LMFDB - Embedded newform 1441.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.59929 q^{2} +1.84862 q^{3} +0.557714 q^{4} -2.20532 q^{5} -2.95647 q^{6} +0.234218 q^{7} +2.30663 q^{8} +0.417399 q^{9} +O(q^{10})$	\(q-1.59929 q^{2} +1.84862 q^{3} +0.557714 q^{4} -2.20532 q^{5} -2.95647 q^{6} +0.234218 q^{7} +2.30663 q^{8} +0.417399 q^{9} +3.52693 q^{10} +1.00000 q^{11} +1.03100 q^{12} +3.74207 q^{13} -0.374582 q^{14} -4.07680 q^{15} -4.80438 q^{16} -7.28503 q^{17} -0.667540 q^{18} -1.61498 q^{19} -1.22994 q^{20} +0.432981 q^{21} -1.59929 q^{22} +0.208342 q^{23} +4.26408 q^{24} -0.136574 q^{25} -5.98464 q^{26} -4.77425 q^{27} +0.130627 q^{28} -0.937441 q^{29} +6.51996 q^{30} +3.89533 q^{31} +3.07033 q^{32} +1.84862 q^{33} +11.6508 q^{34} -0.516525 q^{35} +0.232789 q^{36} +3.40901 q^{37} +2.58282 q^{38} +6.91767 q^{39} -5.08685 q^{40} -2.14713 q^{41} -0.692460 q^{42} +9.65515 q^{43} +0.557714 q^{44} -0.920497 q^{45} -0.333198 q^{46} -1.16811 q^{47} -8.88148 q^{48} -6.94514 q^{49} +0.218421 q^{50} -13.4673 q^{51} +2.08700 q^{52} -2.61773 q^{53} +7.63539 q^{54} -2.20532 q^{55} +0.540254 q^{56} -2.98549 q^{57} +1.49924 q^{58} -1.17369 q^{59} -2.27369 q^{60} -6.06950 q^{61} -6.22975 q^{62} +0.0977624 q^{63} +4.69844 q^{64} -8.25245 q^{65} -2.95647 q^{66} -12.1238 q^{67} -4.06296 q^{68} +0.385145 q^{69} +0.826072 q^{70} -1.12665 q^{71} +0.962783 q^{72} -14.8955 q^{73} -5.45198 q^{74} -0.252474 q^{75} -0.900699 q^{76} +0.234218 q^{77} -11.0633 q^{78} -1.19566 q^{79} +10.5952 q^{80} -10.0780 q^{81} +3.43387 q^{82} -9.02896 q^{83} +0.241479 q^{84} +16.0658 q^{85} -15.4413 q^{86} -1.73297 q^{87} +2.30663 q^{88} +6.26619 q^{89} +1.47214 q^{90} +0.876460 q^{91} +0.116195 q^{92} +7.20099 q^{93} +1.86814 q^{94} +3.56155 q^{95} +5.67587 q^{96} +11.6870 q^{97} +11.1073 q^{98} +0.417399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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 $

$2$	−1.59929	−1.13087	−0.565433	−	0.824794i	$-0.691291\pi$
$2$	−1.59929	−1.13087	−0.565433	+	0.824794i	$0.691291\pi$
$3$	1.84862	1.06730	0.533651	−	0.845705i	$-0.320820\pi$
$3$	1.84862	1.06730	0.533651	+	0.845705i	$0.320820\pi$
$4$	0.557714	0.278857
$5$	−2.20532	−0.986248	−0.493124	−	0.869959i	$-0.664145\pi$
$5$	−2.20532	−0.986248	−0.493124	+	0.869959i	$0.664145\pi$
$6$	−2.95647	−1.20697
$7$	0.234218	0.0885262	0.0442631	−	0.999020i	$-0.485906\pi$
$7$	0.234218	0.0885262	0.0442631	+	0.999020i	$0.485906\pi$
$8$	2.30663	0.815516
$9$	0.417399	0.139133
$10$	3.52693	1.11531
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.03100	0.297625
$13$	3.74207	1.03786	0.518932	−	0.854816i	$-0.326330\pi$
$13$	3.74207	1.03786	0.518932	+	0.854816i	$0.326330\pi$
$14$	−0.374582	−0.100111
$15$	−4.07680	−1.05262
$16$	−4.80438	−1.20110
$17$	−7.28503	−1.76688	−0.883439	−	0.468546i	$-0.844778\pi$
$17$	−7.28503	−1.76688	−0.883439	+	0.468546i	$0.844778\pi$
$18$	−0.667540	−0.157341
$19$	−1.61498	−0.370502	−0.185251	−	0.982691i	$-0.559310\pi$
$19$	−1.61498	−0.370502	−0.185251	+	0.982691i	$0.559310\pi$
$20$	−1.22994	−0.275022
$21$	0.432981	0.0944841
$22$	−1.59929	−0.340969
$23$	0.208342	0.0434422	0.0217211	−	0.999764i	$-0.493085\pi$
$23$	0.208342	0.0434422	0.0217211	+	0.999764i	$0.493085\pi$
$24$	4.26408	0.870401
$25$	−0.136574	−0.0273148
$26$	−5.98464	−1.17368
$27$	−4.77425	−0.918805
$28$	0.130627	0.0246861
$29$	−0.937441	−0.174078	−0.0870392	−	0.996205i	$-0.527741\pi$
$29$	−0.937441	−0.174078	−0.0870392	+	0.996205i	$0.527741\pi$
$30$	6.51996	1.19038
$31$	3.89533	0.699622	0.349811	−	0.936820i	$-0.386246\pi$
$31$	3.89533	0.699622	0.349811	+	0.936820i	$0.386246\pi$
$32$	3.07033	0.542762
$33$	1.84862	0.321804
$34$	11.6508	1.99810
$35$	−0.516525	−0.0873087
$36$	0.232789	0.0387982
$37$	3.40901	0.560437	0.280219	−	0.959936i	$-0.409593\pi$
$37$	3.40901	0.560437	0.280219	+	0.959936i	$0.409593\pi$
$38$	2.58282	0.418989
$39$	6.91767	1.10771
$40$	−5.08685	−0.804301
$41$	−2.14713	−0.335325	−0.167663	−	0.985844i	$-0.553622\pi$
$41$	−2.14713	−0.335325	−0.167663	+	0.985844i	$0.553622\pi$
$42$	−0.692460	−0.106849
$43$	9.65515	1.47240	0.736198	−	0.676766i	$-0.236619\pi$
$43$	9.65515	1.47240	0.736198	+	0.676766i	$0.236619\pi$
$44$	0.557714	0.0840785
$45$	−0.920497	−0.137220
$46$	−0.333198	−0.0491273
$47$	−1.16811	−0.170386	−0.0851929	−	0.996364i	$-0.527151\pi$
$47$	−1.16811	−0.170386	−0.0851929	+	0.996364i	$0.527151\pi$
$48$	−8.88148	−1.28193
$49$	−6.94514	−0.992163
$50$	0.218421	0.0308894
$51$	−13.4673	−1.88579
$52$	2.08700	0.289415
$53$	−2.61773	−0.359573	−0.179787	−	0.983706i	$-0.557541\pi$
$53$	−2.61773	−0.359573	−0.179787	+	0.983706i	$0.557541\pi$
$54$	7.63539	1.03904
$55$	−2.20532	−0.297365
$56$	0.540254	0.0721945
$57$	−2.98549	−0.395438
$58$	1.49924	0.196859
$59$	−1.17369	−0.152802	−0.0764008	−	0.997077i	$-0.524343\pi$
$59$	−1.17369	−0.152802	−0.0764008	+	0.997077i	$0.524343\pi$
$60$	−2.27369	−0.293532
$61$	−6.06950	−0.777119	−0.388560	−	0.921424i	$-0.627027\pi$
$61$	−6.06950	−0.777119	−0.388560	+	0.921424i	$0.627027\pi$
$62$	−6.22975	−0.791179
$63$	0.0977624	0.0123169
$64$	4.69844	0.587305
$65$	−8.25245	−1.02359
$66$	−2.95647	−0.363917
$67$	−12.1238	−1.48116	−0.740580	−	0.671969i	$-0.765449\pi$
$67$	−12.1238	−1.48116	−0.740580	+	0.671969i	$0.765449\pi$
$68$	−4.06296	−0.492706
$69$	0.385145	0.0463660
$70$	0.826072	0.0987345
$71$	−1.12665	−0.133708	−0.0668541	−	0.997763i	$-0.521296\pi$
$71$	−1.12665	−0.133708	−0.0668541	+	0.997763i	$0.521296\pi$
$72$	0.962783	0.113465
$73$	−14.8955	−1.74339	−0.871695	−	0.490050i	$-0.836979\pi$
$73$	−14.8955	−1.74339	−0.871695	+	0.490050i	$0.836979\pi$
$74$	−5.45198	−0.633779
$75$	−0.252474	−0.0291531
$76$	−0.900699	−0.103317
$77$	0.234218	0.0266916
$78$	−11.0633	−1.25267
$79$	−1.19566	−0.134522	−0.0672610	−	0.997735i	$-0.521426\pi$
$79$	−1.19566	−0.134522	−0.0672610	+	0.997735i	$0.521426\pi$
$80$	10.5952	1.18458
$81$	−10.0780	−1.11977
$82$	3.43387	0.379208
$83$	−9.02896	−0.991057	−0.495528	−	0.868592i	$-0.665026\pi$
$83$	−9.02896	−0.991057	−0.495528	+	0.868592i	$0.665026\pi$
$84$	0.241479	0.0263476
$85$	16.0658	1.74258
$86$	−15.4413	−1.66508
$87$	−1.73297	−0.185794
$88$	2.30663	0.245887
$89$	6.26619	0.664215	0.332108	−	0.943242i	$-0.392240\pi$
$89$	6.26619	0.664215	0.332108	+	0.943242i	$0.392240\pi$
$90$	1.47214	0.155177
$91$	0.876460	0.0918780
$92$	0.116195	0.0121142
$93$	7.20099	0.746708
$94$	1.86814	0.192683
$95$	3.56155	0.365407
$96$	5.67587	0.579291
$97$	11.6870	1.18664	0.593318	−	0.804968i	$-0.297817\pi$
$97$	11.6870	1.18664	0.593318	+	0.804968i	$0.297817\pi$
$98$	11.1073	1.12200
$99$	0.417399	0.0419501
$100$	−0.0761692	−0.00761692
$101$	−19.4984	−1.94017	−0.970083	−	0.242774i	$-0.921943\pi$
$101$	−19.4984	−1.94017	−0.970083	+	0.242774i	$0.921943\pi$
$102$	21.5380	2.13258
$103$	−2.75624	−0.271581	−0.135790	−	0.990738i	$-0.543357\pi$
$103$	−2.75624	−0.271581	−0.135790	+	0.990738i	$0.543357\pi$
$104$	8.63156	0.846394
$105$	−0.954860	−0.0931848
$106$	4.18650	0.406629
$107$	−18.3177	−1.77083	−0.885417	−	0.464797i	$-0.846127\pi$
$107$	−18.3177	−1.77083	−0.885417	+	0.464797i	$0.846127\pi$
$108$	−2.66267	−0.256215
$109$	−10.8667	−1.04084	−0.520419	−	0.853911i	$-0.674224\pi$
$109$	−10.8667	−1.04084	−0.520419	+	0.853911i	$0.674224\pi$
$110$	3.52693	0.336280
$111$	6.30196	0.598156
$112$	−1.12527	−0.106328
$113$	−12.2921	−1.15634	−0.578171	−	0.815916i	$-0.696233\pi$
$113$	−12.2921	−1.15634	−0.578171	+	0.815916i	$0.696233\pi$
$114$	4.77465	0.447187
$115$	−0.459460	−0.0428448
$116$	−0.522824	−0.0485430
$117$	1.56193	0.144401
$118$	1.87707	0.172798
$119$	−1.70629	−0.156415
$120$	−9.40365	−0.858432
$121$	1.00000	0.0909091
$122$	9.70686	0.878818
$123$	−3.96923	−0.357893
$124$	2.17248	0.195095
$125$	11.3278	1.01319
$126$	−0.156350	−0.0139288
$127$	−1.12352	−0.0996962	−0.0498481	−	0.998757i	$-0.515874\pi$
$127$	−1.12352	−0.0996962	−0.0498481	+	0.998757i	$0.515874\pi$
$128$	−13.6548	−1.20692
$129$	17.8487	1.57149
$130$	13.1980	1.15754
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.03100	0.0897372
$133$	−0.378258	−0.0327992
$134$	19.3894	1.67499
$135$	10.5287	0.906170
$136$	−16.8038	−1.44092
$137$	15.0416	1.28509	0.642543	−	0.766249i	$-0.277879\pi$
$137$	15.0416	1.28509	0.642543	+	0.766249i	$0.277879\pi$
$138$	−0.615956	−0.0524337
$139$	16.3732	1.38876	0.694379	−	0.719610i	$-0.255679\pi$
$139$	16.3732	1.38876	0.694379	+	0.719610i	$0.255679\pi$
$140$	−0.288073	−0.0243467
$141$	−2.15939	−0.181853
$142$	1.80183	0.151206
$143$	3.74207	0.312927
$144$	−2.00534	−0.167112
$145$	2.06735	0.171684
$146$	23.8222	1.97154
$147$	−12.8389	−1.05894
$148$	1.90125	0.156282
$149$	−14.7447	−1.20793	−0.603966	−	0.797010i	$-0.706414\pi$
$149$	−14.7447	−1.20793	−0.603966	+	0.797010i	$0.706414\pi$
$150$	0.403777	0.0329683
$151$	6.86347	0.558542	0.279271	−	0.960212i	$-0.409907\pi$
$151$	6.86347	0.558542	0.279271	+	0.960212i	$0.409907\pi$
$152$	−3.72516	−0.302151
$153$	−3.04076	−0.245831
$154$	−0.374582	−0.0301847
$155$	−8.59045	−0.690001
$156$	3.85808	0.308894
$157$	−16.6104	−1.32565	−0.662826	−	0.748773i	$-0.730643\pi$
$157$	−16.6104	−1.32565	−0.662826	+	0.748773i	$0.730643\pi$
$158$	1.91220	0.152126
$159$	−4.83920	−0.383773
$160$	−6.77104	−0.535298
$161$	0.0487974	0.00384577
$162$	16.1176	1.26631
$163$	20.8318	1.63168	0.815838	−	0.578280i	$-0.196276\pi$
$163$	20.8318	1.63168	0.815838	+	0.578280i	$0.196276\pi$
$164$	−1.19748	−0.0935078
$165$	−4.07680	−0.317378
$166$	14.4399	1.12075
$167$	−7.76826	−0.601126	−0.300563	−	0.953762i	$-0.597175\pi$
$167$	−7.76826	−0.601126	−0.300563	+	0.953762i	$0.597175\pi$
$168$	0.998725	0.0770533
$169$	1.00308	0.0771598
$170$	−25.6938	−1.97062
$171$	−0.674092	−0.0515491
$172$	5.38481	0.410588
$173$	7.59897	0.577739	0.288870	−	0.957368i	$-0.406721\pi$
$173$	7.59897	0.577739	0.288870	+	0.957368i	$0.406721\pi$
$174$	2.77152	0.210108
$175$	−0.0319881	−0.00241807
$176$	−4.80438	−0.362144
$177$	−2.16971	−0.163085
$178$	−10.0214	−0.751138
$179$	2.57061	0.192136	0.0960682	−	0.995375i	$-0.469373\pi$
$179$	2.57061	0.192136	0.0960682	+	0.995375i	$0.469373\pi$
$180$	−0.513374	−0.0382646
$181$	1.32135	0.0982151	0.0491075	−	0.998793i	$-0.484362\pi$
$181$	1.32135	0.0982151	0.0491075	+	0.998793i	$0.484362\pi$
$182$	−1.40171	−0.103902
$183$	−11.2202	−0.829421
$184$	0.480567	0.0354278
$185$	−7.51794	−0.552730
$186$	−11.5164	−0.844427
$187$	−7.28503	−0.532734
$188$	−0.651469	−0.0475133
$189$	−1.11822	−0.0813383
$190$	−5.69594	−0.413227
$191$	−13.0462	−0.943992	−0.471996	−	0.881601i	$-0.656466\pi$
$191$	−13.0462	−0.943992	−0.471996	+	0.881601i	$0.656466\pi$
$192$	8.68563	0.626831
$193$	−15.9833	−1.15051	−0.575253	−	0.817975i	$-0.695096\pi$
$193$	−15.9833	−1.15051	−0.575253	+	0.817975i	$0.695096\pi$
$194$	−18.6909	−1.34193
$195$	−15.2556	−1.09248
$196$	−3.87340	−0.276672
$197$	−27.8723	−1.98582	−0.992909	−	0.118876i	$-0.962071\pi$
$197$	−27.8723	−1.98582	−0.992909	+	0.118876i	$0.962071\pi$
$198$	−0.667540	−0.0474400
$199$	8.40766	0.596003	0.298002	−	0.954565i	$-0.403680\pi$
$199$	8.40766	0.596003	0.298002	+	0.954565i	$0.403680\pi$
$200$	−0.315025	−0.0222757
$201$	−22.4123	−1.58084
$202$	31.1835	2.19407
$203$	−0.219566	−0.0154105
$204$	−7.51088	−0.525866
$205$	4.73510	0.330714
$206$	4.40802	0.307121
$207$	0.0869615	0.00604425
$208$	−17.9783	−1.24657
$209$	−1.61498	−0.111711
$210$	1.52709	0.105379
$211$	15.0363	1.03514	0.517571	−	0.855640i	$-0.326836\pi$
$211$	15.0363	1.03514	0.517571	+	0.855640i	$0.326836\pi$
$212$	−1.45995	−0.100270
$213$	−2.08274	−0.142707
$214$	29.2952	2.00258
$215$	−21.2927	−1.45215
$216$	−11.0124	−0.749300
$217$	0.912358	0.0619349
$218$	17.3789	1.17705
$219$	−27.5362	−1.86072
$220$	−1.22994	−0.0829223
$221$	−27.2611	−1.83378
$222$	−10.0786	−0.676434
$223$	6.39528	0.428260	0.214130	−	0.976805i	$-0.431308\pi$
$223$	6.39528	0.428260	0.214130	+	0.976805i	$0.431308\pi$
$224$	0.719126	0.0480486
$225$	−0.0570058	−0.00380039
$226$	19.6585	1.30767
$227$	−9.10099	−0.604054	−0.302027	−	0.953299i	$-0.597663\pi$
$227$	−9.10099	−0.604054	−0.302027	+	0.953299i	$0.597663\pi$
$228$	−1.66505	−0.110271
$229$	11.5425	0.762748	0.381374	−	0.924421i	$-0.375451\pi$
$229$	11.5425	0.762748	0.381374	+	0.924421i	$0.375451\pi$
$230$	0.734807	0.0484517
$231$	0.432981	0.0284880
$232$	−2.16233	−0.141964
$233$	−5.35721	−0.350962	−0.175481	−	0.984483i	$-0.556148\pi$
$233$	−5.35721	−0.350962	−0.175481	+	0.984483i	$0.556148\pi$
$234$	−2.49798	−0.163298
$235$	2.57605	0.168043
$236$	−0.654584	−0.0426098
$237$	−2.21032	−0.143576
$238$	2.72884	0.176884
$239$	20.4541	1.32306	0.661532	−	0.749917i	$-0.269907\pi$
$239$	20.4541	1.32306	0.661532	+	0.749917i	$0.269907\pi$
$240$	19.5865	1.26430
$241$	−10.8743	−0.700476	−0.350238	−	0.936661i	$-0.613899\pi$
$241$	−10.8743	−0.700476	−0.350238	+	0.936661i	$0.613899\pi$
$242$	−1.59929	−0.102806
$243$	−4.30760	−0.276333
$244$	−3.38504	−0.216705
$245$	15.3162	0.978519
$246$	6.34793	0.404729
$247$	−6.04338	−0.384531
$248$	8.98508	0.570553
$249$	−16.6911	−1.05776
$250$	−18.1163	−1.14578
$251$	9.40412	0.593583	0.296791	−	0.954942i	$-0.404083\pi$
$251$	9.40412	0.593583	0.296791	+	0.954942i	$0.404083\pi$
$252$	0.0545234	0.00343465
$253$	0.208342	0.0130983
$254$	1.79683	0.112743
$255$	29.6996	1.85986
$256$	12.4410	0.777565
$257$	16.2971	1.01658	0.508292	−	0.861185i	$-0.330277\pi$
$257$	16.2971	1.01658	0.508292	+	0.861185i	$0.330277\pi$
$258$	−28.5452	−1.77715
$259$	0.798451	0.0496134
$260$	−4.60251	−0.285435
$261$	−0.391286	−0.0242200
$262$	−1.59929	−0.0988042
$263$	1.24568	0.0768119	0.0384059	−	0.999262i	$-0.487772\pi$
$263$	1.24568	0.0768119	0.0384059	+	0.999262i	$0.487772\pi$
$264$	4.26408	0.262436
$265$	5.77294	0.354629
$266$	0.604943	0.0370914
$267$	11.5838	0.708918
$268$	−6.76162	−0.413032
$269$	10.5212	0.641489	0.320744	−	0.947166i	$-0.396067\pi$
$269$	10.5212	0.641489	0.320744	+	0.947166i	$0.396067\pi$
$270$	−16.8385	−1.02476
$271$	17.6254	1.07067	0.535334	−	0.844640i	$-0.320186\pi$
$271$	17.6254	1.07067	0.535334	+	0.844640i	$0.320186\pi$
$272$	35.0001	2.12219
$273$	1.62024	0.0980616
$274$	−24.0557	−1.45326
$275$	−0.136574	−0.00823572
$276$	0.214801	0.0129295
$277$	−32.9028	−1.97694	−0.988468	−	0.151427i	$-0.951613\pi$
$277$	−32.9028	−1.97694	−0.988468	+	0.151427i	$0.951613\pi$
$278$	−26.1854	−1.57050
$279$	1.62591	0.0973405
$280$	−1.19143	−0.0712017
$281$	24.0634	1.43550	0.717752	−	0.696298i	$-0.245171\pi$
$281$	24.0634	1.43550	0.717752	+	0.696298i	$0.245171\pi$
$282$	3.45347	0.205651
$283$	32.9569	1.95908	0.979542	−	0.201238i	$-0.0644965\pi$
$283$	32.9569	1.95908	0.979542	+	0.201238i	$0.0644965\pi$
$284$	−0.628346	−0.0372855
$285$	6.58396	0.390000
$286$	−5.98464	−0.353879
$287$	−0.502897	−0.0296851
$288$	1.28155	0.0755161
$289$	36.0716	2.12186
$290$	−3.30629	−0.194152
$291$	21.6049	1.26650
$292$	−8.30744	−0.486156
$293$	−26.7204	−1.56102	−0.780511	−	0.625143i	$-0.785041\pi$
$293$	−26.7204	−1.56102	−0.780511	+	0.625143i	$0.785041\pi$
$294$	20.5331	1.19752
$295$	2.58836	0.150700
$296$	7.86331	0.457045
$297$	−4.77425	−0.277030
$298$	23.5810	1.36601
$299$	0.779629	0.0450871
$300$	−0.140808	−0.00812956
$301$	2.26141	0.130346
$302$	−10.9767	−0.631635
$303$	−36.0452	−2.07074
$304$	7.75900	0.445009
$305$	13.3852	0.766433
$306$	4.86304	0.278002
$307$	19.3288	1.10315	0.551577	−	0.834124i	$-0.314026\pi$
$307$	19.3288	1.10315	0.551577	+	0.834124i	$0.314026\pi$
$308$	0.130627	0.00744315
$309$	−5.09525	−0.289859
$310$	13.7386	0.780299
$311$	−25.9887	−1.47369	−0.736843	−	0.676064i	$-0.763684\pi$
$311$	−25.9887	−1.47369	−0.736843	+	0.676064i	$0.763684\pi$
$312$	15.9565	0.903357
$313$	18.2195	1.02983	0.514914	−	0.857242i	$-0.327824\pi$
$313$	18.2195	1.02983	0.514914	+	0.857242i	$0.327824\pi$
$314$	26.5647	1.49913
$315$	−0.215597	−0.0121475
$316$	−0.666835	−0.0375124
$317$	−8.15749	−0.458171	−0.229085	−	0.973406i	$-0.573573\pi$
$317$	−8.15749	−0.458171	−0.229085	+	0.973406i	$0.573573\pi$
$318$	7.73926	0.433996
$319$	−0.937441	−0.0524866
$320$	−10.3615	−0.579228
$321$	−33.8624	−1.89001
$322$	−0.0780410	−0.00434905
$323$	11.7652	0.654633
$324$	−5.62063	−0.312257
$325$	−0.511069	−0.0283490
$326$	−33.3161	−1.84521
$327$	−20.0883	−1.11089
$328$	−4.95263	−0.273463
$329$	−0.273592	−0.0150836
$330$	6.51996	0.358912
$331$	−6.66395	−0.366284	−0.183142	−	0.983087i	$-0.558627\pi$
$331$	−6.66395	−0.366284	−0.183142	+	0.983087i	$0.558627\pi$
$332$	−5.03558	−0.276363
$333$	1.42291	0.0779753
$334$	12.4237	0.679793
$335$	26.7369	1.46079
$336$	−2.08020	−0.113484
$337$	26.1684	1.42549	0.712743	−	0.701425i	$-0.247453\pi$
$337$	26.1684	1.42549	0.712743	+	0.701425i	$0.247453\pi$
$338$	−1.60421	−0.0872573
$339$	−22.7234	−1.23417
$340$	8.96012	0.485931
$341$	3.89533	0.210944
$342$	1.07807	0.0582951
$343$	−3.26621	−0.176359
$344$	22.2708	1.20076
$345$	−0.849367	−0.0457284
$346$	−12.1529	−0.653345
$347$	8.45778	0.454038	0.227019	−	0.973890i	$-0.427102\pi$
$347$	8.45778	0.454038	0.227019	+	0.973890i	$0.427102\pi$
$348$	−0.966503	−0.0518100
$349$	−22.3643	−1.19713	−0.598567	−	0.801073i	$-0.704263\pi$
$349$	−22.3643	−1.19713	−0.598567	+	0.801073i	$0.704263\pi$
$350$	0.0511581	0.00273452
$351$	−17.8656	−0.953594
$352$	3.07033	0.163649
$353$	17.0355	0.906709	0.453354	−	0.891330i	$-0.350227\pi$
$353$	17.0355	0.906709	0.453354	+	0.891330i	$0.350227\pi$
$354$	3.46999	0.184428
$355$	2.48461	0.131869
$356$	3.49474	0.185221
$357$	−3.15428	−0.166942
$358$	−4.11114	−0.217281
$359$	−9.23321	−0.487310	−0.243655	−	0.969862i	$-0.578347\pi$
$359$	−9.23321	−0.487310	−0.243655	+	0.969862i	$0.578347\pi$
$360$	−2.12324	−0.111905
$361$	−16.3918	−0.862728
$362$	−2.11321	−0.111068
$363$	1.84862	0.0970274
$364$	0.488814	0.0256208
$365$	32.8494	1.71941
$366$	17.9443	0.937964
$367$	25.7557	1.34444	0.672219	−	0.740352i	$-0.265341\pi$
$367$	25.7557	1.34444	0.672219	+	0.740352i	$0.265341\pi$
$368$	−1.00095	−0.0521783
$369$	−0.896209	−0.0466548
$370$	12.0233	0.625064
$371$	−0.613121	−0.0318317
$372$	4.01609	0.208225
$373$	10.9799	0.568519	0.284260	−	0.958747i	$-0.408252\pi$
$373$	10.9799	0.568519	0.284260	+	0.958747i	$0.408252\pi$
$374$	11.6508	0.602450
$375$	20.9408	1.08138
$376$	−2.69439	−0.138952
$377$	−3.50797	−0.180669
$378$	1.78835	0.0919826
$379$	6.36290	0.326840	0.163420	−	0.986557i	$-0.447747\pi$
$379$	6.36290	0.326840	0.163420	+	0.986557i	$0.447747\pi$
$380$	1.98633	0.101896
$381$	−2.07696	−0.106406
$382$	20.8646	1.06753
$383$	16.8313	0.860039	0.430019	−	0.902820i	$-0.358507\pi$
$383$	16.8313	0.860039	0.430019	+	0.902820i	$0.358507\pi$
$384$	−25.2425	−1.28815
$385$	−0.516525	−0.0263246
$386$	25.5619	1.30107
$387$	4.03005	0.204859
$388$	6.51801	0.330902
$389$	12.5414	0.635875	0.317938	−	0.948112i	$-0.397010\pi$
$389$	12.5414	0.635875	0.317938	+	0.948112i	$0.397010\pi$
$390$	24.3981	1.23545
$391$	−1.51777	−0.0767572
$392$	−16.0199	−0.809125
$393$	1.84862	0.0932506
$394$	44.5757	2.24569
$395$	2.63681	0.132672
$396$	0.232789	0.0116981
$397$	12.5962	0.632183	0.316091	−	0.948729i	$-0.397629\pi$
$397$	12.5962	0.632183	0.316091	+	0.948729i	$0.397629\pi$
$398$	−13.4463	−0.674000
$399$	−0.699256	−0.0350066
$400$	0.656154	0.0328077
$401$	26.2865	1.31269	0.656343	−	0.754463i	$-0.272103\pi$
$401$	26.2865	1.31269	0.656343	+	0.754463i	$0.272103\pi$
$402$	35.8437	1.78772
$403$	14.5766	0.726112
$404$	−10.8745	−0.541029
$405$	22.2251	1.10438
$406$	0.351148	0.0174272
$407$	3.40901	0.168978
$408$	−31.0639	−1.53789
$409$	−15.7116	−0.776889	−0.388444	−	0.921472i	$-0.626987\pi$
$409$	−15.7116	−0.776889	−0.388444	+	0.921472i	$0.626987\pi$
$410$	−7.57278	−0.373993
$411$	27.8061	1.37157
$412$	−1.53720	−0.0757322
$413$	−0.274900	−0.0135269
$414$	−0.139076	−0.00683523
$415$	19.9117	0.977428
$416$	11.4894	0.563313
$417$	30.2679	1.48222
$418$	2.58282	0.126330
$419$	−2.99410	−0.146271	−0.0731356	−	0.997322i	$-0.523301\pi$
$419$	−2.99410	−0.146271	−0.0731356	+	0.997322i	$0.523301\pi$
$420$	−0.532539	−0.0259852
$421$	−12.7524	−0.621513	−0.310756	−	0.950490i	$-0.600582\pi$
$421$	−12.7524	−0.621513	−0.310756	+	0.950490i	$0.600582\pi$
$422$	−24.0473	−1.17061
$423$	−0.487566	−0.0237063
$424$	−6.03814	−0.293238
$425$	0.994945	0.0482619
$426$	3.33090	0.161382
$427$	−1.42159	−0.0687954
$428$	−10.2160	−0.493810
$429$	6.91767	0.333988
$430$	34.0531	1.64218
$431$	25.2345	1.21550	0.607752	−	0.794127i	$-0.292072\pi$
$431$	25.2345	1.21550	0.607752	+	0.794127i	$0.292072\pi$
$432$	22.9373	1.10357
$433$	24.8611	1.19475	0.597375	−	0.801962i	$-0.296210\pi$
$433$	24.8611	1.19475	0.597375	+	0.801962i	$0.296210\pi$
$434$	−1.45912	−0.0700400
$435$	3.82175	0.183239
$436$	−6.06049	−0.290245
$437$	−0.336468	−0.0160955
$438$	44.0382	2.10423
$439$	−16.5041	−0.787700	−0.393850	−	0.919175i	$-0.628857\pi$
$439$	−16.5041	−0.787700	−0.393850	+	0.919175i	$0.628857\pi$
$440$	−5.08685	−0.242506
$441$	−2.89889	−0.138043
$442$	43.5982	2.07376
$443$	−17.4844	−0.830710	−0.415355	−	0.909659i	$-0.636343\pi$
$443$	−17.4844	−0.830710	−0.415355	+	0.909659i	$0.636343\pi$
$444$	3.51469	0.166800
$445$	−13.8189	−0.655081
$446$	−10.2279	−0.484304
$447$	−27.2573	−1.28923
$448$	1.10046	0.0519918
$449$	−23.9606	−1.13077	−0.565386	−	0.824827i	$-0.691273\pi$
$449$	−23.9606	−1.13077	−0.565386	+	0.824827i	$0.691273\pi$
$450$	0.0911686	0.00429773
$451$	−2.14713	−0.101104
$452$	−6.85546	−0.322454
$453$	12.6880	0.596132
$454$	14.5551	0.683104
$455$	−1.93287	−0.0906145
$456$	−6.88641	−0.322486
$457$	−27.7204	−1.29671	−0.648353	−	0.761340i	$-0.724542\pi$
$457$	−27.7204	−1.29671	−0.648353	+	0.761340i	$0.724542\pi$
$458$	−18.4597	−0.862565
$459$	34.7805	1.62342
$460$	−0.256247	−0.0119476
$461$	−20.3346	−0.947075	−0.473537	−	0.880774i	$-0.657023\pi$
$461$	−20.3346	−0.947075	−0.473537	+	0.880774i	$0.657023\pi$
$462$	−0.692460	−0.0322161
$463$	−2.96799	−0.137934	−0.0689670	−	0.997619i	$-0.521970\pi$
$463$	−2.96799	−0.137934	−0.0689670	+	0.997619i	$0.521970\pi$
$464$	4.50382	0.209085
$465$	−15.8805	−0.736439
$466$	8.56771	0.396891
$467$	5.78888	0.267877	0.133939	−	0.990990i	$-0.457237\pi$
$467$	5.78888	0.267877	0.133939	+	0.990990i	$0.457237\pi$
$468$	0.871113	0.0402672
$469$	−2.83962	−0.131121
$470$	−4.11983	−0.190034
$471$	−30.7063	−1.41487
$472$	−2.70727	−0.124612
$473$	9.65515	0.443944
$474$	3.53493	0.162365
$475$	0.220565	0.0101202
$476$	−0.951619	−0.0436174
$477$	−1.09264	−0.0500285
$478$	−32.7119	−1.49621
$479$	−32.3712	−1.47908	−0.739540	−	0.673113i	$-0.764957\pi$
$479$	−32.3712	−1.47908	−0.739540	+	0.673113i	$0.764957\pi$
$480$	−12.5171	−0.571324
$481$	12.7567	0.581657
$482$	17.3911	0.792144
$483$	0.0902079	0.00410460
$484$	0.557714	0.0253506
$485$	−25.7736	−1.17032
$486$	6.88908	0.312495
$487$	−26.0442	−1.18017	−0.590087	−	0.807340i	$-0.700907\pi$
$487$	−26.0442	−1.18017	−0.590087	+	0.807340i	$0.700907\pi$
$488$	−14.0001	−0.633753
$489$	38.5102	1.74149
$490$	−24.4950	−1.10657
$491$	13.5492	0.611467	0.305733	−	0.952117i	$-0.401098\pi$
$491$	13.5492	0.611467	0.305733	+	0.952117i	$0.401098\pi$
$492$	−2.21369	−0.0998010
$493$	6.82928	0.307575
$494$	9.66508	0.434853
$495$	−0.920497	−0.0413732
$496$	−18.7147	−0.840314
$497$	−0.263881	−0.0118367
$498$	26.6939	1.19618
$499$	5.34450	0.239253	0.119626	−	0.992819i	$-0.461830\pi$
$499$	5.34450	0.239253	0.119626	+	0.992819i	$0.461830\pi$
$500$	6.31766	0.282534
$501$	−14.3606	−0.641583
$502$	−15.0399	−0.671263
$503$	12.0452	0.537067	0.268534	−	0.963270i	$-0.413461\pi$
$503$	12.0452	0.537067	0.268534	+	0.963270i	$0.413461\pi$
$504$	0.225501	0.0100446
$505$	43.0002	1.91348
$506$	−0.333198	−0.0148125
$507$	1.85431	0.0823527
$508$	−0.626602	−0.0278010
$509$	16.6574	0.738328	0.369164	−	0.929364i	$-0.379644\pi$
$509$	16.6574	0.738328	0.369164	+	0.929364i	$0.379644\pi$
$510$	−47.4981	−2.10325
$511$	−3.48880	−0.154336
$512$	7.41282	0.327603
$513$	7.71033	0.340420
$514$	−26.0637	−1.14962
$515$	6.07839	0.267846
$516$	9.95448	0.438221
$517$	−1.16811	−0.0513733
$518$	−1.27695	−0.0561060
$519$	14.0476	0.616622
$520$	−19.0353	−0.834754
$521$	17.5042	0.766875	0.383437	−	0.923567i	$-0.374740\pi$
$521$	17.5042	0.766875	0.383437	+	0.923567i	$0.374740\pi$
$522$	0.625779	0.0273896
$523$	14.1904	0.620504	0.310252	−	0.950654i	$-0.399587\pi$
$523$	14.1904	0.620504	0.310252	+	0.950654i	$0.399587\pi$
$524$	0.557714	0.0243638
$525$	−0.0591339	−0.00258081
$526$	−1.99220	−0.0868639
$527$	−28.3776	−1.23615
$528$	−8.88148	−0.386517
$529$	−22.9566	−0.998113
$530$	−9.23257	−0.401037
$531$	−0.489897	−0.0212597
$532$	−0.210960	−0.00914627
$533$	−8.03470	−0.348022
$534$	−18.5258	−0.801691
$535$	40.3963	1.74648
$536$	−27.9651	−1.20791
$537$	4.75208	0.205068
$538$	−16.8264	−0.725437
$539$	−6.94514	−0.299148
$540$	5.87202	0.252692
$541$	−5.07724	−0.218288	−0.109144	−	0.994026i	$-0.534811\pi$
$541$	−5.07724	−0.218288	−0.109144	+	0.994026i	$0.534811\pi$
$542$	−28.1881	−1.21078
$543$	2.44267	0.104825
$544$	−22.3674	−0.958995
$545$	23.9644	1.02652
$546$	−2.59123	−0.110894
$547$	−18.6987	−0.799500	−0.399750	−	0.916624i	$-0.630903\pi$
$547$	−18.6987	−0.799500	−0.399750	+	0.916624i	$0.630903\pi$
$548$	8.38888	0.358355
$549$	−2.53340	−0.108123
$550$	0.218421	0.00931350
$551$	1.51395	0.0644965
$552$	0.888385	0.0378122
$553$	−0.280045	−0.0119087
$554$	52.6209	2.23565
$555$	−13.8978	−0.589930
$556$	9.13157	0.387265
$557$	12.0646	0.511192	0.255596	−	0.966784i	$-0.417728\pi$
$557$	12.0646	0.511192	0.255596	+	0.966784i	$0.417728\pi$
$558$	−2.60029	−0.110079
$559$	36.1302	1.52815
$560$	2.48159	0.104866
$561$	−13.4673	−0.568588
$562$	−38.4843	−1.62336
$563$	−16.5806	−0.698788	−0.349394	−	0.936976i	$-0.613612\pi$
$563$	−16.5806	−0.698788	−0.349394	+	0.936976i	$0.613612\pi$
$564$	−1.20432	−0.0507110
$565$	27.1079	1.14044
$566$	−52.7075	−2.21546
$567$	−2.36044	−0.0991294
$568$	−2.59875	−0.109041
$569$	14.0871	0.590560	0.295280	−	0.955411i	$-0.404587\pi$
$569$	14.0871	0.590560	0.295280	+	0.955411i	$0.404587\pi$
$570$	−10.5296	−0.441037
$571$	10.7337	0.449191	0.224595	−	0.974452i	$-0.427894\pi$
$571$	10.7337	0.449191	0.224595	+	0.974452i	$0.427894\pi$
$572$	2.08700	0.0872620
$573$	−24.1175	−1.00752
$574$	0.804275	0.0335698
$575$	−0.0284541	−0.00118662
$576$	1.96112	0.0817134
$577$	−14.4604	−0.601995	−0.300998	−	0.953625i	$-0.597320\pi$
$577$	−14.4604	−0.601995	−0.300998	+	0.953625i	$0.597320\pi$
$578$	−57.6888	−2.39954
$579$	−29.5471	−1.22794
$580$	1.15299	0.0478754
$581$	−2.11475	−0.0877344
$582$	−34.5523	−1.43224
$583$	−2.61773	−0.108415
$584$	−34.3584	−1.42176
$585$	−3.44456	−0.142415
$586$	42.7335	1.76531
$587$	−13.9698	−0.576596	−0.288298	−	0.957541i	$-0.593089\pi$
$587$	−13.9698	−0.576596	−0.288298	+	0.957541i	$0.593089\pi$
$588$	−7.16045	−0.295292
$589$	−6.29090	−0.259212
$590$	−4.13953	−0.170422
$591$	−51.5253	−2.11947
$592$	−16.3782	−0.673139
$593$	−9.14595	−0.375579	−0.187789	−	0.982209i	$-0.560132\pi$
$593$	−9.14595	−0.375579	−0.187789	+	0.982209i	$0.560132\pi$
$594$	7.63539	0.313284
$595$	3.76290	0.154264
$596$	−8.22332	−0.336840
$597$	15.5426	0.636115
$598$	−1.24685	−0.0509875
$599$	−10.6978	−0.437102	−0.218551	−	0.975826i	$-0.570133\pi$
$599$	−10.6978	−0.437102	−0.218551	+	0.975826i	$0.570133\pi$
$600$	−0.582362	−0.0237748
$601$	−35.7633	−1.45881	−0.729407	−	0.684080i	$-0.760204\pi$
$601$	−35.7633	−1.45881	−0.729407	+	0.684080i	$0.760204\pi$
$602$	−3.61664	−0.147403
$603$	−5.06046	−0.206078
$604$	3.82785	0.155753
$605$	−2.20532	−0.0896589
$606$	57.6466	2.34173
$607$	36.4486	1.47940	0.739702	−	0.672934i	$-0.234966\pi$
$607$	36.4486	1.47940	0.739702	+	0.672934i	$0.234966\pi$
$608$	−4.95852	−0.201095
$609$	−0.405894	−0.0164476
$610$	−21.4067	−0.866732
$611$	−4.37113	−0.176837
$612$	−1.69587	−0.0685517
$613$	37.5077	1.51492	0.757462	−	0.652879i	$-0.226439\pi$
$613$	37.5077	1.51492	0.757462	+	0.652879i	$0.226439\pi$
$614$	−30.9123	−1.24752
$615$	8.75341	0.352971
$616$	0.540254	0.0217675
$617$	20.0790	0.808351	0.404176	−	0.914681i	$-0.367558\pi$
$617$	20.0790	0.808351	0.404176	+	0.914681i	$0.367558\pi$
$618$	8.14876	0.327791
$619$	−22.4563	−0.902594	−0.451297	−	0.892374i	$-0.649038\pi$
$619$	−22.4563	−0.902594	−0.451297	+	0.892374i	$0.649038\pi$
$620$	−4.79101	−0.192412
$621$	−0.994675	−0.0399149
$622$	41.5634	1.66654
$623$	1.46766	0.0588004
$624$	−33.2351	−1.33047
$625$	−24.2985	−0.971939
$626$	−29.1382	−1.16460
$627$	−2.98549	−0.119229
$628$	−9.26384	−0.369668
$629$	−24.8347	−0.990225
$630$	0.344801	0.0137372
$631$	−36.2292	−1.44226	−0.721130	−	0.692800i	$-0.756377\pi$
$631$	−36.2292	−1.44226	−0.721130	+	0.692800i	$0.756377\pi$
$632$	−2.75794	−0.109705
$633$	27.7964	1.10481
$634$	13.0462	0.518129
$635$	2.47772	0.0983251
$636$	−2.69889	−0.107018
$637$	−25.9892	−1.02973
$638$	1.49924	0.0593553
$639$	−0.470260	−0.0186032
$640$	30.1132	1.19033
$641$	−32.9693	−1.30221	−0.651105	−	0.758988i	$-0.725694\pi$
$641$	−32.9693	−1.30221	−0.651105	+	0.758988i	$0.725694\pi$
$642$	54.1556	2.13735
$643$	−1.63334	−0.0644126	−0.0322063	−	0.999481i	$-0.510253\pi$
$643$	−1.63334	−0.0644126	−0.0322063	+	0.999481i	$0.510253\pi$
$644$	0.0272150	0.00107242
$645$	−39.3621	−1.54988
$646$	−18.8159	−0.740302
$647$	45.5089	1.78914	0.894571	−	0.446926i	$-0.147481\pi$
$647$	45.5089	1.78914	0.894571	+	0.446926i	$0.147481\pi$
$648$	−23.2461	−0.913194
$649$	−1.17369	−0.0460714
$650$	0.817346	0.0320589
$651$	1.68660	0.0661032
$652$	11.6182	0.455004
$653$	3.21862	0.125954	0.0629772	−	0.998015i	$-0.479940\pi$
$653$	3.21862	0.125954	0.0629772	+	0.998015i	$0.479940\pi$
$654$	32.1270	1.25626
$655$	−2.20532	−0.0861689
$656$	10.3156	0.402758
$657$	−6.21737	−0.242563
$658$	0.437551	0.0170575
$659$	−7.17949	−0.279673	−0.139837	−	0.990175i	$-0.544658\pi$
$659$	−7.17949	−0.279673	−0.139837	+	0.990175i	$0.544658\pi$
$660$	−2.27369	−0.0885031
$661$	38.3063	1.48994	0.744972	−	0.667096i	$-0.232463\pi$
$661$	38.3063	1.48994	0.744972	+	0.667096i	$0.232463\pi$
$662$	10.6576	0.414218
$663$	−50.3954	−1.95719
$664$	−20.8264	−0.808222
$665$	0.834180	0.0323481
$666$	−2.27565	−0.0881795
$667$	−0.195308	−0.00756235
$668$	−4.33247	−0.167628
$669$	11.8224	0.457082
$670$	−42.7599	−1.65196
$671$	−6.06950	−0.234310
$672$	1.32939	0.0512824
$673$	16.2289	0.625579	0.312790	−	0.949822i	$-0.398737\pi$
$673$	16.2289	0.625579	0.312790	+	0.949822i	$0.398737\pi$
$674$	−41.8508	−1.61203
$675$	0.652039	0.0250970
$676$	0.559430	0.0215165
$677$	−17.9016	−0.688013	−0.344007	−	0.938967i	$-0.611784\pi$
$677$	−17.9016	−0.688013	−0.344007	+	0.938967i	$0.611784\pi$
$678$	36.3412	1.39567
$679$	2.73731	0.105048
$680$	37.0578	1.42110
$681$	−16.8243	−0.644708
$682$	−6.22975	−0.238549
$683$	−21.2208	−0.811992	−0.405996	−	0.913875i	$-0.633075\pi$
$683$	−21.2208	−0.811992	−0.405996	+	0.913875i	$0.633075\pi$
$684$	−0.375950	−0.0143748
$685$	−33.1714	−1.26741
$686$	5.22360	0.199438
$687$	21.3376	0.814082
$688$	−46.3870	−1.76849
$689$	−9.79574	−0.373188
$690$	1.35838	0.0517126
$691$	15.6261	0.594446	0.297223	−	0.954808i	$-0.403940\pi$
$691$	15.6261	0.594446	0.297223	+	0.954808i	$0.403940\pi$
$692$	4.23805	0.161107
$693$	0.0977624	0.00371368
$694$	−13.5264	−0.513455
$695$	−36.1081	−1.36966
$696$	−3.99732	−0.151518
$697$	15.6419	0.592479
$698$	35.7669	1.35380
$699$	−9.90345	−0.374583
$700$	−0.0178402	−0.000674297 0
$701$	36.5487	1.38043	0.690213	−	0.723607i	$-0.257517\pi$
$701$	36.5487	1.38043	0.690213	+	0.723607i	$0.257517\pi$
$702$	28.5721	1.07839
$703$	−5.50549	−0.207643
$704$	4.69844	0.177079
$705$	4.76213	0.179352
$706$	−27.2447	−1.02537
$707$	−4.56689	−0.171755
$708$	−1.21008	−0.0454775
$709$	−37.8978	−1.42328	−0.711641	−	0.702543i	$-0.752048\pi$
$709$	−37.8978	−1.42328	−0.711641	+	0.702543i	$0.752048\pi$
$710$	−3.97360	−0.149127
$711$	−0.499066	−0.0187164
$712$	14.4538	0.541678
$713$	0.811560	0.0303932
$714$	5.04459	0.188789
$715$	−8.25245	−0.308624
$716$	1.43367	0.0535786
$717$	37.8118	1.41211
$718$	14.7665	0.551083
$719$	21.2845	0.793780	0.396890	−	0.917866i	$-0.370090\pi$
$719$	21.2845	0.793780	0.396890	+	0.917866i	$0.370090\pi$
$720$	4.42242	0.164814
$721$	−0.645562	−0.0240420
$722$	26.2152	0.975629
$723$	−20.1025	−0.747619
$724$	0.736935	0.0273880
$725$	0.128030	0.00475492
$726$	−2.95647	−0.109725
$727$	−6.14470	−0.227894	−0.113947	−	0.993487i	$-0.536349\pi$
$727$	−6.14470	−0.227894	−0.113947	+	0.993487i	$0.536349\pi$
$728$	2.02167	0.0749280
$729$	22.2708	0.824845
$730$	−52.5355	−1.94443
$731$	−70.3380	−2.60155
$732$	−6.25766	−0.231290
$733$	−16.7286	−0.617886	−0.308943	−	0.951081i	$-0.599975\pi$
$733$	−16.7286	−0.617886	−0.308943	+	0.951081i	$0.599975\pi$
$734$	−41.1908	−1.52038
$735$	28.3139	1.04437
$736$	0.639677	0.0235788
$737$	−12.1238	−0.446586
$738$	1.43329	0.0527603
$739$	−15.1404	−0.556948	−0.278474	−	0.960444i	$-0.589829\pi$
$739$	−15.1404	−0.556948	−0.278474	+	0.960444i	$0.589829\pi$
$740$	−4.19286	−0.154133
$741$	−11.1719	−0.410410
$742$	0.980556	0.0359973
$743$	38.0217	1.39488	0.697440	−	0.716643i	$-0.254323\pi$
$743$	38.0217	1.39488	0.697440	+	0.716643i	$0.254323\pi$
$744$	16.6100	0.608952
$745$	32.5167	1.19132
$746$	−17.5600	−0.642919
$747$	−3.76867	−0.137889
$748$	−4.06296	−0.148557
$749$	−4.29033	−0.156765
$750$	−33.4903	−1.22289
$751$	−26.8157	−0.978520	−0.489260	−	0.872138i	$-0.662733\pi$
$751$	−26.8157	−0.978520	−0.489260	+	0.872138i	$0.662733\pi$
$752$	5.61203	0.204650
$753$	17.3847	0.633532
$754$	5.61024	0.204313
$755$	−15.1361	−0.550860
$756$	−0.623645	−0.0226817
$757$	19.1975	0.697746	0.348873	−	0.937170i	$-0.386564\pi$
$757$	19.1975	0.697746	0.348873	+	0.937170i	$0.386564\pi$
$758$	−10.1761	−0.369612
$759$	0.385145	0.0139799
$760$	8.21517	0.297995
$761$	−47.2006	−1.71102	−0.855509	−	0.517787i	$-0.826756\pi$
$761$	−47.2006	−1.71102	−0.855509	+	0.517787i	$0.826756\pi$
$762$	3.32165	0.120331
$763$	−2.54517	−0.0921413
$764$	−7.27606	−0.263239
$765$	6.70584	0.242450
$766$	−26.9180	−0.972588
$767$	−4.39203	−0.158587
$768$	22.9988	0.829896
$769$	28.4601	1.02630	0.513149	−	0.858300i	$-0.328479\pi$
$769$	28.4601	1.02630	0.513149	+	0.858300i	$0.328479\pi$
$770$	0.826072	0.0297696
$771$	30.1271	1.08500
$772$	−8.91413	−0.320827
$773$	−8.63939	−0.310737	−0.155369	−	0.987857i	$-0.549657\pi$
$773$	−8.63939	−0.310737	−0.155369	+	0.987857i	$0.549657\pi$
$774$	−6.44520	−0.231668
$775$	−0.532001	−0.0191100
$776$	26.9576	0.967721
$777$	1.47603	0.0529524
$778$	−20.0573	−0.719090
$779$	3.46758	0.124239
$780$	−8.50829	−0.304646
$781$	−1.12665	−0.0403145
$782$	2.42736	0.0868020
$783$	4.47558	0.159944
$784$	33.3671	1.19168
$785$	36.6312	1.30742
$786$	−2.95647	−0.105454
$787$	5.47256	0.195076	0.0975379	−	0.995232i	$-0.468903\pi$
$787$	5.47256	0.195076	0.0975379	+	0.995232i	$0.468903\pi$
$788$	−15.5448	−0.553759
$789$	2.30279	0.0819815
$790$	−4.21700	−0.150034
$791$	−2.87903	−0.102366
$792$	0.962783	0.0342110
$793$	−22.7125	−0.806544
$794$	−20.1448	−0.714914
$795$	10.6720	0.378496
$796$	4.68907	0.166200
$797$	2.19446	0.0777317	0.0388659	−	0.999244i	$-0.487625\pi$
$797$	2.19446	0.0777317	0.0388659	+	0.999244i	$0.487625\pi$
$798$	1.11831	0.0395878
$799$	8.50969	0.301051
$800$	−0.419327	−0.0148254
$801$	2.61550	0.0924142
$802$	−42.0396	−1.48447
$803$	−14.8955	−0.525652
$804$	−12.4997	−0.440829
$805$	−0.107614	−0.00379289
$806$	−23.3121	−0.821135
$807$	19.4497	0.684662
$808$	−44.9756	−1.58224
$809$	13.8096	0.485521	0.242761	−	0.970086i	$-0.421947\pi$
$809$	13.8096	0.485521	0.242761	+	0.970086i	$0.421947\pi$
$810$	−35.5443	−1.24890
$811$	19.5365	0.686020	0.343010	−	0.939332i	$-0.388554\pi$
$811$	19.5365	0.686020	0.343010	+	0.939332i	$0.388554\pi$
$812$	−0.122455	−0.00429732
$813$	32.5827	1.14273
$814$	−5.45198	−0.191092
$815$	−45.9408	−1.60924
$816$	64.7018	2.26502
$817$	−15.5929	−0.545527
$818$	25.1273	0.878557
$819$	0.365833	0.0127833
$820$	2.64083	0.0922219
$821$	−20.5186	−0.716103	−0.358052	−	0.933702i	$-0.616559\pi$
$821$	−20.5186	−0.716103	−0.358052	+	0.933702i	$0.616559\pi$
$822$	−44.4699	−1.55107
$823$	14.8301	0.516946	0.258473	−	0.966019i	$-0.416781\pi$
$823$	14.8301	0.516946	0.258473	+	0.966019i	$0.416781\pi$
$824$	−6.35763	−0.221478
$825$	−0.252474	−0.00879000
$826$	0.439643	0.0152971
$827$	7.60652	0.264505	0.132252	−	0.991216i	$-0.457779\pi$
$827$	7.60652	0.264505	0.132252	+	0.991216i	$0.457779\pi$
$828$	0.0484997	0.00168548
$829$	4.44401	0.154347	0.0771734	−	0.997018i	$-0.475410\pi$
$829$	4.44401	0.154347	0.0771734	+	0.997018i	$0.475410\pi$
$830$	−31.8445	−1.10534
$831$	−60.8248	−2.10999
$832$	17.5819	0.609542
$833$	50.5955	1.75303
$834$	−48.4069	−1.67620
$835$	17.1315	0.592859
$836$	−0.900699	−0.0311513
$837$	−18.5973	−0.642817
$838$	4.78842	0.165413
$839$	−13.0586	−0.450833	−0.225416	−	0.974263i	$-0.572374\pi$
$839$	−13.0586	−0.450833	−0.225416	+	0.974263i	$0.572374\pi$
$840$	−2.20251	−0.0759937
$841$	−28.1212	−0.969697
$842$	20.3947	0.702847
$843$	44.4842	1.53212
$844$	8.38596	0.288657
$845$	−2.21210	−0.0760987
$846$	0.779757	0.0268086
$847$	0.234218	0.00804783
$848$	12.5766	0.431882
$849$	60.9248	2.09093
$850$	−1.59120	−0.0545778
$851$	0.710238	0.0243467
$852$	−1.16157	−0.0397949
$853$	−11.7627	−0.402747	−0.201373	−	0.979515i	$-0.564540\pi$
$853$	−11.7627	−0.402747	−0.201373	+	0.979515i	$0.564540\pi$
$854$	2.27352	0.0777983
$855$	1.48659	0.0508402
$856$	−42.2520	−1.44414
$857$	54.1591	1.85004	0.925020	−	0.379918i	$-0.124048\pi$
$857$	54.1591	1.85004	0.925020	+	0.379918i	$0.124048\pi$
$858$	−11.0633	−0.377696
$859$	−31.1714	−1.06356	−0.531778	−	0.846884i	$-0.678476\pi$
$859$	−31.1714	−1.06356	−0.531778	+	0.846884i	$0.678476\pi$
$860$	−11.8752	−0.404942
$861$	−0.929665	−0.0316829
$862$	−40.3572	−1.37457
$863$	−43.9610	−1.49645	−0.748225	−	0.663445i	$-0.769094\pi$
$863$	−43.9610	−1.49645	−0.748225	+	0.663445i	$0.769094\pi$
$864$	−14.6585	−0.498692
$865$	−16.7581	−0.569794
$866$	−39.7601	−1.35110
$867$	66.6827	2.26466
$868$	0.508835	0.0172710
$869$	−1.19566	−0.0405599
$870$	−6.11208	−0.207219
$871$	−45.3681	−1.53724
$872$	−25.0653	−0.848819
$873$	4.87815	0.165100
$874$	0.538109	0.0182018
$875$	2.65317	0.0896936
$876$	−15.3573	−0.518875
$877$	−2.84084	−0.0959285	−0.0479642	−	0.998849i	$-0.515273\pi$
$877$	−2.84084	−0.0959285	−0.0479642	+	0.998849i	$0.515273\pi$
$878$	26.3948	0.890782
$879$	−49.3958	−1.66608
$880$	10.5952	0.357164
$881$	6.50127	0.219033	0.109517	−	0.993985i	$-0.465070\pi$
$881$	6.50127	0.219033	0.109517	+	0.993985i	$0.465070\pi$
$882$	4.63616	0.156108
$883$	38.5549	1.29748	0.648738	−	0.761012i	$-0.275297\pi$
$883$	38.5549	1.29748	0.648738	+	0.761012i	$0.275297\pi$
$884$	−15.2039	−0.511362
$885$	4.78490	0.160843
$886$	27.9626	0.939422
$887$	42.3939	1.42345	0.711724	−	0.702459i	$-0.247915\pi$
$887$	42.3939	1.42345	0.711724	+	0.702459i	$0.247915\pi$
$888$	14.5363	0.487805
$889$	−0.263148	−0.00882572
$890$	22.1004	0.740809
$891$	−10.0780	−0.337625
$892$	3.56674	0.119423
$893$	1.88647	0.0631284
$894$	43.5923	1.45794
$895$	−5.66901	−0.189494
$896$	−3.19820	−0.106844
$897$	1.44124	0.0481215
$898$	38.3199	1.27875
$899$	−3.65164	−0.121789
$900$	−0.0317929	−0.00105976
$901$	19.0703	0.635323
$902$	3.43387	0.114335
$903$	4.18049	0.139118
$904$	−28.3532	−0.943015
$905$	−2.91399	−0.0968644
$906$	−20.2917	−0.674146
$907$	−11.1644	−0.370707	−0.185353	−	0.982672i	$-0.559343\pi$
$907$	−11.1644	−0.370707	−0.185353	+	0.982672i	$0.559343\pi$
$908$	−5.07575	−0.168445
$909$	−8.13862	−0.269941
$910$	3.09122	0.102473
$911$	−11.2619	−0.373123	−0.186561	−	0.982443i	$-0.559734\pi$
$911$	−11.2619	−0.373123	−0.186561	+	0.982443i	$0.559734\pi$
$912$	14.3434	0.474959
$913$	−9.02896	−0.298815
$914$	44.3329	1.46640
$915$	24.7441	0.818015
$916$	6.43740	0.212698
$917$	0.234218	0.00773457
$918$	−55.6240	−1.83587
$919$	−59.0862	−1.94907	−0.974536	−	0.224231i	$-0.928013\pi$
$919$	−59.0862	−1.94907	−0.974536	+	0.224231i	$0.928013\pi$
$920$	−1.05980	−0.0349406
$921$	35.7316	1.17740
$922$	32.5208	1.07101
$923$	−4.21598	−0.138771
$924$	0.241479	0.00794409
$925$	−0.465582	−0.0153082
$926$	4.74666	0.155985
$927$	−1.15045	−0.0377858
$928$	−2.87825	−0.0944831
$929$	−4.83525	−0.158639	−0.0793197	−	0.996849i	$-0.525275\pi$
$929$	−4.83525	−0.158639	−0.0793197	+	0.996849i	$0.525275\pi$
$930$	25.3974	0.832814
$931$	11.2163	0.367599
$932$	−2.98779	−0.0978683
$933$	−48.0433	−1.57287
$934$	−9.25807	−0.302933
$935$	16.0658	0.525408
$936$	3.60280	0.117761
$937$	18.3014	0.597879	0.298940	−	0.954272i	$-0.403367\pi$
$937$	18.3014	0.597879	0.298940	+	0.954272i	$0.403367\pi$
$938$	4.54136	0.148281
$939$	33.6810	1.09914
$940$	1.43670	0.0468599
$941$	60.3459	1.96722	0.983611	−	0.180306i	$-0.0577089\pi$
$941$	60.3459	1.96722	0.983611	+	0.180306i	$0.0577089\pi$
$942$	49.1081	1.60003
$943$	−0.447336	−0.0145673
$944$	5.63886	0.183529
$945$	2.46602	0.0802197
$946$	−15.4413	−0.502041
$947$	5.82608	0.189322	0.0946612	−	0.995510i	$-0.469823\pi$
$947$	5.82608	0.189322	0.0946612	+	0.995510i	$0.469823\pi$
$948$	−1.23273	−0.0400371
$949$	−55.7401	−1.80940
$950$	−0.352746	−0.0114446
$951$	−15.0801	−0.489006
$952$	−3.93576	−0.127559
$953$	11.7563	0.380824	0.190412	−	0.981704i	$-0.439018\pi$
$953$	11.7563	0.380824	0.190412	+	0.981704i	$0.439018\pi$
$954$	1.74744	0.0565755
$955$	28.7711	0.931010
$956$	11.4075	0.368945
$957$	−1.73297	−0.0560190
$958$	51.7708	1.67264
$959$	3.52300	0.113764
$960$	−19.1546	−0.618211
$961$	−15.8264	−0.510528
$962$	−20.4017	−0.657776
$963$	−7.64577	−0.246381
$964$	−6.06475	−0.195333
$965$	35.2484	1.13468
$966$	−0.144268	−0.00464175
$967$	27.7851	0.893509	0.446754	−	0.894657i	$-0.352580\pi$
$967$	27.7851	0.893509	0.446754	+	0.894657i	$0.352580\pi$
$968$	2.30663	0.0741378
$969$	21.7494	0.698691
$970$	41.2193	1.32347
$971$	49.8306	1.59914	0.799569	−	0.600574i	$-0.205061\pi$
$971$	49.8306	1.59914	0.799569	+	0.600574i	$0.205061\pi$
$972$	−2.40241	−0.0770573
$973$	3.83490	0.122941
$974$	41.6521	1.33462
$975$	−0.944773	−0.0302570
$976$	29.1602	0.933395
$977$	42.8213	1.36998	0.684988	−	0.728554i	$-0.259807\pi$
$977$	42.8213	1.36998	0.684988	+	0.728554i	$0.259807\pi$
$978$	−61.5888	−1.96939
$979$	6.26619	0.200268
$980$	8.54208	0.272867
$981$	−4.53573	−0.144815
$982$	−21.6690	−0.691487
$983$	−20.5376	−0.655048	−0.327524	−	0.944843i	$-0.606214\pi$
$983$	−20.5376	−0.655048	−0.327524	+	0.944843i	$0.606214\pi$
$984$	−9.15553	−0.291868
$985$	61.4672	1.95851
$986$	−10.9220	−0.347826
$987$	−0.505767	−0.0160988
$988$	−3.37048	−0.107229
$989$	2.01157	0.0639642
$990$	1.47214	0.0467876
$991$	−41.6727	−1.32378	−0.661888	−	0.749603i	$-0.730244\pi$
$991$	−41.6727	−1.32378	−0.661888	+	0.749603i	$0.730244\pi$
$992$	11.9599	0.379729
$993$	−12.3191	−0.390935
$994$	0.422021	0.0133857
$995$	−18.5416	−0.587807
$996$	−9.30887	−0.294963
$997$	11.7953	0.373562	0.186781	−	0.982402i	$-0.440195\pi$
$997$	11.7953	0.373562	0.186781	+	0.982402i	$0.440195\pi$
$998$	−8.54739	−0.270563
$999$	−16.2755	−0.514933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.7	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.7	✓	23	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.59929 q^{2} +1.84862 q^{3} +0.557714 q^{4} -2.20532 q^{5} -2.95647 q^{6} +0.234218 q^{7} +2.30663 q^{8} +0.417399 q^{9} +O(q^{10})\)	\(q-1.59929 q^{2} +1.84862 q^{3} +0.557714 q^{4} -2.20532 q^{5} -2.95647 q^{6} +0.234218 q^{7} +2.30663 q^{8} +0.417399 q^{9} +3.52693 q^{10} +1.00000 q^{11} +1.03100 q^{12} +3.74207 q^{13} -0.374582 q^{14} -4.07680 q^{15} -4.80438 q^{16} -7.28503 q^{17} -0.667540 q^{18} -1.61498 q^{19} -1.22994 q^{20} +0.432981 q^{21} -1.59929 q^{22} +0.208342 q^{23} +4.26408 q^{24} -0.136574 q^{25} -5.98464 q^{26} -4.77425 q^{27} +0.130627 q^{28} -0.937441 q^{29} +6.51996 q^{30} +3.89533 q^{31} +3.07033 q^{32} +1.84862 q^{33} +11.6508 q^{34} -0.516525 q^{35} +0.232789 q^{36} +3.40901 q^{37} +2.58282 q^{38} +6.91767 q^{39} -5.08685 q^{40} -2.14713 q^{41} -0.692460 q^{42} +9.65515 q^{43} +0.557714 q^{44} -0.920497 q^{45} -0.333198 q^{46} -1.16811 q^{47} -8.88148 q^{48} -6.94514 q^{49} +0.218421 q^{50} -13.4673 q^{51} +2.08700 q^{52} -2.61773 q^{53} +7.63539 q^{54} -2.20532 q^{55} +0.540254 q^{56} -2.98549 q^{57} +1.49924 q^{58} -1.17369 q^{59} -2.27369 q^{60} -6.06950 q^{61} -6.22975 q^{62} +0.0977624 q^{63} +4.69844 q^{64} -8.25245 q^{65} -2.95647 q^{66} -12.1238 q^{67} -4.06296 q^{68} +0.385145 q^{69} +0.826072 q^{70} -1.12665 q^{71} +0.962783 q^{72} -14.8955 q^{73} -5.45198 q^{74} -0.252474 q^{75} -0.900699 q^{76} +0.234218 q^{77} -11.0633 q^{78} -1.19566 q^{79} +10.5952 q^{80} -10.0780 q^{81} +3.43387 q^{82} -9.02896 q^{83} +0.241479 q^{84} +16.0658 q^{85} -15.4413 q^{86} -1.73297 q^{87} +2.30663 q^{88} +6.26619 q^{89} +1.47214 q^{90} +0.876460 q^{91} +0.116195 q^{92} +7.20099 q^{93} +1.86814 q^{94} +3.56155 q^{95} +5.67587 q^{96} +11.6870 q^{97} +11.1073 q^{98} +0.417399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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