LMFDB - Embedded newform 2535.2.a.bm.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2535,2,Mod(1,2535)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2535.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2535, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2535.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,0,-9,10,-9,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.2420769124$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 9x^{7} + 29x^{6} + 17x^{5} - 83x^{4} + 17x^{3} + 70x^{2} - 48x + 8 $ x^9 - 3x^8 - 9x^7 + 29x^6 + 17x^5 - 83x^4 + 17x^3 + 70x^2 - 48x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.35453$ of defining polynomial
Character	$\chi$	$=$	2535.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.224792 q^{2} -1.00000 q^{3} -1.94947 q^{4} -1.00000 q^{5} +0.224792 q^{6} -2.56713 q^{7} +0.887811 q^{8} +1.00000 q^{9} +0.224792 q^{10} -1.92749 q^{11} +1.94947 q^{12} +0.577070 q^{14} +1.00000 q^{15} +3.69936 q^{16} -1.39011 q^{17} -0.224792 q^{18} -7.88294 q^{19} +1.94947 q^{20} +2.56713 q^{21} +0.433285 q^{22} -4.22142 q^{23} -0.887811 q^{24} +1.00000 q^{25} -1.00000 q^{27} +5.00453 q^{28} -6.08029 q^{29} -0.224792 q^{30} -6.16957 q^{31} -2.60721 q^{32} +1.92749 q^{33} +0.312485 q^{34} +2.56713 q^{35} -1.94947 q^{36} +1.81367 q^{37} +1.77202 q^{38} -0.887811 q^{40} +8.49714 q^{41} -0.577070 q^{42} -9.24829 q^{43} +3.75758 q^{44} -1.00000 q^{45} +0.948942 q^{46} -10.1617 q^{47} -3.69936 q^{48} -0.409868 q^{49} -0.224792 q^{50} +1.39011 q^{51} +8.01914 q^{53} +0.224792 q^{54} +1.92749 q^{55} -2.27912 q^{56} +7.88294 q^{57} +1.36680 q^{58} -3.40909 q^{59} -1.94947 q^{60} +6.38709 q^{61} +1.38687 q^{62} -2.56713 q^{63} -6.81265 q^{64} -0.433285 q^{66} -0.561677 q^{67} +2.70997 q^{68} +4.22142 q^{69} -0.577070 q^{70} -13.6250 q^{71} +0.887811 q^{72} -2.59111 q^{73} -0.407699 q^{74} -1.00000 q^{75} +15.3675 q^{76} +4.94811 q^{77} +13.4274 q^{79} -3.69936 q^{80} +1.00000 q^{81} -1.91009 q^{82} +15.2881 q^{83} -5.00453 q^{84} +1.39011 q^{85} +2.07895 q^{86} +6.08029 q^{87} -1.71125 q^{88} +0.352449 q^{89} +0.224792 q^{90} +8.22952 q^{92} +6.16957 q^{93} +2.28428 q^{94} +7.88294 q^{95} +2.60721 q^{96} +3.44031 q^{97} +0.0921353 q^{98} -1.92749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) $ 9 * q - 9 * q^3 + 10 * q^4 - 9 * q^5 + 10 * q^7 - 3 * q^8 + 9 * q^9 - 11 * q^11 - 10 * q^12 + 10 * q^14 + 9 * q^15 + 8 * q^16 + 18 * q^17 - 10 * q^19 - 10 * q^20 - 10 * q^21 + 17 * q^22 - 7 * q^23 + 3 * q^24 + 9 * q^25 - 9 * q^27 + 43 * q^28 - 9 * q^29 - 17 * q^31 - 11 * q^32 + 11 * q^33 + 4 * q^34 - 10 * q^35 + 10 * q^36 - 3 * q^37 + 21 * q^38 + 3 * q^40 - 4 * q^41 - 10 * q^42 + 14 * q^43 - 13 * q^44 - 9 * q^45 - 3 * q^46 + 2 * q^47 - 8 * q^48 + 43 * q^49 - 18 * q^51 + 5 * q^53 + 11 * q^55 + q^56 + 10 * q^57 + 14 * q^58 - 3 * q^59 + 10 * q^60 + 48 * q^61 - 7 * q^62 + 10 * q^63 + 41 * q^64 - 17 * q^66 + 40 * q^67 + 40 * q^68 + 7 * q^69 - 10 * q^70 - 12 * q^71 - 3 * q^72 + 38 * q^73 - 4 * q^74 - 9 * q^75 - 51 * q^76 + 8 * q^77 + 22 * q^79 - 8 * q^80 + 9 * q^81 + 38 * q^82 - 11 * q^83 - 43 * q^84 - 18 * q^85 - 56 * q^86 + 9 * q^87 + 50 * q^88 - 2 * q^89 - 36 * q^92 + 17 * q^93 + 42 * q^94 + 10 * q^95 + 11 * q^96 + 23 * q^97 + 79 * q^98 - 11 * q^99

Coefficient data

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

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

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

$2$	−0.224792	−0.158952	−0.0794761	−	0.996837i	$-0.525325\pi$
$2$	−0.224792	−0.158952	−0.0794761	+	0.996837i	$0.525325\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94947	−0.974734
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.224792	0.0917711
$7$	−2.56713	−0.970282	−0.485141	−	0.874436i	$-0.661232\pi$
$7$	−2.56713	−0.970282	−0.485141	+	0.874436i	$0.661232\pi$
$8$	0.887811	0.313888
$9$	1.00000	0.333333
$10$	0.224792	0.0710856
$11$	−1.92749	−0.581160	−0.290580	−	0.956851i	$-0.593848\pi$
$11$	−1.92749	−0.581160	−0.290580	+	0.956851i	$0.593848\pi$
$12$	1.94947	0.562763
$13$	0	0
$13$	0	0
$14$	0.577070	0.154229
$15$	1.00000	0.258199
$16$	3.69936	0.924841
$17$	−1.39011	−0.337150	−0.168575	−	0.985689i	$-0.553917\pi$
$17$	−1.39011	−0.337150	−0.168575	+	0.985689i	$0.553917\pi$
$18$	−0.224792	−0.0529841
$19$	−7.88294	−1.80847	−0.904235	−	0.427035i	$-0.859558\pi$
$19$	−7.88294	−1.80847	−0.904235	+	0.427035i	$0.859558\pi$
$20$	1.94947	0.435914
$21$	2.56713	0.560193
$22$	0.433285	0.0923767
$23$	−4.22142	−0.880226	−0.440113	−	0.897942i	$-0.645062\pi$
$23$	−4.22142	−0.880226	−0.440113	+	0.897942i	$0.645062\pi$
$24$	−0.887811	−0.181224
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	5.00453	0.945767
$29$	−6.08029	−1.12908	−0.564541	−	0.825405i	$-0.690947\pi$
$29$	−6.08029	−1.12908	−0.564541	+	0.825405i	$0.690947\pi$
$30$	−0.224792	−0.0410413
$31$	−6.16957	−1.10809	−0.554044	−	0.832487i	$-0.686916\pi$
$31$	−6.16957	−1.10809	−0.554044	+	0.832487i	$0.686916\pi$
$32$	−2.60721	−0.460894
$33$	1.92749	0.335533
$34$	0.312485	0.0535908
$35$	2.56713	0.433923
$36$	−1.94947	−0.324911
$37$	1.81367	0.298165	0.149082	−	0.988825i	$-0.452368\pi$
$37$	1.81367	0.298165	0.149082	+	0.988825i	$0.452368\pi$
$38$	1.77202	0.287460
$39$	0	0
$40$	−0.887811	−0.140375
$41$	8.49714	1.32703	0.663515	−	0.748163i	$-0.269064\pi$
$41$	8.49714	1.32703	0.663515	+	0.748163i	$0.269064\pi$
$42$	−0.577070	−0.0890439
$43$	−9.24829	−1.41035	−0.705175	−	0.709033i	$-0.749132\pi$
$43$	−9.24829	−1.41035	−0.705175	+	0.709033i	$0.749132\pi$
$44$	3.75758	0.566477
$45$	−1.00000	−0.149071
$46$	0.948942	0.139914
$47$	−10.1617	−1.48224	−0.741121	−	0.671372i	$-0.765705\pi$
$47$	−10.1617	−1.48224	−0.741121	+	0.671372i	$0.765705\pi$
$48$	−3.69936	−0.533957
$49$	−0.409868	−0.0585526
$50$	−0.224792	−0.0317905
$51$	1.39011	0.194654
$52$	0	0
$53$	8.01914	1.10151	0.550757	−	0.834666i	$-0.314339\pi$
$53$	8.01914	1.10151	0.550757	+	0.834666i	$0.314339\pi$
$54$	0.224792	0.0305904
$55$	1.92749	0.259903
$56$	−2.27912	−0.304560
$57$	7.88294	1.04412
$58$	1.36680	0.179470
$59$	−3.40909	−0.443826	−0.221913	−	0.975066i	$-0.571230\pi$
$59$	−3.40909	−0.443826	−0.221913	+	0.975066i	$0.571230\pi$
$60$	−1.94947	−0.251675
$61$	6.38709	0.817784	0.408892	−	0.912583i	$-0.365915\pi$
$61$	6.38709	0.817784	0.408892	+	0.912583i	$0.365915\pi$
$62$	1.38687	0.176133
$63$	−2.56713	−0.323427
$64$	−6.81265	−0.851581
$65$	0	0
$66$	−0.433285	−0.0533337
$67$	−0.561677	−0.0686198	−0.0343099	−	0.999411i	$-0.510923\pi$
$67$	−0.561677	−0.0686198	−0.0343099	+	0.999411i	$0.510923\pi$
$68$	2.70997	0.328632
$69$	4.22142	0.508199
$70$	−0.577070	−0.0689731
$71$	−13.6250	−1.61698	−0.808492	−	0.588507i	$-0.799716\pi$
$71$	−13.6250	−1.61698	−0.808492	+	0.588507i	$0.799716\pi$
$72$	0.887811	0.104629
$73$	−2.59111	−0.303266	−0.151633	−	0.988437i	$-0.548453\pi$
$73$	−2.59111	−0.303266	−0.151633	+	0.988437i	$0.548453\pi$
$74$	−0.407699	−0.0473940
$75$	−1.00000	−0.115470
$76$	15.3675	1.76278
$77$	4.94811	0.563889
$78$	0	0
$79$	13.4274	1.51070	0.755351	−	0.655320i	$-0.227466\pi$
$79$	13.4274	1.51070	0.755351	+	0.655320i	$0.227466\pi$
$80$	−3.69936	−0.413601
$81$	1.00000	0.111111
$82$	−1.91009	−0.210935
$83$	15.2881	1.67809	0.839045	−	0.544062i	$-0.183114\pi$
$83$	15.2881	1.67809	0.839045	+	0.544062i	$0.183114\pi$
$84$	−5.00453	−0.546039
$85$	1.39011	0.150778
$86$	2.07895	0.224178
$87$	6.08029	0.651876
$88$	−1.71125	−0.182419
$89$	0.352449	0.0373595	0.0186798	−	0.999826i	$-0.494054\pi$
$89$	0.352449	0.0373595	0.0186798	+	0.999826i	$0.494054\pi$
$90$	0.224792	0.0236952
$91$	0	0
$92$	8.22952	0.857986
$93$	6.16957	0.639755
$94$	2.28428	0.235606
$95$	7.88294	0.808772
$96$	2.60721	0.266097
$97$	3.44031	0.349311	0.174656	−	0.984630i	$-0.444119\pi$
$97$	3.44031	0.349311	0.174656	+	0.984630i	$0.444119\pi$
$98$	0.0921353	0.00930707
$99$	−1.92749	−0.193720
$100$	−1.94947	−0.194947
$101$	7.17934	0.714371	0.357186	−	0.934033i	$-0.383736\pi$
$101$	7.17934	0.714371	0.357186	+	0.934033i	$0.383736\pi$
$102$	−0.312485	−0.0309407
$103$	2.10201	0.207117	0.103559	−	0.994623i	$-0.466977\pi$
$103$	2.10201	0.207117	0.103559	+	0.994623i	$0.466977\pi$
$104$	0	0
$105$	−2.56713	−0.250526
$106$	−1.80264	−0.175088
$107$	5.45933	0.527774	0.263887	−	0.964554i	$-0.414995\pi$
$107$	5.45933	0.527774	0.263887	+	0.964554i	$0.414995\pi$
$108$	1.94947	0.187588
$109$	−9.03611	−0.865502	−0.432751	−	0.901513i	$-0.642457\pi$
$109$	−9.03611	−0.865502	−0.432751	+	0.901513i	$0.642457\pi$
$110$	−0.433285	−0.0413121
$111$	−1.81367	−0.172146
$112$	−9.49673	−0.897357
$113$	13.2535	1.24679	0.623394	−	0.781908i	$-0.285753\pi$
$113$	13.2535	1.24679	0.623394	+	0.781908i	$0.285753\pi$
$114$	−1.77202	−0.165965
$115$	4.22142	0.393649
$116$	11.8533	1.10055
$117$	0	0
$118$	0.766339	0.0705472
$119$	3.56858	0.327131
$120$	0.887811	0.0810457
$121$	−7.28478	−0.662253
$122$	−1.43577	−0.129989
$123$	−8.49714	−0.766161
$124$	12.0274	1.08009
$125$	−1.00000	−0.0894427
$126$	0.577070	0.0514095
$127$	18.7084	1.66011	0.830053	−	0.557685i	$-0.188310\pi$
$127$	18.7084	1.66011	0.830053	+	0.557685i	$0.188310\pi$
$128$	6.74585	0.596255
$129$	9.24829	0.814266
$130$	0	0
$131$	−19.3364	−1.68943	−0.844717	−	0.535214i	$-0.820231\pi$
$131$	−19.3364	−1.68943	−0.844717	+	0.535214i	$0.820231\pi$
$132$	−3.75758	−0.327055
$133$	20.2365	1.75473
$134$	0.126261	0.0109073
$135$	1.00000	0.0860663
$136$	−1.23415	−0.105828
$137$	−0.461325	−0.0394137	−0.0197068	−	0.999806i	$-0.506273\pi$
$137$	−0.461325	−0.0394137	−0.0197068	+	0.999806i	$0.506273\pi$
$138$	−0.948942	−0.0807793
$139$	2.02017	0.171348	0.0856742	−	0.996323i	$-0.472696\pi$
$139$	2.02017	0.171348	0.0856742	+	0.996323i	$0.472696\pi$
$140$	−5.00453	−0.422960
$141$	10.1617	0.855773
$142$	3.06279	0.257023
$143$	0	0
$144$	3.69936	0.308280
$145$	6.08029	0.504941
$146$	0.582462	0.0482049
$147$	0.409868	0.0338054
$148$	−3.53569	−0.290632
$149$	−10.2647	−0.840920	−0.420460	−	0.907311i	$-0.638131\pi$
$149$	−10.2647	−0.840920	−0.420460	+	0.907311i	$0.638131\pi$
$150$	0.224792	0.0183542
$151$	9.27340	0.754659	0.377329	−	0.926079i	$-0.376843\pi$
$151$	9.27340	0.754659	0.377329	+	0.926079i	$0.376843\pi$
$152$	−6.99856	−0.567658
$153$	−1.39011	−0.112383
$154$	−1.11230	−0.0896315
$155$	6.16957	0.495552
$156$	0	0
$157$	21.4461	1.71158	0.855791	−	0.517322i	$-0.173071\pi$
$157$	21.4461	1.71158	0.855791	+	0.517322i	$0.173071\pi$
$158$	−3.01838	−0.240130
$159$	−8.01914	−0.635960
$160$	2.60721	0.206118
$161$	10.8369	0.854068
$162$	−0.224792	−0.0176614
$163$	4.69399	0.367662	0.183831	−	0.982958i	$-0.441150\pi$
$163$	4.69399	0.367662	0.183831	+	0.982958i	$0.441150\pi$
$164$	−16.5649	−1.29350
$165$	−1.92749	−0.150055
$166$	−3.43666	−0.266736
$167$	−0.835468	−0.0646505	−0.0323252	−	0.999477i	$-0.510291\pi$
$167$	−0.835468	−0.0646505	−0.0323252	+	0.999477i	$0.510291\pi$
$168$	2.27912	0.175838
$169$	0	0
$170$	−0.312485	−0.0239665
$171$	−7.88294	−0.602823
$172$	18.0292	1.37472
$173$	−14.6458	−1.11350	−0.556749	−	0.830681i	$-0.687952\pi$
$173$	−14.6458	−1.11350	−0.556749	+	0.830681i	$0.687952\pi$
$174$	−1.36680	−0.103617
$175$	−2.56713	−0.194056
$176$	−7.13049	−0.537481
$177$	3.40909	0.256243
$178$	−0.0792279	−0.00593838
$179$	−7.70338	−0.575778	−0.287889	−	0.957664i	$-0.592953\pi$
$179$	−7.70338	−0.575778	−0.287889	+	0.957664i	$0.592953\pi$
$180$	1.94947	0.145305
$181$	2.32303	0.172670	0.0863349	−	0.996266i	$-0.472484\pi$
$181$	2.32303	0.172670	0.0863349	+	0.996266i	$0.472484\pi$
$182$	0	0
$183$	−6.38709	−0.472148
$184$	−3.74782	−0.276293
$185$	−1.81367	−0.133343
$186$	−1.38687	−0.101690
$187$	2.67942	0.195938
$188$	19.8100	1.44479
$189$	2.56713	0.186731
$190$	−1.77202	−0.128556
$191$	12.9959	0.940353	0.470176	−	0.882573i	$-0.344190\pi$
$191$	12.9959	0.940353	0.470176	+	0.882573i	$0.344190\pi$
$192$	6.81265	0.491660
$193$	−18.4364	−1.32708	−0.663541	−	0.748140i	$-0.730947\pi$
$193$	−18.4364	−1.32708	−0.663541	+	0.748140i	$0.730947\pi$
$194$	−0.773357	−0.0555238
$195$	0	0
$196$	0.799025	0.0570732
$197$	−22.8942	−1.63114	−0.815571	−	0.578657i	$-0.803577\pi$
$197$	−22.8942	−1.63114	−0.815571	+	0.578657i	$0.803577\pi$
$198$	0.433285	0.0307922
$199$	10.2538	0.726870	0.363435	−	0.931620i	$-0.381604\pi$
$199$	10.2538	0.726870	0.363435	+	0.931620i	$0.381604\pi$
$200$	0.887811	0.0627777
$201$	0.561677	0.0396176
$202$	−1.61386	−0.113551
$203$	15.6089	1.09553
$204$	−2.70997	−0.189736
$205$	−8.49714	−0.593466
$206$	−0.472516	−0.0329217
$207$	−4.22142	−0.293409
$208$	0	0
$209$	15.1943	1.05101
$210$	0.577070	0.0398216
$211$	13.3665	0.920188	0.460094	−	0.887870i	$-0.347816\pi$
$211$	13.3665	0.920188	0.460094	+	0.887870i	$0.347816\pi$
$212$	−15.6331	−1.07368
$213$	13.6250	0.933566
$214$	−1.22722	−0.0838908
$215$	9.24829	0.630728
$216$	−0.887811	−0.0604079
$217$	15.8381	1.07516
$218$	2.03125	0.137574
$219$	2.59111	0.175091
$220$	−3.75758	−0.253336
$221$	0	0
$222$	0.407699	0.0273629
$223$	14.3328	0.959795	0.479898	−	0.877325i	$-0.340674\pi$
$223$	14.3328	0.959795	0.479898	+	0.877325i	$0.340674\pi$
$224$	6.69304	0.447197
$225$	1.00000	0.0666667
$226$	−2.97930	−0.198180
$227$	−14.2795	−0.947766	−0.473883	−	0.880588i	$-0.657148\pi$
$227$	−14.2795	−0.947766	−0.473883	+	0.880588i	$0.657148\pi$
$228$	−15.3675	−1.01774
$229$	−14.8238	−0.979581	−0.489791	−	0.871840i	$-0.662927\pi$
$229$	−14.8238	−0.979581	−0.489791	+	0.871840i	$0.662927\pi$
$230$	−0.948942	−0.0625714
$231$	−4.94811	−0.325562
$232$	−5.39815	−0.354406
$233$	22.4005	1.46751	0.733754	−	0.679416i	$-0.237767\pi$
$233$	22.4005	1.46751	0.733754	+	0.679416i	$0.237767\pi$
$234$	0	0
$235$	10.1617	0.662879
$236$	6.64592	0.432613
$237$	−13.4274	−0.872204
$238$	−0.802189	−0.0519982
$239$	−10.2447	−0.662678	−0.331339	−	0.943512i	$-0.607500\pi$
$239$	−10.2447	−0.662678	−0.331339	+	0.943512i	$0.607500\pi$
$240$	3.69936	0.238793
$241$	5.31986	0.342682	0.171341	−	0.985212i	$-0.445190\pi$
$241$	5.31986	0.342682	0.171341	+	0.985212i	$0.445190\pi$
$242$	1.63756	0.105267
$243$	−1.00000	−0.0641500
$244$	−12.4514	−0.797122
$245$	0.409868	0.0261855
$246$	1.91009	0.121783
$247$	0	0
$248$	−5.47741	−0.347816
$249$	−15.2881	−0.968846
$250$	0.224792	0.0142171
$251$	20.1943	1.27465	0.637326	−	0.770594i	$-0.280041\pi$
$251$	20.1943	1.27465	0.637326	+	0.770594i	$0.280041\pi$
$252$	5.00453	0.315256
$253$	8.13674	0.511552
$254$	−4.20552	−0.263878
$255$	−1.39011	−0.0870518
$256$	12.1089	0.756805
$257$	−22.5057	−1.40386	−0.701932	−	0.712244i	$-0.747679\pi$
$257$	−22.5057	−1.40386	−0.701932	+	0.712244i	$0.747679\pi$
$258$	−2.07895	−0.129429
$259$	−4.65591	−0.289304
$260$	0	0
$261$	−6.08029	−0.376361
$262$	4.34669	0.268539
$263$	−28.4352	−1.75339	−0.876696	−	0.481046i	$-0.840257\pi$
$263$	−28.4352	−1.75339	−0.876696	+	0.481046i	$0.840257\pi$
$264$	1.71125	0.105320
$265$	−8.01914	−0.492612
$266$	−4.54901	−0.278918
$267$	−0.352449	−0.0215695
$268$	1.09497	0.0668860
$269$	0.602879	0.0367582	0.0183791	−	0.999831i	$-0.494149\pi$
$269$	0.602879	0.0367582	0.0183791	+	0.999831i	$0.494149\pi$
$270$	−0.224792	−0.0136804
$271$	−4.49574	−0.273097	−0.136548	−	0.990633i	$-0.543601\pi$
$271$	−4.49574	−0.273097	−0.136548	+	0.990633i	$0.543601\pi$
$272$	−5.14251	−0.311810
$273$	0	0
$274$	0.103702	0.00626490
$275$	−1.92749	−0.116232
$276$	−8.22952	−0.495359
$277$	5.36093	0.322107	0.161053	−	0.986946i	$-0.448511\pi$
$277$	5.36093	0.322107	0.161053	+	0.986946i	$0.448511\pi$
$278$	−0.454118	−0.0272362
$279$	−6.16957	−0.369363
$280$	2.27912	0.136204
$281$	11.0827	0.661139	0.330570	−	0.943782i	$-0.392759\pi$
$281$	11.0827	0.661139	0.330570	+	0.943782i	$0.392759\pi$
$282$	−2.28428	−0.136027
$283$	16.1957	0.962734	0.481367	−	0.876519i	$-0.340140\pi$
$283$	16.1957	0.962734	0.481367	+	0.876519i	$0.340140\pi$
$284$	26.5614	1.57613
$285$	−7.88294	−0.466945
$286$	0	0
$287$	−21.8132	−1.28759
$288$	−2.60721	−0.153631
$289$	−15.0676	−0.886330
$290$	−1.36680	−0.0802615
$291$	−3.44031	−0.201675
$292$	5.05128	0.295604
$293$	3.03459	0.177282	0.0886412	−	0.996064i	$-0.471748\pi$
$293$	3.03459	0.177282	0.0886412	+	0.996064i	$0.471748\pi$
$294$	−0.0921353	−0.00537344
$295$	3.40909	0.198485
$296$	1.61019	0.0935905
$297$	1.92749	0.111844
$298$	2.30744	0.133666
$299$	0	0
$300$	1.94947	0.112553
$301$	23.7415	1.36844
$302$	−2.08459	−0.119955
$303$	−7.17934	−0.412442
$304$	−29.1619	−1.67255
$305$	−6.38709	−0.365724
$306$	0.312485	0.0178636
$307$	32.7502	1.86915	0.934576	−	0.355763i	$-0.115779\pi$
$307$	32.7502	1.86915	0.934576	+	0.355763i	$0.115779\pi$
$308$	−9.64618	−0.549642
$309$	−2.10201	−0.119579
$310$	−1.38687	−0.0787691
$311$	−21.0600	−1.19421	−0.597103	−	0.802165i	$-0.703682\pi$
$311$	−21.0600	−1.19421	−0.597103	+	0.802165i	$0.703682\pi$
$312$	0	0
$313$	15.6387	0.883950	0.441975	−	0.897027i	$-0.354278\pi$
$313$	15.6387	0.883950	0.441975	+	0.897027i	$0.354278\pi$
$314$	−4.82091	−0.272060
$315$	2.56713	0.144641
$316$	−26.1763	−1.47253
$317$	3.70052	0.207842	0.103921	−	0.994586i	$-0.466861\pi$
$317$	3.70052	0.207842	0.103921	+	0.994586i	$0.466861\pi$
$318$	1.80264	0.101087
$319$	11.7197	0.656177
$320$	6.81265	0.380838
$321$	−5.45933	−0.304710
$322$	−2.43605	−0.135756
$323$	10.9581	0.609726
$324$	−1.94947	−0.108304
$325$	0	0
$326$	−1.05517	−0.0584407
$327$	9.03611	0.499698
$328$	7.54385	0.416540
$329$	26.0864	1.43819
$330$	0.433285	0.0238516
$331$	20.1517	1.10764	0.553820	−	0.832636i	$-0.313170\pi$
$331$	20.1517	1.10764	0.553820	+	0.832636i	$0.313170\pi$
$332$	−29.8037	−1.63569
$333$	1.81367	0.0993883
$334$	0.187807	0.0102763
$335$	0.561677	0.0306877
$336$	9.49673	0.518089
$337$	−14.5745	−0.793921	−0.396960	−	0.917836i	$-0.629935\pi$
$337$	−14.5745	−0.793921	−0.396960	+	0.917836i	$0.629935\pi$
$338$	0	0
$339$	−13.2535	−0.719834
$340$	−2.70997	−0.146969
$341$	11.8918	0.643976
$342$	1.77202	0.0958201
$343$	19.0221	1.02709
$344$	−8.21073	−0.442693
$345$	−4.22142	−0.227273
$346$	3.29226	0.176993
$347$	−16.9595	−0.910432	−0.455216	−	0.890381i	$-0.650438\pi$
$347$	−16.9595	−0.910432	−0.455216	+	0.890381i	$0.650438\pi$
$348$	−11.8533	−0.635405
$349$	−27.2527	−1.45881	−0.729403	−	0.684085i	$-0.760202\pi$
$349$	−27.2527	−1.45881	−0.729403	+	0.684085i	$0.760202\pi$
$350$	0.577070	0.0308457
$351$	0	0
$352$	5.02537	0.267853
$353$	27.7423	1.47657	0.738287	−	0.674486i	$-0.235635\pi$
$353$	27.7423	1.47657	0.738287	+	0.674486i	$0.235635\pi$
$354$	−0.766339	−0.0407304
$355$	13.6250	0.723137
$356$	−0.687088	−0.0364156
$357$	−3.56858	−0.188869
$358$	1.73166	0.0915212
$359$	−32.6221	−1.72173	−0.860864	−	0.508835i	$-0.830076\pi$
$359$	−32.6221	−1.72173	−0.860864	+	0.508835i	$0.830076\pi$
$360$	−0.887811	−0.0467917
$361$	43.1407	2.27056
$362$	−0.522201	−0.0274463
$363$	7.28478	0.382352
$364$	0	0
$365$	2.59111	0.135625
$366$	1.43577	0.0750489
$367$	−35.6986	−1.86345	−0.931727	−	0.363159i	$-0.881698\pi$
$367$	−35.6986	−1.86345	−0.931727	+	0.363159i	$0.881698\pi$
$368$	−15.6166	−0.814069
$369$	8.49714	0.442343
$370$	0.407699	0.0211952
$371$	−20.5861	−1.06878
$372$	−12.0274	−0.623591
$373$	5.07919	0.262990	0.131495	−	0.991317i	$-0.458022\pi$
$373$	5.07919	0.262990	0.131495	+	0.991317i	$0.458022\pi$
$374$	−0.602313	−0.0311448
$375$	1.00000	0.0516398
$376$	−9.02170	−0.465259
$377$	0	0
$378$	−0.577070	−0.0296813
$379$	−16.5306	−0.849119	−0.424560	−	0.905400i	$-0.639571\pi$
$379$	−16.5306	−0.849119	−0.424560	+	0.905400i	$0.639571\pi$
$380$	−15.3675	−0.788338
$381$	−18.7084	−0.958463
$382$	−2.92139	−0.149471
$383$	28.3709	1.44968	0.724842	−	0.688915i	$-0.241913\pi$
$383$	28.3709	1.44968	0.724842	+	0.688915i	$0.241913\pi$
$384$	−6.74585	−0.344248
$385$	−4.94811	−0.252179
$386$	4.14436	0.210943
$387$	−9.24829	−0.470117
$388$	−6.70678	−0.340485
$389$	−36.1830	−1.83455	−0.917275	−	0.398255i	$-0.869616\pi$
$389$	−36.1830	−1.83455	−0.917275	+	0.398255i	$0.869616\pi$
$390$	0	0
$391$	5.86822	0.296768
$392$	−0.363885	−0.0183790
$393$	19.3364	0.975395
$394$	5.14643	0.259274
$395$	−13.4274	−0.675606
$396$	3.75758	0.188826
$397$	14.5197	0.728724	0.364362	−	0.931257i	$-0.381287\pi$
$397$	14.5197	0.728724	0.364362	+	0.931257i	$0.381287\pi$
$398$	−2.30497	−0.115538
$399$	−20.2365	−1.01309
$400$	3.69936	0.184968
$401$	−33.4584	−1.67083	−0.835417	−	0.549617i	$-0.814774\pi$
$401$	−33.4584	−1.67083	−0.835417	+	0.549617i	$0.814774\pi$
$402$	−0.126261	−0.00629732
$403$	0	0
$404$	−13.9959	−0.696322
$405$	−1.00000	−0.0496904
$406$	−3.50876	−0.174137
$407$	−3.49582	−0.173282
$408$	1.23415	0.0610996
$409$	−6.40824	−0.316867	−0.158434	−	0.987370i	$-0.550644\pi$
$409$	−6.40824	−0.316867	−0.158434	+	0.987370i	$0.550644\pi$
$410$	1.91009	0.0943328
$411$	0.461325	0.0227555
$412$	−4.09780	−0.201884
$413$	8.75157	0.430637
$414$	0.948942	0.0466380
$415$	−15.2881	−0.750465
$416$	0	0
$417$	−2.02017	−0.0989280
$418$	−3.41556	−0.167061
$419$	−36.7559	−1.79564	−0.897822	−	0.440358i	$-0.854852\pi$
$419$	−36.7559	−1.79564	−0.897822	+	0.440358i	$0.854852\pi$
$420$	5.00453	0.244196
$421$	−8.07476	−0.393540	−0.196770	−	0.980450i	$-0.563045\pi$
$421$	−8.07476	−0.393540	−0.196770	+	0.980450i	$0.563045\pi$
$422$	−3.00469	−0.146266
$423$	−10.1617	−0.494081
$424$	7.11948	0.345753
$425$	−1.39011	−0.0674301
$426$	−3.06279	−0.148392
$427$	−16.3965	−0.793481
$428$	−10.6428	−0.514439
$429$	0	0
$430$	−2.07895	−0.100256
$431$	−13.6270	−0.656392	−0.328196	−	0.944610i	$-0.606441\pi$
$431$	−13.6270	−0.656392	−0.328196	+	0.944610i	$0.606441\pi$
$432$	−3.69936	−0.177986
$433$	9.17395	0.440872	0.220436	−	0.975401i	$-0.429252\pi$
$433$	9.17395	0.440872	0.220436	+	0.975401i	$0.429252\pi$
$434$	−3.56028	−0.170899
$435$	−6.08029	−0.291528
$436$	17.6156	0.843634
$437$	33.2772	1.59186
$438$	−0.582462	−0.0278311
$439$	30.8988	1.47472	0.737360	−	0.675500i	$-0.236072\pi$
$439$	30.8988	1.47472	0.737360	+	0.675500i	$0.236072\pi$
$440$	1.71125	0.0815805
$441$	−0.409868	−0.0195175
$442$	0	0
$443$	−22.3412	−1.06146	−0.530731	−	0.847540i	$-0.678083\pi$
$443$	−22.3412	−1.06146	−0.530731	+	0.847540i	$0.678083\pi$
$444$	3.53569	0.167796
$445$	−0.352449	−0.0167077
$446$	−3.22191	−0.152562
$447$	10.2647	0.485505
$448$	17.4889	0.826274
$449$	36.5712	1.72590	0.862951	−	0.505287i	$-0.168613\pi$
$449$	36.5712	1.72590	0.862951	+	0.505287i	$0.168613\pi$
$450$	−0.224792	−0.0105968
$451$	−16.3782	−0.771217
$452$	−25.8374	−1.21529
$453$	−9.27340	−0.435702
$454$	3.20993	0.150650
$455$	0	0
$456$	6.99856	0.327737
$457$	17.9289	0.838679	0.419339	−	0.907829i	$-0.362262\pi$
$457$	17.9289	0.838679	0.419339	+	0.907829i	$0.362262\pi$
$458$	3.33227	0.155707
$459$	1.39011	0.0648846
$460$	−8.22952	−0.383703
$461$	10.9081	0.508043	0.254021	−	0.967199i	$-0.418247\pi$
$461$	10.9081	0.508043	0.254021	+	0.967199i	$0.418247\pi$
$462$	1.11230	0.0517488
$463$	38.6347	1.79551	0.897754	−	0.440498i	$-0.145198\pi$
$463$	38.6347	1.79551	0.897754	+	0.440498i	$0.145198\pi$
$464$	−22.4932	−1.04422
$465$	−6.16957	−0.286107
$466$	−5.03547	−0.233264
$467$	33.4060	1.54584	0.772922	−	0.634502i	$-0.218795\pi$
$467$	33.4060	1.54584	0.772922	+	0.634502i	$0.218795\pi$
$468$	0	0
$469$	1.44190	0.0665805
$470$	−2.28428	−0.105366
$471$	−21.4461	−0.988182
$472$	−3.02663	−0.139312
$473$	17.8260	0.819640
$474$	3.01838	0.138639
$475$	−7.88294	−0.361694
$476$	−6.95683	−0.318866
$477$	8.01914	0.367171
$478$	2.30294	0.105334
$479$	15.7956	0.721717	0.360859	−	0.932620i	$-0.382484\pi$
$479$	15.7956	0.721717	0.360859	+	0.932620i	$0.382484\pi$
$480$	−2.60721	−0.119002
$481$	0	0
$482$	−1.19586	−0.0544701
$483$	−10.8369	−0.493096
$484$	14.2015	0.645521
$485$	−3.44031	−0.156217
$486$	0.224792	0.0101968
$487$	22.8236	1.03424	0.517119	−	0.855914i	$-0.327004\pi$
$487$	22.8236	1.03424	0.517119	+	0.855914i	$0.327004\pi$
$488$	5.67053	0.256693
$489$	−4.69399	−0.212270
$490$	−0.0921353	−0.00416225
$491$	−10.0723	−0.454555	−0.227277	−	0.973830i	$-0.572982\pi$
$491$	−10.0723	−0.454555	−0.227277	+	0.973830i	$0.572982\pi$
$492$	16.5649	0.746804
$493$	8.45225	0.380670
$494$	0	0
$495$	1.92749	0.0866342
$496$	−22.8235	−1.02480
$497$	34.9770	1.56893
$498$	3.43666	0.154000
$499$	−37.7742	−1.69101	−0.845503	−	0.533971i	$-0.820699\pi$
$499$	−37.7742	−1.69101	−0.845503	+	0.533971i	$0.820699\pi$
$500$	1.94947	0.0871829
$501$	0.835468	0.0373260
$502$	−4.53952	−0.202609
$503$	−17.3124	−0.771922	−0.385961	−	0.922515i	$-0.626130\pi$
$503$	−17.3124	−0.771922	−0.385961	+	0.922515i	$0.626130\pi$
$504$	−2.27912	−0.101520
$505$	−7.17934	−0.319477
$506$	−1.82908	−0.0813124
$507$	0	0
$508$	−36.4715	−1.61816
$509$	−10.4441	−0.462929	−0.231464	−	0.972843i	$-0.574352\pi$
$509$	−10.4441	−0.462929	−0.231464	+	0.972843i	$0.574352\pi$
$510$	0.312485	0.0138371
$511$	6.65170	0.294254
$512$	−16.2137	−0.716551
$513$	7.88294	0.348040
$514$	5.05910	0.223148
$515$	−2.10201	−0.0926256
$516$	−18.0292	−0.793693
$517$	19.5866	0.861420
$518$	1.04661	0.0459855
$519$	14.6458	0.642879
$520$	0	0
$521$	−18.1205	−0.793874	−0.396937	−	0.917846i	$-0.629927\pi$
$521$	−18.1205	−0.793874	−0.396937	+	0.917846i	$0.629927\pi$
$522$	1.36680	0.0598234
$523$	37.2365	1.62824	0.814119	−	0.580698i	$-0.197220\pi$
$523$	37.2365	1.62824	0.814119	+	0.580698i	$0.197220\pi$
$524$	37.6958	1.64675
$525$	2.56713	0.112039
$526$	6.39202	0.278705
$527$	8.57636	0.373592
$528$	7.13049	0.310315
$529$	−5.17965	−0.225202
$530$	1.80264	0.0783018
$531$	−3.40909	−0.147942
$532$	−39.4504	−1.71039
$533$	0	0
$534$	0.0792279	0.00342852
$535$	−5.45933	−0.236027
$536$	−0.498663	−0.0215390
$537$	7.70338	0.332425
$538$	−0.135523	−0.00584280
$539$	0.790017	0.0340284
$540$	−1.94947	−0.0838918
$541$	−5.62466	−0.241823	−0.120911	−	0.992663i	$-0.538582\pi$
$541$	−5.62466	−0.241823	−0.120911	+	0.992663i	$0.538582\pi$
$542$	1.01061	0.0434093
$543$	−2.32303	−0.0996910
$544$	3.62430	0.155391
$545$	9.03611	0.387064
$546$	0	0
$547$	−42.4758	−1.81613	−0.908066	−	0.418826i	$-0.862442\pi$
$547$	−42.4758	−1.81613	−0.908066	+	0.418826i	$0.862442\pi$
$548$	0.899339	0.0384179
$549$	6.38709	0.272595
$550$	0.433285	0.0184753
$551$	47.9305	2.04191
$552$	3.74782	0.159518
$553$	−34.4699	−1.46581
$554$	−1.20510	−0.0511996
$555$	1.81367	0.0769859
$556$	−3.93825	−0.167019
$557$	−13.4622	−0.570414	−0.285207	−	0.958466i	$-0.592062\pi$
$557$	−13.4622	−0.570414	−0.285207	+	0.958466i	$0.592062\pi$
$558$	1.38687	0.0587110
$559$	0	0
$560$	9.49673	0.401310
$561$	−2.67942	−0.113125
$562$	−2.49131	−0.105090
$563$	−22.9473	−0.967114	−0.483557	−	0.875313i	$-0.660655\pi$
$563$	−22.9473	−0.967114	−0.483557	+	0.875313i	$0.660655\pi$
$564$	−19.8100	−0.834151
$565$	−13.2535	−0.557581
$566$	−3.64067	−0.153029
$567$	−2.56713	−0.107809
$568$	−12.0964	−0.507553
$569$	1.80111	0.0755064	0.0377532	−	0.999287i	$-0.487980\pi$
$569$	1.80111	0.0755064	0.0377532	+	0.999287i	$0.487980\pi$
$570$	1.77202	0.0742220
$571$	17.2755	0.722957	0.361478	−	0.932381i	$-0.382272\pi$
$571$	17.2755	0.722957	0.361478	+	0.932381i	$0.382272\pi$
$572$	0	0
$573$	−12.9959	−0.542913
$574$	4.90345	0.204666
$575$	−4.22142	−0.176045
$576$	−6.81265	−0.283860
$577$	−39.2187	−1.63270	−0.816348	−	0.577561i	$-0.804005\pi$
$577$	−39.2187	−1.63270	−0.816348	+	0.577561i	$0.804005\pi$
$578$	3.38708	0.140884
$579$	18.4364	0.766191
$580$	−11.8533	−0.492183
$581$	−39.2465	−1.62822
$582$	0.773357	0.0320567
$583$	−15.4568	−0.640156
$584$	−2.30041	−0.0951918
$585$	0	0
$586$	−0.682152	−0.0281794
$587$	0.119403	0.00492827	0.00246414	−	0.999997i	$-0.499216\pi$
$587$	0.119403	0.00492827	0.00246414	+	0.999997i	$0.499216\pi$
$588$	−0.799025	−0.0329512
$589$	48.6343	2.00394
$590$	−0.766339	−0.0315497
$591$	22.8942	0.941740
$592$	6.70941	0.275755
$593$	−10.0781	−0.413860	−0.206930	−	0.978356i	$-0.566347\pi$
$593$	−10.0781	−0.413860	−0.206930	+	0.978356i	$0.566347\pi$
$594$	−0.433285	−0.0177779
$595$	−3.56858	−0.146297
$596$	20.0108	0.819673
$597$	−10.2538	−0.419658
$598$	0	0
$599$	2.61113	0.106688	0.0533439	−	0.998576i	$-0.483012\pi$
$599$	2.61113	0.106688	0.0533439	+	0.998576i	$0.483012\pi$
$600$	−0.887811	−0.0362447
$601$	1.14943	0.0468862	0.0234431	−	0.999725i	$-0.492537\pi$
$601$	1.14943	0.0468862	0.0234431	+	0.999725i	$0.492537\pi$
$602$	−5.33691	−0.217516
$603$	−0.561677	−0.0228733
$604$	−18.0782	−0.735591
$605$	7.28478	0.296169
$606$	1.61386	0.0655587
$607$	17.5897	0.713944	0.356972	−	0.934115i	$-0.383809\pi$
$607$	17.5897	0.713944	0.356972	+	0.934115i	$0.383809\pi$
$608$	20.5525	0.833513
$609$	−15.6089	−0.632503
$610$	1.43577	0.0581327
$611$	0	0
$612$	2.70997	0.109544
$613$	2.56465	0.103585	0.0517927	−	0.998658i	$-0.483506\pi$
$613$	2.56465	0.103585	0.0517927	+	0.998658i	$0.483506\pi$
$614$	−7.36200	−0.297106
$615$	8.49714	0.342638
$616$	4.39298	0.176998
$617$	35.3265	1.42219	0.711096	−	0.703095i	$-0.248199\pi$
$617$	35.3265	1.42219	0.711096	+	0.703095i	$0.248199\pi$
$618$	0.472516	0.0190074
$619$	−9.10258	−0.365863	−0.182932	−	0.983126i	$-0.558559\pi$
$619$	−9.10258	−0.365863	−0.182932	+	0.983126i	$0.558559\pi$
$620$	−12.0274	−0.483031
$621$	4.22142	0.169400
$622$	4.73414	0.189822
$623$	−0.904780	−0.0362493
$624$	0	0
$625$	1.00000	0.0400000
$626$	−3.51546	−0.140506
$627$	−15.1943	−0.606801
$628$	−41.8084	−1.66834
$629$	−2.52119	−0.100526
$630$	−0.577070	−0.0229910
$631$	−27.1265	−1.07989	−0.539944	−	0.841701i	$-0.681555\pi$
$631$	−27.1265	−1.07989	−0.539944	+	0.841701i	$0.681555\pi$
$632$	11.9210	0.474192
$633$	−13.3665	−0.531271
$634$	−0.831850	−0.0330370
$635$	−18.7084	−0.742422
$636$	15.6331	0.619892
$637$	0	0
$638$	−2.63450	−0.104301
$639$	−13.6250	−0.538995
$640$	−6.74585	−0.266653
$641$	0.384642	0.0151924	0.00759622	−	0.999971i	$-0.497582\pi$
$641$	0.384642	0.0151924	0.00759622	+	0.999971i	$0.497582\pi$
$642$	1.22722	0.0484344
$643$	10.8866	0.429327	0.214664	−	0.976688i	$-0.431135\pi$
$643$	10.8866	0.429327	0.214664	+	0.976688i	$0.431135\pi$
$644$	−21.1262	−0.832489
$645$	−9.24829	−0.364151
$646$	−2.46330	−0.0969174
$647$	22.6793	0.891616	0.445808	−	0.895129i	$-0.352916\pi$
$647$	22.6793	0.891616	0.445808	+	0.895129i	$0.352916\pi$
$648$	0.887811	0.0348765
$649$	6.57099	0.257934
$650$	0	0
$651$	−15.8381	−0.620743
$652$	−9.15079	−0.358372
$653$	−40.7389	−1.59424	−0.797118	−	0.603823i	$-0.793643\pi$
$653$	−40.7389	−1.59424	−0.797118	+	0.603823i	$0.793643\pi$
$654$	−2.03125	−0.0794281
$655$	19.3364	0.755538
$656$	31.4340	1.22729
$657$	−2.59111	−0.101089
$658$	−5.86404	−0.228604
$659$	15.4087	0.600237	0.300118	−	0.953902i	$-0.402974\pi$
$659$	15.4087	0.600237	0.300118	+	0.953902i	$0.402974\pi$
$660$	3.75758	0.146264
$661$	−34.7726	−1.35250	−0.676249	−	0.736673i	$-0.736395\pi$
$661$	−34.7726	−1.35250	−0.676249	+	0.736673i	$0.736395\pi$
$662$	−4.52996	−0.176062
$663$	0	0
$664$	13.5730	0.526733
$665$	−20.2365	−0.784737
$666$	−0.407699	−0.0157980
$667$	25.6674	0.993847
$668$	1.62872	0.0630170
$669$	−14.3328	−0.554138
$670$	−0.126261	−0.00487788
$671$	−12.3111	−0.475263
$672$	−6.69304	−0.258189
$673$	43.8534	1.69043	0.845213	−	0.534430i	$-0.179474\pi$
$673$	43.8534	1.69043	0.845213	+	0.534430i	$0.179474\pi$
$674$	3.27623	0.126196
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−17.7252	−0.681236	−0.340618	−	0.940202i	$-0.610636\pi$
$677$	−17.7252	−0.681236	−0.340618	+	0.940202i	$0.610636\pi$
$678$	2.97930	0.114419
$679$	−8.83172	−0.338930
$680$	1.23415	0.0473275
$681$	14.2795	0.547193
$682$	−2.67318	−0.102362
$683$	−7.65534	−0.292923	−0.146462	−	0.989216i	$-0.546789\pi$
$683$	−7.65534	−0.292923	−0.146462	+	0.989216i	$0.546789\pi$
$684$	15.3675	0.587592
$685$	0.461325	0.0176263
$686$	−4.27602	−0.163259
$687$	14.8238	0.565561
$688$	−34.2128	−1.30435
$689$	0	0
$690$	0.948942	0.0361256
$691$	−12.4650	−0.474189	−0.237095	−	0.971487i	$-0.576195\pi$
$691$	−12.4650	−0.474189	−0.237095	+	0.971487i	$0.576195\pi$
$692$	28.5515	1.08537
$693$	4.94811	0.187963
$694$	3.81236	0.144715
$695$	−2.02017	−0.0766293
$696$	5.39815	0.204616
$697$	−11.8119	−0.447409
$698$	6.12621	0.231880
$699$	−22.4005	−0.847266
$700$	5.00453	0.189153
$701$	2.78891	0.105336	0.0526679	−	0.998612i	$-0.483228\pi$
$701$	2.78891	0.105336	0.0526679	+	0.998612i	$0.483228\pi$
$702$	0	0
$703$	−14.2970	−0.539222
$704$	13.1313	0.494905
$705$	−10.1617	−0.382713
$706$	−6.23626	−0.234705
$707$	−18.4303	−0.693142
$708$	−6.64592	−0.249769
$709$	23.8129	0.894311	0.447156	−	0.894456i	$-0.352437\pi$
$709$	23.8129	0.894311	0.447156	+	0.894456i	$0.352437\pi$
$710$	−3.06279	−0.114944
$711$	13.4274	0.503567
$712$	0.312908	0.0117267
$713$	26.0443	0.975368
$714$	0.802189	0.0300212
$715$	0	0
$716$	15.0175	0.561230
$717$	10.2447	0.382597
$718$	7.33320	0.273673
$719$	51.6669	1.92685	0.963426	−	0.267976i	$-0.0863547\pi$
$719$	51.6669	1.92685	0.963426	+	0.267976i	$0.0863547\pi$
$720$	−3.69936	−0.137867
$721$	−5.39612	−0.200962
$722$	−9.69770	−0.360911
$723$	−5.31986	−0.197848
$724$	−4.52868	−0.168307
$725$	−6.08029	−0.225816
$726$	−1.63756	−0.0607757
$727$	7.21510	0.267593	0.133797	−	0.991009i	$-0.457283\pi$
$727$	7.21510	0.267593	0.133797	+	0.991009i	$0.457283\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.582462	−0.0215579
$731$	12.8561	0.475500
$732$	12.4514	0.460218
$733$	−26.7214	−0.986979	−0.493490	−	0.869752i	$-0.664279\pi$
$733$	−26.7214	−0.986979	−0.493490	+	0.869752i	$0.664279\pi$
$734$	8.02479	0.296200
$735$	−0.409868	−0.0151182
$736$	11.0061	0.405691
$737$	1.08263	0.0398791
$738$	−1.91009	−0.0703115
$739$	18.3008	0.673205	0.336603	−	0.941647i	$-0.390722\pi$
$739$	18.3008	0.673205	0.336603	+	0.941647i	$0.390722\pi$
$740$	3.53569	0.129974
$741$	0	0
$742$	4.62761	0.169885
$743$	−27.6346	−1.01382	−0.506908	−	0.862000i	$-0.669212\pi$
$743$	−27.6346	−1.01382	−0.506908	+	0.862000i	$0.669212\pi$
$744$	5.47741	0.200812
$745$	10.2647	0.376071
$746$	−1.14176	−0.0418029
$747$	15.2881	0.559363
$748$	−5.22344	−0.190988
$749$	−14.0148	−0.512089
$750$	−0.224792	−0.00820826
$751$	−27.8611	−1.01666	−0.508332	−	0.861161i	$-0.669738\pi$
$751$	−27.8611	−1.01666	−0.508332	+	0.861161i	$0.669738\pi$
$752$	−37.5920	−1.37084
$753$	−20.1943	−0.735921
$754$	0	0
$755$	−9.27340	−0.337494
$756$	−5.00453	−0.182013
$757$	27.7470	1.00848	0.504241	−	0.863563i	$-0.331772\pi$
$757$	27.7470	1.00848	0.504241	+	0.863563i	$0.331772\pi$
$758$	3.71595	0.134969
$759$	−8.13674	−0.295345
$760$	6.99856	0.253864
$761$	−35.3434	−1.28120	−0.640599	−	0.767875i	$-0.721314\pi$
$761$	−35.3434	−1.28120	−0.640599	+	0.767875i	$0.721314\pi$
$762$	4.20552	0.152350
$763$	23.1968	0.839781
$764$	−25.3352	−0.916594
$765$	1.39011	0.0502594
$766$	−6.37756	−0.230431
$767$	0	0
$768$	−12.1089	−0.436941
$769$	−12.9063	−0.465414	−0.232707	−	0.972547i	$-0.574758\pi$
$769$	−12.9063	−0.465414	−0.232707	+	0.972547i	$0.574758\pi$
$770$	1.11230	0.0400844
$771$	22.5057	0.810522
$772$	35.9412	1.29355
$773$	9.83645	0.353793	0.176896	−	0.984230i	$-0.443394\pi$
$773$	9.83645	0.353793	0.176896	+	0.984230i	$0.443394\pi$
$774$	2.07895	0.0747262
$775$	−6.16957	−0.221618
$776$	3.05435	0.109645
$777$	4.65591	0.167030
$778$	8.13366	0.291606
$779$	−66.9824	−2.39989
$780$	0	0
$781$	26.2620	0.939727
$782$	−1.31913	−0.0471720
$783$	6.08029	0.217292
$784$	−1.51625	−0.0541518
$785$	−21.4461	−0.765443
$786$	−4.34669	−0.155041
$787$	2.37007	0.0844837	0.0422419	−	0.999107i	$-0.486550\pi$
$787$	2.37007	0.0844837	0.0422419	+	0.999107i	$0.486550\pi$
$788$	44.6314	1.58993
$789$	28.4352	1.01232
$790$	3.01838	0.107389
$791$	−34.0235	−1.20974
$792$	−1.71125	−0.0608065
$793$	0	0
$794$	−3.26392	−0.115832
$795$	8.01914	0.284410
$796$	−19.9894	−0.708505
$797$	4.86198	0.172220	0.0861100	−	0.996286i	$-0.472556\pi$
$797$	4.86198	0.172220	0.0861100	+	0.996286i	$0.472556\pi$
$798$	4.54901	0.161033
$799$	14.1259	0.499738
$800$	−2.60721	−0.0921788
$801$	0.352449	0.0124532
$802$	7.52120	0.265583
$803$	4.99434	0.176246
$804$	−1.09497	−0.0386167
$805$	−10.8369	−0.381951
$806$	0	0
$807$	−0.602879	−0.0212224
$808$	6.37390	0.224233
$809$	−10.0051	−0.351760	−0.175880	−	0.984412i	$-0.556277\pi$
$809$	−10.0051	−0.351760	−0.175880	+	0.984412i	$0.556277\pi$
$810$	0.224792	0.00789840
$811$	11.0554	0.388209	0.194104	−	0.980981i	$-0.437820\pi$
$811$	11.0554	0.388209	0.194104	+	0.980981i	$0.437820\pi$
$812$	−30.4290	−1.06785
$813$	4.49574	0.157672
$814$	0.785835	0.0275435
$815$	−4.69399	−0.164423
$816$	5.14251	0.180024
$817$	72.9037	2.55058
$818$	1.44052	0.0503667
$819$	0	0
$820$	16.5649	0.578472
$821$	13.1597	0.459276	0.229638	−	0.973276i	$-0.426246\pi$
$821$	13.1597	0.459276	0.229638	+	0.973276i	$0.426246\pi$
$822$	−0.103702	−0.00361704
$823$	−26.3504	−0.918518	−0.459259	−	0.888302i	$-0.651885\pi$
$823$	−26.3504	−0.918518	−0.459259	+	0.888302i	$0.651885\pi$
$824$	1.86619	0.0650117
$825$	1.92749	0.0671066
$826$	−1.96729	−0.0684507
$827$	15.3044	0.532186	0.266093	−	0.963947i	$-0.414267\pi$
$827$	15.3044	0.532186	0.266093	+	0.963947i	$0.414267\pi$
$828$	8.22952	0.285995
$829$	−48.5230	−1.68527	−0.842636	−	0.538483i	$-0.818998\pi$
$829$	−48.5230	−1.68527	−0.842636	+	0.538483i	$0.818998\pi$
$830$	3.43666	0.119288
$831$	−5.36093	−0.185969
$832$	0	0
$833$	0.569760	0.0197410
$834$	0.454118	0.0157248
$835$	0.835468	0.0289126
$836$	−29.6208	−1.02446
$837$	6.16957	0.213252
$838$	8.26246	0.285422
$839$	6.37399	0.220055	0.110027	−	0.993929i	$-0.464906\pi$
$839$	6.37399	0.220055	0.110027	+	0.993929i	$0.464906\pi$
$840$	−2.27912	−0.0786372
$841$	7.96993	0.274825
$842$	1.81514	0.0625540
$843$	−11.0827	−0.381709
$844$	−26.0576	−0.896938
$845$	0	0
$846$	2.28428	0.0785352
$847$	18.7009	0.642572
$848$	29.6657	1.01873
$849$	−16.1957	−0.555835
$850$	0.312485	0.0107182
$851$	−7.65624	−0.262453
$852$	−26.5614	−0.909979
$853$	32.9385	1.12779	0.563897	−	0.825845i	$-0.309302\pi$
$853$	32.9385	1.12779	0.563897	+	0.825845i	$0.309302\pi$
$854$	3.68580	0.126126
$855$	7.88294	0.269591
$856$	4.84685	0.165662
$857$	50.3679	1.72054	0.860268	−	0.509843i	$-0.170296\pi$
$857$	50.3679	1.72054	0.860268	+	0.509843i	$0.170296\pi$
$858$	0	0
$859$	−8.70336	−0.296955	−0.148477	−	0.988916i	$-0.547437\pi$
$859$	−8.70336	−0.296955	−0.148477	+	0.988916i	$0.547437\pi$
$860$	−18.0292	−0.614792
$861$	21.8132	0.743393
$862$	3.06326	0.104335
$863$	38.7639	1.31954	0.659769	−	0.751469i	$-0.270654\pi$
$863$	38.7639	1.31954	0.659769	+	0.751469i	$0.270654\pi$
$864$	2.60721	0.0886991
$865$	14.6458	0.497972
$866$	−2.06223	−0.0700776
$867$	15.0676	0.511723
$868$	−30.8758	−1.04799
$869$	−25.8812	−0.877960
$870$	1.36680	0.0463390
$871$	0	0
$872$	−8.02235	−0.271671
$873$	3.44031	0.116437
$874$	−7.48045	−0.253030
$875$	2.56713	0.0867847
$876$	−5.05128	−0.170667
$877$	33.5072	1.13146	0.565729	−	0.824591i	$-0.308595\pi$
$877$	33.5072	1.13146	0.565729	+	0.824591i	$0.308595\pi$
$878$	−6.94582	−0.234410
$879$	−3.03459	−0.102354
$880$	7.13049	0.240369
$881$	31.5095	1.06158	0.530790	−	0.847503i	$-0.321895\pi$
$881$	31.5095	1.06158	0.530790	+	0.847503i	$0.321895\pi$
$882$	0.0921353	0.00310236
$883$	35.3125	1.18836	0.594181	−	0.804332i	$-0.297476\pi$
$883$	35.3125	1.18836	0.594181	+	0.804332i	$0.297476\pi$
$884$	0	0
$885$	−3.40909	−0.114595
$886$	5.02213	0.168722
$887$	−27.6399	−0.928055	−0.464028	−	0.885821i	$-0.653596\pi$
$887$	−27.6399	−0.928055	−0.464028	+	0.885821i	$0.653596\pi$
$888$	−1.61019	−0.0540345
$889$	−48.0269	−1.61077
$890$	0.0792279	0.00265572
$891$	−1.92749	−0.0645733
$892$	−27.9413	−0.935545
$893$	80.1043	2.68059
$894$	−2.30744	−0.0771722
$895$	7.70338	0.257496
$896$	−17.3174	−0.578535
$897$	0	0
$898$	−8.22094	−0.274336
$899$	37.5128	1.25112
$900$	−1.94947	−0.0649823
$901$	−11.1475	−0.371376
$902$	3.68169	0.122587
$903$	−23.7415	−0.790068
$904$	11.7666	0.391352
$905$	−2.32303	−0.0772203
$906$	2.08459	0.0692559
$907$	−40.9201	−1.35873	−0.679365	−	0.733800i	$-0.737745\pi$
$907$	−40.9201	−1.35873	−0.679365	+	0.733800i	$0.737745\pi$
$908$	27.8375	0.923820
$909$	7.17934	0.238124
$910$	0	0
$911$	29.7453	0.985506	0.492753	−	0.870169i	$-0.335991\pi$
$911$	29.7453	0.985506	0.492753	+	0.870169i	$0.335991\pi$
$912$	29.1619	0.965645
$913$	−29.4677	−0.975239
$914$	−4.03028	−0.133310
$915$	6.38709	0.211151
$916$	28.8984	0.954831
$917$	49.6391	1.63923
$918$	−0.312485	−0.0103136
$919$	−48.2463	−1.59150	−0.795749	−	0.605626i	$-0.792923\pi$
$919$	−48.2463	−1.59150	−0.795749	+	0.605626i	$0.792923\pi$
$920$	3.74782	0.123562
$921$	−32.7502	−1.07916
$922$	−2.45207	−0.0807546
$923$	0	0
$924$	9.64618	0.317336
$925$	1.81367	0.0596330
$926$	−8.68479	−0.285400
$927$	2.10201	0.0690390
$928$	15.8526	0.520387
$929$	−22.9334	−0.752421	−0.376210	−	0.926534i	$-0.622773\pi$
$929$	−22.9334	−0.752421	−0.376210	+	0.926534i	$0.622773\pi$
$930$	1.38687	0.0454774
$931$	3.23096	0.105891
$932$	−43.6691	−1.43043
$933$	21.0600	0.689475
$934$	−7.50941	−0.245715
$935$	−2.67942	−0.0876263
$936$	0	0
$937$	9.38609	0.306630	0.153315	−	0.988177i	$-0.451005\pi$
$937$	9.38609	0.306630	0.153315	+	0.988177i	$0.451005\pi$
$938$	−0.324127	−0.0105831
$939$	−15.6387	−0.510349
$940$	−19.8100	−0.646130
$941$	−11.9963	−0.391069	−0.195535	−	0.980697i	$-0.562644\pi$
$941$	−11.9963	−0.391069	−0.195535	+	0.980697i	$0.562644\pi$
$942$	4.82091	0.157074
$943$	−35.8700	−1.16809
$944$	−12.6115	−0.410469
$945$	−2.56713	−0.0835086
$946$	−4.00715	−0.130284
$947$	−14.8297	−0.481899	−0.240949	−	0.970538i	$-0.577459\pi$
$947$	−14.8297	−0.481899	−0.240949	+	0.970538i	$0.577459\pi$
$948$	26.1763	0.850167
$949$	0	0
$950$	1.77202	0.0574921
$951$	−3.70052	−0.119998
$952$	3.16822	0.102683
$953$	−14.0770	−0.455998	−0.227999	−	0.973661i	$-0.573218\pi$
$953$	−14.0770	−0.455998	−0.227999	+	0.973661i	$0.573218\pi$
$954$	−1.80264	−0.0583627
$955$	−12.9959	−0.420538
$956$	19.9718	0.645935
$957$	−11.7197	−0.378844
$958$	−3.55072	−0.114719
$959$	1.18428	0.0382424
$960$	−6.81265	−0.219877
$961$	7.06362	0.227859
$962$	0	0
$963$	5.45933	0.175925
$964$	−10.3709	−0.334024
$965$	18.4364	0.593489
$966$	2.43605	0.0783787
$967$	39.0969	1.25727	0.628636	−	0.777699i	$-0.283613\pi$
$967$	39.0969	1.25727	0.628636	+	0.777699i	$0.283613\pi$
$968$	−6.46751	−0.207874
$969$	−10.9581	−0.352026
$970$	0.773357	0.0248310
$971$	−27.8569	−0.893970	−0.446985	−	0.894542i	$-0.647502\pi$
$971$	−27.8569	−0.893970	−0.446985	+	0.894542i	$0.647502\pi$
$972$	1.94947	0.0625292
$973$	−5.18602	−0.166256
$974$	−5.13058	−0.164394
$975$	0	0
$976$	23.6282	0.756320
$977$	−33.3833	−1.06803	−0.534013	−	0.845476i	$-0.679317\pi$
$977$	−33.3833	−1.06803	−0.534013	+	0.845476i	$0.679317\pi$
$978$	1.05517	0.0337407
$979$	−0.679342	−0.0217119
$980$	−0.799025	−0.0255239
$981$	−9.03611	−0.288501
$982$	2.26417	0.0722525
$983$	17.7177	0.565108	0.282554	−	0.959251i	$-0.408818\pi$
$983$	17.7177	0.565108	0.282554	+	0.959251i	$0.408818\pi$
$984$	−7.54385	−0.240489
$985$	22.8942	0.729469
$986$	−1.90000	−0.0605084
$987$	−26.0864	−0.830341
$988$	0	0
$989$	39.0409	1.24143
$990$	−0.433285	−0.0137707
$991$	20.4406	0.649318	0.324659	−	0.945831i	$-0.394750\pi$
$991$	20.4406	0.649318	0.324659	+	0.945831i	$0.394750\pi$
$992$	16.0854	0.510711
$993$	−20.1517	−0.639496
$994$	−7.86256	−0.249385
$995$	−10.2538	−0.325066
$996$	29.8037	0.944367
$997$	−23.0154	−0.728904	−0.364452	−	0.931222i	$-0.618744\pi$
$997$	−23.0154	−0.728904	−0.364452	+	0.931222i	$0.618744\pi$
$998$	8.49136	0.268789
$999$	−1.81367	−0.0573819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.bm.1.5	✓	9
3.2	odd	2		7605.2.a.cr.1.5		9
13.12	even	2		2535.2.a.bn.1.5	yes	9
39.38	odd	2		7605.2.a.cq.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.bm.1.5	✓	9	1.1	even	1	trivial
2535.2.a.bn.1.5	yes	9	13.12	even	2
7605.2.a.cq.1.5		9	39.38	odd	2
7605.2.a.cr.1.5		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.a (trivial)

\(f(q)\)	\(=\)	\(q-0.224792 q^{2} -1.00000 q^{3} -1.94947 q^{4} -1.00000 q^{5} +0.224792 q^{6} -2.56713 q^{7} +0.887811 q^{8} +1.00000 q^{9} +0.224792 q^{10} -1.92749 q^{11} +1.94947 q^{12} +0.577070 q^{14} +1.00000 q^{15} +3.69936 q^{16} -1.39011 q^{17} -0.224792 q^{18} -7.88294 q^{19} +1.94947 q^{20} +2.56713 q^{21} +0.433285 q^{22} -4.22142 q^{23} -0.887811 q^{24} +1.00000 q^{25} -1.00000 q^{27} +5.00453 q^{28} -6.08029 q^{29} -0.224792 q^{30} -6.16957 q^{31} -2.60721 q^{32} +1.92749 q^{33} +0.312485 q^{34} +2.56713 q^{35} -1.94947 q^{36} +1.81367 q^{37} +1.77202 q^{38} -0.887811 q^{40} +8.49714 q^{41} -0.577070 q^{42} -9.24829 q^{43} +3.75758 q^{44} -1.00000 q^{45} +0.948942 q^{46} -10.1617 q^{47} -3.69936 q^{48} -0.409868 q^{49} -0.224792 q^{50} +1.39011 q^{51} +8.01914 q^{53} +0.224792 q^{54} +1.92749 q^{55} -2.27912 q^{56} +7.88294 q^{57} +1.36680 q^{58} -3.40909 q^{59} -1.94947 q^{60} +6.38709 q^{61} +1.38687 q^{62} -2.56713 q^{63} -6.81265 q^{64} -0.433285 q^{66} -0.561677 q^{67} +2.70997 q^{68} +4.22142 q^{69} -0.577070 q^{70} -13.6250 q^{71} +0.887811 q^{72} -2.59111 q^{73} -0.407699 q^{74} -1.00000 q^{75} +15.3675 q^{76} +4.94811 q^{77} +13.4274 q^{79} -3.69936 q^{80} +1.00000 q^{81} -1.91009 q^{82} +15.2881 q^{83} -5.00453 q^{84} +1.39011 q^{85} +2.07895 q^{86} +6.08029 q^{87} -1.71125 q^{88} +0.352449 q^{89} +0.224792 q^{90} +8.22952 q^{92} +6.16957 q^{93} +2.28428 q^{94} +7.88294 q^{95} +2.60721 q^{96} +3.44031 q^{97} +0.0921353 q^{98} -1.92749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 9 * q - 9 * q^3 + 10 * q^4 - 9 * q^5 + 10 * q^7 - 3 * q^8 + 9 * q^9 - 11 * q^11 - 10 * q^12 + 10 * q^14 + 9 * q^15 + 8 * q^16 + 18 * q^17 - 10 * q^19 - 10 * q^20 - 10 * q^21 + 17 * q^22 - 7 * q^23 + 3 * q^24 + 9 * q^25 - 9 * q^27 + 43 * q^28 - 9 * q^29 - 17 * q^31 - 11 * q^32 + 11 * q^33 + 4 * q^34 - 10 * q^35 + 10 * q^36 - 3 * q^37 + 21 * q^38 + 3 * q^40 - 4 * q^41 - 10 * q^42 + 14 * q^43 - 13 * q^44 - 9 * q^45 - 3 * q^46 + 2 * q^47 - 8 * q^48 + 43 * q^49 - 18 * q^51 + 5 * q^53 + 11 * q^55 + q^56 + 10 * q^57 + 14 * q^58 - 3 * q^59 + 10 * q^60 + 48 * q^61 - 7 * q^62 + 10 * q^63 + 41 * q^64 - 17 * q^66 + 40 * q^67 + 40 * q^68 + 7 * q^69 - 10 * q^70 - 12 * q^71 - 3 * q^72 + 38 * q^73 - 4 * q^74 - 9 * q^75 - 51 * q^76 + 8 * q^77 + 22 * q^79 - 8 * q^80 + 9 * q^81 + 38 * q^82 - 11 * q^83 - 43 * q^84 - 18 * q^85 - 56 * q^86 + 9 * q^87 + 50 * q^88 - 2 * q^89 - 36 * q^92 + 17 * q^93 + 42 * q^94 + 10 * q^95 + 11 * q^96 + 23 * q^97 + 79 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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