LMFDB - Embedded newform 196.2.i.a.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(29,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("196.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.i (of order $7$, degree $6$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			57.3
Character	$\chi$	$=$	196.57
Dual form			196.2.i.a.141.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.851544 - 0.410082i) q^{3} +(2.34535 - 1.12946i) q^{5} +(-0.840460 - 2.50871i) q^{7} +(-1.31351 + 1.64709i) q^{9} +O(q^{10})$	\(q+(0.851544 - 0.410082i) q^{3} +(2.34535 - 1.12946i) q^{5} +(-0.840460 - 2.50871i) q^{7} +(-1.31351 + 1.64709i) q^{9} +(-0.485964 - 0.609379i) q^{11} +(0.758622 + 0.951282i) q^{13} +(1.53400 - 1.92358i) q^{15} +(0.551443 + 2.41603i) q^{17} +3.79988 q^{19} +(-1.74447 - 1.79162i) q^{21} +(0.252868 - 1.10789i) q^{23} +(1.10755 - 1.38883i) q^{25} +(-1.07401 + 4.70555i) q^{27} +(-0.0485207 - 0.212583i) q^{29} -8.42623 q^{31} +(-0.663715 - 0.319628i) q^{33} +(-4.80467 - 4.93455i) q^{35} +(2.23103 + 9.77480i) q^{37} +(1.03610 + 0.498962i) q^{39} +(-4.43973 + 2.13806i) q^{41} +(-1.24711 - 0.600576i) q^{43} +(-1.22032 + 5.34657i) q^{45} +(2.46780 + 3.09453i) q^{47} +(-5.58725 + 4.21694i) q^{49} +(1.46035 + 1.83122i) q^{51} +(3.07606 - 13.4771i) q^{53} +(-1.82803 - 0.880332i) q^{55} +(3.23577 - 1.55826i) q^{57} +(-11.4933 - 5.53489i) q^{59} +(2.35142 + 10.3023i) q^{61} +(5.23602 + 1.91090i) q^{63} +(2.85368 + 1.37426i) q^{65} -6.92619 q^{67} +(-0.238997 - 1.04711i) q^{69} +(3.01193 - 13.1961i) q^{71} +(-3.38342 + 4.24267i) q^{73} +(0.373597 - 1.63683i) q^{75} +(-1.12032 + 1.73130i) q^{77} +12.5580 q^{79} +(-0.391263 - 1.71423i) q^{81} +(-3.41036 + 4.27646i) q^{83} +(4.02215 + 5.04361i) q^{85} +(-0.128494 - 0.161126i) q^{87} +(3.09335 - 3.87894i) q^{89} +(1.74890 - 2.70268i) q^{91} +(-7.17530 + 3.45544i) q^{93} +(8.91207 - 4.29182i) q^{95} +2.71752 q^{97} +1.64202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9}+O(q^{10}) $ 24 * q + 8 * q^9	$ 24 q + 8 q^{9} - 9 q^{11} + 16 q^{15} - 7 q^{17} + 14 q^{19} - 19 q^{23} - 2 q^{25} - 21 q^{27} + 10 q^{29} + 14 q^{35} - 17 q^{37} - 22 q^{39} - 14 q^{41} + 2 q^{43} - 14 q^{45} + 7 q^{47} - 28 q^{49} - 26 q^{51} - 47 q^{53} - 17 q^{57} - 42 q^{61} - 21 q^{63} + 4 q^{65} + 28 q^{69} - 21 q^{71} - 21 q^{73} + 84 q^{75} - 21 q^{77} - 4 q^{79} + 38 q^{81} - 42 q^{83} + 62 q^{85} + 70 q^{87} - 28 q^{89} + 98 q^{91} + 35 q^{93} + 54 q^{95} + 112 q^{97} - 108 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 9 * q^11 + 16 * q^15 - 7 * q^17 + 14 * q^19 - 19 * q^23 - 2 * q^25 - 21 * q^27 + 10 * q^29 + 14 * q^35 - 17 * q^37 - 22 * q^39 - 14 * q^41 + 2 * q^43 - 14 * q^45 + 7 * q^47 - 28 * q^49 - 26 * q^51 - 47 * q^53 - 17 * q^57 - 42 * q^61 - 21 * q^63 + 4 * q^65 + 28 * q^69 - 21 * q^71 - 21 * q^73 + 84 * q^75 - 21 * q^77 - 4 * q^79 + 38 * q^81 - 42 * q^83 + 62 * q^85 + 70 * q^87 - 28 * q^89 + 98 * q^91 + 35 * q^93 + 54 * q^95 + 112 * q^97 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{6}{7}\right)$

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			0
$2$		0			0
$3$	0.851544	−	0.410082i	0.491639	−	0.236761i	−0.171602	−	0.985166i	$-0.554894\pi$
$3$	0.851544	−	0.410082i	0.491639	−	0.236761i	0.663242	+	0.748405i	$0.269180\pi$
$4$		0			0
$5$	2.34535	−	1.12946i	1.04887	−	0.505111i	0.171633	−	0.985161i	$-0.445096\pi$
$5$	2.34535	−	1.12946i	1.04887	−	0.505111i	0.877241	+	0.480050i	$0.159381\pi$
$6$		0			0
$7$	−0.840460	−	2.50871i	−0.317664	−	0.948203i
$7$	−0.840460	−	2.50871i	−0.317664	−	0.948203i
$8$		0			0
$9$	−1.31351	+	1.64709i	−0.437836	+	0.549029i
$10$		0			0
$11$	−0.485964	−	0.609379i	−0.146524	−	0.183735i	0.703154	−	0.711038i	$-0.251775\pi$
$11$	−0.485964	−	0.609379i	−0.146524	−	0.183735i	−0.849677	+	0.527303i	$0.823203\pi$
$12$		0			0
$13$	0.758622	+	0.951282i	0.210404	+	0.263838i	0.875824	−	0.482631i	$-0.160319\pi$
$13$	0.758622	+	0.951282i	0.210404	+	0.263838i	−0.665420	+	0.746469i	$0.731747\pi$
$14$		0			0
$15$	1.53400	−	1.92358i	0.396077	−	0.496665i
$16$		0			0
$17$	0.551443	+	2.41603i	0.133745	+	0.585973i	0.996734	+	0.0807517i	$0.0257321\pi$
$17$	0.551443	+	2.41603i	0.133745	+	0.585973i	−0.862990	+	0.505222i	$0.831411\pi$
$18$		0			0
$19$	3.79988			0.871752			0.435876	−	0.900007i	$-0.356439\pi$
$19$	3.79988			0.871752			0.435876	+	0.900007i	$0.356439\pi$
$20$		0			0
$21$	−1.74447	−	1.79162i	−0.380674	−	0.390964i
$22$		0			0
$23$	0.252868	−	1.10789i	0.0527267	−	0.231011i	−0.941698	−	0.336459i	$-0.890771\pi$
$23$	0.252868	−	1.10789i	0.0527267	−	0.231011i	0.994425	+	0.105448i	$0.0336278\pi$
$24$		0			0
$25$	1.10755	−	1.38883i	0.221510	−	0.277765i
$26$		0			0
$27$	−1.07401	+	4.70555i	−0.206694	+	0.905584i
$28$		0			0
$29$	−0.0485207	−	0.212583i	−0.00901007	−	0.0394757i	0.970223	−	0.242213i	$-0.0778733\pi$
$29$	−0.0485207	−	0.212583i	−0.00901007	−	0.0394757i	−0.979233	+	0.202737i	$0.935016\pi$
$30$		0			0
$31$	−8.42623			−1.51339			−0.756697	−	0.653765i	$-0.773188\pi$
$31$	−8.42623			−1.51339			−0.756697	+	0.653765i	$0.773188\pi$
$32$		0			0
$33$	−0.663715	−	0.319628i	−0.115538	−	0.0556402i
$34$		0			0
$35$	−4.80467	−	4.93455i	−0.812138	−	0.834090i
$36$		0			0
$37$	2.23103	+	9.77480i	0.366780	+	1.60697i	0.735566	+	0.677453i	$0.236916\pi$
$37$	2.23103	+	9.77480i	0.366780	+	1.60697i	−0.368786	+	0.929514i	$0.620227\pi$
$38$		0			0
$39$	1.03610	+	0.498962i	0.165910	+	0.0798978i
$40$		0			0
$41$	−4.43973	+	2.13806i	−0.693369	+	0.333909i	−0.747161	−	0.664643i	$-0.768584\pi$
$41$	−4.43973	+	2.13806i	−0.693369	+	0.333909i	0.0537916	+	0.998552i	$0.482869\pi$
$42$		0			0
$43$	−1.24711	−	0.600576i	−0.190182	−	0.0915871i	0.336369	−	0.941730i	$-0.390801\pi$
$43$	−1.24711	−	0.600576i	−0.190182	−	0.0915871i	−0.526552	+	0.850143i	$0.676515\pi$
$44$		0			0
$45$	−1.22032	+	5.34657i	−0.181914	+	0.797019i
$46$		0			0
$47$	2.46780	+	3.09453i	0.359966	+	0.451383i	0.928531	−	0.371255i	$-0.121073\pi$
$47$	2.46780	+	3.09453i	0.359966	+	0.451383i	−0.568565	+	0.822638i	$0.692501\pi$
$48$		0			0
$49$	−5.58725	+	4.21694i	−0.798179	+	0.602420i
$50$		0			0
$51$	1.46035	+	1.83122i	0.204490	+	0.256422i
$52$		0			0
$53$	3.07606	−	13.4771i	0.422530	−	1.85122i	−0.0948833	−	0.995488i	$-0.530248\pi$
$53$	3.07606	−	13.4771i	0.422530	−	1.85122i	0.517413	−	0.855736i	$-0.326895\pi$
$54$		0			0
$55$	−1.82803	−	0.880332i	−0.246491	−	0.118704i
$56$		0			0
$57$	3.23577	−	1.55826i	0.428588	−	0.206397i
$58$		0			0
$59$	−11.4933	−	5.53489i	−1.49630	−	0.720582i	−0.506396	−	0.862301i	$-0.669023\pi$
$59$	−11.4933	−	5.53489i	−1.49630	−	0.720582i	−0.989907	+	0.141719i	$0.954737\pi$
$60$		0			0
$61$	2.35142	+	10.3023i	0.301069	+	1.31907i	0.868517	+	0.495659i	$0.165073\pi$
$61$	2.35142	+	10.3023i	0.301069	+	1.31907i	−0.567448	+	0.823409i	$0.692069\pi$
$62$		0			0
$63$	5.23602	+	1.91090i	0.659676	+	0.240751i
$64$		0			0
$65$	2.85368	+	1.37426i	0.353955	+	0.170456i
$66$		0			0
$67$	−6.92619			−0.846169			−0.423085	−	0.906090i	$-0.639053\pi$
$67$	−6.92619			−0.846169			−0.423085	+	0.906090i	$0.639053\pi$
$68$		0			0
$69$	−0.238997	−	1.04711i	−0.0287718	−	0.126058i
$70$		0			0
$71$	3.01193	−	13.1961i	0.357450	−	1.56609i	−0.402071	−	0.915608i	$-0.631710\pi$
$71$	3.01193	−	13.1961i	0.357450	−	1.56609i	0.759521	−	0.650483i	$-0.225433\pi$
$72$		0			0
$73$	−3.38342	+	4.24267i	−0.395999	+	0.496567i	−0.939360	−	0.342932i	$-0.888580\pi$
$73$	−3.38342	+	4.24267i	−0.395999	+	0.496567i	0.543361	+	0.839499i	$0.317151\pi$
$74$		0			0
$75$	0.373597	−	1.63683i	0.0431392	−	0.189005i
$76$		0			0
$77$	−1.12032	+	1.73130i	−0.127673	+	0.197300i
$78$		0			0
$79$	12.5580			1.41289			0.706445	−	0.707768i	$-0.250298\pi$
$79$	12.5580			1.41289			0.706445	+	0.707768i	$0.250298\pi$
$80$		0			0
$81$	−0.391263	−	1.71423i	−0.0434737	−	0.190471i
$82$		0			0
$83$	−3.41036	+	4.27646i	−0.374336	+	0.469403i	−0.932940	−	0.360032i	$-0.882766\pi$
$83$	−3.41036	+	4.27646i	−0.374336	+	0.469403i	0.558604	+	0.829435i	$0.311337\pi$
$84$		0			0
$85$	4.02215	+	5.04361i	0.436263	+	0.547056i
$86$		0			0
$87$	−0.128494	−	0.161126i	−0.0137760	−	0.0172746i
$88$		0			0
$89$	3.09335	−	3.87894i	0.327894	−	0.411166i	−0.590371	−	0.807132i	$-0.701019\pi$
$89$	3.09335	−	3.87894i	0.327894	−	0.411166i	0.918265	+	0.395966i	$0.129590\pi$
$90$		0			0
$91$	1.74890	−	2.70268i	0.183335	−	0.283318i
$92$		0			0
$93$	−7.17530	+	3.45544i	−0.744044	+	0.358313i
$94$		0			0
$95$	8.91207	−	4.29182i	0.914359	−	0.440332i
$96$		0			0
$97$	2.71752			0.275922			0.137961	−	0.990438i	$-0.455945\pi$
$97$	2.71752			0.275922			0.137961	+	0.990438i	$0.455945\pi$
$98$		0			0
$99$	1.64202			0.165029
$100$		0			0
$101$	14.6382	−	7.04939i	1.45656	−	0.701441i	0.472837	−	0.881150i	$-0.343230\pi$
$101$	14.6382	−	7.04939i	1.45656	−	0.701441i	0.983720	+	0.179709i	$0.0575156\pi$
$102$		0			0
$103$	7.10606	−	3.42210i	0.700181	−	0.337190i	−0.0496980	−	0.998764i	$-0.515826\pi$
$103$	7.10606	−	3.42210i	0.700181	−	0.337190i	0.749879	+	0.661575i	$0.230112\pi$
$104$		0			0
$105$	−6.11496	−	2.23167i	−0.596759	−	0.217789i
$106$		0			0
$107$	0.574237	−	0.720070i	0.0555135	−	0.0696118i	−0.753300	−	0.657678i	$-0.771539\pi$
$107$	0.574237	−	0.720070i	0.0555135	−	0.0696118i	0.808813	+	0.588066i	$0.200110\pi$
$108$		0			0
$109$	−6.41120	−	8.03939i	−0.614081	−	0.770033i	0.373417	−	0.927664i	$-0.378186\pi$
$109$	−6.41120	−	8.03939i	−0.614081	−	0.770033i	−0.987498	+	0.157630i	$0.949615\pi$
$110$		0			0
$111$	5.90830	+	7.40877i	0.560791	+	0.703209i
$112$		0			0
$113$	11.4025	−	14.2983i	1.07265	−	1.34507i	0.137630	−	0.990484i	$-0.456051\pi$
$113$	11.4025	−	14.2983i	1.07265	−	1.34507i	0.935025	−	0.354583i	$-0.115377\pi$
$114$		0			0
$115$	−0.658253	−	2.88399i	−0.0613824	−	0.268934i
$116$		0			0
$117$	−2.56330			−0.236977
$118$		0			0
$119$	5.59765	−	3.41399i	0.513136	−	0.312960i
$120$		0			0
$121$	2.31255	−	10.1319i	0.210232	−	0.921085i
$122$		0			0
$123$	−2.90385	+	3.64131i	−0.261831	+	0.328326i
$124$		0			0
$125$	−1.86730	+	8.18118i	−0.167016	+	0.731747i
$126$		0			0
$127$	4.69681	+	20.5781i	0.416775	+	1.82601i	0.550305	+	0.834964i	$0.314512\pi$
$127$	4.69681	+	20.5781i	0.416775	+	1.82601i	−0.133530	+	0.991045i	$0.542631\pi$
$128$		0			0
$129$	−1.30826			−0.115185
$130$		0			0
$131$	−2.07037	−	0.997039i	−0.180889	−	0.0871117i	0.341247	−	0.939974i	$-0.389151\pi$
$131$	−2.07037	−	0.997039i	−0.180889	−	0.0871117i	−0.522137	+	0.852862i	$0.674865\pi$
$132$		0			0
$133$	−3.19365	−	9.53280i	−0.276924	−	0.826598i
$134$		0			0
$135$	2.79581	+	12.2492i	0.240625	+	1.05425i
$136$		0			0
$137$	1.30886	+	0.630314i	0.111824	+	0.0538514i	0.488959	−	0.872307i	$-0.337377\pi$
$137$	1.30886	+	0.630314i	0.111824	+	0.0538514i	−0.377136	+	0.926158i	$0.623091\pi$
$138$		0			0
$139$	−8.09817	+	3.89987i	−0.686878	+	0.330783i	−0.744563	−	0.667552i	$-0.767342\pi$
$139$	−8.09817	+	3.89987i	−0.686878	+	0.330783i	0.0576854	+	0.998335i	$0.481628\pi$
$140$		0			0
$141$	3.37045	+	1.62312i	0.283843	+	0.136692i
$142$		0			0
$143$	0.211029	−	0.924578i	0.0176471	−	0.0773171i
$144$		0			0
$145$	−0.353903	−	0.443780i	−0.0293901	−	0.0368540i
$146$		0			0
$147$	−3.02850	+	5.88215i	−0.249787	+	0.485151i
$148$		0			0
$149$	−8.94342	−	11.2147i	−0.732673	−	0.918743i	0.266307	−	0.963888i	$-0.414196\pi$
$149$	−8.94342	−	11.2147i	−0.732673	−	0.918743i	−0.998980	+	0.0451449i	$0.985625\pi$
$150$		0			0
$151$	−2.83651	+	12.4276i	−0.230832	+	1.01134i	0.718120	+	0.695919i	$0.245003\pi$
$151$	−2.83651	+	12.4276i	−0.230832	+	1.01134i	−0.948952	+	0.315421i	$0.897854\pi$
$152$		0			0
$153$	−4.70374	−	2.26520i	−0.380275	−	0.183131i
$154$		0			0
$155$	−19.7625	+	9.51711i	−1.58736	+	0.764433i
$156$		0			0
$157$	−8.92378	−	4.29747i	−0.712195	−	0.342975i	0.0424586	−	0.999098i	$-0.486481\pi$
$157$	−8.92378	−	4.29747i	−0.712195	−	0.342975i	−0.754654	+	0.656123i	$0.772195\pi$
$158$		0			0
$159$	−2.90732	−	12.7378i	−0.230565	−	1.01017i
$160$		0			0
$161$	−2.99189	+	0.296763i	−0.235794	+	0.0233882i
$162$		0			0
$163$	−2.46877	−	1.18889i	−0.193369	−	0.0931214i	0.334694	−	0.942327i	$-0.391367\pi$
$163$	−2.46877	−	1.18889i	−0.193369	−	0.0931214i	−0.528063	+	0.849205i	$0.677081\pi$
$164$		0			0
$165$	−1.91766			−0.149289
$166$		0			0
$167$	0.707407	+	3.09935i	0.0547408	+	0.239835i	0.994895	−	0.100914i	$-0.0321766\pi$
$167$	0.707407	+	3.09935i	0.0547408	+	0.239835i	−0.940154	+	0.340749i	$0.889319\pi$
$168$		0			0
$169$	2.56334	−	11.2307i	0.197180	−	0.863903i
$170$		0			0
$171$	−4.99118	+	6.25874i	−0.381685	+	0.478618i
$172$		0			0
$173$	−2.57945	+	11.3013i	−0.196112	+	0.859221i	0.777112	+	0.629362i	$0.216684\pi$
$173$	−2.57945	+	11.3013i	−0.196112	+	0.859221i	−0.973224	+	0.229859i	$0.926173\pi$
$174$		0			0
$175$	−4.41501	−	1.61127i	−0.333744	−	0.121801i
$176$		0			0
$177$	−12.0568			−0.906247
$178$		0			0
$179$	2.01494	+	8.82801i	0.150603	+	0.659837i	0.992710	+	0.120526i	$0.0384580\pi$
$179$	2.01494	+	8.82801i	0.150603	+	0.659837i	−0.842107	+	0.539311i	$0.818685\pi$
$180$		0			0
$181$	13.0097	−	16.3137i	0.967006	−	1.21259i	−0.0101251	−	0.999949i	$-0.503223\pi$
$181$	13.0097	−	16.3137i	0.967006	−	1.21259i	0.977131	−	0.212638i	$-0.0682056\pi$
$182$		0			0
$183$	6.22711	+	7.80855i	0.460321	+	0.577224i
$184$		0			0
$185$	16.2728	+	20.4055i	1.19640	+	1.50024i
$186$		0			0
$187$	1.20430	−	1.51014i	0.0880669	−	0.110432i
$188$		0			0
$189$	12.7075	−	1.26045i	0.924337	−	0.0916840i
$190$		0			0
$191$	6.93377	−	3.33913i	0.501710	−	0.241611i	−0.165872	−	0.986147i	$-0.553044\pi$
$191$	6.93377	−	3.33913i	0.501710	−	0.241611i	0.667582	+	0.744537i	$0.267329\pi$
$192$		0			0
$193$	−8.27975	+	3.98732i	−0.595989	+	0.287013i	−0.707459	−	0.706755i	$-0.750159\pi$
$193$	−8.27975	+	3.98732i	−0.595989	+	0.287013i	0.111470	+	0.993768i	$0.464444\pi$
$194$		0			0
$195$	2.99359			0.214376
$196$		0			0
$197$	−19.8283			−1.41271			−0.706356	−	0.707857i	$-0.749662\pi$
$197$	−19.8283			−1.41271			−0.706356	+	0.707857i	$0.749662\pi$
$198$		0			0
$199$	13.2449	−	6.37841i	0.938906	−	0.452154i	0.0991231	−	0.995075i	$-0.468396\pi$
$199$	13.2449	−	6.37841i	0.938906	−	0.452154i	0.839783	+	0.542922i	$0.182682\pi$
$200$		0			0
$201$	−5.89796	+	2.84031i	−0.416010	+	0.200340i
$202$		0			0
$203$	−0.492530	+	0.300392i	−0.0345688	+	0.0210834i
$204$		0			0
$205$	−7.99788	+	10.0290i	−0.558596	+	0.700457i
$206$		0			0
$207$	1.49264	+	1.87172i	0.103746	+	0.130093i
$208$		0			0
$209$	−1.84660	−	2.31557i	−0.127732	−	0.160171i
$210$		0			0
$211$	−2.27767	+	2.85611i	−0.156801	+	0.196623i	−0.854026	−	0.520230i	$-0.825846\pi$
$211$	−2.27767	+	2.85611i	−0.156801	+	0.196623i	0.697225	+	0.716852i	$0.254418\pi$
$212$		0			0
$213$	−2.84670	−	12.4722i	−0.195053	−	0.854582i
$214$		0			0
$215$	−3.60324			−0.245739
$216$		0			0
$217$	7.08191	+	21.1390i	0.480751	+	1.43501i
$218$		0			0
$219$	−1.14129	+	5.00030i	−0.0771210	+	0.337889i
$220$		0			0
$221$	−1.87999	+	2.35743i	−0.126462	+	0.158578i
$222$		0			0
$223$	1.72900	−	7.57526i	0.115783	−	0.507277i	−0.883465	−	0.468497i	$-0.844796\pi$
$223$	1.72900	−	7.57526i	0.115783	−	0.507277i	0.999248	−	0.0387799i	$-0.0123471\pi$
$224$		0			0
$225$	0.832740	+	3.64847i	0.0555160	+	0.243231i
$226$		0			0
$227$	−1.69058			−0.112208			−0.0561038	−	0.998425i	$-0.517868\pi$
$227$	−1.69058			−0.112208			−0.0561038	+	0.998425i	$0.517868\pi$
$228$		0			0
$229$	−6.53887	−	3.14895i	−0.432101	−	0.208089i	0.205174	−	0.978726i	$-0.434224\pi$
$229$	−6.53887	−	3.14895i	−0.432101	−	0.208089i	−0.637275	+	0.770637i	$0.719938\pi$
$230$		0			0
$231$	−0.244029	+	1.93370i	−0.0160559	+	0.127228i
$232$		0			0
$233$	−5.26978	−	23.0884i	−0.345235	−	1.51257i	−0.787854	−	0.615862i	$-0.788808\pi$
$233$	−5.26978	−	23.0884i	−0.345235	−	1.51257i	0.442619	−	0.896710i	$-0.354049\pi$
$234$		0			0
$235$	9.28303	+	4.47047i	0.605558	+	0.291621i
$236$		0			0
$237$	10.6937	−	5.14983i	0.694632	−	0.334517i
$238$		0			0
$239$	−23.8178	−	11.4700i	−1.54065	−	0.741936i	−0.545294	−	0.838245i	$-0.683582\pi$
$239$	−23.8178	−	11.4700i	−1.54065	−	0.741936i	−0.995351	+	0.0963091i	$0.969296\pi$
$240$		0			0
$241$	−0.879955	+	3.85533i	−0.0566829	+	0.248344i	−0.995329	−	0.0965368i	$-0.969223\pi$
$241$	−0.879955	+	3.85533i	−0.0566829	+	0.248344i	0.938647	+	0.344881i	$0.112081\pi$
$242$		0			0
$243$	−10.0641	−	12.6200i	−0.645612	−	0.809572i
$244$		0			0
$245$	−8.34121	+	16.2008i	−0.532900	+	1.03503i
$246$		0			0
$247$	2.88267	+	3.61476i	0.183420	+	0.230002i
$248$		0			0
$249$	−1.15038	+	5.04013i	−0.0729021	+	0.319405i
$250$		0			0
$251$	−17.5791	−	8.46567i	−1.10959	−	0.534348i	−0.212926	−	0.977068i	$-0.568299\pi$
$251$	−17.5791	−	8.46567i	−1.10959	−	0.534348i	−0.896660	+	0.442720i	$0.854014\pi$
$252$		0			0
$253$	−0.798009	+	0.384301i	−0.0501704	+	0.0241608i
$254$		0			0
$255$	5.49333	+	2.64545i	0.344006	+	0.165664i
$256$		0			0
$257$	5.43698	+	23.8210i	0.339150	+	1.48591i	0.800844	+	0.598873i	$0.204385\pi$
$257$	5.43698	+	23.8210i	0.339150	+	1.48591i	−0.461694	+	0.887039i	$0.652758\pi$
$258$		0			0
$259$	22.6470	−	13.8124i	1.40722	−	0.858258i
$260$		0			0
$261$	0.413876	+	0.199312i	0.0256183	+	0.0123371i
$262$		0			0
$263$	23.7909			1.46701			0.733506	−	0.679683i	$-0.237883\pi$
$263$	23.7909			1.46701			0.733506	+	0.679683i	$0.237883\pi$
$264$		0			0
$265$	−8.00745	−	35.0829i	−0.491894	−	2.15513i
$266$		0			0
$267$	1.04344	−	4.57161i	0.0638575	−	0.279778i
$268$		0			0
$269$	1.41144	−	1.76990i	0.0860573	−	0.107912i	−0.736939	−	0.675959i	$-0.763729\pi$
$269$	1.41144	−	1.76990i	0.0860573	−	0.107912i	0.822996	+	0.568047i	$0.192301\pi$
$270$		0			0
$271$	−0.941745	+	4.12605i	−0.0572069	+	0.250640i	−0.995443	−	0.0953549i	$-0.969601\pi$
$271$	−0.941745	+	4.12605i	−0.0572069	+	0.250640i	0.938236	+	0.345995i	$0.112459\pi$
$272$		0			0
$273$	0.380945	−	3.01864i	0.0230559	−	0.182697i
$274$		0			0
$275$	−1.38455			−0.0834916
$276$		0			0
$277$	−1.54439	−	6.76642i	−0.0927935	−	0.406555i	0.907103	−	0.420908i	$-0.138288\pi$
$277$	−1.54439	−	6.76642i	−0.0927935	−	0.406555i	−0.999897	+	0.0143527i	$0.995431\pi$
$278$		0			0
$279$	11.0679	−	13.8787i	0.662619	−	0.830898i
$280$		0			0
$281$	9.85616	+	12.3592i	0.587969	+	0.737290i	0.983449	−	0.181184i	$-0.0579931\pi$
$281$	9.85616	+	12.3592i	0.587969	+	0.737290i	−0.395480	+	0.918475i	$0.629422\pi$
$282$		0			0
$283$	14.4361	+	18.1022i	0.858135	+	1.07607i	0.996324	+	0.0856612i	$0.0273003\pi$
$283$	14.4361	+	18.1022i	0.858135	+	1.07607i	−0.138189	+	0.990406i	$0.544128\pi$
$284$		0			0
$285$	5.82902	−	7.30936i	0.345281	−	0.432969i
$286$		0			0
$287$	9.09519	+	9.34104i	0.536872	+	0.551384i
$288$		0			0
$289$	9.78336	−	4.71142i	0.575492	−	0.277142i
$290$		0			0
$291$	2.31409	−	1.11441i	0.135654	−	0.0653277i
$292$		0			0
$293$	30.6398			1.78999			0.894997	−	0.446071i	$-0.147177\pi$
$293$	30.6398			1.78999			0.894997	+	0.446071i	$0.147177\pi$
$294$		0			0
$295$	−33.2074			−1.93341
$296$		0			0
$297$	3.38940	−	1.63225i	0.196673	−	0.0947126i
$298$		0			0
$299$	1.24575	−	0.599919i	0.0720433	−	0.0346942i
$300$		0			0
$301$	−0.458526	+	3.63340i	−0.0264290	+	0.209426i
$302$		0			0
$303$	9.57426	−	12.0057i	0.550027	−	0.689712i
$304$		0			0
$305$	17.1509	+	21.5066i	0.982059	+	1.23146i
$306$		0			0
$307$	9.58343	+	12.0172i	0.546955	+	0.685860i	0.976087	−	0.217382i	$-0.0697516\pi$
$307$	9.58343	+	12.0172i	0.546955	+	0.685860i	−0.429131	+	0.903242i	$0.641180\pi$
$308$		0			0
$309$	4.64779	−	5.82814i	0.264403	−	0.331551i
$310$		0			0
$311$	−7.11468	−	31.1714i	−0.403436	−	1.76757i	−0.613310	−	0.789842i	$-0.710163\pi$
$311$	−7.11468	−	31.1714i	−0.403436	−	1.76757i	0.209874	−	0.977728i	$-0.432695\pi$
$312$		0			0
$313$	−21.4624			−1.21313			−0.606564	−	0.795034i	$-0.707453\pi$
$313$	−21.4624			−1.21313			−0.606564	+	0.795034i	$0.707453\pi$
$314$		0			0
$315$	14.4386	−	1.43215i	0.813524	−	0.0806925i
$316$		0			0
$317$	1.87310	−	8.20658i	0.105204	−	0.460928i	−0.894695	−	0.446678i	$-0.852607\pi$
$317$	1.87310	−	8.20658i	0.105204	−	0.460928i	0.999898	−	0.0142495i	$-0.00453590\pi$
$318$		0			0
$319$	−0.105964	+	0.132875i	−0.00593287	+	0.00743958i
$320$		0			0
$321$	0.193700	−	0.848656i	0.0108113	−	0.0473673i
$322$		0			0
$323$	2.09542	+	9.18062i	0.116592	+	0.510823i
$324$		0			0
$325$	2.16138			0.119892
$326$		0			0
$327$	−8.75623	−	4.21678i	−0.484220	−	0.233188i
$328$		0			0
$329$	5.68918	−	8.79183i	0.313655	−	0.484709i
$330$		0			0
$331$	−3.80953	−	16.6906i	−0.209391	−	0.917401i	−0.964973	−	0.262347i	$-0.915503\pi$
$331$	−3.80953	−	16.6906i	−0.209391	−	0.917401i	0.755583	−	0.655053i	$-0.227354\pi$
$332$		0			0
$333$	−19.0304	−	9.16458i	−1.04286	−	0.502216i
$334$		0			0
$335$	−16.2444	+	7.82288i	−0.887525	+	0.427410i
$336$		0			0
$337$	9.91724	+	4.77589i	0.540226	+	0.260159i	0.684039	−	0.729446i	$-0.260222\pi$
$337$	9.91724	+	4.77589i	0.540226	+	0.260159i	−0.143812	+	0.989605i	$0.545936\pi$
$338$		0			0
$339$	3.84626	−	16.8515i	0.208900	−	0.915250i
$340$		0			0
$341$	4.09484	+	5.13477i	0.221748	+	0.278063i
$342$		0			0
$343$	15.2750	+	10.4726i	0.824770	+	0.565469i
$344$		0			0
$345$	−1.74321	−	2.18591i	−0.0938511	−	0.117686i
$346$		0			0
$347$	−6.22548	+	27.2756i	−0.334201	+	1.46423i	0.476709	+	0.879061i	$0.341830\pi$
$347$	−6.22548	+	27.2756i	−0.334201	+	1.46423i	−0.810910	+	0.585171i	$0.801027\pi$
$348$		0			0
$349$	9.42280	+	4.53778i	0.504391	+	0.242902i	0.668735	−	0.743501i	$-0.266836\pi$
$349$	9.42280	+	4.53778i	0.504391	+	0.242902i	−0.164344	+	0.986403i	$0.552551\pi$
$350$		0			0
$351$	−5.29108	+	2.54805i	−0.282417	+	0.136005i
$352$		0			0
$353$	20.7374	+	9.98658i	1.10374	+	0.531532i	0.894832	−	0.446403i	$-0.147295\pi$
$353$	20.7374	+	9.98658i	1.10374	+	0.531532i	0.208906	+	0.977936i	$0.433010\pi$
$354$		0			0
$355$	−7.84049	−	34.3514i	−0.416130	−	1.82318i
$356$		0			0
$357$	3.36663	−	5.20266i	0.178181	−	0.275354i
$358$		0			0
$359$	−3.78350	−	1.82204i	−0.199685	−	0.0961634i	0.331369	−	0.943501i	$-0.392490\pi$
$359$	−3.78350	−	1.82204i	−0.199685	−	0.0961634i	−0.531054	+	0.847338i	$0.678204\pi$
$360$		0			0
$361$	−4.56091			−0.240048
$362$		0			0
$363$	−2.18569	−	9.57613i	−0.114719	−	0.502616i
$364$		0			0
$365$	−3.14337	+	13.7720i	−0.164532	+	0.720860i
$366$		0			0
$367$	−16.0054	+	20.0702i	−0.835476	+	1.04765i	0.162664	+	0.986682i	$0.447991\pi$
$367$	−16.0054	+	20.0702i	−0.835476	+	1.04765i	−0.998139	+	0.0609721i	$0.980580\pi$
$368$		0			0
$369$	2.31005	−	10.1210i	0.120256	−	0.526878i
$370$		0			0
$371$	−36.3955	+	3.61003i	−1.88956	+	0.187423i
$372$		0			0
$373$	−31.7337			−1.64311			−0.821554	−	0.570130i	$-0.806893\pi$
$373$	−31.7337			−1.64311			−0.821554	+	0.570130i	$0.806893\pi$
$374$		0			0
$375$	1.76487	+	7.73238i	0.0911373	+	0.399298i
$376$		0			0
$377$	0.165418	−	0.207427i	0.00851945	−	0.0106830i
$378$		0			0
$379$	8.77396	+	11.0022i	0.450688	+	0.565145i	0.954325	−	0.298771i	$-0.0965765\pi$
$379$	8.77396	+	11.0022i	0.450688	+	0.565145i	−0.503637	+	0.863915i	$0.668005\pi$
$380$		0			0
$381$	12.4382	+	15.5971i	0.637230	+	0.799062i
$382$		0			0
$383$	−11.1962	+	14.0396i	−0.572100	+	0.717390i	−0.980743	−	0.195304i	$-0.937431\pi$
$383$	−11.1962	+	14.0396i	−0.572100	+	0.717390i	0.408643	+	0.912694i	$0.366002\pi$
$384$		0			0
$385$	−0.672113	+	5.32588i	−0.0342540	+	0.271432i
$386$		0			0
$387$	2.62729	−	1.26524i	0.133553	−	0.0643156i
$388$		0			0
$389$	−12.4187	+	5.98054i	−0.629654	+	0.303225i	−0.721359	−	0.692561i	$-0.756482\pi$
$389$	−12.4187	+	5.98054i	−0.629654	+	0.303225i	0.0917057	+	0.995786i	$0.470768\pi$
$390$		0			0
$391$	2.81613			0.142418
$392$		0			0
$393$	−2.17188			−0.109557
$394$		0			0
$395$	29.4530	−	14.1838i	1.48194	−	0.713666i
$396$		0			0
$397$	−9.05659	+	4.36143i	−0.454537	+	0.218894i	−0.647122	−	0.762387i	$-0.724027\pi$
$397$	−9.05659	+	4.36143i	−0.454537	+	0.218894i	0.192584	+	0.981280i	$0.438313\pi$
$398$		0			0
$399$	−6.62876	−	6.80794i	−0.331853	−	0.340823i
$400$		0			0
$401$	1.21833	−	1.52774i	0.0608406	−	0.0762917i	−0.750480	−	0.660893i	$-0.770178\pi$
$401$	1.21833	−	1.52774i	0.0608406	−	0.0762917i	0.811321	+	0.584601i	$0.198749\pi$
$402$		0			0
$403$	−6.39232	−	8.01572i	−0.318424	−	0.399291i
$404$		0			0
$405$	−2.85382	−	3.57857i	−0.141807	−	0.177821i
$406$		0			0
$407$	4.87236	−	6.10974i	0.241514	−	0.302849i
$408$		0			0
$409$	−5.72371	−	25.0772i	−0.283019	−	1.23999i	−0.893900	−	0.448266i	$-0.852042\pi$
$409$	−5.72371	−	25.0772i	−0.283019	−	1.23999i	0.610881	−	0.791723i	$-0.290816\pi$
$410$		0			0
$411$	1.37303			0.0677267
$412$		0			0
$413$	−4.22576	+	33.4853i	−0.207936	+	1.64770i
$414$		0			0
$415$	−3.16841	+	13.8817i	−0.155531	+	0.681426i
$416$		0			0
$417$	−5.29668	+	6.64183i	−0.259380	+	0.325252i
$418$		0			0
$419$	−7.38704	+	32.3647i	−0.360880	+	1.58112i	0.390085	+	0.920779i	$0.372446\pi$
$419$	−7.38704	+	32.3647i	−0.360880	+	1.58112i	−0.750965	+	0.660342i	$0.770411\pi$
$420$		0			0
$421$	3.47750	+	15.2359i	0.169483	+	0.742553i	0.986206	+	0.165523i	$0.0529313\pi$
$421$	3.47750	+	15.2359i	0.169483	+	0.742553i	−0.816723	+	0.577030i	$0.804212\pi$
$422$		0			0
$423$	−8.33844			−0.405429
$424$		0			0
$425$	3.96620	+	1.91002i	0.192389	+	0.0926495i
$426$		0			0
$427$	23.8691	−	14.5577i	1.15511	−	0.704495i
$428$		0			0
$429$	−0.199452	−	0.873858i	−0.00962965	−	0.0421903i
$430$		0			0
$431$	−10.2808	−	4.95099i	−0.495211	−	0.238481i	0.169572	−	0.985518i	$-0.445762\pi$
$431$	−10.2808	−	4.95099i	−0.495211	−	0.238481i	−0.664783	+	0.747037i	$0.731476\pi$
$432$		0			0
$433$	−19.8640	+	9.56599i	−0.954602	+	0.459712i	−0.845297	−	0.534296i	$-0.820577\pi$
$433$	−19.8640	+	9.56599i	−0.954602	+	0.459712i	−0.109305	+	0.994008i	$0.534862\pi$
$434$		0			0
$435$	−0.483351	−	0.232769i	−0.0231749	−	0.0111604i
$436$		0			0
$437$	0.960869	−	4.20984i	0.0459646	−	0.201384i
$438$		0			0
$439$	−9.77396	−	12.2562i	−0.466485	−	0.584954i	0.491821	−	0.870696i	$-0.336331\pi$
$439$	−9.77396	−	12.2562i	−0.466485	−	0.584954i	−0.958307	+	0.285742i	$0.907760\pi$
$440$		0			0
$441$	0.393230	−	14.7417i	0.0187252	−	0.701985i
$442$		0			0
$443$	−1.79895	−	2.25581i	−0.0854706	−	0.107177i	0.737258	−	0.675612i	$-0.236120\pi$
$443$	−1.79895	−	2.25581i	−0.0854706	−	0.107177i	−0.822728	+	0.568435i	$0.807549\pi$
$444$		0			0
$445$	2.87388	−	12.5913i	0.136235	−	0.596885i
$446$		0			0
$447$	−12.2147	−	5.88227i	−0.577734	−	0.278222i
$448$		0			0
$449$	−12.4127	+	5.97766i	−0.585794	+	0.282103i	−0.703213	−	0.710979i	$-0.748252\pi$
$449$	−12.4127	+	5.97766i	−0.585794	+	0.282103i	0.117419	+	0.993082i	$0.462538\pi$
$450$		0			0
$451$	3.46044	+	1.66646i	0.162946	+	0.0784705i
$452$		0			0
$453$	2.68091	+	11.7458i	0.125960	+	0.551867i
$454$		0			0
$455$	1.04921	−	8.31406i	0.0491879	−	0.389769i
$456$		0			0
$457$	1.56378	+	0.753077i	0.0731506	+	0.0352275i	0.470101	−	0.882612i	$-0.344217\pi$
$457$	1.56378	+	0.753077i	0.0731506	+	0.0352275i	−0.396951	+	0.917840i	$0.629932\pi$
$458$		0			0
$459$	−11.9610			−0.558292
$460$		0			0
$461$	1.19290	+	5.22642i	0.0555587	+	0.243419i	0.995080	−	0.0990709i	$-0.0315871\pi$
$461$	1.19290	+	5.22642i	0.0555587	+	0.243419i	−0.939522	+	0.342489i	$0.888730\pi$
$462$		0			0
$463$	7.13118	−	31.2438i	0.331414	−	1.45202i	−0.484980	−	0.874525i	$-0.661173\pi$
$463$	7.13118	−	31.2438i	0.331414	−	1.45202i	0.816394	−	0.577495i	$-0.195970\pi$
$464$		0			0
$465$	−12.9258	+	16.2085i	−0.599421	+	0.751651i
$466$		0			0
$467$	−2.53999	+	11.1284i	−0.117537	+	0.514963i	0.881544	+	0.472102i	$0.156504\pi$
$467$	−2.53999	+	11.1284i	−0.117537	+	0.514963i	−0.999081	+	0.0428612i	$0.986353\pi$
$468$		0			0
$469$	5.82119	+	17.3758i	0.268798	+	0.802341i
$470$		0			0
$471$	−9.36131			−0.431346
$472$		0			0
$473$	0.240071	+	1.05182i	0.0110385	+	0.0483628i
$474$		0			0
$475$	4.20856	−	5.27737i	0.193102	−	0.242142i
$476$		0			0
$477$	18.1576	+	22.7689i	0.831378	+	1.04251i
$478$		0			0
$479$	−7.02826	−	8.81316i	−0.321129	−	0.402684i	0.594897	−	0.803802i	$-0.297193\pi$
$479$	−7.02826	−	8.81316i	−0.321129	−	0.402684i	−0.916026	+	0.401119i	$0.868622\pi$
$480$		0			0
$481$	−7.60608	+	9.53773i	−0.346808	+	0.434883i
$482$		0			0
$483$	−2.42603	+	1.47963i	−0.110388	+	0.0673255i
$484$		0			0
$485$	6.37355	−	3.06934i	0.289408	−	0.139372i
$486$		0			0
$487$	−11.4424	+	5.51035i	−0.518503	+	0.249698i	−0.674785	−	0.738015i	$-0.735764\pi$
$487$	−11.4424	+	5.51035i	−0.518503	+	0.249698i	0.156282	+	0.987713i	$0.450049\pi$
$488$		0			0
$489$	−2.58981			−0.117115
$490$		0			0
$491$	−15.9215			−0.718528			−0.359264	−	0.933236i	$-0.616972\pi$
$491$	−15.9215			−0.718528			−0.359264	+	0.933236i	$0.616972\pi$
$492$		0			0
$493$	0.486851	−	0.234455i	0.0219267	−	0.0105593i
$494$		0			0
$495$	3.85112	−	1.85460i	0.173095	−	0.0833581i
$496$		0			0
$497$	−35.6366	+	3.53476i	−1.59852	+	0.158556i
$498$		0			0
$499$	3.21852	−	4.03590i	0.144081	−	0.180672i	−0.704555	−	0.709650i	$-0.748853\pi$
$499$	3.21852	−	4.03590i	0.144081	−	0.180672i	0.848636	+	0.528978i	$0.177425\pi$
$500$		0			0
$501$	1.87338	+	2.34914i	0.0836963	+	0.104952i
$502$		0			0
$503$	14.1329	+	17.7221i	0.630156	+	0.790191i	0.989734	−	0.142924i	$-0.0456505\pi$
$503$	14.1329	+	17.7221i	0.630156	+	0.790191i	−0.359577	+	0.933115i	$0.617079\pi$
$504$		0			0
$505$	26.3698	−	33.0667i	1.17344	−	1.47145i
$506$		0			0
$507$	−2.42272	−	10.6146i	−0.107597	−	0.471413i
$508$		0			0
$509$	31.2491			1.38509			0.692547	−	0.721373i	$-0.256489\pi$
$509$	31.2491			1.38509			0.692547	+	0.721373i	$0.256489\pi$
$510$		0			0
$511$	13.4873	+	4.92222i	0.596641	+	0.217746i
$512$		0			0
$513$	−4.08112	+	17.8805i	−0.180186	+	0.789445i
$514$		0			0
$515$	12.8011	−	16.0521i	0.564084	−	0.707339i
$516$		0			0
$517$	0.686478	−	3.00766i	0.0301913	−	0.132277i
$518$		0			0
$519$	2.43795	+	10.6813i	0.107014	+	0.468859i
$520$		0			0
$521$	11.8554			0.519395			0.259698	−	0.965690i	$-0.416377\pi$
$521$	11.8554			0.519395			0.259698	+	0.965690i	$0.416377\pi$
$522$		0			0
$523$	11.0646	+	5.32842i	0.483820	+	0.232996i	0.659862	−	0.751387i	$-0.270615\pi$
$523$	11.0646	+	5.32842i	0.483820	+	0.232996i	−0.176041	+	0.984383i	$0.556329\pi$
$524$		0			0
$525$	−4.42033	+	0.438448i	−0.192919	+	0.0191355i
$526$		0			0
$527$	−4.64658	−	20.3580i	−0.202408	−	0.886809i
$528$		0			0
$529$	19.5588	+	9.41903i	0.850383	+	0.409523i
$530$		0			0
$531$	24.2130	−	11.6604i	1.05076	−	0.506018i
$532$		0			0
$533$	−5.40198	−	2.60146i	−0.233986	−	0.112682i
$534$		0			0
$535$	0.533496	−	2.33740i	0.0230650	−	0.101055i
$536$		0			0
$537$	5.33602	+	6.69115i	0.230266	+	0.288745i
$538$		0			0
$539$	5.28492	+	1.35547i	0.227638	+	0.0583844i
$540$		0			0
$541$	11.3044	+	14.1753i	0.486016	+	0.609444i	0.963011	−	0.269461i	$-0.0868457\pi$
$541$	11.3044	+	14.1753i	0.486016	+	0.609444i	−0.476996	+	0.878906i	$0.658274\pi$
$542$		0			0
$543$	4.38841	−	19.2269i	0.188325	−	0.825105i
$544$		0			0
$545$	−24.1167	−	11.6140i	−1.03305	−	0.497489i
$546$		0			0
$547$	12.7546	−	6.14231i	0.545349	−	0.262626i	−0.140861	−	0.990029i	$-0.544987\pi$
$547$	12.7546	−	6.14231i	0.545349	−	0.262626i	0.686210	+	0.727403i	$0.259273\pi$
$548$		0			0
$549$	−20.0573	−	9.65910i	−0.856026	−	0.412240i
$550$		0			0
$551$	−0.184373	−	0.807790i	−0.00785455	−	0.0344130i
$552$		0			0
$553$	−10.5545	−	31.5045i	−0.448824	−	1.33971i
$554$		0			0
$555$	22.2250	+	10.7030i	0.943398	+	0.454316i
$556$		0			0
$557$	13.8952			0.588760			0.294380	−	0.955688i	$-0.404887\pi$
$557$	13.8952			0.588760			0.294380	+	0.955688i	$0.404887\pi$
$558$		0			0
$559$	−0.374768	−	1.64196i	−0.0158510	−	0.0694477i
$560$		0			0
$561$	0.406231	−	1.77981i	0.0171511	−	0.0751437i
$562$		0			0
$563$	−21.2749	+	26.6778i	−0.896629	+	1.12434i	0.0950335	+	0.995474i	$0.469704\pi$
$563$	−21.2749	+	26.6778i	−0.896629	+	1.12434i	−0.991662	+	0.128863i	$0.958867\pi$
$564$		0			0
$565$	10.5935	−	46.4131i	0.445672	−	1.95262i
$566$		0			0
$567$	−3.97168	+	2.42231i	−0.166795	+	0.101728i
$568$		0			0
$569$	44.4879			1.86503			0.932515	−	0.361131i	$-0.117609\pi$
$569$	44.4879			1.86503			0.932515	+	0.361131i	$0.117609\pi$
$570$		0			0
$571$	−5.54235	−	24.2826i	−0.231940	−	1.01620i	−0.948028	−	0.318186i	$-0.896926\pi$
$571$	−5.54235	−	24.2826i	−0.231940	−	1.01620i	0.716088	−	0.698010i	$-0.245931\pi$
$572$		0			0
$573$	4.53510	−	5.68683i	0.189456	−	0.237571i
$574$		0			0
$575$	−1.25860	−	1.57823i	−0.0524872	−	0.0658168i
$576$		0			0
$577$	17.8735	+	22.4127i	0.744084	+	0.933052i	0.999429	−	0.0337980i	$-0.0107603\pi$
$577$	17.8735	+	22.4127i	0.744084	+	0.933052i	−0.255344	+	0.966850i	$0.582189\pi$
$578$		0			0
$579$	−5.41544	+	6.79075i	−0.225058	+	0.282214i
$580$		0			0
$581$	13.5947	+	4.96142i	0.564002	+	0.205834i
$582$		0			0
$583$	−9.70753	+	4.67490i	−0.402045	+	0.193615i
$584$		0			0
$585$	−6.01186	+	2.89516i	−0.248560	+	0.119700i
$586$		0			0
$587$	−2.32588			−0.0959993			−0.0479997	−	0.998847i	$-0.515285\pi$
$587$	−2.32588			−0.0959993			−0.0479997	+	0.998847i	$0.515285\pi$
$588$		0			0
$589$	−32.0186			−1.31931
$590$		0			0
$591$	−16.8847	+	8.13125i	−0.694544	+	0.334475i
$592$		0			0
$593$	−23.7923	+	11.4577i	−0.977031	+	0.470513i	−0.853083	−	0.521775i	$-0.825270\pi$
$593$	−23.7923	+	11.4577i	−0.977031	+	0.470513i	−0.123948	+	0.992289i	$0.539556\pi$
$594$		0			0
$595$	9.27250	−	14.3294i	0.380136	−	0.587446i
$596$		0			0
$597$	8.66295	−	10.8630i	0.354551	−	0.444593i
$598$		0			0
$599$	10.1357	+	12.7098i	0.414134	+	0.519307i	0.944522	−	0.328447i	$-0.106525\pi$
$599$	10.1357	+	12.7098i	0.414134	+	0.519307i	−0.530388	+	0.847755i	$0.677954\pi$
$600$		0			0
$601$	6.87076	+	8.61566i	0.280264	+	0.351440i	0.901961	−	0.431818i	$-0.142128\pi$
$601$	6.87076	+	8.61566i	0.280264	+	0.351440i	−0.621697	+	0.783258i	$0.713556\pi$
$602$		0			0
$603$	9.09762	−	11.4081i	0.370484	−	0.464572i
$604$		0			0
$605$	−6.01990	−	26.3749i	−0.244744	−	1.07229i
$606$		0			0
$607$	2.48019			0.100668			0.0503339	−	0.998732i	$-0.483971\pi$
$607$	2.48019			0.100668			0.0503339	+	0.998732i	$0.483971\pi$
$608$		0			0
$609$	−0.296225	+	0.457775i	−0.0120037	+	0.0185500i
$610$		0			0
$611$	−1.07164	+	4.69515i	−0.0433538	+	0.189946i
$612$		0			0
$613$	27.8061	−	34.8678i	1.12308	−	1.40830i	0.221779	−	0.975097i	$-0.428814\pi$
$613$	27.8061	−	34.8678i	1.12308	−	1.40830i	0.901299	−	0.433198i	$-0.142615\pi$
$614$		0			0
$615$	−2.69783	+	11.8199i	−0.108787	+	0.476626i
$616$		0			0
$617$	−7.19816	−	31.5372i	−0.289787	−	1.26964i	−0.884818	−	0.465937i	$-0.845717\pi$
$617$	−7.19816	−	31.5372i	−0.289787	−	1.26964i	0.595031	−	0.803703i	$-0.297140\pi$
$618$		0			0
$619$	−41.1289			−1.65311			−0.826554	−	0.562857i	$-0.809702\pi$
$619$	−41.1289			−1.65311			−0.826554	+	0.562857i	$0.809702\pi$
$620$		0			0
$621$	4.94164	+	2.37977i	0.198301	+	0.0954969i
$622$		0			0
$623$	−12.3310	−	4.50022i	−0.494030	−	0.180298i
$624$		0			0
$625$	6.83726	+	29.9560i	0.273490	+	1.19824i
$626$		0			0
$627$	−2.52204	−	1.21455i	−0.100721	−	0.0485044i
$628$		0			0
$629$	−22.3859	+	10.7805i	−0.892585	+	0.429846i
$630$		0			0
$631$	18.8071	+	9.05704i	0.748700	+	0.360555i	0.769008	−	0.639239i	$-0.220750\pi$
$631$	18.8071	+	9.05704i	0.748700	+	0.360555i	−0.0203082	+	0.999794i	$0.506465\pi$
$632$		0			0
$633$	−0.768299	+	3.36614i	−0.0305371	+	0.133792i
$634$		0			0
$635$	34.2579	+	42.9580i	1.35948	+	1.70474i
$636$		0			0
$637$	−8.25012	−	2.11599i	−0.326882	−	0.0838385i
$638$		0			0
$639$	17.7790	+	22.2941i	0.703325	+	0.881942i
$640$		0			0
$641$	6.52223	−	28.5758i	0.257613	−	1.12867i	−0.666183	−	0.745788i	$-0.732073\pi$
$641$	6.52223	−	28.5758i	0.257613	−	1.12867i	0.923796	−	0.382886i	$-0.125070\pi$
$642$		0			0
$643$	18.6245	+	8.96907i	0.734477	+	0.353705i	0.763443	−	0.645875i	$-0.223507\pi$
$643$	18.6245	+	8.96907i	0.734477	+	0.353705i	−0.0289663	+	0.999580i	$0.509222\pi$
$644$		0			0
$645$	−3.06832	+	1.47763i	−0.120815	+	0.0581815i
$646$		0			0
$647$	−5.84080	−	2.81278i	−0.229626	−	0.110582i	0.315534	−	0.948914i	$-0.397816\pi$
$647$	−5.84080	−	2.81278i	−0.229626	−	0.110582i	−0.545159	+	0.838333i	$0.683531\pi$
$648$		0			0
$649$	2.21249	+	9.69355i	0.0868478	+	0.380505i
$650$		0			0
$651$	14.6993	+	15.0966i	0.576110	+	0.591682i
$652$		0			0
$653$	−14.4107	−	6.93985i	−0.563936	−	0.271577i	0.130120	−	0.991498i	$-0.458464\pi$
$653$	−14.4107	−	6.93985i	−0.563936	−	0.271577i	−0.694056	+	0.719921i	$0.744178\pi$
$654$		0			0
$655$	−5.98187			−0.233731
$656$		0			0
$657$	−2.54391	−	11.1456i	−0.0992472	−	0.434830i
$658$		0			0
$659$	5.26855	−	23.0830i	0.205234	−	0.899188i	−0.762455	−	0.647041i	$-0.776006\pi$
$659$	5.26855	−	23.0830i	0.205234	−	0.899188i	0.967689	−	0.252147i	$-0.0811366\pi$
$660$		0			0
$661$	−15.5781	+	19.5344i	−0.605919	+	0.759799i	−0.986287	−	0.165036i	$-0.947226\pi$
$661$	−15.5781	+	19.5344i	−0.605919	+	0.759799i	0.380368	+	0.924835i	$0.375797\pi$
$662$		0			0
$663$	−0.634154	+	2.77841i	−0.0246285	+	0.107904i
$664$		0			0
$665$	−18.2572	−	18.7507i	−0.707983	−	0.727120i
$666$		0			0
$667$	−0.247788			−0.00959437
$668$		0			0
$669$	−1.63416	−	7.15970i	−0.0631801	−	0.276810i
$670$		0			0
$671$	5.13527	−	6.43943i	0.198245	−	0.248591i
$672$		0			0
$673$	13.4323	+	16.8436i	0.517777	+	0.649271i	0.970135	−	0.242565i	$-0.0779887\pi$
$673$	13.4323	+	16.8436i	0.517777	+	0.649271i	−0.452358	+	0.891836i	$0.649417\pi$
$674$		0			0
$675$	5.34567	+	6.70326i	0.205755	+	0.258009i
$676$		0			0
$677$	18.8228	−	23.6031i	0.723421	−	0.907141i	−0.275105	−	0.961414i	$-0.588713\pi$
$677$	18.8228	−	23.6031i	0.723421	−	0.907141i	0.998526	+	0.0542732i	$0.0172842\pi$
$678$		0			0
$679$	−2.28397	−	6.81747i	−0.0876506	−	0.261631i
$680$		0			0
$681$	−1.43960	+	0.693276i	−0.0551657	+	0.0265664i
$682$		0			0
$683$	33.6594	−	16.2095i	1.28794	−	0.620239i	0.340522	−	0.940237i	$-0.389396\pi$
$683$	33.6594	−	16.2095i	1.28794	−	0.620239i	0.947418	+	0.319997i	$0.103682\pi$
$684$		0			0
$685$	3.78166			0.144490
$686$		0			0
$687$	−6.85947			−0.261705
$688$		0			0
$689$	15.1541	−	7.29784i	0.577326	−	0.278025i
$690$		0			0
$691$	18.9828	−	9.14163i	0.722139	−	0.347764i	−0.0364480	−	0.999336i	$-0.511604\pi$
$691$	18.9828	−	9.14163i	0.722139	−	0.347764i	0.758587	+	0.651572i	$0.225890\pi$
$692$		0			0
$693$	−1.38005	−	4.11935i	−0.0524238	−	0.156481i
$694$		0			0
$695$	−14.5883	+	18.2932i	−0.553366	+	0.693900i
$696$		0			0
$697$	−7.61388	−	9.54750i	−0.288396	−	0.361637i
$698$		0			0
$699$	−13.9556	−	17.4998i	−0.527849	−	0.661902i
$700$		0			0
$701$	8.68862	−	10.8952i	0.328165	−	0.411506i	−0.590190	−	0.807265i	$-0.700947\pi$
$701$	8.68862	−	10.8952i	0.328165	−	0.411506i	0.918354	+	0.395759i	$0.129518\pi$
$702$		0			0
$703$	8.47766	+	37.1431i	0.319741	+	1.40088i
$704$		0			0
$705$	9.73817			0.366761
$706$		0			0
$707$	−29.9877	−	30.7983i	−1.12780	−	1.15829i
$708$		0			0
$709$	−6.64005	+	29.0919i	−0.249372	+	1.09257i	0.682814	+	0.730592i	$0.260756\pi$
$709$	−6.64005	+	29.0919i	−0.249372	+	1.09257i	−0.932186	+	0.361979i	$0.882101\pi$
$710$		0			0
$711$	−16.4951	+	20.6842i	−0.618614	+	0.775718i
$712$		0			0
$713$	−2.13072	+	9.33531i	−0.0797962	+	0.349610i
$714$		0			0
$715$	−0.549339	−	2.40681i	−0.0205441	−	0.0900096i
$716$		0			0
$717$	−24.9856			−0.933103
$718$		0			0
$719$	31.3854	+	15.1144i	1.17048	+	0.563673i	0.915123	−	0.403174i	$-0.132093\pi$
$719$	31.3854	+	15.1144i	1.17048	+	0.563673i	0.255356	+	0.966847i	$0.417807\pi$
$720$		0			0
$721$	−14.5574	−	14.9509i	−0.542147	−	0.556801i
$722$		0			0
$723$	0.831683	+	3.64384i	0.0309306	+	0.135516i
$724$		0			0
$725$	−0.348980	−	0.168060i	−0.0129608	−	0.00624159i
$726$		0			0
$727$	−33.3512	+	16.0611i	−1.23693	+	0.595672i	−0.933977	−	0.357334i	$-0.883686\pi$
$727$	−33.3512	+	16.0611i	−1.23693	+	0.595672i	−0.302950	+	0.953006i	$0.597971\pi$
$728$		0			0
$729$	−8.99268	−	4.33065i	−0.333062	−	0.160394i
$730$		0			0
$731$	0.763300	−	3.34424i	0.0282317	−	0.123691i
$732$		0			0
$733$	−5.35852	−	6.71937i	−0.197921	−	0.248186i	0.672960	−	0.739679i	$-0.265023\pi$
$733$	−5.35852	−	6.71937i	−0.197921	−	0.248186i	−0.870881	+	0.491493i	$0.836451\pi$
$734$		0			0
$735$	−0.459239	+	17.2163i	−0.0169393	+	0.635033i
$736$		0			0
$737$	3.36588	+	4.22068i	0.123984	+	0.155471i
$738$		0			0
$739$	−11.0868	+	48.5743i	−0.407833	+	1.78683i	0.186329	+	0.982487i	$0.440341\pi$
$739$	−11.0868	+	48.5743i	−0.407833	+	1.78683i	−0.594162	+	0.804346i	$0.702516\pi$
$740$		0			0
$741$	3.93707	+	1.89599i	0.144632	+	0.0696511i
$742$		0			0
$743$	34.9309	−	16.8218i	1.28149	−	0.617133i	0.335717	−	0.941963i	$-0.391021\pi$
$743$	34.9309	−	16.8218i	1.28149	−	0.617133i	0.945772	+	0.324830i	$0.105307\pi$
$744$		0			0
$745$	−33.6421	−	16.2012i	−1.23255	−	0.593565i
$746$		0			0
$747$	−2.56416	−	11.2343i	−0.0938179	−	0.411043i
$748$		0			0
$749$	−2.28907	−	0.835403i	−0.0836408	−	0.0305250i
$750$		0			0
$751$	−19.1112	−	9.20346i	−0.697377	−	0.335839i	0.0513843	−	0.998679i	$-0.483637\pi$
$751$	−19.1112	−	9.20346i	−0.697377	−	0.335839i	−0.748761	+	0.662840i	$0.769351\pi$
$752$		0			0
$753$	−18.4410			−0.672029
$754$		0			0
$755$	7.38385	+	32.3508i	0.268726	+	1.17737i
$756$		0			0
$757$	1.03471	−	4.53337i	0.0376072	−	0.164768i	−0.952637	−	0.304109i	$-0.901641\pi$
$757$	1.03471	−	4.53337i	0.0376072	−	0.164768i	0.990244	+	0.139341i	$0.0444984\pi$
$758$		0			0
$759$	−0.521945	+	0.654498i	−0.0189454	+	0.0237568i
$760$		0			0
$761$	−4.09329	+	17.9339i	−0.148382	+	0.650102i	0.844954	+	0.534840i	$0.179628\pi$
$761$	−4.09329	+	17.9339i	−0.148382	+	0.650102i	−0.993335	+	0.115262i	$0.963229\pi$
$762$		0			0
$763$	−14.7801	+	22.8406i	−0.535077	+	0.826886i
$764$		0			0
$765$	−13.5904			−0.491362
$766$		0			0
$767$	−3.45385	−	15.1323i	−0.124711	−	0.546395i
$768$		0			0
$769$	−24.7461	+	31.0307i	−0.892368	+	1.11899i	0.0999140	+	0.994996i	$0.468143\pi$
$769$	−24.7461	+	31.0307i	−0.892368	+	1.11899i	−0.992282	+	0.123999i	$0.960428\pi$
$770$		0			0
$771$	14.3984	+	18.0550i	0.518545	+	0.650235i
$772$		0			0
$773$	−0.389311	−	0.488180i	−0.0140025	−	0.0175586i	0.774781	−	0.632230i	$-0.217860\pi$
$773$	−0.389311	−	0.488180i	−0.0140025	−	0.0175586i	−0.788783	+	0.614671i	$0.789289\pi$
$774$		0			0
$775$	−9.33248	+	11.7026i	−0.335233	+	0.420368i
$776$		0			0
$777$	13.6208	−	21.0490i	0.488642	−	0.755128i
$778$		0			0
$779$	−16.8704	+	8.12438i	−0.604446	+	0.291086i
$780$		0			0
$781$	−9.50513	+	4.57743i	−0.340120	+	0.163793i
$782$		0			0
$783$	1.05243			0.0376109
$784$		0			0
$785$	−25.7833			−0.920244
$786$		0			0
$787$	29.5479	−	14.2295i	1.05327	−	0.507227i	0.174589	−	0.984641i	$-0.444140\pi$
$787$	29.5479	−	14.2295i	1.05327	−	0.507227i	0.878678	+	0.477414i	$0.158426\pi$
$788$		0			0
$789$	20.2590	−	9.75624i	0.721241	−	0.347331i
$790$		0			0
$791$	−45.4535	−	16.5884i	−1.61614	−	0.589815i
$792$		0			0
$793$	−8.01651	+	10.0524i	−0.284675	+	0.356971i
$794$		0			0
$795$	−21.2056	−	26.5909i	−0.752084	−	0.943084i
$796$		0			0
$797$	20.9851	+	26.3145i	0.743330	+	0.932107i	0.999403	−	0.0345509i	$-0.0110001\pi$
$797$	20.9851	+	26.3145i	0.743330	+	0.932107i	−0.256073	+	0.966658i	$0.582429\pi$
$798$		0			0
$799$	−6.11561	+	7.66874i	−0.216355	+	0.271300i
$800$		0			0
$801$	2.32581	+	10.1900i	0.0821784	+	0.360047i
$802$		0			0
$803$	4.22962			0.149260
$804$		0			0
$805$	−6.68187	+	4.07525i	−0.235505	+	0.143634i
$806$		0			0
$807$	0.476105	−	2.08595i	0.0167597	−	0.0734290i
$808$		0			0
$809$	−18.4892	+	23.1847i	−0.650045	+	0.815131i	−0.992219	−	0.124506i	$-0.960265\pi$
$809$	−18.4892	+	23.1847i	−0.650045	+	0.815131i	0.342174	+	0.939637i	$0.388837\pi$
$810$		0			0
$811$	−1.17651	+	5.15461i	−0.0413127	+	0.181003i	−0.991375	−	0.131059i	$-0.958162\pi$
$811$	−1.17651	+	5.15461i	−0.0413127	+	0.181003i	0.950062	+	0.312062i	$0.101020\pi$
$812$		0			0
$813$	0.890084	+	3.89971i	0.0312166	+	0.136769i
$814$		0			0
$815$	−7.13294			−0.249856
$816$		0			0
$817$	−4.73887	−	2.28212i	−0.165792	−	0.0798412i
$818$		0			0
$819$	2.15436	+	6.43059i	0.0752793	+	0.224703i
$820$		0			0
$821$	−1.81856	−	7.96762i	−0.0634681	−	0.278072i	0.933229	−	0.359282i	$-0.116979\pi$
$821$	−1.81856	−	7.96762i	−0.0634681	−	0.278072i	−0.996697	+	0.0812105i	$0.974121\pi$
$822$		0			0
$823$	−26.5460	−	12.7839i	−0.925335	−	0.445618i	−0.0903621	−	0.995909i	$-0.528802\pi$
$823$	−26.5460	−	12.7839i	−0.925335	−	0.445618i	−0.834973	+	0.550291i	$0.814517\pi$
$824$		0			0
$825$	−1.17901	+	0.567780i	−0.0410478	+	0.0197676i
$826$		0			0
$827$	10.4827	+	5.04821i	0.364519	+	0.175543i	0.607173	−	0.794570i	$-0.292304\pi$
$827$	10.4827	+	5.04821i	0.364519	+	0.175543i	−0.242653	+	0.970113i	$0.578018\pi$
$828$		0			0
$829$	−5.95446	+	26.0882i	−0.206807	+	0.906080i	0.759869	+	0.650076i	$0.225263\pi$
$829$	−5.95446	+	26.0882i	−0.206807	+	0.906080i	−0.966676	+	0.256004i	$0.917594\pi$
$830$		0			0
$831$	−4.08991	−	5.12858i	−0.141877	−	0.177909i
$832$		0			0
$833$	−13.2693	−	11.1736i	−0.459754	−	0.387141i
$834$		0			0
$835$	5.15972	+	6.47009i	0.178560	+	0.223907i
$836$		0			0
$837$	9.04987	−	39.6501i	0.312809	−	1.37051i
$838$		0			0
$839$	−33.1891	−	15.9830i	−1.14582	−	0.551796i	−0.238042	−	0.971255i	$-0.576505\pi$
$839$	−33.1891	−	15.9830i	−1.14582	−	0.551796i	−0.907774	+	0.419459i	$0.862220\pi$
$840$		0			0
$841$	26.0853	−	12.5620i	0.899492	−	0.433172i
$842$		0			0
$843$	13.4613	+	6.48260i	0.463631	+	0.223273i
$844$		0			0
$845$	−6.67276	−	29.2353i	−0.229550	−	1.00572i
$846$		0			0
$847$	−27.3617	+	2.71398i	−0.940159	+	0.0932534i
$848$		0			0
$849$	19.7164	+	9.49490i	0.676664	+	0.325864i
$850$		0			0
$851$	11.3935			0.390565
$852$		0			0
$853$	−3.46429	−	15.1780i	−0.118615	−	0.519686i	−0.998970	−	0.0453713i	$-0.985553\pi$
$853$	−3.46429	−	15.1780i	−0.118615	−	0.519686i	0.880355	−	0.474315i	$-0.157304\pi$
$854$		0			0
$855$	−4.63707	+	20.3163i	−0.158584	+	0.694803i
$856$		0			0
$857$	30.1487	−	37.8053i	1.02986	−	1.29140i	0.0741016	−	0.997251i	$-0.476391\pi$
$857$	30.1487	−	37.8053i	1.02986	−	1.29140i	0.955758	−	0.294153i	$-0.0950375\pi$
$858$		0			0
$859$	−0.991298	+	4.34316i	−0.0338226	+	0.148187i	−0.989020	−	0.147784i	$-0.952786\pi$
$859$	−0.991298	+	4.34316i	−0.0338226	+	0.148187i	0.955197	+	0.295971i	$0.0956431\pi$
$860$		0			0
$861$	11.5756	+	4.22453i	0.394494	+	0.143972i
$862$		0			0
$863$	23.9976			0.816888			0.408444	−	0.912783i	$-0.366072\pi$
$863$	23.9976			0.816888			0.408444	+	0.912783i	$0.366072\pi$
$864$		0			0
$865$	6.71468	+	29.4189i	0.228306	+	1.00027i
$866$		0			0
$867$	6.39890	−	8.02396i	0.217318	−	0.272508i
$868$		0			0
$869$	−6.10275	−	7.65261i	−0.207022	−	0.259597i
$870$		0			0
$871$	−5.25437	−	6.58877i	−0.178037	−	0.223252i
$872$		0			0
$873$	−3.56949	+	4.47600i	−0.120809	+	0.151489i
$874$		0			0
$875$	22.0936	−	2.19144i	0.746900	−	0.0740842i
$876$		0			0
$877$	−10.5677	+	5.08913i	−0.356845	+	0.171848i	−0.603713	−	0.797201i	$-0.706313\pi$
$877$	−10.5677	+	5.08913i	−0.356845	+	0.171848i	0.246868	+	0.969049i	$0.420599\pi$
$878$		0			0
$879$	26.0911	−	12.5648i	0.880032	−	0.423801i
$880$		0			0
$881$	12.7706			0.430253			0.215127	−	0.976586i	$-0.430984\pi$
$881$	12.7706			0.430253			0.215127	+	0.976586i	$0.430984\pi$
$882$		0			0
$883$	23.7018			0.797628			0.398814	−	0.917032i	$-0.369422\pi$
$883$	23.7018			0.797628			0.398814	+	0.917032i	$0.369422\pi$
$884$		0			0
$885$	−28.2776	+	13.6178i	−0.950540	+	0.457756i
$886$		0			0
$887$	6.87206	−	3.30941i	0.230741	−	0.111119i	−0.314941	−	0.949111i	$-0.601985\pi$
$887$	6.87206	−	3.30941i	0.230741	−	0.111119i	0.545682	+	0.837992i	$0.316270\pi$
$888$		0			0
$889$	47.6769	−	29.0780i	1.59903	−	0.975245i
$890$		0			0
$891$	−0.854480	+	1.07148i	−0.0286261	+	0.0358961i
$892$		0			0
$893$	9.37735	+	11.7588i	0.313801	+	0.393494i
$894$		0			0
$895$	14.6967	+	18.4290i	0.491255	+	0.616014i
$896$		0			0
$897$	0.814791	−	1.02172i	0.0272051	−	0.0341141i
$898$		0			0
$899$	0.408846	+	1.79127i	0.0136358	+	0.0597423i
$900$		0			0
$901$	34.2574			1.14128
$902$		0			0
$903$	1.09954	+	3.28203i	0.0365903	+	0.109219i
$904$		0			0
$905$	12.0867	−	52.9554i	0.401776	−	1.76030i
$906$		0			0
$907$	15.1987	−	19.0585i	0.504663	−	0.632828i	−0.462611	−	0.886561i	$-0.653087\pi$
$907$	15.1987	−	19.0585i	0.504663	−	0.632828i	0.967274	+	0.253734i	$0.0816587\pi$
$908$		0			0
$909$	−7.61646	+	33.3699i	−0.252622	+	1.10681i
$910$		0			0
$911$	0.532211	+	2.33177i	0.0176329	+	0.0772549i	0.982979	−	0.183719i	$-0.0588136\pi$
$911$	0.532211	+	2.33177i	0.0176329	+	0.0772549i	−0.965346	+	0.260974i	$0.915956\pi$
$912$		0			0
$913$	4.26330			0.141095
$914$		0			0
$915$	23.4242	+	11.2805i	0.774382	+	0.372923i
$916$		0			0
$917$	−0.761215	+	6.03193i	−0.0251375	+	0.199192i
$918$		0			0
$919$	7.64330	+	33.4875i	0.252129	+	1.10465i	0.929446	+	0.368959i	$0.120286\pi$
$919$	7.64330	+	33.4875i	0.252129	+	1.10465i	−0.677316	+	0.735692i	$0.736857\pi$
$920$		0			0
$921$	13.0888	+	6.30322i	0.431290	+	0.207698i
$922$		0			0
$923$	14.8382	−	7.14568i	0.488404	−	0.235203i
$924$		0			0
$925$	16.0465	+	7.72758i	0.527605	+	0.254081i
$926$		0			0
$927$	−3.69738	+	16.1993i	−0.121438	+	0.532054i
$928$		0			0
$929$	−26.3479	−	33.0392i	−0.864447	−	1.08398i	−0.995700	−	0.0926331i	$-0.970472\pi$
$929$	−26.3479	−	33.0392i	−0.864447	−	1.08398i	0.131254	−	0.991349i	$-0.458100\pi$
$930$		0			0
$931$	−21.2309	+	16.0239i	−0.695814	+	0.525161i
$932$		0			0
$933$	−18.8413	−	23.6263i	−0.616837	−	0.773489i
$934$		0			0
$935$	1.11886	−	4.90202i	0.0365905	−	0.160313i
$936$		0			0
$937$	7.48769	+	3.60588i	0.244612	+	0.117799i	0.552173	−	0.833729i	$-0.313799\pi$
$937$	7.48769	+	3.60588i	0.244612	+	0.117799i	−0.307561	+	0.951528i	$0.599513\pi$
$938$		0			0
$939$	−18.2762	+	8.80136i	−0.596422	+	0.287222i
$940$		0			0
$941$	−42.8999	−	20.6595i	−1.39850	−	0.673481i	−0.425641	−	0.904892i	$-0.639951\pi$
$941$	−42.8999	−	20.6595i	−1.39850	−	0.673481i	−0.972856	+	0.231411i	$0.925666\pi$
$942$		0			0
$943$	1.24607	+	5.45937i	0.0405775	+	0.177782i
$944$		0			0
$945$	28.3800	−	17.3089i	0.923203	−	0.563058i
$946$		0			0
$947$	2.16052	+	1.04045i	0.0702073	+	0.0338101i	0.468658	−	0.883380i	$-0.344738\pi$
$947$	2.16052	+	1.04045i	0.0702073	+	0.0338101i	−0.398451	+	0.917190i	$0.630452\pi$
$948$		0			0
$949$	−6.60272			−0.214333
$950$		0			0
$951$	−1.77035	−	7.75639i	−0.0574074	−	0.251518i
$952$		0			0
$953$	2.15472	−	9.44045i	0.0697983	−	0.305806i	−0.927964	−	0.372670i	$-0.878442\pi$
$953$	2.15472	−	9.44045i	0.0697983	−	0.305806i	0.997762	+	0.0668641i	$0.0212994\pi$
$954$		0			0
$955$	12.4907	−	15.6629i	0.404190	−	0.506839i
$956$		0			0
$957$	−0.0357437	+	0.156603i	−0.00115543	+	0.00506226i
$958$		0			0
$959$	0.481230	−	3.81331i	0.0155397	−	0.123138i
$960$		0			0
$961$	40.0013			1.29036
$962$		0			0
$963$	0.431754	+	1.89164i	0.0139131	+	0.0609571i
$964$		0			0
$965$	−14.9154	+	18.7033i	−0.480144	+	0.602082i
$966$		0			0
$967$	−6.97228	−	8.74296i	−0.224213	−	0.281155i	0.656983	−	0.753906i	$-0.271832\pi$
$967$	−6.97228	−	8.74296i	−0.224213	−	0.281155i	−0.881196	+	0.472751i	$0.843261\pi$
$968$		0			0
$969$	5.54915	+	6.95841i	0.178264	+	0.223536i
$970$		0			0
$971$	−2.67932	+	3.35975i	−0.0859833	+	0.107820i	−0.822962	−	0.568096i	$-0.807680\pi$
$971$	−2.67932	+	3.35975i	−0.0859833	+	0.107820i	0.736979	+	0.675916i	$0.236252\pi$
$972$		0			0
$973$	16.5898	+	17.0383i	0.531846	+	0.546222i
$974$		0			0
$975$	1.84051	−	0.886343i	0.0589435	−	0.0283857i
$976$		0			0
$977$	−4.19132	+	2.01843i	−0.134092	+	0.0645754i	−0.499727	−	0.866183i	$-0.666566\pi$
$977$	−4.19132	+	2.01843i	−0.134092	+	0.0645754i	0.365635	+	0.930758i	$0.380852\pi$
$978$		0			0
$979$	−3.86700			−0.123590
$980$		0			0
$981$	21.6627			0.691638
$982$		0			0
$983$	32.3967	−	15.6014i	1.03329	−	0.497608i	0.161188	−	0.986924i	$-0.448468\pi$
$983$	32.3967	−	15.6014i	1.03329	−	0.497608i	0.872107	+	0.489315i	$0.162753\pi$
$984$		0			0
$985$	−46.5045	+	22.3954i	−1.48176	+	0.713576i
$986$		0			0
$987$	1.23922	−	9.81966i	0.0394447	−	0.312563i
$988$		0			0
$989$	−0.980726	+	1.22979i	−0.0311853	+	0.0391051i
$990$		0			0
$991$	−32.5319	−	40.7937i	−1.03341	−	1.29586i	−0.954255	−	0.298993i	$-0.903349\pi$
$991$	−32.5319	−	40.7937i	−1.03341	−	1.29586i	−0.0791547	−	0.996862i	$-0.525222\pi$
$992$		0			0
$993$	−10.0885	−	12.6506i	−0.320149	−	0.401455i
$994$		0			0
$995$	23.8598	−	29.9193i	0.756407	−	0.948505i
$996$		0			0
$997$	−6.48592	−	28.4167i	−0.205411	−	0.899965i	−0.967576	−	0.252582i	$-0.918720\pi$
$997$	−6.48592	−	28.4167i	−0.205411	−	0.899965i	0.762164	−	0.647383i	$-0.224137\pi$
$998$		0			0
$999$	−48.3920			−1.53106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.i.a.57.3	✓	24
4.3	odd	2		784.2.u.e.449.2		24
49.22	even	7		9604.2.a.c.1.5		12
49.27	odd	14		9604.2.a.a.1.8		12
49.43	even	7	inner	196.2.i.a.141.3	yes	24
196.43	odd	14		784.2.u.e.337.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.i.a.57.3	✓	24	1.1	even	1	trivial
196.2.i.a.141.3	yes	24	49.43	even	7	inner
784.2.u.e.337.2		24	196.43	odd	14
784.2.u.e.449.2		24	4.3	odd	2
9604.2.a.a.1.8		12	49.27	odd	14
9604.2.a.c.1.5		12	49.22	even	7

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.i (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.851544 - 0.410082i) q^{3} +(2.34535 - 1.12946i) q^{5} +(-0.840460 - 2.50871i) q^{7} +(-1.31351 + 1.64709i) q^{9} +O(q^{10})\)	\(q+(0.851544 - 0.410082i) q^{3} +(2.34535 - 1.12946i) q^{5} +(-0.840460 - 2.50871i) q^{7} +(-1.31351 + 1.64709i) q^{9} +(-0.485964 - 0.609379i) q^{11} +(0.758622 + 0.951282i) q^{13} +(1.53400 - 1.92358i) q^{15} +(0.551443 + 2.41603i) q^{17} +3.79988 q^{19} +(-1.74447 - 1.79162i) q^{21} +(0.252868 - 1.10789i) q^{23} +(1.10755 - 1.38883i) q^{25} +(-1.07401 + 4.70555i) q^{27} +(-0.0485207 - 0.212583i) q^{29} -8.42623 q^{31} +(-0.663715 - 0.319628i) q^{33} +(-4.80467 - 4.93455i) q^{35} +(2.23103 + 9.77480i) q^{37} +(1.03610 + 0.498962i) q^{39} +(-4.43973 + 2.13806i) q^{41} +(-1.24711 - 0.600576i) q^{43} +(-1.22032 + 5.34657i) q^{45} +(2.46780 + 3.09453i) q^{47} +(-5.58725 + 4.21694i) q^{49} +(1.46035 + 1.83122i) q^{51} +(3.07606 - 13.4771i) q^{53} +(-1.82803 - 0.880332i) q^{55} +(3.23577 - 1.55826i) q^{57} +(-11.4933 - 5.53489i) q^{59} +(2.35142 + 10.3023i) q^{61} +(5.23602 + 1.91090i) q^{63} +(2.85368 + 1.37426i) q^{65} -6.92619 q^{67} +(-0.238997 - 1.04711i) q^{69} +(3.01193 - 13.1961i) q^{71} +(-3.38342 + 4.24267i) q^{73} +(0.373597 - 1.63683i) q^{75} +(-1.12032 + 1.73130i) q^{77} +12.5580 q^{79} +(-0.391263 - 1.71423i) q^{81} +(-3.41036 + 4.27646i) q^{83} +(4.02215 + 5.04361i) q^{85} +(-0.128494 - 0.161126i) q^{87} +(3.09335 - 3.87894i) q^{89} +(1.74890 - 2.70268i) q^{91} +(-7.17530 + 3.45544i) q^{93} +(8.91207 - 4.29182i) q^{95} +2.71752 q^{97} +1.64202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9}+O(q^{10}) \) 24 * q + 8 * q^9	\( 24 q + 8 q^{9} - 9 q^{11} + 16 q^{15} - 7 q^{17} + 14 q^{19} - 19 q^{23} - 2 q^{25} - 21 q^{27} + 10 q^{29} + 14 q^{35} - 17 q^{37} - 22 q^{39} - 14 q^{41} + 2 q^{43} - 14 q^{45} + 7 q^{47} - 28 q^{49} - 26 q^{51} - 47 q^{53} - 17 q^{57} - 42 q^{61} - 21 q^{63} + 4 q^{65} + 28 q^{69} - 21 q^{71} - 21 q^{73} + 84 q^{75} - 21 q^{77} - 4 q^{79} + 38 q^{81} - 42 q^{83} + 62 q^{85} + 70 q^{87} - 28 q^{89} + 98 q^{91} + 35 q^{93} + 54 q^{95} + 112 q^{97} - 108 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 9 * q^11 + 16 * q^15 - 7 * q^17 + 14 * q^19 - 19 * q^23 - 2 * q^25 - 21 * q^27 + 10 * q^29 + 14 * q^35 - 17 * q^37 - 22 * q^39 - 14 * q^41 + 2 * q^43 - 14 * q^45 + 7 * q^47 - 28 * q^49 - 26 * q^51 - 47 * q^53 - 17 * q^57 - 42 * q^61 - 21 * q^63 + 4 * q^65 + 28 * q^69 - 21 * q^71 - 21 * q^73 + 84 * q^75 - 21 * q^77 - 4 * q^79 + 38 * q^81 - 42 * q^83 + 62 * q^85 + 70 * q^87 - 28 * q^89 + 98 * q^91 + 35 * q^93 + 54 * q^95 + 112 * q^97 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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