LMFDB - Embedded newform 875.2.bb.c.493.3

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			493.3
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.c.607.3

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.13877	+	1.75355i	−0.805229	+	1.23994i	0.162189	+	0.986760i	$0.448145\pi$
$2$	−1.13877	+	1.75355i	−0.805229	+	1.23994i	−0.967418	+	0.253185i	$0.918522\pi$
$3$	−0.297680	+	0.775483i	−0.171866	+	0.447725i	−0.992276	−	0.124050i	$-0.960412\pi$
$3$	−0.297680	+	0.775483i	−0.171866	+	0.447725i	0.820410	+	0.571775i	$0.193745\pi$
$4$	−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	0.627822	−	0.778357i	$-0.283946\pi$
$11$	−0.702779	−	0.780515i	−0.211896	−	0.235334i	−0.839718	+	0.543023i	$0.817280\pi$
$12$	1.96737	−	0.103106i	0.567932	−	0.0297640i
$13$	−4.08239	−	2.08008i	−1.13225	−	0.576911i	−0.215554	−	0.976492i	$-0.569156\pi$
$13$	−4.08239	−	2.08008i	−1.13225	−	0.576911i	−0.916698	+	0.399580i	$0.869156\pi$
$14$	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	−0.919641	−	0.392761i	$-0.871520\pi$
$17$	−1.41941	+	1.75283i	−0.344259	+	0.425124i	0.575382	+	0.817885i	$0.304853\pi$
$18$	−4.66535	+	1.25008i	−1.09963	+	0.294646i
$19$	−4.55223	−	2.02678i	−1.04435	−	0.464976i	−0.188434	−	0.982086i	$-0.560341\pi$
$19$	−4.55223	−	2.02678i	−1.04435	−	0.464976i	−0.855919	+	0.517110i	$0.827008\pi$
$20$		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	−0.129793	−	0.991541i	$-0.541431\pi$
$23$	−5.21979	−	3.38977i	−1.08840	−	0.706816i	−0.958609	+	0.284725i	$0.908098\pi$
$24$	−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	−0.872439	−	0.488724i	$-0.837463\pi$
$29$	−0.743348	+	1.02313i	−0.138036	+	0.189991i	0.734402	+	0.678714i	$0.237463\pi$
$30$		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	$0.834322\pi$
$32$	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	−0.882026	−	0.471202i	$-0.843820\pi$
$37$	−0.328991	−	6.27752i	−0.0540858	−	1.03202i	0.827940	−	0.560817i	$-0.189513\pi$
$38$	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	−0.693585	−	0.720374i	$-0.743970\pi$
$41$	−5.32280	+	1.72948i	−0.831282	+	0.270100i	−0.137697	+	0.990474i	$0.543970\pi$
$42$	−4.35431	−	1.46797i	−0.671885	−	0.226513i
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	0.237968	−	0.971273i	$-0.423519\pi$
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	−0.971273	+	0.237968i	$0.923519\pi$
$44$	−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	−0.646897	−	0.762577i	$-0.723934\pi$
$47$	−0.243253	+	0.196982i	−0.0354821	+	0.0287328i	0.611415	+	0.791310i	$0.290600\pi$
$48$	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	0.340341	−	0.940302i	$-0.389457\pi$
$53$	−0.261509	−	0.100384i	−0.0359210	−	0.0137888i	−0.376262	+	0.926513i	$0.622791\pi$
$54$	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	0.623722	−	0.781646i	$-0.285620\pi$
$59$	6.72559	+	1.42957i	0.875597	+	0.186114i	0.251875	+	0.967760i	$0.418953\pi$
$60$		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	$0.823073\pi$
$62$	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	0.999135	−	0.0415894i	$-0.0132421\pi$
$67$	9.54564	+	7.72991i	1.16619	+	0.944359i	0.167051	+	0.985948i	$0.446575\pi$
$68$	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	0.484535	−	0.874772i	$-0.338989\pi$
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	−0.682228	+	0.731140i	$0.738989\pi$
$72$	1.12985	+	1.39524i	0.133154	+	0.164431i
$73$	1.29435	+	0.0678338i	0.151492	+	0.00793934i	0.127931	−	0.991783i	$-0.459166\pi$
$73$	1.29435	+	0.0678338i	0.151492	+	0.00793934i	0.0235607	+	0.999722i	$0.492500\pi$
$74$	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	−0.523363	−	0.852110i	$-0.675323\pi$
$79$	−10.7765	−	1.13266i	−1.21245	−	0.127434i	−0.689090	+	0.724676i	$0.741989\pi$
$80$		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	−0.935220	−	0.354068i	$-0.884798\pi$
$83$	0.579789	−	3.66064i	0.0636401	−	0.401808i	0.998860	−	0.0477399i	$-0.0152019\pi$
$84$	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	−0.721738	−	0.692166i	$-0.756656\pi$
$89$	−10.3731	+	2.20488i	−1.09955	+	0.233716i	−0.377811	+	0.925883i	$0.623323\pi$
$90$		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	0.995269	+	0.0971587i	$0.0309754\pi$
$97$	0.775456	+	4.89604i	0.0787356	+	0.497117i	−0.916533	+	0.399958i	$0.869025\pi$
$98$	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	0.982069	−	0.188524i	$-0.0603704\pi$
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.327767	+	0.944758i	$0.393704\pi$
$102$	3.91190	+	0.205014i	0.387336	+	0.0202994i
$103$	4.27261	+	5.27623i	0.420993	+	0.519883i	0.942880	−	0.333132i	$-0.108105\pi$
$103$	4.27261	+	5.27623i	0.420993	+	0.519883i	−0.521888	+	0.853014i	$0.674772\pi$
$104$	−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	0.998572	−	0.0534166i	$-0.0170111\pi$
$107$	18.9985	+	5.09063i	1.83665	+	0.492130i	0.838081	+	0.545546i	$0.183678\pi$
$108$	8.12981	+	6.58339i	0.782292	+	0.633487i
$109$	3.97502	−	18.7010i	0.380738	−	1.79123i	−0.202880	−	0.979204i	$-0.565030\pi$
$109$	3.97502	−	18.7010i	0.380738	−	1.79123i	0.583618	−	0.812029i	$-0.301637\pi$
$110$		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	−0.998838	−	0.0481952i	$-0.984653\pi$
$113$	−3.96233	+	7.77652i	−0.372745	+	0.731553i	0.626093	+	0.779748i	$0.284653\pi$
$114$	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	−0.989777	−	0.142625i	$-0.954446\pi$
$127$	−5.89827	−	11.5760i	−0.523386	−	1.02720i	0.466390	−	0.884579i	$-0.345554\pi$
$128$	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	−0.839590	−	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
$133$	−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	−0.786710	−	0.617323i	$-0.788217\pi$
$137$	−6.35261	+	4.12544i	−0.542740	+	0.352460i	0.243969	+	0.969783i	$0.421550\pi$
$138$	0.565729	+	10.7947i	0.0481580	+	0.918910i
$139$	2.73221	−	8.40888i	0.231743	−	0.713232i	−0.765794	−	0.643086i	$-0.777654\pi$
$139$	2.73221	−	8.40888i	0.231743	−	0.713232i	0.997537	−	0.0701455i	$-0.0223463\pi$
$140$		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	−0.436242	−	0.899830i	$-0.643691\pi$
$149$	1.52475	−	0.880317i	0.124913	−	0.0721183i	0.561154	+	0.827711i	$0.310357\pi$
$150$		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	$0.248777\pi$
$152$	−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	−0.650072	−	0.759872i	$-0.725261\pi$
$157$	−10.4389	+	2.79709i	−0.833115	+	0.223232i	−0.183043	+	0.983105i	$0.558595\pi$
$158$	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	−0.269265	−	0.963066i	$-0.586781\pi$
$163$	−5.57143	+	0.291986i	−0.436388	+	0.0228701i	−0.167122	+	0.985936i	$0.553448\pi$
$164$	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	−0.257706	−	0.966223i	$-0.582967\pi$
$167$	−10.3561	−	1.64024i	−0.801379	−	0.126926i	−0.543673	+	0.839297i	$0.682967\pi$
$168$	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	−0.431191	−	0.902260i	$-0.641907\pi$
$173$	7.47674	−	11.5132i	0.568446	−	0.875330i	0.999637	+	0.0269305i	$0.00857330\pi$
$174$	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	0.887425	−	0.460953i	$-0.152492\pi$
$179$	−0.654680	−	1.47044i	−0.0489331	−	0.109906i	−0.936358	+	0.351047i	$0.885826\pi$
$180$		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	$0.758736\pi$
$182$	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	−0.810627	−	0.585563i	$-0.800874\pi$
$191$	−1.98374	+	2.20317i	−0.143538	+	0.159415i	0.667089	+	0.744978i	$0.267540\pi$
$192$	5.56517	−	6.87242i	0.401632	−	0.495974i
$193$	16.4661	−	4.41207i	1.18525	−	0.317588i	0.388246	−	0.921556i	$-0.373081\pi$
$193$	16.4661	−	4.41207i	1.18525	−	0.317588i	0.797009	+	0.603968i	$0.206414\pi$
$194$	−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	−0.794320	−	0.607499i	$-0.792173\pi$
$197$	−19.1171	+	3.02785i	−1.36204	+	0.215725i	−0.567716	+	0.823225i	$0.692173\pi$
$198$	4.25441	+	2.76285i	0.302348	+	0.196347i
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	−0.862605	−	0.505878i	$-0.831168\pi$
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	0.869406	+	0.494098i	$0.164502\pi$
$200$		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	−0.860265	−	0.509847i	$-0.829702\pi$
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	0.995650	+	0.0931759i	$0.0297019\pi$
$212$	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	0.594592	−	0.804027i	$-0.297313\pi$
$223$	−6.05349	−	11.8807i	−0.405372	−	0.795587i	−0.999964	+	0.00843996i	$0.997313\pi$
$224$	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	0.977170	+	0.212461i	$0.0681478\pi$
$227$	−0.253949	+	4.84563i	−0.0168552	+	0.321616i	−0.994025	+	0.109155i	$0.965185\pi$
$228$	−9.16491	−	3.51808i	−0.606961	−	0.232991i
$229$	−0.698945	+	6.65002i	−0.0461876	+	0.439446i	0.946852	+	0.321668i	$0.104244\pi$
$229$	−0.698945	+	6.65002i	−0.0461876	+	0.439446i	−0.993040	+	0.117777i	$0.962423\pi$
$230$		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	0.996819	−	0.0796953i	$-0.0253947\pi$
$233$	3.09426	+	8.06082i	0.202712	+	0.528082i	−0.794108	+	0.607777i	$0.792061\pi$
$234$	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	−0.347785	−	0.937574i	$-0.613066\pi$
$239$	−18.2461	−	5.92852i	−1.18024	−	0.383484i	−0.832457	+	0.554090i	$0.813066\pi$
$240$		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	$0.751633\pi$
$242$	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	$-0.838295\pi$
$251$		−	15.4133i		−	0.972880i	0.873714	−	0.486440i	$-0.161705\pi$
$252$	−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	0.0445856	+	0.999006i	$0.485803\pi$
$257$	−7.91188	+	29.5275i	−0.493529	+	1.84188i	−0.538115	+	0.842871i	$0.680863\pi$
$258$	−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	0.831758	−	0.555138i	$-0.187335\pi$
$263$	−0.222055	−	0.341935i	−0.0136925	−	0.0210846i	−0.845451	+	0.534054i	$0.820668\pi$
$264$	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	0.868406	+	0.495854i	$0.165145\pi$
$269$	2.00211	+	19.0488i	0.122071	+	1.16142i	−0.746335	+	0.665570i	$0.768188\pi$
$270$		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	$0.732786\pi$
$272$	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	−0.178497	−	0.983940i	$-0.557124\pi$
$277$	−7.63707	−	0.400242i	−0.458867	−	0.0240482i	−0.280369	+	0.959892i	$0.590457\pi$
$278$	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	−0.0359618	−	0.999353i	$-0.511449\pi$
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	0.939329	+	0.343019i	$0.111449\pi$
$282$	0.525104	+	0.140701i	0.0312695	+	0.00837864i
$283$	−2.21463	−	1.79337i	−0.131646	−	0.106605i	0.561236	−	0.827656i	$-0.310326\pi$
$283$	−2.21463	−	1.79337i	−0.131646	−	0.106605i	−0.692882	+	0.721051i	$0.743659\pi$
$284$	−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	−0.689814	−	0.723987i	$-0.742308\pi$
$293$	0.584948	−	0.584948i	0.0341730	−	0.0341730i	0.723987	+	0.689814i	$0.242308\pi$
$294$	−11.6423	+	3.50150i	−0.678995	+	0.204212i
$295$		0			0
$296$	0.510683	−	4.85883i	0.0296829	−	0.282414i
$297$	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	0.345007	−	0.938600i	$-0.387877\pi$
$307$	−10.4006	−	10.4006i	−0.593593	−	0.593593i	−0.938600	+	0.345007i	$0.887877\pi$
$308$	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	−0.379653	−	0.925129i	$-0.623957\pi$
$311$	8.83036	−	7.95089i	0.500724	−	0.450854i	0.880377	+	0.474275i	$0.157290\pi$
$312$	2.48073	−	1.61100i	0.140443	−	0.0912050i
$313$	−0.527196	−	10.0595i	−0.0297989	−	0.568597i	−0.972206	−	0.234128i	$-0.924777\pi$
$313$	−0.527196	−	10.0595i	−0.0297989	−	0.568597i	0.942407	−	0.334469i	$-0.108557\pi$
$314$	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	0.191981	−	0.981399i	$-0.438509\pi$
$317$	17.6502	−	6.77528i	0.991335	−	0.380538i	0.799354	+	0.600861i	$0.205175\pi$
$318$	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	0.992052	−	0.125830i	$-0.0401594\pi$
$331$	28.4245	+	12.6554i	1.56235	+	0.695605i	0.570302	+	0.821435i	$0.306826\pi$
$332$	−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	0.989060	+	0.147514i	$0.0471271\pi$
$337$	31.0198	+	15.8054i	1.68976	+	0.860974i	0.700696	+	0.713460i	$0.252873\pi$
$338$	−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	−0.385746	−	0.922605i	$-0.626056\pi$
$347$	9.65416	−	25.1500i	0.518263	−	1.35012i	0.904008	−	0.427515i	$-0.140611\pi$
$348$	−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	−0.998710	−	0.0507745i	$-0.983831\pi$
$353$	−4.18132	+	10.8927i	−0.222549	+	0.579760i	0.776161	+	0.630535i	$0.217164\pi$
$354$	−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	0.751802	−	0.659389i	$-0.229185\pi$
$359$	3.30837	+	2.97887i	0.174609	+	0.157219i	−0.577192	+	0.816608i	$0.695852\pi$
$360$		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	−0.154857	−	0.987937i	$-0.549492\pi$
$367$	16.1627	−	19.9593i	0.843688	−	1.04187i	0.998545	−	0.0539306i	$-0.0171750\pi$
$368$	−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	0.981635	+	0.190770i	$0.0610984\pi$
$373$	30.0355	+	19.5053i	1.55518	+	1.00994i	0.573544	+	0.819175i	$0.305568\pi$
$374$	−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	−0.999983	−	0.00584095i	$-0.998141\pi$
$379$	−13.3436	+	18.3659i	−0.685416	+	0.943394i	0.314567	+	0.949235i	$0.398141\pi$
$380$		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	−0.816770	−	0.576964i	$-0.804237\pi$
$383$	−20.3079	+	7.79546i	−1.03768	+	0.398330i	−0.220914	+	0.975293i	$0.570904\pi$
$384$	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	−0.386876	−	0.922132i	$-0.626446\pi$
$389$	9.65968	−	8.69762i	0.489765	−	0.440987i	0.876641	+	0.481145i	$0.159779\pi$
$390$		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	−0.531592	−	0.847001i	$-0.678406\pi$
$397$	3.71351	−	3.00714i	0.186376	−	0.150924i	0.717968	+	0.696077i	$0.245073\pi$
$398$	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	0.990874	−	0.134793i	$-0.0430370\pi$
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	−0.612171	+	0.790725i	$0.709704\pi$
$402$	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	0.449634	−	0.893213i	$-0.351554\pi$
$409$	10.0531	+	2.13685i	0.497094	+	0.105661i	0.0474592	+	0.998873i	$0.484888\pi$
$410$		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	−0.174766	−	0.984610i	$-0.555917\pi$
$419$	14.4852	−	10.5241i	0.707648	−	0.514137i	0.882414	+	0.470473i	$0.155917\pi$
$420$		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	$0.565793\pi$
$422$	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	0.993688	+	0.112178i	$0.0357828\pi$
$431$	0.935006	+	8.89599i	0.0450377	+	0.428505i	−0.948650	+	0.316326i	$0.897551\pi$
$432$	−3.55996	+	13.2859i	−0.171278	+	0.639220i
$433$	−2.75652	+	17.4040i	−0.132470	+	0.836382i	0.828552	+	0.559912i	$0.189165\pi$
$433$	−2.75652	+	17.4040i	−0.132470	+	0.836382i	−0.961022	+	0.276471i	$0.910835\pi$
$434$	−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	−0.796950	−	0.604045i	$-0.793555\pi$
$439$	−26.8046	+	5.69749i	−1.27931	+	0.271926i	−0.482363	+	0.875972i	$0.660221\pi$
$440$		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	0.863692	+	0.504019i	$0.168146\pi$
$443$	−2.86872	+	10.7062i	−0.136297	+	0.508667i	−0.999989	+	0.00464732i	$0.998521\pi$
$444$	−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	$-0.604511\pi$
$449$		−	40.1154i		−	1.89316i	0.322465	−	0.946581i	$-0.395489\pi$
$450$		0			0
$451$	5.09064	+	2.93909i	0.239709	+	0.138396i
$452$	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	−0.610620	−	0.791924i	$-0.709080\pi$
$457$	−32.8230	−	8.79489i	−1.53539	−	0.411408i	−0.924774	+	0.380516i	$0.875746\pi$
$458$	−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	−0.490535	−	0.871422i	$-0.663198\pi$
$461$	−30.0506	−	9.76402i	−1.39959	−	0.454756i	−0.909060	+	0.416666i	$0.863198\pi$
$462$	1.91435	+	4.43027i	0.0890634	+	0.206115i
$463$	8.64582	−	16.9684i	0.401805	−	0.788587i	−0.598113	−	0.801412i	$-0.704082\pi$
$463$	8.64582	−	16.9684i	0.401805	−	0.788587i	0.999918	+	0.0128250i	$0.00408243\pi$
$464$	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	0.974072	−	0.226236i	$-0.0726422\pi$
$467$	2.13538	+	5.56287i	0.0988138	+	0.257419i	−0.875259	+	0.483655i	$0.839309\pi$
$468$	−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	0.0775436	−	0.996989i	$-0.475292\pi$
$479$	19.0483	−	8.48083i	0.870338	−	0.387499i	0.792794	+	0.609490i	$0.208626\pi$
$480$		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	−0.964474	−	0.264176i	$-0.914900\pi$
$487$	−24.6153	+	15.9853i	−1.11542	+	0.724365i	−0.150950	+	0.988541i	$0.548233\pi$
$488$	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	−0.994574	−	0.104036i	$-0.966824\pi$
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	0.743476	−	0.668762i	$-0.233176\pi$
$492$	−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	−0.599549	−	0.800338i	$-0.704653\pi$
$499$	−4.60639	+	2.65950i	−0.206210	+	0.119056i	0.393339	+	0.919394i	$0.371320\pi$
$500$		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	−0.707801	−	0.706412i	$-0.750313\pi$
$503$	−26.0759	+	4.13001i	−1.16267	+	0.184148i	−0.454865	+	0.890560i	$0.650313\pi$
$504$	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	−0.673104	−	0.739548i	$-0.735040\pi$
$509$	2.99499	−	3.32627i	0.132750	−	0.147434i	0.805855	+	0.592113i	$0.201706\pi$
$510$		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	−0.983993	−	0.178206i	$-0.942971\pi$
$521$	−10.4542	−	23.4805i	−0.458006	−	1.02870i	0.525987	−	0.850492i	$-0.323696\pi$
$522$	2.18899	−	5.70250i	0.0958093	−	0.249592i
$523$	11.9816	−	18.4501i	0.523920	−	0.806766i	−0.473330	−	0.880885i	$-0.656948\pi$
$523$	11.9816	−	18.4501i	0.523920	−	0.806766i	0.997249	+	0.0741198i	$0.0236147\pi$
$524$	−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	−0.615223	−	0.788353i	$-0.710934\pi$
$541$	5.42224	−	6.02201i	0.233120	−	0.258906i	0.848343	+	0.529447i	$0.177601\pi$
$542$	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	−0.550444	−	0.834872i	$-0.685542\pi$
$547$	−19.0836	+	3.02255i	−0.815958	+	0.129235i	−0.265514	+	0.964107i	$0.585542\pi$
$548$	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	−0.989656	−	0.143462i	$-0.954177\pi$
$557$	−4.82211	−	17.9964i	−0.204320	−	0.762531i	0.785336	−	0.619069i	$-0.212490\pi$
$558$	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	−0.866926	−	0.498436i	$-0.833908\pi$
$563$	−18.1325	+	11.7754i	−0.764193	+	0.496273i	0.102734	+	0.994709i	$0.467241\pi$
$564$	−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	0.151424	+	0.988469i	$0.451614\pi$
$569$	−16.3273	+	36.6716i	−0.684474	+	1.53735i	−0.835898	+	0.548885i	$0.815053\pi$
$570$		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	$0.121305\pi$
$572$	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	−0.985248	−	0.171130i	$-0.945258\pi$
$577$	0.300036	−	5.72503i	0.0124907	−	0.238336i	0.997739	−	0.0672061i	$-0.0214085\pi$
$578$	−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	−0.749785	−	0.661682i	$-0.769843\pi$
$587$	5.48135	−	10.7577i	0.226239	−	0.444020i	0.976024	+	0.217662i	$0.0698430\pi$
$588$	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	−0.743802	−	0.668401i	$-0.766979\pi$
$593$	−41.9372	−	11.2370i	−1.72215	−	0.461449i	−0.978351	+	0.206951i	$0.933646\pi$
$594$	−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	0.513780	−	0.857922i	$-0.328245\pi$
$599$	0.677665	+	0.391250i	0.0276887	+	0.0159860i	−0.486092	+	0.873908i	$0.661578\pi$
$600$		0			0
$601$		−	7.23002i		−	0.294919i	−0.989068	−	0.147459i	$-0.952890\pi$
$601$		−	7.23002i		−	0.294919i	0.989068	−	0.147459i	$-0.0471095\pi$
$602$	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	−0.955970	−	0.293464i	$-0.905192\pi$
$607$	0.459640	−	1.71540i	0.0186562	−	0.0696260i	0.974626	+	0.223838i	$0.0718586\pi$
$608$	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	0.826414	−	0.563063i	$-0.190377\pi$
$613$	−0.596749	−	0.918913i	−0.0241025	−	0.0371145i	−0.850516	+	0.525948i	$0.823710\pi$
$614$	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	0.650691	+	0.759343i	$0.274479\pi$
$617$	−5.03752	+	31.8056i	−0.202803	+	1.28045i	−0.853494	+	0.521103i	$0.825521\pi$
$618$	3.05185	−	11.3897i	0.122764	−	0.458160i
$619$	−1.93430	−	18.4036i	−0.0777461	−	0.739705i	−0.962065	−	0.272821i	$-0.912043\pi$
$619$	−1.93430	−	18.4036i	−0.0777461	−	0.739705i	0.884319	−	0.466884i	$-0.154623\pi$
$620$		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	−0.0974273	−	0.995243i	$-0.531061\pi$
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	0.916425	+	0.400206i	$0.131061\pi$
$632$	−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	−0.582647	−	0.812725i	$-0.697983\pi$
$641$	−36.5968	−	7.77889i	−1.44549	−	0.307248i	−0.862840	+	0.505478i	$0.831316\pi$
$642$	−12.2419	−	31.8914i	−0.483151	−	1.25865i
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	−0.352392	−	0.935852i	$-0.614632\pi$
$643$	14.7951	−	14.7951i	0.583460	−	0.583460i	0.935852	+	0.352392i	$0.114632\pi$
$644$	17.3464	+	34.9910i	0.683545	+	1.37884i
$645$		0			0
$646$	−2.45636	+	23.3707i	−0.0966442	+	0.919508i
$647$	24.1309	+	9.26299i	0.948684	+	0.364166i	0.783006	−	0.622014i	$-0.213685\pi$
$647$	24.1309	+	9.26299i	0.948684	+	0.364166i	0.165678	+	0.986180i	$0.447019\pi$
$648$	−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	−0.939503	−	0.342542i	$-0.888712\pi$
$653$	−20.4375	+	16.5499i	−0.799780	+	0.647649i	0.139723	+	0.990191i	$0.455379\pi$
$654$	−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	−0.417904	−	0.908491i	$-0.637235\pi$
$659$	−5.69893	+	1.85169i	−0.221999	+	0.0721317i	0.195906	+	0.980623i	$0.437235\pi$
$660$		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	$0.914002\pi$
$662$	−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	−0.127030	−	0.991899i	$-0.540544\pi$
$673$	15.5853	−	7.94108i	0.600767	−	0.306106i	0.727797	+	0.685793i	$0.240544\pi$
$674$	−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	−0.159008	−	0.987277i	$-0.550830\pi$
$677$	−29.2874	−	19.0194i	−1.12560	−	0.730976i	−0.966597	+	0.256301i	$0.917496\pi$
$678$	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	−0.00209925	+	0.999998i	$0.500668\pi$
$683$	−25.6066	+	31.6215i	−0.979808	+	1.20996i	−0.977709	+	0.209965i	$0.932665\pi$
$684$	−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	0.881168	−	0.472803i	$-0.156758\pi$
$691$	13.2239	+	11.9069i	0.503062	+	0.452959i	−0.378106	+	0.925762i	$0.623425\pi$
$692$	−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	0.679886	−	0.733318i	$-0.262029\pi$
$709$	0.576558	+	0.519135i	0.0216531	+	0.0194965i	−0.658233	+	0.752814i	$0.728696\pi$
$710$		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	−0.332888	−	0.942966i	$-0.608023\pi$
$719$	−33.6892	−	14.9994i	−1.25639	−	0.559383i	−0.923506	+	0.383583i	$0.874690\pi$
$720$		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	−0.0928967	−	0.995676i	$-0.529613\pi$
$727$	17.7421	−	9.04006i	0.658019	−	0.335277i	0.750915	+	0.660398i	$0.229613\pi$
$728$	−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	−0.357677	−	0.933845i	$-0.616431\pi$
$733$	0.0374092	−	0.0143601i	0.00138174	−	0.000530401i	0.359059	+	0.933315i	$0.383098\pi$
$734$	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	−0.889534	−	0.456868i	$-0.848971\pi$
$739$	−14.3575	+	12.9276i	−0.528151	+	0.475549i	0.361384	+	0.932417i	$0.382304\pi$
$740$		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	0.328831	−	0.944389i	$-0.393345\pi$
$743$	−16.7789	−	16.7789i	−0.615557	−	0.615557i	−0.944389	+	0.328831i	$0.893345\pi$
$744$	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	0.719227	−	0.694775i	$-0.244496\pi$
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	−0.961306	+	0.275482i	$0.911163\pi$
$752$	−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	−0.727448	−	0.686163i	$-0.759294\pi$
$757$	−1.13591	+	1.13591i	−0.0412853	+	0.0412853i	0.686163	+	0.727448i	$0.259294\pi$
$758$	−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	0.919446	+	0.393217i	$0.128638\pi$
$761$	6.60486	+	31.0734i	0.239426	+	1.12641i	−0.680020	+	0.733194i	$0.738029\pi$
$762$	−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	−0.368495	−	0.929630i	$-0.620127\pi$
$769$	11.1412	−	8.09458i	0.401763	−	0.291898i	0.770259	+	0.637731i	$0.220127\pi$
$770$		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	−0.128891	−	0.991659i	$-0.541142\pi$
$773$	−10.0294	−	0.525618i	−0.360732	−	0.0189052i	−0.231841	+	0.972754i	$0.574475\pi$
$774$	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	0.565504	−	0.824746i	$-0.308682\pi$
$787$	−11.7250	−	18.0549i	−0.417950	−	0.643586i	−0.983454	+	0.181159i	$0.942015\pi$
$788$	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	0.968757	−	0.248013i	$-0.0797776\pi$
$797$	−0.825084	−	5.20937i	−0.0292260	−	0.184526i	−0.997983	+	0.0634877i	$0.979778\pi$
$798$	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	−0.998003	−	0.0631613i	$-0.979882\pi$
$809$	−1.72341	+	8.10801i	−0.0605919	+	0.285063i	0.937411	+	0.348224i	$0.113215\pi$
$810$		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	$0.460775\pi$
$812$	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	0.954703	+	0.297560i	$0.0961729\pi$
$821$	−1.17488	+	11.1783i	−0.0410037	+	0.390124i	−0.995707	+	0.0925640i	$0.970494\pi$
$822$	12.2817	+	4.71451i	0.428374	+	0.164437i
$823$	−0.898326	+	17.1411i	−0.0313137	+	0.597501i	0.937238	+	0.348689i	$0.113373\pi$
$823$	−0.898326	+	17.1411i	−0.0313137	+	0.597501i	−0.968552	+	0.248811i	$0.919960\pi$
$824$	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	0.631046	−	0.775745i	$-0.282626\pi$
$827$	−10.5674	−	20.7397i	−0.367465	−	0.721190i	−0.998511	+	0.0545555i	$0.982626\pi$
$828$	−26.4997	+	21.4590i	−0.920928	+	0.745753i
$829$	−23.1374	+	10.3014i	−0.803596	+	0.357784i	−0.767082	−	0.641549i	$-0.778292\pi$
$829$	−23.1374	+	10.3014i	−0.803596	+	0.357784i	−0.0365142	+	0.999333i	$0.511625\pi$
$830$		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	0.0289189	−	0.999582i	$-0.490794\pi$
$839$	17.1783	−	52.8695i	0.593062	−	1.82526i	0.564144	−	0.825677i	$-0.309206\pi$
$840$		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	0.608616	−	0.793465i	$-0.291725\pi$
$853$	41.8419	−	6.62710i	1.43264	−	0.226908i	0.824023	+	0.566557i	$0.191725\pi$
$854$	−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	0.431164	−	0.902274i	$-0.358103\pi$
$857$	36.7601	−	9.84983i	1.25570	−	0.336464i	0.824536	+	0.565810i	$0.191436\pi$
$858$	5.25969	−	6.49517i	0.179563	−	0.221742i
$859$	34.3314	−	38.1289i	1.17137	−	1.30094i	0.226307	−	0.974056i	$-0.427335\pi$
$859$	34.3314	−	38.1289i	1.17137	−	1.30094i	0.945064	−	0.326884i	$-0.105999\pi$
$860$		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	−0.420025	−	0.907513i	$-0.637979\pi$
$863$	−21.8237	+	1.14373i	−0.742887	+	0.0389331i	−0.322863	+	0.946446i	$0.604645\pi$
$864$	−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	−0.851453	−	0.524431i	$-0.824278\pi$
$877$	−0.771263	+	1.18764i	−0.0260437	+	0.0401038i	0.825409	+	0.564535i	$0.190945\pi$
$878$	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	0.715293	−	0.698825i	$-0.246293\pi$
$881$	−5.05676	−	6.96003i	−0.170367	−	0.234489i	−0.885659	+	0.464335i	$0.846293\pi$
$882$	−2.51208	+	33.7160i	−0.0845860	+	1.13528i
$883$	−40.2254	−	6.37108i	−1.35369	−	0.214404i	−0.562919	−	0.826512i	$-0.690322\pi$
$883$	−40.2254	−	6.37108i	−1.35369	−	0.214404i	−0.790774	+	0.612108i	$0.790322\pi$
$884$	−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	−0.463514	−	0.886090i	$-0.653411\pi$
$887$	−24.7751	+	1.29841i	−0.831866	+	0.0435963i	−0.368353	+	0.929686i	$0.620078\pi$
$888$	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	0.960274	+	0.279060i	$0.0900229\pi$
$907$	8.07670	+	30.1426i	0.268182	+	1.00087i	−0.692091	+	0.721810i	$0.743310\pi$
$908$	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	0.560000	+	0.828492i	$0.310801\pi$
$911$	−11.4702	+	35.3017i	−0.380025	+	1.16960i	−0.940025	+	0.341105i	$0.889199\pi$
$912$	−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	−0.366422	−	0.930449i	$-0.619417\pi$
$919$	17.2862	−	38.8255i	0.570220	−	1.28074i	0.936643	−	0.350287i	$-0.113916\pi$
$920$		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	−0.937186	−	0.348829i	$-0.886579\pi$
$929$	1.58633	−	15.0929i	0.0520459	−	0.495183i	0.989232	−	0.146354i	$-0.0467539\pi$
$930$		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	−0.628076	−	0.778152i	$-0.716157\pi$
$937$	11.3453	−	22.2665i	0.370636	−	0.727415i	0.998712	+	0.0507375i	$0.0161572\pi$
$938$	−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	0.884789	+	0.465992i	$0.154302\pi$
$941$	−3.46764	+	16.3140i	−0.113042	+	0.531820i	−0.997831	+	0.0658284i	$0.979031\pi$
$942$	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	0.471483	−	0.881875i	$-0.343719\pi$
$947$	−15.0527	−	18.5885i	−0.489147	−	0.604047i	−0.960631	+	0.277828i	$0.910385\pi$
$948$	−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	−0.634077	−	0.773270i	$-0.718620\pi$
$953$	−8.33470	−	52.6232i	−0.269987	−	1.70463i	0.364090	−	0.931364i	$-0.381380\pi$
$954$	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	−0.768008	−	0.640441i	$-0.778752\pi$
$967$	4.98535	−	31.4763i	0.160318	−	1.01221i	0.928326	−	0.371768i	$-0.121248\pi$
$968$	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	−0.535937	−	0.844258i	$-0.680042\pi$
$971$	−38.5053	−	4.04707i	−1.23569	−	0.129877i	−0.699757	+	0.714381i	$0.746708\pi$
$972$	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	0.508206	−	0.861236i	$-0.330309\pi$
$977$	28.8691	+	1.51297i	0.923604	+	0.0484040i	0.415398	+	0.909640i	$0.363642\pi$
$978$	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	0.500355	−	0.865820i	$-0.333203\pi$
$983$	−7.60355	−	6.15724i	−0.242516	−	0.196385i	−0.742871	+	0.669435i	$0.766536\pi$
$984$	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	0.571176	−	0.820828i	$-0.306487\pi$
$991$	23.8969	+	5.07944i	0.759110	+	0.161354i	0.187934	+	0.982182i	$0.439821\pi$
$992$	−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	0.0133710	−	0.999911i	$-0.495744\pi$
$997$	−20.3902	−	7.82705i	−0.645763	−	0.247885i	−0.659134	+	0.752025i	$0.729077\pi$
$998$	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.493.3		288
5.2	odd	4		875.2.bb.a.507.3		288
5.3	odd	4		875.2.bb.b.507.16		288
5.4	even	2		175.2.x.a.3.16	✓	288
7.5	odd	6	inner	875.2.bb.c.243.16		288
25.6	even	5		875.2.bb.a.143.3		288
25.8	odd	20		175.2.x.a.17.3	yes	288
25.17	odd	20	inner	875.2.bb.c.857.16		288
25.19	even	10		875.2.bb.b.143.16		288
35.12	even	12		875.2.bb.a.257.3		288
35.19	odd	6		175.2.x.a.103.3	yes	288
35.33	even	12		875.2.bb.b.257.16		288
175.19	odd	30		875.2.bb.b.768.16		288
175.33	even	60		175.2.x.a.117.16	yes	288
175.117	even	60	inner	875.2.bb.c.607.3		288
175.131	odd	30		875.2.bb.a.768.3		288

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