LMFDB - Embedded newform 324.2.l.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40284 - 0.179019i) q^{2} +(1.93590 + 0.502269i) q^{4} +(0.847966 - 2.32977i) q^{5} +(-4.59553 - 0.810316i) q^{7} +(-2.62584 - 1.05116i) q^{8} +O(q^{10})$	\(q+(-1.40284 - 0.179019i) q^{2} +(1.93590 + 0.502269i) q^{4} +(0.847966 - 2.32977i) q^{5} +(-4.59553 - 0.810316i) q^{7} +(-2.62584 - 1.05116i) q^{8} +(-1.60663 + 3.11648i) q^{10} +(-2.23250 + 0.812562i) q^{11} +(-1.53462 + 1.28770i) q^{13} +(6.30172 + 1.95943i) q^{14} +(3.49545 + 1.94469i) q^{16} +(-1.59381 + 0.920188i) q^{17} +(-1.56341 - 0.902634i) q^{19} +(2.81175 - 4.08430i) q^{20} +(3.27729 - 0.740233i) q^{22} +(-0.496152 - 2.81382i) q^{23} +(-0.878547 - 0.737189i) q^{25} +(2.38335 - 1.53171i) q^{26} +(-8.48951 - 3.87689i) q^{28} +(-4.19826 + 5.00329i) q^{29} +(-0.704699 + 0.124257i) q^{31} +(-4.55541 - 3.35383i) q^{32} +(2.40059 - 1.00555i) q^{34} +(-5.78470 + 10.0194i) q^{35} +(-5.60913 - 9.71530i) q^{37} +(2.03162 + 1.54613i) q^{38} +(-4.67560 + 5.22625i) q^{40} +(-4.52704 - 5.39511i) q^{41} +(0.206872 + 0.568377i) q^{43} +(-4.73002 + 0.451729i) q^{44} +(0.192294 + 4.03615i) q^{46} +(0.587034 - 3.32923i) q^{47} +(13.8845 + 5.05353i) q^{49} +(1.10049 + 1.19143i) q^{50} +(-3.61765 + 1.72207i) q^{52} -5.16402i q^{53} +5.89022i q^{55} +(11.2154 + 6.95843i) q^{56} +(6.78516 - 6.26723i) q^{58} +(7.69223 + 2.79974i) q^{59} +(1.01407 - 5.75108i) q^{61} +(1.01082 - 0.0481585i) q^{62} +(5.79011 + 5.52039i) q^{64} +(1.69874 + 4.66724i) q^{65} +(-0.427623 - 0.509621i) q^{67} +(-3.54765 + 0.980874i) q^{68} +(9.90866 - 13.0200i) q^{70} +(-0.933575 - 1.61700i) q^{71} +(0.519326 - 0.899498i) q^{73} +(6.12948 + 14.6331i) q^{74} +(-2.57324 - 2.53266i) q^{76} +(10.9179 - 1.92513i) q^{77} +(8.75072 - 10.4287i) q^{79} +(7.49470 - 6.49456i) q^{80} +(5.38487 + 8.37889i) q^{82} +(-2.22145 - 1.86402i) q^{83} +(0.792326 + 4.49350i) q^{85} +(-0.188458 - 0.834374i) q^{86} +(6.71632 + 0.213061i) q^{88} +(9.13625 + 5.27482i) q^{89} +(8.09585 - 4.67414i) q^{91} +(0.452790 - 5.69649i) q^{92} +(-1.41951 + 4.56528i) q^{94} +(-3.42864 + 2.87697i) q^{95} +(-14.6120 + 5.31834i) q^{97} +(-18.5730 - 9.57486i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−1.40284	−	0.179019i	−0.991956	−	0.126585i
$2$	−1.40284	−	0.179019i	−0.991956	−	0.126585i
$3$		0			0
$3$		0			0
$4$	1.93590	+	0.502269i	0.967952	+	0.251134i
$5$	0.847966	−	2.32977i	0.379222	−	1.04190i	−0.592458	−	0.805602i	$-0.701842\pi$
$5$	0.847966	−	2.32977i	0.379222	−	1.04190i	0.971680	−	0.236302i	$-0.0759355\pi$
$6$		0			0
$7$	−4.59553	−	0.810316i	−1.73695	−	0.306271i	−0.786601	−	0.617462i	$-0.788161\pi$
$7$	−4.59553	−	0.810316i	−1.73695	−	0.306271i	−0.950347	+	0.311191i	$0.899272\pi$
$8$	−2.62584	−	1.05116i	−0.928376	−	0.371643i
$9$		0			0
$10$	−1.60663	+	3.11648i	−0.508061	+	0.985518i
$11$	−2.23250	+	0.812562i	−0.673123	+	0.244997i	−0.655892	−	0.754855i	$-0.727707\pi$
$11$	−2.23250	+	0.812562i	−0.673123	+	0.244997i	−0.0172309	+	0.999852i	$0.505485\pi$
$12$		0			0
$13$	−1.53462	+	1.28770i	−0.425628	+	0.357144i	−0.830299	−	0.557318i	$-0.811830\pi$
$13$	−1.53462	+	1.28770i	−0.425628	+	0.357144i	0.404671	+	0.914462i	$0.367386\pi$
$14$	6.30172	+	1.95943i	1.68421	+	0.523679i
$15$		0			0
$16$	3.49545	+	1.94469i	0.873863	+	0.486172i
$17$	−1.59381	+	0.920188i	−0.386556	+	0.223178i	−0.680667	−	0.732593i	$-0.738310\pi$
$17$	−1.59381	+	0.920188i	−0.386556	+	0.223178i	0.294111	+	0.955771i	$0.404977\pi$
$18$		0			0
$19$	−1.56341	−	0.902634i	−0.358670	−	0.207078i	0.309827	−	0.950793i	$-0.399729\pi$
$19$	−1.56341	−	0.902634i	−0.358670	−	0.207078i	−0.668497	+	0.743715i	$0.733062\pi$
$20$	2.81175	−	4.08430i	0.628727	−	0.913277i
$21$		0			0
$22$	3.27729	−	0.740233i	0.698721	−	0.157818i
$23$	−0.496152	−	2.81382i	−0.103455	−	0.586722i	−0.991826	−	0.127596i	$-0.959274\pi$
$23$	−0.496152	−	2.81382i	−0.103455	−	0.586722i	0.888371	−	0.459126i	$-0.151837\pi$
$24$		0			0
$25$	−0.878547	−	0.737189i	−0.175709	−	0.147438i
$26$	2.38335	−	1.53171i	0.467413	−	0.300393i
$27$		0			0
$28$	−8.48951	−	3.87689i	−1.60437	−	0.732663i
$29$	−4.19826	+	5.00329i	−0.779597	+	0.929088i	−0.998915	−	0.0465658i	$-0.985172\pi$
$29$	−4.19826	+	5.00329i	−0.779597	+	0.929088i	0.219318	+	0.975653i	$0.429617\pi$
$30$		0			0
$31$	−0.704699	+	0.124257i	−0.126568	+	0.0223173i	−0.236573	−	0.971614i	$-0.576024\pi$
$31$	−0.704699	+	0.124257i	−0.126568	+	0.0223173i	0.110005	+	0.993931i	$0.464913\pi$
$32$	−4.55541	−	3.35383i	−0.805291	−	0.592880i
$33$		0			0
$34$	2.40059	−	1.00555i	0.411698	−	0.172451i
$35$	−5.78470	+	10.0194i	−0.977793	+	1.69359i
$36$		0			0
$37$	−5.60913	−	9.71530i	−0.922136	−	1.59719i	−0.796104	−	0.605160i	$-0.793109\pi$
$37$	−5.60913	−	9.71530i	−0.922136	−	1.59719i	−0.126032	−	0.992026i	$-0.540224\pi$
$38$	2.03162	+	1.54613i	0.329572	+	0.250815i
$39$		0			0
$40$	−4.67560	+	5.22625i	−0.739276	+	0.826343i
$41$	−4.52704	−	5.39511i	−0.707005	−	0.842575i	0.286295	−	0.958141i	$-0.407576\pi$
$41$	−4.52704	−	5.39511i	−0.707005	−	0.842575i	−0.993300	+	0.115566i	$0.963132\pi$
$42$		0			0
$43$	0.206872	+	0.568377i	0.0315477	+	0.0866766i	0.954467	−	0.298318i	$-0.0964256\pi$
$43$	0.206872	+	0.568377i	0.0315477	+	0.0866766i	−0.922919	+	0.384995i	$0.874203\pi$
$44$	−4.73002	+	0.451729i	−0.713078	+	0.0681008i
$45$		0			0
$46$	0.192294	+	4.03615i	0.0283522	+	0.595098i
$47$	0.587034	−	3.32923i	0.0856277	−	0.485619i	−0.911592	−	0.411097i	$-0.865146\pi$
$47$	0.587034	−	3.32923i	0.0856277	−	0.485619i	0.997219	−	0.0745219i	$-0.0237431\pi$
$48$		0			0
$49$	13.8845	+	5.05353i	1.98349	+	0.721933i
$50$	1.10049	+	1.19143i	0.155633	+	0.168494i
$51$		0			0
$52$	−3.61765	+	1.72207i	−0.501678	+	0.238809i
$53$		−	5.16402i		−	0.709333i	−0.934993	−	0.354667i	$-0.884594\pi$
$53$		−	5.16402i		−	0.709333i	0.934993	−	0.354667i	$-0.115406\pi$
$54$		0			0
$55$			5.89022i			0.794237i
$56$	11.2154	+	6.95843i	1.49872	+	0.929859i
$57$		0			0
$58$	6.78516	−	6.26723i	0.890935	−	0.822928i
$59$	7.69223	+	2.79974i	1.00144	+	0.364496i	0.790141	−	0.612925i	$-0.210007\pi$
$59$	7.69223	+	2.79974i	1.00144	+	0.364496i	0.211302	+	0.977421i	$0.432230\pi$
$60$		0			0
$61$	1.01407	−	5.75108i	0.129838	−	0.736350i	−0.848478	−	0.529231i	$-0.822480\pi$
$61$	1.01407	−	5.75108i	0.129838	−	0.736350i	0.978316	−	0.207118i	$-0.0664086\pi$
$62$	1.01082	−	0.0481585i	0.128375	−	0.00611614i
$63$		0			0
$64$	5.79011	+	5.52039i	0.723763	+	0.690048i
$65$	1.69874	+	4.66724i	0.210702	+	0.578900i
$66$		0			0
$67$	−0.427623	−	0.509621i	−0.0522424	−	0.0622601i	0.739290	−	0.673387i	$-0.235161\pi$
$67$	−0.427623	−	0.509621i	−0.0522424	−	0.0622601i	−0.791533	+	0.611127i	$0.790717\pi$
$68$	−3.54765	+	0.980874i	−0.430216	+	0.118948i
$69$		0			0
$70$	9.90866	−	13.0200i	1.18431	−	1.55619i
$71$	−0.933575	−	1.61700i	−0.110795	−	0.191902i	0.805296	−	0.592873i	$-0.202006\pi$
$71$	−0.933575	−	1.61700i	−0.110795	−	0.191902i	−0.916091	+	0.400970i	$0.868673\pi$
$72$		0			0
$73$	0.519326	−	0.899498i	0.0607825	−	0.105278i	−0.834033	−	0.551715i	$-0.813974\pi$
$73$	0.519326	−	0.899498i	0.0607825	−	0.105278i	0.894815	+	0.446436i	$0.147307\pi$
$74$	6.12948	+	14.6331i	0.712537	+	1.70107i
$75$		0			0
$76$	−2.57324	−	2.53266i	−0.295171	−	0.290516i
$77$	10.9179	−	1.92513i	1.24421	−	0.219389i
$78$		0			0
$79$	8.75072	−	10.4287i	0.984533	−	1.17332i	−0.000332592	−	1.00000i	$-0.500106\pi$
$79$	8.75072	−	10.4287i	0.984533	−	1.17332i	0.984865	−	0.173321i	$-0.0554497\pi$
$80$	7.49470	−	6.49456i	0.837933	−	0.726114i
$81$		0			0
$82$	5.38487	+	8.37889i	0.594659	+	0.925294i
$83$	−2.22145	−	1.86402i	−0.243836	−	0.204602i	0.512677	−	0.858582i	$-0.328654\pi$
$83$	−2.22145	−	1.86402i	−0.243836	−	0.204602i	−0.756513	+	0.653979i	$0.773098\pi$
$84$		0			0
$85$	0.792326	+	4.49350i	0.0859398	+	0.487389i
$86$	−0.188458	−	0.834374i	−0.0203219	−	0.0899728i
$87$		0			0
$88$	6.71632	+	0.213061i	0.715962	+	0.0227123i
$89$	9.13625	+	5.27482i	0.968441	+	0.559130i	0.898761	−	0.438440i	$-0.144469\pi$
$89$	9.13625	+	5.27482i	0.968441	+	0.559130i	0.0696802	+	0.997569i	$0.477802\pi$
$90$		0			0
$91$	8.09585	−	4.67414i	0.848676	−	0.489983i
$92$	0.452790	−	5.69649i	0.0472066	−	0.593900i
$93$		0			0
$94$	−1.41951	+	4.56528i	−0.146411	+	0.470873i
$95$	−3.42864	+	2.87697i	−0.351771	+	0.295171i
$96$		0			0
$97$	−14.6120	+	5.31834i	−1.48362	+	0.539995i	−0.951763	−	0.306836i	$-0.900730\pi$
$97$	−14.6120	+	5.31834i	−1.48362	+	0.539995i	−0.531862	+	0.846831i	$0.678508\pi$
$98$	−18.5730	−	9.57486i	−1.87615	−	0.967207i
$99$		0			0
$100$	−1.33052	−	1.86839i	−0.133052	−	0.186839i
$101$	−7.77944	−	1.37173i	−0.774083	−	0.136492i	−0.227366	−	0.973809i	$-0.573011\pi$
$101$	−7.77944	−	1.37173i	−0.774083	−	0.136492i	−0.546717	+	0.837318i	$0.684123\pi$
$102$		0			0
$103$	−3.66967	+	10.0823i	−0.361584	+	0.993443i	0.616886	+	0.787053i	$0.288394\pi$
$103$	−3.66967	+	10.0823i	−0.361584	+	0.993443i	−0.978470	+	0.206391i	$0.933828\pi$
$104$	5.38326	−	1.76816i	0.527872	−	0.173382i
$105$		0			0
$106$	−0.924458	+	7.24429i	−0.0897913	+	0.703627i
$107$	12.7270			1.23037			0.615184	−	0.788384i	$-0.289082\pi$
$107$	12.7270			1.23037			0.615184	+	0.788384i	$0.289082\pi$
$108$		0			0
$109$	−3.14870			−0.301591			−0.150795	−	0.988565i	$-0.548183\pi$
$109$	−3.14870			−0.301591			−0.150795	+	0.988565i	$0.548183\pi$
$110$	1.05446	−	8.26302i	0.100539	−	0.787848i
$111$		0			0
$112$	−14.4877	−	11.7693i	−1.36895	−	1.11209i
$113$	0.811474	−	2.22951i	0.0763371	−	0.209734i	−0.895654	−	0.444751i	$-0.853292\pi$
$113$	0.811474	−	2.22951i	0.0763371	−	0.209734i	0.971991	+	0.235017i	$0.0755144\pi$
$114$		0			0
$115$	−6.97626	−	1.23010i	−0.650540	−	0.114708i
$116$	−10.6404	+	7.57724i	−0.987939	+	0.703529i
$117$		0			0
$118$	−10.2897	−	5.30464i	−0.947247	−	0.488332i
$119$	8.07006	−	2.93726i	0.739781	−	0.269258i
$120$		0			0
$121$	−4.10271	+	3.44258i	−0.372974	+	0.312962i
$122$	−2.45213	+	7.88629i	−0.222005	+	0.713991i
$123$		0			0
$124$	−1.42664	−	0.113398i	−0.128116	−	0.0101834i
$125$	8.27317	−	4.77652i	0.739975	−	0.427225i
$126$		0			0
$127$	15.4897	+	8.94299i	1.37449	+	0.793562i	0.991490	−	0.130186i	$-0.0415575\pi$
$127$	15.4897	+	8.94299i	1.37449	+	0.793562i	0.383000	+	0.923748i	$0.374891\pi$
$128$	−7.13432	−	8.78074i	−0.630591	−	0.776115i
$129$		0			0
$130$	−1.54753	−	6.85148i	−0.135727	−	0.600915i
$131$	−0.587315	−	3.33083i	−0.0513140	−	0.291016i	0.948342	−	0.317250i	$-0.102760\pi$
$131$	−0.587315	−	3.33083i	−0.0513140	−	0.291016i	−0.999656	+	0.0262343i	$0.991648\pi$
$132$		0			0
$133$	6.45327	+	5.41494i	0.559570	+	0.469535i
$134$	0.508653	+	0.791468i	0.0439410	+	0.0683724i
$135$		0			0
$136$	5.15237	−	0.740910i	0.441812	−	0.0635325i
$137$	−4.18635	+	4.98910i	−0.357664	+	0.426247i	−0.914633	−	0.404286i	$-0.867520\pi$
$137$	−4.18635	+	4.98910i	−0.357664	+	0.426247i	0.556968	+	0.830534i	$0.311964\pi$
$138$		0			0
$139$	−3.77403	+	0.665463i	−0.320109	+	0.0564438i	−0.331394	−	0.943492i	$-0.607519\pi$
$139$	−3.77403	+	0.665463i	−0.320109	+	0.0564438i	0.0112850	+	0.999936i	$0.496408\pi$
$140$	−16.2311	+	16.4911i	−1.37178	+	1.39375i
$141$		0			0
$142$	1.02018	+	2.43551i	0.0856116	+	0.204384i
$143$	2.37970	−	4.12176i	0.199001	−	0.344679i
$144$		0			0
$145$	8.09652	+	14.0236i	0.672379	+	1.16460i
$146$	−0.889557	+	1.16888i	−0.0736202	+	0.0967373i
$147$		0			0
$148$	−5.97905	−	21.6252i	−0.491475	−	1.77758i
$149$	−1.86523	−	2.22289i	−0.152805	−	0.182106i	0.684211	−	0.729284i	$-0.260147\pi$
$149$	−1.86523	−	2.22289i	−0.152805	−	0.182106i	−0.837016	+	0.547178i	$0.815702\pi$
$150$		0			0
$151$	0.547815	+	1.50511i	0.0445806	+	0.122484i	0.959985	−	0.280051i	$-0.0903514\pi$
$151$	0.547815	+	1.50511i	0.0445806	+	0.122484i	−0.915405	+	0.402535i	$0.868129\pi$
$152$	3.15645	+	4.01357i	0.256022	+	0.325544i
$153$		0			0
$154$	−15.6607	+	0.746123i	−1.26198	+	0.0601243i
$155$	−0.308070	+	1.74715i	−0.0247448	+	0.140335i
$156$		0			0
$157$	−7.36520	−	2.68071i	−0.587807	−	0.213944i	0.0309578	−	0.999521i	$-0.490144\pi$
$157$	−7.36520	−	2.68071i	−0.587807	−	0.213944i	−0.618765	+	0.785577i	$0.712366\pi$
$158$	−14.1428	+	13.0632i	−1.12514	+	1.03925i
$159$		0			0
$160$	−11.6765	+	7.76912i	−0.923107	+	0.614203i
$161$			13.3330i			1.05079i
$162$		0			0
$163$		−	12.5843i		−	0.985676i	−0.870121	−	0.492838i	$-0.835960\pi$
$163$		−	12.5843i		−	0.985676i	0.870121	−	0.492838i	$-0.164040\pi$
$164$	−6.05412	−	12.7182i	−0.472747	−	0.993126i
$165$		0			0
$166$	2.78264	+	3.01259i	0.215975	+	0.233823i
$167$	−7.12937	−	2.59488i	−0.551687	−	0.200798i	0.0511090	−	0.998693i	$-0.483724\pi$
$167$	−7.12937	−	2.59488i	−0.551687	−	0.200798i	−0.602796	+	0.797895i	$0.705947\pi$
$168$		0			0
$169$	−1.56053	+	8.85023i	−0.120041	+	0.680787i
$170$	−0.307082	−	6.44549i	−0.0235521	−	0.494347i
$171$		0			0
$172$	0.115007	+	1.20423i	0.00876920	+	0.0918215i
$173$	0.820320	+	2.25381i	0.0623678	+	0.171354i	0.966963	−	0.254919i	$-0.0820487\pi$
$173$	0.820320	+	2.25381i	0.0623678	+	0.171354i	−0.904595	+	0.426273i	$0.859826\pi$
$174$		0			0
$175$	3.44004	+	4.09968i	0.260042	+	0.309906i
$176$	−9.38376	−	1.50124i	−0.707328	−	0.113160i
$177$		0			0
$178$	−11.8724	−	9.03527i	−0.889873	−	0.677222i
$179$	−12.3836	−	21.4490i	−0.925593	−	1.60317i	−0.790605	−	0.612326i	$-0.790234\pi$
$179$	−12.3836	−	21.4490i	−0.925593	−	1.60317i	−0.134988	−	0.990847i	$-0.543099\pi$
$180$		0			0
$181$	10.8787	−	18.8424i	0.808605	−	1.40054i	−0.105225	−	0.994448i	$-0.533556\pi$
$181$	10.8787	−	18.8424i	0.808605	−	1.40054i	0.913830	−	0.406096i	$-0.133110\pi$
$182$	−12.1939	+	5.10775i	−0.903874	+	0.378612i
$183$		0			0
$184$	−1.65497	+	7.91018i	−0.122006	+	0.583147i
$185$	−27.3908	+	4.82973i	−2.01381	+	0.355089i
$186$		0			0
$187$	2.81047	−	3.34939i	0.205522	−	0.244931i
$188$	2.80861	−	6.15023i	0.204839	−	0.448552i
$189$		0			0
$190$	5.32486	−	3.42213i	0.386306	−	0.248268i
$191$	−7.21505	−	6.05415i	−0.522063	−	0.438063i	0.343287	−	0.939230i	$-0.388460\pi$
$191$	−7.21505	−	6.05415i	−0.522063	−	0.438063i	−0.865350	+	0.501168i	$0.832904\pi$
$192$		0			0
$193$	−0.963275	−	5.46301i	−0.0693381	−	0.393236i	−0.999650	−	0.0264657i	$-0.991575\pi$
$193$	−0.963275	−	5.46301i	−0.0693381	−	0.393236i	0.930312	−	0.366770i	$-0.119536\pi$
$194$	21.4504	−	4.84493i	1.54005	−	0.347846i
$195$		0			0
$196$	24.3408	+	16.7569i	1.73863	+	1.19692i
$197$	13.5445	+	7.81992i	0.965006	+	0.557146i	0.897710	−	0.440587i	$-0.145230\pi$
$197$	13.5445	+	7.81992i	0.965006	+	0.557146i	0.0672958	+	0.997733i	$0.478563\pi$
$198$		0			0
$199$	−13.9609	+	8.06033i	−0.989662	+	0.571382i	−0.905173	−	0.425043i	$-0.860259\pi$
$199$	−13.9609	+	8.06033i	−0.989662	+	0.571382i	−0.0844887	+	0.996424i	$0.526926\pi$
$200$	1.53202	+	2.85924i	0.108330	+	0.202179i
$201$		0			0
$202$	10.6677	+	3.31697i	0.750578	+	0.233381i
$203$	23.3475	−	19.5909i	1.63867	−	1.37501i
$204$		0			0
$205$	−16.4081	+	5.97207i	−1.14599	+	0.417108i
$206$	6.95289	−	13.4870i	0.484431	−	0.939681i
$207$		0			0
$208$	−7.86838	+	1.51673i	−0.545574	+	0.105167i
$209$	4.22375	+	0.744760i	0.292163	+	0.0515162i
$210$		0			0
$211$	3.29026	−	9.03991i	0.226511	−	0.622333i	−0.773423	−	0.633891i	$-0.781457\pi$
$211$	3.29026	−	9.03991i	0.226511	−	0.622333i	0.999933	+	0.0115578i	$0.00367906\pi$
$212$	2.59373	−	9.99706i	0.178138	−	0.686601i
$213$		0			0
$214$	−17.8539	−	2.27838i	−1.22047	−	0.155747i
$215$	1.49961			0.102272
$216$		0			0
$217$	3.33915			0.226677
$218$	4.41711	+	0.563677i	0.299165	+	0.0381770i
$219$		0			0
$220$	−2.95847	+	11.4029i	−0.199460	+	0.768784i
$221$	1.26097	−	3.46450i	0.0848222	−	0.233047i
$222$		0			0
$223$	−10.1708	−	1.79339i	−0.681088	−	0.120094i	−0.177608	−	0.984101i	$-0.556836\pi$
$223$	−10.1708	−	1.79339i	−0.681088	−	0.120094i	−0.503480	+	0.864007i	$0.667947\pi$
$224$	18.2169	+	19.1040i	1.21717	+	1.27644i
$225$		0			0
$226$	−1.53749	+	2.98237i	−0.102272	+	0.198384i
$227$	−12.4052	+	4.51512i	−0.823362	+	0.299679i	−0.719131	−	0.694874i	$-0.755460\pi$
$227$	−12.4052	+	4.51512i	−0.823362	+	0.299679i	−0.104230	+	0.994553i	$0.533238\pi$
$228$		0			0
$229$	13.0462	−	10.9471i	0.862117	−	0.723402i	−0.100306	−	0.994957i	$-0.531982\pi$
$229$	13.0462	−	10.9471i	0.862117	−	0.723402i	0.962423	+	0.271555i	$0.0875377\pi$
$230$	9.56635	+	2.97452i	0.630786	+	0.196134i
$231$		0			0
$232$	16.2833	−	8.72479i	1.06905	−	0.572811i
$233$	−15.8755	+	9.16572i	−1.04004	+	0.600467i	−0.919844	−	0.392284i	$-0.871685\pi$
$233$	−15.8755	+	9.16572i	−1.04004	+	0.600467i	−0.120194	+	0.992750i	$0.538352\pi$
$234$		0			0
$235$	−7.25856	−	4.19073i	−0.473496	−	0.273373i
$236$	13.4852	+	9.28360i	0.877812	+	0.604311i
$237$		0			0
$238$	−11.8468	+	2.67581i	−0.767915	+	0.173447i
$239$	3.60534	+	20.4469i	0.233210	+	1.32260i	0.846350	+	0.532627i	$0.178795\pi$
$239$	3.60534	+	20.4469i	0.233210	+	1.32260i	−0.613140	+	0.789974i	$0.710094\pi$
$240$		0			0
$241$	10.8109	+	9.07140i	0.696390	+	0.584340i	0.920744	−	0.390167i	$-0.127583\pi$
$241$	10.8109	+	9.07140i	0.696390	+	0.584340i	−0.224354	+	0.974508i	$0.572027\pi$
$242$	6.37172	−	4.09492i	0.409590	−	0.263231i
$243$		0			0
$244$	4.85173	−	10.6242i	0.310600	−	0.680145i
$245$	23.5471	−	28.0623i	1.50437	−	1.79284i
$246$		0			0
$247$	3.56156	−	0.628000i	0.226617	−	0.0399587i
$248$	1.98104	+	0.414474i	0.125796	+	0.0263191i
$249$		0			0
$250$	−12.4610	+	5.21962i	−0.788103	+	0.330118i
$251$	−12.3464	+	21.3846i	−0.779297	+	1.34978i	0.153050	+	0.988218i	$0.451090\pi$
$251$	−12.3464	+	21.3846i	−0.779297	+	1.34978i	−0.932347	+	0.361564i	$0.882243\pi$
$252$		0			0
$253$	3.39406	+	5.87868i	0.213383	+	0.369590i
$254$	−20.1286	−	15.3185i	−1.26298	−	0.961169i
$255$		0			0
$256$	8.43637	+	13.5951i	0.527273	+	0.849696i
$257$	13.4321	+	16.0077i	0.837868	+	0.998533i	0.999931	+	0.0117523i	$0.00374095\pi$
$257$	13.4321	+	16.0077i	0.837868	+	0.998533i	−0.162062	+	0.986780i	$0.551815\pi$
$258$		0			0
$259$	17.9045	+	49.1922i	1.11253	+	3.05665i
$260$	0.944382	+	9.88855i	0.0585681	+	0.613262i
$261$		0			0
$262$	0.227626	+	4.77775i	0.0140628	+	0.295171i
$263$	0.464688	−	2.63538i	0.0286539	−	0.162504i	−0.967123	−	0.254308i	$-0.918152\pi$
$263$	0.464688	−	2.63538i	0.0286539	−	0.162504i	0.995777	+	0.0918040i	$0.0292633\pi$
$264$		0			0
$265$	−12.0310	−	4.37892i	−0.739057	−	0.268995i
$266$	−8.08351	−	8.75153i	−0.495632	−	0.536591i
$267$		0			0
$268$	−0.571870	−	1.20136i	−0.0349325	−	0.0733847i
$269$		−	18.9582i		−	1.15590i	−0.816071	−	0.577952i	$-0.803852\pi$
$269$		−	18.9582i		−	1.15590i	0.816071	−	0.577952i	$-0.196148\pi$
$270$		0			0
$271$		−	7.16436i		−	0.435204i	−0.976038	−	0.217602i	$-0.930177\pi$
$271$		−	7.16436i		−	0.435204i	0.976038	−	0.217602i	$-0.0698234\pi$
$272$	−7.36058	+	0.117004i	−0.446300	+	0.00709443i
$273$		0			0
$274$	6.76591	−	6.24946i	0.408744	−	0.377544i
$275$	2.56036	+	0.931896i	0.154396	+	0.0561955i
$276$		0			0
$277$	2.95763	−	16.7735i	0.177707	−	1.00782i	−0.757266	−	0.653106i	$-0.773466\pi$
$277$	2.95763	−	16.7735i	0.177707	−	1.00782i	0.934973	−	0.354719i	$-0.115423\pi$
$278$	5.41348	−	0.257914i	0.324679	−	0.0154686i
$279$		0			0
$280$	25.7218	−	20.2287i	1.53717	−	1.20890i
$281$	−8.47273	−	23.2786i	−0.505441	−	1.38869i	−0.885894	−	0.463887i	$-0.846454\pi$
$281$	−8.47273	−	23.2786i	−0.505441	−	1.38869i	0.380453	−	0.924800i	$-0.375768\pi$
$282$		0			0
$283$	−4.75165	−	5.66279i	−0.282456	−	0.336618i	0.606098	−	0.795390i	$-0.292734\pi$
$283$	−4.75165	−	5.66279i	−0.282456	−	0.336618i	−0.888554	+	0.458772i	$0.848290\pi$
$284$	−0.995143	−	3.59926i	−0.0590509	−	0.213577i
$285$		0			0
$286$	−4.07621	+	5.35615i	−0.241031	+	0.316716i
$287$	16.4324	+	28.4618i	0.969974	+	1.68004i
$288$		0			0
$289$	−6.80651	+	11.7892i	−0.400383	+	0.693483i
$290$	−8.84761	−	21.1222i	−0.519550	−	1.24034i
$291$		0			0
$292$	1.45715	−	1.48050i	0.0852735	−	0.0866398i
$293$	−2.00549	+	0.353621i	−0.117162	+	0.0206588i	−0.231922	−	0.972734i	$-0.574501\pi$
$293$	−2.00549	+	0.353621i	−0.117162	+	0.0206588i	0.114760	+	0.993393i	$0.463390\pi$
$294$		0			0
$295$	13.0455	−	15.5470i	0.759538	−	0.905183i
$296$	4.51632	+	31.4070i	0.262506	+	1.82549i
$297$		0			0
$298$	2.21867	+	3.45226i	0.128524	+	0.199984i
$299$	4.38476	+	3.67925i	0.253577	+	0.212777i
$300$		0			0
$301$	−0.490123	−	2.77962i	−0.0282502	−	0.160215i
$302$	−0.499052	−	2.20949i	−0.0287172	−	0.127142i
$303$		0			0
$304$	−3.70948	−	6.19545i	−0.212753	−	0.355334i
$305$	−12.5388	−	7.23926i	−0.717968	−	0.414519i
$306$		0			0
$307$	7.15348	−	4.13006i	0.408271	−	0.235715i	−0.281776	−	0.959480i	$-0.590923\pi$
$307$	7.15348	−	4.13006i	0.408271	−	0.235715i	0.690046	+	0.723765i	$0.257590\pi$
$308$	22.1030	+	1.75688i	1.25944	+	0.100107i
$309$		0			0
$310$	0.744945	−	2.39582i	0.0423100	−	0.136073i
$311$	−17.7965	+	14.9330i	−1.00915	+	0.846775i	−0.988225	−	0.153006i	$-0.951105\pi$
$311$	−17.7965	+	14.9330i	−1.00915	+	0.846775i	−0.0209220	+	0.999781i	$0.506660\pi$
$312$		0			0
$313$	12.2324	−	4.45222i	0.691414	−	0.251654i	0.0276735	−	0.999617i	$-0.491190\pi$
$313$	12.2324	−	4.45222i	0.691414	−	0.251654i	0.663741	+	0.747963i	$0.268968\pi$
$314$	9.85227	+	5.07911i	0.555996	+	0.286631i
$315$		0			0
$316$	22.1786	−	15.7938i	1.24764	−	0.888468i
$317$	5.90446	+	1.04112i	0.331628	+	0.0584749i	0.336983	−	0.941511i	$-0.390594\pi$
$317$	5.90446	+	1.04112i	0.331628	+	0.0584749i	−0.00535522	+	0.999986i	$0.501705\pi$
$318$		0			0
$319$	5.30711	−	14.5812i	0.297141	−	0.816389i
$320$	17.7710	−	8.80850i	0.993431	−	0.492410i
$321$		0			0
$322$	2.38687	−	18.7041i	0.133015	−	1.04234i
$323$	3.32237			0.184862
$324$		0			0
$325$	2.29752			0.127443
$326$	−2.25282	+	17.6537i	−0.124772	+	0.977746i
$327$		0			0
$328$	6.21614	+	18.9254i	0.343229	+	1.04498i
$329$	−5.39547	+	14.8239i	−0.297462	+	0.817269i
$330$		0			0
$331$	−20.0853	−	3.54158i	−1.10399	−	0.194663i	−0.408187	−	0.912898i	$-0.633839\pi$
$331$	−20.0853	−	3.54158i	−1.10399	−	0.194663i	−0.695800	+	0.718236i	$0.744950\pi$
$332$	−3.36428	−	4.72432i	−0.184639	−	0.259281i
$333$		0			0
$334$	9.53681	+	4.91648i	0.521831	+	0.269018i
$335$	−1.54991	+	0.564120i	−0.0846805	+	0.0308212i
$336$		0			0
$337$	−0.423775	+	0.355590i	−0.0230845	+	0.0193702i	−0.654257	−	0.756272i	$-0.727018\pi$
$337$	−0.423775	+	0.355590i	−0.0230845	+	0.0193702i	0.631172	+	0.775643i	$0.282574\pi$
$338$	3.77353	−	12.1361i	0.205253	−	0.660115i
$339$		0			0
$340$	−0.723079	+	9.09695i	−0.0392145	+	0.493351i
$341$	1.47227	−	0.850016i	0.0797279	−	0.0460309i
$342$		0			0
$343$	−31.4228	−	18.1420i	−1.69667	−	0.979574i
$344$	0.0542436	−	1.70992i	0.00292462	−	0.0921930i
$345$		0			0
$346$	−0.747300	−	3.30858i	−0.0401751	−	0.177870i
$347$	1.00594	+	5.70495i	0.0540015	+	0.306258i	0.999831	−	0.0184072i	$-0.00585952\pi$
$347$	1.00594	+	5.70495i	0.0540015	+	0.306258i	−0.945829	+	0.324665i	$0.894748\pi$
$348$		0			0
$349$	−8.36132	−	7.01598i	−0.447571	−	0.375557i	0.390962	−	0.920407i	$-0.372142\pi$
$349$	−8.36132	−	7.01598i	−0.447571	−	0.375557i	−0.838534	+	0.544850i	$0.816587\pi$
$350$	−4.09189	−	6.36701i	−0.218721	−	0.340331i
$351$		0			0
$352$	12.8951	+	3.78586i	0.687313	+	0.201787i
$353$	−20.7168	+	24.6893i	−1.10264	+	1.31408i	−0.157465	+	0.987525i	$0.550332\pi$
$353$	−20.7168	+	24.6893i	−1.10264	+	1.31408i	−0.945178	+	0.326554i	$0.894112\pi$
$354$		0			0
$355$	−4.55887	+	0.803852i	−0.241960	+	0.0426640i
$356$	15.0375	+	14.8004i	0.796988	+	0.784419i
$357$		0			0
$358$	13.5324	+	32.3064i	0.715208	+	1.70744i
$359$	12.4329	−	21.5345i	0.656185	−	1.13655i	−0.325410	−	0.945573i	$-0.605502\pi$
$359$	12.4329	−	21.5345i	0.656185	−	1.13655i	0.981595	−	0.190973i	$-0.0611643\pi$
$360$		0			0
$361$	−7.87050	−	13.6321i	−0.414237	−	0.717480i
$362$	−18.6341	+	24.4853i	−0.979389	+	1.28692i
$363$		0			0
$364$	18.0205	−	4.98240i	0.944529	−	0.261149i
$365$	−1.65525	−	1.97265i	−0.0866398	−	0.103253i
$366$		0			0
$367$	−5.44785	−	14.9678i	−0.284375	−	0.781315i	−0.996827	−	0.0795941i	$-0.974638\pi$
$367$	−5.44785	−	14.9678i	−0.284375	−	0.781315i	0.712452	−	0.701721i	$-0.247585\pi$
$368$	3.73773	−	10.8004i	0.194842	−	0.563011i
$369$		0			0
$370$	39.2894	−	1.87186i	2.04256	−	0.0973134i
$371$	−4.18449	+	23.7314i	−0.217248	+	1.23208i
$372$		0			0
$373$	−32.2490	−	11.7377i	−1.66979	−	0.607754i	−0.677936	−	0.735121i	$-0.737125\pi$
$373$	−32.2490	−	11.7377i	−1.66979	−	0.607754i	−0.991856	+	0.127367i	$0.959347\pi$
$374$	−4.54224	+	4.19552i	−0.234873	+	0.216945i
$375$		0			0
$376$	−5.04103	+	8.12498i	−0.259971	+	0.419014i
$377$		−	13.0843i		−	0.673874i
$378$		0			0
$379$			20.3118i			1.04335i	0.853145	+	0.521673i	$0.174692\pi$
$379$			20.3118i			1.04335i	−0.853145	+	0.521673i	$0.825308\pi$
$380$	−8.08254	+	3.84745i	−0.414626	+	0.197370i
$381$		0			0
$382$	9.03774	+	9.78461i	0.462411	+	0.500624i
$383$	−23.4300	−	8.52782i	−1.19722	−	0.435751i	−0.334964	−	0.942231i	$-0.608724\pi$
$383$	−23.4300	−	8.52782i	−1.19722	−	0.435751i	−0.862252	+	0.506480i	$0.830947\pi$
$384$		0			0
$385$	4.77294	−	27.0687i	0.243252	−	1.37955i
$386$	0.373337	+	7.83615i	0.0190024	+	0.398850i
$387$		0			0
$388$	−30.9587	+	2.95664i	−1.57169	+	0.150100i
$389$	2.43782	+	6.69786i	0.123602	+	0.339595i	0.986026	−	0.166593i	$-0.0532765\pi$
$389$	2.43782	+	6.69786i	0.123602	+	0.339595i	−0.862423	+	0.506188i	$0.831054\pi$
$390$		0			0
$391$	3.38002	+	4.02815i	0.170935	+	0.203712i
$392$	−31.1463	−	27.8646i	−1.57313	−	1.40738i
$393$		0			0
$394$	−17.6008	−	13.3948i	−0.886716	−	0.674820i
$395$	−16.8761	−	29.2303i	−0.849131	−	1.47074i
$396$		0			0
$397$	−18.3887	+	31.8501i	−0.922901	+	1.59851i	−0.127997	+	0.991775i	$0.540855\pi$
$397$	−18.3887	+	31.8501i	−0.922901	+	1.59851i	−0.794903	+	0.606736i	$0.792478\pi$
$398$	21.0278	−	8.80806i	1.05403	−	0.441508i
$399$		0			0
$400$	−1.63732	−	4.28531i	−0.0818659	−	0.214265i
$401$	36.2027	−	6.38352i	1.80788	−	0.318778i	0.835027	−	0.550209i	$-0.185452\pi$
$401$	36.2027	−	6.38352i	1.80788	−	0.318778i	0.972851	+	0.231431i	$0.0743408\pi$
$402$		0			0
$403$	0.921440	−	1.09813i	0.0459002	−	0.0547017i
$404$	−14.3713	−	6.56290i	−0.714998	−	0.326516i
$405$		0			0
$406$	−36.2598	+	23.3032i	−1.79955	+	1.15652i
$407$	20.4167	+	17.1316i	1.01202	+	0.849182i
$408$		0			0
$409$	1.78158	+	10.1038i	0.0880934	+	0.499602i	0.996646	+	0.0818323i	$0.0260772\pi$
$409$	1.78158	+	10.1038i	0.0880934	+	0.499602i	−0.908553	+	0.417770i	$0.862812\pi$
$410$	24.0871	−	5.44048i	1.18957	−	0.268686i
$411$		0			0
$412$	−12.1682	+	17.6753i	−0.599484	+	0.870800i
$413$	−33.0812	−	19.0994i	−1.62782	−	0.939822i
$414$		0			0
$415$	−6.22644	+	3.59484i	−0.305644	+	0.176464i
$416$	11.3096	−	0.719144i	0.554498	−	0.0352589i
$417$		0			0
$418$	−5.79190	−	1.80091i	−0.283291	−	0.0880853i
$419$	−24.0344	+	20.1673i	−1.17416	+	0.985237i	−0.174160	+	0.984717i	$0.555721\pi$
$419$	−24.0344	+	20.1673i	−1.17416	+	0.985237i	−1.00000		0.000519235i	$0.999835\pi$
$420$		0			0
$421$	19.3207	−	7.03216i	0.941634	−	0.342727i	0.174823	−	0.984600i	$-0.444065\pi$
$421$	19.3207	−	7.03216i	0.941634	−	0.342727i	0.766811	+	0.641873i	$0.221842\pi$
$422$	−6.23401	+	12.0925i	−0.303467	+	0.588654i
$423$		0			0
$424$	−5.42824	+	13.5599i	−0.263619	+	0.658528i
$425$	2.07859	+	0.366512i	0.100827	+	0.0177784i
$426$		0			0
$427$	−9.32038	+	25.6075i	−0.451045	+	1.23924i
$428$	24.6383	+	6.39239i	1.19094	+	0.308988i
$429$		0			0
$430$	−2.10370	−	0.268458i	−0.101450	−	0.0129462i
$431$	−11.1277			−0.536001			−0.268000	−	0.963419i	$-0.586363\pi$
$431$	−11.1277			−0.536001			−0.268000	+	0.963419i	$0.586363\pi$
$432$		0			0
$433$	3.88415			0.186660			0.0933301	−	0.995635i	$-0.470249\pi$
$433$	3.88415			0.186660			0.0933301	+	0.995635i	$0.470249\pi$
$434$	−4.68429	−	0.597772i	−0.224853	−	0.0286940i
$435$		0			0
$436$	−6.09558	−	1.58149i	−0.291925	−	0.0757398i
$437$	−1.76416	+	4.84699i	−0.0843912	+	0.231863i
$438$		0			0
$439$	−13.3089	−	2.34672i	−0.635199	−	0.112003i	−0.153230	−	0.988191i	$-0.548967\pi$
$439$	−13.3089	−	2.34672i	−0.635199	−	0.112003i	−0.481970	+	0.876188i	$0.660079\pi$
$440$	6.19159	−	15.4668i	0.295173	−	0.737350i
$441$		0			0
$442$	−2.38915	+	4.63439i	−0.113640	+	0.220435i
$443$	7.47039	−	2.71900i	0.354929	−	0.129184i	−0.158401	−	0.987375i	$-0.550634\pi$
$443$	7.47039	−	2.71900i	0.354929	−	0.129184i	0.513330	+	0.858191i	$0.328412\pi$
$444$		0			0
$445$	20.0363	−	16.8125i	0.949813	−	0.796988i
$446$	13.9469	+	4.33660i	0.660407	+	0.205344i
$447$		0			0
$448$	−22.1354	−	30.0609i	−1.04580	−	1.42025i
$449$	9.00315	−	5.19797i	0.424885	−	0.245307i	−0.272280	−	0.962218i	$-0.587778\pi$
$449$	9.00315	−	5.19797i	0.424885	−	0.245307i	0.697165	+	0.716911i	$0.254444\pi$
$450$		0			0
$451$	14.4905	+	8.36607i	0.682329	+	0.393943i
$452$	2.69075	−	3.90853i	0.126562	−	0.183842i
$453$		0			0
$454$	18.2108	−	4.11322i	0.854673	−	0.193043i
$455$	−4.02466	−	22.8250i	−0.188679	−	1.07005i
$456$		0			0
$457$	28.6354	+	24.0279i	1.33951	+	1.12398i	0.981753	+	0.190163i	$0.0609016\pi$
$457$	28.6354	+	24.0279i	1.33951	+	1.12398i	0.357753	+	0.933816i	$0.383543\pi$
$458$	−20.2614	+	13.0214i	−0.946754	+	0.608451i
$459$		0			0
$460$	−12.8875	−	5.88532i	−0.600884	−	0.274405i
$461$	8.60771	−	10.2583i	0.400901	−	0.477775i	−0.527393	−	0.849621i	$-0.676831\pi$
$461$	8.60771	−	10.2583i	0.400901	−	0.477775i	0.928294	+	0.371846i	$0.121275\pi$
$462$		0			0
$463$	14.2689	−	2.51599i	0.663131	−	0.116928i	0.168055	−	0.985778i	$-0.446251\pi$
$463$	14.2689	−	2.51599i	0.663131	−	0.116928i	0.495076	+	0.868850i	$0.335140\pi$
$464$	−24.4047	+	9.32445i	−1.13296	+	0.432877i
$465$		0			0
$466$	23.9116	−	10.0160i	1.10768	−	0.463982i
$467$	19.0970	−	33.0769i	0.883702	−	1.53062i	0.0365086	−	0.999333i	$-0.488376\pi$
$467$	19.0970	−	33.0769i	0.883702	−	1.53062i	0.847194	−	0.531284i	$-0.178290\pi$
$468$		0			0
$469$	1.55220	+	2.68849i	0.0716739	+	0.124143i
$470$	9.43235	+	7.17833i	0.435082	+	0.331112i
$471$		0			0
$472$	−17.2556	−	15.4375i	−0.794253	−	0.710568i
$473$	−0.923682	−	1.10080i	−0.0424710	−	0.0506149i
$474$		0			0
$475$	0.708116	+	1.94553i	0.0324906	+	0.0892672i
$476$	17.0982	−	1.63292i	0.783693	−	0.0748447i
$477$		0			0
$478$	−1.39732	−	29.3291i	−0.0639122	−	1.34148i
$479$	5.21540	−	29.5780i	0.238298	−	1.35145i	−0.597259	−	0.802049i	$-0.703743\pi$
$479$	5.21540	−	29.5780i	0.238298	−	1.35145i	0.835556	−	0.549405i	$-0.185145\pi$
$480$		0			0
$481$	21.1183	+	7.68644i	0.962912	+	0.350471i
$482$	−13.5419	−	14.6610i	−0.616819	−	0.667792i
$483$		0			0
$484$	−9.67155	+	4.60385i	−0.439616	+	0.209266i
$485$			38.5524i			1.75057i
$486$		0			0
$487$			14.9474i			0.677331i	0.940907	+	0.338666i	$0.109976\pi$
$487$			14.9474i			0.677331i	−0.940907	+	0.338666i	$0.890024\pi$
$488$	−8.70812	+	14.0355i	−0.394198	+	0.635356i
$489$		0			0
$490$	−38.0564	+	35.1515i	−1.71921	+	1.58798i
$491$	−7.42871	−	2.70383i	−0.335253	−	0.122022i	0.168908	−	0.985632i	$-0.445976\pi$
$491$	−7.42871	−	2.70383i	−0.335253	−	0.122022i	−0.504161	+	0.863610i	$0.668198\pi$
$492$		0			0
$493$	2.08727	−	11.8375i	0.0940059	−	0.533134i
$494$	−5.10872	+	0.243394i	−0.229852	+	0.0109508i
$495$		0			0
$496$	−2.70488	−	0.936084i	−0.121453	−	0.0420314i
$497$	2.97999	+	8.18746i	0.133671	+	0.367258i
$498$		0			0
$499$	−14.1617	−	16.8772i	−0.633963	−	0.755528i	0.349440	−	0.936959i	$-0.386372\pi$
$499$	−14.1617	−	16.8772i	−0.633963	−	0.755528i	−0.983404	+	0.181431i	$0.941927\pi$
$500$	18.4152	−	5.09153i	0.823551	−	0.227700i
$501$		0			0
$502$	21.1482	−	27.7888i	0.943891	−	1.24028i
$503$	15.3597	+	26.6038i	0.684855	+	1.18620i	0.973482	+	0.228762i	$0.0734676\pi$
$503$	15.3597	+	26.6038i	0.684855	+	1.18620i	−0.288628	+	0.957441i	$0.593199\pi$
$504$		0			0
$505$	−9.79250	+	16.9611i	−0.435761	+	0.754759i
$506$	−3.70892	−	8.85444i	−0.164881	−	0.393628i
$507$		0			0
$508$	25.4948	+	25.0928i	1.13115	+	1.11331i
$509$	−17.3155	+	3.05319i	−0.767496	+	0.135330i	−0.543670	−	0.839299i	$-0.682966\pi$
$509$	−17.3155	+	3.05319i	−0.767496	+	0.135330i	−0.223826	+	0.974629i	$0.571855\pi$
$510$		0			0
$511$	−3.11546	+	3.71286i	−0.137820	+	0.164247i
$512$	−9.40107	−	20.5820i	−0.415473	−	0.909606i
$513$		0			0
$514$	−15.9773	−	24.8608i	−0.704729	−	1.09656i
$515$	20.3778	+	17.0990i	0.897952	+	0.753471i
$516$		0			0
$517$	1.39466	+	7.90950i	0.0613370	+	0.347859i
$518$	−16.3107	−	72.2138i	−0.716653	−	3.17289i
$519$		0			0
$520$	0.445423	−	14.0411i	0.0195331	−	0.615743i
$521$	−22.6652	−	13.0858i	−0.992980	−	0.573297i	−0.0868161	−	0.996224i	$-0.527669\pi$
$521$	−22.6652	−	13.0858i	−0.992980	−	0.573297i	−0.906164	+	0.422927i	$0.861003\pi$
$522$		0			0
$523$	7.08428	−	4.09011i	0.309774	−	0.178848i	−0.337051	−	0.941486i	$-0.609430\pi$
$523$	7.08428	−	4.09011i	0.309774	−	0.178848i	0.646825	+	0.762638i	$0.276096\pi$
$524$	0.535986	−	6.74316i	0.0234147	−	0.294576i
$525$		0			0
$526$	−1.12366	+	3.61382i	−0.0489941	+	0.157570i
$527$	1.00882	−	0.846499i	0.0439448	−	0.0368741i
$528$		0			0
$529$	13.9415	−	5.07430i	0.606153	−	0.220622i
$530$	16.0936	+	8.29668i	0.699061	+	0.360385i
$531$		0			0
$532$	9.77316	+	13.7241i	0.423720	+	0.595014i
$533$	13.8946	+	2.44999i	0.601841	+	0.106121i
$534$		0			0
$535$	10.7921	−	29.6510i	0.466583	−	1.28192i
$536$	0.587175	+	1.78769i	0.0253621	+	0.0772163i
$537$		0			0
$538$	−3.39388	+	26.5953i	−0.146321	+	1.14661i
$539$	−35.1033			−1.51201
$540$		0			0
$541$	−7.80321			−0.335486			−0.167743	−	0.985831i	$-0.553648\pi$
$541$	−7.80321			−0.335486			−0.167743	+	0.985831i	$0.553648\pi$
$542$	−1.28256	+	10.0504i	−0.0550905	+	0.431703i
$543$		0			0
$544$	10.3466	+	1.15354i	0.443608	+	0.0494578i
$545$	−2.66999	+	7.33574i	−0.114370	+	0.314228i
$546$		0			0
$547$	39.6028	+	6.98304i	1.69329	+	0.298573i	0.935344	−	0.353740i	$-0.115090\pi$
$547$	39.6028	+	6.98304i	1.69329	+	0.298573i	0.757950	+	0.652313i	$0.226201\pi$
$548$	−10.6102	+	7.55575i	−0.453247	+	0.322765i
$549$		0			0
$550$	−3.42495	−	1.76565i	−0.146040	−	0.0752877i
$551$	11.0797	−	4.03269i	0.472012	−	0.171798i
$552$		0			0
$553$	−48.6648	+	40.8346i	−2.06944	+	1.73646i
$554$	−7.15185	+	23.0011i	−0.303853	+	0.977222i
$555$		0			0
$556$	−7.64040	−	0.607304i	−0.324025	−	0.0257554i
$557$	−27.5205	+	15.8890i	−1.16608	+	0.673238i	−0.952754	−	0.303742i	$-0.901764\pi$
$557$	−27.5205	+	15.8890i	−1.16608	+	0.673238i	−0.213329	+	0.976980i	$0.568431\pi$
$558$		0			0
$559$	−1.04937	−	0.605854i	−0.0443836	−	0.0256249i
$560$	−39.7048	+	23.7729i	−1.67783	+	1.00459i
$561$		0			0
$562$	7.71855	+	34.1729i	0.325587	+	1.44150i
$563$	−4.72244	−	26.7823i	−0.199027	−	1.12874i	−0.906566	−	0.422064i	$-0.861306\pi$
$563$	−4.72244	−	26.7823i	−0.199027	−	1.12874i	0.707539	−	0.706675i	$-0.249805\pi$
$564$		0			0
$565$	−4.50613	−	3.78109i	−0.189574	−	0.159072i
$566$	5.65204	+	8.79461i	0.237573	+	0.369665i
$567$		0			0
$568$	0.751688	+	5.22733i	0.0315401	+	0.219334i
$569$	10.7609	−	12.8243i	0.451121	−	0.537625i	−0.491771	−	0.870725i	$-0.663650\pi$
$569$	10.7609	−	12.8243i	0.451121	−	0.537625i	0.942892	+	0.333100i	$0.108095\pi$
$570$		0			0
$571$	−16.5413	+	2.91668i	−0.692233	+	0.122059i	−0.508687	−	0.860952i	$-0.669869\pi$
$571$	−16.5413	+	2.91668i	−0.692233	+	0.122059i	−0.183546	+	0.983011i	$0.558758\pi$
$572$	6.67711	−	6.78409i	0.279184	−	0.283657i
$573$		0			0
$574$	−17.9568	−	42.8689i	−0.749502	−	1.78931i
$575$	−1.63842	+	2.83783i	−0.0683269	+	0.118346i
$576$		0			0
$577$	−1.22069	−	2.11429i	−0.0508179	−	0.0880192i	0.839497	−	0.543364i	$-0.182849\pi$
$577$	−1.22069	−	2.11429i	−0.0508179	−	0.0880192i	−0.890315	+	0.455344i	$0.849516\pi$
$578$	11.6589	−	15.3199i	0.484947	−	0.637222i
$579$		0			0
$580$	8.63048	+	31.2150i	0.358361	+	1.29613i
$581$	8.69830	+	10.3662i	0.360866	+	0.430064i
$582$		0			0
$583$	4.19609	+	11.5287i	0.173784	+	0.477468i
$584$	−2.30919	+	1.81604i	−0.0955549	+	0.0751485i
$585$		0			0
$586$	2.87668	−	0.137053i	0.118834	−	0.00566162i
$587$	−2.47253	+	14.0224i	−0.102052	+	0.578766i	0.890305	+	0.455365i	$0.150491\pi$
$587$	−2.47253	+	14.0224i	−0.102052	+	0.578766i	−0.992357	+	0.123401i	$0.960620\pi$
$588$		0			0
$589$	1.21389	+	0.441820i	0.0500175	+	0.0182049i
$590$	−21.0839	+	19.4745i	−0.868011	+	0.801754i
$591$		0			0
$592$	−0.713216	−	44.8674i	−0.0293130	−	1.84404i
$593$		−	14.5479i		−	0.597412i	−0.954345	−	0.298706i	$-0.903445\pi$
$593$		−	14.5479i		−	0.597412i	0.954345	−	0.298706i	$-0.0965549\pi$
$594$		0			0
$595$		−	21.2921i		−	0.872890i
$596$	−2.49441	−	5.24015i	−0.102175	−	0.214645i
$597$		0			0
$598$	−5.49245	−	5.94635i	−0.224603	−	0.243164i
$599$	27.4921	+	10.0063i	1.12330	+	0.408846i	0.835854	−	0.548952i	$-0.184973\pi$
$599$	27.4921	+	10.0063i	1.12330	+	0.408846i	0.287442	+	0.957798i	$0.407195\pi$
$600$		0			0
$601$	−1.13737	+	6.45037i	−0.0463945	+	0.263116i	−0.999178	−	0.0405338i	$-0.987094\pi$
$601$	−1.13737	+	6.45037i	−0.0463945	+	0.263116i	0.952784	+	0.303650i	$0.0982053\pi$
$602$	0.189957	+	3.98710i	0.00774208	+	0.162502i
$603$		0			0
$604$	0.304548	+	3.18890i	0.0123919	+	0.129754i
$605$	4.54146	+	12.4776i	0.184636	+	0.507285i
$606$		0			0
$607$	21.3252	+	25.4144i	0.865565	+	1.03154i	0.999179	+	0.0405067i	$0.0128972\pi$
$607$	21.3252	+	25.4144i	0.865565	+	1.03154i	−0.133614	+	0.991033i	$0.542658\pi$
$608$	4.09469	+	9.35528i	0.166061	+	0.379407i
$609$		0			0
$610$	16.2939	+	12.4002i	0.659720	+	0.502069i
$611$	3.38618	+	5.86504i	0.136990	+	0.237274i
$612$		0			0
$613$	4.11508	−	7.12752i	0.166206	−	0.287878i	−0.770877	−	0.636984i	$-0.780182\pi$
$613$	4.11508	−	7.12752i	0.166206	−	0.287878i	0.937083	+	0.349107i	$0.113515\pi$
$614$	−10.7745	+	4.51320i	−0.434825	+	0.182138i
$615$		0			0
$616$	−30.6924	−	6.42147i	−1.23663	−	0.258728i
$617$	18.2737	−	3.22215i	0.735673	−	0.129719i	0.206756	−	0.978392i	$-0.433709\pi$
$617$	18.2737	−	3.22215i	0.735673	−	0.129719i	0.528917	+	0.848673i	$0.322598\pi$
$618$		0			0
$619$	−8.14884	+	9.71141i	−0.327530	+	0.390335i	−0.904530	−	0.426409i	$-0.859778\pi$
$619$	−8.14884	+	9.71141i	−0.327530	+	0.390335i	0.577001	+	0.816744i	$0.304223\pi$
$620$	−1.47393	+	3.22758i	−0.0591946	+	0.129623i
$621$		0			0
$622$	27.6389	−	17.7627i	1.10822	−	0.712220i
$623$	−37.7117	−	31.6438i	−1.51089	−	1.26778i
$624$		0			0
$625$	−5.10856	−	28.9721i	−0.204342	−	1.15888i
$626$	−17.9570	+	4.05591i	−0.717708	+	0.162107i
$627$		0			0
$628$	−12.9119	−	8.88891i	−0.515240	−	0.354706i
$629$	17.8798	+	10.3229i	0.712915	+	0.411602i
$630$		0			0
$631$	−26.9805	+	15.5772i	−1.07408	+	0.620119i	−0.929293	−	0.369344i	$-0.879582\pi$
$631$	−26.9805	+	15.5772i	−1.07408	+	0.620119i	−0.144785	+	0.989463i	$0.546249\pi$
$632$	−33.9403	+	18.1857i	−1.35007	+	0.723388i
$633$		0			0
$634$	−8.09662	−	2.51753i	−0.321558	−	0.0999838i
$635$	33.9698	−	28.5041i	1.34805	−	1.13115i
$636$		0			0
$637$	−27.8148	+	10.1238i	−1.10206	+	0.401118i
$638$	−10.0553	+	19.5049i	−0.398094	+	0.772208i
$639$		0			0
$640$	−26.5068	+	9.17554i	−1.04777	+	0.362695i
$641$	31.4814	+	5.55103i	1.24344	+	0.219252i	0.756390	−	0.654121i	$-0.226961\pi$
$641$	31.4814	+	5.55103i	1.24344	+	0.219252i	0.487052	+	0.873373i	$0.338072\pi$
$642$		0			0
$643$	10.2506	−	28.1633i	0.404244	−	1.11065i	−0.555925	−	0.831233i	$-0.687636\pi$
$643$	10.2506	−	28.1633i	0.404244	−	1.11065i	0.960169	−	0.279420i	$-0.0901421\pi$
$644$	−6.69677	+	25.8115i	−0.263890	+	1.01711i
$645$		0			0
$646$	−4.66075	−	0.594767i	−0.183375	−	0.0234008i
$647$	1.60615			0.0631443			0.0315721	−	0.999501i	$-0.489949\pi$
$647$	1.60615			0.0631443			0.0315721	+	0.999501i	$0.489949\pi$
$648$		0			0
$649$	−19.4478			−0.763394
$650$	−3.22304	−	0.411299i	−0.126418	−	0.0161325i
$651$		0			0
$652$	6.32068	−	24.3619i	0.247537	−	0.954087i
$653$	5.67960	−	15.6046i	0.222260	−	0.610654i	−0.777576	−	0.628790i	$-0.783551\pi$
$653$	5.67960	−	15.6046i	0.222260	−	0.610654i	0.999836	+	0.0181352i	$0.00577293\pi$
$654$		0			0
$655$	−8.25808	−	1.45612i	−0.322670	−	0.0568954i
$656$	−5.33223	−	27.6620i	−0.208189	−	1.08002i
$657$		0			0
$658$	10.2227	−	19.8297i	0.398523	−	0.773040i
$659$	22.5548	−	8.20928i	0.878611	−	0.319788i	0.136962	−	0.990576i	$-0.456266\pi$
$659$	22.5548	−	8.20928i	0.878611	−	0.319788i	0.741649	+	0.670788i	$0.234044\pi$
$660$		0			0
$661$	0.722514	−	0.606261i	0.0281025	−	0.0235808i	−0.628628	−	0.777706i	$-0.716383\pi$
$661$	0.722514	−	0.606261i	0.0281025	−	0.0235808i	0.656731	+	0.754125i	$0.271939\pi$
$662$	27.5424	+	8.56390i	1.07046	+	0.332845i
$663$		0			0
$664$	3.87379	+	7.22973i	0.150332	+	0.280568i
$665$	18.0877	−	10.4429i	0.701411	−	0.404960i
$666$		0			0
$667$	16.1613	+	9.33075i	0.625769	+	0.361288i
$668$	−12.4984	−	8.60429i	−0.483579	−	0.332910i
$669$		0			0
$670$	2.27526	−	0.513906i	0.0879008	−	0.0198539i
$671$	2.40920	+	13.6632i	0.0930061	+	0.527464i
$672$		0			0
$673$	−4.60299	−	3.86237i	−0.177432	−	0.148883i	0.549746	−	0.835332i	$-0.314724\pi$
$673$	−4.60299	−	3.86237i	−0.177432	−	0.148883i	−0.727179	+	0.686448i	$0.759169\pi$
$674$	0.658145	−	0.422971i	0.0253508	−	0.0162922i
$675$		0			0
$676$	−7.46624	+	16.3494i	−0.287163	+	0.628823i
$677$	2.76557	−	3.29588i	0.106290	−	0.126671i	−0.710277	−	0.703922i	$-0.751430\pi$
$677$	2.76557	−	3.29588i	0.106290	−	0.126671i	0.816567	+	0.577251i	$0.195875\pi$
$678$		0			0
$679$	71.4595	−	12.6002i	2.74236	−	0.483553i
$680$	2.64289	−	12.6321i	0.101350	−	0.484419i
$681$		0			0
$682$	−2.21752	+	0.928869i	−0.0849134	+	0.0355682i
$683$	7.98799	−	13.8356i	0.305652	−	0.529405i	−0.671754	−	0.740774i	$-0.734459\pi$
$683$	7.98799	−	13.8356i	0.305652	−	0.529405i	0.977406	+	0.211369i	$0.0677922\pi$
$684$		0			0
$685$	8.07356	+	13.9838i	0.308475	+	0.534294i
$686$	40.8333	+	31.0755i	1.55902	+	1.18647i
$687$		0			0
$688$	−0.382204	+	2.38904i	−0.0145714	+	0.0910811i
$689$	6.64972	+	7.92483i	0.253334	+	0.301912i
$690$		0			0
$691$	−6.40655	−	17.6018i	−0.243717	−	0.669606i	−0.999884	−	0.0152277i	$-0.995153\pi$
$691$	−6.40655	−	17.6018i	−0.243717	−	0.669606i	0.756167	−	0.654378i	$-0.227070\pi$
$692$	0.456042	+	4.77518i	0.0173361	+	0.181525i
$693$		0			0
$694$	−0.389872	−	8.18320i	−0.0147993	−	0.310630i
$695$	−1.64987	+	9.35690i	−0.0625833	+	0.354927i
$696$		0			0
$697$	12.1798	+	4.43307i	0.461342	+	0.167915i
$698$	10.4736	+	11.3391i	0.396431	+	0.429192i
$699$		0			0
$700$	4.60044	+	9.66440i	0.173880	+	0.365280i
$701$		−	2.57851i		−	0.0973888i	−0.998814	−	0.0486944i	$-0.984494\pi$
$701$		−	2.57851i		−	0.0973888i	0.998814	−	0.0486944i	$-0.0155060\pi$
$702$		0			0
$703$			20.2520i			0.763818i
$704$	−17.4120	−	7.61942i	−0.656241	−	0.287168i
$705$		0			0
$706$	33.4821	−	30.9264i	1.26012	−	1.16393i
$707$	34.6391	+	12.6076i	1.30274	+	0.474158i
$708$		0			0
$709$	−5.73026	+	32.4979i	−0.215204	+	1.22048i	0.665347	+	0.746534i	$0.268284\pi$
$709$	−5.73026	+	32.4979i	−0.215204	+	1.22048i	−0.880552	+	0.473950i	$0.842828\pi$
$710$	6.53926	−	0.311549i	0.245414	−	0.0116922i
$711$		0			0
$712$	−18.4457	−	23.4546i	−0.691280	−	0.878996i
$713$	0.699276	+	1.92124i	0.0261881	+	0.0719512i
$714$		0			0
$715$	−7.58484	−	9.03926i	−0.283657	−	0.338049i
$716$	−13.2003	−	47.7431i	−0.493318	−	1.78424i
$717$		0			0
$718$	−21.2965	+	27.9836i	−0.794777	+	1.04434i
$719$	18.8429	+	32.6368i	0.702721	+	1.21715i	0.967508	+	0.252842i	$0.0813651\pi$
$719$	18.8429	+	32.6368i	0.702721	+	1.21715i	−0.264787	+	0.964307i	$0.585302\pi$
$720$		0			0
$721$	25.0340	−	43.3602i	0.932315	−	1.61482i
$722$	8.60063	+	20.5326i	0.320082	+	0.764144i
$723$		0			0
$724$	30.5240	−	31.0131i	1.13442	−	1.15259i
$725$	7.37674	−	1.30072i	0.273965	−	0.0483074i
$726$		0			0
$727$	5.29383	−	6.30894i	0.196337	−	0.233986i	−0.658889	−	0.752240i	$-0.728973\pi$
$727$	5.29383	−	6.30894i	0.196337	−	0.233986i	0.855227	+	0.518254i	$0.173418\pi$
$728$	−26.1717	+	3.76349i	−0.969989	+	0.139484i
$729$		0			0
$730$	1.96891	+	3.06363i	0.0728725	+	0.113390i
$731$	−0.852729	−	0.715525i	−0.0315393	−	0.0264646i
$732$		0			0
$733$	0.159851	+	0.906562i	0.00590425	+	0.0334846i	0.987618	−	0.156881i	$-0.0501438\pi$
$733$	0.159851	+	0.906562i	0.00590425	+	0.0334846i	−0.981713	+	0.190365i	$0.939033\pi$
$734$	4.96292	+	21.9727i	0.183185	+	0.811028i
$735$		0			0
$736$	−7.17690	+	14.4821i	−0.264544	+	0.533818i
$737$	1.36876	+	0.790257i	0.0504191	+	0.0291095i
$738$		0			0
$739$	21.9417	−	12.6681i	0.807139	−	0.466002i	−0.0388223	−	0.999246i	$-0.512361\pi$
$739$	21.9417	−	12.6681i	0.807139	−	0.466002i	0.845961	+	0.533244i	$0.179027\pi$
$740$	−55.4517	−	4.40763i	−2.03845	−	0.162028i
$741$		0			0
$742$	10.1185	−	32.5422i	0.371463	−	1.19466i
$743$	−16.8393	+	14.1298i	−0.617773	+	0.518373i	−0.897103	−	0.441822i	$-0.854332\pi$
$743$	−16.8393	+	14.1298i	−0.617773	+	0.518373i	0.279330	+	0.960195i	$0.409888\pi$
$744$		0			0
$745$	−6.76046	+	2.46061i	−0.247684	+	0.0901497i
$746$	43.1389	+	22.2393i	1.57943	+	0.814237i
$747$		0			0
$748$	7.12309	−	5.07248i	0.260446	−	0.185468i
$749$	−58.4875	−	10.3129i	−2.13709	−	0.376826i
$750$		0			0
$751$	−14.1809	+	38.9618i	−0.517470	+	1.42174i	0.355828	+	0.934551i	$0.384199\pi$
$751$	−14.1809	+	38.9618i	−0.517470	+	1.42174i	−0.873298	+	0.487186i	$0.838023\pi$
$752$	8.52627	−	10.4956i	0.310921	−	0.382734i
$753$		0			0
$754$	−2.34233	+	18.3551i	−0.0853026	+	0.668453i
$755$	3.97108			0.144523
$756$		0			0
$757$	2.67068			0.0970675			0.0485338	−	0.998822i	$-0.484545\pi$
$757$	2.67068			0.0970675			0.0485338	+	0.998822i	$0.484545\pi$
$758$	3.63619	−	28.4941i	0.132072	−	1.03495i
$759$		0			0
$760$	12.0273	−	3.95041i	0.436274	−	0.143296i
$761$	0.975731	−	2.68080i	0.0353702	−	0.0971789i	−0.920750	−	0.390152i	$-0.872422\pi$
$761$	0.975731	−	2.68080i	0.0353702	−	0.0971789i	0.956121	+	0.292973i	$0.0946447\pi$
$762$		0			0
$763$	14.4699	+	2.55144i	0.523847	+	0.0923684i
$764$	−10.9268	−	15.3441i	−0.395319	−	0.555132i
$765$		0			0
$766$	31.3418	+	16.1575i	1.13243	+	0.583796i
$767$	−15.4099	+	5.60875i	−0.556419	+	0.202520i
$768$		0			0
$769$	16.8767	−	14.1612i	0.608590	−	0.510667i	−0.285604	−	0.958348i	$-0.592194\pi$
$769$	16.8767	−	14.1612i	0.608590	−	0.510667i	0.894194	+	0.447680i	$0.147750\pi$
$770$	−11.5415	+	37.1185i	−0.415926	+	1.33766i
$771$		0			0
$772$	0.879088	−	11.0597i	0.0316391	−	0.398047i
$773$	25.5618	−	14.7581i	0.919396	−	0.530813i	0.0359534	−	0.999353i	$-0.488553\pi$
$773$	25.5618	−	14.7581i	0.919396	−	0.530813i	0.883442	+	0.468540i	$0.155220\pi$
$774$		0			0
$775$	0.710712	+	0.410330i	0.0255295	+	0.0147395i
$776$	43.9593	+	1.39451i	1.57805	+	0.0500601i
$777$		0			0
$778$	−2.22082	−	9.83242i	−0.0796204	−	0.352509i
$779$	2.20779	+	12.5210i	0.0791024	+	0.448612i
$780$		0			0
$781$	3.39811	+	2.85135i	0.121594	+	0.102029i
$782$	−4.02050	−	6.25592i	−0.143773	−	0.223711i
$783$		0			0
$784$	38.7049	+	44.6653i	1.38232	+	1.59519i
$785$	−12.4909	+	14.8860i	−0.445818	+	0.531306i
$786$		0			0
$787$	−37.3662	+	6.58868i	−1.33196	+	0.234861i	−0.793902	−	0.608045i	$-0.791954\pi$
$787$	−37.3662	+	6.58868i	−1.33196	+	0.234861i	−0.538060	+	0.842906i	$0.680843\pi$
$788$	22.2932	+	21.9416i	0.794161	+	0.781637i
$789$		0			0
$790$	18.4417	+	44.0265i	0.656126	+	1.56639i
$791$	−5.53576	+	9.58822i	−0.196829	+	0.340918i
$792$		0			0
$793$	5.84945	+	10.1315i	0.207720	+	0.359782i
$794$	31.4981	−	41.3886i	1.11782	−	1.46883i
$795$		0			0
$796$	−31.0754	+	8.59190i	−1.10144	+	0.304532i
$797$	−16.1467	−	19.2429i	−0.571947	−	0.681619i	0.400083	−	0.916479i	$-0.368981\pi$
$797$	−16.1467	−	19.2429i	−0.571947	−	0.681619i	−0.972029	+	0.234860i	$0.924537\pi$
$798$		0			0
$799$	2.12790	+	5.84636i	0.0752797	+	0.206829i
$800$	1.52974	+	6.30470i	0.0540844	+	0.222905i
$801$		0			0
$802$	−51.9293	+	2.47406i	−1.83369	+	0.0873622i
$803$	−0.428494	+	2.43011i	−0.0151212	+	0.0857567i
$804$		0			0
$805$	31.0629	+	11.3060i	1.09482	+	0.398483i
$806$	−1.48922	+	1.37554i	−0.0524554	+	0.0484514i
$807$		0			0
$808$	18.9857	+	11.7794i	0.667914	+	0.414398i
$809$			17.5875i			0.618343i	0.951006	+	0.309171i	$0.100052\pi$
$809$			17.5875i			0.618343i	−0.951006	+	0.309171i	$0.899948\pi$
$810$		0			0
$811$		−	51.1104i		−	1.79473i	−0.441292	−	0.897364i	$-0.645480\pi$
$811$		−	51.1104i		−	1.79473i	0.441292	−	0.897364i	$-0.354520\pi$
$812$	55.0384	−	26.1993i	1.93147	−	0.919416i
$813$		0			0
$814$	−25.5744	−	27.6878i	−0.896381	−	0.970458i
$815$	−29.3184	−	10.6710i	−1.02698	−	0.373790i
$816$		0			0
$817$	0.189610	−	1.07533i	0.00663363	−	0.0376212i
$818$	−0.690487	−	14.4930i	−0.0241423	−	0.506735i
$819$		0			0
$820$	−34.7642	+	3.32007i	−1.21402	+	0.115942i
$821$	3.57660	+	9.82664i	0.124824	+	0.342952i	0.986327	−	0.164801i	$-0.0526983\pi$
$821$	3.57660	+	9.82664i	0.124824	+	0.342952i	−0.861502	+	0.507753i	$0.830476\pi$
$822$		0			0
$823$	14.7797	+	17.6137i	0.515187	+	0.613976i	0.959436	−	0.281927i	$-0.0909737\pi$
$823$	14.7797	+	17.6137i	0.515187	+	0.613976i	−0.444249	+	0.895904i	$0.646529\pi$
$824$	20.2342	−	22.6172i	0.704892	−	0.787909i
$825$		0			0
$826$	42.9884	+	32.7156i	1.49576	+	1.13832i
$827$	−1.77573	−	3.07566i	−0.0617483	−	0.106951i	0.833499	−	0.552521i	$-0.186334\pi$
$827$	−1.77573	−	3.07566i	−0.0617483	−	0.106951i	−0.895247	+	0.445570i	$0.853001\pi$
$828$		0			0
$829$	−1.40521	+	2.43389i	−0.0488049	+	0.0845326i	−0.889396	−	0.457138i	$-0.848875\pi$
$829$	−1.40521	+	2.43389i	−0.0488049	+	0.0845326i	0.840591	+	0.541670i	$0.182208\pi$
$830$	9.37822	−	3.92832i	0.325523	−	0.136354i
$831$		0			0
$832$	−15.9942	−	1.01579i	−0.554500	−	0.0352160i
$833$	−26.7794	+	4.72193i	−0.927852	+	0.163605i
$834$		0			0
$835$	−12.0909	+	14.4094i	−0.418423	+	0.498658i
$836$	7.80270	+	3.56324i	0.269862	+	0.123237i
$837$		0			0
$838$	37.3267	−	23.9888i	1.28943	−	0.828680i
$839$	−9.47819	−	7.95315i	−0.327223	−	0.274573i	0.464344	−	0.885655i	$-0.346290\pi$
$839$	−9.47819	−	7.95315i	−0.327223	−	0.274573i	−0.791567	+	0.611082i	$0.790735\pi$
$840$		0			0
$841$	−2.37174	−	13.4508i	−0.0817840	−	0.463820i
$842$	−28.3627	+	6.40621i	−0.977443	+	0.220773i
$843$		0			0
$844$	10.9101	−	15.8478i	0.375541	−	0.545504i
$845$	19.2957	+	11.1404i	0.663792	+	0.383241i
$846$		0			0
$847$	21.6437	−	12.4960i	0.743687	−	0.429368i
$848$	10.0424	−	18.0506i	0.344858	−	0.619860i
$849$		0			0
$850$	−2.85031	−	0.886264i	−0.0977650	−	0.0303986i
$851$	−24.5541	+	20.6034i	−0.841704	+	0.706274i
$852$		0			0
$853$	31.6292	−	11.5121i	1.08296	−	0.394167i	0.261954	−	0.965080i	$-0.415633\pi$
$853$	31.6292	−	11.5121i	1.08296	−	0.394167i	0.821010	+	0.570913i	$0.193411\pi$
$854$	17.6592	−	34.2547i	0.604286	−	1.17217i
$855$		0			0
$856$	−33.4192	−	13.3782i	−1.14224	−	0.457258i
$857$	−25.5052	−	4.49725i	−0.871239	−	0.153623i	−0.279884	−	0.960034i	$-0.590296\pi$
$857$	−25.5052	−	4.49725i	−0.871239	−	0.153623i	−0.591356	+	0.806411i	$0.701407\pi$
$858$		0			0
$859$	−9.04957	+	24.8635i	−0.308767	+	0.848331i	0.684130	+	0.729360i	$0.260182\pi$
$859$	−9.04957	+	24.8635i	−0.308767	+	0.848331i	−0.992898	+	0.118971i	$0.962040\pi$
$860$	2.90309	+	0.753205i	0.0989947	+	0.0256841i
$861$		0			0
$862$	15.6103	+	1.99206i	0.531689	+	0.0678499i
$863$	13.2516			0.451090			0.225545	−	0.974233i	$-0.427584\pi$
$863$	13.2516			0.451090			0.225545	+	0.974233i	$0.427584\pi$
$864$		0			0
$865$	5.94646			0.202186
$866$	−5.44883	−	0.695336i	−0.185159	−	0.0236285i
$867$		0			0
$868$	6.46428	+	1.67715i	0.219412	+	0.0569263i
$869$	−11.0620	+	30.3925i	−0.375252	+	1.03100i
$870$		0			0
$871$	1.31248	+	0.231425i	0.0444717	+	0.00784155i
$872$	8.26799	+	3.30980i	0.279989	+	0.112084i
$873$		0			0
$874$	3.34253	−	6.48372i	0.113063	−	0.219315i
$875$	−41.8901	+	15.2468i	−1.41614	+	0.515434i
$876$		0			0
$877$	−23.4391	+	19.6678i	−0.791483	+	0.664133i	−0.946112	−	0.323840i	$-0.895026\pi$
$877$	−23.4391	+	19.6678i	−0.791483	+	0.664133i	0.154629	+	0.987973i	$0.450582\pi$
$878$	18.2501	+	5.67461i	0.615912	+	0.191509i
$879$		0			0
$880$	−11.4546	+	20.5890i	−0.386136	+	0.694054i
$881$	18.5204	−	10.6927i	0.623967	−	0.360248i	−0.154445	−	0.988001i	$-0.549359\pi$
$881$	18.5204	−	10.6927i	0.623967	−	0.360248i	0.778412	+	0.627754i	$0.216026\pi$
$882$		0			0
$883$	0.600783	+	0.346862i	0.0202180	+	0.0116728i	0.510075	−	0.860130i	$-0.329618\pi$
$883$	0.600783	+	0.346862i	0.0202180	+	0.0116728i	−0.489857	+	0.871803i	$0.662951\pi$
$884$	4.18123	−	6.07359i	0.140630	−	0.204277i
$885$		0			0
$886$	−10.9665	+	2.47697i	−0.368426	+	0.0832155i
$887$	−4.88382	−	27.6975i	−0.163983	−	0.929992i	−0.950107	−	0.311924i	$-0.899027\pi$
$887$	−4.88382	−	27.6975i	−0.163983	−	0.929992i	0.786125	−	0.618068i	$-0.212084\pi$
$888$		0			0
$889$	−63.9368	−	53.6494i	−2.14437	−	1.79934i
$890$	−31.1175	+	19.9983i	−1.04306	+	0.670344i
$891$		0			0
$892$	−18.7890	−	8.58031i	−0.629101	−	0.287290i
$893$	−3.92285	+	4.67507i	−0.131273	+	0.156445i
$894$		0			0
$895$	−60.4720	+	10.6629i	−2.02136	+	0.356420i
$896$	25.6708	+	46.1332i	0.857602	+	1.54120i
$897$		0			0
$898$	−13.5605	+	5.68017i	−0.452519	+	0.189550i
$899$	2.33681	−	4.04748i	0.0779371	−	0.134991i
$900$		0			0
$901$	4.75188	+	8.23049i	0.158308	+	0.274197i
$902$	−18.8301	−	14.3303i	−0.626973	−	0.477147i
$903$		0			0
$904$	−4.47438	+	5.00134i	−0.148816	+	0.166342i
$905$	−34.6737	−	41.3225i	−1.15259	−	1.37361i
$906$		0			0
$907$	−5.84900	−	16.0700i	−0.194213	−	0.533596i	0.803916	−	0.594743i	$-0.202746\pi$
$907$	−5.84900	−	16.0700i	−0.194213	−	0.533596i	−0.998129	+	0.0611474i	$0.980524\pi$
$908$	−26.2831	+	2.51010i	−0.872234	+	0.0833007i
$909$		0			0
$910$	1.55984	+	32.7402i	0.0517081	+	1.08533i
$911$	7.12328	−	40.3981i	0.236005	−	1.33845i	−0.604482	−	0.796619i	$-0.706620\pi$
$911$	7.12328	−	40.3981i	0.236005	−	1.33845i	0.840487	−	0.541832i	$-0.182269\pi$
$912$		0			0
$913$	6.47400	+	2.35634i	0.214258	+	0.0779836i
$914$	−35.8693	−	38.8335i	−1.18645	−	1.28450i
$915$		0			0
$916$	30.7546	−	14.6398i	1.01616	−	0.483711i
$917$			15.7829i			0.521196i
$918$		0			0
$919$		−	11.9455i		−	0.394044i	−0.980399	−	0.197022i	$-0.936873\pi$
$919$		−	11.9455i		−	0.394044i	0.980399	−	0.197022i	$-0.0631271\pi$
$920$	17.0255	+	10.5633i	0.561315	+	0.348260i
$921$		0			0
$922$	−13.9116	+	12.8497i	−0.458156	+	0.423184i
$923$	3.51489	+	1.27932i	0.115694	+	0.0421092i
$924$		0			0
$925$	−2.23412	+	12.6703i	−0.0734575	+	0.416598i
$926$	−20.4673	+	0.975123i	−0.672598	+	0.0320445i
$927$		0			0
$928$	35.9050	−	8.71180i	1.17864	−	0.285979i
$929$	−18.9806	−	52.1487i	−0.622733	−	1.71094i	−0.700197	−	0.713950i	$-0.746905\pi$
$929$	−18.9806	−	52.1487i	−0.622733	−	1.71094i	0.0774640	−	0.996995i	$-0.475318\pi$
$930$		0			0
$931$	−17.1456	−	20.4333i	−0.561924	−	0.669675i
$932$	−35.3371	+	9.77020i	−1.15751	+	0.320034i
$933$		0			0
$934$	−32.7113	+	42.9828i	−1.07035	+	1.40644i
$935$	−5.42011	−	9.38791i	−0.177257	−	0.307017i
$936$		0			0
$937$	18.9064	−	32.7469i	0.617646	−	1.06979i	−0.372269	−	0.928125i	$-0.621420\pi$
$937$	18.9064	−	32.7469i	0.617646	−	1.06979i	0.989914	−	0.141669i	$-0.0452467\pi$
$938$	−1.69619	−	4.04939i	−0.0553827	−	0.132217i
$939$		0			0
$940$	−11.9470	−	11.7586i	−0.389668	−	0.383523i
$941$	−0.275896	+	0.0486479i	−0.00899395	+	0.00158588i	−0.178143	−	0.984005i	$-0.557009\pi$
$941$	−0.275896	+	0.0486479i	−0.00899395	+	0.00158588i	0.169149	+	0.985590i	$0.445898\pi$
$942$		0			0
$943$	−12.9348	+	15.4151i	−0.421214	+	0.501984i
$944$	21.4432	+	24.7454i	0.697917	+	0.805393i
$945$		0			0
$946$	1.09871	+	1.70960i	0.0357222	+	0.0555840i
$947$	−2.57807	−	2.16325i	−0.0837759	−	0.0702963i	0.599938	−	0.800047i	$-0.295192\pi$
$947$	−2.57807	−	2.16325i	−0.0837759	−	0.0702963i	−0.683714	+	0.729750i	$0.739636\pi$
$948$		0			0
$949$	0.361316	+	2.04913i	0.0117288	+	0.0665175i
$950$	−0.645084	−	2.85603i	−0.0209293	−	0.0926619i
$951$		0			0
$952$	−24.2783	−	0.770175i	−0.786863	−	0.0249615i
$953$	43.7288	+	25.2468i	1.41651	+	0.817825i	0.995991	−	0.0894568i	$-0.0285131\pi$
$953$	43.7288	+	25.2468i	1.41651	+	0.817825i	0.420523	+	0.907282i	$0.361846\pi$
$954$		0			0
$955$	−20.2229	+	11.6757i	−0.654397	+	0.377816i
$956$	−3.29025	+	41.3941i	−0.106414	+	1.33878i
$957$		0			0
$958$	−12.6114	+	40.5595i	−0.407455	+	1.31042i
$959$	23.2813	−	19.5353i	0.751791	−	0.630828i
$960$		0			0
$961$	−28.6493	+	10.4275i	−0.924171	+	0.336371i
$962$	−28.2495	−	14.5634i	−0.910801	−	0.469543i
$963$		0			0
$964$	16.3725	+	22.9913i	0.527324	+	0.740501i
$965$	−13.5444	−	2.38824i	−0.436008	−	0.0768800i
$966$		0			0
$967$	−9.74534	+	26.7751i	−0.313389	+	0.861029i	0.678578	+	0.734529i	$0.262597\pi$
$967$	−9.74534	+	26.7751i	−0.313389	+	0.861029i	−0.991967	+	0.126500i	$0.959625\pi$
$968$	14.3918	−	4.72706i	0.462570	−	0.151933i
$969$		0			0
$970$	6.90160	−	54.0827i	0.221597	−	1.73649i
$971$	−47.1658			−1.51362			−0.756811	−	0.653633i	$-0.773244\pi$
$971$	−47.1658			−1.51362			−0.756811	+	0.653633i	$0.773244\pi$
$972$		0			0
$973$	17.8829			0.573300
$974$	2.67587	−	20.9688i	0.0857403	−	0.671883i
$975$		0			0
$976$	14.7287	−	18.1306i	0.471454	−	0.580345i
$977$	9.95994	−	27.3647i	0.318647	−	0.875475i	−0.672186	−	0.740382i	$-0.734645\pi$
$977$	9.95994	−	27.3647i	0.318647	−	0.875475i	0.990833	−	0.135093i	$-0.0431332\pi$
$978$		0			0
$979$	−24.6828	−	4.35224i	−0.788864	−	0.139098i
$980$	59.6798	−	42.4990i	1.90640	−	1.35758i
$981$		0			0
$982$	9.93723	+	5.12291i	0.317110	+	0.163479i
$983$	17.1941	−	6.25816i	0.548408	−	0.199604i	−0.0529309	−	0.998598i	$-0.516856\pi$
$983$	17.1941	−	6.25816i	0.548408	−	0.199604i	0.601339	+	0.798994i	$0.294634\pi$
$984$		0			0
$985$	29.7039	−	24.9245i	0.946444	−	0.794161i
$986$	−5.04724	+	16.2324i	−0.160737	+	0.516946i
$987$		0			0
$988$	7.21027	+	0.573114i	0.229389	+	0.0182332i
$989$	1.49667	−	0.864102i	0.0475913	−	0.0274768i
$990$		0			0
$991$	−13.9725	−	8.06700i	−0.443850	−	0.256257i	0.261379	−	0.965236i	$-0.415823\pi$
$991$	−13.9725	−	8.06700i	−0.443850	−	0.256257i	−0.705229	+	0.708979i	$0.749156\pi$
$992$	3.62693	+	1.79740i	0.115155	+	0.0570675i
$993$		0			0
$994$	−2.71473	−	12.0191i	−0.0861061	−	0.381224i
$995$	6.94032	+	39.3605i	0.220023	+	1.24781i
$996$		0			0
$997$	5.43694	+	4.56213i	0.172190	+	0.144484i	0.724810	−	0.688949i	$-0.241928\pi$
$997$	5.43694	+	4.56213i	0.172190	+	0.144484i	−0.552620	+	0.833433i	$0.686372\pi$
$998$	16.8452	+	26.2112i	0.533225	+	0.829701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.1		96
3.2	odd	2		108.2.l.a.11.16	yes	96
4.3	odd	2	inner	324.2.l.a.35.10		96
9.2	odd	6		972.2.l.d.755.6		96
9.4	even	3		972.2.l.b.431.12		96
9.5	odd	6		972.2.l.c.431.5		96
9.7	even	3		972.2.l.a.755.11		96
12.11	even	2		108.2.l.a.11.7	✓	96
27.4	even	9		972.2.l.d.215.5		96
27.5	odd	18	inner	324.2.l.a.287.10		96
27.13	even	9		972.2.l.c.539.16		96
27.14	odd	18		972.2.l.b.539.1		96
27.22	even	9		108.2.l.a.59.7	yes	96
27.23	odd	18		972.2.l.a.215.12		96
36.7	odd	6		972.2.l.a.755.12		96
36.11	even	6		972.2.l.d.755.5		96
36.23	even	6		972.2.l.c.431.16		96
36.31	odd	6		972.2.l.b.431.1		96
108.23	even	18		972.2.l.a.215.11		96
108.31	odd	18		972.2.l.d.215.6		96
108.59	even	18	inner	324.2.l.a.287.1		96
108.67	odd	18		972.2.l.c.539.5		96
108.95	even	18		972.2.l.b.539.12		96
108.103	odd	18		108.2.l.a.59.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.7	✓	96	12.11	even	2
108.2.l.a.11.16	yes	96	3.2	odd	2
108.2.l.a.59.7	yes	96	27.22	even	9
108.2.l.a.59.16	yes	96	108.103	odd	18
324.2.l.a.35.1		96	1.1	even	1	trivial
324.2.l.a.35.10		96	4.3	odd	2	inner
324.2.l.a.287.1		96	108.59	even	18	inner
324.2.l.a.287.10		96	27.5	odd	18	inner
972.2.l.a.215.11		96	108.23	even	18
972.2.l.a.215.12		96	27.23	odd	18
972.2.l.a.755.11		96	9.7	even	3
972.2.l.a.755.12		96	36.7	odd	6
972.2.l.b.431.1		96	36.31	odd	6
972.2.l.b.431.12		96	9.4	even	3
972.2.l.b.539.1		96	27.14	odd	18
972.2.l.b.539.12		96	108.95	even	18
972.2.l.c.431.5		96	9.5	odd	6
972.2.l.c.431.16		96	36.23	even	6
972.2.l.c.539.5		96	108.67	odd	18
972.2.l.c.539.16		96	27.13	even	9
972.2.l.d.215.5		96	27.4	even	9
972.2.l.d.215.6		96	108.31	odd	18
972.2.l.d.755.5		96	36.11	even	6
972.2.l.d.755.6		96	9.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40284 - 0.179019i) q^{2} +(1.93590 + 0.502269i) q^{4} +(0.847966 - 2.32977i) q^{5} +(-4.59553 - 0.810316i) q^{7} +(-2.62584 - 1.05116i) q^{8} +O(q^{10})\)	\(q+(-1.40284 - 0.179019i) q^{2} +(1.93590 + 0.502269i) q^{4} +(0.847966 - 2.32977i) q^{5} +(-4.59553 - 0.810316i) q^{7} +(-2.62584 - 1.05116i) q^{8} +(-1.60663 + 3.11648i) q^{10} +(-2.23250 + 0.812562i) q^{11} +(-1.53462 + 1.28770i) q^{13} +(6.30172 + 1.95943i) q^{14} +(3.49545 + 1.94469i) q^{16} +(-1.59381 + 0.920188i) q^{17} +(-1.56341 - 0.902634i) q^{19} +(2.81175 - 4.08430i) q^{20} +(3.27729 - 0.740233i) q^{22} +(-0.496152 - 2.81382i) q^{23} +(-0.878547 - 0.737189i) q^{25} +(2.38335 - 1.53171i) q^{26} +(-8.48951 - 3.87689i) q^{28} +(-4.19826 + 5.00329i) q^{29} +(-0.704699 + 0.124257i) q^{31} +(-4.55541 - 3.35383i) q^{32} +(2.40059 - 1.00555i) q^{34} +(-5.78470 + 10.0194i) q^{35} +(-5.60913 - 9.71530i) q^{37} +(2.03162 + 1.54613i) q^{38} +(-4.67560 + 5.22625i) q^{40} +(-4.52704 - 5.39511i) q^{41} +(0.206872 + 0.568377i) q^{43} +(-4.73002 + 0.451729i) q^{44} +(0.192294 + 4.03615i) q^{46} +(0.587034 - 3.32923i) q^{47} +(13.8845 + 5.05353i) q^{49} +(1.10049 + 1.19143i) q^{50} +(-3.61765 + 1.72207i) q^{52} -5.16402i q^{53} +5.89022i q^{55} +(11.2154 + 6.95843i) q^{56} +(6.78516 - 6.26723i) q^{58} +(7.69223 + 2.79974i) q^{59} +(1.01407 - 5.75108i) q^{61} +(1.01082 - 0.0481585i) q^{62} +(5.79011 + 5.52039i) q^{64} +(1.69874 + 4.66724i) q^{65} +(-0.427623 - 0.509621i) q^{67} +(-3.54765 + 0.980874i) q^{68} +(9.90866 - 13.0200i) q^{70} +(-0.933575 - 1.61700i) q^{71} +(0.519326 - 0.899498i) q^{73} +(6.12948 + 14.6331i) q^{74} +(-2.57324 - 2.53266i) q^{76} +(10.9179 - 1.92513i) q^{77} +(8.75072 - 10.4287i) q^{79} +(7.49470 - 6.49456i) q^{80} +(5.38487 + 8.37889i) q^{82} +(-2.22145 - 1.86402i) q^{83} +(0.792326 + 4.49350i) q^{85} +(-0.188458 - 0.834374i) q^{86} +(6.71632 + 0.213061i) q^{88} +(9.13625 + 5.27482i) q^{89} +(8.09585 - 4.67414i) q^{91} +(0.452790 - 5.69649i) q^{92} +(-1.41951 + 4.56528i) q^{94} +(-3.42864 + 2.87697i) q^{95} +(-14.6120 + 5.31834i) q^{97} +(-18.5730 - 9.57486i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more