LMFDB - Embedded newform 950.2.bb.c.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.c.507.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(-0.400509 + 0.858895i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.890533 - 0.324128i) q^{6} +(-0.243409 - 0.0652212i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.35107 + 1.61014i) q^{9} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.400509 + 0.858895i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.890533 - 0.324128i) q^{6} +(-0.243409 - 0.0652212i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.35107 + 1.61014i) q^{9} +(0.664372 - 1.15073i) q^{11} +(0.245279 - 0.915394i) q^{12} +(-3.16092 + 1.47396i) q^{13} +(0.0437586 - 0.248167i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-1.68782 + 0.147665i) q^{17} +(-1.48626 + 1.48626i) q^{18} +(-1.55826 + 4.07085i) q^{19} +(0.153506 - 0.182941i) q^{21} +(1.20425 + 0.561552i) q^{22} +(-3.65466 + 5.21940i) q^{23} +(0.933288 + 0.164564i) q^{24} +(-1.74385 - 3.02043i) q^{26} +(-4.67024 + 1.25139i) q^{27} +(0.251037 + 0.0219629i) q^{28} +(-3.27388 + 2.74711i) q^{29} +(5.24523 - 3.02834i) q^{31} +(0.422618 + 0.906308i) q^{32} +(0.722266 + 1.03150i) q^{33} +(-0.294206 - 1.66852i) q^{34} +(-1.61014 - 1.35107i) q^{36} +(-1.18909 - 1.18909i) q^{37} +(-4.19117 - 1.19753i) q^{38} -3.30524i q^{39} +(-2.53964 - 6.97759i) q^{41} +(0.195624 + 0.136977i) q^{42} +(-5.37530 + 3.76383i) q^{43} +(-0.454457 + 1.24861i) q^{44} +(-5.51806 - 3.18586i) q^{46} +(-0.109531 + 1.25194i) q^{47} +(-0.0825962 + 0.944079i) q^{48} +(-6.00718 - 3.46825i) q^{49} +(0.549157 - 1.50880i) q^{51} +(2.85695 - 2.00046i) q^{52} +(0.697532 + 0.488417i) q^{53} +(-1.65366 - 4.54340i) q^{54} +0.251996i q^{56} +(-2.87234 - 2.96879i) q^{57} +(-3.02199 - 3.02199i) q^{58} +(2.66338 + 2.23484i) q^{59} +(0.357395 + 2.02689i) q^{61} +(3.47397 + 4.96134i) q^{62} +(-0.223847 - 0.480042i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.964628 + 0.809419i) q^{66} +(-0.964545 - 0.0843868i) q^{67} +(1.63653 - 0.438507i) q^{68} +(-3.01919 - 5.22939i) q^{69} +(-5.06692 - 0.893436i) q^{71} +(1.20560 - 1.72177i) q^{72} +(1.88720 + 0.880018i) q^{73} +(1.08093 - 1.28820i) q^{74} +(0.827690 - 4.27959i) q^{76} +(-0.236766 + 0.236766i) q^{77} +(3.29266 - 0.288070i) q^{78} +(-4.19408 + 1.52652i) q^{79} +(-0.299305 + 1.69744i) q^{81} +(6.72970 - 3.13811i) q^{82} +(-0.295934 + 1.10444i) q^{83} +(-0.119406 + 0.206818i) q^{84} +(-4.21799 - 5.02681i) q^{86} +(-1.04826 - 3.91216i) q^{87} +(-1.28347 - 0.343904i) q^{88} +(0.802651 + 0.292141i) q^{89} +(0.865531 - 0.152616i) q^{91} +(2.69280 - 5.77473i) q^{92} +(0.500259 + 5.71798i) q^{93} -1.25672 q^{94} -0.947686 q^{96} +(-0.871427 - 9.96045i) q^{97} +(2.93149 - 6.28660i) q^{98} +(2.75045 - 0.484978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$	−0.400509	+	0.858895i	−0.231234	+	0.495883i	−0.987350	−	0.158554i	$-0.949317\pi$
$3$	−0.400509	+	0.858895i	−0.231234	+	0.495883i	0.756116	+	0.654437i	$0.227094\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−0.890533	−	0.324128i	−0.363559	−	0.132325i
$7$	−0.243409	−	0.0652212i	−0.0919999	−	0.0246513i	0.212525	−	0.977156i	$-0.431831\pi$
$7$	−0.243409	−	0.0652212i	−0.0919999	−	0.0246513i	−0.304525	+	0.952504i	$0.598498\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	1.35107	+	1.61014i	0.450357	+	0.536714i
$10$		0			0
$11$	0.664372	−	1.15073i	0.200316	−	0.346957i	−0.748314	−	0.663344i	$-0.769137\pi$
$11$	0.664372	−	1.15073i	0.200316	−	0.346957i	0.948630	+	0.316387i	$0.102470\pi$
$12$	0.245279	−	0.915394i	0.0708060	−	0.264251i
$13$	−3.16092	+	1.47396i	−0.876682	+	0.408804i	−0.808241	−	0.588851i	$-0.799580\pi$
$13$	−3.16092	+	1.47396i	−0.876682	+	0.408804i	−0.0684411	+	0.997655i	$0.521803\pi$
$14$	0.0437586	−	0.248167i	0.0116950	−	0.0663255i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−1.68782	+	0.147665i	−0.409355	+	0.0358140i	−0.289974	−	0.957035i	$-0.593647\pi$
$17$	−1.68782	+	0.147665i	−0.409355	+	0.0358140i	−0.119381	+	0.992848i	$0.538091\pi$
$18$	−1.48626	+	1.48626i	−0.350315	+	0.350315i
$19$	−1.55826	+	4.07085i	−0.357489	+	0.933917i
$19$	−1.55826	+	4.07085i	−0.357489	+	0.933917i
$20$		0			0
$21$	0.153506	−	0.182941i	0.0334977	−	0.0399210i
$22$	1.20425	+	0.561552i	0.256747	+	0.119723i
$23$	−3.65466	+	5.21940i	−0.762050	+	1.08832i	0.231266	+	0.972891i	$0.425713\pi$
$23$	−3.65466	+	5.21940i	−0.762050	+	1.08832i	−0.993316	+	0.115429i	$0.963176\pi$
$24$	0.933288	+	0.164564i	0.190507	+	0.0335915i
$25$		0			0
$26$	−1.74385	−	3.02043i	−0.341996	−	0.592355i
$27$	−4.67024	+	1.25139i	−0.898788	+	0.240830i
$28$	0.251037	+	0.0219629i	0.0474415	+	0.00415059i
$29$	−3.27388	+	2.74711i	−0.607943	+	0.510125i	−0.893988	−	0.448091i	$-0.852104\pi$
$29$	−3.27388	+	2.74711i	−0.607943	+	0.510125i	0.286044	+	0.958216i	$0.407660\pi$
$30$		0			0
$31$	5.24523	−	3.02834i	0.942072	−	0.543905i	0.0514627	−	0.998675i	$-0.483612\pi$
$31$	5.24523	−	3.02834i	0.942072	−	0.543905i	0.890609	+	0.454769i	$0.150278\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$	0.722266	+	1.03150i	0.125730	+	0.179562i
$34$	−0.294206	−	1.66852i	−0.0504559	−	0.286149i
$35$		0			0
$36$	−1.61014	−	1.35107i	−0.268357	−	0.225178i
$37$	−1.18909	−	1.18909i	−0.195486	−	0.195486i	0.602576	−	0.798062i	$-0.294141\pi$
$37$	−1.18909	−	1.18909i	−0.195486	−	0.195486i	−0.798062	+	0.602576i	$0.794141\pi$
$38$	−4.19117	−	1.19753i	−0.679898	−	0.194265i
$39$		−	3.30524i		−	0.529261i
$40$		0			0
$41$	−2.53964	−	6.97759i	−0.396625	−	1.08972i	−0.963918	−	0.266201i	$-0.914232\pi$
$41$	−2.53964	−	6.97759i	−0.396625	−	1.08972i	0.567293	−	0.823516i	$-0.307991\pi$
$42$	0.195624	+	0.136977i	0.0301854	+	0.0211360i
$43$	−5.37530	+	3.76383i	−0.819726	+	0.573978i	−0.906479	−	0.422251i	$-0.861240\pi$
$43$	−5.37530	+	3.76383i	−0.819726	+	0.573978i	0.0867526	+	0.996230i	$0.472351\pi$
$44$	−0.454457	+	1.24861i	−0.0685120	+	0.188235i
$45$		0			0
$46$	−5.51806	−	3.18586i	−0.813594	−	0.469729i
$47$	−0.109531	+	1.25194i	−0.0159767	+	0.182614i	0.984013	+	0.178096i	$0.0569938\pi$
$47$	−0.109531	+	1.25194i	−0.0159767	+	0.182614i	−0.999990	+	0.00451826i	$0.998562\pi$
$48$	−0.0825962	+	0.944079i	−0.0119217	+	0.136266i
$49$	−6.00718	−	3.46825i	−0.858169	−	0.495464i
$50$		0			0
$51$	0.549157	−	1.50880i	0.0768974	−	0.211274i
$52$	2.85695	−	2.00046i	0.396188	−	0.277414i
$53$	0.697532	+	0.488417i	0.0958134	+	0.0670893i	0.620501	−	0.784205i	$-0.286929\pi$
$53$	0.697532	+	0.488417i	0.0958134	+	0.0670893i	−0.524688	+	0.851295i	$0.675818\pi$
$54$	−1.65366	−	4.54340i	−0.225035	−	0.618279i
$55$		0			0
$56$			0.251996i			0.0336743i
$57$	−2.87234	−	2.96879i	−0.380450	−	0.393226i
$58$	−3.02199	−	3.02199i	−0.396807	−	0.396807i
$59$	2.66338	+	2.23484i	0.346742	+	0.290951i	0.799480	−	0.600692i	$-0.205108\pi$
$59$	2.66338	+	2.23484i	0.346742	+	0.290951i	−0.452738	+	0.891644i	$0.649553\pi$
$60$		0			0
$61$	0.357395	+	2.02689i	0.0457598	+	0.259516i	0.999102	−	0.0423760i	$-0.0134927\pi$
$61$	0.357395	+	2.02689i	0.0457598	+	0.259516i	−0.953342	+	0.301892i	$0.902382\pi$
$62$	3.47397	+	4.96134i	0.441194	+	0.630091i
$63$	−0.223847	−	0.480042i	−0.0282021	−	0.0604796i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	−0.964628	+	0.809419i	−0.118737	+	0.0996326i
$67$	−0.964545	−	0.0843868i	−0.117838	−	0.0103095i	0.0280842	−	0.999606i	$-0.491059\pi$
$67$	−0.964545	−	0.0843868i	−0.117838	−	0.0103095i	−0.145922	+	0.989296i	$0.546615\pi$
$68$	1.63653	−	0.438507i	0.198459	−	0.0531768i
$69$	−3.01919	−	5.22939i	−0.363468	−	0.629544i
$70$		0			0
$71$	−5.06692	−	0.893436i	−0.601333	−	0.106031i	−0.135309	−	0.990803i	$-0.543203\pi$
$71$	−5.06692	−	0.893436i	−0.601333	−	0.106031i	−0.466024	+	0.884772i	$0.654314\pi$
$72$	1.20560	−	1.72177i	0.142081	−	0.202912i
$73$	1.88720	+	0.880018i	0.220881	+	0.102998i	0.529909	−	0.848054i	$-0.322226\pi$
$73$	1.88720	+	0.880018i	0.220881	+	0.102998i	−0.309028	+	0.951053i	$0.600004\pi$
$74$	1.08093	−	1.28820i	0.125656	−	0.149751i
$75$		0			0
$76$	0.827690	−	4.27959i	0.0949426	−	0.490903i
$77$	−0.236766	+	0.236766i	−0.0269820	+	0.0269820i
$78$	3.29266	−	0.288070i	0.372820	−	0.0326175i
$79$	−4.19408	+	1.52652i	−0.471871	+	0.171747i	−0.567000	−	0.823718i	$-0.691896\pi$
$79$	−4.19408	+	1.52652i	−0.471871	+	0.171747i	0.0951289	+	0.995465i	$0.469674\pi$
$80$		0			0
$81$	−0.299305	+	1.69744i	−0.0332561	+	0.188605i
$82$	6.72970	−	3.13811i	0.743171	−	0.346546i
$83$	−0.295934	+	1.10444i	−0.0324830	+	0.121228i	−0.980264	−	0.197695i	$-0.936654\pi$
$83$	−0.295934	+	1.10444i	−0.0324830	+	0.121228i	0.947781	+	0.318923i	$0.103321\pi$
$84$	−0.119406	+	0.206818i	−0.0130283	+	0.0225657i
$85$		0			0
$86$	−4.21799	−	5.02681i	−0.454838	−	0.542055i
$87$	−1.04826	−	3.91216i	−0.112385	−	0.419427i
$88$	−1.28347	−	0.343904i	−0.136818	−	0.0366603i
$89$	0.802651	+	0.292141i	0.0850809	+	0.0309669i	0.384210	−	0.923246i	$-0.374474\pi$
$89$	0.802651	+	0.292141i	0.0850809	+	0.0309669i	−0.299129	+	0.954213i	$0.596696\pi$
$90$		0			0
$91$	0.865531	−	0.152616i	0.0907323	−	0.0159985i
$92$	2.69280	−	5.77473i	0.280744	−	0.602057i
$93$	0.500259	+	5.71798i	0.0518744	+	0.592927i
$94$	−1.25672			−0.129621
$95$		0			0
$96$	−0.947686			−0.0967228
$97$	−0.871427	−	9.96045i	−0.0884800	−	1.01133i	−0.902556	−	0.430572i	$-0.858312\pi$
$97$	−0.871427	−	9.96045i	−0.0884800	−	1.01133i	0.814076	−	0.580758i	$-0.197244\pi$
$98$	2.93149	−	6.28660i	0.296125	−	0.635043i
$99$	2.75045	−	0.484978i	0.276430	−	0.0487421i
$100$		0			0
$101$	14.8106	+	5.39064i	1.47371	+	0.536388i	0.949106	−	0.314955i	$-0.101990\pi$
$101$	14.8106	+	5.39064i	1.47371	+	0.536388i	0.524608	+	0.851344i	$0.324212\pi$
$102$	1.55092	+	0.415567i	0.153564	+	0.0411473i
$103$	1.83657	+	6.85416i	0.180962	+	0.675360i	0.995459	+	0.0951921i	$0.0303465\pi$
$103$	1.83657	+	6.85416i	0.180962	+	0.675360i	−0.814497	+	0.580168i	$0.802987\pi$
$104$	2.24185	+	2.67173i	0.219831	+	0.261984i
$105$		0			0
$106$	−0.425765	+	0.737446i	−0.0413539	+	0.0716271i
$107$	−2.78505	+	10.3939i	−0.269241	+	1.00482i	0.690363	+	0.723464i	$0.257451\pi$
$107$	−2.78505	+	10.3939i	−0.269241	+	1.00482i	−0.959603	+	0.281357i	$0.909216\pi$
$108$	4.38199	−	2.04335i	0.421657	−	0.196622i
$109$	0.343601	−	1.94866i	0.0329110	−	0.186648i	−0.963920	−	0.266191i	$-0.914235\pi$
$109$	0.343601	−	1.94866i	0.0329110	−	0.186648i	0.996831	+	0.0795428i	$0.0253460\pi$
$110$		0			0
$111$	1.49755	−	0.545063i	0.142141	−	0.0517351i
$112$	−0.251037	+	0.0219629i	−0.0237207	+	0.00207529i
$113$	9.49063	−	9.49063i	0.892803	−	0.892803i	−0.101983	−	0.994786i	$-0.532519\pi$
$113$	9.49063	−	9.49063i	0.892803	−	0.892803i	0.994786	+	0.101983i	$0.0325188\pi$
$114$	2.70716	−	3.12015i	0.253548	−	0.292229i
$115$		0			0
$116$	2.74711	−	3.27388i	0.255063	−	0.303972i
$117$	−6.64392	−	3.09811i	−0.614231	−	0.286420i
$118$	−1.99421	+	2.84802i	−0.183582	+	0.262182i
$119$	0.420460	+	0.0741385i	0.0385435	+	0.00679627i
$120$		0			0
$121$	4.61722	+	7.99726i	0.419747	+	0.727023i
$122$	−1.98803	+	0.532690i	−0.179987	+	0.0482275i
$123$	7.01017	+	0.613310i	0.632085	+	0.0553003i
$124$	−4.63968	+	3.89316i	−0.416656	+	0.349616i
$125$		0			0
$126$	0.458705	−	0.264834i	0.0408647	−	0.0235933i
$127$	2.39673	+	5.13980i	0.212675	+	0.456084i	0.983487	−	0.180979i	$-0.0579267\pi$
$127$	2.39673	+	5.13980i	0.212675	+	0.456084i	−0.770811	+	0.637063i	$0.780149\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$	−1.07987	−	6.12427i	−0.0950776	−	0.539212i
$130$		0			0
$131$	−2.18256	−	1.83139i	−0.190691	−	0.160009i	0.542444	−	0.840092i	$-0.317499\pi$
$131$	−2.18256	−	1.83139i	−0.190691	−	0.160009i	−0.733135	+	0.680083i	$0.761944\pi$
$132$	−0.890411	−	0.890411i	−0.0775004	−	0.0775004i
$133$	0.644800	−	0.889250i	0.0559113	−	0.0771078i
$134$		−	0.968230i		−	0.0836423i
$135$		0			0
$136$	0.579472	+	1.59209i	0.0496893	+	0.136520i
$137$	−7.67295	−	5.37266i	−0.655544	−	0.459017i	0.197885	−	0.980225i	$-0.436593\pi$
$137$	−7.67295	−	5.37266i	−0.655544	−	0.459017i	−0.853430	+	0.521208i	$0.825482\pi$
$138$	4.94635	−	3.46347i	0.421061	−	0.294830i
$139$	−5.80516	+	15.9495i	−0.492387	+	1.35282i	0.406102	+	0.913828i	$0.366888\pi$
$139$	−5.80516	+	15.9495i	−0.492387	+	1.35282i	−0.898489	+	0.438995i	$0.855335\pi$
$140$		0			0
$141$	−1.03142	−	0.595489i	−0.0868610	−	0.0501492i
$142$	0.448424	−	5.12551i	0.0376309	−	0.430123i
$143$	−0.403902	+	4.61662i	−0.0337760	+	0.386061i
$144$	1.82029	+	1.05095i	0.151691	+	0.0875788i
$145$		0			0
$146$	−0.712188	+	1.95672i	−0.0589411	+	0.161939i
$147$	5.38479	−	3.77047i	0.444130	−	0.310983i
$148$	1.37751	+	0.964544i	0.113231	+	0.0792851i
$149$	−3.21393	−	8.83019i	−0.263295	−	0.723398i	−0.998940	−	0.0460301i	$-0.985343\pi$
$149$	−3.21393	−	8.83019i	−0.263295	−	0.723398i	0.735645	−	0.677367i	$-0.236879\pi$
$150$		0			0
$151$			19.4601i			1.58364i	0.610752	+	0.791822i	$0.290867\pi$
$151$			19.4601i			1.58364i	−0.610752	+	0.791822i	$0.709133\pi$
$152$	4.33545	+	0.451550i	0.351651	+	0.0366255i
$153$	−2.51812	−	2.51812i	−0.203578	−	0.203578i
$154$	−0.256501	−	0.215229i	−0.0206694	−	0.0173437i
$155$		0			0
$156$	0.573948	+	3.25502i	0.0459526	+	0.260610i
$157$	13.7860	+	19.6885i	1.10025	+	1.57131i	0.781972	+	0.623314i	$0.214214\pi$
$157$	13.7860	+	19.6885i	1.10025	+	1.57131i	0.318273	+	0.947999i	$0.396897\pi$
$158$	−1.88625	−	4.04507i	−0.150062	−	0.321809i
$159$	−0.698867	+	0.403491i	−0.0554238	+	0.0319989i
$160$		0			0
$161$	1.22999	−	1.03209i	0.0969371	−	0.0813399i
$162$	−1.71707	−	0.150224i	−0.134906	−	0.0118027i
$163$	−15.0150	+	4.02326i	−1.17607	+	0.315126i	−0.793365	−	0.608746i	$-0.791673\pi$
$163$	−15.0150	+	4.02326i	−1.17607	+	0.315126i	−0.382701	+	0.923872i	$0.625006\pi$
$164$	3.71270	+	6.43058i	0.289913	+	0.502144i
$165$		0			0
$166$	−1.12603	−	0.198550i	−0.0873970	−	0.0154104i
$167$	−3.51455	+	5.01929i	−0.271964	+	0.388405i	−0.931781	−	0.363022i	$-0.881745\pi$
$167$	−3.51455	+	5.01929i	−0.271964	+	0.388405i	0.659817	+	0.751427i	$0.270634\pi$
$168$	−0.216438	−	0.100927i	−0.0166985	−	0.00778665i
$169$	−0.537368	+	0.640410i	−0.0413360	+	0.0492623i
$170$		0			0
$171$	−8.65997	+	2.99098i	−0.662244	+	0.228726i
$172$	4.64006	−	4.64006i	0.353801	−	0.353801i
$173$	23.7060	−	2.07400i	1.80233	−	0.157684i	0.864017	−	0.503463i	$-0.167941\pi$
$173$	23.7060	−	2.07400i	1.80233	−	0.157684i	0.938316	+	0.345780i	$0.112386\pi$
$174$	3.80591	−	1.38524i	0.288525	−	0.105015i
$175$		0			0
$176$	0.230734	−	1.30856i	0.0173922	−	0.0986363i
$177$	−2.98620	+	1.39249i	−0.224456	+	0.104666i
$178$	−0.221074	+	0.825059i	−0.0165702	+	0.0618408i
$179$	12.8613	−	22.2765i	0.961300	−	1.66502i	0.242057	−	0.970262i	$-0.422178\pi$
$179$	12.8613	−	22.2765i	0.961300	−	1.66502i	0.719243	−	0.694758i	$-0.244489\pi$
$180$		0			0
$181$	11.2775	+	13.4400i	0.838251	+	0.998988i	0.999926	+	0.0121442i	$0.00386573\pi$
$181$	11.2775	+	13.4400i	0.838251	+	0.998988i	−0.161676	+	0.986844i	$0.551690\pi$
$182$	0.227472	+	0.848936i	0.0168613	+	0.0629273i
$183$	−1.88402	−	0.504823i	−0.139271	−	0.0373176i
$184$	5.98745	+	2.17925i	0.441401	+	0.160657i
$185$		0			0
$186$	−5.65262	+	0.996710i	−0.414470	+	0.0730823i
$187$	−0.951416	+	2.04032i	−0.0695744	+	0.149203i
$188$	−0.109531	−	1.25194i	−0.00798834	−	0.0913071i
$189$	1.21840			0.0886252
$190$		0			0
$191$	−3.47874			−0.251713			−0.125857	−	0.992048i	$-0.540168\pi$
$191$	−3.47874			−0.251713			−0.125857	+	0.992048i	$0.540168\pi$
$192$	−0.0825962	−	0.944079i	−0.00596087	−	0.0681331i
$193$	9.87681	−	21.1809i	0.710949	−	1.52463i	−0.134695	−	0.990887i	$-0.543006\pi$
$193$	9.87681	−	21.1809i	0.710949	−	1.52463i	0.845644	−	0.533747i	$-0.179217\pi$
$194$	9.84660	−	1.73622i	0.706945	−	0.124653i
$195$		0			0
$196$	6.51818	+	2.37242i	0.465584	+	0.169459i
$197$	−10.2293	−	2.74092i	−0.728804	−	0.195282i	−0.124707	−	0.992194i	$-0.539799\pi$
$197$	−10.2293	−	2.74092i	−0.728804	−	0.195282i	−0.604097	+	0.796911i	$0.706466\pi$
$198$	0.722850	+	2.69771i	0.0513707	+	0.191718i
$199$	17.0198	+	20.2834i	1.20650	+	1.43785i	0.867771	+	0.496964i	$0.165552\pi$
$199$	17.0198	+	20.2834i	1.20650	+	1.43785i	0.338727	+	0.940885i	$0.390004\pi$
$200$		0			0
$201$	0.458789	−	0.794645i	0.0323605	−	0.0560499i
$202$	−4.07929	+	15.2241i	−0.287018	+	1.07116i
$203$	0.976060	−	0.455144i	0.0685060	−	0.0319449i
$204$	−0.278814	+	1.58124i	−0.0195209	+	0.110709i
$205$		0			0
$206$	−6.66801	+	2.42696i	−0.464582	+	0.169094i
$207$	−13.3417	+	1.16725i	−0.927311	+	0.0811292i
$208$	−2.46617	+	2.46617i	−0.170998	+	0.170998i
$209$	3.64917	+	4.49769i	0.252418	+	0.311112i
$210$		0			0
$211$	−6.36015	+	7.57973i	−0.437851	+	0.521810i	−0.939170	−	0.343452i	$-0.888404\pi$
$211$	−6.36015	+	7.57973i	−0.437851	+	0.521810i	0.501320	+	0.865262i	$0.332848\pi$
$212$	−0.771748	−	0.359872i	−0.0530039	−	0.0247161i
$213$	2.79672	−	3.99413i	0.191628	−	0.273673i
$214$	−10.5971	−	1.86856i	−0.724404	−	0.127732i
$215$		0			0
$216$	2.41749	+	4.18722i	0.164490	+	0.284904i
$217$	−1.47425	+	0.395024i	−0.100079	+	0.0268160i
$218$	1.97119	+	0.172457i	0.133506	+	0.0116803i
$219$	−1.51169	+	1.26845i	−0.102150	+	0.0857142i
$220$		0			0
$221$	5.11740	−	2.95453i	0.344234	−	0.198743i
$222$	0.673509	+	1.44434i	0.0452030	+	0.0969381i
$223$	−7.49643	−	10.7060i	−0.501998	−	0.716928i	0.485556	−	0.874205i	$-0.338617\pi$
$223$	−7.49643	−	10.7060i	−0.501998	−	0.716928i	−0.987554	+	0.157278i	$0.949728\pi$
$224$	−0.0437586	−	0.248167i	−0.00292374	−	0.0165814i
$225$		0			0
$226$	10.2817	+	8.62735i	0.683927	+	0.573883i
$227$	10.6795	+	10.6795i	0.708824	+	0.708824i	0.966288	−	0.257464i	$-0.0828868\pi$
$227$	10.6795	+	10.6795i	0.708824	+	0.708824i	−0.257464	+	0.966288i	$0.582887\pi$
$228$	3.34422	+	2.42492i	0.221477	+	0.160594i
$229$		−	2.57682i		−	0.170281i	−0.996369	−	0.0851405i	$-0.972866\pi$
$229$		−	2.57682i		−	0.170281i	0.996369	−	0.0851405i	$-0.0271339\pi$
$230$		0			0
$231$	−0.108530	−	0.298184i	−0.00714076	−	0.0196191i
$232$	3.50084	+	2.45132i	0.229842	+	0.160937i
$233$	7.53028	−	5.27276i	0.493325	−	0.345430i	−0.300292	−	0.953847i	$-0.597084\pi$
$233$	7.53028	−	5.27276i	0.493325	−	0.345430i	0.793617	+	0.608417i	$0.208195\pi$
$234$	2.50727	−	6.88866i	0.163905	−	0.450326i
$235$		0			0
$236$	−3.01099	−	1.73840i	−0.195999	−	0.113160i
$237$	0.368647	−	4.21366i	0.0239462	−	0.273707i
$238$	−0.0372109	+	0.425322i	−0.00241202	+	0.0275695i
$239$	21.6035	+	12.4728i	1.39741	+	0.806797i	0.994121	−	0.108275i	$-0.0345326\pi$
$239$	21.6035	+	12.4728i	1.39741	+	0.806797i	0.403292	+	0.915071i	$0.367866\pi$
$240$		0			0
$241$	−0.923124	+	2.53626i	−0.0594636	+	0.163375i	−0.965867	−	0.259038i	$-0.916595\pi$
$241$	−0.923124	+	2.53626i	−0.0594636	+	0.163375i	0.906404	+	0.422413i	$0.138817\pi$
$242$	−7.56441	+	5.29666i	−0.486259	+	0.340482i
$243$	−13.2198	−	9.25662i	−0.848052	−	0.593812i
$244$	−0.703931	−	1.93403i	−0.0450646	−	0.123814i
$245$		0			0
$246$			7.03694i			0.448659i
$247$	−1.07474	−	15.1645i	−0.0683843	−	0.964892i
$248$	−4.28272	−	4.28272i	−0.271953	−	0.271953i
$249$	−0.830075	−	0.696515i	−0.0526038	−	0.0441399i
$250$		0			0
$251$	1.34233	+	7.61273i	0.0847271	+	0.480511i	0.997415	+	0.0718541i	$0.0228916\pi$
$251$	1.34233	+	7.61273i	0.0847271	+	0.480511i	−0.912688	+	0.408657i	$0.865997\pi$
$252$	0.303805	+	0.433878i	0.0191379	+	0.0273318i
$253$	3.57804	+	7.67314i	0.224950	+	0.482406i
$254$	−4.91136	+	2.83557i	−0.308166	+	0.177920i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	29.8143	+	2.60841i	1.85976	+	0.162708i	0.961149	−	0.276030i	$-0.0890188\pi$
$257$	29.8143	+	2.60841i	1.85976	+	0.162708i	0.898615	+	0.438738i	$0.144574\pi$
$258$	6.00685	−	1.60953i	0.373970	−	0.100205i
$259$	0.211882	+	0.366990i	0.0131657	+	0.0228037i
$260$		0			0
$261$	−8.84647	−	1.55987i	−0.547583	−	0.0965536i
$262$	1.63419	−	2.33387i	0.100961	−	0.144187i
$263$	−4.05087	−	1.88895i	−0.249788	−	0.116478i	0.293692	−	0.955900i	$-0.405116\pi$
$263$	−4.05087	−	1.88895i	−0.249788	−	0.116478i	−0.543480	+	0.839422i	$0.682894\pi$
$264$	0.809419	−	0.964628i	0.0498163	−	0.0593687i
$265$		0			0
$266$	0.942064	+	0.564843i	0.0577617	+	0.0346328i
$267$	−0.572388	+	0.572388i	−0.0350296	+	0.0350296i
$268$	0.964545	−	0.0843868i	0.0589190	−	0.00515474i
$269$	7.07105	−	2.57365i	0.431130	−	0.156918i	−0.117334	−	0.993092i	$-0.537435\pi$
$269$	7.07105	−	2.57365i	0.431130	−	0.156918i	0.548464	+	0.836174i	$0.315213\pi$
$270$		0			0
$271$	−1.08789	+	6.16972i	−0.0660845	+	0.374784i	0.933772	+	0.357868i	$0.116496\pi$
$271$	−1.08789	+	6.16972i	−0.0660845	+	0.374784i	−0.999857	+	0.0169165i	$0.994615\pi$
$272$	−1.53552	+	0.716026i	−0.0931048	+	0.0434155i
$273$	−0.215572	+	0.804524i	−0.0130470	+	0.0486920i
$274$	4.68347	−	8.11201i	0.282939	−	0.490064i
$275$		0			0
$276$	3.88139	+	4.62567i	0.233632	+	0.278432i
$277$	0.0830647	+	0.310002i	0.00499087	+	0.0186262i	0.968376	−	0.249494i	$-0.0802643\pi$
$277$	0.0830647	+	0.310002i	0.00499087	+	0.0186262i	−0.963385	+	0.268120i	$0.913598\pi$
$278$	−16.3948	−	4.39297i	−0.983295	−	0.263473i
$279$	11.9627	+	4.35408i	0.716190	+	0.260672i
$280$		0			0
$281$	−24.0298	+	4.23711i	−1.43350	+	0.252765i	−0.835835	−	0.548981i	$-0.815016\pi$
$281$	−24.0298	+	4.23711i	−1.43350	+	0.252765i	−0.597665	+	0.801746i	$0.703905\pi$
$282$	0.503329	−	1.07939i	0.0299728	−	0.0642769i
$283$	−0.965955	−	11.0409i	−0.0574201	−	0.656314i	−0.969304	−	0.245866i	$-0.920928\pi$
$283$	−0.965955	−	11.0409i	−0.0574201	−	0.656314i	0.911884	−	0.410449i	$-0.134628\pi$
$284$	5.14509			0.305305
$285$		0			0
$286$	−4.63425			−0.274029
$287$	0.163083	+	1.86405i	0.00962648	+	0.110031i
$288$	−0.888298	+	1.90496i	−0.0523435	+	0.112251i
$289$	−13.9148	+	2.45356i	−0.818519	+	0.144327i
$290$		0			0
$291$	8.90400	+	3.24079i	0.521961	+	0.189978i
$292$	−2.01135	−	0.538939i	−0.117705	−	0.0315390i
$293$	0.957380	+	3.57299i	0.0559307	+	0.208736i	0.988236	−	0.152936i	$-0.0488727\pi$
$293$	0.957380	+	3.57299i	0.0559307	+	0.208736i	−0.932305	+	0.361672i	$0.882206\pi$
$294$	4.22544	+	5.03568i	0.246433	+	0.293687i
$295$		0			0
$296$	−0.840816	+	1.45634i	−0.0488714	+	0.0846478i
$297$	−1.66277	+	6.20556i	−0.0964839	+	0.360083i
$298$	8.51648	−	3.97130i	0.493346	−	0.230051i
$299$	3.85891	−	21.8850i	0.223166	−	1.26564i
$300$		0			0
$301$	1.55388	−	0.565566i	0.0895641	−	0.0325987i
$302$	−19.3861	+	1.69606i	−1.11554	+	0.0975975i
$303$	−10.5618	+	10.5618i	−0.606759	+	0.606759i
$304$	−0.0719722	+	4.35830i	−0.00412789	+	0.249966i
$305$		0			0
$306$	2.28907	−	2.72801i	0.130857	−	0.155950i
$307$	16.8465	+	7.85567i	0.961483	+	0.448347i	0.839005	−	0.544124i	$-0.183138\pi$
$307$	16.8465	+	7.85567i	0.961483	+	0.448347i	0.122478	+	0.992471i	$0.460916\pi$
$308$	0.192055	−	0.274283i	0.0109433	−	0.0156287i
$309$	−6.62256	−	1.16774i	−0.376744	−	0.0664302i
$310$		0			0
$311$	−6.43055	−	11.1380i	−0.364643	−	0.631581i	0.624076	−	0.781364i	$-0.285476\pi$
$311$	−6.43055	−	11.1380i	−0.364643	−	0.631581i	−0.988719	+	0.149783i	$0.952142\pi$
$312$	−3.19261	+	0.855458i	−0.180746	+	0.0484308i
$313$	−4.82378	−	0.422026i	−0.272656	−	0.0238543i	−0.0499922	−	0.998750i	$-0.515920\pi$
$313$	−4.82378	−	0.422026i	−0.272656	−	0.0238543i	−0.222664	+	0.974895i	$0.571475\pi$
$314$	−18.4120	+	15.4495i	−1.03905	+	0.871868i
$315$		0			0
$316$	3.86528	−	2.23162i	0.217439	−	0.125539i
$317$	−9.00729	−	19.3162i	−0.505900	−	1.08491i	−0.978993	−	0.203893i	$-0.934640\pi$
$317$	−9.00729	−	19.3162i	−0.505900	−	1.08491i	0.473093	−	0.881012i	$-0.343137\pi$
$318$	−0.462866	−	0.661041i	−0.0259562	−	0.0370693i
$319$	0.986098	+	5.59244i	0.0552109	+	0.313116i
$320$		0			0
$321$	−7.81186	−	6.55493i	−0.436016	−	0.365861i
$322$	1.13536	+	1.13536i	0.0632712	+	0.0632712i
$323$	2.02893	−	7.10095i	0.112893	−	0.395107i
$324$		−	1.72363i		−	0.0957570i
$325$		0			0
$326$	−5.31659	−	14.6072i	−0.294459	−	0.809019i
$327$	1.53608	+	1.07557i	0.0849454	+	0.0594794i
$328$	−6.08253	+	4.25903i	−0.335852	+	0.235166i
$329$	0.108314	−	0.297590i	0.00597154	−	0.0164067i
$330$		0			0
$331$	−1.92336	−	1.11045i	−0.105717	−	0.0610360i	0.446209	−	0.894929i	$-0.352774\pi$
$331$	−1.92336	−	1.11045i	−0.105717	−	0.0610360i	−0.551927	+	0.833893i	$0.686107\pi$
$332$	0.0996540	−	1.13905i	0.00546923	−	0.0625135i
$333$	0.308061	−	3.52116i	0.0168817	−	0.192958i
$334$	−5.30651	−	3.06371i	−0.290359	−	0.167639i
$335$		0			0
$336$	0.0816787	−	0.224410i	0.00445594	−	0.0122426i
$337$	15.7522	−	11.0298i	0.858076	−	0.600832i	−0.0595724	−	0.998224i	$-0.518974\pi$
$337$	15.7522	−	11.0298i	0.858076	−	0.600832i	0.917649	+	0.397392i	$0.130085\pi$
$338$	−0.684808	−	0.479508i	−0.0372487	−	0.0260818i
$339$	4.35037	+	11.9525i	0.236279	+	0.649172i
$340$		0			0
$341$		−	8.04777i		−	0.435811i
$342$	−3.73437	−	8.36633i	−0.201932	−	0.452400i
$343$	2.48331	+	2.48331i	0.134086	+	0.134086i
$344$	5.02681	+	4.21799i	0.271027	+	0.227419i
$345$		0			0
$346$	4.13222	+	23.4350i	0.222150	+	1.25987i
$347$	18.5924	+	26.5526i	0.998090	+	1.42542i	0.902845	+	0.429966i	$0.141475\pi$
$347$	18.5924	+	26.5526i	0.998090	+	1.42542i	0.0952452	+	0.995454i	$0.469636\pi$
$348$	1.71167	+	3.67069i	0.0917553	+	0.196770i
$349$	−25.9426	+	14.9779i	−1.38867	+	0.801751i	−0.993166	−	0.116712i	$-0.962765\pi$
$349$	−25.9426	+	14.9779i	−1.38867	+	0.801751i	−0.395507	+	0.918463i	$0.629431\pi$
$350$		0			0
$351$	12.9178	−	10.8393i	0.689500	−	0.578559i
$352$	1.32369	+	0.115808i	0.0705528	+	0.00617257i
$353$	−9.85053	+	2.63944i	−0.524291	+	0.140483i	−0.511251	−	0.859432i	$-0.670818\pi$
$353$	−9.85053	+	2.63944i	−0.524291	+	0.140483i	−0.0130401	+	0.999915i	$0.504151\pi$
$354$	−1.64745	−	2.85347i	−0.0875611	−	0.151660i
$355$		0			0
$356$	−0.841187	−	0.148324i	−0.0445828	−	0.00786115i
$357$	−0.232075	+	0.331438i	−0.0122827	+	0.0175416i
$358$	23.3126	+	10.8709i	1.23211	+	0.574543i
$359$	10.6721	−	12.7185i	0.563250	−	0.671255i	−0.406981	−	0.913437i	$-0.633418\pi$
$359$	10.6721	−	12.7185i	0.563250	−	0.671255i	0.970231	+	0.242181i	$0.0778629\pi$
$360$		0			0
$361$	−14.1437	−	12.6869i	−0.744403	−	0.667731i
$362$	−12.4060	+	12.4060i	−0.652043	+	0.652043i
$363$	−8.71804	+	0.762730i	−0.457579	+	0.0400329i
$364$	−0.825880	+	0.300596i	−0.0432879	+	0.0157555i
$365$		0			0
$366$	0.338698	−	1.92085i	0.0177040	−	0.100405i
$367$	31.4016	−	14.6428i	1.63915	−	0.764348i	0.639160	−	0.769074i	$-0.279282\pi$
$367$	31.4016	−	14.6428i	1.63915	−	0.764348i	0.999989	+	0.00472642i	$0.00150447\pi$
$368$	−1.64912	+	6.15460i	−0.0859663	+	0.320831i
$369$	7.80369	−	13.5164i	0.406244	−	0.703635i
$370$		0			0
$371$	−0.137930	−	0.164379i	−0.00716099	−	0.00853414i
$372$	−1.48558	−	5.54424i	−0.0770235	−	0.287456i
$373$	22.2273	+	5.95578i	1.15089	+	0.308379i	0.783320	−	0.621619i	$-0.213525\pi$
$373$	22.2273	+	5.95578i	1.15089	+	0.308379i	0.367566	+	0.929998i	$0.380191\pi$
$374$	−2.11548	−	0.769970i	−0.109389	−	0.0398142i
$375$		0			0
$376$	1.23763	−	0.218228i	0.0638259	−	0.0112542i
$377$	6.29934	−	13.5090i	0.324432	−	0.695747i
$378$	0.106190	+	1.21376i	0.00546183	+	0.0624290i
$379$	−19.1650			−0.984442			−0.492221	−	0.870470i	$-0.663815\pi$
$379$	−19.1650			−0.984442			−0.492221	+	0.870470i	$0.663815\pi$
$380$		0			0
$381$	−5.37446			−0.275342
$382$	−0.303192	−	3.46551i	−0.0155127	−	0.177311i
$383$	10.4648	−	22.4419i	0.534728	−	1.14673i	−0.434525	−	0.900660i	$-0.643084\pi$
$383$	10.4648	−	22.4419i	0.534728	−	1.14673i	0.969253	−	0.246068i	$-0.0791386\pi$
$384$	0.933288	−	0.164564i	0.0476267	−	0.00839786i
$385$		0			0
$386$	21.9611	+	7.99319i	1.11779	+	0.406843i
$387$	−13.3227	−	3.56981i	−0.677232	−	0.181464i
$388$	2.58780	+	9.65781i	0.131376	+	0.490301i
$389$	9.41742	+	11.2232i	0.477482	+	0.569041i	0.949988	−	0.312286i	$-0.101095\pi$
$389$	9.41742	+	11.2232i	0.477482	+	0.569041i	−0.472506	+	0.881328i	$0.656650\pi$
$390$		0			0
$391$	5.39768	−	9.34905i	0.272972	−	0.472802i
$392$	−1.79530	+	6.70014i	−0.0906762	+	0.338408i
$393$	2.44710	−	1.14110i	0.123440	−	0.0575611i
$394$	1.83895	−	10.4292i	0.0926451	−	0.525416i
$395$		0			0
$396$	−2.62445	+	0.955220i	−0.131883	+	0.0480016i
$397$	−16.8164	+	1.47125i	−0.843992	+	0.0738398i	−0.500946	−	0.865479i	$-0.667014\pi$
$397$	−16.8164	+	1.47125i	−0.843992	+	0.0738398i	−0.343047	+	0.939318i	$0.611459\pi$
$398$	−18.7228	+	18.7228i	−0.938489	+	0.938489i
$399$	0.505524	+	0.909969i	0.0253078	+	0.0455554i
$400$		0			0
$401$	16.6660	−	19.8618i	0.832263	−	0.991852i	−0.167719	−	0.985835i	$-0.553640\pi$
$401$	16.6660	−	19.8618i	0.832263	−	0.991852i	0.999982	−	0.00601718i	$-0.00191534\pi$
$402$	0.831607	+	0.387785i	0.0414768	+	0.0193410i
$403$	−12.1161	+	17.3036i	−0.603547	+	0.861955i
$404$	−15.5217	−	2.73690i	−0.772234	−	0.136166i
$405$		0			0
$406$	0.538482	+	0.932678i	0.0267244	+	0.0462880i
$407$	−2.15832	+	0.578321i	−0.106984	+	0.0286663i
$408$	−1.59952	−	0.139940i	−0.0791880	−	0.00692805i
$409$	−19.5820	+	16.4313i	−0.968270	+	0.812475i	−0.982279	−	0.187427i	$-0.939985\pi$
$409$	−19.5820	+	16.4313i	−0.968270	+	0.812475i	0.0140087	+	0.999902i	$0.495541\pi$
$410$		0			0
$411$	7.68763	−	4.43846i	0.379203	−	0.218933i
$412$	−2.99888	−	6.43111i	−0.147744	−	0.316838i
$413$	−0.502531	−	0.717689i	−0.0247279	−	0.0353151i
$414$	−2.32561	−	13.1892i	−0.114297	−	0.648213i
$415$		0			0
$416$	−2.67173	−	2.24185i	−0.130992	−	0.109916i
$417$	−11.3740	−	11.3740i	−0.556985	−	0.556985i
$418$	−4.16253	+	4.02728i	−0.203596	+	0.196981i
$419$		−	7.70974i		−	0.376645i	−0.982107	−	0.188323i	$-0.939695\pi$
$419$		−	7.70974i		−	0.376645i	0.982107	−	0.188323i	$-0.0603051\pi$
$420$		0			0
$421$	−4.43677	−	12.1899i	−0.216235	−	0.594101i	0.783389	−	0.621532i	$-0.213489\pi$
$421$	−4.43677	−	12.1899i	−0.216235	−	0.594101i	−0.999624	+	0.0274313i	$0.991267\pi$
$422$	−8.10521	−	5.67533i	−0.394555	−	0.276271i
$423$	−2.16379	+	1.51510i	−0.105207	+	0.0736667i
$424$	0.291240	−	0.800176i	0.0141439	−	0.0388600i
$425$		0			0
$426$	4.22268	+	2.43796i	0.204589	+	0.118120i
$427$	0.0452030	−	0.516673i	0.00218753	−	0.0250035i
$428$	0.937848	−	10.7197i	0.0453326	−	0.518154i
$429$	−3.80342	−	2.19591i	−0.183631	−	0.106019i
$430$		0			0
$431$	7.49698	−	20.5978i	0.361117	−	0.992160i	−0.617518	−	0.786556i	$-0.711862\pi$
$431$	7.49698	−	20.5978i	0.361117	−	0.992160i	0.978635	−	0.205604i	$-0.0659158\pi$
$432$	−3.96059	+	2.77324i	−0.190554	+	0.133427i
$433$	4.64847	+	3.25489i	0.223391	+	0.156420i	0.679915	−	0.733291i	$-0.262017\pi$
$433$	4.64847	+	3.25489i	0.223391	+	0.156420i	−0.456524	+	0.889711i	$0.650906\pi$
$434$	−0.522010	−	1.43421i	−0.0250573	−	0.0688443i
$435$		0			0
$436$			1.97872i			0.0947636i
$437$	−15.5525	−	23.0108i	−0.743976	−	1.10075i
$438$	−1.39538	−	1.39538i	−0.0666738	−	0.0666738i
$439$	8.72362	+	7.31999i	0.416356	+	0.349364i	0.826775	−	0.562533i	$-0.190173\pi$
$439$	8.72362	+	7.31999i	0.416356	+	0.349364i	−0.410419	+	0.911897i	$0.634618\pi$
$440$		0			0
$441$	−2.53175	−	14.3583i	−0.120560	−	0.683727i
$442$	3.38930	+	4.84043i	0.161213	+	0.230236i
$443$	11.9700	+	25.6696i	0.568710	+	1.21960i	0.954830	+	0.297153i	$0.0960372\pi$
$443$	11.9700	+	25.6696i	0.568710	+	1.21960i	−0.386120	+	0.922448i	$0.626185\pi$
$444$	−1.38015	+	0.796829i	−0.0654990	+	0.0378158i
$445$		0			0
$446$	10.0119	−	8.40099i	0.474078	−	0.397799i
$447$	8.87141	+	0.776148i	0.419603	+	0.0367105i
$448$	0.243409	−	0.0652212i	0.0115000	−	0.00308141i
$449$	−15.5392	−	26.9148i	−0.733342	−	1.27019i	−0.955447	−	0.295163i	$-0.904626\pi$
$449$	−15.5392	−	26.9148i	−0.733342	−	1.27019i	0.222105	−	0.975023i	$-0.428707\pi$
$450$		0			0
$451$	−9.71656	−	1.71329i	−0.457535	−	0.0806758i
$452$	−7.69841	+	10.9945i	−0.362103	+	0.517136i
$453$	−16.7142	−	7.79397i	−0.785303	−	0.366193i
$454$	−9.70809	+	11.5697i	−0.455623	+	0.542991i
$455$		0			0
$456$	−2.12422	+	3.54284i	−0.0994757	+	0.165909i
$457$	11.2269	−	11.2269i	0.525174	−	0.525174i	−0.393956	−	0.919129i	$-0.628894\pi$
$457$	11.2269	−	11.2269i	0.525174	−	0.525174i	0.919129	+	0.393956i	$0.128894\pi$
$458$	2.56701	−	0.224585i	0.119949	−	0.0104942i
$459$	7.69772	−	2.80174i	0.359299	−	0.130774i
$460$		0			0
$461$	−2.05527	+	11.6560i	−0.0957234	+	0.542875i	0.898800	+	0.438359i	$0.144440\pi$
$461$	−2.05527	+	11.6560i	−0.0957234	+	0.542875i	−0.994523	+	0.104515i	$0.966671\pi$
$462$	0.287590	−	0.134106i	0.0133799	−	0.00623916i
$463$	−0.123800	+	0.462028i	−0.00575348	+	0.0214723i	−0.968743	−	0.248067i	$-0.920205\pi$
$463$	−0.123800	+	0.462028i	−0.00575348	+	0.0214723i	0.962989	+	0.269539i	$0.0868714\pi$
$464$	−2.13687	+	3.70117i	−0.0992017	+	0.171822i
$465$		0			0
$466$	5.90900	+	7.04207i	0.273729	+	0.326218i
$467$	−3.96524	−	14.7985i	−0.183489	−	0.684792i	−0.994949	−	0.100383i	$-0.967993\pi$
$467$	−3.96524	−	14.7985i	−0.183489	−	0.684792i	0.811460	−	0.584409i	$-0.198673\pi$
$468$	7.08097	+	1.89734i	0.327318	+	0.0877045i
$469$	0.229275	+	0.0834493i	0.0105869	+	0.00385333i
$470$		0			0
$471$	−22.4318	+	3.95533i	−1.03360	+	0.182252i
$472$	1.46936	−	3.15104i	0.0676326	−	0.145039i
$473$	0.759934	+	8.68609i	0.0349418	+	0.399387i
$474$	4.22975			0.194279
$475$		0			0
$476$	−0.426947			−0.0195691
$477$	0.155993	+	1.78301i	0.00714245	+	0.0816385i
$478$	−10.5424	+	22.6083i	−0.482200	+	1.03408i
$479$	−15.2012	+	2.68039i	−0.694561	+	0.122470i	−0.509774	−	0.860309i	$-0.670271\pi$
$479$	−15.2012	+	2.68039i	−0.694561	+	0.122470i	−0.184788	+	0.982778i	$0.559160\pi$
$480$		0			0
$481$	5.51131	+	2.00595i	0.251294	+	0.0914636i
$482$	−2.60707	−	0.698561i	−0.118749	−	0.0318186i
$483$	0.393830	+	1.46980i	0.0179199	+	0.0668780i
$484$	−5.93578	−	7.07399i	−0.269808	−	0.321545i
$485$		0			0
$486$	8.06921	−	13.9763i	0.366027	−	0.633977i
$487$	−6.72034	+	25.0806i	−0.304528	+	1.13651i	0.628824	+	0.777548i	$0.283537\pi$
$487$	−6.72034	+	25.0806i	−0.304528	+	1.13651i	−0.933351	+	0.358964i	$0.883130\pi$
$488$	1.86532	−	0.869815i	0.0844392	−	0.0393747i
$489$	2.55809	−	14.5077i	0.115681	−	0.656059i
$490$		0			0
$491$	−0.180218	+	0.0655939i	−0.00813311	+	0.00296021i	−0.346083	−	0.938204i	$-0.612489\pi$
$491$	−0.180218	+	0.0655939i	−0.00813311	+	0.00296021i	0.337950	+	0.941164i	$0.390266\pi$
$492$	−7.01017	+	0.613310i	−0.316043	+	0.0276502i
$493$	5.12005	−	5.12005i	0.230595	−	0.230595i
$494$	15.0131	−	2.39232i	0.675471	−	0.107636i
$495$		0			0
$496$	3.89316	−	4.63968i	0.174808	−	0.208328i
$497$	1.17506	+	0.547941i	0.0527088	+	0.0245785i
$498$	0.621519	−	0.887621i	0.0278509	−	0.0397753i
$499$	−25.4735	−	4.49167i	−1.14035	−	0.201075i	−0.428592	−	0.903498i	$-0.640990\pi$
$499$	−25.4735	−	4.49167i	−1.14035	−	0.201075i	−0.711759	+	0.702424i	$0.752101\pi$
$500$		0			0
$501$	−2.90344	−	5.02890i	−0.129716	−	0.224675i
$502$	−7.46677	+	2.00071i	−0.333258	+	0.0892962i
$503$	−24.3719	−	2.13226i	−1.08669	−	0.0950729i	−0.470293	−	0.882510i	$-0.655852\pi$
$503$	−24.3719	−	2.13226i	−1.08669	−	0.0950729i	−0.616395	+	0.787437i	$0.711407\pi$
$504$	−0.405749	+	0.340464i	−0.0180735	+	0.0151655i
$505$		0			0
$506$	−7.33210	+	4.23319i	−0.325951	+	0.188188i
$507$	−0.334824	−	0.718033i	−0.0148701	−	0.0318890i
$508$	−3.25284	−	4.64553i	−0.144321	−	0.206112i
$509$	−7.08358	−	40.1730i	−0.313974	−	1.78064i	−0.577915	−	0.816097i	$-0.696134\pi$
$509$	−7.08358	−	40.1730i	−0.313974	−	1.78064i	0.263941	−	0.964539i	$-0.414977\pi$
$510$		0			0
$511$	−0.401967	−	0.337290i	−0.0177820	−	0.0149208i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.18324	−	20.9618i	0.0963923	−	0.925488i
$514$			29.9282i			1.32008i
$515$		0			0
$516$	2.12694	+	5.84371i	0.0936331	+	0.257255i
$517$	1.36787	+	0.957794i	0.0601589	+	0.0421237i
$518$	−0.347127	+	0.243061i	−0.0152519	+	0.0106795i
$519$	−7.71311	+	21.1916i	−0.338568	+	0.930208i
$520$		0			0
$521$	−8.07448	−	4.66180i	−0.353749	−	0.204237i	0.312586	−	0.949889i	$-0.398805\pi$
$521$	−8.07448	−	4.66180i	−0.353749	−	0.204237i	−0.666335	+	0.745652i	$0.732138\pi$
$522$	0.782915	−	8.94876i	0.0342673	−	0.391677i
$523$	−1.39384	+	15.9317i	−0.0609483	+	0.696643i	0.902840	+	0.429976i	$0.141478\pi$
$523$	−1.39384	+	15.9317i	−0.0609483	+	0.696643i	−0.963789	+	0.266667i	$0.914078\pi$
$524$	2.46742	+	1.42457i	0.107790	+	0.0622324i
$525$		0			0
$526$	1.52871	−	4.20009i	0.0666549	−	0.183133i
$527$	−8.40581	+	5.88581i	−0.366163	+	0.256390i
$528$	1.03150	+	0.722266i	0.0448904	+	0.0314326i
$529$	−6.01911	−	16.5374i	−0.261700	−	0.719016i
$530$		0			0
$531$			7.30784i			0.317133i
$532$	−0.480588	+	0.987709i	−0.0208361	+	0.0428226i
$533$	18.3123	+	18.3123i	0.793194	+	0.793194i
$534$	−0.620097	−	0.520323i	−0.0268342	−	0.0225166i
$535$		0			0
$536$	0.168131	+	0.953520i	0.00726217	+	0.0411858i
$537$	13.9821	+	19.9684i	0.603370	+	0.861702i
$538$	3.18014	+	6.81984i	0.137106	+	0.294024i
$539$	−7.98201	+	4.60842i	−0.343810	+	0.198499i
$540$		0			0
$541$	26.6122	−	22.3303i	1.14415	−	0.960054i	0.144581	−	0.989493i	$-0.453817\pi$
$541$	26.6122	−	22.3303i	1.14415	−	0.960054i	0.999567	+	0.0294391i	$0.00937213\pi$
$542$	−6.24106	−	0.546022i	−0.268077	−	0.0234537i
$543$	−16.0603	+	4.30335i	−0.689214	+	0.184674i
$544$	−0.847131	−	1.46727i	−0.0363205	−	0.0629089i
$545$		0			0
$546$	−0.820251	−	0.144632i	−0.0351035	−	0.00618970i
$547$	−16.4477	+	23.4898i	−0.703254	+	1.00435i	0.295543	+	0.955329i	$0.404499\pi$
$547$	−16.4477	+	23.4898i	−0.703254	+	1.00435i	−0.998798	+	0.0490221i	$0.984390\pi$
$548$	8.48933	+	3.95864i	0.362646	+	0.169105i
$549$	−2.78071	+	3.31393i	−0.118678	+	0.141435i
$550$		0			0
$551$	−6.08152	−	17.6082i	−0.259081	−	0.750133i
$552$	−4.26978	+	4.26978i	−0.181734	+	0.181734i
$553$	1.12044	−	0.0980256i	0.0476459	−	0.00416847i
$554$	−0.301582	+	0.109767i	−0.0128130	+	0.00466355i
$555$		0			0
$556$	2.94736	−	16.7153i	0.124996	−	0.708886i
$557$	−10.6060	+	4.94565i	−0.449390	+	0.209554i	−0.634119	−	0.773235i	$-0.718637\pi$
$557$	−10.6060	+	4.94565i	−0.449390	+	0.209554i	0.184729	+	0.982790i	$0.440859\pi$
$558$	−3.29489	+	12.2967i	−0.139484	+	0.520561i
$559$	11.4432	−	19.8202i	0.483995	−	0.838304i
$560$		0			0
$561$	−1.37137	−	1.63433i	−0.0578992	−	0.0690016i
$562$	−6.31532	−	23.5691i	−0.266396	−	0.994203i
$563$	−6.43121	−	1.72324i	−0.271043	−	0.0726258i	0.120737	−	0.992684i	$-0.461474\pi$
$563$	−6.43121	−	1.72324i	−0.271043	−	0.0726258i	−0.391781	+	0.920059i	$0.628141\pi$
$564$	1.11915	+	0.407338i	0.0471249	+	0.0171520i
$565$		0			0
$566$	10.9147	−	1.92456i	0.458780	−	0.0808952i
$567$	0.183563	−	0.393651i	0.00770890	−	0.0165318i
$568$	0.448424	+	5.12551i	0.0188155	+	0.215062i
$569$	−32.9286			−1.38044			−0.690220	−	0.723600i	$-0.742486\pi$
$569$	−32.9286			−1.38044			−0.690220	+	0.723600i	$0.742486\pi$
$570$		0			0
$571$	−19.4344			−0.813302			−0.406651	−	0.913583i	$-0.633304\pi$
$571$	−19.4344			−0.813302			−0.406651	+	0.913583i	$0.633304\pi$
$572$	−0.403902	−	4.61662i	−0.0168880	−	0.193031i
$573$	1.39327	−	2.98787i	0.0582046	−	0.124820i
$574$	−1.84274	+	0.324925i	−0.0769145	+	0.0135621i
$575$		0			0
$576$	−1.97513	−	0.718889i	−0.0822972	−	0.0299537i
$577$	37.5199	+	10.0534i	1.56198	+	0.418530i	0.933288	−	0.359128i	$-0.116926\pi$
$577$	37.5199	+	10.0534i	1.56198	+	0.418530i	0.628687	+	0.777658i	$0.283593\pi$
$578$	−3.65698	−	13.6480i	−0.152110	−	0.567683i
$579$	14.2364	+	16.9663i	0.591645	+	0.705095i
$580$		0			0
$581$	0.144066	−	0.249530i	0.00597687	−	0.0103522i
$582$	−2.45242	+	9.15257i	−0.101656	+	0.379386i
$583$	1.02546	−	0.478178i	0.0424700	−	0.0198041i
$584$	0.361588	−	2.05066i	0.0149626	−	0.0848571i
$585$		0			0
$586$	−3.47595	+	1.26514i	−0.143590	+	0.0522626i
$587$	−4.11269	+	0.359814i	−0.169749	+	0.0148511i	−0.171713	−	0.985147i	$-0.554930\pi$
$587$	−4.11269	+	0.359814i	−0.169749	+	0.0148511i	0.00196439	+	0.999998i	$0.499375\pi$
$588$	−4.64825	+	4.64825i	−0.191691	+	0.191691i
$589$	4.15447	+	26.0715i	0.171182	+	1.07426i
$590$		0			0
$591$	6.45107	−	7.68809i	0.265362	−	0.316246i
$592$	−1.52408	−	0.710688i	−0.0626391	−	0.0292091i
$593$	−7.11839	+	10.1661i	−0.292317	+	0.417472i	−0.938269	−	0.345906i	$-0.887572\pi$
$593$	−7.11839	+	10.1661i	−0.292317	+	0.417472i	0.645952	+	0.763378i	$0.276461\pi$
$594$	−6.32686	−	1.11560i	−0.259594	−	0.0457735i
$595$		0			0
$596$	4.69845	+	8.13795i	0.192456	+	0.333343i
$597$	−24.2378	+	6.49451i	−0.991989	+	0.265803i
$598$	22.1380	+	1.93682i	0.905290	+	0.0792026i
$599$	6.68397	−	5.60852i	0.273100	−	0.229158i	−0.495943	−	0.868355i	$-0.665178\pi$
$599$	6.68397	−	5.60852i	0.273100	−	0.229158i	0.769043	+	0.639197i	$0.220733\pi$
$600$		0			0
$601$	−10.7713	+	6.21880i	−0.439370	+	0.253670i	−0.703330	−	0.710863i	$-0.748304\pi$
$601$	−10.7713	+	6.21880i	−0.439370	+	0.253670i	0.263961	+	0.964533i	$0.414971\pi$
$602$	0.698843	+	1.49867i	0.0284827	+	0.0610814i
$603$	−1.16729	−	1.66707i	−0.0475359	−	0.0678882i
$604$	−3.37922	−	19.1645i	−0.137498	−	0.779793i
$605$		0			0
$606$	−11.4421	−	9.60108i	−0.464804	−	0.390017i
$607$	−1.29904	−	1.29904i	−0.0527263	−	0.0527263i	0.680252	−	0.732978i	$-0.261870\pi$
$607$	−1.29904	−	1.29904i	−0.0527263	−	0.0527263i	−0.732978	+	0.680252i	$0.761870\pi$
$608$	−4.34799	+	0.308153i	−0.176334	+	0.0124973i
$609$			1.02062i			0.0413577i
$610$		0			0
$611$	−1.49910	−	4.11873i	−0.0606469	−	0.166626i
$612$	2.91713	+	2.04260i	0.117918	+	0.0825671i
$613$	−21.5522	+	15.0910i	−0.870487	+	0.609521i	−0.921156	−	0.389194i	$-0.872754\pi$
$613$	−21.5522	+	15.0910i	−0.870487	+	0.609521i	0.0506690	+	0.998716i	$0.483865\pi$
$614$	−6.35750	+	17.4671i	−0.256568	+	0.704915i
$615$		0			0
$616$	0.289978	+	0.167419i	0.0116835	+	0.00674550i
$617$	4.17729	−	47.7466i	0.168171	−	1.92221i	−0.177993	−	0.984032i	$-0.556960\pi$
$617$	4.17729	−	47.7466i	0.168171	−	1.92221i	0.346164	−	0.938174i	$-0.387484\pi$
$618$	0.586099	−	6.69914i	0.0235763	−	0.269479i
$619$	27.9533	+	16.1388i	1.12354	+	0.648674i	0.942301	−	0.334766i	$-0.108657\pi$
$619$	27.9533	+	16.1388i	1.12354	+	0.648674i	0.181235	+	0.983440i	$0.441991\pi$
$620$		0			0
$621$	10.5367	−	28.9493i	0.422822	−	1.16169i
$622$	10.5352	−	7.37683i	0.422423	−	0.295784i
$623$	−0.176319	−	0.123460i	−0.00706406	−	0.00494631i
$624$	−1.13046	−	3.10591i	−0.0452545	−	0.124336i
$625$		0			0
$626$		−	4.84220i		−	0.193533i
$627$	−5.32457	+	1.33289i	−0.212643	+	0.0532304i
$628$	−16.9955	−	16.9955i	−0.678193	−	0.678193i
$629$	2.18256	+	1.83138i	0.0870243	+	0.0730220i
$630$		0			0
$631$	4.88225	+	27.6886i	0.194359	+	1.10227i	0.913328	+	0.407224i	$0.133503\pi$
$631$	4.88225	+	27.6886i	0.194359	+	1.10227i	−0.718969	+	0.695042i	$0.755386\pi$
$632$	2.56001	+	3.65608i	0.101832	+	0.145431i
$633$	−3.96289	−	8.49845i	−0.157511	−	0.337783i
$634$	18.4577	−	10.6565i	0.733047	−	0.423225i
$635$		0			0
$636$	0.618184	−	0.518718i	0.0245126	−	0.0205685i
$637$	24.1003	+	2.10850i	0.954889	+	0.0835420i
$638$	−5.48521	+	1.46976i	−0.217162	+	0.0581883i
$639$	−5.40721	−	9.36557i	−0.213906	−	0.370496i
$640$		0			0
$641$	−47.8302	−	8.43376i	−1.88918	−	0.333113i	−0.895473	−	0.445117i	$-0.853162\pi$
$641$	−47.8302	−	8.43376i	−1.88918	−	0.333113i	−0.993708	+	0.112003i	$0.964273\pi$
$642$	5.84914	−	8.35344i	0.230847	−	0.329684i
$643$	−36.2771	−	16.9163i	−1.43063	−	0.667114i	−0.455804	−	0.890080i	$-0.650648\pi$
$643$	−36.2771	−	16.9163i	−1.43063	−	0.667114i	−0.974826	+	0.222966i	$0.928426\pi$
$644$	−1.03209	+	1.22999i	−0.0406699	+	0.0484685i
$645$		0			0
$646$	7.25076	+	1.40233i	0.285277	+	0.0551737i
$647$	23.3750	−	23.3750i	0.918965	−	0.918965i	−0.0779893	−	0.996954i	$-0.524850\pi$
$647$	23.3750	−	23.3750i	0.918965	−	0.918965i	0.996954	+	0.0779893i	$0.0248500\pi$
$648$	1.71707	−	0.150224i	0.0674528	−	0.00590135i
$649$	4.34116	−	1.58005i	0.170406	−	0.0620225i
$650$		0			0
$651$	0.251166	−	1.42444i	0.00984399	−	0.0558280i
$652$	14.0883	−	6.56946i	0.551739	−	0.257280i
$653$	−4.11395	+	15.3535i	−0.160991	+	0.600827i	0.837526	+	0.546397i	$0.184001\pi$
$653$	−4.11395	+	15.3535i	−0.160991	+	0.600827i	−0.998518	+	0.0544304i	$0.982666\pi$
$654$	−0.937603	+	1.62398i	−0.0366632	+	0.0635025i
$655$		0			0
$656$	−4.77295	−	5.68819i	−0.186353	−	0.222086i
$657$	1.13279	+	4.22763i	0.0441944	+	0.164936i
$658$	0.305898	+	0.0819650i	0.0119251	+	0.00319533i
$659$	4.89409	+	1.78130i	0.190647	+	0.0693898i	0.435579	−	0.900150i	$-0.356544\pi$
$659$	4.89409	+	1.78130i	0.190647	+	0.0693898i	−0.244932	+	0.969540i	$0.578766\pi$
$660$		0			0
$661$	−2.01142	+	0.354668i	−0.0782352	+	0.0137950i	−0.212629	−	0.977133i	$-0.568202\pi$
$661$	−2.01142	+	0.354668i	−0.0782352	+	0.0137950i	0.134394	+	0.990928i	$0.457091\pi$
$662$	0.938595	−	2.01282i	0.0364795	−	0.0782306i
$663$	0.488067	+	5.57863i	0.0189549	+	0.216656i
$664$	1.14340			0.0443726
$665$		0			0
$666$	3.53461			0.136963
$667$	−2.37334	−	27.1274i	−0.0918961	−	1.05038i
$668$	2.58956	−	5.55333i	0.100193	−	0.214865i
$669$	12.1977	−	2.15079i	0.471591	−	0.0831543i
$670$		0			0
$671$	2.56984	+	0.935344i	0.0992075	+	0.0361086i
$672$	0.230675	+	0.0618092i	0.00889849	+	0.00238434i
$673$	−6.10515	−	22.7847i	−0.235336	−	0.878287i	−0.977997	−	0.208619i	$-0.933103\pi$
$673$	−6.10515	−	22.7847i	−0.235336	−	0.878287i	0.742661	−	0.669668i	$-0.233564\pi$
$674$	12.3607	+	14.7309i	0.476117	+	0.567414i
$675$		0			0
$676$	0.417998	−	0.723994i	0.0160769	−	0.0278459i
$677$	−7.86981	+	29.3705i	−0.302461	+	1.12880i	0.632648	+	0.774440i	$0.281968\pi$
$677$	−7.86981	+	29.3705i	−0.302461	+	1.12880i	−0.935109	+	0.354361i	$0.884699\pi$
$678$	−11.5279	+	5.37554i	−0.442726	+	0.206446i
$679$	−0.437520	+	2.48130i	−0.0167905	+	0.0952235i
$680$		0			0
$681$	−13.4498	+	4.89534i	−0.515398	+	0.187590i
$682$	8.01715	−	0.701410i	0.306993	−	0.0268584i
$683$	18.2757	−	18.2757i	0.699301	−	0.699301i	−0.264959	−	0.964260i	$-0.585358\pi$
$683$	18.2757	−	18.2757i	0.699301	−	0.699301i	0.964260	+	0.264959i	$0.0853585\pi$
$684$	8.00903	−	4.44933i	0.306233	−	0.170124i
$685$		0			0
$686$	−2.25743	+	2.69030i	−0.0861890	+	0.102716i
$687$	2.21322	+	1.03204i	0.0844395	+	0.0393748i
$688$	−3.76383	+	5.37530i	−0.143495	+	0.204932i
$689$	−2.92475	−	0.515713i	−0.111424	−	0.0196471i
$690$		0			0
$691$	6.89373	+	11.9403i	0.262250	+	0.454230i	0.966839	−	0.255385i	$-0.0822022\pi$
$691$	6.89373	+	11.9403i	0.262250	+	0.454230i	−0.704590	+	0.709615i	$0.748869\pi$
$692$	−22.9857	+	6.15900i	−0.873785	+	0.234130i
$693$	−0.701114	−	0.0613396i	−0.0266331	−	0.00233010i
$694$	−24.8312	+	20.8358i	−0.942578	+	0.790917i
$695$		0			0
$696$	−3.50754	+	2.02508i	−0.132953	+	0.0767605i
$697$	5.31678	+	11.4019i	0.201387	+	0.431877i
$698$	−17.1820	−	24.5384i	−0.650348	−	0.928793i
$699$	1.51280	+	8.57950i	0.0572193	+	0.324507i
$700$		0			0
$701$	33.2408	+	27.8924i	1.25549	+	1.05348i	0.996147	+	0.0876953i	$0.0279502\pi$
$701$	33.2408	+	27.8924i	1.25549	+	1.05348i	0.259342	+	0.965785i	$0.416494\pi$
$702$	11.9239	+	11.9239i	0.450039	+	0.450039i
$703$	6.69354	−	2.98771i	0.252452	−	0.112683i
$704$			1.32874i			0.0500789i
$705$		0			0
$706$	−3.48793	−	9.58300i	−0.131270	−	0.360661i
$707$	−3.25346	−	2.27810i	−0.122359	−	0.0856767i
$708$	2.69903	−	1.88988i	0.101436	−	0.0710260i
$709$	−16.9173	+	46.4799i	−0.635343	+	1.74559i	0.0305393	+	0.999534i	$0.490278\pi$
$709$	−16.9173	+	46.4799i	−0.635343	+	1.74559i	−0.665882	+	0.746057i	$0.731945\pi$
$710$		0			0
$711$	−8.12441	−	4.69063i	−0.304689	−	0.175912i
$712$	0.0744453	−	0.850913i	0.00278995	−	0.0318893i
$713$	−3.36346	+	38.4445i	−0.125963	+	1.43976i
$714$	−0.350404	−	0.202306i	−0.0131135	−	0.00757110i
$715$		0			0
$716$	−8.79766	+	24.1714i	−0.328784	+	0.903327i
$717$	−19.3652	+	13.5597i	−0.723206	+	0.506395i
$718$	13.6002	+	9.52297i	0.507555	+	0.355394i
$719$	−1.63364	−	4.48838i	−0.0609244	−	0.167388i	0.905496	−	0.424355i	$-0.139499\pi$
$719$	−1.63364	−	4.48838i	−0.0609244	−	0.167388i	−0.966420	+	0.256967i	$0.917277\pi$
$720$		0			0
$721$		−	1.78815i		−	0.0665941i
$722$	11.4059	−	15.1956i	0.424484	−	0.565520i
$723$	−1.80866	−	1.80866i	−0.0672649	−	0.0672649i
$724$	−13.4400	−	11.2775i	−0.499494	−	0.419125i
$725$		0			0
$726$	−1.51965	−	8.61839i	−0.0563997	−	0.319859i
$727$	24.9005	+	35.5616i	0.923509	+	1.31891i	0.947688	+	0.319199i	$0.103414\pi$
$727$	24.9005	+	35.5616i	0.923509	+	1.31891i	−0.0241790	+	0.999708i	$0.507697\pi$
$728$	−0.371432	−	0.796539i	−0.0137662	−	0.0295217i
$729$	8.76701	−	5.06164i	0.324704	−	0.187468i
$730$		0			0
$731$	8.51674	−	7.14639i	0.315003	−	0.264319i
$732$	1.94306	+	0.169996i	0.0718177	+	0.00628323i
$733$	35.3672	−	9.47661i	1.30632	−	0.350027i	0.462482	−	0.886629i	$-0.346959\pi$
$733$	35.3672	−	9.47661i	1.30632	−	0.350027i	0.843835	+	0.536602i	$0.180292\pi$
$734$	17.3239	+	30.0059i	0.639437	+	1.10754i
$735$		0			0
$736$	−6.27491	−	1.10644i	−0.231296	−	0.0407838i
$737$	−0.737923	+	1.05386i	−0.0271817	+	0.0388196i
$738$	14.1451	+	6.59597i	0.520688	+	0.242801i
$739$	22.9092	−	27.3021i	0.842729	−	1.00433i	−0.157131	−	0.987578i	$-0.550224\pi$
$739$	22.9092	−	27.3021i	0.842729	−	1.00433i	0.999860	−	0.0167473i	$-0.00533109\pi$
$740$		0			0
$741$	13.4551	+	5.15042i	0.494286	+	0.189205i
$742$	0.151732	−	0.151732i	0.00557026	−	0.00557026i
$743$	−8.85727	+	0.774911i	−0.324942	+	0.0284287i	−0.248460	−	0.968642i	$-0.579924\pi$
$743$	−8.85727	+	0.774911i	−0.324942	+	0.0284287i	−0.0764821	+	0.997071i	$0.524369\pi$
$744$	5.39367	−	1.96314i	0.197742	−	0.0719720i
$745$		0			0
$746$	−3.99588	+	22.6618i	−0.146300	+	0.829707i
$747$	−2.17814	+	1.01568i	−0.0796938	+	0.0371618i
$748$	0.582664	−	2.17453i	0.0213043	−	0.0795088i
$749$	1.35581	−	2.34833i	0.0495403	−	0.0858063i
$750$		0			0
$751$	29.7357	+	35.4376i	1.08507	+	1.29314i	0.953356	+	0.301849i	$0.0976040\pi$
$751$	29.7357	+	35.4376i	1.08507	+	1.29314i	0.131715	+	0.991288i	$0.457952\pi$
$752$	0.325264	+	1.21390i	0.0118611	+	0.0442664i
$753$	−7.07615	−	1.89605i	−0.257869	−	0.0690958i
$754$	14.0066	+	5.09798i	0.510090	+	0.185657i
$755$		0			0
$756$	−1.19989	+	0.211572i	−0.0436394	+	0.00769481i
$757$	−6.84300	+	14.6749i	−0.248713	+	0.533367i	−0.990540	−	0.137224i	$-0.956182\pi$
$757$	−6.84300	+	14.6749i	−0.248713	+	0.533367i	0.741827	+	0.670592i	$0.233960\pi$
$758$	−1.67034	−	19.0921i	−0.0606696	−	0.693457i
$759$	−8.02346			−0.291233
$760$		0			0
$761$	1.87464			0.0679557			0.0339778	−	0.999423i	$-0.489182\pi$
$761$	1.87464			0.0679557			0.0339778	+	0.999423i	$0.489182\pi$
$762$	−0.468415	−	5.35401i	−0.0169689	−	0.193955i
$763$	−0.210730	+	0.451911i	−0.00762893	+	0.0163603i
$764$	3.42589	−	0.604077i	0.123944	−	0.0218548i
$765$		0			0
$766$	23.2686	+	8.46907i	0.840728	+	0.306000i
$767$	−11.7128	−	3.13844i	−0.422925	−	0.113322i
$768$	0.245279	+	0.915394i	0.00885075	+	0.0330314i
$769$	22.0129	+	26.2340i	0.793807	+	0.946022i	0.999468	−	0.0326008i	$-0.0103790\pi$
$769$	22.0129	+	26.2340i	0.793807	+	0.946022i	−0.205661	+	0.978623i	$0.565935\pi$
$770$		0			0
$771$	−14.1812	+	24.5626i	−0.510725	+	0.884602i
$772$	−6.04874	+	22.5742i	−0.217699	+	0.812463i
$773$	16.0621	−	7.48989i	0.577714	−	0.269392i	−0.111721	−	0.993740i	$-0.535636\pi$
$773$	16.0621	−	7.48989i	0.577714	−	0.269392i	0.689436	+	0.724347i	$0.257859\pi$
$774$	2.39508	−	13.5831i	0.0860892	−	0.488236i
$775$		0			0
$776$	−9.39552	+	3.41969i	−0.337279	+	0.122760i
$777$	−0.400067	+	0.0350013i	−0.0143523	+	0.00125566i
$778$	−10.3598	+	10.3598i	−0.371415	+	0.371415i
$779$	32.3622	+	0.534423i	1.15949	+	0.0191477i
$780$		0			0
$781$	−4.39442	+	5.23707i	−0.157245	+	0.187397i
$782$	9.78391	+	4.56231i	0.349872	+	0.163148i
$783$	11.8521	−	16.9265i	0.423559	−	0.604905i
$784$	−6.83112	−	1.20451i	−0.243968	−	0.0430182i
$785$		0			0
$786$	1.35004	+	2.33834i	0.0481543	+	0.0834058i
$787$	−2.34890	+	0.629386i	−0.0837293	+	0.0224352i	−0.300440	−	0.953801i	$-0.597134\pi$
$787$	−2.34890	+	0.629386i	−0.0837293	+	0.0224352i	0.216711	+	0.976236i	$0.430467\pi$
$788$	10.5498	+	0.922988i	0.375821	+	0.0328801i
$789$	3.24483	−	2.72273i	0.115519	−	0.0969318i
$790$		0			0
$791$	−2.92909	+	1.69111i	−0.104147	+	0.0601291i
$792$	−1.18032	−	2.53121i	−0.0419409	−	0.0899425i
$793$	−4.11726	−	5.88005i	−0.146208	−	0.208807i
$794$	−2.93130	−	16.6242i	−0.104028	−	0.589971i
$795$		0			0
$796$	−20.2834	−	17.0198i	−0.718924	−	0.603249i
$797$	−25.0638	−	25.0638i	−0.887806	−	0.887806i	0.106506	−	0.994312i	$-0.466034\pi$
$797$	−25.0638	−	25.0638i	−0.887806	−	0.887806i	−0.994312	+	0.106506i	$0.966034\pi$
$798$	−0.862447	+	0.582909i	−0.0305303	+	0.0206348i
$799$		−	2.12922i		−	0.0753263i
$800$		0			0
$801$	0.614049	+	1.68709i	0.0216964	+	0.0596103i
$802$	21.2388	+	14.8716i	0.749967	+	0.525133i
$803$	2.26647	−	1.58700i	0.0799819	−	0.0560039i
$804$	−0.313830	+	0.862241i	−0.0110679	+	0.0304089i
$805$		0			0
$806$	−18.2938	−	10.5619i	−0.644370	−	0.372027i
$807$	−0.621525	+	7.10406i	−0.0218787	+	0.250075i
$808$	1.37368	−	15.7012i	0.0483258	−	0.552366i
$809$	21.3188	+	12.3084i	0.749529	+	0.432741i	0.825524	−	0.564367i	$-0.190880\pi$
$809$	21.3188	+	12.3084i	0.749529	+	0.432741i	−0.0759946	+	0.997108i	$0.524213\pi$
$810$		0			0
$811$	−6.40366	+	17.5939i	−0.224863	+	0.617806i	−0.999900	−	0.0141095i	$-0.995509\pi$
$811$	−6.40366	+	17.5939i	−0.224863	+	0.617806i	0.775038	+	0.631915i	$0.217731\pi$
$812$	−0.882197	+	0.617721i	−0.0309590	+	0.0216778i
$813$	−4.86344	−	3.40541i	−0.170568	−	0.119433i
$814$	−0.764230	−	2.09970i	−0.0267862	−	0.0735946i
$815$		0			0
$816$		−	1.60563i		−	0.0562082i
$817$	−6.94586	−	27.7471i	−0.243005	−	0.970748i
$818$	−18.0754	−	18.0754i	−0.631993	−	0.631993i
$819$	1.41513	+	1.18743i	0.0494485	+	0.0414923i
$820$		0			0
$821$	3.66649	+	20.7937i	0.127961	+	0.725705i	0.979505	+	0.201421i	$0.0645558\pi$
$821$	3.66649	+	20.7937i	0.127961	+	0.725705i	−0.851544	+	0.524284i	$0.824333\pi$
$822$	5.09159	+	7.27154i	0.177590	+	0.253624i
$823$	−6.60047	−	14.1547i	−0.230078	−	0.493403i	0.757046	−	0.653362i	$-0.226642\pi$
$823$	−6.60047	−	14.1547i	−0.230078	−	0.493403i	−0.987124	+	0.159958i	$0.948864\pi$
$824$	6.14527	−	3.54797i	0.214081	−	0.123600i
$825$		0			0
$826$	0.671159	−	0.563169i	0.0233526	−	0.0195952i
$827$	35.5088	+	3.10662i	1.23476	+	0.108028i	0.685782	−	0.727807i	$-0.259460\pi$
$827$	35.5088	+	3.10662i	1.23476	+	0.108028i	0.548981	+	0.835835i	$0.315016\pi$
$828$	12.9363	−	3.46627i	0.449568	−	0.120461i
$829$	−18.7471	−	32.4709i	−0.651114	−	1.12776i	−0.982853	−	0.184391i	$-0.940969\pi$
$829$	−18.7471	−	32.4709i	−0.651114	−	1.12776i	0.331739	−	0.943371i	$-0.392365\pi$
$830$		0			0
$831$	−0.299527	−	0.0528147i	−0.0103905	−	0.00183212i
$832$	2.00046	−	2.85695i	0.0693534	−	0.0990470i
$833$	10.6512	+	4.96672i	0.369041	+	0.172087i
$834$	10.3394	−	12.3220i	0.358023	−	0.426675i
$835$		0			0
$836$	−4.37475	−	3.79569i	−0.151304	−	0.131277i
$837$	−20.7069	+	20.7069i	−0.715735	+	0.715735i
$838$	7.68040	−	0.671948i	0.265315	−	0.0232121i
$839$	−0.671396	+	0.244368i	−0.0231792	+	0.00843653i	−0.353584	−	0.935403i	$-0.615037\pi$
$839$	−0.671396	+	0.244368i	−0.0231792	+	0.00843653i	0.330405	+	0.943839i	$0.392815\pi$
$840$		0			0
$841$	−1.86414	+	10.5720i	−0.0642806	+	0.364553i
$842$	11.7569	−	5.48231i	0.405168	−	0.188933i
$843$	5.98494	−	22.3361i	0.206132	−	0.769296i
$844$	4.94732	−	8.56901i	0.170294	−	0.294957i
$845$		0			0
$846$	−1.69792	−	2.02350i	−0.0583757	−	0.0695695i
$847$	−0.602281	−	2.24775i	−0.0206946	−	0.0772334i
$848$	0.822514	+	0.220392i	0.0282453	+	0.00756829i
$849$	9.86986	+	3.59234i	0.338733	+	0.123289i
$850$		0			0
$851$	10.5521	−	1.86062i	0.361721	−	0.0637812i
$852$	−2.06066	+	4.41909i	−0.0705969	+	0.151396i
$853$	1.28891	+	14.7323i	0.0441315	+	0.504426i	0.985805	+	0.167897i	$0.0536975\pi$
$853$	1.28891	+	14.7323i	0.0441315	+	0.504426i	−0.941673	+	0.336529i	$0.890747\pi$
$854$	0.518646			0.0177477
$855$		0			0
$856$	10.7606			0.367790
$857$	1.78224	+	20.3711i	0.0608802	+	0.695864i	0.963900	+	0.266265i	$0.0857896\pi$
$857$	1.78224	+	20.3711i	0.0608802	+	0.695864i	−0.903020	+	0.429599i	$0.858655\pi$
$858$	1.85606	−	3.98034i	0.0633649	−	0.135886i
$859$	−56.6346	+	9.98620i	−1.93235	+	0.340725i	−0.999794	−	0.0203086i	$-0.993535\pi$
$859$	−56.6346	+	9.98620i	−1.93235	+	0.340725i	−0.932553	+	0.361033i	$0.882424\pi$
$860$		0			0
$861$	−1.66634	−	0.606497i	−0.0567886	−	0.0206694i
$862$	21.1728	+	5.67324i	0.721149	+	0.193231i
$863$	−1.15517	−	4.31116i	−0.0393225	−	0.146754i	0.943473	−	0.331448i	$-0.107537\pi$
$863$	−1.15517	−	4.31116i	−0.0393225	−	0.146754i	−0.982796	+	0.184694i	$0.940870\pi$
$864$	−3.10787	−	3.70382i	−0.105732	−	0.126006i
$865$		0			0
$866$	−2.83737	+	4.91446i	−0.0964176	+	0.167000i
$867$	3.46566	−	12.9340i	0.117700	−	0.439263i
$868$	1.38326	−	0.645023i	0.0469508	−	0.0218935i
$869$	−1.02982	+	5.84042i	−0.0349343	+	0.198123i
$870$		0			0
$871$	3.17324	−	1.15496i	0.107521	−	0.0391344i
$872$	−1.97119	+	0.172457i	−0.0667530	+	0.00584013i
$873$	14.8604	−	14.8604i	0.502948	−	0.502948i
$874$	21.5677	−	17.4988i	0.729539	−	0.591906i
$875$		0			0
$876$	1.26845	−	1.51169i	0.0428571	−	0.0510751i
$877$	−33.3491	−	15.5509i	−1.12612	−	0.525118i	−0.231896	−	0.972740i	$-0.574493\pi$
$877$	−33.3491	−	15.5509i	−1.12612	−	0.525118i	−0.894223	+	0.447623i	$0.852271\pi$
$878$	−6.53182	+	9.32841i	−0.220438	+	0.314819i
$879$	−3.45226	−	0.608727i	−0.116442	−	0.0205319i
$880$		0			0
$881$	22.0547	+	38.1998i	0.743041	+	1.28699i	0.951104	+	0.308870i	$0.0999507\pi$
$881$	22.0547	+	38.1998i	0.743041	+	1.28699i	−0.208063	+	0.978115i	$0.566716\pi$
$882$	14.0830	−	3.77352i	0.474198	−	0.127061i
$883$	19.9905	+	1.74894i	0.672734	+	0.0588566i	0.418404	−	0.908261i	$-0.362590\pi$
$883$	19.9905	+	1.74894i	0.672734	+	0.0588566i	0.254330	+	0.967118i	$0.418145\pi$
$884$	−4.52661	+	3.79828i	−0.152246	+	0.127750i
$885$		0			0
$886$	−24.5287	+	14.1617i	−0.824058	+	0.475770i
$887$	−17.4755	−	37.4764i	−0.586771	−	1.25834i	−0.945721	−	0.324978i	$-0.894643\pi$
$887$	−17.4755	−	37.4764i	−0.586771	−	1.25834i	0.358950	−	0.933357i	$-0.383135\pi$
$888$	−0.914085	−	1.30545i	−0.0306747	−	0.0438080i
$889$	−0.248161	−	1.40739i	−0.00832306	−	0.0472024i
$890$		0			0
$891$	1.75444	+	1.47215i	0.0587760	+	0.0493189i
$892$	9.24162	+	9.24162i	0.309432	+	0.309432i
$893$	−4.92579	−	2.39673i	−0.164835	−	0.0802036i
$894$			8.90530i			0.297838i
$895$		0			0
$896$	0.0861875	+	0.236798i	0.00287932	+	0.00791088i
$897$	17.2513	+	12.0795i	0.576006	+	0.403324i
$898$	25.4580	−	17.8259i	0.849545	−	0.594857i
$899$	−8.85308	+	24.3236i	−0.295267	+	0.811238i
$900$		0			0
$901$	−1.24943	−	0.721357i	−0.0416245	−	0.0240319i
$902$	0.859919	−	9.82891i	0.0286322	−	0.327267i
$903$	−0.136581	+	1.56113i	−0.00454514	+	0.0519512i
$904$	−11.6236	−	6.71089i	−0.386595	−	0.223201i
$905$		0			0
$906$	6.30757	−	17.3299i	0.209555	−	0.575748i
$907$	−27.0450	+	18.9371i	−0.898014	+	0.628796i	−0.928740	−	0.370732i	$-0.879107\pi$
$907$	−27.0450	+	18.9371i	−0.898014	+	0.628796i	0.0307264	+	0.999528i	$0.490218\pi$
$908$	−12.3717	−	8.66279i	−0.410571	−	0.287485i
$909$	11.3305	+	31.1304i	0.375810	+	1.03253i
$910$		0			0
$911$			31.0023i			1.02715i	0.858045	+	0.513575i	$0.171679\pi$
$911$			31.0023i			1.02715i	−0.858045	+	0.513575i	$0.828321\pi$
$912$	−3.71450	−	1.80736i	−0.122999	−	0.0598476i
$913$	1.07430	+	1.07430i	0.0355541	+	0.0355541i
$914$	12.1627	+	10.2057i	0.402306	+	0.337575i
$915$		0			0
$916$	0.447460	+	2.53767i	0.0147845	+	0.0838471i
$917$	0.411810	+	0.588125i	0.0135992	+	0.0194216i
$918$	3.46198	+	7.42424i	0.114262	+	0.245036i
$919$	23.0915	−	13.3319i	0.761718	−	0.439778i	−0.0681941	−	0.997672i	$-0.521724\pi$
$919$	23.0915	−	13.3319i	0.761718	−	0.439778i	0.829912	+	0.557894i	$0.188390\pi$
$920$		0			0
$921$	−13.4944	+	11.3231i	−0.444655	+	0.373110i
$922$	−11.7908	−	1.03156i	−0.388309	−	0.0339726i
$923$	17.3331	−	4.64438i	0.570524	−	0.152872i
$924$	0.158660	+	0.274808i	0.00521954	+	0.00904052i
$925$		0			0
$926$	−0.471060	−	0.0830606i	−0.0154800	−	0.00272954i
$927$	−8.55484	+	12.2176i	−0.280978	+	0.401278i
$928$	−3.87332	−	1.80616i	−0.127148	−	0.0592901i
$929$	33.7624	−	40.2364i	1.10771	−	1.32011i	0.165075	−	0.986281i	$-0.447213\pi$
$929$	33.7624	−	40.2364i	1.10771	−	1.32011i	0.942632	−	0.333833i	$-0.108342\pi$
$930$		0			0
$931$	23.4795	−	19.0499i	0.769509	−	0.624336i
$932$	−6.50027	+	6.50027i	−0.212923	+	0.212923i
$933$	12.1419	−	1.06228i	0.397508	−	0.0347775i
$934$	14.3966	−	5.23992i	0.471070	−	0.171455i
$935$		0			0
$936$	−1.27297	+	7.21938i	−0.0416084	+	0.235973i
$937$	29.0607	−	13.5512i	0.949371	−	0.442699i	0.114670	−	0.993404i	$-0.463419\pi$
$937$	29.0607	−	13.5512i	0.949371	−	0.442699i	0.834700	+	0.550705i	$0.185641\pi$
$938$	−0.0631491	+	0.235676i	−0.00206189	+	0.00769509i
$939$	2.29444	−	3.97409i	0.0748763	−	0.129690i
$940$		0			0
$941$	30.0847	+	35.8536i	0.980734	+	1.16879i	0.985649	+	0.168805i	$0.0539908\pi$
$941$	30.0847	+	35.8536i	0.980734	+	1.16879i	−0.00491584	+	0.999988i	$0.501565\pi$
$942$	−5.89533	−	22.0017i	−0.192080	−	0.716854i
$943$	45.7004	+	12.2454i	1.48821	+	0.398764i
$944$	3.26712	+	1.18913i	0.106336	+	0.0387030i
$945$		0			0
$946$	−8.58680	+	1.51408i	−0.279181	+	0.0492271i
$947$	−11.3136	+	24.2620i	−0.367641	+	0.788410i	0.632265	+	0.774752i	$0.282125\pi$
$947$	−11.3136	+	24.2620i	−0.367641	+	0.788410i	−0.999907	+	0.0136577i	$0.995652\pi$
$948$	0.368647	+	4.21366i	0.0119731	+	0.136853i
$949$	−7.26242			−0.235748
$950$		0			0
$951$	20.1981			0.654968
$952$	−0.0372109	−	0.425322i	−0.00120601	−	0.0137848i
$953$	−3.39647	+	7.28375i	−0.110022	+	0.235944i	−0.953608	−	0.301051i	$-0.902663\pi$
$953$	−3.39647	+	7.28375i	−0.110022	+	0.235944i	0.843586	+	0.536994i	$0.180440\pi$
$954$	−1.76263	+	0.310800i	−0.0570673	+	0.0100625i
$955$		0			0
$956$	−23.4411	−	8.53188i	−0.758141	−	0.275941i
$957$	−5.19826	−	1.39287i	−0.168036	−	0.0450250i
$958$	−3.99506	−	14.9098i	−0.129075	−	0.481713i
$959$	1.51725	+	1.80819i	0.0489947	+	0.0583896i
$960$		0			0
$961$	2.84166	−	4.92189i	0.0916663	−	0.158771i
$962$	−1.51798	+	5.66517i	−0.0489416	+	0.182652i
$963$	−20.4985	+	9.55862i	−0.660556	+	0.308022i
$964$	0.468682	−	2.65803i	0.0150952	−	0.0856094i
$965$		0			0
$966$	−1.42988	+	0.520433i	−0.0460056	+	0.0167447i
$967$	−29.9244	+	2.61805i	−0.962304	+	0.0841907i	−0.557468	−	0.830199i	$-0.688227\pi$
$967$	−29.9244	+	2.61805i	−0.962304	+	0.0841907i	−0.404836	+	0.914389i	$0.632671\pi$
$968$	6.52973	−	6.52973i	0.209874	−	0.209874i
$969$	5.28636	+	4.58664i	0.169822	+	0.147344i
$970$		0			0
$971$	4.60320	−	5.48588i	0.147724	−	0.176050i	−0.687108	−	0.726555i	$-0.741120\pi$
$971$	4.60320	−	5.48588i	0.147724	−	0.176050i	0.834832	+	0.550505i	$0.185565\pi$
$972$	14.6264	+	6.82039i	0.469141	+	0.218764i
$973$	2.45328	−	3.50364i	0.0786485	−	0.112322i
$974$	−25.5709	−	4.50884i	−0.819345	−	0.144473i
$975$		0			0
$976$	1.02908	+	1.78242i	0.0329400	+	0.0570537i
$977$	−34.7082	+	9.30005i	−1.11042	+	0.297535i	−0.766999	−	0.641648i	$-0.778251\pi$
$977$	−34.7082	+	9.30005i	−1.11042	+	0.297535i	−0.343416	+	0.939183i	$0.611584\pi$
$978$	14.6754	+	1.28393i	0.469268	+	0.0410556i
$979$	0.869434	−	0.729542i	0.0277872	−	0.0233162i
$980$		0			0
$981$	3.60185	−	2.07953i	0.114998	−	0.0663943i
$982$	−0.0810513	−	0.173815i	−0.00258645	−	0.00554666i
$983$	28.4375	+	40.6130i	0.907016	+	1.29535i	0.955031	+	0.296507i	$0.0958218\pi$
$983$	28.4375	+	40.6130i	0.907016	+	1.29535i	−0.0480142	+	0.998847i	$0.515289\pi$
$984$	−1.22195	−	6.93004i	−0.0389544	−	0.220922i
$985$		0			0
$986$	5.54681	+	4.65432i	0.176646	+	0.148224i
$987$	0.212218	+	0.212218i	0.00675496	+	0.00675496i
$988$	3.69170	+	14.7475i	0.117449	+	0.469179i
$989$		−	41.8114i		−	1.32952i
$990$		0			0
$991$	−14.6435	−	40.2327i	−0.465166	−	1.27803i	−0.921553	−	0.388252i	$-0.873079\pi$
$991$	−14.6435	−	40.2327i	−0.465166	−	1.27803i	0.456387	−	0.889782i	$-0.349143\pi$
$992$	4.96134	+	3.47397i	0.157523	+	0.110299i
$993$	1.72409	−	1.20722i	0.0547122	−	0.0383099i
$994$	−0.443443	+	1.21835i	−0.0140651	+	0.0386437i
$995$		0			0
$996$	0.938413	+	0.541793i	0.0297347	+	0.0171674i
$997$	0.237717	−	2.71711i	0.00752856	−	0.0860519i	−0.991501	−	0.130100i	$-0.958470\pi$
$997$	0.237717	−	2.71711i	0.00752856	−	0.0860519i	0.999029	+	0.0440485i	$0.0140256\pi$
$998$	2.25441	−	25.7680i	0.0713622	−	0.815673i
$999$	7.04137	+	4.06534i	0.222779	+	0.128622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.193.4	yes	72
5.2	odd	4	inner	950.2.bb.c.307.3	yes	72
5.3	odd	4	inner	950.2.bb.c.307.4	yes	72
5.4	even	2	inner	950.2.bb.c.193.3	✓	72
19.13	odd	18	inner	950.2.bb.c.393.3	yes	72
95.13	even	36	inner	950.2.bb.c.507.3	yes	72
95.32	even	36	inner	950.2.bb.c.507.4	yes	72
95.89	odd	18	inner	950.2.bb.c.393.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.193.3	✓	72	5.4	even	2	inner
950.2.bb.c.193.4	yes	72	1.1	even	1	trivial
950.2.bb.c.307.3	yes	72	5.2	odd	4	inner
950.2.bb.c.307.4	yes	72	5.3	odd	4	inner
950.2.bb.c.393.3	yes	72	19.13	odd	18	inner
950.2.bb.c.393.4	yes	72	95.89	odd	18	inner
950.2.bb.c.507.3	yes	72	95.13	even	36	inner
950.2.bb.c.507.4	yes	72	95.32	even	36	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.400509 + 0.858895i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.890533 - 0.324128i) q^{6} +(-0.243409 - 0.0652212i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.35107 + 1.61014i) q^{9} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(-0.400509 + 0.858895i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.890533 - 0.324128i) q^{6} +(-0.243409 - 0.0652212i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.35107 + 1.61014i) q^{9} +(0.664372 - 1.15073i) q^{11} +(0.245279 - 0.915394i) q^{12} +(-3.16092 + 1.47396i) q^{13} +(0.0437586 - 0.248167i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-1.68782 + 0.147665i) q^{17} +(-1.48626 + 1.48626i) q^{18} +(-1.55826 + 4.07085i) q^{19} +(0.153506 - 0.182941i) q^{21} +(1.20425 + 0.561552i) q^{22} +(-3.65466 + 5.21940i) q^{23} +(0.933288 + 0.164564i) q^{24} +(-1.74385 - 3.02043i) q^{26} +(-4.67024 + 1.25139i) q^{27} +(0.251037 + 0.0219629i) q^{28} +(-3.27388 + 2.74711i) q^{29} +(5.24523 - 3.02834i) q^{31} +(0.422618 + 0.906308i) q^{32} +(0.722266 + 1.03150i) q^{33} +(-0.294206 - 1.66852i) q^{34} +(-1.61014 - 1.35107i) q^{36} +(-1.18909 - 1.18909i) q^{37} +(-4.19117 - 1.19753i) q^{38} -3.30524i q^{39} +(-2.53964 - 6.97759i) q^{41} +(0.195624 + 0.136977i) q^{42} +(-5.37530 + 3.76383i) q^{43} +(-0.454457 + 1.24861i) q^{44} +(-5.51806 - 3.18586i) q^{46} +(-0.109531 + 1.25194i) q^{47} +(-0.0825962 + 0.944079i) q^{48} +(-6.00718 - 3.46825i) q^{49} +(0.549157 - 1.50880i) q^{51} +(2.85695 - 2.00046i) q^{52} +(0.697532 + 0.488417i) q^{53} +(-1.65366 - 4.54340i) q^{54} +0.251996i q^{56} +(-2.87234 - 2.96879i) q^{57} +(-3.02199 - 3.02199i) q^{58} +(2.66338 + 2.23484i) q^{59} +(0.357395 + 2.02689i) q^{61} +(3.47397 + 4.96134i) q^{62} +(-0.223847 - 0.480042i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.964628 + 0.809419i) q^{66} +(-0.964545 - 0.0843868i) q^{67} +(1.63653 - 0.438507i) q^{68} +(-3.01919 - 5.22939i) q^{69} +(-5.06692 - 0.893436i) q^{71} +(1.20560 - 1.72177i) q^{72} +(1.88720 + 0.880018i) q^{73} +(1.08093 - 1.28820i) q^{74} +(0.827690 - 4.27959i) q^{76} +(-0.236766 + 0.236766i) q^{77} +(3.29266 - 0.288070i) q^{78} +(-4.19408 + 1.52652i) q^{79} +(-0.299305 + 1.69744i) q^{81} +(6.72970 - 3.13811i) q^{82} +(-0.295934 + 1.10444i) q^{83} +(-0.119406 + 0.206818i) q^{84} +(-4.21799 - 5.02681i) q^{86} +(-1.04826 - 3.91216i) q^{87} +(-1.28347 - 0.343904i) q^{88} +(0.802651 + 0.292141i) q^{89} +(0.865531 - 0.152616i) q^{91} +(2.69280 - 5.77473i) q^{92} +(0.500259 + 5.71798i) q^{93} -1.25672 q^{94} -0.947686 q^{96} +(-0.871427 - 9.96045i) q^{97} +(2.93149 - 6.28660i) q^{98} +(2.75045 - 0.484978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

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Database

Properties

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