LMFDB - Embedded newform 980.2.c.e.979.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("980.979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.4
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38298 + 0.295571i) q^{2} +1.66243i q^{3} +(1.82528 - 0.817539i) q^{4} +(2.22517 + 0.220514i) q^{5} +(-0.491366 - 2.29911i) q^{6} +(-2.28268 + 1.67014i) q^{8} +0.236337 q^{9} +O(q^{10})$	\(q+(-1.38298 + 0.295571i) q^{2} +1.66243i q^{3} +(1.82528 - 0.817539i) q^{4} +(2.22517 + 0.220514i) q^{5} +(-0.491366 - 2.29911i) q^{6} +(-2.28268 + 1.67014i) q^{8} +0.236337 q^{9} +(-3.14254 + 0.352730i) q^{10} -4.81346i q^{11} +(1.35910 + 3.03439i) q^{12} -2.14434 q^{13} +(-0.366588 + 3.69918i) q^{15} +(2.66326 - 2.98447i) q^{16} +5.02311 q^{17} +(-0.326849 + 0.0698544i) q^{18} +1.36274 q^{19} +(4.24182 - 1.41666i) q^{20} +(1.42272 + 6.65692i) q^{22} +5.18403 q^{23} +(-2.77649 - 3.79479i) q^{24} +(4.90275 + 0.981360i) q^{25} +(2.96558 - 0.633805i) q^{26} +5.38017i q^{27} -6.43162 q^{29} +(-0.586387 - 5.22425i) q^{30} +4.62144 q^{31} +(-2.80111 + 4.91465i) q^{32} +8.00202 q^{33} +(-6.94687 + 1.48469i) q^{34} +(0.431380 - 0.193215i) q^{36} -9.82080i q^{37} +(-1.88464 + 0.402786i) q^{38} -3.56481i q^{39} +(-5.44764 + 3.21298i) q^{40} -4.71669i q^{41} +0.141753 q^{43} +(-3.93519 - 8.78588i) q^{44} +(0.525889 + 0.0521155i) q^{45} +(-7.16942 + 1.53225i) q^{46} +2.55954i q^{47} +(4.96146 + 4.42747i) q^{48} +(-7.07047 + 0.0919091i) q^{50} +8.35056i q^{51} +(-3.91401 + 1.75308i) q^{52} +4.84781i q^{53} +(-1.59023 - 7.44068i) q^{54} +(1.06143 - 10.7108i) q^{55} +2.26545i q^{57} +(8.89481 - 1.90100i) q^{58} +14.1495 q^{59} +(2.35510 + 7.05172i) q^{60} -10.1807i q^{61} +(-6.39137 + 1.36597i) q^{62} +(2.42126 - 7.62480i) q^{64} +(-4.77152 - 0.472856i) q^{65} +(-11.0666 + 2.36517i) q^{66} -9.64973 q^{67} +(9.16856 - 4.10659i) q^{68} +8.61807i q^{69} +9.58091i q^{71} +(-0.539481 + 0.394716i) q^{72} -1.67523 q^{73} +(2.90275 + 13.5820i) q^{74} +(-1.63144 + 8.15046i) q^{75} +(2.48737 - 1.11409i) q^{76} +(1.05365 + 4.93006i) q^{78} +11.8764i q^{79} +(6.58431 - 6.05366i) q^{80} -8.23513 q^{81} +(1.39412 + 6.52310i) q^{82} +0.811086i q^{83} +(11.1773 + 1.10766i) q^{85} +(-0.196041 + 0.0418981i) q^{86} -10.6921i q^{87} +(8.03915 + 10.9876i) q^{88} +16.0555i q^{89} +(-0.742699 + 0.0833630i) q^{90} +(9.46228 - 4.23815i) q^{92} +7.68281i q^{93} +(-0.756526 - 3.53979i) q^{94} +(3.03232 + 0.300502i) q^{95} +(-8.17024 - 4.65665i) q^{96} +1.76194 q^{97} -1.13760i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) $ 48 * q + 16 * q^4 - 64 * q^9	$ 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) $ 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.38298	+	0.295571i	−0.977916	+	0.209001i
$2$	−1.38298	+	0.295571i	−0.977916	+	0.209001i
$3$			1.66243i			0.959803i	0.877322	+	0.479901i	$0.159328\pi$
$3$			1.66243i			0.959803i	−0.877322	+	0.479901i	$0.840672\pi$
$4$	1.82528	−	0.817539i	0.912638	−	0.408770i
$5$	2.22517	+	0.220514i	0.995125	+	0.0986167i
$5$	2.22517	+	0.220514i	0.995125	+	0.0986167i
$6$	−0.491366	−	2.29911i	−0.200599	−	0.938606i
$7$		0			0
$7$		0			0
$8$	−2.28268	+	1.67014i	−0.807049	+	0.590484i
$9$	0.236337			0.0787789
$10$	−3.14254	+	0.352730i	−0.993760	+	0.111543i
$11$		−	4.81346i		−	1.45131i	−0.688058	−	0.725656i	$-0.741536\pi$
$11$		−	4.81346i		−	1.45131i	0.688058	−	0.725656i	$-0.258464\pi$
$12$	1.35910	+	3.03439i	0.392338	+	0.875952i
$13$	−2.14434			−0.594733			−0.297366	−	0.954763i	$-0.596108\pi$
$13$	−2.14434			−0.594733			−0.297366	+	0.954763i	$0.596108\pi$
$14$		0			0
$15$	−0.366588	+	3.69918i	−0.0946526	+	0.955124i
$16$	2.66326	−	2.98447i	0.665815	−	0.746117i
$17$	5.02311			1.21828			0.609142	−	0.793061i	$-0.291514\pi$
$17$	5.02311			1.21828			0.609142	+	0.793061i	$0.291514\pi$
$18$	−0.326849	+	0.0698544i	−0.0770391	+	0.0164648i
$19$	1.36274			0.312633			0.156317	−	0.987707i	$-0.450038\pi$
$19$	1.36274			0.312633			0.156317	+	0.987707i	$0.450038\pi$
$20$	4.24182	−	1.41666i	0.948500	−	0.316776i
$21$		0			0
$22$	1.42272	+	6.65692i	0.303325	+	1.41926i
$23$	5.18403			1.08094			0.540472	−	0.841362i	$-0.318246\pi$
$23$	5.18403			1.08094			0.540472	+	0.841362i	$0.318246\pi$
$24$	−2.77649	−	3.79479i	−0.566748	−	0.774608i
$25$	4.90275	+	0.981360i	0.980549	+	0.196272i
$26$	2.96558	−	0.633805i	0.581598	−	0.124299i
$27$			5.38017i			1.03541i
$28$		0			0
$29$	−6.43162			−1.19432			−0.597161	−	0.802121i	$-0.703705\pi$
$29$	−6.43162			−1.19432			−0.597161	+	0.802121i	$0.703705\pi$
$30$	−0.586387	−	5.22425i	−0.107059	−	0.953813i
$31$	4.62144			0.830035			0.415018	−	0.909813i	$-0.363775\pi$
$31$	4.62144			0.830035			0.415018	+	0.909813i	$0.363775\pi$
$32$	−2.80111	+	4.91465i	−0.495172	+	0.868795i
$33$	8.00202			1.39297
$34$	−6.94687	+	1.48469i	−1.19138	+	0.254622i
$35$		0			0
$36$	0.431380	−	0.193215i	0.0718966	−	0.0322024i
$37$		−	9.82080i		−	1.61453i	−0.590189	−	0.807265i	$-0.700947\pi$
$37$		−	9.82080i		−	1.61453i	0.590189	−	0.807265i	$-0.299053\pi$
$38$	−1.88464	+	0.402786i	−0.305729	+	0.0653405i
$39$		−	3.56481i		−	0.570826i
$40$	−5.44764	+	3.21298i	−0.861347	+	0.508017i
$41$		−	4.71669i		−	0.736624i	−0.929702	−	0.368312i	$-0.879936\pi$
$41$		−	4.71669i		−	0.736624i	0.929702	−	0.368312i	$-0.120064\pi$
$42$		0			0
$43$	0.141753			0.0216171			0.0108085	−	0.999942i	$-0.496559\pi$
$43$	0.141753			0.0216171			0.0108085	+	0.999942i	$0.496559\pi$
$44$	−3.93519	−	8.78588i	−0.593252	−	1.32452i
$45$	0.525889	+	0.0521155i	0.0783949	+	0.00776892i
$46$	−7.16942	+	1.53225i	−1.05707	+	0.225918i
$47$			2.55954i			0.373347i	0.982422	+	0.186673i	$0.0597706\pi$
$47$			2.55954i			0.373347i	−0.982422	+	0.186673i	$0.940229\pi$
$48$	4.96146	+	4.42747i	0.716125	+	0.639051i
$49$		0			0
$50$	−7.07047	+	0.0919091i	−0.999916	+	0.0129979i
$51$			8.35056i			1.16931i
$52$	−3.91401	+	1.75308i	−0.542775	+	0.243109i
$53$			4.84781i			0.665898i	0.942945	+	0.332949i	$0.108044\pi$
$53$			4.84781i			0.665898i	−0.942945	+	0.332949i	$0.891956\pi$
$54$	−1.59023	−	7.44068i	−0.216402	−	1.01255i
$55$	1.06143	−	10.7108i	0.143124	−	1.44424i
$56$		0			0
$57$			2.26545i			0.300066i
$58$	8.89481	−	1.90100i	1.16795	−	0.249614i
$59$	14.1495			1.84211			0.921054	−	0.389434i	$-0.127329\pi$
$59$	14.1495			1.84211			0.921054	+	0.389434i	$0.127329\pi$
$60$	2.35510	+	7.05172i	0.304042	+	0.910373i
$61$		−	10.1807i		−	1.30351i	−0.758431	−	0.651753i	$-0.774034\pi$
$61$		−	10.1807i		−	1.30351i	0.758431	−	0.651753i	$-0.225966\pi$
$62$	−6.39137	+	1.36597i	−0.811705	+	0.173478i
$63$		0			0
$64$	2.42126	−	7.62480i	0.302657	−	0.953099i
$65$	−4.77152	−	0.472856i	−0.591834	−	0.0586506i
$66$	−11.0666	+	2.36517i	−1.36221	+	0.291132i
$67$	−9.64973			−1.17890			−0.589451	−	0.807804i	$-0.700656\pi$
$67$	−9.64973			−1.17890			−0.589451	+	0.807804i	$0.700656\pi$
$68$	9.16856	−	4.10659i	1.11185	−	0.497997i
$69$			8.61807i			1.03749i
$70$		0			0
$71$			9.58091i			1.13705i	0.822668	+	0.568523i	$0.192485\pi$
$71$			9.58091i			1.13705i	−0.822668	+	0.568523i	$0.807515\pi$
$72$	−0.539481	+	0.394716i	−0.0635785	+	0.0465177i
$73$	−1.67523			−0.196071			−0.0980354	−	0.995183i	$-0.531256\pi$
$73$	−1.67523			−0.196071			−0.0980354	+	0.995183i	$0.531256\pi$
$74$	2.90275	+	13.5820i	0.337438	+	1.57887i
$75$	−1.63144	+	8.15046i	−0.188382	+	0.941134i
$76$	2.48737	−	1.11409i	0.285321	−	0.127795i
$77$		0			0
$78$	1.05365	+	4.93006i	0.119303	+	0.558220i
$79$			11.8764i			1.33620i	0.744074	+	0.668098i	$0.232891\pi$
$79$			11.8764i			1.33620i	−0.744074	+	0.668098i	$0.767109\pi$
$80$	6.58431	−	6.05366i	0.736149	−	0.676820i
$81$	−8.23513			−0.915015
$82$	1.39412	+	6.52310i	0.153955	+	0.720356i
$83$			0.811086i			0.0890282i	0.999009	+	0.0445141i	$0.0141740\pi$
$83$			0.811086i			0.0890282i	−0.999009	+	0.0445141i	$0.985826\pi$
$84$		0			0
$85$	11.1773	+	1.10766i	1.21234	+	0.120143i
$86$	−0.196041	+	0.0418981i	−0.0211397	+	0.00451798i
$87$		−	10.6921i		−	1.14631i
$88$	8.03915	+	10.9876i	0.856976	+	1.17128i
$89$			16.0555i			1.70188i	0.525261	+	0.850941i	$0.323968\pi$
$89$			16.0555i			1.70188i	−0.525261	+	0.850941i	$0.676032\pi$
$90$	−0.742699	+	0.0833630i	−0.0782873	+	0.00878723i
$91$		0			0
$92$	9.46228	−	4.23815i	0.986511	−	0.441857i
$93$			7.68281i			0.796670i
$94$	−0.756526	−	3.53979i	−0.0780297	−	0.365102i
$95$	3.03232	+	0.300502i	0.311109	+	0.0308308i
$96$	−8.17024	−	4.65665i	−0.833872	−	0.475267i
$97$	1.76194			0.178898			0.0894489	−	0.995991i	$-0.471489\pi$
$97$	1.76194			0.178898			0.0894489	+	0.995991i	$0.471489\pi$
$98$		0			0
$99$		−	1.13760i		−	0.114333i
$100$	9.75116	−	2.21694i	0.975116	−	0.221694i
$101$			12.6185i			1.25559i	0.778381	+	0.627793i	$0.216041\pi$
$101$			12.6185i			1.25559i	−0.778381	+	0.627793i	$0.783959\pi$
$102$	−2.46818	−	11.5487i	−0.244387	−	1.14349i
$103$		−	5.73364i		−	0.564952i	−0.959274	−	0.282476i	$-0.908844\pi$
$103$		−	5.73364i		−	0.564952i	0.959274	−	0.282476i	$-0.0911558\pi$
$104$	4.89484	−	3.58135i	0.479979	−	0.351180i
$105$		0			0
$106$	−1.43287	−	6.70443i	−0.139173	−	0.651192i
$107$	−13.2043			−1.27651			−0.638255	−	0.769825i	$-0.720343\pi$
$107$	−13.2043			−1.27651			−0.638255	+	0.769825i	$0.720343\pi$
$108$	4.39850	+	9.82030i	0.423246	+	0.944958i
$109$	−0.461643			−0.0442174			−0.0221087	−	0.999756i	$-0.507038\pi$
$109$	−0.461643			−0.0442174			−0.0221087	+	0.999756i	$0.507038\pi$
$110$	1.69785	+	15.1265i	0.161884	+	1.44226i
$111$	16.3264			1.54963
$112$		0			0
$113$			8.95823i			0.842720i	0.906894	+	0.421360i	$0.138447\pi$
$113$			8.95823i			0.842720i	−0.906894	+	0.421360i	$0.861553\pi$
$114$	−0.669602	−	3.13307i	−0.0627139	−	0.293439i
$115$	11.5353	+	1.14315i	1.07568	+	0.106599i
$116$	−11.7395	+	5.25810i	−1.08998	+	0.488203i
$117$	−0.506786			−0.0468524
$118$	−19.5685	+	4.18219i	−1.80143	+	0.385002i
$119$		0			0
$120$	−5.34135	−	9.05630i	−0.487596	−	0.826723i
$121$	−12.1694			−1.10631
$122$	3.00913	+	14.0797i	0.272434	+	1.27472i
$123$	7.84116			0.707014
$124$	8.43540	−	3.77821i	0.757522	−	0.339293i
$125$	10.6930	+	3.26481i	0.956414	+	0.292014i
$126$		0			0
$127$	−14.5152			−1.28802			−0.644009	−	0.765018i	$-0.722730\pi$
$127$	−14.5152			−1.28802			−0.644009	+	0.765018i	$0.722730\pi$
$128$	−1.09489	+	11.2606i	−0.0967751	+	0.995306i
$129$			0.235654i			0.0207481i
$130$	6.73868	−	0.756372i	0.591021	−	0.0663382i
$131$	16.3717			1.43040			0.715202	−	0.698918i	$-0.246335\pi$
$131$	16.3717			1.43040			0.715202	+	0.698918i	$0.246335\pi$
$132$	14.6059	−	6.54197i	1.27128	−	0.569405i
$133$		0			0
$134$	13.3454	−	2.85218i	1.15287	−	0.246391i
$135$	−1.18640	+	11.9718i	−0.102109	+	1.03037i
$136$	−11.4662	+	8.38930i	−0.983215	+	0.719377i
$137$		−	8.23570i		−	0.703623i	−0.936071	−	0.351812i	$-0.885566\pi$
$137$		−	8.23570i		−	0.703623i	0.936071	−	0.351812i	$-0.114434\pi$
$138$	−2.54725	−	11.9186i	−0.216837	−	1.01458i
$139$	−0.476554			−0.0404207			−0.0202104	−	0.999796i	$-0.506434\pi$
$139$	−0.476554			−0.0404207			−0.0202104	+	0.999796i	$0.506434\pi$
$140$		0			0
$141$	−4.25504			−0.358339
$142$	−2.83184	−	13.2502i	−0.237643	−	1.11193i
$143$			10.3217i			0.863143i
$144$	0.629426	−	0.705340i	0.0524522	−	0.0587783i
$145$	−14.3114	−	1.41826i	−1.18850	−	0.117780i
$146$	2.31681	−	0.495150i	0.191741	−	0.0409789i
$147$		0			0
$148$	−8.02889	−	17.9257i	−0.659971	−	1.47348i
$149$	14.4630			1.18486			0.592430	−	0.805622i	$-0.298169\pi$
$149$	14.4630			1.18486			0.592430	+	0.805622i	$0.298169\pi$
$150$	−0.152792	−	11.7541i	−0.0124754	−	0.959722i
$151$		−	10.9317i		−	0.889605i	−0.895629	−	0.444803i	$-0.853274\pi$
$151$		−	10.9317i		−	0.889605i	0.895629	−	0.444803i	$-0.146726\pi$
$152$	−3.11069	+	2.27596i	−0.252310	+	0.184605i
$153$	1.18715			0.0959750
$154$		0			0
$155$	10.2835	+	1.01909i	0.825989	+	0.0818554i
$156$	−2.91437	−	6.50675i	−0.233336	−	0.520957i
$157$	−13.4455			−1.07307			−0.536533	−	0.843879i	$-0.680266\pi$
$157$	−13.4455			−1.07307			−0.536533	+	0.843879i	$0.680266\pi$
$158$	−3.51031	−	16.4248i	−0.279265	−	1.30669i
$159$	−8.05913			−0.639130
$160$	−7.31670	+	10.3182i	−0.578436	+	0.815728i
$161$		0			0
$162$	11.3890	−	2.43407i	0.894807	−	0.191239i
$163$	16.4270			1.28666			0.643332	−	0.765588i	$-0.277552\pi$
$163$	16.4270			1.28666			0.643332	+	0.765588i	$0.277552\pi$
$164$	−3.85608	−	8.60926i	−0.301110	−	0.672271i
$165$	17.8058	+	1.76455i	1.38618	+	0.137370i
$166$	−0.239734	−	1.12172i	−0.0186069	−	0.0870621i
$167$			14.2832i			1.10527i	0.833424	+	0.552635i	$0.186377\pi$
$167$			14.2832i			1.10527i	−0.833424	+	0.552635i	$0.813623\pi$
$168$		0			0
$169$	−8.40181			−0.646293
$170$	−15.7853	+	1.77180i	−1.21068	+	0.135891i
$171$	0.322065			0.0246289
$172$	0.258738	−	0.115888i	0.0197286	−	0.00883641i
$173$	−17.2249			−1.30959			−0.654793	−	0.755808i	$-0.727244\pi$
$173$	−17.2249			−1.30959			−0.654793	+	0.755808i	$0.727244\pi$
$174$	3.16028	+	14.7870i	0.239580	+	1.12100i
$175$		0			0
$176$	−14.3656	−	12.8195i	−1.08285	−	0.966305i
$177$			23.5225i			1.76806i
$178$	−4.74555	−	22.2045i	−0.355694	−	1.66430i
$179$		−	10.7298i		−	0.801983i	−0.916082	−	0.400991i	$-0.868666\pi$
$179$		−	10.7298i		−	0.801983i	0.916082	−	0.400991i	$-0.131334\pi$
$180$	1.00250	−	0.334810i	0.0747218	−	0.0249553i
$181$		−	4.52237i		−	0.336145i	−0.985775	−	0.168072i	$-0.946246\pi$
$181$		−	4.52237i		−	0.336145i	0.985775	−	0.168072i	$-0.0537542\pi$
$182$		0			0
$183$	16.9247			1.25111
$184$	−11.8335	+	8.65806i	−0.872376	+	0.638280i
$185$	2.16562	−	21.8529i	0.159220	−	1.60666i
$186$	−2.27082	−	10.6252i	−0.166504	−	0.779076i
$187$		−	24.1785i		−	1.76811i
$188$	2.09252	+	4.67186i	0.152613	+	0.340730i
$189$		0			0
$190$	−4.28246	+	0.480677i	−0.310682	+	0.0348720i
$191$		−	11.4909i		−	0.831454i	−0.909490	−	0.415727i	$-0.863527\pi$
$191$		−	11.4909i		−	0.831454i	0.909490	−	0.415727i	$-0.136473\pi$
$192$	12.6757	+	4.02517i	0.914787	+	0.290491i
$193$		−	7.07187i		−	0.509044i	−0.967067	−	0.254522i	$-0.918082\pi$
$193$		−	7.07187i		−	0.509044i	0.967067	−	0.254522i	$-0.0819182\pi$
$194$	−2.43673	+	0.520779i	−0.174947	+	0.0373897i
$195$	0.786089	−	7.93230i	0.0562930	−	0.568044i
$196$		0			0
$197$		−	9.66482i		−	0.688590i	−0.938862	−	0.344295i	$-0.888118\pi$
$197$		−	9.66482i		−	0.688590i	0.938862	−	0.344295i	$-0.111882\pi$
$198$	0.336241	+	1.57328i	0.0238956	+	0.111808i
$199$	−9.41065			−0.667104			−0.333552	−	0.942732i	$-0.608247\pi$
$199$	−9.41065			−0.667104			−0.333552	+	0.942732i	$0.608247\pi$
$200$	−12.8304	+	5.94815i	−0.907247	+	0.420598i
$201$		−	16.0420i		−	1.13151i
$202$	−3.72966	−	17.4511i	−0.262418	−	1.22786i
$203$		0			0
$204$	6.82691	+	15.2421i	0.477979	+	1.06716i
$205$	1.04010	−	10.4954i	0.0726434	−	0.733033i
$206$	1.69470	+	7.92951i	0.118075	+	0.552475i
$207$	1.22518			0.0851556
$208$	−5.71093	+	6.39971i	−0.395982	+	0.443740i
$209$		−	6.55947i		−	0.453728i
$210$		0			0
$211$		−	16.3292i		−	1.12415i	−0.827087	−	0.562075i	$-0.810003\pi$
$211$		−	16.3292i		−	1.12415i	0.827087	−	0.562075i	$-0.189997\pi$
$212$	3.96327	+	8.84858i	0.272199	+	0.607723i
$213$	−15.9276			−1.09134
$214$	18.2613	−	3.90282i	1.24832	−	0.266791i
$215$	0.315424	+	0.0312584i	0.0215117	+	0.00213181i
$216$	−8.98565	−	12.2812i	−0.611396	−	0.835631i
$217$		0			0
$218$	0.638444	−	0.136449i	0.0432409	−	0.00924146i
$219$		−	2.78495i		−	0.188189i
$220$	−6.81905	−	20.4178i	−0.459741	−	1.37657i
$221$	−10.7713			−0.724553
$222$	−22.5791	+	4.82561i	−1.51541	+	0.323873i
$223$			2.93610i			0.196616i	0.995156	+	0.0983079i	$0.0313430\pi$
$223$			2.93610i			0.196616i	−0.995156	+	0.0983079i	$0.968657\pi$
$224$		0			0
$225$	1.15870	+	0.231931i	0.0772466	+	0.0154621i
$226$	−2.64780	−	12.3891i	−0.176129	−	0.824109i
$227$		−	25.1040i		−	1.66621i	−0.553116	−	0.833104i	$-0.686561\pi$
$227$		−	25.1040i		−	1.66621i	0.553116	−	0.833104i	$-0.313439\pi$
$228$	1.85209	+	4.13507i	0.122658	+	0.273852i
$229$			16.7335i			1.10578i	0.833255	+	0.552889i	$0.186475\pi$
$229$			16.7335i			1.10578i	−0.833255	+	0.552889i	$0.813525\pi$
$230$	−16.2910	+	1.82856i	−1.07420	+	0.120572i
$231$		0			0
$232$	14.6813	−	10.7417i	0.963877	−	0.705228i
$233$			8.79554i			0.576215i	0.957598	+	0.288107i	$0.0930260\pi$
$233$			8.79554i			0.576215i	−0.957598	+	0.288107i	$0.906974\pi$
$234$	0.700876	−	0.149791i	0.0458177	−	0.00979217i
$235$	−0.564413	+	5.69540i	−0.0368183	+	0.371527i
$236$	25.8267	−	11.5678i	1.68118	−	0.752998i
$237$	−19.7436			−1.28248
$238$		0			0
$239$			20.9440i			1.35476i	0.735635	+	0.677378i	$0.236884\pi$
$239$			20.9440i			1.35476i	−0.735635	+	0.677378i	$0.763116\pi$
$240$	10.0638	+	10.9459i	0.649613	+	0.706558i
$241$			15.1886i			0.978383i	0.872176	+	0.489191i	$0.162708\pi$
$241$			15.1886i			0.978383i	−0.872176	+	0.489191i	$0.837292\pi$
$242$	16.8300	−	3.59692i	1.08187	−	0.231219i
$243$			2.45021i			0.157181i
$244$	−8.32313	−	18.5826i	−0.532834	−	1.18963i
$245$		0			0
$246$	−10.8442	+	2.31762i	−0.691399	+	0.147766i
$247$	−2.92217			−0.185933
$248$	−10.5493	+	7.71846i	−0.669880	+	0.490123i
$249$	−1.34837			−0.0854495
$250$	−15.7533	−	1.35462i	−0.996323	−	0.0856738i
$251$	−27.8949			−1.76071			−0.880354	−	0.474317i	$-0.842695\pi$
$251$	−27.8949			−1.76071			−0.880354	+	0.474317i	$0.842695\pi$
$252$		0			0
$253$		−	24.9531i		−	1.56879i
$254$	20.0743	−	4.29028i	1.25957	−	0.269196i
$255$	−1.84141	+	18.5814i	−0.115314	+	1.16361i
$256$	−1.81411	−	15.8968i	−0.113382	−	0.993552i
$257$	1.96995			0.122882			0.0614411	−	0.998111i	$-0.480430\pi$
$257$	1.96995			0.122882			0.0614411	+	0.998111i	$0.480430\pi$
$258$	−0.0696525	−	0.325905i	−0.00433637	−	0.0202899i
$259$		0			0
$260$	−9.09591	+	3.03781i	−0.564104	+	0.188397i
$261$	−1.52003			−0.0940874
$262$	−22.6418	+	4.83901i	−1.39881	+	0.298955i
$263$	−2.71666			−0.167517			−0.0837583	−	0.996486i	$-0.526692\pi$
$263$	−2.71666			−0.167517			−0.0837583	+	0.996486i	$0.526692\pi$
$264$	−18.2661	+	13.3645i	−1.12420	+	0.822528i
$265$	−1.06901	+	10.7872i	−0.0656686	+	0.662652i
$266$		0			0
$267$	−26.6911			−1.63347
$268$	−17.6134	+	7.88904i	−1.07591	+	0.481900i
$269$			6.94779i			0.423614i	0.977312	+	0.211807i	$0.0679348\pi$
$269$			6.94779i			0.423614i	−0.977312	+	0.211807i	$0.932065\pi$
$270$	−1.89775	−	16.9074i	−0.115493	−	1.02895i
$271$	−13.0306			−0.791551			−0.395776	−	0.918347i	$-0.629524\pi$
$271$	−13.0306			−0.791551			−0.395776	+	0.918347i	$0.629524\pi$
$272$	13.3778	−	14.9913i	0.811151	−	0.908982i
$273$		0			0
$274$	2.43424	+	11.3898i	0.147058	+	0.688084i
$275$	4.72373	−	23.5992i	0.284852	−	1.42308i
$276$	7.04561	+	15.7303i	0.424096	+	0.946856i
$277$			12.1148i			0.727906i	0.931417	+	0.363953i	$0.118573\pi$
$277$			12.1148i			0.727906i	−0.931417	+	0.363953i	$0.881427\pi$
$278$	0.659065	−	0.140856i	0.0395281	−	0.00844796i
$279$	1.09222			0.0653893
$280$		0			0
$281$	−3.90181			−0.232762			−0.116381	−	0.993205i	$-0.537129\pi$
$281$	−3.90181			−0.232762			−0.116381	+	0.993205i	$0.537129\pi$
$282$	5.88465	−	1.25767i	0.350426	−	0.0748931i
$283$			5.66953i			0.337019i	0.985700	+	0.168509i	$0.0538953\pi$
$283$			5.66953i			0.337019i	−0.985700	+	0.168509i	$0.946105\pi$
$284$	7.83277	+	17.4878i	0.464790	+	1.03771i
$285$	−0.499562	+	5.04100i	−0.0295915	+	0.298603i
$286$	−3.05079	−	14.2747i	−0.180397	−	0.844081i
$287$		0			0
$288$	−0.662006	+	1.16151i	−0.0390091	+	0.0684427i
$289$	8.23165			0.484214
$290$	20.2117	−	2.26862i	1.18687	−	0.133218i
$291$			2.92909i			0.171707i
$292$	−3.05776	+	1.36957i	−0.178942	+	0.0801478i
$293$	−4.21052			−0.245981			−0.122991	−	0.992408i	$-0.539249\pi$
$293$	−4.21052			−0.245981			−0.122991	+	0.992408i	$0.539249\pi$
$294$		0			0
$295$	31.4850	+	3.12016i	1.83313	+	0.181663i
$296$	16.4021	+	22.4177i	0.953354	+	1.30301i
$297$	25.8972			1.50271
$298$	−20.0021	+	4.27486i	−1.15869	+	0.247636i
$299$	−11.1163			−0.642873
$300$	3.68550	+	16.2106i	0.212782	+	0.935919i
$301$		0			0
$302$	3.23108	+	15.1183i	0.185928	+	0.869959i
$303$	−20.9773			−1.20511
$304$	3.62932	−	4.06704i	0.208156	−	0.233261i
$305$	2.24499	−	22.6538i	0.128548	−	1.29715i
$306$	−1.64180	+	0.350886i	−0.0938555	+	0.0200588i
$307$		−	0.464592i		−	0.0265157i	−0.999912	−	0.0132578i	$-0.995780\pi$
$307$		−	0.464592i		−	0.0265157i	0.999912	−	0.0132578i	$-0.00422022\pi$
$308$		0			0
$309$	9.53175			0.542243
$310$	−14.5231	+	1.63012i	−0.824856	+	0.0925846i
$311$	−23.0040			−1.30444			−0.652218	−	0.758032i	$-0.726161\pi$
$311$	−23.0040			−1.30444			−0.652218	+	0.758032i	$0.726161\pi$
$312$	5.95373	+	8.13732i	0.337064	+	0.460685i
$313$	4.64868			0.262759			0.131380	−	0.991332i	$-0.458059\pi$
$313$	4.64868			0.262759			0.131380	+	0.991332i	$0.458059\pi$
$314$	18.5949	−	3.97410i	1.04937	−	0.224271i
$315$		0			0
$316$	9.70939	+	21.6776i	0.546196	+	1.21946i
$317$		−	13.6516i		−	0.766750i	−0.923593	−	0.383375i	$-0.874762\pi$
$317$		−	13.6516i		−	0.766750i	0.923593	−	0.383375i	$-0.125238\pi$
$318$	11.1456	−	2.38205i	0.625015	−	0.133579i
$319$			30.9583i			1.73333i
$320$	7.06908	−	16.4325i	0.395174	−	0.918606i
$321$		−	21.9512i		−	1.22520i
$322$		0			0
$323$	6.84517			0.380876
$324$	−15.0314	+	6.73255i	−0.835077	+	0.374030i
$325$	−10.5132	−	2.10437i	−0.583165	−	0.116729i
$326$	−22.7183	+	4.85535i	−1.25825	+	0.268913i
$327$		−	0.767448i		−	0.0424400i
$328$	7.87754	+	10.7667i	0.434965	+	0.594492i
$329$		0			0
$330$	−25.1467	+	2.82255i	−1.38428	+	0.155376i
$331$		−	0.0738957i		−	0.00406167i	−0.999998	−	0.00203084i	$-0.999354\pi$
$331$		−	0.0738957i		−	0.00406167i	0.999998	−	0.00203084i	$-0.000646436\pi$
$332$	0.663095	+	1.48045i	0.0363920	+	0.0812505i
$333$		−	2.32102i		−	0.127191i
$334$	−4.22171	−	19.7534i	−0.231002	−	1.08086i
$335$	−21.4723	−	2.12790i	−1.17316	−	0.116259i
$336$		0			0
$337$		−	20.7475i		−	1.13019i	−0.825026	−	0.565095i	$-0.808840\pi$
$337$		−	20.7475i		−	1.13019i	0.825026	−	0.565095i	$-0.191160\pi$
$338$	11.6195	−	2.48333i	0.632020	−	0.135076i
$339$	−14.8924			−0.808845
$340$	21.3071	−	7.11606i	1.15554	−	0.385923i
$341$		−	22.2451i		−	1.20464i
$342$	−0.445409	+	0.0951930i	−0.0240850	+	0.00514745i
$343$		0			0
$344$	−0.323576	+	0.236747i	−0.0174461	+	0.0127645i
$345$	−1.90040	+	19.1767i	−0.102314	+	1.03244i
$346$	23.8217	−	5.09119i	1.28067	−	0.273704i
$347$	22.3252			1.19848			0.599241	−	0.800569i	$-0.295469\pi$
$347$	22.3252			1.19848			0.599241	+	0.800569i	$0.295469\pi$
$348$	−8.74121	−	19.5160i	−0.468578	−	1.04617i
$349$		−	0.353911i		−	0.0189444i	−0.999955	−	0.00947221i	$-0.996985\pi$
$349$		−	0.353911i		−	0.0189444i	0.999955	−	0.00947221i	$-0.00301514\pi$
$350$		0			0
$351$		−	11.5369i		−	0.615795i
$352$	23.6564	+	13.4830i	1.26089	+	0.718648i
$353$	34.0609			1.81288			0.906440	−	0.422334i	$-0.138789\pi$
$353$	34.0609			1.81288			0.906440	+	0.422334i	$0.138789\pi$
$354$	−6.95258	−	32.5312i	−0.369526	−	1.72901i
$355$	−2.11272	+	21.3191i	−0.112132	+	1.13150i
$356$	13.1260	+	29.3057i	0.695678	+	1.55320i
$357$		0			0
$358$	3.17142	+	14.8391i	0.167615	+	0.784272i
$359$		−	15.0557i		−	0.794611i	−0.917686	−	0.397305i	$-0.869945\pi$
$359$		−	15.0557i		−	0.794611i	0.917686	−	0.397305i	$-0.130055\pi$
$360$	−1.28748	+	0.759346i	−0.0678560	+	0.0400210i
$361$	−17.1430			−0.902261
$362$	1.33668	+	6.25435i	0.0702544	+	0.328721i
$363$		−	20.2307i		−	1.06184i
$364$		0			0
$365$	−3.72767	−	0.369411i	−0.195115	−	0.0193359i
$366$	−23.4065	+	5.00245i	−1.22348	+	0.261482i
$367$		−	16.4024i		−	0.856201i	−0.903731	−	0.428100i	$-0.859183\pi$
$367$		−	16.4024i		−	0.856201i	0.903731	−	0.428100i	$-0.140817\pi$
$368$	13.8064	−	15.4716i	0.719709	−	0.806511i
$369$		−	1.11473i		−	0.0580304i
$370$	3.46409	+	30.8623i	0.180089	+	1.60445i
$371$		0			0
$372$	6.28100	+	14.0232i	0.325655	+	0.727071i
$373$		−	31.1287i		−	1.61178i	−0.592063	−	0.805892i	$-0.701686\pi$
$373$		−	31.1287i		−	1.61178i	0.592063	−	0.805892i	$-0.298314\pi$
$374$	7.14648	+	33.4385i	0.369536	+	1.72906i
$375$	−5.42751	+	17.7764i	−0.280276	+	0.917969i
$376$	−4.27479	−	5.84261i	−0.220455	−	0.301309i
$377$	13.7916			0.710302
$378$		0			0
$379$		−	30.8008i		−	1.58213i	−0.611731	−	0.791066i	$-0.709526\pi$
$379$		−	30.8008i		−	1.58213i	0.611731	−	0.791066i	$-0.290474\pi$
$380$	5.78048	−	1.93054i	0.296533	−	0.0990346i
$381$		−	24.1305i		−	1.23624i
$382$	3.39639	+	15.8917i	0.173774	+	0.813091i
$383$			21.7981i			1.11383i	0.830570	+	0.556915i	$0.188015\pi$
$383$			21.7981i			1.11383i	−0.830570	+	0.556915i	$0.811985\pi$
$384$	−18.7199	−	1.82017i	−0.955298	−	0.0928850i
$385$		0			0
$386$	2.09024	+	9.78026i	0.106391	+	0.497802i
$387$	0.0335014			0.00170297
$388$	3.21602	−	1.44045i	0.163269	−	0.0731280i
$389$	12.0065			0.608754			0.304377	−	0.952552i	$-0.401552\pi$
$389$	12.0065			0.608754			0.304377	+	0.952552i	$0.401552\pi$
$390$	1.25741	+	11.2026i	0.0636716	+	0.567264i
$391$	26.0400			1.31690
$392$		0			0
$393$			27.2168i			1.37290i
$394$	2.85664	+	13.3663i	0.143916	+	0.673383i
$395$	−2.61890	+	26.4269i	−0.131771	+	1.32968i
$396$	−0.930030	−	2.07643i	−0.0467358	−	0.104344i
$397$	3.78275			0.189851			0.0949253	−	0.995484i	$-0.469739\pi$
$397$	3.78275			0.189851			0.0949253	+	0.995484i	$0.469739\pi$
$398$	13.0148	−	2.78152i	0.652371	−	0.139425i
$399$		0			0
$400$	15.9861	−	12.0185i	0.799306	−	0.600924i
$401$	17.8618			0.891974			0.445987	−	0.895039i	$-0.352853\pi$
$401$	17.8618			0.891974			0.445987	+	0.895039i	$0.352853\pi$
$402$	4.74155	+	22.1858i	0.236487	+	1.10652i
$403$	−9.90994			−0.493649
$404$	10.3161	+	23.0322i	0.513245	+	1.14589i
$405$	−18.3246	−	1.81596i	−0.910555	−	0.0902358i
$406$		0			0
$407$	−47.2720			−2.34319
$408$	−13.9466	−	19.0616i	−0.690460	−	0.943692i
$409$		−	20.2778i		−	1.00267i	−0.865252	−	0.501337i	$-0.832842\pi$
$409$		−	20.2778i		−	1.00267i	0.865252	−	0.501337i	$-0.167158\pi$
$410$	1.66372	+	14.8224i	0.0821652	+	0.732027i
$411$	13.6912			0.675339
$412$	−4.68747	−	10.4655i	−0.230935	−	0.515597i
$413$		0			0
$414$	−1.69440	+	0.362127i	−0.0832750	+	0.0177976i
$415$	−0.178855	+	1.80480i	−0.00877967	+	0.0885943i
$416$	6.00654	−	10.5387i	0.294495	−	0.516701i
$417$		−	0.792235i		−	0.0387959i
$418$	1.93879	+	9.07162i	0.0948294	+	0.443708i
$419$	−5.58588			−0.272888			−0.136444	−	0.990648i	$-0.543567\pi$
$419$	−5.58588			−0.272888			−0.136444	+	0.990648i	$0.543567\pi$
$420$		0			0
$421$	−9.19587			−0.448179			−0.224090	−	0.974569i	$-0.571941\pi$
$421$	−9.19587			−0.448179			−0.224090	+	0.974569i	$0.571941\pi$
$422$	4.82645	+	22.5830i	0.234948	+	1.09932i
$423$			0.604913i			0.0294119i
$424$	−8.09652	−	11.0660i	−0.393202	−	0.537412i
$425$	24.6270	+	4.92948i	1.19459	+	0.239115i
$426$	22.0275	−	4.70773i	1.06724	−	0.228090i
$427$		0			0
$428$	−24.1015	+	10.7951i	−1.16499	+	0.521799i
$429$	−17.1590			−0.828447
$430$	−0.445464	+	0.0500004i	−0.0214822	+	0.00241123i
$431$			2.74398i			0.132173i	0.997814	+	0.0660865i	$0.0210513\pi$
$431$			2.74398i			0.132173i	−0.997814	+	0.0660865i	$0.978949\pi$
$432$	16.0570	+	14.3288i	0.772541	+	0.689394i
$433$	5.66919			0.272444			0.136222	−	0.990678i	$-0.456504\pi$
$433$	5.66919			0.272444			0.136222	+	0.990678i	$0.456504\pi$
$434$		0			0
$435$	2.35775	−	23.7917i	0.113046	−	1.14073i
$436$	−0.842626	+	0.377412i	−0.0403545	+	0.0180747i
$437$	7.06446			0.337939
$438$	0.823151	+	3.85153i	0.0393317	+	0.184033i
$439$	10.9237			0.521360			0.260680	−	0.965425i	$-0.416053\pi$
$439$	10.9237			0.521360			0.260680	+	0.965425i	$0.416053\pi$
$440$	15.4656	+	26.2220i	0.737291	+	1.25008i
$441$		0			0
$442$	14.8964	−	3.18367i	0.708552	−	0.151432i
$443$	−16.6088			−0.789106			−0.394553	−	0.918873i	$-0.629100\pi$
$443$	−16.6088			−0.789106			−0.394553	+	0.918873i	$0.629100\pi$
$444$	29.8001	−	13.3474i	1.41425	−	0.633442i
$445$	−3.54046	+	35.7262i	−0.167834	+	1.69359i
$446$	−0.867827	−	4.06057i	−0.0410928	−	0.192274i
$447$			24.0438i			1.13723i
$448$		0			0
$449$	18.9993			0.896630			0.448315	−	0.893876i	$-0.352024\pi$
$449$	18.9993			0.896630			0.448315	+	0.893876i	$0.352024\pi$
$450$	−1.67101	+	0.0217215i	−0.0787723	+	0.00102396i
$451$	−22.7036			−1.06907
$452$	7.32371	+	16.3512i	0.344478	+	0.769098i
$453$	18.1731			0.853845
$454$	7.42001	+	34.7183i	0.348238	+	1.62941i
$455$		0			0
$456$	−3.78362	−	5.17130i	−0.177184	−	0.242168i
$457$		−	17.5990i		−	0.823248i	−0.911354	−	0.411624i	$-0.864962\pi$
$457$		−	17.5990i		−	0.823248i	0.911354	−	0.411624i	$-0.135038\pi$
$458$	−4.94593	−	23.1421i	−0.231108	−	1.08136i
$459$			27.0252i			1.26143i
$460$	21.9897	−	7.34403i	1.02528	−	0.342417i
$461$			20.9613i			0.976267i	0.872769	+	0.488134i	$0.162322\pi$
$461$			20.9613i			0.976267i	−0.872769	+	0.488134i	$0.837678\pi$
$462$		0			0
$463$	7.63420			0.354791			0.177396	−	0.984140i	$-0.443233\pi$
$463$	7.63420			0.354791			0.177396	+	0.984140i	$0.443233\pi$
$464$	−17.1291	+	19.1950i	−0.795197	+	0.891104i
$465$	−1.69416	+	17.0955i	−0.0785650	+	0.792787i
$466$	−2.59971	−	12.1641i	−0.120429	−	0.563489i
$467$		−	34.9494i		−	1.61726i	−0.588315	−	0.808632i	$-0.700209\pi$
$467$		−	34.9494i		−	1.61726i	0.588315	−	0.808632i	$-0.299791\pi$
$468$	−0.925024	+	0.414318i	−0.0427593	+	0.0191518i
$469$		0			0
$470$	−0.902825	−	8.04346i	−0.0416442	−	0.371017i
$471$		−	22.3521i		−	1.02993i
$472$	−32.2988	+	23.6317i	−1.48667	+	1.08774i
$473$		−	0.682321i		−	0.0313731i
$474$	27.3050	−	5.83564i	1.25416	−	0.268040i
$475$	6.68115	+	1.33733i	0.306552	+	0.0613611i
$476$		0			0
$477$			1.14571i			0.0524587i
$478$	−6.19045	−	28.9652i	−0.283145	−	1.32484i
$479$	−26.6182			−1.21622			−0.608108	−	0.793854i	$-0.708071\pi$
$479$	−26.6182			−1.21622			−0.608108	+	0.793854i	$0.708071\pi$
$480$	−17.1533	−	12.1635i	−0.782938	−	0.555184i
$481$			21.0591i			0.960214i
$482$	−4.48931	−	21.0055i	−0.204482	−	0.956776i
$483$		0			0
$484$	−22.2124	+	9.94894i	−1.00966	+	0.452224i
$485$	3.92061	+	0.388532i	0.178026	+	0.0176423i
$486$	−0.724212	−	3.38860i	−0.0328509	−	0.153710i
$487$	−25.9093			−1.17406			−0.587032	−	0.809564i	$-0.699704\pi$
$487$	−25.9093			−1.17406			−0.587032	+	0.809564i	$0.699704\pi$
$488$	17.0032	+	23.2393i	0.769700	+	1.05199i
$489$			27.3087i			1.23494i
$490$		0			0
$491$			12.9154i			0.582862i	0.956592	+	0.291431i	$0.0941314\pi$
$491$			12.9154i			0.582862i	−0.956592	+	0.291431i	$0.905869\pi$
$492$	14.3123	−	6.41046i	0.645247	−	0.289006i
$493$	−32.3068			−1.45502
$494$	4.04130	−	0.863709i	0.181827	−	0.0388601i
$495$	0.250856	−	2.53134i	0.0112751	−	0.113775i
$496$	12.3081	−	13.7925i	0.552650	−	0.619304i
$497$		0			0
$498$	1.86477	−	0.398540i	0.0835624	−	0.0178590i
$499$		−	18.8481i		−	0.843758i	−0.906652	−	0.421879i	$-0.861371\pi$
$499$		−	18.8481i		−	0.843758i	0.906652	−	0.421879i	$-0.138629\pi$
$500$	22.1868	−	2.78279i	0.992226	−	0.124450i
$501$	−23.7448			−1.06084
$502$	38.5781	−	8.24492i	1.72182	−	0.367989i
$503$		−	27.9050i		−	1.24422i	−0.782930	−	0.622110i	$-0.786276\pi$
$503$		−	27.9050i		−	1.24422i	0.782930	−	0.622110i	$-0.213724\pi$
$504$		0			0
$505$	−2.78255	+	28.0782i	−0.123822	+	1.24946i
$506$	7.37542	+	34.5097i	0.327877	+	1.53414i
$507$		−	13.9674i		−	0.620314i
$508$	−26.4943	+	11.8668i	−1.17549	+	0.526502i
$509$		−	17.1262i		−	0.759103i	−0.925171	−	0.379552i	$-0.876078\pi$
$509$		−	17.1262i		−	0.759103i	0.925171	−	0.379552i	$-0.123922\pi$
$510$	−2.94549	−	26.2420i	−0.130428	−	1.16201i
$511$		0			0
$512$	7.20752	+	21.4488i	0.318530	+	0.947913i
$513$			7.33175i			0.323705i
$514$	−2.72441	+	0.582261i	−0.120168	+	0.0256824i
$515$	1.26435	−	12.7583i	0.0557137	−	0.562198i
$516$	0.192656	+	0.430133i	0.00848121	+	0.0189355i
$517$	12.3202			0.541843
$518$		0			0
$519$		−	28.6352i		−	1.25694i
$520$	11.6816	−	6.88972i	0.512271	−	0.302134i
$521$			10.6559i			0.466844i	0.972376	+	0.233422i	$0.0749923\pi$
$521$			10.6559i			0.466844i	−0.972376	+	0.233422i	$0.925008\pi$
$522$	2.10217	−	0.449277i	0.0920095	−	0.0196643i
$523$			35.5458i			1.55431i	0.629310	+	0.777155i	$0.283338\pi$
$523$			35.5458i			1.55431i	−0.629310	+	0.777155i	$0.716662\pi$
$524$	29.8829	−	13.3845i	1.30544	−	0.584706i
$525$		0			0
$526$	3.75709	−	0.802968i	0.163817	−	0.0350111i
$527$	23.2140			1.01122
$528$	21.3115	−	23.8818i	0.927462	−	1.03932i
$529$	3.87415			0.168441
$530$	−1.70997	−	15.2344i	−0.0742762	−	0.661742i
$531$	3.34405			0.145119
$532$		0			0
$533$			10.1142i			0.438094i
$534$	36.9133	−	7.88914i	1.59740	−	0.341396i
$535$	−29.3818	−	2.91173i	−1.27029	−	0.125885i
$536$	22.0273	−	16.1164i	0.951432	−	0.696123i
$537$	17.8375			0.769745
$538$	−2.05357	−	9.60866i	−0.0885356	−	0.414259i
$539$		0			0
$540$	7.62190	+	22.8217i	0.327994	+	0.982091i
$541$	−13.3429			−0.573658			−0.286829	−	0.957982i	$-0.592601\pi$
$541$	−13.3429			−0.573658			−0.286829	+	0.957982i	$0.592601\pi$
$542$	18.0210	−	3.85147i	0.774070	−	0.165435i
$543$	7.51810			0.322633
$544$	−14.0703	+	24.6868i	−0.603259	+	1.05844i
$545$	−1.02723	−	0.101799i	−0.0440019	−	0.00436057i
$546$		0			0
$547$	−12.8153			−0.547944			−0.273972	−	0.961738i	$-0.588338\pi$
$547$	−12.8153			−0.547944			−0.273972	+	0.961738i	$0.588338\pi$
$548$	−6.73301	−	15.0324i	−0.287620	−	0.642153i
$549$		−	2.40608i		−	0.102689i
$550$	0.442400	+	34.0334i	0.0188640	+	1.45119i
$551$	−8.76460			−0.373385
$552$	−14.3934	−	19.6723i	−0.612623	−	0.837309i
$553$		0			0
$554$	−3.58078	−	16.7545i	−0.152133	−	0.711831i
$555$	36.3289	+	3.60019i	1.54208	+	0.152819i
$556$	−0.869841	+	0.389601i	−0.0368895	+	0.0165228i
$557$			5.48928i			0.232588i	0.993215	+	0.116294i	$0.0371015\pi$
$557$			5.48928i			0.232588i	−0.993215	+	0.116294i	$0.962898\pi$
$558$	−1.51052	+	0.322828i	−0.0639452	+	0.0136664i
$559$	−0.303966			−0.0128564
$560$		0			0
$561$	40.1950			1.69704
$562$	5.39613	−	1.15326i	0.227622	−	0.0486474i
$563$			12.5073i			0.527122i	0.964643	+	0.263561i	$0.0848970\pi$
$563$			12.5073i			0.527122i	−0.964643	+	0.263561i	$0.915103\pi$
$564$	−7.76663	+	3.47867i	−0.327034	+	0.146478i
$565$	−1.97541	+	19.9336i	−0.0831062	+	0.838612i
$566$	−1.67575	−	7.84086i	−0.0704371	−	0.329576i
$567$		0			0
$568$	−16.0015	−	21.8702i	−0.671407	−	0.917652i
$569$	−11.9810			−0.502269			−0.251135	−	0.967952i	$-0.580804\pi$
$569$	−11.9810			−0.502269			−0.251135	+	0.967952i	$0.580804\pi$
$570$	−0.799091	−	7.11927i	−0.0334702	−	0.298193i
$571$			32.3944i			1.35566i	0.735218	+	0.677831i	$0.237080\pi$
$571$			32.3944i			1.35566i	−0.735218	+	0.677831i	$0.762920\pi$
$572$	8.43838	+	18.8399i	0.352827	+	0.787736i
$573$	19.1028			0.798031
$574$		0			0
$575$	25.4160	+	5.08740i	1.05992	+	0.212159i
$576$	0.572233	−	1.80202i	0.0238430	−	0.0750841i
$577$	−1.96815			−0.0819350			−0.0409675	−	0.999160i	$-0.513044\pi$
$577$	−1.96815			−0.0819350			−0.0409675	+	0.999160i	$0.513044\pi$
$578$	−11.3842	+	2.43304i	−0.473521	+	0.101201i
$579$	11.7565			0.488582
$580$	−27.2818	+	9.11145i	−1.13282	+	0.378332i
$581$		0			0
$582$	−0.865756	−	4.05088i	−0.0358868	−	0.167914i
$583$	23.3347			0.966425
$584$	3.82402	−	2.79787i	0.158239	−	0.115777i
$585$	−1.12768	−	0.111753i	−0.0466240	−	0.00462043i
$586$	5.82308	−	1.24451i	0.240549	−	0.0514102i
$587$			42.2233i			1.74274i	0.490626	+	0.871370i	$0.336768\pi$
$587$			42.2233i			1.74274i	−0.490626	+	0.871370i	$0.663232\pi$
$588$		0			0
$589$	6.29780			0.259496
$590$	−44.4654	+	4.99095i	−1.83061	+	0.205474i
$591$	16.0671			0.660910
$592$	−29.3099	−	26.1553i	−1.20463	−	1.07498i
$593$	−23.5752			−0.968119			−0.484060	−	0.875035i	$-0.660838\pi$
$593$	−23.5752			−0.968119			−0.484060	+	0.875035i	$0.660838\pi$
$594$	−35.8154	+	7.65448i	−1.46952	+	0.314067i
$595$		0			0
$596$	26.3990	−	11.8241i	1.08135	−	0.484334i
$597$		−	15.6445i		−	0.640288i
$598$	15.3737	−	3.28566i	0.628676	−	0.134361i
$599$		−	29.4220i		−	1.20215i	−0.799192	−	0.601076i	$-0.794739\pi$
$599$		−	29.4220i		−	1.20215i	0.799192	−	0.601076i	$-0.205261\pi$
$600$	−9.88836	−	21.3296i	−0.403691	−	0.870778i
$601$		−	3.52146i		−	0.143643i	−0.997417	−	0.0718216i	$-0.977119\pi$
$601$		−	3.52146i		−	0.143643i	0.997417	−	0.0718216i	$-0.0228812\pi$
$602$		0			0
$603$	−2.28059			−0.0928726
$604$	−8.93705	−	19.9533i	−0.363644	−	0.811887i
$605$	−27.0789	−	2.68351i	−1.10091	−	0.109100i
$606$	29.0112	−	6.20029i	1.17850	−	0.251869i
$607$		−	11.3158i		−	0.459293i	−0.973274	−	0.229646i	$-0.926243\pi$
$607$		−	11.3158i		−	0.459293i	0.973274	−	0.229646i	$-0.0737570\pi$
$608$	−3.81718	+	6.69737i	−0.154807	+	0.271614i
$609$		0			0
$610$	3.59104	+	31.9933i	0.145397	+	1.29537i
$611$		−	5.48852i		−	0.222042i
$612$	2.16687	−	0.970538i	0.0875904	−	0.0392317i
$613$			34.8323i			1.40686i	0.710764	+	0.703431i	$0.248350\pi$
$613$			34.8323i			1.40686i	−0.710764	+	0.703431i	$0.751650\pi$
$614$	0.137320	+	0.642522i	0.00554179	+	0.0259301i
$615$	17.4479	+	1.72908i	0.703567	+	0.0697233i
$616$		0			0
$617$			41.1278i			1.65574i	0.560918	+	0.827871i	$0.310448\pi$
$617$			41.1278i			1.65574i	−0.560918	+	0.827871i	$0.689552\pi$
$618$	−13.1822	+	2.81731i	−0.530267	+	0.113329i
$619$	21.8585			0.878566			0.439283	−	0.898349i	$-0.355232\pi$
$619$	21.8585			0.878566			0.439283	+	0.898349i	$0.355232\pi$
$620$	19.6033	−	6.54703i	0.787289	−	0.262935i
$621$			27.8910i			1.11923i
$622$	31.8141	−	6.79931i	1.27563	−	0.272628i
$623$		0			0
$624$	−10.6391	−	9.49400i	−0.425903	−	0.380064i
$625$	23.0739	+	9.62272i	0.922955	+	0.384909i
$626$	−6.42904	+	1.37402i	−0.256956	+	0.0549168i
$627$	10.9046			0.435489
$628$	−24.5417	+	10.9922i	−0.979321	+	0.438637i
$629$		−	49.3310i		−	1.96695i
$630$		0			0
$631$		−	9.37906i		−	0.373375i	−0.982419	−	0.186687i	$-0.940225\pi$
$631$		−	9.37906i		−	0.373375i	0.982419	−	0.186687i	$-0.0597751\pi$
$632$	−19.8352	−	27.1099i	−0.789002	−	1.07838i
$633$	27.1461			1.07896
$634$	4.03502	+	18.8799i	0.160251	+	0.749817i
$635$	−32.2988	−	3.20080i	−1.28174	−	0.127020i
$636$	−14.7101	+	6.58865i	−0.583294	+	0.261257i
$637$		0			0
$638$	−9.15040	−	42.8148i	−0.362268	−	1.69505i
$639$			2.26432i			0.0895752i
$640$	−4.91942	+	24.8153i	−0.194457	+	0.980911i
$641$	38.3291			1.51391			0.756954	−	0.653468i	$-0.226686\pi$
$641$	38.3291			1.51391			0.756954	+	0.653468i	$0.226686\pi$
$642$	6.48815	+	30.3581i	0.256067	+	1.19814i
$643$			19.7378i			0.778382i	0.921157	+	0.389191i	$0.127245\pi$
$643$			19.7378i			0.778382i	−0.921157	+	0.389191i	$0.872755\pi$
$644$		0			0
$645$	−0.0519648	+	0.524369i	−0.00204611	+	0.0206470i
$646$	−9.46675	+	2.02324i	−0.372464	+	0.0796032i
$647$			5.26934i			0.207159i	0.994621	+	0.103580i	$0.0330297\pi$
$647$			5.26934i			0.207159i	−0.994621	+	0.103580i	$0.966970\pi$
$648$	18.7982	−	13.7538i	0.738462	−	0.540302i
$649$		−	68.1080i		−	2.67347i
$650$	15.1615	−	0.197084i	0.594682	−	0.00773028i
$651$		0			0
$652$	29.9838	−	13.4297i	1.17426	−	0.525949i
$653$		−	17.6112i		−	0.689181i	−0.938753	−	0.344591i	$-0.888018\pi$
$653$		−	17.6112i		−	0.689181i	0.938753	−	0.344591i	$-0.111982\pi$
$654$	0.226836	+	1.06137i	0.00886998	+	0.0415027i
$655$	36.4298	+	3.61019i	1.42343	+	0.141062i
$656$	−14.0768	−	12.5618i	−0.549608	−	0.490455i
$657$	−0.395918			−0.0154463
$658$		0			0
$659$			37.0188i			1.44205i	0.692910	+	0.721024i	$0.256328\pi$
$659$			37.0188i			1.44205i	−0.692910	+	0.721024i	$0.743672\pi$
$660$	33.9432	−	11.3362i	1.32124	−	0.441260i
$661$			3.40357i			0.132384i	0.997807	+	0.0661918i	$0.0210849\pi$
$661$			3.40357i			0.132384i	−0.997807	+	0.0661918i	$0.978915\pi$
$662$	0.0218415	+	0.102196i	0.000848892	+	0.00397197i
$663$		−	17.9064i		−	0.695428i
$664$	−1.35463	−	1.85145i	−0.0525697	−	0.0718502i
$665$		0			0
$666$	0.686026	+	3.20992i	0.0265830	+	0.124382i
$667$	−33.3417			−1.29100
$668$	11.6771	+	26.0708i	0.451801	+	1.00871i
$669$	−4.88105			−0.188712
$670$	30.3247	−	3.40375i	1.17155	−	0.131498i
$671$	−49.0044			−1.89179
$672$		0			0
$673$			6.69535i			0.258087i	0.991639	+	0.129043i	$0.0411906\pi$
$673$			6.69535i			0.258087i	−0.991639	+	0.129043i	$0.958809\pi$
$674$	6.13238	+	28.6934i	0.236210	+	1.10523i
$675$	−5.27989	+	26.3776i	−0.203223	+	1.01528i
$676$	−15.3356	+	6.86881i	−0.589831	+	0.264185i
$677$	7.74822			0.297788			0.148894	−	0.988853i	$-0.452429\pi$
$677$	7.74822			0.297788			0.148894	+	0.988853i	$0.452429\pi$
$678$	20.5959	−	4.40177i	0.790982	−	0.169049i
$679$		0			0
$680$	−27.3641	+	16.1392i	−1.04936	+	0.618909i
$681$	41.7335			1.59923
$682$	6.57502	+	30.7646i	0.251770	+	1.17804i
$683$	−27.2025			−1.04087			−0.520437	−	0.853900i	$-0.674231\pi$
$683$	−27.2025			−1.04087			−0.520437	+	0.853900i	$0.674231\pi$
$684$	0.587856	−	0.263300i	0.0224772	−	0.0100675i
$685$	1.81608	−	18.3258i	0.0693890	−	0.700193i
$686$		0			0
$687$	−27.8181			−1.06133
$688$	0.377524	−	0.423057i	0.0143930	−	0.0161289i
$689$		−	10.3953i		−	0.396031i
$690$	−3.03985	−	27.0827i	−0.115725	−	1.03102i
$691$	−2.05498			−0.0781750			−0.0390875	−	0.999236i	$-0.512445\pi$
$691$	−2.05498			−0.0781750			−0.0390875	+	0.999236i	$0.512445\pi$
$692$	−31.4402	+	14.0821i	−1.19518	+	0.535319i
$693$		0			0
$694$	−30.8754	+	6.59870i	−1.17201	+	0.250483i
$695$	−1.06041	−	0.105087i	−0.0402237	−	0.00398616i
$696$	17.8573	+	24.4067i	0.676880	+	0.925132i
$697$		−	23.6925i		−	0.897417i
$698$	0.104606	+	0.489452i	0.00395939	+	0.0185260i
$699$	−14.6219			−0.553053
$700$		0			0
$701$	−50.3726			−1.90255			−0.951274	−	0.308348i	$-0.900224\pi$
$701$	−50.3726			−1.90255			−0.951274	+	0.308348i	$0.900224\pi$
$702$	3.40998	+	15.9553i	0.128701	+	0.602196i
$703$		−	13.3832i		−	0.504755i
$704$	−36.7016	−	11.6546i	−1.38324	−	0.439250i
$705$	−9.46819	−	0.938296i	−0.356593	−	0.0353383i
$706$	−47.1056	+	10.0674i	−1.77284	+	0.378893i
$707$		0			0
$708$	19.2306	+	42.9351i	0.722730	+	1.61360i
$709$	−19.9305			−0.748504			−0.374252	−	0.927327i	$-0.622100\pi$
$709$	−19.9305			−0.748504			−0.374252	+	0.927327i	$0.622100\pi$
$710$	−3.37947	−	30.1084i	−0.126829	−	1.12995i
$711$			2.80682i			0.105264i
$712$	−26.8150	−	36.6496i	−1.00493	−	1.37350i
$713$	23.9577			0.897222
$714$		0			0
$715$	−2.27607	+	22.9675i	−0.0851203	+	0.858935i
$716$	−8.77203	−	19.5848i	−0.327826	−	0.731920i
$717$	−34.8179			−1.30030
$718$	4.45004	+	20.8218i	0.166074	+	0.777062i
$719$	−10.3948			−0.387659			−0.193830	−	0.981035i	$-0.562091\pi$
$719$	−10.3948			−0.387659			−0.193830	+	0.981035i	$0.562091\pi$
$720$	1.55612	−	1.43070i	0.0579930	−	0.0533191i
$721$		0			0
$722$	23.7084	−	5.06697i	0.882335	−	0.188573i
$723$	−25.2499			−0.939054
$724$	−3.69721	−	8.25456i	−0.137406	−	0.306778i
$725$	−31.5326	−	6.31174i	−1.17109	−	0.234412i
$726$	5.97961	+	27.9787i	0.221924	+	1.03839i
$727$			3.78185i			0.140261i	0.997538	+	0.0701306i	$0.0223416\pi$
$727$			3.78185i			0.140261i	−0.997538	+	0.0701306i	$0.977658\pi$
$728$		0			0
$729$	−28.7787			−1.06588
$730$	5.26449	−	0.590904i	0.194847	−	0.0218703i
$731$	0.712040			0.0263357
$732$	30.8922	−	13.8366i	1.14181	−	0.511415i
$733$	−21.4770			−0.793272			−0.396636	−	0.917976i	$-0.629823\pi$
$733$	−21.4770			−0.793272			−0.396636	+	0.917976i	$0.629823\pi$
$734$	4.84809	+	22.6843i	0.178946	+	0.837292i
$735$		0			0
$736$	−14.5211	+	25.4777i	−0.535253	+	0.939120i
$737$			46.4486i			1.71096i
$738$	0.329482	+	1.54165i	0.0121284	+	0.0567489i
$739$		−	16.8457i		−	0.619678i	−0.950789	−	0.309839i	$-0.899725\pi$
$739$		−	16.8457i		−	0.619678i	0.950789	−	0.309839i	$-0.100275\pi$
$740$	−13.9128	−	41.6581i	−0.511444	−	1.53138i
$741$		−	4.85789i		−	0.178459i
$742$		0			0
$743$	−13.0015			−0.476979			−0.238490	−	0.971145i	$-0.576652\pi$
$743$	−13.0015			−0.476979			−0.238490	+	0.971145i	$0.576652\pi$
$744$	−12.8314	−	17.5374i	−0.470421	−	0.642952i
$745$	32.1827	+	3.18930i	1.17908	+	0.116847i
$746$	9.20075	+	43.0504i	0.336864	+	1.57619i
$747$			0.191689i			0.00701355i
$748$	−19.7669	−	44.1325i	−0.722749	−	1.61364i
$749$		0			0
$750$	2.25196	−	26.1886i	0.0822300	−	0.956274i
$751$			15.6430i			0.570822i	0.958405	+	0.285411i	$0.0921301\pi$
$751$			15.6430i			0.570822i	−0.958405	+	0.285411i	$0.907870\pi$
$752$	7.63886	+	6.81671i	0.278561	+	0.248580i
$753$		−	46.3732i		−	1.68993i
$754$	−19.0735	+	4.07640i	−0.694616	+	0.148454i
$755$	2.41058	−	24.3248i	0.0877299	−	0.885269i
$756$		0			0
$757$		−	22.2226i		−	0.807695i	−0.914826	−	0.403848i	$-0.867673\pi$
$757$		−	22.2226i		−	0.807695i	0.914826	−	0.403848i	$-0.132327\pi$
$758$	9.10384	+	42.5970i	0.330666	+	1.54719i
$759$	41.4827			1.50573
$760$	−7.42369	+	4.37845i	−0.269286	+	0.158823i
$761$			15.2848i			0.554074i	0.960859	+	0.277037i	$0.0893524\pi$
$761$			15.2848i			0.554074i	−0.960859	+	0.277037i	$0.910648\pi$
$762$	7.13228	+	33.3720i	0.258375	+	1.20894i
$763$		0			0
$764$	−9.39428	−	20.9741i	−0.339873	−	0.758816i
$765$	2.64160	+	0.261782i	0.0955072	+	0.00946474i
$766$	−6.44288	−	30.1463i	−0.232791	−	1.08923i
$767$	−30.3413			−1.09556
$768$	26.4273	−	3.01582i	0.953613	−	0.108824i
$769$			20.4048i			0.735816i	0.929862	+	0.367908i	$0.119926\pi$
$769$			20.4048i			0.735816i	−0.929862	+	0.367908i	$0.880074\pi$
$770$		0			0
$771$			3.27490i			0.117943i
$772$	−5.78153	−	12.9081i	−0.208082	−	0.464573i
$773$	−16.8420			−0.605765			−0.302882	−	0.953028i	$-0.597949\pi$
$773$	−16.8420			−0.605765			−0.302882	+	0.953028i	$0.597949\pi$
$774$	−0.0463318	+	0.00990205i	−0.00166536	+	0.000355922i
$775$	22.6578	+	4.53530i	0.813891	+	0.162913i
$776$	−4.02194	+	2.94269i	−0.144379	+	0.105636i
$777$		0			0
$778$	−16.6048	+	3.54878i	−0.595310	+	0.127230i
$779$		−	6.42761i		−	0.230293i
$780$	−5.05014	−	15.1213i	−0.180824	−

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38298 + 0.295571i) q^{2} +1.66243i q^{3} +(1.82528 - 0.817539i) q^{4} +(2.22517 + 0.220514i) q^{5} +(-0.491366 - 2.29911i) q^{6} +(-2.28268 + 1.67014i) q^{8} +0.236337 q^{9} +O(q^{10})\)	\(q+(-1.38298 + 0.295571i) q^{2} +1.66243i q^{3} +(1.82528 - 0.817539i) q^{4} +(2.22517 + 0.220514i) q^{5} +(-0.491366 - 2.29911i) q^{6} +(-2.28268 + 1.67014i) q^{8} +0.236337 q^{9} +(-3.14254 + 0.352730i) q^{10} -4.81346i q^{11} +(1.35910 + 3.03439i) q^{12} -2.14434 q^{13} +(-0.366588 + 3.69918i) q^{15} +(2.66326 - 2.98447i) q^{16} +5.02311 q^{17} +(-0.326849 + 0.0698544i) q^{18} +1.36274 q^{19} +(4.24182 - 1.41666i) q^{20} +(1.42272 + 6.65692i) q^{22} +5.18403 q^{23} +(-2.77649 - 3.79479i) q^{24} +(4.90275 + 0.981360i) q^{25} +(2.96558 - 0.633805i) q^{26} +5.38017i q^{27} -6.43162 q^{29} +(-0.586387 - 5.22425i) q^{30} +4.62144 q^{31} +(-2.80111 + 4.91465i) q^{32} +8.00202 q^{33} +(-6.94687 + 1.48469i) q^{34} +(0.431380 - 0.193215i) q^{36} -9.82080i q^{37} +(-1.88464 + 0.402786i) q^{38} -3.56481i q^{39} +(-5.44764 + 3.21298i) q^{40} -4.71669i q^{41} +0.141753 q^{43} +(-3.93519 - 8.78588i) q^{44} +(0.525889 + 0.0521155i) q^{45} +(-7.16942 + 1.53225i) q^{46} +2.55954i q^{47} +(4.96146 + 4.42747i) q^{48} +(-7.07047 + 0.0919091i) q^{50} +8.35056i q^{51} +(-3.91401 + 1.75308i) q^{52} +4.84781i q^{53} +(-1.59023 - 7.44068i) q^{54} +(1.06143 - 10.7108i) q^{55} +2.26545i q^{57} +(8.89481 - 1.90100i) q^{58} +14.1495 q^{59} +(2.35510 + 7.05172i) q^{60} -10.1807i q^{61} +(-6.39137 + 1.36597i) q^{62} +(2.42126 - 7.62480i) q^{64} +(-4.77152 - 0.472856i) q^{65} +(-11.0666 + 2.36517i) q^{66} -9.64973 q^{67} +(9.16856 - 4.10659i) q^{68} +8.61807i q^{69} +9.58091i q^{71} +(-0.539481 + 0.394716i) q^{72} -1.67523 q^{73} +(2.90275 + 13.5820i) q^{74} +(-1.63144 + 8.15046i) q^{75} +(2.48737 - 1.11409i) q^{76} +(1.05365 + 4.93006i) q^{78} +11.8764i q^{79} +(6.58431 - 6.05366i) q^{80} -8.23513 q^{81} +(1.39412 + 6.52310i) q^{82} +0.811086i q^{83} +(11.1773 + 1.10766i) q^{85} +(-0.196041 + 0.0418981i) q^{86} -10.6921i q^{87} +(8.03915 + 10.9876i) q^{88} +16.0555i q^{89} +(-0.742699 + 0.0833630i) q^{90} +(9.46228 - 4.23815i) q^{92} +7.68281i q^{93} +(-0.756526 - 3.53979i) q^{94} +(3.03232 + 0.300502i) q^{95} +(-8.17024 - 4.65665i) q^{96} +1.76194 q^{97} -1.13760i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) \) 48 * q + 16 * q^4 - 64 * q^9	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

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