LMFDB - Embedded newform 315.2.bo.b.4.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (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			4.15
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.931541 - 0.537825i) q^{2} +(1.13575 - 1.30770i) q^{3} +(-0.421488 - 0.730038i) q^{4} +(-2.11877 + 0.714718i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(-1.08220 + 2.41430i) q^{7} +3.05805i q^{8} +(-0.420144 - 2.97043i) q^{9} +O(q^{10})$	\(q+(-0.931541 - 0.537825i) q^{2} +(1.13575 - 1.30770i) q^{3} +(-0.421488 - 0.730038i) q^{4} +(-2.11877 + 0.714718i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(-1.08220 + 2.41430i) q^{7} +3.05805i q^{8} +(-0.420144 - 2.97043i) q^{9} +(2.35811 + 0.473738i) q^{10} -5.24290 q^{11} +(-1.43337 - 0.277962i) q^{12} +(-1.08449 - 0.626132i) q^{13} +(2.30659 - 1.66698i) q^{14} +(-1.47176 + 3.58245i) q^{15} +(0.801721 - 1.38862i) q^{16} +(-1.06213 - 0.613221i) q^{17} +(-1.20619 + 2.99305i) q^{18} +(-0.243054 - 0.420982i) q^{19} +(1.41481 + 1.24554i) q^{20} +(1.92806 + 4.15723i) q^{21} +(4.88397 + 2.81976i) q^{22} +6.12474i q^{23} +(3.99900 + 3.47318i) q^{24} +(3.97836 - 3.02864i) 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} +(3.29773 - 2.54565i) q^{30} +(-0.515091 - 0.892163i) q^{31} +(3.80302 - 2.19568i) q^{32} +(-5.95462 + 6.85612i) 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} +0.522883i q^{38} +(-2.05050 + 0.707058i) q^{39} +(-2.18564 - 6.47930i) q^{40} +(-4.83761 + 8.37899i) q^{41} +(0.439793 - 4.90959i) q^{42} +(-2.93537 + 1.69474i) q^{43} +(2.20982 + 3.82751i) q^{44} +(3.01321 + 5.99338i) q^{45} +(3.29404 - 5.70545i) q^{46} +(-1.03977 - 0.600312i) q^{47} +(-0.905342 - 2.62554i) q^{48} +(-4.65769 - 5.22551i) q^{49} +(-5.33488 + 0.681643i) q^{50} +(-2.00822 + 0.692478i) q^{51} +1.05563i q^{52} +(-7.32252 - 4.22766i) q^{53} +(2.54406 + 4.97669i) q^{54} +(11.1085 - 3.74719i) q^{55} +(-7.38305 - 3.30942i) q^{56} +(-0.826566 - 0.160289i) q^{57} +7.35128i q^{58} +(-5.11759 - 8.86393i) q^{59} +(3.23565 - 0.435519i) q^{60} +(-0.242417 + 0.419878i) q^{61} +1.10812i q^{62} +(7.62620 + 2.20025i) q^{63} -7.93045 q^{64} +(2.74529 + 0.551522i) q^{65} +(9.23437 - 3.18421i) q^{66} +(-5.18707 + 2.99476i) q^{67} +1.03386i q^{68} +(8.00931 + 6.95618i) q^{69} +(-3.69570 + 5.18051i) q^{70} +10.9283 q^{71} +(9.08373 - 1.28482i) q^{72} +(-3.19498 - 1.84462i) q^{73} -5.25749 q^{74} +(0.557871 - 8.64227i) q^{75} +(-0.204889 + 0.354877i) q^{76} +(5.67386 - 12.6579i) q^{77} +(2.29040 + 0.444159i) q^{78} +(7.62805 - 13.2122i) q^{79} +(-0.706189 + 3.51517i) q^{80} +(-8.64696 + 2.49602i) q^{81} +(9.01287 - 5.20358i) q^{82} +(7.54680 - 4.35715i) q^{83} +(2.22228 - 3.15978i) q^{84} +(2.68869 + 0.540150i) q^{85} +3.64589 q^{86} +(-11.6208 - 2.25353i) q^{87} -16.0330i q^{88} +(-0.459769 - 0.796344i) q^{89} +(0.416462 - 7.20366i) q^{90} +(2.68531 - 1.94069i) q^{91} +(4.47130 - 2.58150i) q^{92} +(-1.75169 - 0.339692i) q^{93} +(0.645726 + 1.11843i) q^{94} +(0.815859 + 0.718248i) q^{95} +(1.44800 - 7.46694i) 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 + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.931541	−	0.537825i	−0.658699	−	0.380300i	0.133082	−	0.991105i	$-0.457513\pi$
$2$	−0.931541	−	0.537825i	−0.658699	−	0.380300i	−0.791781	+	0.610805i	$0.790846\pi$
$3$	1.13575	−	1.30770i	0.655726	−	0.754999i
$3$	1.13575	−	1.30770i	0.655726	−	0.754999i
$4$	−0.421488	−	0.730038i	−0.210744	−	0.365019i
$5$	−2.11877	+	0.714718i	−0.947542	+	0.319632i
$5$	−2.11877	+	0.714718i	−0.947542	+	0.319632i
$6$	−1.76131	+	0.607338i	−0.719052	+	0.247945i
$7$	−1.08220	+	2.41430i	−0.409033	+	0.912520i
$7$	−1.08220	+	2.41430i	−0.409033	+	0.912520i
$8$			3.05805i			1.08118i
$9$	−0.420144	−	2.97043i	−0.140048	−	0.990145i
$10$	2.35811	+	0.473738i	0.745701	+	0.149809i
$11$	−5.24290			−1.58079			−0.790396	−	0.612596i	$-0.790125\pi$
$11$	−5.24290			−1.58079			−0.790396	+	0.612596i	$0.790125\pi$
$12$	−1.43337	−	0.277962i	−0.413779	−	0.0802408i
$13$	−1.08449	−	0.626132i	−0.300784	−	0.173658i	0.342011	−	0.939696i	$-0.388892\pi$
$13$	−1.08449	−	0.626132i	−0.300784	−	0.173658i	−0.642795	+	0.766038i	$0.722225\pi$
$14$	2.30659	−	1.66698i	0.616461	−	0.445520i
$15$	−1.47176	+	3.58245i	−0.380006	+	0.924984i
$16$	0.801721	−	1.38862i	0.200430	−	0.347155i
$17$	−1.06213	−	0.613221i	−0.257604	−	0.148728i	0.365637	−	0.930758i	$-0.380851\pi$
$17$	−1.06213	−	0.613221i	−0.257604	−	0.148728i	−0.623241	+	0.782030i	$0.714185\pi$
$18$	−1.20619	+	2.99305i	−0.284303	+	0.705468i
$19$	−0.243054	−	0.420982i	−0.0557604	−	0.0965799i	0.836798	−	0.547512i	$-0.184425\pi$
$19$	−0.243054	−	0.420982i	−0.0557604	−	0.0965799i	−0.892558	+	0.450932i	$0.851092\pi$
$20$	1.41481	+	1.24554i	0.316360	+	0.278510i
$21$	1.92806	+	4.15723i	0.420738	+	0.907182i
$22$	4.88397	+	2.81976i	1.04127	+	0.601175i
$23$			6.12474i			1.27710i	0.769581	+	0.638549i	$0.220465\pi$
$23$			6.12474i			1.27710i	−0.769581	+	0.638549i	$0.779535\pi$
$24$	3.99900	+	3.47318i	0.816293	+	0.708960i
$25$	3.97836	−	3.02864i	0.795671	−	0.605729i
$26$	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	$-0.385479\pi$
$30$	3.29773	−	2.54565i	0.602081	−	0.464770i
$31$	−0.515091	−	0.892163i	−0.0925130	−	0.160237i	0.816055	−	0.577974i	$-0.196157\pi$
$31$	−0.515091	−	0.892163i	−0.0925130	−	0.160237i	−0.908568	+	0.417737i	$0.862823\pi$
$32$	3.80302	−	2.19568i	0.672286	−	0.388144i
$33$	−5.95462	+	6.85612i	−1.03657	+	1.19350i
$34$	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	−0.109928	−	0.993940i	$-0.535062\pi$
$37$	4.23290	−	2.44387i	0.695885	−	0.401769i	0.805813	+	0.592170i	$0.201729\pi$
$38$			0.522883i			0.0848228i
$39$	−2.05050	+	0.707058i	−0.328343	+	0.113220i
$40$	−2.18564	−	6.47930i	−0.345580	−	1.02447i
$41$	−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	$0.894057\pi$
$42$	0.439793	−	4.90959i	0.0678616	−	0.757567i
$43$	−2.93537	+	1.69474i	−0.447640	+	0.258445i	−0.706833	−	0.707381i	$-0.749877\pi$
$43$	−2.93537	+	1.69474i	−0.447640	+	0.258445i	0.259193	+	0.965825i	$0.416543\pi$
$44$	2.20982	+	3.82751i	0.333142	+	0.577019i
$45$	3.01321	+	5.99338i	0.449183	+	0.893440i
$46$	3.29404	−	5.70545i	0.485680	−	0.841223i
$47$	−1.03977	−	0.600312i	−0.151666	−	0.0875645i	0.422246	−	0.906481i	$-0.361242\pi$
$47$	−1.03977	−	0.600312i	−0.151666	−	0.0875645i	−0.573913	+	0.818917i	$0.694575\pi$
$48$	−0.905342	−	2.62554i	−0.130675	−	0.378963i
$49$	−4.65769	−	5.22551i	−0.665384	−	0.746501i
$50$	−5.33488	+	0.681643i	−0.754466	+	0.0963989i
$51$	−2.00822	+	0.692478i	−0.281207	+	0.0969663i
$52$			1.05563i			0.146389i
$53$	−7.32252	−	4.22766i	−1.00583	−	0.580713i	−0.0958586	−	0.995395i	$-0.530560\pi$
$53$	−7.32252	−	4.22766i	−1.00583	−	0.580713i	−0.909967	+	0.414682i	$0.863893\pi$
$54$	2.54406	+	4.97669i	0.346203	+	0.677241i
$55$	11.1085	−	3.74719i	1.49787	−	0.505271i
$56$	−7.38305	−	3.30942i	−0.986601	−	0.442240i
$57$	−0.826566	−	0.160289i	−0.109481	−	0.0212308i
$58$			7.35128i			0.965270i
$59$	−5.11759	−	8.86393i	−0.666253	−	1.15398i	−0.978944	−	0.204130i	$-0.934564\pi$
$59$	−5.11759	−	8.86393i	−0.666253	−	1.15398i	0.312690	−	0.949855i	$-0.398770\pi$
$60$	3.23565	−	0.435519i	0.417721	−	0.0562253i
$61$	−0.242417	+	0.419878i	−0.0310383	+	0.0537599i	−0.881127	−	0.472879i	$-0.843215\pi$
$61$	−0.242417	+	0.419878i	−0.0310383	+	0.0537599i	0.850089	+	0.526639i	$0.176548\pi$
$62$			1.10812i			0.140731i
$63$	7.62620	+	2.20025i	0.960811	+	0.277205i
$64$	−7.93045			−0.991306
$65$	2.74529	+	0.551522i	0.340512	+	0.0684079i
$66$	9.23437	−	3.18421i	1.13667	−	0.391949i
$67$	−5.18707	+	2.99476i	−0.633702	+	0.365868i	−0.782184	−	0.623047i	$-0.785894\pi$
$67$	−5.18707	+	2.99476i	−0.633702	+	0.365868i	0.148483	+	0.988915i	$0.452561\pi$
$68$			1.03386i			0.125374i
$69$	8.00931	+	6.95618i	0.964208	+	0.837425i
$70$	−3.69570	+	5.18051i	−0.441720	+	0.619190i
$71$	10.9283			1.29695			0.648473	−	0.761238i	$-0.275408\pi$
$71$	10.9283			1.29695			0.648473	+	0.761238i	$0.275408\pi$
$72$	9.08373	−	1.28482i	1.07053	−	0.151418i
$73$	−3.19498	−	1.84462i	−0.373944	−	0.215897i	0.301236	−	0.953550i	$-0.402601\pi$
$73$	−3.19498	−	1.84462i	−0.373944	−	0.215897i	−0.675180	+	0.737653i	$0.735934\pi$
$74$	−5.25749			−0.611171
$75$	0.557871	−	8.64227i	0.0644174	−	0.997923i
$76$	−0.204889	+	0.354877i	−0.0235023	+	0.0407072i
$77$	5.67386	−	12.6579i	0.646597	−	1.44250i
$78$	2.29040	+	0.444159i	0.259337	+	0.0502911i
$79$	7.62805	−	13.2122i	0.858223	−	1.48649i	−0.0154000	−	0.999881i	$-0.504902\pi$
$79$	7.62805	−	13.2122i	0.858223	−	1.48649i	0.873623	−	0.486604i	$-0.161765\pi$
$80$	−0.706189	+	3.51517i	−0.0789543	+	0.393008i
$81$	−8.64696	+	2.49602i	−0.960773	+	0.277336i
$82$	9.01287	−	5.20358i	0.995305	−	0.574639i
$83$	7.54680	−	4.35715i	0.828369	−	0.478259i	−0.0249251	−	0.999689i	$-0.507935\pi$
$83$	7.54680	−	4.35715i	0.828369	−	0.478259i	0.853294	+	0.521430i	$0.174601\pi$
$84$	2.22228	−	3.15978i	0.242471	−	0.344760i
$85$	2.68869	+	0.540150i	0.291629	+	0.0585875i
$86$	3.64589			0.393146
$87$	−11.6208	−	2.25353i	−1.24588	−	0.241603i
$88$		−	16.0330i		−	1.70913i
$89$	−0.459769	−	0.796344i	−0.0487354	−	0.0844123i	0.840629	−	0.541612i	$-0.182186\pi$
$89$	−0.459769	−	0.796344i	−0.0487354	−	0.0844123i	−0.889364	+	0.457200i	$0.848852\pi$
$90$	0.416462	−	7.20366i	0.0438990	−	0.759332i
$91$	2.68531	−	1.94069i	0.281497	−	0.203440i
$92$	4.47130	−	2.58150i	0.466165	−	0.269140i
$93$	−1.75169	−	0.339692i	−0.181642	−	0.0352244i
$94$	0.645726	+	1.11843i	0.0666016	+	0.115357i
$95$	0.815859	+	0.718248i	0.0837053	+	0.0736907i
$96$	1.44800	−	7.46694i	0.147786	−	0.762092i
$97$	−13.2696	+	7.66120i	−1.34732	+	0.777877i	−0.987870	−	0.155286i	$-0.950370\pi$
$97$	−13.2696	+	7.66120i	−1.34732	+	0.777877i	−0.359453	+	0.933163i	$0.617037\pi$
$98$	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
$101$	13.1988			1.31333			0.656665	−	0.754183i	$-0.271967\pi$
$101$	13.1988			1.31333			0.656665	+	0.754183i	$0.271967\pi$
$102$	2.24317	+	0.435000i	0.222107	+	0.0430714i
$103$			17.5536i			1.72961i	0.502108	+	0.864805i	$0.332558\pi$
$103$			17.5536i			1.72961i	−0.502108	+	0.864805i	$0.667442\pi$
$104$	1.91474	−	3.31643i	0.187756	−	0.325203i
$105$	−7.05637	−	7.43019i	−0.688631	−	0.725112i
$106$	4.54748	+	7.87647i	0.441691	+	0.765031i
$107$	4.60816	−	2.66052i	0.445488	−	0.257203i	−0.260435	−	0.965491i	$-0.583866\pi$
$107$	4.60816	−	2.66052i	0.445488	−	0.257203i	0.705923	+	0.708289i	$0.250533\pi$
$108$	−0.223446	+	4.37452i	−0.0215011	+	0.420939i
$109$	−1.42508	+	2.46830i	−0.136497	+	0.236421i	−0.926169	−	0.377110i	$-0.876918\pi$
$109$	−1.42508	+	2.46830i	−0.136497	+	0.236421i	0.789671	+	0.613531i	$0.210251\pi$
$110$	−12.3633	−	2.48376i	−1.17880	−	0.236817i
$111$	1.61168	−	8.31097i	0.152974	−	0.788843i
$112$	2.48493	+	3.43836i	0.234804	+	0.324895i
$113$	−13.9495	−	8.05374i	−1.31226	−	0.757632i	−0.329788	−	0.944055i	$-0.606977\pi$
$113$	−13.9495	−	8.05374i	−1.31226	−	0.757632i	−0.982470	+	0.186423i	$0.940311\pi$
$114$	0.683772	+	0.593864i	0.0640411	+	0.0556205i
$115$	−4.37746	−	12.9769i	−0.408201	−	1.21010i
$116$	−2.88056	+	4.98927i	−0.267453	+	0.463242i
$117$	−1.40424	+	3.48448i	−0.129822	+	0.322140i
$118$			11.0095i			1.01350i
$119$	2.62993	−	1.90067i	0.241086	−	0.174234i
$120$	−10.9553	−	4.50070i	−1.00008	−	0.410856i
$121$	16.4880			1.49891
$122$	0.451642	−	0.260756i	0.0408898	−	0.0236077i
$123$	5.46286	+	15.8426i	0.492570	+	1.42848i
$124$	−0.434209	+	0.752072i	−0.0389931	+	0.0675380i
$125$	−6.26459	+	9.26039i	−0.560322	+	0.828275i
$126$	−5.92077	−	6.15119i	−0.527464	−	0.547991i
$127$			1.19856i			0.106355i	0.998585	+	0.0531776i	$0.0169349\pi$
$127$			1.19856i			0.106355i	−0.998585	+	0.0531776i	$0.983065\pi$
$128$	−0.218510	−	0.126157i	−0.0193137	−	0.0111508i
$129$	−1.11764	+	5.76337i	−0.0984030	+	0.507436i
$130$	−2.26073	−	1.99026i	−0.198279	−	0.174557i
$131$	−1.62071			−0.141602			−0.0708010	−	0.997490i	$-0.522556\pi$
$131$	−1.62071			−0.141602			−0.0708010	+	0.997490i	$0.522556\pi$
$132$	7.51503	+	1.45733i	0.654099	+	0.126844i
$133$	1.27941	−	0.131219i	0.110939	−	0.0113781i
$134$	6.44263			0.556558
$135$	11.2598	+	2.86661i	0.969087	+	0.246719i
$136$	1.87526	−	3.24804i	0.160802	−	0.278517i
$137$			4.58585i			0.391795i	0.980624	+	0.195898i	$0.0627620\pi$
$137$			4.58585i			0.391795i	−0.980624	+	0.195898i	$0.937238\pi$
$138$	−3.71979	−	10.7876i	−0.316650	−	0.918299i
$139$	−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	$0.824110\pi$
$140$	−4.53820	+	2.06785i	−0.383548	+	0.174765i
$141$	−1.96595	+	0.677901i	−0.165563	+	0.0570896i
$142$	−10.1801	−	5.87750i	−0.854297	−	0.493228i
$143$	5.68588	+	3.28274i	0.475477	+	0.274517i
$144$	−4.46165	−	1.79804i	−0.371804	−	0.149837i
$145$	11.4703	+	10.0979i	0.952554	+	0.838589i
$146$	1.98417	+	3.43668i	0.164211	+	0.284422i
$147$	−12.1234	+	0.155971i	−0.999917	+	0.0128643i
$148$	−3.56823	−	2.06012i	−0.293307	−	0.169341i
$149$	9.19509			0.753291			0.376646	−	0.926357i	$-0.377077\pi$
$149$	9.19509			0.753291			0.376646	+	0.926357i	$0.377077\pi$
$150$	−5.16771	+	7.75059i	−0.421942	+	0.632833i
$151$	−9.04472			−0.736049			−0.368025	−	0.929816i	$-0.619966\pi$
$151$	−9.04472			−0.736049			−0.368025	+	0.929816i	$0.619966\pi$
$152$	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
$155$	1.72900	+	1.52214i	0.138877	+	0.122261i
$156$	1.38044	+	1.19893i	0.110524	+	0.0959911i
$157$	−6.62481	+	3.82483i	−0.528717	+	0.305255i	−0.740494	−	0.672063i	$-0.765408\pi$
$157$	−6.62481	+	3.82483i	−0.528717	+	0.305255i	0.211777	+	0.977318i	$0.432075\pi$
$158$	−14.2117	+	8.20512i	−1.13062	+	0.652764i
$159$	−13.8450	+	4.77407i	−1.09798	+	0.378609i
$160$	−6.48844	+	7.37022i	−0.512956	+	0.582667i
$161$	−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	−0.202066	−	0.979372i	$-0.564766\pi$
$163$	6.95887	−	4.01771i	0.545061	−	0.314691i	0.747128	+	0.664681i	$0.231432\pi$
$164$	8.15597			0.636875
$165$	7.71627	−	18.7824i	0.600710	−	1.46221i
$166$	−9.37354			−0.727527
$167$	17.2584	+	9.96416i	1.33550	+	0.771050i	0.986136	−	0.165938i	$-0.0530651\pi$
$167$	17.2584	+	9.96416i	1.33550	+	0.771050i	0.349362	+	0.936988i	$0.386398\pi$
$168$	−12.7130	+	5.89612i	−0.980830	+	0.454895i
$169$	−5.71592	−	9.90026i	−0.439686	−	0.761558i
$170$	−2.21411	−	1.94921i	−0.169815	−	0.149498i
$171$	−1.14838	+	0.898849i	−0.0878190	+	0.0687367i
$172$	2.47444	+	1.42862i	0.188675	+	0.108931i
$173$	−3.12854	−	1.80627i	−0.237859	−	0.137328i	0.376333	−	0.926484i	$-0.377185\pi$
$173$	−3.12854	−	1.80627i	−0.237859	−	0.137328i	−0.614192	+	0.789156i	$0.710518\pi$
$174$	9.61325	+	8.34921i	0.728778	+	0.632952i
$175$	3.00667	+	12.8825i	0.227283	+	0.973829i
$176$	−4.20334	+	7.28040i	−0.316839	+	0.548781i
$177$	−17.4036	−	3.37495i	−1.30814	−	0.253676i
$178$			0.989102i			0.0741364i
$179$	7.78106	−	13.4772i	0.581584	−	1.00733i	−0.413708	−	0.910409i	$-0.635767\pi$
$179$	7.78106	−	13.4772i	0.581584	−	1.00733i	0.995292	−	0.0969228i	$-0.0309000\pi$
$180$	3.10536	−	4.72589i	0.231460	−	0.352247i
$181$	−12.6543			−0.940589			−0.470295	−	0.882509i	$-0.655852\pi$
$181$	−12.6543			−0.940589			−0.470295	+	0.882509i	$0.655852\pi$
$182$	−3.54523	+	0.363605i	−0.262790	+	0.0269522i
$183$	0.273749	+	0.793884i	0.0202361	+	0.0586856i
$184$	−18.7298			−1.38078
$185$	−7.22186	+	8.20332i	−0.530962	+	0.603120i
$186$	1.44908	+	1.25854i	0.106252	+	0.0922808i
$187$	5.56863	+	3.21505i	0.407219	+	0.235108i
$188$			1.01210i			0.0738147i
$189$	11.5387	−	7.47382i	0.839318	−	0.543641i
$190$	−0.373714	−	1.10787i	−0.0271120	−	0.0803731i
$191$	4.12398	−	7.14294i	0.298401	−	0.516845i	−0.677370	−	0.735643i	$-0.736880\pi$
$191$	4.12398	−	7.14294i	0.298401	−	0.516845i	0.975770	+	0.218798i	$0.0702135\pi$
$192$	−9.00701	+	10.3706i	−0.650025	+	0.748435i
$193$	14.4950	−	8.36870i	1.04337	−	0.602392i	0.122587	−	0.992458i	$-0.460881\pi$
$193$	14.4950	−	8.36870i	1.04337	−	0.602392i	0.920787	+	0.390065i	$0.127548\pi$
$194$	16.4816			1.18331
$195$	3.83919	−	2.96362i	0.274930	−	0.212229i
$196$	−1.85166	+	5.60278i	−0.132262	+	0.400198i
$197$			4.84963i			0.345522i	0.984964	+	0.172761i	$0.0552688\pi$
$197$			4.84963i			0.345522i	−0.984964	+	0.172761i	$0.944731\pi$
$198$	6.32395	−	15.6922i	0.449423	−	1.11520i
$199$	−11.8050	+	20.4468i	−0.836834	+	1.44944i	0.0556949	+	0.998448i	$0.482263\pi$
$199$	−11.8050	+	20.4468i	−0.836834	+	1.44944i	−0.892529	+	0.450991i	$0.851071\pi$
$200$	9.26174	+	12.1660i	0.654904	+	0.860267i
$201$	−1.97498	+	10.1844i	−0.139304	+	0.718353i
$202$	−12.2952	−	7.09865i	−0.865089	−	0.499459i
$203$	17.9874	−	1.84482i	1.26247	−	0.129481i
$204$	1.35198	+	1.17421i	0.0946572	+	0.0822109i
$205$	4.26117	−	21.2107i	0.297613	−	1.48142i
$206$	9.44079	−	16.3519i	0.657771	−	1.13929i
$207$	18.1931	−	2.57327i	1.26451	−	0.178855i
$208$	−1.73892	+	1.00397i	−0.120572	+	0.0696125i
$209$	1.27431	+	2.20717i	0.0881457	+	0.152673i
$210$	2.57715	+	10.7166i	0.177840	+	0.739517i
$211$	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	$0.0396024\pi$
$212$			7.12762i			0.489527i
$213$	12.4118	−	14.2909i	0.850440	−	0.979193i
$214$	−5.72359			−0.391256
$215$	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
$219$	−6.04090	+	2.08304i	−0.408206	+	0.140758i
$220$	−7.41768	−	6.53022i	−0.500100	−	0.440267i
$221$	0.767914	+	1.33007i	0.0516555	+	0.0894699i
$222$	−5.97120	+	6.87521i	−0.400761	+	0.461434i
$223$	−13.1368	+	7.58453i	−0.879704	+	0.507897i	−0.870561	−	0.492061i	$-0.836244\pi$
$223$	−13.1368	+	7.58453i	−0.879704	+	0.507897i	−0.00914337	+	0.999958i	$0.502910\pi$
$224$	1.18539	+	11.5578i	0.0792022	+	0.772238i
$225$	−10.6679	−	10.5450i	−0.711191	−	0.702999i
$226$	8.66301	+	15.0048i	0.576255	+	0.998103i
$227$			23.7515i			1.57644i	0.615392	+	0.788221i	$0.288998\pi$
$227$			23.7515i			1.57644i	−0.615392	+	0.788221i	$0.711002\pi$
$228$	0.231370	+	0.670984i	0.0153229	+	0.0444370i
$229$	7.70695			0.509289			0.254645	−	0.967035i	$-0.418041\pi$
$229$	7.70695			0.509289			0.254645	+	0.967035i	$0.418041\pi$
$230$	−2.90153	+	14.4428i	−0.191321	+	0.952332i
$231$	−10.1086	−	21.7959i	−0.665100	−	1.43407i
$232$	18.0995	−	10.4498i	1.18829	−	0.686060i
$233$	−7.78605	+	4.49528i	−0.510081	+	0.294496i	−0.732867	−	0.680372i	$-0.761818\pi$
$233$	−7.78605	+	4.49528i	−0.510081	+	0.294496i	0.222786	+	0.974867i	$0.428485\pi$
$234$	3.18215	−	2.49070i	0.208024	−	0.162822i
$235$	2.63209	+	0.528779i	0.171698	+	0.0344938i
$236$	−4.31400	+	7.47207i	−0.280818	+	0.486390i
$237$	−8.61396	−	24.9809i	−0.559537	−	1.62268i
$238$	−3.47212	+	0.356107i	−0.225064	+	0.0230830i
$239$	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	$0.0441283\pi$
$240$	3.79473	+	4.91584i	0.244949	+	0.317316i
$241$	−0.933860			−0.0601552			−0.0300776	−	0.999548i	$-0.509575\pi$
$241$	−0.933860			−0.0601552			−0.0300776	+	0.999548i	$0.509575\pi$
$242$	−15.3592	−	8.86764i	−0.987327	−	0.570034i
$243$	−6.55674	+	14.1425i	−0.420615	+	0.907239i
$244$	0.408703			0.0261645
$245$	13.6033	+	7.74271i	0.869084	+	0.494664i
$246$	3.43166	−	17.6961i	0.218794	−	1.12826i
$247$			0.608736i			0.0387329i
$248$	2.72828	−	1.57517i	0.173246	−	0.100024i
$249$	2.87345	−	14.8176i	0.182097	−	0.939024i
$250$	10.8162	−	5.25718i	0.684076	−	0.332493i
$251$	−17.9865			−1.13530			−0.567650	−	0.823270i	$-0.692147\pi$
$251$	−17.9865			−1.13530			−0.567650	+	0.823270i	$0.692147\pi$
$252$	−1.60808	−	6.49479i	−0.101300	−	0.409133i
$253$		−	32.1114i		−	2.01883i
$254$	0.644617	−	1.11651i	0.0404469	−	0.0700561i
$255$	3.76003	−	2.90251i	0.235462	−	0.181762i
$256$	8.06615	+	13.9710i	0.504134	+	0.873186i
$257$		−	15.8421i		−	0.988200i	−0.869405	−	0.494100i	$-0.835498\pi$
$257$		−	15.8421i		−	0.988200i	0.869405	−	0.494100i	$-0.164502\pi$
$258$	4.14082	−	4.76772i	0.257796	−	0.296825i
$259$	1.31938	+	12.8642i	0.0819824	+	0.799345i
$260$	−0.754476	−	2.23663i	−0.0467906	−	0.138710i
$261$	−16.1453	+	12.6370i	−0.999366	+	0.782213i
$262$	1.50976	+	0.871659i	0.0932732	+	0.0538513i
$263$			12.5936i			0.776554i	0.921543	+	0.388277i	$0.126930\pi$
$263$			12.5936i			0.776554i	−0.921543	+	0.388277i	$0.873070\pi$
$264$	−20.9664	−	18.2095i	−1.29039	−	1.12072i
$265$	18.5363	+	3.72389i	1.13868	+	0.228757i
$266$	−1.26240	−	0.565864i	−0.0774025	−	0.0346953i
$267$	−1.56356	−	0.303208i	−0.0956883	−	0.0185561i
$268$	4.37257	+	2.52451i	0.267097	+	0.154209i
$269$	2.32717	−	4.03078i	0.141890	−	0.245761i	−0.786318	−	0.617822i	$-0.788015\pi$
$269$	2.32717	−	4.03078i	0.141890	−	0.245761i	0.928208	+	0.372061i	$0.121349\pi$
$270$	−8.94721	−	8.72616i	−0.544510	−	0.531057i
$271$	6.08992	+	10.5481i	0.369936	+	0.640749i	0.989555	−	0.144154i	$-0.0460462\pi$
$271$	6.08992	+	10.5481i	0.369936	+	0.640749i	−0.619619	+	0.784903i	$0.712713\pi$
$272$	−1.70306	+	0.983264i	−0.103263	+	0.0596191i
$273$	0.512004	−	5.71571i	0.0309879	−	0.345930i
$274$	2.46638	−	4.27190i	0.149000	−	0.258075i
$275$	−20.8581	+	15.8789i	−1.25779	+	0.957531i
$276$	1.70245	−	8.77904i	0.102475	−	0.528436i
$277$		−	12.8413i		−	0.771557i	−0.922591	−	0.385779i	$-0.873933\pi$
$277$		−	12.8413i		−	0.771557i	0.922591	−	0.385779i	$-0.126067\pi$
$278$	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	$0.617374\pi$
$282$	2.19595	+	0.425843i	0.130767	+	0.0253586i
$283$	11.5448	−	6.66542i	0.686270	−	0.396218i	−0.115943	−	0.993256i	$-0.536989\pi$
$283$	11.5448	−	6.66542i	0.686270	−	0.396218i	0.802213	+	0.597038i	$0.203656\pi$
$284$	−4.60613	−	7.97804i	−0.273323	−	0.473410i
$285$	1.86586	−	0.251146i	0.110524	−	0.0148766i
$286$	−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
$290$	−5.25409	−	15.5757i	−0.308531	−	0.914634i
$291$	−5.05241	+	26.0538i	−0.296177	+	1.52730i
$292$			3.10994i			0.181996i
$293$	−5.65831	−	3.26682i	−0.330562	−	0.190850i	0.325529	−	0.945532i	$-0.394458\pi$
$293$	−5.65831	−	3.26682i	−0.330562	−	0.190850i	−0.656090	+	0.754682i	$0.727791\pi$
$294$	11.3773	+	6.37495i	0.663537	+	0.371795i
$295$	17.1782	+	15.1230i	1.00015	+	0.880493i
$296$	7.47346	+	12.9444i	0.434386	+	0.752379i
$297$	22.8675	+	14.8072i	1.32690	+	0.859204i
$298$	−8.56560	−	4.94535i	−0.496192	−	0.286477i
$299$	3.83490	−	6.64224i	0.221778	−	0.384130i
$300$	−6.54432	+	3.23534i	−0.377836	+	0.186793i
$301$	−0.914945	−	8.92090i	−0.0527365	−	0.514192i
$302$	8.42553	+	4.86448i	0.484835	+	0.279919i
$303$	14.9905	−	17.2600i	0.861184	−	0.991563i
$304$	−0.779447			−0.0447043
$305$	0.213531	−	1.06288i	0.0122267	−	0.0608606i
$306$	3.11653	−	2.43934i	0.178160	−	0.139448i
$307$			8.86675i			0.506052i	0.967459	+	0.253026i	$0.0814258\pi$
$307$			8.86675i			0.506052i	−0.967459	+	0.253026i	$0.918574\pi$
$308$	−11.6322	+	1.19302i	−0.662808	+	0.0679788i
$309$	22.9548	+	19.9365i	1.30585	+	1.13415i
$310$	−0.791990	−	2.34784i	−0.0449820	−	0.133348i
$311$	−1.02057	−	1.76767i	−0.0578711	−	0.100236i	0.835638	−	0.549280i	$-0.185098\pi$
$311$	−1.02057	−	1.76767i	−0.0578711	−	0.100236i	−0.893510	+	0.449044i	$0.851765\pi$
$312$	−2.16222	−	6.27054i	−0.122412	−	0.354999i
$313$	3.35081	+	1.93459i	0.189399	+	0.109350i	0.591701	−	0.806157i	$-0.298457\pi$
$313$	3.35081	+	1.93459i	0.189399	+	0.109350i	−0.402302	+	0.915507i	$0.631790\pi$
$314$	8.22837			0.464354
$315$	−17.7307	+	0.788760i	−0.999012	+	0.0444416i
$316$	−12.8605			−0.723460
$317$	−4.31193	−	2.48949i	−0.242182	−	0.139824i	0.373997	−	0.927430i	$-0.377987\pi$
$317$	−4.31193	−	2.48949i	−0.242182	−	0.139824i	−0.616179	+	0.787606i	$0.711320\pi$
$318$	15.4648	+	2.99897i	0.867226	+	0.168174i
$319$	17.9157	+	31.0308i	1.00308	+	1.73739i
$320$	16.8028	−	5.66803i	0.939304	−	0.316853i
$321$	1.75456	−	9.04777i	0.0979300	−	0.504997i
$322$	10.2099	+	14.1272i	0.568973	+	0.787281i
$323$			0.596183i			0.0331725i
$324$	5.46677	+	5.26057i	0.303710	+	0.292254i
$325$	−6.21083	+	0.793563i	−0.344515	+	0.0440190i
$326$	−8.64330			−0.478708
$327$	1.60926	+	4.66694i	0.0889925	+	0.258083i
$328$	−25.6234	−	14.7937i	−1.41481	−	0.816843i
$329$	2.57457	−	1.86066i	0.141941	−	0.102582i
$330$	−17.2897	+	13.3466i	−0.951765	+	0.734705i
$331$	−14.9811	+	25.9481i	−0.823437	+	1.42623i	0.0796711	+	0.996821i	$0.474613\pi$
$331$	−14.9811	+	25.9481i	−0.823437	+	1.42623i	−0.903108	+	0.429413i	$0.858720\pi$
$332$	−6.36176	−	3.67297i	−0.349147	−	0.201580i
$333$	−9.03777	−	11.5468i	−0.495267	−	0.632760i
$334$	−10.7180	−	18.5641i	−0.586461	−	1.01578i
$335$	8.84979	−	10.0525i	0.483516	−	0.549226i
$336$	7.31859	+	0.655587i	0.399262	+	0.0357652i
$337$	13.6534	+	7.88282i	0.743750	+	0.429404i	0.823431	−	0.567416i	$-0.192057\pi$
$337$	13.6534	+	7.88282i	0.743750	+	0.429404i	−0.0796811	+	0.996820i	$0.525390\pi$
$338$			12.2967i			0.668850i
$339$	−26.3750	+	9.09467i	−1.43249	+	0.493955i
$340$	−0.738918	−	2.19051i	−0.0400734	−	0.118797i
$341$	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
$345$	−21.9416	−	9.01413i	−1.18129	−	0.485305i
$346$	1.94291	+	3.36522i	0.104452	+	0.180915i
$347$	−14.3193	+	8.26727i	−0.768702	+	0.443810i	−0.832411	−	0.554158i	$-0.813040\pi$
$347$	−14.3193	+	8.26727i	−0.768702	+	0.443810i	0.0637096	+	0.997968i	$0.479707\pi$
$348$	3.25286	+	9.43346i	0.174372	+	0.505686i
$349$	−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
$353$		−	15.9211i		−	0.847394i	−0.905804	−	0.423697i	$-0.860732\pi$
$353$		−	15.9211i		−	0.847394i	0.905804	−	0.423697i	$-0.139268\pi$
$354$	14.3971	+	12.5040i	0.765195	+	0.664581i
$355$	−23.1544	+	7.81062i	−1.22891	+	0.414545i
$356$	−0.387574	+	0.671298i	−0.0205414	+	0.0355787i
$357$	0.501446	−	5.59785i	0.0265393	−	0.296269i
$358$	−14.4967	+	8.36970i	−0.766177	+	0.442352i
$359$	4.63711	+	8.03171i	0.244737	+	0.423897i	0.962058	−	0.272846i	$-0.0879649\pi$
$359$	4.63711	+	8.03171i	0.244737	+	0.423897i	−0.717320	+	0.696743i	$0.754632\pi$
$360$	−18.3280	+	9.21454i	−0.965972	+	0.485649i
$361$	9.38185	−	16.2498i	0.493782	−	0.855255i
$362$	11.7880	+	6.80582i	0.619565	+	0.357706i
$363$	18.7262	−	21.5613i	0.982871	−	1.13167i
$364$	−2.54860	−	1.14240i	−0.133583	−	0.0598780i
$365$	8.08780	+	1.62482i	0.423335	+	0.0850468i
$366$	0.171963	−	0.886765i	0.00898865	−	0.0463519i
$367$		−	5.19747i		−	0.271306i	−0.990756	−	0.135653i	$-0.956687\pi$
$367$		−	5.19747i		−	0.271306i	0.990756	−	0.135653i	$-0.0433132\pi$
$368$	8.50495	+	4.91034i	0.443351	+	0.255969i
$369$	26.9217	+	10.8494i	1.40149	+	0.564799i
$370$	11.1394	−	3.75762i	0.579110	−	0.195350i
$371$	18.1313	−	13.1036i	0.941328	−	0.680304i
$372$	0.490329	+	1.42198i	0.0254224	+	0.0737262i
$373$		−	20.2585i		−	1.04895i	−0.851427	−	0.524473i	$-0.824262\pi$
$373$		−	20.2585i		−	1.04895i	0.851427	−	0.524473i	$-0.175738\pi$
$374$	−3.45827	−	5.98991i	−0.178823	−	0.309731i
$375$	4.99478	+	18.7097i	0.257929	+	0.966164i
$376$	1.83578	−	3.17967i	0.0946733	−	0.163979i
$377$			8.55830i			0.440775i
$378$	−14.7684	+	0.756359i	−0.759604	+	0.0389029i
$379$	11.3495			0.582986			0.291493	−	0.956573i	$-0.405848\pi$
$379$	11.3495			0.582986			0.291493	+	0.956573i	$0.405848\pi$
$380$	0.180474	−	0.898341i	0.00925813	−	0.0460839i
$381$	1.56736	+	1.36127i	0.0802981	+	0.0697398i
$382$	−7.68331	+	4.43596i	−0.393112	+	0.226963i
$383$		−	25.0897i		−	1.28202i	−0.767531	−	0.641012i	$-0.778515\pi$
$383$		−	25.0897i		−	1.28202i	0.767531	−	0.641012i	$-0.221485\pi$
$384$	−0.413148	+	0.142462i	−0.0210834	+	0.00727000i
$385$	−2.97475	+	30.8744i	−0.151608	+	1.57351i
$386$	−18.0036			−0.916359
$387$	6.26738	+	8.00729i	0.318589	+	0.407033i
$388$	11.1859	+	6.45820i	0.567880	+	0.327866i
$389$	−14.6923			−0.744931			−0.372465	−	0.928046i	$-0.621487\pi$
$389$	−14.6923			−0.744931			−0.372465	+	0.928046i	$0.621487\pi$
$390$	−5.17028	+	0.695921i	−0.261807	+	0.0352393i
$391$	3.75582	−	6.50527i	0.189940	−	0.328986i
$392$	15.9799	−	14.2434i	0.807105	−	0.719402i
$393$	−1.84072	+	2.11940i	−0.0928521	+	0.106909i
$394$	2.60826	−	4.51763i	0.131402	−	0.227595i
$395$	−6.71910	+	33.4454i	−0.338074	+	1.68282i
$396$	10.4409	−	8.17222i	0.524677	−	0.410669i
$397$	−11.2840	+	6.51484i	−0.566329	+	0.326970i	−0.755682	−	0.654939i	$-0.772694\pi$
$397$	−11.2840	+	6.51484i	−0.566329	+	0.326970i	0.189353	+	0.981909i	$0.439361\pi$
$398$	21.9937	−	12.6981i	1.10244	−	0.636496i
$399$	1.28150	−	1.82211i	0.0641550	−	0.0912197i
$400$	−1.01611	−	7.95256i	−0.0508053	−	0.397628i
$401$	−14.9281			−0.745472			−0.372736	−	0.927937i	$-0.621580\pi$
$401$	−14.9281			−0.745472			−0.372736	+	0.927937i	$0.621580\pi$
$402$	7.31721	−	8.42500i	0.364949	−	0.420201i
$403$			1.29006i			0.0642624i
$404$	−5.56313	−	9.63562i	−0.276776	−	0.479390i
$405$	16.5369	−	11.4686i	0.821728	−	0.569880i
$406$	−17.7482	−	7.95555i	−0.880828	−	0.394827i
$407$	−22.1927	+	12.8129i	−1.10005	+	0.635114i
$408$	−2.11763	−	6.14124i	−0.104838	−	0.304036i
$409$	−0.903488	−	1.56489i	−0.0446746	−	0.0773786i	0.842823	−	0.538190i	$-0.180892\pi$
$409$	−0.903488	−	1.56489i	−0.0446746	−	0.0773786i	−0.887498	+	0.460811i	$0.847558\pi$
$410$	−15.3771	+	17.4668i	−0.759420	+	0.862626i
$411$	5.99690	+	5.20838i	0.295805	+	0.256910i
$412$	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
$416$	−5.49913			−0.269617
$417$	11.7180	+	33.9827i	0.573831	+	1.66414i
$418$		−	2.74142i		−	0.134087i
$419$	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	$-0.0303053\pi$
$420$	−2.45015	+	8.28315i	−0.119555	+	0.404176i
$421$	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
$423$	−1.34633	+	3.34079i	−0.0654610	+	0.162435i
$424$	12.9284	−	22.3926i	0.627858	−	1.08748i
$425$	−6.08276	+	0.777199i	−0.295057	+	0.0376997i
$426$	−19.2481	+	6.63715i	−0.932571	+	0.321571i
$427$	−0.751368	−	1.03966i	−0.0363613	−	0.0503126i
$428$	−3.88457	−	2.24276i	−0.187768	−	0.108408i
$429$	10.7506	−	3.70703i	0.519043	−	0.178977i
$430$	−7.72479	+	2.60578i	−0.372523	+	0.125662i
$431$	0.0501982	−	0.0869458i	0.00241796	−	0.00418803i	−0.864814	−	0.502093i	$-0.832564\pi$
$431$	0.0501982	−	0.0869458i	0.00241796	−	0.00418803i	0.867232	+	0.497905i	$0.165897\pi$
$432$	−7.41861	+	3.79236i	−0.356928	+	0.182460i
$433$			32.8267i			1.57755i	0.614682	+	0.788775i	$0.289284\pi$
$433$			32.8267i			1.57755i	−0.614682	+	0.788775i	$0.710716\pi$
$434$	−2.67532	−	1.19920i	−0.128420	−	0.0575636i
$435$	26.2324	−	3.53089i	1.25775	−	0.169293i
$436$	2.40261			0.115064
$437$	2.57841	−	1.48864i	0.123342	−	0.0712115i
$438$	6.74766	+	1.30852i	0.322416	+	0.0625234i
$439$	1.79717	−	3.11279i	0.0857742	−	0.148565i	−0.819947	−	0.572440i	$-0.805997\pi$
$439$	1.79717	−	3.11279i	0.0857742	−	0.148565i	0.905721	+	0.423875i	$0.139330\pi$
$440$	11.4591	+	33.9703i	0.546291	+	1.61947i
$441$	−13.5651	+	16.0308i	−0.645959	+	0.763372i
$442$		−	1.65201i		−	0.0785783i
$443$	−27.2994	−	15.7613i	−1.29703	−	0.748842i	−0.317142	−	0.948378i	$-0.602723\pi$
$443$	−27.2994	−	15.7613i	−1.29703	−	0.748842i	−0.979890	+	0.199536i	$0.936057\pi$
$444$	−6.74663	+	2.32639i	−0.320181	+	0.110405i
$445$	1.54331	+	1.35866i	0.0731597	+	0.0644068i
$446$	16.3166			0.772614
$447$	10.4433	−	12.0244i	0.493952	−	0.568734i
$448$	8.58233	−	19.1465i	0.405477	−	0.904586i
$449$	−34.6142			−1.63355			−0.816773	−	0.576959i	$-0.804239\pi$
$449$	−34.6142			−1.63355			−0.816773	+	0.576959i	$0.804239\pi$
$450$	4.26620	+	15.5605i	0.201110	+	0.733531i
$451$	25.3631	−	43.9302i	1.19430	−	2.06859i
$452$			13.5782i			0.638665i
$453$	−10.2725	+	11.8278i	−0.482646	+	0.555717i
$454$	12.7742	−	22.1255i	0.599521	−	1.03840i
$455$	−4.30250	+	6.03111i	−0.201704	+	0.282743i
$456$	0.490172	−	2.52768i	0.0229544	−	0.118369i
$457$	−15.1667	−	8.75648i	−0.709467	−	0.409611i	0.101397	−	0.994846i	$-0.467669\pi$
$457$	−15.1667	−	8.75648i	−0.709467	−	0.409611i	−0.810864	+	0.585235i	$0.801002\pi$
$458$	−7.17934	−	4.14499i	−0.335468	−	0.193683i
$459$	2.90070	+	5.67435i	0.135393	+	0.264856i
$460$	−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	$0.843647\pi$
$462$	−2.30579	+	25.7405i	−0.107275	+	1.19756i
$463$	3.96653	+	2.29008i	0.184340	+	0.106429i	0.589330	−	0.807892i	$-0.299392\pi$
$463$	3.96653	+	2.29008i	0.184340	+	0.106429i	−0.404990	+	0.914321i	$0.632725\pi$
$464$	−10.9583			−0.508728
$465$	3.95422	−	0.532239i	0.183372	−	0.0246820i
$466$	9.67070			0.447987
$467$	−7.64964	+	4.41652i	−0.353983	+	0.204372i	−0.666438	−	0.745560i	$-0.732182\pi$
$467$	−7.64964	+	4.41652i	−0.353983	+	0.204372i	0.312455	+	0.949933i	$0.398849\pi$
$468$	3.13567	−	0.443515i	0.144946	−	0.0205015i
$469$	−1.61679	−	15.7641i	−0.0746566	−	0.727917i
$470$	−2.16751	−	1.90818i	−0.0999796	−	0.0880179i
$471$	−2.52240	+	13.0073i	−0.116226	+	0.599345i
$472$	27.1063	−	15.6498i	1.24767	−	0.720342i
$473$	15.3898	−	8.88532i	0.707625	−	0.408548i
$474$	−5.41111	+	27.9035i	−0.248540	+	1.28165i
$475$	−2.24196	−	0.938693i	−0.102868	−	0.0430702i
$476$	−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
$479$	−21.8081			−0.996437			−0.498219	−	0.867051i	$-0.666012\pi$
$479$	−21.8081			−0.996437			−0.498219	+	0.867051i	$0.666012\pi$
$480$	2.26877	+	16.8556i	0.103555	+	0.769351i
$481$	−6.12073			−0.279081
$482$	0.869929	+	0.502254i	0.0396242	+	0.0228770i
$483$	−25.4620	+	11.8089i	−1.15856	+	0.537324i
$484$	−6.94947	−	12.0368i	−0.315885	−	0.547129i
$485$	22.6396	−	25.7163i	1.02801	−	1.16772i
$486$	13.7140	−	9.64789i	0.622082	−	0.437637i
$487$	−7.07095	−	4.08241i	−0.320415	−	0.184992i	0.331162	−	0.943574i	$-0.392559\pi$
$487$	−7.07095	−	4.08241i	−0.320415	−	0.184992i	−0.651578	+	0.758582i	$0.725893\pi$
$488$	−1.28401	−	0.741322i	−0.0581243	−	0.0335581i
$489$	2.64960	−	13.6632i	0.119819	−	0.617872i
$490$	−8.50783	−	14.5289i	−0.384344	−	0.656347i
$491$	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	$-0.179735\pi$
$492$	9.26315	−	10.6655i	0.417615	−	0.480840i
$493$			8.38182i			0.377498i
$494$	0.327394	−	0.567062i	0.0147301	−	0.0255133i
$495$	−15.7979	−	31.4227i	−0.710065	−	1.41234i
$496$	−1.65184			−0.0741696
$497$	−11.8266	+	26.3841i	−0.530494	+	1.18349i
$498$	−10.6460	+	12.2577i	−0.477058	+	0.549283i
$499$	−22.9648			−1.02804			−0.514022	−	0.857777i	$-0.671845\pi$
$499$	−22.9648			−1.02804			−0.514022	+	0.857777i	$0.671845\pi$
$500$	9.40089	+	0.670248i	0.420420	+	0.0299744i
$501$	32.6314	−	11.2520i	1.45786	−	0.502703i
$502$	16.7552	+	9.67362i	0.747821	+	0.431755i
$503$			2.13046i			0.0949926i	0.998871	+	0.0474963i	$0.0151242\pi$
$503$			2.13046i			0.0949926i	−0.998871	+	0.0474963i	$0.984876\pi$
$504$	−6.72847	+	23.3213i	−0.299710	+	1.03881i
$505$	−27.9652	+	9.43342i	−1.24443	+	0.419781i
$506$	−17.2703	+	29.9131i	−0.767760	+	1.32980i
$507$	−19.4384	−	3.76953i	−0.863289	−	0.167411i
$508$	0.874996	−	0.505179i	0.0388217	−	0.0224137i
$509$	−13.9001			−0.616111			−0.308056	−	0.951368i	$-0.599678\pi$
$509$	−13.9001			−0.616111			−0.308056	+	0.951368i	$0.599678\pi$
$510$	−5.06366	+	0.681570i	−0.224223	+	0.0301804i
$511$	7.91107	−	5.71739i	0.349965	−	0.252922i
$512$		−	16.8481i		−	0.744587i
$513$	−0.128852	+	2.52260i	−0.00568895	+	0.111376i
$514$	−8.52026	+	14.7575i	−0.375812	+	0.650926i
$515$	−12.5459	−	37.1921i	−0.552838	−	1.63888i
$516$	4.67855	−	1.61327i	0.205962	−	0.0710201i
$517$	5.45141	+	3.14737i	0.239753	+	0.138421i
$518$	5.68966	−	12.6932i	0.249989	−	0.557706i
$519$	−5.91529	+	2.03972i	−0.259652	+	0.0895338i
$520$	−1.68658	+	8.39525i	−0.0739615	+	0.368156i
$521$	−4.12704	+	7.14824i	−0.180809	+	0.313170i	−0.942156	−	0.335174i	$-0.891205\pi$
$521$	−4.12704	+	7.14824i	−0.180809	+	0.313170i	0.761347	+	0.648344i	$0.224538\pi$
$522$	21.8365	−	3.08860i	0.955757	−	0.135184i
$523$	7.38099	−	4.26142i	0.322748	−	0.186339i	−0.329869	−	0.944027i	$-0.607004\pi$
$523$	7.38099	−	4.26142i	0.322748	−	0.186339i	0.652617	+	0.757688i	$0.273671\pi$
$524$	0.683109	+	1.18318i	0.0298418	+	0.0516875i
$525$	20.2613	+	10.6995i	0.884275	+	0.466966i
$526$	6.77315	−	11.7314i	0.295324	−	0.511515i
$527$			1.26346i			0.0550371i
$528$	4.74661	+	13.7654i	0.206570	+	0.599063i
$529$	−14.5125			−0.630978
$530$	−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
$534$	1.29345	+	1.12337i	0.0559729	+	0.0486131i
$535$	−7.86210	+	8.93057i	−0.339908	+	0.386102i
$536$	−9.15811	−	15.8623i	−0.395570	−	0.685148i
$537$	−8.78674	−	25.4820i	−0.379176	−	1.09963i
$538$	−4.33571	+	2.50322i	−0.186926	+	0.107922i
$539$	24.4198	+	27.3968i	1.05183	+	1.18006i
$540$	−2.65312	−	9.42830i	−0.114172	−	0.405730i
$541$	−1.18482	−	2.05217i	−0.0509394	−	0.0882296i	0.839431	−	0.543466i	$-0.182888\pi$
$541$	−1.18482	−	2.05217i	−0.0509394	−	0.0882296i	−0.890371	+	0.455236i	$0.849555\pi$
$542$		−	13.1013i		−	0.562747i
$543$	−14.3722	+	16.5480i	−0.616768	+	0.710144i
$544$	−5.38574			−0.230912
$545$	1.25526	−	6.24829i	0.0537696	−	0.267647i
$546$	−3.55100	+	5.04905i	−0.151969	+	0.216079i
$547$	−26.2840	+	15.1751i	−1.12382	+	0.648840i	−0.942374	−	0.334560i	$-0.891412\pi$
$547$	−26.2840	+	15.1751i	−1.12382	+	0.648840i	−0.181449	+	0.983400i	$0.558079\pi$
$548$	3.34784	−	1.93288i	0.143013	−	0.0825684i
$549$	1.34907	+	0.543674i	0.0575769	+	0.0232034i
$550$	27.9702	−	3.57378i	1.19266	−	0.152387i
$551$	−1.66110	+	2.87710i	−0.0707650	+	0.122569i
$552$	−21.2723	+	24.4929i	−0.905411	+	1.04249i
$553$	23.6431	+	32.7146i	1.00541	+	1.39117i
$554$	−6.90636	+	11.9622i	−0.293423	+	0.508224i
$555$	2.52523	+	18.7609i	0.107190	+	0.796357i
$556$	17.4948			0.741943
$557$	−33.3219	−	19.2384i	−1.41189	−	0.815157i	−0.416327	−	0.909215i	$-0.636683\pi$
$557$	−33.3219	−	19.2384i	−1.41189	−	0.815157i	−0.995567	+	0.0940582i	$0.970016\pi$
$558$	3.29158	−	0.465568i	0.139344	−	0.0197091i
$559$	4.24451			0.179524
$560$	−7.72244	−	5.50907i	−0.326333	−	0.232801i
$561$	10.5289	−	3.63059i	0.444530	−	0.153284i
$562$		−	22.6324i		−	0.954691i
$563$	−26.5987	+	15.3568i	−1.12100	+	0.647211i	−0.941657	−	0.336575i	$-0.890732\pi$
$563$	−26.5987	+	15.3568i	−1.12100	+	0.647211i	−0.179346	+	0.983786i	$0.557398\pi$
$564$	1.32352	+	1.14949i	0.0557301	+	0.0484022i
$565$	35.3119	+	7.09406i	1.48558	+	0.298449i
$566$	−14.3393			−0.602727
$567$	3.33160	−	23.5775i	0.139914	−	0.990164i
$568$			33.4191i			1.40224i
$569$	−7.29098	+	12.6283i	−0.305654	+	0.529408i	−0.977407	−	0.211368i	$-0.932208\pi$
$569$	−7.29098	+	12.6283i	−0.305654	+	0.529408i	0.671753	+	0.740775i	$0.265542\pi$
$570$	−1.87320	−	0.769556i	−0.0784597	−	0.0322332i
$571$	−0.543614	−	0.941567i	−0.0227495	−	0.0394034i	0.854427	−	0.519572i	$-0.173909\pi$
$571$	−0.543614	−	0.941567i	−0.0227495	−	0.0394034i	−0.877176	+	0.480169i	$0.840575\pi$
$572$		−	5.53454i		−	0.231411i
$573$	−4.65699	−	13.5055i	−0.194549	−	0.564201i
$574$	2.80928	+	27.3911i	0.117257	+	1.14328i
$575$	18.5497	+	24.3664i	0.773574	+	1.01615i
$576$	3.33193	+	23.5569i	0.138830	+	0.981536i
$577$	−34.8546	−	20.1233i	−1.45102	−	0.837745i	−0.452478	−	0.891776i	$-0.649460\pi$
$577$	−34.8546	−	20.1233i	−1.45102	−	0.837745i	−0.998539	+	0.0540306i	$0.982793\pi$
$578$			16.6681i			0.693302i
$579$	5.51899	−	28.4598i	0.229361	−	1.18275i
$580$	2.53731	−	12.6299i	0.105356	−	0.524428i
$581$	2.35231	+	22.9355i	0.0975904	+	0.951526i
$582$	18.7189	−	21.5529i	0.775925	−	0.893396i
$583$	38.3912	+	22.1652i	1.59000	+	0.917988i
$584$	5.64094	−	9.77040i	0.233424	−	0.404302i
$585$	0.484842	−	8.38644i	0.0200457	−	0.346736i
$586$	3.51396	+	6.08636i	0.145160	+	0.251425i
$587$	23.5832	−	13.6158i	0.973384	−	0.561983i	0.0731177	−	0.997323i	$-0.476705\pi$
$587$	23.5832	−	13.6158i	0.973384	−	0.561983i	0.900266	+	0.435340i	$0.143372\pi$
$588$	5.22371	+	8.78477i	0.215422	+	0.362278i
$589$	−0.250390	+	0.433688i	−0.0103171	+	0.0178698i
$590$	−7.86867	−	23.3265i	−0.323948	−	0.960338i
$591$	6.34185	+	5.50797i	0.260869	+	0.226568i
$592$		−	7.83720i		−	0.322107i
$593$	−38.1366	+	22.0182i	−1.56608	+	0.904179i	−0.569465	+	0.822015i	$0.692850\pi$
$593$	−38.1366	+	22.0182i	−1.56608	+	0.904179i	−0.996619	+	0.0821636i	$0.973817\pi$
$594$	−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
$597$	13.3308	+	38.6599i	0.545592	+	1.58224i
$598$	−7.14473	+	4.12501i	−0.292170	+	0.168684i
$599$	11.9335	+	20.6694i	0.487590	+	0.844531i	0.999898	−	0.0142710i	$-0.00454276\pi$
$599$	11.9335	+	20.6694i	0.487590	+	0.844531i	−0.512308	+	0.858802i	$0.671209\pi$
$600$	26.4285	+	1.70600i	1.07894	+	0.0696471i
$601$	−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
$605$	−34.9342	+	11.7842i	−1.42028	+	0.479097i
$606$	−23.2472	+	8.01614i	−0.944352	+	0.325633i
$607$		−	29.1247i		−	1.18214i	−0.806622	−	0.591068i	$-0.798706\pi$
$607$		−	29.1247i		−	1.18214i	0.806622	−	0.591068i	$-0.201294\pi$
$608$	−1.84868	−	1.06734i	−0.0749739	−	0.0432862i
$609$	18.0167	−	25.6173i	0.730074	−	1.03807i
$610$	−0.770558	+	0.875278i	−0.0311990	+	0.0354390i
$611$	0.751749	+	1.30207i	0.0304125	+	0.0526760i
$612$	3.07101	−	0.434370i	0.124138	−	0.0175584i
$613$	−27.5261	−	15.8922i	−1.11177	−	0.641880i	−0.172481	−	0.985013i	$-0.555178\pi$
$613$	−27.5261	−	15.8922i	−1.11177	−	0.641880i	−0.939287	+	0.343133i	$0.888512\pi$
$614$	4.76876	−	8.25974i	0.192452	−	0.333336i
$615$	−22.8975	−	29.6623i	−0.923317	−	1.19610i
$616$	38.7085	+	17.3509i	1.55961	+	0.699089i
$617$	−15.5032	−	8.95075i	−0.624134	−	0.360344i	0.154343	−	0.988017i	$-0.450674\pi$
$617$	−15.5032	−	8.95075i	−0.624134	−	0.360344i	−0.778477	+	0.627674i	$0.784007\pi$
$618$	−10.6610	−	30.9174i	−0.428848	−	1.24368i
$619$	46.9324			1.88637			0.943186	−	0.332264i	$-0.107812\pi$
$619$	46.9324			1.88637			0.943186	+	0.332264i	$0.107812\pi$
$620$	0.382469	−	1.90380i	0.0153603	−	0.0764585i
$621$	17.2978	−	26.7137i	0.694137	−	1.07198i
$622$			2.19555i			0.0880335i
$623$	2.42017	−	0.248218i	0.0969622	−	0.00994463i
$624$	−0.662095	+	3.41424i	−0.0265050	+	0.136679i
$625$	6.65465	−	24.0980i	0.266186	−	0.963922i
$626$	−2.08095	−	3.60431i	−0.0831714	−	0.144057i
$627$	4.33360	+	0.840380i	0.173067	+	0.0335615i
$628$	5.58455	+	3.22424i	0.222848	+	0.128661i
$629$	−5.99452			−0.239017
$630$	16.9411	+	8.80126i	0.674949	+	0.350651i
$631$	−2.53639			−0.100972			−0.0504861	−	0.998725i	$-0.516077\pi$
$631$	−2.53639			−0.100972			−0.0504861	+	0.998725i	$0.516077\pi$
$632$	40.4035	+	23.3269i	1.60716	+	0.927896i
$633$	−6.37541	−	18.4890i	−0.253400	−	0.734871i
$634$	2.67783	+	4.63813i	0.106350	+	0.184204i
$635$	−0.856634	−	2.53948i	−0.0339945	−	0.100776i
$636$	9.32077	+	8.09520i	0.369593	+	0.320995i
$637$	1.77937	+	8.58335i	0.0705011	+	0.340085i
$638$		−	38.5420i		−	1.52589i
$639$	−4.59144	−	32.4617i	−0.181635	−	1.28416i
$640$	0.553139	+	0.111124i	0.0218647	+	0.00439257i
$641$	28.4605			1.12412			0.562061	−	0.827096i	$-0.310009\pi$
$641$	28.4605			1.12412			0.562061	+	0.827096i	$0.310009\pi$
$642$	−6.50057	+	7.48472i	−0.256557	+	0.295398i
$643$	−24.7884	−	14.3116i	−0.977560	−	0.564395i	−0.0760274	−	0.997106i	$-0.524224\pi$
$643$	−24.7884	−	14.3116i	−0.977560	−	0.564395i	−0.901533	+	0.432711i	$0.857557\pi$
$644$	1.39369	+	13.5888i	0.0549190	+	0.535472i
$645$	−1.75116	−	13.0100i	−0.0689517	−	0.512270i
$646$	0.320643	−	0.555369i	0.0126155	−	0.0218507i
$647$	−10.8576	−	6.26864i	−0.426857	−	0.246446i	0.271150	−	0.962537i	$-0.412596\pi$
$647$	−10.8576	−	6.26864i	−0.426857	−	0.246446i	−0.698007	+	0.716091i	$0.745929\pi$
$648$	−7.63295	−	26.4428i	−0.299851	−	1.03877i
$649$	26.8310	+	46.4726i	1.05321	+	1.82421i
$650$	6.21244	+	2.60110i	0.243672	+	0.102024i
$651$	2.71580	−	3.86150i	0.106441	−	0.151344i
$652$	−5.86616	−	3.38683i	−0.229737	−	0.132638i
$653$			22.4801i			0.879712i	0.898068	+	0.439856i	$0.144971\pi$
$653$			22.4801i			0.879712i	−0.898068	+	0.439856i	$0.855029\pi$
$654$	1.01091	−	5.21295i	0.0395295	−	0.203843i
$655$	3.43391	−	1.15835i	0.134174	−	0.0452605i
$656$	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	$0.921638\pi$
$660$	−16.9642	+	2.28338i	−0.660330	+	0.0888806i
$661$	−12.8230	−	22.2101i	−0.498758	−	0.863875i	0.501241	−	0.865308i	$-0.332877\pi$
$661$	−12.8230	−	22.2101i	−0.498758	−	0.863875i	−0.999999	+	0.00143328i	$0.999544\pi$
$662$	27.9111	−	16.1145i	1.08479	−	0.626306i
$663$	2.61148	+	0.506423i	0.101422	+	0.0196679i
$664$	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
$668$		−	16.7991i		−	0.649976i
$669$	−5.00184	+	25.7931i	−0.193382	+	0.997217i
$670$	−13.6504	+	4.60466i	−0.527362	+	0.177893i
$671$	1.27097	−	2.20138i	0.0490651	−	0.0849832i
$672$	16.4604	+	11.5766i	0.634974	+	0.446579i
$673$	22.6648	−	13.0855i	0.873663	−	0.504409i	0.00509891	−	0.999987i	$-0.498377\pi$
$673$	22.6648	−	13.0855i	0.873663	−	0.504409i	0.868564	+	0.495578i	$0.165044\pi$
$674$	−8.47916	−	14.6863i	−0.326605	−	0.565696i
$675$	−25.9057	+	1.97388i	−0.997110	+	0.0759745i
$676$	−4.81838	+	8.34567i	−0.185322	+	0.320987i
$677$	13.8808	+	8.01407i	0.533481	+	0.308006i	0.742433	−	0.669920i	$-0.233672\pi$
$677$	13.8808	+	8.01407i	0.533481	+	0.308006i	−0.208952	+	0.977926i	$0.567005\pi$
$678$	29.4607	+	5.71308i	1.13143	+	0.219409i
$679$	−4.13609	−	40.3277i	−0.158729	−	1.54764i
$680$	−1.65180	+	8.22213i	−0.0633438	+	0.315304i
$681$	31.0598	+	26.9758i	1.19021	+	1.03371i
$682$		−	5.80973i		−	0.222466i
$683$	44.4988	+	25.6914i	1.70270	+	0.983055i	0.943006	+	0.332775i	$0.107985\pi$
$683$	44.4988	+	25.6914i	1.70270	+	0.983055i	0.759695	+	0.650280i	$0.225348\pi$
$684$	1.14022	+	0.459508i	0.0435975	+	0.0175697i
$685$	−3.27759	−	9.71635i	−0.125230	−	0.371242i
$686$	−19.4542	−	4.28879i	−0.742765	−	0.163747i
$687$	8.75317	−	10.0784i	0.333954	−	0.384513i
$688$			5.43482i			0.207201i
$689$	5.29414	+	9.16972i	0.201691	+	0.349339i
$690$	15.5914	+	20.1978i	0.593556	+	0.768916i
$691$	−0.877461	+	1.51981i	−0.0333802	+	0.0578162i	−0.882233	−	0.470813i	$-0.843961\pi$
$691$	−0.877461	+	1.51981i	−0.0333802	+	0.0578162i	0.848853	+	0.528629i	$0.177294\pi$
$692$			3.04527i			0.115764i
$693$	−39.9834	−	11.5357i	−1.51884	−	0.438204i
$694$	17.7854			0.675124
$695$	9.14030	−	45.4974i	0.346711	−	1.72581i
$696$	6.89140	−	35.5370i	0.261218	−	1.34703i
$697$	10.2763	−	5.93305i	0.389244	−	0.224730i
$698$			33.9636i			1.28554i
$699$	−2.96454	+	15.2873i	−0.112129	+	0.578219i
$700$	8.13747	−	7.62482i	0.307567	−	0.288191i
$701$	32.1905			1.21582			0.607910	−	0.794006i	$-0.292008\pi$
$701$	32.1905			1.21582			0.607910	+	0.794006i	$0.292008\pi$
$702$	0.357047	−	6.99010i	0.0134759	−	0.263824i
$703$	−2.05765	−	1.18798i	−0.0776057	−	0.0448057i
$704$	41.5785			1.56705
$705$	3.68088	−	2.84141i	0.138630	−	0.107014i
$706$	−8.56277	+	14.8312i	−0.322264	+	0.558178i
$707$	−14.2837	+	31.8659i	−0.537195	+	1.19844i
$708$	4.87158	+	14.1278i	0.183085	+	0.530956i
$709$	−21.4966	+	37.2332i	−0.807322	+	1.39832i	0.107390	+	0.994217i	$0.465751\pi$
$709$	−21.4966	+	37.2332i	−0.807322	+	1.39832i	−0.914712	+	0.404106i	$0.867583\pi$
$710$	25.7701	+	5.17714i	0.967133	+	0.194294i
$711$	−42.4508	−	17.1076i	−1.59203	−	0.641585i
$712$	2.43526	−	1.40600i	0.0912651	−	0.0526920i
$713$	5.46427	−	3.15480i	0.204639	−	0.118148i
$714$	−3.47778	+	4.94493i	−0.130153	+	0.185059i
$715$	−14.3933	−	2.89157i	−0.538279	−	0.108139i
$716$	−13.1185			−0.490261
$717$	−6.55586	−	19.0123i	−0.244833	−	0.710028i
$718$		−	9.97582i		−	0.372294i
$719$	5.96616	+	10.3337i	0.222500	+	0.385382i	0.955567	−	0.294775i	$-0.0952448\pi$
$719$	5.96616	+	10.3337i	0.222500	+	0.385382i	−0.733066	+	0.680157i	$0.761911\pi$
$720$	10.7383	+	0.620808i	0.400192	+	0.0231362i
$721$	−42.3797	−	18.9965i	−1.57830	−	0.707468i
$722$	−17.4792	+	10.0916i	−0.650507	+	0.375570i
$723$	−1.06063	+	1.22121i	−0.0394453	+	0.0454171i
$724$	5.33365	+	9.23814i	0.198223	+	0.343333i
$725$	−31.5200	−	13.1972i	−1.17062	−	0.490132i
$726$	−29.0404	+	10.0138i	−1.07779	+	0.371646i
$727$	20.5189	−	11.8466i	0.761003	−	0.439365i	−0.0686526	−	0.997641i	$-0.521870\pi$
$727$	20.5189	−	11.8466i	0.761003	−	0.439365i	0.829656	+	0.558275i	$0.188537\pi$
$728$	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
$731$	4.15699			0.153752
$732$	0.464184	−	0.534459i	0.0171567	−	0.0197542i
$733$		−	37.9623i		−	1.40217i	−0.713077	−	0.701085i	$-0.752699\pi$
$733$		−	37.9623i		−	1.40217i	0.713077	−	0.701085i	$-0.247301\pi$
$734$	−2.79533	+	4.84165i	−0.103178	+	0.178709i
$735$	25.5751	−	8.99524i	0.943352	−	0.331795i
$736$	13.4480	+	23.2925i	0.495698	+	0.858575i
$737$	27.1953	−	15.7012i	1.00175	−	0.578361i
$738$	−19.2436	−	24.5859i	−0.708367	−	0.905019i
$739$	16.3851	−	28.3798i	0.602735	−	1.04397i	−0.389670	−	0.920954i	$-0.627411\pi$
$739$	16.3851	−	28.3798i	0.602735	−	1.04397i	0.992405	−	0.123013i	$-0.0392556\pi$
$740$	9.03266	+	1.81464i	0.332047	+	0.0667074i
$741$	0.796042	+	0.691372i	0.0292433	+	0.0253982i
$742$	−23.9375	+	2.45507i	−0.878772	+	0.0901285i
$743$	6.39744	+	3.69357i	0.234699	+	0.135504i	0.612738	−	0.790286i	$-0.290068\pi$
$743$	6.39744	+	3.69357i	0.234699	+	0.135504i	−0.378039	+	0.925790i	$0.623401\pi$
$744$	1.03879	−	5.35676i	0.0380840	−	0.196389i
$745$	−19.4823	+	6.57190i	−0.713775	+	0.240776i
$746$	−10.8955	+	18.8716i	−0.398914	+	0.690940i
$747$	−16.1134	−	20.5866i	−0.589557	−	0.753226i
$748$		−	5.42042i		−	0.198190i
$749$	1.43635	+	14.0047i	0.0524830	+	0.511721i
$750$	5.40970	−	20.1152i	0.197534	−	0.734502i
$751$	−19.7955			−0.722349			−0.361174	−	0.932498i	$-0.617624\pi$
$751$	−19.7955			−0.722349			−0.361174	+	0.932498i	$0.617624\pi$
$752$	−1.66721	+	0.962566i	−0.0607970	+	0.0351012i
$753$	−20.4282	+	23.5209i	−0.744445	+	0.857151i
$754$	4.60287	−	7.97240i	0.167627	−	0.290338i
$755$	19.1637	−	6.46442i	0.697437	−	0.235264i
$756$	−10.3196	−	5.27358i	−0.375320	−	0.191798i
$757$		−	29.7453i		−	1.08111i	−0.841308	−	0.540556i	$-0.818214\pi$
$757$		−	29.7453i		−	1.08111i	0.841308	−	0.540556i	$-0.181786\pi$
$758$	−10.5725	−	6.10406i	−0.384012	−	0.221710i
$759$	−41.9920	−	36.4705i	−1.52421	−	1.32380i
$760$	−2.19644	+	2.49494i	−0.0796732	+	0.0905008i
$761$	−19.8046			−0.717916			−0.358958	−	0.933354i	$-0.616868\pi$
$761$	−19.8046			−0.717916			−0.358958	+	0.933354i	$0.616868\pi$
$762$	−0.727933	−	2.11104i	−0.0263702	−	0.0764749i
$763$	−4.41701	−	6.11176i	−0.159906	−	0.221260i
$764$	−6.95282			−0.251544
$765$	0.474844	−	8.21350i	0.0171680	−	0.296960i
$766$	−13.4939	+	23.3721i	−0.487554	+	0.844468i
$767$			12.8171i			0.462800i
$768$	27.4309	+	5.31946i	0.989829	+	0.191949i
$769$	−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	$0.938975\pi$
$770$	19.3762	−	27.1609i	0.698268	−	0.978810i
$771$	−20.7166	−	17.9926i	−0.746090	−	0.647988i
$772$	−12.2189	−	7.05461i	−0.439769	−	0.253901i
$773$	−26.5351	−	15.3201i	−0.954403	−	0.551025i	−0.0599569	−	0.998201i	$-0.519096\pi$
$773$	−26.5351	−	15.3201i	−0.954403	−	0.551025i	−0.894446	+	0.447176i	$0.852430\pi$
$774$	−1.53180	−	10.8299i	−0.0550593	−	0.389272i
$775$	−4.75126	−	1.98932i	−0.170670	−	0.0714584i
$776$	−23.4283	−	40.5791i	−0.841028	−	1.45670i
$777$	18.3210	+	12.8852i	0.657263	+	0.462254i
$778$	13.6865	+	7.90191i	0.490685	+	0.283297i
$779$	4.70321			0.168510
$780$	−3.78173	−	1.55363i	−0.135408	−	0.0556287i
$781$	−57.2957			−2.05020
$782$	−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
$785$	11.3028	−	12.8388i	0.403413	−	0.458237i
$786$	2.85457	−	0.984319i	0.101819	−	0.0351095i
$787$	18.1997	−	10.5076i	0.648747	−	0.374555i	−0.139229	−	0.990260i	$-0.544462\pi$
$787$	18.1997	−	10.5076i	0.648747	−	0.374555i	0.787976	+	0.615706i	$0.211129\pi$
$788$	3.54042	−	2.04406i	0.126122	−	0.0728167i
$789$	16.4686	+	14.3032i	0.586298	+	0.509206i
$790$	24.2469	−	27.5421i	0.862667	−	0.979903i
$791$	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
$794$	14.0154			0.497387
$795$	25.9223	−	20.0105i	0.919370	−	0.709698i
$796$	19.9026			0.705430
$797$	19.8458	+	11.4580i	0.702975	+	0.405863i	0.808454	−	0.588559i	$-0.200304\pi$
$797$	19.8458	+	11.4580i	0.702975	+	0.405863i	−0.105480	+	0.994421i	$0.533638\pi$
$798$	−2.17374	+	1.00815i	−0.0769497	+	0.0356882i
$799$	0.736247	+	1.27522i	0.0260466	+	0.0451140i
$800$	8.47987	−	20.2532i	0.299809	−	0.716058i
$801$	−2.17232	+	1.70029i	−0.0767551	+	0.0600769i
$802$	13.9061	+	8.02870i	0.491042	+	0.283503i
$803$	16.7509	+	9.67116i	0.591128	+	0.341288i
$804$	8.26744	−	2.85079i	0.291570	−	0.100540i
$805$	36.0674	+	3.47510i	1.27121	+	0.122481i
$806$	0.693826	−	1.20174i	0.0244390	−	0.0423296i
$807$	−2.62795	−	7.62119i	−0.0925083	−	0.268279i
$808$			40.3626i			1.41995i
$809$	12.0649	−	20.8971i	0.424180	−	0.734702i	−0.572163	−	0.820140i	$-0.693896\pi$
$809$	12.0649	−	20.8971i	0.424180	−	0.734702i	0.996344	+	0.0854378i	$0.0272289\pi$
$810$	−21.5730	+	1.78950i	−0.757997	+	0.0628766i
$811$	4.77761			0.167764			0.0838822	−	0.996476i	$-0.473268\pi$
$811$	4.77761			0.167764			0.0838822	+	0.996476i	$0.473268\pi$
$812$	−8.92825	−	12.3539i	−0.313320	−	0.433537i
$813$	20.7103	+	4.01618i	0.726341	+	0.140854i
$814$	27.5645			0.966135
$815$	−11.8727	+	13.4862i	−0.415883	+	0.472402i
$816$	−0.648442	+	3.34383i	−0.0227000	+	0.117058i
$817$	1.42691	+	0.823825i	0.0499212	+	0.0288220i
$818$			1.94367i			0.0679590i
$819$	−6.89291	−	7.16116i	−0.240858	−	0.250231i
$820$	−17.2806	+	5.82922i	−0.603465	+	0.203565i
$821$	3.25997	−	5.64644i	0.113774	−	0.197062i	−0.803515	−	0.595284i	$-0.797039\pi$
$821$	3.25997	−	5.64644i	0.113774	−	0.197062i	0.917289	+	0.398222i	$0.130373\pi$
$822$	−2.78516	−	8.07710i	−0.0971436	−	0.281721i
$823$	−4.82761	+	2.78722i	−0.168280	+	0.0971565i	−0.581775	−	0.813350i	$-0.697641\pi$
$823$	−4.82761	+	2.78722i	−0.168280	+	0.0971565i	0.413495	+	0.910507i	$0.364308\pi$
$824$	−53.6798			−1.87003
$825$	−2.92486	+	45.3105i	−0.101831	+	1.57751i
$826$	−26.5802	−	11.9145i	−0.924843	−	0.414557i
$827$		−	4.68443i		−	0.162894i	−0.996678	−	0.0814469i	$-0.974046\pi$
$827$		−	4.68443i		−	0.162894i	0.996678	−	0.0814469i	$-0.0259541\pi$
$828$	−9.54677	−	12.1971i	−0.331773	−	0.423878i
$829$	−2.03293	+	3.52113i	−0.0706064	+	0.122294i	−0.899167	−	0.437605i	$-0.855827\pi$
$829$	−2.03293	+	3.52113i	−0.0706064	+	0.122294i	0.828561	+	0.559899i	$0.189160\pi$
$830$	19.8603	−	6.69943i	0.689363	−	0.232541i
$831$	−16.7925	−	14.5845i	−0.582525	−	0.505930i
$832$	8.60051	+	4.96551i	0.298169	+	0.172148i
$833$	1.74268	+	8.40636i	0.0603801	+	0.291263i
$834$	7.36098	−	37.9585i	0.254890	−	1.31439i
$835$	−43.6882	−	8.77684i	−1.51189	−	0.303735i
$836$	1.07421	−	1.86059i	0.0371523	−	0.0643497i
$837$	−0.273068	+	5.34601i	−0.00943863	+	0.184785i
$838$	−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	$0.497296\pi$
$840$	22.7219	−	21.5787i	0.783979	−	0.744537i
$841$	−8.85356	+	15.3348i	−0.305295	+	0.528787i
$842$		−	26.7369i		−	0.921415i
$843$	35.7770	+	6.93795i	1.23223	+	0.238956i
$844$	−9.51839			−0.327636
$845$	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
$849$	4.39571	−	22.6674i	0.150860	−	0.777944i
$850$	6.08433	+	2.54747i	0.208691	+	0.0873774i
$851$	14.9681	+	25.9254i	0.513098	+	0.888712i
$852$	−15.6643	−	3.03765i	−0.536649	−	0.104068i
$853$	−16.7252	+	9.65632i	−0.572661	+	0.330626i	−0.758212	−	0.652009i	$-0.773927\pi$
$853$	−16.7252	+	9.65632i	−0.572661	+	0.330626i	0.185550	+	0.982635i	$0.440593\pi$
$854$	0.140775	+	1.37259i	0.00481724	+	0.0469691i
$855$	1.79073	−	2.72522i	0.0612417	−	0.0932006i
$856$	8.13601	+	14.0920i	0.278083	+	0.481654i
$857$			14.2679i			0.487381i	0.969853	+	0.243691i	$0.0783582\pi$
$857$			14.2679i			0.487381i	−0.969853	+	0.243691i	$0.921642\pi$
$858$	−12.0083	−	2.32868i	−0.409958	−	0.0794998i
$859$	7.32178			0.249816			0.124908	−	0.992168i	$-0.460136\pi$
$859$	7.32178			0.249816			0.124908	+	0.992168i	$0.460136\pi$
$860$	−6.26383	−	1.25839i	−0.213595	−	0.0429106i
$861$	−44.1606	−	3.95584i	−1.50499	−	0.134815i
$862$	−0.0935233	+	0.0539957i	−0.00318542	+	0.00183910i
$863$	−45.8510	+	26.4721i	−1.56079	+	0.901121i	−0.563610	+	0.826041i	$0.690588\pi$
$863$	−45.8510	+	26.4721i	−1.56079	+	0.901121i	−0.997177	+	0.0750805i	$0.976079\pi$
$864$	−22.7884	−	1.16401i	−0.775278	−	0.0396004i
$865$	7.91963	+	1.59103i	0.269275	+	0.0540967i
$866$	17.6550	−	30.5794i	0.599942	−	1.03913i
$867$	−26.3487	−	5.10959i	−0.894850	−	0.173531i
$868$	−1.34583	−	1.86220i	−0.0456803	−	0.0632072i
$869$	−39.9931	+	69.2700i	−1.35667	+	2.34983i
$870$	−26.3356	−	10.8193i	−0.892859	−	0.366808i
$871$	7.50045			0.254143
$872$	−7.54819	−	4.35795i	−0.255614	−	0.147579i
$873$	28.3322	+	36.1976i	0.958901	+	1.22510i
$874$	−3.20252			−0.108327
$875$	−15.5778	−	25.1462i	−0.526627	−	0.850097i
$876$	4.06686	+	3.53211i	0.137406	+	0.119339i
$877$			43.4353i			1.46671i	0.679847	+	0.733354i	$0.262046\pi$
$877$			43.4353i			1.46671i	−0.679847	+	0.733354i	$0.737954\pi$
$878$	−3.34827	+	1.93313i	−0.112999	+	0.0652399i
$879$	−10.6984	+	3.68905i	−0.360849	+	0.124429i
$880$	3.70247	−	18.4297i	0.124810	−	0.621264i
$881$	27.9517			0.941718			0.470859	−	0.882208i	$-0.343944\pi$
$881$	27.9517			0.941718			0.470859	+	0.882208i	$0.343944\pi$
$882$	21.2583	−	7.63769i	0.715803	−	0.257174i
$883$			30.6255i			1.03063i	0.857001	+	0.515315i	$0.172325\pi$
$883$			30.6255i			1.03063i	−0.857001	+	0.515315i	$0.827675\pi$
$884$	0.647332	−	1.12121i	0.0217721	−	0.0377105i
$885$	39.2864	−	5.28796i	1.32060	−	0.177753i
$886$	16.9537	+	29.3646i	0.569569	+	0.986523i
$887$		−	19.7229i		−	0.662231i	−0.943590	−	0.331115i	$-0.892575\pi$
$887$		−	19.7229i		−	0.662231i	0.943590	−	0.331115i	$-0.107425\pi$
$888$	25.4154	+	4.92860i	0.852884	+	0.165393i
$889$	−2.89369	−	1.29708i	−0.0970512	−	0.0435028i
$890$	−0.706929	−	2.09568i	−0.0236963	−	0.0702473i
$891$	45.3351	−	13.0864i	1.51878	−	0.438410i
$892$	11.0740	+	6.39357i	0.370784	+	0.214072i
$893$			0.583633i			0.0195305i
$894$	−16.1954	+	5.58453i	−0.541656	+	0.186775i
$895$	−6.85387	+	34.1163i	−0.229100	+	1.14038i
$896$	0.541052	−	0.391022i	0.0180753	−	0.0130631i
$897$	−4.33055	−	12.5588i	−0.144593	−	0.419326i
$898$	32.2446	+	18.6164i	1.07601	+	0.621237i
$899$	−3.52026	+	6.09728i	−0.117407	+	0.203356i
$900$	−3.20186	+	12.2325i	−0.106729	+	0.407751i
$901$	5.18497	+	8.98064i	0.172737	+	0.299188i
$902$	−47.2535	+	27.2818i	−1.57337	+	0.908386i
$903$	−12.7050	−	8.93544i	−0.422796	−	0.297353i
$904$	24.6287	−	42.6582i	0.819139	−	1.41879i
$905$	26.8116	−	9.04428i	0.891248	−	0.300642i
$906$	15.9306	−	5.49321i	0.529258	−	0.182500i
$907$			7.76644i			0.257881i	0.991652	+	0.128940i	$0.0411576\pi$
$907$			7.76644i			0.257881i	−0.991652	+	0.128940i	$0.958842\pi$
$908$	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	$0.787323\pi$
$912$	−0.885256	+	1.01928i	−0.0293138	+	0.0337517i
$913$	−39.5671	+	22.8441i	−1.30948	+	0.756028i
$914$	9.41892	+	16.3140i	0.311550	+	0.539621i
$915$	−1.14741	−	1.48640i	−0.0379323	−	0.0491390i
$916$	−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	0.979762	−	0.200164i	$-0.0641475\pi$
$919$	9.59574	+	16.6203i	0.316534	+	0.548253i	−0.663228	+	0.748417i	$0.730814\pi$
$920$	39.6840	−	13.3865i	1.30834	−	0.441340i
$921$	11.5950	+	10.0704i	0.382069	+	0.331831i
$922$			1.49631i			0.0492783i
$923$	−11.8516	−	6.84253i	−0.390101	−	0.225225i
$924$	−11.6512	+	16.5664i	−0.383296	+	0.544995i
$925$	9.43839	−	22.5425i	0.310332	−	0.741193i
$926$	−2.46332	−	4.26660i	−0.0809498	−	0.140209i
$927$	52.1419	−	7.37505i	1.71256	−	0.242228i
$928$	−25.9909	−	15.0058i	−0.853192	−	0.492590i
$929$	5.59666	−	9.69371i	0.183621	−	0.318040i	−0.759490	−	0.650519i	$-0.774552\pi$
$929$	5.59666	−	9.69371i	0.183621	−	0.318040i	0.943111	+	0.332478i	$0.107885\pi$
$930$	−3.96977	−	1.63088i	−0.130174	−	0.0534785i
$931$	−1.06778	+	3.23088i	−0.0349949	+	0.105888i
$932$	6.56345	+	3.78941i	0.214993	+	0.124126i
$933$	−3.47069	−	0.673043i	−0.113625	−	0.0220344i
$934$	9.50127			0.310891
$935$	−14.0965	−	2.83195i	−0.461005	−	0.0926146i
$936$	−10.6557	−	4.29424i	−0.348293	−	0.140361i
$937$		−	14.5502i		−	0.475333i	−0.971347	−	0.237667i	$-0.923617\pi$
$937$		−	14.5502i		−	0.475333i	0.971347	−	0.237667i	$-0.0763826\pi$
$938$	−6.97221	+	15.5544i	−0.227651	+	0.507870i
$939$	6.33555	−	2.18464i	0.206753	−	0.0712929i
$940$	−0.723363	−	2.14440i	−0.0235935	−	0.0699425i
$941$	20.0159	+	34.6685i	0.652499	+	1.13016i	0.982515	+	0.186186i	$0.0596126\pi$
$941$	20.0159	+	34.6685i	0.652499	+	1.13016i	−0.330016	+	0.943975i	$0.607054\pi$
$942$	9.34537	−	10.7602i	0.304489	−	0.350587i
$943$	−51.3192	−	29.6291i	−1.67118	−	0.964857i
$944$	−16.4115			−0.534150
$945$	−19.1062	+	24.0822i	−0.621524	+	0.783395i
$946$	−19.1150			−0.621483
$947$	−15.4476	−	8.91866i	−0.501978	−	0.289817i	0.227552	−	0.973766i	$-0.426928\pi$
$947$	−15.4476	−	8.91866i	−0.501978	−	0.289817i	−0.729530	+	0.683949i	$0.760261\pi$
$948$	−14.6063	+	16.8177i	−0.474392	+	0.546212i
$949$	2.30995	+	4.00096i	0.0749842	+	0.129877i
$950$	1.58363	+	2.08021i	0.0513796	+	0.0674911i
$951$	−8.15278	+	2.81126i	−0.264372	+	0.0911613i
$952$	5.81235	+	8.04247i	0.188379	+	0.260658i
$953$			27.3592i			0.886250i	0.896460	+	0.443125i	$0.146130\pi$
$953$			27.3592i			0.886250i	−0.896460	+	0.443125i	$0.853870\pi$
$954$	21.4859	−	16.8173i	0.695633	−	0.544479i
$955$	−3.63257	+	18.0817i	−0.117547	+	0.585110i
$956$	−9.78780			−0.316560
$957$	60.9266	+	11.8150i	1.96948	+	0.381925i
$958$	20.3151	+	11.7289i	0.656352	+	0.378945i
$959$	−11.0716	−	4.96280i	−0.357521	−	0.160257i
$960$	11.6717	−	28.4104i	0.376702	−	0.916942i
$961$	14.9694	−	25.9277i	0.482883	−	0.836377i
$962$	5.70171	+	3.29188i	0.183831	+	0.106135i
$963$	−9.83900	−	12.5704i	−0.317057	−	0.405077i
$964$	0.393610	+	0.681753i	0.0126773	+	0.0219578i
$965$	−24.7303	+	28.0912i	−0.796097	+	0.904287i
$966$	30.0700	+	2.69362i	0.967486	+	0.0866658i
$967$	−5.81388	−	3.35665i	−0.186962	−	0.107942i	0.403598	−	0.914937i	$-0.367760\pi$
$967$	−5.81388	−	3.35665i	−0.186962	−	0.107942i	−0.590560	+	0.806994i	$0.701093\pi$
$968$			50.4210i			1.62059i
$969$	0.779627	+	0.677115i	0.0250452	+	0.0217521i
$970$	−34.9206	+	11.7797i	−1.12123	+	0.378222i
$971$	−6.31670	−	10.9408i	−0.202712	−	0.351108i	0.746689	−	0.665173i	$-0.231642\pi$
$971$	−6.31670	−	10.9408i	−0.202712	−	0.351108i	−0.949401	+	0.314065i	$0.898309\pi$
$972$	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
$975$	−6.01621	+	9.02317i	−0.192673	+	0.288973i
$976$	0.388701	+	0.673250i	0.0124420	+	0.0215502i
$977$	36.3769	−	21.0022i	1.16380	−	0.671921i	0.211589	−	0.977359i	$-0.432136\pi$
$977$	36.3769	−	21.0022i	1.16380	−	0.671921i	0.952212	+	0.305438i	$0.0988028\pi$
$978$	−9.81663	+	11.3028i	−0.313901	+	0.361424i
$979$	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
$983$			30.0116i			0.957221i	0.878027	+	0.478610i	$0.158859\pi$
$983$			30.0116i			0.957221i	−0.878027	+	0.478610i	$0.841141\pi$
$984$	−48.4474	+	16.7057i	−1.54445	+	0.532558i
$985$	−3.46612	−	10.2753i	−0.110440	−	0.327397i
$986$	4.50796	−	7.80801i	0.143563	−	0.248658i
$987$	0.490890	−	5.48001i	0.0156252	−	0.174431i
$988$	0.444400	−	0.256575i	0.0141383	−	0.00816272i
$989$	−10.3798	−	17.9784i	−0.330059	−	0.571679i
$990$	−2.18347	+	37.7680i	−0.0693952	+	1.20035i
$991$	−19.6179	+	33.9791i	−0.623182	+	1.07938i	0.365707	+	0.930730i	$0.380827\pi$
$991$	−19.6179	+	33.9791i	−0.623182	+	1.07938i	−0.988889	+	0.148653i	$0.952506\pi$
$992$	−3.91780	−	2.26195i	−0.124390	−	0.0718168i
$993$	16.9174	+	49.0613i	0.536858	+	1.55691i
$994$	25.2070	−	18.2172i	0.799516	−	0.577816i
$995$	10.3983	−	51.7594i	0.329649	−	1.64088i
$996$	−12.0285	+	4.14769i	−0.381138	+	0.131425i
$997$			32.6433i			1.03382i	0.856039	+	0.516911i	$0.172918\pi$
$997$			32.6433i			1.03382i	−0.856039	+	0.516911i	$0.827082\pi$
$998$	21.3926	+	12.3510i	0.677172	+	0.390965i
$999$	−25.3643	−	1.29558i	−0.802492	−	0.0409904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.15	yes	84
3.2	odd	2		945.2.bo.b.739.28		84
5.4	even	2	inner	315.2.bo.b.4.28	yes	84
7.2	even	3		315.2.r.b.184.28	yes	84
9.2	odd	6		945.2.r.b.424.15		84
9.7	even	3		315.2.r.b.214.28	yes	84
15.14	odd	2		945.2.bo.b.739.15		84
21.2	odd	6		945.2.r.b.604.15		84
35.9	even	6		315.2.r.b.184.15	✓	84
45.29	odd	6		945.2.r.b.424.28		84
45.34	even	6		315.2.r.b.214.15	yes	84
63.2	odd	6		945.2.bo.b.289.15		84
63.16	even	3	inner	315.2.bo.b.79.28	yes	84
105.44	odd	6		945.2.r.b.604.28		84
315.79	even	6	inner	315.2.bo.b.79.15	yes	84
315.254	odd	6		945.2.bo.b.289.28		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.15	✓	84	35.9	even	6
315.2.r.b.184.28	yes	84	7.2	even	3
315.2.r.b.214.15	yes	84	45.34	even	6
315.2.r.b.214.28	yes	84	9.7	even	3
315.2.bo.b.4.15	yes	84	1.1	even	1	trivial
315.2.bo.b.4.28	yes	84	5.4	even	2	inner
315.2.bo.b.79.15	yes	84	315.79	even	6	inner
315.2.bo.b.79.28	yes	84	63.16	even	3	inner
945.2.r.b.424.15		84	9.2	odd	6
945.2.r.b.424.28		84	45.29	odd	6
945.2.r.b.604.15		84	21.2	odd	6
945.2.r.b.604.28		84	105.44	odd	6
945.2.bo.b.289.15		84	63.2	odd	6
945.2.bo.b.289.28		84	315.254	odd	6
945.2.bo.b.739.15		84	15.14	odd	2
945.2.bo.b.739.28		84	3.2	odd	2

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.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.931541 - 0.537825i) q^{2} +(1.13575 - 1.30770i) q^{3} +(-0.421488 - 0.730038i) q^{4} +(-2.11877 + 0.714718i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(-1.08220 + 2.41430i) q^{7} +3.05805i q^{8} +(-0.420144 - 2.97043i) q^{9} +O(q^{10})\)	\(q+(-0.931541 - 0.537825i) q^{2} +(1.13575 - 1.30770i) q^{3} +(-0.421488 - 0.730038i) q^{4} +(-2.11877 + 0.714718i) q^{5} +(-1.76131 + 0.607338i) q^{6} +(-1.08220 + 2.41430i) q^{7} +3.05805i q^{8} +(-0.420144 - 2.97043i) q^{9} +(2.35811 + 0.473738i) q^{10} -5.24290 q^{11} +(-1.43337 - 0.277962i) q^{12} +(-1.08449 - 0.626132i) q^{13} +(2.30659 - 1.66698i) q^{14} +(-1.47176 + 3.58245i) q^{15} +(0.801721 - 1.38862i) q^{16} +(-1.06213 - 0.613221i) q^{17} +(-1.20619 + 2.99305i) q^{18} +(-0.243054 - 0.420982i) q^{19} +(1.41481 + 1.24554i) q^{20} +(1.92806 + 4.15723i) q^{21} +(4.88397 + 2.81976i) q^{22} +6.12474i q^{23} +(3.99900 + 3.47318i) q^{24} +(3.97836 - 3.02864i) 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} +(3.29773 - 2.54565i) q^{30} +(-0.515091 - 0.892163i) q^{31} +(3.80302 - 2.19568i) q^{32} +(-5.95462 + 6.85612i) 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} +0.522883i q^{38} +(-2.05050 + 0.707058i) q^{39} +(-2.18564 - 6.47930i) q^{40} +(-4.83761 + 8.37899i) q^{41} +(0.439793 - 4.90959i) q^{42} +(-2.93537 + 1.69474i) q^{43} +(2.20982 + 3.82751i) q^{44} +(3.01321 + 5.99338i) q^{45} +(3.29404 - 5.70545i) q^{46} +(-1.03977 - 0.600312i) q^{47} +(-0.905342 - 2.62554i) q^{48} +(-4.65769 - 5.22551i) q^{49} +(-5.33488 + 0.681643i) q^{50} +(-2.00822 + 0.692478i) q^{51} +1.05563i q^{52} +(-7.32252 - 4.22766i) q^{53} +(2.54406 + 4.97669i) q^{54} +(11.1085 - 3.74719i) q^{55} +(-7.38305 - 3.30942i) q^{56} +(-0.826566 - 0.160289i) q^{57} +7.35128i q^{58} +(-5.11759 - 8.86393i) q^{59} +(3.23565 - 0.435519i) q^{60} +(-0.242417 + 0.419878i) q^{61} +1.10812i q^{62} +(7.62620 + 2.20025i) q^{63} -7.93045 q^{64} +(2.74529 + 0.551522i) q^{65} +(9.23437 - 3.18421i) q^{66} +(-5.18707 + 2.99476i) q^{67} +1.03386i q^{68} +(8.00931 + 6.95618i) q^{69} +(-3.69570 + 5.18051i) q^{70} +10.9283 q^{71} +(9.08373 - 1.28482i) q^{72} +(-3.19498 - 1.84462i) q^{73} -5.25749 q^{74} +(0.557871 - 8.64227i) q^{75} +(-0.204889 + 0.354877i) q^{76} +(5.67386 - 12.6579i) q^{77} +(2.29040 + 0.444159i) q^{78} +(7.62805 - 13.2122i) q^{79} +(-0.706189 + 3.51517i) q^{80} +(-8.64696 + 2.49602i) q^{81} +(9.01287 - 5.20358i) q^{82} +(7.54680 - 4.35715i) q^{83} +(2.22228 - 3.15978i) q^{84} +(2.68869 + 0.540150i) q^{85} +3.64589 q^{86} +(-11.6208 - 2.25353i) q^{87} -16.0330i q^{88} +(-0.459769 - 0.796344i) q^{89} +(0.416462 - 7.20366i) q^{90} +(2.68531 - 1.94069i) q^{91} +(4.47130 - 2.58150i) q^{92} +(-1.75169 - 0.339692i) q^{93} +(0.645726 + 1.11843i) q^{94} +(0.815859 + 0.718248i) q^{95} +(1.44800 - 7.46694i) q^{96} +(-13.2696 + 7.66120i) q^{97} +(1.52841 + 7.37280i) q^{98} +(2.20277 + 15.5737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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