LMFDB - Embedded newform 4001.2.a.b.1.100

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:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.100
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)

$f(q)$	$=$	\(q+0.358013 q^{2} -1.99143 q^{3} -1.87183 q^{4} +1.76676 q^{5} -0.712958 q^{6} +1.12698 q^{7} -1.38616 q^{8} +0.965797 q^{9} +0.632522 q^{10} +3.02530 q^{11} +3.72761 q^{12} +3.52268 q^{13} +0.403472 q^{14} -3.51838 q^{15} +3.24739 q^{16} +5.82428 q^{17} +0.345768 q^{18} +2.52638 q^{19} -3.30707 q^{20} -2.24429 q^{21} +1.08309 q^{22} +0.727773 q^{23} +2.76045 q^{24} -1.87856 q^{25} +1.26116 q^{26} +4.05097 q^{27} -2.10950 q^{28} +1.38626 q^{29} -1.25962 q^{30} -5.20922 q^{31} +3.93493 q^{32} -6.02467 q^{33} +2.08517 q^{34} +1.99109 q^{35} -1.80781 q^{36} -0.462962 q^{37} +0.904476 q^{38} -7.01517 q^{39} -2.44902 q^{40} -11.6514 q^{41} -0.803486 q^{42} +3.28335 q^{43} -5.66283 q^{44} +1.70633 q^{45} +0.260552 q^{46} +8.10233 q^{47} -6.46695 q^{48} -5.72993 q^{49} -0.672550 q^{50} -11.5987 q^{51} -6.59385 q^{52} +9.89504 q^{53} +1.45030 q^{54} +5.34497 q^{55} -1.56217 q^{56} -5.03111 q^{57} +0.496297 q^{58} -12.4701 q^{59} +6.58579 q^{60} +5.80931 q^{61} -1.86497 q^{62} +1.08843 q^{63} -5.08602 q^{64} +6.22373 q^{65} -2.15691 q^{66} +12.3929 q^{67} -10.9021 q^{68} -1.44931 q^{69} +0.712837 q^{70} -4.08597 q^{71} -1.33875 q^{72} -3.63984 q^{73} -0.165746 q^{74} +3.74103 q^{75} -4.72894 q^{76} +3.40943 q^{77} -2.51152 q^{78} -17.4188 q^{79} +5.73735 q^{80} -10.9646 q^{81} -4.17134 q^{82} +13.6953 q^{83} +4.20093 q^{84} +10.2901 q^{85} +1.17548 q^{86} -2.76063 q^{87} -4.19355 q^{88} +13.8897 q^{89} +0.610888 q^{90} +3.96997 q^{91} -1.36226 q^{92} +10.3738 q^{93} +2.90074 q^{94} +4.46350 q^{95} -7.83615 q^{96} -2.29162 q^{97} -2.05139 q^{98} +2.92182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	0.358013	0.253153	0.126577	−	0.991957i	$-0.459601\pi$
$2$	0.358013	0.253153	0.126577	+	0.991957i	$0.459601\pi$
$3$	−1.99143	−1.14975	−0.574877	−	0.818240i	$-0.694950\pi$
$3$	−1.99143	−1.14975	−0.574877	+	0.818240i	$0.694950\pi$
$4$	−1.87183	−0.935913
$5$	1.76676	0.790118	0.395059	−	0.918656i	$-0.370724\pi$
$5$	1.76676	0.790118	0.395059	+	0.918656i	$0.370724\pi$
$6$	−0.712958	−0.291064
$7$	1.12698	0.425957	0.212978	−	0.977057i	$-0.431684\pi$
$7$	1.12698	0.425957	0.212978	+	0.977057i	$0.431684\pi$
$8$	−1.38616	−0.490083
$9$	0.965797	0.321932
$10$	0.632522	0.200021
$11$	3.02530	0.912161	0.456080	−	0.889939i	$-0.349253\pi$
$11$	3.02530	0.912161	0.456080	+	0.889939i	$0.349253\pi$
$12$	3.72761	1.07607
$13$	3.52268	0.977016	0.488508	−	0.872559i	$-0.337541\pi$
$13$	3.52268	0.977016	0.488508	+	0.872559i	$0.337541\pi$
$14$	0.403472	0.107832
$15$	−3.51838	−0.908441
$16$	3.24739	0.811847
$17$	5.82428	1.41260	0.706298	−	0.707914i	$-0.250364\pi$
$17$	5.82428	1.41260	0.706298	+	0.707914i	$0.250364\pi$
$18$	0.345768	0.0814982
$19$	2.52638	0.579591	0.289796	−	0.957089i	$-0.406413\pi$
$19$	2.52638	0.579591	0.289796	+	0.957089i	$0.406413\pi$
$20$	−3.30707	−0.739482
$21$	−2.24429	−0.489745
$22$	1.08309	0.230917
$23$	0.727773	0.151751	0.0758755	−	0.997117i	$-0.475825\pi$
$23$	0.727773	0.151751	0.0758755	+	0.997117i	$0.475825\pi$
$24$	2.76045	0.563474
$25$	−1.87856	−0.375713
$26$	1.26116	0.247335
$27$	4.05097	0.779610
$28$	−2.10950	−0.398659
$29$	1.38626	0.257421	0.128711	−	0.991682i	$-0.458916\pi$
$29$	1.38626	0.257421	0.128711	+	0.991682i	$0.458916\pi$
$30$	−1.25962	−0.229975
$31$	−5.20922	−0.935604	−0.467802	−	0.883833i	$-0.654954\pi$
$31$	−5.20922	−0.935604	−0.467802	+	0.883833i	$0.654954\pi$
$32$	3.93493	0.695605
$33$	−6.02467	−1.04876
$34$	2.08517	0.357603
$35$	1.99109	0.336556
$36$	−1.80781	−0.301301
$37$	−0.462962	−0.0761105	−0.0380553	−	0.999276i	$-0.512116\pi$
$37$	−0.462962	−0.0761105	−0.0380553	+	0.999276i	$0.512116\pi$
$38$	0.904476	0.146725
$39$	−7.01517	−1.12333
$40$	−2.44902	−0.387223
$41$	−11.6514	−1.81964	−0.909818	−	0.415007i	$-0.863779\pi$
$41$	−11.6514	−1.81964	−0.909818	+	0.415007i	$0.863779\pi$
$42$	−0.803486	−0.123981
$43$	3.28335	0.500707	0.250353	−	0.968155i	$-0.419453\pi$
$43$	3.28335	0.500707	0.250353	+	0.968155i	$0.419453\pi$
$44$	−5.66283	−0.853704
$45$	1.70633	0.254365
$46$	0.260552	0.0384163
$47$	8.10233	1.18185	0.590923	−	0.806728i	$-0.298764\pi$
$47$	8.10233	1.18185	0.590923	+	0.806728i	$0.298764\pi$
$48$	−6.46695	−0.933424
$49$	−5.72993	−0.818561
$50$	−0.672550	−0.0951130
$51$	−11.5987	−1.62414
$52$	−6.59385	−0.914402
$53$	9.89504	1.35919	0.679594	−	0.733588i	$-0.262156\pi$
$53$	9.89504	1.35919	0.679594	+	0.733588i	$0.262156\pi$
$54$	1.45030	0.197361
$55$	5.34497	0.720715
$56$	−1.56217	−0.208754
$57$	−5.03111	−0.666387
$58$	0.496297	0.0651670
$59$	−12.4701	−1.62346	−0.811732	−	0.584030i	$-0.801475\pi$
$59$	−12.4701	−1.62346	−0.811732	+	0.584030i	$0.801475\pi$
$60$	6.58579	0.850222
$61$	5.80931	0.743807	0.371903	−	0.928271i	$-0.378705\pi$
$61$	5.80931	0.743807	0.371903	+	0.928271i	$0.378705\pi$
$62$	−1.86497	−0.236851
$63$	1.08843	0.137129
$64$	−5.08602	−0.635753
$65$	6.22373	0.771958
$66$	−2.15691	−0.265497
$67$	12.3929	1.51403	0.757016	−	0.653396i	$-0.226656\pi$
$67$	12.3929	1.51403	0.757016	+	0.653396i	$0.226656\pi$
$68$	−10.9021	−1.32207
$69$	−1.44931	−0.174476
$70$	0.712837	0.0852003
$71$	−4.08597	−0.484915	−0.242458	−	0.970162i	$-0.577954\pi$
$71$	−4.08597	−0.484915	−0.242458	+	0.970162i	$0.577954\pi$
$72$	−1.33875	−0.157774
$73$	−3.63984	−0.426011	−0.213005	−	0.977051i	$-0.568325\pi$
$73$	−3.63984	−0.426011	−0.213005	+	0.977051i	$0.568325\pi$
$74$	−0.165746	−0.0192676
$75$	3.74103	0.431977
$76$	−4.72894	−0.542447
$77$	3.40943	0.388541
$78$	−2.51152	−0.284374
$79$	−17.4188	−1.95977	−0.979884	−	0.199569i	$-0.936046\pi$
$79$	−17.4188	−1.95977	−0.979884	+	0.199569i	$0.936046\pi$
$80$	5.73735	0.641456
$81$	−10.9646	−1.21829
$82$	−4.17134	−0.460647
$83$	13.6953	1.50325	0.751627	−	0.659588i	$-0.229269\pi$
$83$	13.6953	1.50325	0.751627	+	0.659588i	$0.229269\pi$
$84$	4.20093	0.458359
$85$	10.2901	1.11612
$86$	1.17548	0.126756
$87$	−2.76063	−0.295971
$88$	−4.19355	−0.447034
$89$	13.8897	1.47230	0.736151	−	0.676817i	$-0.236641\pi$
$89$	13.8897	1.47230	0.736151	+	0.676817i	$0.236641\pi$
$90$	0.610888	0.0643933
$91$	3.96997	0.416166
$92$	−1.36226	−0.142026
$93$	10.3738	1.07571
$94$	2.90074	0.299188
$95$	4.46350	0.457946
$96$	−7.83615	−0.799774
$97$	−2.29162	−0.232679	−0.116340	−	0.993209i	$-0.537116\pi$
$97$	−2.29162	−0.232679	−0.116340	+	0.993209i	$0.537116\pi$
$98$	−2.05139	−0.207221
$99$	2.92182	0.293654
$100$	3.51635	0.351635
$101$	−6.04635	−0.601635	−0.300817	−	0.953682i	$-0.597259\pi$
$101$	−6.04635	−0.601635	−0.300817	+	0.953682i	$0.597259\pi$
$102$	−4.15247	−0.411156
$103$	7.22273	0.711677	0.355838	−	0.934547i	$-0.384195\pi$
$103$	7.22273	0.711677	0.355838	+	0.934547i	$0.384195\pi$
$104$	−4.88301	−0.478819
$105$	−3.96513	−0.386957
$106$	3.54255	0.344083
$107$	5.76804	0.557618	0.278809	−	0.960347i	$-0.410060\pi$
$107$	5.76804	0.557618	0.278809	+	0.960347i	$0.410060\pi$
$108$	−7.58272	−0.729648
$109$	−1.97747	−0.189407	−0.0947036	−	0.995506i	$-0.530190\pi$
$109$	−1.97747	−0.189407	−0.0947036	+	0.995506i	$0.530190\pi$
$110$	1.91357	0.182451
$111$	0.921958	0.0875083
$112$	3.65973	0.345812
$113$	5.72139	0.538224	0.269112	−	0.963109i	$-0.413270\pi$
$113$	5.72139	0.538224	0.269112	+	0.963109i	$0.413270\pi$
$114$	−1.80120	−0.168698
$115$	1.28580	0.119901
$116$	−2.59483	−0.240924
$117$	3.40219	0.314533
$118$	−4.46444	−0.410985
$119$	6.56383	0.601705
$120$	4.87705	0.445211
$121$	−1.84759	−0.167962
$122$	2.07981	0.188297
$123$	23.2029	2.09213
$124$	9.75076	0.875644
$125$	−12.1528	−1.08698
$126$	0.389672	0.0347147
$127$	12.9848	1.15221	0.576106	−	0.817375i	$-0.304572\pi$
$127$	12.9848	1.15221	0.576106	+	0.817375i	$0.304572\pi$
$128$	−9.69073	−0.856548
$129$	−6.53857	−0.575689
$130$	2.22817	0.195424
$131$	−1.36869	−0.119583	−0.0597913	−	0.998211i	$-0.519044\pi$
$131$	−1.36869	−0.119583	−0.0597913	+	0.998211i	$0.519044\pi$
$132$	11.2771	0.981549
$133$	2.84717	0.246881
$134$	4.43681	0.383282
$135$	7.15709	0.615985
$136$	−8.07341	−0.692289
$137$	−18.1904	−1.55411	−0.777055	−	0.629433i	$-0.783287\pi$
$137$	−18.1904	−1.55411	−0.777055	+	0.629433i	$0.783287\pi$
$138$	−0.518871	−0.0441692
$139$	14.0768	1.19398	0.596988	−	0.802250i	$-0.296364\pi$
$139$	14.0768	1.19398	0.596988	+	0.802250i	$0.296364\pi$
$140$	−3.72698	−0.314988
$141$	−16.1352	−1.35883
$142$	−1.46283	−0.122758
$143$	10.6571	0.891196
$144$	3.13632	0.261360
$145$	2.44918	0.203393
$146$	−1.30311	−0.107846
$147$	11.4108	0.941143
$148$	0.866585	0.0712329
$149$	11.5103	0.942964	0.471482	−	0.881876i	$-0.343719\pi$
$149$	11.5103	0.942964	0.471482	+	0.881876i	$0.343719\pi$
$150$	1.33934	0.109356
$151$	−7.53524	−0.613209	−0.306604	−	0.951837i	$-0.599193\pi$
$151$	−7.53524	−0.613209	−0.306604	+	0.951837i	$0.599193\pi$
$152$	−3.50198	−0.284048
$153$	5.62508	0.454761
$154$	1.22062	0.0983605
$155$	−9.20343	−0.739238
$156$	13.1312	1.05134
$157$	−0.916273	−0.0731266	−0.0365633	−	0.999331i	$-0.511641\pi$
$157$	−0.916273	−0.0731266	−0.0365633	+	0.999331i	$0.511641\pi$
$158$	−6.23615	−0.496122
$159$	−19.7053	−1.56273
$160$	6.95208	0.549610
$161$	0.820182	0.0646394
$162$	−3.92548	−0.308415
$163$	−6.39363	−0.500788	−0.250394	−	0.968144i	$-0.580560\pi$
$163$	−6.39363	−0.500788	−0.250394	+	0.968144i	$0.580560\pi$
$164$	21.8093	1.70302
$165$	−10.6441	−0.828645
$166$	4.90309	0.380554
$167$	11.3608	0.879122	0.439561	−	0.898213i	$-0.355134\pi$
$167$	11.3608	0.879122	0.439561	+	0.898213i	$0.355134\pi$
$168$	3.11096	0.240016
$169$	−0.590724	−0.0454403
$170$	3.68399	0.282549
$171$	2.43997	0.186589
$172$	−6.14587	−0.468618
$173$	16.0592	1.22096	0.610478	−	0.792033i	$-0.290977\pi$
$173$	16.0592	1.22096	0.610478	+	0.792033i	$0.290977\pi$
$174$	−0.988342	−0.0749260
$175$	−2.11710	−0.160037
$176$	9.82431	0.740535
$177$	24.8333	1.86658
$178$	4.97268	0.372718
$179$	20.5231	1.53397	0.766983	−	0.641667i	$-0.221757\pi$
$179$	20.5231	1.53397	0.766983	+	0.641667i	$0.221757\pi$
$180$	−3.19395	−0.238063
$181$	−1.18497	−0.0880782	−0.0440391	−	0.999030i	$-0.514023\pi$
$181$	−1.18497	−0.0880782	−0.0440391	+	0.999030i	$0.514023\pi$
$182$	1.42130	0.105354
$183$	−11.5688	−0.855194
$184$	−1.00881	−0.0743706
$185$	−0.817943	−0.0601363
$186$	3.71395	0.272320
$187$	17.6202	1.28852
$188$	−15.1662	−1.10611
$189$	4.56535	0.332080
$190$	1.59799	0.115930
$191$	−8.59050	−0.621587	−0.310793	−	0.950478i	$-0.600595\pi$
$191$	−8.59050	−0.621587	−0.310793	+	0.950478i	$0.600595\pi$
$192$	10.1285	0.730959
$193$	12.8714	0.926506	0.463253	−	0.886226i	$-0.346682\pi$
$193$	12.8714	0.926506	0.463253	+	0.886226i	$0.346682\pi$
$194$	−0.820431	−0.0589035
$195$	−12.3941	−0.887561
$196$	10.7254	0.766102
$197$	−10.4418	−0.743951	−0.371975	−	0.928243i	$-0.621319\pi$
$197$	−10.4418	−0.743951	−0.371975	+	0.928243i	$0.621319\pi$
$198$	1.04605	0.0743395
$199$	12.2029	0.865040	0.432520	−	0.901624i	$-0.357625\pi$
$199$	12.2029	0.865040	0.432520	+	0.901624i	$0.357625\pi$
$200$	2.60400	0.184130
$201$	−24.6796	−1.74076
$202$	−2.16467	−0.152306
$203$	1.56228	0.109650
$204$	21.7107	1.52005
$205$	−20.5851	−1.43773
$206$	2.58583	0.180163
$207$	0.702881	0.0488536
$208$	11.4395	0.793188
$209$	7.64304	0.528680
$210$	−1.41957	−0.0979593
$211$	18.7651	1.29184	0.645922	−	0.763404i	$-0.276473\pi$
$211$	18.7651	1.29184	0.645922	+	0.763404i	$0.276473\pi$
$212$	−18.5218	−1.27208
$213$	8.13692	0.557533
$214$	2.06503	0.141163
$215$	5.80089	0.395618
$216$	−5.61531	−0.382074
$217$	−5.87066	−0.398527
$218$	−0.707959	−0.0479490
$219$	7.24848	0.489807
$220$	−10.0049	−0.674527
$221$	20.5171	1.38013
$222$	0.330073	0.0221530
$223$	−23.9493	−1.60377	−0.801883	−	0.597481i	$-0.796168\pi$
$223$	−23.9493	−1.60377	−0.801883	+	0.597481i	$0.796168\pi$
$224$	4.43457	0.296297
$225$	−1.81431	−0.120954
$226$	2.04833	0.136253
$227$	7.85177	0.521141	0.260570	−	0.965455i	$-0.416089\pi$
$227$	7.85177	0.521141	0.260570	+	0.965455i	$0.416089\pi$
$228$	9.41737	0.623680
$229$	28.5302	1.88533	0.942664	−	0.333745i	$-0.108312\pi$
$229$	28.5302	1.88533	0.942664	+	0.333745i	$0.108312\pi$
$230$	0.460332	0.0303534
$231$	−6.78965	−0.446726
$232$	−1.92158	−0.126158
$233$	4.45331	0.291746	0.145873	−	0.989303i	$-0.453401\pi$
$233$	4.45331	0.291746	0.145873	+	0.989303i	$0.453401\pi$
$234$	1.21803	0.0796251
$235$	14.3149	0.933799
$236$	23.3418	1.51942
$237$	34.6883	2.25325
$238$	2.34993	0.152324
$239$	27.2979	1.76576	0.882878	−	0.469603i	$-0.155603\pi$
$239$	27.2979	1.76576	0.882878	+	0.469603i	$0.155603\pi$
$240$	−11.4255	−0.737516
$241$	−13.5077	−0.870111	−0.435055	−	0.900404i	$-0.643271\pi$
$241$	−13.5077	−0.870111	−0.435055	+	0.900404i	$0.643271\pi$
$242$	−0.661460	−0.0425202
$243$	9.68237	0.621125
$244$	−10.8740	−0.696139
$245$	−10.1234	−0.646760
$246$	8.30693	0.529630
$247$	8.89963	0.566270
$248$	7.22083	0.458523
$249$	−27.2732	−1.72837
$250$	−4.35084	−0.275172
$251$	−25.5782	−1.61448	−0.807239	−	0.590224i	$-0.799039\pi$
$251$	−25.5782	−1.61448	−0.807239	+	0.590224i	$0.799039\pi$
$252$	−2.03735	−0.128341
$253$	2.20173	0.138421
$254$	4.64871	0.291686
$255$	−20.4920	−1.28326
$256$	6.70264	0.418915
$257$	13.0881	0.816412	0.408206	−	0.912890i	$-0.366154\pi$
$257$	13.0881	0.816412	0.408206	+	0.912890i	$0.366154\pi$
$258$	−2.34089	−0.145738
$259$	−0.521747	−0.0324198
$260$	−11.6497	−0.722486
$261$	1.33884	0.0828723
$262$	−0.490007	−0.0302727
$263$	−15.4676	−0.953772	−0.476886	−	0.878965i	$-0.658235\pi$
$263$	−15.4676	−0.953772	−0.476886	+	0.878965i	$0.658235\pi$
$264$	8.35117	0.513979
$265$	17.4821	1.07392
$266$	1.01932	0.0624987
$267$	−27.6603	−1.69279
$268$	−23.1974	−1.41700
$269$	8.27464	0.504513	0.252257	−	0.967660i	$-0.418827\pi$
$269$	8.27464	0.504513	0.252257	+	0.967660i	$0.418827\pi$
$270$	2.56233	0.155939
$271$	−23.4695	−1.42567	−0.712834	−	0.701333i	$-0.752589\pi$
$271$	−23.4695	−1.42567	−0.712834	+	0.701333i	$0.752589\pi$
$272$	18.9137	1.14681
$273$	−7.90593	−0.478489
$274$	−6.51239	−0.393428
$275$	−5.68321	−0.342711
$276$	2.71285	0.163295
$277$	7.83294	0.470636	0.235318	−	0.971918i	$-0.424387\pi$
$277$	7.83294	0.470636	0.235318	+	0.971918i	$0.424387\pi$
$278$	5.03966	0.302259
$279$	−5.03105	−0.301201
$280$	−2.75998	−0.164940
$281$	0.891949	0.0532092	0.0266046	−	0.999646i	$-0.491530\pi$
$281$	0.891949	0.0532092	0.0266046	+	0.999646i	$0.491530\pi$
$282$	−5.77662	−0.343993
$283$	−14.9558	−0.889030	−0.444515	−	0.895771i	$-0.646624\pi$
$283$	−14.9558	−0.889030	−0.444515	+	0.895771i	$0.646624\pi$
$284$	7.64823	0.453839
$285$	−8.88876	−0.526524
$286$	3.81540	0.225609
$287$	−13.1308	−0.775086
$288$	3.80035	0.223938
$289$	16.9223	0.995429
$290$	0.876838	0.0514897
$291$	4.56361	0.267524
$292$	6.81314	0.398709
$293$	−10.8125	−0.631675	−0.315837	−	0.948813i	$-0.602285\pi$
$293$	−10.8125	−0.631675	−0.315837	+	0.948813i	$0.602285\pi$
$294$	4.08520	0.238253
$295$	−22.0316	−1.28273
$296$	0.641742	0.0373005
$297$	12.2554	0.711130
$298$	4.12085	0.238715
$299$	2.56371	0.148263
$300$	−7.00256	−0.404293
$301$	3.70026	0.213279
$302$	−2.69771	−0.155236
$303$	12.0409	0.691731
$304$	8.20414	0.470540
$305$	10.2637	0.587695
$306$	2.01385	0.115124
$307$	14.3563	0.819358	0.409679	−	0.912230i	$-0.365641\pi$
$307$	14.3563	0.819358	0.409679	+	0.912230i	$0.365641\pi$
$308$	−6.38187	−0.363641
$309$	−14.3836	−0.818253
$310$	−3.29495	−0.187140
$311$	6.79593	0.385362	0.192681	−	0.981261i	$-0.438282\pi$
$311$	6.79593	0.385362	0.192681	+	0.981261i	$0.438282\pi$
$312$	9.72418	0.550523
$313$	−5.37854	−0.304013	−0.152007	−	0.988379i	$-0.548573\pi$
$313$	−5.37854	−0.304013	−0.152007	+	0.988379i	$0.548573\pi$
$314$	−0.328038	−0.0185122
$315$	1.92299	0.108348
$316$	32.6050	1.83417
$317$	−10.8135	−0.607347	−0.303673	−	0.952776i	$-0.598213\pi$
$317$	−10.8135	−0.607347	−0.303673	+	0.952776i	$0.598213\pi$
$318$	−7.05475	−0.395611
$319$	4.19383	0.234810
$320$	−8.98577	−0.502320
$321$	−11.4867	−0.641123
$322$	0.293636	0.0163637
$323$	14.7144	0.818728
$324$	20.5239	1.14022
$325$	−6.61758	−0.367077
$326$	−2.28900	−0.126776
$327$	3.93799	0.217772
$328$	16.1507	0.891773
$329$	9.13113	0.503416
$330$	−3.81074	−0.209774
$331$	31.4050	1.72617	0.863086	−	0.505057i	$-0.168528\pi$
$331$	31.4050	1.72617	0.863086	+	0.505057i	$0.168528\pi$
$332$	−25.6352	−1.40692
$333$	−0.447128	−0.0245025
$334$	4.06730	0.222553
$335$	21.8952	1.19627
$336$	−7.28810	−0.397598
$337$	−8.47256	−0.461530	−0.230765	−	0.973010i	$-0.574123\pi$
$337$	−8.47256	−0.461530	−0.230765	+	0.973010i	$0.574123\pi$
$338$	−0.211487	−0.0115034
$339$	−11.3938	−0.618824
$340$	−19.2613	−1.04459
$341$	−15.7594	−0.853421
$342$	0.873541	0.0472357
$343$	−14.3463	−0.774628
$344$	−4.55127	−0.245388
$345$	−2.56058	−0.137857
$346$	5.74939	0.309089
$347$	28.7607	1.54395	0.771976	−	0.635651i	$-0.219268\pi$
$347$	28.7607	1.54395	0.771976	+	0.635651i	$0.219268\pi$
$348$	5.16743	0.277003
$349$	2.73272	0.146279	0.0731397	−	0.997322i	$-0.476698\pi$
$349$	2.73272	0.146279	0.0731397	+	0.997322i	$0.476698\pi$
$350$	−0.757948	−0.0405140
$351$	14.2703	0.761692
$352$	11.9043	0.634503
$353$	−8.74263	−0.465323	−0.232662	−	0.972558i	$-0.574743\pi$
$353$	−8.74263	−0.465323	−0.232662	+	0.972558i	$0.574743\pi$
$354$	8.89063	0.472532
$355$	−7.21892	−0.383140
$356$	−25.9991	−1.37795
$357$	−13.0714	−0.691812
$358$	7.34752	0.388329
$359$	22.8664	1.20684	0.603422	−	0.797422i	$-0.293804\pi$
$359$	22.8664	1.20684	0.603422	+	0.797422i	$0.293804\pi$
$360$	−2.36525	−0.124660
$361$	−12.6174	−0.664074
$362$	−0.424235	−0.0222973
$363$	3.67934	0.193115
$364$	−7.43110	−0.389496
$365$	−6.43071	−0.336599
$366$	−4.14180	−0.216495
$367$	13.7344	0.716932	0.358466	−	0.933543i	$-0.383300\pi$
$367$	13.7344	0.716932	0.358466	+	0.933543i	$0.383300\pi$
$368$	2.36336	0.123199
$369$	−11.2529	−0.585800
$370$	−0.292834	−0.0152237
$371$	11.1515	0.578955
$372$	−19.4180	−1.00677
$373$	−15.7804	−0.817077	−0.408539	−	0.912741i	$-0.633961\pi$
$373$	−15.7804	−0.817077	−0.408539	+	0.912741i	$0.633961\pi$
$374$	6.30825	0.326192
$375$	24.2014	1.24975
$376$	−11.2312	−0.579203
$377$	4.88334	0.251505
$378$	1.63445	0.0840672
$379$	19.1735	0.984876	0.492438	−	0.870347i	$-0.336106\pi$
$379$	19.1735	0.984876	0.492438	+	0.870347i	$0.336106\pi$
$380$	−8.35490	−0.428597
$381$	−25.8583	−1.32476
$382$	−3.07551	−0.157357
$383$	34.8128	1.77885	0.889426	−	0.457079i	$-0.151104\pi$
$383$	34.8128	1.77885	0.889426	+	0.457079i	$0.151104\pi$
$384$	19.2984	0.984818
$385$	6.02365	0.306993
$386$	4.60814	0.234548
$387$	3.17105	0.161194
$388$	4.28952	0.217768
$389$	−35.4524	−1.79751	−0.898753	−	0.438455i	$-0.855526\pi$
$389$	−35.4524	−1.79751	−0.898753	+	0.438455i	$0.855526\pi$
$390$	−4.43725	−0.224689
$391$	4.23875	0.214363
$392$	7.94262	0.401163
$393$	2.72564	0.137490
$394$	−3.73831	−0.188334
$395$	−30.7748	−1.54845
$396$	−5.46914	−0.274835
$397$	12.1621	0.610400	0.305200	−	0.952288i	$-0.401277\pi$
$397$	12.1621	0.610400	0.305200	+	0.952288i	$0.401277\pi$
$398$	4.36879	0.218988
$399$	−5.66994	−0.283852
$400$	−6.10043	−0.305022
$401$	−8.49982	−0.424461	−0.212230	−	0.977220i	$-0.568073\pi$
$401$	−8.49982	−0.424461	−0.212230	+	0.977220i	$0.568073\pi$
$402$	−8.83561	−0.440680
$403$	−18.3504	−0.914099
$404$	11.3177	0.563078
$405$	−19.3718	−0.962595
$406$	0.559315	0.0277583
$407$	−1.40060	−0.0694251
$408$	16.0776	0.795962
$409$	8.21986	0.406446	0.203223	−	0.979132i	$-0.434858\pi$
$409$	8.21986	0.406446	0.203223	+	0.979132i	$0.434858\pi$
$410$	−7.36974	−0.363966
$411$	36.2249	1.78684
$412$	−13.5197	−0.666068
$413$	−14.0535	−0.691526
$414$	0.251640	0.0123674
$415$	24.1963	1.18775
$416$	13.8615	0.679617
$417$	−28.0329	−1.37278
$418$	2.73631	0.133837
$419$	−7.62567	−0.372538	−0.186269	−	0.982499i	$-0.559640\pi$
$419$	−7.62567	−0.372538	−0.186269	+	0.982499i	$0.559640\pi$
$420$	7.42203	0.362158
$421$	7.63033	0.371879	0.185940	−	0.982561i	$-0.440467\pi$
$421$	7.63033	0.371879	0.185940	+	0.982561i	$0.440467\pi$
$422$	6.71815	0.327034
$423$	7.82521	0.380475
$424$	−13.7161	−0.666115
$425$	−10.9413	−0.530731
$426$	2.91312	0.141141
$427$	6.54696	0.316829
$428$	−10.7968	−0.521882
$429$	−21.2230	−1.02465
$430$	2.07679	0.100152
$431$	26.1540	1.25980	0.629898	−	0.776678i	$-0.283097\pi$
$431$	26.1540	1.25980	0.629898	+	0.776678i	$0.283097\pi$
$432$	13.1551	0.632925
$433$	−19.6843	−0.945965	−0.472982	−	0.881072i	$-0.656823\pi$
$433$	−19.6843	−0.945965	−0.472982	+	0.881072i	$0.656823\pi$
$434$	−2.10177	−0.100888
$435$	−4.87737	−0.233852
$436$	3.70148	0.177269
$437$	1.83863	0.0879536
$438$	2.59505	0.123996
$439$	−3.98974	−0.190420	−0.0952100	−	0.995457i	$-0.530352\pi$
$439$	−3.98974	−0.190420	−0.0952100	+	0.995457i	$0.530352\pi$
$440$	−7.40900	−0.353210
$441$	−5.53395	−0.263521
$442$	7.34538	0.349384
$443$	16.9705	0.806295	0.403148	−	0.915135i	$-0.367916\pi$
$443$	16.9705	0.806295	0.403148	+	0.915135i	$0.367916\pi$
$444$	−1.72575	−0.0819002
$445$	24.5397	1.16329
$446$	−8.57417	−0.405999
$447$	−22.9221	−1.08418
$448$	−5.73182	−0.270803
$449$	18.1608	0.857063	0.428531	−	0.903527i	$-0.359031\pi$
$449$	18.1608	0.857063	0.428531	+	0.903527i	$0.359031\pi$
$450$	−0.649547	−0.0306199
$451$	−35.2488	−1.65980
$452$	−10.7095	−0.503731
$453$	15.0059	0.705039
$454$	2.81104	0.131928
$455$	7.01399	0.328821
$456$	6.97394	0.326585
$457$	5.97328	0.279418	0.139709	−	0.990193i	$-0.455383\pi$
$457$	5.97328	0.279418	0.139709	+	0.990193i	$0.455383\pi$
$458$	10.2142	0.477277
$459$	23.5940	1.10127
$460$	−2.40679	−0.112217
$461$	−13.3523	−0.621880	−0.310940	−	0.950429i	$-0.600644\pi$
$461$	−13.3523	−0.621880	−0.310940	+	0.950429i	$0.600644\pi$
$462$	−2.43078	−0.113090
$463$	6.40874	0.297839	0.148920	−	0.988849i	$-0.452420\pi$
$463$	6.40874	0.297839	0.148920	+	0.988849i	$0.452420\pi$
$464$	4.50171	0.208987
$465$	18.3280	0.849941
$466$	1.59434	0.0738565
$467$	−0.0245954	−0.00113814	−0.000569070	−	1.00000i	$-0.500181\pi$
$467$	−0.0245954	−0.00113814	−0.000569070		1.00000i	$0.500181\pi$
$468$	−6.36832	−0.294376
$469$	13.9665	0.644912
$470$	5.12491	0.236394
$471$	1.82470	0.0840775
$472$	17.2856	0.795632
$473$	9.93312	0.456725
$474$	12.4189	0.570417
$475$	−4.74597	−0.217760
$476$	−12.2863	−0.563144
$477$	9.55660	0.437567
$478$	9.77301	0.447007
$479$	−15.8404	−0.723769	−0.361884	−	0.932223i	$-0.617866\pi$
$479$	−15.8404	−0.723769	−0.361884	+	0.932223i	$0.617866\pi$
$480$	−13.8446	−0.631916
$481$	−1.63087	−0.0743612
$482$	−4.83595	−0.220271
$483$	−1.63334	−0.0743193
$484$	3.45836	0.157198
$485$	−4.04875	−0.183844
$486$	3.46641	0.157240
$487$	−15.3626	−0.696146	−0.348073	−	0.937467i	$-0.613164\pi$
$487$	−15.3626	−0.696146	−0.348073	+	0.937467i	$0.613164\pi$
$488$	−8.05266	−0.364527
$489$	12.7325	0.575782
$490$	−3.62431	−0.163729
$491$	34.0697	1.53754	0.768772	−	0.639523i	$-0.220868\pi$
$491$	34.0697	1.53754	0.768772	+	0.639523i	$0.220868\pi$
$492$	−43.4318	−1.95806
$493$	8.07395	0.363632
$494$	3.18618	0.143353
$495$	5.16215	0.232022
$496$	−16.9164	−0.759567
$497$	−4.60479	−0.206553
$498$	−9.76417	−0.437543
$499$	28.3689	1.26997	0.634983	−	0.772526i	$-0.281007\pi$
$499$	28.3689	1.26997	0.634983	+	0.772526i	$0.281007\pi$
$500$	22.7479	1.01732
$501$	−22.6242	−1.01077
$502$	−9.15731	−0.408711
$503$	0.468474	0.0208882	0.0104441	−	0.999945i	$-0.496675\pi$
$503$	0.468474	0.0208882	0.0104441	+	0.999945i	$0.496675\pi$
$504$	−1.50874	−0.0672047
$505$	−10.6824	−0.475363
$506$	0.788246	0.0350418
$507$	1.17639	0.0522451
$508$	−24.3052	−1.07837
$509$	−3.38877	−0.150204	−0.0751022	−	0.997176i	$-0.523928\pi$
$509$	−3.38877	−0.150204	−0.0751022	+	0.997176i	$0.523928\pi$
$510$	−7.33641	−0.324862
$511$	−4.10201	−0.181462
$512$	21.7811	0.962597
$513$	10.2343	0.451855
$514$	4.68570	0.206677
$515$	12.7608	0.562309
$516$	12.2391	0.538795
$517$	24.5120	1.07803
$518$	−0.186792	−0.00820718
$519$	−31.9807	−1.40380
$520$	−8.62710	−0.378323
$521$	4.70012	0.205916	0.102958	−	0.994686i	$-0.467169\pi$
$521$	4.70012	0.205916	0.102958	+	0.994686i	$0.467169\pi$
$522$	0.479323	0.0209794
$523$	−42.1383	−1.84258	−0.921290	−	0.388877i	$-0.872863\pi$
$523$	−42.1383	−1.84258	−0.921290	+	0.388877i	$0.872863\pi$
$524$	2.56194	0.111919
$525$	4.21605	0.184004
$526$	−5.53759	−0.241450
$527$	−30.3400	−1.32163
$528$	−19.5644	−0.851433
$529$	−22.4703	−0.976972
$530$	6.25883	0.271866
$531$	−12.0436	−0.522646
$532$	−5.32940	−0.231059
$533$	−41.0440	−1.77781
$534$	−9.90275	−0.428534
$535$	10.1907	0.440584
$536$	−17.1786	−0.742002
$537$	−40.8703	−1.76368
$538$	2.96243	0.127719
$539$	−17.3347	−0.746659
$540$	−13.3968	−0.576508
$541$	16.4874	0.708850	0.354425	−	0.935084i	$-0.384677\pi$
$541$	16.4874	0.708850	0.354425	+	0.935084i	$0.384677\pi$
$542$	−8.40237	−0.360913
$543$	2.35979	0.101268
$544$	22.9182	0.982609
$545$	−3.49371	−0.149654
$546$	−2.83042	−0.121131
$547$	35.8736	1.53385	0.766923	−	0.641740i	$-0.221787\pi$
$547$	35.8736	1.53385	0.766923	+	0.641740i	$0.221787\pi$
$548$	34.0493	1.45451
$549$	5.61062	0.239455
$550$	−2.03466	−0.0867583
$551$	3.50221	0.149199
$552$	2.00898	0.0855078
$553$	−19.6306	−0.834776
$554$	2.80429	0.119143
$555$	1.62888	0.0691420
$556$	−26.3493	−1.11746
$557$	18.8257	0.797669	0.398835	−	0.917023i	$-0.369415\pi$
$557$	18.8257	0.797669	0.398835	+	0.917023i	$0.369415\pi$
$558$	−1.80118	−0.0762501
$559$	11.5662	0.489199
$560$	6.46586	0.273232
$561$	−35.0894	−1.48147
$562$	0.319329	0.0134701
$563$	−9.15186	−0.385705	−0.192852	−	0.981228i	$-0.561774\pi$
$563$	−9.15186	−0.385705	−0.192852	+	0.981228i	$0.561774\pi$
$564$	30.2024	1.27175
$565$	10.1083	0.425260
$566$	−5.35437	−0.225061
$567$	−12.3569	−0.518940
$568$	5.66382	0.237649
$569$	−0.366116	−0.0153484	−0.00767420	−	0.999971i	$-0.502443\pi$
$569$	−0.366116	−0.0153484	−0.00767420	+	0.999971i	$0.502443\pi$
$570$	−3.18229	−0.133291
$571$	−37.0895	−1.55215	−0.776074	−	0.630642i	$-0.782791\pi$
$571$	−37.0895	−1.55215	−0.776074	+	0.630642i	$0.782791\pi$
$572$	−19.9483	−0.834082
$573$	17.1074	0.714671
$574$	−4.70099	−0.196216
$575$	−1.36717	−0.0570148
$576$	−4.91207	−0.204669
$577$	−19.7970	−0.824160	−0.412080	−	0.911148i	$-0.635197\pi$
$577$	−19.7970	−0.824160	−0.412080	+	0.911148i	$0.635197\pi$
$578$	6.05840	0.251996
$579$	−25.6326	−1.06525
$580$	−4.58444	−0.190359
$581$	15.4343	0.640321
$582$	1.63383	0.0677245
$583$	29.9354	1.23980
$584$	5.04541	0.208780
$585$	6.01086	0.248518
$586$	−3.87103	−0.159911
$587$	−11.5735	−0.477689	−0.238844	−	0.971058i	$-0.576769\pi$
$587$	−11.5735	−0.477689	−0.238844	+	0.971058i	$0.576769\pi$
$588$	−21.3590	−0.880828
$589$	−13.1605	−0.542268
$590$	−7.88759	−0.324727
$591$	20.7942	0.855360
$592$	−1.50342	−0.0617901
$593$	−20.4025	−0.837829	−0.418914	−	0.908026i	$-0.637589\pi$
$593$	−20.4025	−0.837829	−0.418914	+	0.908026i	$0.637589\pi$
$594$	4.38759	0.180025
$595$	11.5967	0.475418
$596$	−21.5454	−0.882533
$597$	−24.3012	−0.994582
$598$	0.917841	0.0375333
$599$	22.6118	0.923892	0.461946	−	0.886908i	$-0.347151\pi$
$599$	22.6118	0.923892	0.461946	+	0.886908i	$0.347151\pi$
$600$	−5.18568	−0.211705
$601$	−29.9646	−1.22228	−0.611141	−	0.791522i	$-0.709289\pi$
$601$	−29.9646	−1.22228	−0.611141	+	0.791522i	$0.709289\pi$
$602$	1.32474	0.0539924
$603$	11.9690	0.487416
$604$	14.1047	0.573910
$605$	−3.26424	−0.132710
$606$	4.31079	0.175114
$607$	−42.1372	−1.71030	−0.855148	−	0.518384i	$-0.826534\pi$
$607$	−42.1372	−1.71030	−0.855148	+	0.518384i	$0.826534\pi$
$608$	9.94114	0.403166
$609$	−3.11117	−0.126071
$610$	3.67452	0.148777
$611$	28.5419	1.15468
$612$	−10.5292	−0.425617
$613$	−2.75222	−0.111161	−0.0555806	−	0.998454i	$-0.517701\pi$
$613$	−2.75222	−0.111161	−0.0555806	+	0.998454i	$0.517701\pi$
$614$	5.13974	0.207423
$615$	40.9939	1.65303
$616$	−4.72603	−0.190417
$617$	34.8603	1.40342	0.701712	−	0.712461i	$-0.252419\pi$
$617$	34.8603	1.40342	0.701712	+	0.712461i	$0.252419\pi$
$618$	−5.14950	−0.207143
$619$	9.77466	0.392877	0.196438	−	0.980516i	$-0.437062\pi$
$619$	9.77466	0.392877	0.196438	+	0.980516i	$0.437062\pi$
$620$	17.2272	0.691862
$621$	2.94819	0.118307
$622$	2.43303	0.0975556
$623$	15.6533	0.627137
$624$	−22.7810	−0.911970
$625$	−12.0782	−0.483127
$626$	−1.92559	−0.0769619
$627$	−15.2206	−0.607852
$628$	1.71511	0.0684401
$629$	−2.69642	−0.107513
$630$	0.688456	0.0274287
$631$	−20.9316	−0.833274	−0.416637	−	0.909073i	$-0.636791\pi$
$631$	−20.9316	−0.833274	−0.416637	+	0.909073i	$0.636791\pi$
$632$	24.1453	0.960448
$633$	−37.3694	−1.48530
$634$	−3.87137	−0.153752
$635$	22.9409	0.910383
$636$	36.8849	1.46258
$637$	−20.1847	−0.799747
$638$	1.50145	0.0594428
$639$	−3.94622	−0.156110
$640$	−17.1212	−0.676774
$641$	−7.51586	−0.296859	−0.148429	−	0.988923i	$-0.547422\pi$
$641$	−7.51586	−0.296859	−0.148429	+	0.988923i	$0.547422\pi$
$642$	−4.11237	−0.162302
$643$	−15.4436	−0.609036	−0.304518	−	0.952507i	$-0.598495\pi$
$643$	−15.4436	−0.609036	−0.304518	+	0.952507i	$0.598495\pi$
$644$	−1.53524	−0.0604969
$645$	−11.5521	−0.454863
$646$	5.26793	0.207264
$647$	−2.86189	−0.112513	−0.0562563	−	0.998416i	$-0.517916\pi$
$647$	−2.86189	−0.112513	−0.0562563	+	0.998416i	$0.517916\pi$
$648$	15.1988	0.597064
$649$	−37.7256	−1.48086
$650$	−2.36918	−0.0929269
$651$	11.6910	0.458207
$652$	11.9678	0.468694
$653$	25.1833	0.985501	0.492750	−	0.870171i	$-0.335992\pi$
$653$	25.1833	0.985501	0.492750	+	0.870171i	$0.335992\pi$
$654$	1.40985	0.0551296
$655$	−2.41814	−0.0944844
$656$	−37.8365	−1.47727
$657$	−3.51534	−0.137147
$658$	3.26906	0.127441
$659$	−41.0517	−1.59915	−0.799574	−	0.600567i	$-0.794941\pi$
$659$	−41.0517	−1.59915	−0.799574	+	0.600567i	$0.794941\pi$
$660$	19.9240	0.775540
$661$	0.294257	0.0114453	0.00572264	−	0.999984i	$-0.498178\pi$
$661$	0.294257	0.0114453	0.00572264	+	0.999984i	$0.498178\pi$
$662$	11.2434	0.436986
$663$	−40.8584	−1.58681
$664$	−18.9839	−0.736719
$665$	5.03026	0.195065
$666$	−0.160077	−0.00620288
$667$	1.00888	0.0390640
$668$	−21.2654	−0.822782
$669$	47.6935	1.84394
$670$	7.83878	0.302838
$671$	17.5749	0.678471
$672$	−8.83115	−0.340669
$673$	−10.3527	−0.399068	−0.199534	−	0.979891i	$-0.563943\pi$
$673$	−10.3527	−0.399068	−0.199534	+	0.979891i	$0.563943\pi$
$674$	−3.03328	−0.116838
$675$	−7.61002	−0.292910
$676$	1.10573	0.0425282
$677$	26.0643	1.00173	0.500867	−	0.865525i	$-0.333015\pi$
$677$	26.0643	1.00173	0.500867	+	0.865525i	$0.333015\pi$
$678$	−4.07911	−0.156657
$679$	−2.58260	−0.0991112
$680$	−14.2638	−0.546991
$681$	−15.6363	−0.599183
$682$	−5.64208	−0.216046
$683$	33.9982	1.30090	0.650452	−	0.759547i	$-0.274579\pi$
$683$	33.9982	1.30090	0.650452	+	0.759547i	$0.274579\pi$
$684$	−4.56720	−0.174631
$685$	−32.1380	−1.22793
$686$	−5.13616	−0.196100
$687$	−56.8159	−2.16766
$688$	10.6623	0.406498
$689$	34.8571	1.32795
$690$	−0.916720	−0.0348989
$691$	39.4493	1.50072	0.750360	−	0.661029i	$-0.229880\pi$
$691$	39.4493	1.50072	0.750360	+	0.661029i	$0.229880\pi$
$692$	−30.0600	−1.14271
$693$	3.29282	0.125084
$694$	10.2967	0.390857
$695$	24.8702	0.943382
$696$	3.82669	0.145050
$697$	−67.8608	−2.57041
$698$	0.978350	0.0370311
$699$	−8.86847	−0.335436
$700$	3.96284	0.149781
$701$	−47.0338	−1.77644	−0.888221	−	0.459416i	$-0.848059\pi$
$701$	−47.0338	−1.77644	−0.888221	+	0.459416i	$0.848059\pi$
$702$	5.10895	0.192825
$703$	−1.16962	−0.0441130
$704$	−15.3867	−0.579909
$705$	−28.5071	−1.07364
$706$	−3.12997	−0.117798
$707$	−6.81409	−0.256270
$708$	−46.4836	−1.74696
$709$	15.3890	0.577947	0.288974	−	0.957337i	$-0.406686\pi$
$709$	15.3890	0.577947	0.288974	+	0.957337i	$0.406686\pi$
$710$	−2.58447	−0.0969933
$711$	−16.8230	−0.630913
$712$	−19.2534	−0.721550
$713$	−3.79113	−0.141979
$714$	−4.67973	−0.175135
$715$	18.8286	0.704150
$716$	−38.4156	−1.43566
$717$	−54.3619	−2.03018
$718$	8.18647	0.305516
$719$	−51.0635	−1.90435	−0.952174	−	0.305558i	$-0.901157\pi$
$719$	−51.0635	−1.90435	−0.952174	+	0.305558i	$0.901157\pi$
$720$	5.54112	0.206505
$721$	8.13984	0.303144
$722$	−4.51719	−0.168113
$723$	26.8997	1.00041
$724$	2.21806	0.0824336
$725$	−2.60417	−0.0967165
$726$	1.31725	0.0488878
$727$	22.7544	0.843915	0.421958	−	0.906616i	$-0.361343\pi$
$727$	22.7544	0.843915	0.421958	+	0.906616i	$0.361343\pi$
$728$	−5.50303	−0.203956
$729$	13.6121	0.504152
$730$	−2.30228	−0.0852111
$731$	19.1232	0.707297
$732$	21.6549	0.800387
$733$	3.90628	0.144282	0.0721409	−	0.997394i	$-0.477017\pi$
$733$	3.90628	0.144282	0.0721409	+	0.997394i	$0.477017\pi$
$734$	4.91710	0.181494
$735$	20.1600	0.743614
$736$	2.86374	0.105559
$737$	37.4922	1.38104
$738$	−4.02866	−0.148297
$739$	−13.9414	−0.512844	−0.256422	−	0.966565i	$-0.582544\pi$
$739$	−13.9414	−0.512844	−0.256422	+	0.966565i	$0.582544\pi$
$740$	1.53105	0.0562824
$741$	−17.7230	−0.651070
$742$	3.99237	0.146564
$743$	7.53431	0.276407	0.138204	−	0.990404i	$-0.455867\pi$
$743$	7.53431	0.276407	0.138204	+	0.990404i	$0.455867\pi$
$744$	−14.3798	−0.527189
$745$	20.3360	0.745054
$746$	−5.64958	−0.206846
$747$	13.2269	0.483946
$748$	−32.9819	−1.20594
$749$	6.50044	0.237521
$750$	8.66441	0.316379
$751$	−1.19242	−0.0435121	−0.0217561	−	0.999763i	$-0.506926\pi$
$751$	−1.19242	−0.0435121	−0.0217561	+	0.999763i	$0.506926\pi$
$752$	26.3114	0.959479
$753$	50.9371	1.85625
$754$	1.74830	0.0636692
$755$	−13.3129	−0.484508
$756$	−8.54554	−0.310798
$757$	−37.5998	−1.36659	−0.683294	−	0.730144i	$-0.739453\pi$
$757$	−37.5998	−1.36659	−0.683294	+	0.730144i	$0.739453\pi$
$758$	6.86436	0.249325
$759$	−4.38459	−0.159150
$760$	−6.18714	−0.224431
$761$	22.0555	0.799512	0.399756	−	0.916622i	$-0.369095\pi$
$761$	22.0555	0.799512	0.399756	+	0.916622i	$0.369095\pi$
$762$	−9.25759	−0.335367
$763$	−2.22856	−0.0806793
$764$	16.0799	0.581751
$765$	9.93815	0.359315
$766$	12.4634	0.450322
$767$	−43.9281	−1.58615
$768$	−13.3478	−0.481649
$769$	−14.7197	−0.530807	−0.265404	−	0.964137i	$-0.585505\pi$
$769$	−14.7197	−0.530807	−0.265404	+	0.964137i	$0.585505\pi$
$770$	2.15654	0.0777164
$771$	−26.0640	−0.938673
$772$	−24.0931	−0.867129
$773$	−19.2059	−0.690790	−0.345395	−	0.938457i	$-0.612255\pi$
$773$	−19.2059	−0.690790	−0.345395	+	0.938457i	$0.612255\pi$
$774$	1.13528	0.0408067
$775$	9.78586	0.351518
$776$	3.17657	0.114032
$777$	1.03902	0.0372748
$778$	−12.6924	−0.455045
$779$	−29.4358	−1.05465
$780$	23.1996	0.830681
$781$	−12.3613	−0.442321
$782$	1.51753	0.0542667
$783$	5.61569	0.200688
$784$	−18.6073	−0.664546
$785$	−1.61883	−0.0577787
$786$	0.975815	0.0348062
$787$	−10.3277	−0.368143	−0.184071	−	0.982913i	$-0.558928\pi$
$787$	−10.3277	−0.368143	−0.184071	+	0.982913i	$0.558928\pi$
$788$	19.5453	0.696273
$789$	30.8026	1.09660
$790$	−11.0178	−0.391995
$791$	6.44787	0.229260
$792$	−4.05012	−0.143915
$793$	20.4644	0.726711
$794$	4.35420	0.154525
$795$	−34.8145	−1.23474
$796$	−22.8417	−0.809602
$797$	−45.2196	−1.60176	−0.800880	−	0.598825i	$-0.795634\pi$
$797$	−45.2196	−1.60176	−0.800880	+	0.598825i	$0.795634\pi$
$798$	−2.02991	−0.0718580
$799$	47.1903	1.66947
$800$	−7.39203	−0.261348
$801$	13.4146	0.473982
$802$	−3.04304	−0.107454
$803$	−11.0116	−0.388590
$804$	46.1959	1.62920
$805$	1.44906	0.0510728
$806$	−6.56969	−0.231407
$807$	−16.4784	−0.580066
$808$	8.38123	0.294851
$809$	−10.3964	−0.365520	−0.182760	−	0.983158i	$-0.558503\pi$
$809$	−10.3964	−0.365520	−0.182760	+	0.983158i	$0.558503\pi$
$810$	−6.93537	−0.243684
$811$	−49.0759	−1.72329	−0.861645	−	0.507512i	$-0.830565\pi$
$811$	−49.0759	−1.72329	−0.861645	+	0.507512i	$0.830565\pi$
$812$	−2.92431	−0.102623
$813$	46.7378	1.63917
$814$	−0.501432	−0.0175752
$815$	−11.2960	−0.395682
$816$	−37.6654	−1.31855
$817$	8.29500	0.290205
$818$	2.94282	0.102893
$819$	3.83419	0.133977
$820$	38.5318	1.34559
$821$	4.31627	0.150639	0.0753195	−	0.997159i	$-0.476002\pi$
$821$	4.31627	0.150639	0.0753195	+	0.997159i	$0.476002\pi$
$822$	12.9690	0.452345
$823$	23.5750	0.821772	0.410886	−	0.911687i	$-0.365219\pi$
$823$	23.5750	0.821772	0.410886	+	0.911687i	$0.365219\pi$
$824$	−10.0119	−0.348781
$825$	11.3177	0.394033
$826$	−5.03132	−0.175062
$827$	−34.9784	−1.21632	−0.608159	−	0.793815i	$-0.708092\pi$
$827$	−34.9784	−1.21632	−0.608159	+	0.793815i	$0.708092\pi$
$828$	−1.31567	−0.0457227
$829$	38.9032	1.35116	0.675582	−	0.737285i	$-0.263892\pi$
$829$	38.9032	1.35116	0.675582	+	0.737285i	$0.263892\pi$
$830$	8.66258	0.300683
$831$	−15.5988	−0.541115
$832$	−17.9164	−0.621140
$833$	−33.3727	−1.15630
$834$	−10.0361	−0.347523
$835$	20.0717	0.694610
$836$	−14.3065	−0.494799
$837$	−21.1024	−0.729406
$838$	−2.73009	−0.0943093
$839$	−25.1617	−0.868677	−0.434339	−	0.900750i	$-0.643018\pi$
$839$	−25.1617	−0.868677	−0.434339	+	0.900750i	$0.643018\pi$
$840$	5.49631	0.189641
$841$	−27.0783	−0.933734
$842$	2.73176	0.0941425
$843$	−1.77626	−0.0611775
$844$	−35.1250	−1.20905
$845$	−1.04367	−0.0359032
$846$	2.80153	0.0963184
$847$	−2.08218	−0.0715447
$848$	32.1331	1.10345
$849$	29.7834	1.02217
$850$	−3.91712	−0.134356
$851$	−0.336931	−0.0115499
$852$	−15.2309	−0.521802
$853$	−30.5156	−1.04484	−0.522418	−	0.852690i	$-0.674970\pi$
$853$	−30.5156	−1.04484	−0.522418	+	0.852690i	$0.674970\pi$
$854$	2.34389	0.0802064
$855$	4.31084	0.147428
$856$	−7.99545	−0.273279
$857$	49.0939	1.67702	0.838508	−	0.544889i	$-0.183428\pi$
$857$	49.0939	1.67702	0.838508	+	0.544889i	$0.183428\pi$
$858$	−7.59810	−0.259395
$859$	−1.85871	−0.0634184	−0.0317092	−	0.999497i	$-0.510095\pi$
$859$	−1.85871	−0.0634184	−0.0317092	+	0.999497i	$0.510095\pi$
$860$	−10.8583	−0.370264
$861$	26.1491	0.891158
$862$	9.36348	0.318921
$863$	−42.9308	−1.46138	−0.730690	−	0.682709i	$-0.760802\pi$
$863$	−42.9308	−1.46138	−0.730690	+	0.682709i	$0.760802\pi$
$864$	15.9403	0.542301
$865$	28.3727	0.964700
$866$	−7.04722	−0.239474
$867$	−33.6996	−1.14450
$868$	10.9889	0.372986
$869$	−52.6970	−1.78762
$870$	−1.74616	−0.0592004
$871$	43.6562	1.47923
$872$	2.74110	0.0928252
$873$	−2.21324	−0.0749070
$874$	0.658253	0.0222657
$875$	−13.6959	−0.463005
$876$	−13.5679	−0.458417
$877$	26.1404	0.882697	0.441348	−	0.897336i	$-0.354500\pi$
$877$	26.1404	0.882697	0.441348	+	0.897336i	$0.354500\pi$
$878$	−1.42838	−0.0482055
$879$	21.5324	0.726270
$880$	17.3572	0.585111
$881$	−3.09816	−0.104380	−0.0521899	−	0.998637i	$-0.516620\pi$
$881$	−3.09816	−0.104380	−0.0521899	+	0.998637i	$0.516620\pi$
$882$	−1.98122	−0.0667113
$883$	0.209441	0.00704825	0.00352413	−	0.999994i	$-0.498878\pi$
$883$	0.209441	0.00704825	0.00352413	+	0.999994i	$0.498878\pi$
$884$	−38.4044	−1.29168
$885$	43.8744	1.47482
$886$	6.07567	0.204116
$887$	20.0478	0.673140	0.336570	−	0.941658i	$-0.390733\pi$
$887$	20.0478	0.673140	0.336570	+	0.941658i	$0.390733\pi$
$888$	−1.27798	−0.0428863
$889$	14.6335	0.490792
$890$	8.78553	0.294492
$891$	−33.1712	−1.11128
$892$	44.8290	1.50099
$893$	20.4696	0.684988
$894$	−8.20639	−0.274463
$895$	36.2593	1.21202
$896$	−10.9212	−0.364852
$897$	−5.10545	−0.170466
$898$	6.50181	0.216968
$899$	−7.22131	−0.240844
$900$	3.39608	0.113203
$901$	57.6315	1.91998
$902$	−12.6195	−0.420184
$903$	−7.36881	−0.245219
$904$	−7.93079	−0.263774
$905$	−2.09356	−0.0695922
$906$	5.37231	0.178483
$907$	56.9694	1.89164	0.945819	−	0.324695i	$-0.105262\pi$
$907$	56.9694	1.89164	0.945819	+	0.324695i	$0.105262\pi$
$908$	−14.6972	−0.487742
$909$	−5.83955	−0.193686
$910$	2.51110	0.0832421
$911$	−37.7032	−1.24916	−0.624581	−	0.780960i	$-0.714730\pi$
$911$	−37.7032	−1.24916	−0.624581	+	0.780960i	$0.714730\pi$
$912$	−16.3380	−0.541004
$913$	41.4323	1.37121
$914$	2.13851	0.0707357
$915$	−20.4394	−0.675704
$916$	−53.4035	−1.76450
$917$	−1.54248	−0.0509370
$918$	8.44696	0.278791
$919$	4.96239	0.163694	0.0818471	−	0.996645i	$-0.473918\pi$
$919$	4.96239	0.163694	0.0818471	+	0.996645i	$0.473918\pi$
$920$	−1.78233	−0.0587616
$921$	−28.5896	−0.942059
$922$	−4.78031	−0.157431
$923$	−14.3936	−0.473770
$924$	12.7091	0.418097
$925$	0.869705	0.0285957
$926$	2.29441	0.0753990
$927$	6.97569	0.229112
$928$	5.45483	0.179063
$929$	−11.6386	−0.381849	−0.190924	−	0.981605i	$-0.561149\pi$
$929$	−11.6386	−0.381849	−0.190924	+	0.981605i	$0.561149\pi$
$930$	6.56166	0.215165
$931$	−14.4760	−0.474431
$932$	−8.33583	−0.273049
$933$	−13.5336	−0.443071
$934$	−0.00880547	−0.000288124 0
$935$	31.1306	1.01808
$936$	−4.71600	−0.154147
$937$	0.273091	0.00892148	0.00446074	−	0.999990i	$-0.498580\pi$
$937$	0.273091	0.00892148	0.00446074	+	0.999990i	$0.498580\pi$
$938$	5.00018	0.163262
$939$	10.7110	0.349540
$940$	−26.7950	−0.873955
$941$	15.2516	0.497189	0.248594	−	0.968608i	$-0.420031\pi$
$941$	15.2516	0.497189	0.248594	+	0.968608i	$0.420031\pi$
$942$	0.653264	0.0212845
$943$	−8.47954	−0.276132
$944$	−40.4952	−1.31801
$945$	8.06587	0.262383
$946$	3.55618	0.115622
$947$	−44.6904	−1.45224	−0.726121	−	0.687567i	$-0.758679\pi$
$947$	−44.6904	−1.45224	−0.726121	+	0.687567i	$0.758679\pi$
$948$	−64.9305	−2.10885
$949$	−12.8220	−0.416219
$950$	−1.69912	−0.0551266
$951$	21.5343	0.698299
$952$	−9.09854	−0.294885
$953$	22.0878	0.715496	0.357748	−	0.933818i	$-0.383545\pi$
$953$	22.0878	0.715496	0.357748	+	0.933818i	$0.383545\pi$
$954$	3.42139	0.110771
$955$	−15.1773	−0.491127
$956$	−51.0970	−1.65259
$957$	−8.35173	−0.269973
$958$	−5.67108	−0.183224
$959$	−20.5001	−0.661983
$960$	17.8945	0.577544
$961$	−3.86402	−0.124646
$962$	−0.583872	−0.0188248
$963$	5.57076	0.179515
$964$	25.2842	0.814348
$965$	22.7407	0.732049
$966$	−0.584755	−0.0188142
$967$	16.8072	0.540483	0.270241	−	0.962793i	$-0.412897\pi$
$967$	16.8072	0.540483	0.270241	+	0.962793i	$0.412897\pi$
$968$	2.56106	0.0823155
$969$	−29.3026	−0.941336
$970$	−1.44950	−0.0465407
$971$	30.7985	0.988372	0.494186	−	0.869356i	$-0.335466\pi$
$971$	30.7985	0.988372	0.494186	+	0.869356i	$0.335466\pi$
$972$	−18.1237	−0.581319
$973$	15.8642	0.508582
$974$	−5.50001	−0.176232
$975$	13.1785	0.422048
$976$	18.8651	0.603857
$977$	−11.6197	−0.371748	−0.185874	−	0.982574i	$-0.559512\pi$
$977$	−11.6197	−0.371748	−0.185874	+	0.982574i	$0.559512\pi$
$978$	4.55839	0.145761
$979$	42.0204	1.34298
$980$	18.9492	0.605311
$981$	−1.90983	−0.0609763
$982$	12.1974	0.389234
$983$	35.7361	1.13980	0.569902	−	0.821713i	$-0.306981\pi$
$983$	35.7361	1.13980	0.569902	+	0.821713i	$0.306981\pi$
$984$	−32.1630	−1.02532
$985$	−18.4482	−0.587809
$986$	2.89058	0.0920547
$987$	−18.1840	−0.578804
$988$	−16.6586	−0.529979
$989$	2.38954	0.0759828
$990$	1.84812	0.0587370
$991$	29.1444	0.925802	0.462901	−	0.886410i	$-0.346809\pi$
$991$	29.1444	0.925802	0.462901	+	0.886410i	$0.346809\pi$
$992$	−20.4979	−0.650810
$993$	−62.5408	−1.98467
$994$	−1.64857	−0.0522895
$995$	21.5596	0.683484
$996$	51.0508	1.61761
$997$	−1.03900	−0.0329055	−0.0164527	−	0.999865i	$-0.505237\pi$
$997$	−1.03900	−0.0329055	−0.0164527	+	0.999865i	$0.505237\pi$
$998$	10.1564	0.321496
$999$	−1.87545	−0.0593366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.100	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.100	✓	184	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q+0.358013 q^{2} -1.99143 q^{3} -1.87183 q^{4} +1.76676 q^{5} -0.712958 q^{6} +1.12698 q^{7} -1.38616 q^{8} +0.965797 q^{9} +0.632522 q^{10} +3.02530 q^{11} +3.72761 q^{12} +3.52268 q^{13} +0.403472 q^{14} -3.51838 q^{15} +3.24739 q^{16} +5.82428 q^{17} +0.345768 q^{18} +2.52638 q^{19} -3.30707 q^{20} -2.24429 q^{21} +1.08309 q^{22} +0.727773 q^{23} +2.76045 q^{24} -1.87856 q^{25} +1.26116 q^{26} +4.05097 q^{27} -2.10950 q^{28} +1.38626 q^{29} -1.25962 q^{30} -5.20922 q^{31} +3.93493 q^{32} -6.02467 q^{33} +2.08517 q^{34} +1.99109 q^{35} -1.80781 q^{36} -0.462962 q^{37} +0.904476 q^{38} -7.01517 q^{39} -2.44902 q^{40} -11.6514 q^{41} -0.803486 q^{42} +3.28335 q^{43} -5.66283 q^{44} +1.70633 q^{45} +0.260552 q^{46} +8.10233 q^{47} -6.46695 q^{48} -5.72993 q^{49} -0.672550 q^{50} -11.5987 q^{51} -6.59385 q^{52} +9.89504 q^{53} +1.45030 q^{54} +5.34497 q^{55} -1.56217 q^{56} -5.03111 q^{57} +0.496297 q^{58} -12.4701 q^{59} +6.58579 q^{60} +5.80931 q^{61} -1.86497 q^{62} +1.08843 q^{63} -5.08602 q^{64} +6.22373 q^{65} -2.15691 q^{66} +12.3929 q^{67} -10.9021 q^{68} -1.44931 q^{69} +0.712837 q^{70} -4.08597 q^{71} -1.33875 q^{72} -3.63984 q^{73} -0.165746 q^{74} +3.74103 q^{75} -4.72894 q^{76} +3.40943 q^{77} -2.51152 q^{78} -17.4188 q^{79} +5.73735 q^{80} -10.9646 q^{81} -4.17134 q^{82} +13.6953 q^{83} +4.20093 q^{84} +10.2901 q^{85} +1.17548 q^{86} -2.76063 q^{87} -4.19355 q^{88} +13.8897 q^{89} +0.610888 q^{90} +3.96997 q^{91} -1.36226 q^{92} +10.3738 q^{93} +2.90074 q^{94} +4.46350 q^{95} -7.83615 q^{96} -2.29162 q^{97} -2.05139 q^{98} +2.92182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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