LMFDB - Embedded newform 207.8.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,8,Mod(1,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	207.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:	$64.6637002752$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 1070 x^{10} + 4076 x^{9} + 403334 x^{8} - 1518684 x^{7} - 64710184 x^{6} + \cdots + 90709421512 $ x^12 - 4x^11 - 1070x^10 + 4076x^9 + 403334x^8 - 1518684x^7 - 64710184x^6 + 248484524x^5 + 4244585785x^4 - 14689737568x^3 - 89785869106x^2 + 190549532712*x + 90709421512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{7} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$10.7226$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.7226 q^{2} +9.42047 q^{4} +342.584 q^{5} +1083.50 q^{7} -1390.07 q^{8} +O(q^{10})$	\(q+11.7226 q^{2} +9.42047 q^{4} +342.584 q^{5} +1083.50 q^{7} -1390.07 q^{8} +4015.99 q^{10} +4333.10 q^{11} -8654.77 q^{13} +12701.5 q^{14} -17501.1 q^{16} +20167.5 q^{17} +49181.6 q^{19} +3227.30 q^{20} +50795.4 q^{22} -12167.0 q^{23} +39238.5 q^{25} -101457. q^{26} +10207.1 q^{28} -167377. q^{29} +265642. q^{31} -27230.5 q^{32} +236417. q^{34} +371190. q^{35} -68962.3 q^{37} +576539. q^{38} -476214. q^{40} -375814. q^{41} +46893.9 q^{43} +40819.8 q^{44} -142629. q^{46} -494488. q^{47} +350433. q^{49} +459979. q^{50} -81532.0 q^{52} +961208. q^{53} +1.48445e6 q^{55} -1.50614e6 q^{56} -1.96210e6 q^{58} +2.04595e6 q^{59} +2.16099e6 q^{61} +3.11402e6 q^{62} +1.92092e6 q^{64} -2.96498e6 q^{65} +3.48408e6 q^{67} +189988. q^{68} +4.35133e6 q^{70} +5.05672e6 q^{71} -1.70553e6 q^{73} -808421. q^{74} +463314. q^{76} +4.69492e6 q^{77} +3.49821e6 q^{79} -5.99558e6 q^{80} -4.40553e6 q^{82} +4.22182e6 q^{83} +6.90907e6 q^{85} +549721. q^{86} -6.02330e6 q^{88} +1.23622e6 q^{89} -9.37746e6 q^{91} -114619. q^{92} -5.79670e6 q^{94} +1.68488e7 q^{95} -3.28306e6 q^{97} +4.10800e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8}+O(q^{10}) $ 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8} + 10270 q^{10} - 460 q^{11} - 21060 q^{13} + 4268 q^{14} + 56676 q^{16} + 73124 q^{17} + 8508 q^{19} + 170538 q^{20} + 124754 q^{22} - 146004 q^{23} + 194064 q^{25} + 206080 q^{26} - 390416 q^{28} + 268640 q^{29} - 191880 q^{31} + 1180172 q^{32} - 221436 q^{34} - 487244 q^{35} + 650332 q^{37} + 1432950 q^{38} + 1775722 q^{40} + 980088 q^{41} - 861276 q^{43} + 800666 q^{44} - 194672 q^{46} + 403868 q^{47} + 1699160 q^{49} + 2919092 q^{50} - 2369520 q^{52} - 201948 q^{53} - 1553512 q^{55} - 4848116 q^{56} + 3720672 q^{58} + 1302676 q^{59} + 2141364 q^{61} + 2160944 q^{62} + 9702136 q^{64} + 9099536 q^{65} - 6159260 q^{67} + 18442208 q^{68} - 10891632 q^{70} + 12584184 q^{71} + 7435872 q^{73} + 22491442 q^{74} + 5721386 q^{76} + 16450568 q^{77} + 3658028 q^{79} + 49905778 q^{80} - 5516316 q^{82} + 26137900 q^{83} + 5169556 q^{85} + 30678550 q^{86} + 14753046 q^{88} + 27235908 q^{89} - 7657216 q^{91} - 7786880 q^{92} - 23519352 q^{94} + 63623628 q^{95} + 22454720 q^{97} + 94951532 q^{98}+O(q^{100}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8 + 10270 * q^10 - 460 * q^11 - 21060 * q^13 + 4268 * q^14 + 56676 * q^16 + 73124 * q^17 + 8508 * q^19 + 170538 * q^20 + 124754 * q^22 - 146004 * q^23 + 194064 * q^25 + 206080 * q^26 - 390416 * q^28 + 268640 * q^29 - 191880 * q^31 + 1180172 * q^32 - 221436 * q^34 - 487244 * q^35 + 650332 * q^37 + 1432950 * q^38 + 1775722 * q^40 + 980088 * q^41 - 861276 * q^43 + 800666 * q^44 - 194672 * q^46 + 403868 * q^47 + 1699160 * q^49 + 2919092 * q^50 - 2369520 * q^52 - 201948 * q^53 - 1553512 * q^55 - 4848116 * q^56 + 3720672 * q^58 + 1302676 * q^59 + 2141364 * q^61 + 2160944 * q^62 + 9702136 * q^64 + 9099536 * q^65 - 6159260 * q^67 + 18442208 * q^68 - 10891632 * q^70 + 12584184 * q^71 + 7435872 * q^73 + 22491442 * q^74 + 5721386 * q^76 + 16450568 * q^77 + 3658028 * q^79 + 49905778 * q^80 - 5516316 * q^82 + 26137900 * q^83 + 5169556 * q^85 + 30678550 * q^86 + 14753046 * q^88 + 27235908 * q^89 - 7657216 * q^91 - 7786880 * q^92 - 23519352 * q^94 + 63623628 * q^95 + 22454720 * q^97 + 94951532 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	11.7226	1.03615	0.518073	−	0.855337i	$-0.326650\pi$
$2$	11.7226	1.03615	0.518073	+	0.855337i	$0.326650\pi$
$3$	0	0
$3$	0	0
$4$	9.42047	0.0735974
$5$	342.584	1.22566	0.612832	−	0.790213i	$-0.290030\pi$
$5$	342.584	1.22566	0.612832	+	0.790213i	$0.290030\pi$
$6$	0	0
$7$	1083.50	1.19395	0.596975	−	0.802259i	$-0.296369\pi$
$7$	1083.50	1.19395	0.596975	+	0.802259i	$0.296369\pi$
$8$	−1390.07	−0.959888
$9$	0	0
$10$	4015.99	1.26997
$11$	4333.10	0.981577	0.490789	−	0.871279i	$-0.336709\pi$
$11$	4333.10	0.981577	0.490789	+	0.871279i	$0.336709\pi$
$12$	0	0
$13$	−8654.77	−1.09258	−0.546291	−	0.837596i	$-0.683961\pi$
$13$	−8654.77	−1.09258	−0.546291	+	0.837596i	$0.683961\pi$
$14$	12701.5	1.23711
$15$	0	0
$16$	−17501.1	−1.06818
$17$	20167.5	0.995593	0.497797	−	0.867294i	$-0.334143\pi$
$17$	20167.5	0.995593	0.497797	+	0.867294i	$0.334143\pi$
$18$	0	0
$19$	49181.6	1.64500	0.822499	−	0.568767i	$-0.192579\pi$
$19$	49181.6	1.64500	0.822499	+	0.568767i	$0.192579\pi$
$20$	3227.30	0.0902057
$21$	0	0
$22$	50795.4	1.01706
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	39238.5	0.502252
$26$	−101457.	−1.13207
$27$	0	0
$28$	10207.1	0.0878717
$29$	−167377.	−1.27439	−0.637196	−	0.770702i	$-0.719906\pi$
$29$	−167377.	−1.27439	−0.637196	+	0.770702i	$0.719906\pi$
$30$	0	0
$31$	265642.	1.60151	0.800756	−	0.598991i	$-0.204431\pi$
$31$	265642.	1.60151	0.800756	+	0.598991i	$0.204431\pi$
$32$	−27230.5	−0.146903
$33$	0	0
$34$	236417.	1.03158
$35$	371190.	1.46338
$36$	0	0
$37$	−68962.3	−0.223824	−0.111912	−	0.993718i	$-0.535697\pi$
$37$	−68962.3	−0.223824	−0.111912	+	0.993718i	$0.535697\pi$
$38$	576539.	1.70446
$39$	0	0
$40$	−476214.	−1.17650
$41$	−375814.	−0.851588	−0.425794	−	0.904820i	$-0.640005\pi$
$41$	−375814.	−0.851588	−0.425794	+	0.904820i	$0.640005\pi$
$42$	0	0
$43$	46893.9	0.0899450	0.0449725	−	0.998988i	$-0.485680\pi$
$43$	46893.9	0.0899450	0.0449725	+	0.998988i	$0.485680\pi$
$44$	40819.8	0.0722415
$45$	0	0
$46$	−142629.	−0.216051
$47$	−494488.	−0.694725	−0.347362	−	0.937731i	$-0.612923\pi$
$47$	−494488.	−0.694725	−0.347362	+	0.937731i	$0.612923\pi$
$48$	0	0
$49$	350433.	0.425519
$50$	459979.	0.520407
$51$	0	0
$52$	−81532.0	−0.0804111
$53$	961208.	0.886854	0.443427	−	0.896311i	$-0.353763\pi$
$53$	961208.	0.886854	0.443427	+	0.896311i	$0.353763\pi$
$54$	0	0
$55$	1.48445e6	1.20308
$56$	−1.50614e6	−1.14606
$57$	0	0
$58$	−1.96210e6	−1.32045
$59$	2.04595e6	1.29692	0.648460	−	0.761249i	$-0.275413\pi$
$59$	2.04595e6	1.29692	0.648460	+	0.761249i	$0.275413\pi$
$60$	0	0
$61$	2.16099e6	1.21898	0.609491	−	0.792793i	$-0.291374\pi$
$61$	2.16099e6	1.21898	0.609491	+	0.792793i	$0.291374\pi$
$62$	3.11402e6	1.65940
$63$	0	0
$64$	1.92092e6	0.915968
$65$	−2.96498e6	−1.33914
$66$	0	0
$67$	3.48408e6	1.41523	0.707614	−	0.706600i	$-0.249772\pi$
$67$	3.48408e6	1.41523	0.707614	+	0.706600i	$0.249772\pi$
$68$	189988.	0.0732731
$69$	0	0
$70$	4.35133e6	1.51628
$71$	5.05672e6	1.67674	0.838369	−	0.545104i	$-0.183510\pi$
$71$	5.05672e6	1.67674	0.838369	+	0.545104i	$0.183510\pi$
$72$	0	0
$73$	−1.70553e6	−0.513132	−0.256566	−	0.966527i	$-0.582591\pi$
$73$	−1.70553e6	−0.513132	−0.256566	+	0.966527i	$0.582591\pi$
$74$	−808421.	−0.231914
$75$	0	0
$76$	463314.	0.121068
$77$	4.69492e6	1.17196
$78$	0	0
$79$	3.49821e6	0.798272	0.399136	−	0.916892i	$-0.369310\pi$
$79$	3.49821e6	0.798272	0.399136	+	0.916892i	$0.369310\pi$
$80$	−5.99558e6	−1.30923
$81$	0	0
$82$	−4.40553e6	−0.882369
$83$	4.22182e6	0.810451	0.405226	−	0.914217i	$-0.367193\pi$
$83$	4.22182e6	0.810451	0.405226	+	0.914217i	$0.367193\pi$
$84$	0	0
$85$	6.90907e6	1.22026
$86$	549721.	0.0931961
$87$	0	0
$88$	−6.02330e6	−0.942204
$89$	1.23622e6	0.185879	0.0929393	−	0.995672i	$-0.470374\pi$
$89$	1.23622e6	0.185879	0.0929393	+	0.995672i	$0.470374\pi$
$90$	0	0
$91$	−9.37746e6	−1.30449
$92$	−114619.	−0.0153461
$93$	0	0
$94$	−5.79670e6	−0.719836
$95$	1.68488e7	2.01621
$96$	0	0
$97$	−3.28306e6	−0.365239	−0.182620	−	0.983184i	$-0.558458\pi$
$97$	−3.28306e6	−0.365239	−0.182620	+	0.983184i	$0.558458\pi$
$98$	4.10800e6	0.440899
$99$	0	0
$100$	369645.	0.0369645
$101$	−6.23084e6	−0.601758	−0.300879	−	0.953662i	$-0.597280\pi$
$101$	−6.23084e6	−0.601758	−0.300879	+	0.953662i	$0.597280\pi$
$102$	0	0
$103$	−1.40341e7	−1.26547	−0.632737	−	0.774367i	$-0.718069\pi$
$103$	−1.40341e7	−1.26547	−0.632737	+	0.774367i	$0.718069\pi$
$104$	1.20307e7	1.04876
$105$	0	0
$106$	1.12679e7	0.918910
$107$	1.70306e6	0.134396	0.0671979	−	0.997740i	$-0.478594\pi$
$107$	1.70306e6	0.134396	0.0671979	+	0.997740i	$0.478594\pi$
$108$	0	0
$109$	−1.53206e7	−1.13314	−0.566568	−	0.824015i	$-0.691729\pi$
$109$	−1.53206e7	−1.13314	−0.566568	+	0.824015i	$0.691729\pi$
$110$	1.74017e7	1.24657
$111$	0	0
$112$	−1.89624e7	−1.27536
$113$	1.02346e7	0.667265	0.333633	−	0.942703i	$-0.391726\pi$
$113$	1.02346e7	0.667265	0.333633	+	0.942703i	$0.391726\pi$
$114$	0	0
$115$	−4.16821e6	−0.255569
$116$	−1.57677e6	−0.0937919
$117$	0	0
$118$	2.39840e7	1.34380
$119$	2.18516e7	1.18869
$120$	0	0
$121$	−711400.	−0.0365061
$122$	2.53325e7	1.26304
$123$	0	0
$124$	2.50247e6	0.117867
$125$	−1.33219e7	−0.610071
$126$	0	0
$127$	−4.02086e7	−1.74183	−0.870916	−	0.491432i	$-0.836474\pi$
$127$	−4.02086e7	−1.74183	−0.870916	+	0.491432i	$0.836474\pi$
$128$	2.60038e7	1.09598
$129$	0	0
$130$	−3.47574e7	−1.38754
$131$	−3.08544e7	−1.19913	−0.599566	−	0.800325i	$-0.704660\pi$
$131$	−3.08544e7	−1.19913	−0.599566	+	0.800325i	$0.704660\pi$
$132$	0	0
$133$	5.32884e7	1.96405
$134$	4.08426e7	1.46638
$135$	0	0
$136$	−2.80342e7	−0.955658
$137$	−3.13769e7	−1.04253	−0.521264	−	0.853395i	$-0.674539\pi$
$137$	−3.13769e7	−1.04253	−0.521264	+	0.853395i	$0.674539\pi$
$138$	0	0
$139$	2.82153e7	0.891112	0.445556	−	0.895254i	$-0.353006\pi$
$139$	2.82153e7	0.891112	0.445556	+	0.895254i	$0.353006\pi$
$140$	3.49678e6	0.107701
$141$	0	0
$142$	5.92782e7	1.73734
$143$	−3.75020e7	−1.07245
$144$	0	0
$145$	−5.73406e7	−1.56198
$146$	−1.99933e7	−0.531680
$147$	0	0
$148$	−649657.	−0.0164728
$149$	−4.22364e6	−0.104601	−0.0523004	−	0.998631i	$-0.516655\pi$
$149$	−4.22364e6	−0.104601	−0.0523004	+	0.998631i	$0.516655\pi$
$150$	0	0
$151$	−5.26920e7	−1.24545	−0.622724	−	0.782442i	$-0.713974\pi$
$151$	−5.26920e7	−1.24545	−0.622724	+	0.782442i	$0.713974\pi$
$152$	−6.83657e7	−1.57901
$153$	0	0
$154$	5.50369e7	1.21432
$155$	9.10044e7	1.96292
$156$	0	0
$157$	−1.15422e7	−0.238034	−0.119017	−	0.992892i	$-0.537974\pi$
$157$	−1.15422e7	−0.238034	−0.119017	+	0.992892i	$0.537974\pi$
$158$	4.10082e7	0.827125
$159$	0	0
$160$	−9.32871e6	−0.180054
$161$	−1.31830e7	−0.248956
$162$	0	0
$163$	1.00400e8	1.81583	0.907915	−	0.419155i	$-0.137674\pi$
$163$	1.00400e8	1.81583	0.907915	+	0.419155i	$0.137674\pi$
$164$	−3.54034e6	−0.0626746
$165$	0	0
$166$	4.94910e7	0.839745
$167$	1.04825e8	1.74164	0.870819	−	0.491603i	$-0.163589\pi$
$167$	1.04825e8	1.74164	0.870819	+	0.491603i	$0.163589\pi$
$168$	0	0
$169$	1.21565e7	0.193734
$170$	8.09926e7	1.26437
$171$	0	0
$172$	441763.	0.00661972
$173$	3.64392e7	0.535066	0.267533	−	0.963549i	$-0.413792\pi$
$173$	3.64392e7	0.535066	0.267533	+	0.963549i	$0.413792\pi$
$174$	0	0
$175$	4.25149e7	0.599665
$176$	−7.58339e7	−1.04850
$177$	0	0
$178$	1.44917e7	0.192597
$179$	7.50893e7	0.978572	0.489286	−	0.872123i	$-0.337257\pi$
$179$	7.50893e7	0.978572	0.489286	+	0.872123i	$0.337257\pi$
$180$	0	0
$181$	−1.43429e8	−1.79789	−0.898943	−	0.438066i	$-0.855664\pi$
$181$	−1.43429e8	−1.79789	−0.898943	+	0.438066i	$0.855664\pi$
$182$	−1.09929e8	−1.35164
$183$	0	0
$184$	1.69129e7	0.200150
$185$	−2.36254e7	−0.274333
$186$	0	0
$187$	8.73880e7	0.977252
$188$	−4.65830e6	−0.0511299
$189$	0	0
$190$	1.97513e8	2.08909
$191$	−4.59546e7	−0.477213	−0.238607	−	0.971116i	$-0.576691\pi$
$191$	−4.59546e7	−0.477213	−0.238607	+	0.971116i	$0.576691\pi$
$192$	0	0
$193$	−1.06856e8	−1.06991	−0.534956	−	0.844880i	$-0.679672\pi$
$193$	−1.06856e8	−1.06991	−0.534956	+	0.844880i	$0.679672\pi$
$194$	−3.84861e7	−0.378441
$195$	0	0
$196$	3.30124e6	0.0313171
$197$	−1.86911e8	−1.74182	−0.870909	−	0.491444i	$-0.836469\pi$
$197$	−1.86911e8	−1.74182	−0.870909	+	0.491444i	$0.836469\pi$
$198$	0	0
$199$	−8.34011e7	−0.750216	−0.375108	−	0.926981i	$-0.622394\pi$
$199$	−8.34011e7	−0.750216	−0.375108	+	0.926981i	$0.622394\pi$
$200$	−5.45441e7	−0.482106
$201$	0	0
$202$	−7.30420e7	−0.623509
$203$	−1.81353e8	−1.52156
$204$	0	0
$205$	−1.28748e8	−1.04376
$206$	−1.64516e8	−1.31121
$207$	0	0
$208$	1.51468e8	1.16707
$209$	2.13109e8	1.61469
$210$	0	0
$211$	−1.87043e8	−1.37073	−0.685367	−	0.728198i	$-0.740358\pi$
$211$	−1.87043e8	−1.37073	−0.685367	+	0.728198i	$0.740358\pi$
$212$	9.05503e6	0.0652701
$213$	0	0
$214$	1.99643e7	0.139254
$215$	1.60651e7	0.110242
$216$	0	0
$217$	2.87823e8	1.91213
$218$	−1.79598e8	−1.17409
$219$	0	0
$220$	1.39842e7	0.0885438
$221$	−1.74545e8	−1.08777
$222$	0	0
$223$	5.61290e7	0.338938	0.169469	−	0.985535i	$-0.445795\pi$
$223$	5.61290e7	0.338938	0.169469	+	0.985535i	$0.445795\pi$
$224$	−2.95043e7	−0.175395
$225$	0	0
$226$	1.19977e8	0.691384
$227$	4.41912e7	0.250752	0.125376	−	0.992109i	$-0.459986\pi$
$227$	4.41912e7	0.250752	0.125376	+	0.992109i	$0.459986\pi$
$228$	0	0
$229$	−2.46218e8	−1.35486	−0.677432	−	0.735585i	$-0.736907\pi$
$229$	−2.46218e8	−1.35486	−0.677432	+	0.735585i	$0.736907\pi$
$230$	−4.88625e7	−0.264806
$231$	0	0
$232$	2.32665e8	1.22327
$233$	1.20493e8	0.624047	0.312024	−	0.950074i	$-0.398993\pi$
$233$	1.20493e8	0.624047	0.312024	+	0.950074i	$0.398993\pi$
$234$	0	0
$235$	−1.69403e8	−0.851499
$236$	1.92738e7	0.0954500
$237$	0	0
$238$	2.56158e8	1.23166
$239$	3.29155e7	0.155958	0.0779791	−	0.996955i	$-0.475153\pi$
$239$	3.29155e7	0.155958	0.0779791	+	0.996955i	$0.475153\pi$
$240$	0	0
$241$	2.31476e8	1.06524	0.532618	−	0.846356i	$-0.321208\pi$
$241$	2.31476e8	1.06524	0.532618	+	0.846356i	$0.321208\pi$
$242$	−8.33949e6	−0.0378256
$243$	0	0
$244$	2.03575e7	0.0897139
$245$	1.20053e8	0.521543
$246$	0	0
$247$	−4.25656e8	−1.79729
$248$	−3.69259e8	−1.53727
$249$	0	0
$250$	−1.56168e8	−0.632123
$251$	−1.82082e8	−0.726792	−0.363396	−	0.931635i	$-0.618383\pi$
$251$	−1.82082e8	−0.726792	−0.363396	+	0.931635i	$0.618383\pi$
$252$	0	0
$253$	−5.27208e7	−0.204673
$254$	−4.71352e8	−1.80479
$255$	0	0
$256$	5.89553e7	0.219626
$257$	−4.36354e7	−0.160351	−0.0801757	−	0.996781i	$-0.525548\pi$
$257$	−4.36354e7	−0.160351	−0.0801757	+	0.996781i	$0.525548\pi$
$258$	0	0
$259$	−7.47208e7	−0.267234
$260$	−2.79315e7	−0.0985570
$261$	0	0
$262$	−3.61695e8	−1.24248
$263$	4.53559e8	1.53741	0.768704	−	0.639605i	$-0.220902\pi$
$263$	4.53559e8	1.53741	0.768704	+	0.639605i	$0.220902\pi$
$264$	0	0
$265$	3.29294e8	1.08698
$266$	6.24681e8	2.03504
$267$	0	0
$268$	3.28216e7	0.104157
$269$	−3.47986e8	−1.09001	−0.545004	−	0.838434i	$-0.683472\pi$
$269$	−3.47986e8	−1.09001	−0.545004	+	0.838434i	$0.683472\pi$
$270$	0	0
$271$	−4.45683e8	−1.36030	−0.680148	−	0.733075i	$-0.738084\pi$
$271$	−4.45683e8	−1.36030	−0.680148	+	0.733075i	$0.738084\pi$
$272$	−3.52954e8	−1.06347
$273$	0	0
$274$	−3.67820e8	−1.08021
$275$	1.70024e8	0.493000
$276$	0	0
$277$	1.94904e8	0.550988	0.275494	−	0.961303i	$-0.411159\pi$
$277$	1.94904e8	0.550988	0.275494	+	0.961303i	$0.411159\pi$
$278$	3.30758e8	0.923322
$279$	0	0
$280$	−5.15978e8	−1.40468
$281$	−2.99594e8	−0.805490	−0.402745	−	0.915312i	$-0.631944\pi$
$281$	−2.99594e8	−0.805490	−0.402745	+	0.915312i	$0.631944\pi$
$282$	0	0
$283$	2.78901e8	0.731471	0.365735	−	0.930719i	$-0.380818\pi$
$283$	2.78901e8	0.731471	0.365735	+	0.930719i	$0.380818\pi$
$284$	4.76367e7	0.123403
$285$	0	0
$286$	−4.39623e8	−1.11122
$287$	−4.07195e8	−1.01675
$288$	0	0
$289$	−3.60865e6	−0.00879431
$290$	−6.72184e8	−1.61843
$291$	0	0
$292$	−1.60669e7	−0.0377652
$293$	2.21505e8	0.514454	0.257227	−	0.966351i	$-0.417191\pi$
$293$	2.21505e8	0.514454	0.257227	+	0.966351i	$0.417191\pi$
$294$	0	0
$295$	7.00909e8	1.58959
$296$	9.58622e7	0.214846
$297$	0	0
$298$	−4.95122e7	−0.108382
$299$	1.05303e8	0.227819
$300$	0	0
$301$	5.08097e7	0.107390
$302$	−6.17690e8	−1.29047
$303$	0	0
$304$	−8.60731e8	−1.75715
$305$	7.40318e8	1.49406
$306$	0	0
$307$	−6.60867e8	−1.30356	−0.651778	−	0.758410i	$-0.725976\pi$
$307$	−6.60867e8	−1.30356	−0.651778	+	0.758410i	$0.725976\pi$
$308$	4.42284e7	0.0862528
$309$	0	0
$310$	1.06681e9	2.03387
$311$	−9.71134e8	−1.83070	−0.915351	−	0.402656i	$-0.868087\pi$
$311$	−9.71134e8	−1.83070	−0.915351	+	0.402656i	$0.868087\pi$
$312$	0	0
$313$	−4.00681e8	−0.738572	−0.369286	−	0.929316i	$-0.620398\pi$
$313$	−4.00681e8	−0.738572	−0.369286	+	0.929316i	$0.620398\pi$
$314$	−1.35305e8	−0.246637
$315$	0	0
$316$	3.29547e7	0.0587507
$317$	−2.39440e8	−0.422172	−0.211086	−	0.977468i	$-0.567700\pi$
$317$	−2.39440e8	−0.422172	−0.211086	+	0.977468i	$0.567700\pi$
$318$	0	0
$319$	−7.25262e8	−1.25091
$320$	6.58077e8	1.12267
$321$	0	0
$322$	−1.54539e8	−0.257955
$323$	9.91873e8	1.63775
$324$	0	0
$325$	−3.39600e8	−0.548752
$326$	1.17695e9	1.88146
$327$	0	0
$328$	5.22406e8	0.817429
$329$	−5.35778e8	−0.829467
$330$	0	0
$331$	−9.97807e8	−1.51234	−0.756169	−	0.654377i	$-0.772931\pi$
$331$	−9.97807e8	−1.51234	−0.756169	+	0.654377i	$0.772931\pi$
$332$	3.97716e7	0.0596471
$333$	0	0
$334$	1.22883e9	1.80459
$335$	1.19359e9	1.73459
$336$	0	0
$337$	1.03753e9	1.47672	0.738358	−	0.674409i	$-0.235602\pi$
$337$	1.03753e9	1.47672	0.738358	+	0.674409i	$0.235602\pi$
$338$	1.42507e8	0.200737
$339$	0	0
$340$	6.50867e7	0.0898082
$341$	1.15105e9	1.57201
$342$	0	0
$343$	−5.12615e8	−0.685902
$344$	−6.51857e7	−0.0863371
$345$	0	0
$346$	4.27164e8	0.554406
$347$	7.31420e8	0.939752	0.469876	−	0.882732i	$-0.344299\pi$
$347$	7.31420e8	0.939752	0.469876	+	0.882732i	$0.344299\pi$
$348$	0	0
$349$	1.35911e9	1.71145	0.855725	−	0.517431i	$-0.173112\pi$
$349$	1.35911e9	1.71145	0.855725	+	0.517431i	$0.173112\pi$
$350$	4.98388e8	0.621340
$351$	0	0
$352$	−1.17992e8	−0.144196
$353$	−1.13739e9	−1.37626	−0.688128	−	0.725590i	$-0.741567\pi$
$353$	−1.13739e9	−1.37626	−0.688128	+	0.725590i	$0.741567\pi$
$354$	0	0
$355$	1.73235e9	2.05512
$356$	1.16457e7	0.0136802
$357$	0	0
$358$	8.80246e8	1.01394
$359$	7.28338e8	0.830811	0.415405	−	0.909636i	$-0.363640\pi$
$359$	7.28338e8	0.830811	0.415405	+	0.909636i	$0.363640\pi$
$360$	0	0
$361$	1.52496e9	1.70602
$362$	−1.68137e9	−1.86287
$363$	0	0
$364$	−8.83400e7	−0.0960070
$365$	−5.84287e8	−0.628928
$366$	0	0
$367$	−1.66014e8	−0.175312	−0.0876562	−	0.996151i	$-0.527938\pi$
$367$	−1.66014e8	−0.175312	−0.0876562	+	0.996151i	$0.527938\pi$
$368$	2.12936e8	0.222731
$369$	0	0
$370$	−2.76952e8	−0.284248
$371$	1.04147e9	1.05886
$372$	0	0
$373$	1.43850e9	1.43526	0.717629	−	0.696426i	$-0.245227\pi$
$373$	1.43850e9	1.43526	0.717629	+	0.696426i	$0.245227\pi$
$374$	1.02442e9	1.01257
$375$	0	0
$376$	6.87370e8	0.666858
$377$	1.44861e9	1.39238
$378$	0	0
$379$	−8.11638e8	−0.765817	−0.382909	−	0.923786i	$-0.625078\pi$
$379$	−8.11638e8	−0.765817	−0.382909	+	0.923786i	$0.625078\pi$
$380$	1.58724e8	0.148388
$381$	0	0
$382$	−5.38710e8	−0.494462
$383$	6.27514e7	0.0570726	0.0285363	−	0.999593i	$-0.490915\pi$
$383$	6.27514e7	0.0570726	0.0285363	+	0.999593i	$0.490915\pi$
$384$	0	0
$385$	1.60840e9	1.43642
$386$	−1.25264e9	−1.10859
$387$	0	0
$388$	−3.09279e7	−0.0268806
$389$	−6.17507e8	−0.531885	−0.265943	−	0.963989i	$-0.585683\pi$
$389$	−6.17507e8	−0.531885	−0.265943	+	0.963989i	$0.585683\pi$
$390$	0	0
$391$	−2.45379e8	−0.207596
$392$	−4.87125e8	−0.408450
$393$	0	0
$394$	−2.19109e9	−1.80478
$395$	1.19843e9	0.978413
$396$	0	0
$397$	−1.88685e9	−1.51346	−0.756728	−	0.653730i	$-0.773203\pi$
$397$	−1.88685e9	−1.51346	−0.756728	+	0.653730i	$0.773203\pi$
$398$	−9.77682e8	−0.777333
$399$	0	0
$400$	−6.86715e8	−0.536496
$401$	2.45780e9	1.90345	0.951724	−	0.306956i	$-0.0993105\pi$
$401$	2.45780e9	1.90345	0.951724	+	0.306956i	$0.0993105\pi$
$402$	0	0
$403$	−2.29907e9	−1.74978
$404$	−5.86974e7	−0.0442878
$405$	0	0
$406$	−2.12594e9	−1.57656
$407$	−2.98821e8	−0.219700
$408$	0	0
$409$	−7.37161e7	−0.0532759	−0.0266380	−	0.999645i	$-0.508480\pi$
$409$	−7.37161e7	−0.0532759	−0.0266380	+	0.999645i	$0.508480\pi$
$410$	−1.50926e9	−1.08149
$411$	0	0
$412$	−1.32207e8	−0.0931356
$413$	2.21679e9	1.54846
$414$	0	0
$415$	1.44633e9	0.993341
$416$	2.35673e8	0.160503
$417$	0	0
$418$	2.49820e9	1.67306
$419$	1.67384e9	1.11164	0.555821	−	0.831302i	$-0.312404\pi$
$419$	1.67384e9	1.11164	0.555821	+	0.831302i	$0.312404\pi$
$420$	0	0
$421$	−2.05445e8	−0.134186	−0.0670931	−	0.997747i	$-0.521372\pi$
$421$	−2.05445e8	−0.134186	−0.0670931	+	0.997747i	$0.521372\pi$
$422$	−2.19264e9	−1.42028
$423$	0	0
$424$	−1.33614e9	−0.851280
$425$	7.91344e8	0.500039
$426$	0	0
$427$	2.34143e9	1.45541
$428$	1.60436e7	0.00989118
$429$	0	0
$430$	1.88325e8	0.114227
$431$	−7.93287e8	−0.477265	−0.238633	−	0.971110i	$-0.576699\pi$
$431$	−7.93287e8	−0.477265	−0.238633	+	0.971110i	$0.576699\pi$
$432$	0	0
$433$	−1.51807e9	−0.898638	−0.449319	−	0.893372i	$-0.648333\pi$
$433$	−1.51807e9	−0.898638	−0.449319	+	0.893372i	$0.648333\pi$
$434$	3.37405e9	1.98124
$435$	0	0
$436$	−1.44327e8	−0.0833959
$437$	−5.98393e8	−0.343006
$438$	0	0
$439$	2.11184e8	0.119134	0.0595669	−	0.998224i	$-0.481028\pi$
$439$	2.11184e8	0.119134	0.0595669	+	0.998224i	$0.481028\pi$
$440$	−2.06348e9	−1.15483
$441$	0	0
$442$	−2.04614e9	−1.12708
$443$	1.75096e9	0.956894	0.478447	−	0.878116i	$-0.341200\pi$
$443$	1.75096e9	0.956894	0.478447	+	0.878116i	$0.341200\pi$
$444$	0	0
$445$	4.23507e8	0.227825
$446$	6.57981e8	0.351189
$447$	0	0
$448$	2.08132e9	1.09362
$449$	2.97176e9	1.54936	0.774679	−	0.632354i	$-0.217911\pi$
$449$	2.97176e9	1.54936	0.774679	+	0.632354i	$0.217911\pi$
$450$	0	0
$451$	−1.62844e9	−0.835899
$452$	9.64152e7	0.0491090
$453$	0	0
$454$	5.18037e8	0.259816
$455$	−3.21256e9	−1.59886
$456$	0	0
$457$	−5.84711e8	−0.286572	−0.143286	−	0.989681i	$-0.545767\pi$
$457$	−5.84711e8	−0.286572	−0.143286	+	0.989681i	$0.545767\pi$
$458$	−2.88633e9	−1.40384
$459$	0	0
$460$	−3.92665e7	−0.0188092
$461$	−2.81304e8	−0.133728	−0.0668640	−	0.997762i	$-0.521299\pi$
$461$	−2.81304e8	−0.133728	−0.0668640	+	0.997762i	$0.521299\pi$
$462$	0	0
$463$	−3.21706e9	−1.50635	−0.753174	−	0.657821i	$-0.771478\pi$
$463$	−3.21706e9	−1.50635	−0.753174	+	0.657821i	$0.771478\pi$
$464$	2.92928e9	1.36128
$465$	0	0
$466$	1.41250e9	0.646603
$467$	−2.78700e9	−1.26627	−0.633137	−	0.774040i	$-0.718233\pi$
$467$	−2.78700e9	−1.26627	−0.633137	+	0.774040i	$0.718233\pi$
$468$	0	0
$469$	3.77501e9	1.68971
$470$	−1.98585e9	−0.882277
$471$	0	0
$472$	−2.84401e9	−1.24490
$473$	2.03196e8	0.0882880
$474$	0	0
$475$	1.92981e9	0.826204
$476$	2.05852e8	0.0874844
$477$	0	0
$478$	3.85857e8	0.161595
$479$	−6.18962e7	−0.0257329	−0.0128665	−	0.999917i	$-0.504096\pi$
$479$	−6.18962e7	−0.0257329	−0.0128665	+	0.999917i	$0.504096\pi$
$480$	0	0
$481$	5.96853e8	0.244546
$482$	2.71351e9	1.10374
$483$	0	0
$484$	−6.70172e6	−0.00268675
$485$	−1.12472e9	−0.447661
$486$	0	0
$487$	−6.45157e8	−0.253113	−0.126556	−	0.991959i	$-0.540392\pi$
$487$	−6.45157e8	−0.253113	−0.126556	+	0.991959i	$0.540392\pi$
$488$	−3.00391e9	−1.17009
$489$	0	0
$490$	1.40733e9	0.540395
$491$	−1.40153e9	−0.534339	−0.267170	−	0.963650i	$-0.586088\pi$
$491$	−1.40153e9	−0.534339	−0.267170	+	0.963650i	$0.586088\pi$
$492$	0	0
$493$	−3.37558e9	−1.26878
$494$	−4.98981e9	−1.86226
$495$	0	0
$496$	−4.64901e9	−1.71070
$497$	5.47897e9	2.00194
$498$	0	0
$499$	2.47067e9	0.890150	0.445075	−	0.895493i	$-0.353177\pi$
$499$	2.47067e9	0.890150	0.445075	+	0.895493i	$0.353177\pi$
$500$	−1.25498e8	−0.0448997
$501$	0	0
$502$	−2.13449e9	−0.753062
$503$	9.09388e8	0.318612	0.159306	−	0.987229i	$-0.449074\pi$
$503$	9.09388e8	0.318612	0.159306	+	0.987229i	$0.449074\pi$
$504$	0	0
$505$	−2.13458e9	−0.737553
$506$	−6.18028e8	−0.212071
$507$	0	0
$508$	−3.78784e8	−0.128194
$509$	−5.66010e8	−0.190244	−0.0951222	−	0.995466i	$-0.530324\pi$
$509$	−5.66010e8	−0.190244	−0.0951222	+	0.995466i	$0.530324\pi$
$510$	0	0
$511$	−1.84795e9	−0.612655
$512$	−2.63738e9	−0.868415
$513$	0	0
$514$	−5.11522e8	−0.166147
$515$	−4.80784e9	−1.55105
$516$	0	0
$517$	−2.14266e9	−0.681926
$518$	−8.75926e8	−0.276894
$519$	0	0
$520$	4.12152e9	1.28542
$521$	−1.65899e9	−0.513939	−0.256970	−	0.966419i	$-0.582724\pi$
$521$	−1.65899e9	−0.513939	−0.256970	+	0.966419i	$0.582724\pi$
$522$	0	0
$523$	4.33759e8	0.132584	0.0662922	−	0.997800i	$-0.478883\pi$
$523$	4.33759e8	0.132584	0.0662922	+	0.997800i	$0.478883\pi$
$524$	−2.90663e8	−0.0882530
$525$	0	0
$526$	5.31692e9	1.59298
$527$	5.35734e9	1.59445
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	3.86020e9	1.12627
$531$	0	0
$532$	5.02001e8	0.144549
$533$	3.25258e9	0.930429
$534$	0	0
$535$	5.83439e8	0.164724
$536$	−4.84310e9	−1.35846
$537$	0	0
$538$	−4.07932e9	−1.12941
$539$	1.51846e9	0.417680
$540$	0	0
$541$	−3.24815e9	−0.881954	−0.440977	−	0.897518i	$-0.645368\pi$
$541$	−3.24815e9	−0.881954	−0.440977	+	0.897518i	$0.645368\pi$
$542$	−5.22458e9	−1.40946
$543$	0	0
$544$	−5.49172e8	−0.146255
$545$	−5.24857e9	−1.38884
$546$	0	0
$547$	3.81804e9	0.997434	0.498717	−	0.866765i	$-0.333805\pi$
$547$	3.81804e9	0.997434	0.498717	+	0.866765i	$0.333805\pi$
$548$	−2.95585e8	−0.0767274
$549$	0	0
$550$	1.99313e9	0.510819
$551$	−8.23187e9	−2.09637
$552$	0	0
$553$	3.79031e9	0.953097
$554$	2.28480e9	0.570904
$555$	0	0
$556$	2.65801e8	0.0655835
$557$	−4.35830e9	−1.06862	−0.534311	−	0.845288i	$-0.679429\pi$
$557$	−4.35830e9	−1.06862	−0.534311	+	0.845288i	$0.679429\pi$
$558$	0	0
$559$	−4.05856e8	−0.0982722
$560$	−6.49622e9	−1.56316
$561$	0	0
$562$	−3.51203e9	−0.834605
$563$	−4.39176e9	−1.03719	−0.518596	−	0.855019i	$-0.673545\pi$
$563$	−4.39176e9	−1.03719	−0.518596	+	0.855019i	$0.673545\pi$
$564$	0	0
$565$	3.50622e9	0.817843
$566$	3.26945e9	0.757910
$567$	0	0
$568$	−7.02918e9	−1.60948
$569$	−6.27750e9	−1.42854	−0.714272	−	0.699868i	$-0.753242\pi$
$569$	−6.27750e9	−1.42854	−0.714272	+	0.699868i	$0.753242\pi$
$570$	0	0
$571$	1.14320e9	0.256977	0.128489	−	0.991711i	$-0.458987\pi$
$571$	1.14320e9	0.256977	0.128489	+	0.991711i	$0.458987\pi$
$572$	−3.53286e8	−0.0789297
$573$	0	0
$574$	−4.77340e9	−1.05350
$575$	−4.77414e8	−0.104727
$576$	0	0
$577$	−4.32504e9	−0.937292	−0.468646	−	0.883386i	$-0.655258\pi$
$577$	−4.32504e9	−0.937292	−0.468646	+	0.883386i	$0.655258\pi$
$578$	−4.23029e7	−0.00911218
$579$	0	0
$580$	−5.40175e8	−0.114957
$581$	4.57435e9	0.967639
$582$	0	0
$583$	4.16501e9	0.870516
$584$	2.37080e9	0.492550
$585$	0	0
$586$	2.59662e9	0.533049
$587$	6.11842e9	1.24855	0.624275	−	0.781205i	$-0.285395\pi$
$587$	6.11842e9	1.24855	0.624275	+	0.781205i	$0.285395\pi$
$588$	0	0
$589$	1.30647e10	2.63448
$590$	8.21651e9	1.64705
$591$	0	0
$592$	1.20692e9	0.239084
$593$	4.98519e9	0.981726	0.490863	−	0.871237i	$-0.336682\pi$
$593$	4.98519e9	0.981726	0.490863	+	0.871237i	$0.336682\pi$
$594$	0	0
$595$	7.48599e9	1.45693
$596$	−3.97887e7	−0.00769835
$597$	0	0
$598$	1.23443e9	0.236054
$599$	3.30610e9	0.628524	0.314262	−	0.949336i	$-0.398243\pi$
$599$	3.30610e9	0.628524	0.314262	+	0.949336i	$0.398243\pi$
$600$	0	0
$601$	−1.67513e9	−0.314766	−0.157383	−	0.987538i	$-0.550306\pi$
$601$	−1.67513e9	−0.314766	−0.157383	+	0.987538i	$0.550306\pi$
$602$	5.95624e8	0.111272
$603$	0	0
$604$	−4.96383e8	−0.0916617
$605$	−2.43714e8	−0.0447442
$606$	0	0
$607$	9.25174e9	1.67905	0.839524	−	0.543323i	$-0.182834\pi$
$607$	9.25174e9	1.67905	0.839524	+	0.543323i	$0.182834\pi$
$608$	−1.33924e9	−0.241655
$609$	0	0
$610$	8.67849e9	1.54807
$611$	4.27968e9	0.759043
$612$	0	0
$613$	1.82423e9	0.319866	0.159933	−	0.987128i	$-0.448872\pi$
$613$	1.82423e9	0.319866	0.159933	+	0.987128i	$0.448872\pi$
$614$	−7.74711e9	−1.35067
$615$	0	0
$616$	−6.52625e9	−1.12495
$617$	1.00585e10	1.72400	0.861999	−	0.506910i	$-0.169212\pi$
$617$	1.00585e10	1.72400	0.861999	+	0.506910i	$0.169212\pi$
$618$	0	0
$619$	−6.26962e9	−1.06249	−0.531244	−	0.847219i	$-0.678275\pi$
$619$	−6.26962e9	−1.06249	−0.531244	+	0.847219i	$0.678275\pi$
$620$	8.57304e8	0.144465
$621$	0	0
$622$	−1.13843e10	−1.89687
$623$	1.33944e9	0.221930
$624$	0	0
$625$	−7.62936e9	−1.24999
$626$	−4.69704e9	−0.765269
$627$	0	0
$628$	−1.08732e8	−0.0175186
$629$	−1.39080e9	−0.222837
$630$	0	0
$631$	3.33072e9	0.527759	0.263879	−	0.964556i	$-0.414998\pi$
$631$	3.33072e9	0.527759	0.263879	+	0.964556i	$0.414998\pi$
$632$	−4.86274e9	−0.766251
$633$	0	0
$634$	−2.80687e9	−0.437431
$635$	−1.37748e10	−2.13490
$636$	0	0
$637$	−3.03292e9	−0.464914
$638$	−8.50199e9	−1.29613
$639$	0	0
$640$	8.90848e9	1.34330
$641$	−1.53183e9	−0.229725	−0.114863	−	0.993381i	$-0.536643\pi$
$641$	−1.53183e9	−0.229725	−0.114863	+	0.993381i	$0.536643\pi$
$642$	0	0
$643$	9.12465e9	1.35356	0.676781	−	0.736185i	$-0.263375\pi$
$643$	9.12465e9	1.35356	0.676781	+	0.736185i	$0.263375\pi$
$644$	−1.24190e8	−0.0183225
$645$	0	0
$646$	1.16274e10	1.69695
$647$	3.35006e9	0.486282	0.243141	−	0.969991i	$-0.421822\pi$
$647$	3.35006e9	0.486282	0.243141	+	0.969991i	$0.421822\pi$
$648$	0	0
$649$	8.86532e9	1.27303
$650$	−3.98101e9	−0.568586
$651$	0	0
$652$	9.45810e8	0.133640
$653$	−1.18785e9	−0.166942	−0.0834709	−	0.996510i	$-0.526601\pi$
$653$	−1.18785e9	−0.166942	−0.0834709	+	0.996510i	$0.526601\pi$
$654$	0	0
$655$	−1.05702e10	−1.46973
$656$	6.57715e9	0.909649
$657$	0	0
$658$	−6.28074e9	−0.859449
$659$	1.75132e9	0.238378	0.119189	−	0.992872i	$-0.461971\pi$
$659$	1.75132e9	0.238378	0.119189	+	0.992872i	$0.461971\pi$
$660$	0	0
$661$	−5.49532e8	−0.0740096	−0.0370048	−	0.999315i	$-0.511782\pi$
$661$	−5.49532e8	−0.0740096	−0.0370048	+	0.999315i	$0.511782\pi$
$662$	−1.16969e10	−1.56700
$663$	0	0
$664$	−5.86861e9	−0.777942
$665$	1.82557e10	2.40726
$666$	0	0
$667$	2.03648e9	0.265729
$668$	9.87502e8	0.128180
$669$	0	0
$670$	1.39920e10	1.79729
$671$	9.36377e9	1.19653
$672$	0	0
$673$	−6.82432e9	−0.862992	−0.431496	−	0.902115i	$-0.642014\pi$
$673$	−6.82432e9	−0.862992	−0.431496	+	0.902115i	$0.642014\pi$
$674$	1.21626e10	1.53009
$675$	0	0
$676$	1.14520e8	0.0142583
$677$	−4.96382e9	−0.614831	−0.307416	−	0.951575i	$-0.599464\pi$
$677$	−4.96382e9	−0.614831	−0.307416	+	0.951575i	$0.599464\pi$
$678$	0	0
$679$	−3.55720e9	−0.436078
$680$	−9.60406e9	−1.17132
$681$	0	0
$682$	1.34934e10	1.62883
$683$	3.69212e8	0.0443408	0.0221704	−	0.999754i	$-0.492942\pi$
$683$	3.69212e8	0.0443408	0.0221704	+	0.999754i	$0.492942\pi$
$684$	0	0
$685$	−1.07492e10	−1.27779
$686$	−6.00921e9	−0.710695
$687$	0	0
$688$	−8.20694e8	−0.0960775
$689$	−8.31904e9	−0.968960
$690$	0	0
$691$	4.68110e8	0.0539728	0.0269864	−	0.999636i	$-0.491409\pi$
$691$	4.68110e8	0.0539728	0.0269864	+	0.999636i	$0.491409\pi$
$692$	3.43274e8	0.0393795
$693$	0	0
$694$	8.57417e9	0.973720
$695$	9.66609e9	1.09220
$696$	0	0
$697$	−7.57924e9	−0.847835
$698$	1.59323e10	1.77331
$699$	0	0
$700$	4.00511e8	0.0441338
$701$	3.36036e9	0.368445	0.184223	−	0.982885i	$-0.441023\pi$
$701$	3.36036e9	0.368445	0.184223	+	0.982885i	$0.441023\pi$
$702$	0	0
$703$	−3.39168e9	−0.368189
$704$	8.32356e9	0.899093
$705$	0	0
$706$	−1.33333e10	−1.42600
$707$	−6.75113e9	−0.718470
$708$	0	0
$709$	3.86979e9	0.407779	0.203890	−	0.978994i	$-0.434642\pi$
$709$	3.86979e9	0.407779	0.203890	+	0.978994i	$0.434642\pi$
$710$	2.03077e10	2.12940
$711$	0	0
$712$	−1.71842e9	−0.178423
$713$	−3.23206e9	−0.333938
$714$	0	0
$715$	−1.28476e10	−1.31447
$716$	7.07377e8	0.0720203
$717$	0	0
$718$	8.53805e9	0.860841
$719$	−6.77777e9	−0.680042	−0.340021	−	0.940418i	$-0.610434\pi$
$719$	−6.77777e9	−0.680042	−0.340021	+	0.940418i	$0.610434\pi$
$720$	0	0
$721$	−1.52059e10	−1.51091
$722$	1.78766e10	1.76768
$723$	0	0
$724$	−1.35117e9	−0.132320
$725$	−6.56762e9	−0.640066
$726$	0	0
$727$	−1.82667e10	−1.76315	−0.881577	−	0.472041i	$-0.843517\pi$
$727$	−1.82667e10	−1.76315	−0.881577	+	0.472041i	$0.843517\pi$
$728$	1.30353e10	1.25216
$729$	0	0
$730$	−6.84939e9	−0.651661
$731$	9.45736e8	0.0895486
$732$	0	0
$733$	−1.88910e10	−1.77171	−0.885854	−	0.463965i	$-0.846426\pi$
$733$	−1.88910e10	−1.77171	−0.885854	+	0.463965i	$0.846426\pi$
$734$	−1.94612e9	−0.181649
$735$	0	0
$736$	3.31313e8	0.0306314
$737$	1.50969e10	1.38916
$738$	0	0
$739$	9.28001e9	0.845849	0.422925	−	0.906165i	$-0.361004\pi$
$739$	9.28001e9	0.845849	0.422925	+	0.906165i	$0.361004\pi$
$740$	−2.22562e8	−0.0201902
$741$	0	0
$742$	1.22088e10	1.09713
$743$	6.57099e9	0.587719	0.293860	−	0.955849i	$-0.405060\pi$
$743$	6.57099e9	0.587719	0.293860	+	0.955849i	$0.405060\pi$
$744$	0	0
$745$	−1.44695e9	−0.128205
$746$	1.68631e10	1.48714
$747$	0	0
$748$	8.23236e8	0.0719232
$749$	1.84526e9	0.160462
$750$	0	0
$751$	−1.31886e10	−1.13621	−0.568106	−	0.822955i	$-0.692324\pi$
$751$	−1.31886e10	−1.13621	−0.568106	+	0.822955i	$0.692324\pi$
$752$	8.65406e9	0.742092
$753$	0	0
$754$	1.69815e10	1.44270
$755$	−1.80514e10	−1.52650
$756$	0	0
$757$	−5.22876e9	−0.438090	−0.219045	−	0.975715i	$-0.570294\pi$
$757$	−5.22876e9	−0.438090	−0.219045	+	0.975715i	$0.570294\pi$
$758$	−9.51455e9	−0.793498
$759$	0	0
$760$	−2.34210e10	−1.93534
$761$	1.56660e9	0.128858	0.0644291	−	0.997922i	$-0.479477\pi$
$761$	1.56660e9	0.128858	0.0644291	+	0.997922i	$0.479477\pi$
$762$	0	0
$763$	−1.65999e10	−1.35291
$764$	−4.32914e8	−0.0351217
$765$	0	0
$766$	7.35613e8	0.0591355
$767$	−1.77072e10	−1.41699
$768$	0	0
$769$	9.21638e9	0.730833	0.365417	−	0.930844i	$-0.380927\pi$
$769$	9.21638e9	0.730833	0.365417	+	0.930844i	$0.380927\pi$
$770$	1.88547e10	1.48834
$771$	0	0
$772$	−1.00663e9	−0.0787428
$773$	1.86318e10	1.45087	0.725434	−	0.688292i	$-0.241639\pi$
$773$	1.86318e10	1.45087	0.725434	+	0.688292i	$0.241639\pi$
$774$	0	0
$775$	1.04234e10	0.804363
$776$	4.56367e9	0.350589
$777$	0	0
$778$	−7.23881e9	−0.551110
$779$	−1.84831e10	−1.40086
$780$	0	0
$781$	2.19113e10	1.64585
$782$	−2.87649e9	−0.215099
$783$	0	0
$784$	−6.13296e9	−0.454531
$785$	−3.95415e9	−0.291749
$786$	0	0
$787$	2.75052e9	0.201142	0.100571	−	0.994930i	$-0.467933\pi$
$787$	2.75052e9	0.201142	0.100571	+	0.994930i	$0.467933\pi$
$788$	−1.76079e9	−0.128193
$789$	0	0
$790$	1.40487e10	1.01378
$791$	1.10893e10	0.796682
$792$	0	0
$793$	−1.87028e10	−1.33184
$794$	−2.21188e10	−1.56816
$795$	0	0
$796$	−7.85677e8	−0.0552139
$797$	2.45287e10	1.71621	0.858104	−	0.513476i	$-0.171643\pi$
$797$	2.45287e10	1.71621	0.858104	+	0.513476i	$0.171643\pi$
$798$	0	0
$799$	−9.97260e9	−0.691663
$800$	−1.06848e9	−0.0737823
$801$	0	0
$802$	2.88119e10	1.97225
$803$	−7.39024e9	−0.503679
$804$	0	0
$805$	−4.51627e9	−0.305136
$806$	−2.69512e10	−1.81303
$807$	0	0
$808$	8.66128e9	0.577620
$809$	−2.66265e10	−1.76805	−0.884026	−	0.467438i	$-0.845177\pi$
$809$	−2.66265e10	−1.76805	−0.884026	+	0.467438i	$0.845177\pi$
$810$	0	0
$811$	7.74902e9	0.510122	0.255061	−	0.966925i	$-0.417904\pi$
$811$	7.74902e9	0.510122	0.255061	+	0.966925i	$0.417904\pi$
$812$	−1.70843e9	−0.111983
$813$	0	0
$814$	−3.50297e9	−0.227641
$815$	3.43952e10	2.22560
$816$	0	0
$817$	2.30632e9	0.147959
$818$	−8.64148e8	−0.0552016
$819$	0	0
$820$	−1.21286e9	−0.0768180
$821$	−2.60493e10	−1.64284	−0.821418	−	0.570327i	$-0.806817\pi$
$821$	−2.60493e10	−1.64284	−0.821418	+	0.570327i	$0.806817\pi$
$822$	0	0
$823$	1.25182e10	0.782788	0.391394	−	0.920223i	$-0.371993\pi$
$823$	1.25182e10	0.782788	0.391394	+	0.920223i	$0.371993\pi$
$824$	1.95083e10	1.21471
$825$	0	0
$826$	2.59867e10	1.60443
$827$	−2.41078e10	−1.48214	−0.741069	−	0.671429i	$-0.765681\pi$
$827$	−2.41078e10	−1.48214	−0.741069	+	0.671429i	$0.765681\pi$
$828$	0	0
$829$	−3.34113e9	−0.203682	−0.101841	−	0.994801i	$-0.532473\pi$
$829$	−3.34113e9	−0.203682	−0.101841	+	0.994801i	$0.532473\pi$
$830$	1.69548e10	1.02925
$831$	0	0
$832$	−1.66252e10	−1.00077
$833$	7.06738e9	0.423644
$834$	0	0
$835$	3.59114e10	2.13466
$836$	2.00759e9	0.118837
$837$	0	0
$838$	1.96218e10	1.15182
$839$	1.23510e10	0.721996	0.360998	−	0.932567i	$-0.382436\pi$
$839$	1.23510e10	0.721996	0.360998	+	0.932567i	$0.382436\pi$
$840$	0	0
$841$	1.07652e10	0.624074
$842$	−2.40836e9	−0.139037
$843$	0	0
$844$	−1.76203e9	−0.100882
$845$	4.16463e9	0.237453
$846$	0	0
$847$	−7.70803e8	−0.0435864
$848$	−1.68222e10	−0.947320
$849$	0	0
$850$	9.27664e9	0.518113
$851$	8.39065e8	0.0466705
$852$	0	0
$853$	−9.64497e8	−0.0532083	−0.0266041	−	0.999646i	$-0.508469\pi$
$853$	−9.64497e8	−0.0532083	−0.0266041	+	0.999646i	$0.508469\pi$
$854$	2.74478e10	1.50801
$855$	0	0
$856$	−2.36736e9	−0.129005
$857$	2.03242e9	0.110301	0.0551507	−	0.998478i	$-0.482436\pi$
$857$	2.03242e9	0.110301	0.0551507	+	0.998478i	$0.482436\pi$
$858$	0	0
$859$	−1.10253e10	−0.593493	−0.296747	−	0.954956i	$-0.595902\pi$
$859$	−1.10253e10	−0.593493	−0.296747	+	0.954956i	$0.595902\pi$
$860$	1.51341e8	0.00811355
$861$	0	0
$862$	−9.29942e9	−0.494516
$863$	6.50704e9	0.344624	0.172312	−	0.985042i	$-0.444876\pi$
$863$	6.50704e9	0.344624	0.172312	+	0.985042i	$0.444876\pi$
$864$	0	0
$865$	1.24835e10	0.655811
$866$	−1.77958e10	−0.931119
$867$	0	0
$868$	2.71143e9	0.140728
$869$	1.51581e10	0.783565
$870$	0	0
$871$	−3.01539e10	−1.54625
$872$	2.12966e10	1.08768
$873$	0	0
$874$	−7.01475e9	−0.355404
$875$	−1.44343e10	−0.728395
$876$	0	0
$877$	1.20449e10	0.602985	0.301492	−	0.953469i	$-0.402515\pi$
$877$	1.20449e10	0.602985	0.301492	+	0.953469i	$0.402515\pi$
$878$	2.47563e9	0.123440
$879$	0	0
$880$	−2.59795e10	−1.28511
$881$	1.64505e9	0.0810521	0.0405261	−	0.999178i	$-0.487097\pi$
$881$	1.64505e9	0.0810521	0.0405261	+	0.999178i	$0.487097\pi$
$882$	0	0
$883$	8.81189e9	0.430732	0.215366	−	0.976533i	$-0.430906\pi$
$883$	8.81189e9	0.430732	0.215366	+	0.976533i	$0.430906\pi$
$884$	−1.64430e9	−0.0800568
$885$	0	0
$886$	2.05259e10	0.991482
$887$	2.99149e10	1.43931	0.719656	−	0.694331i	$-0.244299\pi$
$887$	2.99149e10	1.43931	0.719656	+	0.694331i	$0.244299\pi$
$888$	0	0
$889$	−4.35661e10	−2.07966
$890$	4.96463e9	0.236060
$891$	0	0
$892$	5.28762e8	0.0249450
$893$	−2.43197e10	−1.14282
$894$	0	0
$895$	2.57244e10	1.19940
$896$	2.81752e10	1.30855
$897$	0	0
$898$	3.48369e10	1.60536
$899$	−4.44623e10	−2.04095
$900$	0	0
$901$	1.93852e10	0.882946
$902$	−1.90896e10	−0.866113
$903$	0	0
$904$	−1.42268e10	−0.640500
$905$	−4.91364e10	−2.20360
$906$	0	0
$907$	−4.87204e9	−0.216813	−0.108406	−	0.994107i	$-0.534575\pi$
$907$	−4.87204e9	−0.216813	−0.108406	+	0.994107i	$0.534575\pi$
$908$	4.16301e8	0.0184547
$909$	0	0
$910$	−3.76597e10	−1.65666
$911$	6.29907e9	0.276034	0.138017	−	0.990430i	$-0.455927\pi$
$911$	6.29907e9	0.276034	0.138017	+	0.990430i	$0.455927\pi$
$912$	0	0
$913$	1.82936e10	0.795520
$914$	−6.85436e9	−0.296931
$915$	0	0
$916$	−2.31949e9	−0.0997145
$917$	−3.34308e10	−1.43171
$918$	0	0
$919$	2.84311e10	1.20834	0.604171	−	0.796855i	$-0.293505\pi$
$919$	2.84311e10	1.20834	0.604171	+	0.796855i	$0.293505\pi$
$920$	5.79409e9	0.245317
$921$	0	0
$922$	−3.29763e9	−0.138562
$923$	−4.37648e10	−1.83197
$924$	0	0
$925$	−2.70598e9	−0.112416
$926$	−3.77124e10	−1.56080
$927$	0	0
$928$	4.55776e9	0.187212
$929$	−3.12784e10	−1.27994	−0.639970	−	0.768400i	$-0.721053\pi$
$929$	−3.12784e10	−1.27994	−0.639970	+	0.768400i	$0.721053\pi$
$930$	0	0
$931$	1.72349e10	0.699977
$932$	1.13510e9	0.0459282
$933$	0	0
$934$	−3.26710e10	−1.31204
$935$	2.99377e10	1.19778
$936$	0	0
$937$	−4.18789e10	−1.66305	−0.831527	−	0.555484i	$-0.812533\pi$
$937$	−4.18789e10	−1.66305	−0.831527	+	0.555484i	$0.812533\pi$
$938$	4.42531e10	1.75079
$939$	0	0
$940$	−1.59586e9	−0.0626681
$941$	−3.40294e10	−1.33135	−0.665673	−	0.746243i	$-0.731856\pi$
$941$	−3.40294e10	−1.33135	−0.665673	+	0.746243i	$0.731856\pi$
$942$	0	0
$943$	4.57253e9	0.177568
$944$	−3.58064e10	−1.38535
$945$	0	0
$946$	2.38200e9	0.0914792
$947$	1.37778e10	0.527175	0.263587	−	0.964635i	$-0.415094\pi$
$947$	1.37778e10	0.527175	0.263587	+	0.964635i	$0.415094\pi$
$948$	0	0
$949$	1.47610e10	0.560639
$950$	2.26225e10	0.856067
$951$	0	0
$952$	−3.03751e10	−1.14101
$953$	−2.00997e9	−0.0752255	−0.0376128	−	0.999292i	$-0.511975\pi$
$953$	−2.00997e9	−0.0752255	−0.0376128	+	0.999292i	$0.511975\pi$
$954$	0	0
$955$	−1.57433e10	−0.584903
$956$	3.10080e8	0.0114781
$957$	0	0
$958$	−7.25587e8	−0.0266631
$959$	−3.39969e10	−1.24473
$960$	0	0
$961$	4.30529e10	1.56484
$962$	6.99670e9	0.253385
$963$	0	0
$964$	2.18061e9	0.0783986
$965$	−3.66071e10	−1.31135
$966$	0	0
$967$	2.01519e10	0.716675	0.358338	−	0.933592i	$-0.383344\pi$
$967$	2.01519e10	0.716675	0.358338	+	0.933592i	$0.383344\pi$
$968$	9.88893e8	0.0350417
$969$	0	0
$970$	−1.31847e10	−0.463841
$971$	2.51625e10	0.882035	0.441018	−	0.897498i	$-0.354618\pi$
$971$	2.51625e10	0.882035	0.441018	+	0.897498i	$0.354618\pi$
$972$	0	0
$973$	3.05713e10	1.06394
$974$	−7.56295e9	−0.262262
$975$	0	0
$976$	−3.78196e10	−1.30209
$977$	5.15917e10	1.76990	0.884950	−	0.465687i	$-0.154193\pi$
$977$	5.15917e10	1.76990	0.884950	+	0.465687i	$0.154193\pi$
$978$	0	0
$979$	5.35665e9	0.182454
$980$	1.13095e9	0.0383842
$981$	0	0
$982$	−1.64296e10	−0.553653
$983$	−7.89989e9	−0.265267	−0.132634	−	0.991165i	$-0.542343\pi$
$983$	−7.89989e9	−0.265267	−0.132634	+	0.991165i	$0.542343\pi$
$984$	0	0
$985$	−6.40326e10	−2.13488
$986$	−3.95708e10	−1.31464
$987$	0	0
$988$	−4.00987e9	−0.132276
$989$	−5.70558e8	−0.0187548
$990$	0	0
$991$	4.37936e10	1.42940	0.714699	−	0.699432i	$-0.246564\pi$
$991$	4.37936e10	1.42940	0.714699	+	0.699432i	$0.246564\pi$
$992$	−7.23355e9	−0.235267
$993$	0	0
$994$	6.42280e10	2.07430
$995$	−2.85719e10	−0.919512
$996$	0	0
$997$	−2.62759e10	−0.839700	−0.419850	−	0.907593i	$-0.637917\pi$
$997$	−2.62759e10	−0.839700	−0.419850	+	0.907593i	$0.637917\pi$
$998$	2.89628e10	0.922325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.h.1.10	yes	12
3.2	odd	2		207.8.a.g.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.8.a.g.1.3	✓	12	3.2	odd	2
207.8.a.h.1.10	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q+11.7226 q^{2} +9.42047 q^{4} +342.584 q^{5} +1083.50 q^{7} -1390.07 q^{8} +O(q^{10})\)	\(q+11.7226 q^{2} +9.42047 q^{4} +342.584 q^{5} +1083.50 q^{7} -1390.07 q^{8} +4015.99 q^{10} +4333.10 q^{11} -8654.77 q^{13} +12701.5 q^{14} -17501.1 q^{16} +20167.5 q^{17} +49181.6 q^{19} +3227.30 q^{20} +50795.4 q^{22} -12167.0 q^{23} +39238.5 q^{25} -101457. q^{26} +10207.1 q^{28} -167377. q^{29} +265642. q^{31} -27230.5 q^{32} +236417. q^{34} +371190. q^{35} -68962.3 q^{37} +576539. q^{38} -476214. q^{40} -375814. q^{41} +46893.9 q^{43} +40819.8 q^{44} -142629. q^{46} -494488. q^{47} +350433. q^{49} +459979. q^{50} -81532.0 q^{52} +961208. q^{53} +1.48445e6 q^{55} -1.50614e6 q^{56} -1.96210e6 q^{58} +2.04595e6 q^{59} +2.16099e6 q^{61} +3.11402e6 q^{62} +1.92092e6 q^{64} -2.96498e6 q^{65} +3.48408e6 q^{67} +189988. q^{68} +4.35133e6 q^{70} +5.05672e6 q^{71} -1.70553e6 q^{73} -808421. q^{74} +463314. q^{76} +4.69492e6 q^{77} +3.49821e6 q^{79} -5.99558e6 q^{80} -4.40553e6 q^{82} +4.22182e6 q^{83} +6.90907e6 q^{85} +549721. q^{86} -6.02330e6 q^{88} +1.23622e6 q^{89} -9.37746e6 q^{91} -114619. q^{92} -5.79670e6 q^{94} +1.68488e7 q^{95} -3.28306e6 q^{97} +4.10800e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8}+O(q^{10}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8	\( 12 q + 16 q^{2} + 640 q^{4} + 500 q^{5} - 228 q^{7} + 3072 q^{8} + 10270 q^{10} - 460 q^{11} - 21060 q^{13} + 4268 q^{14} + 56676 q^{16} + 73124 q^{17} + 8508 q^{19} + 170538 q^{20} + 124754 q^{22} - 146004 q^{23} + 194064 q^{25} + 206080 q^{26} - 390416 q^{28} + 268640 q^{29} - 191880 q^{31} + 1180172 q^{32} - 221436 q^{34} - 487244 q^{35} + 650332 q^{37} + 1432950 q^{38} + 1775722 q^{40} + 980088 q^{41} - 861276 q^{43} + 800666 q^{44} - 194672 q^{46} + 403868 q^{47} + 1699160 q^{49} + 2919092 q^{50} - 2369520 q^{52} - 201948 q^{53} - 1553512 q^{55} - 4848116 q^{56} + 3720672 q^{58} + 1302676 q^{59} + 2141364 q^{61} + 2160944 q^{62} + 9702136 q^{64} + 9099536 q^{65} - 6159260 q^{67} + 18442208 q^{68} - 10891632 q^{70} + 12584184 q^{71} + 7435872 q^{73} + 22491442 q^{74} + 5721386 q^{76} + 16450568 q^{77} + 3658028 q^{79} + 49905778 q^{80} - 5516316 q^{82} + 26137900 q^{83} + 5169556 q^{85} + 30678550 q^{86} + 14753046 q^{88} + 27235908 q^{89} - 7657216 q^{91} - 7786880 q^{92} - 23519352 q^{94} + 63623628 q^{95} + 22454720 q^{97} + 94951532 q^{98}+O(q^{100}) \) 12 * q + 16 * q^2 + 640 * q^4 + 500 * q^5 - 228 * q^7 + 3072 * q^8 + 10270 * q^10 - 460 * q^11 - 21060 * q^13 + 4268 * q^14 + 56676 * q^16 + 73124 * q^17 + 8508 * q^19 + 170538 * q^20 + 124754 * q^22 - 146004 * q^23 + 194064 * q^25 + 206080 * q^26 - 390416 * q^28 + 268640 * q^29 - 191880 * q^31 + 1180172 * q^32 - 221436 * q^34 - 487244 * q^35 + 650332 * q^37 + 1432950 * q^38 + 1775722 * q^40 + 980088 * q^41 - 861276 * q^43 + 800666 * q^44 - 194672 * q^46 + 403868 * q^47 + 1699160 * q^49 + 2919092 * q^50 - 2369520 * q^52 - 201948 * q^53 - 1553512 * q^55 - 4848116 * q^56 + 3720672 * q^58 + 1302676 * q^59 + 2141364 * q^61 + 2160944 * q^62 + 9702136 * q^64 + 9099536 * q^65 - 6159260 * q^67 + 18442208 * q^68 - 10891632 * q^70 + 12584184 * q^71 + 7435872 * q^73 + 22491442 * q^74 + 5721386 * q^76 + 16450568 * q^77 + 3658028 * q^79 + 49905778 * q^80 - 5516316 * q^82 + 26137900 * q^83 + 5169556 * q^85 + 30678550 * q^86 + 14753046 * q^88 + 27235908 * q^89 - 7657216 * q^91 - 7786880 * q^92 - 23519352 * q^94 + 63623628 * q^95 + 22454720 * q^97 + 94951532 * q^98

Introduction

L-functions

Modular forms

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Database

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