LMFDB - Embedded newform 2031.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2031,2,Mod(1,2031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2031, 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("2031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2031 = 3 \cdot 677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2031.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:	$16.2176166505$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.82570 q^{2} -1.00000 q^{3} +1.33320 q^{4} +0.0890738 q^{5} +1.82570 q^{6} -3.61025 q^{7} +1.21739 q^{8} +1.00000 q^{9} -0.162622 q^{10} -5.09197 q^{11} -1.33320 q^{12} -3.12793 q^{13} +6.59125 q^{14} -0.0890738 q^{15} -4.88898 q^{16} -5.37516 q^{17} -1.82570 q^{18} +1.56815 q^{19} +0.118753 q^{20} +3.61025 q^{21} +9.29643 q^{22} -6.71613 q^{23} -1.21739 q^{24} -4.99207 q^{25} +5.71068 q^{26} -1.00000 q^{27} -4.81317 q^{28} +8.19556 q^{29} +0.162622 q^{30} +0.829377 q^{31} +6.49106 q^{32} +5.09197 q^{33} +9.81346 q^{34} -0.321579 q^{35} +1.33320 q^{36} +6.20131 q^{37} -2.86298 q^{38} +3.12793 q^{39} +0.108437 q^{40} -5.39696 q^{41} -6.59125 q^{42} -11.8355 q^{43} -6.78859 q^{44} +0.0890738 q^{45} +12.2617 q^{46} -3.72341 q^{47} +4.88898 q^{48} +6.03390 q^{49} +9.11404 q^{50} +5.37516 q^{51} -4.17015 q^{52} -11.5351 q^{53} +1.82570 q^{54} -0.453561 q^{55} -4.39507 q^{56} -1.56815 q^{57} -14.9627 q^{58} -2.47221 q^{59} -0.118753 q^{60} -1.01584 q^{61} -1.51420 q^{62} -3.61025 q^{63} -2.07280 q^{64} -0.278617 q^{65} -9.29643 q^{66} -3.00605 q^{67} -7.16615 q^{68} +6.71613 q^{69} +0.587108 q^{70} -4.34378 q^{71} +1.21739 q^{72} +15.8543 q^{73} -11.3218 q^{74} +4.99207 q^{75} +2.09065 q^{76} +18.3833 q^{77} -5.71068 q^{78} +10.1986 q^{79} -0.435480 q^{80} +1.00000 q^{81} +9.85326 q^{82} -4.82690 q^{83} +4.81317 q^{84} -0.478786 q^{85} +21.6081 q^{86} -8.19556 q^{87} -6.19889 q^{88} -9.78253 q^{89} -0.162622 q^{90} +11.2926 q^{91} -8.95392 q^{92} -0.829377 q^{93} +6.79785 q^{94} +0.139681 q^{95} -6.49106 q^{96} +3.26995 q^{97} -11.0161 q^{98} -5.09197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 3 q^{2} - 38 q^{3} + 49 q^{4} + 3 q^{5} + 3 q^{6} + 7 q^{7} - 12 q^{8} + 38 q^{9} + 14 q^{10} - 12 q^{11} - 49 q^{12} + 24 q^{13} + q^{14} - 3 q^{15} + 71 q^{16} + 12 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 38 * q - 3 * q^2 - 38 * q^3 + 49 * q^4 + 3 * q^5 + 3 * q^6 + 7 * q^7 - 12 * q^8 + 38 * q^9 + 14 * q^10 - 12 * q^11 - 49 * q^12 + 24 * q^13 + q^14 - 3 * q^15 + 71 * q^16 + 12 * q^17 - 3 * q^18 + 16 * q^19 + 6 * q^20 - 7 * q^21 + 20 * q^22 - 35 * q^23 + 12 * q^24 + 85 * q^25 + 33 * q^26 - 38 * q^27 + 23 * q^28 + 13 * q^29 - 14 * q^30 + 27 * q^31 - 22 * q^32 + 12 * q^33 + 45 * q^34 - 23 * q^35 + 49 * q^36 + 28 * q^37 + 16 * q^38 - 24 * q^39 + 52 * q^40 + 53 * q^41 - q^42 + 17 * q^43 - 8 * q^44 + 3 * q^45 + 28 * q^46 - 13 * q^47 - 71 * q^48 + 135 * q^49 - 7 * q^50 - 12 * q^51 + 68 * q^52 + 6 * q^53 + 3 * q^54 + 49 * q^55 + 13 * q^56 - 16 * q^57 + 26 * q^58 + 17 * q^59 - 6 * q^60 + 63 * q^61 + 13 * q^62 + 7 * q^63 + 100 * q^64 + 29 * q^65 - 20 * q^66 + 28 * q^67 - 17 * q^68 + 35 * q^69 + 44 * q^70 - 2 * q^71 - 12 * q^72 + 55 * q^73 - 13 * q^74 - 85 * q^75 + 53 * q^76 - 23 * q^77 - 33 * q^78 + 30 * q^79 + 19 * q^80 + 38 * q^81 + 55 * q^82 - 19 * q^83 - 23 * q^84 + 45 * q^85 + 12 * q^86 - 13 * q^87 + 47 * q^88 + 126 * q^89 + 14 * q^90 + 66 * q^91 - 77 * q^92 - 27 * q^93 + 52 * q^94 - 53 * q^95 + 22 * q^96 + 80 * q^97 + 4 * q^98 - 12 * q^99

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 $

$2$	−1.82570	−1.29097	−0.645484	−	0.763774i	$-0.723344\pi$
$2$	−1.82570	−1.29097	−0.645484	+	0.763774i	$0.723344\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.33320	0.666598
$5$	0.0890738	0.0398350	0.0199175	−	0.999802i	$-0.493660\pi$
$5$	0.0890738	0.0398350	0.0199175	+	0.999802i	$0.493660\pi$
$6$	1.82570	0.745341
$7$	−3.61025	−1.36455	−0.682273	−	0.731097i	$-0.739008\pi$
$7$	−3.61025	−1.36455	−0.682273	+	0.731097i	$0.739008\pi$
$8$	1.21739	0.430411
$9$	1.00000	0.333333
$10$	−0.162622	−0.0514257
$11$	−5.09197	−1.53529	−0.767643	−	0.640878i	$-0.778571\pi$
$11$	−5.09197	−1.53529	−0.767643	+	0.640878i	$0.778571\pi$
$12$	−1.33320	−0.384861
$13$	−3.12793	−0.867532	−0.433766	−	0.901026i	$-0.642816\pi$
$13$	−3.12793	−0.867532	−0.433766	+	0.901026i	$0.642816\pi$
$14$	6.59125	1.76159
$15$	−0.0890738	−0.0229988
$16$	−4.88898	−1.22224
$17$	−5.37516	−1.30367	−0.651834	−	0.758361i	$-0.726000\pi$
$17$	−5.37516	−1.30367	−0.651834	+	0.758361i	$0.726000\pi$
$18$	−1.82570	−0.430323
$19$	1.56815	0.359759	0.179879	−	0.983689i	$-0.442429\pi$
$19$	1.56815	0.359759	0.179879	+	0.983689i	$0.442429\pi$
$20$	0.118753	0.0265540
$21$	3.61025	0.787821
$22$	9.29643	1.98200
$23$	−6.71613	−1.40041	−0.700205	−	0.713942i	$-0.746908\pi$
$23$	−6.71613	−1.40041	−0.700205	+	0.713942i	$0.746908\pi$
$24$	−1.21739	−0.248498
$25$	−4.99207	−0.998413
$26$	5.71068	1.11996
$27$	−1.00000	−0.192450
$28$	−4.81317	−0.909604
$29$	8.19556	1.52188	0.760938	−	0.648824i	$-0.224739\pi$
$29$	8.19556	1.52188	0.760938	+	0.648824i	$0.224739\pi$
$30$	0.162622	0.0296907
$31$	0.829377	0.148960	0.0744802	−	0.997222i	$-0.476270\pi$
$31$	0.829377	0.148960	0.0744802	+	0.997222i	$0.476270\pi$
$32$	6.49106	1.14747
$33$	5.09197	0.886398
$34$	9.81346	1.68299
$35$	−0.321579	−0.0543567
$36$	1.33320	0.222199
$37$	6.20131	1.01949	0.509744	−	0.860326i	$-0.329740\pi$
$37$	6.20131	1.01949	0.509744	+	0.860326i	$0.329740\pi$
$38$	−2.86298	−0.464437
$39$	3.12793	0.500870
$40$	0.108437	0.0171454
$41$	−5.39696	−0.842864	−0.421432	−	0.906860i	$-0.638472\pi$
$41$	−5.39696	−0.842864	−0.421432	+	0.906860i	$0.638472\pi$
$42$	−6.59125	−1.01705
$43$	−11.8355	−1.80489	−0.902446	−	0.430802i	$-0.858231\pi$
$43$	−11.8355	−1.80489	−0.902446	+	0.430802i	$0.858231\pi$
$44$	−6.78859	−1.02342
$45$	0.0890738	0.0132783
$46$	12.2617	1.80788
$47$	−3.72341	−0.543116	−0.271558	−	0.962422i	$-0.587539\pi$
$47$	−3.72341	−0.543116	−0.271558	+	0.962422i	$0.587539\pi$
$48$	4.88898	0.705663
$49$	6.03390	0.861986
$50$	9.11404	1.28892
$51$	5.37516	0.752674
$52$	−4.17015	−0.578296
$53$	−11.5351	−1.58447	−0.792234	−	0.610218i	$-0.791082\pi$
$53$	−11.5351	−1.58447	−0.792234	+	0.610218i	$0.791082\pi$
$54$	1.82570	0.248447
$55$	−0.453561	−0.0611581
$56$	−4.39507	−0.587315
$57$	−1.56815	−0.207707
$58$	−14.9627	−1.96469
$59$	−2.47221	−0.321854	−0.160927	−	0.986966i	$-0.551448\pi$
$59$	−2.47221	−0.321854	−0.160927	+	0.986966i	$0.551448\pi$
$60$	−0.118753	−0.0153309
$61$	−1.01584	−0.130065	−0.0650324	−	0.997883i	$-0.520715\pi$
$61$	−1.01584	−0.130065	−0.0650324	+	0.997883i	$0.520715\pi$
$62$	−1.51420	−0.192303
$63$	−3.61025	−0.454849
$64$	−2.07280	−0.259100
$65$	−0.278617	−0.0345582
$66$	−9.29643	−1.14431
$67$	−3.00605	−0.367247	−0.183624	−	0.982997i	$-0.558783\pi$
$67$	−3.00605	−0.367247	−0.183624	+	0.982997i	$0.558783\pi$
$68$	−7.16615	−0.869023
$69$	6.71613	0.808527
$70$	0.587108	0.0701728
$71$	−4.34378	−0.515511	−0.257756	−	0.966210i	$-0.582983\pi$
$71$	−4.34378	−0.515511	−0.257756	+	0.966210i	$0.582983\pi$
$72$	1.21739	0.143470
$73$	15.8543	1.85560	0.927801	−	0.373076i	$-0.121697\pi$
$73$	15.8543	1.85560	0.927801	+	0.373076i	$0.121697\pi$
$74$	−11.3218	−1.31613
$75$	4.99207	0.576434
$76$	2.09065	0.239814
$77$	18.3833	2.09497
$78$	−5.71068	−0.646607
$79$	10.1986	1.14743	0.573715	−	0.819055i	$-0.305502\pi$
$79$	10.1986	1.14743	0.573715	+	0.819055i	$0.305502\pi$
$80$	−0.435480	−0.0486882
$81$	1.00000	0.111111
$82$	9.85326	1.08811
$83$	−4.82690	−0.529821	−0.264911	−	0.964273i	$-0.585342\pi$
$83$	−4.82690	−0.529821	−0.264911	+	0.964273i	$0.585342\pi$
$84$	4.81317	0.525160
$85$	−0.478786	−0.0519317
$86$	21.6081	2.33006
$87$	−8.19556	−0.878656
$88$	−6.19889	−0.660804
$89$	−9.78253	−1.03695	−0.518473	−	0.855094i	$-0.673499\pi$
$89$	−9.78253	−1.03695	−0.518473	+	0.855094i	$0.673499\pi$
$90$	−0.162622	−0.0171419
$91$	11.2926	1.18379
$92$	−8.95392	−0.933511
$93$	−0.829377	−0.0860024
$94$	6.79785	0.701145
$95$	0.139681	0.0143310
$96$	−6.49106	−0.662491
$97$	3.26995	0.332013	0.166007	−	0.986125i	$-0.446913\pi$
$97$	3.26995	0.332013	0.166007	+	0.986125i	$0.446913\pi$
$98$	−11.0161	−1.11280
$99$	−5.09197	−0.511762
$100$	−6.65541	−0.665541
$101$	−6.74734	−0.671385	−0.335693	−	0.941972i	$-0.608970\pi$
$101$	−6.74734	−0.671385	−0.335693	+	0.941972i	$0.608970\pi$
$102$	−9.81346	−0.971677
$103$	−11.2421	−1.10772	−0.553858	−	0.832611i	$-0.686845\pi$
$103$	−11.2421	−1.10772	−0.553858	+	0.832611i	$0.686845\pi$
$104$	−3.80790	−0.373395
$105$	0.321579	0.0313829
$106$	21.0597	2.04550
$107$	−5.11603	−0.494585	−0.247293	−	0.968941i	$-0.579541\pi$
$107$	−5.11603	−0.494585	−0.247293	+	0.968941i	$0.579541\pi$
$108$	−1.33320	−0.128287
$109$	−8.22366	−0.787684	−0.393842	−	0.919178i	$-0.628854\pi$
$109$	−8.22366	−0.787684	−0.393842	+	0.919178i	$0.628854\pi$
$110$	0.828068	0.0789532
$111$	−6.20131	−0.588602
$112$	17.6504	1.66781
$113$	7.67176	0.721698	0.360849	−	0.932624i	$-0.382487\pi$
$113$	7.67176	0.721698	0.360849	+	0.932624i	$0.382487\pi$
$114$	2.86298	0.268143
$115$	−0.598231	−0.0557853
$116$	10.9263	1.01448
$117$	−3.12793	−0.289177
$118$	4.51352	0.415504
$119$	19.4057	1.77892
$120$	−0.108437	−0.00989892
$121$	14.9281	1.35710
$122$	1.85462	0.167910
$123$	5.39696	0.486628
$124$	1.10572	0.0992968
$125$	−0.890031	−0.0796068
$126$	6.59125	0.587195
$127$	12.1479	1.07795	0.538976	−	0.842321i	$-0.318811\pi$
$127$	12.1479	1.07795	0.538976	+	0.842321i	$0.318811\pi$
$128$	−9.19780	−0.812979
$129$	11.8355	1.04206
$130$	0.508672	0.0446135
$131$	−4.00912	−0.350278	−0.175139	−	0.984544i	$-0.556037\pi$
$131$	−4.00912	−0.350278	−0.175139	+	0.984544i	$0.556037\pi$
$132$	6.78859	0.590871
$133$	−5.66142	−0.490907
$134$	5.48816	0.474104
$135$	−0.0890738	−0.00766625
$136$	−6.54365	−0.561113
$137$	−12.1032	−1.03404	−0.517022	−	0.855972i	$-0.672960\pi$
$137$	−12.1032	−1.03404	−0.517022	+	0.855972i	$0.672960\pi$
$138$	−12.2617	−1.04378
$139$	11.3964	0.966630	0.483315	−	0.875446i	$-0.339433\pi$
$139$	11.3964	0.966630	0.483315	+	0.875446i	$0.339433\pi$
$140$	−0.428728	−0.0362341
$141$	3.72341	0.313568
$142$	7.93045	0.665509
$143$	15.9273	1.33191
$144$	−4.88898	−0.407415
$145$	0.730010	0.0606240
$146$	−28.9452	−2.39552
$147$	−6.03390	−0.497668
$148$	8.26756	0.679589
$149$	−5.83379	−0.477923	−0.238962	−	0.971029i	$-0.576807\pi$
$149$	−5.83379	−0.477923	−0.238962	+	0.971029i	$0.576807\pi$
$150$	−9.11404	−0.744158
$151$	−4.37768	−0.356251	−0.178125	−	0.984008i	$-0.557003\pi$
$151$	−4.37768	−0.356251	−0.178125	+	0.984008i	$0.557003\pi$
$152$	1.90905	0.154844
$153$	−5.37516	−0.434556
$154$	−33.5624	−2.70454
$155$	0.0738757	0.00593384
$156$	4.17015	0.333879
$157$	15.9452	1.27256	0.636282	−	0.771456i	$-0.280471\pi$
$157$	15.9452	1.27256	0.636282	+	0.771456i	$0.280471\pi$
$158$	−18.6196	−1.48129
$159$	11.5351	0.914793
$160$	0.578184	0.0457094
$161$	24.2469	1.91092
$162$	−1.82570	−0.143441
$163$	21.4190	1.67767	0.838834	−	0.544387i	$-0.183238\pi$
$163$	21.4190	1.67767	0.838834	+	0.544387i	$0.183238\pi$
$164$	−7.19521	−0.561852
$165$	0.453561	0.0353097
$166$	8.81250	0.683982
$167$	−12.2941	−0.951344	−0.475672	−	0.879623i	$-0.657795\pi$
$167$	−12.2941	−0.951344	−0.475672	+	0.879623i	$0.657795\pi$
$168$	4.39507	0.339087
$169$	−3.21604	−0.247388
$170$	0.874122	0.0670421
$171$	1.56815	0.119920
$172$	−15.7790	−1.20314
$173$	14.2095	1.08033	0.540166	−	0.841559i	$-0.318362\pi$
$173$	14.2095	1.08033	0.540166	+	0.841559i	$0.318362\pi$
$174$	14.9627	1.13432
$175$	18.0226	1.36238
$176$	24.8945	1.87650
$177$	2.47221	0.185823
$178$	17.8600	1.33866
$179$	3.37466	0.252234	0.126117	−	0.992015i	$-0.459749\pi$
$179$	3.37466	0.252234	0.126117	+	0.992015i	$0.459749\pi$
$180$	0.118753	0.00885132
$181$	20.8237	1.54782	0.773908	−	0.633298i	$-0.218299\pi$
$181$	20.8237	1.54782	0.773908	+	0.633298i	$0.218299\pi$
$182$	−20.6170	−1.52823
$183$	1.01584	0.0750930
$184$	−8.17612	−0.602751
$185$	0.552374	0.0406113
$186$	1.51420	0.111026
$187$	27.3702	2.00150
$188$	−4.96404	−0.362040
$189$	3.61025	0.262607
$190$	−0.255017	−0.0185009
$191$	0.989248	0.0715795	0.0357897	−	0.999359i	$-0.488605\pi$
$191$	0.989248	0.0715795	0.0357897	+	0.999359i	$0.488605\pi$
$192$	2.07280	0.149591
$193$	12.4163	0.893742	0.446871	−	0.894598i	$-0.352538\pi$
$193$	12.4163	0.893742	0.446871	+	0.894598i	$0.352538\pi$
$194$	−5.96996	−0.428618
$195$	0.278617	0.0199522
$196$	8.04438	0.574598
$197$	19.5063	1.38976	0.694882	−	0.719124i	$-0.255457\pi$
$197$	19.5063	1.38976	0.694882	+	0.719124i	$0.255457\pi$
$198$	9.29643	0.660668
$199$	−24.3936	−1.72922	−0.864609	−	0.502445i	$-0.832434\pi$
$199$	−24.3936	−1.72922	−0.864609	+	0.502445i	$0.832434\pi$
$200$	−6.07727	−0.429728
$201$	3.00605	0.212030
$202$	12.3186	0.866737
$203$	−29.5880	−2.07667
$204$	7.16615	0.501731
$205$	−0.480728	−0.0335755
$206$	20.5247	1.43002
$207$	−6.71613	−0.466803
$208$	15.2924	1.06034
$209$	−7.98498	−0.552332
$210$	−0.587108	−0.0405143
$211$	14.8319	1.02107	0.510534	−	0.859857i	$-0.329448\pi$
$211$	14.8319	1.02107	0.510534	+	0.859857i	$0.329448\pi$
$212$	−15.3786	−1.05620
$213$	4.34378	0.297631
$214$	9.34035	0.638494
$215$	−1.05423	−0.0718979
$216$	−1.21739	−0.0828326
$217$	−2.99426	−0.203263
$218$	15.0140	1.01687
$219$	−15.8543	−1.07133
$220$	−0.604686	−0.0407679
$221$	16.8131	1.13097
$222$	11.3218	0.759866
$223$	−6.88052	−0.460754	−0.230377	−	0.973101i	$-0.573996\pi$
$223$	−6.88052	−0.460754	−0.230377	+	0.973101i	$0.573996\pi$
$224$	−23.4343	−1.56577
$225$	−4.99207	−0.332804
$226$	−14.0064	−0.931690
$227$	−17.6493	−1.17143	−0.585714	−	0.810518i	$-0.699186\pi$
$227$	−17.6493	−1.17143	−0.585714	+	0.810518i	$0.699186\pi$
$228$	−2.09065	−0.138457
$229$	25.4186	1.67971	0.839853	−	0.542814i	$-0.182641\pi$
$229$	25.4186	1.67971	0.839853	+	0.542814i	$0.182641\pi$
$230$	1.09219	0.0720171
$231$	−18.3833	−1.20953
$232$	9.97716	0.655032
$233$	−10.6238	−0.695989	−0.347995	−	0.937497i	$-0.613137\pi$
$233$	−10.6238	−0.695989	−0.347995	+	0.937497i	$0.613137\pi$
$234$	5.71068	0.373319
$235$	−0.331659	−0.0216350
$236$	−3.29594	−0.214548
$237$	−10.1986	−0.662469
$238$	−35.4290	−2.29652
$239$	29.3704	1.89981	0.949905	−	0.312538i	$-0.101179\pi$
$239$	29.3704	1.89981	0.949905	+	0.312538i	$0.101179\pi$
$240$	0.435480	0.0281101
$241$	−10.3496	−0.666677	−0.333338	−	0.942807i	$-0.608175\pi$
$241$	−10.3496	−0.666677	−0.333338	+	0.942807i	$0.608175\pi$
$242$	−27.2544	−1.75198
$243$	−1.00000	−0.0641500
$244$	−1.35431	−0.0867010
$245$	0.537463	0.0343372
$246$	−9.85326	−0.628221
$247$	−4.90507	−0.312102
$248$	1.00967	0.0641142
$249$	4.82690	0.305893
$250$	1.62493	0.102770
$251$	9.20452	0.580984	0.290492	−	0.956877i	$-0.406181\pi$
$251$	9.20452	0.580984	0.290492	+	0.956877i	$0.406181\pi$
$252$	−4.81317	−0.303201
$253$	34.1983	2.15003
$254$	−22.1785	−1.39160
$255$	0.478786	0.0299828
$256$	20.9381	1.30863
$257$	7.76335	0.484265	0.242132	−	0.970243i	$-0.422153\pi$
$257$	7.76335	0.484265	0.242132	+	0.970243i	$0.422153\pi$
$258$	−21.6081	−1.34526
$259$	−22.3883	−1.39114
$260$	−0.371451	−0.0230364
$261$	8.19556	0.507292
$262$	7.31946	0.452198
$263$	3.26409	0.201273	0.100636	−	0.994923i	$-0.467912\pi$
$263$	3.26409	0.201273	0.100636	+	0.994923i	$0.467912\pi$
$264$	6.19889	0.381515
$265$	−1.02748	−0.0631173
$266$	10.3361	0.633745
$267$	9.78253	0.598681
$268$	−4.00765	−0.244806
$269$	15.0673	0.918670	0.459335	−	0.888263i	$-0.348088\pi$
$269$	15.0673	0.918670	0.459335	+	0.888263i	$0.348088\pi$
$270$	0.162622	0.00989689
$271$	−5.34308	−0.324569	−0.162285	−	0.986744i	$-0.551886\pi$
$271$	−5.34308	−0.324569	−0.162285	+	0.986744i	$0.551886\pi$
$272$	26.2791	1.59340
$273$	−11.2926	−0.683460
$274$	22.0968	1.33492
$275$	25.4194	1.53285
$276$	8.95392	0.538963
$277$	−28.3622	−1.70412	−0.852059	−	0.523446i	$-0.824646\pi$
$277$	−28.3622	−1.70412	−0.852059	+	0.523446i	$0.824646\pi$
$278$	−20.8065	−1.24789
$279$	0.829377	0.0496535
$280$	−0.391485	−0.0233957
$281$	−21.5231	−1.28396	−0.641980	−	0.766721i	$-0.721887\pi$
$281$	−21.5231	−1.28396	−0.641980	+	0.766721i	$0.721887\pi$
$282$	−6.79785	−0.404806
$283$	−27.1679	−1.61496	−0.807482	−	0.589892i	$-0.799170\pi$
$283$	−27.1679	−1.61496	−0.807482	+	0.589892i	$0.799170\pi$
$284$	−5.79111	−0.343639
$285$	−0.139681	−0.00827400
$286$	−29.0786	−1.71945
$287$	19.4844	1.15013
$288$	6.49106	0.382489
$289$	11.8924	0.699552
$290$	−1.33278	−0.0782636
$291$	−3.26995	−0.191688
$292$	21.1369	1.23694
$293$	−6.99808	−0.408832	−0.204416	−	0.978884i	$-0.565530\pi$
$293$	−6.99808	−0.408832	−0.204416	+	0.978884i	$0.565530\pi$
$294$	11.0161	0.642473
$295$	−0.220209	−0.0128211
$296$	7.54938	0.438799
$297$	5.09197	0.295466
$298$	10.6508	0.616983
$299$	21.0076	1.21490
$300$	6.65541	0.384250
$301$	42.7290	2.46286
$302$	7.99235	0.459908
$303$	6.74734	0.387625
$304$	−7.66666	−0.439713
$305$	−0.0904847	−0.00518114
$306$	9.81346	0.560998
$307$	3.68377	0.210244	0.105122	−	0.994459i	$-0.466477\pi$
$307$	3.68377	0.210244	0.105122	+	0.994459i	$0.466477\pi$
$308$	24.5085	1.39650
$309$	11.2421	0.639540
$310$	−0.134875	−0.00766040
$311$	25.0499	1.42045	0.710224	−	0.703976i	$-0.248594\pi$
$311$	25.0499	1.42045	0.710224	+	0.703976i	$0.248594\pi$
$312$	3.80790	0.215580
$313$	−23.7351	−1.34159	−0.670795	−	0.741643i	$-0.734047\pi$
$313$	−23.7351	−1.34159	−0.670795	+	0.741643i	$0.734047\pi$
$314$	−29.1112	−1.64284
$315$	−0.321579	−0.0181189
$316$	13.5967	0.764875
$317$	16.8244	0.944950	0.472475	−	0.881344i	$-0.343361\pi$
$317$	16.8244	0.944950	0.472475	+	0.881344i	$0.343361\pi$
$318$	−21.0597	−1.18097
$319$	−41.7315	−2.33652
$320$	−0.184632	−0.0103212
$321$	5.11603	0.285549
$322$	−44.2677	−2.46694
$323$	−8.42907	−0.469006
$324$	1.33320	0.0740665
$325$	15.6148	0.866156
$326$	−39.1048	−2.16582
$327$	8.22366	0.454770
$328$	−6.57018	−0.362778
$329$	13.4425	0.741106
$330$	−0.828068	−0.0455837
$331$	15.3426	0.843308	0.421654	−	0.906757i	$-0.361450\pi$
$331$	15.3426	0.843308	0.421654	+	0.906757i	$0.361450\pi$
$332$	−6.43521	−0.353178
$333$	6.20131	0.339829
$334$	22.4453	1.22815
$335$	−0.267760	−0.0146293
$336$	−17.6504	−0.962910
$337$	−6.08398	−0.331416	−0.165708	−	0.986175i	$-0.552991\pi$
$337$	−6.08398	−0.331416	−0.165708	+	0.986175i	$0.552991\pi$
$338$	5.87154	0.319370
$339$	−7.67176	−0.416673
$340$	−0.638316	−0.0346176
$341$	−4.22316	−0.228697
$342$	−2.86298	−0.154812
$343$	3.48785	0.188326
$344$	−14.4083	−0.776846
$345$	0.598231	0.0322077
$346$	−25.9424	−1.39467
$347$	−12.2462	−0.657409	−0.328705	−	0.944433i	$-0.606612\pi$
$347$	−12.2462	−0.657409	−0.328705	+	0.944433i	$0.606612\pi$
$348$	−10.9263	−0.585711
$349$	−1.81732	−0.0972789	−0.0486395	−	0.998816i	$-0.515489\pi$
$349$	−1.81732	−0.0972789	−0.0486395	+	0.998816i	$0.515489\pi$
$350$	−32.9039	−1.75879
$351$	3.12793	0.166957
$352$	−33.0523	−1.76169
$353$	32.3598	1.72234	0.861168	−	0.508320i	$-0.169733\pi$
$353$	32.3598	1.72234	0.861168	+	0.508320i	$0.169733\pi$
$354$	−4.51352	−0.239891
$355$	−0.386917	−0.0205354
$356$	−13.0420	−0.691227
$357$	−19.4057	−1.02706
$358$	−6.16113	−0.325626
$359$	0.321434	0.0169647	0.00848233	−	0.999964i	$-0.497300\pi$
$359$	0.321434	0.0169647	0.00848233	+	0.999964i	$0.497300\pi$
$360$	0.108437	0.00571514
$361$	−16.5409	−0.870574
$362$	−38.0180	−1.99818
$363$	−14.9281	−0.783524
$364$	15.0553	0.789111
$365$	1.41220	0.0739179
$366$	−1.85462	−0.0969427
$367$	−21.9241	−1.14443	−0.572215	−	0.820104i	$-0.693916\pi$
$367$	−21.9241	−1.14443	−0.572215	+	0.820104i	$0.693916\pi$
$368$	32.8350	1.71164
$369$	−5.39696	−0.280955
$370$	−1.00847	−0.0524279
$371$	41.6446	2.16208
$372$	−1.10572	−0.0573290
$373$	−7.52271	−0.389511	−0.194756	−	0.980852i	$-0.562391\pi$
$373$	−7.52271	−0.389511	−0.194756	+	0.980852i	$0.562391\pi$
$374$	−49.9698	−2.58388
$375$	0.890031	0.0459610
$376$	−4.53283	−0.233763
$377$	−25.6351	−1.32028
$378$	−6.59125	−0.339017
$379$	−32.2322	−1.65566	−0.827829	−	0.560981i	$-0.810424\pi$
$379$	−32.2322	−1.65566	−0.827829	+	0.560981i	$0.810424\pi$
$380$	0.186223	0.00955302
$381$	−12.1479	−0.622356
$382$	−1.80607	−0.0924068
$383$	−10.7544	−0.549524	−0.274762	−	0.961512i	$-0.588599\pi$
$383$	−10.7544	−0.549524	−0.274762	+	0.961512i	$0.588599\pi$
$384$	9.19780	0.469373
$385$	1.63747	0.0834531
$386$	−22.6684	−1.15379
$387$	−11.8355	−0.601631
$388$	4.35949	0.221319
$389$	−20.8210	−1.05566	−0.527832	−	0.849349i	$-0.676995\pi$
$389$	−20.8210	−1.05566	−0.527832	+	0.849349i	$0.676995\pi$
$390$	−0.508672	−0.0257576
$391$	36.1003	1.82567
$392$	7.34559	0.371008
$393$	4.00912	0.202233
$394$	−35.6127	−1.79414
$395$	0.908426	0.0457079
$396$	−6.78859	−0.341140
$397$	−5.66416	−0.284276	−0.142138	−	0.989847i	$-0.545398\pi$
$397$	−5.66416	−0.284276	−0.142138	+	0.989847i	$0.545398\pi$
$398$	44.5356	2.23237
$399$	5.66142	0.283425
$400$	24.4061	1.22031
$401$	−1.37239	−0.0685338	−0.0342669	−	0.999413i	$-0.510910\pi$
$401$	−1.37239	−0.0685338	−0.0342669	+	0.999413i	$0.510910\pi$
$402$	−5.48816	−0.273724
$403$	−2.59423	−0.129228
$404$	−8.99553	−0.447544
$405$	0.0890738	0.00442611
$406$	54.0190	2.68092
$407$	−31.5768	−1.56521
$408$	6.54365	0.323959
$409$	−2.81552	−0.139218	−0.0696092	−	0.997574i	$-0.522175\pi$
$409$	−2.81552	−0.139218	−0.0696092	+	0.997574i	$0.522175\pi$
$410$	0.877667	0.0433449
$411$	12.1032	0.597006
$412$	−14.9879	−0.738401
$413$	8.92530	0.439185
$414$	12.2617	0.602628
$415$	−0.429951	−0.0211054
$416$	−20.3036	−0.995466
$417$	−11.3964	−0.558084
$418$	14.5782	0.713043
$419$	−3.73420	−0.182428	−0.0912139	−	0.995831i	$-0.529075\pi$
$419$	−3.73420	−0.182428	−0.0912139	+	0.995831i	$0.529075\pi$
$420$	0.428728	0.0209198
$421$	14.0132	0.682964	0.341482	−	0.939888i	$-0.389071\pi$
$421$	14.0132	0.682964	0.341482	+	0.939888i	$0.389071\pi$
$422$	−27.0786	−1.31817
$423$	−3.72341	−0.181039
$424$	−14.0427	−0.681972
$425$	26.8332	1.30160
$426$	−7.93045	−0.384232
$427$	3.66743	0.177480
$428$	−6.82067	−0.329690
$429$	−15.9273	−0.768979
$430$	1.92471	0.0928179
$431$	−6.92363	−0.333500	−0.166750	−	0.985999i	$-0.553327\pi$
$431$	−6.92363	−0.333500	−0.166750	+	0.985999i	$0.553327\pi$
$432$	4.88898	0.235221
$433$	11.3455	0.545230	0.272615	−	0.962123i	$-0.412112\pi$
$433$	11.3455	0.545230	0.272615	+	0.962123i	$0.412112\pi$
$434$	5.46663	0.262407
$435$	−0.730010	−0.0350013
$436$	−10.9638	−0.525069
$437$	−10.5319	−0.503809
$438$	28.9452	1.38306
$439$	−2.62975	−0.125511	−0.0627555	−	0.998029i	$-0.519989\pi$
$439$	−2.62975	−0.125511	−0.0627555	+	0.998029i	$0.519989\pi$
$440$	−0.552159	−0.0263231
$441$	6.03390	0.287329
$442$	−30.6958	−1.46005
$443$	−9.87644	−0.469244	−0.234622	−	0.972087i	$-0.575385\pi$
$443$	−9.87644	−0.469244	−0.234622	+	0.972087i	$0.575385\pi$
$444$	−8.26756	−0.392361
$445$	−0.871367	−0.0413068
$446$	12.5618	0.594819
$447$	5.83379	0.275929
$448$	7.48332	0.353554
$449$	−6.68632	−0.315547	−0.157774	−	0.987475i	$-0.550432\pi$
$449$	−6.68632	−0.315547	−0.157774	+	0.987475i	$0.550432\pi$
$450$	9.11404	0.429640
$451$	27.4812	1.29404
$452$	10.2280	0.481083
$453$	4.37768	0.205681
$454$	32.2225	1.51228
$455$	1.00588	0.0471562
$456$	−1.90905	−0.0893992
$457$	39.1418	1.83098	0.915489	−	0.402344i	$-0.131804\pi$
$457$	39.1418	1.83098	0.915489	+	0.402344i	$0.131804\pi$
$458$	−46.4068	−2.16845
$459$	5.37516	0.250891
$460$	−0.797560	−0.0371864
$461$	−5.56009	−0.258959	−0.129480	−	0.991582i	$-0.541331\pi$
$461$	−5.56009	−0.258959	−0.129480	+	0.991582i	$0.541331\pi$
$462$	33.5624	1.56147
$463$	−19.4843	−0.905511	−0.452756	−	0.891635i	$-0.649559\pi$
$463$	−19.4843	−0.905511	−0.452756	+	0.891635i	$0.649559\pi$
$464$	−40.0679	−1.86011
$465$	−0.0738757	−0.00342591
$466$	19.3959	0.898500
$467$	−22.6493	−1.04809	−0.524043	−	0.851692i	$-0.675577\pi$
$467$	−22.6493	−1.04809	−0.524043	+	0.851692i	$0.675577\pi$
$468$	−4.17015	−0.192765
$469$	10.8526	0.501126
$470$	0.605511	0.0279301
$471$	−15.9452	−0.734715
$472$	−3.00963	−0.138530
$473$	60.2659	2.77103
$474$	18.6196	0.855226
$475$	−7.82832	−0.359188
$476$	25.8716	1.18582
$477$	−11.5351	−0.528156
$478$	−53.6216	−2.45259
$479$	−19.2755	−0.880720	−0.440360	−	0.897821i	$-0.645149\pi$
$479$	−19.2755	−0.880720	−0.440360	+	0.897821i	$0.645149\pi$
$480$	−0.578184	−0.0263903
$481$	−19.3973	−0.884439
$482$	18.8953	0.860658
$483$	−24.2469	−1.10327
$484$	19.9021	0.904643
$485$	0.291267	0.0132258
$486$	1.82570	0.0828156
$487$	−33.3931	−1.51318	−0.756592	−	0.653887i	$-0.773137\pi$
$487$	−33.3931	−1.51318	−0.756592	+	0.653887i	$0.773137\pi$
$488$	−1.23667	−0.0559813
$489$	−21.4190	−0.968602
$490$	−0.981248	−0.0443283
$491$	−23.4494	−1.05826	−0.529129	−	0.848541i	$-0.677481\pi$
$491$	−23.4494	−1.05826	−0.529129	+	0.848541i	$0.677481\pi$
$492$	7.19521	0.324385
$493$	−44.0525	−1.98402
$494$	8.95521	0.402914
$495$	−0.453561	−0.0203860
$496$	−4.05481	−0.182066
$497$	15.6821	0.703439
$498$	−8.81250	−0.394897
$499$	29.9852	1.34232	0.671160	−	0.741313i	$-0.265796\pi$
$499$	29.9852	1.34232	0.671160	+	0.741313i	$0.265796\pi$
$500$	−1.18659	−0.0530658
$501$	12.2941	0.549259
$502$	−16.8047	−0.750032
$503$	−9.88121	−0.440581	−0.220291	−	0.975434i	$-0.570701\pi$
$503$	−9.88121	−0.440581	−0.220291	+	0.975434i	$0.570701\pi$
$504$	−4.39507	−0.195772
$505$	−0.601011	−0.0267447
$506$	−62.4360	−2.77562
$507$	3.21604	0.142829
$508$	16.1955	0.718561
$509$	−7.37363	−0.326830	−0.163415	−	0.986557i	$-0.552251\pi$
$509$	−7.37363	−0.326830	−0.163415	+	0.986557i	$0.552251\pi$
$510$	−0.874122	−0.0387068
$511$	−57.2379	−2.53205
$512$	−19.8311	−0.876420
$513$	−1.56815	−0.0692356
$514$	−14.1736	−0.625170
$515$	−1.00137	−0.0441259
$516$	15.7790	0.694632
$517$	18.9595	0.833838
$518$	40.8743	1.79592
$519$	−14.2095	−0.623729
$520$	−0.339184	−0.0148742
$521$	37.7485	1.65379	0.826896	−	0.562355i	$-0.190105\pi$
$521$	37.7485	1.65379	0.826896	+	0.562355i	$0.190105\pi$
$522$	−14.9627	−0.654898
$523$	−19.2823	−0.843154	−0.421577	−	0.906793i	$-0.638523\pi$
$523$	−19.2823	−0.843154	−0.421577	+	0.906793i	$0.638523\pi$
$524$	−5.34494	−0.233495
$525$	−18.0226	−0.786571
$526$	−5.95927	−0.259837
$527$	−4.45804	−0.194195
$528$	−24.8945	−1.08340
$529$	22.1064	0.961147
$530$	1.87587	0.0814824
$531$	−2.47221	−0.107285
$532$	−7.54778	−0.327238
$533$	16.8813	0.731212
$534$	−17.8600	−0.772878
$535$	−0.455704	−0.0197018
$536$	−3.65952	−0.158067
$537$	−3.37466	−0.145627
$538$	−27.5085	−1.18597
$539$	−30.7244	−1.32340
$540$	−0.118753	−0.00511031
$541$	−27.0571	−1.16328	−0.581638	−	0.813448i	$-0.697588\pi$
$541$	−27.0571	−1.16328	−0.581638	+	0.813448i	$0.697588\pi$
$542$	9.75489	0.419009
$543$	−20.8237	−0.893632
$544$	−34.8905	−1.49592
$545$	−0.732513	−0.0313774
$546$	20.6170	0.882325
$547$	−27.1856	−1.16237	−0.581186	−	0.813771i	$-0.697411\pi$
$547$	−27.1856	−1.16237	−0.581186	+	0.813771i	$0.697411\pi$
$548$	−16.1359	−0.689292
$549$	−1.01584	−0.0433550
$550$	−46.4084	−1.97886
$551$	12.8519	0.547508
$552$	8.17612	0.347999
$553$	−36.8194	−1.56572
$554$	51.7809	2.19996
$555$	−0.552374	−0.0234470
$556$	15.1936	0.644354
$557$	−39.4146	−1.67005	−0.835025	−	0.550212i	$-0.814547\pi$
$557$	−39.4146	−1.67005	−0.835025	+	0.550212i	$0.814547\pi$
$558$	−1.51420	−0.0641011
$559$	37.0206	1.56580
$560$	1.57219	0.0664372
$561$	−27.3702	−1.15557
$562$	39.2948	1.65755
$563$	−10.2795	−0.433229	−0.216615	−	0.976257i	$-0.569501\pi$
$563$	−10.2795	−0.433229	−0.216615	+	0.976257i	$0.569501\pi$
$564$	4.96404	0.209024
$565$	0.683353	0.0287489
$566$	49.6005	2.08487
$567$	−3.61025	−0.151616
$568$	−5.28805	−0.221882
$569$	21.1332	0.885950	0.442975	−	0.896534i	$-0.353923\pi$
$569$	21.1332	0.885950	0.442975	+	0.896534i	$0.353923\pi$
$570$	0.255017	0.0106815
$571$	7.14958	0.299201	0.149600	−	0.988747i	$-0.452201\pi$
$571$	7.14958	0.299201	0.149600	+	0.988747i	$0.452201\pi$
$572$	21.2343	0.887849
$573$	−0.989248	−0.0413264
$574$	−35.5727	−1.48478
$575$	33.5274	1.39819
$576$	−2.07280	−0.0863666
$577$	6.32513	0.263318	0.131659	−	0.991295i	$-0.457970\pi$
$577$	6.32513	0.263318	0.131659	+	0.991295i	$0.457970\pi$
$578$	−21.7120	−0.903100
$579$	−12.4163	−0.516002
$580$	0.973246	0.0404119
$581$	17.4263	0.722966
$582$	5.96996	0.247463
$583$	58.7363	2.43261
$584$	19.3008	0.798671
$585$	−0.278617	−0.0115194
$586$	12.7764	0.527789
$587$	10.0339	0.414142	0.207071	−	0.978326i	$-0.433607\pi$
$587$	10.0339	0.414142	0.207071	+	0.978326i	$0.433607\pi$
$588$	−8.04438	−0.331745
$589$	1.30059	0.0535898
$590$	0.402037	0.0165516
$591$	−19.5063	−0.802380
$592$	−30.3181	−1.24606
$593$	14.6552	0.601818	0.300909	−	0.953653i	$-0.402710\pi$
$593$	14.6552	0.601818	0.300909	+	0.953653i	$0.402710\pi$
$594$	−9.29643	−0.381437
$595$	1.72854	0.0708632
$596$	−7.77759	−0.318583
$597$	24.3936	0.998365
$598$	−38.3537	−1.56840
$599$	15.4711	0.632131	0.316065	−	0.948737i	$-0.397638\pi$
$599$	15.4711	0.632131	0.316065	+	0.948737i	$0.397638\pi$
$600$	6.07727	0.248104
$601$	−42.0096	−1.71361	−0.856804	−	0.515643i	$-0.827553\pi$
$601$	−42.0096	−1.71361	−0.856804	+	0.515643i	$0.827553\pi$
$602$	−78.0106	−3.17947
$603$	−3.00605	−0.122416
$604$	−5.83631	−0.237476
$605$	1.32971	0.0540602
$606$	−12.3186	−0.500411
$607$	−13.7799	−0.559311	−0.279655	−	0.960100i	$-0.590220\pi$
$607$	−13.7799	−0.559311	−0.279655	+	0.960100i	$0.590220\pi$
$608$	10.1790	0.412812
$609$	29.5880	1.19897
$610$	0.165198	0.00668868
$611$	11.6466	0.471170
$612$	−7.16615	−0.289674
$613$	8.63890	0.348922	0.174461	−	0.984664i	$-0.444182\pi$
$613$	8.63890	0.348922	0.174461	+	0.984664i	$0.444182\pi$
$614$	−6.72548	−0.271418
$615$	0.480728	0.0193848
$616$	22.3795	0.901697
$617$	−44.7530	−1.80169	−0.900845	−	0.434142i	$-0.857052\pi$
$617$	−44.7530	−1.80169	−0.900845	+	0.434142i	$0.857052\pi$
$618$	−20.5247	−0.825625
$619$	13.8584	0.557016	0.278508	−	0.960434i	$-0.410160\pi$
$619$	13.8584	0.557016	0.278508	+	0.960434i	$0.410160\pi$
$620$	0.0984909	0.00395549
$621$	6.71613	0.269509
$622$	−45.7337	−1.83375
$623$	35.3174	1.41496
$624$	−15.2924	−0.612186
$625$	24.8811	0.995242
$626$	43.3334	1.73195
$627$	7.98498	0.318889
$628$	21.2581	0.848289
$629$	−33.3330	−1.32908
$630$	0.587108	0.0233909
$631$	10.6818	0.425237	0.212619	−	0.977135i	$-0.431801\pi$
$631$	10.6818	0.425237	0.212619	+	0.977135i	$0.431801\pi$
$632$	12.4156	0.493866
$633$	−14.8319	−0.589514
$634$	−30.7163	−1.21990
$635$	1.08206	0.0429403
$636$	15.3786	0.609799
$637$	−18.8736	−0.747801
$638$	76.1894	3.01637
$639$	−4.34378	−0.171837
$640$	−0.819283	−0.0323850
$641$	10.8214	0.427421	0.213711	−	0.976897i	$-0.431445\pi$
$641$	10.8214	0.427421	0.213711	+	0.976897i	$0.431445\pi$
$642$	−9.34035	−0.368634
$643$	−32.4201	−1.27852	−0.639261	−	0.768989i	$-0.720760\pi$
$643$	−32.4201	−1.27852	−0.639261	+	0.768989i	$0.720760\pi$
$644$	32.3259	1.27382
$645$	1.05423	0.0415103
$646$	15.3890	0.605472
$647$	−13.3101	−0.523272	−0.261636	−	0.965167i	$-0.584262\pi$
$647$	−13.3101	−0.523272	−0.261636	+	0.965167i	$0.584262\pi$
$648$	1.21739	0.0478234
$649$	12.5884	0.494138
$650$	−28.5081	−1.11818
$651$	2.99426	0.117354
$652$	28.5558	1.11833
$653$	25.4263	0.995010	0.497505	−	0.867461i	$-0.334250\pi$
$653$	25.4263	0.995010	0.497505	+	0.867461i	$0.334250\pi$
$654$	−15.0140	−0.587093
$655$	−0.357107	−0.0139533
$656$	26.3856	1.03019
$657$	15.8543	0.618534
$658$	−24.5419	−0.956745
$659$	−25.3604	−0.987902	−0.493951	−	0.869490i	$-0.664448\pi$
$659$	−25.3604	−0.987902	−0.493951	+	0.869490i	$0.664448\pi$
$660$	0.604686	0.0235374
$661$	11.0526	0.429896	0.214948	−	0.976626i	$-0.431042\pi$
$661$	11.0526	0.429896	0.214948	+	0.976626i	$0.431042\pi$
$662$	−28.0111	−1.08868
$663$	−16.8131	−0.652969
$664$	−5.87620	−0.228041
$665$	−0.504284	−0.0195553
$666$	−11.3218	−0.438709
$667$	−55.0424	−2.13125
$668$	−16.3904	−0.634164
$669$	6.88052	0.266016
$670$	0.488851	0.0188860
$671$	5.17262	0.199687
$672$	23.4343	0.904000
$673$	−16.0181	−0.617451	−0.308726	−	0.951151i	$-0.599903\pi$
$673$	−16.0181	−0.617451	−0.308726	+	0.951151i	$0.599903\pi$
$674$	11.1076	0.427847
$675$	4.99207	0.192145
$676$	−4.28762	−0.164908
$677$	1.00000	0.0384331
$677$	1.00000	0.0384331
$678$	14.0064	0.537911
$679$	−11.8053	−0.453047
$680$	−0.582868	−0.0223520
$681$	17.6493	0.676324
$682$	7.71024	0.295240
$683$	−2.90065	−0.110990	−0.0554952	−	0.998459i	$-0.517674\pi$
$683$	−2.90065	−0.110990	−0.0554952	+	0.998459i	$0.517674\pi$
$684$	2.09065	0.0799382
$685$	−1.07808	−0.0411912
$686$	−6.36779	−0.243123
$687$	−25.4186	−0.969779
$688$	57.8634	2.20602
$689$	36.0810	1.37458
$690$	−1.09219	−0.0415791
$691$	7.72885	0.294019	0.147010	−	0.989135i	$-0.453035\pi$
$691$	7.72885	0.294019	0.147010	+	0.989135i	$0.453035\pi$
$692$	18.9441	0.720147
$693$	18.3833	0.698323
$694$	22.3579	0.848695
$695$	1.01512	0.0385057
$696$	−9.97716	−0.378183
$697$	29.0096	1.09882
$698$	3.31789	0.125584
$699$	10.6238	0.401830
$700$	24.0277	0.908161
$701$	31.4624	1.18832	0.594159	−	0.804348i	$-0.297485\pi$
$701$	31.4624	1.18832	0.594159	+	0.804348i	$0.297485\pi$
$702$	−5.71068	−0.215536
$703$	9.72459	0.366770
$704$	10.5546	0.397792
$705$	0.331659	0.0124910
$706$	−59.0794	−2.22348
$707$	24.3596	0.916136
$708$	3.29594	0.123869
$709$	17.9270	0.673261	0.336631	−	0.941637i	$-0.390713\pi$
$709$	17.9270	0.673261	0.336631	+	0.941637i	$0.390713\pi$
$710$	0.706396	0.0265106
$711$	10.1986	0.382477
$712$	−11.9091	−0.446313
$713$	−5.57020	−0.208606
$714$	35.4290	1.32590
$715$	1.41871	0.0530567
$716$	4.49908	0.168139
$717$	−29.3704	−1.09686
$718$	−0.586844	−0.0219008
$719$	16.3053	0.608084	0.304042	−	0.952659i	$-0.401664\pi$
$719$	16.3053	0.608084	0.304042	+	0.952659i	$0.401664\pi$
$720$	−0.435480	−0.0162294
$721$	40.5867	1.51153
$722$	30.1988	1.12388
$723$	10.3496	0.384906
$724$	27.7621	1.03177
$725$	−40.9128	−1.51946
$726$	27.2544	1.01150
$727$	46.7613	1.73428	0.867140	−	0.498064i	$-0.165956\pi$
$727$	46.7613	1.73428	0.867140	+	0.498064i	$0.165956\pi$
$728$	13.7475	0.509515
$729$	1.00000	0.0370370
$730$	−2.57826	−0.0954257
$731$	63.6176	2.35298
$732$	1.35431	0.0500569
$733$	−34.3505	−1.26877	−0.634383	−	0.773019i	$-0.718746\pi$
$733$	−34.3505	−1.26877	−0.634383	+	0.773019i	$0.718746\pi$
$734$	40.0270	1.47742
$735$	−0.537463	−0.0198246
$736$	−43.5948	−1.60693
$737$	15.3067	0.563830
$738$	9.85326	0.362703
$739$	31.0056	1.14056	0.570280	−	0.821451i	$-0.306835\pi$
$739$	31.0056	1.14056	0.570280	+	0.821451i	$0.306835\pi$
$740$	0.736423	0.0270715
$741$	4.90507	0.180192
$742$	−76.0307	−2.79117
$743$	−32.3758	−1.18775	−0.593876	−	0.804556i	$-0.702403\pi$
$743$	−32.3758	−1.18775	−0.593876	+	0.804556i	$0.702403\pi$
$744$	−1.00967	−0.0370163
$745$	−0.519638	−0.0190381
$746$	13.7343	0.502847
$747$	−4.82690	−0.176607
$748$	36.4898	1.33420
$749$	18.4701	0.674884
$750$	−1.62493	−0.0593342
$751$	5.40999	0.197414	0.0987068	−	0.995117i	$-0.468529\pi$
$751$	5.40999	0.197414	0.0987068	+	0.995117i	$0.468529\pi$
$752$	18.2037	0.663820
$753$	−9.20452	−0.335432
$754$	46.8022	1.70444
$755$	−0.389937	−0.0141913
$756$	4.81317	0.175053
$757$	25.1059	0.912488	0.456244	−	0.889855i	$-0.349194\pi$
$757$	25.1059	0.912488	0.456244	+	0.889855i	$0.349194\pi$
$758$	58.8465	2.13740
$759$	−34.1983	−1.24132
$760$	0.170046	0.00616821
$761$	−22.8176	−0.827138	−0.413569	−	0.910473i	$-0.635718\pi$
$761$	−22.8176	−0.827138	−0.413569	+	0.910473i	$0.635718\pi$
$762$	22.1785	0.803442
$763$	29.6895	1.07483
$764$	1.31886	0.0477148
$765$	−0.478786	−0.0173106
$766$	19.6344	0.709418
$767$	7.73290	0.279219
$768$	−20.9381	−0.755537
$769$	3.19460	0.115200	0.0576002	−	0.998340i	$-0.481655\pi$
$769$	3.19460	0.115200	0.0576002	+	0.998340i	$0.481655\pi$
$770$	−2.98953	−0.107735
$771$	−7.76335	−0.279590
$772$	16.5533	0.595767
$773$	44.8035	1.61147	0.805735	−	0.592276i	$-0.201771\pi$
$773$	44.8035	1.61147	0.805735	+	0.592276i	$0.201771\pi$
$774$	21.6081	0.776686
$775$	−4.14030	−0.148724
$776$	3.98079	0.142902
$777$	22.3883	0.803174
$778$	38.0129	1.36283
$779$	−8.46325	−0.303228
$780$	0.371451	0.0133001
$781$	22.1184	0.791457
$782$	−65.9085	−2.35688
$783$	−8.19556	−0.292885
$784$	−29.4996	−1.05356
$785$	1.42030	0.0506926
$786$	−7.31946	−0.261076
$787$	16.8883	0.602003	0.301002	−	0.953624i	$-0.402679\pi$
$787$	16.8883	0.602003	0.301002	+	0.953624i	$0.402679\pi$
$788$	26.0057	0.926414
$789$	−3.26409	−0.116205
$790$	−1.65852	−0.0590074
$791$	−27.6970	−0.984791
$792$	−6.19889	−0.220268
$793$	3.17748	0.112835
$794$	10.3411	0.366991
$795$	1.02748	0.0364408
$796$	−32.5215	−1.15269
$797$	−51.2579	−1.81565	−0.907824	−	0.419351i	$-0.862258\pi$
$797$	−51.2579	−1.81565	−0.907824	+	0.419351i	$0.862258\pi$
$798$	−10.3361	−0.365893
$799$	20.0140	0.708043
$800$	−32.4038	−1.14565
$801$	−9.78253	−0.345649
$802$	2.50557	0.0884749
$803$	−80.7294	−2.84888
$804$	4.00765	0.141339
$805$	2.15976	0.0761217
$806$	4.73630	0.166829
$807$	−15.0673	−0.530395
$808$	−8.21412	−0.288972
$809$	9.33516	0.328207	0.164103	−	0.986443i	$-0.447527\pi$
$809$	9.33516	0.328207	0.164103	+	0.986443i	$0.447527\pi$
$810$	−0.162622	−0.00571397
$811$	6.16823	0.216596	0.108298	−	0.994118i	$-0.465460\pi$
$811$	6.16823	0.216596	0.108298	+	0.994118i	$0.465460\pi$
$812$	−39.4466	−1.38431
$813$	5.34308	0.187390
$814$	57.6500	2.02063
$815$	1.90788	0.0668300
$816$	−26.2791	−0.919951
$817$	−18.5598	−0.649326
$818$	5.14030	0.179726
$819$	11.2926	0.394596
$820$	−0.640905	−0.0223814
$821$	−51.6821	−1.80372	−0.901859	−	0.432030i	$-0.857798\pi$
$821$	−51.6821	−1.80372	−0.901859	+	0.432030i	$0.857798\pi$
$822$	−22.0968	−0.770715
$823$	49.2507	1.71677	0.858386	−	0.513005i	$-0.171468\pi$
$823$	49.2507	1.71677	0.858386	+	0.513005i	$0.171468\pi$
$824$	−13.6859	−0.476773
$825$	−25.4194	−0.884991
$826$	−16.2950	−0.566974
$827$	5.70388	0.198343	0.0991717	−	0.995070i	$-0.468381\pi$
$827$	5.70388	0.198343	0.0991717	+	0.995070i	$0.468381\pi$
$828$	−8.95392	−0.311170
$829$	−54.3777	−1.88862	−0.944308	−	0.329064i	$-0.893267\pi$
$829$	−54.3777	−1.88862	−0.944308	+	0.329064i	$0.893267\pi$
$830$	0.784963	0.0272465
$831$	28.3622	0.983873
$832$	6.48357	0.224777
$833$	−32.4332	−1.12374
$834$	20.8065	0.720469
$835$	−1.09508	−0.0378968
$836$	−10.6455	−0.368184
$837$	−0.829377	−0.0286675
$838$	6.81755	0.235508
$839$	21.8358	0.753857	0.376928	−	0.926242i	$-0.376980\pi$
$839$	21.8358	0.753857	0.376928	+	0.926242i	$0.376980\pi$
$840$	0.391485	0.0135075
$841$	38.1672	1.31611
$842$	−25.5840	−0.881684
$843$	21.5231	0.741295
$844$	19.7738	0.680643
$845$	−0.286465	−0.00985470
$846$	6.79785	0.233715
$847$	−53.8943	−1.85183
$848$	56.3949	1.93661
$849$	27.1679	0.932400
$850$	−48.9894	−1.68032
$851$	−41.6488	−1.42770
$852$	5.79111	0.198400
$853$	4.18717	0.143366	0.0716830	−	0.997427i	$-0.477163\pi$
$853$	4.18717	0.143366	0.0716830	+	0.997427i	$0.477163\pi$
$854$	−6.69565	−0.229120
$855$	0.139681	0.00477700
$856$	−6.22818	−0.212875
$857$	−26.5397	−0.906579	−0.453289	−	0.891363i	$-0.649750\pi$
$857$	−26.5397	−0.906579	−0.453289	+	0.891363i	$0.649750\pi$
$858$	29.0786	0.992727
$859$	16.9927	0.579784	0.289892	−	0.957059i	$-0.406381\pi$
$859$	16.9927	0.579784	0.289892	+	0.957059i	$0.406381\pi$
$860$	−1.40550	−0.0479271
$861$	−19.4844	−0.664026
$862$	12.6405	0.430537
$863$	−41.2476	−1.40408	−0.702042	−	0.712135i	$-0.747728\pi$
$863$	−41.2476	−1.40408	−0.702042	+	0.712135i	$0.747728\pi$
$864$	−6.49106	−0.220830
$865$	1.26570	0.0430350
$866$	−20.7135	−0.703874
$867$	−11.8924	−0.403887
$868$	−3.99193	−0.135495
$869$	−51.9308	−1.76163
$870$	1.33278	0.0451855
$871$	9.40271	0.318599
$872$	−10.0114	−0.339028
$873$	3.26995	0.110671
$874$	19.2281	0.650402
$875$	3.21324	0.108627
$876$	−21.1369	−0.714148
$877$	−16.9220	−0.571415	−0.285708	−	0.958317i	$-0.592229\pi$
$877$	−16.9220	−0.571415	−0.285708	+	0.958317i	$0.592229\pi$
$878$	4.80114	0.162031
$879$	6.99808	0.236039
$880$	2.21745	0.0747502
$881$	−9.96061	−0.335581	−0.167791	−	0.985823i	$-0.553663\pi$
$881$	−9.96061	−0.335581	−0.167791	+	0.985823i	$0.553663\pi$
$882$	−11.0161	−0.370932
$883$	39.4123	1.32633	0.663165	−	0.748473i	$-0.269213\pi$
$883$	39.4123	1.32633	0.663165	+	0.748473i	$0.269213\pi$
$884$	22.4152	0.753906
$885$	0.220209	0.00740225
$886$	18.0315	0.605779
$887$	16.0523	0.538984	0.269492	−	0.963003i	$-0.413144\pi$
$887$	16.0523	0.538984	0.269492	+	0.963003i	$0.413144\pi$
$888$	−7.54938	−0.253341
$889$	−43.8570	−1.47092
$890$	1.59086	0.0533257
$891$	−5.09197	−0.170587
$892$	−9.17309	−0.307138
$893$	−5.83888	−0.195391
$894$	−10.6508	−0.356215
$895$	0.300594	0.0100477
$896$	33.2064	1.10935
$897$	−21.0076	−0.701423
$898$	12.2072	0.407361
$899$	6.79720	0.226699
$900$	−6.65541	−0.221847
$901$	62.0030	2.06562
$902$	−50.1725	−1.67056
$903$	−42.7290	−1.42193
$904$	9.33949	0.310627
$905$	1.85485	0.0616573
$906$	−7.99235	−0.265528
$907$	2.75942	0.0916249	0.0458125	−	0.998950i	$-0.485412\pi$
$907$	2.75942	0.0916249	0.0458125	+	0.998950i	$0.485412\pi$
$908$	−23.5300	−0.780871
$909$	−6.74734	−0.223795
$910$	−1.83643	−0.0608772
$911$	−48.5699	−1.60919	−0.804596	−	0.593823i	$-0.797618\pi$
$911$	−48.5699	−1.60919	−0.804596	+	0.593823i	$0.797618\pi$
$912$	7.66666	0.253869
$913$	24.5784	0.813427
$914$	−71.4614	−2.36373
$915$	0.0904847	0.00299133
$916$	33.8879	1.11969
$917$	14.4739	0.477971
$918$	−9.81346	−0.323892
$919$	15.9662	0.526676	0.263338	−	0.964704i	$-0.415177\pi$
$919$	15.9662	0.526676	0.263338	+	0.964704i	$0.415177\pi$
$920$	−0.728278	−0.0240106
$921$	−3.68377	−0.121384
$922$	10.1511	0.334308
$923$	13.5870	0.447223
$924$	−24.5085	−0.806271
$925$	−30.9573	−1.01787
$926$	35.5725	1.16899
$927$	−11.2421	−0.369238
$928$	53.1979	1.74631
$929$	26.0601	0.855005	0.427502	−	0.904014i	$-0.359394\pi$
$929$	26.0601	0.855005	0.427502	+	0.904014i	$0.359394\pi$
$930$	0.134875	0.00442273
$931$	9.46207	0.310107
$932$	−14.1636	−0.463945
$933$	−25.0499	−0.820096
$934$	41.3510	1.35305
$935$	2.43796	0.0797300
$936$	−3.80790	−0.124465
$937$	50.9199	1.66348	0.831740	−	0.555166i	$-0.187345\pi$
$937$	50.9199	1.66348	0.831740	+	0.555166i	$0.187345\pi$
$938$	−19.8136	−0.646937
$939$	23.7351	0.774567
$940$	−0.442166	−0.0144219
$941$	−17.4143	−0.567690	−0.283845	−	0.958870i	$-0.591610\pi$
$941$	−17.4143	−0.567690	−0.283845	+	0.958870i	$0.591610\pi$
$942$	29.1112	0.948494
$943$	36.2467	1.18035
$944$	12.0866	0.393385
$945$	0.321579	0.0104610
$946$	−110.028	−3.57731
$947$	4.59817	0.149420	0.0747102	−	0.997205i	$-0.476197\pi$
$947$	4.59817	0.149420	0.0747102	+	0.997205i	$0.476197\pi$
$948$	−13.5967	−0.441601
$949$	−49.5911	−1.60979
$950$	14.2922	0.463700
$951$	−16.8244	−0.545567
$952$	23.6242	0.765665
$953$	−12.7032	−0.411498	−0.205749	−	0.978605i	$-0.565963\pi$
$953$	−12.7032	−0.411498	−0.205749	+	0.978605i	$0.565963\pi$
$954$	21.0597	0.681832
$955$	0.0881161	0.00285137
$956$	39.1565	1.26641
$957$	41.7315	1.34899
$958$	35.1914	1.13698
$959$	43.6955	1.41100
$960$	0.184632	0.00595897
$961$	−30.3121	−0.977811
$962$	35.4137	1.14178
$963$	−5.11603	−0.164862
$964$	−13.7981	−0.444406
$965$	1.10596	0.0356022
$966$	44.2677	1.42429
$967$	−8.38740	−0.269721	−0.134860	−	0.990865i	$-0.543059\pi$
$967$	−8.38740	−0.269721	−0.134860	+	0.990865i	$0.543059\pi$
$968$	18.1733	0.584112
$969$	8.42907	0.270781
$970$	−0.531767	−0.0170740
$971$	−17.7070	−0.568245	−0.284122	−	0.958788i	$-0.591702\pi$
$971$	−17.7070	−0.568245	−0.284122	+	0.958788i	$0.591702\pi$
$972$	−1.33320	−0.0427623
$973$	−41.1439	−1.31901
$974$	60.9658	1.95347
$975$	−15.6148	−0.500075
$976$	4.96642	0.158971
$977$	−0.772680	−0.0247202	−0.0123601	−	0.999924i	$-0.503934\pi$
$977$	−0.772680	−0.0247202	−0.0123601	+	0.999924i	$0.503934\pi$
$978$	39.1048	1.25043
$979$	49.8123	1.59201
$980$	0.716543	0.0228891
$981$	−8.22366	−0.262561
$982$	42.8117	1.36618
$983$	−0.605210	−0.0193032	−0.00965160	−	0.999953i	$-0.503072\pi$
$983$	−0.605210	−0.0193032	−0.00965160	+	0.999953i	$0.503072\pi$
$984$	6.57018	0.209450
$985$	1.73750	0.0553612
$986$	80.4268	2.56131
$987$	−13.4425	−0.427878
$988$	−6.53942	−0.208047
$989$	79.4886	2.52759
$990$	0.828068	0.0263177
$991$	17.2405	0.547662	0.273831	−	0.961778i	$-0.411709\pi$
$991$	17.2405	0.547662	0.273831	+	0.961778i	$0.411709\pi$
$992$	5.38353	0.170927
$993$	−15.3426	−0.486884
$994$	−28.6309	−0.908117
$995$	−2.17283	−0.0688835
$996$	6.43521	0.203907
$997$	−34.3846	−1.08897	−0.544486	−	0.838770i	$-0.683275\pi$
$997$	−34.3846	−1.08897	−0.544486	+	0.838770i	$0.683275\pi$
$998$	−54.7440	−1.73289
$999$	−6.20131	−0.196201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2031.2.a.i.1.9	✓	38
3.2	odd	2		6093.2.a.o.1.30		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2031.2.a.i.1.9	✓	38	1.1	even	1	trivial
6093.2.a.o.1.30		38	3.2	odd	2

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:	\( N \)	\(=\)	\( 2031 = 3 \cdot 677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82570 q^{2} -1.00000 q^{3} +1.33320 q^{4} +0.0890738 q^{5} +1.82570 q^{6} -3.61025 q^{7} +1.21739 q^{8} +1.00000 q^{9} -0.162622 q^{10} -5.09197 q^{11} -1.33320 q^{12} -3.12793 q^{13} +6.59125 q^{14} -0.0890738 q^{15} -4.88898 q^{16} -5.37516 q^{17} -1.82570 q^{18} +1.56815 q^{19} +0.118753 q^{20} +3.61025 q^{21} +9.29643 q^{22} -6.71613 q^{23} -1.21739 q^{24} -4.99207 q^{25} +5.71068 q^{26} -1.00000 q^{27} -4.81317 q^{28} +8.19556 q^{29} +0.162622 q^{30} +0.829377 q^{31} +6.49106 q^{32} +5.09197 q^{33} +9.81346 q^{34} -0.321579 q^{35} +1.33320 q^{36} +6.20131 q^{37} -2.86298 q^{38} +3.12793 q^{39} +0.108437 q^{40} -5.39696 q^{41} -6.59125 q^{42} -11.8355 q^{43} -6.78859 q^{44} +0.0890738 q^{45} +12.2617 q^{46} -3.72341 q^{47} +4.88898 q^{48} +6.03390 q^{49} +9.11404 q^{50} +5.37516 q^{51} -4.17015 q^{52} -11.5351 q^{53} +1.82570 q^{54} -0.453561 q^{55} -4.39507 q^{56} -1.56815 q^{57} -14.9627 q^{58} -2.47221 q^{59} -0.118753 q^{60} -1.01584 q^{61} -1.51420 q^{62} -3.61025 q^{63} -2.07280 q^{64} -0.278617 q^{65} -9.29643 q^{66} -3.00605 q^{67} -7.16615 q^{68} +6.71613 q^{69} +0.587108 q^{70} -4.34378 q^{71} +1.21739 q^{72} +15.8543 q^{73} -11.3218 q^{74} +4.99207 q^{75} +2.09065 q^{76} +18.3833 q^{77} -5.71068 q^{78} +10.1986 q^{79} -0.435480 q^{80} +1.00000 q^{81} +9.85326 q^{82} -4.82690 q^{83} +4.81317 q^{84} -0.478786 q^{85} +21.6081 q^{86} -8.19556 q^{87} -6.19889 q^{88} -9.78253 q^{89} -0.162622 q^{90} +11.2926 q^{91} -8.95392 q^{92} -0.829377 q^{93} +6.79785 q^{94} +0.139681 q^{95} -6.49106 q^{96} +3.26995 q^{97} -11.0161 q^{98} -5.09197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 3 q^{2} - 38 q^{3} + 49 q^{4} + 3 q^{5} + 3 q^{6} + 7 q^{7} - 12 q^{8} + 38 q^{9} + 14 q^{10} - 12 q^{11} - 49 q^{12} + 24 q^{13} + q^{14} - 3 q^{15} + 71 q^{16} + 12 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 38 * q - 3 * q^2 - 38 * q^3 + 49 * q^4 + 3 * q^5 + 3 * q^6 + 7 * q^7 - 12 * q^8 + 38 * q^9 + 14 * q^10 - 12 * q^11 - 49 * q^12 + 24 * q^13 + q^14 - 3 * q^15 + 71 * q^16 + 12 * q^17 - 3 * q^18 + 16 * q^19 + 6 * q^20 - 7 * q^21 + 20 * q^22 - 35 * q^23 + 12 * q^24 + 85 * q^25 + 33 * q^26 - 38 * q^27 + 23 * q^28 + 13 * q^29 - 14 * q^30 + 27 * q^31 - 22 * q^32 + 12 * q^33 + 45 * q^34 - 23 * q^35 + 49 * q^36 + 28 * q^37 + 16 * q^38 - 24 * q^39 + 52 * q^40 + 53 * q^41 - q^42 + 17 * q^43 - 8 * q^44 + 3 * q^45 + 28 * q^46 - 13 * q^47 - 71 * q^48 + 135 * q^49 - 7 * q^50 - 12 * q^51 + 68 * q^52 + 6 * q^53 + 3 * q^54 + 49 * q^55 + 13 * q^56 - 16 * q^57 + 26 * q^58 + 17 * q^59 - 6 * q^60 + 63 * q^61 + 13 * q^62 + 7 * q^63 + 100 * q^64 + 29 * q^65 - 20 * q^66 + 28 * q^67 - 17 * q^68 + 35 * q^69 + 44 * q^70 - 2 * q^71 - 12 * q^72 + 55 * q^73 - 13 * q^74 - 85 * q^75 + 53 * q^76 - 23 * q^77 - 33 * q^78 + 30 * q^79 + 19 * q^80 + 38 * q^81 + 55 * q^82 - 19 * q^83 - 23 * q^84 + 45 * q^85 + 12 * q^86 - 13 * q^87 + 47 * q^88 + 126 * q^89 + 14 * q^90 + 66 * q^91 - 77 * q^92 - 27 * q^93 + 52 * q^94 - 53 * q^95 + 22 * q^96 + 80 * q^97 + 4 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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