LMFDB - Embedded newform 207.8.a.d.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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 775x^{5} - 474x^{4} + 167184x^{3} - 33920x^{2} - 9348928x + 28965760 $ x^7 - 775x^5 - 474x^4 + 167184x^3 - 33920x^2 - 9348928*x + 28965760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\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			$22.2240$ 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)

$f(q)$	$=$	$q-22.2240 q^{2} +365.907 q^{4} +417.971 q^{5} +1389.11 q^{7} -5287.24 q^{8} +O(q^{10})$	\(q-22.2240 q^{2} +365.907 q^{4} +417.971 q^{5} +1389.11 q^{7} -5287.24 q^{8} -9288.99 q^{10} -3388.40 q^{11} +2866.14 q^{13} -30871.5 q^{14} +70667.6 q^{16} -3112.60 q^{17} +16704.2 q^{19} +152938. q^{20} +75303.8 q^{22} +12167.0 q^{23} +96574.8 q^{25} -63697.2 q^{26} +508283. q^{28} +144612. q^{29} -250250. q^{31} -893751. q^{32} +69174.5 q^{34} +580606. q^{35} +547157. q^{37} -371235. q^{38} -2.20991e6 q^{40} +776692. q^{41} -574944. q^{43} -1.23984e6 q^{44} -270400. q^{46} -311646. q^{47} +1.10608e6 q^{49} -2.14628e6 q^{50} +1.04874e6 q^{52} -116768. q^{53} -1.41625e6 q^{55} -7.34454e6 q^{56} -3.21386e6 q^{58} -253456. q^{59} +251888. q^{61} +5.56156e6 q^{62} +1.08173e7 q^{64} +1.19796e6 q^{65} +963675. q^{67} -1.13892e6 q^{68} -1.29034e7 q^{70} +4.64909e6 q^{71} -724338. q^{73} -1.21600e7 q^{74} +6.11218e6 q^{76} -4.70685e6 q^{77} -2.56150e6 q^{79} +2.95370e7 q^{80} -1.72612e7 q^{82} +1.99395e6 q^{83} -1.30098e6 q^{85} +1.27776e7 q^{86} +1.79153e7 q^{88} -4.59998e6 q^{89} +3.98138e6 q^{91} +4.45199e6 q^{92} +6.92602e6 q^{94} +6.98188e6 q^{95} +9.59005e6 q^{97} -2.45814e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8}+O(q^{10}) $ 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8} - 15310 q^{10} - 9040 q^{11} + 3774 q^{13} - 4536 q^{14} + 52002 q^{16} + 40760 q^{17} + 81598 q^{19} + 88946 q^{20} + 245034 q^{22} + 85169 q^{23} + 321325 q^{25} - 412748 q^{26} + 965948 q^{28} - 154126 q^{29} + 243132 q^{31} - 1278286 q^{32} + 984836 q^{34} + 130296 q^{35} + 582114 q^{37} - 772558 q^{38} - 132618 q^{40} - 113062 q^{41} - 659778 q^{43} - 659390 q^{44} + 591032 q^{47} + 3263235 q^{49} + 702684 q^{50} + 1793280 q^{52} - 207128 q^{53} + 184664 q^{55} - 5390508 q^{56} - 1142916 q^{58} - 447148 q^{59} + 2248970 q^{61} + 5729060 q^{62} + 7212922 q^{64} + 827096 q^{65} + 4467570 q^{67} + 5477620 q^{68} - 12744284 q^{70} + 5154608 q^{71} - 13239250 q^{73} + 2827426 q^{74} - 527434 q^{76} + 18415912 q^{77} + 9594446 q^{79} + 55932394 q^{80} - 20889952 q^{82} + 573720 q^{83} + 7477272 q^{85} + 28416910 q^{86} + 26555702 q^{88} + 3810540 q^{89} + 36092068 q^{91} + 7957218 q^{92} + 33545768 q^{94} - 10497320 q^{95} + 49497978 q^{97} + 1023376 q^{98}+O(q^{100}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8 - 15310 * q^10 - 9040 * q^11 + 3774 * q^13 - 4536 * q^14 + 52002 * q^16 + 40760 * q^17 + 81598 * q^19 + 88946 * q^20 + 245034 * q^22 + 85169 * q^23 + 321325 * q^25 - 412748 * q^26 + 965948 * q^28 - 154126 * q^29 + 243132 * q^31 - 1278286 * q^32 + 984836 * q^34 + 130296 * q^35 + 582114 * q^37 - 772558 * q^38 - 132618 * q^40 - 113062 * q^41 - 659778 * q^43 - 659390 * q^44 + 591032 * q^47 + 3263235 * q^49 + 702684 * q^50 + 1793280 * q^52 - 207128 * q^53 + 184664 * q^55 - 5390508 * q^56 - 1142916 * q^58 - 447148 * q^59 + 2248970 * q^61 + 5729060 * q^62 + 7212922 * q^64 + 827096 * q^65 + 4467570 * q^67 + 5477620 * q^68 - 12744284 * q^70 + 5154608 * q^71 - 13239250 * q^73 + 2827426 * q^74 - 527434 * q^76 + 18415912 * q^77 + 9594446 * q^79 + 55932394 * q^80 - 20889952 * q^82 + 573720 * q^83 + 7477272 * q^85 + 28416910 * q^86 + 26555702 * q^88 + 3810540 * q^89 + 36092068 * q^91 + 7957218 * q^92 + 33545768 * q^94 - 10497320 * q^95 + 49497978 * q^97 + 1023376 * 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 $

$2$	−22.2240	−1.96434	−0.982172	−	0.187986i	$-0.939804\pi$
$2$	−22.2240	−1.96434	−0.982172	+	0.187986i	$0.939804\pi$
$3$	0	0
$3$	0	0
$4$	365.907	2.85865
$5$	417.971	1.49538	0.747689	−	0.664049i	$-0.231163\pi$
$5$	417.971	1.49538	0.747689	+	0.664049i	$0.231163\pi$
$6$	0	0
$7$	1389.11	1.53071	0.765354	−	0.643609i	$-0.222564\pi$
$7$	1389.11	1.53071	0.765354	+	0.643609i	$0.222564\pi$
$8$	−5287.24	−3.65102
$9$	0	0
$10$	−9288.99	−2.93744
$11$	−3388.40	−0.767574	−0.383787	−	0.923422i	$-0.625380\pi$
$11$	−3388.40	−0.767574	−0.383787	+	0.923422i	$0.625380\pi$
$12$	0	0
$13$	2866.14	0.361823	0.180911	−	0.983499i	$-0.442095\pi$
$13$	2866.14	0.361823	0.180911	+	0.983499i	$0.442095\pi$
$14$	−30871.5	−3.00684
$15$	0	0
$16$	70667.6	4.31321
$17$	−3112.60	−0.153657	−0.0768286	−	0.997044i	$-0.524479\pi$
$17$	−3112.60	−0.153657	−0.0768286	+	0.997044i	$0.524479\pi$
$18$	0	0
$19$	16704.2	0.558713	0.279356	−	0.960187i	$-0.409879\pi$
$19$	16704.2	0.558713	0.279356	+	0.960187i	$0.409879\pi$
$20$	152938.	4.27476
$21$	0	0
$22$	75303.8	1.50778
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	96574.8	1.23616
$26$	−63697.2	−0.710744
$27$	0	0
$28$	508283.	4.37575
$29$	144612.	1.10106	0.550531	−	0.834815i	$-0.314425\pi$
$29$	144612.	1.10106	0.550531	+	0.834815i	$0.314425\pi$
$30$	0	0
$31$	−250250.	−1.50872	−0.754359	−	0.656462i	$-0.772052\pi$
$31$	−250250.	−1.50872	−0.754359	+	0.656462i	$0.772052\pi$
$32$	−893751.	−4.82161
$33$	0	0
$34$	69174.5	0.301835
$35$	580606.	2.28899
$36$	0	0
$37$	547157.	1.77585	0.887924	−	0.459991i	$-0.152147\pi$
$37$	547157.	1.77585	0.887924	+	0.459991i	$0.152147\pi$
$38$	−371235.	−1.09750
$39$	0	0
$40$	−2.20991e6	−5.45965
$41$	776692.	1.75997	0.879985	−	0.475002i	$-0.157553\pi$
$41$	776692.	1.75997	0.879985	+	0.475002i	$0.157553\pi$
$42$	0	0
$43$	−574944.	−1.10277	−0.551386	−	0.834250i	$-0.685901\pi$
$43$	−574944.	−1.10277	−0.551386	+	0.834250i	$0.685901\pi$
$44$	−1.23984e6	−2.19422
$45$	0	0
$46$	−270400.	−0.409594
$47$	−311646.	−0.437843	−0.218922	−	0.975742i	$-0.570254\pi$
$47$	−311646.	−0.437843	−0.218922	+	0.975742i	$0.570254\pi$
$48$	0	0
$49$	1.10608e6	1.34307
$50$	−2.14628e6	−2.42824
$51$	0	0
$52$	1.04874e6	1.03432
$53$	−116768.	−0.107736	−0.0538679	−	0.998548i	$-0.517155\pi$
$53$	−116768.	−0.107736	−0.0538679	+	0.998548i	$0.517155\pi$
$54$	0	0
$55$	−1.41625e6	−1.14781
$56$	−7.34454e6	−5.58865
$57$	0	0
$58$	−3.21386e6	−2.16286
$59$	−253456.	−0.160665	−0.0803324	−	0.996768i	$-0.525598\pi$
$59$	−253456.	−0.160665	−0.0803324	+	0.996768i	$0.525598\pi$
$60$	0	0
$61$	251888.	0.142086	0.0710432	−	0.997473i	$-0.477367\pi$
$61$	251888.	0.142086	0.0710432	+	0.997473i	$0.477367\pi$
$62$	5.56156e6	2.96364
$63$	0	0
$64$	1.08173e7	5.15808
$65$	1.19796e6	0.541062
$66$	0	0
$67$	963675.	0.391443	0.195722	−	0.980659i	$-0.437295\pi$
$67$	963675.	0.391443	0.195722	+	0.980659i	$0.437295\pi$
$68$	−1.13892e6	−0.439251
$69$	0	0
$70$	−1.29034e7	−4.49636
$71$	4.64909e6	1.54157	0.770786	−	0.637094i	$-0.219864\pi$
$71$	4.64909e6	1.54157	0.770786	+	0.637094i	$0.219864\pi$
$72$	0	0
$73$	−724338.	−0.217927	−0.108964	−	0.994046i	$-0.534753\pi$
$73$	−724338.	−0.217927	−0.108964	+	0.994046i	$0.534753\pi$
$74$	−1.21600e7	−3.48837
$75$	0	0
$76$	6.11218e6	1.59716
$77$	−4.70685e6	−1.17493
$78$	0	0
$79$	−2.56150e6	−0.584520	−0.292260	−	0.956339i	$-0.594407\pi$
$79$	−2.56150e6	−0.584520	−0.292260	+	0.956339i	$0.594407\pi$
$80$	2.95370e7	6.44988
$81$	0	0
$82$	−1.72612e7	−3.45718
$83$	1.99395e6	0.382772	0.191386	−	0.981515i	$-0.438702\pi$
$83$	1.99395e6	0.382772	0.191386	+	0.981515i	$0.438702\pi$
$84$	0	0
$85$	−1.30098e6	−0.229776
$86$	1.27776e7	2.16622
$87$	0	0
$88$	1.79153e7	2.80243
$89$	−4.59998e6	−0.691657	−0.345829	−	0.938298i	$-0.612402\pi$
$89$	−4.59998e6	−0.691657	−0.345829	+	0.938298i	$0.612402\pi$
$90$	0	0
$91$	3.98138e6	0.553845
$92$	4.45199e6	0.596069
$93$	0	0
$94$	6.92602e6	0.860075
$95$	6.98188e6	0.835487
$96$	0	0
$97$	9.59005e6	1.06689	0.533445	−	0.845835i	$-0.320897\pi$
$97$	9.59005e6	1.06689	0.533445	+	0.845835i	$0.320897\pi$
$98$	−2.45814e7	−2.63825
$99$	0	0
$100$	3.53373e7	3.53373
$101$	4.54710e6	0.439147	0.219573	−	0.975596i	$-0.429533\pi$
$101$	4.54710e6	0.439147	0.219573	+	0.975596i	$0.429533\pi$
$102$	0	0
$103$	−1.42961e7	−1.28910	−0.644550	−	0.764562i	$-0.722955\pi$
$103$	−1.42961e7	−1.28910	−0.644550	+	0.764562i	$0.722955\pi$
$104$	−1.51540e7	−1.32102
$105$	0	0
$106$	2.59506e6	0.211630
$107$	8.69305e6	0.686008	0.343004	−	0.939334i	$-0.388556\pi$
$107$	8.69305e6	0.686008	0.343004	+	0.939334i	$0.388556\pi$
$108$	0	0
$109$	−3.43943e6	−0.254386	−0.127193	−	0.991878i	$-0.540597\pi$
$109$	−3.43943e6	−0.254386	−0.127193	+	0.991878i	$0.540597\pi$
$110$	3.14748e7	2.25470
$111$	0	0
$112$	9.81649e7	6.60227
$113$	1.89125e7	1.23303	0.616515	−	0.787343i	$-0.288544\pi$
$113$	1.89125e7	1.23303	0.616515	+	0.787343i	$0.288544\pi$
$114$	0	0
$115$	5.08545e6	0.311808
$116$	5.29145e7	3.14754
$117$	0	0
$118$	5.63281e6	0.315601
$119$	−4.32374e6	−0.235204
$120$	0	0
$121$	−8.00592e6	−0.410830
$122$	−5.59796e6	−0.279107
$123$	0	0
$124$	−9.15682e7	−4.31289
$125$	7.71146e6	0.353144
$126$	0	0
$127$	4.10192e6	0.177695	0.0888473	−	0.996045i	$-0.471682\pi$
$127$	4.10192e6	0.177695	0.0888473	+	0.996045i	$0.471682\pi$
$128$	−1.26003e8	−5.31064
$129$	0	0
$130$	−2.66236e7	−1.06283
$131$	648415.	0.0252002	0.0126001	−	0.999921i	$-0.495989\pi$
$131$	648415.	0.0252002	0.0126001	+	0.999921i	$0.495989\pi$
$132$	0	0
$133$	2.32039e7	0.855226
$134$	−2.14167e7	−0.768929
$135$	0	0
$136$	1.64571e7	0.561005
$137$	−4.20728e7	−1.39791	−0.698956	−	0.715165i	$-0.746352\pi$
$137$	−4.20728e7	−1.39791	−0.698956	+	0.715165i	$0.746352\pi$
$138$	0	0
$139$	2.45140e7	0.774218	0.387109	−	0.922034i	$-0.373474\pi$
$139$	2.45140e7	0.774218	0.387109	+	0.922034i	$0.373474\pi$
$140$	2.12448e8	6.54341
$141$	0	0
$142$	−1.03321e8	−3.02818
$143$	−9.71163e6	−0.277726
$144$	0	0
$145$	6.04436e7	1.64650
$146$	1.60977e7	0.428084
$147$	0	0
$148$	2.00208e8	5.07652
$149$	−6.48888e7	−1.60701	−0.803504	−	0.595300i	$-0.797033\pi$
$149$	−6.48888e7	−1.60701	−0.803504	+	0.595300i	$0.797033\pi$
$150$	0	0
$151$	−2.40931e7	−0.569473	−0.284737	−	0.958606i	$-0.591906\pi$
$151$	−2.40931e7	−0.569473	−0.284737	+	0.958606i	$0.591906\pi$
$152$	−8.83192e7	−2.03987
$153$	0	0
$154$	1.04605e8	2.30797
$155$	−1.04597e8	−2.25611
$156$	0	0
$157$	−3.15613e7	−0.650888	−0.325444	−	0.945561i	$-0.605514\pi$
$157$	−3.15613e7	−0.650888	−0.325444	+	0.945561i	$0.605514\pi$
$158$	5.69267e7	1.14820
$159$	0	0
$160$	−3.73562e8	−7.21013
$161$	1.69013e7	0.319175
$162$	0	0
$163$	1.08520e8	1.96269	0.981347	−	0.192246i	$-0.0615771\pi$
$163$	1.08520e8	1.96269	0.981347	+	0.192246i	$0.0615771\pi$
$164$	2.84197e8	5.03113
$165$	0	0
$166$	−4.43135e7	−0.751896
$167$	−3.10734e7	−0.516274	−0.258137	−	0.966108i	$-0.583109\pi$
$167$	−3.10734e7	−0.516274	−0.258137	+	0.966108i	$0.583109\pi$
$168$	0	0
$169$	−5.45337e7	−0.869084
$170$	2.89130e7	0.451358
$171$	0	0
$172$	−2.10376e8	−3.15244
$173$	1.56813e7	0.230261	0.115130	−	0.993350i	$-0.463271\pi$
$173$	1.56813e7	0.230261	0.115130	+	0.993350i	$0.463271\pi$
$174$	0	0
$175$	1.34153e8	1.89220
$176$	−2.39450e8	−3.31071
$177$	0	0
$178$	1.02230e8	1.35865
$179$	9.85361e7	1.28413	0.642066	−	0.766649i	$-0.278077\pi$
$179$	9.85361e7	1.28413	0.642066	+	0.766649i	$0.278077\pi$
$180$	0	0
$181$	1.45348e7	0.182194	0.0910970	−	0.995842i	$-0.470963\pi$
$181$	1.45348e7	0.182194	0.0910970	+	0.995842i	$0.470963\pi$
$182$	−8.84822e7	−1.08794
$183$	0	0
$184$	−6.43298e7	−0.761290
$185$	2.28696e8	2.65556
$186$	0	0
$187$	1.05467e7	0.117943
$188$	−1.14033e8	−1.25164
$189$	0	0
$190$	−1.55165e8	−1.64118
$191$	−9.98824e7	−1.03722	−0.518612	−	0.855010i	$-0.673551\pi$
$191$	−9.98824e7	−1.03722	−0.518612	+	0.855010i	$0.673551\pi$
$192$	0	0
$193$	2.65643e7	0.265979	0.132989	−	0.991117i	$-0.457542\pi$
$193$	2.65643e7	0.265979	0.132989	+	0.991117i	$0.457542\pi$
$194$	−2.13129e8	−2.09574
$195$	0	0
$196$	4.04720e8	3.83936
$197$	1.54032e8	1.43542	0.717708	−	0.696344i	$-0.245191\pi$
$197$	1.54032e8	1.43542	0.717708	+	0.696344i	$0.245191\pi$
$198$	0	0
$199$	−5.52323e7	−0.496830	−0.248415	−	0.968654i	$-0.579910\pi$
$199$	−5.52323e7	−0.496830	−0.248415	+	0.968654i	$0.579910\pi$
$200$	−5.10614e8	−4.51323
$201$	0	0
$202$	−1.01055e8	−0.862635
$203$	2.00882e8	1.68540
$204$	0	0
$205$	3.24635e8	2.63182
$206$	3.17716e8	2.53223
$207$	0	0
$208$	2.02543e8	1.56062
$209$	−5.66006e7	−0.428853
$210$	0	0
$211$	3.34015e7	0.244781	0.122391	−	0.992482i	$-0.460944\pi$
$211$	3.34015e7	0.244781	0.122391	+	0.992482i	$0.460944\pi$
$212$	−4.27263e7	−0.307978
$213$	0	0
$214$	−1.93194e8	−1.34755
$215$	−2.40310e8	−1.64906
$216$	0	0
$217$	−3.47624e8	−2.30941
$218$	7.64378e7	0.499702
$219$	0	0
$220$	−5.18216e8	−3.28119
$221$	−8.92116e6	−0.0555966
$222$	0	0
$223$	1.79657e8	1.08487	0.542434	−	0.840099i	$-0.317503\pi$
$223$	1.79657e8	1.08487	0.542434	+	0.840099i	$0.317503\pi$
$224$	−1.24152e9	−7.38047
$225$	0	0
$226$	−4.20311e8	−2.42209
$227$	1.68744e8	0.957496	0.478748	−	0.877952i	$-0.341091\pi$
$227$	1.68744e8	0.957496	0.478748	+	0.877952i	$0.341091\pi$
$228$	0	0
$229$	−3.13970e8	−1.72768	−0.863842	−	0.503762i	$-0.831949\pi$
$229$	−3.13970e8	−1.72768	−0.863842	+	0.503762i	$0.831949\pi$
$230$	−1.13019e8	−0.612498
$231$	0	0
$232$	−7.64599e8	−4.02000
$233$	1.78329e8	0.923584	0.461792	−	0.886988i	$-0.347207\pi$
$233$	1.78329e8	0.923584	0.461792	+	0.886988i	$0.347207\pi$
$234$	0	0
$235$	−1.30259e8	−0.654741
$236$	−9.27413e7	−0.459284
$237$	0	0
$238$	9.60908e7	0.462022
$239$	−1.09891e8	−0.520676	−0.260338	−	0.965518i	$-0.583834\pi$
$239$	−1.09891e8	−0.520676	−0.260338	+	0.965518i	$0.583834\pi$
$240$	0	0
$241$	1.68806e8	0.776834	0.388417	−	0.921484i	$-0.373022\pi$
$241$	1.68806e8	0.776834	0.388417	+	0.921484i	$0.373022\pi$
$242$	1.77924e8	0.807012
$243$	0	0
$244$	9.21674e7	0.406175
$245$	4.62307e8	2.00840
$246$	0	0
$247$	4.78767e7	0.202155
$248$	1.32313e9	5.50836
$249$	0	0
$250$	−1.71380e8	−0.693696
$251$	−9.33880e7	−0.372763	−0.186382	−	0.982477i	$-0.559676\pi$
$251$	−9.33880e7	−0.372763	−0.186382	+	0.982477i	$0.559676\pi$
$252$	0	0
$253$	−4.12267e7	−0.160050
$254$	−9.11611e7	−0.349053
$255$	0	0
$256$	1.41568e9	5.27384
$257$	3.05188e8	1.12150	0.560752	−	0.827984i	$-0.310512\pi$
$257$	3.05188e8	1.12150	0.560752	+	0.827984i	$0.310512\pi$
$258$	0	0
$259$	7.60059e8	2.71830
$260$	4.38343e8	1.54670
$261$	0	0
$262$	−1.44104e7	−0.0495018
$263$	2.95191e7	0.100059	0.0500297	−	0.998748i	$-0.484068\pi$
$263$	2.95191e7	0.100059	0.0500297	+	0.998748i	$0.484068\pi$
$264$	0	0
$265$	−4.88058e7	−0.161106
$266$	−5.15685e8	−1.67996
$267$	0	0
$268$	3.52615e8	1.11900
$269$	2.07828e8	0.650986	0.325493	−	0.945544i	$-0.394470\pi$
$269$	2.07828e8	0.650986	0.325493	+	0.945544i	$0.394470\pi$
$270$	0	0
$271$	−2.94736e8	−0.899583	−0.449791	−	0.893134i	$-0.648502\pi$
$271$	−2.94736e8	−0.899583	−0.449791	+	0.893134i	$0.648502\pi$
$272$	−2.19960e8	−0.662755
$273$	0	0
$274$	9.35027e8	2.74598
$275$	−3.27234e8	−0.948842
$276$	0	0
$277$	3.87811e8	1.09633	0.548165	−	0.836370i	$-0.315327\pi$
$277$	3.87811e8	1.09633	0.548165	+	0.836370i	$0.315327\pi$
$278$	−5.44800e8	−1.52083
$279$	0	0
$280$	−3.06981e9	−8.35714
$281$	2.76241e8	0.742705	0.371353	−	0.928492i	$-0.378894\pi$
$281$	2.76241e8	0.742705	0.371353	+	0.928492i	$0.378894\pi$
$282$	0	0
$283$	4.59025e8	1.20388	0.601941	−	0.798540i	$-0.294394\pi$
$283$	4.59025e8	1.20388	0.601941	+	0.798540i	$0.294394\pi$
$284$	1.70113e9	4.40681
$285$	0	0
$286$	2.15831e8	0.545549
$287$	1.07891e9	2.69400
$288$	0	0
$289$	−4.00650e8	−0.976389
$290$	−1.34330e9	−3.23430
$291$	0	0
$292$	−2.65040e8	−0.622976
$293$	1.24865e7	0.0290004	0.0145002	−	0.999895i	$-0.495384\pi$
$293$	1.24865e7	0.0290004	0.0145002	+	0.999895i	$0.495384\pi$
$294$	0	0
$295$	−1.05937e8	−0.240255
$296$	−2.89295e9	−6.48365
$297$	0	0
$298$	1.44209e9	3.15671
$299$	3.48723e7	0.0754453
$300$	0	0
$301$	−7.98659e8	−1.68802
$302$	5.35445e8	1.11864
$303$	0	0
$304$	1.18045e9	2.40984
$305$	1.05282e8	0.212473
$306$	0	0
$307$	2.42015e8	0.477372	0.238686	−	0.971097i	$-0.423283\pi$
$307$	2.42015e8	0.477372	0.238686	+	0.971097i	$0.423283\pi$
$308$	−1.72227e9	−3.35871
$309$	0	0
$310$	2.32457e9	4.43177
$311$	7.42752e8	1.40018	0.700088	−	0.714057i	$-0.253144\pi$
$311$	7.42752e8	1.40018	0.700088	+	0.714057i	$0.253144\pi$
$312$	0	0
$313$	4.76077e8	0.877550	0.438775	−	0.898597i	$-0.355412\pi$
$313$	4.76077e8	0.877550	0.438775	+	0.898597i	$0.355412\pi$
$314$	7.01419e8	1.27857
$315$	0	0
$316$	−9.37269e8	−1.67093
$317$	−3.76385e8	−0.663629	−0.331814	−	0.943345i	$-0.607661\pi$
$317$	−3.76385e8	−0.663629	−0.331814	+	0.943345i	$0.607661\pi$
$318$	0	0
$319$	−4.90003e8	−0.845146
$320$	4.52131e9	7.71328
$321$	0	0
$322$	−3.75614e8	−0.626969
$323$	−5.19936e7	−0.0858502
$324$	0	0
$325$	2.76797e8	0.447270
$326$	−2.41175e9	−3.85540
$327$	0	0
$328$	−4.10656e9	−6.42568
$329$	−4.32909e8	−0.670210
$330$	0	0
$331$	−2.38966e8	−0.362192	−0.181096	−	0.983465i	$-0.557964\pi$
$331$	−2.38966e8	−0.362192	−0.181096	+	0.983465i	$0.557964\pi$
$332$	7.29599e8	1.09421
$333$	0	0
$334$	6.90575e8	1.01414
$335$	4.02788e8	0.585356
$336$	0	0
$337$	−1.35059e8	−0.192229	−0.0961144	−	0.995370i	$-0.530641\pi$
$337$	−1.35059e8	−0.192229	−0.0961144	+	0.995370i	$0.530641\pi$
$338$	1.21196e9	1.70718
$339$	0	0
$340$	−4.76037e8	−0.656847
$341$	8.47947e8	1.15805
$342$	0	0
$343$	3.92468e8	0.525139
$344$	3.03987e9	4.02624
$345$	0	0
$346$	−3.48501e8	−0.452311
$347$	−1.38715e9	−1.78225	−0.891126	−	0.453756i	$-0.850084\pi$
$347$	−1.38715e9	−1.78225	−0.891126	+	0.453756i	$0.850084\pi$
$348$	0	0
$349$	1.40106e9	1.76428	0.882140	−	0.470987i	$-0.156102\pi$
$349$	1.40106e9	1.76428	0.882140	+	0.470987i	$0.156102\pi$
$350$	−2.98141e9	−3.71692
$351$	0	0
$352$	3.02839e9	3.70094
$353$	−1.57265e8	−0.190292	−0.0951459	−	0.995463i	$-0.530332\pi$
$353$	−1.57265e8	−0.190292	−0.0951459	+	0.995463i	$0.530332\pi$
$354$	0	0
$355$	1.94318e9	2.30523
$356$	−1.68316e9	−1.97720
$357$	0	0
$358$	−2.18987e9	−2.52248
$359$	8.77462e8	1.00092	0.500458	−	0.865761i	$-0.333165\pi$
$359$	8.77462e8	1.00092	0.500458	+	0.865761i	$0.333165\pi$
$360$	0	0
$361$	−6.14841e8	−0.687840
$362$	−3.23022e8	−0.357892
$363$	0	0
$364$	1.45681e9	1.58325
$365$	−3.02752e8	−0.325884
$366$	0	0
$367$	−5.25802e8	−0.555253	−0.277626	−	0.960689i	$-0.589548\pi$
$367$	−5.25802e8	−0.555253	−0.277626	+	0.960689i	$0.589548\pi$
$368$	8.59813e8	0.899366
$369$	0	0
$370$	−5.08253e9	−5.21644
$371$	−1.62204e8	−0.164912
$372$	0	0
$373$	−1.12191e9	−1.11937	−0.559687	−	0.828704i	$-0.689079\pi$
$373$	−1.12191e9	−1.11937	−0.559687	+	0.828704i	$0.689079\pi$
$374$	−2.34391e8	−0.231681
$375$	0	0
$376$	1.64775e9	1.59857
$377$	4.14479e8	0.398389
$378$	0	0
$379$	−1.34722e9	−1.27116	−0.635579	−	0.772036i	$-0.719239\pi$
$379$	−1.34722e9	−1.27116	−0.635579	+	0.772036i	$0.719239\pi$
$380$	2.55472e9	2.38836
$381$	0	0
$382$	2.21979e9	2.03746
$383$	−6.72553e8	−0.611689	−0.305845	−	0.952081i	$-0.598939\pi$
$383$	−6.72553e8	−0.611689	−0.305845	+	0.952081i	$0.598939\pi$
$384$	0	0
$385$	−1.96733e9	−1.75697
$386$	−5.90364e8	−0.522474
$387$	0	0
$388$	3.50906e9	3.04986
$389$	−1.43039e9	−1.23205	−0.616027	−	0.787725i	$-0.711259\pi$
$389$	−1.43039e9	−1.23205	−0.616027	+	0.787725i	$0.711259\pi$
$390$	0	0
$391$	−3.78711e7	−0.0320397
$392$	−5.84809e9	−4.90357
$393$	0	0
$394$	−3.42320e9	−2.81965
$395$	−1.07063e9	−0.874078
$396$	0	0
$397$	1.60650e9	1.28859	0.644295	−	0.764777i	$-0.277151\pi$
$397$	1.60650e9	1.28859	0.644295	+	0.764777i	$0.277151\pi$
$398$	1.22748e9	0.975945
$399$	0	0
$400$	6.82471e9	5.33180
$401$	9.04514e8	0.700503	0.350251	−	0.936656i	$-0.386096\pi$
$401$	9.04514e8	0.700503	0.350251	+	0.936656i	$0.386096\pi$
$402$	0	0
$403$	−7.17252e8	−0.545889
$404$	1.66381e9	1.25537
$405$	0	0
$406$	−4.46439e9	−3.31071
$407$	−1.85399e9	−1.36309
$408$	0	0
$409$	2.02789e9	1.46559	0.732796	−	0.680449i	$-0.238215\pi$
$409$	2.02789e9	1.46559	0.732796	+	0.680449i	$0.238215\pi$
$410$	−7.21468e9	−5.16980
$411$	0	0
$412$	−5.23103e9	−3.68508
$413$	−3.52078e8	−0.245931
$414$	0	0
$415$	8.33413e8	0.572390
$416$	−2.56162e9	−1.74457
$417$	0	0
$418$	1.25789e9	0.842415
$419$	−2.49139e9	−1.65460	−0.827298	−	0.561763i	$-0.810123\pi$
$419$	−2.49139e9	−1.65460	−0.827298	+	0.561763i	$0.810123\pi$
$420$	0	0
$421$	2.41551e9	1.57769	0.788845	−	0.614592i	$-0.210679\pi$
$421$	2.41551e9	1.57769	0.788845	+	0.614592i	$0.210679\pi$
$422$	−7.42316e8	−0.480834
$423$	0	0
$424$	6.17382e8	0.393345
$425$	−3.00599e8	−0.189944
$426$	0	0
$427$	3.49899e8	0.217493
$428$	3.18084e9	1.96105
$429$	0	0
$430$	5.34065e9	3.23933
$431$	−1.84369e9	−1.10922	−0.554610	−	0.832110i	$-0.687133\pi$
$431$	−1.84369e9	−1.10922	−0.554610	+	0.832110i	$0.687133\pi$
$432$	0	0
$433$	5.61282e8	0.332256	0.166128	−	0.986104i	$-0.446873\pi$
$433$	5.61282e8	0.332256	0.166128	+	0.986104i	$0.446873\pi$
$434$	7.72560e9	4.53647
$435$	0	0
$436$	−1.25851e9	−0.727200
$437$	2.03240e8	0.116500
$438$	0	0
$439$	−1.32194e9	−0.745736	−0.372868	−	0.927884i	$-0.621626\pi$
$439$	−1.32194e9	−0.745736	−0.372868	+	0.927884i	$0.621626\pi$
$440$	7.48807e9	4.19069
$441$	0	0
$442$	1.98264e8	0.109211
$443$	−1.00810e9	−0.550924	−0.275462	−	0.961312i	$-0.588831\pi$
$443$	−1.00810e9	−0.550924	−0.275462	+	0.961312i	$0.588831\pi$
$444$	0	0
$445$	−1.92266e9	−1.03429
$446$	−3.99270e9	−2.13105
$447$	0	0
$448$	1.50264e10	7.89552
$449$	2.41436e9	1.25875	0.629376	−	0.777101i	$-0.283311\pi$
$449$	2.41436e9	1.25875	0.629376	+	0.777101i	$0.283311\pi$
$450$	0	0
$451$	−2.63174e9	−1.35091
$452$	6.92019e9	3.52479
$453$	0	0
$454$	−3.75016e9	−1.88085
$455$	1.66410e9	0.828208
$456$	0	0
$457$	−3.44028e8	−0.168611	−0.0843057	−	0.996440i	$-0.526867\pi$
$457$	−3.44028e8	−0.168611	−0.0843057	+	0.996440i	$0.526867\pi$
$458$	6.97768e9	3.39377
$459$	0	0
$460$	1.86080e9	0.891348
$461$	−7.39528e8	−0.351562	−0.175781	−	0.984429i	$-0.556245\pi$
$461$	−7.39528e8	−0.351562	−0.175781	+	0.984429i	$0.556245\pi$
$462$	0	0
$463$	1.56007e9	0.730485	0.365242	−	0.930912i	$-0.380986\pi$
$463$	1.56007e9	0.730485	0.365242	+	0.930912i	$0.380986\pi$
$464$	1.02194e10	4.74911
$465$	0	0
$466$	−3.96319e9	−1.81424
$467$	−2.75762e9	−1.25293	−0.626464	−	0.779450i	$-0.715498\pi$
$467$	−2.75762e9	−1.25293	−0.626464	+	0.779450i	$0.715498\pi$
$468$	0	0
$469$	1.33865e9	0.599186
$470$	2.89487e9	1.28614
$471$	0	0
$472$	1.34008e9	0.586590
$473$	1.94814e9	0.846460
$474$	0	0
$475$	1.61321e9	0.690657
$476$	−1.58209e9	−0.672366
$477$	0	0
$478$	2.44221e9	1.02279
$479$	−5.35546e8	−0.222650	−0.111325	−	0.993784i	$-0.535509\pi$
$479$	−5.35546e8	−0.222650	−0.111325	+	0.993784i	$0.535509\pi$
$480$	0	0
$481$	1.56823e9	0.642542
$482$	−3.75155e9	−1.52597
$483$	0	0
$484$	−2.92942e9	−1.17442
$485$	4.00836e9	1.59540
$486$	0	0
$487$	−4.43105e8	−0.173842	−0.0869211	−	0.996215i	$-0.527703\pi$
$487$	−4.43105e8	−0.173842	−0.0869211	+	0.996215i	$0.527703\pi$
$488$	−1.33179e9	−0.518760
$489$	0	0
$490$	−1.02743e10	−3.94518
$491$	−6.05613e8	−0.230893	−0.115446	−	0.993314i	$-0.536830\pi$
$491$	−6.05613e8	−0.230893	−0.115446	+	0.993314i	$0.536830\pi$
$492$	0	0
$493$	−4.50120e8	−0.169186
$494$	−1.06401e9	−0.397102
$495$	0	0
$496$	−1.76846e10	−6.50742
$497$	6.45808e9	2.35970
$498$	0	0
$499$	−1.97569e9	−0.711814	−0.355907	−	0.934521i	$-0.615828\pi$
$499$	−1.97569e9	−0.711814	−0.355907	+	0.934521i	$0.615828\pi$
$500$	2.82168e9	1.00951
$501$	0	0
$502$	2.07546e9	0.732235
$503$	2.83315e9	0.992615	0.496308	−	0.868147i	$-0.334689\pi$
$503$	2.83315e9	0.992615	0.496308	+	0.868147i	$0.334689\pi$
$504$	0	0
$505$	1.90056e9	0.656691
$506$	9.16222e8	0.314394
$507$	0	0
$508$	1.50092e9	0.507966
$509$	−3.31263e9	−1.11342	−0.556711	−	0.830706i	$-0.687937\pi$
$509$	−3.31263e9	−1.11342	−0.556711	+	0.830706i	$0.687937\pi$
$510$	0	0
$511$	−1.00618e9	−0.333583
$512$	−1.53338e10	−5.04899
$513$	0	0
$514$	−6.78249e9	−2.20302
$515$	−5.97534e9	−1.92769
$516$	0	0
$517$	1.05598e9	0.336077
$518$	−1.68916e10	−5.33968
$519$	0	0
$520$	−6.33392e9	−1.97543
$521$	−3.88434e9	−1.20333	−0.601666	−	0.798748i	$-0.705496\pi$
$521$	−3.88434e9	−1.20333	−0.601666	+	0.798748i	$0.705496\pi$
$522$	0	0
$523$	4.56697e9	1.39596	0.697978	−	0.716119i	$-0.254083\pi$
$523$	4.56697e9	1.39596	0.697978	+	0.716119i	$0.254083\pi$
$524$	2.37259e8	0.0720384
$525$	0	0
$526$	−6.56032e8	−0.196551
$527$	7.78929e8	0.231825
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	1.08466e9	0.316467
$531$	0	0
$532$	8.49048e9	2.44479
$533$	2.22611e9	0.636797
$534$	0	0
$535$	3.63344e9	1.02584
$536$	−5.09518e9	−1.42917
$537$	0	0
$538$	−4.61878e9	−1.27876
$539$	−3.74782e9	−1.03090
$540$	0	0
$541$	−2.32364e9	−0.630925	−0.315462	−	0.948938i	$-0.602160\pi$
$541$	−2.32364e9	−0.630925	−0.315462	+	0.948938i	$0.602160\pi$
$542$	6.55022e9	1.76709
$543$	0	0
$544$	2.78189e9	0.740874
$545$	−1.43758e9	−0.380403
$546$	0	0
$547$	−7.56311e7	−0.0197581	−0.00987904	−	0.999951i	$-0.503145\pi$
$547$	−7.56311e7	−0.0197581	−0.00987904	+	0.999951i	$0.503145\pi$
$548$	−1.53947e10	−3.99613
$549$	0	0
$550$	7.27245e9	1.86385
$551$	2.41563e9	0.615177
$552$	0	0
$553$	−3.55819e9	−0.894729
$554$	−8.61873e9	−2.15357
$555$	0	0
$556$	8.96985e9	2.21321
$557$	4.19989e8	0.102978	0.0514891	−	0.998674i	$-0.483603\pi$
$557$	4.19989e8	0.102978	0.0514891	+	0.998674i	$0.483603\pi$
$558$	0	0
$559$	−1.64787e9	−0.399008
$560$	4.10301e10	9.87289
$561$	0	0
$562$	−6.13919e9	−1.45893
$563$	5.79979e9	1.36972	0.684862	−	0.728673i	$-0.259862\pi$
$563$	5.79979e9	1.36972	0.684862	+	0.728673i	$0.259862\pi$
$564$	0	0
$565$	7.90486e9	1.84385
$566$	−1.02014e10	−2.36484
$567$	0	0
$568$	−2.45809e10	−5.62831
$569$	−4.90796e9	−1.11689	−0.558443	−	0.829543i	$-0.688601\pi$
$569$	−4.90796e9	−1.11689	−0.558443	+	0.829543i	$0.688601\pi$
$570$	0	0
$571$	2.03548e9	0.457551	0.228775	−	0.973479i	$-0.426528\pi$
$571$	2.03548e9	0.457551	0.228775	+	0.973479i	$0.426528\pi$
$572$	−3.55355e9	−0.793919
$573$	0	0
$574$	−2.39777e10	−5.29194
$575$	1.17503e9	0.257757
$576$	0	0
$577$	−6.84781e9	−1.48401	−0.742004	−	0.670395i	$-0.766124\pi$
$577$	−6.84781e9	−1.48401	−0.742004	+	0.670395i	$0.766124\pi$
$578$	8.90406e9	1.91796
$579$	0	0
$580$	2.21167e10	4.70677
$581$	2.76981e9	0.585913
$582$	0	0
$583$	3.95658e8	0.0826951
$584$	3.82975e9	0.795656
$585$	0	0
$586$	−2.77500e8	−0.0569667
$587$	−6.60262e9	−1.34736	−0.673679	−	0.739025i	$-0.735287\pi$
$587$	−6.60262e9	−1.34736	−0.673679	+	0.739025i	$0.735287\pi$
$588$	0	0
$589$	−4.18023e9	−0.842940
$590$	2.35435e9	0.471943
$591$	0	0
$592$	3.86663e10	7.65960
$593$	5.35424e9	1.05440	0.527202	−	0.849740i	$-0.323241\pi$
$593$	5.35424e9	1.05440	0.527202	+	0.849740i	$0.323241\pi$
$594$	0	0
$595$	−1.80720e9	−0.351719
$596$	−2.37432e10	−4.59386
$597$	0	0
$598$	−7.75003e8	−0.148200
$599$	−7.78264e8	−0.147956	−0.0739781	−	0.997260i	$-0.523569\pi$
$599$	−7.78264e8	−0.147956	−0.0739781	+	0.997260i	$0.523569\pi$
$600$	0	0
$601$	−3.34777e9	−0.629065	−0.314532	−	0.949247i	$-0.601848\pi$
$601$	−3.34777e9	−0.629065	−0.314532	+	0.949247i	$0.601848\pi$
$602$	1.77494e10	3.31586
$603$	0	0
$604$	−8.81582e9	−1.62792
$605$	−3.34624e9	−0.614347
$606$	0	0
$607$	4.68184e9	0.849682	0.424841	−	0.905268i	$-0.360330\pi$
$607$	4.68184e9	0.849682	0.424841	+	0.905268i	$0.360330\pi$
$608$	−1.49294e10	−2.69389
$609$	0	0
$610$	−2.33978e9	−0.417370
$611$	−8.93221e8	−0.158422
$612$	0	0
$613$	5.69615e9	0.998780	0.499390	−	0.866377i	$-0.333558\pi$
$613$	5.69615e9	0.998780	0.499390	+	0.866377i	$0.333558\pi$
$614$	−5.37854e9	−0.937723
$615$	0	0
$616$	2.48862e10	4.28970
$617$	3.04243e7	0.00521462	0.00260731	−	0.999997i	$-0.499170\pi$
$617$	3.04243e7	0.00521462	0.00260731	+	0.999997i	$0.499170\pi$
$618$	0	0
$619$	−5.77296e9	−0.978320	−0.489160	−	0.872194i	$-0.662697\pi$
$619$	−5.77296e9	−0.978320	−0.489160	+	0.872194i	$0.662697\pi$
$620$	−3.82728e10	−6.44941
$621$	0	0
$622$	−1.65069e10	−2.75043
$623$	−6.38986e9	−1.05873
$624$	0	0
$625$	−4.32174e9	−0.708073
$626$	−1.05803e10	−1.72381
$627$	0	0
$628$	−1.15485e10	−1.86066
$629$	−1.70308e9	−0.272872
$630$	0	0
$631$	7.65501e9	1.21295	0.606475	−	0.795103i	$-0.292583\pi$
$631$	7.65501e9	1.21295	0.606475	+	0.795103i	$0.292583\pi$
$632$	1.35432e10	2.13409
$633$	0	0
$634$	8.36479e9	1.30359
$635$	1.71448e9	0.265721
$636$	0	0
$637$	3.17017e9	0.485953
$638$	1.08898e10	1.66016
$639$	0	0
$640$	−5.26657e10	−7.94141
$641$	1.58157e9	0.237184	0.118592	−	0.992943i	$-0.462162\pi$
$641$	1.58157e9	0.237184	0.118592	+	0.992943i	$0.462162\pi$
$642$	0	0
$643$	9.73525e8	0.144414	0.0722069	−	0.997390i	$-0.476996\pi$
$643$	9.73525e8	0.144414	0.0722069	+	0.997390i	$0.476996\pi$
$644$	6.18429e9	0.912408
$645$	0	0
$646$	1.15551e9	0.168639
$647$	−1.87627e9	−0.272351	−0.136176	−	0.990685i	$-0.543481\pi$
$647$	−1.87627e9	−0.272351	−0.136176	+	0.990685i	$0.543481\pi$
$648$	0	0
$649$	8.58811e8	0.123322
$650$	−6.15154e9	−0.878591
$651$	0	0
$652$	3.97081e10	5.61065
$653$	7.79125e9	1.09499	0.547496	−	0.836808i	$-0.315581\pi$
$653$	7.79125e9	1.09499	0.547496	+	0.836808i	$0.315581\pi$
$654$	0	0
$655$	2.71019e8	0.0376838
$656$	5.48870e10	7.59112
$657$	0	0
$658$	9.62098e9	1.31652
$659$	−1.07630e10	−1.46499	−0.732495	−	0.680773i	$-0.761644\pi$
$659$	−1.07630e10	−1.46499	−0.732495	+	0.680773i	$0.761644\pi$
$660$	0	0
$661$	5.38699e9	0.725506	0.362753	−	0.931885i	$-0.381837\pi$
$661$	5.38699e9	0.725506	0.362753	+	0.931885i	$0.381837\pi$
$662$	5.31079e9	0.711469
$663$	0	0
$664$	−1.05425e10	−1.39751
$665$	9.69858e9	1.27889
$666$	0	0
$667$	1.75949e9	0.229587
$668$	−1.13699e10	−1.47585
$669$	0	0
$670$	−8.95157e9	−1.14984
$671$	−8.53497e8	−0.109062
$672$	0	0
$673$	1.49918e10	1.89584	0.947920	−	0.318509i	$-0.103182\pi$
$673$	1.49918e10	1.89584	0.947920	+	0.318509i	$0.103182\pi$
$674$	3.00155e9	0.377603
$675$	0	0
$676$	−1.99543e10	−2.48440
$677$	7.13258e9	0.883459	0.441729	−	0.897148i	$-0.354365\pi$
$677$	7.13258e9	0.883459	0.441729	+	0.897148i	$0.354365\pi$
$678$	0	0
$679$	1.33216e10	1.63310
$680$	6.87858e9	0.838915
$681$	0	0
$682$	−1.88448e10	−2.27481
$683$	7.64938e9	0.918658	0.459329	−	0.888266i	$-0.348090\pi$
$683$	7.64938e9	0.918658	0.459329	+	0.888266i	$0.348090\pi$
$684$	0	0
$685$	−1.75852e10	−2.09041
$686$	−8.72220e9	−1.03155
$687$	0	0
$688$	−4.06299e10	−4.75649
$689$	−3.34675e8	−0.0389812
$690$	0	0
$691$	6.59503e9	0.760403	0.380201	−	0.924904i	$-0.375855\pi$
$691$	6.59503e9	0.760403	0.380201	+	0.924904i	$0.375855\pi$
$692$	5.73788e9	0.658234
$693$	0	0
$694$	3.08279e10	3.50095
$695$	1.02462e10	1.15775
$696$	0	0
$697$	−2.41753e9	−0.270432
$698$	−3.11372e10	−3.46565
$699$	0	0
$700$	4.90874e10	5.40912
$701$	1.00367e10	1.10046	0.550232	−	0.835012i	$-0.314539\pi$
$701$	1.00367e10	1.10046	0.550232	+	0.835012i	$0.314539\pi$
$702$	0	0
$703$	9.13982e9	0.992188
$704$	−3.66533e10	−3.95921
$705$	0	0
$706$	3.49506e9	0.373799
$707$	6.31641e9	0.672206
$708$	0	0
$709$	2.10293e9	0.221597	0.110798	−	0.993843i	$-0.464659\pi$
$709$	2.10293e9	0.221597	0.110798	+	0.993843i	$0.464659\pi$
$710$	−4.31854e10	−4.52827
$711$	0	0
$712$	2.43212e10	2.52525
$713$	−3.04479e9	−0.314590
$714$	0	0
$715$	−4.05918e9	−0.415305
$716$	3.60550e10	3.67088
$717$	0	0
$718$	−1.95007e10	−1.96614
$719$	6.54106e9	0.656292	0.328146	−	0.944627i	$-0.393576\pi$
$719$	6.54106e9	0.656292	0.328146	+	0.944627i	$0.393576\pi$
$720$	0	0
$721$	−1.98588e10	−1.97324
$722$	1.36642e10	1.35115
$723$	0	0
$724$	5.31838e9	0.520828
$725$	1.39659e10	1.36108
$726$	0	0
$727$	1.06240e10	1.02546	0.512728	−	0.858551i	$-0.328635\pi$
$727$	1.06240e10	1.02546	0.512728	+	0.858551i	$0.328635\pi$
$728$	−2.10505e10	−2.02210
$729$	0	0
$730$	6.72837e9	0.640147
$731$	1.78957e9	0.169449
$732$	0	0
$733$	−7.87271e8	−0.0738346	−0.0369173	−	0.999318i	$-0.511754\pi$
$733$	−7.87271e8	−0.0738346	−0.0369173	+	0.999318i	$0.511754\pi$
$734$	1.16854e10	1.09071
$735$	0	0
$736$	−1.08743e10	−1.00537
$737$	−3.26532e9	−0.300462
$738$	0	0
$739$	2.02276e10	1.84369	0.921845	−	0.387559i	$-0.126682\pi$
$739$	2.02276e10	1.84369	0.921845	+	0.387559i	$0.126682\pi$
$740$	8.36812e10	7.59132
$741$	0	0
$742$	3.60482e9	0.323944
$743$	−1.53934e10	−1.37681	−0.688405	−	0.725327i	$-0.741689\pi$
$743$	−1.53934e10	−1.37681	−0.688405	+	0.725327i	$0.741689\pi$
$744$	0	0
$745$	−2.71216e10	−2.40308
$746$	2.49332e10	2.19884
$747$	0	0
$748$	3.85912e9	0.337158
$749$	1.20756e10	1.05008
$750$	0	0
$751$	−1.36778e10	−1.17835	−0.589176	−	0.808004i	$-0.700548\pi$
$751$	−1.36778e10	−1.17835	−0.589176	+	0.808004i	$0.700548\pi$
$752$	−2.20233e10	−1.88851
$753$	0	0
$754$	−9.21138e9	−0.782573
$755$	−1.00702e10	−0.851578
$756$	0	0
$757$	6.46076e8	0.0541312	0.0270656	−	0.999634i	$-0.491384\pi$
$757$	6.46076e8	0.0541312	0.0270656	+	0.999634i	$0.491384\pi$
$758$	2.99405e10	2.49699
$759$	0	0
$760$	−3.69149e10	−3.05038
$761$	−1.78122e10	−1.46512	−0.732559	−	0.680704i	$-0.761674\pi$
$761$	−1.78122e10	−1.46512	−0.732559	+	0.680704i	$0.761674\pi$
$762$	0	0
$763$	−4.77773e9	−0.389391
$764$	−3.65477e10	−2.96505
$765$	0	0
$766$	1.49468e10	1.20157
$767$	−7.26442e8	−0.0581322
$768$	0	0
$769$	1.39331e10	1.10486	0.552428	−	0.833561i	$-0.313701\pi$
$769$	1.39331e10	1.10486	0.552428	+	0.833561i	$0.313701\pi$
$770$	4.37219e10	3.45129
$771$	0	0
$772$	9.72004e9	0.760339
$773$	−1.31318e10	−1.02257	−0.511287	−	0.859410i	$-0.670831\pi$
$773$	−1.31318e10	−1.02257	−0.511287	+	0.859410i	$0.670831\pi$
$774$	0	0
$775$	−2.41678e10	−1.86501
$776$	−5.07049e10	−3.89524
$777$	0	0
$778$	3.17889e10	2.42018
$779$	1.29740e10	0.983317
$780$	0	0
$781$	−1.57530e10	−1.18327
$782$	8.41647e8	0.0629370
$783$	0	0
$784$	7.81637e10	5.79294
$785$	−1.31917e10	−0.973324
$786$	0	0
$787$	−1.46934e10	−1.07451	−0.537256	−	0.843419i	$-0.680539\pi$
$787$	−1.46934e10	−1.07451	−0.537256	+	0.843419i	$0.680539\pi$
$788$	5.63612e10	4.10335
$789$	0	0
$790$	2.37937e10	1.71699
$791$	2.62714e10	1.88741
$792$	0	0
$793$	7.21946e8	0.0514101
$794$	−3.57029e10	−2.53123
$795$	0	0
$796$	−2.02099e10	−1.42026
$797$	2.12719e9	0.148834	0.0744170	−	0.997227i	$-0.476290\pi$
$797$	2.12719e9	0.148834	0.0744170	+	0.997227i	$0.476290\pi$
$798$	0	0
$799$	9.70030e8	0.0672777
$800$	−8.63138e10	−5.96026
$801$	0	0
$802$	−2.01019e10	−1.37603
$803$	2.45435e9	0.167275
$804$	0	0
$805$	7.06424e9	0.477287
$806$	1.59402e10	1.07231
$807$	0	0
$808$	−2.40416e10	−1.60333
$809$	−1.95324e10	−1.29698	−0.648492	−	0.761221i	$-0.724600\pi$
$809$	−1.95324e10	−1.29698	−0.648492	+	0.761221i	$0.724600\pi$
$810$	0	0
$811$	1.09913e10	0.723563	0.361781	−	0.932263i	$-0.382169\pi$
$811$	1.09913e10	0.723563	0.361781	+	0.932263i	$0.382169\pi$
$812$	7.35039e10	4.81797
$813$	0	0
$814$	4.12030e10	2.67758
$815$	4.53581e10	2.93497
$816$	0	0
$817$	−9.60399e9	−0.616133
$818$	−4.50679e10	−2.87893
$819$	0	0
$820$	1.18786e11	7.52344
$821$	1.66467e10	1.04985	0.524925	−	0.851148i	$-0.324093\pi$
$821$	1.66467e10	1.04985	0.524925	+	0.851148i	$0.324093\pi$
$822$	0	0
$823$	−1.01215e10	−0.632916	−0.316458	−	0.948607i	$-0.602494\pi$
$823$	−1.01215e10	−0.632916	−0.316458	+	0.948607i	$0.602494\pi$
$824$	7.55868e10	4.70653
$825$	0	0
$826$	7.82458e9	0.483093
$827$	1.82045e10	1.11920	0.559601	−	0.828762i	$-0.310954\pi$
$827$	1.82045e10	1.11920	0.559601	+	0.828762i	$0.310954\pi$
$828$	0	0
$829$	−2.44281e10	−1.48918	−0.744592	−	0.667520i	$-0.767356\pi$
$829$	−2.44281e10	−1.48918	−0.744592	+	0.667520i	$0.767356\pi$
$830$	−1.85218e10	−1.12437
$831$	0	0
$832$	3.10039e10	1.86631
$833$	−3.44277e9	−0.206372
$834$	0	0
$835$	−1.29878e10	−0.772026
$836$	−2.07105e10	−1.22594
$837$	0	0
$838$	5.53686e10	3.25020
$839$	−9.80240e9	−0.573014	−0.286507	−	0.958078i	$-0.592494\pi$
$839$	−9.80240e9	−0.573014	−0.286507	+	0.958078i	$0.592494\pi$
$840$	0	0
$841$	3.66277e9	0.212336
$842$	−5.36823e10	−3.09913
$843$	0	0
$844$	1.22218e10	0.699743
$845$	−2.27935e10	−1.29961
$846$	0	0
$847$	−1.11211e10	−0.628862
$848$	−8.25174e9	−0.464687
$849$	0	0
$850$	6.68051e9	0.373116
$851$	6.65725e9	0.370290
$852$	0	0
$853$	−5.25814e9	−0.290075	−0.145038	−	0.989426i	$-0.546330\pi$
$853$	−5.25814e9	−0.290075	−0.145038	+	0.989426i	$0.546330\pi$
$854$	−7.77616e9	−0.427231
$855$	0	0
$856$	−4.59622e10	−2.50463
$857$	−1.79709e10	−0.975299	−0.487650	−	0.873039i	$-0.662146\pi$
$857$	−1.79709e10	−0.975299	−0.487650	+	0.873039i	$0.662146\pi$
$858$	0	0
$859$	−2.84789e10	−1.53302	−0.766509	−	0.642233i	$-0.778008\pi$
$859$	−2.84789e10	−1.53302	−0.766509	+	0.642233i	$0.778008\pi$
$860$	−8.79310e10	−4.71409
$861$	0	0
$862$	4.09742e10	2.17889
$863$	−3.63327e10	−1.92424	−0.962122	−	0.272620i	$-0.912110\pi$
$863$	−3.63327e10	−1.92424	−0.962122	+	0.272620i	$0.912110\pi$
$864$	0	0
$865$	6.55432e9	0.344327
$866$	−1.24739e10	−0.652666
$867$	0	0
$868$	−1.27198e11	−6.60178
$869$	8.67938e9	0.448662
$870$	0	0
$871$	2.76203e9	0.141633
$872$	1.81851e10	0.928768
$873$	0	0
$874$	−4.51681e9	−0.228845
$875$	1.07120e10	0.540560
$876$	0	0
$877$	−1.44465e10	−0.723211	−0.361605	−	0.932331i	$-0.617771\pi$
$877$	−1.44465e10	−0.723211	−0.361605	+	0.932331i	$0.617771\pi$
$878$	2.93788e10	1.46488
$879$	0	0
$880$	−1.00083e11	−4.95076
$881$	−5.80716e9	−0.286120	−0.143060	−	0.989714i	$-0.545694\pi$
$881$	−5.80716e9	−0.286120	−0.143060	+	0.989714i	$0.545694\pi$
$882$	0	0
$883$	−2.13837e10	−1.04525	−0.522626	−	0.852562i	$-0.675048\pi$
$883$	−2.13837e10	−1.04525	−0.522626	+	0.852562i	$0.675048\pi$
$884$	−3.26431e9	−0.158931
$885$	0	0
$886$	2.24041e10	1.08220
$887$	3.30985e10	1.59249	0.796244	−	0.604976i	$-0.206817\pi$
$887$	3.30985e10	1.59249	0.796244	+	0.604976i	$0.206817\pi$
$888$	0	0
$889$	5.69801e9	0.271999
$890$	4.27292e10	2.03170
$891$	0	0
$892$	6.57376e10	3.10125
$893$	−5.20580e9	−0.244629
$894$	0	0
$895$	4.11852e10	1.92026
$896$	−1.75032e11	−8.12904
$897$	0	0
$898$	−5.36568e10	−2.47262
$899$	−3.61892e10	−1.66119
$900$	0	0
$901$	3.63454e8	0.0165544
$902$	5.84879e10	2.65364
$903$	0	0
$904$	−9.99947e10	−4.50181
$905$	6.07513e9	0.272449
$906$	0	0
$907$	−2.88393e9	−0.128339	−0.0641696	−	0.997939i	$-0.520440\pi$
$907$	−2.88393e9	−0.128339	−0.0641696	+	0.997939i	$0.520440\pi$
$908$	6.17445e10	2.73714
$909$	0	0
$910$	−3.69830e10	−1.62689
$911$	1.53447e10	0.672426	0.336213	−	0.941786i	$-0.390854\pi$
$911$	1.53447e10	0.672426	0.336213	+	0.941786i	$0.390854\pi$
$912$	0	0
$913$	−6.75629e9	−0.293806
$914$	7.64568e9	0.331211
$915$	0	0
$916$	−1.14884e11	−4.93884
$917$	9.00718e8	0.0385741
$918$	0	0
$919$	2.33263e10	0.991382	0.495691	−	0.868499i	$-0.334915\pi$
$919$	2.33263e10	0.991382	0.495691	+	0.868499i	$0.334915\pi$
$920$	−2.68880e10	−1.13842
$921$	0	0
$922$	1.64353e10	0.690588
$923$	1.33250e10	0.557776
$924$	0	0
$925$	5.28415e10	2.19523
$926$	−3.46710e10	−1.43492
$927$	0	0
$928$	−1.29247e11	−5.30888
$929$	−4.38112e10	−1.79279	−0.896396	−	0.443254i	$-0.853824\pi$
$929$	−4.38112e10	−1.79279	−0.896396	+	0.443254i	$0.853824\pi$
$930$	0	0
$931$	1.84761e10	0.750390
$932$	6.52518e10	2.64020
$933$	0	0
$934$	6.12855e10	2.46118
$935$	4.40823e9	0.176370
$936$	0	0
$937$	4.87619e9	0.193639	0.0968194	−	0.995302i	$-0.469133\pi$
$937$	4.87619e9	0.193639	0.0968194	+	0.995302i	$0.469133\pi$
$938$	−2.97501e10	−1.17701
$939$	0	0
$940$	−4.76626e10	−1.87167
$941$	−4.25852e9	−0.166608	−0.0833038	−	0.996524i	$-0.526547\pi$
$941$	−4.25852e9	−0.166608	−0.0833038	+	0.996524i	$0.526547\pi$
$942$	0	0
$943$	9.45001e9	0.366979
$944$	−1.79111e10	−0.692981
$945$	0	0
$946$	−4.32955e10	−1.66274
$947$	−2.14348e10	−0.820154	−0.410077	−	0.912051i	$-0.634498\pi$
$947$	−2.14348e10	−0.820154	−0.410077	+	0.912051i	$0.634498\pi$
$948$	0	0
$949$	−2.07606e9	−0.0788510
$950$	−3.58519e10	−1.35669
$951$	0	0
$952$	2.28606e10	0.858735
$953$	1.72741e10	0.646501	0.323251	−	0.946313i	$-0.395224\pi$
$953$	1.72741e10	0.646501	0.323251	+	0.946313i	$0.395224\pi$
$954$	0	0
$955$	−4.17480e10	−1.55104
$956$	−4.02097e10	−1.48843
$957$	0	0
$958$	1.19020e10	0.437361
$959$	−5.84437e10	−2.13980
$960$	0	0
$961$	3.51125e10	1.27623
$962$	−3.48523e10	−1.26217
$963$	0	0
$964$	6.17672e10	2.22069
$965$	1.11031e10	0.397739
$966$	0	0
$967$	3.32959e10	1.18413	0.592064	−	0.805891i	$-0.298313\pi$
$967$	3.32959e10	1.18413	0.592064	+	0.805891i	$0.298313\pi$
$968$	4.23292e10	1.49995
$969$	0	0
$970$	−8.90819e10	−3.13392
$971$	−1.70390e10	−0.597279	−0.298639	−	0.954366i	$-0.596533\pi$
$971$	−1.70390e10	−0.597279	−0.298639	+	0.954366i	$0.596533\pi$
$972$	0	0
$973$	3.40526e10	1.18510
$974$	9.84757e9	0.341486
$975$	0	0
$976$	1.78003e10	0.612849
$977$	3.20940e10	1.10102	0.550508	−	0.834830i	$-0.314434\pi$
$977$	3.20940e10	1.10102	0.550508	+	0.834830i	$0.314434\pi$
$978$	0	0
$979$	1.55866e10	0.530898
$980$	1.69161e11	5.74129
$981$	0	0
$982$	1.34592e10	0.453552
$983$	−2.57963e10	−0.866202	−0.433101	−	0.901345i	$-0.642581\pi$
$983$	−2.57963e10	−0.866202	−0.433101	+	0.901345i	$0.642581\pi$
$984$	0	0
$985$	6.43807e10	2.14649
$986$	1.00035e10	0.332339
$987$	0	0
$988$	1.75184e10	0.577890
$989$	−6.99535e9	−0.229944
$990$	0	0
$991$	−3.80638e10	−1.24238	−0.621189	−	0.783661i	$-0.713350\pi$
$991$	−3.80638e10	−1.24238	−0.621189	+	0.783661i	$0.713350\pi$
$992$	2.23661e11	7.27445
$993$	0	0
$994$	−1.43525e11	−4.63526
$995$	−2.30855e10	−0.742949
$996$	0	0
$997$	2.41942e10	0.773177	0.386589	−	0.922252i	$-0.373653\pi$
$997$	2.41942e10	0.773177	0.386589	+	0.922252i	$0.373653\pi$
$998$	4.39077e10	1.39825
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.d.1.1		7
3.2	odd	2		69.8.a.c.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.c.1.7	✓	7	3.2	odd	2
207.8.a.d.1.1		7	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)

\(f(q)\)	\(=\)	\(q-22.2240 q^{2} +365.907 q^{4} +417.971 q^{5} +1389.11 q^{7} -5287.24 q^{8} +O(q^{10})\)	\(q-22.2240 q^{2} +365.907 q^{4} +417.971 q^{5} +1389.11 q^{7} -5287.24 q^{8} -9288.99 q^{10} -3388.40 q^{11} +2866.14 q^{13} -30871.5 q^{14} +70667.6 q^{16} -3112.60 q^{17} +16704.2 q^{19} +152938. q^{20} +75303.8 q^{22} +12167.0 q^{23} +96574.8 q^{25} -63697.2 q^{26} +508283. q^{28} +144612. q^{29} -250250. q^{31} -893751. q^{32} +69174.5 q^{34} +580606. q^{35} +547157. q^{37} -371235. q^{38} -2.20991e6 q^{40} +776692. q^{41} -574944. q^{43} -1.23984e6 q^{44} -270400. q^{46} -311646. q^{47} +1.10608e6 q^{49} -2.14628e6 q^{50} +1.04874e6 q^{52} -116768. q^{53} -1.41625e6 q^{55} -7.34454e6 q^{56} -3.21386e6 q^{58} -253456. q^{59} +251888. q^{61} +5.56156e6 q^{62} +1.08173e7 q^{64} +1.19796e6 q^{65} +963675. q^{67} -1.13892e6 q^{68} -1.29034e7 q^{70} +4.64909e6 q^{71} -724338. q^{73} -1.21600e7 q^{74} +6.11218e6 q^{76} -4.70685e6 q^{77} -2.56150e6 q^{79} +2.95370e7 q^{80} -1.72612e7 q^{82} +1.99395e6 q^{83} -1.30098e6 q^{85} +1.27776e7 q^{86} +1.79153e7 q^{88} -4.59998e6 q^{89} +3.98138e6 q^{91} +4.45199e6 q^{92} +6.92602e6 q^{94} +6.98188e6 q^{95} +9.59005e6 q^{97} -2.45814e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8}+O(q^{10}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8} - 15310 q^{10} - 9040 q^{11} + 3774 q^{13} - 4536 q^{14} + 52002 q^{16} + 40760 q^{17} + 81598 q^{19} + 88946 q^{20} + 245034 q^{22} + 85169 q^{23} + 321325 q^{25} - 412748 q^{26} + 965948 q^{28} - 154126 q^{29} + 243132 q^{31} - 1278286 q^{32} + 984836 q^{34} + 130296 q^{35} + 582114 q^{37} - 772558 q^{38} - 132618 q^{40} - 113062 q^{41} - 659778 q^{43} - 659390 q^{44} + 591032 q^{47} + 3263235 q^{49} + 702684 q^{50} + 1793280 q^{52} - 207128 q^{53} + 184664 q^{55} - 5390508 q^{56} - 1142916 q^{58} - 447148 q^{59} + 2248970 q^{61} + 5729060 q^{62} + 7212922 q^{64} + 827096 q^{65} + 4467570 q^{67} + 5477620 q^{68} - 12744284 q^{70} + 5154608 q^{71} - 13239250 q^{73} + 2827426 q^{74} - 527434 q^{76} + 18415912 q^{77} + 9594446 q^{79} + 55932394 q^{80} - 20889952 q^{82} + 573720 q^{83} + 7477272 q^{85} + 28416910 q^{86} + 26555702 q^{88} + 3810540 q^{89} + 36092068 q^{91} + 7957218 q^{92} + 33545768 q^{94} - 10497320 q^{95} + 49497978 q^{97} + 1023376 q^{98}+O(q^{100}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8 - 15310 * q^10 - 9040 * q^11 + 3774 * q^13 - 4536 * q^14 + 52002 * q^16 + 40760 * q^17 + 81598 * q^19 + 88946 * q^20 + 245034 * q^22 + 85169 * q^23 + 321325 * q^25 - 412748 * q^26 + 965948 * q^28 - 154126 * q^29 + 243132 * q^31 - 1278286 * q^32 + 984836 * q^34 + 130296 * q^35 + 582114 * q^37 - 772558 * q^38 - 132618 * q^40 - 113062 * q^41 - 659778 * q^43 - 659390 * q^44 + 591032 * q^47 + 3263235 * q^49 + 702684 * q^50 + 1793280 * q^52 - 207128 * q^53 + 184664 * q^55 - 5390508 * q^56 - 1142916 * q^58 - 447148 * q^59 + 2248970 * q^61 + 5729060 * q^62 + 7212922 * q^64 + 827096 * q^65 + 4467570 * q^67 + 5477620 * q^68 - 12744284 * q^70 + 5154608 * q^71 - 13239250 * q^73 + 2827426 * q^74 - 527434 * q^76 + 18415912 * q^77 + 9594446 * q^79 + 55932394 * q^80 - 20889952 * q^82 + 573720 * q^83 + 7477272 * q^85 + 28416910 * q^86 + 26555702 * q^88 + 3810540 * q^89 + 36092068 * q^91 + 7957218 * q^92 + 33545768 * q^94 - 10497320 * q^95 + 49497978 * q^97 + 1023376 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more