LMFDB - Embedded newform 945.2.cs.a.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{18}]$

Embedding invariants

Embedding label			209.3
Character	$\chi$	$=$	945.209
Dual form			945.2.cs.a.104.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.306808 + 1.70466i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(2.02676 + 1.70066i) q^{7} +(-2.81174 + 1.04601i) q^{9} +O(q^{10})$	\(q+(0.306808 + 1.70466i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(2.02676 + 1.70066i) q^{7} +(-2.81174 + 1.04601i) q^{9} +(-6.48531 - 1.14354i) q^{11} +(-2.66153 - 2.21727i) q^{12} +(-5.77616 - 2.10235i) q^{13} +(1.33752 + 3.63470i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-2.93500 + 1.69452i) q^{17} +(-2.87463 + 3.42585i) q^{20} +(-2.27721 + 3.97672i) q^{21} +(4.69846 - 1.71010i) q^{25} +(-2.64575 - 4.47214i) q^{27} -5.29150 q^{28} +(3.67749 + 10.1038i) q^{29} +(-0.0404054 - 11.4061i) q^{33} +(5.12348 + 2.95804i) q^{35} +(2.96311 - 5.21728i) q^{36} +(1.81162 - 10.4914i) q^{39} +(11.4062 - 6.58536i) q^{44} +(-5.78557 + 3.39518i) q^{45} +(-3.77652 + 4.50068i) q^{47} +(6.92816 - 0.0245426i) q^{48} +(1.21554 + 6.89365i) q^{49} +(-3.78906 - 4.48328i) q^{51} +(11.5523 - 4.20470i) q^{52} -14.7253 q^{55} +(-6.72188 - 3.84920i) q^{60} +(-7.47762 - 2.66179i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-13.5360 - 2.38676i) q^{65} +(2.31824 - 6.36931i) q^{68} +(-14.5297 + 8.38871i) q^{71} +(-0.258424 + 0.447604i) q^{73} +(4.35667 + 7.48461i) q^{75} +(-11.1994 - 13.3470i) q^{77} +(4.82115 - 1.75476i) q^{79} -8.94427i q^{80} +(6.81174 - 5.88220i) q^{81} +(1.01767 + 2.79602i) q^{83} +(-1.62348 - 9.02022i) q^{84} +(-5.80518 + 4.87113i) q^{85} +(-16.0953 + 9.36881i) q^{87} +(-8.13153 - 14.0842i) q^{91} +(-3.21237 + 18.2182i) q^{97} +(19.4311 - 3.56836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{9}+O(q^{10}) $ 24 * q - 6 * q^9	$ 24 q - 6 q^{9} - 18 q^{11} - 24 q^{39} + 96 q^{64} - 180 q^{65} - 12 q^{79} + 102 q^{81} + 84 q^{84} + 60 q^{85} + 228 q^{99}+O(q^{100}) $ 24 * q - 6 * q^9 - 18 * q^11 - 24 * q^39 + 96 * q^64 - 180 * q^65 - 12 * q^79 + 102 * q^81 + 84 * q^84 + 60 * q^85 + 228 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$2$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$3$	0.306808	+	1.70466i	0.177136	+	0.984186i
$3$	0.306808	+	1.70466i	0.177136	+	0.984186i
$4$	−1.53209	+	1.28558i	−0.766044	+	0.642788i
$5$	2.20210	−	0.388289i	0.984808	−	0.173648i
$5$	2.20210	−	0.388289i	0.984808	−	0.173648i
$6$		0			0
$7$	2.02676	+	1.70066i	0.766044	+	0.642788i
$7$	2.02676	+	1.70066i	0.766044	+	0.642788i
$8$		0			0
$9$	−2.81174	+	1.04601i	−0.937246	+	0.348669i
$10$		0			0
$11$	−6.48531	−	1.14354i	−1.95539	−	0.344789i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−6.48531	−	1.14354i	−1.95539	−	0.344789i	−0.956868	−	0.290522i	$-0.906171\pi$
$12$	−2.66153	−	2.21727i	−0.768317	−	0.640070i
$13$	−5.77616	−	2.10235i	−1.60202	−	0.583087i	−0.622179	−	0.782875i	$-0.713753\pi$
$13$	−5.77616	−	2.10235i	−1.60202	−	0.583087i	−0.979839	+	0.199788i	$0.935975\pi$
$14$		0			0
$15$	1.33752	+	3.63470i	0.345347	+	0.938475i
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	−2.93500	+	1.69452i	−0.711841	+	0.410982i	−0.811742	−	0.584016i	$-0.801481\pi$
$17$	−2.93500	+	1.69452i	−0.711841	+	0.410982i	0.0999013	+	0.994997i	$0.468147\pi$
$18$		0			0
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−2.87463	+	3.42585i	−0.642788	+	0.766044i
$21$	−2.27721	+	3.97672i	−0.496929	+	0.867791i
$22$		0			0
$23$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$23$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$24$		0			0
$25$	4.69846	−	1.71010i	0.939693	−	0.342020i
$26$		0			0
$27$	−2.64575	−	4.47214i	−0.509175	−	0.860663i
$28$	−5.29150			−1.00000
$29$	3.67749	+	10.1038i	0.682893	+	1.87623i	0.395844	+	0.918318i	$0.370452\pi$
$29$	3.67749	+	10.1038i	0.682893	+	1.87623i	0.287049	+	0.957916i	$0.407326\pi$
$30$		0			0
$31$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$31$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$32$		0			0
$33$	−0.0404054	−	11.4061i	−0.00703368	−	1.98555i
$34$		0			0
$35$	5.12348	+	2.95804i	0.866025	+	0.500000i
$36$	2.96311	−	5.21728i	0.493852	−	0.869546i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	1.81162	−	10.4914i	0.290092	−	1.67997i
$40$		0			0
$41$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$41$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$42$		0			0
$43$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$43$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$44$	11.4062	−	6.58536i	1.71955	−	0.992780i
$45$	−5.78557	+	3.39518i	−0.862461	+	0.506123i
$46$		0			0
$47$	−3.77652	+	4.50068i	−0.550862	+	0.656492i	−0.967586	−	0.252541i	$-0.918734\pi$
$47$	−3.77652	+	4.50068i	−0.550862	+	0.656492i	0.416724	+	0.909033i	$0.363178\pi$
$48$	6.92816	−	0.0245426i	0.999994	−	0.00354242i
$49$	1.21554	+	6.89365i	0.173648	+	0.984808i
$50$		0			0
$51$	−3.78906	−	4.48328i	−0.530575	−	0.627785i
$52$	11.5523	−	4.20470i	1.60202	−	0.583087i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	−14.7253			−1.98556
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$59$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$60$	−6.72188	−	3.84920i	−0.867791	−	0.496929i
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$	−7.47762	−	2.66179i	−0.942092	−	0.335354i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	−13.5360	−	2.38676i	−1.67893	−	0.296041i
$66$		0			0
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$	2.31824	−	6.36931i	0.281128	−	0.772393i
$69$		0			0
$70$		0			0
$71$	−14.5297	+	8.38871i	−1.72435	+	0.995556i	−0.815092	+	0.579331i	$0.803314\pi$
$71$	−14.5297	+	8.38871i	−1.72435	+	0.995556i	−0.909262	+	0.416225i	$0.863353\pi$
$72$		0			0
$73$	−0.258424	+	0.447604i	−0.0302463	+	0.0523881i	−0.880752	−	0.473577i	$-0.842962\pi$
$73$	−0.258424	+	0.447604i	−0.0302463	+	0.0523881i	0.850506	+	0.525965i	$0.176296\pi$
$74$		0			0
$75$	4.35667	+	7.48461i	0.503065	+	0.864249i
$76$		0			0
$77$	−11.1994	−	13.3470i	−1.27629	−	1.52103i
$78$		0			0
$79$	4.82115	−	1.75476i	0.542422	−	0.197425i	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	4.82115	−	1.75476i	0.542422	−	0.197425i	0.598676	+	0.800991i	$0.295694\pi$
$80$		−	8.94427i		−	1.00000i
$81$	6.81174	−	5.88220i	0.756860	−	0.653577i
$82$		0			0
$83$	1.01767	+	2.79602i	0.111704	+	0.306903i	0.982930	−	0.183977i	$-0.0588973\pi$
$83$	1.01767	+	2.79602i	0.111704	+	0.306903i	−0.871227	+	0.490881i	$0.836675\pi$
$84$	−1.62348	−	9.02022i	−0.177136	−	0.984186i
$85$	−5.80518	+	4.87113i	−0.629660	+	0.528348i
$86$		0			0
$87$	−16.0953	+	9.36881i	−1.72560	+	1.00444i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−8.13153	−	14.0842i	−0.852416	−	1.47643i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.21237	+	18.2182i	−0.326167	+	1.84978i	0.175180	+	0.984536i	$0.443949\pi$
$97$	−3.21237	+	18.2182i	−0.326167	+	1.84978i	−0.501347	+	0.865246i	$0.667162\pi$
$98$		0			0
$99$	19.4311	−	3.56836i	1.95290	−	0.358634i
$100$	−5.00000	+	8.66025i	−0.500000	+	0.866025i
$101$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$101$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$102$		0			0
$103$	−2.79670	−	15.8609i	−0.275567	−	1.56282i	−0.737155	−	0.675724i	$-0.763831\pi$
$103$	−2.79670	−	15.8609i	−0.275567	−	1.56282i	0.461588	−	0.887094i	$-0.347280\pi$
$104$		0			0
$105$	−3.47053	+	9.64134i	−0.338689	+	0.940898i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	9.80279	+	3.45040i	0.943274	+	0.332015i
$109$	19.3887			1.85710			0.928552	−	0.371203i	$-0.121054\pi$
$109$	19.3887			1.85710			0.928552	+	0.371203i	$0.121054\pi$
$110$		0			0
$111$		0			0
$112$	8.10705	−	6.80262i	0.766044	−	0.642788i
$113$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$113$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$114$		0			0
$115$		0			0
$116$	−18.6235	−	10.7523i	−1.72915	−	0.998323i
$117$	18.4401	−	0.130648i	1.70479	−	0.0120784i
$118$		0			0
$119$	−8.83034	−	1.55703i	−0.809476	−	0.142732i
$120$		0			0
$121$	30.4150	+	11.0701i	2.76500	+	1.00638i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.68246	−	5.59017i	0.866025	−	0.500000i
$126$		0			0
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$131$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$132$	14.7253	+	17.4232i	1.28167	+	1.51650i
$133$		0			0
$134$		0			0
$135$	−7.56268	−	8.82076i	−0.650892	−	0.759170i
$136$		0			0
$137$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$137$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$138$		0			0
$139$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$139$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$140$	−11.6524	+	2.05463i	−0.984808	+	0.173648i
$141$	−8.83080	−	5.05684i	−0.743688	−	0.425863i
$142$		0			0
$143$	35.0561	+	20.2396i	2.93154	+	1.69252i
$144$	2.16745	+	11.8026i	0.180621	+	0.983553i
$145$	12.0214	+	20.8217i	0.998323	+	1.72915i
$146$		0			0
$147$	−11.3784	+	4.18711i	−0.938475	+	0.345347i
$148$		0			0
$149$	−0.615493	+	1.69105i	−0.0504231	+	0.138536i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−0.615493	+	1.69105i	−0.0504231	+	0.138536i	0.911925	+	0.410358i	$0.134596\pi$
$150$		0			0
$151$	−3.82808	+	21.7101i	−0.311525	+	1.76674i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−3.82808	+	21.7101i	−0.311525	+	1.76674i	−0.591078	+	0.806614i	$0.701298\pi$
$152$		0			0
$153$	6.47996	−	7.83457i	0.523873	−	0.633388i
$154$		0			0
$155$		0			0
$156$	10.7119	+	18.4028i	0.857641	+	1.47340i
$157$	−2.65697	−	15.0684i	−0.212049	−	1.20259i	−0.885954	−	0.463772i	$-0.846496\pi$
$157$	−2.65697	−	15.0684i	−0.212049	−	1.20259i	0.673905	−	0.738818i	$-0.264616\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$	−4.51784	−	25.1017i	−0.351714	−	1.95416i
$166$		0			0
$167$	−20.0888	+	3.54219i	−1.55452	+	0.274103i	−0.883891	−	0.467693i	$-0.845085\pi$
$167$	−20.0888	+	3.54219i	−1.55452	+	0.274103i	−0.670625	+	0.741796i	$0.733974\pi$
$168$		0			0
$169$	18.9856	+	15.9308i	1.46043	+	1.22545i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.8031	−	2.61018i	−1.12546	−	0.198448i	−0.420221	−	0.907422i	$-0.638047\pi$
$173$	−14.8031	−	2.61018i	−1.12546	−	0.198448i	−0.705235	+	0.708974i	$0.749158\pi$
$174$		0			0
$175$	12.4310	+	4.52450i	0.939693	+	0.342020i
$176$	−9.00930	+	24.7528i	−0.679101	+	1.86582i
$177$		0			0
$178$		0			0
$179$	−22.2482	+	12.8450i	−1.66291	+	0.960081i	−0.691594	+	0.722287i	$0.743091\pi$
$179$	−22.2482	+	12.8450i	−1.66291	+	0.960081i	−0.971316	+	0.237794i	$0.923576\pi$
$180$	4.49925	−	12.6395i	0.335354	−	0.942092i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	20.9721	−	7.63322i	1.53363	−	0.558196i
$188$		−	11.7504i		−	0.856989i
$189$	2.24325	−	13.5635i	0.163173	−	0.986598i
$190$		0			0
$191$	−2.02342	−	5.55930i	−0.146409	−	0.402257i	0.844711	−	0.535222i	$-0.179772\pi$
$191$	−2.02342	−	5.55930i	−0.146409	−	0.402257i	−0.991121	+	0.132966i	$0.957550\pi$
$192$	−10.5830	+	8.94427i	−0.763763	+	0.645497i
$193$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$193$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$194$		0			0
$195$	−0.0843332	−	23.8065i	−0.00603923	−	1.70482i
$196$	−10.7246	−	8.99903i	−0.766044	−	0.642788i
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.72973	+	26.7322i	−0.682893	+	1.87623i
$204$	11.5688	+	1.99766i	0.809976	+	0.139864i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−12.2937	+	21.2934i	−0.852416	+	1.47643i
$209$		0			0
$210$		0			0
$211$	1.07847	+	6.11632i	0.0742451	+	0.421065i	0.999163	+	0.0408987i	$0.0130221\pi$
$211$	1.07847	+	6.11632i	0.0742451	+	0.421065i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$	−18.7577	−	22.1944i	−1.28526	−	1.52074i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.842299	−	0.303197i	−0.0569173	−	0.0204882i
$220$	22.5605	−	18.9305i	1.52103	−	1.27629i
$221$	20.5155	−	3.61743i	1.38002	−	0.243335i
$222$		0			0
$223$	13.7754	+	11.5589i	0.922466	+	0.774041i	0.974449	−	0.224607i	$-0.0721099\pi$
$223$	13.7754	+	11.5589i	0.922466	+	0.774041i	−0.0519836	+	0.998648i	$0.516554\pi$
$224$		0			0
$225$	−11.4221	+	9.72298i	−0.761471	+	0.648199i
$226$		0			0
$227$	12.6690	+	2.23388i	0.840870	+	0.148268i	0.577463	−	0.816417i	$-0.304043\pi$
$227$	12.6690	+	2.23388i	0.840870	+	0.148268i	0.263407	+	0.964685i	$0.415154\pi$
$228$		0			0
$229$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$229$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$230$		0			0
$231$	19.3160	−	23.1862i	1.27090	−	1.52554i
$232$		0			0
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$	−6.56870	+	11.3773i	−0.428495	+	0.742175i
$236$		0			0
$237$	4.47043	+	7.68006i	0.290386	+	0.498873i
$238$		0			0
$239$	4.49692	+	5.35922i	0.290882	+	0.346659i	0.891618	−	0.452788i	$-0.149570\pi$
$239$	4.49692	+	5.35922i	0.290882	+	0.346659i	−0.600737	+	0.799447i	$0.705126\pi$
$240$	15.2470	−	2.74417i	0.984186	−	0.177136i
$241$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$241$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$242$		0			0
$243$	12.1170	+	9.80700i	0.777309	+	0.629119i
$244$		0			0
$245$	5.35346	+	14.7085i	0.342020	+	0.939693i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−4.45404	+	2.59262i	−0.282263	+	0.164301i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	14.8783	−	5.53495i	0.937246	−	0.348669i
$253$		0			0
$254$		0			0
$255$	−10.0847	−	8.40137i	−0.631528	−	0.526114i
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$	10.4282	−	28.6513i	0.650495	−	1.78722i	0.0345877	−	0.999402i	$-0.488988\pi$
$257$	10.4282	−	28.6513i	0.650495	−	1.78722i	0.615907	−	0.787819i	$-0.288790\pi$
$258$		0			0
$259$		0			0
$260$	23.8067	−	13.7448i	1.47643	−	0.852416i
$261$	−20.9088	−	24.5626i	−1.29422	−	1.52039i
$262$		0			0
$263$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$263$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	4.63648	+	12.7386i	0.281128	+	0.772393i
$273$	21.5140	−	18.1827i	1.30209	−	1.10046i
$274$		0			0
$275$	−32.4266	+	5.71768i	−1.95539	+	0.344789i
$276$		0			0
$277$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$277$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	25.3529	+	4.47039i	1.51242	+	0.266681i	0.867451	−	0.497523i	$-0.165757\pi$
$281$	25.3529	+	4.47039i	1.51242	+	0.266681i	0.644974	+	0.764204i	$0.276868\pi$
$282$		0			0
$283$	−18.3550	−	6.68068i	−1.09109	−	0.397125i	−0.267067	−	0.963678i	$-0.586054\pi$
$283$	−18.3550	−	6.68068i	−1.09109	−	0.397125i	−0.824025	+	0.566553i	$0.808277\pi$
$284$	11.4764	−	31.5312i	0.681001	−	1.87103i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.75720	+	4.77561i	−0.162188	+	0.280918i
$290$		0			0
$291$	−32.0415	+	0.113505i	−1.87831	+	0.00665378i
$292$	−0.179500	−	1.01799i	−0.0105044	−	0.0595735i
$293$	−5.35006	−	6.37595i	−0.312554	−	0.372487i	0.586783	−	0.809745i	$-0.300394\pi$
$293$	−5.35006	−	6.37595i	−0.312554	−	0.372487i	−0.899336	+	0.437257i	$0.855950\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	12.0445	+	32.0287i	0.698891	+	1.85849i
$298$		0			0
$299$		0			0
$300$	−16.2968	−	5.86627i	−0.940898	−	0.338689i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−15.0131	−	26.0034i	−0.856842	−	1.48409i	−0.874926	−	0.484257i	$-0.839090\pi$
$307$	−15.0131	−	26.0034i	−0.856842	−	1.48409i	0.0180837	−	0.999836i	$-0.494243\pi$
$308$	34.3170	+	6.05102i	1.95539	+	0.344789i
$309$	26.1794	−	9.63367i	1.48929	−	0.548040i
$310$		0			0
$311$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$311$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$312$		0			0
$313$	−5.55328	+	31.4942i	−0.313890	+	1.78016i	0.264488	+	0.964389i	$0.414797\pi$
$313$	−5.55328	+	31.4942i	−0.313890	+	1.78016i	−0.578378	+	0.815769i	$0.696314\pi$
$314$		0			0
$315$	−17.5000	−	2.95804i	−0.986013	−	0.166667i
$316$	−5.13056	+	8.88640i	−0.288617	+	0.499899i
$317$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$317$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$318$		0			0
$319$	−12.2956	−	69.7318i	−0.688421	−	3.90423i
$320$	11.4985	+	13.7034i	0.642788	+	0.766044i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−2.87418	+	17.7690i	−0.159677	+	0.987169i
$325$	−30.7343			−1.70483
$326$		0			0
$327$	5.94862	+	33.0512i	0.328959	+	1.82774i
$328$		0			0
$329$	−15.3082	+	2.69925i	−0.843970	+	0.148815i
$330$		0			0
$331$	22.1732	+	18.6055i	1.21875	+	1.02265i	0.998889	+	0.0471205i	$0.0150045\pi$
$331$	22.1732	+	18.6055i	1.21875	+	1.02265i	0.219860	+	0.975531i	$0.429440\pi$
$332$	−5.15366	−	2.97546i	−0.282844	−	0.163300i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	14.0835	+	11.7327i	0.768317	+	0.640070i
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$		0			0
$339$		0			0
$340$	2.63186	−	14.9260i	0.142732	−	0.809476i
$341$		0			0
$342$		0			0
$343$	−9.26013	+	16.0390i	−0.500000	+	0.866025i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$347$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$348$	12.6151	−	35.0456i	0.676243	−	1.87864i
$349$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$349$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$350$		0			0
$351$	5.88029	+	31.3941i	0.313866	+	1.67569i
$352$		0			0
$353$	12.0241	+	33.0359i	0.639977	+	1.75832i	0.651799	+	0.758392i	$0.274014\pi$
$353$	12.0241	+	33.0359i	0.639977	+	1.75832i	−0.0118225	+	0.999930i	$0.503763\pi$
$354$		0			0
$355$	−28.7385	+	24.1145i	−1.52528	+	1.27986i
$356$		0			0
$357$	−0.0550156	−	15.5304i	−0.00291174	−	0.821958i
$358$		0			0
$359$	21.8765	+	12.6304i	1.15460	+	0.666608i	0.950004	−	0.312239i	$-0.101079\pi$
$359$	21.8765	+	12.6304i	1.15460	+	0.666608i	0.204595	+	0.978847i	$0.434412\pi$
$360$		0			0
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$		0			0
$363$	−9.53928	+	55.2436i	−0.500682	+	2.89954i
$364$	30.5646	+	11.1246i	1.60202	+	0.583087i
$365$	−0.395275	+	1.08601i	−0.0206897	+	0.0568444i
$366$		0			0
$367$	5.01410	−	28.4364i	0.261734	−	1.48437i	−0.516443	−	0.856322i	$-0.672744\pi$
$367$	5.01410	−	28.4364i	0.261734	−	1.48437i	0.778177	−	0.628045i	$-0.216145\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$373$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$374$		0			0
$375$	12.5000	+	14.7902i	0.645497	+	0.763763i
$376$		0			0
$377$		−	66.0927i		−	3.40395i
$378$		0			0
$379$	27.1756			1.39592			0.697958	−	0.716138i	$-0.254092\pi$
$379$	27.1756			1.39592			0.697958	+	0.716138i	$0.254092\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−37.0394	+	6.53104i	−1.89262	+	0.333721i	−0.994388	−	0.105793i	$-0.966262\pi$
$383$	−37.0394	+	6.53104i	−1.89262	+	0.333721i	−0.898236	+	0.439514i	$0.855151\pi$
$384$		0			0
$385$	−29.8447	−	25.0427i	−1.52103	−	1.27629i
$386$		0			0
$387$		0			0
$388$	−18.4993	−	32.0417i	−0.939159	−	1.62667i
$389$	38.8357	+	6.84778i	1.96905	+	0.347196i	0.988689	+	0.149979i	$0.0479205\pi$
$389$	38.8357	+	6.84778i	1.96905	+	0.347196i	0.980360	+	0.197218i	$0.0631906\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.93529	−	5.73614i	0.499899	−	0.288617i
$396$	−25.1828	+	30.4472i	−1.26549	+	1.53003i
$397$	0.115521	−	0.200088i	0.00579782	−	0.0100421i	−0.863112	−	0.505013i	$-0.831488\pi$
$397$	0.115521	−	0.200088i	0.00579782	−	0.0100421i	0.868910	+	0.494971i	$0.164821\pi$
$398$		0			0
$399$		0			0
$400$	−3.47296	−	19.6962i	−0.173648	−	0.984808i
$401$	−19.0139	−	22.6599i	−0.949510	−	1.13158i	−0.991190	−	0.132450i	$-0.957715\pi$
$401$	−19.0139	−	22.6599i	−0.949510	−	1.13158i	0.0416801	−	0.999131i	$-0.486729\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	12.7161	−	15.5981i	0.631869	−	0.775075i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$409$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$410$		0			0
$411$		0			0
$412$	24.6751	+	20.7049i	1.21566	+	1.02006i
$413$		0			0
$414$		0			0
$415$	3.32667	+	5.76196i	0.163300	+	0.282844i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$419$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$420$	−7.07750	−	19.2330i	−0.345347	−	0.938475i
$421$	4.98342	−	28.2624i	0.242877	−	1.37742i	−0.582495	−	0.812834i	$-0.697923\pi$
$421$	4.98342	−	28.2624i	0.242877	−	1.37742i	0.825372	−	0.564590i	$-0.190966\pi$
$422$		0			0
$423$	5.91084	−	16.6050i	0.287395	−	0.807363i
$424$		0			0
$425$	−10.8922	+	12.9808i	−0.528348	+	0.629660i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−23.7462	+	65.9684i	−1.14648	+	3.18499i
$430$		0			0
$431$			10.1456i			0.488698i	0.969687	+	0.244349i	$0.0785743\pi$
$431$			10.1456i			0.488698i	−0.969687	+	0.244349i	$0.921426\pi$
$432$	−19.4545	+	7.31591i	−0.936005	+	0.351987i
$433$	40.1484			1.92941			0.964703	−	0.263339i	$-0.0848238\pi$
$433$	40.1484			1.92941			0.964703	+	0.263339i	$0.0848238\pi$
$434$		0			0
$435$	−31.8056	+	26.8807i	−1.52496	+	1.28883i
$436$	−29.7053	+	24.9257i	−1.42262	+	1.19372i
$437$		0			0
$438$		0			0
$439$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$439$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$440$		0			0
$441$	−10.6286	−	18.1117i	−0.506123	−	0.862461i
$442$		0			0
$443$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$443$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.07151	−	0.530378i	−0.145277	−	0.0250860i
$448$	−3.67544	+	20.8445i	−0.173648	+	0.984808i
$449$	−24.6822	+	14.2503i	−1.16482	+	0.672511i	−0.952455	−	0.304679i	$-0.901451\pi$
$449$	−24.6822	+	14.2503i	−1.16482	+	0.672511i	−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−38.1829	+	0.135260i	−1.79399	+	0.00635509i
$454$		0			0
$455$	−23.3752	−	27.8575i	−1.09585	−	1.30598i
$456$		0			0
$457$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$457$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$458$		0			0
$459$	15.3434	+	8.64242i	0.716168	+	0.403394i
$460$		0			0
$461$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$461$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$462$		0			0
$463$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$463$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$464$	42.3557	−	7.46845i	1.96631	−	0.346714i
$465$		0			0
$466$		0			0
$467$	−23.7669	−	13.7218i	−1.09980	−	0.634970i	−0.163632	−	0.986521i	$-0.552321\pi$
$467$	−23.7669	−	13.7218i	−1.09980	−	0.634970i	−0.936169	+	0.351551i	$0.885654\pi$
$468$	−28.0839	+	23.9063i	−1.29818	+	1.10507i
$469$		0			0
$470$		0			0
$471$	24.8713	−	9.15234i	1.14601	−	0.421717i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	15.5305	−	8.96656i	0.711841	−	0.410982i
$477$		0			0
$478$		0			0
$479$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$479$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−60.8299	+	22.1403i	−2.76500	+	1.00638i
$485$			41.3657i			1.87832i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	37.0635	−	6.53529i	1.67265	−	0.294934i	0.744635	−	0.667472i	$-0.232624\pi$
$491$	37.0635	−	6.53529i	1.67265	−	0.294934i	0.928017	+	0.372539i	$0.121513\pi$
$492$		0			0
$493$	−27.9146	−	23.4231i	−1.25721	−	1.05492i
$494$		0			0
$495$	41.4037	−	15.4028i	1.86096	−	0.692303i
$496$		0			0
$497$	−43.7145	−	7.70804i	−1.96086	−	0.345753i
$498$		0			0
$499$	−18.7934	−	6.84022i	−0.841306	−	0.306210i	−0.114816	−	0.993387i	$-0.536628\pi$
$499$	−18.7934	−	6.84022i	−0.841306	−	0.306210i	−0.726491	+	0.687176i	$0.758850\pi$
$500$	−7.64780	+	21.0122i	−0.342020	+	0.939693i
$501$	−12.2016	−	33.1578i	−0.545129	−	1.48138i
$502$		0			0
$503$	−1.39864	+	0.807506i	−0.0623624	+	0.0360049i	−0.530857	−	0.847461i	$-0.678130\pi$
$503$	−1.39864	+	0.807506i	−0.0623624	+	0.0360049i	0.468495	+	0.883466i	$0.344797\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−21.3317	+	37.2517i	−0.947372	+	1.65440i
$508$		0			0
$509$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$509$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$510$		0			0
$511$	−1.28498	+	0.467696i	−0.0568444	+	0.0206897i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.3172	−	33.8412i	−0.542761	−	1.49122i
$516$		0			0
$517$	29.6386	−	24.8697i	1.30350	−	1.09377i
$518$		0			0
$519$	−0.0922274	−	26.0350i	−0.00404834	−	1.14281i
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	−16.4286	−	28.4552i	−0.718372	−	1.24426i	−0.961644	−	0.274299i	$-0.911554\pi$
$523$	−16.4286	−	28.4552i	−0.718372	−	1.24426i	0.243272	−	0.969958i	$-0.421779\pi$
$524$		0			0
$525$	−3.89882	+	22.5787i	−0.170158	+	0.985417i
$526$		0			0
$527$		0			0
$528$	−44.9593	−	7.76343i	−1.95660	−	0.337860i
$529$	−3.99391	+	22.6506i	−0.173648	+	0.984808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−28.7223	−	33.9847i	−1.23946	−	1.46655i
$538$		0			0
$539$		−	46.0975i		−	1.98556i
$540$	22.9265	+	3.79179i	0.986598	+	0.163173i
$541$	10.0117			0.430438			0.215219	−	0.976566i	$-0.430953\pi$
$541$	10.0117			0.430438			0.215219	+	0.976566i	$0.430953\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	42.6959	−	7.52843i	1.82889	−	0.322483i
$546$		0			0
$547$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$547$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	12.7556	+	4.64265i	0.542422	+	0.197425i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$		0			0
$559$		0			0
$560$	15.2111	−	18.1279i	0.642788	−	0.766044i
$561$	19.4465	+	33.4084i	0.821030	+	1.41050i
$562$		0			0
$563$	−15.4620	−	18.4269i	−0.651646	−	0.776601i	0.334515	−	0.942390i	$-0.391427\pi$
$563$	−15.4620	−	18.4269i	−0.651646	−	0.776601i	−0.986161	+	0.165789i	$0.946983\pi$
$564$	20.0305	−	3.60513i	0.843437	−	0.151803i
$565$		0			0
$566$		0			0
$567$	23.8094	−	0.337394i	0.999900	−	0.0141692i
$568$		0			0
$569$	11.0811	+	30.4452i	0.464546	+	1.27633i	0.922032	+	0.387113i	$0.126528\pi$
$569$	11.0811	+	30.4452i	0.464546	+	1.27633i	−0.457486	+	0.889217i	$0.651250\pi$
$570$		0			0
$571$	−22.5221	+	18.8983i	−0.942519	+	0.790867i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−22.5221	+	18.8983i	−0.942519	+	0.790867i	0.0355029	+	0.999370i	$0.488697\pi$
$572$	−79.7286	+	14.0583i	−3.33362	+	0.587807i
$573$	8.85591	−	5.15488i	0.369961	−	0.215348i
$574$		0			0
$575$		0			0
$576$	−18.4939	−	15.2963i	−0.770579	−	0.637344i
$577$	19.5020	+	33.7785i	0.811880	+	1.40622i	0.911547	+	0.411196i	$0.134889\pi$
$577$	19.5020	+	33.7785i	0.811880	+	1.40622i	−0.0996670	+	0.995021i	$0.531778\pi$
$578$		0			0
$579$		0			0
$580$	−45.1857	−	16.4462i	−1.87623	−	0.682893i
$581$	−2.69250	+	7.39758i	−0.111704	+	0.306903i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	40.5562	−	7.44780i	1.67679	−	0.307929i
$586$		0			0
$587$	−23.6360	+	28.1683i	−0.975561	+	1.16263i	0.0111162	+	0.999938i	$0.496462\pi$
$587$	−23.6360	+	28.1683i	−0.975561	+	1.16263i	−0.986677	+	0.162690i	$0.947983\pi$
$588$	12.0499	−	21.0428i	0.496929	−	0.867791i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	41.8642i		−	1.71916i	−0.511003	−	0.859579i	$-0.670726\pi$
$593$		−	41.8642i		−	1.71916i	0.511003	−	0.859579i	$-0.329274\pi$
$594$		0			0
$595$	−20.0498			−0.821963
$596$	−1.23099	−	3.38211i	−0.0504231	−	0.138536i
$597$		0			0
$598$		0			0
$599$	−14.2381	+	2.51055i	−0.581751	+	0.102578i	−0.456776	−	0.889582i	$-0.650996\pi$
$599$	−14.2381	+	2.51055i	−0.581751	+	0.102578i	−0.124975	+	0.992160i	$0.539885\pi$
$600$		0			0
$601$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$601$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$602$		0			0
$603$		0			0
$604$	−22.0450	−	38.1831i	−0.897000	−	1.55365i
$605$	71.2751	+	12.5677i	2.89775	+	0.510951i
$606$		0			0
$607$	37.5100	+	13.6525i	1.52248	+	0.554139i	0.961767	−	0.273869i	$-0.0883034\pi$
$607$	37.5100	+	13.6525i	1.52248	+	0.554139i	0.560717	+	0.828008i	$0.310526\pi$
$608$		0			0
$609$	−48.5545	−	8.38423i	−1.96753	−	0.339746i
$610$		0			0
$611$	31.2758	−	18.0571i	1.26528	−	0.730512i
$612$	0.144064	+	20.3337i	0.00582343	+	0.821943i
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$617$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$618$		0			0
$619$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$619$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−40.0698	−	14.4237i	−1.60407	−	0.577408i
$625$	19.1511	−	16.0697i	0.766044	−	0.642788i
$626$		0			0
$627$		0			0
$628$	23.4423	+	19.6704i	0.935449	+	0.784935i
$629$		0			0
$630$		0			0
$631$	−12.8200	−	22.2050i	−0.510357	−	0.883965i	−0.999928	−	0.0120014i	$-0.996180\pi$
$631$	−12.8200	−	22.2050i	−0.510357	−	0.883965i	0.489570	−	0.871964i	$-0.337154\pi$
$632$		0			0
$633$	−10.0954	+	3.71497i	−0.401255	+	0.147657i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	7.47174	−	42.3743i	0.296041	−	1.67893i
$638$		0			0
$639$	32.0790	−	38.7850i	1.26902	−	1.53431i
$640$		0			0
$641$	−25.2312	+	30.0694i	−0.996572	+	1.18767i	−0.0143597	+	0.999897i	$0.504571\pi$
$641$	−25.2312	+	30.0694i	−0.996572	+	1.18767i	−0.982213	+	0.187772i	$0.939873\pi$
$642$		0			0
$643$	−0.368634	−	2.09063i	−0.0145375	−	0.0824462i	0.976676	−	0.214719i	$-0.0688836\pi$
$643$	−0.368634	−	2.09063i	−0.0145375	−	0.0824462i	−0.991213	+	0.132273i	$0.957772\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			50.1875i			1.97307i	0.163543	+	0.986536i	$0.447708\pi$
$647$			50.1875i			1.97307i	−0.163543	+	0.986536i	$0.552292\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$653$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.258424	−	1.52886i	0.0100821	−	0.0596464i
$658$		0			0
$659$	11.7032	+	2.06359i	0.455892	+	0.0803860i	0.396878	−	0.917871i	$-0.370093\pi$
$659$	11.7032	+	2.06359i	0.455892	+	0.0803860i	0.0590132	+	0.998257i	$0.481205\pi$
$660$	39.1918	+	32.6499i	1.52554	+	1.27090i
$661$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$661$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$662$		0			0
$663$	12.4608	+	33.8621i	0.483938	+	1.31509i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	26.2240	−	31.2526i	1.01464	−	1.20920i
$669$	−15.4776	+	27.0287i	−0.598399	+	1.04499i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$673$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$674$		0			0
$675$	−20.0788	−	16.4877i	−0.772832	−	0.634611i
$676$	−49.5678			−1.90645
$677$	0.381004	+	1.04680i	0.0146432	+	0.0402318i	0.946799	−	0.321826i	$-0.104297\pi$
$677$	0.381004	+	1.04680i	0.0146432	+	0.0402318i	−0.932156	+	0.362058i	$0.882074\pi$
$678$		0			0
$679$	−37.4937	+	31.4609i	−1.43888	+	1.20736i
$680$		0			0
$681$	0.0789315	+	22.2817i	0.00302466	+	0.853837i
$682$		0			0
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$691$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$692$	26.0352	−	15.0314i	0.989709	−	0.571409i
$693$	45.4509	+	25.8135i	1.72654	+	0.980572i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−24.8619	+	9.04900i	−0.939693	+	0.342020i
$701$		−	27.6284i		−	1.04351i	−0.853095	−	0.521755i	$-0.825277\pi$
$701$		−	27.6284i		−	1.04351i	0.853095	−	0.521755i	$-0.174723\pi$
$702$		0			0
$703$		0			0
$704$	−18.0186	−	49.5057i	−0.679101	−	1.86582i
$705$	−21.4098	−	7.70675i	−0.806340	−	0.290253i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−34.9403	−	29.3184i	−1.31221	−	1.10107i	−0.987895	−	0.155125i	$-0.950422\pi$
$709$	−34.9403	−	29.3184i	−1.31221	−	1.10107i	−0.324314	−	0.945949i	$-0.605134\pi$
$710$		0			0
$711$	−11.7203	+	9.97687i	−0.439547	+	0.374162i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	85.0557	+	30.9578i	3.18090	+	1.15775i
$716$	17.5730	−	48.2814i	0.656734	−	1.80436i
$717$	−7.75597	+	9.30998i	−0.289652	+	0.347688i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	9.35577	+	25.1489i	0.348669	+	0.937246i
$721$	21.3056	−	36.9024i	0.793463	−	1.37432i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	34.5571	+	41.1836i	1.28342	+	1.52952i
$726$		0			0
$727$	−36.2243	+	13.1846i	−1.34349	+	0.488989i	−0.910909	−	0.412608i	$-0.864618\pi$
$727$	−36.2243	+	13.1846i	−1.34349	+	0.488989i	−0.432577	+	0.901597i	$0.642396\pi$
$728$		0			0
$729$	−13.0000	+	23.6643i	−0.481481	+	0.876456i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	5.90330	−	4.95346i	0.218043	−	0.182960i	−0.527223	−	0.849727i	$-0.676767\pi$
$733$	5.90330	−	4.95346i	0.218043	−	0.182960i	0.745266	+	0.666767i	$0.232322\pi$
$734$		0			0
$735$	−23.4305	+	13.6385i	−0.864249	+	0.503065i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	25.8056	+	44.6967i	0.949276	+	1.64419i	0.746955	+	0.664875i	$0.231515\pi$
$739$	25.8056	+	44.6967i	0.949276	+	1.64419i	0.202321	+	0.979319i	$0.435152\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$743$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$744$		0			0
$745$	−0.698758	+	3.96285i	−0.0256005	+	0.145188i
$746$		0			0
$747$	−5.78608	−	6.79719i	−0.211702	−	0.248696i
$748$	−22.3180	+	38.6560i	−0.816029	+	1.41340i
$749$		0			0
$750$		0			0
$751$	−6.87843	−	39.0095i	−0.250997	−	1.42348i	−0.806142	−	0.591723i	$-0.798448\pi$
$751$	−6.87843	−	39.0095i	−0.250997	−	1.42348i	0.555144	−	0.831754i	$-0.312663\pi$
$752$	15.1061	+	18.0027i	0.550862	+	0.656492i
$753$		0			0
$754$		0			0
$755$			49.2942i			1.79400i
$756$	14.0000	+	23.6643i	0.509175	+	0.860663i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$761$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$762$		0			0
$763$	39.2964	+	32.9736i	1.42262	+	1.19372i
$764$	10.2470	+	5.91608i	0.370722	+	0.214036i
$765$	11.2274	−	19.7686i	0.405928	−	0.714735i
$766$		0			0
$767$		0			0
$768$	4.71557	−	27.3087i	0.170158	−	0.985417i
$769$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$769$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$770$		0			0
$771$	52.0403	+	8.98614i	1.87418	+	0.323628i
$772$		0			0
$773$	47.7223	−	27.5525i	1.71645	−	0.990994i	0.791273	−	0.611463i	$-0.209419\pi$
$773$	47.7223	−	27.5525i	1.71645	−	0.990994i	0.925179	−	0.379531i	$-0.123915\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	30.7343	+	36.3653i	1.10046	+	1.30209i
$781$	103.822	−	37.7882i	3.71505	−	1.35217i
$782$		0			0
$783$	35.4560	−	43.1785i	1.26709	−	1.54307i
$784$	28.0000			1.00000
$785$	−11.7018	−	32.1504i	−0.417655	−	1.14750i
$786$		0			0
$787$	42.9098	−	36.0056i	1.52957	−	1.28346i	0.727926	−	0.685656i	$-0.240484\pi$
$787$	42.9098	−	36.0056i	1.52957	−	1.28346i	0.801642	−	0.597804i	$-0.203960\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.8949	+	51.9134i	−0.669293	+	1.83887i	−0.140576	+	0.990070i	$0.544895\pi$
$797$	−18.8949	+	51.9134i	−0.669293	+	1.83887i	−0.528717	+	0.848798i	$0.677327\pi$
$798$		0			0
$799$	3.45757	−	19.6089i	0.122320	−	0.693712i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.18781	−	2.60733i	0.0772062	−	0.0920108i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			6.65514i			0.233982i	0.993133	+	0.116991i	$0.0373249\pi$
$809$			6.65514i			0.233982i	−0.993133	+	0.116991i	$0.962675\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−19.4595	−	53.4644i	−0.682893	−	1.87623i
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−20.2925	+	11.8119i	−0.710381	+	0.413501i
$817$		0			0
$818$		0			0
$819$	37.5959	+	31.0955i	1.31371	+	1.08657i
$820$		0			0
$821$	−24.6738	−	4.35066i	−0.861122	−	0.151839i	−0.274388	−	0.961619i	$-0.588475\pi$
$821$	−24.6738	−	4.35066i	−0.861122	−	0.151839i	−0.586734	+	0.809780i	$0.699586\pi$
$822$		0			0
$823$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$823$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$824$		0			0
$825$	−19.6954	−	53.5220i	−0.685707	−	1.86340i
$826$		0			0
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−8.53913	−	48.4278i	−0.296041	−	1.67893i
$833$	−15.2490	−	18.1731i	−0.528348	−	0.629660i
$834$		0			0
$835$	−42.8620	+	15.6005i	−1.48330	+	0.539878i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$839$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$840$		0			0
$841$	−66.3481	+	55.6727i	−2.28787	+	1.91975i
$842$		0			0
$843$	0.157956	+	44.5896i	0.00544029	+	1.53575i
$844$	−9.51530	−	7.98429i	−0.327530	−	0.274831i
$845$	47.9938	+	27.7092i	1.65104	+	0.953227i
$846$		0			0
$847$	42.8174	+	74.1619i	1.47122	+	2.54823i
$848$		0			0
$849$	5.75682	−	33.3387i	0.197574	−	1.14418i
$850$		0			0
$851$		0			0
$852$	57.2711	+	9.88938i	1.96208	+	0.338805i
$853$	9.72827	−	55.1717i	0.333090	−	1.88904i	−0.112245	−	0.993681i	$-0.535804\pi$
$853$	9.72827	−	55.1717i	0.333090	−	1.88904i	0.445335	−	0.895364i	$-0.353085\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.1051	+	13.2346i	−0.379344	+	0.452085i	−0.921607	−	0.388124i	$-0.873123\pi$
$857$	−11.1051	+	13.2346i	−0.379344	+	0.452085i	0.542263	+	0.840209i	$0.317568\pi$
$858$		0			0
$859$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$859$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−33.6113			−1.14282
$866$		0			0
$867$	−8.98673	−	3.23490i	−0.305205	−	0.109863i
$868$		0			0
$869$	−33.2733	+	5.86698i	−1.12872	+	0.199024i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−10.0241	−	54.5851i	−0.339264	−	1.84743i
$874$		0			0
$875$	29.1310	+	5.13658i	0.984808	+	0.173648i
$876$	1.68026	−	0.618314i	0.0567707	−	0.0208909i
$877$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$877$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$878$		0			0
$879$	9.22740	−	11.0762i	0.311232	−	0.373592i
$880$	−10.2281	+	58.0064i	−0.344789	+	1.95539i
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$		0			0
$883$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$883$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$884$	−26.7811	+	31.9164i	−0.900744	+	1.07347i
$885$		0			0
$886$		0			0
$887$	15.0121	+	17.8907i	0.504056	+	0.600711i	0.956734	−	0.290963i	$-0.0939758\pi$
$887$	15.0121	+	17.8907i	0.504056	+	0.600711i	−0.452678	+	0.891674i	$0.649531\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−50.9027	+	30.3584i	−1.70531	+	1.01704i
$892$	−35.9649			−1.20419
$893$		0			0
$894$		0			0
$895$	−44.0051	+	36.9247i	−1.47093	+	1.23426i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	5.00000	−	29.5804i	0.166667	−	0.986013i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$907$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$908$	−22.2818	+	12.8644i	−0.739449	+	0.426921i
$909$		0			0
$910$		0			0
$911$	−14.1997	+	16.9226i	−0.470458	+	0.560670i	−0.948136	−	0.317865i	$-0.897034\pi$
$911$	−14.1997	+	16.9226i	−0.470458	+	0.560670i	0.477678	+	0.878535i	$0.341479\pi$
$912$		0			0
$913$	−3.40255	−	19.2968i	−0.112608	−	0.638631i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−60.6113			−1.99938			−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−60.6113			−1.99938			−0.999691	+	0.0248659i	$0.992084\pi$
$920$		0			0
$921$	39.7209	−	33.5703i	1.30885	−	1.10618i
$922$		0			0
$923$	101.562	−	17.9081i	3.34294	−	0.589451i
$924$	0.213805	+	60.3554i	0.00703368	+	1.98555i
$925$		0			0
$926$		0			0
$927$	24.4542	+	41.6712i	0.803180	+	1.36866i
$928$		0			0
$929$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$929$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	43.2187	−	24.9523i	1.41340	−	0.816029i
$936$		0			0
$937$	29.7384	−	51.5084i	0.971511	−	1.68271i	0.280512	−	0.959851i	$-0.409496\pi$
$937$	29.7384	−	51.5084i	0.971511	−	1.68271i	0.690999	−	0.722856i	$-0.257171\pi$
$938$		0			0
$939$	−55.3907	+	0.196218i	−1.80761	+	0.00640334i
$940$	−4.56257	−	25.8756i	−0.148815	−	0.843970i
$941$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$941$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−0.326685	−	30.7391i	−0.0106271	−	0.999944i
$946$		0			0
$947$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$947$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$948$	−16.7224	−	6.01945i	−0.543118	−	0.195503i
$949$	2.43372	−	2.04213i	0.0790019	−	0.0662905i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$		0			0
$955$	−6.61438	−	11.4564i	−0.214036	−	0.370722i
$956$	−13.7794	−	2.42968i	−0.445657	−	0.0785813i
$957$	115.097	−	42.3541i	3.72055	−	1.36911i
$958$		0			0
$959$		0			0
$960$	−19.8318	+	23.8054i	−0.640070	+	0.768317i
$961$	5.38309	−	30.5290i	0.173648	−	0.984808i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$967$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	−31.1720	+	0.552180i	−0.999843	+	0.0177112i
$973$		0			0
$974$		0			0
$975$	−9.42953	−	52.3916i	−0.301987	−	1.67787i
$976$		0			0
$977$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$977$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$978$		0			0
$979$		0			0
$980$	−27.1109	−	15.6525i	−0.866025	−	0.500000i
$981$	−54.5160	+	20.2808i	−1.74056	+	0.647515i
$982$		0			0
$983$	−45.6150	−	8.04316i	−1.45489	−	0.256537i	−0.610396	−	0.792096i	$-0.708990\pi$
$983$	−45.6150	−	8.04316i	−1.45489	−	0.256537i	−0.844498	+	0.535559i	$0.820101\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−9.29800	−	25.2672i	−0.295959	−	0.804263i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−30.5023	+	52.8315i	−0.968936	+	1.67825i	−0.270291	+	0.962779i	$0.587120\pi$
$991$	−30.5023	+	52.8315i	−0.968936	+	1.67825i	−0.698645	+	0.715468i	$0.746213\pi$
$992$		0			0
$993$	−24.9132	+	43.5061i	−0.790596	+	1.38062i
$994$		0			0
$995$		0			0
$996$	3.49098	−	9.69813i	0.110616	−	0.307297i
$997$	17.4034	−	6.33430i	0.551170	−	0.200609i	−0.0513964	−	0.998678i	$-0.516367\pi$
$997$	17.4034	−	6.33430i	0.551170	−	0.200609i	0.602566	+	0.798069i	$0.294145\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.a.209.3	yes	24
5.4	even	2	inner	945.2.cs.a.209.2	yes	24
7.6	odd	2	inner	945.2.cs.a.209.2	yes	24
27.23	odd	18	inner	945.2.cs.a.104.3	yes	24
35.34	odd	2	CM	945.2.cs.a.209.3	yes	24
135.104	odd	18	inner	945.2.cs.a.104.2	✓	24
189.104	even	18	inner	945.2.cs.a.104.2	✓	24
945.104	even	18	inner	945.2.cs.a.104.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.a.104.2	✓	24	135.104	odd	18	inner
945.2.cs.a.104.2	✓	24	189.104	even	18	inner
945.2.cs.a.104.3	yes	24	27.23	odd	18	inner
945.2.cs.a.104.3	yes	24	945.104	even	18	inner
945.2.cs.a.209.2	yes	24	5.4	even	2	inner
945.2.cs.a.209.2	yes	24	7.6	odd	2	inner
945.2.cs.a.209.3	yes	24	1.1	even	1	trivial
945.2.cs.a.209.3	yes	24	35.34	odd	2	CM

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.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.306808 + 1.70466i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(2.02676 + 1.70066i) q^{7} +(-2.81174 + 1.04601i) q^{9} +O(q^{10})\)	\(q+(0.306808 + 1.70466i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(2.02676 + 1.70066i) q^{7} +(-2.81174 + 1.04601i) q^{9} +(-6.48531 - 1.14354i) q^{11} +(-2.66153 - 2.21727i) q^{12} +(-5.77616 - 2.10235i) q^{13} +(1.33752 + 3.63470i) q^{15} +(0.694593 - 3.93923i) q^{16} +(-2.93500 + 1.69452i) q^{17} +(-2.87463 + 3.42585i) q^{20} +(-2.27721 + 3.97672i) q^{21} +(4.69846 - 1.71010i) q^{25} +(-2.64575 - 4.47214i) q^{27} -5.29150 q^{28} +(3.67749 + 10.1038i) q^{29} +(-0.0404054 - 11.4061i) q^{33} +(5.12348 + 2.95804i) q^{35} +(2.96311 - 5.21728i) q^{36} +(1.81162 - 10.4914i) q^{39} +(11.4062 - 6.58536i) q^{44} +(-5.78557 + 3.39518i) q^{45} +(-3.77652 + 4.50068i) q^{47} +(6.92816 - 0.0245426i) q^{48} +(1.21554 + 6.89365i) q^{49} +(-3.78906 - 4.48328i) q^{51} +(11.5523 - 4.20470i) q^{52} -14.7253 q^{55} +(-6.72188 - 3.84920i) q^{60} +(-7.47762 - 2.66179i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-13.5360 - 2.38676i) q^{65} +(2.31824 - 6.36931i) q^{68} +(-14.5297 + 8.38871i) q^{71} +(-0.258424 + 0.447604i) q^{73} +(4.35667 + 7.48461i) q^{75} +(-11.1994 - 13.3470i) q^{77} +(4.82115 - 1.75476i) q^{79} -8.94427i q^{80} +(6.81174 - 5.88220i) q^{81} +(1.01767 + 2.79602i) q^{83} +(-1.62348 - 9.02022i) q^{84} +(-5.80518 + 4.87113i) q^{85} +(-16.0953 + 9.36881i) q^{87} +(-8.13153 - 14.0842i) q^{91} +(-3.21237 + 18.2182i) q^{97} +(19.4311 - 3.56836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{9}+O(q^{10}) \) 24 * q - 6 * q^9	\( 24 q - 6 q^{9} - 18 q^{11} - 24 q^{39} + 96 q^{64} - 180 q^{65} - 12 q^{79} + 102 q^{81} + 84 q^{84} + 60 q^{85} + 228 q^{99}+O(q^{100}) \) 24 * q - 6 * q^9 - 18 * q^11 - 24 * q^39 + 96 * q^64 - 180 * q^65 - 12 * q^79 + 102 * q^81 + 84 * q^84 + 60 * q^85 + 228 * q^99

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