LMFDB - Embedded newform 1274.2.m.f.491.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-2,10,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.4
Root			$-1.40613i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.f.589.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.703063 + 1.21774i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.638488i q^{5} +(-1.21774 - 0.703063i) q^{6} +1.00000i q^{8} +(0.511405 - 0.885780i) q^{9} +(-0.319244 - 0.552947i) q^{10} +(-3.93617 + 2.27255i) q^{11} +1.40613 q^{12} +(-2.48206 + 2.61522i) q^{13} +(-0.777512 + 0.448897i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.354210 + 0.613510i) q^{17} +1.02281i q^{18} +(-6.36190 - 3.67305i) q^{19} +(0.552947 + 0.319244i) q^{20} +(2.27255 - 3.93617i) q^{22} +(-3.25276 - 5.63395i) q^{23} +(-1.21774 + 0.703063i) q^{24} +4.59233 q^{25} +(0.841912 - 3.50588i) q^{26} +5.65658 q^{27} +(-3.63276 - 6.29212i) q^{29} +(0.448897 - 0.777512i) q^{30} +6.63998i q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.53475 - 3.19549i) q^{33} -0.708420i q^{34} +(-0.511405 - 0.885780i) q^{36} +(-1.82266 + 1.05231i) q^{37} +7.34609 q^{38} +(-4.92971 - 1.18383i) q^{39} -0.638488 q^{40} +(-4.62167 + 2.66832i) q^{41} +(-5.21162 + 9.02680i) q^{43} +4.54510i q^{44} +(0.565560 + 0.326526i) q^{45} +(5.63395 + 3.25276i) q^{46} +1.94413i q^{47} +(0.703063 - 1.21774i) q^{48} +(-3.97708 + 2.29617i) q^{50} -0.996127 q^{51} +(1.02382 + 3.45714i) q^{52} -6.40142 q^{53} +(-4.89874 + 2.82829i) q^{54} +(-1.45099 - 2.51320i) q^{55} -10.3295i q^{57} +(6.29212 + 3.63276i) q^{58} +(-2.87484 - 1.65979i) q^{59} +0.897794i q^{60} +(3.41517 - 5.91525i) q^{61} +(-3.31999 - 5.75039i) q^{62} -1.00000 q^{64} +(-1.66979 - 1.58476i) q^{65} +6.39098 q^{66} +(3.39810 - 1.96190i) q^{67} +(0.354210 + 0.613510i) q^{68} +(4.57379 - 7.92204i) q^{69} +(-9.11772 - 5.26412i) q^{71} +(0.885780 + 0.511405i) q^{72} +6.41246i q^{73} +(1.05231 - 1.82266i) q^{74} +(3.22870 + 5.59227i) q^{75} +(-6.36190 + 3.67305i) q^{76} +(4.86117 - 1.43962i) q^{78} -10.9684 q^{79} +(0.552947 - 0.319244i) q^{80} +(2.44271 + 4.23090i) q^{81} +(2.66832 - 4.62167i) q^{82} -2.41032i q^{83} +(-0.391718 - 0.226159i) q^{85} -10.4232i q^{86} +(5.10811 - 8.84751i) q^{87} +(-2.27255 - 3.93617i) q^{88} +(4.79196 - 2.76664i) q^{89} -0.653052 q^{90} -6.50552 q^{92} +(-8.08577 + 4.66832i) q^{93} +(-0.972065 - 1.68367i) q^{94} +(2.34519 - 4.06200i) q^{95} +1.40613i q^{96} +(7.96131 + 4.59646i) q^{97} +4.64877i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 10 q^{4} - 16 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{19} + 2 q^{22} - 36 q^{25} + 28 q^{27} + 2 q^{29} - 2 q^{30} + 12 q^{33} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) $ 20 * q - 2 * q^3 + 10 * q^4 - 16 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^19 + 2 * q^22 - 36 * q^25 + 28 * q^27 + 2 * q^29 - 2 * q^30 + 12 * q^33 + 16 * q^36 + 36 * q^37 - 28 * q^38 + 4 * q^39 + 8 * q^40 - 18 * q^41 + 8 * q^43 - 60 * q^45 - 12 * q^46 - 2 * q^48 - 12 * q^50 + 44 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 2 * q^55 + 24 * q^58 + 4 * q^61 + 24 * q^62 - 20 * q^64 + 24 * q^65 + 64 * q^66 + 60 * q^67 - 10 * q^68 + 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 + 16 * q^82 - 12 * q^85 + 64 * q^87 - 2 * q^88 - 18 * q^89 - 52 * q^90 - 60 * q^93 - 16 * q^94 - 12 * q^95 - 78 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.703063	+	1.21774i	0.405914	+	0.703063i	0.994427	−	0.105424i	$-0.0336201\pi$
$3$	0.703063	+	1.21774i	0.405914	+	0.703063i	−0.588514	+	0.808487i	$0.700287\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			0.638488i			0.285540i	0.989756	+	0.142770i	$0.0456010\pi$
$5$			0.638488i			0.285540i	−0.989756	+	0.142770i	$0.954399\pi$
$6$	−1.21774	−	0.703063i	−0.497141	−	0.287024i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.511405	−	0.885780i	0.170468	−	0.295260i
$10$	−0.319244	−	0.552947i	−0.100954	−	0.174857i
$11$	−3.93617	+	2.27255i	−1.18680	+	0.685199i	−0.957578	−	0.288175i	$-0.906952\pi$
$11$	−3.93617	+	2.27255i	−1.18680	+	0.685199i	−0.229222	+	0.973374i	$0.573618\pi$
$12$	1.40613			0.405914
$13$	−2.48206	+	2.61522i	−0.688399	+	0.725333i
$13$	−2.48206	+	2.61522i	−0.688399	+	0.725333i
$14$		0			0
$15$	−0.777512	+	0.448897i	−0.200753	+	0.115905i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.354210	+	0.613510i	−0.0859085	+	0.148798i	−0.905778	−	0.423753i	$-0.860713\pi$
$17$	−0.354210	+	0.613510i	−0.0859085	+	0.148798i	0.819869	+	0.572550i	$0.194046\pi$
$18$			1.02281i			0.241079i
$19$	−6.36190	−	3.67305i	−1.45952	−	0.842654i	−0.460533	−	0.887643i	$-0.652342\pi$
$19$	−6.36190	−	3.67305i	−1.45952	−	0.842654i	−0.998988	+	0.0449884i	$0.985675\pi$
$20$	0.552947	+	0.319244i	0.123643	+	0.0713851i
$21$		0			0
$22$	2.27255	−	3.93617i	0.484509	−	0.839194i
$23$	−3.25276	−	5.63395i	−0.678248	−	1.17476i	−0.975508	−	0.219963i	$-0.929406\pi$
$23$	−3.25276	−	5.63395i	−0.678248	−	1.17476i	0.297261	−	0.954796i	$-0.403927\pi$
$24$	−1.21774	+	0.703063i	−0.248570	+	0.143512i
$25$	4.59233			0.918467
$26$	0.841912	−	3.50588i	0.165113	−	0.687559i
$27$	5.65658			1.08861
$28$		0			0
$29$	−3.63276	−	6.29212i	−0.674586	−	1.16842i	−0.976590	−	0.215111i	$-0.930989\pi$
$29$	−3.63276	−	6.29212i	−0.674586	−	1.16842i	0.302003	−	0.953307i	$-0.402345\pi$
$30$	0.448897	−	0.777512i	0.0819570	−	0.141954i
$31$			6.63998i			1.19258i	0.802771	+	0.596288i	$0.203358\pi$
$31$			6.63998i			1.19258i	−0.802771	+	0.596288i	$0.796642\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.53475	−	3.19549i	−0.963476	−	0.556263i
$34$		−	0.708420i		−	0.121493i
$35$		0			0
$36$	−0.511405	−	0.885780i	−0.0852342	−	0.147630i
$37$	−1.82266	+	1.05231i	−0.299643	+	0.172999i	−0.642283	−	0.766468i	$-0.722012\pi$
$37$	−1.82266	+	1.05231i	−0.299643	+	0.172999i	0.342639	+	0.939467i	$0.388679\pi$
$38$	7.34609			1.19169
$39$	−4.92971	−	1.18383i	−0.789385	−	0.189565i
$40$	−0.638488			−0.100954
$41$	−4.62167	+	2.66832i	−0.721783	+	0.416722i	−0.815409	−	0.578886i	$-0.803488\pi$
$41$	−4.62167	+	2.66832i	−0.721783	+	0.416722i	0.0936256	+	0.995607i	$0.470154\pi$
$42$		0			0
$43$	−5.21162	+	9.02680i	−0.794765	+	1.37657i	0.128223	+	0.991745i	$0.459073\pi$
$43$	−5.21162	+	9.02680i	−0.794765	+	1.37657i	−0.922988	+	0.384828i	$0.874261\pi$
$44$			4.54510i			0.685199i
$45$	0.565560	+	0.326526i	0.0843086	+	0.0486756i
$46$	5.63395	+	3.25276i	0.830680	+	0.479594i
$47$			1.94413i			0.283580i	0.989897	+	0.141790i	$0.0452858\pi$
$47$			1.94413i			0.283580i	−0.989897	+	0.141790i	$0.954714\pi$
$48$	0.703063	−	1.21774i	0.101478	−	0.175766i
$49$		0			0
$50$	−3.97708	+	2.29617i	−0.562444	+	0.324727i
$51$	−0.996127			−0.139486
$52$	1.02382	+	3.45714i	0.141979	+	0.479418i
$53$	−6.40142			−0.879303			−0.439652	−	0.898168i	$-0.644898\pi$
$53$	−6.40142			−0.879303			−0.439652	+	0.898168i	$0.644898\pi$
$54$	−4.89874	+	2.82829i	−0.666634	+	0.384881i
$55$	−1.45099	−	2.51320i	−0.195652	−	0.338879i
$56$		0			0
$57$		−	10.3295i		−	1.36818i
$58$	6.29212	+	3.63276i	0.826196	+	0.477005i
$59$	−2.87484	−	1.65979i	−0.374272	−	0.216086i	0.301051	−	0.953608i	$-0.402663\pi$
$59$	−2.87484	−	1.65979i	−0.374272	−	0.216086i	−0.675323	+	0.737522i	$0.735996\pi$
$60$			0.897794i			0.115905i
$61$	3.41517	−	5.91525i	0.437268	−	0.757370i	−0.560210	−	0.828351i	$-0.689280\pi$
$61$	3.41517	−	5.91525i	0.437268	−	0.757370i	0.997478	+	0.0709807i	$0.0226129\pi$
$62$	−3.31999	−	5.75039i	−0.421639	−	0.730300i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.66979	−	1.58476i	−0.207112	−	0.196566i
$66$	6.39098			0.786675
$67$	3.39810	−	1.96190i	0.415144	−	0.239684i	−0.277853	−	0.960624i	$-0.589623\pi$
$67$	3.39810	−	1.96190i	0.415144	−	0.239684i	0.692998	+	0.720940i	$0.256290\pi$
$68$	0.354210	+	0.613510i	0.0429543	+	0.0743990i
$69$	4.57379	−	7.92204i	0.550620	−	0.953701i
$70$		0			0
$71$	−9.11772	−	5.26412i	−1.08207	−	0.624736i	−0.150619	−	0.988592i	$-0.548127\pi$
$71$	−9.11772	−	5.26412i	−1.08207	−	0.624736i	−0.931455	+	0.363856i	$0.881460\pi$
$72$	0.885780	+	0.511405i	0.104390	+	0.0602697i
$73$			6.41246i			0.750521i	0.926919	+	0.375261i	$0.122447\pi$
$73$			6.41246i			0.750521i	−0.926919	+	0.375261i	$0.877553\pi$
$74$	1.05231	−	1.82266i	0.122329	−	0.211880i
$75$	3.22870	+	5.59227i	0.372818	+	0.645740i
$76$	−6.36190	+	3.67305i	−0.729760	+	0.421327i
$77$		0			0
$78$	4.86117	−	1.43962i	0.550419	−	0.163005i
$79$	−10.9684			−1.23404			−0.617018	−	0.786949i	$-0.711659\pi$
$79$	−10.9684			−1.23404			−0.617018	+	0.786949i	$0.711659\pi$
$80$	0.552947	−	0.319244i	0.0618213	−	0.0356925i
$81$	2.44271	+	4.23090i	0.271413	+	0.470100i
$82$	2.66832	−	4.62167i	0.294667	−	0.510378i
$83$		−	2.41032i		−	0.264567i	−0.991212	−	0.132283i	$-0.957769\pi$
$83$		−	2.41032i		−	0.264567i	0.991212	−	0.132283i	$-0.0422309\pi$
$84$		0			0
$85$	−0.391718	−	0.226159i	−0.0424878	−	0.0245304i
$86$		−	10.4232i		−	1.12397i
$87$	5.10811	−	8.84751i	0.547647	−	0.948553i
$88$	−2.27255	−	3.93617i	−0.242254	−	0.419597i
$89$	4.79196	−	2.76664i	0.507947	−	0.293263i	−0.224043	−	0.974579i	$-0.571925\pi$
$89$	4.79196	−	2.76664i	0.507947	−	0.293263i	0.731989	+	0.681316i	$0.238592\pi$
$90$	−0.653052			−0.0688377
$91$		0			0
$92$	−6.50552			−0.678248
$93$	−8.08577	+	4.66832i	−0.838455	+	0.484082i
$94$	−0.972065	−	1.68367i	−0.100261	−	0.173657i
$95$	2.34519	−	4.06200i	0.240612	−	0.416752i
$96$			1.40613i			0.143512i
$97$	7.96131	+	4.59646i	0.808348	+	0.466700i	0.846382	−	0.532576i	$-0.178776\pi$
$97$	7.96131	+	4.59646i	0.808348	+	0.466700i	−0.0380337	+	0.999276i	$0.512109\pi$
$98$		0			0
$99$			4.64877i			0.467219i
$100$	2.29617	−	3.97708i	0.229617	−	0.397708i
$101$	6.85500	+	11.8732i	0.682098	+	1.18143i	0.974339	+	0.225084i	$0.0722657\pi$
$101$	6.85500	+	11.8732i	0.682098	+	1.18143i	−0.292241	+	0.956345i	$0.594401\pi$
$102$	0.862672	−	0.498064i	0.0854172	−	0.0493157i
$103$	10.8070			1.06485			0.532425	−	0.846477i	$-0.321281\pi$
$103$	10.8070			1.06485			0.532425	+	0.846477i	$0.321281\pi$
$104$	−2.61522	−	2.48206i	−0.256444	−	0.243386i
$105$		0			0
$106$	5.54379	−	3.20071i	0.538461	−	0.310881i
$107$	−7.66173	−	13.2705i	−0.740687	−	1.28291i	−0.952183	−	0.305529i	$-0.901167\pi$
$107$	−7.66173	−	13.2705i	−0.740687	−	1.28291i	0.211495	−	0.977379i	$-0.432167\pi$
$108$	2.82829	−	4.89874i	0.272152	−	0.471381i
$109$		−	1.77368i		−	0.169888i	−0.996386	−	0.0849438i	$-0.972929\pi$
$109$		−	1.77368i		−	0.169888i	0.996386	−	0.0849438i	$-0.0270711\pi$
$110$	2.51320	+	1.45099i	0.239624	+	0.138347i
$111$	−2.56289	−	1.47968i	−0.243259	−	0.140445i
$112$		0			0
$113$	2.62152	−	4.54061i	0.246612	−	0.427145i	−0.715971	−	0.698130i	$-0.754016\pi$
$113$	2.62152	−	4.54061i	0.246612	−	0.427145i	0.962584	+	0.270985i	$0.0873493\pi$
$114$	5.16476	+	8.94563i	0.483724	+	0.837835i
$115$	3.59721	−	2.07685i	0.335441	−	0.193667i
$116$	−7.26552			−0.674586
$117$	1.04718	+	3.53600i	0.0968114	+	0.326903i
$118$	3.31958			0.305592
$119$		0			0
$120$	−0.448897	−	0.777512i	−0.0409785	−	0.0709768i
$121$	4.82895	−	8.36399i	0.438996	−	0.760363i
$122$			6.83034i			0.618390i
$123$	−6.49864	−	3.75199i	−0.585963	−	0.338306i
$124$	5.75039	+	3.31999i	0.516400	+	0.298144i
$125$			6.12459i			0.547800i
$126$		0			0
$127$	0.366918	+	0.635520i	0.0325587	+	0.0563933i	0.881846	−	0.471538i	$-0.156301\pi$
$127$	0.366918	+	0.635520i	0.0325587	+	0.0563933i	−0.849287	+	0.527932i	$0.822968\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−14.6564			−1.29042
$130$	2.23846	+	0.537551i	0.196326	+	0.0471463i
$131$	−19.8711			−1.73615			−0.868074	−	0.496435i	$-0.834642\pi$
$131$	−19.8711			−1.73615			−0.868074	+	0.496435i	$0.834642\pi$
$132$	−5.53475	+	3.19549i	−0.481738	+	0.278132i
$133$		0			0
$134$	−1.96190	+	3.39810i	−0.169482	+	0.293551i
$135$			3.61166i			0.310842i
$136$	−0.613510	−	0.354210i	−0.0526080	−	0.0303733i
$137$	−9.06177	−	5.23181i	−0.774199	−	0.446984i	0.0601714	−	0.998188i	$-0.480835\pi$
$137$	−9.06177	−	5.23181i	−0.774199	−	0.446984i	−0.834370	+	0.551204i	$0.814169\pi$
$138$			9.14758i			0.778694i
$139$	−0.0315662	+	0.0546743i	−0.00267741	+	0.00463741i	−0.867361	−	0.497680i	$-0.834186\pi$
$139$	−0.0315662	+	0.0546743i	−0.00267741	+	0.00463741i	0.864684	+	0.502317i	$0.167519\pi$
$140$		0			0
$141$	−2.36744	+	1.36684i	−0.199375	+	0.115109i
$142$	10.5282			0.883510
$143$	3.82657	−	15.9346i	0.319994	−	1.33251i
$144$	−1.02281			−0.0852342
$145$	4.01744	−	2.31947i	0.333630	−	0.192622i
$146$	−3.20623	−	5.55335i	−0.265349	−	0.459599i
$147$		0			0
$148$			2.10463i			0.172999i
$149$	7.69244	+	4.44123i	0.630189	+	0.363840i	0.780825	−	0.624749i	$-0.214799\pi$
$149$	7.69244	+	4.44123i	0.630189	+	0.363840i	−0.150636	+	0.988589i	$0.548132\pi$
$150$	−5.59227	−	3.22870i	−0.456607	−	0.263622i
$151$		−	13.2306i		−	1.07669i	−0.842724	−	0.538345i	$-0.819050\pi$
$151$		−	13.2306i		−	1.07669i	0.842724	−	0.538345i	$-0.180950\pi$
$152$	3.67305	−	6.36190i	0.297923	−	0.516018i
$153$	0.362290	+	0.627504i	0.0292894	+	0.0507307i
$154$		0			0
$155$	−4.23954			−0.340528
$156$	−3.49008	+	3.67733i	−0.279430	+	0.294422i
$157$	−2.98372			−0.238127			−0.119063	−	0.992887i	$-0.537989\pi$
$157$	−2.98372			−0.238127			−0.119063	+	0.992887i	$0.537989\pi$
$158$	9.49887	−	5.48418i	0.755690	−	0.436298i
$159$	−4.50060	−	7.79527i	−0.356921	−	0.618205i
$160$	−0.319244	+	0.552947i	−0.0252384	+	0.0437143i
$161$		0			0
$162$	−4.23090	−	2.44271i	−0.332411	−	0.191918i
$163$	8.59086	+	4.95993i	0.672888	+	0.388492i	0.797170	−	0.603755i	$-0.206329\pi$
$163$	8.59086	+	4.95993i	0.672888	+	0.388492i	−0.124282	+	0.992247i	$0.539663\pi$
$164$			5.33664i			0.416722i
$165$	2.04028	−	3.53387i	0.158836	−	0.275111i
$166$	1.20516	+	2.08740i	0.0935384	+	0.162013i
$167$	10.4096	−	6.01000i	0.805521	−	0.465068i	−0.0398771	−	0.999205i	$-0.512697\pi$
$167$	10.4096	−	6.01000i	0.805521	−	0.465068i	0.845398	+	0.534137i	$0.179363\pi$
$168$		0			0
$169$	−0.678789	−	12.9823i	−0.0522146	−	0.998636i
$170$	0.452317			0.0346912
$171$	−6.50702	+	3.75683i	−0.497604	+	0.287292i
$172$	5.21162	+	9.02680i	0.397383	+	0.688287i
$173$	−9.75761	+	16.9007i	−0.741857	+	1.28493i	0.209792	+	0.977746i	$0.432721\pi$
$173$	−9.75761	+	16.9007i	−0.741857	+	1.28493i	−0.951649	+	0.307188i	$0.900612\pi$
$174$			10.2162i			0.774490i
$175$		0			0
$176$	3.93617	+	2.27255i	0.296700	+	0.171300i
$177$		−	4.66775i		−	0.350849i
$178$	−2.76664	+	4.79196i	−0.207368	+	0.359173i
$179$	8.07581	+	13.9877i	0.603615	+	1.04549i	0.992269	+	0.124108i	$0.0396068\pi$
$179$	8.07581	+	13.9877i	0.603615	+	1.04549i	−0.388654	+	0.921384i	$0.627060\pi$
$180$	0.565560	−	0.326526i	0.0421543	−	0.0243378i
$181$	−0.281865			−0.0209509			−0.0104754	−	0.999945i	$-0.503334\pi$
$181$	−0.281865			−0.0209509			−0.0104754	+	0.999945i	$0.503334\pi$
$182$		0			0
$183$	9.60432			0.709972
$184$	5.63395	−	3.25276i	0.415340	−	0.239797i
$185$	−0.671889	−	1.16375i	−0.0493983	−	0.0855603i
$186$	4.66832	−	8.08577i	0.342298	−	0.592877i
$187$		−	3.21984i		−	0.235458i
$188$	1.68367	+	0.972065i	0.122794	+	0.0708951i
$189$		0			0
$190$			4.69039i			0.340277i
$191$	−6.21334	+	10.7618i	−0.449581	+	0.778698i	−0.998359	−	0.0572709i	$-0.981760\pi$
$191$	−6.21334	+	10.7618i	−0.449581	+	0.778698i	0.548777	+	0.835969i	$0.315093\pi$
$192$	−0.703063	−	1.21774i	−0.0507392	−	0.0878829i
$193$	−10.0807	+	5.82010i	−0.725626	+	0.418940i	−0.816820	−	0.576893i	$-0.804265\pi$
$193$	−10.0807	+	5.82010i	−0.725626	+	0.418940i	0.0911941	+	0.995833i	$0.470932\pi$
$194$	−9.19293			−0.660014
$195$	0.755864	−	3.14756i	0.0541285	−	0.225401i
$196$		0			0
$197$	4.59712	−	2.65415i	0.327531	−	0.189100i	−0.327213	−	0.944950i	$-0.606110\pi$
$197$	4.59712	−	2.65415i	0.327531	−	0.189100i	0.654744	+	0.755850i	$0.272776\pi$
$198$	−2.32439	−	4.02596i	−0.165187	−	0.286112i
$199$	6.87462	−	11.9072i	0.487329	−	0.844078i	−0.512565	−	0.858648i	$-0.671305\pi$
$199$	6.87462	−	11.9072i	0.487329	−	0.844078i	0.999894	+	0.0145702i	$0.00463799\pi$
$200$			4.59233i			0.324727i
$201$	4.77816	+	2.75867i	0.337025	+	0.194582i
$202$	−11.8732	−	6.85500i	−0.835396	−	0.482316i
$203$		0			0
$204$	−0.498064	+	0.862672i	−0.0348714	+	0.0603991i
$205$	−1.70369	−	2.95088i	−0.118991	−	0.206098i
$206$	−9.35918	+	5.40352i	−0.652085	+	0.376481i
$207$	−6.65392			−0.462479
$208$	3.50588	+	0.841912i	0.243089	+	0.0583761i
$209$	33.3887			2.30954
$210$		0			0
$211$	3.91287	+	6.77729i	0.269373	+	0.466568i	0.968700	−	0.248234i	$-0.0798502\pi$
$211$	3.91287	+	6.77729i	0.269373	+	0.466568i	−0.699327	+	0.714802i	$0.746517\pi$
$212$	−3.20071	+	5.54379i	−0.219826	+	0.380749i
$213$		−	14.8040i		−	1.01436i
$214$	13.2705	+	7.66173i	0.907153	+	0.523745i
$215$	−5.76350	−	3.32756i	−0.393067	−	0.226938i
$216$			5.65658i			0.384881i
$217$		0			0
$218$	0.886839	+	1.53605i	0.0600643	+	0.104034i
$219$	−7.80871	+	4.50836i	−0.527664	+	0.304647i
$220$	−2.90199			−0.195652
$221$	−0.725296	−	2.44910i	−0.0487887	−	0.164745i
$222$	2.95937			0.198620
$223$	−16.9201	+	9.76882i	−1.13305	+	0.654169i	−0.944701	−	0.327933i	$-0.893648\pi$
$223$	−16.9201	+	9.76882i	−1.13305	+	0.654169i	−0.188353	+	0.982101i	$0.560315\pi$
$224$		0			0
$225$	2.34854	−	4.06780i	0.156570	−	0.271186i
$226$			5.24305i			0.348762i
$227$	−4.26499	−	2.46239i	−0.283077	−	0.163435i	0.351738	−	0.936098i	$-0.385591\pi$
$227$	−4.26499	−	2.46239i	−0.283077	−	0.163435i	−0.634816	+	0.772664i	$0.718924\pi$
$228$	−8.94563	−	5.16476i	−0.592439	−	0.342045i
$229$			15.9722i			1.05547i	0.849408	+	0.527736i	$0.176959\pi$
$229$			15.9722i			1.05547i	−0.849408	+	0.527736i	$0.823041\pi$
$230$	−2.07685	+	3.59721i	−0.136943	+	0.237193i
$231$		0			0
$232$	6.29212	−	3.63276i	0.413098	−	0.238502i
$233$	−5.24006			−0.343288			−0.171644	−	0.985159i	$-0.554908\pi$
$233$	−5.24006			−0.343288			−0.171644	+	0.985159i	$0.554908\pi$
$234$	−2.67488	−	2.53867i	−0.174862	−	0.165958i
$235$	−1.24130			−0.0809737
$236$	−2.87484	+	1.65979i	−0.187136	+	0.108043i
$237$	−7.71144	−	13.3566i	−0.500912	−	0.867605i
$238$		0			0
$239$			23.4449i			1.51652i	0.651952	+	0.758261i	$0.273951\pi$
$239$			23.4449i			1.51652i	−0.651952	+	0.758261i	$0.726049\pi$
$240$	0.777512	+	0.448897i	0.0501882	+	0.0289762i
$241$	−9.57480	−	5.52801i	−0.616767	−	0.356091i	0.158842	−	0.987304i	$-0.449224\pi$
$241$	−9.57480	−	5.52801i	−0.616767	−	0.356091i	−0.775609	+	0.631213i	$0.782557\pi$
$242$			9.65791i			0.620834i
$243$	5.05010	−	8.74704i	0.323964	−	0.561123i
$244$	−3.41517	−	5.91525i	−0.218634	−	0.378685i
$245$		0			0
$246$	7.50399			0.478437
$247$	25.3964	−	7.52109i	1.61594	−	0.478555i
$248$	−6.63998			−0.421639
$249$	2.93514	−	1.69460i	0.186007	−	0.107391i
$250$	−3.06229	−	5.30405i	−0.193676	−	0.335457i
$251$	−12.9898	+	22.4990i	−0.819907	+	1.42012i	0.0858425	+	0.996309i	$0.472642\pi$
$251$	−12.9898	+	22.4990i	−0.819907	+	1.42012i	−0.905750	+	0.423813i	$0.860692\pi$
$252$		0			0
$253$	25.6068	+	14.7841i	1.60989	+	0.929469i
$254$	−0.635520	−	0.366918i	−0.0398761	−	0.0230225i
$255$		−	0.636015i		−	0.0398288i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.886678	+	1.53577i	0.0553095	+	0.0957988i	0.892354	−	0.451335i	$-0.149052\pi$
$257$	0.886678	+	1.53577i	0.0553095	+	0.0957988i	−0.837045	+	0.547134i	$0.815719\pi$
$258$	12.6928	−	7.32820i	0.790220	−	0.456234i
$259$		0			0
$260$	−2.20734	+	0.653698i	−0.136893	+	0.0405406i
$261$	−7.43125			−0.459983
$262$	17.2089	−	9.93556i	1.06317	−	0.613821i
$263$	−2.81508	−	4.87586i	−0.173585	−	0.300658i	0.766086	−	0.642739i	$-0.222202\pi$
$263$	−2.81508	−	4.87586i	−0.173585	−	0.300658i	−0.939671	+	0.342080i	$0.888869\pi$
$264$	3.19549	−	5.53475i	0.196669	−	0.340640i
$265$		−	4.08723i		−	0.251077i
$266$		0			0
$267$	6.73810	+	3.89024i	0.412365	+	0.238079i
$268$		−	3.92379i		−	0.239684i
$269$	0.334197	−	0.578847i	0.0203764	−	0.0352929i	−0.855657	−	0.517543i	$-0.826847\pi$
$269$	0.334197	−	0.578847i	0.0203764	−	0.0352929i	0.876034	+	0.482250i	$0.160180\pi$
$270$	−1.80583	−	3.12779i	−0.109899	−	0.190351i
$271$	−18.0500	+	10.4212i	−1.09646	+	0.633040i	−0.935288	−	0.353886i	$-0.884860\pi$
$271$	−18.0500	+	10.4212i	−1.09646	+	0.633040i	−0.161170	+	0.986927i	$0.551527\pi$
$272$	0.708420			0.0429543
$273$		0			0
$274$	10.4636			0.632131
$275$	−18.0762	+	10.4363i	−1.09004	+	0.629333i
$276$	−4.57379	−	7.92204i	−0.275310	−	0.476851i
$277$	3.82091	−	6.61801i	0.229576	−	0.397638i	−0.728106	−	0.685464i	$-0.759599\pi$
$277$	3.82091	−	6.61801i	0.229576	−	0.397638i	0.957683	+	0.287826i	$0.0929326\pi$
$278$		−	0.0631324i		−	0.00378643i
$279$	5.88156	+	3.39572i	0.352120	+	0.203296i
$280$		0			0
$281$			4.17663i			0.249157i	0.992210	+	0.124578i	$0.0397578\pi$
$281$			4.17663i			0.249157i	−0.992210	+	0.124578i	$0.960242\pi$
$282$	1.36684	−	2.36744i	0.0813944	−	0.140979i
$283$	3.44853	+	5.97302i	0.204994	+	0.355059i	0.950131	−	0.311852i	$-0.100949\pi$
$283$	3.44853	+	5.97302i	0.204994	+	0.355059i	−0.745137	+	0.666911i	$0.767616\pi$
$284$	−9.11772	+	5.26412i	−0.541037	+	0.312368i
$285$	6.59528			0.390670
$286$	4.65337	+	15.7130i	0.275159	+	0.929130i
$287$		0			0
$288$	0.885780	−	0.511405i	0.0521951	−	0.0301348i
$289$	8.24907	+	14.2878i	0.485239	+	0.840459i
$290$	−2.31947	+	4.01744i	−0.136204	+	0.235912i
$291$			12.9264i			0.757760i
$292$	5.55335	+	3.20623i	0.324985	+	0.187630i
$293$	−13.3859	−	7.72837i	−0.782014	−	0.451496i	0.0551294	−	0.998479i	$-0.482443\pi$
$293$	−13.3859	−	7.72837i	−0.782014	−	0.451496i	−0.837144	+	0.546983i	$0.815776\pi$
$294$		0			0
$295$	1.05976	−	1.83555i	0.0617013	−	0.106870i
$296$	−1.05231	−	1.82266i	−0.0611645	−	0.105940i
$297$	−22.2652	+	12.8548i	−1.29196	+	0.745914i
$298$	−8.88246			−0.514547
$299$	22.8076	+	5.47708i	1.31900	+	0.316748i
$300$	6.45740			0.372818
$301$		0			0
$302$	6.61530	+	11.4580i	0.380668	+	0.659336i
$303$	−9.63900	+	16.6952i	−0.553746	+	0.959116i
$304$			7.34609i			0.421327i
$305$	3.77681	+	2.18054i	0.216260	+	0.124858i
$306$	−0.627504	−	0.362290i	−0.0358720	−	0.0207107i
$307$			25.0571i			1.43008i	0.699082	+	0.715042i	$0.253592\pi$
$307$			25.0571i			1.43008i	−0.699082	+	0.715042i	$0.746408\pi$
$308$		0			0
$309$	7.59803	+	13.1602i	0.432237	+	0.748656i
$310$	3.67155	−	2.11977i	0.208530	−	0.120395i
$311$	−2.14555			−0.121663			−0.0608315	−	0.998148i	$-0.519375\pi$
$311$	−2.14555			−0.121663			−0.0608315	+	0.998148i	$0.519375\pi$
$312$	1.18383	−	4.92971i	0.0670214	−	0.279090i
$313$	29.7469			1.68139			0.840696	−	0.541507i	$-0.182146\pi$
$313$	29.7469			1.68139			0.840696	+	0.541507i	$0.182146\pi$
$314$	2.58398	−	1.49186i	0.145822	−	0.0841906i
$315$		0			0
$316$	−5.48418	+	9.49887i	−0.308509	+	0.534353i
$317$			6.15558i			0.345732i	0.984945	+	0.172866i	$0.0553027\pi$
$317$			6.15558i			0.345732i	−0.984945	+	0.172866i	$0.944697\pi$
$318$	7.79527	+	4.50060i	0.437137	+	0.252381i
$319$	28.5983	+	16.5112i	1.60120	+	0.924452i
$320$		−	0.638488i		−	0.0356925i
$321$	10.7734	−	18.6600i	0.601310	−	1.04150i
$322$		0			0
$323$	4.50690	−	2.60206i	0.250770	−	0.144782i
$324$	4.88543			0.271413
$325$	−11.3984	+	12.0100i	−0.632271	+	0.666194i
$326$	−9.91987			−0.549411
$327$	2.15988	−	1.24701i	0.119442	−	0.0689597i
$328$	−2.66832	−	4.62167i	−0.147333	−	0.255189i
$329$		0			0
$330$			4.08056i			0.224627i
$331$	24.8252	+	14.3328i	1.36452	+	0.787804i	0.990221	−	0.139505i	$-0.0445511\pi$
$331$	24.8252	+	14.3328i	1.36452	+	0.787804i	0.374296	+	0.927309i	$0.377884\pi$
$332$	−2.08740	−	1.20516i	−0.114561	−	0.0661417i
$333$			2.15263i			0.117964i
$334$	−6.01000	+	10.4096i	−0.328853	+	0.569589i
$335$	1.25265	+	2.16965i	0.0684394	+	0.118540i
$336$		0			0
$337$	21.2688			1.15859			0.579294	−	0.815119i	$-0.303328\pi$
$337$	21.2688			1.15859			0.579294	+	0.815119i	$0.303328\pi$
$338$	7.07898	+	10.9036i	0.385046	+	0.593076i
$339$	7.37238			0.400413
$340$	−0.391718	+	0.226159i	−0.0212439	+	0.0122652i
$341$	−15.0897	−	26.1361i	−0.817151	−	1.41535i
$342$	3.75683	−	6.50702i	0.203146	−	0.351859i
$343$		0			0
$344$	−9.02680	−	5.21162i	−0.486692	−	0.280992i
$345$	5.05812	+	2.92031i	0.272320	+	0.157224i
$346$		−	19.5152i		−	1.04914i
$347$	−6.95294	+	12.0428i	−0.373253	+	0.646494i	−0.990064	−	0.140618i	$-0.955091\pi$
$347$	−6.95294	+	12.0428i	−0.373253	+	0.646494i	0.616811	+	0.787112i	$0.288424\pi$
$348$	−5.10811	−	8.84751i	−0.273824	−	0.474277i
$349$	−5.92236	+	3.41927i	−0.317016	+	0.183030i	−0.650062	−	0.759881i	$-0.725257\pi$
$349$	−5.92236	+	3.41927i	−0.317016	+	0.183030i	0.333045	+	0.942911i	$0.391924\pi$
$350$		0			0
$351$	−14.0399	+	14.7932i	−0.749397	+	0.789603i
$352$	−4.54510			−0.242254
$353$	12.1206	−	6.99785i	0.645116	−	0.372458i	−0.141467	−	0.989943i	$-0.545182\pi$
$353$	12.1206	−	6.99785i	0.645116	−	0.372458i	0.786583	+	0.617485i	$0.211848\pi$
$354$	2.33387	+	4.04239i	0.124044	+	0.214850i
$355$	3.36107	−	5.82155i	0.178387	−	0.308976i
$356$		−	5.53328i		−	0.293263i
$357$		0			0
$358$	−13.9877	−	8.07581i	−0.739274	−	0.426820i
$359$			1.35528i			0.0715287i	0.999360	+	0.0357644i	$0.0113866\pi$
$359$			1.35528i			0.0715287i	−0.999360	+	0.0357644i	$0.988613\pi$
$360$	−0.326526	+	0.565560i	−0.0172094	+	0.0298076i
$361$	17.4825	+	30.2806i	0.920133	+	1.59372i
$362$	0.244102	−	0.140933i	0.0128297	−	0.00740725i
$363$	13.5802			0.712777
$364$		0			0
$365$	−4.09427			−0.214304
$366$	−8.31758	+	4.80216i	−0.434767	+	0.251013i
$367$	−5.92951	−	10.2702i	−0.309518	−	0.536101i	0.668739	−	0.743497i	$-0.266834\pi$
$367$	−5.92951	−	10.2702i	−0.309518	−	0.536101i	−0.978257	+	0.207396i	$0.933501\pi$
$368$	−3.25276	+	5.63395i	−0.169562	+	0.293690i
$369$			5.45837i			0.284151i
$370$	1.16375	+	0.671889i	0.0605003	+	0.0349298i
$371$		0			0
$372$			9.33664i			0.484082i
$373$	19.0720	−	33.0337i	0.987511	−	1.71042i	0.357315	−	0.933984i	$-0.383692\pi$
$373$	19.0720	−	33.0337i	0.987511	−	1.71042i	0.630197	−	0.776436i	$-0.282974\pi$
$374$	1.60992	+	2.78846i	0.0832469	+	0.144188i
$375$	−7.45816	+	4.30597i	−0.385138	+	0.222359i
$376$	−1.94413			−0.100261
$377$	25.4720	+	6.11693i	1.31188	+	0.315038i
$378$		0			0
$379$	−27.4201	+	15.8310i	−1.40848	+	0.813185i	−0.995242	−	0.0974383i	$-0.968935\pi$
$379$	−27.4201	+	15.8310i	−1.40848	+	0.813185i	−0.413237	+	0.910624i	$0.635602\pi$
$380$	−2.34519	−	4.06200i	−0.120306	−	0.208376i
$381$	−0.515932	+	0.893621i	−0.0264320	+	0.0457816i
$382$		−	12.4267i		−	0.635804i
$383$	12.6943	+	7.32908i	0.648650	+	0.374498i	0.787939	−	0.615753i	$-0.211148\pi$
$383$	12.6943	+	7.32908i	0.648650	+	0.374498i	−0.139289	+	0.990252i	$0.544482\pi$
$384$	1.21774	+	0.703063i	0.0621426	+	0.0358780i
$385$		0			0
$386$	5.82010	−	10.0807i	0.296235	−	0.513095i
$387$	5.33050	+	9.23270i	0.270965	+	0.469325i
$388$	7.96131	−	4.59646i	0.404174	−	0.233350i
$389$	16.4655			0.834835			0.417418	−	0.908715i	$-0.362935\pi$
$389$	16.4655			0.834835			0.417418	+	0.908715i	$0.362935\pi$
$390$	0.919181	+	3.10380i	0.0465445	+	0.157167i
$391$	4.60864			0.233069
$392$		0			0
$393$	−13.9706	−	24.1979i	−0.704726	−	1.22062i
$394$	−2.65415	+	4.59712i	−0.133714	+	0.231599i
$395$		−	7.00316i		−	0.352367i
$396$	4.02596	+	2.32439i	0.202312	+	0.116805i
$397$	−14.1163	−	8.15004i	−0.708476	−	0.409039i	0.102020	−	0.994782i	$-0.467469\pi$
$397$	−14.1163	−	8.15004i	−0.708476	−	0.409039i	−0.810497	+	0.585743i	$0.800803\pi$
$398$			13.7492i			0.689187i
$399$		0			0
$400$	−2.29617	−	3.97708i	−0.114808	−	0.198854i
$401$	18.0562	−	10.4248i	0.901684	−	0.520588i	0.0239381	−	0.999713i	$-0.492380\pi$
$401$	18.0562	−	10.4248i	0.901684	−	0.520588i	0.877746	+	0.479126i	$0.159046\pi$
$402$	−5.51734			−0.275180
$403$	−17.3650	−	16.4808i	−0.865013	−	0.820967i
$404$	13.7100			0.682098
$405$	−2.70138	+	1.55964i	−0.134233	+	0.0774993i
$406$		0			0
$407$	4.78287	−	8.28417i	0.237078	−	0.410631i
$408$		−	0.996127i		−	0.0493157i
$409$	1.03993	+	0.600406i	0.0514214	+	0.0296882i	0.525490	−	0.850800i	$-0.323882\pi$
$409$	1.03993	+	0.600406i	0.0514214	+	0.0296882i	−0.474069	+	0.880488i	$0.657215\pi$
$410$	2.95088	+	1.70369i	0.145733	+	0.0841392i
$411$		−	14.7132i		−	0.725747i
$412$	5.40352	−	9.35918i	0.266212	−	0.461094i
$413$		0			0
$414$	5.76246	−	3.32696i	0.283210	−	0.163511i
$415$	1.53896			0.0755445
$416$	−3.45714	+	1.02382i	−0.169500	+	0.0501970i
$417$	−0.0887721			−0.00434719
$418$	−28.9155	+	16.6943i	−1.41430	+	0.816547i
$419$	−9.29434	−	16.0983i	−0.454058	−	0.786452i	0.544575	−	0.838712i	$-0.316691\pi$
$419$	−9.29434	−	16.0983i	−0.454058	−	0.786452i	−0.998634	+	0.0522602i	$0.983357\pi$
$420$		0			0
$421$			21.9581i			1.07017i	0.844797	+	0.535087i	$0.179721\pi$
$421$			21.9581i			1.07017i	−0.844797	+	0.535087i	$0.820279\pi$
$422$	−6.77729	−	3.91287i	−0.329913	−	0.190476i
$423$	1.72207	+	0.994238i	0.0837299	+	0.0483415i
$424$		−	6.40142i		−	0.310881i
$425$	−1.62665	+	2.81744i	−0.0789041	+	0.136666i
$426$	7.40201	+	12.8207i	0.358629	+	0.621163i
$427$		0			0
$428$	−15.3235			−0.740687
$429$	22.0945	−	6.54322i	1.06673	−	0.315910i
$430$	6.65511			0.320938
$431$	23.8430	−	13.7658i	1.14848	−	0.663074i	0.199962	−	0.979804i	$-0.435918\pi$
$431$	23.8430	−	13.7658i	1.14848	−	0.663074i	0.948516	+	0.316730i	$0.102585\pi$
$432$	−2.82829	−	4.89874i	−0.136076	−	0.235691i
$433$	−16.4667	+	28.5212i	−0.791339	+	1.37064i	0.133799	+	0.991008i	$0.457282\pi$
$433$	−16.4667	+	28.5212i	−0.791339	+	1.37064i	−0.925138	+	0.379631i	$0.876051\pi$
$434$		0			0
$435$	5.64903	+	3.26147i	0.270850	+	0.156375i
$436$	−1.53605	−	0.886839i	−0.0735635	−	0.0424719i
$437$			47.7902i			2.28611i
$438$	4.50836	−	7.80871i	0.215418	−	0.373115i
$439$	6.35859	+	11.0134i	0.303479	+	0.525641i	0.976921	−	0.213599i	$-0.0685185\pi$
$439$	6.35859	+	11.0134i	0.303479	+	0.525641i	−0.673443	+	0.739239i	$0.735185\pi$
$440$	2.51320	−	1.45099i	0.119812	−	0.0691734i
$441$		0			0
$442$	1.85268	+	1.75834i	0.0881228	+	0.0836356i
$443$	−28.9869			−1.37721			−0.688604	−	0.725138i	$-0.741776\pi$
$443$	−28.9869			−1.37721			−0.688604	+	0.725138i	$0.741776\pi$
$444$	−2.56289	+	1.47968i	−0.121629	+	0.0702227i
$445$	1.76647	+	3.05961i	0.0837385	+	0.145039i
$446$	9.76882	−	16.9201i	0.462567	−	0.801190i
$447$			12.4899i			0.590750i
$448$		0			0
$449$	−0.0241096	−	0.0139197i	−0.00113780	−	0.000656909i	0.499431	−	0.866354i	$-0.333542\pi$
$449$	−0.0241096	−	0.0139197i	−0.00113780	−	0.000656909i	−0.500569	+	0.865697i	$0.666876\pi$
$450$			4.69709i			0.221423i
$451$	12.1278	−	21.0059i	0.571075	−	0.989130i
$452$	−2.62152	−	4.54061i	−0.123306	−	0.213572i
$453$	16.1114	−	9.30194i	0.756981	−	0.437043i
$454$	4.92479			0.231132
$455$		0			0
$456$	10.3295			0.483724
$457$	26.6615	−	15.3931i	1.24717	−	0.720057i	0.276630	−	0.960977i	$-0.410782\pi$
$457$	26.6615	−	15.3931i	1.24717	−	0.720057i	0.970545	+	0.240920i	$0.0774491\pi$
$458$	−7.98610	−	13.8323i	−0.373166	−	0.646342i
$459$	−2.00362	+	3.47036i	−0.0935208	+	0.161983i
$460$		−	4.15370i		−	0.193667i
$461$	−32.8804	−	18.9835i	−1.53139	−	0.884149i	−0.999298	−	0.0374628i	$-0.988072\pi$
$461$	−32.8804	−	18.9835i	−1.53139	−	0.884149i	−0.532093	−	0.846686i	$-0.678594\pi$
$462$		0			0
$463$		−	13.3969i		−	0.622608i	−0.950310	−	0.311304i	$-0.899234\pi$
$463$		−	13.3969i		−	0.622608i	0.950310	−	0.311304i	$-0.100766\pi$
$464$	−3.63276	+	6.29212i	−0.168647	+	0.292104i
$465$	−2.98067	−	5.16266i	−0.138225	−	0.239413i
$466$	4.53803	−	2.62003i	0.210220	−	0.121371i
$467$	−25.9151			−1.19921			−0.599603	−	0.800298i	$-0.704675\pi$
$467$	−25.9151			−1.19921			−0.599603	+	0.800298i	$0.704675\pi$
$468$	3.58585	+	0.861117i	0.165756	+	0.0398051i
$469$		0			0
$470$	1.07500	−	0.620651i	0.0495860	−	0.0286285i
$471$	−2.09774	−	3.63340i	−0.0966590	−	0.167418i
$472$	1.65979	−	2.87484i	0.0763980	−	0.132325i
$473$		−	47.3747i		−	2.17829i
$474$	13.3566	+	7.71144i	0.613489	+	0.354198i
$475$	−29.2160	−	16.8678i	−1.34052	−	0.773950i
$476$		0			0
$477$	−3.27372	+	5.67025i	−0.149893	+	0.259623i
$478$	−11.7224	−	20.3038i	−0.536171	−	0.928676i
$479$	−0.219038	+	0.126461i	−0.0100081	+	0.00577817i	−0.504996	−	0.863122i	$-0.668506\pi$
$479$	−0.219038	+	0.126461i	−0.0100081	+	0.00577817i	0.494988	+	0.868900i	$0.335173\pi$
$480$	−0.897794			−0.0409785
$481$	1.77191	−	7.37856i	0.0807922	−	0.336434i
$482$	11.0560			0.503588
$483$		0			0
$484$	−4.82895	−	8.36399i	−0.219498	−	0.380181i
$485$	−2.93479	+	5.08320i	−0.133262	+	0.230816i
$486$			10.1002i			0.458155i
$487$	−26.2897	−	15.1783i	−1.19130	−	0.687796i	−0.232697	−	0.972549i	$-0.574755\pi$
$487$	−26.2897	−	15.1783i	−1.19130	−	0.687796i	−0.958601	+	0.284753i	$0.908088\pi$
$488$	5.91525	+	3.41517i	0.267771	+	0.154598i
$489$			13.9486i			0.630777i
$490$		0			0
$491$	−6.74228	−	11.6780i	−0.304275	−	0.527019i	0.672825	−	0.739802i	$-0.265081\pi$
$491$	−6.74228	−	11.6780i	−0.304275	−	0.527019i	−0.977100	+	0.212782i	$0.931747\pi$
$492$	−6.49864	+	3.75199i	−0.292981	+	0.169153i
$493$	5.14704			0.231811
$494$	−18.2334	+	19.2117i	−0.820360	+	0.864374i
$495$	−2.96818			−0.133410
$496$	5.75039	−	3.31999i	0.258200	−	0.149072i
$497$		0			0
$498$	−1.69460	+	2.93514i	−0.0759370	+	0.131527i
$499$			2.02110i			0.0904767i	0.998976	+	0.0452383i	$0.0144047\pi$
$499$			2.02110i			0.0904767i	−0.998976	+	0.0452383i	$0.985595\pi$
$500$	5.30405	+	3.06229i	0.237204	+	0.136950i
$501$	14.6372	+	8.45081i	0.653944	+	0.377555i
$502$		−	25.9796i		−	1.15952i
$503$	2.81234	−	4.87112i	0.125396	−	0.217192i	−0.796492	−	0.604650i	$-0.793313\pi$
$503$	2.81234	−	4.87112i	0.125396	−	0.217192i	0.921888	+	0.387457i	$0.126646\pi$
$504$		0			0
$505$	−7.58090	+	4.37684i	−0.337346	+	0.194767i
$506$	−29.5682			−1.31447
$507$	15.3318	−	9.95394i	0.680909	−	0.442070i
$508$	0.733835			0.0325587
$509$	14.0634	−	8.11950i	0.623348	−	0.359890i	−0.154823	−	0.987942i	$-0.549481\pi$
$509$	14.0634	−	8.11950i	0.623348	−	0.359890i	0.778171	+	0.628052i	$0.216147\pi$
$510$	0.318008	+	0.550805i	0.0140816	+	0.0243901i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−35.9866	−	20.7769i	−1.58885	−	0.917321i
$514$	−1.53577	−	0.886678i	−0.0677400	−	0.0391097i
$515$			6.90017i			0.304058i
$516$	−7.32820	+	12.6928i	−0.322606	+	0.558770i
$517$	−4.41813	−	7.65242i	−0.194309	−	0.336553i
$518$		0			0
$519$	−27.4408			−1.20452
$520$	1.58476	−	1.66979i	0.0694964	−	0.0732251i
$521$	16.6470			0.729319			0.364659	−	0.931141i	$-0.381185\pi$
$521$	16.6470			0.729319			0.364659	+	0.931141i	$0.381185\pi$
$522$	6.43565	−	3.71562i	0.281681	−	0.162628i
$523$	6.40753	+	11.0982i	0.280182	+	0.485289i	0.971429	−	0.237329i	$-0.0762720\pi$
$523$	6.40753	+	11.0982i	0.280182	+	0.485289i	−0.691248	+	0.722618i	$0.742939\pi$
$524$	−9.93556	+	17.2089i	−0.434037	+	0.751774i
$525$		0			0
$526$	4.87586	+	2.81508i	0.212598	+	0.122743i
$527$	−4.07369	−	2.35195i	−0.177453	−	0.102452i
$528$			6.39098i			0.278132i
$529$	−9.66092	+	16.7332i	−0.420040	+	0.727530i
$530$	2.04361	+	3.53964i	0.0887690	+	0.153752i
$531$	−2.94042	+	1.69765i	−0.127603	+	0.0736718i
$532$		0			0
$533$	4.49298	−	18.7096i	0.194613	−	0.810403i
$534$	−7.78048			−0.336695
$535$	8.47305	−	4.89192i	0.366322	−	0.211496i
$536$	1.96190	+	3.39810i	0.0847410	+	0.146776i
$537$	−11.3556	+	19.6685i	−0.490031	+	0.848758i
$538$			0.668394i			0.0288165i
$539$		0			0
$540$	3.12779	+	1.80583i	0.134598	+	0.0777104i
$541$			6.90972i			0.297072i	0.988907	+	0.148536i	$0.0474561\pi$
$541$			6.90972i			0.297072i	−0.988907	+	0.148536i	$0.952544\pi$
$542$	10.4212	−	18.0500i	0.447627	−	0.775313i
$543$	−0.198169	−	0.343239i	−0.00850424	−	0.0147298i
$544$	−0.613510	+	0.354210i	−0.0263040	+	0.0151866i
$545$	1.13247			0.0485098
$546$		0			0
$547$	24.8868			1.06408			0.532041	−	0.846719i	$-0.321425\pi$
$547$	24.8868			1.06408			0.532041	+	0.846719i	$0.321425\pi$
$548$	−9.06177	+	5.23181i	−0.387100	+	0.223492i
$549$	−3.49307	−	6.05018i	−0.149081	−	0.258215i
$550$	10.4363	−	18.0762i	0.445005	−	0.770772i
$551$			53.3731i			2.27377i
$552$	7.92204	+	4.57379i	0.337184	+	0.194674i
$553$		0			0
$554$			7.64182i			0.324670i
$555$	0.944760	−	1.63637i	0.0401028	−	0.0694602i
$556$	0.0315662	+	0.0546743i	0.00133871	+	0.00231871i
$557$	−10.1308	+	5.84900i	−0.429254	+	0.247830i	−0.699029	−	0.715094i	$-0.746384\pi$
$557$	−10.1308	+	5.84900i	−0.429254	+	0.247830i	0.269775	+	0.962923i	$0.413051\pi$
$558$	−6.79144			−0.287505
$559$	−10.6715	−	36.0346i	−0.451358	−	1.52410i
$560$		0			0
$561$	3.92093	−	2.26375i	0.165542	−	0.0955755i
$562$	−2.08831	−	3.61707i	−0.0880903	−	0.152577i
$563$	−12.5615	+	21.7572i	−0.529404	+	0.916955i	0.470008	+	0.882662i	$0.344251\pi$
$563$	−12.5615	+	21.7572i	−0.529404	+	0.916955i	−0.999412	+	0.0342927i	$0.989082\pi$
$564$			2.73369i			0.115109i
$565$	2.89912	+	1.67381i	0.121967	+	0.0704177i
$566$	−5.97302	−	3.44853i	−0.251065	−	0.144952i
$567$		0			0
$568$	5.26412	−	9.11772i	0.220878	−	0.382571i
$569$	12.5379	+	21.7162i	0.525614	+	0.910391i	0.999555	+	0.0298340i	$0.00949788\pi$
$569$	12.5379	+	21.7162i	0.525614	+	0.910391i	−0.473940	+	0.880557i	$0.657169\pi$
$570$	−5.71168	+	3.29764i	−0.239236	+	0.138123i
$571$	9.12402			0.381828			0.190914	−	0.981607i	$-0.438855\pi$
$571$	9.12402			0.381828			0.190914	+	0.981607i	$0.438855\pi$
$572$	−11.8864	−	11.2812i	−0.496997	−	0.471690i
$573$	−17.4735			−0.729964
$574$		0			0
$575$	−14.9378	−	25.8730i	−0.622948	−	1.07898i
$576$	−0.511405	+	0.885780i	−0.0213086	+	0.0369075i
$577$			12.8257i			0.533939i	0.963705	+	0.266970i	$0.0860224\pi$
$577$			12.8257i			0.533939i	−0.963705	+	0.266970i	$0.913978\pi$
$578$	−14.2878	−	8.24907i	−0.594295	−	0.343116i
$579$	−14.1747	−	8.18380i	−0.589082	−	0.340107i
$580$		−	4.63894i		−	0.192622i
$581$		0			0
$582$	−6.46320	−	11.1946i	−0.267908	−	0.464031i
$583$	25.1971	−	14.5475i	1.04356	−	0.602498i
$584$	−6.41246			−0.265349
$585$	−2.25769	+	0.668609i	−0.0933440	+	0.0276436i
$586$	15.4567			0.638512
$587$	6.27507	−	3.62291i	0.259000	−	0.149534i	−0.364878	−	0.931055i	$-0.618889\pi$
$587$	6.27507	−	3.62291i	0.259000	−	0.149534i	0.623878	+	0.781522i	$0.285556\pi$
$588$		0			0
$589$	24.3889	−	42.2429i	1.00493	−	1.74059i
$590$			2.11951i			0.0872589i
$591$	6.46413	+	3.73206i	0.265899	+	0.153517i
$592$	1.82266	+	1.05231i	0.0749109	+	0.0432498i
$593$			15.4794i			0.635664i	0.948147	+	0.317832i	$0.102955\pi$
$593$			15.4794i			0.635664i	−0.948147	+	0.317832i	$0.897045\pi$
$594$	12.8548	−	22.2652i	0.527441	−	0.913554i
$595$		0			0
$596$	7.69244	−	4.44123i	0.315095	−	0.181920i
$597$	19.3332			0.791253
$598$	−22.4905	+	6.66050i	−0.919704	+	0.272368i
$599$	−43.0965			−1.76088			−0.880438	−	0.474162i	$-0.842751\pi$
$599$	−43.0965			−1.76088			−0.880438	+	0.474162i	$0.842751\pi$
$600$	−5.59227	+	3.22870i	−0.228303	+	0.131811i
$601$	−11.6610	−	20.1975i	−0.475664	−	0.823873i	0.523948	−	0.851750i	$-0.324459\pi$
$601$	−11.6610	−	20.1975i	−0.475664	−	0.823873i	−0.999611	+	0.0278770i	$0.991125\pi$
$602$		0			0
$603$		−	4.01330i		−	0.163434i
$604$	−11.4580	−	6.61530i	−0.466221	−	0.269173i
$605$	5.34031	+	3.08323i	0.217114	+	0.125351i
$606$		−	19.2780i		−	0.783115i
$607$	15.7844	−	27.3394i	0.640670	−	1.10967i	−0.344614	−	0.938745i	$-0.611990\pi$
$607$	15.7844	−	27.3394i	0.640670	−	1.10967i	0.985283	−	0.170928i	$-0.0546766\pi$
$608$	−3.67305	−	6.36190i	−0.148962	−	0.258009i
$609$		0			0
$610$	−4.36109			−0.176575
$611$	−5.08433	−	4.82544i	−0.205690	−	0.195216i
$612$	0.724579			0.0292894
$613$	13.6857	−	7.90145i	0.552761	−	0.319137i	−0.197474	−	0.980308i	$-0.563274\pi$
$613$	13.6857	−	7.90145i	0.552761	−	0.319137i	0.750235	+	0.661171i	$0.229940\pi$
$614$	−12.5285	−	21.7001i	−0.505611	−	0.875744i
$615$	2.39560	−	4.14930i	0.0966000	−	0.167316i
$616$		0			0
$617$	14.3413	+	8.27996i	0.577360	+	0.333339i	0.760083	−	0.649826i	$-0.225158\pi$
$617$	14.3413	+	8.27996i	0.577360	+	0.333339i	−0.182724	+	0.983164i	$0.558491\pi$
$618$	−13.1602	−	7.59803i	−0.529380	−	0.305638i
$619$			20.0405i			0.805497i	0.915311	+	0.402749i	$0.131945\pi$
$619$			20.0405i			0.805497i	−0.915311	+	0.402749i	$0.868055\pi$
$620$	−2.11977	+	3.67155i	−0.0851321	+	0.147453i
$621$	−18.3995	−	31.8689i	−0.738346	−	1.27885i
$622$	1.85810	−	1.07278i	0.0745031	−	0.0430144i
$623$		0			0
$624$	1.43962	+	4.86117i	0.0576310	+	0.194602i
$625$	19.0512			0.762048
$626$	−25.7615	+	14.8734i	−1.02964	+	0.594462i
$627$	23.4743	+	40.6588i	0.937475	+	1.62375i
$628$	−1.49186	+	2.58398i	−0.0595317	+	0.103112i
$629$		−	1.49096i		−	0.0594484i
$630$		0			0
$631$	−17.8127	−	10.2842i	−0.709113	−	0.409407i	0.101620	−	0.994823i	$-0.467598\pi$
$631$	−17.8127	−	10.2842i	−0.709113	−	0.409407i	−0.810733	+	0.585417i	$0.800931\pi$
$632$		−	10.9684i		−	0.436298i
$633$	−5.50199	+	9.52972i	−0.218684	+	0.378772i
$634$	−3.07779	−	5.33089i	−0.122235	−	0.211717i
$635$	−0.405772	+	0.234272i	−0.0161026	+	0.00929682i
$636$	−9.00120			−0.356921
$637$		0			0
$638$	−33.0225			−1.30737
$639$	−9.32570	+	5.38420i	−0.368919	+	0.212996i
$640$	0.319244	+	0.552947i	0.0126192	+	0.0218571i
$641$	17.1856	−	29.7664i	0.678792	−	1.17570i	−0.296553	−	0.955017i	$-0.595837\pi$
$641$	17.1856	−	29.7664i	0.678792	−	1.17570i	0.975345	−	0.220686i	$-0.0708296\pi$
$642$			21.5467i			0.850381i
$643$	7.68629	+	4.43768i	0.303118	+	0.175005i	0.643843	−	0.765158i	$-0.277339\pi$
$643$	7.68629	+	4.43768i	0.303118	+	0.175005i	−0.340725	+	0.940163i	$0.610672\pi$
$644$		0			0
$645$		−	9.35793i		−	0.368468i
$646$	−2.60206	+	4.50690i	−0.102377	+	0.177321i
$647$	2.26837	+	3.92893i	0.0891788	+	0.154462i	0.907164	−	0.420777i	$-0.138242\pi$
$647$	2.26837	+	3.92893i	0.0891788	+	0.154462i	−0.817985	+	0.575239i	$0.804909\pi$
$648$	−4.23090	+	2.44271i	−0.166206	+	0.0959588i
$649$	15.0878			0.592248
$650$	3.86634	−	16.1002i	0.151650	−	0.631500i
$651$		0			0
$652$	8.59086	−	4.95993i	0.336444	−	0.194246i
$653$	−13.5725	−	23.5083i	−0.531133	−	0.919949i	−0.999340	−	0.0363305i	$-0.988433\pi$
$653$	−13.5725	−	23.5083i	−0.531133	−	0.919949i	0.468207	−	0.883619i	$-0.344900\pi$
$654$	−1.24701	+	2.15988i	−0.0487619	+	0.0844580i
$655$		−	12.6875i		−	0.495740i
$656$	4.62167	+	2.66832i	0.180446	+	0.104180i
$657$	5.68003	+	3.27936i	0.221599	+	0.127940i
$658$		0			0
$659$	−13.2645	+	22.9748i	−0.516712	+	0.894972i	0.483099	+	0.875566i	$0.339511\pi$
$659$	−13.2645	+	22.9748i	−0.516712	+	0.894972i	−0.999812	+	0.0194066i	$0.993822\pi$
$660$	−2.04028	−	3.53387i	−0.0794178	−	0.137556i
$661$	26.9057	−	15.5340i	1.04651	−	0.604204i	0.124841	−	0.992177i	$-0.460158\pi$
$661$	26.9057	−	15.5340i	1.04651	−	0.604204i	0.921671	+	0.387973i	$0.126825\pi$
$662$	−28.6657			−1.11412
$663$	2.47244	−	2.60510i	0.0960218	−	0.101174i
$664$	2.41032			0.0935384
$665$		0			0
$666$	−1.07632	−	1.86424i	−0.0417064	−	0.0722377i
$667$	−23.6330	+	40.9335i	−0.915073	+	1.58495i
$668$		−	12.0200i		−	0.465068i
$669$	−23.7918	−	13.7362i	−0.919844	−	0.531072i
$670$	−2.16965	−	1.25265i	−0.0838208	−	0.0483940i
$671$			31.0446i			1.19846i
$672$		0			0
$673$	−9.48380	−	16.4264i	−0.365574	−	0.633192i	0.623294	−	0.781987i	$-0.285794\pi$
$673$	−9.48380	−	16.4264i	−0.365574	−	0.633192i	−0.988868	+	0.148795i	$0.952461\pi$
$674$	−18.4194	+	10.6344i	−0.709487	+	0.409623i
$675$	25.9769			0.999851
$676$	−11.5824	−	5.90328i	−0.445476	−	0.227049i
$677$	−16.7713			−0.644574			−0.322287	−	0.946642i	$-0.604452\pi$
$677$	−16.7713			−0.644574			−0.322287	+	0.946642i	$0.604452\pi$
$678$	−6.38467	+	3.68619i	−0.245202	+	0.141567i
$679$		0			0
$680$	0.226159	−	0.391718i	0.00867279	−	0.0150217i
$681$		−	6.92487i		−	0.265362i
$682$	26.1361	+	15.0897i	1.00080	+	0.577813i
$683$	6.44719	+	3.72228i	0.246695	+	0.142429i	0.618250	−	0.785982i	$-0.287842\pi$
$683$	6.44719	+	3.72228i	0.246695	+	0.142429i	−0.371555	+	0.928411i	$0.621175\pi$
$684$			7.51366i			0.287292i
$685$	3.34045	−	5.78583i	0.127632	−	0.221065i
$686$		0			0
$687$	−19.4500	+	11.2295i	−0.742063	+	0.428431i
$688$	10.4232			0.397383
$689$	15.8887	−	16.7412i	0.605311	−	0.637787i
$690$	−5.84062			−0.222349
$691$	−34.9257	+	20.1643i	−1.32863	+	0.767088i	−0.985089	−	0.172048i	$-0.944962\pi$
$691$	−34.9257	+	20.1643i	−1.32863	+	0.767088i	−0.343546	+	0.939136i	$0.611628\pi$
$692$	9.75761	+	16.9007i	0.370929	+	0.642467i
$693$		0			0
$694$		−	13.9059i		−	0.527860i
$695$	−0.0349089	−	0.0201546i	−0.00132417	−	0.000764509i
$696$	8.84751	+	5.10811i	0.335364	+	0.193623i
$697$		−	3.78058i		−	0.143200i
$698$	3.41927	−	5.92236i	0.129421	−	0.224165i
$699$	−3.68409	−	6.38104i	−0.139345	−	0.241353i
$700$		0			0
$701$	1.32063			0.0498794			0.0249397	−	0.999689i	$-0.492061\pi$
$701$	1.32063			0.0498794			0.0249397	+	0.999689i	$0.492061\pi$
$702$	4.76234	−	19.8313i	0.179743	−	0.748483i
$703$	15.4608			0.583114
$704$	3.93617	−	2.27255i	0.148350	−	0.0856499i
$705$	−0.872714	−	1.51158i	−0.0328683	−	0.0569296i
$706$	−6.99785	+	12.1206i	−0.263367	+	0.456166i
$707$		0			0
$708$	−4.04239	−	2.33387i	−0.151922	−	0.0877123i
$709$	−25.0311	−	14.4517i	−0.940063	−	0.542746i	−0.0500830	−	0.998745i	$-0.515949\pi$
$709$	−25.0311	−	14.4517i	−0.940063	−	0.542746i	−0.889980	+	0.455999i	$0.849282\pi$
$710$			6.72215i			0.252278i
$711$	−5.60927	+	9.71555i	−0.210364	+	0.364361i
$712$	2.76664	+	4.79196i	0.103684	+	0.179586i
$713$	37.4093	−	21.5983i	1.40099	−	0.808861i
$714$		0			0
$715$	10.1740	+	2.44322i	0.380487	+	0.0913712i
$716$	16.1516			0.603615
$717$	−28.5497	+	16.4832i	−1.06621	+	0.615577i
$718$	−0.677638	−	1.17370i	−0.0252892	−	0.0438022i
$719$	−15.7289	+	27.2433i	−0.586590	+	1.01600i	0.408086	+	0.912944i	$0.366197\pi$
$719$	−15.7289	+	27.2433i	−0.586590	+	1.01600i	−0.994675	+	0.103059i	$0.967137\pi$
$720$		−	0.653052i		−	0.0243378i
$721$		0			0
$722$	−30.2806	−	17.4825i	−1.12693	−	0.650632i
$723$		−	15.5462i		−	0.578168i
$724$	−0.140933	+	0.244102i	−0.00523772	+	0.00907199i
$725$	−16.6828	−	28.8955i	−0.619585	−	1.07315i
$726$	−11.7608	+	6.79012i	−0.436485	+	0.252005i
$727$	−15.8625			−0.588306			−0.294153	−	0.955758i	$-0.595038\pi$
$727$	−15.8625			−0.588306			−0.294153	+	0.955758i	$0.595038\pi$
$728$		0			0
$729$	28.8584			1.06883
$730$	3.54575	−	2.04714i	0.131234	−	0.0757680i
$731$	−3.69202	−	6.39476i	−0.136554	−	0.236519i
$732$	4.80216	−	8.31758i	0.177493	−	0.307427i
$733$		−	34.7482i		−	1.28345i	−0.766933	−	0.641727i	$-0.778218\pi$
$733$		−	34.7482i		−	1.28345i	0.766933	−	0.641727i	$-0.221782\pi$
$734$	10.2702	+	5.92951i	0.379081	+	0.218862i
$735$		0			0
$736$		−	6.50552i		−	0.239797i
$737$	−8.91701	+	15.4447i	−0.328462	+	0.568913i
$738$	−2.72919	−	4.72709i	−0.100463	−	0.174007i
$739$	21.7681	−	12.5678i	0.800753	−	0.462315i	−0.0429812	−	0.999076i	$-0.513686\pi$
$739$	21.7681	−	12.5678i	0.800753	−	0.462315i	0.843735	+	0.536761i	$0.180352\pi$
$740$	−1.34378			−0.0493983
$741$	27.0140	+	25.6385i	0.992385	+	0.941853i
$742$		0			0
$743$	−23.3693	+	13.4923i	−0.857336	+	0.494983i	−0.863119	−	0.505000i	$-0.831492\pi$
$743$	−23.3693	+	13.4923i	−0.857336	+	0.494983i	0.00578361	+	0.999983i	$0.498159\pi$
$744$	−4.66832	−	8.08577i	−0.171149	−	0.296439i
$745$	−2.83567	+	4.91153i	−0.103891	+	0.179944i
$746$			38.1440i			1.39655i
$747$	−2.13501	−	1.23265i	−0.0781159	−	0.0451003i
$748$	−2.78846	−	1.60992i	−0.101956	−	0.0588645i
$749$		0			0
$750$	4.30597	−	7.45816i	0.157232	−	0.272333i
$751$	−8.27299	−	14.3292i	−0.301886	−	0.522881i	0.674678	−	0.738113i	$-0.264283\pi$
$751$	−8.27299	−	14.3292i	−0.301886	−	0.522881i	−0.976563	+	0.215232i	$0.930949\pi$
$752$	1.68367	−	0.972065i	0.0613970	−	0.0354475i
$753$	−36.5305			−1.33125
$754$	−25.1179	+	7.43859i	−0.914739	+	0.270898i
$755$	8.44757			0.307439
$756$		0			0
$757$	−21.1295	−	36.5974i	−0.767965	−	1.33015i	−0.938665	−	0.344832i	$-0.887936\pi$
$757$	−21.1295	−	36.5974i	−0.767965	−	1.33015i	0.170699	−	0.985323i	$-0.445397\pi$
$758$	15.8310	−	27.4201i	0.575009	−	0.995945i
$759$			41.5767i			1.50914i
$760$	4.06200	+	2.34519i	0.147344	+	0.0850691i
$761$	−19.6009	−	11.3166i	−0.710531	−	0.410225i	0.100726	−	0.994914i	$-0.467883\pi$
$761$	−19.6009	−	11.3166i	−0.710531	−	0.410225i	−0.811258	+	0.584689i	$0.801217\pi$
$762$		−	1.03186i		−	0.0373805i
$763$		0			0
$764$	6.21334	+	10.7618i	0.224791	+	0.389349i
$765$	−0.400654	+	0.231317i	−0.0144857	+	0.00836330i
$766$	−14.6582			−0.529621
$767$	11.4762	−	3.39866i	0.414383	−	0.122718i
$768$	−1.40613			−0.0507392
$769$	−38.9093	+	22.4643i	−1.40311	+	0.810084i	−0.994710	−	0.102721i	$-0.967245\pi$
$769$	−38.9093	+	22.4643i	−1.40311	+	0.810084i	−0.408396	+	0.912805i	$0.633912\pi$
$770$		0			0
$771$	−1.24678	+	2.15949i	−0.0449017	+	0.0777721i
$772$			11.6402i			0.418940i
$773$	−44.7057	−	25.8108i	−1.60795	−	0.928351i	−0.989828	−	0.142270i	$-0.954560\pi$
$773$	−44.7057	−	25.8108i	−1.60795	−	0.928351i	−0.618124	−	0.786081i	$-0.712107\pi$
$774$	−9.23270	−	5.33050i	−0.331863	−	0.191601i
$775$			30.4930i			1.09534i
$776$	−4.59646	+	7.96131i	−0.165003	+	0.285794i
$777$		0			0
$778$	−14.2596	+	8.23276i	−0.511230	+	0.295159i
$779$	39.2034			1.40461
$780$	−2.34793	−	2.22838i	−0.0840695	−	0.0797886i
$781$	47.8519			1.71227
$782$	−3.99120	+	2.30432i	−0.142725	+	0.0824023i
$783$	−20.5490	−	35.5919i	−0.734361	−	1.27195i
$784$		0			0
$785$		−	1.90507i		−	0.0679949i
$786$	24.1979	+	13.9706i	0.863109	+	0.498316i
$787$	8.71313	+	5.03053i	0.310589	+	0.179319i	0.647190	−	0.762329i	$-0.275944\pi$
$787$	8.71313	+	5.03053i	0.310589	+	0.179319i	−0.336601	+	0.941647i	$0.609277\pi$
$788$		−	5.30829i		−	0.189100i
$789$	3.95836	−	6.85607i	0.140921	−	0.244083i
$790$	3.50158	+	6.06491i	0.124581	+	0.215780i
$791$		0			0
$792$	−4.64877			−0.165187
$793$	6.99305	+	23.6134i	0.248331	+	0.838537i
$794$	16.3001			0.578469
$795$	4.97719	−	2.87358i	0.176523	−	0.101915i
$796$	−6.87462	−	11.9072i	−0.243664	−	0.422039i
$797$	17.7635	−	30.7672i	0.629214	−	1.08983i	−0.358495	−	0.933532i	$-0.616710\pi$
$797$	17.7635	−	30.7672i	0.629214	−	1.08983i	0.987710	−	0.156300i	$-0.0499566\pi$
$798$		0			0
$799$	−1.19274	−	0.688630i	−0.0421962	−	0.0243620i
$800$	3.97708	+	2.29617i	0.140611	+	0.0811818i
$801$		−	5.65950i		−	0.199968i
$802$	−10.4248	+	18.0562i	−0.368111	+	0.637587i
$803$	−14.5726	−	25.2405i	−0.514257	−	0.890718i
$804$	4.77816	−	2.75867i	0.168513	−	0.0972909i
$805$		0			0
$806$	23.2790	+	5.59028i	0.819966	+	0.196909i
$807$	0.939847			0.0330842
$808$	−11.8732	+	6.85500i	−0.417698	+	0.241158i
$809$	23.7244	+	41.0918i	0.834104	+	1.44471i	0.894758	+	0.446551i	$0.147348\pi$
$809$	23.7244	+	41.0918i	0.834104	+	1.44471i	−0.0606541	+	0.998159i	$0.519319\pi$
$810$	1.55964	−	2.70138i	0.0548003	−	0.0949168i
$811$			24.4360i			0.858063i	0.903289	+	0.429032i	$0.141145\pi$
$811$			24.4360i			0.858063i	−0.903289	+	0.429032i	$0.858855\pi$
$812$		0			0
$813$	−25.3805	−	14.6535i	−0.890134	−	0.513919i
$814$			9.56573i			0.335279i
$815$	−3.16686	+	5.48516i	−0.110930	+	0.192137i
$816$	0.498064	+	0.862672i	0.0174357	+	0.0301995i
$817$	66.3117	−	38.2851i	2.31995	−	1.33942i
$818$	−1.20081			−0.0419854
$819$		0			0
$820$	−3.40738			−0.118991
$821$	−41.3331	+	23.8637i	−1.44253	+	0.832848i	−0.998018	−	0.0629230i	$-0.979958\pi$
$821$	−41.3331	+	23.8637i	−1.44253	+	0.832848i	−0.444516	+	0.895771i	$0.646624\pi$
$822$	7.35659	+	12.7420i	0.256590	+	0.444428i
$823$	8.53356	−	14.7806i	0.297461	−	0.515218i	−0.678093	−	0.734976i	$-0.737193\pi$
$823$	8.53356	−	14.7806i	0.297461	−	0.515218i	0.975554	+	0.219758i	$0.0705268\pi$
$824$			10.8070i			0.376481i
$825$	−25.4174	−	14.6748i	−0.884921	−	0.510909i
$826$		0			0
$827$			4.18226i			0.145431i	0.997353	+	0.0727157i	$0.0231666\pi$
$827$			4.18226i			0.145431i	−0.997353	+	0.0727157i	$0.976833\pi$
$828$	−3.32696	+	5.76246i	−0.115620	+	0.200259i
$829$	−3.34360	−	5.79129i	−0.116128	−	0.201140i	0.802102	−	0.597187i	$-0.203715\pi$
$829$	−3.34360	−	5.79129i	−0.116128	−	0.201140i	−0.918230	+	0.396047i	$0.870382\pi$
$830$	−1.33278	+	0.769479i	−0.0462613	+	0.0267090i
$831$	10.7454			0.372753
$832$	2.48206	−	2.61522i	0.0860498	−	0.0906666i
$833$		0			0
$834$	0.0768789	−	0.0443861i	0.00266210	−	0.00153696i
$835$	3.83731	+	6.64642i	0.132796	+	0.230009i
$836$	16.6943	−	28.9155i	0.577386	−	1.00006i
$837$			37.5595i			1.29825i
$838$	16.0983	+	9.29434i	0.556105	+	0.321068i
$839$	−37.8216	−	21.8363i	−1.30575	−	0.753874i	−0.324364	−	0.945932i	$-0.605150\pi$
$839$	−37.8216	−	21.8363i	−1.30575	−	0.753874i	−0.981383	+	0.192059i	$0.938484\pi$
$840$		0			0
$841$	−11.8939	+	20.6008i	−0.410133	+	0.710372i
$842$	−10.9791	−	19.0163i	−0.378363	−	0.655345i
$843$	−5.08605	+	2.93643i	−0.175173	+	0.101136i
$844$	7.82574			0.269373
$845$	8.28902	−	0.433399i	0.285151	−	0.0149094i
$846$	−1.98848			−0.0683652
$847$		0			0
$848$	3.20071	+	5.54379i	0.109913	+	0.190375i
$849$	−4.84906	+	8.39882i	−0.166419	+	0.288247i
$850$		−	3.25330i		−	0.111587i
$851$	11.8574	+	6.84585i	0.406465	+	0.234673i
$852$	−12.8207	−	7.40201i	−0.439229	−	0.253589i
$853$		−	5.72664i		−	0.196076i	−0.995183	−	0.0980382i	$-0.968743\pi$
$853$		−	5.72664i		−	0.196076i	0.995183	−	0.0980382i	$-0.0312567\pi$
$854$		0			0
$855$	−2.39869	−	4.15465i	−0.0820334	−	0.142086i
$856$	13.2705	−	7.66173i	0.453577	−	0.261873i
$857$	30.3635			1.03720			0.518599	−	0.855018i	$-0.326454\pi$
$857$	30.3635			1.03720			0.518599	+	0.855018i	$0.326454\pi$
$858$	−15.8628	+	16.7138i	−0.541546	+	0.570601i
$859$	26.4676			0.903062			0.451531	−	0.892255i	$-0.350878\pi$
$859$	26.4676			0.903062			0.451531	+	0.892255i	$0.350878\pi$
$860$	−5.76350	+	3.32756i	−0.196534	+	0.113469i
$861$		0			0
$862$	−13.7658	+	23.8430i	−0.468864	+	0.812096i
$863$		−	17.8703i		−	0.608311i	−0.952622	−	0.304156i	$-0.901626\pi$
$863$		−	17.8703i		−	0.608311i	0.952622	−	0.304156i	$-0.0983743\pi$
$864$	4.89874	+	2.82829i	0.166659	+	0.0962203i
$865$	−10.7909	−	6.23011i	−0.366901	−	0.211830i
$866$		−	32.9334i		−	1.11912i
$867$	−11.5992	+	20.0905i	−0.393931	+	0.682308i
$868$		0			0
$869$	43.1733	−	24.9261i	1.46455	−	0.845560i
$870$	−6.52294			−0.221148
$871$	−3.30349	+	13.7563i	−0.111934	+	0.466116i
$872$	1.77368			0.0600643
$873$	8.14291	−	4.70131i	0.275596	−	0.159115i
$874$	−23.8951	−	41.3875i	−0.808263	−	1.39995i
$875$		0			0
$876$			9.01672i			0.304647i
$877$	−22.4495	−	12.9612i	−0.758065	−	0.437669i	0.0705353	−	0.997509i	$-0.477529\pi$
$877$	−22.4495	−	12.9612i	−0.758065	−	0.437669i	−0.828601	+	0.559840i	$0.810863\pi$
$878$	−11.0134	−	6.35859i	−0.371684	−	0.214592i
$879$		−	21.7341i		−	0.733074i
$880$	−1.45099	+	2.51320i	−0.0489130	+	0.0847198i
$881$	7.54044	+	13.0604i	0.254044	+	0.440017i	0.964635	−	0.263588i	$-0.0849059\pi$
$881$	7.54044	+	13.0604i	0.254044	+	0.440017i	−0.710592	+	0.703605i	$0.751573\pi$
$882$		0			0
$883$	−30.6339			−1.03091			−0.515457	−	0.856916i	$-0.672378\pi$
$883$	−30.6339			−1.03091			−0.515457	+	0.856916i	$0.672378\pi$
$884$	−2.48363	−	0.596427i	−0.0835336	−	0.0200600i
$885$	2.98030			0.100182
$886$	25.1034	−	14.4934i	0.843364	−	0.486916i
$887$	7.73363	+	13.3950i	0.259670	+	0.449761i	0.966153	−	0.257968i	$-0.0830529\pi$
$887$	7.73363	+	13.3950i	0.259670	+	0.449761i	−0.706484	+	0.707729i	$0.749720\pi$
$888$	1.47968	−	2.56289i	0.0496550	−	0.0860049i
$889$		0			0
$890$	−3.05961	−	1.76647i	−0.102558	−	0.0592120i
$891$	−19.2299	−	11.1024i	−0.644225	−	0.371943i
$892$			19.5376i			0.654169i
$893$	7.14087	−	12.3684i	0.238960	−	0.413891i
$894$	−6.24493	−	10.8165i	−0.208862	−	0.361759i
$895$	−8.93099	+	5.15631i	−0.298530	+	0.172356i
$896$		0			0
$897$	9.36549	+	31.6244i	0.312705	+	1.05591i
$898$	0.0278393			0.000929010
$899$	41.7795	−	24.1214i	1.39343	−	0.804495i
$900$	−2.34854	−	4.06780i	−0.0782848	−	0.135593i
$901$	2.26745	−	3.92733i	0.0755396	−	0.130838i
$902$			24.2555i			0.807621i
$903$		0			0
$904$	4.54061	+	2.62152i	0.151019	+	0.0871906i
$905$		−	0.179967i		−	0.00598232i
$906$	−9.30194	+	16.1114i	−0.309036	+	0.535266i
$907$	23.7055	+	41.0591i	0.787127	+	1.36334i	0.927720	+	0.373277i	$0.121766\pi$
$907$	23.7055	+	41.0591i	0.787127	+	1.36334i	−0.140593	+	0.990068i	$0.544901\pi$
$908$	−4.26499	+	2.46239i	−0.141539	+	0.0817174i
$909$	14.0227			0.465105
$910$		0			0
$911$	36.5790			1.21192			0.605958	−	0.795496i	$-0.292790\pi$
$911$	36.5790			1.21192			0.605958	+	0.795496i	$0.292790\pi$
$912$	−8.94563	+	5.16476i	−0.296219	+	0.171022i
$913$	5.47756	+	9.48742i	0.181281	+	0.313988i
$914$	−15.3931	+	26.6615i	−0.509157	+	0.881886i
$915$			6.13224i			0.202726i
$916$	13.8323	+	7.98610i	0.457033	+	0.263868i
$917$		0			0
$918$		−	4.00723i		−	0.132258i
$919$	−3.53379	+	6.12071i	−0.116569	+	0.201904i	−0.918406	−	0.395639i	$-0.870523\pi$
$919$	−3.53379	+	6.12071i	−0.116569	+	0.201904i	0.801837	+	0.597543i	$0.203856\pi$
$920$	2.07685	+	3.59721i	0.0684717	+	0.118596i
$921$	−30.5130	+	17.6167i	−1.00544	+	0.580490i
$922$	37.9670			1.25038
$923$	36.3975	−	10.7790i	1.19804	−	0.354796i
$924$		0			0
$925$	−8.37026	+	4.83257i	−0.275213	+	0.158894i
$926$	6.69846	+	11.6021i	0.220125	+	0.381268i
$927$	5.52678	−	9.57267i	0.181523	−	0.314408i
$928$		−	7.26552i		−	0.238502i
$929$	−41.4922	−	23.9555i	−1.36131	−	0.785955i	−0.371515	−	0.928427i	$-0.621162\pi$
$929$	−41.4922	−	23.9555i	−1.36131	−	0.785955i	−0.989799	+	0.142472i	$0.954495\pi$
$930$	5.16266	+	2.98067i	0.169290	+	0.0977399i
$931$		0			0
$932$	−2.62003	+	4.53803i	−0.0858220	+	0.148648i
$933$	−1.50846	−	2.61272i	−0.0493847	−	0.0855367i
$934$	22.4431	−	12.9575i	0.734360	−	0.423983i
$935$	2.05583			0.0672327
$936$	−3.53600	+	1.04718i	−0.115578	+	0.0342280i
$937$	7.37114			0.240805			0.120402	−	0.992725i	$-0.461582\pi$
$937$	7.37114			0.240805			0.120402	+	0.992725i	$0.461582\pi$
$938$		0			0
$939$	20.9139	+	36.2240i	0.682500	+	1.18212i
$940$	−0.620651	+	1.07500i	−0.0202434	+	0.0350626i
$941$			0.767551i			0.0250214i	0.999922	+	0.0125107i	$0.00398239\pi$
$941$			0.767551i			0.0250214i	−0.999922	+	0.0125107i	$0.996018\pi$
$942$	3.63340	+	2.09774i	0.118383	+	0.0683482i
$943$	30.0664	+	17.3588i	0.979095	+	0.565281i
$944$			3.31958i			0.108043i
$945$		0			0
$946$	23.6873	+	41.0277i	0.770142	+	1.33392i
$947$	27.8306	−	16.0680i	0.904372	−	0.522139i	0.0257556	−	0.999668i	$-0.491801\pi$
$947$	27.8306	−	16.0680i	0.904372	−	0.522139i	0.878616	+	0.477529i	$0.158467\pi$
$948$	−15.4229			−0.500912
$949$	−16.7700	−	15.9161i	−0.544378	−	0.516658i
$950$	33.7357			1.09453
$951$	−7.49590	+	4.32776i	−0.243071	+	0.140337i
$952$		0			0
$953$	−9.10361	+	15.7679i	−0.294895	+	0.510773i	−0.974960	−	0.222378i	$-0.928618\pi$
$953$	−9.10361	+	15.7679i	−0.294895	+	0.510773i	0.680065	+	0.733151i	$0.261951\pi$
$954$		−	6.54744i		−	0.211981i
$955$	−6.87129	−	3.96714i	−0.222350	−	0.128374i
$956$	20.3038	+	11.7224i	0.656673	+	0.379130i
$957$			46.4338i			1.50099i
$958$	0.126461	−	0.219038i	0.00408578	−	0.00707678i
$959$		0			0
$960$	0.777512	−	0.448897i	0.0250941	−	0.0144881i
$961$	−13.0893			−0.422235
$962$	2.15476	+	7.27598i	0.0694723	+	0.234587i
$963$	−15.6730			−0.505055
$964$	−9.57480	+	5.52801i	−0.308384	+	0.178045i
$965$	−3.71606	−	6.43641i	−0.119624	−	0.207195i
$966$		0			0
$967$		−	20.3286i		−	0.653724i	−0.945072	−	0.326862i	$-0.894009\pi$
$967$		−	20.3286i		−	0.653724i	0.945072	−	0.326862i	$-0.105991\pi$
$968$	8.36399	+	4.82895i	0.268829	+	0.155208i
$969$	6.33726	+	3.65882i	0.203582	+	0.117538i
$970$		−	5.86957i		−	0.188461i
$971$	22.3535	−	38.7173i	0.717356	−	1.24250i	−0.244687	−	0.969602i	$-0.578685\pi$
$971$	22.3535	−	38.7173i	0.717356	−	1.24250i	0.962044	−	0.272896i	$-0.0879814\pi$
$972$	−5.05010	−	8.74704i	−0.161982	−	0.280561i
$973$		0			0
$974$	30.3567			0.972691
$975$	−22.6389	−	5.43656i	−0.725024	−	0.174109i
$976$	−6.83034			−0.218634
$977$	17.8956	−	10.3320i	0.572531	−	0.330551i	−0.185629	−	0.982620i	$-0.559432\pi$
$977$	17.8956	−	10.3320i	0.572531	−	0.330551i	0.758160	+	0.652069i	$0.226099\pi$
$978$	−6.97429	−	12.0798i	−0.223013	−	0.386270i
$979$	−12.5746	+	21.7799i	−0.401887	+	0.696089i
$980$		0			0
$981$	−1.57109	−	0.907069i	−0.0501610	−	0.0289605i
$982$	11.6780	+	6.74228i	0.372659	+	0.215155i
$983$		−	56.0189i		−	1.78673i	−0.449335	−	0.893363i	$-0.648339\pi$
$983$		−	56.0189i		−	1.78673i	0.449335	−	0.893363i	$-0.351661\pi$
$984$	3.75199	−	6.49864i	0.119609	−	0.207169i
$985$	1.69464	+	2.93520i	0.0539957	+	0.0935234i
$986$	−4.45746	+	2.57352i	−0.141955	+	0.0819575i
$987$		0			0
$988$	6.18476	−	25.7545i	0.196764	−	0.819360i
$989$	67.8087			2.15619
$990$	2.57052	−	1.48409i	0.0816966	−	0.0471676i
$991$	−2.57214	−	4.45508i	−0.0817068	−	0.141520i	0.822276	−	0.569088i	$-0.192704\pi$
$991$	−2.57214	−	4.45508i	−0.0817068	−	0.141520i	−0.903983	+	0.427568i	$0.859370\pi$
$992$	−3.31999	+	5.75039i	−0.105410	+	0.182575i
$993$			40.3076i			1.27912i
$994$		0			0
$995$	7.60259	+	4.38936i	0.241018	+	0.139152i
$996$		−	3.38921i		−	0.107391i
$997$	11.2980	−	19.5687i	0.357812	−	0.619748i	−0.629783	−	0.776771i	$-0.716856\pi$
$997$	11.2980	−	19.5687i	0.357812	−	0.619748i	0.987595	+	0.157023i	$0.0501896\pi$
$998$	−1.01055	−	1.75032i	−0.0319883	−	0.0554054i
$999$	−10.3100	+	5.95249i	−0.326194	+	0.188328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.f.491.4		20
7.2	even	3		1274.2.v.h.361.7		20
7.3	odd	6		182.2.o.a.23.2	✓	20
7.4	even	3		1274.2.o.h.569.4		20
7.5	odd	6		182.2.v.a.179.9	yes	20
7.6	odd	2		1274.2.m.g.491.2		20
13.4	even	6	inner	1274.2.m.f.589.4		20
21.5	even	6		1638.2.cr.c.361.3		20
21.17	even	6		1638.2.dt.c.1297.8		20
91.4	even	6		1274.2.v.h.667.7		20
91.17	odd	6		182.2.v.a.121.9	yes	20
91.30	even	6		1274.2.o.h.459.9		20
91.69	odd	6		1274.2.m.g.589.2		20
91.82	odd	6		182.2.o.a.95.7	yes	20
273.17	even	6		1638.2.cr.c.667.3		20
273.173	even	6		1638.2.dt.c.1369.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.2	✓	20	7.3	odd	6
182.2.o.a.95.7	yes	20	91.82	odd	6
182.2.v.a.121.9	yes	20	91.17	odd	6
182.2.v.a.179.9	yes	20	7.5	odd	6
1274.2.m.f.491.4		20	1.1	even	1	trivial
1274.2.m.f.589.4		20	13.4	even	6	inner
1274.2.m.g.491.2		20	7.6	odd	2
1274.2.m.g.589.2		20	91.69	odd	6
1274.2.o.h.459.9		20	91.30	even	6
1274.2.o.h.569.4		20	7.4	even	3
1274.2.v.h.361.7		20	7.2	even	3
1274.2.v.h.667.7		20	91.4	even	6
1638.2.cr.c.361.3		20	21.5	even	6
1638.2.cr.c.667.3		20	273.17	even	6
1638.2.dt.c.1297.8		20	21.17	even	6
1638.2.dt.c.1369.3		20	273.173	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.703063 + 1.21774i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.638488i q^{5} +(-1.21774 - 0.703063i) q^{6} +1.00000i q^{8} +(0.511405 - 0.885780i) q^{9} +(-0.319244 - 0.552947i) q^{10} +(-3.93617 + 2.27255i) q^{11} +1.40613 q^{12} +(-2.48206 + 2.61522i) q^{13} +(-0.777512 + 0.448897i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.354210 + 0.613510i) q^{17} +1.02281i q^{18} +(-6.36190 - 3.67305i) q^{19} +(0.552947 + 0.319244i) q^{20} +(2.27255 - 3.93617i) q^{22} +(-3.25276 - 5.63395i) q^{23} +(-1.21774 + 0.703063i) q^{24} +4.59233 q^{25} +(0.841912 - 3.50588i) q^{26} +5.65658 q^{27} +(-3.63276 - 6.29212i) q^{29} +(0.448897 - 0.777512i) q^{30} +6.63998i q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.53475 - 3.19549i) q^{33} -0.708420i q^{34} +(-0.511405 - 0.885780i) q^{36} +(-1.82266 + 1.05231i) q^{37} +7.34609 q^{38} +(-4.92971 - 1.18383i) q^{39} -0.638488 q^{40} +(-4.62167 + 2.66832i) q^{41} +(-5.21162 + 9.02680i) q^{43} +4.54510i q^{44} +(0.565560 + 0.326526i) q^{45} +(5.63395 + 3.25276i) q^{46} +1.94413i q^{47} +(0.703063 - 1.21774i) q^{48} +(-3.97708 + 2.29617i) q^{50} -0.996127 q^{51} +(1.02382 + 3.45714i) q^{52} -6.40142 q^{53} +(-4.89874 + 2.82829i) q^{54} +(-1.45099 - 2.51320i) q^{55} -10.3295i q^{57} +(6.29212 + 3.63276i) q^{58} +(-2.87484 - 1.65979i) q^{59} +0.897794i q^{60} +(3.41517 - 5.91525i) q^{61} +(-3.31999 - 5.75039i) q^{62} -1.00000 q^{64} +(-1.66979 - 1.58476i) q^{65} +6.39098 q^{66} +(3.39810 - 1.96190i) q^{67} +(0.354210 + 0.613510i) q^{68} +(4.57379 - 7.92204i) q^{69} +(-9.11772 - 5.26412i) q^{71} +(0.885780 + 0.511405i) q^{72} +6.41246i q^{73} +(1.05231 - 1.82266i) q^{74} +(3.22870 + 5.59227i) q^{75} +(-6.36190 + 3.67305i) q^{76} +(4.86117 - 1.43962i) q^{78} -10.9684 q^{79} +(0.552947 - 0.319244i) q^{80} +(2.44271 + 4.23090i) q^{81} +(2.66832 - 4.62167i) q^{82} -2.41032i q^{83} +(-0.391718 - 0.226159i) q^{85} -10.4232i q^{86} +(5.10811 - 8.84751i) q^{87} +(-2.27255 - 3.93617i) q^{88} +(4.79196 - 2.76664i) q^{89} -0.653052 q^{90} -6.50552 q^{92} +(-8.08577 + 4.66832i) q^{93} +(-0.972065 - 1.68367i) q^{94} +(2.34519 - 4.06200i) q^{95} +1.40613i q^{96} +(7.96131 + 4.59646i) q^{97} +4.64877i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 10 q^{4} - 16 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{19} + 2 q^{22} - 36 q^{25} + 28 q^{27} + 2 q^{29} - 2 q^{30} + 12 q^{33} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) \) 20 * q - 2 * q^3 + 10 * q^4 - 16 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^19 + 2 * q^22 - 36 * q^25 + 28 * q^27 + 2 * q^29 - 2 * q^30 + 12 * q^33 + 16 * q^36 + 36 * q^37 - 28 * q^38 + 4 * q^39 + 8 * q^40 - 18 * q^41 + 8 * q^43 - 60 * q^45 - 12 * q^46 - 2 * q^48 - 12 * q^50 + 44 * q^51 - 6 * q^52 + 8 * q^53 - 18 * q^54 - 2 * q^55 + 24 * q^58 + 4 * q^61 + 24 * q^62 - 20 * q^64 + 24 * q^65 + 64 * q^66 + 60 * q^67 - 10 * q^68 + 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 + 16 * q^82 - 12 * q^85 + 64 * q^87 - 2 * q^88 - 18 * q^89 - 52 * q^90 - 60 * q^93 - 16 * q^94 - 12 * q^95 - 78 * q^97

Introduction

L-functions

Modular forms

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