LMFDB - Embedded newform 945.2.bv.d.523.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			523.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	945.523
Dual form			945.2.bv.d.262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 1.36603i) q^{2} -1.73205i q^{4} +(0.133975 + 2.23205i) q^{5} +(2.00000 - 1.73205i) q^{7} +(0.366025 + 0.366025i) q^{8} +O(q^{10})$	\(q+(1.36603 - 1.36603i) q^{2} -1.73205i q^{4} +(0.133975 + 2.23205i) q^{5} +(2.00000 - 1.73205i) q^{7} +(0.366025 + 0.366025i) q^{8} +(3.23205 + 2.86603i) q^{10} +(-2.73205 + 4.73205i) q^{11} +(1.00000 + 3.73205i) q^{13} +(0.366025 - 5.09808i) q^{14} +4.46410 q^{16} +(0.732051 - 2.73205i) q^{17} +(1.63397 - 2.83013i) q^{19} +(3.86603 - 0.232051i) q^{20} +(2.73205 + 10.1962i) q^{22} +(-1.23205 + 4.59808i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(6.46410 + 3.73205i) q^{26} +(-3.00000 - 3.46410i) q^{28} +(6.00000 - 3.46410i) q^{29} +0.196152i q^{31} +(5.36603 - 5.36603i) q^{32} +(-2.73205 - 4.73205i) q^{34} +(4.13397 + 4.23205i) q^{35} +(1.09808 + 4.09808i) q^{37} +(-1.63397 - 6.09808i) q^{38} +(-0.767949 + 0.866025i) q^{40} +(2.19615 + 1.26795i) q^{41} +(-0.401924 + 1.50000i) q^{43} +(8.19615 + 4.73205i) q^{44} +(4.59808 + 7.96410i) q^{46} +(-9.29423 - 9.29423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-5.96410 + 7.59808i) q^{50} +(6.46410 - 1.73205i) q^{52} +(1.63397 - 6.09808i) q^{53} +(-10.9282 - 5.46410i) q^{55} +(1.36603 + 0.0980762i) q^{56} +(3.46410 - 12.9282i) q^{58} +3.46410 q^{59} -11.3923i q^{61} +(0.267949 + 0.267949i) q^{62} -5.73205i q^{64} +(-8.19615 + 2.73205i) q^{65} +(0.901924 - 0.901924i) q^{67} +(-4.73205 - 1.26795i) q^{68} +(11.4282 + 0.133975i) q^{70} +6.00000 q^{71} +(-8.83013 - 2.36603i) q^{73} +(7.09808 + 4.09808i) q^{74} +(-4.90192 - 2.83013i) q^{76} +(2.73205 + 14.1962i) q^{77} +4.53590i q^{79} +(0.598076 + 9.96410i) q^{80} +(4.73205 - 1.26795i) q^{82} +(1.36603 + 0.366025i) q^{83} +(6.19615 + 1.26795i) q^{85} +(1.50000 + 2.59808i) q^{86} +(-2.73205 + 0.732051i) q^{88} +(-4.59808 + 7.96410i) q^{89} +(8.46410 + 5.73205i) q^{91} +(7.96410 + 2.13397i) q^{92} -25.3923 q^{94} +(6.53590 + 3.26795i) q^{95} +(2.09808 - 7.83013i) q^{97} +(-8.09808 - 10.8301i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8	$ 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8} + 6 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{19} + 12 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{28} + 24 q^{29} + 18 q^{32} - 4 q^{34} + 20 q^{35} - 6 q^{37} - 10 q^{38} - 10 q^{40} - 12 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} - 6 q^{47} + 4 q^{49} - 10 q^{50} + 12 q^{52} + 10 q^{53} - 16 q^{55} + 2 q^{56} + 8 q^{62} - 12 q^{65} + 14 q^{67} - 12 q^{68} + 18 q^{70} + 24 q^{71} - 18 q^{73} + 18 q^{74} - 30 q^{76} + 4 q^{77} - 8 q^{80} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 6 q^{86} - 4 q^{88} - 8 q^{89} + 20 q^{91} + 18 q^{92} - 60 q^{94} + 40 q^{95} - 2 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8 + 6 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^19 + 12 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^28 + 24 * q^29 + 18 * q^32 - 4 * q^34 + 20 * q^35 - 6 * q^37 - 10 * q^38 - 10 * q^40 - 12 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 - 6 * q^47 + 4 * q^49 - 10 * q^50 + 12 * q^52 + 10 * q^53 - 16 * q^55 + 2 * q^56 + 8 * q^62 - 12 * q^65 + 14 * q^67 - 12 * q^68 + 18 * q^70 + 24 * q^71 - 18 * q^73 + 18 * q^74 - 30 * q^76 + 4 * q^77 - 8 * q^80 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 6 * q^86 - 4 * q^88 - 8 * q^89 + 20 * q^91 + 18 * q^92 - 60 * q^94 + 40 * q^95 - 2 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	−	1.36603i	0.965926	−	0.965926i	−0.0335125	−	0.999438i	$-0.510669\pi$
$2$	1.36603	−	1.36603i	0.965926	−	0.965926i	0.999438	+	0.0335125i	$0.0106693\pi$
$3$		0			0
$3$		0			0
$4$		−	1.73205i		−	0.866025i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	0.366025	+	0.366025i	0.129410	+	0.129410i
$9$		0			0
$10$	3.23205	+	2.86603i	1.02206	+	0.906317i
$11$	−2.73205	+	4.73205i	−0.823744	+	1.42677i	0.0791309	+	0.996864i	$0.474785\pi$
$11$	−2.73205	+	4.73205i	−0.823744	+	1.42677i	−0.902875	+	0.429903i	$0.858548\pi$
$12$		0			0
$13$	1.00000	+	3.73205i	0.277350	+	1.03508i	0.954250	+	0.299010i	$0.0966563\pi$
$13$	1.00000	+	3.73205i	0.277350	+	1.03508i	−0.676900	+	0.736075i	$0.736677\pi$
$14$	0.366025	−	5.09808i	0.0978244	−	1.36252i
$15$		0			0
$16$	4.46410			1.11603
$17$	0.732051	−	2.73205i	0.177548	−	0.662620i	−0.818555	−	0.574428i	$-0.805225\pi$
$17$	0.732051	−	2.73205i	0.177548	−	0.662620i	0.996104	−	0.0881917i	$-0.0281088\pi$
$18$		0			0
$19$	1.63397	−	2.83013i	0.374859	−	0.649276i	−0.615447	−	0.788179i	$-0.711024\pi$
$19$	1.63397	−	2.83013i	0.374859	−	0.649276i	0.990306	+	0.138903i	$0.0443576\pi$
$20$	3.86603	−	0.232051i	0.864470	−	0.0518881i
$21$		0			0
$22$	2.73205	+	10.1962i	0.582475	+	2.17383i
$23$	−1.23205	+	4.59808i	−0.256900	+	0.958765i	0.710123	+	0.704078i	$0.248639\pi$
$23$	−1.23205	+	4.59808i	−0.256900	+	0.958765i	−0.967023	+	0.254688i	$0.918027\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	6.46410	+	3.73205i	1.26771	+	0.731915i
$27$		0			0
$28$	−3.00000	−	3.46410i	−0.566947	−	0.654654i
$29$	6.00000	−	3.46410i	1.11417	−	0.643268i	0.174265	−	0.984699i	$-0.444245\pi$
$29$	6.00000	−	3.46410i	1.11417	−	0.643268i	0.939907	+	0.341431i	$0.110912\pi$
$30$		0			0
$31$			0.196152i			0.0352300i	0.999845	+	0.0176150i	$0.00560732\pi$
$31$			0.196152i			0.0352300i	−0.999845	+	0.0176150i	$0.994393\pi$
$32$	5.36603	−	5.36603i	0.948588	−	0.948588i
$33$		0			0
$34$	−2.73205	−	4.73205i	−0.468543	−	0.811540i
$35$	4.13397	+	4.23205i	0.698769	+	0.715347i
$36$		0			0
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	0.995545	+	0.0942898i	$0.0300580\pi$
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	−0.815022	+	0.579430i	$0.803275\pi$
$38$	−1.63397	−	6.09808i	−0.265066	−	0.989239i
$39$		0			0
$40$	−0.767949	+	0.866025i	−0.121423	+	0.136931i
$41$	2.19615	+	1.26795i	0.342981	+	0.198020i	0.661590	−	0.749866i	$-0.269882\pi$
$41$	2.19615	+	1.26795i	0.342981	+	0.198020i	−0.318608	+	0.947886i	$0.603215\pi$
$42$		0			0
$43$	−0.401924	+	1.50000i	−0.0612928	+	0.228748i	−0.989777	−	0.142624i	$-0.954446\pi$
$43$	−0.401924	+	1.50000i	−0.0612928	+	0.228748i	0.928484	+	0.371372i	$0.121113\pi$
$44$	8.19615	+	4.73205i	1.23562	+	0.713384i
$45$		0			0
$46$	4.59808	+	7.96410i	0.677949	+	1.17424i
$47$	−9.29423	−	9.29423i	−1.35570	−	1.35570i	−0.879141	−	0.476561i	$-0.841883\pi$
$47$	−9.29423	−	9.29423i	−1.35570	−	1.35570i	−0.476561	−	0.879141i	$-0.658117\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−5.96410	+	7.59808i	−0.843451	+	1.07453i
$51$		0			0
$52$	6.46410	−	1.73205i	0.896410	−	0.240192i
$53$	1.63397	−	6.09808i	0.224444	−	0.837635i	−0.758183	−	0.652042i	$-0.773913\pi$
$53$	1.63397	−	6.09808i	0.224444	−	0.837635i	0.982627	−	0.185593i	$-0.0594207\pi$
$54$		0			0
$55$	−10.9282	−	5.46410i	−1.47356	−	0.736779i
$56$	1.36603	+	0.0980762i	0.182543	+	0.0131060i
$57$		0			0
$58$	3.46410	−	12.9282i	0.454859	−	1.69756i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$		0			0
$61$		−	11.3923i		−	1.45864i	−0.684175	−	0.729318i	$-0.739838\pi$
$61$		−	11.3923i		−	1.45864i	0.684175	−	0.729318i	$-0.260162\pi$
$62$	0.267949	+	0.267949i	0.0340296	+	0.0340296i
$63$		0			0
$64$		−	5.73205i		−	0.716506i
$65$	−8.19615	+	2.73205i	−1.01661	+	0.338869i
$66$		0			0
$67$	0.901924	−	0.901924i	0.110188	−	0.110188i	−0.649863	−	0.760051i	$-0.725174\pi$
$67$	0.901924	−	0.901924i	0.110188	−	0.110188i	0.760051	+	0.649863i	$0.225174\pi$
$68$	−4.73205	−	1.26795i	−0.573845	−	0.153761i
$69$		0			0
$70$	11.4282	+	0.133975i	1.36593	+	0.0160130i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−8.83013	−	2.36603i	−1.03349	−	0.276922i	−0.298076	−	0.954542i	$-0.596345\pi$
$73$	−8.83013	−	2.36603i	−1.03349	−	0.276922i	−0.735412	+	0.677620i	$0.763012\pi$
$74$	7.09808	+	4.09808i	0.825135	+	0.476392i
$75$		0			0
$76$	−4.90192	−	2.83013i	−0.562289	−	0.324638i
$77$	2.73205	+	14.1962i	0.311346	+	1.61780i
$78$		0			0
$79$			4.53590i			0.510328i	0.966898	+	0.255164i	$0.0821295\pi$
$79$			4.53590i			0.510328i	−0.966898	+	0.255164i	$0.917870\pi$
$80$	0.598076	+	9.96410i	0.0668670	+	1.11402i
$81$		0			0
$82$	4.73205	−	1.26795i	0.522568	−	0.140022i
$83$	1.36603	+	0.366025i	0.149941	+	0.0401765i	0.333009	−	0.942924i	$-0.391936\pi$
$83$	1.36603	+	0.366025i	0.149941	+	0.0401765i	−0.183068	+	0.983100i	$0.558603\pi$
$84$		0			0
$85$	6.19615	+	1.26795i	0.672067	+	0.137528i
$86$	1.50000	+	2.59808i	0.161749	+	0.280158i
$87$		0			0
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	−4.59808	+	7.96410i	−0.487395	+	0.844193i	−0.999895	−	0.0144942i	$-0.995386\pi$
$89$	−4.59808	+	7.96410i	−0.487395	+	0.844193i	0.512500	+	0.858687i	$0.328720\pi$
$90$		0			0
$91$	8.46410	+	5.73205i	0.887279	+	0.600882i
$92$	7.96410	+	2.13397i	0.830315	+	0.222482i
$93$		0			0
$94$	−25.3923			−2.61902
$95$	6.53590	+	3.26795i	0.670569	+	0.335285i
$96$		0			0
$97$	2.09808	−	7.83013i	0.213027	−	0.795029i	−0.773824	−	0.633400i	$-0.781659\pi$
$97$	2.09808	−	7.83013i	0.213027	−	0.795029i	0.986852	−	0.161629i	$-0.0516747\pi$
$98$	−8.09808	−	10.8301i	−0.818029	−	1.09401i
$99$		0			0
$100$	1.03590	+	8.59808i	0.103590	+	0.859808i
$101$	−15.2321	−	8.79423i	−1.51565	−	0.875058i	−0.999831	−	0.0183580i	$-0.994156\pi$
$101$	−15.2321	−	8.79423i	−1.51565	−	0.875058i	−0.515814	−	0.856700i	$-0.672511\pi$
$102$		0			0
$103$	3.96410	+	1.06218i	0.390595	+	0.104659i	0.448771	−	0.893647i	$-0.351862\pi$
$103$	3.96410	+	1.06218i	0.390595	+	0.104659i	−0.0581764	+	0.998306i	$0.518529\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−6.09808	−	10.5622i	−0.592298	−	1.02589i
$107$	0.633975	+	2.36603i	0.0612886	+	0.228732i	0.989776	−	0.142632i	$-0.0455566\pi$
$107$	0.633975	+	2.36603i	0.0612886	+	0.228732i	−0.928487	+	0.371365i	$0.878890\pi$
$108$		0			0
$109$	−1.73205	+	1.00000i	−0.165900	+	0.0957826i	−0.580651	−	0.814152i	$-0.697202\pi$
$109$	−1.73205	+	1.00000i	−0.165900	+	0.0957826i	0.414751	+	0.909935i	$0.363869\pi$
$110$	−22.3923	+	7.46410i	−2.13502	+	0.711674i
$111$		0			0
$112$	8.92820	−	7.73205i	0.843636	−	0.730610i
$113$	7.09808	−	1.90192i	0.667731	−	0.178918i	0.0909984	−	0.995851i	$-0.470994\pi$
$113$	7.09808	−	1.90192i	0.667731	−	0.178918i	0.576732	+	0.816933i	$0.304328\pi$
$114$		0			0
$115$	−10.4282	−	2.13397i	−0.972435	−	0.198994i
$116$	−6.00000	−	10.3923i	−0.557086	−	0.964901i
$117$		0			0
$118$	4.73205	−	4.73205i	0.435621	−	0.435621i
$119$	−3.26795	−	6.73205i	−0.299572	−	0.617126i
$120$		0			0
$121$	−9.42820	−	16.3301i	−0.857109	−	1.48456i
$122$	−15.5622	−	15.5622i	−1.40893	−	1.40893i
$123$		0			0
$124$	0.339746			0.0305101
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−15.7583	+	15.7583i	−1.39833	+	1.39833i	−0.593468	+	0.804857i	$0.702242\pi$
$127$	−15.7583	+	15.7583i	−1.39833	+	1.39833i	−0.804857	+	0.593468i	$0.797758\pi$
$128$	2.90192	+	2.90192i	0.256496	+	0.256496i
$129$		0			0
$130$	−7.46410	+	14.9282i	−0.654645	+	1.30929i
$131$	4.39230	−	2.53590i	0.383757	−	0.221562i	−0.295694	−	0.955283i	$-0.595551\pi$
$131$	4.39230	−	2.53590i	0.383757	−	0.221562i	0.679452	+	0.733720i	$0.262218\pi$
$132$		0			0
$133$	−1.63397	−	8.49038i	−0.141684	−	0.736209i
$134$		−	2.46410i		−	0.212866i
$135$		0			0
$136$	1.26795	−	0.732051i	0.108726	−	0.0627728i
$137$	−0.535898	−	2.00000i	−0.0457849	−	0.170872i	0.939248	−	0.343240i	$-0.111525\pi$
$137$	−0.535898	−	2.00000i	−0.0457849	−	0.170872i	−0.985032	+	0.172369i	$0.944858\pi$
$138$		0			0
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	−0.974710	−	0.223474i	$-0.928260\pi$
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	0.680889	+	0.732387i	$0.261594\pi$
$140$	7.33013	−	7.16025i	0.619509	−	0.605152i
$141$		0			0
$142$	8.19615	−	8.19615i	0.687806	−	0.687806i
$143$	−20.3923	−	5.46410i	−1.70529	−	0.456931i
$144$		0			0
$145$	8.53590	+	12.9282i	0.708868	+	1.07363i
$146$	−15.2942	+	8.83013i	−1.26576	+	0.730787i
$147$		0			0
$148$	7.09808	−	1.90192i	0.583458	−	0.156337i
$149$	−2.89230	+	1.66987i	−0.236947	+	0.136801i	−0.613773	−	0.789483i	$-0.710349\pi$
$149$	−2.89230	+	1.66987i	−0.236947	+	0.136801i	0.376826	+	0.926284i	$0.377016\pi$
$150$		0			0
$151$	−2.36603	+	4.09808i	−0.192544	+	0.333497i	−0.946093	−	0.323896i	$-0.895007\pi$
$151$	−2.36603	+	4.09808i	−0.192544	+	0.333497i	0.753548	+	0.657392i	$0.228341\pi$
$152$	1.63397	−	0.437822i	0.132533	−	0.0355121i
$153$		0			0
$154$	23.1244	+	15.6603i	1.86341	+	1.26194i
$155$	−0.437822	+	0.0262794i	−0.0351667	+	0.00211082i
$156$		0			0
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	0.666076	−	0.745884i	$-0.267973\pi$
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	−0.745884	+	0.666076i	$0.767973\pi$
$158$	6.19615	+	6.19615i	0.492939	+	0.492939i
$159$		0			0
$160$	12.6962	+	11.2583i	1.00372	+	0.890049i
$161$	5.50000	+	11.3301i	0.433461	+	0.892939i
$162$		0			0
$163$	−8.83013	+	2.36603i	−0.691629	+	0.185321i	−0.587478	−	0.809240i	$-0.699879\pi$
$163$	−8.83013	+	2.36603i	−0.691629	+	0.185321i	−0.104151	+	0.994562i	$0.533212\pi$
$164$	2.19615	−	3.80385i	0.171491	−	0.297031i
$165$		0			0
$166$	2.36603	−	1.36603i	0.183639	−	0.106024i
$167$	−13.5263	+	3.62436i	−1.04669	+	0.280461i	−0.740885	−	0.671632i	$-0.765594\pi$
$167$	−13.5263	+	3.62436i	−1.04669	+	0.280461i	−0.305810	+	0.952093i	$0.598927\pi$
$168$		0			0
$169$	−1.66987	+	0.964102i	−0.128452	+	0.0741617i
$170$	10.1962	−	6.73205i	0.782009	−	0.516325i
$171$		0			0
$172$	2.59808	+	0.696152i	0.198101	+	0.0530811i
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	−0.216088	−	0.976374i	$-0.569330\pi$
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	0.976374	+	0.216088i	$0.0693298\pi$
$174$		0			0
$175$	−8.89230	+	9.79423i	−0.672195	+	0.740374i
$176$	−12.1962	+	21.1244i	−0.919320	+	1.59231i
$177$		0			0
$178$	4.59808	+	17.1603i	0.344640	+	1.28622i
$179$	−10.9019	+	6.29423i	−0.814848	+	0.470453i	−0.848637	−	0.528976i	$-0.822576\pi$
$179$	−10.9019	+	6.29423i	−0.814848	+	0.470453i	0.0337886	+	0.999429i	$0.489243\pi$
$180$		0			0
$181$			11.4641i			0.852120i	0.904695	+	0.426060i	$0.140099\pi$
$181$			11.4641i			0.852120i	−0.904695	+	0.426060i	$0.859901\pi$
$182$	19.3923	−	3.73205i	1.43745	−	0.276638i
$183$		0			0
$184$	−2.13397	+	1.23205i	−0.157319	+	0.0908280i
$185$	−9.00000	+	3.00000i	−0.661693	+	0.220564i
$186$		0			0
$187$	10.9282	+	10.9282i	0.799149	+	0.799149i
$188$	−16.0981	+	16.0981i	−1.17407	+	1.17407i
$189$		0			0
$190$	13.3923	−	4.46410i	0.971580	−	0.323860i
$191$	17.6603			1.27785			0.638926	−	0.769269i	$-0.279379\pi$
$191$	17.6603			1.27785			0.638926	+	0.769269i	$0.279379\pi$
$192$		0			0
$193$	−14.4641	−	14.4641i	−1.04115	−	1.04115i	−0.999116	−	0.0420326i	$-0.986617\pi$
$193$	−14.4641	−	14.4641i	−1.04115	−	1.04115i	−0.0420326	−	0.999116i	$-0.513383\pi$
$194$	−7.83013	−	13.5622i	−0.562170	−	0.973708i
$195$		0			0
$196$	−12.0000	−	1.73205i	−0.857143	−	0.123718i
$197$	17.4641	−	17.4641i	1.24427	−	1.24427i	0.286051	−	0.958214i	$-0.407657\pi$
$197$	17.4641	−	17.4641i	1.24427	−	1.24427i	0.958214	−	0.286051i	$-0.0923428\pi$
$198$		0			0
$199$	−3.92820	−	6.80385i	−0.278463	−	0.482312i	0.692540	−	0.721379i	$-0.256492\pi$
$199$	−3.92820	−	6.80385i	−0.278463	−	0.482312i	−0.971003	+	0.239068i	$0.923158\pi$
$200$	−2.03590	−	1.59808i	−0.143960	−	0.113001i
$201$		0			0
$202$	−32.8205	+	8.79423i	−2.30924	+	0.618760i
$203$	6.00000	−	17.3205i	0.421117	−	1.21566i
$204$		0			0
$205$	−2.53590	+	5.07180i	−0.177115	+	0.354230i
$206$	6.86603	−	3.96410i	0.478379	−	0.276192i
$207$		0			0
$208$	4.46410	+	16.6603i	0.309530	+	1.15518i
$209$	8.92820	+	15.4641i	0.617577	+	1.06967i
$210$		0			0
$211$	−4.46410	+	7.73205i	−0.307321	+	0.532296i	−0.977775	−	0.209655i	$-0.932766\pi$
$211$	−4.46410	+	7.73205i	−0.307321	+	0.532296i	0.670454	+	0.741951i	$0.266099\pi$
$212$	−10.5622	−	2.83013i	−0.725413	−	0.194374i
$213$		0			0
$214$	4.09808	+	2.36603i	0.280139	+	0.161738i
$215$	−3.40192	−	0.696152i	−0.232009	−	0.0474772i
$216$		0			0
$217$	0.339746	+	0.392305i	0.0230635	+	0.0266314i
$218$	−1.00000	+	3.73205i	−0.0677285	+	0.252766i
$219$		0			0
$220$	−9.46410	+	18.9282i	−0.638070	+	1.27614i
$221$	10.9282			0.735111
$222$		0			0
$223$	4.96410	+	1.33013i	0.332421	+	0.0890719i	0.421169	−	0.906982i	$-0.361620\pi$
$223$	4.96410	+	1.33013i	0.332421	+	0.0890719i	−0.0887481	+	0.996054i	$0.528287\pi$
$224$	1.43782	−	20.0263i	0.0960685	−	1.33806i
$225$		0			0
$226$	7.09808	−	12.2942i	0.472157	−	0.817800i
$227$	14.5622	−	3.90192i	0.966526	−	0.258980i	0.259165	−	0.965833i	$-0.416553\pi$
$227$	14.5622	−	3.90192i	0.966526	−	0.258980i	0.707360	+	0.706853i	$0.249886\pi$
$228$		0			0
$229$	−2.33013	−	4.03590i	−0.153979	−	0.266700i	0.778708	−	0.627387i	$-0.215876\pi$
$229$	−2.33013	−	4.03590i	−0.153979	−	0.266700i	−0.932687	+	0.360687i	$0.882542\pi$
$230$	−17.1603	+	11.3301i	−1.13151	+	0.747086i
$231$		0			0
$232$	3.46410	+	0.928203i	0.227429	+	0.0609395i
$233$	11.8301	−	3.16987i	0.775017	−	0.207665i	0.150430	−	0.988621i	$-0.451934\pi$
$233$	11.8301	−	3.16987i	0.775017	−	0.207665i	0.624587	+	0.780955i	$0.285267\pi$
$234$		0			0
$235$	19.5000	−	21.9904i	1.27204	−	1.43449i
$236$		−	6.00000i		−	0.390567i
$237$		0			0
$238$	−13.6603	−	4.73205i	−0.885463	−	0.306733i
$239$	19.0526	+	11.0000i	1.23241	+	0.711531i	0.967531	−	0.252752i	$-0.0813355\pi$
$239$	19.0526	+	11.0000i	1.23241	+	0.711531i	0.264876	+	0.964282i	$0.414669\pi$
$240$		0			0
$241$	8.25833	+	4.76795i	0.531966	+	0.307131i	0.741817	−	0.670603i	$-0.233964\pi$
$241$	8.25833	+	4.76795i	0.531966	+	0.307131i	−0.209851	+	0.977733i	$0.567298\pi$
$242$	−35.1865	−	9.42820i	−2.26188	−	0.606068i
$243$		0			0
$244$	−19.7321			−1.26322
$245$	15.5981	+	1.30385i	0.996525	+	0.0832998i
$246$		0			0
$247$	12.1962	+	3.26795i	0.776023	+	0.207935i
$248$	−0.0717968	+	0.0717968i	−0.00455910	+	0.00455910i
$249$		0			0
$250$	−17.7583	−	12.2942i	−1.12314	−	0.777555i
$251$			5.85641i			0.369653i	0.982771	+	0.184827i	$0.0591723\pi$
$251$			5.85641i			0.369653i	−0.982771	+	0.184827i	$0.940828\pi$
$252$		0			0
$253$	−18.3923	−	18.3923i	−1.15631	−	1.15631i
$254$			43.0526i			2.70136i
$255$		0			0
$256$	19.3923			1.21202
$257$	−3.22243	+	12.0263i	−0.201010	+	0.750179i	0.789619	+	0.613597i	$0.210278\pi$
$257$	−3.22243	+	12.0263i	−0.201010	+	0.750179i	−0.990629	+	0.136581i	$0.956388\pi$
$258$		0			0
$259$	9.29423	+	6.29423i	0.577515	+	0.391104i
$260$	4.73205	+	14.1962i	0.293469	+	0.880408i
$261$		0			0
$262$	2.53590	−	9.46410i	0.156668	−	0.584694i
$263$	−27.4545	+	7.35641i	−1.69292	+	0.453615i	−0.971140	−	0.238511i	$-0.923341\pi$
$263$	−27.4545	+	7.35641i	−1.69292	+	0.453615i	−0.721776	+	0.692127i	$0.756674\pi$
$264$		0			0
$265$	13.8301	+	2.83013i	0.849578	+	0.173853i
$266$	−13.8301	−	9.36603i	−0.847979	−	0.574268i
$267$		0			0
$268$	−1.56218	−	1.56218i	−0.0954252	−	0.0954252i
$269$	−4.96410	−	8.59808i	−0.302667	−	0.524234i	0.674072	−	0.738665i	$-0.264544\pi$
$269$	−4.96410	−	8.59808i	−0.302667	−	0.524234i	−0.976739	+	0.214431i	$0.931210\pi$
$270$		0			0
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	0.167163	−	0.985929i	$-0.446539\pi$
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	−0.770258	+	0.637732i	$0.779873\pi$
$272$	3.26795	−	12.1962i	0.198149	−	0.739500i
$273$		0			0
$274$	−3.46410	−	2.00000i	−0.209274	−	0.120824i
$275$	10.7321	−	25.1244i	0.647167	−	1.51506i
$276$		0			0
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	−0.926562	−	0.376141i	$-0.877251\pi$
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	0.614356	−	0.789029i	$-0.289416\pi$
$278$	3.46410	+	12.9282i	0.207763	+	0.775382i
$279$		0			0
$280$	−0.0358984	+	3.06218i	−0.00214534	+	0.183000i
$281$	−6.86603	−	11.8923i	−0.409593	−	0.709435i	0.585251	−	0.810852i	$-0.300996\pi$
$281$	−6.86603	−	11.8923i	−0.409593	−	0.709435i	−0.994844	+	0.101417i	$0.967663\pi$
$282$		0			0
$283$	15.7583	−	15.7583i	0.936736	−	0.936736i	−0.0613790	−	0.998115i	$-0.519550\pi$
$283$	15.7583	−	15.7583i	0.936736	−	0.936736i	0.998115	+	0.0613790i	$0.0195498\pi$
$284$		−	10.3923i		−	0.616670i
$285$		0			0
$286$	−35.3205	+	20.3923i	−2.08855	+	1.20582i
$287$	6.58846	−	1.26795i	0.388904	−	0.0748447i
$288$		0			0
$289$	7.79423	+	4.50000i	0.458484	+	0.264706i
$290$	29.3205	+	6.00000i	1.72176	+	0.352332i
$291$		0			0
$292$	−4.09808	+	15.2942i	−0.239822	+	0.895027i
$293$	−5.43782	−	20.2942i	−0.317681	−	1.18560i	−0.921468	−	0.388455i	$-0.873009\pi$
$293$	−5.43782	−	20.2942i	−0.317681	−	1.18560i	0.603787	−	0.797146i	$-0.293658\pi$
$294$		0			0
$295$	0.464102	+	7.73205i	0.0270210	+	0.450177i
$296$	−1.09808	+	1.90192i	−0.0638244	+	0.110547i
$297$		0			0
$298$	−1.66987	+	6.23205i	−0.0967331	+	0.361013i
$299$	−18.3923			−1.06365
$300$		0			0
$301$	1.79423	+	3.69615i	0.103418	+	0.213043i
$302$	2.36603	+	8.83013i	0.136149	+	0.508117i
$303$		0			0
$304$	7.29423	−	12.6340i	0.418353	−	0.724608i
$305$	25.4282	−	1.52628i	1.45601	−	0.0873945i
$306$		0			0
$307$	−17.5359	−	17.5359i	−1.00083	−	1.00083i	−1.00000		0.000826926i	$-0.999737\pi$
$307$	−17.5359	−	17.5359i	−1.00083	−	1.00083i	−0.000826926	−	1.00000i	$-0.500263\pi$
$308$	24.5885	−	4.73205i	1.40106	−	0.269634i
$309$		0			0
$310$	−0.562178	+	0.633975i	−0.0319296	+	0.0360073i
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$		0			0
$313$	5.19615	−	5.19615i	0.293704	−	0.293704i	−0.544838	−	0.838542i	$-0.683409\pi$
$313$	5.19615	−	5.19615i	0.293704	−	0.293704i	0.838542	+	0.544838i	$0.183409\pi$
$314$	−2.73205			−0.154179
$315$		0			0
$316$	7.85641			0.441957
$317$	−8.46410	+	8.46410i	−0.475391	+	0.475391i	−0.903654	−	0.428263i	$-0.859126\pi$
$317$	−8.46410	+	8.46410i	−0.475391	+	0.475391i	0.428263	+	0.903654i	$0.359126\pi$
$318$		0			0
$319$			37.8564i			2.11955i
$320$	12.7942	−	0.767949i	0.715219	−	0.0429297i
$321$		0			0
$322$	22.9904	+	7.96410i	1.28120	+	0.443822i
$323$	−6.53590	−	6.53590i	−0.363667	−	0.363667i
$324$		0			0
$325$	−7.19615	−	17.9282i	−0.399171	−	0.994478i
$326$	−8.83013	+	15.2942i	−0.489056	+	0.847069i
$327$		0			0
$328$	0.339746	+	1.26795i	0.0187593	+	0.0700108i
$329$	−34.6865	−	2.49038i	−1.91233	−	0.137299i
$330$		0			0
$331$	18.3397			1.00804			0.504022	−	0.863691i	$-0.331853\pi$
$331$	18.3397			1.00804			0.504022	+	0.863691i	$0.331853\pi$
$332$	0.633975	−	2.36603i	0.0347939	−	0.129853i
$333$		0			0
$334$	−13.5263	+	23.4282i	−0.740125	+	1.28193i
$335$	2.13397	+	1.89230i	0.116591	+	0.103388i
$336$		0			0
$337$	−1.19615	−	4.46410i	−0.0651586	−	0.243175i	0.925663	−	0.378348i	$-0.123508\pi$
$337$	−1.19615	−	4.46410i	−0.0651586	−	0.243175i	−0.990822	+	0.135173i	$0.956841\pi$
$338$	−0.964102	+	3.59808i	−0.0524402	+	0.195710i
$339$		0			0
$340$	2.19615	−	10.7321i	0.119103	−	0.582027i
$341$	−0.928203	−	0.535898i	−0.0502650	−	0.0290205i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−0.696152	+	0.401924i	−0.0375340	+	0.0216703i
$345$		0			0
$346$		−	27.3205i		−	1.46876i
$347$	14.8301	−	14.8301i	0.796123	−	0.796123i	−0.186359	−	0.982482i	$-0.559669\pi$
$347$	14.8301	−	14.8301i	0.796123	−	0.796123i	0.982482	+	0.186359i	$0.0596687\pi$
$348$		0			0
$349$	17.0622	+	29.5526i	0.913317	+	1.58191i	0.809346	+	0.587332i	$0.199822\pi$
$349$	17.0622	+	29.5526i	0.913317	+	1.58191i	0.103971	+	0.994580i	$0.466845\pi$
$350$	1.23205	+	25.5263i	0.0658559	+	1.36444i
$351$		0			0
$352$	10.7321	+	40.0526i	0.572020	+	2.13481i
$353$	2.87564	+	10.7321i	0.153055	+	0.571209i	0.999264	+	0.0383582i	$0.0122128\pi$
$353$	2.87564	+	10.7321i	0.153055	+	0.571209i	−0.846209	+	0.532851i	$0.821121\pi$
$354$		0			0
$355$	0.803848	+	13.3923i	0.0426638	+	0.710790i
$356$	13.7942	+	7.96410i	0.731093	+	0.422097i
$357$		0			0
$358$	−6.29423	+	23.4904i	−0.332660	+	1.24151i
$359$	−17.9545	−	10.3660i	−0.947601	−	0.547098i	−0.0552664	−	0.998472i	$-0.517601\pi$
$359$	−17.9545	−	10.3660i	−0.947601	−	0.547098i	−0.892335	+	0.451374i	$0.850934\pi$
$360$		0			0
$361$	4.16025	+	7.20577i	0.218961	+	0.379251i
$362$	15.6603	+	15.6603i	0.823085	+	0.823085i
$363$		0			0
$364$	9.92820	−	14.6603i	0.520379	−	0.768406i
$365$	4.09808	−	20.0263i	0.214503	−	1.04822i
$366$		0			0
$367$	−6.59808	+	1.76795i	−0.344417	+	0.0922862i	−0.426881	−	0.904308i	$-0.640388\pi$
$367$	−6.59808	+	1.76795i	−0.344417	+	0.0922862i	0.0824642	+	0.996594i	$0.473721\pi$
$368$	−5.50000	+	20.5263i	−0.286707	+	1.07001i
$369$		0			0
$370$	−8.19615	+	16.3923i	−0.426098	+	0.852195i
$371$	−7.29423	−	15.0263i	−0.378697	−	0.780126i
$372$		0			0
$373$	1.09808	−	4.09808i	0.0568562	−	0.212190i	−0.931653	−	0.363348i	$-0.881634\pi$
$373$	1.09808	−	4.09808i	0.0568562	−	0.212190i	0.988510	+	0.151158i	$0.0483002\pi$
$374$	29.8564			1.54384
$375$		0			0
$376$		−	6.80385i		−	0.350882i
$377$	18.9282	+	18.9282i	0.974852	+	0.974852i
$378$		0			0
$379$			12.5359i			0.643926i	0.946752	+	0.321963i	$0.104343\pi$
$379$			12.5359i			0.643926i	−0.946752	+	0.321963i	$0.895657\pi$
$380$	5.66025	−	11.3205i	0.290365	−	0.580730i
$381$		0			0
$382$	24.1244	−	24.1244i	1.23431	−	1.23431i
$383$	−15.7942	−	4.23205i	−0.807047	−	0.216248i	−0.168372	−	0.985724i	$-0.553851\pi$
$383$	−15.7942	−	4.23205i	−0.807047	−	0.216248i	−0.638676	+	0.769476i	$0.720518\pi$
$384$		0			0
$385$	−31.3205	+	8.00000i	−1.59624	+	0.407718i
$386$	−39.5167			−2.01135
$387$		0			0
$388$	−13.5622	−	3.63397i	−0.688515	−	0.184487i
$389$	1.03590	+	0.598076i	0.0525221	+	0.0303237i	0.526031	−	0.850465i	$-0.323680\pi$
$389$	1.03590	+	0.598076i	0.0525221	+	0.0303237i	−0.473509	+	0.880789i	$0.657013\pi$
$390$		0			0
$391$	11.6603	+	6.73205i	0.589684	+	0.340454i
$392$	2.90192	−	2.16987i	0.146569	−	0.109595i
$393$		0			0
$394$		−	47.7128i		−	2.40374i
$395$	−10.1244	+	0.607695i	−0.509412	+	0.0305765i
$396$		0			0
$397$	32.7846	−	8.78461i	1.64541	−	0.440887i	0.687089	−	0.726573i	$-0.258888\pi$
$397$	32.7846	−	8.78461i	1.64541	−	0.440887i	0.958323	+	0.285686i	$0.0922215\pi$
$398$	−14.6603	−	3.92820i	−0.734852	−	0.196903i
$399$		0			0
$400$	−22.1603	+	2.66987i	−1.10801	+	0.133494i
$401$	11.6962	+	20.2583i	0.584078	+	1.01165i	0.994990	+	0.0999776i	$0.0318771\pi$
$401$	11.6962	+	20.2583i	0.584078	+	1.01165i	−0.410912	+	0.911675i	$0.634790\pi$
$402$		0			0
$403$	−0.732051	+	0.196152i	−0.0364660	+	0.00977105i
$404$	−15.2321	+	26.3827i	−0.757823	+	1.31259i
$405$		0			0
$406$	−15.4641	−	31.8564i	−0.767470	−	1.58101i
$407$	−22.3923	−	6.00000i	−1.10995	−	0.297409i
$408$		0			0
$409$	5.39230			0.266632			0.133316	−	0.991074i	$-0.457437\pi$
$409$	5.39230			0.266632			0.133316	+	0.991074i	$0.457437\pi$
$410$	3.46410	+	10.3923i	0.171080	+	0.513239i
$411$		0			0
$412$	1.83975	−	6.86603i	0.0906378	−	0.338265i
$413$	6.92820	−	6.00000i	0.340915	−	0.295241i
$414$		0			0
$415$	−0.633975	+	3.09808i	−0.0311206	+	0.152079i
$416$	25.3923	+	14.6603i	1.24496	+	0.718778i
$417$		0			0
$418$	33.3205	+	8.92820i	1.62976	+	0.436693i
$419$	4.00000	−	6.92820i	0.195413	−	0.338465i	−0.751623	−	0.659593i	$-0.770729\pi$
$419$	4.00000	−	6.92820i	0.195413	−	0.338465i	0.947036	+	0.321128i	$0.104062\pi$
$420$		0			0
$421$	−11.5263	−	19.9641i	−0.561756	−	0.972991i	−0.997343	−	0.0728441i	$-0.976792\pi$
$421$	−11.5263	−	19.9641i	−0.561756	−	0.972991i	0.435587	−	0.900147i	$-0.356541\pi$
$422$	4.46410	+	16.6603i	0.217309	+	0.811008i
$423$		0			0
$424$	2.83013	−	1.63397i	0.137443	−	0.0793528i
$425$	−2.00000	+	14.0000i	−0.0970143	+	0.679100i
$426$		0			0
$427$	−19.7321	−	22.7846i	−0.954901	−	1.10262i
$428$	4.09808	−	1.09808i	0.198088	−	0.0530775i
$429$		0			0
$430$	−5.59808	+	3.69615i	−0.269963	+	0.178244i
$431$	−12.0981	−	20.9545i	−0.582744	−	1.00934i	−0.995153	−	0.0983430i	$-0.968646\pi$
$431$	−12.0981	−	20.9545i	−0.582744	−	1.00934i	0.412409	−	0.910999i	$-0.364688\pi$
$432$		0			0
$433$	9.80385	−	9.80385i	0.471143	−	0.471143i	−0.431141	−	0.902284i	$-0.641889\pi$
$433$	9.80385	−	9.80385i	0.471143	−	0.471143i	0.902284	+	0.431141i	$0.141889\pi$
$434$	1.00000	+	0.0717968i	0.0480015	+	0.00344636i
$435$		0			0
$436$	1.73205	+	3.00000i	0.0829502	+	0.143674i
$437$	11.0000	+	11.0000i	0.526201	+	0.526201i
$438$		0			0
$439$	−5.85641			−0.279511			−0.139756	−	0.990186i	$-0.544632\pi$
$439$	−5.85641			−0.279511			−0.139756	+	0.990186i	$0.544632\pi$
$440$	−2.00000	−	6.00000i	−0.0953463	−	0.286039i
$441$		0			0
$442$	14.9282	−	14.9282i	0.710062	−	0.710062i
$443$	0.660254	+	0.660254i	0.0313696	+	0.0313696i	0.722618	−	0.691248i	$-0.242939\pi$
$443$	0.660254	+	0.660254i	0.0313696	+	0.0313696i	−0.691248	+	0.722618i	$0.742939\pi$
$444$		0			0
$445$	−18.3923	−	9.19615i	−0.871879	−	0.435939i
$446$	8.59808	−	4.96410i	0.407131	−	0.235057i
$447$		0			0
$448$	−9.92820	−	11.4641i	−0.469064	−	0.541628i
$449$		−	1.58846i		−	0.0749639i	−0.999297	−	0.0374820i	$-0.988066\pi$
$449$		−	1.58846i		−	0.0749639i	0.999297	−	0.0374820i	$-0.0119337\pi$
$450$		0			0
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$	−3.29423	−	12.2942i	−0.154947	−	0.578272i
$453$		0			0
$454$	14.5622	−	25.2224i	0.683437	−	1.18375i
$455$	−11.6603	+	19.6603i	−0.546641	+	0.921687i
$456$		0			0
$457$	−7.33975	+	7.33975i	−0.343339	+	0.343339i	−0.857621	−	0.514282i	$-0.828058\pi$
$457$	−7.33975	+	7.33975i	−0.343339	+	0.343339i	0.514282	+	0.857621i	$0.328058\pi$
$458$	−8.69615	−	2.33013i	−0.406345	−	0.108880i
$459$		0			0
$460$	−3.69615	+	18.0622i	−0.172334	+	0.842153i
$461$	−1.03590	+	0.598076i	−0.0482466	+	0.0278552i	−0.523929	−	0.851762i	$-0.675534\pi$
$461$	−1.03590	+	0.598076i	−0.0482466	+	0.0278552i	0.475683	+	0.879617i	$0.342201\pi$
$462$		0			0
$463$	35.1865	−	9.42820i	1.63526	−	0.438166i	0.679824	−	0.733375i	$-0.262056\pi$
$463$	35.1865	−	9.42820i	1.63526	−	0.438166i	0.955433	+	0.295209i	$0.0953894\pi$
$464$	26.7846	−	15.4641i	1.24344	−	0.717903i
$465$		0			0
$466$	11.8301	−	20.4904i	0.548020	−	0.949199i
$467$	−12.9641	+	3.47372i	−0.599907	+	0.160745i	−0.545977	−	0.837800i	$-0.683841\pi$
$467$	−12.9641	+	3.47372i	−0.599907	+	0.160745i	−0.0539300	+	0.998545i	$0.517175\pi$
$468$		0			0
$469$	0.241670	−	3.36603i	0.0111593	−	0.155429i
$470$	−3.40192	−	56.6769i	−0.156919	−	2.61431i
$471$		0			0
$472$	1.26795	+	1.26795i	0.0583621	+	0.0583621i
$473$	−6.00000	−	6.00000i	−0.275880	−	0.275880i
$474$		0			0
$475$	−6.41858	+	15.0263i	−0.294505	+	0.689453i
$476$	−11.6603	+	5.66025i	−0.534447	+	0.259437i
$477$		0			0
$478$	41.0526	−	11.0000i	1.87770	−	0.503128i
$479$	−2.63397	+	4.56218i	−0.120349	+	0.208451i	−0.919905	−	0.392140i	$-0.871735\pi$
$479$	−2.63397	+	4.56218i	−0.120349	+	0.208451i	0.799556	+	0.600591i	$0.205068\pi$
$480$		0			0
$481$	−14.1962	+	8.19615i	−0.647289	+	0.373712i
$482$	17.7942	−	4.76795i	0.810505	−	0.217174i
$483$		0			0
$484$	−28.2846	+	16.3301i	−1.28566	+	0.742279i
$485$	17.7583	+	3.63397i	0.806364	+	0.165010i
$486$		0			0
$487$	−32.4186	−	8.68653i	−1.46903	−	0.393624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−32.4186	−	8.68653i	−1.46903	−	0.393624i	−0.902597	+	0.430486i	$0.858342\pi$
$488$	4.16987	−	4.16987i	0.188761	−	0.188761i
$489$		0			0
$490$	23.0885	−	19.5263i	1.04303	−	0.882107i
$491$	−8.46410	+	14.6603i	−0.381980	+	0.661608i	−0.991345	−	0.131281i	$-0.958091\pi$
$491$	−8.46410	+	14.6603i	−0.381980	+	0.661608i	0.609366	+	0.792889i	$0.291424\pi$
$492$		0			0
$493$	−5.07180	−	18.9282i	−0.228422	−	0.852483i
$494$	21.1244	−	12.1962i	0.950430	−	0.548731i
$495$		0			0
$496$			0.875644i			0.0393176i
$497$	12.0000	−	10.3923i	0.538274	−	0.466159i
$498$		0			0
$499$	6.12436	−	3.53590i	0.274164	−	0.158289i	−0.356615	−	0.934252i	$-0.616069\pi$
$499$	6.12436	−	3.53590i	0.274164	−	0.158289i	0.630778	+	0.775963i	$0.282736\pi$
$500$	−19.0526	+	3.46410i	−0.852056	+	0.154919i
$501$		0			0
$502$	8.00000	+	8.00000i	0.357057	+	0.357057i
$503$	−10.0718	+	10.0718i	−0.449079	+	0.449079i	−0.895048	−	0.445969i	$-0.852859\pi$
$503$	−10.0718	+	10.0718i	−0.449079	+	0.449079i	0.445969	+	0.895048i	$0.352859\pi$
$504$		0			0
$505$	17.5885	−	35.1769i	0.782676	−	1.56535i
$506$	−50.2487			−2.23383
$507$		0			0
$508$	27.2942	+	27.2942i	1.21099	+	1.21099i
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−21.7583	+	10.5622i	−0.962532	+	0.467243i
$512$	20.6865	−	20.6865i	0.914224	−	0.914224i
$513$		0			0
$514$	12.0263	+	20.8301i	0.530456	+	0.918778i
$515$	−1.83975	+	8.99038i	−0.0810689	+	0.396164i
$516$		0			0
$517$	69.3731	−	18.5885i	3.05102	−	0.817519i
$518$	21.2942	−	4.09808i	0.935615	−	0.180059i
$519$		0			0
$520$	−4.00000	−	2.00000i	−0.175412	−	0.0877058i
$521$	−37.6244	+	21.7224i	−1.64835	+	0.951677i	−0.670626	+	0.741796i	$0.733974\pi$
$521$	−37.6244	+	21.7224i	−1.64835	+	0.951677i	−0.977727	+	0.209881i	$0.932692\pi$
$522$		0			0
$523$	−1.33013	−	4.96410i	−0.0581624	−	0.217065i	0.930728	−	0.365713i	$-0.119175\pi$
$523$	−1.33013	−	4.96410i	−0.0581624	−	0.217065i	−0.988890	+	0.148648i	$0.952508\pi$
$524$	−4.39230	−	7.60770i	−0.191879	−	0.332344i
$525$		0			0
$526$	−27.4545	+	47.5526i	−1.19707	+	2.07339i
$527$	0.535898	+	0.143594i	0.0233441	+	0.00625503i
$528$		0			0
$529$	0.294229	+	0.169873i	0.0127925	+	0.00738578i
$530$	22.7583	−	15.0263i	0.988559	−	0.652700i
$531$		0			0
$532$	−14.7058	+	2.83013i	−0.637576	+	0.122702i
$533$	−2.53590	+	9.46410i	−0.109842	+	0.409936i
$534$		0			0
$535$	−5.19615	+	1.73205i	−0.224649	+	0.0748831i
$536$	0.660254			0.0285186
$537$		0			0
$538$	−18.5263	−	4.96410i	−0.798725	−	0.214018i
$539$	30.0526	+	23.6603i	1.29446	+	1.01912i
$540$		0			0
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	−0.739360	−	0.673310i	$-0.764872\pi$
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	0.952784	+	0.303650i	$0.0982053\pi$
$542$	−21.3923	+	5.73205i	−0.918878	+	0.246213i
$543$		0			0
$544$	−10.7321	−	18.5885i	−0.460133	−	0.796974i
$545$	−2.46410	−	3.73205i	−0.105551	−	0.159863i
$546$		0			0
$547$	−12.3660	−	3.31347i	−0.528733	−	0.141674i	−0.0154299	−	0.999881i	$-0.504912\pi$
$547$	−12.3660	−	3.31347i	−0.528733	−	0.141674i	−0.513303	+	0.858207i	$0.671578\pi$
$548$	−3.46410	+	0.928203i	−0.147979	+	0.0396509i
$549$		0			0
$550$	−19.6603	−	48.9808i	−0.838316	−	2.08855i
$551$		−	22.6410i		−	0.964540i
$552$		0			0
$553$	7.85641	+	9.07180i	0.334088	+	0.385772i
$554$	−33.5885	−	19.3923i	−1.42704	−	0.823900i
$555$		0			0
$556$	10.3923	+	6.00000i	0.440732	+	0.254457i
$557$	15.2942	+	4.09808i	0.648037	+	0.173641i	0.567841	−	0.823138i	$-0.307779\pi$
$557$	15.2942	+	4.09808i	0.648037	+	0.173641i	0.0801960	+	0.996779i	$0.474445\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$	18.4545	+	18.8923i	0.779844	+	0.798346i
$561$		0			0
$562$	−25.6244	−	6.86603i	−1.08090	−	0.289626i
$563$	−15.1699	+	15.1699i	−0.639334	+	0.639334i	−0.950391	−	0.311057i	$-0.899317\pi$
$563$	−15.1699	+	15.1699i	−0.639334	+	0.639334i	0.311057	+	0.950391i	$0.399317\pi$
$564$		0			0
$565$	5.19615	+	15.5885i	0.218604	+	0.655811i
$566$		−	43.0526i		−	1.80963i
$567$		0			0
$568$	2.19615	+	2.19615i	0.0921485	+	0.0921485i
$569$		−	18.7846i		−	0.787492i	−0.919219	−	0.393746i	$-0.871179\pi$
$569$		−	18.7846i		−	0.787492i	0.919219	−	0.393746i	$-0.128821\pi$
$570$		0			0
$571$	−20.2487			−0.847382			−0.423691	−	0.905807i	$-0.639266\pi$
$571$	−20.2487			−0.847382			−0.423691	+	0.905807i	$0.639266\pi$
$572$	−9.46410	+	35.3205i	−0.395714	+	1.47682i
$573$		0			0
$574$	7.26795	−	10.7321i	0.303358	−	0.447947i
$575$	3.36603	−	23.5622i	0.140373	−	0.982611i
$576$		0			0
$577$	1.32051	−	4.92820i	0.0549735	−	0.205164i	−0.932977	−	0.359937i	$-0.882798\pi$
$577$	1.32051	−	4.92820i	0.0549735	−	0.205164i	0.987950	+	0.154773i	$0.0494648\pi$
$578$	16.7942	−	4.50000i	0.698548	−	0.187175i
$579$		0			0
$580$	22.3923	−	14.7846i	0.929790	−	0.613898i
$581$	3.36603	−	1.63397i	0.139646	−	0.0677887i
$582$		0			0
$583$	24.3923	+	24.3923i	1.01023	+	1.01023i
$584$	−2.36603	−	4.09808i	−0.0979068	−	0.169580i
$585$		0			0
$586$	−35.1506	−	20.2942i	−1.45206	−	0.838347i
$587$	8.62436	−	32.1865i	0.355965	−	1.32848i	−0.523300	−	0.852148i	$-0.675299\pi$
$587$	8.62436	−	32.1865i	0.355965	−	1.32848i	0.879265	−	0.476332i	$-0.158034\pi$
$588$		0			0
$589$	0.555136	+	0.320508i	0.0228740	+	0.0132063i
$590$	11.1962	+	9.92820i	0.460938	+	0.408738i
$591$		0			0
$592$	4.90192	+	18.2942i	0.201468	+	0.751888i
$593$	0.732051	+	2.73205i	0.0300617	+	0.112192i	0.979326	−	0.202286i	$-0.0648371\pi$
$593$	0.732051	+	2.73205i	0.0300617	+	0.112192i	−0.949265	+	0.314478i	$0.898170\pi$
$594$		0			0
$595$	14.5885	−	8.19615i	0.598068	−	0.336009i
$596$	2.89230	+	5.00962i	0.118473	+	0.205202i
$597$		0			0
$598$	−25.1244	+	25.1244i	−1.02741	+	1.02741i
$599$			30.9808i			1.26584i	0.774217	+	0.632920i	$0.218144\pi$
$599$			30.9808i			1.26584i	−0.774217	+	0.632920i	$0.781856\pi$
$600$		0			0
$601$	20.6603	−	11.9282i	0.842749	−	0.486562i	−0.0154485	−	0.999881i	$-0.504918\pi$
$601$	20.6603	−	11.9282i	0.842749	−	0.486562i	0.858198	+	0.513319i	$0.171584\pi$
$602$	7.50000	+	2.59808i	0.305677	+	0.105890i
$603$		0			0
$604$	7.09808	+	4.09808i	0.288817	+	0.166748i
$605$	35.1865	−	23.2321i	1.43054	−	0.944517i
$606$		0			0
$607$	−1.09808	+	4.09808i	−0.0445695	+	0.166336i	−0.984623	−	0.174690i	$-0.944108\pi$
$607$	−1.09808	+	4.09808i	−0.0445695	+	0.166336i	0.940054	+	0.341026i	$0.110774\pi$
$608$	−6.41858	−	23.9545i	−0.260308	−	0.971483i
$609$		0			0
$610$	32.6506	−	36.8205i	1.32199	−	1.49082i
$611$	25.3923	−	43.9808i	1.02726	−	1.77927i
$612$		0			0
$613$	−11.0981	+	41.4186i	−0.448247	+	1.67288i	0.258971	+	0.965885i	$0.416617\pi$
$613$	−11.0981	+	41.4186i	−0.448247	+	1.67288i	−0.707218	+	0.706996i	$0.750050\pi$
$614$	−47.9090			−1.93345
$615$		0			0
$616$	−4.19615	+	6.19615i	−0.169068	+	0.249650i
$617$	−0.562178	−	2.09808i	−0.0226324	−	0.0844654i	0.953686	−	0.300804i	$-0.0972551\pi$
$617$	−0.562178	−	2.09808i	−0.0226324	−	0.0844654i	−0.976318	+	0.216339i	$0.930588\pi$
$618$		0			0
$619$	12.4904	−	21.6340i	0.502031	−	0.869543i	−0.497966	−	0.867196i	$-0.665920\pi$
$619$	12.4904	−	21.6340i	0.502031	−	0.869543i	0.999997	−	0.00234656i	$-0.000746933\pi$
$620$	0.0455173	+	0.758330i	0.00182802	+	0.0304553i
$621$		0			0
$622$	−21.8564	−	21.8564i	−0.876362	−	0.876362i
$623$	4.59808	+	23.8923i	0.184218	+	0.957225i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		−	14.1962i		−	0.567392i
$627$		0			0
$628$	−1.73205	+	1.73205i	−0.0691164	+	0.0691164i
$629$	12.0000			0.478471
$630$		0			0
$631$	37.3205			1.48571			0.742853	−	0.669455i	$-0.233472\pi$
$631$	37.3205			1.48571			0.742853	+	0.669455i	$0.233472\pi$
$632$	−1.66025	+	1.66025i	−0.0660414	+	0.0660414i
$633$		0			0
$634$			23.1244i			0.918385i
$635$	−37.2846	−	33.0622i	−1.47959	−	1.31203i
$636$		0			0
$637$	26.8564	−	3.19615i	1.06409	−	0.126636i
$638$	51.7128	+	51.7128i	2.04733	+	2.04733i
$639$		0			0
$640$	−6.08846	+	6.86603i	−0.240667	+	0.271403i
$641$	−15.7224	+	27.2321i	−0.620999	+	1.07560i	0.368301	+	0.929706i	$0.379939\pi$
$641$	−15.7224	+	27.2321i	−0.620999	+	1.07560i	−0.989300	+	0.145895i	$0.953394\pi$
$642$		0			0
$643$	0.186533	+	0.696152i	0.00735616	+	0.0274536i	0.969506	−	0.245066i	$-0.0788097\pi$
$643$	0.186533	+	0.696152i	0.00735616	+	0.0274536i	−0.962150	+	0.272520i	$0.912143\pi$
$644$	19.6244	−	9.52628i	0.773308	−	0.375388i
$645$		0			0
$646$	−17.8564			−0.702551
$647$	−5.04552	+	18.8301i	−0.198360	+	0.740289i	0.793012	+	0.609206i	$0.208512\pi$
$647$	−5.04552	+	18.8301i	−0.198360	+	0.740289i	−0.991371	+	0.131082i	$0.958155\pi$
$648$		0			0
$649$	−9.46410	+	16.3923i	−0.371498	+	0.643454i
$650$	−34.3205	−	14.6603i	−1.34616	−	0.575022i
$651$		0			0
$652$	4.09808	+	15.2942i	0.160493	+	0.598968i
$653$	−6.49038	+	24.2224i	−0.253988	+	0.947897i	0.714662	+	0.699470i	$0.246580\pi$
$653$	−6.49038	+	24.2224i	−0.253988	+	0.947897i	−0.968651	+	0.248427i	$0.920086\pi$
$654$		0			0
$655$	6.24871	+	9.46410i	0.244157	+	0.369793i
$656$	9.80385	+	5.66025i	0.382776	+	0.220996i
$657$		0			0
$658$	−50.7846	+	43.9808i	−1.97979	+	1.71455i
$659$	−22.5167	+	13.0000i	−0.877125	+	0.506408i	−0.869709	−	0.493564i	$-0.835694\pi$
$659$	−22.5167	+	13.0000i	−0.877125	+	0.506408i	−0.00741531	+	0.999973i	$0.502360\pi$
$660$		0			0
$661$			11.0000i			0.427850i	0.976850	+	0.213925i	$0.0686249\pi$
$661$			11.0000i			0.427850i	−0.976850	+	0.213925i	$0.931375\pi$
$662$	25.0526	−	25.0526i	0.973695	−	0.973695i
$663$		0			0
$664$	0.366025	+	0.633975i	0.0142045	+	0.0246030i
$665$	18.7321	−	4.78461i	0.726398	−	0.185539i
$666$		0			0
$667$	8.53590	+	31.8564i	0.330511	+	1.23348i
$668$	6.27757	+	23.4282i	0.242886	+	0.906464i
$669$		0			0
$670$	5.50000	−	0.330127i	0.212484	−	0.0127539i
$671$	53.9090	+	31.1244i	2.08113	+	1.20154i
$672$		0			0
$673$	−6.92820	+	25.8564i	−0.267063	+	0.996691i	0.693913	+	0.720059i	$0.255885\pi$
$673$	−6.92820	+	25.8564i	−0.267063	+	0.996691i	−0.960976	+	0.276633i	$0.910782\pi$
$674$	−7.73205	−	4.46410i	−0.297827	−	0.171951i
$675$		0			0
$676$	1.66987	+	2.89230i	0.0642259	+	0.111242i
$677$	35.9090	+	35.9090i	1.38009	+	1.38009i	0.844434	+	0.535660i	$0.179937\pi$
$677$	35.9090	+	35.9090i	1.38009	+	1.38009i	0.535660	+	0.844434i	$0.320063\pi$
$678$		0			0
$679$	−9.36603	−	19.2942i	−0.359435	−	0.740445i
$680$	1.80385	+	2.73205i	0.0691744	+	0.104769i
$681$		0			0
$682$	−2.00000	+	0.535898i	−0.0765840	+	0.0205206i
$683$	4.00962	−	14.9641i	0.153424	−	0.572585i	−0.845811	−	0.533482i	$-0.820883\pi$
$683$	4.00962	−	14.9641i	0.153424	−	0.572585i	0.999235	−	0.0391034i	$-0.0124502\pi$
$684$		0			0
$685$	4.39230	−	1.46410i	0.167821	−	0.0559404i
$686$	−34.9545	−	7.63397i	−1.33457	−	0.291467i
$687$		0			0
$688$	−1.79423	+	6.69615i	−0.0684043	+	0.255288i
$689$	24.3923			0.929273
$690$		0			0
$691$			10.5885i			0.402804i	0.979509	+	0.201402i	$0.0645497\pi$
$691$			10.5885i			0.402804i	−0.979509	+	0.201402i	$0.935450\pi$
$692$	−17.3205	−	17.3205i	−0.658427	−	0.658427i
$693$		0			0
$694$		−	40.5167i		−	1.53799i
$695$	−13.8564	−	6.92820i	−0.525603	−	0.262802i
$696$		0			0
$697$	5.07180	−	5.07180i	0.192108	−	0.192108i
$698$	63.6769	+	17.0622i	2.41021	+	0.645813i
$699$		0			0
$700$	16.9641	+	15.4019i	0.641183	+	0.582138i
$701$	47.4641			1.79269			0.896347	−	0.443353i	$-0.146211\pi$
$701$	47.4641			1.79269			0.896347	+	0.443353i	$0.146211\pi$
$702$		0			0
$703$	13.3923	+	3.58846i	0.505100	+	0.135341i
$704$	27.1244	+	15.6603i	1.02229	+	0.590218i
$705$		0			0
$706$	18.5885	+	10.7321i	0.699586	+	0.403906i
$707$	−45.6962	+	8.79423i	−1.71858	+	0.330741i
$708$		0			0
$709$		−	6.71281i		−	0.252105i	−0.992024	−	0.126052i	$-0.959769\pi$
$709$		−	6.71281i		−	0.252105i	0.992024	−	0.126052i	$-0.0402308\pi$
$710$	19.3923	+	17.1962i	0.727780	+	0.645360i
$711$		0			0
$712$	−4.59808	+	1.23205i	−0.172320	+	0.0461731i
$713$	−0.901924	−	0.241670i	−0.0337773	−	0.00905060i
$714$		0			0
$715$	9.46410	−	46.2487i	0.353937	−	1.72960i
$716$	10.9019	+	18.8827i	0.407424	+	0.705679i
$717$		0			0
$718$	−38.6865	+	10.3660i	−1.44377	+	0.386857i
$719$	−15.5622	+	26.9545i	−0.580371	+	1.00523i	0.415064	+	0.909792i	$0.363759\pi$
$719$	−15.5622	+	26.9545i	−0.580371	+	1.00523i	−0.995435	+	0.0954403i	$0.969574\pi$
$720$		0			0
$721$	9.76795	−	4.74167i	0.363777	−	0.176589i
$722$	15.5263	+	4.16025i	0.577828	+	0.154829i
$723$		0			0
$724$	19.8564			0.737958
$725$	−27.7128	+	20.7846i	−1.02923	+	0.771921i
$726$		0			0
$727$	1.37564	−	5.13397i	0.0510198	−	0.190409i	−0.935713	−	0.352763i	$-0.885242\pi$
$727$	1.37564	−	5.13397i	0.0510198	−	0.190409i	0.986732	+	0.162355i	$0.0519088\pi$
$728$	1.00000	+	5.19615i	0.0370625	+	0.192582i
$729$		0			0
$730$	−21.7583	−	32.9545i	−0.805312	−	1.21970i
$731$	3.80385	+	2.19615i	0.140690	+	0.0812276i
$732$		0			0
$733$	−21.3923	−	5.73205i	−0.790143	−	0.211718i	−0.158891	−	0.987296i	$-0.550792\pi$
$733$	−21.3923	−	5.73205i	−0.790143	−	0.211718i	−0.631252	+	0.775578i	$0.717459\pi$
$734$	−6.59808	+	11.4282i	−0.243539	+	0.421823i
$735$		0			0
$736$	18.0622	+	31.2846i	0.665781	+	1.15317i
$737$	1.80385	+	6.73205i	0.0664456	+	0.247978i
$738$		0			0
$739$	−21.1244	+	12.1962i	−0.777072	+	0.448643i	−0.835392	−	0.549655i	$-0.814759\pi$
$739$	−21.1244	+	12.1962i	−0.777072	+	0.448643i	0.0583196	+	0.998298i	$0.481426\pi$
$740$	5.19615	+	15.5885i	0.191014	+	0.573043i
$741$		0			0
$742$	−30.4904	−	10.5622i	−1.11934	−	0.387750i
$743$	−8.83013	+	2.36603i	−0.323946	+	0.0868011i	−0.417127	−	0.908848i	$-0.636963\pi$
$743$	−8.83013	+	2.36603i	−0.323946	+	0.0868011i	0.0931813	+	0.995649i	$0.470296\pi$
$744$		0			0
$745$	−4.11474	−	6.23205i	−0.150752	−	0.228325i
$746$	−4.09808	−	7.09808i	−0.150041	−	0.259879i
$747$		0			0
$748$	18.9282	−	18.9282i	0.692084	−	0.692084i
$749$	5.36603	+	3.63397i	0.196070	+	0.132783i
$750$		0			0
$751$	23.5622	+	40.8109i	0.859796	+	1.48921i	0.872123	+	0.489286i	$0.162743\pi$
$751$	23.5622	+	40.8109i	0.859796	+	1.48921i	−0.0123270	+	0.999924i	$0.503924\pi$
$752$	−41.4904	−	41.4904i	−1.51300	−	1.51300i
$753$		0			0
$754$	51.7128			1.88327
$755$	−9.46410	−	4.73205i	−0.344434	−	0.172217i
$756$		0			0
$757$	−8.26795	+	8.26795i	−0.300504	+	0.300504i	−0.841211	−	0.540707i	$-0.818157\pi$
$757$	−8.26795	+	8.26795i	−0.300504	+	0.300504i	0.540707	+	0.841211i	$0.318157\pi$
$758$	17.1244	+	17.1244i	0.621985	+	0.621985i
$759$		0			0
$760$	1.19615	+	3.58846i	0.0433890	+	0.130167i
$761$	−16.9641	+	9.79423i	−0.614948	+	0.355041i	−0.774900	−	0.632084i	$-0.782200\pi$
$761$	−16.9641	+	9.79423i	−0.614948	+	0.355041i	0.159951	+	0.987125i	$0.448866\pi$
$762$		0			0
$763$	−1.73205	+	5.00000i	−0.0627044	+	0.181012i
$764$		−	30.5885i		−	1.10665i
$765$		0			0
$766$	−27.3564	+	15.7942i	−0.988427	+	0.570669i
$767$	3.46410	+	12.9282i	0.125081	+	0.466810i
$768$		0			0
$769$	−7.99038	+	13.8397i	−0.288141	+	0.499074i	−0.973366	−	0.229257i	$-0.926370\pi$
$769$	−7.99038	+	13.8397i	−0.288141	+	0.499074i	0.685225	+	0.728331i	$0.259704\pi$
$770$	−31.8564	+	53.7128i	−1.14803	+	1.93568i
$771$		0			0
$772$	−25.0526	+	25.0526i	−0.901661	+	0.901661i
$773$	7.02628	+	1.88269i	0.252718	+	0.0677155i	0.382954	−	0.923768i	$-0.374907\pi$
$773$	7.02628	+	1.88269i	0.252718	+	0.0677155i	−0.130236	+	0.991483i	$0.541574\pi$
$774$		0			0
$775$	−0.117314	−	0.973721i	−0.00421405	−	0.0349771i
$776$	3.63397	−	2.09808i	0.130452	−	0.0753165i
$777$		0			0
$778$	2.23205	−	0.598076i	0.0800229	−	0.0214421i
$779$	7.17691	−	4.14359i	0.257140	−	0.148460i
$780$		0			0
$781$	−16.3923	+	28.3923i	−0.586563	+	1.01596i
$782$	25.1244	−	6.73205i	0.898445	−	0.240738i
$783$		0			0
$784$	4.46410	−	30.9282i	0.159432	−	1.10458i
$785$	2.09808	−	2.36603i	0.0748836	−	0.0844471i
$786$		0			0
$787$	−11.2942	−	11.2942i	−0.402596	−	0.402596i	0.476551	−	0.879147i	$-0.341887\pi$
$787$	−11.2942	−	11.2942i	−0.402596	−	0.402596i	−0.879147	+	0.476551i	$0.841887\pi$
$788$	−30.2487	−	30.2487i	−1.07757	−	1.07757i
$789$		0			0
$790$	−13.0000	+	14.6603i	−0.462519	+	0.521588i
$791$	10.9019	−	16.0981i	0.387628	−	0.572382i
$792$		0			0
$793$	42.5167	−	11.3923i	1.50981	−	0.404553i
$794$	32.7846	−	56.7846i	1.16348	−	2.01521i
$795$		0			0
$796$	−11.7846	+	6.80385i	−0.417694	+	0.241156i
$797$	37.6147	−	10.0788i	1.33238	−	0.357011i	0.478780	−	0.877935i	$-0.341079\pi$
$797$	37.6147	−	10.0788i	1.33238	−	0.357011i	0.853603	+	0.520924i	$0.174413\pi$
$798$		0			0
$799$	−32.1962	+	18.5885i	−1.13902	+	0.657612i
$800$	−23.4282	+	29.8468i	−0.828312	+	1.05524i
$801$		0			0
$802$	43.6506	+	11.6962i	1.54136	+	0.413005i
$803$	35.3205	−	35.3205i	1.24643	−	1.24643i
$804$		0			0
$805$	−24.5526	+	13.7942i	−0.865364	+	0.486183i
$806$	−0.732051	+	1.26795i	−0.0257854	+	0.0446616i
$807$		0			0
$808$	−2.35641	−	8.79423i	−0.0828981	−	0.309380i
$809$	−36.4019	+	21.0167i	−1.27982	+	0.738906i	−0.976816	−	0.214082i	$-0.931324\pi$
$809$	−36.4019	+	21.0167i	−1.27982	+	0.738906i	−0.303008	+	0.952988i	$0.597991\pi$
$810$		0			0
$811$			1.85641i			0.0651872i	0.999469	+	0.0325936i	$0.0103767\pi$
$811$			1.85641i			0.0651872i	−0.999469	+	0.0325936i	$0.989623\pi$
$812$	−30.0000	−	10.3923i	−1.05279	−	0.364698i
$813$		0			0
$814$	−38.7846	+	22.3923i	−1.35940	+	0.784850i
$815$	−6.46410	−	19.3923i	−0.226428	−	0.679283i
$816$		0			0
$817$	3.58846	+	3.58846i	0.125544	+	0.125544i
$818$	7.36603	−	7.36603i	0.257547	−	0.257547i
$819$		0			0
$820$	8.78461	+	4.39230i	0.306772	+	0.153386i
$821$	24.6603			0.860649			0.430324	−	0.902674i	$-0.358399\pi$
$821$	24.6603			0.860649			0.430324	+	0.902674i	$0.358399\pi$
$822$		0			0
$823$	−14.0718	−	14.0718i	−0.490512	−	0.490512i	0.417956	−	0.908468i	$-0.362747\pi$
$823$	−14.0718	−	14.0718i	−0.490512	−	0.490512i	−0.908468	+	0.417956i	$0.862747\pi$
$824$	1.06218	+	1.83975i	0.0370027	+	0.0640906i
$825$		0			0
$826$	1.26795	−	17.6603i	0.0441176	−	0.614479i
$827$	−21.3923	+	21.3923i	−0.743883	+	0.743883i	−0.973323	−	0.229440i	$-0.926311\pi$
$827$	−21.3923	+	21.3923i	−0.743883	+	0.743883i	0.229440	+	0.973323i	$0.426311\pi$
$828$		0			0
$829$	22.1603	+	38.3827i	0.769657	+	1.33309i	0.937749	+	0.347314i	$0.112906\pi$
$829$	22.1603	+	38.3827i	0.769657	+	1.33309i	−0.168091	+	0.985771i	$0.553760\pi$
$830$	3.36603	+	5.09808i	0.116836	+	0.176957i
$831$		0			0
$832$	21.3923	−	5.73205i	0.741645	−	0.198723i
$833$	−18.1962	−	7.80385i	−0.630459	−	0.270387i
$834$		0			0
$835$	−9.90192	−	29.7058i	−0.342670	−	1.02801i
$836$	26.7846	−	15.4641i	0.926365	−	0.534837i
$837$		0			0
$838$	−4.00000	−	14.9282i	−0.138178	−	0.515686i
$839$	0.0262794	+	0.0455173i	0.000907267	+	0.00157143i	0.866479	−	0.499214i	$-0.166378\pi$
$839$	0.0262794	+	0.0455173i	0.000907267	+	0.00157143i	−0.865571	+	0.500786i	$0.833045\pi$
$840$		0			0
$841$	9.50000	−	16.4545i	0.327586	−	0.567396i
$842$	−43.0167	−	11.5263i	−1.48245	−	0.397222i
$843$		0			0
$844$	13.3923	+	7.73205i	0.460982	+	0.266148i
$845$	−2.37564	−	3.59808i	−0.0817247	−	0.123778i
$846$		0			0
$847$	−47.1410	−	16.3301i	−1.61978	−	0.561110i
$848$	7.29423	−	27.2224i	0.250485	−	0.934822i
$849$		0			0
$850$	16.3923	+	21.8564i	0.562251	+	0.749669i
$851$	−20.1962			−0.692315
$852$		0			0
$853$	40.5167	+	10.8564i	1.38726	+	0.371716i	0.873754	−	0.486368i	$-0.161678\pi$
$853$	40.5167	+	10.8564i	1.38726	+	0.371716i	0.513510	+	0.858084i	$0.328345\pi$
$854$	−58.0788	−	4.16987i	−1.98742	−	0.142690i
$855$		0			0
$856$	−0.633975	+	1.09808i	−0.0216688	+	0.0375315i
$857$	−28.7583	+	7.70577i	−0.982366	+	0.263224i	−0.714041	−	0.700104i	$-0.753137\pi$
$857$	−28.7583	+	7.70577i	−0.982366	+	0.263224i	−0.268325	+	0.963328i	$0.586470\pi$
$858$		0			0
$859$	21.4904	+	37.2224i	0.733242	+	1.27001i	0.955490	+	0.295023i	$0.0953272\pi$
$859$	21.4904	+	37.2224i	0.733242	+	1.27001i	−0.222248	+	0.974990i	$0.571339\pi$
$860$	−1.20577	+	5.89230i	−0.0411165	+	0.200926i
$861$		0			0
$862$	−45.1506	−	12.0981i	−1.53784	−	0.412062i
$863$	−24.4282	+	6.54552i	−0.831546	+	0.222812i	−0.649388	−	0.760457i	$-0.724975\pi$
$863$	−24.4282	+	6.54552i	−0.831546	+	0.222812i	−0.182158	+	0.983269i	$0.558308\pi$
$864$		0			0
$865$	23.6603	+	20.9808i	0.804473	+	0.713367i
$866$		−	26.7846i		−	0.910178i
$867$		0			0
$868$	0.679492	−	0.588457i	0.0230635	−	0.0199735i
$869$	−21.4641	−	12.3923i	−0.728120	−	0.420380i
$870$		0			0
$871$	4.26795	+	2.46410i	0.144614	+	0.0834929i
$872$	−1.00000	−	0.267949i	−0.0338643	−	0.00907390i
$873$		0			0
$874$	30.0526			1.01654
$875$	−23.0526	−	18.5359i	−0.779319	−	0.626628i
$876$		0			0
$877$	−11.5622	−	3.09808i	−0.390427	−	0.104615i	0.0582648	−	0.998301i	$-0.481443\pi$
$877$	−11.5622	−	3.09808i	−0.390427	−	0.104615i	−0.448692	+	0.893687i	$0.648110\pi$
$878$	−8.00000	+	8.00000i	−0.269987	+	0.269987i
$879$		0			0
$880$	−48.7846	−	24.3923i	−1.64453	−	0.822264i
$881$		−	17.7846i		−	0.599179i	−0.954068	−	0.299589i	$-0.903150\pi$
$881$		−	17.7846i		−	0.599179i	0.954068	−	0.299589i	$-0.0968497\pi$
$882$		0			0
$883$	−24.5429	−	24.5429i	−0.825936	−	0.825936i	0.161016	−	0.986952i	$-0.448523\pi$
$883$	−24.5429	−	24.5429i	−0.825936	−	0.825936i	−0.986952	+	0.161016i	$0.948523\pi$
$884$		−	18.9282i		−	0.636624i
$885$		0			0
$886$	1.80385			0.0606014
$887$	−4.76795	+	17.7942i	−0.160092	+	0.597472i	0.838523	+	0.544866i	$0.183419\pi$
$887$	−4.76795	+	17.7942i	−0.160092	+	0.597472i	−0.998615	+	0.0526060i	$0.983247\pi$
$888$		0			0
$889$	−4.22243	+	58.8109i	−0.141616	+	1.97245i
$890$	−37.6865	+	12.5622i	−1.26326	+	0.421085i
$891$		0			0
$892$	2.30385	−	8.59808i	0.0771385	−	0.287885i
$893$	−41.4904	+	11.1173i	−1.38842	+	0.372027i
$894$		0			0
$895$	−15.5096	−	23.4904i	−0.518429	−	0.785197i
$896$	10.8301	+	0.777568i	0.361809	+	0.0259767i
$897$		0			0
$898$	−2.16987	−	2.16987i	−0.0724096	−	0.0724096i
$899$	0.679492	+	1.17691i	0.0226623	+	0.0392523i
$900$		0			0
$901$	−15.4641	−	8.92820i	−0.515184	−	0.297442i
$902$	−6.92820	+	25.8564i	−0.230684	+	0.860924i
$903$		0			0
$904$	3.29423	+	1.90192i	0.109564	+	0.0632570i
$905$	−25.5885	+	1.53590i	−0.850589	+	0.0510550i
$906$		0			0
$907$	5.43782	+	20.2942i	0.180560	+	0.673859i	0.995538	+	0.0943664i	$0.0300825\pi$
$907$	5.43782	+	20.2942i	0.180560	+	0.673859i	−0.814978	+	0.579492i	$0.803251\pi$
$908$	−6.75833	−	25.2224i	−0.224283	−	0.837036i
$909$		0			0
$910$	10.9282	+	42.7846i	0.362266	+	1.41830i
$911$	7.43782	+	12.8827i	0.246426	+	0.426822i	0.962532	−	0.271170i	$-0.0874104\pi$
$911$	7.43782	+	12.8827i	0.246426	+	0.426822i	−0.716106	+	0.697992i	$0.754077\pi$
$912$		0			0
$913$	−5.46410	+	5.46410i	−0.180835	+	0.180835i
$914$			20.0526i			0.663280i
$915$		0			0
$916$	−6.99038	+	4.03590i	−0.230969	+	0.133350i
$917$	4.39230	−	12.6795i	0.145047	−	0.418714i
$918$		0			0
$919$	−45.3731	−	26.1962i	−1.49672	−	0.864131i	−0.496727	−	0.867907i	$-0.665465\pi$
$919$	−45.3731	−	26.1962i	−1.49672	−	0.864131i	−0.999993	+	0.00377579i	$0.998798\pi$
$920$	−3.03590	−	4.59808i	−0.100091	−	0.151594i
$921$		0			0
$922$	−0.598076	+	2.23205i	−0.0196966	+	0.0735087i
$923$	6.00000	+	22.3923i	0.197492	+	0.737052i
$924$		0			0
$925$	−7.90192	−	19.6865i	−0.259814	−	0.647289i
$926$	35.1865	−	60.9449i	1.15630	−	2.00277i
$927$		0			0
$928$	13.6077	−	50.7846i	0.446694	−	1.66709i
$929$	36.3205			1.19164			0.595819	−	0.803119i	$-0.296828\pi$
$929$	36.3205			1.19164			0.595819	+	0.803119i	$0.296828\pi$
$930$		0			0
$931$	−17.9737	−	14.1506i	−0.589065	−	0.463768i
$932$	−5.49038	−	20.4904i	−0.179843	−	0.671185i
$933$		0			0
$934$	−12.9641	+	22.4545i	−0.424198	+	0.734733i
$935$	−22.9282	+	25.8564i	−0.749832	+	0.845595i
$936$		0			0
$937$	−9.46410	−	9.46410i	−0.309179	−	0.309179i	0.535412	−	0.844591i	$-0.320156\pi$
$937$	−9.46410	−	9.46410i	−0.309179	−	0.309179i	−0.844591	+	0.535412i	$0.820156\pi$
$938$	−4.26795	−	4.92820i	−0.139353	−	0.160912i
$939$		0			0
$940$	−38.0885	−	33.7750i	−1.24231	−	1.10162i
$941$		−	37.9808i		−	1.23814i	−0.785337	−	0.619069i	$-0.787510\pi$
$941$		−	37.9808i		−	1.23814i	0.785337	−	0.619069i	$-0.212490\pi$
$942$		0			0
$943$	−8.53590	+	8.53590i	−0.277967	+	0.277967i
$944$	15.4641			0.503314
$945$		0			0
$946$	−16.3923			−0.532960
$947$	−18.2224	+	18.2224i	−0.592149	+	0.592149i	−0.938212	−	0.346062i	$-0.887519\pi$
$947$	−18.2224	+	18.2224i	−0.592149	+	0.592149i	0.346062	+	0.938212i	$0.387519\pi$
$948$		0			0
$949$		−	35.3205i		−	1.14655i
$950$	11.7583	+	29.2942i	0.381491	+	0.950430i
$951$		0			0
$952$	1.26795	−	3.66025i	0.0410945	−	0.118630i
$953$	−21.0000	−	21.0000i	−0.680257	−	0.680257i	0.279801	−	0.960058i	$-0.409731\pi$
$953$	−21.0000	−	21.0000i	−0.680257	−	0.680257i	−0.960058	+	0.279801i	$0.909731\pi$
$954$		0			0
$955$	2.36603	+	39.4186i	0.0765628	+	1.27556i
$956$	19.0526	−	33.0000i	0.616204	−	1.06730i
$957$		0			0
$958$	2.63397	+	9.83013i	0.0850999	+	0.317597i
$959$	−4.53590	−	3.07180i	−0.146472	−	0.0991935i
$960$		0			0
$961$	30.9615			0.998759
$962$	−8.19615	+	30.5885i	−0.264255	+	0.986211i
$963$		0			0
$964$	8.25833	−	14.3038i	0.265983	−	0.460696i
$965$	30.3468	−	34.2224i	0.976898	−	1.10166i
$966$		0			0
$967$	0.447441	+	1.66987i	0.0143887	+	0.0536995i	0.972747	−	0.231869i	$-0.0744842\pi$
$967$	0.447441	+	1.66987i	0.0143887	+	0.0536995i	−0.958358	+	0.285569i	$0.907817\pi$
$968$	2.52628	−	9.42820i	0.0811977	−	0.303034i
$969$		0			0
$970$	29.2224	−	19.2942i	0.938276	−	0.619500i
$971$	2.53590	+	1.46410i	0.0813809	+	0.0469853i	0.540138	−	0.841576i	$-0.318372\pi$
$971$	2.53590	+	1.46410i	0.0813809	+	0.0469853i	−0.458757	+	0.888562i	$0.651705\pi$
$972$		0			0
$973$	3.46410	+	18.0000i	0.111054	+	0.577054i
$974$	−56.1506	+	32.4186i	−1.79918	+	1.03876i
$975$		0			0
$976$		−	50.8564i		−	1.62787i
$977$	33.1769	−	33.1769i	1.06142	−	1.06142i	0.0634377	−	0.997986i	$-0.479794\pi$
$977$	33.1769	−	33.1769i	1.06142	−	1.06142i	0.997986	−	0.0634377i	$-0.0202064\pi$
$978$		0			0
$979$	−25.1244	−	43.5167i	−0.802978	−	1.39080i
$980$	2.25833	−	27.0167i	0.0721397	−	0.863016i
$981$		0			0
$982$	8.46410	+	31.5885i	0.270100	+	1.00803i
$983$	0.954483	+	3.56218i	0.0304433	+	0.113616i	0.979476	−	0.201563i	$-0.0646021\pi$
$983$	0.954483	+	3.56218i	0.0304433	+	0.113616i	−0.949032	+	0.315179i	$0.897935\pi$
$984$		0			0
$985$	41.3205	+	36.6410i	1.31658	+	1.16748i
$986$	−32.7846	−	18.9282i	−1.04407	−	0.602797i
$987$		0			0
$988$	5.66025	−	21.1244i	0.180077	−	0.672055i
$989$	−6.40192	−	3.69615i	−0.203569	−	0.117531i
$990$		0			0
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	0.970734	−	0.240159i	$-0.0771997\pi$
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	−0.693351	+	0.720600i	$0.743866\pi$
$992$	1.05256	+	1.05256i	0.0334188	+	0.0334188i
$993$		0			0
$994$	2.19615	−	30.5885i	0.0696577	−	0.970207i
$995$	14.6603	−	9.67949i	0.464761	−	0.306861i
$996$		0			0
$997$	−43.6865	+	11.7058i	−1.38357	+	0.370725i	−0.872415	−	0.488765i	$-0.837447\pi$
$997$	−43.6865	+	11.7058i	−1.38357	+	0.370725i	−0.511151	+	0.859491i	$0.670781\pi$
$998$	3.53590	−	13.1962i	0.111927	−	0.417717i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.d.523.1		4
3.2	odd	2		315.2.bs.c.103.1	yes	4
5.2	odd	4		945.2.bv.a.712.1		4
7.3	odd	6		945.2.cj.d.388.1		4
9.2	odd	6		315.2.cg.c.313.1	yes	4
9.7	even	3		945.2.cj.a.208.1		4
15.2	even	4		315.2.bs.b.292.1	yes	4
21.17	even	6		315.2.cg.a.283.1	yes	4
35.17	even	12		945.2.cj.a.577.1		4
45.2	even	12		315.2.cg.a.187.1	yes	4
45.7	odd	12		945.2.cj.d.397.1		4
63.38	even	6		315.2.bs.b.178.1	✓	4
63.52	odd	6		945.2.bv.a.73.1		4
105.17	odd	12		315.2.cg.c.157.1	yes	4
315.52	even	12	inner	945.2.bv.d.262.1		4
315.227	odd	12		315.2.bs.c.52.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.b.178.1	✓	4	63.38	even	6
315.2.bs.b.292.1	yes	4	15.2	even	4
315.2.bs.c.52.1	yes	4	315.227	odd	12
315.2.bs.c.103.1	yes	4	3.2	odd	2
315.2.cg.a.187.1	yes	4	45.2	even	12
315.2.cg.a.283.1	yes	4	21.17	even	6
315.2.cg.c.157.1	yes	4	105.17	odd	12
315.2.cg.c.313.1	yes	4	9.2	odd	6
945.2.bv.a.73.1		4	63.52	odd	6
945.2.bv.a.712.1		4	5.2	odd	4
945.2.bv.d.262.1		4	315.52	even	12	inner
945.2.bv.d.523.1		4	1.1	even	1	trivial
945.2.cj.a.208.1		4	9.7	even	3
945.2.cj.a.577.1		4	35.17	even	12
945.2.cj.d.388.1		4	7.3	odd	6
945.2.cj.d.397.1		4	45.7	odd	12

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 1.36603i) q^{2} -1.73205i q^{4} +(0.133975 + 2.23205i) q^{5} +(2.00000 - 1.73205i) q^{7} +(0.366025 + 0.366025i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 1.36603i) q^{2} -1.73205i q^{4} +(0.133975 + 2.23205i) q^{5} +(2.00000 - 1.73205i) q^{7} +(0.366025 + 0.366025i) q^{8} +(3.23205 + 2.86603i) q^{10} +(-2.73205 + 4.73205i) q^{11} +(1.00000 + 3.73205i) q^{13} +(0.366025 - 5.09808i) q^{14} +4.46410 q^{16} +(0.732051 - 2.73205i) q^{17} +(1.63397 - 2.83013i) q^{19} +(3.86603 - 0.232051i) q^{20} +(2.73205 + 10.1962i) q^{22} +(-1.23205 + 4.59808i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(6.46410 + 3.73205i) q^{26} +(-3.00000 - 3.46410i) q^{28} +(6.00000 - 3.46410i) q^{29} +0.196152i q^{31} +(5.36603 - 5.36603i) q^{32} +(-2.73205 - 4.73205i) q^{34} +(4.13397 + 4.23205i) q^{35} +(1.09808 + 4.09808i) q^{37} +(-1.63397 - 6.09808i) q^{38} +(-0.767949 + 0.866025i) q^{40} +(2.19615 + 1.26795i) q^{41} +(-0.401924 + 1.50000i) q^{43} +(8.19615 + 4.73205i) q^{44} +(4.59808 + 7.96410i) q^{46} +(-9.29423 - 9.29423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-5.96410 + 7.59808i) q^{50} +(6.46410 - 1.73205i) q^{52} +(1.63397 - 6.09808i) q^{53} +(-10.9282 - 5.46410i) q^{55} +(1.36603 + 0.0980762i) q^{56} +(3.46410 - 12.9282i) q^{58} +3.46410 q^{59} -11.3923i q^{61} +(0.267949 + 0.267949i) q^{62} -5.73205i q^{64} +(-8.19615 + 2.73205i) q^{65} +(0.901924 - 0.901924i) q^{67} +(-4.73205 - 1.26795i) q^{68} +(11.4282 + 0.133975i) q^{70} +6.00000 q^{71} +(-8.83013 - 2.36603i) q^{73} +(7.09808 + 4.09808i) q^{74} +(-4.90192 - 2.83013i) q^{76} +(2.73205 + 14.1962i) q^{77} +4.53590i q^{79} +(0.598076 + 9.96410i) q^{80} +(4.73205 - 1.26795i) q^{82} +(1.36603 + 0.366025i) q^{83} +(6.19615 + 1.26795i) q^{85} +(1.50000 + 2.59808i) q^{86} +(-2.73205 + 0.732051i) q^{88} +(-4.59808 + 7.96410i) q^{89} +(8.46410 + 5.73205i) q^{91} +(7.96410 + 2.13397i) q^{92} -25.3923 q^{94} +(6.53590 + 3.26795i) q^{95} +(2.09808 - 7.83013i) q^{97} +(-8.09808 - 10.8301i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8} + 6 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{19} + 12 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{28} + 24 q^{29} + 18 q^{32} - 4 q^{34} + 20 q^{35} - 6 q^{37} - 10 q^{38} - 10 q^{40} - 12 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} - 6 q^{47} + 4 q^{49} - 10 q^{50} + 12 q^{52} + 10 q^{53} - 16 q^{55} + 2 q^{56} + 8 q^{62} - 12 q^{65} + 14 q^{67} - 12 q^{68} + 18 q^{70} + 24 q^{71} - 18 q^{73} + 18 q^{74} - 30 q^{76} + 4 q^{77} - 8 q^{80} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 6 q^{86} - 4 q^{88} - 8 q^{89} + 20 q^{91} + 18 q^{92} - 60 q^{94} + 40 q^{95} - 2 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8 + 6 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^19 + 12 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^28 + 24 * q^29 + 18 * q^32 - 4 * q^34 + 20 * q^35 - 6 * q^37 - 10 * q^38 - 10 * q^40 - 12 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 - 6 * q^47 + 4 * q^49 - 10 * q^50 + 12 * q^52 + 10 * q^53 - 16 * q^55 + 2 * q^56 + 8 * q^62 - 12 * q^65 + 14 * q^67 - 12 * q^68 + 18 * q^70 + 24 * q^71 - 18 * q^73 + 18 * q^74 - 30 * q^76 + 4 * q^77 - 8 * q^80 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 6 * q^86 - 4 * q^88 - 8 * q^89 + 20 * q^91 + 18 * q^92 - 60 * q^94 + 40 * q^95 - 2 * q^97 - 22 * q^98

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