LMFDB - Embedded newform 875.2.bb.b.768.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			768.16
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.b.507.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.75355 - 1.13877i) q^{2} +(-0.775483 + 0.297680i) q^{3} +(0.964662 - 2.16667i) q^{4} +(-1.02086 + 1.40509i) q^{6} +(-1.53148 + 2.15744i) q^{7} +(-0.121581 - 0.767632i) q^{8} +(-1.71667 + 1.54570i) q^{9} +(-0.702779 + 0.780515i) q^{11} +(-0.103106 + 1.96737i) q^{12} +(2.08008 + 4.08239i) q^{13} +(-0.228707 + 5.52718i) q^{14} +(2.08662 + 2.31743i) q^{16} +(1.75283 - 1.41941i) q^{17} +(-1.25008 + 4.66535i) q^{18} +(4.55223 - 2.02678i) q^{19} +(0.545413 - 2.12895i) q^{21} +(-0.343531 + 2.16897i) q^{22} +(3.38977 + 5.21979i) q^{23} +(0.322792 + 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(2.00245 - 3.93004i) q^{27} +(3.19709 + 5.39942i) q^{28} +(0.743348 + 1.02313i) q^{29} +(-10.1310 - 1.06481i) q^{31} +(7.79943 + 2.08985i) q^{32} +(0.312649 - 0.814479i) q^{33} +(1.45729 - 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-6.27752 - 0.328991i) q^{37} +(5.67452 - 8.73799i) q^{38} +(-2.82832 - 2.54663i) q^{39} +(-5.32280 - 1.72948i) q^{41} +(-1.46797 - 4.35431i) q^{42} +(4.80861 + 4.80861i) q^{43} +(1.01317 + 2.27562i) q^{44} +(11.8882 + 5.29299i) q^{46} +(0.196982 - 0.243253i) q^{47} +(-2.30799 - 1.17598i) q^{48} +(-2.30911 - 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(10.8518 - 0.568717i) q^{52} +(0.100384 + 0.261509i) q^{53} +(-0.963998 - 9.17183i) q^{54} +(1.84232 + 0.913312i) q^{56} +(-2.92684 + 2.92684i) q^{57} +(2.46860 + 0.947608i) q^{58} +(-6.72559 + 1.42957i) q^{59} +(1.10261 - 5.18739i) q^{61} +(-18.9778 + 9.66967i) q^{62} +(-0.705699 - 6.07084i) q^{63} +(10.1249 - 3.28979i) q^{64} +(-0.379257 - 1.78426i) q^{66} +(7.72991 + 9.54564i) q^{67} +(-1.38451 - 5.16706i) q^{68} +(-4.18254 - 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.39524 + 1.12985i) q^{72} +(-0.0678338 - 1.29435i) q^{73} +(-11.3826 + 6.57173i) q^{74} -11.8183i q^{76} +(-0.607621 - 2.71155i) q^{77} +(-7.85959 - 1.24484i) q^{78} +(10.7765 - 1.13266i) q^{79} +(0.341411 - 3.24831i) q^{81} +(-11.3033 + 3.02870i) q^{82} +(3.66064 - 0.579789i) q^{83} +(-4.08659 - 3.23545i) q^{84} +(13.9080 + 2.95623i) q^{86} +(-0.881019 - 0.572141i) q^{87} +(0.684593 + 0.444580i) q^{88} +(10.3731 + 2.20488i) q^{89} +(-11.9931 - 1.76446i) q^{91} +(14.5795 - 2.30917i) q^{92} +(8.17341 - 2.19006i) q^{93} +(0.0684094 - 0.650872i) q^{94} +(-6.67043 + 0.701090i) q^{96} +(4.89604 + 0.775456i) q^{97} +(-11.5743 - 8.95821i) q^{98} -2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.75355	−	1.13877i	1.23994	−	0.805229i	0.253185	−	0.967418i	$-0.418522\pi$
$2$	1.75355	−	1.13877i	1.23994	−	0.805229i	0.986760	+	0.162189i	$0.0518553\pi$
$3$	−0.775483	+	0.297680i	−0.447725	+	0.171866i	−0.571775	−	0.820410i	$-0.693745\pi$
$3$	−0.775483	+	0.297680i	−0.447725	+	0.171866i	0.124050	+	0.992276i	$0.460412\pi$
$4$	0.964662	−	2.16667i	0.482331	−	1.08333i
$5$		0			0
$5$		0			0
$6$	−1.02086	+	1.40509i	−0.416763	+	0.573625i
$7$	−1.53148	+	2.15744i	−0.578847	+	0.815436i
$7$	−1.53148	+	2.15744i	−0.578847	+	0.815436i
$8$	−0.121581	−	0.767632i	−0.0429853	−	0.271399i
$9$	−1.71667	+	1.54570i	−0.572225	+	0.515234i
$10$		0			0
$11$	−0.702779	+	0.780515i	−0.211896	+	0.235334i	−0.839718	−	0.543023i	$-0.817280\pi$
$11$	−0.702779	+	0.780515i	−0.211896	+	0.235334i	0.627822	+	0.778357i	$0.283946\pi$
$12$	−0.103106	+	1.96737i	−0.0297640	+	0.567932i
$13$	2.08008	+	4.08239i	0.576911	+	1.13225i	0.976492	+	0.215554i	$0.0691558\pi$
$13$	2.08008	+	4.08239i	0.576911	+	1.13225i	−0.399580	+	0.916698i	$0.630844\pi$
$14$	−0.228707	+	5.52718i	−0.0611245	+	1.47720i
$15$		0			0
$16$	2.08662	+	2.31743i	0.521655	+	0.579357i
$17$	1.75283	−	1.41941i	0.425124	−	0.344259i	−0.392761	−	0.919641i	$-0.628480\pi$
$17$	1.75283	−	1.41941i	0.425124	−	0.344259i	0.817885	+	0.575382i	$0.195147\pi$
$18$	−1.25008	+	4.66535i	−0.294646	+	1.09963i
$19$	4.55223	−	2.02678i	1.04435	−	0.464976i	0.188434	−	0.982086i	$-0.439659\pi$
$19$	4.55223	−	2.02678i	1.04435	−	0.464976i	0.855919	+	0.517110i	$0.172992\pi$
$20$		0			0
$21$	0.545413	−	2.12895i	0.119019	−	0.464575i
$22$	−0.343531	+	2.16897i	−0.0732411	+	0.462426i
$23$	3.38977	+	5.21979i	0.706816	+	1.08840i	0.991541	+	0.129793i	$0.0414311\pi$
$23$	3.38977	+	5.21979i	0.706816	+	1.08840i	−0.284725	+	0.958609i	$0.591902\pi$
$24$	0.322792	+	0.559093i	0.0658897	+	0.114124i
$25$		0			0
$26$	8.29642	+	4.78994i	1.62706	+	0.939384i
$27$	2.00245	−	3.93004i	0.385373	−	0.756336i
$28$	3.19709	+	5.39942i	0.604194	+	1.02039i
$29$	0.743348	+	1.02313i	0.138036	+	0.189991i	0.872439	−	0.488724i	$-0.162537\pi$
$29$	0.743348	+	1.02313i	0.138036	+	0.189991i	−0.734402	+	0.678714i	$0.762537\pi$
$30$		0			0
$31$	−10.1310	−	1.06481i	−1.81959	−	0.191246i	−0.867574	−	0.497308i	$-0.834322\pi$
$31$	−10.1310	−	1.06481i	−1.81959	−	0.191246i	−0.952012	+	0.306062i	$0.900989\pi$
$32$	7.79943	+	2.08985i	1.37876	+	0.369437i
$33$	0.312649	−	0.814479i	0.0544253	−	0.141783i
$34$	1.45729	−	4.48507i	0.249923	−	0.769184i
$35$		0			0
$36$	1.69301	+	5.21054i	0.282168	+	0.868424i
$37$	−6.27752	−	0.328991i	−1.03202	−	0.0540858i	−0.471202	−	0.882026i	$-0.656180\pi$
$37$	−6.27752	−	0.328991i	−1.03202	−	0.0540858i	−0.560817	+	0.827940i	$0.689513\pi$
$38$	5.67452	−	8.73799i	0.920528	−	1.41749i
$39$	−2.82832	−	2.54663i	−0.452893	−	0.407787i
$40$		0			0
$41$	−5.32280	−	1.72948i	−0.831282	−	0.270100i	−0.137697	−	0.990474i	$-0.543970\pi$
$41$	−5.32280	−	1.72948i	−0.831282	−	0.270100i	−0.693585	+	0.720374i	$0.743970\pi$
$42$	−1.46797	−	4.35431i	−0.226513	−	0.671885i
$43$	4.80861	+	4.80861i	0.733306	+	0.733306i	0.971273	−	0.237968i	$-0.0764812\pi$
$43$	4.80861	+	4.80861i	0.733306	+	0.733306i	−0.237968	+	0.971273i	$0.576481\pi$
$44$	1.01317	+	2.27562i	0.152741	+	0.343063i
$45$		0			0
$46$	11.8882	+	5.29299i	1.75283	+	0.780408i
$47$	0.196982	−	0.243253i	0.0287328	−	0.0354821i	−0.762577	−	0.646897i	$-0.776066\pi$
$47$	0.196982	−	0.243253i	0.0287328	−	0.0354821i	0.791310	+	0.611415i	$0.209400\pi$
$48$	−2.30799	−	1.17598i	−0.333130	−	0.169738i
$49$	−2.30911	−	6.60818i	−0.329873	−	0.944025i
$50$		0			0
$51$	−0.936759	+	1.62251i	−0.131172	+	0.227197i
$52$	10.8518	−	0.568717i	1.50487	−	0.0788669i
$53$	0.100384	+	0.261509i	0.0137888	+	0.0359210i	0.940302	−	0.340341i	$-0.110543\pi$
$53$	0.100384	+	0.261509i	0.0137888	+	0.0359210i	−0.926513	+	0.376262i	$0.877209\pi$
$54$	−0.963998	−	9.17183i	−0.131184	−	1.24813i
$55$		0			0
$56$	1.84232	+	0.913312i	0.246190	+	0.122046i
$57$	−2.92684	+	2.92684i	−0.387670	+	0.387670i
$58$	2.46860	+	0.947608i	0.324143	+	0.124427i
$59$	−6.72559	+	1.42957i	−0.875597	+	0.186114i	−0.623722	−	0.781646i	$-0.714380\pi$
$59$	−6.72559	+	1.42957i	−0.875597	+	0.186114i	−0.251875	+	0.967760i	$0.581047\pi$
$60$		0			0
$61$	1.10261	−	5.18739i	0.141175	−	0.664178i	−0.849461	−	0.527651i	$-0.823073\pi$
$61$	1.10261	−	5.18739i	0.141175	−	0.664178i	0.990636	−	0.136527i	$-0.0435939\pi$
$62$	−18.9778	+	9.66967i	−2.41018	+	1.22805i
$63$	−0.705699	−	6.07084i	−0.0889097	−	0.764854i
$64$	10.1249	−	3.28979i	1.26562	−	0.411224i
$65$		0			0
$66$	−0.379257	−	1.78426i	−0.0466833	−	0.219627i
$67$	7.72991	+	9.54564i	0.944359	+	1.16619i	0.985948	+	0.167051i	$0.0534245\pi$
$67$	7.72991	+	9.54564i	0.944359	+	1.16619i	−0.0415894	+	0.999135i	$0.513242\pi$
$68$	−1.38451	−	5.16706i	−0.167896	−	0.626598i
$69$	−4.18254	−	3.03879i	−0.503518	−	0.365827i
$70$		0			0
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	−0.682228	−	0.731140i	$-0.738989\pi$
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	0.484535	+	0.874772i	$0.338989\pi$
$72$	1.39524	+	1.12985i	0.164431	+	0.133154i
$73$	−0.0678338	−	1.29435i	−0.00793934	−	0.151492i	−0.999722	−	0.0235607i	$-0.992500\pi$
$73$	−0.0678338	−	1.29435i	−0.00793934	−	0.151492i	0.991783	−	0.127931i	$-0.0408336\pi$
$74$	−11.3826	+	6.57173i	−1.32320	+	0.763948i
$75$		0			0
$76$		−	11.8183i		−	1.35566i
$77$	−0.607621	−	2.71155i	−0.0692448	−	0.309010i
$78$	−7.85959	−	1.24484i	−0.889924	−	0.140950i
$79$	10.7765	−	1.13266i	1.21245	−	0.127434i	0.523363	−	0.852110i	$-0.324677\pi$
$79$	10.7765	−	1.13266i	1.21245	−	0.127434i	0.689090	+	0.724676i	$0.258011\pi$
$80$		0			0
$81$	0.341411	−	3.24831i	0.0379346	−	0.360923i
$82$	−11.3033	+	3.02870i	−1.24824	+	0.334464i
$83$	3.66064	−	0.579789i	0.401808	−	0.0636401i	0.0477399	−	0.998860i	$-0.484798\pi$
$83$	3.66064	−	0.579789i	0.401808	−	0.0636401i	0.354068	+	0.935220i	$0.384798\pi$
$84$	−4.08659	−	3.23545i	−0.445883	−	0.353016i
$85$		0			0
$86$	13.9080	+	2.95623i	1.49974	+	0.318779i
$87$	−0.881019	−	0.572141i	−0.0944552	−	0.0613399i
$88$	0.684593	+	0.444580i	0.0729778	+	0.0473924i
$89$	10.3731	+	2.20488i	1.09955	+	0.233716i	0.721738	−	0.692166i	$-0.243344\pi$
$89$	10.3731	+	2.20488i	1.09955	+	0.233716i	0.377811	+	0.925883i	$0.376677\pi$
$90$		0			0
$91$	−11.9931	−	1.76446i	−1.25722	−	0.184966i
$92$	14.5795	−	2.30917i	1.52002	−	0.240748i
$93$	8.17341	−	2.19006i	0.847543	−	0.227098i
$94$	0.0684094	−	0.650872i	0.00705589	−	0.0671323i
$95$		0			0
$96$	−6.67043	+	0.701090i	−0.680798	+	0.0715547i
$97$	4.89604	+	0.775456i	0.497117	+	0.0787356i	0.399958	−	0.916533i	$-0.369025\pi$
$97$	4.89604	+	0.775456i	0.497117	+	0.0787356i	0.0971587	+	0.995269i	$0.469025\pi$
$98$	−11.5743	−	8.95821i	−1.16918	−	0.904916i
$99$		−	2.42618i		−	0.243840i
$100$		0			0
$101$	13.1637	−	7.60006i	1.30984	−	0.756234i	0.327767	−	0.944758i	$-0.393704\pi$
$101$	13.1637	−	7.60006i	1.30984	−	0.756234i	0.982069	+	0.188524i	$0.0603704\pi$
$102$	0.205014	+	3.91190i	0.0202994	+	0.387336i
$103$	−5.27623	−	4.27261i	−0.519883	−	0.420993i	0.333132	−	0.942880i	$-0.391895\pi$
$103$	−5.27623	−	4.27261i	−0.519883	−	0.420993i	−0.853014	+	0.521888i	$0.825228\pi$
$104$	2.88088	−	2.09308i	0.282493	−	0.205243i
$105$		0			0
$106$	0.473825	+	0.344254i	0.0460220	+	0.0334369i
$107$	5.09063	+	18.9985i	0.492130	+	1.83665i	0.545546	+	0.838081i	$0.316322\pi$
$107$	5.09063	+	18.9985i	0.492130	+	1.83665i	−0.0534166	+	0.998572i	$0.517011\pi$
$108$	−6.58339	−	8.12981i	−0.633487	−	0.782292i
$109$	−3.97502	−	18.7010i	−0.380738	−	1.79123i	−0.583618	−	0.812029i	$-0.698363\pi$
$109$	−3.97502	−	18.7010i	−0.380738	−	1.79123i	0.202880	−	0.979204i	$-0.434970\pi$
$110$		0			0
$111$	4.96605	−	1.61357i	0.471356	−	0.153153i
$112$	−8.19534	+	0.952659i	−0.774387	+	0.0900178i
$113$	−7.77652	+	3.96233i	−0.731553	+	0.372745i	−0.779748	−	0.626093i	$-0.784653\pi$
$113$	−7.77652	+	3.96233i	−0.731553	+	0.372745i	0.0481952	+	0.998838i	$0.484653\pi$
$114$	−1.79937	+	8.46535i	−0.168526	+	0.792852i
$115$		0			0
$116$	2.93386	−	0.623612i	0.272402	−	0.0579009i
$117$	−9.88099	−	3.79296i	−0.913498	−	0.350659i
$118$	−10.1657	+	10.1657i	−0.935827	+	0.935827i
$119$	0.377871	+	5.95544i	0.0346393	+	0.545934i
$120$		0			0
$121$	1.03451	+	9.84268i	0.0940461	+	0.894789i
$122$	−3.97374	−	10.3520i	−0.359766	−	0.937222i
$123$	4.64257	−	0.243307i	0.418607	−	0.0219383i
$124$	−12.0801	+	20.9234i	−1.08483	+	1.87897i
$125$		0			0
$126$	−8.15074	−	9.84188i	−0.726126	−	0.876784i
$127$	−11.5760	−	5.89827i	−1.02720	−	0.523386i	−0.142625	−	0.989777i	$-0.545554\pi$
$127$	−11.5760	−	5.89827i	−1.02720	−	0.523386i	−0.884579	+	0.466390i	$0.845554\pi$
$128$	3.84528	−	4.74853i	0.339878	−	0.419715i
$129$	−5.16042	−	2.29757i	−0.454349	−	0.202289i
$130$		0			0
$131$	1.44095	+	3.23643i	0.125896	+	0.282768i	0.965487	−	0.260452i	$-0.0838716\pi$
$131$	1.44095	+	3.23643i	0.125896	+	0.282768i	−0.839590	+	0.543220i	$0.817205\pi$
$132$	−1.46310	−	1.46310i	−0.127347	−	0.127347i
$133$	−2.59900	+	12.9252i	−0.225362	+	1.12075i
$134$	24.4250	+	7.93617i	2.11000	+	0.685580i
$135$		0			0
$136$	−1.30270	−	1.17295i	−0.111705	−	0.100580i
$137$	4.12544	−	6.35261i	0.352460	−	0.542740i	−0.617323	−	0.786710i	$-0.711783\pi$
$137$	4.12544	−	6.35261i	0.352460	−	0.542740i	0.969783	+	0.243969i	$0.0784496\pi$
$138$	−10.7947	−	0.565729i	−0.918910	−	0.0481580i
$139$	−2.73221	−	8.40888i	−0.231743	−	0.713232i	−0.997537	−	0.0701455i	$-0.977654\pi$
$139$	−2.73221	−	8.40888i	−0.231743	−	0.713232i	0.765794	−	0.643086i	$-0.222346\pi$
$140$		0			0
$141$	−0.0803449	+	0.247276i	−0.00676626	+	0.0208244i
$142$	−1.54283	+	4.01920i	−0.129471	+	0.337284i
$143$	−4.64821	−	1.24548i	−0.388703	−	0.104153i
$144$	−7.16410	−	0.752977i	−0.597008	−	0.0627481i
$145$		0			0
$146$	−1.59291	−	2.19245i	−0.131830	−	0.181448i
$147$	3.75780	+	4.43715i	0.309938	+	0.365970i
$148$	−6.76851	+	13.2839i	−0.556368	+	1.09193i
$149$	−1.52475	−	0.880317i	−0.124913	−	0.0721183i	0.436242	−	0.899830i	$-0.356309\pi$
$149$	−1.52475	−	0.880317i	−0.124913	−	0.0721183i	−0.561154	+	0.827711i	$0.689643\pi$
$150$		0			0
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	0.709819	−	0.704385i	$-0.248777\pi$
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	−0.964924	+	0.262529i	$0.915444\pi$
$152$	−2.10929	−	3.24802i	−0.171086	−	0.263449i
$153$	−0.815050	+	5.14602i	−0.0658929	+	0.416031i
$154$	−4.15332	−	4.06289i	−0.334684	−	0.327397i
$155$		0			0
$156$	−8.24606	+	3.67138i	−0.660213	+	0.293946i
$157$	2.79709	−	10.4389i	0.223232	−	0.833115i	−0.759872	−	0.650072i	$-0.774739\pi$
$157$	2.79709	−	10.4389i	0.223232	−	0.833115i	0.983105	−	0.183043i	$-0.0585947\pi$
$158$	17.6073	−	14.2581i	1.40076	−	1.13431i
$159$	−0.155692	−	0.172913i	−0.0123472	−	0.0137129i
$160$		0			0
$161$	−16.4528	−	0.680794i	−1.29666	−	0.0536541i
$162$	−3.10038	−	6.08485i	−0.243589	−	0.478071i
$163$	−0.291986	+	5.57143i	−0.0228701	+	0.436388i	0.963066	+	0.269265i	$0.0867809\pi$
$163$	−0.291986	+	5.57143i	−0.0228701	+	0.436388i	−0.985936	+	0.167122i	$0.946552\pi$
$164$	−8.88192	+	9.86438i	−0.693562	+	0.770278i
$165$		0			0
$166$	5.75886	−	5.18530i	0.446975	−	0.402458i
$167$	−1.64024	−	10.3561i	−0.126926	−	0.801379i	−0.966223	−	0.257706i	$-0.917033\pi$
$167$	−1.64024	−	10.3561i	−0.126926	−	0.801379i	0.839297	−	0.543673i	$-0.182967\pi$
$168$	−1.70056	−	0.159836i	−0.131201	−	0.0123316i
$169$	−4.69799	+	6.46623i	−0.361384	+	0.497402i
$170$		0			0
$171$	−4.68190	+	10.5157i	−0.358034	+	0.804157i
$172$	15.0573	−	5.77997i	1.14811	−	0.440718i
$173$	11.5132	−	7.47674i	0.875330	−	0.568446i	−0.0269305	−	0.999637i	$-0.508573\pi$
$173$	11.5132	−	7.47674i	0.875330	−	0.568446i	0.902260	+	0.431191i	$0.141907\pi$
$174$	−2.19644			−0.166512
$175$		0			0
$176$	−3.27522			−0.246879
$177$	4.79002	−	3.11068i	0.360040	−	0.233813i
$178$	20.7006	−	7.94621i	1.55158	−	0.595594i
$179$	0.654680	−	1.47044i	0.0489331	−	0.109906i	−0.887425	−	0.460953i	$-0.847508\pi$
$179$	0.654680	−	1.47044i	0.0489331	−	0.109906i	0.936358	+	0.351047i	$0.114174\pi$
$180$		0			0
$181$	2.04450	−	2.81402i	0.151967	−	0.209164i	−0.726245	−	0.687436i	$-0.758736\pi$
$181$	2.04450	−	2.81402i	0.151967	−	0.209164i	0.878212	+	0.478271i	$0.158736\pi$
$182$	−23.0398	+	10.5633i	−1.70783	+	0.783005i
$183$	0.689125	+	4.35096i	0.0509416	+	0.321632i
$184$	3.59475	−	3.23672i	0.265008	−	0.238614i
$185$		0			0
$186$	11.8385	−	13.1480i	0.868040	−	0.964056i
$187$	−0.123978	+	2.36565i	−0.00906619	+	0.172993i
$188$	−0.337027	−	0.661452i	−0.0245802	−	0.0482414i
$189$	5.41210	+	10.3390i	0.393672	+	0.752050i
$190$		0			0
$191$	−1.98374	−	2.20317i	−0.143538	−	0.159415i	0.667089	−	0.744978i	$-0.267540\pi$
$191$	−1.98374	−	2.20317i	−0.143538	−	0.159415i	−0.810627	+	0.585563i	$0.800874\pi$
$192$	−6.87242	+	5.56517i	−0.495974	+	0.401632i
$193$	4.41207	−	16.4661i	0.317588	−	1.18525i	−0.603968	−	0.797009i	$-0.706414\pi$
$193$	4.41207	−	16.4661i	0.317588	−	1.18525i	0.921556	−	0.388246i	$-0.126919\pi$
$194$	9.46849	−	4.21564i	0.679798	−	0.302665i
$195$		0			0
$196$	−16.5452	−	1.37159i	−1.18180	−	0.0979705i
$197$	3.02785	−	19.1171i	0.215725	−	1.36204i	−0.607499	−	0.794320i	$-0.707827\pi$
$197$	3.02785	−	19.1171i	0.215725	−	1.36204i	0.823225	−	0.567716i	$-0.192173\pi$
$198$	−2.76285	−	4.25441i	−0.196347	−	0.302348i
$199$	−0.0959424	−	0.166177i	−0.00680118	−	0.0117800i	0.862605	−	0.505878i	$-0.168832\pi$
$199$	−0.0959424	−	0.166177i	−0.00680118	−	0.0117800i	−0.869406	+	0.494098i	$0.835498\pi$
$200$		0			0
$201$	−8.83596	−	5.10144i	−0.623240	−	0.359828i
$202$	14.4284	−	28.3174i	1.01518	−	1.99241i
$203$	−3.34577	+	0.0368211i	−0.234827	+	0.00258434i
$204$	2.61179	+	3.59482i	0.182862	+	0.251688i
$205$		0			0
$206$	−14.1176	−	1.48382i	−0.983621	−	0.103383i
$207$	−13.8874	−	3.72111i	−0.965239	−	0.258635i
$208$	−5.12030	+	13.3388i	−0.355029	+	0.924883i
$209$	−1.61728	+	4.97747i	−0.111869	+	0.344299i
$210$		0			0
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	0.995650	−	0.0931759i	$-0.0297019\pi$
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	−0.860265	+	0.509847i	$0.829702\pi$
$212$	0.663440	+	0.0347694i	0.0455652	+	0.00238797i
$213$	0.931518	−	1.43441i	0.0638266	−	0.0982843i
$214$	30.5615	+	27.5177i	2.08914	+	1.88107i
$215$		0			0
$216$	−3.26028	−	1.05933i	−0.221834	−	0.0720783i
$217$	17.8128	−	20.2263i	1.20921	−	1.37305i
$218$	−28.2665	−	28.2665i	−1.91445	−	1.91445i
$219$	0.437905	+	0.983550i	0.0295908	+	0.0664621i
$220$		0			0
$221$	9.44064	+	4.20325i	0.635046	+	0.282741i
$222$	6.87072	−	8.48463i	0.461132	−	0.569451i
$223$	11.8807	+	6.05349i	0.795587	+	0.405372i	0.804027	−	0.594592i	$-0.202687\pi$
$223$	11.8807	+	6.05349i	0.795587	+	0.405372i	−0.00843996	+	0.999964i	$0.502687\pi$
$224$	−16.4534	+	13.6262i	−1.09934	+	0.910441i
$225$		0			0
$226$	−9.12431	+	15.8038i	−0.606940	+	1.05125i
$227$	4.84563	−	0.253949i	0.321616	−	0.0168552i	0.109155	−	0.994025i	$-0.465185\pi$
$227$	4.84563	−	0.253949i	0.321616	−	0.0168552i	0.212461	+	0.977170i	$0.431852\pi$
$228$	3.51808	+	9.16491i	0.232991	+	0.606961i
$229$	0.698945	+	6.65002i	0.0461876	+	0.439446i	0.993040	+	0.117777i	$0.0375769\pi$
$229$	0.698945	+	6.65002i	0.0461876	+	0.439446i	−0.946852	+	0.321668i	$0.895756\pi$
$230$		0			0
$231$	1.27837	+	1.92189i	0.0841108	+	0.126451i
$232$	0.695011	−	0.695011i	0.0456297	−	0.0456297i
$233$	−8.06082	−	3.09426i	−0.528082	−	0.202712i	0.0796953	−	0.996819i	$-0.474605\pi$
$233$	−8.06082	−	3.09426i	−0.528082	−	0.202712i	−0.607777	+	0.794108i	$0.707939\pi$
$234$	−21.6461	+	4.60101i	−1.41505	+	0.300778i
$235$		0			0
$236$	−3.39053	+	15.9512i	−0.220704	+	1.03833i
$237$	−8.01983	+	4.08631i	−0.520944	+	0.265434i
$238$	7.44447	+	10.0128i	0.482553	+	0.649036i
$239$	18.2461	−	5.92852i	1.18024	−	0.383484i	0.347785	−	0.937574i	$-0.386934\pi$
$239$	18.2461	−	5.92852i	1.18024	−	0.383484i	0.832457	+	0.554090i	$0.186934\pi$
$240$		0			0
$241$	−5.39578	−	25.3851i	−0.347572	−	1.63520i	−0.710725	−	0.703470i	$-0.751633\pi$
$241$	−5.39578	−	25.3851i	−0.347572	−	1.63520i	0.363152	−	0.931730i	$-0.381700\pi$
$242$	13.0226	+	16.0815i	0.837122	+	1.03376i
$243$	4.12698	+	15.4021i	0.264746	+	0.988046i
$244$	−10.1757	−	7.39308i	−0.651433	−	0.473294i
$245$		0			0
$246$	7.86390	−	5.71346i	0.501384	−	0.364277i
$247$	17.7432	+	14.3681i	1.12897	+	0.914222i
$248$	0.414355	+	7.90636i	0.0263115	+	0.502054i
$249$	−2.66617	+	1.53932i	−0.168962	+	0.0975502i
$250$		0			0
$251$			15.4133i			0.972880i	0.873714	+	0.486440i	$0.161705\pi$
$251$			15.4133i			0.972880i	−0.873714	+	0.486440i	$0.838295\pi$
$252$	−13.8343	−	4.32730i	−0.871476	−	0.272594i
$253$	−6.45639	−	1.02259i	−0.405910	−	0.0642898i
$254$	−27.0158	+	2.83947i	−1.69512	+	0.178164i
$255$		0			0
$256$	−0.890203	+	8.46971i	−0.0556377	+	0.529357i
$257$	29.5275	−	7.91188i	1.84188	−	0.493529i	0.842871	−	0.538115i	$-0.180863\pi$
$257$	29.5275	−	7.91188i	1.84188	−	0.493529i	0.999006	+	0.0445856i	$0.0141967\pi$
$258$	−11.6654	+	1.84762i	−0.726257	+	0.115028i
$259$	10.3237	−	13.0395i	0.641484	−	0.810238i
$260$		0			0
$261$	−2.85754	−	0.607389i	−0.176877	−	0.0375964i
$262$	6.21231	+	4.03432i	0.383798	+	0.249241i
$263$	0.341935	+	0.222055i	0.0210846	+	0.0136925i	0.555138	−	0.831758i	$-0.312665\pi$
$263$	0.341935	+	0.222055i	0.0210846	+	0.0136925i	−0.534054	+	0.845451i	$0.679332\pi$
$264$	−0.663232	−	0.140974i	−0.0408191	−	0.00867637i
$265$		0			0
$266$	10.1613	+	25.6245i	0.623027	+	1.57114i
$267$	−8.70053	+	1.37803i	−0.532464	+	0.0843340i
$268$	28.1390	−	7.53982i	1.71886	−	0.460568i
$269$	−2.00211	+	19.0488i	−0.122071	+	1.16142i	0.746335	+	0.665570i	$0.231812\pi$
$269$	−2.00211	+	19.0488i	−0.122071	+	1.16142i	−0.868406	+	0.495854i	$0.834855\pi$
$270$		0			0
$271$	−19.2007	+	2.01808i	−1.16636	+	0.122589i	−0.667851	−	0.744295i	$-0.732786\pi$
$271$	−19.2007	+	2.01808i	−1.16636	+	0.122589i	−0.498509	+	0.866884i	$0.666119\pi$
$272$	6.94688	+	1.10028i	0.421216	+	0.0667141i
$273$	9.82572	−	2.20181i	0.594680	−	0.133259i
$274$		−	15.8375i		−	0.956779i
$275$		0			0
$276$	−10.6188	+	6.13076i	−0.639176	+	0.369028i
$277$	−0.400242	−	7.63707i	−0.0240482	−	0.458867i	−0.983940	−	0.178497i	$-0.942876\pi$
$277$	−0.400242	−	7.63707i	−0.0240482	−	0.458867i	0.959892	−	0.280369i	$-0.0904570\pi$
$278$	−14.3668	−	11.6340i	−0.861664	−	0.697761i
$279$	19.0376	−	13.8316i	1.13975	−	0.828076i
$280$		0			0
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	0.939329	−	0.343019i	$-0.111449\pi$
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	−0.0359618	+	0.999353i	$0.511449\pi$
$282$	0.140701	+	0.525104i	0.00837864	+	0.0312695i
$283$	1.79337	+	2.21463i	0.106605	+	0.131646i	0.827656	−	0.561236i	$-0.189674\pi$
$283$	1.79337	+	2.21463i	0.106605	+	0.131646i	−0.721051	+	0.692882i	$0.756341\pi$
$284$	1.01532	+	4.77671i	0.0602482	+	0.283446i
$285$		0			0
$286$	−9.56917	+	3.10921i	−0.565837	+	0.183852i
$287$	11.8831	−	8.83496i	0.701434	−	0.521511i
$288$	−16.6194	+	8.46799i	−0.979305	+	0.498981i
$289$	−2.47682	+	11.6525i	−0.145695	+	0.685443i
$290$		0			0
$291$	−4.02763	+	0.856099i	−0.236104	+	0.0501854i
$292$	−2.86985	−	1.10163i	−0.167945	−	0.0644682i
$293$	0.584948	−	0.584948i	0.0341730	−	0.0341730i	−0.689814	−	0.723987i	$-0.742308\pi$
$293$	0.584948	−	0.584948i	0.0341730	−	0.0341730i	0.723987	+	0.689814i	$0.242308\pi$
$294$	11.6423	+	3.50150i	0.678995	+	0.204212i
$295$		0			0
$296$	0.510683	+	4.85883i	0.0296829	+	0.282414i
$297$	1.66017	+	4.32490i	0.0963330	+	0.250956i
$298$	−3.67620	+	0.192661i	−0.212957	+	0.0111606i
$299$	−14.2582	+	24.6960i	−0.824575	+	1.42821i
$300$		0			0
$301$	−17.7386	+	3.00998i	−1.02244	+	0.173492i
$302$	−11.6801	−	5.95129i	−0.672112	−	0.342458i
$303$	−7.94583	+	9.81228i	−0.456476	+	0.563701i
$304$	14.1957	+	6.32033i	0.814179	+	0.362496i
$305$		0			0
$306$	4.43089	+	9.95194i	0.253297	+	0.568915i
$307$	−10.4006	−	10.4006i	−0.593593	−	0.593593i	0.345007	−	0.938600i	$-0.387877\pi$
$307$	−10.4006	−	10.4006i	−0.593593	−	0.593593i	−0.938600	+	0.345007i	$0.887877\pi$
$308$	−6.46118	−	1.29922i	−0.368160	−	0.0740299i
$309$	5.36350	+	1.74271i	0.305119	+	0.0991391i
$310$		0			0
$311$	8.83036	+	7.95089i	0.500724	+	0.450854i	0.880377	−	0.474275i	$-0.157290\pi$
$311$	8.83036	+	7.95089i	0.500724	+	0.450854i	−0.379653	+	0.925129i	$0.623957\pi$
$312$	−1.61100	+	2.48073i	−0.0912050	+	0.140443i
$313$	10.0595	+	0.527196i	0.568597	+	0.0297989i	0.334469	−	0.942407i	$-0.391443\pi$
$313$	10.0595	+	0.527196i	0.568597	+	0.0297989i	0.234128	+	0.972206i	$0.424777\pi$
$314$	−6.98263	−	21.4903i	−0.394053	−	1.21277i
$315$		0			0
$316$	7.94161	−	24.4418i	0.446750	−	1.37496i
$317$	−6.77528	+	17.6502i	−0.380538	+	0.991335i	0.600861	+	0.799354i	$0.294825\pi$
$317$	−6.77528	+	17.6502i	−0.380538	+	0.991335i	−0.981399	+	0.191981i	$0.938509\pi$
$318$	−0.469921	−	0.125915i	−0.0263519	−	0.00706096i
$319$	−1.32098	−	0.138841i	−0.0739606	−	0.00777358i
$320$		0			0
$321$	−9.60316	−	13.2176i	−0.535996	−	0.737736i
$322$	−29.6260	+	17.5421i	−1.65099	+	0.977581i
$323$	5.10245	−	10.0141i	0.283908	−	0.557200i
$324$	−6.70866	−	3.87325i	−0.372703	−	0.215180i
$325$		0			0
$326$	5.83254	+	10.1023i	0.323035	+	0.559512i
$327$	8.64948	+	13.3190i	0.478317	+	0.736544i
$328$	−0.680455	+	4.29622i	−0.0375719	+	0.237219i
$329$	0.223129	+	0.797516i	0.0123015	+	0.0439685i
$330$		0			0
$331$	28.4245	−	12.6554i	1.56235	−	0.695605i	0.570302	−	0.821435i	$-0.306826\pi$
$331$	28.4245	−	12.6554i	1.56235	−	0.695605i	0.992052	+	0.125830i	$0.0401594\pi$
$332$	2.27508	−	8.49070i	0.124861	−	0.465988i
$333$	11.2850	−	9.13840i	0.618414	−	0.500781i
$334$	−14.6694	−	16.2920i	−0.802675	−	0.891461i
$335$		0			0
$336$	6.07176	−	3.17836i	0.331241	−	0.173394i
$337$	15.8054	+	31.0198i	0.860974	+	1.68976i	0.713460	+	0.700696i	$0.247127\pi$
$337$	15.8054	+	31.0198i	0.860974	+	1.68976i	0.147514	+	0.989060i	$0.452873\pi$
$338$	−0.874620	+	16.6887i	−0.0475730	+	0.907748i
$339$	4.85105	−	5.38763i	0.263473	−	0.292616i
$340$		0			0
$341$	7.95098	−	7.15909i	0.430570	−	0.387687i
$342$	3.76502	+	23.7714i	0.203589	+	1.28541i
$343$	17.7931	+	5.13855i	0.960738	+	0.277456i
$344$	3.10660	−	4.27587i	0.167497	−	0.230540i
$345$		0			0
$346$	11.6746	−	26.2216i	0.627631	−	1.40968i
$347$	−25.1500	+	9.65416i	−1.35012	+	0.518263i	−0.922605	−	0.385746i	$-0.873944\pi$
$347$	−25.1500	+	9.65416i	−1.35012	+	0.518263i	−0.427515	+	0.904008i	$0.640611\pi$
$348$	−2.08952	+	1.35695i	−0.112010	+	0.0727403i
$349$	28.9278			1.54847			0.774236	−	0.632897i	$-0.218134\pi$
$349$	28.9278			1.54847			0.774236	+	0.632897i	$0.218134\pi$
$350$		0			0
$351$	20.2092			1.07869
$352$	−7.11244	+	4.61887i	−0.379094	+	0.246187i
$353$	−10.8927	+	4.18132i	−0.579760	+	0.222549i	−0.630535	−	0.776161i	$-0.717164\pi$
$353$	−10.8927	+	4.18132i	−0.579760	+	0.222549i	0.0507745	+	0.998710i	$0.483831\pi$
$354$	4.85719	−	10.9094i	0.258157	−	0.579830i
$355$		0			0
$356$	14.7838	−	20.3482i	0.783540	−	1.07845i
$357$	−2.06585	−	4.50586i	−0.109336	−	0.238475i
$358$	−0.526471	−	3.32401i	−0.0278248	−	0.175679i
$359$	−3.30837	+	2.97887i	−0.174609	+	0.157219i	−0.751802	−	0.659389i	$-0.770815\pi$
$359$	−3.30837	+	2.97887i	−0.174609	+	0.157219i	0.577192	+	0.816608i	$0.304148\pi$
$360$		0			0
$361$	3.90148	−	4.33303i	0.205341	−	0.228054i
$362$	0.380623	−	7.26272i	0.0200051	−	0.381720i
$363$	−3.73221	−	7.32488i	−0.195890	−	0.384456i
$364$	−15.3923	+	24.2830i	−0.806778	+	1.27278i
$365$		0			0
$366$	6.16314	+	6.84486i	0.322152	+	0.357787i
$367$	−19.9593	+	16.1627i	−1.04187	+	0.843688i	−0.987937	−	0.154857i	$-0.950508\pi$
$367$	−19.9593	+	16.1627i	−1.04187	+	0.843688i	−0.0539306	+	0.998545i	$0.517175\pi$
$368$	−5.02332	+	18.7473i	−0.261858	+	0.977269i
$369$	11.8108	−	5.25850i	0.614845	−	0.273747i
$370$		0			0
$371$	−0.717927	−	0.183925i	−0.0372729	−	0.00954889i
$372$	3.13945	−	19.8217i	0.162773	−	1.02771i
$373$	−19.5053	−	30.0355i	−1.00994	−	1.55518i	−0.819175	−	0.573544i	$-0.805568\pi$
$373$	−19.5053	−	30.0355i	−1.00994	−	1.55518i	−0.190770	−	0.981635i	$-0.561098\pi$
$374$	2.47652	+	4.28945i	0.128058	+	0.221802i
$375$		0			0
$376$	−0.210678	−	0.121635i	−0.0108649	−	0.00627285i
$377$	−2.63060	+	5.16284i	−0.135483	+	0.265900i
$378$	21.2640	+	11.9667i	1.09370	+	0.615503i
$379$	13.3436	+	18.3659i	0.685416	+	0.943394i	0.999983	−	0.00584095i	$-0.00185924\pi$
$379$	13.3436	+	18.3659i	0.685416	+	0.943394i	−0.314567	+	0.949235i	$0.601859\pi$
$380$		0			0
$381$	10.7328	+	1.12806i	0.549857	+	0.0577923i
$382$	−5.98747	−	1.60434i	−0.306346	−	0.0820850i
$383$	−7.79546	+	20.3079i	−0.398330	+	1.03768i	0.576964	+	0.816770i	$0.304237\pi$
$383$	−7.79546	+	20.3079i	−0.398330	+	1.03768i	−0.975293	+	0.220914i	$0.929096\pi$
$384$	−1.56841	+	4.82707i	−0.0800375	+	0.246330i
$385$		0			0
$386$	−11.0142	−	33.8984i	−0.560610	−	1.72538i
$387$	−15.6875	−	0.822146i	−0.797439	−	0.0417920i
$388$	6.40318	−	9.86003i	0.325072	−	0.500567i
$389$	−9.65968	−	8.69762i	−0.489765	−	0.440987i	0.386876	−	0.922132i	$-0.373554\pi$
$389$	−9.65968	−	8.69762i	−0.489765	−	0.440987i	−0.876641	+	0.481145i	$0.840221\pi$
$390$		0			0
$391$	13.3507	+	4.33792i	0.675176	+	0.219378i
$392$	−4.79190	+	2.57597i	−0.242028	+	0.130106i
$393$	−2.08085	−	2.08085i	−0.104965	−	0.104965i
$394$	−16.4604	−	36.9707i	−0.829264	−	1.86256i
$395$		0			0
$396$	−5.25672	−	2.34044i	−0.264160	−	0.117612i
$397$	−3.00714	+	3.71351i	−0.150924	+	0.186376i	−0.847001	−	0.531592i	$-0.821594\pi$
$397$	−3.00714	+	3.71351i	−0.150924	+	0.186376i	0.696077	+	0.717968i	$0.254927\pi$
$398$	−0.357476	−	0.182143i	−0.0179187	−	0.00913002i
$399$	−1.83208	−	10.7969i	−0.0917187	−	0.540522i
$400$		0			0
$401$	7.58351	−	13.1350i	0.378702	−	0.655932i	−0.612171	−	0.790725i	$-0.709704\pi$
$401$	7.58351	−	13.1350i	0.378702	−	0.655932i	0.990874	+	0.134793i	$0.0430370\pi$
$402$	−21.3036	+	1.11647i	−1.06253	+	0.0556847i
$403$	−16.7264	−	43.5737i	−0.833201	−	2.17056i
$404$	−3.76828	−	35.8528i	−0.187479	−	1.78374i
$405$		0			0
$406$	−5.82504	+	3.87462i	−0.289092	+	0.192294i
$407$	4.66850	−	4.66850i	0.231409	−	0.231409i
$408$	1.35938	+	0.521819i	0.0672996	+	0.0258339i
$409$	−10.0531	+	2.13685i	−0.497094	+	0.105661i	−0.449634	−	0.893213i	$-0.648446\pi$
$409$	−10.0531	+	2.13685i	−0.497094	+	0.105661i	−0.0474592	+	0.998873i	$0.515112\pi$
$410$		0			0
$411$	−1.30816	+	6.15440i	−0.0645267	+	0.303574i
$412$	−14.3471	+	7.31021i	−0.706831	+	0.360148i
$413$	7.21593	−	16.6994i	0.355073	−	0.821725i
$414$	−28.5896	+	9.28933i	−1.40510	+	0.456546i
$415$		0			0
$416$	7.69187	+	36.1874i	0.377125	+	1.77423i
$417$	4.62194	+	5.70761i	0.226337	+	0.279503i
$418$	2.83220	+	10.5699i	0.138528	+	0.516992i
$419$	−14.4852	−	10.5241i	−0.707648	−	0.514137i	0.174766	−	0.984610i	$-0.444083\pi$
$419$	−14.4852	−	10.5241i	−0.707648	−	0.514137i	−0.882414	+	0.470473i	$0.844083\pi$
$420$		0			0
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	−0.205227	−	0.978714i	$-0.565793\pi$
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	0.867394	+	0.497621i	$0.165793\pi$
$422$	10.3409	+	8.37387i	0.503386	+	0.407634i
$423$	0.0378417	+	0.722062i	0.00183992	+	0.0351079i
$424$	0.188538	−	0.108852i	0.00915621	−	0.00528634i
$425$		0			0
$426$		−	3.57609i		−	0.173262i
$427$	9.50286	+	10.3232i	0.459876	+	0.499577i
$428$	46.0741	+	7.29743i	2.22708	+	0.352734i
$429$	3.97536	−	0.417827i	0.191932	−	0.0201729i
$430$		0			0
$431$	0.935006	−	8.89599i	0.0450377	−	0.428505i	−0.948650	−	0.316326i	$-0.897551\pi$
$431$	0.935006	−	8.89599i	0.0450377	−	0.428505i	0.993688	−	0.112178i	$-0.0357828\pi$
$432$	13.2859	−	3.55996i	0.639220	−	0.171278i
$433$	−17.4040	+	2.75652i	−0.836382	+	0.132470i	−0.559912	−	0.828552i	$-0.689165\pi$
$433$	−17.4040	+	2.75652i	−0.836382	+	0.132470i	−0.276471	+	0.961022i	$0.589165\pi$
$434$	8.20245	−	55.7524i	0.393730	−	2.67620i
$435$		0			0
$436$	−44.3534	−	9.42761i	−2.12414	−	0.451501i
$437$	26.0104	+	16.8914i	1.24425	+	0.808024i
$438$	1.88792	+	1.22603i	0.0902083	+	0.0585819i
$439$	26.8046	+	5.69749i	1.27931	+	0.271926i	0.796950	−	0.604045i	$-0.206445\pi$
$439$	26.8046	+	5.69749i	1.27931	+	0.271926i	0.482363	+	0.875972i	$0.339779\pi$
$440$		0			0
$441$	14.1783	+	7.77490i	0.675155	+	0.370233i
$442$	21.3411	−	3.38010i	1.01509	−	0.160775i
$443$	−10.7062	+	2.86872i	−0.508667	+	0.136297i	−0.504019	−	0.863692i	$-0.668146\pi$
$443$	−10.7062	+	2.86872i	−0.508667	+	0.136297i	−0.00464732	+	0.999989i	$0.501479\pi$
$444$	1.29450	−	12.3163i	0.0614341	−	0.584506i
$445$		0			0
$446$	27.7268	−	2.91420i	1.31290	−	0.137992i
$447$	1.44447	+	0.228782i	0.0683212	+	0.0108210i
$448$	−8.40866	+	26.8823i	−0.397272	+	1.27007i
$449$		−	40.1154i		−	1.89316i	−0.322465	−	0.946581i	$-0.604511\pi$
$449$		−	40.1154i		−	1.89316i	0.322465	−	0.946581i	$-0.395489\pi$
$450$		0			0
$451$	5.09064	−	2.93909i	0.239709	−	0.138396i
$452$	1.08334	+	20.6714i	0.0509562	+	0.972303i
$453$	4.04726	+	3.27741i	0.190157	+	0.153986i
$454$	8.20786	−	5.96336i	0.385214	−	0.279874i
$455$		0			0
$456$	2.60259	+	1.89089i	0.121877	+	0.0885490i
$457$	−8.79489	−	32.8230i	−0.411408	−	1.53539i	−0.791924	−	0.610620i	$-0.790920\pi$
$457$	−8.79489	−	32.8230i	−0.411408	−	1.53539i	0.380516	−	0.924774i	$-0.375746\pi$
$458$	8.79845	+	10.8652i	0.411125	+	0.507697i
$459$	−2.06839	−	9.73101i	−0.0965441	−	0.454204i
$460$		0			0
$461$	−30.0506	+	9.76402i	−1.39959	+	0.454756i	−0.909060	−	0.416666i	$-0.863198\pi$
$461$	−30.0506	+	9.76402i	−1.39959	+	0.454756i	−0.490535	+	0.871422i	$0.663198\pi$
$462$	4.43027	+	1.91435i	0.206115	+	0.0890634i
$463$	16.9684	−	8.64582i	0.788587	−	0.401805i	−0.0128250	−	0.999918i	$-0.504082\pi$
$463$	16.9684	−	8.64582i	0.788587	−	0.401805i	0.801412	+	0.598113i	$0.204082\pi$
$464$	−0.819946	+	3.85754i	−0.0380650	+	0.179082i
$465$		0			0
$466$	−17.6587	+	3.75346i	−0.818021	+	0.173876i
$467$	5.56287	+	2.13538i	0.257419	+	0.0988138i	0.483655	−	0.875259i	$-0.339309\pi$
$467$	5.56287	+	2.13538i	0.257419	+	0.0988138i	−0.226236	+	0.974072i	$0.572642\pi$
$468$	−17.7499	+	17.7499i	−0.820489	+	0.820489i
$469$	−32.4324	+	2.05782i	−1.49759	+	0.0950215i
$470$		0			0
$471$	0.938352	+	8.92782i	0.0432370	+	0.411372i
$472$	1.91509	+	4.98897i	0.0881489	+	0.229636i
$473$	−7.13258	+	0.373803i	−0.327956	+	0.0171875i
$474$	−9.40980	+	16.2982i	−0.432206	+	0.748603i
$475$		0			0
$476$	13.2680	+	4.92627i	0.608137	+	0.225795i
$477$	−0.576541	−	0.293762i	−0.0263980	−	0.0134505i
$478$	25.2442	−	31.1740i	1.15464	−	1.42586i
$479$	−19.0483	−	8.48083i	−0.870338	−	0.387499i	−0.0775436	−	0.996989i	$-0.524708\pi$
$479$	−19.0483	−	8.48083i	−0.870338	−	0.387499i	−0.792794	+	0.609490i	$0.791374\pi$
$480$		0			0
$481$	−11.7147	−	26.3117i	−0.534145	−	1.19971i
$482$	−38.3695	−	38.3695i	−1.74768	−	1.74768i
$483$	12.9615	−	4.36972i	0.589769	−	0.198829i
$484$	22.3238	+	7.25343i	1.01472	+	0.329701i
$485$		0			0
$486$	24.7763	+	22.3086i	1.12387	+	1.01194i
$487$	15.9853	−	24.6153i	0.724365	−	1.11542i	−0.264176	−	0.964474i	$-0.585100\pi$
$487$	15.9853	−	24.6153i	0.724365	−	1.11542i	0.988541	−	0.150950i	$-0.0482333\pi$
$488$	−4.11607	−	0.215714i	−0.186326	−	0.00976491i
$489$	−1.43207	−	4.40746i	−0.0647605	−	0.199312i
$490$		0			0
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	0.743476	+	0.668762i	$0.233176\pi$
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	−0.994574	+	0.104036i	$0.966824\pi$
$492$	3.95135	−	10.2936i	0.178141	−	0.464072i
$493$	2.75521	+	0.738256i	0.124088	+	0.0332494i
$494$	47.4754	+	4.98986i	2.13602	+	0.224505i
$495$		0			0
$496$	−18.6720	−	25.6998i	−0.838396	−	1.15395i
$497$	−0.0599495	−	5.44735i	−0.00268910	−	0.244347i
$498$	−2.92234	+	5.73541i	−0.130953	+	0.257010i
$499$	4.60639	+	2.65950i	0.206210	+	0.119056i	0.599549	−	0.800338i	$-0.295347\pi$
$499$	4.60639	+	2.65950i	0.206210	+	0.119056i	−0.393339	+	0.919394i	$0.628680\pi$
$500$		0			0
$501$	4.35478	+	7.54270i	0.194557	+	0.336983i
$502$	17.5522	+	27.0280i	0.783391	+	1.20632i
$503$	−4.13001	+	26.0759i	−0.184148	+	1.16267i	0.706412	+	0.707801i	$0.250313\pi$
$503$	−4.13001	+	26.0759i	−0.184148	+	1.16267i	−0.890560	+	0.454865i	$0.849687\pi$
$504$	−4.57437	+	1.27982i	−0.203759	+	0.0570075i
$505$		0			0
$506$	−12.4861	+	5.55916i	−0.555073	+	0.247135i
$507$	1.71834	−	6.41294i	0.0763143	−	0.284809i
$508$	−23.9465	+	19.3915i	−1.06245	+	0.860359i
$509$	−2.99499	−	3.32627i	−0.132750	−	0.147434i	0.673104	−	0.739548i	$-0.264960\pi$
$509$	−2.99499	−	3.32627i	−0.132750	−	0.147434i	−0.805855	+	0.592113i	$0.798294\pi$
$510$		0			0
$511$	2.89636	+	1.83592i	0.128127	+	0.0812164i
$512$	13.6320	+	26.7543i	0.602454	+	1.18238i
$513$	1.15030	−	21.9490i	0.0507869	−	0.969072i
$514$	42.7681	−	47.4988i	1.88642	−	2.09508i
$515$		0			0
$516$	−9.95612	+	8.96453i	−0.438294	+	0.394641i
$517$	0.0514276	+	0.324701i	0.00226178	+	0.0142803i
$518$	3.25411	−	34.6217i	0.142977	−	1.52119i
$519$	−6.70259	+	9.22532i	−0.294211	+	0.404947i
$520$		0			0
$521$	−10.4542	+	23.4805i	−0.458006	+	1.02870i	0.525987	+	0.850492i	$0.323696\pi$
$521$	−10.4542	+	23.4805i	−0.458006	+	1.02870i	−0.983993	+	0.178206i	$0.942971\pi$
$522$	−5.70250	+	2.18899i	−0.249592	+	0.0958093i
$523$	18.4501	−	11.9816i	0.806766	−	0.523920i	−0.0741198	−	0.997249i	$-0.523615\pi$
$523$	18.4501	−	11.9816i	0.806766	−	0.523920i	0.880885	+	0.473330i	$0.156948\pi$
$524$	8.40229			0.367056
$525$		0			0
$526$	0.852467			0.0371693
$527$	−19.2694	+	12.5137i	−0.839388	+	0.545105i
$528$	2.53988	−	0.974967i	0.110534	−	0.0424300i
$529$	−6.40073	+	14.3763i	−0.278292	+	0.625055i
$530$		0			0
$531$	9.33596	−	12.8499i	0.405146	−	0.557636i
$532$	25.4974	+	18.0996i	1.10545	+	0.784717i
$533$	−4.01144	−	25.3273i	−0.173755	−	1.09705i
$534$	−13.6875	+	12.3243i	−0.592317	+	0.533325i
$535$		0			0
$536$	6.38773	−	7.09429i	0.275908	−	0.306427i
$537$	−0.0699740	+	1.33518i	−0.00301960	+	0.0576174i
$538$	18.1813	+	35.6828i	0.783852	+	1.53840i
$539$	6.78058	+	2.84179i	0.292060	+	0.122405i
$540$		0			0
$541$	5.42224	+	6.02201i	0.233120	+	0.258906i	0.848343	−	0.529447i	$-0.177601\pi$
$541$	5.42224	+	6.02201i	0.233120	+	0.258906i	−0.615223	+	0.788353i	$0.710934\pi$
$542$	−31.3712	+	25.4039i	−1.34751	+	1.09119i
$543$	−0.747801	+	2.79083i	−0.0320912	+	0.119766i
$544$	16.6374	−	7.40747i	0.713324	−	0.317592i
$545$		0			0
$546$	14.7225	−	15.0502i	0.630065	−	0.644088i
$547$	3.02255	−	19.0836i	0.129235	−	0.815958i	−0.834872	−	0.550444i	$-0.814458\pi$
$547$	3.02255	−	19.0836i	0.129235	−	0.815958i	0.964107	−	0.265514i	$-0.0855416\pi$
$548$	−9.78435	−	15.0666i	−0.417967	−	0.643612i
$549$	6.12533	+	10.6094i	0.261423	+	0.452797i
$550$		0			0
$551$	5.45756	+	3.15092i	0.232500	+	0.134234i
$552$	−1.82416	+	3.58011i	−0.0776412	+	0.152379i
$553$	−14.0604	+	24.9844i	−0.597910	+	1.06244i
$554$	−9.39867	−	12.9362i	−0.399311	−	0.549605i
$555$		0			0
$556$	−20.8549	−	2.19194i	−0.884445	−	0.0929589i
$557$	−17.9964	−	4.82211i	−0.762531	−	0.204320i	−0.143462	−	0.989656i	$-0.545823\pi$
$557$	−17.9964	−	4.82211i	−0.762531	−	0.204320i	−0.619069	+	0.785336i	$0.712490\pi$
$558$	17.6323	−	45.9337i	0.746434	−	1.94453i
$559$	−9.62832	+	29.6329i	−0.407235	+	1.25334i
$560$		0			0
$561$	−0.608062	−	1.87142i	−0.0256724	−	0.0790116i
$562$	39.0832	+	2.04826i	1.64862	+	0.0864007i
$563$	−11.7754	+	18.1325i	−0.496273	+	0.764193i	−0.994709	−	0.102734i	$-0.967241\pi$
$563$	−11.7754	+	18.1325i	−0.496273	+	0.764193i	0.498436	+	0.866926i	$0.333908\pi$
$564$	0.458259	+	0.412619i	0.0192962	+	0.0173744i
$565$		0			0
$566$	5.66670	+	1.84122i	0.238189	+	0.0773923i
$567$	6.48517	+	5.71131i	0.272352	+	0.239852i
$568$	1.13157	+	1.13157i	0.0474795	+	0.0474795i
$569$	16.3273	+	36.6716i	0.684474	+	1.53735i	0.835898	+	0.548885i	$0.184947\pi$
$569$	16.3273	+	36.6716i	0.684474	+	1.53735i	−0.151424	+	0.988469i	$0.548386\pi$
$570$		0			0
$571$	30.4188	+	13.5433i	1.27299	+	0.566770i	0.928260	−	0.371932i	$-0.121305\pi$
$571$	30.4188	+	13.5433i	1.27299	+	0.566770i	0.344727	+	0.938703i	$0.387971\pi$
$572$	−7.18251	+	8.86966i	−0.300316	+	0.370859i
$573$	2.19419	+	1.11800i	0.0916638	+	0.0467050i
$574$	10.7765	−	29.0245i	0.449803	−	1.21146i
$575$		0			0
$576$	−12.2962	+	21.2976i	−0.512342	+	0.887402i
$577$	−5.72503	+	0.300036i	−0.238336	+	0.0124907i	−0.171130	−	0.985248i	$-0.554742\pi$
$577$	−5.72503	+	0.300036i	−0.238336	+	0.0124907i	−0.0672061	+	0.997739i	$0.521408\pi$
$578$	8.92628	+	23.2538i	0.371284	+	0.967229i
$579$	1.48014	+	14.0825i	0.0615123	+	0.585251i
$580$		0			0
$581$	−4.35536	+	8.78556i	−0.180691	+	0.364487i
$582$	−6.08774	+	6.08774i	−0.252345	+	0.252345i
$583$	−0.274660	−	0.105432i	−0.0113752	−	0.00436654i
$584$	−0.985333	+	0.209439i	−0.0407734	+	0.00866665i
$585$		0			0
$586$	0.359614	−	1.69185i	0.0148555	−	0.0698898i
$587$	−10.7577	+	5.48135i	−0.444020	+	0.226239i	−0.661682	−	0.749785i	$-0.730157\pi$
$587$	−10.7577	+	5.48135i	−0.444020	+	0.226239i	0.217662	+	0.976024i	$0.430157\pi$
$588$	13.2388	−	3.86154i	0.545960	−	0.159247i
$589$	−48.2769	+	15.6861i	−1.98922	+	0.646335i
$590$		0			0
$591$	3.34273	+	15.7263i	0.137501	+	0.646893i
$592$	−12.3364	−	15.2342i	−0.507023	−	0.626121i
$593$	11.2370	+	41.9372i	0.461449	+	1.72215i	0.668401	+	0.743802i	$0.266979\pi$
$593$	11.2370	+	41.9372i	0.461449	+	1.72215i	−0.206951	+	0.978351i	$0.566354\pi$
$594$	7.83623	+	5.69336i	0.321525	+	0.233601i
$595$		0			0
$596$	−3.37823	+	2.45442i	−0.138377	+	0.100537i
$597$	0.123869	+	0.100307i	0.00506963	+	0.00410531i
$598$	3.12048	+	59.5424i	0.127606	+	2.43487i
$599$	−0.677665	+	0.391250i	−0.0276887	+	0.0159860i	−0.513780	−	0.857922i	$-0.671755\pi$
$599$	−0.677665	+	0.391250i	−0.0276887	+	0.0159860i	0.486092	+	0.873908i	$0.338422\pi$
$600$		0			0
$601$			7.23002i			0.294919i	0.989068	+	0.147459i	$0.0471095\pi$
$601$			7.23002i			0.294919i	−0.989068	+	0.147459i	$0.952890\pi$
$602$	−27.6778	+	25.4783i	−1.12806	+	1.03842i
$603$	−28.0244	−	4.43864i	−1.14124	−	0.180755i
$604$	−14.7882	+	1.55430i	−0.601723	+	0.0632436i
$605$		0			0
$606$	−2.75948	+	26.2547i	−0.112096	+	1.06653i
$607$	−1.71540	+	0.459640i	−0.0696260	+	0.0186562i	−0.293464	−	0.955970i	$-0.594808\pi$
$607$	−1.71540	+	0.459640i	−0.0696260	+	0.0186562i	0.223838	+	0.974626i	$0.428141\pi$
$608$	39.7405	−	6.29427i	1.61169	−	0.255267i
$609$	2.58363	−	1.02452i	0.104694	−	0.0415158i
$610$		0			0
$611$	1.40279	+	0.298173i	0.0567510	+	0.0120628i
$612$	10.3635	+	6.73012i	0.418919	+	0.272049i
$613$	0.918913	+	0.596749i	0.0371145	+	0.0241025i	0.563063	−	0.826414i	$-0.309623\pi$
$613$	0.918913	+	0.596749i	0.0371145	+	0.0241025i	−0.525948	+	0.850516i	$0.676290\pi$
$614$	−30.0818	−	6.39408i	−1.21400	−	0.258044i
$615$		0			0
$616$	−2.00760	+	0.796102i	−0.0808884	+	0.0320759i
$617$	31.8056	−	5.03752i	1.28045	−	0.202803i	0.521103	−	0.853494i	$-0.325521\pi$
$617$	31.8056	−	5.03752i	1.28045	−	0.202803i	0.759343	+	0.650691i	$0.225521\pi$
$618$	11.3897	−	3.05185i	0.458160	−	0.122764i
$619$	1.93430	−	18.4036i	0.0777461	−	0.739705i	−0.884319	−	0.466884i	$-0.845377\pi$
$619$	1.93430	−	18.4036i	0.0777461	−	0.739705i	0.962065	−	0.272821i	$-0.0879567\pi$
$620$		0			0
$621$	27.3018	−	2.86954i	1.09559	−	0.115151i
$622$	24.5386	+	3.88654i	0.983910	+	0.155836i
$623$	−20.6432	+	19.0027i	−0.827051	+	0.761326i
$624$		−	11.8683i		−	0.475111i
$625$		0			0
$626$	18.2402	−	10.5310i	0.729023	−	0.420902i
$627$	−0.227522	−	4.34137i	−0.00908634	−	0.173378i
$628$	−19.9194	−	16.1304i	−0.794869	−	0.643673i
$629$	−11.4704	+	8.33374i	−0.457355	+	0.332288i
$630$		0			0
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	0.916425	−	0.400206i	$-0.131061\pi$
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	−0.0974273	+	0.995243i	$0.531061\pi$
$632$	−2.17968	−	8.13469i	−0.0867031	−	0.323580i
$633$	−3.32675	−	4.10820i	−0.132227	−	0.163286i
$634$	8.21870	+	38.6659i	0.326406	+	1.53562i
$635$		0			0
$636$	−0.524836	+	0.170530i	−0.0208111	+	0.00676194i
$637$	22.1740	−	23.1723i	0.878568	−	0.918118i
$638$	−2.47450	+	1.26082i	−0.0979666	+	0.0499165i
$639$	0.988908	−	4.65245i	0.0391206	−	0.184048i
$640$		0			0
$641$	−36.5968	+	7.77889i	−1.44549	+	0.307248i	−0.862840	−	0.505478i	$-0.831316\pi$
$641$	−36.5968	+	7.77889i	−1.44549	+	0.307248i	−0.582647	+	0.812725i	$0.697983\pi$
$642$	−31.8914	−	12.2419i	−1.25865	−	0.483151i
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	−0.352392	−	0.935852i	$-0.614632\pi$
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	0.935852	+	0.352392i	$0.114632\pi$
$644$	−17.3464	+	34.9910i	−0.683545	+	1.37884i
$645$		0			0
$646$	−2.45636	−	23.3707i	−0.0966442	−	0.919508i
$647$	9.26299	+	24.1309i	0.364166	+	0.948684i	0.986180	+	0.165678i	$0.0529813\pi$
$647$	9.26299	+	24.1309i	0.364166	+	0.948684i	−0.622014	+	0.783006i	$0.713685\pi$
$648$	−2.53501	+	0.132854i	−0.0995848	+	0.00521902i
$649$	3.61080	−	6.25410i	0.141736	−	0.245495i
$650$		0			0
$651$	−7.79252	+	20.9877i	−0.305413	+	0.822572i
$652$	11.7898	+	6.00718i	0.461723	+	0.235259i
$653$	−16.5499	+	20.4375i	−0.647649	+	0.799780i	−0.990191	−	0.139723i	$-0.955379\pi$
$653$	−16.5499	+	20.4375i	−0.647649	+	0.799780i	0.342542	+	0.939503i	$0.388712\pi$
$654$	30.3345	+	13.5058i	1.18617	+	0.528118i
$655$		0			0
$656$	−7.09872	−	15.9440i	−0.277158	−	0.622508i
$657$	2.11712	+	2.11712i	0.0825967	+	0.0825967i
$658$	1.29945	+	1.14439i	0.0506579	+	0.0446130i
$659$	5.69893	+	1.85169i	0.221999	+	0.0721317i	0.417904	−	0.908491i	$-0.362765\pi$
$659$	5.69893	+	1.85169i	0.221999	+	0.0721317i	−0.195906	+	0.980623i	$0.562765\pi$
$660$		0			0
$661$	−34.1915	−	30.7862i	−1.32990	−	1.19744i	−0.963725	−	0.266897i	$-0.914002\pi$
$661$	−34.1915	−	30.7862i	−1.32990	−	1.19744i	−0.366171	−	0.930547i	$-0.619332\pi$
$662$	35.4322	−	54.5608i	1.37711	−	2.12056i
$663$	−8.57228	−	0.449254i	−0.332920	−	0.0174476i
$664$	−0.890129	−	2.73954i	−0.0345437	−	0.106315i
$665$		0			0
$666$	9.38224	−	28.8756i	0.363555	−	1.11891i
$667$	−2.82075	+	7.34830i	−0.109220	+	0.284527i
$668$	−24.0205	−	6.43627i	−0.929381	−	0.249027i
$669$	−11.0152	−	1.15775i	−0.425874	−	0.0447612i
$670$		0			0
$671$	3.27395	+	4.50620i	0.126389	+	0.173960i
$672$	8.70309	−	15.4648i	0.335729	−	0.596566i
$673$	7.94108	−	15.5853i	0.306106	−	0.600767i	−0.685793	−	0.727797i	$-0.740544\pi$
$673$	7.94108	−	15.5853i	0.306106	−	0.600767i	0.991899	+	0.127030i	$0.0405443\pi$
$674$	63.0398	+	36.3960i	2.42820	+	1.40192i
$675$		0			0
$676$	9.47819	+	16.4167i	0.364546	+	0.631412i
$677$	−19.0194	−	29.2874i	−0.730976	−	1.12560i	−0.987277	−	0.159008i	$-0.949170\pi$
$677$	−19.0194	−	29.2874i	−0.730976	−	1.12560i	0.256301	−	0.966597i	$-0.417496\pi$
$678$	2.37128	−	14.9717i	0.0910685	−	0.574984i
$679$	−9.17120	+	9.37531i	−0.351959	+	0.359792i
$680$		0			0
$681$	−3.68211	+	1.63938i	−0.141099	+	0.0628212i
$682$	5.78987	−	21.6081i	0.221706	−	0.827417i
$683$	−31.6215	+	25.6066i	−1.20996	+	0.979808i	−0.209965	+	0.977709i	$0.567335\pi$
$683$	−31.6215	+	25.6066i	−1.20996	+	0.979808i	−0.999998	+	0.00209925i	$0.999332\pi$
$684$	18.2676	+	20.2882i	0.698479	+	0.775740i
$685$		0			0
$686$	37.0527	−	11.2515i	1.41468	−	0.429585i
$687$	−2.52160	−	4.94891i	−0.0962049	−	0.188813i
$688$	−1.10986	+	21.1773i	−0.0423129	+	0.807378i
$689$	−0.858776	+	0.953767i	−0.0327168	+	0.0363356i
$690$		0			0
$691$	13.2239	−	11.9069i	0.503062	−	0.452959i	−0.378106	−	0.925762i	$-0.623425\pi$
$691$	13.2239	−	11.9069i	0.503062	−	0.452959i	0.881168	+	0.472803i	$0.156758\pi$
$692$	−5.09328	−	32.1577i	−0.193618	−	1.22245i
$693$	5.23434	+	3.71565i	0.198836	+	0.141146i
$694$	−33.1078	+	45.5689i	−1.25675	+	1.72977i
$695$		0			0
$696$	−0.332078	+	0.745860i	−0.0125874	+	0.0282717i
$697$	−11.7848	+	4.52377i	−0.446382	+	0.171350i
$698$	50.7263	−	32.9421i	1.92002	−	1.24688i
$699$	7.17212			0.271275
$700$		0			0
$701$	−20.8675			−0.788156			−0.394078	−	0.919077i	$-0.628936\pi$
$701$	−20.8675			−0.788156			−0.394078	+	0.919077i	$0.628936\pi$
$702$	35.4378	−	23.0136i	1.33752	−	0.868592i
$703$	−29.2435	+	11.2255i	−1.10294	+	0.423379i
$704$	−4.54787	+	10.2147i	−0.171404	+	0.384980i
$705$		0			0
$706$	−14.3393	+	19.7364i	−0.539667	+	0.742788i
$707$	−3.76330	+	40.0393i	−0.141533	+	1.50583i
$708$	−2.11905	−	13.3791i	−0.0796387	−	0.502819i
$709$	−0.576558	+	0.519135i	−0.0216531	+	0.0194965i	−0.679886	−	0.733318i	$-0.737971\pi$
$709$	−0.576558	+	0.519135i	−0.0216531	+	0.0194965i	0.658233	+	0.752814i	$0.271304\pi$
$710$		0			0
$711$	−16.7490	+	18.6017i	−0.628137	+	0.697617i
$712$	0.431359	−	8.23081i	0.0161658	−	0.308463i
$713$	−28.7838	−	56.4913i	−1.07796	−	2.11562i
$714$	−8.75368	−	5.54871i	−0.327598	−	0.207655i
$715$		0			0
$716$	−2.55440	−	2.83695i	−0.0954624	−	0.106022i
$717$	−12.3847	+	10.0290i	−0.462516	+	0.374538i
$718$	−2.40915	+	8.99106i	−0.0899086	+	0.335543i
$719$	33.6892	−	14.9994i	1.25639	−	0.559383i	0.332888	−	0.942966i	$-0.391977\pi$
$719$	33.6892	−	14.9994i	1.25639	−	0.559383i	0.923506	+	0.383583i	$0.125310\pi$
$720$		0			0
$721$	17.2984	−	4.83973i	0.644225	−	0.180241i
$722$	1.90712	−	12.0411i	0.0709755	−	0.448122i
$723$	11.7410	+	18.0795i	0.436651	+	0.672384i
$724$	−4.12478	−	7.14434i	−0.153296	−	0.265517i
$725$		0			0
$726$	−14.8859	−	8.59439i	−0.552468	−	0.318968i
$727$	−9.04006	+	17.7421i	−0.335277	+	0.658019i	−0.995676	−	0.0928967i	$-0.970387\pi$
$727$	−9.04006	+	17.7421i	−0.335277	+	0.658019i	0.660398	+	0.750915i	$0.270387\pi$
$728$	0.103679	+	9.42084i	0.00384259	+	0.349160i
$729$	−2.02583	−	2.78831i	−0.0750307	−	0.103271i
$730$		0			0
$731$	15.2541	+	1.60327i	0.564192	+	0.0592990i
$732$	10.0919	+	2.70410i	0.373006	+	0.0999466i
$733$	0.0143601	−	0.0374092i	0.000530401	−	0.00138174i	−0.933315	−	0.359059i	$-0.883098\pi$
$733$	0.0143601	−	0.0374092i	0.000530401	−	0.00138174i	0.933845	+	0.357677i	$0.116431\pi$
$734$	−16.5940	+	51.0711i	−0.612496	+	1.88507i
$735$		0			0
$736$	15.5297	+	47.7955i	0.572432	+	1.76177i
$737$	−12.8829	−	0.675166i	−0.474549	−	0.0248701i
$738$	14.7226	−	22.6707i	0.541945	−	0.834522i
$739$	14.3575	+	12.9276i	0.528151	+	0.475549i	0.889534	−	0.456868i	$-0.151029\pi$
$739$	14.3575	+	12.9276i	0.528151	+	0.475549i	−0.361384	+	0.932417i	$0.617696\pi$
$740$		0			0
$741$	−18.0366	−	5.86045i	−0.662592	−	0.215289i
$742$	−1.46836	+	0.495031i	−0.0539054	+	0.0181731i
$743$	16.7789	+	16.7789i	0.615557	+	0.615557i	0.944389	−	0.328831i	$-0.106655\pi$
$743$	16.7789	+	16.7789i	0.615557	+	0.615557i	−0.328831	+	0.944389i	$0.606655\pi$
$744$	−2.67489	−	6.00790i	−0.0980661	−	0.220260i
$745$		0			0
$746$	−68.4068	−	30.4567i	−2.50455	−	1.11510i
$747$	−5.38795	+	6.65357i	−0.197135	+	0.243441i
$748$	5.00597	+	2.55067i	0.183036	+	0.0932617i
$749$	−48.7843	−	18.1132i	−1.78254	−	0.661840i
$750$		0			0
$751$	−6.63402	+	11.4905i	−0.242079	+	0.419293i	−0.961306	−	0.275482i	$-0.911163\pi$
$751$	−6.63402	+	11.4905i	−0.242079	+	0.419293i	0.719227	+	0.694775i	$0.244496\pi$
$752$	0.974748	−	0.0510844i	0.0355454	−	0.00186286i
$753$	−4.58823	−	11.9528i	−0.167205	−	0.435583i
$754$	1.26639	+	12.0489i	0.0461193	+	0.438796i
$755$		0			0
$756$	27.6220	−	1.75260i	1.00460	−	0.0637416i
$757$	1.13591	−	1.13591i	0.0412853	−	0.0412853i	−0.686163	−	0.727448i	$-0.740706\pi$
$757$	1.13591	−	1.13591i	0.0412853	−	0.0412853i	0.727448	+	0.686163i	$0.240706\pi$
$758$	44.3132	+	17.0102i	1.60953	+	0.617839i
$759$	5.31122	−	1.12894i	0.192785	−	0.0409778i
$760$		0			0
$761$	6.60486	−	31.0734i	0.239426	−	1.12641i	−0.680020	−	0.733194i	$-0.738029\pi$
$761$	6.60486	−	31.0734i	0.239426	−	1.12641i	0.919446	−	0.393217i	$-0.128638\pi$
$762$	20.1050	−	10.2440i	0.728328	−	0.371102i
$763$	46.4340	+	20.0644i	1.68102	+	0.726381i
$764$	−6.68717	+	2.17279i	−0.241933	+	0.0786089i
$765$		0			0
$766$	9.45622	+	44.4880i	0.341667	+	1.60742i
$767$	−19.8259	−	24.4829i	−0.715870	−	0.884026i
$768$	−1.83093	−	6.83311i	−0.0660679	−	0.246569i
$769$	−11.1412	−	8.09458i	−0.401763	−	0.291898i	0.368495	−	0.929630i	$-0.379873\pi$
$769$	−11.1412	−	8.09458i	−0.401763	−	0.291898i	−0.770259	+	0.637731i	$0.779873\pi$
$770$		0			0
$771$	−20.5429	+	14.9253i	−0.739834	+	0.537521i
$772$	−31.4204	−	25.4437i	−1.13084	−	0.915739i
$773$	0.525618	+	10.0294i	0.0189052	+	0.360732i	0.991659	+	0.128891i	$0.0411416\pi$
$773$	0.525618	+	10.0294i	0.0189052	+	0.360732i	−0.972754	+	0.231841i	$0.925525\pi$
$774$	−28.4449	+	16.4227i	−1.02243	+	0.590302i
$775$		0			0
$776$		−	3.85263i		−	0.138301i
$777$	−4.12425	+	13.1851i	−0.147957	+	0.473013i
$778$	−26.8433	−	4.25155i	−0.962377	−	0.152426i
$779$	−27.7359	+	2.91516i	−0.993743	+	0.104447i
$780$		0			0
$781$	0.226050	−	2.15072i	0.00808871	−	0.0769590i
$782$	28.3510	−	7.59663i	1.01383	−	0.271655i
$783$	5.50947	−	0.872614i	0.196892	−	0.0311847i
$784$	10.4957	−	19.1399i	0.374847	−	0.683570i
$785$		0			0
$786$	−6.01847	−	1.27927i	−0.214672	−	0.0456299i
$787$	−18.0549	−	11.7250i	−0.643586	−	0.417950i	0.181159	−	0.983454i	$-0.442015\pi$
$787$	−18.0549	−	11.7250i	−0.643586	−	0.417950i	−0.824746	+	0.565504i	$0.808682\pi$
$788$	−38.4995	−	25.0019i	−1.37149	−	0.890655i
$789$	−0.331266	−	0.0704127i	−0.0117934	−	0.00250676i
$790$		0			0
$791$	3.36111	−	22.8456i	0.119507	−	0.812297i
$792$	−1.86241	+	0.294977i	−0.0661779	+	0.0104815i
$793$	23.4705	−	6.28891i	0.833463	−	0.223326i
$794$	−1.04434	+	9.93624i	−0.0370623	+	0.352624i
$795$		0			0
$796$	−0.452602	+	0.0475704i	−0.0160421	+	0.00168609i
$797$	−5.20937	−	0.825084i	−0.184526	−	0.0292260i	0.0634877	−	0.997983i	$-0.479778\pi$
$797$	−5.20937	−	0.825084i	−0.184526	−	0.0292260i	−0.248013	+	0.968757i	$0.579778\pi$
$798$	−15.5078	−	16.8466i	−0.548970	−	0.596362i
$799$		−	0.705981i		−	0.0249758i
$800$		0			0
$801$	−21.2154	+	12.2487i	−0.749608	+	0.432786i
$802$	−1.65969	−	31.6687i	−0.0586056	−	1.11826i
$803$	1.05793	+	0.856694i	0.0373335	+	0.0302321i
$804$	−19.5768	+	14.2234i	−0.690422	+	0.501621i
$805$		0			0
$806$	−78.9508	−	57.3611i	−2.78092	−	2.02046i
$807$	−4.11784	−	15.3680i	−0.144955	−	0.540979i
$808$	−7.43450	−	9.18084i	−0.261545	−	0.322981i
$809$	1.72341	+	8.10801i	0.0605919	+	0.285063i	0.998003	−	0.0631613i	$-0.0201182\pi$
$809$	1.72341	+	8.10801i	0.0605919	+	0.285063i	−0.937411	+	0.348224i	$0.886785\pi$
$810$		0			0
$811$	22.9445	−	7.45511i	0.805689	−	0.261784i	0.122918	−	0.992417i	$-0.460775\pi$
$811$	22.9445	−	7.45511i	0.805689	−	0.261784i	0.682771	+	0.730632i	$0.260775\pi$
$812$	−3.14776	+	7.28469i	−0.110465	+	0.255643i
$813$	14.2891	−	7.28065i	0.501140	−	0.255343i
$814$	2.87010	−	13.5028i	0.100597	−	0.473271i
$815$		0			0
$816$	−5.71472	+	1.21470i	−0.200055	+	0.0425230i
$817$	31.6359	+	12.1439i	1.10680	+	0.424861i
$818$	−15.1952	+	15.1952i	−0.531288	+	0.531288i
$819$	23.3157	−	15.5088i	0.814715	−	0.541921i
$820$		0			0
$821$	−1.17488	−	11.1783i	−0.0410037	−	0.390124i	−0.995707	−	0.0925640i	$-0.970494\pi$
$821$	−1.17488	−	11.1783i	−0.0410037	−	0.390124i	0.954703	−	0.297560i	$-0.0961729\pi$
$822$	4.71451	+	12.2817i	0.164437	+	0.428374i
$823$	−17.1411	+	0.898326i	−0.597501	+	0.0313137i	−0.348689	−	0.937238i	$-0.613373\pi$
$823$	−17.1411	+	0.898326i	−0.597501	+	0.0313137i	−0.248811	+	0.968552i	$0.580040\pi$
$824$	−2.63830	+	4.56967i	−0.0919096	+	0.159192i
$825$		0			0
$826$	−6.36329	−	37.5005i	−0.221407	−	1.30481i
$827$	−20.7397	−	10.5674i	−0.721190	−	0.367465i	0.0545555	−	0.998511i	$-0.482626\pi$
$827$	−20.7397	−	10.5674i	−0.721190	−	0.367465i	−0.775745	+	0.631046i	$0.782626\pi$
$828$	−21.4590	+	26.4997i	−0.745753	+	0.920928i
$829$	23.1374	+	10.3014i	0.803596	+	0.357784i	0.767082	−	0.641549i	$-0.221708\pi$
$829$	23.1374	+	10.3014i	0.803596	+	0.357784i	0.0365142	+	0.999333i	$0.488375\pi$
$830$		0			0
$831$	2.58378	+	5.80327i	0.0896304	+	0.201313i
$832$	34.4910	+	34.4910i	1.19576	+	1.19576i
$833$	−13.4272	−	8.30543i	−0.465226	−	0.287766i
$834$	14.6044	+	4.74526i	0.505710	+	0.164315i
$835$		0			0
$836$	9.22439	+	8.30568i	0.319032	+	0.287258i
$837$	−24.4717	+	37.6831i	−0.845865	+	1.30252i
$838$	−37.3850	−	1.95926i	−1.29144	−	0.0676816i
$839$	−17.1783	−	52.8695i	−0.593062	−	1.82526i	−0.564144	−	0.825677i	$-0.690794\pi$
$839$	−17.1783	−	52.8695i	−0.593062	−	1.82526i	−0.0289189	−	0.999582i	$-0.509206\pi$
$840$		0			0
$841$	8.46726	−	26.0596i	0.291975	−	0.898605i
$842$	12.5836	−	32.7815i	0.433661	−	1.12973i
$843$	−15.0184	−	4.02417i	−0.517261	−	0.138600i
$844$	15.0108	+	1.57770i	0.516694	+	0.0543068i
$845$		0			0
$846$	0.888617	+	1.22308i	0.0305513	+	0.0420502i
$847$	−22.8193	−	12.8420i	−0.784082	−	0.441257i
$848$	−0.396565	+	0.778302i	−0.0136181	+	0.0267270i
$849$	−2.04998	−	1.18355i	−0.0703550	−	0.0406195i
$850$		0			0
$851$	−19.5621	−	33.8826i	−0.670581	−	1.16148i
$852$	−2.20929	−	3.40201i	−0.0756892	−	0.116551i
$853$	6.62710	−	41.8419i	0.226908	−	1.43264i	−0.566557	−	0.824023i	$-0.691725\pi$
$853$	6.62710	−	41.8419i	0.226908	−	1.43264i	0.793465	−	0.608616i	$-0.208275\pi$
$854$	28.4195	+	7.28074i	0.972494	+	0.249142i
$855$		0			0
$856$	13.9649	−	6.21758i	0.477311	−	0.212513i
$857$	−9.84983	+	36.7601i	−0.336464	+	1.25570i	0.565810	+	0.824536i	$0.308564\pi$
$857$	−9.84983	+	36.7601i	−0.336464	+	1.25570i	−0.902274	+	0.431164i	$0.858103\pi$
$858$	6.49517	−	5.25969i	0.221742	−	0.179563i
$859$	−34.3314	−	38.1289i	−1.17137	−	1.30094i	−0.945064	−	0.326884i	$-0.894001\pi$
$859$	−34.3314	−	38.1289i	−1.17137	−	1.30094i	−0.226307	−	0.974056i	$-0.572665\pi$
$860$		0			0
$861$	−6.58511	+	10.3887i	−0.224420	+	0.354046i
$862$	−8.49088	−	16.6643i	−0.289200	−	0.567588i
$863$	−1.14373	+	21.8237i	−0.0389331	+	0.742887i	0.907513	+	0.420025i	$0.137979\pi$
$863$	−1.14373	+	21.8237i	−0.0389331	+	0.742887i	−0.946446	+	0.322863i	$0.895355\pi$
$864$	23.8312	−	26.4672i	0.810754	−	0.900433i
$865$		0			0
$866$	−27.3797	+	24.6528i	−0.930399	+	0.837735i
$867$	−1.54799	−	9.77363i	−0.0525725	−	0.331930i
$868$	−26.6404	−	58.1060i	−0.904236	−	1.97224i
$869$	−6.68946	+	9.20725i	−0.226924	+	0.312334i
$870$		0			0
$871$	−22.8902	+	51.4123i	−0.775606	+	1.74204i
$872$	−13.8722	+	5.32504i	−0.469772	+	0.180329i
$873$	−9.60352	+	6.23660i	−0.325030	+	0.211077i
$874$	64.8458			2.19344
$875$		0			0
$876$	2.55345			0.0862732
$877$	1.18764	−	0.771263i	0.0401038	−	0.0260437i	−0.524431	−	0.851453i	$-0.675722\pi$
$877$	1.18764	−	0.771263i	0.0401038	−	0.0260437i	0.564535	+	0.825409i	$0.309055\pi$
$878$	53.4912	−	20.5333i	1.80524	−	0.692967i
$879$	−0.279490	+	0.627744i	−0.00942695	+	0.0211733i
$880$		0			0
$881$	−5.05676	+	6.96003i	−0.170367	+	0.234489i	−0.885659	−	0.464335i	$-0.846293\pi$
$881$	−5.05676	+	6.96003i	−0.170367	+	0.234489i	0.715293	+	0.698825i	$0.246293\pi$
$882$	33.7160	−	2.51208i	1.13528	−	0.0845860i
$883$	6.37108	+	40.2254i	0.214404	+	1.35369i	0.826512	+	0.562919i	$0.190322\pi$
$883$	6.37108	+	40.2254i	0.214404	+	1.35369i	−0.612108	+	0.790774i	$0.709678\pi$
$884$	18.2141	−	16.4000i	0.612605	−	0.551592i
$885$		0			0
$886$	−15.5070	+	17.2223i	−0.520968	+	0.578594i
$887$	1.29841	−	24.7751i	0.0435963	−	0.831866i	−0.886090	−	0.463514i	$-0.846589\pi$
$887$	1.29841	−	24.7751i	0.0435963	−	0.831866i	0.929686	−	0.368353i	$-0.120078\pi$
$888$	−1.84240	−	3.61591i	−0.0618269	−	0.121342i
$889$	30.4536	−	15.9414i	1.02138	−	0.534659i
$890$		0			0
$891$	2.29542	+	2.54932i	0.0768994	+	0.0854055i
$892$	24.5767	−	19.9018i	0.822890	−	0.666363i
$893$	0.403688	−	1.50658i	0.0135089	−	0.0504159i
$894$	2.79348	−	1.24374i	0.0934279	−	0.0415968i
$895$		0			0
$896$	4.35568	+	15.5683i	0.145513	+	0.520100i
$897$	3.70552	−	23.3957i	0.123724	−	0.781160i
$898$	−45.6821	−	70.3442i	−1.52443	−	2.34742i
$899$	−6.44144	−	11.1569i	−0.214834	−	0.372103i
$900$		0			0
$901$	0.547146	+	0.315895i	0.0182281	+	0.0105240i
$902$	5.57975	−	10.9509i	0.185785	−	0.364624i
$903$	12.8600	−	7.61461i	0.427953	−	0.253398i
$904$	3.98709	+	5.48776i	0.132609	+	0.182520i
$905$		0			0
$906$	10.8293	+	1.13820i	0.359778	+	0.0378142i
$907$	30.1426	+	8.07670i	1.00087	+	0.268182i	0.721810	−	0.692091i	$-0.243310\pi$
$907$	30.1426	+	8.07670i	1.00087	+	0.268182i	0.279060	+	0.960274i	$0.409977\pi$
$908$	4.12418	−	10.7439i	0.136866	−	0.356547i
$909$	−10.8504	+	33.3940i	−0.359883	+	1.10761i
$910$		0			0
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	−0.940025	−	0.341105i	$-0.889199\pi$
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	0.560000	−	0.828492i	$-0.310801\pi$
$912$	−12.8900	−	0.675534i	−0.426829	−	0.0223692i
$913$	−2.12009	+	3.26465i	−0.0701647	+	0.108044i
$914$	−52.8000	−	47.5413i	−1.74647	−	1.57253i
$915$		0			0
$916$	15.0826	+	4.90064i	0.498344	+	0.161922i
$917$	−9.18920	−	1.84777i	−0.303454	−	0.0610188i
$918$	−14.7084	−	14.7084i	−0.485448	−	0.485448i
$919$	−17.2862	−	38.8255i	−0.570220	−	1.28074i	−0.936643	−	0.350287i	$-0.886084\pi$
$919$	−17.2862	−	38.8255i	−0.570220	−	1.28074i	0.366422	−	0.930449i	$-0.380583\pi$
$920$		0			0
$921$	11.1615	+	4.96943i	0.367785	+	0.163748i
$922$	−41.5761	+	51.3422i	−1.36924	+	1.69087i
$923$	−8.40577	−	4.28295i	−0.276679	−	0.140975i
$924$	5.39729	−	0.915841i	0.177558	−	0.0301290i
$925$		0			0
$926$	19.9093	−	34.4838i	0.654259	−	1.13321i
$927$	15.6617	−	0.820797i	0.514399	−	0.0269585i
$928$	3.65950	+	9.53332i	0.120129	+	0.312947i
$929$	−1.58633	−	15.0929i	−0.0520459	−	0.495183i	−0.989232	−	0.146354i	$-0.953246\pi$
$929$	−1.58633	−	15.0929i	−0.0520459	−	0.495183i	0.937186	−	0.348829i	$-0.113421\pi$
$930$		0			0
$931$	−23.9050	−	25.4019i	−0.783453	−	0.832513i
$932$	−14.4802	+	14.4802i	−0.474315	+	0.474315i
$933$	−9.21461	−	3.53716i	−0.301673	−	0.115801i
$934$	12.1864	−	2.59031i	0.398753	−	0.0847575i
$935$		0			0
$936$	−1.71025	+	8.04611i	−0.0559014	+	0.262995i
$937$	−22.2665	+	11.3453i	−0.727415	+	0.370636i	−0.778152	−	0.628076i	$-0.783843\pi$
$937$	−22.2665	+	11.3453i	−0.727415	+	0.370636i	0.0507375	+	0.998712i	$0.483843\pi$
$938$	−54.5283	+	40.5414i	−1.78041	+	1.32372i
$939$	−7.95790	+	2.58568i	−0.259696	+	0.0843805i
$940$		0			0
$941$	−3.46764	−	16.3140i	−0.113042	−	0.531820i	−0.997831	−	0.0658284i	$-0.979031\pi$
$941$	−3.46764	−	16.3140i	−0.113042	−	0.531820i	0.884789	−	0.465992i	$-0.154302\pi$
$942$	11.8121	+	14.5868i	0.384861	+	0.475263i
$943$	−9.01555	−	33.6465i	−0.293587	−	1.09568i
$944$	−17.3467	−	12.6031i	−0.564586	−	0.410196i
$945$		0			0
$946$	−12.0816	+	8.77782i	−0.392808	+	0.285392i
$947$	−18.5885	−	15.0527i	−0.604047	−	0.489147i	0.277828	−	0.960631i	$-0.410385\pi$
$947$	−18.5885	−	15.0527i	−0.604047	−	0.489147i	−0.881875	+	0.471483i	$0.843719\pi$
$948$	1.11724	+	21.3182i	0.0362863	+	0.692383i
$949$	5.14293	−	2.96927i	0.166947	−	0.0963866i
$950$		0			0
$951$		−	15.7043i		−	0.509247i
$952$	4.52564	−	1.01413i	0.146677	−	0.0328683i
$953$	52.6232	+	8.33470i	1.70463	+	0.269987i	0.931364	−	0.364090i	$-0.118620\pi$
$953$	52.6232	+	8.33470i	1.70463	+	0.269987i	0.773270	+	0.634077i	$0.218620\pi$
$954$	−1.34552	+	0.141420i	−0.0435628	+	0.00457863i
$955$		0			0
$956$	4.75620	−	45.2522i	0.153827	−	1.46356i
$957$	1.06573	−	0.285561i	0.0344500	−	0.00923086i
$958$	−43.0597	+	6.81999i	−1.39120	+	0.220344i
$959$	7.38735	+	18.6293i	0.238550	+	0.601572i
$960$		0			0
$961$	71.1813	+	15.1300i	2.29617	+	0.488066i
$962$	−50.5051	−	32.7984i	−1.62835	−	1.05746i
$963$	−38.1049	−	24.7456i	−1.22791	−	0.797417i
$964$	−60.2062	−	12.7972i	−1.93911	−	0.412171i
$965$		0			0
$966$	17.7525	−	22.4226i	0.571178	−	0.721436i
$967$	−31.4763	+	4.98535i	−1.01221	+	0.160318i	−0.640441	−	0.768008i	$-0.721248\pi$
$967$	−31.4763	+	4.98535i	−1.01221	+	0.160318i	−0.371768	+	0.928326i	$0.621248\pi$
$968$	7.42978	−	1.99080i	0.238802	−	0.0639868i
$969$	−0.975858	+	9.28467i	−0.0313491	+	0.298266i
$970$		0			0
$971$	−38.5053	+	4.04707i	−1.23569	+	0.129877i	−0.699757	−	0.714381i	$-0.746708\pi$
$971$	−38.5053	+	4.04707i	−1.23569	+	0.129877i	−0.535937	+	0.844258i	$0.680042\pi$
$972$	37.3524	+	5.91604i	1.19808	+	0.189757i
$973$	22.3260	+	6.98348i	0.715739	+	0.223880i
$974$		−	61.3676i		−	1.96634i
$975$		0			0
$976$	14.3221	−	8.26889i	0.458441	−	0.264681i
$977$	1.51297	+	28.8691i	0.0484040	+	0.923604i	0.909640	+	0.415398i	$0.136358\pi$
$977$	1.51297	+	28.8691i	0.0484040	+	0.923604i	−0.861236	+	0.508206i	$0.830309\pi$
$978$	−7.53027	−	6.09789i	−0.240792	−	0.194989i
$979$	−9.01096	+	6.54684i	−0.287991	+	0.209238i
$980$		0			0
$981$	35.7300	+	25.9594i	1.14077	+	0.828818i
$982$	9.74367	+	36.3639i	0.310933	+	1.16042i
$983$	6.15724	+	7.60355i	0.196385	+	0.242516i	0.865820	−	0.500355i	$-0.166797\pi$
$983$	6.15724	+	7.60355i	0.196385	+	0.242516i	−0.669435	+	0.742871i	$0.733464\pi$
$984$	−0.751219	−	3.53421i	−0.0239480	−	0.112666i
$985$		0			0
$986$	5.67209	−	1.84297i	0.180636	−	0.0586922i
$987$	−0.410437	−	0.552039i	−0.0130644	−	0.0175716i
$988$	48.2471	−	24.5831i	1.53494	−	0.782093i
$989$	−8.79984	+	41.4000i	−0.279819	+	1.31644i
$990$		0			0
$991$	23.8969	−	5.07944i	0.759110	−	0.161354i	0.187934	−	0.982182i	$-0.439821\pi$
$991$	23.8969	−	5.07944i	0.759110	−	0.161354i	0.571176	+	0.820828i	$0.306487\pi$
$992$	−76.7909	−	29.4773i	−2.43811	−	0.935904i
$993$	−18.2755	+	18.2755i	−0.579955	+	0.579955i
$994$	−6.30838	−	9.48391i	−0.200090	−	0.300811i
$995$		0			0
$996$	0.763228	+	7.26163i	0.0241838	+	0.230094i
$997$	−7.82705	−	20.3902i	−0.247885	−	0.645763i	0.752025	−	0.659134i	$-0.229077\pi$
$997$	−7.82705	−	20.3902i	−0.247885	−	0.645763i	−0.999911	+	0.0133710i	$0.995744\pi$
$998$	11.1061	−	0.582044i	0.351556	−	0.0184243i
$999$	−13.8634	+	24.0121i	−0.438619	+	0.759710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.768.16		288
5.2	odd	4		175.2.x.a.117.16	yes	288
5.3	odd	4		875.2.bb.c.607.3		288
5.4	even	2		875.2.bb.a.768.3		288
7.3	odd	6	inner	875.2.bb.b.143.16		288
25.3	odd	20		875.2.bb.a.257.3		288
25.4	even	10		875.2.bb.c.243.16		288
25.21	even	5		175.2.x.a.103.3	yes	288
25.22	odd	20	inner	875.2.bb.b.257.16		288
35.3	even	12		875.2.bb.c.857.16		288
35.17	even	12		175.2.x.a.17.3	yes	288
35.24	odd	6		875.2.bb.a.143.3		288
175.3	even	60		875.2.bb.a.507.3		288
175.122	even	60	inner	875.2.bb.b.507.16		288
175.129	odd	30		875.2.bb.c.493.3		288
175.171	odd	30		175.2.x.a.3.16	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.16	✓	288	175.171	odd	30
175.2.x.a.17.3	yes	288	35.17	even	12
175.2.x.a.103.3	yes	288	25.21	even	5
175.2.x.a.117.16	yes	288	5.2	odd	4
875.2.bb.a.143.3		288	35.24	odd	6
875.2.bb.a.257.3		288	25.3	odd	20
875.2.bb.a.507.3		288	175.3	even	60
875.2.bb.a.768.3		288	5.4	even	2
875.2.bb.b.143.16		288	7.3	odd	6	inner
875.2.bb.b.257.16		288	25.22	odd	20	inner
875.2.bb.b.507.16		288	175.122	even	60	inner
875.2.bb.b.768.16		288	1.1	even	1	trivial
875.2.bb.c.243.16		288	25.4	even	10
875.2.bb.c.493.3		288	175.129	odd	30
875.2.bb.c.607.3		288	5.3	odd	4
875.2.bb.c.857.16		288	35.3	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75355 - 1.13877i) q^{2} +(-0.775483 + 0.297680i) q^{3} +(0.964662 - 2.16667i) q^{4} +(-1.02086 + 1.40509i) q^{6} +(-1.53148 + 2.15744i) q^{7} +(-0.121581 - 0.767632i) q^{8} +(-1.71667 + 1.54570i) q^{9} +(-0.702779 + 0.780515i) q^{11} +(-0.103106 + 1.96737i) q^{12} +(2.08008 + 4.08239i) q^{13} +(-0.228707 + 5.52718i) q^{14} +(2.08662 + 2.31743i) q^{16} +(1.75283 - 1.41941i) q^{17} +(-1.25008 + 4.66535i) q^{18} +(4.55223 - 2.02678i) q^{19} +(0.545413 - 2.12895i) q^{21} +(-0.343531 + 2.16897i) q^{22} +(3.38977 + 5.21979i) q^{23} +(0.322792 + 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(2.00245 - 3.93004i) q^{27} +(3.19709 + 5.39942i) q^{28} +(0.743348 + 1.02313i) q^{29} +(-10.1310 - 1.06481i) q^{31} +(7.79943 + 2.08985i) q^{32} +(0.312649 - 0.814479i) q^{33} +(1.45729 - 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-6.27752 - 0.328991i) q^{37} +(5.67452 - 8.73799i) q^{38} +(-2.82832 - 2.54663i) q^{39} +(-5.32280 - 1.72948i) q^{41} +(-1.46797 - 4.35431i) q^{42} +(4.80861 + 4.80861i) q^{43} +(1.01317 + 2.27562i) q^{44} +(11.8882 + 5.29299i) q^{46} +(0.196982 - 0.243253i) q^{47} +(-2.30799 - 1.17598i) q^{48} +(-2.30911 - 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(10.8518 - 0.568717i) q^{52} +(0.100384 + 0.261509i) q^{53} +(-0.963998 - 9.17183i) q^{54} +(1.84232 + 0.913312i) q^{56} +(-2.92684 + 2.92684i) q^{57} +(2.46860 + 0.947608i) q^{58} +(-6.72559 + 1.42957i) q^{59} +(1.10261 - 5.18739i) q^{61} +(-18.9778 + 9.66967i) q^{62} +(-0.705699 - 6.07084i) q^{63} +(10.1249 - 3.28979i) q^{64} +(-0.379257 - 1.78426i) q^{66} +(7.72991 + 9.54564i) q^{67} +(-1.38451 - 5.16706i) q^{68} +(-4.18254 - 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.39524 + 1.12985i) q^{72} +(-0.0678338 - 1.29435i) q^{73} +(-11.3826 + 6.57173i) q^{74} -11.8183i q^{76} +(-0.607621 - 2.71155i) q^{77} +(-7.85959 - 1.24484i) q^{78} +(10.7765 - 1.13266i) q^{79} +(0.341411 - 3.24831i) q^{81} +(-11.3033 + 3.02870i) q^{82} +(3.66064 - 0.579789i) q^{83} +(-4.08659 - 3.23545i) q^{84} +(13.9080 + 2.95623i) q^{86} +(-0.881019 - 0.572141i) q^{87} +(0.684593 + 0.444580i) q^{88} +(10.3731 + 2.20488i) q^{89} +(-11.9931 - 1.76446i) q^{91} +(14.5795 - 2.30917i) q^{92} +(8.17341 - 2.19006i) q^{93} +(0.0684094 - 0.650872i) q^{94} +(-6.67043 + 0.701090i) q^{96} +(4.89604 + 0.775456i) q^{97} +(-11.5743 - 8.95821i) q^{98} -2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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