LMFDB - Embedded newform 875.2.bb.b.493.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			493.8
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.b.607.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.504213 + 0.776420i) q^{2} +(0.473408 - 1.23327i) q^{3} +(0.464876 + 1.04413i) q^{4} +(0.718837 + 0.989394i) q^{6} +(-0.0993238 + 2.64389i) q^{7} +(-2.87383 - 0.455170i) q^{8} +(0.932596 + 0.839713i) q^{9} +(-0.526566 - 0.584810i) q^{11} +(1.50777 - 0.0790188i) q^{12} +(-0.729773 - 0.371838i) q^{13} +(-2.00269 - 1.41020i) q^{14} +(0.272873 - 0.303056i) q^{16} +(-4.67910 + 5.77821i) q^{17} +(-1.12220 + 0.300692i) q^{18} +(1.68154 + 0.748668i) q^{19} +(3.21360 + 1.37413i) q^{21} +(0.719560 - 0.113967i) q^{22} +(-3.42753 - 2.22587i) q^{23} +(-1.92184 + 3.32873i) q^{24} +(0.656664 - 0.379125i) q^{26} +(5.00818 - 2.55179i) q^{27} +(-2.80673 + 1.12537i) q^{28} +(-5.50382 + 7.57536i) q^{29} +(4.69555 - 0.493522i) q^{31} +(-1.40844 - 5.25635i) q^{32} +(-0.970509 + 0.372543i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(-0.343540 - 6.55514i) q^{37} +(-1.42913 + 0.928090i) q^{38} +(-0.804057 + 0.723976i) q^{39} +(-2.40999 + 0.783055i) q^{41} +(-2.68724 + 1.80225i) q^{42} +(1.79811 + 1.79811i) q^{43} +(0.365830 - 0.821667i) q^{44} +(3.45641 - 1.53889i) q^{46} +(-8.95355 + 7.25044i) q^{47} +(-0.244570 - 0.479996i) q^{48} +(-6.98027 - 0.525202i) q^{49} +(4.91096 + 8.50604i) q^{51} +(0.0489927 - 0.934836i) q^{52} +(8.40051 + 3.22465i) q^{53} +(-0.543925 + 5.17510i) q^{54} +(1.48886 - 7.55288i) q^{56} +(1.71936 - 1.71936i) q^{57} +(-3.10656 - 8.09287i) q^{58} +(11.1497 + 2.36995i) q^{59} +(1.75779 + 8.26975i) q^{61} +(-1.98438 + 3.89456i) q^{62} +(-2.31273 + 2.38227i) q^{63} +(5.56698 + 1.80882i) q^{64} +(0.200093 - 0.941364i) q^{66} +(-0.709737 - 0.574734i) q^{67} +(-8.20839 - 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(-2.29791 - 2.83768i) q^{72} +(3.70594 + 0.194220i) q^{73} +(5.26276 + 3.03846i) q^{74} +2.10378i q^{76} +(1.59847 - 1.33409i) q^{77} +(-0.156693 - 0.989324i) q^{78} +(-4.86448 - 0.511278i) q^{79} +(-0.382611 - 3.64030i) q^{81} +(0.607171 - 2.26599i) q^{82} +(-0.814213 + 5.14074i) q^{83} +(0.0591594 + 3.99422i) q^{84} +(-2.30272 + 0.489458i) q^{86} +(6.73691 + 10.3739i) q^{87} +(1.24707 + 1.92032i) q^{88} +(-0.565582 + 0.120218i) q^{89} +(1.05558 - 1.89250i) q^{91} +(0.730712 - 4.61354i) q^{92} +(1.61426 - 6.02451i) q^{93} +(-1.11489 - 10.6075i) q^{94} +(-7.14926 - 0.751418i) q^{96} +(1.67483 + 10.5745i) q^{97} +(3.92732 - 5.15481i) q^{98} -0.987555i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.504213	+	0.776420i	−0.356532	+	0.549012i	−0.970740	−	0.240133i	$-0.922809\pi$
$2$	−0.504213	+	0.776420i	−0.356532	+	0.549012i	0.614208	+	0.789144i	$0.289476\pi$
$3$	0.473408	−	1.23327i	0.273322	−	0.712029i	−0.726372	−	0.687302i	$-0.758795\pi$
$3$	0.473408	−	1.23327i	0.273322	−	0.712029i	0.999694	−	0.0247269i	$-0.00787160\pi$
$4$	0.464876	+	1.04413i	0.232438	+	0.522064i
$5$		0			0
$5$		0			0
$6$	0.718837	+	0.989394i	0.293464	+	0.403918i
$7$	−0.0993238	+	2.64389i	−0.0375409	+	0.999295i
$7$	−0.0993238	+	2.64389i	−0.0375409	+	0.999295i
$8$	−2.87383	−	0.455170i	−1.01605	−	0.160927i
$9$	0.932596	+	0.839713i	0.310865	+	0.279904i
$10$		0			0
$11$	−0.526566	−	0.584810i	−0.158765	−	0.176327i	0.658514	−	0.752569i	$-0.271185\pi$
$11$	−0.526566	−	0.584810i	−0.158765	−	0.176327i	−0.817279	+	0.576242i	$0.804519\pi$
$12$	1.50777	−	0.0790188i	0.435255	−	0.0228108i
$13$	−0.729773	−	0.371838i	−0.202403	−	0.103129i	0.349851	−	0.936805i	$-0.386232\pi$
$13$	−0.729773	−	0.371838i	−0.202403	−	0.103129i	−0.552254	+	0.833676i	$0.686232\pi$
$14$	−2.00269	−	1.41020i	−0.535240	−	0.376892i
$15$		0			0
$16$	0.272873	−	0.303056i	0.0682183	−	0.0757641i
$17$	−4.67910	+	5.77821i	−1.13485	+	1.40142i	−0.231328	+	0.972876i	$0.574307\pi$
$17$	−4.67910	+	5.77821i	−1.13485	+	1.40142i	−0.903520	+	0.428545i	$0.859026\pi$
$18$	−1.12220	+	0.300692i	−0.264504	+	0.0708737i
$19$	1.68154	+	0.748668i	0.385771	+	0.171756i	0.590453	−	0.807072i	$-0.298949\pi$
$19$	1.68154	+	0.748668i	0.385771	+	0.171756i	−0.204682	+	0.978829i	$0.565616\pi$
$20$		0			0
$21$	3.21360	+	1.37413i	0.701266	+	0.299860i
$22$	0.719560	−	0.113967i	0.153411	−	0.0242979i
$23$	−3.42753	−	2.22587i	−0.714690	−	0.464125i	0.135381	−	0.990794i	$-0.456774\pi$
$23$	−3.42753	−	2.22587i	−0.714690	−	0.464125i	−0.850071	+	0.526669i	$0.823441\pi$
$24$	−1.92184	+	3.32873i	−0.392294	+	0.679474i
$25$		0			0
$26$	0.656664	−	0.379125i	0.128782	−	0.0743525i
$27$	5.00818	−	2.55179i	0.963824	−	0.491093i
$28$	−2.80673	+	1.12537i	−0.530422	+	0.212675i
$29$	−5.50382	+	7.57536i	−1.02203	+	1.40671i	−0.111266	+	0.993791i	$0.535491\pi$
$29$	−5.50382	+	7.57536i	−1.02203	+	1.40671i	−0.910768	+	0.412919i	$0.864509\pi$
$30$		0			0
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.327005	−	0.945023i	$-0.393961\pi$
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.516340	+	0.856383i	$0.327294\pi$
$32$	−1.40844	−	5.25635i	−0.248979	−	0.929201i
$33$	−0.970509	+	0.372543i	−0.168944	+	0.0648515i
$34$	−2.12705	−	6.54639i	−0.364786	−	1.12270i
$35$		0			0
$36$	−0.443227	+	1.36411i	−0.0738712	+	0.227352i
$37$	−0.343540	−	6.55514i	−0.0564777	−	1.07766i	−0.869027	−	0.494766i	$-0.835254\pi$
$37$	−0.343540	−	6.55514i	−0.0564777	−	1.07766i	0.812549	−	0.582893i	$-0.198079\pi$
$38$	−1.42913	+	0.928090i	−0.231836	+	0.150556i
$39$	−0.804057	+	0.723976i	−0.128752	+	0.115929i
$40$		0			0
$41$	−2.40999	+	0.783055i	−0.376378	+	0.122293i	−0.491096	−	0.871106i	$-0.663404\pi$
$41$	−2.40999	+	0.783055i	−0.376378	+	0.122293i	0.114718	+	0.993398i	$0.463404\pi$
$42$	−2.68724	+	1.80225i	−0.414651	+	0.278094i
$43$	1.79811	+	1.79811i	0.274209	+	0.274209i	0.830792	−	0.556583i	$-0.187888\pi$
$43$	1.79811	+	1.79811i	0.274209	+	0.274209i	−0.556583	+	0.830792i	$0.687888\pi$
$44$	0.365830	−	0.821667i	0.0551509	−	0.123871i
$45$		0			0
$46$	3.45641	−	1.53889i	0.509620	−	0.226898i
$47$	−8.95355	+	7.25044i	−1.30601	+	1.05759i	−0.311797	+	0.950149i	$0.600931\pi$
$47$	−8.95355	+	7.25044i	−1.30601	+	1.05759i	−0.994212	+	0.107437i	$0.965736\pi$
$48$	−0.244570	−	0.479996i	−0.0353006	−	0.0692814i
$49$	−6.98027	−	0.525202i	−0.997181	−	0.0750288i
$50$		0			0
$51$	4.91096	+	8.50604i	0.687673	+	1.19108i
$52$	0.0489927	−	0.934836i	0.00679406	−	0.129638i
$53$	8.40051	+	3.22465i	1.15390	+	0.442940i	0.858691	−	0.512493i	$-0.171278\pi$
$53$	8.40051	+	3.22465i	1.15390	+	0.442940i	0.295207	+	0.955433i	$0.404611\pi$
$54$	−0.543925	+	5.17510i	−0.0740188	+	0.704241i
$55$		0			0
$56$	1.48886	−	7.55288i	0.198957	−	1.00930i
$57$	1.71936	−	1.71936i	0.227735	−	0.227735i
$58$	−3.10656	−	8.09287i	−0.407912	−	1.06265i
$59$	11.1497	+	2.36995i	1.45157	+	0.308541i	0.865169	−	0.501480i	$-0.167211\pi$
$59$	11.1497	+	2.36995i	1.45157	+	0.308541i	0.586401	+	0.810021i	$0.300544\pi$
$60$		0			0
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	0.935022	+	0.354591i	$0.115380\pi$
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	−0.709959	+	0.704243i	$0.751287\pi$
$62$	−1.98438	+	3.89456i	−0.252016	+	0.494609i
$63$	−2.31273	+	2.38227i	−0.291377	+	0.300138i
$64$	5.56698	+	1.80882i	0.695872	+	0.226103i
$65$		0			0
$66$	0.200093	−	0.941364i	0.0246298	−	0.115874i
$67$	−0.709737	−	0.574734i	−0.0867082	−	0.0702149i	0.584986	−	0.811043i	$-0.301100\pi$
$67$	−0.709737	−	0.574734i	−0.0867082	−	0.0702149i	−0.671694	+	0.740828i	$0.734433\pi$
$68$	−8.20839	−	2.19943i	−0.995414	−	0.266720i
$69$	−4.36771	+	3.17333i	−0.525811	+	0.382024i
$70$		0			0
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	−2.29791	−	2.83768i	−0.270811	−	0.334424i
$73$	3.70594	+	0.194220i	0.433747	+	0.0227317i	0.267961	−	0.963430i	$-0.413650\pi$
$73$	3.70594	+	0.194220i	0.433747	+	0.0227317i	0.165787	+	0.986162i	$0.446984\pi$
$74$	5.26276	+	3.03846i	0.611783	+	0.353213i
$75$		0			0
$76$			2.10378i			0.241320i
$77$	1.59847	−	1.33409i	0.182163	−	0.152034i
$78$	−0.156693	−	0.989324i	−0.0177420	−	0.112019i
$79$	−4.86448	−	0.511278i	−0.547297	−	0.0575232i	−0.173155	−	0.984895i	$-0.555396\pi$
$79$	−4.86448	−	0.511278i	−0.547297	−	0.0575232i	−0.374142	+	0.927371i	$0.622063\pi$
$80$		0			0
$81$	−0.382611	−	3.64030i	−0.0425124	−	0.404478i
$82$	0.607171	−	2.26599i	0.0670509	−	0.250237i
$83$	−0.814213	+	5.14074i	−0.0893715	+	0.564269i	0.901849	+	0.432051i	$0.142210\pi$
$83$	−0.814213	+	5.14074i	−0.0893715	+	0.564269i	−0.991221	+	0.132218i	$0.957790\pi$
$84$	0.0591594	+	3.99422i	0.00645482	+	0.435805i
$85$		0			0
$86$	−2.30272	+	0.489458i	−0.248309	+	0.0527796i
$87$	6.73691	+	10.3739i	0.722273	+	1.11220i
$88$	1.24707	+	1.92032i	0.132938	+	0.204707i
$89$	−0.565582	+	0.120218i	−0.0599516	+	0.0127431i	−0.237790	−	0.971317i	$-0.576423\pi$
$89$	−0.565582	+	0.120218i	−0.0599516	+	0.0127431i	0.177838	+	0.984060i	$0.443090\pi$
$90$		0			0
$91$	1.05558	−	1.89250i	0.110655	−	0.198388i
$92$	0.730712	−	4.61354i	0.0761820	−	0.480994i
$93$	1.61426	−	6.02451i	0.167391	−	0.624713i
$94$	−1.11489	−	10.6075i	−0.114992	−	1.09408i
$95$		0			0
$96$	−7.14926	−	0.751418i	−0.729669	−	0.0766913i
$97$	1.67483	+	10.5745i	0.170054	+	1.07368i	0.914082	+	0.405529i	$0.132913\pi$
$97$	1.67483	+	10.5745i	0.170054	+	1.07368i	−0.744029	+	0.668148i	$0.767087\pi$
$98$	3.92732	−	5.15481i	0.396719	−	0.520714i
$99$		−	0.987555i		−	0.0992530i
$100$		0			0
$101$	−5.47339	−	3.16006i	−0.544622	−	0.314438i	0.202328	−	0.979318i	$-0.435149\pi$
$101$	−5.47339	−	3.16006i	−0.544622	−	0.314438i	−0.746950	+	0.664880i	$0.768483\pi$
$102$	−9.08043	−	0.475885i	−0.899097	−	0.0471197i
$103$	6.23115	+	7.69483i	0.613974	+	0.758194i	0.985398	−	0.170269i	$-0.0544637\pi$
$103$	6.23115	+	7.69483i	0.613974	+	0.758194i	−0.371424	+	0.928463i	$0.621130\pi$
$104$	1.92800	+	1.40077i	0.189056	+	0.137357i
$105$		0			0
$106$	−6.73933	+	4.89641i	−0.654582	+	0.475581i
$107$	−5.25791	−	1.40885i	−0.508302	−	0.136199i	−0.00445150	−	0.999990i	$-0.501417\pi$
$107$	−5.25791	−	1.40885i	−0.508302	−	0.136199i	−0.503850	+	0.863791i	$0.668084\pi$
$108$	4.99258	+	4.04291i	0.480412	+	0.389030i
$109$	3.40888	−	16.0375i	0.326512	−	1.53612i	−0.442434	−	0.896801i	$-0.645885\pi$
$109$	3.40888	−	16.0375i	0.326512	−	1.53612i	0.768945	−	0.639315i	$-0.220782\pi$
$110$		0			0
$111$	−8.24689	−	2.67958i	−0.782760	−	0.254334i
$112$	0.774144	+	0.751546i	0.0731497	+	0.0710145i
$113$	−4.26151	+	8.36368i	−0.400889	+	0.786789i	−0.999903	−	0.0139501i	$-0.995559\pi$
$113$	−4.26151	+	8.36368i	−0.400889	+	0.786789i	0.599014	+	0.800739i	$0.295559\pi$
$114$	0.468022	+	2.20187i	0.0438343	+	0.206224i
$115$		0			0
$116$	−10.4682	−	2.22509i	−0.971952	−	0.206595i
$117$	−0.368346	−	0.959574i	−0.0340536	−	0.0887127i
$118$	−7.46191	+	7.46191i	−0.686924	+	0.686924i
$119$	−14.8122	−	12.9449i	−1.35783	−	1.18666i
$120$		0			0
$121$	1.08508	−	10.3239i	0.0986438	−	0.938533i
$122$	−7.30710	−	2.80493i	−0.661554	−	0.253947i
$123$	−0.175193	+	3.34288i	−0.0157966	+	0.301417i
$124$	2.69815	+	4.67333i	0.242301	+	0.419678i
$125$		0			0
$126$	−0.683534	−	2.99683i	−0.0608940	−	0.266979i
$127$	−1.32420	−	2.59888i	−0.117503	−	0.230613i	0.824762	−	0.565480i	$-0.191309\pi$
$127$	−1.32420	−	2.59888i	−0.117503	−	0.230613i	−0.942266	+	0.334866i	$0.891309\pi$
$128$	4.24676	−	3.43896i	0.375365	−	0.303964i
$129$	3.06879	−	1.36632i	0.270192	−	0.120297i
$130$		0			0
$131$	−2.73808	+	6.14983i	−0.239227	+	0.537313i	−0.992763	−	0.120094i	$-0.961680\pi$
$131$	−2.73808	+	6.14983i	−0.239227	+	0.537313i	0.753535	+	0.657408i	$0.228347\pi$
$132$	−0.840150	−	0.840150i	−0.0731256	−	0.0731256i
$133$	−2.14641	+	4.37143i	−0.186117	+	0.379051i
$134$	0.804093	−	0.261266i	0.0694631	−	0.0225699i
$135$		0			0
$136$	16.0770	−	14.4758i	1.37859	−	1.24129i
$137$	16.3347	−	10.6079i	1.39557	−	0.906294i	0.395644	−	0.918404i	$-0.370521\pi$
$137$	16.3347	−	10.6079i	1.39557	−	0.906294i	0.999927	+	0.0121099i	$0.00385480\pi$
$138$	−0.261578	−	4.99121i	−0.0222670	−	0.424880i
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	−0.936700	−	0.350133i	$-0.886137\pi$
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	0.963609	+	0.267315i	$0.0861365\pi$
$140$		0			0
$141$	4.70307	+	14.4746i	0.396070	+	1.21898i
$142$	−0.819711	+	0.314658i	−0.0687886	+	0.0264055i
$143$	0.166819	+	0.622576i	0.0139501	+	0.0520624i
$144$	0.508961	−	0.0534939i	0.0424134	−	0.00445783i
$145$		0			0
$146$	−2.01938	+	2.77944i	−0.167125	+	0.230028i
$147$	−3.95223	+	8.35992i	−0.325974	+	0.689515i
$148$	6.68471	−	3.40603i	0.549480	−	0.279974i
$149$	9.86165	−	5.69362i	0.807897	−	0.466440i	−0.0383277	−	0.999265i	$-0.512203\pi$
$149$	9.86165	−	5.69362i	0.807897	−	0.466440i	0.846225	+	0.532825i	$0.178870\pi$
$150$		0			0
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	−0.998469	−	0.0553124i	$-0.982385\pi$
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	0.547136	+	0.837043i	$0.315718\pi$
$152$	−4.49168	−	2.91693i	−0.364324	−	0.236595i
$153$	−9.21574	+	1.45963i	−0.745049	+	0.118004i
$154$	0.229846	+	1.91375i	0.0185216	+	0.154215i
$155$		0			0
$156$	−1.12971	−	0.502980i	−0.0904493	−	0.0402706i
$157$	16.1035	−	4.31493i	1.28520	−	0.344369i	0.449365	−	0.893348i	$-0.351650\pi$
$157$	16.1035	−	4.31493i	1.28520	−	0.344369i	0.835836	+	0.548979i	$0.184983\pi$
$158$	2.84970	−	3.51909i	0.226710	−	0.279964i
$159$	7.95373	−	8.83352i	0.630772	−	0.700543i
$160$		0			0
$161$	6.22537	−	8.84092i	0.490628	−	0.696762i
$162$	3.01932	+	1.53842i	0.237220	+	0.120870i
$163$	20.5419	−	1.07656i	1.60897	−	0.0843225i	0.773476	−	0.633825i	$-0.218516\pi$
$163$	20.5419	−	1.07656i	1.60897	−	0.0843225i	0.835492	+	0.549503i	$0.185183\pi$
$164$	−1.93796	−	2.15232i	−0.151329	−	0.168068i
$165$		0			0
$166$	−3.58084	−	3.22420i	−0.277927	−	0.250246i
$167$	4.67190	+	0.739956i	0.361522	+	0.0572595i	0.334553	−	0.942377i	$-0.391415\pi$
$167$	4.67190	+	0.739956i	0.361522	+	0.0572595i	0.0269687	+	0.999636i	$0.491415\pi$
$168$	−8.60990	−	5.41176i	−0.664268	−	0.417526i
$169$	−7.24690	−	9.97451i	−0.557454	−	0.767270i
$170$		0			0
$171$	0.939527	+	2.11021i	0.0718475	+	0.161372i
$172$	−1.04156	+	2.71336i	−0.0794182	+	0.206892i
$173$	2.74889	−	4.23292i	0.208994	−	0.321823i	−0.718592	−	0.695432i	$-0.755213\pi$
$173$	2.74889	−	4.23292i	0.208994	−	0.321823i	0.927586	+	0.373609i	$0.121880\pi$
$174$	−11.4514			−0.868126
$175$		0			0
$176$	−0.320916			−0.0241900
$177$	8.20115	−	12.6287i	0.616436	−	0.949228i
$178$	0.191834	−	0.499745i	0.0143786	−	0.0374575i
$179$	1.46827	+	3.29779i	0.109744	+	0.246488i	0.960066	−	0.279774i	$-0.0902596\pi$
$179$	1.46827	+	3.29779i	0.109744	+	0.246488i	−0.850322	+	0.526263i	$0.823593\pi$
$180$		0			0
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	0.446737	−	0.894665i	$-0.352586\pi$
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	−0.988927	+	0.148406i	$0.952586\pi$
$182$	0.937141	+	1.77380i	0.0694655	+	0.131483i
$183$	11.0310	+	1.74714i	0.815434	+	0.129152i
$184$	8.83701	+	7.95688i	0.651473	+	0.586589i
$185$		0			0
$186$	3.86362	+	4.29099i	0.283294	+	0.314630i
$187$	5.84301	−	0.306219i	0.427283	−	0.0223930i
$188$	−11.7327	−	5.97810i	−0.855694	−	0.435998i
$189$	6.24922	+	13.4945i	0.454564	+	0.981581i
$190$		0			0
$191$	15.5218	−	17.2388i	1.12312	−	1.24735i	0.157467	−	0.987524i	$-0.449667\pi$
$191$	15.5218	−	17.2388i	1.12312	−	1.24735i	0.965655	−	0.259828i	$-0.0836660\pi$
$192$	4.86621	−	6.00927i	0.351189	−	0.433682i
$193$	14.4367	−	3.86831i	1.03918	−	0.278447i	0.301406	−	0.953496i	$-0.402544\pi$
$193$	14.4367	−	3.86831i	1.03918	−	0.278447i	0.737773	+	0.675049i	$0.235877\pi$
$194$	−9.05472	−	4.03142i	−0.650091	−	0.289439i
$195$		0			0
$196$	−2.69658	−	7.53245i	−0.192613	−	0.538032i
$197$	−1.48910	+	0.235850i	−0.106094	+	0.0168036i	−0.209256	−	0.977861i	$-0.567104\pi$
$197$	−1.48910	+	0.235850i	−0.106094	+	0.0168036i	0.103162	+	0.994665i	$0.467104\pi$
$198$	0.766758	+	0.497938i	0.0544911	+	0.0353869i
$199$	1.75472	−	3.03927i	0.124389	−	0.215448i	−0.797105	−	0.603841i	$-0.793636\pi$
$199$	1.75472	−	3.03927i	0.124389	−	0.215448i	0.921494	+	0.388393i	$0.126970\pi$
$200$		0			0
$201$	−1.04480	+	0.603214i	−0.0736943	+	0.0425474i
$202$	5.21329	−	2.65630i	0.366806	−	0.186897i
$203$	−19.4817	−	15.3039i	−1.36735	−	1.07412i
$204$	−6.59841	+	9.08193i	−0.461981	+	0.635863i
$205$		0			0
$206$	−9.11625	+	0.958157i	−0.635159	+	0.0667579i
$207$	−1.32741	−	4.95398i	−0.0922616	−	0.344325i
$208$	−0.311823	+	0.119698i	−0.0216211	+	0.00829955i
$209$	−0.447610	−	1.37760i	−0.0309619	−	0.0952908i
$210$		0			0
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	0.538243	+	10.2703i	0.0369666	+	0.705366i
$213$	1.05076	−	0.682368i	0.0719966	−	0.0467551i
$214$	3.74497	−	3.37199i	0.256001	−	0.230504i
$215$		0			0
$216$	−15.5542	+	5.05385i	−1.05833	+	0.343871i
$217$	0.838436	+	12.4635i	0.0569168	+	0.846079i
$218$	10.7331	+	10.7331i	0.726934	+	0.726934i
$219$	1.99395	−	4.47848i	0.134738	−	0.302627i
$220$		0			0
$221$	5.56324	−	2.47691i	0.374224	−	0.166615i
$222$	6.23867	−	5.05197i	0.418712	−	0.339066i
$223$	3.97575	+	7.80285i	0.266236	+	0.522518i	0.984961	−	0.172777i	$-0.0552739\pi$
$223$	3.97575	+	7.80285i	0.266236	+	0.522518i	−0.718725	+	0.695294i	$0.755274\pi$
$224$	14.0371	−	3.20166i	0.937893	−	0.213920i
$225$		0			0
$226$	−4.34502	−	7.52579i	−0.289026	−	0.500608i
$227$	−0.491475	+	9.37790i	−0.0326203	+	0.622433i	0.932587	+	0.360946i	$0.117546\pi$
$227$	−0.491475	+	9.37790i	−0.0326203	+	0.622433i	−0.965207	+	0.261487i	$0.915787\pi$
$228$	2.59453	+	0.995946i	0.171827	+	0.0659581i
$229$	−0.899141	+	8.55475i	−0.0594169	+	0.565314i	0.923800	+	0.382875i	$0.125066\pi$
$229$	−0.899141	+	8.55475i	−0.0594169	+	0.565314i	−0.983217	+	0.182439i	$0.941601\pi$
$230$		0			0
$231$	−0.888568	−	2.60292i	−0.0584635	−	0.171259i
$232$	19.2651	−	19.2651i	1.26482	−	1.26482i
$233$	−0.998293	−	2.60064i	−0.0654004	−	0.170374i	0.896986	−	0.442060i	$-0.145752\pi$
$233$	−0.998293	−	2.60064i	−0.0654004	−	0.170374i	−0.962386	+	0.271686i	$0.912419\pi$
$234$	0.930758	+	0.197839i	0.0608455	+	0.0129331i
$235$		0			0
$236$	2.70871	+	12.7435i	0.176322	+	0.829529i
$237$	−2.93343	+	5.75718i	−0.190547	+	0.373969i
$238$	17.5192	−	4.97347i	1.13560	−	0.322382i
$239$	10.2364	+	3.32600i	0.662136	+	0.215141i	0.620757	−	0.784003i	$-0.286825\pi$
$239$	10.2364	+	3.32600i	0.662136	+	0.215141i	0.0413782	+	0.999144i	$0.486825\pi$
$240$		0			0
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	0.849247	+	0.527995i	$0.177056\pi$
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	−0.990581	+	0.136927i	$0.956277\pi$
$242$	7.46854	+	6.04790i	0.480096	+	0.388774i
$243$	11.6172	+	3.11283i	0.745247	+	0.199688i
$244$	−7.81753	+	5.67977i	−0.500466	+	0.363610i
$245$		0			0
$246$	−2.50714	−	1.82155i	−0.159850	−	0.116137i
$247$	−0.948757	−	1.17162i	−0.0603680	−	0.0745482i
$248$	−13.7189	−	0.718975i	−0.871148	−	0.0456550i
$249$	5.95446	+	3.43781i	0.377349	+	0.217862i
$250$		0			0
$251$		−	29.0617i		−	1.83436i	−0.398477	−	0.917178i	$-0.630461\pi$
$251$		−	29.0617i		−	1.83436i	0.398477	−	0.917178i	$-0.369539\pi$
$252$	−3.56254	−	1.30733i	−0.224419	−	0.0823541i
$253$	0.503111	+	3.17652i	0.0316303	+	0.199706i
$254$	2.68550	+	0.282257i	0.168503	+	0.0177104i
$255$		0			0
$256$	1.75251	+	16.6740i	0.109532	+	1.04213i
$257$	4.81832	−	17.9822i	0.300559	−	1.12170i	−0.636143	−	0.771571i	$-0.719471\pi$
$257$	4.81832	−	17.9822i	0.300559	−	1.12170i	0.936701	−	0.350129i	$-0.113862\pi$
$258$	−0.486492	+	3.07159i	−0.0302876	+	0.191229i
$259$	17.3652	−	0.257200i	1.07902	−	0.0159816i
$260$		0			0
$261$	−11.4940	+	2.44312i	−0.711459	+	0.151225i
$262$	−3.39428	−	5.22673i	−0.209699	−	0.322908i
$263$	−11.2829	−	17.3742i	−0.695735	−	1.07134i	−0.993179	−	0.116599i	$-0.962801\pi$
$263$	−11.2829	−	17.3742i	−0.695735	−	1.07134i	0.297444	−	0.954739i	$-0.403866\pi$
$264$	2.95865	−	0.628881i	0.182092	−	0.0387049i
$265$		0			0
$266$	−2.31182	−	3.87065i	−0.141747	−	0.237325i
$267$	−0.119490	+	0.754428i	−0.00731265	+	0.0461702i
$268$	0.270156	−	1.00824i	0.0165024	−	0.0615879i
$269$	−0.134230	−	1.27711i	−0.00818414	−	0.0778669i	0.989667	−	0.143382i	$-0.0457977\pi$
$269$	−0.134230	−	1.27711i	−0.00818414	−	0.0778669i	−0.997852	+	0.0655149i	$0.979131\pi$
$270$		0			0
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.471636	−	0.881793i	$-0.343664\pi$
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.277995	+	0.960583i	$0.410330\pi$
$272$	0.474322	+	2.99475i	0.0287600	+	0.181583i
$273$	−1.83425	−	2.19774i	−0.111014	−	0.133013i
$274$			18.0313i			1.08931i
$275$		0			0
$276$	−5.34381	−	3.08525i	−0.321660	−	0.185710i
$277$	−1.22836	−	0.0643756i	−0.0738049	−	0.00386795i	0.0153977	−	0.999881i	$-0.495099\pi$
$277$	−1.22836	−	0.0643756i	−0.0738049	−	0.00386795i	−0.0892027	+	0.996013i	$0.528432\pi$
$278$	0.598135	+	0.738635i	0.0358737	+	0.0443004i
$279$	4.79347	+	3.48266i	0.286977	+	0.208501i
$280$		0			0
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	−13.6097	−	3.64670i	−0.810445	−	0.217158i
$283$	11.7176	+	9.48873i	0.696539	+	0.564046i	0.910859	−	0.412717i	$-0.135420\pi$
$283$	11.7176	+	9.48873i	0.696539	+	0.564046i	−0.214320	+	0.976764i	$0.568754\pi$
$284$	−0.225375	+	1.06031i	−0.0133736	+	0.0629177i
$285$		0			0
$286$	−0.567492	−	0.184389i	−0.0335565	−	0.0109032i
$287$	−1.83094	−	6.44953i	−0.108077	−	0.380704i
$288$	3.10033	−	6.08473i	0.182689	−	0.358546i
$289$	−7.95920	−	37.4451i	−0.468188	−	2.20265i
$290$		0			0
$291$	13.8341	+	2.94052i	0.810968	+	0.172377i
$292$	1.52001	+	3.95977i	0.0889520	+	0.231728i
$293$	2.74224	−	2.74224i	0.160203	−	0.160203i	−0.622454	−	0.782657i	$-0.713864\pi$
$293$	2.74224	−	2.74224i	0.160203	−	0.160203i	0.782657	+	0.622454i	$0.213864\pi$
$294$	−4.49804	−	7.28377i	−0.262331	−	0.424798i
$295$		0			0
$296$	−1.99643	+	18.9948i	−0.116040	+	1.10405i
$297$	−4.12945	−	1.58515i	−0.239615	−	0.0919795i
$298$	−0.551727	+	10.5276i	−0.0319607	+	0.609846i
$299$	1.67366	+	2.89886i	0.0967902	+	0.167646i
$300$		0			0
$301$	−4.93259	+	4.57540i	−0.284310	+	0.263722i
$302$	−4.66195	−	9.14958i	−0.268265	−	0.526499i
$303$	−6.48835	+	5.25416i	−0.372746	+	0.301844i
$304$	0.685735	−	0.305309i	0.0393296	−	0.0175107i
$305$		0			0
$306$	3.51341	−	7.89125i	0.200848	−	0.451113i
$307$	19.7851	+	19.7851i	1.12920	+	1.12920i	0.990308	+	0.138889i	$0.0443532\pi$
$307$	19.7851	+	19.7851i	1.12920	+	1.12920i	0.138889	+	0.990308i	$0.455647\pi$
$308$	2.13606	+	1.04882i	0.121713	+	0.0597622i
$309$	12.4397	−	4.04190i	0.707669	−	0.229935i
$310$		0			0
$311$	15.7376	−	14.1702i	0.892396	−	0.803517i	−0.0888962	−	0.996041i	$-0.528334\pi$
$311$	15.7376	−	14.1702i	0.892396	−	0.803517i	0.981292	+	0.192524i	$0.0616673\pi$
$312$	2.64026	−	1.71460i	0.149475	−	0.0970703i
$313$	0.251501	+	4.79892i	0.0142157	+	0.271251i	0.996485	+	0.0837745i	$0.0266975\pi$
$313$	0.251501	+	4.79892i	0.0142157	+	0.271251i	−0.982269	+	0.187477i	$0.939969\pi$
$314$	−4.76941	+	14.6787i	−0.269153	+	0.828369i
$315$		0			0
$316$	−1.72754	−	5.31683i	−0.0971818	−	0.299095i
$317$	−27.7417	+	10.6491i	−1.55813	+	0.598110i	−0.976533	−	0.215366i	$-0.930905\pi$
$317$	−27.7417	+	10.6491i	−1.55813	+	0.598110i	−0.581598	+	0.813477i	$0.697572\pi$
$318$	2.84814	+	10.6294i	0.159716	+	0.596068i
$319$	7.32827	−	0.770232i	0.410304	−	0.0431247i
$320$		0			0
$321$	−4.22663	+	5.81746i	−0.235908	+	0.324699i
$322$	3.72536	+	9.29121i	0.207606	+	0.517779i
$323$	−12.1940	+	6.21317i	−0.678495	+	0.345710i
$324$	3.62308	−	2.09178i	0.201282	−	0.116210i
$325$		0			0
$326$	−9.52165	+	16.4920i	−0.527355	+	0.913406i
$327$	−18.1648	−	11.7964i	−1.00452	−	0.652340i
$328$	7.28234	−	1.15341i	0.402100	−	0.0636864i
$329$	−18.2800	−	24.3923i	−1.00781	−	1.34479i
$330$		0			0
$331$	21.0153	+	9.35662i	1.15511	+	0.514286i	0.892691	−	0.450669i	$-0.148815\pi$
$331$	21.0153	+	9.35662i	1.15511	+	0.514286i	0.262415	+	0.964955i	$0.415481\pi$
$332$	−5.74610	+	1.53966i	−0.315358	+	0.0845000i
$333$	5.18405	−	6.40177i	0.284084	−	0.350815i
$334$	−2.93015	+	3.25426i	−0.160331	+	0.178065i
$335$		0			0
$336$	1.29335	−	0.598940i	0.0705578	−	0.0326749i
$337$	−4.75641	−	2.42351i	−0.259098	−	0.132017i	0.319617	−	0.947547i	$-0.396446\pi$
$337$	−4.75641	−	2.42351i	−0.259098	−	0.132017i	−0.578715	+	0.815530i	$0.696446\pi$
$338$	11.3984	−	0.597364i	0.619991	−	0.0324923i
$339$	8.29724	+	9.21502i	0.450644	+	0.500491i
$340$		0			0
$341$	−2.76113	−	2.48613i	−0.149524	−	0.134632i
$342$	−2.11213	−	0.334529i	−0.114211	−	0.0180893i
$343$	2.08188	−	18.4029i	0.112411	−	0.993662i
$344$	−4.34902	−	5.98591i	−0.234484	−	0.322739i
$345$		0			0
$346$	1.90050	+	4.26859i	0.102171	+	0.229481i
$347$	6.16865	−	16.0699i	0.331151	−	0.862677i	−0.662386	−	0.749163i	$-0.730456\pi$
$347$	6.16865	−	16.0699i	0.331151	−	0.862677i	0.993536	−	0.113514i	$-0.0362107\pi$
$348$	−7.69989	+	11.8568i	−0.412758	+	0.635591i
$349$	−20.0775			−1.07472			−0.537362	−	0.843351i	$-0.680579\pi$
$349$	−20.0775			−1.07472			−0.537362	+	0.843351i	$0.680579\pi$
$350$		0			0
$351$	−4.60369			−0.245727
$352$	−2.33234	+	3.59148i	−0.124314	+	0.191427i
$353$	4.61726	−	12.0284i	0.245752	−	0.640206i	−0.754111	−	0.656747i	$-0.771932\pi$
$353$	4.61726	−	12.0284i	0.245752	−	0.640206i	0.999863	+	0.0165408i	$0.00526535\pi$
$354$	5.67002	+	12.7351i	0.301358	+	0.676861i
$355$		0			0
$356$	−0.388449	−	0.534654i	−0.0205878	−	0.0283366i
$357$	−22.9768	+	12.1392i	−1.21606	+	0.642473i
$358$	−3.30079	−	0.522794i	−0.174452	−	0.0276305i
$359$	5.74355	+	5.17152i	0.303133	+	0.272942i	0.806633	−	0.591053i	$-0.201288\pi$
$359$	5.74355	+	5.17152i	0.303133	+	0.272942i	−0.503499	+	0.863996i	$0.667954\pi$
$360$		0			0
$361$	−10.4464	−	11.6019i	−0.549812	−	0.610628i
$362$	11.4731	−	0.601280i	0.603013	−	0.0316026i
$363$	−12.2184	−	6.22559i	−0.641300	−	0.326759i
$364$	2.46673	+	0.222382i	0.129292	+	0.0116560i
$365$		0			0
$366$	−6.91848	+	7.68375i	−0.361635	+	0.401636i
$367$	−2.08207	+	2.57114i	−0.108683	+	0.134212i	−0.828585	−	0.559864i	$-0.810854\pi$
$367$	−2.08207	+	2.57114i	−0.108683	+	0.134212i	0.719902	+	0.694076i	$0.244187\pi$
$368$	−1.60984	+	0.431357i	−0.0839189	+	0.0224860i
$369$	−2.90509	−	1.29343i	−0.151233	−	0.0673333i
$370$		0			0
$371$	−9.35999	+	21.8897i	−0.485946	+	1.13646i
$372$	7.04080	−	1.11515i	0.365049	−	0.0578180i
$373$	3.18580	+	2.06888i	0.164955	+	0.107123i	0.624476	−	0.781044i	$-0.285312\pi$
$373$	3.18580	+	2.06888i	0.164955	+	0.107123i	−0.459522	+	0.888167i	$0.651979\pi$
$374$	−2.70837	+	4.69103i	−0.140046	+	0.242567i
$375$		0			0
$376$	29.0312	−	16.7612i	1.49717	−	0.864391i
$377$	6.83335	−	3.48176i	0.351935	−	0.179320i
$378$	−13.6283	−	1.95209i	−0.700966	−	0.100404i
$379$	−17.8775	+	24.6063i	−0.918306	+	1.26394i	0.0459436	+	0.998944i	$0.485371\pi$
$379$	−17.8775	+	24.6063i	−0.918306	+	1.26394i	−0.964250	+	0.264996i	$0.914629\pi$
$380$		0			0
$381$	−3.83201	+	0.402760i	−0.196320	+	0.0206340i
$382$	5.55820	+	20.7435i	0.284382	+	1.06133i
$383$	−18.9792	+	7.28545i	−0.969794	+	0.372269i	−0.791135	−	0.611642i	$-0.790509\pi$
$383$	−18.9792	+	7.28545i	−0.969794	+	0.372269i	−0.178659	+	0.983911i	$0.557176\pi$
$384$	−2.23072	−	6.86544i	−0.113836	−	0.350350i
$385$		0			0
$386$	−4.27576	+	13.1594i	−0.217630	+	0.669797i
$387$	0.167013	+	3.18681i	0.00848977	+	0.161994i
$388$	−10.2625	+	6.66457i	−0.521001	+	0.338342i
$389$	8.29482	−	7.46869i	0.420564	−	0.378678i	−0.431502	−	0.902112i	$-0.642016\pi$
$389$	8.29482	−	7.46869i	0.420564	−	0.378678i	0.852066	+	0.523434i	$0.175350\pi$
$390$		0			0
$391$	28.8993	−	9.38994i	1.46150	−	0.474870i
$392$	19.8211	+	4.68655i	1.00112	+	0.236707i
$393$	6.28817	+	6.28817i	0.317196	+	0.317196i
$394$	0.567703	−	1.27508i	0.0286005	−	0.0642377i
$395$		0			0
$396$	1.03113	−	0.459091i	0.0518165	−	0.0230702i
$397$	−8.87732	+	7.18871i	−0.445540	+	0.360791i	−0.825681	−	0.564138i	$-0.809209\pi$
$397$	−8.87732	+	7.18871i	−0.445540	+	0.360791i	0.380141	+	0.924929i	$0.375875\pi$
$398$	1.47500	+	2.89484i	0.0739348	+	0.145105i
$399$	4.37503	+	4.71657i	0.219025	+	0.236124i
$400$		0			0
$401$	14.5815	+	25.2559i	0.728165	+	1.26122i	0.957658	+	0.287908i	$0.0929597\pi$
$401$	14.5815	+	25.2559i	0.728165	+	1.26122i	−0.229493	+	0.973310i	$0.573707\pi$
$402$	0.0584530	−	1.11535i	0.00291537	−	0.0556285i
$403$	−3.61020	−	1.38582i	−0.179837	−	0.0690328i
$404$	0.755064	−	7.18396i	0.0375659	−	0.357415i
$405$		0			0
$406$	21.7052	−	7.40958i	1.07721	−	0.367731i
$407$	−3.65262	+	3.65262i	−0.181054	+	0.181054i
$408$	−10.2416	−	26.6803i	−0.507034	−	1.32087i
$409$	−31.5725	−	6.71095i	−1.56116	−	0.331835i	−0.655287	−	0.755380i	$-0.727452\pi$
$409$	−31.5725	−	6.71095i	−1.56116	−	0.331835i	−0.905875	+	0.423545i	$0.860786\pi$
$410$		0			0
$411$	−5.34941	−	25.1670i	−0.263867	−	1.24140i
$412$	−5.13768	+	10.0833i	−0.253115	+	0.496767i
$413$	−7.37330	+	29.2432i	−0.362816	+	1.43896i
$414$	4.51566	+	1.46723i	0.221933	+	0.0721103i
$415$		0			0
$416$	−0.926673	+	4.35966i	−0.0454339	+	0.213750i
$417$	−1.05398	−	0.853493i	−0.0516134	−	0.0417957i
$418$	1.29529	+	0.347072i	0.0633547	+	0.0169758i
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.983233	−	0.182351i	$-0.941629\pi$
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.130410	+	0.991460i	$0.541629\pi$
$420$		0			0
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	−11.6281	−	14.3595i	−0.566047	−	0.699009i
$423$	−14.4383	−	0.756681i	−0.702015	−	0.0367911i
$424$	−22.6739	−	13.0908i	−1.10114	−	0.635744i
$425$		0			0
$426$			1.15989i			0.0561967i
$427$	−22.0389	+	3.82601i	−1.06654	+	0.185154i
$428$	−0.973254	−	6.14488i	−0.0470440	−	0.297024i
$429$	0.846777	+	0.0889999i	0.0408828	+	0.00429695i
$430$		0			0
$431$	−0.259952	−	2.47328i	−0.0125215	−	0.119134i	0.986476	−	0.163908i	$-0.0524099\pi$
$431$	−0.259952	−	2.47328i	−0.0125215	−	0.119134i	−0.998997	+	0.0447740i	$0.985743\pi$
$432$	0.593260	−	2.21408i	0.0285432	−	0.106525i
$433$	−1.44743	+	9.13869i	−0.0695589	+	0.439178i	0.928189	+	0.372108i	$0.121365\pi$
$433$	−1.44743	+	9.13869i	−0.0695589	+	0.439178i	−0.997748	+	0.0670695i	$0.978635\pi$
$434$	−10.0997	−	5.63329i	−0.484800	−	0.270406i
$435$		0			0
$436$	18.3299	−	3.89615i	0.877845	−	0.186592i
$437$	−4.09709	−	6.30896i	−0.195990	−	0.301798i
$438$	2.47180	+	3.80625i	0.118107	+	0.181869i
$439$	−20.7692	+	4.41462i	−0.991258	+	0.210698i	−0.674874	−	0.737933i	$-0.735802\pi$
$439$	−20.7692	+	4.41462i	−0.991258	+	0.210698i	−0.316384	+	0.948631i	$0.602469\pi$
$440$		0			0
$441$	−6.06875	−	6.35122i	−0.288988	−	0.302439i
$442$	−0.881932	+	5.56830i	−0.0419492	+	0.264857i
$443$	−5.90047	+	22.0209i	−0.280340	+	1.04624i	0.671838	+	0.740698i	$0.265505\pi$
$443$	−5.90047	+	22.0209i	−0.280340	+	1.04624i	−0.952178	+	0.305545i	$0.901161\pi$
$444$	−1.03596	−	9.85649i	−0.0491644	−	0.467768i
$445$		0			0
$446$	−8.06292	−	0.847447i	−0.381790	−	0.0401278i
$447$	−2.35319	−	14.8575i	−0.111302	−	0.702734i
$448$	−5.33525	+	14.5388i	−0.252067	+	0.686893i
$449$			32.5816i			1.53762i	0.639478	+	0.768809i	$0.279150\pi$
$449$			32.5816i			1.53762i	−0.639478	+	0.768809i	$0.720850\pi$
$450$		0			0
$451$	1.72696	+	0.997060i	0.0813193	+	0.0469497i
$452$	−10.7138	−	0.561488i	−0.503936	−	0.0264102i
$453$	9.22132	+	11.3874i	0.433256	+	0.535026i
$454$	−7.03338	−	5.11005i	−0.330093	−	0.239827i
$455$		0			0
$456$	−5.72376	+	4.15856i	−0.268040	+	0.194742i
$457$	7.80380	+	2.09102i	0.365046	+	0.0978138i	0.436679	−	0.899617i	$-0.356154\pi$
$457$	7.80380	+	2.09102i	0.365046	+	0.0978138i	−0.0716332	+	0.997431i	$0.522821\pi$
$458$	−6.18872	−	5.01153i	−0.289180	−	0.234173i
$459$	−8.68897	+	40.8784i	−0.405566	+	1.90804i
$460$		0			0
$461$	−36.2181	−	11.7680i	−1.68684	−	0.548089i	−0.700625	−	0.713530i	$-0.747095\pi$
$461$	−36.2181	−	11.7680i	−1.68684	−	0.548089i	−0.986220	+	0.165441i	$0.947095\pi$
$462$	2.46898	+	0.622523i	0.114868	+	0.0289624i
$463$	−16.6944	+	32.7647i	−0.775856	+	1.52270i	0.0749286	+	0.997189i	$0.476127\pi$
$463$	−16.6944	+	32.7647i	−0.775856	+	1.52270i	−0.850785	+	0.525514i	$0.823873\pi$
$464$	0.793916	+	3.73508i	0.0368566	+	0.173397i
$465$		0			0
$466$	2.52254	+	0.536183i	0.116855	+	0.0248382i
$467$	7.46192	+	19.4390i	0.345297	+	0.899528i	0.990746	+	0.135726i	$0.0433366\pi$
$467$	7.46192	+	19.4390i	0.345297	+	0.899528i	−0.645450	+	0.763803i	$0.723330\pi$
$468$	0.830684	−	0.830684i	0.0383984	−	0.0383984i
$469$	1.59002	−	1.81938i	0.0734205	−	0.0840111i
$470$		0			0
$471$	2.30207	−	21.9027i	0.106074	−	1.00922i
$472$	−30.9637	−	11.8858i	−1.42522	−	0.547091i
$473$	0.104730	−	1.99838i	0.00481551	−	0.0918854i
$474$	−2.99091	−	5.18041i	−0.137377	−	0.237944i
$475$		0			0
$476$	6.63034	−	21.4836i	0.303901	−	0.984699i
$477$	5.12650	+	10.0613i	0.234726	+	0.460676i
$478$	−7.74368	+	6.27071i	−0.354188	+	0.286816i
$479$	1.27864	−	0.569287i	0.0584226	−	0.0260114i	−0.377317	−	0.926084i	$-0.623153\pi$
$479$	1.27864	−	0.569287i	0.0584226	−	0.0260114i	0.435740	+	0.900073i	$0.356487\pi$
$480$		0			0
$481$	−2.18674	+	4.91151i	−0.0997069	+	0.223945i
$482$	−6.90821	−	6.90821i	−0.314660	−	0.314660i
$483$	−7.95610	−	11.8629i	−0.362015	−	0.539782i
$484$	11.2839	−	3.66635i	0.512903	−	0.166652i
$485$		0			0
$486$	−8.27443	+	7.45033i	−0.375336	+	0.337954i
$487$	−22.3089	+	14.4876i	−1.01091	+	0.656494i	−0.940066	−	0.340994i	$-0.889237\pi$
$487$	−22.3089	+	14.4876i	−1.01091	+	0.656494i	−0.0708461	+	0.997487i	$0.522570\pi$
$488$	−1.28745	−	24.5660i	−0.0582801	−	1.11205i
$489$	8.39703	−	25.8434i	0.379727	−	1.16868i
$490$		0			0
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	−3.57184	+	1.37110i	−0.161031	+	0.0618140i
$493$	−18.0191	−	67.2481i	−0.811538	−	3.02870i
$494$	1.38804	−	0.145889i	0.0624510	−	0.00656386i
$495$		0			0
$496$	1.13172	−	1.55769i	0.0508159	−	0.0699421i
$497$	−1.55010	+	1.97327i	−0.0695315	+	0.0885131i
$498$	−5.67150	+	2.88977i	−0.254146	+	0.129494i
$499$	20.4454	−	11.8042i	0.915262	−	0.528427i	0.0331413	−	0.999451i	$-0.489449\pi$
$499$	20.4454	−	11.8042i	0.915262	−	0.528427i	0.882120	+	0.471024i	$0.156116\pi$
$500$		0			0
$501$	3.12428	−	5.41141i	0.139582	−	0.241764i
$502$	22.5641	+	14.6533i	1.00708	+	0.654008i
$503$	3.25409	−	0.515396i	0.145092	−	0.0229804i	−0.0834657	−	0.996511i	$-0.526599\pi$
$503$	3.25409	−	0.515396i	0.145092	−	0.0229804i	0.228558	+	0.973530i	$0.426599\pi$
$504$	7.73075	−	5.79357i	0.344355	−	0.258066i
$505$		0			0
$506$	−2.71999	−	1.21102i	−0.120918	−	0.0538363i
$507$	−15.7320	+	4.21538i	−0.698682	+	0.187211i
$508$	2.09798	−	2.59079i	0.0930828	−	0.114948i
$509$	9.35937	−	10.3946i	0.414847	−	0.460734i	−0.499114	−	0.866536i	$-0.666341\pi$
$509$	9.35937	−	10.3946i	0.414847	−	0.460734i	0.913961	+	0.405802i	$0.133008\pi$
$510$		0			0
$511$	−0.881584	+	9.77879i	−0.0389990	+	0.432588i
$512$	−4.09177	−	2.08486i	−0.180832	−	0.0921387i
$513$	10.3319	−	0.541471i	0.456164	−	0.0239065i
$514$	11.5323	+	12.8079i	0.508668	+	0.564933i
$515$		0			0
$516$	2.85322	+	2.56905i	0.125606	+	0.113096i
$517$	8.95476	+	1.41829i	0.393830	+	0.0623765i
$518$	−8.55605	+	13.6123i	−0.375931	+	0.598092i
$519$	−3.91899	−	5.39402i	−0.172024	−	0.236771i
$520$		0			0
$521$	11.5536	+	25.9498i	0.506172	+	1.13688i	0.968237	+	0.250035i	$0.0804421\pi$
$521$	11.5536	+	25.9498i	0.506172	+	1.13688i	−0.462065	+	0.886846i	$0.652891\pi$
$522$	3.89852	−	10.1560i	0.170634	−	0.444516i
$523$	21.6259	−	33.3009i	0.945633	−	1.45615i	0.0565510	−	0.998400i	$-0.481990\pi$
$523$	21.6259	−	33.3009i	0.945633	−	1.45615i	0.889082	−	0.457748i	$-0.151344\pi$
$524$	−7.69409			−0.336118
$525$		0			0
$526$	19.1787			0.836229
$527$	−19.1193	+	29.4411i	−0.832848	+	1.28247i
$528$	−0.151924	+	0.395776i	−0.00661165	+	0.0172239i
$529$	−2.56144	−	5.75310i	−0.111367	−	0.250135i
$530$		0			0
$531$	8.40811	+	11.5728i	0.364881	+	0.502215i
$532$	−5.56215	−	0.208955i	−0.241150	−	0.00905937i
$533$	2.04992	+	0.324675i	0.0887918	+	0.0140632i
$534$	−0.525505	−	0.473167i	−0.0227408	−	0.0204759i
$535$		0			0
$536$	1.77806	+	1.97474i	0.0768006	+	0.0852958i
$537$	4.76216	−	0.249574i	0.205502	−	0.0107699i
$538$	1.05926	+	0.539718i	0.0456677	+	0.0232689i
$539$	3.36843	+	4.35869i	0.145088	+	0.187742i
$540$		0			0
$541$	−0.882148	+	0.979725i	−0.0379265	+	0.0421217i	−0.761810	−	0.647801i	$-0.775689\pi$
$541$	−0.882148	+	0.979725i	−0.0379265	+	0.0421217i	0.723883	+	0.689923i	$0.242355\pi$
$542$	−7.22928	+	8.92742i	−0.310524	+	0.383465i
$543$	−15.8351	+	4.24301i	−0.679550	+	0.182085i
$544$	36.9625	+	16.4568i	1.58475	+	0.705578i
$545$		0			0
$546$	2.63122	−	0.316016i	0.112606	−	0.0135243i
$547$	21.4047	−	3.39018i	0.915200	−	0.144953i	0.318968	−	0.947766i	$-0.396664\pi$
$547$	21.4047	−	3.39018i	0.915200	−	0.144953i	0.596232	+	0.802812i	$0.296664\pi$
$548$	18.6696	+	12.1242i	0.797528	+	0.517920i
$549$	−5.30491	+	9.18838i	−0.226408	+	0.392150i
$550$		0			0
$551$	−14.9263	+	8.61771i	−0.635882	+	0.367127i
$552$	13.9965	−	7.13156i	0.595730	−	0.303539i
$553$	1.83492	−	12.8104i	0.0780287	−	0.544752i
$554$	0.669337	−	0.921263i	0.0284374	−	0.0391407i
$555$		0			0
$556$	1.16697	−	0.122654i	0.0494906	−	0.00520167i
$557$	−2.91942	−	10.8954i	−0.123700	−	0.461654i	0.876090	−	0.482147i	$-0.160143\pi$
$557$	−2.91942	−	10.8954i	−0.123700	−	0.461654i	−0.999790	+	0.0204931i	$0.993476\pi$
$558$	−5.12093	+	1.96574i	−0.216786	+	0.0832165i
$559$	−0.643607	−	1.98082i	−0.0272217	−	0.0837797i
$560$		0			0
$561$	2.38847	−	7.35097i	0.100841	−	0.310358i
$562$	0.0853991	+	1.62951i	0.00360234	+	0.0687368i
$563$	4.15112	−	2.69577i	0.174949	−	0.113613i	−0.454194	−	0.890903i	$-0.650073\pi$
$563$	4.15112	−	2.69577i	0.174949	−	0.113613i	0.629143	+	0.777290i	$0.283406\pi$
$564$	−12.9270	+	11.6395i	−0.544323	+	0.490111i
$565$		0			0
$566$	−13.2754	+	4.31344i	−0.558007	+	0.181307i
$567$	9.66255	−	0.650012i	0.405789	−	0.0272979i
$568$	−1.95133	−	1.95133i	−0.0818759	−	0.0818759i
$569$	−6.87878	+	15.4500i	−0.288373	+	0.647697i	−0.998404	−	0.0564736i	$-0.982014\pi$
$569$	−6.87878	+	15.4500i	−0.288373	+	0.647697i	0.710031	+	0.704171i	$0.248681\pi$
$570$		0			0
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.224836	−	0.974397i	$-0.427815\pi$
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.874562	+	0.484913i	$0.161149\pi$
$572$	−0.572499	+	0.463601i	−0.0239374	+	0.0193841i
$573$	−13.9119	−	27.3036i	−0.581177	−	1.14062i
$574$	5.93072	+	1.83036i	0.247544	+	0.0763977i
$575$		0			0
$576$	3.67285	+	6.36156i	0.153035	+	0.265065i
$577$	0.543104	−	10.3630i	0.0226097	−	0.431419i	−0.963749	−	0.266810i	$-0.914030\pi$
$577$	0.543104	−	10.3630i	0.0226097	−	0.431419i	0.986359	−	0.164609i	$-0.0526362\pi$
$578$	33.0863	+	12.7006i	1.37621	+	0.528276i
$579$	2.06379	−	19.6357i	0.0857683	−	0.816031i
$580$		0			0
$581$	−13.5107	−	2.66328i	−0.560517	−	0.110492i
$582$	−9.25840	+	9.25840i	−0.383773	+	0.383773i
$583$	−2.53761	−	6.61070i	−0.105097	−	0.273787i
$584$	−10.5618	−	2.24499i	−0.437052	−	0.0928983i
$585$		0			0
$586$	0.746455	+	3.51180i	0.0308358	+	0.145071i
$587$	2.08337	−	4.08885i	0.0859899	−	0.168765i	−0.844007	−	0.536332i	$-0.819809\pi$
$587$	2.08337	−	4.08885i	0.0859899	−	0.168765i	0.929997	+	0.367568i	$0.119809\pi$
$588$	−10.5661	−	0.240310i	−0.435740	−	0.00991023i
$589$	8.26522	+	2.68553i	0.340563	+	0.110655i
$590$		0			0
$591$	−0.414084	+	1.94811i	−0.0170331	+	0.0801345i
$592$	−2.08032	−	1.68461i	−0.0855007	−	0.0692371i
$593$	14.8803	+	3.98715i	0.611059	+	0.163733i	0.551060	−	0.834466i	$-0.314224\pi$
$593$	14.8803	+	3.98715i	0.611059	+	0.163733i	0.0599990	+	0.998198i	$0.480890\pi$
$594$	3.31286	−	2.40693i	0.135928	−	0.0987577i
$595$		0			0
$596$	10.5293	+	7.65000i	0.431298	+	0.313356i
$597$	−2.91754	−	3.60286i	−0.119407	−	0.147455i
$598$	−3.09462	−	0.162182i	−0.126548	−	0.00663211i
$599$	13.4466	+	7.76339i	0.549413	+	0.317204i	0.748885	−	0.662700i	$-0.230589\pi$
$599$	13.4466	+	7.76339i	0.549413	+	0.317204i	−0.199472	+	0.979903i	$0.563923\pi$
$600$		0			0
$601$			41.2449i			1.68241i	0.540714	+	0.841207i	$0.318154\pi$
$601$			41.2449i			1.68241i	−0.540714	+	0.841207i	$0.681846\pi$
$602$	−1.06536	−	6.13674i	−0.0434207	−	0.250115i
$603$	−0.179286	−	1.13197i	−0.00730110	−	0.0460974i
$604$	−12.6082	−	1.32518i	−0.513021	−	0.0539207i
$605$		0			0
$606$	−0.807926	−	7.68690i	−0.0328198	−	0.312259i
$607$	2.89077	−	10.7885i	0.117333	−	0.437891i	−0.882118	−	0.471028i	$-0.843883\pi$
$607$	2.89077	−	10.7885i	0.117333	−	0.437891i	0.999451	+	0.0331368i	$0.0105497\pi$
$608$	1.56693	−	9.89320i	0.0635474	−	0.401222i
$609$	−28.0966	+	16.7812i	−1.13853	+	0.680010i
$610$		0			0
$611$	9.23005	−	1.96191i	0.373408	−	0.0793703i
$612$	−5.80822	−	8.94388i	−0.234783	−	0.361535i
$613$	−1.68999	−	2.60236i	−0.0682580	−	0.105108i	0.802893	−	0.596123i	$-0.203293\pi$
$613$	−1.68999	−	2.60236i	−0.0682580	−	0.105108i	−0.871151	+	0.491015i	$0.836626\pi$
$614$	−25.3375	+	5.38565i	−1.02254	+	0.217347i
$615$		0			0
$616$	−5.20098	+	3.10638i	−0.209554	+	0.125160i
$617$	7.16450	−	45.2349i	0.288432	−	1.82109i	−0.238456	−	0.971153i	$-0.576641\pi$
$617$	7.16450	−	45.2349i	0.288432	−	1.82109i	0.526888	−	0.849935i	$-0.323359\pi$
$618$	−3.13404	+	11.6964i	−0.126070	+	0.470498i
$619$	1.86817	+	17.7745i	0.0750883	+	0.714417i	0.965701	+	0.259655i	$0.0836090\pi$
$619$	1.86817	+	17.7745i	0.0750883	+	0.714417i	−0.890613	+	0.454762i	$0.849724\pi$
$620$		0			0
$621$	−22.8456	−	2.40117i	−0.916764	−	0.0963558i
$622$	3.06692	+	19.3638i	0.122972	+	0.776416i
$623$	−0.261668	−	1.50728i	−0.0104835	−	0.0603878i
$624$			0.441228i			0.0176633i
$625$		0			0
$626$	−3.85279	−	2.22441i	−0.153988	−	0.0889052i
$627$	−1.91086	−	0.100144i	−0.0763123	−	0.00399936i
$628$	11.9915	+	14.8082i	0.478512	+	0.590913i
$629$	39.4844	+	28.6871i	1.57435	+	1.14383i
$630$		0			0
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	13.7470	+	3.68350i	0.546826	+	0.146522i
$633$	20.4899	+	16.5924i	0.814401	+	0.659489i
$634$	5.71961	−	26.9086i	0.227155	−	1.06868i
$635$		0			0
$636$	12.9208	+	4.19823i	0.512344	+	0.166471i
$637$	4.89872	+	2.97881i	0.194094	+	0.118025i
$638$	−3.09699	+	6.07818i	−0.122611	+	0.240637i
$639$	0.247459	+	1.16420i	0.00978931	+	0.0460551i
$640$		0			0
$641$	22.8779	+	4.86285i	0.903622	+	0.192071i	0.636214	−	0.771513i	$-0.280499\pi$
$641$	22.8779	+	4.86285i	0.903622	+	0.192071i	0.267408	+	0.963583i	$0.413833\pi$
$642$	−2.38567	−	6.21488i	−0.0941549	−	0.245282i
$643$	−20.9354	+	20.9354i	−0.825611	+	0.825611i	−0.986906	−	0.161295i	$-0.948433\pi$
$643$	−20.9354	+	20.9354i	−0.825611	+	0.825611i	0.161295	+	0.986906i	$0.448433\pi$
$644$	12.1251	+	2.39015i	0.477795	+	0.0941853i
$645$		0			0
$646$	1.32436	−	12.6005i	0.0521063	−	0.495758i
$647$	18.2066	+	6.98885i	0.715775	+	0.274760i	0.688877	−	0.724878i	$-0.258104\pi$
$647$	18.2066	+	6.98885i	0.715775	+	0.274760i	0.0268974	+	0.999638i	$0.491437\pi$
$648$	−0.557397	+	10.6358i	−0.0218966	+	0.417813i
$649$	−4.48509	−	7.76840i	−0.176055	−	0.304936i
$650$		0			0
$651$	15.7678	+	4.86631i	0.617989	+	0.190726i
$652$	10.6735	+	20.9480i	0.418007	+	0.820385i
$653$	−2.45523	+	1.98821i	−0.0960807	+	0.0778046i	−0.676157	−	0.736757i	$-0.736356\pi$
$653$	−2.45523	+	1.98821i	−0.0960807	+	0.0778046i	0.580077	+	0.814562i	$0.303023\pi$
$654$	18.3179	−	8.15563i	0.716285	−	0.318911i
$655$		0			0
$656$	−0.420313	+	0.944039i	−0.0164105	+	0.0368585i
$657$	3.29305	+	3.29305i	0.128474	+	0.128474i
$658$	28.1557	−	1.89407i	1.09762	−	0.0738385i
$659$	−13.3517	+	4.33824i	−0.520110	+	0.168994i	−0.557295	−	0.830314i	$-0.688161\pi$
$659$	−13.3517	+	4.33824i	−0.520110	+	0.168994i	0.0371852	+	0.999308i	$0.488161\pi$
$660$		0			0
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	−0.832442	−	0.554113i	$-0.813058\pi$
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	0.464063	+	0.885802i	$0.346391\pi$
$662$	−17.8609	+	11.5990i	−0.694182	+	0.450807i
$663$	−0.421021	−	8.03356i	−0.0163511	−	0.311998i
$664$	4.67982	−	14.4030i	0.181612	−	0.558945i
$665$		0			0
$666$	2.35660	+	7.25286i	0.0913163	+	0.281043i
$667$	35.7263	−	13.7140i	1.38333	−	0.531009i
$668$	1.39924	+	5.22205i	0.0541384	+	0.202047i
$669$	11.5052	−	1.20924i	0.444816	−	0.0467520i
$670$		0			0
$671$	3.91065	−	5.38254i	0.150969	−	0.207791i
$672$	2.69676	−	18.8272i	0.104030	−	0.726275i
$673$	29.3231	−	14.9409i	1.13032	−	0.575928i	0.214185	−	0.976793i	$-0.431290\pi$
$673$	29.3231	−	14.9409i	1.13032	−	0.575928i	0.916137	+	0.400865i	$0.131290\pi$
$674$	4.27990	−	2.47100i	0.164856	−	0.0951795i
$675$		0			0
$676$	7.04576	−	12.2036i	0.270991	−	0.469370i
$677$	4.87849	+	3.16813i	0.187496	+	0.121761i	0.634973	−	0.772534i	$-0.281011\pi$
$677$	4.87849	+	3.16813i	0.187496	+	0.121761i	−0.447478	+	0.894295i	$0.647678\pi$
$678$	−11.3383	+	1.79581i	−0.435445	+	0.0689677i
$679$	−28.1241	+	3.37777i	−1.07930	+	0.129627i
$680$		0			0
$681$	11.3328	+	5.04569i	0.434274	+	0.193351i
$682$	3.32248	−	0.890256i	0.127224	−	0.0340897i
$683$	−11.1104	+	13.7202i	−0.425127	+	0.524989i	−0.944037	−	0.329841i	$-0.893005\pi$
$683$	−11.1104	+	13.7202i	−0.425127	+	0.524989i	0.518909	+	0.854829i	$0.326338\pi$
$684$	−1.76657	+	1.96198i	−0.0675465	+	0.0750180i
$685$		0			0
$686$	13.2386	+	10.8954i	0.505454	+	0.415988i
$687$	10.1247	+	5.15877i	0.386280	+	0.196819i
$688$	1.03558	−	0.0542727i	0.0394813	−	0.00206913i
$689$	−4.93142	−	5.47689i	−0.187872	−	0.208653i
$690$		0			0
$691$	25.8993	+	23.3198i	0.985254	+	0.887127i	0.993613	−	0.112838i	$-0.0359942\pi$
$691$	25.8993	+	23.3198i	0.985254	+	0.887127i	−0.00835918	+	0.999965i	$0.502661\pi$
$692$	5.69761	+	0.902413i	0.216591	+	0.0343046i
$693$	2.61098	+	0.0980878i	0.0991831	+	0.00372605i
$694$	9.36667	+	12.8921i	0.355554	+	0.489378i
$695$		0			0
$696$	−14.6388	−	32.8794i	−0.554884	−	1.24629i
$697$	6.75195	−	17.5894i	0.255748	−	0.666247i
$698$	10.1233	−	15.5886i	0.383174	−	0.590037i
$699$	−3.67989			−0.139186
$700$		0			0
$701$	−5.86630			−0.221567			−0.110783	−	0.993845i	$-0.535336\pi$
$701$	−5.86630			−0.221567			−0.110783	+	0.993845i	$0.535336\pi$
$702$	2.32124	−	3.57439i	0.0876095	−	0.134907i
$703$	4.32995	−	11.2799i	0.163307	−	0.425430i
$704$	−1.87356	−	4.20809i	−0.0706125	−	0.158598i
$705$		0			0
$706$	7.01099	+	9.64980i	0.263862	+	0.363175i
$707$	8.89848	−	14.1571i	0.334662	−	0.532434i
$708$	16.9985	+	2.69229i	0.638841	+	0.101183i
$709$	7.00111	+	6.30382i	0.262932	+	0.236745i	0.790043	−	0.613051i	$-0.210058\pi$
$709$	7.00111	+	6.30382i	0.262932	+	0.236745i	−0.527111	+	0.849796i	$0.676725\pi$
$710$		0			0
$711$	−4.10727	−	4.56158i	−0.154035	−	0.171073i
$712$	1.68011	−	0.0880508i	0.0629648	−	0.00329984i
$713$	−17.1927	−	8.76010i	−0.643870	−	0.328068i
$714$	2.16009	−	23.9604i	0.0808393	−	0.896694i
$715$		0			0
$716$	−2.76075	+	3.06613i	−0.103174	+	0.114587i
$717$	8.94783	−	11.0496i	0.334163	−	0.412657i
$718$	−6.91124	+	1.85186i	−0.257925	+	0.0691109i
$719$	38.4705	+	17.1281i	1.43471	+	0.638772i	0.969201	−	0.246273i	$-0.0792059\pi$
$719$	38.4705	+	17.1281i	1.43471	+	0.638772i	0.465505	+	0.885045i	$0.345873\pi$
$720$		0			0
$721$	−20.9632	+	15.7102i	−0.780709	+	0.585078i
$722$	14.2752	−	2.26097i	0.531267	−	0.0841445i
$723$	11.6916	+	7.59259i	0.434814	+	0.282372i
$724$	7.09194	−	12.2836i	0.263570	−	0.456517i
$725$		0			0
$726$	10.9944	−	6.34760i	0.408039	−	0.235581i
$727$	−11.3062	+	5.76081i	−0.419325	+	0.213657i	−0.650905	−	0.759159i	$-0.725610\pi$
$727$	−11.3062	+	5.76081i	−0.419325	+	0.213657i	0.231580	+	0.972816i	$0.425610\pi$
$728$	−3.89498	+	4.95827i	−0.144357	+	0.183766i
$729$	15.7932	−	21.7374i	0.584932	−	0.805090i
$730$		0			0
$731$	−18.8034	+	1.97632i	−0.695469	+	0.0730967i
$732$	3.30381	+	12.3300i	0.122112	+	0.455729i
$733$	−44.0331	+	16.9027i	−1.62640	+	0.624316i	−0.989225	−	0.146404i	$-0.953230\pi$
$733$	−44.0331	+	16.9027i	−1.62640	+	0.624316i	−0.637174	+	0.770720i	$0.719897\pi$
$734$	−0.946479	−	2.91296i	−0.0349352	−	0.107519i
$735$		0			0
$736$	−6.87248	+	21.1513i	−0.253323	+	0.779648i
$737$	0.0376129	+	0.717696i	0.00138549	+	0.0264367i
$738$	2.46903	−	1.60341i	0.0908862	−	0.0590222i
$739$	−33.3478	+	30.0265i	−1.22672	+	1.10454i	−0.235560	+	0.971860i	$0.575692\pi$
$739$	−33.3478	+	30.0265i	−1.22672	+	1.10454i	−0.991159	+	0.132683i	$0.957641\pi$
$740$		0			0
$741$	−1.89407	+	0.615420i	−0.0695804	+	0.0226080i
$742$	−12.2762	−	18.3044i	−0.450673	−	0.671974i
$743$	11.1530	+	11.1530i	0.409164	+	0.409164i	0.881447	−	0.472283i	$-0.156570\pi$
$743$	11.1530	+	11.1530i	0.409164	+	0.409164i	−0.472283	+	0.881447i	$0.656570\pi$
$744$	−7.38130	+	16.5787i	−0.270612	+	0.607804i
$745$		0			0
$746$	−3.21265	+	1.43036i	−0.117623	+	0.0523693i
$747$	−5.07608	+	4.11053i	−0.185724	+	0.150396i
$748$	3.03601	+	5.95850i	0.111007	+	0.217864i
$749$	4.24708	−	13.7614i	0.155185	−	0.502830i
$750$		0			0
$751$	−21.6997	−	37.5850i	−0.791834	−	1.37150i	−0.924830	−	0.380380i	$-0.875793\pi$
$751$	−21.6997	−	37.5850i	−0.791834	−	1.37150i	0.132996	−	0.991117i	$-0.457540\pi$
$752$	−0.245891	+	4.69188i	−0.00896672	+	0.171095i
$753$	−35.8409	−	13.7580i	−1.30611	−	0.501370i
$754$	−0.742151	+	7.06110i	−0.0270276	+	0.257150i
$755$		0			0
$756$	−11.1849	+	12.7983i	−0.406790	+	0.465468i
$757$	−35.7542	+	35.7542i	−1.29951	+	1.29951i	−0.370793	+	0.928716i	$0.620914\pi$
$757$	−35.7542	+	35.7542i	−1.29951	+	1.29951i	−0.928716	+	0.370793i	$0.879086\pi$
$758$	−10.0907	−	26.2873i	−0.366512	−	0.954796i
$759$	4.15568	+	0.883317i	0.150842	+	0.0320624i
$760$		0			0
$761$	−0.918515	−	4.32127i	−0.0332961	−	0.156646i	0.958359	−	0.285567i	$-0.0921820\pi$
$761$	−0.918515	−	4.32127i	−0.0332961	−	0.156646i	−0.991655	+	0.128921i	$0.958849\pi$
$762$	1.61944	−	3.17832i	0.0586660	−	0.115138i
$763$	42.0628	+	10.6056i	1.52278	+	0.383949i
$764$	25.2152	+	8.19292i	0.912255	+	0.296409i
$765$		0			0
$766$	3.91301	−	18.4093i	0.141383	−	0.665154i
$767$	−7.25553	−	5.87541i	−0.261982	−	0.212149i
$768$	21.3932	+	5.73230i	0.771962	+	0.206847i
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.103706	−	0.994608i	$-0.466930\pi$
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.977975	+	0.208720i	$0.0669299\pi$
$770$		0			0
$771$	−19.8959	−	14.4552i	−0.716533	−	0.520592i
$772$	10.7503	+	13.2755i	0.386912	+	0.477797i
$773$	6.48817	+	0.340031i	0.233363	+	0.0122301i	0.168659	−	0.985674i	$-0.446056\pi$
$773$	6.48817	+	0.340031i	0.233363	+	0.0122301i	0.0647042	+	0.997904i	$0.479390\pi$
$774$	−2.55851	−	1.47716i	−0.0919638	−	0.0530953i
$775$		0			0
$776$		−	31.1516i		−	1.11828i
$777$	7.90361	−	21.5377i	0.283540	−	0.772661i
$778$	1.61648	+	10.2061i	0.0579537	+	0.365905i
$779$	−4.63874	−	0.487552i	−0.166200	−	0.0174683i
$780$		0			0
$781$	−0.0780153	−	0.742266i	−0.00279161	−	0.0265604i
$782$	−7.28085	+	27.1725i	−0.260363	+	0.971687i
$783$	−8.23336	+	51.9834i	−0.294236	+	1.85773i
$784$	−2.06389	+	1.97210i	−0.0737105	+	0.0704322i
$785$		0			0
$786$	−8.05284	+	1.71168i	−0.287235	+	0.0610538i
$787$	−3.88508	−	5.98249i	−0.138488	−	0.213253i	0.762621	−	0.646846i	$-0.223912\pi$
$787$	−3.88508	−	5.98249i	−0.138488	−	0.213253i	−0.901109	+	0.433593i	$0.857246\pi$
$788$	−0.938503	−	1.44517i	−0.0334328	−	0.0514820i
$789$	−26.7685	+	5.68981i	−0.952983	+	0.202563i
$790$		0			0
$791$	−21.6893	−	12.0977i	−0.771184	−	0.430143i
$792$	−0.449506	+	2.83807i	−0.0159725	+	0.100846i
$793$	1.79222	−	6.68866i	0.0636436	−	0.237521i
$794$	−1.10540	−	10.5172i	−0.0392291	−	0.373240i
$795$		0			0
$796$	3.98912	+	0.419273i	0.141391	+	0.0148607i
$797$	−4.68404	−	29.5739i	−0.165917	−	1.04756i	−0.920325	−	0.391154i	$-0.872076\pi$
$797$	−4.68404	−	29.5739i	−0.165917	−	1.04756i	0.754408	−	0.656406i	$-0.227924\pi$
$798$	−5.86799	+	1.01870i	−0.207724	+	0.0360616i
$799$		−	85.6610i		−	3.03047i
$800$		0			0
$801$	−0.628409	−	0.362812i	−0.0222037	−	0.0128193i
$802$	−26.9613	−	1.41298i	−0.952038	−	0.0498942i
$803$	−1.83784	−	2.26954i	−0.0648559	−	0.0800903i
$804$	−1.11553	−	0.810483i	−0.0393418	−	0.0285835i
$805$		0			0
$806$	2.89629	−	2.10428i	0.102017	−	0.0741200i
$807$	−1.63857	−	0.439053i	−0.0576803	−	0.0154554i
$808$	14.2912	+	11.5728i	0.502764	+	0.407130i
$809$	0.444905	−	2.09311i	0.0156420	−	0.0735900i	−0.969634	−	0.244560i	$-0.921357\pi$
$809$	0.444905	−	2.09311i	0.0156420	−	0.0735900i	0.985276	+	0.170970i	$0.0546900\pi$
$810$		0			0
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	0.107319	−	0.994225i	$-0.465773\pi$
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	−0.497567	+	0.867425i	$0.665773\pi$
$812$	6.92264	−	27.4559i	0.242937	−	0.963512i
$813$	7.44168	−	14.6051i	0.260991	−	0.512224i
$814$	−0.994268	−	4.67766i	−0.0348491	−	0.163952i
$815$		0			0
$816$	3.91788	+	0.832771i	0.137153	+	0.0291528i
$817$	1.67740	+	4.36978i	0.0586848	+	0.152879i
$818$	21.1298	−	21.1298i	0.738786	−	0.738786i
$819$	2.57359	−	0.878557i	0.0899286	−	0.0306993i
$820$		0			0
$821$	−2.74655	+	26.1317i	−0.0958552	+	0.912001i	0.835892	+	0.548894i	$0.184951\pi$
$821$	−2.74655	+	26.1317i	−0.0958552	+	0.912001i	−0.931747	+	0.363107i	$0.881716\pi$
$822$	22.2374	+	8.53614i	0.775618	+	0.297732i
$823$	1.01911	−	19.4457i	0.0355239	−	0.677835i	−0.921597	−	0.388147i	$-0.873115\pi$
$823$	1.01911	−	19.4457i	0.0355239	−	0.677835i	0.957121	−	0.289688i	$-0.0935515\pi$
$824$	−14.4048	−	24.9499i	−0.501816	−	0.869171i
$825$		0			0
$826$	−18.9873	−	20.4696i	−0.660652	−	0.712228i
$827$	7.82374	+	15.3550i	0.272058	+	0.533944i	0.986099	−	0.166160i	$-0.0531368\pi$
$827$	7.82374	+	15.3550i	0.272058	+	0.533944i	−0.714041	+	0.700104i	$0.753137\pi$
$828$	4.55551	−	3.68898i	0.158315	−	0.128201i
$829$	37.9342	−	16.8894i	1.31751	−	0.586592i	0.376952	−	0.926233i	$-0.376972\pi$
$829$	37.9342	−	16.8894i	1.31751	−	0.586592i	0.940555	+	0.339640i	$0.110305\pi$
$830$		0			0
$831$	−0.660907	+	1.48442i	−0.0229266	+	0.0514940i
$832$	−3.39004	−	3.39004i	−0.117529	−	0.117529i
$833$	35.6961	−	37.8760i	1.23680	−	1.31232i
$834$	1.19410	−	0.387986i	0.0413482	−	0.0134348i
$835$		0			0
$836$	1.23031	−	1.10778i	0.0425512	−	0.0383133i
$837$	22.2568	−	14.4537i	0.769307	−	0.499594i
$838$	−1.36521	−	26.0498i	−0.0471605	−	0.899877i
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	0.501666	+	0.865061i	$0.332720\pi$
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	−0.914327	+	0.404977i	$0.867280\pi$
$840$		0			0
$841$	−18.1325	−	55.8062i	−0.625260	−	1.92435i
$842$	17.9804	−	6.90203i	0.619645	−	0.237860i
$843$	−0.602629	−	2.24904i	−0.0207557	−	0.0774612i
$844$	−22.6866	+	2.38446i	−0.780905	+	0.0820765i
$845$		0			0
$846$	7.86749	−	10.8287i	0.270490	−	0.372298i
$847$	27.1873	+	3.89424i	0.934168	+	0.133808i
$848$	3.26953	−	1.66591i	0.112276	−	0.0572075i
$849$	17.2494	−	9.95893i	0.591997	−	0.341789i
$850$		0			0
$851$	−13.4134	+	23.2326i	−0.459804	+	0.796404i
$852$	1.20095	+	0.779907i	0.0411439	+	0.0267192i
$853$	26.9029	−	4.26100i	0.921138	−	0.145894i	0.322184	−	0.946677i	$-0.395583\pi$
$853$	26.9029	−	4.26100i	0.921138	−	0.145894i	0.598954	+	0.800783i	$0.295583\pi$
$854$	8.14170	−	19.0406i	0.278603	−	0.651554i
$855$		0			0
$856$	14.4691	+	6.44206i	0.494543	+	0.220185i
$857$	37.0493	−	9.92732i	1.26558	−	0.339111i	0.437244	−	0.899343i	$-0.355955\pi$
$857$	37.0493	−	9.92732i	1.26558	−	0.339111i	0.828336	+	0.560232i	$0.189288\pi$
$858$	−0.496057	+	0.612580i	−0.0169351	+	0.0209131i
$859$	−0.603007	+	0.669707i	−0.0205743	+	0.0228501i	−0.753344	−	0.657626i	$-0.771561\pi$
$859$	−0.603007	+	0.669707i	−0.0205743	+	0.0228501i	0.732770	+	0.680477i	$0.238227\pi$
$860$		0			0
$861$	−8.82079	−	0.795217i	−0.300612	−	0.0271009i
$862$	2.05137	+	1.04523i	0.0698701	+	0.0356006i
$863$	−1.17507	+	0.0615826i	−0.0399997	+	0.00209629i	−0.0723253	−	0.997381i	$-0.523042\pi$
$863$	−1.17507	+	0.0615826i	−0.0399997	+	0.00209629i	0.0323256	+	0.999477i	$0.489709\pi$
$864$	−20.4668	−	22.7307i	−0.696296	−	0.773315i
$865$		0			0
$866$	−6.36565	−	5.73166i	−0.216314	−	0.194770i
$867$	−49.9479	−	7.91096i	−1.69632	−	0.268670i
$868$	−12.6237	+	6.66943i	−0.428478	+	0.226375i
$869$	2.26247	+	3.11402i	0.0767490	+	0.105636i
$870$		0			0
$871$	0.304239	+	0.683332i	0.0103087	+	0.0231538i
$872$	−17.0964	+	44.5375i	−0.578956	+	1.50823i
$873$	−7.31759	+	11.2681i	−0.247663	+	0.381367i
$874$	6.96421			0.235568
$875$		0			0
$876$	5.60304			0.189309
$877$	22.5815	−	34.7725i	0.762524	−	1.17418i	−0.217646	−	0.976028i	$-0.569838\pi$
$877$	22.5815	−	34.7725i	0.762524	−	1.17418i	0.980170	−	0.198157i	$-0.0634955\pi$
$878$	7.04448	−	18.3515i	0.237740	−	0.619333i
$879$	−2.08372	−	4.68011i	−0.0702821	−	0.157856i
$880$		0			0
$881$	−20.7423	−	28.5494i	−0.698827	−	0.961852i	−0.999966	−	0.00827221i	$-0.997367\pi$
$881$	−20.7423	−	28.5494i	−0.698827	−	0.961852i	0.301139	−	0.953580i	$-0.402633\pi$
$882$	7.99116	−	1.50953i	0.269076	−	0.0508285i
$883$	−12.7280	−	2.01591i	−0.428330	−	0.0678407i	−0.0614522	−	0.998110i	$-0.519573\pi$
$883$	−12.7280	−	2.01591i	−0.428330	−	0.0678407i	−0.366877	+	0.930269i	$0.619573\pi$
$884$	5.17243	+	4.65728i	0.173968	+	0.156641i
$885$		0			0
$886$	−14.1223	−	15.6845i	−0.474450	−	0.526930i
$887$	−45.7599	+	2.39817i	−1.53647	+	0.0805228i	−0.801671	−	0.597766i	$-0.796055\pi$
$887$	−45.7599	+	2.39817i	−1.53647	+	0.0805228i	−0.734796	+	0.678289i	$0.762722\pi$
$888$	22.4805	+	11.4544i	0.754397	+	0.384384i
$889$	7.00267	−	3.24289i	0.234862	−	0.108763i
$890$		0			0
$891$	−1.92742	+	2.14061i	−0.0645709	+	0.0717132i
$892$	−6.29895	+	7.77856i	−0.210904	+	0.260445i
$893$	−20.4839	+	5.48864i	−0.685467	+	0.183670i
$894$	12.7221	+	5.66427i	0.425492	+	0.189441i
$895$		0			0
$896$	8.67042	+	11.5695i	0.289658	+	0.386511i
$897$	4.36740	−	0.691729i	0.145823	−	0.0230961i
$898$	−25.2970	−	16.4280i	−0.844171	−	0.548211i
$899$	−22.1049	+	38.2867i	−0.737238	+	1.27693i
$900$		0			0
$901$	−57.9395	+	33.4514i	−1.93025	+	1.11443i
$902$	−1.64489	+	0.838114i	−0.0547689	+	0.0279062i
$903$	3.30758	+	8.24925i	0.110069	+	0.274518i
$904$	16.0538	−	22.0961i	0.533940	−	0.734905i
$905$		0			0
$906$	−13.4909	+	1.41795i	−0.448205	+	0.0471083i
$907$	−5.09475	−	19.0139i	−0.169168	−	0.631345i	−0.997472	−	0.0710652i	$-0.977360\pi$
$907$	−5.09475	−	19.0139i	−0.169168	−	0.631345i	0.828303	−	0.560280i	$-0.189307\pi$
$908$	−10.0202	+	3.84640i	−0.332532	+	0.127647i
$909$	−2.45091	−	7.54313i	−0.0812916	−	0.250190i
$910$		0			0
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	−0.0518959	−	0.990232i	−0.00171844	−	0.0327899i
$913$	3.43509	−	2.23078i	0.113685	−	0.0738279i
$914$	−5.55829	+	5.00470i	−0.183852	+	0.165541i
$915$		0			0
$916$	−9.35025	+	3.03808i	−0.308941	+	0.100381i
$917$	−15.9875	−	7.85000i	−0.527954	−	0.259230i
$918$	−27.3577	−	27.3577i	−0.902939	−	0.902939i
$919$	−14.7750	+	33.1853i	−0.487384	+	1.09468i	0.487734	+	0.872992i	$0.337824\pi$
$919$	−14.7750	+	33.1853i	−0.487384	+	1.09468i	−0.975117	+	0.221689i	$0.928843\pi$
$920$		0			0
$921$	33.7668	−	15.0340i	1.11266	−	0.495386i
$922$	27.3985	−	22.1869i	0.902322	−	0.730686i
$923$	−0.352661	−	0.692136i	−0.0116080	−	0.0227819i
$924$	2.30471	−	2.13781i	0.0758193	−	0.0703289i
$925$		0			0
$926$	−17.0216	−	29.4823i	−0.559364	−	0.968847i
$927$	−0.650304	+	12.4085i	−0.0213588	+	0.407550i
$928$	47.5706	+	18.2606i	1.56158	+	0.599434i
$929$	0.343990	−	3.27285i	0.0112860	−	0.107379i	−0.987429	−	0.158065i	$-0.949474\pi$
$929$	0.343990	−	3.27285i	0.0112860	−	0.107379i	0.998715	+	0.0506867i	$0.0161410\pi$
$930$		0			0
$931$	−11.3444	−	6.10905i	−0.371797	−	0.200216i
$932$	2.25132	−	2.25132i	0.0737446	−	0.0737446i
$933$	−10.0254	−	26.1169i	−0.328215	−	0.855030i
$934$	−18.8552	−	4.00780i	−0.616961	−	0.131139i
$935$		0			0
$936$	0.621795	+	2.92532i	0.0203240	+	0.0956170i
$937$	−4.55551	+	8.94070i	−0.148822	+	0.292080i	−0.953368	−	0.301811i	$-0.902409\pi$
$937$	−4.55551	+	8.94070i	−0.148822	+	0.292080i	0.804546	+	0.593891i	$0.202409\pi$
$938$	0.610891	+	2.15188i	0.0199463	+	0.0702614i
$939$	6.03743	+	1.96168i	0.197024	+	0.0640170i
$940$		0			0
$941$	−3.13847	+	14.7653i	−0.102311	+	0.481336i	0.896922	+	0.442188i	$0.145798\pi$
$941$	−3.13847	+	14.7653i	−0.102311	+	0.481336i	−0.999233	+	0.0391481i	$0.987536\pi$
$942$	15.8450	+	12.8310i	0.516257	+	0.418057i
$943$	10.0033	+	2.68038i	0.325752	+	0.0872851i
$944$	3.76069	−	2.73230i	0.122400	−	0.0889288i
$945$		0			0
$946$	1.49877	+	1.08892i	0.0487293	+	0.0354039i
$947$	35.8661	+	44.2910i	1.16549	+	1.43926i	0.876151	+	0.482036i	$0.160103\pi$
$947$	35.8661	+	44.2910i	1.16549	+	1.43926i	0.289341	+	0.957226i	$0.406564\pi$
$948$	−7.37491	−	0.386503i	−0.239526	−	0.0125530i
$949$	−2.63228	−	1.51975i	−0.0854473	−	0.0493330i
$950$		0			0
$951$			39.2544i			1.27291i
$952$	36.6756	+	43.9436i	1.18866	+	1.42422i
$953$	−2.49558	−	15.7565i	−0.0808399	−	0.510403i	−0.994569	−	0.104079i	$-0.966810\pi$
$953$	−2.49558	−	15.7565i	−0.0808399	−	0.510403i	0.913729	−	0.406324i	$-0.133190\pi$
$954$	−10.3967	−	1.09273i	−0.336604	−	0.0353785i
$955$		0			0
$956$	1.28587	+	12.2343i	0.0415881	+	0.395684i
$957$	2.51936	−	9.40237i	0.0814392	−	0.303935i
$958$	−0.202701	+	1.27980i	−0.00654897	+	0.0413486i
$959$	26.4237	+	44.2408i	0.853264	+	1.42861i
$960$		0			0
$961$	−8.51796	+	1.81055i	−0.274773	+	0.0584048i
$962$	−2.71081	−	4.17428i	−0.0873999	−	0.134584i
$963$	−3.72047	−	5.72903i	−0.119891	−	0.184615i
$964$	−11.7979	+	2.50771i	−0.379984	+	0.0807680i
$965$		0			0
$966$	13.2222	−	0.195837i	0.425417	−	0.00630096i
$967$	4.82581	−	30.4690i	0.155188	−	0.979817i	−0.780030	−	0.625743i	$-0.784796\pi$
$967$	4.82581	−	30.4690i	0.155188	−	0.979817i	0.935217	−	0.354074i	$-0.115204\pi$
$968$	−7.81746	+	29.1751i	−0.251263	+	0.937725i
$969$	1.88976	+	17.9799i	0.0607080	+	0.577598i
$970$		0			0
$971$	−4.01132	−	0.421607i	−0.128729	−	0.0135300i	0.0399446	−	0.999202i	$-0.487282\pi$
$971$	−4.01132	−	0.421607i	−0.128729	−	0.0135300i	−0.168674	+	0.985672i	$0.553949\pi$
$972$	2.15038	+	13.5770i	0.0689736	+	0.435482i
$973$	2.54998	+	0.935758i	0.0817487	+	0.0299990i
$974$		−	24.6259i		−	0.789064i
$975$		0			0
$976$	2.98586	+	1.72388i	0.0955749	+	0.0551802i
$977$	24.4967	+	1.28382i	0.783719	+	0.0410730i	0.439998	−	0.897999i	$-0.354979\pi$
$977$	24.4967	+	1.28382i	0.783719	+	0.0410730i	0.343721	+	0.939072i	$0.388312\pi$
$978$	15.8314	+	19.5502i	0.506233	+	0.625146i
$979$	0.368121	+	0.267456i	0.0117652	+	0.00854792i
$980$		0			0
$981$	16.6460	−	12.0940i	0.531467	−	0.386133i
$982$	−0.184678	−	0.0494843i	−0.00589331	−	0.00157911i
$983$	35.4999	+	28.7473i	1.13227	+	0.916896i	0.997262	−	0.0739487i	$-0.0235601\pi$
$983$	35.4999	+	28.7473i	1.13227	+	0.916896i	0.135010	+	0.990844i	$0.456893\pi$
$984$	2.02505	−	9.52713i	0.0645563	−	0.303714i
$985$		0			0
$986$	61.2982	+	19.9170i	1.95213	+	0.634286i
$987$	−38.7362	+	10.9967i	−1.23299	+	0.350029i
$988$	0.782265	−	1.53528i	0.0248872	−	0.0488438i
$989$	−2.16073	−	10.1654i	−0.0687072	−	0.323242i
$990$		0			0
$991$	−44.8481	−	9.53276i	−1.42465	−	0.302818i	−0.569836	−	0.821758i	$-0.692993\pi$
$991$	−44.8481	−	9.53276i	−1.42465	−	0.302818i	−0.854810	+	0.518940i	$0.826327\pi$
$992$	−9.20750	−	23.9864i	−0.292339	−	0.761568i
$993$	21.4880	−	21.4880i	0.681902	−	0.681902i
$994$	−0.750502	−	2.19848i	−0.0238045	−	0.0697314i
$995$		0			0
$996$	−0.821430	+	7.81538i	−0.0260280	+	0.247640i
$997$	−21.2901	−	8.17250i	−0.674264	−	0.258826i	−0.00294638	−	0.999996i	$-0.500938\pi$
$997$	−21.2901	−	8.17250i	−0.674264	−	0.258826i	−0.671317	+	0.741170i	$0.734271\pi$
$998$	−1.14385	+	21.8260i	−0.0362080	+	0.690891i
$999$	−18.4479	−	31.9527i	−0.583665	−	1.01094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.493.8		288
5.2	odd	4		175.2.x.a.122.8	yes	288
5.3	odd	4		875.2.bb.c.507.11		288
5.4	even	2		875.2.bb.a.493.11		288
7.5	odd	6	inner	875.2.bb.b.243.11		288
25.6	even	5		175.2.x.a.108.8	yes	288
25.8	odd	20		875.2.bb.a.857.8		288
25.17	odd	20	inner	875.2.bb.b.857.11		288
25.19	even	10		875.2.bb.c.143.11		288
35.12	even	12		175.2.x.a.47.8	yes	288
35.19	odd	6		875.2.bb.a.243.8		288
35.33	even	12		875.2.bb.c.257.11		288
175.19	odd	30		875.2.bb.c.768.11		288
175.33	even	60		875.2.bb.a.607.11		288
175.117	even	60	inner	875.2.bb.b.607.8		288
175.131	odd	30		175.2.x.a.33.8	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	175.131	odd	30
175.2.x.a.47.8	yes	288	35.12	even	12
175.2.x.a.108.8	yes	288	25.6	even	5
175.2.x.a.122.8	yes	288	5.2	odd	4
875.2.bb.a.243.8		288	35.19	odd	6
875.2.bb.a.493.11		288	5.4	even	2
875.2.bb.a.607.11		288	175.33	even	60
875.2.bb.a.857.8		288	25.8	odd	20
875.2.bb.b.243.11		288	7.5	odd	6	inner
875.2.bb.b.493.8		288	1.1	even	1	trivial
875.2.bb.b.607.8		288	175.117	even	60	inner
875.2.bb.b.857.11		288	25.17	odd	20	inner
875.2.bb.c.143.11		288	25.19	even	10
875.2.bb.c.257.11		288	35.33	even	12
875.2.bb.c.507.11		288	5.3	odd	4
875.2.bb.c.768.11		288	175.19	odd	30

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+(-0.504213 + 0.776420i) q^{2} +(0.473408 - 1.23327i) q^{3} +(0.464876 + 1.04413i) q^{4} +(0.718837 + 0.989394i) q^{6} +(-0.0993238 + 2.64389i) q^{7} +(-2.87383 - 0.455170i) q^{8} +(0.932596 + 0.839713i) q^{9} +(-0.526566 - 0.584810i) q^{11} +(1.50777 - 0.0790188i) q^{12} +(-0.729773 - 0.371838i) q^{13} +(-2.00269 - 1.41020i) q^{14} +(0.272873 - 0.303056i) q^{16} +(-4.67910 + 5.77821i) q^{17} +(-1.12220 + 0.300692i) q^{18} +(1.68154 + 0.748668i) q^{19} +(3.21360 + 1.37413i) q^{21} +(0.719560 - 0.113967i) q^{22} +(-3.42753 - 2.22587i) q^{23} +(-1.92184 + 3.32873i) q^{24} +(0.656664 - 0.379125i) q^{26} +(5.00818 - 2.55179i) q^{27} +(-2.80673 + 1.12537i) q^{28} +(-5.50382 + 7.57536i) q^{29} +(4.69555 - 0.493522i) q^{31} +(-1.40844 - 5.25635i) q^{32} +(-0.970509 + 0.372543i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(-0.343540 - 6.55514i) q^{37} +(-1.42913 + 0.928090i) q^{38} +(-0.804057 + 0.723976i) q^{39} +(-2.40999 + 0.783055i) q^{41} +(-2.68724 + 1.80225i) q^{42} +(1.79811 + 1.79811i) q^{43} +(0.365830 - 0.821667i) q^{44} +(3.45641 - 1.53889i) q^{46} +(-8.95355 + 7.25044i) q^{47} +(-0.244570 - 0.479996i) q^{48} +(-6.98027 - 0.525202i) q^{49} +(4.91096 + 8.50604i) q^{51} +(0.0489927 - 0.934836i) q^{52} +(8.40051 + 3.22465i) q^{53} +(-0.543925 + 5.17510i) q^{54} +(1.48886 - 7.55288i) q^{56} +(1.71936 - 1.71936i) q^{57} +(-3.10656 - 8.09287i) q^{58} +(11.1497 + 2.36995i) q^{59} +(1.75779 + 8.26975i) q^{61} +(-1.98438 + 3.89456i) q^{62} +(-2.31273 + 2.38227i) q^{63} +(5.56698 + 1.80882i) q^{64} +(0.200093 - 0.941364i) q^{66} +(-0.709737 - 0.574734i) q^{67} +(-8.20839 - 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(-2.29791 - 2.83768i) q^{72} +(3.70594 + 0.194220i) q^{73} +(5.26276 + 3.03846i) q^{74} +2.10378i q^{76} +(1.59847 - 1.33409i) q^{77} +(-0.156693 - 0.989324i) q^{78} +(-4.86448 - 0.511278i) q^{79} +(-0.382611 - 3.64030i) q^{81} +(0.607171 - 2.26599i) q^{82} +(-0.814213 + 5.14074i) q^{83} +(0.0591594 + 3.99422i) q^{84} +(-2.30272 + 0.489458i) q^{86} +(6.73691 + 10.3739i) q^{87} +(1.24707 + 1.92032i) q^{88} +(-0.565582 + 0.120218i) q^{89} +(1.05558 - 1.89250i) q^{91} +(0.730712 - 4.61354i) q^{92} +(1.61426 - 6.02451i) q^{93} +(-1.11489 - 10.6075i) q^{94} +(-7.14926 - 0.751418i) q^{96} +(1.67483 + 10.5745i) q^{97} +(3.92732 - 5.15481i) q^{98} -0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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