LMFDB - Embedded newform 1849.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 62x^{8} + 1289x^{6} - 11252x^{4} + 39376x^{2} - 35688 $ x^10 - 62x^8 + 1289x^6 - 11252x^4 + 39376x^2 - 35688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.51834$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.51834 q^{2} -3.84074 q^{3} +22.4521 q^{4} -10.9281 q^{5} +21.1945 q^{6} -14.0538 q^{7} -79.7518 q^{8} -12.2488 q^{9} +O(q^{10})$	\(q-5.51834 q^{2} -3.84074 q^{3} +22.4521 q^{4} -10.9281 q^{5} +21.1945 q^{6} -14.0538 q^{7} -79.7518 q^{8} -12.2488 q^{9} +60.3051 q^{10} +39.1602 q^{11} -86.2327 q^{12} -28.1301 q^{13} +77.5534 q^{14} +41.9720 q^{15} +260.481 q^{16} +20.1300 q^{17} +67.5928 q^{18} +134.739 q^{19} -245.359 q^{20} +53.9767 q^{21} -216.100 q^{22} +180.103 q^{23} +306.306 q^{24} -5.57635 q^{25} +155.232 q^{26} +150.744 q^{27} -315.537 q^{28} +203.883 q^{29} -231.616 q^{30} -14.8891 q^{31} -799.410 q^{32} -150.404 q^{33} -111.084 q^{34} +153.581 q^{35} -275.011 q^{36} +176.205 q^{37} -743.536 q^{38} +108.040 q^{39} +871.537 q^{40} +188.623 q^{41} -297.862 q^{42} +879.230 q^{44} +133.856 q^{45} -993.871 q^{46} -413.619 q^{47} -1000.44 q^{48} -145.492 q^{49} +30.7722 q^{50} -77.3141 q^{51} -631.581 q^{52} -120.503 q^{53} -831.858 q^{54} -427.947 q^{55} +1120.81 q^{56} -517.497 q^{57} -1125.10 q^{58} +139.928 q^{59} +942.360 q^{60} +140.883 q^{61} +82.1629 q^{62} +172.141 q^{63} +2327.57 q^{64} +307.409 q^{65} +829.981 q^{66} +359.087 q^{67} +451.962 q^{68} -691.728 q^{69} -847.513 q^{70} +178.098 q^{71} +976.860 q^{72} -34.4998 q^{73} -972.361 q^{74} +21.4173 q^{75} +3025.18 q^{76} -550.348 q^{77} -596.203 q^{78} -682.916 q^{79} -2846.57 q^{80} -248.252 q^{81} -1040.88 q^{82} +1095.01 q^{83} +1211.89 q^{84} -219.983 q^{85} -783.061 q^{87} -3123.10 q^{88} +570.272 q^{89} -738.662 q^{90} +395.333 q^{91} +4043.70 q^{92} +57.1849 q^{93} +2282.49 q^{94} -1472.44 q^{95} +3070.32 q^{96} +24.2242 q^{97} +802.876 q^{98} -479.664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.51834	−1.95103	−0.975515	−	0.219934i	$-0.929416\pi$
$2$	−5.51834	−1.95103	−0.975515	+	0.219934i	$0.929416\pi$
$3$	−3.84074	−0.739150	−0.369575	−	0.929201i	$-0.620497\pi$
$3$	−3.84074	−0.739150	−0.369575	+	0.929201i	$0.620497\pi$
$4$	22.4521	2.80652
$5$	−10.9281	−0.977440	−0.488720	−	0.872441i	$-0.662536\pi$
$5$	−10.9281	−0.977440	−0.488720	+	0.872441i	$0.662536\pi$
$6$	21.1945	1.44210
$7$	−14.0538	−0.758831	−0.379416	−	0.925226i	$-0.623875\pi$
$7$	−14.0538	−0.758831	−0.379416	+	0.925226i	$0.623875\pi$
$8$	−79.7518	−3.52457
$9$	−12.2488	−0.453657
$10$	60.3051	1.90701
$11$	39.1602	1.07339	0.536693	−	0.843778i	$-0.319673\pi$
$11$	39.1602	1.07339	0.536693	+	0.843778i	$0.319673\pi$
$12$	−86.2327	−2.07444
$13$	−28.1301	−0.600145	−0.300073	−	0.953916i	$-0.597011\pi$
$13$	−28.1301	−0.600145	−0.300073	+	0.953916i	$0.597011\pi$
$14$	77.5534	1.48050
$15$	41.9720	0.722475
$16$	260.481	4.07002
$17$	20.1300	0.287191	0.143596	−	0.989636i	$-0.454134\pi$
$17$	20.1300	0.287191	0.143596	+	0.989636i	$0.454134\pi$
$18$	67.5928	0.885099
$19$	134.739	1.62691	0.813453	−	0.581630i	$-0.197585\pi$
$19$	134.739	1.62691	0.813453	+	0.581630i	$0.197585\pi$
$20$	−245.359	−2.74320
$21$	53.9767	0.560890
$22$	−216.100	−2.09421
$23$	180.103	1.63279	0.816393	−	0.577497i	$-0.195970\pi$
$23$	180.103	1.63279	0.816393	+	0.577497i	$0.195970\pi$
$24$	306.306	2.60518
$25$	−5.57635	−0.0446108
$26$	155.232	1.17090
$27$	150.744	1.07447
$28$	−315.537	−2.12967
$29$	203.883	1.30552	0.652761	−	0.757564i	$-0.273611\pi$
$29$	203.883	1.30552	0.652761	+	0.757564i	$0.273611\pi$
$30$	−231.616	−1.40957
$31$	−14.8891	−0.0862630	−0.0431315	−	0.999069i	$-0.513733\pi$
$31$	−14.8891	−0.0862630	−0.0431315	+	0.999069i	$0.513733\pi$
$32$	−799.410	−4.41616
$33$	−150.404	−0.793393
$34$	−111.084	−0.560318
$35$	153.581	0.741712
$36$	−275.011	−1.27320
$37$	176.205	0.782918	0.391459	−	0.920196i	$-0.371971\pi$
$37$	176.205	0.782918	0.391459	+	0.920196i	$0.371971\pi$
$38$	−743.536	−3.17414
$39$	108.040	0.443597
$40$	871.537	3.44505
$41$	188.623	0.718485	0.359243	−	0.933244i	$-0.383035\pi$
$41$	188.623	0.718485	0.359243	+	0.933244i	$0.383035\pi$
$42$	−297.862	−1.09431
$43$	0	0
$43$	0	0
$44$	879.230	3.01247
$45$	133.856	0.443423
$46$	−993.871	−3.18561
$47$	−413.619	−1.28367	−0.641835	−	0.766843i	$-0.721827\pi$
$47$	−413.619	−1.28367	−0.641835	+	0.766843i	$0.721827\pi$
$48$	−1000.44	−3.00835
$49$	−145.492	−0.424175
$50$	30.7722	0.0870370
$51$	−77.3141	−0.212277
$52$	−631.581	−1.68432
$53$	−120.503	−0.312307	−0.156154	−	0.987733i	$-0.549910\pi$
$53$	−120.503	−0.312307	−0.156154	+	0.987733i	$0.549910\pi$
$54$	−831.858	−2.09632
$55$	−427.947	−1.04917
$56$	1120.81	2.67455
$57$	−517.497	−1.20253
$58$	−1125.10	−2.54711
$59$	139.928	0.308763	0.154382	−	0.988011i	$-0.450661\pi$
$59$	139.928	0.308763	0.154382	+	0.988011i	$0.450661\pi$
$60$	942.360	2.02764
$61$	140.883	0.295709	0.147855	−	0.989009i	$-0.452763\pi$
$61$	140.883	0.295709	0.147855	+	0.989009i	$0.452763\pi$
$62$	82.1629	0.168302
$63$	172.141	0.344249
$64$	2327.57	4.54603
$65$	307.409	0.586606
$66$	829.981	1.54793
$67$	359.087	0.654768	0.327384	−	0.944891i	$-0.393833\pi$
$67$	359.087	0.654768	0.327384	+	0.944891i	$0.393833\pi$
$68$	451.962	0.806006
$69$	−691.728	−1.20687
$70$	−847.513	−1.44710
$71$	178.098	0.297694	0.148847	−	0.988860i	$-0.452444\pi$
$71$	178.098	0.297694	0.148847	+	0.988860i	$0.452444\pi$
$72$	976.860	1.59895
$73$	−34.4998	−0.0553136	−0.0276568	−	0.999617i	$-0.508805\pi$
$73$	−34.4998	−0.0553136	−0.0276568	+	0.999617i	$0.508805\pi$
$74$	−972.361	−1.52750
$75$	21.4173	0.0329741
$76$	3025.18	4.56594
$77$	−550.348	−0.814519
$78$	−596.203	−0.865471
$79$	−682.916	−0.972584	−0.486292	−	0.873797i	$-0.661651\pi$
$79$	−682.916	−0.972584	−0.486292	+	0.873797i	$0.661651\pi$
$80$	−2846.57	−3.97820
$81$	−248.252	−0.340537
$82$	−1040.88	−1.40179
$83$	1095.01	1.44810	0.724051	−	0.689747i	$-0.242278\pi$
$83$	1095.01	1.44810	0.724051	+	0.689747i	$0.242278\pi$
$84$	1211.89	1.57415
$85$	−219.983	−0.280712
$86$	0	0
$87$	−783.061	−0.964977
$88$	−3123.10	−3.78322
$89$	570.272	0.679199	0.339599	−	0.940570i	$-0.389708\pi$
$89$	570.272	0.679199	0.339599	+	0.940570i	$0.389708\pi$
$90$	−738.662	−0.865131
$91$	395.333	0.455409
$92$	4043.70	4.58244
$93$	57.1849	0.0637613
$94$	2282.49	2.50448
$95$	−1472.44	−1.59020
$96$	3070.32	3.26420
$97$	24.2242	0.0253567	0.0126783	−	0.999920i	$-0.495964\pi$
$97$	24.2242	0.0253567	0.0126783	+	0.999920i	$0.495964\pi$
$98$	802.876	0.827578
$99$	−479.664	−0.486950
$100$	−125.201	−0.125201
$101$	1052.39	1.03680	0.518402	−	0.855137i	$-0.326527\pi$
$101$	1052.39	1.03680	0.518402	+	0.855137i	$0.326527\pi$
$102$	426.646	0.414159
$103$	−542.316	−0.518796	−0.259398	−	0.965771i	$-0.583524\pi$
$103$	−542.316	−0.518796	−0.259398	+	0.965771i	$0.583524\pi$
$104$	2243.43	2.11525
$105$	−589.864	−0.548236
$106$	664.974	0.609321
$107$	−1250.83	−1.13012	−0.565058	−	0.825051i	$-0.691146\pi$
$107$	−1250.83	−1.13012	−0.565058	+	0.825051i	$0.691146\pi$
$108$	3384.53	3.01552
$109$	1907.46	1.67616	0.838082	−	0.545545i	$-0.183677\pi$
$109$	1907.46	1.67616	0.838082	+	0.545545i	$0.183677\pi$
$110$	2361.56	2.04696
$111$	−676.758	−0.578694
$112$	−3660.74	−3.08846
$113$	127.663	0.106279	0.0531394	−	0.998587i	$-0.483077\pi$
$113$	127.663	0.106279	0.0531394	+	0.998587i	$0.483077\pi$
$114$	2855.72	2.34617
$115$	−1968.19	−1.59595
$116$	4577.61	3.66397
$117$	344.559	0.272260
$118$	−772.170	−0.602407
$119$	−282.902	−0.217930
$120$	−3347.34	−2.54641
$121$	202.522	0.152157
$122$	−777.443	−0.576938
$123$	−724.449	−0.531068
$124$	−334.291	−0.242098
$125$	1426.95	1.02104
$126$	−949.933	−0.671641
$127$	−1141.00	−0.797226	−0.398613	−	0.917119i	$-0.630508\pi$
$127$	−1141.00	−0.797226	−0.398613	+	0.917119i	$0.630508\pi$
$128$	−6449.05	−4.45329
$129$	0	0
$130$	−1696.39	−1.14449
$131$	−1746.85	−1.16506	−0.582531	−	0.812808i	$-0.697938\pi$
$131$	−1746.85	−1.16506	−0.582531	+	0.812808i	$0.697938\pi$
$132$	−3376.89	−2.22667
$133$	−1893.59	−1.23455
$134$	−1981.57	−1.27747
$135$	−1647.35	−1.05023
$136$	−1605.41	−1.01222
$137$	1108.54	0.691307	0.345653	−	0.938362i	$-0.387657\pi$
$137$	1108.54	0.691307	0.345653	+	0.938362i	$0.387657\pi$
$138$	3817.19	2.35465
$139$	−267.397	−0.163167	−0.0815837	−	0.996666i	$-0.525998\pi$
$139$	−267.397	−0.163167	−0.0815837	+	0.996666i	$0.525998\pi$
$140$	3448.22	2.08163
$141$	1588.60	0.948825
$142$	−982.804	−0.580811
$143$	−1101.58	−0.644187
$144$	−3190.57	−1.84639
$145$	−2228.06	−1.27607
$146$	190.382	0.107919
$147$	558.797	0.313529
$148$	3956.18	2.19727
$149$	−1867.64	−1.02687	−0.513434	−	0.858129i	$-0.671627\pi$
$149$	−1867.64	−1.02687	−0.513434	+	0.858129i	$0.671627\pi$
$150$	−118.188	−0.0643334
$151$	−1799.63	−0.969881	−0.484940	−	0.874547i	$-0.661159\pi$
$151$	−1799.63	−0.969881	−0.484940	+	0.874547i	$0.661159\pi$
$152$	−10745.7	−5.73414
$153$	−246.568	−0.130286
$154$	3037.01	1.58915
$155$	162.709	0.0843169
$156$	2425.73	1.24496
$157$	−1847.94	−0.939375	−0.469687	−	0.882833i	$-0.655633\pi$
$157$	−1847.94	−0.939375	−0.469687	+	0.882833i	$0.655633\pi$
$158$	3768.57	1.89754
$159$	462.818	0.230842
$160$	8736.04	4.31653
$161$	−2531.12	−1.23901
$162$	1369.94	0.664398
$163$	−518.926	−0.249358	−0.124679	−	0.992197i	$-0.539790\pi$
$163$	−518.926	−0.249358	−0.124679	+	0.992197i	$0.539790\pi$
$164$	4234.98	2.01644
$165$	1643.63	0.775494
$166$	−6042.62	−2.82529
$167$	−436.467	−0.202245	−0.101122	−	0.994874i	$-0.532243\pi$
$167$	−436.467	−0.202245	−0.101122	+	0.994874i	$0.532243\pi$
$168$	−4304.74	−1.97689
$169$	−1405.70	−0.639826
$170$	1213.94	0.547677
$171$	−1650.38	−0.738059
$172$	0	0
$173$	4256.95	1.87081	0.935404	−	0.353581i	$-0.115036\pi$
$173$	4256.95	1.87081	0.935404	+	0.353581i	$0.115036\pi$
$174$	4321.20	1.88270
$175$	78.3686	0.0338521
$176$	10200.5	4.36870
$177$	−537.426	−0.228222
$178$	−3146.96	−1.32514
$179$	3377.12	1.41015	0.705077	−	0.709130i	$-0.250912\pi$
$179$	3377.12	1.41015	0.705077	+	0.709130i	$0.250912\pi$
$180$	3005.35	1.24447
$181$	2539.34	1.04281	0.521403	−	0.853311i	$-0.325409\pi$
$181$	2539.34	1.04281	0.521403	+	0.853311i	$0.325409\pi$
$182$	−2181.59	−0.888516
$183$	−541.096	−0.218574
$184$	−14363.5	−5.75486
$185$	−1925.59	−0.765255
$186$	−315.566	−0.124400
$187$	788.296	0.308267
$188$	−9286.62	−3.60264
$189$	−2118.52	−0.815342
$190$	8125.44	3.10254
$191$	3495.47	1.32421	0.662104	−	0.749412i	$-0.269664\pi$
$191$	3495.47	1.32421	0.662104	+	0.749412i	$0.269664\pi$
$192$	−8939.58	−3.36020
$193$	−3696.80	−1.37876	−0.689381	−	0.724399i	$-0.742117\pi$
$193$	−3696.80	−1.37876	−0.689381	+	0.724399i	$0.742117\pi$
$194$	−133.678	−0.0494716
$195$	−1180.68	−0.433590
$196$	−3266.61	−1.19045
$197$	−1348.28	−0.487621	−0.243810	−	0.969823i	$-0.578397\pi$
$197$	−1348.28	−0.487621	−0.243810	+	0.969823i	$0.578397\pi$
$198$	2646.95	0.950053
$199$	−2143.49	−0.763556	−0.381778	−	0.924254i	$-0.624688\pi$
$199$	−2143.49	−0.763556	−0.381778	+	0.924254i	$0.624688\pi$
$200$	444.724	0.157234
$201$	−1379.16	−0.483972
$202$	−5807.48	−2.02283
$203$	−2865.32	−0.990671
$204$	−1735.87	−0.595759
$205$	−2061.29	−0.702276
$206$	2992.68	1.01219
$207$	−2206.04	−0.740726
$208$	−7327.36	−2.44260
$209$	5276.40	1.74630
$210$	3255.07	1.06963
$211$	50.8341	0.0165856	0.00829281	−	0.999966i	$-0.497360\pi$
$211$	50.8341	0.0165856	0.00829281	+	0.999966i	$0.497360\pi$
$212$	−2705.54	−0.876496
$213$	−684.026	−0.220041
$214$	6902.52	2.20489
$215$	0	0
$216$	−12022.1	−3.78704
$217$	209.247	0.0654590
$218$	−10526.0	−3.27024
$219$	132.505	0.0408851
$220$	−9608.32	−2.94451
$221$	−566.260	−0.172356
$222$	3734.58	1.12905
$223$	−5103.07	−1.53241	−0.766204	−	0.642598i	$-0.777857\pi$
$223$	−5103.07	−1.53241	−0.766204	+	0.642598i	$0.777857\pi$
$224$	11234.7	3.35112
$225$	68.3033	0.0202380
$226$	−704.487	−0.207353
$227$	−1555.16	−0.454713	−0.227357	−	0.973812i	$-0.573008\pi$
$227$	−1555.16	−0.454713	−0.227357	+	0.973812i	$0.573008\pi$
$228$	−11618.9	−3.37491
$229$	3739.10	1.07898	0.539491	−	0.841991i	$-0.318617\pi$
$229$	3739.10	1.07898	0.539491	+	0.841991i	$0.318617\pi$
$230$	10861.1	3.11375
$231$	2113.74	0.602051
$232$	−16260.0	−4.60140
$233$	−637.022	−0.179110	−0.0895552	−	0.995982i	$-0.528545\pi$
$233$	−637.022	−0.179110	−0.0895552	+	0.995982i	$0.528545\pi$
$234$	−1901.39	−0.531188
$235$	4520.07	1.25471
$236$	3141.68	0.866550
$237$	2622.90	0.718885
$238$	1561.15	0.425187
$239$	3015.41	0.816111	0.408055	−	0.912957i	$-0.366207\pi$
$239$	3015.41	0.816111	0.408055	+	0.912957i	$0.366207\pi$
$240$	10932.9	2.94048
$241$	−3153.62	−0.842916	−0.421458	−	0.906848i	$-0.638481\pi$
$241$	−3153.62	−0.842916	−0.421458	+	0.906848i	$0.638481\pi$
$242$	−1117.58	−0.296864
$243$	−3116.62	−0.822763
$244$	3163.13	0.829913
$245$	1589.95	0.414606
$246$	3997.76	1.03613
$247$	−3790.22	−0.976380
$248$	1187.43	0.304040
$249$	−4205.63	−1.07036
$250$	−7874.42	−1.99209
$251$	1903.55	0.478688	0.239344	−	0.970935i	$-0.423068\pi$
$251$	1903.55	0.478688	0.239344	+	0.970935i	$0.423068\pi$
$252$	3864.93	0.966142
$253$	7052.87	1.75261
$254$	6296.45	1.55541
$255$	844.897	0.207488
$256$	16967.5	4.14247
$257$	−2274.39	−0.552032	−0.276016	−	0.961153i	$-0.589014\pi$
$257$	−2274.39	−0.552032	−0.276016	+	0.961153i	$0.589014\pi$
$258$	0	0
$259$	−2476.34	−0.594102
$260$	6901.98	1.64632
$261$	−2497.31	−0.592260
$262$	9639.74	2.27307
$263$	7503.35	1.75923	0.879613	−	0.475689i	$-0.157801\pi$
$263$	7503.35	1.75923	0.879613	+	0.475689i	$0.157801\pi$
$264$	11995.0	2.79637
$265$	1316.87	0.305262
$266$	10449.5	2.40864
$267$	−2190.26	−0.502030
$268$	8062.27	1.83762
$269$	3003.38	0.680742	0.340371	−	0.940291i	$-0.389447\pi$
$269$	3003.38	0.680742	0.340371	+	0.940291i	$0.389447\pi$
$270$	9090.64	2.04903
$271$	3083.76	0.691237	0.345619	−	0.938375i	$-0.387669\pi$
$271$	3083.76	0.691237	0.345619	+	0.938375i	$0.387669\pi$
$272$	5243.49	1.16887
$273$	−1518.37	−0.336615
$274$	−6117.31	−1.34876
$275$	−218.371	−0.0478846
$276$	−15530.8	−3.38711
$277$	2719.74	0.589939	0.294970	−	0.955507i	$-0.404690\pi$
$277$	2719.74	0.589939	0.294970	+	0.955507i	$0.404690\pi$
$278$	1475.59	0.318345
$279$	182.372	0.0391338
$280$	−12248.4	−2.61421
$281$	−3258.79	−0.691827	−0.345913	−	0.938266i	$-0.612431\pi$
$281$	−3258.79	−0.691827	−0.345913	+	0.938266i	$0.612431\pi$
$282$	−8766.44	−1.85118
$283$	4726.37	0.992769	0.496385	−	0.868103i	$-0.334661\pi$
$283$	4726.37	0.992769	0.496385	+	0.868103i	$0.334661\pi$
$284$	3998.67	0.835484
$285$	5655.26	1.17540
$286$	6078.90	1.25683
$287$	−2650.85	−0.545209
$288$	9791.77	2.00342
$289$	−4507.78	−0.917521
$290$	12295.2	2.48965
$291$	−93.0388	−0.0187424
$292$	−774.594	−0.155239
$293$	−4532.97	−0.903820	−0.451910	−	0.892064i	$-0.649257\pi$
$293$	−4532.97	−0.903820	−0.451910	+	0.892064i	$0.649257\pi$
$294$	−3083.63	−0.611704
$295$	−1529.15	−0.301798
$296$	−14052.7	−2.75945
$297$	5903.17	1.15332
$298$	10306.3	2.00345
$299$	−5066.32	−0.979909
$300$	480.863	0.0925422
$301$	0	0
$302$	9930.99	1.89227
$303$	−4041.97	−0.766353
$304$	35096.9	6.62154
$305$	−1539.59	−0.289038
$306$	1360.65	0.254193
$307$	−5667.92	−1.05370	−0.526849	−	0.849959i	$-0.676627\pi$
$307$	−5667.92	−1.05370	−0.526849	+	0.849959i	$0.676627\pi$
$308$	−12356.5	−2.28596
$309$	2082.89	0.383468
$310$	−897.886	−0.164505
$311$	−1401.30	−0.255500	−0.127750	−	0.991806i	$-0.540776\pi$
$311$	−1401.30	−0.255500	−0.127750	+	0.991806i	$0.540776\pi$
$312$	−8616.41	−1.56349
$313$	5657.25	1.02162	0.510810	−	0.859694i	$-0.329346\pi$
$313$	5657.25	1.02162	0.510810	+	0.859694i	$0.329346\pi$
$314$	10197.6	1.83275
$315$	−1881.18	−0.336483
$316$	−15332.9	−2.72957
$317$	7145.40	1.26601	0.633006	−	0.774147i	$-0.281821\pi$
$317$	7145.40	1.26601	0.633006	+	0.774147i	$0.281821\pi$
$318$	−2553.99	−0.450380
$319$	7984.10	1.40133
$320$	−25435.9	−4.44348
$321$	4804.11	0.835325
$322$	13967.6	2.41734
$323$	2712.30	0.467233
$324$	−5573.78	−0.955724
$325$	156.863	0.0267729
$326$	2863.61	0.486506
$327$	−7326.06	−1.23894
$328$	−15043.0	−2.53235
$329$	5812.89	0.974089
$330$	−9070.13	−1.51301
$331$	−5559.06	−0.923123	−0.461561	−	0.887108i	$-0.652711\pi$
$331$	−5559.06	−0.923123	−0.461561	+	0.887108i	$0.652711\pi$
$332$	24585.2	4.06412
$333$	−2158.29	−0.355176
$334$	2408.58	0.394585
$335$	−3924.15	−0.639997
$336$	14059.9	2.28283
$337$	5505.04	0.889847	0.444924	−	0.895569i	$-0.353231\pi$
$337$	5505.04	0.889847	0.444924	+	0.895569i	$0.353231\pi$
$338$	7757.12	1.24832
$339$	−490.319	−0.0785560
$340$	−4939.09	−0.787823
$341$	−583.058	−0.0925935
$342$	9107.39	1.43997
$343$	6865.15	1.08071
$344$	0	0
$345$	7559.28	1.17965
$346$	−23491.3	−3.65000
$347$	1466.38	0.226857	0.113428	−	0.993546i	$-0.463817\pi$
$347$	1466.38	0.226857	0.113428	+	0.993546i	$0.463817\pi$
$348$	−17581.4	−2.70822
$349$	9703.58	1.48831	0.744156	−	0.668006i	$-0.232852\pi$
$349$	9703.58	1.48831	0.744156	+	0.668006i	$0.232852\pi$
$350$	−432.465	−0.0660464
$351$	−4240.45	−0.644838
$352$	−31305.0	−4.74024
$353$	1418.43	0.213868	0.106934	−	0.994266i	$-0.465897\pi$
$353$	1418.43	0.213868	0.106934	+	0.994266i	$0.465897\pi$
$354$	2965.70	0.445269
$355$	−1946.27	−0.290978
$356$	12803.8	1.90618
$357$	1086.55	0.161083
$358$	−18636.1	−2.75125
$359$	−7687.74	−1.13020	−0.565102	−	0.825021i	$-0.691163\pi$
$359$	−7687.74	−1.13020	−0.565102	+	0.825021i	$0.691163\pi$
$360$	−10675.2	−1.56287
$361$	11295.6	1.64683
$362$	−14013.0	−2.03454
$363$	−777.832	−0.112467
$364$	8876.08	1.27811
$365$	377.018	0.0540658
$366$	2985.95	0.426443
$367$	888.233	0.126336	0.0631681	−	0.998003i	$-0.479880\pi$
$367$	888.233	0.126336	0.0631681	+	0.998003i	$0.479880\pi$
$368$	46913.4	6.64547
$369$	−2310.39	−0.325946
$370$	10626.1	1.49304
$371$	1693.51	0.236989
$372$	1283.92	0.178947
$373$	−9971.36	−1.38418	−0.692088	−	0.721813i	$-0.743309\pi$
$373$	−9971.36	−1.38418	−0.692088	+	0.721813i	$0.743309\pi$
$374$	−4350.09	−0.601438
$375$	−5480.55	−0.754705
$376$	32986.9	4.52438
$377$	−5735.25	−0.783503
$378$	11690.7	1.59076
$379$	9280.88	1.25785	0.628927	−	0.777464i	$-0.283494\pi$
$379$	9280.88	1.25785	0.628927	+	0.777464i	$0.283494\pi$
$380$	−33059.5	−4.46293
$381$	4382.30	0.589270
$382$	−19289.2	−2.58357
$383$	5552.67	0.740804	0.370402	−	0.928872i	$-0.379220\pi$
$383$	5552.67	0.740804	0.370402	+	0.928872i	$0.379220\pi$
$384$	24769.1	3.29165
$385$	6014.26	0.796143
$386$	20400.2	2.69001
$387$	0	0
$388$	543.885	0.0711639
$389$	10009.6	1.30465	0.652324	−	0.757940i	$-0.273794\pi$
$389$	10009.6	1.30465	0.652324	+	0.757940i	$0.273794\pi$
$390$	6515.38	0.845946
$391$	3625.48	0.468922
$392$	11603.3	1.49503
$393$	6709.20	0.861156
$394$	7440.30	0.951362
$395$	7462.99	0.950642
$396$	−10769.5	−1.36663
$397$	6118.38	0.773483	0.386742	−	0.922188i	$-0.373600\pi$
$397$	6118.38	0.773483	0.386742	+	0.922188i	$0.373600\pi$
$398$	11828.5	1.48972
$399$	7272.77	0.912516
$400$	−1452.53	−0.181567
$401$	8907.83	1.10932	0.554658	−	0.832078i	$-0.312849\pi$
$401$	8907.83	1.10932	0.554658	+	0.832078i	$0.312849\pi$
$402$	7610.67	0.944244
$403$	418.831	0.0517703
$404$	23628.5	2.90981
$405$	2712.92	0.332855
$406$	15811.8	1.93283
$407$	6900.23	0.840373
$408$	6165.94	0.748185
$409$	−3493.18	−0.422315	−0.211157	−	0.977452i	$-0.567723\pi$
$409$	−3493.18	−0.422315	−0.211157	+	0.977452i	$0.567723\pi$
$410$	11374.9	1.37016
$411$	−4257.61	−0.510979
$412$	−12176.1	−1.45601
$413$	−1966.51	−0.234299
$414$	12173.7	1.44518
$415$	−11966.3	−1.41543
$416$	22487.5	2.65033
$417$	1027.00	0.120605
$418$	−29117.0	−3.40708
$419$	−15657.1	−1.82554	−0.912770	−	0.408474i	$-0.866061\pi$
$419$	−15657.1	−1.82554	−0.912770	+	0.408474i	$0.866061\pi$
$420$	−13243.7	−1.53863
$421$	−6522.42	−0.755067	−0.377533	−	0.925996i	$-0.623228\pi$
$421$	−6522.42	−0.755067	−0.377533	+	0.925996i	$0.623228\pi$
$422$	−280.520	−0.0323590
$423$	5066.31	0.582347
$424$	9610.30	1.10075
$425$	−112.252	−0.0128118
$426$	3774.69	0.429306
$427$	−1979.94	−0.224394
$428$	−28083.8	−3.17169
$429$	4230.88	0.476151
$430$	0	0
$431$	−2502.95	−0.279729	−0.139864	−	0.990171i	$-0.544667\pi$
$431$	−2502.95	−0.279729	−0.139864	+	0.990171i	$0.544667\pi$
$432$	39266.0	4.37311
$433$	−8870.52	−0.984504	−0.492252	−	0.870453i	$-0.663826\pi$
$433$	−8870.52	−0.984504	−0.492252	+	0.870453i	$0.663826\pi$
$434$	−1154.70	−0.127713
$435$	8557.38	0.943207
$436$	42826.6	4.70418
$437$	24266.9	2.65639
$438$	−731.206	−0.0797680
$439$	−16253.6	−1.76707	−0.883534	−	0.468368i	$-0.844842\pi$
$439$	−16253.6	−1.76707	−0.883534	+	0.468368i	$0.844842\pi$
$440$	34129.6	3.69787
$441$	1782.10	0.192430
$442$	3124.82	0.336272
$443$	−11588.6	−1.24287	−0.621433	−	0.783467i	$-0.713449\pi$
$443$	−11588.6	−1.24287	−0.621433	+	0.783467i	$0.713449\pi$
$444$	−15194.6	−1.62411
$445$	−6232.00	−0.663876
$446$	28160.5	2.98977
$447$	7173.13	0.759010
$448$	−32711.1	−3.44967
$449$	−1551.25	−0.163047	−0.0815236	−	0.996671i	$-0.525979\pi$
$449$	−1551.25	−0.163047	−0.0815236	+	0.996671i	$0.525979\pi$
$450$	−376.921	−0.0394850
$451$	7386.50	0.771212
$452$	2866.30	0.298273
$453$	6911.91	0.716887
$454$	8581.94	0.887159
$455$	−4320.25	−0.445135
$456$	41271.3	4.23839
$457$	−14608.9	−1.49536	−0.747678	−	0.664062i	$-0.768831\pi$
$457$	−14608.9	−1.49536	−0.747678	+	0.664062i	$0.768831\pi$
$458$	−20633.7	−2.10513
$459$	3034.48	0.308578
$460$	−44190.0	−4.47906
$461$	18448.3	1.86382	0.931911	−	0.362687i	$-0.118141\pi$
$461$	18448.3	1.86382	0.931911	+	0.362687i	$0.118141\pi$
$462$	−11664.3	−1.17462
$463$	−4585.78	−0.460301	−0.230150	−	0.973155i	$-0.573922\pi$
$463$	−4585.78	−0.460301	−0.230150	+	0.973155i	$0.573922\pi$
$464$	53107.7	5.31350
$465$	−624.923	−0.0623228
$466$	3515.31	0.349450
$467$	14399.2	1.42680	0.713400	−	0.700757i	$-0.247154\pi$
$467$	14399.2	1.42680	0.713400	+	0.700757i	$0.247154\pi$
$468$	7736.07	0.764103
$469$	−5046.52	−0.496859
$470$	−24943.3	−2.44798
$471$	7097.46	0.694339
$472$	−11159.5	−1.08826
$473$	0	0
$474$	−14474.1	−1.40257
$475$	−751.351	−0.0725776
$476$	−6351.76	−0.611623
$477$	1476.01	0.141681
$478$	−16640.1	−1.59226
$479$	−10857.3	−1.03567	−0.517833	−	0.855482i	$-0.673261\pi$
$479$	−10857.3	−1.03567	−0.517833	+	0.855482i	$0.673261\pi$
$480$	−33552.8	−3.19056
$481$	−4956.67	−0.469864
$482$	17402.8	1.64455
$483$	9721.37	0.915813
$484$	4547.04	0.427032
$485$	−264.725	−0.0247846
$486$	17198.6	1.60523
$487$	6017.07	0.559876	0.279938	−	0.960018i	$-0.409686\pi$
$487$	6017.07	0.559876	0.279938	+	0.960018i	$0.409686\pi$
$488$	−11235.7	−1.04225
$489$	1993.06	0.184313
$490$	−8773.91	−0.808908
$491$	15072.4	1.38535	0.692675	−	0.721250i	$-0.256432\pi$
$491$	15072.4	1.38535	0.692675	+	0.721250i	$0.256432\pi$
$492$	−16265.4	−1.49045
$493$	4104.17	0.374934
$494$	20915.7	1.90495
$495$	5241.82	0.475964
$496$	−3878.32	−0.351092
$497$	−2502.94	−0.225900
$498$	23208.1	2.08831
$499$	4574.98	0.410430	0.205215	−	0.978717i	$-0.434211\pi$
$499$	4574.98	0.410430	0.205215	+	0.978717i	$0.434211\pi$
$500$	32038.1	2.86558
$501$	1676.35	0.149489
$502$	−10504.4	−0.933935
$503$	787.350	0.0697936	0.0348968	−	0.999391i	$-0.488890\pi$
$503$	787.350	0.0697936	0.0348968	+	0.999391i	$0.488890\pi$
$504$	−13728.6	−1.21333
$505$	−11500.7	−1.01341
$506$	−38920.2	−3.41939
$507$	5398.91	0.472927
$508$	−25618.0	−2.23743
$509$	−10346.9	−0.901018	−0.450509	−	0.892772i	$-0.648757\pi$
$509$	−10346.9	−0.901018	−0.450509	+	0.892772i	$0.648757\pi$
$510$	−4662.43	−0.404816
$511$	484.852	0.0419737
$512$	−42040.3	−3.62878
$513$	20311.1	1.74806
$514$	12550.8	1.07703
$515$	5926.49	0.507092
$516$	0	0
$517$	−16197.4	−1.37787
$518$	13665.3	1.15911
$519$	−16349.8	−1.38281
$520$	−24516.4	−2.06753
$521$	−4423.96	−0.372010	−0.186005	−	0.982549i	$-0.559554\pi$
$521$	−4423.96	−0.372010	−0.186005	+	0.982549i	$0.559554\pi$
$522$	13781.0	1.15552
$523$	12522.3	1.04696	0.523480	−	0.852038i	$-0.324634\pi$
$523$	12522.3	1.04696	0.523480	+	0.852038i	$0.324634\pi$
$524$	−39220.6	−3.26977
$525$	−300.993	−0.0250217
$526$	−41406.1	−3.43230
$527$	−299.717	−0.0247740
$528$	−39177.4	−3.22912
$529$	20270.1	1.66599
$530$	−7266.92	−0.595575
$531$	−1713.94	−0.140073
$532$	−42515.1	−3.46478
$533$	−5305.97	−0.431195
$534$	12086.6	0.979475
$535$	13669.2	1.10462
$536$	−28637.9	−2.30777
$537$	−12970.6	−1.04232
$538$	−16573.7	−1.32815
$539$	−5697.50	−0.455304
$540$	−36986.5	−2.94749
$541$	−10069.2	−0.800199	−0.400100	−	0.916472i	$-0.631025\pi$
$541$	−10069.2	−0.800199	−0.400100	+	0.916472i	$0.631025\pi$
$542$	−17017.3	−1.34862
$543$	−9752.94	−0.770789
$544$	−16092.1	−1.26828
$545$	−20845.0	−1.63835
$546$	8378.89	0.656747
$547$	15032.8	1.17505	0.587527	−	0.809204i	$-0.300101\pi$
$547$	15032.8	1.17505	0.587527	+	0.809204i	$0.300101\pi$
$548$	24889.1	1.94016
$549$	−1725.65	−0.134151
$550$	1205.05	0.0934243
$551$	27471.0	2.12396
$552$	55166.6	4.25371
$553$	9597.54	0.738027
$554$	−15008.4	−1.15099
$555$	7395.68	0.565638
$556$	−6003.62	−0.457932
$557$	−4451.52	−0.338630	−0.169315	−	0.985562i	$-0.554156\pi$
$557$	−4451.52	−0.338630	−0.169315	+	0.985562i	$0.554156\pi$
$558$	−1006.39	−0.0763513
$559$	0	0
$560$	40004.9	3.01878
$561$	−3027.64	−0.227855
$562$	17983.1	1.34977
$563$	−1015.30	−0.0760033	−0.0380016	−	0.999278i	$-0.512099\pi$
$563$	−1015.30	−0.0760033	−0.0380016	+	0.999278i	$0.512099\pi$
$564$	35667.5	2.66289
$565$	−1395.11	−0.103881
$566$	−26081.8	−1.93692
$567$	3488.87	0.258410
$568$	−14203.6	−1.04924
$569$	−26011.4	−1.91644	−0.958219	−	0.286037i	$-0.907662\pi$
$569$	−26011.4	−1.91644	−0.958219	+	0.286037i	$0.907662\pi$
$570$	−31207.7	−2.29324
$571$	19894.8	1.45809	0.729046	−	0.684465i	$-0.239964\pi$
$571$	19894.8	1.45809	0.729046	+	0.684465i	$0.239964\pi$
$572$	−24732.8	−1.80792
$573$	−13425.2	−0.978787
$574$	14628.3	1.06372
$575$	−1004.32	−0.0728399
$576$	−28509.8	−2.06234
$577$	−7066.63	−0.509857	−0.254929	−	0.966960i	$-0.582052\pi$
$577$	−7066.63	−0.509857	−0.254929	+	0.966960i	$0.582052\pi$
$578$	24875.5	1.79011
$579$	14198.4	1.01911
$580$	−50024.6	−3.58131
$581$	−15388.9	−1.09886
$582$	513.420	0.0365669
$583$	−4718.90	−0.335226
$584$	2751.42	0.194957
$585$	−3765.38	−0.266118
$586$	25014.5	1.76338
$587$	−7576.37	−0.532726	−0.266363	−	0.963873i	$-0.585822\pi$
$587$	−7576.37	−0.532726	−0.266363	+	0.963873i	$0.585822\pi$
$588$	12546.2	0.879924
$589$	−2006.13	−0.140342
$590$	8438.36	0.588816
$591$	5178.40	0.360425
$592$	45898.1	3.18649
$593$	−26482.6	−1.83391	−0.916955	−	0.398990i	$-0.869361\pi$
$593$	−26482.6	−1.83391	−0.916955	+	0.398990i	$0.869361\pi$
$594$	−32575.7	−2.25016
$595$	3091.59	0.213013
$596$	−41932.6	−2.88192
$597$	8232.56	0.564382
$598$	27957.7	1.91183
$599$	−5827.52	−0.397506	−0.198753	−	0.980050i	$-0.563689\pi$
$599$	−5827.52	−0.397506	−0.198753	+	0.980050i	$0.563689\pi$
$600$	−1708.07	−0.116219
$601$	27332.7	1.85512	0.927558	−	0.373680i	$-0.121904\pi$
$601$	27332.7	1.85512	0.927558	+	0.373680i	$0.121904\pi$
$602$	0	0
$603$	−4398.37	−0.297041
$604$	−40405.6	−2.72199
$605$	−2213.18	−0.148725
$606$	22305.0	1.49518
$607$	14574.8	0.974583	0.487291	−	0.873239i	$-0.337985\pi$
$607$	14574.8	0.974583	0.487291	+	0.873239i	$0.337985\pi$
$608$	−107712.	−7.18467
$609$	11004.9	0.732254
$610$	8495.99	0.563922
$611$	11635.1	0.770388
$612$	−5535.97	−0.365651
$613$	−14582.9	−0.960845	−0.480423	−	0.877037i	$-0.659517\pi$
$613$	−14582.9	−0.960845	−0.480423	+	0.877037i	$0.659517\pi$
$614$	31277.5	2.05580
$615$	7916.86	0.519087
$616$	43891.2	2.87083
$617$	704.823	0.0459888	0.0229944	−	0.999736i	$-0.492680\pi$
$617$	704.823	0.0459888	0.0229944	+	0.999736i	$0.492680\pi$
$618$	−11494.1	−0.748157
$619$	−27368.9	−1.77714	−0.888569	−	0.458744i	$-0.848300\pi$
$619$	−27368.9	−1.77714	−0.888569	+	0.458744i	$0.848300\pi$
$620$	3653.17	0.236637
$621$	27149.5	1.75438
$622$	7732.87	0.498488
$623$	−8014.46	−0.515397
$624$	28142.4	1.80545
$625$	−14896.9	−0.953399
$626$	−31218.7	−1.99321
$627$	−20265.3	−1.29078
$628$	−41490.2	−2.63637
$629$	3547.01	0.224847
$630$	10381.0	0.656489
$631$	−846.840	−0.0534266	−0.0267133	−	0.999643i	$-0.508504\pi$
$631$	−846.840	−0.0534266	−0.0267133	+	0.999643i	$0.508504\pi$
$632$	54463.8	3.42793
$633$	−195.240	−0.0122593
$634$	−39430.8	−2.47003
$635$	12469.0	0.779241
$636$	10391.3	0.647862
$637$	4092.71	0.254567
$638$	−44059.0	−2.73403
$639$	−2181.47	−0.135051
$640$	70476.0	4.35282
$641$	17004.9	1.04782	0.523911	−	0.851773i	$-0.324472\pi$
$641$	17004.9	1.04782	0.523911	+	0.851773i	$0.324472\pi$
$642$	−26510.7	−1.62974
$643$	21558.4	1.32221	0.661104	−	0.750294i	$-0.270088\pi$
$643$	21558.4	1.32221	0.661104	+	0.750294i	$0.270088\pi$
$644$	−56829.1	−3.47730
$645$	0	0
$646$	−14967.4	−0.911586
$647$	−8696.25	−0.528415	−0.264208	−	0.964466i	$-0.585110\pi$
$647$	−8696.25	−0.528415	−0.264208	+	0.964466i	$0.585110\pi$
$648$	19798.5	1.20025
$649$	5479.60	0.331422
$650$	−865.625	−0.0522348
$651$	−803.662	−0.0483840
$652$	−11651.0	−0.699828
$653$	21936.1	1.31459	0.657294	−	0.753634i	$-0.271701\pi$
$653$	21936.1	1.31459	0.657294	+	0.753634i	$0.271701\pi$
$654$	40427.7	2.41720
$655$	19089.8	1.13878
$656$	49132.6	2.92425
$657$	422.579	0.0250934
$658$	−32077.6	−1.90048
$659$	22253.2	1.31542	0.657710	−	0.753271i	$-0.271525\pi$
$659$	22253.2	1.31542	0.657710	+	0.753271i	$0.271525\pi$
$660$	36903.0	2.17644
$661$	13506.6	0.794774	0.397387	−	0.917651i	$-0.369917\pi$
$661$	13506.6	0.794774	0.397387	+	0.917651i	$0.369917\pi$
$662$	30676.8	1.80104
$663$	2174.85	0.127397
$664$	−87328.7	−5.10393
$665$	20693.3	1.20670
$666$	11910.2	0.692960
$667$	36720.0	2.13164
$668$	−9799.61	−0.567603
$669$	19599.5	1.13268
$670$	21654.8	1.24865
$671$	5517.02	0.317410
$672$	−43149.5	−2.47698
$673$	26198.8	1.50058	0.750289	−	0.661110i	$-0.229914\pi$
$673$	26198.8	1.50058	0.750289	+	0.661110i	$0.229914\pi$
$674$	−30378.7	−1.73612
$675$	−840.601	−0.0479330
$676$	−31560.9	−1.79568
$677$	11559.5	0.656231	0.328116	−	0.944638i	$-0.393586\pi$
$677$	11559.5	0.656231	0.328116	+	0.944638i	$0.393586\pi$
$678$	2705.75	0.153265
$679$	−340.441	−0.0192414
$680$	17544.1	0.989388
$681$	5972.98	0.336101
$682$	3217.52	0.180653
$683$	8850.81	0.495852	0.247926	−	0.968779i	$-0.420251\pi$
$683$	8850.81	0.495852	0.247926	+	0.968779i	$0.420251\pi$
$684$	−37054.6	−2.07137
$685$	−12114.3	−0.675711
$686$	−37884.2	−2.10849
$687$	−14360.9	−0.797530
$688$	0	0
$689$	3389.75	0.187430
$690$	−41714.7	−2.30153
$691$	−29277.8	−1.61184	−0.805920	−	0.592024i	$-0.798329\pi$
$691$	−29277.8	−1.61184	−0.805920	+	0.592024i	$0.798329\pi$
$692$	95577.5	5.25045
$693$	6741.07	0.369513
$694$	−8091.97	−0.442604
$695$	2922.14	0.159486
$696$	62450.5	3.40112
$697$	3796.98	0.206342
$698$	−53547.7	−2.90374
$699$	2446.63	0.132389
$700$	1759.54	0.0950063
$701$	−24827.3	−1.33768	−0.668840	−	0.743407i	$-0.733209\pi$
$701$	−24827.3	−1.33768	−0.668840	+	0.743407i	$0.733209\pi$
$702$	23400.2	1.25810
$703$	23741.7	1.27373
$704$	91148.1	4.87965
$705$	−17360.4	−0.927419
$706$	−7827.40	−0.417264
$707$	−14790.1	−0.786759
$708$	−12066.3	−0.640510
$709$	8614.60	0.456316	0.228158	−	0.973624i	$-0.426730\pi$
$709$	8614.60	0.456316	0.228158	+	0.973624i	$0.426730\pi$
$710$	10740.2	0.567708
$711$	8364.87	0.441220
$712$	−45480.2	−2.39388
$713$	−2681.56	−0.140849
$714$	−5995.97	−0.314277
$715$	12038.2	0.629655
$716$	75823.5	3.95762
$717$	−11581.4	−0.603228
$718$	42423.6	2.20506
$719$	12946.1	0.671500	0.335750	−	0.941951i	$-0.391010\pi$
$719$	12946.1	0.671500	0.335750	+	0.941951i	$0.391010\pi$
$720$	34866.9	1.80474
$721$	7621.57	0.393678
$722$	−62332.9	−3.21301
$723$	12112.2	0.623041
$724$	57013.6	2.92665
$725$	−1136.92	−0.0582404
$726$	4292.34	0.219427
$727$	24459.0	1.24778	0.623888	−	0.781514i	$-0.285552\pi$
$727$	24459.0	1.24778	0.623888	+	0.781514i	$0.285552\pi$
$728$	−31528.6	−1.60512
$729$	18672.9	0.948682
$730$	−2080.51	−0.105484
$731$	0	0
$732$	−12148.8	−0.613430
$733$	25060.3	1.26279	0.631393	−	0.775463i	$-0.282483\pi$
$733$	25060.3	1.26279	0.631393	+	0.775463i	$0.282483\pi$
$734$	−4901.58	−0.246486
$735$	−6106.59	−0.306456
$736$	−143976.	−7.21064
$737$	14061.9	0.702819
$738$	12749.5	0.635931
$739$	16575.6	0.825092	0.412546	−	0.910937i	$-0.364640\pi$
$739$	16575.6	0.825092	0.412546	+	0.910937i	$0.364640\pi$
$740$	−43233.6	−2.14770
$741$	14557.2	0.721691
$742$	−9345.38	−0.462372
$743$	−4394.67	−0.216992	−0.108496	−	0.994097i	$-0.534603\pi$
$743$	−4394.67	−0.216992	−0.108496	+	0.994097i	$0.534603\pi$
$744$	−4560.60	−0.224731
$745$	20409.8	1.00370
$746$	55025.4	2.70057
$747$	−13412.4	−0.656942
$748$	17698.9	0.865156
$749$	17578.9	0.857567
$750$	30243.6	1.47245
$751$	17309.9	0.841073	0.420536	−	0.907276i	$-0.361842\pi$
$751$	17309.9	0.841073	0.420536	+	0.907276i	$0.361842\pi$
$752$	−107740.	−5.22456
$753$	−7311.02	−0.353822
$754$	31649.1	1.52864
$755$	19666.6	0.948000
$756$	−47565.3	−2.28827
$757$	−39830.5	−1.91237	−0.956186	−	0.292761i	$-0.905426\pi$
$757$	−39830.5	−1.91237	−0.956186	+	0.292761i	$0.905426\pi$
$758$	−51215.1	−2.45411
$759$	−27088.2	−1.29544
$760$	117430.	5.60478
$761$	−40495.9	−1.92901	−0.964505	−	0.264064i	$-0.914937\pi$
$761$	−40495.9	−1.92901	−0.964505	+	0.264064i	$0.914937\pi$
$762$	−24183.0	−1.14968
$763$	−26807.0	−1.27193
$764$	78480.8	3.71641
$765$	2694.52	0.127347
$766$	−30641.5	−1.44533
$767$	−3936.18	−0.185303
$768$	−65167.8	−3.06190
$769$	−6701.01	−0.314232	−0.157116	−	0.987580i	$-0.550220\pi$
$769$	−6701.01	−0.314232	−0.157116	+	0.987580i	$0.550220\pi$
$770$	−33188.8	−1.55330
$771$	8735.31	0.408034
$772$	−83000.9	−3.86952
$773$	10325.5	0.480445	0.240222	−	0.970718i	$-0.422780\pi$
$773$	10325.5	0.480445	0.240222	+	0.970718i	$0.422780\pi$
$774$	0	0
$775$	83.0265	0.00384826
$776$	−1931.93	−0.0893712
$777$	9510.98	0.439131
$778$	−55236.6	−2.54541
$779$	25414.8	1.16891
$780$	−26508.7	−1.21688
$781$	6974.34	0.319541
$782$	−20006.6	−0.914880
$783$	30734.2	1.40275
$784$	−37897.9	−1.72640
$785$	20194.5	0.918182
$786$	−37023.7	−1.68014
$787$	9369.98	0.424401	0.212201	−	0.977226i	$-0.431937\pi$
$787$	9369.98	0.424401	0.212201	+	0.977226i	$0.431937\pi$
$788$	−30271.9	−1.36852
$789$	−28818.4	−1.30033
$790$	−41183.3	−1.85473
$791$	−1794.14	−0.0806477
$792$	38254.0	1.71629
$793$	−3963.06	−0.177469
$794$	−33763.4	−1.50909
$795$	−5057.73	−0.225634
$796$	−48125.8	−2.14293
$797$	−8397.25	−0.373207	−0.186603	−	0.982435i	$-0.559748\pi$
$797$	−8397.25	−0.373207	−0.186603	+	0.982435i	$0.559748\pi$
$798$	−40133.6	−1.78035
$799$	−8326.15	−0.368659
$800$	4457.79	0.197008
$801$	−6985.12	−0.308124
$802$	−49156.5	−2.16431
$803$	−1351.02	−0.0593729
$804$	−30965.1	−1.35828
$805$	27660.4	1.21106
$806$	−2311.25	−0.101005
$807$	−11535.2	−0.503170
$808$	−83930.4	−3.65428
$809$	24827.4	1.07897	0.539483	−	0.841996i	$-0.318620\pi$
$809$	24827.4	1.07897	0.539483	+	0.841996i	$0.318620\pi$
$810$	−14970.8	−0.649410
$811$	−7321.18	−0.316993	−0.158497	−	0.987360i	$-0.550665\pi$
$811$	−7321.18	−0.316993	−0.158497	+	0.987360i	$0.550665\pi$
$812$	−64332.6	−2.78033
$813$	−11843.9	−0.510928
$814$	−38077.9	−1.63959
$815$	5670.88	0.243733
$816$	−20138.9	−0.863972
$817$	0	0
$818$	19276.6	0.823948
$819$	−4842.34	−0.206600
$820$	−46280.3	−1.97095
$821$	−20702.3	−0.880044	−0.440022	−	0.897987i	$-0.645029\pi$
$821$	−20702.3	−0.880044	−0.440022	+	0.897987i	$0.645029\pi$
$822$	23495.0	0.996935
$823$	−8015.20	−0.339480	−0.169740	−	0.985489i	$-0.554293\pi$
$823$	−8015.20	−0.339480	−0.169740	+	0.985489i	$0.554293\pi$
$824$	43250.7	1.82853
$825$	838.705	0.0353939
$826$	10851.9	0.457125
$827$	−415.975	−0.0174908	−0.00874539	−	0.999962i	$-0.502784\pi$
$827$	−415.975	−0.0174908	−0.00874539	+	0.999962i	$0.502784\pi$
$828$	−49530.2	−2.07886
$829$	992.238	0.0415704	0.0207852	−	0.999784i	$-0.493383\pi$
$829$	992.238	0.0415704	0.0207852	+	0.999784i	$0.493383\pi$
$830$	66034.4	2.76155
$831$	−10445.8	−0.436053
$832$	−65474.8	−2.72828
$833$	−2928.76	−0.121819
$834$	−5667.34	−0.235304
$835$	4769.76	0.197682
$836$	118467.	4.90102
$837$	−2244.44	−0.0926871
$838$	86401.5	3.56168
$839$	10012.0	0.411983	0.205991	−	0.978554i	$-0.433958\pi$
$839$	10012.0	0.411983	0.205991	+	0.978554i	$0.433958\pi$
$840$	47042.7	1.93230
$841$	17179.3	0.704388
$842$	35992.9	1.47316
$843$	12516.2	0.511364
$844$	1141.33	0.0465478
$845$	15361.6	0.625391
$846$	−27957.7	−1.13618
$847$	−2846.19	−0.115462
$848$	−31388.6	−1.27110
$849$	−18152.7	−0.733805
$850$	619.445	0.0249962
$851$	31735.1	1.27834
$852$	−15357.8	−0.617548
$853$	36642.0	1.47081	0.735403	−	0.677630i	$-0.236993\pi$
$853$	36642.0	1.47081	0.735403	+	0.677630i	$0.236993\pi$
$854$	10926.0	0.437798
$855$	18035.6	0.721408
$856$	99756.0	3.98317
$857$	42826.9	1.70705	0.853523	−	0.521055i	$-0.174461\pi$
$857$	42826.9	1.70705	0.853523	+	0.521055i	$0.174461\pi$
$858$	−23347.4	−0.928985
$859$	−3746.65	−0.148817	−0.0744087	−	0.997228i	$-0.523707\pi$
$859$	−3746.65	−0.148817	−0.0744087	+	0.997228i	$0.523707\pi$
$860$	0	0
$861$	10181.2	0.402991
$862$	13812.2	0.545759
$863$	−17591.3	−0.693877	−0.346939	−	0.937888i	$-0.612779\pi$
$863$	−17591.3	−0.693877	−0.346939	+	0.937888i	$0.612779\pi$
$864$	−120506.	−4.74503
$865$	−46520.4	−1.82860
$866$	48950.6	1.92080
$867$	17313.2	0.678186
$868$	4698.04	0.183712
$869$	−26743.1	−1.04396
$870$	−47222.6	−1.84022
$871$	−10101.2	−0.392956
$872$	−152124.	−5.90775
$873$	−296.716	−0.0115032
$874$	−133913.	−5.18270
$875$	−20054.0	−0.774800
$876$	2975.01	0.114745
$877$	−731.488	−0.0281649	−0.0140824	−	0.999901i	$-0.504483\pi$
$877$	−731.488	−0.0281649	−0.0140824	+	0.999901i	$0.504483\pi$
$878$	89693.0	3.44760
$879$	17410.0	0.668058
$880$	−111472.	−4.27014
$881$	−29344.8	−1.12219	−0.561097	−	0.827750i	$-0.689620\pi$
$881$	−29344.8	−1.12219	−0.561097	+	0.827750i	$0.689620\pi$
$882$	−9834.22	−0.375437
$883$	−33347.2	−1.27092	−0.635460	−	0.772134i	$-0.719190\pi$
$883$	−33347.2	−1.27092	−0.635460	+	0.772134i	$0.719190\pi$
$884$	−12713.7	−0.483721
$885$	5873.05	0.223074
$886$	63949.8	2.42487
$887$	27461.8	1.03954	0.519772	−	0.854305i	$-0.326017\pi$
$887$	27461.8	1.03954	0.519772	+	0.854305i	$0.326017\pi$
$888$	53972.6	2.03964
$889$	16035.4	0.604960
$890$	34390.3	1.29524
$891$	−9721.59	−0.365528
$892$	−114575.	−4.30073
$893$	−55730.6	−2.08841
$894$	−39583.8	−1.48085
$895$	−36905.5	−1.37834
$896$	90633.4	3.37930
$897$	19458.4	0.724299
$898$	8560.35	0.318110
$899$	−3035.63	−0.112618
$900$	1533.55	0.0567983
$901$	−2425.72	−0.0896919
$902$	−40761.2	−1.50466
$903$	0	0
$904$	−10181.3	−0.374587
$905$	−27750.2	−1.01928
$906$	−38142.3	−1.39867
$907$	2422.46	0.0886839	0.0443420	−	0.999016i	$-0.485881\pi$
$907$	2422.46	0.0886839	0.0443420	+	0.999016i	$0.485881\pi$
$908$	−34916.8	−1.27616
$909$	−12890.5	−0.470354
$910$	23840.6	0.868471
$911$	−9822.38	−0.357223	−0.178611	−	0.983920i	$-0.557160\pi$
$911$	−9822.38	−0.357223	−0.178611	+	0.983920i	$0.557160\pi$
$912$	−134798.	−4.89431
$913$	42880.6	1.55437
$914$	80617.2	2.91748
$915$	5913.16	0.213643
$916$	83950.8	3.02818
$917$	24549.8	0.884086
$918$	−16745.3	−0.602045
$919$	14868.7	0.533704	0.266852	−	0.963738i	$-0.414017\pi$
$919$	14868.7	0.533704	0.266852	+	0.963738i	$0.414017\pi$
$920$	156966.	5.62503
$921$	21769.0	0.778841
$922$	−101804.	−3.63637
$923$	−5009.91	−0.178660
$924$	47458.0	1.68967
$925$	−982.582	−0.0349266
$926$	25305.9	0.898060
$927$	6642.69	0.235355
$928$	−162986.	−5.76539
$929$	−3691.42	−0.130368	−0.0651838	−	0.997873i	$-0.520763\pi$
$929$	−3691.42	−0.130368	−0.0651838	+	0.997873i	$0.520763\pi$
$930$	3448.54	0.121594
$931$	−19603.5	−0.690094
$932$	−14302.5	−0.502676
$933$	5382.03	0.188853
$934$	−79459.7	−2.78373
$935$	−8614.58	−0.301312
$936$	−27479.2	−0.959599
$937$	−20303.2	−0.707874	−0.353937	−	0.935269i	$-0.615157\pi$
$937$	−20303.2	−0.707874	−0.353937	+	0.935269i	$0.615157\pi$
$938$	27848.4	0.969386
$939$	−21728.0	−0.755130
$940$	101485.	3.52137
$941$	−6995.70	−0.242352	−0.121176	−	0.992631i	$-0.538667\pi$
$941$	−6995.70	−0.242352	−0.121176	+	0.992631i	$0.538667\pi$
$942$	−39166.2	−1.35468
$943$	33971.5	1.17313
$944$	36448.5	1.25667
$945$	23151.4	0.796948
$946$	0	0
$947$	40139.0	1.37734	0.688671	−	0.725074i	$-0.258194\pi$
$947$	40139.0	1.37734	0.688671	+	0.725074i	$0.258194\pi$
$948$	58889.7	2.01756
$949$	970.483	0.0331962
$950$	4146.22	0.141601
$951$	−27443.6	−0.935773
$952$	22562.0	0.768107
$953$	−13650.1	−0.463977	−0.231989	−	0.972718i	$-0.574523\pi$
$953$	−13650.1	−0.463977	−0.231989	+	0.972718i	$0.574523\pi$
$954$	−8145.11	−0.276423
$955$	−38198.9	−1.29433
$956$	67702.3	2.29043
$957$	−30664.8	−1.03579
$958$	59914.5	2.02061
$959$	−15579.2	−0.524585
$960$	97692.7	3.28439
$961$	−29569.3	−0.992559
$962$	27352.6	0.916719
$963$	15321.1	0.512685
$964$	−70805.5	−2.36566
$965$	40399.0	1.34766
$966$	−53645.9	−1.78678
$967$	−16338.6	−0.543345	−0.271673	−	0.962390i	$-0.587577\pi$
$967$	−16338.6	−0.543345	−0.271673	+	0.962390i	$0.587577\pi$
$968$	−16151.5	−0.536289
$969$	−10417.2	−0.345355
$970$	1460.84	0.0483555
$971$	33263.4	1.09935	0.549677	−	0.835377i	$-0.314751\pi$
$971$	33263.4	1.09935	0.549677	+	0.835377i	$0.314751\pi$
$972$	−69974.8	−2.30910
$973$	3757.92	0.123817
$974$	−33204.3	−1.09233
$975$	−602.470	−0.0197892
$976$	36697.5	1.20354
$977$	−41311.2	−1.35278	−0.676389	−	0.736545i	$-0.736456\pi$
$977$	−41311.2	−1.35278	−0.676389	+	0.736545i	$0.736456\pi$
$978$	−10998.4	−0.359601
$979$	22332.0	0.729043
$980$	35697.9	1.16360
$981$	−23364.0	−0.760404
$982$	−83174.5	−2.70286
$983$	−48290.7	−1.56687	−0.783435	−	0.621473i	$-0.786534\pi$
$983$	−48290.7	−1.56687	−0.783435	+	0.621473i	$0.786534\pi$
$984$	57776.1	1.87178
$985$	14734.2	0.476620
$986$	−22648.2	−0.731508
$987$	−22325.8	−0.719998
$988$	−85098.5	−2.74023
$989$	0	0
$990$	−28926.2	−0.928620
$991$	−50182.0	−1.60856	−0.804280	−	0.594250i	$-0.797449\pi$
$991$	−50182.0	−1.60856	−0.804280	+	0.594250i	$0.797449\pi$
$992$	11902.4	0.380951
$993$	21350.9	0.682326
$994$	13812.1	0.440737
$995$	23424.3	0.746331
$996$	−94425.2	−3.00399
$997$	39031.8	1.23987	0.619935	−	0.784653i	$-0.287159\pi$
$997$	39031.8	1.23987	0.619935	+	0.784653i	$0.287159\pi$
$998$	−25246.3	−0.800761
$999$	26561.9	0.841222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.e.1.1	✓	10
43.42	odd	2	inner	1849.4.a.e.1.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.e.1.1	✓	10	1.1	even	1	trivial
1849.4.a.e.1.10	yes	10	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.51834 q^{2} -3.84074 q^{3} +22.4521 q^{4} -10.9281 q^{5} +21.1945 q^{6} -14.0538 q^{7} -79.7518 q^{8} -12.2488 q^{9} +O(q^{10})\)	\(q-5.51834 q^{2} -3.84074 q^{3} +22.4521 q^{4} -10.9281 q^{5} +21.1945 q^{6} -14.0538 q^{7} -79.7518 q^{8} -12.2488 q^{9} +60.3051 q^{10} +39.1602 q^{11} -86.2327 q^{12} -28.1301 q^{13} +77.5534 q^{14} +41.9720 q^{15} +260.481 q^{16} +20.1300 q^{17} +67.5928 q^{18} +134.739 q^{19} -245.359 q^{20} +53.9767 q^{21} -216.100 q^{22} +180.103 q^{23} +306.306 q^{24} -5.57635 q^{25} +155.232 q^{26} +150.744 q^{27} -315.537 q^{28} +203.883 q^{29} -231.616 q^{30} -14.8891 q^{31} -799.410 q^{32} -150.404 q^{33} -111.084 q^{34} +153.581 q^{35} -275.011 q^{36} +176.205 q^{37} -743.536 q^{38} +108.040 q^{39} +871.537 q^{40} +188.623 q^{41} -297.862 q^{42} +879.230 q^{44} +133.856 q^{45} -993.871 q^{46} -413.619 q^{47} -1000.44 q^{48} -145.492 q^{49} +30.7722 q^{50} -77.3141 q^{51} -631.581 q^{52} -120.503 q^{53} -831.858 q^{54} -427.947 q^{55} +1120.81 q^{56} -517.497 q^{57} -1125.10 q^{58} +139.928 q^{59} +942.360 q^{60} +140.883 q^{61} +82.1629 q^{62} +172.141 q^{63} +2327.57 q^{64} +307.409 q^{65} +829.981 q^{66} +359.087 q^{67} +451.962 q^{68} -691.728 q^{69} -847.513 q^{70} +178.098 q^{71} +976.860 q^{72} -34.4998 q^{73} -972.361 q^{74} +21.4173 q^{75} +3025.18 q^{76} -550.348 q^{77} -596.203 q^{78} -682.916 q^{79} -2846.57 q^{80} -248.252 q^{81} -1040.88 q^{82} +1095.01 q^{83} +1211.89 q^{84} -219.983 q^{85} -783.061 q^{87} -3123.10 q^{88} +570.272 q^{89} -738.662 q^{90} +395.333 q^{91} +4043.70 q^{92} +57.1849 q^{93} +2282.49 q^{94} -1472.44 q^{95} +3070.32 q^{96} +24.2242 q^{97} +802.876 q^{98} -479.664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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