LMFDB - Embedded newform 546.2.bu.a.449.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			449.4
Character	$\chi$	$=$	546.449
Dual form			546.2.bu.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.684122 - 1.59122i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.803802 - 0.803802i) q^{5} +(-1.71406 - 0.248973i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.06396 - 2.17717i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.684122 - 1.59122i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.803802 - 0.803802i) q^{5} +(-1.71406 - 0.248973i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.06396 - 2.17717i) q^{9} +(-0.984452 - 0.568374i) q^{10} +(-3.42199 + 0.916918i) q^{11} +(0.203143 + 1.72010i) q^{12} +(2.52032 - 2.57836i) q^{13} -1.00000i q^{14} +(-0.729126 - 1.82892i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.65463 - 6.33001i) q^{17} +(-1.56880 + 2.55712i) q^{18} +(1.28797 - 4.80679i) q^{19} +(-0.294212 + 1.09801i) q^{20} +(1.07265 - 1.35994i) q^{21} +(1.77135 + 3.06807i) q^{22} +(-0.368272 + 0.637865i) q^{23} +(1.60891 - 0.641415i) q^{24} +3.70781i q^{25} +(-3.14282 - 1.76712i) q^{26} +(-4.87636 + 1.79475i) q^{27} +(-0.965926 + 0.258819i) q^{28} +(1.05961 + 0.611766i) q^{29} +(-1.57789 + 1.17764i) q^{30} +(2.78096 + 2.78096i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.882037 + 6.07241i) q^{33} +(-5.16843 + 5.16843i) q^{34} +(0.984452 - 0.568374i) q^{35} +(2.87602 + 0.853511i) q^{36} +(-0.635866 - 2.37309i) q^{37} -4.97635 q^{38} +(-2.37853 - 5.77430i) q^{39} +1.13675 q^{40} +(-1.57828 - 5.89022i) q^{41} +(-1.59122 - 0.684122i) q^{42} +(2.20536 - 1.27327i) q^{43} +(2.50507 - 2.50507i) q^{44} +(-3.40903 - 0.0910061i) q^{45} +(0.711446 + 0.190631i) q^{46} +(7.99659 + 7.99659i) q^{47} +(-1.03598 - 1.38808i) q^{48} +(0.866025 + 0.500000i) q^{49} +(3.58147 - 0.959651i) q^{50} +(-12.5726 + 1.48482i) q^{51} +(-0.893482 + 3.49309i) q^{52} +7.87957i q^{53} +(2.99569 + 4.24568i) q^{54} +(-2.01358 + 3.48762i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-6.76752 - 5.33788i) q^{57} +(0.316673 - 1.18184i) q^{58} +(0.645602 - 2.40942i) q^{59} +(1.54590 + 1.21933i) q^{60} +(-1.63757 - 2.83635i) q^{61} +(1.96644 - 3.40597i) q^{62} +(-1.43013 - 2.63718i) q^{63} +1.00000i q^{64} +(-0.0466531 - 4.09833i) q^{65} +(6.09379 - 0.719674i) q^{66} +(-1.47511 + 0.395253i) q^{67} +(6.33001 + 3.65463i) q^{68} +(0.763041 + 1.02238i) q^{69} +(-0.803802 - 0.803802i) q^{70} +(4.91302 + 1.31644i) q^{71} +(0.0800584 - 2.99893i) q^{72} +(-11.3512 + 11.3512i) q^{73} +(-2.12765 + 1.22840i) q^{74} +(5.89993 + 2.53659i) q^{75} +(1.28797 + 4.80679i) q^{76} -3.54270 q^{77} +(-4.96194 + 3.79199i) q^{78} +11.0080 q^{79} +(-0.294212 - 1.09801i) q^{80} +(-0.480179 + 8.98718i) q^{81} +(-5.28103 + 3.04900i) q^{82} +(10.0746 - 10.0746i) q^{83} +(-0.248973 + 1.71406i) q^{84} +(-8.02567 - 2.15047i) q^{85} +(-1.80067 - 1.80067i) q^{86} +(1.69836 - 1.26755i) q^{87} +(-3.06807 - 1.77135i) q^{88} +(15.9782 - 4.28134i) q^{89} +(0.794416 + 3.31642i) q^{90} +(3.10178 - 1.83820i) q^{91} -0.736543i q^{92} +(6.32763 - 2.52260i) q^{93} +(5.65444 - 9.79378i) q^{94} +(-2.82843 - 4.89898i) q^{95} +(-1.07265 + 1.35994i) q^{96} +(1.07287 - 4.00399i) q^{97} +(0.258819 - 0.965926i) q^{98} +(9.05912 + 5.55778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.684122	−	1.59122i	0.394978	−	0.918691i
$3$	0.684122	−	1.59122i	0.394978	−	0.918691i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.803802	−	0.803802i	0.359471	−	0.359471i	−0.504147	−	0.863618i	$-0.668193\pi$
$5$	0.803802	−	0.803802i	0.359471	−	0.359471i	0.863618	+	0.504147i	$0.168193\pi$
$6$	−1.71406	−	0.248973i	−0.699763	−	0.101643i
$7$	0.965926	+	0.258819i	0.365086	+	0.0978244i
$7$	0.965926	+	0.258819i	0.365086	+	0.0978244i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.06396	−	2.17717i	−0.687985	−	0.725725i
$10$	−0.984452	−	0.568374i	−0.311311	−	0.179735i
$11$	−3.42199	+	0.916918i	−1.03177	+	0.276461i	−0.734698	−	0.678394i	$-0.762676\pi$
$11$	−3.42199	+	0.916918i	−1.03177	+	0.276461i	−0.297070	+	0.954856i	$0.596009\pi$
$12$	0.203143	+	1.72010i	0.0586422	+	0.496549i
$13$	2.52032	−	2.57836i	0.699012	−	0.715110i
$13$	2.52032	−	2.57836i	0.699012	−	0.715110i
$14$		−	1.00000i		−	0.267261i
$15$	−0.729126	−	1.82892i	−0.188260	−	0.472226i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.65463	−	6.33001i	−0.886378	−	1.53525i	−0.844126	−	0.536145i	$-0.819880\pi$
$17$	−3.65463	−	6.33001i	−0.886378	−	1.53525i	−0.0422523	−	0.999107i	$-0.513453\pi$
$18$	−1.56880	+	2.55712i	−0.369769	+	0.602719i
$19$	1.28797	−	4.80679i	0.295482	−	1.10275i	−0.645352	−	0.763885i	$-0.723289\pi$
$19$	1.28797	−	4.80679i	0.295482	−	1.10275i	0.940834	−	0.338868i	$-0.110044\pi$
$20$	−0.294212	+	1.09801i	−0.0657878	+	0.245523i
$21$	1.07265	−	1.35994i	0.234071	−	0.296762i
$22$	1.77135	+	3.06807i	0.377653	+	0.654115i
$23$	−0.368272	+	0.637865i	−0.0767900	+	0.133004i	−0.901863	−	0.432022i	$-0.857800\pi$
$23$	−0.368272	+	0.637865i	−0.0767900	+	0.133004i	0.825073	+	0.565026i	$0.191134\pi$
$24$	1.60891	−	0.641415i	0.328417	−	0.130928i
$25$			3.70781i			0.741561i
$26$	−3.14282	−	1.76712i	−0.616357	−	0.346560i
$27$	−4.87636	+	1.79475i	−0.938456	+	0.345400i
$28$	−0.965926	+	0.258819i	−0.182543	+	0.0489122i
$29$	1.05961	+	0.611766i	0.196765	+	0.113602i	0.595145	−	0.803618i	$-0.297094\pi$
$29$	1.05961	+	0.611766i	0.196765	+	0.113602i	−0.398381	+	0.917220i	$0.630428\pi$
$30$	−1.57789	+	1.17764i	−0.288082	+	0.215007i
$31$	2.78096	+	2.78096i	0.499475	+	0.499475i	0.911275	−	0.411799i	$-0.135100\pi$
$31$	2.78096	+	2.78096i	0.499475	+	0.499475i	−0.411799	+	0.911275i	$0.635100\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.882037	+	6.07241i	−0.153543	+	1.05707i
$34$	−5.16843	+	5.16843i	−0.886378	+	0.886378i
$35$	0.984452	−	0.568374i	0.166403	−	0.0960727i
$36$	2.87602	+	0.853511i	0.479337	+	0.142252i
$37$	−0.635866	−	2.37309i	−0.104536	−	0.390133i	0.893756	−	0.448553i	$-0.148060\pi$
$37$	−0.635866	−	2.37309i	−0.104536	−	0.390133i	−0.998292	+	0.0584200i	$0.981394\pi$
$38$	−4.97635			−0.807271
$39$	−2.37853	−	5.77430i	−0.380870	−	0.924628i
$40$	1.13675			0.179735
$41$	−1.57828	−	5.89022i	−0.246486	−	0.919898i	−0.972631	−	0.232356i	$-0.925357\pi$
$41$	−1.57828	−	5.89022i	−0.246486	−	0.919898i	0.726145	−	0.687542i	$-0.241310\pi$
$42$	−1.59122	−	0.684122i	−0.245530	−	0.105562i
$43$	2.20536	−	1.27327i	0.336315	−	0.194171i	−0.322326	−	0.946629i	$-0.604465\pi$
$43$	2.20536	−	1.27327i	0.336315	−	0.194171i	0.658641	+	0.752457i	$0.271132\pi$
$44$	2.50507	−	2.50507i	0.377653	−	0.377653i
$45$	−3.40903	−	0.0910061i	−0.508188	−	0.0135664i
$46$	0.711446	+	0.190631i	0.104897	+	0.0281071i
$47$	7.99659	+	7.99659i	1.16642	+	1.16642i	0.983042	+	0.183380i	$0.0587039\pi$
$47$	7.99659	+	7.99659i	1.16642	+	1.16642i	0.183380	+	0.983042i	$0.441296\pi$
$48$	−1.03598	−	1.38808i	−0.149530	−	0.200352i
$49$	0.866025	+	0.500000i	0.123718	+	0.0714286i
$50$	3.58147	−	0.959651i	0.506496	−	0.135715i
$51$	−12.5726	+	1.48482i	−1.76052	+	0.207917i
$52$	−0.893482	+	3.49309i	−0.123904	+	0.484405i
$53$			7.87957i			1.08234i	0.840913	+	0.541171i	$0.182019\pi$
$53$			7.87957i			1.08234i	−0.840913	+	0.541171i	$0.817981\pi$
$54$	2.99569	+	4.24568i	0.407662	+	0.577764i
$55$	−2.01358	+	3.48762i	−0.271511	+	0.470270i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−6.76752	−	5.33788i	−0.896380	−	0.707019i
$58$	0.316673	−	1.18184i	0.0415813	−	0.155183i
$59$	0.645602	−	2.40942i	0.0840502	−	0.313680i	−0.911082	−	0.412224i	$-0.864752\pi$
$59$	0.645602	−	2.40942i	0.0840502	−	0.313680i	0.995133	+	0.0985446i	$0.0314187\pi$
$60$	1.54590	+	1.21933i	0.199575	+	0.157415i
$61$	−1.63757	−	2.83635i	−0.209669	−	0.363157i	0.741941	−	0.670465i	$-0.233905\pi$
$61$	−1.63757	−	2.83635i	−0.209669	−	0.363157i	−0.951610	+	0.307308i	$0.900572\pi$
$62$	1.96644	−	3.40597i	0.249738	−	0.432558i
$63$	−1.43013	−	2.63718i	−0.180180	−	0.332253i
$64$			1.00000i			0.125000i
$65$	−0.0466531	−	4.09833i	−0.00578661	−	0.508336i
$66$	6.09379	−	0.719674i	0.750094	−	0.0885857i
$67$	−1.47511	+	0.395253i	−0.180213	+	0.0482879i	−0.347797	−	0.937570i	$-0.613070\pi$
$67$	−1.47511	+	0.395253i	−0.180213	+	0.0482879i	0.167584	+	0.985858i	$0.446403\pi$
$68$	6.33001	+	3.65463i	0.767626	+	0.443189i
$69$	0.763041	+	1.02238i	0.0918593	+	0.123080i
$70$	−0.803802	−	0.803802i	−0.0960727	−	0.0960727i
$71$	4.91302	+	1.31644i	0.583068	+	0.156233i	0.538283	−	0.842764i	$-0.319073\pi$
$71$	4.91302	+	1.31644i	0.583068	+	0.156233i	0.0447851	+	0.998997i	$0.485740\pi$
$72$	0.0800584	−	2.99893i	0.00943497	−	0.353427i
$73$	−11.3512	+	11.3512i	−1.32855	+	1.32855i	−0.421919	+	0.906634i	$0.638643\pi$
$73$	−11.3512	+	11.3512i	−1.32855	+	1.32855i	−0.906634	+	0.421919i	$0.861357\pi$
$74$	−2.12765	+	1.22840i	−0.247334	+	0.142799i
$75$	5.89993	+	2.53659i	0.681265	+	0.292900i
$76$	1.28797	+	4.80679i	0.147741	+	0.551376i
$77$	−3.54270			−0.403728
$78$	−4.96194	+	3.79199i	−0.561829	+	0.429358i
$79$	11.0080			1.23849			0.619247	−	0.785196i	$-0.287438\pi$
$79$	11.0080			1.23849			0.619247	+	0.785196i	$0.287438\pi$
$80$	−0.294212	−	1.09801i	−0.0328939	−	0.122762i
$81$	−0.480179	+	8.98718i	−0.0533532	+	0.998576i
$82$	−5.28103	+	3.04900i	−0.583192	+	0.336706i
$83$	10.0746	−	10.0746i	1.10583	−	1.10583i	0.112136	−	0.993693i	$-0.464231\pi$
$83$	10.0746	−	10.0746i	1.10583	−	1.10583i	0.993693	−	0.112136i	$-0.0357692\pi$
$84$	−0.248973	+	1.71406i	−0.0271652	+	0.187020i
$85$	−8.02567	−	2.15047i	−0.870506	−	0.233251i
$86$	−1.80067	−	1.80067i	−0.194171	−	0.194171i
$87$	1.69836	−	1.26755i	0.182083	−	0.135895i
$88$	−3.06807	−	1.77135i	−0.327057	−	0.188827i
$89$	15.9782	−	4.28134i	1.69368	−	0.453821i	0.722346	−	0.691531i	$-0.243064\pi$
$89$	15.9782	−	4.28134i	1.69368	−	0.453821i	0.971336	+	0.237710i	$0.0763969\pi$
$90$	0.794416	+	3.31642i	0.0837388	+	0.349581i
$91$	3.10178	−	1.83820i	0.325155	−	0.192696i
$92$		−	0.736543i		−	0.0767900i
$93$	6.32763	−	2.52260i	0.656145	−	0.261581i
$94$	5.65444	−	9.79378i	0.583211	−	1.01015i
$95$	−2.82843	−	4.89898i	−0.290190	−	0.502625i
$96$	−1.07265	+	1.35994i	−0.109477	+	0.138798i
$97$	1.07287	−	4.00399i	0.108933	−	0.406544i	−0.889829	−	0.456295i	$-0.849176\pi$
$97$	1.07287	−	4.00399i	0.108933	−	0.406544i	0.998762	+	0.0497512i	$0.0158428\pi$
$98$	0.258819	−	0.965926i	0.0261447	−	0.0975732i
$99$	9.05912	+	5.55778i	0.910476	+	0.558578i
$100$	−1.85390	−	3.21105i	−0.185390	−	0.321105i
$101$	4.85354	−	8.40658i	0.482945	−	0.836485i	−0.516863	−	0.856068i	$-0.672900\pi$
$101$	4.85354	−	8.40658i	0.482945	−	0.836485i	0.999808	+	0.0195826i	$0.00623372\pi$
$102$	4.68827	+	11.7599i	0.464208	+	1.16441i
$103$			4.41326i			0.434851i	0.976077	+	0.217426i	$0.0697660\pi$
$103$			4.41326i			0.434851i	−0.976077	+	0.217426i	$0.930234\pi$
$104$	3.60532	−	0.0410409i	0.353530	−	0.00402439i
$105$	−0.230922	−	1.95532i	−0.0225357	−	0.190819i
$106$	7.61108	−	2.03938i	0.739253	−	0.198082i
$107$	3.35068	+	1.93452i	0.323923	+	0.187017i	0.653140	−	0.757237i	$-0.273451\pi$
$107$	3.35068	+	1.93452i	0.323923	+	0.187017i	−0.329217	+	0.944254i	$0.606785\pi$
$108$	3.32567	−	3.99248i	0.320013	−	0.384177i
$109$	−9.13766	−	9.13766i	−0.875229	−	0.875229i	0.117807	−	0.993036i	$-0.462413\pi$
$109$	−9.13766	−	9.13766i	−0.875229	−	0.875229i	−0.993036	+	0.117807i	$0.962413\pi$
$110$	3.88993	+	1.04230i	0.370891	+	0.0993798i
$111$	−4.21111	−	0.611677i	−0.399701	−	0.0580578i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−6.11927	+	3.53296i	−0.575652	+	0.332353i	−0.759404	−	0.650620i	$-0.774509\pi$
$113$	−6.11927	+	3.53296i	−0.575652	+	0.332353i	0.183751	+	0.982973i	$0.441176\pi$
$114$	−3.40443	+	7.91846i	−0.318854	+	0.741632i
$115$	0.216700	+	0.808734i	0.0202074	+	0.0754149i
$116$	−1.22353			−0.113602
$117$	−10.8154	−	0.165557i	−0.999883	−	0.0153058i
$118$	−2.49441			−0.229629
$119$	−1.89178	−	7.06020i	−0.173419	−	0.647208i
$120$	0.777673	−	1.80881i	0.0709915	−	0.165121i
$121$	1.34297	−	0.775365i	0.122088	−	0.0704877i
$122$	−2.31587	+	2.31587i	−0.209669	+	0.209669i
$123$	−10.4524	−	1.51824i	−0.942458	−	0.136895i
$124$	−3.79886	−	1.01790i	−0.341148	−	0.0914103i
$125$	6.99935	+	6.99935i	0.626041	+	0.626041i
$126$	−2.17717	+	2.06396i	−0.193958	+	0.183872i
$127$	10.7987	+	6.23461i	0.958226	+	0.553232i	0.895627	−	0.444807i	$-0.146728\pi$
$127$	10.7987	+	6.23461i	0.958226	+	0.553232i	0.0625995	+	0.998039i	$0.480061\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−0.517310	−	4.38028i	−0.0455466	−	0.385663i
$130$	−3.94661	+	1.10579i	−0.346141	+	0.0969842i
$131$			3.30383i			0.288657i	0.989530	+	0.144328i	$0.0461022\pi$
$131$			3.30383i			0.288657i	−0.989530	+	0.144328i	$0.953898\pi$
$132$	−2.27234	−	5.69988i	−0.197782	−	0.496111i
$133$	2.48818	−	4.30965i	0.215752	−	0.373694i
$134$	0.763571	+	1.32254i	0.0659625	+	0.114250i
$135$	−2.47700	+	5.36225i	−0.213186	+	0.461509i
$136$	1.89178	−	7.06020i	0.162218	−	0.605408i
$137$	2.14943	−	8.02180i	0.183639	−	0.685348i	−0.811279	−	0.584659i	$-0.801228\pi$
$137$	2.14943	−	8.02180i	0.183639	−	0.685348i	0.994918	−	0.100690i	$-0.0321049\pi$
$138$	0.790052	−	1.00165i	0.0672537	−	0.0852662i
$139$	9.81828	+	17.0058i	0.832776	+	1.44241i	0.895829	+	0.444400i	$0.146583\pi$
$139$	9.81828	+	17.0058i	0.832776	+	1.44241i	−0.0630528	+	0.998010i	$0.520084\pi$
$140$	−0.568374	+	0.984452i	−0.0480363	+	0.0832014i
$141$	18.1950	−	7.25368i	1.53229	−	0.610870i
$142$		−	5.08633i		−	0.426836i
$143$	−6.26036	+	11.1341i	−0.523518	+	0.931077i
$144$	−2.91747	+	0.698850i	−0.243122	+	0.0582375i
$145$	1.34345	−	0.359978i	0.111568	−	0.0298945i
$146$	13.9023	+	8.02648i	1.15056	+	0.664276i
$147$	1.38808	−	1.03598i	0.114487	−	0.0854458i
$148$	1.73722	+	1.73722i	0.142799	+	0.142799i
$149$	1.54435	+	0.413806i	0.126518	+	0.0339003i	0.321522	−	0.946902i	$-0.395805\pi$
$149$	1.54435	+	0.413806i	0.126518	+	0.0339003i	−0.195005	+	0.980802i	$0.562472\pi$
$150$	0.923144	−	6.35541i	0.0753744	−	0.518917i
$151$	15.8345	−	15.8345i	1.28859	−	1.28859i	0.352954	−	0.935641i	$-0.385177\pi$
$151$	15.8345	−	15.8345i	1.28859	−	1.28859i	0.935641	−	0.352954i	$-0.114823\pi$
$152$	4.30965	−	2.48818i	0.349559	−	0.201818i
$153$	−6.23854	+	21.0216i	−0.504356	+	1.69950i
$154$	0.916918	+	3.42199i	0.0738874	+	0.275752i
$155$	4.47068			0.359094
$156$	4.94702	+	3.81143i	0.396079	+	0.305158i
$157$	4.31592			0.344448			0.172224	−	0.985058i	$-0.444905\pi$
$157$	4.31592			0.344448			0.172224	+	0.985058i	$0.444905\pi$
$158$	−2.84907	−	10.6329i	−0.226660	−	0.845907i
$159$	12.5381	+	5.39058i	0.994338	+	0.427501i
$160$	−0.984452	+	0.568374i	−0.0778278	+	0.0449339i
$161$	−0.520815	+	0.520815i	−0.0410460	+	0.0410460i
$162$	8.80523	−	1.86224i	0.691804	−	0.146311i
$163$	−3.38458	−	0.906895i	−0.265101	−	0.0710335i	0.123820	−	0.992305i	$-0.460485\pi$
$163$	−3.38458	−	0.906895i	−0.265101	−	0.0710335i	−0.388921	+	0.921271i	$0.627152\pi$
$164$	4.31194	+	4.31194i	0.336706	+	0.336706i
$165$	4.17203	+	5.59000i	0.324792	+	0.435181i
$166$	−12.3388	−	7.12380i	−0.957676	−	0.552914i
$167$	0.966456	−	0.258961i	0.0747866	−	0.0200390i	−0.221232	−	0.975221i	$-0.571008\pi$
$167$	0.966456	−	0.258961i	0.0747866	−	0.0200390i	0.296018	+	0.955182i	$0.404341\pi$
$168$	1.72010	−	0.203143i	0.132708	−	0.0156728i
$169$	−0.295931	−	12.9966i	−0.0227639	−	0.999741i
$170$			8.30878i			0.637254i
$171$	−13.1235	+	7.11685i	−1.00358	+	0.544239i
$172$	−1.27327	+	2.20536i	−0.0970857	+	0.168157i
$173$	11.4516	+	19.8347i	0.870649	+	1.50801i	0.861327	+	0.508051i	$0.169634\pi$
$173$	11.4516	+	19.8347i	0.870649	+	1.50801i	0.00932213	+	0.999957i	$0.497033\pi$
$174$	−1.66392	−	1.31242i	−0.126142	−	0.0994943i
$175$	−0.959651	+	3.58147i	−0.0725428	+	0.270733i
$176$	−0.916918	+	3.42199i	−0.0691153	+	0.257942i
$177$	−3.39224	−	2.67563i	−0.254977	−	0.201113i
$178$	−8.27091	−	14.3256i	−0.619931	−	1.07375i
$179$	2.35860	−	4.08522i	0.176290	−	0.305344i	−0.764317	−	0.644841i	$-0.776924\pi$
$179$	2.35860	−	4.08522i	0.176290	−	0.305344i	0.940607	+	0.339497i	$0.110257\pi$
$180$	2.99781	−	1.62570i	0.223443	−	0.121173i
$181$		−	4.61924i		−	0.343345i	−0.985154	−	0.171673i	$-0.945083\pi$
$181$		−	4.61924i		−	0.343345i	0.985154	−	0.171673i	$-0.0549172\pi$
$182$	−2.57836	−	2.52032i	−0.191121	−	0.186819i
$183$	−5.63355	+	0.665320i	−0.416444	+	0.0491818i
$184$	−0.711446	+	0.190631i	−0.0524485	+	0.0140535i
$185$	−2.41860	−	1.39638i	−0.177819	−	0.102664i
$186$	−4.07436	−	5.45912i	−0.298746	−	0.400282i
$187$	18.3102	+	18.3102i	1.33897	+	1.33897i
$188$	−10.9235	−	2.92695i	−0.796681	−	0.213470i
$189$	−5.17472	+	0.471503i	−0.376405	+	0.0342968i
$190$	−4.00000	+	4.00000i	−0.290190	+	0.290190i
$191$	9.14674	−	5.28087i	0.661835	−	0.382110i	−0.131141	−	0.991364i	$-0.541864\pi$
$191$	9.14674	−	5.28087i	0.661835	−	0.382110i	0.792976	+	0.609253i	$0.208531\pi$
$192$	1.59122	+	0.684122i	0.114836	+	0.0493722i
$193$	−1.30905	−	4.88544i	−0.0942275	−	0.351662i	0.902674	−	0.430326i	$-0.141601\pi$
$193$	−1.30905	−	4.88544i	−0.0942275	−	0.351662i	−0.996901	+	0.0786639i	$0.974935\pi$
$194$	−4.14524			−0.297611
$195$	−6.55326	−	2.72952i	−0.469289	−	0.195465i
$196$	−1.00000			−0.0714286
$197$	−3.07482	−	11.4754i	−0.219072	−	0.817586i	−0.984693	−	0.174295i	$-0.944235\pi$
$197$	−3.07482	−	11.4754i	−0.219072	−	0.817586i	0.765622	−	0.643291i	$-0.222431\pi$
$198$	3.02373	−	10.1889i	0.214887	−	0.724093i
$199$	−20.2727	+	11.7045i	−1.43710	+	0.829707i	−0.997647	−	0.0685605i	$-0.978159\pi$
$199$	−20.2727	+	11.7045i	−1.43710	+	0.829707i	−0.439448	+	0.898268i	$0.644826\pi$
$200$	−2.62181	+	2.62181i	−0.185390	+	0.185390i
$201$	−0.380217	+	2.61762i	−0.0268185	+	0.184633i
$202$	−9.37632	−	2.51238i	−0.659715	−	0.176770i
$203$	0.865168	+	0.865168i	0.0607229	+	0.0607229i
$204$	10.1458	−	7.57221i	0.710349	−	0.530161i
$205$	−6.00319	−	3.46594i	−0.419281	−	0.242072i
$206$	4.26288	−	1.14224i	0.297009	−	0.0795833i
$207$	2.14884	−	0.514733i	0.149355	−	0.0357764i
$208$	−0.972767	−	3.47185i	−0.0674493	−	0.240729i
$209$			17.6297i			1.21947i
$210$	−1.82892	+	0.729126i	−0.126208	+	0.0503145i
$211$	−8.19223	+	14.1894i	−0.563976	+	0.976835i	0.433168	+	0.901313i	$0.357396\pi$
$211$	−8.19223	+	14.1894i	−0.563976	+	0.976835i	−0.997144	+	0.0755221i	$0.975938\pi$
$212$	−3.93978	−	6.82391i	−0.270586	−	0.468668i
$213$	5.45585	−	6.91709i	0.373829	−	0.473951i
$214$	1.00138	−	3.73720i	0.0684529	−	0.255470i
$215$	0.749220	−	2.79613i	0.0510964	−	0.190694i
$216$	−4.71719	−	2.17902i	−0.320964	−	0.148264i
$217$	1.96644	+	3.40597i	0.133490	+	0.231212i
$218$	−6.46130	+	11.1913i	−0.437615	+	0.757971i
$219$	10.2966	+	25.8277i	0.695780	+	1.74528i
$220$		−	4.02715i		−	0.271511i
$221$	−25.5319	−	6.53070i	−1.71746	−	0.439302i
$222$	0.499081	+	4.22593i	0.0334961	+	0.283626i
$223$	−19.3357	+	5.18099i	−1.29482	+	0.346945i	−0.839488	−	0.543378i	$-0.817145\pi$
$223$	−19.3357	+	5.18099i	−1.29482	+	0.346945i	−0.455329	+	0.890323i	$0.650478\pi$
$224$	−0.866025	−	0.500000i	−0.0578638	−	0.0334077i
$225$	8.07254	−	7.65275i	0.538169	−	0.510183i
$226$	4.99636	+	4.99636i	0.332353	+	0.332353i
$227$	−11.2325	−	3.00974i	−0.745528	−	0.199763i	−0.133994	−	0.990982i	$-0.542780\pi$
$227$	−11.2325	−	3.00974i	−0.745528	−	0.199763i	−0.611533	+	0.791219i	$0.709447\pi$
$228$	8.52978	+	1.23898i	0.564899	+	0.0820533i
$229$	7.77729	−	7.77729i	0.513937	−	0.513937i	−0.401793	−	0.915731i	$-0.631613\pi$
$229$	7.77729	−	7.77729i	0.513937	−	0.513937i	0.915731	+	0.401793i	$0.131613\pi$
$230$	0.725091	−	0.418632i	0.0478111	−	0.0276038i
$231$	−2.42364	+	5.63721i	−0.159464	+	0.370901i
$232$	0.316673	+	1.18184i	0.0207906	+	0.0775917i
$233$	−27.2445			−1.78485			−0.892424	−	0.451198i	$-0.850997\pi$
$233$	−27.2445			−1.78485			−0.892424	+	0.451198i	$0.850997\pi$
$234$	2.63931	+	10.4897i	0.172537	+	0.685734i
$235$	12.8553			0.838590
$236$	0.645602	+	2.40942i	0.0420251	+	0.156840i
$237$	7.53079	−	17.5161i	0.489178	−	1.13779i
$238$	−6.33001	+	3.65463i	−0.410313	+	0.236895i
$239$	−17.6202	+	17.6202i	−1.13976	+	1.13976i	−0.151265	+	0.988493i	$0.548335\pi$
$239$	−17.6202	+	17.6202i	−1.13976	+	1.13976i	−0.988493	+	0.151265i	$0.951665\pi$
$240$	−1.94846	−	0.283019i	−0.125772	−	0.0182688i
$241$	9.96070	+	2.66896i	0.641625	+	0.171923i	0.564940	−	0.825132i	$-0.308899\pi$
$241$	9.96070	+	2.66896i	0.641625	+	0.171923i	0.0766858	+	0.997055i	$0.475566\pi$
$242$	−1.09653	−	1.09653i	−0.0704877	−	0.0704877i
$243$	13.9721	+	6.91240i	0.896309	+	0.443430i
$244$	2.83635	+	1.63757i	0.181579	+	0.104834i
$245$	1.09801	−	0.294212i	0.0701495	−	0.0187965i
$246$	1.23876	+	10.4892i	0.0789808	+	0.668764i
$247$	−9.14754	−	15.4355i	−0.582044	−	0.982139i
$248$			3.93287i			0.249738i
$249$	−9.13862	−	22.9231i	−0.579137	−	1.45269i
$250$	4.94929	−	8.57242i	0.313020	−	0.542167i
$251$	6.05136	+	10.4813i	0.381958	+	0.661571i	0.991342	−	0.131304i	$-0.0419164\pi$
$251$	6.05136	+	10.4813i	0.381958	+	0.661571i	−0.609384	+	0.792875i	$0.708583\pi$
$252$	2.55712	+	1.56880i	0.161084	+	0.0988250i
$253$	0.675350	−	2.52044i	0.0424589	−	0.158459i
$254$	3.22727	−	12.0443i	0.202497	−	0.755729i
$255$	−8.91240	+	11.2994i	−0.558116	+	0.707596i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.43481	−	9.41337i	0.339014	−	0.587190i	−0.645233	−	0.763986i	$-0.723240\pi$
$257$	5.43481	−	9.41337i	0.339014	−	0.587190i	0.984248	+	0.176796i	$0.0565732\pi$
$258$	−4.09714	+	1.63338i	−0.255077	+	0.101690i
$259$		−	2.45680i		−	0.152658i
$260$	2.08957	+	3.52594i	0.129590	+	0.218669i
$261$	−0.855066	−	3.56961i	−0.0529272	−	0.220954i
$262$	3.19125	−	0.855094i	0.197156	−	0.0528279i
$263$	−18.4531	−	10.6539i	−1.13787	−	0.656949i	−0.191967	−	0.981401i	$-0.561487\pi$
$263$	−18.4531	−	10.6539i	−1.13787	−	0.656949i	−0.945902	+	0.324453i	$0.894820\pi$
$264$	−4.91754	+	3.67015i	−0.302654	+	0.225882i
$265$	6.33361	+	6.33361i	0.389071	+	0.389071i
$266$	−4.80679	−	1.28797i	−0.294723	−	0.0789708i
$267$	4.11847	−	28.3537i	0.252046	−	1.73522i
$268$	1.07985	−	1.07985i	0.0659625	−	0.0659625i
$269$	−27.3497	+	15.7904i	−1.66754	+	0.962756i	−0.698585	+	0.715527i	$0.746187\pi$
$269$	−27.3497	+	15.7904i	−1.66754	+	0.962756i	−0.968957	+	0.247229i	$0.920480\pi$
$270$	5.82063	+	1.00475i	0.354232	+	0.0611469i
$271$	2.99969	+	11.1950i	0.182218	+	0.680047i	0.995209	+	0.0977704i	$0.0311711\pi$
$271$	2.99969	+	11.1950i	0.182218	+	0.680047i	−0.812991	+	0.582276i	$0.802162\pi$
$272$	−7.30926			−0.443189
$273$	−0.802988	−	6.19316i	−0.0485991	−	0.374827i
$274$	−8.30478			−0.501710
$275$	−3.39976	−	12.6881i	−0.205013	−	0.765119i
$276$	−1.17200	−	0.503885i	−0.0705462	−	0.0303303i
$277$	−5.85837	+	3.38233i	−0.351995	+	0.203224i	−0.665564	−	0.746341i	$-0.731809\pi$
$277$	−5.85837	+	3.38233i	−0.351995	+	0.203224i	0.313569	+	0.949566i	$0.398475\pi$
$278$	13.8851	−	13.8851i	0.832776	−	0.832776i
$279$	0.314859	−	11.7944i	0.0188501	−	0.706113i
$280$	1.09801	+	0.294212i	0.0656188	+	0.0175825i
$281$	21.2979	+	21.2979i	1.27053	+	1.27053i	0.945812	+	0.324715i	$0.105268\pi$
$281$	21.2979	+	21.2979i	1.27053	+	1.27053i	0.324715	+	0.945812i	$0.394732\pi$
$282$	−11.7157	−	15.6976i	−0.697661	−	0.934778i
$283$	23.2985	+	13.4514i	1.38495	+	0.799601i	0.992741	−	0.120275i	$-0.0383776\pi$
$283$	23.2985	+	13.4514i	1.38495	+	0.799601i	0.392209	+	0.919876i	$0.371711\pi$
$284$	−4.91302	+	1.31644i	−0.291534	+	0.0781164i
$285$	−9.73034	+	1.14915i	−0.576375	+	0.0680697i
$286$	12.3750	+	3.16534i	0.731748	+	0.187171i
$287$		−	6.09800i		−	0.359954i
$288$	1.43013	+	2.63718i	0.0842714	+	0.155397i
$289$	−18.2127	+	31.5452i	−1.07133	+	1.85560i
$290$	−0.695423	−	1.20451i	−0.0408367	−	0.0707312i
$291$	−5.63726	−	4.44638i	−0.330462	−	0.260652i
$292$	4.15481	−	15.5060i	0.243142	−	0.907418i
$293$	7.03085	−	26.2395i	0.410747	−	1.53293i	−0.382458	−	0.923973i	$-0.624922\pi$
$293$	7.03085	−	26.2395i	0.410747	−	1.53293i	0.793205	−	0.608955i	$-0.208411\pi$
$294$	−1.35994	−	1.07265i	−0.0793131	−	0.0625581i
$295$	−1.41776	−	2.45563i	−0.0825451	−	0.142972i
$296$	1.22840	−	2.12765i	0.0713993	−	0.123667i
$297$	15.0412	−	10.6128i	0.872778	−	0.615819i
$298$		−	1.59883i		−	0.0926175i
$299$	0.716485	+	2.55717i	0.0414354	+	0.147885i
$300$	−6.37779	+	0.753214i	−0.368222	+	0.0434868i
$301$	2.45976	−	0.659091i	0.141778	−	0.0379894i
$302$	−19.3932	−	11.1967i	−1.11596	−	0.644297i
$303$	−10.0563	−	13.4742i	−0.577719	−	0.774070i
$304$	−3.51881	−	3.51881i	−0.201818	−	0.201818i
$305$	−3.59614	−	0.963583i	−0.205914	−	0.0551746i
$306$	21.9200	+	0.585168i	1.25308	+	0.0334518i
$307$	4.41492	−	4.41492i	0.251973	−	0.251973i	−0.569806	−	0.821779i	$-0.692982\pi$
$307$	4.41492	−	4.41492i	0.251973	−	0.251973i	0.821779	+	0.569806i	$0.192982\pi$
$308$	3.06807	−	1.77135i	0.174819	−	0.100932i
$309$	7.02246	+	3.01921i	0.399494	+	0.171757i
$310$	−1.15710	−	4.31834i	−0.0657187	−	0.245265i
$311$	−29.1301			−1.65181			−0.825907	−	0.563806i	$-0.809337\pi$
$311$	−29.1301			−1.65181			−0.825907	+	0.563806i	$0.809337\pi$
$312$	2.40117	−	5.76493i	0.135940	−	0.326375i
$313$	−28.3341			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$313$	−28.3341			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$314$	−1.11704	−	4.16886i	−0.0630384	−	0.235262i
$315$	−3.26931	−	0.970226i	−0.184205	−	0.0546661i
$316$	−9.53318	+	5.50399i	−0.536284	+	0.309623i
$317$	14.7984	−	14.7984i	0.831161	−	0.831161i	−0.156514	−	0.987676i	$-0.550026\pi$
$317$	14.7984	−	14.7984i	0.831161	−	0.831161i	0.987676	+	0.156514i	$0.0500258\pi$
$318$	1.96180	−	13.5061i	0.110012	−	0.757383i
$319$	−4.18691	−	1.12188i	−0.234422	−	0.0628132i
$320$	0.803802	+	0.803802i	0.0449339	+	0.0449339i
$321$	5.37051	−	4.00822i	0.299753	−	0.223717i
$322$	0.637865	+	0.368272i	0.0355468	+	0.0205230i
$323$	−35.1341	+	9.41414i	−1.95491	+	0.523817i
$324$	−4.07774	−	8.02322i	−0.226541	−	0.445734i
$325$	9.56008	+	9.34487i	0.530298	+	0.518360i
$326$			3.50397i			0.194067i
$327$	−20.7913	+	8.28875i	−1.14976	+	0.458369i
$328$	3.04900	−	5.28103i	0.168353	−	0.291596i
$329$	5.65444	+	9.79378i	0.311739	+	0.539949i
$330$	4.31972	−	5.47667i	0.237793	−	0.301481i
$331$	−0.804549	+	3.00262i	−0.0442220	+	0.165039i	−0.984506	−	0.175353i	$-0.943893\pi$
$331$	−0.804549	+	3.00262i	−0.0442220	+	0.165039i	0.940284	+	0.340392i	$0.110560\pi$
$332$	−3.68755	+	13.7621i	−0.202381	+	0.755295i
$333$	−3.85422	+	6.28233i	−0.211210	+	0.344270i
$334$	−0.500274	−	0.866501i	−0.0273738	−	0.0474128i
$335$	−0.867987	+	1.50340i	−0.0474232	+	0.0821394i
$336$	−0.641415	−	1.60891i	−0.0349920	−	0.0877732i
$337$		−	14.3061i		−	0.779305i	−0.920962	−	0.389653i	$-0.872595\pi$
$337$		−	14.3061i		−	0.779305i	0.920962	−	0.389653i	$-0.127405\pi$
$338$	−12.4772	+	3.64962i	−0.678670	+	0.198513i
$339$	1.43539	+	12.1541i	0.0779597	+	0.660119i
$340$	8.02567	−	2.15047i	0.435253	−	0.116626i
$341$	−12.0663	−	6.96649i	−0.653428	−	0.377257i
$342$	10.2710	+	10.8344i	0.555390	+	0.585857i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	2.45976	+	0.659091i	0.132622	+	0.0355358i
$345$	1.43512	+	0.208456i	0.0772644	+	0.0112229i
$346$	16.1950	−	16.1950i	0.870649	−	0.870649i
$347$	20.2438	−	11.6878i	1.08674	−	0.627432i	0.154037	−	0.988065i	$-0.450773\pi$
$347$	20.2438	−	11.6878i	1.08674	−	0.627432i	0.932708	+	0.360633i	$0.117439\pi$
$348$	−0.837045	+	1.94691i	−0.0448703	+	0.104365i
$349$	−6.31414	−	23.5647i	−0.337988	−	1.26139i	−0.900593	−	0.434663i	$-0.856868\pi$
$349$	−6.31414	−	23.5647i	−0.337988	−	1.26139i	0.562605	−	0.826726i	$-0.309799\pi$
$350$	3.70781			0.198191
$351$	−7.66248	+	17.0964i	−0.408993	+	0.912538i
$352$	3.54270			0.188827
$353$	6.14712	+	22.9414i	0.327178	+	1.22104i	0.912104	+	0.409958i	$0.134457\pi$
$353$	6.14712	+	22.9414i	0.327178	+	1.22104i	−0.584926	+	0.811087i	$0.698877\pi$
$354$	−1.70648	+	3.96916i	−0.0906985	+	0.210958i
$355$	5.00725	−	2.89094i	0.265757	−	0.153435i
$356$	−11.6968	+	11.6968i	−0.619931	+	0.619931i
$357$	−12.5285	−	1.81981i	−0.663080	−	0.0963145i
$358$	−4.55647	−	1.22090i	−0.240817	−	0.0645268i
$359$	2.81284	+	2.81284i	0.148456	+	0.148456i	0.777428	−	0.628972i	$-0.216524\pi$
$359$	2.81284	+	2.81284i	0.148456	+	0.148456i	−0.628972	+	0.777428i	$0.716524\pi$
$360$	−2.34619	−	2.47490i	−0.123655	−	0.130439i
$361$	−4.99184	−	2.88204i	−0.262728	−	0.151686i
$362$	−4.46184	+	1.19555i	−0.234509	+	0.0628366i
$363$	−0.315020	−	2.66741i	−0.0165342	−	0.140003i
$364$	−1.76712	+	3.14282i	−0.0926221	+	0.164728i
$365$			18.2482i			0.955152i
$366$	2.10072	+	5.26939i	0.109806	+	0.275436i
$367$	−6.94597	+	12.0308i	−0.362577	+	0.628001i	−0.988384	−	0.151976i	$-0.951436\pi$
$367$	−6.94597	+	12.0308i	−0.362577	+	0.628001i	0.625807	+	0.779978i	$0.284770\pi$
$368$	0.368272	+	0.637865i	0.0191975	+	0.0332510i
$369$	−9.56654	+	15.5933i	−0.498014	+	0.811757i
$370$	−0.722819	+	2.69760i	−0.0375776	+	0.140241i
$371$	−2.03938	+	7.61108i	−0.105879	+	0.395148i
$372$	−4.21859	+	5.34845i	−0.218724	+	0.277304i
$373$	2.38315	+	4.12774i	0.123395	+	0.213727i	0.921104	−	0.389316i	$-0.127288\pi$
$373$	2.38315	+	4.12774i	0.123395	+	0.213727i	−0.797709	+	0.603042i	$0.793955\pi$
$374$	12.9473	−	22.4253i	0.669487	−	1.15959i
$375$	15.9259	−	6.34909i	0.822410	−	0.327866i
$376$			11.3089i			0.583211i
$377$	4.24792	−	1.19021i	0.218779	−	0.0612990i
$378$	1.79475	+	4.87636i	0.0923121	+	0.250813i
$379$	17.3803	−	4.65704i	0.892767	−	0.239216i	0.216859	−	0.976203i	$-0.430419\pi$
$379$	17.3803	−	4.65704i	0.892767	−	0.239216i	0.675907	+	0.736987i	$0.263752\pi$
$380$	4.89898	+	2.82843i	0.251312	+	0.145095i
$381$	17.3082	−	12.9178i	0.886727	−	0.661799i
$382$	−7.46828	−	7.46828i	−0.382110	−	0.382110i
$383$	8.33992	+	2.23467i	0.426150	+	0.114187i	0.465518	−	0.885038i	$-0.345868\pi$
$383$	8.33992	+	2.23467i	0.426150	+	0.114187i	−0.0393685	+	0.999225i	$0.512535\pi$
$384$	0.248973	−	1.71406i	0.0127054	−	0.0874704i
$385$	−2.84763	+	2.84763i	−0.145129	+	0.145129i
$386$	−4.38017	+	2.52889i	−0.222945	+	0.128717i
$387$	−7.32389	−	2.17349i	−0.372294	−	0.110485i
$388$	1.07287	+	4.00399i	0.0544666	+	0.203272i
$389$	3.71381			0.188298			0.0941488	−	0.995558i	$-0.469987\pi$
$389$	3.71381			0.188298			0.0941488	+	0.995558i	$0.469987\pi$
$390$	−0.940408	+	7.03642i	−0.0476194	+	0.356303i
$391$	5.38359			0.272260
$392$	0.258819	+	0.965926i	0.0130723	+	0.0487866i
$393$	5.25711	+	2.26022i	0.265186	+	0.114013i
$394$	−10.2885	+	5.94009i	−0.518329	+	0.299257i
$395$	8.84823	−	8.84823i	0.445203	−	0.445203i
$396$	−10.6243	−	0.283623i	−0.533892	−	0.0142526i
$397$	−9.72596	−	2.60606i	−0.488132	−	0.130795i	0.00635463	−	0.999980i	$-0.497977\pi$
$397$	−9.72596	−	2.60606i	−0.488132	−	0.130795i	−0.494487	+	0.869185i	$0.664644\pi$
$398$	16.5526	+	16.5526i	0.829707	+	0.829707i
$399$	−5.15538	−	6.90756i	−0.258092	−	0.345810i
$400$	3.21105	+	1.85390i	0.160553	+	0.0926952i
$401$	−17.3984	+	4.66188i	−0.868834	+	0.232803i	−0.665583	−	0.746324i	$-0.731817\pi$
$401$	−17.3984	+	4.66188i	−0.868834	+	0.232803i	−0.203250	+	0.979127i	$0.565151\pi$
$402$	2.62683	−	0.310228i	0.131014	−	0.0154728i
$403$	14.1792	−	0.161409i	0.706319	−	0.00804033i
$404$			9.70708i			0.482945i
$405$	6.83794	+	7.60988i	0.339780	+	0.378138i
$406$	0.611766	−	1.05961i	0.0303614	−	0.0525876i
$407$	4.35185	+	7.53763i	0.215713	+	0.373626i
$408$	−9.94013	−	7.84027i	−0.492110	−	0.388151i
$409$	−4.81027	+	17.9522i	−0.237852	+	0.887677i	0.738990	+	0.673716i	$0.235303\pi$
$409$	−4.81027	+	17.9522i	−0.237852	+	0.887677i	−0.976842	+	0.213961i	$0.931364\pi$
$410$	−1.79410	+	6.69569i	−0.0886045	+	0.330677i
$411$	−11.2940	−	8.90811i	−0.557090	−	0.439405i
$412$	−2.20663	−	3.82199i	−0.108713	−	0.188296i
$413$	1.24721	−	2.16023i	0.0613710	−	0.106298i
$414$	−1.05336	−	1.94240i	−0.0517696	−	0.0954636i
$415$		−	16.1959i		−	0.795027i
$416$	−3.10178	+	1.83820i	−0.152077	+	0.0901252i
$417$	33.7768	−	3.98902i	1.65406	−	0.195343i
$418$	17.0290	−	4.56291i	0.832916	−	0.223179i
$419$	−5.64258	−	3.25775i	−0.275658	−	0.159151i	0.355798	−	0.934563i	$-0.384209\pi$
$419$	−5.64258	−	3.25775i	−0.275658	−	0.159151i	−0.631456	+	0.775412i	$0.717542\pi$
$420$	1.17764	+	1.57789i	0.0574630	+	0.0769932i
$421$	−4.04576	−	4.04576i	−0.197178	−	0.197178i	0.601611	−	0.798789i	$-0.294526\pi$
$421$	−4.04576	−	4.04576i	−0.197178	−	0.197178i	−0.798789	+	0.601611i	$0.794526\pi$
$422$	15.8262	+	4.24061i	0.770406	+	0.206430i
$423$	0.905371	−	33.9146i	0.0440206	−	1.64898i
$424$	−5.57170	+	5.57170i	−0.270586	+	0.270586i
$425$	23.4704	−	13.5507i	1.13848	−	0.657304i
$426$	−8.09347	−	3.47967i	−0.392130	−	0.168591i
$427$	−0.847667	−	3.16354i	−0.0410215	−	0.153094i
$428$	−3.86903			−0.187017
$429$	13.4339	+	17.5787i	0.648594	+	0.848706i
$430$	−2.89476			−0.139598
$431$	5.31288	+	19.8280i	0.255913	+	0.955079i	0.967580	+	0.252563i	$0.0812735\pi$
$431$	5.31288	+	19.8280i	0.255913	+	0.955079i	−0.711668	+	0.702516i	$0.752060\pi$
$432$	−0.883878	+	5.12043i	−0.0425256	+	0.246357i
$433$	16.7919	−	9.69483i	0.806969	−	0.465904i	−0.0389329	−	0.999242i	$-0.512396\pi$
$433$	16.7919	−	9.69483i	0.806969	−	0.465904i	0.845902	+	0.533338i	$0.179063\pi$
$434$	2.78096	−	2.78096i	0.133490	−	0.133490i
$435$	0.346283	−	2.38400i	0.0166030	−	0.114304i
$436$	12.4823	+	3.34462i	0.597793	+	0.160178i
$437$	2.59176	+	2.59176i	0.123981	+	0.123981i
$438$	22.2827	−	16.6305i	1.06471	−	0.794634i
$439$	−1.81303	−	1.04675i	−0.0865313	−	0.0499588i	0.456110	−	0.889923i	$-0.349242\pi$
$439$	−1.81303	−	1.04675i	−0.0865313	−	0.0499588i	−0.542641	+	0.839965i	$0.682576\pi$
$440$	−3.88993	+	1.04230i	−0.185445	+	0.0496899i
$441$	−0.698850	−	2.91747i	−0.0332786	−	0.138927i
$442$	0.299979	+	26.3522i	0.0142685	+	1.25345i
$443$			38.6899i			1.83821i	0.394009	+	0.919106i	$0.371088\pi$
$443$			38.6899i			1.83821i	−0.394009	+	0.919106i	$0.628912\pi$
$444$	3.95277	−	1.57583i	0.187590	−	0.0747854i
$445$	9.40193	−	16.2846i	0.445694	−	0.771965i
$446$	10.0089	+	17.3359i	0.473936	+	0.820881i
$447$	1.71498	−	2.17430i	0.0811157	−	0.102841i
$448$	−0.258819	+	0.965926i	−0.0122281	+	0.0456357i
$449$	4.09656	−	15.2886i	0.193329	−	0.721512i	−0.799364	−	0.600846i	$-0.794830\pi$
$449$	4.09656	−	15.2886i	0.193329	−	0.721512i	0.992693	−	0.120666i	$-0.0385030\pi$
$450$	−9.48131	−	5.81680i	−0.446953	−	0.274207i
$451$	10.8017	+	18.7091i	0.508632	+	0.880977i
$452$	3.53296	−	6.11927i	0.166177	−	0.287826i
$453$	−14.3634	−	36.0289i	−0.674854	−	1.69279i
$454$			11.6287i			0.545764i
$455$	1.01566	−	3.97076i	0.0476150	−	0.186152i
$456$	−1.01091	−	8.55981i	−0.0473402	−	0.400850i
$457$	−22.7426	+	6.09386i	−1.06385	+	0.285059i	−0.747965	−	0.663738i	$-0.768969\pi$
$457$	−22.7426	+	6.09386i	−1.06385	+	0.285059i	−0.315888	+	0.948796i	$0.602302\pi$
$458$	−9.52519	−	5.49937i	−0.445083	−	0.256969i
$459$	29.1821	+	24.3082i	1.36210	+	1.13461i
$460$	−0.592035	−	0.592035i	−0.0276038	−	0.0276038i
$461$	33.9606	+	9.09971i	1.58170	+	0.423816i	0.939452	−	0.342680i	$-0.111335\pi$
$461$	33.9606	+	9.09971i	1.58170	+	0.423816i	0.642250	+	0.766496i	$0.278001\pi$
$462$	6.07241	+	0.882037i	0.282514	+	0.0410361i
$463$	−18.5472	+	18.5472i	−0.861964	+	0.861964i	−0.991566	−	0.129602i	$-0.958630\pi$
$463$	−18.5472	+	18.5472i	−0.861964	+	0.861964i	0.129602	+	0.991566i	$0.458630\pi$
$464$	1.05961	−	0.611766i	0.0491912	−	0.0284005i
$465$	3.05849	−	7.11383i	0.141834	−	0.329896i
$466$	7.05140	+	26.3162i	0.326650	+	1.21907i
$467$	−19.1252			−0.885007			−0.442504	−	0.896767i	$-0.645910\pi$
$467$	−19.1252			−0.885007			−0.442504	+	0.896767i	$0.645910\pi$
$468$	9.44918	−	5.26432i	0.436788	−	0.243343i
$469$	−1.52714			−0.0705169
$470$	−3.32721	−	12.4173i	−0.153473	−	0.572768i
$471$	2.95261	−	6.86757i	0.136049	−	0.316441i
$472$	2.16023	−	1.24721i	0.0994325	−	0.0574074i
$473$	−6.37924	+	6.37924i	−0.293318	+	0.293318i
$474$	−18.8684	−	2.74069i	−0.866653	−	0.125884i
$475$	17.8226	+	4.77556i	0.817758	+	0.219118i
$476$	5.16843	+	5.16843i	0.236895	+	0.236895i
$477$	17.1552	−	16.2631i	0.785483	−	0.744635i
$478$	21.5803	+	12.4594i	0.987059	+	0.569879i
$479$	8.26573	−	2.21480i	0.377671	−	0.101197i	−0.0649895	−	0.997886i	$-0.520701\pi$
$479$	8.26573	−	2.21480i	0.377671	−	0.101197i	0.442660	+	0.896689i	$0.354035\pi$
$480$	0.230922	+	1.95532i	0.0105401	+	0.0892475i
$481$	−7.72127	−	4.34145i	−0.352060	−	0.197953i
$482$		−	10.3121i		−	0.469702i
$483$	0.472430	+	1.18503i	0.0214963	+	0.0539208i
$484$	−0.775365	+	1.34297i	−0.0352439	+	0.0610442i
$485$	−2.35604	−	4.08079i	−0.106982	−	0.185299i
$486$	3.06062	−	15.2850i	0.138833	−	0.693344i
$487$	8.46387	−	31.5876i	0.383535	−	1.43137i	−0.456929	−	0.889503i	$-0.651051\pi$
$487$	8.46387	−	31.5876i	0.383535	−	1.43137i	0.840464	−	0.541868i	$-0.182283\pi$
$488$	0.847667	−	3.16354i	0.0383721	−	0.143207i
$489$	−3.75853	+	4.76518i	−0.169967	+	0.215489i
$490$	−0.568374	−	0.984452i	−0.0256765	−	0.0444730i
$491$	−8.47423	+	14.6778i	−0.382437	+	0.662400i	−0.991410	−	0.130791i	$-0.958248\pi$
$491$	−8.47423	+	14.6778i	−0.382437	+	0.662400i	0.608973	+	0.793191i	$0.291582\pi$
$492$	9.81113	−	3.91135i	0.442320	−	0.176337i
$493$		−	8.94312i		−	0.402778i
$494$	−12.5420	+	12.8309i	−0.564292	+	0.577287i
$495$	11.7491	−	2.81438i	0.528082	−	0.126497i
$496$	3.79886	−	1.01790i	0.170574	−	0.0457051i
$497$	4.40489	+	2.54317i	0.197587	+	0.114077i
$498$	−19.7768	+	14.7602i	−0.886218	+	0.661419i
$499$	11.6614	+	11.6614i	0.522037	+	0.522037i	0.918186	−	0.396149i	$-0.129654\pi$
$499$	11.6614	+	11.6614i	0.522037	+	0.522037i	−0.396149	+	0.918186i	$0.629654\pi$
$500$	−9.56129	−	2.56194i	−0.427594	−	0.114573i
$501$	0.249110	−	1.71500i	0.0111294	−	0.0766207i
$502$	8.55791	−	8.55791i	0.381958	−	0.381958i
$503$	−2.15798	+	1.24591i	−0.0962195	+	0.0555523i	−0.547338	−	0.836912i	$-0.684359\pi$
$503$	−2.15798	+	1.24591i	−0.0962195	+	0.0555523i	0.451118	+	0.892464i	$0.351025\pi$
$504$	0.853511	−	2.87602i	0.0380184	−	0.128108i
$505$	−2.85594	−	10.6585i	−0.127088	−	0.474297i
$506$	−2.60935			−0.116000
$507$	−20.8829	−	8.42039i	−0.927444	−	0.373962i
$508$	−12.4692			−0.553232
$509$	−0.307917	−	1.14916i	−0.0136482	−	0.0509358i	0.958766	−	0.284197i	$-0.0917270\pi$
$509$	−0.307917	−	1.14916i	−0.0136482	−	0.0509358i	−0.972414	+	0.233261i	$0.925060\pi$
$510$	13.2211	+	5.68422i	0.585440	+	0.251701i
$511$	−13.9023	+	8.02648i	−0.615000	+	0.355071i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.34636	+	25.7512i	0.103595	+	1.13694i
$514$	−10.4993	−	2.81327i	−0.463102	−	0.124088i
$515$	3.54738	+	3.54738i	0.156316	+	0.156316i
$516$	2.63815	+	3.53478i	0.116138	+	0.155610i
$517$	−34.6964	−	20.0320i	−1.52595	−	0.881006i
$518$	−2.37309	+	0.635866i	−0.104267	+	0.0279384i
$519$	39.3957	−	4.65262i	1.72928	−	0.204227i
$520$	2.86497	−	2.93095i	0.125637	−	0.128531i
$521$		−	12.4355i		−	0.544810i	−0.962183	−	0.272405i	$-0.912181\pi$
$521$		−	12.4355i		−	0.544810i	0.962183	−	0.272405i	$-0.0878190\pi$
$522$	−3.22667	+	1.74981i	−0.141228	+	0.0765873i
$523$	−8.24283	+	14.2770i	−0.360434	+	0.624290i	−0.988032	−	0.154248i	$-0.950705\pi$
$523$	−8.24283	+	14.2770i	−0.360434	+	0.624290i	0.627598	+	0.778537i	$0.284038\pi$
$524$	−1.65191	−	2.86120i	−0.0721642	−	0.124992i
$525$	5.04238	+	3.97717i	0.220067	+	0.173578i
$526$	−5.51487	+	20.5818i	−0.240460	+	0.897409i
$527$	7.44011	−	27.7669i	0.324096	−	1.20954i
$528$	4.81785	+	3.80007i	0.209670	+	0.165377i
$529$	11.2288	+	19.4488i	0.488207	+	0.845599i
$530$	4.47854	−	7.75706i	0.194535	−	0.336945i
$531$	−6.57822	+	3.56734i	−0.285470	+	0.154810i
$532$			4.97635i			0.215752i
$533$	−19.1649	−	10.7759i	−0.830125	−	0.466755i
$534$	−28.4535	+	3.36035i	−1.23130	+	0.145417i
$535$	4.24825	−	1.13832i	0.183668	−	0.0492137i
$536$	−1.32254	−	0.763571i	−0.0571252	−	0.0329812i
$537$	−4.88691	−	6.54785i	−0.210886	−	0.282560i
$538$	22.3310	+	22.3310i	0.962756	+	0.962756i
$539$	−3.42199	−	0.916918i	−0.147395	−	0.0394945i
$540$	−0.535979	−	5.88234i	−0.0230649	−	0.253136i
$541$	10.2201	−	10.2201i	0.439398	−	0.439398i	−0.452412	−	0.891809i	$-0.649436\pi$
$541$	10.2201	−	10.2201i	0.439398	−	0.439398i	0.891809	+	0.452412i	$0.149436\pi$
$542$	10.0371	−	5.79495i	0.431132	−	0.248914i
$543$	−7.35022	−	3.16012i	−0.315428	−	0.135614i
$544$	1.89178	+	7.06020i	0.0811092	+	0.302704i
$545$	−14.6897			−0.629239
$546$	−5.77430	+	2.37853i	−0.247117	+	0.101792i
$547$	23.7481			1.01540			0.507698	−	0.861535i	$-0.330497\pi$
$547$	23.7481			1.01540			0.507698	+	0.861535i	$0.330497\pi$
$548$	2.14943	+	8.02180i	0.0918193	+	0.342674i
$549$	−2.79536	+	9.41937i	−0.119303	+	0.402009i
$550$	−11.3758	+	6.56782i	−0.485066	+	0.280053i
$551$	4.30538	−	4.30538i	0.183415	−	0.183415i
$552$	−0.183379	+	1.26248i	−0.00780515	+	0.0537348i
$553$	10.6329	+	2.84907i	0.452156	+	0.121155i
$554$	4.78334	+	4.78334i	0.203224	+	0.203224i
$555$	−3.87656	+	2.89323i	−0.164551	+	0.122811i
$556$	−17.0058	−	9.81828i	−0.721205	−	0.416388i
$557$	−6.31379	+	1.69178i	−0.267524	+	0.0716828i	−0.390087	−	0.920778i	$-0.627555\pi$
$557$	−6.31379	+	1.69178i	−0.267524	+	0.0716828i	0.122563	+	0.992461i	$0.460889\pi$
$558$	−11.4740	+	2.74849i	−0.485734	+	0.116353i
$559$	2.27528	−	8.89528i	0.0962342	−	0.376230i
$560$		−	1.13675i		−	0.0480363i
$561$	41.6619	−	16.6091i	1.75897	−	0.701238i
$562$	15.0599	−	26.0845i	0.635263	−	1.10031i
$563$	16.3712	+	28.3558i	0.689966	+	1.19506i	0.971848	+	0.235607i	$0.0757078\pi$
$563$	16.3712	+	28.3558i	0.689966	+	1.19506i	−0.281883	+	0.959449i	$0.590959\pi$
$564$	−12.1305	+	15.3794i	−0.510784	+	0.647588i
$565$	−2.07888	+	7.75848i	−0.0874591	+	0.326402i
$566$	6.96294	−	25.9861i	0.292674	−	1.09228i
$567$	−2.78987	+	8.55667i	−0.117164	+	0.359346i
$568$	2.54317	+	4.40489i	0.106709	+	0.184825i
$569$	2.26364	−	3.92075i	0.0948969	−	0.164366i	−0.814669	−	0.579927i	$-0.803081\pi$
$569$	2.26364	−	3.92075i	0.0948969	−	0.164366i	0.909566	+	0.415560i	$0.136415\pi$
$570$	3.62839	+	9.10136i	0.151976	+	0.381214i
$571$		−	17.5173i		−	0.733075i	−0.930403	−	0.366538i	$-0.880543\pi$
$571$		−	17.5173i		−	0.733075i	0.930403	−	0.366538i	$-0.119457\pi$
$572$	−0.145396	−	12.7726i	−0.00607930	−	0.534048i
$573$	−2.14554	−	18.1672i	−0.0896312	−	0.758946i
$574$	−5.89022	+	1.57828i	−0.245853	+	0.0658761i
$575$	−2.36508	−	1.36548i	−0.0986307	−	0.0569445i
$576$	2.17717	−	2.06396i	0.0907156	−	0.0859981i
$577$	−20.4965	−	20.4965i	−0.853279	−	0.853279i	0.137257	−	0.990535i	$-0.456171\pi$
$577$	−20.4965	−	20.4965i	−0.853279	−	0.853279i	−0.990535	+	0.137257i	$0.956171\pi$
$578$	35.1841	+	9.42756i	1.46347	+	0.392135i
$579$	−8.66936	−	1.25925i	−0.360286	−	0.0523327i
$580$	−0.983477	+	0.983477i	−0.0408367	+	0.0408367i
$581$	12.3388	−	7.12380i	0.511899	−	0.295545i
$582$	−2.83585	+	6.59598i	−0.117550	+	0.273412i
$583$	−7.22492	−	26.9638i	−0.299226	−	1.11673i
$584$	−16.0530			−0.664276
$585$	−8.82650	+	8.56035i	−0.364931	+	0.353927i
$586$	−27.1651			−1.12218
$587$	−8.47749	−	31.6384i	−0.349903	−	1.30586i	−0.886778	−	0.462195i	$-0.847062\pi$
$587$	−8.47749	−	31.6384i	−0.349903	−	1.30586i	0.536875	−	0.843662i	$-0.319605\pi$
$588$	−0.684122	+	1.59122i	−0.0282127	+	0.0656208i
$589$	16.9493	−	9.78567i	0.698383	−	0.403212i
$590$	−2.00501	+	2.00501i	−0.0825451	+	0.0825451i
$591$	−20.3634	−	2.95784i	−0.837637	−	0.121669i
$592$	−2.37309	−	0.635866i	−0.0975332	−	0.0261339i
$593$	−6.87228	−	6.87228i	−0.282211	−	0.282211i	0.551779	−	0.833990i	$-0.313949\pi$
$593$	−6.87228	−	6.87228i	−0.282211	−	0.282211i	−0.833990	+	0.551779i	$0.813949\pi$
$594$	−14.1442	−	11.7819i	−0.580342	−	0.483416i
$595$	−7.19562	−	4.15439i	−0.294991	−	0.170313i
$596$	−1.54435	+	0.413806i	−0.0632589	+	0.0169502i
$597$	4.75535	+	40.2656i	0.194624	+	1.64796i
$598$	2.28459	−	1.35391i	0.0934239	−	0.0553657i
$599$			13.4877i			0.551092i	0.961288	+	0.275546i	$0.0888587\pi$
$599$			13.4877i			0.551092i	−0.961288	+	0.275546i	$0.911141\pi$
$600$	2.37824	+	5.96552i	0.0970913	+	0.243541i
$601$	4.31212	−	7.46881i	0.175895	−	0.304659i	−0.764576	−	0.644534i	$-0.777051\pi$
$601$	4.31212	−	7.46881i	0.175895	−	0.304659i	0.940471	+	0.339875i	$0.110385\pi$
$602$	−1.27327	−	2.20536i	−0.0518945	−	0.0898839i
$603$	3.90509	+	2.39578i	0.159027	+	0.0975636i
$604$	−5.79584	+	21.6304i	−0.235829	+	0.880127i
$605$	0.456243	−	1.70272i	0.0185489	−	0.0692255i
$606$	−10.4123	+	13.2010i	−0.422970	+	0.536254i
$607$	−0.674709	−	1.16863i	−0.0273856	−	0.0474332i	0.852008	−	0.523529i	$-0.175385\pi$
$607$	−0.674709	−	1.16863i	−0.0273856	−	0.0474332i	−0.879393	+	0.476096i	$0.842052\pi$
$608$	−2.48818	+	4.30965i	−0.100909	+	0.174779i
$609$	1.96855	−	0.784791i	0.0797697	−	0.0318013i
$610$			3.72300i			0.150740i
$611$	40.7721	−	0.464127i	1.64946	−	0.0187766i
$612$	−5.10808	−	21.3245i	−0.206482	−	0.861993i
$613$	−26.8492	+	7.19422i	−1.08443	+	0.290572i	−0.756409	−	0.654099i	$-0.773048\pi$
$613$	−26.8492	+	7.19422i	−1.08443	+	0.290572i	−0.328020	+	0.944671i	$0.606381\pi$
$614$	−5.40716	−	3.12182i	−0.218215	−	0.125987i
$615$	−9.62199	+	7.18126i	−0.387996	+	0.289577i
$616$	−2.50507	−	2.50507i	−0.100932	−	0.100932i
$617$	−23.6889	−	6.34741i	−0.953678	−	0.255537i	−0.251756	−	0.967791i	$-0.581008\pi$
$617$	−23.6889	−	6.34741i	−0.953678	−	0.255537i	−0.701922	+	0.712254i	$0.747675\pi$
$618$	1.09878	−	7.56460i	0.0441995	−	0.304293i
$619$	24.0336	−	24.0336i	0.965993	−	0.965993i	−0.0334478	−	0.999440i	$-0.510649\pi$
$619$	24.0336	−	24.0336i	0.965993	−	0.965993i	0.999440	+	0.0334478i	$0.0106487\pi$
$620$	−3.87172	+	2.23534i	−0.155492	+	0.0897734i
$621$	0.651015	−	3.77142i	0.0261243	−	0.151342i
$622$	7.53942	+	28.1375i	0.302303	+	1.12821i
$623$	16.5418			0.662734
$624$	−6.18996	−	0.827280i	−0.247797	−	0.0331177i
$625$	−7.28686			−0.291474
$626$	7.33341	+	27.3686i	0.293102	+	1.09387i
$627$	28.0528	+	12.0609i	1.12032	+	0.481665i
$628$	−3.73770	+	2.15796i	−0.149150	+	0.0861120i
$629$	−12.6978	+	12.6978i	−0.506294	+	0.506294i
$630$	−0.0910061	+	3.40903i	−0.00362577	+	0.135819i
$631$	−6.06122	−	1.62410i	−0.241293	−	0.0646544i	0.136146	−	0.990689i	$-0.456529\pi$
$631$	−6.06122	−	1.62410i	−0.241293	−	0.0646544i	−0.377439	+	0.926034i	$0.623195\pi$
$632$	7.78381	+	7.78381i	0.309623	+	0.309623i
$633$	16.9739	+	22.7429i	0.674651	+	0.903948i
$634$	−18.1243	−	10.4641i	−0.719807	−	0.415581i
$635$	13.6914	−	3.66859i	0.543325	−	0.145584i
$636$	−13.5536	+	1.60068i	−0.537436	+	0.0634710i
$637$	3.47185	−	0.972767i	0.137560	−	0.0385424i
$638$			4.33461i			0.171609i
$639$	−7.27414	−	13.4136i	−0.287760	−	0.530633i
$640$	0.568374	−	0.984452i	0.0224669	−	0.0389139i
$641$	16.3293	+	28.2831i	0.644967	+	1.11712i	0.984309	+	0.176453i	$0.0564622\pi$
$641$	16.3293	+	28.2831i	0.644967	+	1.11712i	−0.339342	+	0.940663i	$0.610204\pi$
$642$	−5.26164	−	4.15011i	−0.207660	−	0.163792i
$643$	−1.31535	+	4.90895i	−0.0518723	+	0.193590i	−0.987000	−	0.160721i	$-0.948618\pi$
$643$	−1.31535	+	4.90895i	−0.0518723	+	0.193590i	0.935128	+	0.354311i	$0.115285\pi$
$644$	0.190631	−	0.711446i	0.00751193	−	0.0280349i
$645$	−3.93669	−	3.10507i	−0.155007	−	0.122262i
$646$	18.1867	+	31.5003i	0.715547	+	1.23936i
$647$	20.3193	−	35.1941i	0.798835	−	1.38362i	−0.121540	−	0.992586i	$-0.538783\pi$
$647$	20.3193	−	35.1941i	0.798835	−	1.38362i	0.920375	−	0.391036i	$-0.127883\pi$
$648$	−6.69443	+	6.01536i	−0.262982	+	0.236306i
$649$			8.83696i			0.346881i
$650$	6.55212	−	11.6530i	0.256995	−	0.457067i
$651$	6.76492	−	0.798934i	0.265138	−	0.0313127i
$652$	3.38458	−	0.906895i	0.132550	−	0.0355168i
$653$	7.75553	+	4.47766i	0.303497	+	0.175224i	0.644013	−	0.765015i	$-0.277268\pi$
$653$	7.75553	+	4.47766i	0.303497	+	0.175224i	−0.340516	+	0.940239i	$0.610602\pi$
$654$	13.3875	+	17.9376i	0.523492	+	0.701414i
$655$	2.65562	+	2.65562i	0.103764	+	0.103764i
$656$	−5.89022	−	1.57828i	−0.229974	−	0.0616215i
$657$	48.1417	+	1.28517i	1.87819	+	0.0501394i
$658$	7.99659	−	7.99659i	0.311739	−	0.311739i
$659$	−5.13096	+	2.96236i	−0.199874	+	0.115397i	−0.596597	−	0.802541i	$-0.703481\pi$
$659$	−5.13096	+	2.96236i	−0.199874	+	0.115397i	0.396723	+	0.917938i	$0.370147\pi$
$660$	−6.40809	−	2.75506i	−0.249434	−	0.107241i
$661$	3.20097	+	11.9462i	0.124503	+	0.464653i	0.999821	−	0.0188947i	$-0.00601474\pi$
$661$	3.20097	+	11.9462i	0.124503	+	0.464653i	−0.875318	+	0.483547i	$0.839348\pi$
$662$	3.10854			0.120817
$663$	−27.8587	+	36.1591i	−1.08194	+	1.40430i
$664$	14.2476			0.552914
$665$	−1.46410	−	5.46410i	−0.0567754	−	0.211889i
$666$	7.06582	+	2.09691i	0.273795	+	0.0812534i
$667$	−0.780449	+	0.450592i	−0.0302191	+	0.0174470i
$668$	−0.707495	+	0.707495i	−0.0273738	+	0.0273738i
$669$	−4.98390	+	34.3118i	−0.192689	+	1.32657i
$670$	1.67682	+	0.449303i	0.0647813	+	0.0173581i
$671$	8.20443	+	8.20443i	0.316729	+	0.316729i
$672$	−1.38808	+	1.03598i	−0.0535462	+	0.0399636i
$673$	−19.3563	−	11.1753i	−0.746129	−	0.430778i	0.0781645	−	0.996940i	$-0.475094\pi$
$673$	−19.3563	−	11.1753i	−0.746129	−	0.430778i	−0.824294	+	0.566163i	$0.808427\pi$
$674$	−13.8187	+	3.70270i	−0.532275	+	0.142623i
$675$	−6.65459	−	18.0806i	−0.256135	−	0.695922i
$676$	6.75460	+	11.1074i	0.259792	+	0.427210i
$677$		−	6.02627i		−	0.231608i	−0.993272	−	0.115804i	$-0.963056\pi$
$677$		−	6.02627i		−	0.231608i	0.993272	−	0.115804i	$-0.0369445\pi$
$678$	11.3684	−	4.53219i	0.436602	−	0.174058i
$679$	2.07262	−	3.58988i	0.0795398	−	0.137767i
$680$	−4.15439	−	7.19562i	−0.159314	−	0.275939i
$681$	−12.4736	+	15.8143i	−0.477988	+	0.606007i
$682$	−3.60612	+	13.4582i	−0.138086	+	0.515342i
$683$	−8.87262	+	33.1131i	−0.339501	+	1.26704i	0.559404	+	0.828895i	$0.311030\pi$
$683$	−8.87262	+	33.1131i	−0.339501	+	1.26704i	−0.898906	+	0.438142i	$0.855637\pi$
$684$	7.80689	−	12.7251i	0.298504	−	0.486558i
$685$	−4.72022	−	8.17565i	−0.180350	−	0.312376i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−7.05475	−	17.6960i	−0.269156	−	0.675143i
$688$		−	2.54653i		−	0.0970857i
$689$	20.3164	+	19.8591i	0.773993	+	0.756570i
$690$	−0.170084	−	1.44017i	−0.00647499	−	0.0548265i
$691$	0.587920	−	0.157533i	0.0223655	−	0.00599282i	−0.247619	−	0.968858i	$-0.579648\pi$
$691$	0.587920	−	0.157533i	0.0223655	−	0.00599282i	0.269984	+	0.962865i	$0.412981\pi$
$692$	−19.8347	−	11.4516i	−0.754004	−	0.435324i
$693$	7.31198	+	7.71308i	0.277759	+	0.292996i
$694$	−16.5290	−	16.5290i	−0.627432	−	0.627432i
$695$	21.5612	+	5.77731i	0.817863	+	0.219146i
$696$	2.09721	+	0.304627i	0.0794946	+	0.0115468i
$697$	−31.5171	+	31.5171i	−1.19380	+	1.19380i
$698$	−21.1275	+	12.1980i	−0.799688	+	0.461700i
$699$	−18.6386	+	43.3520i	−0.704975	+	1.63972i
$700$	−0.959651	−	3.58147i	−0.0362714	−	0.135367i
$701$	−14.8844			−0.562176			−0.281088	−	0.959682i	$-0.590695\pi$
$701$	−14.8844			−0.562176			−0.281088	+	0.959682i	$0.590695\pi$
$702$	18.4970	+	2.97652i	0.698126	+	0.112341i
$703$	−12.2259			−0.461108
$704$	−0.916918	−	3.42199i	−0.0345577	−	0.128971i
$705$	8.79462	−	20.4557i	0.331224	−	0.770405i
$706$	20.5687	−	11.8753i	0.774112	−	0.446933i
$707$	6.86394	−	6.86394i	0.258145	−	0.258145i
$708$	4.27558	+	0.621042i	0.160686	+	0.0233402i
$709$	19.0649	+	5.10841i	0.715996	+	0.191850i	0.598384	−	0.801209i	$-0.295810\pi$
$709$	19.0649	+	5.10841i	0.715996	+	0.191850i	0.117611	+	0.993060i	$0.462476\pi$
$710$	−4.08840	−	4.08840i	−0.153435	−	0.153435i
$711$	−22.7200	−	23.9663i	−0.852065	−	0.898806i
$712$	14.3256	+	8.27091i	0.536876	+	0.309965i
$713$	−2.79803	+	0.749729i	−0.104787	+	0.0280776i
$714$	1.48482	+	12.5726i	0.0555681	+	0.470519i
$715$	3.91748	+	13.9817i	0.146506	+	0.522885i
$716$			4.71721i			0.176290i
$717$	15.9833	+	40.0920i	0.596906	+	1.49726i
$718$	1.98898	−	3.44501i	0.0742280	−	0.128567i
$719$	−13.3122	−	23.0574i	−0.496462	−	0.859897i	0.503530	−	0.863978i	$-0.332034\pi$
$719$	−13.3122	−	23.0574i	−0.496462	−	0.859897i	−0.999992	+	0.00408079i	$0.998701\pi$
$720$	−1.78333	+	2.90680i	−0.0664607	+	0.108330i
$721$	−1.14224	+	4.26288i	−0.0425391	+	0.158758i
$722$	−1.49185	+	5.56767i	−0.0555210	+	0.207207i
$723$	11.0612	−	14.0238i	0.411372	−	0.521549i
$724$	2.30962	+	4.00038i	0.0858363	+	0.148673i
$725$	−2.26831	+	3.92883i	−0.0842429	+	0.145913i
$726$	−2.49498	+	0.994661i	−0.0925975	+	0.0369153i
$727$		−	4.91686i		−	0.182356i	−0.995835	−	0.0911782i	$-0.970937\pi$
$727$		−	4.91686i		−	0.182356i	0.995835	−	0.0911782i	$-0.0290633\pi$
$728$	3.49309	+	0.893482i	0.129463	+	0.0331147i
$729$	20.5577	−	17.5037i	0.761397	−	0.648285i
$730$	17.6264	−	4.72297i	0.652381	−	0.174805i
$731$	−16.1196	−	9.30664i	−0.596204	−	0.344219i
$732$	4.54614	−	3.39296i	0.168030	−	0.125407i
$733$	11.6448	+	11.6448i	0.430111	+	0.430111i	0.888666	−	0.458555i	$-0.151633\pi$
$733$	11.6448	+	11.6448i	0.430111	+	0.430111i	−0.458555	+	0.888666i	$0.651633\pi$
$734$	13.4186	+	3.59550i	0.495289	+	0.132712i
$735$	0.283019	−	1.94846i	0.0104393	−	0.0718699i
$736$	0.520815	−	0.520815i	0.0191975	−	0.0191975i
$737$	4.68538	−	2.70510i	0.172588	−	0.0996438i
$738$	17.5380	+	5.20471i	0.645583	+	0.191588i
$739$	−13.4922	−	50.3536i	−0.496318	−	1.85229i	−0.522517	−	0.852629i	$-0.675007\pi$
$739$	−13.4922	−	50.3536i	−0.496318	−	1.85229i	0.0261982	−	0.999657i	$-0.491660\pi$
$740$	2.79276			0.102664
$741$	−30.8193	+	3.99595i	−1.13218	+	0.146795i
$742$	7.87957			0.289268
$743$	−8.74258	−	32.6278i	−0.320734	−	1.19700i	−0.918531	−	0.395349i	$-0.870624\pi$
$743$	−8.74258	−	32.6278i	−0.320734	−	1.19700i	0.597797	−	0.801648i	$-0.296043\pi$
$744$	6.25806	+	2.69056i	0.229432	+	0.0986408i
$745$	1.57397	−	0.908730i	0.0576657	−	0.0332933i
$746$	3.37029	−	3.37029i	0.123395	−	0.123395i
$747$	−42.7276	−	1.14064i	−1.56332	−	0.0417338i
$748$	−25.0122	−	6.70200i	−0.914536	−	0.245049i
$749$	2.73582	+	2.73582i	0.0999647	+	0.0999647i
$750$	−10.2547	−	13.7400i	−0.374448	−	0.501713i
$751$	−36.0862	−	20.8344i	−1.31680	−	0.760257i	−0.333591	−	0.942718i	$-0.608260\pi$
$751$	−36.0862	−	20.8344i	−1.31680	−	0.760257i	−0.983213	+	0.182461i	$0.941594\pi$
$752$	10.9235	−	2.92695i	0.398341	−	0.106735i
$753$	20.8178	−	2.45858i	0.758645	−	0.0895956i
$754$	−2.24910	−	3.79512i	−0.0819073	−	0.138210i
$755$		−	25.4556i		−	0.926425i
$756$	4.24568	−	2.99569i	0.154414	−	0.108952i
$757$	−18.9919	+	32.8949i	−0.690271	+	1.19558i	0.281478	+	0.959568i	$0.409175\pi$
$757$	−18.9919	+	32.8949i	−0.690271	+	1.19558i	−0.971749	+	0.236017i	$0.924158\pi$
$758$	−8.99671	−	15.5828i	−0.326775	−	0.565991i
$759$	−3.54855	−	2.79892i	−0.128804	−	0.101594i
$760$	1.46410	−	5.46410i	0.0531085	−	0.198204i
$761$	−4.65136	+	17.3591i	−0.168612	+	0.629267i	0.828940	+	0.559337i	$0.188944\pi$
$761$	−4.65136	+	17.3591i	−0.168612	+	0.629267i	−0.997552	+	0.0699302i	$0.977722\pi$
$762$	−16.9573	−	13.3751i	−0.614299	−	0.484528i
$763$	−6.46130	−	11.1913i	−0.233915	−	0.405152i
$764$	−5.28087	+	9.14674i	−0.191055	+	0.330917i
$765$	11.8827	+	21.9118i	0.429619	+	0.792221i
$766$		−	8.63412i		−	0.311963i
$767$	−4.58524	−	7.73711i	−0.165563	−	0.279371i
$768$	−1.72010	+	0.203143i	−0.0620686	+	0.00733028i
$769$	−20.9539	+	5.61457i	−0.755616	+	0.202467i	−0.616008	−	0.787740i	$-0.711251\pi$
$769$	−20.9539	+	5.61457i	−0.755616	+	0.202467i	−0.139608	+	0.990207i	$0.544584\pi$
$770$	3.48762	+	2.01358i	0.125685	+	0.0725643i
$771$	−11.2607	−	15.0879i	−0.405543	−	0.543376i
$772$	3.57639	+	3.57639i	0.128717	+	0.128717i
$773$	−17.9218	−	4.80214i	−0.644604	−	0.172721i	−0.0783160	−	0.996929i	$-0.524954\pi$
$773$	−17.9218	−	4.80214i	−0.644604	−	0.172721i	−0.566288	+	0.824207i	$0.691621\pi$
$774$	−0.203871	+	7.63688i	−0.00732800	+	0.274502i
$775$	−10.3113	+	10.3113i	−0.370391	+	0.370391i
$776$	3.58988	−	2.07262i	0.128869	−	0.0744027i
$777$	−3.90931	−	1.68075i	−0.140246	−	0.0602966i
$778$	−0.961205	−	3.58727i	−0.0344609	−	0.128610i
$779$	−30.3458			−1.08725
$780$	7.04005	−	0.912794i	0.252074	−	0.0326833i
$781$	−18.0194			−0.644783
$782$	−1.39338	−	5.20015i	−0.0498270	−	0.185957i
$783$	−6.26500	−	1.08145i	−0.223893	−	0.0386480i
$784$	0.866025	−	0.500000i	0.0309295	−	0.0178571i
$785$	3.46914	−	3.46914i	0.123819	−	0.123819i
$786$	0.822564	−	5.66297i	0.0293399	−	0.201991i
$787$	−9.32858	−	2.49958i	−0.332528	−	0.0891006i	0.0886921	−	0.996059i	$-0.471731\pi$
$787$	−9.32858	−	2.49958i	−0.332528	−	0.0891006i	−0.421220	+	0.906959i	$0.638398\pi$
$788$	8.40056	+	8.40056i	0.299257	+	0.299257i
$789$	−29.5769	+	22.0744i	−1.05297	+	0.785869i
$790$	−10.8368	−	6.25664i	−0.385557	−	0.222601i
$791$	−6.82516	+	1.82880i	−0.242675	+	0.0650245i
$792$	2.47582	+	10.3357i	0.0879743	+	0.367263i
$793$	−11.4403	−	2.92627i	−0.406259	−	0.103915i
$794$			10.0691i			0.357337i
$795$	14.4111	−	5.74520i	0.511110	−	0.203761i
$796$	11.7045	−	20.2727i	0.414854	−	0.718548i
$797$	−20.1450	−	34.8922i	−0.713572	−	1.23594i	−0.963508	−	0.267681i	$-0.913743\pi$
$797$	−20.1450	−	34.8922i	−0.713572	−	1.23594i	0.249935	−	0.968263i	$-0.419591\pi$
$798$	−5.33788	+	6.76752i	−0.188959	+	0.239568i
$799$	21.3939	−	79.8430i	0.756861	−	2.82464i
$800$	0.959651	−	3.58147i	0.0339288	−	0.126624i
$801$	−42.2994	−	25.9508i	−1.49458	−	0.916926i
$802$	9.00606	+	15.5990i	0.318015	+	0.550818i
$803$	28.4354	−	49.2516i	1.00346	−	1.73805i
$804$	−0.979531	−	2.45703i	−0.0345454	−	0.0866529i
$805$			0.837264i			0.0295097i
$806$	−3.82577	−	13.6543i	−0.134757	−	0.480953i
$807$	6.41540	+	54.3219i	0.225833	+	1.91222i
$808$	9.37632	−	2.51238i	0.329858	−	0.0883851i
$809$	17.9443	+	10.3601i	0.630886	+	0.364242i	0.781095	−	0.624412i	$-0.214661\pi$
$809$	17.9443	+	10.3601i	0.630886	+	0.364242i	−0.150209	+	0.988654i	$0.547995\pi$
$810$	5.58079	−	8.57453i	0.196089	−	0.301278i
$811$	−14.2153	−	14.2153i	−0.499166	−	0.499166i	0.412013	−	0.911178i	$-0.364826\pi$
$811$	−14.2153	−	14.2153i	−0.499166	−	0.499166i	−0.911178	+	0.412013i	$0.864826\pi$
$812$	−1.18184	−	0.316673i	−0.0414745	−	0.0111131i
$813$	19.8658	+	2.88557i	0.696725	+	0.101201i
$814$	6.15445	−	6.15445i	0.215713	−	0.215713i
$815$	−3.44949	+	1.99157i	−0.120830	+	0.0697615i
$816$	−5.00042	+	11.6306i	−0.175050	+	0.407154i
$817$	−3.27987	−	12.2406i	−0.114748	−	0.428246i
$818$	18.5854			0.649825
$819$	−10.4040	−	2.95914i	−0.363546	−	0.103401i
$820$	6.93189			0.242072
$821$	9.04585	+	33.7596i	0.315702	+	1.17822i	0.923334	+	0.383998i	$0.125453\pi$
$821$	9.04585	+	33.7596i	0.315702	+	1.17822i	−0.607632	+	0.794219i	$0.707880\pi$
$822$	−5.68148	+	13.2147i	−0.198164	+	0.460916i
$823$	2.44321	−	1.41059i	0.0851650	−	0.0491700i	−0.456813	−	0.889563i	$-0.651009\pi$
$823$	2.44321	−	1.41059i	0.0851650	−	0.0491700i	0.541978	+	0.840393i	$0.317676\pi$
$824$	−3.12065	+	3.12065i	−0.108713	+	0.108713i
$825$	−22.5153	−	3.27042i	−0.783883	−	0.113861i
$826$	−2.40942	−	0.645602i	−0.0838344	−	0.0224634i
$827$	−19.4601	−	19.4601i	−0.676695	−	0.676695i	0.282556	−	0.959251i	$-0.408818\pi$
$827$	−19.4601	−	19.4601i	−0.676695	−	0.676695i	−0.959251	+	0.282556i	$0.908818\pi$
$828$	−1.60358	+	1.52019i	−0.0557284	+	0.0528303i
$829$	40.8051	+	23.5588i	1.41722	+	0.818232i	0.996054	−	0.0887509i	$-0.0282875\pi$
$829$	40.8051	+	23.5588i	1.41722	+	0.818232i	0.421166	+	0.906983i	$0.361621\pi$
$830$	−15.6441	+	4.19181i	−0.543013	+	0.145500i
$831$	1.37419	+	11.6359i	0.0476702	+	0.403644i
$832$	2.57836	+	2.52032i	0.0893887	+	0.0873765i
$833$		−	7.30926i		−	0.253251i
$834$	−12.5952	−	31.5934i	−0.436135	−	1.09399i
$835$	0.568685	−	0.984992i	0.0196802	−	0.0340871i
$836$	−8.81486	−	15.2678i	−0.304868	−	0.528048i
$837$	−18.5521	−	8.56982i	−0.641254	−	0.296216i
$838$	−1.68633	+	6.29348i	−0.0582534	+	0.217405i
$839$	−7.95284	+	29.6804i	−0.274563	+	1.02468i	0.681571	+	0.731752i	$0.261297\pi$
$839$	−7.95284	+	29.6804i	−0.274563	+	1.02468i	−0.956134	+	0.292930i	$0.905370\pi$
$840$	1.21933	−	1.54590i	0.0420709	−	0.0533387i
$841$	−13.7515	−	23.8183i	−0.474189	−	0.821320i
$842$	−2.86079	+	4.95503i	−0.0985892	+	0.170762i
$843$	48.4600	−	19.3193i	1.66905	−	0.665391i
$844$		−	16.3845i		−	0.563976i
$845$	−10.6846	−	10.2088i	−0.367561	−	0.351195i
$846$	−32.9933	+	7.90322i	−1.13433	+	0.271718i
$847$	1.49789	−	0.401359i	0.0514681	−	0.0137908i
$848$	6.82391	+	3.93978i	0.234334	+	0.135293i
$849$	37.3431	−	27.8706i	1.28161	−	0.956516i
$850$	−19.1635	−	19.1635i	−0.657304	−	0.657304i
$851$	1.74788	+	0.468343i	0.0599166	+	0.0160546i
$852$	−1.26636	+	8.71830i	−0.0433848	+	0.298684i
$853$	−10.5415	+	10.5415i	−0.360933	+	0.360933i	−0.864156	−	0.503224i	$-0.832147\pi$
$853$	−10.5415	+	10.5415i	−0.360933	+	0.360933i	0.503224	+	0.864156i	$0.332147\pi$
$854$	−2.83635	+	1.63757i	−0.0970579	+	0.0560364i
$855$	−4.82819	+	16.2693i	−0.165121	+	0.556397i
$856$	1.00138	+	3.73720i	0.0342264	+	0.127735i
$857$	−1.36186			−0.0465204			−0.0232602	−	0.999729i	$-0.507405\pi$
$857$	−1.36186			−0.0465204			−0.0232602	+	0.999729i	$0.507405\pi$
$858$	13.5027	−	17.5258i	0.460976	−	0.598322i
$859$	16.5338			0.564128			0.282064	−	0.959396i	$-0.408981\pi$
$859$	16.5338			0.564128			0.282064	+	0.959396i	$0.408981\pi$
$860$	0.749220	+	2.79613i	0.0255482	+	0.0953472i
$861$	−9.70326	−	4.17178i	−0.330686	−	0.142174i
$862$	17.7773	−	10.2637i	0.605496	−	0.349583i
$863$	2.08850	−	2.08850i	0.0710933	−	0.0710933i	−0.670666	−	0.741759i	$-0.733992\pi$
$863$	2.08850	−	2.08850i	0.0710933	−	0.0710933i	0.741759	+	0.670666i	$0.233992\pi$
$864$	5.17472	−	0.471503i	0.176047	−	0.0160409i
$865$	25.1480	+	6.73839i	0.855058	+	0.229112i
$866$	−13.7106	−	13.7106i	−0.465904	−	0.465904i
$867$	37.7357	+	50.5611i	1.28157	+	1.71714i
$868$	−3.40597	−	1.96644i	−0.115606	−	0.0667452i
$869$	−37.6691	+	10.0934i	−1.27784	+	0.342396i
$870$	−2.39239	+	0.282540i	−0.0811096	+	0.00957901i
$871$	−2.69864	+	4.79953i	−0.0914399	+	0.162626i
$872$		−	12.9226i		−	0.437615i
$873$	−10.9317	+	5.92824i	−0.369983	+	0.200641i
$874$	1.83265	−	3.17424i	0.0619903	−	0.107370i
$875$	4.94929	+	8.57242i	0.167316	+	0.289801i
$876$	−21.8310	−	17.2192i	−0.737601	−	0.581782i
$877$	−8.41329	+	31.3988i	−0.284097	+	1.06026i	0.665400	+	0.746487i	$0.268261\pi$
$877$	−8.41329	+	31.3988i	−0.284097	+	1.06026i	−0.949497	+	0.313777i	$0.898406\pi$
$878$	−0.541840	+	2.02217i	−0.0182862	+	0.0682450i
$879$	−36.9428	−	29.1386i	−1.24605	−	0.982822i
$880$	2.01358	+	3.48762i	0.0678777	+	0.117568i
$881$	15.4817	−	26.8151i	0.521591	−	0.903422i	−0.478093	−	0.878309i	$-0.658672\pi$
$881$	15.4817	−	26.8151i	0.521591	−	0.903422i	0.999685	−	0.0251134i	$-0.00799470\pi$
$882$	−2.63718	+	1.43013i	−0.0887985	+	0.0481551i
$883$			0.856591i			0.0288266i	0.999896	+	0.0144133i	$0.00458805\pi$
$883$			0.856591i			0.0288266i	−0.999896	+	0.0144133i	$0.995412\pi$
$884$	25.3766	−	7.11021i	0.853509	−	0.239142i
$885$	−4.87737	+	0.576015i	−0.163951	+	0.0193625i
$886$	37.3716	−	10.0137i	1.25552	−	0.336416i
$887$	−34.2438	−	19.7707i	−1.14979	−	0.663834i	−0.200958	−	0.979600i	$-0.564405\pi$
$887$	−34.2438	−	19.7707i	−1.14979	−	0.663834i	−0.948837	+	0.315766i	$0.897739\pi$
$888$	−2.54518	−	3.41022i	−0.0854107	−	0.114440i
$889$	8.81707	+	8.81707i	0.295715	+	0.295715i
$890$	−18.1631	−	4.86680i	−0.608830	−	0.163135i
$891$	−6.59735	−	31.1943i	−0.221019	−	1.04505i
$892$	14.1547	−	14.1547i	0.473936	−	0.473936i
$893$	48.7373	−	28.1385i	1.63093	−	0.941619i
$894$	−2.54408	−	1.09379i	−0.0850868	−	0.0365818i
$895$	−1.38786	−	5.17956i	−0.0463910	−	0.173134i
$896$	1.00000			0.0334077
$897$	4.55917	+	0.609328i	0.152226	+	0.0203449i
$898$	−15.8279			−0.528184
$899$	1.24544	+	4.64803i	0.0415376	+	0.155020i
$900$	−3.16465	+	10.6637i	−0.105488	+	0.355458i
$901$	49.8777	−	28.7969i	1.66167	−	0.959364i
$902$	15.2759	−	15.2759i	0.508632	−	0.508632i
$903$	0.634018	−	4.36492i	0.0210988	−	0.145255i
$904$	−6.82516	−	1.82880i	−0.227001	−	0.0608248i
$905$	−3.71295	−	3.71295i	−0.123423	−	0.123423i
$906$	−31.0837	+	23.1990i	−1.03269	+	0.770735i
$907$	46.0351	+	26.5784i	1.52857	+	0.882521i	0.999422	+	0.0339922i	$0.0108221\pi$
$907$	46.0351	+	26.5784i	1.52857	+	0.882521i	0.529149	+	0.848529i	$0.322511\pi$
$908$	11.2325	−	3.00974i	0.372764	−	0.0998817i
$909$	−28.3201	+	6.78379i	−0.939317	+	0.225004i
$910$	−4.09833	+	0.0466531i	−0.135858	+	0.00154654i
$911$		−	8.23986i		−	0.272999i	−0.990640	−	0.136499i	$-0.956415\pi$
$911$		−	8.23986i		−	0.272999i	0.990640	−	0.136499i	$-0.0435852\pi$
$912$	−8.00650	+	3.19190i	−0.265122	+	0.105695i
$913$	−25.2375	+	43.7126i	−0.835240	+	1.44668i
$914$	11.7724	+	20.3904i	0.389397	+	0.674456i
$915$	−3.99347	+	5.06304i	−0.132020	+	0.167379i
$916$	−2.84668	+	10.6240i	−0.0940571	+	0.351026i
$917$	−0.855094	+	3.19125i	−0.0282377	+	0.105384i
$918$	15.9271	−	34.4792i	0.525671	−	1.13798i
$919$	−27.9702	−	48.4459i	−0.922653	−	1.59808i	−0.795293	−	0.606226i	$-0.792683\pi$
$919$	−27.9702	−	48.4459i	−0.922653	−	1.59808i	−0.127360	−	0.991857i	$-0.540650\pi$
$920$	−0.418632	+	0.725091i	−0.0138019	+	0.0239056i
$921$	−4.00477	−	10.0455i	−0.131961	−	0.331009i
$922$		−	35.1586i		−	1.15789i
$923$	15.7767	−	9.34971i	0.519295	−	0.307749i
$924$	−0.719674	−	6.09379i	−0.0236755	−	0.200471i
$925$	8.79894	−	2.35767i	0.289307	−	0.0775197i
$926$	22.7156	+	13.1149i	0.746482	+	0.430982i
$927$	9.60844	−	9.10877i	0.315582	−	0.299171i
$928$	−0.865168	−	0.865168i	−0.0284005	−	0.0284005i
$929$	−54.7075	−	14.6588i	−1.79489	−	0.480941i	−0.801732	−	0.597683i	$-0.796088\pi$
$929$	−54.7075	−	14.6588i	−1.79489	−	0.480941i	−0.993162	+	0.116743i	$0.962755\pi$
$930$	−7.66303	−	1.11308i	−0.251281	−	0.0364993i
$931$	3.51881	−	3.51881i	0.115324	−	0.115324i
$932$	23.5944	−	13.6223i	0.772862	−	0.446212i
$933$	−19.9285	+	46.3523i	−0.652430	+	1.51751i
$934$	4.94996	+	18.4735i	0.161968	+	0.604471i
$935$	29.4355			0.962645
$936$	−7.53057	−	7.76470i	−0.246144	−	0.253797i
$937$	6.90473			0.225568			0.112784	−	0.993620i	$-0.464023\pi$
$937$	6.90473			0.225568			0.112784	+	0.993620i	$0.464023\pi$
$938$	0.395253	+	1.47511i	0.0129055	+	0.0481639i
$939$	−19.3840	+	45.0858i	−0.632572	+	1.47132i
$940$	−11.1331	+	6.42767i	−0.363120	+	0.209647i
$941$	17.8690	−	17.8690i	0.582514	−	0.582514i	−0.353080	−	0.935593i	$-0.614866\pi$
$941$	17.8690	−	17.8690i	0.582514	−	0.582514i	0.935593	+	0.353080i	$0.114866\pi$
$942$	−7.39776	−	1.07455i	−0.241032	−	0.0350107i
$943$	4.33840	+	1.16247i	0.141278	+	0.0378553i
$944$	−1.76382	−	1.76382i	−0.0574074	−	0.0574074i
$945$	−3.78045	+	4.53844i	−0.122978	+	0.147635i
$946$	7.81294	+	4.51080i	0.254021	+	0.146659i
$947$	4.94547	−	1.32513i	0.160706	−	0.0430611i	−0.177569	−	0.984108i	$-0.556823\pi$
$947$	4.94547	−	1.32513i	0.160706	−	0.0430611i	0.338275	+	0.941047i	$0.390157\pi$
$948$	2.23619	+	18.9348i	0.0726281	+	0.614973i
$949$	0.658828	+	57.8760i	0.0213865	+	1.87874i
$950$		−	18.4513i		−	0.598641i
$951$	−13.4236	−	33.6714i	−0.435290	−	1.09187i
$952$	3.65463	−	6.33001i	0.118447	−	0.205157i
$953$	12.2906	+	21.2880i	0.398133	+	0.689586i	0.993496	−	0.113871i	$-0.0363250\pi$
$953$	12.2906	+	21.2880i	0.398133	+	0.689586i	−0.595363	+	0.803457i	$0.702992\pi$
$954$	−20.1490	−	12.3615i	−0.652349	−	0.400217i
$955$	3.10739	−	11.5969i	0.100553	−	0.375268i
$956$	6.44945	−	24.0697i	0.208590	−	0.778469i
$957$	−4.64951	+	5.89479i	−0.150297	+	0.190551i
$958$	−4.27866	−	7.41085i	−0.138237	−	0.239434i
$959$	4.15239	−	7.19215i	0.134088	−	0.232247i
$960$	1.82892	−	0.729126i	0.0590282	−	0.0235324i
$961$		−	15.5325i		−	0.501049i
$962$	−2.19511	+	8.58182i	−0.0707731	+	0.276689i
$963$	−2.70387	−	11.2878i	−0.0871311	−	0.363743i
$964$	−9.96070	+	2.66896i	−0.320813	+	0.0859615i
$965$	−4.97914	−	2.87471i	−0.160284	−	0.0925402i
$966$	1.02238	−	0.763041i	0.0328945	−	0.0245504i
$967$	10.2751	+	10.2751i	0.330425	+	0.330425i	0.852748	−	0.522323i	$-0.174934\pi$
$967$	10.2751	+	10.2751i	0.330425	+	0.330425i	−0.522323	+	0.852748i	$0.674934\pi$
$968$	1.49789	+	0.401359i	0.0481440	+	0.0129002i
$969$	−9.05601	+	62.3464i	−0.290921	+	2.00286i
$970$	−3.33195	+	3.33195i	−0.106982	+	0.106982i
$971$	−23.0605	+	13.3140i	−0.740046	+	0.427266i	−0.822086	−	0.569363i	$-0.807190\pi$
$971$	−23.0605	+	13.3140i	−0.740046	+	0.427266i	0.0820399	+	0.996629i	$0.473857\pi$
$972$	−15.5564	+	0.999725i	−0.498971	+	0.0320662i
$973$	5.08232	+	18.9675i	0.162932	+	0.608069i
$974$	−32.7019			−1.04784
$975$	21.4100	−	8.81914i	0.685669	−	0.282439i
$976$	−3.27513			−0.104834
$977$	−7.41323	−	27.6665i	−0.237170	−	0.885131i	−0.977159	−	0.212512i	$-0.931836\pi$
$977$	−7.41323	−	27.6665i	−0.237170	−	0.885131i	0.739988	−	0.672620i	$-0.234831\pi$
$978$	5.57559	+	2.39714i	0.178288	+	0.0766522i
$979$	−50.7514	+	29.3014i	−1.62202	+	0.936475i
$980$	−0.803802	+	0.803802i	−0.0256765	+	0.0256765i
$981$	−1.03456	+	38.7540i	−0.0330310	+	1.23732i
$982$	16.3710	+	4.38658i	0.522418	+	0.139981i
$983$	34.8726	+	34.8726i	1.11226	+	1.11226i	0.992844	+	0.119420i	$0.0381035\pi$
$983$	34.8726	+	34.8726i	1.11226	+	1.11226i	0.119420	+	0.992844i	$0.461897\pi$
$984$	−6.31738	−	8.46450i	−0.201391	−	0.269838i
$985$	−11.6955	−	6.75238i	−0.372648	−	0.215149i
$986$	−8.63839	+	2.31465i	−0.275102	+	0.0737134i
$987$	19.4524	−	2.29732i	0.619176	−	0.0731244i
$988$	15.6398	+	8.79379i	0.497567	+	0.279768i
$989$			1.87563i			0.0596416i
$990$	−5.75937	−	10.6203i	−0.183045	−	0.337536i
$991$	−14.2683	+	24.7133i	−0.453246	+	0.785045i	−0.998585	−	0.0531700i	$-0.983067\pi$
$991$	−14.2683	+	24.7133i	−0.453246	+	0.785045i	0.545339	+	0.838215i	$0.316401\pi$
$992$	−1.96644	−	3.40597i	−0.0624344	−	0.108140i
$993$	4.22741	+	3.33437i	0.134153	+	0.105813i
$994$	1.31644	−	4.91302i	0.0417549	−	0.155832i
$995$	−6.88718	+	25.7033i	−0.218338	+	0.814850i
$996$	19.3758	+	15.2827i	0.613947	+	0.484250i
$997$	−24.9347	−	43.1881i	−0.789689	−	1.36778i	−0.926157	−	0.377137i	$-0.876909\pi$
$997$	−24.9347	−	43.1881i	−0.789689	−	1.36778i	0.136468	−	0.990644i	$-0.456425\pi$
$998$	8.24588	−	14.2823i	0.261019	−	0.452098i
$999$	7.35981	+	10.4308i	0.232854	+	0.330016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.449.4	yes	56
3.2	odd	2		546.2.bu.b.449.13	yes	56
13.2	odd	12		546.2.bu.b.197.13	yes	56
39.2	even	12	inner	546.2.bu.a.197.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.4	✓	56	39.2	even	12	inner
546.2.bu.a.449.4	yes	56	1.1	even	1	trivial
546.2.bu.b.197.13	yes	56	13.2	odd	12
546.2.bu.b.449.13	yes	56	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.684122 - 1.59122i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.803802 - 0.803802i) q^{5} +(-1.71406 - 0.248973i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.06396 - 2.17717i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.684122 - 1.59122i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.803802 - 0.803802i) q^{5} +(-1.71406 - 0.248973i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.06396 - 2.17717i) q^{9} +(-0.984452 - 0.568374i) q^{10} +(-3.42199 + 0.916918i) q^{11} +(0.203143 + 1.72010i) q^{12} +(2.52032 - 2.57836i) q^{13} -1.00000i q^{14} +(-0.729126 - 1.82892i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.65463 - 6.33001i) q^{17} +(-1.56880 + 2.55712i) q^{18} +(1.28797 - 4.80679i) q^{19} +(-0.294212 + 1.09801i) q^{20} +(1.07265 - 1.35994i) q^{21} +(1.77135 + 3.06807i) q^{22} +(-0.368272 + 0.637865i) q^{23} +(1.60891 - 0.641415i) q^{24} +3.70781i q^{25} +(-3.14282 - 1.76712i) q^{26} +(-4.87636 + 1.79475i) q^{27} +(-0.965926 + 0.258819i) q^{28} +(1.05961 + 0.611766i) q^{29} +(-1.57789 + 1.17764i) q^{30} +(2.78096 + 2.78096i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.882037 + 6.07241i) q^{33} +(-5.16843 + 5.16843i) q^{34} +(0.984452 - 0.568374i) q^{35} +(2.87602 + 0.853511i) q^{36} +(-0.635866 - 2.37309i) q^{37} -4.97635 q^{38} +(-2.37853 - 5.77430i) q^{39} +1.13675 q^{40} +(-1.57828 - 5.89022i) q^{41} +(-1.59122 - 0.684122i) q^{42} +(2.20536 - 1.27327i) q^{43} +(2.50507 - 2.50507i) q^{44} +(-3.40903 - 0.0910061i) q^{45} +(0.711446 + 0.190631i) q^{46} +(7.99659 + 7.99659i) q^{47} +(-1.03598 - 1.38808i) q^{48} +(0.866025 + 0.500000i) q^{49} +(3.58147 - 0.959651i) q^{50} +(-12.5726 + 1.48482i) q^{51} +(-0.893482 + 3.49309i) q^{52} +7.87957i q^{53} +(2.99569 + 4.24568i) q^{54} +(-2.01358 + 3.48762i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-6.76752 - 5.33788i) q^{57} +(0.316673 - 1.18184i) q^{58} +(0.645602 - 2.40942i) q^{59} +(1.54590 + 1.21933i) q^{60} +(-1.63757 - 2.83635i) q^{61} +(1.96644 - 3.40597i) q^{62} +(-1.43013 - 2.63718i) q^{63} +1.00000i q^{64} +(-0.0466531 - 4.09833i) q^{65} +(6.09379 - 0.719674i) q^{66} +(-1.47511 + 0.395253i) q^{67} +(6.33001 + 3.65463i) q^{68} +(0.763041 + 1.02238i) q^{69} +(-0.803802 - 0.803802i) q^{70} +(4.91302 + 1.31644i) q^{71} +(0.0800584 - 2.99893i) q^{72} +(-11.3512 + 11.3512i) q^{73} +(-2.12765 + 1.22840i) q^{74} +(5.89993 + 2.53659i) q^{75} +(1.28797 + 4.80679i) q^{76} -3.54270 q^{77} +(-4.96194 + 3.79199i) q^{78} +11.0080 q^{79} +(-0.294212 - 1.09801i) q^{80} +(-0.480179 + 8.98718i) q^{81} +(-5.28103 + 3.04900i) q^{82} +(10.0746 - 10.0746i) q^{83} +(-0.248973 + 1.71406i) q^{84} +(-8.02567 - 2.15047i) q^{85} +(-1.80067 - 1.80067i) q^{86} +(1.69836 - 1.26755i) q^{87} +(-3.06807 - 1.77135i) q^{88} +(15.9782 - 4.28134i) q^{89} +(0.794416 + 3.31642i) q^{90} +(3.10178 - 1.83820i) q^{91} -0.736543i q^{92} +(6.32763 - 2.52260i) q^{93} +(5.65444 - 9.79378i) q^{94} +(-2.82843 - 4.89898i) q^{95} +(-1.07265 + 1.35994i) q^{96} +(1.07287 - 4.00399i) q^{97} +(0.258819 - 0.965926i) q^{98} +(9.05912 + 5.55778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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