LMFDB - Embedded newform 875.2.bb.a.143.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			143.8
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.a.257.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0420512 - 0.802384i) q^{2} +(2.43882 + 1.97492i) q^{3} +(1.34699 - 0.141575i) q^{4} +(1.48209 - 2.03992i) q^{6} +(0.782993 + 2.52724i) q^{7} +(-0.421625 - 2.66204i) q^{8} +(1.42381 + 6.69848i) q^{9} +(-4.90608 - 1.04282i) q^{11} +(3.56467 + 2.31492i) q^{12} +(0.416175 + 0.816789i) q^{13} +(1.99489 - 0.734535i) q^{14} +(0.531383 - 0.112949i) q^{16} +(0.483913 + 0.185757i) q^{17} +(5.31488 - 1.42412i) q^{18} +(0.116377 - 1.10725i) q^{19} +(-3.08150 + 7.70982i) q^{21} +(-0.630435 + 3.98041i) q^{22} +(5.16039 - 0.270445i) q^{23} +(4.22903 - 7.32490i) q^{24} +(0.637878 - 0.368279i) q^{26} +(-5.48243 + 10.7599i) q^{27} +(1.41248 + 3.29331i) q^{28} +(3.39698 + 4.67555i) q^{29} +(-0.139259 - 0.312781i) q^{31} +(-1.50812 - 5.62839i) q^{32} +(-9.90555 - 12.2323i) q^{33} +(0.128699 - 0.396095i) q^{34} +(2.86619 + 8.82122i) q^{36} +(3.47651 - 5.35336i) q^{37} +(-0.893337 - 0.0468178i) q^{38} +(-0.598115 + 2.81391i) q^{39} +(-6.75808 - 2.19583i) q^{41} +(6.31581 + 2.14834i) q^{42} +(3.02167 + 3.02167i) q^{43} +(-6.75609 - 0.710093i) q^{44} +(-0.434001 - 4.12924i) q^{46} +(-4.57426 - 11.9164i) q^{47} +(1.51901 + 0.773974i) q^{48} +(-5.77384 + 3.95762i) q^{49} +(0.813322 + 1.40871i) q^{51} +(0.676221 + 1.04129i) q^{52} +(3.68942 - 4.55606i) q^{53} +(8.86410 + 3.94655i) q^{54} +(6.39747 - 3.14990i) q^{56} +(2.47056 - 2.47056i) q^{57} +(3.60874 - 2.92230i) q^{58} +(-5.88478 - 6.53571i) q^{59} +(-1.07623 - 0.969040i) q^{61} +(-0.245114 + 0.124892i) q^{62} +(-15.8138 + 8.84316i) q^{63} +(-3.41938 + 1.11102i) q^{64} +(-9.39849 + 8.46244i) q^{66} +(-0.504146 + 1.31334i) q^{67} +(0.678125 + 0.181703i) q^{68} +(13.1194 + 9.53177i) q^{69} +(-6.16371 + 4.47820i) q^{71} +(17.2313 - 6.61447i) q^{72} +(-1.01144 + 0.656834i) q^{73} +(-4.44164 - 2.56438i) q^{74} -1.50794i q^{76} +(-1.20598 - 13.2153i) q^{77} +(2.28299 + 0.361590i) q^{78} +(-1.97771 + 4.44201i) q^{79} +(-15.8523 + 7.05789i) q^{81} +(-1.47772 + 5.51491i) q^{82} +(3.42852 - 0.543025i) q^{83} +(-3.05924 + 10.8213i) q^{84} +(2.29747 - 2.55160i) q^{86} +(-0.949187 + 18.1116i) q^{87} +(-0.707497 + 13.4998i) q^{88} +(2.10268 - 2.33526i) q^{89} +(-1.73836 + 1.69131i) q^{91} +(6.91272 - 1.09487i) q^{92} +(0.278088 - 1.03784i) q^{93} +(-9.36915 + 4.17141i) q^{94} +(7.43756 - 16.7050i) q^{96} +(3.51689 + 0.557021i) q^{97} +(3.41833 + 4.46642i) q^{98} -34.3480i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0420512	−	0.802384i	−0.0297347	−	0.567371i	−0.972355	−	0.233506i	$-0.924980\pi$
$2$	−0.0420512	−	0.802384i	−0.0297347	−	0.567371i	0.942621	−	0.333865i	$-0.108353\pi$
$3$	2.43882	+	1.97492i	1.40805	+	1.14022i	0.970521	+	0.241015i	$0.0774803\pi$
$3$	2.43882	+	1.97492i	1.40805	+	1.14022i	0.437531	+	0.899203i	$0.355853\pi$
$4$	1.34699	−	0.141575i	0.673496	−	0.0707873i
$5$		0			0
$5$		0			0
$6$	1.48209	−	2.03992i	0.605059	−	0.832792i
$7$	0.782993	+	2.52724i	0.295944	+	0.955205i
$7$	0.782993	+	2.52724i	0.295944	+	0.955205i
$8$	−0.421625	−	2.66204i	−0.149067	−	0.941172i
$9$	1.42381	+	6.69848i	0.474602	+	2.23283i
$10$		0			0
$11$	−4.90608	−	1.04282i	−1.47924	−	0.314422i	−0.603560	−	0.797317i	$-0.706252\pi$
$11$	−4.90608	−	1.04282i	−1.47924	−	0.314422i	−0.875678	+	0.482895i	$0.839585\pi$
$12$	3.56467	+	2.31492i	1.02903	+	0.668260i
$13$	0.416175	+	0.816789i	0.115426	+	0.226536i	0.941491	−	0.337039i	$-0.109425\pi$
$13$	0.416175	+	0.816789i	0.115426	+	0.226536i	−0.826065	+	0.563575i	$0.809425\pi$
$14$	1.99489	−	0.734535i	0.533156	−	0.196313i
$15$		0			0
$16$	0.531383	−	0.112949i	0.132846	−	0.0282372i
$17$	0.483913	+	0.185757i	0.117366	+	0.0450526i	0.416342	−	0.909208i	$-0.363312\pi$
$17$	0.483913	+	0.185757i	0.117366	+	0.0450526i	−0.298976	+	0.954261i	$0.596645\pi$
$18$	5.31488	−	1.42412i	1.25273	−	0.335668i
$19$	0.116377	−	1.10725i	0.0266987	−	0.254022i	−0.973029	−	0.230683i	$-0.925904\pi$
$19$	0.116377	−	1.10725i	0.0266987	−	0.254022i	0.999728	−	0.0233383i	$-0.00742947\pi$
$20$		0			0
$21$	−3.08150	+	7.70982i	−0.672439	+	1.68242i
$22$	−0.630435	+	3.98041i	−0.134409	+	0.848626i
$23$	5.16039	−	0.270445i	1.07602	−	0.0563916i	0.493916	−	0.869509i	$-0.335565\pi$
$23$	5.16039	−	0.270445i	1.07602	−	0.0563916i	0.582099	+	0.813118i	$0.302232\pi$
$24$	4.22903	−	7.32490i	0.863248	−	1.49519i
$25$		0			0
$26$	0.637878	−	0.368279i	0.125098	−	0.0722254i
$27$	−5.48243	+	10.7599i	−1.05509	+	2.07074i
$28$	1.41248	+	3.29331i	0.266933	+	0.622378i
$29$	3.39698	+	4.67555i	0.630804	+	0.868227i	0.998083	−	0.0618834i	$-0.0197107\pi$
$29$	3.39698	+	4.67555i	0.630804	+	0.868227i	−0.367279	+	0.930111i	$0.619711\pi$
$30$		0			0
$31$	−0.139259	−	0.312781i	−0.0250116	−	0.0561771i	0.900608	−	0.434633i	$-0.143122\pi$
$31$	−0.139259	−	0.312781i	−0.0250116	−	0.0561771i	−0.925619	+	0.378456i	$0.876455\pi$
$32$	−1.50812	−	5.62839i	−0.266601	−	0.994968i
$33$	−9.90555	−	12.2323i	−1.72434	−	2.12938i
$34$	0.128699	−	0.396095i	0.0220717	−	0.0679298i
$35$		0			0
$36$	2.86619	+	8.82122i	0.477698	+	1.47020i
$37$	3.47651	−	5.35336i	0.571535	−	0.880086i	−0.428187	−	0.903690i	$-0.640847\pi$
$37$	3.47651	−	5.35336i	0.571535	−	0.880086i	0.999721	+	0.0236039i	$0.00751406\pi$
$38$	−0.893337	−	0.0468178i	−0.144918	−	0.00759485i
$39$	−0.598115	+	2.81391i	−0.0957751	+	0.450586i
$40$		0			0
$41$	−6.75808	−	2.19583i	−1.05543	−	0.342931i	−0.270635	−	0.962682i	$-0.587234\pi$
$41$	−6.75808	−	2.19583i	−1.05543	−	0.342931i	−0.784799	+	0.619750i	$0.787234\pi$
$42$	6.31581	+	2.14834i	0.974551	+	0.331496i
$43$	3.02167	+	3.02167i	0.460800	+	0.460800i	0.898918	−	0.438118i	$-0.144355\pi$
$43$	3.02167	+	3.02167i	0.460800	+	0.460800i	−0.438118	+	0.898918i	$0.644355\pi$
$44$	−6.75609	−	0.710093i	−1.01852	−	0.107051i
$45$		0			0
$46$	−0.434001	−	4.12924i	−0.0639899	−	0.608824i
$47$	−4.57426	−	11.9164i	−0.667225	−	1.73818i	−0.674574	−	0.738207i	$-0.735673\pi$
$47$	−4.57426	−	11.9164i	−0.667225	−	1.73818i	0.00734880	−	0.999973i	$-0.497661\pi$
$48$	1.51901	+	0.773974i	0.219250	+	0.111714i
$49$	−5.77384	+	3.95762i	−0.824835	+	0.565374i
$50$		0			0
$51$	0.813322	+	1.40871i	0.113888	+	0.197260i
$52$	0.676221	+	1.04129i	0.0937749	+	0.144401i
$53$	3.68942	−	4.55606i	0.506781	−	0.625822i	−0.457976	−	0.888965i	$-0.651425\pi$
$53$	3.68942	−	4.55606i	0.506781	−	0.625822i	0.964757	+	0.263142i	$0.0847588\pi$
$54$	8.86410	+	3.94655i	1.20625	+	0.537057i
$55$		0			0
$56$	6.39747	−	3.14990i	0.854897	−	0.420924i
$57$	2.47056	−	2.47056i	0.327233	−	0.327233i
$58$	3.60874	−	2.92230i	0.473850	−	0.383717i
$59$	−5.88478	−	6.53571i	−0.766133	−	0.850876i	0.226250	−	0.974069i	$-0.427353\pi$
$59$	−5.88478	−	6.53571i	−0.766133	−	0.850876i	−0.992383	+	0.123193i	$0.960687\pi$
$60$		0			0
$61$	−1.07623	−	0.969040i	−0.137797	−	0.124073i	0.597350	−	0.801981i	$-0.296220\pi$
$61$	−1.07623	−	0.969040i	−0.137797	−	0.124073i	−0.735147	+	0.677908i	$0.762887\pi$
$62$	−0.245114	+	0.124892i	−0.0311295	+	0.0158613i
$63$	−15.8138	+	8.84316i	−1.99235	+	1.11413i
$64$	−3.41938	+	1.11102i	−0.427422	+	0.138878i
$65$		0			0
$66$	−9.39849	+	8.46244i	−1.15687	+	1.04165i
$67$	−0.504146	+	1.31334i	−0.0615912	+	0.160451i	−0.960923	−	0.276817i	$-0.910720\pi$
$67$	−0.504146	+	1.31334i	−0.0615912	+	0.160451i	0.899331	+	0.437268i	$0.144054\pi$
$68$	0.678125	+	0.181703i	0.0822348	+	0.0220347i
$69$	13.1194	+	9.53177i	1.57939	+	1.14749i
$70$		0			0
$71$	−6.16371	+	4.47820i	−0.731498	+	0.531465i	−0.890037	−	0.455888i	$-0.849322\pi$
$71$	−6.16371	+	4.47820i	−0.731498	+	0.531465i	0.158539	+	0.987353i	$0.449322\pi$
$72$	17.2313	−	6.61447i	2.03073	−	0.779523i
$73$	−1.01144	+	0.656834i	−0.118380	+	0.0768766i	−0.602471	−	0.798141i	$-0.705817\pi$
$73$	−1.01144	+	0.656834i	−0.118380	+	0.0768766i	0.484091	+	0.875018i	$0.339150\pi$
$74$	−4.44164	−	2.56438i	−0.516330	−	0.298103i
$75$		0			0
$76$		−	1.50794i		−	0.172972i
$77$	−1.20598	−	13.2153i	−0.137434	−	1.50603i
$78$	2.28299	+	0.361590i	0.258497	+	0.0409420i
$79$	−1.97771	+	4.44201i	−0.222510	+	0.499765i	−0.989961	−	0.141343i	$-0.954858\pi$
$79$	−1.97771	+	4.44201i	−0.222510	+	0.499765i	0.767451	+	0.641107i	$0.221525\pi$
$80$		0			0
$81$	−15.8523	+	7.05789i	−1.76136	+	0.784210i
$82$	−1.47772	+	5.51491i	−0.163186	+	0.609020i
$83$	3.42852	−	0.543025i	0.376329	−	0.0596047i	0.0345952	−	0.999401i	$-0.488986\pi$
$83$	3.42852	−	0.543025i	0.376329	−	0.0596047i	0.341734	+	0.939797i	$0.388986\pi$
$84$	−3.05924	+	10.8213i	−0.333791	+	1.18070i
$85$		0			0
$86$	2.29747	−	2.55160i	0.247743	−	0.275146i
$87$	−0.949187	+	18.1116i	−0.101764	+	1.94176i
$88$	−0.707497	+	13.4998i	−0.0754194	+	1.43909i
$89$	2.10268	−	2.33526i	0.222884	−	0.247537i	−0.621324	−	0.783554i	$-0.713405\pi$
$89$	2.10268	−	2.33526i	0.222884	−	0.247537i	0.844208	+	0.536016i	$0.180071\pi$
$90$		0			0
$91$	−1.73836	+	1.69131i	−0.182229	+	0.177298i
$92$	6.91272	−	1.09487i	0.720700	−	0.114148i
$93$	0.278088	−	1.03784i	0.0288364	−	0.107619i
$94$	−9.36915	+	4.17141i	−0.966354	+	0.430248i
$95$		0			0
$96$	7.43756	−	16.7050i	0.759093	−	1.70495i
$97$	3.51689	+	0.557021i	0.357086	+	0.0565569i	0.332400	−	0.943138i	$-0.392141\pi$
$97$	3.51689	+	0.557021i	0.357086	+	0.0565569i	0.0246858	+	0.999695i	$0.492141\pi$
$98$	3.41833	+	4.46642i	0.345303	+	0.451176i
$99$		−	34.3480i		−	3.45211i
$100$		0			0
$101$	−8.57568	−	4.95117i	−0.853312	−	0.492660i	0.00845468	−	0.999964i	$-0.497309\pi$
$101$	−8.57568	−	4.95117i	−0.853312	−	0.492660i	−0.861767	+	0.507304i	$0.830642\pi$
$102$	1.09613	−	0.711834i	0.108533	−	0.0704821i
$103$	6.93326	−	2.66143i	0.683154	−	0.262238i	0.00805736	−	0.999968i	$-0.497435\pi$
$103$	6.93326	−	2.66143i	0.683154	−	0.262238i	0.675097	+	0.737729i	$0.264102\pi$
$104$	1.99885	−	1.45225i	0.196004	−	0.142405i
$105$		0			0
$106$	−3.81085	−	2.76875i	−0.370143	−	0.268924i
$107$	1.50667	+	0.403711i	0.145655	+	0.0390282i	0.330910	−	0.943662i	$-0.392644\pi$
$107$	1.50667	+	0.403711i	0.145655	+	0.0390282i	−0.185255	+	0.982691i	$0.559311\pi$
$108$	−5.86147	+	15.2696i	−0.564020	+	1.46932i
$109$	4.44021	−	3.99798i	0.425295	−	0.382937i	−0.428504	−	0.903540i	$-0.640959\pi$
$109$	4.44021	−	3.99798i	0.425295	−	0.382937i	0.853799	+	0.520603i	$0.174293\pi$
$110$		0			0
$111$	19.0510	−	6.19005i	1.80824	−	0.587533i
$112$	0.701517	+	1.25449i	0.0662872	+	0.118538i
$113$	2.24970	−	1.14628i	0.211634	−	0.107833i	−0.344960	−	0.938617i	$-0.612108\pi$
$113$	2.24970	−	1.14628i	0.211634	−	0.107833i	0.556595	+	0.830784i	$0.312108\pi$
$114$	−2.08623	−	1.87845i	−0.195393	−	0.175933i
$115$		0			0
$116$	5.23765	+	5.81700i	0.486303	+	0.540095i
$117$	−4.87869	+	3.95069i	−0.451035	+	0.365241i
$118$	−4.99668	+	4.99668i	−0.459982	+	0.459982i
$119$	−0.0905506	+	1.36841i	−0.00830076	+	0.125442i
$120$		0			0
$121$	12.9331	+	5.75820i	1.17574	+	0.523473i
$122$	−0.732286	+	0.904298i	−0.0662981	+	0.0818713i
$123$	−12.1451	−	18.7019i	−1.09509	−	1.68629i
$124$	−0.231863	−	0.401598i	−0.0208219	−	0.0360645i
$125$		0			0
$126$	7.76060	+	12.3169i	0.691369	+	1.09728i
$127$	−8.21389	−	4.18519i	−0.728865	−	0.371375i	0.0498468	−	0.998757i	$-0.484127\pi$
$127$	−8.21389	−	4.18519i	−0.728865	−	0.371375i	−0.778712	+	0.627381i	$0.784127\pi$
$128$	−3.14112	−	8.18289i	−0.277638	−	0.723272i
$129$	1.40176	+	13.3368i	0.123418	+	1.17424i
$130$		0			0
$131$	5.58590	+	0.587102i	0.488043	+	0.0512953i	0.345354	−	0.938472i	$-0.387759\pi$
$131$	5.58590	+	0.587102i	0.488043	+	0.0512953i	0.142688	+	0.989768i	$0.454425\pi$
$132$	−15.0745	−	15.0745i	−1.31207	−	1.31207i
$133$	2.88942	−	0.572860i	0.250544	−	0.0496733i
$134$	1.07501	+	0.349291i	0.0928664	+	0.0301741i
$135$		0			0
$136$	0.290462	−	1.36651i	0.0249069	−	0.117178i
$137$	4.31718	+	0.226254i	0.368841	+	0.0193302i	0.235857	−	0.971788i	$-0.424210\pi$
$137$	4.31718	+	0.226254i	0.368841	+	0.0193302i	0.132985	+	0.991118i	$0.457544\pi$
$138$	7.09646	−	10.9276i	0.604091	−	0.930218i
$139$	−1.99140	−	6.12890i	−0.168908	−	0.519847i	0.830395	−	0.557176i	$-0.188115\pi$
$139$	−1.99140	−	6.12890i	−0.168908	−	0.519847i	−0.999303	+	0.0373290i	$0.988115\pi$
$140$		0			0
$141$	12.3780	−	38.0956i	1.04242	−	3.20823i
$142$	3.85243	+	4.75735i	0.323289	+	0.399228i
$143$	−1.19002	−	4.44123i	−0.0995147	−	0.371394i
$144$	1.51317	+	3.39864i	0.126098	+	0.283220i
$145$		0			0
$146$	0.569565	+	0.783939i	0.0471376	+	0.0648793i
$147$	−21.8973	−	1.75094i	−1.80606	−	0.144415i
$148$	3.92493	−	7.70311i	0.322627	−	0.633192i
$149$	−1.92554	+	1.11171i	−0.157746	+	0.0910749i	−0.576795	−	0.816889i	$-0.695697\pi$
$149$	−1.92554	+	1.11171i	−0.157746	+	0.0910749i	0.419049	+	0.907964i	$0.362364\pi$
$150$		0			0
$151$	6.19286	−	10.7263i	0.503968	−	0.872897i	−0.496022	−	0.868310i	$-0.665206\pi$
$151$	6.19286	−	10.7263i	0.503968	−	0.872897i	0.999989	−	0.00458736i	$-0.00146021\pi$
$152$	−2.99662	+	0.157046i	−0.243058	+	0.0127381i
$153$	−0.555290	+	3.50596i	−0.0448925	+	0.283440i
$154$	−10.5531	+	1.52338i	−0.850390	+	0.122757i
$155$		0			0
$156$	−0.407278	+	3.87499i	−0.0326083	+	0.310248i
$157$	−16.2535	+	4.35511i	−1.29717	+	0.347576i	−0.840380	−	0.541998i	$-0.817668\pi$
$157$	−16.2535	+	4.35511i	−1.29717	+	0.347576i	−0.456791	+	0.889574i	$0.651001\pi$
$158$	3.64736	+	1.40009i	0.290168	+	0.111385i
$159$	17.9957	−	3.82509i	1.42715	−	0.303350i
$160$		0			0
$161$	4.72403	+	12.8298i	0.372306	+	1.01113i
$162$	6.32974	+	12.4228i	0.497312	+	0.976029i
$163$	15.2625	+	9.91155i	1.19545	+	0.776333i	0.979769	−	0.200132i	$-0.0641370\pi$
$163$	15.2625	+	9.91155i	1.19545	+	0.776333i	0.215679	+	0.976464i	$0.430804\pi$
$164$	−9.41395	−	2.00100i	−0.735106	−	0.156252i
$165$		0			0
$166$	−0.579888	−	2.72816i	−0.0450080	−	0.211746i
$167$	0.0529161	+	0.334099i	0.00409477	+	0.0258534i	0.989651	−	0.143494i	$-0.0458339\pi$
$167$	0.0529161	+	0.334099i	0.00409477	+	0.0258534i	−0.985556	+	0.169348i	$0.945834\pi$
$168$	21.8231	+	4.95242i	1.68369	+	0.382087i
$169$	7.14727	−	9.83737i	0.549790	−	0.756721i
$170$		0			0
$171$	7.58262	−	0.796965i	0.579857	−	0.0609455i
$172$	4.49795	+	3.64237i	0.342966	+	0.277728i
$173$	0.931608	+	17.7761i	0.0708288	+	1.35149i	0.770687	+	0.637213i	$0.219913\pi$
$173$	0.931608	+	17.7761i	0.0708288	+	1.35149i	−0.699859	+	0.714281i	$0.746754\pi$
$174$	14.5723			1.10473
$175$		0			0
$176$	−2.72479			−0.205389
$177$	−1.44443	−	27.5613i	−0.108570	−	2.07164i
$178$	−1.96220	−	1.58896i	−0.147073	−	0.119097i
$179$	9.80573	−	1.03062i	0.732915	−	0.0770324i	0.269284	−	0.963061i	$-0.413213\pi$
$179$	9.80573	−	1.03062i	0.732915	−	0.0770324i	0.463631	+	0.886028i	$0.346546\pi$
$180$		0			0
$181$	−12.6158	+	17.3642i	−0.937727	+	1.29067i	0.0190405	+	0.999819i	$0.493939\pi$
$181$	−12.6158	+	17.3642i	−0.937727	+	1.29067i	−0.956768	+	0.290852i	$0.906061\pi$
$182$	1.43018	+	1.32371i	0.106012	+	0.0981197i
$183$	−0.710952	−	4.48877i	−0.0525551	−	0.331820i
$184$	−2.89568	−	13.6231i	−0.213473	−	1.00431i
$185$		0			0
$186$	−0.844440	−	0.179491i	−0.0619174	−	0.0131609i
$187$	−2.18040	−	1.41597i	−0.159447	−	0.103546i
$188$	−7.84855	−	15.4036i	−0.572414	−	1.12343i
$189$	−31.4855	−	5.43048i	−2.29023	−	0.395010i
$190$		0			0
$191$	−0.709623	+	0.150835i	−0.0513465	+	0.0109140i	−0.233513	−	0.972354i	$-0.575022\pi$
$191$	−0.709623	+	0.150835i	−0.0513465	+	0.0109140i	0.182167	+	0.983268i	$0.441689\pi$
$192$	−10.5334	−	4.04340i	−0.760185	−	0.291807i
$193$	−14.2145	+	3.80877i	−1.02318	+	0.274161i	−0.731128	−	0.682240i	$-0.761006\pi$
$193$	−14.2145	+	3.80877i	−1.02318	+	0.274161i	−0.292055	+	0.956401i	$0.594339\pi$
$194$	0.299055	−	2.84532i	0.0214709	−	0.204282i
$195$		0			0
$196$	−7.21702	+	6.14831i	−0.515502	+	0.439165i
$197$	−3.82227	+	24.1329i	−0.272326	+	1.71940i	0.350095	+	0.936714i	$0.386149\pi$
$197$	−3.82227	+	24.1329i	−0.272326	+	1.71940i	−0.622420	+	0.782683i	$0.713851\pi$
$198$	−27.5603	+	1.44438i	−1.95863	+	0.102647i
$199$	−0.487743	+	0.844796i	−0.0345752	+	0.0598860i	−0.882795	−	0.469758i	$-0.844341\pi$
$199$	−0.487743	+	0.844796i	−0.0345752	+	0.0598860i	0.848220	+	0.529644i	$0.177674\pi$
$200$		0			0
$201$	−3.82326	+	2.20736i	−0.269672	+	0.155695i
$202$	−3.61212	+	7.08919i	−0.254148	+	0.498794i
$203$	−9.15640	+	12.2459i	−0.642653	+	0.859494i
$204$	1.29498	+	1.78238i	0.0906665	+	0.124792i
$205$		0			0
$206$	−2.42704	−	5.45122i	−0.169100	−	0.379804i
$207$	9.15896	+	34.1817i	0.636592	+	2.37579i
$208$	0.313403	+	0.387021i	0.0217306	+	0.0268351i
$209$	−1.72562	+	5.31092i	−0.119364	+	0.367364i
$210$		0			0
$211$	−8.83060	−	27.1778i	−0.607923	−	1.87100i	−0.475287	−	0.879831i	$-0.657656\pi$
$211$	−8.83060	−	27.1778i	−0.607923	−	1.87100i	−0.132636	−	0.991165i	$-0.542344\pi$
$212$	4.32460	−	6.65930i	0.297015	−	0.457363i
$213$	−23.8762	−	1.25130i	−1.63597	−	0.0857377i
$214$	0.260574	−	1.22591i	0.0178125	−	0.0838012i
$215$		0			0
$216$	30.9547	+	10.0578i	2.10620	+	0.684347i
$217$	0.681432	−	0.596846i	0.0462586	−	0.0405165i
$218$	−3.39463	−	3.39463i	−0.229913	−	0.229913i
$219$	−3.76390	−	0.395602i	−0.254341	−	0.0267323i
$220$		0			0
$221$	0.0496683	+	0.472562i	0.00334105	+	0.0317880i
$222$	−5.76791	−	15.0259i	−0.387117	−	1.00847i
$223$	19.9284	+	10.1540i	1.33450	+	0.679963i	0.968116	−	0.250501i	$-0.0805952\pi$
$223$	19.9284	+	10.1540i	1.33450	+	0.679963i	0.366385	+	0.930463i	$0.380595\pi$
$224$	13.0434	−	8.21837i	0.871500	−	0.549113i
$225$		0			0
$226$	−1.01436	−	1.75692i	−0.0674742	−	0.116869i
$227$	−3.03877	−	4.67929i	−0.201690	−	0.310575i	0.723324	−	0.690509i	$-0.242613\pi$
$227$	−3.03877	−	4.67929i	−0.201690	−	0.310575i	−0.925014	+	0.379934i	$0.875947\pi$
$228$	2.97805	−	3.67759i	0.197226	−	0.243554i
$229$	−14.5622	−	6.48351i	−0.962298	−	0.428443i	−0.135398	−	0.990791i	$-0.543231\pi$
$229$	−14.5622	−	6.48351i	−0.962298	−	0.428443i	−0.826900	+	0.562349i	$0.809898\pi$
$230$		0			0
$231$	23.1580	−	34.6115i	1.52369	−	2.27727i
$232$	11.0142	−	11.0142i	0.723119	−	0.723119i
$233$	−9.54478	+	7.72921i	−0.625299	+	0.506357i	−0.888796	−	0.458303i	$-0.848458\pi$
$233$	−9.54478	+	7.72921i	−0.625299	+	0.506357i	0.263497	+	0.964660i	$0.415124\pi$
$234$	3.37512	+	3.74845i	0.220639	+	0.245044i
$235$		0			0
$236$	−8.85204	−	7.97041i	−0.576218	−	0.518829i
$237$	−13.5959	+	6.92744i	−0.883146	+	0.449985i
$238$	1.10180	+	0.0151132i	0.0714189	+	0.000979641i
$239$	−14.3549	+	4.66418i	−0.928540	+	0.301701i	−0.733965	−	0.679187i	$-0.762333\pi$
$239$	−14.3549	+	4.66418i	−0.928540	+	0.301701i	−0.194574	+	0.980888i	$0.562333\pi$
$240$		0			0
$241$	−17.2487	+	15.5308i	−1.11108	+	1.00042i	−0.111106	+	0.993809i	$0.535439\pi$
$241$	−17.2487	+	15.5308i	−1.11108	+	1.00042i	−0.999978	+	0.00661623i	$0.997894\pi$
$242$	4.07644	−	10.6195i	0.262043	−	0.682646i
$243$	−17.6057	−	4.71744i	−1.12941	−	0.302624i
$244$	−1.58686	−	1.15292i	−0.101588	−	0.0738083i
$245$		0			0
$246$	−14.4954	+	10.5315i	−0.924191	+	0.671464i
$247$	0.952826	−	0.365756i	0.0606269	−	0.0232725i
$248$	−0.773919	+	0.502589i	−0.0491439	+	0.0319144i
$249$	9.43397	+	5.44671i	0.597854	+	0.345171i
$250$		0			0
$251$		−	22.1623i		−	1.39887i	−0.714697	−	0.699434i	$-0.753435\pi$
$251$		−	22.1623i		−	1.39887i	0.714697	−	0.699434i	$-0.246565\pi$
$252$	−20.0491	+	14.1505i	−1.26298	+	0.891398i
$253$	−25.5993	−	4.05453i	−1.60941	−	0.254906i
$254$	−3.01272	+	6.76669i	−0.189035	+	0.424580i
$255$		0			0
$256$	−13.0028	+	5.78920i	−0.812673	+	0.361825i
$257$	−0.0610358	+	0.227789i	−0.00380731	+	0.0142091i	−0.967803	−	0.251708i	$-0.919008\pi$
$257$	−0.0610358	+	0.227789i	−0.00380731	+	0.0142091i	0.963996	+	0.265917i	$0.0856746\pi$
$258$	10.6423	−	1.68558i	0.662562	−	0.104939i
$259$	16.2513	+	4.59432i	1.00981	+	0.285477i
$260$		0			0
$261$	−26.4824	+	29.4117i	−1.63922	+	1.82054i
$262$	0.236188	−	4.50673i	0.0145917	−	0.278427i
$263$	1.19862	−	22.8710i	0.0739099	−	1.41029i	−0.670176	−	0.742202i	$-0.733782\pi$
$263$	1.19862	−	22.8710i	0.0739099	−	1.41029i	0.744086	−	0.668083i	$-0.232885\pi$
$264$	−28.3865	+	31.5264i	−1.74707	+	1.94032i
$265$		0			0
$266$	−0.581157	−	2.29433i	−0.0356330	−	0.140674i
$267$	9.74001	−	1.54267i	0.596079	−	0.0944096i
$268$	−0.493144	+	1.84044i	−0.0301236	+	0.112423i
$269$	−9.75209	+	4.34191i	−0.594596	+	0.264731i	−0.681894	−	0.731451i	$-0.738843\pi$
$269$	−9.75209	+	4.34191i	−0.594596	+	0.264731i	0.0872981	+	0.996182i	$0.472177\pi$
$270$		0			0
$271$	−7.51186	+	16.8719i	−0.456313	+	1.02490i	0.528125	+	0.849166i	$0.322895\pi$
$271$	−7.51186	+	16.8719i	−0.456313	+	1.02490i	−0.984438	+	0.175730i	$0.943772\pi$
$272$	0.278124	+	0.0440505i	0.0168637	+	0.00267095i
$273$	−7.57973	+	0.691695i	−0.458746	+	0.0418633i
$274$		−	3.47355i		−	0.209845i
$275$		0			0
$276$	19.0211	+	10.9819i	1.14494	+	0.661030i
$277$	8.75448	−	5.68523i	0.526006	−	0.341592i	−0.254163	−	0.967161i	$-0.581800\pi$
$277$	8.75448	−	5.68523i	0.526006	−	0.341592i	0.780169	+	0.625569i	$0.215133\pi$
$278$	−4.83399	+	1.85560i	−0.289924	+	0.111291i
$279$	1.89688	−	1.37816i	0.113563	−	0.0825084i
$280$		0			0
$281$	23.9465	+	17.3981i	1.42853	+	1.03789i	0.990288	+	0.139028i	$0.0443978\pi$
$281$	23.9465	+	17.3981i	1.42853	+	1.03789i	0.438239	+	0.898858i	$0.355602\pi$
$282$	−31.0878	−	8.32996i	−1.85125	−	0.496042i
$283$	−9.98669	+	26.0162i	−0.593647	+	1.54650i	0.226296	+	0.974059i	$0.427338\pi$
$283$	−9.98669	+	26.0162i	−0.593647	+	1.54650i	−0.819943	+	0.572445i	$0.805995\pi$
$284$	−7.66847	+	6.90472i	−0.455040	+	0.409720i
$285$		0			0
$286$	−3.51353	+	1.14161i	−0.207759	+	0.0675051i
$287$	0.257857	−	18.7986i	0.0152208	−	1.10965i
$288$	35.5544	−	18.1159i	2.09506	−	1.06749i
$289$	−12.4338	−	11.1954i	−0.731400	−	0.658555i
$290$		0			0
$291$	7.47699	+	8.30404i	0.438309	+	0.486791i
$292$	−1.26940	+	1.02794i	−0.0742863	+	0.0601559i
$293$	−4.85076	+	4.85076i	−0.283385	+	0.283385i	−0.834457	−	0.551073i	$-0.814219\pi$
$293$	−4.85076	+	4.85076i	−0.283385	+	0.283385i	0.551073	+	0.834457i	$0.314219\pi$
$294$	−0.484122	+	17.6437i	−0.0282346	+	1.02900i
$295$		0			0
$296$	−15.7166	−	6.99749i	−0.913510	−	0.406721i
$297$	38.1178	−	47.0716i	2.21182	−	2.73137i
$298$	0.972990	+	1.49827i	0.0563638	+	0.0867926i
$299$	2.36852	+	4.10240i	0.136975	+	0.237248i
$300$		0			0
$301$	−5.27052	+	10.0024i	−0.303788	+	0.576529i
$302$	−8.86706	−	4.51799i	−0.510242	−	0.259981i
$303$	−11.1364	−	29.0113i	−0.639768	−	1.66665i
$304$	−0.0632223	−	0.601520i	−0.00362605	−	0.0344996i
$305$		0			0
$306$	2.83648	+	0.298126i	0.162151	+	0.0170427i
$307$	−4.10345	−	4.10345i	−0.234196	−	0.234196i	0.580245	−	0.814442i	$-0.302957\pi$
$307$	−4.10345	−	4.10345i	−0.234196	−	0.234196i	−0.814442	+	0.580245i	$0.802957\pi$
$308$	−3.49540	−	17.6302i	−0.199169	−	1.00457i
$309$	22.1650	+	7.20186i	1.26093	+	0.409700i
$310$		0			0
$311$	5.14856	−	24.2220i	0.291948	−	1.37351i	−0.550548	−	0.834804i	$-0.685581\pi$
$311$	5.14856	−	24.2220i	0.291948	−	1.37351i	0.842496	−	0.538703i	$-0.181085\pi$
$312$	7.74291	+	0.405789i	0.438356	+	0.0229733i
$313$	3.89322	−	5.99503i	0.220058	−	0.338859i	−0.711349	−	0.702839i	$-0.751916\pi$
$313$	3.89322	−	5.99503i	0.220058	−	0.338859i	0.931407	+	0.363980i	$0.118582\pi$
$314$	4.17795	+	12.8584i	0.235776	+	0.725642i
$315$		0			0
$316$	−2.03508	+	6.26334i	−0.114482	+	0.352340i
$317$	4.32805	+	5.34470i	0.243088	+	0.300188i	0.884058	−	0.467378i	$-0.154801\pi$
$317$	4.32805	+	5.34470i	0.243088	+	0.300188i	−0.640970	+	0.767566i	$0.721468\pi$
$318$	−3.82593	−	14.2786i	−0.214548	−	0.800703i
$319$	−11.7901	−	26.4810i	−0.660120	−	1.48265i
$320$		0			0
$321$	2.87720	+	3.96013i	0.160590	+	0.221033i
$322$	10.0957	−	4.32999i	0.562614	−	0.241301i
$323$	0.261996	−	0.514197i	0.0145779	−	0.0286107i
$324$	−20.3537	+	11.7512i	−1.13076	+	0.652844i
$325$		0			0
$326$	7.31107	−	12.6631i	0.404923	−	0.701347i
$327$	18.7245	−	0.981311i	1.03547	−	0.0542666i
$328$	−2.99601	+	18.9161i	−0.165427	+	1.04447i
$329$	26.5338	−	20.8907i	1.46286	−	1.15174i
$330$		0			0
$331$	−1.92457	+	18.3111i	−0.105784	+	1.00647i	0.804913	+	0.593392i	$0.202212\pi$
$331$	−1.92457	+	18.3111i	−0.105784	+	1.00647i	−0.910697	+	0.413074i	$0.864455\pi$
$332$	4.54131	−	1.21684i	0.249237	−	0.0667828i
$333$	40.8092	+	15.6652i	2.23633	+	0.858447i
$334$	0.265851	−	0.0565083i	0.0145467	−	0.00309200i
$335$		0			0
$336$	−0.766641	+	4.44491i	−0.0418237	+	0.242490i
$337$	5.72591	+	11.2377i	0.311910	+	0.612158i	0.992740	−	0.120284i	$-0.0383805\pi$
$337$	5.72591	+	11.2377i	0.311910	+	0.612158i	−0.680829	+	0.732442i	$0.738380\pi$
$338$	−8.19390	−	5.32118i	−0.445689	−	0.289434i
$339$	7.75043	+	1.64740i	0.420945	+	0.0894747i
$340$		0			0
$341$	0.357042	+	1.67975i	0.0193349	+	0.0909635i
$342$	−0.958330	−	6.05066i	−0.0518206	−	0.327182i
$343$	−14.5227	−	11.4931i	−0.784153	−	0.620568i
$344$	6.76978	−	9.31780i	0.365002	−	0.502382i
$345$		0			0
$346$	14.2241	−	1.49501i	0.764693	−	0.0803725i
$347$	−7.99918	−	6.47761i	−0.429418	−	0.347736i	0.390117	−	0.920766i	$-0.372435\pi$
$347$	−7.99918	−	6.47761i	−0.429418	−	0.347736i	−0.819535	+	0.573029i	$0.805768\pi$
$348$	1.28559	+	24.5305i	0.0689149	+	1.31497i
$349$	−11.2771			−0.603650			−0.301825	−	0.953363i	$-0.597596\pi$
$349$	−11.2771			−0.603650			−0.301825	+	0.953363i	$0.597596\pi$
$350$		0			0
$351$	−11.0702			−0.590883
$352$	1.52957	+	29.1860i	0.0815266	+	1.55562i
$353$	12.9303	+	10.4707i	0.688208	+	0.557300i	0.908372	−	0.418163i	$-0.137326\pi$
$353$	12.9303	+	10.4707i	0.688208	+	0.557300i	−0.220164	+	0.975463i	$0.570659\pi$
$354$	−22.0540	+	2.31797i	−1.17216	+	0.123199i
$355$		0			0
$356$	2.50168	−	3.44327i	0.132589	−	0.182493i
$357$	−2.92333	+	3.15847i	−0.154719	+	0.167164i
$358$	−1.23930	−	7.82462i	−0.0654990	−	0.413544i
$359$	3.60963	+	16.9820i	0.190509	+	0.896275i	0.964706	+	0.263330i	$0.0848208\pi$
$359$	3.60963	+	16.9820i	0.190509	+	0.896275i	−0.774197	+	0.632945i	$0.781846\pi$
$360$		0			0
$361$	17.3723	+	3.69260i	0.914333	+	0.194348i
$362$	14.4633	+	9.39256i	0.760173	+	0.493662i
$363$	20.1696	+	39.5851i	1.05863	+	2.07768i
$364$	−2.10211	+	2.52429i	−0.110180	+	0.132309i
$365$		0			0
$366$	−3.57182	+	0.759215i	−0.186702	+	0.0396848i
$367$	6.96747	+	2.67456i	0.363699	+	0.139611i	0.533353	−	0.845893i	$-0.320932\pi$
$367$	6.96747	+	2.67456i	0.363699	+	0.139611i	−0.169654	+	0.985504i	$0.554265\pi$
$368$	2.71160	−	0.726570i	0.141352	−	0.0378751i
$369$	5.08655	−	48.3953i	0.264795	−	2.51936i
$370$		0			0
$371$	14.4030	+	5.75668i	0.747768	+	0.298872i
$372$	0.227651	−	1.43733i	0.0118032	−	0.0745222i
$373$	−29.4741	+	1.54467i	−1.52611	+	0.0799802i	−0.796818	−	0.604219i	$-0.793485\pi$
$373$	−29.4741	+	1.54467i	−1.52611	+	0.0799802i	−0.729295	+	0.684199i	$0.760152\pi$
$374$	−1.04446	+	1.80906i	−0.0540080	+	0.0935445i
$375$		0			0
$376$	−29.7932	+	17.2011i	−1.53647	+	0.887079i
$377$	−2.40520	+	4.72046i	−0.123874	+	0.243116i
$378$	−3.03333	+	25.4918i	−0.156018	+	1.31116i
$379$	0.558890	+	0.769246i	0.0287082	+	0.0395135i	0.823130	−	0.567853i	$-0.192226\pi$
$379$	0.558890	+	0.769246i	0.0287082	+	0.0395135i	−0.794422	+	0.607367i	$0.792226\pi$
$380$		0			0
$381$	−11.7668	−	26.4287i	−0.602831	−	1.35398i
$382$	0.150868	+	0.563048i	0.00771909	+	0.0288080i
$383$	6.38001	+	7.87866i	0.326003	+	0.402581i	0.913627	−	0.406554i	$-0.133270\pi$
$383$	6.38001	+	7.87866i	0.326003	+	0.402581i	−0.587623	+	0.809135i	$0.699936\pi$
$384$	8.49991	−	26.1600i	0.433759	−	1.33497i
$385$		0			0
$386$	3.65383	+	11.2453i	0.185975	+	0.572373i
$387$	−15.9383	+	24.5428i	−0.810190	+	1.24758i
$388$	4.81608	+	0.252400i	0.244500	+	0.0128137i
$389$	−2.79772	+	13.1622i	−0.141850	+	0.667352i	0.848549	+	0.529116i	$0.177476\pi$
$389$	−2.79772	+	13.1622i	−0.141850	+	0.667352i	−0.990399	+	0.138235i	$0.955857\pi$
$390$		0			0
$391$	2.54742	+	0.827706i	0.128828	+	0.0418589i
$392$	12.9697	+	13.7016i	0.655070	+	0.692033i
$393$	12.4635	+	12.4635i	0.628702	+	0.628702i
$394$	19.5246	+	2.05212i	0.983634	+	0.103384i
$395$		0			0
$396$	−4.86281	−	46.2665i	−0.244365	−	2.32498i
$397$	9.66717	+	25.1838i	0.485181	+	1.26394i	0.929749	+	0.368195i	$0.120024\pi$
$397$	9.66717	+	25.1838i	0.485181	+	1.26394i	−0.444567	+	0.895745i	$0.646643\pi$
$398$	0.698361	+	0.355833i	0.0350057	+	0.0178363i
$399$	8.17811	+	4.30925i	0.409418	+	0.215732i
$400$		0			0
$401$	−7.65133	−	13.2525i	−0.382089	−	0.661798i	0.609271	−	0.792962i	$-0.291462\pi$
$401$	−7.65133	−	13.2525i	−0.382089	−	0.661798i	−0.991361	+	0.131164i	$0.958129\pi$
$402$	1.93193	+	2.97490i	0.0963557	+	0.148375i
$403$	0.197520	−	0.243917i	0.00983916	−	0.0121504i
$404$	−12.2523	−	5.45509i	−0.609577	−	0.271401i
$405$		0			0
$406$	10.2110	+	6.83199i	0.506761	+	0.339066i
$407$	−22.6386	+	22.6386i	−1.12215	+	1.12215i
$408$	3.40713	−	2.75904i	0.168678	−	0.136593i
$409$	8.68351	+	9.64401i	0.429372	+	0.476866i	0.918542	−	0.395322i	$-0.129367\pi$
$409$	8.68351	+	9.64401i	0.429372	+	0.476866i	−0.489171	+	0.872188i	$0.662700\pi$
$410$		0			0
$411$	10.0820	+	9.07786i	0.497308	+	0.447778i
$412$	8.96225	−	4.56649i	0.441538	−	0.224975i
$413$	11.9095	−	19.9896i	0.586030	−	0.983625i
$414$	27.0417	−	8.78639i	1.32903	−	0.431827i
$415$		0			0
$416$	3.96956	−	3.57421i	0.194624	−	0.175240i
$417$	7.24740	−	18.8801i	0.354907	−	0.924564i
$418$	4.33396	+	1.16128i	0.211981	+	0.0568001i
$419$	14.8800	+	10.8109i	0.726935	+	0.528149i	0.888592	−	0.458698i	$-0.151684\pi$
$419$	14.8800	+	10.8109i	0.726935	+	0.528149i	−0.161658	+	0.986847i	$0.551684\pi$
$420$		0			0
$421$	19.9632	−	14.5041i	0.972947	−	0.706887i	0.0168253	−	0.999858i	$-0.494644\pi$
$421$	19.9632	−	14.5041i	0.972947	−	0.706887i	0.956121	+	0.292971i	$0.0946441\pi$
$422$	−21.4357	+	8.22839i	−1.04347	+	0.400552i
$423$	73.3087	−	47.6072i	3.56439	−	2.31474i
$424$	−13.6839	−	7.90043i	−0.664551	−	0.383679i
$425$		0			0
$426$			19.2105i			0.930754i
$427$	1.60631	−	3.47864i	0.0777350	−	0.168343i
$428$	2.08663	+	0.330490i	0.100861	+	0.0159748i
$429$	5.86880	−	13.1815i	0.283348	−	0.636411i
$430$		0			0
$431$	−27.9846	+	12.4596i	−1.34797	+	0.600156i	−0.948555	−	0.316614i	$-0.897454\pi$
$431$	−27.9846	+	12.4596i	−1.34797	+	0.600156i	−0.399417	+	0.916769i	$0.630787\pi$
$432$	−1.69795	+	6.33685i	−0.0816928	+	0.304882i
$433$	25.6195	−	4.05772i	1.23119	−	0.195002i	0.493263	−	0.869880i	$-0.335804\pi$
$433$	25.6195	−	4.05772i	1.23119	−	0.195002i	0.737929	+	0.674878i	$0.235804\pi$
$434$	−0.507554	−	0.521672i	−0.0243634	−	0.0250411i
$435$		0			0
$436$	5.41491	−	6.01387i	0.259327	−	0.288012i
$437$	0.301100	−	5.74534i	0.0144036	−	0.274837i
$438$	−0.159148	+	3.03673i	−0.00760440	+	0.145101i
$439$	8.91058	−	9.89620i	0.425279	−	0.472320i	−0.491983	−	0.870605i	$-0.663728\pi$
$439$	8.91058	−	9.89620i	0.425279	−	0.472320i	0.917262	+	0.398285i	$0.130394\pi$
$440$		0			0
$441$	−34.7309	−	33.0411i	−1.65385	−	1.57339i
$442$	0.377088	−	0.0597248i	0.0179362	−	0.00284082i
$443$	3.88763	−	14.5088i	0.184707	−	0.689335i	−0.809986	−	0.586449i	$-0.800526\pi$
$443$	3.88763	−	14.5088i	0.184707	−	0.689335i	0.994693	−	0.102886i	$-0.0328077\pi$
$444$	24.7852	−	11.0351i	1.17625	−	0.523702i
$445$		0			0
$446$	7.30940	−	16.4172i	0.346110	−	0.777376i
$447$	−6.89157	−	1.09152i	−0.325960	−	0.0516270i
$448$	−5.48517	−	7.77166i	−0.259150	−	0.367176i
$449$		−	3.87012i		−	0.182642i	−0.995822	−	0.0913211i	$-0.970891\pi$
$449$		−	3.87012i		−	0.182642i	0.995822	−	0.0913211i	$-0.0291090\pi$
$450$		0			0
$451$	30.8658	+	17.8204i	1.45341	+	0.839129i
$452$	2.86805	−	1.86253i	0.134902	−	0.0876062i
$453$	36.2869	−	13.9292i	1.70491	−	0.654452i
$454$	−3.62680	+	2.63503i	−0.170214	+	0.123668i
$455$		0			0
$456$	−7.61836	−	5.53507i	−0.356763	−	0.259203i
$457$	40.9235	+	10.9654i	1.91432	+	0.512941i	0.991949	+	0.126636i	$0.0404181\pi$
$457$	40.9235	+	10.9654i	1.91432	+	0.512941i	0.922371	+	0.386304i	$0.126249\pi$
$458$	−4.58991	+	11.9571i	−0.214472	+	0.558720i
$459$	−4.65174	+	4.18845i	−0.217125	+	0.195500i
$460$		0			0
$461$	−21.8890	+	7.11217i	−1.01947	+	0.331247i	−0.770620	−	0.637295i	$-0.780053\pi$
$461$	−21.8890	+	7.11217i	−1.01947	+	0.331247i	−0.248852	+	0.968541i	$0.580053\pi$
$462$	−28.7455	−	17.1262i	−1.33736	−	0.796782i
$463$	16.0881	−	8.19728i	0.747676	−	0.380960i	−0.0382600	−	0.999268i	$-0.512182\pi$
$463$	16.0881	−	8.19728i	0.747676	−	0.380960i	0.785936	+	0.618308i	$0.212182\pi$
$464$	2.33320	+	2.10082i	0.108316	+	0.0975281i
$465$		0			0
$466$	6.60317	+	7.33356i	0.305886	+	0.339721i
$467$	21.3103	−	17.2567i	0.986121	−	0.798545i	0.00661861	−	0.999978i	$-0.497893\pi$
$467$	21.3103	−	17.2567i	0.986121	−	0.798545i	0.979502	+	0.201433i	$0.0645599\pi$
$468$	−6.01224	+	6.01224i	−0.277916	+	0.277916i
$469$	−3.71387	−	0.245755i	−0.171491	−	0.0113479i
$470$		0			0
$471$	−48.2403	−	21.4780i	−2.22280	−	0.989653i
$472$	−14.9171	+	18.4211i	−0.686616	+	0.847900i
$473$	−11.6735	−	17.9756i	−0.536747	−	0.826518i
$474$	6.13019	+	10.6178i	0.281569	+	0.487691i
$475$		0			0
$476$	0.0717609	+	1.85606i	0.00328916	+	0.0850721i
$477$	35.7717	+	18.2266i	1.63787	+	0.834538i
$478$	4.34610	+	11.3220i	0.198786	+	0.517856i
$479$	3.81683	+	36.3147i	0.174396	+	1.65926i	0.635637	+	0.771988i	$0.280737\pi$
$479$	3.81683	+	36.3147i	0.174396	+	1.65926i	−0.461242	+	0.887275i	$0.652596\pi$
$480$		0			0
$481$	5.81940	+	0.611643i	0.265342	+	0.0278885i
$482$	13.1870	+	13.1870i	0.600650	+	0.600650i
$483$	−13.8167	+	40.6190i	−0.628680	+	1.84823i
$484$	18.2360	+	5.92525i	0.828911	+	0.269330i
$485$		0			0
$486$	−3.04486	+	14.3249i	−0.138118	+	0.649792i
$487$	−36.0175	−	1.88760i	−1.63211	−	0.0855352i	−0.785888	−	0.618368i	$-0.787794\pi$
$487$	−36.0175	−	1.88760i	−1.63211	−	0.0855352i	−0.846220	+	0.532833i	$0.821127\pi$
$488$	−2.12586	+	3.27353i	−0.0962330	+	0.148186i
$489$	17.6479	+	54.3145i	0.798064	+	2.45619i
$490$		0			0
$491$	2.89375	−	8.90606i	0.130593	−	0.401925i	−0.864285	−	0.503002i	$-0.832229\pi$
$491$	2.89375	−	8.90606i	0.130593	−	0.401925i	0.994879	+	0.101077i	$0.0322289\pi$
$492$	−19.0071	−	23.4718i	−0.856907	−	1.05819i
$493$	0.775330	+	2.89357i	0.0349191	+	0.130320i
$494$	−0.333544	−	0.749152i	−0.0150069	−	0.0337060i
$495$		0			0
$496$	−0.109328	−	0.150477i	−0.00490897	−	0.00675662i
$497$	−16.1436	−	12.0708i	−0.724140	−	0.541447i
$498$	3.97364	−	7.79871i	0.178063	−	0.349468i
$499$	27.8046	−	16.0530i	1.24470	−	0.718630i	0.274656	−	0.961543i	$-0.411436\pi$
$499$	27.8046	−	16.0530i	1.24470	−	0.718630i	0.970048	+	0.242912i	$0.0781027\pi$
$500$		0			0
$501$	−0.530765	+	0.919313i	−0.0237128	+	0.0410719i
$502$	−17.7826	+	0.931948i	−0.793678	+	0.0415949i
$503$	5.06296	−	31.9663i	0.225746	−	1.42531i	−0.570979	−	0.820965i	$-0.693436\pi$
$503$	5.06296	−	31.9663i	0.225746	−	1.42531i	0.796725	−	0.604342i	$-0.206564\pi$
$504$	30.2083	+	38.3685i	1.34559	+	1.70907i
$505$		0			0
$506$	−2.17681	+	20.7110i	−0.0967710	+	0.920715i
$507$	36.8589	−	9.87630i	1.63696	−	0.438622i
$508$	−11.6566	−	4.47454i	−0.517177	−	0.198525i
$509$	−25.8085	+	5.48576i	−1.14394	+	0.243152i	−0.740631	−	0.671912i	$-0.765473\pi$
$509$	−25.8085	+	5.48576i	−1.14394	+	0.243152i	−0.403309	+	0.915064i	$0.632140\pi$
$510$		0			0
$511$	−2.45192	−	2.04184i	−0.108467	−	0.0903257i
$512$	−2.76657	−	5.42969i	−0.122266	−	0.239961i
$513$	11.2759	+	7.32265i	0.497843	+	0.323303i
$514$	0.185341	+	0.0393954i	0.00817502	+	0.00173765i
$515$		0			0
$516$	3.77631	+	17.7662i	0.166243	+	0.782111i
$517$	10.0151	+	63.2328i	0.440463	+	2.78097i
$518$	3.00302	−	13.2330i	0.131945	−	0.581423i
$519$	−32.8344	+	45.1926i	−1.44127	+	1.98374i
$520$		0			0
$521$	8.94847	−	0.940522i	0.392039	−	0.0412050i	0.0935417	−	0.995615i	$-0.470181\pi$
$521$	8.94847	−	0.940522i	0.392039	−	0.0412050i	0.298498	+	0.954410i	$0.403514\pi$
$522$	24.7131	+	20.0123i	1.08166	+	0.875913i
$523$	0.356503	+	6.80248i	0.0155888	+	0.297452i	0.995287	+	0.0969736i	$0.0309162\pi$
$523$	0.356503	+	6.80248i	0.0155888	+	0.297452i	−0.979698	+	0.200478i	$0.935750\pi$
$524$	7.60728			0.332326
$525$		0			0
$526$	−18.4017			−0.802353
$527$	−0.00928807	−	0.177227i	−0.000404595	−	0.00772013i
$528$	−6.64527	−	5.38123i	−0.289198	−	0.234188i
$529$	3.68248	−	0.387044i	0.160108	−	0.0168280i
$530$		0			0
$531$	35.4005	−	48.7246i	1.53625	−	2.11447i
$532$	3.81092	−	1.18071i	0.165224	−	0.0511901i
$533$	−1.01901	−	6.43377i	−0.0441382	−	0.278678i
$534$	−1.64739	−	7.75036i	−0.0712895	−	0.335391i
$535$		0			0
$536$	3.70873	+	0.788315i	0.160193	+	0.0340500i
$537$	25.9498	+	16.8520i	1.11982	+	0.727217i
$538$	3.89397	+	7.64234i	0.167881	+	0.329485i
$539$	32.4540	−	13.3953i	1.39789	−	0.576977i
$540$		0			0
$541$	−3.42812	+	0.728670i	−0.147387	+	0.0313280i	−0.281014	−	0.959704i	$-0.590671\pi$
$541$	−3.42812	+	0.728670i	−0.147387	+	0.0313280i	0.133628	+	0.991032i	$0.457337\pi$
$542$	13.8536	+	5.31791i	0.595065	+	0.228424i
$543$	−65.0606	+	17.4329i	−2.79202	+	0.748118i
$544$	0.315711	−	3.00379i	0.0135360	−	0.128787i
$545$		0			0
$546$	0.873742	+	6.05277i	0.0373927	+	0.259035i
$547$	4.73400	−	29.8893i	0.202411	−	1.27798i	−0.651936	−	0.758274i	$-0.726043\pi$
$547$	4.73400	−	29.8893i	0.202411	−	1.27798i	0.854348	−	0.519702i	$-0.173957\pi$
$548$	5.84724	−	0.306441i	0.249782	−	0.0130905i
$549$	4.95876	−	8.58882i	0.211635	−	0.366562i
$550$		0			0
$551$	5.57235	−	3.21720i	0.237390	−	0.137057i
$552$	19.8425	−	38.9431i	0.844552	−	1.65753i
$553$	−12.7745	−	1.52007i	−0.543228	−	0.0646402i
$554$	−4.92987	−	6.78539i	−0.209450	−	0.288283i
$555$		0			0
$556$	−3.55010	−	7.97365i	−0.150558	−	0.338158i
$557$	−3.91007	−	14.5926i	−0.165675	−	0.618307i	−0.997953	−	0.0639490i	$-0.979630\pi$
$557$	−3.91007	−	14.5926i	−0.165675	−	0.618307i	0.832278	−	0.554358i	$-0.187036\pi$
$558$	−1.18558	−	1.46407i	−0.0501897	−	0.0619791i
$559$	−1.21052	+	3.72561i	−0.0511997	+	0.157576i
$560$		0			0
$561$	−2.52119	−	7.75941i	−0.106445	−	0.327603i
$562$	12.9530	−	19.9459i	0.546390	−	0.841367i
$563$	−35.0459	−	1.83668i	−1.47701	−	0.0774067i	−0.703275	−	0.710918i	$-0.748280\pi$
$563$	−35.0459	−	1.83668i	−1.47701	−	0.0774067i	−0.773734	+	0.633511i	$0.781613\pi$
$564$	11.2797	−	53.0669i	0.474962	−	2.23452i
$565$		0			0
$566$	21.2950	+	6.91915i	0.895094	+	0.290834i
$567$	−30.2492	−	34.5362i	−1.27035	−	1.45038i
$568$	14.5199	+	14.5199i	0.609242	+	0.609242i
$569$	2.55943	+	0.269006i	0.107297	+	0.0112773i	0.158025	−	0.987435i	$-0.449487\pi$
$569$	2.55943	+	0.269006i	0.107297	+	0.0112773i	−0.0507279	+	0.998713i	$0.516154\pi$
$570$		0			0
$571$	2.11736	+	20.1454i	0.0886089	+	0.843058i	0.945075	+	0.326854i	$0.105989\pi$
$571$	2.11736	+	20.1454i	0.0886089	+	0.843058i	−0.856466	+	0.516204i	$0.827345\pi$
$572$	−2.23172	−	5.81382i	−0.0933127	−	0.243088i
$573$	−2.02853	−	1.03359i	−0.0847430	−	0.0431787i
$574$	−15.0945	+	0.583602i	−0.630033	+	0.0243591i
$575$		0			0
$576$	−12.3107	−	21.3228i	−0.512946	−	0.888449i
$577$	−21.8264	−	33.6097i	−0.908645	−	1.39919i	−0.916853	−	0.399225i	$-0.869279\pi$
$577$	−21.8264	−	33.6097i	−0.908645	−	1.39919i	0.00820794	−	0.999966i	$-0.497387\pi$
$578$	−8.46019	+	10.4475i	−0.351897	+	0.434557i
$579$	−42.1886	−	18.7836i	−1.75330	−	0.780619i
$580$		0			0
$581$	4.05686	+	8.23950i	0.168307	+	0.341832i
$582$	6.34861	−	6.34861i	0.263158	−	0.263158i
$583$	−22.8517	+	18.5050i	−0.946422	+	0.766397i
$584$	2.17496	+	2.41554i	0.0900006	+	0.0999558i
$585$		0			0
$586$	4.09615	+	3.68819i	0.169211	+	0.152358i
$587$	−17.2988	+	8.81418i	−0.713998	+	0.363800i	−0.772955	−	0.634460i	$-0.781222\pi$
$587$	−17.2988	+	8.81418i	−0.713998	+	0.363800i	0.0589574	+	0.998261i	$0.481222\pi$
$588$	−29.7434	+	0.741595i	−1.22660	+	0.0305829i
$589$	−0.362534	+	0.117795i	−0.0149380	+	0.00485364i
$590$		0			0
$591$	−56.9823	+	51.3071i	−2.34394	+	2.11049i
$592$	1.24270	−	3.23735i	0.0510747	−	0.133054i
$593$	17.2078	+	4.61082i	0.706640	+	0.189344i	0.594203	−	0.804315i	$-0.297468\pi$
$593$	17.2078	+	4.61082i	0.706640	+	0.189344i	0.112437	+	0.993659i	$0.464134\pi$
$594$	−39.3724	−	28.6057i	−1.61547	−	1.17371i
$595$		0			0
$596$	−2.43630	+	1.77007i	−0.0997945	+	0.0725050i
$597$	−2.85792	+	1.09705i	−0.116967	+	0.0448994i
$598$	3.19210	−	2.07297i	0.130535	−	0.0847702i
$599$	−12.9831	−	7.49578i	−0.530474	−	0.306269i	0.210735	−	0.977543i	$-0.432414\pi$
$599$	−12.9831	−	7.49578i	−0.530474	−	0.306269i	−0.741209	+	0.671274i	$0.765747\pi$
$600$		0			0
$601$			20.7383i			0.845932i	0.906145	+	0.422966i	$0.139011\pi$
$601$			20.7383i			0.845932i	−0.906145	+	0.422966i	$0.860989\pi$
$602$	8.24741	+	3.80837i	0.336139	+	0.155217i
$603$	−9.51522	−	1.50706i	−0.387490	−	0.0613723i
$604$	6.82315	−	15.3250i	0.277630	−	0.623567i
$605$		0			0
$606$	−22.8099	+	10.1556i	−0.926588	+	0.412544i
$607$	−5.62452	+	20.9910i	−0.228292	+	0.851999i	0.752766	+	0.658288i	$0.228719\pi$
$607$	−5.62452	+	20.9910i	−0.228292	+	0.851999i	−0.981059	+	0.193711i	$0.937948\pi$
$608$	−6.40757	+	1.01486i	−0.259861	+	0.0411580i
$609$	−46.5154	+	11.7824i	−1.88490	+	0.477448i
$610$		0			0
$611$	7.82946	−	8.69550i	0.316746	−	0.351782i
$612$	−0.251616	+	4.80112i	−0.0101710	+	0.194074i
$613$	−0.370639	+	7.07221i	−0.0149700	+	0.285644i	0.980879	+	0.194620i	$0.0623473\pi$
$613$	−0.370639	+	7.07221i	−0.0149700	+	0.285644i	−0.995849	+	0.0910239i	$0.970986\pi$
$614$	−3.11999	+	3.46510i	−0.125913	+	0.139840i
$615$		0			0
$616$	−34.6713	+	8.78228i	−1.39694	+	0.353848i
$617$	−12.2737	+	1.94396i	−0.494119	+	0.0782608i	−0.398521	−	0.917159i	$-0.630476\pi$
$617$	−12.2737	+	1.94396i	−0.494119	+	0.0782608i	−0.0955982	+	0.995420i	$0.530476\pi$
$618$	4.84659	−	18.0877i	0.194959	−	0.727595i
$619$	−25.0310	+	11.1445i	−1.00608	+	0.447937i	−0.842560	−	0.538603i	$-0.818952\pi$
$619$	−25.0310	+	11.1445i	−1.00608	+	0.447937i	−0.163522	+	0.986540i	$0.552286\pi$
$620$		0			0
$621$	−25.3815	+	57.0079i	−1.01853	+	2.28765i
$622$	−19.6519	−	3.11255i	−0.787969	−	0.124802i
$623$	7.54815	+	3.48548i	0.302410	+	0.139643i
$624$			1.56282i			0.0625628i
$625$		0			0
$626$	−4.97403	−	2.87176i	−0.198802	−	0.114778i
$627$	−14.6971	+	9.54440i	−0.586945	+	0.381167i
$628$	−21.2768	+	8.16739i	−0.849036	+	0.325914i
$629$	2.67675	−	1.94477i	0.106729	−	0.0775432i
$630$		0			0
$631$	29.5709	+	21.4845i	1.17720	+	0.855286i	0.991853	−	0.127387i	$-0.0406590\pi$
$631$	29.5709	+	21.4845i	1.17720	+	0.855286i	0.185347	+	0.982673i	$0.440659\pi$
$632$	12.6586	+	3.39187i	0.503534	+	0.134921i
$633$	32.1376	−	83.7214i	1.27736	−	3.32762i
$634$	4.10650	−	3.69751i	0.163090	−	0.146847i
$635$		0			0
$636$	23.6985	−	7.70010i	0.939705	−	0.305329i
$637$	−5.63547	−	3.06895i	−0.223285	−	0.121596i
$638$	−20.7522	+	10.5738i	−0.821587	+	0.418619i
$639$	−38.7731	−	34.9114i	−1.53384	−	1.38107i
$640$		0			0
$641$	29.7244	+	33.0123i	1.17404	+	1.30391i	0.943703	+	0.330795i	$0.107317\pi$
$641$	29.7244	+	33.0123i	1.17404	+	1.30391i	0.230339	+	0.973110i	$0.426016\pi$
$642$	3.05655	−	2.47515i	0.120633	−	0.0976863i
$643$	9.86123	−	9.86123i	0.388889	−	0.388889i	−0.485402	−	0.874291i	$-0.661327\pi$
$643$	9.86123	−	9.86123i	0.388889	−	0.388889i	0.874291	+	0.485402i	$0.161327\pi$
$644$	8.17960	+	16.6128i	0.322321	+	0.654636i
$645$		0			0
$646$	−0.423601	−	0.188599i	−0.0166663	−	0.00742033i
$647$	−30.5289	+	37.7000i	−1.20021	+	1.48214i	−0.366074	+	0.930586i	$0.619298\pi$
$647$	−30.5289	+	37.7000i	−1.20021	+	1.48214i	−0.834139	+	0.551554i	$0.814035\pi$
$648$	25.4721	+	39.2236i	1.00064	+	1.54085i
$649$	22.0556	+	38.2014i	0.865759	+	1.49954i
$650$		0			0
$651$	2.84061	−	0.109827i	0.111332	−	0.00430445i
$652$	21.9616	+	11.1900i	0.860084	+	0.438235i
$653$	16.2632	+	42.3671i	0.636428	+	1.65795i	0.747599	+	0.664151i	$0.231207\pi$
$653$	16.2632	+	42.3671i	0.636428	+	1.65795i	−0.111171	+	0.993801i	$0.535460\pi$
$654$	−1.57478	−	14.9830i	−0.0615786	−	0.585882i
$655$		0			0
$656$	−3.83914	−	0.403510i	−0.149893	−	0.0157544i
$657$	−5.83988	−	5.83988i	−0.227835	−	0.227835i
$658$	−17.8781	−	20.4119i	−0.696962	−	0.795737i
$659$	−22.0985	−	7.18025i	−0.860837	−	0.279703i	−0.154859	−	0.987937i	$-0.549492\pi$
$659$	−22.0985	−	7.18025i	−0.860837	−	0.279703i	−0.705978	+	0.708234i	$0.749492\pi$
$660$		0			0
$661$	−2.48937	+	11.7116i	−0.0968254	+	0.455528i	0.902848	+	0.429960i	$0.141472\pi$
$661$	−2.48937	+	11.7116i	−0.0968254	+	0.455528i	−0.999673	+	0.0255671i	$0.991861\pi$
$662$	14.7734	+	0.774242i	0.574186	+	0.0300918i
$663$	−0.812139	+	1.25058i	−0.0315408	+	0.0485686i
$664$	−2.89110	−	8.89790i	−0.112197	−	0.345306i
$665$		0			0
$666$	10.8534	−	33.4034i	0.420562	−	1.29436i
$667$	18.7942	+	23.2090i	0.727716	+	0.898654i
$668$	0.118578	+	0.442538i	0.00458790	+	0.0171223i
$669$	28.5483	+	64.1206i	1.10374	+	2.47905i
$670$		0			0
$671$	4.26953	+	5.87650i	0.164823	+	0.226860i
$672$	48.0411	+	5.71654i	1.85323	+	0.220520i
$673$	−10.4791	+	20.5664i	−0.403939	+	0.792775i	−0.999948	−	0.0102030i	$-0.996752\pi$
$673$	−10.4791	+	20.5664i	−0.403939	+	0.792775i	0.596009	+	0.802978i	$0.296752\pi$
$674$	8.77620	−	5.06694i	0.338046	−	0.195171i
$675$		0			0
$676$	8.23459	−	14.2627i	0.316715	−	0.548566i
$677$	−11.5308	+	0.604301i	−0.443163	+	0.0232252i	−0.272613	−	0.962124i	$-0.587888\pi$
$677$	−11.5308	+	0.604301i	−0.443163	+	0.0232252i	−0.170550	+	0.985349i	$0.554554\pi$
$678$	0.995936	−	6.28809i	0.0382487	−	0.241493i
$679$	1.34598	+	9.32416i	0.0516539	+	0.357828i
$680$		0			0
$681$	1.83021	−	17.4132i	0.0701336	−	0.667277i
$682$	1.33279	−	0.357120i	0.0510352	−	0.0136748i
$683$	−13.5163	−	5.18841i	−0.517186	−	0.198529i	0.0857529	−	0.996316i	$-0.472670\pi$
$683$	−13.5163	−	5.18841i	−0.517186	−	0.198529i	−0.602939	+	0.797787i	$0.706004\pi$
$684$	10.1009	−	2.14701i	0.386217	−	0.0820931i
$685$		0			0
$686$	−8.61116	+	12.1361i	−0.328776	+	0.463358i
$687$	−22.7102	−	44.5713i	−0.866448	−	1.70050i
$688$	1.94695	+	1.26437i	0.0742270	+	0.0482036i
$689$	5.25678	+	1.11736i	0.200267	+	0.0425681i
$690$		0			0
$691$	−9.11485	−	42.8820i	−0.346745	−	1.63131i	−0.713263	−	0.700896i	$-0.752784\pi$
$691$	−9.11485	−	42.8820i	−0.346745	−	1.63131i	0.366518	−	0.930411i	$-0.380550\pi$
$692$	3.77152	+	23.8124i	0.143372	+	0.905213i
$693$	86.8056	−	26.8943i	3.29747	−	1.02163i
$694$	−4.86115	+	6.69080i	−0.184527	+	0.253979i
$695$		0			0
$696$	48.6139	−	5.10952i	1.84270	−	0.193676i
$697$	−2.86243	−	2.31795i	−0.108422	−	0.0877986i
$698$	0.474216	+	9.04857i	0.0179493	+	0.342494i
$699$	−38.5425			−1.45781
$700$		0			0
$701$	−30.4358			−1.14955			−0.574773	−	0.818313i	$-0.694910\pi$
$701$	−30.4358			−1.14955			−0.574773	+	0.818313i	$0.694910\pi$
$702$	0.465515	+	8.88255i	0.0175697	+	0.335250i
$703$	−5.52294	−	4.47239i	−0.208302	−	0.168679i
$704$	17.9343	−	1.88498i	0.675926	−	0.0710427i
$705$		0			0
$706$	7.85780	−	10.8153i	0.295732	−	0.407041i
$707$	5.79808	−	25.5495i	0.218059	−	0.960888i
$708$	−5.84762	−	36.9204i	−0.219767	−	1.38755i
$709$	0.889983	+	4.18704i	0.0334240	+	0.157248i	0.991695	−	0.128615i	$-0.0410532\pi$
$709$	0.889983	+	4.18704i	0.0334240	+	0.157248i	−0.958271	+	0.285863i	$0.907720\pi$
$710$		0			0
$711$	−32.5706	−	6.92309i	−1.22149	−	0.259636i
$712$	−7.10310	−	4.61281i	−0.266200	−	0.172872i
$713$	−0.803220	−	1.57641i	−0.0300808	−	0.0590370i
$714$	2.65724	+	2.21281i	0.0994445	+	0.0828125i
$715$		0			0
$716$	13.0623	−	2.77648i	0.488162	−	0.103762i
$717$	−44.2203	−	16.9746i	−1.65144	−	0.633927i
$718$	13.4743	−	3.61042i	0.502856	−	0.134740i
$719$	−1.92780	+	18.3418i	−0.0718947	+	0.684033i	0.897915	+	0.440169i	$0.145082\pi$
$719$	−1.92780	+	18.3418i	−0.0718947	+	0.684033i	−0.969810	+	0.243864i	$0.921585\pi$
$720$		0			0
$721$	12.1547	+	15.4381i	0.452667	+	0.574945i
$722$	2.23236	−	14.0946i	0.0830798	−	0.524545i
$723$	−72.7383	+	3.81205i	−2.70517	+	0.141772i
$724$	−14.5351	+	25.1755i	−0.540193	+	0.935641i
$725$		0			0
$726$	30.9143	−	17.8484i	1.14734	−	0.662415i
$727$	15.6762	−	30.7663i	0.581398	−	1.14106i	−0.393690	−	0.919243i	$-0.628802\pi$
$727$	15.6762	−	30.7663i	0.581398	−	1.14106i	0.975089	−	0.221816i	$-0.0711983\pi$
$728$	5.23527	+	3.91447i	0.194032	+	0.145080i
$729$	−3.02204	−	4.15948i	−0.111927	−	0.154055i
$730$		0			0
$731$	0.900929	+	2.02352i	0.0333221	+	0.0748426i
$732$	−1.59314	−	5.94569i	−0.0588843	−	0.219759i
$733$	−17.6104	−	21.7471i	−0.650456	−	0.803247i	0.340095	−	0.940391i	$-0.389541\pi$
$733$	−17.6104	−	21.7471i	−0.650456	−	0.803247i	−0.990551	+	0.137144i	$0.956208\pi$
$734$	1.85303	−	5.70305i	0.0683967	−	0.210504i
$735$		0			0
$736$	−9.30467	−	28.6368i	−0.342975	−	1.05557i
$737$	3.84296	−	5.91764i	0.141557	−	0.217979i
$738$	−39.0455	−	2.04629i	−1.43728	−	0.0753249i
$739$	−1.73453	+	8.16031i	−0.0638056	+	0.300182i	−0.998467	−	0.0553586i	$-0.982370\pi$
$739$	−1.73453	+	8.16031i	−0.0638056	+	0.300182i	0.934661	+	0.355540i	$0.115703\pi$
$740$		0			0
$741$	3.04611	+	0.989740i	0.111902	+	0.0363590i
$742$	4.01340	−	11.7988i	0.147337	−	0.433149i
$743$	31.5650	+	31.5650i	1.15801	+	1.15801i	0.984903	+	0.173106i	$0.0553802\pi$
$743$	31.5650	+	31.5650i	1.15801	+	1.15801i	0.173106	+	0.984903i	$0.444620\pi$
$744$	−2.88002	−	0.302702i	−0.105587	−	0.0110976i
$745$		0			0
$746$	2.47884	+	23.5846i	0.0907569	+	0.863495i
$747$	8.51899	+	22.1927i	0.311694	+	0.811989i
$748$	−3.13745	−	1.59861i	−0.114717	−	0.0584510i
$749$	0.159440	+	4.12382i	0.00582580	+	0.150681i
$750$		0			0
$751$	22.8072	+	39.5032i	0.832247	+	1.44149i	0.896252	+	0.443544i	$0.146279\pi$
$751$	22.8072	+	39.5032i	0.832247	+	1.44149i	−0.0640055	+	0.997950i	$0.520388\pi$
$752$	−3.77662	−	5.81549i	−0.137719	−	0.212069i
$753$	43.7686	−	54.0497i	1.59502	−	1.96968i
$754$	3.88877	+	1.73139i	0.141621	+	0.0630535i
$755$		0			0
$756$	−43.1795	−	2.85728i	−1.57042	−	0.103918i
$757$	−11.9819	+	11.9819i	−0.435488	+	0.435488i	−0.890490	−	0.455002i	$-0.849638\pi$
$757$	−11.9819	+	11.9819i	−0.435488	+	0.435488i	0.455002	+	0.890490i	$0.349638\pi$
$758$	0.593728	−	0.480792i	0.0215652	−	0.0174631i
$759$	−54.4247	−	60.4447i	−1.97549	−	2.19401i
$760$		0			0
$761$	−17.1557	−	15.4470i	−0.621892	−	0.559954i	0.296794	−	0.954941i	$-0.404082\pi$
$761$	−17.1557	−	15.4470i	−0.621892	−	0.559954i	−0.918687	+	0.394987i	$0.870749\pi$
$762$	−20.7111	+	10.5528i	−0.750285	+	0.382289i
$763$	13.5805	+	8.09106i	0.491647	+	0.292916i
$764$	−0.934503	+	0.303638i	−0.0338091	+	0.0109852i
$765$		0			0
$766$	6.05342	−	5.45053i	0.218719	−	0.196936i
$767$	2.88920	−	7.52662i	0.104323	−	0.271770i
$768$	−43.1446	−	11.5606i	−1.55685	−	0.417155i
$769$	33.2899	+	24.1865i	1.20046	+	0.872188i	0.994330	−	0.106336i	$-0.0339120\pi$
$769$	33.2899	+	24.1865i	1.20046	+	0.872188i	0.206133	+	0.978524i	$0.433912\pi$
$770$		0			0
$771$	−0.598719	+	0.434994i	−0.0215623	+	0.0156659i
$772$	−18.6076	+	7.14280i	−0.669703	+	0.257075i
$773$	15.1818	−	9.85916i	0.546050	−	0.354609i	−0.241945	−	0.970290i	$-0.577785\pi$
$773$	15.1818	−	9.85916i	0.546050	−	0.354609i	0.787996	+	0.615681i	$0.211119\pi$
$774$	20.3630	+	11.7566i	0.731933	+	0.422582i
$775$		0			0
$776$		−	9.59695i		−	0.344510i
$777$	30.5605	+	43.2996i	1.09635	+	1.55337i
$778$	10.6788	+	1.69136i	0.382854	+	0.0606381i
$779$	−3.21783	+	7.22737i	−0.115291	+	0.258947i
$780$		0			0
$781$	34.9096	−	15.5428i	1.24916	−	0.556164i
$782$	0.557016	−	2.07881i	0.0199189	−	0.0743382i
$783$	−68.9320	+	10.9178i	−2.46343	+	0.390169i
$784$	−2.62111	+	2.75516i	−0.0936111	+	0.0983985i
$785$		0			0
$786$	9.47643	−	10.5246i	0.338013	−	0.375401i
$787$	0.803521	−	15.3321i	0.0286424	−	0.546530i	−0.946193	−	0.323603i	$-0.895106\pi$
$787$	0.803521	−	15.3321i	0.0286424	−	0.546530i	0.974835	−	0.222927i	$-0.0715610\pi$
$788$	−1.73197	+	33.0480i	−0.0616989	+	1.17728i
$789$	48.0915	−	53.4110i	1.71210	−	1.90148i
$790$		0			0
$791$	4.65843	+	4.78800i	0.165635	+	0.170242i
$792$	−91.4358	+	14.4820i	−3.24903	+	0.514596i
$793$	0.343602	−	1.28234i	0.0122017	−	0.0455373i
$794$	19.8006	−	8.81579i	0.702697	−	0.312861i
$795$		0			0
$796$	−0.537385	+	1.20699i	−0.0190471	+	0.0427805i
$797$	15.1507	+	2.39964i	0.536667	+	0.0849997i	0.418884	−	0.908040i	$-0.362421\pi$
$797$	15.1507	+	2.39964i	0.536667	+	0.0849997i	0.117783	+	0.993039i	$0.462421\pi$
$798$	3.11377	−	6.74319i	0.110226	−	0.238706i
$799$		−	6.61618i		−	0.234064i
$800$		0			0
$801$	18.6365	+	10.7598i	0.658489	+	0.380179i
$802$	−10.3118	+	6.69659i	−0.364124	+	0.236465i
$803$	5.64714	−	2.16773i	0.199283	−	0.0764977i
$804$	−4.83740	+	3.51458i	−0.170602	+	0.123950i
$805$		0			0
$806$	−0.204021	−	0.148230i	−0.00718632	−	0.00522117i
$807$	−32.3585	−	8.67043i	−1.13907	−	0.305214i
$808$	−9.56448	+	24.9163i	−0.336477	+	0.876553i
$809$	15.3954	−	13.8621i	0.541275	−	0.487366i	−0.352544	−	0.935795i	$-0.614683\pi$
$809$	15.3954	−	13.8621i	0.541275	−	0.487366i	0.893818	+	0.448430i	$0.148016\pi$
$810$		0			0
$811$	−27.8184	+	9.03875i	−0.976837	+	0.317394i	−0.753573	−	0.657364i	$-0.771671\pi$
$811$	−27.8184	+	9.03875i	−0.976837	+	0.317394i	−0.223264	+	0.974758i	$0.571671\pi$
$812$	−10.5999	+	17.7914i	−0.371983	+	0.624357i
$813$	−51.6407	+	26.3122i	−1.81112	+	0.922811i
$814$	19.1168	+	17.2129i	0.670045	+	0.603311i
$815$		0			0
$816$	0.591298	+	0.656703i	0.0206996	+	0.0229892i
$817$	3.69741	−	2.99410i	0.129356	−	0.104750i
$818$	7.37305	−	7.37305i	0.257793	−	0.257793i
$819$	−13.8043	−	9.23625i	−0.482361	−	0.322741i
$820$		0			0
$821$	27.1109	+	12.0706i	0.946179	+	0.421266i	0.821038	−	0.570873i	$-0.193395\pi$
$821$	27.1109	+	12.0706i	0.946179	+	0.421266i	0.125140	+	0.992139i	$0.460062\pi$
$822$	6.85997	−	8.47136i	0.239269	−	0.295472i
$823$	−8.10388	−	12.4789i	−0.282484	−	0.434986i	0.668737	−	0.743499i	$-0.266835\pi$
$823$	−8.10388	−	12.4789i	−0.282484	−	0.434986i	−0.951220	+	0.308513i	$0.900169\pi$
$824$	−10.0081	−	17.3345i	−0.348647	−	0.603875i
$825$		0			0
$826$	−16.5402	−	8.71543i	−0.575506	−	0.303249i
$827$	32.9522	+	16.7900i	1.14586	+	0.583844i	0.920620	−	0.390459i	$-0.127684\pi$
$827$	32.9522	+	16.7900i	1.14586	+	0.583844i	0.225239	+	0.974304i	$0.427684\pi$
$828$	17.1763	+	44.7458i	0.596918	+	1.55502i
$829$	−4.28022	−	40.7236i	−0.148658	−	1.41439i	−0.773579	−	0.633700i	$-0.781535\pi$
$829$	−4.28022	−	40.7236i	−0.148658	−	1.41439i	0.624920	−	0.780689i	$-0.285131\pi$
$830$		0			0
$831$	32.5784	+	3.42413i	1.13013	+	0.118782i
$832$	−2.33053	−	2.33053i	−0.0807967	−	0.0807967i
$833$	−3.52919	+	0.842612i	−0.122279	+	0.0291948i
$834$	−15.4539	−	5.02127i	−0.535124	−	0.173872i
$835$		0			0
$836$	−1.57251	+	7.39807i	−0.0543863	+	0.255867i
$837$	4.12896	+	0.216390i	0.142718	+	0.00747952i
$838$	8.04880	−	12.3941i	0.278041	−	0.428146i
$839$	6.83090	+	21.0234i	0.235829	+	0.725807i	0.997010	+	0.0772679i	$0.0246197\pi$
$839$	6.83090	+	21.0234i	0.235829	+	0.725807i	−0.761181	+	0.648539i	$0.775380\pi$
$840$		0			0
$841$	−1.35975	+	4.18488i	−0.0468879	+	0.144306i
$842$	−12.4773	−	15.4082i	−0.429998	−	0.531003i
$843$	24.0413	+	89.7232i	0.828025	+	3.09023i
$844$	−15.7424	−	35.3581i	−0.541877	−	1.21707i
$845$		0			0
$846$	−41.2820	−	56.8198i	−1.41930	−	1.95350i
$847$	−4.42578	+	37.1937i	−0.152072	+	1.27799i
$848$	1.44589	−	2.83772i	0.0496522	−	0.0974479i
$849$	−75.7356	+	43.7260i	−2.59924	+	1.50067i
$850$		0			0
$851$	16.4924	−	28.5656i	0.565351	−	0.979217i
$852$	−32.3383	+	1.69478i	−1.10789	+	0.0580621i
$853$	2.30932	−	14.5805i	0.0790697	−	0.499226i	−0.916091	−	0.400969i	$-0.868673\pi$
$853$	2.30932	−	14.5805i	0.0790697	−	0.499226i	0.995161	−	0.0982567i	$-0.0313266\pi$
$854$	−2.85875	−	1.14260i	−0.0978244	−	0.0390990i
$855$		0			0
$856$	0.439444	−	4.18103i	0.0150199	−	0.142905i
$857$	−18.6322	+	4.99249i	−0.636465	+	0.170540i	−0.562602	−	0.826728i	$-0.690200\pi$
$857$	−18.6322	+	4.99249i	−0.636465	+	0.170540i	−0.0738633	+	0.997268i	$0.523533\pi$
$858$	−10.8234	−	4.15473i	−0.369506	−	0.141840i
$859$	−29.3200	+	6.23216i	−1.00039	+	0.212639i	−0.678864	−	0.734264i	$-0.737528\pi$
$859$	−29.3200	+	6.23216i	−1.00039	+	0.212639i	−0.321522	+	0.946902i	$0.604194\pi$
$860$		0			0
$861$	37.7545	−	45.3371i	1.28667	−	1.54508i
$862$	11.1741	+	21.9305i	0.380592	+	0.746955i
$863$	21.6157	+	14.0374i	0.735807	+	0.477839i	0.857341	−	0.514749i	$-0.172115\pi$
$863$	21.6157	+	14.0374i	0.735807	+	0.477839i	−0.121534	+	0.992587i	$0.538781\pi$
$864$	68.8289	+	14.6300i	2.34161	+	0.497724i
$865$		0			0
$866$	−4.33318	−	20.3860i	−0.147247	−	0.692745i
$867$	−8.21371	−	51.8593i	−0.278952	−	1.76124i
$868$	0.833385	−	0.900420i	0.0282869	−	0.0305622i
$869$	14.3350	−	19.7304i	0.486282	−	0.669309i
$870$		0			0
$871$	−1.28254	+	0.134800i	−0.0434571	+	0.00456753i
$872$	−12.5149	−	10.1343i	−0.423807	−	0.343192i
$873$	1.27618	+	24.3509i	0.0431921	+	0.824154i
$874$	−4.62263			−0.156363
$875$		0			0
$876$	−5.12595			−0.173190
$877$	−1.12967	−	21.5554i	−0.0381463	−	0.727876i	−0.949025	−	0.315201i	$-0.897928\pi$
$877$	−1.12967	−	21.5554i	−0.0381463	−	0.727876i	0.910879	−	0.412674i	$-0.135405\pi$
$878$	−8.31526	−	6.73356i	−0.280626	−	0.227247i
$879$	−21.4100	+	2.25028i	−0.722141	+	0.0759000i
$880$		0			0
$881$	−18.9856	+	26.1314i	−0.639640	+	0.880388i	−0.998596	−	0.0529657i	$-0.983133\pi$
$881$	−18.9856	+	26.1314i	−0.639640	+	0.880388i	0.358957	+	0.933354i	$0.383133\pi$
$882$	−25.0512	+	29.2569i	−0.843517	+	0.985131i
$883$	2.76060	+	17.4297i	0.0929015	+	0.586557i	0.989592	+	0.143899i	$0.0459642\pi$
$883$	2.76060	+	17.4297i	0.0929015	+	0.586557i	−0.896691	+	0.442657i	$0.854036\pi$
$884$	0.133806	+	0.629506i	0.00450037	+	0.0211726i
$885$		0			0
$886$	−11.8051	−	2.50926i	−0.396601	−	0.0843001i
$887$	−19.3404	−	12.5598i	−0.649387	−	0.421717i	0.177472	−	0.984126i	$-0.443208\pi$
$887$	−19.3404	−	12.5598i	−0.649387	−	0.421717i	−0.826859	+	0.562409i	$0.809875\pi$
$888$	−24.5105	−	48.1046i	−0.822519	−	1.61429i
$889$	4.14553	−	24.0354i	0.139037	−	0.806122i
$890$		0			0
$891$	85.1326	−	18.0955i	2.85205	−	0.606222i
$892$	28.2809	+	10.8560i	0.946914	+	0.363486i
$893$	−13.7268	+	3.67808i	−0.459349	+	0.123082i
$894$	−0.586018	+	5.57559i	−0.0195994	+	0.186476i
$895$		0			0
$896$	18.2206	−	14.3455i	0.608708	−	0.479249i
$897$	−2.32550	+	14.6826i	−0.0776462	+	0.490239i
$898$	−3.10532	+	0.162743i	−0.103626	+	0.00543080i
$899$	0.989361	−	1.71362i	0.0329970	−	0.0571525i
$900$		0			0
$901$	2.63168	−	1.51940i	0.0876739	−	0.0506185i
$902$	13.0008	−	25.5156i	0.432881	−	0.849576i
$903$	−32.6078	+	13.9852i	−1.08512	+	0.465399i
$904$	−3.99998	−	5.50549i	−0.133037	−	0.183110i
$905$		0			0
$906$	−12.7025	−	28.5303i	−0.422012	−	0.947855i
$907$	−10.6692	−	39.8182i	−0.354266	−	1.32214i	−0.881405	−	0.472361i	$-0.843402\pi$
$907$	−10.6692	−	39.8182i	−0.354266	−	1.32214i	0.527139	−	0.849779i	$-0.323265\pi$
$908$	−4.75566	−	5.87275i	−0.157822	−	0.194894i
$909$	20.9552	−	64.4936i	0.695041	−	2.13912i
$910$		0			0
$911$	0.709840	+	2.18466i	0.0235181	+	0.0723812i	0.962127	−	0.272603i	$-0.0878844\pi$
$911$	0.709840	+	2.18466i	0.0235181	+	0.0723812i	−0.938609	+	0.344984i	$0.887884\pi$
$912$	1.03376	−	1.59186i	0.0342314	−	0.0527117i
$913$	−17.3869	−	0.911208i	−0.575422	−	0.0301566i
$914$	7.07760	−	33.2975i	0.234106	−	1.10138i
$915$		0			0
$916$	−20.5331	−	6.67160i	−0.678432	−	0.220436i
$917$	2.88998	+	14.5766i	0.0954355	+	0.481361i
$918$	3.55635	+	3.55635i	0.117377	+	0.117377i
$919$	25.3891	+	2.66851i	0.837511	+	0.0880259i	0.513566	−	0.858050i	$-0.328324\pi$
$919$	25.3891	+	2.66851i	0.837511	+	0.0880259i	0.323945	+	0.946076i	$0.394991\pi$
$920$		0			0
$921$	−1.90360	−	18.1116i	−0.0627258	−	0.596796i
$922$	6.62715	+	17.2643i	0.218254	+	0.568570i
$923$	−6.22293	−	3.17074i	−0.204830	−	0.104366i
$924$	26.2936	−	49.9000i	0.864995	−	1.64159i
$925$		0			0
$926$	−7.25389	−	12.5641i	−0.238378	−	0.412882i
$927$	27.6991	+	42.6529i	0.909759	+	1.40091i
$928$	21.1927	−	26.1708i	0.695685	−	0.859100i
$929$	41.0517	+	18.2774i	1.34686	+	0.599662i	0.948270	−	0.317466i	$-0.102832\pi$
$929$	41.0517	+	18.2774i	1.34686	+	0.599662i	0.398593	+	0.917128i	$0.369499\pi$
$930$		0			0
$931$	3.71015	+	6.85369i	0.121595	+	0.224621i
$932$	−11.7625	+	11.7625i	−0.385293	+	0.385293i
$933$	60.3929	−	48.9052i	1.97718	−	1.60108i
$934$	−14.7426	−	16.3733i	−0.482393	−	0.535752i
$935$		0			0
$936$	12.5739	+	11.3216i	0.410989	+	0.370057i
$937$	50.8942	−	25.9319i	1.66264	−	0.847158i	0.667955	−	0.744202i	$-0.267170\pi$
$937$	50.8942	−	25.9319i	1.66264	−	0.847158i	0.994686	−	0.102956i	$-0.0328301\pi$
$938$	−0.0410173	+	2.99029i	−0.00133926	+	0.0976363i
$939$	21.3345	−	6.93200i	0.696226	−	0.226217i
$940$		0			0
$941$	24.2474	−	21.8325i	0.790444	−	0.711719i	−0.171435	−	0.985195i	$-0.554840\pi$
$941$	24.2474	−	21.8325i	0.790444	−	0.711719i	0.961879	+	0.273477i	$0.0881736\pi$
$942$	−15.2050	+	39.6104i	−0.495407	+	1.29058i
$943$	−35.4682	−	9.50367i	−1.15500	−	0.309482i
$944$	−3.86527	−	2.80828i	−0.125804	−	0.0914018i
$945$		0			0
$946$	−13.9324	+	10.1225i	−0.452983	+	0.329111i
$947$	34.2262	−	13.1382i	1.11220	−	0.426934i	0.268248	−	0.963350i	$-0.413555\pi$
$947$	34.2262	−	13.1382i	1.11220	−	0.426934i	0.843954	+	0.536415i	$0.180222\pi$
$948$	−17.3328	+	11.2560i	−0.562942	+	0.365579i
$949$	−0.957429	−	0.552772i	−0.0310795	−	0.0179437i
$950$		0			0
$951$			21.5823i			0.699854i
$952$	3.68093	−	0.335907i	0.119300	−	0.0108868i
$953$	46.1551	+	7.31025i	1.49511	+	0.236802i	0.849795	−	0.527113i	$-0.176726\pi$
$953$	46.1551	+	7.31025i	1.49511	+	0.236802i	0.645316	+	0.763916i	$0.276726\pi$
$954$	13.1205	−	29.4691i	0.424791	−	0.954096i
$955$		0			0
$956$	−18.6756	+	8.31490i	−0.604011	+	0.268923i
$957$	23.5439	−	87.8669i	0.761065	−	2.84034i
$958$	28.9779	−	4.58964i	0.936232	−	0.148285i
$959$	2.80853	+	11.0877i	0.0906920	+	0.358040i
$960$		0			0
$961$	20.6646	−	22.9504i	0.666600	−	0.740335i
$962$	0.246060	−	4.69511i	0.00793331	−	0.151377i
$963$	−0.559045	+	10.6672i	−0.0180150	+	0.343746i
$964$	−21.0351	+	23.3618i	−0.677493	+	0.752433i
$965$		0			0
$966$	33.1731	+	9.37819i	1.06733	+	0.301738i
$967$	7.10565	−	1.12542i	0.228502	−	0.0361912i	−0.0411332	−	0.999154i	$-0.513097\pi$
$967$	7.10565	−	1.12542i	0.228502	−	0.0361912i	0.269635	+	0.962962i	$0.413097\pi$
$968$	9.87561	−	36.8563i	0.317414	−	1.18461i
$969$	1.65446	−	0.736612i	0.0531488	−	0.0236634i
$970$		0			0
$971$	9.07173	−	20.3754i	0.291126	−	0.653879i	−0.707476	−	0.706737i	$-0.750166\pi$
$971$	9.07173	−	20.3754i	0.291126	−	0.653879i	0.998602	+	0.0528579i	$0.0168330\pi$
$972$	−24.3826	−	3.86183i	−0.782074	−	0.123868i
$973$	13.9299	−	9.83163i	0.446573	−	0.315188i
$974$			28.9792i			0.928555i
$975$		0			0
$976$	−0.681341	−	0.393372i	−0.0218092	−	0.0125915i
$977$	−48.1113	+	31.2438i	−1.53922	+	0.999579i	−0.553178	+	0.833063i	$0.686585\pi$
$977$	−48.1113	+	31.2438i	−1.53922	+	0.999579i	−0.986039	+	0.166516i	$0.946748\pi$
$978$	42.8390	−	16.4444i	1.36984	−	0.525832i
$979$	−12.7512	+	9.26427i	−0.407529	+	0.296087i
$980$		0			0
$981$	33.1024	+	24.0503i	1.05688	+	0.767867i
$982$	−7.26776	−	1.94739i	−0.231924	−	0.0621438i
$983$	−6.67425	+	17.3870i	−0.212875	+	0.554560i	−0.997891	−	0.0649169i	$-0.979322\pi$
$983$	−6.67425	+	17.3870i	−0.212875	+	0.554560i	0.785015	+	0.619477i	$0.212655\pi$
$984$	−44.6644	+	40.2160i	−1.42385	+	1.28204i
$985$		0			0
$986$	2.28915	−	0.743790i	0.0729014	−	0.0236871i
$987$	105.969	+	1.45355i	3.37302	+	0.0462671i
$988$	1.23167	−	0.627566i	0.0391846	−	0.0199655i
$989$	16.4102	+	14.7758i	0.521813	+	0.469843i
$990$		0			0
$991$	−28.2917	−	31.4211i	−0.898714	−	0.998123i	−0.999995	−	0.00326534i	$-0.998961\pi$
$991$	−28.2917	−	31.4211i	−0.898714	−	0.998123i	0.101280	−	0.994858i	$-0.467706\pi$
$992$	−1.55043	+	1.25552i	−0.0492263	+	0.0398626i
$993$	−40.8565	+	40.8565i	−1.29654	+	1.29654i
$994$	−9.00652	+	13.4610i	−0.285670	+	0.426956i
$995$		0			0
$996$	13.4786	+	6.00106i	0.427086	+	0.190151i
$997$	−10.7426	+	13.2661i	−0.340223	+	0.420140i	−0.918327	−	0.395823i	$-0.870459\pi$
$997$	−10.7426	+	13.2661i	−0.340223	+	0.420140i	0.578104	+	0.815963i	$0.303793\pi$
$998$	−14.0499	−	21.6349i	−0.444741	−	0.684841i
$999$	38.5417	+	66.7562i	1.21941	+	2.11207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.143.8		288
5.2	odd	4		875.2.bb.c.857.11		288
5.3	odd	4		175.2.x.a.17.8	yes	288
5.4	even	2		875.2.bb.b.143.11		288
7.5	odd	6	inner	875.2.bb.a.768.8		288
25.3	odd	20		875.2.bb.b.507.11		288
25.4	even	10		175.2.x.a.3.11	✓	288
25.21	even	5		875.2.bb.c.493.8		288
25.22	odd	20	inner	875.2.bb.a.507.8		288
35.12	even	12		875.2.bb.c.607.8		288
35.19	odd	6		875.2.bb.b.768.11		288
35.33	even	12		175.2.x.a.117.11	yes	288
175.47	even	60	inner	875.2.bb.a.257.8		288
175.54	odd	30		175.2.x.a.103.8	yes	288
175.96	odd	30		875.2.bb.c.243.11		288
175.103	even	60		875.2.bb.b.257.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.11	✓	288	25.4	even	10
175.2.x.a.17.8	yes	288	5.3	odd	4
175.2.x.a.103.8	yes	288	175.54	odd	30
175.2.x.a.117.11	yes	288	35.33	even	12
875.2.bb.a.143.8		288	1.1	even	1	trivial
875.2.bb.a.257.8		288	175.47	even	60	inner
875.2.bb.a.507.8		288	25.22	odd	20	inner
875.2.bb.a.768.8		288	7.5	odd	6	inner
875.2.bb.b.143.11		288	5.4	even	2
875.2.bb.b.257.11		288	175.103	even	60
875.2.bb.b.507.11		288	25.3	odd	20
875.2.bb.b.768.11		288	35.19	odd	6
875.2.bb.c.243.11		288	175.96	odd	30
875.2.bb.c.493.8		288	25.21	even	5
875.2.bb.c.607.8		288	35.12	even	12
875.2.bb.c.857.11		288	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0420512 - 0.802384i) q^{2} +(2.43882 + 1.97492i) q^{3} +(1.34699 - 0.141575i) q^{4} +(1.48209 - 2.03992i) q^{6} +(0.782993 + 2.52724i) q^{7} +(-0.421625 - 2.66204i) q^{8} +(1.42381 + 6.69848i) q^{9} +(-4.90608 - 1.04282i) q^{11} +(3.56467 + 2.31492i) q^{12} +(0.416175 + 0.816789i) q^{13} +(1.99489 - 0.734535i) q^{14} +(0.531383 - 0.112949i) q^{16} +(0.483913 + 0.185757i) q^{17} +(5.31488 - 1.42412i) q^{18} +(0.116377 - 1.10725i) q^{19} +(-3.08150 + 7.70982i) q^{21} +(-0.630435 + 3.98041i) q^{22} +(5.16039 - 0.270445i) q^{23} +(4.22903 - 7.32490i) q^{24} +(0.637878 - 0.368279i) q^{26} +(-5.48243 + 10.7599i) q^{27} +(1.41248 + 3.29331i) q^{28} +(3.39698 + 4.67555i) q^{29} +(-0.139259 - 0.312781i) q^{31} +(-1.50812 - 5.62839i) q^{32} +(-9.90555 - 12.2323i) q^{33} +(0.128699 - 0.396095i) q^{34} +(2.86619 + 8.82122i) q^{36} +(3.47651 - 5.35336i) q^{37} +(-0.893337 - 0.0468178i) q^{38} +(-0.598115 + 2.81391i) q^{39} +(-6.75808 - 2.19583i) q^{41} +(6.31581 + 2.14834i) q^{42} +(3.02167 + 3.02167i) q^{43} +(-6.75609 - 0.710093i) q^{44} +(-0.434001 - 4.12924i) q^{46} +(-4.57426 - 11.9164i) q^{47} +(1.51901 + 0.773974i) q^{48} +(-5.77384 + 3.95762i) q^{49} +(0.813322 + 1.40871i) q^{51} +(0.676221 + 1.04129i) q^{52} +(3.68942 - 4.55606i) q^{53} +(8.86410 + 3.94655i) q^{54} +(6.39747 - 3.14990i) q^{56} +(2.47056 - 2.47056i) q^{57} +(3.60874 - 2.92230i) q^{58} +(-5.88478 - 6.53571i) q^{59} +(-1.07623 - 0.969040i) q^{61} +(-0.245114 + 0.124892i) q^{62} +(-15.8138 + 8.84316i) q^{63} +(-3.41938 + 1.11102i) q^{64} +(-9.39849 + 8.46244i) q^{66} +(-0.504146 + 1.31334i) q^{67} +(0.678125 + 0.181703i) q^{68} +(13.1194 + 9.53177i) q^{69} +(-6.16371 + 4.47820i) q^{71} +(17.2313 - 6.61447i) q^{72} +(-1.01144 + 0.656834i) q^{73} +(-4.44164 - 2.56438i) q^{74} -1.50794i q^{76} +(-1.20598 - 13.2153i) q^{77} +(2.28299 + 0.361590i) q^{78} +(-1.97771 + 4.44201i) q^{79} +(-15.8523 + 7.05789i) q^{81} +(-1.47772 + 5.51491i) q^{82} +(3.42852 - 0.543025i) q^{83} +(-3.05924 + 10.8213i) q^{84} +(2.29747 - 2.55160i) q^{86} +(-0.949187 + 18.1116i) q^{87} +(-0.707497 + 13.4998i) q^{88} +(2.10268 - 2.33526i) q^{89} +(-1.73836 + 1.69131i) q^{91} +(6.91272 - 1.09487i) q^{92} +(0.278088 - 1.03784i) q^{93} +(-9.36915 + 4.17141i) q^{94} +(7.43756 - 16.7050i) q^{96} +(3.51689 + 0.557021i) q^{97} +(3.41833 + 4.46642i) q^{98} -34.3480i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more