LMFDB - Embedded newform 369.2.u.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	369.46
Dual form			369.2.u.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42655 - 1.96347i) q^{2} +(-1.20216 + 3.69986i) q^{4} +(-0.110420 - 0.0358775i) q^{5} +(-0.422339 - 2.66654i) q^{7} +(4.36309 - 1.41766i) q^{8} +O(q^{10})$	\(q+(-1.42655 - 1.96347i) q^{2} +(-1.20216 + 3.69986i) q^{4} +(-0.110420 - 0.0358775i) q^{5} +(-0.422339 - 2.66654i) q^{7} +(4.36309 - 1.41766i) q^{8} +(0.0870742 + 0.267987i) q^{10} +(1.53663 - 3.01580i) q^{11} +(-1.03889 - 0.164544i) q^{13} +(-4.63320 + 4.63320i) q^{14} +(-2.71311 - 1.97119i) q^{16} +(-3.25831 - 1.66019i) q^{17} +(-2.25168 + 0.356630i) q^{19} +(0.265483 - 0.365406i) q^{20} +(-8.11352 + 1.28505i) q^{22} +(-6.06568 + 4.40698i) q^{23} +(-4.03418 - 2.93100i) q^{25} +(1.15895 + 2.27456i) q^{26} +(10.3735 + 1.64301i) q^{28} +(-1.31408 + 0.669558i) q^{29} +(-0.964816 - 2.96940i) q^{31} -1.03614i q^{32} +(1.38839 + 8.76594i) q^{34} +(-0.0490344 + 0.309591i) q^{35} +(-0.348766 + 1.07339i) q^{37} +(3.91235 + 3.91235i) q^{38} -0.532633 q^{40} +(1.32339 + 6.26487i) q^{41} +(0.583672 + 0.803355i) q^{43} +(9.31076 + 9.31076i) q^{44} +(17.3060 + 5.62305i) q^{46} +(1.73020 - 10.9241i) q^{47} +(-0.274693 + 0.0892531i) q^{49} +12.1022i q^{50} +(1.85769 - 3.64593i) q^{52} +(-0.482987 + 0.246094i) q^{53} +(-0.277873 + 0.277873i) q^{55} +(-5.62295 - 11.0357i) q^{56} +(3.18926 + 1.62501i) q^{58} +(1.57246 - 1.14246i) q^{59} +(-5.95937 + 8.20238i) q^{61} +(-4.45398 + 6.13037i) q^{62} +(-7.46066 + 5.42048i) q^{64} +(0.108810 + 0.0554416i) q^{65} +(-6.02949 - 11.8335i) q^{67} +(10.0595 - 10.0595i) q^{68} +(0.677824 - 0.345368i) q^{70} +(4.28484 - 8.40947i) q^{71} -10.9108i q^{73} +(2.60511 - 0.846450i) q^{74} +(1.38738 - 8.75960i) q^{76} +(-8.69075 - 2.82380i) q^{77} +(7.58864 + 7.58864i) q^{79} +(0.228859 + 0.314998i) q^{80} +(10.4130 - 11.5356i) q^{82} +0.635212 q^{83} +(0.300218 + 0.300218i) q^{85} +(0.744731 - 2.29205i) q^{86} +(2.42908 - 15.3366i) q^{88} +(-0.753161 - 4.75527i) q^{89} +2.83974i q^{91} +(-9.01328 - 27.7400i) q^{92} +(-23.9173 + 12.1865i) q^{94} +(0.261424 + 0.0414055i) q^{95} +(-1.25412 - 2.46135i) q^{97} +(0.567108 + 0.412028i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−1.42655	−	1.96347i	−1.00872	−	1.38838i	−0.919818	−	0.392344i	$-0.871664\pi$
$2$	−1.42655	−	1.96347i	−1.00872	−	1.38838i	−0.0889021	−	0.996040i	$-0.528336\pi$
$3$		0			0
$3$		0			0
$4$	−1.20216	+	3.69986i	−0.601078	+	1.84993i
$5$	−0.110420	−	0.0358775i	−0.0493811	−	0.0160449i	0.284222	−	0.958758i	$-0.408265\pi$
$5$	−0.110420	−	0.0358775i	−0.0493811	−	0.0160449i	−0.333603	+	0.942714i	$0.608265\pi$
$6$		0			0
$7$	−0.422339	−	2.66654i	−0.159629	−	1.00786i	−0.929275	−	0.369388i	$-0.879567\pi$
$7$	−0.422339	−	2.66654i	−0.159629	−	1.00786i	0.769646	−	0.638471i	$-0.220433\pi$
$8$	4.36309	−	1.41766i	1.54259	−	0.501217i
$9$		0			0
$10$	0.0870742	+	0.267987i	0.0275353	+	0.0847449i
$11$	1.53663	−	3.01580i	0.463311	−	0.909299i	−0.534626	−	0.845089i	$-0.679547\pi$
$11$	1.53663	−	3.01580i	0.463311	−	0.909299i	0.997936	−	0.0642096i	$-0.0204526\pi$
$12$		0			0
$13$	−1.03889	−	0.164544i	−0.288136	−	0.0456362i	0.0106934	−	0.999943i	$-0.496596\pi$
$13$	−1.03889	−	0.164544i	−0.288136	−	0.0456362i	−0.298829	+	0.954307i	$0.596596\pi$
$14$	−4.63320	+	4.63320i	−1.23827	+	1.23827i
$15$		0			0
$16$	−2.71311	−	1.97119i	−0.678278	−	0.492798i
$17$	−3.25831	−	1.66019i	−0.790256	−	0.402655i	0.0117807	−	0.999931i	$-0.496250\pi$
$17$	−3.25831	−	1.66019i	−0.790256	−	0.402655i	−0.802036	+	0.597275i	$0.796250\pi$
$18$		0			0
$19$	−2.25168	+	0.356630i	−0.516570	+	0.0818166i	−0.409276	−	0.912411i	$-0.634219\pi$
$19$	−2.25168	+	0.356630i	−0.516570	+	0.0818166i	−0.107294	+	0.994227i	$0.534219\pi$
$20$	0.265483	−	0.365406i	0.0593638	−	0.0817073i
$21$		0			0
$22$	−8.11352	+	1.28505i	−1.72981	+	0.273975i
$23$	−6.06568	+	4.40698i	−1.26478	+	0.918918i	−0.998982	−	0.0451098i	$-0.985636\pi$
$23$	−6.06568	+	4.40698i	−1.26478	+	0.918918i	−0.265800	+	0.964028i	$0.585636\pi$
$24$		0			0
$25$	−4.03418	−	2.93100i	−0.806836	−	0.586201i
$26$	1.15895	+	2.27456i	0.227288	+	0.446078i
$27$		0			0
$28$	10.3735	+	1.64301i	1.96042	+	0.310499i
$29$	−1.31408	+	0.669558i	−0.244019	+	0.124334i	−0.571723	−	0.820446i	$-0.693725\pi$
$29$	−1.31408	+	0.669558i	−0.244019	+	0.124334i	0.327705	+	0.944780i	$0.393725\pi$
$30$		0			0
$31$	−0.964816	−	2.96940i	−0.173286	−	0.533320i	0.826265	−	0.563282i	$-0.190461\pi$
$31$	−0.964816	−	2.96940i	−0.173286	−	0.533320i	−0.999551	+	0.0299620i	$0.990461\pi$
$32$		−	1.03614i		−	0.183165i
$33$		0			0
$34$	1.38839	+	8.76594i	0.238107	+	1.50335i
$35$	−0.0490344	+	0.309591i	−0.00828833	+	0.0523305i
$36$		0			0
$37$	−0.348766	+	1.07339i	−0.0573368	+	0.176465i	−0.975623	−	0.219452i	$-0.929573\pi$
$37$	−0.348766	+	1.07339i	−0.0573368	+	0.176465i	0.918286	+	0.395917i	$0.129573\pi$
$38$	3.91235	+	3.91235i	0.634668	+	0.634668i
$39$		0			0
$40$	−0.532633			−0.0842167
$41$	1.32339	+	6.26487i	0.206678	+	0.978409i
$41$	1.32339	+	6.26487i	0.206678	+	0.978409i
$42$		0			0
$43$	0.583672	+	0.803355i	0.0890091	+	0.122511i	0.851199	−	0.524843i	$-0.175876\pi$
$43$	0.583672	+	0.803355i	0.0890091	+	0.122511i	−0.762190	+	0.647353i	$0.775876\pi$
$44$	9.31076	+	9.31076i	1.40365	+	1.40365i
$45$		0			0
$46$	17.3060	+	5.62305i	2.55162	+	0.829073i
$47$	1.73020	−	10.9241i	0.252376	−	1.59344i	−0.457563	−	0.889177i	$-0.651278\pi$
$47$	1.73020	−	10.9241i	0.252376	−	1.59344i	0.709939	−	0.704263i	$-0.248722\pi$
$48$		0			0
$49$	−0.274693	+	0.0892531i	−0.0392418	+	0.0127504i
$50$			12.1022i			1.71151i
$51$		0			0
$52$	1.85769	−	3.64593i	0.257616	−	0.505599i
$53$	−0.482987	+	0.246094i	−0.0663434	+	0.0338036i	−0.486847	−	0.873487i	$-0.661853\pi$
$53$	−0.482987	+	0.246094i	−0.0663434	+	0.0338036i	0.420504	+	0.907291i	$0.361853\pi$
$54$		0			0
$55$	−0.277873	+	0.277873i	−0.0374684	+	0.0374684i
$56$	−5.62295	−	11.0357i	−0.751398	−	1.47470i
$57$		0			0
$58$	3.18926	+	1.62501i	0.418770	+	0.213374i
$59$	1.57246	−	1.14246i	0.204717	−	0.148735i	−0.480703	−	0.876883i	$-0.659619\pi$
$59$	1.57246	−	1.14246i	0.204717	−	0.148735i	0.685420	+	0.728148i	$0.259619\pi$
$60$		0			0
$61$	−5.95937	+	8.20238i	−0.763020	+	1.05021i	0.233937	+	0.972252i	$0.424839\pi$
$61$	−5.95937	+	8.20238i	−0.763020	+	1.05021i	−0.996957	+	0.0779548i	$0.975161\pi$
$62$	−4.45398	+	6.13037i	−0.565656	+	0.778558i
$63$		0			0
$64$	−7.46066	+	5.42048i	−0.932582	+	0.677561i
$65$	0.108810	+	0.0554416i	0.0134962	+	0.00687668i
$66$		0			0
$67$	−6.02949	−	11.8335i	−0.736619	−	1.44570i	−0.889254	−	0.457414i	$-0.848776\pi$
$67$	−6.02949	−	11.8335i	−0.736619	−	1.44570i	0.152635	−	0.988283i	$-0.451224\pi$
$68$	10.0595	−	10.0595i	1.21989	−	1.21989i
$69$		0			0
$70$	0.677824	−	0.345368i	0.0810154	−	0.0412794i
$71$	4.28484	−	8.40947i	0.508517	−	0.998021i	−0.483902	−	0.875122i	$-0.660781\pi$
$71$	4.28484	−	8.40947i	0.508517	−	0.998021i	0.992419	−	0.122899i	$-0.0392190\pi$
$72$		0			0
$73$		−	10.9108i		−	1.27702i	−0.769615	−	0.638508i	$-0.779552\pi$
$73$		−	10.9108i		−	1.27702i	0.769615	−	0.638508i	$-0.220448\pi$
$74$	2.60511	−	0.846450i	0.302837	−	0.0983978i
$75$		0			0
$76$	1.38738	−	8.75960i	0.159144	−	1.00480i
$77$	−8.69075	−	2.82380i	−0.990403	−	0.321801i
$78$		0			0
$79$	7.58864	+	7.58864i	0.853789	+	0.853789i	0.990597	−	0.136809i	$-0.0436846\pi$
$79$	7.58864	+	7.58864i	0.853789	+	0.853789i	−0.136809	+	0.990597i	$0.543685\pi$
$80$	0.228859	+	0.314998i	0.0255873	+	0.0352178i
$81$		0			0
$82$	10.4130	−	11.5356i	1.14993	−	1.27389i
$83$	0.635212			0.0697236			0.0348618	−	0.999392i	$-0.488901\pi$
$83$	0.635212			0.0697236			0.0348618	+	0.999392i	$0.488901\pi$
$84$		0			0
$85$	0.300218	+	0.300218i	0.0325632	+	0.0325632i
$86$	0.744731	−	2.29205i	0.0803064	−	0.247158i
$87$		0			0
$88$	2.42908	−	15.3366i	0.258941	−	1.63489i
$89$	−0.753161	−	4.75527i	−0.0798350	−	0.504058i	−0.994909	−	0.100773i	$-0.967868\pi$
$89$	−0.753161	−	4.75527i	−0.0798350	−	0.504058i	0.915074	−	0.403285i	$-0.132132\pi$
$90$		0			0
$91$			2.83974i			0.297685i
$92$	−9.01328	−	27.7400i	−0.939699	−	2.89210i
$93$		0			0
$94$	−23.9173	+	12.1865i	−2.46689	+	1.25694i
$95$	0.261424	+	0.0414055i	0.0268216	+	0.00424812i
$96$		0			0
$97$	−1.25412	−	2.46135i	−0.127337	−	0.249913i	0.818533	−	0.574460i	$-0.194788\pi$
$97$	−1.25412	−	2.46135i	−0.127337	−	0.249913i	−0.945869	+	0.324548i	$0.894788\pi$
$98$	0.567108	+	0.412028i	0.0572866	+	0.0416211i
$99$		0			0
$100$	15.6940	−	11.4024i	1.56940	−	1.14024i
$101$	−9.34392	+	1.47993i	−0.929755	+	0.147259i	−0.602901	−	0.797816i	$-0.705988\pi$
$101$	−9.34392	+	1.47993i	−0.929755	+	0.147259i	−0.326854	+	0.945075i	$0.605988\pi$
$102$		0			0
$103$	3.69313	−	5.08316i	0.363895	−	0.500858i	−0.587334	−	0.809345i	$-0.699822\pi$
$103$	3.69313	−	5.08316i	0.363895	−	0.500858i	0.951229	+	0.308486i	$0.0998225\pi$
$104$	−4.76603	+	0.754866i	−0.467348	+	0.0740207i
$105$		0			0
$106$	1.17220	+	0.597267i	0.113854	+	0.0580117i
$107$	11.1143	+	8.07504i	1.07446	+	0.780644i	0.976709	−	0.214567i	$-0.0688340\pi$
$107$	11.1143	+	8.07504i	1.07446	+	0.780644i	0.0977545	+	0.995211i	$0.468834\pi$
$108$		0			0
$109$	10.4978	−	10.4978i	1.00551	−	1.00551i	0.00552465	−	0.999985i	$-0.498241\pi$
$109$	10.4978	−	10.4978i	1.00551	−	1.00551i	0.999985	−	0.00552465i	$-0.00175856\pi$
$110$	0.941996	+	0.149197i	0.0898158	+	0.0142254i
$111$		0			0
$112$	−4.11042	+	8.06715i	−0.388398	+	0.762274i
$113$	−2.45600	−	7.55880i	−0.231041	−	0.711073i	−0.997622	−	0.0689242i	$-0.978043\pi$
$113$	−2.45600	−	7.55880i	−0.231041	−	0.711073i	0.766580	−	0.642148i	$-0.221957\pi$
$114$		0			0
$115$	0.827882	−	0.268995i	0.0772004	−	0.0250839i
$116$	−0.897537	−	5.66683i	−0.0833342	−	0.526151i
$117$		0			0
$118$	−4.48637	−	1.45771i	−0.413004	−	0.134193i
$119$	−3.05086	+	9.38959i	−0.279672	+	0.860742i
$120$		0			0
$121$	−0.268199	−	0.369145i	−0.0243818	−	0.0335586i
$122$	24.6065			2.22776
$123$		0			0
$124$	12.1462			1.09076
$125$	0.681511	+	0.938019i	0.0609562	+	0.0838990i
$126$		0			0
$127$	−2.50455	+	7.70820i	−0.222243	+	0.683993i	0.776317	+	0.630343i	$0.217086\pi$
$127$	−2.50455	+	7.70820i	−0.222243	+	0.683993i	−0.998560	+	0.0536500i	$0.982914\pi$
$128$	19.3151	+	6.27585i	1.70723	+	0.554712i
$129$		0			0
$130$	−0.0463648	−	0.292736i	−0.00406646	−	0.0256746i
$131$	10.8285	−	3.51838i	0.946087	−	0.307402i	0.204962	−	0.978770i	$-0.434293\pi$
$131$	10.8285	−	3.51838i	0.946087	−	0.307402i	0.741125	+	0.671368i	$0.234293\pi$
$132$		0			0
$133$	1.90194	+	5.85357i	0.164919	+	0.507569i
$134$	−14.6335	+	28.7198i	−1.26414	+	2.48101i
$135$		0			0
$136$	−16.5699	−	2.62441i	−1.42086	−	0.225041i
$137$	−4.26765	+	4.26765i	−0.364610	+	0.364610i	−0.865507	−	0.500897i	$-0.833004\pi$
$137$	−4.26765	+	4.26765i	−0.364610	+	0.364610i	0.500897	+	0.865507i	$0.333004\pi$
$138$		0			0
$139$	14.2798	+	10.3749i	1.21120	+	0.879987i	0.995339	−	0.0964369i	$-0.0307446\pi$
$139$	14.2798	+	10.3749i	1.21120	+	0.879987i	0.215860	+	0.976424i	$0.430745\pi$
$140$	−1.08650	−	0.553597i	−0.0918257	−	0.0467875i
$141$		0			0
$142$	−22.6243	+	3.58334i	−1.89859	+	0.300707i
$143$	−2.09262	+	2.88024i	−0.174993	+	0.240858i
$144$		0			0
$145$	0.169122	−	0.0267864i	0.0140449	−	0.00222449i
$146$	−21.4231	+	15.5648i	−1.77299	+	1.28815i
$147$		0			0
$148$	−3.55212	−	2.58077i	−0.291983	−	0.212138i
$149$	−0.491547	−	0.964715i	−0.0402691	−	0.0790326i	0.869995	−	0.493060i	$-0.164122\pi$
$149$	−0.491547	−	0.964715i	−0.0402691	−	0.0790326i	−0.910264	+	0.414028i	$0.864122\pi$
$150$		0			0
$151$	12.9796	+	2.05577i	1.05626	+	0.167296i	0.660324	−	0.750980i	$-0.270419\pi$
$151$	12.9796	+	2.05577i	1.05626	+	0.167296i	0.395940	+	0.918276i	$0.370419\pi$
$152$	−9.31869	+	4.74811i	−0.755846	+	0.385123i
$153$		0			0
$154$	6.85331	+	21.0923i	0.552255	+	1.69967i
$155$			0.362495i			0.0291163i
$156$		0			0
$157$	−2.56436	−	16.1907i	−0.204658	−	1.29216i	−0.849396	−	0.527757i	$-0.823033\pi$
$157$	−2.56436	−	16.1907i	−0.204658	−	1.29216i	0.644737	−	0.764404i	$-0.276967\pi$
$158$	4.07454	−	25.7256i	0.324153	−	2.04662i
$159$		0			0
$160$	−0.0371741	+	0.114410i	−0.00293887	+	0.00904492i
$161$	14.3132	+	14.3132i	1.12804	+	1.12804i
$162$		0			0
$163$	14.6327			1.14612			0.573059	−	0.819514i	$-0.305757\pi$
$163$	14.6327			1.14612			0.573059	+	0.819514i	$0.305757\pi$
$164$	−24.7700	−	2.63502i	−1.93422	−	0.205761i
$165$		0			0
$166$	−0.906159	−	1.24722i	−0.0703316	−	0.0968032i
$167$	8.21554	+	8.21554i	0.635738	+	0.635738i	0.949501	−	0.313764i	$-0.101590\pi$
$167$	8.21554	+	8.21554i	0.635738	+	0.635738i	−0.313764	+	0.949501i	$0.601590\pi$
$168$		0			0
$169$	−11.3115	−	3.67534i	−0.870117	−	0.282718i
$170$	0.161195	−	1.01774i	0.0123631	−	0.0780573i
$171$		0			0
$172$	−3.67396	+	1.19374i	−0.280137	+	0.0910220i
$173$		−	2.01872i		−	0.153480i	−0.997051	−	0.0767400i	$-0.975549\pi$
$173$		−	2.01872i		−	0.153480i	0.997051	−	0.0767400i	$-0.0244512\pi$
$174$		0			0
$175$	−6.11186	+	11.9952i	−0.462013	+	0.906752i
$176$	−10.1138	+	5.15322i	−0.762354	+	0.388439i
$177$		0			0
$178$	−8.26243	+	8.26243i	−0.619295	+	0.619295i
$179$	−8.10933	−	15.9155i	−0.606120	−	1.18958i	−0.966475	−	0.256762i	$-0.917344\pi$
$179$	−8.10933	−	15.9155i	−0.606120	−	1.18958i	0.360355	−	0.932815i	$-0.382656\pi$
$180$		0			0
$181$	−1.57724	−	0.803644i	−0.117235	−	0.0597344i	0.394389	−	0.918943i	$-0.370956\pi$
$181$	−1.57724	−	0.803644i	−0.117235	−	0.0597344i	−0.511625	+	0.859209i	$0.670956\pi$
$182$	5.57574	−	4.05101i	0.413302	−	0.300281i
$183$		0			0
$184$	−20.2176	+	27.8271i	−1.49046	+	2.05144i
$185$	0.0770212	−	0.106011i	0.00566271	−	0.00779406i
$186$		0			0
$187$	−10.0136	+	7.27532i	−0.732268	+	0.532024i
$188$	38.3375	+	19.5339i	2.79605	+	1.42466i
$189$		0			0
$190$	−0.291635	−	0.572366i	−0.0211574	−	0.0415238i
$191$	3.86040	−	3.86040i	0.279329	−	0.279329i	−0.553512	−	0.832841i	$-0.686713\pi$
$191$	3.86040	−	3.86040i	0.279329	−	0.279329i	0.832841	+	0.553512i	$0.186713\pi$
$192$		0			0
$193$	−5.84374	+	2.97753i	−0.420641	+	0.214328i	−0.651482	−	0.758664i	$-0.725852\pi$
$193$	−5.84374	+	2.97753i	−0.420641	+	0.214328i	0.230841	+	0.972992i	$0.425852\pi$
$194$	−3.04374	+	5.97367i	−0.218527	+	0.428884i
$195$		0			0
$196$		−	1.12362i		−	0.0802586i
$197$	4.06150	−	1.31966i	0.289370	−	0.0940220i	−0.160735	−	0.986998i	$-0.551387\pi$
$197$	4.06150	−	1.31966i	0.289370	−	0.0940220i	0.450105	+	0.892976i	$0.351387\pi$
$198$		0			0
$199$	−2.50210	+	15.7976i	−0.177369	+	1.11986i	0.724952	+	0.688799i	$0.241862\pi$
$199$	−2.50210	+	15.7976i	−0.177369	+	1.11986i	−0.902321	+	0.431064i	$0.858138\pi$
$200$	−21.7567	−	7.06917i	−1.53843	−	0.499866i
$201$		0			0
$202$	16.2353	+	16.2353i	1.14231	+	1.14231i
$203$	2.34039	+	3.22128i	0.164263	+	0.226089i
$204$		0			0
$205$	0.0786403	−	0.739245i	0.00549248	−	0.0516311i
$206$	−15.2491			−1.06245
$207$		0			0
$208$	2.49427	+	2.49427i	0.172947	+	0.172947i
$209$	−2.38446	+	7.33862i	−0.164937	+	0.507623i
$210$		0			0
$211$	3.90790	−	24.6735i	0.269031	−	1.69859i	−0.369691	−	0.929155i	$-0.620536\pi$
$211$	3.90790	−	24.6735i	0.269031	−	1.69859i	0.638722	−	0.769438i	$-0.279464\pi$
$212$	−0.329887	−	2.08283i	−0.0226567	−	0.143049i
$213$		0			0
$214$		−	33.3421i		−	2.27922i
$215$	−0.0356264	−	0.109647i	−0.00242970	−	0.00747785i
$216$		0			0
$217$	−7.51055	+	3.82682i	−0.509849	+	0.259781i
$218$	−35.5878	−	5.63656i	−2.41031	−	0.381756i
$219$		0			0
$220$	−0.694044	−	1.36214i	−0.0467924	−	0.0918353i
$221$	3.11184	+	2.26089i	0.209325	+	0.152084i
$222$		0			0
$223$	−2.68513	+	1.95086i	−0.179809	+	0.130639i	−0.674049	−	0.738686i	$-0.735446\pi$
$223$	−2.68513	+	1.95086i	−0.179809	+	0.130639i	0.494240	+	0.869326i	$0.335446\pi$
$224$	−2.76291	+	0.437603i	−0.184605	+	0.0292386i
$225$		0			0
$226$	−11.3379	+	15.6053i	−0.754186	+	1.03805i
$227$	7.61270	−	1.20573i	0.505272	−	0.0800273i	0.101406	−	0.994845i	$-0.467666\pi$
$227$	7.61270	−	1.20573i	0.505272	−	0.0800273i	0.403867	+	0.914818i	$0.367666\pi$
$228$		0			0
$229$	4.43150	+	2.25796i	0.292842	+	0.149210i	0.594240	−	0.804288i	$-0.297453\pi$
$229$	4.43150	+	2.25796i	0.292842	+	0.149210i	−0.301398	+	0.953499i	$0.597453\pi$
$230$	−1.70918	−	1.24179i	−0.112700	−	0.0818811i
$231$		0			0
$232$	−4.78426	+	4.78426i	−0.314102	+	0.314102i
$233$	10.5733	+	1.67465i	0.692680	+	0.109710i	0.492841	−	0.870119i	$-0.335958\pi$
$233$	10.5733	+	1.67465i	0.692680	+	0.109710i	0.199838	+	0.979829i	$0.435958\pi$
$234$		0			0
$235$	−0.582977	+	1.14416i	−0.0380292	+	0.0746366i
$236$	2.33659	+	7.19128i	0.152099	+	0.468113i
$237$		0			0
$238$	22.7884	−	7.40440i	1.47715	−	0.479956i
$239$	1.44605	+	9.13003i	0.0935375	+	0.590572i	0.989284	+	0.146006i	$0.0466420\pi$
$239$	1.44605	+	9.13003i	0.0935375	+	0.590572i	−0.895746	+	0.444566i	$0.853358\pi$
$240$		0			0
$241$	−26.9539	−	8.75786i	−1.73626	−	0.564144i	−0.741925	−	0.670482i	$-0.766087\pi$
$241$	−26.9539	−	8.75786i	−1.73626	−	0.564144i	−0.994330	+	0.106339i	$0.966087\pi$
$242$	−0.342207	+	1.05320i	−0.0219979	+	0.0677025i
$243$		0			0
$244$	−23.1835	−	31.9094i	−1.48417	−	2.04279i
$245$	0.0335337			0.00214239
$246$		0			0
$247$	2.39792			0.152576
$248$	−8.41916	−	11.5880i	−0.534617	−	0.735838i
$249$		0			0
$250$	0.869568	−	2.67626i	0.0549963	−	0.169261i
$251$	−6.28383	−	2.04174i	−0.396632	−	0.128874i	0.103908	−	0.994587i	$-0.466865\pi$
$251$	−6.28383	−	2.04174i	−0.396632	−	0.128874i	−0.500540	+	0.865713i	$0.666865\pi$
$252$		0			0
$253$	3.96987	+	25.0648i	0.249584	+	1.57581i
$254$	18.7077	−	6.07850i	1.17383	−	0.381399i
$255$		0			0
$256$	−9.53197	−	29.3364i	−0.595748	−	1.83352i
$257$	1.99593	−	3.91722i	0.124502	−	0.244350i	−0.820339	−	0.571877i	$-0.806215\pi$
$257$	1.99593	−	3.91722i	0.124502	−	0.244350i	0.944842	+	0.327527i	$0.106215\pi$
$258$		0			0
$259$	3.00954	+	0.476665i	0.187004	+	0.0296185i
$260$	−0.335933	+	0.335933i	−0.0208337	+	0.0208337i
$261$		0			0
$262$	−22.3555	−	16.2422i	−1.38113	−	1.00345i
$263$	11.1561	+	5.68432i	0.687915	+	0.350510i	0.762757	−	0.646685i	$-0.223845\pi$
$263$	11.1561	+	5.68432i	0.687915	+	0.350510i	−0.0748417	+	0.997195i	$0.523845\pi$
$264$		0			0
$265$	0.0621605	−	0.00984525i	0.00381849	−	0.000604789i
$266$	8.78012	−	12.0848i	0.538344	−	0.740967i
$267$		0			0
$268$	51.0308	−	8.08248i	3.11720	−	0.493716i
$269$	2.86327	−	2.08029i	0.174577	−	0.126838i	−0.497066	−	0.867713i	$-0.665589\pi$
$269$	2.86327	−	2.08029i	0.174577	−	0.126838i	0.671642	+	0.740875i	$0.265589\pi$
$270$		0			0
$271$	3.09632	+	2.24961i	0.188088	+	0.136654i	0.677845	−	0.735205i	$-0.262914\pi$
$271$	3.09632	+	2.24961i	0.188088	+	0.136654i	−0.489756	+	0.871859i	$0.662914\pi$
$272$	5.56760	+	10.9270i	0.337585	+	0.662549i
$273$		0			0
$274$	14.4674	+	2.29141i	0.874009	+	0.138429i
$275$	−15.0384	+	7.66243i	−0.906847	+	0.462062i
$276$		0			0
$277$	9.27253	+	28.5379i	0.557132	+	1.71468i	0.690244	+	0.723576i	$0.257503\pi$
$277$	9.27253	+	28.5379i	0.557132	+	1.71468i	−0.133112	+	0.991101i	$0.542497\pi$
$278$		−	42.8383i		−	2.56927i
$279$		0			0
$280$	0.224952	+	1.42029i	0.0134434	+	0.0848785i
$281$	−0.860451	+	5.43268i	−0.0513302	+	0.324086i	0.948640	+	0.316358i	$0.102460\pi$
$281$	−0.860451	+	5.43268i	−0.0513302	+	0.324086i	−0.999970	+	0.00772841i	$0.997540\pi$
$282$		0			0
$283$	9.37505	−	28.8534i	0.557289	−	1.71516i	−0.132533	−	0.991179i	$-0.542311\pi$
$283$	9.37505	−	28.8534i	0.557289	−	1.71516i	0.689822	−	0.723979i	$-0.257689\pi$
$284$	25.9628	+	25.9628i	1.54061	+	1.54061i
$285$		0			0
$286$	8.64049			0.510923
$287$	16.1466	−	6.17477i	0.953106	−	0.364485i
$288$		0			0
$289$	−2.13201	−	2.93447i	−0.125413	−	0.172616i
$290$	−0.293855	−	0.293855i	−0.0172558	−	0.0172558i
$291$		0			0
$292$	40.3685	+	13.1165i	2.36239	+	0.767587i
$293$	3.14362	−	19.8480i	0.183652	−	1.15953i	−0.707798	−	0.706415i	$-0.750311\pi$
$293$	3.14362	−	19.8480i	0.183652	−	1.15953i	0.891450	−	0.453119i	$-0.149689\pi$
$294$		0			0
$295$	−0.214619	+	0.0697339i	−0.0124956	+	0.00406006i
$296$			5.17774i			0.300950i
$297$		0			0
$298$	−1.19298	+	2.34135i	−0.0691073	+	0.135631i
$299$	7.02671	−	3.58029i	0.406365	−	0.207053i
$300$		0			0
$301$	1.89568	−	1.89568i	0.109265	−	0.109265i
$302$	−14.4796	−	28.4177i	−0.833205	−	1.63526i
$303$		0			0
$304$	6.81204	+	3.47091i	0.390697	+	0.199070i
$305$	0.952313	−	0.691896i	0.0545293	−	0.0396178i
$306$		0			0
$307$	0.132775	−	0.182749i	0.00757787	−	0.0104300i	−0.805211	−	0.592988i	$-0.797948\pi$
$307$	0.132775	−	0.182749i	0.00757787	−	0.0104300i	0.812789	+	0.582558i	$0.197948\pi$
$308$	20.8953	−	28.7599i	1.19062	−	1.63875i
$309$		0			0
$310$	0.711749	−	0.517116i	0.0404246	−	0.0293702i
$311$	−12.9469	−	6.59679i	−0.734153	−	0.374070i	0.0465963	−	0.998914i	$-0.485163\pi$
$311$	−12.9469	−	6.59679i	−0.734153	−	0.374070i	−0.780750	+	0.624844i	$0.785163\pi$
$312$		0			0
$313$	3.71571	+	7.29249i	0.210024	+	0.412196i	0.971855	−	0.235581i	$-0.0756992\pi$
$313$	3.71571	+	7.29249i	0.210024	+	0.412196i	−0.761831	+	0.647776i	$0.775699\pi$
$314$	−28.1319	+	28.1319i	−1.58757	+	1.58757i
$315$		0			0
$316$	−37.1996	+	18.9541i	−2.09264	+	1.06625i
$317$	−4.35992	+	8.55683i	−0.244878	+	0.480600i	−0.980430	−	0.196868i	$-0.936923\pi$
$317$	−4.35992	+	8.55683i	−0.244878	+	0.480600i	0.735552	+	0.677468i	$0.236923\pi$
$318$		0			0
$319$			4.99187i			0.279491i
$320$	1.01828	−	0.330858i	0.0569234	−	0.0184955i
$321$		0			0
$322$	7.68512	−	48.5219i	0.428275	−	2.70402i
$323$	7.92873	+	2.57620i	0.441166	+	0.143344i
$324$		0			0
$325$	3.70878	+	3.70878i	0.205726	+	0.205726i
$326$	−20.8742	−	28.7308i	−1.15611	−	1.59125i
$327$		0			0
$328$	14.6555	+	25.4581i	0.809214	+	1.40569i
$329$	−29.8603			−1.64625
$330$		0			0
$331$	3.24814	+	3.24814i	0.178534	+	0.178534i	0.790716	−	0.612183i	$-0.209708\pi$
$331$	3.24814	+	3.24814i	0.178534	+	0.178534i	−0.612183	+	0.790716i	$0.709708\pi$
$332$	−0.763624	+	2.35019i	−0.0419093	+	0.128984i
$333$		0			0
$334$	4.41114	−	27.8508i	0.241367	−	1.52393i
$335$	0.241216	+	1.52298i	0.0131790	+	0.0832092i
$336$		0			0
$337$		−	17.7306i		−	0.965849i	−0.875662	−	0.482924i	$-0.839575\pi$
$337$		−	17.7306i		−	0.965849i	0.875662	−	0.482924i	$-0.160425\pi$
$338$	8.91999	+	27.4529i	0.485183	+	1.49324i
$339$		0			0
$340$	−1.47167	+	0.749853i	−0.0798125	+	0.0406665i
$341$	−10.4377	−	1.65317i	−0.565232	−	0.0895240i
$342$		0			0
$343$	−8.22572	−	16.1439i	−0.444147	−	0.871688i
$344$	3.68550	+	2.67767i	0.198709	+	0.144370i
$345$		0			0
$346$	−3.96369	+	2.87979i	−0.213089	+	0.154819i
$347$	−15.9671	+	2.52894i	−0.857160	+	0.135761i	−0.569520	−	0.821978i	$-0.692871\pi$
$347$	−15.9671	+	2.52894i	−0.857160	+	0.135761i	−0.287640	+	0.957739i	$0.592871\pi$
$348$		0			0
$349$	−6.28967	+	8.65699i	−0.336678	+	0.463398i	−0.943468	−	0.331465i	$-0.892457\pi$
$349$	−6.28967	+	8.65699i	−0.336678	+	0.463398i	0.606789	+	0.794863i	$0.292457\pi$
$350$	32.2711	−	5.11124i	1.72496	−	0.273207i
$351$		0			0
$352$	−3.12479	−	1.59216i	−0.166552	−	0.0848625i
$353$	−21.0319	−	15.2806i	−1.11942	−	0.813304i	−0.135297	−	0.990805i	$-0.543199\pi$
$353$	−21.0319	−	15.2806i	−1.11942	−	0.813304i	−0.984121	+	0.177501i	$0.943199\pi$
$354$		0			0
$355$	−0.774841	+	0.774841i	−0.0411243	+	0.0411243i
$356$	18.4992	+	2.92999i	0.980458	+	0.155289i
$357$		0			0
$358$	−19.6812	+	38.6266i	−1.04018	+	2.04148i
$359$	3.00578	+	9.25084i	0.158639	+	0.488241i	0.998511	−	0.0545433i	$-0.0173703\pi$
$359$	3.00578	+	9.25084i	0.158639	+	0.488241i	−0.839872	+	0.542784i	$0.817370\pi$
$360$		0			0
$361$	−13.1272	+	4.26529i	−0.690906	+	0.224489i
$362$	0.672073	+	4.24330i	0.0353234	+	0.223023i
$363$		0			0
$364$	−10.5066	−	3.41380i	−0.550696	−	0.178932i
$365$	−0.391454	+	1.20477i	−0.0204896	+	0.0630606i
$366$		0			0
$367$	13.2160	+	18.1902i	0.689868	+	0.949522i	0.999999	−	0.00117139i	$-0.000372866\pi$
$367$	13.2160	+	18.1902i	0.689868	+	0.949522i	−0.310131	+	0.950694i	$0.600373\pi$
$368$	25.1439			1.31072
$369$		0			0
$370$	−0.318023			−0.0165332
$371$	0.860205	+	1.18397i	0.0446596	+	0.0614687i
$372$		0			0
$373$	−0.994171	+	3.05974i	−0.0514762	+	0.158428i	−0.973490	−	0.228730i	$-0.926543\pi$
$373$	−0.994171	+	3.05974i	−0.0514762	+	0.158428i	0.922014	+	0.387157i	$0.126543\pi$
$374$	28.5698	+	9.28288i	1.47731	+	0.480006i
$375$		0			0
$376$	−7.93753	−	50.1156i	−0.409347	−	2.58452i
$377$	1.47536	−	0.479372i	0.0759847	−	0.0246889i
$378$		0			0
$379$	−5.92193	−	18.2258i	−0.304189	−	0.936198i	−0.979978	−	0.199103i	$-0.936197\pi$
$379$	−5.92193	−	18.2258i	−0.304189	−	0.936198i	0.675789	−	0.737095i	$-0.263803\pi$
$380$	−0.467467	+	0.917456i	−0.0239806	+	0.0470645i
$381$		0			0
$382$	−13.0868	−	2.07275i	−0.669581	−	0.106051i
$383$	−20.6909	+	20.6909i	−1.05726	+	1.05726i	−0.0589972	+	0.998258i	$0.518790\pi$
$383$	−20.6909	+	20.6909i	−1.05726	+	1.05726i	−0.998258	+	0.0589972i	$0.981210\pi$
$384$		0			0
$385$	0.858318	+	0.623605i	0.0437439	+	0.0317818i
$386$	14.1827	+	7.22643i	0.721879	+	0.367816i
$387$		0			0
$388$	10.6143	−	1.68114i	0.538859	−	0.0853470i
$389$	5.16511	−	7.10917i	0.261882	−	0.360449i	−0.657746	−	0.753239i	$-0.728490\pi$
$389$	5.16511	−	7.10917i	0.261882	−	0.360449i	0.919628	+	0.392790i	$0.128490\pi$
$390$		0			0
$391$	27.0803	−	4.28910i	1.36951	−	0.216909i
$392$	−1.07198	+	0.778840i	−0.0541432	+	0.0393373i
$393$		0			0
$394$	−8.38504	−	6.09209i	−0.422432	−	0.306915i
$395$	−0.565673	−	1.11020i	−0.0284621	−	0.0558600i
$396$		0			0
$397$	−24.8449	−	3.93505i	−1.24693	−	0.197495i	−0.502137	−	0.864788i	$-0.667453\pi$
$397$	−24.8449	−	3.93505i	−1.24693	−	0.197495i	−0.744795	+	0.667294i	$0.767453\pi$
$398$	34.5875	−	17.6232i	1.73372	−	0.883372i
$399$		0			0
$400$	5.16761	+	15.9043i	0.258381	+	0.795214i
$401$			28.1172i			1.40411i	0.712124	+	0.702054i	$0.247733\pi$
$401$			28.1172i			1.40411i	−0.712124	+	0.702054i	$0.752267\pi$
$402$		0			0
$403$	0.513740	+	3.24363i	0.0255912	+	0.161577i
$404$	5.75731	−	36.3502i	0.286437	−	1.80849i
$405$		0			0
$406$	2.98621	−	9.19060i	0.148203	−	0.456122i
$407$	2.70121	+	2.70121i	0.133894	+	0.133894i
$408$		0			0
$409$	1.43475			0.0709440			0.0354720	−	0.999371i	$-0.488707\pi$
$409$	1.43475			0.0709440			0.0354720	+	0.999371i	$0.488707\pi$
$410$	−1.56367	+	0.900159i	−0.0772242	+	0.0444557i
$411$		0			0
$412$	14.3672	+	19.7748i	0.707822	+	0.974234i
$413$	−3.71053	−	3.71053i	−0.182583	−	0.182583i
$414$		0			0
$415$	−0.0701399	−	0.0227898i	−0.00344303	−	0.00111871i
$416$	−0.170490	+	1.07643i	−0.00835898	+	0.0527765i
$417$		0			0
$418$	17.8107	−	5.78705i	0.871151	−	0.283054i
$419$		−	15.5755i		−	0.760912i	−0.924799	−	0.380456i	$-0.875767\pi$
$419$		−	15.5755i		−	0.760912i	0.924799	−	0.380456i	$-0.124233\pi$
$420$		0			0
$421$	−3.37083	+	6.61562i	−0.164284	+	0.322426i	−0.958443	−	0.285285i	$-0.907912\pi$
$421$	−3.37083	+	6.61562i	−0.164284	+	0.322426i	0.794159	+	0.607710i	$0.207912\pi$
$422$	−54.0205	+	27.5248i	−2.62968	+	1.33989i
$423$		0			0
$424$	−1.75844	+	1.75844i	−0.0853974	+	0.0853974i
$425$	8.27857	+	16.2476i	0.401570	+	0.788125i
$426$		0			0
$427$	24.3889	+	12.4268i	1.18026	+	0.601373i
$428$	−43.2376	+	31.4140i	−2.08997	+	1.51845i
$429$		0			0
$430$	−0.164466	+	0.226368i	−0.00793125	+	0.0109164i
$431$	−20.1133	+	27.6836i	−0.968824	+	1.33347i	−0.0261853	+	0.999657i	$0.508336\pi$
$431$	−20.1133	+	27.6836i	−0.968824	+	1.33347i	−0.942639	+	0.333815i	$0.891664\pi$
$432$		0			0
$433$	−6.78471	+	4.92938i	−0.326053	+	0.236891i	−0.738754	−	0.673975i	$-0.764585\pi$
$433$	−6.78471	+	4.92938i	−0.326053	+	0.236891i	0.412701	+	0.910866i	$0.364585\pi$
$434$	18.2280	+	9.28763i	0.874972	+	0.445820i
$435$		0			0
$436$	26.2204	+	51.4605i	1.25573	+	2.46451i
$437$	12.0863	−	12.0863i	0.578166	−	0.578166i
$438$		0			0
$439$	21.8040	−	11.1097i	1.04065	−	0.530236i	0.151786	−	0.988413i	$-0.451498\pi$
$439$	21.8040	−	11.1097i	1.04065	−	0.530236i	0.888861	+	0.458178i	$0.151498\pi$
$440$	−0.818459	+	1.60632i	−0.0390185	+	0.0765781i
$441$		0			0
$442$		−	9.33528i		−	0.444034i
$443$	13.1456	−	4.27126i	0.624565	−	0.202933i	0.0203990	−	0.999792i	$-0.493506\pi$
$443$	13.1456	−	4.27126i	0.624565	−	0.202933i	0.604166	+	0.796858i	$0.293506\pi$
$444$		0			0
$445$	−0.0874436	+	0.552097i	−0.00414522	+	0.0261719i
$446$	7.66092	+	2.48918i	0.362755	+	0.117866i
$447$		0			0
$448$	17.6049	+	17.6049i	0.831753	+	0.831753i
$449$	−0.627367	−	0.863496i	−0.0296073	−	0.0407509i	0.793957	−	0.607974i	$-0.208018\pi$
$449$	−0.627367	−	0.863496i	−0.0296073	−	0.0407509i	−0.823564	+	0.567223i	$0.808018\pi$
$450$		0			0
$451$	20.9272	+	5.63571i	0.985422	+	0.265375i
$452$	30.9190			1.45431
$453$		0			0
$454$	−13.2273	−	13.2273i	−0.620787	−	0.620787i
$455$	0.101883	−	0.313562i	0.00477633	−	0.0147000i
$456$		0			0
$457$	−4.71510	+	29.7700i	−0.220563	+	1.39258i	0.590223	+	0.807240i	$0.299040\pi$
$457$	−4.71510	+	29.7700i	−0.220563	+	1.39258i	−0.810787	+	0.585342i	$0.800960\pi$
$458$	−1.88829	−	11.9222i	−0.0882342	−	0.557089i
$459$		0			0
$460$			3.38642i			0.157892i
$461$	−0.963390	−	2.96501i	−0.0448695	−	0.138094i	0.926112	−	0.377249i	$-0.123130\pi$
$461$	−0.963390	−	2.96501i	−0.0448695	−	0.138094i	−0.970982	+	0.239154i	$0.923130\pi$
$462$		0			0
$463$	−6.30485	+	3.21248i	−0.293011	+	0.149297i	−0.594317	−	0.804231i	$-0.702577\pi$
$463$	−6.30485	+	3.21248i	−0.293011	+	0.149297i	0.301306	+	0.953528i	$0.402577\pi$
$464$	4.88508	+	0.773720i	0.226784	+	0.0359191i
$465$		0			0
$466$	−11.7952	−	23.1493i	−0.546401	−	1.07237i
$467$	−31.9737	−	23.2303i	−1.47957	−	1.07497i	−0.977695	−	0.210028i	$-0.932644\pi$
$467$	−31.9737	−	23.2303i	−1.47957	−	1.07497i	−0.501873	−	0.864941i	$-0.667356\pi$
$468$		0			0
$469$	−29.0082	+	21.0757i	−1.33947	+	0.973184i
$470$	3.07816	−	0.487533i	0.141985	−	0.0224882i
$471$		0			0
$472$	5.24117	−	7.21386i	0.241245	−	0.332045i
$473$	3.31965	−	0.525780i	0.152638	−	0.0241754i
$474$		0			0
$475$	10.1289	+	5.16096i	0.464748	+	0.236801i
$476$	−31.0725	−	22.5755i	−1.42421	−	1.03475i
$477$		0			0
$478$	15.8637	−	15.8637i	0.725588	−	0.725588i
$479$	−11.5501	−	1.82935i	−0.527737	−	0.0835853i	−0.113120	−	0.993581i	$-0.536084\pi$
$479$	−11.5501	−	1.82935i	−0.527737	−	0.0835853i	−0.414617	+	0.909996i	$0.636084\pi$
$480$		0			0
$481$	0.538949	−	1.05775i	0.0245740	−	0.0482291i
$482$	21.2552	+	65.4168i	0.968148	+	2.97965i
$483$		0			0
$484$	1.68820	−	0.548529i	0.0767363	−	0.0249331i
$485$	0.0501725	+	0.316776i	0.00227821	+	0.0143841i
$486$		0			0
$487$	−23.9864	−	7.79365i	−1.08693	−	0.353164i	−0.289869	−	0.957066i	$-0.593612\pi$
$487$	−23.9864	−	7.79365i	−1.08693	−	0.353164i	−0.797058	+	0.603903i	$0.793612\pi$
$488$	−14.3732	+	44.2361i	−0.650643	+	2.00247i
$489$		0			0
$490$	−0.0478373	−	0.0658424i	−0.00216107	−	0.00297446i
$491$	31.5085			1.42196			0.710980	−	0.703212i	$-0.248252\pi$
$491$	31.5085			1.42196			0.710980	+	0.703212i	$0.248252\pi$
$492$		0			0
$493$	5.39328			0.242901
$494$	−3.42075	−	4.70825i	−0.153907	−	0.211834i
$495$		0			0
$496$	−3.23560	+	9.95815i	−0.145283	+	0.447134i
$497$	−24.2339	−	7.87407i	−1.08704	−	0.353200i
$498$		0			0
$499$	0.773481	+	4.88356i	0.0346257	+	0.218618i	0.998934	−	0.0461643i	$-0.0146998\pi$
$499$	0.773481	+	4.88356i	0.0346257	+	0.218618i	−0.964308	+	0.264783i	$0.914700\pi$
$500$	−4.28982	+	1.39385i	−0.191846	+	0.0623347i
$501$		0			0
$502$	4.95528	+	15.2508i	0.221165	+	0.680675i
$503$	11.0443	−	21.6756i	0.492439	−	0.966466i	−0.502365	−	0.864656i	$-0.667537\pi$
$503$	11.0443	−	21.6756i	0.492439	−	0.966466i	0.994804	−	0.101810i	$-0.0324635\pi$
$504$		0			0
$505$	1.08485	+	0.171823i	0.0482751	+	0.00764602i
$506$	43.5508	−	43.5508i	1.93607	−	1.93607i
$507$		0			0
$508$	−25.5084	−	18.5329i	−1.13175	−	0.822266i
$509$	−29.2644	−	14.9110i	−1.29712	−	0.660917i	−0.337266	−	0.941409i	$-0.609502\pi$
$509$	−29.2644	−	14.9110i	−1.29712	−	0.660917i	−0.959856	+	0.280493i	$0.909502\pi$
$510$		0			0
$511$	−29.0942	+	4.60807i	−1.28705	+	0.203849i
$512$	−20.1286	+	27.7047i	−0.889568	+	1.22438i
$513$		0			0
$514$	−10.5386	+	1.66916i	−0.464839	+	0.0736233i
$515$	−0.590165	+	0.428780i	−0.0260058	+	0.0188943i
$516$		0			0
$517$	−30.2862	−	22.0042i	−1.33198	−	0.967743i
$518$	−3.35734	−	6.58914i	−0.147513	−	0.289510i
$519$		0			0
$520$	0.553346	+	0.0876415i	0.0242658	+	0.00384333i
$521$	37.3756	−	19.0438i	1.63745	−	0.834325i	0.639611	−	0.768699i	$-0.279096\pi$
$521$	37.3756	−	19.0438i	1.63745	−	0.834325i	0.997844	−	0.0656258i	$-0.0209044\pi$
$522$		0			0
$523$	−4.76782	−	14.6739i	−0.208482	−	0.641643i	−0.999552	−	0.0299172i	$-0.990476\pi$
$523$	−4.76782	−	14.6739i	−0.208482	−	0.641643i	0.791070	−	0.611726i	$-0.209524\pi$
$524$			44.2934i			1.93496i
$525$		0			0
$526$	−4.75370	−	30.0137i	−0.207271	−	1.30866i
$527$	−1.78610	+	11.2770i	−0.0778037	+	0.491233i
$528$		0			0
$529$	10.2637	−	31.5884i	0.446247	−	1.37341i
$530$	−0.108006	−	0.108006i	−0.00469147	−	0.00469147i
$531$		0			0
$532$	−23.9438			−1.03810
$533$	−0.344004	−	6.72626i	−0.0149005	−	0.291347i
$534$		0			0
$535$	−0.937529	−	1.29040i	−0.0405329	−	0.0557888i
$536$	−43.0831	−	43.0831i	−1.86091	−	1.86091i
$537$		0			0
$538$	−8.16919	−	2.65433i	−0.352199	−	0.114436i
$539$	−0.152931	+	0.965568i	−0.00658720	+	0.0415900i
$540$		0			0
$541$	8.26506	−	2.68548i	0.355343	−	0.115458i	−0.125905	−	0.992042i	$-0.540184\pi$
$541$	8.26506	−	2.68548i	0.355343	−	0.115458i	0.481248	+	0.876584i	$0.340184\pi$
$542$		−	9.28872i		−	0.398985i
$543$		0			0
$544$	−1.72019	+	3.37606i	−0.0737525	+	0.144748i
$545$	−1.53580	+	0.782530i	−0.0657865	+	0.0335199i
$546$		0			0
$547$	1.94269	−	1.94269i	0.0830635	−	0.0830635i	−0.664354	−	0.747418i	$-0.731293\pi$
$547$	1.94269	−	1.94269i	0.0830635	−	0.0830635i	0.747418	+	0.664354i	$0.231293\pi$
$548$	−10.6593	−	20.9201i	−0.455343	−	0.893661i
$549$		0			0
$550$	36.4979	+	18.5966i	1.55627	+	0.792962i
$551$	2.72010	−	1.97627i	0.115880	−	0.0841919i
$552$		0			0
$553$	17.0305	−	23.4404i	0.724209	−	0.996788i
$554$	42.8057	−	58.9170i	1.81864	−	2.50314i
$555$		0			0
$556$	−55.5522	+	40.3610i	−2.35594	+	1.71169i
$557$	29.7769	+	15.1721i	1.26169	+	0.642862i	0.951452	−	0.307797i	$-0.0995919\pi$
$557$	29.7769	+	15.1721i	1.26169	+	0.642862i	0.310236	+	0.950660i	$0.399592\pi$
$558$		0			0
$559$	−0.474183	−	0.930636i	−0.0200558	−	0.0393617i
$560$	0.743300	−	0.743300i	0.0314101	−	0.0314101i
$561$		0			0
$562$	11.8944	−	6.06049i	0.501734	−	0.255646i
$563$	−7.71260	+	15.1368i	−0.325047	+	0.637941i	−0.994479	−	0.104932i	$-0.966537\pi$
$563$	−7.71260	+	15.1368i	−0.325047	+	0.637941i	0.669432	+	0.742873i	$0.266537\pi$
$564$		0			0
$565$			0.922756i			0.0388206i
$566$	−70.0268	+	22.7531i	−2.94345	+	0.956384i
$567$		0			0
$568$	6.77343	−	42.7657i	0.284207	−	1.79441i
$569$	−24.8527	−	8.07512i	−1.04188	−	0.338526i	−0.262402	−	0.964959i	$-0.584514\pi$
$569$	−24.8527	−	8.07512i	−1.04188	−	0.338526i	−0.779476	+	0.626432i	$0.784514\pi$
$570$		0			0
$571$	−1.00428	−	1.00428i	−0.0420278	−	0.0420278i	0.685781	−	0.727808i	$-0.259461\pi$
$571$	−1.00428	−	1.00428i	−0.0420278	−	0.0420278i	−0.727808	+	0.685781i	$0.759461\pi$
$572$	−8.14082	−	11.2049i	−0.340385	−	0.468499i
$573$		0			0
$574$	−35.1579	−	22.8949i	−1.46746	−	0.955615i
$575$	37.3869			1.55914
$576$		0			0
$577$	23.1743	+	23.1743i	0.964760	+	0.964760i	0.999400	−	0.0346401i	$-0.0110285\pi$
$577$	23.1743	+	23.1743i	0.964760	+	0.964760i	−0.0346401	+	0.999400i	$0.511028\pi$
$578$	−2.72033	+	8.37230i	−0.113151	+	0.348242i
$579$		0			0
$580$	−0.104206	+	0.657930i	−0.00432691	+	0.0273191i
$581$	−0.268275	−	1.69382i	−0.0111299	−	0.0702715i
$582$		0			0
$583$			1.83475i			0.0759875i
$584$	−15.4678	−	47.6050i	−0.640062	−	1.96991i
$585$		0			0
$586$	−43.4556	+	22.1417i	−1.79513	+	0.914667i
$587$	7.53663	+	1.19368i	0.311070	+	0.0492686i	0.310018	−	0.950731i	$-0.399665\pi$
$587$	7.53663	+	1.19368i	0.311070	+	0.0492686i	0.00105233	+	0.999999i	$0.499665\pi$
$588$		0			0
$589$	3.23143	+	6.34204i	0.133149	+	0.261319i
$590$	0.443084	+	0.321920i	0.0182415	+	0.0132532i
$591$		0			0
$592$	3.06210	−	2.22475i	0.125852	−	0.0914366i
$593$	41.5892	−	6.58708i	1.70786	−	0.270499i	0.775322	−	0.631566i	$-0.217587\pi$
$593$	41.5892	−	6.58708i	1.70786	−	0.270499i	0.932540	+	0.361067i	$0.117587\pi$
$594$		0			0
$595$	0.673750	−	0.927337i	0.0276210	−	0.0380171i
$596$	4.16022	−	0.658915i	0.170409	−	0.0269902i
$597$		0			0
$598$	−17.0537	−	8.68931i	−0.697379	−	0.355332i
$599$	−37.0626	−	26.9276i	−1.51434	−	1.10023i	−0.964207	−	0.265151i	$-0.914578\pi$
$599$	−37.0626	−	26.9276i	−1.51434	−	1.10023i	−0.550129	−	0.835079i	$-0.685422\pi$
$600$		0			0
$601$	−8.39569	+	8.39569i	−0.342467	+	0.342467i	−0.857294	−	0.514827i	$-0.827856\pi$
$601$	−8.39569	+	8.39569i	−0.342467	+	0.342467i	0.514827	+	0.857294i	$0.327856\pi$
$602$	−6.42637	−	1.01784i	−0.261919	−	0.0414840i
$603$		0			0
$604$	−23.2095	+	45.5513i	−0.944383	+	1.85346i
$605$	0.0163705	+	0.0503831i	0.000665554	+	0.00204837i
$606$		0			0
$607$	−22.8222	+	7.41539i	−0.926325	+	0.300981i	−0.733059	−	0.680165i	$-0.761908\pi$
$607$	−22.8222	+	7.41539i	−0.926325	+	0.300981i	−0.193266	+	0.981146i	$0.561908\pi$
$608$	0.369519	+	2.33305i	0.0149860	+	0.0946177i
$609$		0			0
$610$	−2.71704	−	0.882818i	−0.110010	−	0.0357443i
$611$	−3.59498	+	11.0642i	−0.145437	+	0.447610i
$612$		0			0
$613$	−10.8769	−	14.9708i	−0.439315	−	0.604665i	0.530745	−	0.847532i	$-0.321912\pi$
$613$	−10.8769	−	14.9708i	−0.439315	−	0.604665i	−0.970060	+	0.242867i	$0.921912\pi$
$614$	−0.548233			−0.0221249
$615$		0			0
$616$	−41.9217			−1.68907
$617$	0.798604	+	1.09918i	0.0321506	+	0.0442515i	0.824790	−	0.565440i	$-0.191293\pi$
$617$	0.798604	+	1.09918i	0.0321506	+	0.0442515i	−0.792639	+	0.609691i	$0.791293\pi$
$618$		0			0
$619$	12.9896	−	39.9780i	0.522097	−	1.60685i	−0.247888	−	0.968789i	$-0.579736\pi$
$619$	12.9896	−	39.9780i	0.522097	−	1.60685i	0.769985	−	0.638062i	$-0.220264\pi$
$620$	−1.34118	−	0.435775i	−0.0538630	−	0.0175012i
$621$		0			0
$622$	5.51678	+	34.8316i	0.221203	+	1.39662i
$623$	−12.3621	+	4.01668i	−0.495276	+	0.160925i
$624$		0			0
$625$	7.66300	+	23.5843i	0.306520	+	0.943371i
$626$	9.01797	−	17.6988i	0.360430	−	0.707385i
$627$		0			0
$628$	62.9861	+	9.97602i	2.51342	+	0.398087i
$629$	2.91842	−	2.91842i	0.116365	−	0.116365i
$630$		0			0
$631$	29.2153	+	21.2262i	1.16304	+	0.845001i	0.990160	−	0.139941i	$-0.0446914\pi$
$631$	29.2153	+	21.2262i	1.16304	+	0.845001i	0.172884	+	0.984942i	$0.444691\pi$
$632$	43.8680	+	22.3519i	1.74498	+	0.889110i
$633$		0			0
$634$	23.0207	−	3.64613i	0.914270	−	0.144806i
$635$	0.553102	−	0.761280i	0.0219492	−	0.0302105i
$636$		0			0
$637$	0.300061	−	0.0475251i	0.0118889	−	0.00188301i
$638$	9.80140	−	7.12114i	0.388041	−	0.281928i
$639$		0			0
$640$	−1.90760	−	1.38595i	−0.0754046	−	0.0547847i
$641$	20.0951	+	39.4388i	0.793708	+	1.55774i	0.829583	+	0.558384i	$0.188578\pi$
$641$	20.0951	+	39.4388i	0.793708	+	1.55774i	−0.0358741	+	0.999356i	$0.511422\pi$
$642$		0			0
$643$	−12.3017	−	1.94839i	−0.485131	−	0.0768372i	−0.0909219	−	0.995858i	$-0.528981\pi$
$643$	−12.3017	−	1.94839i	−0.485131	−	0.0768372i	−0.394209	+	0.919021i	$0.628981\pi$
$644$	−70.1633	+	35.7500i	−2.76482	+	1.40875i
$645$		0			0
$646$	−6.25240	−	19.2429i	−0.245997	−	0.757102i
$647$		−	15.7465i		−	0.619061i	−0.950890	−	0.309530i	$-0.899828\pi$
$647$		−	15.7465i		−	0.619061i	0.950890	−	0.309530i	$-0.100172\pi$
$648$		0			0
$649$	−1.02914	−	6.49776i	−0.0403974	−	0.255059i
$650$	1.99134	−	12.5728i	0.0781069	−	0.493148i
$651$		0			0
$652$	−17.5907	+	54.1387i	−0.688906	+	2.12024i
$653$	−13.7349	−	13.7349i	−0.537489	−	0.537489i	0.385301	−	0.922791i	$-0.374097\pi$
$653$	−13.7349	−	13.7349i	−0.537489	−	0.537489i	−0.922791	+	0.385301i	$0.874097\pi$
$654$		0			0
$655$	−1.32190			−0.0516511
$656$	8.75877	−	19.6060i	0.341973	−	0.765484i
$657$		0			0
$658$	42.5971	+	58.6298i	1.66061	+	2.28563i
$659$	8.94994	+	8.94994i	0.348640	+	0.348640i	0.859603	−	0.510963i	$-0.170711\pi$
$659$	8.94994	+	8.94994i	0.348640	+	0.348640i	−0.510963	+	0.859603i	$0.670711\pi$
$660$		0			0
$661$	35.5255	+	11.5429i	1.38178	+	0.448968i	0.903255	−	0.429105i	$-0.141171\pi$
$661$	35.5255	+	11.5429i	1.38178	+	0.448968i	0.478527	+	0.878073i	$0.341171\pi$
$662$	1.74401	−	11.0112i	0.0677829	−	0.427964i
$663$		0			0
$664$	2.77149	−	0.900512i	0.107555	−	0.0349466i
$665$		−	0.714586i		−	0.0277105i
$666$		0			0
$667$	5.02008	−	9.85246i	0.194378	−	0.381489i
$668$	−40.2727	+	20.5199i	−1.55820	+	0.793941i
$669$		0			0
$670$	2.64622	−	2.64622i	0.102232	−	0.102232i
$671$	15.5794	+	30.5763i	0.601436	+	1.18038i
$672$		0			0
$673$	−9.32618	−	4.75192i	−0.359498	−	0.183173i	0.264908	−	0.964274i	$-0.414659\pi$
$673$	−9.32618	−	4.75192i	−0.359498	−	0.183173i	−0.624405	+	0.781101i	$0.714659\pi$
$674$	−34.8136	+	25.2936i	−1.34097	+	0.974271i
$675$		0			0
$676$	27.1964	−	37.4327i	1.04602	−	1.43972i
$677$	−9.95839	+	13.7066i	−0.382732	+	0.526786i	−0.956306	−	0.292368i	$-0.905557\pi$
$677$	−9.95839	+	13.7066i	−0.382732	+	0.526786i	0.573574	+	0.819154i	$0.305557\pi$
$678$		0			0
$679$	−6.03364	+	4.38370i	−0.231550	+	0.168231i
$680$	1.73548	+	0.884272i	0.0665527	+	0.0339103i
$681$		0			0
$682$	11.6439	+	22.8524i	0.445867	+	0.875064i
$683$	14.4614	−	14.4614i	0.553350	−	0.553350i	−0.374056	−	0.927406i	$-0.622033\pi$
$683$	14.4614	−	14.4614i	0.553350	−	0.553350i	0.927406	+	0.374056i	$0.122033\pi$
$684$		0			0
$685$	0.624345	−	0.318120i	0.0238550	−	0.0121547i
$686$	−19.9637	+	39.1810i	−0.762218	+	1.49594i
$687$		0			0
$688$		−	3.33012i		−	0.126960i
$689$	0.542263	−	0.176192i	0.0206586	−	0.00671238i
$690$		0			0
$691$	−1.41031	+	8.90432i	−0.0536506	+	0.338736i	0.946233	+	0.323486i	$0.104855\pi$
$691$	−1.41031	+	8.90432i	−0.0536506	+	0.338736i	−0.999884	+	0.0152509i	$0.995145\pi$
$692$	7.46895	+	2.42681i	0.283927	+	0.0922535i
$693$		0			0
$694$	27.7433	+	27.7433i	1.05312	+	1.05312i
$695$	−1.20455	−	1.65792i	−0.0456911	−	0.0628884i
$696$		0			0
$697$	6.08889	−	22.6100i	0.230633	−	0.856413i
$698$	25.9703			0.982989
$699$		0			0
$700$	−37.0331	−	37.0331i	−1.39972	−	1.39972i
$701$	−3.66441	+	11.2779i	−0.138403	+	0.425960i	−0.996104	−	0.0881889i	$-0.971892\pi$
$701$	−3.66441	+	11.2779i	−0.138403	+	0.425960i	0.857701	+	0.514149i	$0.171892\pi$
$702$		0			0
$703$	0.402504	−	2.54131i	0.0151807	−	0.0958474i
$704$	4.88286	+	30.8291i	0.184030	+	1.16192i
$705$		0			0
$706$			63.0941i			2.37458i
$707$	7.89260	+	24.2909i	0.296832	+	0.913555i
$708$		0			0
$709$	36.6676	−	18.6831i	1.37708	−	0.701658i	0.400398	−	0.916341i	$-0.368872\pi$
$709$	36.6676	−	18.6831i	1.37708	−	0.701658i	0.976684	+	0.214683i	$0.0688718\pi$
$710$	2.62673	+	0.416033i	0.0985793	+	0.0156134i
$711$		0			0
$712$	−10.0275	−	19.6800i	−0.375795	−	0.737539i
$713$	18.9383	+	13.7595i	0.709246	+	0.515298i
$714$		0			0
$715$	0.334402	−	0.242957i	0.0125059	−	0.00908608i
$716$	68.6336	−	10.8705i	2.56496	−	0.406249i
$717$		0			0
$718$	13.8759	−	19.0985i	0.517843	−	0.712750i
$719$	24.4544	−	3.87320i	0.911996	−	0.144446i	0.317233	−	0.948348i	$-0.397246\pi$
$719$	24.4544	−	3.87320i	0.911996	−	0.144446i	0.594762	+	0.803902i	$0.297246\pi$
$720$		0			0
$721$	−15.1142	−	7.70108i	−0.562883	−	0.286803i
$722$	27.1014	+	19.6903i	1.00861	+	0.732797i
$723$		0			0
$724$	4.86946	−	4.86946i	0.180972	−	0.180972i
$725$	7.26372	+	1.15046i	0.269768	+	0.0427270i
$726$		0			0
$727$	−0.177225	+	0.347823i	−0.00657290	+	0.0129000i	−0.894270	−	0.447529i	$-0.852304\pi$
$727$	−0.177225	+	0.347823i	−0.00657290	+	0.0129000i	0.887697	+	0.460429i	$0.152304\pi$
$728$	4.02577	+	12.3900i	0.149205	+	0.459205i
$729$		0			0
$730$	2.92396	−	0.950052i	0.108221	−	0.0351630i
$731$	−0.568059	−	3.58659i	−0.0210104	−	0.132655i
$732$		0			0
$733$	−9.37877	−	3.04735i	−0.346413	−	0.112556i	0.130643	−	0.991430i	$-0.458296\pi$
$733$	−9.37877	−	3.04735i	−0.346413	−	0.112556i	−0.477055	+	0.878873i	$0.658296\pi$
$734$	16.8628	−	51.8984i	0.622418	−	1.91561i
$735$		0			0
$736$	4.56625	+	6.28490i	0.168314	+	0.231664i
$737$	−44.9527			−1.65585
$738$		0			0
$739$	13.8121			0.508087			0.254044	−	0.967193i	$-0.418239\pi$
$739$	13.8121			0.508087			0.254044	+	0.967193i	$0.418239\pi$
$740$	0.299632	+	0.412409i	0.0110147	+	0.0151604i
$741$		0			0
$742$	1.09757	−	3.37798i	0.0402931	−	0.124010i
$743$	24.8949	+	8.08883i	0.913304	+	0.296750i	0.727717	−	0.685878i	$-0.240581\pi$
$743$	24.8949	+	8.08883i	0.913304	+	0.296750i	0.185587	+	0.982628i	$0.440581\pi$
$744$		0			0
$745$	0.0196648	+	0.124159i	0.000720464	+	0.00454883i
$746$	7.42595	−	2.41284i	0.271883	−	0.0883403i
$747$		0			0
$748$	−14.8797	−	45.7950i	−0.544055	−	1.67443i
$749$	16.8384	−	33.0473i	0.615263	−	1.20752i
$750$		0			0
$751$	−20.6029	−	3.26318i	−0.751812	−	0.119075i	−0.231244	−	0.972896i	$-0.574280\pi$
$751$	−20.6029	−	3.26318i	−0.751812	−	0.119075i	−0.520568	+	0.853820i	$0.674280\pi$
$752$	−26.2277	+	26.2277i	−0.956425	+	0.956425i
$753$		0			0
$754$	−3.04590	−	2.21297i	−0.110925	−	0.0805918i
$755$	−1.35945	−	0.692672i	−0.0494753	−	0.0252089i
$756$		0			0
$757$	44.0377	−	6.97489i	1.60058	−	0.253507i	0.708609	−	0.705602i	$-0.249323\pi$
$757$	44.0377	−	6.97489i	1.60058	−	0.253507i	0.891970	+	0.452095i	$0.149323\pi$
$758$	−27.3380	+	37.6275i	−0.992961	+	1.36669i
$759$		0			0
$760$	1.19932	−	0.189953i	0.0435038	−	0.00689032i
$761$	35.6363	−	25.8913i	1.29182	−	0.938559i	0.291976	−	0.956426i	$-0.405687\pi$
$761$	35.6363	−	25.8913i	1.29182	−	0.938559i	0.999840	+	0.0178662i	$0.00568731\pi$
$762$		0			0
$763$	−32.4266	−	23.5593i	−1.17392	−	0.852903i
$764$	9.64213	+	18.9237i	0.348840	+	0.684637i
$765$		0			0
$766$	70.1425	+	11.1095i	2.53435	+	0.401402i
$767$	−1.82159	+	0.928148i	−0.0657739	+	0.0335135i
$768$		0			0
$769$	−5.91420	−	18.2020i	−0.213272	−	0.656383i	−0.999272	−	0.0381563i	$-0.987852\pi$
$769$	−5.91420	−	18.2020i	−0.213272	−	0.656383i	0.786000	−	0.618226i	$-0.212148\pi$
$770$		−	2.57489i		−	0.0927924i
$771$		0			0
$772$	−3.99136	−	25.2004i	−0.143652	−	0.906984i
$773$	−4.60071	+	29.0477i	−0.165476	+	1.04477i	0.755498	+	0.655151i	$0.227395\pi$
$773$	−4.60071	+	29.0477i	−0.165476	+	1.04477i	−0.920974	+	0.389624i	$0.872605\pi$
$774$		0			0
$775$	−4.81107	+	14.8070i	−0.172819	+	0.531882i
$776$	−8.96120	−	8.96120i	−0.321688	−	0.321688i
$777$		0			0
$778$	−21.3269			−0.764608
$779$	−5.21408	−	13.6345i	−0.186814	−	0.488507i
$780$		0			0
$781$	−18.7771	−	25.8445i	−0.671897	−	0.924787i
$782$	−47.0528	−	47.0528i	−1.68260	−	1.68260i
$783$		0			0
$784$	0.921208	+	0.299319i	0.0329003	+	0.0106899i
$785$	−0.297727	+	1.87978i	−0.0106263	+	0.0670921i
$786$		0			0
$787$	−22.7158	+	7.38080i	−0.809730	+	0.263097i	−0.684483	−	0.729028i	$-0.739972\pi$
$787$	−22.7158	+	7.38080i	−0.809730	+	0.263097i	−0.125246	+	0.992126i	$0.539972\pi$
$788$			16.6134i			0.591828i
$789$		0			0
$790$	−1.37288	+	2.69443i	−0.0488449	+	0.0958635i
$791$	−19.1186	+	9.74142i	−0.679780	+	0.346365i
$792$		0			0
$793$	7.54078	−	7.54078i	0.267781	−	0.267781i
$794$	27.7161	+	54.3959i	0.983607	+	1.93044i
$795$		0			0
$796$	−55.4410	−	28.2486i	−1.96505	−	1.00124i
$797$	−26.5246	+	19.2712i	−0.939548	+	0.682622i	−0.948312	−	0.317340i	$-0.897210\pi$
$797$	−26.5246	+	19.2712i	−0.939548	+	0.682622i	0.00876372	+	0.999962i	$0.497210\pi$
$798$		0			0
$799$	−23.7736	+	32.7215i	−0.841049	+	1.15760i
$800$	−3.03693	+	4.17998i	−0.107372	+	0.147784i
$801$		0			0
$802$	55.2074	−	40.1105i	1.94944	−	1.41635i
$803$	−32.9049	−	16.7659i	−1.16119	−	0.591656i
$804$		0			0
$805$	−1.06693	−	2.09398i	−0.0376045	−	0.0738030i
$806$	5.63590	−	5.63590i	0.198516	−	0.198516i
$807$		0			0
$808$	−38.6704	+	19.7035i	−1.36042	+	0.693168i
$809$	9.00467	−	17.6727i	0.316587	−	0.621338i	−0.676798	−	0.736169i	$-0.736633\pi$
$809$	9.00467	−	17.6727i	0.316587	−	0.621338i	0.993385	+	0.114831i	$0.0366328\pi$
$810$		0			0
$811$		−	12.6254i		−	0.443338i	−0.975122	−	0.221669i	$-0.928850\pi$
$811$		−	12.6254i		−	0.443338i	0.975122	−	0.221669i	$-0.0711505\pi$
$812$	−14.7318	+	4.78664i	−0.516984	+	0.167978i
$813$		0			0
$814$	1.45035	−	9.15716i	0.0508348	−	0.320958i
$815$	−1.61573	−	0.524983i	−0.0565966	−	0.0183894i
$816$		0			0
$817$	−1.60074	−	1.60074i	−0.0560028	−	0.0560028i
$818$	−2.04674	−	2.81710i	−0.0715627	−	0.0984976i
$819$		0			0
$820$	2.64056	+	1.17965i	0.0922124	+	0.0411950i
$821$	3.71560			0.129675			0.0648376	−	0.997896i	$-0.479347\pi$
$821$	3.71560			0.129675			0.0648376	+	0.997896i	$0.479347\pi$
$822$		0			0
$823$	30.0144	+	30.0144i	1.04624	+	1.04624i	0.998878	+	0.0473578i	$0.0150801\pi$
$823$	30.0144	+	30.0144i	1.04624	+	1.04624i	0.0473578	+	0.998878i	$0.484920\pi$
$824$	8.90731	−	27.4139i	0.310301	−	0.955007i
$825$		0			0
$826$	−1.99228	+	12.5788i	−0.0693202	+	0.437671i
$827$	−2.13027	−	13.4500i	−0.0740766	−	0.467702i	−0.996643	−	0.0818642i	$-0.973913\pi$
$827$	−2.13027	−	13.4500i	−0.0740766	−	0.467702i	0.922567	−	0.385837i	$-0.126087\pi$
$828$		0			0
$829$		−	38.0361i		−	1.32105i	−0.750805	−	0.660524i	$-0.770334\pi$
$829$		−	38.0361i		−	1.32105i	0.750805	−	0.660524i	$-0.229666\pi$
$830$	0.0553106	+	0.170228i	0.00191986	+	0.00590872i
$831$		0			0
$832$	8.64270	−	4.40367i	0.299632	−	0.152670i
$833$	1.04321	+	0.165228i	0.0361451	+	0.00572483i
$834$		0			0
$835$	−0.612404	−	1.20191i	−0.0211931	−	0.0415938i
$836$	−24.2853	−	17.6443i	−0.839926	−	0.610242i
$837$		0			0
$838$	−30.5820	+	22.2191i	−1.05644	+	0.767547i
$839$	7.44308	−	1.17887i	0.256964	−	0.0406991i	−0.0266234	−	0.999646i	$-0.508475\pi$
$839$	7.44308	−	1.17887i	0.256964	−	0.0406991i	0.283587	+	0.958946i	$0.408475\pi$
$840$		0			0
$841$	−15.7673	+	21.7018i	−0.543699	+	0.748337i
$842$	17.7982	−	2.81896i	0.613368	−	0.0971479i
$843$		0			0
$844$	86.5904	+	44.1200i	2.98057	+	1.51867i
$845$	1.11715	+	0.811658i	0.0384312	+	0.0279219i
$846$		0			0
$847$	−0.871070	+	0.871070i	−0.0299303	+	0.0299303i
$848$	1.79550	+	0.284379i	0.0616576	+	0.00976561i
$849$		0			0
$850$	20.0920	−	39.4327i	0.689149	−	1.35253i
$851$	−2.61491	−	8.04786i	−0.0896379	−	0.275877i
$852$		0			0
$853$	−44.7084	+	14.5266i	−1.53079	+	0.497383i	−0.948817	−	0.315827i	$-0.897718\pi$
$853$	−44.7084	+	14.5266i	−1.53079	+	0.497383i	−0.581971	+	0.813210i	$0.697718\pi$
$854$	−10.3923	−	65.6142i	−0.355616	−	2.24527i
$855$		0			0
$856$	59.9405	+	19.4759i	2.04873	+	0.665671i
$857$	−6.41959	+	19.7575i	−0.219289	+	0.674903i	0.779532	+	0.626362i	$0.215457\pi$
$857$	−6.41959	+	19.7575i	−0.219289	+	0.674903i	−0.998821	+	0.0485403i	$0.984543\pi$
$858$		0			0
$859$	−7.73097	−	10.6408i	−0.263777	−	0.363058i	0.656499	−	0.754327i	$-0.272036\pi$
$859$	−7.73097	−	10.6408i	−0.263777	−	0.363058i	−0.920277	+	0.391268i	$0.872036\pi$
$860$	0.448506			0.0152939
$861$		0			0
$862$	83.0485			2.82864
$863$	10.8301	+	14.9063i	0.368661	+	0.507418i	0.952536	−	0.304425i	$-0.0984644\pi$
$863$	10.8301	+	14.9063i	0.368661	+	0.507418i	−0.583876	+	0.811843i	$0.698464\pi$
$864$		0			0
$865$	−0.0724265	+	0.222906i	−0.00246257	+	0.00757902i
$866$	19.3574	+	6.28961i	0.657792	+	0.213729i
$867$		0			0
$868$	−5.12982	−	32.3884i	−0.174117	−	1.09933i
$869$	34.5468	−	11.2249i	1.17192	−	0.380779i
$870$		0			0
$871$	4.31683	+	13.2858i	0.146270	+	0.450174i
$872$	30.9207	−	60.6853i	1.04711	−	2.05506i
$873$		0			0
$874$	−40.9728	−	6.48945i	−1.38592	−	0.219509i
$875$	2.21344	−	2.21344i	0.0748280	−	0.0748280i
$876$		0			0
$877$	−15.2047	−	11.0469i	−0.513426	−	0.373026i	0.300696	−	0.953720i	$-0.402781\pi$
$877$	−15.2047	−	11.0469i	−0.513426	−	0.373026i	−0.814122	+	0.580694i	$0.802781\pi$
$878$	−52.9179	−	26.9630i	−1.78589	−	0.909958i
$879$		0			0
$880$	1.30164	−	0.206160i	0.0438784	−	0.00694965i
$881$	−6.74048	+	9.27748i	−0.227093	+	0.312566i	−0.907325	−	0.420431i	$-0.861879\pi$
$881$	−6.74048	+	9.27748i	−0.227093	+	0.312566i	0.680232	+	0.732997i	$0.261879\pi$
$882$		0			0
$883$	36.1792	−	5.73023i	1.21753	−	0.192837i	0.485576	−	0.874194i	$-0.338610\pi$
$883$	36.1792	−	5.73023i	1.21753	−	0.192837i	0.731951	+	0.681357i	$0.238610\pi$
$884$	−12.1059	+	8.79543i	−0.407165	+	0.295822i
$885$		0			0
$886$	−27.1393	−	19.7178i	−0.911761	−	0.662433i
$887$	−20.8224	−	40.8663i	−0.699149	−	1.37216i	−0.918071	−	0.396415i	$-0.870254\pi$
$887$	−20.8224	−	40.8663i	−0.699149	−	1.37216i	0.218922	−	0.975742i	$-0.429746\pi$
$888$		0			0
$889$	21.6120	+	3.42301i	0.724844	+	0.114804i
$890$	1.20877	−	0.615899i	0.0405181	−	0.0206450i
$891$		0			0
$892$	−3.98995	−	12.2798i	−0.133594	−	0.411159i
$893$			25.2145i			0.843772i
$894$		0			0
$895$	0.324422	+	2.04832i	0.0108442	+	0.0684678i
$896$	8.57732	−	54.1551i	0.286548	−	1.80919i
$897$		0			0
$898$	−0.800483	+	2.46363i	−0.0267125	+	0.0822125i
$899$	3.25603	+	3.25603i	0.108595	+	0.108595i
$900$		0			0
$901$	1.98228			0.0660394
$902$	−18.7880	−	49.1295i	−0.625572	−	1.63583i
$903$		0			0
$904$	−21.4316	−	29.4980i	−0.712803	−	0.981089i
$905$	0.145326	+	0.145326i	0.00483078	+	0.00483078i
$906$		0			0
$907$	−4.33501	−	1.40853i	−0.143942	−	0.0467695i	0.236160	−	0.971714i	$-0.424111\pi$
$907$	−4.33501	−	1.40853i	−0.143942	−	0.0467695i	−0.380102	+	0.924945i	$0.624111\pi$
$908$	−4.69061	+	29.6153i	−0.155663	+	0.982820i
$909$		0			0
$910$	−0.761012	+	0.247268i	−0.0252273	+	0.00819684i
$911$			0.497074i			0.0164688i	0.999966	+	0.00823439i	$0.00262112\pi$
$911$			0.497074i			0.0164688i	−0.999966	+	0.00823439i	$0.997379\pi$
$912$		0			0
$913$	0.976085	−	1.91567i	0.0323037	−	0.0633996i
$914$	65.1789	−	33.2103i	2.15593	−	1.09850i
$915$		0			0
$916$	−13.6815	+	13.6815i	−0.452049	+	0.452049i
$917$	−13.9552	−	27.3886i	−0.460841	−	0.904452i
$918$		0			0
$919$	−19.8412	−	10.1096i	−0.654502	−	0.333485i	0.0950101	−	0.995476i	$-0.469712\pi$
$919$	−19.8412	−	10.1096i	−0.654502	−	0.333485i	−0.749512	+	0.661991i	$0.769712\pi$
$920$	3.23078	−	2.34730i	0.106516	−	0.0773882i
$921$		0			0
$922$	−4.44739	+	6.12131i	−0.146467	+	0.201595i
$923$	−5.83520	+	8.03146i	−0.192068	+	0.264359i
$924$		0			0
$925$	4.55310	−	3.30802i	0.149705	−	0.108767i
$926$	15.3018	+	7.79664i	0.502847	+	0.256214i
$927$		0			0
$928$	0.693756	+	1.36157i	0.0227737	+	0.0446958i
$929$	6.13292	−	6.13292i	0.201215	−	0.201215i	−0.599306	−	0.800520i	$-0.704557\pi$
$929$	6.13292	−	6.13292i	0.201215	−	0.201215i	0.800520	+	0.599306i	$0.204557\pi$
$930$		0			0
$931$	0.586689	−	0.298933i	0.0192280	−	0.00979713i
$932$	−18.9067	+	37.1065i	−0.619310	+	1.21546i
$933$		0			0
$934$			95.9186i			3.13855i
$935$	1.36672	−	0.444074i	0.0446965	−	0.0145228i
$936$		0			0
$937$	−4.33799	+	27.3890i	−0.141716	+	0.894759i	0.809699	+	0.586846i	$0.199630\pi$
$937$	−4.33799	+	27.3890i	−0.141716	+	0.894759i	−0.951415	+	0.307913i	$0.900370\pi$
$938$	82.7630	+	26.8913i	2.70231	+	0.878033i
$939$		0			0
$940$	−3.53239	−	3.53239i	−0.115214	−	0.115214i
$941$	−15.4910	−	21.3216i	−0.504993	−	0.695063i	0.478072	−	0.878321i	$-0.341336\pi$
$941$	−15.4910	−	21.3216i	−0.504993	−	0.695063i	−0.983065	+	0.183257i	$0.941336\pi$
$942$		0			0
$943$	−35.6364	−	32.1686i	−1.16048	−	1.04755i
$944$	−6.51826			−0.212151
$945$		0			0
$946$	−5.76799	−	5.76799i	−0.187533	−	0.187533i
$947$	17.4125	−	53.5901i	0.565830	−	1.74144i	−0.0996438	−	0.995023i	$-0.531770\pi$
$947$	17.4125	−	53.5901i	0.565830	−	1.74144i	0.665474	−	0.746421i	$-0.268230\pi$
$948$		0			0
$949$	−1.79531	+	11.3351i	−0.0582782	+	0.367954i
$950$	−4.31602	−	27.2503i	−0.140030	−	0.884115i
$951$		0			0
$952$			45.2927i			1.46795i
$953$	9.02900	+	27.7884i	0.292478	+	0.900154i	0.984057	+	0.177854i	$0.0569154\pi$
$953$	9.02900	+	27.7884i	0.292478	+	0.900154i	−0.691579	+	0.722301i	$0.743085\pi$
$954$		0			0
$955$	−0.564766	+	0.287763i	−0.0182754	+	0.00931178i
$956$	−35.5182	−	5.62552i	−1.14874	−	0.181942i
$957$		0			0
$958$	12.8848	+	25.2879i	0.416291	+	0.817016i
$959$	13.1823	+	9.57748i	0.425678	+	0.309273i
$960$		0			0
$961$	17.1931	−	12.4915i	0.554615	−	0.402952i
$962$	−2.84569	+	0.450713i	−0.0917488	+	0.0145316i
$963$		0			0
$964$	64.8057	−	89.1973i	2.08725	−	2.87285i
$965$	0.752090	−	0.119119i	0.0242106	−	0.00383459i
$966$		0			0
$967$	−17.8304	−	9.08505i	−0.573388	−	0.292156i	0.143153	−	0.989701i	$-0.454276\pi$
$967$	−17.8304	−	9.08505i	−0.573388	−	0.292156i	−0.716541	+	0.697545i	$0.754276\pi$
$968$	−1.69350	−	1.23040i	−0.0544311	−	0.0395465i
$969$		0			0
$970$	0.550408	−	0.550408i	0.0176725	−	0.0176725i
$971$	3.43652	+	0.544291i	0.110283	+	0.0174671i	0.211332	−	0.977414i	$-0.432220\pi$
$971$	3.43652	+	0.544291i	0.110283	+	0.0174671i	−0.101049	+	0.994881i	$0.532220\pi$
$972$		0			0
$973$	21.6342	−	42.4595i	0.693561	−	1.36119i
$974$	18.9151	+	58.2146i	0.606078	+	1.86532i
$975$		0			0
$976$	32.3369	−	10.5069i	1.03508	−	0.336318i
$977$	0.933392	+	5.89321i	0.0298619	+	0.188540i	0.998110	−	0.0614501i	$-0.0195725\pi$
$977$	0.933392	+	5.89321i	0.0298619	+	0.188540i	−0.968248	+	0.249991i	$0.919572\pi$
$978$		0			0
$979$	−15.4983	−	5.03570i	−0.495328	−	0.160942i
$980$	−0.0403127	+	0.124070i	−0.00128774	+	0.00396326i
$981$		0			0
$982$	−44.9484	−	61.8661i	−1.43436	−	1.97423i
$983$	−42.8287			−1.36602			−0.683011	−	0.730408i	$-0.739330\pi$
$983$	−42.8287			−1.36602			−0.683011	+	0.730408i	$0.739330\pi$
$984$		0			0
$985$	−0.495816			−0.0157980
$986$	−7.69376	−	10.5895i	−0.245019	−	0.337240i
$987$		0			0
$988$	−2.88268	+	8.87196i	−0.0917101	+	0.282255i
$989$	−7.08074	−	2.30067i	−0.225154	−	0.0731571i
$990$		0			0
$991$	4.88595	+	30.8487i	0.155207	+	0.979940i	0.935192	+	0.354141i	$0.115227\pi$
$991$	4.88595	+	30.8487i	0.155207	+	0.979940i	−0.779985	+	0.625799i	$0.784773\pi$
$992$	−3.07671	+	0.999685i	−0.0976857	+	0.0317400i
$993$		0			0
$994$	19.1102	+	58.8153i	0.606140	+	1.86551i
$995$	0.843059	−	1.65460i	0.0267268	−	0.0524542i
$996$		0			0
$997$	43.0807	+	6.82332i	1.36438	+	0.216097i	0.795315	−	0.606196i	$-0.207305\pi$
$997$	43.0807	+	6.82332i	1.36438	+	0.216097i	0.569065	+	0.822293i	$0.307305\pi$
$998$	8.48534	−	8.48534i	0.268599	−	0.268599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.46.1		24
3.2	odd	2		41.2.g.a.5.3	✓	24
12.11	even	2		656.2.bs.d.497.3		24
41.33	even	20	inner	369.2.u.a.361.1		24
123.74	odd	20		41.2.g.a.33.3	yes	24
123.101	even	40		1681.2.a.m.1.22		24
123.104	even	40		1681.2.a.m.1.21		24
492.443	even	20		656.2.bs.d.33.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.3	✓	24	3.2	odd	2
41.2.g.a.33.3	yes	24	123.74	odd	20
369.2.u.a.46.1		24	1.1	even	1	trivial
369.2.u.a.361.1		24	41.33	even	20	inner
656.2.bs.d.33.3		24	492.443	even	20
656.2.bs.d.497.3		24	12.11	even	2
1681.2.a.m.1.21		24	123.104	even	40
1681.2.a.m.1.22		24	123.101	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42655 - 1.96347i) q^{2} +(-1.20216 + 3.69986i) q^{4} +(-0.110420 - 0.0358775i) q^{5} +(-0.422339 - 2.66654i) q^{7} +(4.36309 - 1.41766i) q^{8} +O(q^{10})\)	\(q+(-1.42655 - 1.96347i) q^{2} +(-1.20216 + 3.69986i) q^{4} +(-0.110420 - 0.0358775i) q^{5} +(-0.422339 - 2.66654i) q^{7} +(4.36309 - 1.41766i) q^{8} +(0.0870742 + 0.267987i) q^{10} +(1.53663 - 3.01580i) q^{11} +(-1.03889 - 0.164544i) q^{13} +(-4.63320 + 4.63320i) q^{14} +(-2.71311 - 1.97119i) q^{16} +(-3.25831 - 1.66019i) q^{17} +(-2.25168 + 0.356630i) q^{19} +(0.265483 - 0.365406i) q^{20} +(-8.11352 + 1.28505i) q^{22} +(-6.06568 + 4.40698i) q^{23} +(-4.03418 - 2.93100i) q^{25} +(1.15895 + 2.27456i) q^{26} +(10.3735 + 1.64301i) q^{28} +(-1.31408 + 0.669558i) q^{29} +(-0.964816 - 2.96940i) q^{31} -1.03614i q^{32} +(1.38839 + 8.76594i) q^{34} +(-0.0490344 + 0.309591i) q^{35} +(-0.348766 + 1.07339i) q^{37} +(3.91235 + 3.91235i) q^{38} -0.532633 q^{40} +(1.32339 + 6.26487i) q^{41} +(0.583672 + 0.803355i) q^{43} +(9.31076 + 9.31076i) q^{44} +(17.3060 + 5.62305i) q^{46} +(1.73020 - 10.9241i) q^{47} +(-0.274693 + 0.0892531i) q^{49} +12.1022i q^{50} +(1.85769 - 3.64593i) q^{52} +(-0.482987 + 0.246094i) q^{53} +(-0.277873 + 0.277873i) q^{55} +(-5.62295 - 11.0357i) q^{56} +(3.18926 + 1.62501i) q^{58} +(1.57246 - 1.14246i) q^{59} +(-5.95937 + 8.20238i) q^{61} +(-4.45398 + 6.13037i) q^{62} +(-7.46066 + 5.42048i) q^{64} +(0.108810 + 0.0554416i) q^{65} +(-6.02949 - 11.8335i) q^{67} +(10.0595 - 10.0595i) q^{68} +(0.677824 - 0.345368i) q^{70} +(4.28484 - 8.40947i) q^{71} -10.9108i q^{73} +(2.60511 - 0.846450i) q^{74} +(1.38738 - 8.75960i) q^{76} +(-8.69075 - 2.82380i) q^{77} +(7.58864 + 7.58864i) q^{79} +(0.228859 + 0.314998i) q^{80} +(10.4130 - 11.5356i) q^{82} +0.635212 q^{83} +(0.300218 + 0.300218i) q^{85} +(0.744731 - 2.29205i) q^{86} +(2.42908 - 15.3366i) q^{88} +(-0.753161 - 4.75527i) q^{89} +2.83974i q^{91} +(-9.01328 - 27.7400i) q^{92} +(-23.9173 + 12.1865i) q^{94} +(0.261424 + 0.0414055i) q^{95} +(-1.25412 - 2.46135i) q^{97} +(0.567108 + 0.412028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Introduction

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