LMFDB - Embedded newform 3721.2.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3721,2,Mod(1,3721)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3721, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3721.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3721 = 61^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3721.a (trivial)

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:	yes
Analytic conductor:	$29.7123345921$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{14} + 111x^{12} - 361x^{10} + 624x^{8} - 558x^{6} + 229x^{4} - 34x^{2} + 1 $ x^16 - 17x^14 + 111x^12 - 361x^10 + 624x^8 - 558x^6 + 229x^4 - 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.776536$ of defining polynomial
Character	$\chi$	$=$	3721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.776536 q^{2} -1.79600 q^{3} -1.39699 q^{4} -0.637773 q^{5} +1.39466 q^{6} -1.38239 q^{7} +2.63789 q^{8} +0.225616 q^{9} +O(q^{10})$	\(q-0.776536 q^{2} -1.79600 q^{3} -1.39699 q^{4} -0.637773 q^{5} +1.39466 q^{6} -1.38239 q^{7} +2.63789 q^{8} +0.225616 q^{9} +0.495253 q^{10} -0.172452 q^{11} +2.50900 q^{12} +2.97038 q^{13} +1.07348 q^{14} +1.14544 q^{15} +0.745570 q^{16} +8.03402 q^{17} -0.175199 q^{18} -1.65785 q^{19} +0.890963 q^{20} +2.48278 q^{21} +0.133915 q^{22} -0.642119 q^{23} -4.73764 q^{24} -4.59325 q^{25} -2.30661 q^{26} +4.98279 q^{27} +1.93119 q^{28} -0.820197 q^{29} -0.889475 q^{30} +4.46583 q^{31} -5.85473 q^{32} +0.309723 q^{33} -6.23871 q^{34} +0.881652 q^{35} -0.315183 q^{36} -10.9347 q^{37} +1.28738 q^{38} -5.33481 q^{39} -1.68237 q^{40} -2.61351 q^{41} -1.92797 q^{42} +9.79585 q^{43} +0.240914 q^{44} -0.143892 q^{45} +0.498628 q^{46} -10.4380 q^{47} -1.33904 q^{48} -5.08899 q^{49} +3.56682 q^{50} -14.4291 q^{51} -4.14960 q^{52} +4.55190 q^{53} -3.86932 q^{54} +0.109985 q^{55} -3.64659 q^{56} +2.97750 q^{57} +0.636913 q^{58} -8.14238 q^{59} -1.60017 q^{60} -3.46788 q^{62} -0.311890 q^{63} +3.05527 q^{64} -1.89443 q^{65} -0.240511 q^{66} +4.62100 q^{67} -11.2235 q^{68} +1.15325 q^{69} -0.684635 q^{70} -6.51473 q^{71} +0.595149 q^{72} +12.4750 q^{73} +8.49119 q^{74} +8.24947 q^{75} +2.31601 q^{76} +0.238396 q^{77} +4.14267 q^{78} +2.25127 q^{79} -0.475504 q^{80} -9.62594 q^{81} +2.02948 q^{82} +4.47196 q^{83} -3.46842 q^{84} -5.12388 q^{85} -7.60683 q^{86} +1.47307 q^{87} -0.454908 q^{88} -10.7042 q^{89} +0.111737 q^{90} -4.10624 q^{91} +0.897035 q^{92} -8.02064 q^{93} +8.10547 q^{94} +1.05733 q^{95} +10.5151 q^{96} -12.2741 q^{97} +3.95178 q^{98} -0.0389079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} + 2 q^{4} + 10 q^{5} + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^3 + 2 * q^4 + 10 * q^5 + 6 * q^9	$ 16 q + 6 q^{3} + 2 q^{4} + 10 q^{5} + 6 q^{9} + 10 q^{12} - 12 q^{13} + 18 q^{14} + 32 q^{15} - 6 q^{16} + 32 q^{19} + 2 q^{20} - 6 q^{22} - 2 q^{25} + 24 q^{27} + 16 q^{34} - 12 q^{36} - 12 q^{39} + 38 q^{41} + 40 q^{42} + 104 q^{45} + 28 q^{46} + 6 q^{47} + 20 q^{48} + 20 q^{49} - 54 q^{52} + 32 q^{56} + 64 q^{57} - 26 q^{58} - 14 q^{60} + 16 q^{62} + 18 q^{64} - 60 q^{65} - 18 q^{66} - 52 q^{70} + 54 q^{73} + 24 q^{74} + 88 q^{75} + 66 q^{76} - 42 q^{77} + 14 q^{80} + 16 q^{81} - 64 q^{83} - 20 q^{86} + 88 q^{88} + 68 q^{95} - 30 q^{97}+O(q^{100}) $ 16 * q + 6 * q^3 + 2 * q^4 + 10 * q^5 + 6 * q^9 + 10 * q^12 - 12 * q^13 + 18 * q^14 + 32 * q^15 - 6 * q^16 + 32 * q^19 + 2 * q^20 - 6 * q^22 - 2 * q^25 + 24 * q^27 + 16 * q^34 - 12 * q^36 - 12 * q^39 + 38 * q^41 + 40 * q^42 + 104 * q^45 + 28 * q^46 + 6 * q^47 + 20 * q^48 + 20 * q^49 - 54 * q^52 + 32 * q^56 + 64 * q^57 - 26 * q^58 - 14 * q^60 + 16 * q^62 + 18 * q^64 - 60 * q^65 - 18 * q^66 - 52 * q^70 + 54 * q^73 + 24 * q^74 + 88 * q^75 + 66 * q^76 - 42 * q^77 + 14 * q^80 + 16 * q^81 - 64 * q^83 - 20 * q^86 + 88 * q^88 + 68 * q^95 - 30 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	−0.776536	−0.549094	−0.274547	−	0.961574i	$-0.588528\pi$
$2$	−0.776536	−0.549094	−0.274547	+	0.961574i	$0.588528\pi$
$3$	−1.79600	−1.03692	−0.518461	−	0.855102i	$-0.673495\pi$
$3$	−1.79600	−1.03692	−0.518461	+	0.855102i	$0.673495\pi$
$4$	−1.39699	−0.698496
$5$	−0.637773	−0.285221	−0.142610	−	0.989779i	$-0.545550\pi$
$5$	−0.637773	−0.285221	−0.142610	+	0.989779i	$0.545550\pi$
$6$	1.39466	0.569367
$7$	−1.38239	−0.522495	−0.261248	−	0.965272i	$-0.584134\pi$
$7$	−1.38239	−0.522495	−0.261248	+	0.965272i	$0.584134\pi$
$8$	2.63789	0.932634
$9$	0.225616	0.0752053
$10$	0.495253	0.156613
$11$	−0.172452	−0.0519962	−0.0259981	−	0.999662i	$-0.508276\pi$
$11$	−0.172452	−0.0519962	−0.0259981	+	0.999662i	$0.508276\pi$
$12$	2.50900	0.724285
$13$	2.97038	0.823836	0.411918	−	0.911221i	$-0.364859\pi$
$13$	2.97038	0.823836	0.411918	+	0.911221i	$0.364859\pi$
$14$	1.07348	0.286899
$15$	1.14544	0.295751
$16$	0.745570	0.186392
$17$	8.03402	1.94854	0.974269	−	0.225390i	$-0.0723658\pi$
$17$	8.03402	1.94854	0.974269	+	0.225390i	$0.0723658\pi$
$18$	−0.175199	−0.0412947
$19$	−1.65785	−0.380337	−0.190169	−	0.981751i	$-0.560903\pi$
$19$	−1.65785	−0.380337	−0.190169	+	0.981751i	$0.560903\pi$
$20$	0.890963	0.199225
$21$	2.48278	0.541786
$22$	0.133915	0.0285508
$23$	−0.642119	−0.133891	−0.0669455	−	0.997757i	$-0.521325\pi$
$23$	−0.642119	−0.133891	−0.0669455	+	0.997757i	$0.521325\pi$
$24$	−4.73764	−0.967068
$25$	−4.59325	−0.918649
$26$	−2.30661	−0.452364
$27$	4.98279	0.958939
$28$	1.93119	0.364961
$29$	−0.820197	−0.152307	−0.0761534	−	0.997096i	$-0.524264\pi$
$29$	−0.820197	−0.152307	−0.0761534	+	0.997096i	$0.524264\pi$
$30$	−0.889475	−0.162395
$31$	4.46583	0.802088	0.401044	−	0.916059i	$-0.368648\pi$
$31$	4.46583	0.802088	0.401044	+	0.916059i	$0.368648\pi$
$32$	−5.85473	−1.03498
$33$	0.309723	0.0539159
$34$	−6.23871	−1.06993
$35$	0.881652	0.149026
$36$	−0.315183	−0.0525306
$37$	−10.9347	−1.79765	−0.898827	−	0.438304i	$-0.855579\pi$
$37$	−10.9347	−1.79765	−0.898827	+	0.438304i	$0.855579\pi$
$38$	1.28738	0.208841
$39$	−5.33481	−0.854253
$40$	−1.68237	−0.266006
$41$	−2.61351	−0.408161	−0.204081	−	0.978954i	$-0.565420\pi$
$41$	−2.61351	−0.408161	−0.204081	+	0.978954i	$0.565420\pi$
$42$	−1.92797	−0.297492
$43$	9.79585	1.49385	0.746927	−	0.664906i	$-0.231529\pi$
$43$	9.79585	1.49385	0.746927	+	0.664906i	$0.231529\pi$
$44$	0.240914	0.0363191
$45$	−0.143892	−0.0214501
$46$	0.498628	0.0735188
$47$	−10.4380	−1.52254	−0.761268	−	0.648438i	$-0.775423\pi$
$47$	−10.4380	−1.52254	−0.761268	+	0.648438i	$0.775423\pi$
$48$	−1.33904	−0.193274
$49$	−5.08899	−0.726999
$50$	3.56682	0.504425
$51$	−14.4291	−2.02048
$52$	−4.14960	−0.575446
$53$	4.55190	0.625251	0.312626	−	0.949876i	$-0.398791\pi$
$53$	4.55190	0.625251	0.312626	+	0.949876i	$0.398791\pi$
$54$	−3.86932	−0.526548
$55$	0.109985	0.0148304
$56$	−3.64659	−0.487297
$57$	2.97750	0.394380
$58$	0.636913	0.0836307
$59$	−8.14238	−1.06005	−0.530024	−	0.847983i	$-0.677817\pi$
$59$	−8.14238	−1.06005	−0.530024	+	0.847983i	$0.677817\pi$
$60$	−1.60017	−0.206581
$61$	0	0
$61$	0	0
$62$	−3.46788	−0.440421
$63$	−0.311890	−0.0392944
$64$	3.05527	0.381909
$65$	−1.89443	−0.234975
$66$	−0.240511	−0.0296049
$67$	4.62100	0.564545	0.282272	−	0.959334i	$-0.408912\pi$
$67$	4.62100	0.564545	0.282272	+	0.959334i	$0.408912\pi$
$68$	−11.2235	−1.36105
$69$	1.15325	0.138834
$70$	−0.684635	−0.0818295
$71$	−6.51473	−0.773157	−0.386578	−	0.922257i	$-0.626343\pi$
$71$	−6.51473	−0.773157	−0.386578	+	0.922257i	$0.626343\pi$
$72$	0.595149	0.0701390
$73$	12.4750	1.46009	0.730044	−	0.683400i	$-0.239500\pi$
$73$	12.4750	1.46009	0.730044	+	0.683400i	$0.239500\pi$
$74$	8.49119	0.987081
$75$	8.24947	0.952567
$76$	2.31601	0.265664
$77$	0.238396	0.0271678
$78$	4.14267	0.469065
$79$	2.25127	0.253288	0.126644	−	0.991948i	$-0.459579\pi$
$79$	2.25127	0.253288	0.126644	+	0.991948i	$0.459579\pi$
$80$	−0.475504	−0.0531630
$81$	−9.62594	−1.06955
$82$	2.02948	0.224119
$83$	4.47196	0.490861	0.245431	−	0.969414i	$-0.421071\pi$
$83$	4.47196	0.490861	0.245431	+	0.969414i	$0.421071\pi$
$84$	−3.46842	−0.378436
$85$	−5.12388	−0.555763
$86$	−7.60683	−0.820266
$87$	1.47307	0.157930
$88$	−0.454908	−0.0484934
$89$	−10.7042	−1.13464	−0.567319	−	0.823498i	$-0.692019\pi$
$89$	−10.7042	−1.13464	−0.567319	+	0.823498i	$0.692019\pi$
$90$	0.111737	0.0117781
$91$	−4.10624	−0.430451
$92$	0.897035	0.0935223
$93$	−8.02064	−0.831701
$94$	8.10547	0.836015
$95$	1.05733	0.108480
$96$	10.5151	1.07319
$97$	−12.2741	−1.24624	−0.623122	−	0.782124i	$-0.714136\pi$
$97$	−12.2741	−1.24624	−0.623122	+	0.782124i	$0.714136\pi$
$98$	3.95178	0.399191
$99$	−0.0389079	−0.00391039
$100$	6.41673	0.641673
$101$	−11.9559	−1.18966	−0.594828	−	0.803853i	$-0.702780\pi$
$101$	−11.9559	−1.18966	−0.594828	+	0.803853i	$0.702780\pi$
$102$	11.2047	1.10943
$103$	10.3990	1.02465	0.512323	−	0.858793i	$-0.328785\pi$
$103$	10.3990	1.02465	0.512323	+	0.858793i	$0.328785\pi$
$104$	7.83554	0.768338
$105$	−1.58345	−0.154529
$106$	−3.53471	−0.343322
$107$	14.0722	1.36041	0.680205	−	0.733022i	$-0.261891\pi$
$107$	14.0722	1.36041	0.680205	+	0.733022i	$0.261891\pi$
$108$	−6.96092	−0.669815
$109$	8.99979	0.862023	0.431012	−	0.902346i	$-0.358157\pi$
$109$	8.99979	0.862023	0.431012	+	0.902346i	$0.358157\pi$
$110$	−0.0854074	−0.00814327
$111$	19.6387	1.86403
$112$	−1.03067	−0.0973891
$113$	−4.92346	−0.463160	−0.231580	−	0.972816i	$-0.574390\pi$
$113$	−4.92346	−0.463160	−0.231580	+	0.972816i	$0.574390\pi$
$114$	−2.31214	−0.216552
$115$	0.409526	0.0381885
$116$	1.14581	0.106386
$117$	0.670165	0.0619568
$118$	6.32285	0.582066
$119$	−11.1062	−1.01810
$120$	3.02154	0.275828
$121$	−10.9703	−0.997296
$122$	0	0
$123$	4.69386	0.423231
$124$	−6.23873	−0.560255
$125$	6.11831	0.547238
$126$	0.242193	0.0215763
$127$	−7.01954	−0.622883	−0.311442	−	0.950265i	$-0.600812\pi$
$127$	−7.01954	−0.622883	−0.311442	+	0.950265i	$0.600812\pi$
$128$	9.33694	0.825277
$129$	−17.5934	−1.54901
$130$	1.47109	0.129023
$131$	0.566735	0.0495159	0.0247580	−	0.999693i	$-0.492118\pi$
$131$	0.566735	0.0495159	0.0247580	+	0.999693i	$0.492118\pi$
$132$	−0.432681	−0.0376601
$133$	2.29180	0.198724
$134$	−3.58837	−0.309988
$135$	−3.17789	−0.273509
$136$	21.1928	1.81727
$137$	12.0744	1.03158	0.515791	−	0.856714i	$-0.327498\pi$
$137$	12.0744	1.03158	0.515791	+	0.856714i	$0.327498\pi$
$138$	−0.895537	−0.0762331
$139$	3.57511	0.303237	0.151619	−	0.988439i	$-0.451551\pi$
$139$	3.57511	0.303237	0.151619	+	0.988439i	$0.451551\pi$
$140$	−1.23166	−0.104094
$141$	18.7466	1.57875
$142$	5.05893	0.424536
$143$	−0.512248	−0.0428363
$144$	0.168212	0.0140177
$145$	0.523099	0.0434410
$146$	−9.68728	−0.801725
$147$	9.13983	0.753840
$148$	15.2757	1.25565
$149$	12.6955	1.04006	0.520029	−	0.854148i	$-0.325921\pi$
$149$	12.6955	1.04006	0.520029	+	0.854148i	$0.325921\pi$
$150$	−6.40601	−0.523049
$151$	18.2540	1.48549	0.742745	−	0.669574i	$-0.233523\pi$
$151$	18.2540	1.48549	0.742745	+	0.669574i	$0.233523\pi$
$152$	−4.37323	−0.354715
$153$	1.81260	0.146540
$154$	−0.185123	−0.0149177
$155$	−2.84819	−0.228772
$156$	7.45269	0.596692
$157$	−16.5294	−1.31919	−0.659596	−	0.751620i	$-0.729273\pi$
$157$	−16.5294	−1.31919	−0.659596	+	0.751620i	$0.729273\pi$
$158$	−1.74819	−0.139079
$159$	−8.17521	−0.648336
$160$	3.73399	0.295198
$161$	0.887660	0.0699574
$162$	7.47489	0.587283
$163$	4.48277	0.351118	0.175559	−	0.984469i	$-0.443827\pi$
$163$	4.48277	0.351118	0.175559	+	0.984469i	$0.443827\pi$
$164$	3.65105	0.285099
$165$	−0.197533	−0.0153779
$166$	−3.47264	−0.269529
$167$	15.0167	1.16203	0.581015	−	0.813893i	$-0.302656\pi$
$167$	15.0167	1.16203	0.581015	+	0.813893i	$0.302656\pi$
$168$	6.54928	0.505288
$169$	−4.17682	−0.321294
$170$	3.97888	0.305166
$171$	−0.374037	−0.0286034
$172$	−13.6847	−1.04345
$173$	−11.7379	−0.892417	−0.446208	−	0.894929i	$-0.647226\pi$
$173$	−11.7379	−0.892417	−0.446208	+	0.894929i	$0.647226\pi$
$174$	−1.14390	−0.0867185
$175$	6.34967	0.479990
$176$	−0.128575	−0.00969169
$177$	14.6237	1.09919
$178$	8.31216	0.623023
$179$	17.2510	1.28940	0.644699	−	0.764437i	$-0.276983\pi$
$179$	17.2510	1.28940	0.644699	+	0.764437i	$0.276983\pi$
$180$	0.201015	0.0149828
$181$	2.07415	0.154171	0.0770853	−	0.997024i	$-0.475439\pi$
$181$	2.07415	0.154171	0.0770853	+	0.997024i	$0.475439\pi$
$182$	3.18864	0.236358
$183$	0	0
$184$	−1.69384	−0.124871
$185$	6.97385	0.512728
$186$	6.22831	0.456682
$187$	−1.38548	−0.101316
$188$	14.5818	1.06348
$189$	−6.88818	−0.501041
$190$	−0.821057	−0.0595657
$191$	−21.3914	−1.54782	−0.773912	−	0.633293i	$-0.781703\pi$
$191$	−21.3914	−1.54782	−0.773912	+	0.633293i	$0.781703\pi$
$192$	−5.48727	−0.396010
$193$	−14.0056	−1.00815	−0.504074	−	0.863661i	$-0.668166\pi$
$193$	−14.0056	−1.00815	−0.504074	+	0.863661i	$0.668166\pi$
$194$	9.53127	0.684305
$195$	3.40240	0.243651
$196$	7.10928	0.507806
$197$	−10.7214	−0.763867	−0.381933	−	0.924190i	$-0.624742\pi$
$197$	−10.7214	−0.763867	−0.381933	+	0.924190i	$0.624742\pi$
$198$	0.0302133	0.00214717
$199$	19.8466	1.40688	0.703442	−	0.710752i	$-0.251645\pi$
$199$	19.8466	1.40688	0.703442	+	0.710752i	$0.251645\pi$
$200$	−12.1165	−0.856763
$201$	−8.29931	−0.585388
$202$	9.28418	0.653233
$203$	1.13383	0.0795796
$204$	20.1573	1.41130
$205$	1.66682	0.116416
$206$	−8.07522	−0.562627
$207$	−0.144872	−0.0100693
$208$	2.21463	0.153557
$209$	0.285900	0.0197761
$210$	1.22960	0.0848507
$211$	−14.7446	−1.01506	−0.507530	−	0.861634i	$-0.669441\pi$
$211$	−14.7446	−1.01506	−0.507530	+	0.861634i	$0.669441\pi$
$212$	−6.35896	−0.436735
$213$	11.7005	0.801702
$214$	−10.9276	−0.746993
$215$	−6.24753	−0.426078
$216$	13.1440	0.894339
$217$	−6.17354	−0.419087
$218$	−6.98866	−0.473332
$219$	−22.4051	−1.51400
$220$	−0.153648	−0.0103590
$221$	23.8641	1.60528
$222$	−15.2502	−1.02352
$223$	17.4934	1.17145	0.585723	−	0.810511i	$-0.300811\pi$
$223$	17.4934	1.17145	0.585723	+	0.810511i	$0.300811\pi$
$224$	8.09354	0.540772
$225$	−1.03631	−0.0690872
$226$	3.82325	0.254319
$227$	−28.0375	−1.86091	−0.930457	−	0.366401i	$-0.880590\pi$
$227$	−28.0375	−1.86091	−0.930457	+	0.366401i	$0.880590\pi$
$228$	−4.15955	−0.275473
$229$	1.03613	0.0684694	0.0342347	−	0.999414i	$-0.489101\pi$
$229$	1.03613	0.0684694	0.0342347	+	0.999414i	$0.489101\pi$
$230$	−0.318012	−0.0209691
$231$	−0.428159	−0.0281708
$232$	−2.16359	−0.142046
$233$	7.36539	0.482523	0.241261	−	0.970460i	$-0.422439\pi$
$233$	7.36539	0.482523	0.241261	+	0.970460i	$0.422439\pi$
$234$	−0.520408	−0.0340201
$235$	6.65706	0.434259
$236$	11.3748	0.740439
$237$	−4.04328	−0.262639
$238$	8.62434	0.559033
$239$	17.4949	1.13165	0.565827	−	0.824524i	$-0.308557\pi$
$239$	17.4949	1.13165	0.565827	+	0.824524i	$0.308557\pi$
$240$	0.854005	0.0551258
$241$	−6.64363	−0.427954	−0.213977	−	0.976839i	$-0.568642\pi$
$241$	−6.64363	−0.427954	−0.213977	+	0.976839i	$0.568642\pi$
$242$	8.51880	0.547609
$243$	2.33981	0.150099
$244$	0	0
$245$	3.24562	0.207355
$246$	−3.64495	−0.232394
$247$	−4.92446	−0.313336
$248$	11.7804	0.748054
$249$	−8.03163	−0.508984
$250$	−4.75109	−0.300485
$251$	13.5362	0.854400	0.427200	−	0.904157i	$-0.359500\pi$
$251$	13.5362	0.854400	0.427200	+	0.904157i	$0.359500\pi$
$252$	0.435707	0.0274470
$253$	0.110735	0.00696182
$254$	5.45093	0.342021
$255$	9.20249	0.576282
$256$	−13.3610	−0.835064
$257$	21.2807	1.32745	0.663726	−	0.747976i	$-0.268974\pi$
$257$	21.2807	1.32745	0.663726	+	0.747976i	$0.268974\pi$
$258$	13.6619	0.850551
$259$	15.1161	0.939266
$260$	2.64650	0.164129
$261$	−0.185049	−0.0114543
$262$	−0.440091	−0.0271889
$263$	13.1380	0.810121	0.405061	−	0.914290i	$-0.367250\pi$
$263$	13.1380	0.810121	0.405061	+	0.914290i	$0.367250\pi$
$264$	0.817015	0.0502838
$265$	−2.90308	−0.178335
$266$	−1.77967	−0.109118
$267$	19.2247	1.17653
$268$	−6.45550	−0.394332
$269$	13.5534	0.826364	0.413182	−	0.910649i	$-0.364417\pi$
$269$	13.5534	0.826364	0.413182	+	0.910649i	$0.364417\pi$
$270$	2.46775	0.150182
$271$	−17.0427	−1.03527	−0.517634	−	0.855602i	$-0.673187\pi$
$271$	−17.0427	−1.03527	−0.517634	+	0.855602i	$0.673187\pi$
$272$	5.98992	0.363192
$273$	7.37480	0.446343
$274$	−9.37618	−0.566436
$275$	0.792114	0.0477663
$276$	−1.61107	−0.0969753
$277$	7.85844	0.472168	0.236084	−	0.971733i	$-0.424136\pi$
$277$	7.85844	0.472168	0.236084	+	0.971733i	$0.424136\pi$
$278$	−2.77620	−0.166506
$279$	1.00756	0.0603212
$280$	2.32570	0.138987
$281$	14.6879	0.876206	0.438103	−	0.898925i	$-0.355651\pi$
$281$	14.6879	0.876206	0.438103	+	0.898925i	$0.355651\pi$
$282$	−14.5574	−0.866882
$283$	−15.6790	−0.932017	−0.466008	−	0.884780i	$-0.654308\pi$
$283$	−15.6790	−0.932017	−0.466008	+	0.884780i	$0.654308\pi$
$284$	9.10103	0.540047
$285$	−1.89897	−0.112485
$286$	0.397779	0.0235212
$287$	3.61289	0.213262
$288$	−1.32092	−0.0778360
$289$	47.5455	2.79680
$290$	−0.406205	−0.0238532
$291$	22.0443	1.29226
$292$	−17.4275	−1.01987
$293$	0.475754	0.0277938	0.0138969	−	0.999903i	$-0.495576\pi$
$293$	0.475754	0.0277938	0.0138969	+	0.999903i	$0.495576\pi$
$294$	−7.09741	−0.413929
$295$	5.19299	0.302348
$296$	−28.8445	−1.67655
$297$	−0.859292	−0.0498612
$298$	−9.85854	−0.571090
$299$	−1.90734	−0.110304
$300$	−11.5244	−0.665364
$301$	−13.5417	−0.780531
$302$	−14.1749	−0.815674
$303$	21.4728	1.23358
$304$	−1.23604	−0.0708920
$305$	0	0
$306$	−1.40755	−0.0804643
$307$	7.72802	0.441061	0.220531	−	0.975380i	$-0.429221\pi$
$307$	7.72802	0.441061	0.220531	+	0.975380i	$0.429221\pi$
$308$	−0.333037	−0.0189766
$309$	−18.6766	−1.06248
$310$	2.21172	0.125617
$311$	−3.31042	−0.187716	−0.0938582	−	0.995586i	$-0.529920\pi$
$311$	−3.31042	−0.187716	−0.0938582	+	0.995586i	$0.529920\pi$
$312$	−14.0726	−0.796705
$313$	3.79061	0.214258	0.107129	−	0.994245i	$-0.465834\pi$
$313$	3.79061	0.214258	0.107129	+	0.994245i	$0.465834\pi$
$314$	12.8357	0.724360
$315$	0.198915	0.0112076
$316$	−3.14501	−0.176921
$317$	−2.04795	−0.115025	−0.0575123	−	0.998345i	$-0.518317\pi$
$317$	−2.04795	−0.115025	−0.0575123	+	0.998345i	$0.518317\pi$
$318$	6.34834	0.355997
$319$	0.141444	0.00791937
$320$	−1.94857	−0.108928
$321$	−25.2737	−1.41064
$322$	−0.689300	−0.0384132
$323$	−13.3192	−0.741101
$324$	13.4474	0.747076
$325$	−13.6437	−0.756817
$326$	−3.48103	−0.192796
$327$	−16.1636	−0.893850
$328$	−6.89413	−0.380665
$329$	14.4294	0.795518
$330$	0.153392	0.00844393
$331$	21.0430	1.15663	0.578315	−	0.815813i	$-0.303710\pi$
$331$	21.0430	1.15663	0.578315	+	0.815813i	$0.303710\pi$
$332$	−6.24729	−0.342864
$333$	−2.46704	−0.135193
$334$	−11.6610	−0.638064
$335$	−2.94715	−0.161020
$336$	1.85108	0.100985
$337$	−4.44526	−0.242149	−0.121074	−	0.992643i	$-0.538634\pi$
$337$	−4.44526	−0.242149	−0.121074	+	0.992643i	$0.538634\pi$
$338$	3.24345	0.176420
$339$	8.84254	0.480261
$340$	7.15802	0.388198
$341$	−0.770141	−0.0417055
$342$	0.290454	0.0157059
$343$	16.7117	0.902349
$344$	25.8404	1.39322
$345$	−0.735508	−0.0395984
$346$	9.11491	0.490021
$347$	19.4255	1.04281	0.521407	−	0.853308i	$-0.325407\pi$
$347$	19.4255	1.04281	0.521407	+	0.853308i	$0.325407\pi$
$348$	−2.05787	−0.110314
$349$	13.7706	0.737124	0.368562	−	0.929603i	$-0.379850\pi$
$349$	13.7706	0.737124	0.368562	+	0.929603i	$0.379850\pi$
$350$	−4.93075	−0.263560
$351$	14.8008	0.790009
$352$	1.00966	0.0538150
$353$	11.1114	0.591400	0.295700	−	0.955281i	$-0.404447\pi$
$353$	11.1114	0.591400	0.295700	+	0.955281i	$0.404447\pi$
$354$	−11.3558	−0.603556
$355$	4.15492	0.220520
$356$	14.9536	0.792540
$357$	19.9467	1.05569
$358$	−13.3960	−0.708000
$359$	13.4983	0.712413	0.356207	−	0.934407i	$-0.384070\pi$
$359$	13.4983	0.712413	0.356207	+	0.934407i	$0.384070\pi$
$360$	−0.379570	−0.0200051
$361$	−16.2515	−0.855344
$362$	−1.61066	−0.0846542
$363$	19.7026	1.03412
$364$	5.73638	0.300668
$365$	−7.95621	−0.416447
$366$	0	0
$367$	28.8255	1.50468	0.752340	−	0.658775i	$-0.228925\pi$
$367$	28.8255	1.50468	0.752340	+	0.658775i	$0.228925\pi$
$368$	−0.478744	−0.0249563
$369$	−0.589648	−0.0306959
$370$	−5.41545	−0.281536
$371$	−6.29251	−0.326691
$372$	11.2048	0.580940
$373$	32.1882	1.66664	0.833320	−	0.552791i	$-0.186437\pi$
$373$	32.1882	1.66664	0.833320	+	0.552791i	$0.186437\pi$
$374$	1.07588	0.0556323
$375$	−10.9885	−0.567443
$376$	−27.5342	−1.41997
$377$	−2.43630	−0.125476
$378$	5.34892	0.275119
$379$	−12.1417	−0.623677	−0.311838	−	0.950135i	$-0.600945\pi$
$379$	−12.1417	−0.623677	−0.311838	+	0.950135i	$0.600945\pi$
$380$	−1.47708	−0.0757729
$381$	12.6071	0.645881
$382$	16.6112	0.849901
$383$	14.9388	0.763338	0.381669	−	0.924299i	$-0.375349\pi$
$383$	14.9388	0.763338	0.381669	+	0.924299i	$0.375349\pi$
$384$	−16.7691	−0.855747
$385$	−0.152043	−0.00774880
$386$	10.8759	0.553568
$387$	2.21010	0.112346
$388$	17.1468	0.870497
$389$	14.3927	0.729741	0.364870	−	0.931058i	$-0.381113\pi$
$389$	14.3927	0.729741	0.364870	+	0.931058i	$0.381113\pi$
$390$	−2.64208	−0.133787
$391$	−5.15880	−0.260892
$392$	−13.4242	−0.678024
$393$	−1.01786	−0.0513441
$394$	8.32554	0.419434
$395$	−1.43580	−0.0722429
$396$	0.0543539	0.00273139
$397$	−7.94937	−0.398968	−0.199484	−	0.979901i	$-0.563927\pi$
$397$	−7.94937	−0.398968	−0.199484	+	0.979901i	$0.563927\pi$
$398$	−15.4116	−0.772512
$399$	−4.11608	−0.206062
$400$	−3.42458	−0.171229
$401$	−2.56339	−0.128010	−0.0640049	−	0.997950i	$-0.520387\pi$
$401$	−2.56339	−0.128010	−0.0640049	+	0.997950i	$0.520387\pi$
$402$	6.44472	0.321433
$403$	13.2652	0.660789
$404$	16.7023	0.830970
$405$	6.13916	0.305058
$406$	−0.880463	−0.0436967
$407$	1.88571	0.0934712
$408$	−38.0623	−1.88437
$409$	−7.82985	−0.387161	−0.193581	−	0.981084i	$-0.562010\pi$
$409$	−7.82985	−0.387161	−0.193581	+	0.981084i	$0.562010\pi$
$410$	−1.29435	−0.0639233
$411$	−21.6856	−1.06967
$412$	−14.5274	−0.715711
$413$	11.2560	0.553870
$414$	0.112498	0.00552900
$415$	−2.85209	−0.140004
$416$	−17.3908	−0.852655
$417$	−6.42090	−0.314433
$418$	−0.222011	−0.0108589
$419$	20.8508	1.01863	0.509313	−	0.860581i	$-0.329899\pi$
$419$	20.8508	1.01863	0.509313	+	0.860581i	$0.329899\pi$
$420$	2.21206	0.107938
$421$	−15.8643	−0.773179	−0.386589	−	0.922252i	$-0.626347\pi$
$421$	−15.8643	−0.773179	−0.386589	+	0.922252i	$0.626347\pi$
$422$	11.4497	0.557364
$423$	−2.35497	−0.114503
$424$	12.0074	0.583130
$425$	−36.9022	−1.79002
$426$	−9.08583	−0.440210
$427$	0	0
$428$	−19.6587	−0.950241
$429$	0.919998	0.0444179
$430$	4.85143	0.233957
$431$	29.6706	1.42918	0.714591	−	0.699543i	$-0.246613\pi$
$431$	29.6706	1.42918	0.714591	+	0.699543i	$0.246613\pi$
$432$	3.71502	0.178739
$433$	9.22627	0.443386	0.221693	−	0.975117i	$-0.428842\pi$
$433$	9.22627	0.443386	0.221693	+	0.975117i	$0.428842\pi$
$434$	4.79397	0.230118
$435$	−0.939486	−0.0450449
$436$	−12.5726	−0.602120
$437$	1.06454	0.0509238
$438$	17.3984	0.831326
$439$	−13.2532	−0.632542	−0.316271	−	0.948669i	$-0.602431\pi$
$439$	−13.2532	−0.632542	−0.316271	+	0.948669i	$0.602431\pi$
$440$	0.290128	0.0138313
$441$	−1.14816	−0.0546741
$442$	−18.5314	−0.881447
$443$	−36.9043	−1.75338	−0.876688	−	0.481060i	$-0.840252\pi$
$443$	−36.9043	−1.75338	−0.876688	+	0.481060i	$0.840252\pi$
$444$	−27.4351	−1.30201
$445$	6.82682	0.323622
$446$	−13.5843	−0.643234
$447$	−22.8012	−1.07846
$448$	−4.22359	−0.199546
$449$	−13.2432	−0.624987	−0.312493	−	0.949920i	$-0.601164\pi$
$449$	−13.2432	−0.624987	−0.312493	+	0.949920i	$0.601164\pi$
$450$	0.804731	0.0379354
$451$	0.450704	0.0212228
$452$	6.87804	0.323516
$453$	−32.7842	−1.54034
$454$	21.7721	1.02182
$455$	2.61885	0.122773
$456$	7.85431	0.367812
$457$	−3.96420	−0.185437	−0.0927187	−	0.995692i	$-0.529556\pi$
$457$	−3.96420	−0.185437	−0.0927187	+	0.995692i	$0.529556\pi$
$458$	−0.804593	−0.0375962
$459$	40.0319	1.86853
$460$	−0.572104	−0.0266745
$461$	−22.5096	−1.04838	−0.524189	−	0.851602i	$-0.675631\pi$
$461$	−22.5096	−1.04838	−0.524189	+	0.851602i	$0.675631\pi$
$462$	0.332481	0.0154684
$463$	29.8890	1.38906	0.694529	−	0.719464i	$-0.255613\pi$
$463$	29.8890	1.38906	0.694529	+	0.719464i	$0.255613\pi$
$464$	−0.611514	−0.0283888
$465$	5.11534	0.237218
$466$	−5.71949	−0.264950
$467$	−20.5522	−0.951044	−0.475522	−	0.879704i	$-0.657741\pi$
$467$	−20.5522	−0.951044	−0.475522	+	0.879704i	$0.657741\pi$
$468$	−0.936216	−0.0432766
$469$	−6.38803	−0.294972
$470$	−5.16944	−0.238449
$471$	29.6868	1.36790
$472$	−21.4787	−0.988637
$473$	−1.68931	−0.0776747
$474$	3.13976	0.144214
$475$	7.61492	0.349397
$476$	15.5152	0.711140
$477$	1.02698	0.0470222
$478$	−13.5854	−0.621384
$479$	18.4124	0.841283	0.420642	−	0.907227i	$-0.361805\pi$
$479$	18.4124	0.841283	0.420642	+	0.907227i	$0.361805\pi$
$480$	−6.70625	−0.306097
$481$	−32.4803	−1.48097
$482$	5.15902	0.234987
$483$	−1.59424	−0.0725403
$484$	15.3254	0.696607
$485$	7.82808	0.355455
$486$	−1.81695	−0.0824185
$487$	22.6094	1.02453	0.512264	−	0.858828i	$-0.328807\pi$
$487$	22.6094	1.02453	0.512264	+	0.858828i	$0.328807\pi$
$488$	0	0
$489$	−8.05105	−0.364081
$490$	−2.52034	−0.113857
$491$	8.63809	0.389832	0.194916	−	0.980820i	$-0.437557\pi$
$491$	8.63809	0.389832	0.194916	+	0.980820i	$0.437557\pi$
$492$	−6.55728	−0.295625
$493$	−6.58948	−0.296775
$494$	3.82402	0.172051
$495$	0.0248144	0.00111532
$496$	3.32959	0.149503
$497$	9.00592	0.403971
$498$	6.23685	0.279480
$499$	−33.7367	−1.51026	−0.755132	−	0.655573i	$-0.772427\pi$
$499$	−33.7367	−1.51026	−0.755132	+	0.655573i	$0.772427\pi$
$500$	−8.54723	−0.382244
$501$	−26.9701	−1.20493
$502$	−10.5114	−0.469146
$503$	−24.0744	−1.07343	−0.536713	−	0.843765i	$-0.680334\pi$
$503$	−24.0744	−1.07343	−0.536713	+	0.843765i	$0.680334\pi$
$504$	−0.822729	−0.0366473
$505$	7.62514	0.339314
$506$	−0.0859894	−0.00382269
$507$	7.50156	0.333156
$508$	9.80624	0.435082
$509$	−3.20965	−0.142265	−0.0711326	−	0.997467i	$-0.522661\pi$
$509$	−3.20965	−0.142265	−0.0711326	+	0.997467i	$0.522661\pi$
$510$	−7.14606	−0.316433
$511$	−17.2453	−0.762889
$512$	−8.29857	−0.366748
$513$	−8.26073	−0.364720
$514$	−16.5252	−0.728896
$515$	−6.63221	−0.292250
$516$	24.5778	1.08198
$517$	1.80005	0.0791660
$518$	−11.7382	−0.515745
$519$	21.0813	0.925366
$520$	−4.99729	−0.219146
$521$	−10.2837	−0.450539	−0.225269	−	0.974297i	$-0.572326\pi$
$521$	−10.2837	−0.450539	−0.225269	+	0.974297i	$0.572326\pi$
$522$	0.143698	0.00628947
$523$	−9.39173	−0.410672	−0.205336	−	0.978692i	$-0.565829\pi$
$523$	−9.39173	−0.410672	−0.205336	+	0.978692i	$0.565829\pi$
$524$	−0.791725	−0.0345867
$525$	−11.4040	−0.497712
$526$	−10.2021	−0.444833
$527$	35.8786	1.56290
$528$	0.230920	0.0100495
$529$	−22.5877	−0.982073
$530$	2.25434	0.0979224
$531$	−1.83705	−0.0797212
$532$	−3.20163	−0.138808
$533$	−7.76312	−0.336258
$534$	−14.9286	−0.646026
$535$	−8.97486	−0.388017
$536$	12.1897	0.526514
$537$	−30.9827	−1.33700
$538$	−10.5247	−0.453751
$539$	0.877606	0.0378012
$540$	4.43949	0.191045
$541$	−9.90454	−0.425829	−0.212915	−	0.977071i	$-0.568296\pi$
$541$	−9.90454	−0.425829	−0.212915	+	0.977071i	$0.568296\pi$
$542$	13.2342	0.568459
$543$	−3.72518	−0.159863
$544$	−47.0371	−2.01670
$545$	−5.73982	−0.245867
$546$	−5.72680	−0.245084
$547$	14.4051	0.615918	0.307959	−	0.951400i	$-0.400354\pi$
$547$	14.4051	0.615918	0.307959	+	0.951400i	$0.400354\pi$
$548$	−16.8678	−0.720556
$549$	0	0
$550$	−0.615105	−0.0262282
$551$	1.35977	0.0579280
$552$	3.04213	0.129482
$553$	−3.11214	−0.132342
$554$	−6.10236	−0.259265
$555$	−12.5250	−0.531658
$556$	−4.99441	−0.211810
$557$	19.2728	0.816614	0.408307	−	0.912845i	$-0.366119\pi$
$557$	19.2728	0.816614	0.408307	+	0.912845i	$0.366119\pi$
$558$	−0.782409	−0.0331220
$559$	29.0975	1.23069
$560$	0.657333	0.0277774
$561$	2.48833	0.105057
$562$	−11.4057	−0.481119
$563$	−40.1372	−1.69158	−0.845790	−	0.533516i	$-0.820870\pi$
$563$	−40.1372	−1.69158	−0.845790	+	0.533516i	$0.820870\pi$
$564$	−26.1889	−1.10275
$565$	3.14005	0.132103
$566$	12.1753	0.511765
$567$	13.3068	0.558835
$568$	−17.1851	−0.721072
$569$	7.61046	0.319047	0.159523	−	0.987194i	$-0.449004\pi$
$569$	7.61046	0.319047	0.159523	+	0.987194i	$0.449004\pi$
$570$	1.47462	0.0617650
$571$	4.39777	0.184041	0.0920205	−	0.995757i	$-0.470667\pi$
$571$	4.39777	0.184041	0.0920205	+	0.995757i	$0.470667\pi$
$572$	0.715607	0.0299210
$573$	38.4189	1.60497
$574$	−2.80554	−0.117101
$575$	2.94941	0.122999
$576$	0.689318	0.0287216
$577$	5.88829	0.245133	0.122566	−	0.992460i	$-0.460888\pi$
$577$	5.88829	0.245133	0.122566	+	0.992460i	$0.460888\pi$
$578$	−36.9208	−1.53570
$579$	25.1541	1.04537
$580$	−0.730765	−0.0303434
$581$	−6.18200	−0.256473
$582$	−17.1182	−0.709571
$583$	−0.784983	−0.0325107
$584$	32.9076	1.36173
$585$	−0.427413	−0.0176714
$586$	−0.369440	−0.0152614
$587$	−40.7272	−1.68099	−0.840497	−	0.541817i	$-0.817737\pi$
$587$	−40.7272	−1.68099	−0.840497	+	0.541817i	$0.817737\pi$
$588$	−12.7683	−0.526554
$589$	−7.40369	−0.305064
$590$	−4.03254	−0.166017
$591$	19.2556	0.792069
$592$	−8.15258	−0.335069
$593$	21.7442	0.892925	0.446463	−	0.894802i	$-0.352684\pi$
$593$	21.7442	0.892925	0.446463	+	0.894802i	$0.352684\pi$
$594$	0.667271	0.0273785
$595$	7.08321	0.290383
$596$	−17.7356	−0.726477
$597$	−35.6444	−1.45883
$598$	1.48112	0.0605674
$599$	25.8881	1.05776	0.528880	−	0.848697i	$-0.322612\pi$
$599$	25.8881	1.05776	0.528880	+	0.848697i	$0.322612\pi$
$600$	21.7612	0.888396
$601$	26.3199	1.07361	0.536806	−	0.843706i	$-0.319631\pi$
$601$	26.3199	1.07361	0.536806	+	0.843706i	$0.319631\pi$
$602$	10.5156	0.428585
$603$	1.04257	0.0424567
$604$	−25.5007	−1.03761
$605$	6.99653	0.284449
$606$	−16.6744	−0.677351
$607$	16.5092	0.670087	0.335044	−	0.942203i	$-0.391249\pi$
$607$	16.5092	0.670087	0.335044	+	0.942203i	$0.391249\pi$
$608$	9.70628	0.393642
$609$	−2.03637	−0.0825177
$610$	0	0
$611$	−31.0048	−1.25432
$612$	−2.53219	−0.102358
$613$	−27.4676	−1.10941	−0.554703	−	0.832048i	$-0.687168\pi$
$613$	−27.4676	−1.10941	−0.554703	+	0.832048i	$0.687168\pi$
$614$	−6.00108	−0.242184
$615$	−2.99361	−0.120714
$616$	0.628862	0.0253376
$617$	29.3450	1.18138	0.590692	−	0.806897i	$-0.298855\pi$
$617$	29.3450	1.18138	0.590692	+	0.806897i	$0.298855\pi$
$618$	14.5031	0.583400
$619$	20.8472	0.837920	0.418960	−	0.908005i	$-0.362395\pi$
$619$	20.8472	0.837920	0.418960	+	0.908005i	$0.362395\pi$
$620$	3.97889	0.159796
$621$	−3.19955	−0.128393
$622$	2.57066	0.103074
$623$	14.7973	0.592843
$624$	−3.97747	−0.159226
$625$	19.0641	0.762566
$626$	−2.94354	−0.117648
$627$	−0.513476	−0.0205062
$628$	23.0915	0.921450
$629$	−87.8497	−3.50280
$630$	−0.154464	−0.00615401
$631$	−24.7125	−0.983789	−0.491894	−	0.870655i	$-0.663695\pi$
$631$	−24.7125	−0.983789	−0.491894	+	0.870655i	$0.663695\pi$
$632$	5.93860	0.236225
$633$	26.4813	1.05254
$634$	1.59031	0.0631593
$635$	4.47687	0.177659
$636$	11.4207	0.452860
$637$	−15.1163	−0.598928
$638$	−0.109837	−0.00434848
$639$	−1.46983	−0.0581454
$640$	−5.95484	−0.235386
$641$	9.48935	0.374807	0.187403	−	0.982283i	$-0.439993\pi$
$641$	9.48935	0.374807	0.187403	+	0.982283i	$0.439993\pi$
$642$	19.6259	0.774573
$643$	−27.1514	−1.07075	−0.535374	−	0.844615i	$-0.679829\pi$
$643$	−27.1514	−1.07075	−0.535374	+	0.844615i	$0.679829\pi$
$644$	−1.24005	−0.0488650
$645$	11.2206	0.441809
$646$	10.3429	0.406934
$647$	29.0591	1.14243	0.571216	−	0.820800i	$-0.306472\pi$
$647$	29.0591	1.14243	0.571216	+	0.820800i	$0.306472\pi$
$648$	−25.3922	−0.997498
$649$	1.40417	0.0551185
$650$	10.5948	0.415563
$651$	11.0877	0.434560
$652$	−6.26239	−0.245254
$653$	3.28618	0.128598	0.0642990	−	0.997931i	$-0.479519\pi$
$653$	3.28618	0.128598	0.0642990	+	0.997931i	$0.479519\pi$
$654$	12.5516	0.490808
$655$	−0.361448	−0.0141230
$656$	−1.94855	−0.0760781
$657$	2.81456	0.109806
$658$	−11.2049	−0.436814
$659$	49.2051	1.91676	0.958379	−	0.285499i	$-0.0921593\pi$
$659$	49.2051	1.91676	0.958379	+	0.285499i	$0.0921593\pi$
$660$	0.275952	0.0107414
$661$	34.1474	1.32818	0.664090	−	0.747653i	$-0.268819\pi$
$661$	34.1474	1.32818	0.664090	+	0.747653i	$0.268819\pi$
$662$	−16.3407	−0.635099
$663$	−42.8600	−1.66454
$664$	11.7965	0.457794
$665$	−1.46165	−0.0566803
$666$	1.91575	0.0742337
$667$	0.526664	0.0203925
$668$	−20.9783	−0.811674
$669$	−31.4182	−1.21470
$670$	2.28857	0.0884150
$671$	0	0
$672$	−14.5360	−0.560738
$673$	−13.4523	−0.518549	−0.259274	−	0.965804i	$-0.583483\pi$
$673$	−13.4523	−0.518549	−0.259274	+	0.965804i	$0.583483\pi$
$674$	3.45191	0.132962
$675$	−22.8872	−0.880929
$676$	5.83498	0.224422
$677$	21.9459	0.843449	0.421725	−	0.906724i	$-0.361425\pi$
$677$	21.9459	0.843449	0.421725	+	0.906724i	$0.361425\pi$
$678$	−6.86655	−0.263708
$679$	16.9676	0.651157
$680$	−13.5162	−0.518323
$681$	50.3553	1.92962
$682$	0.598043	0.0229002
$683$	33.8144	1.29387	0.646936	−	0.762544i	$-0.276050\pi$
$683$	33.8144	1.29387	0.646936	+	0.762544i	$0.276050\pi$
$684$	0.522527	0.0199793
$685$	−7.70070	−0.294229
$686$	−12.9773	−0.495474
$687$	−1.86089	−0.0709974
$688$	7.30349	0.278443
$689$	13.5209	0.515105
$690$	0.571149	0.0217433
$691$	32.4520	1.23453	0.617266	−	0.786754i	$-0.288240\pi$
$691$	32.4520	1.23453	0.617266	+	0.786754i	$0.288240\pi$
$692$	16.3978	0.623349
$693$	0.0537859	0.00204316
$694$	−15.0846	−0.572602
$695$	−2.28011	−0.0864895
$696$	3.88580	0.147291
$697$	−20.9970	−0.795317
$698$	−10.6934	−0.404750
$699$	−13.2282	−0.500338
$700$	−8.87044	−0.335271
$701$	18.3927	0.694684	0.347342	−	0.937738i	$-0.387084\pi$
$701$	18.3927	0.694684	0.347342	+	0.937738i	$0.387084\pi$
$702$	−11.4934	−0.433789
$703$	18.1281	0.683715
$704$	−0.526887	−0.0198578
$705$	−11.9561	−0.450292
$706$	−8.62840	−0.324734
$707$	16.5277	0.621590
$708$	−20.4292	−0.767777
$709$	−26.9537	−1.01227	−0.506134	−	0.862455i	$-0.668926\pi$
$709$	−26.9537	−1.01227	−0.506134	+	0.862455i	$0.668926\pi$
$710$	−3.22644	−0.121086
$711$	0.507922	0.0190486
$712$	−28.2363	−1.05820
$713$	−2.86760	−0.107392
$714$	−15.4893	−0.579673
$715$	0.326698	0.0122178
$716$	−24.0994	−0.900639
$717$	−31.4209	−1.17344
$718$	−10.4819	−0.391182
$719$	25.6949	0.958259	0.479129	−	0.877744i	$-0.340952\pi$
$719$	25.6949	0.958259	0.479129	+	0.877744i	$0.340952\pi$
$720$	−0.107281	−0.00399813
$721$	−14.3755	−0.535373
$722$	12.6199	0.469664
$723$	11.9320	0.443754
$724$	−2.89758	−0.107688
$725$	3.76737	0.139917
$726$	−15.2998	−0.567828
$727$	−8.57047	−0.317861	−0.158931	−	0.987290i	$-0.550805\pi$
$727$	−8.57047	−0.317861	−0.158931	+	0.987290i	$0.550805\pi$
$728$	−10.8318	−0.401453
$729$	24.6755	0.913908
$730$	6.17828	0.228669
$731$	78.7001	2.91083
$732$	0	0
$733$	33.5419	1.23890	0.619450	−	0.785036i	$-0.287356\pi$
$733$	33.5419	1.23890	0.619450	+	0.785036i	$0.287356\pi$
$734$	−22.3841	−0.826210
$735$	−5.82913	−0.215011
$736$	3.75944	0.138575
$737$	−0.796900	−0.0293542
$738$	0.457883	0.0168549
$739$	−27.9772	−1.02916	−0.514579	−	0.857443i	$-0.672052\pi$
$739$	−27.9772	−1.02916	−0.514579	+	0.857443i	$0.672052\pi$
$740$	−9.74242	−0.358138
$741$	8.84432	0.324904
$742$	4.88636	0.179384
$743$	−36.3522	−1.33363	−0.666816	−	0.745223i	$-0.732343\pi$
$743$	−36.3522	−1.33363	−0.666816	+	0.745223i	$0.732343\pi$
$744$	−21.1575	−0.775673
$745$	−8.09687	−0.296646
$746$	−24.9953	−0.915142
$747$	1.00894	0.0369153
$748$	1.93551	0.0707692
$749$	−19.4533	−0.710808
$750$	8.53295	0.311579
$751$	−10.0759	−0.367677	−0.183838	−	0.982957i	$-0.558852\pi$
$751$	−10.0759	−0.367677	−0.183838	+	0.982957i	$0.558852\pi$
$752$	−7.78224	−0.283789
$753$	−24.3111	−0.885946
$754$	1.89188	0.0688980
$755$	−11.6419	−0.423692
$756$	9.62273	0.349975
$757$	−41.4655	−1.50709	−0.753545	−	0.657396i	$-0.771658\pi$
$757$	−41.4655	−1.50709	−0.753545	+	0.657396i	$0.771658\pi$
$758$	9.42846	0.342457
$759$	−0.198879	−0.00721886
$760$	2.78912	0.101172
$761$	−6.71167	−0.243298	−0.121649	−	0.992573i	$-0.538818\pi$
$761$	−6.71167	−0.243298	−0.121649	+	0.992573i	$0.538818\pi$
$762$	−9.78986	−0.354649
$763$	−12.4412	−0.450403
$764$	29.8835	1.08115
$765$	−1.15603	−0.0417963
$766$	−11.6005	−0.419144
$767$	−24.1860	−0.873306
$768$	23.9964	0.865895
$769$	−21.3582	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$769$	−21.3582	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$770$	0.118067	0.00425482
$771$	−38.2201	−1.37646
$772$	19.5657	0.704187
$773$	−28.3574	−1.01995	−0.509973	−	0.860190i	$-0.670345\pi$
$773$	−28.3574	−1.01995	−0.509973	+	0.860190i	$0.670345\pi$
$774$	−1.71622	−0.0616883
$775$	−20.5127	−0.736837
$776$	−32.3776	−1.16229
$777$	−27.1484	−0.973944
$778$	−11.1765	−0.400696
$779$	4.33281	0.155239
$780$	−4.75312	−0.170189
$781$	1.12348	0.0402012
$782$	4.00599	0.143254
$783$	−4.08687	−0.146053
$784$	−3.79420	−0.135507
$785$	10.5420	0.376261
$786$	0.790403	0.0281927
$787$	−13.5892	−0.484402	−0.242201	−	0.970226i	$-0.577869\pi$
$787$	−13.5892	−0.484402	−0.242201	+	0.970226i	$0.577869\pi$
$788$	14.9777	0.533558
$789$	−23.5958	−0.840032
$790$	1.11495	0.0396681
$791$	6.80616	0.241999
$792$	−0.102634	−0.00364696
$793$	0	0
$794$	6.17298	0.219071
$795$	5.21392	0.184919
$796$	−27.7255	−0.982703
$797$	17.7156	0.627517	0.313759	−	0.949503i	$-0.398412\pi$
$797$	17.7156	0.627517	0.313759	+	0.949503i	$0.398412\pi$
$798$	3.19628	0.113147
$799$	−83.8590	−2.96672
$800$	26.8922	0.950784
$801$	−2.41503	−0.0853308
$802$	1.99057	0.0702894
$803$	−2.15134	−0.0759190
$804$	11.5941	0.408891
$805$	−0.566126	−0.0199533
$806$	−10.3009	−0.362835
$807$	−24.3419	−0.856874
$808$	−31.5383	−1.10951
$809$	47.7157	1.67759	0.838797	−	0.544444i	$-0.183259\pi$
$809$	47.7157	1.67759	0.838797	+	0.544444i	$0.183259\pi$
$810$	−4.76728	−0.167505
$811$	−1.71349	−0.0601689	−0.0300845	−	0.999547i	$-0.509578\pi$
$811$	−1.71349	−0.0601689	−0.0300845	+	0.999547i	$0.509578\pi$
$812$	−1.58396	−0.0555860
$813$	30.6086	1.07349
$814$	−1.46432	−0.0513244
$815$	−2.85899	−0.100146
$816$	−10.7579	−0.376602
$817$	−16.2401	−0.568168
$818$	6.08016	0.212588
$819$	−0.926432	−0.0323721
$820$	−2.32854	−0.0813161
$821$	40.1046	1.39966	0.699831	−	0.714309i	$-0.253259\pi$
$821$	40.1046	1.39966	0.699831	+	0.714309i	$0.253259\pi$
$822$	16.8396	0.587349
$823$	27.4859	0.958099	0.479049	−	0.877788i	$-0.340981\pi$
$823$	27.4859	0.958099	0.479049	+	0.877788i	$0.340981\pi$
$824$	27.4314	0.955620
$825$	−1.42264	−0.0495298
$826$	−8.74067	−0.304127
$827$	44.6267	1.55182	0.775911	−	0.630843i	$-0.217291\pi$
$827$	44.6267	1.55182	0.775911	+	0.630843i	$0.217291\pi$
$828$	0.202385	0.00703337
$829$	14.7791	0.513298	0.256649	−	0.966505i	$-0.417382\pi$
$829$	14.7791	0.513298	0.256649	+	0.966505i	$0.417382\pi$
$830$	2.21475	0.0768752
$831$	−14.1138	−0.489601
$832$	9.07534	0.314631
$833$	−40.8851	−1.41658
$834$	4.98606	0.172653
$835$	−9.57727	−0.331435
$836$	−0.399399	−0.0138135
$837$	22.2523	0.769153
$838$	−16.1914	−0.559322
$839$	−47.6276	−1.64429	−0.822143	−	0.569281i	$-0.807222\pi$
$839$	−47.6276	−1.64429	−0.822143	+	0.569281i	$0.807222\pi$
$840$	−4.17695	−0.144119
$841$	−28.3273	−0.976803
$842$	12.3192	0.424548
$843$	−26.3794	−0.908556
$844$	20.5981	0.709016
$845$	2.66386	0.0916396
$846$	1.82872	0.0628727
$847$	15.1652	0.521083
$848$	3.39376	0.116542
$849$	28.1594	0.966428
$850$	28.6559	0.982890
$851$	7.02138	0.240690
$852$	−16.3454	−0.559986
$853$	−21.8547	−0.748289	−0.374145	−	0.927370i	$-0.622064\pi$
$853$	−21.8547	−0.748289	−0.374145	+	0.927370i	$0.622064\pi$
$854$	0	0
$855$	0.238551	0.00815827
$856$	37.1208	1.26876
$857$	33.9239	1.15882	0.579409	−	0.815037i	$-0.303283\pi$
$857$	33.9239	1.15882	0.579409	+	0.815037i	$0.303283\pi$
$858$	−0.714411	−0.0243896
$859$	9.02537	0.307942	0.153971	−	0.988075i	$-0.450794\pi$
$859$	9.02537	0.307942	0.153971	+	0.988075i	$0.450794\pi$
$860$	8.72774	0.297614
$861$	−6.48875	−0.221136
$862$	−23.0403	−0.784755
$863$	−25.2985	−0.861170	−0.430585	−	0.902550i	$-0.641693\pi$
$863$	−25.2985	−0.861170	−0.430585	+	0.902550i	$0.641693\pi$
$864$	−29.1729	−0.992483
$865$	7.48612	0.254536
$866$	−7.16453	−0.243461
$867$	−85.3918	−2.90006
$868$	8.62438	0.292731
$869$	−0.388236	−0.0131700
$870$	0.729545	0.0247339
$871$	13.7261	0.465093
$872$	23.7404	0.803952
$873$	−2.76923	−0.0937241
$874$	−0.826652	−0.0279619
$875$	−8.45791	−0.285929
$876$	31.2997	1.05752
$877$	25.4397	0.859038	0.429519	−	0.903058i	$-0.358683\pi$
$877$	25.4397	0.859038	0.429519	+	0.903058i	$0.358683\pi$
$878$	10.2916	0.347325
$879$	−0.854454	−0.0288200
$880$	0.0820015	0.00276427
$881$	48.5337	1.63514	0.817570	−	0.575829i	$-0.195320\pi$
$881$	48.5337	1.63514	0.817570	+	0.575829i	$0.195320\pi$
$882$	0.891585	0.0300212
$883$	16.6730	0.561092	0.280546	−	0.959841i	$-0.409484\pi$
$883$	16.6730	0.561092	0.280546	+	0.959841i	$0.409484\pi$
$884$	−33.3380	−1.12128
$885$	−9.32661	−0.313511
$886$	28.6575	0.962768
$887$	−49.0075	−1.64551	−0.822756	−	0.568395i	$-0.807565\pi$
$887$	−49.0075	−1.64551	−0.822756	+	0.568395i	$0.807565\pi$
$888$	51.8047	1.73845
$889$	9.70376	0.325454
$890$	−5.30127	−0.177699
$891$	1.66001	0.0556125
$892$	−24.4382	−0.818251
$893$	17.3046	0.579077
$894$	17.7059	0.592175
$895$	−11.0022	−0.367763
$896$	−12.9073	−0.431203
$897$	3.42558	0.114377
$898$	10.2838	0.343176
$899$	−3.66286	−0.122163
$900$	1.44771	0.0482572
$901$	36.5701	1.21833
$902$	−0.349988	−0.0116533
$903$	24.3209	0.809350
$904$	−12.9875	−0.431959
$905$	−1.32284	−0.0439726
$906$	25.4581	0.845789
$907$	14.4989	0.481429	0.240714	−	0.970596i	$-0.422618\pi$
$907$	14.4989	0.481429	0.240714	+	0.970596i	$0.422618\pi$
$908$	39.1682	1.29984
$909$	−2.69744	−0.0894684
$910$	−2.03363	−0.0674141
$911$	−38.7505	−1.28386	−0.641930	−	0.766763i	$-0.721866\pi$
$911$	−38.7505	−1.28386	−0.641930	+	0.766763i	$0.721866\pi$
$912$	2.21993	0.0735094
$913$	−0.771197	−0.0255229
$914$	3.07834	0.101823
$915$	0	0
$916$	−1.44747	−0.0478256
$917$	−0.783451	−0.0258718
$918$	−31.0862	−1.02600
$919$	45.0557	1.48625	0.743125	−	0.669152i	$-0.233343\pi$
$919$	45.0557	1.48625	0.743125	+	0.669152i	$0.233343\pi$
$920$	1.08028	0.0356159
$921$	−13.8795	−0.457346
$922$	17.4795	0.575658
$923$	−19.3513	−0.636955
$924$	0.598135	0.0196772
$925$	50.2258	1.65141
$926$	−23.2099	−0.762724
$927$	2.34618	0.0770588
$928$	4.80204	0.157635
$929$	18.4731	0.606084	0.303042	−	0.952977i	$-0.401998\pi$
$929$	18.4731	0.606084	0.303042	+	0.952977i	$0.401998\pi$
$930$	−3.97225	−0.130255
$931$	8.43679	0.276505
$932$	−10.2894	−0.337040
$933$	5.94551	0.194647
$934$	15.9595	0.522212
$935$	0.883623	0.0288976
$936$	1.76782	0.0577830
$937$	−23.5456	−0.769203	−0.384601	−	0.923083i	$-0.625661\pi$
$937$	−23.5456	−0.769203	−0.384601	+	0.923083i	$0.625661\pi$
$938$	4.96054	0.161967
$939$	−6.80793	−0.222168
$940$	−9.29985	−0.303328
$941$	−17.8219	−0.580977	−0.290489	−	0.956878i	$-0.593818\pi$
$941$	−17.8219	−0.580977	−0.290489	+	0.956878i	$0.593818\pi$
$942$	−23.0529	−0.751104
$943$	1.67818	0.0546491
$944$	−6.07071	−0.197585
$945$	4.39309	0.142907
$946$	1.31181	0.0426507
$947$	−49.6515	−1.61346	−0.806729	−	0.590922i	$-0.798764\pi$
$947$	−49.6515	−1.61346	−0.806729	+	0.590922i	$0.798764\pi$
$948$	5.64843	0.183453
$949$	37.0555	1.20287
$950$	−5.91326	−0.191852
$951$	3.67813	0.119271
$952$	−29.2968	−0.949516
$953$	54.8623	1.77716	0.888582	−	0.458718i	$-0.151691\pi$
$953$	54.8623	1.77716	0.888582	+	0.458718i	$0.151691\pi$
$954$	−0.797487	−0.0258196
$955$	13.6428	0.441471
$956$	−24.4403	−0.790455
$957$	−0.254034	−0.00821176
$958$	−14.2979	−0.461944
$959$	−16.6915	−0.538997
$960$	3.49963	0.112950
$961$	−11.0563	−0.356656
$962$	25.2221	0.813193
$963$	3.17491	0.102310
$964$	9.28110	0.298924
$965$	8.93241	0.287544
$966$	1.23798	0.0398315
$967$	−52.8168	−1.69847	−0.849237	−	0.528013i	$-0.822937\pi$
$967$	−52.8168	−1.69847	−0.849237	+	0.528013i	$0.822937\pi$
$968$	−28.9383	−0.930112
$969$	23.9213	0.768464
$970$	−6.07878	−0.195178
$971$	52.0298	1.66972	0.834859	−	0.550464i	$-0.185549\pi$
$971$	52.0298	1.66972	0.834859	+	0.550464i	$0.185549\pi$
$972$	−3.26870	−0.104844
$973$	−4.94221	−0.158440
$974$	−17.5570	−0.562562
$975$	24.5041	0.784759
$976$	0	0
$977$	0.851462	0.0272407	0.0136203	−	0.999907i	$-0.495664\pi$
$977$	0.851462	0.0272407	0.0136203	+	0.999907i	$0.495664\pi$
$978$	6.25193	0.199915
$979$	1.84595	0.0589969
$980$	−4.53410	−0.144837
$981$	2.03049	0.0648287
$982$	−6.70779	−0.214054
$983$	17.9387	0.572155	0.286077	−	0.958206i	$-0.407649\pi$
$983$	17.9387	0.572155	0.286077	+	0.958206i	$0.407649\pi$
$984$	12.3819	0.394719
$985$	6.83780	0.217870
$986$	5.11697	0.162958
$987$	−25.9152	−0.824889
$988$	6.87943	0.218864
$989$	−6.29010	−0.200014
$990$	−0.0192692	−0.000612417 0
$991$	3.94249	0.125237	0.0626187	−	0.998038i	$-0.480055\pi$
$991$	3.94249	0.125237	0.0626187	+	0.998038i	$0.480055\pi$
$992$	−26.1463	−0.830145
$993$	−37.7933	−1.19933
$994$	−6.99342	−0.221818
$995$	−12.6576	−0.401273
$996$	11.2201	0.355523
$997$	−48.7837	−1.54500	−0.772498	−	0.635017i	$-0.780993\pi$
$997$	−48.7837	−1.54500	−0.772498	+	0.635017i	$0.780993\pi$
$998$	26.1978	0.829277
$999$	−54.4854	−1.72384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3721.2.a.k.1.6		16
61.8	odd	20		61.2.g.a.3.2	✓	16
61.23	odd	20		61.2.g.a.41.2	yes	16
61.60	even	2	inner	3721.2.a.k.1.11		16
183.8	even	20		549.2.y.b.64.3		16
183.23	even	20		549.2.y.b.163.3		16
244.23	even	20		976.2.bd.b.529.1		16
244.191	even	20		976.2.bd.b.369.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.2	✓	16	61.8	odd	20
61.2.g.a.41.2	yes	16	61.23	odd	20
549.2.y.b.64.3		16	183.8	even	20
549.2.y.b.163.3		16	183.23	even	20
976.2.bd.b.369.1		16	244.191	even	20
976.2.bd.b.529.1		16	244.23	even	20
3721.2.a.k.1.6		16	1.1	even	1	trivial
3721.2.a.k.1.11		16	61.60	even	2	inner

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:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.a (trivial)

\(f(q)\)	\(=\)	\(q-0.776536 q^{2} -1.79600 q^{3} -1.39699 q^{4} -0.637773 q^{5} +1.39466 q^{6} -1.38239 q^{7} +2.63789 q^{8} +0.225616 q^{9} +O(q^{10})\)	\(q-0.776536 q^{2} -1.79600 q^{3} -1.39699 q^{4} -0.637773 q^{5} +1.39466 q^{6} -1.38239 q^{7} +2.63789 q^{8} +0.225616 q^{9} +0.495253 q^{10} -0.172452 q^{11} +2.50900 q^{12} +2.97038 q^{13} +1.07348 q^{14} +1.14544 q^{15} +0.745570 q^{16} +8.03402 q^{17} -0.175199 q^{18} -1.65785 q^{19} +0.890963 q^{20} +2.48278 q^{21} +0.133915 q^{22} -0.642119 q^{23} -4.73764 q^{24} -4.59325 q^{25} -2.30661 q^{26} +4.98279 q^{27} +1.93119 q^{28} -0.820197 q^{29} -0.889475 q^{30} +4.46583 q^{31} -5.85473 q^{32} +0.309723 q^{33} -6.23871 q^{34} +0.881652 q^{35} -0.315183 q^{36} -10.9347 q^{37} +1.28738 q^{38} -5.33481 q^{39} -1.68237 q^{40} -2.61351 q^{41} -1.92797 q^{42} +9.79585 q^{43} +0.240914 q^{44} -0.143892 q^{45} +0.498628 q^{46} -10.4380 q^{47} -1.33904 q^{48} -5.08899 q^{49} +3.56682 q^{50} -14.4291 q^{51} -4.14960 q^{52} +4.55190 q^{53} -3.86932 q^{54} +0.109985 q^{55} -3.64659 q^{56} +2.97750 q^{57} +0.636913 q^{58} -8.14238 q^{59} -1.60017 q^{60} -3.46788 q^{62} -0.311890 q^{63} +3.05527 q^{64} -1.89443 q^{65} -0.240511 q^{66} +4.62100 q^{67} -11.2235 q^{68} +1.15325 q^{69} -0.684635 q^{70} -6.51473 q^{71} +0.595149 q^{72} +12.4750 q^{73} +8.49119 q^{74} +8.24947 q^{75} +2.31601 q^{76} +0.238396 q^{77} +4.14267 q^{78} +2.25127 q^{79} -0.475504 q^{80} -9.62594 q^{81} +2.02948 q^{82} +4.47196 q^{83} -3.46842 q^{84} -5.12388 q^{85} -7.60683 q^{86} +1.47307 q^{87} -0.454908 q^{88} -10.7042 q^{89} +0.111737 q^{90} -4.10624 q^{91} +0.897035 q^{92} -8.02064 q^{93} +8.10547 q^{94} +1.05733 q^{95} +10.5151 q^{96} -12.2741 q^{97} +3.95178 q^{98} -0.0389079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} + 2 q^{4} + 10 q^{5} + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^3 + 2 * q^4 + 10 * q^5 + 6 * q^9	\( 16 q + 6 q^{3} + 2 q^{4} + 10 q^{5} + 6 q^{9} + 10 q^{12} - 12 q^{13} + 18 q^{14} + 32 q^{15} - 6 q^{16} + 32 q^{19} + 2 q^{20} - 6 q^{22} - 2 q^{25} + 24 q^{27} + 16 q^{34} - 12 q^{36} - 12 q^{39} + 38 q^{41} + 40 q^{42} + 104 q^{45} + 28 q^{46} + 6 q^{47} + 20 q^{48} + 20 q^{49} - 54 q^{52} + 32 q^{56} + 64 q^{57} - 26 q^{58} - 14 q^{60} + 16 q^{62} + 18 q^{64} - 60 q^{65} - 18 q^{66} - 52 q^{70} + 54 q^{73} + 24 q^{74} + 88 q^{75} + 66 q^{76} - 42 q^{77} + 14 q^{80} + 16 q^{81} - 64 q^{83} - 20 q^{86} + 88 q^{88} + 68 q^{95} - 30 q^{97}+O(q^{100}) \) 16 * q + 6 * q^3 + 2 * q^4 + 10 * q^5 + 6 * q^9 + 10 * q^12 - 12 * q^13 + 18 * q^14 + 32 * q^15 - 6 * q^16 + 32 * q^19 + 2 * q^20 - 6 * q^22 - 2 * q^25 + 24 * q^27 + 16 * q^34 - 12 * q^36 - 12 * q^39 + 38 * q^41 + 40 * q^42 + 104 * q^45 + 28 * q^46 + 6 * q^47 + 20 * q^48 + 20 * q^49 - 54 * q^52 + 32 * q^56 + 64 * q^57 - 26 * q^58 - 14 * q^60 + 16 * q^62 + 18 * q^64 - 60 * q^65 - 18 * q^66 - 52 * q^70 + 54 * q^73 + 24 * q^74 + 88 * q^75 + 66 * q^76 - 42 * q^77 + 14 * q^80 + 16 * q^81 - 64 * q^83 - 20 * q^86 + 88 * q^88 + 68 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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