LMFDB - Embedded newform 127.4.a.b.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,4,Mod(1,127)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("127.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	127.a (trivial)

Newform invariants

comment:select newform

sage:traces = [13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.49324257073$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 55 x^{11} + 264 x^{10} + 1126 x^{9} - 5085 x^{8} - 10823 x^{7} + 44242 x^{6} + \cdots - 130048 $ x^13 - 5x^12 - 55x^11 + 264x^10 + 1126x^9 - 5085x^8 - 10823x^7 + 44242x^6 + 52047x^5 - 178872x^4 - 113160x^3 + 298560x^2 + 65136x - 130048
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$5.48248$ of defining polynomial
Character	$\chi$	$=$	127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.48248 q^{2} -7.80738 q^{3} +12.0927 q^{4} -5.99266 q^{5} -34.9964 q^{6} -20.2899 q^{7} +18.3452 q^{8} +33.9551 q^{9} -26.8620 q^{10} -8.70120 q^{11} -94.4119 q^{12} -57.1649 q^{13} -90.9491 q^{14} +46.7870 q^{15} -14.5090 q^{16} -34.0983 q^{17} +152.203 q^{18} +58.9447 q^{19} -72.4672 q^{20} +158.411 q^{21} -39.0030 q^{22} +147.409 q^{23} -143.228 q^{24} -89.0880 q^{25} -256.241 q^{26} -54.3011 q^{27} -245.359 q^{28} +127.619 q^{29} +209.722 q^{30} -98.1327 q^{31} -211.798 q^{32} +67.9335 q^{33} -152.845 q^{34} +121.591 q^{35} +410.607 q^{36} -72.2719 q^{37} +264.219 q^{38} +446.308 q^{39} -109.937 q^{40} -15.2752 q^{41} +710.074 q^{42} +427.027 q^{43} -105.221 q^{44} -203.482 q^{45} +660.756 q^{46} -356.718 q^{47} +113.277 q^{48} +68.6803 q^{49} -399.335 q^{50} +266.218 q^{51} -691.275 q^{52} -582.203 q^{53} -243.404 q^{54} +52.1434 q^{55} -372.223 q^{56} -460.204 q^{57} +572.049 q^{58} -79.1281 q^{59} +565.779 q^{60} -297.291 q^{61} -439.878 q^{62} -688.946 q^{63} -833.310 q^{64} +342.570 q^{65} +304.511 q^{66} -162.865 q^{67} -412.339 q^{68} -1150.87 q^{69} +545.028 q^{70} +1137.70 q^{71} +622.915 q^{72} -756.758 q^{73} -323.957 q^{74} +695.543 q^{75} +712.798 q^{76} +176.547 q^{77} +2000.57 q^{78} +55.7276 q^{79} +86.9475 q^{80} -492.839 q^{81} -68.4710 q^{82} -789.369 q^{83} +1915.61 q^{84} +204.340 q^{85} +1914.14 q^{86} -996.368 q^{87} -159.626 q^{88} -1351.23 q^{89} -912.103 q^{90} +1159.87 q^{91} +1782.56 q^{92} +766.159 q^{93} -1598.98 q^{94} -353.236 q^{95} +1653.59 q^{96} +1221.35 q^{97} +307.858 q^{98} -295.450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 8 q^{2} - 16 q^{3} + 34 q^{4} - 46 q^{5} - 2 q^{6} - 26 q^{7} - 117 q^{8} + 3 q^{9} - 25 q^{10} - 53 q^{11} - 255 q^{12} - 75 q^{13} - 152 q^{14} - 62 q^{15} + 82 q^{16} - 479 q^{17} - 292 q^{18}+ \cdots + 1769 q^{99}+O(q^{100}) $ 13 * q - 8 * q^2 - 16 * q^3 + 34 * q^4 - 46 * q^5 - 2 * q^6 - 26 * q^7 - 117 * q^8 + 3 * q^9 - 25 * q^10 - 53 * q^11 - 255 * q^12 - 75 * q^13 - 152 * q^14 - 62 * q^15 + 82 * q^16 - 479 * q^17 - 292 * q^18 - 209 * q^19 - 533 * q^20 - 174 * q^21 - 407 * q^22 - 376 * q^23 + 108 * q^24 + 9 * q^25 - 622 * q^26 - 562 * q^27 - 258 * q^28 - 158 * q^29 - 287 * q^30 - 307 * q^31 - 609 * q^32 - 494 * q^33 + 948 * q^34 - 512 * q^35 + 1556 * q^36 - 171 * q^37 + 712 * q^38 - 154 * q^39 + 1897 * q^40 - 641 * q^41 + 1489 * q^42 + 530 * q^43 + 1328 * q^44 - 566 * q^45 + 2051 * q^46 - 555 * q^47 + 268 * q^48 + 357 * q^49 + 808 * q^50 + 1228 * q^51 + 2473 * q^52 - 1640 * q^53 + 2957 * q^54 + 540 * q^55 + 551 * q^56 + 968 * q^57 + 1328 * q^58 - 860 * q^59 + 4466 * q^60 + 191 * q^61 + 367 * q^62 + 120 * q^63 + 1915 * q^64 - 1584 * q^65 + 3416 * q^66 + 912 * q^67 - 1873 * q^68 - 2142 * q^69 + 2329 * q^70 + 115 * q^71 - 1864 * q^72 - 2563 * q^73 + 470 * q^74 + 44 * q^75 - 192 * q^76 - 3338 * q^77 + 4226 * q^78 + 169 * q^79 - 3194 * q^80 - 395 * q^81 + 54 * q^82 - 1688 * q^83 + 853 * q^84 + 480 * q^85 - 485 * q^86 - 1068 * q^87 - 1192 * q^88 - 2752 * q^89 + 4948 * q^90 - 398 * q^91 - 846 * q^92 - 804 * q^93 + 531 * q^94 - 1766 * q^95 + 3965 * q^96 - 2124 * q^97 - 1479 * q^98 + 1769 * 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 $

$2$	4.48248	1.58480	0.792398	−	0.610004i	$-0.208832\pi$
$2$	4.48248	1.58480	0.792398	+	0.610004i	$0.208832\pi$
$3$	−7.80738	−1.50253	−0.751265	−	0.660001i	$-0.770556\pi$
$3$	−7.80738	−1.50253	−0.751265	+	0.660001i	$0.770556\pi$
$4$	12.0927	1.51158
$5$	−5.99266	−0.536000	−0.268000	−	0.963419i	$-0.586363\pi$
$5$	−5.99266	−0.536000	−0.268000	+	0.963419i	$0.586363\pi$
$6$	−34.9964	−2.38121
$7$	−20.2899	−1.09555	−0.547776	−	0.836625i	$-0.684525\pi$
$7$	−20.2899	−1.09555	−0.547776	+	0.836625i	$0.684525\pi$
$8$	18.3452	0.810753
$9$	33.9551	1.25760
$10$	−26.8620	−0.849451
$11$	−8.70120	−0.238501	−0.119251	−	0.992864i	$-0.538049\pi$
$11$	−8.70120	−0.238501	−0.119251	+	0.992864i	$0.538049\pi$
$12$	−94.4119	−2.27120
$13$	−57.1649	−1.21959	−0.609796	−	0.792559i	$-0.708749\pi$
$13$	−57.1649	−1.21959	−0.609796	+	0.792559i	$0.708749\pi$
$14$	−90.9491	−1.73623
$15$	46.7870	0.805356
$16$	−14.5090	−0.226703
$17$	−34.0983	−0.486473	−0.243237	−	0.969967i	$-0.578209\pi$
$17$	−34.0983	−0.486473	−0.243237	+	0.969967i	$0.578209\pi$
$18$	152.203	1.99304
$19$	58.9447	0.711729	0.355864	−	0.934538i	$-0.384186\pi$
$19$	58.9447	0.711729	0.355864	+	0.934538i	$0.384186\pi$
$20$	−72.4672	−0.810208
$21$	158.411	1.64610
$22$	−39.0030	−0.377976
$23$	147.409	1.33638	0.668192	−	0.743989i	$-0.267069\pi$
$23$	147.409	1.33638	0.668192	+	0.743989i	$0.267069\pi$
$24$	−143.228	−1.21818
$25$	−89.0880	−0.712704
$26$	−256.241	−1.93280
$27$	−54.3011	−0.387047
$28$	−245.359	−1.65602
$29$	127.619	0.817180	0.408590	−	0.912718i	$-0.366021\pi$
$29$	127.619	0.817180	0.408590	+	0.912718i	$0.366021\pi$
$30$	209.722	1.27633
$31$	−98.1327	−0.568553	−0.284277	−	0.958742i	$-0.591753\pi$
$31$	−98.1327	−0.568553	−0.284277	+	0.958742i	$0.591753\pi$
$32$	−211.798	−1.17003
$33$	67.9335	0.358355
$34$	−152.845	−0.770961
$35$	121.591	0.587216
$36$	410.607	1.90096
$37$	−72.2719	−0.321120	−0.160560	−	0.987026i	$-0.551330\pi$
$37$	−72.2719	−0.321120	−0.160560	+	0.987026i	$0.551330\pi$
$38$	264.219	1.12795
$39$	446.308	1.83247
$40$	−109.937	−0.434564
$41$	−15.2752	−0.0581852	−0.0290926	−	0.999577i	$-0.509262\pi$
$41$	−15.2752	−0.0581852	−0.0290926	+	0.999577i	$0.509262\pi$
$42$	710.074	2.60873
$43$	427.027	1.51444	0.757221	−	0.653159i	$-0.226557\pi$
$43$	427.027	1.51444	0.757221	+	0.653159i	$0.226557\pi$
$44$	−105.221	−0.360514
$45$	−203.482	−0.674072
$46$	660.756	2.11790
$47$	−356.718	−1.10708	−0.553540	−	0.832823i	$-0.686723\pi$
$47$	−356.718	−1.10708	−0.553540	+	0.832823i	$0.686723\pi$
$48$	113.277	0.340628
$49$	68.6803	0.200234
$50$	−399.335	−1.12949
$51$	266.218	0.730941
$52$	−691.275	−1.84351
$53$	−582.203	−1.50890	−0.754450	−	0.656357i	$-0.772096\pi$
$53$	−582.203	−1.50890	−0.754450	+	0.656357i	$0.772096\pi$
$54$	−243.404	−0.613390
$55$	52.1434	0.127837
$56$	−372.223	−0.888222
$57$	−460.204	−1.06939
$58$	572.049	1.29506
$59$	−79.1281	−0.174603	−0.0873017	−	0.996182i	$-0.527824\pi$
$59$	−79.1281	−0.174603	−0.0873017	+	0.996182i	$0.527824\pi$
$60$	565.779	1.21736
$61$	−297.291	−0.624004	−0.312002	−	0.950081i	$-0.601000\pi$
$61$	−297.291	−0.624004	−0.312002	+	0.950081i	$0.601000\pi$
$62$	−439.878	−0.901041
$63$	−688.946	−1.37776
$64$	−833.310	−1.62756
$65$	342.570	0.653701
$66$	304.511	0.567920
$67$	−162.865	−0.296972	−0.148486	−	0.988915i	$-0.547440\pi$
$67$	−162.865	−0.296972	−0.148486	+	0.988915i	$0.547440\pi$
$68$	−412.339	−0.735344
$69$	−1150.87	−2.00796
$70$	545.028	0.930618
$71$	1137.70	1.90168	0.950842	−	0.309675i	$-0.100220\pi$
$71$	1137.70	1.90168	0.950842	+	0.309675i	$0.100220\pi$
$72$	622.915	1.01960
$73$	−756.758	−1.21331	−0.606657	−	0.794964i	$-0.707490\pi$
$73$	−756.758	−1.21331	−0.606657	+	0.794964i	$0.707490\pi$
$74$	−323.957	−0.508909
$75$	695.543	1.07086
$76$	712.798	1.07584
$77$	176.547	0.261290
$78$	2000.57	2.90410
$79$	55.7276	0.0793651	0.0396825	−	0.999212i	$-0.487365\pi$
$79$	55.7276	0.0793651	0.0396825	+	0.999212i	$0.487365\pi$
$80$	86.9475	0.121513
$81$	−492.839	−0.676047
$82$	−68.4710	−0.0922117
$83$	−789.369	−1.04391	−0.521955	−	0.852973i	$-0.674797\pi$
$83$	−789.369	−1.04391	−0.521955	+	0.852973i	$0.674797\pi$
$84$	1915.61	2.48821
$85$	204.340	0.260750
$86$	1914.14	2.40008
$87$	−996.368	−1.22784
$88$	−159.626	−0.193365
$89$	−1351.23	−1.60933	−0.804664	−	0.593730i	$-0.797655\pi$
$89$	−1351.23	−1.60933	−0.804664	+	0.593730i	$0.797655\pi$
$90$	−912.103	−1.06827
$91$	1159.87	1.33613
$92$	1782.56	2.02005
$93$	766.159	0.854268
$94$	−1598.98	−1.75450
$95$	−353.236	−0.381487
$96$	1653.59	1.75801
$97$	1221.35	1.27844	0.639222	−	0.769022i	$-0.279256\pi$
$97$	1221.35	1.27844	0.639222	+	0.769022i	$0.279256\pi$
$98$	307.858	0.317330
$99$	−295.450	−0.299938
$100$	−1077.31	−1.07731
$101$	1035.00	1.01966	0.509832	−	0.860274i	$-0.329708\pi$
$101$	1035.00	1.01966	0.509832	+	0.860274i	$0.329708\pi$
$102$	1193.32	1.15839
$103$	−1436.04	−1.37376	−0.686878	−	0.726772i	$-0.741020\pi$
$103$	−1436.04	−1.37376	−0.686878	+	0.726772i	$0.741020\pi$
$104$	−1048.70	−0.988787
$105$	−949.303	−0.882310
$106$	−2609.72	−2.39130
$107$	−1344.95	−1.21515	−0.607574	−	0.794263i	$-0.707857\pi$
$107$	−1344.95	−1.21515	−0.607574	+	0.794263i	$0.707857\pi$
$108$	−656.645	−0.585052
$109$	491.906	0.432257	0.216129	−	0.976365i	$-0.430657\pi$
$109$	491.906	0.432257	0.216129	+	0.976365i	$0.430657\pi$
$110$	233.732	0.202595
$111$	564.254	0.482492
$112$	294.386	0.248365
$113$	866.204	0.721111	0.360556	−	0.932738i	$-0.382587\pi$
$113$	866.204	0.721111	0.360556	+	0.932738i	$0.382587\pi$
$114$	−2062.85	−1.69477
$115$	−883.370	−0.716302
$116$	1543.25	1.23523
$117$	−1941.04	−1.53375
$118$	−354.690	−0.276711
$119$	691.851	0.532957
$120$	858.318	0.652945
$121$	−1255.29	−0.943117
$122$	−1332.60	−0.988919
$123$	119.260	0.0874250
$124$	−1186.68	−0.859414
$125$	1282.96	0.918010
$126$	−3088.19	−2.18347
$127$	127.000	0.0887357
$127$	127.000	0.0887357
$128$	−2040.91	−1.40932
$129$	−3333.96	−2.27549
$130$	1535.56	1.03598
$131$	1372.81	0.915594	0.457797	−	0.889057i	$-0.348639\pi$
$131$	1372.81	0.915594	0.457797	+	0.889057i	$0.348639\pi$
$132$	821.497	0.541683
$133$	−1195.98	−0.779736
$134$	−730.039	−0.470640
$135$	325.408	0.207457
$136$	−625.541	−0.394410
$137$	−1734.43	−1.08163	−0.540813	−	0.841143i	$-0.681883\pi$
$137$	−1734.43	−1.08163	−0.540813	+	0.841143i	$0.681883\pi$
$138$	−5158.77	−3.18220
$139$	−1159.62	−0.707608	−0.353804	−	0.935320i	$-0.615112\pi$
$139$	−1159.62	−0.707608	−0.353804	+	0.935320i	$0.615112\pi$
$140$	1470.35	0.887625
$141$	2785.03	1.66342
$142$	5099.70	3.01378
$143$	497.403	0.290874
$144$	−492.655	−0.285101
$145$	−764.777	−0.438009
$146$	−3392.16	−1.92285
$147$	−536.212	−0.300858
$148$	−873.959	−0.485398
$149$	3378.34	1.85748	0.928739	−	0.370735i	$-0.120894\pi$
$149$	3378.34	1.85748	0.928739	+	0.370735i	$0.120894\pi$
$150$	3117.76	1.69709
$151$	−1035.75	−0.558199	−0.279099	−	0.960262i	$-0.590036\pi$
$151$	−1035.75	−0.558199	−0.279099	+	0.960262i	$0.590036\pi$
$152$	1081.36	0.577036
$153$	−1157.81	−0.611787
$154$	791.367	0.414092
$155$	588.076	0.304745
$156$	5397.04	2.76993
$157$	1974.36	1.00364	0.501819	−	0.864973i	$-0.332664\pi$
$157$	1974.36	1.00364	0.501819	+	0.864973i	$0.332664\pi$
$158$	249.798	0.125778
$159$	4545.48	2.26717
$160$	1269.24	0.627137
$161$	−2990.91	−1.46408
$162$	−2209.14	−1.07140
$163$	3758.38	1.80600	0.903002	−	0.429636i	$-0.141358\pi$
$163$	3758.38	1.80600	0.903002	+	0.429636i	$0.141358\pi$
$164$	−184.718	−0.0879517
$165$	−407.103	−0.192078
$166$	−3538.33	−1.65438
$167$	708.610	0.328346	0.164173	−	0.986432i	$-0.447504\pi$
$167$	708.610	0.328346	0.164173	+	0.986432i	$0.447504\pi$
$168$	2906.09	1.33458
$169$	1070.83	0.487403
$170$	915.948	0.413235
$171$	2001.47	0.895068
$172$	5163.89	2.28920
$173$	−2153.41	−0.946363	−0.473181	−	0.880965i	$-0.656895\pi$
$173$	−2153.41	−0.946363	−0.473181	+	0.880965i	$0.656895\pi$
$174$	−4466.20	−1.94587
$175$	1807.59	0.780804
$176$	126.246	0.0540689
$177$	617.782	0.262347
$178$	−6056.87	−2.55046
$179$	−791.823	−0.330635	−0.165317	−	0.986240i	$-0.552865\pi$
$179$	−791.823	−0.330635	−0.165317	+	0.986240i	$0.552865\pi$
$180$	−2460.63	−1.01891
$181$	3423.95	1.40608	0.703040	−	0.711150i	$-0.251825\pi$
$181$	3423.95	1.40608	0.703040	+	0.711150i	$0.251825\pi$
$182$	5199.10	2.11749
$183$	2321.06	0.937584
$184$	2704.25	1.08348
$185$	433.101	0.172120
$186$	3434.29	1.35384
$187$	296.696	0.116024
$188$	−4313.67	−1.67344
$189$	1101.76	0.424030
$190$	−1583.37	−0.604579
$191$	−1191.56	−0.451404	−0.225702	−	0.974196i	$-0.572468\pi$
$191$	−1191.56	−0.451404	−0.225702	+	0.974196i	$0.572468\pi$
$192$	6505.96	2.44546
$193$	−3571.53	−1.33204	−0.666021	−	0.745933i	$-0.732004\pi$
$193$	−3571.53	−1.33204	−0.666021	+	0.745933i	$0.732004\pi$
$194$	5474.67	2.02607
$195$	−2674.57	−0.982206
$196$	830.526	0.302670
$197$	−4386.46	−1.58641	−0.793204	−	0.608956i	$-0.791589\pi$
$197$	−4386.46	−1.58641	−0.793204	+	0.608956i	$0.791589\pi$
$198$	−1324.35	−0.475341
$199$	−1350.45	−0.481061	−0.240531	−	0.970642i	$-0.577321\pi$
$199$	−1350.45	−0.481061	−0.240531	+	0.970642i	$0.577321\pi$
$200$	−1634.34	−0.577827
$201$	1271.55	0.446209
$202$	4639.35	1.61596
$203$	−2589.37	−0.895263
$204$	3219.28	1.10488
$205$	91.5394	0.0311873
$206$	−6437.01	−2.17713
$207$	5005.27	1.68063
$208$	829.405	0.276485
$209$	−512.890	−0.169748
$210$	−4255.24	−1.39828
$211$	4659.45	1.52024	0.760118	−	0.649785i	$-0.225141\pi$
$211$	4659.45	1.52024	0.760118	+	0.649785i	$0.225141\pi$
$212$	−7040.38	−2.28083
$213$	−8882.42	−2.85734
$214$	−6028.69	−1.92576
$215$	−2559.03	−0.811741
$216$	−996.167	−0.313799
$217$	1991.10	0.622880
$218$	2204.96	0.685040
$219$	5908.30	1.82304
$220$	630.552	0.193235
$221$	1949.22	0.593299
$222$	2529.26	0.764651
$223$	3249.25	0.975722	0.487861	−	0.872921i	$-0.337777\pi$
$223$	3249.25	0.975722	0.487861	+	0.872921i	$0.337777\pi$
$224$	4297.37	1.28183
$225$	−3024.99	−0.896294
$226$	3882.74	1.14281
$227$	−2213.55	−0.647217	−0.323608	−	0.946191i	$-0.604896\pi$
$227$	−2213.55	−0.647217	−0.323608	+	0.946191i	$0.604896\pi$
$228$	−5565.08	−1.61648
$229$	5292.29	1.52718	0.763590	−	0.645701i	$-0.223435\pi$
$229$	5292.29	1.52718	0.763590	+	0.645701i	$0.223435\pi$
$230$	−3959.69	−1.13519
$231$	−1378.37	−0.392596
$232$	2341.20	0.662531
$233$	−5572.29	−1.56675	−0.783375	−	0.621550i	$-0.786503\pi$
$233$	−5572.29	−1.56675	−0.783375	+	0.621550i	$0.786503\pi$
$234$	−8700.68	−2.43069
$235$	2137.69	0.593395
$236$	−956.868	−0.263927
$237$	−435.086	−0.119248
$238$	3101.21	0.844628
$239$	294.219	0.0796294	0.0398147	−	0.999207i	$-0.487323\pi$
$239$	294.219	0.0796294	0.0398147	+	0.999207i	$0.487323\pi$
$240$	−678.832	−0.182577
$241$	2884.22	0.770908	0.385454	−	0.922727i	$-0.374045\pi$
$241$	2884.22	0.770908	0.385454	+	0.922727i	$0.374045\pi$
$242$	−5626.81	−1.49465
$243$	5313.91	1.40283
$244$	−3595.04	−0.943232
$245$	−411.578	−0.107325
$246$	534.579	0.138551
$247$	−3369.57	−0.868019
$248$	−1800.27	−0.460956
$249$	6162.90	1.56851
$250$	5750.83	1.45486
$251$	2422.46	0.609181	0.304590	−	0.952483i	$-0.401480\pi$
$251$	2422.46	0.609181	0.304590	+	0.952483i	$0.401480\pi$
$252$	−8331.18	−2.08260
$253$	−1282.63	−0.318729
$254$	569.275	0.140628
$255$	−1595.36	−0.391784
$256$	−2481.87	−0.605926
$257$	3089.95	0.749983	0.374991	−	0.927028i	$-0.377646\pi$
$257$	3089.95	0.749983	0.374991	+	0.927028i	$0.377646\pi$
$258$	−14944.4	−3.60620
$259$	1466.39	0.351803
$260$	4142.58	0.988123
$261$	4333.31	1.02768
$262$	6153.59	1.45103
$263$	2815.98	0.660232	0.330116	−	0.943940i	$-0.392912\pi$
$263$	2815.98	0.660232	0.330116	+	0.943940i	$0.392912\pi$
$264$	1246.26	0.290537
$265$	3488.95	0.808771
$266$	−5360.97	−1.23572
$267$	10549.6	2.41806
$268$	−1969.47	−0.448897
$269$	−3784.44	−0.857774	−0.428887	−	0.903358i	$-0.641094\pi$
$269$	−3784.44	−0.857774	−0.428887	+	0.903358i	$0.641094\pi$
$270$	1458.64	0.328777
$271$	1369.04	0.306876	0.153438	−	0.988158i	$-0.450965\pi$
$271$	1369.04	0.306876	0.153438	+	0.988158i	$0.450965\pi$
$272$	494.732	0.110285
$273$	−9055.54	−2.00757
$274$	−7774.57	−1.71416
$275$	775.172	0.169981
$276$	−13917.1	−3.03519
$277$	5440.34	1.18007	0.590033	−	0.807379i	$-0.299115\pi$
$277$	5440.34	1.18007	0.590033	+	0.807379i	$0.299115\pi$
$278$	−5197.97	−1.12142
$279$	−3332.11	−0.715011
$280$	2230.61	0.476087
$281$	−3506.57	−0.744428	−0.372214	−	0.928147i	$-0.621401\pi$
$281$	−3506.57	−0.744428	−0.372214	+	0.928147i	$0.621401\pi$
$282$	12483.9	2.63618
$283$	−4260.58	−0.894930	−0.447465	−	0.894301i	$-0.647673\pi$
$283$	−4260.58	−0.894930	−0.447465	+	0.894301i	$0.647673\pi$
$284$	13757.8	2.87455
$285$	2757.85	0.573195
$286$	2229.60	0.460976
$287$	309.933	0.0637449
$288$	−7191.63	−1.47143
$289$	−3750.31	−0.763344
$290$	−3428.10	−0.694155
$291$	−9535.52	−1.92090
$292$	−9151.21	−1.83402
$293$	−5874.40	−1.17128	−0.585642	−	0.810570i	$-0.699158\pi$
$293$	−5874.40	−1.17128	−0.585642	+	0.810570i	$0.699158\pi$
$294$	−2403.56	−0.476798
$295$	474.188	0.0935874
$296$	−1325.84	−0.260349
$297$	472.485	0.0923110
$298$	15143.3	2.94372
$299$	−8426.60	−1.62984
$300$	8410.96	1.61869
$301$	−8664.34	−1.65915
$302$	−4642.73	−0.884632
$303$	−8080.61	−1.53207
$304$	−855.229	−0.161351
$305$	1781.57	0.334466
$306$	−5189.87	−0.969559
$307$	5101.93	0.948477	0.474239	−	0.880396i	$-0.342723\pi$
$307$	5101.93	0.948477	0.474239	+	0.880396i	$0.342723\pi$
$308$	2134.92	0.394961
$309$	11211.7	2.06411
$310$	2636.04	0.482958
$311$	−7090.92	−1.29289	−0.646446	−	0.762960i	$-0.723745\pi$
$311$	−7090.92	−1.29289	−0.646446	+	0.762960i	$0.723745\pi$
$312$	8187.62	1.48568
$313$	9643.89	1.74155	0.870775	−	0.491682i	$-0.163618\pi$
$313$	9643.89	1.74155	0.870775	+	0.491682i	$0.163618\pi$
$314$	8850.04	1.59056
$315$	4128.62	0.738481
$316$	673.894	0.119967
$317$	−4662.64	−0.826120	−0.413060	−	0.910704i	$-0.635540\pi$
$317$	−4662.64	−0.826120	−0.413060	+	0.910704i	$0.635540\pi$
$318$	20375.0	3.59300
$319$	−1110.44	−0.194898
$320$	4993.75	0.872372
$321$	10500.5	1.82580
$322$	−13406.7	−2.32027
$323$	−2009.91	−0.346237
$324$	−5959.73	−1.02190
$325$	5092.71	0.869208
$326$	16846.9	2.86215
$327$	−3840.49	−0.649479
$328$	−280.228	−0.0471738
$329$	7237.78	1.21286
$330$	−1824.83	−0.304405
$331$	−2759.66	−0.458261	−0.229131	−	0.973396i	$-0.573588\pi$
$331$	−2759.66	−0.458261	−0.229131	+	0.973396i	$0.573588\pi$
$332$	−9545.56	−1.57795
$333$	−2454.00	−0.403839
$334$	3176.33	0.520362
$335$	975.994	0.159177
$336$	−2298.38	−0.373176
$337$	−2462.01	−0.397965	−0.198982	−	0.980003i	$-0.563764\pi$
$337$	−2462.01	−0.397965	−0.198982	+	0.980003i	$0.563764\pi$
$338$	4799.96	0.772435
$339$	−6762.78	−1.08349
$340$	2471.01	0.394145
$341$	853.872	0.135601
$342$	8971.58	1.41850
$343$	5565.92	0.876185
$344$	7833.91	1.22784
$345$	6896.80	1.07626
$346$	−9652.63	−1.49979
$347$	−5933.71	−0.917977	−0.458989	−	0.888442i	$-0.651788\pi$
$347$	−5933.71	−0.917977	−0.458989	+	0.888442i	$0.651788\pi$
$348$	−12048.7	−1.85598
$349$	−8965.75	−1.37515	−0.687573	−	0.726116i	$-0.741324\pi$
$349$	−8965.75	−1.37515	−0.687573	+	0.726116i	$0.741324\pi$
$350$	8102.48	1.23742
$351$	3104.12	0.472039
$352$	1842.90	0.279054
$353$	5153.48	0.777031	0.388515	−	0.921442i	$-0.372988\pi$
$353$	5153.48	0.777031	0.388515	+	0.921442i	$0.372988\pi$
$354$	2769.20	0.415766
$355$	−6817.83	−1.01930
$356$	−16340.0	−2.43263
$357$	−5401.54	−0.800784
$358$	−3549.33	−0.523989
$359$	−1783.87	−0.262254	−0.131127	−	0.991366i	$-0.541860\pi$
$359$	−1783.87	−0.262254	−0.131127	+	0.991366i	$0.541860\pi$
$360$	−3732.92	−0.546506
$361$	−3384.52	−0.493442
$362$	15347.8	2.22835
$363$	9800.51	1.41706
$364$	14025.9	2.01966
$365$	4535.00	0.650336
$366$	10404.1	1.48588
$367$	−8063.33	−1.14687	−0.573436	−	0.819250i	$-0.694390\pi$
$367$	−8063.33	−1.14687	−0.573436	+	0.819250i	$0.694390\pi$
$368$	−2138.75	−0.302962
$369$	−518.673	−0.0731735
$370$	1941.37	0.272775
$371$	11812.8	1.65308
$372$	9264.89	1.29130
$373$	−3328.88	−0.462099	−0.231049	−	0.972942i	$-0.574216\pi$
$373$	−3328.88	−0.462099	−0.231049	+	0.972942i	$0.574216\pi$
$374$	1329.93	0.183875
$375$	−10016.5	−1.37934
$376$	−6544.08	−0.897568
$377$	−7295.32	−0.996626
$378$	4938.64	0.672001
$379$	−4980.68	−0.675040	−0.337520	−	0.941318i	$-0.609588\pi$
$379$	−4980.68	−0.675040	−0.337520	+	0.941318i	$0.609588\pi$
$380$	−4271.56	−0.576648
$381$	−991.537	−0.133328
$382$	−5341.14	−0.715384
$383$	3259.30	0.434836	0.217418	−	0.976079i	$-0.430236\pi$
$383$	3259.30	0.434836	0.217418	+	0.976079i	$0.430236\pi$
$384$	15934.2	2.11754
$385$	−1057.98	−0.140052
$386$	−16009.3	−2.11102
$387$	14499.7	1.90456
$388$	14769.3	1.93247
$389$	−13363.9	−1.74184	−0.870922	−	0.491422i	$-0.836477\pi$
$389$	−13363.9	−1.74184	−0.870922	+	0.491422i	$0.836477\pi$
$390$	−11988.7	−1.55660
$391$	−5026.38	−0.650115
$392$	1259.96	0.162340
$393$	−10718.0	−1.37571
$394$	−19662.2	−2.51414
$395$	−333.957	−0.0425397
$396$	−3572.78	−0.453381
$397$	−6376.83	−0.806156	−0.403078	−	0.915166i	$-0.632060\pi$
$397$	−6376.83	−0.806156	−0.403078	+	0.915166i	$0.632060\pi$
$398$	−6053.39	−0.762384
$399$	9337.49	1.17158
$400$	1292.58	0.161572
$401$	−15399.4	−1.91772	−0.958862	−	0.283874i	$-0.908380\pi$
$401$	−15399.4	−1.91772	−0.958862	+	0.283874i	$0.908380\pi$
$402$	5699.69	0.707151
$403$	5609.74	0.693403
$404$	12515.9	1.54130
$405$	2953.42	0.362362
$406$	−11606.8	−1.41881
$407$	628.852	0.0765873
$408$	4883.83	0.592612
$409$	2084.12	0.251964	0.125982	−	0.992033i	$-0.459792\pi$
$409$	2084.12	0.251964	0.125982	+	0.992033i	$0.459792\pi$
$410$	410.324	0.0494255
$411$	13541.4	1.62517
$412$	−17365.5	−2.07655
$413$	1605.50	0.191287
$414$	22436.1	2.66346
$415$	4730.42	0.559536
$416$	12107.4	1.42696
$417$	9053.57	1.06320
$418$	−2299.02	−0.269016
$419$	−16396.9	−1.91179	−0.955897	−	0.293702i	$-0.905113\pi$
$419$	−16396.9	−1.91179	−0.955897	+	0.293702i	$0.905113\pi$
$420$	−11479.6	−1.33368
$421$	11887.3	1.37614	0.688069	−	0.725646i	$-0.258459\pi$
$421$	11887.3	1.37614	0.688069	+	0.725646i	$0.258459\pi$
$422$	20885.9	2.40926
$423$	−12112.4	−1.39226
$424$	−10680.7	−1.22335
$425$	3037.75	0.346711
$426$	−39815.3	−4.52830
$427$	6032.01	0.683628
$428$	−16264.0	−1.83679
$429$	−3883.41	−0.437047
$430$	−11470.8	−1.28644
$431$	17178.6	1.91987	0.959937	−	0.280217i	$-0.0904063\pi$
$431$	17178.6	1.91987	0.959937	+	0.280217i	$0.0904063\pi$
$432$	787.855	0.0877447
$433$	−3841.73	−0.426378	−0.213189	−	0.977011i	$-0.568385\pi$
$433$	−3841.73	−0.426378	−0.213189	+	0.977011i	$0.568385\pi$
$434$	8925.08	0.987138
$435$	5970.90	0.658121
$436$	5948.44	0.653392
$437$	8688.96	0.951143
$438$	26483.8	2.88915
$439$	−6038.50	−0.656496	−0.328248	−	0.944591i	$-0.606458\pi$
$439$	−6038.50	−0.656496	−0.328248	+	0.944591i	$0.606458\pi$
$440$	956.583	0.103644
$441$	2332.05	0.251814
$442$	8737.36	0.940258
$443$	9137.40	0.979980	0.489990	−	0.871728i	$-0.337000\pi$
$443$	9137.40	0.979980	0.489990	+	0.871728i	$0.337000\pi$
$444$	6823.32	0.729326
$445$	8097.48	0.862600
$446$	14564.7	1.54632
$447$	−26375.9	−2.79092
$448$	16907.8	1.78307
$449$	−8984.62	−0.944344	−0.472172	−	0.881506i	$-0.656530\pi$
$449$	−8984.62	−0.944344	−0.472172	+	0.881506i	$0.656530\pi$
$450$	−13559.5	−1.42044
$451$	132.913	0.0138772
$452$	10474.7	1.09002
$453$	8086.48	0.838711
$454$	−9922.18	−1.02571
$455$	−6950.71	−0.716164
$456$	−8442.55	−0.867014
$457$	10388.7	1.06337	0.531686	−	0.846942i	$-0.321559\pi$
$457$	10388.7	1.06337	0.531686	+	0.846942i	$0.321559\pi$
$458$	23722.6	2.42027
$459$	1851.58	0.188288
$460$	−10682.3	−1.08275
$461$	4180.70	0.422375	0.211187	−	0.977446i	$-0.432267\pi$
$461$	4180.70	0.422375	0.211187	+	0.977446i	$0.432267\pi$
$462$	−6178.50	−0.622186
$463$	−5078.19	−0.509727	−0.254864	−	0.966977i	$-0.582031\pi$
$463$	−5078.19	−0.509727	−0.254864	+	0.966977i	$0.582031\pi$
$464$	−1851.62	−0.185257
$465$	−4591.33	−0.457888
$466$	−24977.7	−2.48298
$467$	3968.97	0.393280	0.196640	−	0.980476i	$-0.436997\pi$
$467$	3968.97	0.393280	0.196640	+	0.980476i	$0.436997\pi$
$468$	−23472.3	−2.31839
$469$	3304.51	0.325348
$470$	9582.18	0.940410
$471$	−15414.6	−1.50800
$472$	−1451.62	−0.141560
$473$	−3715.65	−0.361196
$474$	−1950.27	−0.188985
$475$	−5251.27	−0.507252
$476$	8366.31	0.805608
$477$	−19768.8	−1.89759
$478$	1318.83	0.126196
$479$	843.501	0.0804604	0.0402302	−	0.999190i	$-0.487191\pi$
$479$	843.501	0.0804604	0.0402302	+	0.999190i	$0.487191\pi$
$480$	−9909.40	−0.942292
$481$	4131.41	0.391635
$482$	12928.5	1.22173
$483$	23351.1	2.19982
$484$	−15179.8	−1.42560
$485$	−7319.13	−0.685246
$486$	23819.5	2.22320
$487$	4366.33	0.406277	0.203139	−	0.979150i	$-0.434886\pi$
$487$	4366.33	0.406277	0.203139	+	0.979150i	$0.434886\pi$
$488$	−5453.88	−0.505913
$489$	−29343.0	−2.71358
$490$	−1844.89	−0.170089
$491$	−11403.8	−1.04816	−0.524078	−	0.851670i	$-0.675590\pi$
$491$	−11403.8	−1.04816	−0.524078	+	0.851670i	$0.675590\pi$
$492$	1442.16	0.132150
$493$	−4351.58	−0.397536
$494$	−15104.0	−1.37563
$495$	1770.53	0.160767
$496$	1423.81	0.128893
$497$	−23083.7	−2.08339
$498$	27625.1	2.48576
$499$	13001.5	1.16639	0.583194	−	0.812333i	$-0.301803\pi$
$499$	13001.5	1.16639	0.583194	+	0.812333i	$0.301803\pi$
$500$	15514.4	1.38765
$501$	−5532.38	−0.493350
$502$	10858.6	0.965428
$503$	−9223.90	−0.817641	−0.408821	−	0.912615i	$-0.634060\pi$
$503$	−9223.90	−0.817641	−0.408821	+	0.912615i	$0.634060\pi$
$504$	−12638.9	−1.11702
$505$	−6202.39	−0.546540
$506$	−5749.37	−0.505120
$507$	−8360.33	−0.732338
$508$	1535.77	0.134131
$509$	17452.8	1.51981	0.759903	−	0.650037i	$-0.225247\pi$
$509$	17452.8	1.51981	0.759903	+	0.650037i	$0.225247\pi$
$510$	−7151.15	−0.620899
$511$	15354.6	1.32925
$512$	5202.35	0.449050
$513$	−3200.77	−0.275472
$514$	13850.6	1.18857
$515$	8605.69	0.736334
$516$	−40316.4	−3.43960
$517$	3103.88	0.264040
$518$	6573.07	0.557537
$519$	16812.5	1.42194
$520$	6284.53	0.529990
$521$	−1764.28	−0.148358	−0.0741788	−	0.997245i	$-0.523634\pi$
$521$	−1764.28	−0.148358	−0.0741788	+	0.997245i	$0.523634\pi$
$522$	19424.0	1.62867
$523$	−1343.12	−0.112296	−0.0561478	−	0.998422i	$-0.517882\pi$
$523$	−1343.12	−0.112296	−0.0561478	+	0.998422i	$0.517882\pi$
$524$	16600.9	1.38400
$525$	−14112.5	−1.17318
$526$	12622.6	1.04633
$527$	3346.16	0.276586
$528$	−985.648	−0.0812402
$529$	9562.29	0.785920
$530$	15639.1	1.28174
$531$	−2686.80	−0.219581
$532$	−14462.6	−1.17863
$533$	873.208	0.0709622
$534$	47288.3	3.83214
$535$	8059.81	0.651319
$536$	−2987.79	−0.240771
$537$	6182.06	0.496788
$538$	−16963.7	−1.35940
$539$	−597.601	−0.0477560
$540$	3935.05	0.313588
$541$	5800.90	0.460999	0.230499	−	0.973072i	$-0.425964\pi$
$541$	5800.90	0.460999	0.230499	+	0.973072i	$0.425964\pi$
$542$	6136.72	0.486337
$543$	−26732.1	−2.11268
$544$	7221.95	0.569189
$545$	−2947.83	−0.231690
$546$	−40591.3	−3.18159
$547$	−20172.9	−1.57684	−0.788420	−	0.615138i	$-0.789100\pi$
$547$	−20172.9	−1.57684	−0.788420	+	0.615138i	$0.789100\pi$
$548$	−20973.9	−1.63496
$549$	−10094.6	−0.784745
$550$	3474.70	0.269385
$551$	7522.46	0.581611
$552$	−21113.1	−1.62796
$553$	−1130.71	−0.0869486
$554$	24386.2	1.87016
$555$	−3381.38	−0.258616
$556$	−14022.9	−1.06961
$557$	−7029.36	−0.534728	−0.267364	−	0.963596i	$-0.586153\pi$
$557$	−7029.36	−0.534728	−0.267364	+	0.963596i	$0.586153\pi$
$558$	−14936.1	−1.13315
$559$	−24411.0	−1.84700
$560$	−1764.16	−0.133124
$561$	−2316.42	−0.174330
$562$	−15718.1	−1.17977
$563$	11312.5	0.846826	0.423413	−	0.905937i	$-0.360832\pi$
$563$	11312.5	0.846826	0.423413	+	0.905937i	$0.360832\pi$
$564$	33678.5	2.51439
$565$	−5190.87	−0.386516
$566$	−19098.0	−1.41828
$567$	9999.65	0.740645
$568$	20871.3	1.54180
$569$	−927.916	−0.0683660	−0.0341830	−	0.999416i	$-0.510883\pi$
$569$	−927.916	−0.0683660	−0.0341830	+	0.999416i	$0.510883\pi$
$570$	12362.0	0.908398
$571$	15832.0	1.16033	0.580164	−	0.814499i	$-0.302988\pi$
$571$	15832.0	1.16033	0.580164	+	0.814499i	$0.302988\pi$
$572$	6014.92	0.439679
$573$	9302.95	0.678248
$574$	1389.27	0.101023
$575$	−13132.3	−0.952445
$576$	−28295.1	−2.04681
$577$	−14721.1	−1.06212	−0.531062	−	0.847333i	$-0.678207\pi$
$577$	−14721.1	−1.06212	−0.531062	+	0.847333i	$0.678207\pi$
$578$	−16810.7	−1.20974
$579$	27884.2	2.00143
$580$	−9248.18	−0.662086
$581$	16016.2	1.14366
$582$	−42742.8	−3.04424
$583$	5065.87	0.359874
$584$	−13882.9	−0.983697
$585$	11632.0	0.822092
$586$	−26331.9	−1.85625
$587$	8796.43	0.618513	0.309257	−	0.950979i	$-0.399920\pi$
$587$	8796.43	0.618513	0.309257	+	0.950979i	$0.399920\pi$
$588$	−6484.23	−0.454771
$589$	−5784.40	−0.404656
$590$	2125.54	0.148317
$591$	34246.8	2.38363
$592$	1048.59	0.0727988
$593$	−25527.4	−1.76777	−0.883883	−	0.467708i	$-0.845080\pi$
$593$	−25527.4	−1.76777	−0.883883	+	0.467708i	$0.845080\pi$
$594$	2117.91	0.146294
$595$	−4146.03	−0.285665
$596$	40853.0	2.80773
$597$	10543.5	0.722809
$598$	−37772.1	−2.58297
$599$	1545.78	0.105441	0.0527204	−	0.998609i	$-0.483211\pi$
$599$	1545.78	0.105441	0.0527204	+	0.998609i	$0.483211\pi$
$600$	12759.9	0.868202
$601$	25564.6	1.73511	0.867556	−	0.497340i	$-0.165690\pi$
$601$	25564.6	1.73511	0.867556	+	0.497340i	$0.165690\pi$
$602$	−38837.7	−2.62942
$603$	−5530.09	−0.373471
$604$	−12524.9	−0.843763
$605$	7522.53	0.505511
$606$	−36221.2	−2.42803
$607$	−14665.6	−0.980658	−0.490329	−	0.871538i	$-0.663123\pi$
$607$	−14665.6	−0.980658	−0.490329	+	0.871538i	$0.663123\pi$
$608$	−12484.4	−0.832745
$609$	20216.2	1.34516
$610$	7985.84	0.530061
$611$	20391.8	1.35018
$612$	−14001.0	−0.924766
$613$	18431.9	1.21445	0.607225	−	0.794530i	$-0.292283\pi$
$613$	18431.9	1.21445	0.607225	+	0.794530i	$0.292283\pi$
$614$	22869.3	1.50314
$615$	−714.683	−0.0468598
$616$	3238.79	0.211842
$617$	−17954.8	−1.17153	−0.585763	−	0.810482i	$-0.699205\pi$
$617$	−17954.8	−1.17153	−0.585763	+	0.810482i	$0.699205\pi$
$618$	50256.2	3.27120
$619$	17919.5	1.16356	0.581781	−	0.813345i	$-0.302356\pi$
$619$	17919.5	1.16356	0.581781	+	0.813345i	$0.302356\pi$
$620$	7111.40	0.460646
$621$	−8004.45	−0.517243
$622$	−31784.9	−2.04897
$623$	27416.4	1.76310
$624$	−6475.48	−0.415427
$625$	3447.67	0.220651
$626$	43228.6	2.76000
$627$	4004.32	0.255052
$628$	23875.3	1.51708
$629$	2464.35	0.156216
$630$	18506.5	1.17034
$631$	−23214.4	−1.46458	−0.732290	−	0.680993i	$-0.761548\pi$
$631$	−23214.4	−1.46458	−0.732290	+	0.680993i	$0.761548\pi$
$632$	1022.34	0.0643455
$633$	−36378.1	−2.28420
$634$	−20900.2	−1.30923
$635$	−761.068	−0.0475623
$636$	54966.9	3.42701
$637$	−3926.10	−0.244204
$638$	−4977.52	−0.308874
$639$	38630.6	2.39155
$640$	12230.5	0.755395
$641$	−1102.69	−0.0679463	−0.0339731	−	0.999423i	$-0.510816\pi$
$641$	−1102.69	−0.0679463	−0.0339731	+	0.999423i	$0.510816\pi$
$642$	47068.3	2.89352
$643$	26164.4	1.60470	0.802350	−	0.596854i	$-0.203583\pi$
$643$	26164.4	1.60470	0.802350	+	0.596854i	$0.203583\pi$
$644$	−36168.0	−2.21307
$645$	19979.3	1.21967
$646$	−9009.40	−0.548716
$647$	22462.7	1.36491	0.682456	−	0.730927i	$-0.260912\pi$
$647$	22462.7	1.36491	0.682456	+	0.730927i	$0.260912\pi$
$648$	−9041.24	−0.548107
$649$	688.509	0.0416431
$650$	22828.0	1.37752
$651$	−15545.3	−0.935895
$652$	45448.7	2.72992
$653$	22228.2	1.33209	0.666047	−	0.745910i	$-0.267985\pi$
$653$	22228.2	1.33209	0.666047	+	0.745910i	$0.267985\pi$
$654$	−17214.9	−1.02929
$655$	−8226.78	−0.490759
$656$	221.629	0.0131908
$657$	−25695.8	−1.52586
$658$	32443.2	1.92214
$659$	95.8262	0.00566443	0.00283221	−	0.999996i	$-0.499098\pi$
$659$	95.8262	0.00566443	0.00283221	+	0.999996i	$0.499098\pi$
$660$	−4922.95	−0.290342
$661$	8655.48	0.509318	0.254659	−	0.967031i	$-0.418037\pi$
$661$	8655.48	0.509318	0.254659	+	0.967031i	$0.418037\pi$
$662$	−12370.1	−0.726251
$663$	−15218.3	−0.891449
$664$	−14481.2	−0.846352
$665$	7167.12	0.417939
$666$	−11000.0	−0.640003
$667$	18812.1	1.09207
$668$	8568.97	0.496322
$669$	−25368.1	−1.46605
$670$	4374.88	0.252263
$671$	2586.79	0.148826
$672$	−33551.1	−1.92599
$673$	16241.9	0.930282	0.465141	−	0.885237i	$-0.346004\pi$
$673$	16241.9	0.930282	0.465141	+	0.885237i	$0.346004\pi$
$674$	−11035.9	−0.630693
$675$	4837.58	0.275850
$676$	12949.1	0.736750
$677$	11.9360	0.000677604 0	0.000338802	−	1.00000i	$-0.499892\pi$
$677$	11.9360	0.000677604 0	0.000338802		1.00000i	$0.499892\pi$
$678$	−30314.0	−1.71711
$679$	−24781.0	−1.40060
$680$	3748.66	0.211404
$681$	17282.0	0.972463
$682$	3827.47	0.214899
$683$	−25012.6	−1.40129	−0.700644	−	0.713511i	$-0.747104\pi$
$683$	−25012.6	−1.40129	−0.700644	+	0.713511i	$0.747104\pi$
$684$	24203.1	1.35297
$685$	10393.9	0.579751
$686$	24949.1	1.38858
$687$	−41318.9	−2.29464
$688$	−6195.73	−0.343329
$689$	33281.6	1.84024
$690$	30914.8	1.70566
$691$	12198.3	0.671555	0.335777	−	0.941941i	$-0.391001\pi$
$691$	12198.3	0.671555	0.335777	+	0.941941i	$0.391001\pi$
$692$	−26040.4	−1.43050
$693$	5994.66	0.328598
$694$	−26597.7	−1.45481
$695$	6949.20	0.379278
$696$	−18278.6	−0.995473
$697$	520.860	0.0283055
$698$	−40188.8	−2.17933
$699$	43504.9	2.35409
$700$	21858.5	1.18025
$701$	−26331.6	−1.41873	−0.709367	−	0.704840i	$-0.751019\pi$
$701$	−26331.6	−1.41873	−0.709367	+	0.704840i	$0.751019\pi$
$702$	13914.2	0.748086
$703$	−4260.05	−0.228550
$704$	7250.80	0.388174
$705$	−16689.8	−0.891593
$706$	23100.4	1.23144
$707$	−21000.0	−1.11709
$708$	7470.63	0.396558
$709$	29196.0	1.54651	0.773256	−	0.634094i	$-0.218627\pi$
$709$	29196.0	1.54651	0.773256	+	0.634094i	$0.218627\pi$
$710$	−30560.8	−1.61539
$711$	1892.24	0.0998093
$712$	−24788.7	−1.30477
$713$	−14465.6	−0.759805
$714$	−24212.3	−1.26908
$715$	−2980.77	−0.155908
$716$	−9575.23	−0.499781
$717$	−2297.08	−0.119646
$718$	−7996.17	−0.415619
$719$	−12729.8	−0.660282	−0.330141	−	0.943932i	$-0.607096\pi$
$719$	−12729.8	−0.660282	−0.330141	+	0.943932i	$0.607096\pi$
$720$	2952.31	0.152814
$721$	29137.1	1.50502
$722$	−15171.0	−0.782005
$723$	−22518.2	−1.15831
$724$	41404.7	2.12541
$725$	−11369.3	−0.582407
$726$	43930.6	2.24576
$727$	−31504.9	−1.60722	−0.803611	−	0.595155i	$-0.797091\pi$
$727$	−31504.9	−1.60722	−0.803611	+	0.595155i	$0.797091\pi$
$728$	21278.1	1.08327
$729$	−28181.0	−1.43174
$730$	20328.1	1.03065
$731$	−14560.9	−0.736736
$732$	28067.8	1.41723
$733$	−24769.0	−1.24811	−0.624054	−	0.781381i	$-0.714516\pi$
$733$	−24769.0	−1.24811	−0.624054	+	0.781381i	$0.714516\pi$
$734$	−36143.7	−1.81756
$735$	3213.34	0.161260
$736$	−31220.9	−1.56361
$737$	1417.12	0.0708281
$738$	−2324.94	−0.115965
$739$	−22258.6	−1.10798	−0.553989	−	0.832524i	$-0.686895\pi$
$739$	−22258.6	−1.10798	−0.553989	+	0.832524i	$0.686895\pi$
$740$	5237.34	0.260174
$741$	26307.5	1.30422
$742$	52950.9	2.61979
$743$	12747.8	0.629436	0.314718	−	0.949185i	$-0.398090\pi$
$743$	12747.8	0.629436	0.314718	+	0.949185i	$0.398090\pi$
$744$	14055.4	0.692600
$745$	−20245.2	−0.995608
$746$	−14921.6	−0.732333
$747$	−26803.1	−1.31282
$748$	3587.84	0.175380
$749$	27288.8	1.33126
$750$	−44898.9	−2.18597
$751$	−2079.69	−0.101051	−0.0505253	−	0.998723i	$-0.516090\pi$
$751$	−2079.69	−0.101051	−0.0505253	+	0.998723i	$0.516090\pi$
$752$	5175.63	0.250978
$753$	−18913.1	−0.915312
$754$	−32701.1	−1.57945
$755$	6206.89	0.299195
$756$	13323.3	0.640955
$757$	1497.14	0.0718817	0.0359409	−	0.999354i	$-0.488557\pi$
$757$	1497.14	0.0718817	0.0359409	+	0.999354i	$0.488557\pi$
$758$	−22325.8	−1.06980
$759$	10014.0	0.478900
$760$	−6480.20	−0.309291
$761$	15622.5	0.744173	0.372087	−	0.928198i	$-0.378642\pi$
$761$	15622.5	0.744173	0.372087	+	0.928198i	$0.378642\pi$
$762$	−4444.55	−0.211298
$763$	−9980.72	−0.473560
$764$	−14409.1	−0.682334
$765$	6938.37	0.327918
$766$	14609.7	0.689127
$767$	4523.35	0.212945
$768$	19376.9	0.910421
$769$	−195.022	−0.00914520	−0.00457260	−	0.999990i	$-0.501456\pi$
$769$	−195.022	−0.00914520	−0.00457260	+	0.999990i	$0.501456\pi$
$770$	−4742.40	−0.221953
$771$	−24124.4	−1.12687
$772$	−43189.2	−2.01349
$773$	15353.1	0.714377	0.357188	−	0.934032i	$-0.383735\pi$
$773$	15353.1	0.714377	0.357188	+	0.934032i	$0.383735\pi$
$774$	64994.9	3.01834
$775$	8742.44	0.405210
$776$	22405.9	1.03650
$777$	−11448.7	−0.528595
$778$	−59903.5	−2.76047
$779$	−900.395	−0.0414121
$780$	−32342.7	−1.48468
$781$	−9899.32	−0.453554
$782$	−22530.7	−1.03030
$783$	−6929.85	−0.316287
$784$	−996.482	−0.0453937
$785$	−11831.7	−0.537950
$786$	−48043.4	−2.18022
$787$	−27041.7	−1.22482	−0.612410	−	0.790540i	$-0.709800\pi$
$787$	−27041.7	−1.22482	−0.612410	+	0.790540i	$0.709800\pi$
$788$	−53044.0	−2.39799
$789$	−21985.4	−0.992019
$790$	−1496.95	−0.0674168
$791$	−17575.2	−0.790015
$792$	−5420.10	−0.243176
$793$	16994.6	0.761030
$794$	−28584.0	−1.27759
$795$	−27239.5	−1.21520
$796$	−16330.6	−0.727163
$797$	−16608.2	−0.738134	−0.369067	−	0.929403i	$-0.620323\pi$
$797$	−16608.2	−0.738134	−0.369067	+	0.929403i	$0.620323\pi$
$798$	41855.1	1.85671
$799$	12163.5	0.538565
$800$	18868.7	0.833886
$801$	−45881.2	−2.02389
$802$	−69027.3	−3.03920
$803$	6584.71	0.289376
$804$	15376.4	0.674481
$805$	17923.5	0.784746
$806$	25145.6	1.09890
$807$	29546.5	1.28883
$808$	18987.3	0.826695
$809$	3737.98	0.162448	0.0812239	−	0.996696i	$-0.474117\pi$
$809$	3737.98	0.162448	0.0812239	+	0.996696i	$0.474117\pi$
$810$	13238.6	0.574269
$811$	−14001.4	−0.606233	−0.303117	−	0.952954i	$-0.598027\pi$
$811$	−14001.4	−0.606233	−0.303117	+	0.952954i	$0.598027\pi$
$812$	−31312.4	−1.35326
$813$	−10688.6	−0.461091
$814$	2818.82	0.121375
$815$	−22522.7	−0.968019
$816$	−3862.56	−0.165707
$817$	25171.0	1.07787
$818$	9342.05	0.399312
$819$	39383.5	1.68031
$820$	1106.95	0.0471421
$821$	29196.5	1.24113	0.620564	−	0.784156i	$-0.286904\pi$
$821$	29196.5	1.24113	0.620564	+	0.784156i	$0.286904\pi$
$822$	60699.0	2.57557
$823$	−20622.6	−0.873463	−0.436731	−	0.899592i	$-0.643864\pi$
$823$	−20622.6	−0.873463	−0.436731	+	0.899592i	$0.643864\pi$
$824$	−26344.4	−1.11378
$825$	−6052.06	−0.255401
$826$	7196.63	0.303151
$827$	−4618.12	−0.194181	−0.0970906	−	0.995276i	$-0.530954\pi$
$827$	−4618.12	−0.194181	−0.0970906	+	0.995276i	$0.530954\pi$
$828$	60527.0	2.54041
$829$	17840.5	0.747437	0.373718	−	0.927542i	$-0.378083\pi$
$829$	17840.5	0.747437	0.373718	+	0.927542i	$0.378083\pi$
$830$	21204.0	0.886750
$831$	−42474.8	−1.77308
$832$	47636.1	1.98496
$833$	−2341.88	−0.0974085
$834$	40582.5	1.68496
$835$	−4246.46	−0.175994
$836$	−6202.20	−0.256588
$837$	5328.72	0.220057
$838$	−73498.9	−3.02981
$839$	3178.71	0.130800	0.0654001	−	0.997859i	$-0.479168\pi$
$839$	3178.71	0.130800	0.0654001	+	0.997859i	$0.479168\pi$
$840$	−17415.2	−0.715335
$841$	−8102.43	−0.332217
$842$	53284.8	2.18090
$843$	27377.1	1.11853
$844$	56345.1	2.29796
$845$	−6417.10	−0.261248
$846$	−54293.7	−2.20645
$847$	25469.7	1.03323
$848$	8447.18	0.342072
$849$	33263.9	1.34466
$850$	13616.6	0.549467
$851$	−10653.5	−0.429139
$852$	−107412.	−4.31910
$853$	20694.2	0.830661	0.415331	−	0.909670i	$-0.363666\pi$
$853$	20694.2	0.830661	0.415331	+	0.909670i	$0.363666\pi$
$854$	27038.4	1.08341
$855$	−11994.2	−0.479757
$856$	−24673.3	−0.985184
$857$	19147.6	0.763209	0.381605	−	0.924326i	$-0.375372\pi$
$857$	19147.6	0.763209	0.381605	+	0.924326i	$0.375372\pi$
$858$	−17407.3	−0.692630
$859$	24033.8	0.954624	0.477312	−	0.878734i	$-0.341611\pi$
$859$	24033.8	0.954624	0.477312	+	0.878734i	$0.341611\pi$
$860$	−30945.4	−1.22701
$861$	−2419.77	−0.0957786
$862$	77002.9	3.04261
$863$	−23599.9	−0.930882	−0.465441	−	0.885079i	$-0.654104\pi$
$863$	−23599.9	−0.930882	−0.465441	+	0.885079i	$0.654104\pi$
$864$	11500.9	0.452856
$865$	12904.7	0.507251
$866$	−17220.5	−0.675723
$867$	29280.1	1.14695
$868$	24077.7	0.941533
$869$	−484.897	−0.0189287
$870$	26764.5	1.04299
$871$	9310.15	0.362184
$872$	9024.13	0.350454
$873$	41471.0	1.60777
$874$	38948.1	1.50737
$875$	−26031.1	−1.00573
$876$	71447.0	2.75567
$877$	−11519.0	−0.443521	−0.221760	−	0.975101i	$-0.571180\pi$
$877$	−11519.0	−0.443521	−0.221760	+	0.975101i	$0.571180\pi$
$878$	−27067.5	−1.04041
$879$	45863.7	1.75989
$880$	−756.548	−0.0289809
$881$	34539.7	1.32085	0.660427	−	0.750890i	$-0.270375\pi$
$881$	34539.7	1.32085	0.660427	+	0.750890i	$0.270375\pi$
$882$	10453.4	0.399073
$883$	3728.90	0.142115	0.0710575	−	0.997472i	$-0.477363\pi$
$883$	3728.90	0.142115	0.0710575	+	0.997472i	$0.477363\pi$
$884$	23571.3	0.896819
$885$	−3702.16	−0.140618
$886$	40958.3	1.55307
$887$	19658.2	0.744147	0.372074	−	0.928203i	$-0.378647\pi$
$887$	19658.2	0.744147	0.372074	+	0.928203i	$0.378647\pi$
$888$	10351.4	0.391181
$889$	−2576.82	−0.0972145
$890$	36296.8	1.36705
$891$	4288.29	0.161238
$892$	39292.1	1.47488
$893$	−21026.7	−0.787940
$894$	−118230.	−4.42303
$895$	4745.13	0.177220
$896$	41409.9	1.54398
$897$	65789.6	2.44889
$898$	−40273.4	−1.49659
$899$	−12523.6	−0.464610
$900$	−36580.2	−1.35482
$901$	19852.1	0.734040
$902$	595.780	0.0219926
$903$	67645.7	2.49292
$904$	15890.7	0.584643
$905$	−20518.6	−0.753659
$906$	36247.5	1.32919
$907$	−18626.3	−0.681892	−0.340946	−	0.940083i	$-0.610747\pi$
$907$	−18626.3	−0.681892	−0.340946	+	0.940083i	$0.610747\pi$
$908$	−26767.6	−0.978321
$909$	35143.4	1.28233
$910$	−31156.5	−1.13497
$911$	−3653.75	−0.132881	−0.0664403	−	0.997790i	$-0.521164\pi$
$911$	−3653.75	−0.132881	−0.0664403	+	0.997790i	$0.521164\pi$
$912$	6677.09	0.242435
$913$	6868.46	0.248973
$914$	46567.0	1.68523
$915$	−13909.4	−0.502545
$916$	63997.8	2.30846
$917$	−27854.2	−1.00308
$918$	8299.65	0.298398
$919$	−44548.5	−1.59904	−0.799521	−	0.600638i	$-0.794913\pi$
$919$	−44548.5	−1.59904	−0.799521	+	0.600638i	$0.794913\pi$
$920$	−16205.6	−0.580743
$921$	−39832.7	−1.42512
$922$	18739.9	0.669378
$923$	−65036.2	−2.31928
$924$	−16668.1	−0.593441
$925$	6438.56	0.228863
$926$	−22762.9	−0.807814
$927$	−48760.8	−1.72763
$928$	−27029.4	−0.956126
$929$	12777.8	0.451267	0.225633	−	0.974212i	$-0.427555\pi$
$929$	12777.8	0.451267	0.225633	+	0.974212i	$0.427555\pi$
$930$	−20580.6	−0.725659
$931$	4048.34	0.142512
$932$	−67383.7	−2.36827
$933$	55361.5	1.94261
$934$	17790.8	0.623269
$935$	−1778.00	−0.0621891
$936$	−35608.8	−1.24350
$937$	−34627.4	−1.20729	−0.603643	−	0.797255i	$-0.706285\pi$
$937$	−34627.4	−1.20729	−0.603643	+	0.797255i	$0.706285\pi$
$938$	14812.4	0.515611
$939$	−75293.5	−2.61673
$940$	25850.4	0.896964
$941$	21761.8	0.753893	0.376946	−	0.926235i	$-0.376974\pi$
$941$	21761.8	0.753893	0.376946	+	0.926235i	$0.376974\pi$
$942$	−69095.6	−2.38987
$943$	−2251.70	−0.0777577
$944$	1148.07	0.0395831
$945$	−6602.51	−0.227280
$946$	−16655.3	−0.572422
$947$	8871.49	0.304419	0.152209	−	0.988348i	$-0.451361\pi$
$947$	8871.49	0.304419	0.152209	+	0.988348i	$0.451361\pi$
$948$	−5261.34	−0.180254
$949$	43260.0	1.47975
$950$	−23538.7	−0.803891
$951$	36403.0	1.24127
$952$	12692.2	0.432096
$953$	−21681.9	−0.736985	−0.368493	−	0.929631i	$-0.620126\pi$
$953$	−21681.9	−0.736985	−0.368493	+	0.929631i	$0.620126\pi$
$954$	−88613.2	−3.00729
$955$	7140.61	0.241953
$956$	3557.89	0.120366
$957$	8669.60	0.292841
$958$	3780.98	0.127513
$959$	35191.5	1.18498
$960$	−38988.1	−1.31076
$961$	−20161.0	−0.676747
$962$	18519.0	0.620661
$963$	−45667.8	−1.52817
$964$	34877.9	1.16529
$965$	21403.0	0.713974
$966$	104671.	3.48627
$967$	34370.9	1.14301	0.571506	−	0.820598i	$-0.306360\pi$
$967$	34370.9	1.14301	0.571506	+	0.820598i	$0.306360\pi$
$968$	−23028.6	−0.764635
$969$	15692.2	0.520232
$970$	−32807.9	−1.08598
$971$	−28443.6	−0.940060	−0.470030	−	0.882650i	$-0.655757\pi$
$971$	−28443.6	−0.940060	−0.470030	+	0.882650i	$0.655757\pi$
$972$	64259.2	2.12049
$973$	23528.5	0.775221
$974$	19572.0	0.643867
$975$	−39760.7	−1.30601
$976$	4313.40	0.141464
$977$	−13505.7	−0.442258	−0.221129	−	0.975245i	$-0.570974\pi$
$977$	−13505.7	−0.442258	−0.221129	+	0.975245i	$0.570974\pi$
$978$	−131530.	−4.30047
$979$	11757.3	0.383827
$980$	−4977.07	−0.162231
$981$	16702.7	0.543605
$982$	−51117.2	−1.66111
$983$	8992.66	0.291782	0.145891	−	0.989301i	$-0.453395\pi$
$983$	8992.66	0.291782	0.145891	+	0.989301i	$0.453395\pi$
$984$	2187.85	0.0708801
$985$	26286.6	0.850315
$986$	−19505.9	−0.630014
$987$	−56508.1	−1.82236
$988$	−40747.0	−1.31208
$989$	62947.4	2.02388
$990$	7936.39	0.254783
$991$	−42022.2	−1.34700	−0.673502	−	0.739186i	$-0.735211\pi$
$991$	−42022.2	−1.34700	−0.673502	+	0.739186i	$0.735211\pi$
$992$	20784.3	0.665225
$993$	21545.7	0.688552
$994$	−103472.	−3.30176
$995$	8092.82	0.257849
$996$	74525.8	2.37092
$997$	−14379.8	−0.456784	−0.228392	−	0.973569i	$-0.573347\pi$
$997$	−14379.8	−0.456784	−0.228392	+	0.973569i	$0.573347\pi$
$998$	58279.1	1.84849
$999$	3924.44	0.124288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.4.a.b.1.13	✓	13
3.2	odd	2		1143.4.a.d.1.1		13
4.3	odd	2		2032.4.a.g.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.4.a.b.1.13	✓	13	1.1	even	1	trivial
1143.4.a.d.1.1		13	3.2	odd	2
2032.4.a.g.1.11		13	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	127.a (trivial)

\(f(q)\)	\(=\)	\(q+4.48248 q^{2} -7.80738 q^{3} +12.0927 q^{4} -5.99266 q^{5} -34.9964 q^{6} -20.2899 q^{7} +18.3452 q^{8} +33.9551 q^{9} -26.8620 q^{10} -8.70120 q^{11} -94.4119 q^{12} -57.1649 q^{13} -90.9491 q^{14} +46.7870 q^{15} -14.5090 q^{16} -34.0983 q^{17} +152.203 q^{18} +58.9447 q^{19} -72.4672 q^{20} +158.411 q^{21} -39.0030 q^{22} +147.409 q^{23} -143.228 q^{24} -89.0880 q^{25} -256.241 q^{26} -54.3011 q^{27} -245.359 q^{28} +127.619 q^{29} +209.722 q^{30} -98.1327 q^{31} -211.798 q^{32} +67.9335 q^{33} -152.845 q^{34} +121.591 q^{35} +410.607 q^{36} -72.2719 q^{37} +264.219 q^{38} +446.308 q^{39} -109.937 q^{40} -15.2752 q^{41} +710.074 q^{42} +427.027 q^{43} -105.221 q^{44} -203.482 q^{45} +660.756 q^{46} -356.718 q^{47} +113.277 q^{48} +68.6803 q^{49} -399.335 q^{50} +266.218 q^{51} -691.275 q^{52} -582.203 q^{53} -243.404 q^{54} +52.1434 q^{55} -372.223 q^{56} -460.204 q^{57} +572.049 q^{58} -79.1281 q^{59} +565.779 q^{60} -297.291 q^{61} -439.878 q^{62} -688.946 q^{63} -833.310 q^{64} +342.570 q^{65} +304.511 q^{66} -162.865 q^{67} -412.339 q^{68} -1150.87 q^{69} +545.028 q^{70} +1137.70 q^{71} +622.915 q^{72} -756.758 q^{73} -323.957 q^{74} +695.543 q^{75} +712.798 q^{76} +176.547 q^{77} +2000.57 q^{78} +55.7276 q^{79} +86.9475 q^{80} -492.839 q^{81} -68.4710 q^{82} -789.369 q^{83} +1915.61 q^{84} +204.340 q^{85} +1914.14 q^{86} -996.368 q^{87} -159.626 q^{88} -1351.23 q^{89} -912.103 q^{90} +1159.87 q^{91} +1782.56 q^{92} +766.159 q^{93} -1598.98 q^{94} -353.236 q^{95} +1653.59 q^{96} +1221.35 q^{97} +307.858 q^{98} -295.450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 8 q^{2} - 16 q^{3} + 34 q^{4} - 46 q^{5} - 2 q^{6} - 26 q^{7} - 117 q^{8} + 3 q^{9} - 25 q^{10} - 53 q^{11} - 255 q^{12} - 75 q^{13} - 152 q^{14} - 62 q^{15} + 82 q^{16} - 479 q^{17} - 292 q^{18}+ \cdots + 1769 q^{99}+O(q^{100}) \) 13 * q - 8 * q^2 - 16 * q^3 + 34 * q^4 - 46 * q^5 - 2 * q^6 - 26 * q^7 - 117 * q^8 + 3 * q^9 - 25 * q^10 - 53 * q^11 - 255 * q^12 - 75 * q^13 - 152 * q^14 - 62 * q^15 + 82 * q^16 - 479 * q^17 - 292 * q^18 - 209 * q^19 - 533 * q^20 - 174 * q^21 - 407 * q^22 - 376 * q^23 + 108 * q^24 + 9 * q^25 - 622 * q^26 - 562 * q^27 - 258 * q^28 - 158 * q^29 - 287 * q^30 - 307 * q^31 - 609 * q^32 - 494 * q^33 + 948 * q^34 - 512 * q^35 + 1556 * q^36 - 171 * q^37 + 712 * q^38 - 154 * q^39 + 1897 * q^40 - 641 * q^41 + 1489 * q^42 + 530 * q^43 + 1328 * q^44 - 566 * q^45 + 2051 * q^46 - 555 * q^47 + 268 * q^48 + 357 * q^49 + 808 * q^50 + 1228 * q^51 + 2473 * q^52 - 1640 * q^53 + 2957 * q^54 + 540 * q^55 + 551 * q^56 + 968 * q^57 + 1328 * q^58 - 860 * q^59 + 4466 * q^60 + 191 * q^61 + 367 * q^62 + 120 * q^63 + 1915 * q^64 - 1584 * q^65 + 3416 * q^66 + 912 * q^67 - 1873 * q^68 - 2142 * q^69 + 2329 * q^70 + 115 * q^71 - 1864 * q^72 - 2563 * q^73 + 470 * q^74 + 44 * q^75 - 192 * q^76 - 3338 * q^77 + 4226 * q^78 + 169 * q^79 - 3194 * q^80 - 395 * q^81 + 54 * q^82 - 1688 * q^83 + 853 * q^84 + 480 * q^85 - 485 * q^86 - 1068 * q^87 - 1192 * q^88 - 2752 * q^89 + 4948 * q^90 - 398 * q^91 - 846 * q^92 - 804 * q^93 + 531 * q^94 - 1766 * q^95 + 3965 * q^96 - 2124 * q^97 - 1479 * q^98 + 1769 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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