LMFDB - Embedded newform 414.8.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,8,Mod(1,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, 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("414.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	414.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:	$129.327400550$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 $ x^4 - 2x^3 - 8367x^2 - 89140*x + 11077220
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$33.2734$ of defining polynomial
Character	$\chi$	$=$	414.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +64.0000 q^{4} +427.795 q^{5} +345.429 q^{7} -512.000 q^{8} +O(q^{10})$	\(q-8.00000 q^{2} +64.0000 q^{4} +427.795 q^{5} +345.429 q^{7} -512.000 q^{8} -3422.36 q^{10} -2181.54 q^{11} -2610.39 q^{13} -2763.43 q^{14} +4096.00 q^{16} -37979.0 q^{17} -26348.1 q^{19} +27378.9 q^{20} +17452.3 q^{22} +12167.0 q^{23} +104884. q^{25} +20883.1 q^{26} +22107.4 q^{28} -250851. q^{29} +179145. q^{31} -32768.0 q^{32} +303832. q^{34} +147773. q^{35} +434281. q^{37} +210785. q^{38} -219031. q^{40} +200429. q^{41} +841346. q^{43} -139619. q^{44} -97336.0 q^{46} +200025. q^{47} -704222. q^{49} -839072. q^{50} -167065. q^{52} +1.62417e6 q^{53} -933254. q^{55} -176859. q^{56} +2.00681e6 q^{58} +2.18662e6 q^{59} +2.54771e6 q^{61} -1.43316e6 q^{62} +262144. q^{64} -1.11671e6 q^{65} +4.66306e6 q^{67} -2.43066e6 q^{68} -1.18218e6 q^{70} -4.02892e6 q^{71} -2.58030e6 q^{73} -3.47425e6 q^{74} -1.68628e6 q^{76} -753568. q^{77} +1.22032e6 q^{79} +1.75225e6 q^{80} -1.60343e6 q^{82} +2.16585e6 q^{83} -1.62473e7 q^{85} -6.73077e6 q^{86} +1.11695e6 q^{88} -1.19998e6 q^{89} -901704. q^{91} +778688. q^{92} -1.60020e6 q^{94} -1.12716e7 q^{95} +8.97814e6 q^{97} +5.63378e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8}+O(q^{10}) $ 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8} + 2160 q^{10} - 4120 q^{11} + 8036 q^{13} - 16176 q^{14} + 16384 q^{16} - 37182 q^{17} + 5702 q^{19} - 17280 q^{20} + 32960 q^{22} + 48668 q^{23} + 121480 q^{25} - 64288 q^{26} + 129408 q^{28} - 217716 q^{29} + 222852 q^{31} - 131072 q^{32} + 297456 q^{34} - 68440 q^{35} + 486428 q^{37} - 45616 q^{38} + 138240 q^{40} - 338336 q^{41} + 730974 q^{43} - 263680 q^{44} - 389344 q^{46} - 338248 q^{47} - 310552 q^{49} - 971840 q^{50} + 514304 q^{52} + 375502 q^{53} + 424840 q^{55} - 1035264 q^{56} + 1741728 q^{58} - 71392 q^{59} + 2101164 q^{61} - 1782816 q^{62} + 1048576 q^{64} - 1578780 q^{65} + 4337162 q^{67} - 2379648 q^{68} + 547520 q^{70} - 2288016 q^{71} - 1107328 q^{73} - 3891424 q^{74} + 364928 q^{76} - 5826200 q^{77} + 60610 q^{79} - 1105920 q^{80} + 2706688 q^{82} - 1485464 q^{83} - 8843820 q^{85} - 5847792 q^{86} + 2109440 q^{88} - 1485090 q^{89} - 2898412 q^{91} + 3114752 q^{92} + 2705984 q^{94} - 8545200 q^{95} + 1935444 q^{97} + 2484416 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8 + 2160 * q^10 - 4120 * q^11 + 8036 * q^13 - 16176 * q^14 + 16384 * q^16 - 37182 * q^17 + 5702 * q^19 - 17280 * q^20 + 32960 * q^22 + 48668 * q^23 + 121480 * q^25 - 64288 * q^26 + 129408 * q^28 - 217716 * q^29 + 222852 * q^31 - 131072 * q^32 + 297456 * q^34 - 68440 * q^35 + 486428 * q^37 - 45616 * q^38 + 138240 * q^40 - 338336 * q^41 + 730974 * q^43 - 263680 * q^44 - 389344 * q^46 - 338248 * q^47 - 310552 * q^49 - 971840 * q^50 + 514304 * q^52 + 375502 * q^53 + 424840 * q^55 - 1035264 * q^56 + 1741728 * q^58 - 71392 * q^59 + 2101164 * q^61 - 1782816 * q^62 + 1048576 * q^64 - 1578780 * q^65 + 4337162 * q^67 - 2379648 * q^68 + 547520 * q^70 - 2288016 * q^71 - 1107328 * q^73 - 3891424 * q^74 + 364928 * q^76 - 5826200 * q^77 + 60610 * q^79 - 1105920 * q^80 + 2706688 * q^82 - 1485464 * q^83 - 8843820 * q^85 - 5847792 * q^86 + 2109440 * q^88 - 1485090 * q^89 - 2898412 * q^91 + 3114752 * q^92 + 2705984 * q^94 - 8545200 * q^95 + 1935444 * q^97 + 2484416 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	64.0000	0.500000
$5$	427.795	1.53053	0.765264	−	0.643717i	$-0.222609\pi$
$5$	427.795	1.53053	0.765264	+	0.643717i	$0.222609\pi$
$6$	0	0
$7$	345.429	0.380641	0.190320	−	0.981722i	$-0.439047\pi$
$7$	345.429	0.380641	0.190320	+	0.981722i	$0.439047\pi$
$8$	−512.000	−0.353553
$9$	0	0
$10$	−3422.36	−1.08225
$11$	−2181.54	−0.494185	−0.247092	−	0.968992i	$-0.579475\pi$
$11$	−2181.54	−0.494185	−0.247092	+	0.968992i	$0.579475\pi$
$12$	0	0
$13$	−2610.39	−0.329537	−0.164768	−	0.986332i	$-0.552688\pi$
$13$	−2610.39	−0.329537	−0.164768	+	0.986332i	$0.552688\pi$
$14$	−2763.43	−0.269154
$15$	0	0
$16$	4096.00	0.250000
$17$	−37979.0	−1.87488	−0.937438	−	0.348152i	$-0.886809\pi$
$17$	−37979.0	−1.87488	−0.937438	+	0.348152i	$0.886809\pi$
$18$	0	0
$19$	−26348.1	−0.881276	−0.440638	−	0.897685i	$-0.645248\pi$
$19$	−26348.1	−0.881276	−0.440638	+	0.897685i	$0.645248\pi$
$20$	27378.9	0.765264
$21$	0	0
$22$	17452.3	0.349442
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	104884.	1.34251
$26$	20883.1	0.233018
$27$	0	0
$28$	22107.4	0.190320
$29$	−250851.	−1.90995	−0.954977	−	0.296679i	$-0.904121\pi$
$29$	−250851.	−1.90995	−0.954977	+	0.296679i	$0.904121\pi$
$30$	0	0
$31$	179145.	1.08003	0.540017	−	0.841654i	$-0.318418\pi$
$31$	179145.	1.08003	0.540017	+	0.841654i	$0.318418\pi$
$32$	−32768.0	−0.176777
$33$	0	0
$34$	303832.	1.32574
$35$	147773.	0.582581
$36$	0	0
$37$	434281.	1.40950	0.704749	−	0.709456i	$-0.251059\pi$
$37$	434281.	1.40950	0.704749	+	0.709456i	$0.251059\pi$
$38$	210785.	0.623157
$39$	0	0
$40$	−219031.	−0.541123
$41$	200429.	0.454168	0.227084	−	0.973875i	$-0.427081\pi$
$41$	200429.	0.454168	0.227084	+	0.973875i	$0.427081\pi$
$42$	0	0
$43$	841346.	1.61375	0.806873	−	0.590725i	$-0.201158\pi$
$43$	841346.	1.61375	0.806873	+	0.590725i	$0.201158\pi$
$44$	−139619.	−0.247092
$45$	0	0
$46$	−97336.0	−0.147442
$47$	200025.	0.281024	0.140512	−	0.990079i	$-0.455125\pi$
$47$	200025.	0.281024	0.140512	+	0.990079i	$0.455125\pi$
$48$	0	0
$49$	−704222.	−0.855113
$50$	−839072.	−0.949301
$51$	0	0
$52$	−167065.	−0.164768
$53$	1.62417e6	1.49853	0.749266	−	0.662269i	$-0.230407\pi$
$53$	1.62417e6	1.49853	0.749266	+	0.662269i	$0.230407\pi$
$54$	0	0
$55$	−933254.	−0.756364
$56$	−176859.	−0.134577
$57$	0	0
$58$	2.00681e6	1.35054
$59$	2.18662e6	1.38609	0.693044	−	0.720895i	$-0.256269\pi$
$59$	2.18662e6	1.38609	0.693044	+	0.720895i	$0.256269\pi$
$60$	0	0
$61$	2.54771e6	1.43713	0.718564	−	0.695460i	$-0.244800\pi$
$61$	2.54771e6	1.43713	0.718564	+	0.695460i	$0.244800\pi$
$62$	−1.43316e6	−0.763700
$63$	0	0
$64$	262144.	0.125000
$65$	−1.11671e6	−0.504365
$66$	0	0
$67$	4.66306e6	1.89413	0.947063	−	0.321048i	$-0.104035\pi$
$67$	4.66306e6	1.89413	0.947063	+	0.321048i	$0.104035\pi$
$68$	−2.43066e6	−0.937438
$69$	0	0
$70$	−1.18218e6	−0.411947
$71$	−4.02892e6	−1.33593	−0.667966	−	0.744192i	$-0.732835\pi$
$71$	−4.02892e6	−1.33593	−0.667966	+	0.744192i	$0.732835\pi$
$72$	0	0
$73$	−2.58030e6	−0.776319	−0.388160	−	0.921592i	$-0.626889\pi$
$73$	−2.58030e6	−0.776319	−0.388160	+	0.921592i	$0.626889\pi$
$74$	−3.47425e6	−0.996666
$75$	0	0
$76$	−1.68628e6	−0.440638
$77$	−753568.	−0.188107
$78$	0	0
$79$	1.22032e6	0.278471	0.139236	−	0.990259i	$-0.455535\pi$
$79$	1.22032e6	0.278471	0.139236	+	0.990259i	$0.455535\pi$
$80$	1.75225e6	0.382632
$81$	0	0
$82$	−1.60343e6	−0.321145
$83$	2.16585e6	0.415771	0.207886	−	0.978153i	$-0.433342\pi$
$83$	2.16585e6	0.415771	0.207886	+	0.978153i	$0.433342\pi$
$84$	0	0
$85$	−1.62473e7	−2.86955
$86$	−6.73077e6	−1.14109
$87$	0	0
$88$	1.11695e6	0.174721
$89$	−1.19998e6	−0.180430	−0.0902148	−	0.995922i	$-0.528755\pi$
$89$	−1.19998e6	−0.180430	−0.0902148	+	0.995922i	$0.528755\pi$
$90$	0	0
$91$	−901704.	−0.125435
$92$	778688.	0.104257
$93$	0	0
$94$	−1.60020e6	−0.198714
$95$	−1.12716e7	−1.34882
$96$	0	0
$97$	8.97814e6	0.998815	0.499408	−	0.866367i	$-0.333551\pi$
$97$	8.97814e6	0.998815	0.499408	+	0.866367i	$0.333551\pi$
$98$	5.63378e6	0.604656
$99$	0	0
$100$	6.71257e6	0.671257
$101$	9.74940e6	0.941571	0.470785	−	0.882248i	$-0.343971\pi$
$101$	9.74940e6	0.941571	0.470785	+	0.882248i	$0.343971\pi$
$102$	0	0
$103$	−1.50223e7	−1.35459	−0.677294	−	0.735713i	$-0.736847\pi$
$103$	−1.50223e7	−1.35459	−0.677294	+	0.735713i	$0.736847\pi$
$104$	1.33652e6	0.116509
$105$	0	0
$106$	−1.29934e7	−1.05962
$107$	1.75798e7	1.38730	0.693650	−	0.720312i	$-0.256001\pi$
$107$	1.75798e7	1.38730	0.693650	+	0.720312i	$0.256001\pi$
$108$	0	0
$109$	1.64602e7	1.21742	0.608711	−	0.793392i	$-0.291687\pi$
$109$	1.64602e7	1.21742	0.608711	+	0.793392i	$0.291687\pi$
$110$	7.46604e6	0.534830
$111$	0	0
$112$	1.41488e6	0.0951602
$113$	−1.70487e6	−0.111152	−0.0555761	−	0.998454i	$-0.517700\pi$
$113$	−1.70487e6	−0.111152	−0.0555761	+	0.998454i	$0.517700\pi$
$114$	0	0
$115$	5.20499e6	0.319137
$116$	−1.60545e7	−0.954977
$117$	0	0
$118$	−1.74929e7	−0.980112
$119$	−1.31190e7	−0.713654
$120$	0	0
$121$	−1.47280e7	−0.755781
$122$	−2.03817e7	−1.01620
$123$	0	0
$124$	1.14653e7	0.540017
$125$	1.14474e7	0.524228
$126$	0	0
$127$	1.90880e7	0.826889	0.413444	−	0.910529i	$-0.364326\pi$
$127$	1.90880e7	0.826889	0.413444	+	0.910529i	$0.364326\pi$
$128$	−2.09715e6	−0.0883883
$129$	0	0
$130$	8.93371e6	0.356640
$131$	−3.31709e6	−0.128916	−0.0644582	−	0.997920i	$-0.520532\pi$
$131$	−3.31709e6	−0.128916	−0.0644582	+	0.997920i	$0.520532\pi$
$132$	0	0
$133$	−9.10140e6	−0.335450
$134$	−3.73045e7	−1.33935
$135$	0	0
$136$	1.94453e7	0.662869
$137$	5.17700e7	1.72011	0.860055	−	0.510202i	$-0.170429\pi$
$137$	5.17700e7	1.72011	0.860055	+	0.510202i	$0.170429\pi$
$138$	0	0
$139$	−1.27587e7	−0.402954	−0.201477	−	0.979493i	$-0.564574\pi$
$139$	−1.27587e7	−0.402954	−0.201477	+	0.979493i	$0.564574\pi$
$140$	9.45746e6	0.291291
$141$	0	0
$142$	3.22314e7	0.944647
$143$	5.69468e6	0.162852
$144$	0	0
$145$	−1.07313e8	−2.92324
$146$	2.06424e7	0.548941
$147$	0	0
$148$	2.77940e7	0.704749
$149$	4.76667e7	1.18049	0.590246	−	0.807223i	$-0.299031\pi$
$149$	4.76667e7	1.18049	0.590246	+	0.807223i	$0.299031\pi$
$150$	0	0
$151$	4.87918e7	1.15326	0.576631	−	0.817005i	$-0.304367\pi$
$151$	4.87918e7	1.15326	0.576631	+	0.817005i	$0.304367\pi$
$152$	1.34902e7	0.311578
$153$	0	0
$154$	6.02854e6	0.133012
$155$	7.66372e7	1.65302
$156$	0	0
$157$	1.52646e7	0.314801	0.157401	−	0.987535i	$-0.449689\pi$
$157$	1.52646e7	0.314801	0.157401	+	0.987535i	$0.449689\pi$
$158$	−9.76259e6	−0.196909
$159$	0	0
$160$	−1.40180e7	−0.270562
$161$	4.20283e6	0.0793691
$162$	0	0
$163$	−7.21694e7	−1.30526	−0.652629	−	0.757678i	$-0.726334\pi$
$163$	−7.21694e7	−1.30526	−0.652629	+	0.757678i	$0.726334\pi$
$164$	1.28274e7	0.227084
$165$	0	0
$166$	−1.73268e7	−0.293995
$167$	−3.34621e7	−0.555962	−0.277981	−	0.960587i	$-0.589665\pi$
$167$	−3.34621e7	−0.555962	−0.277981	+	0.960587i	$0.589665\pi$
$168$	0	0
$169$	−5.59344e7	−0.891405
$170$	1.29978e8	2.02908
$171$	0	0
$172$	5.38461e7	0.806873
$173$	4.16573e7	0.611688	0.305844	−	0.952082i	$-0.401061\pi$
$173$	4.16573e7	0.611688	0.305844	+	0.952082i	$0.401061\pi$
$174$	0	0
$175$	3.62299e7	0.511016
$176$	−8.93560e6	−0.123546
$177$	0	0
$178$	9.59982e6	0.127583
$179$	6.94962e7	0.905682	0.452841	−	0.891591i	$-0.350411\pi$
$179$	6.94962e7	0.905682	0.452841	+	0.891591i	$0.350411\pi$
$180$	0	0
$181$	3.54533e7	0.444408	0.222204	−	0.975000i	$-0.428675\pi$
$181$	3.54533e7	0.444408	0.222204	+	0.975000i	$0.428675\pi$
$182$	7.21363e6	0.0886960
$183$	0	0
$184$	−6.22950e6	−0.0737210
$185$	1.85783e8	2.15728
$186$	0	0
$187$	8.28529e7	0.926536
$188$	1.28016e7	0.140512
$189$	0	0
$190$	9.01729e7	0.953758
$191$	−5.59759e7	−0.581279	−0.290639	−	0.956833i	$-0.593868\pi$
$191$	−5.59759e7	−0.581279	−0.290639	+	0.956833i	$0.593868\pi$
$192$	0	0
$193$	8.02723e7	0.803740	0.401870	−	0.915697i	$-0.368360\pi$
$193$	8.02723e7	0.803740	0.401870	+	0.915697i	$0.368360\pi$
$194$	−7.18251e7	−0.706269
$195$	0	0
$196$	−4.50702e7	−0.427556
$197$	−3.52484e7	−0.328479	−0.164240	−	0.986420i	$-0.552517\pi$
$197$	−3.52484e7	−0.328479	−0.164240	+	0.986420i	$0.552517\pi$
$198$	0	0
$199$	4.36909e7	0.393012	0.196506	−	0.980503i	$-0.437041\pi$
$199$	4.36909e7	0.393012	0.196506	+	0.980503i	$0.437041\pi$
$200$	−5.37006e7	−0.474651
$201$	0	0
$202$	−7.79952e7	−0.665791
$203$	−8.66511e7	−0.727006
$204$	0	0
$205$	8.57425e7	0.695116
$206$	1.20179e8	0.957838
$207$	0	0
$208$	−1.06922e7	−0.0823842
$209$	5.74796e7	0.435514
$210$	0	0
$211$	−1.86224e8	−1.36473	−0.682365	−	0.731012i	$-0.739048\pi$
$211$	−1.86224e8	−1.36473	−0.682365	+	0.731012i	$0.739048\pi$
$212$	1.03947e8	0.749266
$213$	0	0
$214$	−1.40638e8	−0.980970
$215$	3.59924e8	2.46988
$216$	0	0
$217$	6.18817e7	0.411105
$218$	−1.31681e8	−0.860848
$219$	0	0
$220$	−5.97283e7	−0.378182
$221$	9.91401e7	0.617841
$222$	0	0
$223$	4.97859e7	0.300635	0.150317	−	0.988638i	$-0.451970\pi$
$223$	4.97859e7	0.300635	0.150317	+	0.988638i	$0.451970\pi$
$224$	−1.13190e7	−0.0672884
$225$	0	0
$226$	1.36390e7	0.0785964
$227$	−1.75842e8	−0.997773	−0.498886	−	0.866667i	$-0.666257\pi$
$227$	−1.75842e8	−0.997773	−0.498886	+	0.866667i	$0.666257\pi$
$228$	0	0
$229$	4.00032e7	0.220125	0.110063	−	0.993925i	$-0.464895\pi$
$229$	4.00032e7	0.220125	0.110063	+	0.993925i	$0.464895\pi$
$230$	−4.16399e7	−0.225664
$231$	0	0
$232$	1.28436e8	0.675271
$233$	−1.16608e8	−0.603923	−0.301962	−	0.953320i	$-0.597641\pi$
$233$	−1.16608e8	−0.603923	−0.301962	+	0.953320i	$0.597641\pi$
$234$	0	0
$235$	8.55700e7	0.430114
$236$	1.39944e8	0.693044
$237$	0	0
$238$	1.04952e8	0.504630
$239$	7.54954e7	0.357707	0.178854	−	0.983876i	$-0.442761\pi$
$239$	7.54954e7	0.357707	0.178854	+	0.983876i	$0.442761\pi$
$240$	0	0
$241$	4.32182e8	1.98887	0.994436	−	0.105346i	$-0.0335949\pi$
$241$	4.32182e8	1.98887	0.994436	+	0.105346i	$0.0335949\pi$
$242$	1.17824e8	0.534418
$243$	0	0
$244$	1.63053e8	0.718564
$245$	−3.01263e8	−1.30877
$246$	0	0
$247$	6.87789e7	0.290413
$248$	−9.17220e7	−0.381850
$249$	0	0
$250$	−9.15789e7	−0.370685
$251$	1.77661e8	0.709141	0.354571	−	0.935029i	$-0.384627\pi$
$251$	1.77661e8	0.709141	0.354571	+	0.935029i	$0.384627\pi$
$252$	0	0
$253$	−2.65428e7	−0.103045
$254$	−1.52704e8	−0.584699
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	3.32079e8	1.22033	0.610163	−	0.792276i	$-0.291104\pi$
$257$	3.32079e8	1.22033	0.610163	+	0.792276i	$0.291104\pi$
$258$	0	0
$259$	1.50013e8	0.536513
$260$	−7.14697e7	−0.252183
$261$	0	0
$262$	2.65368e7	0.0911577
$263$	−3.55827e8	−1.20613	−0.603064	−	0.797693i	$-0.706054\pi$
$263$	−3.55827e8	−1.20613	−0.603064	+	0.797693i	$0.706054\pi$
$264$	0	0
$265$	6.94812e8	2.29354
$266$	7.28112e7	0.237199
$267$	0	0
$268$	2.98436e8	0.947063
$269$	−2.51996e6	−0.00789332	−0.00394666	−	0.999992i	$-0.501256\pi$
$269$	−2.51996e6	−0.00789332	−0.00394666	+	0.999992i	$0.501256\pi$
$270$	0	0
$271$	−4.75682e7	−0.145186	−0.0725929	−	0.997362i	$-0.523127\pi$
$271$	−4.75682e7	−0.145186	−0.0725929	+	0.997362i	$0.523127\pi$
$272$	−1.55562e8	−0.468719
$273$	0	0
$274$	−4.14160e8	−1.21630
$275$	−2.28809e8	−0.663451
$276$	0	0
$277$	−6.57962e7	−0.186004	−0.0930018	−	0.995666i	$-0.529646\pi$
$277$	−6.57962e7	−0.186004	−0.0930018	+	0.995666i	$0.529646\pi$
$278$	1.02070e8	0.284932
$279$	0	0
$280$	−7.56597e7	−0.205973
$281$	−1.33552e8	−0.359069	−0.179535	−	0.983752i	$-0.557459\pi$
$281$	−1.33552e8	−0.359069	−0.179535	+	0.983752i	$0.557459\pi$
$282$	0	0
$283$	−1.61478e8	−0.423508	−0.211754	−	0.977323i	$-0.567917\pi$
$283$	−1.61478e8	−0.423508	−0.211754	+	0.977323i	$0.567917\pi$
$284$	−2.57851e8	−0.667966
$285$	0	0
$286$	−4.55575e7	−0.115154
$287$	6.92338e7	0.172875
$288$	0	0
$289$	1.03207e9	2.51516
$290$	8.58504e8	2.06704
$291$	0	0
$292$	−1.65139e8	−0.388160
$293$	1.53715e8	0.357009	0.178505	−	0.983939i	$-0.442874\pi$
$293$	1.53715e8	0.357009	0.178505	+	0.983939i	$0.442874\pi$
$294$	0	0
$295$	9.35425e8	2.12145
$296$	−2.22352e8	−0.498333
$297$	0	0
$298$	−3.81333e8	−0.834734
$299$	−3.17606e7	−0.0687132
$300$	0	0
$301$	2.90625e8	0.614257
$302$	−3.90335e8	−0.815479
$303$	0	0
$304$	−1.07922e8	−0.220319
$305$	1.08990e9	2.19957
$306$	0	0
$307$	−4.52238e8	−0.892037	−0.446019	−	0.895024i	$-0.647159\pi$
$307$	−4.52238e8	−0.892037	−0.446019	+	0.895024i	$0.647159\pi$
$308$	−4.82283e7	−0.0940534
$309$	0	0
$310$	−6.13098e8	−1.16886
$311$	−7.24988e8	−1.36669	−0.683344	−	0.730096i	$-0.739475\pi$
$311$	−7.24988e8	−1.36669	−0.683344	+	0.730096i	$0.739475\pi$
$312$	0	0
$313$	−5.66818e8	−1.04481	−0.522407	−	0.852696i	$-0.674966\pi$
$313$	−5.66818e8	−1.04481	−0.522407	+	0.852696i	$0.674966\pi$
$314$	−1.22117e8	−0.222598
$315$	0	0
$316$	7.81007e7	0.139236
$317$	9.63349e8	1.69854	0.849271	−	0.527958i	$-0.177042\pi$
$317$	9.63349e8	1.69854	0.849271	+	0.527958i	$0.177042\pi$
$318$	0	0
$319$	5.47243e8	0.943871
$320$	1.12144e8	0.191316
$321$	0	0
$322$	−3.36226e7	−0.0561224
$323$	1.00068e9	1.65228
$324$	0	0
$325$	−2.73788e8	−0.442408
$326$	5.77355e8	0.922957
$327$	0	0
$328$	−1.02619e8	−0.160573
$329$	6.90945e7	0.106969
$330$	0	0
$331$	−4.26221e8	−0.646006	−0.323003	−	0.946398i	$-0.604692\pi$
$331$	−4.26221e8	−0.646006	−0.323003	+	0.946398i	$0.604692\pi$
$332$	1.38614e8	0.207886
$333$	0	0
$334$	2.67697e8	0.393125
$335$	1.99483e9	2.89901
$336$	0	0
$337$	−2.41775e8	−0.344118	−0.172059	−	0.985087i	$-0.555042\pi$
$337$	−2.41775e8	−0.344118	−0.172059	+	0.985087i	$0.555042\pi$
$338$	4.47475e8	0.630319
$339$	0	0
$340$	−1.03982e9	−1.43477
$341$	−3.90812e8	−0.533737
$342$	0	0
$343$	−5.27734e8	−0.706131
$344$	−4.30769e8	−0.570545
$345$	0	0
$346$	−3.33258e8	−0.432528
$347$	−1.34412e9	−1.72697	−0.863484	−	0.504375i	$-0.831723\pi$
$347$	−1.34412e9	−1.72697	−0.863484	+	0.504375i	$0.831723\pi$
$348$	0	0
$349$	3.27029e8	0.411811	0.205905	−	0.978572i	$-0.433986\pi$
$349$	3.27029e8	0.411811	0.205905	+	0.978572i	$0.433986\pi$
$350$	−2.89839e8	−0.361343
$351$	0	0
$352$	7.14848e7	0.0873604
$353$	−1.52857e9	−1.84958	−0.924789	−	0.380480i	$-0.875759\pi$
$353$	−1.52857e9	−1.84958	−0.924789	+	0.380480i	$0.875759\pi$
$354$	0	0
$355$	−1.72355e9	−2.04468
$356$	−7.67985e7	−0.0902148
$357$	0	0
$358$	−5.55970e8	−0.640414
$359$	4.65294e7	0.0530759	0.0265379	−	0.999648i	$-0.491552\pi$
$359$	4.65294e7	0.0530759	0.0265379	+	0.999648i	$0.491552\pi$
$360$	0	0
$361$	−1.99648e8	−0.223352
$362$	−2.83627e8	−0.314244
$363$	0	0
$364$	−5.77091e7	−0.0627176
$365$	−1.10384e9	−1.18818
$366$	0	0
$367$	4.58322e8	0.483993	0.241997	−	0.970277i	$-0.422198\pi$
$367$	4.58322e8	0.483993	0.241997	+	0.970277i	$0.422198\pi$
$368$	4.98360e7	0.0521286
$369$	0	0
$370$	−1.48627e9	−1.52543
$371$	5.61035e8	0.570402
$372$	0	0
$373$	7.39771e8	0.738102	0.369051	−	0.929409i	$-0.379683\pi$
$373$	7.39771e8	0.738102	0.369051	+	0.929409i	$0.379683\pi$
$374$	−6.62823e8	−0.655160
$375$	0	0
$376$	−1.02413e8	−0.0993568
$377$	6.54820e8	0.629400
$378$	0	0
$379$	3.93984e8	0.371742	0.185871	−	0.982574i	$-0.440489\pi$
$379$	3.93984e8	0.371742	0.185871	+	0.982574i	$0.440489\pi$
$380$	−7.21383e8	−0.674409
$381$	0	0
$382$	4.47807e8	0.411026
$383$	−1.33816e9	−1.21706	−0.608530	−	0.793531i	$-0.708240\pi$
$383$	−1.33816e9	−1.21706	−0.608530	+	0.793531i	$0.708240\pi$
$384$	0	0
$385$	−3.22373e8	−0.287903
$386$	−6.42179e8	−0.568330
$387$	0	0
$388$	5.74601e8	0.499408
$389$	1.71698e9	1.47891	0.739455	−	0.673206i	$-0.235083\pi$
$389$	1.71698e9	1.47891	0.739455	+	0.673206i	$0.235083\pi$
$390$	0	0
$391$	−4.62091e8	−0.390939
$392$	3.60562e8	0.302328
$393$	0	0
$394$	2.81987e8	0.232270
$395$	5.22049e8	0.426208
$396$	0	0
$397$	−9.91563e7	−0.0795341	−0.0397671	−	0.999209i	$-0.512662\pi$
$397$	−9.91563e7	−0.0795341	−0.0397671	+	0.999209i	$0.512662\pi$
$398$	−3.49528e8	−0.277901
$399$	0	0
$400$	4.29605e8	0.335629
$401$	−1.41606e9	−1.09667	−0.548334	−	0.836259i	$-0.684738\pi$
$401$	−1.41606e9	−1.09667	−0.548334	+	0.836259i	$0.684738\pi$
$402$	0	0
$403$	−4.67638e8	−0.355911
$404$	6.23961e8	0.470785
$405$	0	0
$406$	6.93209e8	0.514071
$407$	−9.47403e8	−0.696553
$408$	0	0
$409$	−1.39619e9	−1.00905	−0.504524	−	0.863397i	$-0.668332\pi$
$409$	−1.39619e9	−1.00905	−0.504524	+	0.863397i	$0.668332\pi$
$410$	−6.85940e8	−0.491521
$411$	0	0
$412$	−9.61429e8	−0.677294
$413$	7.55320e8	0.527601
$414$	0	0
$415$	9.26540e8	0.636350
$416$	8.55373e7	0.0582544
$417$	0	0
$418$	−4.59837e8	−0.307955
$419$	9.81338e8	0.651733	0.325866	−	0.945416i	$-0.394344\pi$
$419$	9.81338e8	0.651733	0.325866	+	0.945416i	$0.394344\pi$
$420$	0	0
$421$	−1.16824e9	−0.763037	−0.381518	−	0.924361i	$-0.624599\pi$
$421$	−1.16824e9	−0.763037	−0.381518	+	0.924361i	$0.624599\pi$
$422$	1.48979e9	0.965010
$423$	0	0
$424$	−8.31575e8	−0.529811
$425$	−3.98339e9	−2.51705
$426$	0	0
$427$	8.80052e8	0.547030
$428$	1.12511e9	0.693650
$429$	0	0
$430$	−2.87939e9	−1.74647
$431$	−1.91210e9	−1.15037	−0.575187	−	0.818022i	$-0.695071\pi$
$431$	−1.91210e9	−1.15037	−0.575187	+	0.818022i	$0.695071\pi$
$432$	0	0
$433$	1.67730e9	0.992894	0.496447	−	0.868067i	$-0.334638\pi$
$433$	1.67730e9	0.992894	0.496447	+	0.868067i	$0.334638\pi$
$434$	−4.95053e8	−0.290695
$435$	0	0
$436$	1.05345e9	0.608711
$437$	−3.20578e8	−0.183759
$438$	0	0
$439$	−1.78469e8	−0.100679	−0.0503393	−	0.998732i	$-0.516030\pi$
$439$	−1.78469e8	−0.100679	−0.0503393	+	0.998732i	$0.516030\pi$
$440$	4.77826e8	0.267415
$441$	0	0
$442$	−7.93121e8	−0.436879
$443$	−1.00078e7	−0.00546921	−0.00273461	−	0.999996i	$-0.500870\pi$
$443$	−1.00078e7	−0.00546921	−0.00273461	+	0.999996i	$0.500870\pi$
$444$	0	0
$445$	−5.13345e8	−0.276153
$446$	−3.98287e8	−0.212581
$447$	0	0
$448$	9.05520e7	0.0475801
$449$	−2.38685e9	−1.24441	−0.622203	−	0.782856i	$-0.713762\pi$
$449$	−2.38685e9	−1.24441	−0.622203	+	0.782856i	$0.713762\pi$
$450$	0	0
$451$	−4.37244e8	−0.224443
$452$	−1.09112e8	−0.0555761
$453$	0	0
$454$	1.40673e9	0.705532
$455$	−3.85745e8	−0.191982
$456$	0	0
$457$	1.40659e9	0.689385	0.344692	−	0.938716i	$-0.387983\pi$
$457$	1.40659e9	0.689385	0.344692	+	0.938716i	$0.387983\pi$
$458$	−3.20025e8	−0.155652
$459$	0	0
$460$	3.33119e8	0.159569
$461$	8.75198e8	0.416057	0.208029	−	0.978123i	$-0.433295\pi$
$461$	8.75198e8	0.416057	0.208029	+	0.978123i	$0.433295\pi$
$462$	0	0
$463$	−8.95572e8	−0.419341	−0.209670	−	0.977772i	$-0.567239\pi$
$463$	−8.95572e8	−0.419341	−0.209670	+	0.977772i	$0.567239\pi$
$464$	−1.02749e9	−0.477489
$465$	0	0
$466$	9.32862e8	0.427038
$467$	2.18071e9	0.990807	0.495403	−	0.868663i	$-0.335020\pi$
$467$	2.18071e9	0.990807	0.495403	+	0.868663i	$0.335020\pi$
$468$	0	0
$469$	1.61075e9	0.720981
$470$	−6.84560e8	−0.304137
$471$	0	0
$472$	−1.11955e9	−0.490056
$473$	−1.83543e9	−0.797489
$474$	0	0
$475$	−2.76350e9	−1.18313
$476$	−8.39619e8	−0.356827
$477$	0	0
$478$	−6.03963e8	−0.252937
$479$	−1.86608e9	−0.775812	−0.387906	−	0.921699i	$-0.626801\pi$
$479$	−1.86608e9	−0.775812	−0.387906	+	0.921699i	$0.626801\pi$
$480$	0	0
$481$	−1.13364e9	−0.464482
$482$	−3.45745e9	−1.40634
$483$	0	0
$484$	−9.42594e8	−0.377891
$485$	3.84081e9	1.52871
$486$	0	0
$487$	−9.54001e8	−0.374281	−0.187140	−	0.982333i	$-0.559922\pi$
$487$	−9.54001e8	−0.374281	−0.187140	+	0.982333i	$0.559922\pi$
$488$	−1.30443e9	−0.508102
$489$	0	0
$490$	2.41010e9	0.925443
$491$	−1.21183e9	−0.462017	−0.231008	−	0.972952i	$-0.574202\pi$
$491$	−1.21183e9	−0.462017	−0.231008	+	0.972952i	$0.574202\pi$
$492$	0	0
$493$	9.52708e9	3.58093
$494$	−5.50232e8	−0.205353
$495$	0	0
$496$	7.33776e8	0.270009
$497$	−1.39170e9	−0.508510
$498$	0	0
$499$	−1.17097e9	−0.421884	−0.210942	−	0.977499i	$-0.567653\pi$
$499$	−1.17097e9	−0.421884	−0.210942	+	0.977499i	$0.567653\pi$
$500$	7.32631e8	0.262114
$501$	0	0
$502$	−1.42128e9	−0.501439
$503$	3.36243e9	1.17806	0.589028	−	0.808113i	$-0.299511\pi$
$503$	3.36243e9	1.17806	0.589028	+	0.808113i	$0.299511\pi$
$504$	0	0
$505$	4.17075e9	1.44110
$506$	2.12343e8	0.0728636
$507$	0	0
$508$	1.22163e9	0.413444
$509$	3.89948e9	1.31067	0.655336	−	0.755337i	$-0.272527\pi$
$509$	3.89948e9	1.31067	0.655336	+	0.755337i	$0.272527\pi$
$510$	0	0
$511$	−8.91310e8	−0.295499
$512$	−1.34218e8	−0.0441942
$513$	0	0
$514$	−2.65663e9	−0.862900
$515$	−6.42648e9	−2.07323
$516$	0	0
$517$	−4.36364e8	−0.138878
$518$	−1.20010e9	−0.379372
$519$	0	0
$520$	5.71758e8	0.178320
$521$	4.08573e9	1.26572	0.632860	−	0.774266i	$-0.281881\pi$
$521$	4.08573e9	1.26572	0.632860	+	0.774266i	$0.281881\pi$
$522$	0	0
$523$	−6.17299e9	−1.88686	−0.943430	−	0.331571i	$-0.892421\pi$
$523$	−6.17299e9	−1.88686	−0.943430	+	0.331571i	$0.892421\pi$
$524$	−2.12294e8	−0.0644582
$525$	0	0
$526$	2.84661e9	0.852861
$527$	−6.80374e9	−2.02493
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−5.55850e9	−1.62178
$531$	0	0
$532$	−5.82489e8	−0.167725
$533$	−5.23197e8	−0.149665
$534$	0	0
$535$	7.52056e9	2.12330
$536$	−2.38748e9	−0.669675
$537$	0	0
$538$	2.01596e7	0.00558142
$539$	1.53629e9	0.422584
$540$	0	0
$541$	6.18398e9	1.67910	0.839552	−	0.543280i	$-0.182818\pi$
$541$	6.18398e9	1.67910	0.839552	+	0.543280i	$0.182818\pi$
$542$	3.80546e8	0.102662
$543$	0	0
$544$	1.24450e9	0.331434
$545$	7.04158e9	1.86330
$546$	0	0
$547$	−3.11011e9	−0.812494	−0.406247	−	0.913763i	$-0.633163\pi$
$547$	−3.11011e9	−0.812494	−0.406247	+	0.913763i	$0.633163\pi$
$548$	3.31328e9	0.860055
$549$	0	0
$550$	1.83047e9	0.469130
$551$	6.60946e9	1.68320
$552$	0	0
$553$	4.21535e8	0.105997
$554$	5.26369e8	0.131524
$555$	0	0
$556$	−8.16559e8	−0.201477
$557$	−5.56754e9	−1.36512	−0.682559	−	0.730831i	$-0.739133\pi$
$557$	−5.56754e9	−1.36512	−0.682559	+	0.730831i	$0.739133\pi$
$558$	0	0
$559$	−2.19624e9	−0.531789
$560$	6.05277e8	0.145645
$561$	0	0
$562$	1.06842e9	0.253900
$563$	6.88023e9	1.62489	0.812445	−	0.583038i	$-0.198136\pi$
$563$	6.88023e9	1.62489	0.812445	+	0.583038i	$0.198136\pi$
$564$	0	0
$565$	−7.29337e8	−0.170121
$566$	1.29182e9	0.299465
$567$	0	0
$568$	2.06281e9	0.472323
$569$	−8.40627e9	−1.91298	−0.956490	−	0.291765i	$-0.905758\pi$
$569$	−8.40627e9	−1.91298	−0.956490	+	0.291765i	$0.905758\pi$
$570$	0	0
$571$	−5.25925e8	−0.118222	−0.0591109	−	0.998251i	$-0.518827\pi$
$571$	−5.25925e8	−0.118222	−0.0591109	+	0.998251i	$0.518827\pi$
$572$	3.64460e8	0.0814261
$573$	0	0
$574$	−5.53870e8	−0.122241
$575$	1.27612e9	0.279934
$576$	0	0
$577$	−1.66741e9	−0.361349	−0.180674	−	0.983543i	$-0.557828\pi$
$577$	−1.66741e9	−0.361349	−0.180674	+	0.983543i	$0.557828\pi$
$578$	−8.25654e9	−1.77849
$579$	0	0
$580$	−6.86803e9	−1.46162
$581$	7.48146e8	0.158259
$582$	0	0
$583$	−3.54320e9	−0.740552
$584$	1.32111e9	0.274470
$585$	0	0
$586$	−1.22972e9	−0.252444
$587$	1.24841e9	0.254756	0.127378	−	0.991854i	$-0.459344\pi$
$587$	1.24841e9	0.254756	0.127378	+	0.991854i	$0.459344\pi$
$588$	0	0
$589$	−4.72012e9	−0.951809
$590$	−7.48340e9	−1.50009
$591$	0	0
$592$	1.77881e9	0.352375
$593$	2.61091e9	0.514163	0.257081	−	0.966390i	$-0.417239\pi$
$593$	2.61091e9	0.514163	0.257081	+	0.966390i	$0.417239\pi$
$594$	0	0
$595$	−5.61227e9	−1.09227
$596$	3.05067e9	0.590246
$597$	0	0
$598$	2.54085e8	0.0485876
$599$	6.36475e9	1.21001	0.605003	−	0.796223i	$-0.293172\pi$
$599$	6.36475e9	1.21001	0.605003	+	0.796223i	$0.293172\pi$
$600$	0	0
$601$	−1.44570e9	−0.271656	−0.135828	−	0.990732i	$-0.543369\pi$
$601$	−1.44570e9	−0.271656	−0.135828	+	0.990732i	$0.543369\pi$
$602$	−2.32500e9	−0.434345
$603$	0	0
$604$	3.12268e9	0.576631
$605$	−6.30059e9	−1.15674
$606$	0	0
$607$	−4.03112e9	−0.731586	−0.365793	−	0.930696i	$-0.619202\pi$
$607$	−4.03112e9	−0.731586	−0.365793	+	0.930696i	$0.619202\pi$
$608$	8.63375e8	0.155789
$609$	0	0
$610$	−8.71919e9	−1.55533
$611$	−5.22145e8	−0.0926076
$612$	0	0
$613$	2.16682e9	0.379936	0.189968	−	0.981790i	$-0.439162\pi$
$613$	2.16682e9	0.379936	0.189968	+	0.981790i	$0.439162\pi$
$614$	3.61791e9	0.630766
$615$	0	0
$616$	3.85827e8	0.0665058
$617$	3.74148e9	0.641276	0.320638	−	0.947202i	$-0.396103\pi$
$617$	3.74148e9	0.641276	0.320638	+	0.947202i	$0.396103\pi$
$618$	0	0
$619$	1.01384e10	1.71811	0.859054	−	0.511885i	$-0.171053\pi$
$619$	1.01384e10	1.71811	0.859054	+	0.511885i	$0.171053\pi$
$620$	4.90478e9	0.826511
$621$	0	0
$622$	5.79990e9	0.966394
$623$	−4.14506e8	−0.0686789
$624$	0	0
$625$	−3.29693e9	−0.540169
$626$	4.53455e9	0.738795
$627$	0	0
$628$	9.76934e8	0.157401
$629$	−1.64936e10	−2.64264
$630$	0	0
$631$	8.21596e9	1.30183	0.650917	−	0.759149i	$-0.274385\pi$
$631$	8.21596e9	1.30183	0.650917	+	0.759149i	$0.274385\pi$
$632$	−6.24806e8	−0.0984544
$633$	0	0
$634$	−7.70679e9	−1.20105
$635$	8.16575e9	1.26558
$636$	0	0
$637$	1.83830e9	0.281791
$638$	−4.37794e9	−0.667417
$639$	0	0
$640$	−8.97152e8	−0.135281
$641$	−8.20911e8	−0.123110	−0.0615549	−	0.998104i	$-0.519606\pi$
$641$	−8.20911e8	−0.123110	−0.0615549	+	0.998104i	$0.519606\pi$
$642$	0	0
$643$	5.92103e9	0.878333	0.439166	−	0.898406i	$-0.355274\pi$
$643$	5.92103e9	0.878333	0.439166	+	0.898406i	$0.355274\pi$
$644$	2.68981e8	0.0396845
$645$	0	0
$646$	−8.00541e9	−1.16834
$647$	1.09657e10	1.59174	0.795870	−	0.605468i	$-0.207014\pi$
$647$	1.09657e10	1.59174	0.795870	+	0.605468i	$0.207014\pi$
$648$	0	0
$649$	−4.77020e9	−0.684984
$650$	2.19031e9	0.312830
$651$	0	0
$652$	−4.61884e9	−0.652629
$653$	6.73255e9	0.946201	0.473101	−	0.881008i	$-0.343135\pi$
$653$	6.73255e9	0.946201	0.473101	+	0.881008i	$0.343135\pi$
$654$	0	0
$655$	−1.41904e9	−0.197310
$656$	8.20956e8	0.113542
$657$	0	0
$658$	−5.52756e8	−0.0756385
$659$	1.25637e10	1.71009	0.855043	−	0.518557i	$-0.173531\pi$
$659$	1.25637e10	1.71009	0.855043	+	0.518557i	$0.173531\pi$
$660$	0	0
$661$	7.27312e9	0.979526	0.489763	−	0.871856i	$-0.337083\pi$
$661$	7.27312e9	0.979526	0.489763	+	0.871856i	$0.337083\pi$
$662$	3.40977e9	0.456796
$663$	0	0
$664$	−1.10891e9	−0.146997
$665$	−3.89354e9	−0.513415
$666$	0	0
$667$	−3.05210e9	−0.398253
$668$	−2.14157e9	−0.277981
$669$	0	0
$670$	−1.59587e10	−2.04991
$671$	−5.55794e9	−0.710207
$672$	0	0
$673$	−2.38576e9	−0.301699	−0.150849	−	0.988557i	$-0.548201\pi$
$673$	−2.38576e9	−0.301699	−0.150849	+	0.988557i	$0.548201\pi$
$674$	1.93420e9	0.243328
$675$	0	0
$676$	−3.57980e9	−0.445703
$677$	1.25080e10	1.54928	0.774639	−	0.632404i	$-0.217932\pi$
$677$	1.25080e10	1.54928	0.774639	+	0.632404i	$0.217932\pi$
$678$	0	0
$679$	3.10131e9	0.380190
$680$	8.31859e9	1.01454
$681$	0	0
$682$	3.12649e9	0.377409
$683$	6.33284e9	0.760548	0.380274	−	0.924874i	$-0.375830\pi$
$683$	6.33284e9	0.760548	0.380274	+	0.924874i	$0.375830\pi$
$684$	0	0
$685$	2.21470e10	2.63267
$686$	4.22187e9	0.499310
$687$	0	0
$688$	3.44615e9	0.403436
$689$	−4.23972e9	−0.493821
$690$	0	0
$691$	−2.30362e9	−0.265606	−0.132803	−	0.991142i	$-0.542398\pi$
$691$	−2.30362e9	−0.265606	−0.132803	+	0.991142i	$0.542398\pi$
$692$	2.66607e9	0.305844
$693$	0	0
$694$	1.07530e10	1.22115
$695$	−5.45813e9	−0.616733
$696$	0	0
$697$	−7.61208e9	−0.851508
$698$	−2.61624e9	−0.291194
$699$	0	0
$700$	2.31871e9	0.255508
$701$	5.07693e9	0.556657	0.278329	−	0.960486i	$-0.410220\pi$
$701$	5.07693e9	0.556657	0.278329	+	0.960486i	$0.410220\pi$
$702$	0	0
$703$	−1.14425e10	−1.24216
$704$	−5.71879e8	−0.0617731
$705$	0	0
$706$	1.22285e10	1.30785
$707$	3.36772e9	0.358400
$708$	0	0
$709$	8.96481e8	0.0944669	0.0472334	−	0.998884i	$-0.484960\pi$
$709$	8.96481e8	0.0944669	0.0472334	+	0.998884i	$0.484960\pi$
$710$	1.37884e10	1.44581
$711$	0	0
$712$	6.14388e8	0.0637915
$713$	2.17965e9	0.225203
$714$	0	0
$715$	2.43616e9	0.249250
$716$	4.44776e9	0.452841
$717$	0	0
$718$	−3.72235e8	−0.0375303
$719$	4.13828e9	0.415210	0.207605	−	0.978213i	$-0.433433\pi$
$719$	4.13828e9	0.415210	0.207605	+	0.978213i	$0.433433\pi$
$720$	0	0
$721$	−5.18914e9	−0.515611
$722$	1.59718e9	0.157934
$723$	0	0
$724$	2.26901e9	0.222204
$725$	−2.63103e10	−2.56414
$726$	0	0
$727$	1.34281e10	1.29611	0.648057	−	0.761591i	$-0.275582\pi$
$727$	1.34281e10	1.29611	0.648057	+	0.761591i	$0.275582\pi$
$728$	4.61672e8	0.0443480
$729$	0	0
$730$	8.83073e9	0.840169
$731$	−3.19535e10	−3.02557
$732$	0	0
$733$	2.59875e8	0.0243725	0.0121863	−	0.999926i	$-0.496121\pi$
$733$	2.59875e8	0.0243725	0.0121863	+	0.999926i	$0.496121\pi$
$734$	−3.66658e9	−0.342235
$735$	0	0
$736$	−3.98688e8	−0.0368605
$737$	−1.01727e10	−0.936049
$738$	0	0
$739$	−1.08950e10	−0.993056	−0.496528	−	0.868021i	$-0.665392\pi$
$739$	−1.08950e10	−0.993056	−0.496528	+	0.868021i	$0.665392\pi$
$740$	1.18901e10	1.07864
$741$	0	0
$742$	−4.48828e9	−0.403335
$743$	1.77102e10	1.58403	0.792014	−	0.610503i	$-0.209033\pi$
$743$	1.77102e10	1.58403	0.792014	+	0.610503i	$0.209033\pi$
$744$	0	0
$745$	2.03916e10	1.80678
$746$	−5.91817e9	−0.521917
$747$	0	0
$748$	5.30259e9	0.463268
$749$	6.07256e9	0.528063
$750$	0	0
$751$	−2.21088e10	−1.90470	−0.952348	−	0.305013i	$-0.901339\pi$
$751$	−2.21088e10	−1.90470	−0.952348	+	0.305013i	$0.901339\pi$
$752$	8.19304e8	0.0702559
$753$	0	0
$754$	−5.23856e9	−0.445053
$755$	2.08729e10	1.76510
$756$	0	0
$757$	−1.59200e10	−1.33385	−0.666925	−	0.745125i	$-0.732390\pi$
$757$	−1.59200e10	−1.33385	−0.666925	+	0.745125i	$0.732390\pi$
$758$	−3.15188e9	−0.262861
$759$	0	0
$760$	5.77106e9	0.476879
$761$	6.68228e7	0.00549640	0.00274820	−	0.999996i	$-0.499125\pi$
$761$	6.68228e7	0.00549640	0.00274820	+	0.999996i	$0.499125\pi$
$762$	0	0
$763$	5.68581e9	0.463400
$764$	−3.58246e9	−0.290639
$765$	0	0
$766$	1.07053e10	0.860591
$767$	−5.70793e9	−0.456767
$768$	0	0
$769$	−6.62635e9	−0.525451	−0.262726	−	0.964871i	$-0.584621\pi$
$769$	−6.62635e9	−0.525451	−0.262726	+	0.964871i	$0.584621\pi$
$770$	2.57898e9	0.203578
$771$	0	0
$772$	5.13743e9	0.401870
$773$	3.61939e9	0.281843	0.140922	−	0.990021i	$-0.454993\pi$
$773$	3.61939e9	0.281843	0.140922	+	0.990021i	$0.454993\pi$
$774$	0	0
$775$	1.87894e10	1.44996
$776$	−4.59681e9	−0.353135
$777$	0	0
$778$	−1.37359e10	−1.04575
$779$	−5.28092e9	−0.400247
$780$	0	0
$781$	8.78926e9	0.660197
$782$	3.69673e9	0.276435
$783$	0	0
$784$	−2.88449e9	−0.213778
$785$	6.53012e9	0.481812
$786$	0	0
$787$	1.01537e10	0.742525	0.371263	−	0.928528i	$-0.378925\pi$
$787$	1.01537e10	0.742525	0.371263	+	0.928528i	$0.378925\pi$
$788$	−2.25590e9	−0.164240
$789$	0	0
$790$	−4.17639e9	−0.301374
$791$	−5.88912e8	−0.0423090
$792$	0	0
$793$	−6.65052e9	−0.473587
$794$	7.93250e8	0.0562391
$795$	0	0
$796$	2.79622e9	0.196506
$797$	−1.25904e10	−0.880916	−0.440458	−	0.897773i	$-0.645184\pi$
$797$	−1.25904e10	−0.880916	−0.440458	+	0.897773i	$0.645184\pi$
$798$	0	0
$799$	−7.59677e9	−0.526884
$800$	−3.43684e9	−0.237325
$801$	0	0
$802$	1.13285e10	0.775461
$803$	5.62904e9	0.383645
$804$	0	0
$805$	1.79795e9	0.121477
$806$	3.74110e9	0.251667
$807$	0	0
$808$	−4.99169e9	−0.332896
$809$	−2.20668e10	−1.46528	−0.732638	−	0.680618i	$-0.761711\pi$
$809$	−2.20668e10	−1.46528	−0.732638	+	0.680618i	$0.761711\pi$
$810$	0	0
$811$	7.09047e9	0.466769	0.233384	−	0.972385i	$-0.425020\pi$
$811$	7.09047e9	0.466769	0.233384	+	0.972385i	$0.425020\pi$
$812$	−5.54567e9	−0.363503
$813$	0	0
$814$	7.57922e9	0.492537
$815$	−3.08737e10	−1.99773
$816$	0	0
$817$	−2.21679e10	−1.42216
$818$	1.11695e10	0.713505
$819$	0	0
$820$	5.48752e9	0.347558
$821$	−3.26295e9	−0.205783	−0.102891	−	0.994693i	$-0.532809\pi$
$821$	−3.26295e9	−0.205783	−0.102891	+	0.994693i	$0.532809\pi$
$822$	0	0
$823$	4.72161e9	0.295250	0.147625	−	0.989043i	$-0.452837\pi$
$823$	4.72161e9	0.295250	0.147625	+	0.989043i	$0.452837\pi$
$824$	7.69143e9	0.478919
$825$	0	0
$826$	−6.04256e9	−0.373071
$827$	−1.78452e10	−1.09712	−0.548558	−	0.836112i	$-0.684823\pi$
$827$	−1.78452e10	−1.09712	−0.548558	+	0.836112i	$0.684823\pi$
$828$	0	0
$829$	−2.93379e10	−1.78850	−0.894248	−	0.447572i	$-0.852289\pi$
$829$	−2.93379e10	−1.78850	−0.894248	+	0.447572i	$0.852289\pi$
$830$	−7.41232e9	−0.449967
$831$	0	0
$832$	−6.84299e8	−0.0411921
$833$	2.67457e10	1.60323
$834$	0	0
$835$	−1.43149e10	−0.850916
$836$	3.67869e9	0.217757
$837$	0	0
$838$	−7.85070e9	−0.460845
$839$	1.90554e9	0.111391	0.0556957	−	0.998448i	$-0.482262\pi$
$839$	1.90554e9	0.111391	0.0556957	+	0.998448i	$0.482262\pi$
$840$	0	0
$841$	4.56764e10	2.64793
$842$	9.34594e9	0.539549
$843$	0	0
$844$	−1.19183e10	−0.682365
$845$	−2.39285e10	−1.36432
$846$	0	0
$847$	−5.08749e9	−0.287681
$848$	6.65260e9	0.374633
$849$	0	0
$850$	3.18671e10	1.77982
$851$	5.28390e9	0.293901
$852$	0	0
$853$	1.63652e8	0.00902818	0.00451409	−	0.999990i	$-0.498563\pi$
$853$	1.63652e8	0.00902818	0.00451409	+	0.999990i	$0.498563\pi$
$854$	−7.04042e9	−0.386808
$855$	0	0
$856$	−9.00085e9	−0.490485
$857$	6.70099e9	0.363669	0.181834	−	0.983329i	$-0.441797\pi$
$857$	6.70099e9	0.363669	0.181834	+	0.983329i	$0.441797\pi$
$858$	0	0
$859$	1.52632e10	0.821620	0.410810	−	0.911721i	$-0.365246\pi$
$859$	1.52632e10	0.821620	0.410810	+	0.911721i	$0.365246\pi$
$860$	2.30351e10	1.23494
$861$	0	0
$862$	1.52968e10	0.813437
$863$	1.65285e9	0.0875376	0.0437688	−	0.999042i	$-0.486064\pi$
$863$	1.65285e9	0.0875376	0.0437688	+	0.999042i	$0.486064\pi$
$864$	0	0
$865$	1.78208e10	0.936205
$866$	−1.34184e10	−0.702082
$867$	0	0
$868$	3.96043e9	0.205553
$869$	−2.66219e9	−0.137616
$870$	0	0
$871$	−1.21724e10	−0.624184
$872$	−8.42760e9	−0.430424
$873$	0	0
$874$	2.56462e9	0.129937
$875$	3.95425e9	0.199543
$876$	0	0
$877$	−1.13923e10	−0.570313	−0.285156	−	0.958481i	$-0.592045\pi$
$877$	−1.13923e10	−0.570313	−0.285156	+	0.958481i	$0.592045\pi$
$878$	1.42775e9	0.0711905
$879$	0	0
$880$	−3.82261e9	−0.189091
$881$	1.15694e10	0.570024	0.285012	−	0.958524i	$-0.408002\pi$
$881$	1.15694e10	0.570024	0.285012	+	0.958524i	$0.408002\pi$
$882$	0	0
$883$	−2.51966e10	−1.23163	−0.615814	−	0.787892i	$-0.711173\pi$
$883$	−2.51966e10	−1.23163	−0.615814	+	0.787892i	$0.711173\pi$
$884$	6.34497e9	0.308920
$885$	0	0
$886$	8.00622e7	0.00386732
$887$	3.78563e10	1.82140	0.910700	−	0.413069i	$-0.135543\pi$
$887$	3.78563e10	1.82140	0.910700	+	0.413069i	$0.135543\pi$
$888$	0	0
$889$	6.59354e9	0.314747
$890$	4.10676e9	0.195269
$891$	0	0
$892$	3.18630e9	0.150317
$893$	−5.27030e9	−0.247659
$894$	0	0
$895$	2.97302e10	1.38617
$896$	−7.24416e8	−0.0336442
$897$	0	0
$898$	1.90948e10	0.879928
$899$	−4.49386e10	−2.06282
$900$	0	0
$901$	−6.16844e10	−2.80956
$902$	3.49795e9	0.158705
$903$	0	0
$904$	8.72895e8	0.0392982
$905$	1.51668e10	0.680179
$906$	0	0
$907$	−9.07644e9	−0.403915	−0.201957	−	0.979394i	$-0.564730\pi$
$907$	−9.07644e9	−0.403915	−0.201957	+	0.979394i	$0.564730\pi$
$908$	−1.12539e10	−0.498886
$909$	0	0
$910$	3.08596e9	0.135752
$911$	3.63398e10	1.59246	0.796229	−	0.604995i	$-0.206825\pi$
$911$	3.63398e10	1.59246	0.796229	+	0.604995i	$0.206825\pi$
$912$	0	0
$913$	−4.72489e9	−0.205468
$914$	−1.12527e10	−0.487469
$915$	0	0
$916$	2.56020e9	0.110063
$917$	−1.14582e9	−0.0490708
$918$	0	0
$919$	2.16445e10	0.919904	0.459952	−	0.887944i	$-0.347867\pi$
$919$	2.16445e10	0.919904	0.459952	+	0.887944i	$0.347867\pi$
$920$	−2.66495e9	−0.112832
$921$	0	0
$922$	−7.00158e9	−0.294197
$923$	1.05171e10	0.440239
$924$	0	0
$925$	4.55491e10	1.89227
$926$	7.16458e9	0.296519
$927$	0	0
$928$	8.21989e9	0.337635
$929$	−7.00431e9	−0.286623	−0.143311	−	0.989678i	$-0.545775\pi$
$929$	−7.00431e9	−0.286623	−0.143311	+	0.989678i	$0.545775\pi$
$930$	0	0
$931$	1.85549e10	0.753591
$932$	−7.46289e9	−0.301962
$933$	0	0
$934$	−1.74457e10	−0.700606
$935$	3.54441e10	1.41809
$936$	0	0
$937$	−3.16263e10	−1.25591	−0.627957	−	0.778248i	$-0.716109\pi$
$937$	−3.16263e10	−1.25591	−0.627957	+	0.778248i	$0.716109\pi$
$938$	−1.28860e10	−0.509811
$939$	0	0
$940$	5.47648e9	0.215057
$941$	2.31615e10	0.906155	0.453077	−	0.891471i	$-0.350326\pi$
$941$	2.31615e10	0.906155	0.453077	+	0.891471i	$0.350326\pi$
$942$	0	0
$943$	2.43861e9	0.0947005
$944$	8.95639e9	0.346522
$945$	0	0
$946$	1.46835e10	0.563910
$947$	−1.11874e10	−0.428060	−0.214030	−	0.976827i	$-0.568659\pi$
$947$	−1.11874e10	−0.428060	−0.214030	+	0.976827i	$0.568659\pi$
$948$	0	0
$949$	6.73560e9	0.255826
$950$	2.21080e10	0.836597
$951$	0	0
$952$	6.71695e9	0.252315
$953$	1.85383e10	0.693817	0.346908	−	0.937899i	$-0.387232\pi$
$953$	1.85383e10	0.693817	0.346908	+	0.937899i	$0.387232\pi$
$954$	0	0
$955$	−2.39463e10	−0.889663
$956$	4.83170e9	0.178854
$957$	0	0
$958$	1.49287e10	0.548582
$959$	1.78828e10	0.654743
$960$	0	0
$961$	4.58016e9	0.166475
$962$	9.06915e9	0.328438
$963$	0	0
$964$	2.76596e10	0.994436
$965$	3.43401e10	1.23015
$966$	0	0
$967$	−7.91753e9	−0.281577	−0.140788	−	0.990040i	$-0.544964\pi$
$967$	−7.91753e9	−0.281577	−0.140788	+	0.990040i	$0.544964\pi$
$968$	7.54076e9	0.267209
$969$	0	0
$970$	−3.07265e10	−1.08096
$971$	3.25866e10	1.14228	0.571139	−	0.820853i	$-0.306502\pi$
$971$	3.25866e10	1.14228	0.571139	+	0.820853i	$0.306502\pi$
$972$	0	0
$973$	−4.40723e9	−0.153381
$974$	7.63201e9	0.264656
$975$	0	0
$976$	1.04354e10	0.359282
$977$	−6.25658e9	−0.214638	−0.107319	−	0.994225i	$-0.534227\pi$
$977$	−6.25658e9	−0.214638	−0.107319	+	0.994225i	$0.534227\pi$
$978$	0	0
$979$	2.61780e9	0.0891656
$980$	−1.92808e10	−0.654387
$981$	0	0
$982$	9.69467e9	0.326695
$983$	−8.04489e9	−0.270136	−0.135068	−	0.990836i	$-0.543125\pi$
$983$	−8.04489e9	−0.270136	−0.135068	+	0.990836i	$0.543125\pi$
$984$	0	0
$985$	−1.50791e10	−0.502746
$986$	−7.62166e10	−2.53210
$987$	0	0
$988$	4.40185e9	0.145207
$989$	1.02367e10	0.336489
$990$	0	0
$991$	−3.99983e10	−1.30552	−0.652761	−	0.757564i	$-0.726389\pi$
$991$	−3.99983e10	−1.30552	−0.652761	+	0.757564i	$0.726389\pi$
$992$	−5.87021e9	−0.190925
$993$	0	0
$994$	1.11336e10	0.359571
$995$	1.86908e10	0.601515
$996$	0	0
$997$	3.00799e10	0.961267	0.480633	−	0.876922i	$-0.340407\pi$
$997$	3.00799e10	0.961267	0.480633	+	0.876922i	$0.340407\pi$
$998$	9.36774e9	0.298317
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.8.a.i.1.4		4
3.2	odd	2		138.8.a.h.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.8.a.h.1.1	✓	4	3.2	odd	2
414.8.a.i.1.4		4	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	414.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +64.0000 q^{4} +427.795 q^{5} +345.429 q^{7} -512.000 q^{8} +O(q^{10})\)	\(q-8.00000 q^{2} +64.0000 q^{4} +427.795 q^{5} +345.429 q^{7} -512.000 q^{8} -3422.36 q^{10} -2181.54 q^{11} -2610.39 q^{13} -2763.43 q^{14} +4096.00 q^{16} -37979.0 q^{17} -26348.1 q^{19} +27378.9 q^{20} +17452.3 q^{22} +12167.0 q^{23} +104884. q^{25} +20883.1 q^{26} +22107.4 q^{28} -250851. q^{29} +179145. q^{31} -32768.0 q^{32} +303832. q^{34} +147773. q^{35} +434281. q^{37} +210785. q^{38} -219031. q^{40} +200429. q^{41} +841346. q^{43} -139619. q^{44} -97336.0 q^{46} +200025. q^{47} -704222. q^{49} -839072. q^{50} -167065. q^{52} +1.62417e6 q^{53} -933254. q^{55} -176859. q^{56} +2.00681e6 q^{58} +2.18662e6 q^{59} +2.54771e6 q^{61} -1.43316e6 q^{62} +262144. q^{64} -1.11671e6 q^{65} +4.66306e6 q^{67} -2.43066e6 q^{68} -1.18218e6 q^{70} -4.02892e6 q^{71} -2.58030e6 q^{73} -3.47425e6 q^{74} -1.68628e6 q^{76} -753568. q^{77} +1.22032e6 q^{79} +1.75225e6 q^{80} -1.60343e6 q^{82} +2.16585e6 q^{83} -1.62473e7 q^{85} -6.73077e6 q^{86} +1.11695e6 q^{88} -1.19998e6 q^{89} -901704. q^{91} +778688. q^{92} -1.60020e6 q^{94} -1.12716e7 q^{95} +8.97814e6 q^{97} +5.63378e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8}+O(q^{10}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8} + 2160 q^{10} - 4120 q^{11} + 8036 q^{13} - 16176 q^{14} + 16384 q^{16} - 37182 q^{17} + 5702 q^{19} - 17280 q^{20} + 32960 q^{22} + 48668 q^{23} + 121480 q^{25} - 64288 q^{26} + 129408 q^{28} - 217716 q^{29} + 222852 q^{31} - 131072 q^{32} + 297456 q^{34} - 68440 q^{35} + 486428 q^{37} - 45616 q^{38} + 138240 q^{40} - 338336 q^{41} + 730974 q^{43} - 263680 q^{44} - 389344 q^{46} - 338248 q^{47} - 310552 q^{49} - 971840 q^{50} + 514304 q^{52} + 375502 q^{53} + 424840 q^{55} - 1035264 q^{56} + 1741728 q^{58} - 71392 q^{59} + 2101164 q^{61} - 1782816 q^{62} + 1048576 q^{64} - 1578780 q^{65} + 4337162 q^{67} - 2379648 q^{68} + 547520 q^{70} - 2288016 q^{71} - 1107328 q^{73} - 3891424 q^{74} + 364928 q^{76} - 5826200 q^{77} + 60610 q^{79} - 1105920 q^{80} + 2706688 q^{82} - 1485464 q^{83} - 8843820 q^{85} - 5847792 q^{86} + 2109440 q^{88} - 1485090 q^{89} - 2898412 q^{91} + 3114752 q^{92} + 2705984 q^{94} - 8545200 q^{95} + 1935444 q^{97} + 2484416 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8 + 2160 * q^10 - 4120 * q^11 + 8036 * q^13 - 16176 * q^14 + 16384 * q^16 - 37182 * q^17 + 5702 * q^19 - 17280 * q^20 + 32960 * q^22 + 48668 * q^23 + 121480 * q^25 - 64288 * q^26 + 129408 * q^28 - 217716 * q^29 + 222852 * q^31 - 131072 * q^32 + 297456 * q^34 - 68440 * q^35 + 486428 * q^37 - 45616 * q^38 + 138240 * q^40 - 338336 * q^41 + 730974 * q^43 - 263680 * q^44 - 389344 * q^46 - 338248 * q^47 - 310552 * q^49 - 971840 * q^50 + 514304 * q^52 + 375502 * q^53 + 424840 * q^55 - 1035264 * q^56 + 1741728 * q^58 - 71392 * q^59 + 2101164 * q^61 - 1782816 * q^62 + 1048576 * q^64 - 1578780 * q^65 + 4337162 * q^67 - 2379648 * q^68 + 547520 * q^70 - 2288016 * q^71 - 1107328 * q^73 - 3891424 * q^74 + 364928 * q^76 - 5826200 * q^77 + 60610 * q^79 - 1105920 * q^80 + 2706688 * q^82 - 1485464 * q^83 - 8843820 * q^85 - 5847792 * q^86 + 2109440 * q^88 - 1485090 * q^89 - 2898412 * q^91 + 3114752 * q^92 + 2705984 * q^94 - 8545200 * q^95 + 1935444 * q^97 + 2484416 * q^98

Introduction

L-functions

Modular forms

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Groups

Database

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