LMFDB - Embedded newform 297.2.n.b.280.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			280.1
Character	$\chi$	$=$	297.280
Dual form			297.2.n.b.262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55841 + 1.73079i) q^{2} +(-0.357932 - 3.40549i) q^{4} +(0.212128 + 0.235592i) q^{5} +(-1.29586 - 0.576953i) q^{7} +(2.68358 + 1.94973i) q^{8} -0.738340 q^{10} +(-2.21923 - 2.46476i) q^{11} +(-4.10532 - 0.872613i) q^{13} +(3.01805 - 1.34372i) q^{14} +(-0.857827 + 0.182337i) q^{16} +(1.92957 - 5.93860i) q^{17} +(-2.50622 - 1.82087i) q^{19} +(0.726379 - 0.806725i) q^{20} +(7.72443 + 7.98214e-5i) q^{22} +(-2.26025 + 3.91487i) q^{23} +(0.512137 - 4.87266i) q^{25} +(7.90807 - 5.74555i) q^{26} +(-1.50098 + 4.61954i) q^{28} +(-2.67527 - 1.19111i) q^{29} +(9.33325 + 1.98384i) q^{31} +(-2.29583 + 3.97649i) q^{32} +(7.27140 + 12.5944i) q^{34} +(-0.138962 - 0.427681i) q^{35} +(-0.685637 + 0.498145i) q^{37} +(7.05725 - 1.50006i) q^{38} +(0.109920 + 1.04582i) q^{40} +(3.53506 - 1.57391i) q^{41} +(-1.77651 - 3.07700i) q^{43} +(-7.59937 + 8.43978i) q^{44} +(-3.25341 - 10.0130i) q^{46} +(-0.778841 + 7.41018i) q^{47} +(-3.33754 - 3.70672i) q^{49} +(7.63541 + 8.47998i) q^{50} +(-1.50225 + 14.2930i) q^{52} +(-2.06517 - 6.35595i) q^{53} +(0.109916 - 1.04568i) q^{55} +(-2.35263 - 4.07487i) q^{56} +(6.23070 - 2.77409i) q^{58} +(-1.26216 - 12.0086i) q^{59} +(-4.51935 + 0.960618i) q^{61} +(-17.9786 + 13.0622i) q^{62} +(-3.84663 - 11.8387i) q^{64} +(-0.665272 - 1.15229i) q^{65} +(-4.98385 + 8.63229i) q^{67} +(-20.9145 - 4.44552i) q^{68} +(0.956783 + 0.425987i) q^{70} +(-0.905630 + 2.78724i) q^{71} +(-3.43158 + 2.49319i) q^{73} +(0.206320 - 1.96300i) q^{74} +(-5.30392 + 9.18665i) q^{76} +(1.45376 + 4.47436i) q^{77} +(-2.26299 + 2.51331i) q^{79} +(-0.224926 - 0.163418i) q^{80} +(-2.78496 + 8.57123i) q^{82} +(-13.1927 + 2.80420i) q^{83} +(1.80840 - 0.805152i) q^{85} +(8.09416 + 1.72047i) q^{86} +(-1.14986 - 10.9413i) q^{88} -2.69745 q^{89} +(4.81645 + 3.49936i) q^{91} +(14.1411 + 6.29601i) q^{92} +(-11.6117 - 12.8961i) q^{94} +(-0.102656 - 0.976702i) q^{95} +(-3.51792 + 3.90704i) q^{97} +11.6168 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.55841	+	1.73079i	−1.10196	+	1.22385i	−0.129303	+	0.991605i	$0.541274\pi$
$2$	−1.55841	+	1.73079i	−1.10196	+	1.22385i	−0.972657	+	0.232245i	$0.925393\pi$
$3$		0			0
$3$		0			0
$4$	−0.357932	−	3.40549i	−0.178966	−	1.70275i
$5$	0.212128	+	0.235592i	0.0948664	+	0.105360i	0.788708	−	0.614767i	$-0.210750\pi$
$5$	0.212128	+	0.235592i	0.0948664	+	0.105360i	−0.693842	+	0.720127i	$0.744083\pi$
$6$		0			0
$7$	−1.29586	−	0.576953i	−0.489788	−	0.218068i	0.146956	−	0.989143i	$-0.453052\pi$
$7$	−1.29586	−	0.576953i	−0.489788	−	0.218068i	−0.636744	+	0.771075i	$0.719719\pi$
$8$	2.68358	+	1.94973i	0.948787	+	0.689334i
$9$		0			0
$10$	−0.738340			−0.233484
$11$	−2.21923	−	2.46476i	−0.669123	−	0.743152i
$11$	−2.21923	−	2.46476i	−0.669123	−	0.743152i
$12$		0			0
$13$	−4.10532	−	0.872613i	−1.13861	−	0.242019i	−0.400238	−	0.916411i	$-0.631072\pi$
$13$	−4.10532	−	0.872613i	−1.13861	−	0.242019i	−0.738373	+	0.674392i	$0.764406\pi$
$14$	3.01805	−	1.34372i	0.806609	−	0.359125i
$15$		0			0
$16$	−0.857827	+	0.182337i	−0.214457	+	0.0455842i
$17$	1.92957	−	5.93860i	0.467989	−	1.44032i	−0.387195	−	0.921998i	$-0.626556\pi$
$17$	1.92957	−	5.93860i	0.467989	−	1.44032i	0.855184	−	0.518325i	$-0.173444\pi$
$18$		0			0
$19$	−2.50622	−	1.82087i	−0.574966	−	0.417737i	0.261940	−	0.965084i	$-0.415638\pi$
$19$	−2.50622	−	1.82087i	−0.574966	−	0.417737i	−0.836906	+	0.547347i	$0.815638\pi$
$20$	0.726379	−	0.806725i	0.162423	−	0.180389i
$21$		0			0
$22$	7.72443		7.98214e-5i	1.64685		1.70180e-5i
$23$	−2.26025	+	3.91487i	−0.471295	+	0.816306i	−0.999461	−	0.0328349i	$-0.989546\pi$
$23$	−2.26025	+	3.91487i	−0.471295	+	0.816306i	0.528166	+	0.849141i	$0.322880\pi$
$24$		0			0
$25$	0.512137	−	4.87266i	0.102427	−	0.974532i
$26$	7.90807	−	5.74555i	1.55090	−	1.12679i
$27$		0			0
$28$	−1.50098	+	4.61954i	−0.283659	+	0.873011i
$29$	−2.67527	−	1.19111i	−0.496785	−	0.221183i	0.143021	−	0.989720i	$-0.454318\pi$
$29$	−2.67527	−	1.19111i	−0.496785	−	0.221183i	−0.639805	+	0.768537i	$0.720985\pi$
$30$		0			0
$31$	9.33325	+	1.98384i	1.67630	+	0.356309i	0.945334	−	0.326103i	$-0.105736\pi$
$31$	9.33325	+	1.98384i	1.67630	+	0.356309i	0.730967	+	0.682412i	$0.239069\pi$
$32$	−2.29583	+	3.97649i	−0.405848	+	0.702950i
$33$		0			0
$34$	7.27140	+	12.5944i	1.24703	+	2.15993i
$35$	−0.138962	−	0.427681i	−0.0234889	−	0.0722913i
$36$		0			0
$37$	−0.685637	+	0.498145i	−0.112718	+	0.0818945i	−0.642716	−	0.766104i	$-0.722193\pi$
$37$	−0.685637	+	0.498145i	−0.112718	+	0.0818945i	0.529998	+	0.847999i	$0.322193\pi$
$38$	7.05725	−	1.50006i	1.14484	−	0.243343i
$39$		0			0
$40$	0.109920	+	1.04582i	0.0173799	+	0.165359i
$41$	3.53506	−	1.57391i	0.552084	−	0.245804i	−0.111682	−	0.993744i	$-0.535624\pi$
$41$	3.53506	−	1.57391i	0.552084	−	0.245804i	0.663766	+	0.747940i	$0.268957\pi$
$42$		0			0
$43$	−1.77651	−	3.07700i	−0.270915	−	0.469239i	0.698181	−	0.715921i	$-0.253993\pi$
$43$	−1.77651	−	3.07700i	−0.270915	−	0.469239i	−0.969096	+	0.246682i	$0.920660\pi$
$44$	−7.59937	+	8.43978i	−1.14565	+	1.27235i
$45$		0			0
$46$	−3.25341	−	10.0130i	−0.479689	−	1.47633i
$47$	−0.778841	+	7.41018i	−0.113606	+	1.08089i	0.778059	+	0.628191i	$0.216204\pi$
$47$	−0.778841	+	7.41018i	−0.113606	+	1.08089i	−0.891665	+	0.452695i	$0.850462\pi$
$48$		0			0
$49$	−3.33754	−	3.70672i	−0.476792	−	0.529531i
$50$	7.63541	+	8.47998i	1.07981	+	1.19925i
$51$		0			0
$52$	−1.50225	+	14.2930i	−0.208325	+	1.98208i
$53$	−2.06517	−	6.35595i	−0.283673	−	0.873057i	−0.986793	−	0.161986i	$-0.948210\pi$
$53$	−2.06517	−	6.35595i	−0.283673	−	0.873057i	0.703120	−	0.711071i	$-0.251790\pi$
$54$		0			0
$55$	0.109916	−	1.04568i	0.0148210	−	0.140999i
$56$	−2.35263	−	4.07487i	−0.314383	−	0.544528i
$57$		0			0
$58$	6.23070	−	2.77409i	0.818132	−	0.364256i
$59$	−1.26216	−	12.0086i	−0.164319	−	1.56339i	−0.696998	−	0.717073i	$-0.745482\pi$
$59$	−1.26216	−	12.0086i	−0.164319	−	1.56339i	0.532680	−	0.846317i	$-0.321185\pi$
$60$		0			0
$61$	−4.51935	+	0.960618i	−0.578644	+	0.122995i	−0.487931	−	0.872882i	$-0.662248\pi$
$61$	−4.51935	+	0.960618i	−0.578644	+	0.122995i	−0.0907135	+	0.995877i	$0.528915\pi$
$62$	−17.9786	+	13.0622i	−2.28329	+	1.65890i
$63$		0			0
$64$	−3.84663	−	11.8387i	−0.480828	−	1.47984i
$65$	−0.665272	−	1.15229i	−0.0825169	−	0.142923i
$66$		0			0
$67$	−4.98385	+	8.63229i	−0.608875	+	1.05460i	0.382552	+	0.923934i	$0.375045\pi$
$67$	−4.98385	+	8.63229i	−0.608875	+	1.05460i	−0.991426	+	0.130668i	$0.958288\pi$
$68$	−20.9145	−	4.44552i	−2.53626	−	0.539098i
$69$		0			0
$70$	0.956783	+	0.425987i	0.114357	+	0.0509152i
$71$	−0.905630	+	2.78724i	−0.107479	+	0.330785i	−0.990304	−	0.138916i	$-0.955638\pi$
$71$	−0.905630	+	2.78724i	−0.107479	+	0.330785i	0.882826	+	0.469701i	$0.155638\pi$
$72$		0			0
$73$	−3.43158	+	2.49319i	−0.401636	+	0.291806i	−0.770207	−	0.637794i	$-0.779847\pi$
$73$	−3.43158	+	2.49319i	−0.401636	+	0.291806i	0.368571	+	0.929600i	$0.379847\pi$
$74$	0.206320	−	1.96300i	0.0239842	−	0.228195i
$75$		0			0
$76$	−5.30392	+	9.18665i	−0.608401	+	1.05378i
$77$	1.45376	+	4.47436i	0.165671	+	0.509901i
$78$		0			0
$79$	−2.26299	+	2.51331i	−0.254606	+	0.282769i	−0.856875	−	0.515525i	$-0.827597\pi$
$79$	−2.26299	+	2.51331i	−0.254606	+	0.282769i	0.602268	+	0.798294i	$0.294264\pi$
$80$	−0.224926	−	0.163418i	−0.0251475	−	0.0182707i
$81$		0			0
$82$	−2.78496	+	8.57123i	−0.307548	+	0.946534i
$83$	−13.1927	+	2.80420i	−1.44809	+	0.307801i	−0.863838	−	0.503770i	$-0.831946\pi$
$83$	−13.1927	+	2.80420i	−1.44809	+	0.307801i	−0.584253	+	0.811571i	$0.698613\pi$
$84$		0			0
$85$	1.80840	−	0.805152i	0.196149	−	0.0873310i
$86$	8.09416	+	1.72047i	0.872815	+	0.185523i
$87$		0			0
$88$	−1.14986	−	10.9413i	−0.122575	−	1.16634i
$89$	−2.69745			−0.285929			−0.142965	−	0.989728i	$-0.545664\pi$
$89$	−2.69745			−0.285929			−0.142965	+	0.989728i	$0.545664\pi$
$90$		0			0
$91$	4.81645	+	3.49936i	0.504902	+	0.366833i
$92$	14.1411	+	6.29601i	1.47431	+	0.656404i
$93$		0			0
$94$	−11.6117	−	12.8961i	−1.19765	−	1.33013i
$95$	−0.102656	−	0.976702i	−0.0105322	−	0.100208i
$96$		0			0
$97$	−3.51792	+	3.90704i	−0.357190	+	0.396700i	−0.894781	−	0.446506i	$-0.852668\pi$
$97$	−3.51792	+	3.90704i	−0.357190	+	0.396700i	0.537590	+	0.843206i	$0.319335\pi$
$98$	11.6168			1.17347
$99$		0			0
$100$	−16.7771			−1.67771
$101$	6.37664	−	7.08198i	0.634500	−	0.704683i	−0.337059	−	0.941484i	$-0.609432\pi$
$101$	6.37664	−	7.08198i	0.634500	−	0.704683i	0.971558	+	0.236800i	$0.0760987\pi$
$102$		0			0
$103$	−0.996745	−	9.48339i	−0.0982122	−	0.934426i	−0.927050	−	0.374938i	$-0.877664\pi$
$103$	−0.996745	−	9.48339i	−0.0982122	−	0.934426i	0.828838	−	0.559489i	$-0.189003\pi$
$104$	−9.31558	−	10.3460i	−0.913468	−	1.01451i
$105$		0			0
$106$	14.2192	+	6.33078i	1.38109	+	0.614900i
$107$	4.18472	+	3.04038i	0.404552	+	0.293924i	0.771393	−	0.636359i	$-0.219560\pi$
$107$	4.18472	+	3.04038i	0.404552	+	0.293924i	−0.366840	+	0.930284i	$0.619560\pi$
$108$		0			0
$109$	14.4767			1.38661			0.693307	−	0.720643i	$-0.256153\pi$
$109$	14.4767			1.38661			0.693307	+	0.720643i	$0.256153\pi$
$110$	1.63855	+	1.81983i	0.156229	+	0.173514i
$111$		0			0
$112$	1.21682	+	0.258643i	0.114979	+	0.0244395i
$113$	6.78911	−	3.02271i	0.638666	−	0.284352i	−0.0617453	−	0.998092i	$-0.519667\pi$
$113$	6.78911	−	3.02271i	0.638666	−	0.284352i	0.700411	+	0.713740i	$0.253000\pi$
$114$		0			0
$115$	−1.40177	+	0.297956i	−0.130716	+	0.0277845i
$116$	−3.09874	+	9.53694i	−0.287711	+	0.885482i
$117$		0			0
$118$	22.7513	+	16.5298i	2.09443	+	1.52169i
$119$	−5.92674	+	6.58231i	−0.543303	+	0.603400i
$120$		0			0
$121$	−1.15004	+	10.9397i	−0.104549	+	0.994520i
$122$	5.38037	−	9.31907i	0.487116	−	0.843709i
$123$		0			0
$124$	3.41530	−	32.4944i	0.306703	−	2.91808i
$125$	2.53897	−	1.84467i	0.227092	−	0.164992i
$126$		0			0
$127$	−4.08040	+	12.5582i	−0.362077	+	1.11436i	0.589715	+	0.807612i	$0.299240\pi$
$127$	−4.08040	+	12.5582i	−0.362077	+	1.11436i	−0.951791	+	0.306746i	$0.900760\pi$
$128$	18.0955	+	8.05664i	1.59943	+	0.712113i
$129$		0			0
$130$	3.03112	+	0.644285i	0.265847	+	0.0565075i
$131$	−3.65021	+	6.32236i	−0.318921	+	0.552387i	−0.980263	−	0.197697i	$-0.936654\pi$
$131$	−3.65021	+	6.32236i	−0.318921	+	0.552387i	0.661342	+	0.750084i	$0.269987\pi$
$132$		0			0
$133$	2.19714	+	3.80556i	0.190516	+	0.329984i
$134$	−7.17377	−	22.0786i	−0.619719	−	1.90730i
$135$		0			0
$136$	16.7568	−	12.1746i	1.43689	−	1.04396i
$137$	9.59302	−	2.03906i	0.819587	−	0.174209i	0.221008	−	0.975272i	$-0.429065\pi$
$137$	9.59302	−	2.03906i	0.819587	−	0.174209i	0.598579	+	0.801064i	$0.295732\pi$
$138$		0			0
$139$	0.990605	+	9.42498i	0.0840220	+	0.799416i	0.952674	+	0.303994i	$0.0983202\pi$
$139$	0.990605	+	9.42498i	0.0840220	+	0.799416i	−0.868652	+	0.495423i	$0.835013\pi$
$140$	−1.40673	+	0.626314i	−0.118890	+	0.0529332i
$141$		0			0
$142$	−3.41278	−	5.91111i	−0.286394	−	0.496049i
$143$	6.95987	+	12.0551i	0.582014	+	1.00810i
$144$		0			0
$145$	−0.286884	−	0.882938i	−0.0238244	−	0.0733240i
$146$	1.03262	−	9.82474i	0.0854604	−	0.813101i
$147$		0			0
$148$	1.94184	+	2.15663i	0.159618	+	0.177274i
$149$	2.76180	+	3.06729i	0.226256	+	0.251282i	0.845575	−	0.533857i	$-0.179258\pi$
$149$	2.76180	+	3.06729i	0.226256	+	0.251282i	−0.619319	+	0.785139i	$0.712591\pi$
$150$		0			0
$151$	1.85802	−	17.6779i	0.151204	−	1.43861i	−0.611186	−	0.791487i	$-0.709307\pi$
$151$	1.85802	−	17.6779i	0.151204	−	1.43861i	0.762389	−	0.647119i	$-0.224026\pi$
$152$	−3.17541	−	9.77291i	−0.257560	−	0.792688i
$153$		0			0
$154$	−10.0097	−	4.45673i	−0.806605	−	0.359134i
$155$	1.51246	+	2.61967i	0.121484	+	0.210417i
$156$		0			0
$157$	−1.84286	+	0.820493i	−0.147076	+	0.0654825i	−0.478955	−	0.877840i	$-0.658984\pi$
$157$	−1.84286	+	0.820493i	−0.147076	+	0.0654825i	0.331879	+	0.943322i	$0.392318\pi$
$158$	−0.823335	−	7.83351i	−0.0655010	−	0.623200i
$159$		0			0
$160$	−1.42384	+	0.302646i	−0.112564	+	0.0239262i
$161$	5.18765	−	3.76905i	0.408844	−	0.297043i
$162$		0			0
$163$	−0.488377	−	1.50307i	−0.0382526	−	0.117729i	0.930107	−	0.367289i	$-0.119714\pi$
$163$	−0.488377	−	1.50307i	−0.0382526	−	0.117729i	−0.968359	+	0.249560i	$0.919714\pi$
$164$	−6.62526	−	11.4753i	−0.517346	−	0.896069i
$165$		0			0
$166$	15.7062	−	27.2039i	1.21904	−	2.11143i
$167$	14.9868	+	3.18555i	1.15971	+	0.246505i	0.747297	−	0.664490i	$-0.231351\pi$
$167$	14.9868	+	3.18555i	1.15971	+	0.246505i	0.412417	+	0.910995i	$0.364685\pi$
$168$		0			0
$169$	4.21612	+	1.87714i	0.324317	+	0.144395i
$170$	−1.42468	+	4.38471i	−0.109268	+	0.336292i
$171$		0			0
$172$	−9.84284	+	7.15124i	−0.750510	+	0.545277i
$173$	−0.103069	+	0.980638i	−0.00783620	+	0.0745565i	−0.997741	−	0.0671768i	$-0.978601\pi$
$173$	−0.103069	+	0.980638i	−0.00783620	+	0.0745565i	0.989905	+	0.141733i	$0.0452675\pi$
$174$		0			0
$175$	−3.47495	+	6.01879i	−0.262682	+	0.454978i
$176$	2.35313	+	1.70969i	0.177374	+	0.128872i
$177$		0			0
$178$	4.20373	−	4.66871i	0.315083	−	0.349935i
$179$	−9.08186	−	6.59836i	−0.678810	−	0.493185i	0.194153	−	0.980971i	$-0.437804\pi$
$179$	−9.08186	−	6.59836i	−0.678810	−	0.493185i	−0.872963	+	0.487787i	$0.837804\pi$
$180$		0			0
$181$	5.53932	−	17.0483i	0.411735	−	1.26719i	−0.503405	−	0.864051i	$-0.667919\pi$
$181$	5.53932	−	17.0483i	0.411735	−	1.26719i	0.915139	−	0.403138i	$-0.132081\pi$
$182$	−13.5626	+	2.88283i	−1.00533	+	0.213689i
$183$		0			0
$184$	−13.6985	+	6.09896i	−1.00987	+	0.449621i
$185$	−0.262801	−	0.0558602i	−0.0193216	−	0.00410692i
$186$		0			0
$187$	−18.9194	+	8.42321i	−1.38352	+	0.615966i
$188$	25.5141			1.86081
$189$		0			0
$190$	1.85044	+	1.34442i	0.134245	+	0.0975348i
$191$	−11.7737	−	5.24200i	−0.851917	−	0.379298i	−0.0661416	−	0.997810i	$-0.521069\pi$
$191$	−11.7737	−	5.24200i	−0.851917	−	0.379298i	−0.785775	+	0.618513i	$0.787736\pi$
$192$		0			0
$193$	−15.4911	−	17.2046i	−1.11507	−	1.23841i	−0.968447	−	0.249219i	$-0.919826\pi$
$193$	−15.4911	−	17.2046i	−1.11507	−	1.23841i	−0.146624	−	0.989192i	$-0.546841\pi$
$194$	−1.27991	−	12.1775i	−0.0918921	−	0.874295i
$195$		0			0
$196$	−11.4286	+	12.6927i	−0.816327	+	0.906623i
$197$	−1.07766			−0.0767801			−0.0383900	−	0.999263i	$-0.512223\pi$
$197$	−1.07766			−0.0767801			−0.0383900	+	0.999263i	$0.512223\pi$
$198$		0			0
$199$	16.4307			1.16474			0.582371	−	0.812923i	$-0.302125\pi$
$199$	16.4307			1.16474			0.582371	+	0.812923i	$0.302125\pi$
$200$	10.8747	−	12.0776i	0.768960	−	0.854017i
$201$		0			0
$202$	2.31999	+	22.0732i	0.163234	+	1.55307i
$203$	2.77955	+	3.08701i	0.195086	+	0.216665i
$204$		0			0
$205$	1.12069	+	0.498961i	0.0782721	+	0.0348490i
$206$	17.9671	+	13.0538i	1.25182	+	0.909503i
$207$		0			0
$208$	3.68076			0.255215
$209$	1.07386	+	10.2182i	0.0742807	+	0.706804i
$210$		0			0
$211$	14.6231	+	3.10824i	1.00670	+	0.213980i	0.681618	−	0.731708i	$-0.261276\pi$
$211$	14.6231	+	3.10824i	1.00670	+	0.213980i	0.325077	+	0.945688i	$0.394610\pi$
$212$	−20.9060	+	9.30793i	−1.43583	+	0.639271i
$213$		0			0
$214$	−11.7837	+	2.50471i	−0.805520	+	0.171219i
$215$	0.348070	−	1.07125i	0.0237382	−	0.0730585i
$216$		0			0
$217$	−10.9500	−	7.95563i	−0.743333	−	0.540063i
$218$	−22.5605	+	25.0560i	−1.52799	+	1.69701i
$219$		0			0
$220$	−3.60038		3.72050e-5i	−0.242738		2.50836e-6i
$221$	−13.1036	+	22.6961i	−0.881444	+	1.52671i
$222$		0			0
$223$	−0.201351	+	1.91573i	−0.0134835	+	0.128286i	−0.999193	−	0.0401676i	$-0.987211\pi$
$223$	−0.201351	+	1.91573i	−0.0134835	+	0.128286i	0.985710	+	0.168454i	$0.0538775\pi$
$224$	5.26931	−	3.82838i	0.352070	−	0.255794i
$225$		0			0
$226$	−5.34854	+	16.4611i	−0.355779	+	1.09498i
$227$	14.6269	+	6.51230i	0.970819	+	0.432236i	0.829978	−	0.557796i	$-0.188353\pi$
$227$	14.6269	+	6.51230i	0.970819	+	0.432236i	0.140841	+	0.990032i	$0.455020\pi$
$228$		0			0
$229$	0.511498	+	0.108722i	0.0338007	+	0.00718457i	0.224781	−	0.974409i	$-0.427833\pi$
$229$	0.511498	+	0.108722i	0.0338007	+	0.00718457i	−0.190980	+	0.981594i	$0.561167\pi$
$230$	1.66883	−	2.89050i	0.110040	−	0.190594i
$231$		0			0
$232$	−4.85695	−	8.41248i	−0.318874	−	0.552306i
$233$	3.16820	+	9.75073i	0.207556	+	0.638792i	0.999599	+	0.0283260i	$0.00901764\pi$
$233$	3.16820	+	9.75073i	0.207556	+	0.638792i	−0.792043	+	0.610466i	$0.790982\pi$
$234$		0			0
$235$	−1.91099	+	1.38842i	−0.124659	+	0.0905703i
$236$	−40.4435	+	8.59653i	−2.63265	+	0.559587i
$237$		0			0
$238$	−2.15630	−	20.5158i	−0.139772	−	1.32984i
$239$	8.80753	−	3.92137i	0.569712	−	0.253652i	−0.101602	−	0.994825i	$-0.532397\pi$
$239$	8.80753	−	3.92137i	0.569712	−	0.253652i	0.671314	+	0.741173i	$0.265730\pi$
$240$		0			0
$241$	0.139366	+	0.241388i	0.00897733	+	0.0155492i	0.870479	−	0.492205i	$-0.163809\pi$
$241$	0.139366	+	0.241388i	0.00897733	+	0.0155492i	−0.861502	+	0.507754i	$0.830476\pi$
$242$	−17.1421	−	19.0390i	−1.10193	−	1.22387i
$243$		0			0
$244$	4.88900	+	15.0468i	0.312986	+	0.963272i
$245$	0.165286	−	1.57259i	0.0105598	−	0.100469i
$246$		0			0
$247$	8.69991	+	9.66223i	0.553562	+	0.614793i
$248$	21.1785	+	23.5211i	1.34484	+	1.49359i
$249$		0			0
$250$	−0.764019	+	7.26916i	−0.0483208	+	0.459742i
$251$	−1.36753	−	4.20881i	−0.0863175	−	0.265658i	0.898576	−	0.438817i	$-0.144602\pi$
$251$	−1.36753	−	4.20881i	−0.0863175	−	0.265658i	−0.984894	+	0.173159i	$0.944602\pi$
$252$		0			0
$253$	14.6652	−	3.11703i	0.921993	−	0.195966i
$254$	−15.3766	−	26.6330i	−0.964813	−	1.67111i
$255$		0			0
$256$	−19.4009	+	8.63785i	−1.21256	+	0.539866i
$257$	0.382002	+	3.63450i	0.0238286	+	0.226714i	0.999955	+	0.00950980i	$0.00302711\pi$
$257$	0.382002	+	3.63450i	0.0238286	+	0.226714i	−0.976126	+	0.217204i	$0.930306\pi$
$258$		0			0
$259$	1.17589	−	0.249944i	0.0730665	−	0.0155308i
$260$	−3.68598	+	2.67802i	−0.228595	+	0.166084i
$261$		0			0
$262$	−5.25413	−	16.1705i	−0.324601	−	0.999019i
$263$	−7.22621	−	12.5162i	−0.445587	−	0.771780i	0.552506	−	0.833509i	$-0.313672\pi$
$263$	−7.22621	−	12.5162i	−0.445587	−	0.771780i	−0.998093	+	0.0617294i	$0.980338\pi$
$264$		0			0
$265$	1.05933	−	1.83481i	0.0650741	−	0.112712i
$266$	−10.0107	−	2.12783i	−0.613793	−	0.130466i
$267$		0			0
$268$	31.1811	+	13.8827i	1.90469	+	0.848021i
$269$	−0.283600	+	0.872830i	−0.0172914	+	0.0532174i	−0.959330	−	0.282287i	$-0.908907\pi$
$269$	−0.283600	+	0.872830i	−0.0172914	+	0.0532174i	0.942039	+	0.335505i	$0.108907\pi$
$270$		0			0
$271$	2.13921	−	1.55422i	0.129948	−	0.0944124i	−0.520913	−	0.853610i	$-0.674408\pi$
$271$	2.13921	−	1.55422i	0.129948	−	0.0944124i	0.650860	+	0.759197i	$0.274408\pi$
$272$	−0.572411	+	5.44612i	−0.0347075	+	0.330220i
$273$		0			0
$274$	−11.4206	+	19.7811i	−0.689947	+	1.19502i
$275$	−13.1465	+	9.55126i	−0.792761	+	0.575962i
$276$		0			0
$277$	19.3409	−	21.4802i	1.16208	−	1.29062i	0.212478	−	0.977166i	$-0.431847\pi$
$277$	19.3409	−	21.4802i	1.16208	−	1.29062i	0.949603	−	0.313456i	$-0.101487\pi$
$278$	−17.8564	−	12.9734i	−1.07095	−	0.778094i
$279$		0			0
$280$	0.460948	−	1.41865i	0.0275469	−	0.0847807i
$281$	8.55152	−	1.81768i	0.510141	−	0.108434i	0.0543523	−	0.998522i	$-0.482691\pi$
$281$	8.55152	−	1.81768i	0.510141	−	0.108434i	0.455789	+	0.890088i	$0.349357\pi$
$282$		0			0
$283$	−21.2100	+	9.44331i	−1.26081	+	0.561347i	−0.924778	−	0.380506i	$-0.875750\pi$
$283$	−21.2100	+	9.44331i	−1.26081	+	0.561347i	−0.336027	+	0.941852i	$0.609083\pi$
$284$	9.81609	+	2.08647i	0.582478	+	0.123809i
$285$		0			0
$286$	−31.7112	−	6.74076i	−1.87512	−	0.398590i
$287$	−5.48901			−0.324006
$288$		0			0
$289$	−17.7905	−	12.9255i	−1.04650	−	0.760326i
$290$	1.97526	+	0.879441i	0.115991	+	0.0516426i
$291$		0			0
$292$	9.71881	+	10.7938i	0.568751	+	0.631662i
$293$	−2.19253	−	20.8605i	−0.128089	−	1.21868i	−0.850032	−	0.526731i	$-0.823418\pi$
$293$	−2.19253	−	20.8605i	−0.128089	−	1.21868i	0.721944	−	0.691952i	$-0.243249\pi$
$294$		0			0
$295$	2.56139	−	2.84472i	0.149130	−	0.165626i
$296$	−2.81121			−0.163398
$297$		0			0
$298$	−9.61284			−0.556857
$299$	12.6952	−	14.0995i	0.734183	−	0.815393i
$300$		0			0
$301$	0.526816	+	5.01232i	0.0303652	+	0.288905i
$302$	27.7011	+	30.7652i	1.59402	+	1.77034i
$303$		0			0
$304$	2.48191	+	1.10502i	0.142347	+	0.0633772i
$305$	−1.18499	−	0.860949i	−0.0678526	−	0.0492978i
$306$		0			0
$307$	23.1324			1.32024			0.660118	−	0.751162i	$-0.270506\pi$
$307$	23.1324			1.32024			0.660118	+	0.751162i	$0.270506\pi$
$308$	14.7171	−	6.55228i	0.838582	−	0.373351i
$309$		0			0
$310$	−6.89111	−	1.46475i	−0.391389	−	0.0831923i
$311$	−18.6499	+	8.30346i	−1.05754	+	0.470846i	−0.860447	−	0.509540i	$-0.829816\pi$
$311$	−18.6499	+	8.30346i	−1.05754	+	0.470846i	−0.197090	+	0.980385i	$0.563149\pi$
$312$		0			0
$313$	33.2955	−	7.07718i	1.88197	−	0.400026i	0.884222	−	0.467066i	$-0.154689\pi$
$313$	33.2955	−	7.07718i	1.88197	−	0.400026i	0.997750	+	0.0670406i	$0.0213557\pi$
$314$	1.45182	−	4.46825i	0.0819311	−	0.252158i
$315$		0			0
$316$	9.36904	+	6.80701i	0.527050	+	0.382924i
$317$	18.3478	−	20.3773i	1.03052	−	1.14451i	0.0411371	−	0.999154i	$-0.486902\pi$
$317$	18.3478	−	20.3773i	1.03052	−	1.14451i	0.989380	−	0.145352i	$-0.0464314\pi$
$318$		0			0
$319$	3.00125	+	9.23722i	0.168038	+	0.517185i
$320$	1.97312	−	3.41755i	0.110301	−	0.191047i
$321$		0			0
$322$	−1.56105	+	14.8524i	−0.0869941	+	0.827694i
$323$	−15.6494	+	11.3699i	−0.870754	+	0.632640i
$324$		0			0
$325$	−6.35443	+	19.5569i	−0.352480	+	1.08482i
$326$	3.36258	+	1.49712i	0.186236	+	0.0829176i
$327$		0			0
$328$	12.5553	+	2.66872i	0.693252	+	0.147355i
$329$	5.28459	−	9.15318i	0.291349	−	0.504631i
$330$		0			0
$331$	8.98622	+	15.5646i	0.493927	+	0.855507i	0.999976	−	0.00699827i	$-0.00222764\pi$
$331$	8.98622	+	15.5646i	0.493927	+	0.855507i	−0.506048	+	0.862505i	$0.668894\pi$
$332$	14.2718	+	43.9241i	0.783266	+	2.41065i
$333$		0			0
$334$	−28.8690	+	20.9746i	−1.57964	+	1.14768i
$335$	−3.09091	+	0.656993i	−0.168874	+	0.0358954i
$336$		0			0
$337$	−1.14690	−	10.9120i	−0.0624757	−	0.594417i	−0.980312	−	0.197457i	$-0.936732\pi$
$337$	−1.14690	−	10.9120i	−0.0624757	−	0.594417i	0.917836	−	0.396960i	$-0.129935\pi$
$338$	−9.81935	+	4.37186i	−0.534102	+	0.237798i
$339$		0			0
$340$	−3.38922	−	5.87031i	−0.183806	−	0.318362i
$341$	−15.8229	−	27.4068i	−0.856860	−	1.48416i
$342$		0			0
$343$	5.25475	+	16.1724i	0.283730	+	0.873230i
$344$	1.23194	−	11.7211i	0.0664215	−	0.631959i
$345$		0			0
$346$	−1.53665	−	1.70662i	−0.0826108	−	0.0917486i
$347$	−14.7870	−	16.4226i	−0.793807	−	0.881612i	0.201389	−	0.979511i	$-0.435454\pi$
$347$	−14.7870	−	16.4226i	−0.793807	−	0.881612i	−0.995196	+	0.0978989i	$0.968788\pi$
$348$		0			0
$349$	1.92371	−	18.3029i	0.102974	−	0.979732i	−0.814022	−	0.580835i	$-0.802726\pi$
$349$	1.92371	−	18.3029i	0.102974	−	0.979732i	0.916996	−	0.398897i	$-0.130607\pi$
$350$	−5.00185	−	15.3941i	−0.267360	−	0.822850i
$351$		0			0
$352$	14.8960	−	3.16609i	0.793961	−	0.168753i
$353$	16.5354	+	28.6401i	0.880089	+	1.52436i	0.851241	+	0.524776i	$0.175851\pi$
$353$	16.5354	+	28.6401i	0.880089	+	1.52436i	0.0288486	+	0.999584i	$0.490816\pi$
$354$		0			0
$355$	−0.848761	+	0.377893i	−0.0450475	+	0.0200565i
$356$	0.965504	+	9.18616i	0.0511716	+	0.486865i
$357$		0			0
$358$	25.5736	−	5.43583i	1.35161	−	0.287293i
$359$	2.42595	−	1.76256i	0.128037	−	0.0930242i	−0.521924	−	0.852992i	$-0.674785\pi$
$359$	2.42595	−	1.76256i	0.128037	−	0.0930242i	0.649960	+	0.759968i	$0.274785\pi$
$360$		0			0
$361$	−2.90578	−	8.94306i	−0.152936	−	0.470687i
$362$	20.8744	+	36.1555i	1.09713	+	1.90029i
$363$		0			0
$364$	10.1931	−	17.6549i	0.534262	−	0.925370i
$365$	−1.31531	−	0.279578i	−0.0688464	−	0.0146338i
$366$		0			0
$367$	1.51873	+	0.676183i	0.0792772	+	0.0352965i	0.445992	−	0.895037i	$-0.352851\pi$
$367$	1.51873	+	0.676183i	0.0792772	+	0.0352965i	−0.366715	+	0.930333i	$0.619518\pi$
$368$	1.22508	−	3.77040i	0.0638616	−	0.196546i
$369$		0			0
$370$	0.506234	−	0.367800i	0.0263178	−	0.0191210i
$371$	−0.990914	+	9.42791i	−0.0514457	+	0.489473i
$372$		0			0
$373$	10.7543	−	18.6271i	0.556839	−	0.964473i	−0.440919	−	0.897547i	$-0.645348\pi$
$373$	10.7543	−	18.6271i	0.556839	−	0.964473i	0.997758	−	0.0669259i	$-0.0213191\pi$
$374$	14.9053	−	45.8721i	0.770734	−	2.37199i
$375$		0			0
$376$	−16.5380	+	18.3673i	−0.852880	+	0.947219i
$377$	9.94346	+	7.22435i	0.512114	+	0.372073i
$378$		0			0
$379$	3.83779	−	11.8115i	0.197134	−	0.606715i	−0.802811	−	0.596233i	$-0.796663\pi$
$379$	3.83779	−	11.8115i	0.197134	−	0.606715i	0.999945	−	0.0104822i	$-0.00333665\pi$
$380$	−3.28941	+	0.699185i	−0.168743	+	0.0358674i
$381$		0			0
$382$	27.4210	−	12.2086i	1.40298	−	0.624648i
$383$	0.782202	+	0.166262i	0.0399686	+	0.00849560i	0.227853	−	0.973696i	$-0.426830\pi$
$383$	0.782202	+	0.166262i	0.0399686	+	0.00849560i	−0.187884	+	0.982191i	$0.560163\pi$
$384$		0			0
$385$	−0.745741	+	1.29163i	−0.0380065	+	0.0658275i
$386$	53.9188			2.74439
$387$		0			0
$388$	14.5646	+	10.5818i	0.739404	+	0.537209i
$389$	1.58654	+	0.706374i	0.0804408	+	0.0358146i	0.446563	−	0.894752i	$-0.352648\pi$
$389$	1.58654	+	0.706374i	0.0804408	+	0.0358146i	−0.366122	+	0.930567i	$0.619315\pi$
$390$		0			0
$391$	18.8875	+	20.9767i	0.955184	+	1.06084i
$392$	−1.72945	−	16.4546i	−0.0873502	−	0.831081i
$393$		0			0
$394$	1.67943	−	1.86520i	0.0846086	−	0.0939673i
$395$	−1.07216			−0.0539461
$396$		0			0
$397$	−24.7599			−1.24267			−0.621333	−	0.783547i	$-0.713409\pi$
$397$	−24.7599			−1.24267			−0.621333	+	0.783547i	$0.713409\pi$
$398$	−25.6057	+	28.4380i	−1.28350	+	1.42547i
$399$		0			0
$400$	0.449140	+	4.27328i	0.0224570	+	0.213664i
$401$	−14.6221	−	16.2395i	−0.730191	−	0.810960i	0.257681	−	0.966230i	$-0.417042\pi$
$401$	−14.6221	−	16.2395i	−0.730191	−	0.810960i	−0.987872	+	0.155271i	$0.950375\pi$
$402$		0			0
$403$	−36.5849	−	16.2886i	−1.82242	−	0.811395i
$404$	−26.4000	−	19.1807i	−1.31345	−	0.954278i
$405$		0			0
$406$	−9.67462			−0.480143
$407$	2.74939	+	0.584431i	0.136282	+	0.0289692i
$408$		0			0
$409$	−7.85919	−	1.67052i	−0.388612	−	0.0826020i	0.00946221	−	0.999955i	$-0.496988\pi$
$409$	−7.85919	−	1.67052i	−0.388612	−	0.0826020i	−0.398074	+	0.917353i	$0.630321\pi$
$410$	−2.61008	+	1.16208i	−0.128903	+	0.0573911i
$411$		0			0
$412$	−31.9389	+	6.78881i	−1.57351	+	0.334461i
$413$	−5.29283	+	16.2897i	−0.260443	+	0.801562i
$414$		0			0
$415$	−3.45919	−	2.51325i	−0.169805	−	0.123371i
$416$	12.8950	−	14.3214i	0.632231	−	0.702164i
$417$		0			0
$418$	−19.3590	−	14.0654i	−0.946877	−	0.687962i
$419$	−2.79840	+	4.84698i	−0.136711	+	0.236790i	−0.926250	−	0.376910i	$-0.876986\pi$
$419$	−2.79840	+	4.84698i	−0.136711	+	0.236790i	0.789539	+	0.613701i	$0.210320\pi$
$420$		0			0
$421$	−3.95686	+	37.6470i	−0.192846	+	1.83480i	0.287567	+	0.957760i	$0.407154\pi$
$421$	−3.95686	+	37.6470i	−0.192846	+	1.83480i	−0.480413	+	0.877043i	$0.659513\pi$
$422$	−28.1684	+	20.4656i	−1.37122	+	0.996248i
$423$		0			0
$424$	6.85035	−	21.0832i	0.332682	−	1.02389i
$425$	−27.9486	−	12.4435i	−1.35571	−	0.603599i
$426$		0			0
$427$	6.41067	+	1.36263i	0.310234	+	0.0659423i
$428$	8.85614	−	15.3393i	0.428078	−	0.741452i
$429$		0			0
$430$	1.31167	+	2.27187i	0.0632542	+	0.109560i
$431$	9.20389	+	28.3267i	0.443336	+	1.36445i	0.884299	+	0.466922i	$0.154637\pi$
$431$	9.20389	+	28.3267i	0.443336	+	1.36445i	−0.440963	+	0.897525i	$0.645363\pi$
$432$		0			0
$433$	0.225935	−	0.164152i	0.0108578	−	0.00788862i	−0.582343	−	0.812943i	$-0.697864\pi$
$433$	0.225935	−	0.164152i	0.0108578	−	0.00788862i	0.593201	+	0.805054i	$0.297864\pi$
$434$	30.8340	−	6.55397i	1.48008	−	0.314601i
$435$		0			0
$436$	−5.18166	−	49.3002i	−0.248156	−	2.36105i
$437$	12.7932	−	5.69588i	0.611980	−	0.272471i
$438$		0			0
$439$	−7.49827	−	12.9874i	−0.357873	−	0.619854i	0.629732	−	0.776812i	$-0.283165\pi$
$439$	−7.49827	−	12.9874i	−0.357873	−	0.619854i	−0.987605	+	0.156958i	$0.949831\pi$
$440$	2.33375	−	2.59184i	0.111257	−	0.123561i
$441$		0			0
$442$	−18.8614	−	58.0493i	−0.897143	−	2.76112i
$443$	1.51564	−	14.4204i	0.0720104	−	0.685133i	−0.897655	−	0.440698i	$-0.854731\pi$
$443$	1.51564	−	14.4204i	0.0720104	−	0.685133i	0.969666	−	0.244435i	$-0.0786024\pi$
$444$		0			0
$445$	−0.572205	−	0.635498i	−0.0271251	−	0.0301255i
$446$	−3.00192	−	3.33397i	−0.142145	−	0.157868i
$447$		0			0
$448$	−1.84569	+	17.5606i	−0.0872008	+	0.829660i
$449$	6.55787	+	20.1830i	0.309485	+	0.952497i	0.977965	+	0.208767i	$0.0669450\pi$
$449$	6.55787	+	20.1830i	0.309485	+	0.952497i	−0.668481	+	0.743730i	$0.733055\pi$
$450$		0			0
$451$	−11.7244	−	5.22020i	−0.552082	−	0.245809i
$452$	−12.7238	−	22.0383i	−0.598479	−	1.03660i
$453$		0			0
$454$	−34.0660	+	15.1672i	−1.59880	+	0.711830i
$455$	0.197284	+	1.87703i	0.00924880	+	0.0879964i
$456$		0			0
$457$	3.13937	−	0.667293i	0.146853	−	0.0312146i	−0.133898	−	0.990995i	$-0.542750\pi$
$457$	3.13937	−	0.667293i	0.146853	−	0.0312146i	0.280752	+	0.959780i	$0.409416\pi$
$458$	−0.985297	+	0.715860i	−0.0460399	+	0.0334499i
$459$		0			0
$460$	1.51642	+	4.66707i	0.0707037	+	0.217603i
$461$	13.1628	+	22.7986i	0.613052	+	1.06184i	0.990723	+	0.135897i	$0.0433918\pi$
$461$	13.1628	+	22.7986i	0.613052	+	1.06184i	−0.377671	+	0.925940i	$0.623275\pi$
$462$		0			0
$463$	−1.81412	+	3.14215i	−0.0843093	+	0.146028i	−0.905097	−	0.425206i	$-0.860202\pi$
$463$	−1.81412	+	3.14215i	−0.0843093	+	0.146028i	0.820787	+	0.571234i	$0.193535\pi$
$464$	2.51210	+	0.533963i	0.116621	+	0.0247886i
$465$		0			0
$466$	−21.8138	−	9.71212i	−1.01050	−	0.449905i
$467$	5.71532	−	17.5899i	0.264473	−	0.813965i	−0.727341	−	0.686276i	$-0.759244\pi$
$467$	5.71532	−	17.5899i	0.264473	−	0.813965i	0.991814	−	0.127689i	$-0.0407559\pi$
$468$		0			0
$469$	11.4388	−	8.31077i	0.528194	−	0.383756i
$470$	0.575050	−	5.47123i	0.0265251	−	0.252369i
$471$		0			0
$472$	20.0265	−	34.6869i	0.921795	−	1.59660i
$473$	−3.64158	+	11.2072i	−0.167440	+	0.515309i
$474$		0			0
$475$	−10.1560	+	11.2794i	−0.465990	+	0.517535i
$476$	24.5374	+	17.8275i	1.12467	+	0.817120i
$477$		0			0
$478$	−6.93867	+	21.3550i	−0.317367	+	0.976756i
$479$	−0.153567	+	0.0326418i	−0.00701668	+	0.00149144i	−0.211419	−	0.977396i	$-0.567808\pi$
$479$	−0.153567	+	0.0326418i	−0.00701668	+	0.00149144i	0.204402	+	0.978887i	$0.434475\pi$
$480$		0			0
$481$	3.24945	−	1.44675i	0.148162	−	0.0659660i
$482$	−0.634980	−	0.134969i	−0.0289225	−	0.00614767i
$483$		0			0
$484$	37.6668		0.000778469i	1.71213		3.53850e-5i
$485$	−1.66671			−0.0756816
$486$		0			0
$487$	−14.5028	−	10.5369i	−0.657187	−	0.477474i	0.208525	−	0.978017i	$-0.433134\pi$
$487$	−14.5028	−	10.5369i	−0.657187	−	0.477474i	−0.865712	+	0.500543i	$0.833134\pi$
$488$	−14.0010	−	6.23364i	−0.633795	−	0.282184i
$489$		0			0
$490$	2.46424	+	2.73682i	0.111323	+	0.123637i
$491$	−0.694902	−	6.61155i	−0.0313605	−	0.298375i	−0.998949	−	0.0458419i	$-0.985403\pi$
$491$	−0.694902	−	6.61155i	−0.0313605	−	0.298375i	0.967588	−	0.252533i	$-0.0812637\pi$
$492$		0			0
$493$	−12.2356	+	13.5890i	−0.551065	+	0.612019i
$494$	−30.2813			−1.36242
$495$		0			0
$496$	−8.36804			−0.375736
$497$	2.78168	−	3.08936i	0.124775	−	0.138577i
$498$		0			0
$499$	−3.54846	−	33.7614i	−0.158851	−	1.51137i	−0.725968	−	0.687729i	$-0.758608\pi$
$499$	−3.54846	−	33.7614i	−0.158851	−	1.51137i	0.567117	−	0.823638i	$-0.308059\pi$
$500$	−7.19078	−	7.98617i	−0.321582	−	0.357153i
$501$		0			0
$502$	9.41572	+	4.19215i	0.420244	+	0.187105i
$503$	2.53812	+	1.84405i	0.113169	+	0.0822222i	0.642930	−	0.765925i	$-0.277718\pi$
$503$	2.53812	+	1.84405i	0.113169	+	0.0822222i	−0.529761	+	0.848147i	$0.677718\pi$
$504$		0			0
$505$	3.02112			0.134438
$506$	−17.4594	+	30.2399i	−0.776167	+	1.34433i
$507$		0			0
$508$	44.2273	+	9.40080i	1.96227	+	0.417093i
$509$	−20.8320	+	9.27502i	−0.923364	+	0.411108i	−0.812655	−	0.582745i	$-0.801979\pi$
$509$	−20.8320	+	9.27502i	−0.923364	+	0.411108i	−0.110709	+	0.993853i	$0.535312\pi$
$510$		0			0
$511$	5.88530	−	1.25096i	0.260350	−	0.0553391i
$512$	3.04225	−	9.36310i	0.134450	−	0.413794i
$513$		0			0
$514$	−6.88586	−	5.00287i	−0.303722	−	0.220667i
$515$	2.02277	−	2.24652i	0.0891340	−	0.0989933i
$516$		0			0
$517$	19.9927	−	14.5252i	0.879279	−	0.638819i
$518$	−1.39992	+	2.42474i	−0.0615090	+	0.106537i
$519$		0			0
$520$	0.461339	−	4.38935i	0.0202311	−	0.192486i
$521$	4.26200	−	3.09653i	0.186722	−	0.135661i	−0.490497	−	0.871443i	$-0.663185\pi$
$521$	4.26200	−	3.09653i	0.186722	−	0.135661i	0.677219	+	0.735781i	$0.263185\pi$
$522$		0			0
$523$	3.67595	−	11.3134i	0.160738	−	0.494701i	−0.837959	−	0.545733i	$-0.816251\pi$
$523$	3.67595	−	11.3134i	0.160738	−	0.494701i	0.998697	+	0.0510325i	$0.0162512\pi$
$524$	22.8373	+	10.1678i	0.997651	+	0.444183i
$525$		0			0
$526$	32.9242	+	6.99825i	1.43556	+	0.305138i
$527$	29.7904	−	51.5985i	1.29769	−	2.24767i
$528$		0			0
$529$	1.28255	+	2.22144i	0.0557629	+	0.0965843i
$530$	1.52480	+	4.69285i	0.0662331	+	0.203845i
$531$		0			0
$532$	12.1734	−	8.84448i	0.527783	−	0.383457i
$533$	−15.8860	+	3.37667i	−0.688099	+	0.146260i
$534$		0			0
$535$	0.171408	+	1.63083i	0.00741060	+	0.0705071i
$536$	−30.2052	+	13.4482i	−1.30467	+	0.580875i
$537$		0			0
$538$	−1.06872	−	1.85108i	−0.0460757	−	0.0798055i
$539$	−1.72938	+	16.4523i	−0.0744895	+	0.708650i
$540$		0			0
$541$	12.5401	+	38.5945i	0.539142	+	1.65931i	0.734525	+	0.678581i	$0.237405\pi$
$541$	12.5401	+	38.5945i	0.539142	+	1.65931i	−0.195383	+	0.980727i	$0.562595\pi$
$542$	−0.643724	+	6.12462i	−0.0276503	+	0.263075i
$543$		0			0
$544$	19.1848	+	21.3069i	0.822542	+	0.913526i
$545$	3.07090	+	3.41058i	0.131543	+	0.146093i
$546$		0			0
$547$	−2.46000	+	23.4054i	−0.105182	+	1.00074i	0.806887	+	0.590706i	$0.201151\pi$
$547$	−2.46000	+	23.4054i	−0.105182	+	1.00074i	−0.912069	+	0.410036i	$0.865516\pi$
$548$	−10.3776	−	31.9391i	−0.443311	−	1.36437i
$549$		0			0
$550$	3.95635	−	37.6384i	0.168699	−	1.60491i
$551$	4.53595	+	7.85650i	0.193238	+	0.334698i
$552$		0			0
$553$	4.38257	−	1.95125i	0.186366	−	0.0829755i
$554$	7.03671	+	66.9498i	0.298961	+	2.84443i
$555$		0			0
$556$	31.7421	−	6.74700i	1.34617	−	0.286136i
$557$	−5.08590	+	3.69513i	−0.215497	+	0.156568i	−0.690297	−	0.723526i	$-0.742520\pi$
$557$	−5.08590	+	3.69513i	−0.215497	+	0.156568i	0.474800	+	0.880093i	$0.342520\pi$
$558$		0			0
$559$	4.60811	+	14.1823i	0.194902	+	0.599847i
$560$	0.197187	+	0.341538i	0.00833268	+	0.0144326i
$561$		0			0
$562$	−10.1807	+	17.6335i	−0.429448	+	0.743826i
$563$	−16.5956	−	3.52751i	−0.699423	−	0.148667i	−0.155542	−	0.987829i	$-0.549712\pi$
$563$	−16.5956	−	3.52751i	−0.699423	−	0.148667i	−0.543881	+	0.839162i	$0.683046\pi$
$564$		0			0
$565$	2.15228	+	0.958259i	0.0905473	+	0.0403142i
$566$	16.7095	−	51.4265i	0.702352	−	2.16162i
$567$		0			0
$568$	−7.86471	+	5.71404i	−0.329996	+	0.239756i
$569$	2.32581	−	22.1286i	0.0975031	−	0.927680i	−0.830979	−	0.556303i	$-0.812219\pi$
$569$	2.32581	−	22.1286i	0.0975031	−	0.927680i	0.928482	−	0.371376i	$-0.121114\pi$
$570$		0			0
$571$	−17.6576	+	30.5838i	−0.738947	+	1.27989i	0.214023	+	0.976829i	$0.431343\pi$
$571$	−17.6576	+	30.5838i	−0.738947	+	1.27989i	−0.952970	+	0.303065i	$0.901990\pi$
$572$	38.5625	−	28.0167i	1.61238	−	1.17144i
$573$		0			0
$574$	8.55411	−	9.50030i	0.357042	−	0.396535i
$575$	17.9182	+	13.0184i	0.747243	+	0.542904i
$576$		0			0
$577$	−11.8156	+	36.3646i	−0.491889	+	1.51388i	0.329859	+	0.944030i	$0.392999\pi$
$577$	−11.8156	+	36.3646i	−0.491889	+	1.51388i	−0.821749	+	0.569850i	$0.807001\pi$
$578$	50.0962	−	10.6483i	2.08373	−	0.442910i
$579$		0			0
$580$	−2.90415	+	1.29301i	−0.120588	+	0.0536894i
$581$	18.7138	+	3.97774i	0.776379	+	0.165025i
$582$		0			0
$583$	−11.0828	+	19.1955i	−0.459001	+	0.794995i
$584$	−14.0700			−0.582219
$585$		0			0
$586$	39.5219	+	28.7143i	1.63263	+	1.18618i
$587$	11.3185	+	5.03932i	0.467165	+	0.207995i	0.626799	−	0.779181i	$-0.284365\pi$
$587$	11.3185	+	5.03932i	0.467165	+	0.207995i	−0.159634	+	0.987176i	$0.551031\pi$
$588$		0			0
$589$	−19.7788	−	21.9666i	−0.814973	−	0.905119i
$590$	0.931901	+	8.86645i	0.0383658	+	0.365026i
$591$		0			0
$592$	0.497328	−	0.552339i	0.0204401	−	0.0227010i
$593$	−4.18039			−0.171668			−0.0858340	−	0.996309i	$-0.527355\pi$
$593$	−4.18039			−0.171668			−0.0858340	+	0.996309i	$0.527355\pi$
$594$		0			0
$595$	−2.80796			−0.115115
$596$	9.45710	−	10.5032i	0.387378	−	0.430227i
$597$		0			0
$598$	4.61885	+	43.9454i	0.188879	+	1.79706i
$599$	29.4944	+	32.7569i	1.20511	+	1.33841i	0.925709	+	0.378236i	$0.123469\pi$
$599$	29.4944	+	32.7569i	1.20511	+	1.33841i	0.279401	+	0.960174i	$0.409864\pi$
$600$		0			0
$601$	−1.59991	−	0.712324i	−0.0652616	−	0.0290563i	0.373846	−	0.927491i	$-0.378039\pi$
$601$	−1.59991	−	0.712324i	−0.0652616	−	0.0290563i	−0.439108	+	0.898434i	$0.644705\pi$
$602$	−9.49624	−	6.89943i	−0.387038	−	0.281200i
$603$		0			0
$604$	−60.8670			−2.47664
$605$	−2.82126	+	2.04968i	−0.114701	+	0.0833312i
$606$		0			0
$607$	10.6316	+	2.25982i	0.431525	+	0.0917234i	0.418553	−	0.908192i	$-0.362538\pi$
$607$	10.6316	+	2.25982i	0.431525	+	0.0917234i	0.0129718	+	0.999916i	$0.495871\pi$
$608$	12.9945	−	5.78553i	0.526997	−	0.234634i
$609$		0			0
$610$	3.33682	−	0.709263i	0.135104	−	0.0287172i
$611$	9.66362	−	29.7416i	0.390948	−	1.20321i
$612$		0			0
$613$	−14.3951	−	10.4586i	−0.581412	−	0.422421i	0.257821	−	0.966193i	$-0.416996\pi$
$613$	−14.3951	−	10.4586i	−0.581412	−	0.422421i	−0.839233	+	0.543772i	$0.816996\pi$
$614$	−36.0497	+	40.0372i	−1.45485	+	1.61577i
$615$		0			0
$616$	−4.82254	+	14.8417i	−0.194306	+	0.597990i
$617$	1.99805	−	3.46073i	0.0804386	−	0.139324i	−0.823000	−	0.568042i	$-0.807701\pi$
$617$	1.99805	−	3.46073i	0.0804386	−	0.139324i	0.903438	+	0.428718i	$0.141035\pi$
$618$		0			0
$619$	1.14724	−	10.9153i	0.0461115	−	0.438721i	−0.946972	−	0.321315i	$-0.895875\pi$
$619$	1.14724	−	10.9153i	0.0461115	−	0.438721i	0.993084	−	0.117407i	$-0.0374581\pi$
$620$	8.37989	−	6.08835i	0.336544	−	0.244514i
$621$		0			0
$622$	14.6926	−	45.2191i	0.589118	−	1.81312i
$623$	3.49552	+	1.55630i	0.140045	+	0.0623520i
$624$		0			0
$625$	−22.9890	−	4.88646i	−0.919560	−	0.195458i
$626$	−39.6388	+	68.6565i	−1.58429	+	2.74407i
$627$		0			0
$628$	3.45380	+	5.98216i	0.137822	+	0.238714i
$629$	1.63530	+	5.03293i	0.0652037	+	0.200676i
$630$		0			0
$631$	−6.99735	+	5.08388i	−0.278560	+	0.202386i	−0.718289	−	0.695745i	$-0.755075\pi$
$631$	−6.99735	+	5.08388i	−0.278560	+	0.202386i	0.439729	+	0.898131i	$0.355075\pi$
$632$	−10.9732	+	2.33242i	−0.436490	+	0.0927788i
$633$		0			0
$634$	6.67542	+	63.5123i	0.265115	+	2.52240i
$635$	−3.82417	+	1.70263i	−0.151757	+	0.0675668i
$636$		0			0
$637$	10.4672	+	18.1296i	0.414724	+	0.718323i
$638$	−20.6648	−	9.20082i	−0.818128	−	0.364264i
$639$		0			0
$640$	1.94048	+	5.97219i	0.0767042	+	0.236071i
$641$	3.87671	−	36.8844i	0.153121	−	1.45685i	−0.600546	−	0.799591i	$-0.705050\pi$
$641$	3.87671	−	36.8844i	0.153121	−	1.45685i	0.753666	−	0.657257i	$-0.228283\pi$
$642$		0			0
$643$	−27.2554	−	30.2702i	−1.07485	−	1.19374i	−0.980155	−	0.198234i	$-0.936479\pi$
$643$	−27.2554	−	30.2702i	−1.07485	−	1.19374i	−0.0946941	−	0.995506i	$-0.530187\pi$
$644$	−14.6923	−	16.3175i	−0.578958	−	0.642998i
$645$		0			0
$646$	4.70916	−	44.8047i	0.185280	−	1.76282i
$647$	0.175813	+	0.541098i	0.00691193	+	0.0212727i	0.954453	−	0.298361i	$-0.0964400\pi$
$647$	0.175813	+	0.541098i	0.00691193	+	0.0212727i	−0.947541	+	0.319634i	$0.896440\pi$
$648$		0			0
$649$	−26.7973	+	29.7608i	−1.05189	+	1.16821i
$650$	−23.9461	−	41.4758i	−0.939242	−	1.62682i
$651$		0			0
$652$	−4.94388	+	2.20116i	−0.193617	+	0.0862040i
$653$	−3.81817	−	36.3275i	−0.149417	−	1.42160i	−0.770290	−	0.637694i	$-0.779889\pi$
$653$	−3.81817	−	36.3275i	−0.149417	−	1.42160i	0.620873	−	0.783911i	$-0.286778\pi$
$654$		0			0
$655$	−2.26381	+	0.481187i	−0.0884542	+	0.0188015i
$656$	−2.74549	+	1.99472i	−0.107193	+	0.0778806i
$657$		0			0
$658$	7.60666	+	23.4109i	0.296538	+	0.912651i
$659$	−12.0035	−	20.7907i	−0.467590	−	0.809889i	0.531725	−	0.846917i	$-0.321544\pi$
$659$	−12.0035	−	20.7907i	−0.467590	−	0.809889i	−0.999314	+	0.0370284i	$0.988211\pi$
$660$		0			0
$661$	−6.49165	+	11.2439i	−0.252496	+	0.437336i	−0.964212	−	0.265131i	$-0.914585\pi$
$661$	−6.49165	+	11.2439i	−0.252496	+	0.437336i	0.711717	+	0.702467i	$0.247918\pi$
$662$	−40.9431	−	8.70273i	−1.59130	−	0.338241i
$663$		0			0
$664$	−40.8712	−	18.1970i	−1.58611	−	0.706181i
$665$	−0.430484	+	1.32489i	−0.0166935	+	0.0513772i
$666$		0			0
$667$	10.7098	−	7.78112i	0.414685	−	0.301286i
$668$	5.48410	−	52.1777i	0.212186	−	2.01882i
$669$		0			0
$670$	3.67978	−	6.37356i	0.142162	−	0.246232i
$671$	12.3972	+	9.00727i	0.478588	+	0.347722i
$672$		0			0
$673$	11.3924	−	12.6525i	0.439144	−	0.487719i	−0.482423	−	0.875939i	$-0.660243\pi$
$673$	11.3924	−	12.6525i	0.439144	−	0.487719i	0.921567	+	0.388219i	$0.126910\pi$
$674$	20.6737	+	15.0204i	0.796323	+	0.578562i
$675$		0			0
$676$	4.88349	−	15.0298i	0.187827	−	0.578071i
$677$	−34.6574	+	7.36665i	−1.33199	+	0.283123i	−0.818270	−	0.574834i	$-0.805067\pi$
$677$	−34.6574	+	7.36665i	−1.33199	+	0.283123i	−0.513721	+	0.857957i	$0.671733\pi$
$678$		0			0
$679$	6.81290	−	3.03330i	0.261455	−	0.116407i
$680$	6.42281	+	1.36521i	0.246304	+	0.0523535i
$681$		0			0
$682$	72.0939	+	15.3248i	2.76062	+	0.586817i
$683$	−23.8967			−0.914381			−0.457191	−	0.889369i	$-0.651144\pi$
$683$	−23.8967			−0.914381			−0.457191	+	0.889369i	$0.651144\pi$
$684$		0			0
$685$	2.51533	+	1.82749i	0.0961058	+	0.0698250i
$686$	−36.1801	−	16.1084i	−1.38136	−	0.615022i
$687$		0			0
$688$	2.08499	+	2.31561i	0.0794894	+	0.0882819i
$689$	2.93192	+	27.8953i	0.111697	+	1.06273i
$690$		0			0
$691$	−0.396537	+	0.440399i	−0.0150850	+	0.0167536i	−0.750640	−	0.660711i	$-0.770255\pi$
$691$	−0.396537	+	0.440399i	−0.0150850	+	0.0167536i	0.735555	+	0.677465i	$0.236921\pi$
$692$	3.37645			0.128353
$693$		0			0
$694$	51.4682			1.95371
$695$	−2.01031	+	2.23268i	−0.0762555	+	0.0846903i
$696$		0			0
$697$	−2.52569	−	24.0303i	−0.0956672	−	0.910213i
$698$	28.6805	+	31.8529i	1.08557	+	1.20565i
$699$		0			0
$700$	21.7407	+	9.67960i	0.821723	+	0.365855i
$701$	−20.5701	−	14.9451i	−0.776922	−	0.564467i	0.127131	−	0.991886i	$-0.459423\pi$
$701$	−20.5701	−	14.9451i	−0.776922	−	0.564467i	−0.904054	+	0.427419i	$0.859423\pi$
$702$		0			0
$703$	2.62542			0.0990194
$704$	−20.6430	+	35.7538i	−0.778011	+	1.34752i
$705$		0			0
$706$	−75.3387	−	16.0137i	−2.83541	−	0.602685i
$707$	−12.3492	+	5.49821i	−0.464439	+	0.206782i
$708$		0			0
$709$	−14.7746	+	3.14044i	−0.554871	+	0.117942i	−0.476809	−	0.879007i	$-0.658207\pi$
$709$	−14.7746	+	3.14044i	−0.554871	+	0.117942i	−0.0780624	+	0.996948i	$0.524873\pi$
$710$	0.668663	−	2.05793i	0.0250945	−	0.0772329i
$711$		0			0
$712$	−7.23882	−	5.25931i	−0.271286	−	0.197101i
$713$	−28.8620	+	32.0545i	−1.08089	+	1.20045i
$714$		0			0
$715$	−1.36371	+	4.19692i	−0.0509998	+	0.156956i
$716$	−19.2200	+	33.2900i	−0.718284	+	1.24410i
$717$		0			0
$718$	−0.730010	+	6.94558i	−0.0272437	+	0.259207i
$719$	9.74281	−	7.07857i	0.363345	−	0.263986i	−0.391101	−	0.920348i	$-0.627906\pi$
$719$	9.74281	−	7.07857i	0.363345	−	0.263986i	0.754446	+	0.656362i	$0.227906\pi$
$720$		0			0
$721$	−4.17983	+	12.8642i	−0.155665	+	0.479088i
$722$	20.0069	+	8.90765i	0.744580	+	0.331508i
$723$		0			0
$724$	−60.0405	−	12.7620i	−2.23139	−	0.474296i
$725$	−7.17396	+	12.4257i	−0.266434	+	0.461477i
$726$		0			0
$727$	−24.7966	−	42.9489i	−0.919654	−	1.59289i	−0.799940	−	0.600079i	$-0.795136\pi$
$727$	−24.7966	−	42.9489i	−0.919654	−	1.59289i	−0.119714	−	0.992808i	$-0.538198\pi$
$728$	6.10251	+	18.7816i	0.226174	+	0.696092i
$729$		0			0
$730$	2.53368	−	1.84082i	0.0937755	−	0.0681319i
$731$	−21.7010	+	4.61269i	−0.802640	+	0.170606i
$732$		0			0
$733$	3.37265	+	32.0886i	0.124572	+	1.18522i	0.860964	+	0.508666i	$0.169861\pi$
$733$	3.37265	+	32.0886i	0.124572	+	1.18522i	−0.736392	+	0.676555i	$0.763472\pi$
$734$	−3.53713	+	1.57483i	−0.130558	+	0.0581281i
$735$		0			0
$736$	−10.3783	−	17.9757i	−0.382548	−	0.662593i
$737$	32.3368	−	6.87305i	1.19114	−	0.253172i
$738$		0			0
$739$	−0.968005	−	2.97921i	−0.0356086	−	0.109592i	0.931672	−	0.363300i	$-0.118350\pi$
$739$	−0.968005	−	2.97921i	−0.0356086	−	0.109592i	−0.967281	+	0.253708i	$0.918350\pi$
$740$	−0.0961664	+	0.914963i	−0.00353515	+	0.0336347i
$741$		0			0
$742$	−14.7735	−	16.4076i	−0.542351	−	0.602341i
$743$	−5.21170	−	5.78818i	−0.191199	−	0.212348i	0.639922	−	0.768440i	$-0.278967\pi$
$743$	−5.21170	−	5.78818i	−0.191199	−	0.212348i	−0.831121	+	0.556092i	$0.812300\pi$
$744$		0			0
$745$	−0.136774	+	1.30132i	−0.00501100	+	0.0476765i
$746$	15.4798	+	47.6420i	0.566756	+	1.74430i
$747$		0			0
$748$	35.4570	+	61.4148i	1.29644	+	2.24555i
$749$	−3.66865	−	6.35428i	−0.134049	−	0.232180i
$750$		0			0
$751$	45.3932	−	20.2103i	1.65642	−	0.737486i	0.656562	−	0.754272i	$-0.272010\pi$
$751$	45.3932	−	20.2103i	1.65642	−	0.737486i	0.999859	+	0.0167864i	$0.00534354\pi$
$752$	−0.683037	−	6.49866i	−0.0249078	−	0.236982i
$753$		0			0
$754$	−27.9997	+	5.95153i	−1.01969	+	0.216742i
$755$	4.55890	−	3.31224i	0.165915	−	0.120545i
$756$		0			0
$757$	−8.35296	−	25.7078i	−0.303594	−	0.934365i	−0.980198	−	0.198018i	$-0.936549\pi$
$757$	−8.35296	−	25.7078i	−0.303594	−	0.934365i	0.676605	−	0.736346i	$-0.263451\pi$
$758$	14.4623	+	25.0495i	0.525295	+	0.909838i
$759$		0			0
$760$	1.62882	−	2.82121i	0.0590836	−	0.102336i
$761$	43.5379	+	9.25426i	1.57825	+	0.335467i	0.911976	−	0.410243i	$-0.134556\pi$
$761$	43.5379	+	9.25426i	1.57825	+	0.335467i	0.666271	+	0.745710i	$0.267889\pi$
$762$		0			0
$763$	−18.7597	−	8.35235i	−0.679147	−	0.302376i
$764$	−13.6374	+	41.9716i	−0.493384	+	1.51848i
$765$		0			0
$766$	−1.50675	+	1.09472i	−0.0544412	+	0.0395538i
$767$	−5.29732	+	50.4006i	−0.191275	+	1.81986i
$768$		0			0
$769$	1.65952	−	2.87438i	0.0598440	−	0.103653i	−0.834551	−	0.550930i	$-0.814273\pi$
$769$	1.65952	−	2.87438i	0.0598440	−	0.103653i	0.894395	+	0.447277i	$0.147606\pi$
$770$	−1.07337	−	3.30360i	−0.0386815	−	0.119054i
$771$		0			0
$772$	−53.0453	+	58.9127i	−1.90914	+	2.12032i
$773$	23.0471	+	16.7447i	0.828946	+	0.602264i	0.919261	−	0.393649i	$-0.128787\pi$
$773$	23.0471	+	16.7447i	0.828946	+	0.602264i	−0.0903152	+	0.995913i	$0.528787\pi$
$774$		0			0
$775$	14.4465	−	44.4617i	0.518934	−	1.59711i
$776$	−17.0583	+	3.62585i	−0.612357	+	0.130160i
$777$		0			0
$778$	−3.69506	+	1.64515i	−0.132474	+	0.0589813i
$779$	−11.7255	−	2.49234i	−0.420111	−	0.0892973i
$780$		0			0
$781$	8.87968	−	3.95338i	0.317740	−	0.141463i
$782$	−65.7407			−2.35088
$783$		0			0
$784$	3.53890	+	2.57116i	0.126389	+	0.0918273i
$785$	−0.584222	−	0.260113i	−0.0208518	−	0.00928382i
$786$		0			0
$787$	8.73129	+	9.69708i	0.311237	+	0.345663i	0.878386	−	0.477951i	$-0.158621\pi$
$787$	8.73129	+	9.69708i	0.311237	+	0.345663i	−0.567150	+	0.823615i	$0.691954\pi$
$788$	0.385729	+	3.66996i	0.0137410	+	0.130737i
$789$		0			0
$790$	1.67086	−	1.85568i	0.0594464	−	0.0660220i
$791$	−10.5417			−0.374819
$792$		0			0
$793$	19.3917			0.688618
$794$	38.5861	−	42.8542i	1.36937	−	1.52084i
$795$		0			0
$796$	−5.88107	−	55.9547i	−0.208449	−	1.98326i
$797$	−33.5725	−	37.2861i	−1.18920	−	1.32074i	−0.935445	−	0.353471i	$-0.885001\pi$
$797$	−33.5725	−	37.2861i	−1.18920	−	1.32074i	−0.253754	−	0.967269i	$-0.581666\pi$
$798$		0			0
$799$	42.5033	+	18.9237i	1.50366	+	0.669472i
$800$	18.2003	+	13.2233i	0.643477	+	0.467514i
$801$		0			0
$802$	50.8941			1.79713
$803$	13.7606	+	2.92505i	0.485600	+	0.103223i
$804$		0			0
$805$	1.98840	+	0.422648i	0.0700820	+	0.0148964i
$806$	85.2062	−	37.9363i	3.00126	−	1.33625i
$807$		0			0
$808$	30.9202	−	6.57229i	1.08777	−	0.231212i
$809$	10.8621	−	33.4301i	0.381892	−	1.17534i	−0.556819	−	0.830634i	$-0.687978\pi$
$809$	10.8621	−	33.4301i	0.381892	−	1.17534i	0.938710	−	0.344707i	$-0.112022\pi$
$810$		0			0
$811$	−17.8837	−	12.9933i	−0.627981	−	0.456255i	0.227719	−	0.973727i	$-0.426873\pi$
$811$	−17.8837	−	12.9933i	−0.627981	−	0.456255i	−0.855700	+	0.517472i	$0.826873\pi$
$812$	9.51789	−	10.5707i	0.334012	−	0.370958i
$813$		0			0
$814$	−5.29620	+	3.84783i	−0.185632	+	0.134866i
$815$	0.250512	−	0.433900i	0.00877506	−	0.0151989i
$816$		0			0
$817$	−1.15052	+	10.9464i	−0.0402515	+	0.382967i
$818$	15.1391	−	10.9992i	0.529327	−	0.384579i
$819$		0			0
$820$	1.29808	−	3.99508i	0.0453309	−	0.139514i
$821$	−2.31785	−	1.03197i	−0.0808934	−	0.0360160i	0.365891	−	0.930658i	$-0.380764\pi$
$821$	−2.31785	−	1.03197i	−0.0808934	−	0.0360160i	−0.446784	+	0.894642i	$0.647431\pi$
$822$		0			0
$823$	10.1460	+	2.15660i	0.353668	+	0.0751745i	0.381320	−	0.924443i	$-0.375470\pi$
$823$	10.1460	+	2.15660i	0.353668	+	0.0751745i	−0.0276517	+	0.999618i	$0.508803\pi$
$824$	15.8152	−	27.3928i	0.550950	−	0.954273i
$825$		0			0
$826$	−19.9455	−	34.5467i	−0.693994	−	1.20203i
$827$	−16.2925	−	50.1431i	−0.566546	−	1.74365i	−0.663314	−	0.748341i	$-0.730851\pi$
$827$	−16.2925	−	50.1431i	−0.566546	−	1.74365i	0.0967683	−	0.995307i	$-0.469149\pi$
$828$		0			0
$829$	−30.6163	+	22.2440i	−1.06335	+	0.772566i	−0.974705	−	0.223497i	$-0.928253\pi$
$829$	−30.6163	+	22.2440i	−1.06335	+	0.772566i	−0.0886419	+	0.996064i	$0.528253\pi$
$830$	9.74073	−	2.07046i	0.338106	−	0.0718666i
$831$		0			0
$832$	5.46104	+	51.9583i	0.189327	+	1.80133i
$833$	−28.4527	+	12.6680i	−0.985829	+	0.438919i
$834$		0			0
$835$	2.42863	+	4.20651i	0.0840462	+	0.145572i
$836$	34.4135	−	7.31444i	1.19021	−	0.252975i
$837$		0			0
$838$	−4.02803	−	12.3970i	−0.139146	−	0.428247i
$839$	−2.10265	+	20.0054i	−0.0725915	+	0.690662i	0.896346	+	0.443355i	$0.146212\pi$
$839$	−2.10265	+	20.0054i	−0.0725915	+	0.690662i	−0.968937	+	0.247306i	$0.920455\pi$
$840$		0			0
$841$	−13.6665	−	15.1781i	−0.471257	−	0.523384i
$842$	−58.9925	−	65.5178i	−2.03302	−	2.25789i
$843$		0			0
$844$	5.35100	−	50.9114i	0.184189	−	1.75244i
$845$	0.452118	+	1.39148i	0.0155533	+	0.0478682i
$846$		0			0
$847$	7.80199	−	13.5128i	0.268079	−	0.464305i
$848$	2.93048	+	5.07575i	0.100633	+	0.174302i
$849$		0			0
$850$	65.0923	−	28.9810i	2.23265	−	0.994039i
$851$	−0.400459	−	3.81011i	−0.0137275	−	0.130609i
$852$		0			0
$853$	−8.92089	+	1.89619i	−0.305446	+	0.0649245i	−0.358085	−	0.933689i	$-0.616570\pi$
$853$	−8.92089	+	1.89619i	−0.305446	+	0.0649245i	0.0526390	+	0.998614i	$0.483237\pi$
$854$	−12.3489	+	8.97197i	−0.422569	+	0.307014i
$855$		0			0
$856$	5.30210	+	16.3182i	0.181222	+	0.557744i
$857$	−0.922678	−	1.59813i	−0.0315181	−	0.0545909i	0.849836	−	0.527047i	$-0.176701\pi$
$857$	−0.922678	−	1.59813i	−0.0315181	−	0.0545909i	−0.881354	+	0.472456i	$0.843368\pi$
$858$		0			0
$859$	−14.2555	+	24.6913i	−0.486392	+	0.842456i	−0.999878	−	0.0156422i	$-0.995021\pi$
$859$	−14.2555	+	24.6913i	−0.486392	+	0.842456i	0.513485	+	0.858098i	$0.328354\pi$
$860$	−3.77271	−	0.801915i	−0.128648	−	0.0273451i
$861$		0			0
$862$	−63.3708	−	28.2145i	−2.15842	−	0.960989i
$863$	3.30628	−	10.1757i	0.112547	−	0.346385i	−0.878880	−	0.477042i	$-0.841709\pi$
$863$	3.30628	−	10.1757i	0.112547	−	0.346385i	0.991428	+	0.130658i	$0.0417089\pi$
$864$		0			0
$865$	−0.252894	+	0.183738i	−0.00859865	+	0.00624729i
$866$	−0.0679878	+	0.646861i	−0.00231032	+	0.0219812i
$867$		0			0
$868$	−23.1735	+	40.1376i	−0.786559	+	1.36236i
$869$	11.2168		0.000115910i	0.380503		3.93198e-6i
$870$		0			0
$871$	27.9930	−	31.0893i	0.948506	−	1.05342i
$872$	38.8492	+	28.2256i	1.31560	+	0.955840i
$873$		0			0
$874$	−10.0786	+	31.0187i	−0.340913	+	1.04922i
$875$	−4.35443	+	0.925562i	−0.147207	+	0.0312897i
$876$		0			0
$877$	37.3021	−	16.6080i	1.25960	−	0.560811i	0.335171	−	0.942157i	$-0.391206\pi$
$877$	37.3021	−	16.6080i	1.25960	−	0.560811i	0.924432	+	0.381346i	$0.124539\pi$
$878$	34.1637	+	7.26173i	1.15297	+	0.245071i
$879$		0			0
$880$	0.0963762	+	0.917050i	0.00324884	+	0.0309137i
$881$	−21.0458			−0.709050			−0.354525	−	0.935047i	$-0.615357\pi$
$881$	−21.0458			−0.709050			−0.354525	+	0.935047i	$0.615357\pi$
$882$		0			0
$883$	−10.2973	−	7.48145i	−0.346533	−	0.251771i	0.400880	−	0.916130i	$-0.368704\pi$
$883$	−10.2973	−	7.48145i	−0.346533	−	0.251771i	−0.747413	+	0.664360i	$0.768704\pi$
$884$	81.9816	+	36.5006i	2.75734	+	1.22765i
$885$		0			0
$886$	22.5966	+	25.0961i	0.759148	+	0.843119i
$887$	1.12107	+	10.6662i	0.0376417	+	0.358137i	0.997089	+	0.0762484i	$0.0242942\pi$
$887$	1.12107	+	10.6662i	0.0376417	+	0.358137i	−0.959447	+	0.281889i	$0.909039\pi$
$888$		0			0
$889$	12.5331	−	13.9194i	0.420346	−	0.466842i
$890$	1.99164			0.0667599
$891$		0			0
$892$	6.59606			0.220852
$893$	15.4450	−	17.1534i	0.516846	−	0.574015i
$894$		0			0
$895$	−0.371996	−	3.53931i	−0.0124345	−	0.118306i
$896$	−18.8009	−	20.8805i	−0.628094	−	0.697569i
$897$		0			0
$898$	−45.1523	−	20.1031i	−1.50675	−	0.670850i
$899$	−22.6060	−	16.4242i	−0.753952	−	0.547778i
$900$		0			0
$901$	−41.7304			−1.39024
$902$	27.3065	−	12.1573i	0.909206	−	0.404793i
$903$		0			0
$904$	24.1126	+	5.12529i	0.801972	+	0.170464i
$905$	5.19148	−	2.31139i	0.172571	−	0.0768334i
$906$		0			0
$907$	12.9561	−	2.75391i	0.430201	−	0.0914421i	0.0122784	−	0.999925i	$-0.496092\pi$
$907$	12.9561	−	2.75391i	0.430201	−	0.0914421i	0.417923	+	0.908483i	$0.362758\pi$
$908$	16.9422	−	52.1426i	0.562245	−	1.73041i
$909$		0			0
$910$	−3.55618	−	2.58372i	−0.117886	−	0.0856494i
$911$	38.2237	−	42.4518i	1.26641	−	1.40649i	0.392973	−	0.919550i	$-0.371447\pi$
$911$	38.2237	−	42.4518i	1.26641	−	1.40649i	0.873436	−	0.486939i	$-0.161887\pi$
$912$		0			0
$913$	36.1894	+	26.2937i	1.19769	+	0.870195i
$914$	−3.73747	+	6.47348i	−0.123624	+	0.214124i
$915$		0			0
$916$	0.187172	−	1.78082i	0.00618432	−	0.0588399i
$917$	8.37786	−	6.08687i	0.276661	−	0.201006i
$918$		0			0
$919$	5.12287	−	15.7666i	0.168988	−	0.520091i	−0.830320	−	0.557287i	$-0.811842\pi$
$919$	5.12287	−	15.7666i	0.168988	−	0.520091i	0.999308	+	0.0371955i	$0.0118424\pi$
$920$	−4.34269	−	1.93349i	−0.143174	−	0.0637454i
$921$		0			0
$922$	−59.9725	−	12.7475i	−1.97509	−	0.419818i
$923$	6.15009	−	10.6523i	0.202433	−	0.350624i
$924$		0			0
$925$	2.07615	+	3.59600i	0.0682634	+	0.118236i
$926$	−2.61125	−	8.03660i	−0.0858109	−	0.264099i
$927$		0			0
$928$	10.8784	−	7.90359i	0.357100	−	0.259448i
$929$	−7.20288	+	1.53102i	−0.236319	+	0.0502311i	−0.324549	−	0.945869i	$-0.605212\pi$
$929$	−7.20288	+	1.53102i	−0.236319	+	0.0502311i	0.0882298	+	0.996100i	$0.471879\pi$
$930$		0			0
$931$	1.61515	+	15.3671i	0.0529343	+	0.503636i
$932$	32.0720	−	14.2794i	1.05055	−	0.467737i
$933$		0			0
$934$	21.5376	+	37.3043i	0.704733	+	1.22063i
$935$	−5.99776	−	2.67045i	−0.196148	−	0.0873330i
$936$		0			0
$937$	14.6033	+	44.9444i	0.477069	+	1.46827i	0.843147	+	0.537684i	$0.180701\pi$
$937$	14.6033	+	44.9444i	0.477069	+	1.46827i	−0.366077	+	0.930584i	$0.619299\pi$
$938$	−3.44213	+	32.7496i	−0.112389	+	1.06931i
$939$		0			0
$940$	5.41225	+	6.01091i	0.176528	+	0.196054i
$941$	37.5574	+	41.7118i	1.22434	+	1.35976i	0.912209	+	0.409725i	$0.134375\pi$
$941$	37.5574	+	41.7118i	1.22434	+	1.35976i	0.312128	+	0.950040i	$0.398958\pi$
$942$		0			0
$943$	−1.82847	+	17.3967i	−0.0595432	+	0.566516i
$944$	3.27233	+	10.0712i	0.106505	+	0.327789i
$945$		0			0
$946$	−13.7223	−	23.7682i	−0.446149	−	0.772772i
$947$	−6.39323	−	11.0734i	−0.207752	−	0.359837i	0.743254	−	0.669009i	$-0.233281\pi$
$947$	−6.39323	−	11.0734i	−0.207752	−	0.359837i	−0.951006	+	0.309172i	$0.899948\pi$
$948$		0			0
$949$	16.2633	−	7.24091i	0.527930	−	0.235050i
$950$	−3.69502	−	35.1558i	−0.119882	−	1.14060i
$951$		0			0
$952$	−28.7386	+	6.10858i	−0.931424	+	0.197980i
$953$	−18.8480	+	13.6939i	−0.610547	+	0.443588i	−0.849607	−	0.527417i	$-0.823161\pi$
$953$	−18.8480	+	13.6939i	−0.610547	+	0.443588i	0.239060	+	0.971005i	$0.423161\pi$
$954$		0			0
$955$	−1.26256	−	3.88576i	−0.0408555	−	0.125740i
$956$	−16.5067	−	28.5904i	−0.533864	−	0.924680i
$957$		0			0
$958$	0.182825	−	0.316662i	0.00590680	−	0.0102309i
$959$	−13.6076	−	2.89239i	−0.439413	−	0.0934001i
$960$		0			0
$961$	54.8540	+	24.4226i	1.76949	+	0.787826i
$962$	−2.55995	+	7.87872i	−0.0825362	+	0.254020i
$963$		0			0
$964$	0.772163	−	0.561009i	0.0248697	−	0.0180689i
$965$	0.767170	−	7.29913i	0.0246961	−	0.234967i
$966$		0			0
$967$	27.7586	−	48.0794i	0.892657	−	1.54613i	0.0559798	−	0.998432i	$-0.482172\pi$
$967$	27.7586	−	48.0794i	0.892657	−	1.54613i	0.836677	−	0.547696i	$-0.184495\pi$
$968$	−24.4157	+	27.1153i	−0.784752	+	0.871519i
$969$		0			0
$970$	2.59742	−	2.88473i	0.0833981	−	0.0926230i
$971$	−3.65698	−	2.65695i	−0.117358	−	0.0852656i	0.527558	−	0.849519i	$-0.323108\pi$
$971$	−3.65698	−	2.65695i	−0.117358	−	0.0852656i	−0.644916	+	0.764253i	$0.723108\pi$
$972$		0			0
$973$	4.15409	−	12.7850i	0.133174	−	0.409867i
$974$	40.8385	−	8.68049i	1.30855	−	0.278141i
$975$		0			0
$976$	3.70167	−	1.64809i	0.118487	−	0.0527540i
$977$	−26.4484	−	5.62178i	−0.846159	−	0.179857i	−0.235623	−	0.971845i	$-0.575713\pi$
$977$	−26.4484	−	5.62178i	−0.846159	−	0.179857i	−0.610537	+	0.791988i	$0.709046\pi$
$978$		0			0
$979$	5.98627	+	6.64856i	0.191322	+	0.212489i
$980$	−5.41462			−0.172964
$981$		0			0
$982$	12.5261	+	9.10076i	0.399725	+	0.290417i
$983$	−9.71793	−	4.32670i	−0.309954	−	0.138000i	0.245864	−	0.969304i	$-0.420928\pi$
$983$	−9.71793	−	4.32670i	−0.309954	−	0.138000i	−0.555818	+	0.831304i	$0.687595\pi$
$984$		0			0
$985$	−0.228602	−	0.253888i	−0.00728385	−	0.00808953i
$986$	−4.45163	−	42.3545i	−0.141769	−	1.34884i
$987$		0			0
$988$	29.7907	−	33.0859i	0.947768	−	1.05260i
$989$	16.0614			0.510723
$990$		0			0
$991$	−18.7938			−0.597005			−0.298502	−	0.954409i	$-0.596487\pi$
$991$	−18.7938			−0.597005			−0.298502	+	0.954409i	$0.596487\pi$
$992$	−29.3162	+	32.5590i	−0.930792	+	1.03375i
$993$		0			0
$994$	1.01205	+	9.62897i	0.0321001	+	0.305412i
$995$	3.48541	+	3.87094i	0.110495	+	0.122717i
$996$		0			0
$997$	−23.8686	−	10.6270i	−0.755926	−	0.336560i	−0.00767052	−	0.999971i	$-0.502442\pi$
$997$	−23.8686	−	10.6270i	−0.755926	−	0.336560i	−0.748256	+	0.663411i	$0.769108\pi$
$998$	63.9637	+	46.4723i	2.02473	+	1.47106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.280.1		72
3.2	odd	2		99.2.m.b.49.9	yes	72
9.2	odd	6		99.2.m.b.16.1	✓	72
9.4	even	3		891.2.f.e.82.1		36
9.5	odd	6		891.2.f.f.82.9		36
9.7	even	3	inner	297.2.n.b.181.9		72
11.9	even	5	inner	297.2.n.b.64.9		72
33.8	even	10		1089.2.e.o.364.18		36
33.14	odd	10		1089.2.e.p.364.1		36
33.20	odd	10		99.2.m.b.31.1	yes	72
99.14	odd	30		9801.2.a.cm.1.18		18
99.20	odd	30		99.2.m.b.97.9	yes	72
99.31	even	15		891.2.f.e.163.1		36
99.41	even	30		9801.2.a.co.1.1		18
99.47	odd	30		1089.2.e.p.727.1		36
99.58	even	15		9801.2.a.cp.1.1		18
99.74	even	30		1089.2.e.o.727.18		36
99.85	odd	30		9801.2.a.cn.1.18		18
99.86	odd	30		891.2.f.f.163.9		36
99.97	even	15	inner	297.2.n.b.262.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	9.2	odd	6
99.2.m.b.31.1	yes	72	33.20	odd	10
99.2.m.b.49.9	yes	72	3.2	odd	2
99.2.m.b.97.9	yes	72	99.20	odd	30
297.2.n.b.64.9		72	11.9	even	5	inner
297.2.n.b.181.9		72	9.7	even	3	inner
297.2.n.b.262.1		72	99.97	even	15	inner
297.2.n.b.280.1		72	1.1	even	1	trivial
891.2.f.e.82.1		36	9.4	even	3
891.2.f.e.163.1		36	99.31	even	15
891.2.f.f.82.9		36	9.5	odd	6
891.2.f.f.163.9		36	99.86	odd	30
1089.2.e.o.364.18		36	33.8	even	10
1089.2.e.o.727.18		36	99.74	even	30
1089.2.e.p.364.1		36	33.14	odd	10
1089.2.e.p.727.1		36	99.47	odd	30
9801.2.a.cm.1.18		18	99.14	odd	30
9801.2.a.cn.1.18		18	99.85	odd	30
9801.2.a.co.1.1		18	99.41	even	30
9801.2.a.cp.1.1		18	99.58	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.55841 + 1.73079i) q^{2} +(-0.357932 - 3.40549i) q^{4} +(0.212128 + 0.235592i) q^{5} +(-1.29586 - 0.576953i) q^{7} +(2.68358 + 1.94973i) q^{8} -0.738340 q^{10} +(-2.21923 - 2.46476i) q^{11} +(-4.10532 - 0.872613i) q^{13} +(3.01805 - 1.34372i) q^{14} +(-0.857827 + 0.182337i) q^{16} +(1.92957 - 5.93860i) q^{17} +(-2.50622 - 1.82087i) q^{19} +(0.726379 - 0.806725i) q^{20} +(7.72443 + 7.98214e-5i) q^{22} +(-2.26025 + 3.91487i) q^{23} +(0.512137 - 4.87266i) q^{25} +(7.90807 - 5.74555i) q^{26} +(-1.50098 + 4.61954i) q^{28} +(-2.67527 - 1.19111i) q^{29} +(9.33325 + 1.98384i) q^{31} +(-2.29583 + 3.97649i) q^{32} +(7.27140 + 12.5944i) q^{34} +(-0.138962 - 0.427681i) q^{35} +(-0.685637 + 0.498145i) q^{37} +(7.05725 - 1.50006i) q^{38} +(0.109920 + 1.04582i) q^{40} +(3.53506 - 1.57391i) q^{41} +(-1.77651 - 3.07700i) q^{43} +(-7.59937 + 8.43978i) q^{44} +(-3.25341 - 10.0130i) q^{46} +(-0.778841 + 7.41018i) q^{47} +(-3.33754 - 3.70672i) q^{49} +(7.63541 + 8.47998i) q^{50} +(-1.50225 + 14.2930i) q^{52} +(-2.06517 - 6.35595i) q^{53} +(0.109916 - 1.04568i) q^{55} +(-2.35263 - 4.07487i) q^{56} +(6.23070 - 2.77409i) q^{58} +(-1.26216 - 12.0086i) q^{59} +(-4.51935 + 0.960618i) q^{61} +(-17.9786 + 13.0622i) q^{62} +(-3.84663 - 11.8387i) q^{64} +(-0.665272 - 1.15229i) q^{65} +(-4.98385 + 8.63229i) q^{67} +(-20.9145 - 4.44552i) q^{68} +(0.956783 + 0.425987i) q^{70} +(-0.905630 + 2.78724i) q^{71} +(-3.43158 + 2.49319i) q^{73} +(0.206320 - 1.96300i) q^{74} +(-5.30392 + 9.18665i) q^{76} +(1.45376 + 4.47436i) q^{77} +(-2.26299 + 2.51331i) q^{79} +(-0.224926 - 0.163418i) q^{80} +(-2.78496 + 8.57123i) q^{82} +(-13.1927 + 2.80420i) q^{83} +(1.80840 - 0.805152i) q^{85} +(8.09416 + 1.72047i) q^{86} +(-1.14986 - 10.9413i) q^{88} -2.69745 q^{89} +(4.81645 + 3.49936i) q^{91} +(14.1411 + 6.29601i) q^{92} +(-11.6117 - 12.8961i) q^{94} +(-0.102656 - 0.976702i) q^{95} +(-3.51792 + 3.90704i) q^{97} +11.6168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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