LMFDB - Embedded newform 315.2.r.b.184.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.15
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07565i q^{2} +(-0.564624 - 1.63744i) q^{3} +0.842975 q^{4} +(0.440420 + 2.19227i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(2.63194 + 0.269937i) q^{7} -3.05805i q^{8} +(-2.36240 + 1.84907i) q^{9} +O(q^{10})$	\(q-1.07565i q^{2} +(-0.564624 - 1.63744i) q^{3} +0.842975 q^{4} +(0.440420 + 2.19227i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(2.63194 + 0.269937i) q^{7} -3.05805i q^{8} +(-2.36240 + 1.84907i) q^{9} +(2.35811 - 0.473738i) q^{10} +(2.62145 - 4.54048i) q^{11} +(-0.475964 - 1.38032i) q^{12} +(1.08449 + 0.626132i) q^{13} +(0.290358 - 2.83105i) q^{14} +(3.34103 - 1.95897i) q^{15} -1.60344 q^{16} +(-1.06213 + 0.613221i) q^{17} +(1.98896 + 2.54112i) q^{18} +(-0.243054 + 0.420982i) q^{19} +(0.371263 + 1.84803i) q^{20} +(-1.04405 - 4.46206i) q^{21} +(-4.88397 - 2.81976i) q^{22} +(-5.30418 + 3.06237i) q^{23} +(-5.00736 + 1.72665i) q^{24} +(-4.61206 + 1.93104i) q^{25} +(0.673499 - 1.16653i) q^{26} +(4.36161 + 2.82425i) q^{27} +(2.21866 + 0.227550i) q^{28} +(-3.41713 - 5.91864i) q^{29} +(-2.10716 - 3.59378i) q^{30} +1.03018 q^{31} -4.39135i q^{32} +(-8.91488 - 1.72879i) q^{33} +(0.659611 + 1.14248i) q^{34} +(0.567388 + 5.88881i) q^{35} +(-1.99144 + 1.55872i) q^{36} +(4.23290 + 2.44387i) q^{37} +(0.452830 + 0.261441i) q^{38} +(0.412921 - 2.12932i) q^{39} +(6.70406 - 1.34683i) q^{40} +(-4.83761 + 8.37899i) q^{41} +(-4.79962 + 1.12304i) q^{42} +(2.93537 - 1.69474i) q^{43} +(2.20982 - 3.82751i) q^{44} +(-5.09411 - 4.36464i) q^{45} +(3.29404 + 5.70545i) q^{46} -1.20062i q^{47} +(0.905342 + 2.62554i) q^{48} +(6.85427 + 1.42092i) q^{49} +(2.07712 + 4.96097i) q^{50} +(1.60381 + 1.39293i) q^{51} +(0.914200 + 0.527814i) q^{52} +(-7.32252 + 4.22766i) q^{53} +(3.03791 - 4.69157i) q^{54} +(11.1085 + 3.74719i) q^{55} +(0.825481 - 8.04862i) q^{56} +(0.826566 + 0.160289i) q^{57} +(-6.36639 + 3.67564i) q^{58} +10.2352 q^{59} +(2.81640 - 1.65136i) q^{60} +0.484834 q^{61} -1.10812i q^{62} +(-6.71684 + 4.22896i) q^{63} -7.93045 q^{64} +(-0.895015 + 2.65326i) q^{65} +(-1.85958 + 9.58930i) q^{66} +5.98951i q^{67} +(-0.895349 + 0.516930i) q^{68} +(8.00931 + 6.95618i) q^{69} +(6.33430 - 0.610311i) q^{70} +10.9283 q^{71} +(5.65455 + 7.22433i) q^{72} +(-3.19498 + 1.84462i) q^{73} +(2.62875 - 4.55312i) q^{74} +(5.76603 + 6.46165i) q^{75} +(-0.204889 + 0.354877i) q^{76} +(8.12515 - 11.2427i) q^{77} +(-2.29040 - 0.444159i) q^{78} -15.2561 q^{79} +(-0.706189 - 3.51517i) q^{80} +(2.16186 - 8.73650i) q^{81} +(9.01287 + 5.20358i) q^{82} +(-7.54680 + 4.35715i) q^{83} +(-0.880112 - 3.76140i) q^{84} +(-1.81213 - 2.05840i) q^{85} +(-1.82294 - 3.15743i) q^{86} +(-7.76201 + 8.93714i) q^{87} +(-13.8850 - 8.01652i) q^{88} +(-0.459769 + 0.796344i) q^{89} +(-4.69483 + 5.47948i) q^{90} +(2.68531 + 1.94069i) q^{91} +(-4.47130 + 2.58150i) q^{92} +(-0.581665 - 1.68686i) q^{93} -1.29145 q^{94} +(-1.02995 - 0.347430i) q^{95} +(-7.19056 + 2.47946i) q^{96} +(13.2696 - 7.66120i) q^{97} +(1.52841 - 7.37280i) q^{98} +(2.20277 + 15.5737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.07565i		−	0.760600i	−0.924863	−	0.380300i	$-0.875821\pi$
$2$		−	1.07565i		−	0.760600i	0.924863	−	0.380300i	$-0.124179\pi$
$3$	−0.564624	−	1.63744i	−0.325986	−	0.945375i
$3$	−0.564624	−	1.63744i	−0.325986	−	0.945375i
$4$	0.842975			0.421488
$5$	0.440420	+	2.19227i	0.196962	+	0.980411i
$5$	0.440420	+	2.19227i	0.196962	+	0.980411i
$6$	−1.76131	+	0.607338i	−0.719052	+	0.247945i
$7$	2.63194	+	0.269937i	0.994782	+	0.102027i
$7$	2.63194	+	0.269937i	0.994782	+	0.102027i
$8$		−	3.05805i		−	1.08118i
$9$	−2.36240	+	1.84907i	−0.787466	+	0.616357i
$10$	2.35811	−	0.473738i	0.745701	−	0.149809i
$11$	2.62145	−	4.54048i	0.790396	−	1.36901i	−0.135325	−	0.990801i	$-0.543208\pi$
$11$	2.62145	−	4.54048i	0.790396	−	1.36901i	0.925722	−	0.378205i	$-0.123459\pi$
$12$	−0.475964	−	1.38032i	−0.137399	−	0.398464i
$13$	1.08449	+	0.626132i	0.300784	+	0.173658i	0.642795	−	0.766038i	$-0.277775\pi$
$13$	1.08449	+	0.626132i	0.300784	+	0.173658i	−0.342011	+	0.939696i	$0.611108\pi$
$14$	0.290358	−	2.83105i	0.0776015	−	0.756631i
$15$	3.34103	−	1.95897i	0.862649	−	0.505803i
$16$	−1.60344			−0.400861
$17$	−1.06213	+	0.613221i	−0.257604	+	0.148728i	−0.623241	−	0.782030i	$-0.714185\pi$
$17$	−1.06213	+	0.613221i	−0.257604	+	0.148728i	0.365637	+	0.930758i	$0.380851\pi$
$18$	1.98896	+	2.54112i	0.468802	+	0.598947i
$19$	−0.243054	+	0.420982i	−0.0557604	+	0.0965799i	−0.892558	−	0.450932i	$-0.851092\pi$
$19$	−0.243054	+	0.420982i	−0.0557604	+	0.0965799i	0.836798	+	0.547512i	$0.184425\pi$
$20$	0.371263	+	1.84803i	0.0830170	+	0.413231i
$21$	−1.04405	−	4.46206i	−0.227831	−	0.973701i
$22$	−4.88397	−	2.81976i	−1.04127	−	0.601175i
$23$	−5.30418	+	3.06237i	−1.10600	+	0.638549i	−0.937790	−	0.347203i	$-0.887132\pi$
$23$	−5.30418	+	3.06237i	−1.10600	+	0.638549i	−0.168209	+	0.985751i	$0.553798\pi$
$24$	−5.00736	+	1.72665i	−1.02212	+	0.352450i
$25$	−4.61206	+	1.93104i	−0.922412	+	0.386207i
$26$	0.673499	−	1.16653i	0.132084	−	0.228776i
$27$	4.36161	+	2.82425i	0.839392	+	0.543527i
$28$	2.21866	+	0.227550i	0.419288	+	0.0430030i
$29$	−3.41713	−	5.91864i	−0.634545	−	1.09906i	−0.986611	−	0.163089i	$-0.947854\pi$
$29$	−3.41713	−	5.91864i	−0.634545	−	1.09906i	0.352066	−	0.935975i	$-0.385479\pi$
$30$	−2.10716	−	3.59378i	−0.384714	−	0.656131i
$31$	1.03018			0.185026			0.0925130	−	0.995711i	$-0.470510\pi$
$31$	1.03018			0.185026			0.0925130	+	0.995711i	$0.470510\pi$
$32$		−	4.39135i		−	0.776289i
$33$	−8.91488	−	1.72879i	−1.55188	−	0.300944i
$34$	0.659611	+	1.14248i	0.113122	+	0.195934i
$35$	0.567388	+	5.88881i	0.0959060	+	0.995390i
$36$	−1.99144	+	1.55872i	−0.331907	+	0.259787i
$37$	4.23290	+	2.44387i	0.695885	+	0.401769i	0.805813	−	0.592170i	$-0.201729\pi$
$37$	4.23290	+	2.44387i	0.695885	+	0.401769i	−0.109928	+	0.993940i	$0.535062\pi$
$38$	0.452830	+	0.261441i	0.0734587	+	0.0424114i
$39$	0.412921	−	2.12932i	0.0661203	−	0.340964i
$40$	6.70406	−	1.34683i	1.06000	−	0.212952i
$41$	−4.83761	+	8.37899i	−0.755508	+	1.30858i	0.189613	+	0.981859i	$0.439277\pi$
$41$	−4.83761	+	8.37899i	−0.755508	+	1.30858i	−0.945121	+	0.326720i	$0.894057\pi$
$42$	−4.79962	+	1.12304i	−0.740597	+	0.173288i
$43$	2.93537	−	1.69474i	0.447640	−	0.258445i	−0.259193	−	0.965825i	$-0.583457\pi$
$43$	2.93537	−	1.69474i	0.447640	−	0.258445i	0.706833	+	0.707381i	$0.250123\pi$
$44$	2.20982	−	3.82751i	0.333142	−	0.577019i
$45$	−5.09411	−	4.36464i	−0.759385	−	0.650642i
$46$	3.29404	+	5.70545i	0.485680	+	0.841223i
$47$		−	1.20062i		−	0.175129i	−0.996159	−	0.0875645i	$-0.972092\pi$
$47$		−	1.20062i		−	0.175129i	0.996159	−	0.0875645i	$-0.0279084\pi$
$48$	0.905342	+	2.62554i	0.130675	+	0.378963i
$49$	6.85427	+	1.42092i	0.979181	+	0.202989i
$50$	2.07712	+	4.96097i	0.293749	+	0.701587i
$51$	1.60381	+	1.39293i	0.224579	+	0.195049i
$52$	0.914200	+	0.527814i	0.126777	+	0.0731946i
$53$	−7.32252	+	4.22766i	−1.00583	+	0.580713i	−0.909967	−	0.414682i	$-0.863893\pi$
$53$	−7.32252	+	4.22766i	−1.00583	+	0.580713i	−0.0958586	+	0.995395i	$0.530560\pi$
$54$	3.03791	−	4.69157i	0.413407	−	0.638441i
$55$	11.1085	+	3.74719i	1.49787	+	0.505271i
$56$	0.825481	−	8.04862i	0.110310	−	1.07554i
$57$	0.826566	+	0.160289i	0.109481	+	0.0212308i
$58$	−6.36639	+	3.67564i	−0.835948	+	0.482635i
$59$	10.2352			1.33251			0.666253	−	0.745725i	$-0.267897\pi$
$59$	10.2352			1.33251			0.666253	+	0.745725i	$0.267897\pi$
$60$	2.81640	−	1.65136i	0.363596	−	0.213190i
$61$	0.484834			0.0620766			0.0310383	−	0.999518i	$-0.490119\pi$
$61$	0.484834			0.0620766			0.0310383	+	0.999518i	$0.490119\pi$
$62$		−	1.10812i		−	0.140731i
$63$	−6.71684	+	4.22896i	−0.846242	+	0.532798i
$64$	−7.93045			−0.991306
$65$	−0.895015	+	2.65326i	−0.111013	+	0.329096i
$66$	−1.85958	+	9.58930i	−0.228898	+	1.18036i
$67$			5.98951i			0.731736i	0.930667	+	0.365868i	$0.119228\pi$
$67$			5.98951i			0.731736i	−0.930667	+	0.365868i	$0.880772\pi$
$68$	−0.895349	+	0.516930i	−0.108577	+	0.0626869i
$69$	8.00931	+	6.95618i	0.964208	+	0.837425i
$70$	6.33430	−	0.610311i	0.757094	−	0.0729461i
$71$	10.9283			1.29695			0.648473	−	0.761238i	$-0.275408\pi$
$71$	10.9283			1.29695			0.648473	+	0.761238i	$0.275408\pi$
$72$	5.65455	+	7.22433i	0.666396	+	0.851396i
$73$	−3.19498	+	1.84462i	−0.373944	+	0.215897i	−0.675180	−	0.737653i	$-0.735934\pi$
$73$	−3.19498	+	1.84462i	−0.373944	+	0.215897i	0.301236	+	0.953550i	$0.402601\pi$
$74$	2.62875	−	4.55312i	0.305586	−	0.529290i
$75$	5.76603	+	6.46165i	0.665804	+	0.746127i
$76$	−0.204889	+	0.354877i	−0.0235023	+	0.0407072i
$77$	8.12515	−	11.2427i	0.925947	−	1.28122i
$78$	−2.29040	−	0.444159i	−0.259337	−	0.0502911i
$79$	−15.2561			−1.71645			−0.858223	−	0.513277i	$-0.828431\pi$
$79$	−15.2561			−1.71645			−0.858223	+	0.513277i	$0.828431\pi$
$80$	−0.706189	−	3.51517i	−0.0789543	−	0.393008i
$81$	2.16186	−	8.73650i	0.240207	−	0.970722i
$82$	9.01287	+	5.20358i	0.995305	+	0.574639i
$83$	−7.54680	+	4.35715i	−0.828369	+	0.478259i	−0.853294	−	0.521430i	$-0.825399\pi$
$83$	−7.54680	+	4.35715i	−0.828369	+	0.478259i	0.0249251	+	0.999689i	$0.492065\pi$
$84$	−0.880112	−	3.76140i	−0.0960281	−	0.410403i
$85$	−1.81213	−	2.05840i	−0.196553	−	0.223264i
$86$	−1.82294	−	3.15743i	−0.196573	−	0.340475i
$87$	−7.76201	+	8.93714i	−0.832175	+	0.958162i
$88$	−13.8850	−	8.01652i	−1.48015	−	0.854563i
$89$	−0.459769	+	0.796344i	−0.0487354	+	0.0844123i	−0.889364	−	0.457200i	$-0.848852\pi$
$89$	−0.459769	+	0.796344i	−0.0487354	+	0.0844123i	0.840629	+	0.541612i	$0.182186\pi$
$90$	−4.69483	+	5.47948i	−0.494878	+	0.577588i
$91$	2.68531	+	1.94069i	0.281497	+	0.203440i
$92$	−4.47130	+	2.58150i	−0.466165	+	0.269140i
$93$	−0.581665	−	1.68686i	−0.0603159	−	0.174919i
$94$	−1.29145			−0.133203
$95$	−1.02995	−	0.347430i	−0.105671	−	0.0356456i
$96$	−7.19056	+	2.47946i	−0.733884	+	0.253059i
$97$	13.2696	−	7.66120i	1.34732	−	0.777877i	0.359453	−	0.933163i	$-0.382963\pi$
$97$	13.2696	−	7.66120i	1.34732	−	0.777877i	0.987870	+	0.155286i	$0.0496298\pi$
$98$	1.52841	−	7.37280i	0.154393	−	0.744765i
$99$	2.20277	+	15.5737i	0.221387	+	1.56521i
$100$	−3.88785	+	1.62782i	−0.388785	+	0.162782i
$101$	−6.59940	+	11.4305i	−0.656665	+	1.13738i	0.324809	+	0.945780i	$0.394700\pi$
$101$	−6.59940	+	11.4305i	−0.656665	+	1.13738i	−0.981474	+	0.191597i	$0.938633\pi$
$102$	1.49831	−	1.72514i	0.148355	−	0.170815i
$103$	−15.2019	+	8.77681i	−1.49789	+	0.864805i	−0.999997	−	0.00243557i	$-0.999225\pi$
$103$	−15.2019	+	8.77681i	−1.49789	+	0.864805i	−0.497889	+	0.867241i	$0.665891\pi$
$104$	1.91474	−	3.31643i	0.187756	−	0.325203i
$105$	9.32219	−	4.25402i	0.909753	−	0.415150i
$106$	4.54748	+	7.87647i	0.441691	+	0.765031i
$107$	4.60816	+	2.66052i	0.445488	+	0.257203i	0.705923	−	0.708289i	$-0.250533\pi$
$107$	4.60816	+	2.66052i	0.445488	+	0.257203i	−0.260435	+	0.965491i	$0.583866\pi$
$108$	3.67673	+	2.38077i	0.353793	+	0.229090i
$109$	−1.42508	−	2.46830i	−0.136497	−	0.236421i	0.789671	−	0.613531i	$-0.210251\pi$
$109$	−1.42508	−	2.46830i	−0.136497	−	0.236421i	−0.926169	+	0.377110i	$0.876918\pi$
$110$	4.03067	−	11.9488i	0.384309	−	1.13928i
$111$	1.61168	−	8.31097i	0.152974	−	0.788843i
$112$	−4.22017	−	0.432829i	−0.398769	−	0.0408985i
$113$	13.9495	+	8.05374i	1.31226	+	0.757632i	0.982470	−	0.186423i	$-0.0596895\pi$
$113$	13.9495	+	8.05374i	1.31226	+	0.757632i	0.329788	+	0.944055i	$0.393023\pi$
$114$	0.172415	−	0.889096i	0.0161482	−	0.0832715i
$115$	−9.04960	−	10.2795i	−0.843880	−	0.958564i
$116$	−2.88056	−	4.98927i	−0.267453	−	0.463242i
$117$	−3.71977	+	0.526131i	−0.343893	+	0.0486408i
$118$		−	11.0095i		−	1.01350i
$119$	−2.96100	+	1.32725i	−0.271434	+	0.121669i
$120$	−5.99061	−	10.2170i	−0.546866	−	0.932682i
$121$	−8.24398	−	14.2790i	−0.749453	−	1.29809i
$122$		−	0.521512i		−	0.0472154i
$123$	16.4515	+	3.19031i	1.48338	+	0.287660i
$124$	0.868417			0.0779862
$125$	−6.26459	−	9.26039i	−0.560322	−	0.828275i
$126$	4.54888	+	7.22497i	0.405247	+	0.643652i
$127$		−	1.19856i		−	0.106355i	−0.998585	−	0.0531776i	$-0.983065\pi$
$127$		−	1.19856i		−	0.106355i	0.998585	−	0.0531776i	$-0.0169349\pi$
$128$		−	0.252314i		−	0.0223016i
$129$	−4.43240	−	3.84959i	−0.390251	−	0.338938i
$130$	2.85398	+	0.962724i	0.250310	+	0.0844365i
$131$	0.810355	+	1.40358i	0.0708010	+	0.122631i	0.899253	−	0.437430i	$-0.144111\pi$
$131$	0.810355	+	1.40358i	0.0708010	+	0.122631i	−0.828452	+	0.560061i	$0.810778\pi$
$132$	−7.51503	−	1.45733i	−0.654099	−	0.126844i
$133$	−0.753344	+	1.04239i	−0.0653232	+	0.0903869i
$134$	6.44263			0.556558
$135$	−4.27057	+	10.8057i	−0.367552	+	0.930003i
$136$	1.87526	+	3.24804i	0.160802	+	0.278517i
$137$	3.97146	+	2.29292i	0.339305	+	0.195898i	0.659965	−	0.751297i	$-0.270571\pi$
$137$	3.97146	+	2.29292i	0.339305	+	0.195898i	−0.320660	+	0.947194i	$0.603905\pi$
$138$	7.48242	−	8.61522i	0.636946	−	0.733376i
$139$	−10.3768	+	17.9731i	−0.880148	+	1.52446i	−0.0289718	+	0.999580i	$0.509223\pi$
$139$	−10.3768	+	17.9731i	−0.880148	+	1.52446i	−0.851176	+	0.524880i	$0.824110\pi$
$140$	0.478294	+	4.96412i	0.0404232	+	0.419545i
$141$	−1.96595	+	0.677901i	−0.165563	+	0.0570896i
$142$		−	11.7550i		−	0.986457i
$143$	5.68588	−	3.28274i	0.475477	−	0.274517i
$144$	3.78797	−	2.96488i	0.315664	−	0.247073i
$145$	11.4703	−	10.0979i	0.952554	−	0.838589i
$146$	1.98417	+	3.43668i	0.164211	+	0.284422i
$147$	−1.54342	−	12.0257i	−0.127299	−	0.991864i
$148$	3.56823	+	2.06012i	0.293307	+	0.169341i
$149$	−4.59755	−	7.96318i	−0.376646	−	0.652369i	0.613926	−	0.789363i	$-0.289589\pi$
$149$	−4.59755	−	7.96318i	−0.376646	−	0.652369i	−0.990572	+	0.136994i	$0.956256\pi$
$150$	6.95048	−	6.20224i	0.567504	−	0.506410i
$151$	4.52236	−	7.83296i	0.368025	−	0.637437i	−0.621232	−	0.783627i	$-0.713368\pi$
$151$	4.52236	−	7.83296i	0.368025	−	0.637437i	0.989257	+	0.146189i	$0.0467009\pi$
$152$	1.28738	+	0.743271i	0.104421	+	0.0602873i
$153$	1.37528	−	3.41263i	0.111185	−	0.275894i
$154$	−12.0932	−	8.73983i	−0.974497	−	0.704275i
$155$	0.453713	+	2.25843i	0.0364431	+	0.181402i
$156$	0.348082	−	1.79496i	0.0278689	−	0.143712i
$157$			7.64967i			0.610510i	0.952271	+	0.305255i	$0.0987417\pi$
$157$			7.64967i			0.610510i	−0.952271	+	0.305255i	$0.901258\pi$
$158$			16.4102i			1.30553i
$159$	11.0570	+	9.60312i	0.876877	+	0.761577i
$160$	9.62701	−	1.93404i	0.761082	−	0.152899i
$161$	−14.7870	+	6.62820i	−1.16538	+	0.522375i
$162$	−9.39742	−	2.32541i	−0.738331	−	0.182701i
$163$	6.95887	+	4.01771i	0.545061	+	0.314691i	0.747128	−	0.664681i	$-0.231432\pi$
$163$	6.95887	+	4.01771i	0.545061	+	0.314691i	−0.202066	+	0.979372i	$0.564766\pi$
$164$	−4.07799	+	7.06328i	−0.318437	+	0.551550i
$165$	−0.136326	−	20.3052i	−0.0106130	−	1.58076i
$166$	4.68677	+	8.11772i	0.363764	+	0.630057i
$167$	−17.2584	−	9.96416i	−1.33550	−	0.771050i	−0.349362	−	0.936988i	$-0.613602\pi$
$167$	−17.2584	−	9.96416i	−1.33550	−	0.771050i	−0.986136	+	0.165938i	$0.946935\pi$
$168$	−13.6452	+	3.19277i	−1.05275	+	0.246327i
$169$	−5.71592	−	9.90026i	−0.439686	−	0.761558i
$170$	−2.21411	+	1.94921i	−0.169815	+	0.149498i
$171$	−0.204235	−	1.44395i	−0.0156183	−	0.110422i
$172$	2.47444	−	1.42862i	0.188675	−	0.108931i
$173$		−	3.61253i		−	0.274656i	−0.990526	−	0.137328i	$-0.956149\pi$
$173$		−	3.61253i		−	0.274656i	0.990526	−	0.137328i	$-0.0438514\pi$
$174$	9.61325	+	8.34921i	0.728778	+	0.632952i
$175$	−12.6599	+	3.83742i	−0.957002	+	0.290081i
$176$	−4.20334	+	7.28040i	−0.316839	+	0.548781i
$177$	−5.77903	−	16.7595i	−0.434378	−	1.25972i
$178$	0.856588	+	0.494551i	0.0642040	+	0.0370682i
$179$	7.78106	+	13.4772i	0.581584	+	1.00733i	0.995292	+	0.0969228i	$0.0309000\pi$
$179$	7.78106	+	13.4772i	0.581584	+	1.00733i	−0.413708	+	0.910409i	$0.635767\pi$
$180$	−4.29421	−	3.67928i	−0.320071	−	0.274238i
$181$	−12.6543			−0.940589			−0.470295	−	0.882509i	$-0.655852\pi$
$181$	−12.6543			−0.940589			−0.470295	+	0.882509i	$0.655852\pi$
$182$	2.08750	−	2.88845i	0.154736	−	0.214106i
$183$	−0.273749	−	0.793884i	−0.0202361	−	0.0586856i
$184$	9.36488	+	16.2205i	0.690388	+	1.19579i
$185$	−3.49335	+	10.3560i	−0.256836	+	0.761386i
$186$	−1.81447	+	0.625669i	−0.133043	+	0.0458763i
$187$			6.43010i			0.470216i
$188$		−	1.01210i		−	0.0738147i
$189$	10.7171	+	8.61063i	0.779557	+	0.626331i
$190$	−0.373714	+	1.10787i	−0.0271120	+	0.0803731i
$191$	−8.24796			−0.596801			−0.298401	−	0.954441i	$-0.596453\pi$
$191$	−8.24796			−0.596801			−0.298401	+	0.954441i	$0.596453\pi$
$192$	4.47772	+	12.9856i	0.323152	+	0.937156i
$193$		−	16.7374i		−	1.20478i	−0.798200	−	0.602392i	$-0.794214\pi$
$193$		−	16.7374i		−	1.20478i	0.798200	−	0.602392i	$-0.205786\pi$
$194$	−8.24078	−	14.2734i	−0.591653	−	1.02477i
$195$	4.84989	−	0.0325614i	0.347308	−	0.00233177i
$196$	5.77798	+	1.19780i	0.412713	+	0.0855572i
$197$		−	4.84963i		−	0.345522i	−0.984964	−	0.172761i	$-0.944731\pi$
$197$		−	4.84963i		−	0.345522i	0.984964	−	0.172761i	$-0.0552688\pi$
$198$	16.7518	−	2.36941i	1.19050	−	0.168387i
$199$	−11.8050	−	20.4468i	−0.836834	−	1.44944i	−0.892529	−	0.450991i	$-0.851071\pi$
$199$	−11.8050	−	20.4468i	−0.836834	−	1.44944i	0.0556949	−	0.998448i	$-0.482263\pi$
$200$	5.90520	+	14.1039i	0.417561	+	0.997297i
$201$	9.80745	−	3.38182i	0.691764	−	0.238535i
$202$	12.2952	+	7.09865i	0.865089	+	0.499459i
$203$	−7.39604	−	16.5000i	−0.519100	−	1.15807i
$204$	1.35198	+	1.17421i	0.0946572	+	0.0822109i
$205$	−20.4996	−	6.91506i	−1.43175	−	0.482968i
$206$	9.44079	+	16.3519i	0.657771	+	1.13929i
$207$	6.86805	−	17.0424i	0.477363	−	1.18453i
$208$	−1.73892	−	1.00397i	−0.120572	−	0.0696125i
$209$	1.27431	+	2.20717i	0.0881457	+	0.152673i
$210$	−4.57585	−	10.0274i	−0.315763	−	0.691958i
$211$	5.64571	−	9.77866i	0.388667	−	0.673190i	−0.603604	−	0.797284i	$-0.706269\pi$
$211$	5.64571	−	9.77866i	0.388667	−	0.673190i	0.992270	+	0.124094i	$0.0396024\pi$
$212$	−6.17270	+	3.56381i	−0.423943	+	0.244764i
$213$	−6.17036	−	17.8943i	−0.422786	−	1.22610i
$214$	2.86179	−	4.95677i	0.195628	−	0.338838i
$215$	5.00811	+	5.68871i	0.341550	+	0.387967i
$216$	8.63669	−	13.3380i	0.587652	−	0.907536i
$217$	2.71138	+	0.278084i	0.184061	+	0.0188776i
$218$	−2.65503	+	1.53288i	−0.179822	+	0.103820i
$219$	4.82441	+	4.19006i	0.326004	+	0.283138i
$220$	9.36417	+	3.15879i	0.631333	+	0.212966i
$221$	−1.53583			−0.103311
$222$	−8.93971	−	1.73360i	−0.599994	−	0.116352i
$223$	13.1368	−	7.58453i	0.879704	−	0.507897i	0.00914337	−	0.999958i	$-0.497090\pi$
$223$	13.1368	−	7.58453i	0.879704	−	0.507897i	0.870561	+	0.492061i	$0.163756\pi$
$224$	1.18539	−	11.5578i	0.0792022	−	0.772238i
$225$	7.32490	−	13.0899i	0.488327	−	0.872661i
$226$	8.66301	−	15.0048i	0.576255	−	0.998103i
$227$	20.5694	+	11.8757i	1.36524	+	0.788221i	0.990316	−	0.138835i	$-0.0443357\pi$
$227$	20.5694	+	11.8757i	1.36524	+	0.788221i	0.374923	+	0.927056i	$0.377669\pi$
$228$	0.696775	+	0.135120i	0.0461450	+	0.00894853i
$229$	−3.85347	−	6.67441i	−0.254645	−	0.441058i	0.710154	−	0.704046i	$-0.248625\pi$
$229$	−3.85347	−	6.67441i	−0.254645	−	0.441058i	−0.964799	+	0.262989i	$0.915292\pi$
$230$	−11.0571	+	9.73421i	−0.729084	+	0.641855i
$231$	−22.9968	−	6.95654i	−1.51308	−	0.457707i
$232$	−18.0995	+	10.4498i	−1.18829	+	0.686060i
$233$	−7.78605	−	4.49528i	−0.510081	−	0.294496i	0.222786	−	0.974867i	$-0.428485\pi$
$233$	−7.78605	−	4.49528i	−0.510081	−	0.294496i	−0.732867	+	0.680372i	$0.761818\pi$
$234$	0.565933	+	4.00117i	0.0369962	+	0.261565i
$235$	2.63209	−	0.528779i	0.171698	−	0.0344938i
$236$	8.62800			0.561635
$237$	8.61396	+	24.9809i	0.559537	+	1.62268i
$238$	1.42766	+	3.18500i	0.0925416	+	0.206453i
$239$	5.80551	−	10.0554i	0.375527	−	0.650432i	−0.614879	−	0.788622i	$-0.710795\pi$
$239$	5.80551	−	10.0554i	0.375527	−	0.650432i	0.990406	+	0.138190i	$0.0441283\pi$
$240$	−5.35714	+	3.14109i	−0.345802	+	0.202756i
$241$	0.466930	−	0.808747i	0.0300776	−	0.0520959i	−0.850595	−	0.525822i	$-0.823758\pi$
$241$	0.466930	−	0.808747i	0.0300776	−	0.0520959i	0.880672	+	0.473726i	$0.157091\pi$
$242$	−15.3592	+	8.86764i	−0.987327	+	0.570034i
$243$	−15.5261	+	1.39292i	−0.996000	+	0.0893560i
$244$	0.408703			0.0261645
$245$	−0.0962762	+	15.6522i	−0.00615086	+	0.999981i
$246$	3.43166	−	17.6961i	0.218794	−	1.12826i
$247$	−0.527181	+	0.304368i	−0.0335437	+	0.0193665i
$248$		−	3.15035i		−	0.200047i
$249$	11.3957	+	9.89726i	0.722170	+	0.627213i
$250$	−9.96095	+	6.73851i	−0.629986	+	0.426181i
$251$	−17.9865			−1.13530			−0.567650	−	0.823270i	$-0.692147\pi$
$251$	−17.9865			−1.13530			−0.567650	+	0.823270i	$0.692147\pi$
$252$	−5.66213	+	3.56491i	−0.356681	+	0.224568i
$253$			32.1114i			2.01883i
$254$	−1.28923			−0.0808938
$255$	−2.34732	+	4.12946i	−0.146995	+	0.258597i
$256$	−16.1323			−1.00827
$257$	13.7196	−	7.92103i	0.855806	−	0.494100i	−0.00679943	−	0.999977i	$-0.502164\pi$
$257$	13.7196	−	7.92103i	0.855806	−	0.494100i	0.862606	+	0.505877i	$0.168831\pi$
$258$	−4.14082	+	4.76772i	−0.257796	+	0.296825i
$259$	10.4811	+	7.57474i	0.651262	+	0.470671i
$260$	−0.754476	+	2.23663i	−0.0467906	+	0.138710i
$261$	19.0166	+	7.66368i	1.17710	+	0.474370i
$262$	1.50976	−	0.871659i	0.0932732	−	0.0538513i
$263$	10.9064	+	6.29680i	0.672516	+	0.388277i	0.797029	−	0.603941i	$-0.206404\pi$
$263$	10.9064	+	6.29680i	0.672516	+	0.388277i	−0.124514	+	0.992218i	$0.539737\pi$
$264$	−5.28673	+	27.2622i	−0.325376	+	1.67787i
$265$	−12.4931	−	14.1910i	−0.767447	−	0.871744i
$266$	1.12125	+	0.810335i	0.0687483	+	0.0496848i
$267$	1.56356	+	0.303208i	0.0956883	+	0.0185561i
$268$			5.04901i			0.308417i
$269$	2.32717	+	4.03078i	0.141890	+	0.245761i	0.928208	−	0.372061i	$-0.121349\pi$
$269$	2.32717	+	4.03078i	0.141890	+	0.245761i	−0.786318	+	0.617822i	$0.788015\pi$
$270$	11.6231	+	4.59364i	0.707360	+	0.279560i
$271$	6.08992	−	10.5481i	0.369936	−	0.640749i	−0.619619	−	0.784903i	$-0.712713\pi$
$271$	6.08992	−	10.5481i	0.369936	−	0.640749i	0.989555	+	0.144154i	$0.0460462\pi$
$272$	1.70306	−	0.983264i	0.103263	−	0.0596191i
$273$	1.66157	−	5.49278i	0.100563	−	0.332438i
$274$	2.46638	−	4.27190i	0.149000	−	0.258075i
$275$	−3.32244	+	26.0031i	−0.200351	+	1.56804i
$276$	6.75165	+	5.86389i	0.406402	+	0.352964i
$277$	−11.1209	−	6.42064i	−0.668188	−	0.385779i	0.127202	−	0.991877i	$-0.459401\pi$
$277$	−11.1209	−	6.42064i	−0.668188	−	0.385779i	−0.795390	+	0.606098i	$0.792734\pi$
$278$	19.3328	+	11.1618i	1.15950	+	0.669440i
$279$	−2.43370	+	1.90488i	−0.145702	+	0.114042i
$280$	18.0083	−	1.73510i	1.07620	−	0.103692i
$281$	10.5203	+	18.2218i	0.627591	+	1.08702i	0.988034	+	0.154238i	$0.0492923\pi$
$281$	10.5203	+	18.2218i	0.627591	+	1.08702i	−0.360443	+	0.932781i	$0.617374\pi$
$282$	0.729185	+	2.11467i	0.0434223	+	0.125927i
$283$		−	13.3308i		−	0.792436i	−0.918156	−	0.396218i	$-0.870322\pi$
$283$		−	13.3308i		−	0.792436i	0.918156	−	0.396218i	$-0.129678\pi$
$284$	9.21225			0.546647
$285$	0.0126398	+	1.88265i	0.000748718	+	0.111518i
$286$	−3.53109	−	6.11602i	−0.208798	−	0.361648i
$287$	−14.9941	+	20.7472i	−0.885076	+	1.22467i
$288$	8.11993	+	10.3741i	0.478471	+	0.611302i
$289$	−7.74792	+	13.4198i	−0.455760	+	0.789400i
$290$	−10.8619	−	12.3380i	−0.637831	−	0.724512i
$291$	−20.0371	−	17.4024i	−1.17459	−	1.02015i
$292$	−2.69329	+	1.55497i	−0.157613	+	0.0909978i
$293$	5.65831	+	3.26682i	0.330562	+	0.190850i	0.656090	−	0.754682i	$-0.272209\pi$
$293$	5.65831	+	3.26682i	0.330562	+	0.190850i	−0.325529	+	0.945532i	$0.605542\pi$
$294$	−12.9355	+	1.66018i	−0.754412	+	0.0968235i
$295$	4.50778	+	22.4382i	0.262453	+	1.30640i
$296$	7.47346	−	12.9444i	0.434386	−	0.752379i
$297$	24.2572	−	12.4002i	1.40754	−	0.719531i
$298$	−8.56560	+	4.94535i	−0.496192	+	0.286477i
$299$	−7.66979			−0.443556
$300$	4.86062	+	5.44701i	0.280628	+	0.314483i
$301$	8.18320	−	3.66809i	0.471672	−	0.211425i
$302$	−8.42553	−	4.86448i	−0.484835	−	0.279919i
$303$	22.4429	+	4.35217i	1.28931	+	0.250026i
$304$	0.389723	−	0.675021i	0.0223522	−	0.0387151i
$305$	0.213531	+	1.06288i	0.0122267	+	0.0608606i
$306$	−3.67079	−	1.47933i	−0.209845	−	0.0845674i
$307$		−	8.86675i		−	0.506052i	−0.967459	−	0.253026i	$-0.918574\pi$
$307$		−	8.86675i		−	0.506052i	0.967459	−	0.253026i	$-0.0814258\pi$
$308$	6.84930	−	9.47729i	0.390275	−	0.540019i
$309$	22.9548	+	19.9365i	1.30585	+	1.13415i
$310$	2.42928	−	0.488037i	0.137974	−	0.0277186i
$311$	2.04113			0.115742			0.0578711	−	0.998324i	$-0.481569\pi$
$311$	2.04113			0.115742			0.0578711	+	0.998324i	$0.481569\pi$
$312$	−6.51155	−	1.26273i	−0.368644	−	0.0714882i
$313$			3.86919i			0.218699i	0.994003	+	0.109350i	$0.0348768\pi$
$313$			3.86919i			0.218699i	−0.994003	+	0.109350i	$0.965123\pi$
$314$	8.22837			0.464354
$315$	−12.2292	−	12.8626i	−0.689039	−	0.724724i
$316$	−12.8605			−0.723460
$317$		−	4.97899i		−	0.279648i	−0.990176	−	0.139824i	$-0.955346\pi$
$317$		−	4.97899i		−	0.279648i	0.990176	−	0.139824i	$-0.0446537\pi$
$318$	10.3296	−	11.8935i	0.579256	−	0.666952i
$319$	−35.8313			−2.00617
$320$	−3.49273	−	17.3857i	−0.195250	−	0.971887i
$321$	1.75456	−	9.04777i	0.0979300	−	0.504997i
$322$	7.12963	+	15.9056i	0.397319	+	0.886385i
$323$		−	0.596183i		−	0.0331725i
$324$	1.82240	−	7.36465i	0.101244	−	0.409147i
$325$	−6.21083	−	0.793563i	−0.344515	−	0.0440190i
$326$	4.32165	−	7.48532i	0.239354	−	0.414574i
$327$	−3.23706	+	3.72713i	−0.179010	+	0.206111i
$328$	25.6234	+	14.7937i	1.41481	+	0.816843i
$329$	0.324093	−	3.15998i	0.0178678	−	0.174215i
$330$	−21.8413	+	0.146639i	−1.20232	+	0.00807222i
$331$	29.9622			1.64687			0.823437	−	0.567408i	$-0.192054\pi$
$331$	29.9622			1.64687			0.823437	+	0.567408i	$0.192054\pi$
$332$	−6.36176	+	3.67297i	−0.349147	+	0.201580i
$333$	−14.5187	+	2.05355i	−0.795619	+	0.112534i
$334$	−10.7180	+	18.5641i	−0.586461	+	1.01578i
$335$	−13.1306	+	2.63790i	−0.717402	+	0.144124i
$336$	1.67408	+	7.15465i	0.0913286	+	0.390318i
$337$	−13.6534	−	7.88282i	−0.743750	−	0.429404i	0.0796811	−	0.996820i	$-0.474610\pi$
$337$	−13.6534	−	7.88282i	−0.743750	−	0.429404i	−0.823431	+	0.567416i	$0.807943\pi$
$338$	−10.6492	+	6.14833i	−0.579241	+	0.334425i
$339$	5.31128	−	27.3887i	0.288469	−	1.48755i
$340$	−1.52758	−	1.73518i	−0.0828445	−	0.0941031i
$341$	2.70057	−	4.67752i	0.146244	−	0.253302i
$342$	−1.55319	+	0.219686i	−0.0839868	+	0.0118793i
$343$	17.6565	+	5.59001i	0.953361	+	0.301832i
$344$	−5.18258	−	8.97650i	−0.279426	−	0.483980i
$345$	−11.7223	+	20.6222i	−0.631109	+	1.11026i
$346$	−3.88582			−0.208903
$347$			16.5345i			0.887620i	0.896121	+	0.443810i	$0.146374\pi$
$347$			16.5345i			0.887620i	−0.896121	+	0.443810i	$0.853626\pi$
$348$	−6.54318	+	7.53379i	−0.350751	+	0.403854i
$349$	−15.7874	−	27.3447i	−0.845083	−	1.46373i	−0.885549	−	0.464545i	$-0.846218\pi$
$349$	−15.7874	−	27.3447i	−0.845083	−	1.46373i	0.0404667	−	0.999181i	$-0.487116\pi$
$350$	4.12772	+	13.6177i	0.220636	+	0.727896i
$351$	2.96178	+	5.79382i	0.158088	+	0.309251i
$352$	−19.9389	−	11.5117i	−1.06274	−	0.613576i
$353$	−13.7881	−	7.96055i	−0.733865	−	0.423697i	0.0859694	−	0.996298i	$-0.472601\pi$
$353$	−13.7881	−	7.96055i	−0.733865	−	0.423697i	−0.819835	+	0.572601i	$0.805935\pi$
$354$	−18.0273	+	6.21622i	−0.958142	+	0.330388i
$355$	4.81303	+	23.9576i	0.255449	+	1.27154i
$356$	−0.387574	+	0.671298i	−0.0205414	+	0.0355787i
$357$	3.84515	+	4.09905i	0.203507	+	0.216945i
$358$	14.4967	−	8.36970i	0.766177	−	0.442352i
$359$	4.63711	−	8.03171i	0.244737	−	0.423897i	−0.717320	−	0.696743i	$-0.754632\pi$
$359$	4.63711	−	8.03171i	0.244737	−	0.423897i	0.962058	+	0.272846i	$0.0879649\pi$
$360$	−13.3473	+	15.5780i	−0.703463	+	0.821034i
$361$	9.38185	+	16.2498i	0.493782	+	0.855255i
$362$			13.6116i			0.715412i
$363$	−18.7262	+	21.5613i	−0.982871	+	1.13167i
$364$	2.26365	+	1.63595i	0.118647	+	0.0857472i
$365$	−5.45103	−	6.19183i	−0.285320	−	0.324095i
$366$	−0.853942	+	0.294458i	−0.0446363	+	0.0153916i
$367$	−4.50114	−	2.59873i	−0.234958	−	0.135653i	0.377899	−	0.925847i	$-0.376646\pi$
$367$	−4.50114	−	2.59873i	−0.234958	−	0.135653i	−0.612857	+	0.790194i	$0.709980\pi$
$368$	8.50495	−	4.91034i	0.443351	−	0.255969i
$369$	−4.06499	−	28.7396i	−0.211615	−	1.49612i
$370$	11.1394	+	3.75762i	0.579110	+	0.195350i
$371$	−20.4137	+	9.15034i	−1.05982	+	0.475062i
$372$	−0.490329	−	1.42198i	−0.0254224	−	0.0737262i
$373$	17.5444	−	10.1293i	0.908414	−	0.524473i	0.0284935	−	0.999594i	$-0.490929\pi$
$373$	17.5444	−	10.1293i	0.908414	−	0.524473i	0.879921	+	0.475121i	$0.157596\pi$
$374$	6.91655			0.357646
$375$	−11.6262	+	15.4865i	−0.600373	+	0.799720i
$376$	−3.67157			−0.189347
$377$		−	8.55830i		−	0.440775i
$378$	9.26203	−	11.5279i	0.476387	−	0.592931i
$379$	11.3495			0.582986			0.291493	−	0.956573i	$-0.405848\pi$
$379$	11.3495			0.582986			0.291493	+	0.956573i	$0.405848\pi$
$380$	−0.868223	−	0.292875i	−0.0445389	−	0.0150242i
$381$	−1.96257	+	0.676737i	−0.100546	+	0.0346703i
$382$			8.87192i			0.453927i
$383$	21.7283	−	12.5449i	1.11027	−	0.641012i	0.171367	−	0.985207i	$-0.445181\pi$
$383$	21.7283	−	12.5449i	1.11027	−	0.641012i	0.938898	+	0.344195i	$0.111848\pi$
$384$	−0.413148	+	0.142462i	−0.0210834	+	0.00727000i
$385$	28.2254	+	12.8610i	1.43850	+	0.655457i
$386$	−18.0036			−0.916359
$387$	−3.80082	+	9.43135i	−0.193207	+	0.479423i
$388$	11.1859	−	6.45820i	0.567880	−	0.327866i
$389$	7.34617	−	12.7239i	0.372465	−	0.645129i	−0.617479	−	0.786588i	$-0.711846\pi$
$389$	7.34617	−	12.7239i	0.372465	−	0.645129i	0.989944	+	0.141459i	$0.0451792\pi$
$390$	−0.0350247	−	5.21679i	−0.00177355	−	0.264162i
$391$	3.75582	−	6.50527i	0.189940	−	0.328986i
$392$	4.34524	−	20.9607i	0.219468	−	1.05867i
$393$	1.84072	−	2.11940i	0.0928521	−	0.106909i
$394$	−5.21651			−0.262804
$395$	−6.71910	−	33.4454i	−0.338074	−	1.68282i
$396$	1.85688	+	13.1282i	0.0933118	+	0.659718i
$397$	−11.2840	−	6.51484i	−0.566329	−	0.326970i	0.189353	−	0.981909i	$-0.439361\pi$
$397$	−11.2840	−	6.51484i	−0.566329	−	0.326970i	−0.755682	+	0.654939i	$0.772694\pi$
$398$	−21.9937	+	12.6981i	−1.10244	+	0.636496i
$399$	2.13221	+	0.644993i	0.106744	+	0.0322901i
$400$	7.39517	−	3.09631i	0.369759	−	0.154815i
$401$	7.46404	+	12.9281i	0.372736	+	0.645598i	0.989985	−	0.141170i	$-0.0450863\pi$
$401$	7.46404	+	12.9281i	0.372736	+	0.645598i	−0.617249	+	0.786768i	$0.711753\pi$
$402$	−3.63766	−	10.5494i	−0.181430	−	0.526156i
$403$	1.11722	+	0.645029i	0.0556529	+	0.0321312i
$404$	−5.56313	+	9.63562i	−0.276776	+	0.479390i
$405$	20.1048	+	0.891647i	0.999018	+	0.0443063i
$406$	−17.7482	+	7.95555i	−0.880828	+	0.394827i
$407$	22.1927	−	12.8129i	1.10005	−	0.635114i
$408$	4.25965	−	4.90454i	0.210884	−	0.242811i
$409$	1.80698			0.0893492			0.0446746	−	0.999002i	$-0.485775\pi$
$409$	1.80698			0.0893492			0.0446746	+	0.999002i	$0.485775\pi$
$410$	−7.43819	+	22.0504i	−0.367346	+	1.08899i
$411$	1.51214	−	7.79765i	0.0745882	−	0.384630i
$412$	−12.8148	+	7.39864i	−0.631341	+	0.364505i
$413$	26.9384	+	2.76286i	1.32555	+	0.135951i
$414$	−18.3316	−	7.38763i	−0.900951	−	0.363082i
$415$	−12.8758	−	14.6256i	−0.632047	−	0.717943i
$416$	2.74957	−	4.76239i	0.134809	−	0.233495i
$417$	35.2888	+	6.84328i	1.72810	+	0.335117i
$418$	2.37414	−	1.37071i	0.116123	−	0.0670436i
$419$	11.8736	−	20.5657i	0.580063	−	1.00470i	−0.415408	−	0.909635i	$-0.636361\pi$
$419$	11.8736	−	20.5657i	0.580063	−	1.00470i	0.995471	−	0.0950632i	$-0.0303053\pi$
$420$	7.85838	−	3.58604i	0.383450	−	0.174981i
$421$	12.4283	+	21.5264i	0.605716	+	1.04913i	0.991938	+	0.126725i	$0.0404466\pi$
$421$	12.4283	+	21.5264i	0.605716	+	1.04913i	−0.386222	+	0.922406i	$0.626220\pi$
$422$	−10.5184	−	6.07281i	−0.512029	−	0.295620i
$423$	2.22004	+	2.83635i	0.107942	+	0.137908i
$424$	12.9284	+	22.3926i	0.627858	+	1.08748i
$425$	3.71445	−	4.87922i	0.180177	−	0.236677i
$426$	−19.2481	+	6.63715i	−0.932571	+	0.321571i
$427$	1.27606	+	0.130875i	0.0617526	+	0.00633347i
$428$	3.88457	+	2.24276i	0.187768	+	0.108408i
$429$	−8.58567	−	7.45675i	−0.414520	−	0.360015i
$430$	6.11907	−	5.38698i	0.295088	−	0.259783i
$431$	0.0501982	+	0.0869458i	0.00241796	+	0.00418803i	0.867232	−	0.497905i	$-0.165897\pi$
$431$	0.0501982	+	0.0869458i	0.00241796	+	0.00418803i	−0.864814	+	0.502093i	$0.832564\pi$
$432$	−6.99359	−	4.52852i	−0.336479	−	0.217879i
$433$		−	32.8267i		−	1.57755i	−0.614682	−	0.788775i	$-0.710716\pi$
$433$		−	32.8267i		−	1.57755i	0.614682	−	0.788775i	$-0.289284\pi$
$434$	0.299122	−	2.91650i	0.0143583	−	0.139996i
$435$	−23.0111	−	13.0803i	−1.10330	−	0.627152i
$436$	−1.20130	−	2.08072i	−0.0575320	−	0.0996483i
$437$		−	2.97729i		−	0.142423i
$438$	4.50704	−	5.18938i	0.215355	−	0.247958i
$439$	−3.59434			−0.171548			−0.0857742	−	0.996315i	$-0.527336\pi$
$439$	−3.59434			−0.171548			−0.0857742	+	0.996315i	$0.527336\pi$
$440$	11.4591	−	33.9703i	0.546291	−	1.61947i
$441$	−18.8199	+	9.31726i	−0.896186	+	0.443679i
$442$			1.65201i			0.0785783i
$443$		−	31.5226i		−	1.49768i	−0.662749	−	0.748842i	$-0.730610\pi$
$443$		−	31.5226i		−	1.49768i	0.662749	−	0.748842i	$-0.269390\pi$
$444$	1.35861	−	7.00595i	0.0644766	−	0.332487i
$445$	−1.94829	−	0.657211i	−0.0923578	−	0.0311548i
$446$	−8.15830	−	14.1306i	−0.386307	−	0.669103i
$447$	−10.4433	+	12.0244i	−0.493952	+	0.568734i
$448$	−20.8725	−	2.14072i	−0.986133	−	0.101140i
$449$	−34.6142			−1.63355			−0.816773	−	0.576959i	$-0.804239\pi$
$449$	−34.6142			−1.63355			−0.816773	+	0.576959i	$0.804239\pi$
$450$	−14.0802	−	7.87904i	−0.663746	−	0.371421i
$451$	25.3631	+	43.9302i	1.19430	+	2.06859i
$452$	11.7591	+	6.78910i	0.553100	+	0.319333i
$453$	−15.3794	−	2.98240i	−0.722588	−	0.140126i
$454$	12.7742	−	22.1255i	0.599521	−	1.03840i
$455$	−3.07184	+	6.74163i	−0.144010	+	0.316052i
$456$	0.490172	−	2.52768i	0.0229544	−	0.118369i
$457$		−	17.5130i		−	0.819222i	−0.912260	−	0.409611i	$-0.865664\pi$
$457$		−	17.5130i		−	0.819222i	0.912260	−	0.409611i	$-0.134336\pi$
$458$	−7.17934	+	4.14499i	−0.335468	+	0.193683i
$459$	−6.36448	−	0.325091i	−0.297068	−	0.0151739i
$460$	−7.62859	−	8.66532i	−0.355685	−	0.404023i
$461$	−0.695537	−	1.20470i	−0.0323944	−	0.0561087i	0.849374	−	0.527792i	$-0.176980\pi$
$461$	−0.695537	−	1.20470i	−0.0323944	−	0.0561087i	−0.881768	+	0.471683i	$0.843647\pi$
$462$	−7.48281	+	24.7365i	−0.348132	+	1.15085i
$463$	−3.96653	−	2.29008i	−0.184340	−	0.106429i	0.404990	−	0.914321i	$-0.367275\pi$
$463$	−3.96653	−	2.29008i	−0.184340	−	0.106429i	−0.589330	+	0.807892i	$0.700608\pi$
$464$	5.47917	+	9.49020i	0.254364	+	0.440572i
$465$	3.44186	−	2.01809i	0.159613	−	0.0935867i
$466$	−4.83535	+	8.37507i	−0.223993	+	0.387968i
$467$	−7.64964	−	4.41652i	−0.353983	−	0.204372i	0.312455	−	0.949933i	$-0.398849\pi$
$467$	−7.64964	−	4.41652i	−0.353983	−	0.204372i	−0.666438	+	0.745560i	$0.732182\pi$
$468$	−3.13567	+	0.443515i	−0.144946	+	0.0205015i
$469$	−1.61679	+	15.7641i	−0.0746566	+	0.727917i
$470$	−0.568782	−	2.83121i	−0.0262359	−	0.130594i
$471$	12.5259	−	4.31919i	0.577161	−	0.199018i
$472$		−	31.2997i		−	1.44068i
$473$		−	17.7706i		−	0.817095i
$474$	26.8707	−	9.26561i	1.23421	−	0.425584i
$475$	0.308048	−	2.41094i	0.0141342	−	0.110622i
$476$	−2.49605	+	1.11884i	−0.114406	+	0.0512821i
$477$	9.48147	−	23.5273i	0.434127	−	1.07724i
$478$	−10.8161	−	6.24470i	−0.494719	−	0.285626i
$479$	10.9040	−	18.8864i	0.498219	−	0.862940i	−0.501779	−	0.864996i	$-0.667321\pi$
$479$	10.9040	−	18.8864i	0.498219	−	0.862940i	0.999998	+	0.00205577i	$0.000654372\pi$
$480$	−8.60251	−	14.6716i	−0.392649	−	0.669665i
$481$	3.06037	+	5.30071i	0.139541	+	0.241691i
$482$	−0.869929	−	0.502254i	−0.0396242	−	0.0228770i
$483$	19.2023	+	20.4703i	0.873736	+	0.931430i
$484$	−6.94947	−	12.0368i	−0.315885	−	0.547129i
$485$	22.6396	+	25.7163i	1.02801	+	1.16772i
$486$	1.49830	+	16.7007i	0.0679642	+	0.757557i
$487$	−7.07095	+	4.08241i	−0.320415	+	0.184992i	−0.651578	−	0.758582i	$-0.725893\pi$
$487$	−7.07095	+	4.08241i	−0.320415	+	0.184992i	0.331162	+	0.943574i	$0.392559\pi$
$488$		−	1.48264i		−	0.0671162i
$489$	2.64960	−	13.6632i	0.119819	−	0.617872i
$490$	16.8363	+	0.103560i	0.760586	+	0.00467834i
$491$	19.6284	−	33.9974i	0.885818	−	1.53428i	0.0410454	−	0.999157i	$-0.486931\pi$
$491$	19.6284	−	33.9974i	0.885818	−	1.53428i	0.844773	−	0.535125i	$-0.179735\pi$
$492$	13.8682	+	2.68935i	0.625227	+	0.121245i
$493$	7.25887	+	4.19091i	0.326923	+	0.188749i
$494$	0.327394	+	0.567062i	0.0147301	+	0.0255133i
$495$	−33.1715	+	11.6880i	−1.49095	+	0.525338i
$496$	−1.65184			−0.0741696
$497$	28.7626	+	2.94994i	1.29018	+	0.132323i
$498$	10.6460	−	12.2577i	0.477058	−	0.549283i
$499$	11.4824	+	19.8881i	0.514022	+	0.890313i	0.999868	+	0.0162678i	$0.00517844\pi$
$499$	11.4824	+	19.8881i	0.514022	+	0.890313i	−0.485845	+	0.874045i	$0.661488\pi$
$500$	−5.28090	−	7.80628i	−0.236169	−	0.349108i
$501$	−6.57116	+	33.8856i	−0.293578	+	1.51390i
$502$			19.3472i			0.863509i
$503$		−	2.13046i		−	0.0949926i	−0.998871	−	0.0474963i	$-0.984876\pi$
$503$		−	2.13046i		−	0.0949926i	0.998871	−	0.0474963i	$-0.0151242\pi$
$504$	12.9324	+	20.5404i	0.576053	+	0.914943i
$505$	−27.9652	−	9.43342i	−1.24443	−	0.419781i
$506$	34.5407			1.53552
$507$	−12.9837	+	14.9494i	−0.576627	+	0.663925i
$508$		−	1.01036i		−	0.0448274i
$509$	6.95005	+	12.0378i	0.308056	+	0.533568i	0.977937	−	0.208900i	$-0.0669884\pi$
$509$	6.95005	+	12.0378i	0.308056	+	0.533568i	−0.669881	+	0.742468i	$0.733655\pi$
$510$	4.44186	+	2.52490i	0.196689	+	0.111804i
$511$	−8.90694	+	3.99250i	−0.394020	+	0.176618i
$512$			16.8481i			0.744587i
$513$	−2.24907	+	1.14971i	−0.0992986	+	0.0507611i
$514$	−8.52026	−	14.7575i	−0.375812	−	0.650926i
$515$	−25.9363	−	29.4611i	−1.14289	−	1.29821i
$516$	−3.73641	−	3.24511i	−0.164486	−	0.142858i
$517$	−5.45141	−	3.14737i	−0.239753	−	0.138421i
$518$	8.14778	−	11.2740i	0.357993	−	0.495350i
$519$	−5.91529	+	2.03972i	−0.259652	+	0.0895338i
$520$	8.11379	+	2.73700i	0.355813	+	0.120025i
$521$	−4.12704	−	7.14824i	−0.180809	−	0.313170i	0.761347	−	0.648344i	$-0.224538\pi$
$521$	−4.12704	−	7.14824i	−0.180809	−	0.313170i	−0.942156	+	0.335174i	$0.891205\pi$
$522$	8.24344	−	20.4553i	0.360806	−	0.895302i
$523$	7.38099	+	4.26142i	0.322748	+	0.186339i	0.652617	−	0.757688i	$-0.273671\pi$
$523$	7.38099	+	4.26142i	0.322748	+	0.186339i	−0.329869	+	0.944027i	$0.607004\pi$
$524$	0.683109	+	1.18318i	0.0298418	+	0.0516875i
$525$	13.4316	+	18.5632i	0.586205	+	0.810163i
$526$	6.77315	−	11.7314i	0.295324	−	0.511515i
$527$	−1.09419	+	0.631729i	−0.0476635	+	0.0275185i
$528$	14.2945	+	2.77202i	0.622088	+	0.120637i
$529$	7.25624	−	12.5682i	0.315489	−	0.546443i
$530$	−15.2645	+	13.4383i	−0.663048	+	0.583720i
$531$	−24.1796	+	18.9256i	−1.04930	+	0.821301i
$532$	−0.635050	+	0.878711i	−0.0275329	+	0.0380969i
$533$	−10.4927	+	6.05797i	−0.454490	+	0.262400i
$534$	0.326146	−	1.68184i	0.0141137	−	0.0727805i
$535$	−3.80305	+	11.2741i	−0.164420	+	0.487420i
$536$	18.3162			0.791140
$537$	17.6747	−	20.3505i	0.762718	−	0.878190i
$538$	4.33571	−	2.50322i	0.186926	−	0.107922i
$539$	24.4198	−	27.3968i	1.05183	−	1.18006i
$540$	−3.59998	+	9.10890i	−0.154919	+	0.391985i
$541$	−1.18482	+	2.05217i	−0.0509394	+	0.0882296i	−0.890371	−	0.455236i	$-0.849555\pi$
$541$	−1.18482	+	2.05217i	−0.0509394	+	0.0882296i	0.839431	+	0.543466i	$0.182888\pi$
$542$	−11.3460	−	6.55063i	−0.487353	−	0.281374i
$543$	7.14494	+	20.7207i	0.306619	+	0.889209i
$544$	2.69287	+	4.66419i	0.115456	+	0.199975i
$545$	4.78355	−	4.21124i	0.204905	−	0.180390i
$546$	−5.90831	−	1.78727i	−0.252853	−	0.0764879i
$547$	26.2840	−	15.1751i	1.12382	−	0.648840i	0.181449	−	0.983400i	$-0.441921\pi$
$547$	26.2840	−	15.1751i	1.12382	−	0.648840i	0.942374	+	0.334560i	$0.108588\pi$
$548$	3.34784	+	1.93288i	0.143013	+	0.0825684i
$549$	−1.14537	+	0.896492i	−0.0488832	+	0.0382614i
$550$	27.9702	+	3.57378i	1.19266	+	0.152387i
$551$	3.32219			0.141530
$552$	21.2723	−	24.4929i	0.905411	−	1.04249i
$553$	−40.1532	−	4.11819i	−1.70749	−	0.175123i
$554$	−6.90636	+	11.9622i	−0.293423	+	0.508224i
$555$	18.9297	−	0.127091i	0.803520	−	0.00539472i
$556$	−8.74738	+	15.1509i	−0.370971	+	0.642541i
$557$	−33.3219	+	19.2384i	−1.41189	+	0.815157i	−0.995567	−	0.0940582i	$-0.970016\pi$
$557$	−33.3219	+	19.2384i	−1.41189	+	0.815157i	−0.416327	+	0.909215i	$0.636683\pi$
$558$	2.04899	+	2.61781i	0.0867405	+	0.110821i
$559$	4.24451			0.179524
$560$	−0.909773	−	9.44237i	−0.0384449	−	0.399013i
$561$	10.5289	−	3.63059i	0.444530	−	0.153284i
$562$	19.6003	−	11.3162i	0.826787	−	0.477346i
$563$			30.7136i			1.29442i	0.762310	+	0.647211i	$0.224065\pi$
$563$			30.7136i			1.29442i	−0.762310	+	0.647211i	$0.775935\pi$
$564$	−1.65724	+	0.571454i	−0.0697826	+	0.0240625i
$565$	−11.5123	+	34.1280i	−0.484326	+	1.43578i
$566$	−14.3393			−0.602727
$567$	8.04821	−	22.4104i	0.337993	−	0.941149i
$568$		−	33.4191i		−	1.40224i
$569$	14.5820			0.611307			0.305654	−	0.952143i	$-0.401125\pi$
$569$	14.5820			0.611307			0.305654	+	0.952143i	$0.401125\pi$
$570$	2.02507	−	0.0135960i	0.0848209	−	0.000569475i
$571$	1.08723			0.0454991			0.0227495	−	0.999741i	$-0.492758\pi$
$571$	1.08723			0.0454991			0.0227495	+	0.999741i	$0.492758\pi$
$572$	4.79306	−	2.76727i	0.200408	−	0.115705i
$573$	4.65699	+	13.5055i	0.194549	+	0.564201i
$574$	22.3167	+	16.1285i	0.931482	+	0.673188i
$575$	18.5497	−	24.3664i	0.773574	−	1.01615i
$576$	18.7349	−	14.6640i	0.780620	−	0.610999i
$577$	−34.8546	+	20.1233i	−1.45102	+	0.837745i	−0.998539	−	0.0540306i	$-0.982793\pi$
$577$	−34.8546	+	20.1233i	−1.45102	+	0.837745i	−0.452478	+	0.891776i	$0.649460\pi$
$578$	14.4350	+	8.33406i	0.600417	+	0.346651i
$579$	−27.4064	+	9.45034i	−1.13897	+	0.392743i
$580$	9.66915	−	8.51232i	0.401490	−	0.353455i
$581$	−21.0389	+	9.43061i	−0.872841	+	0.391247i
$582$	−18.7189	+	21.5529i	−0.775925	+	0.893396i
$583$			44.3303i			1.83598i
$584$	5.64094	+	9.77040i	0.233424	+	0.404302i
$585$	−2.79168	−	7.92300i	−0.115422	−	0.327576i
$586$	3.51396	−	6.08636i	0.145160	−	0.251425i
$587$	−23.5832	+	13.6158i	−0.973384	+	0.561983i	−0.900266	−	0.435340i	$-0.856628\pi$
$587$	−23.5832	+	13.6158i	−0.973384	+	0.561983i	−0.0731177	+	0.997323i	$0.523295\pi$
$588$	−1.30106	−	10.1374i	−0.0536549	−	0.418059i
$589$	−0.250390	+	0.433688i	−0.0103171	+	0.0178698i
$590$	24.1357	−	4.84880i	0.993651	−	0.199622i
$591$	−7.94097	+	2.73822i	−0.326648	+	0.112635i
$592$	−6.78721	−	3.91860i	−0.278953	−	0.161053i
$593$	−38.1366	−	22.0182i	−1.56608	−	0.904179i	−0.996619	−	0.0821636i	$-0.973817\pi$
$593$	−38.1366	−	22.0182i	−1.56608	−	0.904179i	−0.569465	−	0.822015i	$-0.692850\pi$
$594$	−13.3383	−	26.0923i	−0.547275	−	1.07058i
$595$	−4.21378	−	5.90674i	−0.172748	−	0.242153i
$596$	−3.87562	−	6.71277i	−0.158751	−	0.274966i
$597$	−26.8150	+	30.8747i	−1.09747	+	1.26362i
$598$			8.25002i			0.337368i
$599$	−23.8670			−0.975180			−0.487590	−	0.873073i	$-0.662124\pi$
$599$	−23.8670			−0.975180			−0.487590	+	0.873073i	$0.662124\pi$
$600$	19.7600	−	17.6328i	0.806700	−	0.719856i
$601$	−17.8029	−	30.8356i	−0.726196	−	1.25781i	−0.958480	−	0.285161i	$-0.907953\pi$
$601$	−17.8029	−	30.8356i	−0.726196	−	1.25781i	0.232283	−	0.972648i	$-0.425380\pi$
$602$	−3.94558	−	8.80227i	−0.160810	−	0.358754i
$603$	−11.0750	−	14.1496i	−0.451011	−	0.576217i
$604$	3.81224	−	6.60299i	0.155118	−	0.268672i
$605$	27.6725	−	24.3618i	1.12505	−	0.990446i
$606$	4.68141	−	24.1407i	0.190169	−	0.980650i
$607$	25.2228	−	14.5624i	1.02376	−	0.591068i	0.108569	−	0.994089i	$-0.465373\pi$
$607$	25.2228	−	14.5624i	1.02376	−	0.591068i	0.915191	+	0.403021i	$0.132040\pi$
$608$	1.84868	+	1.06734i	0.0749739	+	0.0432862i
$609$	−22.8417	+	21.4268i	−0.925591	+	0.868258i
$610$	1.14329	−	0.229684i	0.0462905	−	0.00929965i
$611$	0.751749	−	1.30207i	0.0304125	−	0.0526760i
$612$	1.15933	−	2.87676i	0.0468632	−	0.116286i
$613$	−27.5261	+	15.8922i	−1.11177	+	0.641880i	−0.939287	−	0.343133i	$-0.888512\pi$
$613$	−27.5261	+	15.8922i	−1.11177	+	0.641880i	−0.172481	+	0.985013i	$0.555178\pi$
$614$	−9.53753			−0.384903
$615$	0.251576	+	37.4711i	0.0101445	+	1.51098i
$616$	−34.3806	−	24.8471i	−1.38524	−	1.00112i
$617$	15.5032	+	8.95075i	0.624134	+	0.360344i	0.778477	−	0.627674i	$-0.215993\pi$
$617$	15.5032	+	8.95075i	0.624134	+	0.360344i	−0.154343	+	0.988017i	$0.549326\pi$
$618$	21.4447	−	24.6914i	0.862634	−	0.993233i
$619$	−23.4662	+	40.6447i	−0.943186	+	1.63365i	−0.183844	+	0.982955i	$0.558854\pi$
$619$	−23.4662	+	40.6447i	−0.943186	+	1.63365i	−0.759342	+	0.650691i	$0.774479\pi$
$620$	0.382469	+	1.90380i	0.0153603	+	0.0764585i
$621$	−31.7837	−	1.62348i	−1.27543	−	0.0651478i
$622$		−	2.19555i		−	0.0880335i
$623$	−1.42505	+	1.97182i	−0.0570934	+	0.0789995i
$624$	−0.662095	+	3.41424i	−0.0265050	+	0.136679i
$625$	17.5422	−	17.8121i	0.701688	−	0.712485i
$626$	4.16189			0.166343
$627$	2.89459	−	3.33282i	0.115599	−	0.133100i
$628$			6.44848i			0.257322i
$629$	−5.99452			−0.239017
$630$	−13.8356	+	13.1544i	−0.551225	+	0.524083i
$631$	−2.53639			−0.100972			−0.0504861	−	0.998725i	$-0.516077\pi$
$631$	−2.53639			−0.100972			−0.0504861	+	0.998725i	$0.516077\pi$
$632$			46.6539i			1.85579i
$633$	−19.1996	−	3.72323i	−0.763117	−	0.147985i
$634$	−5.35565			−0.212700
$635$	2.62757	−	0.527871i	0.104272	−	0.0209479i
$636$	9.32077	+	8.09520i	0.369593	+	0.320995i
$637$	6.54372	+	5.83265i	0.259271	+	0.231098i
$638$			38.5420i			1.52589i
$639$	−25.8169	+	20.2071i	−1.02130	+	0.799382i
$640$	0.553139	−	0.111124i	0.0218647	−	0.00439257i
$641$	−14.2302	+	24.6475i	−0.562061	+	0.973518i	0.435256	+	0.900307i	$0.356658\pi$
$641$	−14.2302	+	24.6475i	−0.562061	+	0.973518i	−0.997316	+	0.0732107i	$0.976675\pi$
$642$	−9.73224	−	1.88729i	−0.384101	−	0.0744856i
$643$	24.7884	+	14.3116i	0.977560	+	0.564395i	0.901533	−	0.432711i	$-0.142443\pi$
$643$	24.7884	+	14.3116i	0.977560	+	0.564395i	0.0760274	+	0.997106i	$0.475776\pi$
$644$	−12.4650	+	5.58741i	−0.491192	+	0.220175i
$645$	6.48721	−	11.4124i	0.255434	−	0.449365i
$646$	−0.641285			−0.0252310
$647$	−10.8576	+	6.26864i	−0.426857	+	0.246446i	−0.698007	−	0.716091i	$-0.745929\pi$
$647$	−10.8576	+	6.26864i	−0.426857	+	0.246446i	0.271150	+	0.962537i	$0.412596\pi$
$648$	−26.7166	−	6.61108i	−1.04953	−	0.259708i
$649$	26.8310	−	46.4726i	1.05321	−	1.82421i
$650$	−0.853597	+	6.68068i	−0.0334808	+	0.262038i
$651$	−1.07557	−	4.59673i	−0.0421547	−	0.180160i
$652$	5.86616	+	3.38683i	0.229737	+	0.132638i
$653$	−19.4683	+	11.2400i	−0.761853	+	0.439856i	−0.829961	−	0.557822i	$-0.811637\pi$
$653$	−19.4683	+	11.2400i	−0.761853	+	0.439856i	0.0681075	+	0.997678i	$0.478304\pi$
$654$	4.00910	+	3.48195i	0.156768	+	0.136155i
$655$	−2.72012	+	2.39468i	−0.106284	+	0.0935678i
$656$	7.75683	−	13.4352i	0.302853	−	0.524558i
$657$	4.13698	−	10.2655i	0.161399	−	0.400494i
$658$	−3.39903	−	0.348611i	−0.132508	−	0.0135903i
$659$	−7.03059	−	12.1773i	−0.273873	−	0.474362i	0.695977	−	0.718064i	$-0.254971\pi$
$659$	−7.03059	−	12.1773i	−0.273873	−	0.474362i	−0.969850	+	0.243702i	$0.921638\pi$
$660$	−0.114919	−	17.1168i	−0.00447323	−	0.666269i
$661$	25.6461			0.997516			0.498758	−	0.866741i	$-0.333790\pi$
$661$	25.6461			0.997516			0.498758	+	0.866741i	$0.333790\pi$
$662$		−	32.2289i		−	1.25261i
$663$	0.867165	+	2.51482i	0.0336779	+	0.0976676i
$664$	13.3244	+	23.0785i	0.517086	+	0.895619i
$665$	−2.61699	−	1.19244i	−0.101482	−	0.0462408i
$666$	2.20890	+	15.6170i	0.0855933	+	0.605148i
$667$	36.2502	+	20.9290i	1.40361	+	0.810376i
$668$	−14.5484	−	8.39954i	−0.562896	−	0.324988i
$669$	−19.8365	−	17.2283i	−0.766925	−	0.666083i
$670$	2.83746	+	14.1239i	0.109621	+	0.545656i
$671$	1.27097	−	2.20138i	0.0490651	−	0.0849832i
$672$	−19.5945	+	4.58481i	−0.755873	+	0.176863i
$673$	−22.6648	+	13.0855i	−0.873663	+	0.504409i	−0.868564	−	0.495578i	$-0.834956\pi$
$673$	−22.6648	+	13.0855i	−0.873663	+	0.504409i	−0.00509891	+	0.999987i	$0.501623\pi$
$674$	−8.47916	+	14.6863i	−0.326605	+	0.565696i
$675$	−25.5697	−	4.60318i	−0.984179	−	0.177177i
$676$	−4.81838	−	8.34567i	−0.185322	−	0.320987i
$677$			16.0281i			0.616011i	0.951385	+	0.308006i	$0.0996616\pi$
$677$			16.0281i			0.616011i	−0.951385	+	0.308006i	$0.900338\pi$
$678$	−29.4607	−	5.71308i	−1.13143	−	0.219409i
$679$	36.9929	−	16.5819i	1.41966	−	0.636355i
$680$	−6.29467	+	5.54157i	−0.241390	+	0.212510i
$681$	7.83181	−	40.3864i	0.300116	−	1.54761i
$682$	−5.03138	−	2.90487i	−0.192661	−	0.111233i
$683$	44.4988	−	25.6914i	1.70270	−	0.983055i	0.759695	−	0.650280i	$-0.225348\pi$
$683$	44.4988	−	25.6914i	1.70270	−	0.983055i	0.943006	−	0.332775i	$-0.107985\pi$
$684$	−0.172165	−	1.21722i	−0.00658291	−	0.0465414i
$685$	−3.27759	+	9.71635i	−0.125230	+	0.371242i
$686$	6.01289	−	18.9922i	0.229573	−	0.725127i
$687$	−8.75317	+	10.0784i	−0.333954	+	0.384513i
$688$	−4.70669	+	2.71741i	−0.179441	+	0.103600i
$689$	−10.5883			−0.403382
$690$	22.1823	+	12.6091i	0.844464	+	0.480021i
$691$	1.75492			0.0667603			0.0333802	−	0.999443i	$-0.489373\pi$
$691$	1.75492			0.0667603			0.0333802	+	0.999443i	$0.489373\pi$
$692$		−	3.04527i		−	0.115764i
$693$	1.59366	+	41.5837i	0.0605380	+	1.57963i
$694$	17.7854			0.675124
$695$	−43.9720	−	14.8330i	−1.66795	−	0.562646i
$696$	27.3302	+	23.7366i	1.03595	+	0.899734i
$697$		−	11.8661i		−	0.449460i
$698$	−29.4133	+	16.9818i	−1.11331	+	0.642770i
$699$	−2.96454	+	15.2873i	−0.112129	+	0.578219i
$700$	−10.6720	+	3.23485i	−0.403364	+	0.122266i
$701$	32.1905			1.21582			0.607910	−	0.794006i	$-0.292008\pi$
$701$	32.1905			1.21582			0.607910	+	0.794006i	$0.292008\pi$
$702$	6.23212	−	3.18584i	0.235216	−	0.120242i
$703$	−2.05765	+	1.18798i	−0.0776057	+	0.0448057i
$704$	−20.7893	+	36.0080i	−0.783525	+	1.35710i
$705$	−2.35198	−	4.01132i	−0.0885808	−	0.151075i
$706$	−8.56277	+	14.8312i	−0.322264	+	0.558178i
$707$	−20.4548	+	28.3030i	−0.769281	+	1.06444i
$708$	−4.87158	−	14.1278i	−0.183085	−	0.530956i
$709$	42.9932			1.61464			0.807322	−	0.590111i	$-0.200916\pi$
$709$	42.9932			1.61464			0.807322	+	0.590111i	$0.200916\pi$
$710$	25.7701	−	5.17714i	0.967133	−	0.194294i
$711$	36.0410	−	28.2096i	1.35164	−	1.05794i
$712$	2.43526	+	1.40600i	0.0912651	+	0.0526920i
$713$	−5.46427	+	3.15480i	−0.204639	+	0.118148i
$714$	4.40914	−	4.13603i	0.165008	−	0.154787i
$715$	9.70082	+	11.0192i	0.362790	+	0.412094i
$716$	6.55924	+	11.3609i	0.245130	+	0.424578i
$717$	−19.7431	−	3.82861i	−0.737319	−	0.142982i
$718$	−8.63932	−	4.98791i	−0.322416	−	0.186147i
$719$	5.96616	−	10.3337i	0.222500	−	0.385382i	−0.733066	−	0.680157i	$-0.761911\pi$
$719$	5.96616	−	10.3337i	0.222500	−	0.385382i	0.955567	+	0.294775i	$0.0952448\pi$
$720$	8.16811	+	6.99845i	0.304407	+	0.260817i
$721$	−42.3797	+	18.9965i	−1.57830	+	0.707468i
$722$	17.4792	−	10.0916i	0.650507	−	0.375570i
$723$	−1.58791	−	0.307931i	−0.0590551	−	0.0114521i
$724$	−10.6673			−0.396447
$725$	27.1891	+	20.6985i	1.00978	+	0.768724i
$726$	23.1924	+	20.1429i	0.860750	+	0.747571i
$727$	−20.5189	+	11.8466i	−0.761003	+	0.439365i	−0.829656	−	0.558275i	$-0.811463\pi$
$727$	−20.5189	+	11.8466i	−0.761003	+	0.439365i	0.0686526	+	0.997641i	$0.478130\pi$
$728$	5.93472	−	8.21180i	0.219955	−	0.304350i
$729$	11.0472	+	24.6365i	0.409157	+	0.912464i
$730$	−6.66025	+	5.86341i	−0.246507	+	0.217015i
$731$	−2.07849	+	3.60006i	−0.0768759	+	0.133153i
$732$	−0.230763	−	0.669225i	−0.00852926	−	0.0247353i
$733$	32.8763	−	18.9812i	1.21432	−	0.701085i	0.250619	−	0.968086i	$-0.419366\pi$
$733$	32.8763	−	18.9812i	1.21432	−	0.701085i	0.963696	+	0.267000i	$0.0860325\pi$
$734$	−2.79533	+	4.84165i	−0.103178	+	0.178709i
$735$	25.6838	−	8.67995i	0.947362	−	0.320165i
$736$	13.4480	+	23.2925i	0.495698	+	0.858575i
$737$	27.1953	+	15.7012i	1.00175	+	0.578361i
$738$	−30.9138	+	4.37251i	−1.13795	+	0.160954i
$739$	16.3851	+	28.3798i	0.602735	+	1.04397i	0.992405	+	0.123013i	$0.0392556\pi$
$739$	16.3851	+	28.3798i	0.602735	+	1.04397i	−0.389670	+	0.920954i	$0.627411\pi$
$740$	−2.94481	+	8.72983i	−0.108253	+	0.320915i
$741$	0.796042	+	0.691372i	0.0292433	+	0.0253982i
$742$	9.84257	+	21.9580i	0.361332	+	0.806103i
$743$	−6.39744	−	3.69357i	−0.234699	−	0.135504i	0.378039	−	0.925790i	$-0.376599\pi$
$743$	−6.39744	−	3.69357i	−0.234699	−	0.135504i	−0.612738	+	0.790286i	$0.709932\pi$
$744$	−5.15849	+	1.77876i	−0.189119	+	0.0652125i
$745$	15.4326	−	13.5862i	0.565405	−	0.497760i
$746$	−10.8955	−	18.8716i	−0.398914	−	0.690940i
$747$	9.77187	−	24.2479i	0.357534	−	0.887184i
$748$			5.42042i			0.198190i
$749$	11.4103	+	8.24627i	0.416922	+	0.301312i
$750$	16.6581	+	12.5057i	0.608267	+	0.456644i
$751$	9.89776	+	17.1434i	0.361174	+	0.625572i	0.988154	−	0.153463i	$-0.0490426\pi$
$751$	9.89776	+	17.1434i	0.361174	+	0.625572i	−0.626980	+	0.779035i	$0.715709\pi$
$752$			1.92513i			0.0702023i
$753$	10.1556	+	29.4518i	0.370092	+	1.07328i
$754$	−9.20574			−0.335253
$755$	19.1637	+	6.46442i	0.697437	+	0.235264i
$756$	9.03428	+	7.25855i	0.328574	+	0.263991i
$757$			29.7453i			1.08111i	0.841308	+	0.540556i	$0.181786\pi$
$757$			29.7453i			1.08111i	−0.841308	+	0.540556i	$0.818214\pi$
$758$		−	12.2081i		−	0.443419i
$759$	52.5804	−	18.1309i	1.90855	−	0.658109i
$760$	−1.06246	+	3.14964i	−0.0385394	+	0.114249i
$761$	9.90229	+	17.1513i	0.358958	+	0.621733i	0.987787	−	0.155810i	$-0.0497988\pi$
$761$	9.90229	+	17.1513i	0.358958	+	0.621733i	−0.628829	+	0.777544i	$0.716465\pi$
$762$	0.727933	+	2.11104i	0.0263702	+	0.0764749i
$763$	−3.08443	−	6.88112i	−0.111664	−	0.249113i
$764$	−6.95282			−0.251544
$765$	8.08709	+	1.51200i	0.292389	+	0.0546664i
$766$	−13.4939	−	23.3721i	−0.487554	−	0.844468i
$767$	11.1000	+	6.40857i	0.400797	+	0.231400i
$768$	9.10868	+	26.4156i	0.328681	+	0.953192i
$769$	−18.1874	+	31.5016i	−0.655856	+	1.13598i	0.325823	+	0.945431i	$0.394359\pi$
$769$	−18.1874	+	31.5016i	−0.655856	+	1.13598i	−0.981678	+	0.190545i	$0.938975\pi$
$770$	13.8339	−	30.3607i	0.498541	−	1.09412i
$771$	−20.7166	−	17.9926i	−0.746090	−	0.647988i
$772$		−	14.1092i		−	0.507802i
$773$	−26.5351	+	15.3201i	−0.954403	+	0.551025i	−0.894446	−	0.447176i	$-0.852430\pi$
$773$	−26.5351	+	15.3201i	−0.954403	+	0.551025i	−0.0599569	+	0.998201i	$0.519096\pi$
$774$	10.1448	+	4.08836i	0.364649	+	0.146953i
$775$	−4.75126	+	1.98932i	−0.170670	+	0.0714584i
$776$	−23.4283	−	40.5791i	−0.841028	−	1.45670i
$777$	6.48529	−	21.4390i	0.232659	−	0.769119i
$778$	−13.6865	−	7.90191i	−0.490685	−	0.283297i
$779$	−2.35160	−	4.07310i	−0.0842549	−	0.145934i
$780$	4.08833	−	0.0274485i	0.146386	−	0.000982813i
$781$	28.6479	−	49.6196i	1.02510	−	1.77553i
$782$	−6.99740	−	4.03995i	−0.250226	−	0.144468i
$783$	1.81155	−	35.4656i	0.0647394	−	1.26744i
$784$	−10.9904	−	2.27836i	−0.392515	−	0.0813701i
$785$	−16.7701	+	3.36907i	−0.598551	+	0.120247i
$786$	−2.27973	−	1.97997i	−0.0813154	−	0.0706233i
$787$		−	21.0151i		−	0.749109i	−0.927205	−	0.374555i	$-0.877796\pi$
$787$		−	21.0151i		−	0.749109i	0.927205	−	0.374555i	$-0.122204\pi$
$788$		−	4.08812i		−	0.145633i
$789$	4.15261	−	21.4138i	0.147837	−	0.762352i
$790$	−35.9756	+	7.22740i	−1.27995	+	0.257139i
$791$	34.5403	+	24.9625i	1.22811	+	0.887564i
$792$	47.6251	−	6.73618i	1.69228	−	0.239360i
$793$	0.525798	+	0.303570i	0.0186716	+	0.0107801i
$794$	−7.00769	+	12.1377i	−0.248694	+	0.430750i
$795$	−16.1829	+	28.4693i	−0.573948	+	1.00970i
$796$	−9.95132	−	17.2362i	−0.352715	−	0.610920i
$797$	−19.8458	−	11.4580i	−0.702975	−	0.405863i	0.105480	−	0.994421i	$-0.466362\pi$
$797$	−19.8458	−	11.4580i	−0.702975	−	0.405863i	−0.808454	+	0.588559i	$0.799696\pi$
$798$	0.693788	−	2.29351i	0.0245598	−	0.0811894i
$799$	0.736247	+	1.27522i	0.0260466	+	0.0451140i
$800$	8.47987	+	20.2532i	0.299809	+	0.716058i
$801$	−0.386339	−	2.73143i	−0.0136506	−	0.0965103i
$802$	13.9061	−	8.02870i	0.491042	−	0.283503i
$803$			19.3423i			0.682576i
$804$	8.26744	−	2.85079i	0.291570	−	0.100540i
$805$	−21.0433	−	29.4978i	−0.741677	−	1.03966i
$806$	0.693826	−	1.20174i	0.0244390	−	0.0423296i
$807$	5.28617	−	6.08647i	0.186082	−	0.214254i
$808$	34.9550	+	20.1813i	1.22971	+	0.709975i
$809$	12.0649	+	20.8971i	0.424180	+	0.734702i	0.996344	−	0.0854378i	$-0.0272289\pi$
$809$	12.0649	+	20.8971i	0.424180	+	0.734702i	−0.572163	+	0.820140i	$0.693896\pi$
$810$	0.959101	−	21.6258i	0.0336994	−	0.759853i
$811$	4.77761			0.167764			0.0838822	−	0.996476i	$-0.473268\pi$
$811$	4.77761			0.167764			0.0838822	+	0.996476i	$0.473268\pi$
$812$	−6.23467	−	13.9091i	−0.218794	−	0.488112i
$813$	−20.7103	−	4.01618i	−0.726341	−	0.140854i
$814$	−13.7822	−	23.8716i	−0.483068	−	0.836698i
$815$	−5.74306	+	17.0252i	−0.201170	+	0.596366i
$816$	−2.57162	−	2.23348i	−0.0900248	−	0.0781876i
$817$			1.64765i			0.0576440i
$818$		−	1.94367i		−	0.0679590i
$819$	−9.93224	+	0.380644i	−0.347061	+	0.0133008i
$820$	−17.2806	−	5.82922i	−0.603465	−	0.203565i
$821$	−6.51994			−0.227548			−0.113774	−	0.993507i	$-0.536294\pi$
$821$	−6.51994			−0.227548			−0.113774	+	0.993507i	$0.536294\pi$
$822$	−8.38755	−	1.62653i	−0.292550	−	0.0567318i
$823$			5.57445i			0.194313i	0.995269	+	0.0971565i	$0.0309747\pi$
$823$			5.57445i			0.194313i	−0.995269	+	0.0971565i	$0.969025\pi$
$824$	26.8399	+	46.4881i	0.935013	+	1.61949i
$825$	44.4543	−	9.24168i	1.54770	−	0.321754i
$826$	2.97187	−	28.9763i	0.103405	−	1.00822i
$827$			4.68443i			0.162894i	0.996678	+	0.0814469i	$0.0259541\pi$
$827$			4.68443i			0.162894i	−0.996678	+	0.0814469i	$0.974046\pi$
$828$	5.78960	−	14.3663i	0.201202	−	0.499263i
$829$	−2.03293	−	3.52113i	−0.0706064	−	0.122294i	0.828561	−	0.559899i	$-0.189160\pi$
$829$	−2.03293	−	3.52113i	−0.0706064	−	0.122294i	−0.899167	+	0.437605i	$0.855827\pi$
$830$	−15.7321	+	13.8499i	−0.546068	+	0.480735i
$831$	−4.23428	+	21.8350i	−0.146885	+	0.757447i
$832$	−8.60051	−	4.96551i	−0.298169	−	0.172148i
$833$	−8.15146	+	2.69398i	−0.282431	+	0.0933408i
$834$	7.36098	−	37.9585i	0.254890	−	1.31439i
$835$	14.2431	−	42.2235i	0.492904	−	1.46120i
$836$	1.07421	+	1.86059i	0.0371523	+	0.0643497i
$837$	4.49325	+	2.90949i	0.155309	+	0.100567i
$838$	−22.1215	−	12.7718i	−0.764173	−	0.441196i
$839$	25.2070	+	43.6597i	0.870241	+	1.50730i	0.861747	+	0.507338i	$0.169370\pi$
$839$	25.2070	+	43.6597i	0.870241	+	1.50730i	0.00849402	+	0.999964i	$0.497296\pi$
$840$	−13.0090	−	28.5077i	−0.448854	−	0.983610i
$841$	−8.85356	+	15.3348i	−0.305295	+	0.528787i
$842$	23.1549	−	13.3685i	0.797969	−	0.460708i
$843$	23.8970	−	27.5148i	0.823055	−	0.947662i
$844$	4.75919	−	8.24316i	0.163818	−	0.283741i
$845$	19.1866	−	16.8911i	0.660039	−	0.581071i
$846$	3.05093	−	2.38799i	0.104893	−	0.0821007i
$847$	−17.8433	−	39.8069i	−0.613102	−	1.36778i
$848$	11.7412	−	6.77881i	0.403196	−	0.232785i
$849$	−21.8284	+	7.52691i	−0.749149	+	0.258323i
$850$	−5.24834	−	3.99545i	−0.180017	−	0.137043i
$851$	−29.9361			−1.02620
$852$	−5.20146	−	15.0845i	−0.178199	−	0.516786i
$853$	16.7252	−	9.65632i	0.572661	−	0.330626i	−0.185550	−	0.982635i	$-0.559407\pi$
$853$	16.7252	−	9.65632i	0.572661	−	0.330626i	0.758212	+	0.652009i	$0.226073\pi$
$854$	0.140775	−	1.37259i	0.00481724	−	0.0469691i
$855$	3.07558	−	1.08368i	0.105183	−	0.0370612i
$856$	8.13601	−	14.0920i	0.278083	−	0.481654i
$857$	12.3563	+	7.13394i	0.422085	+	0.243691i	0.695969	−	0.718072i	$-0.254975\pi$
$857$	12.3563	+	7.13394i	0.422085	+	0.243691i	−0.273884	+	0.961763i	$0.588308\pi$
$858$	−8.02086	+	9.23518i	−0.273828	+	0.315284i
$859$	−3.66089	−	6.34085i	−0.124908	−	0.216347i	0.796789	−	0.604258i	$-0.206530\pi$
$859$	−3.66089	−	6.34085i	−0.124908	−	0.216347i	−0.921697	+	0.387911i	$0.873197\pi$
$860$	4.22171	+	4.79544i	0.143959	+	0.163523i
$861$	42.4383	+	12.8376i	1.44629	+	0.437504i
$862$	0.0935233	−	0.0539957i	0.00318542	−	0.00183910i
$863$	−45.8510	−	26.4721i	−1.56079	−	0.901121i	−0.997177	−	0.0750805i	$-0.976079\pi$
$863$	−45.8510	−	26.4721i	−1.56079	−	0.901121i	−0.563610	−	0.826041i	$-0.690588\pi$
$864$	12.4023	−	19.1534i	0.421934	−	0.651610i
$865$	7.91963	−	1.59103i	0.269275	−	0.0540967i
$866$	−35.3101			−1.19988
$867$	26.3487	+	5.10959i	0.894850	+	0.173531i
$868$	2.28563	+	0.234418i	0.0775792	+	0.00795667i
$869$	−39.9931	+	69.2700i	−1.35667	+	2.34983i
$870$	−14.0698	+	24.7520i	−0.477012	+	0.839170i
$871$	−3.75022	+	6.49558i	−0.127072	+	0.220094i
$872$	−7.54819	+	4.35795i	−0.255614	+	0.147579i
$873$	−17.1820	+	42.6353i	−0.581521	+	1.44298i
$874$	−3.20252			−0.108327
$875$	−13.9883	−	26.0639i	−0.472892	−	0.881120i
$876$	4.06686	+	3.53211i	0.137406	+	0.119339i
$877$	−37.6161	+	21.7177i	−1.27021	+	0.733354i	−0.975027	−	0.222088i	$-0.928713\pi$
$877$	−37.6161	+	21.7177i	−1.27021	+	0.733354i	−0.295179	+	0.955442i	$0.595379\pi$
$878$			3.86625i			0.130480i
$879$	2.15440	−	11.1096i	0.0726662	−	0.374719i
$880$	−17.8118	−	6.00840i	−0.600436	−	0.202543i
$881$	27.9517			0.941718			0.470859	−	0.882208i	$-0.343944\pi$
$881$	27.9517			0.941718			0.470859	+	0.882208i	$0.343944\pi$
$882$	10.0221	+	20.2436i	0.337462	+	0.681639i
$883$		−	30.6255i		−	1.03063i	−0.857001	−	0.515315i	$-0.827675\pi$
$883$		−	30.6255i		−	1.03063i	0.857001	−	0.515315i	$-0.172325\pi$
$884$	−1.29466			−0.0435443
$885$	34.1960	−	20.0504i	1.14949	−	0.673986i
$886$	−33.9073			−1.13914
$887$	17.0806	−	9.86146i	0.573509	−	0.331115i	−0.185041	−	0.982731i	$-0.559242\pi$
$887$	17.0806	−	9.86146i	0.573509	−	0.331115i	0.758550	+	0.651615i	$0.225908\pi$
$888$	−25.4154	−	4.92860i	−0.852884	−	0.165393i
$889$	0.323537	−	3.15455i	0.0108511	−	0.105800i
$890$	−0.706929	+	2.09568i	−0.0236963	+	0.0702473i
$891$	−34.0007	−	32.7182i	−1.13907	−	1.09610i
$892$	11.0740	−	6.39357i	0.370784	−	0.214072i
$893$	0.505441	+	0.291817i	0.0169139	+	0.00976527i
$894$	12.9341	+	11.2334i	0.432579	+	0.375700i
$895$	−26.1186	+	22.9938i	−0.873050	+	0.768597i
$896$	0.0681089	−	0.664076i	0.00227536	−	0.0221852i
$897$	4.33055	+	12.5588i	0.144593	+	0.419326i
$898$			37.2328i			1.24247i
$899$	−3.52026	−	6.09728i	−0.117407	−	0.203356i
$900$	6.17471	−	11.0345i	0.205824	−	0.367816i
$901$	5.18497	−	8.98064i	0.172737	−	0.299188i
$902$	47.2535	−	27.2818i	1.57337	−	0.908386i
$903$	−10.6267	−	11.3284i	−0.353634	−	0.376985i
$904$	24.6287	−	42.6582i	0.819139	−	1.41879i
$905$	−5.57323	−	27.7417i	−0.185260	−	0.922164i
$906$	−3.20803	+	16.5429i	−0.106580	+	0.549600i
$907$	6.72594	+	3.88322i	0.223331	+	0.128940i	0.607492	−	0.794326i	$-0.292176\pi$
$907$	6.72594	+	3.88322i	0.223331	+	0.128940i	−0.384161	+	0.923266i	$0.625509\pi$
$908$	17.3395	+	10.0110i	0.575431	+	0.332225i
$909$	−5.54540	−	39.2062i	−0.183929	−	1.30039i
$910$	7.25164	+	3.30423i	0.240389	+	0.109534i
$911$	4.34760	+	7.53026i	0.144042	+	0.249489i	0.929015	−	0.370041i	$-0.120657\pi$
$911$	4.34760	+	7.53026i	0.144042	+	0.249489i	−0.784973	+	0.619530i	$0.787323\pi$
$912$	−1.32535	−	0.257015i	−0.0438867	−	0.00851060i
$913$			45.6881i			1.51206i
$914$	−18.8378			−0.623100
$915$	1.61984	−	0.949773i	0.0535503	−	0.0313985i
$916$	−3.24838	−	5.62636i	−0.107330	−	0.185900i
$917$	1.75393	+	3.91288i	0.0579199	+	0.129215i
$918$	−0.349684	+	6.84596i	−0.0115413	+	0.225950i
$919$	9.59574	−	16.6203i	0.316534	−	0.548253i	−0.663228	−	0.748417i	$-0.730814\pi$
$919$	9.59574	−	16.6203i	0.316534	−	0.548253i	0.979762	+	0.200164i	$0.0641475\pi$
$920$	−31.4351	+	27.6741i	−1.03638	+	0.912389i
$921$	−14.5187	+	5.00638i	−0.478409	+	0.164966i
$922$	−1.29584	+	0.748155i	−0.0426763	+	0.0246392i
$923$	11.8516	+	6.84253i	0.390101	+	0.225225i
$924$	−19.3857	−	5.86419i	−0.637744	−	0.192918i
$925$	−24.2416	−	3.09737i	−0.797059	−	0.101841i
$926$	−2.46332	+	4.26660i	−0.0809498	+	0.140209i
$927$	19.6840	−	48.8437i	0.646506	−	1.60424i
$928$	−25.9909	+	15.0058i	−0.853192	+	0.492590i
$929$	−11.1933			−0.367241			−0.183621	−	0.982997i	$-0.558782\pi$
$929$	−11.1933			−0.367241			−0.183621	+	0.982997i	$0.558782\pi$
$930$	−2.17076	−	3.70224i	−0.0711821	−	0.121401i
$931$	−2.26414	+	2.54016i	−0.0742042	+	0.0832505i
$932$	−6.56345	−	3.78941i	−0.214993	−	0.124126i
$933$	−1.15247	−	3.34223i	−0.0377303	−	0.109420i
$934$	−4.75063	+	8.22834i	−0.155446	+	0.269240i
$935$	−14.0965	+	2.83195i	−0.461005	+	0.0926146i
$936$	1.60893	+	11.3752i	0.0525897	+	0.371811i
$937$			14.5502i			0.475333i	0.971347	+	0.237667i	$0.0763826\pi$
$937$			14.5502i			0.475333i	−0.971347	+	0.237667i	$0.923617\pi$
$938$	16.9566	+	1.73910i	0.553654	+	0.0567838i
$939$	6.33555	−	2.18464i	0.206753	−	0.0712929i
$940$	2.21878	−	0.445748i	0.0723688	−	0.0145387i
$941$	−40.0317			−1.30500			−0.652499	−	0.757790i	$-0.726279\pi$
$941$	−40.0317			−1.30500			−0.652499	+	0.757790i	$0.726279\pi$
$942$	−4.64594	−	13.4734i	−0.151373	−	0.438988i
$943$		−	59.2583i		−	1.92971i
$944$	−16.4115			−0.534150
$945$	−14.1567	+	27.2871i	−0.460519	+	0.887650i
$946$	−19.1150			−0.621483
$947$		−	17.8373i		−	0.579635i	−0.957082	−	0.289817i	$-0.906405\pi$
$947$		−	17.8373i		−	0.579635i	0.957082	−	0.289817i	$-0.0935946\pi$
$948$	7.26136	+	21.0583i	0.235838	+	0.683941i
$949$	−4.61991			−0.149968
$950$	−2.59333	−	0.331352i	−0.0841388	−	0.0107505i
$951$	−8.15278	+	2.81126i	−0.264372	+	0.0911613i
$952$	4.05881	+	9.05487i	0.131547	+	0.293470i
$953$		−	27.3592i		−	0.886250i	−0.896460	−	0.443125i	$-0.853870\pi$
$953$		−	27.3592i		−	0.886250i	0.896460	−	0.443125i	$-0.146130\pi$
$954$	−25.3071	−	10.1987i	−0.819349	−	0.330197i
$955$	−3.63257	−	18.0817i	−0.117547	−	0.585110i
$956$	4.89390	−	8.47648i	0.158280	−	0.274149i
$957$	20.2312	+	58.6715i	0.653983	+	1.89658i
$958$	−20.3151	−	11.7289i	−0.656352	−	0.378945i
$959$	9.83372	+	7.10689i	0.317547	+	0.229494i
$960$	−26.4958	+	15.5355i	−0.855149	+	0.501405i
$961$	−29.9387			−0.965765
$962$	5.70171	−	3.29188i	0.183831	−	0.106135i
$963$	−15.8058	+	2.23561i	−0.509335	+	0.0720414i
$964$	0.393610	−	0.681753i	0.0126773	−	0.0219578i
$965$	36.6928	−	7.37149i	1.18118	−	0.237297i
$966$	22.0189	−	20.6550i	0.708446	−	0.664564i
$967$	5.81388	+	3.35665i	0.186962	+	0.107942i	0.590560	−	0.806994i	$-0.298907\pi$
$967$	5.81388	+	3.35665i	0.186962	+	0.107942i	−0.403598	+	0.914937i	$0.632240\pi$
$968$	−43.6659	+	25.2105i	−1.40347	+	0.810296i
$969$	−0.976212	+	0.336619i	−0.0313605	+	0.0108138i
$970$	27.6618	−	24.3523i	0.888166	−	0.781905i
$971$	−6.31670	+	10.9408i	−0.202712	+	0.351108i	−0.949401	−	0.314065i	$-0.898309\pi$
$971$	−6.31670	+	10.9408i	−0.202712	+	0.351108i	0.746689	+	0.665173i	$0.231642\pi$
$972$	−13.0881	+	1.17420i	−0.419802	+	0.0376624i
$973$	−32.1628	+	44.5032i	−1.03109	+	1.42671i
$974$	4.39125	+	7.60587i	0.140705	+	0.243708i
$975$	2.20737	+	10.6179i	0.0706925	+	0.340045i
$976$	−0.777403			−0.0248841
$977$		−	42.0045i		−	1.34384i	−0.740623	−	0.671921i	$-0.765470\pi$
$977$		−	42.0045i		−	1.34384i	0.740623	−	0.671921i	$-0.234530\pi$
$978$	−14.6968	−	2.85004i	−0.469953	−	0.0911342i
$979$	2.41052	+	4.17515i	0.0770406	+	0.133438i
$980$	−0.0811584	+	13.1944i	−0.00259251	+	0.421480i
$981$	7.93067	+	3.19605i	0.253207	+	0.102042i
$982$	−36.5694	−	21.1133i	−1.16698	−	0.673753i
$983$	25.9908	+	15.0058i	0.828978	+	0.478610i	0.853502	−	0.521089i	$-0.174474\pi$
$983$	25.9908	+	15.0058i	0.828978	+	0.478610i	−0.0245249	+	0.999699i	$0.507807\pi$
$984$	9.75611	−	50.3095i	0.311013	−	1.60381i
$985$	10.6317	−	2.13588i	0.338754	−	0.0680547i
$986$	4.50796	−	7.80801i	0.143563	−	0.248658i
$987$	−5.35725	+	1.25352i	−0.170523	+	0.0398999i
$988$	−0.444400	+	0.256575i	−0.0141383	+	0.00816272i
$989$	−10.3798	+	17.9784i	−0.330059	+	0.571679i
$990$	12.5722	+	35.6809i	0.399572	+	1.13402i
$991$	−19.6179	−	33.9791i	−0.623182	−	1.07938i	−0.988889	−	0.148653i	$-0.952506\pi$
$991$	−19.6179	−	33.9791i	−0.623182	−	1.07938i	0.365707	−	0.930730i	$-0.380827\pi$
$992$		−	4.52389i		−	0.143634i
$993$	−16.9174	−	49.0613i	−0.536858	−	1.55691i
$994$	3.17311	−	30.9385i	0.100645	−	0.981309i
$995$	39.6258	−	34.8849i	1.25622	−	1.10593i
$996$	9.60625	+	8.34314i	0.304386	+	0.264363i
$997$	28.2699	+	16.3216i	0.895316	+	0.516911i	0.875678	−	0.482896i	$-0.160415\pi$
$997$	28.2699	+	16.3216i	0.895316	+	0.516911i	0.0196387	+	0.999807i	$0.493748\pi$
$998$	21.3926	−	12.3510i	0.677172	−	0.390965i
$999$	11.5602	+	22.6140i	0.365747	+	0.715474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.15	✓	84
3.2	odd	2		945.2.r.b.604.28		84
5.4	even	2	inner	315.2.r.b.184.28	yes	84
7.4	even	3		315.2.bo.b.4.28	yes	84
9.2	odd	6		945.2.bo.b.289.28		84
9.7	even	3		315.2.bo.b.79.15	yes	84
15.14	odd	2		945.2.r.b.604.15		84
21.11	odd	6		945.2.bo.b.739.15		84
35.4	even	6		315.2.bo.b.4.15	yes	84
45.29	odd	6		945.2.bo.b.289.15		84
45.34	even	6		315.2.bo.b.79.28	yes	84
63.11	odd	6		945.2.r.b.424.28		84
63.25	even	3	inner	315.2.r.b.214.15	yes	84
105.74	odd	6		945.2.bo.b.739.28		84
315.74	odd	6		945.2.r.b.424.15		84
315.214	even	6	inner	315.2.r.b.214.28	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.15	✓	84	1.1	even	1	trivial
315.2.r.b.184.28	yes	84	5.4	even	2	inner
315.2.r.b.214.15	yes	84	63.25	even	3	inner
315.2.r.b.214.28	yes	84	315.214	even	6	inner
315.2.bo.b.4.15	yes	84	35.4	even	6
315.2.bo.b.4.28	yes	84	7.4	even	3
315.2.bo.b.79.15	yes	84	9.7	even	3
315.2.bo.b.79.28	yes	84	45.34	even	6
945.2.r.b.424.15		84	315.74	odd	6
945.2.r.b.424.28		84	63.11	odd	6
945.2.r.b.604.15		84	15.14	odd	2
945.2.r.b.604.28		84	3.2	odd	2
945.2.bo.b.289.15		84	45.29	odd	6
945.2.bo.b.289.28		84	9.2	odd	6
945.2.bo.b.739.15		84	21.11	odd	6
945.2.bo.b.739.28		84	105.74	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.07565i q^{2} +(-0.564624 - 1.63744i) q^{3} +0.842975 q^{4} +(0.440420 + 2.19227i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(2.63194 + 0.269937i) q^{7} -3.05805i q^{8} +(-2.36240 + 1.84907i) q^{9} +O(q^{10})\)	\(q-1.07565i q^{2} +(-0.564624 - 1.63744i) q^{3} +0.842975 q^{4} +(0.440420 + 2.19227i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(2.63194 + 0.269937i) q^{7} -3.05805i q^{8} +(-2.36240 + 1.84907i) q^{9} +(2.35811 - 0.473738i) q^{10} +(2.62145 - 4.54048i) q^{11} +(-0.475964 - 1.38032i) q^{12} +(1.08449 + 0.626132i) q^{13} +(0.290358 - 2.83105i) q^{14} +(3.34103 - 1.95897i) q^{15} -1.60344 q^{16} +(-1.06213 + 0.613221i) q^{17} +(1.98896 + 2.54112i) q^{18} +(-0.243054 + 0.420982i) q^{19} +(0.371263 + 1.84803i) q^{20} +(-1.04405 - 4.46206i) q^{21} +(-4.88397 - 2.81976i) q^{22} +(-5.30418 + 3.06237i) q^{23} +(-5.00736 + 1.72665i) q^{24} +(-4.61206 + 1.93104i) q^{25} +(0.673499 - 1.16653i) q^{26} +(4.36161 + 2.82425i) q^{27} +(2.21866 + 0.227550i) q^{28} +(-3.41713 - 5.91864i) q^{29} +(-2.10716 - 3.59378i) q^{30} +1.03018 q^{31} -4.39135i q^{32} +(-8.91488 - 1.72879i) q^{33} +(0.659611 + 1.14248i) q^{34} +(0.567388 + 5.88881i) q^{35} +(-1.99144 + 1.55872i) q^{36} +(4.23290 + 2.44387i) q^{37} +(0.452830 + 0.261441i) q^{38} +(0.412921 - 2.12932i) q^{39} +(6.70406 - 1.34683i) q^{40} +(-4.83761 + 8.37899i) q^{41} +(-4.79962 + 1.12304i) q^{42} +(2.93537 - 1.69474i) q^{43} +(2.20982 - 3.82751i) q^{44} +(-5.09411 - 4.36464i) q^{45} +(3.29404 + 5.70545i) q^{46} -1.20062i q^{47} +(0.905342 + 2.62554i) q^{48} +(6.85427 + 1.42092i) q^{49} +(2.07712 + 4.96097i) q^{50} +(1.60381 + 1.39293i) q^{51} +(0.914200 + 0.527814i) q^{52} +(-7.32252 + 4.22766i) q^{53} +(3.03791 - 4.69157i) q^{54} +(11.1085 + 3.74719i) q^{55} +(0.825481 - 8.04862i) q^{56} +(0.826566 + 0.160289i) q^{57} +(-6.36639 + 3.67564i) q^{58} +10.2352 q^{59} +(2.81640 - 1.65136i) q^{60} +0.484834 q^{61} -1.10812i q^{62} +(-6.71684 + 4.22896i) q^{63} -7.93045 q^{64} +(-0.895015 + 2.65326i) q^{65} +(-1.85958 + 9.58930i) q^{66} +5.98951i q^{67} +(-0.895349 + 0.516930i) q^{68} +(8.00931 + 6.95618i) q^{69} +(6.33430 - 0.610311i) q^{70} +10.9283 q^{71} +(5.65455 + 7.22433i) q^{72} +(-3.19498 + 1.84462i) q^{73} +(2.62875 - 4.55312i) q^{74} +(5.76603 + 6.46165i) q^{75} +(-0.204889 + 0.354877i) q^{76} +(8.12515 - 11.2427i) q^{77} +(-2.29040 - 0.444159i) q^{78} -15.2561 q^{79} +(-0.706189 - 3.51517i) q^{80} +(2.16186 - 8.73650i) q^{81} +(9.01287 + 5.20358i) q^{82} +(-7.54680 + 4.35715i) q^{83} +(-0.880112 - 3.76140i) q^{84} +(-1.81213 - 2.05840i) q^{85} +(-1.82294 - 3.15743i) q^{86} +(-7.76201 + 8.93714i) q^{87} +(-13.8850 - 8.01652i) q^{88} +(-0.459769 + 0.796344i) q^{89} +(-4.69483 + 5.47948i) q^{90} +(2.68531 + 1.94069i) q^{91} +(-4.47130 + 2.58150i) q^{92} +(-0.581665 - 1.68686i) q^{93} -1.29145 q^{94} +(-1.02995 - 0.347430i) q^{95} +(-7.19056 + 2.47946i) q^{96} +(13.2696 - 7.66120i) q^{97} +(1.52841 - 7.37280i) q^{98} +(2.20277 + 15.5737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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