LMFDB - Embedded newform 531.8.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-5.66556$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.66556 q^{2} -95.9014 q^{4} -117.894 q^{5} +1197.66 q^{7} -1268.53 q^{8} +O(q^{10})$	\(q+5.66556 q^{2} -95.9014 q^{4} -117.894 q^{5} +1197.66 q^{7} -1268.53 q^{8} -667.937 q^{10} +6536.63 q^{11} +11916.5 q^{13} +6785.43 q^{14} +5088.45 q^{16} -29402.4 q^{17} +3457.38 q^{19} +11306.2 q^{20} +37033.7 q^{22} +37722.6 q^{23} -64225.9 q^{25} +67514.0 q^{26} -114857. q^{28} +207751. q^{29} +111488. q^{31} +191200. q^{32} -166581. q^{34} -141197. q^{35} -49565.3 q^{37} +19588.0 q^{38} +149552. q^{40} -112884. q^{41} -38995.6 q^{43} -626872. q^{44} +213720. q^{46} -1.22368e6 q^{47} +610852. q^{49} -363876. q^{50} -1.14281e6 q^{52} +475269. q^{53} -770631. q^{55} -1.51927e6 q^{56} +1.17702e6 q^{58} +205379. q^{59} +699413. q^{61} +631640. q^{62} +431937. q^{64} -1.40489e6 q^{65} -3.23969e6 q^{67} +2.81973e6 q^{68} -799963. q^{70} -5.13542e6 q^{71} +5.08296e6 q^{73} -280816. q^{74} -331568. q^{76} +7.82867e6 q^{77} +7.01416e6 q^{79} -599899. q^{80} -639551. q^{82} -6.20880e6 q^{83} +3.46637e6 q^{85} -220932. q^{86} -8.29189e6 q^{88} -1.44794e6 q^{89} +1.42720e7 q^{91} -3.61765e6 q^{92} -6.93283e6 q^{94} -407605. q^{95} -1.19209e7 q^{97} +3.46082e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) $ 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

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 $

$2$	5.66556	0.500770	0.250385	−	0.968146i	$-0.419443\pi$
$2$	5.66556	0.500770	0.250385	+	0.968146i	$0.419443\pi$
$3$	0	0
$3$	0	0
$4$	−95.9014	−0.749230
$5$	−117.894	−0.421791	−0.210896	−	0.977509i	$-0.567638\pi$
$5$	−117.894	−0.421791	−0.210896	+	0.977509i	$0.567638\pi$
$6$	0	0
$7$	1197.66	1.31975	0.659874	−	0.751376i	$-0.270609\pi$
$7$	1197.66	1.31975	0.659874	+	0.751376i	$0.270609\pi$
$8$	−1268.53	−0.875961
$9$	0	0
$10$	−667.937	−0.211220
$11$	6536.63	1.48074	0.740371	−	0.672199i	$-0.234650\pi$
$11$	6536.63	1.48074	0.740371	+	0.672199i	$0.234650\pi$
$12$	0	0
$13$	11916.5	1.50435	0.752175	−	0.658964i	$-0.229005\pi$
$13$	11916.5	1.50435	0.752175	+	0.658964i	$0.229005\pi$
$14$	6785.43	0.660890
$15$	0	0
$16$	5088.45	0.310574
$17$	−29402.4	−1.45148	−0.725741	−	0.687968i	$-0.758503\pi$
$17$	−29402.4	−1.45148	−0.725741	+	0.687968i	$0.758503\pi$
$18$	0	0
$19$	3457.38	0.115640	0.0578202	−	0.998327i	$-0.481585\pi$
$19$	3457.38	0.115640	0.0578202	+	0.998327i	$0.481585\pi$
$20$	11306.2	0.316018
$21$	0	0
$22$	37033.7	0.741511
$23$	37722.6	0.646479	0.323239	−	0.946317i	$-0.395228\pi$
$23$	37722.6	0.646479	0.323239	+	0.946317i	$0.395228\pi$
$24$	0	0
$25$	−64225.9	−0.822092
$26$	67514.0	0.753333
$27$	0	0
$28$	−114857.	−0.988795
$29$	207751.	1.58179	0.790896	−	0.611951i	$-0.209615\pi$
$29$	207751.	1.58179	0.790896	+	0.611951i	$0.209615\pi$
$30$	0	0
$31$	111488.	0.672141	0.336071	−	0.941837i	$-0.390902\pi$
$31$	111488.	0.672141	0.336071	+	0.941837i	$0.390902\pi$
$32$	191200.	1.03149
$33$	0	0
$34$	−166581.	−0.726858
$35$	−141197.	−0.556658
$36$	0	0
$37$	−49565.3	−0.160869	−0.0804344	−	0.996760i	$-0.525631\pi$
$37$	−49565.3	−0.160869	−0.0804344	+	0.996760i	$0.525631\pi$
$38$	19588.0	0.0579092
$39$	0	0
$40$	149552.	0.369473
$41$	−112884.	−0.255793	−0.127896	−	0.991788i	$-0.540823\pi$
$41$	−112884.	−0.255793	−0.127896	+	0.991788i	$0.540823\pi$
$42$	0	0
$43$	−38995.6	−0.0747956	−0.0373978	−	0.999300i	$-0.511907\pi$
$43$	−38995.6	−0.0747956	−0.0373978	+	0.999300i	$0.511907\pi$
$44$	−626872.	−1.10942
$45$	0	0
$46$	213720.	0.323737
$47$	−1.22368e6	−1.71919	−0.859597	−	0.510972i	$-0.829285\pi$
$47$	−1.22368e6	−1.71919	−0.859597	+	0.510972i	$0.829285\pi$
$48$	0	0
$49$	610852.	0.741737
$50$	−363876.	−0.411679
$51$	0	0
$52$	−1.14281e6	−1.12710
$53$	475269.	0.438504	0.219252	−	0.975668i	$-0.429638\pi$
$53$	475269.	0.438504	0.219252	+	0.975668i	$0.429638\pi$
$54$	0	0
$55$	−770631.	−0.624564
$56$	−1.51927e6	−1.15605
$57$	0	0
$58$	1.17702e6	0.792114
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	699413.	0.394529	0.197265	−	0.980350i	$-0.436794\pi$
$61$	699413.	0.394529	0.197265	+	0.980350i	$0.436794\pi$
$62$	631640.	0.336588
$63$	0	0
$64$	431937.	0.205964
$65$	−1.40489e6	−0.634521
$66$	0	0
$67$	−3.23969e6	−1.31596	−0.657979	−	0.753036i	$-0.728589\pi$
$67$	−3.23969e6	−1.31596	−0.657979	+	0.753036i	$0.728589\pi$
$68$	2.81973e6	1.08749
$69$	0	0
$70$	−799963.	−0.278758
$71$	−5.13542e6	−1.70283	−0.851417	−	0.524490i	$-0.824256\pi$
$71$	−5.13542e6	−1.70283	−0.851417	+	0.524490i	$0.824256\pi$
$72$	0	0
$73$	5.08296e6	1.52928	0.764639	−	0.644459i	$-0.222917\pi$
$73$	5.08296e6	1.52928	0.764639	+	0.644459i	$0.222917\pi$
$74$	−280816.	−0.0805583
$75$	0	0
$76$	−331568.	−0.0866412
$77$	7.82867e6	1.95421
$78$	0	0
$79$	7.01416e6	1.60059	0.800296	−	0.599605i	$-0.204675\pi$
$79$	7.01416e6	1.60059	0.800296	+	0.599605i	$0.204675\pi$
$80$	−599899.	−0.130998
$81$	0	0
$82$	−639551.	−0.128093
$83$	−6.20880e6	−1.19188	−0.595942	−	0.803027i	$-0.703221\pi$
$83$	−6.20880e6	−1.19188	−0.595942	+	0.803027i	$0.703221\pi$
$84$	0	0
$85$	3.46637e6	0.612222
$86$	−220932.	−0.0374554
$87$	0	0
$88$	−8.29189e6	−1.29707
$89$	−1.44794e6	−0.217714	−0.108857	−	0.994057i	$-0.534719\pi$
$89$	−1.44794e6	−0.217714	−0.108857	+	0.994057i	$0.534719\pi$
$90$	0	0
$91$	1.42720e7	1.98536
$92$	−3.61765e6	−0.484361
$93$	0	0
$94$	−6.93283e6	−0.860921
$95$	−407605.	−0.0487761
$96$	0	0
$97$	−1.19209e7	−1.32620	−0.663098	−	0.748532i	$-0.730759\pi$
$97$	−1.19209e7	−1.32620	−0.663098	+	0.748532i	$0.730759\pi$
$98$	3.46082e6	0.371439
$99$	0	0
$100$	6.15936e6	0.615936
$101$	1.33614e7	1.29041	0.645205	−	0.764009i	$-0.276772\pi$
$101$	1.33614e7	1.29041	0.645205	+	0.764009i	$0.276772\pi$
$102$	0	0
$103$	2.58316e6	0.232928	0.116464	−	0.993195i	$-0.462844\pi$
$103$	2.58316e6	0.232928	0.116464	+	0.993195i	$0.462844\pi$
$104$	−1.51165e7	−1.31775
$105$	0	0
$106$	2.69266e6	0.219590
$107$	4.52462e6	0.357058	0.178529	−	0.983935i	$-0.442866\pi$
$107$	4.52462e6	0.357058	0.178529	+	0.983935i	$0.442866\pi$
$108$	0	0
$109$	−312613.	−0.0231214	−0.0115607	−	0.999933i	$-0.503680\pi$
$109$	−312613.	−0.0231214	−0.0115607	+	0.999933i	$0.503680\pi$
$110$	−4.36606e6	−0.312763
$111$	0	0
$112$	6.09425e6	0.409880
$113$	−4.97336e6	−0.324246	−0.162123	−	0.986771i	$-0.551834\pi$
$113$	−4.97336e6	−0.324246	−0.162123	+	0.986771i	$0.551834\pi$
$114$	0	0
$115$	−4.44728e6	−0.272679
$116$	−1.99236e7	−1.18513
$117$	0	0
$118$	1.16359e6	0.0651947
$119$	−3.52141e7	−1.91559
$120$	0	0
$121$	2.32403e7	1.19260
$122$	3.96257e6	0.197568
$123$	0	0
$124$	−1.06918e7	−0.503588
$125$	1.67824e7	0.768543
$126$	0	0
$127$	4.34322e7	1.88148	0.940738	−	0.339134i	$-0.110134\pi$
$127$	4.34322e7	1.88148	0.940738	+	0.339134i	$0.110134\pi$
$128$	−2.20265e7	−0.928347
$129$	0	0
$130$	−7.95951e6	−0.317749
$131$	3.43447e7	1.33478	0.667391	−	0.744707i	$-0.267411\pi$
$131$	3.43447e7	1.33478	0.667391	+	0.744707i	$0.267411\pi$
$132$	0	0
$133$	4.14077e6	0.152616
$134$	−1.83547e7	−0.658992
$135$	0	0
$136$	3.72978e7	1.27144
$137$	5.15704e7	1.71348	0.856738	−	0.515752i	$-0.172487\pi$
$137$	5.15704e7	1.71348	0.856738	+	0.515752i	$0.172487\pi$
$138$	0	0
$139$	6.25955e7	1.97693	0.988466	−	0.151444i	$-0.0483924\pi$
$139$	6.25955e7	1.97693	0.988466	+	0.151444i	$0.0483924\pi$
$140$	1.35410e7	0.417065
$141$	0	0
$142$	−2.90951e7	−0.852728
$143$	7.78940e7	2.22755
$144$	0	0
$145$	−2.44926e7	−0.667186
$146$	2.87978e7	0.765816
$147$	0	0
$148$	4.75338e6	0.120528
$149$	4.84710e6	0.120041	0.0600206	−	0.998197i	$-0.480883\pi$
$149$	4.84710e6	0.120041	0.0600206	+	0.998197i	$0.480883\pi$
$150$	0	0
$151$	7.66941e7	1.81277	0.906385	−	0.422452i	$-0.138831\pi$
$151$	7.66941e7	1.81277	0.906385	+	0.422452i	$0.138831\pi$
$152$	−4.38578e6	−0.101297
$153$	0	0
$154$	4.43538e7	0.978608
$155$	−1.31437e7	−0.283503
$156$	0	0
$157$	−4.97181e6	−0.102534	−0.0512668	−	0.998685i	$-0.516326\pi$
$157$	−4.97181e6	−0.102534	−0.0512668	+	0.998685i	$0.516326\pi$
$158$	3.97392e7	0.801529
$159$	0	0
$160$	−2.25414e7	−0.435073
$161$	4.51790e7	0.853190
$162$	0	0
$163$	1.80568e7	0.326577	0.163288	−	0.986578i	$-0.447790\pi$
$163$	1.80568e7	0.326577	0.163288	+	0.986578i	$0.447790\pi$
$164$	1.08257e7	0.191648
$165$	0	0
$166$	−3.51763e7	−0.596860
$167$	3.89288e7	0.646790	0.323395	−	0.946264i	$-0.395176\pi$
$167$	3.89288e7	0.646790	0.323395	+	0.946264i	$0.395176\pi$
$168$	0	0
$169$	7.92556e7	1.26307
$170$	1.96390e7	0.306582
$171$	0	0
$172$	3.73973e6	0.0560391
$173$	−9.04299e7	−1.32786	−0.663928	−	0.747797i	$-0.731112\pi$
$173$	−9.04299e7	−1.32786	−0.663928	+	0.747797i	$0.731112\pi$
$174$	0	0
$175$	−7.69210e7	−1.08496
$176$	3.32613e7	0.459881
$177$	0	0
$178$	−8.20342e6	−0.109025
$179$	−1.14493e7	−0.149208	−0.0746042	−	0.997213i	$-0.523769\pi$
$179$	−1.14493e7	−0.149208	−0.0746042	+	0.997213i	$0.523769\pi$
$180$	0	0
$181$	−9.25112e7	−1.15963	−0.579815	−	0.814748i	$-0.696875\pi$
$181$	−9.25112e7	−1.15963	−0.579815	+	0.814748i	$0.696875\pi$
$182$	8.08589e7	0.994210
$183$	0	0
$184$	−4.78522e7	−0.566291
$185$	5.84347e6	0.0678531
$186$	0	0
$187$	−1.92193e8	−2.14927
$188$	1.17353e8	1.28807
$189$	0	0
$190$	−2.30931e6	−0.0244256
$191$	−2.78323e7	−0.289023	−0.144511	−	0.989503i	$-0.546161\pi$
$191$	−2.78323e7	−0.289023	−0.144511	+	0.989503i	$0.546161\pi$
$192$	0	0
$193$	−3.52675e7	−0.353122	−0.176561	−	0.984290i	$-0.556497\pi$
$193$	−3.52675e7	−0.353122	−0.176561	+	0.984290i	$0.556497\pi$
$194$	−6.75386e7	−0.664119
$195$	0	0
$196$	−5.85816e7	−0.555731
$197$	−1.76100e8	−1.64107	−0.820536	−	0.571595i	$-0.806325\pi$
$197$	−1.76100e8	−1.64107	−0.820536	+	0.571595i	$0.806325\pi$
$198$	0	0
$199$	1.94813e8	1.75239	0.876196	−	0.481954i	$-0.160073\pi$
$199$	1.94813e8	1.75239	0.876196	+	0.481954i	$0.160073\pi$
$200$	8.14724e7	0.720121
$201$	0	0
$202$	7.57000e7	0.646199
$203$	2.48815e8	2.08757
$204$	0	0
$205$	1.33084e7	0.107891
$206$	1.46351e7	0.116643
$207$	0	0
$208$	6.06368e7	0.467212
$209$	2.25996e7	0.171234
$210$	0	0
$211$	9.43223e7	0.691235	0.345617	−	0.938376i	$-0.387670\pi$
$211$	9.43223e7	0.691235	0.345617	+	0.938376i	$0.387670\pi$
$212$	−4.55789e7	−0.328540
$213$	0	0
$214$	2.56345e7	0.178804
$215$	4.59736e6	0.0315481
$216$	0	0
$217$	1.33525e8	0.887058
$218$	−1.77113e6	−0.0115785
$219$	0	0
$220$	7.39045e7	0.467942
$221$	−3.50375e8	−2.18354
$222$	0	0
$223$	−3.04202e8	−1.83694	−0.918470	−	0.395492i	$-0.870574\pi$
$223$	−3.04202e8	−1.83694	−0.918470	+	0.395492i	$0.870574\pi$
$224$	2.28994e8	1.36130
$225$	0	0
$226$	−2.81769e7	−0.162373
$227$	−1.54534e8	−0.876866	−0.438433	−	0.898764i	$-0.644466\pi$
$227$	−1.54534e8	−0.876866	−0.438433	+	0.898764i	$0.644466\pi$
$228$	0	0
$229$	1.18030e8	0.649485	0.324742	−	0.945803i	$-0.394722\pi$
$229$	1.18030e8	0.649485	0.324742	+	0.945803i	$0.394722\pi$
$230$	−2.51963e7	−0.136550
$231$	0	0
$232$	−2.63537e8	−1.38559
$233$	6.82032e7	0.353231	0.176615	−	0.984280i	$-0.443485\pi$
$233$	6.82032e7	0.353231	0.176615	+	0.984280i	$0.443485\pi$
$234$	0	0
$235$	1.44265e8	0.725141
$236$	−1.96961e7	−0.0975414
$237$	0	0
$238$	−1.99508e8	−0.959270
$239$	8.01024e7	0.379536	0.189768	−	0.981829i	$-0.439226\pi$
$239$	8.01024e7	0.379536	0.189768	+	0.981829i	$0.439226\pi$
$240$	0	0
$241$	9.44904e7	0.434839	0.217419	−	0.976078i	$-0.430236\pi$
$241$	9.44904e7	0.434839	0.217419	+	0.976078i	$0.430236\pi$
$242$	1.31670e8	0.597216
$243$	0	0
$244$	−6.70746e7	−0.295593
$245$	−7.20159e7	−0.312858
$246$	0	0
$247$	4.12000e7	0.173964
$248$	−1.41425e8	−0.588770
$249$	0	0
$250$	9.50815e7	0.384863
$251$	2.37800e8	0.949191	0.474596	−	0.880204i	$-0.342594\pi$
$251$	2.37800e8	0.949191	0.474596	+	0.880204i	$0.342594\pi$
$252$	0	0
$253$	2.46579e8	0.957268
$254$	2.46068e8	0.942187
$255$	0	0
$256$	−1.80080e8	−0.670852
$257$	−673684.	−0.00247566	−0.00123783	−	0.999999i	$-0.500394\pi$
$257$	−673684.	−0.00247566	−0.00123783	+	0.999999i	$0.500394\pi$
$258$	0	0
$259$	−5.93625e7	−0.212307
$260$	1.34731e8	0.475402
$261$	0	0
$262$	1.94582e8	0.668419
$263$	3.23561e7	0.109676	0.0548380	−	0.998495i	$-0.482536\pi$
$263$	3.23561e7	0.109676	0.0548380	+	0.998495i	$0.482536\pi$
$264$	0	0
$265$	−5.60314e7	−0.184957
$266$	2.34598e7	0.0764256
$267$	0	0
$268$	3.10691e8	0.985955
$269$	−2.61753e8	−0.819896	−0.409948	−	0.912109i	$-0.634453\pi$
$269$	−2.61753e8	−0.819896	−0.409948	+	0.912109i	$0.634453\pi$
$270$	0	0
$271$	6.21861e8	1.89802	0.949011	−	0.315244i	$-0.102086\pi$
$271$	6.21861e8	1.89802	0.949011	+	0.315244i	$0.102086\pi$
$272$	−1.49613e8	−0.450793
$273$	0	0
$274$	2.92175e8	0.858057
$275$	−4.19821e8	−1.21731
$276$	0	0
$277$	2.81765e8	0.796541	0.398270	−	0.917268i	$-0.369611\pi$
$277$	2.81765e8	0.796541	0.398270	+	0.917268i	$0.369611\pi$
$278$	3.54639e8	0.989988
$279$	0	0
$280$	1.79113e8	0.487611
$281$	−2.34019e8	−0.629186	−0.314593	−	0.949227i	$-0.601868\pi$
$281$	−2.34019e8	−0.629186	−0.314593	+	0.949227i	$0.601868\pi$
$282$	0	0
$283$	−3.59081e8	−0.941759	−0.470879	−	0.882198i	$-0.656063\pi$
$283$	−3.59081e8	−0.941759	−0.470879	+	0.882198i	$0.656063\pi$
$284$	4.92494e8	1.27581
$285$	0	0
$286$	4.41314e8	1.11549
$287$	−1.35197e8	−0.337582
$288$	0	0
$289$	4.54163e8	1.10680
$290$	−1.38764e8	−0.334107
$291$	0	0
$292$	−4.87463e8	−1.14578
$293$	−2.48310e8	−0.576711	−0.288355	−	0.957523i	$-0.593108\pi$
$293$	−2.48310e8	−0.576711	−0.288355	+	0.957523i	$0.593108\pi$
$294$	0	0
$295$	−2.42130e7	−0.0549125
$296$	6.28750e7	0.140915
$297$	0	0
$298$	2.74616e7	0.0601130
$299$	4.49523e8	0.972530
$300$	0	0
$301$	−4.67036e7	−0.0987114
$302$	4.34516e8	0.907781
$303$	0	0
$304$	1.75927e7	0.0359150
$305$	−8.24567e7	−0.166409
$306$	0	0
$307$	1.92429e8	0.379566	0.189783	−	0.981826i	$-0.439222\pi$
$307$	1.92429e8	0.379566	0.189783	+	0.981826i	$0.439222\pi$
$308$	−7.50780e8	−1.46415
$309$	0	0
$310$	−7.44667e7	−0.141970
$311$	4.80733e8	0.906238	0.453119	−	0.891450i	$-0.350311\pi$
$311$	4.80733e8	0.906238	0.453119	+	0.891450i	$0.350311\pi$
$312$	0	0
$313$	7.85937e8	1.44871	0.724357	−	0.689425i	$-0.242137\pi$
$313$	7.85937e8	1.44871	0.724357	+	0.689425i	$0.242137\pi$
$314$	−2.81681e7	−0.0513457
$315$	0	0
$316$	−6.72668e8	−1.19921
$317$	2.09039e8	0.368570	0.184285	−	0.982873i	$-0.441003\pi$
$317$	2.09039e8	0.368570	0.184285	+	0.982873i	$0.441003\pi$
$318$	0	0
$319$	1.35799e9	2.34222
$320$	−5.09229e7	−0.0868736
$321$	0	0
$322$	2.55964e8	0.427252
$323$	−1.01655e8	−0.167850
$324$	0	0
$325$	−7.65351e8	−1.23671
$326$	1.02302e8	0.163540
$327$	0	0
$328$	1.43196e8	0.224065
$329$	−1.46555e9	−2.26890
$330$	0	0
$331$	7.95790e8	1.20615	0.603074	−	0.797685i	$-0.293942\pi$
$331$	7.95790e8	1.20615	0.603074	+	0.797685i	$0.293942\pi$
$332$	5.95432e8	0.892995
$333$	0	0
$334$	2.20554e8	0.323893
$335$	3.81941e8	0.555060
$336$	0	0
$337$	2.75834e8	0.392593	0.196297	−	0.980545i	$-0.437108\pi$
$337$	2.75834e8	0.392593	0.196297	+	0.980545i	$0.437108\pi$
$338$	4.49027e8	0.632506
$339$	0	0
$340$	−3.32430e8	−0.458695
$341$	7.28753e8	0.995268
$342$	0	0
$343$	−2.54732e8	−0.340843
$344$	4.94670e7	0.0655181
$345$	0	0
$346$	−5.12337e8	−0.664950
$347$	−4.81631e8	−0.618816	−0.309408	−	0.950929i	$-0.600131\pi$
$347$	−4.81631e8	−0.618816	−0.309408	+	0.950929i	$0.600131\pi$
$348$	0	0
$349$	−3.21673e8	−0.405066	−0.202533	−	0.979275i	$-0.564917\pi$
$349$	−3.21673e8	−0.405066	−0.202533	+	0.979275i	$0.564917\pi$
$350$	−4.35801e8	−0.543313
$351$	0	0
$352$	1.24981e9	1.52737
$353$	−1.17516e9	−1.42195	−0.710977	−	0.703216i	$-0.751747\pi$
$353$	−1.17516e9	−1.42195	−0.710977	+	0.703216i	$0.751747\pi$
$354$	0	0
$355$	6.05437e8	0.718240
$356$	1.38860e8	0.163118
$357$	0	0
$358$	−6.48668e7	−0.0747191
$359$	−3.28816e8	−0.375079	−0.187539	−	0.982257i	$-0.560051\pi$
$359$	−3.28816e8	−0.375079	−0.187539	+	0.982257i	$0.560051\pi$
$360$	0	0
$361$	−8.81918e8	−0.986627
$362$	−5.24128e8	−0.580707
$363$	0	0
$364$	−1.36870e9	−1.48749
$365$	−5.99251e8	−0.645036
$366$	0	0
$367$	−6.95555e8	−0.734515	−0.367257	−	0.930119i	$-0.619703\pi$
$367$	−6.95555e8	−0.734515	−0.367257	+	0.930119i	$0.619703\pi$
$368$	1.91950e8	0.200780
$369$	0	0
$370$	3.31065e7	0.0339788
$371$	5.69211e8	0.578715
$372$	0	0
$373$	1.04776e9	1.04540	0.522699	−	0.852517i	$-0.324925\pi$
$373$	1.04776e9	1.04540	0.522699	+	0.852517i	$0.324925\pi$
$374$	−1.08888e9	−1.07629
$375$	0	0
$376$	1.55227e9	1.50595
$377$	2.47567e9	2.37957
$378$	0	0
$379$	9.05666e8	0.854537	0.427268	−	0.904125i	$-0.359476\pi$
$379$	9.05666e8	0.854537	0.427268	+	0.904125i	$0.359476\pi$
$380$	3.90899e7	0.0365445
$381$	0	0
$382$	−1.57686e8	−0.144734
$383$	−1.13004e9	−1.02777	−0.513887	−	0.857858i	$-0.671795\pi$
$383$	−1.13004e9	−1.02777	−0.513887	+	0.857858i	$0.671795\pi$
$384$	0	0
$385$	−9.22955e8	−0.824267
$386$	−1.99810e8	−0.176833
$387$	0	0
$388$	1.14323e9	0.993626
$389$	9.69975e8	0.835482	0.417741	−	0.908566i	$-0.362822\pi$
$389$	9.69975e8	0.835482	0.417741	+	0.908566i	$0.362822\pi$
$390$	0	0
$391$	−1.10914e9	−0.938352
$392$	−7.74883e8	−0.649733
$393$	0	0
$394$	−9.97706e8	−0.821799
$395$	−8.26929e8	−0.675116
$396$	0	0
$397$	−1.37378e9	−1.10192	−0.550961	−	0.834531i	$-0.685739\pi$
$397$	−1.37378e9	−1.10192	−0.550961	+	0.834531i	$0.685739\pi$
$398$	1.10372e9	0.877546
$399$	0	0
$400$	−3.26811e8	−0.255321
$401$	−5.72339e8	−0.443249	−0.221625	−	0.975132i	$-0.571136\pi$
$401$	−5.72339e8	−0.443249	−0.221625	+	0.975132i	$0.571136\pi$
$402$	0	0
$403$	1.32855e9	1.01114
$404$	−1.28138e9	−0.966813
$405$	0	0
$406$	1.40968e9	1.04539
$407$	−3.23990e8	−0.238205
$408$	0	0
$409$	1.07412e8	0.0776286	0.0388143	−	0.999246i	$-0.487642\pi$
$409$	1.07412e8	0.0776286	0.0388143	+	0.999246i	$0.487642\pi$
$410$	7.53994e7	0.0540287
$411$	0	0
$412$	−2.47729e8	−0.174516
$413$	2.45975e8	0.171817
$414$	0	0
$415$	7.31982e8	0.502727
$416$	2.27845e9	1.55172
$417$	0	0
$418$	1.28040e8	0.0857486
$419$	−4.96522e8	−0.329753	−0.164877	−	0.986314i	$-0.552723\pi$
$419$	−4.96522e8	−0.329753	−0.164877	+	0.986314i	$0.552723\pi$
$420$	0	0
$421$	2.13271e9	1.39298	0.696490	−	0.717566i	$-0.254744\pi$
$421$	2.13271e9	1.39298	0.696490	+	0.717566i	$0.254744\pi$
$422$	5.34389e8	0.346150
$423$	0	0
$424$	−6.02891e8	−0.384113
$425$	1.88840e9	1.19325
$426$	0	0
$427$	8.37660e8	0.520679
$428$	−4.33918e8	−0.267519
$429$	0	0
$430$	2.60466e7	0.0157984
$431$	2.75546e8	0.165777	0.0828885	−	0.996559i	$-0.473585\pi$
$431$	2.75546e8	0.165777	0.0828885	+	0.996559i	$0.473585\pi$
$432$	0	0
$433$	1.42964e9	0.846289	0.423144	−	0.906062i	$-0.360926\pi$
$433$	1.42964e9	0.846289	0.423144	+	0.906062i	$0.360926\pi$
$434$	7.56492e8	0.444212
$435$	0	0
$436$	2.99800e7	0.0173232
$437$	1.30421e8	0.0747591
$438$	0	0
$439$	−2.29794e9	−1.29632	−0.648161	−	0.761503i	$-0.724462\pi$
$439$	−2.29794e9	−1.29632	−0.648161	+	0.761503i	$0.724462\pi$
$440$	9.77566e8	0.547094
$441$	0	0
$442$	−1.98507e9	−1.09345
$443$	5.72726e8	0.312992	0.156496	−	0.987679i	$-0.449980\pi$
$443$	5.72726e8	0.312992	0.156496	+	0.987679i	$0.449980\pi$
$444$	0	0
$445$	1.70704e8	0.0918300
$446$	−1.72347e9	−0.919884
$447$	0	0
$448$	5.17315e8	0.271820
$449$	2.51611e9	1.31180	0.655899	−	0.754848i	$-0.272290\pi$
$449$	2.51611e9	1.31180	0.655899	+	0.754848i	$0.272290\pi$
$450$	0	0
$451$	−7.37880e8	−0.378763
$452$	4.76952e8	0.242935
$453$	0	0
$454$	−8.75521e8	−0.439108
$455$	−1.68259e9	−0.837409
$456$	0	0
$457$	−9.31683e8	−0.456627	−0.228314	−	0.973588i	$-0.573321\pi$
$457$	−9.31683e8	−0.456627	−0.228314	+	0.973588i	$0.573321\pi$
$458$	6.68708e8	0.325242
$459$	0	0
$460$	4.26500e8	0.204299
$461$	2.12369e8	0.100957	0.0504786	−	0.998725i	$-0.483925\pi$
$461$	2.12369e8	0.100957	0.0504786	+	0.998725i	$0.483925\pi$
$462$	0	0
$463$	3.14522e9	1.47271	0.736355	−	0.676596i	$-0.236545\pi$
$463$	3.14522e9	1.47271	0.736355	+	0.676596i	$0.236545\pi$
$464$	1.05713e9	0.491264
$465$	0	0
$466$	3.86409e8	0.176887
$467$	−3.87688e9	−1.76146	−0.880732	−	0.473615i	$-0.842949\pi$
$467$	−3.87688e9	−1.76146	−0.880732	+	0.473615i	$0.842949\pi$
$468$	0	0
$469$	−3.88006e9	−1.73673
$470$	8.17341e8	0.363129
$471$	0	0
$472$	−2.60529e8	−0.114040
$473$	−2.54900e8	−0.110753
$474$	0	0
$475$	−2.22054e8	−0.0950671
$476$	3.37709e9	1.43522
$477$	0	0
$478$	4.53825e8	0.190060
$479$	3.88318e9	1.61441	0.807205	−	0.590272i	$-0.200979\pi$
$479$	3.88318e9	1.61441	0.807205	+	0.590272i	$0.200979\pi$
$480$	0	0
$481$	−5.90648e8	−0.242003
$482$	5.35342e8	0.217754
$483$	0	0
$484$	−2.22878e9	−0.893528
$485$	1.40541e9	0.559378
$486$	0	0
$487$	−1.79849e9	−0.705597	−0.352799	−	0.935699i	$-0.614770\pi$
$487$	−1.79849e9	−0.705597	−0.352799	+	0.935699i	$0.614770\pi$
$488$	−8.87224e8	−0.345592
$489$	0	0
$490$	−4.08011e8	−0.156670
$491$	1.24531e9	0.474780	0.237390	−	0.971414i	$-0.423708\pi$
$491$	1.24531e9	0.474780	0.237390	+	0.971414i	$0.423708\pi$
$492$	0	0
$493$	−6.10837e9	−2.29594
$494$	2.33421e8	0.0871157
$495$	0	0
$496$	5.67299e8	0.208750
$497$	−6.15051e9	−2.24731
$498$	0	0
$499$	3.02782e9	1.09088	0.545442	−	0.838148i	$-0.316362\pi$
$499$	3.02782e9	1.09088	0.545442	+	0.838148i	$0.316362\pi$
$500$	−1.60945e9	−0.575815
$501$	0	0
$502$	1.34727e9	0.475326
$503$	3.67205e9	1.28653	0.643267	−	0.765642i	$-0.277579\pi$
$503$	3.67205e9	1.28653	0.643267	+	0.765642i	$0.277579\pi$
$504$	0	0
$505$	−1.57523e9	−0.544284
$506$	1.39701e9	0.479371
$507$	0	0
$508$	−4.16521e9	−1.40966
$509$	7.51140e8	0.252469	0.126235	−	0.992000i	$-0.459711\pi$
$509$	7.51140e8	0.252469	0.126235	+	0.992000i	$0.459711\pi$
$510$	0	0
$511$	6.08767e9	2.01826
$512$	1.79913e9	0.592405
$513$	0	0
$514$	−3.81680e6	−0.00123973
$515$	−3.04540e8	−0.0982469
$516$	0	0
$517$	−7.99873e9	−2.54568
$518$	−3.36322e8	−0.106317
$519$	0	0
$520$	1.78214e9	0.555816
$521$	−2.30813e9	−0.715036	−0.357518	−	0.933906i	$-0.616377\pi$
$521$	−2.30813e9	−0.715036	−0.357518	+	0.933906i	$0.616377\pi$
$522$	0	0
$523$	−9.93626e8	−0.303716	−0.151858	−	0.988402i	$-0.548526\pi$
$523$	−9.93626e8	−0.303716	−0.151858	+	0.988402i	$0.548526\pi$
$524$	−3.29371e9	−1.00006
$525$	0	0
$526$	1.83316e8	0.0549224
$527$	−3.27800e9	−0.975601
$528$	0	0
$529$	−1.98183e9	−0.582065
$530$	−3.17450e8	−0.0926210
$531$	0	0
$532$	−3.97106e8	−0.114345
$533$	−1.34519e9	−0.384802
$534$	0	0
$535$	−5.33427e8	−0.150604
$536$	4.10964e9	1.15273
$537$	0	0
$538$	−1.48298e9	−0.410579
$539$	3.99291e9	1.09832
$540$	0	0
$541$	−7.57542e8	−0.205691	−0.102846	−	0.994697i	$-0.532795\pi$
$541$	−7.57542e8	−0.205691	−0.102846	+	0.994697i	$0.532795\pi$
$542$	3.52320e9	0.950472
$543$	0	0
$544$	−5.62175e9	−1.49719
$545$	3.68552e7	0.00975240
$546$	0	0
$547$	−7.20248e9	−1.88160	−0.940798	−	0.338969i	$-0.889922\pi$
$547$	−7.20248e9	−1.88160	−0.940798	+	0.338969i	$0.889922\pi$
$548$	−4.94567e9	−1.28379
$549$	0	0
$550$	−2.37852e9	−0.609590
$551$	7.18273e8	0.182919
$552$	0	0
$553$	8.40060e9	2.11238
$554$	1.59636e9	0.398884
$555$	0	0
$556$	−6.00300e9	−1.48118
$557$	2.72425e9	0.667966	0.333983	−	0.942579i	$-0.391607\pi$
$557$	2.72425e9	0.667966	0.333983	+	0.942579i	$0.391607\pi$
$558$	0	0
$559$	−4.64693e8	−0.112519
$560$	−7.18477e8	−0.172884
$561$	0	0
$562$	−1.32585e9	−0.315077
$563$	−4.08861e9	−0.965599	−0.482799	−	0.875731i	$-0.660380\pi$
$563$	−4.08861e9	−0.965599	−0.482799	+	0.875731i	$0.660380\pi$
$564$	0	0
$565$	5.86330e8	0.136764
$566$	−2.03440e9	−0.471604
$567$	0	0
$568$	6.51443e9	1.49162
$569$	6.62224e9	1.50699	0.753497	−	0.657451i	$-0.228365\pi$
$569$	6.62224e9	1.50699	0.753497	+	0.657451i	$0.228365\pi$
$570$	0	0
$571$	1.73743e9	0.390555	0.195277	−	0.980748i	$-0.437439\pi$
$571$	1.73743e9	0.390555	0.195277	+	0.980748i	$0.437439\pi$
$572$	−7.47014e9	−1.66895
$573$	0	0
$574$	−7.65966e8	−0.169051
$575$	−2.42277e9	−0.531465
$576$	0	0
$577$	3.85948e9	0.836399	0.418200	−	0.908355i	$-0.362661\pi$
$577$	3.85948e9	0.836399	0.418200	+	0.908355i	$0.362661\pi$
$578$	2.57309e9	0.554252
$579$	0	0
$580$	2.34887e9	0.499875
$581$	−7.43604e9	−1.57299
$582$	0	0
$583$	3.10665e9	0.649311
$584$	−6.44787e9	−1.33959
$585$	0	0
$586$	−1.40682e9	−0.288799
$587$	2.98276e9	0.608674	0.304337	−	0.952564i	$-0.401565\pi$
$587$	2.98276e9	0.608674	0.304337	+	0.952564i	$0.401565\pi$
$588$	0	0
$589$	3.85455e8	0.0777267
$590$	−1.37180e8	−0.0274985
$591$	0	0
$592$	−2.52211e8	−0.0499618
$593$	−2.61405e9	−0.514781	−0.257390	−	0.966308i	$-0.582863\pi$
$593$	−2.61405e9	−0.514781	−0.257390	+	0.966308i	$0.582863\pi$
$594$	0	0
$595$	4.15155e9	0.807980
$596$	−4.64844e8	−0.0899384
$597$	0	0
$598$	2.54680e9	0.487014
$599$	2.42519e8	0.0461054	0.0230527	−	0.999734i	$-0.492661\pi$
$599$	2.42519e8	0.0461054	0.0230527	+	0.999734i	$0.492661\pi$
$600$	0	0
$601$	6.57764e9	1.23597	0.617987	−	0.786188i	$-0.287948\pi$
$601$	6.57764e9	1.23597	0.617987	+	0.786188i	$0.287948\pi$
$602$	−2.64602e8	−0.0494317
$603$	0	0
$604$	−7.35507e9	−1.35818
$605$	−2.73990e9	−0.503027
$606$	0	0
$607$	3.79055e9	0.687927	0.343963	−	0.938983i	$-0.388230\pi$
$607$	3.79055e9	0.687927	0.343963	+	0.938983i	$0.388230\pi$
$608$	6.61053e8	0.119282
$609$	0	0
$610$	−4.67164e8	−0.0833326
$611$	−1.45820e10	−2.58627
$612$	0	0
$613$	−5.87144e9	−1.02952	−0.514758	−	0.857336i	$-0.672118\pi$
$613$	−5.87144e9	−1.02952	−0.514758	+	0.857336i	$0.672118\pi$
$614$	1.09022e9	0.190075
$615$	0	0
$616$	−9.93089e9	−1.71181
$617$	4.89410e9	0.838832	0.419416	−	0.907794i	$-0.362235\pi$
$617$	4.89410e9	0.838832	0.419416	+	0.907794i	$0.362235\pi$
$618$	0	0
$619$	9.45629e9	1.60252	0.801260	−	0.598316i	$-0.204163\pi$
$619$	9.45629e9	1.60252	0.801260	+	0.598316i	$0.204163\pi$
$620$	1.26050e9	0.212409
$621$	0	0
$622$	2.72362e9	0.453817
$623$	−1.73415e9	−0.287328
$624$	0	0
$625$	3.03911e9	0.497928
$626$	4.45278e9	0.725473
$627$	0	0
$628$	4.76804e8	0.0768212
$629$	1.45734e9	0.233498
$630$	0	0
$631$	2.37404e9	0.376171	0.188086	−	0.982153i	$-0.439772\pi$
$631$	2.37404e9	0.376171	0.188086	+	0.982153i	$0.439772\pi$
$632$	−8.89766e9	−1.40206
$633$	0	0
$634$	1.18432e9	0.184569
$635$	−5.12041e9	−0.793590
$636$	0	0
$637$	7.27925e9	1.11583
$638$	7.69377e9	1.17292
$639$	0	0
$640$	2.59680e9	0.391569
$641$	−1.19471e10	−1.79168	−0.895841	−	0.444375i	$-0.853426\pi$
$641$	−1.19471e10	−1.79168	−0.895841	+	0.444375i	$0.853426\pi$
$642$	0	0
$643$	3.95645e9	0.586904	0.293452	−	0.955974i	$-0.405196\pi$
$643$	3.95645e9	0.586904	0.293452	+	0.955974i	$0.405196\pi$
$644$	−4.33272e9	−0.639235
$645$	0	0
$646$	−5.75935e8	−0.0840542
$647$	−8.69167e9	−1.26165	−0.630824	−	0.775926i	$-0.717283\pi$
$647$	−8.69167e9	−1.26165	−0.630824	+	0.775926i	$0.717283\pi$
$648$	0	0
$649$	1.34249e9	0.192776
$650$	−4.33615e9	−0.619309
$651$	0	0
$652$	−1.73168e9	−0.244681
$653$	−2.95452e9	−0.415231	−0.207616	−	0.978210i	$-0.566570\pi$
$653$	−2.95452e9	−0.415231	−0.207616	+	0.978210i	$0.566570\pi$
$654$	0	0
$655$	−4.04904e9	−0.562999
$656$	−5.74404e8	−0.0794427
$657$	0	0
$658$	−8.30319e9	−1.13620
$659$	6.81330e9	0.927382	0.463691	−	0.885997i	$-0.346525\pi$
$659$	6.81330e9	0.927382	0.463691	+	0.885997i	$0.346525\pi$
$660$	0	0
$661$	−9.65769e9	−1.30067	−0.650336	−	0.759646i	$-0.725372\pi$
$661$	−9.65769e9	−1.30067	−0.650336	+	0.759646i	$0.725372\pi$
$662$	4.50860e9	0.604003
$663$	0	0
$664$	7.87603e9	1.04404
$665$	−4.88173e8	−0.0643722
$666$	0	0
$667$	7.83690e9	1.02259
$668$	−3.73332e9	−0.484594
$669$	0	0
$670$	2.16391e9	0.277957
$671$	4.57180e9	0.584196
$672$	0	0
$673$	−5.74382e9	−0.726354	−0.363177	−	0.931720i	$-0.618308\pi$
$673$	−5.74382e9	−0.726354	−0.363177	+	0.931720i	$0.618308\pi$
$674$	1.56275e9	0.196599
$675$	0	0
$676$	−7.60072e9	−0.946327
$677$	6.39314e9	0.791870	0.395935	−	0.918279i	$-0.370421\pi$
$677$	6.39314e9	0.791870	0.395935	+	0.918279i	$0.370421\pi$
$678$	0	0
$679$	−1.42772e10	−1.75025
$680$	−4.39719e9	−0.536283
$681$	0	0
$682$	4.12880e9	0.498400
$683$	1.10711e10	1.32959	0.664794	−	0.747027i	$-0.268519\pi$
$683$	1.10711e10	1.32959	0.664794	+	0.747027i	$0.268519\pi$
$684$	0	0
$685$	−6.07985e9	−0.722729
$686$	−1.44320e9	−0.170684
$687$	0	0
$688$	−1.98427e8	−0.0232296
$689$	5.66356e9	0.659663
$690$	0	0
$691$	1.01541e10	1.17077	0.585383	−	0.810757i	$-0.300944\pi$
$691$	1.01541e10	1.17077	0.585383	+	0.810757i	$0.300944\pi$
$692$	8.67236e9	0.994869
$693$	0	0
$694$	−2.72871e9	−0.309884
$695$	−7.37965e9	−0.833852
$696$	0	0
$697$	3.31906e9	0.371279
$698$	−1.82246e9	−0.202845
$699$	0	0
$700$	7.37683e9	0.812880
$701$	−6.42013e9	−0.703933	−0.351966	−	0.936013i	$-0.614487\pi$
$701$	−6.42013e9	−0.703933	−0.351966	+	0.936013i	$0.614487\pi$
$702$	0	0
$703$	−1.71366e8	−0.0186029
$704$	2.82341e9	0.304979
$705$	0	0
$706$	−6.65794e9	−0.712071
$707$	1.60025e10	1.70302
$708$	0	0
$709$	−1.49237e10	−1.57259	−0.786293	−	0.617854i	$-0.788002\pi$
$709$	−1.49237e10	−1.57259	−0.786293	+	0.617854i	$0.788002\pi$
$710$	3.43014e9	0.359673
$711$	0	0
$712$	1.83676e9	0.190709
$713$	4.20560e9	0.434525
$714$	0	0
$715$	−9.18326e9	−0.939562
$716$	1.09800e9	0.111791
$717$	0	0
$718$	−1.86293e9	−0.187828
$719$	3.46295e9	0.347452	0.173726	−	0.984794i	$-0.444419\pi$
$719$	3.46295e9	0.347452	0.173726	+	0.984794i	$0.444419\pi$
$720$	0	0
$721$	3.09376e9	0.307406
$722$	−4.99656e9	−0.494073
$723$	0	0
$724$	8.87195e9	0.868828
$725$	−1.33430e10	−1.30038
$726$	0	0
$727$	−1.19482e10	−1.15327	−0.576637	−	0.817000i	$-0.695635\pi$
$727$	−1.19482e10	−1.15327	−0.576637	+	0.817000i	$0.695635\pi$
$728$	−1.81044e10	−1.73910
$729$	0	0
$730$	−3.39510e9	−0.323015
$731$	1.14656e9	0.108564
$732$	0	0
$733$	−4.90087e9	−0.459631	−0.229815	−	0.973234i	$-0.573812\pi$
$733$	−4.90087e9	−0.459631	−0.229815	+	0.973234i	$0.573812\pi$
$734$	−3.94071e9	−0.367823
$735$	0	0
$736$	7.21258e9	0.666835
$737$	−2.11767e10	−1.94859
$738$	0	0
$739$	−1.16073e10	−1.05797	−0.528986	−	0.848631i	$-0.677428\pi$
$739$	−1.16073e10	−1.05797	−0.528986	+	0.848631i	$0.677428\pi$
$740$	−5.60397e8	−0.0508375
$741$	0	0
$742$	3.22490e9	0.289803
$743$	1.83926e10	1.64506	0.822531	−	0.568720i	$-0.192561\pi$
$743$	1.83926e10	1.64506	0.822531	+	0.568720i	$0.192561\pi$
$744$	0	0
$745$	−5.71445e8	−0.0506323
$746$	5.93617e9	0.523504
$747$	0	0
$748$	1.84315e10	1.61030
$749$	5.41897e9	0.471227
$750$	0	0
$751$	−1.54442e10	−1.33054	−0.665268	−	0.746604i	$-0.731683\pi$
$751$	−1.54442e10	−1.33054	−0.665268	+	0.746604i	$0.731683\pi$
$752$	−6.22663e9	−0.533938
$753$	0	0
$754$	1.40261e10	1.19162
$755$	−9.04180e9	−0.764611
$756$	0	0
$757$	−1.95008e10	−1.63387	−0.816933	−	0.576732i	$-0.804328\pi$
$757$	−1.95008e10	−1.63387	−0.816933	+	0.576732i	$0.804328\pi$
$758$	5.13111e9	0.427926
$759$	0	0
$760$	5.17059e8	0.0427260
$761$	9.37201e9	0.770880	0.385440	−	0.922733i	$-0.374050\pi$
$761$	9.37201e9	0.770880	0.385440	+	0.922733i	$0.374050\pi$
$762$	0	0
$763$	−3.74405e8	−0.0305144
$764$	2.66916e9	0.216544
$765$	0	0
$766$	−6.40231e9	−0.514679
$767$	2.44741e9	0.195850
$768$	0	0
$769$	−1.02340e10	−0.811528	−0.405764	−	0.913978i	$-0.632994\pi$
$769$	−1.02340e10	−0.811528	−0.405764	+	0.913978i	$0.632994\pi$
$770$	−5.22906e9	−0.412768
$771$	0	0
$772$	3.38220e9	0.264569
$773$	−2.44487e10	−1.90383	−0.951913	−	0.306367i	$-0.900887\pi$
$773$	−2.44487e10	−1.90383	−0.951913	+	0.306367i	$0.900887\pi$
$774$	0	0
$775$	−7.16040e9	−0.552562
$776$	1.51220e10	1.16170
$777$	0	0
$778$	5.49546e9	0.418384
$779$	−3.90283e8	−0.0295800
$780$	0	0
$781$	−3.35684e10	−2.52146
$782$	−6.28388e9	−0.469899
$783$	0	0
$784$	3.10829e9	0.230364
$785$	5.86148e8	0.0432478
$786$	0	0
$787$	−3.61895e8	−0.0264649	−0.0132325	−	0.999912i	$-0.504212\pi$
$787$	−3.61895e8	−0.0264649	−0.0132325	+	0.999912i	$0.504212\pi$
$788$	1.68882e10	1.22954
$789$	0	0
$790$	−4.68502e9	−0.338078
$791$	−5.95640e9	−0.427924
$792$	0	0
$793$	8.33458e9	0.593510
$794$	−7.78325e9	−0.551810
$795$	0	0
$796$	−1.86828e10	−1.31294
$797$	5.22352e9	0.365476	0.182738	−	0.983162i	$-0.441504\pi$
$797$	5.22352e9	0.365476	0.182738	+	0.983162i	$0.441504\pi$
$798$	0	0
$799$	3.59791e10	2.49538
$800$	−1.22800e10	−0.847978
$801$	0	0
$802$	−3.24262e9	−0.221966
$803$	3.32254e10	2.26447
$804$	0	0
$805$	−5.32634e9	−0.359868
$806$	7.52697e9	0.506346
$807$	0	0
$808$	−1.69493e10	−1.13035
$809$	2.37703e10	1.57839	0.789194	−	0.614144i	$-0.210498\pi$
$809$	2.37703e10	1.57839	0.789194	+	0.614144i	$0.210498\pi$
$810$	0	0
$811$	1.74347e10	1.14774	0.573868	−	0.818948i	$-0.305442\pi$
$811$	1.74347e10	1.14774	0.573868	+	0.818948i	$0.305442\pi$
$812$	−2.38617e10	−1.56407
$813$	0	0
$814$	−1.83559e9	−0.119286
$815$	−2.12880e9	−0.137747
$816$	0	0
$817$	−1.34823e8	−0.00864940
$818$	6.08550e8	0.0388741
$819$	0	0
$820$	−1.27629e9	−0.0808353
$821$	2.87309e9	0.181196	0.0905978	−	0.995888i	$-0.471122\pi$
$821$	2.87309e9	0.181196	0.0905978	+	0.995888i	$0.471122\pi$
$822$	0	0
$823$	6.48563e9	0.405558	0.202779	−	0.979225i	$-0.435003\pi$
$823$	6.48563e9	0.405558	0.202779	+	0.979225i	$0.435003\pi$
$824$	−3.27681e9	−0.204036
$825$	0	0
$826$	1.39359e9	0.0860406
$827$	1.45803e10	0.896388	0.448194	−	0.893936i	$-0.352067\pi$
$827$	1.45803e10	0.896388	0.448194	+	0.893936i	$0.352067\pi$
$828$	0	0
$829$	2.97207e9	0.181183	0.0905916	−	0.995888i	$-0.471124\pi$
$829$	2.97207e9	0.181183	0.0905916	+	0.995888i	$0.471124\pi$
$830$	4.14709e9	0.251750
$831$	0	0
$832$	5.14720e9	0.309841
$833$	−1.79605e10	−1.07662
$834$	0	0
$835$	−4.58948e9	−0.272810
$836$	−2.16733e9	−0.128293
$837$	0	0
$838$	−2.81307e9	−0.165130
$839$	1.23558e10	0.722276	0.361138	−	0.932512i	$-0.382388\pi$
$839$	1.23558e10	0.722276	0.361138	+	0.932512i	$0.382388\pi$
$840$	0	0
$841$	2.59104e10	1.50206
$842$	1.20830e10	0.697562
$843$	0	0
$844$	−9.04564e9	−0.517894
$845$	−9.34377e9	−0.532750
$846$	0	0
$847$	2.78341e10	1.57393
$848$	2.41838e9	0.136188
$849$	0	0
$850$	1.06988e10	0.597545
$851$	−1.86973e9	−0.103998
$852$	0	0
$853$	−3.00088e9	−0.165549	−0.0827746	−	0.996568i	$-0.526378\pi$
$853$	−3.00088e9	−0.165549	−0.0827746	+	0.996568i	$0.526378\pi$
$854$	4.74582e9	0.260741
$855$	0	0
$856$	−5.73961e9	−0.312769
$857$	−6.68872e9	−0.363003	−0.181502	−	0.983391i	$-0.558096\pi$
$857$	−6.68872e9	−0.363003	−0.181502	+	0.983391i	$0.558096\pi$
$858$	0	0
$859$	9.56843e9	0.515068	0.257534	−	0.966269i	$-0.417090\pi$
$859$	9.56843e9	0.515068	0.257534	+	0.966269i	$0.417090\pi$
$860$	−4.40893e8	−0.0236368
$861$	0	0
$862$	1.56113e9	0.0830161
$863$	−3.10651e10	−1.64526	−0.822632	−	0.568575i	$-0.807495\pi$
$863$	−3.10651e10	−1.64526	−0.822632	+	0.568575i	$0.807495\pi$
$864$	0	0
$865$	1.06612e10	0.560078
$866$	8.09971e9	0.423796
$867$	0	0
$868$	−1.28052e10	−0.664610
$869$	4.58490e10	2.37006
$870$	0	0
$871$	−3.86060e10	−1.97966
$872$	3.96558e8	0.0202534
$873$	0	0
$874$	7.38911e8	0.0374371
$875$	2.00996e10	1.01428
$876$	0	0
$877$	−3.23289e10	−1.61843	−0.809213	−	0.587515i	$-0.800106\pi$
$877$	−3.23289e10	−1.61843	−0.809213	+	0.587515i	$0.800106\pi$
$878$	−1.30191e10	−0.649159
$879$	0	0
$880$	−3.92132e9	−0.193974
$881$	−1.05719e10	−0.520881	−0.260440	−	0.965490i	$-0.583868\pi$
$881$	−1.05719e10	−0.520881	−0.260440	+	0.965490i	$0.583868\pi$
$882$	0	0
$883$	1.62742e10	0.795493	0.397746	−	0.917495i	$-0.369792\pi$
$883$	1.62742e10	0.795493	0.397746	+	0.917495i	$0.369792\pi$
$884$	3.36015e10	1.63597
$885$	0	0
$886$	3.24481e9	0.156737
$887$	5.54686e9	0.266879	0.133440	−	0.991057i	$-0.457398\pi$
$887$	5.54686e9	0.266879	0.133440	+	0.991057i	$0.457398\pi$
$888$	0	0
$889$	5.20171e10	2.48308
$890$	9.67136e8	0.0459857
$891$	0	0
$892$	2.91734e10	1.37629
$893$	−4.23072e9	−0.198808
$894$	0	0
$895$	1.34981e9	0.0629348
$896$	−2.63803e10	−1.22519
$897$	0	0
$898$	1.42552e10	0.656909
$899$	2.31616e10	1.06319
$900$	0	0
$901$	−1.39740e10	−0.636481
$902$	−4.18051e9	−0.189673
$903$	0	0
$904$	6.30884e9	0.284027
$905$	1.09065e10	0.489121
$906$	0	0
$907$	2.33401e10	1.03867	0.519335	−	0.854571i	$-0.326180\pi$
$907$	2.33401e10	1.03867	0.519335	+	0.854571i	$0.326180\pi$
$908$	1.48200e10	0.656974
$909$	0	0
$910$	−9.53280e9	−0.419349
$911$	−1.77936e10	−0.779740	−0.389870	−	0.920870i	$-0.627480\pi$
$911$	−1.77936e10	−0.779740	−0.389870	+	0.920870i	$0.627480\pi$
$912$	0	0
$913$	−4.05846e10	−1.76487
$914$	−5.27851e9	−0.228665
$915$	0	0
$916$	−1.13193e10	−0.486613
$917$	4.11334e10	1.76158
$918$	0	0
$919$	2.41659e10	1.02706	0.513532	−	0.858070i	$-0.328337\pi$
$919$	2.41659e10	1.02706	0.513532	+	0.858070i	$0.328337\pi$
$920$	5.64150e9	0.238856
$921$	0	0
$922$	1.20319e9	0.0505563
$923$	−6.11965e10	−2.56166
$924$	0	0
$925$	3.18338e9	0.132249
$926$	1.78194e10	0.737489
$927$	0	0
$928$	3.97220e10	1.63160
$929$	2.78712e10	1.14052	0.570258	−	0.821466i	$-0.306843\pi$
$929$	2.78712e10	1.14052	0.570258	+	0.821466i	$0.306843\pi$
$930$	0	0
$931$	2.11195e9	0.0857747
$932$	−6.54078e9	−0.264651
$933$	0	0
$934$	−2.19647e10	−0.882088
$935$	2.26584e10	0.906543
$936$	0	0
$937$	1.83113e10	0.727162	0.363581	−	0.931563i	$-0.381554\pi$
$937$	1.83113e10	0.727162	0.363581	+	0.931563i	$0.381554\pi$
$938$	−2.19827e10	−0.869704
$939$	0	0
$940$	−1.38352e10	−0.543297
$941$	−3.20558e9	−0.125413	−0.0627066	−	0.998032i	$-0.519973\pi$
$941$	−3.20558e9	−0.125413	−0.0627066	+	0.998032i	$0.519973\pi$
$942$	0	0
$943$	−4.25828e9	−0.165365
$944$	1.04506e9	0.0404333
$945$	0	0
$946$	−1.44415e9	−0.0554618
$947$	−1.13660e10	−0.434895	−0.217448	−	0.976072i	$-0.569773\pi$
$947$	−1.13660e10	−0.434895	−0.217448	+	0.976072i	$0.569773\pi$
$948$	0	0
$949$	6.05713e10	2.30057
$950$	−1.25806e9	−0.0476067
$951$	0	0
$952$	4.46701e10	1.67798
$953$	2.26241e10	0.846732	0.423366	−	0.905959i	$-0.360848\pi$
$953$	2.26241e10	0.846732	0.423366	+	0.905959i	$0.360848\pi$
$954$	0	0
$955$	3.28127e9	0.121907
$956$	−7.68193e9	−0.284359
$957$	0	0
$958$	2.20004e10	0.808447
$959$	6.17639e10	2.26136
$960$	0	0
$961$	−1.50831e10	−0.548226
$962$	−3.34635e9	−0.121188
$963$	0	0
$964$	−9.06176e9	−0.325794
$965$	4.15784e9	0.148944
$966$	0	0
$967$	4.77814e10	1.69928	0.849642	−	0.527359i	$-0.176818\pi$
$967$	4.77814e10	1.69928	0.849642	+	0.527359i	$0.176818\pi$
$968$	−2.94810e10	−1.04467
$969$	0	0
$970$	7.96242e9	0.280120
$971$	−2.36126e9	−0.0827707	−0.0413854	−	0.999143i	$-0.513177\pi$
$971$	−2.36126e9	−0.0827707	−0.0413854	+	0.999143i	$0.513177\pi$
$972$	0	0
$973$	7.49683e10	2.60905
$974$	−1.01895e10	−0.353342
$975$	0	0
$976$	3.55893e9	0.122531
$977$	2.09178e10	0.717604	0.358802	−	0.933414i	$-0.383185\pi$
$977$	2.09178e10	0.717604	0.358802	+	0.933414i	$0.383185\pi$
$978$	0	0
$979$	−9.46467e9	−0.322379
$980$	6.90643e9	0.234403
$981$	0	0
$982$	7.05538e9	0.237755
$983$	5.00358e9	0.168013	0.0840066	−	0.996465i	$-0.473228\pi$
$983$	5.00358e9	0.168013	0.0840066	+	0.996465i	$0.473228\pi$
$984$	0	0
$985$	2.07612e10	0.692190
$986$	−3.46073e10	−1.14974
$987$	0	0
$988$	−3.95114e9	−0.130339
$989$	−1.47102e9	−0.0483538
$990$	0	0
$991$	2.88517e10	0.941702	0.470851	−	0.882213i	$-0.343947\pi$
$991$	2.88517e10	0.941702	0.470851	+	0.882213i	$0.343947\pi$
$992$	2.13165e10	0.693306
$993$	0	0
$994$	−3.48461e10	−1.12539
$995$	−2.29673e10	−0.739144
$996$	0	0
$997$	−4.64145e10	−1.48327	−0.741636	−	0.670802i	$-0.765950\pi$
$997$	−4.64145e10	−1.48327	−0.741636	+	0.670802i	$0.765950\pi$
$998$	1.71543e10	0.546282
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.11		17
3.2	odd	2		177.8.a.c.1.7	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.7	✓	17	3.2	odd	2
531.8.a.c.1.11		17	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q+5.66556 q^{2} -95.9014 q^{4} -117.894 q^{5} +1197.66 q^{7} -1268.53 q^{8} +O(q^{10})\)	\(q+5.66556 q^{2} -95.9014 q^{4} -117.894 q^{5} +1197.66 q^{7} -1268.53 q^{8} -667.937 q^{10} +6536.63 q^{11} +11916.5 q^{13} +6785.43 q^{14} +5088.45 q^{16} -29402.4 q^{17} +3457.38 q^{19} +11306.2 q^{20} +37033.7 q^{22} +37722.6 q^{23} -64225.9 q^{25} +67514.0 q^{26} -114857. q^{28} +207751. q^{29} +111488. q^{31} +191200. q^{32} -166581. q^{34} -141197. q^{35} -49565.3 q^{37} +19588.0 q^{38} +149552. q^{40} -112884. q^{41} -38995.6 q^{43} -626872. q^{44} +213720. q^{46} -1.22368e6 q^{47} +610852. q^{49} -363876. q^{50} -1.14281e6 q^{52} +475269. q^{53} -770631. q^{55} -1.51927e6 q^{56} +1.17702e6 q^{58} +205379. q^{59} +699413. q^{61} +631640. q^{62} +431937. q^{64} -1.40489e6 q^{65} -3.23969e6 q^{67} +2.81973e6 q^{68} -799963. q^{70} -5.13542e6 q^{71} +5.08296e6 q^{73} -280816. q^{74} -331568. q^{76} +7.82867e6 q^{77} +7.01416e6 q^{79} -599899. q^{80} -639551. q^{82} -6.20880e6 q^{83} +3.46637e6 q^{85} -220932. q^{86} -8.29189e6 q^{88} -1.44794e6 q^{89} +1.42720e7 q^{91} -3.61765e6 q^{92} -6.93283e6 q^{94} -407605. q^{95} -1.19209e7 q^{97} +3.46082e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more