LMFDB - Embedded newform 74.7.d.b.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,7,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, 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:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 $ x^20 + 10424x^18 + 44844916x^16 + 103219343022x^14 + 138101513095620x^12 + 109787124347520192x^10 + 51172837440825906441x^8 + 13199761586736849750156x^6 + 1629475196758519705300656x^4 + 65381450766316829487245376*x^2 + 736627437450607950694158336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Root			$4.34837i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 4.00000i) q^{2} -7.34837i q^{3} -32.0000i q^{4} +(166.447 + 166.447i) q^{5} +(29.3935 + 29.3935i) q^{6} -272.903 q^{7} +(128.000 + 128.000i) q^{8} +675.001 q^{9} +O(q^{10})$	\(q+(-4.00000 + 4.00000i) q^{2} -7.34837i q^{3} -32.0000i q^{4} +(166.447 + 166.447i) q^{5} +(29.3935 + 29.3935i) q^{6} -272.903 q^{7} +(128.000 + 128.000i) q^{8} +675.001 q^{9} -1331.57 q^{10} -847.494i q^{11} -235.148 q^{12} +(60.3898 + 60.3898i) q^{13} +(1091.61 - 1091.61i) q^{14} +(1223.11 - 1223.11i) q^{15} -1024.00 q^{16} +(296.654 + 296.654i) q^{17} +(-2700.01 + 2700.01i) q^{18} +(6092.66 + 6092.66i) q^{19} +(5326.29 - 5326.29i) q^{20} +2005.40i q^{21} +(3389.98 + 3389.98i) q^{22} +(1726.81 + 1726.81i) q^{23} +(940.592 - 940.592i) q^{24} +39784.0i q^{25} -483.118 q^{26} -10317.1i q^{27} +8732.91i q^{28} +(-29907.1 + 29907.1i) q^{29} +9784.90i q^{30} +(-645.539 + 645.539i) q^{31} +(4096.00 - 4096.00i) q^{32} -6227.70 q^{33} -2373.23 q^{34} +(-45423.8 - 45423.8i) q^{35} -21600.0i q^{36} +(5510.20 + 50352.4i) q^{37} -48741.3 q^{38} +(443.767 - 443.767i) q^{39} +42610.3i q^{40} +38038.5i q^{41} +(-8021.58 - 8021.58i) q^{42} +(79921.9 + 79921.9i) q^{43} -27119.8 q^{44} +(112352. + 112352. i) q^{45} -13814.5 q^{46} +177704. q^{47} +7524.73i q^{48} -43172.8 q^{49} +(-159136. - 159136. i) q^{50} +(2179.93 - 2179.93i) q^{51} +(1932.47 - 1932.47i) q^{52} -27269.4 q^{53} +(41268.5 + 41268.5i) q^{54} +(141063. - 141063. i) q^{55} +(-34931.6 - 34931.6i) q^{56} +(44771.1 - 44771.1i) q^{57} -239257. i q^{58} +(-236897. - 236897. i) q^{59} +(-39139.6 - 39139.6i) q^{60} +(197119. - 197119. i) q^{61} -5164.32i q^{62} -184210. q^{63} +32768.0i q^{64} +20103.4i q^{65} +(24910.8 - 24910.8i) q^{66} +24811.2i q^{67} +(9492.93 - 9492.93i) q^{68} +(12689.2 - 12689.2i) q^{69} +363391. q^{70} -279996. q^{71} +(86400.2 + 86400.2i) q^{72} +286589. i q^{73} +(-223450. - 179369. i) q^{74} +292347. q^{75} +(194965. - 194965. i) q^{76} +231284. i q^{77} +3550.13i q^{78} +(-446529. - 446529. i) q^{79} +(-170441. - 170441. i) q^{80} +416262. q^{81} +(-152154. - 152154. i) q^{82} +568952. q^{83} +64172.7 q^{84} +98754.2i q^{85} -639375. q^{86} +(219769. + 219769. i) q^{87} +(108479. - 108479. i) q^{88} +(21574.1 - 21574.1i) q^{89} -898814. q^{90} +(-16480.6 - 16480.6i) q^{91} +(55257.9 - 55257.9i) q^{92} +(4743.67 + 4743.67i) q^{93} +(-710816. + 710816. i) q^{94} +2.02821e6i q^{95} +(-30098.9 - 30098.9i) q^{96} +(-1.13802e6 - 1.13802e6i) q^{97} +(172691. - 172691. i) q^{98} -572060. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) $ 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$3$		−	7.34837i		−	0.272162i	−0.990698	−	0.136081i	$-0.956549\pi$
$3$		−	7.34837i		−	0.272162i	0.990698	−	0.136081i	$-0.0434507\pi$
$4$		−	32.0000i		−	0.500000i
$5$	166.447	+	166.447i	1.33157	+	1.33157i	0.903964	+	0.427609i	$0.140644\pi$
$5$	166.447	+	166.447i	1.33157	+	1.33157i	0.427609	+	0.903964i	$0.359356\pi$
$6$	29.3935	+	29.3935i	0.136081	+	0.136081i
$7$	−272.903			−0.795637			−0.397818	−	0.917464i	$-0.630233\pi$
$7$	−272.903			−0.795637			−0.397818	+	0.917464i	$0.630233\pi$
$8$	128.000	+	128.000i	0.250000	+	0.250000i
$9$	675.001			0.925928
$10$	−1331.57			−1.33157
$11$		−	847.494i		−	0.636735i	−0.947967	−	0.318367i	$-0.896865\pi$
$11$		−	847.494i		−	0.636735i	0.947967	−	0.318367i	$-0.103135\pi$
$12$	−235.148			−0.136081
$13$	60.3898	+	60.3898i	0.0274874	+	0.0274874i	0.720717	−	0.693230i	$-0.243813\pi$
$13$	60.3898	+	60.3898i	0.0274874	+	0.0274874i	−0.693230	+	0.720717i	$0.743813\pi$
$14$	1091.61	−	1091.61i	0.397818	−	0.397818i
$15$	1223.11	−	1223.11i	0.362404	−	0.362404i
$16$	−1024.00			−0.250000
$17$	296.654	+	296.654i	0.0603815	+	0.0603815i	0.736653	−	0.676271i	$-0.236405\pi$
$17$	296.654	+	296.654i	0.0603815	+	0.0603815i	−0.676271	+	0.736653i	$0.736405\pi$
$18$	−2700.01	+	2700.01i	−0.462964	+	0.462964i
$19$	6092.66	+	6092.66i	0.888272	+	0.888272i	0.994357	−	0.106085i	$-0.0338315\pi$
$19$	6092.66	+	6092.66i	0.888272	+	0.888272i	−0.106085	+	0.994357i	$0.533831\pi$
$20$	5326.29	−	5326.29i	0.665786	−	0.665786i
$21$			2005.40i			0.216542i
$22$	3389.98	+	3389.98i	0.318367	+	0.318367i
$23$	1726.81	+	1726.81i	0.141926	+	0.141926i	0.774500	−	0.632574i	$-0.218002\pi$
$23$	1726.81	+	1726.81i	0.141926	+	0.141926i	−0.632574	+	0.774500i	$0.718002\pi$
$24$	940.592	−	940.592i	0.0680405	−	0.0680405i
$25$			39784.0i			2.54617i
$26$	−483.118			−0.0274874
$27$		−	10317.1i		−	0.524164i
$28$			8732.91i			0.397818i
$29$	−29907.1	+	29907.1i	−1.22625	+	1.22625i	−0.260883	+	0.965370i	$0.584014\pi$
$29$	−29907.1	+	29907.1i	−1.22625	+	1.22625i	−0.965370	+	0.260883i	$0.915986\pi$
$30$			9784.90i			0.362404i
$31$	−645.539	+	645.539i	−0.0216689	+	0.0216689i	−0.717858	−	0.696189i	$-0.754877\pi$
$31$	−645.539	+	645.539i	−0.0216689	+	0.0216689i	0.696189	+	0.717858i	$0.254877\pi$
$32$	4096.00	−	4096.00i	0.125000	−	0.125000i
$33$	−6227.70			−0.173295
$34$	−2373.23			−0.0603815
$35$	−45423.8	−	45423.8i	−1.05945	−	1.05945i
$36$		−	21600.0i		−	0.462964i
$37$	5510.20	+	50352.4i	0.108783	+	0.994065i
$37$	5510.20	+	50352.4i	0.108783	+	0.994065i
$38$	−48741.3			−0.888272
$39$	443.767	−	443.767i	0.00748102	−	0.00748102i
$40$			42610.3i			0.665786i
$41$			38038.5i			0.551915i	0.961170	+	0.275958i	$0.0889949\pi$
$41$			38038.5i			0.551915i	−0.961170	+	0.275958i	$0.911005\pi$
$42$	−8021.58	−	8021.58i	−0.108271	−	0.108271i
$43$	79921.9	+	79921.9i	1.00522	+	1.00522i	0.999986	+	0.00523198i	$0.00166540\pi$
$43$	79921.9	+	79921.9i	1.00522	+	1.00522i	0.00523198	+	0.999986i	$0.498335\pi$
$44$	−27119.8			−0.318367
$45$	112352.	+	112352.i	1.23294	+	1.23294i
$46$	−13814.5			−0.141926
$47$	177704.			1.71161			0.855803	−	0.517302i	$-0.173064\pi$
$47$	177704.			1.71161			0.855803	+	0.517302i	$0.173064\pi$
$48$			7524.73i			0.0680405i
$49$	−43172.8			−0.366962
$50$	−159136.	−	159136.i	−1.27309	−	1.27309i
$51$	2179.93	−	2179.93i	0.0164335	−	0.0164335i
$52$	1932.47	−	1932.47i	0.0137437	−	0.0137437i
$53$	−27269.4			−0.183167			−0.0915837	−	0.995797i	$-0.529193\pi$
$53$	−27269.4			−0.183167			−0.0915837	+	0.995797i	$0.529193\pi$
$54$	41268.5	+	41268.5i	0.262082	+	0.262082i
$55$	141063.	−	141063.i	0.847859	−	0.847859i
$56$	−34931.6	−	34931.6i	−0.198909	−	0.198909i
$57$	44771.1	−	44771.1i	0.241754	−	0.241754i
$58$		−	239257.i		−	1.22625i
$59$	−236897.	−	236897.i	−1.15346	−	1.15346i	−0.985853	−	0.167611i	$-0.946395\pi$
$59$	−236897.	−	236897.i	−1.15346	−	1.15346i	−0.167611	−	0.985853i	$-0.553605\pi$
$60$	−39139.6	−	39139.6i	−0.181202	−	0.181202i
$61$	197119.	−	197119.i	0.868438	−	0.868438i	−0.123862	−	0.992299i	$-0.539528\pi$
$61$	197119.	−	197119.i	0.868438	−	0.868438i	0.992299	+	0.123862i	$0.0395280\pi$
$62$		−	5164.32i		−	0.0216689i
$63$	−184210.			−0.736702
$64$			32768.0i			0.125000i
$65$			20103.4i			0.0732029i
$66$	24910.8	−	24910.8i	0.0866475	−	0.0866475i
$67$			24811.2i			0.0824940i	0.999149	+	0.0412470i	$0.0131331\pi$
$67$			24811.2i			0.0824940i	−0.999149	+	0.0412470i	$0.986867\pi$
$68$	9492.93	−	9492.93i	0.0301907	−	0.0301907i
$69$	12689.2	−	12689.2i	0.0386268	−	0.0386268i
$70$	363391.			1.05945
$71$	−279996.			−0.782307			−0.391153	−	0.920326i	$-0.627924\pi$
$71$	−279996.			−0.782307			−0.391153	+	0.920326i	$0.627924\pi$
$72$	86400.2	+	86400.2i	0.231482	+	0.231482i
$73$			286589.i			0.736700i	0.929687	+	0.368350i	$0.120077\pi$
$73$			286589.i			0.736700i	−0.929687	+	0.368350i	$0.879923\pi$
$74$	−223450.	−	179369.i	−0.551424	−	0.442641i
$75$	292347.			0.692972
$76$	194965.	−	194965.i	0.444136	−	0.444136i
$77$			231284.i			0.506610i
$78$			3550.13i			0.00748102i
$79$	−446529.	−	446529.i	−0.905667	−	0.905667i	0.0902519	−	0.995919i	$-0.471233\pi$
$79$	−446529.	−	446529.i	−0.905667	−	0.905667i	−0.995919	+	0.0902519i	$0.971233\pi$
$80$	−170441.	−	170441.i	−0.332893	−	0.332893i
$81$	416262.			0.783270
$82$	−152154.	−	152154.i	−0.275958	−	0.275958i
$83$	568952.			0.995042			0.497521	−	0.867452i	$-0.334244\pi$
$83$	568952.			0.995042			0.497521	+	0.867452i	$0.334244\pi$
$84$	64172.7			0.108271
$85$			98754.2i			0.160805i
$86$	−639375.			−1.00522
$87$	219769.	+	219769.i	0.333740	+	0.333740i
$88$	108479.	−	108479.i	0.159184	−	0.159184i
$89$	21574.1	−	21574.1i	0.0306029	−	0.0306029i	−0.691640	−	0.722243i	$-0.743111\pi$
$89$	21574.1	−	21574.1i	0.0306029	−	0.0306029i	0.722243	+	0.691640i	$0.243111\pi$
$90$	−898814.			−1.23294
$91$	−16480.6	−	16480.6i	−0.0218700	−	0.0218700i
$92$	55257.9	−	55257.9i	0.0709628	−	0.0709628i
$93$	4743.67	+	4743.67i	0.00589746	+	0.00589746i
$94$	−710816.	+	710816.i	−0.855803	+	0.855803i
$95$			2.02821e6i			2.36560i
$96$	−30098.9	−	30098.9i	−0.0340202	−	0.0340202i
$97$	−1.13802e6	−	1.13802e6i	−1.24690	−	1.24690i	−0.957080	−	0.289824i	$-0.906403\pi$
$97$	−1.13802e6	−	1.13802e6i	−1.24690	−	1.24690i	−0.289824	−	0.957080i	$-0.593597\pi$
$98$	172691.	−	172691.i	0.183481	−	0.183481i
$99$		−	572060.i		−	0.589571i
$100$	1.27309e6			1.27309
$101$		−	88345.0i		−	0.0857467i	−0.999081	−	0.0428734i	$-0.986349\pi$
$101$		−	88345.0i		−	0.0857467i	0.999081	−	0.0428734i	$-0.0136512\pi$
$102$			17439.4i			0.0164335i
$103$	−130709.	+	130709.i	−0.119617	+	0.119617i	−0.764381	−	0.644764i	$-0.776956\pi$
$103$	−130709.	+	130709.i	−0.119617	+	0.119617i	0.644764	+	0.764381i	$0.276956\pi$
$104$			15459.8i			0.0137437i
$105$	−333791.	+	333791.i	−0.288342	+	0.288342i
$106$	109078.	−	109078.i	0.0915837	−	0.0915837i
$107$	652379.			0.532536			0.266268	−	0.963899i	$-0.414209\pi$
$107$	652379.			0.532536			0.266268	+	0.963899i	$0.414209\pi$
$108$	−330148.			−0.262082
$109$	228489.	+	228489.i	0.176435	+	0.176435i	0.789800	−	0.613365i	$-0.210184\pi$
$109$	228489.	+	228489.i	0.176435	+	0.176435i	−0.613365	+	0.789800i	$0.710184\pi$
$110$			1.12850e6i			0.847859i
$111$	370008.	−	40491.0i	0.270547	−	0.0296067i
$112$	279453.			0.198909
$113$	848896.	−	848896.i	0.588327	−	0.588327i	−0.348851	−	0.937178i	$-0.613428\pi$
$113$	848896.	−	848896.i	0.588327	−	0.588327i	0.937178	+	0.348851i	$0.113428\pi$
$114$			358169.i			0.241754i
$115$			574843.i			0.377969i
$116$	957027.	+	957027.i	0.613127	+	0.613127i
$117$	40763.2	+	40763.2i	0.0254513	+	0.0254513i
$118$	1.89518e6			1.15346
$119$	−80957.9	−	80957.9i	−0.0480417	−	0.0480417i
$120$	313117.			0.181202
$121$	1.05331e6			0.594569
$122$			1.57695e6i			0.868438i
$123$	279521.			0.150210
$124$	20657.3	+	20657.3i	0.0108345	+	0.0108345i
$125$	−4.02118e6	+	4.02118e6i	−2.05884	+	2.05884i
$126$	736841.	−	736841.i	0.368351	−	0.368351i
$127$	−1.97426e6			−0.963816			−0.481908	−	0.876222i	$-0.660056\pi$
$127$	−1.97426e6			−0.963816			−0.481908	+	0.876222i	$0.660056\pi$
$128$	−131072.	−	131072.i	−0.0625000	−	0.0625000i
$129$	587296.	−	587296.i	0.273582	−	0.273582i
$130$	−80413.4	−	80413.4i	−0.0366015	−	0.0366015i
$131$	−96469.8	+	96469.8i	−0.0429119	+	0.0429119i	−0.728237	−	0.685325i	$-0.759660\pi$
$131$	−96469.8	+	96469.8i	−0.0429119	+	0.0429119i	0.685325	+	0.728237i	$0.259660\pi$
$132$			199287.i			0.0866475i
$133$	−1.66271e6	−	1.66271e6i	−0.706742	−	0.706742i
$134$	−99244.6	−	99244.6i	−0.0412470	−	0.0412470i
$135$	1.71725e6	−	1.71725e6i	0.697963	−	0.697963i
$136$			75943.5i			0.0301907i
$137$	3.26760e6			1.27077			0.635386	−	0.772195i	$-0.280841\pi$
$137$	3.26760e6			1.27077			0.635386	+	0.772195i	$0.280841\pi$
$138$			101514.i			0.0386268i
$139$		−	2.50566e6i		−	0.932993i	−0.884523	−	0.466497i	$-0.845516\pi$
$139$		−	2.50566e6i		−	0.932993i	0.884523	−	0.466497i	$-0.154484\pi$
$140$	−1.45356e6	+	1.45356e6i	−0.529724	+	0.529724i
$141$		−	1.30584e6i		−	0.465834i
$142$	1.11998e6	−	1.11998e6i	0.391153	−	0.391153i
$143$	51180.0	−	51180.0i	0.0175022	−	0.0175022i
$144$	−691201.			−0.231482
$145$	−9.95587e6			−3.26569
$146$	−1.14636e6	−	1.14636e6i	−0.368350	−	0.368350i
$147$			317250.i			0.0998732i
$148$	1.61128e6	−	176326.i	0.497033	−	0.0543917i
$149$	−198872.			−0.0601195			−0.0300598	−	0.999548i	$-0.509570\pi$
$149$	−198872.			−0.0601195			−0.0300598	+	0.999548i	$0.509570\pi$
$150$	−1.16939e6	+	1.16939e6i	−0.346486	+	0.346486i
$151$			2.44799e6i			0.711016i	0.934673	+	0.355508i	$0.115692\pi$
$151$			2.44799e6i			0.711016i	−0.934673	+	0.355508i	$0.884308\pi$
$152$			1.55972e6i			0.444136i
$153$	200242.	+	200242.i	0.0559089	+	0.0559089i
$154$	−925136.	−	925136.i	−0.253305	−	0.253305i
$155$	−214896.			−0.0577076
$156$	−14200.5	−	14200.5i	−0.00374051	−	0.00374051i
$157$	7.04163e6			1.81959			0.909797	−	0.415053i	$-0.136237\pi$
$157$	7.04163e6			1.81959			0.909797	+	0.415053i	$0.136237\pi$
$158$	3.57223e6			0.905667
$159$			200386.i			0.0498512i
$160$	1.36353e6			0.332893
$161$	−471252.	−	471252.i	−0.112921	−	0.112921i
$162$	−1.66505e6	+	1.66505e6i	−0.391635	+	0.391635i
$163$	3.30974e6	−	3.30974e6i	0.764242	−	0.764242i	−0.212844	−	0.977086i	$-0.568273\pi$
$163$	3.30974e6	−	3.30974e6i	0.764242	−	0.764242i	0.977086	+	0.212844i	$0.0682726\pi$
$164$	1.21723e6			0.275958
$165$	−1.03658e6	−	1.03658e6i	−0.230755	−	0.230755i
$166$	−2.27581e6	+	2.27581e6i	−0.497521	+	0.497521i
$167$	−4.00516e6	−	4.00516e6i	−0.859945	−	0.859945i	0.131386	−	0.991331i	$-0.458057\pi$
$167$	−4.00516e6	−	4.00516e6i	−0.859945	−	0.859945i	−0.991331	+	0.131386i	$0.958057\pi$
$168$	−256691.	+	256691.i	−0.0541355	+	0.0541355i
$169$		−	4.81952e6i		−	0.998489i
$170$	−395017.	−	395017.i	−0.0804023	−	0.0804023i
$171$	4.11255e6	+	4.11255e6i	0.822476	+	0.822476i
$172$	2.55750e6	−	2.55750e6i	0.502609	−	0.502609i
$173$			5.74948e6i			1.11043i	0.831707	+	0.555214i	$0.187364\pi$
$173$			5.74948e6i			1.11043i	−0.831707	+	0.555214i	$0.812636\pi$
$174$	−1.75815e6			−0.333740
$175$		−	1.08572e7i		−	2.02583i
$176$			867834.i			0.159184i
$177$	−1.74081e6	+	1.74081e6i	−0.313929	+	0.313929i
$178$			172593.i			0.0306029i
$179$	5.15327e6	−	5.15327e6i	0.898513	−	0.898513i	−0.0967920	−	0.995305i	$-0.530858\pi$
$179$	5.15327e6	−	5.15327e6i	0.898513	−	0.898513i	0.995305	+	0.0967920i	$0.0308582\pi$
$180$	3.59525e6	−	3.59525e6i	0.616470	−	0.616470i
$181$	4.23220e6			0.713725			0.356862	−	0.934157i	$-0.383847\pi$
$181$	4.23220e6			0.713725			0.356862	+	0.934157i	$0.383847\pi$
$182$	131845.			0.0218700
$183$	−1.44850e6	−	1.44850e6i	−0.236356	−	0.236356i
$184$			442063.i			0.0709628i
$185$	−7.46383e6	+	9.29814e6i	−1.17882	+	1.46852i
$186$	−37949.3			−0.00589746
$187$	251413.	−	251413.i	0.0384470	−	0.0384470i
$188$		−	5.68653e6i		−	0.855803i
$189$			2.81558e6i			0.417044i
$190$	−8.11282e6	−	8.11282e6i	−1.18280	−	1.18280i
$191$	−9.30591e6	−	9.30591e6i	−1.33555	−	1.33555i	−0.900323	−	0.435223i	$-0.856670\pi$
$191$	−9.30591e6	−	9.30591e6i	−1.33555	−	1.33555i	−0.435223	−	0.900323i	$-0.643330\pi$
$192$	240792.			0.0340202
$193$	−1.19415e6	−	1.19415e6i	−0.166107	−	0.166107i	0.619159	−	0.785266i	$-0.287474\pi$
$193$	−1.19415e6	−	1.19415e6i	−0.166107	−	0.166107i	−0.785266	+	0.619159i	$0.787474\pi$
$194$	9.10412e6			1.24690
$195$	147727.			0.0199231
$196$			1.38153e6i			0.183481i
$197$	−4.27079e6			−0.558611			−0.279306	−	0.960202i	$-0.590104\pi$
$197$	−4.27079e6			−0.558611			−0.279306	+	0.960202i	$0.590104\pi$
$198$	2.28824e6	+	2.28824e6i	0.294785	+	0.294785i
$199$	543970.	−	543970.i	0.0690265	−	0.0690265i	−0.671751	−	0.740777i	$-0.734457\pi$
$199$	543970.	−	543970.i	0.0690265	−	0.0690265i	0.740777	+	0.671751i	$0.234457\pi$
$200$	−5.09235e6	+	5.09235e6i	−0.636543	+	0.636543i
$201$	182322.			0.0224517
$202$	353380.	+	353380.i	0.0428734	+	0.0428734i
$203$	8.16175e6	−	8.16175e6i	0.975652	−	0.975652i
$204$	−69757.6	−	69757.6i	−0.00821677	−	0.00821677i
$205$	−6.33139e6	+	6.33139e6i	−0.734915	+	0.734915i
$206$		−	1.04567e6i		−	0.119617i
$207$	1.16560e6	+	1.16560e6i	0.131413	+	0.131413i
$208$	−61839.2	−	61839.2i	−0.00687185	−	0.00687185i
$209$	5.16349e6	−	5.16349e6i	0.565594	−	0.565594i
$210$		−	2.67033e6i		−	0.288342i
$211$	1.81475e7			1.93183			0.965916	−	0.258857i	$-0.0833459\pi$
$211$	1.81475e7			1.93183			0.965916	+	0.258857i	$0.0833459\pi$
$212$			872621.i			0.0915837i
$213$			2.05752e6i			0.212914i
$214$	−2.60952e6	+	2.60952e6i	−0.266268	+	0.266268i
$215$			2.66055e7i			2.67704i
$216$	1.32059e6	−	1.32059e6i	0.131041	−	0.131041i
$217$	176170.	−	176170.i	0.0172406	−	0.0172406i
$218$	−1.82791e6			−0.176435
$219$	2.10596e6			0.200502
$220$	−4.51400e6	−	4.51400e6i	−0.423930	−	0.423930i
$221$			35829.8i			0.00331946i
$222$	−1.31807e6	+	1.64200e6i	−0.120470	+	0.150077i
$223$	1.44159e6			0.129995			0.0649976	−	0.997885i	$-0.479296\pi$
$223$	1.44159e6			0.129995			0.0649976	+	0.997885i	$0.479296\pi$
$224$	−1.11781e6	+	1.11781e6i	−0.0994546	+	0.0994546i
$225$			2.68542e7i			2.35757i
$226$			6.79117e6i			0.588327i
$227$	−5.24976e6	−	5.24976e6i	−0.448810	−	0.448810i	0.446149	−	0.894959i	$-0.352795\pi$
$227$	−5.24976e6	−	5.24976e6i	−0.448810	−	0.448810i	−0.894959	+	0.446149i	$0.852795\pi$
$228$	−1.43268e6	−	1.43268e6i	−0.120877	−	0.120877i
$229$	7.67416e6			0.639035			0.319517	−	0.947580i	$-0.396479\pi$
$229$	7.67416e6			0.639035			0.319517	+	0.947580i	$0.396479\pi$
$230$	−2.29937e6	−	2.29937e6i	−0.188984	−	0.188984i
$231$	1.69956e6			0.137880
$232$	−7.65622e6			−0.613127
$233$			1.34852e7i			1.06608i	0.846089	+	0.533041i	$0.178951\pi$
$233$			1.34852e7i			1.06608i	−0.846089	+	0.533041i	$0.821049\pi$
$234$	−326106.			−0.0254513
$235$	2.95782e7	+	2.95782e7i	2.27913	+	2.27913i
$236$	−7.58072e6	+	7.58072e6i	−0.576732	+	0.576732i
$237$	−3.28126e6	+	3.28126e6i	−0.246488	+	0.246488i
$238$	647663.			0.0480417
$239$	−1.28642e7	−	1.28642e7i	−0.942303	−	0.942303i	0.0561209	−	0.998424i	$-0.482127\pi$
$239$	−1.28642e7	−	1.28642e7i	−0.942303	−	0.942303i	−0.998424	+	0.0561209i	$0.982127\pi$
$240$	−1.25247e6	+	1.25247e6i	−0.0906009	+	0.0906009i
$241$	−1.00918e7	−	1.00918e7i	−0.720974	−	0.720974i	0.247830	−	0.968804i	$-0.420283\pi$
$241$	−1.00918e7	−	1.00918e7i	−0.720974	−	0.720974i	−0.968804	+	0.247830i	$0.920283\pi$
$242$	−4.21326e6	+	4.21326e6i	−0.297284	+	0.297284i
$243$		−	1.05800e7i		−	0.737341i
$244$	−6.30780e6	−	6.30780e6i	−0.434219	−	0.434219i
$245$	−7.18596e6	−	7.18596e6i	−0.488637	−	0.488637i
$246$	−1.11809e6	+	1.11809e6i	−0.0751051	+	0.0751051i
$247$			735869.i			0.0488326i
$248$	−165258.			−0.0108345
$249$		−	4.18087e6i		−	0.270813i
$250$		−	3.21694e7i		−	2.05884i
$251$	−4.66127e6	+	4.66127e6i	−0.294770	+	0.294770i	−0.838961	−	0.544191i	$-0.816837\pi$
$251$	−4.66127e6	+	4.66127e6i	−0.294770	+	0.294770i	0.544191	+	0.838961i	$0.316837\pi$
$252$			5.89472e6i			0.368351i
$253$	1.46346e6	−	1.46346e6i	0.0903690	−	0.0903690i
$254$	7.89705e6	−	7.89705e6i	0.481908	−	0.481908i
$255$	725683.			0.0437649
$256$	1.04858e6			0.0625000
$257$	1.06533e7	+	1.06533e7i	0.627603	+	0.627603i	0.947464	−	0.319862i	$-0.103636\pi$
$257$	1.06533e7	+	1.06533e7i	0.627603	+	0.627603i	−0.319862	+	0.947464i	$0.603636\pi$
$258$			4.69837e6i			0.273582i
$259$	−1.50375e6	−	1.37413e7i	−0.0865520	−	0.790915i
$260$	643307.			0.0366015
$261$	−2.01873e7	+	2.01873e7i	−1.13542	+	1.13542i
$262$		−	771758.i		−	0.0429119i
$263$			2.85461e7i			1.56920i	0.620000	+	0.784602i	$0.287133\pi$
$263$			2.85461e7i			1.56920i	−0.620000	+	0.784602i	$0.712867\pi$
$264$	−797146.	−	797146.i	−0.0433238	−	0.0433238i
$265$	−4.53890e6	−	4.53890e6i	−0.243901	−	0.243901i
$266$	1.33017e7			0.706742
$267$	−158535.	−	158535.i	−0.00832895	−	0.00832895i
$268$	793957.			0.0412470
$269$	−1.67080e7			−0.858355			−0.429178	−	0.903220i	$-0.641197\pi$
$269$	−1.67080e7			−0.858355			−0.429178	+	0.903220i	$0.641197\pi$
$270$			1.37380e7i			0.697963i
$271$	−1.75842e6			−0.0883515			−0.0441757	−	0.999024i	$-0.514066\pi$
$271$	−1.75842e6			−0.0883515			−0.0441757	+	0.999024i	$0.514066\pi$
$272$	−303774.	−	303774.i	−0.0150954	−	0.0150954i
$273$	−121105.	+	121105.i	−0.00595218	+	0.00595218i
$274$	−1.30704e7	+	1.30704e7i	−0.635386	+	0.635386i
$275$	3.37167e7			1.62124
$276$	−406056.	−	406056.i	−0.0193134	−	0.0193134i
$277$	1.35380e7	−	1.35380e7i	0.636963	−	0.636963i	−0.312842	−	0.949805i	$-0.601281\pi$
$277$	1.35380e7	−	1.35380e7i	0.636963	−	0.636963i	0.949805	+	0.312842i	$0.101281\pi$
$278$	1.00227e7	+	1.00227e7i	0.466497	+	0.466497i
$279$	−435740.	+	435740.i	−0.0200639	+	0.0200639i
$280$		−	1.16285e7i		−	0.529724i
$281$	73639.8	+	73639.8i	0.00331889	+	0.00331889i	0.708764	−	0.705445i	$-0.249253\pi$
$281$	73639.8	+	73639.8i	0.00331889	+	0.00331889i	−0.705445	+	0.708764i	$0.749253\pi$
$282$	5.22334e6	+	5.22334e6i	0.232917	+	0.232917i
$283$	−1.60420e7	+	1.60420e7i	−0.707783	+	0.707783i	−0.966069	−	0.258286i	$-0.916842\pi$
$283$	−1.60420e7	+	1.60420e7i	−0.707783	+	0.707783i	0.258286	+	0.966069i	$0.416842\pi$
$284$			8.95988e6i			0.391153i
$285$	1.49040e7			0.643826
$286$			409440.i			0.0175022i
$287$		−	1.03808e7i		−	0.439124i
$288$	2.76481e6	−	2.76481e6i	0.115741	−	0.115741i
$289$		−	2.39616e7i		−	0.992708i
$290$	3.98235e7	−	3.98235e7i	1.63285	−	1.63285i
$291$	−8.36256e6	+	8.36256e6i	−0.339360	+	0.339360i
$292$	9.17085e6			0.368350
$293$	−2.20186e7			−0.875359			−0.437680	−	0.899131i	$-0.644200\pi$
$293$	−2.20186e7			−0.875359			−0.437680	+	0.899131i	$0.644200\pi$
$294$	−1.26900e6	−	1.26900e6i	−0.0499366	−	0.0499366i
$295$		−	7.88615e7i		−	3.07184i
$296$	−5.73980e6	+	7.15041e6i	−0.221321	+	0.275712i
$297$	−8.74371e6			−0.333754
$298$	795490.	−	795490.i	0.0300598	−	0.0300598i
$299$			208563.i			0.00780233i
$300$		−	9.35512e6i		−	0.346486i
$301$	−2.18110e7	−	2.18110e7i	−0.799788	−	0.799788i
$302$	−9.79197e6	−	9.79197e6i	−0.355508	−	0.355508i
$303$	−649192.			−0.0233370
$304$	−6.23888e6	−	6.23888e6i	−0.222068	−	0.222068i
$305$	6.56195e7			2.31278
$306$	−1.60194e6			−0.0559089
$307$		−	1.96382e7i		−	0.678713i	−0.940658	−	0.339357i	$-0.889791\pi$
$307$		−	1.96382e7i		−	0.678713i	0.940658	−	0.339357i	$-0.110209\pi$
$308$	7.40109e6			0.253305
$309$	960498.	+	960498.i	0.0325552	+	0.0325552i
$310$	859583.	−	859583.i	0.0288538	−	0.0288538i
$311$	2.44088e7	−	2.44088e7i	0.811457	−	0.811457i	−0.173395	−	0.984852i	$-0.555474\pi$
$311$	2.44088e7	−	2.44088e7i	0.811457	−	0.811457i	0.984852	+	0.173395i	$0.0554737\pi$
$312$	113604.			0.00374051
$313$	−1.47802e7	−	1.47802e7i	−0.482000	−	0.482000i	0.423770	−	0.905770i	$-0.360706\pi$
$313$	−1.47802e7	−	1.47802e7i	−0.482000	−	0.482000i	−0.905770	+	0.423770i	$0.860706\pi$
$314$	−2.81665e7	+	2.81665e7i	−0.909797	+	0.909797i
$315$	−3.06612e7	−	3.06612e7i	−0.980973	−	0.980973i
$316$	−1.42889e7	+	1.42889e7i	−0.452834	+	0.452834i
$317$		−	1.25856e7i		−	0.395089i	−0.980294	−	0.197544i	$-0.936703\pi$
$317$		−	1.25856e7i		−	0.395089i	0.980294	−	0.197544i	$-0.0632967\pi$
$318$	−801543.	−	801543.i	−0.0249256	−	0.0249256i
$319$	2.53461e7	+	2.53461e7i	0.780799	+	0.780799i
$320$	−5.45412e6	+	5.45412e6i	−0.166447	+	0.166447i
$321$		−	4.79393e6i		−	0.144936i
$322$	3.77002e6			0.112921
$323$			3.61483e6i			0.107270i
$324$		−	1.33204e7i		−	0.391635i
$325$	−2.40255e6	+	2.40255e6i	−0.0699877	+	0.0699877i
$326$			2.64779e7i			0.764242i
$327$	1.67902e6	−	1.67902e6i	0.0480189	−	0.0480189i
$328$	−4.86893e6	+	4.86893e6i	−0.137979	+	0.137979i
$329$	−4.84960e7			−1.36182
$330$	8.29264e6			0.230755
$331$	5.91341e6	+	5.91341e6i	0.163062	+	0.163062i	0.783922	−	0.620859i	$-0.213216\pi$
$331$	5.91341e6	+	5.91341e6i	0.163062	+	0.163062i	−0.620859	+	0.783922i	$0.713216\pi$
$332$		−	1.82065e7i		−	0.497521i
$333$	3.71939e6	+	3.39879e7i	0.100725	+	0.920433i
$334$	3.20413e7			0.859945
$335$	−4.12973e6	+	4.12973e6i	−0.109847	+	0.109847i
$336$		−	2.05353e6i		−	0.0541355i
$337$			4.86887e7i			1.27215i	0.771627	+	0.636075i	$0.219443\pi$
$337$			4.86887e7i			1.27215i	−0.771627	+	0.636075i	$0.780557\pi$
$338$	1.92781e7	+	1.92781e7i	0.499244	+	0.499244i
$339$	−6.23800e6	−	6.23800e6i	−0.160120	−	0.160120i
$340$	3.16013e6			0.0804023
$341$	547091.	+	547091.i	0.0137974	+	0.0137974i
$342$	−3.29004e7			−0.822476
$343$	4.38888e7			1.08761
$344$			2.04600e7i			0.502609i
$345$	4.22416e6			0.102869
$346$	−2.29979e7	−	2.29979e7i	−0.555214	−	0.555214i
$347$	−2.88115e6	+	2.88115e6i	−0.0689569	+	0.0689569i	−0.740744	−	0.671787i	$-0.765527\pi$
$347$	−2.88115e6	+	2.88115e6i	−0.0689569	+	0.0689569i	0.671787	+	0.740744i	$0.265527\pi$
$348$	7.03259e6	−	7.03259e6i	0.166870	−	0.166870i
$349$	−5.75251e7			−1.35326			−0.676630	−	0.736324i	$-0.736560\pi$
$349$	−5.75251e7			−1.35326			−0.676630	+	0.736324i	$0.736560\pi$
$350$	4.34287e7	+	4.34287e7i	1.01291	+	1.01291i
$351$	623049.	−	623049.i	0.0144079	−	0.0144079i
$352$	−3.47134e6	−	3.47134e6i	−0.0795919	−	0.0795919i
$353$	5.90382e7	−	5.90382e7i	1.34217	−	1.34217i	0.448281	−	0.893893i	$-0.352036\pi$
$353$	5.90382e7	−	5.90382e7i	1.34217	−	1.34217i	0.893893	−	0.448281i	$-0.147964\pi$
$354$		−	1.39265e7i		−	0.313929i
$355$	−4.66044e7	−	4.66044e7i	−1.04170	−	1.04170i
$356$	−690372.	−	690372.i	−0.0153015	−	0.0153015i
$357$	−594909.	+	594909.i	−0.0130751	+	0.0130751i
$358$			4.12262e7i			0.898513i
$359$	−2.38656e7			−0.515809			−0.257904	−	0.966170i	$-0.583032\pi$
$359$	−2.38656e7			−0.515809			−0.257904	+	0.966170i	$0.583032\pi$
$360$			2.87620e7i			0.616470i
$361$			2.71951e7i			0.578056i
$362$	−1.69288e7	+	1.69288e7i	−0.356862	+	0.356862i
$363$		−	7.74015e6i		−	0.161819i
$364$	−527379.	+	527379.i	−0.0109350	+	0.0109350i
$365$	−4.77018e7	+	4.77018e7i	−0.980970	+	0.980970i
$366$	1.15880e7			0.236356
$367$	−4.57814e7			−0.926171			−0.463086	−	0.886314i	$-0.653258\pi$
$367$	−4.57814e7			−0.926171			−0.463086	+	0.886314i	$0.653258\pi$
$368$	−1.76825e6	−	1.76825e6i	−0.0354814	−	0.0354814i
$369$			2.56761e7i			0.511033i
$370$	−7.33723e6	−	6.70479e7i	−0.144853	−	1.32367i
$371$	7.44192e6			0.145735
$372$	151797.	−	151797.i	0.00294873	−	0.00294873i
$373$			1.59431e7i			0.307218i	0.988132	+	0.153609i	$0.0490897\pi$
$373$			1.59431e7i			0.307218i	−0.988132	+	0.153609i	$0.950910\pi$
$374$			2.01130e6i			0.0384470i
$375$	2.95491e7	+	2.95491e7i	0.560339	+	0.560339i
$376$	2.27461e7	+	2.27461e7i	0.427902	+	0.427902i
$377$	−3.61217e6			−0.0674130
$378$	−1.12623e7	−	1.12623e7i	−0.208522	−	0.208522i
$379$	−6.64854e7			−1.22126			−0.610630	−	0.791916i	$-0.709084\pi$
$379$	−6.64854e7			−1.22126			−0.610630	+	0.791916i	$0.709084\pi$
$380$	6.49026e7			1.18280
$381$			1.45076e7i			0.262314i
$382$	7.44473e7			1.33555
$383$	1.26421e7	+	1.26421e7i	0.225021	+	0.225021i	0.810609	−	0.585588i	$-0.199136\pi$
$383$	1.26421e7	+	1.26421e7i	0.225021	+	0.225021i	−0.585588	+	0.810609i	$0.699136\pi$
$384$	−963166.	+	963166.i	−0.0170101	+	0.0170101i
$385$	−3.84964e7	+	3.84964e7i	−0.674588	+	0.674588i
$386$	9.55323e6			0.166107
$387$	5.39474e7	+	5.39474e7i	0.930760	+	0.930760i
$388$	−3.64165e7	+	3.64165e7i	−0.623452	+	0.623452i
$389$	−2.15962e7	−	2.15962e7i	−0.366883	−	0.366883i	0.499456	−	0.866339i	$-0.333533\pi$
$389$	−2.15962e7	−	2.15962e7i	−0.366883	−	0.366883i	−0.866339	+	0.499456i	$0.833533\pi$
$390$	−590908.	+	590908.i	−0.00996153	+	0.00996153i
$391$			1.02453e6i			0.0171394i
$392$	−5.52611e6	−	5.52611e6i	−0.0917406	−	0.0917406i
$393$	708896.	+	708896.i	0.0116790	+	0.0116790i
$394$	1.70832e7	−	1.70832e7i	0.279306	−	0.279306i
$395$		−	1.48647e8i		−	2.41192i
$396$	−1.83059e7			−0.294785
$397$		−	3.43484e7i		−	0.548952i	−0.961594	−	0.274476i	$-0.911496\pi$
$397$		−	3.43484e7i		−	0.548952i	0.961594	−	0.274476i	$-0.0885044\pi$
$398$			4.35176e6i			0.0690265i
$399$	−1.22182e7	+	1.22182e7i	−0.192348	+	0.192348i
$400$		−	4.07388e7i		−	0.636543i
$401$	−8.25802e7	+	8.25802e7i	−1.28069	+	1.28069i	−0.340409	+	0.940277i	$0.610566\pi$
$401$	−8.25802e7	+	8.25802e7i	−1.28069	+	1.28069i	−0.940277	+	0.340409i	$0.889434\pi$
$402$	−729286.	+	729286.i	−0.0112259	+	0.0112259i
$403$	−77968.0			−0.00119125
$404$	−2.82704e6			−0.0428734
$405$	6.92854e7	+	6.92854e7i	1.04298	+	1.04298i
$406$			6.52940e7i			0.975652i
$407$	4.26734e7	−	4.66986e6i	0.632956	−	0.0692661i
$408$	558061.			0.00821677
$409$	8.82522e7	−	8.82522e7i	1.28990	−	1.28990i	0.355053	−	0.934846i	$-0.384463\pi$
$409$	8.82522e7	−	8.82522e7i	1.28990	−	1.28990i	0.934846	−	0.355053i	$-0.115537\pi$
$410$		−	5.06511e7i		−	0.734915i
$411$		−	2.40116e7i		−	0.345856i
$412$	4.18268e6	+	4.18268e6i	0.0598086	+	0.0598086i
$413$	6.46501e7	+	6.46501e7i	0.917739	+	0.917739i
$414$	−9.32479e6			−0.131413
$415$	9.47001e7	+	9.47001e7i	1.32497	+	1.32497i
$416$	494713.			0.00687185
$417$	−1.84126e7			−0.253925
$418$			4.13080e7i			0.565594i
$419$	−1.15427e8			−1.56915			−0.784576	−	0.620033i	$-0.787119\pi$
$419$	−1.15427e8			−1.56915			−0.784576	+	0.620033i	$0.787119\pi$
$420$	1.06813e7	+	1.06813e7i	0.144171	+	0.144171i
$421$	9.52716e7	−	9.52716e7i	1.27678	−	1.27678i	0.334326	−	0.942458i	$-0.391492\pi$
$421$	9.52716e7	−	9.52716e7i	1.27678	−	1.27678i	0.942458	−	0.334326i	$-0.108508\pi$
$422$	−7.25900e7	+	7.25900e7i	−0.965916	+	0.965916i
$423$	1.19950e8			1.58482
$424$	−3.49049e6	−	3.49049e6i	−0.0457919	−	0.0457919i
$425$	−1.18021e7	+	1.18021e7i	−0.153742	+	0.153742i
$426$	−8.23006e6	−	8.23006e6i	−0.106457	−	0.106457i
$427$	−5.37944e7	+	5.37944e7i	−0.690961	+	0.690961i
$428$		−	2.08761e7i		−	0.266268i
$429$	−376090.	−	376090.i	−0.00476343	−	0.00476343i
$430$	−1.06422e8	−	1.06422e8i	−1.33852	−	1.33852i
$431$	−6.84874e7	+	6.84874e7i	−0.855419	+	0.855419i	−0.990794	−	0.135376i	$-0.956776\pi$
$431$	−6.84874e7	+	6.84874e7i	−0.855419	+	0.855419i	0.135376	+	0.990794i	$0.456776\pi$
$432$			1.05647e7i			0.131041i
$433$	1.09279e8			1.34609			0.673045	−	0.739602i	$-0.264986\pi$
$433$	1.09279e8			1.34609			0.673045	+	0.739602i	$0.264986\pi$
$434$			1.40936e6i			0.0172406i
$435$			7.31595e7i			0.888797i
$436$	7.31163e6	−	7.31163e6i	0.0882176	−	0.0882176i
$437$			2.10417e7i			0.252137i
$438$	−8.42385e6	+	8.42385e6i	−0.100251	+	0.100251i
$439$	2.04194e6	−	2.04194e6i	0.0241351	−	0.0241351i	−0.694936	−	0.719071i	$-0.744567\pi$
$439$	2.04194e6	−	2.04194e6i	0.0241351	−	0.0241351i	0.719071	+	0.694936i	$0.244567\pi$
$440$	3.61120e7			0.423930
$441$	−2.91417e7			−0.339781
$442$	−143319.	−	143319.i	−0.00165973	−	0.00165973i
$443$		−	1.01578e8i		−	1.16839i	−0.811614	−	0.584194i	$-0.801411\pi$
$443$		−	1.01578e8i		−	1.16839i	0.811614	−	0.584194i	$-0.198589\pi$
$444$	−1.29571e6	−	1.18403e7i	−0.0148033	−	0.135273i
$445$	7.18188e6			0.0815001
$446$	−5.76636e6	+	5.76636e6i	−0.0649976	+	0.0649976i
$447$			1.46139e6i			0.0163623i
$448$		−	8.94250e6i		−	0.0994546i
$449$	−3.25266e7	−	3.25266e7i	−0.359335	−	0.359335i	0.504233	−	0.863568i	$-0.331775\pi$
$449$	−3.25266e7	−	3.25266e7i	−0.359335	−	0.359335i	−0.863568	+	0.504233i	$0.831775\pi$
$450$	−1.07417e8	−	1.07417e8i	−1.17879	−	1.17879i
$451$	3.22374e7			0.351424
$452$	−2.71647e7	−	2.71647e7i	−0.294164	−	0.294164i
$453$	1.79888e7			0.193512
$454$	4.19981e7			0.448810
$455$		−	5.48627e6i		−	0.0582429i
$456$	1.14614e7			0.120877
$457$	−1.07799e8	−	1.07799e8i	−1.12945	−	1.12945i	−0.990267	−	0.139178i	$-0.955554\pi$
$457$	−1.07799e8	−	1.07799e8i	−1.12945	−	1.12945i	−0.139178	−	0.990267i	$-0.544446\pi$
$458$	−3.06966e7	+	3.06966e7i	−0.319517	+	0.319517i
$459$	3.06062e6	−	3.06062e6i	0.0316498	−	0.0316498i
$460$	1.83950e7			0.188984
$461$	2.00158e7	+	2.00158e7i	0.204301	+	0.204301i	0.801840	−	0.597539i	$-0.203855\pi$
$461$	2.00158e7	+	2.00158e7i	0.204301	+	0.204301i	−0.597539	+	0.801840i	$0.703855\pi$
$462$	−6.79825e6	+	6.79825e6i	−0.0689399	+	0.0689399i
$463$	6.36169e7	+	6.36169e7i	0.640958	+	0.640958i	0.950791	−	0.309833i	$-0.100273\pi$
$463$	6.36169e7	+	6.36169e7i	0.640958	+	0.640958i	−0.309833	+	0.950791i	$0.600273\pi$
$464$	3.06249e7	−	3.06249e7i	0.306563	−	0.306563i
$465$			1.57913e6i			0.0157058i
$466$	−5.39409e7	−	5.39409e7i	−0.533041	−	0.533041i
$467$	−1.29146e8	−	1.29146e8i	−1.26803	−	1.26803i	−0.947104	−	0.320926i	$-0.896006\pi$
$467$	−1.29146e8	−	1.29146e8i	−1.26803	−	1.26803i	−0.320926	−	0.947104i	$-0.603994\pi$
$468$	1.30442e6	−	1.30442e6i	0.0127257	−	0.0127257i
$469$		−	6.77105e6i		−	0.0656353i
$470$	−2.36626e8			−2.27913
$471$		−	5.17446e7i		−	0.495224i
$472$		−	6.06457e7i		−	0.576732i
$473$	6.77333e7	−	6.77333e7i	0.640058	−	0.640058i
$474$		−	2.62501e7i		−	0.246488i
$475$	−2.42390e8	+	2.42390e8i	−2.26170	+	2.26170i
$476$	−2.59065e6	+	2.59065e6i	−0.0240209	+	0.0240209i
$477$	−1.84069e7			−0.169600
$478$	1.02914e8			0.942303
$479$	1.02535e8	+	1.02535e8i	0.932961	+	0.932961i	0.997890	−	0.0649289i	$-0.0206821\pi$
$479$	1.02535e8	+	1.02535e8i	0.932961	+	0.932961i	−0.0649289	+	0.997890i	$0.520682\pi$
$480$		−	1.00197e7i		−	0.0906009i
$481$	−2.70801e6	+	3.37353e6i	−0.0243341	+	0.0303144i
$482$	8.07348e7			0.720974
$483$	−3.46294e6	+	3.46294e6i	−0.0307329	+	0.0307329i
$484$		−	3.37061e7i		−	0.297284i
$485$		−	3.78838e8i		−	3.32069i
$486$	4.23201e7	+	4.23201e7i	0.368670	+	0.368670i
$487$	1.44418e8	+	1.44418e8i	1.25036	+	1.25036i	0.955560	+	0.294798i	$0.0952525\pi$
$487$	1.44418e8	+	1.44418e8i	1.25036	+	1.25036i	0.294798	+	0.955560i	$0.404748\pi$
$488$	5.04624e7			0.434219
$489$	−2.43212e7	−	2.43212e7i	−0.207998	−	0.207998i
$490$	5.74877e7			0.488637
$491$	6.30835e7			0.532931			0.266466	−	0.963844i	$-0.414144\pi$
$491$	6.30835e7			0.532931			0.266466	+	0.963844i	$0.414144\pi$
$492$		−	8.94468e6i		−	0.0751051i
$493$	−1.77441e7			−0.148086
$494$	−2.94348e6	−	2.94348e6i	−0.0244163	−	0.0244163i
$495$	9.52174e7	−	9.52174e7i	0.785056	−	0.785056i
$496$	661032.	−	661032.i	0.00541724	−	0.00541724i
$497$	7.64119e7			0.622432
$498$	1.67235e7	+	1.67235e7i	0.135406	+	0.135406i
$499$	−1.18286e8	+	1.18286e8i	−0.951988	+	0.951988i	−0.998899	−	0.0469113i	$-0.985062\pi$
$499$	−1.18286e8	+	1.18286e8i	−0.951988	+	0.951988i	0.0469113	+	0.998899i	$0.485062\pi$
$500$	1.28678e8	+	1.28678e8i	1.02942	+	1.02942i
$501$	−2.94314e7	+	2.94314e7i	−0.234044	+	0.234044i
$502$		−	3.72901e7i		−	0.294770i
$503$	−1.37751e7	−	1.37751e7i	−0.108240	−	0.108240i	0.650912	−	0.759153i	$-0.274386\pi$
$503$	−1.37751e7	−	1.37751e7i	−0.108240	−	0.108240i	−0.759153	+	0.650912i	$0.774386\pi$
$504$	−2.35789e7	−	2.35789e7i	−0.184176	−	0.184176i
$505$	1.47047e7	−	1.47047e7i	0.114178	−	0.114178i
$506$			1.17077e7i			0.0903690i
$507$	−3.54156e7			−0.271751
$508$			6.31764e7i			0.481908i
$509$			1.72430e8i			1.30756i	0.756687	+	0.653778i	$0.226817\pi$
$509$			1.72430e8i			1.30756i	−0.756687	+	0.653778i	$0.773183\pi$
$510$	−2.90273e6	+	2.90273e6i	−0.0218825	+	0.0218825i
$511$		−	7.82111e7i		−	0.586146i
$512$	−4.19430e6	+	4.19430e6i	−0.0312500	+	0.0312500i
$513$	6.28587e7	−	6.28587e7i	0.465601	−	0.465601i
$514$	−8.52264e7			−0.627603
$515$	−4.35121e7			−0.318558
$516$	−1.87935e7	−	1.87935e7i	−0.136791	−	0.136791i
$517$		−	1.50603e8i		−	1.08984i
$518$	6.09804e7	+	4.89503e7i	0.438733	+	0.352181i
$519$	4.22494e7			0.302216
$520$	−2.57323e6	+	2.57323e6i	−0.0183007	+	0.0183007i
$521$			7.64112e7i			0.540311i	0.962817	+	0.270156i	$0.0870752\pi$
$521$			7.64112e7i			0.540311i	−0.962817	+	0.270156i	$0.912925\pi$
$522$		−	1.61499e8i		−	1.13542i
$523$	1.30809e8	+	1.30809e8i	0.914391	+	0.914391i	0.996614	−	0.0822230i	$-0.0262020\pi$
$523$	1.30809e8	+	1.30809e8i	0.914391	+	0.914391i	−0.0822230	+	0.996614i	$0.526202\pi$
$524$	3.08703e6	+	3.08703e6i	0.0214559	+	0.0214559i
$525$	−7.97826e7			−0.551354
$526$	−1.14184e8	−	1.14184e8i	−0.784602	−	0.784602i
$527$	−383004.			−0.00261681
$528$	6.37717e6			0.0433238
$529$		−	1.42072e8i		−	0.959714i
$530$	3.63112e7			0.243901
$531$	−1.59906e8	−	1.59906e8i	−1.06802	−	1.06802i
$532$	−5.32066e7	+	5.32066e7i	−0.353371	+	0.353371i
$533$	−2.29714e6	+	2.29714e6i	−0.0151707	+	0.0151707i
$534$	1.26828e6			0.00832895
$535$	1.08586e8	+	1.08586e8i	0.709110	+	0.709110i
$536$	−3.17583e6	+	3.17583e6i	−0.0206235	+	0.0206235i
$537$	−3.78682e7	−	3.78682e7i	−0.244541	−	0.244541i
$538$	6.68319e7	−	6.68319e7i	0.429178	−	0.429178i
$539$			3.65887e7i			0.233658i
$540$	−5.49520e7	−	5.49520e7i	−0.348982	−	0.348982i
$541$	8.39789e7	+	8.39789e7i	0.530369	+	0.530369i	0.920682	−	0.390313i	$-0.127633\pi$
$541$	8.39789e7	+	8.39789e7i	0.530369	+	0.530369i	−0.390313	+	0.920682i	$0.627633\pi$
$542$	7.03366e6	−	7.03366e6i	0.0441757	−	0.0441757i
$543$		−	3.10998e7i		−	0.194249i
$544$	2.43019e6			0.0150954
$545$			7.60623e7i			0.469872i
$546$		−	968844.i		−	0.00595218i
$547$	2.30751e7	−	2.30751e7i	0.140988	−	0.140988i	−0.633090	−	0.774078i	$-0.718214\pi$
$547$	2.30751e7	−	2.30751e7i	0.140988	−	0.140988i	0.774078	+	0.633090i	$0.218214\pi$
$548$		−	1.04563e8i		−	0.635386i
$549$	1.33055e8	−	1.33055e8i	0.804111	−	0.804111i
$550$	−1.34867e8	+	1.34867e8i	−0.810619	+	0.810619i
$551$	−3.64428e8			−2.17849
$552$	3.24844e6			0.0193134
$553$	1.21859e8	+	1.21859e8i	0.720582	+	0.720582i
$554$			1.08304e8i			0.636963i
$555$	6.83262e7	+	5.48470e7i	0.399676	+	0.320829i
$556$	−8.01813e7			−0.466497
$557$	−2.93020e7	+	2.93020e7i	−0.169563	+	0.169563i	−0.786787	−	0.617224i	$-0.788257\pi$
$557$	−2.93020e7	+	2.93020e7i	−0.169563	+	0.169563i	0.617224	+	0.786787i	$0.288257\pi$
$558$		−	3.48592e6i		−	0.0200639i
$559$			9.65293e6i			0.0552617i
$560$	4.65140e7	+	4.65140e7i	0.264862	+	0.264862i
$561$	−1.84747e6	−	1.84747e6i	−0.0104638	−	0.0104638i
$562$	−589118.			−0.00331889
$563$	7.28404e7	+	7.28404e7i	0.408176	+	0.408176i	0.881102	−	0.472926i	$-0.156802\pi$
$563$	7.28404e7	+	7.28404e7i	0.408176	+	0.408176i	−0.472926	+	0.881102i	$0.656802\pi$
$564$	−4.17867e7			−0.232917
$565$	2.82592e8			1.56680
$566$		−	1.28336e8i		−	0.707783i
$567$	−1.13599e8			−0.623198
$568$	−3.58395e7	−	3.58395e7i	−0.195577	−	0.195577i
$569$	2.24718e8	−	2.24718e8i	1.21983	−	1.21983i	0.252145	−	0.967689i	$-0.418864\pi$
$569$	2.24718e8	−	2.24718e8i	1.21983	−	1.21983i	0.967689	−	0.252145i	$-0.0811360\pi$
$570$	−5.96160e7	+	5.96160e7i	−0.321913	+	0.321913i
$571$	−1.14769e8			−0.616475			−0.308237	−	0.951309i	$-0.599739\pi$
$571$	−1.14769e8			−0.616475			−0.308237	+	0.951309i	$0.599739\pi$
$572$	−1.63776e6	−	1.63776e6i	−0.00875109	−	0.00875109i
$573$	−6.83833e7	+	6.83833e7i	−0.363485	+	0.363485i
$574$	4.15234e7	+	4.15234e7i	0.219562	+	0.219562i
$575$	−6.86993e7	+	6.86993e7i	−0.361367	+	0.361367i
$576$			2.21184e7i			0.115741i
$577$	1.69821e8	+	1.69821e8i	0.884023	+	0.884023i	0.993941	−	0.109918i	$-0.0350589\pi$
$577$	1.69821e8	+	1.69821e8i	0.884023	+	0.884023i	−0.109918	+	0.993941i	$0.535059\pi$
$578$	9.58462e7	+	9.58462e7i	0.496354	+	0.496354i
$579$	−8.77509e6	+	8.77509e6i	−0.0452081	+	0.0452081i
$580$			3.18588e8i			1.63285i
$581$	−1.55269e8			−0.791692
$582$		−	6.69005e7i		−	0.339360i
$583$			2.31107e7i			0.116629i
$584$	−3.66834e7	+	3.66834e7i	−0.184175	+	0.184175i
$585$			1.35698e7i			0.0677806i
$586$	8.80743e7	−	8.80743e7i	0.437680	−	0.437680i
$587$	−8.86765e7	+	8.86765e7i	−0.438424	+	0.438424i	−0.891481	−	0.453057i	$-0.850333\pi$
$587$	−8.86765e7	+	8.86765e7i	−0.438424	+	0.438424i	0.453057	+	0.891481i	$0.350333\pi$
$588$	1.01520e7			0.0499366
$589$	−7.86611e6			−0.0384958
$590$	3.15446e8	+	3.15446e8i	1.53592	+	1.53592i
$591$			3.13834e7i			0.152033i
$592$	−5.64245e6	−	5.15609e7i	−0.0271958	−	0.248516i
$593$	−3.01193e8			−1.44438			−0.722190	−	0.691695i	$-0.756864\pi$
$593$	−3.01193e8			−1.44438			−0.722190	+	0.691695i	$0.756864\pi$
$594$	3.49748e7	−	3.49748e7i	0.166877	−	0.166877i
$595$		−	2.69503e7i		−	0.127942i
$596$			6.36392e6i			0.0300598i
$597$	−3.99729e6	−	3.99729e6i	−0.0187864	−	0.0187864i
$598$	−834253.	−	834253.i	−0.00390116	−	0.00390116i
$599$	−1.22182e8			−0.568494			−0.284247	−	0.958751i	$-0.591744\pi$
$599$	−1.22182e8			−0.568494			−0.284247	+	0.958751i	$0.591744\pi$
$600$	3.74205e7	+	3.74205e7i	0.173243	+	0.173243i
$601$	1.16434e8			0.536360			0.268180	−	0.963369i	$-0.413578\pi$
$601$	1.16434e8			0.536360			0.268180	+	0.963369i	$0.413578\pi$
$602$	1.74488e8			0.799788
$603$			1.67476e7i			0.0763835i
$604$	7.83358e7			0.355508
$605$	1.75321e8	+	1.75321e8i	0.791711	+	0.791711i
$606$	2.59677e6	−	2.59677e6i	0.0116685	−	0.0116685i
$607$	−2.57023e8	+	2.57023e8i	−1.14923	+	1.14923i	−0.162521	+	0.986705i	$0.551962\pi$
$607$	−2.57023e8	+	2.57023e8i	−1.14923	+	1.14923i	−0.986705	+	0.162521i	$0.948038\pi$
$608$	4.99111e7			0.222068
$609$	−5.99756e7	−	5.99756e7i	−0.265535	−	0.265535i
$610$	−2.62478e8	+	2.62478e8i	−1.15639	+	1.15639i
$611$	1.07315e7	+	1.07315e7i	0.0470476	+	0.0470476i
$612$	6.40774e6	−	6.40774e6i	0.0279544	−	0.0279544i
$613$		−	1.20183e7i		−	0.0521750i	−0.999660	−	0.0260875i	$-0.991695\pi$
$613$		−	1.20183e7i		−	0.0521750i	0.999660	−	0.0260875i	$-0.00830486\pi$
$614$	7.85528e7	+	7.85528e7i	0.339357	+	0.339357i
$615$	4.65254e7	+	4.65254e7i	0.200016	+	0.200016i
$616$	−2.96044e7	+	2.96044e7i	−0.126652	+	0.126652i
$617$			1.22138e8i			0.519988i	0.965610	+	0.259994i	$0.0837206\pi$
$617$			1.22138e8i			0.519988i	−0.965610	+	0.259994i	$0.916279\pi$
$618$	−7.68398e6			−0.0325552
$619$		−	2.79029e8i		−	1.17646i	−0.808693	−	0.588230i	$-0.799825\pi$
$619$		−	2.79029e8i		−	1.17646i	0.808693	−	0.588230i	$-0.200175\pi$
$620$			6.87666e6i			0.0288538i
$621$	1.78157e7	−	1.78157e7i	0.0743923	−	0.0743923i
$622$			1.95271e8i			0.811457i
$623$	−5.88765e6	+	5.88765e6i	−0.0243488	+	0.0243488i
$624$	−454417.	+	454417.i	−0.00187026	+	0.00187026i
$625$	−7.16998e8			−2.93682
$626$	1.18241e8			0.482000
$627$	−3.79433e7	−	3.79433e7i	−0.153933	−	0.153933i
$628$		−	2.25332e8i		−	0.909797i
$629$	−1.33026e7	+	1.65719e7i	−0.0534546	+	0.0665916i
$630$	2.45289e8			0.980973
$631$	−3.19616e7	+	3.19616e7i	−0.127216	+	0.127216i	−0.767848	−	0.640632i	$-0.778672\pi$
$631$	−3.19616e7	+	3.19616e7i	−0.127216	+	0.127216i	0.640632	+	0.767848i	$0.278672\pi$
$632$		−	1.14311e8i		−	0.452834i
$633$		−	1.33355e8i		−	0.525771i
$634$	5.03422e7	+	5.03422e7i	0.197544	+	0.197544i
$635$	−3.28609e8	−	3.28609e8i	−1.28339	−	1.28339i
$636$	6.41235e6			0.0249256
$637$	−2.60719e6	−	2.60719e6i	−0.0100868	−	0.0100868i
$638$	−2.02769e8			−0.780799
$639$	−1.88998e8			−0.724359
$640$		−	4.36330e7i		−	0.166447i
$641$	5.68908e7			0.216007			0.108003	−	0.994151i	$-0.465554\pi$
$641$	5.68908e7			0.216007			0.108003	+	0.994151i	$0.465554\pi$
$642$	1.91757e7	+	1.91757e7i	0.0724680	+	0.0724680i
$643$	3.38647e8	−	3.38647e8i	1.27384	−	1.27384i	0.329778	−	0.944059i	$-0.393026\pi$
$643$	3.38647e8	−	3.38647e8i	1.27384	−	1.27384i	0.944059	−	0.329778i	$-0.106974\pi$
$644$	−1.50801e7	+	1.50801e7i	−0.0564606	+	0.0564606i
$645$	1.95507e8			0.728589
$646$	−1.44593e7	−	1.44593e7i	−0.0536352	−	0.0536352i
$647$	1.22663e8	−	1.22663e8i	0.452900	−	0.452900i	−0.443416	−	0.896316i	$-0.646234\pi$
$647$	1.22663e8	−	1.22663e8i	0.452900	−	0.452900i	0.896316	+	0.443416i	$0.146234\pi$
$648$	5.32815e7	+	5.32815e7i	0.195818	+	0.195818i
$649$	−2.00769e8	+	2.00769e8i	−0.734451	+	0.734451i
$650$		−	1.92204e7i		−	0.0699877i
$651$	−1.29456e6	−	1.29456e6i	−0.00469224	−	0.00469224i
$652$	−1.05912e8	−	1.05912e8i	−0.382121	−	0.382121i
$653$	1.10213e8	−	1.10213e8i	0.395816	−	0.395816i	−0.480938	−	0.876754i	$-0.659704\pi$
$653$	1.10213e8	−	1.10213e8i	0.395816	−	0.395816i	0.876754	+	0.480938i	$0.159704\pi$
$654$			1.34322e7i			0.0480189i
$655$	−3.21141e7			−0.114281
$656$		−	3.89515e7i		−	0.137979i
$657$			1.93448e8i			0.682131i
$658$	1.93984e8	−	1.93984e8i	0.680908	−	0.680908i
$659$		−	2.48028e8i		−	0.866653i	−0.901237	−	0.433326i	$-0.857340\pi$
$659$		−	2.48028e8i		−	0.866653i	0.901237	−	0.433326i	$-0.142660\pi$
$660$	−3.31706e7	+	3.31706e7i	−0.115378	+	0.115378i
$661$	−5.20128e7	+	5.20128e7i	−0.180097	+	0.180097i	−0.791398	−	0.611301i	$-0.790646\pi$
$661$	−5.20128e7	+	5.20128e7i	−0.180097	+	0.180097i	0.611301	+	0.791398i	$0.290646\pi$
$662$	−4.73073e7			−0.163062
$663$	263291.			0.000903430
$664$	7.28258e7	+	7.28258e7i	0.248760	+	0.248760i
$665$		−	5.53504e8i		−	1.88216i
$666$	−1.50829e8	−	1.21074e8i	−0.510579	−	0.409854i
$667$	−1.03288e8			−0.348074
$668$	−1.28165e8	+	1.28165e8i	−0.429972	+	0.429972i
$669$		−	1.05933e7i		−	0.0353797i
$670$		−	3.30379e7i		−	0.109847i
$671$	−1.67057e8	−	1.67057e8i	−0.552965	−	0.552965i
$672$	8.21410e6	+	8.21410e6i	0.0270678	+	0.0270678i
$673$	5.74694e8			1.88535			0.942673	−	0.333717i	$-0.108303\pi$
$673$	5.74694e8			1.88535			0.942673	+	0.333717i	$0.108303\pi$
$674$	−1.94755e8	−	1.94755e8i	−0.636075	−	0.636075i
$675$	4.10456e8			1.33461
$676$	−1.54224e8			−0.499244
$677$		−	8.37798e7i		−	0.270006i	−0.990845	−	0.135003i	$-0.956896\pi$
$677$		−	8.37798e7i		−	0.270006i	0.990845	−	0.135003i	$-0.0431044\pi$
$678$	4.99040e7			0.160120
$679$	3.10568e8	+	3.10568e8i	0.992082	+	0.992082i
$680$	−1.26405e7	+	1.26405e7i	−0.0402012	+	0.0402012i
$681$	−3.85772e7	+	3.85772e7i	−0.122149	+	0.122149i
$682$	−4.37673e6			−0.0137974
$683$	1.35801e7	+	1.35801e7i	0.0426226	+	0.0426226i	0.728097	−	0.685474i	$-0.240405\pi$
$683$	1.35801e7	+	1.35801e7i	0.0426226	+	0.0426226i	−0.685474	+	0.728097i	$0.740405\pi$
$684$	1.31602e8	−	1.31602e8i	0.411238	−	0.411238i
$685$	5.43881e8	+	5.43881e8i	1.69212	+	1.69212i
$686$	−1.75555e8	+	1.75555e8i	−0.543803	+	0.543803i
$687$		−	5.63926e7i		−	0.173921i
$688$	−8.18400e7	−	8.18400e7i	−0.251305	−	0.251305i
$689$	−1.64679e6	−	1.64679e6i	−0.00503480	−	0.00503480i
$690$	−1.68966e7	+	1.68966e7i	−0.0514343	+	0.0514343i
$691$		−	2.27786e8i		−	0.690388i	−0.938531	−	0.345194i	$-0.887813\pi$
$691$		−	2.27786e8i		−	0.690388i	0.938531	−	0.345194i	$-0.112187\pi$
$692$	1.83984e8			0.555214
$693$			1.56117e8i			0.469084i
$694$		−	2.30492e7i		−	0.0689569i
$695$	4.17059e8	−	4.17059e8i	1.24235	−	1.24235i
$696$			5.62608e7i			0.166870i
$697$	−1.12843e7	+	1.12843e7i	−0.0333254	+	0.0333254i
$698$	2.30100e8	−	2.30100e8i	0.676630	−	0.676630i
$699$	9.90945e7			0.290147
$700$	−3.47430e8			−1.01291
$701$	−1.01173e8	−	1.01173e8i	−0.293703	−	0.293703i	0.544838	−	0.838541i	$-0.316591\pi$
$701$	−1.01173e8	−	1.01173e8i	−0.293703	−	0.293703i	−0.838541	+	0.544838i	$0.816591\pi$
$702$			4.98439e6i			0.0144079i
$703$	−2.73208e8	+	3.40352e8i	−0.786372	+	0.979630i
$704$	2.77707e7			0.0795919
$705$	2.17352e8	−	2.17352e8i	0.620292	−	0.620292i
$706$			4.72305e8i			1.34217i
$707$			2.41096e7i			0.0682232i
$708$	5.57059e7	+	5.57059e7i	0.156965	+	0.156965i
$709$	−2.55052e8	−	2.55052e8i	−0.715632	−	0.715632i	0.252076	−	0.967707i	$-0.418887\pi$
$709$	−2.55052e8	−	2.55052e8i	−0.715632	−	0.715632i	−0.967707	+	0.252076i	$0.918887\pi$
$710$	3.72835e8			1.04170
$711$	−3.01408e8	−	3.01408e8i	−0.838582	−	0.838582i
$712$	5.52297e6			0.0153015
$713$	−2.22945e6			−0.00615076
$714$		−	4.75927e6i		−	0.0130751i
$715$	1.70375e7			0.0466109
$716$	−1.64905e8	−	1.64905e8i	−0.449256	−	0.449256i
$717$	−9.45313e7	+	9.45313e7i	−0.256459	+	0.256459i
$718$	9.54623e7	−	9.54623e7i	0.257904	−	0.257904i
$719$	5.05119e8			1.35896			0.679481	−	0.733694i	$-0.262205\pi$
$719$	5.05119e8			1.35896			0.679481	+	0.733694i	$0.262205\pi$
$720$	−1.15048e8	−	1.15048e8i	−0.308235	−	0.308235i
$721$	3.56709e7	−	3.56709e7i	0.0951718	−	0.0951718i
$722$	−1.08781e8	−	1.08781e8i	−0.289028	−	0.289028i
$723$	−7.41587e7	+	7.41587e7i	−0.196222	+	0.196222i
$724$		−	1.35431e8i		−	0.356862i
$725$	−1.18982e9	−	1.18982e9i	−3.12225	−	3.12225i
$726$	3.09606e7	+	3.09606e7i	0.0809095	+	0.0809095i
$727$	−2.37670e8	+	2.37670e8i	−0.618545	+	0.618545i	−0.945158	−	0.326613i	$-0.894093\pi$
$727$	−2.37670e8	+	2.37670e8i	−0.618545	+	0.618545i	0.326613	+	0.945158i	$0.394093\pi$
$728$		−	4.21903e6i		−	0.0109350i
$729$	2.25709e8			0.582594
$730$		−	3.81614e8i		−	0.980970i
$731$			4.74183e7i			0.121393i
$732$	−4.63521e7	+	4.63521e7i	−0.118178	+	0.118178i
$733$		−	1.28704e6i		−	0.00326799i	−0.999999	−	0.00163399i	$-0.999480\pi$
$733$		−	1.28704e6i		−	0.00326799i	0.999999	−	0.00163399i	$-0.000520117\pi$
$734$	1.83126e8	−	1.83126e8i	0.463086	−	0.463086i
$735$	−5.28051e7	+	5.28051e7i	−0.132988	+	0.132988i
$736$	1.41460e7			0.0354814
$737$	2.10273e7			0.0525268
$738$	−1.02704e8	−	1.02704e8i	−0.255517	−	0.255517i
$739$			5.56842e8i			1.37974i	0.723932	+	0.689872i	$0.242333\pi$
$739$			5.56842e8i			1.37974i	−0.723932	+	0.689872i	$0.757667\pi$
$740$	2.97541e8	+	2.38843e8i	0.734262	+	0.589409i
$741$	5.40744e6			0.0132904
$742$	−2.97677e7	+	2.97677e7i	−0.0728674	+	0.0728674i
$743$		−	1.39597e8i		−	0.340337i	−0.985415	−	0.170168i	$-0.945569\pi$
$743$		−	1.39597e8i		−	0.340337i	0.985415	−	0.170168i	$-0.0544311\pi$
$744$			1.21438e6i			0.00294873i
$745$	−3.31016e7	−	3.31016e7i	−0.0800536	−	0.0800536i
$746$	−6.37726e7	−	6.37726e7i	−0.153609	−	0.153609i
$747$	3.84043e8			0.921337
$748$	−8.04521e6	−	8.04521e6i	−0.0192235	−	0.0192235i
$749$	−1.78037e8			−0.423705
$750$	−2.36393e8			−0.560339
$751$			6.58929e8i			1.55567i	0.628466	+	0.777837i	$0.283683\pi$
$751$			6.58929e8i			1.55567i	−0.628466	+	0.777837i	$0.716317\pi$
$752$	−1.81969e8			−0.427902
$753$	3.42527e7	+	3.42527e7i	0.0802251	+	0.0802251i
$754$	1.44487e7	−	1.44487e7i	0.0337065	−	0.0337065i
$755$	−4.07460e8	+	4.07460e8i	−0.946770	+	0.946770i
$756$	9.00985e7			0.208522
$757$	8.40686e7	+	8.40686e7i	0.193797	+	0.193797i	0.797334	−	0.603538i	$-0.206243\pi$
$757$	8.40686e7	+	8.40686e7i	0.193797	+	0.193797i	−0.603538	+	0.797334i	$0.706243\pi$
$758$	2.65941e8	−	2.65941e8i	0.610630	−	0.610630i
$759$	−1.07541e7	−	1.07541e7i	−0.0245950	−	0.0245950i
$760$	−2.59610e8	+	2.59610e8i	−0.591400	+	0.591400i
$761$		−	4.75413e8i		−	1.07874i	−0.842069	−	0.539370i	$-0.818662\pi$
$761$		−	4.75413e8i		−	1.07874i	0.842069	−	0.539370i	$-0.181338\pi$
$762$	−5.80305e7	−	5.80305e7i	−0.131157	−	0.131157i
$763$	−6.23553e7	−	6.23553e7i	−0.140378	−	0.140378i
$764$	−2.97789e8	+	2.97789e8i	−0.667773	+	0.667773i
$765$			6.66592e7i			0.148894i
$766$	−1.01137e8			−0.225021
$767$		−	2.86124e7i		−	0.0634115i
$768$		−	7.70533e6i		−	0.0170101i
$769$	−4.57125e8	+	4.57125e8i	−1.00521	+	1.00521i	−0.00522124	+	0.999986i	$0.501662\pi$
$769$	−4.57125e8	+	4.57125e8i	−1.00521	+	1.00521i	−0.999986	+	0.00522124i	$0.998338\pi$
$770$		−	3.07972e8i		−	0.674588i
$771$	7.82844e7	−	7.82844e7i	0.170810	−	0.170810i
$772$	−3.82129e7	+	3.82129e7i	−0.0830536	+	0.0830536i
$773$	5.22174e8			1.13052			0.565258	−	0.824914i	$-0.308777\pi$
$773$	5.22174e8			1.13052			0.565258	+	0.824914i	$0.308777\pi$
$774$	−4.31579e8			−0.930760
$775$	−2.56821e7	−	2.56821e7i	−0.0551729	−	0.0551729i
$776$		−	2.91332e8i		−	0.623452i
$777$	−1.00976e8	+	1.10501e7i	−0.215257	+	0.0235562i
$778$	1.72769e8			0.366883
$779$	−2.31756e8	+	2.31756e8i	−0.490251	+	0.490251i
$780$		−	4.72726e6i		−	0.00996153i
$781$			2.37295e8i			0.498122i
$782$	−4.09812e6	−	4.09812e6i	−0.00856968	−	0.00856968i
$783$	3.08555e8	+	3.08555e8i	0.642758	+	0.642758i
$784$	4.42089e7			0.0917406
$785$	1.17206e9	+	1.17206e9i	2.42292	+	2.42292i
$786$	−5.67117e6			−0.0116790
$787$	2.17908e8			0.447043			0.223522	−	0.974699i	$-0.428245\pi$
$787$	2.17908e8			0.447043			0.223522	+	0.974699i	$0.428245\pi$
$788$			1.36665e8i			0.279306i
$789$	2.09767e8			0.427078
$790$	5.94586e8	+	5.94586e8i	1.20596	+	1.20596i
$791$	−2.31666e8	+	2.31666e8i	−0.468095	+	0.468095i
$792$	7.32237e7	−	7.32237e7i	0.147393	−	0.147393i
$793$	2.38079e7			0.0477422
$794$	1.37393e8	+	1.37393e8i	0.274476	+	0.274476i
$795$	−3.33536e7	+	3.33536e7i	−0.0663805	+	0.0663805i
$796$	−1.74070e7	−	1.74070e7i	−0.0345132	−	0.0345132i
$797$	−5.58598e8	+	5.58598e8i	−1.10338	+	1.10338i	−0.109378	+	0.994000i	$0.534886\pi$
$797$	−5.58598e8	+	5.58598e8i	−1.10338	+	1.10338i	−0.994000	+	0.109378i	$0.965114\pi$
$798$		−	9.77456e7i		−	0.192348i
$799$	5.27167e7	+	5.27167e7i	0.103349	+	0.103349i
$800$	1.62955e8	+	1.62955e8i	0.318272	+	0.318272i
$801$	1.45626e7	−	1.45626e7i	0.0283361	−	0.0283361i
$802$		−	6.60642e8i		−	1.28069i
$803$	2.42882e8			0.469083
$804$		−	5.83429e6i		−	0.0112259i
$805$		−	1.56877e8i		−	0.300726i
$806$	311872.	−	311872.i	0.000595623	−	0.000595623i
$807$			1.22776e8i			0.233612i
$808$	1.13082e7	−	1.13082e7i	0.0214367	−	0.0214367i
$809$	−3.93282e8	+	3.93282e8i	−0.742776	+	0.742776i	−0.973111	−	0.230335i	$-0.926018\pi$
$809$	−3.93282e8	+	3.93282e8i	−0.742776	+	0.742776i	0.230335	+	0.973111i	$0.426018\pi$
$810$	−5.54283e8			−1.04298
$811$	−5.07636e8			−0.951677			−0.475839	−	0.879533i	$-0.657855\pi$
$811$	−5.07636e8			−0.951677			−0.475839	+	0.879533i	$0.657855\pi$
$812$	−2.61176e8	−	2.61176e8i	−0.487826	−	0.487826i
$813$			1.29215e7i			0.0240459i
$814$	−1.52014e8	+	1.89373e8i	−0.281845	+	0.351111i
$815$	1.10179e9			2.03529
$816$	−2.23224e6	+	2.23224e6i	−0.00410839	+	0.00410839i
$817$			9.73874e8i			1.78582i
$818$			7.06018e8i			1.28990i
$819$	−1.11244e7	−	1.11244e7i	−0.0202500	−	0.0202500i
$820$	2.02604e8	+	2.02604e8i	0.367458	+	0.367458i
$821$	1.84641e8			0.333656			0.166828	−	0.985986i	$-0.446647\pi$
$821$	1.84641e8			0.333656			0.166828	+	0.985986i	$0.446647\pi$
$822$	9.60462e7	+	9.60462e7i	0.172928	+	0.172928i
$823$	7.29995e7			0.130954			0.0654772	−	0.997854i	$-0.479143\pi$
$823$	7.29995e7			0.130954			0.0654772	+	0.997854i	$0.479143\pi$
$824$	−3.34615e7			−0.0598086
$825$		−	2.47763e8i		−	0.441239i
$826$	−5.17201e8			−0.917739
$827$	1.85066e7	+	1.85066e7i	0.0327197	+	0.0327197i	0.723277	−	0.690558i	$-0.242635\pi$
$827$	1.85066e7	+	1.85066e7i	0.0327197	+	0.0327197i	−0.690558	+	0.723277i	$0.742635\pi$
$828$	3.72991e7	−	3.72991e7i	0.0657064	−	0.0657064i
$829$	3.82275e8	−	3.82275e8i	0.670983	−	0.670983i	−0.286959	−	0.957943i	$-0.592644\pi$
$829$	3.82275e8	−	3.82275e8i	0.670983	−	0.670983i	0.957943	+	0.286959i	$0.0926445\pi$
$830$	−7.57601e8			−1.32497
$831$	−9.94821e7	−	9.94821e7i	−0.173357	−	0.173357i
$832$	−1.97885e6	+	1.97885e6i	−0.00343592	+	0.00343592i
$833$	−1.28074e7	−	1.28074e7i	−0.0221577	−	0.0221577i
$834$	7.36502e7	−	7.36502e7i	0.126963	−	0.126963i
$835$		−	1.33329e9i		−	2.29016i
$836$	−1.65232e8	−	1.65232e8i	−0.282797	−	0.282797i
$837$	6.66011e6	+	6.66011e6i	0.0113581	+	0.0113581i
$838$	4.61707e8	−	4.61707e8i	0.784576	−	0.784576i
$839$			7.74575e8i			1.31153i	0.754966	+	0.655764i	$0.227653\pi$
$839$			7.74575e8i			1.31153i	−0.754966	+	0.655764i	$0.772347\pi$
$840$	−8.54506e7			−0.144171
$841$		−	1.19405e9i		−	2.00740i
$842$			7.62173e8i			1.27678i
$843$	541132.	−	541132.i	0.000903277	−	0.000903277i
$844$		−	5.80720e8i		−	0.965916i
$845$	8.02192e8	−	8.02192e8i	1.32956	−	1.32956i
$846$	−4.79802e8	+	4.79802e8i	−0.792412	+	0.792412i
$847$	−2.87453e8			−0.473061
$848$	2.79239e7			0.0457919
$849$	1.17883e8	+	1.17883e8i	0.192632	+	0.192632i
$850$		−	9.44166e7i		−	0.153742i
$851$	−7.74339e7	+	9.64640e7i	−0.125644	+	0.156522i
$852$	6.58405e7			0.106457
$853$	1.11787e8	−	1.11787e8i	0.180113	−	0.180113i	−0.611292	−	0.791405i	$-0.709350\pi$
$853$	1.11787e8	−	1.11787e8i	0.180113	−	0.180113i	0.791405	+	0.611292i	$0.209350\pi$
$854$		−	4.30355e8i		−	0.690961i
$855$			1.36904e9i			2.19037i
$856$	8.35046e7	+	8.35046e7i	0.133134	+	0.133134i
$857$	−6.62264e8	−	6.62264e8i	−1.05218	−	1.05218i	−0.998562	−	0.0536143i	$-0.982926\pi$
$857$	−6.62264e8	−	6.62264e8i	−1.05218	−	1.05218i	−0.0536143	−	0.998562i	$-0.517074\pi$
$858$	3.00872e6			0.00476343
$859$	−1.00889e8	−	1.00889e8i	−0.159172	−	0.159172i	0.623028	−	0.782200i	$-0.285902\pi$
$859$	−1.00889e8	−	1.00889e8i	−0.159172	−	0.159172i	−0.782200	+	0.623028i	$0.785902\pi$
$860$	8.51375e8			1.33852
$861$	−7.62823e7			−0.119513
$862$		−	5.47899e8i		−	0.855419i
$863$	2.37926e8			0.370177			0.185088	−	0.982722i	$-0.440743\pi$
$863$	2.37926e8			0.370177			0.185088	+	0.982722i	$0.440743\pi$
$864$	−4.22590e7	−	4.22590e7i	−0.0655205	−	0.0655205i
$865$	−9.56982e8	+	9.56982e8i	−1.47862	+	1.47862i
$866$	−4.37117e8	+	4.37117e8i	−0.673045	+	0.673045i
$867$	−1.76079e8			−0.270177
$868$	−5.63744e6	−	5.63744e6i	−0.00862030	−	0.00862030i
$869$	−3.78431e8	+	3.78431e8i	−0.576670	+	0.576670i
$870$	−2.92638e8	−	2.92638e8i	−0.444399	−	0.444399i
$871$	−1.49834e6	+	1.49834e6i	−0.00226755	+	0.00226755i
$872$			5.84931e7i			0.0882176i
$873$	−7.68162e8	−	7.68162e8i	−1.15454	−	1.15454i
$874$	−8.41669e7	−	8.41669e7i	−0.126069	−	0.126069i
$875$	1.09739e9	−	1.09739e9i	1.63809	−	1.63809i
$876$		−	6.73908e7i		−	0.100251i
$877$	−8.23387e8			−1.22069			−0.610344	−	0.792136i	$-0.708969\pi$
$877$	−8.23387e8			−1.22069			−0.610344	+	0.792136i	$0.708969\pi$
$878$			1.63355e7i			0.0241351i
$879$			1.61801e8i			0.238240i
$880$	−1.44448e8	+	1.44448e8i	−0.211965	+	0.211965i
$881$			8.18606e8i			1.19715i	0.801068	+	0.598573i	$0.204265\pi$
$881$			8.18606e8i			1.19715i	−0.801068	+	0.598573i	$0.795735\pi$
$882$	1.16567e8	−	1.16567e8i	0.169890	−	0.169890i
$883$	3.62941e8	−	3.62941e8i	0.527173	−	0.527173i	−0.392555	−	0.919728i	$-0.628409\pi$
$883$	3.62941e8	−	3.62941e8i	0.527173	−	0.527173i	0.919728	+	0.392555i	$0.128409\pi$
$884$	1.14655e6			0.00165973
$885$	−5.79504e8			−0.836039
$886$	4.06311e8	+	4.06311e8i	0.584194	+	0.584194i
$887$		−	3.88707e8i		−	0.556995i	−0.960437	−	0.278497i	$-0.910164\pi$
$887$		−	3.88707e8i		−	0.556995i	0.960437	−	0.278497i	$-0.0898364\pi$
$888$	5.25439e7	+	4.21782e7i	0.0750384	+	0.0602350i
$889$	5.38783e8			0.766847
$890$	−2.87275e7	+	2.87275e7i	−0.0407500	+	0.0407500i
$891$		−	3.52780e8i		−	0.498736i
$892$		−	4.61309e7i		−	0.0649976i
$893$	1.08269e9	+	1.08269e9i	1.52037	+	1.52037i
$894$	−5.84555e6	−	5.84555e6i	−0.00818113	−	0.00818113i
$895$	1.71549e9			2.39287
$896$	3.57700e7	+	3.57700e7i	0.0497273	+	0.0497273i
$897$	1.53260e6			0.00212350
$898$	2.60213e8			0.359335
$899$		−	3.86124e7i		−	0.0531432i
$900$	8.59335e8			1.17879
$901$	−8.08959e6	−	8.08959e6i	−0.0110599	−	0.0110599i
$902$	−1.28950e8	+	1.28950e8i	−0.175712	+	0.175712i
$903$	−1.60275e8	+	1.60275e8i	−0.217672	+	0.217672i
$904$	2.17317e8			0.294164
$905$	7.04436e8	+	7.04436e8i	0.950377	+	0.950377i
$906$	−7.19551e7	+	7.19551e7i	−0.0967558	+	0.0967558i
$907$	−7.10773e8	−	7.10773e8i	−0.952597	−	0.952597i	0.0463289	−	0.998926i	$-0.485248\pi$
$907$	−7.10773e8	−	7.10773e8i	−0.952597	−	0.952597i	−0.998926	+	0.0463289i	$0.985248\pi$
$908$	−1.67992e8	+	1.67992e8i	−0.224405	+	0.224405i
$909$		−	5.96330e7i		−	0.0793953i
$910$	2.19451e7	+	2.19451e7i	0.0291215	+	0.0291215i
$911$	−5.18145e8	−	5.18145e8i	−0.685325	−	0.685325i	0.275870	−	0.961195i	$-0.411034\pi$
$911$	−5.18145e8	−	5.18145e8i	−0.685325	−	0.685325i	−0.961195	+	0.275870i	$0.911034\pi$
$912$	−4.58457e7	+	4.58457e7i	−0.0604385	+	0.0604385i
$913$		−	4.82183e8i		−	0.633578i
$914$	8.62390e8			1.12945
$915$		−	4.82197e8i		−	0.629450i
$916$		−	2.45573e8i		−	0.319517i
$917$	2.63269e7	−	2.63269e7i	0.0341422	−	0.0341422i
$918$			2.44849e7i			0.0316498i
$919$	1.02070e9	−	1.02070e9i	1.31508	−	1.31508i	0.397454	−	0.917622i	$-0.369894\pi$
$919$	1.02070e9	−	1.02070e9i	1.31508	−	1.31508i	0.917622	−	0.397454i	$-0.130106\pi$
$920$	−7.35799e7	+	7.35799e7i	−0.0944921	+	0.0944921i
$921$	−1.44309e8			−0.184720
$922$	−1.60127e8			−0.204301
$923$	−1.69089e7	−	1.69089e7i	−0.0215036	−	0.0215036i
$924$		−	5.43860e7i		−	0.0689399i
$925$	−2.00322e9	+	2.19218e8i	−2.53106	+	0.276981i
$926$	−5.08936e8			−0.640958
$927$	−8.82287e7	+	8.82287e7i	−0.110757	+	0.110757i
$928$			2.44999e8i			0.306563i
$929$			7.13325e8i			0.889693i	0.895607	+	0.444847i	$0.146742\pi$
$929$			7.13325e8i			0.889693i	−0.895607	+	0.444847i	$0.853258\pi$
$930$	−6.31654e6	−	6.31654e6i	−0.00785290	−	0.00785290i
$931$	−2.63037e8	−	2.63037e8i	−0.325963	−	0.325963i
$932$	4.31527e8			0.533041
$933$	−1.79365e8	−	1.79365e8i	−0.220848	−	0.220848i
$934$	1.03317e9			1.26803
$935$	8.36936e7			0.102390
$936$			1.04354e7i			0.0127257i
$937$	−5.43286e8			−0.660404			−0.330202	−	0.943910i	$-0.607117\pi$
$937$	−5.43286e8			−0.660404			−0.330202	+	0.943910i	$0.607117\pi$
$938$	2.70842e7	+	2.70842e7i	0.0328176	+	0.0328176i
$939$	−1.08610e8	+	1.08610e8i	−0.131182	+	0.131182i
$940$	9.46504e8	−	9.46504e8i	1.13956	−	1.13956i
$941$	−3.57012e8			−0.428463			−0.214232	−	0.976783i	$-0.568725\pi$
$941$	−3.57012e8			−0.428463			−0.214232	+	0.976783i	$0.568725\pi$
$942$	2.06978e8	+	2.06978e8i	0.247612	+	0.247612i
$943$	−6.56853e7	+	6.56853e7i	−0.0783309	+	0.0783309i
$944$	2.42583e8	+	2.42583e8i	0.288366	+	0.288366i
$945$	−4.68644e8	+	4.68644e8i	−0.555325	+	0.555325i
$946$			5.41867e8i			0.640058i
$947$	−8.34300e8	−	8.34300e8i	−0.982363	−	0.982363i	0.0174838	−	0.999847i	$-0.494434\pi$
$947$	−8.34300e8	−	8.34300e8i	−0.982363	−	0.982363i	−0.999847	+	0.0174838i	$0.994434\pi$
$948$	1.05000e8	+	1.05000e8i	0.123244	+	0.123244i
$949$	−1.73071e7	+	1.73071e7i	−0.0202500	+	0.0202500i
$950$		−	1.93912e9i		−	2.26170i
$951$	−9.24834e7			−0.107528
$952$		−	2.07252e7i		−	0.0240209i
$953$		−	1.70262e8i		−	0.196715i	−0.995151	−	0.0983577i	$-0.968641\pi$
$953$		−	1.70262e8i		−	0.196715i	0.995151	−	0.0983577i	$-0.0313589\pi$
$954$	7.36276e7	−	7.36276e7i	0.0847999	−	0.0847999i
$955$		−	3.09787e9i		−	3.55675i
$956$	−4.11656e8	+	4.11656e8i	−0.471152	+	0.471152i
$957$	1.86253e8	−	1.86253e8i	0.212504	−	0.212504i
$958$	−8.20276e8			−0.932961
$959$	−8.91739e8			−1.01107
$960$	4.00789e7	+	4.00789e7i	0.0453004	+	0.0453004i
$961$			8.86670e8i			0.999061i
$962$	−2.66208e6	−	2.43262e7i	−0.00299017	−	0.0273243i
$963$	4.40357e8			0.493090
$964$	−3.22939e8	+	3.22939e8i	−0.360487	+	0.360487i
$965$		−	3.97526e8i		−	0.442368i
$966$		−	2.77035e7i		−	0.0307329i
$967$	−3.30225e8	−	3.30225e8i	−0.365199	−	0.365199i	0.500524	−	0.865723i	$-0.333141\pi$
$967$	−3.30225e8	−	3.30225e8i	−0.365199	−	0.365199i	−0.865723	+	0.500524i	$0.833141\pi$
$968$	1.34824e8	+	1.34824e8i	0.148642	+	0.148642i
$969$	2.65631e7			0.0291949
$970$	1.51535e9	+	1.51535e9i	1.66034	+	1.66034i
$971$	−1.12142e9			−1.22493			−0.612464	−	0.790498i	$-0.709822\pi$
$971$	−1.12142e9			−1.22493			−0.612464	+	0.790498i	$0.709822\pi$
$972$	−3.38561e8			−0.368670
$973$			6.83804e8i			0.742324i
$974$	−1.15534e9			−1.25036
$975$	1.76548e7	+	1.76548e7i	0.0190480	+	0.0190480i
$976$	−2.01850e8	+	2.01850e8i	−0.217109	+	0.217109i
$977$	3.47629e8	−	3.47629e8i	0.372763	−	0.372763i	−0.495720	−	0.868483i	$-0.665096\pi$
$977$	3.47629e8	−	3.47629e8i	0.372763	−	0.372763i	0.868483	+	0.495720i	$0.165096\pi$
$978$	1.94570e8			0.207998
$979$	−1.82839e7	−	1.82839e7i	−0.0194860	−	0.0194860i
$980$	−2.29951e8	+	2.29951e8i	−0.244319	+	0.244319i
$981$	1.54230e8	+	1.54230e8i	0.163366	+	0.163366i
$982$	−2.52334e8	+	2.52334e8i	−0.266466	+	0.266466i
$983$			1.52162e8i			0.160194i	0.996787	+	0.0800970i	$0.0255230\pi$
$983$			1.52162e8i			0.160194i	−0.996787	+	0.0800970i	$0.974477\pi$
$984$	3.57787e7	+	3.57787e7i	0.0375526	+	0.0375526i
$985$	−7.10859e8	−	7.10859e8i	−0.743832	−	0.743832i
$986$	7.09765e7	−	7.09765e7i	0.0740430	−	0.0740430i
$987$			3.56367e8i			0.370635i
$988$	2.35478e7			0.0244163
$989$			2.76020e8i			0.285332i
$990$			7.61739e8i			0.785056i
$991$	1.10684e9	−	1.10684e9i	1.13727	−	1.13727i	0.148333	−	0.988937i	$-0.452609\pi$
$991$	1.10684e9	−	1.10684e9i	1.13727	−	1.13727i	0.988937	−	0.148333i	$-0.0473907\pi$
$992$			5.28826e6i			0.00541724i
$993$	4.34539e7	−	4.34539e7i	0.0443794	−	0.0443794i
$994$	−3.05648e8	+	3.05648e8i	−0.311216	+	0.311216i
$995$	1.81084e8			0.183828
$996$	−1.33788e8			−0.135406
$997$	1.07176e9	+	1.07176e9i	1.08146	+	1.08146i	0.996373	+	0.0850883i	$0.0271172\pi$
$997$	1.07176e9	+	1.07176e9i	1.08146	+	1.08146i	0.0850883	+	0.996373i	$0.472883\pi$
$998$		−	9.46287e8i		−	0.951988i
$999$	5.19492e8	−	5.68494e7i	0.521054	−	0.0570203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.43.6	yes	20
37.31	odd	4	inner	74.7.d.b.31.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.5	✓	20	37.31	odd	4	inner
74.7.d.b.43.6	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 4.00000i) q^{2} -7.34837i q^{3} -32.0000i q^{4} +(166.447 + 166.447i) q^{5} +(29.3935 + 29.3935i) q^{6} -272.903 q^{7} +(128.000 + 128.000i) q^{8} +675.001 q^{9} +O(q^{10})\)	\(q+(-4.00000 + 4.00000i) q^{2} -7.34837i q^{3} -32.0000i q^{4} +(166.447 + 166.447i) q^{5} +(29.3935 + 29.3935i) q^{6} -272.903 q^{7} +(128.000 + 128.000i) q^{8} +675.001 q^{9} -1331.57 q^{10} -847.494i q^{11} -235.148 q^{12} +(60.3898 + 60.3898i) q^{13} +(1091.61 - 1091.61i) q^{14} +(1223.11 - 1223.11i) q^{15} -1024.00 q^{16} +(296.654 + 296.654i) q^{17} +(-2700.01 + 2700.01i) q^{18} +(6092.66 + 6092.66i) q^{19} +(5326.29 - 5326.29i) q^{20} +2005.40i q^{21} +(3389.98 + 3389.98i) q^{22} +(1726.81 + 1726.81i) q^{23} +(940.592 - 940.592i) q^{24} +39784.0i q^{25} -483.118 q^{26} -10317.1i q^{27} +8732.91i q^{28} +(-29907.1 + 29907.1i) q^{29} +9784.90i q^{30} +(-645.539 + 645.539i) q^{31} +(4096.00 - 4096.00i) q^{32} -6227.70 q^{33} -2373.23 q^{34} +(-45423.8 - 45423.8i) q^{35} -21600.0i q^{36} +(5510.20 + 50352.4i) q^{37} -48741.3 q^{38} +(443.767 - 443.767i) q^{39} +42610.3i q^{40} +38038.5i q^{41} +(-8021.58 - 8021.58i) q^{42} +(79921.9 + 79921.9i) q^{43} -27119.8 q^{44} +(112352. + 112352. i) q^{45} -13814.5 q^{46} +177704. q^{47} +7524.73i q^{48} -43172.8 q^{49} +(-159136. - 159136. i) q^{50} +(2179.93 - 2179.93i) q^{51} +(1932.47 - 1932.47i) q^{52} -27269.4 q^{53} +(41268.5 + 41268.5i) q^{54} +(141063. - 141063. i) q^{55} +(-34931.6 - 34931.6i) q^{56} +(44771.1 - 44771.1i) q^{57} -239257. i q^{58} +(-236897. - 236897. i) q^{59} +(-39139.6 - 39139.6i) q^{60} +(197119. - 197119. i) q^{61} -5164.32i q^{62} -184210. q^{63} +32768.0i q^{64} +20103.4i q^{65} +(24910.8 - 24910.8i) q^{66} +24811.2i q^{67} +(9492.93 - 9492.93i) q^{68} +(12689.2 - 12689.2i) q^{69} +363391. q^{70} -279996. q^{71} +(86400.2 + 86400.2i) q^{72} +286589. i q^{73} +(-223450. - 179369. i) q^{74} +292347. q^{75} +(194965. - 194965. i) q^{76} +231284. i q^{77} +3550.13i q^{78} +(-446529. - 446529. i) q^{79} +(-170441. - 170441. i) q^{80} +416262. q^{81} +(-152154. - 152154. i) q^{82} +568952. q^{83} +64172.7 q^{84} +98754.2i q^{85} -639375. q^{86} +(219769. + 219769. i) q^{87} +(108479. - 108479. i) q^{88} +(21574.1 - 21574.1i) q^{89} -898814. q^{90} +(-16480.6 - 16480.6i) q^{91} +(55257.9 - 55257.9i) q^{92} +(4743.67 + 4743.67i) q^{93} +(-710816. + 710816. i) q^{94} +2.02821e6i q^{95} +(-30098.9 - 30098.9i) q^{96} +(-1.13802e6 - 1.13802e6i) q^{97} +(172691. - 172691. i) q^{98} -572060. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

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