LMFDB - Embedded newform 504.2.cs.a.85.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.18
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.152619 - 1.40595i) q^{2} +(-1.40449 + 1.01361i) q^{3} +(-1.95342 + 0.429150i) q^{4} +(1.92732 + 1.11274i) q^{5} +(1.63945 + 1.81995i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.901492 + 2.68092i) q^{8} +(0.945172 - 2.84722i) q^{9} +O(q^{10})$	\(q+(-0.152619 - 1.40595i) q^{2} +(-1.40449 + 1.01361i) q^{3} +(-1.95342 + 0.429150i) q^{4} +(1.92732 + 1.11274i) q^{5} +(1.63945 + 1.81995i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.901492 + 2.68092i) q^{8} +(0.945172 - 2.84722i) q^{9} +(1.27031 - 2.87955i) q^{10} +(-3.09577 + 1.78734i) q^{11} +(2.30856 - 2.58275i) q^{12} +(-4.12235 - 2.38004i) q^{13} +(1.14128 - 0.835149i) q^{14} +(-3.83478 + 0.390731i) q^{15} +(3.63166 - 1.67661i) q^{16} -5.20955 q^{17} +(-4.14731 - 0.894330i) q^{18} +7.87807i q^{19} +(-4.24239 - 1.34653i) q^{20} +(-1.58006 - 0.709515i) q^{21} +(2.98539 + 4.07972i) q^{22} +(1.97738 - 3.42492i) q^{23} +(-3.98355 - 2.85155i) q^{24} +(-0.0236271 - 0.0409234i) q^{25} +(-2.71708 + 6.15908i) q^{26} +(1.55850 + 4.95692i) q^{27} +(-1.34836 - 1.47713i) q^{28} +(-0.176344 + 0.101812i) q^{29} +(1.13461 + 5.33190i) q^{30} +(-4.64469 + 8.04483i) q^{31} +(-2.91150 - 4.85007i) q^{32} +(2.53629 - 5.64821i) q^{33} +(0.795074 + 7.32439i) q^{34} +2.22548i q^{35} +(-0.624430 + 5.96742i) q^{36} +7.27495i q^{37} +(11.0762 - 1.20234i) q^{38} +(8.20224 - 0.835737i) q^{39} +(-1.24569 + 6.17011i) q^{40} +(0.428588 - 0.742336i) q^{41} +(-0.756399 + 2.32978i) q^{42} +(-0.822626 + 0.474943i) q^{43} +(5.28028 - 4.81997i) q^{44} +(4.98986 - 4.43577i) q^{45} +(-5.11706 - 2.25739i) q^{46} +(0.992629 + 1.71928i) q^{47} +(-3.40118 + 6.03589i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.0539305 + 0.0394643i) q^{50} +(7.31675 - 5.28047i) q^{51} +(9.07406 + 2.88010i) q^{52} +3.27639i q^{53} +(6.73135 - 2.94770i) q^{54} -7.95537 q^{55} +(-1.87100 + 2.12117i) q^{56} +(-7.98532 - 11.0646i) q^{57} +(0.170057 + 0.232393i) q^{58} +(-5.73790 - 3.31278i) q^{59} +(7.32324 - 2.40896i) q^{60} +(-2.64229 + 1.52553i) q^{61} +(12.0195 + 5.30243i) q^{62} +(2.93835 - 0.605066i) q^{63} +(-6.37462 + 4.83365i) q^{64} +(-5.29673 - 9.17420i) q^{65} +(-8.32821 - 2.70389i) q^{66} +(-6.71827 - 3.87879i) q^{67} +(10.1764 - 2.23568i) q^{68} +(0.694343 + 6.81455i) q^{69} +(3.12892 - 0.339649i) q^{70} -10.7120 q^{71} +(8.48522 - 0.0328190i) q^{72} +7.19666 q^{73} +(10.2282 - 1.11029i) q^{74} +(0.0746645 + 0.0335276i) q^{75} +(-3.38087 - 15.3891i) q^{76} +(-3.09577 - 1.78734i) q^{77} +(-2.42682 - 11.4044i) q^{78} +(-0.360153 - 0.623804i) q^{79} +(8.86500 + 0.809716i) q^{80} +(-7.21330 - 5.38222i) q^{81} +(-1.10910 - 0.489280i) q^{82} +(9.34963 - 5.39801i) q^{83} +(3.39100 + 0.707895i) q^{84} +(-10.0405 - 5.79686i) q^{85} +(0.793297 + 1.08409i) q^{86} +(0.144474 - 0.321738i) q^{87} +(-7.58252 - 6.68821i) q^{88} +16.9394 q^{89} +(-6.99803 - 6.33853i) q^{90} -4.76008i q^{91} +(-2.39284 + 7.53887i) q^{92} +(-1.63095 - 16.0068i) q^{93} +(2.26574 - 1.65799i) q^{94} +(-8.76623 + 15.1836i) q^{95} +(9.00527 + 3.86072i) q^{96} +(6.09153 + 10.5508i) q^{97} +(1.29390 + 0.570806i) q^{98} +(2.16292 + 10.5037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.152619	−	1.40595i	−0.107918	−	0.994160i
$2$	−0.152619	−	1.40595i	−0.107918	−	0.994160i
$3$	−1.40449	+	1.01361i	−0.810881	+	0.585211i
$3$	−1.40449	+	1.01361i	−0.810881	+	0.585211i
$4$	−1.95342	+	0.429150i	−0.976708	+	0.214575i
$5$	1.92732	+	1.11274i	0.861923	+	0.497632i	0.864656	−	0.502365i	$-0.167536\pi$
$5$	1.92732	+	1.11274i	0.861923	+	0.497632i	−0.00273255	+	0.999996i	$0.500870\pi$
$6$	1.63945	+	1.81995i	0.669301	+	0.742991i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	0.901492	+	2.68092i	0.318726	+	0.947847i
$9$	0.945172	−	2.84722i	0.315057	−	0.949073i
$10$	1.27031	−	2.87955i	0.401709	−	0.910593i
$11$	−3.09577	+	1.78734i	−0.933409	+	0.538904i	−0.887888	−	0.460060i	$-0.847828\pi$
$11$	−3.09577	+	1.78734i	−0.933409	+	0.538904i	−0.0455205	+	0.998963i	$0.514495\pi$
$12$	2.30856	−	2.58275i	0.666423	−	0.745574i
$13$	−4.12235	−	2.38004i	−1.14334	−	0.660105i	−0.196081	−	0.980588i	$-0.562821\pi$
$13$	−4.12235	−	2.38004i	−1.14334	−	0.660105i	−0.947254	+	0.320483i	$0.896155\pi$
$14$	1.14128	−	0.835149i	0.305021	−	0.223203i
$15$	−3.83478	+	0.390731i	−0.990137	+	0.100886i
$16$	3.63166	−	1.67661i	0.907915	−	0.419154i
$17$	−5.20955			−1.26350			−0.631751	−	0.775172i	$-0.717663\pi$
$17$	−5.20955			−1.26350			−0.631751	+	0.775172i	$0.717663\pi$
$18$	−4.14731	−	0.894330i	−0.977530	−	0.210796i
$19$			7.87807i			1.80735i	0.428216	+	0.903676i	$0.359142\pi$
$19$			7.87807i			1.80735i	−0.428216	+	0.903676i	$0.640858\pi$
$20$	−4.24239	−	1.34653i	−0.948626	−	0.301094i
$21$	−1.58006	−	0.709515i	−0.344797	−	0.154829i
$22$	2.98539	+	4.07972i	0.636488	+	0.869800i
$23$	1.97738	−	3.42492i	0.412311	−	0.714144i	−0.582831	−	0.812594i	$-0.698055\pi$
$23$	1.97738	−	3.42492i	0.412311	−	0.714144i	0.995142	+	0.0984493i	$0.0313882\pi$
$24$	−3.98355	−	2.85155i	−0.813139	−	0.582070i
$25$	−0.0236271	−	0.0409234i	−0.00472543	−	0.00818468i
$26$	−2.71708	+	6.15908i	−0.532864	+	1.20789i
$27$	1.55850	+	4.95692i	0.299933	+	0.953960i
$28$	−1.34836	−	1.47713i	−0.254816	−	0.279152i
$29$	−0.176344	+	0.101812i	−0.0327462	+	0.0189060i	−0.516284	−	0.856418i	$-0.672685\pi$
$29$	−0.176344	+	0.101812i	−0.0327462	+	0.0189060i	0.483538	+	0.875324i	$0.339352\pi$
$30$	1.13461	+	5.33190i	0.207150	+	0.973467i
$31$	−4.64469	+	8.04483i	−0.834210	+	1.44489i	0.0604612	+	0.998171i	$0.480743\pi$
$31$	−4.64469	+	8.04483i	−0.834210	+	1.44489i	−0.894672	+	0.446724i	$0.852590\pi$
$32$	−2.91150	−	4.85007i	−0.514686	−	0.857379i
$33$	2.53629	−	5.64821i	0.441511	−	0.983227i
$34$	0.795074	+	7.32439i	0.136354	+	1.25612i
$35$			2.22548i			0.376174i
$36$	−0.624430	+	5.96742i	−0.104072	+	0.994570i
$37$			7.27495i			1.19599i	0.801498	+	0.597997i	$0.204036\pi$
$37$			7.27495i			1.19599i	−0.801498	+	0.597997i	$0.795964\pi$
$38$	11.0762	−	1.20234i	1.79680	−	0.195045i
$39$	8.20224	−	0.835737i	1.31341	−	0.133825i
$40$	−1.24569	+	6.17011i	−0.196962	+	0.975579i
$41$	0.428588	−	0.742336i	0.0669341	−	0.115933i	−0.830616	−	0.556845i	$-0.812012\pi$
$41$	0.428588	−	0.742336i	0.0669341	−	0.115933i	0.897550	+	0.440912i	$0.145345\pi$
$42$	−0.756399	+	2.32978i	−0.116715	+	0.359492i
$43$	−0.822626	+	0.474943i	−0.125449	+	0.0724282i	−0.561411	−	0.827537i	$-0.689741\pi$
$43$	−0.822626	+	0.474943i	−0.125449	+	0.0724282i	0.435962	+	0.899965i	$0.356408\pi$
$44$	5.28028	−	4.81997i	0.796032	−	0.726637i
$45$	4.98986	−	4.43577i	0.743844	−	0.661245i
$46$	−5.11706	−	2.25739i	−0.754469	−	0.332835i
$47$	0.992629	+	1.71928i	0.144790	+	0.250783i	0.929295	−	0.369340i	$-0.120416\pi$
$47$	0.992629	+	1.71928i	0.144790	+	0.250783i	−0.784505	+	0.620123i	$0.787083\pi$
$48$	−3.40118	+	6.03589i	−0.490918	+	0.871206i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.0539305	+	0.0394643i	−0.00762692	+	0.00558110i
$51$	7.31675	−	5.28047i	1.02455	−	0.739414i
$52$	9.07406	+	2.88010i	1.25835	+	0.399398i
$53$			3.27639i			0.450047i	0.974353	+	0.225023i	$0.0722459\pi$
$53$			3.27639i			0.450047i	−0.974353	+	0.225023i	$0.927754\pi$
$54$	6.73135	−	2.94770i	0.916021	−	0.401131i
$55$	−7.95537			−1.07270
$56$	−1.87100	+	2.12117i	−0.250022	+	0.283454i
$57$	−7.98532	−	11.0646i	−1.05768	−	1.46555i
$58$	0.170057	+	0.232393i	0.0223295	+	0.0305147i
$59$	−5.73790	−	3.31278i	−0.747011	−	0.431287i	0.0776021	−	0.996984i	$-0.475274\pi$
$59$	−5.73790	−	3.31278i	−0.747011	−	0.431287i	−0.824613	+	0.565698i	$0.808607\pi$
$60$	7.32324	−	2.40896i	0.945427	−	0.310995i
$61$	−2.64229	+	1.52553i	−0.338311	+	0.195324i	−0.659525	−	0.751683i	$-0.729243\pi$
$61$	−2.64229	+	1.52553i	−0.338311	+	0.195324i	0.321214	+	0.947007i	$0.395909\pi$
$62$	12.0195	+	5.30243i	1.52648	+	0.673409i
$63$	2.93835	−	0.605066i	0.370197	−	0.0762312i
$64$	−6.37462	+	4.83365i	−0.796828	+	0.604206i
$65$	−5.29673	−	9.17420i	−0.656978	−	1.13792i
$66$	−8.32821	−	2.70389i	−1.02513	−	0.332825i
$67$	−6.71827	−	3.87879i	−0.820767	−	0.473870i	0.0299137	−	0.999552i	$-0.490477\pi$
$67$	−6.71827	−	3.87879i	−0.820767	−	0.473870i	−0.850681	+	0.525682i	$0.823810\pi$
$68$	10.1764	−	2.23568i	1.23407	−	0.271116i
$69$	0.694343	+	6.81455i	0.0835891	+	0.820375i
$70$	3.12892	−	0.339649i	0.373977	−	0.0405958i
$71$	−10.7120			−1.27128			−0.635639	−	0.771987i	$-0.719263\pi$
$71$	−10.7120			−1.27128			−0.635639	+	0.771987i	$0.719263\pi$
$72$	8.48522	−	0.0328190i	0.999993	−	0.00386775i
$73$	7.19666			0.842305			0.421153	−	0.906990i	$-0.361626\pi$
$73$	7.19666			0.842305			0.421153	+	0.906990i	$0.361626\pi$
$74$	10.2282	−	1.11029i	1.18901	−	0.129069i
$75$	0.0746645	+	0.0335276i	0.00862152	+	0.00387143i
$76$	−3.38087	−	15.3891i	−0.387812	−	1.76525i
$77$	−3.09577	−	1.78734i	−0.352795	−	0.203686i
$78$	−2.42682	−	11.4044i	−0.274784	−	1.29130i
$79$	−0.360153	−	0.623804i	−0.0405204	−	0.0701834i	0.845054	−	0.534681i	$-0.179568\pi$
$79$	−0.360153	−	0.623804i	−0.0405204	−	0.0701834i	−0.885574	+	0.464498i	$0.846235\pi$
$80$	8.86500	+	0.809716i	0.991138	+	0.0905290i
$81$	−7.21330	−	5.38222i	−0.801478	−	0.598024i
$82$	−1.10910	−	0.489280i	−0.122480	−	0.0540320i
$83$	9.34963	−	5.39801i	1.02626	−	0.592509i	0.110346	−	0.993893i	$-0.464804\pi$
$83$	9.34963	−	5.39801i	1.02626	−	0.592509i	0.915910	+	0.401385i	$0.131471\pi$
$84$	3.39100	+	0.707895i	0.369988	+	0.0772377i
$85$	−10.0405	−	5.79686i	−1.08904	−	0.628758i
$86$	0.793297	+	1.08409i	0.0855434	+	0.116900i
$87$	0.144474	−	0.321738i	0.0154893	−	0.0344940i
$88$	−7.58252	−	6.68821i	−0.808299	−	0.712966i
$89$	16.9394			1.79557			0.897787	−	0.440429i	$-0.145174\pi$
$89$	16.9394			1.79557			0.897787	+	0.440429i	$0.145174\pi$
$90$	−6.99803	−	6.33853i	−0.737658	−	0.668140i
$91$		−	4.76008i		−	0.498992i
$92$	−2.39284	+	7.53887i	−0.249470	+	0.785982i
$93$	−1.63095	−	16.0068i	−0.169122	−	1.65983i
$94$	2.26574	−	1.65799i	0.233693	−	0.171008i
$95$	−8.76623	+	15.1836i	−0.899396	+	1.55780i
$96$	9.00527	+	3.86072i	0.919096	+	0.394033i
$97$	6.09153	+	10.5508i	0.618501	+	1.07127i	0.989759	+	0.142745i	$0.0455930\pi$
$97$	6.09153	+	10.5508i	0.618501	+	1.07127i	−0.371259	+	0.928529i	$0.621074\pi$
$98$	1.29390	+	0.570806i	0.130704	+	0.0576601i
$99$	2.16292	+	10.5037i	0.217382	+	1.05566i
$100$	0.0637158	+	0.0698008i	0.00637158	+	0.00698008i
$101$	5.24945	−	3.03077i	0.522340	−	0.301573i	−0.215552	−	0.976492i	$-0.569155\pi$
$101$	5.24945	−	3.03077i	0.522340	−	0.301573i	0.737891	+	0.674920i	$0.235822\pi$
$102$	−8.54078	−	9.48111i	−0.845663	−	0.938770i
$103$	−6.67670	+	11.5644i	−0.657875	+	1.13947i	0.323290	+	0.946300i	$0.395211\pi$
$103$	−6.67670	+	11.5644i	−0.657875	+	1.13947i	−0.981165	+	0.193172i	$0.938122\pi$
$104$	2.66442	−	13.1973i	0.261268	−	1.29410i
$105$	−2.25577	−	3.12565i	−0.220141	−	0.305033i
$106$	4.60646	−	0.500038i	0.447419	−	0.0485680i
$107$		−	10.8905i		−	1.05282i	−0.850230	−	0.526411i	$-0.823537\pi$
$107$		−	10.8905i		−	1.05282i	0.850230	−	0.526411i	$-0.176463\pi$
$108$	−5.17166	−	9.01410i	−0.497643	−	0.867382i
$109$			9.18075i			0.879356i	0.898155	+	0.439678i	$0.144907\pi$
$109$			9.18075i			0.879356i	−0.898155	+	0.439678i	$0.855093\pi$
$110$	1.21414	+	11.1849i	0.115764	+	1.06644i
$111$	−7.37399	−	10.2176i	−0.699908	−	0.969809i
$112$	3.26782	+	2.30680i	0.308780	+	0.217972i
$113$	5.39653	−	9.34706i	0.507663	−	0.879298i	−0.492298	−	0.870427i	$-0.663843\pi$
$113$	5.39653	−	9.34706i	0.507663	−	0.879298i	0.999961	−	0.00887098i	$-0.00282376\pi$
$114$	−14.3377	+	12.9157i	−1.34285	+	1.20966i
$115$	7.62207	−	4.40060i	0.710762	−	0.410359i
$116$	0.300780	−	0.274559i	0.0279267	−	0.0254922i
$117$	−10.6728	+	9.48769i	−0.986704	+	0.877137i
$118$	−3.78190	+	8.57281i	−0.348152	+	0.789191i
$119$	−2.60477	−	4.51160i	−0.238779	−	0.413578i
$120$	−4.50455	−	9.92849i	−0.411207	−	0.906343i
$121$	0.889177	−	1.54010i	0.0808343	−	0.140009i
$122$	2.54809	+	3.48212i	0.230693	+	0.315256i
$123$	0.150496	+	1.47702i	0.0135698	+	0.133179i
$124$	5.62056	−	17.7082i	0.504742	−	1.59024i
$125$		−	11.2325i		−	1.00467i
$126$	−1.29914	−	4.03884i	−0.115737	−	0.359808i
$127$	22.1491			1.96541			0.982707	−	0.185168i	$-0.0592830\pi$
$127$	22.1491			1.96541			0.982707	+	0.185168i	$0.0592830\pi$
$128$	7.76878	+	8.22472i	0.686670	+	0.726970i
$129$	0.673959	−	1.50088i	0.0593388	−	0.132145i
$130$	−12.0901	+	8.84711i	−1.06037	+	0.775943i
$131$	−12.5880	−	7.26768i	−1.09982	−	0.634980i	−0.163645	−	0.986519i	$-0.552325\pi$
$131$	−12.5880	−	7.26768i	−1.09982	−	0.634980i	−0.936173	+	0.351539i	$0.885658\pi$
$132$	−2.53050	+	12.1217i	−0.220252	+	1.05506i
$133$	−6.82261	+	3.93903i	−0.591595	+	0.341558i
$134$	−4.42807	+	10.0376i	−0.382527	+	0.867113i
$135$	−2.51203	+	11.2878i	−0.216201	+	0.971497i
$136$	−4.69637	−	13.9664i	−0.402710	−	1.19761i
$137$	5.79515	+	10.0375i	0.495113	+	0.857561i	0.999984	−	0.00563408i	$-0.00179339\pi$
$137$	5.79515	+	10.0375i	0.495113	+	0.857561i	−0.504871	+	0.863195i	$0.668460\pi$
$138$	9.47498	−	2.01624i	0.806564	−	0.171634i
$139$	9.13552	+	5.27440i	0.774865	+	0.447369i	0.834607	−	0.550845i	$-0.185695\pi$
$139$	9.13552	+	5.27440i	0.774865	+	0.447369i	−0.0597424	+	0.998214i	$0.519028\pi$
$140$	−0.955063	−	4.34728i	−0.0807175	−	0.367412i
$141$	−3.13683	−	1.40857i	−0.264168	−	0.118623i
$142$	1.63485	+	15.0605i	0.137193	+	1.26385i
$143$	17.0158			1.42293
$144$	−1.34114	−	11.9248i	−0.111762	−	0.993735i
$145$	−0.453161			−0.0376330
$146$	−1.09834	−	10.1182i	−0.0908996	−	0.837386i
$147$	−0.175572	−	1.72313i	−0.0144809	−	0.142121i
$148$	−3.12204	−	14.2110i	−0.256630	−	1.16814i
$149$	1.21645	+	0.702316i	0.0996552	+	0.0575360i	0.548999	−	0.835823i	$-0.315009\pi$
$149$	1.21645	+	0.702316i	0.0996552	+	0.0575360i	−0.449344	+	0.893359i	$0.648342\pi$
$150$	0.0357431	−	0.110092i	0.00291841	−	0.00898896i
$151$	−0.717653	−	1.24301i	−0.0584018	−	0.101155i	0.835346	−	0.549724i	$-0.185267\pi$
$151$	−0.717653	−	1.24301i	−0.0584018	−	0.101155i	−0.893748	+	0.448569i	$0.851934\pi$
$152$	−21.1204	+	7.10202i	−1.71309	+	0.576050i
$153$	−4.92392	+	14.8327i	−0.398075	+	1.19915i
$154$	−2.04045	+	4.62529i	−0.164424	+	0.372716i
$155$	−17.9036	+	10.3366i	−1.43805	+	0.830259i
$156$	−15.6637	+	5.15253i	−1.25410	+	0.412533i
$157$	−14.1154	−	8.14953i	−1.12653	−	0.650403i	−0.183471	−	0.983025i	$-0.558733\pi$
$157$	−14.1154	−	8.14953i	−1.12653	−	0.650403i	−0.943060	+	0.332622i	$0.892067\pi$
$158$	−0.822074	+	0.601563i	−0.0654007	+	0.0478578i
$159$	−3.32100	−	4.60165i	−0.263372	−	0.364935i
$160$	−0.214541	−	12.5874i	−0.0169609	−	0.995119i
$161$	3.95475			0.311678
$162$	−6.46627	+	10.9630i	−0.508038	+	0.861334i
$163$		−	16.0401i		−	1.25636i	−0.778068	−	0.628180i	$-0.783800\pi$
$163$		−	16.0401i		−	1.25636i	0.778068	−	0.628180i	$-0.216200\pi$
$164$	−0.518636	+	1.63402i	−0.0404987	+	0.127595i
$165$	11.1732	−	8.06368i	0.869834	−	0.627757i
$166$	−9.01628	−	12.3213i	−0.699799	−	0.956319i
$167$	−4.82280	+	8.35333i	−0.373199	+	0.646400i	−0.990056	−	0.140676i	$-0.955073\pi$
$167$	−4.82280	+	8.35333i	−0.373199	+	0.646400i	0.616856	+	0.787076i	$0.288406\pi$
$168$	0.477738	−	4.87563i	0.0368583	−	0.376163i
$169$	4.82920	+	8.36442i	0.371477	+	0.643417i
$170$	−6.61776	+	15.0011i	−0.507559	+	1.15054i
$171$	22.4306	+	7.44613i	1.71531	+	0.569420i
$172$	1.40311	−	1.28079i	0.106986	−	0.0976594i
$173$	0.174357	−	0.100665i	0.0132561	−	0.00765342i	−0.493357	−	0.869827i	$-0.664230\pi$
$173$	0.174357	−	0.100665i	0.0132561	−	0.00765342i	0.506613	+	0.862173i	$0.330897\pi$
$174$	−0.474399	−	0.154021i	−0.0359641	−	0.0116763i
$175$	0.0236271	−	0.0409234i	0.00178604	−	0.00309352i
$176$	−8.24609	+	11.6814i	−0.621572	+	0.880521i
$177$	11.4167	−	1.16326i	0.858131	−	0.0874361i
$178$	−2.58527	−	23.8161i	−0.193774	−	1.78509i
$179$			3.13911i			0.234628i	0.993095	+	0.117314i	$0.0374284\pi$
$179$			3.13911i			0.234628i	−0.993095	+	0.117314i	$0.962572\pi$
$180$	−7.84365	+	10.8063i	−0.584631	+	0.805454i
$181$			16.9831i			1.26234i	0.775643	+	0.631172i	$0.217426\pi$
$181$			16.9831i			1.26234i	−0.775643	+	0.631172i	$0.782574\pi$
$182$	−6.69246	+	0.726478i	−0.496078	+	0.0538501i
$183$	2.16477	−	4.82086i	0.160025	−	0.356368i
$184$	10.9645	+	2.21364i	0.808314	+	0.163192i
$185$	−8.09511	+	14.0211i	−0.595164	+	1.03085i
$186$	−22.2559	+	4.73598i	−1.63188	+	0.347259i
$187$	16.1275	−	9.31124i	1.17936	−	0.680905i
$188$	−2.67685	−	2.93249i	−0.195229	−	0.213874i
$189$	−3.51357	+	3.82816i	−0.255575	+	0.278458i
$190$	22.6853	+	10.0076i	1.64576	+	0.726029i
$191$	−0.660007	−	1.14317i	−0.0477564	−	0.0827166i	0.841159	−	0.540788i	$-0.181874\pi$
$191$	−0.660007	−	1.14317i	−0.0477564	−	0.0827166i	−0.888915	+	0.458071i	$0.848540\pi$
$192$	4.05362	−	13.2502i	0.292545	−	0.956252i
$193$	11.3909	−	19.7296i	0.819936	−	1.42017i	−0.0857929	−	0.996313i	$-0.527342\pi$
$193$	11.3909	−	19.7296i	0.819936	−	1.42017i	0.905729	−	0.423858i	$-0.139324\pi$
$194$	13.9043	−	10.1747i	0.998271	−	0.730498i
$195$	16.7383	+	7.51621i	1.19865	+	0.538247i
$196$	0.605053	−	1.90628i	0.0432181	−	0.136163i
$197$		−	11.3310i		−	0.807301i	−0.914913	−	0.403651i	$-0.867741\pi$
$197$		−	11.3310i		−	0.807301i	0.914913	−	0.403651i	$-0.132259\pi$
$198$	14.4376	−	4.64402i	1.02603	−	0.330036i
$199$	6.02928			0.427404			0.213702	−	0.976899i	$-0.431448\pi$
$199$	6.02928			0.427404			0.213702	+	0.976899i	$0.431448\pi$
$200$	0.0884125	−	0.100234i	0.00625171	−	0.00708765i
$201$	13.3673	−	1.36201i	0.942859	−	0.0960691i
$202$	−5.06229	−	6.91793i	−0.356181	−	0.486744i
$203$	−0.176344	−	0.101812i	−0.0123769	−	0.00714581i
$204$	−12.0265	+	13.4549i	−0.842026	+	0.942034i
$205$	1.65205	−	0.953812i	0.115384	−	0.0666171i
$206$	17.2780	+	7.62219i	1.20381	+	0.531063i
$207$	−7.88252	−	8.86716i	−0.547873	−	0.616310i
$208$	−18.9614	−	1.73191i	−1.31474	−	0.120086i
$209$	−14.0808	−	24.3887i	−0.973989	−	1.68700i
$210$	−4.05025	+	3.64855i	−0.279494	+	0.251774i
$211$	9.17956	+	5.29982i	0.631947	+	0.364855i	0.781506	−	0.623898i	$-0.214452\pi$
$211$	9.17956	+	5.29982i	0.631947	+	0.364855i	−0.149559	+	0.988753i	$0.547785\pi$
$212$	−1.40606	−	6.40015i	−0.0965688	−	0.439564i
$213$	15.0448	−	10.8578i	1.03086	−	0.743965i
$214$	−15.3115	+	1.66209i	−1.04667	+	0.113618i
$215$	−2.11395			−0.144170
$216$	−11.8841	+	8.64683i	−0.808612	+	0.588342i
$217$	−9.28937			−0.630604
$218$	12.9077	−	1.40115i	0.874220	−	0.0948981i
$219$	−10.1076	+	7.29464i	−0.683010	+	0.492926i
$220$	15.5401	−	3.41405i	1.04772	−	0.230175i
$221$	21.4756	+	12.3989i	1.44461	+	0.834043i
$222$	−13.2400	+	11.9269i	−0.888613	+	0.800480i
$223$	7.32036	+	12.6792i	0.490208	+	0.849065i	0.999936	−	0.0112706i	$-0.00358761\pi$
$223$	7.32036	+	12.6792i	0.490208	+	0.849065i	−0.509729	+	0.860335i	$0.670254\pi$
$224$	2.74453	−	4.94647i	0.183377	−	0.330500i
$225$	−0.138849	+	0.0285920i	−0.00925663	+	0.00190613i
$226$	−13.9652	−	6.16074i	−0.928948	−	0.409806i
$227$	16.9213	−	9.76954i	1.12311	−	0.648427i	0.180916	−	0.983499i	$-0.442094\pi$
$227$	16.9213	−	9.76954i	1.12311	−	0.648427i	0.942193	+	0.335072i	$0.108760\pi$
$228$	20.3470	+	18.1870i	1.34752	+	1.20446i
$229$	10.4382	+	6.02650i	0.689776	+	0.398242i	0.803528	−	0.595267i	$-0.202954\pi$
$229$	10.4382	+	6.02650i	0.689776	+	0.398242i	−0.113752	+	0.993509i	$0.536287\pi$
$230$	−7.35032	−	10.0447i	−0.484666	−	0.662326i
$231$	6.15964	−	0.627614i	0.405275	−	0.0412940i
$232$	−0.431922	−	0.380980i	−0.0283571	−	0.0250126i
$233$	−24.4274			−1.60029			−0.800145	−	0.599807i	$-0.795244\pi$
$233$	−24.4274			−1.60029			−0.800145	+	0.599807i	$0.795244\pi$
$234$	14.9681	+	13.5575i	0.978497	+	0.886282i
$235$			4.41815i			0.288208i
$236$	12.6302	+	4.00881i	0.822154	+	0.260951i
$237$	1.13813	+	0.511068i	0.0739293	+	0.0331975i
$238$	−5.94557	+	4.35075i	−0.385394	+	0.282017i
$239$	−9.64827	+	16.7113i	−0.624095	+	1.08096i	0.364620	+	0.931156i	$0.381199\pi$
$239$	−9.64827	+	16.7113i	−0.624095	+	1.08096i	−0.988715	+	0.149808i	$0.952135\pi$
$240$	−13.2715	+	7.84846i	−0.856674	+	0.506616i
$241$	7.92988	+	13.7350i	0.510808	+	0.884746i	0.999922	+	0.0125258i	$0.00398718\pi$
$241$	7.92988	+	13.7350i	0.510808	+	0.884746i	−0.489113	+	0.872220i	$0.662679\pi$
$242$	−2.30102	−	1.01509i	−0.147915	−	0.0652527i
$243$	15.5865	+	0.247758i	0.999874	+	0.0158937i
$244$	4.50682	−	4.11393i	0.288519	−	0.263368i
$245$	−1.92732	+	1.11274i	−0.123132	+	0.0710902i
$246$	2.05366	−	0.437012i	0.130937	−	0.0278628i
$247$	18.7501	−	32.4762i	1.19304	−	2.06641i
$248$	−25.7547	−	5.19966i	−1.63542	−	0.330179i
$249$	−7.65994	+	17.0584i	−0.485429	+	1.08103i
$250$	−15.7924	+	1.71430i	−0.998802	+	0.108422i
$251$			6.47190i			0.408503i	0.978918	+	0.204251i	$0.0654760\pi$
$251$			6.47190i			0.408503i	−0.978918	+	0.204251i	$0.934524\pi$
$252$	−5.48015	+	2.44294i	−0.345217	+	0.153891i
$253$			14.1370i			0.888785i
$254$	−3.38036	−	31.1406i	−0.212103	−	1.95394i
$255$	19.9775	−	2.03553i	1.25104	−	0.127470i
$256$	10.3779	−	12.1778i	0.648620	−	0.761112i
$257$	0.944655	−	1.63619i	0.0589259	−	0.102063i	−0.835058	−	0.550163i	$-0.814566\pi$
$257$	0.944655	−	1.63619i	0.0589259	−	0.102063i	0.893984	+	0.448100i	$0.147899\pi$
$258$	−2.21302	−	0.718494i	−0.137777	−	0.0447315i
$259$	−6.30029	+	3.63747i	−0.391481	+	0.226022i
$260$	14.2838	+	15.6479i	0.885844	+	0.970444i
$261$	0.123206	+	0.598319i	0.00762627	+	0.0370350i
$262$	−8.29686	+	18.8073i	−0.512582	+	1.16192i
$263$	8.39638	+	14.5430i	0.517743	+	0.896757i	0.999788	+	0.0206104i	$0.00656096\pi$
$263$	8.39638	+	14.5430i	0.517743	+	0.896757i	−0.482045	+	0.876147i	$0.660106\pi$
$264$	17.4288	+	1.70776i	1.07267	+	0.105106i
$265$	−3.64577	+	6.31465i	−0.223958	+	0.387906i
$266$	6.57936	+	8.99110i	0.403406	+	0.551280i
$267$	−23.7912	+	17.1700i	−1.45600	+	1.05079i
$268$	14.7882	+	4.69375i	0.903330	+	0.286717i
$269$			10.9255i			0.666138i	0.942903	+	0.333069i	$0.108084\pi$
$269$			10.9255i			0.666138i	−0.942903	+	0.333069i	$0.891916\pi$
$270$	16.2535	+	1.80908i	0.989155	+	0.110097i
$271$	−25.1684			−1.52887			−0.764435	−	0.644701i	$-0.776982\pi$
$271$	−25.1684			−1.52887			−0.764435	+	0.644701i	$0.776982\pi$
$272$	−18.9193	+	8.73441i	−1.14715	+	0.529601i
$273$	4.82489	+	6.68548i	0.292016	+	0.404624i
$274$	13.2278	−	9.67962i	0.799121	−	0.584767i
$275$	0.146288	+	0.0844595i	0.00882150	+	0.00509310i
$276$	−4.28080	−	13.0137i	−0.257674	−	0.783331i
$277$	−11.0002	+	6.35098i	−0.660939	+	0.381594i	−0.792635	−	0.609697i	$-0.791291\pi$
$277$	−11.0002	+	6.35098i	−0.660939	+	0.381594i	0.131695	+	0.991290i	$0.457958\pi$
$278$	6.02131	−	13.6491i	0.361134	−	0.818619i
$279$	18.5154	+	20.8282i	1.10849	+	1.24695i
$280$	−5.96632	+	2.00625i	−0.356556	+	0.119896i
$281$	2.56684	+	4.44589i	0.153125	+	0.265220i	0.932375	−	0.361494i	$-0.117733\pi$
$281$	2.56684	+	4.44589i	0.153125	+	0.265220i	−0.779250	+	0.626713i	$0.784400\pi$
$282$	−1.50165	+	4.62521i	−0.0894218	+	0.275427i
$283$	−0.467277	−	0.269782i	−0.0277767	−	0.0160369i	0.486047	−	0.873932i	$-0.338438\pi$
$283$	−0.467277	−	0.269782i	−0.0277767	−	0.0160369i	−0.513824	+	0.857896i	$0.671772\pi$
$284$	20.9249	−	4.59704i	1.24167	−	0.272784i
$285$	−3.07821	−	30.2107i	−0.182337	−	1.78953i
$286$	−2.59693	−	23.9234i	−0.153559	−	1.41462i
$287$	0.857175			0.0505975
$288$	−16.5611	+	3.70554i	−0.975870	+	0.218351i
$289$	10.1394			0.596435
$290$	0.0691608	+	0.637124i	0.00406126	+	0.0374132i
$291$	−19.2499	−	8.64406i	−1.12845	−	0.506724i
$292$	−14.0581	+	3.08844i	−0.822686	+	0.180738i
$293$	15.2121	+	8.78271i	0.888701	+	0.513092i	0.873517	−	0.486793i	$-0.161833\pi$
$293$	15.2121	+	8.78271i	0.888701	+	0.513092i	0.0151835	+	0.999885i	$0.495167\pi$
$294$	−2.39585	+	0.509828i	−0.139729	+	0.0297338i
$295$	−7.37251	−	12.7696i	−0.429244	−	0.743472i
$296$	−19.5035	+	6.55831i	−1.13362	+	0.381194i
$297$	−13.6845	−	12.5599i	−0.794053	−	0.728799i
$298$	0.801772	−	1.81745i	0.0464454	−	0.105282i
$299$	−16.3029	+	9.41248i	−0.942820	+	0.544338i
$300$	−0.160239	−	0.0334511i	−0.00925141	−	0.00193130i
$301$	−0.822626	−	0.474943i	−0.0474154	−	0.0273753i
$302$	−1.63809	+	1.19869i	−0.0942615	+	0.0689771i
$303$	−4.30075	+	9.57760i	−0.247072	+	0.550218i
$304$	13.2085	+	28.6105i	0.757559	+	1.64092i
$305$	−6.79006			−0.388798
$306$	21.6056	+	4.65906i	1.23511	+	0.266340i
$307$		−	1.19639i		−	0.0682818i	−0.999417	−	0.0341409i	$-0.989131\pi$
$307$		−	1.19639i		−	0.0682818i	0.999417	−	0.0341409i	$-0.0108695\pi$
$308$	6.81435	+	2.16287i	0.388284	+	0.123241i
$309$	−2.34448	−	23.0096i	−0.133373	−	1.30897i
$310$	17.2653	+	23.5941i	0.980601	+	1.34005i
$311$	−10.4269	+	18.0599i	−0.591254	+	1.02408i	0.402809	+	0.915284i	$0.368034\pi$
$311$	−10.4269	+	18.0599i	−0.591254	+	1.02408i	−0.994064	+	0.108799i	$0.965300\pi$
$312$	9.63480	+	21.2361i	0.545463	+	1.20226i
$313$	4.77943	+	8.27822i	0.270150	+	0.467913i	0.968900	−	0.247453i	$-0.0795935\pi$
$313$	4.77943	+	8.27822i	0.270150	+	0.467913i	−0.698750	+	0.715366i	$0.746260\pi$
$314$	−9.30359	+	21.0894i	−0.525032	+	1.19014i
$315$	6.33642	+	2.10346i	0.357017	+	0.118516i
$316$	0.971234	+	1.06399i	0.0546362	+	0.0598540i
$317$	9.73589	−	5.62102i	0.546822	−	0.315708i	−0.201017	−	0.979588i	$-0.564425\pi$
$317$	9.73589	−	5.62102i	0.546822	−	0.315708i	0.747839	+	0.663880i	$0.231091\pi$
$318$	−5.96287	+	5.37147i	−0.334381	+	0.301217i
$319$	0.363946	−	0.630373i	0.0203771	−	0.0352941i
$320$	−17.6645	+	2.22270i	−0.987477	+	0.124253i
$321$	11.0387	+	15.2955i	0.616122	+	0.853714i
$322$	−0.603569	−	5.56020i	−0.0336356	−	0.309858i
$323$		−	41.0412i		−	2.28359i
$324$	16.4003	+	7.41812i	0.911130	+	0.412118i
$325$			0.224934i			0.0124771i
$326$	−22.5517	+	2.44802i	−1.24902	+	0.135584i
$327$	−9.30574	−	12.8942i	−0.514608	−	0.713053i
$328$	2.37651	+	0.479798i	0.131221	+	0.0264924i
$329$	−0.992629	+	1.71928i	−0.0547254	+	0.0947872i
$330$	−13.0424	−	14.4784i	−0.717961	−	0.797008i
$331$	−18.3530	+	10.5961i	−1.00877	+	0.582415i	−0.910832	−	0.412777i	$-0.864559\pi$
$331$	−18.3530	+	10.5961i	−1.00877	+	0.582415i	−0.0979403	+	0.995192i	$0.531225\pi$
$332$	−15.9472	+	14.5569i	−0.875214	+	0.798916i
$333$	20.7134	+	6.87607i	1.13508	+	0.376807i
$334$	12.4805	+	5.50576i	0.682900	+	0.301262i
$335$	−8.63217	−	14.9514i	−0.471626	−	0.816880i
$336$	−6.92782	+	0.0724339i	−0.377944	+	0.00395160i
$337$	5.92381	−	10.2603i	0.322690	−	0.558916i	−0.658352	−	0.752710i	$-0.728746\pi$
$337$	5.92381	−	10.2603i	0.322690	−	0.558916i	0.981042	+	0.193794i	$0.0620794\pi$
$338$	11.0230	−	8.06620i	0.599570	−	0.438743i
$339$	1.89496	+	18.5978i	0.102920	+	1.01010i
$340$	22.1009	+	7.01482i	1.19859	+	0.380432i
$341$		−	33.2066i		−	1.79824i
$342$	7.04559	−	32.6728i	0.380982	−	1.76674i
$343$	−1.00000			−0.0539949
$344$	−2.01487	−	1.77723i	−0.108635	−	0.0958220i
$345$	−6.24459	+	13.9064i	−0.336197	+	0.748697i
$346$	−0.168141	−	0.229775i	−0.00903929	−	0.0123528i
$347$	−19.7957	−	11.4291i	−1.06269	−	0.613544i	−0.136515	−	0.990638i	$-0.543590\pi$
$347$	−19.7957	−	11.4291i	−1.06269	−	0.613544i	−0.926175	+	0.377094i	$0.876923\pi$
$348$	−0.144145	+	0.690490i	−0.00772696	+	0.0370141i
$349$	10.5469	−	6.08927i	0.564564	−	0.325951i	−0.190411	−	0.981704i	$-0.560982\pi$
$349$	10.5469	−	6.08927i	0.564564	−	0.325951i	0.754975	+	0.655753i	$0.227649\pi$
$350$	−0.0611424	−	0.0269730i	−0.00326820	−	0.00144177i
$351$	5.37300	−	24.1435i	0.286790	−	1.28868i
$352$	17.6821	+	9.81082i	0.942457	+	0.522919i
$353$	3.19150	+	5.52785i	0.169867	+	0.294218i	0.938373	−	0.345625i	$-0.112333\pi$
$353$	3.19150	+	5.52785i	0.169867	+	0.294218i	−0.768506	+	0.639842i	$0.779000\pi$
$354$	−3.37789	−	15.8738i	−0.179533	−	0.843683i
$355$	−20.6454	−	11.9196i	−1.09574	−	0.632628i
$356$	−33.0897	+	7.26955i	−1.75375	+	0.385285i
$357$	8.23140	+	3.69625i	0.435652	+	0.195626i
$358$	4.41344	−	0.479087i	0.233258	−	0.0253205i
$359$	−4.52677			−0.238914			−0.119457	−	0.992839i	$-0.538115\pi$
$359$	−4.52677			−0.238914			−0.119457	+	0.992839i	$0.538115\pi$
$360$	16.3902	+	9.37857i	0.863842	+	0.494294i
$361$	−43.0639			−2.26652
$362$	23.8775	−	2.59194i	1.25497	−	0.136229i
$363$	0.312229	+	3.06433i	0.0163878	+	0.160836i
$364$	2.04279	+	9.29842i	0.107071	+	0.487370i
$365$	13.8703	+	8.00800i	0.726003	+	0.419158i
$366$	−7.10829	−	2.30782i	−0.371556	−	0.120632i
$367$	−14.1596	−	24.5252i	−0.739125	−	1.28020i	−0.952890	−	0.303318i	$-0.901906\pi$
$367$	−14.1596	−	24.5252i	−0.739125	−	1.28020i	0.213764	−	0.976885i	$-0.431428\pi$
$368$	1.43890	−	15.7534i	0.0750076	−	0.821205i
$369$	−1.70850	−	1.92192i	−0.0889411	−	0.100051i
$370$	20.9486	+	9.24147i	1.08906	+	0.480441i
$371$	−2.83744	+	1.63820i	−0.147312	+	0.0850509i
$372$	10.0552	+	30.5680i	0.521340	+	1.58488i
$373$	3.16804	+	1.82907i	0.164035	+	0.0947057i	0.579770	−	0.814780i	$-0.303142\pi$
$373$	3.16804	+	1.82907i	0.164035	+	0.0947057i	−0.415735	+	0.909486i	$0.636476\pi$
$374$	−15.5525	−	21.2535i	−0.804203	−	1.09899i
$375$	11.3855	+	15.7760i	0.587943	+	0.814668i
$376$	−3.71441	+	4.21108i	−0.191556	+	0.217170i
$377$	0.969268			0.0499199
$378$	5.91846	+	4.35567i	0.304413	+	0.224032i
$379$		−	8.01531i		−	0.411719i	−0.978582	−	0.205859i	$-0.934001\pi$
$379$		−	8.01531i		−	0.411719i	0.978582	−	0.205859i	$-0.0659989\pi$
$380$	10.6081	−	33.4218i	0.544182	−	1.71450i
$381$	−31.1081	+	22.4506i	−1.59372	+	1.15018i
$382$	−1.50651	+	1.10241i	−0.0770797	+	0.0564041i
$383$	−0.0917017	+	0.158832i	−0.00468574	+	0.00811593i	−0.868359	−	0.495937i	$-0.834825\pi$
$383$	−0.0917017	+	0.158832i	−0.00468574	+	0.00811593i	0.863673	+	0.504052i	$0.168158\pi$
$384$	−19.2479	−	3.67698i	−0.982238	−	0.187640i
$385$	−3.97769	−	6.88955i	−0.202722	−	0.351124i
$386$	−29.4774	−	13.0040i	−1.50036	−	0.661886i
$387$	0.574744	+	2.79110i	0.0292159	+	0.141880i
$388$	−16.4272	−	17.9960i	−0.833963	−	0.913607i
$389$	−22.7467	+	13.1328i	−1.15330	+	0.665859i	−0.949690	−	0.313192i	$-0.898602\pi$
$389$	−22.7467	+	13.1328i	−1.15330	+	0.665859i	−0.203612	+	0.979052i	$0.565268\pi$
$390$	8.01288	−	24.6804i	0.405748	−	1.24974i
$391$	−10.3012	+	17.8423i	−0.520956	+	0.902322i
$392$	−2.77249	−	0.559743i	−0.140032	−	0.0282713i
$393$	25.0463	−	2.55200i	1.26342	−	0.128731i
$394$	−15.9309	+	1.72932i	−0.802586	+	0.0871221i
$395$		−	1.60303i		−	0.0806570i
$396$	−8.73272	−	19.5898i	−0.438836	−	0.984425i
$397$		−	10.1734i		−	0.510589i	−0.966863	−	0.255294i	$-0.917828\pi$
$397$		−	10.1734i		−	0.510589i	0.966863	−	0.255294i	$-0.0821723\pi$
$398$	−0.920180	−	8.47689i	−0.0461245	−	0.424908i
$399$	5.58961	−	12.4478i	0.279830	−	0.623170i
$400$	−0.154418	−	0.109006i	−0.00772092	−	0.00545031i
$401$	1.49105	−	2.58258i	0.0744597	−	0.128968i	−0.826392	−	0.563096i	$-0.809610\pi$
$401$	1.49105	−	2.58258i	0.0744597	−	0.128968i	0.900851	+	0.434128i	$0.142943\pi$
$402$	−3.95503	−	18.5860i	−0.197259	−	0.926985i
$403$	38.2941	−	22.1091i	1.90756	−	1.10133i
$404$	−8.95370	+	8.17315i	−0.445463	+	0.406629i
$405$	−7.91333	−	18.3998i	−0.393217	−	0.914292i
$406$	−0.116230	+	0.263470i	−0.00576839	+	0.0130758i
$407$	−13.0028	−	22.5215i	−0.644525	−	1.11635i
$408$	20.7525	+	14.8553i	1.02740	+	0.735446i
$409$	−17.8325	+	30.8868i	−0.881762	+	1.52726i	−0.0323806	+	0.999476i	$0.510309\pi$
$409$	−17.8325	+	30.8868i	−0.881762	+	1.52726i	−0.849381	+	0.527780i	$0.823024\pi$
$410$	−1.59315	−	2.17714i	−0.0786800	−	0.107521i
$411$	−18.3134	−	8.22349i	−0.903331	−	0.405635i
$412$	8.07951	−	25.4553i	0.398049	−	1.25409i
$413$		−	6.62555i		−	0.326022i
$414$	−11.2638	+	12.4358i	−0.553585	+	0.611184i
$415$	24.0263			1.17940
$416$	0.458883	+	26.9232i	0.0224986	+	1.32002i
$417$	−18.1769	+	1.85207i	−0.890128	+	0.0906964i
$418$	−32.1403	+	23.5191i	−1.57204	+	1.15036i
$419$	15.7714	+	9.10563i	0.770484	+	0.444839i	0.833047	−	0.553202i	$-0.186594\pi$
$419$	15.7714	+	9.10563i	0.770484	+	0.444839i	−0.0625632	+	0.998041i	$0.519927\pi$
$420$	5.74784	+	5.13764i	0.280466	+	0.250691i
$421$	−17.3170	+	9.99796i	−0.843978	+	0.487271i	−0.858614	−	0.512622i	$-0.828674\pi$
$421$	−17.3170	+	9.99796i	−0.843978	+	0.487271i	0.0146368	+	0.999893i	$0.495341\pi$
$422$	6.05033	−	13.7149i	0.294526	−	0.667631i
$423$	5.83338	−	1.20121i	0.283629	−	0.0584050i
$424$	−8.78373	+	2.95364i	−0.426576	+	0.143442i
$425$	0.123087	+	0.213192i	0.00597058	+	0.0103413i
$426$	−17.5617	−	19.4952i	−0.850868	−	0.944548i
$427$	−2.64229	−	1.52553i	−0.127870	−	0.0738255i
$428$	4.67364	+	21.2736i	0.225909	+	1.02830i
$429$	−23.8985	+	17.2474i	−1.15383	+	0.832715i
$430$	0.322628	+	2.97212i	0.0155585	+	0.143328i
$431$	16.5295			0.796199			0.398100	−	0.917342i	$-0.369670\pi$
$431$	16.5295			0.796199			0.398100	+	0.917342i	$0.369670\pi$
$432$	13.9708	+	15.3889i	0.672170	+	0.740397i
$433$	−5.66320			−0.272156			−0.136078	−	0.990698i	$-0.543450\pi$
$433$	−5.66320			−0.272156			−0.136078	+	0.990698i	$0.543450\pi$
$434$	1.41773	+	13.0604i	0.0680533	+	0.626921i
$435$	0.636459	−	0.459330i	0.0305159	−	0.0220232i
$436$	−3.93991	−	17.9338i	−0.188688	−	0.858874i
$437$	26.9817	+	15.5779i	1.29071	+	0.745192i
$438$	11.7985	+	13.0976i	0.563756	+	0.625825i
$439$	−18.9769	−	32.8690i	−0.905720	−	1.56875i	−0.819948	−	0.572438i	$-0.805998\pi$
$439$	−18.9769	−	32.8690i	−0.905720	−	1.56875i	−0.0857723	−	0.996315i	$-0.527336\pi$
$440$	−7.17171	−	21.3277i	−0.341898	−	1.01676i
$441$	1.99318	+	2.24215i	0.0949132	+	0.106769i
$442$	14.1548	−	32.0860i	0.673274	−	1.52618i
$443$	−25.6172	+	14.7901i	−1.21711	+	0.702700i	−0.964299	−	0.264816i	$-0.914689\pi$
$443$	−25.6172	+	14.7901i	−1.21711	+	0.702700i	−0.252813	+	0.967515i	$0.581356\pi$
$444$	18.7893	+	16.7946i	0.891702	+	0.797037i
$445$	32.6477	+	18.8491i	1.54765	+	0.893535i
$446$	16.7092	−	12.2272i	0.791204	−	0.578974i
$447$	−2.42036	+	0.246614i	−0.114479	+	0.0116644i
$448$	−7.37338	−	3.10376i	−0.348359	−	0.146639i
$449$	24.3818			1.15065			0.575324	−	0.817926i	$-0.304876\pi$
$449$	24.3818			1.15065			0.575324	+	0.817926i	$0.304876\pi$
$450$	0.0613900	+	0.190852i	0.00289395	+	0.00899687i
$451$			3.06413i			0.144284i
$452$	−6.53037	+	20.5746i	−0.307163	+	0.967748i
$453$	2.26787	+	1.01837i	0.106554	+	0.0478473i
$454$	−16.3180	−	22.2996i	−0.765843	−	1.04657i
$455$	5.29673	−	9.17420i	0.248314	−	0.430093i
$456$	22.4647	−	31.3827i	1.05201	−	1.46963i
$457$	7.81624	+	13.5381i	0.365628	+	0.633287i	0.988877	−	0.148737i	$-0.0475208\pi$
$457$	7.81624	+	13.5381i	0.365628	+	0.633287i	−0.623248	+	0.782024i	$0.714187\pi$
$458$	6.87992	−	15.5954i	0.321477	−	0.728725i
$459$	−8.11908	−	25.8233i	−0.378966	−	1.20533i
$460$	−13.0006	+	11.8672i	−0.606154	+	0.553312i
$461$	0.380140	−	0.219474i	0.0177049	−	0.0102219i	−0.491121	−	0.871091i	$-0.663413\pi$
$461$	0.380140	−	0.219474i	0.0177049	−	0.0102219i	0.508826	+	0.860869i	$0.330080\pi$
$462$	−1.82247	−	8.56439i	−0.0847891	−	0.398451i
$463$	−6.04020	+	10.4619i	−0.280712	+	0.486208i	−0.971560	−	0.236792i	$-0.923904\pi$
$463$	−6.04020	+	10.4619i	−0.280712	+	0.486208i	0.690848	+	0.723000i	$0.257237\pi$
$464$	−0.469721	+	0.665408i	−0.0218063	+	0.0308908i
$465$	14.6680	−	32.6650i	0.680212	−	1.51480i
$466$	3.72807	+	34.3438i	0.172700	+	1.59094i
$467$			18.1355i			0.839213i	0.907706	+	0.419606i	$0.137832\pi$
$467$			18.1355i			0.839213i	−0.907706	+	0.419606i	$0.862168\pi$
$468$	16.7768	−	23.1136i	0.775509	−	1.06843i
$469$		−	7.75759i		−	0.358212i
$470$	6.21171	−	0.674291i	0.286525	−	0.0311027i
$471$	28.0854	−	2.86166i	1.29411	−	0.131858i
$472$	3.70861	−	18.3693i	0.170702	−	0.845514i
$473$	1.69777	−	2.94063i	0.0780636	−	0.135210i
$474$	0.544839	−	1.67815i	0.0250253	−	0.0770802i
$475$	0.322397	−	0.186136i	0.0147926	−	0.00854051i
$476$	7.02436	+	7.69519i	0.321961	+	0.352709i
$477$	9.32860	+	3.09675i	0.427127	+	0.141791i
$478$	24.9678	+	11.0146i	1.14200	+	0.503795i
$479$	−6.01148	−	10.4122i	−0.274671	−	0.475745i	0.695381	−	0.718641i	$-0.255236\pi$
$479$	−6.01148	−	10.4122i	−0.274671	−	0.475745i	−0.970052	+	0.242897i	$0.921902\pi$
$480$	13.0601	+	17.4613i	0.596107	+	0.796998i
$481$	17.3147	−	29.9899i	0.789481	−	1.36742i
$482$	18.1005	−	13.2453i	0.824454	−	0.603305i
$483$	−5.55440	+	4.00859i	−0.252734	+	0.182397i
$484$	−1.07600	+	3.39004i	−0.0489090	+	0.154093i
$485$			27.1131i			1.23114i
$486$	−2.03045	−	21.9517i	−0.0921032	−	0.995749i
$487$	34.6368			1.56955			0.784773	−	0.619784i	$-0.212780\pi$
$487$	34.6368			1.56955			0.784773	+	0.619784i	$0.212780\pi$
$488$	−6.47182	−	5.70852i	−0.292966	−	0.258412i
$489$	16.2585	+	22.5282i	0.735235	+	1.01876i
$490$	1.85860	+	2.53990i	0.0839632	+	0.114741i
$491$	11.3680	+	6.56334i	0.513033	+	0.296199i	0.734079	−	0.679064i	$-0.237614\pi$
$491$	11.3680	+	6.56334i	0.513033	+	0.296199i	−0.221047	+	0.975263i	$0.570947\pi$
$492$	−0.927845	−	2.82066i	−0.0418305	−	0.127165i
$493$	0.918671	−	0.530395i	0.0413749	−	0.0238878i
$494$	−48.5216	−	21.4054i	−2.18309	−	0.963072i
$495$	−7.51919	+	22.6507i	−0.337963	+	1.01807i
$496$	−3.37984	+	37.0035i	−0.151759	+	1.66150i
$497$	−5.35599	−	9.27684i	−0.240249	−	0.416123i
$498$	25.1523	+	8.16610i	1.12710	+	0.365932i
$499$	6.36516	+	3.67492i	0.284944	+	0.164512i	0.635659	−	0.771970i	$-0.280728\pi$
$499$	6.36516	+	3.67492i	0.284944	+	0.164512i	−0.350716	+	0.936482i	$0.614062\pi$
$500$	4.82044	+	21.9418i	0.215577	+	0.981268i
$501$	−1.69350	−	16.6206i	−0.0756598	−	0.742554i
$502$	9.09920	−	0.987733i	0.406117	−	0.0440847i
$503$	−17.7890			−0.793171			−0.396586	−	0.917998i	$-0.629805\pi$
$503$	−17.7890			−0.793171			−0.396586	+	0.917998i	$0.629805\pi$
$504$	4.27103	+	7.33200i	0.190247	+	0.326593i
$505$	13.4898			0.600289
$506$	19.8760	−	2.15757i	0.883594	−	0.0959156i
$507$	−15.2608	−	6.85278i	−0.677758	−	0.304342i
$508$	−43.2664	+	9.50527i	−1.91963	+	0.421728i
$509$	−4.11128	−	2.37365i	−0.182229	−	0.105210i	0.406110	−	0.913824i	$-0.366885\pi$
$509$	−4.11128	−	2.37365i	−0.182229	−	0.105210i	−0.588340	+	0.808614i	$0.700218\pi$
$510$	−5.91080	−	27.7768i	−0.261735	−	1.22998i
$511$	3.59833	+	6.23249i	0.159181	+	0.275709i
$512$	−18.7053	−	12.7323i	−0.826665	−	0.562695i
$513$	−39.0510	+	12.2780i	−1.72414	+	0.542085i
$514$	−2.44458	−	1.07843i	−0.107826	−	0.0475674i
$515$	−25.7363	+	14.8588i	−1.13407	+	0.654758i
$516$	−0.672420	+	3.22107i	−0.0296017	+	0.141800i
$517$	−6.14589	−	3.54833i	−0.270296	−	0.156056i
$518$	6.07566	+	8.30277i	0.266949	+	0.364803i
$519$	−0.142847	+	0.318114i	−0.00627027	+	0.0139636i
$520$	19.8203	−	22.4706i	0.869178	−	0.985399i
$521$	−14.1484			−0.619851			−0.309925	−	0.950761i	$-0.600304\pi$
$521$	−14.1484			−0.619851			−0.309925	+	0.950761i	$0.600304\pi$
$522$	0.822406	−	0.264537i	0.0359957	−	0.0115785i
$523$		−	13.0034i		−	0.568597i	−0.958736	−	0.284299i	$-0.908239\pi$
$523$		−	13.0034i		−	0.568597i	0.958736	−	0.284299i	$-0.0917607\pi$
$524$	27.7085	+	8.79466i	1.21045	+	0.384197i
$525$	0.00829652	+	0.0814252i	0.000362090	+	0.00355369i
$526$	19.1653	−	14.0245i	0.835646	−	0.611495i
$527$	24.1967	−	41.9100i	1.05403	−	1.82563i
$528$	−0.258928	−	24.7648i	−0.0112684	−	1.07775i
$529$	3.67997	+	6.37389i	0.159998	+	0.277126i
$530$	9.43452	+	4.16205i	0.409810	+	0.180788i
$531$	−14.8555	+	13.2059i	−0.644674	+	0.573087i
$532$	11.6369	−	10.6225i	0.504526	−	0.460543i
$533$	−3.53358	+	2.04011i	−0.153056	+	0.0883671i
$534$	27.7713	+	30.8289i	1.20178	+	1.33410i
$535$	12.1182	−	20.9894i	0.523917	−	0.907452i
$536$	4.34225	−	21.5078i	0.187557	−	0.928996i
$537$	−3.18185	−	4.40884i	−0.137307	−	0.190256i
$538$	15.3607	−	1.66743i	0.662247	−	0.0718880i
$539$		−	3.57468i		−	0.153972i
$540$	0.0628984	−	23.1277i	0.00270672	−	0.995260i
$541$			9.14238i			0.393062i	0.980498	+	0.196531i	$0.0629676\pi$
$541$			9.14238i			0.393062i	−0.980498	+	0.196531i	$0.937032\pi$
$542$	3.84116	+	35.3856i	0.164992	+	1.51994i
$543$	−17.2143	−	23.8525i	−0.738737	−	1.02361i
$544$	15.1676	+	25.2667i	0.650306	+	1.08330i
$545$	−10.2158	+	17.6942i	−0.437595	+	0.757938i
$546$	8.66311	−	7.80390i	0.370747	−	0.333976i
$547$	13.6771	−	7.89646i	0.584789	−	0.337628i	−0.178245	−	0.983986i	$-0.557042\pi$
$547$	13.6771	−	7.89646i	0.584789	−	0.337628i	0.763034	+	0.646358i	$0.223709\pi$
$548$	−15.6279	−	17.1204i	−0.667591	−	0.731347i
$549$	1.84609	+	8.96508i	0.0787893	+	0.382620i
$550$	0.0964199	−	0.218564i	0.00411136	−	0.00931962i
$551$	−0.802083	−	1.38925i	−0.0341699	−	0.0591840i
$552$	−17.6433	+	8.00474i	−0.750948	+	0.340704i
$553$	0.360153	−	0.623804i	0.0153153	−	0.0265268i
$554$	10.6080	+	14.4965i	0.450692	+	0.615899i
$555$	−2.84255	−	27.8978i	−0.120659	−	1.18420i
$556$	−20.1090	−	6.38258i	−0.852811	−	0.270682i
$557$			15.3318i			0.649630i	0.945778	+	0.324815i	$0.105302\pi$
$557$			15.3318i			0.649630i	−0.945778	+	0.324815i	$0.894698\pi$
$558$	26.4577	−	29.2105i	1.12004	−	1.23658i
$559$	4.52154			0.191241
$560$	3.73127	+	8.08218i	0.157675	+	0.341534i
$561$	−13.2129	+	29.4246i	−0.557850	+	1.24231i
$562$	5.85898	−	4.28738i	0.247146	−	0.180852i
$563$	−25.9327	−	14.9723i	−1.09293	−	0.631006i	−0.158578	−	0.987346i	$-0.550691\pi$
$563$	−25.9327	−	14.9723i	−1.09293	−	0.631006i	−0.934356	+	0.356340i	$0.884024\pi$
$564$	6.73201	+	1.40535i	0.283469	+	0.0591761i
$565$	20.8017	−	12.0099i	0.875133	−	0.505258i
$566$	−0.307987	+	0.698144i	−0.0129456	+	0.0293452i
$567$	1.05449	−	8.93801i	0.0442844	−	0.375361i
$568$	−9.65676	−	28.7179i	−0.405189	−	1.20498i
$569$	−14.4287	−	24.9913i	−0.604884	−	1.04769i	−0.992070	−	0.125689i	$-0.959886\pi$
$569$	−14.4287	−	24.9913i	−0.604884	−	1.04769i	0.387185	−	0.922002i	$-0.373447\pi$
$570$	−42.0051	+	8.93853i	−1.75940	+	0.374394i
$571$	32.8883	+	18.9880i	1.37633	+	0.794625i	0.991716	−	0.128452i	$-0.0410010\pi$
$571$	32.8883	+	18.9880i	1.37633	+	0.794625i	0.384615	+	0.923077i	$0.374334\pi$
$572$	−33.2389	+	7.30232i	−1.38979	+	0.305325i
$573$	2.08570	+	0.936570i	0.0871314	+	0.0391258i
$574$	−0.130821	−	1.20515i	−0.00546036	−	0.0503020i
$575$	−0.186879			−0.00779339
$576$	7.73734	+	22.7186i	0.322389	+	0.946607i
$577$	−35.6095			−1.48244			−0.741221	−	0.671261i	$-0.765753\pi$
$577$	−35.6095			−1.48244			−0.741221	+	0.671261i	$0.765753\pi$
$578$	−1.54746	−	14.2555i	−0.0643659	−	0.592952i
$579$	3.99985	+	39.2560i	0.166228	+	1.63143i
$580$	0.885211	−	0.194474i	0.0367564	−	0.00807509i
$581$	9.34963	+	5.39801i	0.387888	+	0.223947i
$582$	−9.21525	+	28.3838i	−0.381984	+	1.17655i
$583$	−5.85603	−	10.1429i	−0.242532	−	0.420078i
$584$	6.48773	+	19.2936i	0.268464	+	0.798376i
$585$	−31.1273	+	6.40974i	−1.28695	+	0.265010i
$586$	10.0264	−	22.7279i	0.414189	−	0.938882i
$587$	−20.6601	+	11.9281i	−0.852733	+	0.492325i	−0.861572	−	0.507635i	$-0.830520\pi$
$587$	−20.6601	+	11.9281i	−0.852733	+	0.492325i	0.00883923	+	0.999961i	$0.497186\pi$
$588$	1.08245	+	3.29064i	0.0446393	+	0.135704i
$589$	−63.3777	−	36.5912i	−2.61143	−	1.50771i
$590$	−16.8282	+	12.3143i	−0.692807	+	0.506971i
$591$	11.4853	+	15.9143i	0.472441	+	0.654626i
$592$	12.1973	+	26.4201i	0.501305	+	1.08586i
$593$	46.4133			1.90597			0.952983	−	0.303025i	$-0.0979966\pi$
$593$	46.4133			1.90597			0.952983	+	0.303025i	$0.0979966\pi$
$594$	−15.5701	+	21.1566i	−0.638851	+	0.868066i
$595$		−	11.5937i		−	0.475297i
$596$	−2.67762	−	0.849877i	−0.109680	−	0.0348123i
$597$	−8.46805	+	6.11136i	−0.346574	+	0.250121i
$598$	15.7216	+	21.4846i	0.642906	+	0.878571i
$599$	12.5560	−	21.7477i	0.513025	−	0.888586i	−0.486861	−	0.873480i	$-0.661858\pi$
$599$	12.5560	−	21.7477i	0.513025	−	0.888586i	0.999886	−	0.0151061i	$-0.00480861\pi$
$600$	−0.0225752	+	0.230394i	−0.000921627	+	0.00940581i
$601$	−0.808642	−	1.40061i	−0.0329852	−	0.0571320i	0.849062	−	0.528294i	$-0.177168\pi$
$601$	−0.808642	−	1.40061i	−0.0329852	−	0.0571320i	−0.882047	+	0.471162i	$0.843835\pi$
$602$	−0.542201	+	1.22906i	−0.0220985	+	0.0500928i
$603$	−17.3937	+	15.4622i	−0.708326	+	0.629671i
$604$	1.93531	+	2.12014i	0.0787468	+	0.0862672i
$605$	3.42746	−	1.97884i	0.139346	−	0.0804514i
$606$	14.1220	+	4.58494i	0.573669	+	0.186251i
$607$	−5.21572	+	9.03389i	−0.211700	+	0.366674i	−0.952247	−	0.305330i	$-0.901233\pi$
$607$	−5.21572	+	9.03389i	−0.211700	+	0.366674i	0.740547	+	0.672005i	$0.234567\pi$
$608$	38.2092	−	22.9370i	1.54959	−	0.930219i
$609$	0.350871	−	0.0357507i	0.0142180	−	0.00144869i
$610$	1.03629	+	9.54651i	0.0419581	+	0.386527i
$611$		−	9.45000i		−	0.382306i
$612$	3.25300	−	31.0876i	0.131495	−	1.25664i
$613$		−	12.1681i		−	0.491467i	−0.969337	−	0.245733i	$-0.920971\pi$
$613$		−	12.1681i		−	0.491467i	0.969337	−	0.245733i	$-0.0790288\pi$
$614$	−1.68207	+	0.182592i	−0.0678830	+	0.00736881i
$615$	−1.35349	+	3.01416i	−0.0545779	+	0.121543i
$616$	2.00090	−	9.91076i	0.0806187	−	0.399316i
$617$	−4.15062	+	7.18908i	−0.167098	+	0.289422i	−0.937398	−	0.348259i	$-0.886773\pi$
$617$	−4.15062	+	7.18908i	−0.167098	+	0.289422i	0.770301	+	0.637681i	$0.220106\pi$
$618$	−31.9927	+	6.80793i	−1.28693	+	0.273855i
$619$	−1.21845	+	0.703470i	−0.0489735	+	0.0282749i	−0.524287	−	0.851542i	$-0.675668\pi$
$619$	−1.21845	+	0.703470i	−0.0489735	+	0.0282749i	0.475313	+	0.879817i	$0.342335\pi$
$620$	30.5372	−	27.8751i	1.22640	−	1.11949i
$621$	20.0588	+	4.46397i	0.804931	+	0.179133i
$622$	26.9827	+	11.9034i	1.08191	+	0.477285i
$623$	8.46971	+	14.6700i	0.339332	+	0.587740i
$624$	28.3865	−	16.7871i	1.13637	−	0.672022i
$625$	12.3807	−	21.4441i	0.495230	−	0.857763i
$626$	10.9094	−	7.98308i	0.436026	−	0.319068i
$627$	44.4970	+	19.9811i	1.77704	+	0.797967i
$628$	31.0706	+	9.86180i	1.23985	+	0.393528i
$629$		−	37.8992i		−	1.51114i
$630$	1.99031	−	9.22974i	0.0792959	−	0.367722i
$631$	−21.7906			−0.867471			−0.433736	−	0.901040i	$-0.642805\pi$
$631$	−21.7906			−0.867471			−0.433736	+	0.901040i	$0.642805\pi$
$632$	1.34769	−	1.52790i	0.0536082	−	0.0607764i
$633$	−18.2646	+	1.86100i	−0.725951	+	0.0739681i
$634$	−9.38877	−	12.8303i	−0.372876	−	0.509558i
$635$	42.6884	+	24.6461i	1.69404	+	0.978052i
$636$	8.46208	+	7.56373i	0.335543	+	0.299921i
$637$	4.12235	−	2.38004i	0.163334	−	0.0943007i
$638$	−0.941820	−	0.415485i	−0.0372870	−	0.0164492i
$639$	−10.1247	+	30.4993i	−0.400525	+	1.20653i
$640$	5.82095	+	24.4963i	0.230093	+	0.968301i
$641$	18.6038	+	32.2228i	0.734808	+	1.27272i	0.954808	+	0.297225i	$0.0960610\pi$
$641$	18.6038	+	32.2228i	0.734808	+	1.27272i	−0.220000	+	0.975500i	$0.570606\pi$
$642$	19.8201	−	17.8543i	0.782237	−	0.704655i
$643$	−18.2350	−	10.5280i	−0.719118	−	0.415183i	0.0953098	−	0.995448i	$-0.469616\pi$
$643$	−18.2350	−	10.5280i	−0.719118	−	0.415183i	−0.814428	+	0.580265i	$0.802949\pi$
$644$	−7.72527	+	1.69718i	−0.304418	+	0.0668783i
$645$	2.96902	−	2.14273i	0.116905	−	0.0843700i
$646$	−57.7020	+	6.26365i	−2.27026	+	0.246440i
$647$	16.5335			0.649999			0.324999	−	0.945714i	$-0.394636\pi$
$647$	16.5335			0.649999			0.324999	+	0.945714i	$0.394636\pi$
$648$	7.92655	−	24.1903i	0.311384	−	0.950284i
$649$	23.6842			0.929688
$650$	0.316247	−	0.0343292i	0.0124042	−	0.00134650i
$651$	13.0468	−	9.41584i	0.511345	−	0.369036i
$652$	6.88362	+	31.3330i	0.269583	+	1.22710i
$653$	−28.6149	−	16.5208i	−1.11979	−	0.646509i	−0.178440	−	0.983951i	$-0.557105\pi$
$653$	−28.6149	−	16.5208i	−1.11979	−	0.646509i	−0.941346	+	0.337442i	$0.890438\pi$
$654$	−16.7085	+	15.0513i	−0.653354	+	0.588554i
$655$	−16.1741	−	28.0143i	−0.631972	−	1.09461i
$656$	0.311874	−	3.41449i	0.0121766	−	0.133313i
$657$	6.80208	−	20.4905i	0.265374	−	0.799409i
$658$	2.56873	+	1.13320i	0.100139	+	0.0441766i
$659$	29.2059	−	16.8621i	1.13770	−	0.656853i	0.191842	−	0.981426i	$-0.438554\pi$
$659$	29.2059	−	16.8621i	1.13770	−	0.656853i	0.945861	+	0.324573i	$0.105221\pi$
$660$	−18.3654	+	20.5467i	−0.714873	+	0.799779i
$661$	−0.867694	−	0.500963i	−0.0337494	−	0.0194852i	0.483030	−	0.875604i	$-0.339536\pi$
$661$	−0.867694	−	0.500963i	−0.0337494	−	0.0194852i	−0.516780	+	0.856118i	$0.672869\pi$
$662$	17.6987	+	24.1863i	0.687878	+	0.940028i
$663$	−42.7300	+	4.35381i	−1.65949	+	0.169088i
$664$	22.9002	+	20.1993i	0.888701	+	0.783885i
$665$	−17.5325			−0.679879
$666$	6.50620	−	30.1715i	0.252110	−	1.16912i
$667$			0.805284i			0.0311807i
$668$	5.83610	−	18.3872i	0.225805	−	0.711423i
$669$	−23.1332	−	10.3878i	−0.894382	−	0.401616i
$670$	−19.7035	+	14.4183i	−0.761212	+	0.557027i
$671$	5.45328	−	9.44536i	0.210522	−	0.364634i
$672$	1.15915	+	9.72915i	0.0447153	+	0.375310i
$673$	−5.31645	−	9.20837i	−0.204934	−	0.354957i	0.745178	−	0.666866i	$-0.232365\pi$
$673$	−5.31645	−	9.20837i	−0.204934	−	0.354957i	−0.950112	+	0.311910i	$0.899031\pi$
$674$	−15.3297	−	6.76269i	−0.590476	−	0.260489i
$675$	0.166031	−	0.180897i	0.00639054	−	0.00696272i
$676$	−13.0230	−	14.2667i	−0.500885	−	0.548720i
$677$	−32.5295	+	18.7809i	−1.25021	+	0.721809i	−0.971151	−	0.238464i	$-0.923356\pi$
$677$	−32.5295	+	18.7809i	−1.25021	+	0.721809i	−0.279059	+	0.960274i	$0.590023\pi$
$678$	25.8585	−	5.50260i	0.993090	−	0.211326i
$679$	−6.09153	+	10.5508i	−0.233771	+	0.404904i
$680$	6.48951	−	32.1435i	0.248861	−	1.23265i
$681$	−13.8633	+	30.8729i	−0.531242	+	1.18305i
$682$	−46.6869	+	5.06794i	−1.78773	+	0.194061i
$683$			10.5030i			0.401886i	0.979603	+	0.200943i	$0.0644006\pi$
$683$			10.5030i			0.401886i	−0.979603	+	0.200943i	$0.935599\pi$
$684$	−47.0117	−	4.91930i	−1.79754	−	0.188094i
$685$			25.7939i			0.985535i
$686$	0.152619	+	1.40595i	0.00582701	+	0.0536796i
$687$	−20.7689	+	2.11617i	−0.792382	+	0.0807368i
$688$	−2.19120	+	3.10406i	−0.0835388	+	0.118341i
$689$	7.79795	−	13.5064i	0.297078	−	0.514554i
$690$	20.5049	+	6.65723i	0.780606	+	0.253436i
$691$	−42.3070	+	24.4260i	−1.60944	+	0.929208i	−0.619939	+	0.784650i	$0.712843\pi$
$691$	−42.3070	+	24.4260i	−1.60944	+	0.929208i	−0.989496	+	0.144558i	$0.953824\pi$
$692$	−0.297391	+	0.271466i	−0.0113051	+	0.0103196i
$693$	−8.01498	+	7.12498i	−0.304464	+	0.270655i
$694$	−13.0475	+	29.5762i	−0.495278	+	1.12270i
$695$	11.7380	+	20.3309i	0.445249	+	0.771195i
$696$	0.992796	+	0.0972791i	0.0376318	+	0.00368735i
$697$	−2.23275	+	3.86723i	−0.0845714	+	0.146482i
$698$	−10.1709	−	13.8992i	−0.384974	−	0.526091i
$699$	34.3079	−	24.7599i	1.29765	−	0.936506i
$700$	−0.0285913	+	0.0900799i	−0.00108065	+	0.00340470i
$701$			41.8366i			1.58015i	0.613012	+	0.790074i	$0.289958\pi$
$701$			41.8366i			1.58015i	−0.613012	+	0.790074i	$0.710042\pi$
$702$	−34.7646	−	3.86945i	−1.31211	−	0.146043i
$703$	−57.3125			−2.16158
$704$	11.0950	−	26.3575i	0.418157	−	0.993385i
$705$	−4.47830	−	6.20523i	−0.168662	−	0.233703i
$706$	7.28482	−	5.33076i	0.274168	−	0.200626i
$707$	5.24945	+	3.03077i	0.197426	+	0.113984i
$708$	−21.8023	+	7.17180i	−0.819381	+	0.269533i
$709$	−15.0535	+	8.69117i	−0.565348	+	0.326404i	−0.755289	−	0.655392i	$-0.772504\pi$
$709$	−15.0535	+	8.69117i	−0.565348	+	0.326404i	0.189941	+	0.981795i	$0.439170\pi$
$710$	−13.6076	+	30.8456i	−0.510683	+	1.15762i
$711$	−2.11651	+	0.435833i	−0.0793754	+	0.0163450i
$712$	15.2708	+	45.4132i	0.572296	+	1.70193i
$713$	18.3686	+	31.8153i	0.687909	+	1.19149i
$714$	3.94050	−	12.1371i	0.147469	−	0.454219i
$715$	32.7949	+	18.9341i	1.22646	+	0.708096i
$716$	−1.34715	−	6.13198i	−0.0503453	−	0.229163i
$717$	−3.38793	−	33.2504i	−0.126525	−	1.24176i
$718$	0.690870	+	6.36443i	0.0257830	+	0.237519i
$719$	32.6491			1.21761			0.608803	−	0.793322i	$-0.291650\pi$
$719$	32.6491			1.21761			0.608803	+	0.793322i	$0.291650\pi$
$720$	10.6844	−	24.4753i	0.398184	−	0.912140i
$721$	−13.3534			−0.497306
$722$	6.57236	+	60.5459i	0.244598	+	2.25329i
$723$	−25.0594	−	11.2527i	−0.931968	−	0.418494i
$724$	−7.28829	−	33.1750i	−0.270867	−	1.23294i
$725$	0.00833299	+	0.00481106i	0.000309480	+	0.000178678i
$726$	4.26066	−	0.906654i	0.158128	−	0.0336491i
$727$	4.33945	+	7.51615i	0.160941	+	0.278758i	0.935207	−	0.354103i	$-0.115214\pi$
$727$	4.33945	+	7.51615i	0.160941	+	0.278758i	−0.774265	+	0.632861i	$0.781880\pi$
$728$	12.7614	−	4.29118i	0.472968	−	0.159042i
$729$	−22.1422	+	15.4507i	−0.820080	+	0.572249i
$730$	9.14202	−	20.7231i	0.338361	−	0.766997i
$731$	4.28551	−	2.47424i	0.158505	−	0.0915131i
$732$	−2.15983	+	10.3461i	−0.0798296	+	0.382404i
$733$	9.56725	+	5.52366i	0.353375	+	0.204021i	0.666171	−	0.745799i	$-0.267932\pi$
$733$	9.56725	+	5.52366i	0.353375	+	0.204021i	−0.312796	+	0.949820i	$0.601266\pi$
$734$	−32.3202	+	23.6508i	−1.19296	+	0.872965i
$735$	1.57901	−	3.51639i	0.0582426	−	0.129704i
$736$	−22.3682	+	0.381247i	−0.824503	+	0.0140530i
$737$	27.7309			1.02148
$738$	−2.44138	+	2.69540i	−0.0898684	+	0.0992189i
$739$		−	9.90356i		−	0.364308i	−0.983270	−	0.182154i	$-0.941693\pi$
$739$		−	9.90356i		−	0.364308i	0.983270	−	0.182154i	$-0.0583070\pi$
$740$	9.79594	−	30.8631i	0.360106	−	1.13455i
$741$	6.58399	+	64.6178i	0.241869	+	2.37379i
$742$	2.73627	+	3.73929i	0.100452	+	0.137274i
$743$	−7.99555	+	13.8487i	−0.293328	+	0.508060i	−0.974595	−	0.223976i	$-0.928096\pi$
$743$	−7.99555	+	13.8487i	−0.293328	+	0.508060i	0.681266	+	0.732036i	$0.261430\pi$
$744$	41.4426	−	18.8025i	1.51936	−	0.689331i
$745$	1.56299	+	2.70717i	0.0572634	+	0.0991832i
$746$	2.08809	−	4.73328i	0.0764503	−	0.173298i
$747$	−6.53231	−	31.7225i	−0.239005	−	1.16066i
$748$	−27.5079	+	25.1098i	−1.00579	+	0.918107i
$749$	9.43143	−	5.44524i	0.344617	−	0.198965i
$750$	20.4427	−	18.4152i	0.746461	−	0.672427i
$751$	−22.7410	+	39.3886i	−0.829831	+	1.43731i	0.0683388	+	0.997662i	$0.478230\pi$
$751$	−22.7410	+	39.3886i	−0.829831	+	1.43731i	−0.898170	+	0.439648i	$0.855103\pi$
$752$	6.48747	+	4.57960i	0.236574	+	0.167001i
$753$	−6.56002	−	9.08971i	−0.239060	−	0.331247i
$754$	−0.147928	−	1.36275i	−0.00538724	−	0.0496283i
$755$		−	3.19424i		−	0.116250i
$756$	5.22061	−	8.98584i	0.189872	−	0.326812i
$757$		−	13.8844i		−	0.504637i	−0.967644	−	0.252319i	$-0.918807\pi$
$757$		−	13.8844i		−	0.504637i	0.967644	−	0.252319i	$-0.0811931\pi$
$758$	−11.2692	+	1.22329i	−0.409314	+	0.0444317i
$759$	−14.3295	−	19.8552i	−0.520126	−	0.720699i
$760$	−48.6085	−	9.81366i	−1.76322	−	0.355979i
$761$	−7.84243	+	13.5835i	−0.284288	+	0.492401i	−0.972436	−	0.233169i	$-0.925091\pi$
$761$	−7.84243	+	13.5835i	−0.284288	+	0.492401i	0.688148	+	0.725570i	$0.258424\pi$
$762$	36.3122	+	40.3102i	1.31545	+	1.46028i
$763$	−7.95076	+	4.59037i	−0.287837	+	0.166183i
$764$	1.77986	+	1.94984i	0.0643930	+	0.0705426i
$765$	−25.9949	+	23.1084i	−0.939848	+	0.835484i
$766$	0.237306	+	0.104688i	0.00857421	+	0.00378252i
$767$	15.7691	+	27.3129i	0.569389	+	0.986211i
$768$	−2.23208	+	27.6228i	−0.0805433	+	0.996751i
$769$	17.0320	−	29.5003i	0.614190	−	1.06381i	−0.376336	−	0.926483i	$-0.622816\pi$
$769$	17.0320	−	29.5003i	0.614190	−	1.06381i	0.990526	−	0.137325i	$-0.0438504\pi$
$770$	−9.07933	+	6.64392i	−0.327196	+	0.239430i
$771$	0.331710	+	3.25552i	0.0119462	+	0.117245i
$772$	−13.7842	+	43.4286i	−0.496105	+	1.56303i
$773$			33.3658i			1.20009i	0.799968	+	0.600043i	$0.204850\pi$
$773$			33.3658i			1.20009i	−0.799968	+	0.600043i	$0.795150\pi$
$774$	3.83644	−	1.23404i	0.137898	−	0.0443566i
$775$	0.438962			0.0157680
$776$	−22.7944	+	25.8424i	−0.818272	+	0.927687i
$777$	5.16168	−	11.4948i	0.185174	−	0.412375i
$778$	21.9357	+	29.9765i	0.786432	+	1.07471i
$779$	5.84817	+	3.37644i	0.209532	+	0.120974i
$780$	−35.9224	−	7.49905i	−1.28623	−	0.268509i
$781$	33.1618	−	19.1460i	1.18662	−	0.685096i
$782$	26.6576	+	11.7600i	0.953273	+	0.420537i
$783$	−0.779506	−	0.715448i	−0.0278573	−	0.0255680i
$784$	−0.363839	+	3.98342i	−0.0129943	+	0.142265i
$785$	−18.1366	−	31.4135i	−0.647323	−	1.12120i
$786$	−7.41053	−	34.8245i	−0.264325	−	1.24215i
$787$	−24.1796	−	13.9601i	−0.861911	−	0.497625i	0.00274056	−	0.999996i	$-0.499128\pi$
$787$	−24.1796	−	13.9601i	−0.861911	−	0.497625i	−0.864652	+	0.502372i	$0.832461\pi$
$788$	4.86270	+	22.1342i	0.173227	+	0.788497i
$789$	−26.5336	−	11.9147i	−0.944620	−	0.424175i
$790$	−2.25378	+	0.244652i	−0.0801859	+	0.00870431i
$791$	10.7931			0.383757
$792$	−26.2096	+	15.2676i	−0.931317	+	0.542510i
$793$	14.5233			0.515737
$794$	−14.3033	+	1.55265i	−0.507607	+	0.0551015i
$795$	−1.28019	−	12.5643i	−0.0454036	−	0.445608i
$796$	−11.7777	+	2.58746i	−0.417449	+	0.0917102i
$797$	14.0398	+	8.10586i	0.497314	+	0.287124i	0.727604	−	0.685998i	$-0.240634\pi$
$797$	14.0398	+	8.10586i	0.497314	+	0.287124i	−0.230290	+	0.973122i	$0.573967\pi$
$798$	−18.3541	−	5.95896i	−0.649729	−	0.210945i
$799$	−5.17115	−	8.95669i	−0.182942	−	0.316865i
$800$	−0.129691	+	0.233742i	−0.00458526	+	0.00826402i
$801$	16.0107	−	48.2302i	0.565709	−	1.70413i
$802$	−3.85855	−	1.70220i	−0.136250	−	0.0601069i
$803$	−22.2792	+	12.8629i	−0.786215	+	0.453921i
$804$	−25.5274	+	8.39717i	−0.900283	+	0.296145i
$805$	7.62207	+	4.40060i	0.268643	+	0.155101i
$806$	−36.9288	−	50.4655i	−1.30076	−	1.77757i
$807$	−11.0742	−	15.3447i	−0.389831	−	0.540159i
$808$	12.8576	+	11.3411i	0.452328	+	0.398979i
$809$	35.2925			1.24082			0.620410	−	0.784278i	$-0.286966\pi$
$809$	35.2925			1.24082			0.620410	+	0.784278i	$0.286966\pi$
$810$	−24.6615	+	13.9339i	−0.866517	+	0.489588i
$811$		−	25.7340i		−	0.903644i	−0.892108	−	0.451822i	$-0.850774\pi$
$811$		−	25.7340i		−	0.903644i	0.892108	−	0.451822i	$-0.149226\pi$
$812$	0.388165	+	0.123203i	0.0136219	+	0.00432359i
$813$	35.3487	−	25.5110i	1.23973	−	0.894710i
$814$	−29.6798	+	21.7186i	−1.04028	+	0.761235i
$815$	17.8485	−	30.9145i	0.625205	−	1.08289i
$816$	17.7186	−	31.4443i	0.620276	−	1.10077i
$817$	−3.74164	−	6.48070i	−0.130903	−	0.226731i
$818$	46.1471	+	20.3578i	1.61349	+	0.711794i
$819$	−13.5530	−	4.49910i	−0.473580	−	0.157211i
$820$	−2.81781	+	2.57217i	−0.0984023	+	0.0898240i
$821$	35.0358	−	20.2280i	1.22276	−	0.705960i	0.257254	−	0.966344i	$-0.417182\pi$
$821$	35.0358	−	20.2280i	1.22276	−	0.705960i	0.965505	+	0.260384i	$0.0838490\pi$
$822$	−8.76689	+	27.0028i	−0.305780	+	0.941831i
$823$	5.51915	−	9.55944i	0.192385	−	0.333221i	−0.753655	−	0.657270i	$-0.771711\pi$
$823$	5.51915	−	9.55944i	0.192385	−	0.333221i	0.946040	+	0.324049i	$0.105044\pi$
$824$	−37.0221	−	7.47447i	−1.28973	−	0.260385i
$825$	−0.291069	+	0.0296574i	−0.0101337	+	0.00103254i
$826$	−9.31522	+	1.01118i	−0.324118	+	0.0351836i
$827$		−	27.8260i		−	0.967605i	−0.875177	−	0.483802i	$-0.839255\pi$
$827$		−	27.8260i		−	0.967605i	0.875177	−	0.483802i	$-0.160745\pi$
$828$	19.2032	+	13.9385i	0.667357	+	0.484395i
$829$			5.62325i			0.195304i	0.995221	+	0.0976519i	$0.0311332\pi$
$829$			5.62325i			0.195304i	−0.995221	+	0.0976519i	$0.968867\pi$
$830$	−3.66686	−	33.7799i	−0.127279	−	1.17252i
$831$	9.01223	−	20.0699i	0.312631	−	0.696216i
$832$	37.7827	−	4.75415i	1.30988	−	0.164820i
$833$	2.60477	−	4.51160i	0.0902501	−	0.156318i
$834$	5.37807	+	25.2733i	0.186227	+	0.875142i
$835$	−18.5901	+	10.7330i	−0.643338	+	0.371432i
$836$	37.9720	+	41.5984i	1.31329	+	1.43871i
$837$	−47.1164	−	10.4855i	−1.62858	−	0.362432i
$838$	10.3951	−	23.5636i	0.359092	−	0.813990i
$839$	−10.7884	−	18.6860i	−0.372456	−	0.645112i	0.617487	−	0.786581i	$-0.288151\pi$
$839$	−10.7884	−	18.6860i	−0.372456	−	0.645112i	−0.989943	+	0.141469i	$0.954817\pi$
$840$	6.34605	−	8.86530i	0.218960	−	0.305882i
$841$	−14.4793	+	25.0788i	−0.499285	+	0.864787i
$842$	16.6996	+	22.8210i	0.575505	+	0.786463i
$843$	−8.11151	−	3.64242i	−0.279375	−	0.125452i
$844$	−20.2059	−	6.41335i	−0.695516	−	0.220756i
$845$			21.4945i			0.739435i
$846$	−2.57913	−	8.01814i	−0.0886724	−	0.275669i
$847$	1.77835			0.0611050
$848$	5.49325	+	11.8987i	0.188639	+	0.408605i
$849$	0.929740	−	0.0947324i	0.0319086	−	0.00325121i
$850$	0.280953	−	0.205591i	0.00963662	−	0.00705173i
$851$	24.9161	+	14.3853i	0.854112	+	0.493122i
$852$	−24.7292	+	27.6663i	−0.847208	+	0.947832i
$853$	44.7691	−	25.8474i	1.53286	−	0.885000i	0.533636	−	0.845714i	$-0.320825\pi$
$853$	44.7691	−	25.8474i	1.53286	−	0.885000i	0.999228	−	0.0392856i	$-0.0125082\pi$
$854$	−1.74156	+	3.94777i	−0.0595950	+	0.135090i
$855$	34.9453	+	39.3104i	1.19510	+	1.34439i
$856$	29.1964	−	9.81768i	0.997914	−	0.335561i
$857$	−10.8404	−	18.7761i	−0.370300	−	0.641378i	0.619312	−	0.785145i	$-0.287412\pi$
$857$	−10.8404	−	18.7761i	−0.370300	−	0.641378i	−0.989612	+	0.143767i	$0.954078\pi$
$858$	27.8965	+	30.9679i	0.952370	+	1.05723i
$859$	41.6383	+	24.0399i	1.42068	+	0.820231i	0.996357	−	0.0852798i	$-0.0271784\pi$
$859$	41.6383	+	24.0399i	1.42068	+	0.820231i	0.424324	+	0.905510i	$0.360512\pi$
$860$	4.12942	−	0.907201i	0.140812	−	0.0309353i
$861$	−1.20389	+	0.868845i	−0.0410285	+	0.0296102i
$862$	−2.52271	−	23.2398i	−0.0859240	−	0.791549i
$863$	21.2543			0.723506			0.361753	−	0.932274i	$-0.382178\pi$
$863$	21.2543			0.723506			0.361753	+	0.932274i	$0.382178\pi$
$864$	19.5038	−	21.9909i	0.663534	−	0.748146i
$865$	0.448055			0.0152343
$866$	0.864310	+	7.96220i	0.0293704	+	0.270567i
$867$	−14.2407	+	10.2774i	−0.483638	+	0.349040i
$868$	18.1460	−	3.98653i	0.615916	−	0.135312i
$869$	2.22990	+	1.28743i	0.0756442	+	0.0436732i
$870$	−0.742933	−	0.824730i	−0.0251878	−	0.0279610i
$871$	18.4634	+	31.9795i	0.625608	+	1.08358i
$872$	−24.6128	+	8.27637i	−0.833495	+	0.280273i
$873$	35.7981	−	7.37155i	1.21158	−	0.249489i
$874$	17.7839	−	40.3125i	0.601550	−	1.36359i
$875$	9.72767	−	5.61627i	0.328855	−	0.189865i
$876$	16.6139	−	18.5871i	0.561331	−	0.628001i
$877$	47.3642	+	27.3457i	1.59937	+	0.923399i	0.991608	+	0.129284i	$0.0412678\pi$
$877$	47.3642	+	27.3457i	1.59937	+	0.923399i	0.607767	+	0.794116i	$0.292066\pi$
$878$	−43.3161	+	31.6971i	−1.46185	+	1.06973i
$879$	−30.2675	+	3.08400i	−1.02090	+	0.104021i
$880$	−28.8912	+	13.3381i	−0.973923	+	0.449627i
$881$	−4.30524			−0.145047			−0.0725236	−	0.997367i	$-0.523105\pi$
$881$	−4.30524			−0.145047			−0.0725236	+	0.997367i	$0.523105\pi$
$882$	2.84817	−	3.14451i	0.0959028	−	0.105881i
$883$		−	7.41422i		−	0.249508i	−0.992188	−	0.124754i	$-0.960186\pi$
$883$		−	7.41422i		−	0.249508i	0.992188	−	0.124754i	$-0.0398142\pi$
$884$	−47.2718	−	15.0040i	−1.58992	−	0.504640i
$885$	23.2980	+	10.4618i	0.783154	+	0.351670i
$886$	24.7039	+	33.7594i	0.829944	+	1.13417i
$887$	−22.5385	+	39.0378i	−0.756769	+	1.31076i	0.187721	+	0.982222i	$0.439890\pi$
$887$	−22.5385	+	39.0378i	−0.756769	+	1.31076i	−0.944490	+	0.328540i	$0.893443\pi$
$888$	20.7449	−	28.9801i	0.696152	−	0.972509i
$889$	11.0745	+	19.1817i	0.371428	+	0.643333i
$890$	21.5184	−	48.7779i	0.721298	−	1.63504i
$891$	31.9506	+	3.76946i	1.07038	+	0.126282i
$892$	−19.7410	−	21.6263i	−0.660977	−	0.724102i
$893$	−13.5446	+	7.82000i	−0.453254	+	0.261686i
$894$	0.716120	+	3.36528i	0.0239506	+	0.112552i
$895$	−3.49301	+	6.05007i	−0.116758	+	0.202231i
$896$	−3.23843	+	10.8403i	−0.108188	+	0.362150i
$897$	13.3566	−	29.7446i	0.445963	−	0.993142i
$898$	−3.72112	−	34.2797i	−0.124175	−	1.14393i
$899$		−	1.89154i		−	0.0630864i
$900$	0.258960	−	0.115439i	0.00863202	−	0.00384797i
$901$		−	17.0685i		−	0.568635i
$902$	4.30803	−	0.467643i	0.143442	−	0.0155708i
$903$	1.63678	−	0.166773i	0.0544686	−	0.00554987i
$904$	29.9236	+	6.04134i	0.995245	+	0.200932i
$905$	−18.8977	+	32.7318i	−0.628182	+	1.08804i
$906$	1.08566	−	3.34394i	0.0360688	−	0.111095i
$907$	20.2365	−	11.6836i	0.671942	−	0.387946i	−0.124870	−	0.992173i	$-0.539851\pi$
$907$	20.2365	−	11.6836i	0.671942	−	0.387946i	0.796812	+	0.604227i	$0.206518\pi$
$908$	−28.8618	+	26.3457i	−0.957812	+	0.874314i
$909$	−3.66763	−	17.8109i	−0.121648	−	0.590751i
$910$	−13.7069	−	6.04680i	−0.454379	−	0.200450i
$911$	−12.7105	−	22.0153i	−0.421119	−	0.729399i	0.574930	−	0.818202i	$-0.305029\pi$
$911$	−12.7105	−	22.0153i	−0.421119	−	0.729399i	−0.996049	+	0.0888031i	$0.971696\pi$
$912$	−47.5511	−	26.7947i	−1.57458	−	0.887263i
$913$	−19.2962	+	33.4220i	−0.638610	+	1.10611i
$914$	17.8411	−	13.0555i	0.590131	−	0.431836i
$915$	9.53656	−	6.88250i	0.315269	−	0.227529i
$916$	−22.9764	−	7.29270i	−0.759162	−	0.240958i
$917$		−	14.5354i		−	0.480000i
$918$	−35.0673	+	15.3562i	−1.15739	+	0.506829i
$919$	24.1333			0.796083			0.398042	−	0.917367i	$-0.369690\pi$
$919$	24.1333			0.796083			0.398042	+	0.917367i	$0.369690\pi$
$920$	18.6689	+	16.4670i	0.615495	+	0.542902i
$921$	1.21268	+	1.68032i	0.0399592	+	0.0553684i
$922$	−0.366586	−	0.500963i	−0.0120729	−	0.0164983i
$923$	44.1585	+	25.4949i	1.45350	+	0.839176i
$924$	−11.7630	+	3.86940i	−0.386974	+	0.127294i
$925$	0.297715	−	0.171886i	0.00978882	−	0.00565158i
$926$	15.6309	+	6.89556i	0.513662	+	0.226602i
$927$	26.6157	+	29.9403i	0.874174	+	0.983370i
$928$	1.00722	+	0.558853i	0.0330636	+	0.0183452i
$929$	−0.0662280	−	0.114710i	−0.00217287	−	0.00376352i	0.864937	−	0.501881i	$-0.167358\pi$
$929$	−0.0662280	−	0.114710i	−0.00217287	−	0.00376352i	−0.867110	+	0.498117i	$0.834025\pi$
$930$	−48.1641	−	15.6373i	−1.57936	−	0.512766i
$931$	−6.82261	−	3.93903i	−0.223602	−	0.129097i
$932$	47.7168	−	10.4830i	1.56302	−	0.343382i
$933$	−3.66134	−	35.9337i	−0.119867	−	1.17642i
$934$	25.4977	−	2.76782i	0.834312	−	0.0905659i
$935$	41.4439			1.35536
$936$	−35.0572	−	20.0599i	−1.14588	−	0.655678i
$937$	−40.8298			−1.33385			−0.666925	−	0.745124i	$-0.732390\pi$
$937$	−40.8298			−1.33385			−0.666925	+	0.745124i	$0.732390\pi$
$938$	−10.9068	+	1.18395i	−0.356120	+	0.0386574i
$939$	−15.1036	−	6.78216i	−0.492887	−	0.221327i
$940$	−1.89605	−	8.63047i	−0.0618422	−	0.281495i
$941$	−34.5257	−	19.9334i	−1.12551	−	0.649812i	−0.182706	−	0.983168i	$-0.558486\pi$
$941$	−34.5257	−	19.9334i	−1.12551	−	0.649812i	−0.942801	+	0.333356i	$0.891819\pi$
$942$	−8.30971	−	39.0500i	−0.270745	−	1.27232i
$943$	−1.69496	−	2.93575i	−0.0551954	−	0.0956013i
$944$	−26.3923	−	2.41064i	−0.858998	−	0.0784596i
$945$	−11.0315	+	3.46840i	−0.358855	+	0.112827i
$946$	−4.39350	−	1.93820i	−0.142845	−	0.0630162i
$947$	2.82050	−	1.62842i	0.0916539	−	0.0529164i	−0.453473	−	0.891270i	$-0.649815\pi$
$947$	2.82050	−	1.62842i	0.0916539	−	0.0529164i	0.545126	+	0.838354i	$0.316482\pi$
$948$	−2.44256	−	0.509901i	−0.0793307	−	0.0165608i
$949$	−29.6672	−	17.1283i	−0.963037	−	0.556010i
$950$	−0.310903	−	0.424868i	−0.0100870	−	0.0137845i
$951$	−7.97639	+	17.7631i	−0.258652	+	0.576008i
$952$	9.74704	−	11.0504i	0.315903	−	0.358144i
$953$	40.7380			1.31963			0.659817	−	0.751427i	$-0.270634\pi$
$953$	40.7380			1.31963			0.659817	+	0.751427i	$0.270634\pi$
$954$	2.93017	−	13.5882i	0.0948679	−	0.439934i
$955$		−	2.93766i		−	0.0950604i
$956$	11.6754	−	36.7847i	0.377610	−	1.18970i
$957$	0.127797	+	1.25425i	0.00413110	+	0.0405442i
$958$	−13.7216	+	10.0410i	−0.443324	+	0.324409i
$959$	−5.79515	+	10.0375i	−0.187135	+	0.324127i
$960$	22.5566	−	21.0268i	0.728012	−	0.678636i
$961$	−27.6462	−	47.8847i	−0.891814	−	1.54467i
$962$	−44.8070	−	19.7666i	−1.44463	−	0.637302i
$963$	−31.0076	−	10.2934i	−0.999204	−	0.331699i
$964$	−21.3847	−	23.4270i	−0.688755	−	0.754532i
$965$	43.9079	−	25.3502i	1.41344	−	0.816052i
$966$	6.48361	+	7.19745i	0.208607	+	0.231574i
$967$	−15.0077	+	25.9941i	−0.482615	+	0.835913i	−0.999801	−	0.0199599i	$-0.993646\pi$
$967$	−15.0077	+	25.9941i	−0.482615	+	0.835913i	0.517186	+	0.855873i	$0.326979\pi$
$968$	4.93047	+	0.995421i	0.158471	+	0.0319940i
$969$	41.5999	+	57.6418i	1.33638	+	1.85172i
$970$	38.1198	−	4.13796i	1.22395	−	0.132862i
$971$			49.5236i			1.58929i	0.607075	+	0.794645i	$0.292343\pi$
$971$			49.5236i			1.58929i	−0.607075	+	0.794645i	$0.707657\pi$
$972$	−30.5532	+	6.20496i	−0.979995	+	0.199024i
$973$			10.5488i			0.338179i
$974$	−5.28623	−	48.6978i	−0.169382	−	1.56038i
$975$	−0.227997	−	0.315917i	−0.00730173	−	0.0101175i
$976$	−7.03819	+	9.97032i	−0.225287	+	0.319142i
$977$	3.99749	−	6.92386i	0.127891	−	0.221514i	−0.794968	−	0.606651i	$-0.792513\pi$
$977$	3.99749	−	6.92386i	0.127891	−	0.221514i	0.922859	+	0.385137i	$0.125846\pi$
$978$	29.1922	−	26.2969i	0.933465	−	0.840884i
$979$	−52.4405	+	30.2765i	−1.67600	+	0.967642i
$980$	3.28732	−	3.00075i	0.105010	−	0.0958554i
$981$	26.1396	+	8.67738i	0.834573	+	0.277048i
$982$	7.49278	−	16.9846i	0.239104	−	0.542002i
$983$	10.8800	+	18.8448i	0.347019	+	0.601055i	0.985718	−	0.168401i	$-0.0538605\pi$
$983$	10.8800	+	18.8448i	0.347019	+	0.601055i	−0.638699	+	0.769457i	$0.720527\pi$
$984$	−3.82411	+	1.73499i	−0.121908	+	0.0553095i
$985$	12.6085	−	21.8385i	0.401739	−	0.695832i
$986$	−0.885918	−	1.21066i	−0.0282134	−	0.0385553i
$987$	−0.348556	−	3.42086i	−0.0110946	−	0.108887i
$988$	−22.6896	+	71.4861i	−0.721854	+	2.27427i
$989$			3.75657i			0.119452i
$990$	32.9934	+	7.11473i	1.04860	+	0.226121i
$991$	47.4065			1.50592			0.752959	−	0.658067i	$-0.228626\pi$
$991$	47.4065			1.50592			0.752959	+	0.658067i	$0.228626\pi$
$992$	52.5410	−	0.895516i	1.66818	−	0.0284327i
$993$	15.0362	−	33.4850i	0.477159	−	1.06261i
$994$	−12.2254	+	8.94609i	−0.387766	+	0.283753i
$995$	11.6203	+	6.70901i	0.368390	+	0.212690i
$996$	7.64245	−	36.6093i	0.242160	−	1.16001i
$997$	−27.7806	+	16.0391i	−0.879820	+	0.507965i	−0.870599	−	0.491993i	$-0.836269\pi$
$997$	−27.7806	+	16.0391i	−0.879820	+	0.507965i	−0.00922119	+	0.999957i	$0.502935\pi$
$998$	4.19533	−	9.50998i	0.132801	−	0.301033i
$999$	−36.0613	+	11.3380i	−1.14093	+	0.358718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.18	yes	72
8.5	even	2	inner	504.2.cs.a.85.8	✓	72
9.7	even	3	inner	504.2.cs.a.421.8	yes	72
72.61	even	6	inner	504.2.cs.a.421.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.8	✓	72	8.5	even	2	inner
504.2.cs.a.85.18	yes	72	1.1	even	1	trivial
504.2.cs.a.421.8	yes	72	9.7	even	3	inner
504.2.cs.a.421.18	yes	72	72.61	even	6	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.152619 - 1.40595i) q^{2} +(-1.40449 + 1.01361i) q^{3} +(-1.95342 + 0.429150i) q^{4} +(1.92732 + 1.11274i) q^{5} +(1.63945 + 1.81995i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.901492 + 2.68092i) q^{8} +(0.945172 - 2.84722i) q^{9} +O(q^{10})\)	\(q+(-0.152619 - 1.40595i) q^{2} +(-1.40449 + 1.01361i) q^{3} +(-1.95342 + 0.429150i) q^{4} +(1.92732 + 1.11274i) q^{5} +(1.63945 + 1.81995i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.901492 + 2.68092i) q^{8} +(0.945172 - 2.84722i) q^{9} +(1.27031 - 2.87955i) q^{10} +(-3.09577 + 1.78734i) q^{11} +(2.30856 - 2.58275i) q^{12} +(-4.12235 - 2.38004i) q^{13} +(1.14128 - 0.835149i) q^{14} +(-3.83478 + 0.390731i) q^{15} +(3.63166 - 1.67661i) q^{16} -5.20955 q^{17} +(-4.14731 - 0.894330i) q^{18} +7.87807i q^{19} +(-4.24239 - 1.34653i) q^{20} +(-1.58006 - 0.709515i) q^{21} +(2.98539 + 4.07972i) q^{22} +(1.97738 - 3.42492i) q^{23} +(-3.98355 - 2.85155i) q^{24} +(-0.0236271 - 0.0409234i) q^{25} +(-2.71708 + 6.15908i) q^{26} +(1.55850 + 4.95692i) q^{27} +(-1.34836 - 1.47713i) q^{28} +(-0.176344 + 0.101812i) q^{29} +(1.13461 + 5.33190i) q^{30} +(-4.64469 + 8.04483i) q^{31} +(-2.91150 - 4.85007i) q^{32} +(2.53629 - 5.64821i) q^{33} +(0.795074 + 7.32439i) q^{34} +2.22548i q^{35} +(-0.624430 + 5.96742i) q^{36} +7.27495i q^{37} +(11.0762 - 1.20234i) q^{38} +(8.20224 - 0.835737i) q^{39} +(-1.24569 + 6.17011i) q^{40} +(0.428588 - 0.742336i) q^{41} +(-0.756399 + 2.32978i) q^{42} +(-0.822626 + 0.474943i) q^{43} +(5.28028 - 4.81997i) q^{44} +(4.98986 - 4.43577i) q^{45} +(-5.11706 - 2.25739i) q^{46} +(0.992629 + 1.71928i) q^{47} +(-3.40118 + 6.03589i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.0539305 + 0.0394643i) q^{50} +(7.31675 - 5.28047i) q^{51} +(9.07406 + 2.88010i) q^{52} +3.27639i q^{53} +(6.73135 - 2.94770i) q^{54} -7.95537 q^{55} +(-1.87100 + 2.12117i) q^{56} +(-7.98532 - 11.0646i) q^{57} +(0.170057 + 0.232393i) q^{58} +(-5.73790 - 3.31278i) q^{59} +(7.32324 - 2.40896i) q^{60} +(-2.64229 + 1.52553i) q^{61} +(12.0195 + 5.30243i) q^{62} +(2.93835 - 0.605066i) q^{63} +(-6.37462 + 4.83365i) q^{64} +(-5.29673 - 9.17420i) q^{65} +(-8.32821 - 2.70389i) q^{66} +(-6.71827 - 3.87879i) q^{67} +(10.1764 - 2.23568i) q^{68} +(0.694343 + 6.81455i) q^{69} +(3.12892 - 0.339649i) q^{70} -10.7120 q^{71} +(8.48522 - 0.0328190i) q^{72} +7.19666 q^{73} +(10.2282 - 1.11029i) q^{74} +(0.0746645 + 0.0335276i) q^{75} +(-3.38087 - 15.3891i) q^{76} +(-3.09577 - 1.78734i) q^{77} +(-2.42682 - 11.4044i) q^{78} +(-0.360153 - 0.623804i) q^{79} +(8.86500 + 0.809716i) q^{80} +(-7.21330 - 5.38222i) q^{81} +(-1.10910 - 0.489280i) q^{82} +(9.34963 - 5.39801i) q^{83} +(3.39100 + 0.707895i) q^{84} +(-10.0405 - 5.79686i) q^{85} +(0.793297 + 1.08409i) q^{86} +(0.144474 - 0.321738i) q^{87} +(-7.58252 - 6.68821i) q^{88} +16.9394 q^{89} +(-6.99803 - 6.33853i) q^{90} -4.76008i q^{91} +(-2.39284 + 7.53887i) q^{92} +(-1.63095 - 16.0068i) q^{93} +(2.26574 - 1.65799i) q^{94} +(-8.76623 + 15.1836i) q^{95} +(9.00527 + 3.86072i) q^{96} +(6.09153 + 10.5508i) q^{97} +(1.29390 + 0.570806i) q^{98} +(2.16292 + 10.5037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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