LMFDB - Embedded newform 531.8.a.a.1.8

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5 x^{13} - 1169 x^{12} + 5113 x^{11} + 509966 x^{10} - 1844082 x^{9} - 104172650 x^{8} + \cdots - 143083653176 $ x^14 - 5x^13 - 1169x^12 + 5113x^11 + 509966x^10 - 1844082x^9 - 104172650x^8 + 278779842x^7 + 10354430077x^6 - 15604625737x^5 - 463520315741x^4 + 183357846869x^3 + 6367098630660x^2 - 2745299080272*x - 143083653176
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	no (minimal twist has level 59)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.0470033$ 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)

$f(q)$	$=$	$q+1.04700 q^{2} -126.904 q^{4} +45.6259 q^{5} -399.043 q^{7} -266.885 q^{8} +O(q^{10})$	\(q+1.04700 q^{2} -126.904 q^{4} +45.6259 q^{5} -399.043 q^{7} -266.885 q^{8} +47.7705 q^{10} +7630.37 q^{11} -10793.2 q^{13} -417.799 q^{14} +15964.3 q^{16} -16279.6 q^{17} -1165.90 q^{19} -5790.10 q^{20} +7989.02 q^{22} +48614.1 q^{23} -76043.3 q^{25} -11300.5 q^{26} +50640.0 q^{28} -11854.8 q^{29} -62996.4 q^{31} +50875.9 q^{32} -17044.8 q^{34} -18206.7 q^{35} +79351.5 q^{37} -1220.70 q^{38} -12176.9 q^{40} +634420. q^{41} +592064. q^{43} -968323. q^{44} +50899.2 q^{46} +18247.6 q^{47} -664308. q^{49} -79617.6 q^{50} +1.36969e6 q^{52} +582919. q^{53} +348143. q^{55} +106499. q^{56} -12412.0 q^{58} -205379. q^{59} +3.18008e6 q^{61} -65957.5 q^{62} -1.99016e6 q^{64} -492448. q^{65} +2.62410e6 q^{67} +2.06594e6 q^{68} -19062.5 q^{70} -835207. q^{71} +793009. q^{73} +83081.3 q^{74} +147957. q^{76} -3.04484e6 q^{77} +1.48627e6 q^{79} +728384. q^{80} +664239. q^{82} -7.81392e6 q^{83} -742771. q^{85} +619893. q^{86} -2.03643e6 q^{88} -775444. q^{89} +4.30693e6 q^{91} -6.16932e6 q^{92} +19105.3 q^{94} -53195.1 q^{95} +7.61284e6 q^{97} -695533. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 9 q^{2} + 575 q^{4} + 430 q^{5} - 2390 q^{7} + 2463 q^{8}+O(q^{10}) $ 14 * q + 9 * q^2 + 575 * q^4 + 430 * q^5 - 2390 * q^7 + 2463 * q^8	\( 14 q + 9 q^{2} + 575 q^{4} + 430 q^{5} - 2390 q^{7} + 2463 q^{8} - 5362 q^{10} + 5030 q^{11} - 24364 q^{13} + 12717 q^{14} + 33859 q^{16} - 14504 q^{17} - 80234 q^{19} + 190220 q^{20} - 266687 q^{22} + 113272 q^{23} - 62580 q^{25} + 386729 q^{26} - 617413 q^{28} + 490250 q^{29} - 379844 q^{31} + 700263 q^{32} - 709263 q^{34} + 611196 q^{35} - 1203748 q^{37} + 340 q^{38} - 927130 q^{40} + 681860 q^{41} - 967090 q^{43} - 218679 q^{44} - 136632 q^{46} - 287456 q^{47} + 341754 q^{49} - 2153697 q^{50} + 1661397 q^{52} + 1227618 q^{53} + 975320 q^{55} - 4449921 q^{56} - 265424 q^{58} - 2875306 q^{59} - 4711840 q^{61} - 17057148 q^{62} + 2117595 q^{64} - 4072956 q^{65} + 7298936 q^{67} - 13001951 q^{68} + 12397514 q^{70} - 5657790 q^{71} + 4750028 q^{73} - 1875491 q^{74} + 3128138 q^{76} + 8640944 q^{77} - 17385506 q^{79} - 20096996 q^{80} - 941109 q^{82} + 15067470 q^{83} - 28577148 q^{85} - 3286963 q^{86} - 20655117 q^{88} + 15451868 q^{89} - 24287002 q^{91} - 13921944 q^{92} - 12765942 q^{94} + 43655474 q^{95} + 2400932 q^{97} - 19642950 q^{98}+O(q^{100}) \) 14 * q + 9 * q^2 + 575 * q^4 + 430 * q^5 - 2390 * q^7 + 2463 * q^8 - 5362 * q^10 + 5030 * q^11 - 24364 * q^13 + 12717 * q^14 + 33859 * q^16 - 14504 * q^17 - 80234 * q^19 + 190220 * q^20 - 266687 * q^22 + 113272 * q^23 - 62580 * q^25 + 386729 * q^26 - 617413 * q^28 + 490250 * q^29 - 379844 * q^31 + 700263 * q^32 - 709263 * q^34 + 611196 * q^35 - 1203748 * q^37 + 340 * q^38 - 927130 * q^40 + 681860 * q^41 - 967090 * q^43 - 218679 * q^44 - 136632 * q^46 - 287456 * q^47 + 341754 * q^49 - 2153697 * q^50 + 1661397 * q^52 + 1227618 * q^53 + 975320 * q^55 - 4449921 * q^56 - 265424 * q^58 - 2875306 * q^59 - 4711840 * q^61 - 17057148 * q^62 + 2117595 * q^64 - 4072956 * q^65 + 7298936 * q^67 - 13001951 * q^68 + 12397514 * q^70 - 5657790 * q^71 + 4750028 * q^73 - 1875491 * q^74 + 3128138 * q^76 + 8640944 * q^77 - 17385506 * q^79 - 20096996 * q^80 - 941109 * q^82 + 15067470 * q^83 - 28577148 * q^85 - 3286963 * q^86 - 20655117 * q^88 + 15451868 * q^89 - 24287002 * q^91 - 13921944 * q^92 - 12765942 * q^94 + 43655474 * q^95 + 2400932 * q^97 - 19642950 * 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 $

$2$	1.04700	0.0925429	0.0462714	−	0.998929i	$-0.485266\pi$
$2$	1.04700	0.0925429	0.0462714	+	0.998929i	$0.485266\pi$
$3$	0	0
$3$	0	0
$4$	−126.904	−0.991436
$5$	45.6259	0.163236	0.0816182	−	0.996664i	$-0.473991\pi$
$5$	45.6259	0.163236	0.0816182	+	0.996664i	$0.473991\pi$
$6$	0	0
$7$	−399.043	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$7$	−399.043	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$8$	−266.885	−0.184293
$9$	0	0
$10$	47.7705	0.0151064
$11$	7630.37	1.72851	0.864254	−	0.503056i	$-0.167791\pi$
$11$	7630.37	1.72851	0.864254	+	0.503056i	$0.167791\pi$
$12$	0	0
$13$	−10793.2	−1.36253	−0.681266	−	0.732036i	$-0.738570\pi$
$13$	−10793.2	−1.36253	−0.681266	+	0.732036i	$0.738570\pi$
$14$	−417.799	−0.0406930
$15$	0	0
$16$	15964.3	0.974381
$17$	−16279.6	−0.803660	−0.401830	−	0.915714i	$-0.631626\pi$
$17$	−16279.6	−0.803660	−0.401830	+	0.915714i	$0.631626\pi$
$18$	0	0
$19$	−1165.90	−0.0389962	−0.0194981	−	0.999810i	$-0.506207\pi$
$19$	−1165.90	−0.0389962	−0.0194981	+	0.999810i	$0.506207\pi$
$20$	−5790.10	−0.161838
$21$	0	0
$22$	7989.02	0.159961
$23$	48614.1	0.833135	0.416567	−	0.909105i	$-0.363233\pi$
$23$	48614.1	0.833135	0.416567	+	0.909105i	$0.363233\pi$
$24$	0	0
$25$	−76043.3	−0.973354
$26$	−11300.5	−0.126093
$27$	0	0
$28$	50640.0	0.435954
$29$	−11854.8	−0.0902610	−0.0451305	−	0.998981i	$-0.514370\pi$
$29$	−11854.8	−0.0902610	−0.0451305	+	0.998981i	$0.514370\pi$
$30$	0	0
$31$	−62996.4	−0.379796	−0.189898	−	0.981804i	$-0.560816\pi$
$31$	−62996.4	−0.379796	−0.189898	+	0.981804i	$0.560816\pi$
$32$	50875.9	0.274465
$33$	0	0
$34$	−17044.8	−0.0743730
$35$	−18206.7	−0.0717783
$36$	0	0
$37$	79351.5	0.257543	0.128771	−	0.991674i	$-0.458897\pi$
$37$	79351.5	0.257543	0.128771	+	0.991674i	$0.458897\pi$
$38$	−1220.70	−0.00360882
$39$	0	0
$40$	−12176.9	−0.0300834
$41$	634420.	1.43758	0.718792	−	0.695225i	$-0.244695\pi$
$41$	634420.	1.43758	0.718792	+	0.695225i	$0.244695\pi$
$42$	0	0
$43$	592064.	1.13561	0.567805	−	0.823163i	$-0.307793\pi$
$43$	592064.	1.13561	0.567805	+	0.823163i	$0.307793\pi$
$44$	−968323.	−1.71370
$45$	0	0
$46$	50899.2	0.0771007
$47$	18247.6	0.0256368	0.0128184	−	0.999918i	$-0.495920\pi$
$47$	18247.6	0.0256368	0.0128184	+	0.999918i	$0.495920\pi$
$48$	0	0
$49$	−664308.	−0.806646
$50$	−79617.6	−0.0900770
$51$	0	0
$52$	1.36969e6	1.35086
$53$	582919.	0.537827	0.268913	−	0.963164i	$-0.413335\pi$
$53$	582919.	0.537827	0.268913	+	0.963164i	$0.413335\pi$
$54$	0	0
$55$	348143.	0.282155
$56$	106499.	0.0810374
$57$	0	0
$58$	−12412.0	−0.00835302
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	3.18008e6	1.79384	0.896921	−	0.442191i	$-0.145799\pi$
$61$	3.18008e6	1.79384	0.896921	+	0.442191i	$0.145799\pi$
$62$	−65957.5	−0.0351474
$63$	0	0
$64$	−1.99016e6	−0.948981
$65$	−492448.	−0.222415
$66$	0	0
$67$	2.62410e6	1.06591	0.532953	−	0.846145i	$-0.321082\pi$
$67$	2.62410e6	1.06591	0.532953	+	0.846145i	$0.321082\pi$
$68$	2.06594e6	0.796777
$69$	0	0
$70$	−19062.5	−0.00664257
$71$	−835207.	−0.276943	−0.138471	−	0.990366i	$-0.544219\pi$
$71$	−835207.	−0.276943	−0.138471	+	0.990366i	$0.544219\pi$
$72$	0	0
$73$	793009.	0.238588	0.119294	−	0.992859i	$-0.461937\pi$
$73$	793009.	0.238588	0.119294	+	0.992859i	$0.461937\pi$
$74$	83081.3	0.0238337
$75$	0	0
$76$	147957.	0.0386622
$77$	−3.04484e6	−0.760059
$78$	0	0
$79$	1.48627e6	0.339158	0.169579	−	0.985517i	$-0.445759\pi$
$79$	1.48627e6	0.339158	0.169579	+	0.985517i	$0.445759\pi$
$80$	728384.	0.159054
$81$	0	0
$82$	664239.	0.133038
$83$	−7.81392e6	−1.50001	−0.750007	−	0.661430i	$-0.769950\pi$
$83$	−7.81392e6	−1.50001	−0.750007	+	0.661430i	$0.769950\pi$
$84$	0	0
$85$	−742771.	−0.131186
$86$	619893.	0.105093
$87$	0	0
$88$	−2.03643e6	−0.318552
$89$	−775444.	−0.116596	−0.0582982	−	0.998299i	$-0.518567\pi$
$89$	−775444.	−0.116596	−0.0582982	+	0.998299i	$0.518567\pi$
$90$	0	0
$91$	4.30693e6	0.599133
$92$	−6.16932e6	−0.825999
$93$	0	0
$94$	19105.3	0.00237250
$95$	−53195.1	−0.00636560
$96$	0	0
$97$	7.61284e6	0.846926	0.423463	−	0.905913i	$-0.360814\pi$
$97$	7.61284e6	0.846926	0.423463	+	0.905913i	$0.360814\pi$
$98$	−695533.	−0.0746494
$99$	0	0
$100$	9.65018e6	0.965018
$101$	−4.62228e6	−0.446407	−0.223204	−	0.974772i	$-0.571651\pi$
$101$	−4.62228e6	−0.446407	−0.223204	+	0.974772i	$0.571651\pi$
$102$	0	0
$103$	−1.97679e7	−1.78250	−0.891250	−	0.453513i	$-0.850171\pi$
$103$	−1.97679e7	−1.78250	−0.891250	+	0.453513i	$0.850171\pi$
$104$	2.88053e6	0.251106
$105$	0	0
$106$	610318.	0.0497721
$107$	1.87902e7	1.48282	0.741408	−	0.671054i	$-0.234158\pi$
$107$	1.87902e7	1.48282	0.741408	+	0.671054i	$0.234158\pi$
$108$	0	0
$109$	−1.79499e7	−1.32761	−0.663803	−	0.747907i	$-0.731059\pi$
$109$	−1.79499e7	−1.32761	−0.663803	+	0.747907i	$0.731059\pi$
$110$	364507.	0.0261115
$111$	0	0
$112$	−6.37042e6	−0.428455
$113$	−2.59528e7	−1.69204	−0.846019	−	0.533153i	$-0.821007\pi$
$113$	−2.59528e7	−1.69204	−0.846019	+	0.533153i	$0.821007\pi$
$114$	0	0
$115$	2.21807e6	0.135998
$116$	1.50442e6	0.0894880
$117$	0	0
$118$	−215032.	−0.0120481
$119$	6.49625e6	0.353385
$120$	0	0
$121$	3.87354e7	1.98774
$122$	3.32956e6	0.166007
$123$	0	0
$124$	7.99449e6	0.376543
$125$	−7.03407e6	−0.322123
$126$	0	0
$127$	−2.93481e7	−1.27136	−0.635678	−	0.771954i	$-0.719279\pi$
$127$	−2.93481e7	−1.27136	−0.635678	+	0.771954i	$0.719279\pi$
$128$	−8.59582e6	−0.362287
$129$	0	0
$130$	−515595.	−0.0205829
$131$	3.53905e6	0.137543	0.0687714	−	0.997632i	$-0.478092\pi$
$131$	3.53905e6	0.137543	0.0687714	+	0.997632i	$0.478092\pi$
$132$	0	0
$133$	465243.	0.0171474
$134$	2.74744e6	0.0986420
$135$	0	0
$136$	4.34478e6	0.148109
$137$	3.69569e7	1.22793	0.613966	−	0.789333i	$-0.289573\pi$
$137$	3.69569e7	1.22793	0.613966	+	0.789333i	$0.289573\pi$
$138$	0	0
$139$	2.92929e7	0.925148	0.462574	−	0.886581i	$-0.346926\pi$
$139$	2.92929e7	0.925148	0.462574	+	0.886581i	$0.346926\pi$
$140$	2.31050e6	0.0711635
$141$	0	0
$142$	−874465.	−0.0256291
$143$	−8.23558e7	−2.35515
$144$	0	0
$145$	−540885.	−0.0147339
$146$	830283.	0.0220796
$147$	0	0
$148$	−1.00700e7	−0.255337
$149$	3.15472e7	0.781284	0.390642	−	0.920543i	$-0.372253\pi$
$149$	3.15472e7	0.781284	0.390642	+	0.920543i	$0.372253\pi$
$150$	0	0
$151$	−7.10068e7	−1.67834	−0.839171	−	0.543868i	$-0.816959\pi$
$151$	−7.10068e7	−1.67834	−0.839171	+	0.543868i	$0.816959\pi$
$152$	311160.	0.00718674
$153$	0	0
$154$	−3.18796e6	−0.0703381
$155$	−2.87427e6	−0.0619965
$156$	0	0
$157$	−3.82152e7	−0.788111	−0.394056	−	0.919087i	$-0.628928\pi$
$157$	−3.82152e7	−0.788111	−0.394056	+	0.919087i	$0.628928\pi$
$158$	1.55613e6	0.0313866
$159$	0	0
$160$	2.32126e6	0.0448027
$161$	−1.93991e7	−0.366346
$162$	0	0
$163$	−5.03333e7	−0.910329	−0.455165	−	0.890407i	$-0.650420\pi$
$163$	−5.03333e7	−0.910329	−0.455165	+	0.890407i	$0.650420\pi$
$164$	−8.05103e7	−1.42527
$165$	0	0
$166$	−8.18120e6	−0.138816
$167$	5.50022e7	0.913845	0.456923	−	0.889506i	$-0.348952\pi$
$167$	5.50022e7	0.913845	0.456923	+	0.889506i	$0.348952\pi$
$168$	0	0
$169$	5.37438e7	0.856495
$170$	−777684.	−0.0121404
$171$	0	0
$172$	−7.51351e7	−1.12588
$173$	−4.15378e7	−0.609932	−0.304966	−	0.952363i	$-0.598645\pi$
$173$	−4.15378e7	−0.609932	−0.304966	+	0.952363i	$0.598645\pi$
$174$	0	0
$175$	3.03445e7	0.428003
$176$	1.21813e8	1.68422
$177$	0	0
$178$	−811892.	−0.0107902
$179$	−1.01372e8	−1.32109	−0.660544	−	0.750787i	$-0.729674\pi$
$179$	−1.01372e8	−1.32109	−0.660544	+	0.750787i	$0.729674\pi$
$180$	0	0
$181$	−1.02231e8	−1.28146	−0.640731	−	0.767765i	$-0.721369\pi$
$181$	−1.02231e8	−1.28146	−0.640731	+	0.767765i	$0.721369\pi$
$182$	4.50937e6	0.0554455
$183$	0	0
$184$	−1.29744e7	−0.153541
$185$	3.62049e6	0.0420403
$186$	0	0
$187$	−1.24219e8	−1.38913
$188$	−2.31569e6	−0.0254172
$189$	0	0
$190$	−55695.5	−0.000589091 0
$191$	−1.56413e8	−1.62426	−0.812130	−	0.583476i	$-0.801692\pi$
$191$	−1.56413e8	−1.62426	−0.812130	+	0.583476i	$0.801692\pi$
$192$	0	0
$193$	−1.15639e8	−1.15786	−0.578928	−	0.815378i	$-0.696529\pi$
$193$	−1.15639e8	−1.15786	−0.578928	+	0.815378i	$0.696529\pi$
$194$	7.97067e6	0.0783770
$195$	0	0
$196$	8.43032e7	0.799738
$197$	4.53901e7	0.422990	0.211495	−	0.977379i	$-0.432167\pi$
$197$	4.53901e7	0.422990	0.211495	+	0.977379i	$0.432167\pi$
$198$	0	0
$199$	−1.48637e8	−1.33703	−0.668516	−	0.743698i	$-0.733070\pi$
$199$	−1.48637e8	−1.33703	−0.668516	+	0.743698i	$0.733070\pi$
$200$	2.02948e7	0.179383
$201$	0	0
$202$	−4.83954e6	−0.0413118
$203$	4.73056e6	0.0396896
$204$	0	0
$205$	2.89460e7	0.234666
$206$	−2.06970e7	−0.164958
$207$	0	0
$208$	−1.72305e8	−1.32763
$209$	−8.89623e6	−0.0674053
$210$	0	0
$211$	5.88038e7	0.430940	0.215470	−	0.976510i	$-0.430872\pi$
$211$	5.88038e7	0.430940	0.215470	+	0.976510i	$0.430872\pi$
$212$	−7.39746e7	−0.533221
$213$	0	0
$214$	1.96734e7	0.137224
$215$	2.70135e7	0.185373
$216$	0	0
$217$	2.51383e7	0.167004
$218$	−1.87936e7	−0.122860
$219$	0	0
$220$	−4.41806e7	−0.279739
$221$	1.75708e8	1.09501
$222$	0	0
$223$	3.14766e6	0.0190073	0.00950366	−	0.999955i	$-0.496975\pi$
$223$	3.14766e6	0.0190073	0.00950366	+	0.999955i	$0.496975\pi$
$224$	−2.03017e7	−0.120688
$225$	0	0
$226$	−2.71727e7	−0.156586
$227$	3.35850e8	1.90570	0.952850	−	0.303443i	$-0.0981362\pi$
$227$	3.35850e8	1.90570	0.952850	+	0.303443i	$0.0981362\pi$
$228$	0	0
$229$	1.77524e8	0.976860	0.488430	−	0.872603i	$-0.337570\pi$
$229$	1.77524e8	0.976860	0.488430	+	0.872603i	$0.337570\pi$
$230$	2.32232e6	0.0125856
$231$	0	0
$232$	3.16386e6	0.0166345
$233$	1.83990e8	0.952901	0.476451	−	0.879201i	$-0.341923\pi$
$233$	1.83990e8	0.952901	0.476451	+	0.879201i	$0.341923\pi$
$234$	0	0
$235$	832565.	0.00418486
$236$	2.60634e7	0.129074
$237$	0	0
$238$	6.80159e6	0.0327033
$239$	7.80447e7	0.369786	0.184893	−	0.982759i	$-0.440806\pi$
$239$	7.80447e7	0.369786	0.184893	+	0.982759i	$0.440806\pi$
$240$	0	0
$241$	5.53125e7	0.254544	0.127272	−	0.991868i	$-0.459378\pi$
$241$	5.53125e7	0.254544	0.127272	+	0.991868i	$0.459378\pi$
$242$	4.05561e7	0.183951
$243$	0	0
$244$	−4.03565e8	−1.77848
$245$	−3.03097e7	−0.131674
$246$	0	0
$247$	1.25837e7	0.0531336
$248$	1.68128e7	0.0699938
$249$	0	0
$250$	−7.36470e6	−0.0298102
$251$	−4.39894e8	−1.75586	−0.877930	−	0.478789i	$-0.841076\pi$
$251$	−4.39894e8	−1.75586	−0.877930	+	0.478789i	$0.841076\pi$
$252$	0	0
$253$	3.70944e8	1.44008
$254$	−3.07276e7	−0.117655
$255$	0	0
$256$	2.45740e8	0.915454
$257$	6.14273e7	0.225733	0.112867	−	0.993610i	$-0.463997\pi$
$257$	6.14273e7	0.225733	0.112867	+	0.993610i	$0.463997\pi$
$258$	0	0
$259$	−3.16646e7	−0.113247
$260$	6.24935e7	0.220510
$261$	0	0
$262$	3.70540e6	0.0127286
$263$	−2.33744e8	−0.792310	−0.396155	−	0.918184i	$-0.629656\pi$
$263$	−2.33744e8	−0.792310	−0.396155	+	0.918184i	$0.629656\pi$
$264$	0	0
$265$	2.65962e7	0.0877929
$266$	487110.	0.00158687
$267$	0	0
$268$	−3.33008e8	−1.05678
$269$	2.91448e8	0.912909	0.456455	−	0.889747i	$-0.349119\pi$
$269$	2.91448e8	0.912909	0.456455	+	0.889747i	$0.349119\pi$
$270$	0	0
$271$	−3.08708e8	−0.942227	−0.471113	−	0.882073i	$-0.656148\pi$
$271$	−3.08708e8	−0.942227	−0.471113	+	0.882073i	$0.656148\pi$
$272$	−2.59891e8	−0.783070
$273$	0	0
$274$	3.86940e7	0.113636
$275$	−5.80238e8	−1.68245
$276$	0	0
$277$	−1.46213e8	−0.413339	−0.206669	−	0.978411i	$-0.566262\pi$
$277$	−1.46213e8	−0.413339	−0.206669	+	0.978411i	$0.566262\pi$
$278$	3.06698e7	0.0856159
$279$	0	0
$280$	4.85910e6	0.0132282
$281$	−6.34299e8	−1.70538	−0.852692	−	0.522414i	$-0.825031\pi$
$281$	−6.34299e8	−1.70538	−0.852692	+	0.522414i	$0.825031\pi$
$282$	0	0
$283$	2.44879e7	0.0642243	0.0321121	−	0.999484i	$-0.489777\pi$
$283$	2.44879e7	0.0642243	0.0321121	+	0.999484i	$0.489777\pi$
$284$	1.05991e8	0.274571
$285$	0	0
$286$	−8.62268e7	−0.217952
$287$	−2.53160e8	−0.632134
$288$	0	0
$289$	−1.45314e8	−0.354131
$290$	−566309.	−0.00136352
$291$	0	0
$292$	−1.00636e8	−0.236544
$293$	2.69929e8	0.626922	0.313461	−	0.949601i	$-0.398511\pi$
$293$	2.69929e8	0.626922	0.313461	+	0.949601i	$0.398511\pi$
$294$	0	0
$295$	−9.37061e6	−0.0212516
$296$	−2.11777e7	−0.0474634
$297$	0	0
$298$	3.30300e7	0.0723023
$299$	−5.24700e8	−1.13517
$300$	0	0
$301$	−2.36259e8	−0.499350
$302$	−7.43443e7	−0.155319
$303$	0	0
$304$	−1.86127e7	−0.0379972
$305$	1.45094e8	0.292820
$306$	0	0
$307$	−7.89237e8	−1.55676	−0.778382	−	0.627790i	$-0.783960\pi$
$307$	−7.89237e8	−1.55676	−0.778382	+	0.627790i	$0.783960\pi$
$308$	3.86402e8	0.753550
$309$	0	0
$310$	−3.00937e6	−0.00573733
$311$	−7.34416e8	−1.38446	−0.692230	−	0.721677i	$-0.743372\pi$
$311$	−7.34416e8	−1.38446	−0.692230	+	0.721677i	$0.743372\pi$
$312$	0	0
$313$	−5.15821e8	−0.950811	−0.475405	−	0.879767i	$-0.657699\pi$
$313$	−5.15821e8	−0.950811	−0.475405	+	0.879767i	$0.657699\pi$
$314$	−4.00115e7	−0.0729341
$315$	0	0
$316$	−1.88613e8	−0.336253
$317$	7.45878e7	0.131511	0.0657553	−	0.997836i	$-0.479054\pi$
$317$	7.45878e7	0.131511	0.0657553	+	0.997836i	$0.479054\pi$
$318$	0	0
$319$	−9.04563e7	−0.156017
$320$	−9.08028e7	−0.154908
$321$	0	0
$322$	−2.03109e7	−0.0339027
$323$	1.89803e7	0.0313397
$324$	0	0
$325$	8.20747e8	1.32623
$326$	−5.26991e7	−0.0842445
$327$	0	0
$328$	−1.69317e8	−0.264937
$329$	−7.28158e6	−0.0112730
$330$	0	0
$331$	3.87123e8	0.586747	0.293373	−	0.955998i	$-0.405222\pi$
$331$	3.87123e8	0.586747	0.293373	+	0.955998i	$0.405222\pi$
$332$	9.91616e8	1.48717
$333$	0	0
$334$	5.75875e7	0.0845699
$335$	1.19727e8	0.173994
$336$	0	0
$337$	6.81120e8	0.969435	0.484718	−	0.874671i	$-0.338922\pi$
$337$	6.81120e8	0.969435	0.484718	+	0.874671i	$0.338922\pi$
$338$	5.62699e7	0.0792625
$339$	0	0
$340$	9.42605e7	0.130063
$341$	−4.80686e8	−0.656480
$342$	0	0
$343$	5.93716e8	0.794418
$344$	−1.58013e8	−0.209285
$345$	0	0
$346$	−4.34902e7	−0.0564449
$347$	−8.46454e8	−1.08755	−0.543776	−	0.839230i	$-0.683006\pi$
$347$	−8.46454e8	−1.08755	−0.543776	+	0.839230i	$0.683006\pi$
$348$	0	0
$349$	−8.77313e8	−1.10475	−0.552377	−	0.833595i	$-0.686279\pi$
$349$	−8.77313e8	−1.10475	−0.552377	+	0.833595i	$0.686279\pi$
$350$	3.17708e7	0.0396086
$351$	0	0
$352$	3.88202e8	0.474415
$353$	−4.93604e8	−0.597265	−0.298633	−	0.954368i	$-0.596531\pi$
$353$	−4.93604e8	−0.597265	−0.298633	+	0.954368i	$0.596531\pi$
$354$	0	0
$355$	−3.81071e7	−0.0452071
$356$	9.84067e7	0.115598
$357$	0	0
$358$	−1.06137e8	−0.122257
$359$	1.16371e8	0.132744	0.0663718	−	0.997795i	$-0.478858\pi$
$359$	1.16371e8	0.132744	0.0663718	+	0.997795i	$0.478858\pi$
$360$	0	0
$361$	−8.92512e8	−0.998479
$362$	−1.07036e8	−0.118590
$363$	0	0
$364$	−5.46566e8	−0.594002
$365$	3.61818e7	0.0389462
$366$	0	0
$367$	−1.02293e8	−0.108023	−0.0540113	−	0.998540i	$-0.517201\pi$
$367$	−1.02293e8	−0.108023	−0.0540113	+	0.998540i	$0.517201\pi$
$368$	7.76088e8	0.811790
$369$	0	0
$370$	3.79066e6	0.00389053
$371$	−2.32609e8	−0.236493
$372$	0	0
$373$	−4.28192e8	−0.427226	−0.213613	−	0.976918i	$-0.568523\pi$
$373$	−4.28192e8	−0.427226	−0.213613	+	0.976918i	$0.568523\pi$
$374$	−1.30058e8	−0.128554
$375$	0	0
$376$	−4.87002e6	−0.00472469
$377$	1.27951e8	0.122984
$378$	0	0
$379$	−1.73361e9	−1.63574	−0.817868	−	0.575406i	$-0.804844\pi$
$379$	−1.73361e9	−1.63574	−0.817868	+	0.575406i	$0.804844\pi$
$380$	6.75067e6	0.00631108
$381$	0	0
$382$	−1.63765e8	−0.150314
$383$	−9.28289e8	−0.844282	−0.422141	−	0.906530i	$-0.638721\pi$
$383$	−9.28289e8	−0.844282	−0.422141	+	0.906530i	$0.638721\pi$
$384$	0	0
$385$	−1.38924e8	−0.124069
$386$	−1.21075e8	−0.107151
$387$	0	0
$388$	−9.66098e8	−0.839673
$389$	−6.27218e7	−0.0540250	−0.0270125	−	0.999635i	$-0.508599\pi$
$389$	−6.27218e7	−0.0540250	−0.0270125	+	0.999635i	$0.508599\pi$
$390$	0	0
$391$	−7.91418e8	−0.669557
$392$	1.77294e8	0.148659
$393$	0	0
$394$	4.75236e7	0.0391447
$395$	6.78123e7	0.0553629
$396$	0	0
$397$	9.87552e8	0.792124	0.396062	−	0.918224i	$-0.370377\pi$
$397$	9.87552e8	0.792124	0.396062	+	0.918224i	$0.370377\pi$
$398$	−1.55624e8	−0.123733
$399$	0	0
$400$	−1.21397e9	−0.948417
$401$	−3.03463e8	−0.235018	−0.117509	−	0.993072i	$-0.537491\pi$
$401$	−3.03463e8	−0.235018	−0.117509	+	0.993072i	$0.537491\pi$
$402$	0	0
$403$	6.79931e8	0.517484
$404$	5.86585e8	0.442584
$405$	0	0
$406$	4.95291e6	0.00367299
$407$	6.05481e8	0.445164
$408$	0	0
$409$	−2.12651e9	−1.53686	−0.768432	−	0.639931i	$-0.778963\pi$
$409$	−2.12651e9	−1.53686	−0.768432	+	0.639931i	$0.778963\pi$
$410$	3.03066e7	0.0217167
$411$	0	0
$412$	2.50862e9	1.76723
$413$	8.19550e7	0.0572467
$414$	0	0
$415$	−3.56517e8	−0.244857
$416$	−5.49112e8	−0.373968
$417$	0	0
$418$	−9.31438e6	−0.00623788
$419$	3.10868e8	0.206456	0.103228	−	0.994658i	$-0.467083\pi$
$419$	3.10868e8	0.206456	0.103228	+	0.994658i	$0.467083\pi$
$420$	0	0
$421$	6.45741e8	0.421765	0.210883	−	0.977511i	$-0.432366\pi$
$421$	6.45741e8	0.421765	0.210883	+	0.977511i	$0.432366\pi$
$422$	6.15677e7	0.0398804
$423$	0	0
$424$	−1.55572e8	−0.0991179
$425$	1.23795e9	0.782245
$426$	0	0
$427$	−1.26899e9	−0.788788
$428$	−2.38454e9	−1.47012
$429$	0	0
$430$	2.82832e7	0.0171549
$431$	−2.52751e9	−1.52063	−0.760313	−	0.649556i	$-0.774955\pi$
$431$	−2.52751e9	−1.52063	−0.760313	+	0.649556i	$0.774955\pi$
$432$	0	0
$433$	1.83259e9	1.08482	0.542409	−	0.840115i	$-0.317513\pi$
$433$	1.83259e9	1.08482	0.542409	+	0.840115i	$0.317513\pi$
$434$	2.63198e7	0.0154550
$435$	0	0
$436$	2.27791e9	1.31624
$437$	−5.66791e7	−0.0324891
$438$	0	0
$439$	2.67837e7	0.0151093	0.00755466	−	0.999971i	$-0.497595\pi$
$439$	2.67837e7	0.0151093	0.00755466	+	0.999971i	$0.497595\pi$
$440$	−9.29141e7	−0.0519993
$441$	0	0
$442$	1.83967e8	0.101336
$443$	−2.75298e9	−1.50449	−0.752246	−	0.658883i	$-0.771029\pi$
$443$	−2.75298e9	−1.50449	−0.752246	+	0.658883i	$0.771029\pi$
$444$	0	0
$445$	−3.53803e7	−0.0190328
$446$	3.29561e6	0.00175899
$447$	0	0
$448$	7.94158e8	0.417286
$449$	−1.10746e9	−0.577387	−0.288694	−	0.957422i	$-0.593221\pi$
$449$	−1.10746e9	−0.577387	−0.288694	+	0.957422i	$0.593221\pi$
$450$	0	0
$451$	4.84086e9	2.48487
$452$	3.29351e9	1.67755
$453$	0	0
$454$	3.51636e8	0.176359
$455$	1.96508e8	0.0978002
$456$	0	0
$457$	4.92024e8	0.241146	0.120573	−	0.992704i	$-0.461527\pi$
$457$	4.92024e8	0.241146	0.120573	+	0.992704i	$0.461527\pi$
$458$	1.85868e8	0.0904015
$459$	0	0
$460$	−2.81481e8	−0.134833
$461$	3.98165e9	1.89282	0.946411	−	0.322964i	$-0.104679\pi$
$461$	3.98165e9	1.89282	0.946411	+	0.322964i	$0.104679\pi$
$462$	0	0
$463$	−2.76256e9	−1.29354	−0.646768	−	0.762686i	$-0.723880\pi$
$463$	−2.76256e9	−1.29354	−0.646768	+	0.762686i	$0.723880\pi$
$464$	−1.89253e8	−0.0879486
$465$	0	0
$466$	1.92638e8	0.0881842
$467$	3.39978e9	1.54469	0.772346	−	0.635202i	$-0.219083\pi$
$467$	3.39978e9	1.54469	0.772346	+	0.635202i	$0.219083\pi$
$468$	0	0
$469$	−1.04713e9	−0.468700
$470$	871698.	0.000387279 0
$471$	0	0
$472$	5.48126e7	0.0239929
$473$	4.51767e9	1.96291
$474$	0	0
$475$	8.86586e7	0.0379571
$476$	−8.24399e8	−0.350359
$477$	0	0
$478$	8.17131e7	0.0342211
$479$	−1.05808e8	−0.0439890	−0.0219945	−	0.999758i	$-0.507002\pi$
$479$	−1.05808e8	−0.0439890	−0.0219945	+	0.999758i	$0.507002\pi$
$480$	0	0
$481$	−8.56453e8	−0.350910
$482$	5.79124e7	0.0235563
$483$	0	0
$484$	−4.91567e9	−1.97071
$485$	3.47343e8	0.138249
$486$	0	0
$487$	3.42694e9	1.34448	0.672241	−	0.740333i	$-0.265332\pi$
$487$	3.42694e9	1.34448	0.672241	+	0.740333i	$0.265332\pi$
$488$	−8.48717e8	−0.330593
$489$	0	0
$490$	−3.17343e7	−0.0121855
$491$	4.02092e9	1.53299	0.766496	−	0.642249i	$-0.221999\pi$
$491$	4.02092e9	1.53299	0.766496	+	0.642249i	$0.221999\pi$
$492$	0	0
$493$	1.92991e8	0.0725392
$494$	1.31752e7	0.00491714
$495$	0	0
$496$	−1.00569e9	−0.370066
$497$	3.33283e8	0.121777
$498$	0	0
$499$	2.61447e9	0.941958	0.470979	−	0.882144i	$-0.343901\pi$
$499$	2.61447e9	0.941958	0.470979	+	0.882144i	$0.343901\pi$
$500$	8.92650e8	0.319364
$501$	0	0
$502$	−4.60570e8	−0.162492
$503$	3.84561e9	1.34734	0.673671	−	0.739032i	$-0.264717\pi$
$503$	3.84561e9	1.34734	0.673671	+	0.739032i	$0.264717\pi$
$504$	0	0
$505$	−2.10896e8	−0.0728699
$506$	3.88379e8	0.133269
$507$	0	0
$508$	3.72439e9	1.26047
$509$	3.30098e9	1.10951	0.554755	−	0.832014i	$-0.312812\pi$
$509$	3.30098e9	1.10951	0.554755	+	0.832014i	$0.312812\pi$
$510$	0	0
$511$	−3.16444e8	−0.104912
$512$	1.35756e9	0.447005
$513$	0	0
$514$	6.43146e7	0.0208900
$515$	−9.01927e8	−0.290969
$516$	0	0
$517$	1.39236e8	0.0443134
$518$	−3.31530e7	−0.0104802
$519$	0	0
$520$	1.31427e8	0.0409895
$521$	−2.85291e8	−0.0883804	−0.0441902	−	0.999023i	$-0.514071\pi$
$521$	−2.85291e8	−0.0883804	−0.0441902	+	0.999023i	$0.514071\pi$
$522$	0	0
$523$	4.97451e9	1.52053	0.760263	−	0.649615i	$-0.225070\pi$
$523$	4.97451e9	1.52053	0.760263	+	0.649615i	$0.225070\pi$
$524$	−4.49119e8	−0.136365
$525$	0	0
$526$	−2.44731e8	−0.0733227
$527$	1.02556e9	0.305226
$528$	0	0
$529$	−1.04149e9	−0.305887
$530$	2.78463e7	0.00812461
$531$	0	0
$532$	−5.90410e7	−0.0170006
$533$	−6.84739e9	−1.95875
$534$	0	0
$535$	8.57319e8	0.242050
$536$	−7.00333e8	−0.196439
$537$	0	0
$538$	3.05147e8	0.0844833
$539$	−5.06892e9	−1.39429
$540$	0	0
$541$	−1.19739e9	−0.325122	−0.162561	−	0.986698i	$-0.551976\pi$
$541$	−1.19739e9	−0.325122	−0.162561	+	0.986698i	$0.551976\pi$
$542$	−3.23218e8	−0.0871964
$543$	0	0
$544$	−8.28239e8	−0.220577
$545$	−8.18981e8	−0.216714
$546$	0	0
$547$	2.87851e9	0.751989	0.375995	−	0.926622i	$-0.377301\pi$
$547$	2.87851e9	0.751989	0.375995	+	0.926622i	$0.377301\pi$
$548$	−4.68998e9	−1.21741
$549$	0	0
$550$	−6.07511e8	−0.155699
$551$	1.38214e7	0.00351984
$552$	0	0
$553$	−5.93084e8	−0.149134
$554$	−1.53085e8	−0.0382516
$555$	0	0
$556$	−3.71738e9	−0.917225
$557$	−7.60163e8	−0.186386	−0.0931931	−	0.995648i	$-0.529707\pi$
$557$	−7.60163e8	−0.186386	−0.0931931	+	0.995648i	$0.529707\pi$
$558$	0	0
$559$	−6.39024e9	−1.54730
$560$	−2.90656e8	−0.0699394
$561$	0	0
$562$	−6.64113e8	−0.157821
$563$	3.49652e9	0.825766	0.412883	−	0.910784i	$-0.364522\pi$
$563$	3.49652e9	0.825766	0.412883	+	0.910784i	$0.364522\pi$
$564$	0	0
$565$	−1.18412e9	−0.276202
$566$	2.56389e7	0.00594350
$567$	0	0
$568$	2.22904e8	0.0510387
$569$	−4.56391e9	−1.03859	−0.519294	−	0.854595i	$-0.673805\pi$
$569$	−4.56391e9	−1.03859	−0.519294	+	0.854595i	$0.673805\pi$
$570$	0	0
$571$	−3.82957e9	−0.860842	−0.430421	−	0.902628i	$-0.641635\pi$
$571$	−3.82957e9	−0.860842	−0.430421	+	0.902628i	$0.641635\pi$
$572$	1.04513e10	2.33498
$573$	0	0
$574$	−2.65060e8	−0.0584995
$575$	−3.69678e9	−0.810935
$576$	0	0
$577$	6.27659e9	1.36022	0.680109	−	0.733111i	$-0.261932\pi$
$577$	6.27659e9	1.36022	0.680109	+	0.733111i	$0.261932\pi$
$578$	−1.52144e8	−0.0327723
$579$	0	0
$580$	6.86404e7	0.0146077
$581$	3.11809e9	0.659586
$582$	0	0
$583$	4.44789e9	0.929638
$584$	−2.11642e8	−0.0439701
$585$	0	0
$586$	2.82617e8	0.0580172
$587$	−1.60999e9	−0.328541	−0.164271	−	0.986415i	$-0.552527\pi$
$587$	−1.60999e9	−0.328541	−0.164271	+	0.986415i	$0.552527\pi$
$588$	0	0
$589$	7.34473e7	0.0148106
$590$	−9.81106e6	−0.00196668
$591$	0	0
$592$	1.26679e9	0.250945
$593$	2.78148e9	0.547753	0.273877	−	0.961765i	$-0.411694\pi$
$593$	2.78148e9	0.547753	0.273877	+	0.961765i	$0.411694\pi$
$594$	0	0
$595$	2.96397e8	0.0576853
$596$	−4.00346e9	−0.774593
$597$	0	0
$598$	−5.49363e8	−0.105052
$599$	−9.69947e9	−1.84397	−0.921986	−	0.387224i	$-0.873434\pi$
$599$	−9.69947e9	−1.84397	−0.921986	+	0.387224i	$0.873434\pi$
$600$	0	0
$601$	6.38608e9	1.19998	0.599989	−	0.800008i	$-0.295171\pi$
$601$	6.38608e9	1.19998	0.599989	+	0.800008i	$0.295171\pi$
$602$	−2.47364e8	−0.0462113
$603$	0	0
$604$	9.01103e9	1.66397
$605$	1.76734e9	0.324471
$606$	0	0
$607$	7.47612e9	1.35680	0.678400	−	0.734693i	$-0.262674\pi$
$607$	7.47612e9	1.35680	0.678400	+	0.734693i	$0.262674\pi$
$608$	−5.93161e7	−0.0107031
$609$	0	0
$610$	1.51914e8	0.0270984
$611$	−1.96950e8	−0.0349310
$612$	0	0
$613$	−1.06933e9	−0.187500	−0.0937501	−	0.995596i	$-0.529885\pi$
$613$	−1.06933e9	−0.187500	−0.0937501	+	0.995596i	$0.529885\pi$
$614$	−8.26334e8	−0.144068
$615$	0	0
$616$	8.12623e8	0.140074
$617$	4.37316e9	0.749544	0.374772	−	0.927117i	$-0.377721\pi$
$617$	4.37316e9	0.749544	0.374772	+	0.927117i	$0.377721\pi$
$618$	0	0
$619$	2.09428e9	0.354910	0.177455	−	0.984129i	$-0.443214\pi$
$619$	2.09428e9	0.354910	0.177455	+	0.984129i	$0.443214\pi$
$620$	3.64756e8	0.0614655
$621$	0	0
$622$	−7.68936e8	−0.128122
$623$	3.09435e8	0.0512698
$624$	0	0
$625$	5.61994e9	0.920772
$626$	−5.40067e8	−0.0879908
$627$	0	0
$628$	4.84966e9	0.781362
$629$	−1.29181e9	−0.206977
$630$	0	0
$631$	−1.28290e8	−0.0203278	−0.0101639	−	0.999948i	$-0.503235\pi$
$631$	−1.28290e8	−0.0203278	−0.0101639	+	0.999948i	$0.503235\pi$
$632$	−3.96662e8	−0.0625045
$633$	0	0
$634$	7.80937e7	0.0121704
$635$	−1.33904e9	−0.207531
$636$	0	0
$637$	7.16998e9	1.09908
$638$	−9.47081e7	−0.0144383
$639$	0	0
$640$	−3.92192e8	−0.0591384
$641$	−7.27091e9	−1.09040	−0.545200	−	0.838306i	$-0.683546\pi$
$641$	−7.27091e9	−1.09040	−0.545200	+	0.838306i	$0.683546\pi$
$642$	0	0
$643$	−2.09075e9	−0.310145	−0.155072	−	0.987903i	$-0.549561\pi$
$643$	−2.09075e9	−0.310145	−0.155072	+	0.987903i	$0.549561\pi$
$644$	2.46182e9	0.363208
$645$	0	0
$646$	1.98725e7	0.00290027
$647$	2.61971e8	0.0380266	0.0190133	−	0.999819i	$-0.493948\pi$
$647$	2.61971e8	0.0380266	0.0190133	+	0.999819i	$0.493948\pi$
$648$	0	0
$649$	−1.56712e9	−0.225033
$650$	8.59325e8	0.122733
$651$	0	0
$652$	6.38748e9	0.902533
$653$	−5.83822e8	−0.0820510	−0.0410255	−	0.999158i	$-0.513062\pi$
$653$	−5.83822e8	−0.0820510	−0.0410255	+	0.999158i	$0.513062\pi$
$654$	0	0
$655$	1.61473e8	0.0224520
$656$	1.01280e10	1.40075
$657$	0	0
$658$	−7.62384e6	−0.00104324
$659$	5.10247e9	0.694515	0.347258	−	0.937770i	$-0.387113\pi$
$659$	5.10247e9	0.694515	0.347258	+	0.937770i	$0.387113\pi$
$660$	0	0
$661$	−8.35701e9	−1.12550	−0.562750	−	0.826627i	$-0.690257\pi$
$661$	−8.35701e9	−1.12550	−0.562750	+	0.826627i	$0.690257\pi$
$662$	4.05319e8	0.0542992
$663$	0	0
$664$	2.08542e9	0.276443
$665$	2.12271e7	0.00279908
$666$	0	0
$667$	−5.76310e8	−0.0751996
$668$	−6.97999e9	−0.906019
$669$	0	0
$670$	1.25355e8	0.0161020
$671$	2.42652e10	3.10067
$672$	0	0
$673$	2.73137e9	0.345405	0.172702	−	0.984974i	$-0.444750\pi$
$673$	2.73137e9	0.345405	0.172702	+	0.984974i	$0.444750\pi$
$674$	7.13135e8	0.0897144
$675$	0	0
$676$	−6.82029e9	−0.849160
$677$	1.15909e10	1.43568	0.717838	−	0.696210i	$-0.245132\pi$
$677$	1.15909e10	1.43568	0.717838	+	0.696210i	$0.245132\pi$
$678$	0	0
$679$	−3.03785e9	−0.372410
$680$	1.98235e8	0.0241768
$681$	0	0
$682$	−5.03280e8	−0.0607525
$683$	−1.30752e10	−1.57027	−0.785135	−	0.619324i	$-0.787407\pi$
$683$	−1.30752e10	−1.57027	−0.785135	+	0.619324i	$0.787407\pi$
$684$	0	0
$685$	1.68620e9	0.200443
$686$	6.21623e8	0.0735178
$687$	0	0
$688$	9.45186e9	1.10652
$689$	−6.29154e9	−0.732807
$690$	0	0
$691$	5.35573e8	0.0617512	0.0308756	−	0.999523i	$-0.490170\pi$
$691$	5.35573e8	0.0617512	0.0308756	+	0.999523i	$0.490170\pi$
$692$	5.27130e9	0.604709
$693$	0	0
$694$	−8.86240e8	−0.100645
$695$	1.33652e9	0.151018
$696$	0	0
$697$	−1.03281e10	−1.15533
$698$	−9.18549e8	−0.102237
$699$	0	0
$700$	−3.85083e9	−0.424338
$701$	−9.08901e9	−0.996560	−0.498280	−	0.867016i	$-0.666035\pi$
$701$	−9.08901e9	−0.996560	−0.498280	+	0.867016i	$0.666035\pi$
$702$	0	0
$703$	−9.25156e7	−0.0100432
$704$	−1.51856e10	−1.64032
$705$	0	0
$706$	−5.16805e8	−0.0552726
$707$	1.84449e9	0.196294
$708$	0	0
$709$	−1.59144e10	−1.67698	−0.838489	−	0.544918i	$-0.816561\pi$
$709$	−1.59144e10	−1.67698	−0.838489	+	0.544918i	$0.816561\pi$
$710$	−3.98983e7	−0.00418360
$711$	0	0
$712$	2.06954e8	0.0214879
$713$	−3.06252e9	−0.316421
$714$	0	0
$715$	−3.75756e9	−0.384446
$716$	1.28645e10	1.30977
$717$	0	0
$718$	1.21841e8	0.0122845
$719$	−8.22348e9	−0.825096	−0.412548	−	0.910936i	$-0.635361\pi$
$719$	−8.22348e9	−0.825096	−0.412548	+	0.910936i	$0.635361\pi$
$720$	0	0
$721$	7.88822e9	0.783801
$722$	−9.34463e8	−0.0924022
$723$	0	0
$724$	1.29734e10	1.27049
$725$	9.01476e8	0.0878559
$726$	0	0
$727$	−1.24376e10	−1.20051	−0.600257	−	0.799808i	$-0.704935\pi$
$727$	−1.24376e10	−1.20051	−0.600257	+	0.799808i	$0.704935\pi$
$728$	−1.14946e9	−0.110416
$729$	0	0
$730$	3.78824e7	0.00360419
$731$	−9.63855e9	−0.912643
$732$	0	0
$733$	8.16789e9	0.766031	0.383015	−	0.923742i	$-0.374886\pi$
$733$	8.16789e9	0.766031	0.383015	+	0.923742i	$0.374886\pi$
$734$	−1.07101e8	−0.00999672
$735$	0	0
$736$	2.47329e9	0.228666
$737$	2.00229e10	1.84243
$738$	0	0
$739$	8.70396e9	0.793343	0.396672	−	0.917961i	$-0.370165\pi$
$739$	8.70396e9	0.793343	0.396672	+	0.917961i	$0.370165\pi$
$740$	−4.59453e8	−0.0416803
$741$	0	0
$742$	−2.43543e8	−0.0218858
$743$	1.93107e10	1.72718	0.863590	−	0.504195i	$-0.168211\pi$
$743$	1.93107e10	1.72718	0.863590	+	0.504195i	$0.168211\pi$
$744$	0	0
$745$	1.43937e9	0.127534
$746$	−4.48318e8	−0.0395367
$747$	0	0
$748$	1.57639e10	1.37723
$749$	−7.49808e9	−0.652024
$750$	0	0
$751$	1.80579e10	1.55571	0.777854	−	0.628445i	$-0.216308\pi$
$751$	1.80579e10	1.55571	0.777854	+	0.628445i	$0.216308\pi$
$752$	2.91310e8	0.0249800
$753$	0	0
$754$	1.33965e8	0.0113813
$755$	−3.23975e9	−0.273966
$756$	0	0
$757$	−2.07804e10	−1.74108	−0.870538	−	0.492102i	$-0.836229\pi$
$757$	−2.07804e10	−1.74108	−0.870538	+	0.492102i	$0.836229\pi$
$758$	−1.81509e9	−0.151376
$759$	0	0
$760$	1.41970e7	0.00117314
$761$	−1.72676e10	−1.42032	−0.710160	−	0.704041i	$-0.751377\pi$
$761$	−1.72676e10	−1.42032	−0.710160	+	0.704041i	$0.751377\pi$
$762$	0	0
$763$	7.16277e9	0.583775
$764$	1.98494e10	1.61035
$765$	0	0
$766$	−9.71921e8	−0.0781323
$767$	2.21669e9	0.177387
$768$	0	0
$769$	−3.61626e9	−0.286759	−0.143380	−	0.989668i	$-0.545797\pi$
$769$	−3.61626e9	−0.286759	−0.143380	+	0.989668i	$0.545797\pi$
$770$	−1.45454e8	−0.0114817
$771$	0	0
$772$	1.46751e10	1.14794
$773$	1.71407e10	1.33475	0.667376	−	0.744721i	$-0.267417\pi$
$773$	1.71407e10	1.33475	0.667376	+	0.744721i	$0.267417\pi$
$774$	0	0
$775$	4.79046e9	0.369676
$776$	−2.03175e9	−0.156083
$777$	0	0
$778$	−6.56700e7	−0.00499963
$779$	−7.39668e8	−0.0560603
$780$	0	0
$781$	−6.37294e9	−0.478698
$782$	−8.28617e8	−0.0619627
$783$	0	0
$784$	−1.06052e10	−0.785981
$785$	−1.74361e9	−0.128648
$786$	0	0
$787$	−2.04068e10	−1.49233	−0.746164	−	0.665762i	$-0.768106\pi$
$787$	−2.04068e10	−1.49233	−0.746164	+	0.665762i	$0.768106\pi$
$788$	−5.76018e9	−0.419367
$789$	0	0
$790$	7.09997e7	0.00512344
$791$	1.03563e10	0.744023
$792$	0	0
$793$	−3.43232e10	−2.44417
$794$	1.03397e9	0.0733054
$795$	0	0
$796$	1.88626e10	1.32558
$797$	−9.47421e9	−0.662886	−0.331443	−	0.943475i	$-0.607535\pi$
$797$	−9.47421e9	−0.662886	−0.331443	+	0.943475i	$0.607535\pi$
$798$	0	0
$799$	−2.97064e8	−0.0206033
$800$	−3.86877e9	−0.267152
$801$	0	0
$802$	−3.17727e8	−0.0217492
$803$	6.05095e9	0.412400
$804$	0	0
$805$	−8.85103e8	−0.0598010
$806$	7.11890e8	0.0478895
$807$	0	0
$808$	1.23362e9	0.0822698
$809$	−2.25327e10	−1.49621	−0.748106	−	0.663579i	$-0.769037\pi$
$809$	−2.25327e10	−1.49621	−0.748106	+	0.663579i	$0.769037\pi$
$810$	0	0
$811$	2.45506e10	1.61618	0.808090	−	0.589060i	$-0.200502\pi$
$811$	2.45506e10	1.61618	0.808090	+	0.589060i	$0.200502\pi$
$812$	−6.00326e8	−0.0393497
$813$	0	0
$814$	6.33941e8	0.0411968
$815$	−2.29650e9	−0.148599
$816$	0	0
$817$	−6.90285e8	−0.0442845
$818$	−2.22646e9	−0.142226
$819$	0	0
$820$	−3.67336e9	−0.232656
$821$	−7.18995e9	−0.453445	−0.226722	−	0.973959i	$-0.572801\pi$
$821$	−7.18995e9	−0.453445	−0.226722	+	0.973959i	$0.572801\pi$
$822$	0	0
$823$	2.32419e9	0.145336	0.0726679	−	0.997356i	$-0.476849\pi$
$823$	2.32419e9	0.145336	0.0726679	+	0.997356i	$0.476849\pi$
$824$	5.27575e9	0.328503
$825$	0	0
$826$	8.58071e7	0.00529777
$827$	−8.26522e9	−0.508142	−0.254071	−	0.967186i	$-0.581770\pi$
$827$	−8.26522e9	−0.508142	−0.254071	+	0.967186i	$0.581770\pi$
$828$	0	0
$829$	−8.40607e9	−0.512450	−0.256225	−	0.966617i	$-0.582479\pi$
$829$	−8.40607e9	−0.512450	−0.256225	+	0.966617i	$0.582479\pi$
$830$	−3.73275e8	−0.0226598
$831$	0	0
$832$	2.14801e10	1.29302
$833$	1.08147e10	0.648269
$834$	0	0
$835$	2.50953e9	0.149173
$836$	1.12896e9	0.0668280
$837$	0	0
$838$	3.25480e8	0.0191060
$839$	2.46464e10	1.44074	0.720372	−	0.693588i	$-0.243971\pi$
$839$	2.46464e10	1.44074	0.720372	+	0.693588i	$0.243971\pi$
$840$	0	0
$841$	−1.71093e10	−0.991853
$842$	6.76093e8	0.0390314
$843$	0	0
$844$	−7.46242e9	−0.427249
$845$	2.45211e9	0.139811
$846$	0	0
$847$	−1.54571e10	−0.874048
$848$	9.30586e9	0.524048
$849$	0	0
$850$	1.29614e9	0.0723912
$851$	3.85760e9	0.214568
$852$	0	0
$853$	−2.48229e10	−1.36940	−0.684701	−	0.728824i	$-0.740067\pi$
$853$	−2.48229e10	−1.36940	−0.684701	+	0.728824i	$0.740067\pi$
$854$	−1.32864e9	−0.0729967
$855$	0	0
$856$	−5.01482e9	−0.273273
$857$	5.96585e9	0.323772	0.161886	−	0.986809i	$-0.448242\pi$
$857$	5.96585e9	0.323772	0.161886	+	0.986809i	$0.448242\pi$
$858$	0	0
$859$	1.17433e10	0.632143	0.316071	−	0.948735i	$-0.397636\pi$
$859$	1.17433e10	0.632143	0.316071	+	0.948735i	$0.397636\pi$
$860$	−3.42811e9	−0.183785
$861$	0	0
$862$	−2.64631e9	−0.140723
$863$	1.24460e9	0.0659160	0.0329580	−	0.999457i	$-0.489507\pi$
$863$	1.24460e9	0.0659160	0.0329580	+	0.999457i	$0.489507\pi$
$864$	0	0
$865$	−1.89520e9	−0.0995631
$866$	1.91872e9	0.100392
$867$	0	0
$868$	−3.19014e9	−0.165573
$869$	1.13408e10	0.586237
$870$	0	0
$871$	−2.83223e10	−1.45233
$872$	4.79056e9	0.244669
$873$	0	0
$874$	−5.93432e7	−0.00300664
$875$	2.80689e9	0.141644
$876$	0	0
$877$	−6.61320e9	−0.331065	−0.165532	−	0.986204i	$-0.552934\pi$
$877$	−6.61320e9	−0.331065	−0.165532	+	0.986204i	$0.552934\pi$
$878$	2.80426e7	0.00139826
$879$	0	0
$880$	5.55784e9	0.274927
$881$	5.40905e9	0.266505	0.133253	−	0.991082i	$-0.457458\pi$
$881$	5.40905e9	0.266505	0.133253	+	0.991082i	$0.457458\pi$
$882$	0	0
$883$	9.03523e9	0.441649	0.220824	−	0.975314i	$-0.429125\pi$
$883$	9.03523e9	0.441649	0.220824	+	0.975314i	$0.429125\pi$
$884$	−2.22980e10	−1.08563
$885$	0	0
$886$	−2.88238e9	−0.139230
$887$	1.10545e10	0.531870	0.265935	−	0.963991i	$-0.414319\pi$
$887$	1.10545e10	0.531870	0.265935	+	0.963991i	$0.414319\pi$
$888$	0	0
$889$	1.17111e10	0.559041
$890$	−3.70433e7	−0.00176135
$891$	0	0
$892$	−3.99450e8	−0.0188445
$893$	−2.12748e7	−0.000999738 0
$894$	0	0
$895$	−4.62519e9	−0.215650
$896$	3.43010e9	0.159305
$897$	0	0
$898$	−1.15952e9	−0.0534331
$899$	7.46809e8	0.0342808
$900$	0	0
$901$	−9.48968e9	−0.432230
$902$	5.06839e9	0.229957
$903$	0	0
$904$	6.92642e9	0.311831
$905$	−4.66437e9	−0.209181
$906$	0	0
$907$	1.82725e10	0.813153	0.406577	−	0.913617i	$-0.366722\pi$
$907$	1.82725e10	0.813153	0.406577	+	0.913617i	$0.366722\pi$
$908$	−4.26206e10	−1.88938
$909$	0	0
$910$	2.05744e8	0.00905072
$911$	−3.94744e10	−1.72982	−0.864911	−	0.501926i	$-0.832625\pi$
$911$	−3.94744e10	−1.72982	−0.864911	+	0.501926i	$0.832625\pi$
$912$	0	0
$913$	−5.96231e10	−2.59279
$914$	5.15151e8	0.0223163
$915$	0	0
$916$	−2.25284e10	−0.968494
$917$	−1.41223e9	−0.0604803
$918$	0	0
$919$	−3.67275e10	−1.56094	−0.780471	−	0.625192i	$-0.785021\pi$
$919$	−3.67275e10	−1.56094	−0.780471	+	0.625192i	$0.785021\pi$
$920$	−5.91969e8	−0.0250635
$921$	0	0
$922$	4.16880e9	0.175167
$923$	9.01452e9	0.377343
$924$	0	0
$925$	−6.03415e9	−0.250680
$926$	−2.89241e9	−0.119708
$927$	0	0
$928$	−6.03123e8	−0.0247735
$929$	1.46040e10	0.597607	0.298804	−	0.954315i	$-0.403412\pi$
$929$	1.46040e10	0.597607	0.298804	+	0.954315i	$0.403412\pi$
$930$	0	0
$931$	7.74515e8	0.0314562
$932$	−2.33490e10	−0.944740
$933$	0	0
$934$	3.55958e9	0.142950
$935$	−5.66762e9	−0.226757
$936$	0	0
$937$	−3.40171e10	−1.35086	−0.675428	−	0.737426i	$-0.736041\pi$
$937$	−3.40171e10	−1.35086	−0.675428	+	0.737426i	$0.736041\pi$
$938$	−1.09635e9	−0.0433748
$939$	0	0
$940$	−1.05656e8	−0.00414902
$941$	2.21318e9	0.0865872	0.0432936	−	0.999062i	$-0.486215\pi$
$941$	2.21318e9	0.0865872	0.0432936	+	0.999062i	$0.486215\pi$
$942$	0	0
$943$	3.08418e10	1.19770
$944$	−3.27872e9	−0.126854
$945$	0	0
$946$	4.73001e9	0.181653
$947$	−5.66644e9	−0.216813	−0.108406	−	0.994107i	$-0.534575\pi$
$947$	−5.66644e9	−0.216813	−0.108406	+	0.994107i	$0.534575\pi$
$948$	0	0
$949$	−8.55907e9	−0.325083
$950$	9.28259e7	0.00351266
$951$	0	0
$952$	−1.73375e9	−0.0651265
$953$	−1.49175e10	−0.558304	−0.279152	−	0.960247i	$-0.590053\pi$
$953$	−1.49175e10	−0.558304	−0.279152	+	0.960247i	$0.590053\pi$
$954$	0	0
$955$	−7.13648e9	−0.265138
$956$	−9.90417e9	−0.366619
$957$	0	0
$958$	−1.10781e8	−0.00407087
$959$	−1.47474e10	−0.539946
$960$	0	0
$961$	−2.35441e10	−0.855755
$962$	−8.96709e8	−0.0324742
$963$	0	0
$964$	−7.01936e9	−0.252364
$965$	−5.27615e9	−0.189004
$966$	0	0
$967$	−2.59933e10	−0.924418	−0.462209	−	0.886771i	$-0.652943\pi$
$967$	−2.59933e10	−0.924418	−0.462209	+	0.886771i	$0.652943\pi$
$968$	−1.03379e10	−0.366327
$969$	0	0
$970$	3.63669e8	0.0127940
$971$	−3.07398e10	−1.07754	−0.538770	−	0.842453i	$-0.681111\pi$
$971$	−3.07398e10	−1.07754	−0.538770	+	0.842453i	$0.681111\pi$
$972$	0	0
$973$	−1.16891e10	−0.406806
$974$	3.58802e9	0.124422
$975$	0	0
$976$	5.07677e10	1.74789
$977$	−4.79208e10	−1.64397	−0.821983	−	0.569512i	$-0.807132\pi$
$977$	−4.79208e10	−1.64397	−0.821983	+	0.569512i	$0.807132\pi$
$978$	0	0
$979$	−5.91692e9	−0.201538
$980$	3.84641e9	0.130546
$981$	0	0
$982$	4.20991e9	0.141868
$983$	−2.22035e9	−0.0745562	−0.0372781	−	0.999305i	$-0.511869\pi$
$983$	−2.22035e9	−0.0745562	−0.0372781	+	0.999305i	$0.511869\pi$
$984$	0	0
$985$	2.07097e9	0.0690473
$986$	2.02062e8	0.00671298
$987$	0	0
$988$	−1.59692e9	−0.0526786
$989$	2.87827e10	0.946115
$990$	0	0
$991$	−1.78351e10	−0.582127	−0.291064	−	0.956704i	$-0.594009\pi$
$991$	−1.78351e10	−0.582127	−0.291064	+	0.956704i	$0.594009\pi$
$992$	−3.20500e9	−0.104241
$993$	0	0
$994$	3.48949e8	0.0112696
$995$	−6.78171e9	−0.218252
$996$	0	0
$997$	5.15263e10	1.64663	0.823314	−	0.567586i	$-0.192123\pi$
$997$	5.15263e10	1.64663	0.823314	+	0.567586i	$0.192123\pi$
$998$	2.73736e9	0.0871715
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.a.1.8		14
3.2	odd	2		59.8.a.a.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.8.a.a.1.7	✓	14	3.2	odd	2
531.8.a.a.1.8		14	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)

\(f(q)\)	\(=\)	\(q+1.04700 q^{2} -126.904 q^{4} +45.6259 q^{5} -399.043 q^{7} -266.885 q^{8} +O(q^{10})\)	\(q+1.04700 q^{2} -126.904 q^{4} +45.6259 q^{5} -399.043 q^{7} -266.885 q^{8} +47.7705 q^{10} +7630.37 q^{11} -10793.2 q^{13} -417.799 q^{14} +15964.3 q^{16} -16279.6 q^{17} -1165.90 q^{19} -5790.10 q^{20} +7989.02 q^{22} +48614.1 q^{23} -76043.3 q^{25} -11300.5 q^{26} +50640.0 q^{28} -11854.8 q^{29} -62996.4 q^{31} +50875.9 q^{32} -17044.8 q^{34} -18206.7 q^{35} +79351.5 q^{37} -1220.70 q^{38} -12176.9 q^{40} +634420. q^{41} +592064. q^{43} -968323. q^{44} +50899.2 q^{46} +18247.6 q^{47} -664308. q^{49} -79617.6 q^{50} +1.36969e6 q^{52} +582919. q^{53} +348143. q^{55} +106499. q^{56} -12412.0 q^{58} -205379. q^{59} +3.18008e6 q^{61} -65957.5 q^{62} -1.99016e6 q^{64} -492448. q^{65} +2.62410e6 q^{67} +2.06594e6 q^{68} -19062.5 q^{70} -835207. q^{71} +793009. q^{73} +83081.3 q^{74} +147957. q^{76} -3.04484e6 q^{77} +1.48627e6 q^{79} +728384. q^{80} +664239. q^{82} -7.81392e6 q^{83} -742771. q^{85} +619893. q^{86} -2.03643e6 q^{88} -775444. q^{89} +4.30693e6 q^{91} -6.16932e6 q^{92} +19105.3 q^{94} -53195.1 q^{95} +7.61284e6 q^{97} -695533. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 9 q^{2} + 575 q^{4} + 430 q^{5} - 2390 q^{7} + 2463 q^{8}+O(q^{10}) \) 14 * q + 9 * q^2 + 575 * q^4 + 430 * q^5 - 2390 * q^7 + 2463 * q^8	\( 14 q + 9 q^{2} + 575 q^{4} + 430 q^{5} - 2390 q^{7} + 2463 q^{8} - 5362 q^{10} + 5030 q^{11} - 24364 q^{13} + 12717 q^{14} + 33859 q^{16} - 14504 q^{17} - 80234 q^{19} + 190220 q^{20} - 266687 q^{22} + 113272 q^{23} - 62580 q^{25} + 386729 q^{26} - 617413 q^{28} + 490250 q^{29} - 379844 q^{31} + 700263 q^{32} - 709263 q^{34} + 611196 q^{35} - 1203748 q^{37} + 340 q^{38} - 927130 q^{40} + 681860 q^{41} - 967090 q^{43} - 218679 q^{44} - 136632 q^{46} - 287456 q^{47} + 341754 q^{49} - 2153697 q^{50} + 1661397 q^{52} + 1227618 q^{53} + 975320 q^{55} - 4449921 q^{56} - 265424 q^{58} - 2875306 q^{59} - 4711840 q^{61} - 17057148 q^{62} + 2117595 q^{64} - 4072956 q^{65} + 7298936 q^{67} - 13001951 q^{68} + 12397514 q^{70} - 5657790 q^{71} + 4750028 q^{73} - 1875491 q^{74} + 3128138 q^{76} + 8640944 q^{77} - 17385506 q^{79} - 20096996 q^{80} - 941109 q^{82} + 15067470 q^{83} - 28577148 q^{85} - 3286963 q^{86} - 20655117 q^{88} + 15451868 q^{89} - 24287002 q^{91} - 13921944 q^{92} - 12765942 q^{94} + 43655474 q^{95} + 2400932 q^{97} - 19642950 q^{98}+O(q^{100}) \) 14 * q + 9 * q^2 + 575 * q^4 + 430 * q^5 - 2390 * q^7 + 2463 * q^8 - 5362 * q^10 + 5030 * q^11 - 24364 * q^13 + 12717 * q^14 + 33859 * q^16 - 14504 * q^17 - 80234 * q^19 + 190220 * q^20 - 266687 * q^22 + 113272 * q^23 - 62580 * q^25 + 386729 * q^26 - 617413 * q^28 + 490250 * q^29 - 379844 * q^31 + 700263 * q^32 - 709263 * q^34 + 611196 * q^35 - 1203748 * q^37 + 340 * q^38 - 927130 * q^40 + 681860 * q^41 - 967090 * q^43 - 218679 * q^44 - 136632 * q^46 - 287456 * q^47 + 341754 * q^49 - 2153697 * q^50 + 1661397 * q^52 + 1227618 * q^53 + 975320 * q^55 - 4449921 * q^56 - 265424 * q^58 - 2875306 * q^59 - 4711840 * q^61 - 17057148 * q^62 + 2117595 * q^64 - 4072956 * q^65 + 7298936 * q^67 - 13001951 * q^68 + 12397514 * q^70 - 5657790 * q^71 + 4750028 * q^73 - 1875491 * q^74 + 3128138 * q^76 + 8640944 * q^77 - 17385506 * q^79 - 20096996 * q^80 - 941109 * q^82 + 15067470 * q^83 - 28577148 * q^85 - 3286963 * q^86 - 20655117 * q^88 + 15451868 * q^89 - 24287002 * q^91 - 13921944 * q^92 - 12765942 * q^94 + 43655474 * q^95 + 2400932 * q^97 - 19642950 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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