LMFDB - Embedded newform 37.7.i.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(2,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.i (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	37.2
Dual form			37.7.i.a.19.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.35059 + 0.730582i) q^{2} +(1.76500 - 2.10345i) q^{3} +(6.17099 + 1.08811i) q^{4} +(-100.792 + 216.150i) q^{5} +(16.2756 - 16.2756i) q^{6} +(-148.724 + 54.1313i) q^{7} +(-467.463 - 125.256i) q^{8} +(125.280 + 710.500i) q^{9} +O(q^{10})$	\(q+(8.35059 + 0.730582i) q^{2} +(1.76500 - 2.10345i) q^{3} +(6.17099 + 1.08811i) q^{4} +(-100.792 + 216.150i) q^{5} +(16.2756 - 16.2756i) q^{6} +(-148.724 + 54.1313i) q^{7} +(-467.463 - 125.256i) q^{8} +(125.280 + 710.500i) q^{9} +(-999.591 + 1731.34i) q^{10} +(1605.92 - 927.177i) q^{11} +(13.1806 - 11.0598i) q^{12} +(1255.96 + 1793.69i) q^{13} +(-1281.48 + 343.373i) q^{14} +(276.761 + 593.516i) q^{15} +(-4188.93 - 1524.65i) q^{16} +(-5535.91 - 3876.29i) q^{17} +(527.086 + 6024.62i) q^{18} +(2837.53 - 248.252i) q^{19} +(-857.183 + 1224.18i) q^{20} +(-148.637 + 408.376i) q^{21} +(14087.8 - 6569.23i) q^{22} +(5331.93 + 19899.0i) q^{23} +(-1088.54 + 762.207i) q^{24} +(-26518.1 - 31603.0i) q^{25} +(9177.55 + 15896.0i) q^{26} +(3449.17 + 1991.38i) q^{27} +(-976.678 + 172.215i) q^{28} +(-585.478 + 2185.04i) q^{29} +(1877.51 + 5158.41i) q^{30} +(11315.3 + 11315.3i) q^{31} +(-5795.13 - 2702.32i) q^{32} +(884.181 - 5014.44i) q^{33} +(-43396.2 - 36413.8i) q^{34} +(3289.81 - 37602.8i) q^{35} +4520.80i q^{36} +(50539.4 + 3390.84i) q^{37} +23876.5 q^{38} +(5989.71 + 524.032i) q^{39} +(74190.8 - 88417.1i) q^{40} +(9664.09 + 1704.04i) q^{41} +(-1539.56 + 3301.59i) q^{42} +(88716.9 - 88716.9i) q^{43} +(10919.0 - 3974.18i) q^{44} +(-166202. - 44533.6i) q^{45} +(29986.9 + 170064. i) q^{46} +(-57277.5 + 99207.5i) q^{47} +(-10600.5 + 6120.20i) q^{48} +(-70935.6 + 59522.0i) q^{49} +(-198353. - 283277. i) q^{50} +(-17924.5 + 4802.85i) q^{51} +(5798.76 + 12435.5i) q^{52} +(211603. + 77017.3i) q^{53} +(27347.8 + 19149.1i) q^{54} +(38545.0 + 440571. i) q^{55} +(76303.4 - 6675.69i) q^{56} +(4486.07 - 6406.78i) q^{57} +(-6485.44 + 17818.6i) q^{58} +(-85982.2 + 40094.2i) q^{59} +(1062.08 + 3963.73i) q^{60} +(-215515. + 150905. i) q^{61} +(86222.9 + 102756. i) q^{62} +(-57092.5 - 98887.1i) q^{63} +(200656. + 115849. i) q^{64} +(-514297. + 90684.4i) q^{65} +(11046.9 - 41227.6i) q^{66} +(9005.35 + 24742.0i) q^{67} +(-29944.2 - 29944.2i) q^{68} +(51267.5 + 23906.4i) q^{69} +(54943.8 - 311602. i) q^{70} +(-63054.7 - 52909.1i) q^{71} +(30430.7 - 347824. i) q^{72} -138198. i q^{73} +(419557. + 65238.7i) q^{74} -113280. q^{75} +(17780.5 + 1555.59i) q^{76} +(-188650. + 224824. i) q^{77} +(49634.8 + 8751.96i) q^{78} +(212689. - 456114. i) q^{79} +(751764. - 751764. i) q^{80} +(-483950. + 176143. i) q^{81} +(79456.0 + 21290.2i) q^{82} +(94833.9 + 537830. i) q^{83} +(-1361.59 + 2358.35i) q^{84} +(1.39584e6 - 805886. i) q^{85} +(805654. - 676024. i) q^{86} +(3562.74 + 5088.12i) q^{87} +(-866842. + 232270. i) q^{88} +(-46710.8 - 100172. i) q^{89} +(-1.35535e6 - 493306. i) q^{90} +(-283886. - 198779. i) q^{91} +(11250.9 + 128598. i) q^{92} +(43772.8 - 3829.62i) q^{93} +(-550780. + 786596. i) q^{94} +(-232342. + 638354. i) q^{95} +(-15912.6 + 7420.17i) q^{96} +(216679. + 808658. i) q^{97} +(-635840. + 445220. i) q^{98} +(859949. + 1.02485e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9}+O(q^{10}) $ 216 * q - 12 * q^2 - 12 * q^3 - 282 * q^4 + 186 * q^5 - 12 * q^6 - 12 * q^7 + 1782 * q^8 - 972 * q^9	\( 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9} - 6 q^{10} - 18 q^{11} - 12300 q^{12} - 12 q^{13} - 2508 q^{14} - 5724 q^{15} + 21138 q^{16} + 14652 q^{17} - 36462 q^{18} + 25692 q^{19} + 15156 q^{20} + 22308 q^{21} - 396 q^{22} - 45372 q^{23} - 130632 q^{24} + 54042 q^{25} + 48834 q^{26} - 18 q^{27} - 261132 q^{28} - 63852 q^{29} + 140076 q^{30} + 255300 q^{31} + 444198 q^{32} + 151134 q^{33} + 121740 q^{34} + 64380 q^{35} - 323412 q^{37} - 530748 q^{38} - 734844 q^{39} - 873996 q^{40} + 143244 q^{41} + 682356 q^{42} + 298788 q^{43} + 410502 q^{44} - 296748 q^{45} + 1696848 q^{46} + 97674 q^{47} - 18 q^{48} - 827124 q^{49} - 701574 q^{50} + 1150788 q^{51} + 452802 q^{52} + 147876 q^{53} - 1733052 q^{54} - 481266 q^{55} - 1608972 q^{56} + 238596 q^{57} + 2880600 q^{58} + 1700916 q^{59} - 2913120 q^{60} - 212628 q^{61} - 3373512 q^{62} - 1185486 q^{63} - 2139876 q^{64} - 2189010 q^{65} + 4562748 q^{66} - 486876 q^{67} + 6077478 q^{68} + 3324612 q^{69} + 6153942 q^{70} + 2088276 q^{71} + 1397046 q^{72} - 212106 q^{74} - 5357160 q^{75} - 2036850 q^{76} - 4623426 q^{77} - 7419738 q^{78} - 2895996 q^{79} - 8321832 q^{80} - 337890 q^{81} - 5343312 q^{82} + 2697348 q^{83} + 1737582 q^{84} + 6365610 q^{85} + 9282138 q^{86} + 9292260 q^{87} + 11436912 q^{88} - 618732 q^{89} - 2893080 q^{90} - 2103804 q^{91} - 1911270 q^{92} + 2397036 q^{93} + 751476 q^{94} - 8155788 q^{95} - 5338512 q^{96} - 8958252 q^{97} + 1386858 q^{98} - 12128778 q^{99}+O(q^{100}) \) 216 * q - 12 * q^2 - 12 * q^3 - 282 * q^4 + 186 * q^5 - 12 * q^6 - 12 * q^7 + 1782 * q^8 - 972 * q^9 - 6 * q^10 - 18 * q^11 - 12300 * q^12 - 12 * q^13 - 2508 * q^14 - 5724 * q^15 + 21138 * q^16 + 14652 * q^17 - 36462 * q^18 + 25692 * q^19 + 15156 * q^20 + 22308 * q^21 - 396 * q^22 - 45372 * q^23 - 130632 * q^24 + 54042 * q^25 + 48834 * q^26 - 18 * q^27 - 261132 * q^28 - 63852 * q^29 + 140076 * q^30 + 255300 * q^31 + 444198 * q^32 + 151134 * q^33 + 121740 * q^34 + 64380 * q^35 - 323412 * q^37 - 530748 * q^38 - 734844 * q^39 - 873996 * q^40 + 143244 * q^41 + 682356 * q^42 + 298788 * q^43 + 410502 * q^44 - 296748 * q^45 + 1696848 * q^46 + 97674 * q^47 - 18 * q^48 - 827124 * q^49 - 701574 * q^50 + 1150788 * q^51 + 452802 * q^52 + 147876 * q^53 - 1733052 * q^54 - 481266 * q^55 - 1608972 * q^56 + 238596 * q^57 + 2880600 * q^58 + 1700916 * q^59 - 2913120 * q^60 - 212628 * q^61 - 3373512 * q^62 - 1185486 * q^63 - 2139876 * q^64 - 2189010 * q^65 + 4562748 * q^66 - 486876 * q^67 + 6077478 * q^68 + 3324612 * q^69 + 6153942 * q^70 + 2088276 * q^71 + 1397046 * q^72 - 212106 * q^74 - 5357160 * q^75 - 2036850 * q^76 - 4623426 * q^77 - 7419738 * q^78 - 2895996 * q^79 - 8321832 * q^80 - 337890 * q^81 - 5343312 * q^82 + 2697348 * q^83 + 1737582 * q^84 + 6365610 * q^85 + 9282138 * q^86 + 9292260 * q^87 + 11436912 * q^88 - 618732 * q^89 - 2893080 * q^90 - 2103804 * q^91 - 1911270 * q^92 + 2397036 * q^93 + 751476 * q^94 - 8155788 * q^95 - 5338512 * q^96 - 8958252 * q^97 + 1386858 * q^98 - 12128778 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{36}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	8.35059	+	0.730582i	1.04382	+	0.0913228i	0.596149	−	0.802874i	$-0.296697\pi$
$2$	8.35059	+	0.730582i	1.04382	+	0.0913228i	0.447675	+	0.894196i	$0.352252\pi$
$3$	1.76500	−	2.10345i	0.0653705	−	0.0779055i	−0.732368	−	0.680909i	$-0.761585\pi$
$3$	1.76500	−	2.10345i	0.0653705	−	0.0779055i	0.797739	+	0.603003i	$0.206029\pi$
$4$	6.17099	+	1.08811i	0.0964217	+	0.0170017i
$5$	−100.792	+	216.150i	−0.806338	+	1.72920i	−0.131392	+	0.991330i	$0.541945\pi$
$5$	−100.792	+	216.150i	−0.806338	+	1.72920i	−0.674946	+	0.737867i	$0.735833\pi$
$6$	16.2756	−	16.2756i	0.0753499	−	0.0753499i
$7$	−148.724	+	54.1313i	−0.433599	+	0.157817i	−0.549593	−	0.835433i	$-0.685217\pi$
$7$	−148.724	+	54.1313i	−0.433599	+	0.157817i	0.115994	+	0.993250i	$0.462995\pi$
$8$	−467.463	−	125.256i	−0.913014	−	0.244641i
$9$	125.280	+	710.500i	0.171852	+	0.974622i
$10$	−999.591	+	1731.34i	−0.999591	+	1.73134i
$11$	1605.92	−	927.177i	1.20655	−	0.696602i	0.244546	−	0.969638i	$-0.421361\pi$
$11$	1605.92	−	927.177i	1.20655	−	0.696602i	0.962004	+	0.273036i	$0.0880277\pi$
$12$	13.1806	−	11.0598i	0.00762767	−	0.00640037i
$13$	1255.96	+	1793.69i	0.571669	+	0.816428i	0.996026	−	0.0890669i	$-0.0283885\pi$
$13$	1255.96	+	1793.69i	0.571669	+	0.816428i	−0.424356	+	0.905495i	$0.639500\pi$
$14$	−1281.48	+	343.373i	−0.467013	+	0.125136i
$15$	276.761	+	593.516i	0.0820033	+	0.175857i
$16$	−4188.93	−	1524.65i	−1.02269	−	0.372228i
$17$	−5535.91	−	3876.29i	−1.12679	−	0.788986i	−0.147023	−	0.989133i	$-0.546969\pi$
$17$	−5535.91	−	3876.29i	−1.12679	−	0.788986i	−0.979766	+	0.200147i	$0.935858\pi$
$18$	527.086	+	6024.62i	0.0903783	+	1.03303i
$19$	2837.53	−	248.252i	0.413695	−	0.0361936i	0.121591	−	0.992580i	$-0.461200\pi$
$19$	2837.53	−	248.252i	0.413695	−	0.0361936i	0.292104	+	0.956387i	$0.405645\pi$
$20$	−857.183	+	1224.18i	−0.107148	+	0.153023i
$21$	−148.637	+	408.376i	−0.0160498	+	0.0440963i
$22$	14087.8	−	6569.23i	1.32304	−	0.616945i
$23$	5331.93	+	19899.0i	0.438229	+	1.63549i	0.733219	+	0.679992i	$0.238017\pi$
$23$	5331.93	+	19899.0i	0.438229	+	1.63549i	−0.294990	+	0.955500i	$0.595316\pi$
$24$	−1088.54	+	762.207i	−0.0787431	+	0.0551365i
$25$	−26518.1	−	31603.0i	−1.69716	−	2.02259i
$26$	9177.55	+	15896.0i	0.522164	+	0.904414i
$27$	3449.17	+	1991.38i	0.175236	+	0.101173i
$28$	−976.678	+	172.215i	−0.0444915	+	0.00784505i
$29$	−585.478	+	2185.04i	−0.0240058	+	0.0895910i	−0.976889	−	0.213745i	$-0.931434\pi$
$29$	−585.478	+	2185.04i	−0.0240058	+	0.0895910i	0.952884	+	0.303336i	$0.0981005\pi$
$30$	1877.51	+	5158.41i	0.0695374	+	0.191052i
$31$	11315.3	+	11315.3i	0.379824	+	0.379824i	0.871038	−	0.491215i	$-0.163447\pi$
$31$	11315.3	+	11315.3i	0.379824	+	0.379824i	−0.491215	+	0.871038i	$0.663447\pi$
$32$	−5795.13	−	2702.32i	−0.176853	−	0.0824681i
$33$	884.181	−	5014.44i	0.0246036	−	0.139534i
$34$	−43396.2	−	36413.8i	−1.10412	−	0.926464i
$35$	3289.81	−	37602.8i	0.0767304	−	0.877032i
$36$			4520.80i			0.0968965i
$37$	50539.4	+	3390.84i	0.997757	+	0.0669425i
$37$	50539.4	+	3390.84i	0.997757	+	0.0669425i
$38$	23876.5			0.435130
$39$	5989.71	+	524.032i	0.100975	+	0.00883413i
$40$	74190.8	−	88417.1i	1.15923	−	1.38152i
$41$	9664.09	+	1704.04i	0.140220	+	0.0247245i	0.243317	−	0.969947i	$-0.421764\pi$
$41$	9664.09	+	1704.04i	0.140220	+	0.0247245i	−0.103098	+	0.994671i	$0.532875\pi$
$42$	−1539.56	+	3301.59i	−0.0207801	+	0.0445631i
$43$	88716.9	−	88716.9i	1.11584	−	1.11584i	0.123492	−	0.992346i	$-0.460591\pi$
$43$	88716.9	−	88716.9i	1.11584	−	1.11584i	0.992346	−	0.123492i	$-0.0394095\pi$
$44$	10919.0	−	3974.18i	0.128181	−	0.0466541i
$45$	−166202.	−	44533.6i	−1.82389	−	0.488709i
$46$	29986.9	+	170064.i	0.308076	+	1.74719i
$47$	−57277.5	+	99207.5i	−0.551684	+	0.955545i	0.446469	+	0.894799i	$0.352681\pi$
$47$	−57277.5	+	99207.5i	−0.551684	+	0.955545i	−0.998153	+	0.0607459i	$0.980652\pi$
$48$	−10600.5	+	6120.20i	−0.0958523	+	0.0553404i
$49$	−70935.6	+	59522.0i	−0.602943	+	0.505929i
$50$	−198353.	−	283277.i	−1.58682	−	2.26622i
$51$	−17924.5	+	4802.85i	−0.135125	+	0.0362067i
$52$	5798.76	+	12435.5i	0.0412406	+	0.0884408i
$53$	211603.	+	77017.3i	1.42133	+	0.517321i	0.934433	−	0.356139i	$-0.115907\pi$
$53$	211603.	+	77017.3i	1.42133	+	0.517321i	0.486896	+	0.873460i	$0.338129\pi$
$54$	27347.8	+	19149.1i	0.173676	+	0.121609i
$55$	38545.0	+	440571.i	0.231675	+	2.64806i
$56$	76303.4	−	6675.69i	0.434490	−	0.0380130i
$57$	4486.07	−	6406.78i	0.0242238	−	0.0345951i
$58$	−6485.44	+	17818.6i	−0.0332396	+	0.0913250i
$59$	−85982.2	+	40094.2i	−0.418652	+	0.195220i	−0.620517	−	0.784193i	$-0.713077\pi$
$59$	−85982.2	+	40094.2i	−0.418652	+	0.195220i	0.201866	+	0.979413i	$0.435300\pi$
$60$	1062.08	+	3963.73i	0.00491703	+	0.0183506i
$61$	−215515.	+	150905.i	−0.949484	+	0.664836i	−0.942169	−	0.335137i	$-0.891217\pi$
$61$	−215515.	+	150905.i	−0.949484	+	0.664836i	−0.00731488	+	0.999973i	$0.502328\pi$
$62$	86222.9	+	102756.i	0.361783	+	0.431156i
$63$	−57092.5	−	98887.1i	−0.228327	−	0.395474i
$64$	200656.	+	115849.i	0.765443	+	0.441929i
$65$	−514297.	+	90684.4i	−1.87272	+	0.330212i
$66$	11046.9	−	41227.6i	0.0384245	−	0.143402i
$67$	9005.35	+	24742.0i	0.0299417	+	0.0822641i	0.953763	−	0.300560i	$-0.0971737\pi$
$67$	9005.35	+	24742.0i	0.0299417	+	0.0822641i	−0.923821	+	0.382824i	$0.874951\pi$
$68$	−29944.2	−	29944.2i	−0.0952328	−	0.0952328i
$69$	51267.5	+	23906.4i	0.156061	+	0.0727725i
$70$	54943.8	−	311602.i	0.160186	−	0.908460i
$71$	−63054.7	−	52909.1i	−0.176174	−	0.147828i	0.550437	−	0.834877i	$-0.314461\pi$
$71$	−63054.7	−	52909.1i	−0.176174	−	0.147828i	−0.726611	+	0.687049i	$0.758906\pi$
$72$	30430.7	−	347824.i	0.0815294	−	0.931886i
$73$		−	138198.i		−	0.355250i	−0.984098	−	0.177625i	$-0.943159\pi$
$73$		−	138198.i		−	0.355250i	0.984098	−	0.177625i	$-0.0568413\pi$
$74$	419557.	+	65238.7i	1.03537	+	0.160994i
$75$	−113280.			−0.268515
$76$	17780.5	+	1555.59i	0.0405045	+	0.00354369i
$77$	−188650.	+	224824.i	−0.413223	+	0.492460i
$78$	49634.8	+	8751.96i	0.104593	+	0.0184426i
$79$	212689.	−	456114.i	0.431385	−	0.925107i	−0.563691	−	0.825986i	$-0.690619\pi$
$79$	212689.	−	456114.i	0.431385	−	0.925107i	0.995075	−	0.0991212i	$-0.0316032\pi$
$80$	751764.	−	751764.i	1.46829	−	1.46829i
$81$	−483950.	+	176143.i	−0.910637	+	0.331445i
$82$	79456.0	+	21290.2i	0.144107	+	0.0386133i
$83$	94833.9	+	537830.i	0.165855	+	0.940612i	0.948178	+	0.317739i	$0.102924\pi$
$83$	94833.9	+	537830.i	0.165855	+	0.940612i	−0.782323	+	0.622873i	$0.785965\pi$
$84$	−1361.59	+	2358.35i	−0.00229726	+	0.00397897i
$85$	1.39584e6	−	805886.i	2.27289	−	1.31225i
$86$	805654.	−	676024.i	1.26664	−	1.06284i
$87$	3562.74	+	5088.12i	0.00541036	+	0.00772680i
$88$	−866842.	+	232270.i	−1.27201	+	0.340835i
$89$	−46710.8	−	100172.i	−0.0662594	−	0.142094i	0.870389	−	0.492365i	$-0.163867\pi$
$89$	−46710.8	−	100172.i	−0.0662594	−	0.142094i	−0.936648	+	0.350271i	$0.886090\pi$
$90$	−1.35535e6	−	493306.i	−1.85919	−	0.676688i
$91$	−283886.	−	198779.i	−0.376722	−	0.263783i
$92$	11250.9	+	128598.i	0.0144485	+	0.165148i
$93$	43772.8	−	3829.62i	0.0544196	−	0.00476110i
$94$	−550780.	+	786596.i	−0.663124	+	0.947040i
$95$	−232342.	+	638354.i	−0.270992	+	0.744545i
$96$	−15912.6	+	7420.17i	−0.0179857	+	0.00838688i
$97$	216679.	+	808658.i	0.237412	+	0.886032i	0.977047	+	0.213024i	$0.0683313\pi$
$97$	216679.	+	808658.i	0.237412	+	0.886032i	−0.739635	+	0.673008i	$0.765002\pi$
$98$	−635840.	+	445220.i	−0.675569	+	0.473039i
$99$	859949.	+	1.02485e6i	0.886272	+	1.05622i
$100$	−129255.	−	223876.i	−0.129255	−	0.223876i
$101$	−192341.	−	111048.i	−0.186684	−	0.107782i	0.403745	−	0.914872i	$-0.367708\pi$
$101$	−192341.	−	111048.i	−0.186684	−	0.107782i	−0.590429	+	0.807089i	$0.701042\pi$
$102$	−153189.	+	27011.3i	−0.144353	+	0.0254534i
$103$	341385.	−	1.27407e6i	0.312415	−	1.16595i	−0.613956	−	0.789340i	$-0.710423\pi$
$103$	341385.	−	1.27407e6i	0.312415	−	1.16595i	0.926372	−	0.376610i	$-0.122910\pi$
$104$	−362442.	−	995802.i	−0.322210	−	0.885264i
$105$	−73289.0	−	73289.0i	−0.0633098	−	0.0633098i
$106$	1.71075e6	+	797734.i	1.43637	+	0.669792i
$107$	129142.	−	732398.i	0.105418	−	0.597855i	−0.885635	−	0.464383i	$-0.846276\pi$
$107$	129142.	−	732398.i	0.105418	−	0.597855i	0.991053	−	0.133472i	$-0.0426127\pi$
$108$	19117.9	+	16041.9i	0.0151764	+	0.0127345i
$109$	51849.4	−	592641.i	0.0400372	−	0.457628i	−0.949542	−	0.313640i	$-0.898452\pi$
$109$	51849.4	−	592641.i	0.0400372	−	0.457628i	0.989579	−	0.143988i	$-0.0459928\pi$
$110$			3.70719e6i			2.78527i
$111$	96334.6	−	100322.i	0.0704391	−	0.0733547i
$112$	705528.			0.502181
$113$	1.36678e6	+	119578.i	0.947249	+	0.0828735i	0.550300	−	0.834967i	$-0.314513\pi$
$113$	1.36678e6	+	119578.i	0.947249	+	0.0828735i	0.396949	+	0.917841i	$0.370069\pi$
$114$	42142.1	−	50222.9i	0.0284447	−	0.0338991i
$115$	−4.83859e6	−	853174.i	−3.18145	−	0.560976i
$116$	−5990.54	+	12846.8i	−0.00383789	+	0.00823038i
$117$	−1.11707e6	+	1.11707e6i	−0.697467	+	0.697467i
$118$	−747295.	+	271993.i	−0.454827	+	0.165543i
$119$	1.03315e6	+	276833.i	0.613090	+	0.164277i
$120$	−55034.0	−	312113.i	−0.0318484	−	0.180621i
$121$	833535.	−	1.44373e6i	0.470509	−	0.814945i
$122$	−1.90993e6	+	1.10270e6i	−1.05181	+	0.607262i
$123$	20641.5	−	17320.3i	0.0110924	−	0.00930764i
$124$	57514.4	+	82139.1i	0.0301656	+	0.0430809i
$125$	5.90429e6	−	1.58205e6i	3.02300	−	0.810010i
$126$	−404511.	−	867477.i	−0.202217	−	0.433657i
$127$	−2.73615e6	−	995878.i	−1.33576	−	0.486178i	−0.427287	−	0.904116i	$-0.640530\pi$
$127$	−2.73615e6	−	995878.i	−1.33576	−	0.486178i	−0.908475	+	0.417939i	$0.862753\pi$
$128$	1.92618e6	+	1.34873e6i	0.918476	+	0.643124i
$129$	−30025.9	−	343197.i	−0.0139871	−	0.159873i
$130$	−4.36094e6	+	381533.i	−1.98495	+	0.173661i
$131$	240109.	−	342911.i	0.106806	−	0.152534i	−0.762191	−	0.647352i	$-0.775876\pi$
$131$	240109.	−	342911.i	0.106806	−	0.152534i	0.868997	+	0.494818i	$0.164765\pi$
$132$	10912.5	−	29982.0i	0.00474465	−	0.0130358i
$133$	−408573.	+	190520.i	−0.173666	+	0.0809817i
$134$	57124.0	+	213190.i	0.0237413	+	0.0886037i
$135$	−778086.	+	544821.i	−0.316247	+	0.221438i
$136$	2.10230e6	+	2.50543e6i	0.835755	+	0.996014i
$137$	295748.	+	512251.i	0.115017	+	0.199214i	0.917786	−	0.397075i	$-0.129975\pi$
$137$	295748.	+	512251.i	0.115017	+	0.199214i	−0.802770	+	0.596289i	$0.796641\pi$
$138$	410648.	+	237088.i	0.156255	+	0.0902137i
$139$	524683.	−	92515.7i	0.195367	−	0.0344486i	−0.0751081	−	0.997175i	$-0.523930\pi$
$139$	524683.	−	92515.7i	0.195367	−	0.0344486i	0.270476	+	0.962727i	$0.412819\pi$
$140$	61217.4	−	228467.i	0.0223096	−	0.0832604i
$141$	107583.	+	295582.i	0.0383784	+	0.105444i
$142$	−487889.	−	487889.i	−0.170395	−	0.170395i
$143$	3.68004e6	+	1.71603e6i	1.25847	+	0.586836i
$144$	558471.	−	3.16724e6i	0.187031	−	1.06070i
$145$	−413283.	−	346786.i	−0.135564	−	0.113752i
$146$	100965.	−	1.15404e6i	0.0324424	−	0.370818i
$147$			254266.i			0.0800454i
$148$	308188.	+	75917.3i	0.0950673	+	0.0234183i
$149$	611310.			0.184800			0.0924001	−	0.995722i	$-0.470546\pi$
$149$	611310.			0.184800			0.0924001	+	0.995722i	$0.470546\pi$
$150$	−945954.	−	82760.2i	−0.280283	−	0.0245215i
$151$	−1.44733e6	+	1.72487e6i	−0.420376	+	0.500985i	−0.934120	−	0.356959i	$-0.883814\pi$
$151$	−1.44733e6	+	1.72487e6i	−0.420376	+	0.500985i	0.513744	+	0.857944i	$0.328258\pi$
$152$	−1.35754e6	−	239370.i	−0.386564	−	0.0681616i
$153$	2.06056e6	−	4.41889e6i	0.575322	−	1.23378i
$154$	−1.73959e6	+	1.73959e6i	−0.476305	+	0.476305i
$155$	−3.58630e6	+	1.30531e6i	−0.963057	+	0.350524i
$156$	36392.2	+	9751.27i	0.00958595	+	0.00256855i
$157$	−333559.	−	1.89171e6i	−0.0861934	−	0.488827i	−0.997093	−	0.0761984i	$-0.975722\pi$
$157$	−333559.	−	1.89171e6i	−0.0861934	−	0.488827i	0.910899	−	0.412629i	$-0.135389\pi$
$158$	2.10931e6	−	3.65344e6i	0.534773	−	0.926254i
$159$	535482.	−	309161.i	0.133215	−	0.0769118i
$160$	1.16821e6	−	980244.i	0.285207	−	0.239317i
$161$	−1.87015e6	−	2.67085e6i	−0.448124	−	0.639988i
$162$	−4.16995e6	+	1.11734e6i	−0.980813	+	0.262808i
$163$	−1.02672e6	−	2.20180e6i	−0.237076	−	0.508411i	0.751389	−	0.659859i	$-0.229384\pi$
$163$	−1.02672e6	−	2.20180e6i	−0.237076	−	0.508411i	−0.988465	+	0.151448i	$0.951606\pi$
$164$	57782.8	+	21031.2i	0.0130999	+	0.00476796i
$165$	994751.	+	696532.i	0.221443	+	0.155056i
$166$	398991.	+	4.56048e6i	0.0872245	+	0.996980i
$167$	8.12436e6	−	710790.i	1.74437	−	0.152613i	0.830075	−	0.557651i	$-0.188297\pi$
$167$	8.12436e6	−	710790.i	1.74437	−	0.152613i	0.914300	+	0.405038i	$0.132742\pi$
$168$	120634.	−	172283.i	0.0254414	−	0.0363341i
$169$	10960.2	−	30112.8i	0.00227069	−	0.00623866i
$170$	1.22448e7	−	5.70986e6i	2.49233	−	1.16219i
$171$	531870.	+	1.98497e6i	0.106370	+	0.396977i
$172$	644005.	−	450937.i	0.126562	−	0.0886198i
$173$	−3.40039e6	−	4.05242e6i	−0.656735	−	0.782666i	0.330179	−	0.943918i	$-0.392891\pi$
$173$	−3.40039e6	−	4.05242e6i	−0.656735	−	0.782666i	−0.986913	+	0.161253i	$0.948447\pi$
$174$	26033.7	+	45091.7i	0.00494183	+	0.00855951i
$175$	5.65459e6	+	3.26468e6i	1.05508	+	0.609153i
$176$	−8.14071e6	+	1.43543e6i	−1.49322	+	0.263295i
$177$	−67422.9	+	251626.i	−0.0121587	+	0.0453769i
$178$	−316880.	−	870619.i	−0.0561868	−	0.154372i
$179$	1.96239e6	+	1.96239e6i	0.342158	+	0.342158i	0.857178	−	0.515020i	$-0.172216\pi$
$179$	1.96239e6	+	1.96239e6i	0.342158	+	0.342158i	−0.515020	+	0.857178i	$0.672216\pi$
$180$	−977171.	−	455662.i	−0.167553	−	0.0781314i
$181$	−263870.	+	1.49648e6i	−0.0444994	+	0.252368i	−0.998940	−	0.0460326i	$-0.985342\pi$
$181$	−263870.	+	1.49648e6i	−0.0444994	+	0.252368i	0.954441	+	0.298401i	$0.0964533\pi$
$182$	−2.22540e6	−	1.86733e6i	−0.369142	−	0.309747i
$183$	−62963.2	+	719673.i	−0.0102739	+	0.117431i
$184$		−	9.96992e6i		−	1.60044i
$185$	−5.82691e6	+	1.05823e7i	−0.920286	+	1.67134i
$186$	368327.			0.0572393
$187$	−1.24842e7	−	1.09223e6i	−1.90914	−	0.167028i
$188$	−461408.	+	549884.i	−0.0694403	+	0.0827557i
$189$	−620772.	−	109459.i	−0.0919489	−	0.0162131i
$190$	−2.40656e6	+	5.16089e6i	−0.350862	+	0.752426i
$191$	2.78168e6	−	2.78168e6i	0.399216	−	0.399216i	−0.478741	−	0.877956i	$-0.658907\pi$
$191$	2.78168e6	−	2.78168e6i	0.399216	−	0.399216i	0.877956	+	0.478741i	$0.158907\pi$
$192$	597841.	−	217596.i	0.0844660	−	0.0307431i
$193$	−1.28822e6	−	345176.i	−0.179191	−	0.0480141i	0.168108	−	0.985769i	$-0.446234\pi$
$193$	−1.28822e6	−	345176.i	−0.179191	−	0.0480141i	−0.347299	+	0.937755i	$0.612901\pi$
$194$	1.21861e6	+	6.91107e6i	0.166901	+	0.946543i
$195$	−716986.	+	1.24186e6i	−0.0966956	+	0.167482i
$196$	−502509.	+	290124.i	−0.0667384	+	0.0385315i
$197$	−3.70022e6	+	3.10485e6i	−0.483981	+	0.406109i	−0.851864	−	0.523764i	$-0.824527\pi$
$197$	−3.70022e6	+	3.10485e6i	−0.483981	+	0.406109i	0.367882	+	0.929872i	$0.380083\pi$
$198$	6.43235e6	+	9.18635e6i	0.828656	+	1.18344i
$199$	−4.04845e6	+	1.08478e6i	−0.513723	+	0.137652i	−0.506362	−	0.862321i	$-0.669010\pi$
$199$	−4.04845e6	+	1.08478e6i	−0.513723	+	0.137652i	−0.00736148	+	0.999973i	$0.502343\pi$
$200$	8.43774e6	+	1.80948e7i	1.05472	+	2.26185i
$201$	67938.0	+	24727.4i	0.00836613	+	0.00304502i
$202$	−1.52503e6	−	1.06784e6i	−0.185023	−	0.129554i
$203$	−31203.8	−	356661.i	−0.00373009	−	0.0426351i
$204$	−115838.	+	10134.5i	−0.0136446	+	0.00119375i
$205$	−1.34239e6	+	1.91714e6i	−0.155818	+	0.222531i
$206$	3.78158e6	−	1.03898e7i	0.432585	−	1.18852i
$207$	−1.34703e7	+	6.28129e6i	−1.51868	+	0.708171i
$208$	−2.52637e6	−	9.42855e6i	−0.280742	−	1.04774i
$209$	4.32668e6	−	3.02957e6i	0.473931	−	0.331850i
$210$	−558463.	−	665550.i	−0.0603026	−	0.0718659i
$211$	−1.16048e6	−	2.01002e6i	−0.123536	−	0.213970i	0.797624	−	0.603155i	$-0.206090\pi$
$211$	−1.16048e6	−	2.01002e6i	−0.123536	−	0.213970i	−0.921160	+	0.389185i	$0.872757\pi$
$212$	1.22200e6	+	705521.i	0.128252	+	0.0740461i
$213$	−222583.	+	39247.5i	−0.0230332	+	0.00406137i
$214$	1.61349e6	−	6.02161e6i	0.164636	−	0.614429i
$215$	1.02342e7	+	2.81181e7i	1.02976	+	2.82925i
$216$	−1.36293e6	−	1.36293e6i	−0.135242	−	0.135242i
$217$	−2.29538e6	−	1.07035e6i	−0.224634	−	0.104748i
$218$	865947.	−	4.91103e6i	0.0835837	−	0.474027i
$219$	−290693.	−	243920.i	−0.0276759	−	0.0232228i
$220$	−241530.	+	2.76070e6i	−0.0226831	+	0.259269i
$221$		−	1.47982e7i		−	1.37098i
$222$	877745.	−	767369.i	0.0802250	−	0.0701367i
$223$	4.63499e6			0.417960			0.208980	−	0.977920i	$-0.432986\pi$
$223$	4.63499e6			0.417960			0.208980	+	0.977920i	$0.432986\pi$
$224$	1.00816e6	+	88202.4i	0.0896983	+	0.00784759i
$225$	1.91317e7	−	2.28003e7i	1.67960	−	2.00167i
$226$	1.13261e7	+	1.99709e6i	0.981193	+	0.173011i
$227$	−6.03520e6	+	1.29425e7i	−0.515958	+	1.10647i	0.459881	+	0.887981i	$0.347892\pi$
$227$	−6.03520e6	+	1.29425e7i	−0.515958	+	1.10647i	−0.975838	+	0.218494i	$0.929886\pi$
$228$	34654.8	−	34654.8i	0.00292388	−	0.00292388i
$229$	2.79426e6	−	1.01703e6i	0.232681	−	0.0846889i	−0.223048	−	0.974807i	$-0.571601\pi$
$229$	2.79426e6	−	1.01703e6i	0.232681	−	0.0846889i	0.455729	+	0.890118i	$0.349379\pi$
$230$	−3.97818e7	−	1.06595e7i	−3.26965	−	0.876099i
$231$	139939.	+	793631.i	0.0113528	+	0.0643847i
$232$	547379.	−	948088.i	0.0438353	−	0.0759250i
$233$	1.02547e7	−	5.92056e6i	0.810692	−	0.468053i	−0.0365043	−	0.999333i	$-0.511622\pi$
$233$	1.02547e7	−	5.92056e6i	0.810692	−	0.468053i	0.847196	+	0.531280i	$0.178289\pi$
$234$	−1.01443e7	+	8.51210e6i	−0.791727	+	0.664338i
$235$	−1.56706e7	−	2.23799e7i	−1.20748	−	1.72446i
$236$	−574222.	+	153862.i	−0.0436862	+	0.0117057i
$237$	−584015.	−	1.25242e6i	−0.0438711	−	0.0940820i
$238$	8.42520e6	+	3.06652e6i	0.624956	+	0.227465i
$239$	232903.	+	163081.i	0.0170601	+	0.0119456i	0.582075	−	0.813135i	$-0.302241\pi$
$239$	232903.	+	163081.i	0.0170601	+	0.0119456i	−0.565015	+	0.825080i	$0.691130\pi$
$240$	−254431.	−	2.90816e6i	−0.0184051	−	0.210371i
$241$	1.90561e7	−	1.66719e6i	1.36139	−	0.119106i	0.617059	−	0.786917i	$-0.288324\pi$
$241$	1.90561e7	−	1.66719e6i	1.36139	−	0.119106i	0.744331	+	0.667811i	$0.232769\pi$
$242$	8.01528e6	−	1.14470e7i	0.565552	−	0.807692i
$243$	−1.47670e6	+	4.05719e6i	−0.102913	+	0.282752i
$244$	−1.49414e6	+	696730.i	−0.102854	+	0.0479617i
$245$	−5.71591e6	−	2.13321e7i	−0.388676	−	1.45056i
$246$	185023.	−	129554.i	0.0124285	−	0.00870255i
$247$	4.00911e6	+	4.77787e6i	0.266046	+	0.317062i
$248$	−3.87218e6	−	6.70681e6i	−0.253864	−	0.439705i
$249$	1.29868e6	+	749793.i	0.0841209	+	0.0485672i
$250$	5.04602e7	−	8.89749e6i	3.22945	−	0.569439i
$251$	921284.	−	3.43828e6i	0.0582602	−	0.217430i	−0.930658	−	0.365890i	$-0.880765\pi$
$251$	921284.	−	3.43828e6i	0.0582602	−	0.217430i	0.988918	+	0.148459i	$0.0474314\pi$
$252$	−244717.	−	672354.i	−0.0152919	−	0.0420142i
$253$	2.70126e7	+	2.70126e7i	1.66803	+	1.66803i
$254$	−2.21209e7	−	1.03152e7i	−1.34990	−	0.629470i
$255$	768514.	−	4.35846e6i	0.0463481	−	0.262853i
$256$	3.74001e6	+	3.13824e6i	0.222922	+	0.187054i
$257$	−699463.	+	7.99489e6i	−0.0412064	+	0.470992i	0.947356	+	0.320181i	$0.103744\pi$
$257$	−699463.	+	7.99489e6i	−0.0412064	+	0.470992i	−0.988563	+	0.150810i	$0.951812\pi$
$258$		−	2.88784e6i		−	0.168156i
$259$	−7.69999e6	+	2.23146e6i	−0.443191	+	0.128437i
$260$	−3.27240e6			−0.186185
$261$	−1.62582e6	−	142240.i	−0.0914429	−	0.00800021i
$262$	2.25558e6	−	2.68809e6i	0.125416	−	0.149465i
$263$	1.63630e6	+	288525.i	0.0899491	+	0.0158605i	0.218442	−	0.975850i	$-0.429903\pi$
$263$	1.63630e6	+	288525.i	0.0899491	+	0.0158605i	−0.128492	+	0.991710i	$0.541014\pi$
$264$	−1.04141e6	+	2.23332e6i	−0.0565993	+	0.121378i
$265$	−3.79752e7	+	3.79752e7i	−2.04062	+	2.04062i
$266$	−3.55101e6	+	1.29246e6i	−0.188672	+	0.0686710i
$267$	−293151.	−	78549.5i	−0.0154013	−	0.00412677i
$268$	28649.9	+	162481.i	0.00148840	+	0.00844111i
$269$	1.51537e6	−	2.62469e6i	0.0778503	−	0.134841i	−0.824472	−	0.565903i	$-0.808528\pi$
$269$	1.51537e6	−	2.62469e6i	0.0778503	−	0.134841i	0.902322	+	0.431062i	$0.141861\pi$
$270$	−6.89552e6	+	3.98113e6i	−0.350328	+	0.202262i
$271$	−2.00253e7	+	1.68032e7i	−1.00617	+	0.844278i	−0.987827	−	0.155554i	$-0.950284\pi$
$271$	−2.00253e7	+	1.68032e7i	−1.00617	+	0.844278i	−0.0183436	+	0.999832i	$0.505839\pi$
$272$	1.72796e7	+	2.46778e7i	0.858672	+	1.22631i
$273$	−919183.	+	246294.i	−0.0451766	+	0.0121050i
$274$	2.09543e6	+	4.49367e6i	0.101864	+	0.218449i
$275$	−7.18874e7	−	2.61649e7i	−3.45665	−	1.25812i
$276$	290358.	+	203311.i	0.0138104	+	0.00967016i
$277$	−980043.	−	1.12019e7i	−0.0461111	−	0.527053i	−0.983762	−	0.179475i	$-0.942560\pi$
$277$	−980043.	−	1.12019e7i	−0.0461111	−	0.527053i	0.937651	−	0.347577i	$-0.112996\pi$
$278$	4.44900e6	−	389237.i	0.207075	−	0.0181167i
$279$	−6.62195e6	+	9.45712e6i	−0.304911	+	0.435458i
$280$	−6.24785e6	+	1.71658e7i	−0.284614	+	0.781971i
$281$	2.86489e7	−	1.33592e7i	1.29119	−	0.602090i	0.348982	−	0.937129i	$-0.386527\pi$
$281$	2.86489e7	−	1.33592e7i	1.29119	−	0.602090i	0.942204	+	0.335040i	$0.108750\pi$
$282$	682435.	+	2.54688e6i	0.0304309	+	0.113570i
$283$	1.50932e7	−	1.05683e7i	0.665918	−	0.466281i	−0.191098	−	0.981571i	$-0.561205\pi$
$283$	1.50932e7	−	1.05683e7i	0.665918	−	0.466281i	0.857016	+	0.515290i	$0.172316\pi$
$284$	−331539.	−	395112.i	−0.0144737	−	0.0172491i
$285$	932661.	+	1.61542e6i	0.0402893	+	0.0697831i
$286$	2.94768e7	+	1.70184e7i	1.26003	+	0.727481i
$287$	−1.52953e6	+	269697.i	−0.0647011	+	0.0114086i
$288$	1.19398e6	−	4.45599e6i	0.0499826	−	0.186538i
$289$	7.36519e6	+	2.02357e7i	0.305134	+	0.838349i
$290$	−3.19780e6	−	3.19780e6i	−0.131117	−	0.131117i
$291$	2.08341e6	+	971510.i	0.0845465	+	0.0394247i
$292$	150375.	−	852819.i	0.00603986	−	0.0342538i
$293$	2.74627e7	+	2.30439e7i	1.09179	+	0.916122i	0.996846	−	0.0793603i	$-0.0252878\pi$
$293$	2.74627e7	+	2.30439e7i	1.09179	+	0.916122i	0.0949458	+	0.995482i	$0.469732\pi$
$294$	−185762.	+	2.12327e6i	−0.00730997	+	0.0835533i
$295$		−	2.26262e7i		−	0.881345i
$296$	−2.32006e7	−	7.91547e6i	−0.894589	−	0.305212i
$297$	7.38545e6			0.281908
$298$	5.10480e6	+	446612.i	0.192899	+	0.0168765i
$299$	−2.89961e7	+	3.45562e7i	−1.08474	+	1.29274i
$300$	−699048.	−	123261.i	−0.0258907	−	0.00456522i
$301$	−8.39201e6	+	1.79967e7i	−0.307728	+	0.659924i
$302$	−1.33463e7	+	1.33463e7i	−0.484550	+	0.484550i
$303$	−573067.	+	208579.i	−0.0206005	+	0.00749796i
$304$	−1.22647e7	−	3.28633e6i	−0.436554	−	0.116974i
$305$	−1.08959e7	−	6.17936e7i	−0.384028	−	2.17793i
$306$	2.04353e7	−	3.53949e7i	0.713208	−	1.23531i
$307$	3.31779e7	−	1.91553e7i	1.14666	−	0.662023i	0.198587	−	0.980083i	$-0.436365\pi$
$307$	3.31779e7	−	1.91553e7i	1.14666	−	0.662023i	0.948071	+	0.318060i	$0.103031\pi$
$308$	−1.40879e6	+	1.18212e6i	−0.0482164	+	0.0404583i
$309$	−2.07739e6	−	2.96682e6i	−0.0704112	−	0.100558i
$310$	−3.09014e7	+	8.28000e6i	−1.03727	+	0.277936i
$311$	2.34733e7	+	5.03387e7i	0.780357	+	1.67348i	0.738402	+	0.674360i	$0.235581\pi$
$311$	2.34733e7	+	5.03387e7i	0.780357	+	1.67348i	0.0419542	+	0.999120i	$0.486642\pi$
$312$	−2.73433e6	−	995215.i	−0.0900300	−	0.0327682i
$313$	1.30963e7	+	9.17012e6i	0.427086	+	0.299049i	0.767287	−	0.641304i	$-0.221606\pi$
$313$	1.30963e7	+	9.17012e6i	0.427086	+	0.299049i	−0.340201	+	0.940353i	$0.610495\pi$
$314$	−1.40337e6	−	1.60406e7i	−0.0453297	−	0.518121i
$315$	2.71289e7	−	2.37347e6i	0.867961	−	0.0759368i
$316$	1.80881e6	−	2.58324e6i	0.0573233	−	0.0818661i
$317$	−1.36353e6	+	3.74628e6i	−0.0428044	+	0.117604i	−0.959253	−	0.282548i	$-0.908820\pi$
$317$	−1.36353e6	+	3.74628e6i	−0.0428044	+	0.117604i	0.916449	+	0.400152i	$0.131043\pi$
$318$	4.69746e6	−	2.19046e6i	0.146077	−	0.0681169i
$319$	1.08568e6	+	4.05183e6i	0.0334450	+	0.124819i
$320$	−4.52653e7	+	3.16951e7i	−1.38139	+	0.967258i
$321$	−1.31263e6	−	1.56433e6i	−0.0396850	−	0.0472947i
$322$	−1.36656e7	−	2.36695e7i	−0.409318	−	0.708959i
$323$	−1.66706e7	−	9.62480e6i	−0.494703	−	0.285617i
$324$	−3.17811e6	+	560387.i	−0.0934403	+	0.0164760i
$325$	2.33805e7	−	8.72573e7i	0.681089	−	2.54186i
$326$	−6.96509e6	−	1.91364e7i	−0.201036	−	0.552342i
$327$	−1.15508e6	−	1.15508e6i	−0.0330345	−	0.0330345i
$328$	−4.30416e6	−	2.00706e6i	−0.121974	−	0.0568774i
$329$	3.14833e6	−	1.78551e7i	0.0884083	−	0.501388i
$330$	7.79789e6	+	6.54321e6i	0.216988	+	0.182074i
$331$	−5.50405e6	+	6.29116e7i	−0.151774	+	1.73479i	0.414041	+	0.910258i	$0.364117\pi$
$331$	−5.50405e6	+	6.29116e7i	−0.151774	+	1.73479i	−0.565815	+	0.824532i	$0.691438\pi$
$332$			3.42213e6i			0.0935153i
$333$	3.92240e6	+	3.63330e7i	0.106223	+	0.983940i
$334$	6.83625e7			1.83476
$335$	−6.25565e6	−	547298.i	−0.166394	−	0.0145576i
$336$	1.24526e6	−	1.48404e6i	0.0328278	−	0.0391227i
$337$	−4.66819e7	−	8.23128e6i	−1.21972	−	0.215069i	−0.473513	−	0.880787i	$-0.657014\pi$
$337$	−4.66819e7	−	8.23128e6i	−1.21972	−	0.215069i	−0.746203	+	0.665718i	$0.768125\pi$
$338$	113524.	−	243453.i	0.00293993	−	0.00630470i
$339$	2.66390e6	−	2.66390e6i	0.0683784	−	0.0683784i
$340$	9.49058e6	−	3.45429e6i	0.241466	−	0.0878865i
$341$	2.86628e7	+	7.68018e6i	0.722862	+	0.193690i
$342$	2.99125e6	+	1.69642e7i	0.0747781	+	0.424088i
$343$	1.66380e7	−	2.88178e7i	0.412304	−	0.714132i
$344$	−5.25842e7	+	3.03595e7i	−1.29176	+	0.745795i
$345$	−1.03347e7	+	8.67187e6i	−0.251676	+	0.211181i
$346$	−2.54346e7	−	3.63244e7i	−0.614040	−	0.876940i
$347$	5.81828e7	−	1.55900e7i	1.39253	−	0.373129i	0.516876	−	0.856060i	$-0.327095\pi$
$347$	5.81828e7	−	1.55900e7i	1.39253	−	0.373129i	0.875658	+	0.482931i	$0.160428\pi$
$348$	16449.2	+	35275.4i	0.000390307	+	0.000837017i
$349$	−3.75449e7	−	1.36652e7i	−0.883233	−	0.321470i	−0.139719	−	0.990191i	$-0.544620\pi$
$349$	−3.75449e7	−	1.36652e7i	−0.883233	−	0.321470i	−0.743514	+	0.668721i	$0.766842\pi$
$350$	4.48341e7	+	3.13932e7i	1.04569	+	0.732202i
$351$	760087.	+	8.68784e6i	0.0175769	+	0.200905i
$352$	−1.18120e7	+	1.03342e6i	−0.270830	+	0.0236946i
$353$	4.26122e7	−	6.08566e7i	0.968746	−	1.38351i	0.0456442	−	0.998958i	$-0.485466\pi$
$353$	4.26122e7	−	6.08566e7i	0.968746	−	1.38351i	0.923102	−	0.384555i	$-0.125645\pi$
$354$	−746854.	+	2.05197e6i	−0.0168355	+	0.0462552i
$355$	1.77917e7	−	8.29642e6i	0.397679	−	0.185441i
$356$	−179254.	−	668985.i	−0.00397300	−	0.0148275i
$357$	2.40582e6	−	1.68458e6i	0.0528761	−	0.0370242i
$358$	1.49535e7	+	1.78208e7i	0.325906	+	0.388400i
$359$	−1.35911e7	−	2.35404e7i	−0.293745	−	0.508781i	0.680947	−	0.732332i	$-0.261568\pi$
$359$	−1.35911e7	−	2.35404e7i	−0.293745	−	0.508781i	−0.974692	+	0.223551i	$0.928235\pi$
$360$	7.21150e7	+	4.16356e7i	1.54567	+	0.892395i
$361$	−3.83412e7	+	6.76058e6i	−0.814974	+	0.143702i
$362$	−3.29677e6	+	1.23037e7i	−0.0694965	+	0.259365i
$363$	−1.56561e6	−	4.30148e6i	−0.0327313	−	0.0899286i
$364$	−1.53557e6	−	1.53557e6i	−0.0318394	−	0.0318394i
$365$	2.98715e7	+	1.39293e7i	0.614297	+	0.286451i
$366$	−1.05156e6	+	5.96370e6i	−0.0214482	+	0.121639i
$367$	−5.65802e7	−	4.74764e7i	−1.14463	−	0.960460i	−0.145052	−	0.989424i	$-0.546335\pi$
$367$	−5.65802e7	−	4.74764e7i	−1.14463	−	0.960460i	−0.999580	+	0.0289636i	$0.990779\pi$
$368$	8.00391e6	−	9.14851e7i	0.160605	−	1.83572i
$369$			7.07982e6i			0.140910i
$370$	−5.63894e7	+	8.41115e7i	−1.11325	+	1.66054i
$371$	−3.56396e7			−0.697929
$372$	274289.	+	23997.1i	0.00532818	+	0.000466155i
$373$	1.31956e7	−	1.57259e7i	0.254274	−	0.303032i	−0.623774	−	0.781605i	$-0.714401\pi$
$373$	1.31956e7	−	1.57259e7i	0.254274	−	0.303032i	0.878048	+	0.478573i	$0.158846\pi$
$374$	−1.03453e8	−	1.82415e7i	−1.97755	−	0.348695i
$375$	7.09333e6	−	1.52117e7i	0.134511	−	0.288459i
$376$	3.92015e7	−	3.92015e7i	0.737461	−	0.737461i
$377$	−4.65462e6	+	1.69414e6i	−0.0868680	+	0.0316174i
$378$	−5.10384e6	−	1.36757e6i	−0.0944979	−	0.0253206i
$379$	1.11892e7	+	6.34571e7i	0.205533	+	1.16564i	0.896599	+	0.442844i	$0.146030\pi$
$379$	1.11892e7	+	6.34571e7i	0.205533	+	1.16564i	−0.691066	+	0.722792i	$0.742859\pi$
$380$	−2.12838e6	+	3.68646e6i	−0.0387881	+	0.0671830i
$381$	−6.92410e6	+	3.99763e6i	−0.125195	+	0.0722816i
$382$	2.52610e7	−	2.11965e7i	0.453169	−	0.380254i
$383$	1.37158e7	+	1.95882e7i	0.244132	+	0.348656i	0.922453	−	0.386109i	$-0.126181\pi$
$383$	1.37158e7	+	1.95882e7i	0.244132	+	0.348656i	−0.678321	+	0.734765i	$0.737292\pi$
$384$	6.23670e6	−	1.67112e6i	0.110144	−	0.0295130i
$385$	−2.95813e7	−	6.34372e7i	−0.518363	−	1.11163i
$386$	−1.05052e7	−	3.82357e6i	−0.182659	−	0.0664825i
$387$	7.41478e7	+	5.19189e7i	1.27928	+	0.895761i
$388$	457215.	+	5.22599e6i	0.00782753	+	0.0894691i
$389$	−1.00760e8	+	8.81532e6i	−1.71174	+	0.149758i	−0.900470	−	0.434917i	$-0.856778\pi$
$389$	−1.00760e8	+	8.81532e6i	−1.71174	+	0.149758i	−0.811268	+	0.584675i	$0.801222\pi$
$390$	−6.89454e6	+	9.84642e6i	−0.116228	+	0.165991i
$391$	4.76173e7	−	1.30827e8i	0.796589	−	2.18861i
$392$	4.06153e7	−	1.89392e7i	0.674266	−	0.314415i
$393$	−297503.	−	1.11030e6i	−0.00490132	−	0.0182920i
$394$	−3.31674e7	+	2.32240e7i	−0.542279	+	0.379708i
$395$	7.71514e7	+	9.19455e7i	1.25185	+	1.49190i
$396$	4.19159e6	+	7.26004e6i	0.0674983	+	0.116911i
$397$	4.95997e7	+	2.86364e7i	0.792698	+	0.457664i	0.840912	−	0.541173i	$-0.182019\pi$
$397$	4.95997e7	+	2.86364e7i	0.792698	+	0.457664i	−0.0482135	+	0.998837i	$0.515353\pi$
$398$	−3.45995e7	+	6.10082e6i	−0.548807	+	0.0967696i
$399$	−320382.	+	1.19568e6i	−0.00504370	+	0.0188233i
$400$	6.28990e7	+	1.72814e8i	0.982797	+	2.70021i
$401$	1.25212e7	+	1.25212e7i	0.194184	+	0.194184i	0.797501	−	0.603317i	$-0.206155\pi$
$401$	1.25212e7	+	1.25212e7i	0.194184	+	0.194184i	−0.603317	+	0.797501i	$0.706155\pi$
$402$	549258.	+	256123.i	0.00845469	+	0.00394249i
$403$	−6.08465e6	+	3.45078e7i	−0.0929653	+	0.527232i
$404$	−1.06610e6	−	894566.i	−0.0161679	−	0.0135665i
$405$	1.07051e7	−	1.22359e8i	0.161148	−	1.84193i
$406$		−	3.00113e6i		−	0.0448442i
$407$	8.43060e7	−	4.14136e7i	1.25048	−	0.614270i
$408$	8.98062e6			0.132229
$409$	−6.39453e7	−	5.59449e6i	−0.934628	−	0.0817693i	−0.390343	−	0.920670i	$-0.627643\pi$
$409$	−6.39453e7	−	5.59449e6i	−0.934628	−	0.0817693i	−0.544285	+	0.838900i	$0.683199\pi$
$410$	−1.26104e7	+	1.50285e7i	−0.182969	+	0.218054i
$411$	1.59949e6	+	282033.i	0.0230386	+	0.00406233i
$412$	3.49301e6	−	7.49078e6i	0.0499468	−	0.107111i
$413$	1.06173e7	−	1.06173e7i	0.150718	−	0.150718i
$414$	−1.17074e8	+	4.26114e7i	−1.64990	+	0.600516i
$415$	−1.25810e8	−	3.37108e7i	−1.76024	−	0.471655i
$416$	−2.43132e6	−	1.37887e7i	−0.0337724	−	0.191533i
$417$	731465.	−	1.26693e6i	0.0100875	−	0.0174721i
$418$	3.83437e7	−	2.21377e7i	0.525007	−	0.303113i
$419$	−5.00564e7	+	4.20023e7i	−0.680484	+	0.570993i	−0.916148	−	0.400841i	$-0.868718\pi$
$419$	−5.00564e7	+	4.20023e7i	−0.680484	+	0.570993i	0.235664	+	0.971835i	$0.424274\pi$
$420$	−372519.	−	532012.i	−0.00502806	−	0.00718081i
$421$	−9.97299e7	+	2.67225e7i	−1.33653	+	0.358122i	−0.855146	−	0.518387i	$-0.826533\pi$
$421$	−9.97299e7	+	2.67225e7i	−1.33653	+	0.358122i	−0.481385	+	0.876509i	$0.659866\pi$
$422$	−8.22225e6	−	1.76327e7i	−0.109409	−	0.234628i
$423$	−7.76627e7	−	2.82669e7i	−1.02610	−	0.373471i
$424$	−8.92698e7	−	6.25074e7i	−1.17113	−	0.820037i
$425$	2.42994e7	+	2.77743e8i	0.316540	+	3.61807i
$426$	−1.88738e6	+	165124.i	−0.0244135	+	0.00213590i
$427$	2.38836e7	−	3.41094e7i	0.306773	−	0.438117i
$428$	1.59386e6	−	4.37910e6i	0.0203292	−	0.0558539i
$429$	1.01049e7	−	4.71197e6i	0.127985	−	0.0596803i
$430$	6.49187e7	+	2.42280e8i	0.816516	+	3.04728i
$431$	3.49673e7	−	2.44844e7i	0.436748	−	0.305814i	−0.334446	−	0.942415i	$-0.608549\pi$
$431$	3.49673e7	−	2.44844e7i	0.436748	−	0.305814i	0.771193	+	0.636601i	$0.219660\pi$
$432$	−1.14122e7	−	1.36005e7i	−0.141553	−	0.168696i
$433$	7.33354e7	+	1.27021e8i	0.903338	+	1.56463i	0.823133	+	0.567849i	$0.192224\pi$
$433$	7.33354e7	+	1.27021e8i	0.903338	+	1.56463i	0.0802047	+	0.996778i	$0.474443\pi$
$434$	−1.83858e7	−	1.06150e7i	−0.224912	−	0.129853i
$435$	−1.45889e6	+	257242.i	−0.0177237	+	0.00312517i
$436$	964822.	−	3.60077e6i	0.0116409	−	0.0434446i
$437$	2.00695e7	+	5.51405e7i	0.240488	+	0.660734i
$438$	−2.24925e6	−	2.24925e6i	−0.0267680	−	0.0267680i
$439$	−5.69843e7	−	2.65722e7i	−0.673537	−	0.314075i	0.0555901	−	0.998454i	$-0.482296\pi$
$439$	−5.69843e7	−	2.65722e7i	−0.673537	−	0.314075i	−0.729127	+	0.684378i	$0.760074\pi$
$440$	3.71660e7	−	2.10779e8i	0.436302	−	2.47439i
$441$	−5.11772e7	−	4.29428e7i	−0.596707	−	0.500696i
$442$	1.08113e7	−	1.23574e8i	0.125202	−	1.43106i
$443$			8.90623e7i			1.02443i	0.858857	+	0.512215i	$0.171175\pi$
$443$			8.90623e7i			1.02443i	−0.858857	+	0.512215i	$0.828825\pi$
$444$	703642.	−	514264.i	0.00803901	−	0.00587540i
$445$	2.63602e7			0.299136
$446$	3.87049e7	+	3.38624e6i	0.436277	+	0.0381693i
$447$	1.07896e6	−	1.28586e6i	0.0120805	−	0.0143970i
$448$	−3.61135e7	−	6.36779e6i	−0.401639	−	0.0708198i
$449$	1.93295e7	−	4.14522e7i	0.213541	−	0.457940i	−0.770137	−	0.637879i	$-0.779812\pi$
$449$	1.93295e7	−	4.14522e7i	0.213541	−	0.457940i	0.983678	+	0.179938i	$0.0575898\pi$
$450$	1.76419e8	−	1.76419e8i	1.93601	−	1.93601i
$451$	1.70997e7	−	6.22378e6i	0.186405	−	0.0678460i
$452$	8.30429e6	+	2.22513e6i	0.0899264	+	0.0240957i
$453$	1.07362e6	+	6.08879e6i	0.0115493	+	0.0654992i
$454$	−5.98531e7	+	1.03669e8i	−0.639615	+	1.10785i
$455$	7.15797e7	−	4.13265e7i	0.759898	−	0.438728i
$456$	−2.89956e6	+	2.43302e6i	−0.0305800	+	0.0256597i
$457$	−1.32711e7	−	1.89532e7i	−0.139046	−	0.198579i	0.743589	−	0.668637i	$-0.233122\pi$
$457$	−1.32711e7	−	1.89532e7i	−0.139046	−	0.198579i	−0.882636	+	0.470058i	$0.844233\pi$
$458$	2.40768e7	−	6.45135e6i	0.250612	−	0.0671513i
$459$	−1.13751e7	−	2.43941e7i	−0.117630	−	0.252259i
$460$	−2.89305e7	−	1.05299e7i	−0.297223	−	0.108180i
$461$	5.22968e7	+	3.66186e7i	0.533792	+	0.373765i	0.809173	−	0.587570i	$-0.199915\pi$
$461$	5.22968e7	+	3.66186e7i	0.533792	+	0.373765i	−0.275381	+	0.961335i	$0.588804\pi$
$462$	588758.	+	6.72953e6i	0.00597050	+	0.0682431i
$463$	4.70065e7	−	4.11254e6i	0.473604	−	0.0414350i	0.152144	−	0.988358i	$-0.451382\pi$
$463$	4.70065e7	−	4.11254e6i	0.473604	−	0.0414350i	0.321460	+	0.946923i	$0.395827\pi$
$464$	5.78394e6	−	8.26032e6i	0.0578988	−	0.0826881i
$465$	−3.58419e6	+	9.84748e6i	−0.0356477	+	0.0979414i
$466$	8.99584e7	−	4.19483e7i	0.888964	−	0.414531i
$467$	1.01117e6	+	3.77373e6i	0.00992824	+	0.0370527i	0.970712	−	0.240245i	$-0.0772278\pi$
$467$	1.01117e6	+	3.77373e6i	0.00992824	+	0.0370527i	−0.960784	+	0.277298i	$0.910561\pi$
$468$	−8.10894e6	+	5.67794e6i	−0.0791091	+	0.0553928i
$469$	−2.67863e6	−	3.19227e6i	−0.0259654	−	0.0309443i
$470$	−1.14508e8	−	1.98334e8i	−1.10292	−	1.91031i
$471$	−4.56785e6	−	2.63725e6i	−0.0437169	−	0.0252399i
$472$	4.52156e7	−	7.97272e6i	0.429994	−	0.0758195i
$473$	6.02158e7	−	2.24728e8i	0.569019	−	2.12361i
$474$	−3.96187e6	−	1.08852e7i	−0.0372019	−	0.102211i
$475$	−8.30914e7	−	8.30914e7i	−0.775310	−	0.775310i
$476$	6.07436e6	+	2.83252e6i	0.0563222	+	0.0262635i
$477$	−2.82110e7	+	1.59993e8i	−0.259935	+	1.47416i
$478$	1.82574e6	+	1.53197e6i	0.0167168	+	0.0140271i
$479$	−3.85607e6	+	4.40750e7i	−0.0350863	+	0.401039i	0.958262	+	0.285891i	$0.0922896\pi$
$479$	−3.85607e6	+	4.40750e7i	−0.0350863	+	0.401039i	−0.993348	+	0.115147i	$0.963266\pi$
$480$		−	4.18740e6i		−	0.0378635i
$481$	5.73932e7	+	9.49109e7i	0.515733	+	0.852866i
$482$	1.60348e8			1.43193
$483$	−8.91881e6	−	780295.i	−0.0791527	−	0.00692496i
$484$	6.71467e6	−	8.00223e6i	0.0592228	−	0.0705790i
$485$	−1.96631e8	−	3.46713e7i	−1.72356	−	0.303910i
$486$	−1.52954e7	+	3.28011e7i	−0.133245	+	0.285746i
$487$	8.85952e6	−	8.85952e6i	0.0767049	−	0.0767049i	−0.667713	−	0.744418i	$-0.732727\pi$
$487$	8.85952e6	−	8.85952e6i	0.0767049	−	0.0767049i	0.744418	+	0.667713i	$0.232727\pi$
$488$	1.19647e8	−	4.35480e7i	1.02954	−	0.374721i
$489$	−6.44353e6	−	1.72654e6i	−0.0551058	−	0.0147656i
$490$	−3.21464e7	−	1.82311e8i	−0.273240	−	1.54962i
$491$	2.77677e7	−	4.80950e7i	0.234582	−	0.406308i	−0.724569	−	0.689202i	$-0.757961\pi$
$491$	2.77677e7	−	4.80950e7i	0.234582	−	0.406308i	0.959151	+	0.282894i	$0.0912944\pi$
$492$	146225.	−	84423.0i	0.00122780	−	0.000708868i
$493$	1.17110e7	−	9.82668e6i	0.0977356	−	0.0820099i
$494$	2.99878e7	+	4.28271e7i	0.248751	+	0.355253i
$495$	−3.08197e8	+	8.25811e7i	−2.54105	+	0.680871i
$496$	−3.01473e7	−	6.46510e7i	−0.247060	−	0.529823i
$497$	1.22418e7	+	4.45565e6i	0.0997186	+	0.0362946i
$498$	1.02970e7	+	7.21001e6i	0.0833722	+	0.0583778i
$499$	−1.13475e7	−	1.29702e8i	−0.0913266	−	1.04387i	−0.894185	−	0.447698i	$-0.852244\pi$
$499$	−1.13475e7	−	1.29702e8i	−0.0913266	−	1.04387i	0.802858	−	0.596170i	$-0.203311\pi$
$500$	3.81568e7	−	3.33828e6i	0.305254	−	0.0267063i
$501$	1.28444e7	−	1.83437e7i	0.102141	−	0.145873i
$502$	1.02052e7	−	2.80386e7i	0.0806698	−	0.221638i
$503$	−1.97575e8	+	9.21306e7i	−1.55249	+	0.723936i	−0.994384	−	0.105836i	$-0.966248\pi$
$503$	−1.97575e8	+	9.21306e7i	−1.55249	+	0.723936i	−0.558102	+	0.829772i	$0.688470\pi$
$504$	1.43024e7	+	5.33772e7i	0.111716	+	0.416931i
$505$	4.33895e7	−	3.03817e7i	0.336908	−	0.235905i
$506$	2.05836e8	+	2.45306e8i	1.58880	+	1.89346i
$507$	−43996.1	−	76203.4i	−0.000337590	−	0.000584724i
$508$	−1.58011e7	−	9.12279e6i	−0.120531	−	0.0695884i
$509$	3.99595e7	−	7.04594e6i	0.303017	−	0.0534300i	−0.0200725	−	0.999799i	$-0.506390\pi$
$509$	3.99595e7	−	7.04594e6i	0.303017	−	0.0534300i	0.323089	+	0.946369i	$0.395279\pi$
$510$	9.60177e6	−	3.58343e7i	0.0723837	−	0.270140i
$511$	7.48084e6	+	2.05534e7i	0.0560645	+	0.154036i
$512$	−7.74753e7	−	7.74753e7i	−0.577236	−	0.577236i
$513$	1.02815e7	+	4.79434e6i	0.0761561	+	0.0355122i
$514$	−1.16819e7	+	6.62511e7i	−0.0860246	+	0.487870i
$515$	2.40980e8	+	2.02206e8i	1.76425	+	1.48038i
$516$	188148.	−	2.15054e6i	0.00136946	−	0.0156530i
$517$			2.12426e8i			1.53722i
$518$	−6.59298e7	+	1.30085e7i	−0.474343	+	0.0935921i
$519$	−1.45258e7			−0.103905
$520$	2.51774e8	+	2.20273e7i	1.79061	+	0.156658i
$521$	−5.48900e7	+	6.54154e7i	−0.388133	+	0.462559i	−0.924364	−	0.381513i	$-0.875403\pi$
$521$	−5.48900e7	+	6.54154e7i	−0.388133	+	0.462559i	0.536231	+	0.844071i	$0.319848\pi$
$522$	−1.34726e7	−	2.37558e6i	−0.0947197	−	0.0167016i
$523$	6.29653e7	−	1.35030e8i	0.440146	−	0.943895i	−0.553658	−	0.832744i	$-0.686768\pi$
$523$	6.29653e7	−	1.35030e8i	0.440146	−	0.943895i	0.993804	−	0.111151i	$-0.0354538\pi$
$524$	1.85483e6	−	1.85483e6i	0.0128917	−	0.0128917i
$525$	1.68475e7	−	6.13198e6i	0.116428	−	0.0423763i
$526$	1.34533e7	+	3.60481e6i	0.0924426	+	0.0247699i
$527$	−1.87792e7	−	1.06502e8i	−0.128305	−	0.727657i
$528$	−1.13490e7	+	1.96571e7i	−0.0771004	+	0.133542i
$529$	−2.39339e8	+	1.38183e8i	−1.61677	+	0.933440i
$530$	−3.44860e8	+	2.89372e8i	−2.31641	+	1.94370i
$531$	−3.92588e7	−	5.60673e7i	−0.262212	−	0.374478i
$532$	−2.72860e6	+	731127.i	−0.0181220	+	0.00485577i
$533$	9.08116e6	+	1.94746e7i	0.0599735	+	0.128614i
$534$	−2.39060e6	−	870106.i	−0.0156994	−	0.00571411i
$535$	1.45291e8	+	1.01734e8i	0.948807	+	0.664362i
$536$	−1.11058e6	−	1.26939e7i	−0.00721197	−	0.0824332i
$537$	7.59142e6	−	664163.i	0.0490230	−	0.00428896i
$538$	1.45718e7	−	2.08106e7i	0.0935761	−	0.133641i
$539$	−5.87293e7	+	1.61357e8i	−0.375049	+	1.03044i
$540$	−5.39438e6	+	2.51544e6i	−0.0342579	+	0.0159747i
$541$	−2.55046e7	−	9.51846e7i	−0.161075	−	0.601139i	−0.998508	−	0.0545999i	$-0.982612\pi$
$541$	−2.55046e7	−	9.51846e7i	−0.161075	−	0.601139i	0.837434	−	0.546539i	$-0.184055\pi$
$542$	−1.79500e8	+	1.25687e8i	−1.12737	+	0.789391i
$543$	2.68204e6	+	3.19633e6i	0.0167520	+	0.0199642i
$544$	2.16064e7	+	3.74234e7i	0.134210	+	0.232459i
$545$	1.22873e8	+	7.09409e7i	0.759046	+	0.438235i
$546$	−7.85566e6	+	1.38517e6i	−0.0482620	+	0.00850988i
$547$	3.22617e7	−	1.20402e8i	0.197118	−	0.735653i	−0.794591	−	0.607145i	$-0.792315\pi$
$547$	3.22617e7	−	1.20402e8i	0.197118	−	0.735653i	0.991708	−	0.128508i	$-0.0410188\pi$
$548$	1.26767e6	+	3.48290e6i	0.00770309	+	0.0211641i
$549$	−1.34218e8	−	1.34218e8i	−0.811135	−	0.811135i
$550$	−5.81187e8	−	2.71012e8i	−3.49324	−	1.62892i
$551$	−1.11888e6	+	6.34546e6i	−0.00668847	+	0.0379322i
$552$	−2.09712e7	−	1.75969e7i	−0.124683	−	0.104621i
$553$	−6.94209e6	+	7.93484e7i	−0.0410501	+	0.469205i
$554$		−	9.42589e7i		−	0.554361i
$555$	1.19748e7	+	3.09344e7i	0.0700471	+	0.180952i
$556$	3.33848e6			0.0194234
$557$	8.86618e7	+	7.75690e6i	0.513063	+	0.0448872i	0.340748	−	0.940155i	$-0.389320\pi$
$557$	8.86618e7	+	7.75690e6i	0.513063	+	0.0448872i	0.172315	+	0.985042i	$0.444875\pi$
$558$	−6.22064e7	+	7.41347e7i	−0.358041	+	0.426696i
$559$	2.70556e8	+	4.77063e7i	1.54889	+	0.273111i
$560$	−7.11118e7	+	1.52500e8i	−0.404928	+	0.868370i
$561$	−2.43322e7	+	2.43322e7i	−0.137814	+	0.137814i
$562$	2.48995e8	−	9.06269e7i	1.40276	−	0.510561i
$563$	1.65663e8	+	4.43893e7i	0.928326	+	0.248744i	0.691141	−	0.722720i	$-0.257108\pi$
$563$	1.65663e8	+	4.43893e7i	0.928326	+	0.248744i	0.237186	+	0.971464i	$0.423775\pi$
$564$	342268.	+	1.94110e6i	0.00190778	+	0.0108196i
$565$	−1.63608e8	+	2.83377e8i	−0.907108	+	1.57116i
$566$	1.33758e8	−	7.72252e7i	0.737684	−	0.425902i
$567$	6.24403e7	−	5.23936e7i	0.342543	−	0.287428i
$568$	2.28485e7	+	3.26311e7i	0.124685	+	0.178068i
$569$	6.71193e7	−	1.79846e7i	0.364343	−	0.0976255i	−0.0720027	−	0.997404i	$-0.522939\pi$
$569$	6.71193e7	−	1.79846e7i	0.364343	−	0.0976255i	0.436346	+	0.899779i	$0.356272\pi$
$570$	6.60808e6	+	1.41711e7i	0.0356821	+	0.0765206i
$571$	−2.05589e8	−	7.48282e7i	−1.10431	−	0.401936i	−0.275407	−	0.961328i	$-0.588813\pi$
$571$	−2.05589e8	−	7.48282e7i	−1.10431	−	0.401936i	−0.828903	+	0.559392i	$0.811035\pi$
$572$	2.08422e7	+	1.45939e7i	0.111367	+	0.0779800i
$573$	−941449.	−	1.07608e7i	−0.00500418	−	0.0571980i
$574$	−1.29695e7	+	1.13468e6i	−0.0685785	+	0.00599984i
$575$	4.87477e8	−	6.96189e8i	2.56419	−	3.66204i
$576$	−5.71723e7	+	1.57080e8i	−0.299170	+	0.821964i
$577$	1.43524e8	−	6.69264e7i	0.747132	−	0.348393i	−0.0114816	−	0.999934i	$-0.503655\pi$
$577$	1.43524e8	−	6.69264e7i	0.747132	−	0.348393i	0.758614	+	0.651541i	$0.225877\pi$
$578$	4.67199e7	+	1.74361e8i	0.241946	+	0.902954i
$579$	−2.99977e6	+	2.10046e6i	−0.0154544	+	0.0108213i
$580$	−2.17302e6	−	2.58971e6i	−0.0111373	−	0.0132729i
$581$	−4.32175e7	−	7.48550e7i	−0.220359	−	0.381674i
$582$	1.66879e7	+	9.63479e6i	0.0846513	+	0.0488735i
$583$	4.11226e8	−	7.25103e7i	2.07527	−	0.365926i
$584$	−1.73102e7	+	6.46025e7i	−0.0869087	+	0.324348i
$585$	−1.28863e8	−	3.54047e8i	−0.643664	−	1.76845i
$586$	2.12494e8	+	2.12494e8i	1.05598	+	1.05598i
$587$	−2.91369e8	−	1.35868e8i	−1.44055	−	0.671741i	−0.463766	−	0.885957i	$-0.653502\pi$
$587$	−2.91369e8	−	1.35868e8i	−1.44055	−	0.671741i	−0.976786	+	0.214217i	$0.931280\pi$
$588$	−276670.	+	1.56907e6i	−0.00136091	+	0.00771811i
$589$	3.49167e7	+	2.92986e7i	0.170878	+	0.143384i
$590$	1.65303e7	−	1.88942e8i	0.0804869	−	0.919969i
$591$			1.32633e7i			0.0642523i
$592$	−2.06536e8	−	9.12587e7i	−0.995477	−	0.439855i
$593$	−2.59763e8			−1.24570			−0.622849	−	0.782342i	$-0.714025\pi$
$593$	−2.59763e8			−1.24570			−0.622849	+	0.782342i	$0.714025\pi$
$594$	6.16729e7	+	5.39568e6i	0.294262	+	0.0257446i
$595$	−1.63971e8	+	1.95413e8i	−0.778425	+	0.927691i
$596$	3.77239e6	+	665173.i	0.0178188	+	0.00314193i
$597$	−4.86375e6	+	1.04303e7i	−0.0228585	+	0.0490202i
$598$	−2.67381e8	+	2.67381e8i	−1.25034	+	1.25034i
$599$	2.47621e8	−	9.01266e7i	1.15214	−	0.419346i	0.305859	−	0.952077i	$-0.401056\pi$
$599$	2.47621e8	−	9.01266e7i	1.15214	−	0.419346i	0.846285	+	0.532731i	$0.178834\pi$
$600$	5.29541e7	+	1.41890e7i	0.245158	+	0.0656899i
$601$	−6.41784e7	−	3.63974e8i	−0.295642	−	1.67667i	−0.664583	−	0.747214i	$-0.731391\pi$
$601$	−6.41784e7	−	3.63974e8i	−0.295642	−	1.67667i	0.368941	−	0.929453i	$-0.379720\pi$
$602$	−8.32264e7	+	1.44152e8i	−0.381480	+	0.660743i
$603$	−1.64510e7	+	9.49799e6i	−0.0750309	+	0.0433191i
$604$	−1.08083e7	+	9.06927e6i	−0.0490510	+	0.0411587i
$605$	2.28047e8	+	3.25685e8i	1.02981	+	1.47072i
$606$	−4.93783e6	+	1.32309e6i	−0.0221880	+	0.00594526i
$607$	−4.13285e7	−	8.86292e7i	−0.184792	−	0.396288i	0.791987	−	0.610538i	$-0.209047\pi$
$607$	−4.13285e7	−	8.86292e7i	−0.184792	−	0.396288i	−0.976779	+	0.214250i	$0.931269\pi$
$608$	−1.71147e7	−	6.22926e6i	−0.0761482	−	0.0277157i
$609$	−805293.	−	563872.i	−0.00356535	−	0.00249648i
$610$	−4.58417e7	−	5.23973e8i	−0.201963	−	2.30845i
$611$	−2.49886e8	+	2.18622e7i	−1.09551	+	0.0958451i
$612$	1.75239e7	−	2.50268e7i	0.0764500	−	0.109182i
$613$	1.16099e8	−	3.18980e8i	0.504021	−	1.38479i	−0.383297	−	0.923625i	$-0.625211\pi$
$613$	1.16099e8	−	3.18980e8i	0.504021	−	1.38479i	0.887317	−	0.461160i	$-0.152567\pi$
$614$	2.91050e8	−	1.35719e8i	1.25737	−	0.586320i
$615$	1.66327e6	+	6.20741e6i	0.00715052	+	0.0266861i
$616$	1.16348e8	−	8.14674e7i	0.497754	−	0.348531i
$617$	−2.05434e8	−	2.44827e8i	−0.874615	−	1.04233i	−0.998746	−	0.0500599i	$-0.984059\pi$
$617$	−2.05434e8	−	2.44827e8i	−0.874615	−	1.04233i	0.124131	−	0.992266i	$-0.460386\pi$
$618$	−1.51799e7	−	2.62924e7i	−0.0643137	−	0.111395i
$619$	1.45486e8	+	8.39965e7i	0.613409	+	0.354152i	0.774298	−	0.632821i	$-0.218103\pi$
$619$	1.45486e8	+	8.39965e7i	0.613409	+	0.354152i	−0.160890	+	0.986972i	$0.551436\pi$
$620$	−2.35514e7	+	4.15274e6i	−0.0988191	+	0.0174245i
$621$	−2.12358e7	+	7.92530e7i	−0.0886734	+	0.330934i
$622$	1.59240e8	+	4.37507e8i	0.661728	+	1.81808i
$623$	1.23695e7	+	1.23695e7i	0.0511548	+	0.0511548i
$624$	−2.42915e7	−	1.13273e7i	−0.0999773	−	0.0466202i
$625$	−1.41213e8	+	8.00856e8i	−0.578407	+	3.28031i
$626$	1.02662e8	+	8.61439e7i	0.418493	+	0.351157i
$627$	1.26405e6	−	1.44481e7i	0.00512816	−	0.0586151i
$628$		−	1.20367e7i		−	0.0485990i
$629$	−2.66638e8	−	2.14677e8i	−1.07144	−	0.862646i
$630$	2.28276e8			0.912934
$631$	2.12536e8	+	1.85945e7i	0.845949	+	0.0740109i	0.501884	−	0.864935i	$-0.332640\pi$
$631$	2.12536e8	+	1.85945e7i	0.845949	+	0.0740109i	0.344065	+	0.938946i	$0.388196\pi$
$632$	−1.56556e8	+	1.86576e8i	−0.620179	+	0.739101i
$633$	−6.27623e6	−	1.10667e6i	−0.0247450	−	0.00436321i
$634$	−1.41233e7	+	3.02875e7i	−0.0554202	+	0.118849i
$635$	4.91042e8	−	4.91042e8i	1.91777	−	1.91777i
$636$	3.64086e6	−	1.32516e6i	0.0141525	−	0.00515108i
$637$	−1.95856e8	−	5.24796e7i	−0.757739	−	0.203035i
$638$	6.10592e6	+	3.46284e7i	0.0235120	+	0.133343i
$639$	2.96924e7	−	5.14288e7i	0.113800	−	0.197108i
$640$	−4.85672e8	+	2.80403e8i	−1.85269	+	1.06965i
$641$	−1.64363e8	+	1.37917e8i	−0.624064	+	0.523652i	−0.899078	−	0.437789i	$-0.855762\pi$
$641$	−1.64363e8	+	1.37917e8i	−0.624064	+	0.523652i	0.275014	+	0.961440i	$0.411317\pi$
$642$	−9.81835e6	−	1.40221e7i	−0.0371051	−	0.0529915i
$643$	−1.61298e8	+	4.32196e7i	−0.606730	+	0.162573i	−0.549088	−	0.835765i	$-0.685025\pi$
$643$	−1.61298e8	+	4.32196e7i	−0.606730	+	0.162573i	−0.0576420	+	0.998337i	$0.518358\pi$
$644$	−8.63448e6	−	1.85167e7i	−0.0323280	−	0.0693276i
$645$	7.72084e7	+	2.81015e7i	0.287730	+	0.104725i
$646$	−1.32178e8	−	9.25521e7i	−0.490300	−	0.343312i
$647$	2.30663e7	+	2.63649e8i	0.0851659	+	0.973451i	0.911779	+	0.410681i	$0.134709\pi$
$647$	2.30663e7	+	2.63649e8i	0.0851659	+	0.973451i	−0.826613	+	0.562770i	$0.809736\pi$
$648$	2.48292e8	−	2.17227e7i	0.912509	−	0.0798342i
$649$	−1.00906e8	+	1.44109e8i	−0.369133	+	0.527177i
$650$	2.58990e8	−	7.11569e8i	0.943067	−	2.59106i
$651$	−6.30278e6	+	2.93904e6i	−0.0228449	+	0.0106528i
$652$	−3.94005e6	−	1.47045e7i	−0.0142154	−	0.0530526i
$653$	3.74998e8	−	2.62576e8i	1.34676	−	0.943010i	0.346770	−	0.937950i	$-0.387278\pi$
$653$	3.74998e8	−	2.62576e8i	1.34676	−	0.943010i	0.999987	−	0.00505931i	$-0.00161043\pi$
$654$	−8.80170e6	−	1.04895e7i	−0.0314654	−	0.0374990i
$655$	4.99190e7	+	8.64622e7i	0.177640	+	0.307682i
$656$	−3.78842e7	−	2.18724e7i	−0.134198	−	0.0774793i
$657$	9.81897e7	−	1.73135e7i	0.346234	−	0.0610504i
$658$	3.93351e7	−	1.46800e8i	0.138071	−	0.515288i
$659$	1.06051e8	+	2.91372e8i	0.370559	+	1.01810i	0.975146	+	0.221563i	$0.0711159\pi$
$659$	1.06051e8	+	2.91372e8i	0.370559	+	1.01810i	−0.604587	+	0.796539i	$0.706662\pi$
$660$	5.38069e6	+	5.38069e6i	0.0187157	+	0.0187157i
$661$	−1.08393e8	−	5.05443e7i	−0.375314	−	0.175012i	0.225802	−	0.974173i	$-0.427500\pi$
$661$	−1.08393e8	−	5.05443e7i	−0.375314	−	0.175012i	−0.601117	+	0.799161i	$0.705277\pi$
$662$	−9.19243e7	+	5.21328e8i	−0.316852	+	1.79696i
$663$	−3.11272e7	−	2.61188e7i	−0.106807	−	0.0896217i
$664$	2.30352e7	−	2.63294e8i	0.0786844	−	0.899367i
$665$		−	1.07516e8i		−	0.365601i
$666$	6.21008e6	+	3.06268e8i	0.0210220	+	1.03676i
$667$	−4.66018e7			−0.157045
$668$	5.09088e7	+	4.45394e6i	0.170790	+	0.0149422i
$669$	8.18078e6	−	9.74947e6i	0.0273222	−	0.0325614i
$670$	−5.18385e7	−	9.14053e6i	−0.172357	−	0.0303911i
$671$	−2.06183e8	+	4.42162e8i	−0.682474	+	1.46357i
$672$	1.96493e6	−	1.96493e6i	0.00647500	−	0.00647500i
$673$	5.20614e8	−	1.89488e8i	1.70793	−	0.621637i	0.711244	−	0.702945i	$-0.248132\pi$
$673$	5.20614e8	−	1.89488e8i	1.70793	−	0.621637i	0.996689	+	0.0813082i	$0.0259098\pi$
$674$	−3.83808e8	−	1.02841e8i	−1.25353	−	0.335882i
$675$	−2.85318e7	−	1.61812e8i	−0.0927720	−	0.526136i
$676$	100401.	−	173900.i	0.000325012	−	0.000562937i
$677$	−8.58485e7	+	4.95647e7i	−0.276673	+	0.159737i	−0.631916	−	0.775037i	$-0.717731\pi$
$677$	−8.58485e7	+	4.95647e7i	−0.276673	+	0.159737i	0.355243	+	0.934774i	$0.384398\pi$
$678$	2.41914e7	−	2.02990e7i	0.0776196	−	0.0651306i
$679$	−7.59991e7	−	1.08538e8i	−0.242772	−	0.346715i
$680$	−7.53444e8	+	2.01885e8i	−2.39621	+	0.642062i
$681$	1.65718e7	+	3.55383e7i	0.0524721	+	0.112527i
$682$	2.33740e8	+	8.50746e7i	0.736853	+	0.268193i
$683$	−1.09840e8	−	7.69111e7i	−0.344747	−	0.241394i	0.388360	−	0.921508i	$-0.373042\pi$
$683$	−1.09840e8	−	7.69111e7i	−0.344747	−	0.241394i	−0.733107	+	0.680113i	$0.761931\pi$
$684$	1.12230e6	+	1.28279e7i	0.00350704	+	0.0400856i
$685$	−1.40532e8	+	1.22950e7i	−0.437223	+	0.0382521i
$686$	1.59991e8	−	2.28490e8i	0.495590	−	0.707775i
$687$	2.79261e6	−	7.67265e6i	0.00861273	−	0.0236633i
$688$	−5.06891e8	+	2.36367e8i	−1.55650	+	0.725809i
$689$	1.27619e8	+	4.76282e8i	0.390174	+	1.45615i
$690$	−9.26367e7	+	6.48649e7i	−0.281991	+	0.197452i
$691$	−2.04766e8	−	2.44030e8i	−0.620616	−	0.739621i	0.360560	−	0.932736i	$-0.382586\pi$
$691$	−2.04766e8	−	2.44030e8i	−0.620616	−	0.739621i	−0.981176	+	0.193115i	$0.938141\pi$
$692$	−1.65743e7	−	2.87074e7i	−0.0500168	−	0.0866316i
$693$	−1.83372e8	−	1.05870e8i	−0.550976	−	0.318106i
$694$	4.97251e8	−	8.76787e7i	1.48764	−	0.262310i
$695$	−3.28867e7	+	1.22735e8i	−0.0979639	+	0.365606i
$696$	−1.02813e6	−	2.82476e6i	−0.00304944	−	0.00837827i
$697$	−4.68942e7	−	4.68942e7i	−0.138491	−	0.138491i
$698$	−3.03539e8	−	1.41543e8i	−0.892582	−	0.416218i
$699$	5.64600e6	−	3.20201e7i	0.0165314	−	0.0937542i
$700$	3.13421e7	+	2.62991e7i	0.0913764	+	0.0766739i
$701$	1.93520e6	−	2.21194e7i	0.00561787	−	0.0642125i	−0.992868	−	0.119217i	$-0.961962\pi$
$701$	1.93520e6	−	2.21194e7i	0.00561787	−	0.0642125i	0.998486	+	0.0550042i	$0.0175172\pi$
$702$			7.31039e7i			0.211315i
$703$	1.44249e8	−	2.92488e6i	0.415190	−	0.00841865i
$704$	4.29650e8			1.23139
$705$	−7.47335e7	−	6.53833e6i	−0.213279	−	0.0186595i
$706$	4.00298e8	−	4.77057e8i	1.13755	−	1.35568i
$707$	3.46170e7	+	6.10391e6i	0.0979560	+	0.0172723i
$708$	−689863.	+	1.47942e6i	−0.00194385	+	0.00416860i
$709$	2.26278e8	−	2.26278e8i	0.634897	−	0.634897i	−0.314395	−	0.949292i	$-0.601802\pi$
$709$	2.26278e8	−	2.26278e8i	0.634897	−	0.634897i	0.949292	+	0.314395i	$0.101802\pi$
$710$	1.54633e8	−	5.62817e7i	0.432042	−	0.157251i
$711$	3.50715e8	+	9.39737e7i	0.975764	+	0.261455i
$712$	9.28845e6	+	5.26774e7i	0.0257337	+	0.145943i
$713$	−1.64832e8	+	2.85497e8i	−0.454749	+	0.787648i
$714$	2.13208e7	−	1.23096e7i	0.0585745	−	0.0338180i
$715$	−7.41839e8	+	6.22476e8i	−2.02951	+	1.70296i
$716$	9.97460e6	+	1.42452e7i	0.0271742	+	0.0388087i
$717$	754106.	−	202062.i	0.00204586	−	0.000548186i
$718$	−9.62953e7	−	2.06506e8i	−0.260155	−	0.557904i
$719$	6.55545e8	+	2.38599e8i	1.76366	+	0.641921i	0.999993	−	0.00368354i	$-0.00117251\pi$
$719$	6.55545e8	+	2.38599e8i	1.76366	+	0.641921i	0.763672	+	0.645605i	$0.223395\pi$
$720$	6.28310e8	+	4.39947e8i	1.68336	+	1.17870i
$721$	1.81945e7	+	2.07964e8i	0.0485439	+	0.554859i
$722$	−3.25111e8	+	2.84435e7i	−0.863813	+	0.0755739i
$723$	3.01272e7	−	4.30261e7i	0.0797157	−	0.113846i
$724$	−3.25667e6	+	8.94764e6i	−0.00858141	+	0.0235772i
$725$	8.45794e7	−	3.94400e7i	0.221948	−	0.103496i
$726$	−9.93120e6	−	3.70637e7i	−0.0259532	−	0.0968588i
$727$	2.46771e7	−	1.72791e7i	0.0642230	−	0.0449694i	−0.541024	−	0.841007i	$-0.681963\pi$
$727$	2.46771e7	−	1.72791e7i	0.0642230	−	0.0449694i	0.605247	+	0.796038i	$0.293074\pi$
$728$	1.07808e8	+	1.28481e8i	0.279420	+	0.332999i
$729$	−1.81793e8	−	3.14874e8i	−0.469239	−	0.812746i
$730$	2.39268e8	+	1.38142e8i	0.615058	+	0.355104i
$731$	−8.35022e8	+	1.47237e8i	−2.13769	+	0.376933i
$732$	−1.17163e6	+	4.37258e6i	−0.00298715	+	0.0111482i
$733$	1.63173e8	+	4.48313e8i	0.414319	+	1.13833i	0.954871	+	0.297022i	$0.0959934\pi$
$733$	1.63173e8	+	4.48313e8i	0.414319	+	1.13833i	−0.540551	+	0.841311i	$0.681784\pi$
$734$	−4.37793e8	−	4.37793e8i	−1.10708	−	1.10708i
$735$	−5.49595e7	−	2.56281e7i	−0.138414	−	0.0645437i
$736$	2.28742e7	−	1.29726e8i	0.0573737	−	0.325382i
$737$	3.74021e7	+	3.13841e7i	0.0934315	+	0.0783984i
$738$	−5.17239e6	+	5.91207e7i	−0.0128683	+	0.147086i
$739$		−	2.99897e8i		−	0.743086i	−0.928416	−	0.371543i	$-0.878829\pi$
$739$		−	2.99897e8i		−	0.743086i	0.928416	−	0.371543i	$-0.121171\pi$
$740$	−4.74725e7	+	5.89629e7i	−0.117151	+	0.145507i
$741$	1.71261e7			0.0420924
$742$	−2.97612e8	−	2.60377e7i	−0.728515	−	0.0637368i
$743$	−3.79344e8	+	4.52085e8i	−0.924841	+	1.10218i	0.0696719	+	0.997570i	$0.477805\pi$
$743$	−3.79344e8	+	4.52085e8i	−0.924841	+	1.10218i	−0.994513	+	0.104613i	$0.966640\pi$
$744$	−2.09419e7	−	3.69261e6i	−0.0508506	−	0.00896634i
$745$	−6.16153e7	+	1.32134e8i	−0.149011	+	0.319556i
$746$	1.21680e8	−	1.21680e8i	0.293092	−	0.293092i
$747$	−3.70247e8	+	1.34759e8i	−0.888239	+	0.323293i
$748$	−7.58516e7	−	2.03244e7i	−0.181242	−	0.0485638i
$749$	2.04391e7	+	1.15916e8i	0.0486426	+	0.275866i
$750$	7.03469e7	−	1.21844e8i	0.166748	−	0.288817i
$751$	2.88524e8	−	1.66579e8i	0.681180	−	0.393280i	−0.119119	−	0.992880i	$-0.538007\pi$
$751$	2.88524e8	−	1.66579e8i	0.681180	−	0.393280i	0.800300	+	0.599600i	$0.204674\pi$
$752$	3.91188e8	−	3.28246e8i	0.919882	−	0.771873i
$753$	−5.60617e6	−	8.00644e6i	−0.0131305	−	0.0187523i
$754$	−4.01065e7	+	1.07465e7i	−0.0935624	+	0.0250700i
$755$	−2.26949e8	−	4.86694e8i	−0.527336	−	1.13088i
$756$	−3.71167e6	−	1.35094e6i	−0.00859022	−	0.00312658i
$757$	−4.32316e8	−	3.02711e8i	−0.996584	−	0.697816i	−0.0430411	−	0.999073i	$-0.513705\pi$
$757$	−4.32316e8	−	3.02711e8i	−0.996584	−	0.697816i	−0.953543	+	0.301258i	$0.902594\pi$
$758$	4.70759e7	+	5.38079e8i	0.108091	+	1.23549i
$759$	1.04497e8	−	9.14229e6i	0.238989	−	0.0209088i
$760$	1.88569e8	−	2.69305e8i	0.429566	−	0.613484i
$761$	1.57150e8	−	4.31766e8i	0.356583	−	0.979704i	−0.623623	−	0.781725i	$-0.714340\pi$
$761$	1.57150e8	−	4.31766e8i	0.356583	−	0.979704i	0.980206	−	0.197979i	$-0.0634378\pi$
$762$	−6.07409e7	+	2.83240e7i	−0.137283	+	0.0640161i
$763$	2.43692e7	+	9.09469e7i	0.0548614	+	0.204746i
$764$	2.01925e7	−	1.41390e7i	0.0452804	−	0.0317057i
$765$	7.47453e8	+	8.90779e8i	1.66955	+	1.98969i
$766$	1.00224e8	+	1.73593e8i	0.222990	+	0.386231i
$767$	−1.79907e8	−	1.03869e8i	−0.398714	−	0.230197i
$768$	1.32022e7	−	2.32791e6i	0.0291450	−	0.00513905i
$769$	1.14235e8	−	4.26331e8i	0.251200	−	0.937492i	−0.718965	−	0.695046i	$-0.755384\pi$
$769$	1.14235e8	−	4.26331e8i	0.251200	−	0.937492i	0.970165	−	0.242445i	$-0.0779495\pi$
$770$	−2.00675e8	−	5.51350e8i	−0.439563	−	1.20769i
$771$	1.55823e7	+	1.55823e7i	0.0339992	+	0.0339992i
$772$	−7.57397e6	−	3.53180e6i	−0.0164616	−	0.00767617i
$773$	4.96452e7	−	2.81552e8i	0.107483	−	0.609565i	−0.882717	−	0.469905i	$-0.844288\pi$
$773$	4.96452e7	−	2.81552e8i	0.107483	−	0.609565i	0.990200	−	0.139660i	$-0.0446009\pi$
$774$	5.81247e8	+	4.87725e8i	1.25354	+	1.05184i
$775$	5.75377e7	−	6.57659e8i	0.123608	−	1.41285i
$776$		−	4.05158e8i		−	0.867040i
$777$	−8.89675e6	+	2.01351e7i	−0.0189657	+	0.0429230i
$778$	−8.47842e8			−1.80043
$779$	2.78452e7	+	2.43614e6i	0.0589031	+	0.00515336i
$780$	−5.77579e6	+	6.88332e6i	−0.0121710	+	0.0145049i
$781$	−1.50317e8	−	2.65049e7i	−0.315540	−	0.0556382i
$782$	4.93213e8	−	1.05770e9i	1.03137	−	2.21178i
$783$	−6.37065e6	+	6.37065e6i	−0.0132708	+	0.0132708i
$784$	3.87895e8	−	1.41182e8i	0.804944	−	0.292976i
$785$	4.42513e8	+	1.18571e8i	0.914780	+	0.245115i
$786$	−1.67316e6	−	9.48898e6i	−0.00344565	−	0.0195412i
$787$	−1.98702e8	+	3.44162e8i	−0.407641	+	0.706056i	−0.994625	−	0.103543i	$-0.966982\pi$
$787$	−1.98702e8	+	3.44162e8i	−0.407641	+	0.706056i	0.586984	+	0.809599i	$0.300315\pi$
$788$	−2.62124e7	+	1.51338e7i	−0.0535709	+	0.0309292i
$789$	3.49498e6	−	2.93264e6i	0.00711563	−	0.00597073i
$790$	5.77087e8	+	8.24165e8i	1.17047	+	1.67160i
$791$	−2.09747e8	+	5.62015e7i	−0.423805	+	0.113558i
$792$	−2.73626e8	−	5.86792e8i	−0.550784	−	1.18116i
$793$	−5.41355e8	−	1.97037e8i	−1.08558	−	0.395119i
$794$	3.93266e8	+	2.75368e8i	0.785642	+	0.550113i
$795$	1.28526e7	+	1.46905e8i	0.0255793	+	0.292372i
$796$	−2.61633e7	+	2.28899e6i	−0.0518744	+	0.00453842i
$797$	−3.03568e8	+	4.33539e8i	−0.599626	+	0.856355i	−0.998150	−	0.0608034i	$-0.980634\pi$
$797$	−3.03568e8	+	4.33539e8i	−0.599626	+	0.856355i	0.398524	+	0.917158i	$0.369523\pi$
$798$	−3.54892e6	+	9.75058e6i	−0.00698373	+	0.0191877i
$799$	7.01640e8	−	3.27180e8i	1.37554	−	0.641426i
$800$	6.82745e7	+	2.54804e8i	0.133349	+	0.497664i
$801$	6.53200e7	−	4.57376e7i	0.127101	−	0.0889970i
$802$	9.54118e7	+	1.13707e8i	0.184960	+	0.220427i
$803$	−1.28134e8	−	2.21935e8i	−0.247468	−	0.428626i
$804$	392339.	+	226517.i	0.000754906	+	0.000435845i
$805$	7.65800e8	−	1.35031e8i	1.46800	−	0.258849i
$806$	−7.60213e7	+	2.83715e8i	−0.145188	+	0.541848i
$807$	−2.84628e6	−	7.82008e6i	−0.00541572	−	0.0148796i
$808$	7.60029e7	+	7.60029e7i	0.144077	+	0.144077i
$809$	−8.52739e7	−	3.97639e7i	−0.161054	−	0.0751006i	0.340420	−	0.940274i	$-0.389431\pi$
$809$	−8.52739e7	−	3.97639e7i	−0.161054	−	0.0751006i	−0.501474	+	0.865173i	$0.667209\pi$
$810$	1.78787e8	−	1.01395e9i	0.336420	−	1.90793i
$811$	−4.66711e8	−	3.91617e8i	−0.874955	−	0.734175i	0.0901803	−	0.995925i	$-0.471256\pi$
$811$	−4.66711e8	−	3.91617e8i	−0.874955	−	0.734175i	−0.965135	+	0.261751i	$0.915700\pi$
$812$	195529.	−	2.23490e6i	0.000365210	−	0.00417437i
$813$			7.17801e7i			0.133577i
$814$	7.34261e8	−	2.84235e8i	1.36137	−	0.526993i
$815$	5.79403e8			1.07031
$816$	8.24071e7	+	7.20969e6i	0.151668	+	0.0132692i
$817$	2.29713e8	−	2.73762e8i	0.421230	−	0.502003i
$818$	−5.29894e8	−	9.34346e7i	−0.968120	−	0.170706i
$819$	1.05667e8	−	2.26604e8i	0.192349	−	0.412493i
$820$	−1.03700e7	+	1.03700e7i	−0.0188077	+	0.0188077i
$821$	−8.39069e8	+	3.05396e8i	−1.51624	+	0.551866i	−0.960206	−	0.279293i	$-0.909900\pi$
$821$	−8.39069e8	+	3.05396e8i	−1.51624	+	0.551866i	−0.556035	+	0.831159i	$0.687678\pi$
$822$	1.31506e7	+	3.52370e6i	0.0236773	+	0.00634430i
$823$	−1.15196e8	−	6.53309e8i	−0.206651	−	1.17198i	−0.894820	−	0.446427i	$-0.852696\pi$
$823$	−1.15196e8	−	6.53309e8i	−0.206651	−	1.17198i	0.688169	−	0.725551i	$-0.258415\pi$
$824$	−3.19170e8	+	5.52818e8i	−0.570479	+	0.988099i
$825$	−1.81918e8	+	1.05030e8i	−0.323977	+	0.187048i
$826$	9.64177e7	−	8.09040e7i	0.171087	−	0.143559i
$827$	−3.28330e8	−	4.68904e8i	−0.580489	−	0.829024i	0.416289	−	0.909232i	$-0.363330\pi$
$827$	−3.28330e8	−	4.68904e8i	−0.580489	−	0.829024i	−0.996778	+	0.0802083i	$0.974441\pi$
$828$	−8.99597e7	+	2.41046e7i	−0.158474	+	0.0424629i
$829$	3.16534e7	+	6.78809e7i	0.0555593	+	0.119147i	0.932127	−	0.362131i	$-0.117951\pi$
$829$	3.16534e7	+	6.78809e7i	0.0555593	+	0.119147i	−0.876568	+	0.481278i	$0.840173\pi$
$830$	−1.02596e9	−	3.73420e8i	−1.79431	−	0.653075i
$831$	−2.52925e7	−	1.77100e7i	−0.0440746	−	0.0308614i
$832$	4.42182e7	+	5.05417e8i	0.0767771	+	0.877566i
$833$	6.23418e8	−	5.45420e7i	1.07856	−	0.0943618i
$834$	7.03376e6	−	1.00453e7i	0.0121252	−	0.0173166i
$835$	−6.65236e8	+	1.82772e9i	−1.14266	+	3.13943i
$836$	2.99964e7	−	1.39875e7i	0.0513393	−	0.0239399i
$837$	1.64954e7	+	6.15616e7i	0.0281310	+	0.104986i
$838$	−4.48687e8	+	3.14174e8i	−0.762450	+	0.533873i
$839$	2.54388e6	+	3.03168e6i	0.00430736	+	0.00513331i	0.768194	−	0.640217i	$-0.221156\pi$
$839$	2.54388e6	+	3.03168e6i	0.00430736	+	0.00513331i	−0.763886	+	0.645351i	$0.776711\pi$
$840$	2.50800e7	+	4.34398e7i	0.0423145	+	0.0732908i
$841$	5.10701e8	+	2.94853e8i	0.858575	+	0.495699i
$842$	−8.52327e8	+	1.50288e8i	−1.42781	+	0.251761i
$843$	2.24650e7	−	8.38405e7i	0.0374993	−	0.139949i
$844$	−4.97421e6	−	1.36665e7i	−0.00827364	−	0.0227317i
$845$	5.40418e6	+	5.40418e6i	0.00895694	+	0.00895694i
$846$	−6.27878e8	−	2.92784e8i	−1.03697	−	0.483545i
$847$	−4.58164e7	+	2.59838e8i	−0.0753999	+	0.427614i
$848$	−7.68968e8	−	6.45241e8i	−1.26102	−	1.05812i
$849$	4.40950e6	−	5.04009e7i	0.00720554	−	0.0823597i
$850$			2.33707e9i			3.80553i
$851$	2.01998e8	+	1.02376e9i	0.327762	+	1.66116i
$852$	−1.41627e6			−0.00228995
$853$	2.19884e8	+	1.92373e7i	0.354280	+	0.0309955i	0.262907	−	0.964821i	$-0.415319\pi$
$853$	2.19884e8	+	1.92373e7i	0.354280	+	0.0309955i	0.0913730	+	0.995817i	$0.470874\pi$
$854$	2.24362e8	−	2.67385e8i	0.360227	−	0.429302i
$855$	−4.82658e8	−	8.51057e7i	−0.772221	−	0.136163i
$856$	−1.52106e8	+	3.26193e8i	−0.242508	+	0.520060i
$857$	3.14126e8	−	3.14126e8i	0.499070	−	0.499070i	−0.412078	−	0.911149i	$-0.635197\pi$
$857$	3.14126e8	−	3.14126e8i	0.499070	−	0.499070i	0.911149	+	0.412078i	$0.135197\pi$
$858$	8.78241e7	−	3.19653e7i	0.139044	−	0.0506078i
$859$	3.02010e8	+	8.09233e7i	0.476476	+	0.127671i	0.489061	−	0.872249i	$-0.337339\pi$
$859$	3.02010e8	+	8.09233e7i	0.476476	+	0.127671i	−0.0125850	+	0.999921i	$0.504006\pi$
$860$	3.25592e7	+	1.84653e8i	0.0511892	+	0.290309i
$861$	−2.13233e6	+	3.69330e6i	−0.00334076	+	0.00578636i
$862$	3.09886e8	−	1.78913e8i	0.483816	−	0.279331i
$863$	3.89341e8	−	3.26696e8i	0.605756	−	0.508290i	−0.287534	−	0.957770i	$-0.592835\pi$
$863$	3.89341e8	−	3.26696e8i	0.605756	−	0.508290i	0.893290	+	0.449481i	$0.148391\pi$
$864$	−1.46071e7	−	2.08611e7i	−0.0226476	−	0.0323441i
$865$	1.21866e9	−	3.26540e8i	1.88293	−	0.504531i
$866$	5.19595e8	+	1.11428e9i	0.800040	+	1.71569i
$867$	5.55644e7	+	2.02238e7i	0.0852588	+	0.0310316i
$868$	−1.30001e7	−	9.10276e6i	−0.0198787	−	0.0139192i
$869$	−8.13367e7	−	9.29682e8i	−0.123944	−	1.41669i
$870$	−1.23706e7	+	1.08228e6i	−0.0187859	+	0.00164355i
$871$	−3.30692e7	+	4.72277e7i	−0.0500460	+	0.0714731i
$872$	−9.84698e7	+	2.70543e8i	−0.148509	+	0.408026i
$873$	−5.47405e8	+	2.55259e8i	−0.822747	+	0.383653i
$874$	1.27308e8	+	4.75119e8i	0.190687	+	0.711652i
$875$	−7.92474e8	+	5.54896e8i	−1.18293	+	0.828300i
$876$	−1.52845e6	−	1.82153e6i	−0.00227373	−	0.00270972i
$877$	3.05314e8	+	5.28820e8i	0.452635	+	0.783988i	0.998549	−	0.0538540i	$-0.0171506\pi$
$877$	3.05314e8	+	5.28820e8i	0.452635	+	0.783988i	−0.545913	+	0.837842i	$0.683817\pi$
$878$	−4.56439e8	−	2.63525e8i	−0.674372	−	0.389349i
$879$	9.69434e7	−	1.70937e7i	0.142742	−	0.0251693i
$880$	5.10253e8	−	1.90429e9i	0.748752	−	2.79438i
$881$	−1.46064e8	−	4.01308e8i	−0.213607	−	0.586881i	0.785897	−	0.618357i	$-0.212201\pi$
$881$	−1.46064e8	−	4.01308e8i	−0.213607	−	0.586881i	−0.999505	+	0.0314762i	$0.989979\pi$
$882$	−3.95987e8	−	3.95987e8i	−0.577132	−	0.577132i
$883$	7.83179e8	+	3.65202e8i	1.13757	+	0.530459i	0.897814	−	0.440374i	$-0.145154\pi$
$883$	7.83179e8	+	3.65202e8i	1.13757	+	0.530459i	0.239758	+	0.970833i	$0.422932\pi$
$884$	1.61021e7	−	9.13194e7i	0.0233091	−	0.132192i
$885$	−4.75931e7	−	3.99354e7i	−0.0686616	−	0.0576140i
$886$	−6.50673e7	+	7.43723e8i	−0.0935539	+	1.06933i
$887$			8.97615e8i			1.28623i	0.765769	+	0.643116i	$0.222359\pi$
$887$			8.97615e8i			1.28623i	−0.765769	+	0.643116i	$0.777641\pi$
$888$	−5.75989e7	+	3.48304e7i	−0.0822574	+	0.0497415i
$889$	4.60841e8			0.655912
$890$	2.20123e8	+	1.92583e7i	0.312245	+	0.0273179i
$891$	−6.13868e8	+	7.31579e8i	−0.867844	+	1.03426i
$892$	2.86025e7	+	5.04339e6i	0.0403004	+	0.00710605i
$893$	−1.37898e8	+	2.95724e8i	−0.193644	+	0.415272i
$894$	9.94942e6	−	9.94942e6i	0.0139247	−	0.0139247i
$895$	−6.21965e8	+	2.26377e8i	−0.867554	+	0.315764i
$896$	−3.59479e8	−	9.63221e7i	−0.499746	−	0.133907i
$897$	2.15090e7	+	1.21984e8i	0.0298018	+	0.169015i
$898$	1.91697e8	−	3.32029e8i	0.264720	−	0.458508i
$899$	−3.13493e7	+	1.80995e7i	−0.0431468	+	0.0249108i
$900$	1.42871e8	−	1.19883e8i	0.195982	−	0.164449i
$901$	−8.72876e8	−	1.24660e9i	−1.19338	−	1.70432i
$902$	1.47340e8	−	3.94795e7i	0.200770	−	0.0537963i
$903$	2.30433e7	+	4.94165e7i	0.0312954	+	0.0671133i
$904$	−6.23942e8	−	2.27096e8i	−0.844577	−	0.307401i
$905$	−2.96868e8	−	2.07869e8i	−0.400514	−	0.280443i
$906$	4.51699e6	+	5.16294e7i	0.00607385	+	0.0694244i
$907$	−1.31686e9	+	1.15210e8i	−1.76489	+	0.154407i	−0.922887	−	0.385072i	$-0.874177\pi$
$907$	−1.31686e9	+	1.15210e8i	−1.76489	+	0.154407i	−0.841999	+	0.539479i	$0.818621\pi$
$908$	−5.13261e7	+	7.33012e7i	−0.0685615	+	0.0979160i
$909$	5.48032e7	−	1.50570e8i	0.0729649	−	0.200469i
$910$	6.27925e8	−	2.92806e8i	0.833266	−	0.388558i
$911$	−1.58388e8	−	5.91111e8i	−0.209491	−	0.781833i	−0.988033	−	0.154240i	$-0.950707\pi$
$911$	−1.58388e8	−	5.91111e8i	−0.209491	−	0.781833i	0.778542	−	0.627593i	$-0.215960\pi$
$912$	−2.85599e7	+	1.99979e7i	−0.0376507	+	0.0263633i
$913$	6.50959e8	+	7.75783e8i	0.855345	+	1.01936i
$914$	−9.69751e7	−	1.67966e8i	−0.127005	−	0.219980i
$915$	−1.49211e8	−	8.61469e7i	−0.194777	−	0.112454i
$916$	1.83500e7	−	3.23560e6i	0.0238753	−	0.00420987i
$917$	−1.71478e7	+	6.39966e7i	−0.0222383	+	0.0829944i
$918$	−7.71673e7	−	2.12016e8i	−0.0997483	−	0.274056i
$919$	−3.20921e7	−	3.20921e7i	−0.0413478	−	0.0413478i	0.686131	−	0.727478i	$-0.259308\pi$
$919$	−3.20921e7	−	3.20921e7i	−0.0413478	−	0.0413478i	−0.727478	+	0.686131i	$0.759308\pi$
$920$	2.15500e9	+	1.00489e9i	2.76747	+	1.29049i
$921$	1.82670e7	−	1.03597e8i	0.0233823	−	0.132608i
$922$	4.09956e8	+	3.43994e8i	0.523052	+	0.438893i
$923$	1.57088e7	−	1.79552e8i	0.0199773	−	0.228342i
$924$			5.04976e6i			0.00640110i
$925$	−1.23305e9	−	1.68711e9i	−1.55795	−	2.13167i
$926$	3.95537e8			0.498143
$927$	9.47992e8	+	8.29385e7i	1.19005	+	0.104116i
$928$	9.29758e6	−	1.10804e7i	0.0116339	−	0.0138648i
$929$	−7.32116e8	−	1.29092e8i	−0.913130	−	0.161009i	−0.302706	−	0.953084i	$-0.597890\pi$
$929$	−7.32116e8	−	1.29092e8i	−0.913130	−	0.161009i	−0.610424	+	0.792075i	$0.709001\pi$
$930$	−3.71245e7	+	7.96137e7i	−0.0461543	+	0.0989781i
$931$	−1.86506e8	+	1.86506e8i	−0.231123	+	0.231123i
$932$	6.97240e7	−	2.53774e7i	0.0861260	−	0.0313473i
$933$	1.47315e8	+	3.94730e7i	0.181386	+	0.0486021i
$934$	5.68683e6	+	3.22516e7i	0.00697959	+	0.0395832i
$935$	1.49440e9	−	2.58838e9i	1.82823	−	3.16659i
$936$	6.62110e8	−	3.82269e8i	0.807426	−	0.466167i
$937$	2.28214e8	−	1.91494e8i	0.277411	−	0.232775i	−0.493457	−	0.869770i	$-0.664267\pi$
$937$	2.28214e8	−	1.91494e8i	0.277411	−	0.232775i	0.770868	+	0.636995i	$0.219823\pi$
$938$	−2.00360e7	−	2.86143e7i	−0.0242774	−	0.0346717i
$939$	4.24039e7	−	1.13621e7i	0.0512164	−	0.0137234i
$940$	−7.23510e7	−	1.55157e8i	−0.0871086	−	0.186805i
$941$	−1.50628e8	−	5.48240e7i	−0.180774	−	0.0657964i	0.250047	−	0.968234i	$-0.419554\pi$
$941$	−1.50628e8	−	5.48240e7i	−0.180774	−	0.0657964i	−0.430821	+	0.902437i	$0.641776\pi$
$942$	−3.62175e7	−	2.53598e7i	−0.0433277	−	0.0303384i
$943$	1.76195e7	+	2.01392e8i	0.0210116	+	0.240163i
$944$	4.21303e8	−	3.68593e7i	0.500817	−	0.0438158i
$945$	8.62285e7	−	1.23147e8i	0.102177	−	0.145925i
$946$	6.67021e8	−	1.83262e9i	0.787890	−	2.16471i
$947$	2.47728e7	−	1.15517e7i	0.0291692	−	0.0136018i	−0.407979	−	0.912991i	$-0.633766\pi$
$947$	2.47728e7	−	1.15517e7i	0.0291692	−	0.0136018i	0.437148	+	0.899390i	$0.355989\pi$
$948$	−2.24117e6	−	8.36417e6i	−0.00263057	−	0.00981743i
$949$	2.47885e8	−	1.73571e8i	0.290036	−	0.203085i
$950$	−6.33158e8	−	7.54568e8i	−0.738484	−	0.880091i
$951$	5.47346e6	+	9.48032e6i	0.00636386	+	0.0110225i
$952$	−4.48286e8	−	2.58818e8i	−0.519570	−	0.299974i
$953$	1.72537e7	−	3.04229e6i	0.0199344	−	0.00351497i	−0.163672	−	0.986515i	$-0.552334\pi$
$953$	1.72537e7	−	3.04229e6i	0.0199344	−	0.00351497i	0.183606	+	0.983000i	$0.441223\pi$
$954$	−3.52467e8	+	1.31542e9i	−0.405951	+	1.51503i
$955$	3.20888e8	+	8.81632e8i	0.368420	+	1.01223i
$956$	1.25979e6	+	1.25979e6i	0.00144187	+	0.00144187i
$957$	1.04391e7	+	4.86781e6i	0.0119104	+	0.00555390i
$958$	−6.44009e7	+	3.65236e8i	−0.0732479	+	0.415410i
$959$	−7.17137e7	−	6.01750e7i	−0.0813105	−	0.0682276i
$960$	−1.32244e7	+	1.51155e8i	−0.0149472	+	0.170848i
$961$		−	6.31430e8i		−	0.711468i
$962$	4.09927e8	+	8.34493e8i	0.460449	+	0.937340i
$963$	5.36548e8			0.600799
$964$	1.19409e8	+	1.04469e7i	0.133293	+	0.0116616i
$965$	2.04452e8	−	2.43656e8i	0.227515	−	0.271141i
$966$	−7.39073e7	−	1.30319e7i	−0.0819891	−	0.0144569i
$967$	3.73387e8	−	8.00731e8i	0.412933	−	0.885539i	−0.584324	−	0.811521i	$-0.698640\pi$
$967$	3.73387e8	−	8.00731e8i	0.412933	−	0.885539i	0.997257	−	0.0740177i	$-0.0235821\pi$
$968$	−5.70483e8	+	5.70483e8i	−0.628950	+	0.628950i
$969$	−4.96690e7	+	1.80780e7i	−0.0545902	+	0.0198692i
$970$	−1.61665e9	−	4.33181e8i	−1.77134	−	0.474629i
$971$	2.32095e8	+	1.31628e9i	0.253518	+	1.43777i	0.799848	+	0.600202i	$0.204913\pi$
$971$	2.32095e8	+	1.31628e9i	0.253518	+	1.43777i	−0.546330	+	0.837570i	$0.683976\pi$
$972$	−1.35274e7	+	2.34301e7i	−0.0147304	+	0.0255138i
$973$	−7.30251e7	+	4.21611e7i	−0.0792746	+	0.0457692i
$974$	8.04548e7	−	6.75096e7i	0.0870714	−	0.0730615i
$975$	−1.42275e8	−	2.03189e8i	−0.153502	−	0.219223i
$976$	1.13285e9	−	3.03548e8i	1.21850	−	0.326496i
$977$	2.51286e8	+	5.38884e8i	0.269454	+	0.577845i	0.993748	−	0.111646i	$-0.0356122\pi$
$977$	2.51286e8	+	5.38884e8i	0.269454	+	0.577845i	−0.724295	+	0.689491i	$0.757834\pi$
$978$	−5.25459e7	−	1.91252e7i	−0.0561723	−	0.0204451i
$979$	−1.67891e8	−	1.17558e8i	−0.178928	−	0.125287i
$980$	−1.20611e7	−	1.37860e8i	−0.0128148	−	0.146473i
$981$	4.27567e8	−	3.74073e7i	0.452895	−	0.0396232i
$982$	2.67014e8	−	3.81336e8i	0.281968	−	0.402692i
$983$	−4.68371e8	+	1.28684e9i	−0.493093	+	1.35476i	0.404742	+	0.914431i	$0.367361\pi$
$983$	−4.68371e8	+	1.28684e9i	−0.493093	+	1.35476i	−0.897835	+	0.440331i	$0.854861\pi$
$984$	−1.18186e7	+	5.51111e6i	−0.0124046	+	0.00578434i
$985$	−2.98159e8	−	1.11275e9i	−0.311989	−	1.16436i
$986$	1.04973e8	−	7.35028e7i	0.109508	−	0.0766784i
$987$	−3.20005e7	−	3.81367e7i	−0.0332816	−	0.0396635i
$988$	1.95413e7	+	3.38466e7i	0.0202620	+	0.0350949i
$989$	2.23841e9	+	1.29235e9i	2.31394	+	1.33595i
$990$	−2.63396e9	+	4.64438e8i	−2.71458	+	0.478654i
$991$	−3.91253e8	+	1.46017e9i	−0.402010	+	1.50032i	0.407496	+	0.913207i	$0.366402\pi$
$991$	−3.91253e8	+	1.46017e9i	−0.402010	+	1.50032i	−0.809505	+	0.587113i	$0.800265\pi$
$992$	−3.49963e7	−	9.61514e7i	−0.0358498	−	0.0984965i
$993$	1.22617e8	+	1.22617e8i	0.125228	+	0.125228i
$994$	9.89712e7	+	4.61510e7i	0.100774	+	0.0469918i
$995$	1.73578e8	−	9.84408e8i	0.176208	−	0.999323i
$996$	7.19828e6	+	6.04008e6i	0.00728536	+	0.00611314i
$997$	1.08082e8	−	1.23538e9i	0.109060	−	1.24656i	−0.722595	−	0.691272i	$-0.757051\pi$
$997$	1.08082e8	−	1.23538e9i	0.109060	−	1.24656i	0.831655	−	0.555293i	$-0.187394\pi$
$998$		−	1.09138e9i		−	1.09795i
$999$	1.67566e8	+	1.12339e8i	0.168070	+	0.112676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.i.a.2.13	✓	216
37.19	odd	36	inner	37.7.i.a.19.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.i.a.2.13	✓	216	1.1	even	1	trivial
37.7.i.a.19.13	yes	216	37.19	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.i (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(8.35059 + 0.730582i) q^{2} +(1.76500 - 2.10345i) q^{3} +(6.17099 + 1.08811i) q^{4} +(-100.792 + 216.150i) q^{5} +(16.2756 - 16.2756i) q^{6} +(-148.724 + 54.1313i) q^{7} +(-467.463 - 125.256i) q^{8} +(125.280 + 710.500i) q^{9} +O(q^{10})\)	\(q+(8.35059 + 0.730582i) q^{2} +(1.76500 - 2.10345i) q^{3} +(6.17099 + 1.08811i) q^{4} +(-100.792 + 216.150i) q^{5} +(16.2756 - 16.2756i) q^{6} +(-148.724 + 54.1313i) q^{7} +(-467.463 - 125.256i) q^{8} +(125.280 + 710.500i) q^{9} +(-999.591 + 1731.34i) q^{10} +(1605.92 - 927.177i) q^{11} +(13.1806 - 11.0598i) q^{12} +(1255.96 + 1793.69i) q^{13} +(-1281.48 + 343.373i) q^{14} +(276.761 + 593.516i) q^{15} +(-4188.93 - 1524.65i) q^{16} +(-5535.91 - 3876.29i) q^{17} +(527.086 + 6024.62i) q^{18} +(2837.53 - 248.252i) q^{19} +(-857.183 + 1224.18i) q^{20} +(-148.637 + 408.376i) q^{21} +(14087.8 - 6569.23i) q^{22} +(5331.93 + 19899.0i) q^{23} +(-1088.54 + 762.207i) q^{24} +(-26518.1 - 31603.0i) q^{25} +(9177.55 + 15896.0i) q^{26} +(3449.17 + 1991.38i) q^{27} +(-976.678 + 172.215i) q^{28} +(-585.478 + 2185.04i) q^{29} +(1877.51 + 5158.41i) q^{30} +(11315.3 + 11315.3i) q^{31} +(-5795.13 - 2702.32i) q^{32} +(884.181 - 5014.44i) q^{33} +(-43396.2 - 36413.8i) q^{34} +(3289.81 - 37602.8i) q^{35} +4520.80i q^{36} +(50539.4 + 3390.84i) q^{37} +23876.5 q^{38} +(5989.71 + 524.032i) q^{39} +(74190.8 - 88417.1i) q^{40} +(9664.09 + 1704.04i) q^{41} +(-1539.56 + 3301.59i) q^{42} +(88716.9 - 88716.9i) q^{43} +(10919.0 - 3974.18i) q^{44} +(-166202. - 44533.6i) q^{45} +(29986.9 + 170064. i) q^{46} +(-57277.5 + 99207.5i) q^{47} +(-10600.5 + 6120.20i) q^{48} +(-70935.6 + 59522.0i) q^{49} +(-198353. - 283277. i) q^{50} +(-17924.5 + 4802.85i) q^{51} +(5798.76 + 12435.5i) q^{52} +(211603. + 77017.3i) q^{53} +(27347.8 + 19149.1i) q^{54} +(38545.0 + 440571. i) q^{55} +(76303.4 - 6675.69i) q^{56} +(4486.07 - 6406.78i) q^{57} +(-6485.44 + 17818.6i) q^{58} +(-85982.2 + 40094.2i) q^{59} +(1062.08 + 3963.73i) q^{60} +(-215515. + 150905. i) q^{61} +(86222.9 + 102756. i) q^{62} +(-57092.5 - 98887.1i) q^{63} +(200656. + 115849. i) q^{64} +(-514297. + 90684.4i) q^{65} +(11046.9 - 41227.6i) q^{66} +(9005.35 + 24742.0i) q^{67} +(-29944.2 - 29944.2i) q^{68} +(51267.5 + 23906.4i) q^{69} +(54943.8 - 311602. i) q^{70} +(-63054.7 - 52909.1i) q^{71} +(30430.7 - 347824. i) q^{72} -138198. i q^{73} +(419557. + 65238.7i) q^{74} -113280. q^{75} +(17780.5 + 1555.59i) q^{76} +(-188650. + 224824. i) q^{77} +(49634.8 + 8751.96i) q^{78} +(212689. - 456114. i) q^{79} +(751764. - 751764. i) q^{80} +(-483950. + 176143. i) q^{81} +(79456.0 + 21290.2i) q^{82} +(94833.9 + 537830. i) q^{83} +(-1361.59 + 2358.35i) q^{84} +(1.39584e6 - 805886. i) q^{85} +(805654. - 676024. i) q^{86} +(3562.74 + 5088.12i) q^{87} +(-866842. + 232270. i) q^{88} +(-46710.8 - 100172. i) q^{89} +(-1.35535e6 - 493306. i) q^{90} +(-283886. - 198779. i) q^{91} +(11250.9 + 128598. i) q^{92} +(43772.8 - 3829.62i) q^{93} +(-550780. + 786596. i) q^{94} +(-232342. + 638354. i) q^{95} +(-15912.6 + 7420.17i) q^{96} +(216679. + 808658. i) q^{97} +(-635840. + 445220. i) q^{98} +(859949. + 1.02485e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9}+O(q^{10}) \) 216 * q - 12 * q^2 - 12 * q^3 - 282 * q^4 + 186 * q^5 - 12 * q^6 - 12 * q^7 + 1782 * q^8 - 972 * q^9	\( 216 q - 12 q^{2} - 12 q^{3} - 282 q^{4} + 186 q^{5} - 12 q^{6} - 12 q^{7} + 1782 q^{8} - 972 q^{9} - 6 q^{10} - 18 q^{11} - 12300 q^{12} - 12 q^{13} - 2508 q^{14} - 5724 q^{15} + 21138 q^{16} + 14652 q^{17} - 36462 q^{18} + 25692 q^{19} + 15156 q^{20} + 22308 q^{21} - 396 q^{22} - 45372 q^{23} - 130632 q^{24} + 54042 q^{25} + 48834 q^{26} - 18 q^{27} - 261132 q^{28} - 63852 q^{29} + 140076 q^{30} + 255300 q^{31} + 444198 q^{32} + 151134 q^{33} + 121740 q^{34} + 64380 q^{35} - 323412 q^{37} - 530748 q^{38} - 734844 q^{39} - 873996 q^{40} + 143244 q^{41} + 682356 q^{42} + 298788 q^{43} + 410502 q^{44} - 296748 q^{45} + 1696848 q^{46} + 97674 q^{47} - 18 q^{48} - 827124 q^{49} - 701574 q^{50} + 1150788 q^{51} + 452802 q^{52} + 147876 q^{53} - 1733052 q^{54} - 481266 q^{55} - 1608972 q^{56} + 238596 q^{57} + 2880600 q^{58} + 1700916 q^{59} - 2913120 q^{60} - 212628 q^{61} - 3373512 q^{62} - 1185486 q^{63} - 2139876 q^{64} - 2189010 q^{65} + 4562748 q^{66} - 486876 q^{67} + 6077478 q^{68} + 3324612 q^{69} + 6153942 q^{70} + 2088276 q^{71} + 1397046 q^{72} - 212106 q^{74} - 5357160 q^{75} - 2036850 q^{76} - 4623426 q^{77} - 7419738 q^{78} - 2895996 q^{79} - 8321832 q^{80} - 337890 q^{81} - 5343312 q^{82} + 2697348 q^{83} + 1737582 q^{84} + 6365610 q^{85} + 9282138 q^{86} + 9292260 q^{87} + 11436912 q^{88} - 618732 q^{89} - 2893080 q^{90} - 2103804 q^{91} - 1911270 q^{92} + 2397036 q^{93} + 751476 q^{94} - 8155788 q^{95} - 5338512 q^{96} - 8958252 q^{97} + 1386858 q^{98} - 12128778 q^{99}+O(q^{100}) \) 216 * q - 12 * q^2 - 12 * q^3 - 282 * q^4 + 186 * q^5 - 12 * q^6 - 12 * q^7 + 1782 * q^8 - 972 * q^9 - 6 * q^10 - 18 * q^11 - 12300 * q^12 - 12 * q^13 - 2508 * q^14 - 5724 * q^15 + 21138 * q^16 + 14652 * q^17 - 36462 * q^18 + 25692 * q^19 + 15156 * q^20 + 22308 * q^21 - 396 * q^22 - 45372 * q^23 - 130632 * q^24 + 54042 * q^25 + 48834 * q^26 - 18 * q^27 - 261132 * q^28 - 63852 * q^29 + 140076 * q^30 + 255300 * q^31 + 444198 * q^32 + 151134 * q^33 + 121740 * q^34 + 64380 * q^35 - 323412 * q^37 - 530748 * q^38 - 734844 * q^39 - 873996 * q^40 + 143244 * q^41 + 682356 * q^42 + 298788 * q^43 + 410502 * q^44 - 296748 * q^45 + 1696848 * q^46 + 97674 * q^47 - 18 * q^48 - 827124 * q^49 - 701574 * q^50 + 1150788 * q^51 + 452802 * q^52 + 147876 * q^53 - 1733052 * q^54 - 481266 * q^55 - 1608972 * q^56 + 238596 * q^57 + 2880600 * q^58 + 1700916 * q^59 - 2913120 * q^60 - 212628 * q^61 - 3373512 * q^62 - 1185486 * q^63 - 2139876 * q^64 - 2189010 * q^65 + 4562748 * q^66 - 486876 * q^67 + 6077478 * q^68 + 3324612 * q^69 + 6153942 * q^70 + 2088276 * q^71 + 1397046 * q^72 - 212106 * q^74 - 5357160 * q^75 - 2036850 * q^76 - 4623426 * q^77 - 7419738 * q^78 - 2895996 * q^79 - 8321832 * q^80 - 337890 * q^81 - 5343312 * q^82 + 2697348 * q^83 + 1737582 * q^84 + 6365610 * q^85 + 9282138 * q^86 + 9292260 * q^87 + 11436912 * q^88 - 618732 * q^89 - 2893080 * q^90 - 2103804 * q^91 - 1911270 * q^92 + 2397036 * q^93 + 751476 * q^94 - 8155788 * q^95 - 5338512 * q^96 - 8958252 * q^97 + 1386858 * q^98 - 12128778 * q^99

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