LMFDB - Embedded newform 27.7.f.a.2.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.14
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.4695 + 1.84606i) q^{2} +(-18.3558 - 19.8006i) q^{3} +(46.0625 + 16.7654i) q^{4} +(-137.909 - 164.354i) q^{5} +(-155.623 - 241.189i) q^{6} +(506.532 - 184.363i) q^{7} +(-137.929 - 79.6334i) q^{8} +(-55.1285 + 726.913i) q^{9} +O(q^{10})$	\(q+(10.4695 + 1.84606i) q^{2} +(-18.3558 - 19.8006i) q^{3} +(46.0625 + 16.7654i) q^{4} +(-137.909 - 164.354i) q^{5} +(-155.623 - 241.189i) q^{6} +(506.532 - 184.363i) q^{7} +(-137.929 - 79.6334i) q^{8} +(-55.1285 + 726.913i) q^{9} +(-1140.44 - 1975.29i) q^{10} +(198.615 - 236.700i) q^{11} +(-513.550 - 1219.81i) q^{12} +(375.382 + 2128.90i) q^{13} +(5643.49 - 995.099i) q^{14} +(-722.871 + 5747.53i) q^{15} +(-3700.27 - 3104.90i) q^{16} +(1302.84 - 752.193i) q^{17} +(-1919.09 + 7508.65i) q^{18} +(5043.14 - 8734.98i) q^{19} +(-3596.99 - 9882.65i) q^{20} +(-12948.3 - 6645.52i) q^{21} +(2516.36 - 2111.48i) q^{22} +(-503.858 + 1384.34i) q^{23} +(955.010 + 4192.82i) q^{24} +(-5279.97 + 29944.2i) q^{25} +22981.5i q^{26} +(15405.2 - 12251.5i) q^{27} +26423.0 q^{28} +(6736.49 + 1187.82i) q^{29} +(-18178.4 + 58839.4i) q^{30} +(43864.1 + 15965.2i) q^{31} +(-26456.3 - 31529.4i) q^{32} +(-8332.53 + 412.124i) q^{33} +(15028.7 - 5469.99i) q^{34} +(-100156. - 57825.2i) q^{35} +(-14726.3 + 32559.1i) q^{36} +(2057.61 + 3563.88i) q^{37} +(68924.5 - 82141.1i) q^{38} +(35263.0 - 46510.5i) q^{39} +(5933.64 + 33651.4i) q^{40} +(925.411 - 163.175i) q^{41} +(-123294. - 93478.6i) q^{42} +(-31232.5 - 26207.1i) q^{43} +(13117.0 - 7573.13i) q^{44} +(127074. - 91187.4i) q^{45} +(-7830.72 + 13563.2i) q^{46} +(-13871.0 - 38110.1i) q^{47} +(6442.63 + 130261. i) q^{48} +(132461. - 111148. i) q^{49} +(-110557. + 303754. i) q^{50} +(-38808.5 - 11989.9i) q^{51} +(-18400.7 + 104356. i) q^{52} -182216. i q^{53} +(183902. - 99828.2i) q^{54} -66293.3 q^{55} +(-84546.9 - 14907.9i) q^{56} +(-265529. + 60480.3i) q^{57} +(68335.0 + 24871.9i) q^{58} +(151982. + 181125. i) q^{59} +(-129657. + 252627. i) q^{60} +(-132078. + 48072.5i) q^{61} +(429763. + 248124. i) q^{62} +(106091. + 378368. i) q^{63} +(-64207.6 - 111211. i) q^{64} +(298124. - 355290. i) q^{65} +(-87998.4 - 11067.6i) q^{66} +(32441.2 + 183983. i) q^{67} +(72622.7 - 12805.3i) q^{68} +(36659.5 - 15434.0i) q^{69} +(-941837. - 790295. i) q^{70} +(-427176. + 246630. i) q^{71} +(65490.4 - 95872.3i) q^{72} +(26578.8 - 46035.8i) q^{73} +(14963.0 + 41110.5i) q^{74} +(689832. - 445103. i) q^{75} +(378745. - 317805. i) q^{76} +(56966.1 - 156513. i) q^{77} +(455048. - 421844. i) q^{78} +(-127957. + 725680. i) q^{79} +1.03635e6i q^{80} +(-525363. - 80147.2i) q^{81} +9989.83 q^{82} +(-61397.6 - 10826.1i) q^{83} +(-485016. - 523192. i) q^{84} +(-303299. - 110392. i) q^{85} +(-278609. - 332033. i) q^{86} +(-100134. - 155190. i) q^{87} +(-46244.0 + 16831.4i) q^{88} +(212109. + 122461. i) q^{89} +(1.49874e6 - 720102. i) q^{90} +(582632. + 1.00915e6i) q^{91} +(-46417.9 + 55318.7i) q^{92} +(-489040. - 1.16159e6i) q^{93} +(-74868.6 - 424601. i) q^{94} +(-2.13112e6 + 375775. i) q^{95} +(-138674. + 1.10260e6i) q^{96} +(580975. + 487496. i) q^{97} +(1.59198e6 - 919132. i) q^{98} +(161111. + 157424. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	10.4695	+	1.84606i	1.30869	+	0.230757i	0.784119	−	0.620610i	$-0.213115\pi$
$2$	10.4695	+	1.84606i	1.30869	+	0.230757i	0.524570	+	0.851367i	$0.324226\pi$
$3$	−18.3558	−	19.8006i	−0.679845	−	0.733356i
$3$	−18.3558	−	19.8006i	−0.679845	−	0.733356i
$4$	46.0625	+	16.7654i	0.719726	+	0.261959i
$5$	−137.909	−	164.354i	−1.10327	−	1.31483i	−0.944866	−	0.327457i	$-0.893808\pi$
$5$	−137.909	−	164.354i	−1.10327	−	1.31483i	−0.158408	−	0.987374i	$-0.550636\pi$
$6$	−155.623	−	241.189i	−0.720478	−	1.11661i
$7$	506.532	−	184.363i	1.47677	−	0.537500i	0.526840	−	0.849965i	$-0.323377\pi$
$7$	506.532	−	184.363i	1.47677	−	0.537500i	0.949929	+	0.312465i	$0.101155\pi$
$8$	−137.929	−	79.6334i	−0.269393	−	0.155534i
$9$	−55.1285	+	726.913i	−0.0756221	+	0.997137i
$10$	−1140.44	−	1975.29i	−1.14044	−	1.97529i
$11$	198.615	−	236.700i	0.149222	−	0.177836i	−0.686255	−	0.727361i	$-0.740747\pi$
$11$	198.615	−	236.700i	0.149222	−	0.177836i	0.835477	+	0.549525i	$0.185191\pi$
$12$	−513.550	−	1219.81i	−0.297193	−	0.705907i
$13$	375.382	+	2128.90i	0.170861	+	0.969002i	0.942813	+	0.333322i	$0.108169\pi$
$13$	375.382	+	2128.90i	0.170861	+	0.969002i	−0.771952	+	0.635681i	$0.780719\pi$
$14$	5643.49	−	995.099i	2.05666	−	0.362645i
$15$	−722.871	+	5747.53i	−0.214184	+	1.70297i
$16$	−3700.27	−	3104.90i	−0.903387	−	0.758032i
$17$	1302.84	−	752.193i	0.265182	−	0.153103i	−0.361514	−	0.932367i	$-0.617740\pi$
$17$	1302.84	−	752.193i	0.265182	−	0.153103i	0.626696	+	0.779264i	$0.284407\pi$
$18$	−1919.09	+	7508.65i	−0.329062	+	1.28749i
$19$	5043.14	−	8734.98i	0.735259	−	1.27351i	−0.219350	−	0.975646i	$-0.570394\pi$
$19$	5043.14	−	8734.98i	0.735259	−	1.27351i	0.954609	−	0.297860i	$-0.0962729\pi$
$20$	−3596.99	−	9882.65i	−0.449624	−	1.23533i
$21$	−12948.3	−	6645.52i	−1.39815	−	0.717581i
$22$	2516.36	−	2111.48i	0.236322	−	0.198298i
$23$	−503.858	+	1384.34i	−0.0414118	+	0.113778i	−0.958675	−	0.284504i	$-0.908171\pi$
$23$	−503.858	+	1384.34i	−0.0414118	+	0.113778i	0.917263	+	0.398282i	$0.130393\pi$
$24$	955.010	+	4192.82i	0.0690835	+	0.303300i
$25$	−5279.97	+	29944.2i	−0.337918	+	1.91643i
$26$			22981.5i			1.30755i
$27$	15405.2	−	12251.5i	0.782667	−	0.622440i
$28$	26423.0			1.20367
$29$	6736.49	+	1187.82i	0.276210	+	0.0487033i	0.310037	−	0.950724i	$-0.399658\pi$
$29$	6736.49	+	1187.82i	0.276210	+	0.0487033i	−0.0338271	+	0.999428i	$0.510770\pi$
$30$	−18178.4	+	58839.4i	−0.673274	+	2.17924i
$31$	43864.1	+	15965.2i	1.47239	+	0.535907i	0.948749	−	0.316030i	$-0.102350\pi$
$31$	43864.1	+	15965.2i	1.47239	+	0.535907i	0.523644	+	0.851937i	$0.324572\pi$
$32$	−26456.3	−	31529.4i	−0.807381	−	0.962199i
$33$	−8332.53	+	412.124i	−0.231865	+	0.0114679i
$34$	15028.7	−	5469.99i	0.382370	−	0.139171i
$35$	−100156.	−	57825.2i	−2.33600	−	1.34869i
$36$	−14726.3	+	32559.1i	−0.315636	+	0.697856i
$37$	2057.61	+	3563.88i	0.0406216	+	0.0703587i	0.885621	−	0.464408i	$-0.153733\pi$
$37$	2057.61	+	3563.88i	0.0406216	+	0.0703587i	−0.845000	+	0.534767i	$0.820400\pi$
$38$	68924.5	−	82141.1i	1.25610	−	1.49696i
$39$	35263.0	−	46510.5i	0.594465	−	0.784073i
$40$	5933.64	+	33651.4i	0.0927132	+	0.525803i
$41$	925.411	−	163.175i	0.0134271	−	0.00236756i	−0.166931	−	0.985969i	$-0.553386\pi$
$41$	925.411	−	163.175i	0.0134271	−	0.00236756i	0.180358	+	0.983601i	$0.442274\pi$
$42$	−123294.	−	93478.6i	−1.66416	−	1.26172i
$43$	−31232.5	−	26207.1i	−0.392826	−	0.329621i	0.424887	−	0.905247i	$-0.360314\pi$
$43$	−31232.5	−	26207.1i	−0.392826	−	0.329621i	−0.817713	+	0.575626i	$0.804758\pi$
$44$	13117.0	−	7573.13i	0.153985	−	0.0889032i
$45$	127074.	−	91187.4i	1.39450	−	1.00068i
$46$	−7830.72	+	13563.2i	−0.0804504	+	0.139344i
$47$	−13871.0	−	38110.1i	−0.133602	−	0.367068i	0.854794	−	0.518967i	$-0.173683\pi$
$47$	−13871.0	−	38110.1i	−0.133602	−	0.367068i	−0.988396	+	0.151899i	$0.951461\pi$
$48$	6442.63	+	130261.i	0.0582559	+	1.17785i
$49$	132461.	−	111148.i	1.12590	−	0.944739i
$50$	−110557.	+	303754.i	−0.884460	+	2.43003i
$51$	−38808.5	−	11989.9i	−0.292561	−	0.0903864i
$52$	−18400.7	+	104356.i	−0.130866	+	0.742175i
$53$		−	182216.i		−	1.22393i	−0.790883	−	0.611967i	$-0.790379\pi$
$53$		−	182216.i		−	1.22393i	0.790883	−	0.611967i	$-0.209621\pi$
$54$	183902.	−	99828.2i	1.16790	−	0.633975i
$55$	−66293.3			−0.398457
$56$	−84546.9	−	14907.9i	−0.481431	−	0.0848892i
$57$	−265529.	+	60480.3i	−1.43380	+	0.326580i
$58$	68335.0	+	24871.9i	0.350235	+	0.127475i
$59$	151982.	+	181125.i	0.740009	+	0.881908i	0.996410	−	0.0846623i	$-0.0269811\pi$
$59$	151982.	+	181125.i	0.740009	+	0.881908i	−0.256401	+	0.966571i	$0.582537\pi$
$60$	−129657.	+	252627.i	−0.600263	+	1.16957i
$61$	−132078.	+	48072.5i	−0.581891	+	0.211791i	−0.616159	−	0.787622i	$-0.711312\pi$
$61$	−132078.	+	48072.5i	−0.581891	+	0.211791i	0.0342681	+	0.999413i	$0.489090\pi$
$62$	429763.	+	248124.i	1.80324	+	1.04110i
$63$	106091.	+	378368.i	0.424285	+	1.51319i
$64$	−64207.6	−	111211.i	−0.244933	−	0.424236i
$65$	298124.	−	355290.i	1.08557	−	1.29373i
$66$	−87998.4	−	11067.6i	−0.306086	−	0.0384966i
$67$	32441.2	+	183983.i	0.107863	+	0.611722i	0.990038	+	0.140800i	$0.0449674\pi$
$67$	32441.2	+	183983.i	0.107863	+	0.611722i	−0.882175	+	0.470922i	$0.843921\pi$
$68$	72622.7	−	12805.3i	0.230965	−	0.0407253i
$69$	36659.5	−	15434.0i	0.111593	−	0.0469818i
$70$	−941837.	−	790295.i	−2.74588	−	2.30407i
$71$	−427176.	+	246630.i	−1.19353	+	0.689082i	−0.959104	−	0.283053i	$-0.908653\pi$
$71$	−427176.	+	246630.i	−1.19353	+	0.689082i	−0.234421	+	0.972135i	$0.575319\pi$
$72$	65490.4	−	95872.3i	0.175461	−	0.256860i
$73$	26578.8	−	46035.8i	0.0683230	−	0.118339i	−0.829840	−	0.558001i	$-0.811569\pi$
$73$	26578.8	−	46035.8i	0.0683230	−	0.118339i	0.898163	+	0.439662i	$0.144902\pi$
$74$	14963.0	+	41110.5i	0.0369253	+	0.101451i
$75$	689832.	−	445103.i	1.63516	−	1.05506i
$76$	378745.	−	317805.i	0.862792	−	0.723968i
$77$	56966.1	−	156513.i	0.124780	−	0.342830i
$78$	455048.	−	421844.i	0.958900	−	0.888932i
$79$	−127957.	+	725680.i	−0.259527	+	1.47185i	0.524653	+	0.851316i	$0.324195\pi$
$79$	−127957.	+	725680.i	−0.259527	+	1.47185i	−0.784180	+	0.620534i	$0.786916\pi$
$80$			1.03635e6i			2.02412i
$81$	−525363.	−	80147.2i	−0.988563	−	0.150811i
$82$	9989.83			0.0181183
$83$	−61397.6	−	10826.1i	−0.107378	−	0.0189337i	0.119701	−	0.992810i	$-0.461806\pi$
$83$	−61397.6	−	10826.1i	−0.107378	−	0.0189337i	−0.227079	+	0.973876i	$0.572918\pi$
$84$	−485016.	−	523192.i	−0.818311	−	0.882721i
$85$	−303299.	−	110392.i	−0.493872	−	0.179755i
$86$	−278609.	−	332033.i	−0.438026	−	0.522018i
$87$	−100134.	−	155190.i	−0.152063	−	0.235671i
$88$	−46244.0	+	16831.4i	−0.0678589	+	0.0246986i
$89$	212109.	+	122461.i	0.300877	+	0.173711i	0.642837	−	0.766003i	$-0.277757\pi$
$89$	212109.	+	122461.i	0.300877	+	0.173711i	−0.341960	+	0.939715i	$0.611091\pi$
$90$	1.49874e6	−	720102.i	2.05588	−	0.987795i
$91$	582632.	+	1.00915e6i	0.773162	+	1.33916i
$92$	−46417.9	+	55318.7i	−0.0596104	+	0.0710409i
$93$	−489040.	−	1.16159e6i	−0.607988	−	1.44412i
$94$	−74868.6	−	424601.i	−0.0901397	−	0.511208i
$95$	−2.13112e6	+	375775.i	−2.48564	+	0.438285i
$96$	−138674.	+	1.10260e6i	−0.156741	+	1.24624i
$97$	580975.	+	487496.i	0.636564	+	0.534141i	0.902961	−	0.429722i	$-0.141389\pi$
$97$	580975.	+	487496.i	0.636564	+	0.534141i	−0.266397	+	0.963864i	$0.585833\pi$
$98$	1.59198e6	−	919132.i	1.69145	−	0.976562i
$99$	161111.	+	157424.i	0.166042	+	0.162243i
$100$	−745234.	+	1.29078e6i	−0.745234	+	1.29078i
$101$	−199827.	−	549019.i	−0.193950	−	0.532873i	0.804154	−	0.594421i	$-0.202619\pi$
$101$	−199827.	−	549019.i	−0.193950	−	0.532873i	−0.998104	+	0.0615478i	$0.980396\pi$
$102$	−384172.	−	197171.i	−0.362014	−	0.185798i
$103$	837606.	−	702835.i	0.766528	−	0.643193i	−0.173289	−	0.984871i	$-0.555440\pi$
$103$	837606.	−	702835.i	0.766528	−	0.643193i	0.939817	+	0.341678i	$0.110995\pi$
$104$	117755.	−	323530.i	0.104684	−	0.287617i
$105$	693473.	+	3.04458e6i	0.599048	+	2.63002i
$106$	336381.	−	1.90771e6i	0.282432	−	1.60175i
$107$			209138.i			0.170719i	0.996350	+	0.0853593i	$0.0272038\pi$
$107$			209138.i			0.170719i	−0.996350	+	0.0853593i	$0.972796\pi$
$108$	915005.	−	306059.i	0.726360	−	0.242960i
$109$	438605.			0.338684			0.169342	−	0.985557i	$-0.445836\pi$
$109$	438605.			0.338684			0.169342	+	0.985557i	$0.445836\pi$
$110$	−694059.	−	122381.i	−0.521457	−	0.0919469i
$111$	32798.0	−	106160.i	0.0239816	−	0.0776231i
$112$	−2.44673e6	−	890538.i	−1.74154	−	0.633867i
$113$	248073.	+	295642.i	0.171927	+	0.204895i	0.845127	−	0.534566i	$-0.179525\pi$
$113$	248073.	+	295642.i	0.171927	+	0.204895i	−0.673199	+	0.739461i	$0.735080\pi$
$114$	−2.89161e6	+	143018.i	−1.95175	+	0.0965329i
$115$	297008.	−	108102.i	0.195288	−	0.0710789i
$116$	290385.	+	167654.i	0.186037	+	0.107409i
$117$	−1.56822e6	+	155507.i	−0.979149	+	0.0970941i
$118$	1.25681e6	+	2.17686e6i	0.764935	+	1.32491i
$119$	521252.	−	621204.i	0.309319	−	0.368632i
$120$	557401.	−	735188.i	0.322570	−	0.425456i
$121$	291049.	+	1.65062e6i	0.164290	+	0.931734i
$122$	−1.47154e6	+	259472.i	−0.810387	+	0.142893i
$123$	−20217.6	−	15328.5i	−0.0108646	−	0.00823729i
$124$	1.75283e6	+	1.47080e6i	0.919335	+	0.771413i
$125$	2.74640e6	−	1.58564e6i	1.40616	−	0.811846i
$126$	412233.	+	4.15718e6i	0.206078	+	2.07820i
$127$	−887067.	+	1.53645e6i	−0.433057	+	0.750077i	−0.997135	−	0.0756445i	$-0.975899\pi$
$127$	−887067.	+	1.53645e6i	−0.433057	+	0.750077i	0.564077	+	0.825722i	$0.309232\pi$
$128$	434013.	+	1.19244e6i	0.206953	+	0.568600i
$129$	54379.6	+	1.09948e6i	0.0253318	+	0.512172i
$130$	3.77710e6	−	3.16936e6i	1.71921	−	1.44259i
$131$	493171.	−	1.35498e6i	0.219373	−	0.602723i	−0.780372	−	0.625316i	$-0.784970\pi$
$131$	493171.	−	1.35498e6i	0.219373	−	0.602723i	0.999745	+	0.0225934i	$0.00719232\pi$
$132$	−390727.	−	120715.i	−0.169884	−	0.0524853i
$133$	944110.	−	5.35431e6i	0.401299	−	2.27588i
$134$			1.98610e6i			0.825444i
$135$	−4.13810e6	−	842317.i	−1.68190	−	0.342353i
$136$	−239599.			−0.0952507
$137$	−127131.	−	22416.7i	−0.0494414	−	0.00871785i	0.148873	−	0.988856i	$-0.452436\pi$
$137$	−127131.	−	22416.7i	−0.0494414	−	0.00871785i	−0.198314	+	0.980139i	$0.563547\pi$
$138$	412299.	−	93910.5i	0.156883	−	0.0357336i
$139$	−61437.8	−	22361.5i	−0.0228766	−	0.00832639i	0.330557	−	0.943786i	$-0.392764\pi$
$139$	−61437.8	−	22361.5i	−0.0228766	−	0.00832639i	−0.353433	+	0.935460i	$0.614986\pi$
$140$	−3.64398e6	−	4.34272e6i	−1.32798	−	1.58263i
$141$	−499991.	+	974195.i	−0.178363	+	0.347527i
$142$	−4.92762e6	+	1.79351e6i	−1.72096	+	0.626380i
$143$	578466.	+	333978.i	0.197820	+	0.114211i
$144$	2.46098e6	−	2.51861e6i	0.824177	−	0.843476i
$145$	−733801.	−	1.27098e6i	−0.240699	−	0.416903i
$146$	363252.	−	432907.i	0.116721	−	0.139103i
$147$	−4.63221e6	−	582596.i	−1.45827	−	0.183407i
$148$	35028.7	+	198658.i	0.0108054	+	0.0612802i
$149$	6.10515e6	−	1.07650e6i	1.84560	−	0.325429i	0.862156	−	0.506643i	$-0.169114\pi$
$149$	6.10515e6	−	1.07650e6i	1.84560	−	0.325429i	0.983444	+	0.181214i	$0.0580026\pi$
$150$	8.04389e6	−	3.38655e6i	2.38337	−	1.00342i
$151$	−2.50196e6	−	2.09939e6i	−0.726691	−	0.609766i	0.202536	−	0.979275i	$-0.435082\pi$
$151$	−2.50196e6	−	2.09939e6i	−0.726691	−	0.609766i	−0.929227	+	0.369509i	$0.879526\pi$
$152$	−1.39119e6	+	803206.i	−0.396147	+	0.228716i
$153$	474955.	+	988516.i	0.132611	+	0.276000i
$154$	885340.	−	1.53345e6i	0.242408	−	0.419864i
$155$	−3.42532e6	−	9.41098e6i	−0.919826	−	2.52720i
$156$	2.40407e6	−	1.55119e6i	0.633247	−	0.408593i
$157$	1.50662e6	−	1.26420e6i	0.389318	−	0.326676i	−0.427030	−	0.904238i	$-0.640440\pi$
$157$	1.50662e6	−	1.26420e6i	0.389318	−	0.326676i	0.816347	+	0.577561i	$0.195996\pi$
$158$	−2.67929e6	+	7.36130e6i	−0.679280	+	1.86631i
$159$	−3.60798e6	+	3.34471e6i	−0.897579	+	0.832085i
$160$	−1.53341e6	+	8.69638e6i	−0.374367	+	2.12314i
$161$			794104.i			0.190283i
$162$	−5.35234e6	−	1.80895e6i	−1.25892	−	0.425483i
$163$	6.40851e6			1.47977			0.739885	−	0.672733i	$-0.234880\pi$
$163$	6.40851e6			1.47977			0.739885	+	0.672733i	$0.234880\pi$
$164$	45362.4	+	7998.62i	0.0102841	+	0.00181336i
$165$	1.21687e6	+	1.31265e6i	0.270889	+	0.292211i
$166$	−622817.	−	226687.i	−0.136156	−	0.0495567i
$167$	3.35169e6	+	3.99439e6i	0.719640	+	0.857633i	0.994596	−	0.103824i	$-0.0331078\pi$
$167$	3.35169e6	+	3.99439e6i	0.719640	+	0.857633i	−0.274956	+	0.961457i	$0.588663\pi$
$168$	1.25674e6	+	1.94773e6i	0.265044	+	0.410771i
$169$	144420.	−	52564.6i	0.0299204	−	0.0108901i
$170$	−2.97160e6	−	1.71566e6i	−0.604845	−	0.349207i
$171$	6.07155e6	+	4.14747e6i	1.21426	+	0.829459i
$172$	−999272.	−	1.73079e6i	−0.196381	−	0.340141i
$173$	−4.71688e6	+	5.62136e6i	−0.910996	+	1.08568i	0.0850085	+	0.996380i	$0.472908\pi$
$173$	−4.71688e6	+	5.62136e6i	−0.910996	+	1.08568i	−0.996005	+	0.0893026i	$0.971536\pi$
$174$	−761865.	−	1.80962e6i	−0.144621	−	0.343510i
$175$	2.84611e6	+	1.61411e7i	0.531053	+	3.01175i
$176$	−1.46986e6	+	259176.i	−0.269611	+	0.0475397i
$177$	796637.	−	6.33405e6i	0.143662	−	1.14225i
$178$	1.99461e6	+	1.67368e6i	0.353670	+	0.296764i
$179$	−6.50680e6	+	3.75670e6i	−1.13451	+	0.655010i	−0.945065	−	0.326881i	$-0.894002\pi$
$179$	−6.50680e6	+	3.75670e6i	−1.13451	+	0.655010i	−0.189445	+	0.981891i	$0.560669\pi$
$180$	7.38212e6	−	2.06988e6i	1.26579	−	0.354918i
$181$	2.14311e6	−	3.71197e6i	0.361417	−	0.625993i	−0.626777	−	0.779198i	$-0.715626\pi$
$181$	2.14311e6	−	3.71197e6i	0.361417	−	0.625993i	0.988194	+	0.153206i	$0.0489597\pi$
$182$	4.23693e6	+	1.16409e7i	0.702809	+	1.93095i
$183$	3.37627e6	+	1.73282e6i	0.550914	+	0.282748i
$184$	179736.	−	150817.i	0.0288524	−	0.0242101i
$185$	301974.	−	829667.i	0.0476930	−	0.131035i
$186$	−2.97564e6	−	1.30641e7i	−0.462426	−	2.03021i
$187$	80718.6	−	457778.i	0.0123438	−	0.0700051i
$188$		−	1.98800e6i		−	0.299187i
$189$	5.54453e6	−	9.04592e6i	0.821257	−	1.33988i
$190$	−2.30055e7			−3.35406
$191$	1.32096e7	+	2.32922e6i	1.89579	+	0.334280i	0.994992	−	0.0999520i	$-0.0318689\pi$
$191$	1.32096e7	+	2.32922e6i	1.89579	+	0.334280i	0.900801	+	0.434232i	$0.142980\pi$
$192$	−1.02346e6	+	3.31272e6i	−0.144600	+	0.468037i
$193$	−1.20450e7	−	4.38402e6i	−1.67546	−	0.609818i	−0.682786	−	0.730619i	$-0.739232\pi$
$193$	−1.20450e7	−	4.38402e6i	−1.67546	−	0.609818i	−0.992677	+	0.120800i	$0.961454\pi$
$194$	5.18258e6	+	6.17636e6i	0.709808	+	0.845917i
$195$	−1.25073e7	+	618604.i	−1.68678	+	0.0834275i
$196$	7.96490e6	−	2.89899e6i	1.05782	−	0.385015i
$197$	−1.11061e7	−	6.41209e6i	−1.45265	−	0.838689i	−0.454021	−	0.890991i	$-0.650011\pi$
$197$	−1.11061e7	−	6.41209e6i	−1.45265	−	0.838689i	−0.998631	+	0.0523014i	$0.983344\pi$
$198$	1.39614e6	+	1.94558e6i	0.179859	+	0.250641i
$199$	−7.28378e6	−	1.26159e7i	−0.924267	−	1.60088i	−0.792736	−	0.609566i	$-0.791344\pi$
$199$	−7.28378e6	−	1.26159e7i	−0.924267	−	1.60088i	−0.131531	−	0.991312i	$-0.541989\pi$
$200$	3.11282e6	−	3.70971e6i	0.389103	−	0.463714i
$201$	3.04750e6	−	4.01952e6i	0.375280	−	0.494978i
$202$	−1.07857e6	−	6.11686e6i	−0.130856	−	0.742120i
$203$	3.63124e6	−	640285.i	0.434077	−	0.0765394i
$204$	−1.58660e6	−	1.20292e6i	−0.186886	−	0.141692i
$205$	−154441.	−	129591.i	−0.0179267	−	0.0150423i
$206$	1.00668e7	−	5.81207e6i	1.15157	−	0.664858i
$207$	−978516.	−	442577.i	−0.110321	−	0.0498974i
$208$	5.22100e6	−	9.04303e6i	0.580181	−	1.00490i
$209$	−1.06593e6	−	2.92861e6i	−0.116758	−	0.320791i
$210$	1.63985e6	+	3.31555e7i	0.177071	+	3.58012i
$211$	−4.77661e6	+	4.00805e6i	−0.508478	+	0.426664i	−0.860593	−	0.509293i	$-0.829907\pi$
$211$	−4.77661e6	+	4.00805e6i	−0.508478	+	0.426664i	0.352115	+	0.935957i	$0.385463\pi$
$212$	3.05491e6	−	8.39330e6i	0.320620	−	0.880897i
$213$	1.27246e7	+	3.93125e6i	1.31675	+	0.406810i
$214$	−386080.	+	2.18957e6i	−0.0393946	+	0.223418i
$215$			8.74738e6i			0.880162i
$216$	−3.10046e6	+	463065.i	−0.307656	+	0.0459495i
$217$	2.51619e7			2.46244
$218$	4.59199e6	+	809691.i	0.443232	+	0.0781538i
$219$	−1.39941e6	+	318748.i	−0.133234	+	0.0303470i
$220$	−3.05363e6	−	1.11143e6i	−0.286780	−	0.104379i
$221$	2.09040e6	+	2.49125e6i	0.193666	+	0.230802i
$222$	539356.	−	1.05089e6i	0.0492965	−	0.0960506i
$223$	−6.51504e6	+	2.37128e6i	−0.587493	+	0.213830i	−0.618626	−	0.785685i	$-0.712311\pi$
$223$	−6.51504e6	+	2.37128e6i	−0.587493	+	0.213830i	0.0311334	+	0.999515i	$0.490088\pi$
$224$	−1.92138e7	−	1.10931e7i	−1.70950	−	0.986979i
$225$	−2.14757e7	−	5.48885e6i	−1.88539	−	0.481875i
$226$	2.05144e6	+	3.55319e6i	0.177719	+	0.307817i
$227$	1.25385e6	−	1.49428e6i	0.107193	−	0.127748i	−0.709780	−	0.704423i	$-0.751206\pi$
$227$	1.25385e6	−	1.49428e6i	0.107193	−	0.127748i	0.816974	+	0.576675i	$0.195650\pi$
$228$	−1.32449e7	−	1.66582e6i	−1.11749	−	0.140547i
$229$	−712832.	−	4.04267e6i	−0.0593582	−	0.336637i	0.940638	−	0.339412i	$-0.110228\pi$
$229$	−712832.	−	4.04267e6i	−0.0593582	−	0.336637i	−0.999996	+	0.00277454i	$0.999117\pi$
$230$	3.30909e6	−	583482.i	0.271973	−	0.0479561i
$231$	−4.14471e6	+	1.74496e6i	−0.336247	+	0.141563i
$232$	−834568.	−	700285.i	−0.0668340	−	0.0560804i
$233$	1.34143e7	−	7.74474e6i	1.06047	−	0.612265i	0.134910	−	0.990858i	$-0.456925\pi$
$233$	1.34143e7	−	7.74474e6i	1.06047	−	0.612265i	0.925563	+	0.378593i	$0.123592\pi$
$234$	−1.67055e7	−	1.26694e6i	−1.30381	−	0.0988797i
$235$	−4.35061e6	+	7.53548e6i	−0.335233	+	0.580641i
$236$	3.96405e6	+	1.08911e7i	0.301580	+	0.828585i
$237$	1.67177e7	−	1.07868e7i	1.25583	−	0.810304i
$238$	6.60403e6	−	5.54144e6i	0.489867	−	0.411048i
$239$	−1.39030e6	+	3.81981e6i	−0.101839	+	0.279800i	−0.980140	−	0.198308i	$-0.936455\pi$
$239$	−1.39030e6	+	3.81981e6i	−0.101839	+	0.279800i	0.878301	+	0.478109i	$0.158678\pi$
$240$	2.05203e7	−	1.90230e7i	1.48440	−	1.37609i
$241$	−2.32085e6	+	1.31622e7i	−0.165805	+	0.940325i	0.782426	+	0.622743i	$0.213982\pi$
$241$	−2.32085e6	+	1.31622e7i	−0.165805	+	0.940325i	−0.948231	+	0.317582i	$0.897129\pi$
$242$			1.78185e7i			1.25726i
$243$	8.05649e6	+	1.18737e7i	0.561471	+	0.827496i
$244$	−6.88981e6			−0.474283
$245$	−3.65351e7	−	6.44212e6i	−2.48434	−	0.438057i
$246$	−183371.	−	197805.i	−0.0123176	−	0.0132871i
$247$	2.04890e7	+	7.45738e6i	1.35966	+	0.494875i
$248$	−4.77877e6	−	5.69512e6i	−0.313300	−	0.373377i
$249$	912640.	+	1.41443e6i	0.0591155	+	0.0916186i
$250$	3.16807e7	−	1.15308e7i	2.02756	−	0.737973i
$251$	−1.72709e7	−	9.97137e6i	−1.09218	−	0.630571i	−0.158024	−	0.987435i	$-0.550512\pi$
$251$	−1.72709e7	−	9.97137e6i	−1.09218	−	0.630571i	−0.934156	+	0.356864i	$0.883846\pi$
$252$	−1.45666e6	+	1.92072e7i	−0.0910242	+	1.20023i
$253$	227599.	+	394213.i	0.0140543	+	0.0243427i
$254$	−1.21235e7	+	1.44483e7i	−0.739823	+	0.881687i
$255$	3.38147e6	+	8.03184e6i	0.203932	+	0.484389i
$256$	3.76973e6	+	2.13792e7i	0.224693	+	1.27430i
$257$	6.90629e6	−	1.21777e6i	0.406861	−	0.0717405i	0.0335273	−	0.999438i	$-0.489326\pi$
$257$	6.90629e6	−	1.21777e6i	0.406861	−	0.0717405i	0.373333	+	0.927697i	$0.378215\pi$
$258$	−1.46037e6	+	1.16114e7i	−0.0850360	+	0.676120i
$259$	1.69929e6	+	1.42587e6i	0.0978065	+	0.0820694i
$260$	1.96889e7	−	1.13674e7i	1.12022	−	0.646757i
$261$	−1.23482e6	+	4.83136e6i	−0.0694514	+	0.271736i
$262$	7.66462e6	−	1.32755e7i	0.426174	−	0.738155i
$263$	1.74777e6	+	4.80196e6i	0.0960764	+	0.263968i	0.978416	−	0.206646i	$-0.0662548\pi$
$263$	1.74777e6	+	4.80196e6i	0.0960764	+	0.263968i	−0.882339	+	0.470614i	$0.844033\pi$
$264$	1.18212e6	+	606704.i	0.0642464	+	0.0329735i
$265$	−2.99478e7	+	2.51292e7i	−1.60927	+	1.35033i
$266$	1.97687e7	−	5.43142e7i	1.05035	−	2.88581i
$267$	−1.46863e6	−	6.44776e6i	−0.0771574	−	0.338747i
$268$	−1.59022e6	+	9.01861e6i	−0.0826141	+	0.468528i
$269$			2.72690e6i			0.140092i	0.997544	+	0.0700458i	$0.0223146\pi$
$269$			2.72690e6i			0.140092i	−0.997544	+	0.0700458i	$0.977685\pi$
$270$	−4.17690e7	−	1.64578e7i	−2.12208	−	0.836144i
$271$	−2.39140e7			−1.20156			−0.600778	−	0.799416i	$-0.705142\pi$
$271$	−2.39140e7			−1.20156			−0.600778	+	0.799416i	$0.705142\pi$
$272$	−7.15634e6	−	1.26186e6i	−0.355618	−	0.0627051i
$273$	9.28707e6	−	3.00602e7i	0.456448	−	1.47742i
$274$	−1.28962e6	−	469383.i	−0.0626917	−	0.0228179i
$275$	6.03911e6	+	7.19713e6i	0.290385	+	0.346068i
$276$	1.94738e6	−	96316.7i	0.0926241	−	0.00458115i
$277$	3.51151e7	−	1.27809e7i	1.65217	−	0.601341i	0.663066	−	0.748561i	$-0.269255\pi$
$277$	3.51151e7	−	1.27809e7i	1.65217	−	0.601341i	0.989104	+	0.147220i	$0.0470326\pi$
$278$	−601943.	−	347532.i	−0.0280170	−	0.0161756i
$279$	−1.40235e7	+	3.10052e7i	−0.645718	+	1.42765i
$280$	9.20963e6	+	1.59515e7i	0.419535	+	0.726656i
$281$	−5.31646e6	+	6.33591e6i	−0.239609	+	0.285555i	−0.872426	−	0.488747i	$-0.837454\pi$
$281$	−5.31646e6	+	6.33591e6i	−0.239609	+	0.285555i	0.632817	+	0.774302i	$0.281899\pi$
$282$	−7.03309e6	+	9.27634e6i	−0.313616	+	0.413647i
$283$	−367718.	−	2.08543e6i	−0.0162239	−	0.0920105i	0.975621	−	0.219464i	$-0.0704308\pi$
$283$	−367718.	−	2.08543e6i	−0.0162239	−	0.0920105i	−0.991845	+	0.127453i	$0.959320\pi$
$284$	−2.38116e7	+	4.19863e6i	−1.03952	+	0.183296i
$285$	4.65591e7	+	3.52999e7i	2.01127	+	1.52489i
$286$	5.43972e6	+	4.56447e6i	0.232530	+	0.195116i
$287$	438667.	−	253264.i	0.0185562	−	0.0107134i
$288$	2.43776e7	−	1.74932e7i	1.02050	−	0.732306i
$289$	−1.09372e7	+	1.89438e7i	−0.453119	+	0.784825i
$290$	−5.33623e6	−	1.46612e7i	−0.218797	−	0.601139i
$291$	−1.01155e6	−	2.04521e7i	−0.0410495	−	0.829961i
$292$	1.99609e6	−	1.67492e6i	0.0801738	−	0.0672738i
$293$	−1.15760e7	+	3.18048e7i	−0.460210	+	1.26442i	0.465119	+	0.885248i	$0.346012\pi$
$293$	−1.15760e7	+	3.18048e7i	−0.460210	+	1.26442i	−0.925328	+	0.379167i	$0.876211\pi$
$294$	−4.74215e7	−	1.46508e7i	−1.86609	−	0.576528i
$295$	8.80890e6	−	4.99577e7i	0.343127	−	1.94597i
$296$		−	655417.i		−	0.0252722i
$297$	159782.	−	6.07974e6i	0.00609901	−	0.232068i
$298$	6.59052e7			2.49041
$299$	−3.13625e6	−	553006.i	−0.117327	−	0.0206879i
$300$	3.92377e7	−	8.93728e6i	1.45325	−	0.331010i
$301$	−2.06518e7	−	7.51666e6i	−0.757285	−	0.275629i
$302$	−2.23187e7	−	2.65984e7i	−0.810305	−	0.965683i
$303$	−7.20294e6	+	1.40344e7i	−0.258930	+	0.504505i
$304$	−4.57822e7	+	1.66634e7i	−1.62958	+	0.593119i
$305$	2.61157e7	+	1.50779e7i	0.920455	+	0.531425i
$306$	3.14769e6	+	1.12261e7i	0.109857	+	0.391799i
$307$	−1.30208e7	−	2.25526e7i	−0.450009	−	0.779438i	0.548377	−	0.836231i	$-0.315246\pi$
$307$	−1.30208e7	−	2.25526e7i	−0.450009	−	0.779438i	−0.998386	+	0.0567931i	$0.981912\pi$
$308$	5.24800e6	−	6.25432e6i	0.179615	−	0.214056i
$309$	−2.92915e7	−	3.68401e6i	−0.992810	−	0.124866i
$310$	−1.84882e7	−	1.04852e8i	−0.620596	−	3.51958i
$311$	2.28254e7	−	4.02473e6i	0.758816	−	0.133800i	0.219164	−	0.975688i	$-0.429667\pi$
$311$	2.28254e7	−	4.02473e6i	0.758816	−	0.133800i	0.539652	+	0.841888i	$0.318556\pi$
$312$	−8.56759e6	+	3.60703e6i	−0.282095	+	0.118764i
$313$	2.03375e7	+	1.70652e7i	0.663230	+	0.556516i	0.911053	−	0.412289i	$-0.135271\pi$
$313$	2.03375e7	+	1.70652e7i	0.663230	+	0.556516i	−0.247823	+	0.968805i	$0.579715\pi$
$314$	1.81073e7	−	1.04543e7i	0.584879	−	0.337680i
$315$	4.75553e7	−	6.96169e7i	1.52148	−	2.22732i
$316$	−1.80603e7	+	3.12814e7i	−0.572353	+	0.991344i
$317$	1.87086e7	+	5.14013e7i	0.587303	+	1.61360i	0.775413	+	0.631454i	$0.217542\pi$
$317$	1.87086e7	+	5.14013e7i	0.587303	+	1.61360i	−0.188110	+	0.982148i	$0.560236\pi$
$318$	−4.39483e7	+	2.83570e7i	−1.36666	+	0.881818i
$319$	1.61912e6	−	1.35861e6i	0.0498779	−	0.0418525i
$320$	−9.42311e6	+	2.58898e7i	−0.287570	+	0.790093i
$321$	4.14105e6	−	3.83889e6i	0.125198	−	0.116062i
$322$	−1.46596e6	+	8.31388e6i	−0.0439092	+	0.249021i
$323$		−	1.51737e7i		−	0.450280i
$324$	−2.28558e7	−	1.24997e7i	−0.671988	−	0.367506i
$325$	−6.57302e7			−1.91476
$326$	6.70940e7	+	1.18305e7i	1.93656	+	0.341468i
$327$	−8.05096e6	−	8.68466e6i	−0.230252	−	0.248376i
$328$	−140635.	−	51187.1i	−0.00398541	−	0.00145057i
$329$	−1.40522e7	−	1.67467e7i	−0.394598	−	0.470264i
$330$	1.03168e7	+	1.59892e7i	0.287080	+	0.444923i
$331$	−4.68782e7	+	1.70623e7i	−1.29267	+	0.470492i	−0.894602	−	0.446865i	$-0.852541\pi$
$331$	−4.68782e7	+	1.70623e7i	−1.29267	+	0.470492i	−0.398066	+	0.917357i	$0.630318\pi$
$332$	−2.64662e6	−	1.52803e6i	−0.0723232	−	0.0417558i
$333$	−2.70406e6	+	1.29923e6i	−0.0732291	+	0.0351846i
$334$	2.77167e7	+	4.80068e7i	0.743880	+	1.28844i
$335$	2.57644e7	−	3.07048e7i	0.685308	−	0.816718i
$336$	2.72786e7	+	6.47934e7i	0.719124	+	1.70810i
$337$	−5.31132e6	−	3.01220e7i	−0.138775	−	0.787034i	−0.972156	−	0.234335i	$-0.924709\pi$
$337$	−5.31132e6	−	3.01220e7i	−0.138775	−	0.787034i	0.833381	−	0.552700i	$-0.186402\pi$
$338$	1.60904e6	−	283718.i	0.0416695	−	0.00734745i
$339$	1.30031e6	−	1.03388e7i	0.0333771	−	0.265381i
$340$	−1.21199e7	−	1.01698e7i	−0.308364	−	0.258748i
$341$	1.24910e7	−	7.21169e6i	0.315017	−	0.181875i
$342$	5.59097e7	+	5.46304e7i	1.39768	+	1.36570i
$343$	1.48953e7	−	2.57994e7i	0.369119	−	0.639333i
$344$	2.22090e6	+	6.10188e6i	0.0545574	+	0.149895i
$345$	−7.59231e6	−	3.89664e6i	−0.184891	−	0.0948927i
$346$	−5.97608e7	+	5.01453e7i	−1.44274	+	1.21060i
$347$	−2.17219e7	+	5.96804e7i	−0.519888	+	1.42838i	0.350757	+	0.936467i	$0.385924\pi$
$347$	−2.17219e7	+	5.96804e7i	−0.519888	+	1.42838i	−0.870644	+	0.491913i	$0.836298\pi$
$348$	−2.01060e6	−	8.82723e6i	−0.0477077	−	0.209453i
$349$	9.58260e6	−	5.43456e7i	0.225428	−	1.27846i	−0.636438	−	0.771328i	$-0.719593\pi$
$349$	9.58260e6	−	5.43456e7i	0.225428	−	1.27846i	0.861866	−	0.507136i	$-0.169296\pi$
$350$			1.74244e8i			4.06399i
$351$	3.18650e7	+	2.81972e7i	0.736874	+	0.652056i
$352$	−1.27176e7			−0.291593
$353$	−4.36642e6	−	769918.i	−0.0992663	−	0.0175033i	0.123794	−	0.992308i	$-0.460494\pi$
$353$	−4.36642e6	−	769918.i	−0.0992663	−	0.0175033i	−0.223061	+	0.974805i	$0.571605\pi$
$354$	2.00334e7	−	6.48438e7i	0.451591	−	1.46170i
$355$	9.94461e7	+	3.61954e7i	2.22281	+	0.809037i
$356$	7.71716e6	+	9.19696e6i	0.171044	+	0.203842i
$357$	−2.18682e7	+	1.08159e6i	−0.480628	+	0.0237716i
$358$	−7.50582e7	+	2.73189e7i	−1.63587	+	0.595408i
$359$	−4.97871e7	−	2.87446e7i	−1.07605	−	0.621259i	−0.146223	−	0.989252i	$-0.546712\pi$
$359$	−4.97871e7	−	2.87446e7i	−1.07605	−	0.621259i	−0.929829	+	0.367993i	$0.880045\pi$
$360$	−2.47887e7	+	2.45809e6i	−0.531308	+	0.0526854i
$361$	−2.73437e7	−	4.73606e7i	−0.581212	−	1.00669i
$362$	2.92898e7	−	3.49063e7i	0.617435	−	0.735830i
$363$	2.73409e7	−	3.60615e7i	0.571601	−	0.753917i
$364$	9.91873e6	+	5.62519e7i	0.205661	+	1.16636i
$365$	−1.12316e7	+	1.98044e6i	−0.230974	+	0.0407270i
$366$	3.21490e7	+	2.43746e7i	0.655729	+	0.497157i
$367$	2.32730e7	+	1.95284e7i	0.470820	+	0.395065i	0.847094	−	0.531444i	$-0.178350\pi$
$367$	2.32730e7	+	1.95284e7i	0.470820	+	0.395065i	−0.376274	+	0.926509i	$0.622795\pi$
$368$	6.16264e6	−	3.55800e6i	0.123658	−	0.0713942i
$369$	67597.4	+	681688.i	0.00134540	+	0.0135677i
$370$	4.69314e6	−	8.12875e6i	0.0926527	−	0.160479i
$371$	−3.35937e7	−	9.22980e7i	−0.657864	−	1.80747i
$372$	−3.05189e6	−	6.17047e7i	−0.0592843	−	1.19864i
$373$	2.03681e7	−	1.70909e7i	0.392486	−	0.329335i	−0.425095	−	0.905149i	$-0.639759\pi$
$373$	2.03681e7	−	1.70909e7i	0.392486	−	0.329335i	0.817581	+	0.575814i	$0.195315\pi$
$374$	1.69017e6	−	4.64370e6i	0.0323084	−	0.0887666i
$375$	−8.18090e7	−	2.52748e7i	−1.55134	−	0.479285i
$376$	−1.12163e6	+	6.36109e6i	−0.0211002	+	0.119665i
$377$			1.47872e7i			0.275970i
$378$	7.47478e7	−	8.44709e7i	1.38396	−	1.56398i
$379$	4.06138e7			0.746029			0.373014	−	0.927826i	$-0.378324\pi$
$379$	4.06138e7			0.746029			0.373014	+	0.927826i	$0.378324\pi$
$380$	−1.04465e8	−	1.84200e7i	−1.90379	−	0.335690i
$381$	4.67054e7	−	1.06382e7i	0.844486	−	0.192351i
$382$	1.33999e8	+	4.87715e7i	2.40387	+	0.874936i
$383$	4.66997e7	+	5.56545e7i	0.831224	+	0.990614i	0.999988	+	0.00495714i	$0.00157791\pi$
$383$	4.66997e7	+	5.56545e7i	0.831224	+	0.990614i	−0.168764	+	0.985656i	$0.553978\pi$
$384$	1.56444e7	−	3.04819e7i	0.276290	−	0.538330i
$385$	−3.35797e7	+	1.22220e7i	−0.588429	+	0.214171i
$386$	−1.18012e8	−	6.81343e7i	−2.05194	−	1.18469i
$387$	2.07721e7	−	2.12585e7i	0.358383	−	0.366775i
$388$	1.85881e7	+	3.21955e7i	0.318229	+	0.551189i
$389$	−3.58725e7	+	4.27512e7i	−0.609415	+	0.726273i	−0.979212	−	0.202840i	$-0.934983\pi$
$389$	−3.58725e7	+	4.27512e7i	−0.609415	+	0.726273i	0.369797	+	0.929113i	$0.379427\pi$
$390$	−1.32087e8	−	1.66127e7i	−2.22672	−	0.280056i
$391$	384845.	+	2.18257e6i	0.00643807	+	0.0365121i
$392$	−2.71212e7	+	4.78221e6i	−0.450248	+	0.0793908i
$393$	−3.58819e7	+	1.51066e7i	−0.591150	+	0.248879i
$394$	−1.04438e8	−	8.76340e7i	−1.70754	−	1.43279i
$395$	1.36915e8	−	7.90477e7i	2.22156	−	1.28262i
$396$	4.78188e6	+	9.95244e6i	0.0770040	+	0.160267i
$397$	3.94608e6	−	6.83482e6i	0.0630659	−	0.109233i	−0.832768	−	0.553621i	$-0.813245\pi$
$397$	3.94608e6	−	6.83482e6i	0.0630659	−	0.109233i	0.895834	+	0.444388i	$0.146579\pi$
$398$	−5.29680e7	−	1.45528e8i	−0.840164	−	2.30833i
$399$	−1.23349e8	+	7.95888e7i	−1.94185	+	1.25295i
$400$	1.12511e8	−	9.44080e7i	1.75798	−	1.47512i
$401$	−5.41723e6	+	1.48837e7i	−0.0840126	+	0.230823i	−0.974585	−	0.224019i	$-0.928082\pi$
$401$	−5.41723e6	+	1.48837e7i	−0.0840126	+	0.230823i	0.890572	+	0.454842i	$0.150304\pi$
$402$	3.93261e7	−	3.64565e7i	0.605344	−	0.561174i
$403$	−1.75225e7	+	9.93752e7i	−0.267721	+	1.51832i
$404$		−	2.86394e7i		−	0.434330i
$405$	5.92799e7	+	9.73984e7i	0.892364	+	1.46618i
$406$	3.91993e7			0.585734
$407$	1.25224e6	+	220804.i	0.0185740	+	0.00327509i
$408$	4.39803e6	+	4.74420e6i	0.0647557	+	0.0698526i
$409$	−5.61932e7	−	2.04526e7i	−0.821322	−	0.298937i	−0.103030	−	0.994678i	$-0.532854\pi$
$409$	−5.61932e7	−	2.04526e7i	−0.821322	−	0.298937i	−0.718292	+	0.695741i	$0.755076\pi$
$410$	−1.37769e6	−	1.64187e6i	−0.0199894	−	0.0238225i
$411$	1.88973e6	+	2.92875e6i	0.0272192	+	0.0421849i
$412$	5.03655e7	−	1.83315e7i	0.720181	−	0.262124i
$413$	1.10377e8	+	6.37260e7i	1.56685	+	0.904620i
$414$	−9.42756e6	−	6.43996e6i	−0.132861	−	0.0907575i
$415$	6.68799e6	+	1.15839e7i	0.0935732	+	0.162073i
$416$	5.71916e7	−	6.81583e7i	0.794423	−	0.946757i
$417$	684968.	+	1.62697e6i	0.00944631	+	0.0224373i
$418$	−5.75335e6	−	3.26288e7i	−0.0787756	−	0.446759i
$419$	−6.56106e7	+	1.15689e7i	−0.891932	+	0.157272i	−0.600789	−	0.799408i	$-0.705147\pi$
$419$	−6.56106e7	+	1.15689e7i	−0.891932	+	0.157272i	−0.291143	+	0.956679i	$0.594036\pi$
$420$	−1.91004e7	+	1.51867e8i	−0.257807	+	2.04982i
$421$	−3.72193e7	−	3.12307e7i	−0.498794	−	0.418538i	0.358371	−	0.933579i	$-0.383332\pi$
$421$	−3.72193e7	−	3.12307e7i	−0.498794	−	0.418538i	−0.857165	+	0.515041i	$0.827777\pi$
$422$	−5.74079e7	+	3.31444e7i	−0.763896	+	0.441035i
$423$	2.84674e7	−	7.98201e6i	0.376120	−	0.105461i
$424$	−1.45104e7	+	2.51328e7i	−0.190363	+	0.329719i
$425$	1.56449e7	+	4.29840e7i	0.203801	+	0.559938i
$426$	1.25963e8	+	6.46486e7i	1.62935	+	0.836239i
$427$	−5.80391e7	+	4.87005e7i	−0.745481	+	0.625533i
$428$	−3.50627e6	+	9.63340e6i	−0.0447213	+	0.122871i
$429$	−4.00525e6	−	1.75844e7i	−0.0507292	−	0.222718i
$430$	−1.61482e7	+	9.15808e7i	−0.203104	+	1.15186i
$431$			1.03222e7i			0.128926i	0.997920	+	0.0644632i	$0.0205335\pi$
$431$			1.03222e7i			0.128926i	−0.997920	+	0.0644632i	$0.979466\pi$
$432$	−9.50433e7	−	2.49784e6i	−1.17888	−	0.0309823i
$433$	−3.63900e7			−0.448248			−0.224124	−	0.974561i	$-0.571952\pi$
$433$	−3.63900e7			−0.448248			−0.224124	+	0.974561i	$0.571952\pi$
$434$	2.63433e8	+	4.64504e7i	3.22256	+	0.568225i
$435$	−1.16967e7	+	3.78596e7i	−0.142100	+	0.459947i
$436$	2.02033e7	+	7.35338e6i	0.243760	+	0.0887213i
$437$	9.55114e6	+	1.13826e7i	0.114449	+	0.136395i
$438$	−1.52396e7	+	753744.i	−0.181364	+	0.00897019i
$439$	6.94860e7	−	2.52908e7i	0.821304	−	0.298930i	0.103019	−	0.994679i	$-0.467150\pi$
$439$	6.94860e7	−	2.52908e7i	0.821304	−	0.298930i	0.718285	+	0.695749i	$0.244928\pi$
$440$	9.14378e6	+	5.27916e6i	0.107342	+	0.0619736i
$441$	7.34923e7	+	1.02415e8i	0.856892	+	1.19412i
$442$	1.72865e7	+	2.99412e7i	0.200189	+	0.346738i
$443$	1.57705e7	−	1.87946e7i	0.181399	−	0.216183i	−0.667681	−	0.744448i	$-0.732713\pi$
$443$	1.57705e7	−	1.87946e7i	0.181399	−	0.216183i	0.849080	+	0.528265i	$0.177157\pi$
$444$	3.29056e6	−	4.34011e6i	0.0375942	−	0.0495852i
$445$	−9.12483e6	−	5.17495e7i	−0.103549	−	0.587254i
$446$	−7.25869e7	+	1.27990e7i	−0.818189	+	0.144269i
$447$	−1.33380e8	−	1.01126e8i	−1.49338	−	1.13224i
$448$	−5.30263e7	−	4.44944e7i	−0.589736	−	0.494847i
$449$	−1.07334e8	+	6.19695e7i	−1.18577	+	0.684603i	−0.957342	−	0.288958i	$-0.906691\pi$
$449$	−1.07334e8	+	6.19695e7i	−1.18577	+	0.684603i	−0.228426	+	0.973561i	$0.573358\pi$
$450$	−2.14708e8	−	9.71111e7i	−2.35619	−	1.06569i
$451$	145177.	−	251453.i	0.00158259	−	0.00274112i
$452$	6.47033e6	+	1.77771e7i	0.0700666	+	0.192506i
$453$	4.35622e6	+	8.80764e7i	0.0468614	+	0.947469i
$454$	1.58857e7	−	1.33297e7i	0.169762	−	0.142447i
$455$	8.55071e7	−	2.34929e8i	0.907753	−	2.49403i
$456$	4.14404e7	+	1.28030e7i	0.437049	+	0.135026i
$457$	2.59796e7	−	1.47338e8i	0.272198	−	1.54371i	−0.475527	−	0.879701i	$-0.657742\pi$
$457$	2.59796e7	−	1.47338e8i	0.272198	−	1.54371i	0.747724	−	0.664009i	$-0.231146\pi$
$458$		−	4.36407e7i		−	0.454251i
$459$	1.08550e7	−	2.75494e7i	0.112252	−	0.284888i
$460$	1.54933e7			0.159173
$461$	−8.70162e7	−	1.53433e7i	−0.888172	−	0.156609i	−0.289096	−	0.957300i	$-0.593355\pi$
$461$	−8.70162e7	−	1.53433e7i	−0.888172	−	0.156609i	−0.599077	+	0.800691i	$0.704466\pi$
$462$	−4.66144e7	+	1.06175e7i	−0.472710	+	0.107670i
$463$	6.51717e6	+	2.37205e6i	0.0656623	+	0.0238991i	0.374642	−	0.927169i	$-0.377765\pi$
$463$	6.51717e6	+	2.37205e6i	0.0656623	+	0.0238991i	−0.308980	+	0.951068i	$0.599988\pi$
$464$	−2.12388e7	−	2.53114e7i	−0.212606	−	0.253374i
$465$	−1.23469e8	+	2.40570e8i	−1.22800	+	2.39266i
$466$	1.54738e8	−	5.63201e7i	1.52911	−	0.556552i
$467$	−8.10669e7	−	4.68040e7i	−0.795963	−	0.459550i	0.0460945	−	0.998937i	$-0.485322\pi$
$467$	−8.10669e7	−	4.68040e7i	−0.795963	−	0.459550i	−0.842058	+	0.539388i	$0.818656\pi$
$468$	−7.48431e7	−	1.91287e7i	−0.730154	−	0.186616i
$469$	5.03521e7	+	8.72124e7i	0.488089	+	0.845395i
$470$	−5.94597e7	+	7.08614e7i	−0.572703	+	0.682521i
$471$	−5.26872e7	−	6.62649e6i	−0.504245	−	0.0634192i
$472$	−6.53915e6	−	3.70853e7i	−0.0621864	−	0.352676i
$473$	−1.24064e7	+	2.18759e6i	−0.117237	+	0.0206720i
$474$	1.94939e8	−	8.20709e7i	1.83047	−	0.770645i
$475$	2.34934e8	+	1.97133e8i	2.19213	+	1.83941i
$476$	3.44249e7	−	1.98752e7i	0.319192	−	0.184285i
$477$	1.32455e8	+	1.00453e7i	1.22043	+	0.0925564i
$478$	−2.16073e7	+	3.74250e7i	−0.197842	+	0.342672i
$479$	4.10254e7	+	1.12716e8i	0.373290	+	1.02561i	0.974081	+	0.226199i	$0.0726301\pi$
$479$	4.10254e7	+	1.12716e8i	0.373290	+	1.02561i	−0.600791	+	0.799406i	$0.705148\pi$
$480$	2.00341e8	−	1.29267e8i	1.81153	−	1.16886i
$481$	−6.81475e6	+	5.71825e6i	−0.0612371	+	0.0513840i
$482$	−4.85964e7	+	1.33518e8i	−0.433974	+	1.19233i
$483$	1.57237e7	−	1.45764e7i	0.139545	−	0.129363i
$484$	−1.42669e7	+	8.09113e7i	−0.125832	+	0.713630i
$485$		−	1.62716e8i		−	1.42628i
$486$	6.24281e7	+	1.39184e8i	0.543840	+	1.21250i
$487$	−2.80599e6			−0.0242940			−0.0121470	−	0.999926i	$-0.503867\pi$
$487$	−2.80599e6			−0.0242940			−0.0121470	+	0.999926i	$0.503867\pi$
$488$	2.20456e7	+	3.88724e6i	0.189698	+	0.0334489i
$489$	−1.17633e8	−	1.26892e8i	−1.00601	−	1.08520i
$490$	−3.70612e8	−	1.34892e8i	−3.15015	−	1.14656i
$491$	−6.42997e7	−	7.66294e7i	−0.543206	−	0.647368i	0.422697	−	0.906271i	$-0.361083\pi$
$491$	−6.42997e7	−	7.66294e7i	−0.543206	−	0.647368i	−0.965903	+	0.258903i	$0.916639\pi$
$492$	−674286.	−	1.04502e6i	−0.00566173	−	0.00877468i
$493$	9.67002e6	−	3.51960e6i	0.0807024	−	0.0293733i
$494$	2.00743e8	+	1.15899e8i	1.66517	+	0.961389i
$495$	3.65465e6	−	4.81894e7i	0.0301322	−	0.397316i
$496$	−1.12739e8	−	1.95269e8i	−0.923907	−	1.60025i
$497$	−1.70909e8	+	2.03681e8i	−1.39218	+	1.65914i
$498$	6.94378e6	+	1.64932e7i	0.0562222	+	0.133542i
$499$	2.74266e7	+	1.55544e8i	0.220735	+	1.25185i	0.870673	+	0.491862i	$0.163684\pi$
$499$	2.74266e7	+	1.55544e8i	0.220735	+	1.25185i	−0.649938	+	0.759987i	$0.725205\pi$
$500$	1.53090e8	−	2.69939e7i	1.22472	−	0.215951i
$501$	1.75684e7	−	1.39686e8i	0.139707	−	1.11081i
$502$	−1.62410e8	−	1.36279e8i	−1.28382	−	1.07725i
$503$	1.94459e8	−	1.12271e8i	1.52800	−	0.882193i	0.528557	−	0.848898i	$-0.322733\pi$
$503$	1.94459e8	−	1.12271e8i	1.52800	−	0.882193i	0.999446	−	0.0332951i	$-0.0106001\pi$
$504$	1.54977e7	−	6.06364e7i	0.121053	−	0.473633i
$505$	−6.26755e7	+	1.08557e8i	−0.486658	+	0.842916i
$506$	1.65511e6	+	4.54738e6i	0.0127754	+	0.0351002i
$507$	−3.69176e6	−	1.89474e6i	−0.0283276	−	0.0145387i
$508$	−6.66196e7	+	5.59005e7i	−0.508172	+	0.426407i
$509$	8.52130e6	−	2.34121e7i	0.0646178	−	0.177536i	−0.903182	−	0.429259i	$-0.858775\pi$
$509$	8.52130e6	−	2.34121e7i	0.0646178	−	0.177536i	0.967799	+	0.251723i	$0.0809971\pi$
$510$	2.05752e7	+	9.03318e7i	0.155107	+	0.680974i
$511$	4.97573e6	−	2.82187e7i	0.0372901	−	0.211483i
$512$			1.49575e8i			1.11442i
$513$	−2.93257e7	−	1.96351e8i	−0.217218	−	1.45439i
$514$	7.45536e7			0.549009
$515$	−2.31027e8	−	4.07363e7i	−1.69138	−	0.298236i
$516$	−1.59283e7	+	5.15562e7i	−0.115936	+	0.375260i
$517$	−1.17756e7	−	4.28598e6i	−0.0852143	−	0.0310155i
$518$	1.51585e7	+	1.80652e7i	0.109060	+	0.129973i
$519$	1.97888e8	−	9.78748e6i	1.41553	−	0.0700114i
$520$	−6.94129e7	+	2.52642e7i	−0.493663	+	0.179679i
$521$	−2.50971e6	−	1.44898e6i	−0.0177464	−	0.0102459i	0.491101	−	0.871103i	$-0.336595\pi$
$521$	−2.50971e6	−	1.44898e6i	−0.0177464	−	0.0102459i	−0.508847	+	0.860857i	$0.669928\pi$
$522$	−2.18469e7	+	4.83024e7i	−0.153595	+	0.339592i
$523$	−890685.	−	1.54271e6i	−0.00622615	−	0.0107840i	0.862896	−	0.505382i	$-0.168649\pi$
$523$	−890685.	−	1.54271e6i	−0.00622615	−	0.0107840i	−0.869122	+	0.494598i	$0.835315\pi$
$524$	4.54333e7	−	5.41453e7i	0.315777	−	0.376329i
$525$	2.67361e8	−	3.52638e8i	1.84765	−	2.43698i
$526$	9.43361e6	+	5.35006e7i	0.0648217	+	0.367622i
$527$	6.91567e7	−	1.21942e7i	0.472500	−	0.0833146i
$528$	3.21123e7	+	2.43467e7i	0.218157	+	0.165401i
$529$	1.11740e8	+	9.37606e7i	0.754814	+	0.633364i
$530$	−3.59929e8	+	2.07805e8i	−2.41763	+	1.39582i
$531$	−1.40041e8	+	1.00493e8i	−0.935344	+	0.671198i
$532$	1.33255e8	−	2.30805e8i	0.885012	−	1.53288i
$533$	694766.	+	1.90885e6i	0.00458835	+	0.0126064i
$534$	−3.47286e6	−	7.02161e7i	−0.0228068	−	0.461119i
$535$	3.43726e7	−	2.88420e7i	0.224466	−	0.188349i
$536$	1.01766e7	−	2.79600e7i	0.0660860	−	0.181570i
$537$	1.93823e8	+	5.98813e7i	1.25165	+	0.386695i
$538$	−5.03401e6	+	2.85493e7i	−0.0323272	+	0.183336i
$539$		−	5.34289e7i		−	0.341201i
$540$	−1.76490e8	−	1.08176e8i	−1.12083	−	0.686989i
$541$	−2.34732e8			−1.48245			−0.741226	−	0.671256i	$-0.765755\pi$
$541$	−2.34732e8			−1.48245			−0.741226	+	0.671256i	$0.765755\pi$
$542$	−2.50368e8	−	4.41466e7i	−1.57246	−	0.277268i
$543$	−1.12838e8	+	2.57014e7i	−0.704783	+	0.160531i
$544$	−5.81844e7	−	2.11774e7i	−0.361418	−	0.131545i
$545$	−6.04877e7	−	7.20865e7i	−0.373661	−	0.445312i
$546$	1.52724e8	−	2.97571e8i	0.938273	−	1.82816i
$547$	1.15068e8	−	4.18814e7i	0.703061	−	0.255893i	0.0343439	−	0.999410i	$-0.489066\pi$
$547$	1.15068e8	−	4.18814e7i	0.703061	−	0.255893i	0.668717	+	0.743517i	$0.266844\pi$
$548$	−5.48016e6	−	3.16397e6i	−0.0333005	−	0.0192261i
$549$	−2.76633e7	−	9.86595e7i	−0.167181	−	0.596241i
$550$	4.99402e7	+	8.64989e7i	0.300166	+	0.519904i
$551$	4.43487e7	−	5.28527e7i	0.265110	−	0.315946i
$552$	−6.28547e6	−	790527.i	−0.0373698	−	0.00470002i
$553$	6.89739e7	+	3.91170e8i	0.407858	+	2.31308i
$554$	3.91232e8	−	6.89848e7i	2.30094	−	0.405718i
$555$	−2.19709e7	+	9.24994e6i	−0.128519	+	0.0541078i
$556$	−2.45508e6	−	2.06005e6i	−0.0142837	−	0.0119854i
$557$	3.23361e7	−	1.86693e7i	0.187121	−	0.108034i	−0.403513	−	0.914974i	$-0.632211\pi$
$557$	3.23361e7	−	1.86693e7i	0.187121	−	0.108034i	0.590634	+	0.806939i	$0.298878\pi$
$558$	−2.04056e8	+	2.98721e8i	−1.17449	+	1.71935i
$559$	4.40682e7	−	7.63284e7i	0.252284	−	0.436969i
$560$	1.91064e8	+	5.24943e8i	1.08796	+	2.98915i
$561$	−1.05459e7	+	6.80460e6i	−0.0597305	+	0.0385402i
$562$	−6.73572e7	+	5.65194e7i	−0.379468	+	0.318411i
$563$	−8.70786e7	+	2.39246e8i	−0.487962	+	1.34067i	0.414560	+	0.910022i	$0.363935\pi$
$563$	−8.70786e7	+	2.39246e8i	−0.487962	+	1.34067i	−0.902522	+	0.430643i	$0.858287\pi$
$564$	−3.93636e7	+	3.64913e7i	−0.219410	+	0.203401i
$565$	1.43783e7	−	8.15437e7i	0.0797193	−	0.452111i
$566$		−	2.25123e7i		−	0.124157i
$567$	−2.80889e8	+	5.62601e7i	−1.54094	+	0.308639i
$568$	7.85600e7			0.428703
$569$	1.95182e8	+	3.44159e7i	1.05951	+	0.186819i	0.676137	−	0.736776i	$-0.263653\pi$
$569$	1.95182e8	+	3.44159e7i	1.05951	+	0.186819i	0.383368	+	0.923596i	$0.374764\pi$
$570$	4.22285e8	+	4.55524e8i	2.28024	+	2.45972i
$571$	−1.30229e8	−	4.73997e7i	−0.699521	−	0.254605i	−0.0323148	−	0.999478i	$-0.510288\pi$
$571$	−1.30229e8	−	4.73997e7i	−0.699521	−	0.254605i	−0.667207	+	0.744873i	$0.732510\pi$
$572$	2.10463e7	+	2.50820e7i	0.112457	+	0.134022i
$573$	−1.96354e8	−	3.04314e8i	−1.04370	−	1.61755i
$574$	5.06017e6	−	1.84175e6i	0.0267565	−	0.00973857i
$575$	−3.87925e7	−	2.23969e7i	−0.204054	−	0.117811i
$576$	8.43802e7	−	4.05424e7i	0.441543	−	0.212150i
$577$	−9.40011e7	−	1.62815e8i	−0.489334	−	0.847551i	0.510591	−	0.859824i	$-0.329427\pi$
$577$	−9.40011e7	−	1.62815e8i	−0.489334	−	0.847551i	−0.999925	+	0.0122725i	$0.996093\pi$
$578$	−1.49478e8	+	1.78141e8i	−0.774096	+	0.922532i
$579$	1.34289e8	+	3.18971e8i	0.691840	+	1.64329i
$580$	−1.24922e7	−	7.08469e7i	−0.0640259	−	0.363109i
$581$	−3.30957e7	+	5.83567e6i	−0.168750	+	0.0297552i
$582$	2.71652e7	−	2.15990e8i	0.137799	−	1.09563i
$583$	−4.31304e7	−	3.61907e7i	−0.217660	−	0.182638i
$584$	−7.33198e6	+	4.23312e6i	−0.0368114	+	0.0212531i
$585$	2.41830e8	+	2.36297e8i	1.20793	+	1.18029i
$586$	−1.79909e8	+	3.11611e8i	−0.894044	+	1.54853i
$587$	−4.80646e7	−	1.32056e8i	−0.237635	−	0.652897i	−0.999984	−	0.00573038i	$-0.998176\pi$
$587$	−4.80646e7	−	1.32056e8i	−0.237635	−	0.652897i	0.762348	−	0.647167i	$-0.224046\pi$
$588$	−2.03604e8	−	1.04497e8i	−1.00151	−	0.514008i
$589$	3.60669e8	−	3.02637e8i	1.76507	−	1.48107i
$590$	1.84450e8	−	5.06772e8i	0.898095	−	2.46749i
$591$	7.68976e7	+	3.37606e8i	0.372520	+	1.63549i
$592$	3.45178e6	−	1.95760e7i	0.0166371	−	0.0943536i
$593$		−	6.98326e7i		−	0.334884i	−0.985882	−	0.167442i	$-0.946449\pi$
$593$		−	6.98326e7i		−	0.334884i	0.985882	−	0.167442i	$-0.0535507\pi$
$594$	1.28964e7	−	6.33570e7i	0.0615332	−	0.302298i
$595$	−1.73983e8			−0.825953
$596$	2.99266e8	+	5.27687e7i	1.41358	+	0.249252i
$597$	−1.16102e8	+	3.75798e8i	−0.545655	+	1.76617i
$598$	−3.18142e7	−	1.15794e7i	−0.148771	−	0.0541481i
$599$	1.01146e8	+	1.20541e8i	0.470617	+	0.560859i	0.948178	−	0.317739i	$-0.102924\pi$
$599$	1.01146e8	+	1.20541e8i	0.470617	+	0.560859i	−0.477561	+	0.878598i	$0.658479\pi$
$600$	−1.30593e8	+	6.45907e6i	−0.604597	+	0.0299031i
$601$	−2.48645e8	+	9.04994e7i	−1.14540	+	0.416891i	−0.843860	−	0.536563i	$-0.819722\pi$
$601$	−2.48645e8	+	9.04994e7i	−1.14540	+	0.416891i	−0.301538	+	0.953454i	$0.597500\pi$
$602$	−2.02339e8	−	1.16820e8i	−0.927448	−	0.535462i
$603$	−1.35528e8	+	1.34392e7i	−0.618127	+	0.0612945i
$604$	−8.00494e7	−	1.38650e8i	−0.363285	−	0.629228i
$605$	2.31148e8	−	2.75471e8i	1.04382	−	1.24397i
$606$	−1.01320e8	+	1.33636e8i	−0.455277	+	0.600491i
$607$	−5.07484e7	−	2.87808e8i	−0.226911	−	1.28688i	−0.858998	−	0.511979i	$-0.828912\pi$
$607$	−5.07484e7	−	2.87808e8i	−0.226911	−	1.28688i	0.632087	−	0.774898i	$-0.282199\pi$
$608$	−4.08831e8	+	7.20879e7i	−1.81900	+	0.320739i
$609$	−7.93323e7	−	6.01478e7i	−0.351235	−	0.266298i
$610$	2.45584e8	+	2.06070e8i	1.08196	+	0.907871i
$611$	7.59257e7	−	4.38357e7i	0.332863	−	0.192178i
$612$	5.30478e6	+	5.34963e7i	0.0231427	+	0.233383i
$613$	2.16665e8	−	3.75275e8i	0.940606	−	1.62918i	0.176288	−	0.984339i	$-0.443591\pi$
$613$	2.16665e8	−	3.75275e8i	0.940606	−	1.62918i	0.764318	−	0.644839i	$-0.223076\pi$
$614$	−9.46875e7	−	2.60152e8i	−0.409061	−	1.12389i
$615$	268901.	+	5.43679e6i	0.00115603	+	0.0233731i
$616$	−2.03210e7	+	1.70513e7i	−0.0869365	+	0.0729484i
$617$	−1.34111e8	+	3.68467e8i	−0.570964	+	1.56871i	0.232020	+	0.972711i	$0.425467\pi$
$617$	−1.34111e8	+	3.68467e8i	−0.570964	+	1.56871i	−0.802984	+	0.596000i	$0.796756\pi$
$618$	−2.99867e8	−	9.26435e7i	−1.27047	−	0.392509i
$619$	1.50868e7	−	8.55617e7i	0.0636101	−	0.360751i	−0.936343	−	0.351086i	$-0.885812\pi$
$619$	1.50868e7	−	8.55617e7i	0.0636101	−	0.360751i	0.999953	−	0.00966484i	$-0.00307646\pi$
$620$		−	4.90920e8i		−	2.05985i
$621$	9.19815e6	+	2.74991e7i	0.0384084	+	0.114827i
$622$	2.46400e8			1.02393
$623$	1.30017e8	+	2.29255e7i	0.537696	+	0.0948103i
$624$	−2.74893e8	+	6.26132e7i	−1.13138	+	0.257699i
$625$	−1.92916e8	−	7.02156e7i	−0.790183	−	0.287603i
$626$	1.81420e8	+	2.16208e8i	0.739542	+	0.881352i
$627$	−3.84223e7	+	7.48629e7i	−0.155876	+	0.303714i
$628$	9.05934e7	−	3.29733e7i	0.365778	−	0.133132i
$629$	5.36145e6	+	3.09544e6i	0.0215442	+	0.0124386i
$630$	6.26398e8	−	6.41065e8i	2.50512	−	2.56378i
$631$	1.06182e8	+	1.83913e8i	0.422634	+	0.732024i	0.996196	−	0.0871380i	$-0.0277721\pi$
$631$	1.06182e8	+	1.83913e8i	0.422634	+	0.732024i	−0.573562	+	0.819162i	$0.694439\pi$
$632$	7.54373e7	−	8.99027e7i	0.298838	−	0.356141i
$633$	1.67040e8	+	2.10088e7i	0.658583	+	0.0828303i
$634$	1.00980e8	+	5.72684e8i	0.396247	+	2.24723i
$635$	3.74856e8	−	6.60971e7i	1.46401	−	0.258144i
$636$	−2.22268e8	+	9.35767e7i	−0.863983	+	0.363745i
$637$	2.86345e8	+	2.40272e8i	1.10783	+	0.929577i
$638$	1.94595e7	−	1.12350e7i	0.0749324	−	0.0432623i
$639$	−1.55729e8	−	3.24116e8i	−0.596852	−	1.24222i
$640$	1.36128e8	−	2.35780e8i	0.519286	−	0.899430i
$641$	−8.03061e7	−	2.20639e8i	−0.304912	−	0.837738i	−0.993628	−	0.112708i	$-0.964048\pi$
$641$	−8.03061e7	−	2.20639e8i	−0.304912	−	0.837738i	0.688716	−	0.725031i	$-0.258175\pi$
$642$	5.04416e7	−	3.25467e7i	0.190627	−	0.122999i
$643$	−2.42941e8	+	2.03852e8i	−0.913836	+	0.766800i	−0.972845	−	0.231458i	$-0.925650\pi$
$643$	−2.42941e8	+	2.03852e8i	−0.913836	+	0.766800i	0.0590087	+	0.998257i	$0.481206\pi$
$644$	−1.33134e7	+	3.65784e7i	−0.0498463	+	0.136952i
$645$	1.73203e8	−	1.60565e8i	0.645472	−	0.598374i
$646$	2.80115e7	−	1.58861e8i	0.103905	−	0.589277i
$647$		−	2.64449e8i		−	0.976402i	−0.872731	−	0.488201i	$-0.837653\pi$
$647$		−	2.64449e8i		−	0.976402i	0.872731	−	0.488201i	$-0.162347\pi$
$648$	6.60804e7	+	5.28911e7i	0.242855	+	0.194383i
$649$	7.30583e7			0.267261
$650$	−6.88163e8	−	1.21342e8i	−2.50583	−	0.441845i
$651$	−4.61868e8	−	4.98222e8i	−1.67407	−	1.80584i
$652$	2.95192e8	+	1.07441e8i	1.06503	+	0.387639i
$653$	−9.98814e7	−	1.19034e8i	−0.358711	−	0.427496i	0.556264	−	0.831006i	$-0.312234\pi$
$653$	−9.98814e7	−	1.19034e8i	−0.358711	−	0.427496i	−0.914975	+	0.403510i	$0.867790\pi$
$654$	−6.82573e7	−	1.05787e8i	−0.244014	−	0.378179i
$655$	−2.90708e8	+	1.05809e8i	−1.03451	+	0.376530i
$656$	−3.93092e6	−	2.26952e6i	−0.0139246	−	0.00803936i
$657$	3.19988e7	+	2.18583e7i	0.112833	+	0.0770764i
$658$	−1.16204e8	−	2.01271e8i	−0.407890	−	0.706486i
$659$	−8.87361e7	+	1.05752e8i	−0.310059	+	0.369514i	−0.898460	−	0.439055i	$-0.855313\pi$
$659$	−8.87361e7	+	1.05752e8i	−0.310059	+	0.369514i	0.588401	+	0.808569i	$0.299758\pi$
$660$	3.40449e7	+	8.08651e7i	0.118419	+	0.281274i
$661$	2.52061e7	+	1.42951e8i	0.0872772	+	0.494973i	0.996842	+	0.0794113i	$0.0253040\pi$
$661$	2.52061e7	+	1.42951e8i	0.0872772	+	0.494973i	−0.909565	+	0.415562i	$0.863585\pi$
$662$	−5.22290e8	+	9.20938e7i	−1.80027	+	0.317436i
$663$	1.09571e7	−	8.71201e7i	0.0375973	−	0.298936i
$664$	7.60640e6	+	6.38253e6i	0.0259821	+	0.0218016i
$665$	−1.01020e9	+	5.83241e8i	−3.43513	+	1.98328i
$666$	−3.07087e7	+	8.61044e6i	−0.103953	+	0.0291476i
$667$	−5.03859e6	+	8.72709e6i	−0.0169797	+	0.0294098i
$668$	8.74199e7	+	2.40184e8i	0.293279	+	0.805777i
$669$	1.66542e8	+	8.54751e7i	0.556218	+	0.285470i
$670$	3.26424e8	−	2.73902e8i	1.08532	−	0.910690i
$671$	−1.48539e7	+	4.08108e7i	−0.0491670	+	0.135085i
$672$	1.33035e8	+	5.84067e8i	0.438386	+	1.92466i
$673$	1.48572e7	−	8.42595e7i	0.0487408	−	0.276423i	−0.950691	−	0.310141i	$-0.899624\pi$
$673$	1.48572e7	−	8.42595e7i	0.0487408	−	0.276423i	0.999431	+	0.0337182i	$0.0107349\pi$
$674$		−	3.25167e8i		−	1.06201i
$675$	2.85522e8	+	5.25985e8i	0.928385	+	1.71026i
$676$	7.53361e6			0.0243873
$677$	4.84567e8	+	8.54423e7i	1.56167	+	0.275364i	0.886650	−	0.462440i	$-0.153026\pi$
$677$	4.84567e8	+	8.54423e7i	1.56167	+	0.275364i	0.675015	+	0.737804i	$0.264137\pi$
$678$	3.26996e7	−	1.05841e8i	0.104919	−	0.339599i
$679$	3.84158e8	+	1.39822e8i	1.22716	+	0.446650i
$680$	3.30429e7	+	3.93790e7i	0.105088	+	0.125238i
$681$	−5.26031e7	+	2.60173e6i	−0.166560	+	0.00823797i
$682$	1.44088e8	−	5.24438e7i	0.454229	−	0.165326i
$683$	2.98588e8	+	1.72390e8i	0.937152	+	0.541065i	0.889066	−	0.457778i	$-0.151355\pi$
$683$	2.98588e8	+	1.72390e8i	0.937152	+	0.541065i	0.0480854	+	0.998843i	$0.484688\pi$
$684$	2.10137e8	+	2.92835e8i	0.656649	+	0.915069i
$685$	1.38483e7	+	2.39860e7i	0.0430849	+	0.0746252i
$686$	2.03574e8	−	2.42610e8i	0.630593	−	0.751512i
$687$	−6.69628e7	+	8.83210e7i	−0.206520	+	0.272392i
$688$	3.41981e7	+	1.93947e8i	0.105012	+	0.595550i
$689$	3.87918e8	−	6.84005e7i	1.18599	−	0.209123i
$690$	−7.22944e7	−	5.48118e7i	−0.220068	−	0.166850i
$691$	1.03614e8	+	8.69422e7i	0.314039	+	0.263510i	0.786159	−	0.618025i	$-0.212067\pi$
$691$	1.03614e8	+	8.69422e7i	0.314039	+	0.263510i	−0.472120	+	0.881534i	$0.656511\pi$
$692$	−3.11515e8	+	1.79853e8i	−0.940072	+	0.542751i
$693$	1.10631e8	+	5.00377e7i	0.332412	+	0.150348i
$694$	−3.37591e8	+	5.84725e8i	−1.00998	+	1.74934i
$695$	4.79763e6	+	1.31814e7i	0.0142913	+	0.0392651i
$696$	1.45309e6	+	2.93793e7i	0.00430986	+	0.0871391i
$697$	1.08292e6	−	908678.i	0.00319815	−	0.00268356i
$698$	2.00650e8	−	5.51282e8i	0.590030	−	1.62109i
$699$	−3.99581e8	−	1.23450e8i	−1.16997	−	0.361460i
$700$	−1.39513e8	+	7.91216e8i	−0.406743	+	2.30675i
$701$			2.23610e8i			0.649139i	0.945862	+	0.324569i	$0.105219\pi$
$701$			2.23610e8i			0.649139i	−0.945862	+	0.324569i	$0.894781\pi$
$702$	2.81558e8	+	3.54036e8i	0.813872	+	1.02338i
$703$	4.15072e7			0.119470
$704$	−3.90762e7	−	6.89018e6i	−0.111994	−	0.0197475i
$705$	2.29066e8	−	5.21751e7i	0.653723	−	0.148900i
$706$	−4.42930e7	−	1.61213e7i	−0.125870	−	0.0458128i
$707$	−2.02437e8	−	2.41255e8i	−0.572838	−	0.682682i
$708$	1.42888e8	−	2.78406e8i	0.402620	−	0.784475i
$709$	−4.72520e8	+	1.71983e8i	−1.32581	+	0.482556i	−0.905316	−	0.424738i	$-0.860366\pi$
$709$	−4.72520e8	+	1.71983e8i	−1.32581	+	0.482556i	−0.420496	+	0.907294i	$0.638144\pi$
$710$	9.74334e8	+	5.62532e8i	2.72228	+	1.57171i
$711$	−5.20452e8	−	1.33019e8i	−1.44801	−	0.370088i
$712$	−1.95040e7	−	3.37819e7i	−0.0540361	−	0.0935933i
$713$	−4.42025e7	+	5.26785e7i	−0.121949	+	0.145333i
$714$	−2.30946e8	−	2.90463e7i	−0.634478	−	0.0797986i
$715$	−2.48853e7	−	1.41132e8i	−0.0680809	−	0.386106i
$716$	−3.62702e8	+	6.39542e7i	−0.988123	+	0.174233i
$717$	1.01155e8	−	4.25870e7i	0.274428	−	0.115537i
$718$	−4.68182e8	−	3.92852e8i	−1.26486	−	1.06134i
$719$	−2.62933e7	+	1.51805e7i	−0.0707390	+	0.0408412i	−0.534952	−	0.844882i	$-0.679670\pi$
$719$	−2.62933e7	+	1.51805e7i	−0.0707390	+	0.0408412i	0.464213	+	0.885723i	$0.346337\pi$
$720$	−7.53335e8	−	5.71323e7i	−2.01832	−	0.153068i
$721$	2.94698e8	−	5.10431e8i	0.786268	−	1.36186i
$722$	−1.98844e8	−	5.46320e8i	−0.528326	−	1.45156i
$723$	3.03221e8	−	1.95649e8i	0.802314	−	0.517681i
$724$	1.60950e8	−	1.35053e8i	0.424106	−	0.355867i
$725$	−7.11369e7	+	1.95447e8i	−0.186673	+	0.512879i
$726$	3.52818e8	−	3.27073e8i	0.922020	−	0.854742i
$727$	5.94743e7	−	3.37296e8i	0.154784	−	0.877824i	−0.804199	−	0.594360i	$-0.797405\pi$
$727$	5.94743e7	−	3.37296e8i	0.154784	−	0.877824i	0.958983	−	0.283464i	$-0.0914836\pi$
$728$		−	1.85588e8i		−	0.481012i
$729$	8.72224e7	−	3.77474e8i	0.225136	−	0.974327i
$730$	−1.21246e8			−0.311672
$731$	−6.04036e7	−	1.06508e7i	−0.154636	−	0.0272665i
$732$	1.26468e8	+	1.36422e8i	0.322439	+	0.347818i
$733$	−2.66126e8	−	9.68620e7i	−0.675734	−	0.245947i	−0.0187193	−	0.999825i	$-0.505959\pi$
$733$	−2.66126e8	−	9.68620e7i	−0.675734	−	0.245947i	−0.657015	+	0.753878i	$0.728181\pi$
$734$	2.07607e8	+	2.47416e8i	0.524993	+	0.625662i
$735$	5.43073e8	+	8.41667e8i	1.36772	+	2.11972i
$736$	5.69775e7	−	2.07381e7i	0.142912	−	0.0520159i
$737$	4.99921e7	+	2.88629e7i	0.124882	+	0.0721005i
$738$	−550724.	+	7.26174e6i	−0.00137014	+	0.0180664i
$739$	1.54895e8	+	2.68286e8i	0.383800	+	0.664760i	0.991602	−	0.129328i	$-0.0412820\pi$
$739$	1.54895e8	+	2.68286e8i	0.383800	+	0.664760i	−0.607802	+	0.794088i	$0.707949\pi$
$740$	2.78194e7	−	3.31538e7i	0.0686518	−	0.0818161i
$741$	−2.28431e8	−	5.42581e8i	−0.561437	−	1.33355i
$742$	−1.81323e8	−	1.02833e9i	−0.443854	−	2.51722i
$743$	−2.87999e8	+	5.07820e7i	−0.702141	+	0.123806i	−0.513310	−	0.858203i	$-0.671581\pi$
$743$	−2.87999e8	+	5.07820e7i	−0.702141	+	0.123806i	−0.188831	+	0.982010i	$0.560470\pi$
$744$	−2.50486e7	+	1.99161e8i	−0.0608225	+	0.483599i
$745$	−1.01888e9	−	8.54945e8i	−2.46409	−	2.06761i
$746$	2.44795e8	−	1.41332e8i	0.589639	−	0.340428i
$747$	1.12543e7	−	4.40338e7i	0.0269997	−	0.105639i
$748$	1.13929e7	−	1.97331e7i	0.0272226	−	0.0471510i
$749$	3.85571e7	+	1.05935e8i	0.0917613	+	0.252112i
$750$	−8.09842e8	−	4.15639e8i	−1.91963	−	0.985219i
$751$	−2.67516e8	+	2.24473e8i	−0.631583	+	0.529961i	−0.901420	−	0.432945i	$-0.857474\pi$
$751$	−2.67516e8	+	2.24473e8i	−0.631583	+	0.529961i	0.269837	+	0.962906i	$0.413030\pi$
$752$	−6.70017e7	+	1.84086e8i	−0.157555	+	0.432879i
$753$	1.19583e8	+	5.25008e8i	0.280080	+	1.22965i
$754$	−2.72980e7	+	1.54815e8i	−0.0636820	+	0.361159i
$755$			7.00733e8i			1.62821i
$756$	4.07053e8	−	3.23721e8i	0.942075	−	0.749214i
$757$	3.37653e8			0.778364			0.389182	−	0.921161i	$-0.372758\pi$
$757$	3.37653e8			0.778364			0.389182	+	0.921161i	$0.372758\pi$
$758$	4.25206e8	+	7.49753e7i	0.976320	+	0.172152i
$759$	3.62789e6	−	1.17427e7i	0.00829716	−

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(10.4695 + 1.84606i) q^{2} +(-18.3558 - 19.8006i) q^{3} +(46.0625 + 16.7654i) q^{4} +(-137.909 - 164.354i) q^{5} +(-155.623 - 241.189i) q^{6} +(506.532 - 184.363i) q^{7} +(-137.929 - 79.6334i) q^{8} +(-55.1285 + 726.913i) q^{9} +O(q^{10})\)	\(q+(10.4695 + 1.84606i) q^{2} +(-18.3558 - 19.8006i) q^{3} +(46.0625 + 16.7654i) q^{4} +(-137.909 - 164.354i) q^{5} +(-155.623 - 241.189i) q^{6} +(506.532 - 184.363i) q^{7} +(-137.929 - 79.6334i) q^{8} +(-55.1285 + 726.913i) q^{9} +(-1140.44 - 1975.29i) q^{10} +(198.615 - 236.700i) q^{11} +(-513.550 - 1219.81i) q^{12} +(375.382 + 2128.90i) q^{13} +(5643.49 - 995.099i) q^{14} +(-722.871 + 5747.53i) q^{15} +(-3700.27 - 3104.90i) q^{16} +(1302.84 - 752.193i) q^{17} +(-1919.09 + 7508.65i) q^{18} +(5043.14 - 8734.98i) q^{19} +(-3596.99 - 9882.65i) q^{20} +(-12948.3 - 6645.52i) q^{21} +(2516.36 - 2111.48i) q^{22} +(-503.858 + 1384.34i) q^{23} +(955.010 + 4192.82i) q^{24} +(-5279.97 + 29944.2i) q^{25} +22981.5i q^{26} +(15405.2 - 12251.5i) q^{27} +26423.0 q^{28} +(6736.49 + 1187.82i) q^{29} +(-18178.4 + 58839.4i) q^{30} +(43864.1 + 15965.2i) q^{31} +(-26456.3 - 31529.4i) q^{32} +(-8332.53 + 412.124i) q^{33} +(15028.7 - 5469.99i) q^{34} +(-100156. - 57825.2i) q^{35} +(-14726.3 + 32559.1i) q^{36} +(2057.61 + 3563.88i) q^{37} +(68924.5 - 82141.1i) q^{38} +(35263.0 - 46510.5i) q^{39} +(5933.64 + 33651.4i) q^{40} +(925.411 - 163.175i) q^{41} +(-123294. - 93478.6i) q^{42} +(-31232.5 - 26207.1i) q^{43} +(13117.0 - 7573.13i) q^{44} +(127074. - 91187.4i) q^{45} +(-7830.72 + 13563.2i) q^{46} +(-13871.0 - 38110.1i) q^{47} +(6442.63 + 130261. i) q^{48} +(132461. - 111148. i) q^{49} +(-110557. + 303754. i) q^{50} +(-38808.5 - 11989.9i) q^{51} +(-18400.7 + 104356. i) q^{52} -182216. i q^{53} +(183902. - 99828.2i) q^{54} -66293.3 q^{55} +(-84546.9 - 14907.9i) q^{56} +(-265529. + 60480.3i) q^{57} +(68335.0 + 24871.9i) q^{58} +(151982. + 181125. i) q^{59} +(-129657. + 252627. i) q^{60} +(-132078. + 48072.5i) q^{61} +(429763. + 248124. i) q^{62} +(106091. + 378368. i) q^{63} +(-64207.6 - 111211. i) q^{64} +(298124. - 355290. i) q^{65} +(-87998.4 - 11067.6i) q^{66} +(32441.2 + 183983. i) q^{67} +(72622.7 - 12805.3i) q^{68} +(36659.5 - 15434.0i) q^{69} +(-941837. - 790295. i) q^{70} +(-427176. + 246630. i) q^{71} +(65490.4 - 95872.3i) q^{72} +(26578.8 - 46035.8i) q^{73} +(14963.0 + 41110.5i) q^{74} +(689832. - 445103. i) q^{75} +(378745. - 317805. i) q^{76} +(56966.1 - 156513. i) q^{77} +(455048. - 421844. i) q^{78} +(-127957. + 725680. i) q^{79} +1.03635e6i q^{80} +(-525363. - 80147.2i) q^{81} +9989.83 q^{82} +(-61397.6 - 10826.1i) q^{83} +(-485016. - 523192. i) q^{84} +(-303299. - 110392. i) q^{85} +(-278609. - 332033. i) q^{86} +(-100134. - 155190. i) q^{87} +(-46244.0 + 16831.4i) q^{88} +(212109. + 122461. i) q^{89} +(1.49874e6 - 720102. i) q^{90} +(582632. + 1.00915e6i) q^{91} +(-46417.9 + 55318.7i) q^{92} +(-489040. - 1.16159e6i) q^{93} +(-74868.6 - 424601. i) q^{94} +(-2.13112e6 + 375775. i) q^{95} +(-138674. + 1.10260e6i) q^{96} +(580975. + 487496. i) q^{97} +(1.59198e6 - 919132. i) q^{98} +(161111. + 157424. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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