LMFDB - Embedded newform 875.2.bb.a.607.11

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			607.11
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.a.493.11

$q$-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	0.970740	−	0.240133i	$-0.0771909\pi$
$2$	0.504213	+	0.776420i	0.356532	+	0.549012i	−0.614208	+	0.789144i	$0.710524\pi$
$3$	−0.473408	−	1.23327i	−0.273322	−	0.712029i	−0.999694	−	0.0247269i	$-0.992128\pi$
$3$	−0.473408	−	1.23327i	−0.273322	−	0.712029i	0.726372	−	0.687302i	$-0.241205\pi$
$4$	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	−0.349851	−	0.936805i	$-0.613768\pi$
$13$	0.729773	−	0.371838i	0.202403	−	0.103129i	0.552254	+	0.833676i	$0.313768\pi$
$14$	−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	$0.140974\pi$
$17$	4.67910	+	5.77821i	1.13485	+	1.40142i	0.231328	+	0.972876i	$0.425693\pi$
$18$	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	−0.135381	−	0.990794i	$-0.543226\pi$
$23$	3.42753	−	2.22587i	0.714690	−	0.464125i	0.850071	+	0.526669i	$0.176559\pi$
$24$	−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	$-0.801921\pi$
$37$	0.343540	−	6.55514i	0.0564777	−	1.07766i	0.869027	−	0.494766i	$-0.164746\pi$
$38$	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	−0.830792	−	0.556583i	$-0.812112\pi$
$43$	−1.79811	+	1.79811i	−0.274209	+	0.274209i	0.556583	+	0.830792i	$0.312112\pi$
$44$	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	$0.0342643\pi$
$47$	8.95355	+	7.25044i	1.30601	+	1.05759i	0.311797	+	0.950149i	$0.399069\pi$
$48$	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	$-0.828722\pi$
$53$	−8.40051	+	3.22465i	−1.15390	+	0.442940i	−0.295207	+	0.955433i	$0.595389\pi$
$54$	−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	−0.584986	−	0.811043i	$-0.698900\pi$
$67$	0.709737	−	0.574734i	0.0867082	−	0.0702149i	0.671694	+	0.740828i	$0.265567\pi$
$68$	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	−0.267961	−	0.963430i	$-0.586350\pi$
$73$	−3.70594	+	0.194220i	−0.433747	+	0.0227317i	−0.165787	+	0.986162i	$0.553016\pi$
$74$	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	$0.0422100\pi$
$83$	0.814213	+	5.14074i	0.0893715	+	0.564269i	−0.901849	+	0.432051i	$0.857790\pi$
$84$	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	$0.232913\pi$
$97$	−1.67483	+	10.5745i	−0.170054	+	1.07368i	−0.914082	+	0.405529i	$0.867087\pi$
$98$	−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	−0.985398	−	0.170269i	$-0.945536\pi$
$103$	−6.23115	+	7.69483i	−0.613974	+	0.758194i	0.371424	+	0.928463i	$0.378870\pi$
$104$	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	$-0.498583\pi$
$107$	5.25791	−	1.40885i	0.508302	−	0.136199i	0.503850	+	0.863791i	$0.331916\pi$
$108$	−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	0.999903	−	0.0139501i	$-0.00444059\pi$
$113$	4.26151	+	8.36368i	0.400889	+	0.786789i	−0.599014	+	0.800739i	$0.704441\pi$
$114$	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	$-0.808691\pi$
$127$	1.32420	−	2.59888i	0.117503	−	0.230613i	0.942266	+	0.334866i	$0.108691\pi$
$128$	−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	−0.395644	−	0.918404i	$-0.629479\pi$
$137$	−16.3347	−	10.6079i	−1.39557	−	0.906294i	−0.999927	+	0.0121099i	$0.996145\pi$
$138$	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	−0.449365	−	0.893348i	$-0.648350\pi$
$157$	−16.1035	−	4.31493i	−1.28520	−	0.344369i	−0.835836	+	0.548979i	$0.815017\pi$
$158$	−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	$-0.781484\pi$
$163$	−20.5419	−	1.07656i	−1.60897	−	0.0843225i	−0.835492	+	0.549503i	$0.814817\pi$
$164$	−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	$-0.608585\pi$
$167$	−4.67190	+	0.739956i	−0.361522	+	0.0572595i	−0.0269687	+	0.999636i	$0.508585\pi$
$168$	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	$-0.244787\pi$
$173$	−2.74889	−	4.23292i	−0.208994	−	0.321823i	−0.927586	+	0.373609i	$0.878120\pi$
$174$	−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	−0.301406	−	0.953496i	$-0.597456\pi$
$193$	−14.4367	−	3.86831i	−1.03918	−	0.278447i	−0.737773	+	0.675049i	$0.764123\pi$
$194$	−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	$-0.432896\pi$
$197$	1.48910	+	0.235850i	0.106094	+	0.0168036i	−0.103162	+	0.994665i	$0.532896\pi$
$198$	−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	−0.984961	−	0.172777i	$-0.944726\pi$
$223$	−3.97575	+	7.80285i	−0.266236	+	0.522518i	0.718725	+	0.695294i	$0.244726\pi$
$224$	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	$0.0842129\pi$
$227$	0.491475	+	9.37790i	0.0326203	+	0.622433i	−0.932587	+	0.360946i	$0.882454\pi$
$228$	−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	−0.896986	−	0.442060i	$-0.854248\pi$
$233$	0.998293	−	2.60064i	0.0654004	−	0.170374i	0.962386	+	0.271686i	$0.0875812\pi$
$234$	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	$-0.886138\pi$
$257$	−4.81832	−	17.9822i	−0.300559	−	1.12170i	0.636143	−	0.771571i	$-0.280529\pi$
$258$	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	$-0.596134\pi$
$263$	11.2829	−	17.3742i	0.695735	−	1.07134i	0.993179	−	0.116599i	$-0.0371991\pi$
$264$	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	−0.0153977	−	0.999881i	$-0.504901\pi$
$277$	1.22836	−	0.0643756i	0.0738049	−	0.00386795i	0.0892027	+	0.996013i	$0.471568\pi$
$278$	−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	−0.910859	−	0.412717i	$-0.864580\pi$
$283$	−11.7176	+	9.48873i	−0.696539	+	0.564046i	0.214320	+	0.976764i	$0.431246\pi$
$284$	−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	$-0.286136\pi$
$293$	−2.74224	−	2.74224i	−0.160203	−	0.160203i	−0.782657	+	0.622454i	$0.786136\pi$
$294$	−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	$0.544353\pi$
$307$	−19.7851	+	19.7851i	−1.12920	+	1.12920i	−0.990308	+	0.138889i	$0.955647\pi$
$308$	−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	$0.0600309\pi$
$313$	−0.251501	+	4.79892i	−0.0142157	+	0.271251i	−0.996485	+	0.0837745i	$0.973302\pi$
$314$	−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	$-0.0690945\pi$
$317$	27.7417	+	10.6491i	1.55813	+	0.598110i	0.581598	+	0.813477i	$0.302428\pi$
$318$	−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	−0.319617	−	0.947547i	$-0.603554\pi$
$337$	4.75641	−	2.42351i	0.259098	−	0.132017i	0.578715	+	0.815530i	$0.303554\pi$
$338$	−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	$-0.963789\pi$
$347$	−6.16865	−	16.0699i	−0.331151	−	0.862677i	0.662386	−	0.749163i	$-0.269544\pi$
$348$	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	$-0.228068\pi$
$353$	−4.61726	−	12.0284i	−0.245752	−	0.640206i	−0.999863	+	0.0165408i	$0.994735\pi$
$354$	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	0.828585	−	0.559864i	$-0.189146\pi$
$367$	2.08207	+	2.57114i	0.108683	+	0.134212i	−0.719902	+	0.694076i	$0.755813\pi$
$368$	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	$-0.714688\pi$
$373$	−3.18580	+	2.06888i	−0.164955	+	0.107123i	0.459522	+	0.888167i	$0.348021\pi$
$374$	−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	0.791135	−	0.611642i	$-0.209491\pi$
$383$	18.9792	+	7.28545i	0.969794	+	0.372269i	0.178659	+	0.983911i	$0.442824\pi$
$384$	−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	0.825681	−	0.564138i	$-0.190791\pi$
$397$	8.87732	+	7.18871i	0.445540	+	0.360791i	−0.380141	+	0.924929i	$0.624125\pi$
$398$	−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	$0.0213649\pi$
$433$	1.44743	+	9.13869i	0.0695589	+	0.439178i	−0.928189	+	0.372108i	$0.878635\pi$
$434$	−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	$0.0988386\pi$
$443$	5.90047	+	22.0209i	0.280340	+	1.04624i	−0.671838	+	0.740698i	$0.734495\pi$
$444$	−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	−0.436679	−	0.899617i	$-0.643846\pi$
$457$	−7.80380	+	2.09102i	−0.365046	+	0.0978138i	0.0716332	+	0.997431i	$0.477179\pi$
$458$	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	$0.176127\pi$
$463$	16.6944	+	32.7647i	0.775856	+	1.52270i	−0.0749286	+	0.997189i	$0.523873\pi$
$464$	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	$0.276670\pi$
$467$	−7.46192	+	19.4390i	−0.345297	+	0.899528i	−0.990746	+	0.135726i	$0.956663\pi$
$468$	−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	0.940066	−	0.340994i	$-0.110763\pi$
$487$	22.3089	+	14.4876i	1.01091	+	0.656494i	0.0708461	+	0.997487i	$0.477430\pi$
$488$	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	0.0834657	−	0.996511i	$-0.473401\pi$
$503$	−3.25409	−	0.515396i	−0.145092	−	0.0229804i	−0.228558	+	0.973530i	$0.573401\pi$
$504$	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	$-0.848656\pi$
$523$	−21.6259	−	33.3009i	−0.945633	−	1.45615i	−0.0565510	−	0.998400i	$-0.518010\pi$
$524$	−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	−0.318968	−	0.947766i	$-0.603336\pi$
$547$	−21.4047	−	3.39018i	−0.915200	−	0.144953i	−0.596232	+	0.802812i	$0.703336\pi$
$548$	−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	$-0.839857\pi$
$557$	2.91942	−	10.8954i	0.123700	−	0.461654i	0.999790	+	0.0204931i	$0.00652362\pi$
$558$	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	$-0.349927\pi$
$563$	−4.15112	−	2.69577i	−0.174949	−	0.113613i	−0.629143	+	0.777290i	$0.716594\pi$
$564$	−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	$-0.947364\pi$
$577$	−0.543104	−	10.3630i	−0.0226097	−	0.431419i	0.963749	−	0.266810i	$-0.0859696\pi$
$578$	−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	$-0.180191\pi$
$587$	−2.08337	−	4.08885i	−0.0859899	−	0.168765i	−0.929997	+	0.367568i	$0.880191\pi$
$588$	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	$-0.685776\pi$
$593$	−14.8803	+	3.98715i	−0.611059	+	0.163733i	−0.0599990	+	0.998198i	$0.519110\pi$
$594$	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	0.882118	−	0.471028i	$-0.156117\pi$
$607$	−2.89077	−	10.7885i	−0.117333	−	0.437891i	−0.999451	+	0.0331368i	$0.989450\pi$
$608$	−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	$-0.796707\pi$
$613$	1.68999	−	2.60236i	0.0682580	−	0.105108i	0.871151	+	0.491015i	$0.163374\pi$
$614$	−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	$-0.676641\pi$
$617$	−7.16450	−	45.2349i	−0.288432	−	1.82109i	0.238456	−	0.971153i	$-0.423359\pi$
$618$	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	0.986906	−	0.161295i	$-0.0515672\pi$
$643$	20.9354	+	20.9354i	0.825611	+	0.825611i	−0.161295	+	0.986906i	$0.551567\pi$
$644$	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	$-0.741896\pi$
$647$	−18.2066	+	6.98885i	−0.715775	+	0.274760i	−0.0268974	+	0.999638i	$0.508563\pi$
$648$	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	$-0.263644\pi$
$653$	2.45523	+	1.98821i	0.0960807	+	0.0778046i	−0.580077	+	0.814562i	$0.696977\pi$
$654$	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	−0.214185	−	0.976793i	$-0.568710\pi$
$673$	−29.3231	−	14.9409i	−1.13032	−	0.575928i	−0.916137	+	0.400865i	$0.868710\pi$
$674$	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	$-0.718989\pi$
$677$	−4.87849	+	3.16813i	−0.187496	+	0.121761i	0.447478	+	0.894295i	$0.352322\pi$
$678$	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	$-0.106995\pi$
$683$	11.1104	+	13.7202i	0.425127	+	0.524989i	−0.518909	+	0.854829i	$0.673662\pi$
$684$	−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	0.650905	−	0.759159i	$-0.274390\pi$
$727$	11.3062	+	5.76081i	0.419325	+	0.213657i	−0.231580	+	0.972816i	$0.574390\pi$
$728$	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	$-0.0467699\pi$
$733$	44.0331	+	16.9027i	1.62640	+	0.624316i	0.637174	+	0.770720i	$0.280103\pi$
$734$	−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	−0.881447	−	0.472283i	$-0.843430\pi$
$743$	−11.1530	+	11.1530i	−0.409164	+	0.409164i	0.472283	+	0.881447i	$0.343430\pi$
$744$	−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	$0.120914\pi$
$757$	35.7542	+	35.7542i	1.29951	+	1.29951i	0.370793	+	0.928716i	$0.379086\pi$
$758$	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	−0.168659	−	0.985674i	$-0.553944\pi$
$773$	−6.48817	+	0.340031i	−0.233363	+	0.0122301i	−0.0647042	+	0.997904i	$0.520610\pi$
$774$	−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	$-0.776088\pi$
$787$	3.88508	−	5.98249i	0.138488	−	0.213253i	0.901109	+	0.433593i	$0.142754\pi$
$788$	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	$-0.772076\pi$
$797$	4.68404	−	29.5739i	0.165917	−	1.04756i	0.920325	−	0.391154i	$-0.127924\pi$
$798$	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	$-0.906448\pi$
$823$	−1.01911	−	19.4457i	−0.0355239	−	0.677835i	0.921597	−	0.388147i	$-0.126885\pi$
$824$	−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	$-0.946863\pi$
$827$	−7.82374	+	15.3550i	−0.272058	+	0.533944i	0.714041	+	0.700104i	$0.246863\pi$
$828$	−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	−0.322184	−	0.946677i	$-0.604417\pi$
$853$	−26.9029	−	4.26100i	−0.921138	−	0.145894i	−0.598954	+	0.800783i	$0.704417\pi$
$854$	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	$-0.644045\pi$
$857$	−37.0493	−	9.92732i	−1.26558	−	0.339111i	−0.828336	+	0.560232i	$0.810712\pi$
$858$	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	0.0723253	−	0.997381i	$-0.476958\pi$
$863$	1.17507	+	0.0615826i	0.0399997	+	0.00209629i	−0.0323256	+	0.999477i	$0.510291\pi$
$864$	−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	$-0.936504\pi$
$877$	−22.5815	−	34.7725i	−0.762524	−	1.17418i	0.217646	−	0.976028i	$-0.430162\pi$
$878$	−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	0.0614522	−	0.998110i	$-0.480427\pi$
$883$	12.7280	−	2.01591i	0.428330	−	0.0678407i	0.366877	+	0.930269i	$0.380427\pi$
$884$	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	$-0.203945\pi$
$887$	45.7599	+	2.39817i	1.53647	+	0.0805228i	0.734796	+	0.678289i	$0.237278\pi$
$888$	−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	$-0.810693\pi$
$907$	5.09475	−	19.0139i	0.169168	−	0.631345i	0.997472	−	0.0710652i	$-0.0226398\pi$
$908$	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	0.953368	−	0.301811i	$-0.0975911\pi$
$937$	4.55551	+	8.94070i	0.148822	+	0.292080i	−0.804546	+	0.593891i	$0.797591\pi$
$938$	−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	$0.593436\pi$
$947$	−35.8661	+	44.2910i	−1.16549	+	1.43926i	−0.876151	+	0.482036i	$0.839897\pi$
$948$	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	$-0.866810\pi$
$953$	2.49558	−	15.7565i	0.0808399	−	0.510403i	0.994569	−	0.104079i	$-0.0331895\pi$
$954$	−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	$-0.884796\pi$
$967$	−4.82581	−	30.4690i	−0.155188	−	0.979817i	0.780030	−	0.625743i	$-0.215204\pi$
$968$	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	−0.439998	−	0.897999i	$-0.645021\pi$
$977$	−24.4967	+	1.28382i	−0.783719	+	0.0410730i	−0.343721	+	0.939072i	$0.611688\pi$
$978$	−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	$-0.976440\pi$
$983$	−35.4999	+	28.7473i	−1.13227	+	0.916896i	−0.135010	+	0.990844i	$0.543107\pi$
$984$	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	0.00294638	−	0.999996i	$-0.499062\pi$
$997$	21.2901	−	8.17250i	0.674264	−	0.258826i	0.671317	+	0.741170i	$0.265729\pi$
$998$	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.a.607.11		288
5.2	odd	4		175.2.x.a.33.8	✓	288
5.3	odd	4		875.2.bb.c.768.11		288
5.4	even	2		875.2.bb.b.607.8		288
7.3	odd	6	inner	875.2.bb.a.857.8		288
25.3	odd	20	inner	875.2.bb.a.243.8		288
25.4	even	10		175.2.x.a.47.8	yes	288
25.21	even	5		875.2.bb.c.257.11		288
25.22	odd	20		875.2.bb.b.243.11		288
35.3	even	12		875.2.bb.c.143.11		288
35.17	even	12		175.2.x.a.108.8	yes	288
35.24	odd	6		875.2.bb.b.857.11		288
175.3	even	60	inner	875.2.bb.a.493.11		288
175.122	even	60		875.2.bb.b.493.8		288
175.129	odd	30		175.2.x.a.122.8	yes	288
175.171	odd	30		875.2.bb.c.507.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	5.2	odd	4
175.2.x.a.47.8	yes	288	25.4	even	10
175.2.x.a.108.8	yes	288	35.17	even	12
175.2.x.a.122.8	yes	288	175.129	odd	30
875.2.bb.a.243.8		288	25.3	odd	20	inner
875.2.bb.a.493.11		288	175.3	even	60	inner
875.2.bb.a.607.11		288	1.1	even	1	trivial
875.2.bb.a.857.8		288	7.3	odd	6	inner
875.2.bb.b.243.11		288	25.22	odd	20
875.2.bb.b.493.8		288	175.122	even	60
875.2.bb.b.607.8		288	5.4	even	2
875.2.bb.b.857.11		288	35.24	odd	6
875.2.bb.c.143.11		288	35.3	even	12
875.2.bb.c.257.11		288	25.21	even	5
875.2.bb.c.507.11		288	175.171	odd	30
875.2.bb.c.768.11		288	5.3	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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