LMFDB - Embedded newform 2535.2.a.bm.1.8

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			1.8
Root			$-1.47773$ 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)

$f(q)$	$=$	\(q+1.57796 q^{2} -1.00000 q^{3} +0.489955 q^{4} -1.00000 q^{5} -1.57796 q^{6} -4.24018 q^{7} -2.38279 q^{8} +1.00000 q^{9} -1.57796 q^{10} -0.930991 q^{11} -0.489955 q^{12} -6.69083 q^{14} +1.00000 q^{15} -4.73985 q^{16} +6.69540 q^{17} +1.57796 q^{18} -4.08272 q^{19} -0.489955 q^{20} +4.24018 q^{21} -1.46907 q^{22} +4.83891 q^{23} +2.38279 q^{24} +1.00000 q^{25} -1.00000 q^{27} -2.07750 q^{28} +5.09615 q^{29} +1.57796 q^{30} -10.0387 q^{31} -2.71372 q^{32} +0.930991 q^{33} +10.5651 q^{34} +4.24018 q^{35} +0.489955 q^{36} -6.44972 q^{37} -6.44237 q^{38} +2.38279 q^{40} +10.1522 q^{41} +6.69083 q^{42} +4.26956 q^{43} -0.456143 q^{44} -1.00000 q^{45} +7.63560 q^{46} +3.33450 q^{47} +4.73985 q^{48} +10.9791 q^{49} +1.57796 q^{50} -6.69540 q^{51} -6.11103 q^{53} -1.57796 q^{54} +0.930991 q^{55} +10.1035 q^{56} +4.08272 q^{57} +8.04152 q^{58} +1.90578 q^{59} +0.489955 q^{60} +4.34579 q^{61} -15.8406 q^{62} -4.24018 q^{63} +5.19757 q^{64} +1.46907 q^{66} +10.0323 q^{67} +3.28045 q^{68} -4.83891 q^{69} +6.69083 q^{70} +9.28521 q^{71} -2.38279 q^{72} +15.2909 q^{73} -10.1774 q^{74} -1.00000 q^{75} -2.00035 q^{76} +3.94757 q^{77} +2.83883 q^{79} +4.73985 q^{80} +1.00000 q^{81} +16.0197 q^{82} -0.543160 q^{83} +2.07750 q^{84} -6.69540 q^{85} +6.73719 q^{86} -5.09615 q^{87} +2.21835 q^{88} +12.4023 q^{89} -1.57796 q^{90} +2.37085 q^{92} +10.0387 q^{93} +5.26171 q^{94} +4.08272 q^{95} +2.71372 q^{96} -1.73935 q^{97} +17.3246 q^{98} -0.930991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.57796	1.11579	0.557893	−	0.829913i	$-0.311610\pi$
$2$	1.57796	1.11579	0.557893	+	0.829913i	$0.311610\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.489955	0.244977
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.57796	−0.644199
$7$	−4.24018	−1.60264	−0.801319	−	0.598237i	$-0.795868\pi$
$7$	−4.24018	−1.60264	−0.801319	+	0.598237i	$0.795868\pi$
$8$	−2.38279	−0.842443
$9$	1.00000	0.333333
$10$	−1.57796	−0.498994
$11$	−0.930991	−0.280704	−0.140352	−	0.990102i	$-0.544823\pi$
$11$	−0.930991	−0.280704	−0.140352	+	0.990102i	$0.544823\pi$
$12$	−0.489955	−0.141438
$13$	0	0
$13$	0	0
$14$	−6.69083	−1.78820
$15$	1.00000	0.258199
$16$	−4.73985	−1.18496
$17$	6.69540	1.62387	0.811937	−	0.583745i	$-0.198413\pi$
$17$	6.69540	1.62387	0.811937	+	0.583745i	$0.198413\pi$
$18$	1.57796	0.371929
$19$	−4.08272	−0.936641	−0.468320	−	0.883559i	$-0.655141\pi$
$19$	−4.08272	−0.936641	−0.468320	+	0.883559i	$0.655141\pi$
$20$	−0.489955	−0.109557
$21$	4.24018	0.925283
$22$	−1.46907	−0.313206
$23$	4.83891	1.00898	0.504491	−	0.863417i	$-0.331680\pi$
$23$	4.83891	1.00898	0.504491	+	0.863417i	$0.331680\pi$
$24$	2.38279	0.486385
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−2.07750	−0.392610
$29$	5.09615	0.946332	0.473166	−	0.880973i	$-0.343111\pi$
$29$	5.09615	0.946332	0.473166	+	0.880973i	$0.343111\pi$
$30$	1.57796	0.288095
$31$	−10.0387	−1.80300	−0.901498	−	0.432784i	$-0.857531\pi$
$31$	−10.0387	−1.80300	−0.901498	+	0.432784i	$0.857531\pi$
$32$	−2.71372	−0.479722
$33$	0.930991	0.162065
$34$	10.5651	1.81189
$35$	4.24018	0.716721
$36$	0.489955	0.0816592
$37$	−6.44972	−1.06033	−0.530164	−	0.847895i	$-0.677870\pi$
$37$	−6.44972	−1.06033	−0.530164	+	0.847895i	$0.677870\pi$
$38$	−6.44237	−1.04509
$39$	0	0
$40$	2.38279	0.376752
$41$	10.1522	1.58551	0.792753	−	0.609543i	$-0.208647\pi$
$41$	10.1522	1.58551	0.792753	+	0.609543i	$0.208647\pi$
$42$	6.69083	1.03242
$43$	4.26956	0.651102	0.325551	−	0.945525i	$-0.394450\pi$
$43$	4.26956	0.651102	0.325551	+	0.945525i	$0.394450\pi$
$44$	−0.456143	−0.0687662
$45$	−1.00000	−0.149071
$46$	7.63560	1.12581
$47$	3.33450	0.486387	0.243193	−	0.969978i	$-0.421805\pi$
$47$	3.33450	0.486387	0.243193	+	0.969978i	$0.421805\pi$
$48$	4.73985	0.684139
$49$	10.9791	1.56845
$50$	1.57796	0.223157
$51$	−6.69540	−0.937544
$52$	0	0
$53$	−6.11103	−0.839415	−0.419707	−	0.907660i	$-0.637867\pi$
$53$	−6.11103	−0.839415	−0.419707	+	0.907660i	$0.637867\pi$
$54$	−1.57796	−0.214733
$55$	0.930991	0.125535
$56$	10.1035	1.35013
$57$	4.08272	0.540770
$58$	8.04152	1.05590
$59$	1.90578	0.248111	0.124056	−	0.992275i	$-0.460410\pi$
$59$	1.90578	0.248111	0.124056	+	0.992275i	$0.460410\pi$
$60$	0.489955	0.0632529
$61$	4.34579	0.556422	0.278211	−	0.960520i	$-0.410259\pi$
$61$	4.34579	0.556422	0.278211	+	0.960520i	$0.410259\pi$
$62$	−15.8406	−2.01176
$63$	−4.24018	−0.534213
$64$	5.19757	0.649697
$65$	0	0
$66$	1.46907	0.180829
$67$	10.0323	1.22564	0.612819	−	0.790224i	$-0.290036\pi$
$67$	10.0323	1.22564	0.612819	+	0.790224i	$0.290036\pi$
$68$	3.28045	0.397812
$69$	−4.83891	−0.582536
$70$	6.69083	0.799707
$71$	9.28521	1.10195	0.550976	−	0.834521i	$-0.314256\pi$
$71$	9.28521	1.10195	0.550976	+	0.834521i	$0.314256\pi$
$72$	−2.38279	−0.280814
$73$	15.2909	1.78966	0.894830	−	0.446407i	$-0.147297\pi$
$73$	15.2909	1.78966	0.894830	+	0.446407i	$0.147297\pi$
$74$	−10.1774	−1.18310
$75$	−1.00000	−0.115470
$76$	−2.00035	−0.229456
$77$	3.94757	0.449867
$78$	0	0
$79$	2.83883	0.319393	0.159697	−	0.987166i	$-0.448948\pi$
$79$	2.83883	0.319393	0.159697	+	0.987166i	$0.448948\pi$
$80$	4.73985	0.529932
$81$	1.00000	0.111111
$82$	16.0197	1.76909
$83$	−0.543160	−0.0596196	−0.0298098	−	0.999556i	$-0.509490\pi$
$83$	−0.543160	−0.0596196	−0.0298098	+	0.999556i	$0.509490\pi$
$84$	2.07750	0.226674
$85$	−6.69540	−0.726218
$86$	6.73719	0.726490
$87$	−5.09615	−0.546365
$88$	2.21835	0.236477
$89$	12.4023	1.31464	0.657318	−	0.753613i	$-0.271691\pi$
$89$	12.4023	1.31464	0.657318	+	0.753613i	$0.271691\pi$
$90$	−1.57796	−0.166331
$91$	0	0
$92$	2.37085	0.247178
$93$	10.0387	1.04096
$94$	5.26171	0.542703
$95$	4.08272	0.418878
$96$	2.71372	0.276968
$97$	−1.73935	−0.176604	−0.0883020	−	0.996094i	$-0.528144\pi$
$97$	−1.73935	−0.176604	−0.0883020	+	0.996094i	$0.528144\pi$
$98$	17.3246	1.75005
$99$	−0.930991	−0.0935681
$100$	0.489955	0.0489955
$101$	0.0423894	0.00421791	0.00210895	−	0.999998i	$-0.499329\pi$
$101$	0.0423894	0.00421791	0.00210895	+	0.999998i	$0.499329\pi$
$102$	−10.5651	−1.04610
$103$	−8.92296	−0.879205	−0.439603	−	0.898192i	$-0.644881\pi$
$103$	−8.92296	−0.879205	−0.439603	+	0.898192i	$0.644881\pi$
$104$	0	0
$105$	−4.24018	−0.413799
$106$	−9.64296	−0.936607
$107$	−20.2229	−1.95502	−0.977509	−	0.210894i	$-0.932363\pi$
$107$	−20.2229	−1.95502	−0.977509	+	0.210894i	$0.932363\pi$
$108$	−0.489955	−0.0471459
$109$	−12.8717	−1.23288	−0.616442	−	0.787400i	$-0.711427\pi$
$109$	−12.8717	−1.23288	−0.616442	+	0.787400i	$0.711427\pi$
$110$	1.46907	0.140070
$111$	6.44972	0.612180
$112$	20.0978	1.89907
$113$	5.19844	0.489028	0.244514	−	0.969646i	$-0.421372\pi$
$113$	5.19844	0.489028	0.244514	+	0.969646i	$0.421372\pi$
$114$	6.44237	0.603383
$115$	−4.83891	−0.451231
$116$	2.49689	0.231830
$117$	0	0
$118$	3.00724	0.276839
$119$	−28.3897	−2.60248
$120$	−2.38279	−0.217518
$121$	−10.1333	−0.921205
$122$	6.85748	0.620847
$123$	−10.1522	−0.915393
$124$	−4.91849	−0.441693
$125$	−1.00000	−0.0894427
$126$	−6.69083	−0.596067
$127$	6.52609	0.579097	0.289548	−	0.957163i	$-0.406495\pi$
$127$	6.52609	0.579097	0.289548	+	0.957163i	$0.406495\pi$
$128$	13.6290	1.20464
$129$	−4.26956	−0.375914
$130$	0	0
$131$	−6.92440	−0.604988	−0.302494	−	0.953151i	$-0.597819\pi$
$131$	−6.92440	−0.604988	−0.302494	+	0.953151i	$0.597819\pi$
$132$	0.456143	0.0397022
$133$	17.3115	1.50110
$134$	15.8305	1.36755
$135$	1.00000	0.0860663
$136$	−15.9537	−1.36802
$137$	13.0533	1.11522	0.557611	−	0.830102i	$-0.311718\pi$
$137$	13.0533	1.11522	0.557611	+	0.830102i	$0.311718\pi$
$138$	−7.63560	−0.649986
$139$	8.85123	0.750751	0.375376	−	0.926873i	$-0.377514\pi$
$139$	8.85123	0.750751	0.375376	+	0.926873i	$0.377514\pi$
$140$	2.07750	0.175581
$141$	−3.33450	−0.280816
$142$	14.6517	1.22954
$143$	0	0
$144$	−4.73985	−0.394988
$145$	−5.09615	−0.423213
$146$	24.1284	1.99688
$147$	−10.9791	−0.905544
$148$	−3.16007	−0.259756
$149$	0.285807	0.0234142	0.0117071	−	0.999931i	$-0.496273\pi$
$149$	0.285807	0.0234142	0.0117071	+	0.999931i	$0.496273\pi$
$150$	−1.57796	−0.128840
$151$	−17.3570	−1.41250	−0.706248	−	0.707964i	$-0.749614\pi$
$151$	−17.3570	−1.41250	−0.706248	+	0.707964i	$0.749614\pi$
$152$	9.72827	0.789067
$153$	6.69540	0.541291
$154$	6.22910	0.501955
$155$	10.0387	0.806324
$156$	0	0
$157$	−9.45243	−0.754386	−0.377193	−	0.926135i	$-0.623111\pi$
$157$	−9.45243	−0.754386	−0.377193	+	0.926135i	$0.623111\pi$
$158$	4.47956	0.356375
$159$	6.11103	0.484636
$160$	2.71372	0.214538
$161$	−20.5179	−1.61703
$162$	1.57796	0.123976
$163$	13.6851	1.07190	0.535950	−	0.844250i	$-0.319954\pi$
$163$	13.6851	1.07190	0.535950	+	0.844250i	$0.319954\pi$
$164$	4.97412	0.388413
$165$	−0.930991	−0.0724775
$166$	−0.857085	−0.0665227
$167$	−15.7127	−1.21589	−0.607943	−	0.793981i	$-0.708005\pi$
$167$	−15.7127	−1.21589	−0.607943	+	0.793981i	$0.708005\pi$
$168$	−10.1035	−0.779499
$169$	0	0
$170$	−10.5651	−0.810304
$171$	−4.08272	−0.312214
$172$	2.09189	0.159505
$173$	13.3150	1.01232	0.506161	−	0.862439i	$-0.331064\pi$
$173$	13.3150	1.01232	0.506161	+	0.862439i	$0.331064\pi$
$174$	−8.04152	−0.609626
$175$	−4.24018	−0.320528
$176$	4.41276	0.332624
$177$	−1.90578	−0.143247
$178$	19.5703	1.46685
$179$	8.88543	0.664128	0.332064	−	0.943257i	$-0.392255\pi$
$179$	8.88543	0.664128	0.332064	+	0.943257i	$0.392255\pi$
$180$	−0.489955	−0.0365191
$181$	4.30351	0.319878	0.159939	−	0.987127i	$-0.448870\pi$
$181$	4.30351	0.319878	0.159939	+	0.987127i	$0.448870\pi$
$182$	0	0
$183$	−4.34579	−0.321250
$184$	−11.5301	−0.850011
$185$	6.44972	0.474193
$186$	15.8406	1.16149
$187$	−6.23336	−0.455828
$188$	1.63375	0.119154
$189$	4.24018	0.308428
$190$	6.44237	0.467379
$191$	−16.9244	−1.22460	−0.612302	−	0.790624i	$-0.709756\pi$
$191$	−16.9244	−1.22460	−0.612302	+	0.790624i	$0.709756\pi$
$192$	−5.19757	−0.375103
$193$	21.6528	1.55860	0.779301	−	0.626650i	$-0.215575\pi$
$193$	21.6528	1.55860	0.779301	+	0.626650i	$0.215575\pi$
$194$	−2.74462	−0.197052
$195$	0	0
$196$	5.37928	0.384234
$197$	9.14280	0.651398	0.325699	−	0.945474i	$-0.394400\pi$
$197$	9.14280	0.651398	0.325699	+	0.945474i	$0.394400\pi$
$198$	−1.46907	−0.104402
$199$	14.6362	1.03754	0.518768	−	0.854915i	$-0.326391\pi$
$199$	14.6362	1.03754	0.518768	+	0.854915i	$0.326391\pi$
$200$	−2.38279	−0.168489
$201$	−10.0323	−0.707622
$202$	0.0668888	0.00470628
$203$	−21.6086	−1.51663
$204$	−3.28045	−0.229677
$205$	−10.1522	−0.709060
$206$	−14.0801	−0.981005
$207$	4.83891	0.336328
$208$	0	0
$209$	3.80098	0.262919
$210$	−6.69083	−0.461711
$211$	−19.5073	−1.34294	−0.671468	−	0.741034i	$-0.734336\pi$
$211$	−19.5073	−1.34294	−0.671468	+	0.741034i	$0.734336\pi$
$212$	−2.99413	−0.205638
$213$	−9.28521	−0.636212
$214$	−31.9109	−2.18138
$215$	−4.26956	−0.291181
$216$	2.38279	0.162128
$217$	42.5657	2.88955
$218$	−20.3110	−1.37563
$219$	−15.2909	−1.03326
$220$	0.456143	0.0307532
$221$	0	0
$222$	10.1774	0.683062
$223$	7.82273	0.523849	0.261924	−	0.965088i	$-0.415643\pi$
$223$	7.82273	0.523849	0.261924	+	0.965088i	$0.415643\pi$
$224$	11.5067	0.768821
$225$	1.00000	0.0666667
$226$	8.20293	0.545651
$227$	19.3814	1.28639	0.643194	−	0.765703i	$-0.277609\pi$
$227$	19.3814	1.28639	0.643194	+	0.765703i	$0.277609\pi$
$228$	2.00035	0.132476
$229$	−24.0463	−1.58903	−0.794513	−	0.607247i	$-0.792274\pi$
$229$	−24.0463	−1.58903	−0.794513	+	0.607247i	$0.792274\pi$
$230$	−7.63560	−0.503477
$231$	−3.94757	−0.259731
$232$	−12.1431	−0.797231
$233$	13.6914	0.896955	0.448477	−	0.893794i	$-0.351966\pi$
$233$	13.6914	0.896955	0.448477	+	0.893794i	$0.351966\pi$
$234$	0	0
$235$	−3.33450	−0.217519
$236$	0.933745	0.0607816
$237$	−2.83883	−0.184402
$238$	−44.7978	−2.90381
$239$	5.92813	0.383459	0.191729	−	0.981448i	$-0.438590\pi$
$239$	5.92813	0.383459	0.191729	+	0.981448i	$0.438590\pi$
$240$	−4.73985	−0.305956
$241$	−23.1085	−1.48855	−0.744275	−	0.667873i	$-0.767205\pi$
$241$	−23.1085	−1.48855	−0.744275	+	0.667873i	$0.767205\pi$
$242$	−15.9899	−1.02787
$243$	−1.00000	−0.0641500
$244$	2.12924	0.136311
$245$	−10.9791	−0.701431
$246$	−16.0197	−1.02138
$247$	0	0
$248$	23.9200	1.51892
$249$	0.543160	0.0344214
$250$	−1.57796	−0.0997989
$251$	−3.50105	−0.220984	−0.110492	−	0.993877i	$-0.535243\pi$
$251$	−3.50105	−0.220984	−0.110492	+	0.993877i	$0.535243\pi$
$252$	−2.07750	−0.130870
$253$	−4.50498	−0.283226
$254$	10.2979	0.646148
$255$	6.69540	0.419282
$256$	11.1108	0.694428
$257$	−9.31537	−0.581077	−0.290538	−	0.956863i	$-0.593834\pi$
$257$	−9.31537	−0.581077	−0.290538	+	0.956863i	$0.593834\pi$
$258$	−6.73719	−0.419439
$259$	27.3480	1.69932
$260$	0	0
$261$	5.09615	0.315444
$262$	−10.9264	−0.675037
$263$	13.5759	0.837123	0.418562	−	0.908188i	$-0.362534\pi$
$263$	13.5759	0.837123	0.418562	+	0.908188i	$0.362534\pi$
$264$	−2.21835	−0.136530
$265$	6.11103	0.375398
$266$	27.3168	1.67490
$267$	−12.4023	−0.759006
$268$	4.91536	0.300253
$269$	−25.6988	−1.56688	−0.783442	−	0.621465i	$-0.786538\pi$
$269$	−25.6988	−1.56688	−0.783442	+	0.621465i	$0.786538\pi$
$270$	1.57796	0.0960315
$271$	19.4492	1.18145	0.590727	−	0.806871i	$-0.298841\pi$
$271$	19.4492	1.18145	0.590727	+	0.806871i	$0.298841\pi$
$272$	−31.7352	−1.92423
$273$	0	0
$274$	20.5976	1.24435
$275$	−0.930991	−0.0561408
$276$	−2.37085	−0.142708
$277$	−19.0529	−1.14478	−0.572388	−	0.819983i	$-0.693983\pi$
$277$	−19.0529	−1.14478	−0.572388	+	0.819983i	$0.693983\pi$
$278$	13.9669	0.837677
$279$	−10.0387	−0.600998
$280$	−10.1035	−0.603797
$281$	−5.09810	−0.304127	−0.152064	−	0.988371i	$-0.548592\pi$
$281$	−5.09810	−0.304127	−0.152064	+	0.988371i	$0.548592\pi$
$282$	−5.26171	−0.313330
$283$	2.64104	0.156993	0.0784966	−	0.996914i	$-0.474988\pi$
$283$	2.64104	0.156993	0.0784966	+	0.996914i	$0.474988\pi$
$284$	4.54934	0.269953
$285$	−4.08272	−0.241840
$286$	0	0
$287$	−43.0472	−2.54099
$288$	−2.71372	−0.159907
$289$	27.8284	1.63697
$290$	−8.04152	−0.472214
$291$	1.73935	0.101962
$292$	7.49183	0.438426
$293$	22.5407	1.31684	0.658419	−	0.752651i	$-0.271225\pi$
$293$	22.5407	1.31684	0.658419	+	0.752651i	$0.271225\pi$
$294$	−17.3246	−1.01039
$295$	−1.90578	−0.110959
$296$	15.3683	0.893266
$297$	0.930991	0.0540216
$298$	0.450992	0.0261253
$299$	0	0
$300$	−0.489955	−0.0282876
$301$	−18.1037	−1.04348
$302$	−27.3887	−1.57604
$303$	−0.0423894	−0.00243521
$304$	19.3515	1.10988
$305$	−4.34579	−0.248839
$306$	10.5651	0.603965
$307$	26.6912	1.52335	0.761674	−	0.647960i	$-0.224378\pi$
$307$	26.6912	1.52335	0.761674	+	0.647960i	$0.224378\pi$
$308$	1.93413	0.110207
$309$	8.92296	0.507609
$310$	15.8406	0.899685
$311$	17.1305	0.971384	0.485692	−	0.874130i	$-0.338568\pi$
$311$	17.1305	0.971384	0.485692	+	0.874130i	$0.338568\pi$
$312$	0	0
$313$	25.1929	1.42399	0.711994	−	0.702186i	$-0.247792\pi$
$313$	25.1929	1.42399	0.711994	+	0.702186i	$0.247792\pi$
$314$	−14.9156	−0.841733
$315$	4.24018	0.238907
$316$	1.39090	0.0782442
$317$	−0.244299	−0.0137212	−0.00686060	−	0.999976i	$-0.502184\pi$
$317$	−0.244299	−0.0137212	−0.00686060	+	0.999976i	$0.502184\pi$
$318$	9.64296	0.540750
$319$	−4.74447	−0.265639
$320$	−5.19757	−0.290553
$321$	20.2229	1.12873
$322$	−32.3763	−1.80426
$323$	−27.3355	−1.52099
$324$	0.489955	0.0272197
$325$	0	0
$326$	21.5945	1.19601
$327$	12.8717	0.711806
$328$	−24.1905	−1.33570
$329$	−14.1389	−0.779502
$330$	−1.46907	−0.0808694
$331$	18.8657	1.03695	0.518475	−	0.855093i	$-0.326500\pi$
$331$	18.8657	1.03695	0.518475	+	0.855093i	$0.326500\pi$
$332$	−0.266124	−0.0146055
$333$	−6.44972	−0.353443
$334$	−24.7940	−1.35667
$335$	−10.0323	−0.548122
$336$	−20.0978	−1.09643
$337$	−1.35150	−0.0736209	−0.0368104	−	0.999322i	$-0.511720\pi$
$337$	−1.35150	−0.0736209	−0.0368104	+	0.999322i	$0.511720\pi$
$338$	0	0
$339$	−5.19844	−0.282341
$340$	−3.28045	−0.177907
$341$	9.34589	0.506108
$342$	−6.44237	−0.348363
$343$	−16.8723	−0.911017
$344$	−10.1735	−0.548516
$345$	4.83891	0.260518
$346$	21.0106	1.12953
$347$	−25.3185	−1.35917	−0.679583	−	0.733599i	$-0.737839\pi$
$347$	−25.3185	−1.35917	−0.679583	+	0.733599i	$0.737839\pi$
$348$	−2.49689	−0.133847
$349$	8.63448	0.462193	0.231097	−	0.972931i	$-0.425769\pi$
$349$	8.63448	0.462193	0.231097	+	0.972931i	$0.425769\pi$
$350$	−6.69083	−0.357640
$351$	0	0
$352$	2.52644	0.134660
$353$	15.7788	0.839821	0.419910	−	0.907566i	$-0.362062\pi$
$353$	15.7788	0.839821	0.419910	+	0.907566i	$0.362062\pi$
$354$	−3.00724	−0.159833
$355$	−9.28521	−0.492808
$356$	6.07655	0.322056
$357$	28.3897	1.50254
$358$	14.0208	0.741024
$359$	−13.3184	−0.702917	−0.351458	−	0.936203i	$-0.614314\pi$
$359$	−13.3184	−0.702917	−0.351458	+	0.936203i	$0.614314\pi$
$360$	2.38279	0.125584
$361$	−2.33138	−0.122704
$362$	6.79077	0.356915
$363$	10.1333	0.531858
$364$	0	0
$365$	−15.2909	−0.800360
$366$	−6.85748	−0.358446
$367$	16.9622	0.885420	0.442710	−	0.896665i	$-0.354017\pi$
$367$	16.9622	0.885420	0.442710	+	0.896665i	$0.354017\pi$
$368$	−22.9357	−1.19561
$369$	10.1522	0.528502
$370$	10.1774	0.529098
$371$	25.9119	1.34528
$372$	4.91849	0.255012
$373$	28.0710	1.45346	0.726730	−	0.686923i	$-0.241039\pi$
$373$	28.0710	1.45346	0.726730	+	0.686923i	$0.241039\pi$
$374$	−9.83598	−0.508607
$375$	1.00000	0.0516398
$376$	−7.94541	−0.409753
$377$	0	0
$378$	6.69083	0.344139
$379$	2.65873	0.136570	0.0682850	−	0.997666i	$-0.478247\pi$
$379$	2.65873	0.136570	0.0682850	+	0.997666i	$0.478247\pi$
$380$	2.00035	0.102616
$381$	−6.52609	−0.334342
$382$	−26.7059	−1.36639
$383$	9.06323	0.463110	0.231555	−	0.972822i	$-0.425619\pi$
$383$	9.06323	0.463110	0.231555	+	0.972822i	$0.425619\pi$
$384$	−13.6290	−0.695502
$385$	−3.94757	−0.201187
$386$	34.1672	1.73906
$387$	4.26956	0.217034
$388$	−0.852202	−0.0432640
$389$	11.4337	0.579710	0.289855	−	0.957071i	$-0.406393\pi$
$389$	11.4337	0.579710	0.289855	+	0.957071i	$0.406393\pi$
$390$	0	0
$391$	32.3985	1.63846
$392$	−26.1610	−1.32133
$393$	6.92440	0.349290
$394$	14.4270	0.726820
$395$	−2.83883	−0.142837
$396$	−0.456143	−0.0229221
$397$	−26.0927	−1.30956	−0.654778	−	0.755821i	$-0.727238\pi$
$397$	−26.0927	−1.30956	−0.654778	+	0.755821i	$0.727238\pi$
$398$	23.0954	1.15767
$399$	−17.3115	−0.866658
$400$	−4.73985	−0.236993
$401$	−4.05294	−0.202394	−0.101197	−	0.994866i	$-0.532267\pi$
$401$	−4.05294	−0.202394	−0.101197	+	0.994866i	$0.532267\pi$
$402$	−15.8305	−0.789554
$403$	0	0
$404$	0.0207689	0.00103329
$405$	−1.00000	−0.0496904
$406$	−34.0975	−1.69223
$407$	6.00463	0.297638
$408$	15.9537	0.789828
$409$	−15.0236	−0.742867	−0.371434	−	0.928459i	$-0.621134\pi$
$409$	−15.0236	−0.742867	−0.371434	+	0.928459i	$0.621134\pi$
$410$	−16.0197	−0.791159
$411$	−13.0533	−0.643874
$412$	−4.37185	−0.215385
$413$	−8.08084	−0.397632
$414$	7.63560	0.375269
$415$	0.543160	0.0266627
$416$	0	0
$417$	−8.85123	−0.433446
$418$	5.99778	0.293361
$419$	3.41250	0.166711	0.0833557	−	0.996520i	$-0.473436\pi$
$419$	3.41250	0.166711	0.0833557	+	0.996520i	$0.473436\pi$
$420$	−2.07750	−0.101372
$421$	13.0288	0.634984	0.317492	−	0.948261i	$-0.397159\pi$
$421$	13.0288	0.634984	0.317492	+	0.948261i	$0.397159\pi$
$422$	−30.7817	−1.49843
$423$	3.33450	0.162129
$424$	14.5613	0.707159
$425$	6.69540	0.324775
$426$	−14.6517	−0.709876
$427$	−18.4270	−0.891743
$428$	−9.90829	−0.478935
$429$	0	0
$430$	−6.73719	−0.324896
$431$	13.5106	0.650782	0.325391	−	0.945580i	$-0.394504\pi$
$431$	13.5106	0.650782	0.325391	+	0.945580i	$0.394504\pi$
$432$	4.73985	0.228046
$433$	39.3271	1.88994	0.944970	−	0.327158i	$-0.106091\pi$
$433$	39.3271	1.88994	0.944970	+	0.327158i	$0.106091\pi$
$434$	67.1669	3.22412
$435$	5.09615	0.244342
$436$	−6.30655	−0.302029
$437$	−19.7559	−0.945054
$438$	−24.1284	−1.15290
$439$	9.61407	0.458855	0.229427	−	0.973326i	$-0.426315\pi$
$439$	9.61407	0.458855	0.229427	+	0.973326i	$0.426315\pi$
$440$	−2.21835	−0.105756
$441$	10.9791	0.522816
$442$	0	0
$443$	23.6194	1.12219	0.561095	−	0.827751i	$-0.310380\pi$
$443$	23.6194	1.12219	0.561095	+	0.827751i	$0.310380\pi$
$444$	3.16007	0.149970
$445$	−12.4023	−0.587923
$446$	12.3439	0.584503
$447$	−0.285807	−0.0135182
$448$	−22.0387	−1.04123
$449$	−35.6727	−1.68350	−0.841750	−	0.539867i	$-0.818475\pi$
$449$	−35.6727	−1.68350	−0.841750	+	0.539867i	$0.818475\pi$
$450$	1.57796	0.0743857
$451$	−9.45160	−0.445058
$452$	2.54700	0.119801
$453$	17.3570	0.815505
$454$	30.5831	1.43533
$455$	0	0
$456$	−9.72827	−0.455568
$457$	−32.5254	−1.52147	−0.760737	−	0.649060i	$-0.775162\pi$
$457$	−32.5254	−1.52147	−0.760737	+	0.649060i	$0.775162\pi$
$458$	−37.9441	−1.77301
$459$	−6.69540	−0.312515
$460$	−2.37085	−0.110541
$461$	7.12442	0.331817	0.165909	−	0.986141i	$-0.446944\pi$
$461$	7.12442	0.331817	0.165909	+	0.986141i	$0.446944\pi$
$462$	−6.22910	−0.289804
$463$	−14.6017	−0.678599	−0.339300	−	0.940678i	$-0.610190\pi$
$463$	−14.6017	−0.678599	−0.339300	+	0.940678i	$0.610190\pi$
$464$	−24.1550	−1.12137
$465$	−10.0387	−0.465531
$466$	21.6045	1.00081
$467$	10.0300	0.464134	0.232067	−	0.972700i	$-0.425451\pi$
$467$	10.0300	0.464134	0.232067	+	0.972700i	$0.425451\pi$
$468$	0	0
$469$	−42.5387	−1.96425
$470$	−5.26171	−0.242704
$471$	9.45243	0.435545
$472$	−4.54107	−0.209020
$473$	−3.97492	−0.182767
$474$	−4.47956	−0.205753
$475$	−4.08272	−0.187328
$476$	−13.9097	−0.637549
$477$	−6.11103	−0.279805
$478$	9.35435	0.427858
$479$	1.68123	0.0768174	0.0384087	−	0.999262i	$-0.487771\pi$
$479$	1.68123	0.0768174	0.0384087	+	0.999262i	$0.487771\pi$
$480$	−2.71372	−0.123864
$481$	0	0
$482$	−36.4643	−1.66090
$483$	20.5179	0.933595
$484$	−4.96484	−0.225674
$485$	1.73935	0.0789797
$486$	−1.57796	−0.0715777
$487$	38.5971	1.74900	0.874500	−	0.485025i	$-0.161190\pi$
$487$	38.5971	1.74900	0.874500	+	0.485025i	$0.161190\pi$
$488$	−10.3551	−0.468754
$489$	−13.6851	−0.618861
$490$	−17.3246	−0.782647
$491$	15.2496	0.688203	0.344102	−	0.938932i	$-0.388184\pi$
$491$	15.2496	0.688203	0.344102	+	0.938932i	$0.388184\pi$
$492$	−4.97412	−0.224251
$493$	34.1208	1.53672
$494$	0	0
$495$	0.930991	0.0418449
$496$	47.5817	2.13648
$497$	−39.3710	−1.76603
$498$	0.857085	0.0384069
$499$	17.6082	0.788250	0.394125	−	0.919057i	$-0.371048\pi$
$499$	17.6082	0.788250	0.394125	+	0.919057i	$0.371048\pi$
$500$	−0.489955	−0.0219114
$501$	15.7127	0.701992
$502$	−5.52451	−0.246571
$503$	−4.28127	−0.190892	−0.0954461	−	0.995435i	$-0.530428\pi$
$503$	−4.28127	−0.190892	−0.0954461	+	0.995435i	$0.530428\pi$
$504$	10.1035	0.450044
$505$	−0.0423894	−0.00188631
$506$	−7.10868	−0.316019
$507$	0	0
$508$	3.19749	0.141866
$509$	21.4062	0.948812	0.474406	−	0.880306i	$-0.342663\pi$
$509$	21.4062	0.948812	0.474406	+	0.880306i	$0.342663\pi$
$510$	10.5651	0.467829
$511$	−64.8360	−2.86818
$512$	−9.72553	−0.429812
$513$	4.08272	0.180257
$514$	−14.6993	−0.648357
$515$	8.92296	0.393193
$516$	−2.09189	−0.0920904
$517$	−3.10439	−0.136531
$518$	43.1540	1.89608
$519$	−13.3150	−0.584465
$520$	0	0
$521$	−4.41184	−0.193286	−0.0966431	−	0.995319i	$-0.530811\pi$
$521$	−4.41184	−0.193286	−0.0966431	+	0.995319i	$0.530811\pi$
$522$	8.04152	0.351968
$523$	−33.6618	−1.47193	−0.735964	−	0.677020i	$-0.763271\pi$
$523$	−33.6618	−1.47193	−0.735964	+	0.677020i	$0.763271\pi$
$524$	−3.39264	−0.148208
$525$	4.24018	0.185057
$526$	21.4221	0.934050
$527$	−67.2128	−2.92784
$528$	−4.41276	−0.192041
$529$	0.415061	0.0180462
$530$	9.64296	0.418863
$531$	1.90578	0.0827037
$532$	8.48185	0.367735
$533$	0	0
$534$	−19.5703	−0.846888
$535$	20.2229	0.874311
$536$	−23.9048	−1.03253
$537$	−8.88543	−0.383434
$538$	−40.5517	−1.74831
$539$	−10.2215	−0.440270
$540$	0.489955	0.0210843
$541$	1.52048	0.0653706	0.0326853	−	0.999466i	$-0.489594\pi$
$541$	1.52048	0.0653706	0.0326853	+	0.999466i	$0.489594\pi$
$542$	30.6900	1.31825
$543$	−4.30351	−0.184681
$544$	−18.1694	−0.779008
$545$	12.8717	0.551363
$546$	0	0
$547$	−7.63513	−0.326454	−0.163227	−	0.986589i	$-0.552190\pi$
$547$	−7.63513	−0.326454	−0.163227	+	0.986589i	$0.552190\pi$
$548$	6.39555	0.273204
$549$	4.34579	0.185474
$550$	−1.46907	−0.0626411
$551$	−20.8062	−0.886373
$552$	11.5301	0.490754
$553$	−12.0372	−0.511872
$554$	−30.0647	−1.27732
$555$	−6.44972	−0.273775
$556$	4.33670	0.183917
$557$	35.8920	1.52079	0.760396	−	0.649460i	$-0.225005\pi$
$557$	35.8920	1.52079	0.760396	+	0.649460i	$0.225005\pi$
$558$	−15.8406	−0.670585
$559$	0	0
$560$	−20.0978	−0.849289
$561$	6.23336	0.263173
$562$	−8.04460	−0.339341
$563$	−40.7167	−1.71601	−0.858003	−	0.513645i	$-0.828295\pi$
$563$	−40.7167	−1.71601	−0.858003	+	0.513645i	$0.828295\pi$
$564$	−1.63375	−0.0687935
$565$	−5.19844	−0.218700
$566$	4.16745	0.175171
$567$	−4.24018	−0.178071
$568$	−22.1247	−0.928332
$569$	23.7908	0.997364	0.498682	−	0.866785i	$-0.333818\pi$
$569$	23.7908	0.997364	0.498682	+	0.866785i	$0.333818\pi$
$570$	−6.44237	−0.269841
$571$	−20.2045	−0.845531	−0.422766	−	0.906239i	$-0.638941\pi$
$571$	−20.2045	−0.845531	−0.422766	+	0.906239i	$0.638941\pi$
$572$	0	0
$573$	16.9244	0.707025
$574$	−67.9266	−2.83520
$575$	4.83891	0.201797
$576$	5.19757	0.216566
$577$	18.1369	0.755048	0.377524	−	0.926000i	$-0.376776\pi$
$577$	18.1369	0.755048	0.377524	+	0.926000i	$0.376776\pi$
$578$	43.9121	1.82650
$579$	−21.6528	−0.899859
$580$	−2.49689	−0.103678
$581$	2.30310	0.0955486
$582$	2.74462	0.113768
$583$	5.68931	0.235627
$584$	−36.4349	−1.50769
$585$	0	0
$586$	35.5682	1.46931
$587$	40.4882	1.67113	0.835564	−	0.549394i	$-0.185141\pi$
$587$	40.4882	1.67113	0.835564	+	0.549394i	$0.185141\pi$
$588$	−5.37928	−0.221838
$589$	40.9850	1.68876
$590$	−3.00724	−0.123806
$591$	−9.14280	−0.376085
$592$	30.5707	1.25645
$593$	12.2048	0.501192	0.250596	−	0.968092i	$-0.419373\pi$
$593$	12.2048	0.501192	0.250596	+	0.968092i	$0.419373\pi$
$594$	1.46907	0.0602765
$595$	28.3897	1.16387
$596$	0.140033	0.00573596
$597$	−14.6362	−0.599021
$598$	0	0
$599$	39.0287	1.59467	0.797335	−	0.603536i	$-0.206242\pi$
$599$	39.0287	1.59467	0.797335	+	0.603536i	$0.206242\pi$
$600$	2.38279	0.0972770
$601$	−33.6723	−1.37352	−0.686761	−	0.726883i	$-0.740968\pi$
$601$	−33.6723	−1.37352	−0.686761	+	0.726883i	$0.740968\pi$
$602$	−28.5669	−1.16430
$603$	10.0323	0.408546
$604$	−8.50417	−0.346030
$605$	10.1333	0.411975
$606$	−0.0668888	−0.00271717
$607$	−1.08799	−0.0441603	−0.0220802	−	0.999756i	$-0.507029\pi$
$607$	−1.08799	−0.0441603	−0.0220802	+	0.999756i	$0.507029\pi$
$608$	11.0794	0.449327
$609$	21.6086	0.875625
$610$	−6.85748	−0.277651
$611$	0	0
$612$	3.28045	0.132604
$613$	18.8465	0.761202	0.380601	−	0.924739i	$-0.375717\pi$
$613$	18.8465	0.761202	0.380601	+	0.924739i	$0.375717\pi$
$614$	42.1177	1.69973
$615$	10.1522	0.409376
$616$	−9.40623	−0.378988
$617$	−33.2812	−1.33985	−0.669926	−	0.742428i	$-0.733674\pi$
$617$	−33.2812	−1.33985	−0.669926	+	0.742428i	$0.733674\pi$
$618$	14.0801	0.566383
$619$	−22.4565	−0.902601	−0.451301	−	0.892372i	$-0.649040\pi$
$619$	−22.4565	−0.902601	−0.451301	+	0.892372i	$0.649040\pi$
$620$	4.91849	0.197531
$621$	−4.83891	−0.194179
$622$	27.0313	1.08386
$623$	−52.5878	−2.10689
$624$	0	0
$625$	1.00000	0.0400000
$626$	39.7534	1.58887
$627$	−3.80098	−0.151796
$628$	−4.63127	−0.184808
$629$	−43.1835	−1.72184
$630$	6.69083	0.266569
$631$	−18.7673	−0.747115	−0.373558	−	0.927607i	$-0.621862\pi$
$631$	−18.7673	−0.747115	−0.373558	+	0.927607i	$0.621862\pi$
$632$	−6.76434	−0.269071
$633$	19.5073	0.775344
$634$	−0.385494	−0.0153099
$635$	−6.52609	−0.258980
$636$	2.99413	0.118725
$637$	0	0
$638$	−7.48658	−0.296397
$639$	9.28521	0.367317
$640$	−13.6290	−0.538733
$641$	−20.4213	−0.806594	−0.403297	−	0.915069i	$-0.632136\pi$
$641$	−20.4213	−0.806594	−0.403297	+	0.915069i	$0.632136\pi$
$642$	31.9109	1.25942
$643$	12.5023	0.493043	0.246521	−	0.969137i	$-0.420712\pi$
$643$	12.5023	0.493043	0.246521	+	0.969137i	$0.420712\pi$
$644$	−10.0528	−0.396137
$645$	4.26956	0.168114
$646$	−43.1343	−1.69709
$647$	42.4256	1.66792	0.833961	−	0.551824i	$-0.186068\pi$
$647$	42.4256	1.66792	0.833961	+	0.551824i	$0.186068\pi$
$648$	−2.38279	−0.0936048
$649$	−1.77426	−0.0696458
$650$	0	0
$651$	−42.5657	−1.66828
$652$	6.70508	0.262591
$653$	4.93671	0.193188	0.0965942	−	0.995324i	$-0.469205\pi$
$653$	4.93671	0.193188	0.0965942	+	0.995324i	$0.469205\pi$
$654$	20.3110	0.794223
$655$	6.92440	0.270559
$656$	−48.1199	−1.87877
$657$	15.2909	0.596553
$658$	−22.3106	−0.869757
$659$	−41.2628	−1.60737	−0.803686	−	0.595053i	$-0.797131\pi$
$659$	−41.2628	−1.60737	−0.803686	+	0.595053i	$0.797131\pi$
$660$	−0.456143	−0.0177554
$661$	23.6968	0.921699	0.460850	−	0.887478i	$-0.347545\pi$
$661$	23.6968	0.921699	0.460850	+	0.887478i	$0.347545\pi$
$662$	29.7693	1.15701
$663$	0	0
$664$	1.29424	0.0502261
$665$	−17.3115	−0.671310
$666$	−10.1774	−0.394366
$667$	24.6598	0.954833
$668$	−7.69851	−0.297864
$669$	−7.82273	−0.302444
$670$	−15.8305	−0.611586
$671$	−4.04589	−0.156190
$672$	−11.5067	−0.443879
$673$	5.88324	0.226782	0.113391	−	0.993550i	$-0.463829\pi$
$673$	5.88324	0.226782	0.113391	+	0.993550i	$0.463829\pi$
$674$	−2.13261	−0.0821451
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	33.2940	1.27959	0.639796	−	0.768545i	$-0.279019\pi$
$677$	33.2940	1.27959	0.639796	+	0.768545i	$0.279019\pi$
$678$	−8.20293	−0.315032
$679$	7.37515	0.283032
$680$	15.9537	0.611798
$681$	−19.3814	−0.742697
$682$	14.7474	0.564708
$683$	13.3530	0.510940	0.255470	−	0.966817i	$-0.417770\pi$
$683$	13.3530	0.510940	0.255470	+	0.966817i	$0.417770\pi$
$684$	−2.00035	−0.0764853
$685$	−13.0533	−0.498743
$686$	−26.6238	−1.01650
$687$	24.0463	0.917425
$688$	−20.2371	−0.771532
$689$	0	0
$690$	7.63560	0.290682
$691$	−14.3836	−0.547178	−0.273589	−	0.961847i	$-0.588211\pi$
$691$	−14.3836	−0.547178	−0.273589	+	0.961847i	$0.588211\pi$
$692$	6.52376	0.247996
$693$	3.94757	0.149956
$694$	−39.9515	−1.51654
$695$	−8.85123	−0.335746
$696$	12.1431	0.460282
$697$	67.9730	2.57466
$698$	13.6249	0.515709
$699$	−13.6914	−0.517857
$700$	−2.07750	−0.0785220
$701$	−23.1908	−0.875903	−0.437952	−	0.898999i	$-0.644296\pi$
$701$	−23.1908	−0.875903	−0.437952	+	0.898999i	$0.644296\pi$
$702$	0	0
$703$	26.3324	0.993146
$704$	−4.83889	−0.182373
$705$	3.33450	0.125585
$706$	24.8983	0.937060
$707$	−0.179739	−0.00675978
$708$	−0.933745	−0.0350923
$709$	−34.8997	−1.31069	−0.655343	−	0.755331i	$-0.727476\pi$
$709$	−34.8997	−1.31069	−0.655343	+	0.755331i	$0.727476\pi$
$710$	−14.6517	−0.549868
$711$	2.83883	0.106464
$712$	−29.5520	−1.10751
$713$	−48.5761	−1.81919
$714$	44.7978	1.67652
$715$	0	0
$716$	4.35346	0.162696
$717$	−5.92813	−0.221390
$718$	−21.0159	−0.784305
$719$	14.6065	0.544732	0.272366	−	0.962194i	$-0.412194\pi$
$719$	14.6065	0.544732	0.272366	+	0.962194i	$0.412194\pi$
$720$	4.73985	0.176644
$721$	37.8350	1.40905
$722$	−3.67882	−0.136912
$723$	23.1085	0.859415
$724$	2.10853	0.0783628
$725$	5.09615	0.189266
$726$	15.9899	0.593440
$727$	−24.4509	−0.906832	−0.453416	−	0.891299i	$-0.649795\pi$
$727$	−24.4509	−0.906832	−0.453416	+	0.891299i	$0.649795\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−24.1284	−0.893030
$731$	28.5864	1.05731
$732$	−2.12924	−0.0786991
$733$	31.1538	1.15069	0.575345	−	0.817911i	$-0.304868\pi$
$733$	31.1538	1.15069	0.575345	+	0.817911i	$0.304868\pi$
$734$	26.7657	0.987939
$735$	10.9791	0.404972
$736$	−13.1314	−0.484031
$737$	−9.33995	−0.344041
$738$	16.0197	0.589695
$739$	28.5784	1.05127	0.525637	−	0.850709i	$-0.323827\pi$
$739$	28.5784	1.05127	0.525637	+	0.850709i	$0.323827\pi$
$740$	3.16007	0.116167
$741$	0	0
$742$	40.8879	1.50104
$743$	19.9932	0.733481	0.366740	−	0.930323i	$-0.380474\pi$
$743$	19.9932	0.733481	0.366740	+	0.930323i	$0.380474\pi$
$744$	−23.9200	−0.876950
$745$	−0.285807	−0.0104712
$746$	44.2949	1.62175
$747$	−0.543160	−0.0198732
$748$	−3.05406	−0.111668
$749$	85.7486	3.13319
$750$	1.57796	0.0576189
$751$	8.57420	0.312877	0.156439	−	0.987688i	$-0.449999\pi$
$751$	8.57420	0.312877	0.156439	+	0.987688i	$0.449999\pi$
$752$	−15.8050	−0.576351
$753$	3.50105	0.127585
$754$	0	0
$755$	17.3570	0.631688
$756$	2.07750	0.0755579
$757$	14.1052	0.512663	0.256331	−	0.966589i	$-0.417486\pi$
$757$	14.1052	0.512663	0.256331	+	0.966589i	$0.417486\pi$
$758$	4.19537	0.152383
$759$	4.50498	0.163520
$760$	−9.72827	−0.352881
$761$	−9.09450	−0.329676	−0.164838	−	0.986321i	$-0.552710\pi$
$761$	−9.09450	−0.329676	−0.164838	+	0.986321i	$0.552710\pi$
$762$	−10.2979	−0.373054
$763$	54.5783	1.97587
$764$	−8.29217	−0.300000
$765$	−6.69540	−0.242073
$766$	14.3014	0.516731
$767$	0	0
$768$	−11.1108	−0.400928
$769$	24.0929	0.868814	0.434407	−	0.900717i	$-0.356958\pi$
$769$	24.0929	0.868814	0.434407	+	0.900717i	$0.356958\pi$
$770$	−6.22910	−0.224481
$771$	9.31537	0.335485
$772$	10.6089	0.381822
$773$	4.74663	0.170724	0.0853622	−	0.996350i	$-0.472795\pi$
$773$	4.74663	0.170724	0.0853622	+	0.996350i	$0.472795\pi$
$774$	6.73719	0.242163
$775$	−10.0387	−0.360599
$776$	4.14450	0.148779
$777$	−27.3480	−0.981104
$778$	18.0419	0.646832
$779$	−41.4486	−1.48505
$780$	0	0
$781$	−8.64444	−0.309323
$782$	51.1234	1.82817
$783$	−5.09615	−0.182122
$784$	−52.0395	−1.85855
$785$	9.45243	0.337372
$786$	10.9264	0.389733
$787$	53.0147	1.88977	0.944885	−	0.327403i	$-0.106173\pi$
$787$	53.0147	1.88977	0.944885	+	0.327403i	$0.106173\pi$
$788$	4.47956	0.159578
$789$	−13.5759	−0.483313
$790$	−4.47956	−0.159376
$791$	−22.0423	−0.783735
$792$	2.21835	0.0788258
$793$	0	0
$794$	−41.1732	−1.46118
$795$	−6.11103	−0.216736
$796$	7.17110	0.254173
$797$	−20.5997	−0.729679	−0.364840	−	0.931070i	$-0.618876\pi$
$797$	−20.5997	−0.729679	−0.364840	+	0.931070i	$0.618876\pi$
$798$	−27.3168	−0.967005
$799$	22.3258	0.789831
$800$	−2.71372	−0.0959444
$801$	12.4023	0.438212
$802$	−6.39538	−0.225829
$803$	−14.2356	−0.502365
$804$	−4.91536	−0.173351
$805$	20.5179	0.723160
$806$	0	0
$807$	25.6988	0.904641
$808$	−0.101005	−0.00355335
$809$	5.78481	0.203383	0.101692	−	0.994816i	$-0.467575\pi$
$809$	5.78481	0.203383	0.101692	+	0.994816i	$0.467575\pi$
$810$	−1.57796	−0.0554438
$811$	55.5401	1.95028	0.975139	−	0.221595i	$-0.0711263\pi$
$811$	55.5401	1.95028	0.975139	+	0.221595i	$0.0711263\pi$
$812$	−10.5872	−0.371540
$813$	−19.4492	−0.682113
$814$	9.47506	0.332101
$815$	−13.6851	−0.479368
$816$	31.7352	1.11096
$817$	−17.4314	−0.609848
$818$	−23.7066	−0.828881
$819$	0	0
$820$	−4.97412	−0.173704
$821$	−40.6664	−1.41927	−0.709634	−	0.704571i	$-0.751140\pi$
$821$	−40.6664	−1.41927	−0.709634	+	0.704571i	$0.751140\pi$
$822$	−20.5976	−0.718426
$823$	15.4559	0.538758	0.269379	−	0.963034i	$-0.413182\pi$
$823$	15.4559	0.538758	0.269379	+	0.963034i	$0.413182\pi$
$824$	21.2615	0.740681
$825$	0.930991	0.0324129
$826$	−12.7512	−0.443672
$827$	−27.2475	−0.947489	−0.473745	−	0.880662i	$-0.657098\pi$
$827$	−27.2475	−0.947489	−0.473745	+	0.880662i	$0.657098\pi$
$828$	2.37085	0.0823927
$829$	44.0881	1.53124	0.765621	−	0.643292i	$-0.222432\pi$
$829$	44.0881	1.53124	0.765621	+	0.643292i	$0.222432\pi$
$830$	0.857085	0.0297498
$831$	19.0529	0.660937
$832$	0	0
$833$	73.5098	2.54696
$834$	−13.9669	−0.483633
$835$	15.7127	0.543760
$836$	1.86231	0.0644092
$837$	10.0387	0.346987
$838$	5.38478	0.186014
$839$	−42.1746	−1.45603	−0.728014	−	0.685563i	$-0.759556\pi$
$839$	−42.1746	−1.45603	−0.728014	+	0.685563i	$0.759556\pi$
$840$	10.1035	0.348602
$841$	−3.02922	−0.104456
$842$	20.5589	0.708506
$843$	5.09810	0.175588
$844$	−9.55768	−0.328989
$845$	0	0
$846$	5.26171	0.180901
$847$	42.9668	1.47636
$848$	28.9654	0.994676
$849$	−2.64104	−0.0906401
$850$	10.5651	0.362379
$851$	−31.2096	−1.06985
$852$	−4.54934	−0.155858
$853$	−12.7253	−0.435705	−0.217852	−	0.975982i	$-0.569905\pi$
$853$	−12.7253	−0.435705	−0.217852	+	0.975982i	$0.569905\pi$
$854$	−29.0770	−0.994994
$855$	4.08272	0.139626
$856$	48.1868	1.64699
$857$	−7.31935	−0.250024	−0.125012	−	0.992155i	$-0.539897\pi$
$857$	−7.31935	−0.250024	−0.125012	+	0.992155i	$0.539897\pi$
$858$	0	0
$859$	−30.1263	−1.02790	−0.513949	−	0.857821i	$-0.671818\pi$
$859$	−30.1263	−1.02790	−0.513949	+	0.857821i	$0.671818\pi$
$860$	−2.09189	−0.0713329
$861$	43.0472	1.46704
$862$	21.3191	0.726133
$863$	−1.08303	−0.0368668	−0.0184334	−	0.999830i	$-0.505868\pi$
$863$	−1.08303	−0.0368668	−0.0184334	+	0.999830i	$0.505868\pi$
$864$	2.71372	0.0923225
$865$	−13.3150	−0.452724
$866$	62.0565	2.10877
$867$	−27.8284	−0.945103
$868$	20.8553	0.707874
$869$	−2.64292	−0.0896551
$870$	8.04152	0.272633
$871$	0	0
$872$	30.6705	1.03864
$873$	−1.73935	−0.0588680
$874$	−31.1740	−1.05448
$875$	4.24018	0.143344
$876$	−7.49183	−0.253126
$877$	−47.4920	−1.60369	−0.801845	−	0.597532i	$-0.796148\pi$
$877$	−47.4920	−1.60369	−0.801845	+	0.597532i	$0.796148\pi$
$878$	15.1706	0.511983
$879$	−22.5407	−0.760277
$880$	−4.41276	−0.148754
$881$	7.42921	0.250297	0.125148	−	0.992138i	$-0.460059\pi$
$881$	7.42921	0.250297	0.125148	+	0.992138i	$0.460059\pi$
$882$	17.3246	0.583351
$883$	18.6025	0.626024	0.313012	−	0.949749i	$-0.398662\pi$
$883$	18.6025	0.626024	0.313012	+	0.949749i	$0.398662\pi$
$884$	0	0
$885$	1.90578	0.0640620
$886$	37.2704	1.25212
$887$	−1.00388	−0.0337068	−0.0168534	−	0.999858i	$-0.505365\pi$
$887$	−1.00388	−0.0337068	−0.0168534	+	0.999858i	$0.505365\pi$
$888$	−15.3683	−0.515727
$889$	−27.6718	−0.928083
$890$	−19.5703	−0.655996
$891$	−0.930991	−0.0311894
$892$	3.83278	0.128331
$893$	−13.6138	−0.455570
$894$	−0.450992	−0.0150834
$895$	−8.88543	−0.297007
$896$	−57.7894	−1.93061
$897$	0	0
$898$	−56.2901	−1.87843
$899$	−51.1585	−1.70623
$900$	0.489955	0.0163318
$901$	−40.9158	−1.36310
$902$	−14.9142	−0.496590
$903$	18.1037	0.602453
$904$	−12.3868	−0.411979
$905$	−4.30351	−0.143054
$906$	27.3887	0.909929
$907$	19.2704	0.639863	0.319931	−	0.947441i	$-0.396340\pi$
$907$	19.2704	0.639863	0.319931	+	0.947441i	$0.396340\pi$
$908$	9.49601	0.315136
$909$	0.0423894	0.00140597
$910$	0	0
$911$	−33.0518	−1.09505	−0.547527	−	0.836788i	$-0.684431\pi$
$911$	−33.0518	−1.09505	−0.547527	+	0.836788i	$0.684431\pi$
$912$	−19.3515	−0.640792
$913$	0.505677	0.0167355
$914$	−51.3237	−1.69764
$915$	4.34579	0.143667
$916$	−11.7816	−0.389276
$917$	29.3607	0.969576
$918$	−10.5651	−0.348699
$919$	−13.4338	−0.443139	−0.221570	−	0.975145i	$-0.571118\pi$
$919$	−13.4338	−0.443139	−0.221570	+	0.975145i	$0.571118\pi$
$920$	11.5301	0.380136
$921$	−26.6912	−0.879506
$922$	11.2420	0.370237
$923$	0	0
$924$	−1.93413	−0.0636282
$925$	−6.44972	−0.212066
$926$	−23.0409	−0.757171
$927$	−8.92296	−0.293068
$928$	−13.8295	−0.453976
$929$	14.0098	0.459647	0.229823	−	0.973232i	$-0.426185\pi$
$929$	14.0098	0.459647	0.229823	+	0.973232i	$0.426185\pi$
$930$	−15.8406	−0.519433
$931$	−44.8248	−1.46907
$932$	6.70818	0.219734
$933$	−17.1305	−0.560829
$934$	15.8270	0.517874
$935$	6.23336	0.203853
$936$	0	0
$937$	20.1806	0.659273	0.329636	−	0.944108i	$-0.393074\pi$
$937$	20.1806	0.659273	0.329636	+	0.944108i	$0.393074\pi$
$938$	−67.1243	−2.19168
$939$	−25.1929	−0.822140
$940$	−1.63375	−0.0532872
$941$	−9.82880	−0.320410	−0.160205	−	0.987084i	$-0.551215\pi$
$941$	−9.82880	−0.320410	−0.160205	+	0.987084i	$0.551215\pi$
$942$	14.9156	0.485975
$943$	49.1256	1.59975
$944$	−9.03311	−0.294003
$945$	−4.24018	−0.137933
$946$	−6.27226	−0.203929
$947$	−30.4220	−0.988583	−0.494291	−	0.869296i	$-0.664572\pi$
$947$	−30.4220	−0.988583	−0.494291	+	0.869296i	$0.664572\pi$
$948$	−1.39090	−0.0451743
$949$	0	0
$950$	−6.44237	−0.209018
$951$	0.244299	0.00792193
$952$	67.6467	2.19244
$953$	3.86690	0.125261	0.0626305	−	0.998037i	$-0.480051\pi$
$953$	3.86690	0.125261	0.0626305	+	0.998037i	$0.480051\pi$
$954$	−9.64296	−0.312202
$955$	16.9244	0.547659
$956$	2.90452	0.0939388
$957$	4.74447	0.153367
$958$	2.65291	0.0857117
$959$	−55.3486	−1.78730
$960$	5.19757	0.167751
$961$	69.7745	2.25079
$962$	0	0
$963$	−20.2229	−0.651673
$964$	−11.3221	−0.364661
$965$	−21.6528	−0.697028
$966$	32.3763	1.04169
$967$	7.41143	0.238335	0.119168	−	0.992874i	$-0.461977\pi$
$967$	7.41143	0.238335	0.119168	+	0.992874i	$0.461977\pi$
$968$	24.1454	0.776063
$969$	27.3355	0.878142
$970$	2.74462	0.0881245
$971$	2.06539	0.0662814	0.0331407	−	0.999451i	$-0.489449\pi$
$971$	2.06539	0.0662814	0.0331407	+	0.999451i	$0.489449\pi$
$972$	−0.489955	−0.0157153
$973$	−37.5308	−1.20318
$974$	60.9046	1.95151
$975$	0	0
$976$	−20.5984	−0.659339
$977$	−2.73365	−0.0874572	−0.0437286	−	0.999043i	$-0.513924\pi$
$977$	−2.73365	−0.0874572	−0.0437286	+	0.999043i	$0.513924\pi$
$978$	−21.5945	−0.690517
$979$	−11.5464	−0.369024
$980$	−5.37928	−0.171835
$981$	−12.8717	−0.410962
$982$	24.0632	0.767887
$983$	−22.8404	−0.728496	−0.364248	−	0.931302i	$-0.618674\pi$
$983$	−22.8404	−0.728496	−0.364248	+	0.931302i	$0.618674\pi$
$984$	24.1905	0.771166
$985$	−9.14280	−0.291314
$986$	53.8412	1.71465
$987$	14.1389	0.450046
$988$	0	0
$989$	20.6600	0.656950
$990$	1.46907	0.0466900
$991$	29.5431	0.938468	0.469234	−	0.883074i	$-0.344530\pi$
$991$	29.5431	0.938468	0.469234	+	0.883074i	$0.344530\pi$
$992$	27.2421	0.864936
$993$	−18.8657	−0.598684
$994$	−62.1258	−1.97051
$995$	−14.6362	−0.464000
$996$	0.266124	0.00843246
$997$	7.41595	0.234866	0.117433	−	0.993081i	$-0.462534\pi$
$997$	7.41595	0.234866	0.117433	+	0.993081i	$0.462534\pi$
$998$	27.7850	0.879518
$999$	6.44972	0.204060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.2.a.bm.1.8	✓	9
3.2	odd	2		7605.2.a.cr.1.2		9
13.12	even	2		2535.2.a.bn.1.2	yes	9
39.38	odd	2		7605.2.a.cq.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.bm.1.8	✓	9	1.1	even	1	trivial
2535.2.a.bn.1.2	yes	9	13.12	even	2
7605.2.a.cq.1.8		9	39.38	odd	2
7605.2.a.cr.1.2		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)

\(f(q)\)	\(=\)	\(q+1.57796 q^{2} -1.00000 q^{3} +0.489955 q^{4} -1.00000 q^{5} -1.57796 q^{6} -4.24018 q^{7} -2.38279 q^{8} +1.00000 q^{9} -1.57796 q^{10} -0.930991 q^{11} -0.489955 q^{12} -6.69083 q^{14} +1.00000 q^{15} -4.73985 q^{16} +6.69540 q^{17} +1.57796 q^{18} -4.08272 q^{19} -0.489955 q^{20} +4.24018 q^{21} -1.46907 q^{22} +4.83891 q^{23} +2.38279 q^{24} +1.00000 q^{25} -1.00000 q^{27} -2.07750 q^{28} +5.09615 q^{29} +1.57796 q^{30} -10.0387 q^{31} -2.71372 q^{32} +0.930991 q^{33} +10.5651 q^{34} +4.24018 q^{35} +0.489955 q^{36} -6.44972 q^{37} -6.44237 q^{38} +2.38279 q^{40} +10.1522 q^{41} +6.69083 q^{42} +4.26956 q^{43} -0.456143 q^{44} -1.00000 q^{45} +7.63560 q^{46} +3.33450 q^{47} +4.73985 q^{48} +10.9791 q^{49} +1.57796 q^{50} -6.69540 q^{51} -6.11103 q^{53} -1.57796 q^{54} +0.930991 q^{55} +10.1035 q^{56} +4.08272 q^{57} +8.04152 q^{58} +1.90578 q^{59} +0.489955 q^{60} +4.34579 q^{61} -15.8406 q^{62} -4.24018 q^{63} +5.19757 q^{64} +1.46907 q^{66} +10.0323 q^{67} +3.28045 q^{68} -4.83891 q^{69} +6.69083 q^{70} +9.28521 q^{71} -2.38279 q^{72} +15.2909 q^{73} -10.1774 q^{74} -1.00000 q^{75} -2.00035 q^{76} +3.94757 q^{77} +2.83883 q^{79} +4.73985 q^{80} +1.00000 q^{81} +16.0197 q^{82} -0.543160 q^{83} +2.07750 q^{84} -6.69540 q^{85} +6.73719 q^{86} -5.09615 q^{87} +2.21835 q^{88} +12.4023 q^{89} -1.57796 q^{90} +2.37085 q^{92} +10.0387 q^{93} +5.26171 q^{94} +4.08272 q^{95} +2.71372 q^{96} -1.73935 q^{97} +17.3246 q^{98} -0.930991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 10 q^{4} - 9 q^{5} + 10 q^{7} - 3 q^{8} + 9 q^{9} - 11 q^{11} - 10 q^{12} + 10 q^{14} + 9 q^{15} + 8 q^{16} + 18 q^{17} - 10 q^{19} - 10 q^{20} - 10 q^{21} + 17 q^{22} - 7 q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 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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