LMFDB - Embedded newform 637.6.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,6,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	637.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:	$102.164493221$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 250x^{6} + 210x^{5} + 20076x^{4} - 12252x^{3} - 544784x^{2} + 65648x + 2393792 $ x^8 - x^7 - 250x^6 + 210x^5 + 20076x^4 - 12252x^3 - 544784x^2 + 65648x + 2393792
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-10.5454$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+10.5454 q^{2} -20.9360 q^{3} +79.2064 q^{4} +47.3313 q^{5} -220.779 q^{6} +497.812 q^{8} +195.317 q^{9} +499.129 q^{10} -565.192 q^{11} -1658.27 q^{12} +169.000 q^{13} -990.929 q^{15} +2715.04 q^{16} -1584.92 q^{17} +2059.70 q^{18} +122.512 q^{19} +3748.94 q^{20} -5960.20 q^{22} -3589.38 q^{23} -10422.2 q^{24} -884.748 q^{25} +1782.18 q^{26} +998.301 q^{27} +281.224 q^{29} -10449.8 q^{30} -1091.47 q^{31} +12701.3 q^{32} +11832.9 q^{33} -16713.7 q^{34} +15470.3 q^{36} +12227.0 q^{37} +1291.94 q^{38} -3538.19 q^{39} +23562.1 q^{40} -18476.7 q^{41} -18009.0 q^{43} -44766.8 q^{44} +9244.59 q^{45} -37851.6 q^{46} +1825.98 q^{47} -56842.2 q^{48} -9330.06 q^{50} +33181.9 q^{51} +13385.9 q^{52} +16450.0 q^{53} +10527.5 q^{54} -26751.3 q^{55} -2564.91 q^{57} +2965.63 q^{58} -17850.9 q^{59} -78487.8 q^{60} +40378.3 q^{61} -11510.0 q^{62} +47060.0 q^{64} +7998.99 q^{65} +124783. q^{66} -25650.2 q^{67} -125536. q^{68} +75147.3 q^{69} +62754.5 q^{71} +97230.9 q^{72} -1546.40 q^{73} +128939. q^{74} +18523.1 q^{75} +9703.73 q^{76} -37311.7 q^{78} -75500.7 q^{79} +128507. q^{80} -68362.4 q^{81} -194845. q^{82} -73741.0 q^{83} -75016.2 q^{85} -189913. q^{86} -5887.71 q^{87} -281359. q^{88} +77074.6 q^{89} +97488.3 q^{90} -284302. q^{92} +22850.9 q^{93} +19255.8 q^{94} +5798.66 q^{95} -265916. q^{96} -47473.9 q^{97} -110391. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 28 q^{3} + 245 q^{4} - 219 q^{5} - 435 q^{6} - 57 q^{8} + 930 q^{9} + 948 q^{10} + 184 q^{11} - 463 q^{12} + 1352 q^{13} - 256 q^{15} + 4953 q^{16} - 2278 q^{17} - 5308 q^{18} - 4959 q^{19}+ \cdots + 90754 q^{99}+O(q^{100}) $ 8 * q - q^2 - 28 * q^3 + 245 * q^4 - 219 * q^5 - 435 * q^6 - 57 * q^8 + 930 * q^9 + 948 * q^10 + 184 * q^11 - 463 * q^12 + 1352 * q^13 - 256 * q^15 + 4953 * q^16 - 2278 * q^17 - 5308 * q^18 - 4959 * q^19 - 6684 * q^20 - 2009 * q^22 + 1889 * q^23 - 26021 * q^24 + 4505 * q^25 - 169 * q^26 - 9016 * q^27 + 15265 * q^29 + 24204 * q^30 - 6805 * q^31 + 1335 * q^32 + 12892 * q^33 - 5828 * q^34 + 58838 * q^36 + 5534 * q^37 - 506 * q^38 - 4732 * q^39 + 56256 * q^40 - 31176 * q^41 - 391 * q^43 + 14047 * q^44 - 29403 * q^45 - 30027 * q^46 - 1539 * q^47 + 106629 * q^48 - 24367 * q^50 - 71892 * q^51 + 41405 * q^52 + 19553 * q^53 + 8155 * q^54 - 69414 * q^55 + 54432 * q^57 - 148020 * q^58 - 90596 * q^59 - 299448 * q^60 + 58218 * q^61 - 7697 * q^62 + 61681 * q^64 - 37011 * q^65 + 145411 * q^66 - 89884 * q^67 - 120612 * q^68 - 24278 * q^69 + 2308 * q^71 - 317742 * q^72 + 69187 * q^73 + 52027 * q^74 + 154856 * q^75 + 47258 * q^76 - 73515 * q^78 - 167799 * q^79 - 173400 * q^80 + 163984 * q^81 + 49553 * q^82 - 101449 * q^83 + 24684 * q^85 - 357720 * q^86 - 61908 * q^87 - 270819 * q^88 - 51833 * q^89 + 567124 * q^90 - 542963 * q^92 + 132644 * q^93 + 122399 * q^94 + 188103 * q^95 - 871725 * q^96 - 295025 * q^97 + 90754 * q^99

Coefficient data

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

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

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

$2$	10.5454	1.86419	0.932094	−	0.362216i	$-0.117980\pi$
$2$	10.5454	1.86419	0.932094	+	0.362216i	$0.117980\pi$
$3$	−20.9360	−1.34305	−0.671523	−	0.740984i	$-0.734360\pi$
$3$	−20.9360	−1.34305	−0.671523	+	0.740984i	$0.734360\pi$
$4$	79.2064	2.47520
$5$	47.3313	0.846688	0.423344	−	0.905969i	$-0.360856\pi$
$5$	47.3313	0.846688	0.423344	+	0.905969i	$0.360856\pi$
$6$	−220.779	−2.50369
$7$	0	0
$7$	0	0
$8$	497.812	2.75005
$9$	195.317	0.803772
$10$	499.129	1.57839
$11$	−565.192	−1.40836	−0.704181	−	0.710021i	$-0.748686\pi$
$11$	−565.192	−1.40836	−0.704181	+	0.710021i	$0.748686\pi$
$12$	−1658.27	−3.32430
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	0	0
$15$	−990.929	−1.13714
$16$	2715.04	2.65141
$17$	−1584.92	−1.33010	−0.665050	−	0.746799i	$-0.731590\pi$
$17$	−1584.92	−1.33010	−0.665050	+	0.746799i	$0.731590\pi$
$18$	2059.70	1.49838
$19$	122.512	0.0778565	0.0389282	−	0.999242i	$-0.487606\pi$
$19$	122.512	0.0778565	0.0389282	+	0.999242i	$0.487606\pi$
$20$	3748.94	2.09572
$21$	0	0
$22$	−5960.20	−2.62545
$23$	−3589.38	−1.41481	−0.707407	−	0.706806i	$-0.750135\pi$
$23$	−3589.38	−1.41481	−0.707407	+	0.706806i	$0.750135\pi$
$24$	−10422.2	−3.69344
$25$	−884.748	−0.283119
$26$	1782.18	0.517033
$27$	998.301	0.263543
$28$	0	0
$29$	281.224	0.0620951	0.0310475	−	0.999518i	$-0.490116\pi$
$29$	281.224	0.0620951	0.0310475	+	0.999518i	$0.490116\pi$
$30$	−10449.8	−2.11984
$31$	−1091.47	−0.203988	−0.101994	−	0.994785i	$-0.532522\pi$
$31$	−1091.47	−0.203988	−0.101994	+	0.994785i	$0.532522\pi$
$32$	12701.3	2.19268
$33$	11832.9	1.89149
$34$	−16713.7	−2.47956
$35$	0	0
$36$	15470.3	1.98949
$37$	12227.0	1.46830	0.734149	−	0.678988i	$-0.237581\pi$
$37$	12227.0	1.46830	0.734149	+	0.678988i	$0.237581\pi$
$38$	1291.94	0.145139
$39$	−3538.19	−0.372494
$40$	23562.1	2.32843
$41$	−18476.7	−1.71658	−0.858292	−	0.513161i	$-0.828474\pi$
$41$	−18476.7	−1.71658	−0.858292	+	0.513161i	$0.828474\pi$
$42$	0	0
$43$	−18009.0	−1.48531	−0.742656	−	0.669673i	$-0.766434\pi$
$43$	−18009.0	−1.48531	−0.742656	+	0.669673i	$0.766434\pi$
$44$	−44766.8	−3.48597
$45$	9244.59	0.680544
$46$	−37851.6	−2.63748
$47$	1825.98	0.120573	0.0602867	−	0.998181i	$-0.480799\pi$
$47$	1825.98	0.120573	0.0602867	+	0.998181i	$0.480799\pi$
$48$	−56842.2	−3.56096
$49$	0	0
$50$	−9330.06	−0.527788
$51$	33181.9	1.78639
$52$	13385.9	0.686497
$53$	16450.0	0.804410	0.402205	−	0.915550i	$-0.368244\pi$
$53$	16450.0	0.804410	0.402205	+	0.915550i	$0.368244\pi$
$54$	10527.5	0.491294
$55$	−26751.3	−1.19244
$56$	0	0
$57$	−2564.91	−0.104565
$58$	2965.63	0.115757
$59$	−17850.9	−0.667621	−0.333810	−	0.942640i	$-0.608334\pi$
$59$	−17850.9	−0.667621	−0.333810	+	0.942640i	$0.608334\pi$
$60$	−78487.8	−2.81465
$61$	40378.3	1.38939	0.694693	−	0.719306i	$-0.255540\pi$
$61$	40378.3	1.38939	0.694693	+	0.719306i	$0.255540\pi$
$62$	−11510.0	−0.380273
$63$	0	0
$64$	47060.0	1.43616
$65$	7998.99	0.234829
$66$	124783.	3.52610
$67$	−25650.2	−0.698078	−0.349039	−	0.937108i	$-0.613492\pi$
$67$	−25650.2	−0.698078	−0.349039	+	0.937108i	$0.613492\pi$
$68$	−125536.	−3.29226
$69$	75147.3	1.90016
$70$	0	0
$71$	62754.5	1.47740	0.738701	−	0.674033i	$-0.235439\pi$
$71$	62754.5	1.47740	0.738701	+	0.674033i	$0.235439\pi$
$72$	97230.9	2.21041
$73$	−1546.40	−0.0339637	−0.0169819	−	0.999856i	$-0.505406\pi$
$73$	−1546.40	−0.0339637	−0.0169819	+	0.999856i	$0.505406\pi$
$74$	128939.	2.73718
$75$	18523.1	0.380242
$76$	9703.73	0.192710
$77$	0	0
$78$	−37311.7	−0.694399
$79$	−75500.7	−1.36108	−0.680539	−	0.732711i	$-0.738254\pi$
$79$	−75500.7	−1.36108	−0.680539	+	0.732711i	$0.738254\pi$
$80$	128507.	2.24492
$81$	−68362.4	−1.15772
$82$	−194845.	−3.20004
$83$	−73741.0	−1.17494	−0.587468	−	0.809248i	$-0.699875\pi$
$83$	−73741.0	−1.17494	−0.587468	+	0.809248i	$0.699875\pi$
$84$	0	0
$85$	−75016.2	−1.12618
$86$	−189913.	−2.76890
$87$	−5887.71	−0.0833966
$88$	−281359.	−3.87306
$89$	77074.6	1.03142	0.515711	−	0.856763i	$-0.327528\pi$
$89$	77074.6	1.03142	0.515711	+	0.856763i	$0.327528\pi$
$90$	97488.3	1.26866
$91$	0	0
$92$	−284302.	−3.50195
$93$	22850.9	0.273966
$94$	19255.8	0.224771
$95$	5798.66	0.0659202
$96$	−265916.	−2.94487
$97$	−47473.9	−0.512302	−0.256151	−	0.966637i	$-0.582454\pi$
$97$	−47473.9	−0.512302	−0.256151	+	0.966637i	$0.582454\pi$
$98$	0	0
$99$	−110391.	−1.13200
$100$	−70077.7	−0.700777
$101$	−183143.	−1.78643	−0.893217	−	0.449626i	$-0.851557\pi$
$101$	−183143.	−1.78643	−0.893217	+	0.449626i	$0.851557\pi$
$102$	349917.	3.33016
$103$	−35947.8	−0.333871	−0.166936	−	0.985968i	$-0.553387\pi$
$103$	−35947.8	−0.333871	−0.166936	+	0.985968i	$0.553387\pi$
$104$	84130.2	0.762726
$105$	0	0
$106$	173473.	1.49957
$107$	−56317.4	−0.475536	−0.237768	−	0.971322i	$-0.576416\pi$
$107$	−56317.4	−0.475536	−0.237768	+	0.971322i	$0.576416\pi$
$108$	79071.8	0.652322
$109$	198764.	1.60240	0.801199	−	0.598398i	$-0.204196\pi$
$109$	198764.	1.60240	0.801199	+	0.598398i	$0.204196\pi$
$110$	−282104.	−2.22294
$111$	−255984.	−1.97199
$112$	0	0
$113$	−263390.	−1.94045	−0.970227	−	0.242197i	$-0.922132\pi$
$113$	−263390.	−1.94045	−0.970227	+	0.242197i	$0.922132\pi$
$114$	−27048.2	−0.194929
$115$	−169890.	−1.19791
$116$	22274.7	0.153698
$117$	33008.5	0.222926
$118$	−188245.	−1.24457
$119$	0	0
$120$	−493296.	−3.12719
$121$	158391.	0.983482
$122$	425807.	2.59008
$123$	386829.	2.30545
$124$	−86451.0	−0.504912
$125$	−189787.	−1.08640
$126$	0	0
$127$	133322.	0.733486	0.366743	−	0.930322i	$-0.380473\pi$
$127$	133322.	0.733486	0.366743	+	0.930322i	$0.380473\pi$
$128$	89824.9	0.484587
$129$	377036.	1.99484
$130$	84352.9	0.437766
$131$	−355376.	−1.80930	−0.904649	−	0.426158i	$-0.859867\pi$
$131$	−355376.	−1.80930	−0.904649	+	0.426158i	$0.859867\pi$
$132$	937238.	4.68182
$133$	0	0
$134$	−270493.	−1.30135
$135$	47250.9	0.223139
$136$	−788991.	−3.65784
$137$	13834.2	0.0629730	0.0314865	−	0.999504i	$-0.489976\pi$
$137$	13834.2	0.0629730	0.0314865	+	0.999504i	$0.489976\pi$
$138$	792461.	3.54226
$139$	304201.	1.33544	0.667718	−	0.744414i	$-0.267271\pi$
$139$	304201.	1.33544	0.667718	+	0.744414i	$0.267271\pi$
$140$	0	0
$141$	−38228.7	−0.161935
$142$	661774.	2.75416
$143$	−95517.4	−0.390609
$144$	530293.	2.13113
$145$	13310.7	0.0525752
$146$	−16307.5	−0.0633148
$147$	0	0
$148$	968453.	3.63433
$149$	61346.6	0.226373	0.113186	−	0.993574i	$-0.463894\pi$
$149$	61346.6	0.226373	0.113186	+	0.993574i	$0.463894\pi$
$150$	195334.	0.708843
$151$	−251294.	−0.896892	−0.448446	−	0.893810i	$-0.648022\pi$
$151$	−251294.	−0.896892	−0.448446	+	0.893810i	$0.648022\pi$
$152$	60988.0	0.214109
$153$	−309561.	−1.06910
$154$	0	0
$155$	−51660.5	−0.172715
$156$	−280247.	−0.921996
$157$	−141718.	−0.458856	−0.229428	−	0.973326i	$-0.573685\pi$
$157$	−141718.	−0.458856	−0.229428	+	0.973326i	$0.573685\pi$
$158$	−796188.	−2.53731
$159$	−344398.	−1.08036
$160$	601171.	1.85651
$161$	0	0
$162$	−720911.	−2.15821
$163$	388256.	1.14459	0.572293	−	0.820049i	$-0.306054\pi$
$163$	388256.	1.14459	0.572293	+	0.820049i	$0.306054\pi$
$164$	−1.46347e6	−4.24889
$165$	560065.	1.60151
$166$	−777632.	−2.19030
$167$	188989.	0.524378	0.262189	−	0.965017i	$-0.415556\pi$
$167$	188989.	0.524378	0.262189	+	0.965017i	$0.415556\pi$
$168$	0	0
$169$	28561.0	0.0769231
$170$	−791079.	−2.09941
$171$	23928.6	0.0625789
$172$	−1.42643e6	−3.67644
$173$	77256.1	0.196253	0.0981267	−	0.995174i	$-0.468715\pi$
$173$	77256.1	0.196253	0.0981267	+	0.995174i	$0.468715\pi$
$174$	−62088.5	−0.155467
$175$	0	0
$176$	−1.53452e6	−3.73414
$177$	373726.	0.896645
$178$	812785.	1.92276
$179$	455688.	1.06300	0.531502	−	0.847057i	$-0.321628\pi$
$179$	455688.	1.06300	0.531502	+	0.847057i	$0.321628\pi$
$180$	732230.	1.68448
$181$	−234722.	−0.532547	−0.266273	−	0.963898i	$-0.585792\pi$
$181$	−234722.	−0.532547	−0.266273	+	0.963898i	$0.585792\pi$
$182$	0	0
$183$	−845360.	−1.86601
$184$	−1.78683e6	−3.89081
$185$	578718.	1.24319
$186$	240973.	0.510724
$187$	895783.	1.87326
$188$	144629.	0.298443
$189$	0	0
$190$	61149.4	0.122888
$191$	−205385.	−0.407366	−0.203683	−	0.979037i	$-0.565291\pi$
$191$	−205385.	−0.407366	−0.203683	+	0.979037i	$0.565291\pi$
$192$	−985248.	−1.92882
$193$	18128.1	0.0350315	0.0175158	−	0.999847i	$-0.494424\pi$
$193$	18128.1	0.0350315	0.0175158	+	0.999847i	$0.494424\pi$
$194$	−500634.	−0.955027
$195$	−167467.	−0.315386
$196$	0	0
$197$	331912.	0.609337	0.304668	−	0.952459i	$-0.401454\pi$
$197$	331912.	0.609337	0.304668	+	0.952459i	$0.401454\pi$
$198$	−1.16413e6	−2.11026
$199$	−363902.	−0.651407	−0.325703	−	0.945472i	$-0.605601\pi$
$199$	−363902.	−0.651407	−0.325703	+	0.945472i	$0.605601\pi$
$200$	−440438.	−0.778592
$201$	537013.	0.937551
$202$	−1.93132e6	−3.33025
$203$	0	0
$204$	2.62821e6	4.42166
$205$	−874527.	−1.45341
$206$	−379085.	−0.622399
$207$	−701065.	−1.13719
$208$	458842.	0.735369
$209$	−69242.8	−0.109650
$210$	0	0
$211$	86433.6	0.133652	0.0668261	−	0.997765i	$-0.478713\pi$
$211$	86433.6	0.133652	0.0668261	+	0.997765i	$0.478713\pi$
$212$	1.30295e6	1.99107
$213$	−1.31383e6	−1.98422
$214$	−593892.	−0.886488
$215$	−852388.	−1.25760
$216$	496966.	0.724757
$217$	0	0
$218$	2.09605e6	2.98717
$219$	32375.5	0.0456149
$220$	−2.11887e6	−2.95153
$221$	−267851.	−0.368904
$222$	−2.69946e6	−3.67616
$223$	828294.	1.11538	0.557689	−	0.830050i	$-0.311688\pi$
$223$	828294.	1.11538	0.557689	+	0.830050i	$0.311688\pi$
$224$	0	0
$225$	−172806.	−0.227563
$226$	−2.77757e6	−3.61737
$227$	−476437.	−0.613678	−0.306839	−	0.951761i	$-0.599271\pi$
$227$	−476437.	−0.613678	−0.306839	+	0.951761i	$0.599271\pi$
$228$	−203157.	−0.258819
$229$	634312.	0.799308	0.399654	−	0.916666i	$-0.369130\pi$
$229$	634312.	0.799308	0.399654	+	0.916666i	$0.369130\pi$
$230$	−1.79156e6	−2.23312
$231$	0	0
$232$	139997.	0.170764
$233$	−381598.	−0.460486	−0.230243	−	0.973133i	$-0.573952\pi$
$233$	−381598.	−0.460486	−0.230243	+	0.973133i	$0.573952\pi$
$234$	348089.	0.415576
$235$	86426.0	0.102088
$236$	−1.41390e6	−1.65249
$237$	1.58068e6	1.82799
$238$	0	0
$239$	−436062.	−0.493803	−0.246901	−	0.969041i	$-0.579412\pi$
$239$	−436062.	−0.493803	−0.246901	+	0.969041i	$0.579412\pi$
$240$	−2.69041e6	−3.01503
$241$	540410.	0.599351	0.299675	−	0.954041i	$-0.403122\pi$
$241$	540410.	0.599351	0.299675	+	0.954041i	$0.403122\pi$
$242$	1.67030e6	1.83340
$243$	1.18865e6	1.29133
$244$	3.19822e6	3.43901
$245$	0	0
$246$	4.07928e6	4.29780
$247$	20704.5	0.0215935
$248$	−543344.	−0.560978
$249$	1.54384e6	1.57799
$250$	−2.00138e6	−2.02526
$251$	445577.	0.446415	0.223207	−	0.974771i	$-0.428347\pi$
$251$	445577.	0.446415	0.223207	+	0.974771i	$0.428347\pi$
$252$	0	0
$253$	2.02869e6	1.99257
$254$	1.40594e6	1.36736
$255$	1.57054e6	1.51251
$256$	−558675.	−0.532794
$257$	−823745.	−0.777965	−0.388983	−	0.921245i	$-0.627173\pi$
$257$	−823745.	−0.777965	−0.388983	+	0.921245i	$0.627173\pi$
$258$	3.97601e6	3.71876
$259$	0	0
$260$	633571.	0.581248
$261$	54927.7	0.0499103
$262$	−3.74760e6	−3.37287
$263$	−1.57117e6	−1.40067	−0.700334	−	0.713816i	$-0.746965\pi$
$263$	−1.57117e6	−1.40067	−0.700334	+	0.713816i	$0.746965\pi$
$264$	5.89054e6	5.20170
$265$	778602.	0.681084
$266$	0	0
$267$	−1.61363e6	−1.38525
$268$	−2.03166e6	−1.72788
$269$	1.61767e6	1.36304	0.681519	−	0.731800i	$-0.261319\pi$
$269$	1.61767e6	1.36304	0.681519	+	0.731800i	$0.261319\pi$
$270$	498281.	0.415973
$271$	1.62925e6	1.34761	0.673807	−	0.738907i	$-0.264658\pi$
$271$	1.62925e6	1.34761	0.673807	+	0.738907i	$0.264658\pi$
$272$	−4.30312e6	−3.52664
$273$	0	0
$274$	145888.	0.117393
$275$	500052.	0.398734
$276$	5.95214e6	4.70328
$277$	1.42189e6	1.11344	0.556721	−	0.830699i	$-0.312059\pi$
$277$	1.42189e6	1.11344	0.556721	+	0.830699i	$0.312059\pi$
$278$	3.20793e6	2.48950
$279$	−213181.	−0.163960
$280$	0	0
$281$	−1.90371e6	−1.43825	−0.719126	−	0.694879i	$-0.755458\pi$
$281$	−1.90371e6	−1.43825	−0.719126	+	0.694879i	$0.755458\pi$
$282$	−403139.	−0.301878
$283$	1.04222e6	0.773556	0.386778	−	0.922173i	$-0.373588\pi$
$283$	1.04222e6	0.773556	0.386778	+	0.922173i	$0.373588\pi$
$284$	4.97055e6	3.65686
$285$	−121401.	−0.0885338
$286$	−1.00727e6	−0.728169
$287$	0	0
$288$	2.48078e6	1.76241
$289$	1.09211e6	0.769168
$290$	140367.	0.0980100
$291$	993915.	0.688045
$292$	−122485.	−0.0840670
$293$	2.49381e6	1.69705	0.848524	−	0.529157i	$-0.177492\pi$
$293$	2.49381e6	1.69705	0.848524	+	0.529157i	$0.177492\pi$
$294$	0	0
$295$	−844905.	−0.565266
$296$	6.08673e6	4.03789
$297$	−564232.	−0.371164
$298$	646927.	0.422002
$299$	−606605.	−0.392399
$300$	1.46715e6	0.941175
$301$	0	0
$302$	−2.65001e6	−1.67198
$303$	3.83428e6	2.39926
$304$	332626.	0.206429
$305$	1.91116e6	1.17638
$306$	−3.26446e6	−1.99300
$307$	2.24762e6	1.36106	0.680530	−	0.732721i	$-0.261750\pi$
$307$	2.24762e6	1.36106	0.680530	+	0.732721i	$0.261750\pi$
$308$	0	0
$309$	752603.	0.448404
$310$	−544782.	−0.321973
$311$	803100.	0.470835	0.235418	−	0.971894i	$-0.424354\pi$
$311$	803100.	0.470835	0.235418	+	0.971894i	$0.424354\pi$
$312$	−1.76135e6	−1.02438
$313$	138328.	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$313$	138328.	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$314$	−1.49448e6	−0.855394
$315$	0	0
$316$	−5.98014e6	−3.36894
$317$	2.95651e6	1.65246	0.826232	−	0.563330i	$-0.190480\pi$
$317$	2.95651e6	1.65246	0.826232	+	0.563330i	$0.190480\pi$
$318$	−3.63183e6	−2.01399
$319$	−158945.	−0.0874524
$320$	2.22741e6	1.21598
$321$	1.17906e6	0.638666
$322$	0	0
$323$	−194172.	−0.103557
$324$	−5.41473e6	−2.86559
$325$	−149522.	−0.0785232
$326$	4.09433e6	2.13373
$327$	−4.16131e6	−2.15209
$328$	−9.19793e6	−4.72069
$329$	0	0
$330$	5.90613e6	2.98551
$331$	−1.50820e6	−0.756639	−0.378320	−	0.925675i	$-0.623498\pi$
$331$	−1.50820e6	−0.756639	−0.378320	+	0.925675i	$0.623498\pi$
$332$	−5.84076e6	−2.90820
$333$	2.38813e6	1.18018
$334$	1.99297e6	0.977540
$335$	−1.21406e6	−0.591055
$336$	0	0
$337$	−2.60970e6	−1.25174	−0.625872	−	0.779926i	$-0.715257\pi$
$337$	−2.60970e6	−1.25174	−0.625872	+	0.779926i	$0.715257\pi$
$338$	301188.	0.143399
$339$	5.51434e6	2.60612
$340$	−5.94176e6	−2.78752
$341$	616887.	0.287290
$342$	252338.	0.116659
$343$	0	0
$344$	−8.96508e6	−4.08468
$345$	3.55682e6	1.60884
$346$	814699.	0.365853
$347$	1.66208e6	0.741016	0.370508	−	0.928829i	$-0.379184\pi$
$347$	1.66208e6	0.741016	0.370508	+	0.928829i	$0.379184\pi$
$348$	−466344.	−0.206423
$349$	−876744.	−0.385309	−0.192654	−	0.981267i	$-0.561710\pi$
$349$	−876744.	−0.385309	−0.192654	+	0.981267i	$0.561710\pi$
$350$	0	0
$351$	168713.	0.0730938
$352$	−7.17870e6	−3.08808
$353$	506945.	0.216533	0.108266	−	0.994122i	$-0.465470\pi$
$353$	506945.	0.216533	0.108266	+	0.994122i	$0.465470\pi$
$354$	3.94111e6	1.67152
$355$	2.97025e6	1.25090
$356$	6.10479e6	2.55297
$357$	0	0
$358$	4.80543e6	1.98164
$359$	−1.75965e6	−0.720594	−0.360297	−	0.932838i	$-0.617325\pi$
$359$	−1.75965e6	−0.720594	−0.360297	+	0.932838i	$0.617325\pi$
$360$	4.60206e6	1.87153
$361$	−2.46109e6	−0.993938
$362$	−2.47525e6	−0.992767
$363$	−3.31607e6	−1.32086
$364$	0	0
$365$	−73193.3	−0.0287567
$366$	−8.91469e6	−3.47859
$367$	−2.17152e6	−0.841587	−0.420793	−	0.907157i	$-0.638248\pi$
$367$	−2.17152e6	−0.841587	−0.420793	+	0.907157i	$0.638248\pi$
$368$	−9.74531e6	−3.75125
$369$	−3.60881e6	−1.37974
$370$	6.10284e6	2.31754
$371$	0	0
$372$	1.80994e6	0.678120
$373$	4.92257e6	1.83197	0.915987	−	0.401207i	$-0.131409\pi$
$373$	4.92257e6	1.83197	0.915987	+	0.401207i	$0.131409\pi$
$374$	9.44643e6	3.49211
$375$	3.97337e6	1.45909
$376$	908994.	0.331582
$377$	47526.8	0.0172221
$378$	0	0
$379$	−2.28253e6	−0.816241	−0.408120	−	0.912928i	$-0.633816\pi$
$379$	−2.28253e6	−0.816241	−0.408120	+	0.912928i	$0.633816\pi$
$380$	459290.	0.163165
$381$	−2.79123e6	−0.985105
$382$	−2.16587e6	−0.759407
$383$	−3.06754e6	−1.06854	−0.534272	−	0.845312i	$-0.679414\pi$
$383$	−3.06754e6	−1.06854	−0.534272	+	0.845312i	$0.679414\pi$
$384$	−1.88058e6	−0.650823
$385$	0	0
$386$	191169.	0.0653053
$387$	−3.51745e6	−1.19385
$388$	−3.76024e6	−1.26805
$389$	5.07035e6	1.69889	0.849443	−	0.527680i	$-0.176938\pi$
$389$	5.07035e6	1.69889	0.849443	+	0.527680i	$0.176938\pi$
$390$	−1.76601e6	−0.587939
$391$	5.68887e6	1.88185
$392$	0	0
$393$	7.44016e6	2.42997
$394$	3.50016e6	1.13592
$395$	−3.57355e6	−1.15241
$396$	−8.74369e6	−2.80193
$397$	708622.	0.225651	0.112826	−	0.993615i	$-0.464010\pi$
$397$	708622.	0.225651	0.112826	+	0.993615i	$0.464010\pi$
$398$	−3.83751e6	−1.21435
$399$	0	0
$400$	−2.40213e6	−0.750665
$401$	1.66439e6	0.516885	0.258443	−	0.966027i	$-0.416791\pi$
$401$	1.66439e6	0.516885	0.258443	+	0.966027i	$0.416791\pi$
$402$	5.66304e6	1.74777
$403$	−184458.	−0.0565762
$404$	−1.45061e7	−4.42178
$405$	−3.23568e6	−0.980230
$406$	0	0
$407$	−6.91058e6	−2.06789
$408$	1.65183e7	4.91265
$409$	2.86555e6	0.847031	0.423515	−	0.905889i	$-0.360796\pi$
$409$	2.86555e6	0.847031	0.423515	+	0.905889i	$0.360796\pi$
$410$	−9.22227e6	−2.70943
$411$	−289634.	−0.0845756
$412$	−2.84729e6	−0.826397
$413$	0	0
$414$	−7.39304e6	−2.11993
$415$	−3.49026e6	−0.994804
$416$	2.14653e6	0.608139
$417$	−6.36875e6	−1.79355
$418$	−730196.	−0.204408
$419$	979119.	0.272458	0.136229	−	0.990677i	$-0.456502\pi$
$419$	979119.	0.272458	0.136229	+	0.990677i	$0.456502\pi$
$420$	0	0
$421$	−1.38633e6	−0.381208	−0.190604	−	0.981667i	$-0.561045\pi$
$421$	−1.38633e6	−0.381208	−0.190604	+	0.981667i	$0.561045\pi$
$422$	911480.	0.249153
$423$	356644.	0.0969135
$424$	8.18903e6	2.21217
$425$	1.40225e6	0.376577
$426$	−1.38549e7	−3.69896
$427$	0	0
$428$	−4.46070e6	−1.17705
$429$	1.99975e6	0.524606
$430$	−8.98881e6	−2.34440
$431$	−3.17560e6	−0.823441	−0.411720	−	0.911310i	$-0.635072\pi$
$431$	−3.17560e6	−0.823441	−0.411720	+	0.911310i	$0.635072\pi$
$432$	2.71043e6	0.698761
$433$	4.41385e6	1.13135	0.565676	−	0.824628i	$-0.308615\pi$
$433$	4.41385e6	1.13135	0.565676	+	0.824628i	$0.308615\pi$
$434$	0	0
$435$	−278673.	−0.0706109
$436$	1.57433e7	3.96625
$437$	−439742.	−0.110153
$438$	341414.	0.0850347
$439$	−4.16949e6	−1.03258	−0.516288	−	0.856415i	$-0.672687\pi$
$439$	−4.16949e6	−1.03258	−0.516288	+	0.856415i	$0.672687\pi$
$440$	−1.33171e7	−3.27928
$441$	0	0
$442$	−2.82461e6	−0.687706
$443$	−4.62749e6	−1.12031	−0.560153	−	0.828389i	$-0.689258\pi$
$443$	−4.62749e6	−1.12031	−0.560153	+	0.828389i	$0.689258\pi$
$444$	−2.02755e7	−4.88107
$445$	3.64804e6	0.873292
$446$	8.73472e6	2.07928
$447$	−1.28435e6	−0.304029
$448$	0	0
$449$	4.38061e6	1.02546	0.512730	−	0.858550i	$-0.328634\pi$
$449$	4.38061e6	1.02546	0.512730	+	0.858550i	$0.328634\pi$
$450$	−1.82232e6	−0.424221
$451$	1.04429e7	2.41757
$452$	−2.08622e7	−4.80301
$453$	5.26110e6	1.20457
$454$	−5.02424e6	−1.14401
$455$	0	0
$456$	−1.27684e6	−0.287558
$457$	−2.43273e6	−0.544884	−0.272442	−	0.962172i	$-0.587831\pi$
$457$	−2.43273e6	−0.544884	−0.272442	+	0.962172i	$0.587831\pi$
$458$	6.68910e6	1.49006
$459$	−1.58223e6	−0.350539
$460$	−1.34564e7	−2.96506
$461$	1.86839e6	0.409464	0.204732	−	0.978818i	$-0.434368\pi$
$461$	1.86839e6	0.409464	0.204732	+	0.978818i	$0.434368\pi$
$462$	0	0
$463$	3.66203e6	0.793906	0.396953	−	0.917839i	$-0.370068\pi$
$463$	3.66203e6	0.793906	0.396953	+	0.917839i	$0.370068\pi$
$464$	763535.	0.164639
$465$	1.08156e6	0.231964
$466$	−4.02412e6	−0.858433
$467$	460989.	0.0978135	0.0489068	−	0.998803i	$-0.484426\pi$
$467$	460989.	0.0978135	0.0489068	+	0.998803i	$0.484426\pi$
$468$	2.61448e6	0.551787
$469$	0	0
$470$	911400.	0.190311
$471$	2.96701e6	0.616264
$472$	−8.88638e6	−1.83599
$473$	1.01785e7	2.09186
$474$	1.66690e7	3.40772
$475$	−108392.	−0.0220427
$476$	0	0
$477$	3.21297e6	0.646562
$478$	−4.59847e6	−0.920541
$479$	4.25527e6	0.847400	0.423700	−	0.905803i	$-0.360731\pi$
$479$	4.25527e6	0.847400	0.423700	+	0.905803i	$0.360731\pi$
$480$	−1.25861e7	−2.49338
$481$	2.06636e6	0.407233
$482$	5.69886e6	1.11730
$483$	0	0
$484$	1.25456e7	2.43431
$485$	−2.24700e6	−0.433760
$486$	1.25348e7	2.40728
$487$	5.38051e6	1.02802	0.514009	−	0.857785i	$-0.328160\pi$
$487$	5.38051e6	1.02802	0.514009	+	0.857785i	$0.328160\pi$
$488$	2.01008e7	3.82088
$489$	−8.12852e6	−1.53723
$490$	0	0
$491$	−9.27857e6	−1.73691	−0.868455	−	0.495768i	$-0.834887\pi$
$491$	−9.27857e6	−1.73691	−0.868455	+	0.495768i	$0.834887\pi$
$492$	3.06393e7	5.70645
$493$	−445717.	−0.0825927
$494$	218339.	0.0402544
$495$	−5.22497e6	−0.958452
$496$	−2.96337e6	−0.540857
$497$	0	0
$498$	1.62805e7	2.94167
$499$	−4.18990e6	−0.753274	−0.376637	−	0.926361i	$-0.622920\pi$
$499$	−4.18990e6	−0.753274	−0.376637	+	0.926361i	$0.622920\pi$
$500$	−1.50323e7	−2.68906
$501$	−3.95667e6	−0.704264
$502$	4.69881e6	0.832201
$503$	−5.65368e6	−0.996348	−0.498174	−	0.867077i	$-0.665996\pi$
$503$	−5.65368e6	−0.996348	−0.498174	+	0.867077i	$0.665996\pi$
$504$	0	0
$505$	−8.66840e6	−1.51255
$506$	2.13934e7	3.71453
$507$	−597953.	−0.103311
$508$	1.05599e7	1.81552
$509$	−6.81804e6	−1.16645	−0.583224	−	0.812312i	$-0.698209\pi$
$509$	−6.81804e6	−1.16645	−0.583224	+	0.812312i	$0.698209\pi$
$510$	1.65620e7	2.81961
$511$	0	0
$512$	−8.76587e6	−1.47782
$513$	122304.	0.0205186
$514$	−8.68676e6	−1.45027
$515$	−1.70145e6	−0.282685
$516$	2.98637e7	4.93763
$517$	−1.03203e6	−0.169811
$518$	0	0
$519$	−1.61743e6	−0.263577
$520$	3.98199e6	0.645791
$521$	−6.09883e6	−0.984355	−0.492178	−	0.870495i	$-0.663799\pi$
$521$	−6.09883e6	−0.984355	−0.492178	+	0.870495i	$0.663799\pi$
$522$	579237.	0.0930422
$523$	−6.06138e6	−0.968986	−0.484493	−	0.874795i	$-0.660996\pi$
$523$	−6.06138e6	−0.968986	−0.484493	+	0.874795i	$0.660996\pi$
$524$	−2.81480e7	−4.47837
$525$	0	0
$526$	−1.65687e7	−2.61111
$527$	1.72988e6	0.271325
$528$	3.21267e7	5.01512
$529$	6.44729e6	1.00170
$530$	8.21070e6	1.26967
$531$	−3.48657e6	−0.536615
$532$	0	0
$533$	−3.12257e6	−0.476095
$534$	−1.70165e7	−2.58236
$535$	−2.66558e6	−0.402630
$536$	−1.27690e7	−1.91975
$537$	−9.54029e6	−1.42766
$538$	1.70590e7	2.54096
$539$	0	0
$540$	3.74257e6	0.552313
$541$	1.42169e6	0.208839	0.104420	−	0.994533i	$-0.466702\pi$
$541$	1.42169e6	0.208839	0.104420	+	0.994533i	$0.466702\pi$
$542$	1.71812e7	2.51221
$543$	4.91414e6	0.715234
$544$	−2.01306e7	−2.91648
$545$	9.40774e6	1.35673
$546$	0	0
$547$	−4.79167e6	−0.684728	−0.342364	−	0.939567i	$-0.611228\pi$
$547$	−4.79167e6	−0.684728	−0.342364	+	0.939567i	$0.611228\pi$
$548$	1.09576e6	0.155871
$549$	7.88655e6	1.11675
$550$	5.27327e6	0.743316
$551$	34453.3	0.00483451
$552$	3.74092e7	5.22553
$553$	0	0
$554$	1.49945e7	2.07567
$555$	−1.21160e7	−1.66966
$556$	2.40946e7	3.30547
$557$	−7.93011e6	−1.08303	−0.541516	−	0.840690i	$-0.682149\pi$
$557$	−7.93011e6	−1.08303	−0.541516	+	0.840690i	$0.682149\pi$
$558$	−2.24809e6	−0.305653
$559$	−3.04352e6	−0.411952
$560$	0	0
$561$	−1.87541e7	−2.51588
$562$	−2.00755e7	−2.68117
$563$	−2.89581e6	−0.385035	−0.192517	−	0.981294i	$-0.561665\pi$
$563$	−2.89581e6	−0.385035	−0.192517	+	0.981294i	$0.561665\pi$
$564$	−3.02796e6	−0.400822
$565$	−1.24666e7	−1.64296
$566$	1.09906e7	1.44205
$567$	0	0
$568$	3.12399e7	4.06293
$569$	−460757.	−0.0596611	−0.0298305	−	0.999555i	$-0.509497\pi$
$569$	−460757.	−0.0596611	−0.0298305	+	0.999555i	$0.509497\pi$
$570$	−1.28022e6	−0.165044
$571$	1.12080e7	1.43859	0.719297	−	0.694703i	$-0.244464\pi$
$571$	1.12080e7	1.43859	0.719297	+	0.694703i	$0.244464\pi$
$572$	−7.56559e6	−0.966835
$573$	4.29994e6	0.547111
$574$	0	0
$575$	3.17569e6	0.400561
$576$	9.19159e6	1.15434
$577$	2.59789e6	0.324849	0.162424	−	0.986721i	$-0.448069\pi$
$577$	2.59789e6	0.324849	0.162424	+	0.986721i	$0.448069\pi$
$578$	1.15168e7	1.43387
$579$	−379530.	−0.0470489
$580$	1.05429e6	0.130134
$581$	0	0
$582$	1.04813e7	1.28265
$583$	−9.29743e6	−1.13290
$584$	−769818.	−0.0934019
$585$	1.56234e6	0.188749
$586$	2.62983e7	3.16362
$587$	−1.34937e7	−1.61635	−0.808177	−	0.588939i	$-0.799546\pi$
$587$	−1.34937e7	−1.61635	−0.808177	+	0.588939i	$0.799546\pi$
$588$	0	0
$589$	−133718.	−0.0158818
$590$	−8.90990e6	−1.05376
$591$	−6.94891e6	−0.818367
$592$	3.31967e7	3.89306
$593$	−1.44345e7	−1.68564	−0.842821	−	0.538194i	$-0.819107\pi$
$593$	−1.44345e7	−1.68564	−0.842821	+	0.538194i	$0.819107\pi$
$594$	−5.95007e6	−0.691920
$595$	0	0
$596$	4.85904e6	0.560318
$597$	7.61867e6	0.874869
$598$	−6.39692e6	−0.731506
$599$	7.05761e6	0.803694	0.401847	−	0.915707i	$-0.368368\pi$
$599$	7.05761e6	0.803694	0.401847	+	0.915707i	$0.368368\pi$
$600$	9.22102e6	1.04568
$601$	−2.35971e6	−0.266485	−0.133242	−	0.991083i	$-0.542539\pi$
$601$	−2.35971e6	−0.266485	−0.133242	+	0.991083i	$0.542539\pi$
$602$	0	0
$603$	−5.00991e6	−0.561096
$604$	−1.99041e7	−2.21999
$605$	7.49684e6	0.832703
$606$	4.04342e7	4.47268
$607$	−4.27931e6	−0.471414	−0.235707	−	0.971824i	$-0.575741\pi$
$607$	−4.27931e6	−0.471414	−0.235707	+	0.971824i	$0.575741\pi$
$608$	1.55607e6	0.170714
$609$	0	0
$610$	2.01540e7	2.19299
$611$	308591.	0.0334410
$612$	−2.45192e7	−2.64623
$613$	−4.64215e6	−0.498963	−0.249481	−	0.968380i	$-0.580260\pi$
$613$	−4.64215e6	−0.498963	−0.249481	+	0.968380i	$0.580260\pi$
$614$	2.37022e7	2.53727
$615$	1.83091e7	1.95200
$616$	0	0
$617$	1.70525e6	0.180333	0.0901667	−	0.995927i	$-0.471260\pi$
$617$	1.70525e6	0.180333	0.0901667	+	0.995927i	$0.471260\pi$
$618$	7.93653e6	0.835910
$619$	8.83129e6	0.926398	0.463199	−	0.886254i	$-0.346702\pi$
$619$	8.83129e6	0.926398	0.463199	+	0.886254i	$0.346702\pi$
$620$	−4.09184e6	−0.427503
$621$	−3.58328e6	−0.372865
$622$	8.46905e6	0.877725
$623$	0	0
$624$	−9.60633e6	−0.987634
$625$	−6.21801e6	−0.636724
$626$	1.45873e6	0.148778
$627$	1.44967e6	0.147265
$628$	−1.12250e7	−1.13576
$629$	−1.93787e7	−1.95298
$630$	0	0
$631$	7.19286e6	0.719165	0.359582	−	0.933113i	$-0.382919\pi$
$631$	7.19286e6	0.719165	0.359582	+	0.933113i	$0.382919\pi$
$632$	−3.75851e7	−3.74303
$633$	−1.80957e6	−0.179501
$634$	3.11778e7	3.08050
$635$	6.31029e6	0.621034
$636$	−2.72785e7	−2.67410
$637$	0	0
$638$	−1.67615e6	−0.163028
$639$	1.22570e7	1.18749
$640$	4.25153e6	0.410294
$641$	−1.60215e7	−1.54013	−0.770066	−	0.637964i	$-0.779777\pi$
$641$	−1.60215e7	−1.54013	−0.770066	+	0.637964i	$0.779777\pi$
$642$	1.24337e7	1.19059
$643$	3.26167e6	0.311109	0.155554	−	0.987827i	$-0.450284\pi$
$643$	3.26167e6	0.311109	0.155554	+	0.987827i	$0.450284\pi$
$644$	0	0
$645$	1.78456e7	1.68901
$646$	−2.04763e6	−0.193050
$647$	−1.06996e6	−0.100486	−0.0502431	−	0.998737i	$-0.516000\pi$
$647$	−1.06996e6	−0.100486	−0.0502431	+	0.998737i	$0.516000\pi$
$648$	−3.40316e7	−3.18379
$649$	1.00892e7	0.940251
$650$	−1.57678e6	−0.146382
$651$	0	0
$652$	3.07523e7	2.83308
$653$	1.77899e7	1.63264	0.816319	−	0.577602i	$-0.196011\pi$
$653$	1.77899e7	1.63264	0.816319	+	0.577602i	$0.196011\pi$
$654$	−4.38829e7	−4.01191
$655$	−1.68204e7	−1.53191
$656$	−5.01651e7	−4.55137
$657$	−302038.	−0.0272991
$658$	0	0
$659$	4.31144e6	0.386731	0.193365	−	0.981127i	$-0.438060\pi$
$659$	4.31144e6	0.386731	0.193365	+	0.981127i	$0.438060\pi$
$660$	4.43607e7	3.96404
$661$	−7.41111e6	−0.659750	−0.329875	−	0.944025i	$-0.607007\pi$
$661$	−7.41111e6	−0.659750	−0.329875	+	0.944025i	$0.607007\pi$
$662$	−1.59046e7	−1.41052
$663$	5.60773e6	0.495454
$664$	−3.67092e7	−3.23113
$665$	0	0
$666$	2.51839e7	2.20007
$667$	−1.00942e6	−0.0878531
$668$	1.49691e7	1.29794
$669$	−1.73412e7	−1.49800
$670$	−1.28028e7	−1.10184
$671$	−2.28215e7	−1.95676
$672$	0	0
$673$	−1.80495e7	−1.53613	−0.768066	−	0.640370i	$-0.778781\pi$
$673$	−1.80495e7	−1.53613	−0.768066	+	0.640370i	$0.778781\pi$
$674$	−2.75204e7	−2.33349
$675$	−883245.	−0.0746142
$676$	2.26221e6	0.190400
$677$	1.54749e7	1.29764	0.648821	−	0.760941i	$-0.275262\pi$
$677$	1.54749e7	1.29764	0.648821	+	0.760941i	$0.275262\pi$
$678$	5.81511e7	4.85830
$679$	0	0
$680$	−3.73440e7	−3.09705
$681$	9.97469e6	0.824198
$682$	6.50535e6	0.535562
$683$	−554378.	−0.0454730	−0.0227365	−	0.999741i	$-0.507238\pi$
$683$	−554378.	−0.0454730	−0.0227365	+	0.999741i	$0.507238\pi$
$684$	1.89530e6	0.154895
$685$	654793.	0.0533185
$686$	0	0
$687$	−1.32800e7	−1.07351
$688$	−4.88951e7	−3.93817
$689$	2.78006e6	0.223103
$690$	3.75082e7	2.99919
$691$	2.88772e6	0.230070	0.115035	−	0.993361i	$-0.463302\pi$
$691$	2.88772e6	0.230070	0.115035	+	0.993361i	$0.463302\pi$
$692$	6.11917e6	0.485766
$693$	0	0
$694$	1.75273e7	1.38139
$695$	1.43982e7	1.13070
$696$	−2.93097e6	−0.229345
$697$	2.92841e7	2.28323
$698$	−9.24565e6	−0.718288
$699$	7.98914e6	0.618454
$700$	0	0
$701$	1.52188e7	1.16973	0.584866	−	0.811130i	$-0.301147\pi$
$701$	1.52188e7	1.16973	0.584866	+	0.811130i	$0.301147\pi$
$702$	1.77915e6	0.136261
$703$	1.49795e6	0.114317
$704$	−2.65979e7	−2.02263
$705$	−1.80942e6	−0.137109
$706$	5.34595e6	0.403658
$707$	0	0
$708$	2.96015e7	2.21937
$709$	−2.27767e6	−0.170167	−0.0850835	−	0.996374i	$-0.527116\pi$
$709$	−2.27767e6	−0.170167	−0.0850835	+	0.996374i	$0.527116\pi$
$710$	3.13226e7	2.33191
$711$	−1.47465e7	−1.09400
$712$	3.83686e7	2.83646
$713$	3.91768e6	0.288606
$714$	0	0
$715$	−4.52096e6	−0.330724
$716$	3.60934e7	2.63115
$717$	9.12940e6	0.663200
$718$	−1.85563e7	−1.34332
$719$	1.21691e7	0.877879	0.438939	−	0.898517i	$-0.355354\pi$
$719$	1.21691e7	0.877879	0.438939	+	0.898517i	$0.355354\pi$
$720$	2.50994e7	1.80440
$721$	0	0
$722$	−2.59533e7	−1.85289
$723$	−1.13140e7	−0.804955
$724$	−1.85915e7	−1.31816
$725$	−248812.	−0.0175803
$726$	−3.49694e7	−2.46234
$727$	−1.38530e7	−0.972095	−0.486047	−	0.873932i	$-0.661562\pi$
$727$	−1.38530e7	−0.972095	−0.486047	+	0.873932i	$0.661562\pi$
$728$	0	0
$729$	−8.27350e6	−0.576594
$730$	−771855.	−0.0536079
$731$	2.85428e7	1.97562
$732$	−6.69579e7	−4.61874
$733$	−3.28701e6	−0.225965	−0.112983	−	0.993597i	$-0.536040\pi$
$733$	−3.28701e6	−0.225965	−0.112983	+	0.993597i	$0.536040\pi$
$734$	−2.28996e7	−1.56888
$735$	0	0
$736$	−4.55899e7	−3.10223
$737$	1.44973e7	0.983147
$738$	−3.80565e7	−2.57210
$739$	−8.02971e6	−0.540865	−0.270433	−	0.962739i	$-0.587167\pi$
$739$	−8.02971e6	−0.540865	−0.270433	+	0.962739i	$0.587167\pi$
$740$	4.58381e7	3.07714
$741$	−433470.	−0.0290011
$742$	0	0
$743$	2.00914e7	1.33517	0.667587	−	0.744532i	$-0.267327\pi$
$743$	2.00914e7	1.33517	0.667587	+	0.744532i	$0.267327\pi$
$744$	1.13755e7	0.753419
$745$	2.90361e6	0.191667
$746$	5.19106e7	3.41515
$747$	−1.44028e7	−0.944380
$748$	7.09517e7	4.63670
$749$	0	0
$750$	4.19010e7	2.72001
$751$	−7.47195e6	−0.483431	−0.241715	−	0.970347i	$-0.577710\pi$
$751$	−7.47195e6	−0.483431	−0.241715	+	0.970347i	$0.577710\pi$
$752$	4.95761e6	0.319689
$753$	−9.32861e6	−0.599555
$754$	501192.	0.0321052
$755$	−1.18941e7	−0.759388
$756$	0	0
$757$	−2.42248e7	−1.53646	−0.768228	−	0.640176i	$-0.778861\pi$
$757$	−2.42248e7	−1.53646	−0.768228	+	0.640176i	$0.778861\pi$
$758$	−2.40703e7	−1.52163
$759$	−4.24726e7	−2.67611
$760$	2.88664e6	0.181284
$761$	−1.54929e7	−0.969776	−0.484888	−	0.874576i	$-0.661140\pi$
$761$	−1.54929e7	−0.969776	−0.484888	+	0.874576i	$0.661140\pi$
$762$	−2.94347e7	−1.83642
$763$	0	0
$764$	−1.62678e7	−1.00831
$765$	−1.46519e7	−0.905192
$766$	−3.23485e7	−1.99197
$767$	−3.01680e6	−0.185165
$768$	1.16964e7	0.715567
$769$	2.63582e7	1.60731	0.803656	−	0.595094i	$-0.202885\pi$
$769$	2.63582e7	1.60731	0.803656	+	0.595094i	$0.202885\pi$
$770$	0	0
$771$	1.72459e7	1.04484
$772$	1.43586e6	0.0867099
$773$	−5.63865e6	−0.339411	−0.169706	−	0.985495i	$-0.554282\pi$
$773$	−5.63865e6	−0.339411	−0.169706	+	0.985495i	$0.554282\pi$
$774$	−3.70931e7	−2.22557
$775$	965672.	0.0577531
$776$	−2.36331e7	−1.40885
$777$	0	0
$778$	5.34691e7	3.16704
$779$	−2.26362e6	−0.133647
$780$	−1.32644e7	−0.780643
$781$	−3.54683e7	−2.08072
$782$	5.99916e7	3.50812
$783$	280746.	0.0163647
$784$	0	0
$785$	−6.70770e6	−0.388508
$786$	7.84598e7	4.52992
$787$	−2.56511e7	−1.47628	−0.738141	−	0.674647i	$-0.764296\pi$
$787$	−2.56511e7	−1.47628	−0.738141	+	0.674647i	$0.764296\pi$
$788$	2.62895e7	1.50823
$789$	3.28941e7	1.88116
$790$	−3.76846e7	−2.14831
$791$	0	0
$792$	−5.49541e7	−3.11306
$793$	6.82393e6	0.385347
$794$	7.47273e6	0.420657
$795$	−1.63008e7	−0.914728
$796$	−2.88234e7	−1.61236
$797$	1.12754e7	0.628761	0.314380	−	0.949297i	$-0.398203\pi$
$797$	1.12754e7	0.628761	0.314380	+	0.949297i	$0.398203\pi$
$798$	0	0
$799$	−2.89403e6	−0.160375
$800$	−1.12375e7	−0.620790
$801$	1.50539e7	0.829027
$802$	1.75517e7	0.963572
$803$	874014.	0.0478332
$804$	4.25349e7	2.32063
$805$	0	0
$806$	−1.94519e6	−0.105469
$807$	−3.38675e7	−1.83062
$808$	−9.11708e7	−4.91278
$809$	1.41748e7	0.761458	0.380729	−	0.924687i	$-0.375673\pi$
$809$	1.41748e7	0.761458	0.380729	+	0.924687i	$0.375673\pi$
$810$	−3.41217e7	−1.82733
$811$	1.08255e7	0.577959	0.288979	−	0.957335i	$-0.406684\pi$
$811$	1.08255e7	0.577959	0.288979	+	0.957335i	$0.406684\pi$
$812$	0	0
$813$	−3.41101e7	−1.80991
$814$	−7.28751e7	−3.85495
$815$	1.83766e7	0.969108
$816$	9.00902e7	4.73644
$817$	−2.20632e6	−0.115641
$818$	3.02184e7	1.57902
$819$	0	0
$820$	−6.92681e7	−3.59748
$821$	1.07177e7	0.554935	0.277468	−	0.960735i	$-0.410505\pi$
$821$	1.07177e7	0.554935	0.277468	+	0.960735i	$0.410505\pi$
$822$	−3.05432e6	−0.157665
$823$	2.21626e7	1.14057	0.570283	−	0.821448i	$-0.306833\pi$
$823$	2.21626e7	1.14057	0.570283	+	0.821448i	$0.306833\pi$
$824$	−1.78952e7	−0.918162
$825$	−1.04691e7	−0.535519
$826$	0	0
$827$	1.68800e7	0.858240	0.429120	−	0.903248i	$-0.358824\pi$
$827$	1.68800e7	0.858240	0.429120	+	0.903248i	$0.358824\pi$
$828$	−5.55288e7	−2.81477
$829$	−2.51198e7	−1.26949	−0.634747	−	0.772720i	$-0.718896\pi$
$829$	−2.51198e7	−1.26949	−0.634747	+	0.772720i	$0.718896\pi$
$830$	−3.68063e7	−1.85450
$831$	−2.97688e7	−1.49540
$832$	7.95313e6	0.398318
$833$	0	0
$834$	−6.71613e7	−3.34352
$835$	8.94508e6	0.443985
$836$	−5.48447e6	−0.271406
$837$	−1.08961e6	−0.0537598
$838$	1.03252e7	0.507914
$839$	−3.11719e7	−1.52883	−0.764414	−	0.644726i	$-0.776971\pi$
$839$	−3.11719e7	−1.52883	−0.764414	+	0.644726i	$0.776971\pi$
$840$	0	0
$841$	−2.04321e7	−0.996144
$842$	−1.46195e7	−0.710644
$843$	3.98561e7	1.93164
$844$	6.84609e6	0.330816
$845$	1.35183e6	0.0651298
$846$	3.76097e6	0.180665
$847$	0	0
$848$	4.46626e7	2.13282
$849$	−2.18199e7	−1.03892
$850$	1.47874e7	0.702011
$851$	−4.38872e7	−2.07737
$852$	−1.04064e8	−4.91134
$853$	2.01270e7	0.947121	0.473560	−	0.880761i	$-0.342969\pi$
$853$	2.01270e7	0.947121	0.473560	+	0.880761i	$0.342969\pi$
$854$	0	0
$855$	1.13257e6	0.0529848
$856$	−2.80355e7	−1.30775
$857$	−1.08390e7	−0.504126	−0.252063	−	0.967711i	$-0.581109\pi$
$857$	−1.08390e7	−0.504126	−0.252063	+	0.967711i	$0.581109\pi$
$858$	2.10883e7	0.977965
$859$	−9.56603e6	−0.442332	−0.221166	−	0.975236i	$-0.570986\pi$
$859$	−9.56603e6	−0.442332	−0.221166	+	0.975236i	$0.570986\pi$
$860$	−6.75146e7	−3.11280
$861$	0	0
$862$	−3.34881e7	−1.53505
$863$	−8.82553e6	−0.403380	−0.201690	−	0.979449i	$-0.564643\pi$
$863$	−8.82553e6	−0.403380	−0.201690	+	0.979449i	$0.564643\pi$
$864$	1.26798e7	0.577866
$865$	3.65663e6	0.166165
$866$	4.65460e7	2.10905
$867$	−2.28644e7	−1.03303
$868$	0	0
$869$	4.26724e7	1.91689
$870$	−2.93873e6	−0.131632
$871$	−4.33489e6	−0.193612
$872$	9.89468e7	4.40667
$873$	−9.27245e6	−0.411774
$874$	−4.63727e6	−0.205345
$875$	0	0
$876$	2.56435e6	0.112906
$877$	2.70383e7	1.18708	0.593541	−	0.804804i	$-0.297729\pi$
$877$	2.70383e7	1.18708	0.593541	+	0.804804i	$0.297729\pi$
$878$	−4.39692e7	−1.92492
$879$	−5.22104e7	−2.27921
$880$	−7.26308e7	−3.16165
$881$	2.91334e7	1.26459	0.632297	−	0.774726i	$-0.282112\pi$
$881$	2.91334e7	1.26459	0.632297	+	0.774726i	$0.282112\pi$
$882$	0	0
$883$	−2.14179e7	−0.924431	−0.462216	−	0.886768i	$-0.652945\pi$
$883$	−2.14179e7	−0.924431	−0.462216	+	0.886768i	$0.652945\pi$
$884$	−2.12155e7	−0.913110
$885$	1.76890e7	0.759179
$886$	−4.87990e7	−2.08846
$887$	−1.11025e6	−0.0473819	−0.0236910	−	0.999719i	$-0.507542\pi$
$887$	−1.11025e6	−0.0473819	−0.0236910	+	0.999719i	$0.507542\pi$
$888$	−1.27432e8	−5.42307
$889$	0	0
$890$	3.84702e7	1.62798
$891$	3.86379e7	1.63049
$892$	6.56061e7	2.76078
$893$	223705.	0.00938742
$894$	−1.35441e7	−0.566768
$895$	2.15683e7	0.900033
$896$	0	0
$897$	1.26999e7	0.527010
$898$	4.61955e7	1.91165
$899$	−306946.	−0.0126667
$900$	−1.36873e7	−0.563265
$901$	−2.60720e7	−1.06995
$902$	1.10125e8	4.50681
$903$	0	0
$904$	−1.31119e8	−5.33634
$905$	−1.11097e7	−0.450901
$906$	5.54806e7	2.24554
$907$	−3.19985e7	−1.29155	−0.645776	−	0.763527i	$-0.723466\pi$
$907$	−3.19985e7	−1.29155	−0.645776	+	0.763527i	$0.723466\pi$
$908$	−3.77368e7	−1.51898
$909$	−3.57709e7	−1.43589
$910$	0	0
$911$	−2.62475e7	−1.04783	−0.523917	−	0.851769i	$-0.675530\pi$
$911$	−2.62475e7	−1.04783	−0.523917	+	0.851769i	$0.675530\pi$
$912$	−6.96385e6	−0.277244
$913$	4.16778e7	1.65473
$914$	−2.56542e7	−1.01577
$915$	−4.00120e7	−1.57993
$916$	5.02415e7	1.97845
$917$	0	0
$918$	−1.66853e7	−0.653471
$919$	9.77282e6	0.381708	0.190854	−	0.981618i	$-0.438874\pi$
$919$	9.77282e6	0.381708	0.190854	+	0.981618i	$0.438874\pi$
$920$	−8.45732e7	−3.29430
$921$	−4.70562e7	−1.82796
$922$	1.97030e7	0.763319
$923$	1.06055e7	0.409758
$924$	0	0
$925$	−1.08178e7	−0.415704
$926$	3.86177e7	1.47999
$927$	−7.02120e6	−0.268356
$928$	3.57192e6	0.136155
$929$	−4.64936e7	−1.76748	−0.883739	−	0.467980i	$-0.844982\pi$
$929$	−4.64936e7	−1.76748	−0.883739	+	0.467980i	$0.844982\pi$
$930$	1.14056e7	0.432424
$931$	0	0
$932$	−3.02250e7	−1.13979
$933$	−1.68137e7	−0.632353
$934$	4.86134e6	0.182343
$935$	4.23986e7	1.58607
$936$	1.64320e7	0.613058
$937$	−1.70196e6	−0.0633287	−0.0316643	−	0.999499i	$-0.510081\pi$
$937$	−1.70196e6	−0.0633287	−0.0316643	+	0.999499i	$0.510081\pi$
$938$	0	0
$939$	−2.89604e6	−0.107187
$940$	6.84549e6	0.252688
$941$	8.19489e6	0.301696	0.150848	−	0.988557i	$-0.451800\pi$
$941$	8.19489e6	0.301696	0.150848	+	0.988557i	$0.451800\pi$
$942$	3.12884e7	1.14883
$943$	6.63199e7	2.42865
$944$	−4.84659e7	−1.77013
$945$	0	0
$946$	1.07337e8	3.89962
$947$	1.60008e7	0.579785	0.289892	−	0.957059i	$-0.406381\pi$
$947$	1.60008e7	0.579785	0.289892	+	0.957059i	$0.406381\pi$
$948$	1.25200e8	4.52464
$949$	−261342.	−0.00941985
$950$	−1.14304e6	−0.0410917
$951$	−6.18976e7	−2.21933
$952$	0	0
$953$	2.39151e7	0.852982	0.426491	−	0.904492i	$-0.359750\pi$
$953$	2.39151e7	0.852982	0.426491	+	0.904492i	$0.359750\pi$
$954$	3.38822e7	1.20531
$955$	−9.72113e6	−0.344912
$956$	−3.45389e7	−1.22226
$957$	3.32768e6	0.117453
$958$	4.48737e7	1.57971
$959$	0	0
$960$	−4.66331e7	−1.63311
$961$	−2.74379e7	−0.958389
$962$	2.17906e7	0.759158
$963$	−1.09997e7	−0.382222
$964$	4.28039e7	1.48351
$965$	858026.	0.0296608
$966$	0	0
$967$	2.74831e7	0.945147	0.472573	−	0.881291i	$-0.343325\pi$
$967$	2.74831e7	0.945147	0.472573	+	0.881291i	$0.343325\pi$
$968$	7.88488e7	2.70462
$969$	4.06518e6	0.139082
$970$	−2.36956e7	−0.808610
$971$	2.50885e7	0.853940	0.426970	−	0.904266i	$-0.359581\pi$
$971$	2.50885e7	0.853940	0.426970	+	0.904266i	$0.359581\pi$
$972$	9.41485e7	3.19630
$973$	0	0
$974$	5.67398e7	1.91642
$975$	3.13040e6	0.105460
$976$	1.09629e8	3.68383
$977$	3.28322e7	1.10043	0.550217	−	0.835022i	$-0.314545\pi$
$977$	3.28322e7	1.10043	0.550217	+	0.835022i	$0.314545\pi$
$978$	−8.57189e7	−2.86569
$979$	−4.35619e7	−1.45261
$980$	0	0
$981$	3.88218e7	1.28796
$982$	−9.78466e7	−3.23793
$983$	−2.97714e7	−0.982687	−0.491344	−	0.870966i	$-0.663494\pi$
$983$	−2.97714e7	−0.982687	−0.491344	+	0.870966i	$0.663494\pi$
$984$	1.92568e8	6.34010
$985$	1.57098e7	0.515918
$986$	−4.70028e6	−0.153968
$987$	0	0
$988$	1.63993e6	0.0534482
$989$	6.46410e7	2.10144
$990$	−5.50996e7	−1.78674
$991$	−4.94780e6	−0.160040	−0.0800199	−	0.996793i	$-0.525498\pi$
$991$	−4.94780e6	−0.160040	−0.0800199	+	0.996793i	$0.525498\pi$
$992$	−1.38631e7	−0.447281
$993$	3.15757e7	1.01620
$994$	0	0
$995$	−1.72240e7	−0.551538
$996$	1.22282e8	3.90584
$997$	−3.06523e7	−0.976620	−0.488310	−	0.872670i	$-0.662386\pi$
$997$	−3.06523e7	−0.976620	−0.488310	+	0.872670i	$0.662386\pi$
$998$	−4.41844e7	−1.40424
$999$	1.22062e7	0.386960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.6.a.e.1.8		8
7.6	odd	2		91.6.a.c.1.8	✓	8
21.20	even	2		819.6.a.j.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.6.a.c.1.8	✓	8	7.6	odd	2
637.6.a.e.1.8		8	1.1	even	1	trivial
819.6.a.j.1.1		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+10.5454 q^{2} -20.9360 q^{3} +79.2064 q^{4} +47.3313 q^{5} -220.779 q^{6} +497.812 q^{8} +195.317 q^{9} +499.129 q^{10} -565.192 q^{11} -1658.27 q^{12} +169.000 q^{13} -990.929 q^{15} +2715.04 q^{16} -1584.92 q^{17} +2059.70 q^{18} +122.512 q^{19} +3748.94 q^{20} -5960.20 q^{22} -3589.38 q^{23} -10422.2 q^{24} -884.748 q^{25} +1782.18 q^{26} +998.301 q^{27} +281.224 q^{29} -10449.8 q^{30} -1091.47 q^{31} +12701.3 q^{32} +11832.9 q^{33} -16713.7 q^{34} +15470.3 q^{36} +12227.0 q^{37} +1291.94 q^{38} -3538.19 q^{39} +23562.1 q^{40} -18476.7 q^{41} -18009.0 q^{43} -44766.8 q^{44} +9244.59 q^{45} -37851.6 q^{46} +1825.98 q^{47} -56842.2 q^{48} -9330.06 q^{50} +33181.9 q^{51} +13385.9 q^{52} +16450.0 q^{53} +10527.5 q^{54} -26751.3 q^{55} -2564.91 q^{57} +2965.63 q^{58} -17850.9 q^{59} -78487.8 q^{60} +40378.3 q^{61} -11510.0 q^{62} +47060.0 q^{64} +7998.99 q^{65} +124783. q^{66} -25650.2 q^{67} -125536. q^{68} +75147.3 q^{69} +62754.5 q^{71} +97230.9 q^{72} -1546.40 q^{73} +128939. q^{74} +18523.1 q^{75} +9703.73 q^{76} -37311.7 q^{78} -75500.7 q^{79} +128507. q^{80} -68362.4 q^{81} -194845. q^{82} -73741.0 q^{83} -75016.2 q^{85} -189913. q^{86} -5887.71 q^{87} -281359. q^{88} +77074.6 q^{89} +97488.3 q^{90} -284302. q^{92} +22850.9 q^{93} +19255.8 q^{94} +5798.66 q^{95} -265916. q^{96} -47473.9 q^{97} -110391. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 28 q^{3} + 245 q^{4} - 219 q^{5} - 435 q^{6} - 57 q^{8} + 930 q^{9} + 948 q^{10} + 184 q^{11} - 463 q^{12} + 1352 q^{13} - 256 q^{15} + 4953 q^{16} - 2278 q^{17} - 5308 q^{18} - 4959 q^{19}+ \cdots + 90754 q^{99}+O(q^{100}) \) 8 * q - q^2 - 28 * q^3 + 245 * q^4 - 219 * q^5 - 435 * q^6 - 57 * q^8 + 930 * q^9 + 948 * q^10 + 184 * q^11 - 463 * q^12 + 1352 * q^13 - 256 * q^15 + 4953 * q^16 - 2278 * q^17 - 5308 * q^18 - 4959 * q^19 - 6684 * q^20 - 2009 * q^22 + 1889 * q^23 - 26021 * q^24 + 4505 * q^25 - 169 * q^26 - 9016 * q^27 + 15265 * q^29 + 24204 * q^30 - 6805 * q^31 + 1335 * q^32 + 12892 * q^33 - 5828 * q^34 + 58838 * q^36 + 5534 * q^37 - 506 * q^38 - 4732 * q^39 + 56256 * q^40 - 31176 * q^41 - 391 * q^43 + 14047 * q^44 - 29403 * q^45 - 30027 * q^46 - 1539 * q^47 + 106629 * q^48 - 24367 * q^50 - 71892 * q^51 + 41405 * q^52 + 19553 * q^53 + 8155 * q^54 - 69414 * q^55 + 54432 * q^57 - 148020 * q^58 - 90596 * q^59 - 299448 * q^60 + 58218 * q^61 - 7697 * q^62 + 61681 * q^64 - 37011 * q^65 + 145411 * q^66 - 89884 * q^67 - 120612 * q^68 - 24278 * q^69 + 2308 * q^71 - 317742 * q^72 + 69187 * q^73 + 52027 * q^74 + 154856 * q^75 + 47258 * q^76 - 73515 * q^78 - 167799 * q^79 - 173400 * q^80 + 163984 * q^81 + 49553 * q^82 - 101449 * q^83 + 24684 * q^85 - 357720 * q^86 - 61908 * q^87 - 270819 * q^88 - 51833 * q^89 + 567124 * q^90 - 542963 * q^92 + 132644 * q^93 + 122399 * q^94 + 188103 * q^95 - 871725 * q^96 - 295025 * q^97 + 90754 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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