LMFDB - Embedded newform 4001.2.a.a.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.75222 q^{2} -2.39793 q^{3} +1.07026 q^{4} -1.87948 q^{5} +4.20169 q^{6} -0.610730 q^{7} +1.62910 q^{8} +2.75008 q^{9} +3.29326 q^{10} +2.33584 q^{11} -2.56641 q^{12} +1.51936 q^{13} +1.07013 q^{14} +4.50687 q^{15} -4.99506 q^{16} -6.58782 q^{17} -4.81873 q^{18} -2.33384 q^{19} -2.01154 q^{20} +1.46449 q^{21} -4.09290 q^{22} +6.92929 q^{23} -3.90648 q^{24} -1.46754 q^{25} -2.66225 q^{26} +0.599300 q^{27} -0.653641 q^{28} -3.90459 q^{29} -7.89702 q^{30} +0.969877 q^{31} +5.49422 q^{32} -5.60118 q^{33} +11.5433 q^{34} +1.14786 q^{35} +2.94330 q^{36} +3.91378 q^{37} +4.08938 q^{38} -3.64333 q^{39} -3.06187 q^{40} -4.63610 q^{41} -2.56610 q^{42} -7.06881 q^{43} +2.49996 q^{44} -5.16873 q^{45} -12.1416 q^{46} +4.03611 q^{47} +11.9778 q^{48} -6.62701 q^{49} +2.57145 q^{50} +15.7971 q^{51} +1.62612 q^{52} -10.3645 q^{53} -1.05010 q^{54} -4.39017 q^{55} -0.994942 q^{56} +5.59638 q^{57} +6.84168 q^{58} +6.78540 q^{59} +4.82353 q^{60} +4.95132 q^{61} -1.69943 q^{62} -1.67955 q^{63} +0.363058 q^{64} -2.85562 q^{65} +9.81448 q^{66} +10.0456 q^{67} -7.05069 q^{68} -16.6160 q^{69} -2.01129 q^{70} +4.45183 q^{71} +4.48016 q^{72} +0.0554320 q^{73} -6.85779 q^{74} +3.51906 q^{75} -2.49781 q^{76} -1.42657 q^{77} +6.38391 q^{78} +4.37186 q^{79} +9.38814 q^{80} -9.68731 q^{81} +8.12345 q^{82} -13.1767 q^{83} +1.56739 q^{84} +12.3817 q^{85} +12.3861 q^{86} +9.36293 q^{87} +3.80532 q^{88} +11.6764 q^{89} +9.05672 q^{90} -0.927922 q^{91} +7.41615 q^{92} -2.32570 q^{93} -7.07214 q^{94} +4.38641 q^{95} -13.1748 q^{96} +13.8586 q^{97} +11.6120 q^{98} +6.42374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18}+ \cdots - 131 q^{99}+O(q^{100}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−1.75222	−1.23900	−0.619502	−	0.784995i	$-0.712665\pi$
$2$	−1.75222	−1.23900	−0.619502	+	0.784995i	$0.712665\pi$
$3$	−2.39793	−1.38445	−0.692223	−	0.721683i	$-0.743369\pi$
$3$	−2.39793	−1.38445	−0.692223	+	0.721683i	$0.743369\pi$
$4$	1.07026	0.535131
$5$	−1.87948	−0.840531	−0.420265	−	0.907401i	$-0.638063\pi$
$5$	−1.87948	−0.840531	−0.420265	+	0.907401i	$0.638063\pi$
$6$	4.20169	1.71533
$7$	−0.610730	−0.230834	−0.115417	−	0.993317i	$-0.536820\pi$
$7$	−0.610730	−0.230834	−0.115417	+	0.993317i	$0.536820\pi$
$8$	1.62910	0.575975
$9$	2.75008	0.916692
$10$	3.29326	1.04142
$11$	2.33584	0.704282	0.352141	−	0.935947i	$-0.385454\pi$
$11$	2.33584	0.704282	0.352141	+	0.935947i	$0.385454\pi$
$12$	−2.56641	−0.740860
$13$	1.51936	0.421396	0.210698	−	0.977551i	$-0.432426\pi$
$13$	1.51936	0.421396	0.210698	+	0.977551i	$0.432426\pi$
$14$	1.07013	0.286005
$15$	4.50687	1.16367
$16$	−4.99506	−1.24877
$17$	−6.58782	−1.59778	−0.798890	−	0.601477i	$-0.794579\pi$
$17$	−6.58782	−1.59778	−0.798890	+	0.601477i	$0.794579\pi$
$18$	−4.81873	−1.13579
$19$	−2.33384	−0.535419	−0.267709	−	0.963500i	$-0.586267\pi$
$19$	−2.33384	−0.535419	−0.267709	+	0.963500i	$0.586267\pi$
$20$	−2.01154	−0.449794
$21$	1.46449	0.319578
$22$	−4.09290	−0.872608
$23$	6.92929	1.44486	0.722429	−	0.691445i	$-0.243026\pi$
$23$	6.92929	1.44486	0.722429	+	0.691445i	$0.243026\pi$
$24$	−3.90648	−0.797406
$25$	−1.46754	−0.293508
$26$	−2.66225	−0.522111
$27$	0.599300	0.115335
$28$	−0.653641	−0.123527
$29$	−3.90459	−0.725064	−0.362532	−	0.931971i	$-0.618088\pi$
$29$	−3.90459	−0.725064	−0.362532	+	0.931971i	$0.618088\pi$
$30$	−7.89702	−1.44179
$31$	0.969877	0.174195	0.0870975	−	0.996200i	$-0.472241\pi$
$31$	0.969877	0.174195	0.0870975	+	0.996200i	$0.472241\pi$
$32$	5.49422	0.971251
$33$	−5.60118	−0.975041
$34$	11.5433	1.97966
$35$	1.14786	0.194023
$36$	2.94330	0.490550
$37$	3.91378	0.643422	0.321711	−	0.946838i	$-0.395742\pi$
$37$	3.91378	0.643422	0.321711	+	0.946838i	$0.395742\pi$
$38$	4.08938	0.663386
$39$	−3.64333	−0.583400
$40$	−3.06187	−0.484125
$41$	−4.63610	−0.724037	−0.362019	−	0.932171i	$-0.617912\pi$
$41$	−4.63610	−0.724037	−0.362019	+	0.932171i	$0.617912\pi$
$42$	−2.56610	−0.395958
$43$	−7.06881	−1.07798	−0.538992	−	0.842311i	$-0.681195\pi$
$43$	−7.06881	−1.07798	−0.538992	+	0.842311i	$0.681195\pi$
$44$	2.49996	0.376883
$45$	−5.16873	−0.770508
$46$	−12.1416	−1.79018
$47$	4.03611	0.588727	0.294364	−	0.955694i	$-0.404892\pi$
$47$	4.03611	0.588727	0.294364	+	0.955694i	$0.404892\pi$
$48$	11.9778	1.72885
$49$	−6.62701	−0.946716
$50$	2.57145	0.363657
$51$	15.7971	2.21204
$52$	1.62612	0.225502
$53$	−10.3645	−1.42367	−0.711836	−	0.702346i	$-0.752136\pi$
$53$	−10.3645	−1.42367	−0.711836	+	0.702346i	$0.752136\pi$
$54$	−1.05010	−0.142901
$55$	−4.39017	−0.591971
$56$	−0.994942	−0.132955
$57$	5.59638	0.741259
$58$	6.84168	0.898357
$59$	6.78540	0.883384	0.441692	−	0.897167i	$-0.354378\pi$
$59$	6.78540	0.883384	0.441692	+	0.897167i	$0.354378\pi$
$60$	4.82353	0.622716
$61$	4.95132	0.633951	0.316976	−	0.948434i	$-0.397333\pi$
$61$	4.95132	0.633951	0.316976	+	0.948434i	$0.397333\pi$
$62$	−1.69943	−0.215828
$63$	−1.67955	−0.211604
$64$	0.363058	0.0453822
$65$	−2.85562	−0.354196
$66$	9.81448	1.20808
$67$	10.0456	1.22726	0.613631	−	0.789593i	$-0.289708\pi$
$67$	10.0456	1.22726	0.613631	+	0.789593i	$0.289708\pi$
$68$	−7.05069	−0.855021
$69$	−16.6160	−2.00033
$70$	−2.01129	−0.240396
$71$	4.45183	0.528334	0.264167	−	0.964477i	$-0.414903\pi$
$71$	4.45183	0.528334	0.264167	+	0.964477i	$0.414903\pi$
$72$	4.48016	0.527992
$73$	0.0554320	0.00648783	0.00324391	−	0.999995i	$-0.498967\pi$
$73$	0.0554320	0.00648783	0.00324391	+	0.999995i	$0.498967\pi$
$74$	−6.85779	−0.797202
$75$	3.51906	0.406346
$76$	−2.49781	−0.286519
$77$	−1.42657	−0.162572
$78$	6.38391	0.722835
$79$	4.37186	0.491873	0.245936	−	0.969286i	$-0.420905\pi$
$79$	4.37186	0.491873	0.245936	+	0.969286i	$0.420905\pi$
$80$	9.38814	1.04963
$81$	−9.68731	−1.07637
$82$	8.12345	0.897085
$83$	−13.1767	−1.44633	−0.723167	−	0.690673i	$-0.757315\pi$
$83$	−13.1767	−1.44633	−0.723167	+	0.690673i	$0.757315\pi$
$84$	1.56739	0.171016
$85$	12.3817	1.34298
$86$	12.3861	1.33563
$87$	9.36293	1.00381
$88$	3.80532	0.405649
$89$	11.6764	1.23769	0.618847	−	0.785512i	$-0.287600\pi$
$89$	11.6764	1.23769	0.618847	+	0.785512i	$0.287600\pi$
$90$	9.05672	0.954662
$91$	−0.927922	−0.0972726
$92$	7.41615	0.773187
$93$	−2.32570	−0.241164
$94$	−7.07214	−0.729435
$95$	4.38641	0.450036
$96$	−13.1748	−1.34464
$97$	13.8586	1.40712	0.703562	−	0.710634i	$-0.251592\pi$
$97$	13.8586	1.40712	0.703562	+	0.710634i	$0.251592\pi$
$98$	11.6120	1.17298
$99$	6.42374	0.645610
$100$	−1.57065	−0.157065
$101$	6.27475	0.624361	0.312180	−	0.950023i	$-0.398941\pi$
$101$	6.27475	0.624361	0.312180	+	0.950023i	$0.398941\pi$
$102$	−27.6800	−2.74073
$103$	6.20460	0.611357	0.305679	−	0.952135i	$-0.401117\pi$
$103$	6.20460	0.611357	0.305679	+	0.952135i	$0.401117\pi$
$104$	2.47520	0.242713
$105$	−2.75248	−0.268615
$106$	18.1608	1.76393
$107$	6.91973	0.668956	0.334478	−	0.942404i	$-0.391440\pi$
$107$	6.91973	0.668956	0.334478	+	0.942404i	$0.391440\pi$
$108$	0.641407	0.0617195
$109$	10.4036	0.996486	0.498243	−	0.867037i	$-0.333979\pi$
$109$	10.4036	0.996486	0.498243	+	0.867037i	$0.333979\pi$
$110$	7.69253	0.733454
$111$	−9.38498	−0.890783
$112$	3.05064	0.288258
$113$	10.7723	1.01337	0.506686	−	0.862130i	$-0.330870\pi$
$113$	10.7723	1.01337	0.506686	+	0.862130i	$0.330870\pi$
$114$	−9.80607	−0.918422
$115$	−13.0235	−1.21445
$116$	−4.17893	−0.388004
$117$	4.17837	0.386290
$118$	−11.8895	−1.09452
$119$	4.02338	0.368822
$120$	7.34216	0.670245
$121$	−5.54385	−0.503987
$122$	−8.67578	−0.785468
$123$	11.1171	1.00239
$124$	1.03802	0.0932171
$125$	12.1556	1.08723
$126$	2.94294	0.262178
$127$	3.69183	0.327597	0.163798	−	0.986494i	$-0.447625\pi$
$127$	3.69183	0.327597	0.163798	+	0.986494i	$0.447625\pi$
$128$	−11.6246	−1.02748
$129$	16.9505	1.49241
$130$	5.00367	0.438851
$131$	2.85891	0.249785	0.124892	−	0.992170i	$-0.460141\pi$
$131$	2.85891	0.249785	0.124892	+	0.992170i	$0.460141\pi$
$132$	−5.99473	−0.521774
$133$	1.42534	0.123593
$134$	−17.6020	−1.52058
$135$	−1.12637	−0.0969429
$136$	−10.7322	−0.920281
$137$	10.7938	0.922176	0.461088	−	0.887354i	$-0.347459\pi$
$137$	10.7938	0.922176	0.461088	+	0.887354i	$0.347459\pi$
$138$	29.1148	2.47841
$139$	−14.2798	−1.21120	−0.605598	−	0.795771i	$-0.707066\pi$
$139$	−14.2798	−1.21120	−0.605598	+	0.795771i	$0.707066\pi$
$140$	1.22851	0.103828
$141$	−9.67832	−0.815061
$142$	−7.80056	−0.654608
$143$	3.54899	0.296782
$144$	−13.7368	−1.14473
$145$	7.33861	0.609438
$146$	−0.0971289	−0.00803844
$147$	15.8911	1.31068
$148$	4.18877	0.344315
$149$	−3.81194	−0.312286	−0.156143	−	0.987734i	$-0.549906\pi$
$149$	−3.81194	−0.312286	−0.156143	+	0.987734i	$0.549906\pi$
$150$	−6.16615	−0.503464
$151$	3.70713	0.301682	0.150841	−	0.988558i	$-0.451802\pi$
$151$	3.70713	0.301682	0.150841	+	0.988558i	$0.451802\pi$
$152$	−3.80206	−0.308388
$153$	−18.1170	−1.46467
$154$	2.49965	0.201428
$155$	−1.82287	−0.146416
$156$	−3.89932	−0.312195
$157$	−15.2284	−1.21536	−0.607679	−	0.794182i	$-0.707899\pi$
$157$	−15.2284	−1.21536	−0.607679	+	0.794182i	$0.707899\pi$
$158$	−7.66044	−0.609432
$159$	24.8533	1.97100
$160$	−10.3263	−0.816366
$161$	−4.23193	−0.333523
$162$	16.9743	1.33362
$163$	−3.24862	−0.254452	−0.127226	−	0.991874i	$-0.540607\pi$
$163$	−3.24862	−0.254452	−0.127226	+	0.991874i	$0.540607\pi$
$164$	−4.96184	−0.387455
$165$	10.5273	0.819552
$166$	23.0885	1.79201
$167$	8.70119	0.673318	0.336659	−	0.941627i	$-0.390703\pi$
$167$	8.70119	0.673318	0.336659	+	0.941627i	$0.390703\pi$
$168$	2.38580	0.184069
$169$	−10.6915	−0.822426
$170$	−21.6954	−1.66396
$171$	−6.41823	−0.490814
$172$	−7.56547	−0.576862
$173$	24.0238	1.82649	0.913246	−	0.407408i	$-0.133567\pi$
$173$	24.0238	1.82649	0.913246	+	0.407408i	$0.133567\pi$
$174$	−16.4059	−1.24373
$175$	0.896270	0.0677517
$176$	−11.6677	−0.879483
$177$	−16.2709	−1.22300
$178$	−20.4595	−1.53351
$179$	21.1231	1.57881	0.789406	−	0.613871i	$-0.210389\pi$
$179$	21.1231	1.57881	0.789406	+	0.613871i	$0.210389\pi$
$180$	−5.53189	−0.412322
$181$	−2.44328	−0.181608	−0.0908038	−	0.995869i	$-0.528944\pi$
$181$	−2.44328	−0.181608	−0.0908038	+	0.995869i	$0.528944\pi$
$182$	1.62592	0.120521
$183$	−11.8729	−0.877671
$184$	11.2885	0.832202
$185$	−7.35589	−0.540816
$186$	4.07513	0.298803
$187$	−15.3881	−1.12529
$188$	4.31969	0.315046
$189$	−0.366010	−0.0266233
$190$	−7.68593	−0.557596
$191$	−10.8126	−0.782369	−0.391185	−	0.920312i	$-0.627935\pi$
$191$	−10.8126	−0.782369	−0.391185	+	0.920312i	$0.627935\pi$
$192$	−0.870588	−0.0628293
$193$	−15.4966	−1.11547	−0.557736	−	0.830019i	$-0.688330\pi$
$193$	−15.4966	−1.11547	−0.557736	+	0.830019i	$0.688330\pi$
$194$	−24.2832	−1.74343
$195$	6.84758	0.490366
$196$	−7.09263	−0.506617
$197$	1.15213	0.0820856	0.0410428	−	0.999157i	$-0.486932\pi$
$197$	1.15213	0.0820856	0.0410428	+	0.999157i	$0.486932\pi$
$198$	−11.2558	−0.799913
$199$	−13.0606	−0.925840	−0.462920	−	0.886400i	$-0.653198\pi$
$199$	−13.0606	−0.925840	−0.462920	+	0.886400i	$0.653198\pi$
$200$	−2.39077	−0.169053
$201$	−24.0886	−1.69908
$202$	−10.9947	−0.773586
$203$	2.38465	0.167370
$204$	16.9071	1.18373
$205$	8.71348	0.608576
$206$	−10.8718	−0.757474
$207$	19.0561	1.32449
$208$	−7.58932	−0.526225
$209$	−5.45147	−0.377086
$210$	4.82295	0.332815
$211$	−2.56314	−0.176454	−0.0882270	−	0.996100i	$-0.528120\pi$
$211$	−2.56314	−0.176454	−0.0882270	+	0.996100i	$0.528120\pi$
$212$	−11.0927	−0.761850
$213$	−10.6752	−0.731451
$214$	−12.1249	−0.828838
$215$	13.2857	0.906078
$216$	0.976321	0.0664302
$217$	−0.592333	−0.0402102
$218$	−18.2294	−1.23465
$219$	−0.132922	−0.00898205
$220$	−4.69863	−0.316782
$221$	−10.0093	−0.673298
$222$	16.4445	1.10368
$223$	−13.6415	−0.913502	−0.456751	−	0.889595i	$-0.650987\pi$
$223$	−13.6415	−0.913502	−0.456751	+	0.889595i	$0.650987\pi$
$224$	−3.35549	−0.224198
$225$	−4.03584	−0.269056
$226$	−18.8754	−1.25557
$227$	−19.8683	−1.31871	−0.659353	−	0.751833i	$-0.729170\pi$
$227$	−19.8683	−1.31871	−0.659353	+	0.751833i	$0.729170\pi$
$228$	5.98959	0.396670
$229$	−10.0766	−0.665878	−0.332939	−	0.942948i	$-0.608040\pi$
$229$	−10.0766	−0.665878	−0.332939	+	0.942948i	$0.608040\pi$
$230$	22.8200	1.50470
$231$	3.42081	0.225073
$232$	−6.36097	−0.417618
$233$	10.1106	0.662366	0.331183	−	0.943566i	$-0.392552\pi$
$233$	10.1106	0.662366	0.331183	+	0.943566i	$0.392552\pi$
$234$	−7.32140	−0.478615
$235$	−7.58580	−0.494843
$236$	7.26215	0.472726
$237$	−10.4834	−0.680971
$238$	−7.04983	−0.456972
$239$	−9.67476	−0.625808	−0.312904	−	0.949785i	$-0.601302\pi$
$239$	−9.67476	−0.625808	−0.312904	+	0.949785i	$0.601302\pi$
$240$	−22.5121	−1.45315
$241$	−16.5743	−1.06764	−0.533821	−	0.845597i	$-0.679245\pi$
$241$	−16.5743	−1.06764	−0.533821	+	0.845597i	$0.679245\pi$
$242$	9.71403	0.624442
$243$	21.4316	1.37484
$244$	5.29920	0.339247
$245$	12.4554	0.795744
$246$	−19.4795	−1.24197
$247$	−3.54595	−0.225623
$248$	1.58003	0.100332
$249$	31.5969	2.00237
$250$	−21.2993	−1.34709
$251$	2.70795	0.170924	0.0854622	−	0.996341i	$-0.472763\pi$
$251$	2.70795	0.170924	0.0854622	+	0.996341i	$0.472763\pi$
$252$	−1.79756	−0.113236
$253$	16.1857	1.01759
$254$	−6.46888	−0.405894
$255$	−29.6905	−1.85929
$256$	19.6427	1.22767
$257$	30.2476	1.88680	0.943398	−	0.331662i	$-0.107609\pi$
$257$	30.2476	1.88680	0.943398	+	0.331662i	$0.107609\pi$
$258$	−29.7010	−1.84910
$259$	−2.39026	−0.148524
$260$	−3.05626	−0.189541
$261$	−10.7379	−0.664660
$262$	−5.00944	−0.309484
$263$	−0.453414	−0.0279587	−0.0139794	−	0.999902i	$-0.504450\pi$
$263$	−0.453414	−0.0279587	−0.0139794	+	0.999902i	$0.504450\pi$
$264$	−9.12490	−0.561599
$265$	19.4799	1.19664
$266$	−2.49751	−0.153132
$267$	−27.9991	−1.71352
$268$	10.7514	0.656746
$269$	5.91568	0.360685	0.180343	−	0.983604i	$-0.442279\pi$
$269$	5.91568	0.360685	0.180343	+	0.983604i	$0.442279\pi$
$270$	1.97365	0.120113
$271$	−19.5712	−1.18886	−0.594432	−	0.804146i	$-0.702623\pi$
$271$	−19.5712	−1.18886	−0.594432	+	0.804146i	$0.702623\pi$
$272$	32.9066	1.99525
$273$	2.22509	0.134669
$274$	−18.9131	−1.14258
$275$	−3.42794	−0.206712
$276$	−17.7834	−1.07044
$277$	32.4876	1.95199	0.975995	−	0.217795i	$-0.0698863\pi$
$277$	32.4876	1.95199	0.975995	+	0.217795i	$0.0698863\pi$
$278$	25.0213	1.50068
$279$	2.66724	0.159683
$280$	1.86998	0.111753
$281$	−12.4608	−0.743349	−0.371675	−	0.928363i	$-0.621216\pi$
$281$	−12.4608	−0.743349	−0.371675	+	0.928363i	$0.621216\pi$
$282$	16.9585	1.00986
$283$	27.5926	1.64021	0.820106	−	0.572211i	$-0.193914\pi$
$283$	27.5926	1.64021	0.820106	+	0.572211i	$0.193914\pi$
$284$	4.76462	0.282728
$285$	−10.5183	−0.623051
$286$	−6.21860	−0.367713
$287$	2.83141	0.167133
$288$	15.1095	0.890338
$289$	26.3993	1.55290
$290$	−12.8588	−0.755096
$291$	−33.2319	−1.94809
$292$	0.0593268	0.00347184
$293$	7.04808	0.411753	0.205877	−	0.978578i	$-0.433995\pi$
$293$	7.04808	0.411753	0.205877	+	0.978578i	$0.433995\pi$
$294$	−27.8447	−1.62393
$295$	−12.7531	−0.742511
$296$	6.37595	0.370595
$297$	1.39987	0.0812286
$298$	6.67933	0.386923
$299$	10.5281	0.608857
$300$	3.76631	0.217448
$301$	4.31713	0.248836
$302$	−6.49570	−0.373786
$303$	−15.0464	−0.864394
$304$	11.6577	0.668613
$305$	−9.30592	−0.532855
$306$	31.7449	1.81474
$307$	−25.5358	−1.45741	−0.728704	−	0.684829i	$-0.759877\pi$
$307$	−25.5358	−1.45741	−0.728704	+	0.684829i	$0.759877\pi$
$308$	−1.52680	−0.0869975
$309$	−14.8782	−0.846391
$310$	3.19406	0.181410
$311$	−19.5720	−1.10983	−0.554913	−	0.831908i	$-0.687249\pi$
$311$	−19.5720	−1.10983	−0.554913	+	0.831908i	$0.687249\pi$
$312$	−5.93536	−0.336024
$313$	−19.6768	−1.11220	−0.556099	−	0.831116i	$-0.687702\pi$
$313$	−19.6768	−1.11220	−0.556099	+	0.831116i	$0.687702\pi$
$314$	26.6835	1.50583
$315$	3.15670	0.177860
$316$	4.67903	0.263216
$317$	21.9727	1.23411	0.617054	−	0.786920i	$-0.288326\pi$
$317$	21.9727	1.23411	0.617054	+	0.786920i	$0.288326\pi$
$318$	−43.5484	−2.44207
$319$	−9.12049	−0.510649
$320$	−0.682362	−0.0381452
$321$	−16.5930	−0.926133
$322$	7.41525	0.413236
$323$	15.3749	0.855481
$324$	−10.3680	−0.575997
$325$	−2.22973	−0.123683
$326$	5.69229	0.315267
$327$	−24.9472	−1.37958
$328$	−7.55269	−0.417027
$329$	−2.46497	−0.135898
$330$	−18.4462	−1.01543
$331$	−30.5674	−1.68014	−0.840069	−	0.542480i	$-0.817485\pi$
$331$	−30.5674	−1.68014	−0.840069	+	0.542480i	$0.817485\pi$
$332$	−14.1026	−0.773978
$333$	10.7632	0.589820
$334$	−15.2464	−0.834244
$335$	−18.8805	−1.03155
$336$	−7.31522	−0.399078
$337$	15.5416	0.846606	0.423303	−	0.905988i	$-0.360871\pi$
$337$	15.5416	0.846606	0.423303	+	0.905988i	$0.360871\pi$
$338$	18.7339	1.01899
$339$	−25.8312	−1.40296
$340$	13.2517	0.718672
$341$	2.26548	0.122682
$342$	11.2461	0.608121
$343$	8.32242	0.449369
$344$	−11.5158	−0.620891
$345$	31.2295	1.68134
$346$	−42.0948	−2.26303
$347$	18.6287	1.00004	0.500021	−	0.866013i	$-0.333326\pi$
$347$	18.6287	1.00004	0.500021	+	0.866013i	$0.333326\pi$
$348$	10.0208	0.537170
$349$	−22.2554	−1.19130	−0.595651	−	0.803243i	$-0.703106\pi$
$349$	−22.2554	−1.19130	−0.595651	+	0.803243i	$0.703106\pi$
$350$	−1.57046	−0.0839446
$351$	0.910555	0.0486018
$352$	12.8336	0.684035
$353$	−11.7167	−0.623619	−0.311810	−	0.950145i	$-0.600935\pi$
$353$	−11.7167	−0.623619	−0.311810	+	0.950145i	$0.600935\pi$
$354$	28.5102	1.51530
$355$	−8.36714	−0.444081
$356$	12.4968	0.662328
$357$	−9.64779	−0.510615
$358$	−37.0122	−1.95615
$359$	10.4582	0.551960	0.275980	−	0.961163i	$-0.410998\pi$
$359$	10.4582	0.551960	0.275980	+	0.961163i	$0.410998\pi$
$360$	−8.42039	−0.443793
$361$	−13.5532	−0.713327
$362$	4.28116	0.225013
$363$	13.2938	0.697743
$364$	−0.993119	−0.0520536
$365$	−0.104184	−0.00545322
$366$	20.8039	1.08744
$367$	−8.61868	−0.449891	−0.224946	−	0.974371i	$-0.572220\pi$
$367$	−8.61868	−0.449891	−0.224946	+	0.974371i	$0.572220\pi$
$368$	−34.6123	−1.80429
$369$	−12.7496	−0.663719
$370$	12.8891	0.670073
$371$	6.32990	0.328632
$372$	−2.48911	−0.129054
$373$	18.5096	0.958390	0.479195	−	0.877708i	$-0.340929\pi$
$373$	18.5096	0.958390	0.479195	+	0.877708i	$0.340929\pi$
$374$	26.9632	1.39424
$375$	−29.1484	−1.50522
$376$	6.57524	0.339092
$377$	−5.93249	−0.305539
$378$	0.641329	0.0329864
$379$	−11.2857	−0.579708	−0.289854	−	0.957071i	$-0.593607\pi$
$379$	−11.2857	−0.579708	−0.289854	+	0.957071i	$0.593607\pi$
$380$	4.69460	0.240828
$381$	−8.85275	−0.453540
$382$	18.9459	0.969359
$383$	−22.5718	−1.15337	−0.576683	−	0.816968i	$-0.695653\pi$
$383$	−22.5718	−1.15337	−0.576683	+	0.816968i	$0.695653\pi$
$384$	27.8750	1.42249
$385$	2.68121	0.136647
$386$	27.1534	1.38207
$387$	−19.4398	−0.988179
$388$	14.8323	0.752995
$389$	0.448333	0.0227314	0.0113657	−	0.999935i	$-0.496382\pi$
$389$	0.448333	0.0227314	0.0113657	+	0.999935i	$0.496382\pi$
$390$	−11.9984	−0.607565
$391$	−45.6489	−2.30856
$392$	−10.7961	−0.545284
$393$	−6.85548	−0.345813
$394$	−2.01877	−0.101704
$395$	−8.21684	−0.413434
$396$	6.87508	0.345486
$397$	24.6629	1.23780	0.618899	−	0.785471i	$-0.287579\pi$
$397$	24.6629	1.23780	0.618899	+	0.785471i	$0.287579\pi$
$398$	22.8850	1.14712
$399$	−3.41788	−0.171108
$400$	7.33045	0.366523
$401$	−15.2360	−0.760848	−0.380424	−	0.924812i	$-0.624222\pi$
$401$	−15.2360	−0.760848	−0.380424	+	0.924812i	$0.624222\pi$
$402$	42.2084	2.10517
$403$	1.47360	0.0734051
$404$	6.71562	0.334115
$405$	18.2071	0.904720
$406$	−4.17842	−0.207371
$407$	9.14197	0.453150
$408$	25.7352	1.27408
$409$	20.6393	1.02055	0.510274	−	0.860012i	$-0.329544\pi$
$409$	20.6393	1.02055	0.510274	+	0.860012i	$0.329544\pi$
$410$	−15.2679	−0.754028
$411$	−25.8828	−1.27670
$412$	6.64054	0.327156
$413$	−4.14405	−0.203915
$414$	−33.3904	−1.64105
$415$	24.7655	1.21569
$416$	8.34773	0.409281
$417$	34.2419	1.67684
$418$	9.55215	0.467211
$419$	1.58967	0.0776607	0.0388303	−	0.999246i	$-0.487637\pi$
$419$	1.58967	0.0776607	0.0388303	+	0.999246i	$0.487637\pi$
$420$	−2.94588	−0.143744
$421$	−16.8457	−0.821009	−0.410504	−	0.911859i	$-0.634647\pi$
$421$	−16.8457	−0.821009	−0.410504	+	0.911859i	$0.634647\pi$
$422$	4.49118	0.218627
$423$	11.0996	0.539682
$424$	−16.8848	−0.819999
$425$	9.66788	0.468961
$426$	18.7052	0.906270
$427$	−3.02392	−0.146338
$428$	7.40592	0.357979
$429$	−8.51024	−0.410878
$430$	−23.2794	−1.12263
$431$	−1.48206	−0.0713884	−0.0356942	−	0.999363i	$-0.511364\pi$
$431$	−1.48206	−0.0713884	−0.0356942	+	0.999363i	$0.511364\pi$
$432$	−2.99354	−0.144027
$433$	−25.0583	−1.20422	−0.602112	−	0.798412i	$-0.705674\pi$
$433$	−25.0583	−1.20422	−0.602112	+	0.798412i	$0.705674\pi$
$434$	1.03790	0.0498206
$435$	−17.5975	−0.843735
$436$	11.1346	0.533250
$437$	−16.1718	−0.773604
$438$	0.232908	0.0111288
$439$	33.0379	1.57681	0.788406	−	0.615156i	$-0.210907\pi$
$439$	33.0379	1.57681	0.788406	+	0.615156i	$0.210907\pi$
$440$	−7.15204	−0.340960
$441$	−18.2248	−0.867847
$442$	17.5384	0.834219
$443$	−1.10436	−0.0524697	−0.0262349	−	0.999656i	$-0.508352\pi$
$443$	−1.10436	−0.0524697	−0.0262349	+	0.999656i	$0.508352\pi$
$444$	−10.0444	−0.476685
$445$	−21.9456	−1.04032
$446$	23.9028	1.13183
$447$	9.14076	0.432343
$448$	−0.221730	−0.0104758
$449$	−10.9829	−0.518316	−0.259158	−	0.965835i	$-0.583445\pi$
$449$	−10.9829	−0.518316	−0.259158	+	0.965835i	$0.583445\pi$
$450$	7.07167	0.333362
$451$	−10.8292	−0.509926
$452$	11.5292	0.542287
$453$	−8.88946	−0.417663
$454$	34.8136	1.63388
$455$	1.74401	0.0817606
$456$	9.11708	0.426946
$457$	−17.7699	−0.831241	−0.415620	−	0.909538i	$-0.636436\pi$
$457$	−17.7699	−0.831241	−0.415620	+	0.909538i	$0.636436\pi$
$458$	17.6563	0.825026
$459$	−3.94808	−0.184280
$460$	−13.9385	−0.649888
$461$	−37.8233	−1.76161	−0.880803	−	0.473483i	$-0.842997\pi$
$461$	−37.8233	−1.76161	−0.880803	+	0.473483i	$0.842997\pi$
$462$	−5.99400	−0.278866
$463$	−5.29997	−0.246311	−0.123155	−	0.992387i	$-0.539301\pi$
$463$	−5.29997	−0.246311	−0.123155	+	0.992387i	$0.539301\pi$
$464$	19.5037	0.905435
$465$	4.37111	0.202706
$466$	−17.7159	−0.820675
$467$	−25.2728	−1.16948	−0.584742	−	0.811219i	$-0.698804\pi$
$467$	−25.2728	−1.16948	−0.584742	+	0.811219i	$0.698804\pi$
$468$	4.47195	0.206716
$469$	−6.13514	−0.283294
$470$	13.2920	0.613113
$471$	36.5167	1.68260
$472$	11.0541	0.508807
$473$	−16.5116	−0.759204
$474$	18.3692	0.843726
$475$	3.42500	0.157150
$476$	4.30607	0.197368
$477$	−28.5031	−1.30507
$478$	16.9523	0.775379
$479$	29.8372	1.36329	0.681647	−	0.731681i	$-0.261264\pi$
$479$	29.8372	1.36329	0.681647	+	0.731681i	$0.261264\pi$
$480$	24.7618	1.13022
$481$	5.94646	0.271135
$482$	29.0417	1.32281
$483$	10.1479	0.461744
$484$	−5.93337	−0.269699
$485$	−26.0469	−1.18273
$486$	−37.5528	−1.70343
$487$	0.556325	0.0252095	0.0126047	−	0.999921i	$-0.495988\pi$
$487$	0.556325	0.0252095	0.0126047	+	0.999921i	$0.495988\pi$
$488$	8.06620	0.365140
$489$	7.78997	0.352275
$490$	−21.8245	−0.985929
$491$	−15.6072	−0.704344	−0.352172	−	0.935935i	$-0.614557\pi$
$491$	−15.6072	−0.704344	−0.352172	+	0.935935i	$0.614557\pi$
$492$	11.8982	0.536410
$493$	25.7227	1.15849
$494$	6.21327	0.279548
$495$	−12.0733	−0.542655
$496$	−4.84460	−0.217529
$497$	−2.71886	−0.121958
$498$	−55.3646	−2.48095
$499$	2.08565	0.0933665	0.0466832	−	0.998910i	$-0.485135\pi$
$499$	2.08565	0.0933665	0.0466832	+	0.998910i	$0.485135\pi$
$500$	13.0097	0.581812
$501$	−20.8649	−0.932173
$502$	−4.74492	−0.211776
$503$	11.3329	0.505311	0.252655	−	0.967556i	$-0.418696\pi$
$503$	11.3329	0.505311	0.252655	+	0.967556i	$0.418696\pi$
$504$	−2.73617	−0.121879
$505$	−11.7933	−0.524795
$506$	−28.3609	−1.26079
$507$	25.6376	1.13860
$508$	3.95122	0.175307
$509$	−32.6803	−1.44853	−0.724265	−	0.689522i	$-0.757821\pi$
$509$	−32.6803	−1.44853	−0.724265	+	0.689522i	$0.757821\pi$
$510$	52.0241	2.30367
$511$	−0.0338540	−0.00149761
$512$	−11.1691	−0.493607
$513$	−1.39867	−0.0617527
$514$	−53.0004	−2.33775
$515$	−11.6614	−0.513865
$516$	18.1415	0.798634
$517$	9.42770	0.414630
$518$	4.18826	0.184022
$519$	−57.6073	−2.52868
$520$	−4.65210	−0.204008
$521$	−14.5210	−0.636177	−0.318089	−	0.948061i	$-0.603041\pi$
$521$	−14.5210	−0.636177	−0.318089	+	0.948061i	$0.603041\pi$
$522$	18.8151	0.823516
$523$	−40.2081	−1.75818	−0.879089	−	0.476657i	$-0.841848\pi$
$523$	−40.2081	−1.75818	−0.879089	+	0.476657i	$0.841848\pi$
$524$	3.05979	0.133667
$525$	−2.14920	−0.0937986
$526$	0.794480	0.0346410
$527$	−6.38937	−0.278325
$528$	27.9783	1.21760
$529$	25.0151	1.08761
$530$	−34.1330	−1.48264
$531$	18.6604	0.809791
$532$	1.52549	0.0661384
$533$	−7.04393	−0.305106
$534$	49.0606	2.12306
$535$	−13.0055	−0.562278
$536$	16.3653	0.706872
$537$	−50.6517	−2.18578
$538$	−10.3655	−0.446890
$539$	−15.4796	−0.666755
$540$	−1.20552	−0.0518771
$541$	27.4177	1.17878	0.589389	−	0.807849i	$-0.299369\pi$
$541$	27.4177	1.17878	0.589389	+	0.807849i	$0.299369\pi$
$542$	34.2929	1.47301
$543$	5.85882	0.251426
$544$	−36.1949	−1.55185
$545$	−19.5534	−0.837578
$546$	−3.89884	−0.166855
$547$	0.966715	0.0413338	0.0206669	−	0.999786i	$-0.493421\pi$
$547$	0.966715	0.0413338	0.0206669	+	0.999786i	$0.493421\pi$
$548$	11.5522	0.493485
$549$	13.6165	0.581138
$550$	6.00648	0.256117
$551$	9.11266	0.388213
$552$	−27.0691	−1.15214
$553$	−2.67003	−0.113541
$554$	−56.9253	−2.41852
$555$	17.6389	0.748731
$556$	−15.2831	−0.648148
$557$	45.2307	1.91649	0.958243	−	0.285954i	$-0.0923106\pi$
$557$	45.2307	1.91649	0.958243	+	0.285954i	$0.0923106\pi$
$558$	−4.67357	−0.197848
$559$	−10.7401	−0.454258
$560$	−5.73362	−0.242290
$561$	36.8996	1.55790
$562$	21.8340	0.921013
$563$	9.46655	0.398967	0.199484	−	0.979901i	$-0.436074\pi$
$563$	9.46655	0.398967	0.199484	+	0.979901i	$0.436074\pi$
$564$	−10.3583	−0.436164
$565$	−20.2464	−0.851771
$566$	−48.3483	−2.03223
$567$	5.91633	0.248463
$568$	7.25248	0.304307
$569$	24.0225	1.00707	0.503537	−	0.863974i	$-0.332032\pi$
$569$	24.0225	1.00707	0.503537	+	0.863974i	$0.332032\pi$
$570$	18.4303	0.771962
$571$	−15.6877	−0.656510	−0.328255	−	0.944589i	$-0.606460\pi$
$571$	−15.6877	−0.656510	−0.328255	+	0.944589i	$0.606460\pi$
$572$	3.79835	0.158817
$573$	25.9278	1.08315
$574$	−4.96124	−0.207078
$575$	−10.1690	−0.424077
$576$	0.998437	0.0416016
$577$	−24.4939	−1.01970	−0.509848	−	0.860265i	$-0.670298\pi$
$577$	−24.4939	−1.01970	−0.509848	+	0.860265i	$0.670298\pi$
$578$	−46.2573	−1.92405
$579$	37.1599	1.54431
$580$	7.85423	0.326129
$581$	8.04743	0.333864
$582$	58.2294	2.41369
$583$	−24.2098	−1.00267
$584$	0.0903045	0.00373683
$585$	−7.85318	−0.324689
$586$	−12.3498	−0.510164
$587$	−29.0867	−1.20054	−0.600269	−	0.799798i	$-0.704940\pi$
$587$	−29.0867	−1.20054	−0.600269	+	0.799798i	$0.704940\pi$
$588$	17.0076	0.701383
$589$	−2.26353	−0.0932673
$590$	22.3461	0.919975
$591$	−2.76272	−0.113643
$592$	−19.5496	−0.803483
$593$	38.2893	1.57235	0.786176	−	0.618003i	$-0.212058\pi$
$593$	38.2893	1.57235	0.786176	+	0.618003i	$0.212058\pi$
$594$	−2.45287	−0.100643
$595$	−7.56188	−0.310007
$596$	−4.07977	−0.167114
$597$	31.3184	1.28178
$598$	−18.4475	−0.754376
$599$	16.8481	0.688394	0.344197	−	0.938897i	$-0.388151\pi$
$599$	16.8481	0.688394	0.344197	+	0.938897i	$0.388151\pi$
$600$	5.73291	0.234045
$601$	−16.2755	−0.663891	−0.331945	−	0.943299i	$-0.607705\pi$
$601$	−16.2755	−0.663891	−0.331945	+	0.943299i	$0.607705\pi$
$602$	−7.56455	−0.308308
$603$	27.6261	1.12502
$604$	3.96760	0.161439
$605$	10.4196	0.423616
$606$	26.3646	1.07099
$607$	18.2569	0.741026	0.370513	−	0.928827i	$-0.379182\pi$
$607$	18.2569	0.741026	0.370513	+	0.928827i	$0.379182\pi$
$608$	−12.8226	−0.520026
$609$	−5.71822	−0.231714
$610$	16.3060	0.660210
$611$	6.13232	0.248087
$612$	−19.3899	−0.783791
$613$	22.5486	0.910731	0.455366	−	0.890305i	$-0.349509\pi$
$613$	22.5486	0.910731	0.455366	+	0.890305i	$0.349509\pi$
$614$	44.7443	1.80573
$615$	−20.8943	−0.842540
$616$	−2.32403	−0.0936376
$617$	−30.7802	−1.23916	−0.619582	−	0.784932i	$-0.712698\pi$
$617$	−30.7802	−1.23916	−0.619582	+	0.784932i	$0.712698\pi$
$618$	26.0698	1.04868
$619$	−9.88972	−0.397501	−0.198751	−	0.980050i	$-0.563688\pi$
$619$	−9.88972	−0.397501	−0.198751	+	0.980050i	$0.563688\pi$
$620$	−1.95095	−0.0783519
$621$	4.15272	0.166643
$622$	34.2944	1.37508
$623$	−7.13111	−0.285702
$624$	18.1987	0.728530
$625$	−15.5086	−0.620345
$626$	34.4780	1.37802
$627$	13.0722	0.522055
$628$	−16.2984	−0.650376
$629$	−25.7833	−1.02805
$630$	−5.53121	−0.220369
$631$	−22.3039	−0.887905	−0.443952	−	0.896050i	$-0.646424\pi$
$631$	−22.3039	−0.887905	−0.443952	+	0.896050i	$0.646424\pi$
$632$	7.12221	0.283306
$633$	6.14624	0.244291
$634$	−38.5009	−1.52907
$635$	−6.93873	−0.275355
$636$	26.5996	1.05474
$637$	−10.0688	−0.398942
$638$	15.9811	0.632696
$639$	12.2429	0.484320
$640$	21.8483	0.863628
$641$	−27.5328	−1.08748	−0.543740	−	0.839253i	$-0.682992\pi$
$641$	−27.5328	−1.08748	−0.543740	+	0.839253i	$0.682992\pi$
$642$	29.0746	1.14748
$643$	−37.0807	−1.46232	−0.731160	−	0.682206i	$-0.761021\pi$
$643$	−37.0807	−1.46232	−0.731160	+	0.682206i	$0.761021\pi$
$644$	−4.52927	−0.178478
$645$	−31.8582	−1.25442
$646$	−26.9401	−1.05994
$647$	14.7128	0.578419	0.289210	−	0.957266i	$-0.406608\pi$
$647$	14.7128	0.578419	0.289210	+	0.957266i	$0.406608\pi$
$648$	−15.7816	−0.619961
$649$	15.8496	0.622151
$650$	3.90696	0.153244
$651$	1.42037	0.0556689
$652$	−3.47687	−0.136165
$653$	2.66952	0.104466	0.0522332	−	0.998635i	$-0.483366\pi$
$653$	2.66952	0.104466	0.0522332	+	0.998635i	$0.483366\pi$
$654$	43.7128	1.70931
$655$	−5.37328	−0.209952
$656$	23.1576	0.904153
$657$	0.152442	0.00594734
$658$	4.31917	0.168379
$659$	35.7737	1.39355	0.696773	−	0.717292i	$-0.254619\pi$
$659$	35.7737	1.39355	0.696773	+	0.717292i	$0.254619\pi$
$660$	11.2670	0.438567
$661$	12.4033	0.482431	0.241216	−	0.970472i	$-0.422454\pi$
$661$	12.4033	0.482431	0.241216	+	0.970472i	$0.422454\pi$
$662$	53.5607	2.08170
$663$	24.0016	0.932145
$664$	−21.4663	−0.833053
$665$	−2.67891	−0.103884
$666$	−18.8595	−0.730789
$667$	−27.0560	−1.04761
$668$	9.31255	0.360313
$669$	32.7114	1.26469
$670$	33.0827	1.27810
$671$	11.5655	0.446480
$672$	8.04623	0.310390
$673$	−8.44199	−0.325415	−0.162707	−	0.986674i	$-0.552023\pi$
$673$	−8.44199	−0.325415	−0.162707	+	0.986674i	$0.552023\pi$
$674$	−27.2323	−1.04895
$675$	−0.879496	−0.0338518
$676$	−11.4427	−0.440105
$677$	−7.52530	−0.289221	−0.144610	−	0.989489i	$-0.546193\pi$
$677$	−7.52530	−0.289221	−0.144610	+	0.989489i	$0.546193\pi$
$678$	45.2619	1.73827
$679$	−8.46384	−0.324812
$680$	20.1711	0.773525
$681$	47.6429	1.82568
$682$	−3.96961	−0.152004
$683$	16.2657	0.622390	0.311195	−	0.950346i	$-0.399271\pi$
$683$	16.2657	0.622390	0.311195	+	0.950346i	$0.399271\pi$
$684$	−6.86918	−0.262650
$685$	−20.2868	−0.775118
$686$	−14.5827	−0.556770
$687$	24.1629	0.921873
$688$	35.3091	1.34615
$689$	−15.7474	−0.599929
$690$	−54.7207	−2.08318
$691$	−15.9419	−0.606458	−0.303229	−	0.952918i	$-0.598065\pi$
$691$	−15.9419	−0.606458	−0.303229	+	0.952918i	$0.598065\pi$
$692$	25.7117	0.977412
$693$	−3.92317	−0.149029
$694$	−32.6416	−1.23906
$695$	26.8386	1.01805
$696$	15.2532	0.578170
$697$	30.5418	1.15685
$698$	38.9962	1.47603
$699$	−24.2445	−0.917011
$700$	0.959244	0.0362560
$701$	17.8163	0.672914	0.336457	−	0.941699i	$-0.390771\pi$
$701$	17.8163	0.672914	0.336457	+	0.941699i	$0.390771\pi$
$702$	−1.59549	−0.0602178
$703$	−9.13413	−0.344500
$704$	0.848045	0.0319619
$705$	18.1902	0.685084
$706$	20.5303	0.772667
$707$	−3.83218	−0.144124
$708$	−17.4141	−0.654464
$709$	5.95032	0.223469	0.111735	−	0.993738i	$-0.464359\pi$
$709$	5.95032	0.223469	0.111735	+	0.993738i	$0.464359\pi$
$710$	14.6610	0.550219
$711$	12.0229	0.450896
$712$	19.0220	0.712880
$713$	6.72056	0.251687
$714$	16.9050	0.632654
$715$	−6.67027	−0.249454
$716$	22.6072	0.844871
$717$	23.1994	0.866398
$718$	−18.3249	−0.683881
$719$	−26.3963	−0.984417	−0.492208	−	0.870477i	$-0.663810\pi$
$719$	−26.3963	−0.984417	−0.492208	+	0.870477i	$0.663810\pi$
$720$	25.8181	0.962184
$721$	−3.78933	−0.141122
$722$	23.7482	0.883815
$723$	39.7440	1.47809
$724$	−2.61495	−0.0971838
$725$	5.73013	0.212812
$726$	−23.2936	−0.864506
$727$	46.5418	1.72614	0.863070	−	0.505085i	$-0.168539\pi$
$727$	46.5418	1.72614	0.863070	+	0.505085i	$0.168539\pi$
$728$	−1.51168	−0.0560266
$729$	−22.3296	−0.827022
$730$	0.182552	0.00675656
$731$	46.5680	1.72238
$732$	−12.7071	−0.469669
$733$	38.9711	1.43943	0.719716	−	0.694269i	$-0.244272\pi$
$733$	38.9711	1.43943	0.719716	+	0.694269i	$0.244272\pi$
$734$	15.1018	0.557417
$735$	−29.8671	−1.10166
$736$	38.0711	1.40332
$737$	23.4649	0.864339
$738$	22.3401	0.822351
$739$	−17.0207	−0.626118	−0.313059	−	0.949734i	$-0.601354\pi$
$739$	−17.0207	−0.626118	−0.313059	+	0.949734i	$0.601354\pi$
$740$	−7.87273	−0.289407
$741$	8.50294	0.312363
$742$	−11.0914	−0.407177
$743$	28.1274	1.03189	0.515947	−	0.856621i	$-0.327440\pi$
$743$	28.1274	1.03189	0.515947	+	0.856621i	$0.327440\pi$
$744$	−3.78880	−0.138904
$745$	7.16447	0.262486
$746$	−32.4328	−1.18745
$747$	−36.2370	−1.32584
$748$	−16.4693	−0.602176
$749$	−4.22609	−0.154418
$750$	51.0743	1.86497
$751$	13.0842	0.477448	0.238724	−	0.971087i	$-0.423271\pi$
$751$	13.0842	0.477448	0.238724	+	0.971087i	$0.423271\pi$
$752$	−20.1606	−0.735182
$753$	−6.49348	−0.236636
$754$	10.3950	0.378564
$755$	−6.96750	−0.253573
$756$	−0.391727	−0.0142470
$757$	−12.8587	−0.467357	−0.233679	−	0.972314i	$-0.575076\pi$
$757$	−12.8587	−0.467357	−0.233679	+	0.972314i	$0.575076\pi$
$758$	19.7750	0.718260
$759$	−38.8122	−1.40879
$760$	7.14591	0.259209
$761$	−24.1562	−0.875660	−0.437830	−	0.899058i	$-0.644253\pi$
$761$	−24.1562	−0.875660	−0.437830	+	0.899058i	$0.644253\pi$
$762$	15.5119	0.561938
$763$	−6.35381	−0.230023
$764$	−11.5723	−0.418670
$765$	34.0506	1.23110
$766$	39.5507	1.42902
$767$	10.3095	0.372254
$768$	−47.1019	−1.69964
$769$	11.9745	0.431813	0.215906	−	0.976414i	$-0.430729\pi$
$769$	11.9745	0.431813	0.215906	+	0.976414i	$0.430729\pi$
$770$	−4.69806	−0.169306
$771$	−72.5318	−2.61217
$772$	−16.5854	−0.596923
$773$	−13.0859	−0.470666	−0.235333	−	0.971915i	$-0.575618\pi$
$773$	−13.0859	−0.470666	−0.235333	+	0.971915i	$0.575618\pi$
$774$	34.0627	1.22436
$775$	−1.42333	−0.0511276
$776$	22.5770	0.810468
$777$	5.73169	0.205623
$778$	−0.785577	−0.0281643
$779$	10.8199	0.387663
$780$	7.32871	0.262410
$781$	10.3987	0.372096
$782$	79.9868	2.86032
$783$	−2.34002	−0.0836254
$784$	33.1023	1.18223
$785$	28.6215	1.02155
$786$	12.0123	0.428464
$787$	−37.1430	−1.32401	−0.662003	−	0.749501i	$-0.730293\pi$
$787$	−37.1430	−1.32401	−0.662003	+	0.749501i	$0.730293\pi$
$788$	1.23308	0.0439265
$789$	1.08726	0.0387074
$790$	14.3977	0.512247
$791$	−6.57897	−0.233921
$792$	10.4649	0.371855
$793$	7.52285	0.267144
$794$	−43.2148	−1.53364
$795$	−46.7114	−1.65668
$796$	−13.9782	−0.495445
$797$	36.7149	1.30051	0.650255	−	0.759716i	$-0.274662\pi$
$797$	36.7149	1.30051	0.650255	+	0.759716i	$0.274662\pi$
$798$	5.98886	0.212003
$799$	−26.5892	−0.940657
$800$	−8.06299	−0.285070
$801$	32.1109	1.13458
$802$	26.6967	0.942694
$803$	0.129480	0.00456926
$804$	−25.7811	−0.909229
$805$	7.95384	0.280336
$806$	−2.58206	−0.0909492
$807$	−14.1854	−0.499349
$808$	10.2222	0.359616
$809$	−37.6797	−1.32475	−0.662373	−	0.749174i	$-0.730451\pi$
$809$	−37.6797	−1.32475	−0.662373	+	0.749174i	$0.730451\pi$
$810$	−31.9029	−1.12095
$811$	7.39136	0.259546	0.129773	−	0.991544i	$-0.458575\pi$
$811$	7.39136	0.259546	0.129773	+	0.991544i	$0.458575\pi$
$812$	2.55220	0.0895646
$813$	46.9303	1.64592
$814$	−16.0187	−0.561455
$815$	6.10573	0.213874
$816$	−78.9077	−2.76232
$817$	16.4974	0.577172
$818$	−36.1645	−1.26446
$819$	−2.55186	−0.0891690
$820$	9.32570	0.325668
$821$	43.6054	1.52184	0.760920	−	0.648845i	$-0.224748\pi$
$821$	43.6054	1.52184	0.760920	+	0.648845i	$0.224748\pi$
$822$	45.3522	1.58184
$823$	−24.3386	−0.848390	−0.424195	−	0.905571i	$-0.639443\pi$
$823$	−24.3386	−0.848390	−0.424195	+	0.905571i	$0.639443\pi$
$824$	10.1079	0.352126
$825$	8.21996	0.286182
$826$	7.26127	0.252652
$827$	−35.3925	−1.23072	−0.615358	−	0.788248i	$-0.710989\pi$
$827$	−35.3925	−1.23072	−0.615358	+	0.788248i	$0.710989\pi$
$828$	20.3950	0.708775
$829$	−21.0917	−0.732546	−0.366273	−	0.930507i	$-0.619366\pi$
$829$	−21.0917	−0.732546	−0.366273	+	0.930507i	$0.619366\pi$
$830$	−43.3945	−1.50624
$831$	−77.9030	−2.70242
$832$	0.551617	0.0191239
$833$	43.6575	1.51264
$834$	−59.9993	−2.07761
$835$	−16.3537	−0.565945
$836$	−5.83449	−0.201790
$837$	0.581247	0.0200908
$838$	−2.78545	−0.0962219
$839$	−21.8559	−0.754549	−0.377274	−	0.926102i	$-0.623139\pi$
$839$	−21.8559	−0.754549	−0.377274	+	0.926102i	$0.623139\pi$
$840$	−4.48408	−0.154715
$841$	−13.7542	−0.474283
$842$	29.5173	1.01723
$843$	29.8802	1.02913
$844$	−2.74323	−0.0944259
$845$	20.0946	0.691274
$846$	−19.4489	−0.668667
$847$	3.38580	0.116337
$848$	51.7713	1.77783
$849$	−66.1653	−2.27079
$850$	−16.9402	−0.581045
$851$	27.1197	0.929653
$852$	−11.4252	−0.391422
$853$	−51.5179	−1.76394	−0.881970	−	0.471306i	$-0.843783\pi$
$853$	−51.5179	−1.76394	−0.881970	+	0.471306i	$0.843783\pi$
$854$	5.29856	0.181313
$855$	12.0630	0.412544
$856$	11.2730	0.385302
$857$	−51.0722	−1.74459	−0.872297	−	0.488977i	$-0.837370\pi$
$857$	−51.0722	−1.74459	−0.872297	+	0.488977i	$0.837370\pi$
$858$	14.9118	0.509080
$859$	−34.7298	−1.18496	−0.592482	−	0.805584i	$-0.701852\pi$
$859$	−34.7298	−1.18496	−0.592482	+	0.805584i	$0.701852\pi$
$860$	14.2192	0.484870
$861$	−6.78952	−0.231386
$862$	2.59689	0.0884505
$863$	4.60780	0.156851	0.0784257	−	0.996920i	$-0.475011\pi$
$863$	4.60780	0.156851	0.0784257	+	0.996920i	$0.475011\pi$
$864$	3.29269	0.112020
$865$	−45.1523	−1.53522
$866$	43.9075	1.49204
$867$	−63.3038	−2.14991
$868$	−0.633951	−0.0215177
$869$	10.2120	0.346417
$870$	30.8346	1.04539
$871$	15.2629	0.517163
$872$	16.9486	0.573951
$873$	38.1121	1.28990
$874$	28.3365	0.958498
$875$	−7.42381	−0.250971
$876$	−0.142262	−0.00480657
$877$	3.75295	0.126728	0.0633640	−	0.997990i	$-0.479817\pi$
$877$	3.75295	0.126728	0.0633640	+	0.997990i	$0.479817\pi$
$878$	−57.8895	−1.95368
$879$	−16.9008	−0.570051
$880$	21.9292	0.739233
$881$	−43.8499	−1.47734	−0.738670	−	0.674068i	$-0.764546\pi$
$881$	−43.8499	−1.47734	−0.738670	+	0.674068i	$0.764546\pi$
$882$	31.9338	1.07527
$883$	−44.9016	−1.51106	−0.755530	−	0.655114i	$-0.772621\pi$
$883$	−44.9016	−1.51106	−0.755530	+	0.655114i	$0.772621\pi$
$884$	−10.7126	−0.360302
$885$	30.5809	1.02797
$886$	1.93508	0.0650102
$887$	26.1956	0.879563	0.439782	−	0.898105i	$-0.355056\pi$
$887$	26.1956	0.879563	0.439782	+	0.898105i	$0.355056\pi$
$888$	−15.2891	−0.513069
$889$	−2.25471	−0.0756206
$890$	38.4534	1.28896
$891$	−22.6280	−0.758066
$892$	−14.6000	−0.488843
$893$	−9.41962	−0.315215
$894$	−16.0166	−0.535675
$895$	−39.7005	−1.32704
$896$	7.09950	0.237178
$897$	−25.2457	−0.842930
$898$	19.2445	0.642196
$899$	−3.78697	−0.126302
$900$	−4.31941	−0.143980
$901$	68.2793	2.27471
$902$	18.9751	0.631801
$903$	−10.3522	−0.344499
$904$	17.5492	0.583677
$905$	4.59211	0.152647
$906$	15.5762	0.517486
$907$	20.0701	0.666418	0.333209	−	0.942853i	$-0.391869\pi$
$907$	20.0701	0.666418	0.333209	+	0.942853i	$0.391869\pi$
$908$	−21.2643	−0.705680
$909$	17.2560	0.572347
$910$	−3.05589	−0.101302
$911$	16.6924	0.553044	0.276522	−	0.961008i	$-0.410818\pi$
$911$	16.6924	0.553044	0.276522	+	0.961008i	$0.410818\pi$
$912$	−27.9543	−0.925658
$913$	−30.7787	−1.01863
$914$	31.1367	1.02991
$915$	22.3150	0.737710
$916$	−10.7846	−0.356332
$917$	−1.74603	−0.0576588
$918$	6.91788	0.228324
$919$	−7.73132	−0.255033	−0.127516	−	0.991836i	$-0.540701\pi$
$919$	−7.73132	−0.255033	−0.127516	+	0.991836i	$0.540701\pi$
$920$	−21.2166	−0.699491
$921$	61.2332	2.01770
$922$	66.2746	2.18264
$923$	6.76394	0.222638
$924$	3.66116	0.120443
$925$	−5.74363	−0.188849
$926$	9.28670	0.305180
$927$	17.0631	0.560426
$928$	−21.4527	−0.704219
$929$	−27.8769	−0.914611	−0.457306	−	0.889310i	$-0.651185\pi$
$929$	−27.8769	−0.914611	−0.457306	+	0.889310i	$0.651185\pi$
$930$	−7.65914	−0.251153
$931$	15.4664	0.506889
$932$	10.8210	0.354453
$933$	46.9323	1.53650
$934$	44.2833	1.44900
$935$	28.9217	0.945839
$936$	6.80699	0.222493
$937$	−14.9024	−0.486841	−0.243421	−	0.969921i	$-0.578270\pi$
$937$	−14.9024	−0.486841	−0.243421	+	0.969921i	$0.578270\pi$
$938$	10.7501	0.351003
$939$	47.1836	1.53978
$940$	−8.11879	−0.264806
$941$	5.21996	0.170166	0.0850828	−	0.996374i	$-0.472885\pi$
$941$	5.21996	0.170166	0.0850828	+	0.996374i	$0.472885\pi$
$942$	−63.9851	−2.08475
$943$	−32.1249	−1.04613
$944$	−33.8935	−1.10314
$945$	0.687911	0.0223777
$946$	28.9319	0.940657
$947$	53.3817	1.73467	0.867336	−	0.497723i	$-0.165831\pi$
$947$	53.3817	1.73467	0.867336	+	0.497723i	$0.165831\pi$
$948$	−11.2200	−0.364409
$949$	0.0842214	0.00273394
$950$	−6.00133	−0.194709
$951$	−52.6890	−1.70856
$952$	6.55450	0.212432
$953$	42.2370	1.36819	0.684096	−	0.729392i	$-0.260197\pi$
$953$	42.2370	1.36819	0.684096	+	0.729392i	$0.260197\pi$
$954$	49.9436	1.61698
$955$	20.3220	0.657606
$956$	−10.3545	−0.334889
$957$	21.8703	0.706967
$958$	−52.2812	−1.68913
$959$	−6.59210	−0.212870
$960$	1.63626	0.0528100
$961$	−30.0593	−0.969656
$962$	−10.4195	−0.335938
$963$	19.0298	0.613226
$964$	−17.7388	−0.571329
$965$	29.1257	0.937588
$966$	−17.7813	−0.572103
$967$	10.5859	0.340419	0.170210	−	0.985408i	$-0.445556\pi$
$967$	10.5859	0.340419	0.170210	+	0.985408i	$0.445556\pi$
$968$	−9.03151	−0.290284
$969$	−36.8679	−1.18437
$970$	45.6399	1.46541
$971$	−15.9006	−0.510276	−0.255138	−	0.966905i	$-0.582121\pi$
$971$	−15.9006	−0.510276	−0.255138	+	0.966905i	$0.582121\pi$
$972$	22.9374	0.735718
$973$	8.72109	0.279585
$974$	−0.974801	−0.0312346
$975$	5.34673	0.171232
$976$	−24.7321	−0.791656
$977$	24.0355	0.768963	0.384481	−	0.923133i	$-0.374380\pi$
$977$	24.0355	0.768963	0.384481	+	0.923133i	$0.374380\pi$
$978$	−13.6497	−0.436470
$979$	27.2741	0.871685
$980$	13.3305	0.425827
$981$	28.6108	0.913471
$982$	27.3472	0.872684
$983$	−23.6694	−0.754936	−0.377468	−	0.926023i	$-0.623205\pi$
$983$	−23.6694	−0.754936	−0.377468	+	0.926023i	$0.623205\pi$
$984$	18.1108	0.577352
$985$	−2.16540	−0.0689954
$986$	−45.0717	−1.43538
$987$	5.91084	0.188144
$988$	−3.79509	−0.120738
$989$	−48.9818	−1.55753
$990$	21.1551	0.672352
$991$	−3.88356	−0.123365	−0.0616827	−	0.998096i	$-0.519647\pi$
$991$	−3.88356	−0.123365	−0.0616827	+	0.998096i	$0.519647\pi$
$992$	5.32872	0.169187
$993$	73.2986	2.32606
$994$	4.76404	0.151106
$995$	24.5471	0.778197
$996$	33.8170	1.07153
$997$	−29.7586	−0.942465	−0.471232	−	0.882009i	$-0.656191\pi$
$997$	−29.7586	−0.942465	−0.471232	+	0.882009i	$0.656191\pi$
$998$	−3.65451	−0.115681
$999$	2.34553	0.0742092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.31	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.31	✓	149	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.75222 q^{2} -2.39793 q^{3} +1.07026 q^{4} -1.87948 q^{5} +4.20169 q^{6} -0.610730 q^{7} +1.62910 q^{8} +2.75008 q^{9} +3.29326 q^{10} +2.33584 q^{11} -2.56641 q^{12} +1.51936 q^{13} +1.07013 q^{14} +4.50687 q^{15} -4.99506 q^{16} -6.58782 q^{17} -4.81873 q^{18} -2.33384 q^{19} -2.01154 q^{20} +1.46449 q^{21} -4.09290 q^{22} +6.92929 q^{23} -3.90648 q^{24} -1.46754 q^{25} -2.66225 q^{26} +0.599300 q^{27} -0.653641 q^{28} -3.90459 q^{29} -7.89702 q^{30} +0.969877 q^{31} +5.49422 q^{32} -5.60118 q^{33} +11.5433 q^{34} +1.14786 q^{35} +2.94330 q^{36} +3.91378 q^{37} +4.08938 q^{38} -3.64333 q^{39} -3.06187 q^{40} -4.63610 q^{41} -2.56610 q^{42} -7.06881 q^{43} +2.49996 q^{44} -5.16873 q^{45} -12.1416 q^{46} +4.03611 q^{47} +11.9778 q^{48} -6.62701 q^{49} +2.57145 q^{50} +15.7971 q^{51} +1.62612 q^{52} -10.3645 q^{53} -1.05010 q^{54} -4.39017 q^{55} -0.994942 q^{56} +5.59638 q^{57} +6.84168 q^{58} +6.78540 q^{59} +4.82353 q^{60} +4.95132 q^{61} -1.69943 q^{62} -1.67955 q^{63} +0.363058 q^{64} -2.85562 q^{65} +9.81448 q^{66} +10.0456 q^{67} -7.05069 q^{68} -16.6160 q^{69} -2.01129 q^{70} +4.45183 q^{71} +4.48016 q^{72} +0.0554320 q^{73} -6.85779 q^{74} +3.51906 q^{75} -2.49781 q^{76} -1.42657 q^{77} +6.38391 q^{78} +4.37186 q^{79} +9.38814 q^{80} -9.68731 q^{81} +8.12345 q^{82} -13.1767 q^{83} +1.56739 q^{84} +12.3817 q^{85} +12.3861 q^{86} +9.36293 q^{87} +3.80532 q^{88} +11.6764 q^{89} +9.05672 q^{90} -0.927922 q^{91} +7.41615 q^{92} -2.32570 q^{93} -7.07214 q^{94} +4.38641 q^{95} -13.1748 q^{96} +13.8586 q^{97} +11.6120 q^{98} +6.42374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18}+ \cdots - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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