LMFDB - Embedded newform 1890.2.bk.b.341.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 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("1890.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bk (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.5
Character	$\chi$	$=$	1890.341
Dual form			1890.2.bk.b.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.55256 + 0.696025i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.55256 + 0.696025i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(-1.26877 - 0.732523i) q^{11} +(-6.03529 - 3.48448i) q^{13} +(-0.696025 + 2.55256i) q^{14} +1.00000 q^{16} +(3.30332 + 5.72151i) q^{17} +(-3.08388 - 1.78048i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.732523 - 1.26877i) q^{22} +(-5.51016 + 3.18129i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.48448 - 6.03529i) q^{26} +(-2.55256 - 0.696025i) q^{28} +(-1.49409 + 0.862614i) q^{29} +7.84985i q^{31} +1.00000i q^{32} +(-5.72151 + 3.30332i) q^{34} +(0.673503 + 2.55859i) q^{35} +(-2.75951 + 4.77962i) q^{37} +(1.78048 - 3.08388i) q^{38} +(0.866025 - 0.500000i) q^{40} +(-0.632413 + 1.09537i) q^{41} +(-3.24581 - 5.62191i) q^{43} +(1.26877 + 0.732523i) q^{44} +(-3.18129 - 5.51016i) q^{46} -5.39759 q^{47} +(6.03110 + 3.55329i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(6.03529 + 3.48448i) q^{52} +(-5.60809 + 3.23783i) q^{53} -1.46505i q^{55} +(0.696025 - 2.55256i) q^{56} +(-0.862614 - 1.49409i) q^{58} +1.49328 q^{59} +3.73592i q^{61} -7.84985 q^{62} -1.00000 q^{64} -6.96896i q^{65} +12.5498 q^{67} +(-3.30332 - 5.72151i) q^{68} +(-2.55859 + 0.673503i) q^{70} +14.2133i q^{71} +(-1.11022 + 0.640987i) q^{73} +(-4.77962 - 2.75951i) q^{74} +(3.08388 + 1.78048i) q^{76} +(-2.72875 - 2.75290i) q^{77} +0.994011 q^{79} +(0.500000 + 0.866025i) q^{80} +(-1.09537 - 0.632413i) q^{82} +(5.93463 + 10.2791i) q^{83} +(-3.30332 + 5.72151i) q^{85} +(5.62191 - 3.24581i) q^{86} +(-0.732523 + 1.26877i) q^{88} +(-2.18741 + 3.78871i) q^{89} +(-12.9801 - 13.0950i) q^{91} +(5.51016 - 3.18129i) q^{92} -5.39759i q^{94} -3.56096i q^{95} +(9.04933 - 5.22463i) q^{97} +(-3.55329 + 6.03110i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.55256	+	0.696025i	0.964776	+	0.263073i
$7$	2.55256	+	0.696025i	0.964776	+	0.263073i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	−1.26877	−	0.732523i	−0.382548	−	0.220864i	0.296378	−	0.955071i	$-0.404221\pi$
$11$	−1.26877	−	0.732523i	−0.382548	−	0.220864i	−0.678926	+	0.734206i	$0.737554\pi$
$12$		0			0
$13$	−6.03529	−	3.48448i	−1.67389	−	0.966420i	−0.965428	−	0.260671i	$-0.916056\pi$
$13$	−6.03529	−	3.48448i	−1.67389	−	0.966420i	−0.708461	−	0.705750i	$-0.750610\pi$
$14$	−0.696025	+	2.55256i	−0.186020	+	0.682200i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.30332	+	5.72151i	0.801172	+	1.38767i	0.918845	+	0.394618i	$0.129123\pi$
$17$	3.30332	+	5.72151i	0.801172	+	1.38767i	−0.117673	+	0.993052i	$0.537544\pi$
$18$		0			0
$19$	−3.08388	−	1.78048i	−0.707491	−	0.408470i	0.102640	−	0.994719i	$-0.467271\pi$
$19$	−3.08388	−	1.78048i	−0.707491	−	0.408470i	−0.810131	+	0.586249i	$0.800604\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	0.732523	−	1.26877i	0.156175	−	0.270502i
$23$	−5.51016	+	3.18129i	−1.14895	+	0.663346i	−0.948631	−	0.316385i	$-0.897531\pi$
$23$	−5.51016	+	3.18129i	−1.14895	+	0.663346i	−0.200318	+	0.979731i	$0.564197\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.48448	−	6.03529i	0.683362	−	1.18362i
$27$		0			0
$28$	−2.55256	−	0.696025i	−0.482388	−	0.131536i
$29$	−1.49409	+	0.862614i	−0.277446	+	0.160183i	−0.632267	−	0.774751i	$-0.717875\pi$
$29$	−1.49409	+	0.862614i	−0.277446	+	0.160183i	0.354821	+	0.934934i	$0.384542\pi$
$30$		0			0
$31$			7.84985i			1.40987i	0.709269	+	0.704937i	$0.249025\pi$
$31$			7.84985i			1.40987i	−0.709269	+	0.704937i	$0.750975\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−5.72151	+	3.30332i	−0.981231	+	0.566514i
$35$	0.673503	+	2.55859i	0.113843	+	0.432481i
$36$		0			0
$37$	−2.75951	+	4.77962i	−0.453661	+	0.785764i	−0.998610	−	0.0527049i	$-0.983216\pi$
$37$	−2.75951	+	4.77962i	−0.453661	+	0.785764i	0.544949	+	0.838469i	$0.316549\pi$
$38$	1.78048	−	3.08388i	0.288832	−	0.500272i
$39$		0			0
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−0.632413	+	1.09537i	−0.0987663	+	0.171068i	−0.911174	−	0.412021i	$-0.864823\pi$
$41$	−0.632413	+	1.09537i	−0.0987663	+	0.171068i	0.812408	+	0.583089i	$0.198156\pi$
$42$		0			0
$43$	−3.24581	−	5.62191i	−0.494981	−	0.857333i	0.505002	−	0.863118i	$-0.331492\pi$
$43$	−3.24581	−	5.62191i	−0.494981	−	0.857333i	−0.999983	+	0.00578540i	$0.998158\pi$
$44$	1.26877	+	0.732523i	0.191274	+	0.110432i
$45$		0			0
$46$	−3.18129	−	5.51016i	−0.469056	−	0.812429i
$47$	−5.39759			−0.787320			−0.393660	−	0.919256i	$-0.628791\pi$
$47$	−5.39759			−0.787320			−0.393660	+	0.919256i	$0.628791\pi$
$48$		0			0
$49$	6.03110	+	3.55329i	0.861586	+	0.507612i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$	6.03529	+	3.48448i	0.836945	+	0.483210i
$53$	−5.60809	+	3.23783i	−0.770331	+	0.444751i	−0.832993	−	0.553284i	$-0.813374\pi$
$53$	−5.60809	+	3.23783i	−0.770331	+	0.444751i	0.0626620	+	0.998035i	$0.480041\pi$
$54$		0			0
$55$		−	1.46505i		−	0.197547i
$56$	0.696025	−	2.55256i	0.0930102	−	0.341100i
$57$		0			0
$58$	−0.862614	−	1.49409i	−0.113267	−	0.196184i
$59$	1.49328			0.194409			0.0972045	−	0.995264i	$-0.469010\pi$
$59$	1.49328			0.194409			0.0972045	+	0.995264i	$0.469010\pi$
$60$		0			0
$61$			3.73592i			0.478335i	0.970978	+	0.239167i	$0.0768745\pi$
$61$			3.73592i			0.478335i	−0.970978	+	0.239167i	$0.923126\pi$
$62$	−7.84985			−0.996932
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	6.96896i		−	0.864393i
$66$		0			0
$67$	12.5498			1.53320			0.766602	−	0.642123i	$-0.221946\pi$
$67$	12.5498			1.53320			0.766602	+	0.642123i	$0.221946\pi$
$68$	−3.30332	−	5.72151i	−0.400586	−	0.693835i
$69$		0			0
$70$	−2.55859	+	0.673503i	−0.305810	+	0.0804991i
$71$			14.2133i			1.68681i	0.537281	+	0.843403i	$0.319451\pi$
$71$			14.2133i			1.68681i	−0.537281	+	0.843403i	$0.680549\pi$
$72$		0			0
$73$	−1.11022	+	0.640987i	−0.129942	+	0.0750218i	−0.563562	−	0.826074i	$-0.690569\pi$
$73$	−1.11022	+	0.640987i	−0.129942	+	0.0750218i	0.433620	+	0.901096i	$0.357236\pi$
$74$	−4.77962	−	2.75951i	−0.555619	−	0.320787i
$75$		0			0
$76$	3.08388	+	1.78048i	0.353745	+	0.204235i
$77$	−2.72875	−	2.75290i	−0.310970	−	0.313722i
$78$		0			0
$79$	0.994011			0.111835			0.0559175	−	0.998435i	$-0.482192\pi$
$79$	0.994011			0.111835			0.0559175	+	0.998435i	$0.482192\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−1.09537	−	0.632413i	−0.120964	−	0.0698383i
$83$	5.93463	+	10.2791i	0.651411	+	1.12828i	0.982781	+	0.184776i	$0.0591559\pi$
$83$	5.93463	+	10.2791i	0.651411	+	1.12828i	−0.331370	+	0.943501i	$0.607511\pi$
$84$		0			0
$85$	−3.30332	+	5.72151i	−0.358295	+	0.620585i
$86$	5.62191	−	3.24581i	0.606226	−	0.350005i
$87$		0			0
$88$	−0.732523	+	1.26877i	−0.0780873	+	0.135251i
$89$	−2.18741	+	3.78871i	−0.231865	+	0.401602i	−0.958357	−	0.285573i	$-0.907816\pi$
$89$	−2.18741	+	3.78871i	−0.231865	+	0.401602i	0.726492	+	0.687175i	$0.241149\pi$
$90$		0			0
$91$	−12.9801	−	13.0950i	−1.36069	−	1.37273i
$92$	5.51016	−	3.18129i	0.574474	−	0.331673i
$93$		0			0
$94$		−	5.39759i		−	0.556719i
$95$		−	3.56096i		−	0.365347i
$96$		0			0
$97$	9.04933	−	5.22463i	0.918820	−	0.530481i	0.0355618	−	0.999367i	$-0.488678\pi$
$97$	9.04933	−	5.22463i	0.918820	−	0.530481i	0.883259	+	0.468886i	$0.155345\pi$
$98$	−3.55329	+	6.03110i	−0.358936	+	0.609233i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	1.01983	−	1.76640i	0.101477	−	0.175763i	−0.810816	−	0.585301i	$-0.800977\pi$
$101$	1.01983	−	1.76640i	0.101477	−	0.175763i	0.912293	+	0.409537i	$0.134310\pi$
$102$		0			0
$103$	−2.75430	+	1.59020i	−0.271389	+	0.156687i	−0.629519	−	0.776985i	$-0.716748\pi$
$103$	−2.75430	+	1.59020i	−0.271389	+	0.156687i	0.358130	+	0.933672i	$0.383415\pi$
$104$	−3.48448	+	6.03529i	−0.341681	+	0.591809i
$105$		0			0
$106$	−3.23783	−	5.60809i	−0.314486	−	0.544706i
$107$	−13.7903	−	7.96185i	−1.33316	−	0.769701i	−0.347379	−	0.937725i	$-0.612928\pi$
$107$	−13.7903	−	7.96185i	−1.33316	−	0.769701i	−0.985783	+	0.168024i	$0.946261\pi$
$108$		0			0
$109$	−3.60853	−	6.25017i	−0.345635	−	0.598657i	0.639834	−	0.768513i	$-0.279003\pi$
$109$	−3.60853	−	6.25017i	−0.345635	−	0.598657i	−0.985469	+	0.169856i	$0.945670\pi$
$110$	1.46505			0.139687
$111$		0			0
$112$	2.55256	+	0.696025i	0.241194	+	0.0657682i
$113$	−5.42707	−	3.13332i	−0.510536	−	0.294758i	0.222518	−	0.974929i	$-0.428572\pi$
$113$	−5.42707	−	3.13332i	−0.510536	−	0.294758i	−0.733054	+	0.680170i	$0.761906\pi$
$114$		0			0
$115$	−5.51016	−	3.18129i	−0.513825	−	0.296657i
$116$	1.49409	−	0.862614i	0.138723	−	0.0800917i
$117$		0			0
$118$			1.49328i			0.137468i
$119$	4.44959	+	16.9037i	0.407893	+	1.54956i
$120$		0			0
$121$	−4.42682	−	7.66748i	−0.402438	−	0.697043i
$122$	−3.73592			−0.338234
$123$		0			0
$124$		−	7.84985i		−	0.704937i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.914380			−0.0811381			−0.0405691	−	0.999177i	$-0.512917\pi$
$127$	−0.914380			−0.0811381			−0.0405691	+	0.999177i	$0.512917\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	6.96896			0.611218
$131$	−4.94937	−	8.57256i	−0.432429	−	0.748988i	0.564653	−	0.825328i	$-0.309010\pi$
$131$	−4.94937	−	8.57256i	−0.432429	−	0.748988i	−0.997082	+	0.0763399i	$0.975677\pi$
$132$		0			0
$133$	−6.63252	−	6.69123i	−0.575113	−	0.580204i
$134$			12.5498i			1.08414i
$135$		0			0
$136$	5.72151	−	3.30332i	0.490616	−	0.283257i
$137$	−10.4341	−	6.02412i	−0.891444	−	0.514675i	−0.0170294	−	0.999855i	$-0.505421\pi$
$137$	−10.4341	−	6.02412i	−0.891444	−	0.514675i	−0.874414	+	0.485180i	$0.838754\pi$
$138$		0			0
$139$	−15.6077	−	9.01113i	−1.32383	−	0.764314i	−0.339494	−	0.940608i	$-0.610256\pi$
$139$	−15.6077	−	9.01113i	−1.32383	−	0.764314i	−0.984338	+	0.176294i	$0.943589\pi$
$140$	−0.673503	−	2.55859i	−0.0569214	−	0.216240i
$141$		0			0
$142$	−14.2133			−1.19275
$143$	5.10492	+	8.84199i	0.426895	+	0.739404i
$144$		0			0
$145$	−1.49409	−	0.862614i	−0.124078	−	0.0716362i
$146$	−0.640987	−	1.11022i	−0.0530484	−	0.0918826i
$147$		0			0
$148$	2.75951	−	4.77962i	0.226831	−	0.392882i
$149$	7.44381	−	4.29769i	0.609821	−	0.352080i	−0.163075	−	0.986614i	$-0.552141\pi$
$149$	7.44381	−	4.29769i	0.609821	−	0.352080i	0.772895	+	0.634534i	$0.218808\pi$
$150$		0			0
$151$	1.30386	−	2.25835i	0.106106	−	0.183782i	−0.808083	−	0.589068i	$-0.799495\pi$
$151$	1.30386	−	2.25835i	0.106106	−	0.183782i	0.914190	+	0.405287i	$0.132828\pi$
$152$	−1.78048	+	3.08388i	−0.144416	+	0.250136i
$153$		0			0
$154$	2.75290	−	2.72875i	0.221835	−	0.219889i
$155$	−6.79817	+	3.92493i	−0.546042	+	0.315258i
$156$		0			0
$157$			7.79034i			0.621737i	0.950453	+	0.310868i	$0.100620\pi$
$157$			7.79034i			0.621737i	−0.950453	+	0.310868i	$0.899380\pi$
$158$			0.994011i			0.0790793i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−16.2793	+	4.28523i	−1.28299	+	0.337723i
$162$		0			0
$163$	−4.14705	+	7.18290i	−0.324822	+	0.562608i	−0.981476	−	0.191584i	$-0.938638\pi$
$163$	−4.14705	+	7.18290i	−0.324822	+	0.562608i	0.656654	+	0.754192i	$0.271971\pi$
$164$	0.632413	−	1.09537i	0.0493832	−	0.0855342i
$165$		0			0
$166$	−10.2791	+	5.93463i	−0.797812	+	0.460617i
$167$	−6.88497	+	11.9251i	−0.532775	+	0.922793i	0.466493	+	0.884525i	$0.345517\pi$
$167$	−6.88497	+	11.9251i	−0.532775	+	0.922793i	−0.999268	+	0.0382680i	$0.987816\pi$
$168$		0			0
$169$	17.7832	+	30.8014i	1.36794	+	2.36934i
$170$	−5.72151	−	3.30332i	−0.438820	−	0.253353i
$171$		0			0
$172$	3.24581	+	5.62191i	0.247491	+	0.428666i
$173$	−11.6394			−0.884929			−0.442464	−	0.896786i	$-0.645896\pi$
$173$	−11.6394			−0.884929			−0.442464	+	0.896786i	$0.645896\pi$
$174$		0			0
$175$	−1.87905	+	1.86257i	−0.142043	+	0.140797i
$176$	−1.26877	−	0.732523i	−0.0956370	−	0.0552160i
$177$		0			0
$178$	−3.78871	−	2.18741i	−0.283976	−	0.163953i
$179$	−1.21808	+	0.703262i	−0.0910439	+	0.0525642i	−0.544831	−	0.838546i	$-0.683406\pi$
$179$	−1.21808	+	0.703262i	−0.0910439	+	0.0525642i	0.453787	+	0.891110i	$0.350073\pi$
$180$		0			0
$181$		−	10.1582i		−	0.755054i	−0.925998	−	0.377527i	$-0.876774\pi$
$181$		−	10.1582i		−	0.755054i	0.925998	−	0.377527i	$-0.123226\pi$
$182$	13.0950	−	12.9801i	0.970669	−	0.962153i
$183$		0			0
$184$	3.18129	+	5.51016i	0.234528	+	0.406215i
$185$	−5.51903			−0.405767
$186$		0			0
$187$		−	9.67903i		−	0.707801i
$188$	5.39759			0.393660
$189$		0			0
$190$	3.56096			0.258339
$191$		−	17.1243i		−	1.23907i	−0.784968	−	0.619536i	$-0.787321\pi$
$191$		−	17.1243i		−	1.23907i	0.784968	−	0.619536i	$-0.212679\pi$
$192$		0			0
$193$	1.93306			0.139144			0.0695722	−	0.997577i	$-0.477837\pi$
$193$	1.93306			0.139144			0.0695722	+	0.997577i	$0.477837\pi$
$194$	5.22463	+	9.04933i	0.375107	+	0.649704i
$195$		0			0
$196$	−6.03110	−	3.55329i	−0.430793	−	0.253806i
$197$			22.0136i			1.56840i	0.620508	+	0.784200i	$0.286927\pi$
$197$			22.0136i			1.56840i	−0.620508	+	0.784200i	$0.713073\pi$
$198$		0			0
$199$	23.0430	−	13.3039i	1.63348	−	0.943088i	0.650468	−	0.759534i	$-0.274573\pi$
$199$	23.0430	−	13.3039i	1.63348	−	0.943088i	0.983010	−	0.183554i	$-0.0587604\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$		0			0
$202$	1.76640	+	1.01983i	0.124283	+	0.0717550i
$203$	−4.41416	+	1.16195i	−0.309813	+	0.0815527i
$204$		0			0
$205$	−1.26483			−0.0883393
$206$	−1.59020	−	2.75430i	−0.110794	−	0.191901i
$207$		0			0
$208$	−6.03529	−	3.48448i	−0.418472	−	0.241605i
$209$	2.60849	+	4.51803i	0.180433	+	0.312519i
$210$		0			0
$211$	−3.44298	+	5.96341i	−0.237024	+	0.410538i	−0.959859	−	0.280483i	$-0.909505\pi$
$211$	−3.44298	+	5.96341i	−0.237024	+	0.410538i	0.722835	+	0.691021i	$0.242839\pi$
$212$	5.60809	−	3.23783i	0.385165	−	0.222375i
$213$		0			0
$214$	7.96185	−	13.7903i	0.544261	−	0.942688i
$215$	3.24581	−	5.62191i	0.221362	−	0.383411i
$216$		0			0
$217$	−5.46369	+	20.0372i	−0.370900	+	1.36021i
$218$	6.25017	−	3.60853i	0.423315	−	0.244401i
$219$		0			0
$220$			1.46505i			0.0987734i
$221$		−	46.0413i		−	3.09708i
$222$		0			0
$223$	11.6938	−	6.75140i	0.783072	−	0.452107i	−0.0544458	−	0.998517i	$-0.517339\pi$
$223$	11.6938	−	6.75140i	0.783072	−	0.452107i	0.837518	+	0.546410i	$0.184006\pi$
$224$	−0.696025	+	2.55256i	−0.0465051	+	0.170550i
$225$		0			0
$226$	3.13332	−	5.42707i	0.208426	−	0.361004i
$227$	10.7490	−	18.6179i	0.713438	−	1.23571i	−0.250120	−	0.968215i	$-0.580470\pi$
$227$	10.7490	−	18.6179i	0.713438	−	1.23571i	0.963559	−	0.267497i	$-0.0861965\pi$
$228$		0			0
$229$	19.4936	−	11.2546i	1.28817	−	0.743727i	0.309845	−	0.950787i	$-0.399723\pi$
$229$	19.4936	−	11.2546i	1.28817	−	0.743727i	0.978328	+	0.207060i	$0.0663896\pi$
$230$	3.18129	−	5.51016i	0.209768	−	0.363329i
$231$		0			0
$232$	0.862614	+	1.49409i	0.0566334	+	0.0980919i
$233$	15.4408	+	8.91477i	1.01156	+	0.584026i	0.911649	−	0.410970i	$-0.134810\pi$
$233$	15.4408	+	8.91477i	1.01156	+	0.584026i	0.0999142	+	0.994996i	$0.468143\pi$
$234$		0			0
$235$	−2.69880	−	4.67445i	−0.176050	−	0.304928i
$236$	−1.49328			−0.0972045
$237$		0			0
$238$	−16.9037	+	4.44959i	−1.09570	+	0.288424i
$239$	−13.7144	−	7.91804i	−0.887114	−	0.512175i	−0.0141164	−	0.999900i	$-0.504494\pi$
$239$	−13.7144	−	7.91804i	−0.887114	−	0.512175i	−0.872997	+	0.487725i	$0.837827\pi$
$240$		0			0
$241$	22.8842	+	13.2122i	1.47410	+	0.851073i	0.999575	−	0.0291688i	$-0.00928603\pi$
$241$	22.8842	+	13.2122i	1.47410	+	0.851073i	0.474526	+	0.880241i	$0.342619\pi$
$242$	7.66748	−	4.42682i	0.492884	−	0.284567i
$243$		0			0
$244$		−	3.73592i		−	0.239167i
$245$	−0.0616877	+	6.99973i	−0.00394109	+	0.447196i
$246$		0			0
$247$	12.4081	+	21.4914i	0.789507	+	1.36747i
$248$	7.84985			0.498466
$249$		0			0
$250$		−	1.00000i		−	0.0632456i
$251$	27.9912			1.76679			0.883395	−	0.468628i	$-0.155252\pi$
$251$	27.9912			1.76679			0.883395	+	0.468628i	$0.155252\pi$
$252$		0			0
$253$	9.32149			0.586037
$254$		−	0.914380i		−	0.0573733i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.21520	+	12.4971i	0.450072	+	0.779547i	0.998390	−	0.0567229i	$-0.0180651\pi$
$257$	7.21520	+	12.4971i	0.450072	+	0.779547i	−0.548318	+	0.836270i	$0.684732\pi$
$258$		0			0
$259$	−10.3706	+	10.2796i	−0.644395	+	0.638741i
$260$			6.96896i			0.432196i
$261$		0			0
$262$	8.57256	−	4.94937i	0.529615	−	0.305773i
$263$	1.39555	+	0.805722i	0.0860534	+	0.0496830i	0.542409	−	0.840114i	$-0.317512\pi$
$263$	1.39555	+	0.805722i	0.0860534	+	0.0496830i	−0.456356	+	0.889797i	$0.650846\pi$
$264$		0			0
$265$	−5.60809	−	3.23783i	−0.344502	−	0.198898i
$266$	6.69123	−	6.63252i	0.410266	−	0.406666i
$267$		0			0
$268$	−12.5498			−0.766602
$269$	−2.06266	−	3.57264i	−0.125763	−	0.217828i	0.796268	−	0.604944i	$-0.206804\pi$
$269$	−2.06266	−	3.57264i	−0.125763	−	0.217828i	−0.922031	+	0.387116i	$0.873471\pi$
$270$		0			0
$271$	−4.02680	−	2.32488i	−0.244611	−	0.141226i	0.372683	−	0.927959i	$-0.378438\pi$
$271$	−4.02680	−	2.32488i	−0.244611	−	0.141226i	−0.617294	+	0.786732i	$0.711771\pi$
$272$	3.30332	+	5.72151i	0.200293	+	0.346918i
$273$		0			0
$274$	6.02412	−	10.4341i	0.363930	−	0.630346i
$275$	1.26877	−	0.732523i	0.0765096	−	0.0441728i
$276$		0			0
$277$	−11.7120	+	20.2858i	−0.703705	+	1.21885i	0.263452	+	0.964673i	$0.415139\pi$
$277$	−11.7120	+	20.2858i	−0.703705	+	1.21885i	−0.967157	+	0.254180i	$0.918194\pi$
$278$	9.01113	−	15.6077i	0.540452	−	0.936090i
$279$		0			0
$280$	2.55859	−	0.673503i	0.152905	−	0.0402495i
$281$	17.5671	−	10.1424i	1.04797	−	0.605043i	0.125887	−	0.992045i	$-0.459822\pi$
$281$	17.5671	−	10.1424i	1.04797	−	0.605043i	0.922079	+	0.387001i	$0.126489\pi$
$282$		0			0
$283$		−	5.74367i		−	0.341426i	−0.985321	−	0.170713i	$-0.945393\pi$
$283$		−	5.74367i		−	0.341426i	0.985321	−	0.170713i	$-0.0546071\pi$
$284$		−	14.2133i		−	0.843403i
$285$		0			0
$286$	−8.84199	+	5.10492i	−0.522838	+	0.301860i
$287$	−2.37668	+	2.35582i	−0.140291	+	0.139060i
$288$		0			0
$289$	−13.3238	+	23.0775i	−0.783753	+	1.35750i
$290$	0.862614	−	1.49409i	0.0506545	−	0.0877361i
$291$		0			0
$292$	1.11022	−	0.640987i	0.0649708	−	0.0375109i
$293$	−10.7874	+	18.6844i	−0.630209	+	1.09155i	0.357300	+	0.933990i	$0.383697\pi$
$293$	−10.7874	+	18.6844i	−0.630209	+	1.09155i	−0.987509	+	0.157564i	$0.949636\pi$
$294$		0			0
$295$	0.746642	+	1.29322i	0.0434712	+	0.0752943i
$296$	4.77962	+	2.75951i	0.277810	+	0.160393i
$297$		0			0
$298$	4.29769	+	7.44381i	0.248958	+	0.431208i
$299$	44.3406			2.56428
$300$		0			0
$301$	−4.37213	−	16.6094i	−0.252005	−	0.957350i
$302$	2.25835	+	1.30386i	0.129953	+	0.0750285i
$303$		0			0
$304$	−3.08388	−	1.78048i	−0.176873	−	0.102117i
$305$	−3.23540	+	1.86796i	−0.185258	+	0.106959i
$306$		0			0
$307$		−	5.22295i		−	0.298090i	−0.988830	−	0.149045i	$-0.952380\pi$
$307$		−	5.22295i		−	0.298090i	0.988830	−	0.149045i	$-0.0476199\pi$
$308$	2.72875	+	2.75290i	0.155485	+	0.156861i
$309$		0			0
$310$	−3.92493	−	6.79817i	−0.222921	−	0.386110i
$311$	13.2357			0.750526			0.375263	−	0.926918i	$-0.377552\pi$
$311$	13.2357			0.750526			0.375263	+	0.926918i	$0.377552\pi$
$312$		0			0
$313$			30.9549i			1.74968i	0.484416	+	0.874838i	$0.339032\pi$
$313$			30.9549i			1.74968i	−0.484416	+	0.874838i	$0.660968\pi$
$314$	−7.79034			−0.439634
$315$		0			0
$316$	−0.994011			−0.0559175
$317$			15.1480i			0.850796i	0.905006	+	0.425398i	$0.139866\pi$
$317$			15.1480i			0.850796i	−0.905006	+	0.425398i	$0.860134\pi$
$318$		0			0
$319$	2.52754			0.141515
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−4.28523	−	16.2793i	−0.238806	−	0.907208i
$323$		−	23.5259i		−	1.30902i
$324$		0			0
$325$	6.03529	−	3.48448i	0.334778	−	0.193284i
$326$	−7.18290	−	4.14705i	−0.397824	−	0.229684i
$327$		0			0
$328$	1.09537	+	0.632413i	0.0604818	+	0.0349192i
$329$	−13.7777	−	3.75686i	−0.759587	−	0.207122i
$330$		0			0
$331$	1.30322			0.0716313			0.0358157	−	0.999358i	$-0.488597\pi$
$331$	1.30322			0.0716313			0.0358157	+	0.999358i	$0.488597\pi$
$332$	−5.93463	−	10.2791i	−0.325705	−	0.564138i
$333$		0			0
$334$	−11.9251	−	6.88497i	−0.652513	−	0.376729i
$335$	6.27490	+	10.8685i	0.342835	+	0.593807i
$336$		0			0
$337$	8.12095	−	14.0659i	0.442377	−	0.766219i	−0.555489	−	0.831524i	$-0.687469\pi$
$337$	8.12095	−	14.0659i	0.442377	−	0.766219i	0.997865	+	0.0653053i	$0.0208021\pi$
$338$	−30.8014	+	17.7832i	−1.67537	+	0.967277i
$339$		0			0
$340$	3.30332	−	5.72151i	0.179147	−	0.310293i
$341$	5.75020	−	9.95964i	0.311391	−	0.539345i
$342$		0			0
$343$	12.9215	+	13.2678i	0.697698	+	0.716392i
$344$	−5.62191	+	3.24581i	−0.303113	+	0.175002i
$345$		0			0
$346$		−	11.6394i		−	0.625739i
$347$			5.07209i			0.272284i	0.990689	+	0.136142i	$0.0434703\pi$
$347$			5.07209i			0.272284i	−0.990689	+	0.136142i	$0.956530\pi$
$348$		0			0
$349$	−20.4996	+	11.8354i	−1.09732	+	0.633536i	−0.935515	−	0.353287i	$-0.885064\pi$
$349$	−20.4996	+	11.8354i	−1.09732	+	0.633536i	−0.161802	+	0.986823i	$0.551731\pi$
$350$	−1.86257	−	1.87905i	−0.0995584	−	0.100440i
$351$		0			0
$352$	0.732523	−	1.26877i	0.0390436	−	0.0676255i
$353$	−0.272379	+	0.471774i	−0.0144973	+	0.0251100i	−0.873183	−	0.487392i	$-0.837948\pi$
$353$	−0.272379	+	0.471774i	−0.0144973	+	0.0251100i	0.858686	+	0.512502i	$0.171281\pi$
$354$		0			0
$355$	−12.3091	+	7.10664i	−0.653297	+	0.377181i
$356$	2.18741	−	3.78871i	0.115933	−	0.200801i
$357$		0			0
$358$	−0.703262	−	1.21808i	−0.0371685	−	0.0643778i
$359$	−5.44862	−	3.14576i	−0.287567	−	0.166027i	0.349277	−	0.937019i	$-0.386427\pi$
$359$	−5.44862	−	3.14576i	−0.287567	−	0.166027i	−0.636844	+	0.770993i	$0.719761\pi$
$360$		0			0
$361$	−3.15979	−	5.47291i	−0.166305	−	0.288048i
$362$	10.1582			0.533904
$363$		0			0
$364$	12.9801	+	13.0950i	0.680345	+	0.686367i
$365$	−1.11022	−	0.640987i	−0.0581117	−	0.0335508i
$366$		0			0
$367$	21.0875	+	12.1749i	1.10076	+	0.635522i	0.936420	−	0.350882i	$-0.114118\pi$
$367$	21.0875	+	12.1749i	1.10076	+	0.635522i	0.164337	+	0.986404i	$0.447452\pi$
$368$	−5.51016	+	3.18129i	−0.287237	+	0.165836i
$369$		0			0
$370$		−	5.51903i		−	0.286921i
$371$	−16.5686	+	4.36138i	−0.860198	+	0.226432i
$372$		0			0
$373$	−1.08878	−	1.88581i	−0.0563746	−	0.0976437i	0.836461	−	0.548027i	$-0.184621\pi$
$373$	−1.08878	−	1.88581i	−0.0563746	−	0.0976437i	−0.892835	+	0.450383i	$0.851287\pi$
$374$	9.67903			0.500491
$375$		0			0
$376$			5.39759i			0.278360i
$377$	12.0230			0.619218
$378$		0			0
$379$	−22.5954			−1.16065			−0.580323	−	0.814387i	$-0.697074\pi$
$379$	−22.5954			−1.16065			−0.580323	+	0.814387i	$0.697074\pi$
$380$			3.56096i			0.182673i
$381$		0			0
$382$	17.1243			0.876156
$383$	−3.26282	−	5.65138i	−0.166723	−	0.288772i	0.770543	−	0.637388i	$-0.219985\pi$
$383$	−3.26282	−	5.65138i	−0.166723	−	0.288772i	−0.937266	+	0.348616i	$0.886652\pi$
$384$		0			0
$385$	1.01971	−	3.73962i	0.0519692	−	0.190588i
$386$			1.93306i			0.0983900i
$387$		0			0
$388$	−9.04933	+	5.22463i	−0.459410	+	0.265241i
$389$	30.0342	+	17.3402i	1.52279	+	0.879184i	0.999637	+	0.0269467i	$0.00857846\pi$
$389$	30.0342	+	17.3402i	1.52279	+	0.879184i	0.523155	+	0.852238i	$0.324755\pi$
$390$		0			0
$391$	−36.4036	−	21.0176i	−1.84101	−	1.06291i
$392$	3.55329	−	6.03110i	0.179468	−	0.304616i
$393$		0			0
$394$	−22.0136			−1.10903
$395$	0.497005	+	0.860839i	0.0250071	+	0.0433135i
$396$		0			0
$397$	23.8417	+	13.7650i	1.19658	+	0.690845i	0.959791	−	0.280717i	$-0.0905721\pi$
$397$	23.8417	+	13.7650i	1.19658	+	0.690845i	0.236788	+	0.971561i	$0.423905\pi$
$398$	13.3039	+	23.0430i	0.666864	+	1.15504i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−12.1926	+	7.03938i	−0.608868	+	0.351530i	−0.772522	−	0.634988i	$-0.781005\pi$
$401$	−12.1926	+	7.03938i	−0.608868	+	0.351530i	0.163655	+	0.986518i	$0.447672\pi$
$402$		0			0
$403$	27.3526	−	47.3762i	1.36253	−	2.35997i
$404$	−1.01983	+	1.76640i	−0.0507385	+	0.0878816i
$405$		0			0
$406$	−1.16195	−	4.41416i	−0.0576665	−	0.219071i
$407$	7.00236	−	4.04282i	0.347094	−	0.200395i
$408$		0			0
$409$			32.7642i			1.62009i	0.586371	+	0.810043i	$0.300556\pi$
$409$			32.7642i			1.62009i	−0.586371	+	0.810043i	$0.699444\pi$
$410$		−	1.26483i		−	0.0624653i
$411$		0			0
$412$	2.75430	−	1.59020i	0.135695	−	0.0783433i
$413$	3.81169	+	1.03936i	0.187561	+	0.0511437i
$414$		0			0
$415$	−5.93463	+	10.2791i	−0.291320	+	0.504581i
$416$	3.48448	−	6.03529i	0.170841	−	0.295905i
$417$		0			0
$418$	−4.51803	+	2.60849i	−0.220984	+	0.127585i
$419$	5.81259	−	10.0677i	0.283964	−	0.491839i	−0.688394	−	0.725337i	$-0.741684\pi$
$419$	5.81259	−	10.0677i	0.283964	−	0.491839i	0.972357	+	0.233498i	$0.0750172\pi$
$420$		0			0
$421$	11.4508	+	19.8333i	0.558076	+	0.966615i	0.997657	+	0.0684126i	$0.0217934\pi$
$421$	11.4508	+	19.8333i	0.558076	+	0.966615i	−0.439582	+	0.898203i	$0.644873\pi$
$422$	−5.96341	−	3.44298i	−0.290294	−	0.167601i
$423$		0			0
$424$	3.23783	+	5.60809i	0.157243	+	0.272353i
$425$	−6.60663			−0.320469
$426$		0			0
$427$	−2.60029	+	9.53614i	−0.125837	+	0.461486i
$428$	13.7903	+	7.96185i	0.666581	+	0.384851i
$429$		0			0
$430$	5.62191	+	3.24581i	0.271112	+	0.156527i
$431$	8.34407	−	4.81745i	0.401920	−	0.232048i	−0.285392	−	0.958411i	$-0.592124\pi$
$431$	8.34407	−	4.81745i	0.401920	−	0.232048i	0.687312	+	0.726362i	$0.258791\pi$
$432$		0			0
$433$			37.8458i			1.81875i	0.415972	+	0.909377i	$0.363441\pi$
$433$			37.8458i			1.81875i	−0.415972	+	0.909377i	$0.636559\pi$
$434$	−20.0372	−	5.46369i	−0.961816	−	0.262266i
$435$		0			0
$436$	3.60853	+	6.25017i	0.172817	+	0.299329i
$437$	22.6569			1.08383
$438$		0			0
$439$		−	32.3974i		−	1.54624i	−0.634257	−	0.773122i	$-0.718694\pi$
$439$		−	32.3974i		−	1.54624i	0.634257	−	0.773122i	$-0.281306\pi$
$440$	−1.46505			−0.0698434
$441$		0			0
$442$	46.0413			2.18996
$443$		−	21.9018i		−	1.04059i	−0.853988	−	0.520293i	$-0.825823\pi$
$443$		−	21.9018i		−	1.04059i	0.853988	−	0.520293i	$-0.174177\pi$
$444$		0			0
$445$	−4.37482			−0.207387
$446$	6.75140	+	11.6938i	0.319688	+	0.553716i
$447$		0			0
$448$	−2.55256	−	0.696025i	−0.120597	−	0.0328841i
$449$		−	25.8522i		−	1.22004i	−0.792385	−	0.610021i	$-0.791161\pi$
$449$		−	25.8522i		−	1.22004i	0.792385	−	0.610021i	$-0.208839\pi$
$450$		0			0
$451$	1.60477	−	0.926515i	0.0755657	−	0.0436279i
$452$	5.42707	+	3.13332i	0.255268	+	0.147379i
$453$		0			0
$454$	18.6179	+	10.7490i	0.873780	+	0.504477i
$455$	4.85057	−	17.7887i	0.227398	−	0.833945i
$456$		0			0
$457$	−22.2463			−1.04064			−0.520318	−	0.853973i	$-0.674187\pi$
$457$	−22.2463			−1.04064			−0.520318	+	0.853973i	$0.674187\pi$
$458$	11.2546	+	19.4936i	0.525894	+	0.910876i
$459$		0			0
$460$	5.51016	+	3.18129i	0.256913	+	0.148329i
$461$	−7.05369	−	12.2173i	−0.328523	−	0.569018i	0.653696	−	0.756757i	$-0.273217\pi$
$461$	−7.05369	−	12.2173i	−0.328523	−	0.569018i	−0.982219	+	0.187739i	$0.939884\pi$
$462$		0			0
$463$	3.33243	−	5.77194i	0.154871	−	0.268245i	−0.778141	−	0.628090i	$-0.783837\pi$
$463$	3.33243	−	5.77194i	0.154871	−	0.268245i	0.933012	+	0.359845i	$0.117170\pi$
$464$	−1.49409	+	0.862614i	−0.0693615	+	0.0400459i
$465$		0			0
$466$	−8.91477	+	15.4408i	−0.412969	+	0.715283i
$467$	1.75717	−	3.04350i	0.0813119	−	0.140836i	−0.822502	−	0.568763i	$-0.807422\pi$
$467$	1.75717	−	3.04350i	0.0813119	−	0.140836i	0.903814	+	0.427926i	$0.140756\pi$
$468$		0			0
$469$	32.0341	+	8.73498i	1.47920	+	0.403344i
$470$	4.67445	−	2.69880i	0.215616	−	0.124486i
$471$		0			0
$472$		−	1.49328i		−	0.0687340i
$473$			9.51053i			0.437294i
$474$		0			0
$475$	3.08388	−	1.78048i	0.141498	−	0.0816940i
$476$	−4.44959	−	16.9037i	−0.203947	−	0.774779i
$477$		0			0
$478$	7.91804	−	13.7144i	0.362163	−	0.627284i
$479$	0.500486	−	0.866868i	0.0228678	−	0.0396082i	−0.854365	−	0.519673i	$-0.826054\pi$
$479$	0.500486	−	0.866868i	0.0228678	−	0.0396082i	0.877233	+	0.480065i	$0.159387\pi$
$480$		0			0
$481$	33.3089	−	19.2309i	1.51876	−	0.876855i
$482$	−13.2122	+	22.8842i	−0.601799	+	1.04235i
$483$		0			0
$484$	4.42682	+	7.66748i	0.201219	+	0.348522i
$485$	9.04933	+	5.22463i	0.410909	+	0.237238i
$486$		0			0
$487$	−14.4755	−	25.0723i	−0.655948	−	1.13613i	−0.981655	−	0.190664i	$-0.938936\pi$
$487$	−14.4755	−	25.0723i	−0.655948	−	1.13613i	0.325708	−	0.945471i	$-0.394397\pi$
$488$	3.73592			0.169117
$489$		0			0
$490$	−6.99973	−	0.0616877i	−0.316215	−	0.00278677i
$491$	−30.6555	−	17.6990i	−1.38346	−	0.798743i	−0.390896	−	0.920435i	$-0.627835\pi$
$491$	−30.6555	−	17.6990i	−1.38346	−	0.798743i	−0.992568	+	0.121691i	$0.961168\pi$
$492$		0			0
$493$	−9.87092	−	5.69898i	−0.444564	−	0.256669i
$494$	−21.4914	+	12.4081i	−0.966945	+	0.558266i
$495$		0			0
$496$			7.84985i			0.352469i
$497$	−9.89280	+	36.2802i	−0.443753	+	1.62739i
$498$		0			0
$499$	−8.31844	−	14.4080i	−0.372384	−	0.644989i	0.617547	−	0.786534i	$-0.288126\pi$
$499$	−8.31844	−	14.4080i	−0.372384	−	0.644989i	−0.989932	+	0.141545i	$0.954793\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$			27.9912i			1.24931i
$503$	−12.7352			−0.567834			−0.283917	−	0.958849i	$-0.591634\pi$
$503$	−12.7352			−0.567834			−0.283917	+	0.958849i	$0.591634\pi$
$504$		0			0
$505$	2.03966			0.0907638
$506$			9.32149i			0.414391i
$507$		0			0
$508$	0.914380			0.0405691
$509$	4.73445	+	8.20032i	0.209851	+	0.363473i	0.951667	−	0.307130i	$-0.0993688\pi$
$509$	4.73445	+	8.20032i	0.209851	+	0.363473i	−0.741816	+	0.670603i	$0.766035\pi$
$510$		0			0
$511$	−3.28005	+	0.863414i	−0.145101	+	0.0381952i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.4971	+	7.21520i	−0.551223	+	0.318249i
$515$	−2.75430	−	1.59020i	−0.121369	−	0.0700724i
$516$		0			0
$517$	6.84829	+	3.95386i	0.301187	+	0.173891i
$518$	−10.2796	−	10.3706i	−0.451658	−	0.455656i
$519$		0			0
$520$	−6.96896			−0.305609
$521$	2.37330	+	4.11068i	0.103976	+	0.180092i	0.913320	−	0.407244i	$-0.133510\pi$
$521$	2.37330	+	4.11068i	0.103976	+	0.180092i	−0.809343	+	0.587336i	$0.800177\pi$
$522$		0			0
$523$	30.1376	+	17.3999i	1.31782	+	0.760846i	0.983378	−	0.181569i	$-0.0581176\pi$
$523$	30.1376	+	17.3999i	1.31782	+	0.760846i	0.334446	+	0.942415i	$0.391451\pi$
$524$	4.94937	+	8.57256i	0.216214	+	0.374494i
$525$		0			0
$526$	−0.805722	+	1.39555i	−0.0351312	+	0.0608490i
$527$	−44.9130	+	25.9305i	−1.95644	+	1.12955i
$528$		0			0
$529$	8.74127	−	15.1403i	0.380055	−	0.658275i
$530$	3.23783	−	5.60809i	0.140642	−	0.243600i
$531$		0			0
$532$	6.63252	+	6.69123i	0.287556	+	0.290102i
$533$	7.63360	−	4.40726i	0.330648	−	0.190900i
$534$		0			0
$535$		−	15.9237i		−	0.688442i
$536$		−	12.5498i		−	0.542069i
$537$		0			0
$538$	3.57264	−	2.06266i	0.154027	−	0.0889277i
$539$	−5.04920	−	8.92622i	−0.217484	−	0.384479i
$540$		0			0
$541$	−0.542248	+	0.939202i	−0.0233131	+	0.0403794i	−0.877447	−	0.479674i	$-0.840755\pi$
$541$	−0.542248	+	0.939202i	−0.0233131	+	0.0403794i	0.854133	+	0.520054i	$0.174088\pi$
$542$	2.32488	−	4.02680i	0.0998620	−	0.172966i
$543$		0			0
$544$	−5.72151	+	3.30332i	−0.245308	+	0.141629i
$545$	3.60853	−	6.25017i	0.154573	−	0.267728i
$546$		0			0
$547$	−8.77785	−	15.2037i	−0.375314	−	0.650063i	0.615060	−	0.788480i	$-0.289132\pi$
$547$	−8.77785	−	15.2037i	−0.375314	−	0.650063i	−0.990374	+	0.138417i	$0.955798\pi$
$548$	10.4341	+	6.02412i	0.445722	+	0.257338i
$549$		0			0
$550$	0.732523	+	1.26877i	0.0312349	+	0.0541004i
$551$	6.14347			0.261721
$552$		0			0
$553$	2.53727	+	0.691856i	0.107896	+	0.0294207i
$554$	−20.2858	−	11.7120i	−0.861859	−	0.497595i
$555$		0			0
$556$	15.6077	+	9.01113i	0.661916	+	0.382157i
$557$	−27.9379	+	16.1300i	−1.18377	+	0.683449i	−0.956883	−	0.290472i	$-0.906188\pi$
$557$	−27.9379	+	16.1300i	−1.18377	+	0.683449i	−0.226885	+	0.973922i	$0.572854\pi$
$558$		0			0
$559$			45.2398i			1.91344i
$560$	0.673503	+	2.55859i	0.0284607	+	0.108120i
$561$		0			0
$562$	10.1424	+	17.5671i	0.427830	+	0.741024i
$563$	35.5704			1.49911			0.749557	−	0.661940i	$-0.230267\pi$
$563$	35.5704			1.49911			0.749557	+	0.661940i	$0.230267\pi$
$564$		0			0
$565$		−	6.26664i		−	0.263640i
$566$	5.74367			0.241425
$567$		0			0
$568$	14.2133			0.596376
$569$		−	41.9657i		−	1.75929i	−0.475627	−	0.879647i	$-0.657779\pi$
$569$		−	41.9657i		−	1.75929i	0.475627	−	0.879647i	$-0.342221\pi$
$570$		0			0
$571$	6.77247			0.283419			0.141709	−	0.989908i	$-0.454740\pi$
$571$	6.77247			0.283419			0.141709	+	0.989908i	$0.454740\pi$
$572$	−5.10492	−	8.84199i	−0.213448	−	0.369702i
$573$		0			0
$574$	−2.35582	−	2.37668i	−0.0983302	−	0.0992006i
$575$		−	6.36259i		−	0.265338i
$576$		0			0
$577$	−30.1675	+	17.4172i	−1.25589	+	0.725087i	−0.972273	−	0.233851i	$-0.924867\pi$
$577$	−30.1675	+	17.4172i	−1.25589	+	0.725087i	−0.283616	+	0.958938i	$0.591534\pi$
$578$	−23.0775	−	13.3238i	−0.959897	−	0.554197i
$579$		0			0
$580$	1.49409	+	0.862614i	0.0620388	+	0.0358181i
$581$	7.99399	+	30.3686i	0.331647	+	1.25990i
$582$		0			0
$583$	9.48715			0.392918
$584$	0.640987	+	1.11022i	0.0265242	+	0.0459413i
$585$		0			0
$586$	−18.6844	−	10.7874i	−0.771845	−	0.445625i
$587$	20.1646	+	34.9261i	0.832281	+	1.44155i	0.896225	+	0.443599i	$0.146299\pi$
$587$	20.1646	+	34.9261i	0.832281	+	1.44155i	−0.0639444	+	0.997953i	$0.520368\pi$
$588$		0			0
$589$	13.9765	−	24.2080i	0.575892	−	0.997474i
$590$	−1.29322	+	0.746642i	−0.0532411	+	0.0307388i
$591$		0			0
$592$	−2.75951	+	4.77962i	−0.113415	+	0.196441i
$593$	−13.7783	+	23.8647i	−0.565806	+	0.980005i	0.431168	+	0.902272i	$0.358102\pi$
$593$	−13.7783	+	23.8647i	−0.565806	+	0.980005i	−0.996974	+	0.0777332i	$0.975232\pi$
$594$		0			0
$595$	−12.4142	+	12.3053i	−0.508933	+	0.504468i
$596$	−7.44381	+	4.29769i	−0.304910	+	0.176040i
$597$		0			0
$598$			44.3406i			1.81322i
$599$			14.1442i			0.577917i	0.957342	+	0.288959i	$0.0933090\pi$
$599$			14.1442i			0.577917i	−0.957342	+	0.288959i	$0.906691\pi$
$600$		0			0
$601$	10.7893	−	6.22920i	0.440104	−	0.254094i	−0.263537	−	0.964649i	$-0.584889\pi$
$601$	10.7893	−	6.22920i	0.440104	−	0.254094i	0.703642	+	0.710555i	$0.251556\pi$
$602$	16.6094	−	4.37213i	0.676949	−	0.178195i
$603$		0			0
$604$	−1.30386	+	2.25835i	−0.0530532	+	0.0918908i
$605$	4.42682	−	7.66748i	0.179976	−	0.311727i
$606$		0			0
$607$	6.89996	−	3.98369i	0.280061	−	0.161693i	−0.353390	−	0.935476i	$-0.614971\pi$
$607$	6.89996	−	3.98369i	0.280061	−	0.161693i	0.633451	+	0.773783i	$0.281638\pi$
$608$	1.78048	−	3.08388i	0.0722080	−	0.125068i
$609$		0			0
$610$	−1.86796	−	3.23540i	−0.0756314	−	0.130997i
$611$	32.5760	+	18.8078i	1.31789	+	0.760882i
$612$		0			0
$613$	3.28676	+	5.69283i	0.132751	+	0.229931i	0.924736	−	0.380609i	$-0.124286\pi$
$613$	3.28676	+	5.69283i	0.132751	+	0.229931i	−0.791985	+	0.610540i	$0.790952\pi$
$614$	5.22295			0.210781
$615$		0			0
$616$	−2.75290	+	2.72875i	−0.110918	+	0.109944i
$617$	6.77484	+	3.91146i	0.272745	+	0.157469i	0.630134	−	0.776486i	$-0.283000\pi$
$617$	6.77484	+	3.91146i	0.272745	+	0.157469i	−0.357389	+	0.933955i	$0.616333\pi$
$618$		0			0
$619$	39.8161	+	22.9878i	1.60034	+	0.923959i	0.991418	+	0.130732i	$0.0417327\pi$
$619$	39.8161	+	22.9878i	1.60034	+	0.923959i	0.608926	+	0.793227i	$0.291601\pi$
$620$	6.79817	−	3.92493i	0.273021	−	0.157629i
$621$		0			0
$622$			13.2357i			0.530702i
$623$	−8.22053	+	8.14840i	−0.329349	+	0.326459i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−30.9549			−1.23721
$627$		0			0
$628$		−	7.79034i		−	0.310868i
$629$	−36.4622			−1.45384
$630$		0			0
$631$	−24.0931			−0.959131			−0.479566	−	0.877506i	$-0.659206\pi$
$631$	−24.0931			−0.959131			−0.479566	+	0.877506i	$0.659206\pi$
$632$		−	0.994011i		−	0.0395396i
$633$		0			0
$634$	−15.1480			−0.601604
$635$	−0.457190	−	0.791877i	−0.0181430	−	0.0314247i
$636$		0			0
$637$	−24.0181	−	42.4604i	−0.951632	−	1.68234i
$638$			2.52754i			0.100066i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	−20.6665	−	11.9318i	−0.816279	−	0.471279i	0.0328524	−	0.999460i	$-0.489541\pi$
$641$	−20.6665	−	11.9318i	−0.816279	−	0.471279i	−0.849132	+	0.528181i	$0.822874\pi$
$642$		0			0
$643$	−12.9563	−	7.48033i	−0.510947	−	0.294996i	0.222276	−	0.974984i	$-0.428652\pi$
$643$	−12.9563	−	7.48033i	−0.510947	−	0.294996i	−0.733223	+	0.679988i	$0.761985\pi$
$644$	16.2793	−	4.28523i	0.641493	−	0.168862i
$645$		0			0
$646$	23.5259			0.925616
$647$	3.99382	+	6.91751i	0.157013	+	0.271955i	0.933790	−	0.357821i	$-0.116480\pi$
$647$	3.99382	+	6.91751i	0.157013	+	0.271955i	−0.776777	+	0.629776i	$0.783147\pi$
$648$		0			0
$649$	−1.89463	−	1.09387i	−0.0743708	−	0.0429380i
$650$	3.48448	+	6.03529i	0.136672	+	0.236724i
$651$		0			0
$652$	4.14705	−	7.18290i	0.162411	−	0.281304i
$653$	−24.4998	+	14.1449i	−0.958750	+	0.553535i	−0.895788	−	0.444481i	$-0.853388\pi$
$653$	−24.4998	+	14.1449i	−0.958750	+	0.553535i	−0.0629620	+	0.998016i	$0.520055\pi$
$654$		0			0
$655$	4.94937	−	8.57256i	0.193388	−	0.334958i
$656$	−0.632413	+	1.09537i	−0.0246916	+	0.0427671i
$657$		0			0
$658$	3.75686	−	13.7777i	0.146458	−	0.537109i
$659$	0.349881	−	0.202004i	0.0136294	−	0.00786894i	−0.493170	−	0.869933i	$-0.664162\pi$
$659$	0.349881	−	0.202004i	0.0136294	−	0.00786894i	0.506799	+	0.862064i	$0.330829\pi$
$660$		0			0
$661$		−	3.41898i		−	0.132983i	−0.997787	−	0.0664915i	$-0.978819\pi$
$661$		−	3.41898i		−	0.132983i	0.997787	−	0.0664915i	$-0.0211805\pi$
$662$			1.30322i			0.0506510i
$663$		0			0
$664$	10.2791	−	5.93463i	0.398906	−	0.230308i
$665$	2.47852	−	9.08955i	0.0961127	−	0.352478i
$666$		0			0
$667$	5.48846	−	9.50629i	0.212514	−	0.368085i
$668$	6.88497	−	11.9251i	0.266387	−	0.461397i
$669$		0			0
$670$	−10.8685	+	6.27490i	−0.419885	+	0.242421i
$671$	2.73665	−	4.74001i	0.105647	−	0.182986i
$672$		0			0
$673$	9.47604	+	16.4130i	0.365274	+	0.632674i	0.988820	−	0.149113i	$-0.0476418\pi$
$673$	9.47604	+	16.4130i	0.365274	+	0.632674i	−0.623546	+	0.781787i	$0.714309\pi$
$674$	14.0659	+	8.12095i	0.541798	+	0.312807i
$675$		0			0
$676$	−17.7832	−	30.8014i	−0.683968	−	1.18467i
$677$	15.3569			0.590214			0.295107	−	0.955464i	$-0.404645\pi$
$677$	15.3569			0.590214			0.295107	+	0.955464i	$0.404645\pi$
$678$		0			0
$679$	26.7354	−	7.03762i	1.02601	−	0.270079i
$680$	5.72151	+	3.30332i	0.219410	+	0.126676i
$681$		0			0
$682$	9.95964	+	5.75020i	0.381374	+	0.220187i
$683$	26.9763	−	15.5748i	1.03222	−	0.595951i	0.114599	−	0.993412i	$-0.463442\pi$
$683$	26.9763	−	15.5748i	1.03222	−	0.595951i	0.917619	+	0.397460i	$0.130108\pi$
$684$		0			0
$685$		−	12.0482i		−	0.460340i
$686$	−13.2678	+	12.9215i	−0.506566	+	0.493347i
$687$		0			0
$688$	−3.24581	−	5.62191i	−0.123745	−	0.214333i
$689$	45.1286			1.71926
$690$		0			0
$691$			26.8062i			1.01976i	0.860247	+	0.509878i	$0.170309\pi$
$691$			26.8062i			1.01976i	−0.860247	+	0.509878i	$0.829691\pi$
$692$	11.6394			0.442464
$693$		0			0
$694$	−5.07209			−0.192534
$695$		−	18.0223i		−	0.683624i
$696$		0			0
$697$	−8.35624			−0.316515
$698$	−11.8354	−	20.4996i	−0.447978	−	0.775921i
$699$		0			0
$700$	1.87905	−	1.86257i	0.0710216	−	0.0703984i
$701$			9.39873i			0.354985i	0.984122	+	0.177493i	$0.0567985\pi$
$701$			9.39873i			0.354985i	−0.984122	+	0.177493i	$0.943201\pi$
$702$		0			0
$703$	17.0200	−	9.82652i	0.641922	−	0.370614i
$704$	1.26877	+	0.732523i	0.0478185	+	0.0276080i
$705$		0			0
$706$	−0.471774	−	0.272379i	−0.0177554	−	0.0102511i
$707$	3.83263	−	3.79901i	0.144141	−	0.142876i
$708$		0			0
$709$	20.2298			0.759745			0.379873	−	0.925039i	$-0.375968\pi$
$709$	20.2298			0.759745			0.379873	+	0.925039i	$0.375968\pi$
$710$	−7.10664	−	12.3091i	−0.266707	−	0.461951i
$711$		0			0
$712$	3.78871	+	2.18741i	0.141988	+	0.0819767i
$713$	−24.9727	−	43.2540i	−0.935234	−	1.61987i
$714$		0			0
$715$	−5.10492	+	8.84199i	−0.190913	+	0.330672i
$716$	1.21808	−	0.703262i	0.0455220	−	0.0262821i
$717$		0			0
$718$	3.14576	−	5.44862i	0.117399	−	0.203341i
$719$	0.154148	−	0.266992i	0.00574874	−	0.00995710i	−0.863137	−	0.504970i	$-0.831503\pi$
$719$	0.154148	−	0.266992i	0.00574874	−	0.00995710i	0.868885	+	0.495013i	$0.164837\pi$
$720$		0			0
$721$	−8.13732	+	2.14200i	−0.303050	+	0.0797724i
$722$	5.47291	−	3.15979i	0.203681	−	0.117595i
$723$		0			0
$724$			10.1582i			0.377527i
$725$		−	1.72523i		−	0.0640734i
$726$		0			0
$727$	3.69340	−	2.13238i	0.136980	−	0.0790857i	−0.429944	−	0.902856i	$-0.641467\pi$
$727$	3.69340	−	2.13238i	0.136980	−	0.0790857i	0.566924	+	0.823770i	$0.308133\pi$
$728$	−13.0950	+	12.9801i	−0.485335	+	0.481076i
$729$		0			0
$730$	0.640987	−	1.11022i	0.0237240	−	0.0410911i
$731$	21.4439	−	37.1419i	0.793130	−	1.37374i
$732$		0			0
$733$	2.60873	−	1.50615i	0.0963558	−	0.0556310i	−0.451048	−	0.892500i	$-0.648950\pi$
$733$	2.60873	−	1.50615i	0.0963558	−	0.0556310i	0.547404	+	0.836869i	$0.315616\pi$
$734$	−12.1749	+	21.0875i	−0.449382	+	0.778353i
$735$		0			0
$736$	−3.18129	−	5.51016i	−0.117264	−	0.203107i
$737$	−15.9228	−	9.19303i	−0.586524	−	0.338630i
$738$		0			0
$739$	9.01920	+	15.6217i	0.331776	+	0.574654i	0.982860	−	0.184352i	$-0.0590187\pi$
$739$	9.01920	+	15.6217i	0.331776	+	0.574654i	−0.651084	+	0.759006i	$0.725685\pi$
$740$	5.51903			0.202884
$741$		0			0
$742$	−4.36138	−	16.5686i	−0.160111	−	0.608252i
$743$	−1.82145	−	1.05161i	−0.0668225	−	0.0385800i	0.466217	−	0.884671i	$-0.345617\pi$
$743$	−1.82145	−	1.05161i	−0.0668225	−	0.0385800i	−0.533039	+	0.846091i	$0.678950\pi$
$744$		0			0
$745$	7.44381	+	4.29769i	0.272720	+	0.157455i
$746$	1.88581	−	1.08878i	0.0690445	−	0.0398629i
$747$		0			0
$748$			9.67903i			0.353900i
$749$	−29.6590	−	29.9215i	−1.08371	−	1.09331i
$750$		0			0
$751$	3.40069	+	5.89017i	0.124093	+	0.214935i	0.921378	−	0.388668i	$-0.127065\pi$
$751$	3.40069	+	5.89017i	0.124093	+	0.214935i	−0.797285	+	0.603603i	$0.793731\pi$
$752$	−5.39759			−0.196830
$753$		0			0
$754$			12.0230i			0.437853i
$755$	2.60771			0.0949044
$756$		0			0
$757$	−26.9017			−0.977761			−0.488880	−	0.872351i	$-0.662595\pi$
$757$	−26.9017			−0.977761			−0.488880	+	0.872351i	$0.662595\pi$
$758$		−	22.5954i		−	0.820700i
$759$		0			0
$760$	−3.56096			−0.129170
$761$	−2.08165	−	3.60553i	−0.0754598	−	0.130700i	0.825826	−	0.563925i	$-0.190709\pi$
$761$	−2.08165	−	3.60553i	−0.0754598	−	0.130700i	−0.901286	+	0.433224i	$0.857376\pi$
$762$		0			0
$763$	−4.86072	−	18.4655i	−0.175970	−	0.668497i
$764$			17.1243i			0.619536i
$765$		0			0
$766$	5.65138	−	3.26282i	0.204193	−	0.117891i
$767$	−9.01241	−	5.20332i	−0.325419	−	0.187881i
$768$		0			0
$769$	−15.1341	−	8.73768i	−0.545750	−	0.315089i	0.201656	−	0.979456i	$-0.435368\pi$
$769$	−15.1341	−	8.73768i	−0.545750	−	0.315089i	−0.747406	+	0.664368i	$0.768701\pi$
$770$	3.73962	+	1.01971i	0.134766	+	0.0367478i
$771$		0			0
$772$	−1.93306			−0.0695722
$773$	−9.80159	−	16.9768i	−0.352539	−	0.610615i	0.634155	−	0.773206i	$-0.281348\pi$
$773$	−9.80159	−	16.9768i	−0.352539	−	0.610615i	−0.986694	+	0.162591i	$0.948015\pi$
$774$		0			0
$775$	−6.79817	−	3.92493i	−0.244197	−	0.140987i
$776$	−5.22463	−	9.04933i	−0.187553	−	0.324852i
$777$		0			0
$778$	−17.3402	+	30.0342i	−0.621677	+	1.07678i
$779$	3.90057	−	2.25200i	0.139753	−	0.0806862i
$780$		0			0
$781$	10.4116	−	18.0334i	0.372555	−	0.645284i
$782$	21.0176	−	36.4036i	0.751589	−	1.30179i
$783$		0			0
$784$	6.03110	+	3.55329i	0.215396	+	0.126903i
$785$	−6.74663	+	3.89517i	−0.240798	+	0.139025i
$786$		0			0
$787$		−	29.0422i		−	1.03524i	−0.855610	−	0.517620i	$-0.826818\pi$
$787$		−	29.0422i		−	1.03524i	0.855610	−	0.517620i	$-0.173182\pi$
$788$		−	22.0136i		−	0.784200i
$789$		0			0
$790$	−0.860839	+	0.497005i	−0.0306273	+	0.0176827i
$791$	−11.6720	−	11.7754i	−0.415010	−	0.418684i
$792$		0			0
$793$	13.0177	−	22.5473i	0.462273	−	0.800680i
$794$	−13.7650	+	23.8417i	−0.488501	+	0.846109i
$795$		0			0
$796$	−23.0430	+	13.3039i	−0.816739	+	0.471544i
$797$	14.0345	−	24.3085i	0.497129	−	0.861052i	−0.502866	−	0.864365i	$-0.667721\pi$
$797$	14.0345	−	24.3085i	0.497129	−	0.861052i	0.999995	+	0.00331218i	$0.00105430\pi$
$798$		0			0
$799$	−17.8300	−	30.8824i	−0.630778	−	1.09254i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	−7.03938	−	12.1926i	−0.248569	−	0.430534i
$803$	1.87815			0.0662785
$804$		0			0
$805$	−11.8507	−	11.9556i	−0.417684	−	0.421381i
$806$	47.3762	+	27.3526i	1.66875	+	0.963455i
$807$		0			0
$808$	−1.76640	−	1.01983i	−0.0621417	−	0.0358775i
$809$	2.46533	−	1.42336i	0.0866764	−	0.0500427i	−0.456035	−	0.889962i	$-0.650731\pi$
$809$	2.46533	−	1.42336i	0.0866764	−	0.0500427i	0.542712	+	0.839919i	$0.317398\pi$
$810$		0			0
$811$			5.05522i			0.177513i	0.996053	+	0.0887564i	$0.0282893\pi$
$811$			5.05522i			0.177513i	−0.996053	+	0.0887564i	$0.971711\pi$
$812$	4.41416	−	1.16195i	0.154907	−	0.0407764i
$813$		0			0
$814$	4.04282	+	7.00236i	0.141701	+	0.245433i
$815$	−8.29410			−0.290530
$816$		0			0
$817$			23.1164i			0.808740i
$818$	−32.7642			−1.14557
$819$		0			0
$820$	1.26483			0.0441696
$821$			39.0748i			1.36372i	0.731482	+	0.681861i	$0.238829\pi$
$821$			39.0748i			1.36372i	−0.731482	+	0.681861i	$0.761171\pi$
$822$		0			0
$823$	−32.7968			−1.14322			−0.571612	−	0.820524i	$-0.693682\pi$
$823$	−32.7968			−1.14322			−0.571612	+	0.820524i	$0.693682\pi$
$824$	1.59020	+	2.75430i	0.0553971	+	0.0959506i
$825$		0			0
$826$	−1.03936	+	3.81169i	−0.0361641	+	0.132626i
$827$			53.3096i			1.85376i	0.375361	+	0.926879i	$0.377519\pi$
$827$			53.3096i			1.85376i	−0.375361	+	0.926879i	$0.622481\pi$
$828$		0			0
$829$	39.1781	−	22.6195i	1.36071	−	0.785607i	0.370992	−	0.928636i	$-0.379018\pi$
$829$	39.1781	−	22.6195i	1.36071	−	0.785607i	0.989718	+	0.143029i	$0.0456844\pi$
$830$	−10.2791	−	5.93463i	−0.356792	−	0.205994i
$831$		0			0
$832$	6.03529	+	3.48448i	0.209236	+	0.120803i
$833$	−0.407548	+	46.2446i	−0.0141207	+	1.60228i
$834$		0			0
$835$	−13.7699			−0.476528
$836$	−2.60849	−	4.51803i	−0.0902164	−	0.156259i
$837$		0			0
$838$	10.0677	+	5.81259i	0.347783	+	0.200793i
$839$	19.1888	+	33.2360i	0.662472	+	1.14744i	0.979964	+	0.199175i	$0.0638261\pi$
$839$	19.1888	+	33.2360i	0.662472	+	1.14744i	−0.317492	+	0.948261i	$0.602841\pi$
$840$		0			0
$841$	−13.0118	+	22.5371i	−0.448683	+	0.777141i
$842$	−19.8333	+	11.4508i	−0.683500	+	0.394619i
$843$		0			0
$844$	3.44298	−	5.96341i	0.118512	−	0.205269i
$845$	−17.7832	+	30.8014i	−0.611760	+	1.05960i
$846$		0			0
$847$	−5.96296	−	22.6528i	−0.204890	−	0.778361i
$848$	−5.60809	+	3.23783i	−0.192583	+	0.111188i
$849$		0			0
$850$		−	6.60663i		−	0.226606i
$851$		−	35.1153i		−	1.20374i
$852$		0			0
$853$	−43.3554	+	25.0313i	−1.48446	+	0.857054i	−0.999844	−	0.0176720i	$-0.994375\pi$
$853$	−43.3554	+	25.0313i	−1.48446	+	0.857054i	−0.484618	+	0.874726i	$0.661041\pi$
$854$	−9.53614	−	2.60029i	−0.326320	−	0.0889801i
$855$		0			0
$856$	−7.96185	+	13.7903i	−0.272130	+	0.471344i
$857$	−15.7216	+	27.2305i	−0.537038	+	0.930178i	0.462023	+	0.886868i	$0.347124\pi$
$857$	−15.7216	+	27.2305i	−0.537038	+	0.930178i	−0.999062	+	0.0433100i	$0.986210\pi$
$858$		0			0
$859$	−26.1528	+	15.0993i	−0.892323	+	0.515183i	−0.874702	−	0.484662i	$-0.838943\pi$
$859$	−26.1528	+	15.0993i	−0.892323	+	0.515183i	−0.0176215	+	0.999845i	$0.505609\pi$
$860$	−3.24581	+	5.62191i	−0.110681	+	0.191705i
$861$		0			0
$862$	4.81745	+	8.34407i	0.164083	+	0.284200i
$863$	−13.8288	−	7.98404i	−0.470736	−	0.271780i	0.245812	−	0.969318i	$-0.420946\pi$
$863$	−13.8288	−	7.98404i	−0.470736	−	0.271780i	−0.716548	+	0.697538i	$0.754279\pi$
$864$		0			0
$865$	−5.81971	−	10.0800i	−0.197876	−	0.342731i
$866$	−37.8458			−1.28605
$867$		0			0
$868$	5.46369	−	20.0372i	0.185450	−	0.680107i
$869$	−1.26117	−	0.728136i	−0.0427822	−	0.0247003i
$870$		0			0
$871$	−75.7418	−	43.7295i	−2.56641	−	1.48172i
$872$	−6.25017	+	3.60853i	−0.211657	+	0.122200i
$873$		0			0
$874$			22.6569i			0.766382i
$875$	−2.55256	−	0.696025i	−0.0862922	−	0.0235299i
$876$		0			0
$877$	−25.2758	−	43.7790i	−0.853503	−	1.47831i	−0.878027	−	0.478611i	$-0.841140\pi$
$877$	−25.2758	−	43.7790i	−0.853503	−	1.47831i	0.0245242	−	0.999699i	$-0.492193\pi$
$878$	32.3974			1.09336
$879$		0			0
$880$		−	1.46505i		−	0.0493867i
$881$	7.58608			0.255581			0.127791	−	0.991801i	$-0.459211\pi$
$881$	7.58608			0.255581			0.127791	+	0.991801i	$0.459211\pi$
$882$		0			0
$883$	−19.9066			−0.669910			−0.334955	−	0.942234i	$-0.608721\pi$
$883$	−19.9066			−0.669910			−0.334955	+	0.942234i	$0.608721\pi$
$884$			46.0413i			1.54854i
$885$		0			0
$886$	21.9018			0.735806
$887$	17.5255	+	30.3551i	0.588449	+	1.01922i	0.994436	+	0.105345i	$0.0335947\pi$
$887$	17.5255	+	30.3551i	0.588449	+	1.01922i	−0.405987	+	0.913879i	$0.633072\pi$
$888$		0			0
$889$	−2.33401	−	0.636431i	−0.0782801	−	0.0213452i
$890$		−	4.37482i		−	0.146644i
$891$		0			0
$892$	−11.6938	+	6.75140i	−0.391536	+	0.226053i
$893$	16.6455	+	9.61030i	0.557021	+	0.321596i
$894$		0			0
$895$	−1.21808	−	0.703262i	−0.0407161	−	0.0235074i
$896$	0.696025	−	2.55256i	0.0232526	−	0.0852750i
$897$		0			0
$898$	25.8522			0.862700
$899$	−6.77139	−	11.7284i	−0.225839	−	0.391164i
$900$		0			0
$901$	−37.0506	−	21.3912i	−1.23433	−	0.712643i
$902$	0.926515	+	1.60477i	0.0308496	+	0.0534330i
$903$		0			0
$904$	−3.13332	+	5.42707i	−0.104213	+	0.180502i
$905$	8.79728	−	5.07911i	0.292431	−	0.168835i
$906$		0			0
$907$	−2.06535	+	3.57729i	−0.0685789	+	0.118782i	−0.898276	−	0.439432i	$-0.855180\pi$
$907$	−2.06535	+	3.57729i	−0.0685789	+	0.118782i	0.829697	+	0.558214i	$0.188513\pi$
$908$	−10.7490	+	18.6179i	−0.356719	+	0.617856i
$909$		0			0
$910$	17.7887	+	4.85057i	0.589688	+	0.160795i
$911$	22.0418	−	12.7258i	0.730276	−	0.421625i	−0.0882472	−	0.996099i	$-0.528127\pi$
$911$	22.0418	−	12.7258i	0.730276	−	0.421625i	0.818523	+	0.574474i	$0.194793\pi$
$912$		0			0
$913$		−	17.3890i		−	0.575493i
$914$		−	22.2463i		−	0.735841i
$915$		0			0
$916$	−19.4936	+	11.2546i	−0.644086	+	0.371863i
$917$	−6.66684	−	25.3268i	−0.220158	−	0.836366i
$918$		0			0
$919$	3.41703	−	5.91848i	0.112718	−	0.195232i	−0.804148	−	0.594430i	$-0.797378\pi$
$919$	3.41703	−	5.91848i	0.112718	−	0.195232i	0.916865	+	0.399197i	$0.130711\pi$
$920$	−3.18129	+	5.51016i	−0.104884	+	0.181665i
$921$		0			0
$922$	12.2173	−	7.05369i	0.402357	−	0.232301i
$923$	49.5259	−	85.7813i	1.63016	−	2.82353i
$924$		0			0
$925$	−2.75951	−	4.77962i	−0.0907323	−	0.157153i
$926$	5.77194	+	3.33243i	0.189678	+	0.109510i
$927$		0			0
$928$	−0.862614	−	1.49409i	−0.0283167	−	0.0490460i
$929$	−36.1564			−1.18625			−0.593126	−	0.805110i	$-0.702106\pi$
$929$	−36.1564			−1.18625			−0.593126	+	0.805110i	$0.702106\pi$
$930$		0			0
$931$	−12.2726	−	21.6962i	−0.402219	−	0.711063i
$932$	−15.4408	−	8.91477i	−0.505782	−	0.292013i
$933$		0			0
$934$	3.04350	+	1.75717i	0.0995864	+	0.0574962i
$935$	8.38228	−	4.83951i	0.274130	−	0.158269i
$936$		0			0
$937$		−	25.1125i		−	0.820391i	−0.911998	−	0.410195i	$-0.865461\pi$
$937$		−	25.1125i		−	0.820391i	0.911998	−	0.410195i	$-0.134539\pi$
$938$	−8.73498	+	32.0341i	−0.285207	+	1.04595i
$939$		0			0
$940$	2.69880	+	4.67445i	0.0880250	+	0.152464i
$941$	−2.72207			−0.0887370			−0.0443685	−	0.999015i	$-0.514128\pi$
$941$	−2.72207			−0.0887370			−0.0443685	+	0.999015i	$0.514128\pi$
$942$		0			0
$943$		−	8.04757i		−	0.262065i
$944$	1.49328			0.0486023
$945$		0			0
$946$	−9.51053			−0.309214
$947$			4.50181i			0.146289i	0.997321	+	0.0731446i	$0.0233034\pi$
$947$			4.50181i			0.146289i	−0.997321	+	0.0731446i	$0.976697\pi$
$948$		0			0
$949$	8.93402			0.290010
$950$	1.78048	+	3.08388i	0.0577664	+	0.100054i
$951$		0			0
$952$	16.9037	−	4.44959i	0.547851	−	0.144212i
$953$		−	18.8442i		−	0.610423i	−0.952285	−	0.305211i	$-0.901273\pi$
$953$		−	18.8442i		−	0.610423i	0.952285	−	0.305211i	$-0.0987271\pi$
$954$		0			0
$955$	14.8301	−	8.56216i	0.479890	−	0.277065i
$956$	13.7144	+	7.91804i	0.443557	+	0.256088i
$957$		0			0
$958$	0.866868	+	0.500486i	0.0280072	+	0.0161700i
$959$	−22.4407	−	22.6393i	−0.724647	−	0.731061i
$960$		0			0
$961$	−30.6202			−0.987747
$962$	19.2309	+	33.3089i	0.620030	+	1.07392i
$963$		0			0
$964$	−22.8842	−	13.2122i	−0.737050	−	0.425536i
$965$	0.966528	+	1.67408i	0.0311136	+	0.0538904i
$966$		0			0
$967$	−17.7127	+	30.6793i	−0.569602	+	0.986579i	0.427003	+	0.904250i	$0.359569\pi$
$967$	−17.7127	+	30.6793i	−0.569602	+	0.986579i	−0.996605	+	0.0823294i	$0.973764\pi$
$968$	−7.66748	+	4.42682i	−0.246442	+	0.142283i
$969$		0			0
$970$	−5.22463	+	9.04933i	−0.167753	+	0.290556i
$971$	0.536311	−	0.928919i	0.0172111	−	0.0298104i	−0.857292	−	0.514831i	$-0.827855\pi$
$971$	0.536311	−	0.928919i	0.0172111	−	0.0298104i	0.874503	+	0.485021i	$0.161188\pi$
$972$		0			0
$973$	−33.5677	−	33.8648i	−1.07613	−	1.08566i
$974$	25.0723	−	14.4755i	0.803368	−	0.463825i
$975$		0			0
$976$			3.73592i			0.119584i
$977$			7.75308i			0.248043i	0.992280	+	0.124021i	$0.0395792\pi$
$977$			7.75308i			0.248043i	−0.992280	+	0.124021i	$0.960421\pi$
$978$		0			0
$979$	5.55063	−	3.20466i	0.177399	−	0.102421i
$980$	0.0616877	−	6.99973i	0.00197054	−	0.223598i
$981$		0			0
$982$	17.6990	−	30.6555i	0.564797	−	0.978257i
$983$	10.7940	−	18.6958i	0.344275	−	0.596302i	−0.640947	−	0.767585i	$-0.721458\pi$
$983$	10.7940	−	18.6958i	0.344275	−	0.596302i	0.985222	+	0.171283i	$0.0547913\pi$
$984$		0			0
$985$	−19.0643	+	11.0068i	−0.607439	+	0.350705i
$986$	5.69898	−	9.87092i	0.181492	−	0.314354i
$987$		0			0
$988$	−12.4081	−	21.4914i	−0.394754	−	0.683733i
$989$	35.7699	+	20.6518i	1.13742	+	0.656687i
$990$		0			0
$991$	−3.97525	−	6.88534i	−0.126278	−	0.218720i	0.795954	−	0.605357i	$-0.206970\pi$
$991$	−3.97525	−	6.88534i	−0.126278	−	0.218720i	−0.922232	+	0.386637i	$0.873636\pi$
$992$	−7.84985			−0.249233
$993$		0			0
$994$	−36.2802	−	9.89280i	−1.15074	−	0.313780i
$995$	23.0430	+	13.3039i	0.730513	+	0.421762i
$996$		0			0
$997$	49.5700	+	28.6192i	1.56990	+	0.906380i	0.996180	+	0.0873264i	$0.0278323\pi$
$997$	49.5700	+	28.6192i	1.56990	+	0.906380i	0.573717	+	0.819054i	$0.305501\pi$
$998$	14.4080	−	8.31844i	0.456076	−	0.263316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.b.341.5		28
3.2	odd	2		630.2.bk.b.131.4	yes	28
7.3	odd	6		1890.2.t.b.1151.3		28
9.2	odd	6		1890.2.t.b.1601.3		28
9.7	even	3		630.2.t.b.551.14	yes	28
21.17	even	6		630.2.t.b.311.14	✓	28
63.38	even	6	inner	1890.2.bk.b.521.5		28
63.52	odd	6		630.2.bk.b.101.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.14	✓	28	21.17	even	6
630.2.t.b.551.14	yes	28	9.7	even	3
630.2.bk.b.101.11	yes	28	63.52	odd	6
630.2.bk.b.131.4	yes	28	3.2	odd	2
1890.2.t.b.1151.3		28	7.3	odd	6
1890.2.t.b.1601.3		28	9.2	odd	6
1890.2.bk.b.341.5		28	1.1	even	1	trivial
1890.2.bk.b.521.5		28	63.38	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.55256 + 0.696025i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.55256 + 0.696025i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(-1.26877 - 0.732523i) q^{11} +(-6.03529 - 3.48448i) q^{13} +(-0.696025 + 2.55256i) q^{14} +1.00000 q^{16} +(3.30332 + 5.72151i) q^{17} +(-3.08388 - 1.78048i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.732523 - 1.26877i) q^{22} +(-5.51016 + 3.18129i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.48448 - 6.03529i) q^{26} +(-2.55256 - 0.696025i) q^{28} +(-1.49409 + 0.862614i) q^{29} +7.84985i q^{31} +1.00000i q^{32} +(-5.72151 + 3.30332i) q^{34} +(0.673503 + 2.55859i) q^{35} +(-2.75951 + 4.77962i) q^{37} +(1.78048 - 3.08388i) q^{38} +(0.866025 - 0.500000i) q^{40} +(-0.632413 + 1.09537i) q^{41} +(-3.24581 - 5.62191i) q^{43} +(1.26877 + 0.732523i) q^{44} +(-3.18129 - 5.51016i) q^{46} -5.39759 q^{47} +(6.03110 + 3.55329i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(6.03529 + 3.48448i) q^{52} +(-5.60809 + 3.23783i) q^{53} -1.46505i q^{55} +(0.696025 - 2.55256i) q^{56} +(-0.862614 - 1.49409i) q^{58} +1.49328 q^{59} +3.73592i q^{61} -7.84985 q^{62} -1.00000 q^{64} -6.96896i q^{65} +12.5498 q^{67} +(-3.30332 - 5.72151i) q^{68} +(-2.55859 + 0.673503i) q^{70} +14.2133i q^{71} +(-1.11022 + 0.640987i) q^{73} +(-4.77962 - 2.75951i) q^{74} +(3.08388 + 1.78048i) q^{76} +(-2.72875 - 2.75290i) q^{77} +0.994011 q^{79} +(0.500000 + 0.866025i) q^{80} +(-1.09537 - 0.632413i) q^{82} +(5.93463 + 10.2791i) q^{83} +(-3.30332 + 5.72151i) q^{85} +(5.62191 - 3.24581i) q^{86} +(-0.732523 + 1.26877i) q^{88} +(-2.18741 + 3.78871i) q^{89} +(-12.9801 - 13.0950i) q^{91} +(5.51016 - 3.18129i) q^{92} -5.39759i q^{94} -3.56096i q^{95} +(9.04933 - 5.22463i) q^{97} +(-3.55329 + 6.03110i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

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