LMFDB - Embedded newform 207.12.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,12,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, 12, names="a")

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

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 12 $
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:	$159.047038376$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} + \cdots - 51\!\cdots\!56 $ x^11 - x^10 - 16849x^9 - 2148x^8 + 97176782x^7 + 169360278x^6 - 226650696110x^5 - 940430954112x^4 + 180101325169073x^3 + 1690347715497299x^2 - 9620508603737857*x - 51108001263703556
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$46.0566$ 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)

$f(q)$	$=$	$q+43.0566 q^{2} -194.133 q^{4} +11277.9 q^{5} -9281.65 q^{7} -96538.5 q^{8} +O(q^{10})$	\(q+43.0566 q^{2} -194.133 q^{4} +11277.9 q^{5} -9281.65 q^{7} -96538.5 q^{8} +485588. q^{10} +775928. q^{11} -1.35775e6 q^{13} -399636. q^{14} -3.75903e6 q^{16} -5.04724e6 q^{17} +1.10360e7 q^{19} -2.18942e6 q^{20} +3.34088e7 q^{22} +6.43634e6 q^{23} +7.83629e7 q^{25} -5.84601e7 q^{26} +1.80188e6 q^{28} +3.22957e7 q^{29} +2.54882e8 q^{31} +3.58600e7 q^{32} -2.17317e8 q^{34} -1.04678e8 q^{35} -3.12485e8 q^{37} +4.75174e8 q^{38} -1.08875e9 q^{40} -8.65298e8 q^{41} +7.75261e8 q^{43} -1.50634e8 q^{44} +2.77127e8 q^{46} +2.34472e9 q^{47} -1.89118e9 q^{49} +3.37404e9 q^{50} +2.63585e8 q^{52} +4.77808e9 q^{53} +8.75084e9 q^{55} +8.96037e8 q^{56} +1.39054e9 q^{58} +1.57779e9 q^{59} -9.63652e9 q^{61} +1.09743e10 q^{62} +9.24250e9 q^{64} -1.53126e10 q^{65} +1.06227e10 q^{67} +9.79838e8 q^{68} -4.50705e9 q^{70} -1.06427e10 q^{71} +1.53965e9 q^{73} -1.34545e10 q^{74} -2.14246e9 q^{76} -7.20189e9 q^{77} +2.42947e10 q^{79} -4.23940e10 q^{80} -3.72567e10 q^{82} -1.34063e10 q^{83} -5.69222e10 q^{85} +3.33801e10 q^{86} -7.49070e10 q^{88} +4.54047e10 q^{89} +1.26022e10 q^{91} -1.24951e9 q^{92} +1.00956e11 q^{94} +1.24463e11 q^{95} -9.36141e10 q^{97} -8.14276e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 32 q^{2} + 11264 q^{4} - 1034 q^{5} + 159584 q^{7} - 115497 q^{8}+O(q^{10}) $ 11 * q - 32 * q^2 + 11264 * q^4 - 1034 * q^5 + 159584 * q^7 - 115497 * q^8	\( 11 q - 32 q^{2} + 11264 q^{4} - 1034 q^{5} + 159584 q^{7} - 115497 q^{8} - 627650 q^{10} + 771396 q^{11} + 3433434 q^{13} - 4585896 q^{14} + 18802384 q^{16} - 29035398 q^{17} + 21398428 q^{19} - 72466260 q^{20} + 100463524 q^{22} + 70799773 q^{23} + 233562509 q^{25} - 328796191 q^{26} + 499445210 q^{28} - 226699042 q^{29} + 251932328 q^{31} - 806116648 q^{32} + 325378622 q^{34} + 355232072 q^{35} + 573876170 q^{37} + 770782036 q^{38} - 1009699226 q^{40} + 1733596378 q^{41} + 647370308 q^{43} + 4662321170 q^{44} - 205962976 q^{46} + 5436527248 q^{47} + 4356386219 q^{49} + 10296502416 q^{50} - 5616607137 q^{52} + 3387203910 q^{53} - 10571441512 q^{55} - 635842210 q^{56} + 1991171353 q^{58} - 15113662084 q^{59} + 23895772578 q^{61} - 7557529251 q^{62} + 32993181147 q^{64} - 3660035708 q^{65} + 46806014468 q^{67} - 40754169364 q^{68} - 12274756860 q^{70} - 45541532768 q^{71} + 63786612542 q^{73} + 41720765910 q^{74} + 5581739704 q^{76} - 19147126968 q^{77} + 21847812496 q^{79} + 67715736674 q^{80} - 30216129401 q^{82} - 40153340788 q^{83} + 116854272412 q^{85} + 47307463306 q^{86} - 263050721364 q^{88} - 37300228382 q^{89} + 109416811256 q^{91} + 72498967552 q^{92} - 378035850441 q^{94} + 255722421456 q^{95} - 243602730 q^{97} + 514347061348 q^{98}+O(q^{100}) \) 11 * q - 32 * q^2 + 11264 * q^4 - 1034 * q^5 + 159584 * q^7 - 115497 * q^8 - 627650 * q^10 + 771396 * q^11 + 3433434 * q^13 - 4585896 * q^14 + 18802384 * q^16 - 29035398 * q^17 + 21398428 * q^19 - 72466260 * q^20 + 100463524 * q^22 + 70799773 * q^23 + 233562509 * q^25 - 328796191 * q^26 + 499445210 * q^28 - 226699042 * q^29 + 251932328 * q^31 - 806116648 * q^32 + 325378622 * q^34 + 355232072 * q^35 + 573876170 * q^37 + 770782036 * q^38 - 1009699226 * q^40 + 1733596378 * q^41 + 647370308 * q^43 + 4662321170 * q^44 - 205962976 * q^46 + 5436527248 * q^47 + 4356386219 * q^49 + 10296502416 * q^50 - 5616607137 * q^52 + 3387203910 * q^53 - 10571441512 * q^55 - 635842210 * q^56 + 1991171353 * q^58 - 15113662084 * q^59 + 23895772578 * q^61 - 7557529251 * q^62 + 32993181147 * q^64 - 3660035708 * q^65 + 46806014468 * q^67 - 40754169364 * q^68 - 12274756860 * q^70 - 45541532768 * q^71 + 63786612542 * q^73 + 41720765910 * q^74 + 5581739704 * q^76 - 19147126968 * q^77 + 21847812496 * q^79 + 67715736674 * q^80 - 30216129401 * q^82 - 40153340788 * q^83 + 116854272412 * q^85 + 47307463306 * q^86 - 263050721364 * q^88 - 37300228382 * q^89 + 109416811256 * q^91 + 72498967552 * q^92 - 378035850441 * q^94 + 255722421456 * q^95 - 243602730 * q^97 + 514347061348 * 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 $

$2$	43.0566	0.951424	0.475712	−	0.879601i	$-0.342190\pi$
$2$	43.0566	0.951424	0.475712	+	0.879601i	$0.342190\pi$
$3$	0	0
$3$	0	0
$4$	−194.133	−0.0947917
$5$	11277.9	1.61396	0.806981	−	0.590578i	$-0.201100\pi$
$5$	11277.9	1.61396	0.806981	+	0.590578i	$0.201100\pi$
$6$	0	0
$7$	−9281.65	−0.208730	−0.104365	−	0.994539i	$-0.533281\pi$
$7$	−9281.65	−0.208730	−0.104365	+	0.994539i	$0.533281\pi$
$8$	−96538.5	−1.04161
$9$	0	0
$10$	485588.	1.53556
$11$	775928.	1.45265	0.726326	−	0.687350i	$-0.241226\pi$
$11$	775928.	1.45265	0.726326	+	0.687350i	$0.241226\pi$
$12$	0	0
$13$	−1.35775e6	−1.01422	−0.507109	−	0.861882i	$-0.669286\pi$
$13$	−1.35775e6	−1.01422	−0.507109	+	0.861882i	$0.669286\pi$
$14$	−399636.	−0.198591
$15$	0	0
$16$	−3.75903e6	−0.896223
$17$	−5.04724e6	−0.862154	−0.431077	−	0.902315i	$-0.641866\pi$
$17$	−5.04724e6	−0.862154	−0.431077	+	0.902315i	$0.641866\pi$
$18$	0	0
$19$	1.10360e7	1.02251	0.511256	−	0.859429i	$-0.329181\pi$
$19$	1.10360e7	1.02251	0.511256	+	0.859429i	$0.329181\pi$
$20$	−2.18942e6	−0.152990
$21$	0	0
$22$	3.34088e7	1.38209
$23$	6.43634e6	0.208514
$23$	6.43634e6	0.208514
$24$	0	0
$25$	7.83629e7	1.60487
$26$	−5.84601e7	−0.964952
$27$	0	0
$28$	1.80188e6	0.0197859
$29$	3.22957e7	0.292385	0.146193	−	0.989256i	$-0.453298\pi$
$29$	3.22957e7	0.292385	0.146193	+	0.989256i	$0.453298\pi$
$30$	0	0
$31$	2.54882e8	1.59901	0.799503	−	0.600663i	$-0.205096\pi$
$31$	2.54882e8	1.59901	0.799503	+	0.600663i	$0.205096\pi$
$32$	3.58600e7	0.188923
$33$	0	0
$34$	−2.17317e8	−0.820274
$35$	−1.04678e8	−0.336883
$36$	0	0
$37$	−3.12485e8	−0.740831	−0.370416	−	0.928866i	$-0.620785\pi$
$37$	−3.12485e8	−0.740831	−0.370416	+	0.928866i	$0.620785\pi$
$38$	4.75174e8	0.972842
$39$	0	0
$40$	−1.08875e9	−1.68112
$41$	−8.65298e8	−1.16642	−0.583209	−	0.812322i	$-0.698203\pi$
$41$	−8.65298e8	−1.16642	−0.583209	+	0.812322i	$0.698203\pi$
$42$	0	0
$43$	7.75261e8	0.804214	0.402107	−	0.915593i	$-0.368278\pi$
$43$	7.75261e8	0.804214	0.402107	+	0.915593i	$0.368278\pi$
$44$	−1.50634e8	−0.137699
$45$	0	0
$46$	2.77127e8	0.198386
$47$	2.34472e9	1.49126	0.745630	−	0.666360i	$-0.232149\pi$
$47$	2.34472e9	1.49126	0.745630	+	0.666360i	$0.232149\pi$
$48$	0	0
$49$	−1.89118e9	−0.956432
$50$	3.37404e9	1.52691
$51$	0	0
$52$	2.63585e8	0.0961395
$53$	4.77808e9	1.56941	0.784705	−	0.619870i	$-0.212815\pi$
$53$	4.77808e9	1.56941	0.784705	+	0.619870i	$0.212815\pi$
$54$	0	0
$55$	8.75084e9	2.34453
$56$	8.96037e8	0.217416
$57$	0	0
$58$	1.39054e9	0.278182
$59$	1.57779e9	0.287318	0.143659	−	0.989627i	$-0.454113\pi$
$59$	1.57779e9	0.287318	0.143659	+	0.989627i	$0.454113\pi$
$60$	0	0
$61$	−9.63652e9	−1.46085	−0.730426	−	0.682992i	$-0.760679\pi$
$61$	−9.63652e9	−1.46085	−0.730426	+	0.682992i	$0.760679\pi$
$62$	1.09743e10	1.52133
$63$	0	0
$64$	9.24250e9	1.07597
$65$	−1.53126e10	−1.63691
$66$	0	0
$67$	1.06227e10	0.961226	0.480613	−	0.876933i	$-0.340414\pi$
$67$	1.06227e10	0.961226	0.480613	+	0.876933i	$0.340414\pi$
$68$	9.79838e8	0.0817251
$69$	0	0
$70$	−4.50705e9	−0.320519
$71$	−1.06427e10	−0.700055	−0.350027	−	0.936739i	$-0.613828\pi$
$71$	−1.06427e10	−0.700055	−0.350027	+	0.936739i	$0.613828\pi$
$72$	0	0
$73$	1.53965e9	0.0869251	0.0434626	−	0.999055i	$-0.486161\pi$
$73$	1.53965e9	0.0869251	0.0434626	+	0.999055i	$0.486161\pi$
$74$	−1.34545e10	−0.704845
$75$	0	0
$76$	−2.14246e9	−0.0969256
$77$	−7.20189e9	−0.303213
$78$	0	0
$79$	2.42947e10	0.888307	0.444154	−	0.895951i	$-0.353504\pi$
$79$	2.42947e10	0.888307	0.444154	+	0.895951i	$0.353504\pi$
$80$	−4.23940e10	−1.44647
$81$	0	0
$82$	−3.72567e10	−1.10976
$83$	−1.34063e10	−0.373577	−0.186788	−	0.982400i	$-0.559808\pi$
$83$	−1.34063e10	−0.373577	−0.186788	+	0.982400i	$0.559808\pi$
$84$	0	0
$85$	−5.69222e10	−1.39148
$86$	3.33801e10	0.765149
$87$	0	0
$88$	−7.49070e10	−1.51310
$89$	4.54047e10	0.861899	0.430949	−	0.902376i	$-0.358179\pi$
$89$	4.54047e10	0.861899	0.430949	+	0.902376i	$0.358179\pi$
$90$	0	0
$91$	1.26022e10	0.211698
$92$	−1.24951e9	−0.0197654
$93$	0	0
$94$	1.00956e11	1.41882
$95$	1.24463e11	1.65029
$96$	0	0
$97$	−9.36141e10	−1.10687	−0.553435	−	0.832892i	$-0.686683\pi$
$97$	−9.36141e10	−1.10687	−0.553435	+	0.832892i	$0.686683\pi$
$98$	−8.14276e10	−0.909972
$99$	0	0
$100$	−1.52129e10	−0.152129
$101$	1.57667e11	1.49270	0.746352	−	0.665551i	$-0.231803\pi$
$101$	1.57667e11	1.49270	0.746352	+	0.665551i	$0.231803\pi$
$102$	0	0
$103$	8.81920e10	0.749591	0.374796	−	0.927107i	$-0.377713\pi$
$103$	8.81920e10	0.749591	0.374796	+	0.927107i	$0.377713\pi$
$104$	1.31075e11	1.05642
$105$	0	0
$106$	2.05728e11	1.49317
$107$	−1.40209e10	−0.0966422	−0.0483211	−	0.998832i	$-0.515387\pi$
$107$	−1.40209e10	−0.0966422	−0.0483211	+	0.998832i	$0.515387\pi$
$108$	0	0
$109$	2.33589e11	1.45414	0.727071	−	0.686562i	$-0.240881\pi$
$109$	2.33589e11	1.45414	0.727071	+	0.686562i	$0.240881\pi$
$110$	3.76781e11	2.23064
$111$	0	0
$112$	3.48900e10	0.187069
$113$	−2.56226e11	−1.30825	−0.654126	−	0.756386i	$-0.726963\pi$
$113$	−2.56226e11	−1.30825	−0.654126	+	0.756386i	$0.726963\pi$
$114$	0	0
$115$	7.25884e10	0.336534
$116$	−6.26967e9	−0.0277157
$117$	0	0
$118$	6.79342e10	0.273362
$119$	4.68467e10	0.179958
$120$	0	0
$121$	3.16753e11	1.11020
$122$	−4.14915e11	−1.38989
$123$	0	0
$124$	−4.94811e10	−0.151572
$125$	3.33091e11	0.976241
$126$	0	0
$127$	5.69763e11	1.53029	0.765145	−	0.643858i	$-0.222667\pi$
$127$	5.69763e11	1.53029	0.765145	+	0.643858i	$0.222667\pi$
$128$	3.24509e11	0.834780
$129$	0	0
$130$	−6.59307e11	−1.55740
$131$	2.47403e11	0.560289	0.280145	−	0.959958i	$-0.409618\pi$
$131$	2.47403e11	0.560289	0.280145	+	0.959958i	$0.409618\pi$
$132$	0	0
$133$	−1.02433e11	−0.213429
$134$	4.57379e11	0.914534
$135$	0	0
$136$	4.87253e11	0.898029
$137$	3.51747e11	0.622684	0.311342	−	0.950298i	$-0.399222\pi$
$137$	3.51747e11	0.622684	0.311342	+	0.950298i	$0.399222\pi$
$138$	0	0
$139$	−7.27582e11	−1.18932	−0.594662	−	0.803975i	$-0.702714\pi$
$139$	−7.27582e11	−1.18932	−0.594662	+	0.803975i	$0.702714\pi$
$140$	2.03214e10	0.0319337
$141$	0	0
$142$	−4.58239e11	−0.666049
$143$	−1.05352e12	−1.47331
$144$	0	0
$145$	3.64227e11	0.471899
$146$	6.62919e10	0.0827027
$147$	0	0
$148$	6.06637e10	0.0702247
$149$	4.22980e10	0.0471841	0.0235920	−	0.999722i	$-0.492490\pi$
$149$	4.22980e10	0.0471841	0.0235920	+	0.999722i	$0.492490\pi$
$150$	0	0
$151$	6.22347e11	0.645148	0.322574	−	0.946544i	$-0.395452\pi$
$151$	6.22347e11	0.645148	0.322574	+	0.946544i	$0.395452\pi$
$152$	−1.06540e12	−1.06506
$153$	0	0
$154$	−3.10089e11	−0.288484
$155$	2.87453e12	2.58073
$156$	0	0
$157$	1.52607e12	1.27681	0.638405	−	0.769701i	$-0.279595\pi$
$157$	1.52607e12	1.27681	0.638405	+	0.769701i	$0.279595\pi$
$158$	1.04605e12	0.845157
$159$	0	0
$160$	4.04426e11	0.304915
$161$	−5.97399e10	−0.0435233
$162$	0	0
$163$	9.36709e11	0.637636	0.318818	−	0.947816i	$-0.396714\pi$
$163$	9.36709e11	0.637636	0.318818	+	0.947816i	$0.396714\pi$
$164$	1.67983e11	0.110567
$165$	0	0
$166$	−5.77229e11	−0.355430
$167$	2.71869e12	1.61964	0.809821	−	0.586678i	$-0.199564\pi$
$167$	2.71869e12	1.61964	0.809821	+	0.586678i	$0.199564\pi$
$168$	0	0
$169$	5.13259e10	0.0286391
$170$	−2.45088e12	−1.32389
$171$	0	0
$172$	−1.50504e11	−0.0762328
$173$	−7.83243e11	−0.384276	−0.192138	−	0.981368i	$-0.561542\pi$
$173$	−7.83243e11	−0.384276	−0.192138	+	0.981368i	$0.561542\pi$
$174$	0	0
$175$	−7.27337e11	−0.334986
$176$	−2.91674e12	−1.30190
$177$	0	0
$178$	1.95497e12	0.820031
$179$	−2.95711e12	−1.20275	−0.601375	−	0.798967i	$-0.705380\pi$
$179$	−2.95711e12	−1.20275	−0.601375	+	0.798967i	$0.705380\pi$
$180$	0	0
$181$	8.41355e11	0.321919	0.160960	−	0.986961i	$-0.448541\pi$
$181$	8.41355e11	0.321919	0.160960	+	0.986961i	$0.448541\pi$
$182$	5.42606e11	0.201415
$183$	0	0
$184$	−6.21355e11	−0.217191
$185$	−3.52417e12	−1.19567
$186$	0	0
$187$	−3.91629e12	−1.25241
$188$	−4.55189e11	−0.141359
$189$	0	0
$190$	5.35896e12	1.57013
$191$	3.38839e12	0.964517	0.482259	−	0.876029i	$-0.339817\pi$
$191$	3.38839e12	0.964517	0.482259	+	0.876029i	$0.339817\pi$
$192$	0	0
$193$	−1.51781e12	−0.407993	−0.203996	−	0.978972i	$-0.565393\pi$
$193$	−1.51781e12	−0.407993	−0.203996	+	0.978972i	$0.565393\pi$
$194$	−4.03070e12	−1.05310
$195$	0	0
$196$	3.67141e11	0.0906618
$197$	3.52739e12	0.847012	0.423506	−	0.905893i	$-0.360799\pi$
$197$	3.52739e12	0.847012	0.423506	+	0.905893i	$0.360799\pi$
$198$	0	0
$199$	7.38754e12	1.67806	0.839030	−	0.544085i	$-0.183123\pi$
$199$	7.38754e12	1.67806	0.839030	+	0.544085i	$0.183123\pi$
$200$	−7.56504e12	−1.67165
$201$	0	0
$202$	6.78861e12	1.42020
$203$	−2.99757e11	−0.0610297
$204$	0	0
$205$	−9.75874e12	−1.88255
$206$	3.79724e12	0.713179
$207$	0	0
$208$	5.10383e12	0.908966
$209$	8.56317e12	1.48535
$210$	0	0
$211$	−1.63283e12	−0.268775	−0.134387	−	0.990929i	$-0.542907\pi$
$211$	−1.63283e12	−0.268775	−0.134387	+	0.990929i	$0.542907\pi$
$212$	−9.27585e11	−0.148767
$213$	0	0
$214$	−6.03694e11	−0.0919477
$215$	8.74332e12	1.29797
$216$	0	0
$217$	−2.36573e12	−0.333761
$218$	1.00575e13	1.38351
$219$	0	0
$220$	−1.69883e12	−0.222242
$221$	6.85289e12	0.874412
$222$	0	0
$223$	1.20694e13	1.46558	0.732790	−	0.680455i	$-0.238218\pi$
$223$	1.20694e13	1.46558	0.732790	+	0.680455i	$0.238218\pi$
$224$	−3.32840e11	−0.0394341
$225$	0	0
$226$	−1.10322e13	−1.24470
$227$	1.54635e12	0.170281	0.0851405	−	0.996369i	$-0.472866\pi$
$227$	1.54635e12	0.170281	0.0851405	+	0.996369i	$0.472866\pi$
$228$	0	0
$229$	8.77961e12	0.921255	0.460628	−	0.887594i	$-0.347624\pi$
$229$	8.77961e12	0.921255	0.460628	+	0.887594i	$0.347624\pi$
$230$	3.12541e12	0.320187
$231$	0	0
$232$	−3.11778e12	−0.304552
$233$	−1.10337e13	−1.05260	−0.526302	−	0.850298i	$-0.676422\pi$
$233$	−1.10337e13	−1.05260	−0.526302	+	0.850298i	$0.676422\pi$
$234$	0	0
$235$	2.64436e13	2.40684
$236$	−3.06302e11	−0.0272354
$237$	0	0
$238$	2.01706e12	0.171216
$239$	2.43995e12	0.202392	0.101196	−	0.994867i	$-0.467733\pi$
$239$	2.43995e12	0.202392	0.101196	+	0.994867i	$0.467733\pi$
$240$	0	0
$241$	−7.83601e12	−0.620871	−0.310435	−	0.950595i	$-0.600475\pi$
$241$	−7.83601e12	−0.620871	−0.310435	+	0.950595i	$0.600475\pi$
$242$	1.36383e13	1.05627
$243$	0	0
$244$	1.87077e12	0.138477
$245$	−2.13285e13	−1.54364
$246$	0	0
$247$	−1.49842e13	−1.03705
$248$	−2.46059e13	−1.66554
$249$	0	0
$250$	1.43417e13	0.928820
$251$	−4.45929e12	−0.282527	−0.141264	−	0.989972i	$-0.545117\pi$
$251$	−4.45929e12	−0.282527	−0.141264	+	0.989972i	$0.545117\pi$
$252$	0	0
$253$	4.99414e12	0.302899
$254$	2.45320e13	1.45595
$255$	0	0
$256$	−4.95641e12	−0.281739
$257$	−2.14811e13	−1.19516	−0.597578	−	0.801811i	$-0.703870\pi$
$257$	−2.14811e13	−1.19516	−0.597578	+	0.801811i	$0.703870\pi$
$258$	0	0
$259$	2.90037e12	0.154634
$260$	2.97268e12	0.155166
$261$	0	0
$262$	1.06523e13	0.533073
$263$	1.13326e13	0.555358	0.277679	−	0.960674i	$-0.410435\pi$
$263$	1.13326e13	0.555358	0.277679	+	0.960674i	$0.410435\pi$
$264$	0	0
$265$	5.38867e13	2.53297
$266$	−4.41039e12	−0.203062
$267$	0	0
$268$	−2.06223e12	−0.0911163
$269$	−2.21638e13	−0.959413	−0.479707	−	0.877429i	$-0.659257\pi$
$269$	−2.21638e13	−0.959413	−0.479707	+	0.877429i	$0.659257\pi$
$270$	0	0
$271$	−2.48907e12	−0.103444	−0.0517221	−	0.998662i	$-0.516471\pi$
$271$	−2.48907e12	−0.103444	−0.0517221	+	0.998662i	$0.516471\pi$
$272$	1.89727e13	0.772682
$273$	0	0
$274$	1.51450e13	0.592436
$275$	6.08040e13	2.33132
$276$	0	0
$277$	−3.31407e13	−1.22102	−0.610511	−	0.792008i	$-0.709036\pi$
$277$	−3.31407e13	−1.22102	−0.610511	+	0.792008i	$0.709036\pi$
$278$	−3.13272e13	−1.13155
$279$	0	0
$280$	1.01054e13	0.350901
$281$	−4.91827e13	−1.67466	−0.837331	−	0.546696i	$-0.815885\pi$
$281$	−4.91827e13	−1.67466	−0.837331	+	0.546696i	$0.815885\pi$
$282$	0	0
$283$	1.81902e13	0.595679	0.297840	−	0.954616i	$-0.403734\pi$
$283$	1.81902e13	0.595679	0.297840	+	0.954616i	$0.403734\pi$
$284$	2.06611e12	0.0663594
$285$	0	0
$286$	−4.53608e13	−1.40174
$287$	8.03139e12	0.243467
$288$	0	0
$289$	−8.79729e12	−0.256691
$290$	1.56824e13	0.448976
$291$	0	0
$292$	−2.98897e11	−0.00823978
$293$	6.91895e13	1.87184	0.935919	−	0.352216i	$-0.114572\pi$
$293$	6.91895e13	1.87184	0.935919	+	0.352216i	$0.114572\pi$
$294$	0	0
$295$	1.77942e13	0.463721
$296$	3.01668e13	0.771658
$297$	0	0
$298$	1.82121e12	0.0448921
$299$	−8.73895e12	−0.211479
$300$	0	0
$301$	−7.19570e12	−0.167864
$302$	2.67961e13	0.613810
$303$	0	0
$304$	−4.14848e13	−0.916398
$305$	−1.08680e14	−2.35776
$306$	0	0
$307$	−2.22110e12	−0.0464843	−0.0232422	−	0.999730i	$-0.507399\pi$
$307$	−2.22110e12	−0.0464843	−0.0232422	+	0.999730i	$0.507399\pi$
$308$	1.39813e12	0.0287421
$309$	0	0
$310$	1.23768e14	2.45537
$311$	3.59445e13	0.700567	0.350284	−	0.936644i	$-0.386085\pi$
$311$	3.59445e13	0.700567	0.350284	+	0.936644i	$0.386085\pi$
$312$	0	0
$313$	2.47593e13	0.465848	0.232924	−	0.972495i	$-0.425171\pi$
$313$	2.47593e13	0.465848	0.232924	+	0.972495i	$0.425171\pi$
$314$	6.57073e13	1.21479
$315$	0	0
$316$	−4.71642e12	−0.0842042
$317$	4.47519e12	0.0785210	0.0392605	−	0.999229i	$-0.487500\pi$
$317$	4.47519e12	0.0785210	0.0392605	+	0.999229i	$0.487500\pi$
$318$	0	0
$319$	2.50591e13	0.424734
$320$	1.04236e14	1.73657
$321$	0	0
$322$	−2.57219e12	−0.0414091
$323$	−5.57015e13	−0.881562
$324$	0	0
$325$	−1.06397e14	−1.62769
$326$	4.03315e13	0.606662
$327$	0	0
$328$	8.35346e13	1.21495
$329$	−2.17629e13	−0.311271
$330$	0	0
$331$	−1.00551e14	−1.39102	−0.695509	−	0.718517i	$-0.744821\pi$
$331$	−1.00551e14	−1.39102	−0.695509	+	0.718517i	$0.744821\pi$
$332$	2.60261e12	0.0354120
$333$	0	0
$334$	1.17057e14	1.54097
$335$	1.19802e14	1.55138
$336$	0	0
$337$	9.02286e13	1.13078	0.565392	−	0.824822i	$-0.308725\pi$
$337$	9.02286e13	1.13078	0.565392	+	0.824822i	$0.308725\pi$
$338$	2.20992e12	0.0272480
$339$	0	0
$340$	1.10505e13	0.131901
$341$	1.97770e14	2.32280
$342$	0	0
$343$	3.59061e13	0.408367
$344$	−7.48426e13	−0.837678
$345$	0	0
$346$	−3.37238e13	−0.365609
$347$	−1.15206e14	−1.22931	−0.614656	−	0.788796i	$-0.710705\pi$
$347$	−1.15206e14	−1.22931	−0.614656	+	0.788796i	$0.710705\pi$
$348$	0	0
$349$	8.72795e13	0.902345	0.451172	−	0.892437i	$-0.351006\pi$
$349$	8.72795e13	0.902345	0.451172	+	0.892437i	$0.351006\pi$
$350$	−3.13166e13	−0.318714
$351$	0	0
$352$	2.78248e13	0.274440
$353$	−1.59272e14	−1.54660	−0.773300	−	0.634040i	$-0.781395\pi$
$353$	−1.59272e14	−1.54660	−0.773300	+	0.634040i	$0.781395\pi$
$354$	0	0
$355$	−1.20028e14	−1.12986
$356$	−8.81458e12	−0.0817009
$357$	0	0
$358$	−1.27323e14	−1.14433
$359$	6.67697e13	0.590963	0.295481	−	0.955348i	$-0.404520\pi$
$359$	6.67697e13	0.590963	0.295481	+	0.955348i	$0.404520\pi$
$360$	0	0
$361$	5.30377e12	0.0455297
$362$	3.62258e13	0.306282
$363$	0	0
$364$	−2.44650e12	−0.0200673
$365$	1.73640e13	0.140294
$366$	0	0
$367$	−4.83510e13	−0.379090	−0.189545	−	0.981872i	$-0.560701\pi$
$367$	−4.83510e13	−0.379090	−0.189545	+	0.981872i	$0.560701\pi$
$368$	−2.41944e13	−0.186875
$369$	0	0
$370$	−1.51739e14	−1.13759
$371$	−4.43485e13	−0.327584
$372$	0	0
$373$	1.48654e14	1.06605	0.533027	−	0.846098i	$-0.321054\pi$
$373$	1.48654e14	1.06605	0.533027	+	0.846098i	$0.321054\pi$
$374$	−1.68622e14	−1.19157
$375$	0	0
$376$	−2.26356e14	−1.55331
$377$	−4.38495e13	−0.296543
$378$	0	0
$379$	−1.52989e14	−1.00495	−0.502475	−	0.864592i	$-0.667577\pi$
$379$	−1.52989e14	−1.00495	−0.502475	+	0.864592i	$0.667577\pi$
$380$	−2.41625e13	−0.156434
$381$	0	0
$382$	1.45892e14	0.917665
$383$	−1.16163e14	−0.720233	−0.360116	−	0.932907i	$-0.617263\pi$
$383$	−1.16163e14	−0.720233	−0.360116	+	0.932907i	$0.617263\pi$
$384$	0	0
$385$	−8.12222e13	−0.489374
$386$	−6.53517e13	−0.388174
$387$	0	0
$388$	1.81736e13	0.104922
$389$	−2.30945e14	−1.31458	−0.657289	−	0.753638i	$-0.728297\pi$
$389$	−2.30945e14	−1.31458	−0.657289	+	0.753638i	$0.728297\pi$
$390$	0	0
$391$	−3.24858e13	−0.179771
$392$	1.82572e14	0.996230
$393$	0	0
$394$	1.51877e14	0.805868
$395$	2.73994e14	1.43369
$396$	0	0
$397$	−2.86990e14	−1.46056	−0.730279	−	0.683149i	$-0.760610\pi$
$397$	−2.86990e14	−1.46056	−0.730279	+	0.683149i	$0.760610\pi$
$398$	3.18082e14	1.59655
$399$	0	0
$400$	−2.94569e14	−1.43832
$401$	−2.89581e14	−1.39468	−0.697342	−	0.716739i	$-0.745634\pi$
$401$	−2.89581e14	−1.39468	−0.697342	+	0.716739i	$0.745634\pi$
$402$	0	0
$403$	−3.46066e14	−1.62174
$404$	−3.06085e13	−0.141496
$405$	0	0
$406$	−1.29065e13	−0.0580652
$407$	−2.42466e14	−1.07617
$408$	0	0
$409$	−1.31711e13	−0.0569041	−0.0284521	−	0.999595i	$-0.509058\pi$
$409$	−1.31711e13	−0.0569041	−0.0284521	+	0.999595i	$0.509058\pi$
$410$	−4.20178e14	−1.79111
$411$	0	0
$412$	−1.71210e13	−0.0710551
$413$	−1.46445e13	−0.0599721
$414$	0	0
$415$	−1.51195e14	−0.602938
$416$	−4.86890e13	−0.191610
$417$	0	0
$418$	3.68700e14	1.41320
$419$	−1.52680e14	−0.577571	−0.288785	−	0.957394i	$-0.593251\pi$
$419$	−1.52680e14	−0.577571	−0.288785	+	0.957394i	$0.593251\pi$
$420$	0	0
$421$	−3.07188e14	−1.13202	−0.566009	−	0.824399i	$-0.691513\pi$
$421$	−3.07188e14	−1.13202	−0.566009	+	0.824399i	$0.691513\pi$
$422$	−7.03042e13	−0.255719
$423$	0	0
$424$	−4.61269e14	−1.63471
$425$	−3.95516e14	−1.38365
$426$	0	0
$427$	8.94428e13	0.304924
$428$	2.72194e12	0.00916088
$429$	0	0
$430$	3.76457e14	1.23492
$431$	3.68520e14	1.19354	0.596769	−	0.802413i	$-0.296451\pi$
$431$	3.68520e14	1.19354	0.596769	+	0.802413i	$0.296451\pi$
$432$	0	0
$433$	3.19287e14	1.00809	0.504043	−	0.863678i	$-0.331845\pi$
$433$	3.19287e14	1.00809	0.504043	+	0.863678i	$0.331845\pi$
$434$	−1.01860e14	−0.317548
$435$	0	0
$436$	−4.53475e13	−0.137841
$437$	7.10317e13	0.213208
$438$	0	0
$439$	−4.07703e14	−1.19341	−0.596705	−	0.802461i	$-0.703524\pi$
$439$	−4.07703e14	−1.19341	−0.596705	+	0.802461i	$0.703524\pi$
$440$	−8.44793e14	−2.44208
$441$	0	0
$442$	2.95062e14	0.831937
$443$	−5.90010e14	−1.64300	−0.821502	−	0.570206i	$-0.806863\pi$
$443$	−5.90010e14	−1.64300	−0.821502	+	0.570206i	$0.806863\pi$
$444$	0	0
$445$	5.12070e14	1.39107
$446$	5.19668e14	1.39439
$447$	0	0
$448$	−8.57857e13	−0.224588
$449$	4.34355e14	1.12329	0.561643	−	0.827380i	$-0.310169\pi$
$449$	4.34355e14	1.12329	0.561643	+	0.827380i	$0.310169\pi$
$450$	0	0
$451$	−6.71409e14	−1.69440
$452$	4.97420e13	0.124011
$453$	0	0
$454$	6.65806e13	0.162010
$455$	1.42126e14	0.341673
$456$	0	0
$457$	2.72471e13	0.0639412	0.0319706	−	0.999489i	$-0.489822\pi$
$457$	2.72471e13	0.0639412	0.0319706	+	0.999489i	$0.489822\pi$
$458$	3.78020e14	0.876504
$459$	0	0
$460$	−1.40918e13	−0.0319007
$461$	−2.69205e14	−0.602182	−0.301091	−	0.953595i	$-0.597351\pi$
$461$	−2.69205e14	−0.602182	−0.301091	+	0.953595i	$0.597351\pi$
$462$	0	0
$463$	−3.78520e14	−0.826787	−0.413394	−	0.910552i	$-0.635657\pi$
$463$	−3.78520e14	−0.826787	−0.413394	+	0.910552i	$0.635657\pi$
$464$	−1.21400e14	−0.262042
$465$	0	0
$466$	−4.75074e14	−1.00147
$467$	2.49842e13	0.0520502	0.0260251	−	0.999661i	$-0.491715\pi$
$467$	2.49842e13	0.0520502	0.0260251	+	0.999661i	$0.491715\pi$
$468$	0	0
$469$	−9.85966e13	−0.200637
$470$	1.13857e15	2.28992
$471$	0	0
$472$	−1.52318e14	−0.299274
$473$	6.01547e14	1.16824
$474$	0	0
$475$	8.64816e14	1.64100
$476$	−9.09451e12	−0.0170585
$477$	0	0
$478$	1.05056e14	0.192560
$479$	−7.03196e14	−1.27418	−0.637091	−	0.770789i	$-0.719862\pi$
$479$	−7.03196e14	−1.27418	−0.637091	+	0.770789i	$0.719862\pi$
$480$	0	0
$481$	4.24276e14	0.751365
$482$	−3.37391e14	−0.590711
$483$	0	0
$484$	−6.14923e13	−0.105238
$485$	−1.05577e15	−1.78645
$486$	0	0
$487$	2.43606e12	0.00402975	0.00201487	−	0.999998i	$-0.499359\pi$
$487$	2.43606e12	0.00402975	0.00201487	+	0.999998i	$0.499359\pi$
$488$	9.30296e14	1.52164
$489$	0	0
$490$	−9.18332e14	−1.46866
$491$	6.69777e14	1.05921	0.529605	−	0.848244i	$-0.322340\pi$
$491$	6.69777e14	1.05921	0.529605	+	0.848244i	$0.322340\pi$
$492$	0	0
$493$	−1.63004e14	−0.252081
$494$	−6.45167e14	−0.986675
$495$	0	0
$496$	−9.58109e14	−1.43306
$497$	9.87821e13	0.146123
$498$	0	0
$499$	−1.01952e15	−1.47518	−0.737588	−	0.675251i	$-0.764035\pi$
$499$	−1.01952e15	−1.47518	−0.737588	+	0.675251i	$0.764035\pi$
$500$	−6.46640e13	−0.0925396
$501$	0	0
$502$	−1.92002e14	−0.268803
$503$	8.07323e14	1.11795	0.558977	−	0.829183i	$-0.311194\pi$
$503$	8.07323e14	1.11795	0.558977	+	0.829183i	$0.311194\pi$
$504$	0	0
$505$	1.77816e15	2.40917
$506$	2.15030e14	0.288185
$507$	0	0
$508$	−1.10610e14	−0.145059
$509$	−1.38546e15	−1.79741	−0.898705	−	0.438555i	$-0.855491\pi$
$509$	−1.38546e15	−1.79741	−0.898705	+	0.438555i	$0.855491\pi$
$510$	0	0
$511$	−1.42905e13	−0.0181439
$512$	−8.78000e14	−1.10283
$513$	0	0
$514$	−9.24903e14	−1.13710
$515$	9.94621e14	1.20981
$516$	0	0
$517$	1.81934e15	2.16628
$518$	1.24880e14	0.147123
$519$	0	0
$520$	1.47825e15	1.70502
$521$	−4.52345e12	−0.00516253	−0.00258127	−	0.999997i	$-0.500822\pi$
$521$	−4.52345e12	−0.00516253	−0.00258127	+	0.999997i	$0.500822\pi$
$522$	0	0
$523$	7.44037e14	0.831448	0.415724	−	0.909491i	$-0.363528\pi$
$523$	7.44037e14	0.831448	0.415724	+	0.909491i	$0.363528\pi$
$524$	−4.80292e13	−0.0531108
$525$	0	0
$526$	4.87943e14	0.528381
$527$	−1.28645e15	−1.37859
$528$	0	0
$529$	4.14265e13	0.0434783
$530$	2.32018e15	2.40993
$531$	0	0
$532$	1.98856e13	0.0202313
$533$	1.17486e15	1.18300
$534$	0	0
$535$	−1.58127e14	−0.155977
$536$	−1.02550e15	−1.00122
$537$	0	0
$538$	−9.54295e14	−0.912809
$539$	−1.46742e15	−1.38936
$540$	0	0
$541$	−1.10221e15	−1.02254	−0.511271	−	0.859419i	$-0.670825\pi$
$541$	−1.10221e15	−1.02254	−0.511271	+	0.859419i	$0.670825\pi$
$542$	−1.07171e14	−0.0984193
$543$	0	0
$544$	−1.80994e14	−0.162881
$545$	2.63440e15	2.34693
$546$	0	0
$547$	−9.96151e14	−0.869751	−0.434876	−	0.900491i	$-0.643208\pi$
$547$	−9.96151e14	−0.869751	−0.434876	+	0.900491i	$0.643208\pi$
$548$	−6.82859e13	−0.0590253
$549$	0	0
$550$	2.61801e15	2.21808
$551$	3.56416e14	0.298967
$552$	0	0
$553$	−2.25495e14	−0.185417
$554$	−1.42693e15	−1.16171
$555$	0	0
$556$	1.41248e14	0.112738
$557$	−1.20532e15	−0.952572	−0.476286	−	0.879290i	$-0.658017\pi$
$557$	−1.20532e15	−0.952572	−0.476286	+	0.879290i	$0.658017\pi$
$558$	0	0
$559$	−1.05261e15	−0.815649
$560$	3.93486e14	0.301922
$561$	0	0
$562$	−2.11764e15	−1.59331
$563$	−6.75619e14	−0.503391	−0.251696	−	0.967806i	$-0.580988\pi$
$563$	−6.75619e14	−0.503391	−0.251696	+	0.967806i	$0.580988\pi$
$564$	0	0
$565$	−2.88969e15	−2.11147
$566$	7.83208e14	0.566744
$567$	0	0
$568$	1.02743e15	0.729185
$569$	2.26192e14	0.158986	0.0794931	−	0.996835i	$-0.474670\pi$
$569$	2.26192e14	0.158986	0.0794931	+	0.996835i	$0.474670\pi$
$570$	0	0
$571$	2.55601e15	1.76224	0.881118	−	0.472896i	$-0.156792\pi$
$571$	2.55601e15	1.76224	0.881118	+	0.472896i	$0.156792\pi$
$572$	2.04523e14	0.139657
$573$	0	0
$574$	3.45804e14	0.231641
$575$	5.04371e14	0.334639
$576$	0	0
$577$	1.35677e15	0.883160	0.441580	−	0.897222i	$-0.354418\pi$
$577$	1.35677e15	0.883160	0.441580	+	0.897222i	$0.354418\pi$
$578$	−3.78781e14	−0.244222
$579$	0	0
$580$	−7.07088e13	−0.0447321
$581$	1.24433e14	0.0779768
$582$	0	0
$583$	3.70745e15	2.27981
$584$	−1.48635e14	−0.0905422
$585$	0	0
$586$	2.97906e15	1.78091
$587$	6.34386e14	0.375703	0.187851	−	0.982197i	$-0.439848\pi$
$587$	6.34386e14	0.375703	0.187851	+	0.982197i	$0.439848\pi$
$588$	0	0
$589$	2.81289e15	1.63500
$590$	7.66156e14	0.441195
$591$	0	0
$592$	1.17464e15	0.663950
$593$	3.05825e15	1.71266	0.856331	−	0.516428i	$-0.172738\pi$
$593$	3.05825e15	1.71266	0.856331	+	0.516428i	$0.172738\pi$
$594$	0	0
$595$	5.28332e14	0.290445
$596$	−8.21146e12	−0.00447266
$597$	0	0
$598$	−3.76269e14	−0.201206
$599$	2.03183e15	1.07656	0.538281	−	0.842765i	$-0.319074\pi$
$599$	2.03183e15	1.07656	0.538281	+	0.842765i	$0.319074\pi$
$600$	0	0
$601$	−2.04310e15	−1.06287	−0.531436	−	0.847099i	$-0.678347\pi$
$601$	−2.04310e15	−1.06287	−0.531436	+	0.847099i	$0.678347\pi$
$602$	−3.09822e14	−0.159710
$603$	0	0
$604$	−1.20818e14	−0.0611547
$605$	3.57230e15	1.79182
$606$	0	0
$607$	−2.55573e15	−1.25886	−0.629430	−	0.777057i	$-0.716711\pi$
$607$	−2.55573e15	−1.25886	−0.629430	+	0.777057i	$0.716711\pi$
$608$	3.95752e14	0.193176
$609$	0	0
$610$	−4.67938e15	−2.24323
$611$	−3.18355e15	−1.51246
$612$	0	0
$613$	5.21912e14	0.243537	0.121768	−	0.992559i	$-0.461143\pi$
$613$	5.21912e14	0.243537	0.121768	+	0.992559i	$0.461143\pi$
$614$	−9.56328e13	−0.0442263
$615$	0	0
$616$	6.95260e14	0.315830
$617$	−2.14862e15	−0.967369	−0.483685	−	0.875242i	$-0.660702\pi$
$617$	−2.14862e15	−0.967369	−0.483685	+	0.875242i	$0.660702\pi$
$618$	0	0
$619$	3.10647e15	1.37394	0.686972	−	0.726684i	$-0.258939\pi$
$619$	3.10647e15	1.37394	0.686972	+	0.726684i	$0.258939\pi$
$620$	−5.58043e14	−0.244632
$621$	0	0
$622$	1.54764e15	0.666537
$623$	−4.21431e14	−0.179905
$624$	0	0
$625$	−6.97525e13	−0.0292563
$626$	1.06605e15	0.443219
$627$	0	0
$628$	−2.96261e14	−0.121031
$629$	1.57718e15	0.638710
$630$	0	0
$631$	−4.20442e15	−1.67319	−0.836594	−	0.547823i	$-0.815457\pi$
$631$	−4.20442e15	−1.67319	−0.836594	+	0.547823i	$0.815457\pi$
$632$	−2.34538e15	−0.925271
$633$	0	0
$634$	1.92686e14	0.0747068
$635$	6.42573e15	2.46983
$636$	0	0
$637$	2.56775e15	0.970031
$638$	1.07896e15	0.404102
$639$	0	0
$640$	3.65978e15	1.34730
$641$	3.32182e15	1.21243	0.606216	−	0.795300i	$-0.292687\pi$
$641$	3.32182e15	1.21243	0.606216	+	0.795300i	$0.292687\pi$
$642$	0	0
$643$	−5.66843e14	−0.203377	−0.101689	−	0.994816i	$-0.532425\pi$
$643$	−5.66843e14	−0.203377	−0.101689	+	0.994816i	$0.532425\pi$
$644$	1.15975e13	0.00412565
$645$	0	0
$646$	−2.39831e15	−0.838740
$647$	−3.92250e15	−1.36016	−0.680080	−	0.733138i	$-0.738055\pi$
$647$	−3.92250e15	−1.36016	−0.680080	+	0.733138i	$0.738055\pi$
$648$	0	0
$649$	1.22425e15	0.417374
$650$	−4.58110e15	−1.54863
$651$	0	0
$652$	−1.81847e14	−0.0604426
$653$	4.67327e15	1.54028	0.770138	−	0.637877i	$-0.220187\pi$
$653$	4.67327e15	1.54028	0.770138	+	0.637877i	$0.220187\pi$
$654$	0	0
$655$	2.79018e15	0.904286
$656$	3.25268e15	1.04537
$657$	0	0
$658$	−9.37035e14	−0.296151
$659$	−4.45160e15	−1.39523	−0.697616	−	0.716471i	$-0.745756\pi$
$659$	−4.45160e15	−1.39523	−0.697616	+	0.716471i	$0.745756\pi$
$660$	0	0
$661$	−2.44869e15	−0.754789	−0.377395	−	0.926053i	$-0.623180\pi$
$661$	−2.44869e15	−0.754789	−0.377395	+	0.926053i	$0.623180\pi$
$662$	−4.32938e15	−1.32345
$663$	0	0
$664$	1.29423e15	0.389122
$665$	−1.15522e15	−0.344467
$666$	0	0
$667$	2.07866e14	0.0609665
$668$	−5.27788e14	−0.153529
$669$	0	0
$670$	5.15827e15	1.47602
$671$	−7.47725e15	−2.12211
$672$	0	0
$673$	1.13697e15	0.317443	0.158722	−	0.987323i	$-0.449263\pi$
$673$	1.13697e15	0.317443	0.158722	+	0.987323i	$0.449263\pi$
$674$	3.88493e15	1.07586
$675$	0	0
$676$	−9.96408e12	−0.00271475
$677$	−1.80153e15	−0.486859	−0.243430	−	0.969919i	$-0.578273\pi$
$677$	−1.80153e15	−0.486859	−0.243430	+	0.969919i	$0.578273\pi$
$678$	0	0
$679$	8.68893e14	0.231038
$680$	5.49519e15	1.44938
$681$	0	0
$682$	8.51530e15	2.20997
$683$	−6.34274e15	−1.63291	−0.816456	−	0.577407i	$-0.804065\pi$
$683$	−6.34274e15	−1.63291	−0.816456	+	0.577407i	$0.804065\pi$
$684$	0	0
$685$	3.96697e15	1.00499
$686$	1.54599e15	0.388530
$687$	0	0
$688$	−2.91423e15	−0.720755
$689$	−6.48744e15	−1.59172
$690$	0	0
$691$	−1.89940e15	−0.458657	−0.229328	−	0.973349i	$-0.573653\pi$
$691$	−1.89940e15	−0.458657	−0.229328	+	0.973349i	$0.573653\pi$
$692$	1.52054e14	0.0364262
$693$	0	0
$694$	−4.96036e15	−1.16960
$695$	−8.20560e15	−1.91952
$696$	0	0
$697$	4.36736e15	1.00563
$698$	3.75796e15	0.858513
$699$	0	0
$700$	1.41200e14	0.0317539
$701$	2.36214e15	0.527057	0.263528	−	0.964652i	$-0.415114\pi$
$701$	2.36214e15	0.527057	0.263528	+	0.964652i	$0.415114\pi$
$702$	0	0
$703$	−3.44859e15	−0.757508
$704$	7.17152e15	1.56301
$705$	0	0
$706$	−6.85769e15	−1.47147
$707$	−1.46341e15	−0.311573
$708$	0	0
$709$	−4.74181e14	−0.0994008	−0.0497004	−	0.998764i	$-0.515827\pi$
$709$	−4.74181e14	−0.0994008	−0.0497004	+	0.998764i	$0.515827\pi$
$710$	−5.16798e15	−1.07498
$711$	0	0
$712$	−4.38331e15	−0.897764
$713$	1.64051e15	0.333416
$714$	0	0
$715$	−1.18815e16	−2.37786
$716$	5.74074e14	0.114011
$717$	0	0
$718$	2.87488e15	0.562257
$719$	−3.29693e15	−0.639883	−0.319942	−	0.947437i	$-0.603663\pi$
$719$	−3.29693e15	−0.639883	−0.319942	+	0.947437i	$0.603663\pi$
$720$	0	0
$721$	−8.18567e14	−0.156463
$722$	2.28362e14	0.0433181
$723$	0	0
$724$	−1.63335e14	−0.0305153
$725$	2.53078e15	0.469241
$726$	0	0
$727$	−1.40399e15	−0.256404	−0.128202	−	0.991748i	$-0.540921\pi$
$727$	−1.40399e15	−0.256404	−0.128202	+	0.991748i	$0.540921\pi$
$728$	−1.21659e15	−0.220507
$729$	0	0
$730$	7.47633e14	0.133479
$731$	−3.91293e15	−0.693356
$732$	0	0
$733$	1.58845e14	0.0277270	0.0138635	−	0.999904i	$-0.495587\pi$
$733$	1.58845e14	0.0277270	0.0138635	+	0.999904i	$0.495587\pi$
$734$	−2.08183e15	−0.360676
$735$	0	0
$736$	2.30807e14	0.0393932
$737$	8.24249e15	1.39633
$738$	0	0
$739$	6.35407e15	1.06049	0.530246	−	0.847844i	$-0.322099\pi$
$739$	6.35407e15	1.06049	0.530246	+	0.847844i	$0.322099\pi$
$740$	6.84160e14	0.113340
$741$	0	0
$742$	−1.90949e15	−0.311671
$743$	3.51051e15	0.568764	0.284382	−	0.958711i	$-0.408212\pi$
$743$	3.51051e15	0.568764	0.284382	+	0.958711i	$0.408212\pi$
$744$	0	0
$745$	4.77033e14	0.0761533
$746$	6.40054e15	1.01427
$747$	0	0
$748$	7.60284e14	0.118718
$749$	1.30138e14	0.0201722
$750$	0	0
$751$	2.90087e15	0.443107	0.221554	−	0.975148i	$-0.428887\pi$
$751$	2.90087e15	0.443107	0.221554	+	0.975148i	$0.428887\pi$
$752$	−8.81388e15	−1.33650
$753$	0	0
$754$	−1.88801e15	−0.282138
$755$	7.01877e15	1.04124
$756$	0	0
$757$	3.63111e15	0.530899	0.265449	−	0.964125i	$-0.414480\pi$
$757$	3.63111e15	0.530899	0.265449	+	0.964125i	$0.414480\pi$
$758$	−6.58718e15	−0.956134
$759$	0	0
$760$	−1.20155e16	−1.71897
$761$	3.06289e15	0.435027	0.217513	−	0.976057i	$-0.430205\pi$
$761$	3.06289e15	0.435027	0.217513	+	0.976057i	$0.430205\pi$
$762$	0	0
$763$	−2.16809e15	−0.303524
$764$	−6.57800e14	−0.0914283
$765$	0	0
$766$	−5.00156e15	−0.685247
$767$	−2.14225e15	−0.291404
$768$	0	0
$769$	−3.72035e15	−0.498871	−0.249436	−	0.968391i	$-0.580245\pi$
$769$	−3.72035e15	−0.498871	−0.249436	+	0.968391i	$0.580245\pi$
$770$	−3.49715e15	−0.465602
$771$	0	0
$772$	2.94658e14	0.0386744
$773$	−6.10032e15	−0.794997	−0.397498	−	0.917603i	$-0.630122\pi$
$773$	−6.10032e15	−0.794997	−0.397498	+	0.917603i	$0.630122\pi$
$774$	0	0
$775$	1.99733e16	2.56620
$776$	9.03737e15	1.15293
$777$	0	0
$778$	−9.94372e15	−1.25072
$779$	−9.54946e15	−1.19268
$780$	0	0
$781$	−8.25799e15	−1.01694
$782$	−1.39872e15	−0.171039
$783$	0	0
$784$	7.10900e15	0.857176
$785$	1.72109e16	2.06072
$786$	0	0
$787$	3.85840e14	0.0455561	0.0227780	−	0.999741i	$-0.492749\pi$
$787$	3.85840e14	0.0455561	0.0227780	+	0.999741i	$0.492749\pi$
$788$	−6.84785e14	−0.0802898
$789$	0	0
$790$	1.17972e16	1.36405
$791$	2.37820e15	0.273072
$792$	0	0
$793$	1.30840e16	1.48162
$794$	−1.23568e16	−1.38961
$795$	0	0
$796$	−1.43417e15	−0.159066
$797$	1.23028e16	1.35514	0.677568	−	0.735460i	$-0.263034\pi$
$797$	1.23028e16	1.35514	0.677568	+	0.735460i	$0.263034\pi$
$798$	0	0
$799$	−1.18344e16	−1.28569
$800$	2.81010e15	0.303198
$801$	0	0
$802$	−1.24684e16	−1.32694
$803$	1.19465e15	0.126272
$804$	0	0
$805$	−6.73740e14	−0.0702450
$806$	−1.49004e16	−1.54296
$807$	0	0
$808$	−1.52210e16	−1.55482
$809$	1.19957e15	0.121705	0.0608524	−	0.998147i	$-0.480618\pi$
$809$	1.19957e15	0.121705	0.0608524	+	0.998147i	$0.480618\pi$
$810$	0	0
$811$	1.66206e16	1.66354	0.831769	−	0.555122i	$-0.187328\pi$
$811$	1.66206e16	1.66354	0.831769	+	0.555122i	$0.187328\pi$
$812$	5.81929e13	0.00578511
$813$	0	0
$814$	−1.04397e16	−1.02389
$815$	1.05641e16	1.02912
$816$	0	0
$817$	8.55581e15	0.822318
$818$	−5.67102e14	−0.0541400
$819$	0	0
$820$	1.89450e15	0.178451
$821$	1.54131e16	1.44212	0.721062	−	0.692871i	$-0.243654\pi$
$821$	1.54131e16	1.44212	0.721062	+	0.692871i	$0.243654\pi$
$822$	0	0
$823$	1.89575e16	1.75017	0.875087	−	0.483965i	$-0.160804\pi$
$823$	1.89575e16	1.75017	0.875087	+	0.483965i	$0.160804\pi$
$824$	−8.51393e15	−0.780783
$825$	0	0
$826$	−6.30542e14	−0.0570589
$827$	1.74650e16	1.56996	0.784981	−	0.619520i	$-0.212673\pi$
$827$	1.74650e16	1.56996	0.784981	+	0.619520i	$0.212673\pi$
$828$	0	0
$829$	−1.08283e16	−0.960525	−0.480262	−	0.877125i	$-0.659459\pi$
$829$	−1.08283e16	−0.960525	−0.480262	+	0.877125i	$0.659459\pi$
$830$	−6.50994e15	−0.573650
$831$	0	0
$832$	−1.25490e16	−1.09127
$833$	9.54522e15	0.824591
$834$	0	0
$835$	3.06611e16	2.61404
$836$	−1.66240e15	−0.140799
$837$	0	0
$838$	−6.57388e15	−0.549515
$839$	1.31359e16	1.09086	0.545431	−	0.838156i	$-0.316366\pi$
$839$	1.31359e16	1.09086	0.545431	+	0.838156i	$0.316366\pi$
$840$	0	0
$841$	−1.11575e16	−0.914511
$842$	−1.32265e16	−1.07703
$843$	0	0
$844$	3.16988e14	0.0254776
$845$	5.78849e14	0.0462225
$846$	0	0
$847$	−2.93999e15	−0.231732
$848$	−1.79610e16	−1.40654
$849$	0	0
$850$	−1.70296e16	−1.31644
$851$	−2.01126e15	−0.154474
$852$	0	0
$853$	5.36688e15	0.406914	0.203457	−	0.979084i	$-0.434782\pi$
$853$	5.36688e15	0.406914	0.203457	+	0.979084i	$0.434782\pi$
$854$	3.85110e15	0.290113
$855$	0	0
$856$	1.35356e15	0.100664
$857$	−8.55485e15	−0.632147	−0.316073	−	0.948735i	$-0.602365\pi$
$857$	−8.55485e15	−0.632147	−0.316073	+	0.948735i	$0.602365\pi$
$858$	0	0
$859$	−8.08289e15	−0.589663	−0.294832	−	0.955549i	$-0.595264\pi$
$859$	−8.08289e15	−0.589663	−0.294832	+	0.955549i	$0.595264\pi$
$860$	−1.69737e15	−0.123037
$861$	0	0
$862$	1.58672e16	1.13556
$863$	−2.88640e15	−0.205256	−0.102628	−	0.994720i	$-0.532725\pi$
$863$	−2.88640e15	−0.205256	−0.102628	+	0.994720i	$0.532725\pi$
$864$	0	0
$865$	−8.83334e15	−0.620207
$866$	1.37474e16	0.959118
$867$	0	0
$868$	4.59267e14	0.0316378
$869$	1.88510e16	1.29040
$870$	0	0
$871$	−1.44230e16	−0.974893
$872$	−2.25504e16	−1.51465
$873$	0	0
$874$	3.05838e15	0.202852
$875$	−3.09163e15	−0.203771
$876$	0	0
$877$	8.43019e15	0.548706	0.274353	−	0.961629i	$-0.411536\pi$
$877$	8.43019e15	0.548706	0.274353	+	0.961629i	$0.411536\pi$
$878$	−1.75543e16	−1.13544
$879$	0	0
$880$	−3.28947e16	−2.10122
$881$	−2.84876e16	−1.80838	−0.904188	−	0.427135i	$-0.859523\pi$
$881$	−2.84876e16	−1.80838	−0.904188	+	0.427135i	$0.859523\pi$
$882$	0	0
$883$	2.33282e16	1.46251	0.731254	−	0.682106i	$-0.238936\pi$
$883$	2.33282e16	1.46251	0.731254	+	0.682106i	$0.238936\pi$
$884$	−1.33038e15	−0.0828871
$885$	0	0
$886$	−2.54038e16	−1.56319
$887$	4.96192e15	0.303438	0.151719	−	0.988424i	$-0.451519\pi$
$887$	4.96192e15	0.303438	0.151719	+	0.988424i	$0.451519\pi$
$888$	0	0
$889$	−5.28834e15	−0.319418
$890$	2.20480e16	1.32350
$891$	0	0
$892$	−2.34308e15	−0.138925
$893$	2.58764e16	1.52483
$894$	0	0
$895$	−3.33500e16	−1.94119
$896$	−3.01198e15	−0.174244
$897$	0	0
$898$	1.87018e16	1.06872
$899$	8.23159e15	0.467526
$900$	0	0
$901$	−2.41161e16	−1.35307
$902$	−2.89085e16	−1.61209
$903$	0	0
$904$	2.47357e16	1.36269
$905$	9.48871e15	0.519565
$906$	0	0
$907$	−1.03369e16	−0.559180	−0.279590	−	0.960120i	$-0.590198\pi$
$907$	−1.03369e16	−0.559180	−0.279590	+	0.960120i	$0.590198\pi$
$908$	−3.00199e14	−0.0161412
$909$	0	0
$910$	6.11945e15	0.325076
$911$	−8.39263e15	−0.443146	−0.221573	−	0.975144i	$-0.571119\pi$
$911$	−8.39263e15	−0.443146	−0.221573	+	0.975144i	$0.571119\pi$
$912$	0	0
$913$	−1.04023e16	−0.542677
$914$	1.17316e15	0.0608352
$915$	0	0
$916$	−1.70442e15	−0.0873274
$917$	−2.29631e15	−0.116949
$918$	0	0
$919$	1.62657e16	0.818535	0.409267	−	0.912414i	$-0.365784\pi$
$919$	1.62657e16	0.818535	0.409267	+	0.912414i	$0.365784\pi$
$920$	−7.00758e15	−0.350538
$921$	0	0
$922$	−1.15910e16	−0.572931
$923$	1.44502e16	0.710008
$924$	0	0
$925$	−2.44872e16	−1.18894
$926$	−1.62978e16	−0.786626
$927$	0	0
$928$	1.15812e15	0.0552384
$929$	−2.54810e16	−1.20818	−0.604088	−	0.796917i	$-0.706463\pi$
$929$	−2.54810e16	−1.20818	−0.604088	+	0.796917i	$0.706463\pi$
$930$	0	0
$931$	−2.08711e16	−0.977962
$932$	2.14202e15	0.0997781
$933$	0	0
$934$	1.07573e15	0.0495219
$935$	−4.41676e16	−2.02134
$936$	0	0
$937$	4.04656e16	1.83028	0.915141	−	0.403134i	$-0.132079\pi$
$937$	4.04656e16	1.83028	0.915141	+	0.403134i	$0.132079\pi$
$938$	−4.24523e15	−0.190891
$939$	0	0
$940$	−5.13358e15	−0.228148
$941$	2.45413e15	0.108431	0.0542156	−	0.998529i	$-0.482734\pi$
$941$	2.45413e15	0.108431	0.0542156	+	0.998529i	$0.482734\pi$
$942$	0	0
$943$	−5.56935e15	−0.243215
$944$	−5.93096e15	−0.257501
$945$	0	0
$946$	2.59005e16	1.11149
$947$	5.77920e15	0.246572	0.123286	−	0.992371i	$-0.460657\pi$
$947$	5.77920e15	0.246572	0.123286	+	0.992371i	$0.460657\pi$
$948$	0	0
$949$	−2.09046e15	−0.0881610
$950$	3.72360e16	1.56129
$951$	0	0
$952$	−4.52251e15	−0.187446
$953$	−2.59433e16	−1.06909	−0.534545	−	0.845140i	$-0.679517\pi$
$953$	−2.59433e16	−1.06909	−0.534545	+	0.845140i	$0.679517\pi$
$954$	0	0
$955$	3.82139e16	1.55669
$956$	−4.73677e14	−0.0191851
$957$	0	0
$958$	−3.02772e16	−1.21229
$959$	−3.26479e15	−0.129973
$960$	0	0
$961$	3.95564e16	1.55682
$962$	1.82679e16	0.714867
$963$	0	0
$964$	1.52123e15	0.0588534
$965$	−1.71177e16	−0.658485
$966$	0	0
$967$	−1.54657e16	−0.588200	−0.294100	−	0.955775i	$-0.595020\pi$
$967$	−1.54657e16	−0.588200	−0.294100	+	0.955775i	$0.595020\pi$
$968$	−3.05788e16	−1.15640
$969$	0	0
$970$	−4.54578e16	−1.69967
$971$	5.60106e15	0.208240	0.104120	−	0.994565i	$-0.466797\pi$
$971$	5.60106e15	0.208240	0.104120	+	0.994565i	$0.466797\pi$
$972$	0	0
$973$	6.75316e15	0.248248
$974$	1.04888e14	0.00383400
$975$	0	0
$976$	3.62240e16	1.30925
$977$	1.92165e16	0.690645	0.345323	−	0.938484i	$-0.387770\pi$
$977$	1.92165e16	0.690645	0.345323	+	0.938484i	$0.387770\pi$
$978$	0	0
$979$	3.52308e16	1.25204
$980$	4.14058e15	0.146325
$981$	0	0
$982$	2.88383e16	1.00776
$983$	−2.38430e16	−0.828544	−0.414272	−	0.910153i	$-0.635964\pi$
$983$	−2.38430e16	−0.828544	−0.414272	+	0.910153i	$0.635964\pi$
$984$	0	0
$985$	3.97816e16	1.36705
$986$	−7.01839e15	−0.239836
$987$	0	0
$988$	2.90893e15	0.0983038
$989$	4.98985e15	0.167690
$990$	0	0
$991$	−3.56181e16	−1.18377	−0.591883	−	0.806024i	$-0.701615\pi$
$991$	−3.56181e16	−1.18377	−0.591883	+	0.806024i	$0.701615\pi$
$992$	9.14007e15	0.302089
$993$	0	0
$994$	4.25321e15	0.139025
$995$	8.33159e16	2.70833
$996$	0	0
$997$	3.21478e16	1.03354	0.516771	−	0.856123i	$-0.327134\pi$
$997$	3.21478e16	1.03354	0.516771	+	0.856123i	$0.327134\pi$
$998$	−4.38971e16	−1.40352
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.12.a.d.1.8		11
3.2	odd	2		23.12.a.b.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.12.a.b.1.4	✓	11	3.2	odd	2
207.12.a.d.1.8		11	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q+43.0566 q^{2} -194.133 q^{4} +11277.9 q^{5} -9281.65 q^{7} -96538.5 q^{8} +O(q^{10})\)	\(q+43.0566 q^{2} -194.133 q^{4} +11277.9 q^{5} -9281.65 q^{7} -96538.5 q^{8} +485588. q^{10} +775928. q^{11} -1.35775e6 q^{13} -399636. q^{14} -3.75903e6 q^{16} -5.04724e6 q^{17} +1.10360e7 q^{19} -2.18942e6 q^{20} +3.34088e7 q^{22} +6.43634e6 q^{23} +7.83629e7 q^{25} -5.84601e7 q^{26} +1.80188e6 q^{28} +3.22957e7 q^{29} +2.54882e8 q^{31} +3.58600e7 q^{32} -2.17317e8 q^{34} -1.04678e8 q^{35} -3.12485e8 q^{37} +4.75174e8 q^{38} -1.08875e9 q^{40} -8.65298e8 q^{41} +7.75261e8 q^{43} -1.50634e8 q^{44} +2.77127e8 q^{46} +2.34472e9 q^{47} -1.89118e9 q^{49} +3.37404e9 q^{50} +2.63585e8 q^{52} +4.77808e9 q^{53} +8.75084e9 q^{55} +8.96037e8 q^{56} +1.39054e9 q^{58} +1.57779e9 q^{59} -9.63652e9 q^{61} +1.09743e10 q^{62} +9.24250e9 q^{64} -1.53126e10 q^{65} +1.06227e10 q^{67} +9.79838e8 q^{68} -4.50705e9 q^{70} -1.06427e10 q^{71} +1.53965e9 q^{73} -1.34545e10 q^{74} -2.14246e9 q^{76} -7.20189e9 q^{77} +2.42947e10 q^{79} -4.23940e10 q^{80} -3.72567e10 q^{82} -1.34063e10 q^{83} -5.69222e10 q^{85} +3.33801e10 q^{86} -7.49070e10 q^{88} +4.54047e10 q^{89} +1.26022e10 q^{91} -1.24951e9 q^{92} +1.00956e11 q^{94} +1.24463e11 q^{95} -9.36141e10 q^{97} -8.14276e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} + 11264 q^{4} - 1034 q^{5} + 159584 q^{7} - 115497 q^{8}+O(q^{10}) \) 11 * q - 32 * q^2 + 11264 * q^4 - 1034 * q^5 + 159584 * q^7 - 115497 * q^8	\( 11 q - 32 q^{2} + 11264 q^{4} - 1034 q^{5} + 159584 q^{7} - 115497 q^{8} - 627650 q^{10} + 771396 q^{11} + 3433434 q^{13} - 4585896 q^{14} + 18802384 q^{16} - 29035398 q^{17} + 21398428 q^{19} - 72466260 q^{20} + 100463524 q^{22} + 70799773 q^{23} + 233562509 q^{25} - 328796191 q^{26} + 499445210 q^{28} - 226699042 q^{29} + 251932328 q^{31} - 806116648 q^{32} + 325378622 q^{34} + 355232072 q^{35} + 573876170 q^{37} + 770782036 q^{38} - 1009699226 q^{40} + 1733596378 q^{41} + 647370308 q^{43} + 4662321170 q^{44} - 205962976 q^{46} + 5436527248 q^{47} + 4356386219 q^{49} + 10296502416 q^{50} - 5616607137 q^{52} + 3387203910 q^{53} - 10571441512 q^{55} - 635842210 q^{56} + 1991171353 q^{58} - 15113662084 q^{59} + 23895772578 q^{61} - 7557529251 q^{62} + 32993181147 q^{64} - 3660035708 q^{65} + 46806014468 q^{67} - 40754169364 q^{68} - 12274756860 q^{70} - 45541532768 q^{71} + 63786612542 q^{73} + 41720765910 q^{74} + 5581739704 q^{76} - 19147126968 q^{77} + 21847812496 q^{79} + 67715736674 q^{80} - 30216129401 q^{82} - 40153340788 q^{83} + 116854272412 q^{85} + 47307463306 q^{86} - 263050721364 q^{88} - 37300228382 q^{89} + 109416811256 q^{91} + 72498967552 q^{92} - 378035850441 q^{94} + 255722421456 q^{95} - 243602730 q^{97} + 514347061348 q^{98}+O(q^{100}) \) 11 * q - 32 * q^2 + 11264 * q^4 - 1034 * q^5 + 159584 * q^7 - 115497 * q^8 - 627650 * q^10 + 771396 * q^11 + 3433434 * q^13 - 4585896 * q^14 + 18802384 * q^16 - 29035398 * q^17 + 21398428 * q^19 - 72466260 * q^20 + 100463524 * q^22 + 70799773 * q^23 + 233562509 * q^25 - 328796191 * q^26 + 499445210 * q^28 - 226699042 * q^29 + 251932328 * q^31 - 806116648 * q^32 + 325378622 * q^34 + 355232072 * q^35 + 573876170 * q^37 + 770782036 * q^38 - 1009699226 * q^40 + 1733596378 * q^41 + 647370308 * q^43 + 4662321170 * q^44 - 205962976 * q^46 + 5436527248 * q^47 + 4356386219 * q^49 + 10296502416 * q^50 - 5616607137 * q^52 + 3387203910 * q^53 - 10571441512 * q^55 - 635842210 * q^56 + 1991171353 * q^58 - 15113662084 * q^59 + 23895772578 * q^61 - 7557529251 * q^62 + 32993181147 * q^64 - 3660035708 * q^65 + 46806014468 * q^67 - 40754169364 * q^68 - 12274756860 * q^70 - 45541532768 * q^71 + 63786612542 * q^73 + 41720765910 * q^74 + 5581739704 * q^76 - 19147126968 * q^77 + 21847812496 * q^79 + 67715736674 * q^80 - 30216129401 * q^82 - 40153340788 * q^83 + 116854272412 * q^85 + 47307463306 * q^86 - 263050721364 * q^88 - 37300228382 * q^89 + 109416811256 * q^91 + 72498967552 * q^92 - 378035850441 * q^94 + 255722421456 * q^95 - 243602730 * q^97 + 514347061348 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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