LMFDB - Embedded newform 875.2.bb.a.507.3

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			507.3
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.a.768.3

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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	$-0.581478\pi$
$2$	−1.75355	−	1.13877i	−1.23994	−	0.805229i	−0.986760	+	0.162189i	$0.948145\pi$
$3$	0.775483	+	0.297680i	0.447725	+	0.171866i	0.571775	−	0.820410i	$-0.306255\pi$
$3$	0.775483	+	0.297680i	0.447725	+	0.171866i	−0.124050	+	0.992276i	$0.539588\pi$
$4$	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	0.627822	−	0.778357i	$-0.283946\pi$
$11$	−0.702779	−	0.780515i	−0.211896	−	0.235334i	−0.839718	+	0.543023i	$0.817280\pi$
$12$	0.103106	+	1.96737i	0.0297640	+	0.567932i
$13$	−2.08008	+	4.08239i	−0.576911	+	1.13225i	0.399580	+	0.916698i	$0.369156\pi$
$13$	−2.08008	+	4.08239i	−0.576911	+	1.13225i	−0.976492	+	0.215554i	$0.930844\pi$
$14$	−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	$-0.371520\pi$
$17$	−1.75283	−	1.41941i	−0.425124	−	0.344259i	−0.817885	+	0.575382i	$0.804853\pi$
$18$	1.25008	+	4.66535i	0.294646	+	1.09963i
$19$	4.55223	+	2.02678i	1.04435	+	0.464976i	0.855919	−	0.517110i	$-0.172992\pi$
$19$	4.55223	+	2.02678i	1.04435	+	0.464976i	0.188434	+	0.982086i	$0.439659\pi$
$20$		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	0.284725	+	0.958609i	$0.408098\pi$
$23$	−3.38977	+	5.21979i	−0.706816	+	1.08840i	−0.991541	+	0.129793i	$0.958569\pi$
$24$	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	−0.734402	−	0.678714i	$-0.762537\pi$
$29$	0.743348	−	1.02313i	0.138036	−	0.189991i	0.872439	+	0.488724i	$0.162537\pi$
$30$		0			0
$31$	−10.1310	+	1.06481i	−1.81959	+	0.191246i	−0.952012	−	0.306062i	$-0.900989\pi$
$31$	−10.1310	+	1.06481i	−1.81959	+	0.191246i	−0.867574	+	0.497308i	$0.834322\pi$
$32$	−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	$-0.343820\pi$
$37$	6.27752	−	0.328991i	1.03202	−	0.0540858i	0.560817	+	0.827940i	$0.310487\pi$
$38$	−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	−0.693585	−	0.720374i	$-0.743970\pi$
$41$	−5.32280	+	1.72948i	−0.831282	+	0.270100i	−0.137697	+	0.990474i	$0.543970\pi$
$42$	1.46797	−	4.35431i	0.226513	−	0.671885i
$43$	−4.80861	+	4.80861i	−0.733306	+	0.733306i	−0.971273	−	0.237968i	$-0.923519\pi$
$43$	−4.80861	+	4.80861i	−0.733306	+	0.733306i	0.237968	+	0.971273i	$0.423519\pi$
$44$	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	$-0.223934\pi$
$47$	−0.196982	−	0.243253i	−0.0287328	−	0.0354821i	−0.791310	+	0.611415i	$0.790600\pi$
$48$	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	$-0.889457\pi$
$53$	−0.100384	+	0.261509i	−0.0137888	+	0.0359210i	0.926513	+	0.376262i	$0.122791\pi$
$54$	−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	−0.251875	−	0.967760i	$-0.581047\pi$
$59$	−6.72559	−	1.42957i	−0.875597	−	0.186114i	−0.623722	+	0.781646i	$0.714380\pi$
$60$		0			0
$61$	1.10261	+	5.18739i	0.141175	+	0.664178i	0.990636	+	0.136527i	$0.0435939\pi$
$61$	1.10261	+	5.18739i	0.141175	+	0.664178i	−0.849461	+	0.527651i	$0.823073\pi$
$62$	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	0.0415894	+	0.999135i	$0.486758\pi$
$67$	−7.72991	+	9.54564i	−0.944359	+	1.16619i	−0.985948	+	0.167051i	$0.946575\pi$
$68$	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	0.484535	−	0.874772i	$-0.338989\pi$
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	−0.682228	+	0.731140i	$0.738989\pi$
$72$	−1.39524	+	1.12985i	−0.164431	+	0.133154i
$73$	0.0678338	−	1.29435i	0.00793934	−	0.151492i	−0.991783	−	0.127931i	$-0.959166\pi$
$73$	0.0678338	−	1.29435i	0.00793934	−	0.151492i	0.999722	−	0.0235607i	$-0.00750028\pi$
$74$	−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	0.689090	−	0.724676i	$-0.258011\pi$
$79$	10.7765	+	1.13266i	1.21245	+	0.127434i	0.523363	+	0.852110i	$0.324677\pi$
$80$		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	$-0.515202\pi$
$83$	−3.66064	−	0.579789i	−0.401808	−	0.0636401i	−0.354068	+	0.935220i	$0.615202\pi$
$84$	−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	0.377811	−	0.925883i	$-0.376677\pi$
$89$	10.3731	−	2.20488i	1.09955	−	0.233716i	0.721738	+	0.692166i	$0.243344\pi$
$90$		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	$-0.630975\pi$
$97$	−4.89604	+	0.775456i	−0.497117	+	0.0787356i	−0.0971587	+	0.995269i	$0.530975\pi$
$98$	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	0.982069	−	0.188524i	$-0.0603704\pi$
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.327767	+	0.944758i	$0.393704\pi$
$102$	−0.205014	+	3.91190i	−0.0202994	+	0.387336i
$103$	5.27623	−	4.27261i	0.519883	−	0.420993i	−0.333132	−	0.942880i	$-0.608105\pi$
$103$	5.27623	−	4.27261i	0.519883	−	0.420993i	0.853014	+	0.521888i	$0.174772\pi$
$104$	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	0.0534166	+	0.998572i	$0.482989\pi$
$107$	−5.09063	+	18.9985i	−0.492130	+	1.83665i	−0.545546	+	0.838081i	$0.683678\pi$
$108$	6.58339	−	8.12981i	0.633487	−	0.782292i
$109$	−3.97502	+	18.7010i	−0.380738	+	1.79123i	0.202880	+	0.979204i	$0.434970\pi$
$109$	−3.97502	+	18.7010i	−0.380738	+	1.79123i	−0.583618	+	0.812029i	$0.698363\pi$
$110$		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	$-0.215347\pi$
$113$	7.77652	+	3.96233i	0.731553	+	0.372745i	−0.0481952	+	0.998838i	$0.515347\pi$
$114$	−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	$-0.454446\pi$
$127$	11.5760	−	5.89827i	1.02720	−	0.523386i	0.884579	+	0.466390i	$0.154446\pi$
$128$	−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	−0.839590	−	0.543220i	$-0.817205\pi$
$131$	1.44095	−	3.23643i	0.125896	−	0.282768i	0.965487	+	0.260452i	$0.0838716\pi$
$132$	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	$-0.288217\pi$
$137$	−4.12544	−	6.35261i	−0.352460	−	0.542740i	−0.969783	+	0.243969i	$0.921550\pi$
$138$	10.7947	−	0.565729i	0.918910	−	0.0481580i
$139$	−2.73221	+	8.40888i	−0.231743	+	0.713232i	0.765794	+	0.643086i	$0.222346\pi$
$139$	−2.73221	+	8.40888i	−0.231743	+	0.713232i	−0.997537	+	0.0701455i	$0.977654\pi$
$140$		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	−0.561154	−	0.827711i	$-0.689643\pi$
$149$	−1.52475	+	0.880317i	−0.124913	+	0.0721183i	0.436242	+	0.899830i	$0.356309\pi$
$150$		0			0
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	−0.964924	−	0.262529i	$-0.915444\pi$
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	0.709819	+	0.704385i	$0.248777\pi$
$152$	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	−0.983105	−	0.183043i	$-0.941405\pi$
$157$	−2.79709	−	10.4389i	−0.223232	−	0.833115i	0.759872	−	0.650072i	$-0.225261\pi$
$158$	−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	0.985936	+	0.167122i	$0.0534475\pi$
$163$	0.291986	+	5.57143i	0.0228701	+	0.436388i	−0.963066	+	0.269265i	$0.913219\pi$
$164$	−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	−0.839297	−	0.543673i	$-0.817033\pi$
$167$	1.64024	−	10.3561i	0.126926	−	0.801379i	0.966223	−	0.257706i	$-0.0829667\pi$
$168$	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	$-0.491427\pi$
$173$	−11.5132	−	7.47674i	−0.875330	−	0.568446i	−0.902260	+	0.431191i	$0.858093\pi$
$174$	−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	0.936358	−	0.351047i	$-0.114174\pi$
$179$	0.654680	+	1.47044i	0.0489331	+	0.109906i	−0.887425	+	0.460953i	$0.847508\pi$
$180$		0			0
$181$	2.04450	+	2.81402i	0.151967	+	0.209164i	0.878212	−	0.478271i	$-0.158736\pi$
$181$	2.04450	+	2.81402i	0.151967	+	0.209164i	−0.726245	+	0.687436i	$0.758736\pi$
$182$	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	−0.810627	−	0.585563i	$-0.800874\pi$
$191$	−1.98374	+	2.20317i	−0.143538	+	0.159415i	0.667089	+	0.744978i	$0.267540\pi$
$192$	6.87242	+	5.56517i	0.495974	+	0.401632i
$193$	−4.41207	−	16.4661i	−0.317588	−	1.18525i	−0.921556	−	0.388246i	$-0.873081\pi$
$193$	−4.41207	−	16.4661i	−0.317588	−	1.18525i	0.603968	−	0.797009i	$-0.293586\pi$
$194$	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	−0.823225	−	0.567716i	$-0.807827\pi$
$197$	−3.02785	−	19.1171i	−0.215725	−	1.36204i	0.607499	−	0.794320i	$-0.292173\pi$
$198$	2.76285	−	4.25441i	0.196347	−	0.302348i
$199$	−0.0959424	+	0.166177i	−0.00680118	+	0.0117800i	−0.869406	−	0.494098i	$-0.835498\pi$
$199$	−0.0959424	+	0.166177i	−0.00680118	+	0.0117800i	0.862605	+	0.505878i	$0.168832\pi$
$200$		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	−0.860265	−	0.509847i	$-0.829702\pi$
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	0.995650	+	0.0931759i	$0.0297019\pi$
$212$	−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	$-0.797313\pi$
$223$	−11.8807	+	6.05349i	−0.795587	+	0.405372i	0.00843996	+	0.999964i	$0.497313\pi$
$224$	−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	$-0.534815\pi$
$227$	−4.84563	−	0.253949i	−0.321616	−	0.0168552i	−0.212461	+	0.977170i	$0.568148\pi$
$228$	−3.51808	+	9.16491i	−0.232991	+	0.606961i
$229$	0.698945	−	6.65002i	0.0461876	−	0.439446i	−0.946852	−	0.321668i	$-0.895756\pi$
$229$	0.698945	−	6.65002i	0.0461876	−	0.439446i	0.993040	−	0.117777i	$-0.0375769\pi$
$230$		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	$-0.525395\pi$
$233$	8.06082	−	3.09426i	0.528082	−	0.202712i	0.607777	+	0.794108i	$0.292061\pi$
$234$	−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	0.832457	−	0.554090i	$-0.186934\pi$
$239$	18.2461	+	5.92852i	1.18024	+	0.383484i	0.347785	+	0.937574i	$0.386934\pi$
$240$		0			0
$241$	−5.39578	+	25.3851i	−0.347572	+	1.63520i	0.363152	+	0.931730i	$0.381700\pi$
$241$	−5.39578	+	25.3851i	−0.347572	+	1.63520i	−0.710725	+	0.703470i	$0.751633\pi$
$242$	−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	$-0.838295\pi$
$251$		−	15.4133i		−	0.972880i	0.873714	−	0.486440i	$-0.161705\pi$
$252$	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	$-0.819137\pi$
$257$	−29.5275	−	7.91188i	−1.84188	−	0.493529i	−0.999006	+	0.0445856i	$0.985803\pi$
$258$	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	$-0.687335\pi$
$263$	−0.341935	+	0.222055i	−0.0210846	+	0.0136925i	0.534054	+	0.845451i	$0.320668\pi$
$264$	−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	−0.868406	−	0.495854i	$-0.834855\pi$
$269$	−2.00211	−	19.0488i	−0.122071	−	1.16142i	0.746335	−	0.665570i	$-0.231812\pi$
$270$		0			0
$271$	−19.2007	−	2.01808i	−1.16636	−	0.122589i	−0.498509	−	0.866884i	$-0.666119\pi$
$271$	−19.2007	−	2.01808i	−1.16636	−	0.122589i	−0.667851	+	0.744295i	$0.732786\pi$
$272$	−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	−0.959892	−	0.280369i	$-0.909543\pi$
$277$	0.400242	−	7.63707i	0.0240482	−	0.458867i	0.983940	−	0.178497i	$-0.0571236\pi$
$278$	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	−0.0359618	−	0.999353i	$-0.511449\pi$
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	0.939329	+	0.343019i	$0.111449\pi$
$282$	−0.140701	+	0.525104i	−0.00837864	+	0.0312695i
$283$	−1.79337	+	2.21463i	−0.106605	+	0.131646i	−0.827656	−	0.561236i	$-0.810326\pi$
$283$	−1.79337	+	2.21463i	−0.106605	+	0.131646i	0.721051	+	0.692882i	$0.243659\pi$
$284$	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	$-0.257692\pi$
$293$	−0.584948	−	0.584948i	−0.0341730	−	0.0341730i	−0.723987	+	0.689814i	$0.757692\pi$
$294$	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	$-0.612123\pi$
$307$	10.4006	−	10.4006i	0.593593	−	0.593593i	0.938600	+	0.345007i	$0.112123\pi$
$308$	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	−0.379653	−	0.925129i	$-0.623957\pi$
$311$	8.83036	−	7.95089i	0.500724	−	0.450854i	0.880377	+	0.474275i	$0.157290\pi$
$312$	1.61100	+	2.48073i	0.0912050	+	0.140443i
$313$	−10.0595	+	0.527196i	−0.568597	+	0.0297989i	−0.334469	−	0.942407i	$-0.608557\pi$
$313$	−10.0595	+	0.527196i	−0.568597	+	0.0297989i	−0.234128	+	0.972206i	$0.575223\pi$
$314$	−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	0.981399	+	0.191981i	$0.0614913\pi$
$317$	6.77528	+	17.6502i	0.380538	+	0.991335i	−0.600861	+	0.799354i	$0.705175\pi$
$318$	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	0.992052	−	0.125830i	$-0.0401594\pi$
$331$	28.4245	+	12.6554i	1.56235	+	0.695605i	0.570302	+	0.821435i	$0.306826\pi$
$332$	−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	−0.147514	+	0.989060i	$0.547127\pi$
$337$	−15.8054	+	31.0198i	−0.860974	+	1.68976i	−0.713460	+	0.700696i	$0.752873\pi$
$338$	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	$-0.126056\pi$
$347$	25.1500	+	9.65416i	1.35012	+	0.518263i	0.427515	+	0.904008i	$0.359389\pi$
$348$	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	$-0.282836\pi$
$353$	10.8927	+	4.18132i	0.579760	+	0.222549i	−0.0507745	+	0.998710i	$0.516169\pi$
$354$	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	0.577192	−	0.816608i	$-0.304148\pi$
$359$	−3.30837	−	2.97887i	−0.174609	−	0.157219i	−0.751802	+	0.659389i	$0.770815\pi$
$360$		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	$-0.0494917\pi$
$367$	19.9593	+	16.1627i	1.04187	+	0.843688i	0.0539306	+	0.998545i	$0.482825\pi$
$368$	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	0.190770	−	0.981635i	$-0.438902\pi$
$373$	19.5053	−	30.0355i	1.00994	−	1.55518i	0.819175	−	0.573544i	$-0.194432\pi$
$374$	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	−0.314567	−	0.949235i	$-0.601859\pi$
$379$	13.3436	−	18.3659i	0.685416	−	0.943394i	0.999983	+	0.00584095i	$0.00185924\pi$
$380$		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	0.975293	+	0.220914i	$0.0709041\pi$
$383$	7.79546	+	20.3079i	0.398330	+	1.03768i	−0.576964	+	0.816770i	$0.695763\pi$
$384$	−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	−0.876641	−	0.481145i	$-0.840221\pi$
$389$	−9.65968	+	8.69762i	−0.489765	+	0.440987i	0.386876	+	0.922132i	$0.373554\pi$
$390$		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	$-0.178406\pi$
$397$	3.00714	+	3.71351i	0.150924	+	0.186376i	−0.696077	+	0.717968i	$0.745073\pi$
$398$	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	0.990874	−	0.134793i	$-0.0430370\pi$
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	−0.612171	+	0.790725i	$0.709704\pi$
$402$	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	−0.0474592	−	0.998873i	$-0.515112\pi$
$409$	−10.0531	−	2.13685i	−0.497094	−	0.105661i	−0.449634	+	0.893213i	$0.648446\pi$
$410$		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	−0.882414	−	0.470473i	$-0.844083\pi$
$419$	−14.4852	+	10.5241i	−0.707648	+	0.514137i	0.174766	+	0.984610i	$0.444083\pi$
$420$		0			0
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	0.867394	−	0.497621i	$-0.165793\pi$
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	−0.205227	+	0.978714i	$0.565793\pi$
$422$	−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	0.993688	+	0.112178i	$0.0357828\pi$
$431$	0.935006	+	8.89599i	0.0450377	+	0.428505i	−0.948650	+	0.316326i	$0.897551\pi$
$432$	−13.2859	−	3.55996i	−0.639220	−	0.171278i
$433$	17.4040	+	2.75652i	0.836382	+	0.132470i	0.559912	−	0.828552i	$-0.310835\pi$
$433$	17.4040	+	2.75652i	0.836382	+	0.132470i	0.276471	+	0.961022i	$0.410835\pi$
$434$	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	0.482363	−	0.875972i	$-0.339779\pi$
$439$	26.8046	−	5.69749i	1.27931	−	0.271926i	0.796950	+	0.604045i	$0.206445\pi$
$440$		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	$-0.331854\pi$
$443$	10.7062	+	2.86872i	0.508667	+	0.136297i	0.00464732	+	0.999989i	$0.498521\pi$
$444$	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	$0.395489\pi$
$449$			40.1154i			1.89316i	−0.322465	+	0.946581i	$0.604511\pi$
$450$		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	−0.380516	−	0.924774i	$-0.624254\pi$
$457$	8.79489	−	32.8230i	0.411408	−	1.53539i	0.791924	−	0.610620i	$-0.209080\pi$
$458$	−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	−0.490535	−	0.871422i	$-0.663198\pi$
$461$	−30.0506	−	9.76402i	−1.39959	−	0.454756i	−0.909060	+	0.416666i	$0.863198\pi$
$462$	−4.43027	+	1.91435i	−0.206115	+	0.0890634i
$463$	−16.9684	−	8.64582i	−0.788587	−	0.401805i	0.0128250	−	0.999918i	$-0.495918\pi$
$463$	−16.9684	−	8.64582i	−0.788587	−	0.401805i	−0.801412	+	0.598113i	$0.795918\pi$
$464$	−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	$-0.660691\pi$
$467$	−5.56287	+	2.13538i	−0.257419	+	0.0988138i	0.226236	+	0.974072i	$0.427358\pi$
$468$	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	−0.792794	−	0.609490i	$-0.791374\pi$
$479$	−19.0483	+	8.48083i	−0.870338	+	0.387499i	−0.0775436	+	0.996989i	$0.524708\pi$
$480$		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	−0.988541	−	0.150950i	$-0.951767\pi$
$487$	−15.9853	−	24.6153i	−0.724365	−	1.11542i	0.264176	−	0.964474i	$-0.414900\pi$
$488$	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	−0.994574	−	0.104036i	$-0.966824\pi$
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	0.743476	−	0.668762i	$-0.233176\pi$
$492$	−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	−0.393339	−	0.919394i	$-0.628680\pi$
$499$	4.60639	−	2.65950i	0.206210	−	0.119056i	0.599549	+	0.800338i	$0.295347\pi$
$500$		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	0.890560	+	0.454865i	$0.150313\pi$
$503$	4.13001	+	26.0759i	0.184148	+	1.16267i	−0.706412	+	0.707801i	$0.749687\pi$
$504$	−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	−0.805855	−	0.592113i	$-0.798294\pi$
$509$	−2.99499	+	3.32627i	−0.132750	+	0.147434i	0.673104	+	0.739548i	$0.264960\pi$
$510$		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	−0.983993	−	0.178206i	$-0.942971\pi$
$521$	−10.4542	−	23.4805i	−0.458006	−	1.02870i	0.525987	−	0.850492i	$-0.323696\pi$
$522$	5.70250	+	2.18899i	0.249592	+	0.0958093i
$523$	−18.4501	−	11.9816i	−0.806766	−	0.523920i	0.0741198	−	0.997249i	$-0.476385\pi$
$523$	−18.4501	−	11.9816i	−0.806766	−	0.523920i	−0.880885	+	0.473330i	$0.843052\pi$
$524$	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	−0.615223	−	0.788353i	$-0.710934\pi$
$541$	5.42224	−	6.02201i	0.233120	−	0.258906i	0.848343	+	0.529447i	$0.177601\pi$
$542$	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	−0.964107	−	0.265514i	$-0.914458\pi$
$547$	−3.02255	−	19.0836i	−0.129235	−	0.815958i	0.834872	−	0.550444i	$-0.185542\pi$
$548$	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	$-0.454177\pi$
$557$	17.9964	−	4.82211i	0.762531	−	0.204320i	0.619069	+	0.785336i	$0.287510\pi$
$558$	−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	$-0.0327589\pi$
$563$	11.7754	+	18.1325i	0.496273	+	0.764193i	−0.498436	+	0.866926i	$0.666092\pi$
$564$	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	−0.151424	−	0.988469i	$-0.548386\pi$
$569$	16.3273	−	36.6716i	0.684474	−	1.53735i	0.835898	−	0.548885i	$-0.184947\pi$
$570$		0			0
$571$	30.4188	−	13.5433i	1.27299	−	0.566770i	0.344727	−	0.938703i	$-0.387971\pi$
$571$	30.4188	−	13.5433i	1.27299	−	0.566770i	0.928260	+	0.371932i	$0.121305\pi$
$572$	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	$-0.445258\pi$
$577$	5.72503	+	0.300036i	0.238336	+	0.0124907i	0.0672061	+	0.997739i	$0.478592\pi$
$578$	−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	$-0.269843\pi$
$587$	10.7577	+	5.48135i	0.444020	+	0.226239i	−0.217662	+	0.976024i	$0.569843\pi$
$588$	−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	0.206951	+	0.978351i	$0.433646\pi$
$593$	−11.2370	+	41.9372i	−0.461449	+	1.72215i	−0.668401	+	0.743802i	$0.733021\pi$
$594$	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	0.486092	−	0.873908i	$-0.338422\pi$
$599$	−0.677665	−	0.391250i	−0.0276887	−	0.0159860i	−0.513780	+	0.857922i	$0.671755\pi$
$600$		0			0
$601$		−	7.23002i		−	0.294919i	−0.989068	−	0.147459i	$-0.952890\pi$
$601$		−	7.23002i		−	0.294919i	0.989068	−	0.147459i	$-0.0471095\pi$
$602$	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	$-0.405192\pi$
$607$	1.71540	+	0.459640i	0.0696260	+	0.0186562i	−0.223838	+	0.974626i	$0.571859\pi$
$608$	−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	$-0.690377\pi$
$613$	−0.918913	+	0.596749i	−0.0371145	+	0.0241025i	0.525948	+	0.850516i	$0.323710\pi$
$614$	−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	$-0.674479\pi$
$617$	−31.8056	−	5.03752i	−1.28045	−	0.202803i	−0.759343	+	0.650691i	$0.774479\pi$
$618$	−11.3897	−	3.05185i	−0.458160	−	0.122764i
$619$	1.93430	+	18.4036i	0.0777461	+	0.739705i	0.962065	+	0.272821i	$0.0879567\pi$
$619$	1.93430	+	18.4036i	0.0777461	+	0.739705i	−0.884319	+	0.466884i	$0.845377\pi$
$620$		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	−0.0974273	−	0.995243i	$-0.531061\pi$
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	0.916425	+	0.400206i	$0.131061\pi$
$632$	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	−0.582647	−	0.812725i	$-0.697983\pi$
$641$	−36.5968	−	7.77889i	−1.44549	−	0.307248i	−0.862840	+	0.505478i	$0.831316\pi$
$642$	31.8914	−	12.2419i	1.25865	−	0.483151i
$643$	−14.7951	−	14.7951i	−0.583460	−	0.583460i	0.352392	−	0.935852i	$-0.385368\pi$
$643$	−14.7951	−	14.7951i	−0.583460	−	0.583460i	−0.935852	+	0.352392i	$0.885368\pi$
$644$	−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	0.622014	+	0.783006i	$0.286315\pi$
$647$	−9.26299	+	24.1309i	−0.364166	+	0.948684i	−0.986180	+	0.165678i	$0.947019\pi$
$648$	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	$-0.0446212\pi$
$653$	16.5499	+	20.4375i	0.647649	+	0.799780i	−0.342542	+	0.939503i	$0.611288\pi$
$654$	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	−0.195906	−	0.980623i	$-0.562765\pi$
$659$	5.69893	−	1.85169i	0.221999	−	0.0721317i	0.417904	+	0.908491i	$0.362765\pi$
$660$		0			0
$661$	−34.1915	+	30.7862i	−1.32990	+	1.19744i	−0.366171	+	0.930547i	$0.619332\pi$
$661$	−34.1915	+	30.7862i	−1.32990	+	1.19744i	−0.963725	+	0.266897i	$0.914002\pi$
$662$	−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	$-0.259456\pi$
$673$	−7.94108	−	15.5853i	−0.306106	−	0.600767i	−0.991899	+	0.127030i	$0.959456\pi$
$674$	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	−0.256301	−	0.966597i	$-0.582504\pi$
$677$	19.0194	−	29.2874i	0.730976	−	1.12560i	0.987277	−	0.159008i	$-0.0508295\pi$
$678$	−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	0.999998	+	0.00209925i	$0.000668214\pi$
$683$	31.6215	+	25.6066i	1.20996	+	0.979808i	0.209965	+	0.977709i	$0.432665\pi$
$684$	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	0.881168	−	0.472803i	$-0.156758\pi$
$691$	13.2239	+	11.9069i	0.503062	+	0.452959i	−0.378106	+	0.925762i	$0.623425\pi$
$692$	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	0.658233	−	0.752814i	$-0.271304\pi$
$709$	−0.576558	−	0.519135i	−0.0216531	−	0.0194965i	−0.679886	+	0.733318i	$0.737971\pi$
$710$		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	0.923506	−	0.383583i	$-0.125310\pi$
$719$	33.6892	+	14.9994i	1.25639	+	0.559383i	0.332888	+	0.942966i	$0.391977\pi$
$720$		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	$-0.0296126\pi$
$727$	9.04006	+	17.7421i	0.335277	+	0.658019i	−0.660398	+	0.750915i	$0.729613\pi$
$728$	−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	$-0.116902\pi$
$733$	−0.0143601	−	0.0374092i	−0.000530401	−	0.00138174i	−0.933845	+	0.357677i	$0.883569\pi$
$734$	−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	−0.361384	−	0.932417i	$-0.617696\pi$
$739$	14.3575	−	12.9276i	0.528151	−	0.475549i	0.889534	+	0.456868i	$0.151029\pi$
$740$		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	$-0.893345\pi$
$743$	−16.7789	+	16.7789i	−0.615557	+	0.615557i	0.328831	+	0.944389i	$0.393345\pi$
$744$	−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	0.719227	−	0.694775i	$-0.244496\pi$
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	−0.961306	+	0.275482i	$0.911163\pi$
$752$	−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	$-0.259294\pi$
$757$	−1.13591	−	1.13591i	−0.0412853	−	0.0412853i	−0.727448	+	0.686163i	$0.759294\pi$
$758$	−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	0.919446	+	0.393217i	$0.128638\pi$
$761$	6.60486	+	31.0734i	0.239426	+	1.12641i	−0.680020	+	0.733194i	$0.738029\pi$
$762$	−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	−0.770259	−	0.637731i	$-0.779873\pi$
$769$	−11.1412	+	8.09458i	−0.401763	+	0.291898i	0.368495	+	0.929630i	$0.379873\pi$
$770$		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	0.972754	+	0.231841i	$0.0744750\pi$
$773$	−0.525618	+	10.0294i	−0.0189052	+	0.360732i	−0.991659	+	0.128891i	$0.958858\pi$
$774$	−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	$-0.557985\pi$
$787$	18.0549	−	11.7250i	0.643586	−	0.417950i	0.824746	+	0.565504i	$0.191318\pi$
$788$	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	$-0.520222\pi$
$797$	5.20937	−	0.825084i	0.184526	−	0.0292260i	0.248013	+	0.968757i	$0.420222\pi$
$798$	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	−0.937411	−	0.348224i	$-0.886785\pi$
$809$	1.72341	−	8.10801i	0.0605919	−	0.285063i	0.998003	+	0.0631613i	$0.0201182\pi$
$810$		0			0
$811$	22.9445	+	7.45511i	0.805689	+	0.261784i	0.682771	−	0.730632i	$-0.260775\pi$
$811$	22.9445	+	7.45511i	0.805689	+	0.261784i	0.122918	+	0.992417i	$0.460775\pi$
$812$	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	0.954703	+	0.297560i	$0.0961729\pi$
$821$	−1.17488	+	11.1783i	−0.0410037	+	0.390124i	−0.995707	+	0.0925640i	$0.970494\pi$
$822$	−4.71451	+	12.2817i	−0.164437	+	0.428374i
$823$	17.1411	+	0.898326i	0.597501	+	0.0313137i	0.348689	−	0.937238i	$-0.386627\pi$
$823$	17.1411	+	0.898326i	0.597501	+	0.0313137i	0.248811	+	0.968552i	$0.419960\pi$
$824$	−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	$-0.517374\pi$
$827$	20.7397	−	10.5674i	0.721190	−	0.367465i	0.775745	+	0.631046i	$0.217374\pi$
$828$	21.4590	+	26.4997i	0.745753	+	0.920928i
$829$	23.1374	−	10.3014i	0.803596	−	0.357784i	0.0365142	−	0.999333i	$-0.488375\pi$
$829$	23.1374	−	10.3014i	0.803596	−	0.357784i	0.767082	+	0.641549i	$0.221708\pi$
$830$		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	−0.0289189	+	0.999582i	$0.509206\pi$
$839$	−17.1783	+	52.8695i	−0.593062	+	1.82526i	−0.564144	+	0.825677i	$0.690794\pi$
$840$		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	−0.793465	−	0.608616i	$-0.791725\pi$
$853$	−6.62710	−	41.8419i	−0.226908	−	1.43264i	0.566557	−	0.824023i	$-0.308275\pi$
$854$	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	0.902274	+	0.431164i	$0.141897\pi$
$857$	9.84983	+	36.7601i	0.336464	+	1.25570i	−0.565810	+	0.824536i	$0.691436\pi$
$858$	−6.49517	−	5.25969i	−0.221742	−	0.179563i
$859$	−34.3314	+	38.1289i	−1.17137	+	1.30094i	−0.226307	+	0.974056i	$0.572665\pi$
$859$	−34.3314	+	38.1289i	−1.17137	+	1.30094i	−0.945064	+	0.326884i	$0.894001\pi$
$860$		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	0.946446	+	0.322863i	$0.104645\pi$
$863$	1.14373	+	21.8237i	0.0389331	+	0.742887i	−0.907513	+	0.420025i	$0.862021\pi$
$864$	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	$-0.324278\pi$
$877$	−1.18764	−	0.771263i	−0.0401038	−	0.0260437i	−0.564535	+	0.825409i	$0.690945\pi$
$878$	−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	0.715293	−	0.698825i	$-0.246293\pi$
$881$	−5.05676	−	6.96003i	−0.170367	−	0.234489i	−0.885659	+	0.464335i	$0.846293\pi$
$882$	−33.7160	−	2.51208i	−1.13528	−	0.0845860i
$883$	−6.37108	+	40.2254i	−0.214404	+	1.35369i	0.612108	+	0.790774i	$0.290322\pi$
$883$	−6.37108	+	40.2254i	−0.214404	+	1.35369i	−0.826512	+	0.562919i	$0.809678\pi$
$884$	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	−0.929686	−	0.368353i	$-0.879922\pi$
$887$	−1.29841	−	24.7751i	−0.0435963	−	0.831866i	0.886090	−	0.463514i	$-0.153411\pi$
$888$	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	$-0.756690\pi$
$907$	−30.1426	+	8.07670i	−1.00087	+	0.268182i	−0.279060	+	0.960274i	$0.590023\pi$
$908$	−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	0.560000	+	0.828492i	$0.310801\pi$
$911$	−11.4702	+	35.3017i	−0.380025	+	1.16960i	−0.940025	+	0.341105i	$0.889199\pi$
$912$	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	0.366422	+	0.930449i	$0.380583\pi$
$919$	−17.2862	+	38.8255i	−0.570220	+	1.28074i	−0.936643	+	0.350287i	$0.886084\pi$
$920$		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	0.937186	+	0.348829i	$0.113421\pi$
$929$	−1.58633	+	15.0929i	−0.0520459	+	0.495183i	−0.989232	+	0.146354i	$0.953246\pi$
$930$		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	$-0.216157\pi$
$937$	22.2665	+	11.3453i	0.727415	+	0.370636i	−0.0507375	+	0.998712i	$0.516157\pi$
$938$	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	0.884789	+	0.465992i	$0.154302\pi$
$941$	−3.46764	+	16.3140i	−0.113042	+	0.531820i	−0.997831	+	0.0658284i	$0.979031\pi$
$942$	−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	$-0.589615\pi$
$947$	18.5885	−	15.0527i	0.604047	−	0.489147i	0.881875	+	0.471483i	$0.156281\pi$
$948$	−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	$-0.881380\pi$
$953$	−52.6232	+	8.33470i	−1.70463	+	0.269987i	−0.773270	+	0.634077i	$0.781380\pi$
$954$	−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	$-0.278752\pi$
$967$	31.4763	+	4.98535i	1.01221	+	0.160318i	0.371768	+	0.928326i	$0.378752\pi$
$968$	−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	−0.535937	−	0.844258i	$-0.680042\pi$
$971$	−38.5053	−	4.04707i	−1.23569	−	0.129877i	−0.699757	+	0.714381i	$0.746708\pi$
$972$	−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	0.861236	+	0.508206i	$0.169691\pi$
$977$	−1.51297	+	28.8691i	−0.0484040	+	0.923604i	−0.909640	+	0.415398i	$0.863642\pi$
$978$	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	$-0.833203\pi$
$983$	−6.15724	+	7.60355i	−0.196385	+	0.242516i	0.669435	+	0.742871i	$0.266536\pi$
$984$	−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	0.571176	−	0.820828i	$-0.306487\pi$
$991$	23.8969	+	5.07944i	0.759110	+	0.161354i	0.187934	+	0.982182i	$0.439821\pi$
$992$	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	$-0.770923\pi$
$997$	7.82705	−	20.3902i	0.247885	−	0.645763i	0.999911	+	0.0133710i	$0.00425626\pi$
$998$	−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.a.507.3		288
5.2	odd	4		175.2.x.a.3.16	✓	288
5.3	odd	4		875.2.bb.c.493.3		288
5.4	even	2		875.2.bb.b.507.16		288
7.5	odd	6	inner	875.2.bb.a.257.3		288
25.6	even	5		875.2.bb.c.857.16		288
25.8	odd	20	inner	875.2.bb.a.143.3		288
25.17	odd	20		875.2.bb.b.143.16		288
25.19	even	10		175.2.x.a.17.3	yes	288
35.12	even	12		175.2.x.a.103.3	yes	288
35.19	odd	6		875.2.bb.b.257.16		288
35.33	even	12		875.2.bb.c.243.16		288
175.19	odd	30		175.2.x.a.117.16	yes	288
175.33	even	60	inner	875.2.bb.a.768.3		288
175.117	even	60		875.2.bb.b.768.16		288
175.131	odd	30		875.2.bb.c.607.3		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.16	✓	288	5.2	odd	4
175.2.x.a.17.3	yes	288	25.19	even	10
175.2.x.a.103.3	yes	288	35.12	even	12
175.2.x.a.117.16	yes	288	175.19	odd	30
875.2.bb.a.143.3		288	25.8	odd	20	inner
875.2.bb.a.257.3		288	7.5	odd	6	inner
875.2.bb.a.507.3		288	1.1	even	1	trivial
875.2.bb.a.768.3		288	175.33	even	60	inner
875.2.bb.b.143.16		288	25.17	odd	20
875.2.bb.b.257.16		288	35.19	odd	6
875.2.bb.b.507.16		288	5.4	even	2
875.2.bb.b.768.16		288	175.117	even	60
875.2.bb.c.243.16		288	35.33	even	12
875.2.bb.c.493.3		288	5.3	odd	4
875.2.bb.c.607.3		288	175.131	odd	30
875.2.bb.c.857.16		288	25.6	even	5

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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