LMFDB - Embedded newform 1872.2.by.h.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(433,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1872.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.by (of order $6$, degree $2$, 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:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1872.433
Dual form			1872.2.by.h.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(1.09808 + 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +(2.86603 + 4.96410i) q^{17} +(-4.09808 + 2.36603i) q^{19} +(2.09808 - 3.63397i) q^{23} -8.92820 q^{25} +(-2.23205 + 3.86603i) q^{29} -1.46410i q^{31} +(5.09808 + 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +(-8.13397 - 4.69615i) q^{41} +(4.83013 + 8.36603i) q^{43} -2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} +6.46410 q^{53} +(2.36603 - 4.09808i) q^{55} +(-6.92820 + 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(9.33013 + 9.69615i) q^{65} +(11.3660 + 6.56218i) q^{67} +(4.09808 - 2.36603i) q^{71} +6.26795i q^{73} -3.46410 q^{77} +2.53590 q^{79} -0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} +(8.19615 + 4.73205i) q^{89} +(2.73205 - 9.46410i) q^{91} +(8.83013 + 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{7} - 6 q^{11} + 8 q^{17} - 6 q^{19} - 2 q^{23} - 8 q^{25} - 2 q^{29} + 10 q^{35} - 12 q^{37} - 36 q^{41} + 2 q^{43} - 6 q^{49} + 12 q^{53} + 6 q^{55} + 8 q^{61} + 20 q^{65} + 42 q^{67} + 6 q^{71}+ \cdots + 18 q^{95}+O(q^{100}) $ 4 * q - 6 * q^7 - 6 * q^11 + 8 * q^17 - 6 * q^19 - 2 * q^23 - 8 * q^25 - 2 * q^29 + 10 * q^35 - 12 * q^37 - 36 * q^41 + 2 * q^43 - 6 * q^49 + 12 * q^53 + 6 * q^55 + 8 * q^61 + 20 * q^65 + 42 * q^67 + 6 * q^71 + 24 * q^79 + 36 * q^85 + 12 * q^89 + 4 * q^91 + 18 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$		−	3.73205i		−	1.66902i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$		−	3.73205i		−	1.66902i	0.550990	−	0.834512i	$-0.314250\pi$
$6$		0			0
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.875338	−	0.483512i	$-0.839361\pi$
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.0189356	+	0.999821i	$0.506028\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	0.656322	−	0.754481i	$-0.272111\pi$
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	−0.325239	+	0.945632i	$0.605445\pi$
$12$		0			0
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.890011	−	0.455938i	$-0.849304\pi$
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.0501517	+	0.998742i	$0.515970\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	−0.560015	−	0.828482i	$-0.689205\pi$
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	0.997494	+	0.0707462i	$0.0225381\pi$
$24$		0			0
$25$	−8.92820			−1.78564
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.23205	+	3.86603i	−0.414481	+	0.717903i	−0.995374	−	0.0960774i	$-0.969370\pi$
$29$	−2.23205	+	3.86603i	−0.414481	+	0.717903i	0.580892	+	0.813980i	$0.302704\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.09808	+	8.83013i	0.861732	+	1.49256i
$36$		0			0
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	0.730124	−	0.683314i	$-0.239462\pi$
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	−0.226705	+	0.973963i	$0.572795\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.295267	−	0.955415i	$-0.595408\pi$
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.975047	+	0.221999i	$0.928742\pi$
$42$		0			0
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	0.954023	+	0.299732i	$0.0968974\pi$
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	−0.217436	+	0.976075i	$0.569769\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	2.19615i		−	0.320342i	−0.987089	−	0.160171i	$-0.948795\pi$
$47$		−	2.19615i		−	0.320342i	0.987089	−	0.160171i	$-0.0512045\pi$
$48$		0			0
$49$	0.232051	−	0.401924i	0.0331501	−	0.0574177i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$		0			0
$55$	2.36603	−	4.09808i	0.319035	−	0.552584i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$		0			0
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.33013	+	9.69615i	1.15726	+	1.20266i
$66$		0			0
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.993155	−	0.116800i	$-0.0372638\pi$
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.395426	+	0.918498i	$0.370597\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	−0.236708	−	0.971581i	$-0.576068\pi$
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	0.723060	+	0.690785i	$0.242735\pi$
$72$		0			0
$73$			6.26795i			0.733608i	0.930298	+	0.366804i	$0.119548\pi$
$73$			6.26795i			0.733608i	−0.930298	+	0.366804i	$0.880452\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.46410			−0.394771
$78$		0			0
$79$	2.53590			0.285311			0.142655	−	0.989772i	$-0.454436\pi$
$79$	2.53590			0.285311			0.142655	+	0.989772i	$0.454436\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	0.196152i		−	0.0215305i	−0.999942	−	0.0107653i	$-0.996573\pi$
$83$		−	0.196152i		−	0.0215305i	0.999942	−	0.0107653i	$-0.00342676\pi$
$84$		0			0
$85$	18.5263	−	10.6962i	2.00946	−	1.16016i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$		0			0
$91$	2.73205	−	9.46410i	0.286397	−	0.992107i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.83013	+	15.2942i	0.905952	+	1.56915i
$96$		0			0
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	−0.909997	−	0.414615i	$-0.863916\pi$
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	0.814065	+	0.580773i	$0.197250\pi$
$102$		0			0
$103$	−15.2679			−1.50440			−0.752198	−	0.658937i	$-0.771006\pi$
$103$	−15.2679			−1.50440			−0.752198	+	0.658937i	$0.771006\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	−0.999966	−	0.00823695i	$-0.997378\pi$
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	0.507116	+	0.861878i	$0.330711\pi$
$108$		0			0
$109$			1.46410i			0.140236i	0.997539	+	0.0701178i	$0.0223375\pi$
$109$			1.46410i			0.140236i	−0.997539	+	0.0701178i	$0.977662\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	0.832796	−	0.553580i	$-0.186739\pi$
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	−0.895812	+	0.444432i	$0.853405\pi$
$114$		0			0
$115$	−13.5622	−	7.83013i	−1.26468	−	0.730163i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−13.5622	−	7.83013i	−1.24324	−	0.717787i
$120$		0			0
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			14.6603i			1.31125i
$126$		0			0
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	−0.560173	−	0.828375i	$-0.689266\pi$
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	0.997481	+	0.0709368i	$0.0225989\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$		0			0
$133$	6.46410	−	11.1962i	0.560509	−	0.970830i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.0110599	−	0.999939i	$-0.496479\pi$
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.871502	+	0.490391i	$0.163146\pi$
$138$		0			0
$139$	8.92820	+	15.4641i	0.757280	+	1.31165i	0.944233	+	0.329279i	$0.106806\pi$
$139$	8.92820	+	15.4641i	0.757280	+	1.31165i	−0.186952	+	0.982369i	$0.559861\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.43782	+	1.09808i	−0.371109	+	0.0918257i
$144$		0			0
$145$	14.4282	+	8.33013i	1.19820	+	0.691779i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.888778	−	0.458338i	$-0.848445\pi$
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.0474568	+	0.998873i	$0.515112\pi$
$150$		0			0
$151$			6.73205i			0.547847i	0.961752	+	0.273923i	$0.0883214\pi$
$151$			6.73205i			0.547847i	−0.961752	+	0.273923i	$0.911679\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.46410			−0.438887
$156$		0			0
$157$	7.58846			0.605625			0.302812	−	0.953050i	$-0.402074\pi$
$157$	7.58846			0.605625			0.302812	+	0.953050i	$0.402074\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			11.4641i			0.903498i
$162$		0			0
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.881492	−	0.472199i	$-0.843460\pi$
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.0318096	+	0.999494i	$0.510127\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.19615	−	4.73205i	−0.634237	−	0.366177i	0.148154	−	0.988964i	$-0.452667\pi$
$167$	−8.19615	−	4.73205i	−0.634237	−	0.366177i	−0.782391	+	0.622787i	$0.786000\pi$
$168$		0			0
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	0.770383	−	0.637582i	$-0.220065\pi$
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	−0.937353	+	0.348380i	$0.886732\pi$
$174$		0			0
$175$	21.1244	−	12.1962i	1.59685	−	0.921942i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	0.392921	+	0.919572i	$0.371465\pi$
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	−0.992833	+	0.119506i	$0.961869\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.59808	−	11.4282i	0.485100	−	0.840218i
$186$		0			0
$187$			7.26795i			0.531485i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	0.963706	−	0.266966i	$-0.0860212\pi$
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	−0.713052	+	0.701111i	$0.752688\pi$
$192$		0			0
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	0.0875652	−	0.996159i	$-0.472091\pi$
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	−0.818916	+	0.573913i	$0.805425\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.165086	−	0.986279i	$-0.552790\pi$
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.936686	+	0.350171i	$0.886123\pi$
$198$		0			0
$199$	7.09808	+	12.2942i	0.503169	+	0.871515i	0.999993	+	0.00366345i	$0.00116611\pi$
$199$	7.09808	+	12.2942i	0.503169	+	0.871515i	−0.496824	+	0.867851i	$0.665501\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	12.1962i		−	0.856002i
$204$		0			0
$205$	−17.5263	+	30.3564i	−1.22409	+	2.12018i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.00000			−0.415029
$210$		0			0
$211$	8.19615	−	14.1962i	0.564246	−	0.977303i	−0.432873	−	0.901455i	$-0.642500\pi$
$211$	8.19615	−	14.1962i	0.564246	−	0.977303i	0.997119	−	0.0758485i	$-0.0241665\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	31.2224	−	18.0263i	2.12935	−	1.22938i
$216$		0			0
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−19.8564	−	5.73205i	−1.33569	−	0.385579i
$222$		0			0
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.997090	−	0.0762356i	$-0.975710\pi$
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.564567	−	0.825387i	$-0.690957\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.5622	+	6.09808i	−0.701036	+	0.404744i	−0.807733	−	0.589548i	$-0.799306\pi$
$227$	−10.5622	+	6.09808i	−0.701036	+	0.404744i	0.106697	+	0.994292i	$0.465973\pi$
$228$		0			0
$229$			11.8564i			0.783493i	0.920073	+	0.391747i	$0.128129\pi$
$229$			11.8564i			0.783493i	−0.920073	+	0.391747i	$0.871871\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.85641			−0.514690			−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641			−0.514690			−0.257345	+	0.966320i	$0.582848\pi$
$234$		0			0
$235$	−8.19615			−0.534658
$236$		0			0
$237$		0			0
$238$		0			0
$239$			7.66025i			0.495501i	0.968824	+	0.247750i	$0.0796913\pi$
$239$			7.66025i			0.495501i	−0.968824	+	0.247750i	$0.920309\pi$
$240$		0			0
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	−0.828592	−	0.559853i	$-0.810857\pi$
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	0.0705514	+	0.997508i	$0.477524\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.50000	−	0.866025i	−0.0958315	−	0.0553283i
$246$		0			0
$247$	4.73205	−	16.3923i	0.301093	−	1.04302i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	0.996413	−	0.0846203i	$-0.0269677\pi$
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	−0.571490	+	0.820609i	$0.693634\pi$
$252$		0			0
$253$	4.60770	−	2.66025i	0.289683	−	0.167249i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	−0.974117	−	0.226044i	$-0.927421\pi$
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	0.682818	+	0.730588i	$0.260754\pi$
$258$		0			0
$259$	−9.66025			−0.600259
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	−0.668414	−	0.743790i	$-0.733026\pi$
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	0.978348	+	0.206969i	$0.0663598\pi$
$264$		0			0
$265$		−	24.1244i		−	1.48195i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.73205	+	4.73205i	0.166576	+	0.288518i	0.937214	−	0.348755i	$-0.113396\pi$
$269$	2.73205	+	4.73205i	0.166576	+	0.288518i	−0.770638	+	0.637273i	$0.780062\pi$
$270$		0			0
$271$	18.9282	+	10.9282i	1.14981	+	0.663841i	0.948840	−	0.315757i	$-0.102258\pi$
$271$	18.9282	+	10.9282i	1.14981	+	0.663841i	0.200966	+	0.979598i	$0.435592\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.80385	−	5.66025i	−0.591194	−	0.341326i
$276$		0			0
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	0.766987	−	0.641663i	$-0.221755\pi$
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	−0.939190	+	0.343399i	$0.888422\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			12.3205i			0.734980i	0.930027	+	0.367490i	$0.119783\pi$
$281$			12.3205i			0.734980i	−0.930027	+	0.367490i	$0.880217\pi$
$282$		0			0
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	0.178797	+	0.983886i	$0.442780\pi$
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	−0.941469	+	0.337100i	$0.890554\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.6603			1.51468
$288$		0			0
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.545368	−	0.838196i	$-0.316390\pi$
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.998584	−	0.0532048i	$-0.0169436\pi$
$294$		0			0
$295$	14.9282	+	25.8564i	0.869154	+	1.50542i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.63397	+	14.6865i	0.210158	+	0.849344i
$300$		0			0
$301$	−22.8564	−	13.1962i	−1.31742	−	0.760614i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	29.7224	−	17.1603i	1.70190	−	0.982593i
$306$		0			0
$307$		−	22.5885i		−	1.28919i	−0.764524	−	0.644596i	$-0.777026\pi$
$307$		−	22.5885i		−	1.28919i	0.764524	−	0.644596i	$-0.222974\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.66025			0.0941444			0.0470722	−	0.998891i	$-0.485011\pi$
$311$	1.66025			0.0941444			0.0470722	+	0.998891i	$0.485011\pi$
$312$		0			0
$313$	6.53590			0.369431			0.184715	−	0.982792i	$-0.440864\pi$
$313$	6.53590			0.369431			0.184715	+	0.982792i	$0.440864\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	20.6603i		−	1.16040i	−0.814476	−	0.580198i	$-0.802975\pi$
$317$		−	20.6603i		−	1.16040i	0.814476	−	0.580198i	$-0.197025\pi$
$318$		0			0
$319$	−4.90192	+	2.83013i	−0.274455	+	0.158457i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−23.4904	−	13.5622i	−1.30704	−	0.754620i
$324$		0			0
$325$	23.1962	−	22.3205i	1.28669	−	1.23812i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.893708	−	0.448649i	$-0.851905\pi$
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.0583130	+	0.998298i	$0.518572\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	24.4904	−	42.4186i	1.33805	−	2.31757i
$336$		0			0
$337$	20.8564			1.13612			0.568060	−	0.822987i	$-0.307694\pi$
$337$	20.8564			1.13612			0.568060	+	0.822987i	$0.307694\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.928203	−	1.60770i	0.0502650	−	0.0870616i
$342$		0			0
$343$		−	17.8564i		−	0.964155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.840936	−	0.541135i	$-0.817995\pi$
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.0481683	−	0.998839i	$-0.515338\pi$
$348$		0			0
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.0946674	−	0.995509i	$-0.530179\pi$
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.909470	+	0.415770i	$0.863512\pi$
$354$		0			0
$355$	−8.83013	−	15.2942i	−0.468654	−	0.811733i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			1.12436i			0.0593412i	0.999560	+	0.0296706i	$0.00944584\pi$
$359$			1.12436i			0.0593412i	−0.999560	+	0.0296706i	$0.990554\pi$
$360$		0			0
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.3923			1.22441
$366$		0			0
$367$	−5.63397	+	9.75833i	−0.294091	+	0.509381i	−0.974773	−	0.223198i	$-0.928350\pi$
$367$	−5.63397	+	9.75833i	−0.294091	+	0.509381i	0.680682	+	0.732579i	$0.261684\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−15.2942	+	8.83013i	−0.794037	+	0.458437i
$372$		0			0
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	0.987205	−	0.159456i	$-0.0509741\pi$
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	−0.631696	+	0.775216i	$0.717641\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.86603	−	15.6244i	−0.199110	−	0.804695i
$378$		0			0
$379$	−4.73205	−	2.73205i	−0.243069	−	0.140336i	0.373517	−	0.927623i	$-0.378152\pi$
$379$	−4.73205	−	2.73205i	−0.243069	−	0.140336i	−0.616587	+	0.787287i	$0.711485\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	−0.532045	−	0.846716i	$-0.678576\pi$
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	0.467255	+	0.884122i	$0.345243\pi$
$384$		0			0
$385$			12.9282i			0.658882i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.7846			0.597503			0.298752	−	0.954331i	$-0.403430\pi$
$389$	11.7846			0.597503			0.298752	+	0.954331i	$0.403430\pi$
$390$		0			0
$391$	24.0526			1.21639
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	9.46410i		−	0.476191i
$396$		0			0
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.872744	−	0.488177i	$-0.837662\pi$
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.0135983	+	0.999908i	$0.504329\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	0.315198	−	0.949026i	$-0.397929\pi$
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	−0.664281	+	0.747483i	$0.731262\pi$
$402$		0			0
$403$	3.66025	+	3.80385i	0.182330	+	0.189483i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.24167	+	3.88269i	0.111115	+	0.192458i
$408$		0			0
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	−0.0697281	−	0.997566i	$-0.522213\pi$
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	0.829053	+	0.559169i	$0.188880\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.9282	−	18.9282i	0.537742	−	0.931396i
$414$		0			0
$415$	−0.732051			−0.0359350
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	−0.569979	−	0.821659i	$-0.693049\pi$
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	0.996567	+	0.0827863i	$0.0263819\pi$
$420$		0			0
$421$		−	22.7128i		−	1.10695i	−0.832864	−	0.553477i	$-0.813301\pi$
$421$		−	22.7128i		−	1.10695i	0.832864	−	0.553477i	$-0.186699\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−25.5885	−	44.3205i	−1.24122	−	2.14986i
$426$		0			0
$427$	−21.7583	−	12.5622i	−1.05296	−	0.607926i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	0.200624	−	0.979668i	$-0.435703\pi$
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	−0.748106	+	0.663579i	$0.769036\pi$
$432$		0			0
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	0.978126	−	0.208012i	$-0.0666992\pi$
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	−0.669207	+	0.743076i	$0.733366\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			19.8564i			0.949861i
$438$		0			0
$439$	0.169873	−	0.294229i	0.00810760	−	0.0140428i	−0.861943	−	0.507005i	$-0.830753\pi$
$439$	0.169873	−	0.294229i	0.00810760	−	0.0140428i	0.870051	+	0.492962i	$0.164086\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.6077			0.741544			0.370772	−	0.928724i	$-0.379093\pi$
$443$	15.6077			0.741544			0.370772	+	0.928724i	$0.379093\pi$
$444$		0			0
$445$	17.6603	−	30.5885i	0.837176	−	1.45003i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	−0.250495	−	0.968118i	$-0.580593\pi$
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	0.713167	+	0.700994i	$0.247260\pi$
$450$		0			0
$451$	−5.95448	−	10.3135i	−0.280386	−	0.485642i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−35.3205	−	10.1962i	−1.65585	−	0.478003i
$456$		0			0
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	0.472617	−	0.881268i	$-0.343309\pi$
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	−0.526892	+	0.849932i	$0.676643\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.876607	−	0.481207i	$-0.840199\pi$
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.0215666	+	0.999767i	$0.506865\pi$
$462$		0			0
$463$			10.0526i			0.467182i	0.972335	+	0.233591i	$0.0750477\pi$
$463$			10.0526i			0.467182i	−0.972335	+	0.233591i	$0.924952\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.5885			−0.860171			−0.430086	−	0.902788i	$-0.641517\pi$
$467$	−18.5885			−0.860171			−0.430086	+	0.902788i	$0.641517\pi$
$468$		0			0
$469$	−35.8564			−1.65570
$470$		0			0
$471$		0			0
$472$		0			0
$473$			12.2487i			0.563196i
$474$		0			0
$475$	36.5885	−	21.1244i	1.67879	−	0.969252i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.984390	−	0.176000i	$-0.0563159\pi$
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.339775	+	0.940507i	$0.389649\pi$
$480$		0			0
$481$	−12.3756	+	3.06218i	−0.564281	+	0.139623i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	11.1962	+	19.3923i	0.508391	+	0.880559i
$486$		0			0
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	−0.437441	−	0.899247i	$-0.644115\pi$
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	0.560051	+	0.828458i	$0.310782\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	−0.750530	−	0.660836i	$-0.770202\pi$
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	0.947566	+	0.319560i	$0.103535\pi$
$492$		0			0
$493$	−25.5885			−1.15245
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.46410	+	11.1962i	−0.289955	+	0.502216i
$498$		0			0
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.808908	−	0.587935i	$-0.799941\pi$
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.104713	−	0.994502i	$-0.533392\pi$
$504$		0			0
$505$	6.23205	+	3.59808i	0.277323	+	0.160112i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	0.739842	−	0.672781i	$-0.234900\pi$
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	−0.212725	+	0.977112i	$0.568234\pi$
$510$		0			0
$511$	−8.56218	−	14.8301i	−0.378768	−	0.656046i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			56.9808i			2.51087i
$516$		0			0
$517$	1.39230	−	2.41154i	0.0612335	−	0.106060i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−41.4449			−1.81573			−0.907866	−	0.419260i	$-0.862290\pi$
$521$	−41.4449			−1.81573			−0.907866	+	0.419260i	$0.862290\pi$
$522$		0			0
$523$	−11.2224	+	19.4378i	−0.490723	+	0.849957i	−0.999943	−	0.0106796i	$-0.996601\pi$
$523$	−11.2224	+	19.4378i	−0.490723	+	0.849957i	0.509220	+	0.860636i	$0.329934\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.26795	−	4.19615i	0.316597	−	0.182787i
$528$		0			0
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	32.8731	−	8.13397i	1.42389	−	0.352322i
$534$		0			0
$535$	32.9545	+	19.0263i	1.42475	+	0.822578i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.509619	−	0.294229i	0.0219508	−	0.0126733i
$540$		0			0
$541$		−	5.67949i		−	0.244180i	−0.992519	−	0.122090i	$-0.961040\pi$
$541$		−	5.67949i		−	0.244180i	0.992519	−	0.122090i	$-0.0389597\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.46410			0.234056
$546$		0			0
$547$	4.19615			0.179415			0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615			0.179415			0.0897073	+	0.995968i	$0.471407\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	21.1244i		−	0.899928i
$552$		0			0
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.997734	−	0.0672780i	$-0.978569\pi$
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.557132	−	0.830424i	$-0.688098\pi$
$558$		0			0
$559$	−33.4641	−	9.66025i	−1.41538	−	0.408585i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	0.954273	+	0.298938i	$0.0966324\pi$
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	−0.218248	+	0.975893i	$0.570034\pi$
$564$		0			0
$565$	−4.33013	+	2.50000i	−0.182170	+	0.105176i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	0.342656	+	0.939461i	$0.388674\pi$
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	−0.984925	+	0.172982i	$0.944660\pi$
$570$		0			0
$571$	14.0526			0.588081			0.294041	−	0.955793i	$-0.405000\pi$
$571$	14.0526			0.588081			0.294041	+	0.955793i	$0.405000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18.7321	+	32.4449i	−0.781181	+	1.35304i
$576$		0			0
$577$			3.73205i			0.155367i	0.996978	+	0.0776837i	$0.0247524\pi$
$577$			3.73205i			0.155367i	−0.996978	+	0.0776837i	$0.975248\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.267949	+	0.464102i	0.0111164	+	0.0192542i
$582$		0			0
$583$	7.09808	+	4.09808i	0.293972	+	0.169725i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	0.185999	−	0.982550i	$-0.440448\pi$
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	−0.757914	+	0.652355i	$0.773781\pi$
$588$		0			0
$589$	3.46410	+	6.00000i	0.142736	+	0.247226i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	9.14359i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$		−	9.14359i		−	0.375482i	0.982219	−	0.187741i	$-0.0601166\pi$
$594$		0			0
$595$	−29.2224	+	50.6147i	−1.19800	+	2.07500i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.53590			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$599$	−2.53590			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$600$		0			0
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−30.3564	+	17.5263i	−1.23416	+	0.712545i
$606$		0			0
$607$	−20.3923	−	35.3205i	−0.827698	−	1.43362i	−0.899840	−	0.436221i	$-0.856317\pi$
$607$	−20.3923	−	35.3205i	−0.827698	−	1.43362i	0.0721415	−	0.997394i	$-0.477017\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.49038	+	5.70577i	0.222117	+	0.230831i
$612$		0			0
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	0.655187	−	0.755466i	$-0.272590\pi$
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	−0.326659	+	0.945142i	$0.605923\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	−0.250934	−	0.968004i	$-0.580738\pi$
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	0.712849	+	0.701318i	$0.247404\pi$
$618$		0			0
$619$			17.4641i			0.701942i	0.936386	+	0.350971i	$0.114148\pi$
$619$			17.4641i			0.701942i	−0.936386	+	0.350971i	$0.885852\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25.8564			−1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$		0			0
$627$		0			0
$628$		0			0
$629$			20.2679i			0.808136i
$630$		0			0
$631$	−6.67949	+	3.85641i	−0.265906	+	0.153521i	−0.627026	−	0.778998i	$-0.715728\pi$
$631$	−6.67949	+	3.85641i	−0.265906	+	0.153521i	0.361119	+	0.932520i	$0.382395\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.8564	−	18.3923i	−1.26418	−	0.729876i
$636$		0			0
$637$	0.401924	+	1.62436i	0.0159248	+	0.0643593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	0.999885	+	0.0151806i	$0.00483233\pi$
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	−0.486796	+	0.873516i	$0.661834\pi$
$642$		0			0
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	−0.997484	−	0.0708966i	$-0.977414\pi$
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	0.560140	+	0.828398i	$0.310747\pi$
$648$		0			0
$649$	−10.1436			−0.398171
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	−0.984751	−	0.173972i	$-0.944340\pi$
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	0.643039	+	0.765833i	$0.277673\pi$
$654$		0			0
$655$		−	24.3923i		−	0.953086i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	0.948404	−	0.317064i	$-0.102697\pi$
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	−0.748788	+	0.662810i	$0.769364\pi$
$660$		0			0
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	0.679446	−	0.733726i	$-0.262220\pi$
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	−0.295702	+	0.955280i	$0.595554\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−41.7846	−	24.1244i	−1.62034	−	0.935502i
$666$		0			0
$667$	9.36603	+	16.2224i	0.362654	+	0.628135i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			11.6603i			0.450139i
$672$		0			0
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	−0.460720	−	0.887545i	$-0.652409\pi$
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	0.998997	−	0.0447770i	$-0.0142577\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	45.4641			1.74733			0.873664	−	0.486530i	$-0.161738\pi$
$677$	45.4641			1.74733			0.873664	+	0.486530i	$0.161738\pi$
$678$		0			0
$679$	8.19615	−	14.1962i	0.314539	−	0.544798i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.78461	−	5.07180i	0.336134	−	0.194067i	−0.322427	−	0.946594i	$-0.604499\pi$
$683$	8.78461	−	5.07180i	0.336134	−	0.194067i	0.658561	+	0.752527i	$0.271165\pi$
$684$		0			0
$685$	−22.2583	−	38.5526i	−0.850447	−	1.47302i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.7942	+	16.1603i	−0.639809	+	0.615657i
$690$		0			0
$691$	37.8109	+	21.8301i	1.43839	+	0.830457i	0.997738	−	0.0672190i	$-0.0214126\pi$
$691$	37.8109	+	21.8301i	1.43839	+	0.830457i	0.440656	+	0.897676i	$0.354746\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	57.7128	−	33.3205i	2.18917	−	1.26392i
$696$		0			0
$697$		−	53.8372i		−	2.03923i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.32051			−0.125414			−0.0627069	−	0.998032i	$-0.519973\pi$
$701$	−3.32051			−0.125414			−0.0627069	+	0.998032i	$0.519973\pi$
$702$		0			0
$703$	−16.7321			−0.631061
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	5.26795i		−	0.198122i
$708$		0			0
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	−0.698275	−	0.715830i	$-0.746049\pi$
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	0.270789	+	0.962639i	$0.412715\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−5.32051	−	3.07180i	−0.199255	−	0.115040i
$714$		0			0
$715$	4.09808	+	16.5622i	0.153259	+	0.619390i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	−0.998315	−	0.0580299i	$-0.981518\pi$
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	0.448902	−	0.893581i	$-0.351815\pi$
$720$		0			0
$721$	36.1244	−	20.8564i	1.34534	−	0.776733i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	19.9282	−	34.5167i	0.740115	−	1.28192i
$726$		0			0
$727$	−30.9808			−1.14901			−0.574506	−	0.818500i	$-0.694806\pi$
$727$	−30.9808			−1.14901			−0.574506	+	0.818500i	$0.694806\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−27.6865	+	47.9545i	−1.02402	+	1.77366i
$732$		0			0
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.32051	+	14.4115i	0.306490	+	0.530856i
$738$		0			0
$739$	−2.53590	−	1.46410i	−0.0932845	−	0.0538578i	0.452632	−	0.891697i	$-0.350485\pi$
$739$	−2.53590	−	1.46410i	−0.0932845	−	0.0538578i	−0.545917	+	0.837840i	$0.683818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	41.9090	+	24.1962i	1.53749	+	0.887671i	0.998985	+	0.0450491i	$0.0143444\pi$
$743$	41.9090	+	24.1962i	1.53749	+	0.887671i	0.538506	+	0.842622i	$0.318989\pi$
$744$		0			0
$745$	24.6244	+	42.6506i	0.902167	+	1.56260i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	27.8564i		−	1.01785i
$750$		0			0
$751$	24.9545	−	43.2224i	0.910602	−	1.57721i	0.0973862	−	0.995247i	$-0.468952\pi$
$751$	24.9545	−	43.2224i	0.910602	−	1.57721i	0.813216	−	0.581962i	$-0.197715\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.1244			0.914369
$756$		0			0
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	−0.991109	−	0.133056i	$-0.957521\pi$
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	0.610784	+	0.791797i	$0.290854\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	−0.311667	−	0.950191i	$-0.600887\pi$
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	0.667056	+	0.745007i	$0.267554\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$		0			0
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.990879	−	0.134751i	$-0.0430235\pi$
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.378742	+	0.925502i	$0.376357\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.524459	−	0.851436i	$-0.324268\pi$
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.999594	−	0.0284768i	$-0.00906566\pi$
$774$		0			0
$775$			13.0718i			0.469553i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	44.4449			1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	28.3205i		−	1.01080i
$786$		0			0
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	−0.426029	−	0.904710i	$-0.640088\pi$
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	0.570487	+	0.821307i	$0.306754\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.16987	+	1.83013i	0.112708	+	0.0650718i
$792$		0			0
$793$	−31.8564	−	9.19615i	−1.13125	−	0.326565i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	10.9019	−	6.29423i	0.385682	−	0.222674i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.97372	+	6.88269i	−0.140230	+	0.242885i
$804$		0			0
$805$	42.7846			1.50796
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.7942	+	46.4090i	−0.942035	+	1.63165i	−0.180453	+	0.983584i	$0.557756\pi$
$809$	−26.7942	+	46.4090i	−0.942035	+	1.63165i	−0.761582	+	0.648069i	$0.775577\pi$
$810$		0			0
$811$		−	17.1769i		−	0.603163i	−0.953440	−	0.301582i	$-0.902485\pi$
$811$		−	17.1769i		−	0.603163i	0.953440	−	0.301582i	$-0.0975145\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	25.1244	+	43.5167i	0.880068	+	1.52432i
$816$		0			0
$817$	−39.5885	−	22.8564i	−1.38502	−	0.799644i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	0.485907	−	0.874010i	$-0.338489\pi$
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	−0.513962	+	0.857813i	$0.671823\pi$
$822$		0			0
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	−0.959177	−	0.282806i	$-0.908735\pi$
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	0.234671	−	0.972075i	$-0.424599\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	26.5359i		−	0.922744i	−0.887207	−	0.461372i	$-0.847357\pi$
$827$		−	26.5359i		−	0.922744i	0.887207	−	0.461372i	$-0.152643\pi$
$828$		0			0
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	−0.951886	−	0.306452i	$-0.900858\pi$
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	0.741338	+	0.671132i	$0.234192\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.66025			0.0921723
$834$		0			0
$835$	−17.6603	+	30.5885i	−0.611158	+	1.05856i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.971396	−	0.237464i	$-0.923684\pi$
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.280048	+	0.959986i	$0.590350\pi$
$840$		0			0
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−48.4808	−	1.86603i	−1.66779	−	0.0641932i
$846$		0			0
$847$	22.2224	+	12.8301i	0.763572	+	0.440848i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.8494	−	7.41858i	0.440471	−	0.254306i
$852$		0			0
$853$			54.1769i			1.85498i	0.373845	+	0.927491i	$0.378039\pi$
$853$			54.1769i			1.85498i	−0.373845	+	0.927491i	$0.621961\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	39.4449			1.34741			0.673705	−	0.739000i	$-0.264702\pi$
$857$	39.4449			1.34741			0.673705	+	0.739000i	$0.264702\pi$
$858$		0			0
$859$	47.1244			1.60786			0.803931	−	0.594722i	$-0.202738\pi$
$859$	47.1244			1.60786			0.803931	+	0.594722i	$0.202738\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	17.1244i		−	0.582920i	−0.956583	−	0.291460i	$-0.905859\pi$
$863$		−	17.1244i		−	0.582920i	0.956583	−	0.291460i	$-0.0941410\pi$
$864$		0			0
$865$	−14.1962	+	8.19615i	−0.482684	+	0.278678i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.78461	+	1.60770i	0.0944614	+	0.0545373i
$870$		0			0
$871$	−45.9352	+	11.3660i	−1.55646	+	0.385123i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.0263	−	34.6865i	−0.677012	−	1.17262i
$876$		0			0
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	−0.107506	−	0.994204i	$-0.534287\pi$
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	0.807253	+	0.590205i	$0.200953\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	−0.530440	−	0.847722i	$-0.677973\pi$
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	0.999369	+	0.0355135i	$0.0113067\pi$
$882$		0			0
$883$	42.9282			1.44465			0.722325	−	0.691554i	$-0.243074\pi$
$883$	42.9282			1.44465			0.722325	+	0.691554i	$0.243074\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	0.350852	+	0.936431i	$0.385892\pi$
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	−0.986399	+	0.164369i	$0.947441\pi$
$888$		0			0
$889$			26.9282i			0.903143i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.19615	+	9.00000i	0.173883	+	0.301174i
$894$		0			0
$895$	51.8827	+	29.9545i	1.73425	+	1.00127i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.66025	+	3.26795i	0.188780	+	0.108992i
$900$		0			0
$901$	18.5263	+	32.0885i	0.617200	+	1.06902i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			71.6410i			2.38143i
$906$		0			0
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	0.387985	+	0.921666i	$0.373171\pi$
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	−0.992178	+	0.124828i	$0.960162\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$		0			0
$913$	0.124356	−	0.215390i	0.00411557	−	0.00712838i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.4641	+	8.92820i	−0.510670	+	0.294835i
$918$		0			0
$919$	22.9808	+	39.8038i	0.758065	+	1.31301i	0.943836	+	0.330415i	$0.107189\pi$
$919$	22.9808	+	39.8038i	0.758065	+	1.31301i	−0.185770	+	0.982593i	$0.559478\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.73205	+	16.3923i	−0.155757	+	0.539559i
$924$		0			0
$925$	−27.3397	−	15.7846i	−0.898925	−	0.518995i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.175020	−	0.984565i	$-0.444001\pi$
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.940168	+	0.340711i	$0.110668\pi$
$930$		0			0
$931$			2.19615i			0.0719760i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	27.1244			0.887061
$936$		0			0
$937$	−5.24871			−0.171468			−0.0857340	−	0.996318i	$-0.527324\pi$
$937$	−5.24871			−0.171468			−0.0857340	+	0.996318i	$0.527324\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	12.6410i		−	0.412085i	−0.978543	−	0.206043i	$-0.933941\pi$
$941$		−	12.6410i		−	0.412085i	0.978543	−	0.206043i	$-0.0660586\pi$
$942$		0			0
$943$	−34.1314	+	19.7058i	−1.11147	+	0.641708i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.2487	+	10.5359i	0.593003	+	0.342371i	0.766284	−	0.642502i	$-0.222103\pi$
$947$	18.2487	+	10.5359i	0.593003	+	0.342371i	−0.173281	+	0.984872i	$0.555437\pi$
$948$		0			0
$949$	−15.6699	−	16.2846i	−0.508666	−	0.528621i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$		0			0
$955$	22.3923	−	12.9282i	0.724598	−	0.418347i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.2942	+	28.2224i	−0.526168	+	0.911350i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.8923	+	37.9186i	−0.704738	+	1.22064i
$966$		0			0
$967$			43.1244i			1.38679i	0.720560	+	0.693393i	$0.243885\pi$
$967$			43.1244i			1.38679i	−0.720560	+	0.693393i	$0.756115\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	0.514495	−	0.857493i	$-0.327979\pi$
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	−0.999859	+	0.0168189i	$0.994646\pi$
$972$		0			0
$973$	−42.2487	−	24.3923i	−1.35443	−	0.781981i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.975461	−	0.220174i	$-0.0706625\pi$
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.297054	+	0.954861i	$0.403996\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$		0			0
$985$	−33.3205	+	57.7128i	−1.06168	+	1.83888i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	40.5359			1.28897
$990$		0			0
$991$	11.2942	−	19.5622i	0.358773	−	0.621413i	−0.628983	−	0.777419i	$-0.716529\pi$
$991$	11.2942	−	19.5622i	0.358773	−	0.621413i	0.987756	+	0.156006i	$0.0498619\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	45.8827	−	26.4904i	1.45458	−	0.839802i
$996$		0			0
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	0.646123	−	0.763234i	$-0.276389\pi$
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	−0.984041	+	0.177942i	$0.943056\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.by.h.433.1		4
3.2	odd	2		624.2.bv.e.433.2		4
4.3	odd	2		234.2.l.c.199.2		4
12.11	even	2		78.2.i.a.43.1	✓	4
13.10	even	6	inner	1872.2.by.h.1297.2		4
39.20	even	12		8112.2.a.bj.1.1		2
39.23	odd	6		624.2.bv.e.49.1		4
39.32	even	12		8112.2.a.bp.1.2		2
52.7	even	12		3042.2.a.y.1.2		2
52.19	even	12		3042.2.a.p.1.1		2
52.23	odd	6		234.2.l.c.127.2		4
52.35	odd	6		3042.2.b.i.1351.1		4
52.43	odd	6		3042.2.b.i.1351.4		4
60.23	odd	4		1950.2.y.b.199.1		4
60.47	odd	4		1950.2.y.g.199.2		4
60.59	even	2		1950.2.bc.d.901.2		4
156.11	odd	12		1014.2.e.i.991.1		4
156.23	even	6		78.2.i.a.49.1	yes	4
156.35	even	6		1014.2.b.e.337.4		4
156.47	odd	4		1014.2.e.i.529.1		4
156.59	odd	12		1014.2.a.i.1.1		2
156.71	odd	12		1014.2.a.k.1.2		2
156.83	odd	4		1014.2.e.g.529.2		4
156.95	even	6		1014.2.b.e.337.1		4
156.107	even	6		1014.2.i.a.361.2		4
156.119	odd	12		1014.2.e.g.991.2		4
156.155	even	2		1014.2.i.a.823.2		4
780.23	odd	12		1950.2.y.g.49.2		4
780.179	even	6		1950.2.bc.d.751.2		4
780.647	odd	12		1950.2.y.b.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	12.11	even	2
78.2.i.a.49.1	yes	4	156.23	even	6
234.2.l.c.127.2		4	52.23	odd	6
234.2.l.c.199.2		4	4.3	odd	2
624.2.bv.e.49.1		4	39.23	odd	6
624.2.bv.e.433.2		4	3.2	odd	2
1014.2.a.i.1.1		2	156.59	odd	12
1014.2.a.k.1.2		2	156.71	odd	12
1014.2.b.e.337.1		4	156.95	even	6
1014.2.b.e.337.4		4	156.35	even	6
1014.2.e.g.529.2		4	156.83	odd	4
1014.2.e.g.991.2		4	156.119	odd	12
1014.2.e.i.529.1		4	156.47	odd	4
1014.2.e.i.991.1		4	156.11	odd	12
1014.2.i.a.361.2		4	156.107	even	6
1014.2.i.a.823.2		4	156.155	even	2
1872.2.by.h.433.1		4	1.1	even	1	trivial
1872.2.by.h.1297.2		4	13.10	even	6	inner
1950.2.y.b.49.1		4	780.647	odd	12
1950.2.y.b.199.1		4	60.23	odd	4
1950.2.y.g.49.2		4	780.23	odd	12
1950.2.y.g.199.2		4	60.47	odd	4
1950.2.bc.d.751.2		4	780.179	even	6
1950.2.bc.d.901.2		4	60.59	even	2
3042.2.a.p.1.1		2	52.19	even	12
3042.2.a.y.1.2		2	52.7	even	12
3042.2.b.i.1351.1		4	52.35	odd	6
3042.2.b.i.1351.4		4	52.43	odd	6
8112.2.a.bj.1.1		2	39.20	even	12
8112.2.a.bp.1.2		2	39.32	even	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:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(1.09808 + 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +(2.86603 + 4.96410i) q^{17} +(-4.09808 + 2.36603i) q^{19} +(2.09808 - 3.63397i) q^{23} -8.92820 q^{25} +(-2.23205 + 3.86603i) q^{29} -1.46410i q^{31} +(5.09808 + 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +(-8.13397 - 4.69615i) q^{41} +(4.83013 + 8.36603i) q^{43} -2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} +6.46410 q^{53} +(2.36603 - 4.09808i) q^{55} +(-6.92820 + 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(9.33013 + 9.69615i) q^{65} +(11.3660 + 6.56218i) q^{67} +(4.09808 - 2.36603i) q^{71} +6.26795i q^{73} -3.46410 q^{77} +2.53590 q^{79} -0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} +(8.19615 + 4.73205i) q^{89} +(2.73205 - 9.46410i) q^{91} +(8.83013 + 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{7} - 6 q^{11} + 8 q^{17} - 6 q^{19} - 2 q^{23} - 8 q^{25} - 2 q^{29} + 10 q^{35} - 12 q^{37} - 36 q^{41} + 2 q^{43} - 6 q^{49} + 12 q^{53} + 6 q^{55} + 8 q^{61} + 20 q^{65} + 42 q^{67} + 6 q^{71}+ \cdots + 18 q^{95}+O(q^{100}) \) 4 * q - 6 * q^7 - 6 * q^11 + 8 * q^17 - 6 * q^19 - 2 * q^23 - 8 * q^25 - 2 * q^29 + 10 * q^35 - 12 * q^37 - 36 * q^41 + 2 * q^43 - 6 * q^49 + 12 * q^53 + 6 * q^55 + 8 * q^61 + 20 * q^65 + 42 * q^67 + 6 * q^71 + 24 * q^79 + 36 * q^85 + 12 * q^89 + 4 * q^91 + 18 * q^95

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