LMFDB - Embedded newform 875.2.bb.c.507.11

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 = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

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

Embedding invariants

Embedding label			507.11
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.c.768.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.776420 + 0.504213i) q^{2} +(1.23327 + 0.473408i) q^{3} +(-0.464876 - 1.04413i) q^{4} +(0.718837 + 0.989394i) q^{6} +(2.64389 + 0.0993238i) q^{7} +(0.455170 - 2.87383i) q^{8} +(-0.932596 - 0.839713i) q^{9} +(-0.526566 - 0.584810i) q^{11} +(-0.0790188 - 1.50777i) q^{12} +(0.371838 - 0.729773i) q^{13} +(2.00269 + 1.41020i) q^{14} +(0.272873 - 0.303056i) q^{16} +(5.77821 + 4.67910i) q^{17} +(-0.300692 - 1.12220i) q^{18} +(-1.68154 - 0.748668i) q^{19} +(3.21360 + 1.37413i) q^{21} +(-0.113967 - 0.719560i) q^{22} +(2.22587 - 3.42753i) q^{23} +(1.92184 - 3.32873i) q^{24} +(0.656664 - 0.379125i) q^{26} +(-2.55179 - 5.00818i) q^{27} +(-1.12537 - 2.80673i) q^{28} +(5.50382 - 7.57536i) q^{29} +(4.69555 - 0.493522i) q^{31} +(-5.25635 + 1.40844i) q^{32} +(-0.372543 - 0.970509i) q^{33} +(2.12705 + 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(-6.55514 + 0.343540i) q^{37} +(-0.928090 - 1.42913i) q^{38} +(0.804057 - 0.723976i) q^{39} +(-2.40999 + 0.783055i) q^{41} +(1.80225 + 2.68724i) q^{42} +(-1.79811 + 1.79811i) q^{43} +(-0.365830 + 0.821667i) q^{44} +(3.45641 - 1.53889i) q^{46} +(7.25044 + 8.95355i) q^{47} +(0.479996 - 0.244570i) q^{48} +(6.98027 + 0.525202i) q^{49} +(4.91096 + 8.50604i) q^{51} +(-0.934836 - 0.0489927i) q^{52} +(-3.22465 + 8.40051i) q^{53} +(0.543925 - 5.17510i) q^{54} +(1.48886 - 7.55288i) q^{56} +(-1.71936 - 1.71936i) q^{57} +(8.09287 - 3.10656i) q^{58} +(-11.1497 - 2.36995i) q^{59} +(1.75779 + 8.26975i) q^{61} +(3.89456 + 1.98438i) q^{62} +(-2.38227 - 2.31273i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(0.200093 - 0.941364i) q^{66} +(-0.574734 + 0.709737i) q^{67} +(2.19943 - 8.20839i) q^{68} +(4.36771 - 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(-2.83768 + 2.29791i) q^{72} +(-0.194220 + 3.70594i) q^{73} +(-5.26276 - 3.03846i) q^{74} +2.10378i q^{76} +(-1.33409 - 1.59847i) q^{77} +(0.989324 - 0.156693i) q^{78} +(4.86448 + 0.511278i) q^{79} +(-0.382611 - 3.64030i) q^{81} +(-2.26599 - 0.607171i) q^{82} +(-5.14074 - 0.814213i) q^{83} +(-0.0591594 - 3.99422i) q^{84} +(-2.30272 + 0.489458i) q^{86} +(10.3739 - 6.73691i) q^{87} +(-1.92032 + 1.24707i) q^{88} +(0.565582 - 0.120218i) q^{89} +(1.05558 - 1.89250i) q^{91} +(-4.61354 - 0.730712i) q^{92} +(6.02451 + 1.61426i) q^{93} +(1.11489 + 10.6075i) q^{94} +(-7.14926 - 0.751418i) q^{96} +(10.5745 - 1.67483i) q^{97} +(5.15481 + 3.92732i) q^{98} +0.987555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.776420	+	0.504213i	0.549012	+	0.356532i	0.789144	−	0.614208i	$-0.210524\pi$
$2$	0.776420	+	0.504213i	0.549012	+	0.356532i	−0.240133	+	0.970740i	$0.577191\pi$
$3$	1.23327	+	0.473408i	0.712029	+	0.273322i	0.687302	−	0.726372i	$-0.258795\pi$
$3$	1.23327	+	0.473408i	0.712029	+	0.273322i	0.0247269	+	0.999694i	$0.492128\pi$
$4$	−0.464876	−	1.04413i	−0.232438	−	0.522064i
$5$		0			0
$5$		0			0
$6$	0.718837	+	0.989394i	0.293464	+	0.403918i
$7$	2.64389	+	0.0993238i	0.999295	+	0.0375409i
$7$	2.64389	+	0.0993238i	0.999295	+	0.0375409i
$8$	0.455170	−	2.87383i	0.160927	−	1.01605i
$9$	−0.932596	−	0.839713i	−0.310865	−	0.279904i
$10$		0			0
$11$	−0.526566	−	0.584810i	−0.158765	−	0.176327i	0.658514	−	0.752569i	$-0.271185\pi$
$11$	−0.526566	−	0.584810i	−0.158765	−	0.176327i	−0.817279	+	0.576242i	$0.804519\pi$
$12$	−0.0790188	−	1.50777i	−0.0228108	−	0.435255i
$13$	0.371838	−	0.729773i	0.103129	−	0.202403i	−0.833676	−	0.552254i	$-0.813768\pi$
$13$	0.371838	−	0.729773i	0.103129	−	0.202403i	0.936805	+	0.349851i	$0.113768\pi$
$14$	2.00269	+	1.41020i	0.535240	+	0.376892i
$15$		0			0
$16$	0.272873	−	0.303056i	0.0682183	−	0.0757641i
$17$	5.77821	+	4.67910i	1.40142	+	1.13485i	0.972876	+	0.231328i	$0.0743071\pi$
$17$	5.77821	+	4.67910i	1.40142	+	1.13485i	0.428545	+	0.903520i	$0.359026\pi$
$18$	−0.300692	−	1.12220i	−0.0708737	−	0.264504i
$19$	−1.68154	−	0.748668i	−0.385771	−	0.171756i	0.204682	−	0.978829i	$-0.434384\pi$
$19$	−1.68154	−	0.748668i	−0.385771	−	0.171756i	−0.590453	+	0.807072i	$0.701051\pi$
$20$		0			0
$21$	3.21360	+	1.37413i	0.701266	+	0.299860i
$22$	−0.113967	−	0.719560i	−0.0242979	−	0.153411i
$23$	2.22587	−	3.42753i	0.464125	−	0.714690i	−0.526669	−	0.850071i	$-0.676559\pi$
$23$	2.22587	−	3.42753i	0.464125	−	0.714690i	0.990794	+	0.135381i	$0.0432258\pi$
$24$	1.92184	−	3.32873i	0.392294	−	0.679474i
$25$		0			0
$26$	0.656664	−	0.379125i	0.128782	−	0.0743525i
$27$	−2.55179	−	5.00818i	−0.491093	−	0.963824i
$28$	−1.12537	−	2.80673i	−0.212675	−	0.530422i
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.111266	−	0.993791i	$-0.464509\pi$
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.910768	−	0.412919i	$-0.135491\pi$
$30$		0			0
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.327005	−	0.945023i	$-0.393961\pi$
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.516340	+	0.856383i	$0.327294\pi$
$32$	−5.25635	+	1.40844i	−0.929201	+	0.248979i
$33$	−0.372543	−	0.970509i	−0.0648515	−	0.168944i
$34$	2.12705	+	6.54639i	0.364786	+	1.12270i
$35$		0			0
$36$	−0.443227	+	1.36411i	−0.0738712	+	0.227352i
$37$	−6.55514	+	0.343540i	−1.07766	+	0.0564777i	−0.582893	−	0.812549i	$-0.698079\pi$
$37$	−6.55514	+	0.343540i	−1.07766	+	0.0564777i	−0.494766	+	0.869027i	$0.664746\pi$
$38$	−0.928090	−	1.42913i	−0.150556	−	0.231836i
$39$	0.804057	−	0.723976i	0.128752	−	0.115929i
$40$		0			0
$41$	−2.40999	+	0.783055i	−0.376378	+	0.122293i	−0.491096	−	0.871106i	$-0.663404\pi$
$41$	−2.40999	+	0.783055i	−0.376378	+	0.122293i	0.114718	+	0.993398i	$0.463404\pi$
$42$	1.80225	+	2.68724i	0.278094	+	0.414651i
$43$	−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
$47$	7.25044	+	8.95355i	1.05759	+	1.30601i	0.950149	+	0.311797i	$0.100931\pi$
$47$	7.25044	+	8.95355i	1.05759	+	1.30601i	0.107437	+	0.994212i	$0.465736\pi$
$48$	0.479996	−	0.244570i	0.0692814	−	0.0353006i
$49$	6.98027	+	0.525202i	0.997181	+	0.0750288i
$50$		0			0
$51$	4.91096	+	8.50604i	0.687673	+	1.19108i
$52$	−0.934836	−	0.0489927i	−0.129638	−	0.00679406i
$53$	−3.22465	+	8.40051i	−0.442940	+	1.15390i	0.512493	+	0.858691i	$0.328722\pi$
$53$	−3.22465	+	8.40051i	−0.442940	+	1.15390i	−0.955433	+	0.295207i	$0.904611\pi$
$54$	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
$58$	8.09287	−	3.10656i	1.06265	−	0.407912i
$59$	−11.1497	−	2.36995i	−1.45157	−	0.308541i	−0.586401	−	0.810021i	$-0.699456\pi$
$59$	−11.1497	−	2.36995i	−1.45157	−	0.308541i	−0.865169	+	0.501480i	$0.832789\pi$
$60$		0			0
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	0.935022	+	0.354591i	$0.115380\pi$
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	−0.709959	+	0.704243i	$0.751287\pi$
$62$	3.89456	+	1.98438i	0.494609	+	0.252016i
$63$	−2.38227	−	2.31273i	−0.300138	−	0.291377i
$64$	−5.56698	−	1.80882i	−0.695872	−	0.226103i
$65$		0			0
$66$	0.200093	−	0.941364i	0.0246298	−	0.115874i
$67$	−0.574734	+	0.709737i	−0.0702149	+	0.0867082i	−0.811043	−	0.584986i	$-0.801100\pi$
$67$	−0.574734	+	0.709737i	−0.0702149	+	0.0867082i	0.740828	+	0.671694i	$0.234433\pi$
$68$	2.19943	−	8.20839i	0.266720	−	0.995414i
$69$	4.36771	−	3.17333i	0.525811	−	0.382024i
$70$		0			0
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	−2.83768	+	2.29791i	−0.334424	+	0.270811i
$73$	−0.194220	+	3.70594i	−0.0227317	+	0.433747i	0.963430	+	0.267961i	$0.0863497\pi$
$73$	−0.194220	+	3.70594i	−0.0227317	+	0.433747i	−0.986162	+	0.165787i	$0.946984\pi$
$74$	−5.26276	−	3.03846i	−0.611783	−	0.353213i
$75$		0			0
$76$			2.10378i			0.241320i
$77$	−1.33409	−	1.59847i	−0.152034	−	0.182163i
$78$	0.989324	−	0.156693i	0.112019	−	0.0177420i
$79$	4.86448	+	0.511278i	0.547297	+	0.0575232i	0.374142	−	0.927371i	$-0.377937\pi$
$79$	4.86448	+	0.511278i	0.547297	+	0.0575232i	0.173155	+	0.984895i	$0.444604\pi$
$80$		0			0
$81$	−0.382611	−	3.64030i	−0.0425124	−	0.404478i
$82$	−2.26599	−	0.607171i	−0.250237	−	0.0670509i
$83$	−5.14074	−	0.814213i	−0.564269	−	0.0893715i	−0.132218	−	0.991221i	$-0.542210\pi$
$83$	−5.14074	−	0.814213i	−0.564269	−	0.0893715i	−0.432051	+	0.901849i	$0.642210\pi$
$84$	−0.0591594	−	3.99422i	−0.00645482	−	0.435805i
$85$		0			0
$86$	−2.30272	+	0.489458i	−0.248309	+	0.0527796i
$87$	10.3739	−	6.73691i	1.11220	−	0.722273i
$88$	−1.92032	+	1.24707i	−0.204707	+	0.132938i
$89$	0.565582	−	0.120218i	0.0599516	−	0.0127431i	−0.177838	−	0.984060i	$-0.556910\pi$
$89$	0.565582	−	0.120218i	0.0599516	−	0.0127431i	0.237790	+	0.971317i	$0.423577\pi$
$90$		0			0
$91$	1.05558	−	1.89250i	0.110655	−	0.198388i
$92$	−4.61354	−	0.730712i	−0.480994	−	0.0761820i
$93$	6.02451	+	1.61426i	0.624713	+	0.167391i
$94$	1.11489	+	10.6075i	0.114992	+	1.09408i
$95$		0			0
$96$	−7.14926	−	0.751418i	−0.729669	−	0.0766913i
$97$	10.5745	−	1.67483i	1.07368	−	0.170054i	0.405529	−	0.914082i	$-0.367087\pi$
$97$	10.5745	−	1.67483i	1.07368	−	0.170054i	0.668148	+	0.744029i	$0.267087\pi$
$98$	5.15481	+	3.92732i	0.520714	+	0.396719i
$99$			0.987555i			0.0992530i
$100$		0			0
$101$	−5.47339	−	3.16006i	−0.544622	−	0.314438i	0.202328	−	0.979318i	$-0.435149\pi$
$101$	−5.47339	−	3.16006i	−0.544622	−	0.314438i	−0.746950	+	0.664880i	$0.768483\pi$
$102$	−0.475885	+	9.08043i	−0.0471197	+	0.899097i
$103$	−7.69483	+	6.23115i	−0.758194	+	0.613974i	−0.928463	−	0.371424i	$-0.878870\pi$
$103$	−7.69483	+	6.23115i	−0.758194	+	0.613974i	0.170269	+	0.985398i	$0.445536\pi$
$104$	−1.92800	−	1.40077i	−0.189056	−	0.137357i
$105$		0			0
$106$	−6.73933	+	4.89641i	−0.654582	+	0.475581i
$107$	−1.40885	+	5.25791i	−0.136199	+	0.508302i	0.863791	+	0.503850i	$0.168084\pi$
$107$	−1.40885	+	5.25791i	−0.136199	+	0.508302i	−0.999990	+	0.00445150i	$0.998583\pi$
$108$	−4.04291	+	4.99258i	−0.389030	+	0.480412i
$109$	−3.40888	+	16.0375i	−0.326512	+	1.53612i	0.442434	+	0.896801i	$0.354115\pi$
$109$	−3.40888	+	16.0375i	−0.326512	+	1.53612i	−0.768945	+	0.639315i	$0.779218\pi$
$110$		0			0
$111$	−8.24689	−	2.67958i	−0.782760	−	0.254334i
$112$	0.751546	−	0.774144i	0.0710145	−	0.0731497i
$113$	−8.36368	−	4.26151i	−0.786789	−	0.400889i	0.0139501	−	0.999903i	$-0.495559\pi$
$113$	−8.36368	−	4.26151i	−0.786789	−	0.400889i	−0.800739	+	0.599014i	$0.795559\pi$
$114$	−0.468022	−	2.20187i	−0.0438343	−	0.206224i
$115$		0			0
$116$	−10.4682	−	2.22509i	−0.971952	−	0.206595i
$117$	−0.959574	+	0.368346i	−0.0887127	+	0.0340536i
$118$	−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
$122$	−2.80493	+	7.30710i	−0.253947	+	0.661554i
$123$	−3.34288	−	0.175193i	−0.301417	−	0.0157966i
$124$	−2.69815	−	4.67333i	−0.242301	−	0.419678i
$125$		0			0
$126$	−0.683534	−	2.99683i	−0.0608940	−	0.266979i
$127$	−2.59888	+	1.32420i	−0.230613	+	0.117503i	−0.565480	−	0.824762i	$-0.691309\pi$
$127$	−2.59888	+	1.32420i	−0.230613	+	0.117503i	0.334866	+	0.942266i	$0.391309\pi$
$128$	3.43896	+	4.24676i	0.303964	+	0.375365i
$129$	−3.06879	+	1.36632i	−0.270192	+	0.120297i
$130$		0			0
$131$	−2.73808	+	6.14983i	−0.239227	+	0.537313i	−0.992763	−	0.120094i	$-0.961680\pi$
$131$	−2.73808	+	6.14983i	−0.239227	+	0.537313i	0.753535	+	0.657408i	$0.228347\pi$
$132$	−0.840150	+	0.840150i	−0.0731256	+	0.0731256i
$133$	−4.37143	−	2.14641i	−0.379051	−	0.186117i
$134$	−0.804093	+	0.261266i	−0.0694631	+	0.0225699i
$135$		0			0
$136$	16.0770	−	14.4758i	1.37859	−	1.24129i
$137$	−10.6079	−	16.3347i	−0.906294	−	1.39557i	−0.918404	−	0.395644i	$-0.870521\pi$
$137$	−10.6079	−	16.3347i	−0.906294	−	1.39557i	0.0121099	−	0.999927i	$-0.496145\pi$
$138$	4.99121	−	0.261578i	0.424880	−	0.0222670i
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	−0.963609	−	0.267315i	$-0.913863\pi$
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	0.936700	+	0.350133i	$0.113863\pi$
$140$		0			0
$141$	4.70307	+	14.4746i	0.396070	+	1.21898i
$142$	0.314658	+	0.819711i	0.0264055	+	0.0687886i
$143$	−0.622576	+	0.166819i	−0.0520624	+	0.0139501i
$144$	−0.508961	+	0.0534939i	−0.0424134	+	0.00445783i
$145$		0			0
$146$	−2.01938	+	2.77944i	−0.167125	+	0.230028i
$147$	8.35992	+	3.95223i	0.689515	+	0.325974i
$148$	3.40603	+	6.68471i	0.279974	+	0.549480i
$149$	−9.86165	+	5.69362i	−0.807897	+	0.466440i	−0.846225	−	0.532825i	$-0.821130\pi$
$149$	−9.86165	+	5.69362i	−0.807897	+	0.466440i	0.0383277	+	0.999265i	$0.487797\pi$
$150$		0			0
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	−0.998469	−	0.0553124i	$-0.982385\pi$
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	0.547136	+	0.837043i	$0.315718\pi$
$152$	−2.91693	+	4.49168i	−0.236595	+	0.364324i
$153$	−1.45963	−	9.21574i	−0.118004	−	0.745049i
$154$	−0.229846	−	1.91375i	−0.0185216	−	0.154215i
$155$		0			0
$156$	−1.12971	−	0.502980i	−0.0904493	−	0.0402706i
$157$	−4.31493	−	16.1035i	−0.344369	−	1.28520i	−0.893348	−	0.449365i	$-0.851650\pi$
$157$	−4.31493	−	16.1035i	−0.344369	−	1.28520i	0.548979	−	0.835836i	$-0.315017\pi$
$158$	3.51909	+	2.84970i	0.279964	+	0.226710i
$159$	−7.95373	+	8.83352i	−0.630772	+	0.700543i
$160$		0			0
$161$	6.22537	−	8.84092i	0.490628	−	0.696762i
$162$	1.53842	−	3.01932i	0.120870	−	0.237220i
$163$	1.07656	+	20.5419i	0.0843225	+	1.60897i	0.633825	+	0.773476i	$0.281484\pi$
$163$	1.07656	+	20.5419i	0.0843225	+	1.60897i	−0.549503	+	0.835492i	$0.685183\pi$
$164$	1.93796	+	2.15232i	0.151329	+	0.168068i
$165$		0			0
$166$	−3.58084	−	3.22420i	−0.277927	−	0.250246i
$167$	0.739956	−	4.67190i	0.0572595	−	0.361522i	−0.942377	−	0.334553i	$-0.891415\pi$
$167$	0.739956	−	4.67190i	0.0572595	−	0.361522i	0.999636	−	0.0269687i	$-0.00858546\pi$
$168$	5.41176	−	8.60990i	0.417526	−	0.664268i
$169$	7.24690	+	9.97451i	0.557454	+	0.767270i
$170$		0			0
$171$	0.939527	+	2.11021i	0.0718475	+	0.161372i
$172$	2.71336	+	1.04156i	0.206892	+	0.0794182i
$173$	4.23292	+	2.74889i	0.321823	+	0.208994i	0.695432	−	0.718592i	$-0.255213\pi$
$173$	4.23292	+	2.74889i	0.321823	+	0.208994i	−0.373609	+	0.927586i	$0.621880\pi$
$174$	11.4514			0.868126
$175$		0			0
$176$	−0.320916			−0.0241900
$177$	−12.6287	−	8.20115i	−0.949228	−	0.616436i
$178$	0.499745	+	0.191834i	0.0374575	+	0.0143786i
$179$	−1.46827	−	3.29779i	−0.109744	−	0.246488i	0.850322	−	0.526263i	$-0.176407\pi$
$179$	−1.46827	−	3.29779i	−0.109744	−	0.246488i	−0.960066	+	0.279774i	$0.909740\pi$
$180$		0			0
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	0.446737	−	0.894665i	$-0.352586\pi$
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	−0.988927	+	0.148406i	$0.952586\pi$
$182$	1.77380	−	0.937141i	0.131483	−	0.0694655i
$183$	−1.74714	+	11.0310i	−0.129152	+	0.815434i
$184$	−8.83701	−	7.95688i	−0.651473	−	0.586589i
$185$		0			0
$186$	3.86362	+	4.29099i	0.283294	+	0.314630i
$187$	−0.306219	−	5.84301i	−0.0223930	−	0.427283i
$188$	5.97810	−	11.7327i	0.435998	−	0.855694i
$189$	−6.24922	−	13.4945i	−0.454564	−	0.981581i
$190$		0			0
$191$	15.5218	−	17.2388i	1.12312	−	1.24735i	0.157467	−	0.987524i	$-0.449667\pi$
$191$	15.5218	−	17.2388i	1.12312	−	1.24735i	0.965655	−	0.259828i	$-0.0836660\pi$
$192$	−6.00927	−	4.86621i	−0.433682	−	0.351189i
$193$	3.86831	+	14.4367i	0.278447	+	1.03918i	0.953496	+	0.301406i	$0.0974560\pi$
$193$	3.86831	+	14.4367i	0.278447	+	1.03918i	−0.675049	+	0.737773i	$0.735877\pi$
$194$	9.05472	+	4.03142i	0.650091	+	0.289439i
$195$		0			0
$196$	−2.69658	−	7.53245i	−0.192613	−	0.538032i
$197$	0.235850	+	1.48910i	0.0168036	+	0.106094i	0.994665	−	0.103162i	$-0.0328960\pi$
$197$	0.235850	+	1.48910i	0.0168036	+	0.106094i	−0.977861	+	0.209256i	$0.932896\pi$
$198$	−0.497938	+	0.766758i	−0.0353869	+	0.0544911i
$199$	−1.75472	+	3.03927i	−0.124389	+	0.215448i	−0.921494	−	0.388393i	$-0.873030\pi$
$199$	−1.75472	+	3.03927i	−0.124389	+	0.215448i	0.797105	+	0.603841i	$0.206364\pi$
$200$		0			0
$201$	−1.04480	+	0.603214i	−0.0736943	+	0.0425474i
$202$	−2.65630	−	5.21329i	−0.186897	−	0.366806i
$203$	15.3039	−	19.4817i	1.07412	−	1.36735i
$204$	6.59841	−	9.08193i	0.461981	−	0.635863i
$205$		0			0
$206$	−9.11625	+	0.958157i	−0.635159	+	0.0667579i
$207$	−4.95398	+	1.32741i	−0.344325	+	0.0922616i
$208$	−0.119698	−	0.311823i	−0.00829955	−	0.0216211i
$209$	0.447610	+	1.37760i	0.0309619	+	0.0952908i
$210$		0			0
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	10.2703	−	0.538243i	0.705366	−	0.0369666i
$213$	0.682368	+	1.05076i	0.0467551	+	0.0719966i
$214$	−3.74497	+	3.37199i	−0.256001	+	0.230504i
$215$		0			0
$216$	−15.5542	+	5.05385i	−1.05833	+	0.343871i
$217$	12.4635	−	0.838436i	0.846079	−	0.0569168i
$218$	−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
$222$	−5.05197	−	6.23867i	−0.339066	−	0.418712i
$223$	−7.80285	+	3.97575i	−0.522518	+	0.266236i	−0.695294	−	0.718725i	$-0.744726\pi$
$223$	−7.80285	+	3.97575i	−0.522518	+	0.266236i	0.172777	+	0.984961i	$0.444726\pi$
$224$	−14.0371	+	3.20166i	−0.937893	+	0.213920i
$225$		0			0
$226$	−4.34502	−	7.52579i	−0.289026	−	0.500608i
$227$	9.37790	+	0.491475i	0.622433	+	0.0326203i	0.360946	−	0.932587i	$-0.382454\pi$
$227$	9.37790	+	0.491475i	0.622433	+	0.0326203i	0.261487	+	0.965207i	$0.415787\pi$
$228$	−0.995946	+	2.59453i	−0.0659581	+	0.171827i
$229$	0.899141	−	8.55475i	0.0594169	−	0.565314i	−0.923800	−	0.382875i	$-0.874934\pi$
$229$	0.899141	−	8.55475i	0.0594169	−	0.565314i	0.983217	−	0.182439i	$-0.0583993\pi$
$230$		0			0
$231$	−0.888568	−	2.60292i	−0.0584635	−	0.171259i
$232$	−19.2651	−	19.2651i	−1.26482	−	1.26482i
$233$	2.60064	−	0.998293i	0.170374	−	0.0654004i	−0.271686	−	0.962386i	$-0.587581\pi$
$233$	2.60064	−	0.998293i	0.170374	−	0.0654004i	0.442060	+	0.896986i	$0.354248\pi$
$234$	−0.930758	−	0.197839i	−0.0608455	−	0.0129331i
$235$		0			0
$236$	2.70871	+	12.7435i	0.176322	+	0.829529i
$237$	5.75718	+	2.93343i	0.373969	+	0.190547i
$238$	4.97347	+	17.5192i	0.322382	+	1.13560i
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.0413782	−	0.999144i	$-0.513175\pi$
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.620757	+	0.784003i	$0.713175\pi$
$240$		0			0
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	0.849247	+	0.527995i	$0.177056\pi$
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	−0.990581	+	0.136927i	$0.956277\pi$
$242$	6.04790	−	7.46854i	0.388774	−	0.480096i
$243$	−3.11283	+	11.6172i	−0.199688	+	0.745247i
$244$	7.81753	−	5.67977i	0.500466	−	0.363610i
$245$		0			0
$246$	−2.50714	−	1.82155i	−0.159850	−	0.116137i
$247$	−1.17162	+	0.948757i	−0.0745482	+	0.0603680i
$248$	0.718975	−	13.7189i	0.0456550	−	0.871148i
$249$	−5.95446	−	3.43781i	−0.377349	−	0.217862i
$250$		0			0
$251$		−	29.0617i		−	1.83436i	−0.398477	−	0.917178i	$-0.630461\pi$
$251$		−	29.0617i		−	1.83436i	0.398477	−	0.917178i	$-0.369539\pi$
$252$	−1.30733	+	3.56254i	−0.0823541	+	0.224419i
$253$	−3.17652	+	0.503111i	−0.199706	+	0.0316303i
$254$	−2.68550	−	0.282257i	−0.168503	−	0.0177104i
$255$		0			0
$256$	1.75251	+	16.6740i	0.109532	+	1.04213i
$257$	−17.9822	−	4.81832i	−1.12170	−	0.300559i	−0.350129	−	0.936701i	$-0.613862\pi$
$257$	−17.9822	−	4.81832i	−1.12170	−	0.300559i	−0.771571	+	0.636143i	$0.780529\pi$
$258$	−3.07159	−	0.486492i	−0.191229	−	0.0302876i
$259$	−17.3652	+	0.257200i	−1.07902	+	0.0159816i
$260$		0			0
$261$	−11.4940	+	2.44312i	−0.711459	+	0.151225i
$262$	−5.22673	+	3.39428i	−0.322908	+	0.209699i
$263$	17.3742	−	11.2829i	1.07134	−	0.695735i	0.116599	−	0.993179i	$-0.462801\pi$
$263$	17.3742	−	11.2829i	1.07134	−	0.695735i	0.954739	+	0.297444i	$0.0961342\pi$
$264$	−2.95865	+	0.628881i	−0.182092	+	0.0387049i
$265$		0			0
$266$	−2.31182	−	3.87065i	−0.141747	−	0.237325i
$267$	0.754428	+	0.119490i	0.0461702	+	0.00731265i
$268$	1.00824	+	0.270156i	0.0615879	+	0.0165024i
$269$	0.134230	+	1.27711i	0.00818414	+	0.0778669i	0.997852	−	0.0655149i	$-0.0208690\pi$
$269$	0.134230	+	1.27711i	0.00818414	+	0.0778669i	−0.989667	+	0.143382i	$0.954202\pi$
$270$		0			0
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.471636	−	0.881793i	$-0.343664\pi$
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.277995	+	0.960583i	$0.410330\pi$
$272$	2.99475	−	0.474322i	0.181583	−	0.0287600i
$273$	2.19774	−	1.83425i	0.133013	−	0.111014i
$274$		−	18.0313i		−	1.08931i
$275$		0			0
$276$	−5.34381	−	3.08525i	−0.321660	−	0.185710i
$277$	−0.0643756	+	1.22836i	−0.00386795	+	0.0738049i	−0.999881	−	0.0153977i	$-0.995099\pi$
$277$	−0.0643756	+	1.22836i	−0.00386795	+	0.0738049i	0.996013	+	0.0892027i	$0.0284319\pi$
$278$	−0.738635	+	0.598135i	−0.0443004	+	0.0358737i
$279$	−4.79347	−	3.48266i	−0.286977	−	0.208501i
$280$		0			0
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	−3.64670	+	13.6097i	−0.217158	+	0.810445i
$283$	−9.48873	+	11.7176i	−0.564046	+	0.696539i	−0.976764	−	0.214320i	$-0.931246\pi$
$283$	−9.48873	+	11.7176i	−0.564046	+	0.696539i	0.412717	+	0.910859i	$0.364580\pi$
$284$	0.225375	−	1.06031i	0.0133736	−	0.0629177i
$285$		0			0
$286$	−0.567492	−	0.184389i	−0.0335565	−	0.0109032i
$287$	−6.44953	+	1.83094i	−0.380704	+	0.108077i
$288$	6.08473	+	3.10033i	0.358546	+	0.182689i
$289$	7.95920	+	37.4451i	0.468188	+	2.20265i
$290$		0			0
$291$	13.8341	+	2.94052i	0.810968	+	0.172377i
$292$	3.95977	−	1.52001i	0.231728	−	0.0889520i
$293$	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
$297$	−1.58515	+	4.12945i	−0.0919795	+	0.239615i
$298$	−10.5276	−	0.551727i	−0.609846	−	0.0319607i
$299$	−1.67366	−	2.89886i	−0.0967902	−	0.167646i
$300$		0			0
$301$	−4.93259	+	4.57540i	−0.284310	+	0.263722i
$302$	−9.14958	+	4.66195i	−0.526499	+	0.268265i
$303$	−5.25416	−	6.48835i	−0.301844	−	0.372746i
$304$	−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	$-0.0443532\pi$
$308$	−1.04882	+	2.13606i	−0.0597622	+	0.121713i
$309$	−12.4397	+	4.04190i	−0.707669	+	0.229935i
$310$		0			0
$311$	15.7376	−	14.1702i	0.892396	−	0.803517i	−0.0888962	−	0.996041i	$-0.528334\pi$
$311$	15.7376	−	14.1702i	0.892396	−	0.803517i	0.981292	+	0.192524i	$0.0616673\pi$
$312$	−1.71460	−	2.64026i	−0.0970703	−	0.149475i
$313$	−4.79892	+	0.251501i	−0.271251	+	0.0142157i	−0.187477	−	0.982269i	$-0.560031\pi$
$313$	−4.79892	+	0.251501i	−0.271251	+	0.0142157i	−0.0837745	+	0.996485i	$0.526698\pi$
$314$	4.76941	−	14.6787i	0.269153	−	0.828369i
$315$		0			0
$316$	−1.72754	−	5.31683i	−0.0971818	−	0.299095i
$317$	10.6491	+	27.7417i	0.598110	+	1.55813i	0.813477	+	0.581598i	$0.197572\pi$
$317$	10.6491	+	27.7417i	0.598110	+	1.55813i	−0.215366	+	0.976533i	$0.569095\pi$
$318$	−10.6294	+	2.84814i	−0.596068	+	0.159716i
$319$	−7.32827	+	0.770232i	−0.410304	+	0.0431247i
$320$		0			0
$321$	−4.22663	+	5.81746i	−0.235908	+	0.324699i
$322$	9.29121	−	3.72536i	0.517779	−	0.207606i
$323$	−6.21317	−	12.1940i	−0.345710	−	0.678495i
$324$	−3.62308	+	2.09178i	−0.201282	+	0.116210i
$325$		0			0
$326$	−9.52165	+	16.4920i	−0.527355	+	0.913406i
$327$	−11.7964	+	18.1648i	−0.652340	+	1.00452i
$328$	1.15341	+	7.28234i	0.0636864	+	0.402100i
$329$	18.2800	+	24.3923i	1.00781	+	1.34479i
$330$		0			0
$331$	21.0153	+	9.35662i	1.15511	+	0.514286i	0.892691	−	0.450669i	$-0.148815\pi$
$331$	21.0153	+	9.35662i	1.15511	+	0.514286i	0.262415	+	0.964955i	$0.415481\pi$
$332$	1.53966	+	5.74610i	0.0845000	+	0.315358i
$333$	6.40177	+	5.18405i	0.350815	+	0.284084i
$334$	2.93015	−	3.25426i	0.160331	−	0.178065i
$335$		0			0
$336$	1.29335	−	0.598940i	0.0705578	−	0.0326749i
$337$	−2.42351	+	4.75641i	−0.132017	+	0.259098i	−0.947547	−	0.319617i	$-0.896446\pi$
$337$	−2.42351	+	4.75641i	−0.132017	+	0.259098i	0.815530	+	0.578715i	$0.196446\pi$
$338$	0.597364	+	11.3984i	0.0324923	+	0.619991i
$339$	−8.29724	−	9.21502i	−0.450644	−	0.500491i
$340$		0			0
$341$	−2.76113	−	2.48613i	−0.149524	−	0.134632i
$342$	−0.334529	+	2.11213i	−0.0180893	+	0.114211i
$343$	18.4029	+	2.08188i	0.993662	+	0.112411i
$344$	4.34902	+	5.98591i	0.234484	+	0.322739i
$345$		0			0
$346$	1.90050	+	4.26859i	0.102171	+	0.229481i
$347$	−16.0699	−	6.16865i	−0.862677	−	0.331151i	−0.113514	−	0.993536i	$-0.536211\pi$
$347$	−16.0699	−	6.16865i	−0.862677	−	0.331151i	−0.749163	+	0.662386i	$0.769544\pi$
$348$	−11.8568	−	7.69989i	−0.635591	−	0.412758i
$349$	20.0775			1.07472			0.537362	−	0.843351i	$-0.319421\pi$
$349$	20.0775			1.07472			0.537362	+	0.843351i	$0.319421\pi$
$350$		0			0
$351$	−4.60369			−0.245727
$352$	3.59148	+	2.33234i	0.191427	+	0.124314i
$353$	12.0284	+	4.61726i	0.640206	+	0.245752i	0.656747	−	0.754111i	$-0.271932\pi$
$353$	12.0284	+	4.61726i	0.640206	+	0.245752i	−0.0165408	+	0.999863i	$0.505265\pi$
$354$	−5.67002	−	12.7351i	−0.301358	−	0.676861i
$355$		0			0
$356$	−0.388449	−	0.534654i	−0.0205878	−	0.0283366i
$357$	12.1392	+	22.9768i	0.642473	+	1.21606i
$358$	0.522794	−	3.30079i	0.0276305	−	0.174452i
$359$	−5.74355	−	5.17152i	−0.303133	−	0.272942i	0.503499	−	0.863996i	$-0.332046\pi$
$359$	−5.74355	−	5.17152i	−0.303133	−	0.272942i	−0.806633	+	0.591053i	$0.798712\pi$
$360$		0			0
$361$	−10.4464	−	11.6019i	−0.549812	−	0.610628i
$362$	−0.601280	−	11.4731i	−0.0316026	−	0.603013i
$363$	6.22559	−	12.2184i	0.326759	−	0.641300i
$364$	−2.46673	−	0.222382i	−0.129292	−	0.0116560i
$365$		0			0
$366$	−6.91848	+	7.68375i	−0.361635	+	0.401636i
$367$	2.57114	+	2.08207i	0.134212	+	0.108683i	0.694076	−	0.719902i	$-0.255813\pi$
$367$	2.57114	+	2.08207i	0.134212	+	0.108683i	−0.559864	+	0.828585i	$0.689146\pi$
$368$	−0.431357	−	1.60984i	−0.0224860	−	0.0839189i
$369$	2.90509	+	1.29343i	0.151233	+	0.0673333i
$370$		0			0
$371$	−9.35999	+	21.8897i	−0.485946	+	1.13646i
$372$	−1.11515	−	7.04080i	−0.0578180	−	0.365049i
$373$	−2.06888	+	3.18580i	−0.107123	+	0.164955i	−0.888167	−	0.459522i	$-0.848021\pi$
$373$	−2.06888	+	3.18580i	−0.107123	+	0.164955i	0.781044	+	0.624476i	$0.214688\pi$
$374$	2.70837	−	4.69103i	0.140046	−	0.242567i
$375$		0			0
$376$	29.0312	−	16.7612i	1.49717	−	0.864391i
$377$	−3.48176	−	6.83335i	−0.179320	−	0.351935i
$378$	1.95209	−	13.6283i	0.100404	−	0.700966i
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	−0.0459436	−	0.998944i	$-0.514629\pi$
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	0.964250	−	0.264996i	$-0.0853705\pi$
$380$		0			0
$381$	−3.83201	+	0.402760i	−0.196320	+	0.0206340i
$382$	20.7435	−	5.55820i	1.06133	−	0.284382i
$383$	−7.28545	−	18.9792i	−0.372269	−	0.969794i	−0.983911	−	0.178659i	$-0.942824\pi$
$383$	−7.28545	−	18.9792i	−0.372269	−	0.969794i	0.611642	−	0.791135i	$-0.290509\pi$
$384$	2.23072	+	6.86544i	0.113836	+	0.350350i
$385$		0			0
$386$	−4.27576	+	13.1594i	−0.217630	+	0.669797i
$387$	3.18681	−	0.167013i	0.161994	−	0.00848977i
$388$	−6.66457	−	10.2625i	−0.338342	−	0.521001i
$389$	−8.29482	+	7.46869i	−0.420564	+	0.378678i	−0.852066	−	0.523434i	$-0.824650\pi$
$389$	−8.29482	+	7.46869i	−0.420564	+	0.378678i	0.431502	+	0.902112i	$0.357984\pi$
$390$		0			0
$391$	28.8993	−	9.38994i	1.46150	−	0.474870i
$392$	4.68655	−	19.8211i	0.236707	−	1.00112i
$393$	−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
$397$	7.18871	+	8.87732i	0.360791	+	0.445540i	0.924929	−	0.380141i	$-0.124125\pi$
$397$	7.18871	+	8.87732i	0.360791	+	0.445540i	−0.564138	+	0.825681i	$0.690791\pi$
$398$	−2.89484	+	1.47500i	−0.145105	+	0.0739348i
$399$	−4.37503	−	4.71657i	−0.219025	−	0.236124i
$400$		0			0
$401$	14.5815	+	25.2559i	0.728165	+	1.26122i	0.957658	+	0.287908i	$0.0929597\pi$
$401$	14.5815	+	25.2559i	0.728165	+	1.26122i	−0.229493	+	0.973310i	$0.573707\pi$
$402$	−1.11535	−	0.0584530i	−0.0556285	−	0.00291537i
$403$	1.38582	−	3.61020i	0.0690328	−	0.179837i
$404$	−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
$408$	26.6803	−	10.2416i	1.32087	−	0.507034i
$409$	31.5725	+	6.71095i	1.56116	+	0.331835i	0.905875	−	0.423545i	$-0.139214\pi$
$409$	31.5725	+	6.71095i	1.56116	+	0.331835i	0.655287	+	0.755380i	$0.272548\pi$
$410$		0			0
$411$	−5.34941	−	25.1670i	−0.263867	−	1.24140i
$412$	10.0833	+	5.13768i	0.496767	+	0.253115i
$413$	−29.2432	−	7.37330i	−1.43896	−	0.362816i
$414$	−4.51566	−	1.46723i	−0.221933	−	0.0721103i
$415$		0			0
$416$	−0.926673	+	4.35966i	−0.0454339	+	0.213750i
$417$	−0.853493	+	1.05398i	−0.0417957	+	0.0516134i
$418$	−0.347072	+	1.29529i	−0.0169758	+	0.0633547i
$419$	22.7957	−	16.5620i	1.11364	−	0.809109i	0.130410	−	0.991460i	$-0.458371\pi$
$419$	22.7957	−	16.5620i	1.11364	−	0.809109i	0.983233	+	0.182351i	$0.0583708\pi$
$420$		0			0
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	−14.3595	+	11.6281i	−0.699009	+	0.566047i
$423$	0.756681	−	14.4383i	0.0367911	−	0.702015i
$424$	22.6739	+	13.0908i	1.10114	+	0.635744i
$425$		0			0
$426$			1.15989i			0.0561967i
$427$	3.82601	+	22.0389i	0.185154	+	1.06654i
$428$	6.14488	−	0.973254i	0.297024	−	0.0470440i
$429$	−0.846777	−	0.0889999i	−0.0408828	−	0.00429695i
$430$		0			0
$431$	−0.259952	−	2.47328i	−0.0125215	−	0.119134i	0.986476	−	0.163908i	$-0.0524099\pi$
$431$	−0.259952	−	2.47328i	−0.0125215	−	0.119134i	−0.998997	+	0.0447740i	$0.985743\pi$
$432$	−2.21408	−	0.593260i	−0.106525	−	0.0285432i
$433$	−9.13869	−	1.44743i	−0.439178	−	0.0695589i	−0.0670695	−	0.997748i	$-0.521365\pi$
$433$	−9.13869	−	1.44743i	−0.439178	−	0.0695589i	−0.372108	+	0.928189i	$0.621365\pi$
$434$	10.0997	+	5.63329i	0.484800	+	0.270406i
$435$		0			0
$436$	18.3299	−	3.89615i	0.877845	−	0.186592i
$437$	−6.30896	+	4.09709i	−0.301798	+	0.195990i
$438$	−3.80625	+	2.47180i	−0.181869	+	0.118107i
$439$	20.7692	−	4.41462i	0.991258	−	0.210698i	0.316384	−	0.948631i	$-0.397531\pi$
$439$	20.7692	−	4.41462i	0.991258	−	0.210698i	0.674874	+	0.737933i	$0.264198\pi$
$440$		0			0
$441$	−6.06875	−	6.35122i	−0.288988	−	0.302439i
$442$	5.56830	+	0.881932i	0.264857	+	0.0419492i
$443$	−22.0209	−	5.90047i	−1.04624	−	0.280340i	−0.305545	−	0.952178i	$-0.598839\pi$
$443$	−22.0209	−	5.90047i	−1.04624	−	0.280340i	−0.740698	+	0.671838i	$0.765505\pi$
$444$	1.03596	+	9.85649i	0.0491644	+	0.467768i
$445$		0			0
$446$	−8.06292	−	0.847447i	−0.381790	−	0.0401278i
$447$	−14.8575	+	2.35319i	−0.702734	+	0.111302i
$448$	−14.5388	−	5.33525i	−0.686893	−	0.252067i
$449$		−	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
$452$	−0.561488	+	10.7138i	−0.0264102	+	0.503936i
$453$	−11.3874	+	9.22132i	−0.535026	+	0.433256i
$454$	7.03338	+	5.11005i	0.330093	+	0.239827i
$455$		0			0
$456$	−5.72376	+	4.15856i	−0.268040	+	0.194742i
$457$	2.09102	−	7.80380i	0.0978138	−	0.365046i	−0.899617	−	0.436679i	$-0.856154\pi$
$457$	2.09102	−	7.80380i	0.0978138	−	0.365046i	0.997431	+	0.0716332i	$0.0228211\pi$
$458$	5.01153	−	6.18872i	0.234173	−	0.289180i
$459$	8.68897	−	40.8784i	0.405566	−	1.90804i
$460$		0			0
$461$	−36.2181	−	11.7680i	−1.68684	−	0.548089i	−0.700625	−	0.713530i	$-0.747095\pi$
$461$	−36.2181	−	11.7680i	−1.68684	−	0.548089i	−0.986220	+	0.165441i	$0.947095\pi$
$462$	0.622523	−	2.46898i	0.0289624	−	0.114868i
$463$	−32.7647	−	16.6944i	−1.52270	−	0.775856i	−0.525514	−	0.850785i	$-0.676127\pi$
$463$	−32.7647	−	16.6944i	−1.52270	−	0.775856i	−0.997189	+	0.0749286i	$0.976127\pi$
$464$	−0.793916	−	3.73508i	−0.0368566	−	0.173397i
$465$		0			0
$466$	2.52254	+	0.536183i	0.116855	+	0.0248382i
$467$	19.4390	−	7.46192i	0.899528	−	0.345297i	0.135726	−	0.990746i	$-0.456663\pi$
$467$	19.4390	−	7.46192i	0.899528	−	0.345297i	0.763803	+	0.645450i	$0.223330\pi$
$468$	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
$472$	−11.8858	+	30.9637i	−0.547091	+	1.42522i
$473$	1.99838	+	0.104730i	0.0918854	+	0.00481551i
$474$	2.99091	+	5.18041i	0.137377	+	0.237944i
$475$		0			0
$476$	6.63034	−	21.4836i	0.303901	−	0.984699i
$477$	10.0613	−	5.12650i	0.460676	−	0.234726i
$478$	−6.27071	−	7.74368i	−0.286816	−	0.354188i
$479$	−1.27864	+	0.569287i	−0.0584226	+	0.0260114i	−0.435740	−	0.900073i	$-0.643513\pi$
$479$	−1.27864	+	0.569287i	−0.0584226	+	0.0260114i	0.377317	+	0.926084i	$0.376847\pi$
$480$		0			0
$481$	−2.18674	+	4.91151i	−0.0997069	+	0.223945i
$482$	−6.90821	+	6.90821i	−0.314660	+	0.314660i
$483$	11.8629	−	7.95610i	0.539782	−	0.362015i
$484$	−11.2839	+	3.66635i	−0.512903	+	0.166652i
$485$		0			0
$486$	−8.27443	+	7.45033i	−0.375336	+	0.337954i
$487$	14.4876	+	22.3089i	0.656494	+	1.01091i	0.997487	+	0.0708461i	$0.0225699\pi$
$487$	14.4876	+	22.3089i	0.656494	+	1.01091i	−0.340994	+	0.940066i	$0.610763\pi$
$488$	24.5660	−	1.28745i	1.11205	−	0.0582801i
$489$	−8.39703	+	25.8434i	−0.379727	+	1.16868i
$490$		0			0
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	1.37110	+	3.57184i	0.0618140	+	0.161031i
$493$	67.2481	−	18.0191i	3.02870	−	0.811538i
$494$	−1.38804	+	0.145889i	−0.0624510	+	0.00656386i
$495$		0			0
$496$	1.13172	−	1.55769i	0.0508159	−	0.0699421i
$497$	1.97327	+	1.55010i	0.0885131	+	0.0695315i
$498$	−2.88977	−	5.67150i	−0.129494	−	0.254146i
$499$	−20.4454	+	11.8042i	−0.915262	+	0.528427i	−0.882120	−	0.471024i	$-0.843884\pi$
$499$	−20.4454	+	11.8042i	−0.915262	+	0.528427i	−0.0331413	+	0.999451i	$0.510551\pi$
$500$		0			0
$501$	3.12428	−	5.41141i	0.139582	−	0.241764i
$502$	14.6533	−	22.5641i	0.654008	−	1.00708i
$503$	0.515396	+	3.25409i	0.0229804	+	0.145092i	0.996511	−	0.0834657i	$-0.0265989\pi$
$503$	0.515396	+	3.25409i	0.0229804	+	0.145092i	−0.973530	+	0.228558i	$0.926599\pi$
$504$	−7.73075	+	5.79357i	−0.344355	+	0.258066i
$505$		0			0
$506$	−2.71999	−	1.21102i	−0.120918	−	0.0538363i
$507$	4.21538	+	15.7320i	0.187211	+	0.698682i
$508$	2.59079	+	2.09798i	0.114948	+	0.0930828i
$509$	−9.35937	+	10.3946i	−0.414847	+	0.460734i	−0.913961	−	0.405802i	$-0.866992\pi$
$509$	−9.35937	+	10.3946i	−0.414847	+	0.460734i	0.499114	+	0.866536i	$0.333659\pi$
$510$		0			0
$511$	−0.881584	+	9.77879i	−0.0389990	+	0.432588i
$512$	−2.08486	+	4.09177i	−0.0921387	+	0.180832i
$513$	0.541471	+	10.3319i	0.0239065	+	0.456164i
$514$	−11.5323	−	12.8079i	−0.508668	−	0.564933i
$515$		0			0
$516$	2.85322	+	2.56905i	0.125606	+	0.113096i
$517$	1.41829	−	8.95476i	0.0623765	−	0.393830i
$518$	−13.6123	−	8.55605i	−0.598092	−	0.375931i
$519$	3.91899	+	5.39402i	0.172024	+	0.236771i
$520$		0			0
$521$	11.5536	+	25.9498i	0.506172	+	1.13688i	0.968237	+	0.250035i	$0.0804421\pi$
$521$	11.5536	+	25.9498i	0.506172	+	1.13688i	−0.462065	+	0.886846i	$0.652891\pi$
$522$	−10.1560	−	3.89852i	−0.444516	−	0.170634i
$523$	33.3009	+	21.6259i	1.45615	+	0.945633i	0.998400	+	0.0565510i	$0.0180103\pi$
$523$	33.3009	+	21.6259i	1.45615	+	0.945633i	0.457748	+	0.889082i	$0.348656\pi$
$524$	7.69409			0.336118
$525$		0			0
$526$	19.1787			0.836229
$527$	29.4411	+	19.1193i	1.28247	+	0.832848i
$528$	−0.395776	−	0.151924i	−0.0172239	−	0.00661165i
$529$	2.56144	+	5.75310i	0.111367	+	0.250135i
$530$		0			0
$531$	8.40811	+	11.5728i	0.364881	+	0.502215i
$532$	−0.208955	+	5.56215i	−0.00905937	+	0.241150i
$533$	−0.324675	+	2.04992i	−0.0140632	+	0.0887918i
$534$	0.525505	+	0.473167i	0.0227408	+	0.0204759i
$535$		0			0
$536$	1.77806	+	1.97474i	0.0768006	+	0.0852958i
$537$	−0.249574	−	4.76216i	−0.0107699	−	0.205502i
$538$	−0.539718	+	1.05926i	−0.0232689	+	0.0456677i
$539$	−3.36843	−	4.35869i	−0.145088	−	0.187742i
$540$		0			0
$541$	−0.882148	+	0.979725i	−0.0379265	+	0.0421217i	−0.761810	−	0.647801i	$-0.775689\pi$
$541$	−0.882148	+	0.979725i	−0.0379265	+	0.0421217i	0.723883	+	0.689923i	$0.242355\pi$
$542$	8.92742	+	7.22928i	0.383465	+	0.310524i
$543$	−4.24301	−	15.8351i	−0.182085	−	0.679550i
$544$	−36.9625	−	16.4568i	−1.58475	−	0.705578i
$545$		0			0
$546$	2.63122	−	0.316016i	0.112606	−	0.0135243i
$547$	−3.39018	−	21.4047i	−0.144953	−	0.915200i	−0.947766	−	0.318968i	$-0.896664\pi$
$547$	−3.39018	−	21.4047i	−0.144953	−	0.915200i	0.802812	−	0.596232i	$-0.203336\pi$
$548$	−12.1242	+	18.6696i	−0.517920	+	0.797528i
$549$	5.30491	−	9.18838i	0.226408	−	0.392150i
$550$		0			0
$551$	−14.9263	+	8.61771i	−0.635882	+	0.367127i
$552$	−7.13156	−	13.9965i	−0.303539	−	0.595730i
$553$	12.8104	+	1.83492i	0.544752	+	0.0780287i
$554$	−0.669337	+	0.921263i	−0.0284374	+	0.0391407i
$555$		0			0
$556$	1.16697	−	0.122654i	0.0494906	−	0.00520167i
$557$	−10.8954	+	2.91942i	−0.461654	+	0.123700i	−0.482147	−	0.876090i	$-0.660143\pi$
$557$	−10.8954	+	2.91942i	−0.461654	+	0.123700i	0.0204931	+	0.999790i	$0.493476\pi$
$558$	−1.96574	−	5.12093i	−0.0832165	−	0.216786i
$559$	0.643607	+	1.98082i	0.0272217	+	0.0837797i
$560$		0			0
$561$	2.38847	−	7.35097i	0.100841	−	0.310358i
$562$	1.62951	−	0.0853991i	0.0687368	−	0.00360234i
$563$	2.69577	+	4.15112i	0.113613	+	0.174949i	0.890903	−	0.454194i	$-0.150073\pi$
$563$	2.69577	+	4.15112i	0.113613	+	0.174949i	−0.777290	+	0.629143i	$0.783406\pi$
$564$	12.9270	−	11.6395i	0.544323	−	0.490111i
$565$		0			0
$566$	−13.2754	+	4.31344i	−0.558007	+	0.181307i
$567$	−0.650012	−	9.66255i	−0.0272979	−	0.405789i
$568$	1.95133	−	1.95133i	0.0818759	−	0.0818759i
$569$	6.87878	−	15.4500i	0.288373	−	0.647697i	−0.710031	−	0.704171i	$-0.751319\pi$
$569$	6.87878	−	15.4500i	0.288373	−	0.647697i	0.998404	+	0.0564736i	$0.0179857\pi$
$570$		0			0
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.224836	−	0.974397i	$-0.427815\pi$
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.874562	+	0.484913i	$0.161149\pi$
$572$	0.463601	+	0.572499i	0.0193841	+	0.0239374i
$573$	27.3036	−	13.9119i	1.14062	−	0.581177i
$574$	−5.93072	−	1.83036i	−0.247544	−	0.0763977i
$575$		0			0
$576$	3.67285	+	6.36156i	0.153035	+	0.265065i
$577$	−10.3630	−	0.543104i	−0.431419	−	0.0226097i	−0.164609	−	0.986359i	$-0.552636\pi$
$577$	−10.3630	−	0.543104i	−0.431419	−	0.0226097i	−0.266810	+	0.963749i	$0.585970\pi$
$578$	−12.7006	+	33.0863i	−0.528276	+	1.37621i
$579$	−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
$583$	6.61070	−	2.53761i	0.273787	−	0.105097i
$584$	10.5618	+	2.24499i	0.437052	+	0.0928983i
$585$		0			0
$586$	0.746455	+	3.51180i	0.0308358	+	0.145071i
$587$	−4.08885	−	2.08337i	−0.168765	−	0.0859899i	0.367568	−	0.929997i	$-0.380191\pi$
$587$	−4.08885	−	2.08337i	−0.168765	−	0.0859899i	−0.536332	+	0.844007i	$0.680191\pi$
$588$	0.240310	−	10.5661i	0.00991023	−	0.435740i
$589$	−8.26522	−	2.68553i	−0.340563	−	0.110655i
$590$		0			0
$591$	−0.414084	+	1.94811i	−0.0170331	+	0.0801345i
$592$	−1.68461	+	2.08032i	−0.0692371	+	0.0855007i
$593$	−3.98715	+	14.8803i	−0.163733	+	0.611059i	0.834466	+	0.551060i	$0.185776\pi$
$593$	−3.98715	+	14.8803i	−0.163733	+	0.611059i	−0.998198	+	0.0599990i	$0.980890\pi$
$594$	−3.31286	+	2.40693i	−0.135928	+	0.0987577i
$595$		0			0
$596$	10.5293	+	7.65000i	0.431298	+	0.313356i
$597$	−3.60286	+	2.91754i	−0.147455	+	0.119407i
$598$	0.162182	−	3.09462i	0.00663211	−	0.126548i
$599$	−13.4466	−	7.76339i	−0.549413	−	0.317204i	0.199472	−	0.979903i	$-0.436077\pi$
$599$	−13.4466	−	7.76339i	−0.549413	−	0.317204i	−0.748885	+	0.662700i	$0.769411\pi$
$600$		0			0
$601$			41.2449i			1.68241i	0.540714	+	0.841207i	$0.318154\pi$
$601$			41.2449i			1.68241i	−0.540714	+	0.841207i	$0.681846\pi$
$602$	−6.13674	+	1.06536i	−0.250115	+	0.0434207i
$603$	1.13197	−	0.179286i	0.0460974	−	0.00730110i
$604$	12.6082	+	1.32518i	0.513021	+	0.0539207i
$605$		0			0
$606$	−0.807926	−	7.68690i	−0.0328198	−	0.312259i
$607$	−10.7885	−	2.89077i	−0.437891	−	0.117333i	0.0331368	−	0.999451i	$-0.489450\pi$
$607$	−10.7885	−	2.89077i	−0.437891	−	0.117333i	−0.471028	+	0.882118i	$0.656117\pi$
$608$	9.89320	+	1.56693i	0.401222	+	0.0635474i
$609$	28.0966	−	16.7812i	1.13853	−	0.680010i
$610$		0			0
$611$	9.23005	−	1.96191i	0.373408	−	0.0793703i
$612$	−8.94388	+	5.80822i	−0.361535	+	0.234783i
$613$	2.60236	−	1.68999i	0.105108	−	0.0682580i	−0.491015	−	0.871151i	$-0.663374\pi$
$613$	2.60236	−	1.68999i	0.105108	−	0.0682580i	0.596123	+	0.802893i	$0.296707\pi$
$614$	25.3375	−	5.38565i	1.02254	−	0.217347i
$615$		0			0
$616$	−5.20098	+	3.10638i	−0.209554	+	0.125160i
$617$	−45.2349	−	7.16450i	−1.82109	−	0.288432i	−0.849935	−	0.526888i	$-0.823359\pi$
$617$	−45.2349	−	7.16450i	−1.82109	−	0.288432i	−0.971153	+	0.238456i	$0.923359\pi$
$618$	−11.6964	−	3.13404i	−0.470498	−	0.126070i
$619$	−1.86817	−	17.7745i	−0.0750883	−	0.714417i	−0.965701	−	0.259655i	$-0.916391\pi$
$619$	−1.86817	−	17.7745i	−0.0750883	−	0.714417i	0.890613	−	0.454762i	$-0.150276\pi$
$620$		0			0
$621$	−22.8456	−	2.40117i	−0.916764	−	0.0963558i
$622$	19.3638	−	3.06692i	0.776416	−	0.122972i
$623$	1.50728	−	0.261668i	0.0603878	−	0.0104835i
$624$		−	0.441228i		−	0.0176633i
$625$		0			0
$626$	−3.85279	−	2.22441i	−0.153988	−	0.0889052i
$627$	−0.100144	+	1.91086i	−0.00399936	+	0.0763123i
$628$	−14.8082	+	11.9915i	−0.590913	+	0.478512i
$629$	−39.4844	−	28.6871i	−1.57435	−	1.14383i
$630$		0			0
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	3.68350	−	13.7470i	0.146522	−	0.546826i
$633$	−16.5924	+	20.4899i	−0.659489	+	0.814401i
$634$	−5.71961	+	26.9086i	−0.227155	+	1.06868i
$635$		0			0
$636$	12.9208	+	4.19823i	0.512344	+	0.166471i
$637$	2.97881	−	4.89872i	0.118025	−	0.194094i
$638$	−6.07818	−	3.09699i	−0.240637	−	0.122611i
$639$	−0.247459	−	1.16420i	−0.00978931	−	0.0460551i
$640$		0			0
$641$	22.8779	+	4.86285i	0.903622	+	0.192071i	0.636214	−	0.771513i	$-0.280499\pi$
$641$	22.8779	+	4.86285i	0.903622	+	0.192071i	0.267408	+	0.963583i	$0.413833\pi$
$642$	−6.21488	+	2.38567i	−0.245282	+	0.0941549i
$643$	−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
$647$	6.98885	−	18.2066i	0.274760	−	0.715775i	−0.724878	−	0.688877i	$-0.758104\pi$
$647$	6.98885	−	18.2066i	0.274760	−	0.715775i	0.999638	−	0.0268974i	$-0.00856275\pi$
$648$	−10.6358	−	0.557397i	−0.417813	−	0.0218966i
$649$	4.48509	+	7.76840i	0.176055	+	0.304936i
$650$		0			0
$651$	15.7678	+	4.86631i	0.617989	+	0.190726i
$652$	20.9480	−	10.6735i	0.820385	−	0.418007i
$653$	−1.98821	−	2.45523i	−0.0778046	−	0.0960807i	0.736757	−	0.676157i	$-0.236356\pi$
$653$	−1.98821	−	2.45523i	−0.0778046	−	0.0960807i	−0.814562	+	0.580077i	$0.803023\pi$
$654$	−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
$658$	1.89407	+	28.1557i	0.0738385	+	1.09762i
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	−0.0371852	−	0.999308i	$-0.511839\pi$
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	0.557295	+	0.830314i	$0.311839\pi$
$660$		0			0
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	−0.832442	−	0.554113i	$-0.813058\pi$
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	0.464063	+	0.885802i	$0.346391\pi$
$662$	11.5990	+	17.8609i	0.450807	+	0.694182i
$663$	8.03356	−	0.421021i	0.311998	−	0.0163511i
$664$	−4.67982	+	14.4030i	−0.181612	+	0.558945i
$665$		0			0
$666$	2.35660	+	7.25286i	0.0913163	+	0.281043i
$667$	−13.7140	−	35.7263i	−0.531009	−	1.38333i
$668$	−5.22205	+	1.39924i	−0.202047	+	0.0541384i
$669$	−11.5052	+	1.20924i	−0.444816	+	0.0467520i
$670$		0			0
$671$	3.91065	−	5.38254i	0.150969	−	0.207791i
$672$	−18.8272	−	2.69676i	−0.726275	−	0.104030i
$673$	14.9409	+	29.3231i	0.575928	+	1.13032i	0.976793	+	0.214185i	$0.0687095\pi$
$673$	14.9409	+	29.3231i	0.575928	+	1.13032i	−0.400865	+	0.916137i	$0.631290\pi$
$674$	−4.27990	+	2.47100i	−0.164856	+	0.0951795i
$675$		0			0
$676$	7.04576	−	12.2036i	0.270991	−	0.469370i
$677$	3.16813	−	4.87849i	0.121761	−	0.187496i	−0.772534	−	0.634973i	$-0.781011\pi$
$677$	3.16813	−	4.87849i	0.121761	−	0.187496i	0.894295	+	0.447478i	$0.147678\pi$
$678$	−1.79581	−	11.3383i	−0.0689677	−	0.435445i
$679$	28.1241	−	3.37777i	1.07930	−	0.129627i
$680$		0			0
$681$	11.3328	+	5.04569i	0.434274	+	0.193351i
$682$	−0.890256	−	3.32248i	−0.0340897	−	0.127224i
$683$	−13.7202	−	11.1104i	−0.524989	−	0.425127i	0.329841	−	0.944037i	$-0.393005\pi$
$683$	−13.7202	−	11.1104i	−0.524989	−	0.425127i	−0.854829	+	0.518909i	$0.826338\pi$
$684$	1.76657	−	1.96198i	0.0675465	−	0.0750180i
$685$		0			0
$686$	13.2386	+	10.8954i	0.505454	+	0.415988i
$687$	5.15877	−	10.1247i	0.196819	−	0.386280i
$688$	0.0542727	+	1.03558i	0.00206913	+	0.0394813i
$689$	4.93142	+	5.47689i	0.187872	+	0.208653i
$690$		0			0
$691$	25.8993	+	23.3198i	0.985254	+	0.887127i	0.993613	−	0.112838i	$-0.0359942\pi$
$691$	25.8993	+	23.3198i	0.985254	+	0.887127i	−0.00835918	+	0.999965i	$0.502661\pi$
$692$	0.902413	−	5.69761i	0.0343046	−	0.216591i
$693$	−0.0980878	+	2.61098i	−0.00372605	+	0.0991831i
$694$	−9.36667	−	12.8921i	−0.355554	−	0.489378i
$695$		0			0
$696$	−14.6388	−	32.8794i	−0.554884	−	1.24629i
$697$	−17.5894	−	6.75195i	−0.666247	−	0.255748i
$698$	15.5886	+	10.1233i	0.590037	+	0.383174i
$699$	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	$0.535336\pi$
$702$	−3.57439	−	2.32124i	−0.134907	−	0.0876095i
$703$	11.2799	+	4.32995i	0.425430	+	0.163307i
$704$	1.87356	+	4.20809i	0.0706125	+	0.158598i
$705$		0			0
$706$	7.01099	+	9.64980i	0.263862	+	0.363175i
$707$	−14.1571	−	8.89848i	−0.532434	−	0.334662i
$708$	−2.69229	+	16.9985i	−0.101183	+	0.638841i
$709$	−7.00111	−	6.30382i	−0.262932	−	0.236745i	0.527111	−	0.849796i	$-0.323275\pi$
$709$	−7.00111	−	6.30382i	−0.262932	−	0.236745i	−0.790043	+	0.613051i	$0.789942\pi$
$710$		0			0
$711$	−4.10727	−	4.56158i	−0.154035	−	0.171073i
$712$	−0.0880508	−	1.68011i	−0.00329984	−	0.0629648i
$713$	8.76010	−	17.1927i	0.328068	−	0.643870i
$714$	−2.16009	+	23.9604i	−0.0808393	+	0.896694i
$715$		0			0
$716$	−2.76075	+	3.06613i	−0.103174	+	0.114587i
$717$	−11.0496	−	8.94783i	−0.412657	−	0.334163i
$718$	−1.85186	−	6.91124i	−0.0691109	−	0.257925i
$719$	−38.4705	−	17.1281i	−1.43471	−	0.638772i	−0.465505	−	0.885045i	$-0.654127\pi$
$719$	−38.4705	−	17.1281i	−1.43471	−	0.638772i	−0.969201	+	0.246273i	$0.920794\pi$
$720$		0			0
$721$	−20.9632	+	15.7102i	−0.780709	+	0.585078i
$722$	−2.26097	−	14.2752i	−0.0841445	−	0.531267i
$723$	−7.59259	+	11.6916i	−0.282372	+	0.434814i
$724$	−7.09194	+	12.2836i	−0.263570	+	0.456517i
$725$		0			0
$726$	10.9944	−	6.34760i	0.408039	−	0.235581i
$727$	5.76081	+	11.3062i	0.213657	+	0.419325i	0.972816	−	0.231580i	$-0.0743896\pi$
$727$	5.76081	+	11.3062i	0.213657	+	0.419325i	−0.759159	+	0.650905i	$0.774390\pi$
$728$	−4.95827	−	3.89498i	−0.183766	−	0.144357i
$729$	−15.7932	+	21.7374i	−0.584932	+	0.805090i
$730$		0			0
$731$	−18.8034	+	1.97632i	−0.695469	+	0.0730967i
$732$	12.3300	−	3.30381i	0.455729	−	0.122112i
$733$	−16.9027	−	44.0331i	−0.624316	−	1.62640i	−0.770720	−	0.637174i	$-0.780103\pi$
$733$	−16.9027	−	44.0331i	−0.624316	−	1.62640i	0.146404	−	0.989225i	$-0.453230\pi$
$734$	0.946479	+	2.91296i	0.0349352	+	0.107519i
$735$		0			0
$736$	−6.87248	+	21.1513i	−0.253323	+	0.779648i
$737$	0.717696	−	0.0376129i	0.0264367	−	0.00138549i
$738$	1.60341	+	2.46903i	0.0590222	+	0.0908862i
$739$	33.3478	−	30.0265i	1.22672	−	1.10454i	0.235560	−	0.971860i	$-0.424308\pi$
$739$	33.3478	−	30.0265i	1.22672	−	1.10454i	0.991159	−	0.132683i	$-0.0423591\pi$
$740$		0			0
$741$	−1.89407	+	0.615420i	−0.0695804	+	0.0226080i
$742$	−18.3044	+	12.2762i	−0.671974	+	0.450673i
$743$	−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
$747$	4.11053	+	5.07608i	0.150396	+	0.185724i
$748$	−5.95850	+	3.03601i	−0.217864	+	0.111007i
$749$	−4.24708	+	13.7614i	−0.155185	+	0.502830i
$750$		0			0
$751$	−21.6997	−	37.5850i	−0.791834	−	1.37150i	−0.924830	−	0.380380i	$-0.875793\pi$
$751$	−21.6997	−	37.5850i	−0.791834	−	1.37150i	0.132996	−	0.991117i	$-0.457540\pi$
$752$	4.69188	+	0.245891i	0.171095	+	0.00896672i
$753$	13.7580	−	35.8409i	0.501370	−	1.30611i
$754$	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	$0.379086\pi$
$758$	26.2873	−	10.0907i	0.954796	−	0.366512i
$759$	−4.15568	−	0.883317i	−0.150842	−	0.0320624i
$760$		0			0
$761$	−0.918515	−	4.32127i	−0.0332961	−	0.156646i	0.958359	−	0.285567i	$-0.0921820\pi$
$761$	−0.918515	−	4.32127i	−0.0332961	−	0.156646i	−0.991655	+	0.128921i	$0.958849\pi$
$762$	−3.17832	−	1.61944i	−0.115138	−	0.0586660i
$763$	−10.6056	+	42.0628i	−0.383949	+	1.52278i
$764$	−25.2152	−	8.19292i	−0.912255	−	0.296409i
$765$		0			0
$766$	3.91301	−	18.4093i	0.141383	−	0.665154i
$767$	−5.87541	+	7.25553i	−0.212149	+	0.261982i
$768$	−5.73230	+	21.3932i	−0.206847	+	0.771962i
$769$	−29.9959	+	21.7933i	−1.08168	+	0.785888i	−0.977975	−	0.208720i	$-0.933070\pi$
$769$	−29.9959	+	21.7933i	−1.08168	+	0.785888i	−0.103706	+	0.994608i	$0.533070\pi$
$770$		0			0
$771$	−19.8959	−	14.4552i	−0.716533	−	0.520592i
$772$	13.2755	−	10.7503i	0.477797	−	0.386912i
$773$	−0.340031	+	6.48817i	−0.0122301	+	0.233363i	0.985674	+	0.168659i	$0.0539437\pi$
$773$	−0.340031	+	6.48817i	−0.0122301	+	0.233363i	−0.997904	+	0.0647042i	$0.979390\pi$
$774$	2.55851	+	1.47716i	0.0919638	+	0.0530953i
$775$		0			0
$776$		−	31.1516i		−	1.11828i
$777$	−21.5377	−	7.90361i	−0.772661	−	0.283540i
$778$	−10.2061	+	1.61648i	−0.365905	+	0.0579537i
$779$	4.63874	+	0.487552i	0.166200	+	0.0174683i
$780$		0			0
$781$	−0.0780153	−	0.742266i	−0.00279161	−	0.0265604i
$782$	27.1725	+	7.28085i	0.971687	+	0.260363i
$783$	−51.9834	−	8.23336i	−1.85773	−	0.294236i
$784$	2.06389	−	1.97210i	0.0737105	−	0.0704322i
$785$		0			0
$786$	−8.05284	+	1.71168i	−0.287235	+	0.0610538i
$787$	−5.98249	+	3.88508i	−0.213253	+	0.138488i	−0.646846	−	0.762621i	$-0.723912\pi$
$787$	−5.98249	+	3.88508i	−0.213253	+	0.138488i	0.433593	+	0.901109i	$0.357246\pi$
$788$	1.44517	−	0.938503i	0.0514820	−	0.0334328i
$789$	26.7685	−	5.68981i	0.952983	−	0.202563i
$790$		0			0
$791$	−21.6893	−	12.0977i	−0.771184	−	0.430143i
$792$	2.83807	+	0.449506i	0.100846	+	0.0159725i
$793$	6.68866	+	1.79222i	0.237521	+	0.0636436i
$794$	1.10540	+	10.5172i	0.0392291	+	0.373240i
$795$		0			0
$796$	3.98912	+	0.419273i	0.141391	+	0.0148607i
$797$	−29.5739	+	4.68404i	−1.04756	+	0.165917i	−0.656406	−	0.754408i	$-0.727924\pi$
$797$	−29.5739	+	4.68404i	−1.04756	+	0.165917i	−0.391154	+	0.920325i	$0.627924\pi$
$798$	−1.01870	−	5.86799i	−0.0360616	−	0.207724i
$799$			85.6610i			3.03047i
$800$		0			0
$801$	−0.628409	−	0.362812i	−0.0222037	−	0.0128193i
$802$	−1.41298	+	26.9613i	−0.0498942	+	0.952038i
$803$	2.26954	−	1.83784i	0.0800903	−	0.0648559i
$804$	1.11553	+	0.810483i	0.0393418	+	0.0285835i
$805$		0			0
$806$	2.89629	−	2.10428i	0.102017	−	0.0741200i
$807$	−0.439053	+	1.63857i	−0.0154554	+	0.0576803i
$808$	−11.5728	+	14.2912i	−0.407130	+	0.502764i
$809$	−0.444905	+	2.09311i	−0.0156420	+	0.0735900i	−0.985276	−	0.170970i	$-0.945310\pi$
$809$	−0.444905	+	2.09311i	−0.0156420	+	0.0735900i	0.969634	+	0.244560i	$0.0786434\pi$
$810$		0			0
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	0.107319	−	0.994225i	$-0.465773\pi$
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	−0.497567	+	0.867425i	$0.665773\pi$
$812$	−27.4559	−	6.92264i	−0.963512	−	0.242937i
$813$	14.6051	+	7.44168i	0.512224	+	0.260991i
$814$	0.994268	+	4.67766i	0.0348491	+	0.163952i
$815$		0			0
$816$	3.91788	+	0.832771i	0.137153	+	0.0291528i
$817$	4.36978	−	1.67740i	0.152879	−	0.0586848i
$818$	21.1298	+	21.1298i	0.738786	+	0.738786i
$819$	−2.57359	+	0.878557i	−0.0899286	+	0.0306993i
$820$		0			0
$821$	−2.74655	+	26.1317i	−0.0958552	+	0.912001i	0.835892	+	0.548894i	$0.184951\pi$
$821$	−2.74655	+	26.1317i	−0.0958552	+	0.912001i	−0.931747	+	0.363107i	$0.881716\pi$
$822$	8.53614	−	22.2374i	0.297732	−	0.775618i
$823$	19.4457	+	1.01911i	0.677835	+	0.0355239i	0.388147	−	0.921597i	$-0.373115\pi$
$823$	19.4457	+	1.01911i	0.677835	+	0.0355239i	0.289688	+	0.957121i	$0.406448\pi$
$824$	14.4048	+	24.9499i	0.501816	+	0.869171i
$825$		0			0
$826$	−18.9873	−	20.4696i	−0.660652	−	0.712228i
$827$	15.3550	−	7.82374i	0.533944	−	0.272058i	−0.166160	−	0.986099i	$-0.553137\pi$
$827$	15.3550	−	7.82374i	0.533944	−	0.272058i	0.700104	+	0.714041i	$0.253137\pi$
$828$	3.68898	+	4.55551i	0.128201	+	0.158315i
$829$	−37.9342	+	16.8894i	−1.31751	+	0.586592i	−0.940555	−	0.339640i	$-0.889695\pi$
$829$	−37.9342	+	16.8894i	−1.31751	+	0.586592i	−0.376952	+	0.926233i	$0.623028\pi$
$830$		0			0
$831$	−0.660907	+	1.48442i	−0.0229266	+	0.0514940i
$832$	−3.39004	+	3.39004i	−0.117529	+	0.117529i
$833$	37.8760	+	35.6961i	1.31232	+	1.23680i
$834$	−1.19410	+	0.387986i	−0.0413482	+	0.0134348i
$835$		0			0
$836$	1.23031	−	1.10778i	0.0425512	−	0.0383133i
$837$	−14.4537	−	22.2568i	−0.499594	−	0.769307i
$838$	26.0498	−	1.36521i	0.899877	−	0.0471605i
$839$	11.9529	−	36.7873i	0.412660	−	1.27004i	−0.501666	−	0.865061i	$-0.667280\pi$
$839$	11.9529	−	36.7873i	0.412660	−	1.27004i	0.914327	−	0.404977i	$-0.132720\pi$
$840$		0			0
$841$	−18.1325	−	55.8062i	−0.625260	−	1.92435i
$842$	−6.90203	−	17.9804i	−0.237860	−	0.619645i
$843$	2.24904	−	0.602629i	0.0774612	−	0.0207557i
$844$	22.6866	−	2.38446i	0.780905	−	0.0820765i
$845$		0			0
$846$	7.86749	−	10.8287i	0.270490	−	0.372298i
$847$	3.89424	−	27.1873i	0.133808	−	0.934168i
$848$	1.66591	+	3.26953i	0.0572075	+	0.112276i
$849$	−17.2494	+	9.95893i	−0.591997	+	0.341789i
$850$		0			0
$851$	−13.4134	+	23.2326i	−0.459804	+	0.796404i
$852$	0.779907	−	1.20095i	0.0267192	−	0.0411439i
$853$	4.26100	+	26.9029i	0.145894	+	0.921138i	0.946677	+	0.322184i	$0.104417\pi$
$853$	4.26100	+	26.9029i	0.145894	+	0.921138i	−0.800783	+	0.598954i	$0.795583\pi$
$854$	−8.14170	+	19.0406i	−0.278603	+	0.651554i
$855$		0			0
$856$	14.4691	+	6.44206i	0.494543	+	0.220185i
$857$	−9.92732	−	37.0493i	−0.339111	−	1.26558i	−0.899343	−	0.437244i	$-0.855955\pi$
$857$	−9.92732	−	37.0493i	−0.339111	−	1.26558i	0.560232	−	0.828336i	$-0.310712\pi$
$858$	−0.612580	−	0.496057i	−0.0209131	−	0.0169351i
$859$	0.603007	−	0.669707i	0.0205743	−	0.0228501i	−0.732770	−	0.680477i	$-0.761773\pi$
$859$	0.603007	−	0.669707i	0.0205743	−	0.0228501i	0.753344	+	0.657626i	$0.228439\pi$
$860$		0			0
$861$	−8.82079	−	0.795217i	−0.300612	−	0.0271009i
$862$	1.04523	−	2.05137i	0.0356006	−	0.0698701i
$863$	−0.0615826	−	1.17507i	−0.00209629	−	0.0399997i	0.997381	−	0.0723253i	$-0.0230420\pi$
$863$	−0.0615826	−	1.17507i	−0.00209629	−	0.0399997i	−0.999477	+	0.0323256i	$0.989709\pi$
$864$	20.4668	+	22.7307i	0.696296	+	0.773315i
$865$		0			0
$866$	−6.36565	−	5.73166i	−0.216314	−	0.194770i
$867$	−7.91096	+	49.9479i	−0.268670	+	1.69632i
$868$	−6.66943	−	12.6237i	−0.226375	−	0.428478i
$869$	−2.26247	−	3.11402i	−0.0767490	−	0.105636i
$870$		0			0
$871$	0.304239	+	0.683332i	0.0103087	+	0.0231538i
$872$	44.5375	+	17.0964i	1.50823	+	0.578956i
$873$	−11.2681	−	7.31759i	−0.381367	−	0.247663i
$874$	−6.96421			−0.235568
$875$		0			0
$876$	5.60304			0.189309
$877$	−34.7725	−	22.5815i	−1.17418	−	0.762524i	−0.198157	−	0.980170i	$-0.563496\pi$
$877$	−34.7725	−	22.5815i	−1.17418	−	0.762524i	−0.976028	+	0.217646i	$0.930162\pi$
$878$	18.3515	+	7.04448i	0.619333	+	0.237740i
$879$	2.08372	+	4.68011i	0.0702821	+	0.157856i
$880$		0			0
$881$	−20.7423	−	28.5494i	−0.698827	−	0.961852i	−0.999966	−	0.00827221i	$-0.997367\pi$
$881$	−20.7423	−	28.5494i	−0.698827	−	0.961852i	0.301139	−	0.953580i	$-0.402633\pi$
$882$	−1.50953	−	7.99116i	−0.0508285	−	0.269076i
$883$	2.01591	−	12.7280i	0.0678407	−	0.428330i	−0.930269	−	0.366877i	$-0.880427\pi$
$883$	2.01591	−	12.7280i	0.0678407	−	0.428330i	0.998110	−	0.0614522i	$-0.0195732\pi$
$884$	−5.17243	−	4.65728i	−0.173968	−	0.156641i
$885$		0			0
$886$	−14.1223	−	15.6845i	−0.474450	−	0.526930i
$887$	2.39817	+	45.7599i	0.0805228	+	1.53647i	0.678289	+	0.734796i	$0.262722\pi$
$887$	2.39817	+	45.7599i	0.0805228	+	1.53647i	−0.597766	+	0.801671i	$0.703945\pi$
$888$	−11.4544	+	22.4805i	−0.384384	+	0.754397i
$889$	−7.00267	+	3.24289i	−0.234862	+	0.108763i
$890$		0			0
$891$	−1.92742	+	2.14061i	−0.0645709	+	0.0717132i
$892$	7.77856	+	6.29895i	0.260445	+	0.210904i
$893$	−5.48864	−	20.4839i	−0.183670	−	0.685467i
$894$	−12.7221	−	5.66427i	−0.425492	−	0.189441i
$895$		0			0
$896$	8.67042	+	11.5695i	0.289658	+	0.386511i
$897$	−0.691729	−	4.36740i	−0.0230961	−	0.145823i
$898$	16.4280	−	25.2970i	0.548211	−	0.844171i
$899$	22.1049	−	38.2867i	0.737238	−	1.27693i
$900$		0			0
$901$	−57.9395	+	33.4514i	−1.93025	+	1.11443i
$902$	0.838114	+	1.64489i	0.0279062	+	0.0547689i
$903$	−8.24925	+	3.30758i	−0.274518	+	0.110069i
$904$	−16.0538	+	22.0961i	−0.533940	+	0.734905i
$905$		0			0
$906$	−13.4909	+	1.41795i	−0.448205	+	0.0471083i
$907$	−19.0139	+	5.09475i	−0.631345	+	0.169168i	−0.560280	−	0.828303i	$-0.689307\pi$
$907$	−19.0139	+	5.09475i	−0.631345	+	0.169168i	−0.0710652	+	0.997472i	$0.522640\pi$
$908$	−3.84640	−	10.0202i	−0.127647	−	0.332532i
$909$	2.45091	+	7.54313i	0.0812916	+	0.250190i
$910$		0			0
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	−0.990232	+	0.0518959i	−0.0327899	+	0.00171844i
$913$	2.23078	+	3.43509i	0.0738279	+	0.113685i
$914$	5.55829	−	5.00470i	0.183852	−	0.165541i
$915$		0			0
$916$	−9.35025	+	3.03808i	−0.308941	+	0.100381i
$917$	−7.85000	+	15.9875i	−0.259230	+	0.527954i
$918$	27.3577	−	27.3577i	0.902939	−	0.902939i
$919$	14.7750	−	33.1853i	0.487384	−	1.09468i	−0.487734	−	0.872992i	$-0.662176\pi$
$919$	14.7750	−	33.1853i	0.487384	−	1.09468i	0.975117	−	0.221689i	$-0.0711571\pi$
$920$		0			0
$921$	33.7668	−	15.0340i	1.11266	−	0.495386i
$922$	−22.1869	−	27.3985i	−0.730686	−	0.902322i
$923$	0.692136	−	0.352661i	0.0227819	−	0.0116080i
$924$	−2.30471	+	2.13781i	−0.0758193	+	0.0703289i
$925$		0			0
$926$	−17.0216	−	29.4823i	−0.559364	−	0.968847i
$927$	12.4085	+	0.650304i	0.407550	+	0.0213588i
$928$	−18.2606	+	47.5706i	−0.599434	+	1.56158i
$929$	−0.343990	+	3.27285i	−0.0112860	+	0.107379i	−0.998715	−	0.0506867i	$-0.983859\pi$
$929$	−0.343990	+	3.27285i	−0.0112860	+	0.107379i	0.987429	+	0.158065i	$0.0505257\pi$
$930$		0			0
$931$	−11.3444	−	6.10905i	−0.371797	−	0.200216i
$932$	−2.25132	−	2.25132i	−0.0737446	−	0.0737446i
$933$	26.1169	−	10.0254i	0.855030	−	0.328215i
$934$	18.8552	+	4.00780i	0.616961	+	0.131139i
$935$		0			0
$936$	0.621795	+	2.92532i	0.0203240	+	0.0956170i
$937$	8.94070	+	4.55551i	0.292080	+	0.148822i	0.593891	−	0.804546i	$-0.297591\pi$
$937$	8.94070	+	4.55551i	0.292080	+	0.148822i	−0.301811	+	0.953368i	$0.597591\pi$
$938$	−2.15188	+	0.610891i	−0.0702614	+	0.0199463i
$939$	−6.03743	−	1.96168i	−0.197024	−	0.0640170i
$940$		0			0
$941$	−3.13847	+	14.7653i	−0.102311	+	0.481336i	0.896922	+	0.442188i	$0.145798\pi$
$941$	−3.13847	+	14.7653i	−0.102311	+	0.481336i	−0.999233	+	0.0391481i	$0.987536\pi$
$942$	12.8310	−	15.8450i	0.418057	−	0.516257i
$943$	−2.68038	+	10.0033i	−0.0872851	+	0.325752i
$944$	−3.76069	+	2.73230i	−0.122400	+	0.0889288i
$945$		0			0
$946$	1.49877	+	1.08892i	0.0487293	+	0.0354039i
$947$	44.2910	−	35.8661i	1.43926	−	1.16549i	0.482036	−	0.876151i	$-0.339897\pi$
$947$	44.2910	−	35.8661i	1.43926	−	1.16549i	0.957226	−	0.289341i	$-0.0934361\pi$
$948$	0.386503	−	7.37491i	0.0125530	−	0.239526i
$949$	2.63228	+	1.51975i	0.0854473	+	0.0493330i
$950$		0			0
$951$			39.2544i			1.27291i
$952$	43.9436	−	36.6756i	1.42422	−	1.18866i
$953$	15.7565	−	2.49558i	0.510403	−	0.0808399i	0.104079	−	0.994569i	$-0.466810\pi$
$953$	15.7565	−	2.49558i	0.510403	−	0.0808399i	0.406324	+	0.913729i	$0.366810\pi$
$954$	10.3967	+	1.09273i	0.336604	+	0.0353785i
$955$		0			0
$956$	1.28587	+	12.2343i	0.0415881	+	0.395684i
$957$	−9.40237	−	2.51936i	−0.303935	−	0.0814392i
$958$	−1.27980	−	0.202701i	−0.0413486	−	0.00654897i
$959$	−26.4237	−	44.2408i	−0.853264	−	1.42861i
$960$		0			0
$961$	−8.51796	+	1.81055i	−0.274773	+	0.0584048i
$962$	−4.17428	+	2.71081i	−0.134584	+	0.0873999i
$963$	5.72903	−	3.72047i	0.184615	−	0.119891i
$964$	11.7979	−	2.50771i	0.379984	−	0.0807680i
$965$		0			0
$966$	13.2222	−	0.195837i	0.425417	−	0.00630096i
$967$	−30.4690	−	4.82581i	−0.979817	−	0.155188i	−0.354074	−	0.935217i	$-0.615204\pi$
$967$	−30.4690	−	4.82581i	−0.979817	−	0.155188i	−0.625743	+	0.780030i	$0.715204\pi$
$968$	−29.1751	−	7.81746i	−0.937725	−	0.251263i
$969$	−1.88976	−	17.9799i	−0.0607080	−	0.577598i
$970$		0			0
$971$	−4.01132	−	0.421607i	−0.128729	−	0.0135300i	0.0399446	−	0.999202i	$-0.487282\pi$
$971$	−4.01132	−	0.421607i	−0.128729	−	0.0135300i	−0.168674	+	0.985672i	$0.553949\pi$
$972$	13.5770	−	2.15038i	0.435482	−	0.0689736i
$973$	−0.935758	+	2.54998i	−0.0299990	+	0.0817487i
$974$			24.6259i			0.789064i
$975$		0			0
$976$	2.98586	+	1.72388i	0.0955749	+	0.0551802i
$977$	1.28382	−	24.4967i	0.0410730	−	0.783719i	−0.897999	−	0.439998i	$-0.854979\pi$
$977$	1.28382	−	24.4967i	0.0410730	−	0.783719i	0.939072	−	0.343721i	$-0.111688\pi$
$978$	−19.5502	+	15.8314i	−0.625146	+	0.506233i
$979$	−0.368121	−	0.267456i	−0.0117652	−	0.00854792i
$980$		0			0
$981$	16.6460	−	12.0940i	0.531467	−	0.386133i
$982$	−0.0494843	+	0.184678i	−0.00157911	+	0.00589331i
$983$	−28.7473	+	35.4999i	−0.916896	+	1.13227i	0.0739487	+	0.997262i	$0.476440\pi$
$983$	−28.7473	+	35.4999i	−0.916896	+	1.13227i	−0.990844	+	0.135010i	$0.956893\pi$
$984$	−2.02505	+	9.52713i	−0.0645563	+	0.303714i
$985$		0			0
$986$	61.2982	+	19.9170i	1.95213	+	0.634286i
$987$	10.9967	+	38.7362i	0.350029	+	1.23299i
$988$	1.53528	+	0.782265i	0.0488438	+	0.0248872i
$989$	2.16073	+	10.1654i	0.0687072	+	0.323242i
$990$		0			0
$991$	−44.8481	−	9.53276i	−1.42465	−	0.302818i	−0.569836	−	0.821758i	$-0.692993\pi$
$991$	−44.8481	−	9.53276i	−1.42465	−	0.302818i	−0.854810	+	0.518940i	$0.826327\pi$
$992$	−23.9864	+	9.20750i	−0.761568	+	0.292339i
$993$	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
$997$	−8.17250	+	21.2901i	−0.258826	+	0.674264i	0.741170	+	0.671317i	$0.234271\pi$
$997$	−8.17250	+	21.2901i	−0.258826	+	0.674264i	−0.999996	+	0.00294638i	$0.999062\pi$
$998$	−21.8260	−	1.14385i	−0.690891	−	0.0362080i
$999$	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.c.507.11		288
5.2	odd	4		875.2.bb.b.493.8		288
5.3	odd	4		875.2.bb.a.493.11		288
5.4	even	2		175.2.x.a.122.8	yes	288
7.5	odd	6	inner	875.2.bb.c.257.11		288
25.6	even	5		875.2.bb.a.857.8		288
25.8	odd	20	inner	875.2.bb.c.143.11		288
25.17	odd	20		175.2.x.a.108.8	yes	288
25.19	even	10		875.2.bb.b.857.11		288
35.12	even	12		875.2.bb.b.243.11		288
35.19	odd	6		175.2.x.a.47.8	yes	288
35.33	even	12		875.2.bb.a.243.8		288
175.19	odd	30		875.2.bb.b.607.8		288
175.33	even	60	inner	875.2.bb.c.768.11		288
175.117	even	60		175.2.x.a.33.8	✓	288
175.131	odd	30		875.2.bb.a.607.11		288

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.776420 + 0.504213i) q^{2} +(1.23327 + 0.473408i) q^{3} +(-0.464876 - 1.04413i) q^{4} +(0.718837 + 0.989394i) q^{6} +(2.64389 + 0.0993238i) q^{7} +(0.455170 - 2.87383i) q^{8} +(-0.932596 - 0.839713i) q^{9} +(-0.526566 - 0.584810i) q^{11} +(-0.0790188 - 1.50777i) q^{12} +(0.371838 - 0.729773i) q^{13} +(2.00269 + 1.41020i) q^{14} +(0.272873 - 0.303056i) q^{16} +(5.77821 + 4.67910i) q^{17} +(-0.300692 - 1.12220i) q^{18} +(-1.68154 - 0.748668i) q^{19} +(3.21360 + 1.37413i) q^{21} +(-0.113967 - 0.719560i) q^{22} +(2.22587 - 3.42753i) q^{23} +(1.92184 - 3.32873i) q^{24} +(0.656664 - 0.379125i) q^{26} +(-2.55179 - 5.00818i) q^{27} +(-1.12537 - 2.80673i) q^{28} +(5.50382 - 7.57536i) q^{29} +(4.69555 - 0.493522i) q^{31} +(-5.25635 + 1.40844i) q^{32} +(-0.372543 - 0.970509i) q^{33} +(2.12705 + 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(-6.55514 + 0.343540i) q^{37} +(-0.928090 - 1.42913i) q^{38} +(0.804057 - 0.723976i) q^{39} +(-2.40999 + 0.783055i) q^{41} +(1.80225 + 2.68724i) q^{42} +(-1.79811 + 1.79811i) q^{43} +(-0.365830 + 0.821667i) q^{44} +(3.45641 - 1.53889i) q^{46} +(7.25044 + 8.95355i) q^{47} +(0.479996 - 0.244570i) q^{48} +(6.98027 + 0.525202i) q^{49} +(4.91096 + 8.50604i) q^{51} +(-0.934836 - 0.0489927i) q^{52} +(-3.22465 + 8.40051i) q^{53} +(0.543925 - 5.17510i) q^{54} +(1.48886 - 7.55288i) q^{56} +(-1.71936 - 1.71936i) q^{57} +(8.09287 - 3.10656i) q^{58} +(-11.1497 - 2.36995i) q^{59} +(1.75779 + 8.26975i) q^{61} +(3.89456 + 1.98438i) q^{62} +(-2.38227 - 2.31273i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(0.200093 - 0.941364i) q^{66} +(-0.574734 + 0.709737i) q^{67} +(2.19943 - 8.20839i) q^{68} +(4.36771 - 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(-2.83768 + 2.29791i) q^{72} +(-0.194220 + 3.70594i) q^{73} +(-5.26276 - 3.03846i) q^{74} +2.10378i q^{76} +(-1.33409 - 1.59847i) q^{77} +(0.989324 - 0.156693i) q^{78} +(4.86448 + 0.511278i) q^{79} +(-0.382611 - 3.64030i) q^{81} +(-2.26599 - 0.607171i) q^{82} +(-5.14074 - 0.814213i) q^{83} +(-0.0591594 - 3.99422i) q^{84} +(-2.30272 + 0.489458i) q^{86} +(10.3739 - 6.73691i) q^{87} +(-1.92032 + 1.24707i) q^{88} +(0.565582 - 0.120218i) q^{89} +(1.05558 - 1.89250i) q^{91} +(-4.61354 - 0.730712i) q^{92} +(6.02451 + 1.61426i) q^{93} +(1.11489 + 10.6075i) q^{94} +(-7.14926 - 0.751418i) q^{96} +(10.5745 - 1.67483i) q^{97} +(5.15481 + 3.92732i) q^{98} +0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more