LMFDB - Embedded newform 875.2.bb.c.607.3

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 = [288,8] 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			607.3
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.c.493.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13877 - 1.75355i) q^{2} +(-0.297680 - 0.775483i) q^{3} +(-0.964662 + 2.16667i) q^{4} +(-1.02086 + 1.40509i) q^{6} +(2.15744 + 1.53148i) q^{7} +(0.767632 - 0.121581i) q^{8} +(1.71667 - 1.54570i) q^{9} +(-0.702779 + 0.780515i) q^{11} +(1.96737 + 0.103106i) q^{12} +(-4.08239 + 2.08008i) q^{13} +(0.228707 - 5.52718i) q^{14} +(2.08662 + 2.31743i) q^{16} +(-1.41941 - 1.75283i) q^{17} +(-4.66535 - 1.25008i) q^{18} +(-4.55223 + 2.02678i) q^{19} +(0.545413 - 2.12895i) q^{21} +(2.16897 + 0.343531i) q^{22} +(-5.21979 + 3.38977i) q^{23} +(-0.322792 - 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(-3.93004 - 2.00245i) q^{27} +(-5.39942 + 3.19709i) q^{28} +(-0.743348 - 1.02313i) q^{29} +(-10.1310 - 1.06481i) q^{31} +(2.08985 - 7.79943i) q^{32} +(0.814479 + 0.312649i) q^{33} +(-1.45729 + 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-0.328991 + 6.27752i) q^{37} +(8.73799 + 5.67452i) q^{38} +(2.82832 + 2.54663i) q^{39} +(-5.32280 - 1.72948i) q^{41} +(-4.35431 + 1.46797i) q^{42} +(-4.80861 + 4.80861i) q^{43} +(-1.01317 - 2.27562i) q^{44} +(11.8882 + 5.29299i) q^{46} +(-0.243253 - 0.196982i) q^{47} +(1.17598 - 2.30799i) q^{48} +(2.30911 + 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(-0.568717 - 10.8518i) q^{52} +(-0.261509 + 0.100384i) q^{53} +(0.963998 + 9.17183i) q^{54} +(1.84232 + 0.913312i) q^{56} +(2.92684 + 2.92684i) q^{57} +(-0.947608 + 2.46860i) q^{58} +(6.72559 - 1.42957i) q^{59} +(1.10261 - 5.18739i) q^{61} +(9.66967 + 18.9778i) q^{62} +(6.07084 - 0.705699i) q^{63} +(-10.1249 + 3.28979i) q^{64} +(-0.379257 - 1.78426i) q^{66} +(9.54564 - 7.72991i) q^{67} +(5.16706 - 1.38451i) q^{68} +(4.18254 + 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.12985 - 1.39524i) q^{72} +(1.29435 - 0.0678338i) q^{73} +(11.3826 - 6.57173i) q^{74} -11.8183i q^{76} +(-2.71155 + 0.607621i) q^{77} +(1.24484 - 7.85959i) q^{78} +(-10.7765 + 1.13266i) q^{79} +(0.341411 - 3.24831i) q^{81} +(3.02870 + 11.3033i) q^{82} +(0.579789 + 3.66064i) q^{83} +(4.08659 + 3.23545i) q^{84} +(13.9080 + 2.95623i) q^{86} +(-0.572141 + 0.881019i) q^{87} +(-0.444580 + 0.684593i) q^{88} +(-10.3731 - 2.20488i) q^{89} +(-11.9931 - 1.76446i) q^{91} +(-2.30917 - 14.5795i) q^{92} +(2.19006 + 8.17341i) q^{93} +(-0.0684094 + 0.650872i) q^{94} +(-6.67043 + 0.701090i) q^{96} +(0.775456 - 4.89604i) q^{97} +(8.95821 - 11.5743i) q^{98} +2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.13877	−	1.75355i	−0.805229	−	1.23994i	−0.967418	−	0.253185i	$-0.918522\pi$
$2$	−1.13877	−	1.75355i	−0.805229	−	1.23994i	0.162189	−	0.986760i	$-0.448145\pi$
$3$	−0.297680	−	0.775483i	−0.171866	−	0.447725i	0.820410	−	0.571775i	$-0.193745\pi$
$3$	−0.297680	−	0.775483i	−0.171866	−	0.447725i	−0.992276	+	0.124050i	$0.960412\pi$
$4$	−0.964662	+	2.16667i	−0.482331	+	1.08333i
$5$		0			0
$5$		0			0
$6$	−1.02086	+	1.40509i	−0.416763	+	0.573625i
$7$	2.15744	+	1.53148i	0.815436	+	0.578847i
$7$	2.15744	+	1.53148i	0.815436	+	0.578847i
$8$	0.767632	−	0.121581i	0.271399	−	0.0429853i
$9$	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	$0.283946\pi$
$12$	1.96737	+	0.103106i	0.567932	+	0.0297640i
$13$	−4.08239	+	2.08008i	−1.13225	+	0.576911i	−0.916698	−	0.399580i	$-0.869156\pi$
$13$	−4.08239	+	2.08008i	−1.13225	+	0.576911i	−0.215554	+	0.976492i	$0.569156\pi$
$14$	0.228707	−	5.52718i	0.0611245	−	1.47720i
$15$		0			0
$16$	2.08662	+	2.31743i	0.521655	+	0.579357i
$17$	−1.41941	−	1.75283i	−0.344259	−	0.425124i	0.575382	−	0.817885i	$-0.304853\pi$
$17$	−1.41941	−	1.75283i	−0.344259	−	0.425124i	−0.919641	+	0.392761i	$0.871520\pi$
$18$	−4.66535	−	1.25008i	−1.09963	−	0.294646i
$19$	−4.55223	+	2.02678i	−1.04435	+	0.464976i	−0.855919	−	0.517110i	$-0.827008\pi$
$19$	−4.55223	+	2.02678i	−1.04435	+	0.464976i	−0.188434	+	0.982086i	$0.560341\pi$
$20$		0			0
$21$	0.545413	−	2.12895i	0.119019	−	0.464575i
$22$	2.16897	+	0.343531i	0.462426	+	0.0732411i
$23$	−5.21979	+	3.38977i	−1.08840	+	0.706816i	−0.958609	−	0.284725i	$-0.908098\pi$
$23$	−5.21979	+	3.38977i	−1.08840	+	0.706816i	−0.129793	+	0.991541i	$0.541431\pi$
$24$	−0.322792	−	0.559093i	−0.0658897	−	0.114124i
$25$		0			0
$26$	8.29642	+	4.78994i	1.62706	+	0.939384i
$27$	−3.93004	−	2.00245i	−0.756336	−	0.385373i
$28$	−5.39942	+	3.19709i	−1.02039	+	0.604194i
$29$	−0.743348	−	1.02313i	−0.138036	−	0.189991i	0.734402	−	0.678714i	$-0.237463\pi$
$29$	−0.743348	−	1.02313i	−0.138036	−	0.189991i	−0.872439	+	0.488724i	$0.837463\pi$
$30$		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	$0.900989\pi$
$32$	2.08985	−	7.79943i	0.369437	−	1.37876i
$33$	0.814479	+	0.312649i	0.141783	+	0.0544253i
$34$	−1.45729	+	4.48507i	−0.249923	+	0.769184i
$35$		0			0
$36$	1.69301	+	5.21054i	0.282168	+	0.868424i
$37$	−0.328991	+	6.27752i	−0.0540858	+	1.03202i	0.827940	+	0.560817i	$0.189513\pi$
$37$	−0.328991	+	6.27752i	−0.0540858	+	1.03202i	−0.882026	+	0.471202i	$0.843820\pi$
$38$	8.73799	+	5.67452i	1.41749	+	0.920528i
$39$	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	$0.743970\pi$
$42$	−4.35431	+	1.46797i	−0.671885	+	0.226513i
$43$	−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
$47$	−0.243253	−	0.196982i	−0.0354821	−	0.0287328i	0.611415	−	0.791310i	$-0.290600\pi$
$47$	−0.243253	−	0.196982i	−0.0354821	−	0.0287328i	−0.646897	+	0.762577i	$0.723934\pi$
$48$	1.17598	−	2.30799i	0.169738	−	0.333130i
$49$	2.30911	+	6.60818i	0.329873	+	0.944025i
$50$		0			0
$51$	−0.936759	+	1.62251i	−0.131172	+	0.227197i
$52$	−0.568717	−	10.8518i	−0.0788669	−	1.50487i
$53$	−0.261509	+	0.100384i	−0.0359210	+	0.0137888i	−0.376262	−	0.926513i	$-0.622791\pi$
$53$	−0.261509	+	0.100384i	−0.0359210	+	0.0137888i	0.340341	+	0.940302i	$0.389457\pi$
$54$	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
$58$	−0.947608	+	2.46860i	−0.124427	+	0.324143i
$59$	6.72559	−	1.42957i	0.875597	−	0.186114i	0.251875	−	0.967760i	$-0.418953\pi$
$59$	6.72559	−	1.42957i	0.875597	−	0.186114i	0.623722	+	0.781646i	$0.285620\pi$
$60$		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	$-0.0435939\pi$
$62$	9.66967	+	18.9778i	1.22805	+	2.41018i
$63$	6.07084	−	0.705699i	0.764854	−	0.0889097i
$64$	−10.1249	+	3.28979i	−1.26562	+	0.411224i
$65$		0			0
$66$	−0.379257	−	1.78426i	−0.0466833	−	0.219627i
$67$	9.54564	−	7.72991i	1.16619	−	0.944359i	0.167051	−	0.985948i	$-0.446575\pi$
$67$	9.54564	−	7.72991i	1.16619	−	0.944359i	0.999135	+	0.0415894i	$0.0132421\pi$
$68$	5.16706	−	1.38451i	0.626598	−	0.167896i
$69$	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	$0.338989\pi$
$72$	1.12985	−	1.39524i	0.133154	−	0.164431i
$73$	1.29435	−	0.0678338i	0.151492	−	0.00793934i	0.0235607	−	0.999722i	$-0.492500\pi$
$73$	1.29435	−	0.0678338i	0.151492	−	0.00793934i	0.127931	+	0.991783i	$0.459166\pi$
$74$	11.3826	−	6.57173i	1.32320	−	0.763948i
$75$		0			0
$76$		−	11.8183i		−	1.35566i
$77$	−2.71155	+	0.607621i	−0.309010	+	0.0692448i
$78$	1.24484	−	7.85959i	0.140950	−	0.889924i
$79$	−10.7765	+	1.13266i	−1.21245	+	0.127434i	−0.689090	−	0.724676i	$-0.741989\pi$
$79$	−10.7765	+	1.13266i	−1.21245	+	0.127434i	−0.523363	+	0.852110i	$0.675323\pi$
$80$		0			0
$81$	0.341411	−	3.24831i	0.0379346	−	0.360923i
$82$	3.02870	+	11.3033i	0.334464	+	1.24824i
$83$	0.579789	+	3.66064i	0.0636401	+	0.401808i	0.998860	+	0.0477399i	$0.0152019\pi$
$83$	0.579789	+	3.66064i	0.0636401	+	0.401808i	−0.935220	+	0.354068i	$0.884798\pi$
$84$	4.08659	+	3.23545i	0.445883	+	0.353016i
$85$		0			0
$86$	13.9080	+	2.95623i	1.49974	+	0.318779i
$87$	−0.572141	+	0.881019i	−0.0613399	+	0.0944552i
$88$	−0.444580	+	0.684593i	−0.0473924	+	0.0729778i
$89$	−10.3731	−	2.20488i	−1.09955	−	0.233716i	−0.377811	−	0.925883i	$-0.623323\pi$
$89$	−10.3731	−	2.20488i	−1.09955	−	0.233716i	−0.721738	+	0.692166i	$0.756656\pi$
$90$		0			0
$91$	−11.9931	−	1.76446i	−1.25722	−	0.184966i
$92$	−2.30917	−	14.5795i	−0.240748	−	1.52002i
$93$	2.19006	+	8.17341i	0.227098	+	0.847543i
$94$	−0.0684094	+	0.650872i	−0.00705589	+	0.0671323i
$95$		0			0
$96$	−6.67043	+	0.701090i	−0.680798	+	0.0715547i
$97$	0.775456	−	4.89604i	0.0787356	−	0.497117i	−0.916533	−	0.399958i	$-0.869025\pi$
$97$	0.775456	−	4.89604i	0.0787356	−	0.497117i	0.995269	−	0.0971587i	$-0.0309754\pi$
$98$	8.95821	−	11.5743i	0.904916	−	1.16918i
$99$			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	$0.0603704\pi$
$102$	3.91190	−	0.205014i	0.387336	−	0.0202994i
$103$	4.27261	−	5.27623i	0.420993	−	0.519883i	−0.521888	−	0.853014i	$-0.674772\pi$
$103$	4.27261	−	5.27623i	0.420993	−	0.519883i	0.942880	+	0.333132i	$0.108105\pi$
$104$	−2.88088	+	2.09308i	−0.282493	+	0.205243i
$105$		0			0
$106$	0.473825	+	0.344254i	0.0460220	+	0.0334369i
$107$	18.9985	−	5.09063i	1.83665	−	0.492130i	0.838081	−	0.545546i	$-0.183678\pi$
$107$	18.9985	−	5.09063i	1.83665	−	0.492130i	0.998572	+	0.0534166i	$0.0170111\pi$
$108$	8.12981	−	6.58339i	0.782292	−	0.633487i
$109$	3.97502	+	18.7010i	0.380738	+	1.79123i	0.583618	+	0.812029i	$0.301637\pi$
$109$	3.97502	+	18.7010i	0.380738	+	1.79123i	−0.202880	+	0.979204i	$0.565030\pi$
$110$		0			0
$111$	4.96605	−	1.61357i	0.471356	−	0.153153i
$112$	0.952659	+	8.19534i	0.0900178	+	0.774387i
$113$	−3.96233	−	7.77652i	−0.372745	−	0.731553i	0.626093	−	0.779748i	$-0.284653\pi$
$113$	−3.96233	−	7.77652i	−0.372745	−	0.731553i	−0.998838	+	0.0481952i	$0.984653\pi$
$114$	1.79937	−	8.46535i	0.168526	−	0.792852i
$115$		0			0
$116$	2.93386	−	0.623612i	0.272402	−	0.0579009i
$117$	−3.79296	+	9.88099i	−0.350659	+	0.913498i
$118$	−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
$122$	−10.3520	+	3.97374i	−0.937222	+	0.359766i
$123$	0.243307	+	4.64257i	0.0219383	+	0.418607i
$124$	12.0801	−	20.9234i	1.08483	−	1.87897i
$125$		0			0
$126$	−8.15074	−	9.84188i	−0.726126	−	0.876784i
$127$	−5.89827	+	11.5760i	−0.523386	+	1.02720i	0.466390	+	0.884579i	$0.345554\pi$
$127$	−5.89827	+	11.5760i	−0.523386	+	1.02720i	−0.989777	+	0.142625i	$0.954446\pi$
$128$	4.74853	+	3.84528i	0.419715	+	0.339878i
$129$	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
$133$	−12.9252	−	2.59900i	−1.12075	−	0.225362i
$134$	−24.4250	−	7.93617i	−2.11000	−	0.685580i
$135$		0			0
$136$	−1.30270	−	1.17295i	−0.111705	−	0.100580i
$137$	−6.35261	−	4.12544i	−0.542740	−	0.352460i	0.243969	−	0.969783i	$-0.421550\pi$
$137$	−6.35261	−	4.12544i	−0.542740	−	0.352460i	−0.786710	+	0.617323i	$0.788217\pi$
$138$	0.565729	−	10.7947i	0.0481580	−	0.918910i
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	0.997537	+	0.0701455i	$0.0223463\pi$
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	−0.765794	+	0.643086i	$0.777654\pi$
$140$		0			0
$141$	−0.0803449	+	0.247276i	−0.00676626	+	0.0208244i
$142$	4.01920	+	1.54283i	0.337284	+	0.129471i
$143$	1.24548	−	4.64821i	0.104153	−	0.388703i
$144$	7.16410	+	0.752977i	0.597008	+	0.0627481i
$145$		0			0
$146$	−1.59291	−	2.19245i	−0.131830	−	0.181448i
$147$	4.43715	−	3.75780i	0.365970	−	0.309938i
$148$	−13.2839	−	6.76851i	−1.09193	−	0.556368i
$149$	1.52475	+	0.880317i	0.124913	+	0.0721183i	0.561154	−	0.827711i	$-0.310357\pi$
$149$	1.52475	+	0.880317i	0.124913	+	0.0721183i	−0.436242	+	0.899830i	$0.643691\pi$
$150$		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	$0.915444\pi$
$152$	−3.24802	+	2.10929i	−0.263449	+	0.171086i
$153$	−5.14602	−	0.815050i	−0.416031	−	0.0658929i
$154$	4.15332	+	4.06289i	0.334684	+	0.327397i
$155$		0			0
$156$	−8.24606	+	3.67138i	−0.660213	+	0.293946i
$157$	−10.4389	−	2.79709i	−0.833115	−	0.223232i	−0.183043	−	0.983105i	$-0.558595\pi$
$157$	−10.4389	−	2.79709i	−0.833115	−	0.223232i	−0.650072	+	0.759872i	$0.725261\pi$
$158$	14.2581	+	17.6073i	1.13431	+	1.40076i
$159$	0.155692	+	0.172913i	0.0123472	+	0.0137129i
$160$		0			0
$161$	−16.4528	−	0.680794i	−1.29666	−	0.0536541i
$162$	−6.08485	+	3.10038i	−0.478071	+	0.243589i
$163$	−5.57143	−	0.291986i	−0.436388	−	0.0228701i	−0.167122	−	0.985936i	$-0.553448\pi$
$163$	−5.57143	−	0.291986i	−0.436388	−	0.0228701i	−0.269265	+	0.963066i	$0.586781\pi$
$164$	8.88192	−	9.86438i	0.693562	−	0.770278i
$165$		0			0
$166$	5.75886	−	5.18530i	0.446975	−	0.402458i
$167$	−10.3561	+	1.64024i	−0.801379	+	0.126926i	−0.543673	−	0.839297i	$-0.682967\pi$
$167$	−10.3561	+	1.64024i	−0.801379	+	0.126926i	−0.257706	+	0.966223i	$0.582967\pi$
$168$	0.159836	−	1.70056i	0.0123316	−	0.131201i
$169$	4.69799	−	6.46623i	0.361384	−	0.497402i
$170$		0			0
$171$	−4.68190	+	10.5157i	−0.358034	+	0.804157i
$172$	−5.77997	−	15.0573i	−0.440718	−	1.14811i
$173$	7.47674	+	11.5132i	0.568446	+	0.875330i	0.999637	−	0.0269305i	$-0.00857330\pi$
$173$	7.47674	+	11.5132i	0.568446	+	0.875330i	−0.431191	+	0.902260i	$0.641907\pi$
$174$	2.19644			0.166512
$175$		0			0
$176$	−3.27522			−0.246879
$177$	−3.11068	−	4.79002i	−0.233813	−	0.360040i
$178$	7.94621	+	20.7006i	0.595594	+	1.55158i
$179$	−0.654680	+	1.47044i	−0.0489331	+	0.109906i	−0.936358	−	0.351047i	$-0.885826\pi$
$179$	−0.654680	+	1.47044i	−0.0489331	+	0.109906i	0.887425	+	0.460953i	$0.152492\pi$
$180$		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	$0.158736\pi$
$182$	10.5633	+	23.0398i	0.783005	+	1.70783i
$183$	−4.35096	+	0.689125i	−0.321632	+	0.0509416i
$184$	−3.59475	+	3.23672i	−0.265008	+	0.238614i
$185$		0			0
$186$	11.8385	−	13.1480i	0.868040	−	0.964056i
$187$	2.36565	+	0.123978i	0.172993	+	0.00906619i
$188$	0.661452	−	0.337027i	0.0482414	−	0.0245802i
$189$	−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	$0.800874\pi$
$192$	5.56517	+	6.87242i	0.401632	+	0.495974i
$193$	16.4661	+	4.41207i	1.18525	+	0.317588i	0.797009	−	0.603968i	$-0.206414\pi$
$193$	16.4661	+	4.41207i	1.18525	+	0.317588i	0.388246	+	0.921556i	$0.373081\pi$
$194$	−9.46849	+	4.21564i	−0.679798	+	0.302665i
$195$		0			0
$196$	−16.5452	−	1.37159i	−1.18180	−	0.0979705i
$197$	−19.1171	−	3.02785i	−1.36204	−	0.215725i	−0.567716	−	0.823225i	$-0.692173\pi$
$197$	−19.1171	−	3.02785i	−1.36204	−	0.215725i	−0.794320	+	0.607499i	$0.792173\pi$
$198$	4.25441	−	2.76285i	0.302348	−	0.196347i
$199$	0.0959424	+	0.166177i	0.00680118	+	0.0117800i	0.869406	−	0.494098i	$-0.164502\pi$
$199$	0.0959424	+	0.166177i	0.00680118	+	0.0117800i	−0.862605	+	0.505878i	$0.831168\pi$
$200$		0			0
$201$	−8.83596	−	5.10144i	−0.623240	−	0.359828i
$202$	−28.3174	−	14.4284i	−1.99241	−	1.01518i
$203$	−0.0368211	−	3.34577i	−0.00258434	−	0.234827i
$204$	−2.61179	−	3.59482i	−0.182862	−	0.251688i
$205$		0			0
$206$	−14.1176	−	1.48382i	−0.983621	−	0.103383i
$207$	−3.72111	+	13.8874i	−0.258635	+	0.965239i
$208$	−13.3388	−	5.12030i	−0.924883	−	0.355029i
$209$	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	$0.829702\pi$
$212$	0.0347694	−	0.663440i	0.00238797	−	0.0455652i
$213$	1.43441	+	0.931518i	0.0982843	+	0.0638266i
$214$	−30.5615	−	27.5177i	−2.08914	−	1.88107i
$215$		0			0
$216$	−3.26028	−	1.05933i	−0.221834	−	0.0720783i
$217$	−20.2263	−	17.8128i	−1.37305	−	1.20921i
$218$	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
$222$	−8.48463	−	6.87072i	−0.569451	−	0.461132i
$223$	−6.05349	+	11.8807i	−0.405372	+	0.795587i	−0.999964	−	0.00843996i	$-0.997313\pi$
$223$	−6.05349	+	11.8807i	−0.405372	+	0.795587i	0.594592	+	0.804027i	$0.297313\pi$
$224$	16.4534	−	13.6262i	1.09934	−	0.910441i
$225$		0			0
$226$	−9.12431	+	15.8038i	−0.606940	+	1.05125i
$227$	−0.253949	−	4.84563i	−0.0168552	−	0.321616i	−0.994025	−	0.109155i	$-0.965185\pi$
$227$	−0.253949	−	4.84563i	−0.0168552	−	0.321616i	0.977170	−	0.212461i	$-0.0681478\pi$
$228$	−9.16491	+	3.51808i	−0.606961	+	0.232991i
$229$	−0.698945	−	6.65002i	−0.0461876	−	0.439446i	−0.993040	−	0.117777i	$-0.962423\pi$
$229$	−0.698945	−	6.65002i	−0.0461876	−	0.439446i	0.946852	−	0.321668i	$-0.104244\pi$
$230$		0			0
$231$	1.27837	+	1.92189i	0.0841108	+	0.126451i
$232$	−0.695011	−	0.695011i	−0.0456297	−	0.0456297i
$233$	3.09426	−	8.06082i	0.202712	−	0.528082i	−0.794108	−	0.607777i	$-0.792061\pi$
$233$	3.09426	−	8.06082i	0.202712	−	0.528082i	0.996819	+	0.0796953i	$0.0253947\pi$
$234$	21.6461	−	4.60101i	1.41505	−	0.300778i
$235$		0			0
$236$	−3.39053	+	15.9512i	−0.220704	+	1.03833i
$237$	4.08631	+	8.01983i	0.265434	+	0.520944i
$238$	−10.0128	+	7.44447i	−0.649036	+	0.482553i
$239$	−18.2461	+	5.92852i	−1.18024	+	0.383484i	−0.832457	−	0.554090i	$-0.813066\pi$
$239$	−18.2461	+	5.92852i	−1.18024	+	0.383484i	−0.347785	+	0.937574i	$0.613066\pi$
$240$		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	$-0.381700\pi$
$242$	16.0815	−	13.0226i	1.03376	−	0.837122i
$243$	−15.4021	+	4.12698i	−0.988046	+	0.264746i
$244$	10.1757	+	7.39308i	0.651433	+	0.473294i
$245$		0			0
$246$	7.86390	−	5.71346i	0.501384	−	0.364277i
$247$	14.3681	−	17.7432i	0.914222	−	1.12897i
$248$	−7.90636	+	0.414355i	−0.502054	+	0.0263115i
$249$	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	$0.838295\pi$
$252$	−4.32730	+	13.8343i	−0.272594	+	0.871476i
$253$	1.02259	−	6.45639i	0.0642898	−	0.405910i
$254$	27.0158	−	2.83947i	1.69512	−	0.178164i
$255$		0			0
$256$	−0.890203	+	8.46971i	−0.0556377	+	0.529357i
$257$	−7.91188	−	29.5275i	−0.493529	−	1.84188i	−0.538115	−	0.842871i	$-0.680863\pi$
$257$	−7.91188	−	29.5275i	−0.493529	−	1.84188i	0.0445856	−	0.999006i	$-0.485803\pi$
$258$	−1.84762	−	11.6654i	−0.115028	−	0.726257i
$259$	−10.3237	+	13.0395i	−0.641484	+	0.810238i
$260$		0			0
$261$	−2.85754	−	0.607389i	−0.176877	−	0.0375964i
$262$	4.03432	−	6.21231i	0.249241	−	0.383798i
$263$	−0.222055	+	0.341935i	−0.0136925	+	0.0210846i	−0.845451	−	0.534054i	$-0.820668\pi$
$263$	−0.222055	+	0.341935i	−0.0136925	+	0.0210846i	0.831758	+	0.555138i	$0.187335\pi$
$264$	0.663232	+	0.140974i	0.0408191	+	0.00867637i
$265$		0			0
$266$	10.1613	+	25.6245i	0.623027	+	1.57114i
$267$	1.37803	+	8.70053i	0.0843340	+	0.532464i
$268$	7.53982	+	28.1390i	0.460568	+	1.71886i
$269$	2.00211	−	19.0488i	0.122071	−	1.16142i	−0.746335	−	0.665570i	$-0.768188\pi$
$269$	2.00211	−	19.0488i	0.122071	−	1.16142i	0.868406	−	0.495854i	$-0.165145\pi$
$270$		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	$0.666119\pi$
$272$	1.10028	−	6.94688i	0.0667141	−	0.421216i
$273$	2.20181	+	9.82572i	0.133259	+	0.594680i
$274$			15.8375i			0.956779i
$275$		0			0
$276$	−10.6188	+	6.13076i	−0.639176	+	0.369028i
$277$	−7.63707	+	0.400242i	−0.458867	+	0.0240482i	−0.280369	−	0.959892i	$-0.590457\pi$
$277$	−7.63707	+	0.400242i	−0.458867	+	0.0240482i	−0.178497	+	0.983940i	$0.557124\pi$
$278$	11.6340	−	14.3668i	0.697761	−	0.861664i
$279$	−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	$0.511449\pi$
$282$	0.525104	−	0.140701i	0.0312695	−	0.00837864i
$283$	−2.21463	+	1.79337i	−0.131646	+	0.106605i	−0.692882	−	0.721051i	$-0.743659\pi$
$283$	−2.21463	+	1.79337i	−0.131646	+	0.106605i	0.561236	+	0.827656i	$0.310326\pi$
$284$	−1.01532	−	4.77671i	−0.0602482	−	0.283446i
$285$		0			0
$286$	−9.56917	+	3.10921i	−0.565837	+	0.183852i
$287$	−8.83496	−	11.8831i	−0.521511	−	0.701434i
$288$	−8.46799	−	16.6194i	−0.498981	−	0.979305i
$289$	2.47682	−	11.6525i	0.145695	−	0.685443i
$290$		0			0
$291$	−4.02763	+	0.856099i	−0.236104	+	0.0501854i
$292$	−1.10163	+	2.86985i	−0.0644682	+	0.167945i
$293$	0.584948	+	0.584948i	0.0341730	+	0.0341730i	0.723987	−	0.689814i	$-0.242308\pi$
$293$	0.584948	+	0.584948i	0.0341730	+	0.0341730i	−0.689814	+	0.723987i	$0.742308\pi$
$294$	−11.6423	−	3.50150i	−0.678995	−	0.204212i
$295$		0			0
$296$	0.510683	+	4.85883i	0.0296829	+	0.282414i
$297$	4.32490	−	1.66017i	0.250956	−	0.0963330i
$298$	−0.192661	−	3.67620i	−0.0111606	−	0.212957i
$299$	14.2582	−	24.6960i	0.824575	−	1.42821i
$300$		0			0
$301$	−17.7386	+	3.00998i	−1.02244	+	0.173492i
$302$	−5.95129	+	11.6801i	−0.342458	+	0.672112i
$303$	−9.81228	−	7.94583i	−0.563701	−	0.456476i
$304$	−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	−0.938600	−	0.345007i	$-0.887877\pi$
$307$	−10.4006	+	10.4006i	−0.593593	+	0.593593i	0.345007	+	0.938600i	$0.387877\pi$
$308$	1.29922	−	6.46118i	0.0740299	−	0.368160i
$309$	−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	$0.623957\pi$
$312$	2.48073	+	1.61100i	0.140443	+	0.0912050i
$313$	−0.527196	+	10.0595i	−0.0297989	+	0.568597i	0.942407	+	0.334469i	$0.108557\pi$
$313$	−0.527196	+	10.0595i	−0.0297989	+	0.568597i	−0.972206	+	0.234128i	$0.924777\pi$
$314$	6.98263	+	21.4903i	0.394053	+	1.21277i
$315$		0			0
$316$	7.94161	−	24.4418i	0.446750	−	1.37496i
$317$	17.6502	+	6.77528i	0.991335	+	0.380538i	0.799354	−	0.600861i	$-0.205175\pi$
$317$	17.6502	+	6.77528i	0.991335	+	0.380538i	0.191981	+	0.981399i	$0.438509\pi$
$318$	0.125915	−	0.469921i	0.00706096	−	0.0263519i
$319$	1.32098	+	0.138841i	0.0739606	+	0.00777358i
$320$		0			0
$321$	−9.60316	−	13.2176i	−0.535996	−	0.737736i
$322$	17.5421	+	29.6260i	0.977581	+	1.65099i
$323$	10.0141	+	5.10245i	0.557200	+	0.283908i
$324$	6.70866	+	3.87325i	0.372703	+	0.215180i
$325$		0			0
$326$	5.83254	+	10.1023i	0.323035	+	0.559512i
$327$	13.3190	−	8.64948i	0.736544	−	0.478317i
$328$	−4.29622	−	0.680455i	−0.237219	−	0.0375719i
$329$	−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	$0.0401594\pi$
$332$	−8.49070	−	2.27508i	−0.465988	−	0.124861i
$333$	9.13840	+	11.2850i	0.500781	+	0.618414i
$334$	14.6694	+	16.2920i	0.802675	+	0.891461i
$335$		0			0
$336$	6.07176	−	3.17836i	0.331241	−	0.173394i
$337$	31.0198	−	15.8054i	1.68976	−	0.860974i	0.700696	−	0.713460i	$-0.252873\pi$
$337$	31.0198	−	15.8054i	1.68976	−	0.860974i	0.989060	−	0.147514i	$-0.0471271\pi$
$338$	−16.6887	−	0.874620i	−0.907748	−	0.0475730i
$339$	−4.85105	+	5.38763i	−0.263473	+	0.292616i
$340$		0			0
$341$	7.95098	−	7.15909i	0.430570	−	0.387687i
$342$	23.7714	−	3.76502i	1.28541	−	0.203589i
$343$	−5.13855	+	17.7931i	−0.277456	+	0.960738i
$344$	−3.10660	+	4.27587i	−0.167497	+	0.230540i
$345$		0			0
$346$	11.6746	−	26.2216i	0.627631	−	1.40968i
$347$	9.65416	+	25.1500i	0.518263	+	1.35012i	0.904008	+	0.427515i	$0.140611\pi$
$347$	9.65416	+	25.1500i	0.518263	+	1.35012i	−0.385746	+	0.922605i	$0.626056\pi$
$348$	−1.35695	−	2.08952i	−0.0727403	−	0.112010i
$349$	−28.9278			−1.54847			−0.774236	−	0.632897i	$-0.781866\pi$
$349$	−28.9278			−1.54847			−0.774236	+	0.632897i	$0.781866\pi$
$350$		0			0
$351$	20.2092			1.07869
$352$	4.61887	+	7.11244i	0.246187	+	0.379094i
$353$	−4.18132	−	10.8927i	−0.222549	−	0.579760i	0.776161	−	0.630535i	$-0.217164\pi$
$353$	−4.18132	−	10.8927i	−0.222549	−	0.579760i	−0.998710	+	0.0507745i	$0.983831\pi$
$354$	−4.85719	+	10.9094i	−0.258157	+	0.579830i
$355$		0			0
$356$	14.7838	−	20.3482i	0.783540	−	1.07845i
$357$	−4.50586	+	2.06585i	−0.238475	+	0.109336i
$358$	3.32401	−	0.526471i	0.175679	−	0.0278248i
$359$	3.30837	−	2.97887i	0.174609	−	0.157219i	−0.577192	−	0.816608i	$-0.695852\pi$
$359$	3.30837	−	2.97887i	0.174609	−	0.157219i	0.751802	+	0.659389i	$0.229185\pi$
$360$		0			0
$361$	3.90148	−	4.33303i	0.205341	−	0.228054i
$362$	−7.26272	−	0.380623i	−0.381720	−	0.0200051i
$363$	7.32488	−	3.73221i	0.384456	−	0.195890i
$364$	15.3923	−	24.2830i	0.806778	−	1.27278i
$365$		0			0
$366$	6.16314	+	6.84486i	0.322152	+	0.357787i
$367$	16.1627	+	19.9593i	0.843688	+	1.04187i	0.998545	+	0.0539306i	$0.0171750\pi$
$367$	16.1627	+	19.9593i	0.843688	+	1.04187i	−0.154857	+	0.987937i	$0.549492\pi$
$368$	−18.7473	−	5.02332i	−0.977269	−	0.261858i
$369$	−11.8108	+	5.25850i	−0.614845	+	0.273747i
$370$		0			0
$371$	−0.717927	−	0.183925i	−0.0372729	−	0.00954889i
$372$	−19.8217	−	3.13945i	−1.02771	−	0.162773i
$373$	30.0355	−	19.5053i	1.55518	−	1.00994i	0.573544	−	0.819175i	$-0.305568\pi$
$373$	30.0355	−	19.5053i	1.55518	−	1.00994i	0.981635	−	0.190770i	$-0.0610984\pi$
$374$	−2.47652	−	4.28945i	−0.128058	−	0.221802i
$375$		0			0
$376$	−0.210678	−	0.121635i	−0.0108649	−	0.00627285i
$377$	5.16284	+	2.63060i	0.265900	+	0.135483i
$378$	−11.9667	+	21.2640i	−0.615503	+	1.09370i
$379$	−13.3436	−	18.3659i	−0.685416	−	0.943394i	0.314567	−	0.949235i	$-0.398141\pi$
$379$	−13.3436	−	18.3659i	−0.685416	−	0.943394i	−0.999983	+	0.00584095i	$0.998141\pi$
$380$		0			0
$381$	10.7328	+	1.12806i	0.549857	+	0.0577923i
$382$	−1.60434	+	5.98747i	−0.0820850	+	0.306346i
$383$	−20.3079	−	7.79546i	−1.03768	−	0.398330i	−0.220914	−	0.975293i	$-0.570904\pi$
$383$	−20.3079	−	7.79546i	−1.03768	−	0.398330i	−0.816770	+	0.576964i	$0.804237\pi$
$384$	1.56841	−	4.82707i	0.0800375	−	0.246330i
$385$		0			0
$386$	−11.0142	−	33.8984i	−0.560610	−	1.72538i
$387$	−0.822146	+	15.6875i	−0.0417920	+	0.797439i
$388$	9.86003	+	6.40318i	0.500567	+	0.325072i
$389$	9.65968	+	8.69762i	0.489765	+	0.440987i	0.876641	−	0.481145i	$-0.159779\pi$
$389$	9.65968	+	8.69762i	0.489765	+	0.440987i	−0.386876	+	0.922132i	$0.626446\pi$
$390$		0			0
$391$	13.3507	+	4.33792i	0.675176	+	0.219378i
$392$	2.57597	+	4.79190i	0.130106	+	0.242028i
$393$	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
$397$	3.71351	+	3.00714i	0.186376	+	0.150924i	0.717968	−	0.696077i	$-0.245073\pi$
$397$	3.71351	+	3.00714i	0.186376	+	0.150924i	−0.531592	+	0.847001i	$0.678406\pi$
$398$	0.182143	−	0.357476i	0.00913002	−	0.0179187i
$399$	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	$0.0430370\pi$
$402$	1.11647	+	21.3036i	0.0556847	+	1.06253i
$403$	43.5737	−	16.7264i	2.17056	−	0.833201i
$404$	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
$408$	−0.521819	+	1.35938i	−0.0258339	+	0.0672996i
$409$	10.0531	−	2.13685i	0.497094	−	0.105661i	0.0474592	−	0.998873i	$-0.484888\pi$
$409$	10.0531	−	2.13685i	0.497094	−	0.105661i	0.449634	+	0.893213i	$0.351554\pi$
$410$		0			0
$411$	−1.30816	+	6.15440i	−0.0645267	+	0.303574i
$412$	7.31021	+	14.3471i	0.360148	+	0.706831i
$413$	16.6994	+	7.21593i	0.821725	+	0.355073i
$414$	28.5896	−	9.28933i	1.40510	−	0.456546i
$415$		0			0
$416$	7.69187	+	36.1874i	0.377125	+	1.77423i
$417$	5.70761	−	4.62194i	0.279503	−	0.226337i
$418$	−10.5699	+	2.83220i	−0.516992	+	0.138528i
$419$	14.4852	+	10.5241i	0.707648	+	0.514137i	0.882414	−	0.470473i	$-0.155917\pi$
$419$	14.4852	+	10.5241i	0.707648	+	0.514137i	−0.174766	+	0.984610i	$0.555917\pi$
$420$		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	$0.165793\pi$
$422$	8.37387	−	10.3409i	0.407634	−	0.503386i
$423$	−0.722062	+	0.0378417i	−0.0351079	+	0.00183992i
$424$	−0.188538	+	0.108852i	−0.00915621	+	0.00528634i
$425$		0			0
$426$		−	3.57609i		−	0.173262i
$427$	10.3232	−	9.50286i	0.499577	−	0.459876i
$428$	−7.29743	+	46.0741i	−0.352734	+	2.22708i
$429$	−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	$-0.0357828\pi$
$432$	−3.55996	−	13.2859i	−0.171278	−	0.639220i
$433$	−2.75652	−	17.4040i	−0.132470	−	0.836382i	−0.961022	−	0.276471i	$-0.910835\pi$
$433$	−2.75652	−	17.4040i	−0.132470	−	0.836382i	0.828552	−	0.559912i	$-0.189165\pi$
$434$	−8.20245	+	55.7524i	−0.393730	+	2.67620i
$435$		0			0
$436$	−44.3534	−	9.42761i	−2.12414	−	0.451501i
$437$	16.8914	−	26.0104i	0.808024	−	1.24425i
$438$	−1.22603	+	1.88792i	−0.0585819	+	0.0902083i
$439$	−26.8046	−	5.69749i	−1.27931	−	0.271926i	−0.482363	−	0.875972i	$-0.660221\pi$
$439$	−26.8046	−	5.69749i	−1.27931	−	0.271926i	−0.796950	+	0.604045i	$0.793555\pi$
$440$		0			0
$441$	14.1783	+	7.77490i	0.675155	+	0.370233i
$442$	−3.38010	−	21.3411i	−0.160775	−	1.01509i
$443$	−2.86872	−	10.7062i	−0.136297	−	0.508667i	−0.999989	−	0.00464732i	$-0.998521\pi$
$443$	−2.86872	−	10.7062i	−0.136297	−	0.508667i	0.863692	−	0.504019i	$-0.168146\pi$
$444$	−1.29450	+	12.3163i	−0.0614341	+	0.584506i
$445$		0			0
$446$	27.7268	−	2.91420i	1.31290	−	0.137992i
$447$	0.228782	−	1.44447i	0.0108210	−	0.0683212i
$448$	−26.8823	−	8.40866i	−1.27007	−	0.397272i
$449$			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
$452$	20.6714	−	1.08334i	0.972303	−	0.0509562i
$453$	−3.27741	+	4.04726i	−0.153986	+	0.190157i
$454$	−8.20786	+	5.96336i	−0.385214	+	0.279874i
$455$		0			0
$456$	2.60259	+	1.89089i	0.121877	+	0.0885490i
$457$	−32.8230	+	8.79489i	−1.53539	+	0.411408i	−0.924774	−	0.380516i	$-0.875746\pi$
$457$	−32.8230	+	8.79489i	−1.53539	+	0.411408i	−0.610620	+	0.791924i	$0.709080\pi$
$458$	−10.8652	+	8.79845i	−0.507697	+	0.411125i
$459$	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	$0.663198\pi$
$462$	1.91435	−	4.43027i	0.0890634	−	0.206115i
$463$	8.64582	+	16.9684i	0.401805	+	0.788587i	0.999918	−	0.0128250i	$-0.00408243\pi$
$463$	8.64582	+	16.9684i	0.401805	+	0.788587i	−0.598113	+	0.801412i	$0.704082\pi$
$464$	0.819946	−	3.85754i	0.0380650	−	0.179082i
$465$		0			0
$466$	−17.6587	+	3.75346i	−0.818021	+	0.173876i
$467$	2.13538	−	5.56287i	0.0988138	−	0.257419i	−0.875259	−	0.483655i	$-0.839309\pi$
$467$	2.13538	−	5.56287i	0.0988138	−	0.257419i	0.974072	+	0.226236i	$0.0726422\pi$
$468$	−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
$472$	4.98897	−	1.91509i	0.229636	−	0.0881489i
$473$	−0.373803	−	7.13258i	−0.0171875	−	0.327956i
$474$	9.40980	−	16.2982i	0.432206	−	0.748603i
$475$		0			0
$476$	13.2680	+	4.92627i	0.608137	+	0.225795i
$477$	−0.293762	+	0.576541i	−0.0134505	+	0.0263980i
$478$	31.1740	+	25.2442i	1.42586	+	1.15464i
$479$	19.0483	+	8.48083i	0.870338	+	0.387499i	0.792794	−	0.609490i	$-0.208626\pi$
$479$	19.0483	+	8.48083i	0.870338	+	0.387499i	0.0775436	+	0.996989i	$0.475292\pi$
$480$		0			0
$481$	−11.7147	−	26.3117i	−0.534145	−	1.19971i
$482$	−38.3695	+	38.3695i	−1.74768	+	1.74768i
$483$	4.36972	+	12.9615i	0.198829	+	0.589769i
$484$	−22.3238	−	7.25343i	−1.01472	−	0.329701i
$485$		0			0
$486$	24.7763	+	22.3086i	1.12387	+	1.01194i
$487$	−24.6153	−	15.9853i	−1.11542	−	0.724365i	−0.150950	−	0.988541i	$-0.548233\pi$
$487$	−24.6153	−	15.9853i	−1.11542	−	0.724365i	−0.964474	+	0.264176i	$0.914900\pi$
$488$	0.215714	−	4.11607i	0.00976491	−	0.186326i
$489$	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	$0.966824\pi$
$492$	−10.2936	−	3.95135i	−0.464072	−	0.178141i
$493$	−0.738256	+	2.75521i	−0.0332494	+	0.124088i
$494$	−47.4754	−	4.98986i	−2.13602	−	0.224505i
$495$		0			0
$496$	−18.6720	−	25.6998i	−0.838396	−	1.15395i
$497$	−5.44735	+	0.0599495i	−0.244347	+	0.00268910i
$498$	−5.73541	−	2.92234i	−0.257010	−	0.130953i
$499$	−4.60639	−	2.65950i	−0.206210	−	0.119056i	0.393339	−	0.919394i	$-0.371320\pi$
$499$	−4.60639	−	2.65950i	−0.206210	−	0.119056i	−0.599549	+	0.800338i	$0.704653\pi$
$500$		0			0
$501$	4.35478	+	7.54270i	0.194557	+	0.336983i
$502$	27.0280	−	17.5522i	1.20632	−	0.783391i
$503$	−26.0759	−	4.13001i	−1.16267	−	0.184148i	−0.454865	−	0.890560i	$-0.650313\pi$
$503$	−26.0759	−	4.13001i	−1.16267	−	0.184148i	−0.707801	+	0.706412i	$0.750313\pi$
$504$	4.57437	−	1.27982i	0.203759	−	0.0570075i
$505$		0			0
$506$	−12.4861	+	5.55916i	−0.555073	+	0.247135i
$507$	−6.41294	−	1.71834i	−0.284809	−	0.0763143i
$508$	−19.3915	−	23.9465i	−0.860359	−	1.06245i
$509$	2.99499	+	3.32627i	0.132750	+	0.147434i	0.805855	−	0.592113i	$-0.201706\pi$
$509$	2.99499	+	3.32627i	0.132750	+	0.147434i	−0.673104	+	0.739548i	$0.735040\pi$
$510$		0			0
$511$	2.89636	+	1.83592i	0.128127	+	0.0812164i
$512$	26.7543	−	13.6320i	1.18238	−	0.602454i
$513$	21.9490	+	1.15030i	0.969072	+	0.0507869i
$514$	−42.7681	+	47.4988i	−1.88642	+	2.09508i
$515$		0			0
$516$	−9.95612	+	8.96453i	−0.438294	+	0.394641i
$517$	0.324701	−	0.0514276i	0.0142803	−	0.00226178i
$518$	34.6217	+	3.25411i	1.52119	+	0.142977i
$519$	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	$0.942971\pi$
$522$	2.18899	+	5.70250i	0.0958093	+	0.249592i
$523$	11.9816	+	18.4501i	0.523920	+	0.806766i	0.997249	−	0.0741198i	$-0.0236147\pi$
$523$	11.9816	+	18.4501i	0.523920	+	0.806766i	−0.473330	+	0.880885i	$0.656948\pi$
$524$	−8.40229			−0.367056
$525$		0			0
$526$	0.852467			0.0371693
$527$	12.5137	+	19.2694i	0.545105	+	0.839388i
$528$	0.974967	+	2.53988i	0.0424300	+	0.110534i
$529$	6.40073	−	14.3763i	0.278292	−	0.625055i
$530$		0			0
$531$	9.33596	−	12.8499i	0.405146	−	0.557636i
$532$	18.0996	−	25.4974i	0.784717	−	1.10545i
$533$	25.3273	−	4.01144i	1.09705	−	0.173755i
$534$	13.6875	−	12.3243i	0.592317	−	0.533325i
$535$		0			0
$536$	6.38773	−	7.09429i	0.275908	−	0.306427i
$537$	1.33518	+	0.0699740i	0.0576174	+	0.00301960i
$538$	−35.6828	+	18.1813i	−1.53840	+	0.783852i
$539$	−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	$0.710934\pi$
$542$	25.4039	+	31.3712i	1.09119	+	1.34751i
$543$	−2.79083	−	0.747801i	−0.119766	−	0.0320912i
$544$	−16.6374	+	7.40747i	−0.713324	+	0.317592i
$545$		0			0
$546$	14.7225	−	15.0502i	0.630065	−	0.644088i
$547$	−19.0836	−	3.02255i	−0.815958	−	0.129235i	−0.265514	−	0.964107i	$-0.585542\pi$
$547$	−19.0836	−	3.02255i	−0.815958	−	0.129235i	−0.550444	+	0.834872i	$0.685542\pi$
$548$	15.0666	−	9.78435i	0.643612	−	0.417967i
$549$	−6.12533	−	10.6094i	−0.261423	−	0.452797i
$550$		0			0
$551$	5.45756	+	3.15092i	0.232500	+	0.134234i
$552$	3.58011	+	1.82416i	0.152379	+	0.0776412i
$553$	−24.9844	−	14.0604i	−1.06244	−	0.597910i
$554$	9.39867	+	12.9362i	0.399311	+	0.549605i
$555$		0			0
$556$	−20.8549	−	2.19194i	−0.884445	−	0.0929589i
$557$	−4.82211	+	17.9964i	−0.204320	+	0.762531i	0.785336	+	0.619069i	$0.212490\pi$
$557$	−4.82211	+	17.9964i	−0.204320	+	0.762531i	−0.989656	+	0.143462i	$0.954177\pi$
$558$	45.9337	+	17.6323i	1.94453	+	0.746434i
$559$	9.62832	−	29.6329i	0.407235	−	1.25334i
$560$		0			0
$561$	−0.608062	−	1.87142i	−0.0256724	−	0.0790116i
$562$	2.04826	−	39.0832i	0.0864007	−	1.64862i
$563$	−18.1325	−	11.7754i	−0.764193	−	0.496273i	0.102734	−	0.994709i	$-0.467241\pi$
$563$	−18.1325	−	11.7754i	−0.764193	−	0.496273i	−0.866926	+	0.498436i	$0.833908\pi$
$564$	−0.458259	−	0.412619i	−0.0192962	−	0.0173744i
$565$		0			0
$566$	5.66670	+	1.84122i	0.238189	+	0.0773923i
$567$	5.71131	−	6.48517i	0.239852	−	0.272352i
$568$	−1.13157	+	1.13157i	−0.0474795	+	0.0474795i
$569$	−16.3273	−	36.6716i	−0.684474	−	1.53735i	−0.835898	−	0.548885i	$-0.815053\pi$
$569$	−16.3273	−	36.6716i	−0.684474	−	1.53735i	0.151424	−	0.988469i	$-0.451614\pi$
$570$		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	$0.387971\pi$
$572$	8.86966	+	7.18251i	0.370859	+	0.300316i
$573$	−1.11800	+	2.19419i	−0.0467050	+	0.0916638i
$574$	−10.7765	+	29.0245i	−0.449803	+	1.21146i
$575$		0			0
$576$	−12.2962	+	21.2976i	−0.512342	+	0.887402i
$577$	0.300036	+	5.72503i	0.0124907	+	0.238336i	0.997739	+	0.0672061i	$0.0214085\pi$
$577$	0.300036	+	5.72503i	0.0124907	+	0.238336i	−0.985248	+	0.171130i	$0.945258\pi$
$578$	−23.2538	+	8.92628i	−0.967229	+	0.371284i
$579$	−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
$583$	0.105432	−	0.274660i	0.00436654	−	0.0113752i
$584$	0.985333	−	0.209439i	0.0407734	−	0.00866665i
$585$		0			0
$586$	0.359614	−	1.69185i	0.0148555	−	0.0698898i
$587$	5.48135	+	10.7577i	0.226239	+	0.444020i	0.976024	−	0.217662i	$-0.0698430\pi$
$587$	5.48135	+	10.7577i	0.226239	+	0.444020i	−0.749785	+	0.661682i	$0.769843\pi$
$588$	3.86154	+	13.2388i	0.159247	+	0.545960i
$589$	48.2769	−	15.6861i	1.98922	−	0.646335i
$590$		0			0
$591$	3.34273	+	15.7263i	0.137501	+	0.646893i
$592$	−15.2342	+	12.3364i	−0.626121	+	0.507023i
$593$	−41.9372	+	11.2370i	−1.72215	+	0.461449i	−0.978351	−	0.206951i	$-0.933646\pi$
$593$	−41.9372	+	11.2370i	−1.72215	+	0.461449i	−0.743802	+	0.668401i	$0.766979\pi$
$594$	−7.83623	−	5.69336i	−0.321525	−	0.233601i
$595$		0			0
$596$	−3.37823	+	2.45442i	−0.138377	+	0.100537i
$597$	0.100307	−	0.123869i	0.00410531	−	0.00506963i
$598$	−59.5424	+	3.12048i	−2.43487	+	0.127606i
$599$	0.677665	−	0.391250i	0.0276887	−	0.0159860i	−0.486092	−	0.873908i	$-0.661578\pi$
$599$	0.677665	−	0.391250i	0.0276887	−	0.0159860i	0.513780	+	0.857922i	$0.328245\pi$
$600$		0			0
$601$			7.23002i			0.294919i	0.989068	+	0.147459i	$0.0471095\pi$
$601$			7.23002i			0.294919i	−0.989068	+	0.147459i	$0.952890\pi$
$602$	25.4783	+	27.6778i	1.03842	+	1.12806i
$603$	4.43864	−	28.0244i	0.180755	−	1.14124i
$604$	14.7882	−	1.55430i	0.601723	−	0.0632436i
$605$		0			0
$606$	−2.75948	+	26.2547i	−0.112096	+	1.06653i
$607$	0.459640	+	1.71540i	0.0186562	+	0.0696260i	0.974626	−	0.223838i	$-0.0718586\pi$
$607$	0.459640	+	1.71540i	0.0186562	+	0.0696260i	−0.955970	+	0.293464i	$0.905192\pi$
$608$	6.29427	+	39.7405i	0.255267	+	1.61169i
$609$	−2.58363	+	1.02452i	−0.104694	+	0.0415158i
$610$		0			0
$611$	1.40279	+	0.298173i	0.0567510	+	0.0120628i
$612$	6.73012	−	10.3635i	0.272049	−	0.418919i
$613$	−0.596749	+	0.918913i	−0.0241025	+	0.0371145i	−0.850516	−	0.525948i	$-0.823710\pi$
$613$	−0.596749	+	0.918913i	−0.0241025	+	0.0371145i	0.826414	+	0.563063i	$0.190377\pi$
$614$	30.0818	+	6.39408i	1.21400	+	0.258044i
$615$		0			0
$616$	−2.00760	+	0.796102i	−0.0808884	+	0.0320759i
$617$	−5.03752	−	31.8056i	−0.202803	−	1.28045i	−0.853494	−	0.521103i	$-0.825521\pi$
$617$	−5.03752	−	31.8056i	−0.202803	−	1.28045i	0.650691	−	0.759343i	$-0.274479\pi$
$618$	3.05185	+	11.3897i	0.122764	+	0.458160i
$619$	−1.93430	+	18.4036i	−0.0777461	+	0.739705i	0.884319	+	0.466884i	$0.154623\pi$
$619$	−1.93430	+	18.4036i	−0.0777461	+	0.739705i	−0.962065	+	0.272821i	$0.912043\pi$
$620$		0			0
$621$	27.3018	−	2.86954i	1.09559	−	0.115151i
$622$	3.88654	−	24.5386i	0.155836	−	0.983910i
$623$	−19.0027	−	20.6432i	−0.761326	−	0.827051i
$624$			11.8683i			0.475111i
$625$		0			0
$626$	18.2402	−	10.5310i	0.729023	−	0.420902i
$627$	−4.34137	+	0.227522i	−0.173378	+	0.00908634i
$628$	16.1304	−	19.9194i	0.643673	−	0.794869i
$629$	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	$0.531061\pi$
$632$	−8.13469	+	2.17968i	−0.323580	+	0.0867031i
$633$	4.10820	−	3.32675i	0.163286	−	0.132227i
$634$	−8.21870	−	38.6659i	−0.326406	−	1.53562i
$635$		0			0
$636$	−0.524836	+	0.170530i	−0.0208111	+	0.00676194i
$637$	−23.1723	−	22.1740i	−0.918118	−	0.878568i
$638$	−1.26082	−	2.47450i	−0.0499165	−	0.0979666i
$639$	−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	$0.697983\pi$
$642$	−12.2419	+	31.8914i	−0.483151	+	1.25865i
$643$	14.7951	+	14.7951i	0.583460	+	0.583460i	0.935852	−	0.352392i	$-0.114632\pi$
$643$	14.7951	+	14.7951i	0.583460	+	0.583460i	−0.352392	+	0.935852i	$0.614632\pi$
$644$	17.3464	−	34.9910i	0.683545	−	1.37884i
$645$		0			0
$646$	−2.45636	−	23.3707i	−0.0966442	−	0.919508i
$647$	24.1309	−	9.26299i	0.948684	−	0.364166i	0.165678	−	0.986180i	$-0.447019\pi$
$647$	24.1309	−	9.26299i	0.948684	−	0.364166i	0.783006	+	0.622014i	$0.213685\pi$
$648$	−0.132854	−	2.53501i	−0.00521902	−	0.0995848i
$649$	−3.61080	+	6.25410i	−0.141736	+	0.245495i
$650$		0			0
$651$	−7.79252	+	20.9877i	−0.305413	+	0.822572i
$652$	6.00718	−	11.7898i	0.235259	−	0.461723i
$653$	−20.4375	−	16.5499i	−0.799780	−	0.647649i	0.139723	−	0.990191i	$-0.455379\pi$
$653$	−20.4375	−	16.5499i	−0.799780	−	0.647649i	−0.939503	+	0.342542i	$0.888712\pi$
$654$	−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
$658$	−1.14439	+	1.29945i	−0.0446130	+	0.0506579i
$659$	−5.69893	−	1.85169i	−0.221999	−	0.0721317i	0.195906	−	0.980623i	$-0.437235\pi$
$659$	−5.69893	−	1.85169i	−0.221999	−	0.0721317i	−0.417904	+	0.908491i	$0.637235\pi$
$660$		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	$-0.619332\pi$
$662$	−54.5608	−	35.4322i	−2.12056	−	1.37711i
$663$	0.449254	−	8.57228i	0.0174476	−	0.332920i
$664$	0.890129	+	2.73954i	0.0345437	+	0.106315i
$665$		0			0
$666$	9.38224	−	28.8756i	0.363555	−	1.11891i
$667$	7.34830	+	2.82075i	0.284527	+	0.109220i
$668$	6.43627	−	24.0205i	0.249027	−	0.929381i
$669$	11.0152	+	1.15775i	0.425874	+	0.0447612i
$670$		0			0
$671$	3.27395	+	4.50620i	0.126389	+	0.173960i
$672$	−15.4648	−	8.70309i	−0.596566	−	0.335729i
$673$	15.5853	+	7.94108i	0.600767	+	0.306106i	0.727797	−	0.685793i	$-0.240544\pi$
$673$	15.5853	+	7.94108i	0.600767	+	0.306106i	−0.127030	+	0.991899i	$0.540544\pi$
$674$	−63.0398	−	36.3960i	−2.42820	−	1.40192i
$675$		0			0
$676$	9.47819	+	16.4167i	0.364546	+	0.631412i
$677$	−29.2874	+	19.0194i	−1.12560	+	0.730976i	−0.966597	−	0.256301i	$-0.917496\pi$
$677$	−29.2874	+	19.0194i	−1.12560	+	0.730976i	−0.159008	+	0.987277i	$0.550830\pi$
$678$	14.9717	+	2.37128i	0.574984	+	0.0910685i
$679$	9.17120	−	9.37531i	0.351959	−	0.359792i
$680$		0			0
$681$	−3.68211	+	1.63938i	−0.141099	+	0.0628212i
$682$	−21.6081	−	5.78987i	−0.827417	−	0.221706i
$683$	−25.6066	−	31.6215i	−0.979808	−	1.20996i	−0.977709	−	0.209965i	$-0.932665\pi$
$683$	−25.6066	−	31.6215i	−0.979808	−	1.20996i	−0.00209925	−	0.999998i	$-0.500668\pi$
$684$	−18.2676	−	20.2882i	−0.698479	−	0.775740i
$685$		0			0
$686$	37.0527	−	11.2515i	1.41468	−	0.429585i
$687$	−4.94891	+	2.52160i	−0.188813	+	0.0962049i
$688$	−21.1773	−	1.10986i	−0.807378	−	0.0423129i
$689$	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	$0.156758\pi$
$692$	−32.1577	+	5.09328i	−1.22245	+	0.193618i
$693$	−3.71565	+	5.23434i	−0.141146	+	0.198836i
$694$	33.1078	−	45.5689i	1.25675	−	1.72977i
$695$		0			0
$696$	−0.332078	+	0.745860i	−0.0125874	+	0.0282717i
$697$	4.52377	+	11.7848i	0.171350	+	0.446382i
$698$	32.9421	+	50.7263i	1.24688	+	1.92002i
$699$	−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	$0.628936\pi$
$702$	−23.0136	−	35.4378i	−0.868592	−	1.33752i
$703$	−11.2255	−	29.2435i	−0.423379	−	1.10294i
$704$	4.54787	−	10.2147i	0.171404	−	0.384980i
$705$		0			0
$706$	−14.3393	+	19.7364i	−0.539667	+	0.742788i
$707$	40.0393	+	3.76330i	1.50583	+	0.141533i
$708$	13.3791	−	2.11905i	0.502819	−	0.0796387i
$709$	0.576558	−	0.519135i	0.0216531	−	0.0194965i	−0.658233	−	0.752814i	$-0.728696\pi$
$709$	0.576558	−	0.519135i	0.0216531	−	0.0194965i	0.679886	+	0.733318i	$0.262029\pi$
$710$		0			0
$711$	−16.7490	+	18.6017i	−0.628137	+	0.697617i
$712$	−8.23081	−	0.431359i	−0.308463	−	0.0161658i
$713$	56.4913	−	28.7838i	2.11562	−	1.07796i
$714$	8.75368	+	5.54871i	0.327598	+	0.207655i
$715$		0			0
$716$	−2.55440	−	2.83695i	−0.0954624	−	0.106022i
$717$	10.0290	+	12.3847i	0.374538	+	0.462516i
$718$	−8.99106	−	2.40915i	−0.335543	−	0.0899086i
$719$	−33.6892	+	14.9994i	−1.25639	+	0.559383i	−0.923506	−	0.383583i	$-0.874690\pi$
$719$	−33.6892	+	14.9994i	−1.25639	+	0.559383i	−0.332888	+	0.942966i	$0.608023\pi$
$720$		0			0
$721$	17.2984	−	4.83973i	0.644225	−	0.180241i
$722$	−12.0411	−	1.90712i	−0.448122	−	0.0709755i
$723$	−18.0795	+	11.7410i	−0.672384	+	0.436651i
$724$	4.12478	+	7.14434i	0.153296	+	0.265517i
$725$		0			0
$726$	−14.8859	−	8.59439i	−0.552468	−	0.318968i
$727$	17.7421	+	9.04006i	0.658019	+	0.335277i	0.750915	−	0.660398i	$-0.229613\pi$
$727$	17.7421	+	9.04006i	0.658019	+	0.335277i	−0.0928967	+	0.995676i	$0.529613\pi$
$728$	−9.42084	+	0.103679i	−0.349160	+	0.00384259i
$729$	2.02583	+	2.78831i	0.0750307	+	0.103271i
$730$		0			0
$731$	15.2541	+	1.60327i	0.564192	+	0.0592990i
$732$	2.70410	−	10.0919i	0.0999466	−	0.373006i
$733$	0.0374092	+	0.0143601i	0.00138174	+	0.000530401i	0.359059	−	0.933315i	$-0.383098\pi$
$733$	0.0374092	+	0.0143601i	0.00138174	+	0.000530401i	−0.357677	+	0.933845i	$0.616431\pi$
$734$	16.5940	−	51.0711i	0.612496	−	1.88507i
$735$		0			0
$736$	15.5297	+	47.7955i	0.572432	+	1.76177i
$737$	−0.675166	+	12.8829i	−0.0248701	+	0.474549i
$738$	22.6707	+	14.7226i	0.834522	+	0.541945i
$739$	−14.3575	−	12.9276i	−0.528151	−	0.475549i	0.361384	−	0.932417i	$-0.382304\pi$
$739$	−14.3575	−	12.9276i	−0.528151	−	0.475549i	−0.889534	+	0.456868i	$0.848971\pi$
$740$		0			0
$741$	−18.0366	−	5.86045i	−0.662592	−	0.215289i
$742$	0.495031	+	1.46836i	0.0181731	+	0.0539054i
$743$	−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
$747$	6.65357	+	5.38795i	0.243441	+	0.197135i
$748$	−2.55067	+	5.00597i	−0.0932617	+	0.183036i
$749$	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	$0.244496\pi$
$752$	−0.0510844	−	0.974748i	−0.00186286	−	0.0355454i
$753$	11.9528	−	4.58823i	0.435583	−	0.167205i
$754$	−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	$0.759294\pi$
$758$	−17.0102	+	44.3132i	−0.617839	+	1.60953i
$759$	−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	$-0.128638\pi$
$762$	−10.2440	−	20.1050i	−0.371102	−	0.728328i
$763$	−20.0644	+	46.4340i	−0.726381	+	1.68102i
$764$	6.68717	−	2.17279i	0.241933	−	0.0786089i
$765$		0			0
$766$	9.45622	+	44.4880i	0.341667	+	1.60742i
$767$	−24.4829	+	19.8259i	−0.884026	+	0.715870i
$768$	6.83311	−	1.83093i	0.246569	−	0.0660679i
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	0.770259	−	0.637731i	$-0.220127\pi$
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	−0.368495	+	0.929630i	$0.620127\pi$
$770$		0			0
$771$	−20.5429	+	14.9253i	−0.739834	+	0.537521i
$772$	−25.4437	+	31.4204i	−0.915739	+	1.13084i
$773$	−10.0294	+	0.525618i	−0.360732	+	0.0189052i	−0.231841	−	0.972754i	$-0.574475\pi$
$773$	−10.0294	+	0.525618i	−0.360732	+	0.0189052i	−0.128891	+	0.991659i	$0.541142\pi$
$774$	28.4449	−	16.4227i	1.02243	−	0.590302i
$775$		0			0
$776$		−	3.85263i		−	0.138301i
$777$	13.1851	+	4.12425i	0.473013	+	0.147957i
$778$	4.25155	−	26.8433i	0.152426	−	0.962377i
$779$	27.7359	−	2.91516i	0.993743	−	0.104447i
$780$		0			0
$781$	0.226050	−	2.15072i	0.00808871	−	0.0769590i
$782$	−7.59663	−	28.3510i	−0.271655	−	1.01383i
$783$	0.872614	+	5.50947i	0.0311847	+	0.196892i
$784$	−10.4957	+	19.1399i	−0.374847	+	0.683570i
$785$		0			0
$786$	−6.01847	−	1.27927i	−0.214672	−	0.0456299i
$787$	−11.7250	+	18.0549i	−0.417950	+	0.643586i	−0.983454	−	0.181159i	$-0.942015\pi$
$787$	−11.7250	+	18.0549i	−0.417950	+	0.643586i	0.565504	+	0.824746i	$0.308682\pi$
$788$	25.0019	−	38.4995i	0.890655	−	1.37149i
$789$	0.331266	+	0.0704127i	0.0117934	+	0.00250676i
$790$		0			0
$791$	3.36111	−	22.8456i	0.119507	−	0.812297i
$792$	0.294977	+	1.86241i	0.0104815	+	0.0661779i
$793$	6.28891	+	23.4705i	0.223326	+	0.833463i
$794$	1.04434	−	9.93624i	0.0370623	−	0.352624i
$795$		0			0
$796$	−0.452602	+	0.0475704i	−0.0160421	+	0.00168609i
$797$	−0.825084	+	5.20937i	−0.0292260	+	0.184526i	−0.997983	−	0.0634877i	$-0.979778\pi$
$797$	−0.825084	+	5.20937i	−0.0292260	+	0.184526i	0.968757	+	0.248013i	$0.0797776\pi$
$798$	16.8466	−	15.5078i	0.596362	−	0.548970i
$799$			0.705981i			0.0249758i
$800$		0			0
$801$	−21.2154	+	12.2487i	−0.749608	+	0.432786i
$802$	−31.6687	+	1.65969i	−1.11826	+	0.0586056i
$803$	−0.856694	+	1.05793i	−0.0302321	+	0.0373335i
$804$	19.5768	−	14.2234i	0.690422	−	0.501621i
$805$		0			0
$806$	−78.9508	−	57.3611i	−2.78092	−	2.02046i
$807$	−15.3680	+	4.11784i	−0.540979	+	0.144955i
$808$	9.18084	−	7.43450i	0.322981	−	0.261545i
$809$	−1.72341	−	8.10801i	−0.0605919	−	0.285063i	0.937411	−	0.348224i	$-0.113215\pi$
$809$	−1.72341	−	8.10801i	−0.0605919	−	0.285063i	−0.998003	+	0.0631613i	$0.979882\pi$
$810$		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	$0.260775\pi$
$812$	7.28469	+	3.14776i	0.255643	+	0.110465i
$813$	7.28065	+	14.2891i	0.255343	+	0.501140i
$814$	−2.87010	+	13.5028i	−0.100597	+	0.473271i
$815$		0			0
$816$	−5.71472	+	1.21470i	−0.200055	+	0.0425230i
$817$	12.1439	−	31.6359i	0.424861	−	1.10680i
$818$	−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	$-0.0961729\pi$
$822$	12.2817	−	4.71451i	0.428374	−	0.164437i
$823$	−0.898326	−	17.1411i	−0.0313137	−	0.597501i	−0.968552	−	0.248811i	$-0.919960\pi$
$823$	−0.898326	−	17.1411i	−0.0313137	−	0.597501i	0.937238	−	0.348689i	$-0.113373\pi$
$824$	2.63830	−	4.56967i	0.0919096	−	0.159192i
$825$		0			0
$826$	−6.36329	−	37.5005i	−0.221407	−	1.30481i
$827$	−10.5674	+	20.7397i	−0.367465	+	0.721190i	−0.998511	−	0.0545555i	$-0.982626\pi$
$827$	−10.5674	+	20.7397i	−0.367465	+	0.721190i	0.631046	+	0.775745i	$0.282626\pi$
$828$	−26.4997	−	21.4590i	−0.920928	−	0.745753i
$829$	−23.1374	−	10.3014i	−0.803596	−	0.357784i	−0.0365142	−	0.999333i	$-0.511625\pi$
$829$	−23.1374	−	10.3014i	−0.803596	−	0.357784i	−0.767082	+	0.641549i	$0.778292\pi$
$830$		0			0
$831$	2.58378	+	5.80327i	0.0896304	+	0.201313i
$832$	34.4910	−	34.4910i	1.19576	−	1.19576i
$833$	8.30543	−	13.4272i	0.287766	−	0.465226i
$834$	−14.6044	−	4.74526i	−0.505710	−	0.164315i
$835$		0			0
$836$	9.22439	+	8.30568i	0.319032	+	0.287258i
$837$	37.6831	+	24.4717i	1.30252	+	0.845865i
$838$	1.95926	−	37.3850i	0.0676816	−	1.29144i
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.564144	+	0.825677i	$0.309206\pi$
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.0289189	+	0.999582i	$0.490794\pi$
$840$		0			0
$841$	8.46726	−	26.0596i	0.291975	−	0.898605i
$842$	−32.7815	−	12.5836i	−1.12973	−	0.433661i
$843$	4.02417	−	15.0184i	0.138600	−	0.517261i
$844$	−15.0108	−	1.57770i	−0.516694	−	0.0543068i
$845$		0			0
$846$	0.888617	+	1.22308i	0.0305513	+	0.0420502i
$847$	−12.8420	+	22.8193i	−0.441257	+	0.784082i
$848$	−0.778302	−	0.396565i	−0.0267270	−	0.0136181i
$849$	2.04998	+	1.18355i	0.0703550	+	0.0406195i
$850$		0			0
$851$	−19.5621	−	33.8826i	−0.670581	−	1.16148i
$852$	−3.40201	+	2.20929i	−0.116551	+	0.0756892i
$853$	41.8419	+	6.62710i	1.43264	+	0.226908i	0.824023	−	0.566557i	$-0.191725\pi$
$853$	41.8419	+	6.62710i	1.43264	+	0.226908i	0.608616	+	0.793465i	$0.291725\pi$
$854$	−28.4195	−	7.28074i	−0.972494	−	0.249142i
$855$		0			0
$856$	13.9649	−	6.21758i	0.477311	−	0.212513i
$857$	36.7601	+	9.84983i	1.25570	+	0.336464i	0.824536	−	0.565810i	$-0.191436\pi$
$857$	36.7601	+	9.84983i	1.25570	+	0.336464i	0.431164	+	0.902274i	$0.358103\pi$
$858$	5.25969	+	6.49517i	0.179563	+	0.221742i
$859$	34.3314	+	38.1289i	1.17137	+	1.30094i	0.945064	+	0.326884i	$0.105999\pi$
$859$	34.3314	+	38.1289i	1.17137	+	1.30094i	0.226307	+	0.974056i	$0.427335\pi$
$860$		0			0
$861$	−6.58511	+	10.3887i	−0.224420	+	0.354046i
$862$	−16.6643	+	8.49088i	−0.567588	+	0.289200i
$863$	−21.8237	−	1.14373i	−0.742887	−	0.0389331i	−0.322863	−	0.946446i	$-0.604645\pi$
$863$	−21.8237	−	1.14373i	−0.742887	−	0.0389331i	−0.420025	+	0.907513i	$0.637979\pi$
$864$	−23.8312	+	26.4672i	−0.810754	+	0.900433i
$865$		0			0
$866$	−27.3797	+	24.6528i	−0.930399	+	0.837735i
$867$	−9.77363	+	1.54799i	−0.331930	+	0.0525725i
$868$	58.1060	−	26.6404i	1.97224	−	0.904236i
$869$	6.68946	−	9.20725i	0.226924	−	0.312334i
$870$		0			0
$871$	−22.8902	+	51.4123i	−0.775606	+	1.74204i
$872$	5.32504	+	13.8722i	0.180329	+	0.469772i
$873$	−6.23660	−	9.60352i	−0.211077	−	0.325030i
$874$	−64.8458			−2.19344
$875$		0			0
$876$	2.55345			0.0862732
$877$	−0.771263	−	1.18764i	−0.0260437	−	0.0401038i	0.825409	−	0.564535i	$-0.190945\pi$
$877$	−0.771263	−	1.18764i	−0.0260437	−	0.0401038i	−0.851453	+	0.524431i	$0.824278\pi$
$878$	20.5333	+	53.4912i	0.692967	+	1.80524i
$879$	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	$0.246293\pi$
$882$	−2.51208	−	33.7160i	−0.0845860	−	1.13528i
$883$	−40.2254	+	6.37108i	−1.35369	+	0.214404i	−0.790774	−	0.612108i	$-0.790322\pi$
$883$	−40.2254	+	6.37108i	−1.35369	+	0.214404i	−0.562919	+	0.826512i	$0.690322\pi$
$884$	−18.2141	+	16.4000i	−0.612605	+	0.551592i
$885$		0			0
$886$	−15.5070	+	17.2223i	−0.520968	+	0.578594i
$887$	−24.7751	−	1.29841i	−0.831866	−	0.0435963i	−0.368353	−	0.929686i	$-0.620078\pi$
$887$	−24.7751	−	1.29841i	−0.831866	−	0.0435963i	−0.463514	+	0.886090i	$0.653411\pi$
$888$	3.61591	−	1.84240i	0.121342	−	0.0618269i
$889$	−30.4536	+	15.9414i	−1.02138	+	0.534659i
$890$		0			0
$891$	2.29542	+	2.54932i	0.0768994	+	0.0854055i
$892$	−19.9018	−	24.5767i	−0.666363	−	0.822890i
$893$	1.50658	+	0.403688i	0.0504159	+	0.0135089i
$894$	−2.79348	+	1.24374i	−0.0934279	+	0.0415968i
$895$		0			0
$896$	4.35568	+	15.5683i	0.145513	+	0.520100i
$897$	−23.3957	−	3.70552i	−0.781160	−	0.123724i
$898$	70.3442	−	45.6821i	2.34742	−	1.52443i
$899$	6.44144	+	11.1569i	0.214834	+	0.372103i
$900$		0			0
$901$	0.547146	+	0.315895i	0.0182281	+	0.0105240i
$902$	−10.9509	−	5.57975i	−0.364624	−	0.185785i
$903$	7.61461	+	12.8600i	0.253398	+	0.427953i
$904$	−3.98709	−	5.48776i	−0.132609	−	0.182520i
$905$		0			0
$906$	10.8293	+	1.13820i	0.359778	+	0.0378142i
$907$	8.07670	−	30.1426i	0.268182	−	1.00087i	−0.692091	−	0.721810i	$-0.743310\pi$
$907$	8.07670	−	30.1426i	0.268182	−	1.00087i	0.960274	−	0.279060i	$-0.0900229\pi$
$908$	10.7439	+	4.12418i	0.356547	+	0.136866i
$909$	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	$-0.310801\pi$
$912$	−0.675534	+	12.8900i	−0.0223692	+	0.426829i
$913$	−3.26465	−	2.12009i	−0.108044	−	0.0701647i
$914$	52.8000	+	47.5413i	1.74647	+	1.57253i
$915$		0			0
$916$	15.0826	+	4.90064i	0.498344	+	0.161922i
$917$	−1.84777	+	9.18920i	−0.0610188	+	0.303454i
$918$	14.7084	−	14.7084i	0.485448	−	0.485448i
$919$	17.2862	+	38.8255i	0.570220	+	1.28074i	0.936643	+	0.350287i	$0.113916\pi$
$919$	17.2862	+	38.8255i	0.570220	+	1.28074i	−0.366422	+	0.930449i	$0.619417\pi$
$920$		0			0
$921$	11.1615	+	4.96943i	0.367785	+	0.163748i
$922$	51.3422	+	41.5761i	1.69087	+	1.36924i
$923$	4.28295	−	8.40577i	0.140975	−	0.276679i
$924$	−5.39729	+	0.915841i	−0.177558	+	0.0301290i
$925$		0			0
$926$	19.9093	−	34.4838i	0.654259	−	1.13321i
$927$	−0.820797	−	15.6617i	−0.0269585	−	0.514399i
$928$	−9.53332	+	3.65950i	−0.312947	+	0.120129i
$929$	1.58633	+	15.0929i	0.0520459	+	0.495183i	0.989232	+	0.146354i	$0.0467539\pi$
$929$	1.58633	+	15.0929i	0.0520459	+	0.495183i	−0.937186	+	0.348829i	$0.886579\pi$
$930$		0			0
$931$	−23.9050	−	25.4019i	−0.783453	−	0.832513i
$932$	14.4802	+	14.4802i	0.474315	+	0.474315i
$933$	3.53716	−	9.21461i	0.115801	−	0.301673i
$934$	−12.1864	+	2.59031i	−0.398753	+	0.0847575i
$935$		0			0
$936$	−1.71025	+	8.04611i	−0.0559014	+	0.262995i
$937$	11.3453	+	22.2665i	0.370636	+	0.727415i	0.998712	−	0.0507375i	$-0.0161572\pi$
$937$	11.3453	+	22.2665i	0.370636	+	0.727415i	−0.628076	+	0.778152i	$0.716157\pi$
$938$	−40.5414	−	54.5283i	−1.32372	−	1.78041i
$939$	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	$-0.154302\pi$
$942$	14.5868	−	11.8121i	0.475263	−	0.384861i
$943$	33.6465	−	9.01555i	1.09568	−	0.293587i
$944$	17.3467	+	12.6031i	0.564586	+	0.410196i
$945$		0			0
$946$	−12.0816	+	8.77782i	−0.392808	+	0.285392i
$947$	−15.0527	+	18.5885i	−0.489147	+	0.604047i	−0.960631	−	0.277828i	$-0.910385\pi$
$947$	−15.0527	+	18.5885i	−0.489147	+	0.604047i	0.471483	+	0.881875i	$0.343719\pi$
$948$	−21.3182	+	1.11724i	−0.692383	+	0.0362863i
$949$	−5.14293	+	2.96927i	−0.166947	+	0.0963866i
$950$		0			0
$951$		−	15.7043i		−	0.509247i
$952$	−1.01413	−	4.52564i	−0.0328683	−	0.146677i
$953$	−8.33470	+	52.6232i	−0.269987	+	1.70463i	0.364090	+	0.931364i	$0.381380\pi$
$953$	−8.33470	+	52.6232i	−0.269987	+	1.70463i	−0.634077	+	0.773270i	$0.718620\pi$
$954$	1.34552	−	0.141420i	0.0435628	−	0.00457863i
$955$		0			0
$956$	4.75620	−	45.2522i	0.153827	−	1.46356i
$957$	−0.285561	−	1.06573i	−0.00923086	−	0.0344500i
$958$	−6.81999	−	43.0597i	−0.220344	−	1.39120i
$959$	−7.38735	−	18.6293i	−0.238550	−	0.601572i
$960$		0			0
$961$	71.1813	+	15.1300i	2.29617	+	0.488066i
$962$	−32.7984	+	50.5051i	−1.05746	+	1.62835i
$963$	24.7456	−	38.1049i	0.797417	−	1.22791i
$964$	60.2062	+	12.7972i	1.93911	+	0.412171i
$965$		0			0
$966$	17.7525	−	22.4226i	0.571178	−	0.721436i
$967$	4.98535	+	31.4763i	0.160318	+	1.01221i	0.928326	+	0.371768i	$0.121248\pi$
$967$	4.98535	+	31.4763i	0.160318	+	1.01221i	−0.768008	+	0.640441i	$0.778752\pi$
$968$	1.99080	+	7.42978i	0.0639868	+	0.238802i
$969$	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	$0.680042\pi$
$972$	5.91604	−	37.3524i	0.189757	−	1.19808i
$973$	−6.98348	+	22.3260i	−0.223880	+	0.715739i
$974$			61.3676i			1.96634i
$975$		0			0
$976$	14.3221	−	8.26889i	0.458441	−	0.264681i
$977$	28.8691	−	1.51297i	0.923604	−	0.0484040i	0.415398	−	0.909640i	$-0.363642\pi$
$977$	28.8691	−	1.51297i	0.923604	−	0.0484040i	0.508206	+	0.861236i	$0.330309\pi$
$978$	6.09789	−	7.53027i	0.194989	−	0.240792i
$979$	9.01096	−	6.54684i	0.287991	−	0.209238i
$980$		0			0
$981$	35.7300	+	25.9594i	1.14077	+	0.828818i
$982$	36.3639	−	9.74367i	1.16042	−	0.310933i
$983$	−7.60355	+	6.15724i	−0.242516	+	0.196385i	−0.742871	−	0.669435i	$-0.766536\pi$
$983$	−7.60355	+	6.15724i	−0.242516	+	0.196385i	0.500355	+	0.865820i	$0.333203\pi$
$984$	0.751219	+	3.53421i	0.0239480	+	0.112666i
$985$		0			0
$986$	5.67209	−	1.84297i	0.180636	−	0.0586922i
$987$	−0.552039	+	0.410437i	−0.0175716	+	0.0130644i
$988$	24.5831	+	48.2471i	0.782093	+	1.53494i
$989$	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	$0.306487\pi$
$992$	−29.4773	+	76.7909i	−0.935904	+	2.43811i
$993$	−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
$997$	−20.3902	+	7.82705i	−0.645763	+	0.247885i	−0.659134	−	0.752025i	$-0.729077\pi$
$997$	−20.3902	+	7.82705i	−0.645763	+	0.247885i	0.0133710	+	0.999911i	$0.495744\pi$
$998$	0.582044	+	11.1061i	0.0184243	+	0.351556i
$999$	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.c.607.3		288
5.2	odd	4		875.2.bb.b.768.16		288
5.3	odd	4		875.2.bb.a.768.3		288
5.4	even	2		175.2.x.a.117.16	yes	288
7.3	odd	6	inner	875.2.bb.c.857.16		288
25.3	odd	20	inner	875.2.bb.c.243.16		288
25.4	even	10		875.2.bb.b.257.16		288
25.21	even	5		875.2.bb.a.257.3		288
25.22	odd	20		175.2.x.a.103.3	yes	288
35.3	even	12		875.2.bb.a.143.3		288
35.17	even	12		875.2.bb.b.143.16		288
35.24	odd	6		175.2.x.a.17.3	yes	288
175.3	even	60	inner	875.2.bb.c.493.3		288
175.122	even	60		175.2.x.a.3.16	✓	288
175.129	odd	30		875.2.bb.b.507.16		288
175.171	odd	30		875.2.bb.a.507.3		288

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-1.13877 - 1.75355i) q^{2} +(-0.297680 - 0.775483i) q^{3} +(-0.964662 + 2.16667i) q^{4} +(-1.02086 + 1.40509i) q^{6} +(2.15744 + 1.53148i) q^{7} +(0.767632 - 0.121581i) q^{8} +(1.71667 - 1.54570i) q^{9} +(-0.702779 + 0.780515i) q^{11} +(1.96737 + 0.103106i) q^{12} +(-4.08239 + 2.08008i) q^{13} +(0.228707 - 5.52718i) q^{14} +(2.08662 + 2.31743i) q^{16} +(-1.41941 - 1.75283i) q^{17} +(-4.66535 - 1.25008i) q^{18} +(-4.55223 + 2.02678i) q^{19} +(0.545413 - 2.12895i) q^{21} +(2.16897 + 0.343531i) q^{22} +(-5.21979 + 3.38977i) q^{23} +(-0.322792 - 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(-3.93004 - 2.00245i) q^{27} +(-5.39942 + 3.19709i) q^{28} +(-0.743348 - 1.02313i) q^{29} +(-10.1310 - 1.06481i) q^{31} +(2.08985 - 7.79943i) q^{32} +(0.814479 + 0.312649i) q^{33} +(-1.45729 + 4.48507i) q^{34} +(1.69301 + 5.21054i) q^{36} +(-0.328991 + 6.27752i) q^{37} +(8.73799 + 5.67452i) q^{38} +(2.82832 + 2.54663i) q^{39} +(-5.32280 - 1.72948i) q^{41} +(-4.35431 + 1.46797i) q^{42} +(-4.80861 + 4.80861i) q^{43} +(-1.01317 - 2.27562i) q^{44} +(11.8882 + 5.29299i) q^{46} +(-0.243253 - 0.196982i) q^{47} +(1.17598 - 2.30799i) q^{48} +(2.30911 + 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(-0.568717 - 10.8518i) q^{52} +(-0.261509 + 0.100384i) q^{53} +(0.963998 + 9.17183i) q^{54} +(1.84232 + 0.913312i) q^{56} +(2.92684 + 2.92684i) q^{57} +(-0.947608 + 2.46860i) q^{58} +(6.72559 - 1.42957i) q^{59} +(1.10261 - 5.18739i) q^{61} +(9.66967 + 18.9778i) q^{62} +(6.07084 - 0.705699i) q^{63} +(-10.1249 + 3.28979i) q^{64} +(-0.379257 - 1.78426i) q^{66} +(9.54564 - 7.72991i) q^{67} +(5.16706 - 1.38451i) q^{68} +(4.18254 + 3.03879i) q^{69} +(-1.66579 + 1.21027i) q^{71} +(1.12985 - 1.39524i) q^{72} +(1.29435 - 0.0678338i) q^{73} +(11.3826 - 6.57173i) q^{74} -11.8183i q^{76} +(-2.71155 + 0.607621i) q^{77} +(1.24484 - 7.85959i) q^{78} +(-10.7765 + 1.13266i) q^{79} +(0.341411 - 3.24831i) q^{81} +(3.02870 + 11.3033i) q^{82} +(0.579789 + 3.66064i) q^{83} +(4.08659 + 3.23545i) q^{84} +(13.9080 + 2.95623i) q^{86} +(-0.572141 + 0.881019i) q^{87} +(-0.444580 + 0.684593i) q^{88} +(-10.3731 - 2.20488i) q^{89} +(-11.9931 - 1.76446i) q^{91} +(-2.30917 - 14.5795i) q^{92} +(2.19006 + 8.17341i) q^{93} +(-0.0684094 + 0.650872i) q^{94} +(-6.67043 + 0.701090i) q^{96} +(0.775456 - 4.89604i) q^{97} +(8.95821 - 11.5743i) q^{98} +2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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