LMFDB - Embedded newform 875.2.bb.b.607.8

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			607.8
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.b.493.8

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.504213	−	0.776420i	−0.356532	−	0.549012i	0.614208	−	0.789144i	$-0.289476\pi$
$2$	−0.504213	−	0.776420i	−0.356532	−	0.549012i	−0.970740	+	0.240133i	$0.922809\pi$
$3$	0.473408	+	1.23327i	0.273322	+	0.712029i	0.999694	+	0.0247269i	$0.00787160\pi$
$3$	0.473408	+	1.23327i	0.273322	+	0.712029i	−0.726372	+	0.687302i	$0.758795\pi$
$4$	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	−0.817279	−	0.576242i	$-0.804519\pi$
$11$	−0.526566	+	0.584810i	−0.158765	+	0.176327i	0.658514	+	0.752569i	$0.271185\pi$
$12$	1.50777	+	0.0790188i	0.435255	+	0.0228108i
$13$	−0.729773	+	0.371838i	−0.202403	+	0.103129i	−0.552254	−	0.833676i	$-0.686232\pi$
$13$	−0.729773	+	0.371838i	−0.202403	+	0.103129i	0.349851	+	0.936805i	$0.386232\pi$
$14$	−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	−0.903520	−	0.428545i	$-0.859026\pi$
$17$	−4.67910	−	5.77821i	−1.13485	−	1.40142i	−0.231328	−	0.972876i	$-0.574307\pi$
$18$	−1.12220	−	0.300692i	−0.264504	−	0.0708737i
$19$	1.68154	−	0.748668i	0.385771	−	0.171756i	−0.204682	−	0.978829i	$-0.565616\pi$
$19$	1.68154	−	0.748668i	0.385771	−	0.171756i	0.590453	+	0.807072i	$0.298949\pi$
$20$		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	−0.850071	−	0.526669i	$-0.823441\pi$
$23$	−3.42753	+	2.22587i	−0.714690	+	0.464125i	0.135381	+	0.990794i	$0.456774\pi$
$24$	−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	−0.910768	−	0.412919i	$-0.864509\pi$
$29$	−5.50382	−	7.57536i	−1.02203	−	1.40671i	−0.111266	−	0.993791i	$-0.535491\pi$
$30$		0			0
$31$	4.69555	+	0.493522i	0.843345	+	0.0886392i	0.516340	−	0.856383i	$-0.327294\pi$
$31$	4.69555	+	0.493522i	0.843345	+	0.0886392i	0.327005	+	0.945023i	$0.393961\pi$
$32$	−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	0.812549	+	0.582893i	$0.198079\pi$
$37$	−0.343540	+	6.55514i	−0.0564777	+	1.07766i	−0.869027	+	0.494766i	$0.835254\pi$
$38$	−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	0.114718	−	0.993398i	$-0.463404\pi$
$41$	−2.40999	−	0.783055i	−0.376378	−	0.122293i	−0.491096	+	0.871106i	$0.663404\pi$
$42$	−2.68724	−	1.80225i	−0.414651	−	0.278094i
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	−0.556583	−	0.830792i	$-0.687888\pi$
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	0.830792	+	0.556583i	$0.187888\pi$
$44$	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	−0.994212	−	0.107437i	$-0.965736\pi$
$47$	−8.95355	−	7.25044i	−1.30601	−	1.05759i	−0.311797	−	0.950149i	$-0.600931\pi$
$48$	−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	0.295207	−	0.955433i	$-0.404611\pi$
$53$	8.40051	−	3.22465i	1.15390	−	0.442940i	0.858691	+	0.512493i	$0.171278\pi$
$54$	−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	0.586401	−	0.810021i	$-0.300544\pi$
$59$	11.1497	−	2.36995i	1.45157	−	0.308541i	0.865169	+	0.501480i	$0.167211\pi$
$60$		0			0
$61$	1.75779	−	8.26975i	0.225062	−	1.05883i	−0.709959	−	0.704243i	$-0.751287\pi$
$61$	1.75779	−	8.26975i	0.225062	−	1.05883i	0.935022	−	0.354591i	$-0.115380\pi$
$62$	−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	−0.671694	−	0.740828i	$-0.734433\pi$
$67$	−0.709737	+	0.574734i	−0.0867082	+	0.0702149i	0.584986	+	0.811043i	$0.301100\pi$
$68$	−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	−0.541323	−	0.840815i	$-0.682076\pi$
$71$	0.767293	−	0.557471i	0.0910610	−	0.0661597i	0.632384	+	0.774655i	$0.282076\pi$
$72$	−2.29791	+	2.83768i	−0.270811	+	0.334424i
$73$	3.70594	−	0.194220i	0.433747	−	0.0227317i	0.165787	−	0.986162i	$-0.446984\pi$
$73$	3.70594	−	0.194220i	0.433747	−	0.0227317i	0.267961	+	0.963430i	$0.413650\pi$
$74$	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	−0.374142	−	0.927371i	$-0.622063\pi$
$79$	−4.86448	+	0.511278i	−0.547297	+	0.0575232i	−0.173155	+	0.984895i	$0.555396\pi$
$80$		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	−0.991221	−	0.132218i	$-0.957790\pi$
$83$	−0.814213	−	5.14074i	−0.0893715	−	0.564269i	0.901849	−	0.432051i	$-0.142210\pi$
$84$	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	0.177838	−	0.984060i	$-0.443090\pi$
$89$	−0.565582	−	0.120218i	−0.0599516	−	0.0127431i	−0.237790	+	0.971317i	$0.576423\pi$
$90$		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	−0.744029	−	0.668148i	$-0.767087\pi$
$97$	1.67483	−	10.5745i	0.170054	−	1.07368i	0.914082	−	0.405529i	$-0.132913\pi$
$98$	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	−0.746950	−	0.664880i	$-0.768483\pi$
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	0.202328	+	0.979318i	$0.435149\pi$
$102$	−9.08043	+	0.475885i	−0.899097	+	0.0471197i
$103$	6.23115	−	7.69483i	0.613974	−	0.758194i	−0.371424	−	0.928463i	$-0.621130\pi$
$103$	6.23115	−	7.69483i	0.613974	−	0.758194i	0.985398	+	0.170269i	$0.0544637\pi$
$104$	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	−0.503850	−	0.863791i	$-0.668084\pi$
$107$	−5.25791	+	1.40885i	−0.508302	+	0.136199i	−0.00445150	+	0.999990i	$0.501417\pi$
$108$	4.99258	−	4.04291i	0.480412	−	0.389030i
$109$	3.40888	+	16.0375i	0.326512	+	1.53612i	0.768945	+	0.639315i	$0.220782\pi$
$109$	3.40888	+	16.0375i	0.326512	+	1.53612i	−0.442434	+	0.896801i	$0.645885\pi$
$110$		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	0.599014	−	0.800739i	$-0.295559\pi$
$113$	−4.26151	−	8.36368i	−0.400889	−	0.786789i	−0.999903	+	0.0139501i	$0.995559\pi$
$114$	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	−0.942266	−	0.334866i	$-0.891309\pi$
$127$	−1.32420	+	2.59888i	−0.117503	+	0.230613i	0.824762	+	0.565480i	$0.191309\pi$
$128$	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	0.753535	−	0.657408i	$-0.228347\pi$
$131$	−2.73808	−	6.14983i	−0.239227	−	0.537313i	−0.992763	+	0.120094i	$0.961680\pi$
$132$	−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	0.999927	−	0.0121099i	$-0.00385480\pi$
$137$	16.3347	+	10.6079i	1.39557	+	0.906294i	0.395644	+	0.918404i	$0.370521\pi$
$138$	−0.261578	+	4.99121i	−0.0222670	+	0.424880i
$139$	0.317252	+	0.976401i	0.0269090	+	0.0828172i	0.963609	−	0.267315i	$-0.0861365\pi$
$139$	0.317252	+	0.976401i	0.0269090	+	0.0828172i	−0.936700	+	0.350133i	$0.886137\pi$
$140$		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	0.846225	−	0.532825i	$-0.178870\pi$
$149$	9.86165	+	5.69362i	0.807897	+	0.466440i	−0.0383277	+	0.999265i	$0.512203\pi$
$150$		0			0
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	0.547136	−	0.837043i	$-0.315718\pi$
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	−0.998469	+	0.0553124i	$0.982385\pi$
$152$	−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	0.835836	−	0.548979i	$-0.184983\pi$
$157$	16.1035	+	4.31493i	1.28520	+	0.344369i	0.449365	+	0.893348i	$0.351650\pi$
$158$	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	0.835492	−	0.549503i	$-0.185183\pi$
$163$	20.5419	+	1.07656i	1.60897	+	0.0843225i	0.773476	+	0.633825i	$0.218516\pi$
$164$	−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	0.0269687	−	0.999636i	$-0.491415\pi$
$167$	4.67190	−	0.739956i	0.361522	−	0.0572595i	0.334553	+	0.942377i	$0.391415\pi$
$168$	−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	0.927586	−	0.373609i	$-0.121880\pi$
$173$	2.74889	+	4.23292i	0.208994	+	0.321823i	−0.718592	+	0.695432i	$0.755213\pi$
$174$	−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	−0.850322	−	0.526263i	$-0.823593\pi$
$179$	1.46827	−	3.29779i	0.109744	−	0.246488i	0.960066	+	0.279774i	$0.0902596\pi$
$180$		0			0
$181$	−7.29441	+	10.0399i	−0.542189	+	0.746259i	−0.988927	−	0.148406i	$-0.952586\pi$
$181$	−7.29441	+	10.0399i	−0.542189	+	0.746259i	0.446737	+	0.894665i	$0.352586\pi$
$182$	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	0.965655	+	0.259828i	$0.0836660\pi$
$191$	15.5218	+	17.2388i	1.12312	+	1.24735i	0.157467	+	0.987524i	$0.449667\pi$
$192$	4.86621	+	6.00927i	0.351189	+	0.433682i
$193$	14.4367	+	3.86831i	1.03918	+	0.278447i	0.737773	−	0.675049i	$-0.235877\pi$
$193$	14.4367	+	3.86831i	1.03918	+	0.278447i	0.301406	+	0.953496i	$0.402544\pi$
$194$	−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	0.103162	−	0.994665i	$-0.467104\pi$
$197$	−1.48910	−	0.235850i	−0.106094	−	0.0168036i	−0.209256	+	0.977861i	$0.567104\pi$
$198$	0.766758	−	0.497938i	0.0544911	−	0.0353869i
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	0.921494	−	0.388393i	$-0.126970\pi$
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	−0.797105	+	0.603841i	$0.793636\pi$
$200$		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	−0.903384	−	0.428833i	$-0.858925\pi$
$211$	−6.16756	−	18.9818i	−0.424593	−	1.30676i	0.478791	−	0.877929i	$-0.341075\pi$
$212$	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	−0.718725	−	0.695294i	$-0.755274\pi$
$223$	3.97575	−	7.80285i	0.266236	−	0.522518i	0.984961	+	0.172777i	$0.0552739\pi$
$224$	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	−0.965207	−	0.261487i	$-0.915787\pi$
$227$	−0.491475	−	9.37790i	−0.0326203	−	0.622433i	0.932587	−	0.360946i	$-0.117546\pi$
$228$	2.59453	−	0.995946i	0.171827	−	0.0659581i
$229$	−0.899141	−	8.55475i	−0.0594169	−	0.565314i	−0.983217	−	0.182439i	$-0.941601\pi$
$229$	−0.899141	−	8.55475i	−0.0594169	−	0.565314i	0.923800	−	0.382875i	$-0.125066\pi$
$230$		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	−0.962386	−	0.271686i	$-0.912419\pi$
$233$	−0.998293	+	2.60064i	−0.0654004	+	0.170374i	0.896986	+	0.442060i	$0.145752\pi$
$234$	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	0.0413782	−	0.999144i	$-0.486825\pi$
$239$	10.2364	−	3.32600i	0.662136	−	0.215141i	0.620757	+	0.784003i	$0.286825\pi$
$240$		0			0
$241$	−2.19409	−	10.3224i	−0.141334	−	0.664922i	−0.990581	−	0.136927i	$-0.956277\pi$
$241$	−2.19409	−	10.3224i	−0.141334	−	0.664922i	0.849247	−	0.527995i	$-0.177056\pi$
$242$	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	$0.369539\pi$
$251$			29.0617i			1.83436i	−0.398477	+	0.917178i	$0.630461\pi$
$252$	−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	0.936701	+	0.350129i	$0.113862\pi$
$257$	4.81832	+	17.9822i	0.300559	+	1.12170i	−0.636143	+	0.771571i	$0.719471\pi$
$258$	−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	0.297444	+	0.954739i	$0.403866\pi$
$263$	−11.2829	+	17.3742i	−0.695735	+	1.07134i	−0.993179	+	0.116599i	$0.962801\pi$
$264$	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	−0.997852	−	0.0655149i	$-0.979131\pi$
$269$	−0.134230	+	1.27711i	−0.00818414	+	0.0778669i	0.989667	+	0.143382i	$0.0457977\pi$
$270$		0			0
$271$	12.3405	−	1.29704i	0.749631	−	0.0787894i	0.277995	−	0.960583i	$-0.410330\pi$
$271$	12.3405	−	1.29704i	0.749631	−	0.0787894i	0.471636	+	0.881793i	$0.343664\pi$
$272$	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	−0.0892027	−	0.996013i	$-0.528432\pi$
$277$	−1.22836	+	0.0643756i	−0.0738049	+	0.00386795i	0.0153977	+	0.999881i	$0.495099\pi$
$278$	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	0.629505	−	0.776996i	$-0.283258\pi$
$281$	1.42595	+	1.03602i	0.0850652	+	0.0618035i	−0.544440	+	0.838800i	$0.683258\pi$
$282$	−13.6097	+	3.64670i	−0.810445	+	0.217158i
$283$	11.7176	−	9.48873i	0.696539	−	0.564046i	−0.214320	−	0.976764i	$-0.568754\pi$
$283$	11.7176	−	9.48873i	0.696539	−	0.564046i	0.910859	+	0.412717i	$0.135420\pi$
$284$	−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	0.782657	−	0.622454i	$-0.213864\pi$
$293$	2.74224	+	2.74224i	0.160203	+	0.160203i	−0.622454	+	0.782657i	$0.713864\pi$
$294$	−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	0.138889	−	0.990308i	$-0.455647\pi$
$307$	19.7851	−	19.7851i	1.12920	−	1.12920i	0.990308	−	0.138889i	$-0.0443532\pi$
$308$	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	0.981292	−	0.192524i	$-0.0616673\pi$
$311$	15.7376	+	14.1702i	0.892396	+	0.803517i	−0.0888962	+	0.996041i	$0.528334\pi$
$312$	2.64026	+	1.71460i	0.149475	+	0.0970703i
$313$	0.251501	−	4.79892i	0.0142157	−	0.271251i	−0.982269	−	0.187477i	$-0.939969\pi$
$313$	0.251501	−	4.79892i	0.0142157	−	0.271251i	0.996485	−	0.0837745i	$-0.0266975\pi$
$314$	−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	−0.581598	−	0.813477i	$-0.697572\pi$
$317$	−27.7417	−	10.6491i	−1.55813	−	0.598110i	−0.976533	+	0.215366i	$0.930905\pi$
$318$	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	0.262415	−	0.964955i	$-0.415481\pi$
$331$	21.0153	−	9.35662i	1.15511	−	0.514286i	0.892691	+	0.450669i	$0.148815\pi$
$332$	−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	−0.578715	−	0.815530i	$-0.696446\pi$
$337$	−4.75641	+	2.42351i	−0.259098	+	0.132017i	0.319617	+	0.947547i	$0.396446\pi$
$338$	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	0.993536	+	0.113514i	$0.0362107\pi$
$347$	6.16865	+	16.0699i	0.331151	+	0.862677i	−0.662386	+	0.749163i	$0.730456\pi$
$348$	−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	0.999863	−	0.0165408i	$-0.00526535\pi$
$353$	4.61726	+	12.0284i	0.245752	+	0.640206i	−0.754111	+	0.656747i	$0.771932\pi$
$354$	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	−0.503499	−	0.863996i	$-0.667954\pi$
$359$	5.74355	−	5.17152i	0.303133	−	0.272942i	0.806633	+	0.591053i	$0.201288\pi$
$360$		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	0.719902	−	0.694076i	$-0.244187\pi$
$367$	−2.08207	−	2.57114i	−0.108683	−	0.134212i	−0.828585	+	0.559864i	$0.810854\pi$
$368$	−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	−0.459522	−	0.888167i	$-0.651979\pi$
$373$	3.18580	−	2.06888i	0.164955	−	0.107123i	0.624476	+	0.781044i	$0.285312\pi$
$374$	−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	−0.964250	−	0.264996i	$-0.914629\pi$
$379$	−17.8775	−	24.6063i	−0.918306	−	1.26394i	0.0459436	−	0.998944i	$-0.485371\pi$
$380$		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	−0.178659	−	0.983911i	$-0.557176\pi$
$383$	−18.9792	−	7.28545i	−0.969794	−	0.372269i	−0.791135	+	0.611642i	$0.790509\pi$
$384$	−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	0.852066	−	0.523434i	$-0.175350\pi$
$389$	8.29482	+	7.46869i	0.420564	+	0.378678i	−0.431502	+	0.902112i	$0.642016\pi$
$390$		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	0.380141	−	0.924929i	$-0.375875\pi$
$397$	−8.87732	−	7.18871i	−0.445540	−	0.360791i	−0.825681	+	0.564138i	$0.809209\pi$
$398$	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	−0.229493	−	0.973310i	$-0.573707\pi$
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	0.957658	−	0.287908i	$-0.0929597\pi$
$402$	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	−0.905875	−	0.423545i	$-0.860786\pi$
$409$	−31.5725	+	6.71095i	−1.56116	+	0.331835i	−0.655287	+	0.755380i	$0.727452\pi$
$410$		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	−0.130410	−	0.991460i	$-0.541629\pi$
$419$	−22.7957	−	16.5620i	−1.11364	−	0.809109i	−0.983233	+	0.182351i	$0.941629\pi$
$420$		0			0
$421$	−16.8306	+	12.2282i	−0.820274	+	0.595964i	−0.916791	−	0.399368i	$-0.869230\pi$
$421$	−16.8306	+	12.2282i	−0.820274	+	0.595964i	0.0965173	+	0.995331i	$0.469230\pi$
$422$	−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	−0.998997	−	0.0447740i	$-0.985743\pi$
$431$	−0.259952	+	2.47328i	−0.0125215	+	0.119134i	0.986476	+	0.163908i	$0.0524099\pi$
$432$	0.593260	+	2.21408i	0.0285432	+	0.106525i
$433$	−1.44743	−	9.13869i	−0.0695589	−	0.439178i	−0.997748	−	0.0670695i	$-0.978635\pi$
$433$	−1.44743	−	9.13869i	−0.0695589	−	0.439178i	0.928189	−	0.372108i	$-0.121365\pi$
$434$	−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	−0.316384	−	0.948631i	$-0.602469\pi$
$439$	−20.7692	−	4.41462i	−0.991258	−	0.210698i	−0.674874	+	0.737933i	$0.735802\pi$
$440$		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	−0.952178	−	0.305545i	$-0.901161\pi$
$443$	−5.90047	−	22.0209i	−0.280340	−	1.04624i	0.671838	−	0.740698i	$-0.265505\pi$
$444$	−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	$-0.720850\pi$
$449$		−	32.5816i		−	1.53762i	0.639478	−	0.768809i	$-0.279150\pi$
$450$		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	−0.0716332	−	0.997431i	$-0.522821\pi$
$457$	7.80380	−	2.09102i	0.365046	−	0.0978138i	0.436679	+	0.899617i	$0.356154\pi$
$458$	−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	−0.986220	−	0.165441i	$-0.947095\pi$
$461$	−36.2181	+	11.7680i	−1.68684	+	0.548089i	−0.700625	+	0.713530i	$0.747095\pi$
$462$	2.46898	−	0.622523i	0.114868	−	0.0289624i
$463$	−16.6944	−	32.7647i	−0.775856	−	1.52270i	−0.850785	−	0.525514i	$-0.823873\pi$
$463$	−16.6944	−	32.7647i	−0.775856	−	1.52270i	0.0749286	−	0.997189i	$-0.476127\pi$
$464$	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	−0.645450	−	0.763803i	$-0.723330\pi$
$467$	7.46192	−	19.4390i	0.345297	−	0.899528i	0.990746	−	0.135726i	$-0.0433366\pi$
$468$	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	0.435740	−	0.900073i	$-0.356487\pi$
$479$	1.27864	+	0.569287i	0.0584226	+	0.0260114i	−0.377317	+	0.926084i	$0.623153\pi$
$480$		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	−0.0708461	−	0.997487i	$-0.522570\pi$
$487$	−22.3089	−	14.4876i	−1.01091	−	0.656494i	−0.940066	+	0.340994i	$0.889237\pi$
$488$	−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	−0.949606	−	0.313446i	$-0.898517\pi$
$491$	0.0638187	−	0.196414i	0.00288010	−	0.00886403i	0.952486	+	0.304582i	$0.0985166\pi$
$492$	−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	0.882120	−	0.471024i	$-0.156116\pi$
$499$	20.4454	+	11.8042i	0.915262	+	0.528427i	0.0331413	+	0.999451i	$0.489449\pi$
$500$		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	0.228558	−	0.973530i	$-0.426599\pi$
$503$	3.25409	+	0.515396i	0.145092	+	0.0229804i	−0.0834657	+	0.996511i	$0.526599\pi$
$504$	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	0.913961	−	0.405802i	$-0.133008\pi$
$509$	9.35937	+	10.3946i	0.414847	+	0.460734i	−0.499114	+	0.866536i	$0.666341\pi$
$510$		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	−0.462065	−	0.886846i	$-0.652891\pi$
$521$	11.5536	−	25.9498i	0.506172	−	1.13688i	0.968237	−	0.250035i	$-0.0804421\pi$
$522$	3.89852	+	10.1560i	0.170634	+	0.444516i
$523$	21.6259	+	33.3009i	0.945633	+	1.45615i	0.889082	+	0.457748i	$0.151344\pi$
$523$	21.6259	+	33.3009i	0.945633	+	1.45615i	0.0565510	+	0.998400i	$0.481990\pi$
$524$	−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	0.723883	−	0.689923i	$-0.242355\pi$
$541$	−0.882148	−	0.979725i	−0.0379265	−	0.0421217i	−0.761810	+	0.647801i	$0.775689\pi$
$542$	−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	0.596232	−	0.802812i	$-0.296664\pi$
$547$	21.4047	+	3.39018i	0.915200	+	0.144953i	0.318968	+	0.947766i	$0.396664\pi$
$548$	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	−0.999790	−	0.0204931i	$-0.993476\pi$
$557$	−2.91942	+	10.8954i	−0.123700	+	0.461654i	0.876090	+	0.482147i	$0.160143\pi$
$558$	−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	0.629143	−	0.777290i	$-0.283406\pi$
$563$	4.15112	+	2.69577i	0.174949	+	0.113613i	−0.454194	+	0.890903i	$0.650073\pi$
$564$	−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	0.710031	−	0.704171i	$-0.248681\pi$
$569$	−6.87878	−	15.4500i	−0.288373	−	0.647697i	−0.998404	+	0.0564736i	$0.982014\pi$
$570$		0			0
$571$	26.2708	+	11.6965i	1.09940	+	0.489484i	0.874562	−	0.484913i	$-0.161149\pi$
$571$	26.2708	+	11.6965i	1.09940	+	0.489484i	0.224836	+	0.974397i	$0.427815\pi$
$572$	−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	0.986359	+	0.164609i	$0.0526362\pi$
$577$	0.543104	+	10.3630i	0.0226097	+	0.431419i	−0.963749	+	0.266810i	$0.914030\pi$
$578$	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	0.929997	−	0.367568i	$-0.119809\pi$
$587$	2.08337	+	4.08885i	0.0859899	+	0.168765i	−0.844007	+	0.536332i	$0.819809\pi$
$588$	−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	0.0599990	−	0.998198i	$-0.480890\pi$
$593$	14.8803	−	3.98715i	0.611059	−	0.163733i	0.551060	+	0.834466i	$0.314224\pi$
$594$	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	−0.199472	−	0.979903i	$-0.563923\pi$
$599$	13.4466	−	7.76339i	0.549413	−	0.317204i	0.748885	+	0.662700i	$0.230589\pi$
$600$		0			0
$601$		−	41.2449i		−	1.68241i	−0.540714	−	0.841207i	$-0.681846\pi$
$601$		−	41.2449i		−	1.68241i	0.540714	−	0.841207i	$-0.318154\pi$
$602$	−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	0.999451	−	0.0331368i	$-0.0105497\pi$
$607$	2.89077	+	10.7885i	0.117333	+	0.437891i	−0.882118	+	0.471028i	$0.843883\pi$
$608$	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	−0.871151	−	0.491015i	$-0.836626\pi$
$613$	−1.68999	+	2.60236i	−0.0682580	+	0.105108i	0.802893	+	0.596123i	$0.203293\pi$
$614$	−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	0.526888	+	0.849935i	$0.323359\pi$
$617$	7.16450	+	45.2349i	0.288432	+	1.82109i	−0.238456	+	0.971153i	$0.576641\pi$
$618$	−3.13404	−	11.6964i	−0.126070	−	0.470498i
$619$	1.86817	−	17.7745i	0.0750883	−	0.714417i	−0.890613	−	0.454762i	$-0.849724\pi$
$619$	1.86817	−	17.7745i	0.0750883	−	0.714417i	0.965701	−	0.259655i	$-0.0836090\pi$
$620$		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	0.588942	−	0.808175i	$-0.299545\pi$
$631$	0.0581461	+	0.0422456i	0.00231476	+	0.00168177i	−0.586627	+	0.809857i	$0.699545\pi$
$632$	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	0.267408	−	0.963583i	$-0.413833\pi$
$641$	22.8779	−	4.86285i	0.903622	−	0.192071i	0.636214	+	0.771513i	$0.280499\pi$
$642$	−2.38567	+	6.21488i	−0.0941549	+	0.245282i
$643$	−20.9354	−	20.9354i	−0.825611	−	0.825611i	0.161295	−	0.986906i	$-0.448433\pi$
$643$	−20.9354	−	20.9354i	−0.825611	−	0.825611i	−0.986906	+	0.161295i	$0.948433\pi$
$644$	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	0.0268974	−	0.999638i	$-0.491437\pi$
$647$	18.2066	−	6.98885i	0.715775	−	0.274760i	0.688877	+	0.724878i	$0.258104\pi$
$648$	−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	0.580077	−	0.814562i	$-0.303023\pi$
$653$	−2.45523	−	1.98821i	−0.0960807	−	0.0778046i	−0.676157	+	0.736757i	$0.736356\pi$
$654$	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	0.0371852	−	0.999308i	$-0.488161\pi$
$659$	−13.3517	−	4.33824i	−0.520110	−	0.168994i	−0.557295	+	0.830314i	$0.688161\pi$
$660$		0			0
$661$	−9.47098	−	8.52771i	−0.368378	−	0.331689i	0.464063	−	0.885802i	$-0.346391\pi$
$661$	−9.47098	−	8.52771i	−0.368378	−	0.331689i	−0.832442	+	0.554113i	$0.813058\pi$
$662$	−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	0.916137	−	0.400865i	$-0.131290\pi$
$673$	29.3231	+	14.9409i	1.13032	+	0.575928i	0.214185	+	0.976793i	$0.431290\pi$
$674$	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	−0.447478	−	0.894295i	$-0.647678\pi$
$677$	4.87849	−	3.16813i	0.187496	−	0.121761i	0.634973	+	0.772534i	$0.281011\pi$
$678$	−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	0.518909	−	0.854829i	$-0.326338\pi$
$683$	−11.1104	−	13.7202i	−0.425127	−	0.524989i	−0.944037	+	0.329841i	$0.893005\pi$
$684$	−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	−0.00835918	−	0.999965i	$-0.502661\pi$
$691$	25.8993	−	23.3198i	0.985254	−	0.887127i	0.993613	+	0.112838i	$0.0359942\pi$
$692$	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	−0.527111	−	0.849796i	$-0.676725\pi$
$709$	7.00111	−	6.30382i	0.262932	−	0.236745i	0.790043	+	0.613051i	$0.210058\pi$
$710$		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	0.465505	−	0.885045i	$-0.345873\pi$
$719$	38.4705	−	17.1281i	1.43471	−	0.638772i	0.969201	+	0.246273i	$0.0792059\pi$
$720$		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	0.231580	−	0.972816i	$-0.425610\pi$
$727$	−11.3062	−	5.76081i	−0.419325	−	0.213657i	−0.650905	+	0.759159i	$0.725610\pi$
$728$	−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	−0.637174	−	0.770720i	$-0.719897\pi$
$733$	−44.0331	−	16.9027i	−1.62640	−	0.624316i	−0.989225	+	0.146404i	$0.953230\pi$
$734$	−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	−0.991159	−	0.132683i	$-0.957641\pi$
$739$	−33.3478	−	30.0265i	−1.22672	−	1.10454i	−0.235560	−	0.971860i	$-0.575692\pi$
$740$		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	−0.472283	−	0.881447i	$-0.656570\pi$
$743$	11.1530	−	11.1530i	0.409164	−	0.409164i	0.881447	+	0.472283i	$0.156570\pi$
$744$	−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	0.132996	+	0.991117i	$0.457540\pi$
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	−0.924830	+	0.380380i	$0.875793\pi$
$752$	−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	−0.928716	−	0.370793i	$-0.879086\pi$
$757$	−35.7542	−	35.7542i	−1.29951	−	1.29951i	−0.370793	−	0.928716i	$-0.620914\pi$
$758$	−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	−0.991655	−	0.128921i	$-0.958849\pi$
$761$	−0.918515	+	4.32127i	−0.0332961	+	0.156646i	0.958359	+	0.285567i	$0.0921820\pi$
$762$	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	0.977975	−	0.208720i	$-0.0669299\pi$
$769$	29.9959	+	21.7933i	1.08168	+	0.785888i	0.103706	+	0.994608i	$0.466930\pi$
$770$		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	0.0647042	−	0.997904i	$-0.479390\pi$
$773$	6.48817	−	0.340031i	0.233363	−	0.0122301i	0.168659	+	0.985674i	$0.446056\pi$
$774$	−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	−0.901109	−	0.433593i	$-0.857246\pi$
$787$	−3.88508	+	5.98249i	−0.138488	+	0.213253i	0.762621	+	0.646846i	$0.223912\pi$
$788$	−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	0.754408	+	0.656406i	$0.227924\pi$
$797$	−4.68404	+	29.5739i	−0.165917	+	1.04756i	−0.920325	+	0.391154i	$0.872076\pi$
$798$	−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	0.985276	−	0.170970i	$-0.0546900\pi$
$809$	0.444905	+	2.09311i	0.0156420	+	0.0735900i	−0.969634	+	0.244560i	$0.921357\pi$
$810$		0			0
$811$	−11.1135	+	3.61100i	−0.390248	+	0.126799i	−0.497567	−	0.867425i	$-0.665773\pi$
$811$	−11.1135	+	3.61100i	−0.390248	+	0.126799i	0.107319	+	0.994225i	$0.465773\pi$
$812$	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	−0.931747	−	0.363107i	$-0.881716\pi$
$821$	−2.74655	−	26.1317i	−0.0958552	−	0.912001i	0.835892	−	0.548894i	$-0.184951\pi$
$822$	22.2374	−	8.53614i	0.775618	−	0.297732i
$823$	1.01911	+	19.4457i	0.0355239	+	0.677835i	0.957121	+	0.289688i	$0.0935515\pi$
$823$	1.01911	+	19.4457i	0.0355239	+	0.677835i	−0.921597	+	0.388147i	$0.873115\pi$
$824$	−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	−0.714041	−	0.700104i	$-0.753137\pi$
$827$	7.82374	−	15.3550i	0.272058	−	0.533944i	0.986099	+	0.166160i	$0.0531368\pi$
$828$	4.55551	+	3.68898i	0.158315	+	0.128201i
$829$	37.9342	+	16.8894i	1.31751	+	0.586592i	0.940555	−	0.339640i	$-0.110305\pi$
$829$	37.9342	+	16.8894i	1.31751	+	0.586592i	0.376952	+	0.926233i	$0.376972\pi$
$830$		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	−0.914327	−	0.404977i	$-0.867280\pi$
$839$	−11.9529	−	36.7873i	−0.412660	−	1.27004i	0.501666	−	0.865061i	$-0.332720\pi$
$840$		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	0.598954	−	0.800783i	$-0.295583\pi$
$853$	26.9029	+	4.26100i	0.921138	+	0.145894i	0.322184	+	0.946677i	$0.395583\pi$
$854$	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	0.828336	−	0.560232i	$-0.189288\pi$
$857$	37.0493	+	9.92732i	1.26558	+	0.339111i	0.437244	+	0.899343i	$0.355955\pi$
$858$	−0.496057	−	0.612580i	−0.0169351	−	0.0209131i
$859$	−0.603007	−	0.669707i	−0.0205743	−	0.0228501i	0.732770	−	0.680477i	$-0.238227\pi$
$859$	−0.603007	−	0.669707i	−0.0205743	−	0.0228501i	−0.753344	+	0.657626i	$0.771561\pi$
$860$		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	0.0323256	−	0.999477i	$-0.489709\pi$
$863$	−1.17507	−	0.0615826i	−0.0399997	−	0.00209629i	−0.0723253	+	0.997381i	$0.523042\pi$
$864$	−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	0.980170	+	0.198157i	$0.0634955\pi$
$877$	22.5815	+	34.7725i	0.762524	+	1.17418i	−0.217646	+	0.976028i	$0.569838\pi$
$878$	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	0.301139	+	0.953580i	$0.402633\pi$
$881$	−20.7423	+	28.5494i	−0.698827	+	0.961852i	−0.999966	+	0.00827221i	$0.997367\pi$
$882$	7.99116	+	1.50953i	0.269076	+	0.0508285i
$883$	−12.7280	+	2.01591i	−0.428330	+	0.0678407i	−0.366877	−	0.930269i	$-0.619573\pi$
$883$	−12.7280	+	2.01591i	−0.428330	+	0.0678407i	−0.0614522	+	0.998110i	$0.519573\pi$
$884$	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	−0.734796	−	0.678289i	$-0.762722\pi$
$887$	−45.7599	−	2.39817i	−1.53647	−	0.0805228i	−0.801671	+	0.597766i	$0.796055\pi$
$888$	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	0.828303	+	0.560280i	$0.189307\pi$
$907$	−5.09475	+	19.0139i	−0.169168	+	0.631345i	−0.997472	+	0.0710652i	$0.977360\pi$
$908$	−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	0.954085	+	0.299537i	$0.0968323\pi$
$911$	10.8138	+	33.2815i	0.358278	+	1.10267i	−0.595807	+	0.803128i	$0.703168\pi$
$912$	−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	−0.975117	−	0.221689i	$-0.928843\pi$
$919$	−14.7750	−	33.1853i	−0.487384	−	1.09468i	0.487734	−	0.872992i	$-0.337824\pi$
$920$		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	0.998715	−	0.0506867i	$-0.0161410\pi$
$929$	0.343990	+	3.27285i	0.0112860	+	0.107379i	−0.987429	+	0.158065i	$0.949474\pi$
$930$		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	0.804546	−	0.593891i	$-0.202409\pi$
$937$	−4.55551	−	8.94070i	−0.148822	−	0.292080i	−0.953368	+	0.301811i	$0.902409\pi$
$938$	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	−0.999233	−	0.0391481i	$-0.987536\pi$
$941$	−3.13847	−	14.7653i	−0.102311	−	0.481336i	0.896922	−	0.442188i	$-0.145798\pi$
$942$	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	0.289341	−	0.957226i	$-0.406564\pi$
$947$	35.8661	−	44.2910i	1.16549	−	1.43926i	0.876151	−	0.482036i	$-0.160103\pi$
$948$	−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	0.913729	+	0.406324i	$0.133190\pi$
$953$	−2.49558	+	15.7565i	−0.0808399	+	0.510403i	−0.994569	+	0.104079i	$0.966810\pi$
$954$	−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	0.935217	+	0.354074i	$0.115204\pi$
$967$	4.82581	+	30.4690i	0.155188	+	0.979817i	−0.780030	+	0.625743i	$0.784796\pi$
$968$	−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	−0.168674	−	0.985672i	$-0.553949\pi$
$971$	−4.01132	+	0.421607i	−0.128729	+	0.0135300i	0.0399446	+	0.999202i	$0.487282\pi$
$972$	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	0.343721	−	0.939072i	$-0.388312\pi$
$977$	24.4967	−	1.28382i	0.783719	−	0.0410730i	0.439998	+	0.897999i	$0.354979\pi$
$978$	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	0.135010	−	0.990844i	$-0.456893\pi$
$983$	35.4999	−	28.7473i	1.13227	−	0.916896i	0.997262	+	0.0739487i	$0.0235601\pi$
$984$	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	−0.854810	−	0.518940i	$-0.826327\pi$
$991$	−44.8481	+	9.53276i	−1.42465	+	0.302818i	−0.569836	+	0.821758i	$0.692993\pi$
$992$	−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	−0.671317	−	0.741170i	$-0.734271\pi$
$997$	−21.2901	+	8.17250i	−0.674264	+	0.258826i	−0.00294638	+	0.999996i	$0.500938\pi$
$998$	−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.607.8		288
5.2	odd	4		875.2.bb.c.768.11		288
5.3	odd	4		175.2.x.a.33.8	✓	288
5.4	even	2		875.2.bb.a.607.11		288
7.3	odd	6	inner	875.2.bb.b.857.11		288
25.3	odd	20	inner	875.2.bb.b.243.11		288
25.4	even	10		875.2.bb.c.257.11		288
25.21	even	5		175.2.x.a.47.8	yes	288
25.22	odd	20		875.2.bb.a.243.8		288
35.3	even	12		175.2.x.a.108.8	yes	288
35.17	even	12		875.2.bb.c.143.11		288
35.24	odd	6		875.2.bb.a.857.8		288
175.3	even	60	inner	875.2.bb.b.493.8		288
175.122	even	60		875.2.bb.a.493.11		288
175.129	odd	30		875.2.bb.c.507.11		288
175.171	odd	30		175.2.x.a.122.8	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	5.3	odd	4
175.2.x.a.47.8	yes	288	25.21	even	5
175.2.x.a.108.8	yes	288	35.3	even	12
175.2.x.a.122.8	yes	288	175.171	odd	30
875.2.bb.a.243.8		288	25.22	odd	20
875.2.bb.a.493.11		288	175.122	even	60
875.2.bb.a.607.11		288	5.4	even	2
875.2.bb.a.857.8		288	35.24	odd	6
875.2.bb.b.243.11		288	25.3	odd	20	inner
875.2.bb.b.493.8		288	175.3	even	60	inner
875.2.bb.b.607.8		288	1.1	even	1	trivial
875.2.bb.b.857.11		288	7.3	odd	6	inner
875.2.bb.c.143.11		288	35.17	even	12
875.2.bb.c.257.11		288	25.4	even	10
875.2.bb.c.507.11		288	175.129	odd	30
875.2.bb.c.768.11		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 $\F_{q}$
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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