LMFDB - Embedded newform 207.8.a.e.1.1

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:	$1$
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} - 757x^{6} - 1170x^{5} + 170343x^{4} + 424132x^{3} - 9973075x^{2} - 5161010x + 130545120 $ x^8 - 757x^6 - 1170x^5 + 170343x^4 + 424132x^3 - 9973075x^2 - 5161010x + 130545120
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-18.5379$ 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)

$f(q)$	$=$	$q-21.5379 q^{2} +335.881 q^{4} -54.7305 q^{5} -565.198 q^{7} -4477.33 q^{8} +O(q^{10})$	\(q-21.5379 q^{2} +335.881 q^{4} -54.7305 q^{5} -565.198 q^{7} -4477.33 q^{8} +1178.78 q^{10} +890.150 q^{11} +12435.5 q^{13} +12173.2 q^{14} +53439.5 q^{16} +2692.57 q^{17} -56073.6 q^{19} -18383.0 q^{20} -19172.0 q^{22} -12167.0 q^{23} -75129.6 q^{25} -267836. q^{26} -189839. q^{28} +72626.2 q^{29} +207276. q^{31} -577876. q^{32} -57992.3 q^{34} +30933.6 q^{35} -160422. q^{37} +1.20771e6 q^{38} +245047. q^{40} +562941. q^{41} +7553.70 q^{43} +298985. q^{44} +262052. q^{46} -374615. q^{47} -504095. q^{49} +1.61813e6 q^{50} +4.17687e6 q^{52} -96348.3 q^{53} -48718.4 q^{55} +2.53058e6 q^{56} -1.56422e6 q^{58} +1.29931e6 q^{59} +1.20681e6 q^{61} -4.46429e6 q^{62} +5.60599e6 q^{64} -680604. q^{65} +3.81931e6 q^{67} +904384. q^{68} -666244. q^{70} +649906. q^{71} -2.81315e6 q^{73} +3.45515e6 q^{74} -1.88341e7 q^{76} -503111. q^{77} -807658. q^{79} -2.92477e6 q^{80} -1.21246e7 q^{82} +4.40700e6 q^{83} -147366. q^{85} -162691. q^{86} -3.98549e6 q^{88} +1.28241e7 q^{89} -7.02854e6 q^{91} -4.08667e6 q^{92} +8.06842e6 q^{94} +3.06894e6 q^{95} -2.57777e6 q^{97} +1.08571e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8}+O(q^{10}) $ 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8} + 11720 q^{10} - 6932 q^{11} + 12404 q^{13} - 30222 q^{14} + 27058 q^{16} - 24434 q^{17} - 14682 q^{19} + 3760 q^{20} + 36294 q^{22} - 97336 q^{23} + 144644 q^{25} - 325840 q^{26} - 21566 q^{28} - 255356 q^{29} + 450764 q^{31} - 647588 q^{32} + 191822 q^{34} - 1022616 q^{35} + 206240 q^{37} - 737372 q^{38} + 590028 q^{40} - 1053344 q^{41} + 1587806 q^{43} - 589366 q^{44} + 292008 q^{46} - 443336 q^{47} + 1944828 q^{49} + 1556112 q^{50} - 614236 q^{52} + 375530 q^{53} + 407792 q^{55} + 1316922 q^{56} - 1413384 q^{58} - 624008 q^{59} - 2005568 q^{61} + 3908272 q^{62} - 5082310 q^{64} - 646124 q^{65} - 2712286 q^{67} + 2289698 q^{68} - 16499468 q^{70} + 6287176 q^{71} - 10358312 q^{73} + 2000150 q^{74} - 25107464 q^{76} + 2156840 q^{77} - 8800574 q^{79} - 2384344 q^{80} - 31799800 q^{82} - 384948 q^{83} - 17826684 q^{85} + 11563928 q^{86} - 25202782 q^{88} + 3445530 q^{89} - 16316740 q^{91} - 6837854 q^{92} - 24237616 q^{94} - 26164288 q^{95} - 28043764 q^{97} + 9998012 q^{98}+O(q^{100}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8 + 11720 * q^10 - 6932 * q^11 + 12404 * q^13 - 30222 * q^14 + 27058 * q^16 - 24434 * q^17 - 14682 * q^19 + 3760 * q^20 + 36294 * q^22 - 97336 * q^23 + 144644 * q^25 - 325840 * q^26 - 21566 * q^28 - 255356 * q^29 + 450764 * q^31 - 647588 * q^32 + 191822 * q^34 - 1022616 * q^35 + 206240 * q^37 - 737372 * q^38 + 590028 * q^40 - 1053344 * q^41 + 1587806 * q^43 - 589366 * q^44 + 292008 * q^46 - 443336 * q^47 + 1944828 * q^49 + 1556112 * q^50 - 614236 * q^52 + 375530 * q^53 + 407792 * q^55 + 1316922 * q^56 - 1413384 * q^58 - 624008 * q^59 - 2005568 * q^61 + 3908272 * q^62 - 5082310 * q^64 - 646124 * q^65 - 2712286 * q^67 + 2289698 * q^68 - 16499468 * q^70 + 6287176 * q^71 - 10358312 * q^73 + 2000150 * q^74 - 25107464 * q^76 + 2156840 * q^77 - 8800574 * q^79 - 2384344 * q^80 - 31799800 * q^82 - 384948 * q^83 - 17826684 * q^85 + 11563928 * q^86 - 25202782 * q^88 + 3445530 * q^89 - 16316740 * q^91 - 6837854 * q^92 - 24237616 * q^94 - 26164288 * q^95 - 28043764 * q^97 + 9998012 * 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 $

$2$	−21.5379	−1.90370	−0.951850	−	0.306564i	$-0.900820\pi$
$2$	−21.5379	−1.90370	−0.951850	+	0.306564i	$0.900820\pi$
$3$	0	0
$3$	0	0
$4$	335.881	2.62407
$5$	−54.7305	−0.195810	−0.0979050	−	0.995196i	$-0.531214\pi$
$5$	−54.7305	−0.195810	−0.0979050	+	0.995196i	$0.531214\pi$
$6$	0	0
$7$	−565.198	−0.622812	−0.311406	−	0.950277i	$-0.600800\pi$
$7$	−565.198	−0.622812	−0.311406	+	0.950277i	$0.600800\pi$
$8$	−4477.33	−3.09175
$9$	0	0
$10$	1178.78	0.372763
$11$	890.150	0.201646	0.100823	−	0.994904i	$-0.467852\pi$
$11$	890.150	0.201646	0.100823	+	0.994904i	$0.467852\pi$
$12$	0	0
$13$	12435.5	1.56987	0.784934	−	0.619579i	$-0.212697\pi$
$13$	12435.5	1.56987	0.784934	+	0.619579i	$0.212697\pi$
$14$	12173.2	1.18565
$15$	0	0
$16$	53439.5	3.26169
$17$	2692.57	0.132922	0.0664608	−	0.997789i	$-0.478829\pi$
$17$	2692.57	0.132922	0.0664608	+	0.997789i	$0.478829\pi$
$18$	0	0
$19$	−56073.6	−1.87551	−0.937757	−	0.347291i	$-0.887102\pi$
$19$	−56073.6	−1.87551	−0.937757	+	0.347291i	$0.887102\pi$
$20$	−18383.0	−0.513819
$21$	0	0
$22$	−19172.0	−0.383873
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	0	0
$25$	−75129.6	−0.961658
$26$	−267836.	−2.98856
$27$	0	0
$28$	−189839.	−1.63430
$29$	72626.2	0.552969	0.276484	−	0.961018i	$-0.410831\pi$
$29$	72626.2	0.552969	0.276484	+	0.961018i	$0.410831\pi$
$30$	0	0
$31$	207276.	1.24963	0.624817	−	0.780771i	$-0.285173\pi$
$31$	207276.	1.24963	0.624817	+	0.780771i	$0.285173\pi$
$32$	−577876.	−3.11752
$33$	0	0
$34$	−57992.3	−0.253043
$35$	30933.6	0.121953
$36$	0	0
$37$	−160422.	−0.520664	−0.260332	−	0.965519i	$-0.583832\pi$
$37$	−160422.	−0.520664	−0.260332	+	0.965519i	$0.583832\pi$
$38$	1.20771e6	3.57042
$39$	0	0
$40$	245047.	0.605395
$41$	562941.	1.27561	0.637807	−	0.770196i	$-0.279842\pi$
$41$	562941.	1.27561	0.637807	+	0.770196i	$0.279842\pi$
$42$	0	0
$43$	7553.70	0.0144884	0.00724419	−	0.999974i	$-0.497694\pi$
$43$	7553.70	0.0144884	0.00724419	+	0.999974i	$0.497694\pi$
$44$	298985.	0.529133
$45$	0	0
$46$	262052.	0.396949
$47$	−374615.	−0.526311	−0.263156	−	0.964753i	$-0.584763\pi$
$47$	−374615.	−0.526311	−0.263156	+	0.964753i	$0.584763\pi$
$48$	0	0
$49$	−504095.	−0.612105
$50$	1.61813e6	1.83071
$51$	0	0
$52$	4.17687e6	4.11945
$53$	−96348.3	−0.0888952	−0.0444476	−	0.999012i	$-0.514153\pi$
$53$	−96348.3	−0.0888952	−0.0444476	+	0.999012i	$0.514153\pi$
$54$	0	0
$55$	−48718.4	−0.0394842
$56$	2.53058e6	1.92558
$57$	0	0
$58$	−1.56422e6	−1.05269
$59$	1.29931e6	0.823625	0.411812	−	0.911269i	$-0.364896\pi$
$59$	1.29931e6	0.823625	0.411812	+	0.911269i	$0.364896\pi$
$60$	0	0
$61$	1.20681e6	0.680747	0.340374	−	0.940290i	$-0.389446\pi$
$61$	1.20681e6	0.680747	0.340374	+	0.940290i	$0.389446\pi$
$62$	−4.46429e6	−2.37893
$63$	0	0
$64$	5.60599e6	2.67314
$65$	−680604.	−0.307396
$66$	0	0
$67$	3.81931e6	1.55140	0.775699	−	0.631103i	$-0.217398\pi$
$67$	3.81931e6	1.55140	0.775699	+	0.631103i	$0.217398\pi$
$68$	904384.	0.348796
$69$	0	0
$70$	−666244.	−0.232162
$71$	649906.	0.215499	0.107750	−	0.994178i	$-0.465635\pi$
$71$	649906.	0.215499	0.107750	+	0.994178i	$0.465635\pi$
$72$	0	0
$73$	−2.81315e6	−0.846374	−0.423187	−	0.906042i	$-0.639089\pi$
$73$	−2.81315e6	−0.846374	−0.423187	+	0.906042i	$0.639089\pi$
$74$	3.45515e6	0.991187
$75$	0	0
$76$	−1.88341e7	−4.92149
$77$	−503111.	−0.125587
$78$	0	0
$79$	−807658.	−0.184303	−0.0921516	−	0.995745i	$-0.529374\pi$
$79$	−807658.	−0.184303	−0.0921516	+	0.995745i	$0.529374\pi$
$80$	−2.92477e6	−0.638670
$81$	0	0
$82$	−1.21246e7	−2.42839
$83$	4.40700e6	0.845999	0.422999	−	0.906130i	$-0.360977\pi$
$83$	4.40700e6	0.845999	0.422999	+	0.906130i	$0.360977\pi$
$84$	0	0
$85$	−147366.	−0.0260274
$86$	−162691.	−0.0275815
$87$	0	0
$88$	−3.98549e6	−0.623437
$89$	1.28241e7	1.92824	0.964121	−	0.265464i	$-0.0855250\pi$
$89$	1.28241e7	1.92824	0.964121	+	0.265464i	$0.0855250\pi$
$90$	0	0
$91$	−7.02854e6	−0.977733
$92$	−4.08667e6	−0.547157
$93$	0	0
$94$	8.06842e6	1.00194
$95$	3.06894e6	0.367244
$96$	0	0
$97$	−2.57777e6	−0.286776	−0.143388	−	0.989667i	$-0.545800\pi$
$97$	−2.57777e6	−0.286776	−0.143388	+	0.989667i	$0.545800\pi$
$98$	1.08571e7	1.16526
$99$	0	0
$100$	−2.52346e7	−2.52346
$101$	−1.36859e7	−1.32174	−0.660872	−	0.750499i	$-0.729813\pi$
$101$	−1.36859e7	−1.32174	−0.660872	+	0.750499i	$0.729813\pi$
$102$	0	0
$103$	1.78977e7	1.61386	0.806932	−	0.590645i	$-0.201127\pi$
$103$	1.78977e7	1.61386	0.806932	+	0.590645i	$0.201127\pi$
$104$	−5.56780e7	−4.85364
$105$	0	0
$106$	2.07514e6	0.169230
$107$	−2.05198e7	−1.61931	−0.809655	−	0.586907i	$-0.800346\pi$
$107$	−2.05198e7	−1.61931	−0.809655	+	0.586907i	$0.800346\pi$
$108$	0	0
$109$	−1.99672e7	−1.47681	−0.738405	−	0.674358i	$-0.764421\pi$
$109$	−1.99672e7	−1.47681	−0.738405	+	0.674358i	$0.764421\pi$
$110$	1.04929e6	0.0751661
$111$	0	0
$112$	−3.02039e7	−2.03142
$113$	−3.03308e7	−1.97747	−0.988734	−	0.149685i	$-0.952174\pi$
$113$	−3.03308e7	−1.97747	−0.988734	+	0.149685i	$0.952174\pi$
$114$	0	0
$115$	665906.	0.0408292
$116$	2.43938e7	1.45103
$117$	0	0
$118$	−2.79843e7	−1.56793
$119$	−1.52183e6	−0.0827853
$120$	0	0
$121$	−1.86948e7	−0.959339
$122$	−2.59922e7	−1.29594
$123$	0	0
$124$	6.96201e7	3.27913
$125$	8.38770e6	0.384112
$126$	0	0
$127$	1.95967e7	0.848926	0.424463	−	0.905445i	$-0.360463\pi$
$127$	1.95967e7	0.848926	0.424463	+	0.905445i	$0.360463\pi$
$128$	−4.67731e7	−1.97134
$129$	0	0
$130$	1.46588e7	0.585189
$131$	1.49391e7	0.580597	0.290299	−	0.956936i	$-0.406245\pi$
$131$	1.49391e7	0.580597	0.290299	+	0.956936i	$0.406245\pi$
$132$	0	0
$133$	3.16926e7	1.16809
$134$	−8.22599e7	−2.95339
$135$	0	0
$136$	−1.20555e7	−0.410960
$137$	−3.18774e7	−1.05916	−0.529578	−	0.848261i	$-0.677650\pi$
$137$	−3.18774e7	−1.05916	−0.529578	+	0.848261i	$0.677650\pi$
$138$	0	0
$139$	4.39284e7	1.38737	0.693687	−	0.720277i	$-0.255985\pi$
$139$	4.39284e7	1.38737	0.693687	+	0.720277i	$0.255985\pi$
$140$	1.03900e7	0.320013
$141$	0	0
$142$	−1.39976e7	−0.410246
$143$	1.10695e7	0.316557
$144$	0	0
$145$	−3.97487e6	−0.108277
$146$	6.05893e7	1.61124
$147$	0	0
$148$	−5.38827e7	−1.36626
$149$	−6.05704e7	−1.50006	−0.750030	−	0.661404i	$-0.769961\pi$
$149$	−6.05704e7	−1.50006	−0.750030	+	0.661404i	$0.769961\pi$
$150$	0	0
$151$	1.59550e7	0.377117	0.188559	−	0.982062i	$-0.439618\pi$
$151$	1.59550e7	0.377117	0.188559	+	0.982062i	$0.439618\pi$
$152$	2.51060e8	5.79862
$153$	0	0
$154$	1.08359e7	0.239081
$155$	−1.13443e7	−0.244691
$156$	0	0
$157$	−3.40669e7	−0.702562	−0.351281	−	0.936270i	$-0.614254\pi$
$157$	−3.40669e7	−0.702562	−0.351281	+	0.936270i	$0.614254\pi$
$158$	1.73953e7	0.350858
$159$	0	0
$160$	3.16275e7	0.610442
$161$	6.87676e6	0.129865
$162$	0	0
$163$	−7.41885e7	−1.34178	−0.670888	−	0.741559i	$-0.734087\pi$
$163$	−7.41885e7	−1.34178	−0.670888	+	0.741559i	$0.734087\pi$
$164$	1.89081e8	3.34731
$165$	0	0
$166$	−9.49175e7	−1.61053
$167$	−1.05052e8	−1.74540	−0.872700	−	0.488258i	$-0.837633\pi$
$167$	−1.05052e8	−1.74540	−0.872700	+	0.488258i	$0.837633\pi$
$168$	0	0
$169$	9.18943e7	1.46449
$170$	3.17395e6	0.0495483
$171$	0	0
$172$	2.53715e6	0.0380186
$173$	−8.92240e7	−1.31015	−0.655074	−	0.755565i	$-0.727362\pi$
$173$	−8.92240e7	−1.31015	−0.655074	+	0.755565i	$0.727362\pi$
$174$	0	0
$175$	4.24631e7	0.598933
$176$	4.75691e7	0.657705
$177$	0	0
$178$	−2.76204e8	−3.67079
$179$	−4.09274e7	−0.533369	−0.266685	−	0.963784i	$-0.585928\pi$
$179$	−4.09274e7	−0.533369	−0.266685	+	0.963784i	$0.585928\pi$
$180$	0	0
$181$	4.48333e7	0.561986	0.280993	−	0.959710i	$-0.409336\pi$
$181$	4.48333e7	0.561986	0.280993	+	0.959710i	$0.409336\pi$
$182$	1.51380e8	1.86131
$183$	0	0
$184$	5.44757e7	0.644674
$185$	8.77997e6	0.101951
$186$	0	0
$187$	2.39679e6	0.0268031
$188$	−1.25826e8	−1.38108
$189$	0	0
$190$	−6.60984e7	−0.699123
$191$	−1.08477e8	−1.12648	−0.563239	−	0.826294i	$-0.690445\pi$
$191$	−1.08477e8	−1.12648	−0.563239	+	0.826294i	$0.690445\pi$
$192$	0	0
$193$	8.81302e6	0.0882417	0.0441209	−	0.999026i	$-0.485951\pi$
$193$	8.81302e6	0.0882417	0.0441209	+	0.999026i	$0.485951\pi$
$194$	5.55197e7	0.545935
$195$	0	0
$196$	−1.69316e8	−1.60621
$197$	−1.04354e7	−0.0972475	−0.0486238	−	0.998817i	$-0.515484\pi$
$197$	−1.04354e7	−0.0972475	−0.0486238	+	0.998817i	$0.515484\pi$
$198$	0	0
$199$	−1.41236e8	−1.27046	−0.635230	−	0.772323i	$-0.719095\pi$
$199$	−1.41236e8	−1.27046	−0.635230	+	0.772323i	$0.719095\pi$
$200$	3.36380e8	2.97320
$201$	0	0
$202$	2.94765e8	2.51620
$203$	−4.10482e7	−0.344396
$204$	0	0
$205$	−3.08101e7	−0.249778
$206$	−3.85479e8	−3.07231
$207$	0	0
$208$	6.64549e8	5.12042
$209$	−4.99139e7	−0.378189
$210$	0	0
$211$	5.31949e7	0.389835	0.194918	−	0.980820i	$-0.437556\pi$
$211$	5.31949e7	0.389835	0.194918	+	0.980820i	$0.437556\pi$
$212$	−3.23616e7	−0.233267
$213$	0	0
$214$	4.41953e8	3.08268
$215$	−413418.	−0.00283697
$216$	0	0
$217$	−1.17152e8	−0.778288
$218$	4.30052e8	2.81140
$219$	0	0
$220$	−1.63636e7	−0.103609
$221$	3.34836e7	0.208670
$222$	0	0
$223$	−1.70709e8	−1.03084	−0.515419	−	0.856938i	$-0.672364\pi$
$223$	−1.70709e8	−1.03084	−0.515419	+	0.856938i	$0.672364\pi$
$224$	3.26614e8	1.94163
$225$	0	0
$226$	6.53262e8	3.76450
$227$	1.95923e8	1.11172	0.555860	−	0.831276i	$-0.312389\pi$
$227$	1.95923e8	1.11172	0.555860	+	0.831276i	$0.312389\pi$
$228$	0	0
$229$	−2.03625e8	−1.12049	−0.560244	−	0.828328i	$-0.689293\pi$
$229$	−2.03625e8	−1.12049	−0.560244	+	0.828328i	$0.689293\pi$
$230$	−1.43422e7	−0.0777265
$231$	0	0
$232$	−3.25172e8	−1.70964
$233$	−3.21437e7	−0.166475	−0.0832376	−	0.996530i	$-0.526526\pi$
$233$	−3.21437e7	−0.166475	−0.0832376	+	0.996530i	$0.526526\pi$
$234$	0	0
$235$	2.05029e7	0.103057
$236$	4.36413e8	2.16125
$237$	0	0
$238$	3.27771e7	0.157598
$239$	−4.43634e7	−0.210200	−0.105100	−	0.994462i	$-0.533516\pi$
$239$	−4.43634e7	−0.210200	−0.105100	+	0.994462i	$0.533516\pi$
$240$	0	0
$241$	1.09153e8	0.502316	0.251158	−	0.967946i	$-0.419189\pi$
$241$	1.09153e8	0.502316	0.251158	+	0.967946i	$0.419189\pi$
$242$	4.02647e8	1.82629
$243$	0	0
$244$	4.05346e8	1.78633
$245$	2.75894e7	0.119856
$246$	0	0
$247$	−6.97305e8	−2.94431
$248$	−9.28043e8	−3.86356
$249$	0	0
$250$	−1.80654e8	−0.731234
$251$	1.36741e8	0.545810	0.272905	−	0.962041i	$-0.412016\pi$
$251$	1.36741e8	0.545810	0.272905	+	0.962041i	$0.412016\pi$
$252$	0	0
$253$	−1.08305e7	−0.0420460
$254$	−4.22072e8	−1.61610
$255$	0	0
$256$	2.89828e8	1.07969
$257$	−4.31493e8	−1.58565	−0.792825	−	0.609449i	$-0.791391\pi$
$257$	−4.31493e8	−1.58565	−0.792825	+	0.609449i	$0.791391\pi$
$258$	0	0
$259$	9.06700e7	0.324276
$260$	−2.28602e8	−0.806629
$261$	0	0
$262$	−3.21757e8	−1.10528
$263$	−2.44909e8	−0.830157	−0.415078	−	0.909786i	$-0.636246\pi$
$263$	−2.44909e8	−0.830157	−0.415078	+	0.909786i	$0.636246\pi$
$264$	0	0
$265$	5.27319e6	0.0174066
$266$	−6.82593e8	−2.22370
$267$	0	0
$268$	1.28283e9	4.07098
$269$	6.20750e8	1.94439	0.972195	−	0.234171i	$-0.0752376\pi$
$269$	6.20750e8	1.94439	0.972195	+	0.234171i	$0.0752376\pi$
$270$	0	0
$271$	8.27788e7	0.252654	0.126327	−	0.991989i	$-0.459681\pi$
$271$	8.27788e7	0.252654	0.126327	+	0.991989i	$0.459681\pi$
$272$	1.43889e8	0.433549
$273$	0	0
$274$	6.86571e8	2.01632
$275$	−6.68766e7	−0.193914
$276$	0	0
$277$	−5.28652e8	−1.49448	−0.747242	−	0.664552i	$-0.768622\pi$
$277$	−5.28652e8	−1.49448	−0.747242	+	0.664552i	$0.768622\pi$
$278$	−9.46125e8	−2.64114
$279$	0	0
$280$	−1.38500e8	−0.377047
$281$	9.61867e7	0.258608	0.129304	−	0.991605i	$-0.458726\pi$
$281$	9.61867e7	0.258608	0.129304	+	0.991605i	$0.458726\pi$
$282$	0	0
$283$	−3.04630e8	−0.798950	−0.399475	−	0.916744i	$-0.630808\pi$
$283$	−3.04630e8	−0.798950	−0.399475	+	0.916744i	$0.630808\pi$
$284$	2.18291e8	0.565486
$285$	0	0
$286$	−2.38414e8	−0.602630
$287$	−3.18173e8	−0.794468
$288$	0	0
$289$	−4.03089e8	−0.982332
$290$	8.56104e7	0.206126
$291$	0	0
$292$	−9.44883e8	−2.22095
$293$	−5.54091e8	−1.28690	−0.643450	−	0.765488i	$-0.722498\pi$
$293$	−5.54091e8	−1.28690	−0.643450	+	0.765488i	$0.722498\pi$
$294$	0	0
$295$	−7.11117e7	−0.161274
$296$	7.18261e8	1.60976
$297$	0	0
$298$	1.30456e9	2.85566
$299$	−1.51303e8	−0.327340
$300$	0	0
$301$	−4.26933e6	−0.00902354
$302$	−3.43636e8	−0.717918
$303$	0	0
$304$	−2.99654e9	−6.11734
$305$	−6.60495e7	−0.133297
$306$	0	0
$307$	6.73332e8	1.32814	0.664071	−	0.747669i	$-0.268827\pi$
$307$	6.73332e8	1.32814	0.664071	+	0.747669i	$0.268827\pi$
$308$	−1.68985e8	−0.329550
$309$	0	0
$310$	2.44333e8	0.465818
$311$	4.87910e8	0.919767	0.459884	−	0.887979i	$-0.347891\pi$
$311$	4.87910e8	0.919767	0.459884	+	0.887979i	$0.347891\pi$
$312$	0	0
$313$	−4.65266e8	−0.857622	−0.428811	−	0.903394i	$-0.641067\pi$
$313$	−4.65266e8	−0.857622	−0.428811	+	0.903394i	$0.641067\pi$
$314$	7.33731e8	1.33747
$315$	0	0
$316$	−2.71277e8	−0.483625
$317$	4.54827e7	0.0801934	0.0400967	−	0.999196i	$-0.487233\pi$
$317$	4.54827e7	0.0801934	0.0400967	+	0.999196i	$0.487233\pi$
$318$	0	0
$319$	6.46482e7	0.111504
$320$	−3.06819e8	−0.523428
$321$	0	0
$322$	−1.48111e8	−0.247225
$323$	−1.50982e8	−0.249297
$324$	0	0
$325$	−9.34277e8	−1.50968
$326$	1.59786e9	2.55434
$327$	0	0
$328$	−2.52047e9	−3.94388
$329$	2.11731e8	0.327793
$330$	0	0
$331$	5.74770e8	0.871157	0.435578	−	0.900151i	$-0.356544\pi$
$331$	5.74770e8	0.871157	0.435578	+	0.900151i	$0.356544\pi$
$332$	1.48023e9	2.21996
$333$	0	0
$334$	2.26259e9	3.32272
$335$	−2.09033e8	−0.303779
$336$	0	0
$337$	6.94857e8	0.988987	0.494494	−	0.869181i	$-0.335354\pi$
$337$	6.94857e8	0.988987	0.494494	+	0.869181i	$0.335354\pi$
$338$	−1.97921e9	−2.78794
$339$	0	0
$340$	−4.94974e7	−0.0682977
$341$	1.84507e8	0.251983
$342$	0	0
$343$	7.50378e8	1.00404
$344$	−3.38204e7	−0.0447944
$345$	0	0
$346$	1.92170e9	2.49413
$347$	−1.21676e9	−1.56334	−0.781669	−	0.623694i	$-0.785631\pi$
$347$	−1.21676e9	−1.56334	−0.781669	+	0.623694i	$0.785631\pi$
$348$	0	0
$349$	−1.31017e9	−1.64982	−0.824912	−	0.565261i	$-0.808775\pi$
$349$	−1.31017e9	−1.64982	−0.824912	+	0.565261i	$0.808775\pi$
$350$	−9.14565e8	−1.14019
$351$	0	0
$352$	−5.14396e8	−0.628635
$353$	8.00528e8	0.968646	0.484323	−	0.874889i	$-0.339066\pi$
$353$	8.00528e8	0.968646	0.484323	+	0.874889i	$0.339066\pi$
$354$	0	0
$355$	−3.55697e7	−0.0421969
$356$	4.30737e9	5.05985
$357$	0	0
$358$	8.81490e8	1.01538
$359$	−2.84701e7	−0.0324757	−0.0162378	−	0.999868i	$-0.505169\pi$
$359$	−2.84701e7	−0.0324757	−0.0162378	+	0.999868i	$0.505169\pi$
$360$	0	0
$361$	2.25037e9	2.51756
$362$	−9.65615e8	−1.06985
$363$	0	0
$364$	−2.36076e9	−2.56564
$365$	1.53965e8	0.165728
$366$	0	0
$367$	−1.47636e8	−0.155906	−0.0779529	−	0.996957i	$-0.524838\pi$
$367$	−1.47636e8	−0.155906	−0.0779529	+	0.996957i	$0.524838\pi$
$368$	−6.50198e8	−0.680108
$369$	0	0
$370$	−1.89102e8	−0.194084
$371$	5.44558e7	0.0553650
$372$	0	0
$373$	−1.17802e9	−1.17537	−0.587683	−	0.809091i	$-0.699960\pi$
$373$	−1.17802e9	−1.17537	−0.587683	+	0.809091i	$0.699960\pi$
$374$	−5.16219e7	−0.0510250
$375$	0	0
$376$	1.67727e9	1.62722
$377$	9.03147e8	0.868088
$378$	0	0
$379$	−1.50793e9	−1.42280	−0.711399	−	0.702788i	$-0.751938\pi$
$379$	−1.50793e9	−1.42280	−0.711399	+	0.702788i	$0.751938\pi$
$380$	1.03080e9	0.963676
$381$	0	0
$382$	2.33638e9	2.14448
$383$	7.42514e7	0.0675319	0.0337659	−	0.999430i	$-0.489250\pi$
$383$	7.42514e7	0.0675319	0.0337659	+	0.999430i	$0.489250\pi$
$384$	0	0
$385$	2.75355e7	0.0245912
$386$	−1.89814e8	−0.167986
$387$	0	0
$388$	−8.65824e8	−0.752521
$389$	−1.56330e9	−1.34654	−0.673271	−	0.739396i	$-0.735111\pi$
$389$	−1.56330e9	−1.34654	−0.673271	+	0.739396i	$0.735111\pi$
$390$	0	0
$391$	−3.27605e7	−0.0277161
$392$	2.25700e9	1.89247
$393$	0	0
$394$	2.24757e8	0.185130
$395$	4.42036e7	0.0360884
$396$	0	0
$397$	−3.60628e8	−0.289263	−0.144631	−	0.989486i	$-0.546200\pi$
$397$	−3.60628e8	−0.289263	−0.144631	+	0.989486i	$0.546200\pi$
$398$	3.04194e9	2.41857
$399$	0	0
$400$	−4.01488e9	−3.13663
$401$	1.19634e9	0.926507	0.463253	−	0.886226i	$-0.346682\pi$
$401$	1.19634e9	0.926507	0.463253	+	0.886226i	$0.346682\pi$
$402$	0	0
$403$	2.57759e9	1.96176
$404$	−4.59682e9	−3.46835
$405$	0	0
$406$	8.84092e8	0.655626
$407$	−1.42799e8	−0.104990
$408$	0	0
$409$	6.44935e8	0.466106	0.233053	−	0.972464i	$-0.425129\pi$
$409$	6.44935e8	0.466106	0.233053	+	0.972464i	$0.425129\pi$
$410$	6.63584e8	0.475502
$411$	0	0
$412$	6.01150e9	4.23490
$413$	−7.34365e8	−0.512964
$414$	0	0
$415$	−2.41197e8	−0.165655
$416$	−7.18620e9	−4.89410
$417$	0	0
$418$	1.07504e9	0.719959
$419$	1.87982e9	1.24844	0.624218	−	0.781250i	$-0.285418\pi$
$419$	1.87982e9	1.24844	0.624218	+	0.781250i	$0.285418\pi$
$420$	0	0
$421$	1.34590e9	0.879076	0.439538	−	0.898224i	$-0.355142\pi$
$421$	1.34590e9	0.879076	0.439538	+	0.898224i	$0.355142\pi$
$422$	−1.14571e9	−0.742130
$423$	0	0
$424$	4.31383e8	0.274841
$425$	−2.02292e8	−0.127825
$426$	0	0
$427$	−6.82088e8	−0.423978
$428$	−6.89222e9	−4.24919
$429$	0	0
$430$	8.90415e6	0.00540074
$431$	3.61149e8	0.217278	0.108639	−	0.994081i	$-0.465351\pi$
$431$	3.61149e8	0.217278	0.108639	+	0.994081i	$0.465351\pi$
$432$	0	0
$433$	−2.03487e9	−1.20456	−0.602281	−	0.798284i	$-0.705741\pi$
$433$	−2.03487e9	−1.20456	−0.602281	+	0.798284i	$0.705741\pi$
$434$	2.52321e9	1.48163
$435$	0	0
$436$	−6.70661e9	−3.87526
$437$	6.82247e8	0.391072
$438$	0	0
$439$	−2.51793e9	−1.42043	−0.710213	−	0.703987i	$-0.751401\pi$
$439$	−2.51793e9	−1.42043	−0.710213	+	0.703987i	$0.751401\pi$
$440$	2.18128e8	0.122075
$441$	0	0
$442$	−7.21166e8	−0.397244
$443$	−8.85785e8	−0.484078	−0.242039	−	0.970267i	$-0.577816\pi$
$443$	−8.85785e8	−0.484078	−0.242039	+	0.970267i	$0.577816\pi$
$444$	0	0
$445$	−7.01869e8	−0.377569
$446$	3.67672e9	1.96241
$447$	0	0
$448$	−3.16849e9	−1.66487
$449$	8.25873e8	0.430577	0.215289	−	0.976550i	$-0.430931\pi$
$449$	8.25873e8	0.430577	0.215289	+	0.976550i	$0.430931\pi$
$450$	0	0
$451$	5.01102e8	0.257222
$452$	−1.01876e10	−5.18902
$453$	0	0
$454$	−4.21978e9	−2.11638
$455$	3.84676e8	0.191450
$456$	0	0
$457$	−1.26103e9	−0.618041	−0.309021	−	0.951055i	$-0.600001\pi$
$457$	−1.26103e9	−0.618041	−0.309021	+	0.951055i	$0.600001\pi$
$458$	4.38566e9	2.13307
$459$	0	0
$460$	2.23666e8	0.107139
$461$	2.91819e9	1.38727	0.693634	−	0.720328i	$-0.256009\pi$
$461$	2.91819e9	1.38727	0.693634	+	0.720328i	$0.256009\pi$
$462$	0	0
$463$	8.59303e8	0.402358	0.201179	−	0.979554i	$-0.435523\pi$
$463$	8.59303e8	0.402358	0.201179	+	0.979554i	$0.435523\pi$
$464$	3.88111e9	1.80361
$465$	0	0
$466$	6.92307e8	0.316919
$467$	−3.45880e9	−1.57151	−0.785754	−	0.618539i	$-0.787725\pi$
$467$	−3.45880e9	−1.57151	−0.785754	+	0.618539i	$0.787725\pi$
$468$	0	0
$469$	−2.15866e9	−0.966229
$470$	−4.41589e8	−0.196189
$471$	0	0
$472$	−5.81742e9	−2.54644
$473$	6.72392e6	0.00292152
$474$	0	0
$475$	4.21278e9	1.80360
$476$	−5.11156e8	−0.217235
$477$	0	0
$478$	9.55495e8	0.400157
$479$	−2.91208e9	−1.21068	−0.605339	−	0.795968i	$-0.706962\pi$
$479$	−2.91208e9	−1.21068	−0.605339	+	0.795968i	$0.706962\pi$
$480$	0	0
$481$	−1.99493e9	−0.817373
$482$	−2.35093e9	−0.956259
$483$	0	0
$484$	−6.27924e9	−2.51738
$485$	1.41083e8	0.0561536
$486$	0	0
$487$	1.75754e9	0.689530	0.344765	−	0.938689i	$-0.387959\pi$
$487$	1.75754e9	0.689530	0.344765	+	0.938689i	$0.387959\pi$
$488$	−5.40330e9	−2.10470
$489$	0	0
$490$	−5.94217e8	−0.228170
$491$	9.74766e8	0.371634	0.185817	−	0.982584i	$-0.440507\pi$
$491$	9.74766e8	0.371634	0.185817	+	0.982584i	$0.440507\pi$
$492$	0	0
$493$	1.95551e8	0.0735015
$494$	1.50185e10	5.60508
$495$	0	0
$496$	1.10767e10	4.07592
$497$	−3.67325e8	−0.134216
$498$	0	0
$499$	−4.71158e7	−0.0169752	−0.00848760	−	0.999964i	$-0.502702\pi$
$499$	−4.71158e7	−0.0169752	−0.00848760	+	0.999964i	$0.502702\pi$
$500$	2.81727e9	1.00794
$501$	0	0
$502$	−2.94512e9	−1.03906
$503$	−5.67881e7	−0.0198962	−0.00994809	−	0.999951i	$-0.503167\pi$
$503$	−5.67881e7	−0.0198962	−0.00994809	+	0.999951i	$0.503167\pi$
$504$	0	0
$505$	7.49034e8	0.258810
$506$	2.33265e8	0.0800430
$507$	0	0
$508$	6.58217e9	2.22764
$509$	4.54481e9	1.52758	0.763789	−	0.645466i	$-0.223337\pi$
$509$	4.54481e9	1.52758	0.763789	+	0.645466i	$0.223337\pi$
$510$	0	0
$511$	1.58998e9	0.527132
$512$	−2.55330e8	−0.0840730
$513$	0	0
$514$	9.29345e9	3.01860
$515$	−9.79550e8	−0.316010
$516$	0	0
$517$	−3.33463e8	−0.106128
$518$	−1.95284e9	−0.617324
$519$	0	0
$520$	3.04729e9	0.950390
$521$	1.70629e7	0.00528593	0.00264297	−	0.999997i	$-0.499159\pi$
$521$	1.70629e7	0.00528593	0.00264297	+	0.999997i	$0.499159\pi$
$522$	0	0
$523$	−1.82834e8	−0.0558856	−0.0279428	−	0.999610i	$-0.508896\pi$
$523$	−1.82834e8	−0.0558856	−0.0279428	+	0.999610i	$0.508896\pi$
$524$	5.01776e9	1.52353
$525$	0	0
$526$	5.27483e9	1.58037
$527$	5.58105e8	0.166104
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−1.13573e8	−0.0331369
$531$	0	0
$532$	1.06450e10	3.06516
$533$	7.00048e9	2.00255
$534$	0	0
$535$	1.12306e9	0.317077
$536$	−1.71003e10	−4.79653
$537$	0	0
$538$	−1.33696e10	−3.70154
$539$	−4.48720e8	−0.123428
$540$	0	0
$541$	−1.96073e9	−0.532387	−0.266194	−	0.963920i	$-0.585766\pi$
$541$	−1.96073e9	−0.532387	−0.266194	+	0.963920i	$0.585766\pi$
$542$	−1.78288e9	−0.480978
$543$	0	0
$544$	−1.55597e9	−0.414386
$545$	1.09282e9	0.289174
$546$	0	0
$547$	−2.88969e9	−0.754910	−0.377455	−	0.926028i	$-0.623201\pi$
$547$	−2.88969e9	−0.754910	−0.377455	+	0.926028i	$0.623201\pi$
$548$	−1.07070e10	−2.77930
$549$	0	0
$550$	1.44038e9	0.369154
$551$	−4.07241e9	−1.03710
$552$	0	0
$553$	4.56486e8	0.114786
$554$	1.13861e10	2.84505
$555$	0	0
$556$	1.47547e10	3.64057
$557$	−4.50918e9	−1.10562	−0.552808	−	0.833309i	$-0.686444\pi$
$557$	−4.50918e9	−1.10562	−0.552808	+	0.833309i	$0.686444\pi$
$558$	0	0
$559$	9.39344e7	0.0227449
$560$	1.65307e9	0.397772
$561$	0	0
$562$	−2.07166e9	−0.492313
$563$	2.34598e9	0.554046	0.277023	−	0.960863i	$-0.410652\pi$
$563$	2.34598e9	0.554046	0.277023	+	0.960863i	$0.410652\pi$
$564$	0	0
$565$	1.66002e9	0.387208
$566$	6.56108e9	1.52096
$567$	0	0
$568$	−2.90984e9	−0.666270
$569$	−5.31334e9	−1.20913	−0.604567	−	0.796554i	$-0.706654\pi$
$569$	−5.31334e9	−1.20913	−0.604567	+	0.796554i	$0.706654\pi$
$570$	0	0
$571$	−6.82398e9	−1.53395	−0.766975	−	0.641677i	$-0.778239\pi$
$571$	−6.82398e9	−1.53395	−0.766975	+	0.641677i	$0.778239\pi$
$572$	3.71804e9	0.830669
$573$	0	0
$574$	6.85278e9	1.51243
$575$	9.14101e8	0.200520
$576$	0	0
$577$	2.32589e9	0.504050	0.252025	−	0.967721i	$-0.418903\pi$
$577$	2.32589e9	0.504050	0.252025	+	0.967721i	$0.418903\pi$
$578$	8.68169e9	1.87006
$579$	0	0
$580$	−1.33509e9	−0.284126
$581$	−2.49083e9	−0.526898
$582$	0	0
$583$	−8.57644e7	−0.0179253
$584$	1.25954e10	2.61677
$585$	0	0
$586$	1.19340e10	2.44987
$587$	2.10001e8	0.0428536	0.0214268	−	0.999770i	$-0.493179\pi$
$587$	2.10001e8	0.0428536	0.0214268	+	0.999770i	$0.493179\pi$
$588$	0	0
$589$	−1.16227e10	−2.34371
$590$	1.53160e9	0.307017
$591$	0	0
$592$	−8.57285e9	−1.69824
$593$	6.51352e7	0.0128270	0.00641348	−	0.999979i	$-0.497959\pi$
$593$	6.51352e7	0.0128270	0.00641348	+	0.999979i	$0.497959\pi$
$594$	0	0
$595$	8.32908e7	0.0162102
$596$	−2.03445e10	−3.93627
$597$	0	0
$598$	3.25876e9	0.623157
$599$	2.77059e7	0.00526718	0.00263359	−	0.999997i	$-0.499162\pi$
$599$	2.77059e7	0.00526718	0.00263359	+	0.999997i	$0.499162\pi$
$600$	0	0
$601$	6.25558e8	0.117546	0.0587729	−	0.998271i	$-0.481281\pi$
$601$	6.25558e8	0.117546	0.0587729	+	0.998271i	$0.481281\pi$
$602$	9.19525e7	0.0171781
$603$	0	0
$604$	5.35897e9	0.989583
$605$	1.02318e9	0.187848
$606$	0	0
$607$	5.77739e9	1.04851	0.524253	−	0.851562i	$-0.324344\pi$
$607$	5.77739e9	1.04851	0.524253	+	0.851562i	$0.324344\pi$
$608$	3.24036e10	5.84696
$609$	0	0
$610$	1.42257e9	0.253757
$611$	−4.65854e9	−0.826239
$612$	0	0
$613$	−3.43198e8	−0.0601774	−0.0300887	−	0.999547i	$-0.509579\pi$
$613$	−3.43198e8	−0.0601774	−0.0300887	+	0.999547i	$0.509579\pi$
$614$	−1.45022e10	−2.52838
$615$	0	0
$616$	2.25259e9	0.388284
$617$	−6.69767e9	−1.14796	−0.573978	−	0.818871i	$-0.694601\pi$
$617$	−6.69767e9	−1.14796	−0.573978	+	0.818871i	$0.694601\pi$
$618$	0	0
$619$	−9.34901e9	−1.58434	−0.792170	−	0.610301i	$-0.791049\pi$
$619$	−9.34901e9	−1.58434	−0.792170	+	0.610301i	$0.791049\pi$
$620$	−3.81035e9	−0.642087
$621$	0	0
$622$	−1.05085e10	−1.75096
$623$	−7.24814e9	−1.20093
$624$	0	0
$625$	5.41043e9	0.886446
$626$	1.00209e10	1.63266
$627$	0	0
$628$	−1.14425e10	−1.84357
$629$	−4.31947e8	−0.0692075
$630$	0	0
$631$	1.13983e10	1.80608	0.903038	−	0.429561i	$-0.141332\pi$
$631$	1.13983e10	1.80608	0.903038	+	0.429561i	$0.141332\pi$
$632$	3.61615e9	0.569819
$633$	0	0
$634$	−9.79601e8	−0.152664
$635$	−1.07254e9	−0.166228
$636$	0	0
$637$	−6.26869e9	−0.960924
$638$	−1.39239e9	−0.212270
$639$	0	0
$640$	2.55992e9	0.386007
$641$	1.05373e10	1.58025	0.790124	−	0.612947i	$-0.210016\pi$
$641$	1.05373e10	1.58025	0.790124	+	0.612947i	$0.210016\pi$
$642$	0	0
$643$	9.34452e9	1.38618	0.693089	−	0.720852i	$-0.256249\pi$
$643$	9.34452e9	1.38618	0.693089	+	0.720852i	$0.256249\pi$
$644$	2.30978e9	0.340776
$645$	0	0
$646$	3.25184e9	0.474586
$647$	6.73299e9	0.977334	0.488667	−	0.872471i	$-0.337483\pi$
$647$	6.73299e9	0.977334	0.488667	+	0.872471i	$0.337483\pi$
$648$	0	0
$649$	1.15658e9	0.166080
$650$	2.01224e10	2.87397
$651$	0	0
$652$	−2.49185e10	−3.52092
$653$	−2.89741e9	−0.407205	−0.203603	−	0.979054i	$-0.565265\pi$
$653$	−2.89741e9	−0.407205	−0.203603	+	0.979054i	$0.565265\pi$
$654$	0	0
$655$	−8.17625e8	−0.113687
$656$	3.00833e10	4.16065
$657$	0	0
$658$	−4.56025e9	−0.624020
$659$	−4.09714e9	−0.557675	−0.278838	−	0.960338i	$-0.589949\pi$
$659$	−4.09714e9	−0.557675	−0.278838	+	0.960338i	$0.589949\pi$
$660$	0	0
$661$	1.19350e10	1.60738	0.803691	−	0.595047i	$-0.202867\pi$
$661$	1.19350e10	1.60738	0.803691	+	0.595047i	$0.202867\pi$
$662$	−1.23793e10	−1.65842
$663$	0	0
$664$	−1.97316e10	−2.61561
$665$	−1.73456e9	−0.228724
$666$	0	0
$667$	−8.83643e8	−0.115302
$668$	−3.52849e10	−4.58005
$669$	0	0
$670$	4.50213e9	0.578304
$671$	1.07424e9	0.137270
$672$	0	0
$673$	−9.75181e9	−1.23320	−0.616599	−	0.787278i	$-0.711490\pi$
$673$	−9.75181e9	−1.23320	−0.616599	+	0.787278i	$0.711490\pi$
$674$	−1.49658e10	−1.88273
$675$	0	0
$676$	3.08656e10	3.84292
$677$	1.09587e10	1.35737	0.678684	−	0.734430i	$-0.262551\pi$
$677$	1.09587e10	1.35737	0.678684	+	0.734430i	$0.262551\pi$
$678$	0	0
$679$	1.45695e9	0.178608
$680$	6.59805e8	0.0804701
$681$	0	0
$682$	−3.97389e9	−0.479701
$683$	5.39763e9	0.648233	0.324116	−	0.946017i	$-0.394933\pi$
$683$	5.39763e9	0.648233	0.324116	+	0.946017i	$0.394933\pi$
$684$	0	0
$685$	1.74466e9	0.207393
$686$	−1.61616e10	−1.91139
$687$	0	0
$688$	4.03665e8	0.0472566
$689$	−1.19814e9	−0.139554
$690$	0	0
$691$	−1.91440e9	−0.220729	−0.110364	−	0.993891i	$-0.535202\pi$
$691$	−1.91440e9	−0.220729	−0.110364	+	0.993891i	$0.535202\pi$
$692$	−2.99687e10	−3.43792
$693$	0	0
$694$	2.62065e10	2.97612
$695$	−2.40422e9	−0.271661
$696$	0	0
$697$	1.51576e9	0.169557
$698$	2.82183e10	3.14077
$699$	0	0
$700$	1.42625e10	1.57164
$701$	−1.00810e10	−1.10532	−0.552661	−	0.833406i	$-0.686388\pi$
$701$	−1.00810e10	−1.10532	−0.552661	+	0.833406i	$0.686388\pi$
$702$	0	0
$703$	8.99542e9	0.976512
$704$	4.99017e9	0.539027
$705$	0	0
$706$	−1.72417e10	−1.84401
$707$	7.73521e9	0.823198
$708$	0	0
$709$	−1.08851e9	−0.114702	−0.0573509	−	0.998354i	$-0.518265\pi$
$709$	−1.08851e9	−0.114702	−0.0573509	+	0.998354i	$0.518265\pi$
$710$	7.66097e8	0.0803303
$711$	0	0
$712$	−5.74177e10	−5.96164
$713$	−2.52193e9	−0.260567
$714$	0	0
$715$	−6.05840e8	−0.0619850
$716$	−1.37467e10	−1.39960
$717$	0	0
$718$	6.13186e8	0.0618240
$719$	−1.83367e10	−1.83980	−0.919899	−	0.392156i	$-0.871729\pi$
$719$	−1.83367e10	−1.83980	−0.919899	+	0.392156i	$0.871729\pi$
$720$	0	0
$721$	−1.01157e10	−1.00513
$722$	−4.84683e10	−4.79267
$723$	0	0
$724$	1.50587e10	1.47469
$725$	−5.45638e9	−0.531767
$726$	0	0
$727$	1.27508e9	0.123074	0.0615369	−	0.998105i	$-0.480400\pi$
$727$	1.27508e9	0.123074	0.0615369	+	0.998105i	$0.480400\pi$
$728$	3.14691e10	3.02290
$729$	0	0
$730$	−3.31608e9	−0.315497
$731$	2.03389e7	0.00192582
$732$	0	0
$733$	−1.44780e10	−1.35782	−0.678912	−	0.734220i	$-0.737548\pi$
$733$	−1.44780e10	−1.35782	−0.678912	+	0.734220i	$0.737548\pi$
$734$	3.17978e9	0.296798
$735$	0	0
$736$	7.03102e9	0.650049
$737$	3.39976e9	0.312832
$738$	0	0
$739$	−1.82585e9	−0.166422	−0.0832109	−	0.996532i	$-0.526518\pi$
$739$	−1.82585e9	−0.166422	−0.0832109	+	0.996532i	$0.526518\pi$
$740$	2.94903e9	0.267527
$741$	0	0
$742$	−1.17286e9	−0.105398
$743$	1.29792e9	0.116088	0.0580439	−	0.998314i	$-0.481514\pi$
$743$	1.29792e9	0.116088	0.0580439	+	0.998314i	$0.481514\pi$
$744$	0	0
$745$	3.31505e9	0.293727
$746$	2.53722e10	2.23754
$747$	0	0
$748$	8.05037e8	0.0703332
$749$	1.15977e10	1.00853
$750$	0	0
$751$	−1.52504e10	−1.31383	−0.656917	−	0.753963i	$-0.728140\pi$
$751$	−1.52504e10	−1.31383	−0.656917	+	0.753963i	$0.728140\pi$
$752$	−2.00192e10	−1.71666
$753$	0	0
$754$	−1.94519e10	−1.65258
$755$	−8.73224e8	−0.0738433
$756$	0	0
$757$	−1.60955e9	−0.134856	−0.0674280	−	0.997724i	$-0.521479\pi$
$757$	−1.60955e9	−0.134856	−0.0674280	+	0.997724i	$0.521479\pi$
$758$	3.24776e10	2.70858
$759$	0	0
$760$	−1.37406e10	−1.13543
$761$	1.60947e9	0.132384	0.0661920	−	0.997807i	$-0.478915\pi$
$761$	1.60947e9	0.132384	0.0661920	+	0.997807i	$0.478915\pi$
$762$	0	0
$763$	1.12854e10	0.919775
$764$	−3.64356e10	−2.95596
$765$	0	0
$766$	−1.59922e9	−0.128560
$767$	1.61576e10	1.29298
$768$	0	0
$769$	−1.07804e10	−0.854855	−0.427428	−	0.904050i	$-0.640580\pi$
$769$	−1.07804e10	−0.854855	−0.427428	+	0.904050i	$0.640580\pi$
$770$	−5.93057e8	−0.0468144
$771$	0	0
$772$	2.96013e9	0.231553
$773$	2.94937e9	0.229668	0.114834	−	0.993385i	$-0.463366\pi$
$773$	2.94937e9	0.229668	0.114834	+	0.993385i	$0.463366\pi$
$774$	0	0
$775$	−1.55726e10	−1.20172
$776$	1.15415e10	0.886638
$777$	0	0
$778$	3.36703e10	2.56341
$779$	−3.15661e10	−2.39243
$780$	0	0
$781$	5.78514e8	0.0434545
$782$	7.05593e8	0.0527631
$783$	0	0
$784$	−2.69385e10	−1.99649
$785$	1.86450e9	0.137569
$786$	0	0
$787$	−1.46253e10	−1.06953	−0.534765	−	0.845001i	$-0.679600\pi$
$787$	−1.46253e10	−1.06953	−0.534765	+	0.845001i	$0.679600\pi$
$788$	−3.50507e9	−0.255185
$789$	0	0
$790$	−9.52052e8	−0.0687014
$791$	1.71429e10	1.23159
$792$	0	0
$793$	1.50074e10	1.06868
$794$	7.76717e9	0.550669
$795$	0	0
$796$	−4.74387e10	−3.33378
$797$	−4.11710e9	−0.288063	−0.144031	−	0.989573i	$-0.546007\pi$
$797$	−4.11710e9	−0.288063	−0.144031	+	0.989573i	$0.546007\pi$
$798$	0	0
$799$	−1.00868e9	−0.0699582
$800$	4.34156e10	2.99799
$801$	0	0
$802$	−2.57666e10	−1.76379
$803$	−2.50412e9	−0.170668
$804$	0	0
$805$	−3.76369e8	−0.0254289
$806$	−5.55159e10	−3.73461
$807$	0	0
$808$	6.12761e10	4.08650
$809$	9.51685e9	0.631936	0.315968	−	0.948770i	$-0.397671\pi$
$809$	9.51685e9	0.631936	0.315968	+	0.948770i	$0.397671\pi$
$810$	0	0
$811$	−1.01219e10	−0.666327	−0.333164	−	0.942869i	$-0.608116\pi$
$811$	−1.01219e10	−0.666327	−0.333164	+	0.942869i	$0.608116\pi$
$812$	−1.37873e10	−0.903719
$813$	0	0
$814$	3.07560e9	0.199869
$815$	4.06037e9	0.262733
$816$	0	0
$817$	−4.23563e8	−0.0271732
$818$	−1.38905e10	−0.887325
$819$	0	0
$820$	−1.03485e10	−0.655436
$821$	−2.18569e10	−1.37844	−0.689218	−	0.724554i	$-0.742046\pi$
$821$	−2.18569e10	−1.37844	−0.689218	+	0.724554i	$0.742046\pi$
$822$	0	0
$823$	−3.86655e9	−0.241782	−0.120891	−	0.992666i	$-0.538575\pi$
$823$	−3.86655e9	−0.241782	−0.120891	+	0.992666i	$0.538575\pi$
$824$	−8.01338e10	−4.98966
$825$	0	0
$826$	1.58167e10	0.976529
$827$	−1.12726e10	−0.693035	−0.346518	−	0.938044i	$-0.612636\pi$
$827$	−1.12726e10	−0.693035	−0.346518	+	0.938044i	$0.612636\pi$
$828$	0	0
$829$	−1.59797e10	−0.974154	−0.487077	−	0.873359i	$-0.661937\pi$
$829$	−1.59797e10	−0.974154	−0.487077	+	0.873359i	$0.661937\pi$
$830$	5.19489e9	0.315357
$831$	0	0
$832$	6.97135e10	4.19648
$833$	−1.35731e9	−0.0813620
$834$	0	0
$835$	5.74953e9	0.341766
$836$	−1.67651e10	−0.992396
$837$	0	0
$838$	−4.04873e10	−2.37665
$839$	−2.40926e9	−0.140837	−0.0704186	−	0.997518i	$-0.522433\pi$
$839$	−2.40926e9	−0.140837	−0.0704186	+	0.997518i	$0.522433\pi$
$840$	0	0
$841$	−1.19753e10	−0.694226
$842$	−2.89879e10	−1.67350
$843$	0	0
$844$	1.78672e10	1.02296
$845$	−5.02943e9	−0.286761
$846$	0	0
$847$	1.05663e10	0.597488
$848$	−5.14880e9	−0.289948
$849$	0	0
$850$	4.35694e9	0.243341
$851$	1.95185e9	0.108566
$852$	0	0
$853$	1.71764e10	0.947570	0.473785	−	0.880640i	$-0.342887\pi$
$853$	1.71764e10	0.947570	0.473785	+	0.880640i	$0.342887\pi$
$854$	1.46907e10	0.807126
$855$	0	0
$856$	9.18738e10	5.00649
$857$	4.41092e9	0.239385	0.119692	−	0.992811i	$-0.461809\pi$
$857$	4.41092e9	0.239385	0.119692	+	0.992811i	$0.461809\pi$
$858$	0	0
$859$	2.39855e10	1.29114	0.645570	−	0.763701i	$-0.276620\pi$
$859$	2.39855e10	1.29114	0.645570	+	0.763701i	$0.276620\pi$
$860$	−1.38859e8	−0.00744441
$861$	0	0
$862$	−7.77839e9	−0.413632
$863$	1.76729e10	0.935985	0.467993	−	0.883732i	$-0.344977\pi$
$863$	1.76729e10	0.935985	0.467993	+	0.883732i	$0.344977\pi$
$864$	0	0
$865$	4.88327e9	0.256540
$866$	4.38268e10	2.29312
$867$	0	0
$868$	−3.93491e10	−2.04228
$869$	−7.18937e8	−0.0371639
$870$	0	0
$871$	4.74952e10	2.43549
$872$	8.93997e10	4.56592
$873$	0	0
$874$	−1.46942e10	−0.744483
$875$	−4.74071e9	−0.239230
$876$	0	0
$877$	−1.28667e10	−0.644122	−0.322061	−	0.946719i	$-0.604376\pi$
$877$	−1.28667e10	−0.644122	−0.322061	+	0.946719i	$0.604376\pi$
$878$	5.42310e10	2.70407
$879$	0	0
$880$	−2.60348e9	−0.128785
$881$	4.58163e8	0.0225738	0.0112869	−	0.999936i	$-0.496407\pi$
$881$	4.58163e8	0.0225738	0.0112869	+	0.999936i	$0.496407\pi$
$882$	0	0
$883$	−3.51665e9	−0.171897	−0.0859483	−	0.996300i	$-0.527392\pi$
$883$	−3.51665e9	−0.171897	−0.0859483	+	0.996300i	$0.527392\pi$
$884$	1.12465e10	0.547564
$885$	0	0
$886$	1.90780e10	0.921539
$887$	8.81338e9	0.424043	0.212021	−	0.977265i	$-0.431995\pi$
$887$	8.81338e9	0.424043	0.212021	+	0.977265i	$0.431995\pi$
$888$	0	0
$889$	−1.10760e10	−0.528722
$890$	1.51168e10	0.718778
$891$	0	0
$892$	−5.73381e10	−2.70499
$893$	2.10060e10	0.987104
$894$	0	0
$895$	2.23998e9	0.104439
$896$	2.64360e10	1.22777
$897$	0	0
$898$	−1.77876e10	−0.819690
$899$	1.50537e10	0.691009
$900$	0	0
$901$	−2.59424e8	−0.0118161
$902$	−1.07927e10	−0.489674
$903$	0	0
$904$	1.35801e11	6.11383
$905$	−2.45375e9	−0.110042
$906$	0	0
$907$	2.98196e10	1.32701	0.663507	−	0.748170i	$-0.269067\pi$
$907$	2.98196e10	1.32701	0.663507	+	0.748170i	$0.269067\pi$
$908$	6.58070e10	2.91724
$909$	0	0
$910$	−8.28511e9	−0.364463
$911$	1.93274e10	0.846951	0.423475	−	0.905908i	$-0.360810\pi$
$911$	1.93274e10	0.846951	0.423475	+	0.905908i	$0.360810\pi$
$912$	0	0
$913$	3.92289e9	0.170592
$914$	2.71599e10	1.17656
$915$	0	0
$916$	−6.83939e10	−2.94024
$917$	−8.44354e9	−0.361603
$918$	0	0
$919$	1.92553e9	0.0818361	0.0409180	−	0.999163i	$-0.486972\pi$
$919$	1.92553e9	0.0818361	0.0409180	+	0.999163i	$0.486972\pi$
$920$	−2.98148e9	−0.126234
$921$	0	0
$922$	−6.28517e10	−2.64094
$923$	8.08193e9	0.338306
$924$	0	0
$925$	1.20524e10	0.500701
$926$	−1.85076e10	−0.765969
$927$	0	0
$928$	−4.19690e10	−1.72389
$929$	2.99271e10	1.22464	0.612321	−	0.790609i	$-0.290236\pi$
$929$	2.99271e10	1.22464	0.612321	+	0.790609i	$0.290236\pi$
$930$	0	0
$931$	2.82664e10	1.14801
$932$	−1.07965e10	−0.436843
$933$	0	0
$934$	7.44954e10	2.99168
$935$	−1.31178e8	−0.00524831
$936$	0	0
$937$	−6.02696e9	−0.239337	−0.119668	−	0.992814i	$-0.538183\pi$
$937$	−6.02696e9	−0.239337	−0.119668	+	0.992814i	$0.538183\pi$
$938$	4.64931e10	1.83941
$939$	0	0
$940$	6.88653e9	0.270429
$941$	−1.83486e10	−0.717860	−0.358930	−	0.933364i	$-0.616858\pi$
$941$	−1.83486e10	−0.717860	−0.358930	+	0.933364i	$0.616858\pi$
$942$	0	0
$943$	−6.84930e9	−0.265984
$944$	6.94342e10	2.68641
$945$	0	0
$946$	−1.44819e8	−0.00556170
$947$	−1.62700e10	−0.622533	−0.311267	−	0.950323i	$-0.600753\pi$
$947$	−1.62700e10	−0.622533	−0.311267	+	0.950323i	$0.600753\pi$
$948$	0	0
$949$	−3.49830e10	−1.32870
$950$	−9.07345e10	−3.43352
$951$	0	0
$952$	6.81375e9	0.255951
$953$	−4.87166e10	−1.82327	−0.911636	−	0.410998i	$-0.865180\pi$
$953$	−4.87166e10	−1.82327	−0.911636	+	0.410998i	$0.865180\pi$
$954$	0	0
$955$	5.93703e9	0.220576
$956$	−1.49008e10	−0.551580
$957$	0	0
$958$	6.27200e10	2.30477
$959$	1.80170e10	0.659656
$960$	0	0
$961$	1.54507e10	0.561587
$962$	4.29667e10	1.55603
$963$	0	0
$964$	3.66625e10	1.31811
$965$	−4.82341e8	−0.0172786
$966$	0	0
$967$	3.96535e10	1.41023	0.705113	−	0.709095i	$-0.250896\pi$
$967$	3.96535e10	1.41023	0.705113	+	0.709095i	$0.250896\pi$
$968$	8.37028e10	2.96603
$969$	0	0
$970$	−3.03862e9	−0.106900
$971$	−4.46486e10	−1.56509	−0.782547	−	0.622591i	$-0.786080\pi$
$971$	−4.46486e10	−1.56509	−0.782547	+	0.622591i	$0.786080\pi$
$972$	0	0
$973$	−2.48282e10	−0.864073
$974$	−3.78536e10	−1.31266
$975$	0	0
$976$	6.44915e10	2.22038
$977$	−2.37557e10	−0.814962	−0.407481	−	0.913214i	$-0.633593\pi$
$977$	−2.37557e10	−0.814962	−0.407481	+	0.913214i	$0.633593\pi$
$978$	0	0
$979$	1.14154e10	0.388821
$980$	9.26675e9	0.314511
$981$	0	0
$982$	−2.09944e10	−0.707479
$983$	−2.14111e10	−0.718955	−0.359477	−	0.933154i	$-0.617045\pi$
$983$	−2.14111e10	−0.718955	−0.359477	+	0.933154i	$0.617045\pi$
$984$	0	0
$985$	5.71137e8	0.0190420
$986$	−4.21176e9	−0.139925
$987$	0	0
$988$	−2.34212e11	−7.72609
$989$	−9.19058e7	−0.00302104
$990$	0	0
$991$	1.26347e10	0.412387	0.206194	−	0.978511i	$-0.433892\pi$
$991$	1.26347e10	0.412387	0.206194	+	0.978511i	$0.433892\pi$
$992$	−1.19780e11	−3.89577
$993$	0	0
$994$	7.91141e9	0.255506
$995$	7.72994e9	0.248769
$996$	0	0
$997$	−6.85313e9	−0.219006	−0.109503	−	0.993986i	$-0.534926\pi$
$997$	−6.85313e9	−0.219006	−0.109503	+	0.993986i	$0.534926\pi$
$998$	1.01478e9	0.0323157
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.e.1.1		8
3.2	odd	2		69.8.a.d.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.d.1.8	✓	8	3.2	odd	2
207.8.a.e.1.1		8	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)

\(f(q)\)	\(=\)	\(q-21.5379 q^{2} +335.881 q^{4} -54.7305 q^{5} -565.198 q^{7} -4477.33 q^{8} +O(q^{10})\)	\(q-21.5379 q^{2} +335.881 q^{4} -54.7305 q^{5} -565.198 q^{7} -4477.33 q^{8} +1178.78 q^{10} +890.150 q^{11} +12435.5 q^{13} +12173.2 q^{14} +53439.5 q^{16} +2692.57 q^{17} -56073.6 q^{19} -18383.0 q^{20} -19172.0 q^{22} -12167.0 q^{23} -75129.6 q^{25} -267836. q^{26} -189839. q^{28} +72626.2 q^{29} +207276. q^{31} -577876. q^{32} -57992.3 q^{34} +30933.6 q^{35} -160422. q^{37} +1.20771e6 q^{38} +245047. q^{40} +562941. q^{41} +7553.70 q^{43} +298985. q^{44} +262052. q^{46} -374615. q^{47} -504095. q^{49} +1.61813e6 q^{50} +4.17687e6 q^{52} -96348.3 q^{53} -48718.4 q^{55} +2.53058e6 q^{56} -1.56422e6 q^{58} +1.29931e6 q^{59} +1.20681e6 q^{61} -4.46429e6 q^{62} +5.60599e6 q^{64} -680604. q^{65} +3.81931e6 q^{67} +904384. q^{68} -666244. q^{70} +649906. q^{71} -2.81315e6 q^{73} +3.45515e6 q^{74} -1.88341e7 q^{76} -503111. q^{77} -807658. q^{79} -2.92477e6 q^{80} -1.21246e7 q^{82} +4.40700e6 q^{83} -147366. q^{85} -162691. q^{86} -3.98549e6 q^{88} +1.28241e7 q^{89} -7.02854e6 q^{91} -4.08667e6 q^{92} +8.06842e6 q^{94} +3.06894e6 q^{95} -2.57777e6 q^{97} +1.08571e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8}+O(q^{10}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8	\( 8 q - 24 q^{2} + 562 q^{4} - 378 q^{5} + 126 q^{7} - 4188 q^{8} + 11720 q^{10} - 6932 q^{11} + 12404 q^{13} - 30222 q^{14} + 27058 q^{16} - 24434 q^{17} - 14682 q^{19} + 3760 q^{20} + 36294 q^{22} - 97336 q^{23} + 144644 q^{25} - 325840 q^{26} - 21566 q^{28} - 255356 q^{29} + 450764 q^{31} - 647588 q^{32} + 191822 q^{34} - 1022616 q^{35} + 206240 q^{37} - 737372 q^{38} + 590028 q^{40} - 1053344 q^{41} + 1587806 q^{43} - 589366 q^{44} + 292008 q^{46} - 443336 q^{47} + 1944828 q^{49} + 1556112 q^{50} - 614236 q^{52} + 375530 q^{53} + 407792 q^{55} + 1316922 q^{56} - 1413384 q^{58} - 624008 q^{59} - 2005568 q^{61} + 3908272 q^{62} - 5082310 q^{64} - 646124 q^{65} - 2712286 q^{67} + 2289698 q^{68} - 16499468 q^{70} + 6287176 q^{71} - 10358312 q^{73} + 2000150 q^{74} - 25107464 q^{76} + 2156840 q^{77} - 8800574 q^{79} - 2384344 q^{80} - 31799800 q^{82} - 384948 q^{83} - 17826684 q^{85} + 11563928 q^{86} - 25202782 q^{88} + 3445530 q^{89} - 16316740 q^{91} - 6837854 q^{92} - 24237616 q^{94} - 26164288 q^{95} - 28043764 q^{97} + 9998012 q^{98}+O(q^{100}) \) 8 * q - 24 * q^2 + 562 * q^4 - 378 * q^5 + 126 * q^7 - 4188 * q^8 + 11720 * q^10 - 6932 * q^11 + 12404 * q^13 - 30222 * q^14 + 27058 * q^16 - 24434 * q^17 - 14682 * q^19 + 3760 * q^20 + 36294 * q^22 - 97336 * q^23 + 144644 * q^25 - 325840 * q^26 - 21566 * q^28 - 255356 * q^29 + 450764 * q^31 - 647588 * q^32 + 191822 * q^34 - 1022616 * q^35 + 206240 * q^37 - 737372 * q^38 + 590028 * q^40 - 1053344 * q^41 + 1587806 * q^43 - 589366 * q^44 + 292008 * q^46 - 443336 * q^47 + 1944828 * q^49 + 1556112 * q^50 - 614236 * q^52 + 375530 * q^53 + 407792 * q^55 + 1316922 * q^56 - 1413384 * q^58 - 624008 * q^59 - 2005568 * q^61 + 3908272 * q^62 - 5082310 * q^64 - 646124 * q^65 - 2712286 * q^67 + 2289698 * q^68 - 16499468 * q^70 + 6287176 * q^71 - 10358312 * q^73 + 2000150 * q^74 - 25107464 * q^76 + 2156840 * q^77 - 8800574 * q^79 - 2384344 * q^80 - 31799800 * q^82 - 384948 * q^83 - 17826684 * q^85 + 11563928 * q^86 - 25202782 * q^88 + 3445530 * q^89 - 16316740 * q^91 - 6837854 * q^92 - 24237616 * q^94 - 26164288 * q^95 - 28043764 * q^97 + 9998012 * q^98

Introduction

L-functions

Modular forms

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Database

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