LMFDB - Embedded newform 625.8.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,8,Mod(1,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("625.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	625.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:	$195.240640928$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	no (minimal twist has level 25)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.5105 q^{2} +29.2192 q^{3} +28.5132 q^{4} -365.548 q^{6} -461.143 q^{7} +1244.63 q^{8} -1333.24 q^{9} +O(q^{10})$	\(q-12.5105 q^{2} +29.2192 q^{3} +28.5132 q^{4} -365.548 q^{6} -461.143 q^{7} +1244.63 q^{8} -1333.24 q^{9} -976.006 q^{11} +833.135 q^{12} -1918.23 q^{13} +5769.14 q^{14} -19220.7 q^{16} +4120.53 q^{17} +16679.5 q^{18} +32264.9 q^{19} -13474.2 q^{21} +12210.4 q^{22} -80729.2 q^{23} +36367.2 q^{24} +23998.1 q^{26} -102859. q^{27} -13148.7 q^{28} +64135.7 q^{29} +233155. q^{31} +81148.1 q^{32} -28518.1 q^{33} -51550.0 q^{34} -38014.9 q^{36} +251706. q^{37} -403651. q^{38} -56049.3 q^{39} -383881. q^{41} +168570. q^{42} +660240. q^{43} -27829.1 q^{44} +1.00996e6 q^{46} +370161. q^{47} -561614. q^{48} -610890. q^{49} +120399. q^{51} -54695.0 q^{52} -855542. q^{53} +1.28682e6 q^{54} -573954. q^{56} +942756. q^{57} -802371. q^{58} +2.10557e6 q^{59} -2.20549e6 q^{61} -2.91689e6 q^{62} +614813. q^{63} +1.44504e6 q^{64} +356777. q^{66} +4.31857e6 q^{67} +117490. q^{68} -2.35884e6 q^{69} -615188. q^{71} -1.65939e6 q^{72} -3.74907e6 q^{73} -3.14897e6 q^{74} +919977. q^{76} +450079. q^{77} +701206. q^{78} +2.40458e6 q^{79} -89659.4 q^{81} +4.80255e6 q^{82} +376052. q^{83} -384194. q^{84} -8.25995e6 q^{86} +1.87399e6 q^{87} -1.21477e6 q^{88} +5.32443e6 q^{89} +884580. q^{91} -2.30185e6 q^{92} +6.81259e6 q^{93} -4.63090e6 q^{94} +2.37108e6 q^{96} +3.46278e6 q^{97} +7.64255e6 q^{98} +1.30125e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 3582 q^{4} - 1982 q^{6} + 37148 q^{9}+O(q^{10}) $ 64 * q + 3582 * q^4 - 1982 * q^6 + 37148 * q^9	$ 64 q + 3582 q^{4} - 1982 q^{6} + 37148 q^{9} - 17432 q^{11} - 34836 q^{14} + 164154 q^{16} - 123910 q^{19} - 193882 q^{21} - 544720 q^{24} - 708942 q^{26} - 666400 q^{29} - 900872 q^{31} - 911986 q^{34} + 309704 q^{36} - 1745894 q^{39} - 1862362 q^{41} - 3617976 q^{44} - 2373242 q^{46} + 3298162 q^{49} - 3922092 q^{51} - 7598090 q^{54} - 11353310 q^{56} - 12112530 q^{59} - 9276582 q^{61} - 4640288 q^{64} - 16518624 q^{66} - 17766944 q^{69} - 22846802 q^{71} - 20547876 q^{74} - 22436480 q^{76} - 23545670 q^{79} - 1824616 q^{81} - 31121786 q^{84} - 15273782 q^{86} - 29694630 q^{89} - 31731942 q^{91} + 3544204 q^{94} - 40852262 q^{96} - 57867624 q^{99}+O(q^{100}) $ 64 * q + 3582 * q^4 - 1982 * q^6 + 37148 * q^9 - 17432 * q^11 - 34836 * q^14 + 164154 * q^16 - 123910 * q^19 - 193882 * q^21 - 544720 * q^24 - 708942 * q^26 - 666400 * q^29 - 900872 * q^31 - 911986 * q^34 + 309704 * q^36 - 1745894 * q^39 - 1862362 * q^41 - 3617976 * q^44 - 2373242 * q^46 + 3298162 * q^49 - 3922092 * q^51 - 7598090 * q^54 - 11353310 * q^56 - 12112530 * q^59 - 9276582 * q^61 - 4640288 * q^64 - 16518624 * q^66 - 17766944 * q^69 - 22846802 * q^71 - 20547876 * q^74 - 22436480 * q^76 - 23545670 * q^79 - 1824616 * q^81 - 31121786 * q^84 - 15273782 * q^86 - 29694630 * q^89 - 31731942 * q^91 + 3544204 * q^94 - 40852262 * q^96 - 57867624 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−12.5105	−1.10578	−0.552892	−	0.833253i	$-0.686476\pi$
$2$	−12.5105	−1.10578	−0.552892	+	0.833253i	$0.686476\pi$
$3$	29.2192	0.624805	0.312402	−	0.949950i	$-0.398866\pi$
$3$	29.2192	0.624805	0.312402	+	0.949950i	$0.398866\pi$
$4$	28.5132	0.222760
$5$	0	0
$5$	0	0
$6$	−365.548	−0.690899
$7$	−461.143	−0.508151	−0.254075	−	0.967184i	$-0.581771\pi$
$7$	−461.143	−0.508151	−0.254075	+	0.967184i	$0.581771\pi$
$8$	1244.63	0.859460
$9$	−1333.24	−0.609619
$10$	0	0
$11$	−976.006	−0.221095	−0.110547	−	0.993871i	$-0.535260\pi$
$11$	−976.006	−0.221095	−0.110547	+	0.993871i	$0.535260\pi$
$12$	833.135	0.139181
$13$	−1918.23	−0.242158	−0.121079	−	0.992643i	$-0.538636\pi$
$13$	−1918.23	−0.242158	−0.121079	+	0.992643i	$0.538636\pi$
$14$	5769.14	0.561905
$15$	0	0
$16$	−19220.7	−1.17314
$17$	4120.53	0.203415	0.101707	−	0.994814i	$-0.467569\pi$
$17$	4120.53	0.203415	0.101707	+	0.994814i	$0.467569\pi$
$18$	16679.5	0.674107
$19$	32264.9	1.07918	0.539589	−	0.841929i	$-0.318580\pi$
$19$	32264.9	1.07918	0.539589	+	0.841929i	$0.318580\pi$
$20$	0	0
$21$	−13474.2	−0.317495
$22$	12210.4	0.244483
$23$	−80729.2	−1.38351	−0.691756	−	0.722131i	$-0.743163\pi$
$23$	−80729.2	−1.38351	−0.691756	+	0.722131i	$0.743163\pi$
$24$	36367.2	0.536995
$25$	0	0
$26$	23998.1	0.267775
$27$	−102859.	−1.00570
$28$	−13148.7	−0.113196
$29$	64135.7	0.488322	0.244161	−	0.969735i	$-0.421487\pi$
$29$	64135.7	0.488322	0.244161	+	0.969735i	$0.421487\pi$
$30$	0	0
$31$	233155.	1.40565	0.702826	−	0.711362i	$-0.251921\pi$
$31$	233155.	1.40565	0.702826	+	0.711362i	$0.251921\pi$
$32$	81148.1	0.437777
$33$	−28518.1	−0.138141
$34$	−51550.0	−0.224933
$35$	0	0
$36$	−38014.9	−0.135799
$37$	251706.	0.816935	0.408467	−	0.912773i	$-0.366063\pi$
$37$	251706.	0.816935	0.408467	+	0.912773i	$0.366063\pi$
$38$	−403651.	−1.19334
$39$	−56049.3	−0.151302
$40$	0	0
$41$	−383881.	−0.869867	−0.434934	−	0.900463i	$-0.643228\pi$
$41$	−383881.	−0.869867	−0.434934	+	0.900463i	$0.643228\pi$
$42$	168570.	0.351081
$43$	660240.	1.26637	0.633187	−	0.773998i	$-0.281746\pi$
$43$	660240.	1.26637	0.633187	+	0.773998i	$0.281746\pi$
$44$	−27829.1	−0.0492510
$45$	0	0
$46$	1.00996e6	1.52987
$47$	370161.	0.520053	0.260027	−	0.965601i	$-0.416269\pi$
$47$	370161.	0.520053	0.260027	+	0.965601i	$0.416269\pi$
$48$	−561614.	−0.732982
$49$	−610890.	−0.741783
$50$	0	0
$51$	120399.	0.127094
$52$	−54695.0	−0.0539431
$53$	−855542.	−0.789361	−0.394681	−	0.918818i	$-0.629145\pi$
$53$	−855542.	−0.789361	−0.394681	+	0.918818i	$0.629145\pi$
$54$	1.28682e6	1.11208
$55$	0	0
$56$	−573954.	−0.436736
$57$	942756.	0.674275
$58$	−802371.	−0.539979
$59$	2.10557e6	1.33471	0.667356	−	0.744739i	$-0.267426\pi$
$59$	2.10557e6	1.33471	0.667356	+	0.744739i	$0.267426\pi$
$60$	0	0
$61$	−2.20549e6	−1.24408	−0.622042	−	0.782984i	$-0.713697\pi$
$61$	−2.20549e6	−1.24408	−0.622042	+	0.782984i	$0.713697\pi$
$62$	−2.91689e6	−1.55435
$63$	614813.	0.309778
$64$	1.44504e6	0.689050
$65$	0	0
$66$	356777.	0.152754
$67$	4.31857e6	1.75420	0.877098	−	0.480311i	$-0.159476\pi$
$67$	4.31857e6	1.75420	0.877098	+	0.480311i	$0.159476\pi$
$68$	117490.	0.0453126
$69$	−2.35884e6	−0.864425
$70$	0	0
$71$	−615188.	−0.203988	−0.101994	−	0.994785i	$-0.532522\pi$
$71$	−615188.	−0.203988	−0.101994	+	0.994785i	$0.532522\pi$
$72$	−1.65939e6	−0.523943
$73$	−3.74907e6	−1.12796	−0.563979	−	0.825789i	$-0.690730\pi$
$73$	−3.74907e6	−1.12796	−0.563979	+	0.825789i	$0.690730\pi$
$74$	−3.14897e6	−0.903354
$75$	0	0
$76$	919977.	0.240397
$77$	450079.	0.112349
$78$	701206.	0.167307
$79$	2.40458e6	0.548712	0.274356	−	0.961628i	$-0.411535\pi$
$79$	2.40458e6	0.548712	0.274356	+	0.961628i	$0.411535\pi$
$80$	0	0
$81$	−89659.4	−0.0187456
$82$	4.80255e6	0.961886
$83$	376052.	0.0721896	0.0360948	−	0.999348i	$-0.488508\pi$
$83$	376052.	0.0721896	0.0360948	+	0.999348i	$0.488508\pi$
$84$	−384194.	−0.0707251
$85$	0	0
$86$	−8.25995e6	−1.40034
$87$	1.87399e6	0.305106
$88$	−1.21477e6	−0.190022
$89$	5.32443e6	0.800586	0.400293	−	0.916387i	$-0.368908\pi$
$89$	5.32443e6	0.800586	0.400293	+	0.916387i	$0.368908\pi$
$90$	0	0
$91$	884580.	0.123053
$92$	−2.30185e6	−0.308191
$93$	6.81259e6	0.878258
$94$	−4.63090e6	−0.575067
$95$	0	0
$96$	2.37108e6	0.273525
$97$	3.46278e6	0.385234	0.192617	−	0.981274i	$-0.438303\pi$
$97$	3.46278e6	0.385234	0.192617	+	0.981274i	$0.438303\pi$
$98$	7.64255e6	0.820252
$99$	1.30125e6	0.134784
$100$	0	0
$101$	−4.87609e6	−0.470920	−0.235460	−	0.971884i	$-0.575660\pi$
$101$	−4.87609e6	−0.470920	−0.235460	+	0.971884i	$0.575660\pi$
$102$	−1.50625e6	−0.140539
$103$	3.91471e6	0.352996	0.176498	−	0.984301i	$-0.443523\pi$
$103$	3.91471e6	0.352996	0.176498	+	0.984301i	$0.443523\pi$
$104$	−2.38749e6	−0.208126
$105$	0	0
$106$	1.07033e7	0.872863
$107$	−7.96860e6	−0.628838	−0.314419	−	0.949284i	$-0.601810\pi$
$107$	−7.96860e6	−0.628838	−0.314419	+	0.949284i	$0.601810\pi$
$108$	−2.93283e6	−0.224029
$109$	−2.35426e7	−1.74125	−0.870625	−	0.491948i	$-0.836285\pi$
$109$	−2.35426e7	−1.74125	−0.870625	+	0.491948i	$0.836285\pi$
$110$	0	0
$111$	7.35465e6	0.510425
$112$	8.86349e6	0.596131
$113$	−2.13662e7	−1.39301	−0.696504	−	0.717553i	$-0.745262\pi$
$113$	−2.13662e7	−1.39301	−0.696504	+	0.717553i	$0.745262\pi$
$114$	−1.17944e7	−0.745603
$115$	0	0
$116$	1.82872e6	0.108779
$117$	2.55746e6	0.147624
$118$	−2.63418e7	−1.47590
$119$	−1.90016e6	−0.103365
$120$	0	0
$121$	−1.85346e7	−0.951117
$122$	2.75918e7	1.37569
$123$	−1.12167e7	−0.543497
$124$	6.64799e6	0.313123
$125$	0	0
$126$	−7.69164e6	−0.342548
$127$	1.35753e7	0.588079	0.294039	−	0.955793i	$-0.405000\pi$
$127$	1.35753e7	0.588079	0.294039	+	0.955793i	$0.405000\pi$
$128$	−2.84652e7	−1.19972
$129$	1.92917e7	0.791237
$130$	0	0
$131$	2.03856e7	0.792270	0.396135	−	0.918192i	$-0.370351\pi$
$131$	2.03856e7	0.792270	0.396135	+	0.918192i	$0.370351\pi$
$132$	−813145.	−0.0307722
$133$	−1.48788e7	−0.548385
$134$	−5.40276e7	−1.93976
$135$	0	0
$136$	5.12855e6	0.174827
$137$	5.17061e7	1.71799	0.858994	−	0.511986i	$-0.171090\pi$
$137$	5.17061e7	1.71799	0.858994	+	0.511986i	$0.171090\pi$
$138$	2.95104e7	0.955868
$139$	4.95819e7	1.56593	0.782964	−	0.622067i	$-0.213707\pi$
$139$	4.95819e7	1.56593	0.782964	+	0.622067i	$0.213707\pi$
$140$	0	0
$141$	1.08158e7	0.324932
$142$	7.69633e6	0.225566
$143$	1.87221e6	0.0535399
$144$	2.56257e7	0.715167
$145$	0	0
$146$	4.69028e7	1.24728
$147$	−1.78497e7	−0.463469
$148$	7.17695e6	0.181980
$149$	−4.98650e7	−1.23493	−0.617467	−	0.786597i	$-0.711841\pi$
$149$	−4.98650e7	−1.23493	−0.617467	+	0.786597i	$0.711841\pi$
$150$	0	0
$151$	−5.87598e7	−1.38887	−0.694434	−	0.719556i	$-0.744345\pi$
$151$	−5.87598e7	−1.38887	−0.694434	+	0.719556i	$0.744345\pi$
$152$	4.01579e7	0.927511
$153$	−5.49365e6	−0.124005
$154$	−5.63072e6	−0.124234
$155$	0	0
$156$	−1.59815e6	−0.0337039
$157$	5.67439e7	1.17023	0.585114	−	0.810951i	$-0.301050\pi$
$157$	5.67439e7	1.17023	0.585114	+	0.810951i	$0.301050\pi$
$158$	−3.00826e7	−0.606757
$159$	−2.49983e7	−0.493197
$160$	0	0
$161$	3.72277e7	0.703033
$162$	1.12169e6	0.0207286
$163$	3.73870e7	0.676183	0.338092	−	0.941113i	$-0.390219\pi$
$163$	3.73870e7	0.676183	0.338092	+	0.941113i	$0.390219\pi$
$164$	−1.09457e7	−0.193771
$165$	0	0
$166$	−4.70461e6	−0.0798262
$167$	3.80297e7	0.631851	0.315926	−	0.948784i	$-0.397685\pi$
$167$	3.80297e7	0.631851	0.315926	+	0.948784i	$0.397685\pi$
$168$	−1.67705e7	−0.272874
$169$	−5.90689e7	−0.941359
$170$	0	0
$171$	−4.30168e7	−0.657887
$172$	1.88256e7	0.282097
$173$	9.24627e7	1.35770	0.678852	−	0.734275i	$-0.262478\pi$
$173$	9.24627e7	1.35770	0.678852	+	0.734275i	$0.262478\pi$
$174$	−2.34447e7	−0.337382
$175$	0	0
$176$	1.87595e7	0.259374
$177$	6.15231e7	0.833934
$178$	−6.66114e7	−0.885276
$179$	1.16062e8	1.51254	0.756268	−	0.654262i	$-0.227021\pi$
$179$	1.16062e8	1.51254	0.756268	+	0.654262i	$0.227021\pi$
$180$	0	0
$181$	−5.30434e7	−0.664900	−0.332450	−	0.943121i	$-0.607875\pi$
$181$	−5.30434e7	−0.664900	−0.332450	+	0.943121i	$0.607875\pi$
$182$	−1.10666e7	−0.136070
$183$	−6.44426e7	−0.777310
$184$	−1.00478e8	−1.18907
$185$	0	0
$186$	−8.52291e7	−0.971164
$187$	−4.02167e6	−0.0449739
$188$	1.05545e7	0.115847
$189$	4.74325e7	0.511046
$190$	0	0
$191$	7.05071e7	0.732177	0.366089	−	0.930580i	$-0.380697\pi$
$191$	7.05071e7	0.732177	0.366089	+	0.930580i	$0.380697\pi$
$192$	4.22230e7	0.430522
$193$	1.84498e8	1.84732	0.923659	−	0.383216i	$-0.125183\pi$
$193$	1.84498e8	1.84732	0.923659	+	0.383216i	$0.125183\pi$
$194$	−4.33212e7	−0.425985
$195$	0	0
$196$	−1.74184e7	−0.165239
$197$	1.48333e8	1.38231	0.691156	−	0.722706i	$-0.257102\pi$
$197$	1.48333e8	1.38231	0.691156	+	0.722706i	$0.257102\pi$
$198$	−1.62793e7	−0.149042
$199$	−7.16422e7	−0.644441	−0.322221	−	0.946665i	$-0.604429\pi$
$199$	−7.16422e7	−0.644441	−0.322221	+	0.946665i	$0.604429\pi$
$200$	0	0
$201$	1.26185e8	1.09603
$202$	6.10025e7	0.520736
$203$	−2.95757e7	−0.248142
$204$	3.43296e6	0.0283115
$205$	0	0
$206$	−4.89751e7	−0.390337
$207$	1.07631e8	0.843416
$208$	3.68698e7	0.284085
$209$	−3.14908e7	−0.238600
$210$	0	0
$211$	5.49095e7	0.402401	0.201201	−	0.979550i	$-0.435516\pi$
$211$	5.49095e7	0.402401	0.201201	+	0.979550i	$0.435516\pi$
$212$	−2.43943e7	−0.175838
$213$	−1.79753e7	−0.127452
$214$	9.96914e7	0.695359
$215$	0	0
$216$	−1.28021e8	−0.864357
$217$	−1.07518e8	−0.714284
$218$	2.94530e8	1.92545
$219$	−1.09545e8	−0.704754
$220$	0	0
$221$	−7.90414e6	−0.0492586
$222$	−9.20106e7	−0.564420
$223$	−1.95421e8	−1.18006	−0.590031	−	0.807381i	$-0.700884\pi$
$223$	−1.95421e8	−1.18006	−0.590031	+	0.807381i	$0.700884\pi$
$224$	−3.74209e7	−0.222457
$225$	0	0
$226$	2.67303e8	1.54037
$227$	−2.28599e8	−1.29713	−0.648566	−	0.761158i	$-0.724631\pi$
$227$	−2.28599e8	−1.29713	−0.648566	+	0.761158i	$0.724631\pi$
$228$	2.68810e7	0.150201
$229$	−5.32721e7	−0.293140	−0.146570	−	0.989200i	$-0.546823\pi$
$229$	−5.32721e7	−0.293140	−0.146570	+	0.989200i	$0.546823\pi$
$230$	0	0
$231$	1.31510e7	0.0701965
$232$	7.98253e7	0.419694
$233$	5.65786e6	0.0293026	0.0146513	−	0.999893i	$-0.495336\pi$
$233$	5.65786e6	0.0293026	0.0146513	+	0.999893i	$0.495336\pi$
$234$	−3.19952e7	−0.163241
$235$	0	0
$236$	6.00366e7	0.297320
$237$	7.02600e7	0.342838
$238$	2.37720e7	0.114300
$239$	−2.68379e8	−1.27162	−0.635809	−	0.771846i	$-0.719333\pi$
$239$	−2.68379e8	−1.27162	−0.635809	+	0.771846i	$0.719333\pi$
$240$	0	0
$241$	−2.21921e8	−1.02127	−0.510634	−	0.859798i	$-0.670589\pi$
$241$	−2.21921e8	−1.02127	−0.510634	+	0.859798i	$0.670589\pi$
$242$	2.31877e8	1.05173
$243$	2.22332e8	0.993985
$244$	−6.28855e7	−0.277132
$245$	0	0
$246$	1.40327e8	0.600991
$247$	−6.18916e7	−0.261332
$248$	2.90192e8	1.20810
$249$	1.09880e7	0.0451044
$250$	0	0
$251$	−1.47393e8	−0.588326	−0.294163	−	0.955755i	$-0.595041\pi$
$251$	−1.47393e8	−0.588326	−0.294163	+	0.955755i	$0.595041\pi$
$252$	1.75303e7	0.0690061
$253$	7.87922e7	0.305887
$254$	−1.69834e8	−0.650288
$255$	0	0
$256$	1.71149e8	0.637580
$257$	−2.69911e7	−0.0991870	−0.0495935	−	0.998769i	$-0.515793\pi$
$257$	−2.69911e7	−0.0991870	−0.0495935	+	0.998769i	$0.515793\pi$
$258$	−2.41349e8	−0.874938
$259$	−1.16073e8	−0.415126
$260$	0	0
$261$	−8.55081e7	−0.297691
$262$	−2.55034e8	−0.876080
$263$	5.50491e7	0.186597	0.0932986	−	0.995638i	$-0.470259\pi$
$263$	5.50491e7	0.186597	0.0932986	+	0.995638i	$0.470259\pi$
$264$	−3.54946e7	−0.118727
$265$	0	0
$266$	1.86141e8	0.606396
$267$	1.55576e8	0.500210
$268$	1.23136e8	0.390764
$269$	−5.42136e8	−1.69815	−0.849074	−	0.528274i	$-0.822839\pi$
$269$	−5.42136e8	−1.69815	−0.849074	+	0.528274i	$0.822839\pi$
$270$	0	0
$271$	−1.15188e8	−0.351573	−0.175787	−	0.984428i	$-0.556247\pi$
$271$	−1.15188e8	−0.351573	−0.175787	+	0.984428i	$0.556247\pi$
$272$	−7.91995e7	−0.238633
$273$	2.58467e7	0.0768841
$274$	−6.46871e8	−1.89972
$275$	0	0
$276$	−6.72583e7	−0.192559
$277$	−2.50840e8	−0.709116	−0.354558	−	0.935034i	$-0.615369\pi$
$277$	−2.50840e8	−0.709116	−0.354558	+	0.935034i	$0.615369\pi$
$278$	−6.20296e8	−1.73158
$279$	−3.10850e8	−0.856912
$280$	0	0
$281$	−6.94695e8	−1.86776	−0.933882	−	0.357580i	$-0.883602\pi$
$281$	−6.94695e8	−1.86776	−0.933882	+	0.357580i	$0.883602\pi$
$282$	−1.35311e8	−0.359304
$283$	−6.28595e8	−1.64861	−0.824306	−	0.566145i	$-0.808434\pi$
$283$	−6.28595e8	−1.64861	−0.824306	+	0.566145i	$0.808434\pi$
$284$	−1.75410e7	−0.0454402
$285$	0	0
$286$	−2.34223e7	−0.0592036
$287$	1.77024e8	0.442024
$288$	−1.08190e8	−0.266877
$289$	−3.93360e8	−0.958622
$290$	0	0
$291$	1.01180e8	0.240696
$292$	−1.06898e8	−0.251264
$293$	−1.95280e8	−0.453546	−0.226773	−	0.973948i	$-0.572818\pi$
$293$	−1.95280e8	−0.453546	−0.226773	+	0.973948i	$0.572818\pi$
$294$	2.23309e8	0.512497
$295$	0	0
$296$	3.13281e8	0.702123
$297$	1.00391e8	0.222354
$298$	6.23837e8	1.36557
$299$	1.54857e8	0.335029
$300$	0	0
$301$	−3.04465e8	−0.643510
$302$	7.35116e8	1.53579
$303$	−1.42476e8	−0.294233
$304$	−6.20154e8	−1.26602
$305$	0	0
$306$	6.87284e7	0.137123
$307$	−6.50343e8	−1.28280	−0.641398	−	0.767208i	$-0.721645\pi$
$307$	−6.50343e8	−1.28280	−0.641398	+	0.767208i	$0.721645\pi$
$308$	1.28332e7	0.0250269
$309$	1.14385e8	0.220554
$310$	0	0
$311$	2.94232e8	0.554662	0.277331	−	0.960774i	$-0.410550\pi$
$311$	2.94232e8	0.554662	0.277331	+	0.960774i	$0.410550\pi$
$312$	−6.97607e7	−0.130038
$313$	5.07872e8	0.936158	0.468079	−	0.883687i	$-0.344946\pi$
$313$	5.07872e8	0.936158	0.468079	+	0.883687i	$0.344946\pi$
$314$	−7.09896e8	−1.29402
$315$	0	0
$316$	6.85624e7	0.122231
$317$	−1.10737e9	−1.95247	−0.976235	−	0.216716i	$-0.930465\pi$
$317$	−1.10737e9	−1.95247	−0.976235	+	0.216716i	$0.930465\pi$
$318$	3.12742e8	0.545369
$319$	−6.25968e7	−0.107965
$320$	0	0
$321$	−2.32836e8	−0.392901
$322$	−4.65738e8	−0.777403
$323$	1.32949e8	0.219521
$324$	−2.55648e6	−0.00417575
$325$	0	0
$326$	−4.67731e8	−0.747713
$327$	−6.87895e8	−1.08794
$328$	−4.77790e8	−0.747616
$329$	−1.70697e8	−0.264266
$330$	0	0
$331$	8.74616e8	1.32562	0.662810	−	0.748787i	$-0.269364\pi$
$331$	8.74616e8	1.32562	0.662810	+	0.748787i	$0.269364\pi$
$332$	1.07225e7	0.0160809
$333$	−3.35584e8	−0.498019
$334$	−4.75771e8	−0.698692
$335$	0	0
$336$	2.58984e8	0.372466
$337$	−2.36617e8	−0.336775	−0.168388	−	0.985721i	$-0.553856\pi$
$337$	−2.36617e8	−0.336775	−0.168388	+	0.985721i	$0.553856\pi$
$338$	7.38983e8	1.04094
$339$	−6.24305e8	−0.870357
$340$	0	0
$341$	−2.27560e8	−0.310782
$342$	5.38163e8	0.727482
$343$	6.61479e8	0.885088
$344$	8.21756e8	1.08840
$345$	0	0
$346$	−1.15676e9	−1.50133
$347$	2.18796e8	0.281116	0.140558	−	0.990072i	$-0.455110\pi$
$347$	2.18796e8	0.281116	0.140558	+	0.990072i	$0.455110\pi$
$348$	5.34337e7	0.0679653
$349$	6.31810e8	0.795605	0.397803	−	0.917471i	$-0.369773\pi$
$349$	6.31810e8	0.795605	0.397803	+	0.917471i	$0.369773\pi$
$350$	0	0
$351$	1.97307e8	0.243538
$352$	−7.92010e7	−0.0967902
$353$	−1.07542e9	−1.30127	−0.650636	−	0.759389i	$-0.725498\pi$
$353$	−1.07542e9	−1.30127	−0.650636	+	0.759389i	$0.725498\pi$
$354$	−7.69686e8	−0.922151
$355$	0	0
$356$	1.51817e8	0.178338
$357$	−5.55211e7	−0.0645832
$358$	−1.45200e9	−1.67254
$359$	5.13054e8	0.585239	0.292619	−	0.956229i	$-0.405473\pi$
$359$	5.13054e8	0.585239	0.292619	+	0.956229i	$0.405473\pi$
$360$	0	0
$361$	1.47153e8	0.164625
$362$	6.63601e8	0.735236
$363$	−5.41566e8	−0.594262
$364$	2.52222e7	0.0274113
$365$	0	0
$366$	8.06211e8	0.859537
$367$	−1.00090e9	−1.05696	−0.528479	−	0.848946i	$-0.677237\pi$
$367$	−1.00090e9	−1.05696	−0.528479	+	0.848946i	$0.677237\pi$
$368$	1.55167e9	1.62305
$369$	5.11804e8	0.530288
$370$	0	0
$371$	3.94527e8	0.401115
$372$	1.94249e8	0.195640
$373$	−4.21073e8	−0.420123	−0.210061	−	0.977688i	$-0.567366\pi$
$373$	−4.21073e8	−0.420123	−0.210061	+	0.977688i	$0.567366\pi$
$374$	5.03132e7	0.0497314
$375$	0	0
$376$	4.60714e8	0.446965
$377$	−1.23027e8	−0.118251
$378$	−5.93406e8	−0.565107
$379$	−1.82445e9	−1.72145	−0.860724	−	0.509073i	$-0.829988\pi$
$379$	−1.82445e9	−1.72145	−0.860724	+	0.509073i	$0.829988\pi$
$380$	0	0
$381$	3.96659e8	0.367434
$382$	−8.82081e8	−0.809630
$383$	−2.04708e8	−0.186182	−0.0930912	−	0.995658i	$-0.529675\pi$
$383$	−2.04708e8	−0.186182	−0.0930912	+	0.995658i	$0.529675\pi$
$384$	−8.31731e8	−0.749590
$385$	0	0
$386$	−2.30817e9	−2.04274
$387$	−8.80256e8	−0.772006
$388$	9.87351e7	0.0858145
$389$	−1.49282e9	−1.28583	−0.642914	−	0.765938i	$-0.722275\pi$
$389$	−1.49282e9	−1.28583	−0.642914	+	0.765938i	$0.722275\pi$
$390$	0	0
$391$	−3.32647e8	−0.281427
$392$	−7.60333e8	−0.637533
$393$	5.95650e8	0.495014
$394$	−1.85572e9	−1.52854
$395$	0	0
$396$	3.71028e7	0.0300243
$397$	−9.84566e8	−0.789729	−0.394865	−	0.918739i	$-0.629208\pi$
$397$	−9.84566e8	−0.789729	−0.394865	+	0.918739i	$0.629208\pi$
$398$	8.96282e8	0.712613
$399$	−4.34746e8	−0.342634
$400$	0	0
$401$	−5.25610e8	−0.407060	−0.203530	−	0.979069i	$-0.565241\pi$
$401$	−5.25610e8	−0.407060	−0.203530	+	0.979069i	$0.565241\pi$
$402$	−1.57864e9	−1.21197
$403$	−4.47245e8	−0.340391
$404$	−1.39033e8	−0.104902
$405$	0	0
$406$	3.70008e8	0.274391
$407$	−2.45667e8	−0.180620
$408$	1.49852e8	0.109233
$409$	1.65035e9	1.19274	0.596368	−	0.802711i	$-0.296610\pi$
$409$	1.65035e9	1.19274	0.596368	+	0.802711i	$0.296610\pi$
$410$	0	0
$411$	1.51081e9	1.07341
$412$	1.11621e8	0.0786332
$413$	−9.70969e8	−0.678235
$414$	−1.34652e9	−0.932636
$415$	0	0
$416$	−1.55661e8	−0.106011
$417$	1.44875e9	0.978399
$418$	3.93966e8	0.263841
$419$	−1.84787e9	−1.22722	−0.613609	−	0.789610i	$-0.710283\pi$
$419$	−1.84787e9	−1.22722	−0.613609	+	0.789610i	$0.710283\pi$
$420$	0	0
$421$	1.23521e9	0.806775	0.403387	−	0.915029i	$-0.367833\pi$
$421$	1.23521e9	0.806775	0.403387	+	0.915029i	$0.367833\pi$
$422$	−6.86947e8	−0.444969
$423$	−4.93512e8	−0.317034
$424$	−1.06483e9	−0.678425
$425$	0	0
$426$	2.24881e8	0.140935
$427$	1.01704e9	0.632183
$428$	−2.27211e8	−0.140080
$429$	5.47044e7	0.0334520
$430$	0	0
$431$	−1.36512e9	−0.821296	−0.410648	−	0.911794i	$-0.634697\pi$
$431$	−1.36512e9	−0.821296	−0.410648	+	0.911794i	$0.634697\pi$
$432$	1.97701e9	1.17982
$433$	−2.48522e9	−1.47115	−0.735576	−	0.677442i	$-0.763088\pi$
$433$	−2.48522e9	−1.47115	−0.735576	+	0.677442i	$0.763088\pi$
$434$	1.34510e9	0.789844
$435$	0	0
$436$	−6.71275e8	−0.387880
$437$	−2.60472e9	−1.49306
$438$	1.37046e9	0.779306
$439$	2.69349e9	1.51946	0.759731	−	0.650238i	$-0.225331\pi$
$439$	2.69349e9	1.51946	0.759731	+	0.650238i	$0.225331\pi$
$440$	0	0
$441$	8.14461e8	0.452205
$442$	9.88850e7	0.0544694
$443$	−1.48287e8	−0.0810382	−0.0405191	−	0.999179i	$-0.512901\pi$
$443$	−1.48287e8	−0.0810382	−0.0405191	+	0.999179i	$0.512901\pi$
$444$	2.09705e8	0.113702
$445$	0	0
$446$	2.44482e9	1.30489
$447$	−1.45702e9	−0.771592
$448$	−6.66372e8	−0.350142
$449$	−1.17652e9	−0.613392	−0.306696	−	0.951808i	$-0.599223\pi$
$449$	−1.17652e9	−0.613392	−0.306696	+	0.951808i	$0.599223\pi$
$450$	0	0
$451$	3.74670e8	0.192323
$452$	−6.09220e8	−0.310306
$453$	−1.71692e9	−0.867772
$454$	2.85990e9	1.43435
$455$	0	0
$456$	1.17338e9	0.579513
$457$	−2.79917e8	−0.137190	−0.0685950	−	0.997645i	$-0.521852\pi$
$457$	−2.79917e8	−0.137190	−0.0685950	+	0.997645i	$0.521852\pi$
$458$	6.66462e8	0.324150
$459$	−4.23832e8	−0.204574
$460$	0	0
$461$	−2.71308e6	−0.00128976	−0.000644880	−	1.00000i	$-0.500205\pi$
$461$	−2.71308e6	−0.00128976	−0.000644880		1.00000i	$0.500205\pi$
$462$	−1.64525e8	−0.0776222
$463$	1.77497e8	0.0831106	0.0415553	−	0.999136i	$-0.486769\pi$
$463$	1.77497e8	0.0831106	0.0415553	+	0.999136i	$0.486769\pi$
$464$	−1.23273e9	−0.572870
$465$	0	0
$466$	−7.07828e7	−0.0324024
$467$	1.63216e9	0.741573	0.370787	−	0.928718i	$-0.379088\pi$
$467$	1.63216e9	0.741573	0.370787	+	0.928718i	$0.379088\pi$
$468$	7.29214e7	0.0328848
$469$	−1.99148e9	−0.891397
$470$	0	0
$471$	1.65801e9	0.731164
$472$	2.62066e9	1.14713
$473$	−6.44398e8	−0.279989
$474$	−8.78989e8	−0.379105
$475$	0	0
$476$	−5.41796e7	−0.0230256
$477$	1.14064e9	0.481210
$478$	3.35757e9	1.40614
$479$	−2.94453e9	−1.22417	−0.612085	−	0.790792i	$-0.709669\pi$
$479$	−2.94453e9	−1.22417	−0.612085	+	0.790792i	$0.709669\pi$
$480$	0	0
$481$	−4.82831e8	−0.197828
$482$	2.77635e9	1.12930
$483$	1.08777e9	0.439258
$484$	−5.28481e8	−0.211871
$485$	0	0
$486$	−2.78149e9	−1.09913
$487$	2.57408e8	0.100988	0.0504940	−	0.998724i	$-0.483920\pi$
$487$	2.57408e8	0.100988	0.0504940	+	0.998724i	$0.483920\pi$
$488$	−2.74502e9	−1.06924
$489$	1.09242e9	0.422482
$490$	0	0
$491$	−3.10225e9	−1.18275	−0.591374	−	0.806398i	$-0.701414\pi$
$491$	−3.10225e9	−1.18275	−0.591374	+	0.806398i	$0.701414\pi$
$492$	−3.19824e8	−0.121069
$493$	2.64273e8	0.0993320
$494$	7.74297e8	0.288977
$495$	0	0
$496$	−4.48139e9	−1.64902
$497$	2.83690e8	0.103657
$498$	−1.37465e8	−0.0498758
$499$	−9.86282e8	−0.355344	−0.177672	−	0.984090i	$-0.556857\pi$
$499$	−9.86282e8	−0.355344	−0.177672	+	0.984090i	$0.556857\pi$
$500$	0	0
$501$	1.11120e9	0.394784
$502$	1.84396e9	0.650561
$503$	1.15261e9	0.403827	0.201913	−	0.979403i	$-0.435284\pi$
$503$	1.15261e9	0.403827	0.201913	+	0.979403i	$0.435284\pi$
$504$	7.65216e8	0.266242
$505$	0	0
$506$	−9.85732e8	−0.338245
$507$	−1.72595e9	−0.588166
$508$	3.87075e8	0.131000
$509$	−5.48463e9	−1.84347	−0.921733	−	0.387825i	$-0.873226\pi$
$509$	−5.48463e9	−1.84347	−0.921733	+	0.387825i	$0.873226\pi$
$510$	0	0
$511$	1.72886e9	0.573173
$512$	1.50238e9	0.494692
$513$	−3.31872e9	−1.08533
$514$	3.37673e8	0.109679
$515$	0	0
$516$	5.50069e8	0.176256
$517$	−3.61279e8	−0.114981
$518$	1.45213e9	0.459040
$519$	2.70169e9	0.848300
$520$	0	0
$521$	−2.70913e9	−0.839263	−0.419632	−	0.907694i	$-0.637841\pi$
$521$	−2.70913e9	−0.839263	−0.419632	+	0.907694i	$0.637841\pi$
$522$	1.06975e9	0.329182
$523$	2.42758e9	0.742025	0.371012	−	0.928628i	$-0.379011\pi$
$523$	2.42758e9	0.742025	0.371012	+	0.928628i	$0.379011\pi$
$524$	5.81258e8	0.176486
$525$	0	0
$526$	−6.88693e8	−0.206336
$527$	9.60721e8	0.285930
$528$	5.48138e8	0.162058
$529$	3.11237e9	0.914107
$530$	0	0
$531$	−2.80722e9	−0.813666
$532$	−4.24241e8	−0.122158
$533$	7.36373e8	0.210646
$534$	−1.94633e9	−0.553124
$535$	0	0
$536$	5.37503e9	1.50766
$537$	3.39125e9	0.945039
$538$	6.78241e9	1.87779
$539$	5.96232e8	0.164004
$540$	0	0
$541$	−4.45289e9	−1.20907	−0.604535	−	0.796579i	$-0.706641\pi$
$541$	−4.45289e9	−1.20907	−0.604535	+	0.796579i	$0.706641\pi$
$542$	1.44107e9	0.388764
$543$	−1.54989e9	−0.415433
$544$	3.34373e8	0.0890503
$545$	0	0
$546$	−3.23356e8	−0.0850173
$547$	5.12140e9	1.33793	0.668964	−	0.743294i	$-0.266738\pi$
$547$	5.12140e9	1.33793	0.668964	+	0.743294i	$0.266738\pi$
$548$	1.47431e9	0.382698
$549$	2.94044e9	0.758418
$550$	0	0
$551$	2.06933e9	0.526987
$552$	−2.93589e9	−0.742939
$553$	−1.10886e9	−0.278828
$554$	3.13814e9	0.784130
$555$	0	0
$556$	1.41374e9	0.348825
$557$	2.27708e9	0.558323	0.279161	−	0.960244i	$-0.409944\pi$
$557$	2.27708e9	0.558323	0.279161	+	0.960244i	$0.409944\pi$
$558$	3.88890e9	0.947561
$559$	−1.26649e9	−0.306663
$560$	0	0
$561$	−1.17510e8	−0.0280999
$562$	8.69100e9	2.06535
$563$	2.22027e9	0.524357	0.262178	−	0.965019i	$-0.415559\pi$
$563$	2.22027e9	0.524357	0.262178	+	0.965019i	$0.415559\pi$
$564$	3.08394e8	0.0723817
$565$	0	0
$566$	7.86405e9	1.82301
$567$	4.13458e7	0.00952557
$568$	−7.65683e8	−0.175319
$569$	2.40464e9	0.547213	0.273606	−	0.961842i	$-0.411783\pi$
$569$	2.40464e9	0.547213	0.273606	+	0.961842i	$0.411783\pi$
$570$	0	0
$571$	−2.48806e9	−0.559287	−0.279643	−	0.960104i	$-0.590216\pi$
$571$	−2.48806e9	−0.559287	−0.279643	+	0.960104i	$0.590216\pi$
$572$	5.33827e7	0.0119265
$573$	2.06016e9	0.457468
$574$	−2.21466e9	−0.488783
$575$	0	0
$576$	−1.92659e9	−0.420058
$577$	3.13386e9	0.679147	0.339574	−	0.940579i	$-0.389717\pi$
$577$	3.13386e9	0.679147	0.339574	+	0.940579i	$0.389717\pi$
$578$	4.92114e9	1.06003
$579$	5.39089e9	1.15421
$580$	0	0
$581$	−1.73414e8	−0.0366832
$582$	−1.26581e9	−0.266158
$583$	8.35014e8	0.174524
$584$	−4.66621e9	−0.969435
$585$	0	0
$586$	2.44306e9	0.501524
$587$	−2.38296e9	−0.486277	−0.243139	−	0.969992i	$-0.578177\pi$
$587$	−2.38296e9	−0.486277	−0.243139	+	0.969992i	$0.578177\pi$
$588$	−5.08954e8	−0.103242
$589$	7.52271e9	1.51695
$590$	0	0
$591$	4.33417e9	0.863675
$592$	−4.83796e9	−0.958377
$593$	−5.24016e9	−1.03194	−0.515969	−	0.856607i	$-0.672568\pi$
$593$	−5.24016e9	−1.03194	−0.515969	+	0.856607i	$0.672568\pi$
$594$	−1.25594e9	−0.245876
$595$	0	0
$596$	−1.42181e9	−0.275093
$597$	−2.09333e9	−0.402650
$598$	−1.93735e9	−0.370470
$599$	6.71444e9	1.27649	0.638243	−	0.769835i	$-0.279662\pi$
$599$	6.71444e9	1.27649	0.638243	+	0.769835i	$0.279662\pi$
$600$	0	0
$601$	3.71405e9	0.697891	0.348945	−	0.937143i	$-0.386540\pi$
$601$	3.71405e9	0.697891	0.348945	+	0.937143i	$0.386540\pi$
$602$	3.80902e9	0.711583
$603$	−5.75768e9	−1.06939
$604$	−1.67543e9	−0.309384
$605$	0	0
$606$	1.78245e9	0.325358
$607$	−5.42079e9	−0.983789	−0.491895	−	0.870655i	$-0.663695\pi$
$607$	−5.42079e9	−0.983789	−0.491895	+	0.870655i	$0.663695\pi$
$608$	2.61824e9	0.472440
$609$	−8.64180e8	−0.155040
$610$	0	0
$611$	−7.10054e8	−0.125935
$612$	−1.56642e8	−0.0276234
$613$	2.77503e9	0.486582	0.243291	−	0.969953i	$-0.421773\pi$
$613$	2.77503e9	0.486582	0.243291	+	0.969953i	$0.421773\pi$
$614$	8.13613e9	1.41850
$615$	0	0
$616$	5.60182e8	0.0965599
$617$	1.00341e10	1.71981	0.859906	−	0.510453i	$-0.170522\pi$
$617$	1.00341e10	1.71981	0.859906	+	0.510453i	$0.170522\pi$
$618$	−1.43102e9	−0.243885
$619$	5.53759e9	0.938434	0.469217	−	0.883083i	$-0.344536\pi$
$619$	5.53759e9	0.938434	0.469217	+	0.883083i	$0.344536\pi$
$620$	0	0
$621$	8.30369e9	1.39140
$622$	−3.68100e9	−0.613337
$623$	−2.45532e9	−0.406819
$624$	1.07731e9	0.177498
$625$	0	0
$626$	−6.35375e9	−1.03519
$627$	−9.20136e8	−0.149079
$628$	1.61795e9	0.260680
$629$	1.03716e9	0.166177
$630$	0	0
$631$	−7.91682e9	−1.25443	−0.627217	−	0.778844i	$-0.715806\pi$
$631$	−7.91682e9	−1.25443	−0.627217	+	0.778844i	$0.715806\pi$
$632$	2.99282e9	0.471596
$633$	1.60441e9	0.251422
$634$	1.38537e10	2.15901
$635$	0	0
$636$	−7.12782e8	−0.109864
$637$	1.17183e9	0.179629
$638$	7.83119e8	0.119387
$639$	8.20192e8	0.124355
$640$	0	0
$641$	−1.16040e10	−1.74022	−0.870112	−	0.492854i	$-0.835954\pi$
$641$	−1.16040e10	−1.74022	−0.870112	+	0.492854i	$0.835954\pi$
$642$	2.91290e9	0.434464
$643$	−1.33576e10	−1.98149	−0.990744	−	0.135742i	$-0.956658\pi$
$643$	−1.33576e10	−1.98149	−0.990744	+	0.135742i	$0.956658\pi$
$644$	1.06148e9	0.156607
$645$	0	0
$646$	−1.66326e9	−0.242743
$647$	4.80733e9	0.697813	0.348907	−	0.937158i	$-0.386553\pi$
$647$	4.80733e9	0.697813	0.348907	+	0.937158i	$0.386553\pi$
$648$	−1.11593e8	−0.0161111
$649$	−2.05505e9	−0.295098
$650$	0	0
$651$	−3.14158e9	−0.446288
$652$	1.06602e9	0.150626
$653$	5.34858e9	0.751696	0.375848	−	0.926681i	$-0.377352\pi$
$653$	5.34858e9	0.751696	0.375848	+	0.926681i	$0.377352\pi$
$654$	8.60593e9	1.20303
$655$	0	0
$656$	7.37845e9	1.02047
$657$	4.99839e9	0.687625
$658$	2.13551e9	0.292221
$659$	−2.02525e9	−0.275663	−0.137832	−	0.990456i	$-0.544013\pi$
$659$	−2.02525e9	−0.275663	−0.137832	+	0.990456i	$0.544013\pi$
$660$	0	0
$661$	2.82247e9	0.380123	0.190061	−	0.981772i	$-0.439131\pi$
$661$	2.82247e9	0.380123	0.190061	+	0.981772i	$0.439131\pi$
$662$	−1.09419e10	−1.46585
$663$	−2.30953e8	−0.0307770
$664$	4.68046e8	0.0620441
$665$	0	0
$666$	4.19833e9	0.550702
$667$	−5.17762e9	−0.675600
$668$	1.08435e9	0.140751
$669$	−5.71006e9	−0.737308
$670$	0	0
$671$	2.15257e9	0.275060
$672$	−1.09341e9	−0.138992
$673$	−4.18476e9	−0.529197	−0.264599	−	0.964359i	$-0.585239\pi$
$673$	−4.18476e9	−0.529197	−0.264599	+	0.964359i	$0.585239\pi$
$674$	2.96020e9	0.372401
$675$	0	0
$676$	−1.68425e9	−0.209697
$677$	−1.33079e9	−0.164835	−0.0824173	−	0.996598i	$-0.526264\pi$
$677$	−1.33079e9	−0.164835	−0.0824173	+	0.996598i	$0.526264\pi$
$678$	7.81038e9	0.962428
$679$	−1.59684e9	−0.195757
$680$	0	0
$681$	−6.67950e9	−0.810455
$682$	2.84690e9	0.343658
$683$	−2.57804e9	−0.309612	−0.154806	−	0.987945i	$-0.549475\pi$
$683$	−2.57804e9	−0.309612	−0.154806	+	0.987945i	$0.549475\pi$
$684$	−1.22655e9	−0.146551
$685$	0	0
$686$	−8.27545e9	−0.978717
$687$	−1.55657e9	−0.183155
$688$	−1.26903e10	−1.48563
$689$	1.64113e9	0.191150
$690$	0	0
$691$	−4.84462e9	−0.558582	−0.279291	−	0.960207i	$-0.590099\pi$
$691$	−4.84462e9	−0.558582	−0.279291	+	0.960207i	$0.590099\pi$
$692$	2.63641e9	0.302442
$693$	−6.00062e8	−0.0684904
$694$	−2.73725e9	−0.310854
$695$	0	0
$696$	2.33243e9	0.262227
$697$	−1.58179e9	−0.176944
$698$	−7.90428e9	−0.879768
$699$	1.65318e8	0.0183084
$700$	0	0
$701$	6.11894e9	0.670908	0.335454	−	0.942057i	$-0.391110\pi$
$701$	6.11894e9	0.670908	0.335454	+	0.942057i	$0.391110\pi$
$702$	−2.46841e9	−0.269301
$703$	8.12127e9	0.881618
$704$	−1.41037e9	−0.152345
$705$	0	0
$706$	1.34541e10	1.43893
$707$	2.24858e9	0.239299
$708$	1.75422e9	0.185767
$709$	7.40120e9	0.779903	0.389951	−	0.920835i	$-0.372492\pi$
$709$	7.40120e9	0.779903	0.389951	+	0.920835i	$0.372492\pi$
$710$	0	0
$711$	−3.20587e9	−0.334505
$712$	6.62695e9	0.688072
$713$	−1.88224e10	−1.94474
$714$	6.94598e8	0.0714151
$715$	0	0
$716$	3.30931e9	0.336932
$717$	−7.84184e9	−0.794513
$718$	−6.41858e9	−0.647148
$719$	7.80060e9	0.782667	0.391333	−	0.920249i	$-0.372014\pi$
$719$	7.80060e9	0.782667	0.391333	+	0.920249i	$0.372014\pi$
$720$	0	0
$721$	−1.80524e9	−0.179375
$722$	−1.84097e9	−0.182040
$723$	−6.48437e9	−0.638093
$724$	−1.51244e9	−0.148113
$725$	0	0
$726$	6.77528e9	0.657126
$727$	5.90928e8	0.0570379	0.0285190	−	0.999593i	$-0.490921\pi$
$727$	5.90928e8	0.0570379	0.0285190	+	0.999593i	$0.490921\pi$
$728$	1.10098e9	0.105759
$729$	6.69245e9	0.639792
$730$	0	0
$731$	2.72054e9	0.257599
$732$	−1.83747e9	−0.173153
$733$	1.50795e10	1.41424	0.707122	−	0.707092i	$-0.249993\pi$
$733$	1.50795e10	1.41424	0.707122	+	0.707092i	$0.249993\pi$
$734$	1.25217e10	1.16877
$735$	0	0
$736$	−6.55102e9	−0.605670
$737$	−4.21495e9	−0.387844
$738$	−6.40294e9	−0.586384
$739$	−1.39633e10	−1.27272	−0.636361	−	0.771391i	$-0.719561\pi$
$739$	−1.39633e10	−1.27272	−0.636361	+	0.771391i	$0.719561\pi$
$740$	0	0
$741$	−1.80843e9	−0.163281
$742$	−4.93575e9	−0.443546
$743$	−8.75841e9	−0.783365	−0.391683	−	0.920100i	$-0.628107\pi$
$743$	−8.75841e9	−0.783365	−0.391683	+	0.920100i	$0.628107\pi$
$744$	8.47917e9	0.754828
$745$	0	0
$746$	5.26784e9	0.464565
$747$	−5.01367e8	−0.0440082
$748$	−1.14671e8	−0.0100184
$749$	3.67467e9	0.319545
$750$	0	0
$751$	−3.62726e9	−0.312492	−0.156246	−	0.987718i	$-0.549939\pi$
$751$	−3.62726e9	−0.312492	−0.156246	+	0.987718i	$0.549939\pi$
$752$	−7.11474e9	−0.610094
$753$	−4.30670e9	−0.367589
$754$	1.53913e9	0.130761
$755$	0	0
$756$	1.35246e9	0.113840
$757$	−7.68437e8	−0.0643832	−0.0321916	−	0.999482i	$-0.510249\pi$
$757$	−7.68437e8	−0.0643832	−0.0321916	+	0.999482i	$0.510249\pi$
$758$	2.28248e10	1.90355
$759$	2.30225e9	0.191120
$760$	0	0
$761$	−9.97476e9	−0.820458	−0.410229	−	0.911983i	$-0.634551\pi$
$761$	−9.97476e9	−0.820458	−0.410229	+	0.911983i	$0.634551\pi$
$762$	−4.96241e9	−0.406303
$763$	1.08565e10	0.884817
$764$	2.01039e9	0.163100
$765$	0	0
$766$	2.56100e9	0.205878
$767$	−4.03897e9	−0.323212
$768$	5.00084e9	0.398363
$769$	−3.11961e9	−0.247377	−0.123688	−	0.992321i	$-0.539472\pi$
$769$	−3.11961e9	−0.247377	−0.123688	+	0.992321i	$0.539472\pi$
$770$	0	0
$771$	−7.88659e8	−0.0619725
$772$	5.26064e9	0.411508
$773$	−1.74261e10	−1.35698	−0.678489	−	0.734611i	$-0.737365\pi$
$773$	−1.74261e10	−1.35698	−0.678489	+	0.734611i	$0.737365\pi$
$774$	1.10125e10	0.853673
$775$	0	0
$776$	4.30989e9	0.331093
$777$	−3.39155e9	−0.259373
$778$	1.86759e10	1.42185
$779$	−1.23859e10	−0.938741
$780$	0	0
$781$	6.00428e8	0.0451006
$782$	4.16159e9	0.311197
$783$	−6.59691e9	−0.491105
$784$	1.17417e10	0.870213
$785$	0	0
$786$	−7.45190e9	−0.547379
$787$	−5.71501e9	−0.417932	−0.208966	−	0.977923i	$-0.567010\pi$
$787$	−5.71501e9	−0.417932	−0.208966	+	0.977923i	$0.567010\pi$
$788$	4.22945e9	0.307923
$789$	1.60849e9	0.116587
$790$	0	0
$791$	9.85289e9	0.707858
$792$	1.61957e9	0.115841
$793$	4.23064e9	0.301266
$794$	1.23174e10	0.873270
$795$	0	0
$796$	−2.04275e9	−0.143556
$797$	−3.66054e9	−0.256119	−0.128059	−	0.991767i	$-0.540875\pi$
$797$	−3.66054e9	−0.256119	−0.128059	+	0.991767i	$0.540875\pi$
$798$	5.43890e9	0.378879
$799$	1.52526e9	0.105786
$800$	0	0
$801$	−7.09873e9	−0.488053
$802$	6.57566e9	0.450121
$803$	3.65911e9	0.249385
$804$	3.59795e9	0.244151
$805$	0	0
$806$	5.59527e9	0.376399
$807$	−1.58408e10	−1.06101
$808$	−6.06894e9	−0.404737
$809$	1.88709e10	1.25307	0.626533	−	0.779395i	$-0.284473\pi$
$809$	1.88709e10	1.25307	0.626533	+	0.779395i	$0.284473\pi$
$810$	0	0
$811$	2.80285e10	1.84513	0.922564	−	0.385845i	$-0.126090\pi$
$811$	2.80285e10	1.84513	0.922564	+	0.385845i	$0.126090\pi$
$812$	−8.43300e8	−0.0552759
$813$	−3.36571e9	−0.219665
$814$	3.07342e9	0.199727
$815$	0	0
$816$	−2.31415e9	−0.149099
$817$	2.13026e10	1.36664
$818$	−2.06467e10	−1.31891
$819$	−1.17935e9	−0.0750155
$820$	0	0
$821$	−9.10545e9	−0.574249	−0.287125	−	0.957893i	$-0.592699\pi$
$821$	−9.10545e9	−0.574249	−0.287125	+	0.957893i	$0.592699\pi$
$822$	−1.89011e10	−1.18696
$823$	8.98135e9	0.561619	0.280810	−	0.959763i	$-0.409397\pi$
$823$	8.98135e9	0.561619	0.280810	+	0.959763i	$0.409397\pi$
$824$	4.87238e9	0.303386
$825$	0	0
$826$	1.21473e10	0.749982
$827$	−1.69765e10	−1.04370	−0.521852	−	0.853036i	$-0.674759\pi$
$827$	−1.69765e10	−1.04370	−0.521852	+	0.853036i	$0.674759\pi$
$828$	3.06891e9	0.187879
$829$	−6.63956e9	−0.404761	−0.202381	−	0.979307i	$-0.564868\pi$
$829$	−6.63956e9	−0.404761	−0.202381	+	0.979307i	$0.564868\pi$
$830$	0	0
$831$	−7.32935e9	−0.443059
$832$	−2.77193e9	−0.166859
$833$	−2.51719e9	−0.150889
$834$	−1.81246e10	−1.08190
$835$	0	0
$836$	−8.97904e8	−0.0531505
$837$	−2.39819e10	−1.41366
$838$	2.31178e10	1.35704
$839$	−6.01260e9	−0.351476	−0.175738	−	0.984437i	$-0.556231\pi$
$839$	−6.01260e9	−0.351476	−0.175738	+	0.984437i	$0.556231\pi$
$840$	0	0
$841$	−1.31365e10	−0.761541
$842$	−1.54531e10	−0.892119
$843$	−2.02985e10	−1.16699
$844$	1.56565e9	0.0896387
$845$	0	0
$846$	6.17409e9	0.350572
$847$	8.54710e9	0.483311
$848$	1.64441e10	0.926029
$849$	−1.83671e10	−1.03006
$850$	0	0
$851$	−2.03200e10	−1.13024
$852$	−5.12535e8	−0.0283913
$853$	−1.07212e9	−0.0591454	−0.0295727	−	0.999563i	$-0.509415\pi$
$853$	−1.07212e9	−0.0591454	−0.0295727	+	0.999563i	$0.509415\pi$
$854$	−1.27238e10	−0.699058
$855$	0	0
$856$	−9.91797e9	−0.540461
$857$	−1.01013e10	−0.548207	−0.274104	−	0.961700i	$-0.588381\pi$
$857$	−1.01013e10	−0.548207	−0.274104	+	0.961700i	$0.588381\pi$
$858$	−6.84381e8	−0.0369907
$859$	2.75889e10	1.48511	0.742555	−	0.669785i	$-0.233614\pi$
$859$	2.75889e10	1.48511	0.742555	+	0.669785i	$0.233614\pi$
$860$	0	0
$861$	5.17251e9	0.276179
$862$	1.70783e10	0.908176
$863$	−1.67192e10	−0.885480	−0.442740	−	0.896650i	$-0.645994\pi$
$863$	−1.67192e10	−0.885480	−0.442740	+	0.896650i	$0.645994\pi$
$864$	−8.34678e9	−0.440272
$865$	0	0
$866$	3.10914e10	1.62678
$867$	−1.14937e10	−0.598952
$868$	−3.06568e9	−0.159114
$869$	−2.34689e9	−0.121317
$870$	0	0
$871$	−8.28403e9	−0.424794
$872$	−2.93018e10	−1.49653
$873$	−4.61671e9	−0.234846
$874$	3.25864e10	1.65100
$875$	0	0
$876$	−3.12348e9	−0.156991
$877$	6.63225e9	0.332019	0.166009	−	0.986124i	$-0.446912\pi$
$877$	6.63225e9	0.332019	0.166009	+	0.986124i	$0.446912\pi$
$878$	−3.36970e10	−1.68020
$879$	−5.70594e9	−0.283378
$880$	0	0
$881$	−1.44206e10	−0.710505	−0.355253	−	0.934770i	$-0.615605\pi$
$881$	−1.44206e10	−0.710505	−0.355253	+	0.934770i	$0.615605\pi$
$882$	−1.01893e10	−0.500041
$883$	−1.41136e10	−0.689883	−0.344941	−	0.938624i	$-0.612101\pi$
$883$	−1.41136e10	−0.689883	−0.344941	+	0.938624i	$0.612101\pi$
$884$	−2.25373e8	−0.0109728
$885$	0	0
$886$	1.85515e9	0.0896108
$887$	4.14206e10	1.99289	0.996446	−	0.0842313i	$-0.0268435\pi$
$887$	4.14206e10	1.99289	0.996446	+	0.0842313i	$0.0268435\pi$
$888$	9.15383e9	0.438690
$889$	−6.26014e9	−0.298833
$890$	0	0
$891$	8.75082e7	0.00414454
$892$	−5.57209e9	−0.262870
$893$	1.19432e10	0.561230
$894$	1.82280e10	0.853215
$895$	0	0
$896$	1.31265e10	0.609638
$897$	4.52481e9	0.209328
$898$	1.47189e10	0.678279
$899$	1.49535e10	0.686412
$900$	0	0
$901$	−3.52529e9	−0.160568
$902$	−4.68732e9	−0.212668
$903$	−8.89624e9	−0.402068
$904$	−2.65931e10	−1.19723
$905$	0	0
$906$	2.14795e10	0.959569
$907$	−1.46229e10	−0.650740	−0.325370	−	0.945587i	$-0.605489\pi$
$907$	−1.46229e10	−0.650740	−0.325370	+	0.945587i	$0.605489\pi$
$908$	−6.51811e9	−0.288949
$909$	6.50099e9	0.287082
$910$	0	0
$911$	1.98316e9	0.0869048	0.0434524	−	0.999055i	$-0.486164\pi$
$911$	1.98316e9	0.0869048	0.0434524	+	0.999055i	$0.486164\pi$
$912$	−1.81204e10	−0.791018
$913$	−3.67029e8	−0.0159607
$914$	3.50191e9	0.151703
$915$	0	0
$916$	−1.51896e9	−0.0652998
$917$	−9.40066e9	−0.402593
$918$	5.30237e9	0.226214
$919$	2.70716e10	1.15056	0.575281	−	0.817956i	$-0.304893\pi$
$919$	2.70716e10	1.15056	0.575281	+	0.817956i	$0.304893\pi$
$920$	0	0
$921$	−1.90025e10	−0.801498
$922$	3.39420e7	0.00142620
$923$	1.18007e9	0.0493973
$924$	3.74976e8	0.0156369
$925$	0	0
$926$	−2.22057e9	−0.0919024
$927$	−5.21924e9	−0.215193
$928$	5.20449e9	0.213776
$929$	3.85484e10	1.57743	0.788717	−	0.614757i	$-0.210746\pi$
$929$	3.85484e10	1.57743	0.788717	+	0.614757i	$0.210746\pi$
$930$	0	0
$931$	−1.97103e10	−0.800515
$932$	1.61324e8	0.00652744
$933$	8.59723e9	0.346556
$934$	−2.04192e10	−0.820021
$935$	0	0
$936$	3.18309e9	0.126877
$937$	−1.38428e10	−0.549712	−0.274856	−	0.961485i	$-0.588630\pi$
$937$	−1.38428e10	−0.549712	−0.274856	+	0.961485i	$0.588630\pi$
$938$	2.49145e10	0.985693
$939$	1.48396e10	0.584916
$940$	0	0
$941$	−4.80825e10	−1.88115	−0.940574	−	0.339587i	$-0.889713\pi$
$941$	−4.80825e10	−1.88115	−0.940574	+	0.339587i	$0.889713\pi$
$942$	−2.07426e10	−0.808510
$943$	3.09904e10	1.20347
$944$	−4.04705e10	−1.56580
$945$	0	0
$946$	8.06176e9	0.309607
$947$	3.12208e10	1.19459	0.597296	−	0.802021i	$-0.296242\pi$
$947$	3.12208e10	1.19459	0.597296	+	0.802021i	$0.296242\pi$
$948$	2.00334e9	0.0763704
$949$	7.19158e9	0.273145
$950$	0	0
$951$	−3.23564e10	−1.21991
$952$	−2.36500e9	−0.0888384
$953$	1.25062e10	0.468060	0.234030	−	0.972229i	$-0.424809\pi$
$953$	1.25062e10	0.468060	0.234030	+	0.972229i	$0.424809\pi$
$954$	−1.42700e10	−0.532114
$955$	0	0
$956$	−7.65237e9	−0.283265
$957$	−1.82903e9	−0.0674573
$958$	3.68376e10	1.35367
$959$	−2.38439e10	−0.872997
$960$	0	0
$961$	2.68484e10	0.975859
$962$	6.04047e9	0.218755
$963$	1.06240e10	0.383352
$964$	−6.32770e9	−0.227497
$965$	0	0
$966$	−1.36085e10	−0.485725
$967$	6.10155e8	0.0216994	0.0108497	−	0.999941i	$-0.496546\pi$
$967$	6.10155e8	0.0216994	0.0108497	+	0.999941i	$0.496546\pi$
$968$	−2.30687e10	−0.817448
$969$	3.88466e9	0.137158
$970$	0	0
$971$	−1.30898e10	−0.458845	−0.229423	−	0.973327i	$-0.573684\pi$
$971$	−1.30898e10	−0.458845	−0.229423	+	0.973327i	$0.573684\pi$
$972$	6.33940e9	0.221420
$973$	−2.28644e10	−0.795728
$974$	−3.22030e9	−0.111671
$975$	0	0
$976$	4.23910e10	1.45948
$977$	3.47814e10	1.19321	0.596604	−	0.802536i	$-0.296516\pi$
$977$	3.47814e10	1.19321	0.596604	+	0.802536i	$0.296516\pi$
$978$	−1.36667e10	−0.467174
$979$	−5.19668e9	−0.177005
$980$	0	0
$981$	3.13878e10	1.06150
$982$	3.88108e10	1.30786
$983$	−2.24923e10	−0.755262	−0.377631	−	0.925956i	$-0.623261\pi$
$983$	−2.24923e10	−0.755262	−0.377631	+	0.925956i	$0.623261\pi$
$984$	−1.39607e10	−0.467114
$985$	0	0
$986$	−3.30620e9	−0.109840
$987$	−4.98764e9	−0.165114
$988$	−1.76473e9	−0.0582142
$989$	−5.33006e10	−1.75205
$990$	0	0
$991$	5.87302e9	0.191692	0.0958460	−	0.995396i	$-0.469444\pi$
$991$	5.87302e9	0.191692	0.0958460	+	0.995396i	$0.469444\pi$
$992$	1.89200e10	0.615363
$993$	2.55556e10	0.828254
$994$	−3.54911e9	−0.114622
$995$	0	0
$996$	3.13302e8	0.0100474
$997$	3.22135e10	1.02945	0.514725	−	0.857355i	$-0.327894\pi$
$997$	3.22135e10	1.02945	0.514725	+	0.857355i	$0.327894\pi$
$998$	1.23389e10	0.392934
$999$	−2.58901e10	−0.821590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.8.a.g.1.15		64
5.4	even	2	inner	625.8.a.g.1.50		64
25.3	odd	20		25.8.e.a.9.13	✓	64
25.17	odd	20		25.8.e.a.14.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.e.a.9.13	✓	64	25.3	odd	20
25.8.e.a.14.13	yes	64	25.17	odd	20
625.8.a.g.1.15		64	1.1	even	1	trivial
625.8.a.g.1.50		64	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)

\(f(q)\)	\(=\)	\(q-12.5105 q^{2} +29.2192 q^{3} +28.5132 q^{4} -365.548 q^{6} -461.143 q^{7} +1244.63 q^{8} -1333.24 q^{9} +O(q^{10})\)	\(q-12.5105 q^{2} +29.2192 q^{3} +28.5132 q^{4} -365.548 q^{6} -461.143 q^{7} +1244.63 q^{8} -1333.24 q^{9} -976.006 q^{11} +833.135 q^{12} -1918.23 q^{13} +5769.14 q^{14} -19220.7 q^{16} +4120.53 q^{17} +16679.5 q^{18} +32264.9 q^{19} -13474.2 q^{21} +12210.4 q^{22} -80729.2 q^{23} +36367.2 q^{24} +23998.1 q^{26} -102859. q^{27} -13148.7 q^{28} +64135.7 q^{29} +233155. q^{31} +81148.1 q^{32} -28518.1 q^{33} -51550.0 q^{34} -38014.9 q^{36} +251706. q^{37} -403651. q^{38} -56049.3 q^{39} -383881. q^{41} +168570. q^{42} +660240. q^{43} -27829.1 q^{44} +1.00996e6 q^{46} +370161. q^{47} -561614. q^{48} -610890. q^{49} +120399. q^{51} -54695.0 q^{52} -855542. q^{53} +1.28682e6 q^{54} -573954. q^{56} +942756. q^{57} -802371. q^{58} +2.10557e6 q^{59} -2.20549e6 q^{61} -2.91689e6 q^{62} +614813. q^{63} +1.44504e6 q^{64} +356777. q^{66} +4.31857e6 q^{67} +117490. q^{68} -2.35884e6 q^{69} -615188. q^{71} -1.65939e6 q^{72} -3.74907e6 q^{73} -3.14897e6 q^{74} +919977. q^{76} +450079. q^{77} +701206. q^{78} +2.40458e6 q^{79} -89659.4 q^{81} +4.80255e6 q^{82} +376052. q^{83} -384194. q^{84} -8.25995e6 q^{86} +1.87399e6 q^{87} -1.21477e6 q^{88} +5.32443e6 q^{89} +884580. q^{91} -2.30185e6 q^{92} +6.81259e6 q^{93} -4.63090e6 q^{94} +2.37108e6 q^{96} +3.46278e6 q^{97} +7.64255e6 q^{98} +1.30125e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 3582 q^{4} - 1982 q^{6} + 37148 q^{9}+O(q^{10}) \) 64 * q + 3582 * q^4 - 1982 * q^6 + 37148 * q^9	\( 64 q + 3582 q^{4} - 1982 q^{6} + 37148 q^{9} - 17432 q^{11} - 34836 q^{14} + 164154 q^{16} - 123910 q^{19} - 193882 q^{21} - 544720 q^{24} - 708942 q^{26} - 666400 q^{29} - 900872 q^{31} - 911986 q^{34} + 309704 q^{36} - 1745894 q^{39} - 1862362 q^{41} - 3617976 q^{44} - 2373242 q^{46} + 3298162 q^{49} - 3922092 q^{51} - 7598090 q^{54} - 11353310 q^{56} - 12112530 q^{59} - 9276582 q^{61} - 4640288 q^{64} - 16518624 q^{66} - 17766944 q^{69} - 22846802 q^{71} - 20547876 q^{74} - 22436480 q^{76} - 23545670 q^{79} - 1824616 q^{81} - 31121786 q^{84} - 15273782 q^{86} - 29694630 q^{89} - 31731942 q^{91} + 3544204 q^{94} - 40852262 q^{96} - 57867624 q^{99}+O(q^{100}) \) 64 * q + 3582 * q^4 - 1982 * q^6 + 37148 * q^9 - 17432 * q^11 - 34836 * q^14 + 164154 * q^16 - 123910 * q^19 - 193882 * q^21 - 544720 * q^24 - 708942 * q^26 - 666400 * q^29 - 900872 * q^31 - 911986 * q^34 + 309704 * q^36 - 1745894 * q^39 - 1862362 * q^41 - 3617976 * q^44 - 2373242 * q^46 + 3298162 * q^49 - 3922092 * q^51 - 7598090 * q^54 - 11353310 * q^56 - 12112530 * q^59 - 9276582 * q^61 - 4640288 * q^64 - 16518624 * q^66 - 17766944 * q^69 - 22846802 * q^71 - 20547876 * q^74 - 22436480 * q^76 - 23545670 * q^79 - 1824616 * q^81 - 31121786 * q^84 - 15273782 * q^86 - 29694630 * q^89 - 31731942 * q^91 + 3544204 * q^94 - 40852262 * q^96 - 57867624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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