LMFDB - Embedded newform 775.2.ck.a.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	775.49
Dual form			775.2.ck.a.174.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35633 + 1.86683i) q^{2} +(-1.03422 - 2.32289i) q^{3} +(-1.02738 + 3.16196i) q^{4} +(2.93370 - 5.08132i) q^{6} +(1.19043 - 1.07187i) q^{7} +(-2.90713 + 0.944583i) q^{8} +(-2.31884 + 2.57533i) q^{9} +(-0.717625 + 0.152536i) q^{11} +(8.40743 - 0.883657i) q^{12} +(1.88559 + 0.198183i) q^{13} +(3.61560 + 0.768520i) q^{14} +(-0.326952 - 0.237545i) q^{16} +(0.910495 - 4.28354i) q^{17} +(-7.95280 - 0.835873i) q^{18} +(-0.484806 - 4.61262i) q^{19} +(-3.72099 - 1.65669i) q^{21} +(-1.25809 - 1.13279i) q^{22} +(6.77006 - 2.19973i) q^{23} +(5.20077 + 5.77604i) q^{24} +(2.18751 + 3.78887i) q^{26} +(1.12557 + 0.365721i) q^{27} +(2.16617 + 4.86530i) q^{28} +(-0.104314 + 0.0757884i) q^{29} +(4.81795 - 2.79058i) q^{31} +5.18091i q^{32} +(1.09651 + 1.50921i) q^{33} +(9.23157 - 4.11016i) q^{34} +(-5.76075 - 9.97791i) q^{36} +(7.30014 + 4.21474i) q^{37} +(7.95341 - 7.16128i) q^{38} +(-1.48975 - 4.58499i) q^{39} +(-6.73647 - 2.99927i) q^{41} +(-1.95413 - 9.19348i) q^{42} +(0.229229 - 0.0240929i) q^{43} +(0.254963 - 2.42581i) q^{44} +(13.2889 + 9.65498i) q^{46} +(4.72375 - 6.50168i) q^{47} +(-0.213651 + 1.00515i) q^{48} +(-0.463478 + 4.40970i) q^{49} +(-10.8919 + 2.31514i) q^{51} +(-2.56387 + 5.75854i) q^{52} +(4.26137 + 3.83695i) q^{53} +(0.843912 + 2.59729i) q^{54} +(-2.44826 + 4.24051i) q^{56} +(-10.2132 + 5.89661i) q^{57} +(-0.282968 - 0.0919419i) q^{58} +(-8.68208 + 3.86551i) q^{59} -7.84044 q^{61} +(11.7443 + 5.20934i) q^{62} +5.55122i q^{63} +(-10.3258 + 7.50212i) q^{64} +(-1.33021 + 4.09397i) q^{66} +(-4.17994 + 2.41329i) q^{67} +(12.6090 + 7.27978i) q^{68} +(-12.1115 - 13.4511i) q^{69} +(-2.27840 + 2.53042i) q^{71} +(4.30854 - 9.67714i) q^{72} +(-0.559708 - 2.63322i) q^{73} +(2.03321 + 19.3447i) q^{74} +(15.0830 + 3.20599i) q^{76} +(-0.690782 + 0.950780i) q^{77} +(6.53879 - 8.99987i) q^{78} +(4.42900 + 0.941413i) q^{79} +(0.772154 + 7.34656i) q^{81} +(-3.53775 - 16.6438i) q^{82} +(-1.08613 + 2.43949i) q^{83} +(9.06128 - 10.0636i) q^{84} +(0.355888 + 0.395253i) q^{86} +(0.283932 + 0.163928i) q^{87} +(1.94214 - 1.12130i) q^{88} +(0.681255 - 2.09669i) q^{89} +(2.45708 - 1.78518i) q^{91} +23.6666i q^{92} +(-11.4650 - 8.30552i) q^{93} +18.5445 q^{94} +(12.0347 - 5.35820i) q^{96} +(-11.6884 - 3.79778i) q^{97} +(-8.86077 + 5.11577i) q^{98} +(1.27122 - 2.20182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{13}{15}\right)$	$-1$

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 $

$2$	1.35633	+	1.86683i	0.959070	+	1.32005i	0.947379	+	0.320115i	$0.103722\pi$
$2$	1.35633	+	1.86683i	0.959070	+	1.32005i	0.0116917	+	0.999932i	$0.496278\pi$
$3$	−1.03422	−	2.32289i	−0.597107	−	1.34112i	−0.918966	−	0.394336i	$-0.870975\pi$
$3$	−1.03422	−	2.32289i	−0.597107	−	1.34112i	0.321860	−	0.946787i	$-0.395692\pi$
$4$	−1.02738	+	3.16196i	−0.513691	+	1.58098i
$5$		0			0
$5$		0			0
$6$	2.93370	−	5.08132i	1.19768	−	2.07444i
$7$	1.19043	−	1.07187i	0.449939	−	0.405127i	−0.412764	−	0.910838i	$-0.635436\pi$
$7$	1.19043	−	1.07187i	0.449939	−	0.405127i	0.862703	+	0.505711i	$0.168770\pi$
$8$	−2.90713	+	0.944583i	−1.02782	+	0.333960i
$9$	−2.31884	+	2.57533i	−0.772945	+	0.858443i
$10$		0			0
$11$	−0.717625	+	0.152536i	−0.216372	+	0.0459913i	−0.314822	−	0.949151i	$-0.601945\pi$
$11$	−0.717625	+	0.152536i	−0.216372	+	0.0459913i	0.0984501	+	0.995142i	$0.468612\pi$
$12$	8.40743	−	0.883657i	2.42702	−	0.255090i
$13$	1.88559	+	0.198183i	0.522968	+	0.0549662i	0.362335	−	0.932048i	$-0.381980\pi$
$13$	1.88559	+	0.198183i	0.522968	+	0.0549662i	0.160633	+	0.987014i	$0.448646\pi$
$14$	3.61560	+	0.768520i	0.966310	+	0.205396i
$15$		0			0
$16$	−0.326952	−	0.237545i	−0.0817381	−	0.0593862i
$17$	0.910495	−	4.28354i	0.220828	−	1.03891i	−0.718404	−	0.695626i	$-0.755127\pi$
$17$	0.910495	−	4.28354i	0.220828	−	1.03891i	0.939231	−	0.343285i	$-0.111540\pi$
$18$	−7.95280	−	0.835873i	−1.87449	−	0.197017i
$19$	−0.484806	−	4.61262i	−0.111222	−	1.05821i	−0.897706	−	0.440596i	$-0.854767\pi$
$19$	−0.484806	−	4.61262i	−0.111222	−	1.05821i	0.786483	−	0.617611i	$-0.211900\pi$
$20$		0			0
$21$	−3.72099	−	1.65669i	−0.811987	−	0.361520i
$22$	−1.25809	−	1.13279i	−0.268227	−	0.241512i
$23$	6.77006	−	2.19973i	1.41166	−	0.458675i	0.498714	−	0.866766i	$-0.333806\pi$
$23$	6.77006	−	2.19973i	1.41166	−	0.458675i	0.912941	+	0.408092i	$0.133806\pi$
$24$	5.20077	+	5.77604i	1.06160	+	1.17903i
$25$		0			0
$26$	2.18751	+	3.78887i	0.429005	+	0.743059i
$27$	1.12557	+	0.365721i	0.216617	+	0.0703831i
$28$	2.16617	+	4.86530i	0.409368	+	0.919455i
$29$	−0.104314	+	0.0757884i	−0.0193706	+	0.0140736i	−0.597428	−	0.801922i	$-0.703811\pi$
$29$	−0.104314	+	0.0757884i	−0.0193706	+	0.0140736i	0.578058	+	0.815996i	$0.303811\pi$
$30$		0			0
$31$	4.81795	−	2.79058i	0.865330	−	0.501203i
$31$	4.81795	−	2.79058i	0.865330	−	0.501203i
$32$			5.18091i			0.915865i
$33$	1.09651	+	1.50921i	0.190877	+	0.262720i
$34$	9.23157	−	4.11016i	1.58320	−	0.704887i
$35$		0			0
$36$	−5.76075	−	9.97791i	−0.960125	−	1.66298i
$37$	7.30014	+	4.21474i	1.20014	+	0.692899i	0.960585	−	0.277985i	$-0.0896666\pi$
$37$	7.30014	+	4.21474i	1.20014	+	0.692899i	0.239550	+	0.970884i	$0.423000\pi$
$38$	7.95341	−	7.16128i	1.29021	−	1.16171i
$39$	−1.48975	−	4.58499i	−0.238551	−	0.734186i
$40$		0			0
$41$	−6.73647	−	2.99927i	−1.05206	−	0.468407i	−0.193489	−	0.981102i	$-0.561980\pi$
$41$	−6.73647	−	2.99927i	−1.05206	−	0.468407i	−0.858570	+	0.512696i	$0.828647\pi$
$42$	−1.95413	−	9.19348i	−0.301529	−	1.41858i
$43$	0.229229	−	0.0240929i	0.0349571	−	0.00367414i	−0.0870338	−	0.996205i	$-0.527739\pi$
$43$	0.229229	−	0.0240929i	0.0349571	−	0.00367414i	0.121991	+	0.992531i	$0.461072\pi$
$44$	0.254963	−	2.42581i	0.0384371	−	0.365705i
$45$		0			0
$46$	13.2889	+	9.65498i	1.95935	+	1.42355i
$47$	4.72375	−	6.50168i	0.689030	−	0.948368i	−0.310968	−	0.950420i	$-0.600653\pi$
$47$	4.72375	−	6.50168i	0.689030	−	0.948368i	0.999998	+	0.00205222i	$0.000653243\pi$
$48$	−0.213651	+	1.00515i	−0.0308379	+	0.145081i
$49$	−0.463478	+	4.40970i	−0.0662111	+	0.629957i
$50$		0			0
$51$	−10.8919	+	2.31514i	−1.52517	+	0.324184i
$52$	−2.56387	+	5.75854i	−0.355545	+	0.798566i
$53$	4.26137	+	3.83695i	0.585344	+	0.527046i	0.907726	−	0.419563i	$-0.137817\pi$
$53$	4.26137	+	3.83695i	0.585344	+	0.527046i	−0.322382	+	0.946610i	$0.604483\pi$
$54$	0.843912	+	2.59729i	0.114842	+	0.353447i
$55$		0			0
$56$	−2.44826	+	4.24051i	−0.327162	+	0.566662i
$57$	−10.2132	+	5.89661i	−1.35278	+	0.781025i
$58$	−0.282968	−	0.0919419i	−0.0371555	−	0.0120726i
$59$	−8.68208	+	3.86551i	−1.13031	+	0.503247i	−0.884718	−	0.466127i	$-0.845649\pi$
$59$	−8.68208	+	3.86551i	−1.13031	+	0.503247i	−0.245592	+	0.969373i	$0.578982\pi$
$60$		0			0
$61$	−7.84044			−1.00387			−0.501933	−	0.864907i	$-0.667377\pi$
$61$	−7.84044			−1.00387			−0.501933	+	0.864907i	$0.667377\pi$
$62$	11.7443	+	5.20934i	1.49152	+	0.661587i
$63$			5.55122i			0.699388i
$64$	−10.3258	+	7.50212i	−1.29072	+	0.937765i
$65$		0			0
$66$	−1.33021	+	4.09397i	−0.163738	+	0.503933i
$67$	−4.17994	+	2.41329i	−0.510661	+	0.294830i	−0.733105	−	0.680115i	$-0.761930\pi$
$67$	−4.17994	+	2.41329i	−0.510661	+	0.294830i	0.222444	+	0.974945i	$0.428596\pi$
$68$	12.6090	+	7.27978i	1.52906	+	0.882804i
$69$	−12.1115	−	13.4511i	−1.45805	−	1.61933i
$70$		0			0
$71$	−2.27840	+	2.53042i	−0.270396	+	0.300306i	−0.863016	−	0.505177i	$-0.831427\pi$
$71$	−2.27840	+	2.53042i	−0.270396	+	0.300306i	0.592619	+	0.805483i	$0.298094\pi$
$72$	4.30854	−	9.67714i	0.507766	−	1.14046i
$73$	−0.559708	−	2.63322i	−0.0655088	−	0.308195i	0.933179	−	0.359413i	$-0.117023\pi$
$73$	−0.559708	−	2.63322i	−0.0655088	−	0.308195i	−0.998687	+	0.0512180i	$0.983690\pi$
$74$	2.03321	+	19.3447i	0.236356	+	2.24877i
$75$		0			0
$76$	15.0830	+	3.20599i	1.73014	+	0.367752i
$77$	−0.690782	+	0.950780i	−0.0787219	+	0.108351i
$78$	6.53879	−	8.99987i	0.740372	−	1.01903i
$79$	4.42900	+	0.941413i	0.498301	+	0.105917i	0.450204	−	0.892925i	$-0.351351\pi$
$79$	4.42900	+	0.941413i	0.498301	+	0.105917i	0.0480968	+	0.998843i	$0.484684\pi$
$80$		0			0
$81$	0.772154	+	7.34656i	0.0857949	+	0.816284i
$82$	−3.53775	−	16.6438i	−0.390680	−	1.83800i
$83$	−1.08613	+	2.43949i	−0.119218	+	0.267768i	−0.963291	−	0.268461i	$-0.913485\pi$
$83$	−1.08613	+	2.43949i	−0.119218	+	0.267768i	0.844072	+	0.536229i	$0.180152\pi$
$84$	9.06128	−	10.0636i	0.988666	−	1.09803i
$85$		0			0
$86$	0.355888	+	0.395253i	0.0383764	+	0.0426213i
$87$	0.283932	+	0.163928i	0.0304407	+	0.0175749i
$88$	1.94214	−	1.12130i	0.207033	−	0.119531i
$89$	0.681255	−	2.09669i	0.0722129	−	0.222248i	−0.908436	−	0.418025i	$-0.862723\pi$
$89$	0.681255	−	2.09669i	0.0722129	−	0.222248i	0.980649	+	0.195776i	$0.0627226\pi$
$90$		0			0
$91$	2.45708	−	1.78518i	0.257572	−	0.187137i
$92$			23.6666i			2.46741i
$93$	−11.4650	−	8.30552i	−1.18887	−	0.861243i
$94$	18.5445			1.91272
$95$		0			0
$96$	12.0347	−	5.35820i	1.22829	−	0.546869i
$97$	−11.6884	−	3.79778i	−1.18677	−	0.385606i	−0.351894	−	0.936040i	$-0.614462\pi$
$97$	−11.6884	−	3.79778i	−1.18677	−	0.385606i	−0.834879	+	0.550434i	$0.814462\pi$
$98$	−8.86077	+	5.11577i	−0.895073	+	0.516771i
$99$	1.27122	−	2.20182i	0.127763	−	0.221292i
$100$		0			0
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	0.998207	+	0.0598605i	$0.0190656\pi$
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	−0.772381	+	0.635159i	$0.780934\pi$
$102$	−19.0949	−	17.1932i	−1.89068	−	1.70238i
$103$	−2.27315	+	5.10558i	−0.223980	+	0.503068i	−0.990225	−	0.139481i	$-0.955456\pi$
$103$	−2.27315	+	5.10558i	−0.223980	+	0.503068i	0.766245	+	0.642549i	$0.222123\pi$
$104$	−5.66885	+	1.20495i	−0.555876	+	0.118155i
$105$		0			0
$106$	−1.38311	+	13.1594i	−0.134340	+	1.27816i
$107$	−0.379264	+	1.78430i	−0.0366649	+	0.172495i	−0.992670	−	0.120855i	$-0.961437\pi$
$107$	−0.379264	+	1.78430i	−0.0366649	+	0.172495i	0.956005	+	0.293349i	$0.0947699\pi$
$108$	−2.31279	+	3.18328i	−0.222548	+	0.306312i
$109$	9.51832	+	6.91546i	0.911689	+	0.662381i	0.941442	−	0.337176i	$-0.109472\pi$
$109$	9.51832	+	6.91546i	0.911689	+	0.662381i	−0.0297521	+	0.999557i	$0.509472\pi$
$110$		0			0
$111$	2.24045	−	21.3164i	0.212654	−	2.02326i
$112$	−0.643829	+	0.0676692i	−0.0608361	+	0.00639414i
$113$	−2.29837	−	10.8130i	−0.216212	−	1.01720i	−0.943630	−	0.331003i	$-0.892613\pi$
$113$	−2.29837	−	10.8130i	−0.216212	−	1.01720i	0.727417	−	0.686195i	$-0.240720\pi$
$114$	−24.8605	−	11.0686i	−2.32840	−	1.03667i
$115$		0			0
$116$	−0.132470	−	0.407700i	−0.0122995	−	0.0378540i
$117$	−4.88276	+	4.39646i	−0.451411	+	0.406452i
$118$	−18.9920	−	10.9650i	−1.74836	−	1.00941i
$119$	−3.50750	−	6.07518i	−0.321532	−	0.556911i
$120$		0			0
$121$	−9.55728	+	4.25518i	−0.868844	+	0.386834i
$122$	−10.6342	−	14.6368i	−0.962777	−	1.32515i
$123$			18.7500i			1.69063i
$124$	3.87381	+	18.1012i	0.347879	+	1.62553i
$125$		0			0
$126$	−10.3632	+	7.52929i	−0.923225	+	0.670762i
$127$	0.523483	+	1.17576i	0.0464516	+	0.104332i	0.935281	−	0.353907i	$-0.115147\pi$
$127$	0.523483	+	1.17576i	0.0464516	+	0.104332i	−0.888829	+	0.458239i	$0.848480\pi$
$128$	−18.1557	−	5.89913i	−1.60475	−	0.521414i
$129$	−0.293038	−	0.507557i	−0.0258006	−	0.0446879i
$130$		0			0
$131$	−5.36666	−	5.96028i	−0.468888	−	0.520752i	0.461594	−	0.887091i	$-0.347278\pi$
$131$	−5.36666	−	5.96028i	−0.468888	−	0.520752i	−0.930481	+	0.366339i	$0.880611\pi$
$132$	−5.89859	+	1.91657i	−0.513406	+	0.166816i
$133$	−5.52123	−	4.97134i	−0.478752	−	0.431070i
$134$	−10.1746	−	4.53001i	−0.878949	−	0.391334i
$135$		0			0
$136$	1.39924	+	13.3128i	0.119983	+	1.14157i
$137$	−16.3865	−	1.72229i	−1.39999	−	0.147145i	−0.625745	−	0.780028i	$-0.715205\pi$
$137$	−16.3865	−	1.72229i	−1.39999	−	0.147145i	−0.774248	+	0.632883i	$0.781872\pi$
$138$	8.68382	−	40.8542i	0.739216	−	3.47774i
$139$	5.93804	+	4.31424i	0.503658	+	0.365929i	0.810412	−	0.585860i	$-0.199243\pi$
$139$	5.93804	+	4.31424i	0.503658	+	0.365929i	−0.306755	+	0.951789i	$0.599243\pi$
$140$		0			0
$141$	−19.9881	−	4.24861i	−1.68330	−	0.357797i
$142$	−7.81413	−	0.821298i	−0.655747	−	0.0689218i
$143$	−1.38338	+	0.145399i	−0.115684	+	0.0121588i
$144$	1.36990	−	0.291182i	0.114159	−	0.0242652i
$145$		0			0
$146$	4.15662	−	4.61639i	0.344004	−	0.382055i
$147$	10.7226	−	3.48398i	0.884385	−	0.287354i
$148$	−20.8269	+	18.7526i	−1.71196	+	1.54145i
$149$	−3.18096	+	5.50959i	−0.260595	+	0.451363i	−0.966400	−	0.257043i	$-0.917252\pi$
$149$	−3.18096	+	5.50959i	−0.260595	+	0.451363i	0.705805	+	0.708406i	$0.250585\pi$
$150$		0			0
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	−0.996181	−	0.0873120i	$-0.972172\pi$
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	0.857248	+	0.514904i	$0.172172\pi$
$152$	5.76639	+	12.9515i	0.467716	+	1.05051i
$153$	8.92024	+	12.2777i	0.721159	+	0.992590i
$154$	−2.71187			−0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	4.69903	+	6.46767i	0.375024	+	0.516176i	0.954258	−	0.298985i	$-0.0966482\pi$
$157$	4.69903	+	6.46767i	0.375024	+	0.516176i	−0.579234	+	0.815161i	$0.696648\pi$
$158$	4.24973	+	9.54505i	0.338090	+	0.759363i
$159$	4.50565	−	13.8670i	0.357321	−	1.09972i
$160$		0			0
$161$	5.70146	−	9.87521i	0.449338	−	0.778276i
$162$	−12.6675	+	11.4058i	−0.995250	+	0.896127i
$163$	16.2302	−	5.27350i	1.27124	−	0.413052i	0.405756	−	0.913981i	$-0.367008\pi$
$163$	16.2302	−	5.27350i	1.27124	−	0.413052i	0.865488	+	0.500929i	$0.167008\pi$
$164$	16.4045	−	18.2190i	1.28098	−	1.42267i
$165$		0			0
$166$	−6.02725	+	1.28113i	−0.467805	+	0.0994351i
$167$	24.2387	−	2.54759i	1.87565	−	0.197138i	0.903034	−	0.429570i	$-0.141335\pi$
$167$	24.2387	−	2.54759i	1.87565	−	0.197138i	0.972613	+	0.232431i	$0.0746680\pi$
$168$	12.3823	+	1.30143i	0.955314	+	0.100408i
$169$	−9.19975	−	1.95547i	−0.707673	−	0.150421i
$170$		0			0
$171$	13.0032	+	9.44737i	0.994379	+	0.722458i
$172$	−0.159325	+	0.749565i	−0.0121484	+	0.0571538i
$173$	−8.92444	−	0.937997i	−0.678513	−	0.0713146i	−0.240998	−	0.970526i	$-0.577475\pi$
$173$	−8.92444	−	0.937997i	−0.678513	−	0.0713146i	−0.437515	+	0.899211i	$0.644141\pi$
$174$	0.0790797	+	0.752393i	0.00599501	+	0.0570387i
$175$		0			0
$176$	0.270863	+	0.120596i	0.0204171	+	0.00909027i
$177$	17.9583	+	16.1698i	1.34983	+	1.21539i
$178$	4.83816	−	1.57201i	0.362635	−	0.117827i
$179$	7.55483	+	8.39049i	0.564675	+	0.627135i	0.956088	−	0.293080i	$-0.0946803\pi$
$179$	7.55483	+	8.39049i	0.564675	+	0.627135i	−0.391413	+	0.920215i	$0.628014\pi$
$180$		0			0
$181$	7.47052	+	12.9393i	0.555279	+	0.961772i	0.997882	+	0.0650542i	$0.0207220\pi$
$181$	7.47052	+	12.9393i	0.555279	+	0.961772i	−0.442602	+	0.896718i	$0.645945\pi$
$182$	6.66523	+	2.16567i	0.494060	+	0.160530i
$183$	8.10873	+	18.2125i	0.599415	+	1.34631i
$184$	−17.6036	+	12.7898i	−1.29775	+	0.942874i
$185$		0			0
$186$	−0.0453903	−	32.6683i	−0.00332818	−	2.39536i
$187$			3.21286i			0.234947i
$188$	15.7050	+	21.6160i	1.14540	+	1.57651i
$189$	1.73192	−	0.771100i	0.125979	−	0.0560893i
$190$		0			0
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	0.822225	−	0.569163i	$-0.192733\pi$
$191$	−1.13046	−	1.95802i	−0.0817975	−	0.141677i	−0.904022	+	0.427486i	$0.859399\pi$
$192$	28.1057	+	16.2269i	2.02836	+	1.17107i
$193$	−19.0723	+	17.1727i	−1.37285	+	1.23612i	−0.430033	+	0.902813i	$0.641498\pi$
$193$	−19.0723	+	17.1727i	−1.37285	+	1.23612i	−0.942818	+	0.333307i	$0.891835\pi$
$194$	−8.76347	−	26.9712i	−0.629181	−	1.93642i
$195$		0			0
$196$	−13.4671	−	5.99594i	−0.961936	−	0.428282i
$197$	−1.28816	−	6.06032i	−0.0917776	−	0.431780i	−0.999914	−	0.0131056i	$-0.995828\pi$
$197$	−1.28816	−	6.06032i	−0.0917776	−	0.431780i	0.908136	−	0.418674i	$-0.137505\pi$
$198$	5.83463	−	0.613244i	0.414649	−	0.0435813i
$199$	−0.477625	+	4.54430i	−0.0338579	+	0.322137i	0.964463	+	0.264217i	$0.0851135\pi$
$199$	−0.477625	+	4.54430i	−0.0338579	+	0.322137i	−0.998321	+	0.0579199i	$0.981553\pi$
$200$		0			0
$201$	9.92879	+	7.21369i	0.700323	+	0.508814i
$202$	−9.96132	+	13.7106i	−0.700876	+	0.964673i
$203$	−0.0429430	+	0.202031i	−0.00301401	+	0.0141798i
$204$	3.86974	−	36.8182i	0.270936	−	2.57779i
$205$		0			0
$206$	−12.6144	+	2.68127i	−0.878886	+	0.186813i
$207$	−10.0336	+	22.5359i	−0.697386	+	1.56636i
$208$	−0.569420	−	0.512708i	−0.0394822	−	0.0355499i
$209$	1.05150	+	3.23618i	0.0727336	+	0.223851i
$210$		0			0
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	−0.344435	−	0.938810i	$-0.611930\pi$
$211$	9.30839	−	16.1226i	0.640816	−	1.10993i	0.985251	−	0.171115i	$-0.0547371\pi$
$212$	−16.5103	+	9.53225i	−1.13394	+	0.654678i
$213$	8.23426	+	2.67547i	0.564203	+	0.183321i
$214$	−3.84539	+	1.71208i	−0.262865	+	0.117035i
$215$		0			0
$216$	−3.61764			−0.246149
$217$	2.74430	−	8.48618i	0.186295	−	0.576080i
$218$			27.1487i			1.83874i
$219$	−5.53783	+	4.02347i	−0.374212	+	0.271881i
$220$		0			0
$221$	2.56575	−	7.89656i	0.172591	−	0.531180i
$222$	42.8329	−	24.7296i	2.87475	−	1.65974i
$223$	−5.38231	−	3.10748i	−0.360426	−	0.208092i	0.308842	−	0.951113i	$-0.400059\pi$
$223$	−5.38231	−	3.10748i	−0.360426	−	0.208092i	−0.669268	+	0.743021i	$0.733392\pi$
$224$	5.55324	+	6.16750i	0.371042	+	0.412084i
$225$		0			0
$226$	17.0686	−	18.9566i	1.13539	−	1.26097i
$227$	−5.30702	+	11.9198i	−0.352239	+	0.791142i	0.647342	+	0.762200i	$0.275881\pi$
$227$	−5.30702	+	11.9198i	−0.352239	+	0.791142i	−0.999581	+	0.0289423i	$0.990786\pi$
$228$	−8.15194	−	38.3519i	−0.539876	−	2.53992i
$229$	1.59698	+	15.1942i	0.105531	+	1.00406i	0.911275	+	0.411799i	$0.135099\pi$
$229$	1.59698	+	15.1942i	0.105531	+	1.00406i	−0.805743	+	0.592265i	$0.798234\pi$
$230$		0			0
$231$	2.92298	+	0.621299i	0.192318	+	0.0408785i
$232$	0.231665	−	0.318860i	0.0152096	−	0.0209342i
$233$	7.67721	−	10.5668i	0.502951	−	0.692253i	−0.479760	−	0.877400i	$-0.659276\pi$
$233$	7.67721	−	10.5668i	0.502951	−	0.692253i	0.982711	+	0.185147i	$0.0592762\pi$
$234$	−14.8301	−	3.15223i	−0.969471	−	0.206068i
$235$		0			0
$236$	−3.30277	−	31.4237i	−0.214992	−	2.04551i
$237$	−2.39375	−	11.2617i	−0.155491	−	0.731527i
$238$	6.58398	−	14.7879i	0.426776	−	0.958554i
$239$	15.6859	−	17.4210i	1.01464	−	1.12687i	0.0227507	−	0.999741i	$-0.492758\pi$
$239$	15.6859	−	17.4210i	1.01464	−	1.12687i	0.991886	−	0.127128i	$-0.0405757\pi$
$240$		0			0
$241$	16.5356	+	18.3647i	1.06515	+	1.18297i	0.982475	+	0.186395i	$0.0596805\pi$
$241$	16.5356	+	18.3647i	1.06515	+	1.18297i	0.0826776	+	0.996576i	$0.473653\pi$
$242$	−20.9065	−	12.0704i	−1.34392	−	0.775914i
$243$	19.3415	−	11.1668i	1.24076	−	0.716353i
$244$	8.05513	−	24.7911i	0.515677	−	1.58709i
$245$		0			0
$246$	−35.0030	+	25.4312i	−2.23171	+	1.62143i
$247$		−	8.79358i		−	0.559522i
$248$	−11.3705	+	12.6635i	−0.722025	+	0.804134i
$249$	6.78996			0.430296
$250$		0			0
$251$	−21.1889	+	9.43391i	−1.33743	+	0.595463i	−0.945827	−	0.324671i	$-0.894747\pi$
$251$	−21.1889	+	9.43391i	−1.33743	+	0.595463i	−0.391605	+	0.920134i	$0.628080\pi$
$252$	−17.5527	−	5.70323i	−1.10572	−	0.359270i
$253$	−4.52282	+	2.61125i	−0.284348	+	0.164168i
$254$	−1.48493	+	2.57198i	−0.0931729	+	0.161380i
$255$		0			0
$256$	−5.72420	−	17.6173i	−0.357763	−	1.10108i
$257$	−11.4044	−	10.2686i	−0.711386	−	0.640535i	0.231814	−	0.972760i	$-0.425534\pi$
$257$	−11.4044	−	10.2686i	−0.711386	−	0.640535i	−0.943200	+	0.332225i	$0.892201\pi$
$258$	0.550066	−	1.23547i	0.0342456	−	0.0769169i
$259$	13.2079	−	2.80743i	0.820700	−	0.174445i
$260$		0			0
$261$	0.0467066	−	0.444383i	0.00289106	−	0.0275066i
$262$	3.84786	−	18.1028i	0.237722	−	1.11839i
$263$	−4.00039	+	5.50607i	−0.246675	+	0.339519i	−0.914343	−	0.404940i	$-0.867292\pi$
$263$	−4.00039	+	5.50607i	−0.246675	+	0.339519i	0.667668	+	0.744459i	$0.267292\pi$
$264$	−4.61325	−	3.35173i	−0.283926	−	0.206284i
$265$		0			0
$266$	1.79202	−	17.0500i	0.109876	−	1.04540i
$267$	−5.57495	+	0.585951i	−0.341181	+	0.0358596i
$268$	−3.33632	−	15.6962i	−0.203798	−	0.958796i
$269$	−9.61017	−	4.27873i	−0.585943	−	0.260878i	0.0922822	−	0.995733i	$-0.470584\pi$
$269$	−9.61017	−	4.27873i	−0.585943	−	0.260878i	−0.678225	+	0.734854i	$0.737250\pi$
$270$		0			0
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	0.935162	−	0.354220i	$-0.115254\pi$
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	−0.964767	+	0.263105i	$0.915254\pi$
$272$	−1.31522	+	1.18423i	−0.0797470	+	0.0718046i
$273$	−6.68794	−	3.86128i	−0.404772	−	0.233695i
$274$	−19.0103	−	32.9268i	−1.14845	−	1.98918i
$275$		0			0
$276$	54.9750	−	24.4765i	3.30911	−	1.47331i
$277$	7.11300	+	9.79020i	0.427379	+	0.588236i	0.967349	−	0.253448i	$-0.0815646\pi$
$277$	7.11300	+	9.79020i	0.427379	+	0.588236i	−0.539970	+	0.841684i	$0.681565\pi$
$278$			16.9368i			1.01580i
$279$	−3.98538	+	18.8787i	−0.238599	+	1.13024i
$280$		0			0
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.0667525	−	0.997770i	$-0.478736\pi$
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.969563	+	0.244842i	$0.0787362\pi$
$282$	−19.1791	−	43.0769i	−1.14210	−	2.56519i
$283$	−0.655094	−	0.212853i	−0.0389413	−	0.0126528i	0.289482	−	0.957184i	$-0.406517\pi$
$283$	−0.655094	−	0.212853i	−0.0389413	−	0.0126528i	−0.328423	+	0.944531i	$0.606517\pi$
$284$	−5.66030	−	9.80392i	−0.335877	−	0.581756i
$285$		0			0
$286$	−2.14775	−	2.38532i	−0.126999	−	0.141047i
$287$	−11.2341	+	3.65018i	−0.663127	+	0.215463i
$288$	−13.3426	−	12.0137i	−0.786217	−	0.707913i
$289$	−1.98947	−	0.885767i	−0.117027	−	0.0521040i
$290$		0			0
$291$	3.26649	+	31.0785i	0.191485	+	1.82186i
$292$	8.90116	+	0.935550i	0.520901	+	0.0547489i
$293$	1.87368	−	8.81495i	0.109461	−	0.514975i	−0.888918	−	0.458066i	$-0.848542\pi$
$293$	1.87368	−	8.81495i	0.109461	−	0.514975i	0.998379	−	0.0569086i	$-0.0181244\pi$
$294$	21.0474	+	15.2918i	1.22751	+	0.891837i
$295$		0			0
$296$	−25.2036	−	5.35719i	−1.46493	−	0.311380i
$297$	−0.863526	−	0.0907602i	−0.0501068	−	0.00526644i
$298$	−14.5999	+	1.53451i	−0.845749	+	0.0888918i
$299$	13.2015	−	2.80607i	0.763463	−	0.162279i
$300$		0			0
$301$	0.247056	−	0.274384i	0.0142401	−	0.0158152i
$302$	−12.1245	+	3.93949i	−0.697688	+	0.226692i
$303$	13.8779	−	12.4957i	0.797265	−	0.717861i
$304$	−0.937195	+	1.62327i	−0.0537518	+	0.0931009i
$305$		0			0
$306$	−10.8215	+	33.3051i	−0.618623	+	1.90393i
$307$	12.7441	+	28.6238i	0.727346	+	1.63365i	0.772776	+	0.634679i	$0.218868\pi$
$307$	12.7441	+	28.6238i	0.727346	+	1.63365i	−0.0454296	+	0.998968i	$0.514466\pi$
$308$	−2.29663	−	3.16104i	−0.130863	−	0.180117i
$309$	14.2107			0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	8.66180	+	11.9219i	0.490378	+	0.674947i
$313$	−8.81346	−	19.7953i	−0.498166	−	1.11890i	−0.971289	−	0.237903i	$-0.923540\pi$
$313$	−8.81346	−	19.7953i	−0.498166	−	1.11890i	0.473123	−	0.880996i	$-0.343127\pi$
$314$	−5.70058	+	17.5446i	−0.321702	+	0.990098i
$315$		0			0
$316$	−7.52698	+	13.0371i	−0.423426	+	0.733395i
$317$	0.755070	−	0.679868i	0.0424089	−	0.0381852i	−0.647654	−	0.761935i	$-0.724250\pi$
$317$	0.755070	−	0.679868i	0.0424089	−	0.0381852i	0.690063	+	0.723750i	$0.257583\pi$
$318$	31.9984	−	10.3969i	1.79438	−	0.583030i
$319$	0.0632977	−	0.0702992i	0.00354399	−	0.00393600i
$320$		0			0
$321$	4.53698	−	0.964364i	0.253229	−	0.0538256i
$322$	26.1684	−	2.75041i	1.45831	−	0.153274i
$323$	−20.1998	−	2.12308i	−1.12394	−	0.118131i
$324$	−24.0228	−	5.10620i	−1.33460	−	0.283678i
$325$		0			0
$326$	31.8582	+	23.1463i	1.76446	+	1.28196i
$327$	6.21986	−	29.2621i	0.343959	−	1.61820i
$328$	22.4168	+	2.35610i	1.23776	+	0.130094i
$329$	−1.34565	−	12.8030i	−0.0741881	−	0.705853i
$330$		0			0
$331$	24.3820	+	10.8556i	1.34016	+	0.596676i	0.946537	−	0.322597i	$-0.104556\pi$
$331$	24.3820	+	10.8556i	1.34016	+	0.596676i	0.393621	+	0.919273i	$0.371222\pi$
$332$	−6.59768	−	5.94058i	−0.362095	−	0.326032i
$333$	−27.7822	+	9.02697i	−1.52245	+	0.494675i
$334$	37.6316	+	41.7941i	2.05911	+	2.28687i
$335$		0			0
$336$	0.823049	+	1.42556i	0.0449010	+	0.0777708i
$337$	−30.3782	−	9.87048i	−1.65481	−	0.537679i	−0.675033	−	0.737788i	$-0.735871\pi$
$337$	−30.3782	−	9.87048i	−1.65481	−	0.537679i	−0.979774	+	0.200108i	$0.935871\pi$
$338$	−8.82738	−	19.8266i	−0.480146	−	1.07843i
$339$	−22.7404	+	16.5218i	−1.23509	+	0.897343i
$340$		0			0
$341$	−3.03182	+	2.73750i	−0.164182	+	0.148244i
$342$			37.0885i			2.00552i
$343$	10.7658	+	14.8178i	0.581298	+	0.800088i
$344$	−0.643640	+	0.286567i	−0.0347027	+	0.0154507i
$345$		0			0
$346$	−10.3534	−	17.9326i	−0.556603	−	0.964065i
$347$	2.70314	+	1.56066i	0.145112	+	0.0837804i	0.570798	−	0.821090i	$-0.306634\pi$
$347$	2.70314	+	1.56066i	0.145112	+	0.0837804i	−0.425686	+	0.904871i	$0.639967\pi$
$348$	−0.810041	+	0.729364i	−0.0434227	+	0.0390980i
$349$	6.80655	+	20.9484i	0.364346	+	1.12134i	0.950389	+	0.311063i	$0.100685\pi$
$349$	6.80655	+	20.9484i	0.364346	+	1.12134i	−0.586043	+	0.810280i	$0.699315\pi$
$350$		0			0
$351$	2.04989	+	0.912671i	0.109415	+	0.0487147i
$352$	−0.790275	−	3.71795i	−0.0421218	−	0.198167i
$353$	4.90537	−	0.515575i	0.261087	−	0.0274413i	0.0269192	−	0.999638i	$-0.491430\pi$
$353$	4.90537	−	0.515575i	0.261087	−	0.0274413i	0.234167	+	0.972196i	$0.424764\pi$
$354$	−5.82873	+	55.4567i	−0.309794	+	2.94749i
$355$		0			0
$356$	5.92973	+	4.30820i	0.314275	+	0.228334i
$357$	−10.4845	+	14.4306i	−0.554897	+	0.763750i
$358$	−5.41676	+	25.4838i	−0.286285	+	1.34686i
$359$	−0.0377201	+	0.358883i	−0.00199079	+	0.0189411i	−0.995472	−	0.0950532i	$-0.969698\pi$
$359$	−0.0377201	+	0.358883i	−0.00199079	+	0.0189411i	0.993481	+	0.113994i	$0.0363646\pi$
$360$		0			0
$361$	−2.45641	+	0.522126i	−0.129285	+	0.0274803i
$362$	−14.0230	+	31.4962i	−0.737033	+	1.65540i
$363$	19.7686	+	17.7998i	1.03758	+	0.934246i
$364$	3.12029	+	9.60325i	0.163547	+	0.503347i
$365$		0			0
$366$	−23.0015	+	39.8398i	−1.20231	+	2.08246i
$367$	25.4498	−	14.6935i	1.32847	−	0.766992i	0.343406	−	0.939187i	$-0.388419\pi$
$367$	25.4498	−	14.6935i	1.32847	−	0.766992i	0.985063	+	0.172195i	$0.0550859\pi$
$368$	−2.73602	−	0.888987i	−0.142625	−	0.0463416i
$369$	23.3449	−	10.3938i	1.21528	−	0.541080i
$370$		0			0
$371$	9.18555			0.476890
$372$	38.0407	−	27.7190i	1.97232	−	1.43716i
$373$			17.7284i			0.917941i	0.888451	+	0.458971i	$0.151782\pi$
$373$			17.7284i			0.917941i	−0.888451	+	0.458971i	$0.848218\pi$
$374$	−5.99786	+	4.35770i	−0.310142	+	0.225331i
$375$		0			0
$376$	−7.59116	+	23.3632i	−0.391484	+	1.20486i
$377$	−0.211713	+	0.122233i	−0.0109038	+	0.00629530i
$378$	3.78857	+	2.18733i	0.194863	+	0.112504i
$379$	1.64634	+	1.82845i	0.0845669	+	0.0939211i	0.783943	−	0.620833i	$-0.213205\pi$
$379$	1.64634	+	1.82845i	0.0845669	+	0.0939211i	−0.699376	+	0.714754i	$0.746539\pi$
$380$		0			0
$381$	2.18978	−	2.43199i	0.112186	−	0.124595i
$382$	2.12201	−	4.76611i	0.108571	−	0.243855i
$383$	3.97484	+	18.7001i	0.203105	+	0.955533i	0.955082	+	0.296343i	$0.0957672\pi$
$383$	3.97484	+	18.7001i	0.203105	+	0.955533i	−0.751977	+	0.659190i	$0.770899\pi$
$384$	5.07387	+	48.2747i	0.258925	+	2.46351i
$385$		0			0
$386$	−57.9268	−	12.3127i	−2.94840	−	0.626701i
$387$	−0.469497	+	0.646208i	−0.0238659	+	0.0328486i
$388$	24.0168	−	33.0563i	1.21927	−	1.67818i
$389$	5.15587	+	1.09591i	0.261413	+	0.0555651i	0.336754	−	0.941593i	$-0.390671\pi$
$389$	5.15587	+	1.09591i	0.261413	+	0.0555651i	−0.0753405	+	0.997158i	$0.524004\pi$
$390$		0			0
$391$	−3.25851	−	31.0027i	−0.164790	−	1.56787i
$392$	−2.81793	−	13.2573i	−0.142327	−	0.669597i
$393$	−8.29480	+	18.6304i	−0.418417	+	0.939781i
$394$	9.56640	−	10.6246i	0.481949	−	0.535258i
$395$		0			0
$396$	5.65604	+	6.28167i	0.284227	+	0.315666i
$397$	14.6579	+	8.46275i	0.735660	+	0.424733i	0.820489	−	0.571662i	$-0.193701\pi$
$397$	14.6579	+	8.46275i	0.735660	+	0.424733i	−0.0848295	+	0.996395i	$0.527035\pi$
$398$	−9.13124	+	5.27193i	−0.457708	+	0.264258i
$399$	−5.83773	+	17.9667i	−0.292252	+	0.899460i
$400$		0			0
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.584524	+	0.811377i	$0.698719\pi$
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.952293	+	0.305186i	$0.901281\pi$
$402$			28.3195i			1.41245i
$403$	9.63773	−	4.30705i	0.480089	−	0.214549i
$404$	−24.4175			−1.21482
$405$		0			0
$406$	−0.435402	+	0.193854i	−0.0216087	+	0.00962079i
$407$	−5.88166	−	1.91107i	−0.291543	−	0.0947281i
$408$	29.4772	−	17.0187i	1.45934	−	0.842550i
$409$	0.249342	−	0.431873i	0.0123292	−	0.0213547i	−0.859795	−	0.510639i	$-0.829409\pi$
$409$	0.249342	−	0.431873i	0.0123292	−	0.0213547i	0.872124	+	0.489285i	$0.162742\pi$
$410$		0			0
$411$	12.9465	+	39.8453i	0.638605	+	1.96542i
$412$	−13.8082	−	12.4330i	−0.680283	−	0.612529i
$413$	−6.19208	+	13.9076i	−0.304692	+	0.684350i
$414$	−55.6796	+	11.8351i	−2.73650	+	0.581662i
$415$		0			0
$416$	−1.02677	+	9.76908i	−0.0503416	+	0.478968i
$417$	3.88028	−	18.2553i	0.190018	−	0.893966i
$418$	−4.61521	+	6.35229i	−0.225737	+	0.310701i
$419$	10.9298	+	7.94098i	0.533957	+	0.387942i	0.821836	−	0.569725i	$-0.192950\pi$
$419$	10.9298	+	7.94098i	0.533957	+	0.387942i	−0.287879	+	0.957667i	$0.592950\pi$
$420$		0			0
$421$	3.23151	−	30.7458i	0.157494	−	1.49846i	−0.575264	−	0.817968i	$-0.695101\pi$
$421$	3.23151	−	30.7458i	0.157494	−	1.49846i	0.732758	−	0.680489i	$-0.238233\pi$
$422$	42.7234	−	4.49041i	2.07974	−	0.218590i
$423$	5.79037	+	27.2415i	0.281537	+	1.32453i
$424$	−16.0127	−	7.12930i	−0.777644	−	0.346229i
$425$		0			0
$426$	6.17373	+	19.0008i	0.299118	+	0.920591i
$427$	−9.33347	+	8.40390i	−0.451678	+	0.406693i
$428$	−5.25223	−	3.03237i	−0.253876	−	0.146575i
$429$	1.76846	+	3.06306i	0.0853820	+	0.147886i
$430$		0			0
$431$	−11.0126	+	4.90313i	−0.530458	+	0.236175i	−0.654446	−	0.756108i	$-0.727098\pi$
$431$	−11.0126	+	4.90313i	−0.530458	+	0.236175i	0.123988	+	0.992284i	$0.460432\pi$
$432$	−0.281134	−	0.386948i	−0.0135261	−	0.0186170i
$433$		−	32.3919i		−	1.55665i	−0.627860	−	0.778327i	$-0.716069\pi$
$433$		−	32.3919i		−	1.55665i	0.627860	−	0.778327i	$-0.283931\pi$
$434$	19.5644	−	6.38693i	0.939122	−	0.306583i
$435$		0			0
$436$	−31.6454	+	22.9917i	−1.51554	+	1.10110i
$437$	−13.4287	−	30.1613i	−0.642380	−	1.44281i
$438$	−15.0222	−	4.88102i	−0.717790	−	0.233224i
$439$	6.18408	+	10.7111i	0.295150	+	0.511215i	0.975020	−	0.222118i	$-0.0712971\pi$
$439$	6.18408	+	10.7111i	0.295150	+	0.511215i	−0.679870	+	0.733333i	$0.737964\pi$
$440$		0			0
$441$	−10.2817	−	11.4190i	−0.489604	−	0.543760i
$442$	18.2215	−	5.92053i	0.866709	−	0.281611i
$443$	−3.51017	−	3.16058i	−0.166773	−	0.150163i	0.581518	−	0.813533i	$-0.302459\pi$
$443$	−3.51017	−	3.16058i	−0.166773	−	0.150163i	−0.748292	+	0.663370i	$0.769126\pi$
$444$	65.0998	+	28.9843i	3.08950	+	1.37553i
$445$		0			0
$446$	−1.49906	−	14.2626i	−0.0709826	−	0.675354i
$447$	16.0880	+	1.69092i	0.760937	+	0.0799777i
$448$	−4.25083	+	19.9986i	−0.200833	+	0.944844i
$449$	−12.9315	−	9.39528i	−0.610275	−	0.443390i	0.239236	−	0.970961i	$-0.423103\pi$
$449$	−12.9315	−	9.39528i	−0.610275	−	0.443390i	−0.849511	+	0.527571i	$0.823103\pi$
$450$		0			0
$451$	5.29175	+	1.12480i	0.249179	+	0.0529646i
$452$	36.5515	+	3.84171i	1.71924	+	0.180699i
$453$	13.9709	−	1.46840i	0.656411	−	0.0689916i
$454$	−29.4502	+	6.25984i	−1.38217	+	0.293789i
$455$		0			0
$456$	24.1213	−	26.7894i	1.12958	−	1.25453i
$457$	4.33468	−	1.40842i	0.202768	−	0.0658832i	−0.205872	−	0.978579i	$-0.566003\pi$
$457$	4.33468	−	1.40842i	0.202768	−	0.0658832i	0.408640	+	0.912696i	$0.366003\pi$
$458$	−26.1990	+	23.5897i	−1.22420	+	1.10227i
$459$	2.59141	−	4.48846i	0.120957	−	0.209503i
$460$		0			0
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	0.751171	+	0.660107i	$0.229489\pi$
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	−0.995712	+	0.0925105i	$0.970511\pi$
$462$	2.80467	+	6.29939i	0.130485	+	0.293074i
$463$	−16.1217	−	22.1896i	−0.749239	−	1.03124i	−0.998034	−	0.0626822i	$-0.980035\pi$
$463$	−16.1217	−	22.1896i	−0.749239	−	1.03124i	0.248795	−	0.968556i	$-0.419965\pi$
$464$	0.0521088			0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	−13.4665	−	18.5350i	−0.623153	−	0.857697i	0.374425	−	0.927257i	$-0.377840\pi$
$467$	−13.4665	−	18.5350i	−0.623153	−	0.857697i	−0.997578	+	0.0695608i	$0.977840\pi$
$468$	−8.88495	−	19.9559i	−0.410707	−	0.922463i
$469$	−2.38919	+	7.35318i	−0.110323	+	0.339538i
$470$		0			0
$471$	10.1639	−	17.6043i	0.468327	−	0.811165i
$472$	21.5886	−	19.4385i	0.993696	−	0.894728i
$473$	−0.160825	+	0.0522553i	−0.00739476	+	0.00240270i
$474$	17.7770	−	19.7433i	0.816524	−	0.906841i
$475$		0			0
$476$	22.8130	−	4.84905i	1.04563	−	0.222256i
$477$	−19.7628	+	2.07716i	−0.904878	+	0.0951065i
$478$	53.7972	+	5.65432i	2.46063	+	0.258622i
$479$	8.84935	+	1.88099i	0.404337	+	0.0859445i	0.405591	−	0.914055i	$-0.367066\pi$
$479$	8.84935	+	1.88099i	0.404337	+	0.0859445i	−0.00125373	+	0.999999i	$0.500399\pi$
$480$		0			0
$481$	12.9298	+	9.39403i	0.589547	+	0.428331i
$482$	−11.8559	+	55.7777i	−0.540022	+	2.54060i
$483$	−28.8356	−	3.03075i	−1.31207	−	0.137904i
$484$	−3.63570	−	34.5914i	−0.165259	−	1.57234i
$485$		0			0
$486$	47.0800	+	20.9614i	2.13559	+	0.950828i
$487$	17.5551	+	15.8066i	0.795496	+	0.716268i	0.962970	−	0.269609i	$-0.0868944\pi$
$487$	17.5551	+	15.8066i	0.795496	+	0.716268i	−0.167474	+	0.985876i	$0.553561\pi$
$488$	22.7931	−	7.40594i	1.03180	−	0.335251i
$489$	−29.0353	−	32.2470i	−1.31302	−	1.45826i
$490$		0			0
$491$	−4.61346	−	7.99074i	−0.208202	−	0.360617i	0.742946	−	0.669351i	$-0.233428\pi$
$491$	−4.61346	−	7.99074i	−0.208202	−	0.360617i	−0.951148	+	0.308734i	$0.900095\pi$
$492$	−59.2867	−	19.2634i	−2.67285	−	0.868462i
$493$	0.229666	+	0.515838i	0.0103436	+	0.0232322i
$494$	16.4161	−	11.9270i	0.738596	−	0.536621i
$495$		0			0
$496$	−2.23813	−	0.232093i	−0.100495	−	0.0104213i
$497$			5.45442i			0.244664i
$498$	9.20943	+	12.6757i	0.412684	+	0.568011i
$499$	−25.9574	+	11.5570i	−1.16201	+	0.517362i	−0.894884	−	0.446298i	$-0.852742\pi$
$499$	−25.9574	+	11.5570i	−1.16201	+	0.517362i	−0.267130	+	0.963660i	$0.586075\pi$
$500$		0			0
$501$	−30.9859	−	53.6692i	−1.38435	−	2.39776i
$502$	−46.3506	−	26.7606i	−2.06873	−	1.19438i
$503$	−13.5833	+	12.2304i	−0.605647	+	0.545327i	−0.913880	−	0.405984i	$-0.866929\pi$
$503$	−13.5833	+	12.2304i	−0.605647	+	0.545327i	0.308233	+	0.951311i	$0.400262\pi$
$504$	−5.24359	−	16.1381i	−0.233568	−	0.718848i
$505$		0			0
$506$	−11.0092	−	4.90161i	−0.489419	−	0.217903i
$507$	4.97221	+	23.3924i	0.220824	+	1.03889i
$508$	−4.25553	+	0.447274i	−0.188809	+	0.0198446i
$509$	1.08567	−	10.3295i	0.0481215	−	0.457845i	−0.943756	−	0.330644i	$-0.892734\pi$
$509$	1.08567	−	10.3295i	0.0481215	−	0.457845i	0.991877	−	0.127201i	$-0.0405993\pi$
$510$		0			0
$511$	−3.48875	−	2.53472i	−0.154333	−	0.112130i
$512$	2.68292	−	3.69272i	0.118569	−	0.163197i
$513$	1.14125	−	5.36915i	0.0503873	−	0.237054i
$514$	3.70152	−	35.2176i	0.163267	−	1.55338i
$515$		0			0
$516$	1.90594	−	0.405120i	0.0839042	−	0.0178344i
$517$	−2.39814	+	5.38631i	−0.105470	+	0.236890i
$518$	23.1553	+	20.8491i	1.01739	+	0.916058i
$519$	7.05096	+	21.7006i	0.309503	+	0.952552i
$520$		0			0
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	−0.949376	−	0.314141i	$-0.898284\pi$
$521$	−4.62522	+	8.01111i	−0.202635	+	0.350973i	0.746742	+	0.665114i	$0.231617\pi$
$522$	0.892937	−	0.515537i	0.0390828	−	0.0225645i
$523$	−6.25335	−	2.03184i	−0.273440	−	0.0888461i	0.169087	−	0.985601i	$-0.445918\pi$
$523$	−6.25335	−	2.03184i	−0.273440	−	0.0888461i	−0.442527	+	0.896755i	$0.645918\pi$
$524$	24.3598	−	10.8457i	1.06416	−	0.473796i
$525$		0			0
$526$	−15.7047			−0.684759
$527$	−7.56684	−	23.1787i	−0.329617	−	1.00968i
$528$		−	0.753909i		−	0.0328097i
$529$	22.3875	−	16.2655i	0.973371	−	0.707195i
$530$		0			0
$531$	10.1774	−	31.3227i	0.441660	−	1.35929i
$532$	21.3916	−	12.3504i	0.927443	−	0.535460i
$533$	−12.1078	−	6.99044i	−0.524447	−	0.302790i
$534$	−8.65534	−	9.61273i	−0.374553	−	0.415983i
$535$		0			0
$536$	9.87206	−	10.9640i	0.426408	−	0.473574i
$537$	11.6769	−	26.2267i	0.503894	−	1.13176i
$538$	−5.04692	−	23.7439i	−0.217588	−	1.02367i
$539$	−0.340034	−	3.23520i	−0.0146463	−	0.139350i
$540$		0			0
$541$	2.15513	+	0.458087i	0.0926562	+	0.0196947i	0.254006	−	0.967203i	$-0.418252\pi$
$541$	2.15513	+	0.458087i	0.0926562	+	0.0196947i	−0.161350	+	0.986897i	$0.551585\pi$
$542$	2.13912	−	2.94425i	0.0918831	−	0.126466i
$543$	22.3305	−	30.7353i	0.958294	−	1.31898i
$544$	22.1927	+	4.71720i	0.951503	+	0.202248i
$545$		0			0
$546$	−1.86270	−	17.7224i	−0.0797162	−	0.758449i
$547$	−1.01117	−	4.75717i	−0.0432344	−	0.203402i	0.951229	−	0.308486i	$-0.0998222\pi$
$547$	−1.01117	−	4.75717i	−0.0432344	−	0.203402i	−0.994463	+	0.105084i	$0.966489\pi$
$548$	22.2810	−	50.0440i	0.951797	−	2.13777i
$549$	18.1807	−	20.1917i	0.775933	−	0.861761i
$550$		0			0
$551$	0.400155	+	0.444417i	0.0170472	+	0.0189328i
$552$	47.9152	+	27.6639i	2.03941	+	1.17745i
$553$	6.28147	−	3.62661i	0.267115	−	0.154219i
$554$	−8.62905	+	26.5575i	−0.366613	+	1.12832i
$555$		0			0
$556$	−19.7421	+	14.3435i	−0.837251	+	0.608298i
$557$		−	11.0363i		−	0.467623i	−0.972282	−	0.233811i	$-0.924880\pi$
$557$		−	11.0363i		−	0.467623i	0.972282	−	0.233811i	$-0.0751198\pi$
$558$	−40.6488	+	18.1657i	−1.72080	+	0.769016i
$559$	0.437007			0.0184834
$560$		0			0
$561$	7.46313	−	3.32280i	0.315094	−	0.140289i
$562$	47.1238	+	15.3115i	1.98780	+	0.645875i
$563$	−9.69292	+	5.59621i	−0.408508	+	0.235852i	−0.690148	−	0.723668i	$-0.742455\pi$
$563$	−9.69292	+	5.59621i	−0.408508	+	0.235852i	0.281641	+	0.959520i	$0.409121\pi$
$564$	33.9694	−	58.8366i	1.43037	−	2.47747i
$565$		0			0
$566$	−0.491164	−	1.51165i	−0.0206452	−	0.0635393i
$567$	8.79372	+	7.91790i	0.369301	+	0.332521i
$568$	4.23341	−	9.50839i	0.177630	−	0.398963i
$569$	−45.8966	+	9.75563i	−1.92409	+	0.408977i	−0.924471	+	0.381252i	$0.875493\pi$
$569$	−45.8966	+	9.75563i	−1.92409	+	0.408977i	−0.999616	+	0.0277250i	$0.991174\pi$
$570$		0			0
$571$	2.13862	−	20.3476i	0.0894983	−	0.851520i	−0.854029	−	0.520225i	$-0.825848\pi$
$571$	2.13862	−	20.3476i	0.0894983	−	0.851520i	0.943527	−	0.331295i	$-0.107485\pi$
$572$	0.961511	−	4.52355i	0.0402028	−	0.189139i
$573$	−3.37913	+	4.65097i	−0.141165	+	0.194297i
$574$	−22.0514	−	16.0213i	−0.920407	−	0.668715i
$575$		0			0
$576$	4.62337	−	43.9885i	0.192641	−	1.83285i
$577$	−3.62836	+	0.381356i	−0.151051	+	0.0158761i	−0.179752	−	0.983712i	$-0.557530\pi$
$577$	−3.62836	+	0.381356i	−0.151051	+	0.0158761i	0.0287013	+	0.999588i	$0.490863\pi$
$578$	−1.04480	−	4.91538i	−0.0434578	−	0.204453i
$579$	59.6153	+	26.5425i	2.47753	+	1.10307i
$580$		0			0
$581$	1.32184	+	4.06822i	0.0548393	+	0.168778i
$582$	−53.5879	+	48.2507i	−2.22129	+	2.00006i
$583$	−3.64334	−	2.10348i	−0.150892	−	0.0871173i
$584$	4.11443	+	7.12641i	0.170256	+	0.294893i
$585$		0			0
$586$	18.9973	−	8.45815i	0.784772	−	0.349403i
$587$	−13.4442	−	18.5043i	−0.554901	−	0.763755i	0.435766	−	0.900060i	$-0.356477\pi$
$587$	−13.4442	−	18.5043i	−0.554901	−	0.763755i	−0.990667	+	0.136305i	$0.956477\pi$
$588$			37.4838i			1.54580i
$589$	−15.2076	−	20.8705i	−0.626620	−	0.859954i
$590$		0			0
$591$	−12.7452	+	9.25996i	−0.524269	+	0.380904i
$592$	−1.38561	−	3.11213i	−0.0569482	−	0.127908i
$593$	−18.5073	−	6.01340i	−0.760005	−	0.246941i	−0.0967243	−	0.995311i	$-0.530837\pi$
$593$	−18.5073	−	6.01340i	−0.760005	−	0.246941i	−0.663281	+	0.748371i	$0.730837\pi$
$594$	−1.00179	−	1.73515i	−0.0411040	−	0.0711943i
$595$		0			0
$596$	−14.1530	−	15.7185i	−0.579731	−	0.643856i
$597$	11.0499	−	3.59033i	0.452242	−	0.146942i
$598$	23.1440	+	20.8390i	0.946430	+	0.852169i
$599$	−32.1311	−	14.3057i	−1.31284	−	0.584514i	−0.373541	−	0.927614i	$-0.621857\pi$
$599$	−32.1311	−	14.3057i	−1.31284	−	0.584514i	−0.939299	+	0.343099i	$0.888523\pi$
$600$		0			0
$601$	−0.615470	−	5.85580i	−0.0251055	−	0.238863i	−0.999877	−	0.0156596i	$-0.995015\pi$
$601$	−0.615470	−	5.85580i	−0.0251055	−	0.238863i	0.974772	−	0.223204i	$-0.0716515\pi$
$602$	0.847317	+	0.0890566i	0.0345341	+	0.00362968i
$603$	3.47758	−	16.3607i	0.141618	−	0.666261i
$604$	−14.8600	−	10.7964i	−0.604645	−	0.439300i
$605$		0			0
$606$	42.1504	+	8.95935i	1.71224	+	0.363949i
$607$	38.6718	+	4.06457i	1.56964	+	0.164976i	0.849023	−	0.528356i	$-0.177191\pi$
$607$	38.6718	+	4.06457i	1.56964	+	0.164976i	0.720618	+	0.693332i	$0.243858\pi$
$608$	23.8976	−	2.51174i	0.969175	−	0.101864i
$609$	0.513709	−	0.109192i	0.0208166	−	0.00442469i
$610$		0			0
$611$	10.1956	−	11.3233i	0.412469	−	0.458093i
$612$	−47.9859	+	15.5916i	−1.93972	+	0.630252i
$613$	33.8892	−	30.5139i	1.36877	−	1.23245i	0.423609	−	0.905845i	$-0.360763\pi$
$613$	33.8892	−	30.5139i	1.36877	−	1.23245i	0.945162	−	0.326602i	$-0.105904\pi$
$614$	−36.1505	+	62.6144i	−1.45891	+	2.52691i
$615$		0			0
$616$	1.11010	−	3.41654i	0.0447272	−	0.137656i
$617$	2.69523	+	6.05359i	0.108506	+	0.243708i	0.959635	−	0.281248i	$-0.0907483\pi$
$617$	2.69523	+	6.05359i	0.108506	+	0.243708i	−0.851129	+	0.524956i	$0.824082\pi$
$618$	19.2743	+	26.5288i	0.775328	+	1.06715i
$619$	−41.5360			−1.66947			−0.834736	−	0.550650i	$-0.814380\pi$
$619$	−41.5360			−1.66947			−0.834736	+	0.550650i	$0.814380\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	−24.0260	−	33.0689i	−0.963353	−	1.32594i
$623$	−1.43638	−	3.22617i	−0.0575474	−	0.129254i
$624$	−0.602062	+	1.85296i	−0.0241018	+	0.0741776i
$625$		0			0
$626$	25.0006	−	43.3022i	0.999223	−	1.73071i
$627$	6.42982	−	5.78944i	0.256782	−	0.231208i
$628$	−25.2782	+	8.21338i	−1.00871	+	0.327750i
$629$	24.7008	−	27.4330i	0.984884	−	1.09382i
$630$		0			0
$631$	−10.9012	+	2.31712i	−0.433969	+	0.0922429i	−0.419716	−	0.907655i	$-0.637870\pi$
$631$	−10.9012	+	2.31712i	−0.433969	+	0.0922429i	−0.0142529	+	0.999898i	$0.504537\pi$
$632$	−13.7649	+	1.44675i	−0.547538	+	0.0575486i
$633$	−47.0780	−	4.94810i	−1.87118	−	0.196669i
$634$	2.29332	+	0.487460i	0.0910794	+	0.0193595i
$635$		0			0
$636$	39.2177	+	28.4934i	1.55508	+	1.12983i
$637$	−1.74786	+	8.22302i	−0.0692526	+	0.325808i
$638$	0.217089	+	0.0228170i	0.00859464	+	0.000903334i
$639$	−1.23343	−	11.7353i	−0.0487936	−	0.464240i
$640$		0			0
$641$	16.0357	+	7.13957i	0.633374	+	0.281996i	0.698203	−	0.715900i	$-0.253983\pi$
$641$	16.0357	+	7.13957i	0.633374	+	0.281996i	−0.0648289	+	0.997896i	$0.520650\pi$
$642$	7.95394	+	7.16176i	0.313917	+	0.282652i
$643$	2.08857	−	0.678617i	0.0823651	−	0.0267621i	−0.267545	−	0.963545i	$-0.586212\pi$
$643$	2.08857	−	0.678617i	0.0823651	−	0.0267621i	0.349910	+	0.936783i	$0.386212\pi$
$644$	25.3674	+	28.1734i	0.999617	+	1.11019i
$645$		0			0
$646$	−23.4341	−	40.5891i	−0.922003	−	1.59696i
$647$	30.8566	+	10.0259i	1.21310	+	0.394160i	0.844564	−	0.535454i	$-0.179860\pi$
$647$	30.8566	+	10.0259i	1.21310	+	0.394160i	0.368535	+	0.929614i	$0.379860\pi$
$648$	−9.18418	−	20.6280i	−0.360789	−	0.810345i
$649$	5.64084	−	4.09831i	0.221422	−	0.160873i
$650$		0			0
$651$	−22.5507	+	2.40186i	−0.883832	+	0.0941362i
$652$			56.7370i			2.22199i
$653$	−9.69256	−	13.3407i	−0.379299	−	0.522061i	0.576099	−	0.817380i	$-0.304574\pi$
$653$	−9.69256	−	13.3407i	−0.379299	−	0.522061i	−0.955399	+	0.295319i	$0.904574\pi$
$654$	63.0636	−	28.0777i	2.46598	−	1.09793i
$655$		0			0
$656$	1.49004	+	2.58083i	0.0581764	+	0.100764i
$657$	8.07927	+	4.66457i	0.315202	+	0.181982i
$658$	22.0759	−	19.8772i	0.860607	−	0.774894i
$659$	6.10043	+	18.7752i	0.237639	+	0.731377i	0.996760	+	0.0804282i	$0.0256288\pi$
$659$	6.10043	+	18.7752i	0.237639	+	0.731377i	−0.759122	+	0.650949i	$0.774371\pi$
$660$		0			0
$661$	10.7623	+	4.79169i	0.418605	+	0.186375i	0.605220	−	0.796058i	$-0.293085\pi$
$661$	10.7623	+	4.79169i	0.418605	+	0.186375i	−0.186615	+	0.982433i	$0.559752\pi$
$662$	12.8046	+	60.2408i	0.497664	+	2.34132i
$663$	−20.9964	+	2.20681i	−0.815433	+	0.0857055i
$664$	0.853219	−	8.11783i	0.0331113	−	0.315033i
$665$		0			0
$666$	−54.5336	−	39.6210i	−2.11313	−	1.53528i
$667$	−0.539497	+	0.742554i	−0.0208894	+	0.0287518i
$668$	−16.8470	+	79.2591i	−0.651832	+	3.06663i
$669$	−1.65185	+	15.7163i	−0.0638644	+	0.607629i
$670$		0			0
$671$	5.62649	−	1.19595i	0.217208	−	0.0461690i
$672$	8.58318	−	19.2781i	0.331104	−	0.743671i
$673$	37.4412	+	33.7122i	1.44325	+	1.29951i	0.881482	+	0.472217i	$0.156546\pi$
$673$	37.4412	+	33.7122i	1.44325	+	1.29951i	0.561770	+	0.827293i	$0.310120\pi$
$674$	−22.7764	−	70.0985i	−0.877314	−	2.70009i
$675$		0			0
$676$	15.6348	−	27.0802i	0.601337	−	1.04155i
$677$	3.44674	−	1.98998i	0.132469	−	0.0764810i	−0.432301	−	0.901729i	$-0.642298\pi$
$677$	3.44674	−	1.98998i	0.132469	−	0.0764810i	0.564770	+	0.825248i	$0.308965\pi$
$678$	−61.6869	−	20.0433i	−2.36907	−	0.769758i
$679$	−17.9849	+	8.00737i	−0.690195	+	0.307295i
$680$		0			0
$681$	33.1770			1.27134
$682$	−9.22259	−	1.94693i	−0.353151	−	0.0745519i
$683$			5.23244i			0.200214i	0.994977	+	0.100107i	$0.0319185\pi$
$683$			5.23244i			0.200214i	−0.994977	+	0.100107i	$0.968082\pi$
$684$	−43.2314	+	31.4095i	−1.65300	+	1.20097i
$685$		0			0
$686$	−13.0604	+	40.1958i	−0.498648	+	1.53468i
$687$	33.6430	−	19.4238i	1.28356	−	0.741064i
$688$	−0.0806701	−	0.0465749i	−0.00307552	−	0.00177565i
$689$	7.27477	+	8.07945i	0.277147	+	0.307803i
$690$		0			0
$691$	6.15301	−	6.83361i	0.234072	−	0.259963i	−0.614653	−	0.788797i	$-0.710704\pi$
$691$	6.15301	−	6.83361i	0.234072	−	0.259963i	0.848725	+	0.528834i	$0.177371\pi$
$692$	12.1347	−	27.2550i	0.461293	−	1.03608i
$693$	−0.846760	−	3.98369i	−0.0321658	−	0.151328i
$694$	0.752867	+	7.16305i	0.0285785	+	0.271906i
$695$		0			0
$696$	−0.980270	−	0.208363i	−0.0371570	−	0.00789797i
$697$	−18.9810	+	26.1251i	−0.718957	+	0.989560i
$698$	−29.8751	+	41.1196i	−1.13079	+	1.55640i
$699$	−32.4854	−	6.90499i	−1.22871	−	0.261171i
$700$		0			0
$701$	4.23908	+	40.3321i	0.160108	+	1.52332i	0.719542	+	0.694449i	$0.244352\pi$
$701$	4.23908	+	40.3321i	0.160108	+	1.52332i	−0.559434	+	0.828875i	$0.688981\pi$
$702$	1.07653	+	5.06468i	0.0406310	+	0.191154i
$703$	15.9018	−	35.7161i	0.599749	−	1.34706i
$704$	6.26569	−	6.95876i	0.236147	−	0.262268i
$705$		0			0
$706$	7.61579	+	8.45820i	0.286624	+	0.318328i
$707$	10.1885	+	5.88235i	0.383179	+	0.221229i
$708$	−69.5782	+	40.1710i	−2.61491	+	1.50972i
$709$	11.5220	−	35.4612i	0.432719	−	1.33177i	−0.462687	−	0.886521i	$-0.653115\pi$
$709$	11.5220	−	35.4612i	0.432719	−	1.33177i	0.895406	−	0.445250i	$-0.146885\pi$
$710$		0			0
$711$	−12.6946	+	9.22314i	−0.476083	+	0.345895i
$712$			6.73883i			0.252548i
$713$	26.4793	−	29.4906i	0.991658	−	1.10443i
$714$	−41.1599			−1.54037
$715$		0			0
$716$	−34.2921	+	15.2678i	−1.28156	+	0.570585i
$717$	−56.6897	−	18.4196i	−2.11712	−	0.687893i
$718$	−0.721134	+	0.416347i	−0.0269125	+	0.0155379i
$719$	−9.28994	+	16.0906i	−0.346456	+	0.600080i	−0.985617	−	0.168993i	$-0.945948\pi$
$719$	−9.28994	+	16.0906i	−0.346456	+	0.600080i	0.639161	+	0.769073i	$0.279282\pi$
$720$		0			0
$721$	2.76647	+	8.51433i	0.103029	+	0.317090i
$722$	−4.30642	−	3.87752i	−0.160268	−	0.144306i
$723$	25.5577	−	57.4036i	0.950501	−	2.13486i
$724$	−48.5887	+	10.3278i	−1.80578	+	0.383831i
$725$		0			0
$726$	−6.41630	+	61.0470i	−0.238131	+	2.26567i
$727$	−3.40501	+	16.0193i	−0.126285	+	0.594123i	0.868806	+	0.495153i	$0.164888\pi$
$727$	−3.40501	+	16.0193i	−0.126285	+	0.594123i	−0.995090	+	0.0989697i	$0.968445\pi$
$728$	−5.45681	+	7.51065i	−0.202243	+	0.278363i
$729$	−28.0140	−	20.3534i	−1.03756	−	0.753829i
$730$		0			0
$731$	0.105509	−	1.00385i	0.00390238	−	0.0371287i
$732$	−65.9179	+	6.92826i	−2.43640	+	0.256076i
$733$	0.239377	+	1.12618i	0.00884158	+	0.0415964i	0.982347	−	0.187067i	$-0.0598980\pi$
$733$	0.239377	+	1.12618i	0.00884158	+	0.0415964i	−0.973506	+	0.228663i	$0.926565\pi$
$734$	61.9485	+	27.5812i	2.28656	+	1.01804i
$735$		0			0
$736$	11.3966	+	35.0751i	0.420084	+	1.29289i
$737$	2.63151	−	2.36943i	0.0969331	−	0.0872789i
$738$	51.0668	+	29.4834i	1.87979	+	1.08530i
$739$	−10.3579	−	17.9404i	−0.381022	−	0.659949i	0.610187	−	0.792257i	$-0.291094\pi$
$739$	−10.3579	−	17.9404i	−0.381022	−	0.659949i	−0.991209	+	0.132309i	$0.957761\pi$
$740$		0			0
$741$	−20.4266	+	9.09449i	−0.750389	+	0.334095i
$742$	12.4586	+	17.1479i	0.457371	+	0.629517i
$743$		−	35.2367i		−	1.29271i	−0.763038	−	0.646354i	$-0.776293\pi$
$743$		−	35.2367i		−	1.29271i	0.763038	−	0.646354i	$-0.223707\pi$
$744$	41.1756	+	13.3155i	1.50957	+	0.488171i
$745$		0			0
$746$	−33.0959	+	24.0456i	−1.21173	+	0.880370i
$747$	−3.76392	−	8.45390i	−0.137715	−	0.309312i
$748$	−10.1589	−	3.30083i	−0.371447	−	0.120690i
$749$	1.46104	+	2.53060i	0.0533853	+	0.0924660i
$750$		0			0
$751$	−28.8702	−	32.0636i	−1.05349	−	1.17002i	−0.985033	−	0.172364i	$-0.944859\pi$
$751$	−28.8702	−	32.0636i	−1.05349	−	1.17002i	−0.0684559	−	0.997654i	$-0.521807\pi$
$752$	−3.08888	+	1.00364i	−0.112640	+	0.0365989i
$753$	43.8279	+	39.4629i	1.59718	+	1.43811i
$754$	−0.515340	−	0.229444i	−0.0187676	−	0.00835586i
$755$		0			0
$756$	0.658843	+	6.26847i	0.0239619	+	0.227982i
$757$	−27.1888	−	2.85766i	−0.988194	−	0.103863i	−0.403382	−	0.915032i	$-0.632165\pi$
$757$	−27.1888	−	2.85766i	−0.988194	−	0.103863i	−0.584813	+	0.811168i	$0.698832\pi$
$758$	−1.18042	+	5.55342i	−0.0428746	+	0.201709i
$759$	10.7433	+	7.80543i	0.389955	+	0.283319i
$760$		0			0
$761$	−16.8163	−	3.57441i	−0.609589	−	0.129572i	−0.107235	−	0.994234i	$-0.534200\pi$
$761$	−16.8163	−	3.57441i	−0.609589	−	0.129572i	−0.502355	+	0.864662i	$0.667533\pi$
$762$	7.51017	+	0.789351i	0.272065	+	0.0285952i
$763$	18.7433	−	1.97000i	0.678554	−	0.0713189i
$764$	7.35260	−	1.56284i	0.266008	−	0.0565417i
$765$		0			0
$766$	−29.5188	+	32.7839i	−1.06656	+	1.18453i
$767$	−17.1369	+	5.56812i	−0.618778	+	0.201053i
$768$	−35.0030	+	31.5169i	−1.26306	+	1.13727i
$769$	7.02837	−	12.1735i	0.253450	−	0.438987i	−0.711024	−	0.703168i	$-0.751768\pi$
$769$	7.02837	−	12.1735i	0.253450	−	0.438987i	0.964473	+	0.264181i	$0.0851015\pi$
$770$		0			0
$771$	−12.0581	+	37.1111i	−0.434263	+	1.33652i
$772$	−34.7050	−	77.9486i	−1.24906	−	2.80543i
$773$	13.0705	+	17.9900i	0.470112	+	0.647054i	0.976567	−	0.215212i	$-0.0690443\pi$
$773$	13.0705	+	17.9900i	0.470112	+	0.647054i	−0.506455	+	0.862266i	$0.669044\pi$
$774$	−1.84315			−0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	−20.1813	−	27.7771i	−0.723998	−	0.996498i
$778$	4.94718	+	11.1116i	0.177365	+	0.398369i
$779$	−10.5686	+	32.5268i	−0.378659	+	1.16539i
$780$		0			0
$781$	1.24906	−	2.16343i	0.0446948	−	0.0774136i
$782$	53.4571	−	48.1330i	1.91162	−	1.72123i
$783$	−0.145130	+	0.0471557i	−0.00518654	+	0.00168521i
$784$	1.19904	−	1.33166i	0.0428227	−	0.0475594i
$785$		0			0
$786$	−46.0303	+	9.78404i	−1.64185	+	0.348985i
$787$	−31.8583	+	3.34845i	−1.13563	+	0.119359i	−0.653630	−	0.756814i	$-0.726755\pi$
$787$	−31.8583	+	3.34845i	−1.13563	+	0.119359i	−0.481997	+	0.876173i	$0.660088\pi$
$788$	20.4859	+	2.15316i	0.729780	+	0.0767030i
$789$	16.9273	+	3.59801i	0.602628	+	0.128093i
$790$		0			0
$791$	−14.3261	−	10.4085i	−0.509377	−	0.370084i
$792$	−1.61580	+	7.60176i	−0.0574151	+	0.270117i
$793$	−14.7838	−	1.55384i	−0.524990	−	0.0551786i
$794$	4.08247	+	38.8421i	0.144881	+	1.37845i
$795$		0			0
$796$	−13.8782	−	6.17896i	−0.491899	−	0.219008i
$797$	−19.3584	−	17.4304i	−0.685709	−	0.617415i	0.250808	−	0.968037i	$-0.419304\pi$
$797$	−19.3584	−	17.4304i	−0.685709	−	0.617415i	−0.936517	+	0.350622i	$0.885970\pi$
$798$	−41.4586	+	13.4707i	−1.46762	+	0.476859i
$799$	−23.5493	−	26.1541i	−0.833114	−	0.925267i
$800$		0			0
$801$	3.81994	+	6.61633i	0.134971	+	0.233776i
$802$	−83.4814	−	27.1247i	−2.94783	−	0.957808i
$803$	0.803320	+	1.80429i	0.0283485	+	0.0636719i
$804$	−33.0100	+	23.9832i	−1.16417	+	0.845822i
$805$		0			0
$806$	21.1125	+	12.1502i	0.743655	+	0.427973i
$807$			26.7486i			0.941594i
$808$	−13.1956	−	18.1621i	−0.464218	−	0.638942i
$809$	7.97472	−	3.55057i	0.280376	−	0.124831i	−0.261731	−	0.965141i	$-0.584293\pi$
$809$	7.97472	−	3.55057i	0.280376	−	0.124831i	0.542107	+	0.840309i	$0.317627\pi$
$810$		0			0
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.852170	+	0.523264i	$0.175286\pi$
$811$	25.0392	+	43.3692i	0.879245	+	1.52290i	0.0270750	+	0.999633i	$0.491381\pi$
$812$	−0.594695	−	0.343347i	−0.0208697	−	0.0120491i
$813$	−2.98018	+	2.68337i	−0.104520	+	0.0941098i
$814$	−4.40984	−	13.5721i	−0.154565	−	0.475701i
$815$		0			0
$816$	4.11107	+	1.83037i	0.143916	+	0.0640756i
$817$	−0.222263	−	1.04567i	−0.00777600	−	0.0365832i
$818$	1.14442	−	0.120284i	0.0400138	−	0.00420562i
$819$	−1.10016	+	10.4673i	−0.0384427	+	0.365758i
$820$		0			0
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.989283	+	0.146013i	$0.0466441\pi$
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.444572	+	0.895743i	$0.353356\pi$
$822$	−56.8246	+	78.2123i	−1.98199	+	2.72797i
$823$	−1.31592	+	6.19089i	−0.0458699	+	0.215801i	−0.995113	−	0.0987423i	$-0.968518\pi$
$823$	−1.31592	+	6.19089i	−0.0458699	+	0.215801i	0.949243	+	0.314543i	$0.101851\pi$
$824$	1.78569	−	16.9897i	0.0622076	−	0.591866i
$825$		0			0
$826$	−34.3617	+	7.30380i	−1.19560	+	0.254132i
$827$	1.50389	−	3.37779i	0.0522953	−	0.117457i	−0.885508	−	0.464624i	$-0.846190\pi$
$827$	1.50389	−	3.37779i	0.0522953	−	0.117457i	0.937803	+	0.347167i	$0.112856\pi$
$828$	−60.9493	−	54.8790i	−2.11813	−	1.90718i
$829$	−8.04729	−	24.7670i	−0.279494	−	0.860193i	−0.987995	−	0.154484i	$-0.950628\pi$
$829$	−8.04729	−	24.7670i	−0.279494	−	0.860193i	0.708501	−	0.705709i	$-0.249372\pi$
$830$		0			0
$831$	15.3852	−	26.6479i	0.533707	−	0.924407i
$832$	−20.9570	+	12.0995i	−0.726553	+	0.419475i
$833$	18.4671	+	6.00033i	0.639848	+	0.207899i
$834$	39.3425	−	17.5164i	1.36232	−	0.606543i
$835$		0			0
$836$	−11.3130			−0.391267
$837$	6.44354	−	1.37898i	0.222721	−	0.0476644i
$838$			31.1747i			1.07691i
$839$	6.06196	−	4.40427i	0.209282	−	0.152052i	−0.478207	−	0.878247i	$-0.658713\pi$
$839$	6.06196	−	4.40427i	0.209282	−	0.152052i	0.687489	+	0.726195i	$0.258713\pi$
$840$		0			0
$841$	−8.95636	+	27.5648i	−0.308840	+	0.950511i
$842$	61.7800	−	35.6687i	2.12908	−	1.22923i
$843$	−47.2843	−	27.2996i	−1.62856	−	0.940249i
$844$	41.4157	+	45.9968i	1.42559	+	1.58328i
$845$		0			0
$846$	−43.0016	+	47.7581i	−1.47843	+	1.64196i
$847$	−6.81627	+	15.3096i	−0.234210	+	0.526044i
$848$	−0.481816	−	2.26677i	−0.0165456	−	0.0778411i
$849$	0.183076	+	1.74185i	0.00628315	+	0.0597801i
$850$		0			0
$851$	58.6937	+	12.4757i	2.01199	+	0.427662i
$852$	−16.9195	+	23.2877i	−0.579652	+	0.797822i
$853$	−25.6198	+	35.2626i	−0.877204	+	1.20737i	0.0999836	+	0.994989i	$0.468121\pi$
$853$	−25.6198	+	35.2626i	−0.877204	+	1.20737i	−0.977187	+	0.212378i	$0.931879\pi$
$854$	−28.3479	−	6.02553i	−0.970045	−	0.206189i
$855$		0			0
$856$	−0.582848	−	5.54543i	−0.0199213	−	0.189539i
$857$	8.15487	+	38.3657i	0.278565	+	1.31055i	0.865499	+	0.500911i	$0.167002\pi$
$857$	8.15487	+	38.3657i	0.278565	+	1.31055i	−0.586933	+	0.809635i	$0.699665\pi$
$858$	−3.31959	+	7.45593i	−0.113329	+	0.254541i
$859$	12.1790	−	13.5262i	0.415544	−	0.461508i	−0.498639	−	0.866809i	$-0.666167\pi$
$859$	12.1790	−	13.5262i	0.415544	−	0.461508i	0.914183	+	0.405302i	$0.132833\pi$
$860$		0			0
$861$	20.0975	+	22.3205i	0.684920	+	0.760681i
$862$	−24.0900	−	13.9084i	−0.820509	−	0.473721i
$863$	38.9258	−	22.4738i	1.32505	−	0.765018i	0.340521	−	0.940237i	$-0.389397\pi$
$863$	38.9258	−	22.4738i	1.32505	−	0.765018i	0.984530	+	0.175219i	$0.0560633\pi$
$864$	−1.89477	+	5.83151i	−0.0644614	+	0.198392i
$865$		0			0
$866$	60.4700	−	43.9340i	2.05486	−	1.49294i
$867$			5.53740i			0.188060i
$868$	24.0135	+	17.3959i	0.815072	+	0.590456i
$869$	−3.32196			−0.112690
$870$		0			0
$871$	−8.35992	+	3.72208i	−0.283265	+	0.126118i
$872$	−34.2032	−	11.1133i	−1.15827	−	0.376343i
$873$	36.8839	−	21.2949i	1.24833	−	0.720724i
$874$	38.0922	−	65.9776i	1.28849	−	2.23173i
$875$		0			0
$876$	−7.03257	−	21.6440i	−0.237608	−	0.731283i
$877$	31.6959	+	28.5391i	1.07029	+	0.963698i	0.999429	−	0.0337881i	$-0.0107571\pi$
$877$	31.6959	+	28.5391i	1.07029	+	0.963698i	0.0708657	+	0.997486i	$0.477424\pi$
$878$	−11.6082	+	26.0725i	−0.391758	+	0.879903i
$879$	−22.4140	+	4.76424i	−0.756005	+	0.160694i
$880$		0			0
$881$	0.932030	−	8.86768i	0.0314009	−	0.298760i	−0.967539	−	0.252722i	$-0.918674\pi$
$881$	0.932030	−	8.86768i	0.0314009	−	0.298760i	0.998940	−	0.0460372i	$-0.0146593\pi$
$882$	7.37189	−	34.6820i	0.248225	−	1.16780i
$883$	27.6661	−	38.0791i	0.931038	−	1.28146i	−0.0284158	−	0.999596i	$-0.509046\pi$
$883$	27.6661	−	38.0791i	0.931038	−	1.28146i	0.959453	−	0.281867i	$-0.0909538\pi$
$884$	22.3326	+	16.2256i	0.751126	+	0.545725i
$885$		0			0
$886$	1.13930	−	10.8397i	0.0382754	−	0.364166i
$887$	−3.13928	+	0.329951i	−0.105407	+	0.0110787i	−0.157085	−	0.987585i	$-0.550210\pi$
$887$	−3.13928	+	0.329951i	−0.105407	+	0.0110787i	0.0516783	+	0.998664i	$0.483543\pi$
$888$	13.6219	+	64.0858i	0.457120	+	2.15058i
$889$	1.88343	+	0.838557i	0.0631682	+	0.0281243i
$890$		0			0
$891$	−1.67473	−	5.15429i	−0.0561056	−	0.172675i
$892$	15.3554	−	13.8261i	0.514137	−	0.462931i
$893$	−32.2799	−	18.6368i	−1.08021	−	0.623657i
$894$	18.6640	+	32.3270i	0.624217	+	1.08118i
$895$		0			0
$896$	−27.9361	+	12.4379i	−0.933279	+	0.415522i
$897$	−20.1714	−	27.7636i	−0.673505	−	0.927000i
$898$		−	36.8840i		−	1.23083i
$899$	−0.291086	+	0.656241i	−0.00970825	+	0.0218869i
$900$		0			0
$901$	20.3157	−	14.7602i	0.676815	−	0.491735i
$902$	5.07756	+	11.4044i	0.169064	+	0.379724i
$903$	−0.892875	−	0.290113i	−0.0297130	−	0.00965434i
$904$	16.8954	+	29.2637i	0.561932	+	0.973295i
$905$		0			0
$906$	21.6904	+	24.0897i	0.720616	+	0.800326i
$907$	25.6435	−	8.33208i	0.851478	−	0.276662i	0.149413	−	0.988775i	$-0.452262\pi$
$907$	25.6435	−	8.33208i	0.851478	−	0.276662i	0.702065	+	0.712113i	$0.252262\pi$
$908$	−32.2374	−	29.0267i	−1.06984	−	0.963285i
$909$	−23.2510	−	10.3520i	−0.771185	−	0.343354i
$910$		0			0
$911$	−0.530798	−	5.05020i	−0.0175861	−	0.167321i	0.982204	−	0.187818i	$-0.0601416\pi$
$911$	−0.530798	−	5.05020i	−0.0175861	−	0.167321i	−0.999790	+	0.0204976i	$0.993475\pi$
$912$	4.73995	+	0.498189i	0.156955	+	0.0164967i
$913$	0.407324	−	1.91631i	0.0134805	−	0.0634206i
$914$	8.50854	+	6.18181i	0.281437	+	0.204476i
$915$		0			0
$916$	−49.6843	−	10.5607i	−1.64161	−	0.348936i
$917$	−12.7772	−	1.34294i	−0.421942	−	0.0443479i
$918$	11.8940	−	1.25011i	0.392560	−	0.0412598i
$919$	−48.2001	+	10.2453i	−1.58998	+	0.337960i	−0.916120	−	0.400903i	$-0.868696\pi$
$919$	−48.2001	+	10.2453i	−1.58998	+	0.337960i	−0.673856	+	0.738863i	$0.735363\pi$
$920$		0			0
$921$	53.3098	−	59.2066i	1.75662	−	1.95092i
$922$	−37.2882	+	12.1157i	−1.22802	+	0.399009i
$923$	−4.79762	+	4.31979i	−0.157915	+	0.142188i
$924$	−4.96754	+	8.60403i	−0.163420	+	0.283052i
$925$		0			0
$926$	19.5578	−	60.1929i	0.642711	−	1.97806i
$927$	−7.87748	−	17.6931i	−0.258730	−	0.581118i
$928$	−0.392653	−	0.540441i	−0.0128895	−	0.0177408i
$929$	39.9606			1.31107			0.655533	−	0.755167i	$-0.272444\pi$
$929$	39.9606			1.31107			0.655533	+	0.755167i	$0.272444\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	25.5243	+	35.1311i	0.836075	+	1.15076i
$933$	18.3201	+	41.1476i	0.599773	+	1.34711i
$934$	16.3367	−	50.2791i	0.534552	−	1.64518i
$935$		0			0
$936$	10.0420	−	17.3932i	0.328232	−	0.568515i
$937$	33.5079	−	30.1706i	1.09465	−	0.985631i	0.0947033	−	0.995506i	$-0.469810\pi$
$937$	33.5079	−	30.1706i	1.09465	−	0.985631i	0.999951	+	0.00987411i	$0.00314308\pi$
$938$	−16.9677	+	5.51313i	−0.554014	+	0.180010i
$939$	−36.8674	+	40.9454i	−1.20312	+	1.33620i
$940$		0			0
$941$	−49.0955	+	10.4356i	−1.60047	+	0.340190i	−0.919795	−	0.392398i	$-0.871646\pi$
$941$	−49.0955	+	10.4356i	−1.60047	+	0.340190i	−0.680672	+	0.732588i	$0.738312\pi$
$942$	46.6499	−	4.90310i	1.51993	−	0.159752i
$943$	−52.2038	−	5.48684i	−1.69999	−	0.178676i
$944$	3.75686	+	0.798545i	0.122275	+	0.0259904i
$945$		0			0
$946$	−0.315684	−	0.229358i	−0.0102638	−	0.00745707i
$947$	−6.30512	+	29.6633i	−0.204889	+	0.963926i	0.748722	+	0.662884i	$0.230668\pi$
$947$	−6.30512	+	29.6633i	−0.204889	+	0.963926i	−0.953611	+	0.301042i	$0.902666\pi$
$948$	38.0684	+	4.00115i	1.23640	+	0.129951i
$949$	−0.533519	−	5.07609i	−0.0173188	−	0.164777i
$950$		0			0
$951$	−2.36017	−	1.05081i	−0.0765337	−	0.0340750i
$952$	15.9353	+	14.3482i	0.516465	+	0.465027i
$953$	33.7411	−	10.9631i	1.09298	−	0.355131i	0.293583	−	0.955934i	$-0.405152\pi$
$953$	33.7411	−	10.9631i	1.09298	−	0.355131i	0.799397	+	0.600803i	$0.205152\pi$
$954$	−30.6826	−	34.0765i	−0.993387	−	1.10327i
$955$		0			0
$956$	38.9689	+	67.4962i	1.26035	+	2.18298i
$957$	−0.228761	−	0.0743291i	−0.00739481	−	0.00240272i
$958$	8.49116	+	19.0715i	0.274337	+	0.616171i
$959$	−21.3530	+	15.5139i	−0.689524	+	0.500969i
$960$		0			0
$961$	15.4253	−	26.8898i	0.497592	−	0.867411i
$962$			36.8791i			1.18903i
$963$	−3.71570	−	5.11422i	−0.119737	−	0.164804i
$964$	−75.0567	+	33.4174i	−2.41741	+	1.07630i
$965$		0			0
$966$	−33.4527	−	57.9418i	−1.07632	−	1.86425i
$967$	−30.6957	−	17.7222i	−0.987107	−	0.569906i	−0.0826987	−	0.996575i	$-0.526354\pi$
$967$	−30.6957	−	17.7222i	−0.987107	−	0.569906i	−0.904408	+	0.426668i	$0.859687\pi$
$968$	23.7649	−	21.3980i	0.763832	−	0.687757i
$969$	15.9593	+	49.1176i	0.512686	+	1.57789i
$970$		0			0
$971$	−36.6306	−	16.3090i	−1.17553	−	0.523381i	−0.276394	−	0.961044i	$-0.589140\pi$
$971$	−36.6306	−	16.3090i	−1.17553	−	0.523381i	−0.899139	+	0.437663i	$0.855806\pi$
$972$	15.4379	+	72.6297i	0.495171	+	2.32960i
$973$	11.6931	−	1.22899i	0.374863	−	0.0393997i
$974$	−5.69784	+	54.2113i	−0.182571	+	1.73704i
$975$		0			0
$976$	2.56345	+	1.86246i	0.0820540	+	0.0596157i
$977$	22.7302	−	31.2854i	0.727202	−	1.00091i	−0.272052	−	0.962283i	$-0.587702\pi$
$977$	22.7302	−	31.2854i	0.727202	−	1.00091i	0.999254	−	0.0386252i	$-0.0122978\pi$
$978$	20.8181	−	97.9415i	0.665690	−	3.13182i
$979$	−0.169065	+	1.60855i	−0.00540335	+	0.0514095i
$980$		0			0
$981$	−39.8810	+	8.47697i	−1.27330	+	0.270649i
$982$	8.65997	−	19.4506i	0.276351	−	0.620694i
$983$	−16.0368	−	14.4396i	−0.511493	−	0.460551i	0.372512	−	0.928027i	$-0.378497\pi$
$983$	−16.0368	−	14.4396i	−0.511493	−	0.460551i	−0.884005	+	0.467477i	$0.845163\pi$
$984$	−17.7109	−	54.5086i	−0.564604	−	1.73767i
$985$		0			0
$986$	−0.651478	+	1.12839i	−0.0207473	+	0.0359354i
$987$	−28.3483	+	16.3669i	−0.902338	+	0.520965i
$988$	27.8049	+	9.03438i	0.884593	+	0.287422i
$989$	1.49890	−	0.667352i	0.0476621	−	0.0212206i
$990$		0			0
$991$	46.8764			1.48908			0.744538	−	0.667580i	$-0.232670\pi$
$991$	46.8764			1.48908			0.744538	+	0.667580i	$0.232670\pi$
$992$	14.4578	+	24.9614i	0.459034	+	0.792525i
$993$		−	67.8639i		−	2.15360i
$994$	−10.1825	+	7.39800i	−0.322968	+	0.234650i
$995$		0			0
$996$	−6.97589	+	21.4696i	−0.221039	+	0.680290i
$997$	−38.5718	+	22.2695i	−1.22158	+	0.705281i	−0.965255	−	0.261309i	$-0.915846\pi$
$997$	−38.5718	+	22.2695i	−1.22158	+	0.705281i	−0.256327	+	0.966590i	$0.582512\pi$
$998$	−56.7818	−	32.7830i	−1.79740	−	1.03773i
$999$	6.67543	+	7.41382i	0.211201	+	0.234563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.a.49.4		32
5.2	odd	4		31.2.g.a.18.1	✓	16
5.3	odd	4		775.2.bl.a.576.2		16
5.4	even	2	inner	775.2.ck.a.49.1		32
15.2	even	4		279.2.y.c.235.2		16
20.7	even	4		496.2.bg.c.49.2		16
31.19	even	15	inner	775.2.ck.a.174.1		32
155.2	odd	20		961.2.g.k.816.1		16
155.7	odd	60		961.2.g.t.448.2		16
155.12	even	60		961.2.g.l.732.1		16
155.17	even	60		961.2.c.i.521.8		16
155.19	even	30	inner	775.2.ck.a.174.4		32
155.22	even	60		961.2.a.j.1.8		8
155.27	even	20		961.2.g.m.846.2		16
155.37	even	12		961.2.g.j.338.1		16
155.42	even	60		961.2.d.q.628.4		16
155.47	odd	20		961.2.g.t.547.2		16
155.52	even	60		961.2.d.n.374.1		16
155.57	even	12		961.2.d.n.388.1		16
155.67	odd	12		961.2.d.o.388.1		16
155.72	odd	60		961.2.d.o.374.1		16
155.77	even	20		961.2.g.n.547.2		16
155.82	odd	60		961.2.d.p.628.4		16
155.87	odd	12		961.2.g.k.338.1		16
155.92	even	4		961.2.g.l.235.1		16
155.97	odd	20		961.2.g.s.846.2		16
155.102	odd	60		961.2.a.i.1.8		8
155.107	odd	60		961.2.c.j.521.8		16
155.112	odd	60		31.2.g.a.19.1	yes	16
155.117	even	60		961.2.g.n.448.2		16
155.122	even	20		961.2.g.j.816.1		16
155.127	even	60		961.2.g.m.844.2		16
155.132	odd	20		961.2.c.j.439.8		16
155.137	even	60		961.2.d.q.531.4		16
155.142	odd	60		961.2.d.p.531.4		16
155.143	odd	60		775.2.bl.a.701.2		16
155.147	even	20		961.2.c.i.439.8		16
155.152	odd	60		961.2.g.s.844.2		16
465.257	even	60		8649.2.a.bf.1.1		8
465.332	odd	60		8649.2.a.be.1.1		8
465.422	even	60		279.2.y.c.19.2		16
620.267	even	60		496.2.bg.c.81.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	5.2	odd	4
31.2.g.a.19.1	yes	16	155.112	odd	60
279.2.y.c.19.2		16	465.422	even	60
279.2.y.c.235.2		16	15.2	even	4
496.2.bg.c.49.2		16	20.7	even	4
496.2.bg.c.81.2		16	620.267	even	60
775.2.bl.a.576.2		16	5.3	odd	4
775.2.bl.a.701.2		16	155.143	odd	60
775.2.ck.a.49.1		32	5.4	even	2	inner
775.2.ck.a.49.4		32	1.1	even	1	trivial
775.2.ck.a.174.1		32	31.19	even	15	inner
775.2.ck.a.174.4		32	155.19	even	30	inner
961.2.a.i.1.8		8	155.102	odd	60
961.2.a.j.1.8		8	155.22	even	60
961.2.c.i.439.8		16	155.147	even	20
961.2.c.i.521.8		16	155.17	even	60
961.2.c.j.439.8		16	155.132	odd	20
961.2.c.j.521.8		16	155.107	odd	60
961.2.d.n.374.1		16	155.52	even	60
961.2.d.n.388.1		16	155.57	even	12
961.2.d.o.374.1		16	155.72	odd	60
961.2.d.o.388.1		16	155.67	odd	12
961.2.d.p.531.4		16	155.142	odd	60
961.2.d.p.628.4		16	155.82	odd	60
961.2.d.q.531.4		16	155.137	even	60
961.2.d.q.628.4		16	155.42	even	60
961.2.g.j.338.1		16	155.37	even	12
961.2.g.j.816.1		16	155.122	even	20
961.2.g.k.338.1		16	155.87	odd	12
961.2.g.k.816.1		16	155.2	odd	20
961.2.g.l.235.1		16	155.92	even	4
961.2.g.l.732.1		16	155.12	even	60
961.2.g.m.844.2		16	155.127	even	60
961.2.g.m.846.2		16	155.27	even	20
961.2.g.n.448.2		16	155.117	even	60
961.2.g.n.547.2		16	155.77	even	20
961.2.g.s.844.2		16	155.152	odd	60
961.2.g.s.846.2		16	155.97	odd	20
961.2.g.t.448.2		16	155.7	odd	60
961.2.g.t.547.2		16	155.47	odd	20
8649.2.a.be.1.1		8	465.332	odd	60
8649.2.a.bf.1.1		8	465.257	even	60

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35633 + 1.86683i) q^{2} +(-1.03422 - 2.32289i) q^{3} +(-1.02738 + 3.16196i) q^{4} +(2.93370 - 5.08132i) q^{6} +(1.19043 - 1.07187i) q^{7} +(-2.90713 + 0.944583i) q^{8} +(-2.31884 + 2.57533i) q^{9} +(-0.717625 + 0.152536i) q^{11} +(8.40743 - 0.883657i) q^{12} +(1.88559 + 0.198183i) q^{13} +(3.61560 + 0.768520i) q^{14} +(-0.326952 - 0.237545i) q^{16} +(0.910495 - 4.28354i) q^{17} +(-7.95280 - 0.835873i) q^{18} +(-0.484806 - 4.61262i) q^{19} +(-3.72099 - 1.65669i) q^{21} +(-1.25809 - 1.13279i) q^{22} +(6.77006 - 2.19973i) q^{23} +(5.20077 + 5.77604i) q^{24} +(2.18751 + 3.78887i) q^{26} +(1.12557 + 0.365721i) q^{27} +(2.16617 + 4.86530i) q^{28} +(-0.104314 + 0.0757884i) q^{29} +(4.81795 - 2.79058i) q^{31} +5.18091i q^{32} +(1.09651 + 1.50921i) q^{33} +(9.23157 - 4.11016i) q^{34} +(-5.76075 - 9.97791i) q^{36} +(7.30014 + 4.21474i) q^{37} +(7.95341 - 7.16128i) q^{38} +(-1.48975 - 4.58499i) q^{39} +(-6.73647 - 2.99927i) q^{41} +(-1.95413 - 9.19348i) q^{42} +(0.229229 - 0.0240929i) q^{43} +(0.254963 - 2.42581i) q^{44} +(13.2889 + 9.65498i) q^{46} +(4.72375 - 6.50168i) q^{47} +(-0.213651 + 1.00515i) q^{48} +(-0.463478 + 4.40970i) q^{49} +(-10.8919 + 2.31514i) q^{51} +(-2.56387 + 5.75854i) q^{52} +(4.26137 + 3.83695i) q^{53} +(0.843912 + 2.59729i) q^{54} +(-2.44826 + 4.24051i) q^{56} +(-10.2132 + 5.89661i) q^{57} +(-0.282968 - 0.0919419i) q^{58} +(-8.68208 + 3.86551i) q^{59} -7.84044 q^{61} +(11.7443 + 5.20934i) q^{62} +5.55122i q^{63} +(-10.3258 + 7.50212i) q^{64} +(-1.33021 + 4.09397i) q^{66} +(-4.17994 + 2.41329i) q^{67} +(12.6090 + 7.27978i) q^{68} +(-12.1115 - 13.4511i) q^{69} +(-2.27840 + 2.53042i) q^{71} +(4.30854 - 9.67714i) q^{72} +(-0.559708 - 2.63322i) q^{73} +(2.03321 + 19.3447i) q^{74} +(15.0830 + 3.20599i) q^{76} +(-0.690782 + 0.950780i) q^{77} +(6.53879 - 8.99987i) q^{78} +(4.42900 + 0.941413i) q^{79} +(0.772154 + 7.34656i) q^{81} +(-3.53775 - 16.6438i) q^{82} +(-1.08613 + 2.43949i) q^{83} +(9.06128 - 10.0636i) q^{84} +(0.355888 + 0.395253i) q^{86} +(0.283932 + 0.163928i) q^{87} +(1.94214 - 1.12130i) q^{88} +(0.681255 - 2.09669i) q^{89} +(2.45708 - 1.78518i) q^{91} +23.6666i q^{92} +(-11.4650 - 8.30552i) q^{93} +18.5445 q^{94} +(12.0347 - 5.35820i) q^{96} +(-11.6884 - 3.79778i) q^{97} +(-8.86077 + 5.11577i) q^{98} +(1.27122 - 2.20182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more