LMFDB - Embedded newform 6014.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.380224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 8x^{3} - 2x^{2} + 5x + 2 $ x^5 - 8x^3 - 2x^2 + 5*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.82726$ of defining polynomial
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.82726 q^{3} +1.00000 q^{4} -0.0813392 q^{5} +2.82726 q^{6} +1.00000 q^{8} +4.99338 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.82726 q^{3} +1.00000 q^{4} -0.0813392 q^{5} +2.82726 q^{6} +1.00000 q^{8} +4.99338 q^{9} -0.0813392 q^{10} -1.39609 q^{11} +2.82726 q^{12} +0.459934 q^{13} -0.229967 q^{15} +1.00000 q^{16} +4.67863 q^{17} +4.99338 q^{18} -2.88989 q^{19} -0.0813392 q^{20} -1.39609 q^{22} +7.66426 q^{23} +2.82726 q^{24} -4.99338 q^{25} +0.459934 q^{26} +5.63581 q^{27} +7.25212 q^{29} -0.229967 q^{30} -1.00000 q^{31} +1.00000 q^{32} -3.94712 q^{33} +4.67863 q^{34} +4.99338 q^{36} -2.88989 q^{38} +1.30035 q^{39} -0.0813392 q^{40} +9.73155 q^{41} +1.39609 q^{43} -1.39609 q^{44} -0.406158 q^{45} +7.66426 q^{46} -1.14170 q^{47} +2.82726 q^{48} -7.00000 q^{49} -4.99338 q^{50} +13.2277 q^{51} +0.459934 q^{52} -2.48177 q^{53} +5.63581 q^{54} +0.113557 q^{55} -8.17047 q^{57} +7.25212 q^{58} +1.07270 q^{59} -0.229967 q^{60} -5.26849 q^{61} -1.00000 q^{62} +1.00000 q^{64} -0.0374106 q^{65} -3.94712 q^{66} +10.5005 q^{67} +4.67863 q^{68} +21.6688 q^{69} -7.54007 q^{71} +4.99338 q^{72} +5.32226 q^{73} -14.1176 q^{75} -2.88989 q^{76} +1.30035 q^{78} -6.38916 q^{79} -0.0813392 q^{80} +0.953731 q^{81} +9.73155 q^{82} -2.44670 q^{83} -0.380556 q^{85} +1.39609 q^{86} +20.5036 q^{87} -1.39609 q^{88} +10.7721 q^{89} -0.406158 q^{90} +7.66426 q^{92} -2.82726 q^{93} -1.14170 q^{94} +0.235061 q^{95} +2.82726 q^{96} -1.00000 q^{97} -7.00000 q^{98} -6.97123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{4} - 4 q^{5} + 5 q^{8} + q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^4 - 4 * q^5 + 5 * q^8 + q^9	$ 5 q + 5 q^{2} + 5 q^{4} - 4 q^{5} + 5 q^{8} + q^{9} - 4 q^{10} + 4 q^{11} + 5 q^{16} + 14 q^{17} + q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - q^{25} + 6 q^{27} + 12 q^{29} - 5 q^{31} + 5 q^{32} + 14 q^{34} + q^{36} - 10 q^{38} + 20 q^{39} - 4 q^{40} + 2 q^{41} - 4 q^{43} + 4 q^{44} + 2 q^{45} + 40 q^{47} - 35 q^{49} - q^{50} + 6 q^{51} + 30 q^{53} + 6 q^{54} - 12 q^{55} + 4 q^{57} + 12 q^{58} + 22 q^{59} - 16 q^{61} - 5 q^{62} + 5 q^{64} + 12 q^{65} + 4 q^{67} + 14 q^{68} + 34 q^{69} - 40 q^{71} + q^{72} + 18 q^{73} - 6 q^{75} - 10 q^{76} + 20 q^{78} + 20 q^{79} - 4 q^{80} + 9 q^{81} + 2 q^{82} + 38 q^{83} - 38 q^{85} - 4 q^{86} + 20 q^{87} + 4 q^{88} + 18 q^{89} + 2 q^{90} + 40 q^{94} + 8 q^{95} - 5 q^{97} - 35 q^{98} - 34 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 5 * q^4 - 4 * q^5 + 5 * q^8 + q^9 - 4 * q^10 + 4 * q^11 + 5 * q^16 + 14 * q^17 + q^18 - 10 * q^19 - 4 * q^20 + 4 * q^22 - q^25 + 6 * q^27 + 12 * q^29 - 5 * q^31 + 5 * q^32 + 14 * q^34 + q^36 - 10 * q^38 + 20 * q^39 - 4 * q^40 + 2 * q^41 - 4 * q^43 + 4 * q^44 + 2 * q^45 + 40 * q^47 - 35 * q^49 - q^50 + 6 * q^51 + 30 * q^53 + 6 * q^54 - 12 * q^55 + 4 * q^57 + 12 * q^58 + 22 * q^59 - 16 * q^61 - 5 * q^62 + 5 * q^64 + 12 * q^65 + 4 * q^67 + 14 * q^68 + 34 * q^69 - 40 * q^71 + q^72 + 18 * q^73 - 6 * q^75 - 10 * q^76 + 20 * q^78 + 20 * q^79 - 4 * q^80 + 9 * q^81 + 2 * q^82 + 38 * q^83 - 38 * q^85 - 4 * q^86 + 20 * q^87 + 4 * q^88 + 18 * q^89 + 2 * q^90 + 40 * q^94 + 8 * q^95 - 5 * q^97 - 35 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.82726	1.63232	0.816159	−	0.577828i	$-0.196099\pi$
$3$	2.82726	1.63232	0.816159	+	0.577828i	$0.196099\pi$
$4$	1.00000	0.500000
$5$	−0.0813392	−0.0363760	−0.0181880	−	0.999835i	$-0.505790\pi$
$5$	−0.0813392	−0.0363760	−0.0181880	+	0.999835i	$0.505790\pi$
$6$	2.82726	1.15422
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	4.99338	1.66446
$10$	−0.0813392	−0.0257217
$11$	−1.39609	−0.420938	−0.210469	−	0.977601i	$-0.567499\pi$
$11$	−1.39609	−0.420938	−0.210469	+	0.977601i	$0.567499\pi$
$12$	2.82726	0.816159
$13$	0.459934	0.127563	0.0637813	−	0.997964i	$-0.479684\pi$
$13$	0.459934	0.127563	0.0637813	+	0.997964i	$0.479684\pi$
$14$	0	0
$15$	−0.229967	−0.0593772
$16$	1.00000	0.250000
$17$	4.67863	1.13473	0.567367	−	0.823465i	$-0.307962\pi$
$17$	4.67863	1.13473	0.567367	+	0.823465i	$0.307962\pi$
$18$	4.99338	1.17695
$19$	−2.88989	−0.662987	−0.331493	−	0.943458i	$-0.607552\pi$
$19$	−2.88989	−0.662987	−0.331493	+	0.943458i	$0.607552\pi$
$20$	−0.0813392	−0.0181880
$21$	0	0
$22$	−1.39609	−0.297648
$23$	7.66426	1.59811	0.799055	−	0.601258i	$-0.205334\pi$
$23$	7.66426	1.59811	0.799055	+	0.601258i	$0.205334\pi$
$24$	2.82726	0.577111
$25$	−4.99338	−0.998677
$26$	0.459934	0.0902004
$27$	5.63581	1.08461
$28$	0	0
$29$	7.25212	1.34668	0.673342	−	0.739331i	$-0.264858\pi$
$29$	7.25212	1.34668	0.673342	+	0.739331i	$0.264858\pi$
$30$	−0.229967	−0.0419860
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−3.94712	−0.687105
$34$	4.67863	0.802378
$35$	0	0
$36$	4.99338	0.832231
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−2.88989	−0.468802
$39$	1.30035	0.208223
$40$	−0.0813392	−0.0128609
$41$	9.73155	1.51981	0.759907	−	0.650032i	$-0.225245\pi$
$41$	9.73155	1.51981	0.759907	+	0.650032i	$0.225245\pi$
$42$	0	0
$43$	1.39609	0.212902	0.106451	−	0.994318i	$-0.466051\pi$
$43$	1.39609	0.212902	0.106451	+	0.994318i	$0.466051\pi$
$44$	−1.39609	−0.210469
$45$	−0.406158	−0.0605464
$46$	7.66426	1.13003
$47$	−1.14170	−0.166534	−0.0832668	−	0.996527i	$-0.526535\pi$
$47$	−1.14170	−0.166534	−0.0832668	+	0.996527i	$0.526535\pi$
$48$	2.82726	0.408079
$49$	−7.00000	−1.00000
$50$	−4.99338	−0.706171
$51$	13.2277	1.85225
$52$	0.459934	0.0637813
$53$	−2.48177	−0.340898	−0.170449	−	0.985367i	$-0.554522\pi$
$53$	−2.48177	−0.340898	−0.170449	+	0.985367i	$0.554522\pi$
$54$	5.63581	0.766937
$55$	0.113557	0.0153120
$56$	0	0
$57$	−8.17047	−1.08220
$58$	7.25212	0.952250
$59$	1.07270	0.139653	0.0698267	−	0.997559i	$-0.477755\pi$
$59$	1.07270	0.139653	0.0698267	+	0.997559i	$0.477755\pi$
$60$	−0.229967	−0.0296886
$61$	−5.26849	−0.674560	−0.337280	−	0.941404i	$-0.609507\pi$
$61$	−5.26849	−0.674560	−0.337280	+	0.941404i	$0.609507\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.0374106	−0.00464022
$66$	−3.94712	−0.485856
$67$	10.5005	1.28284	0.641419	−	0.767191i	$-0.278346\pi$
$67$	10.5005	1.28284	0.641419	+	0.767191i	$0.278346\pi$
$68$	4.67863	0.567367
$69$	21.6688	2.60862
$70$	0	0
$71$	−7.54007	−0.894841	−0.447421	−	0.894324i	$-0.647657\pi$
$71$	−7.54007	−0.894841	−0.447421	+	0.894324i	$0.647657\pi$
$72$	4.99338	0.588476
$73$	5.32226	0.622924	0.311462	−	0.950259i	$-0.399181\pi$
$73$	5.32226	0.622924	0.311462	+	0.950259i	$0.399181\pi$
$74$	0	0
$75$	−14.1176	−1.63016
$76$	−2.88989	−0.331493
$77$	0	0
$78$	1.30035	0.147236
$79$	−6.38916	−0.718837	−0.359418	−	0.933176i	$-0.617025\pi$
$79$	−6.38916	−0.718837	−0.359418	+	0.933176i	$0.617025\pi$
$80$	−0.0813392	−0.00909400
$81$	0.953731	0.105970
$82$	9.73155	1.07467
$83$	−2.44670	−0.268560	−0.134280	−	0.990943i	$-0.542872\pi$
$83$	−2.44670	−0.268560	−0.134280	+	0.990943i	$0.542872\pi$
$84$	0	0
$85$	−0.380556	−0.0412771
$86$	1.39609	0.150545
$87$	20.5036	2.19822
$88$	−1.39609	−0.148824
$89$	10.7721	1.14184	0.570918	−	0.821007i	$-0.306587\pi$
$89$	10.7721	1.14184	0.570918	+	0.821007i	$0.306587\pi$
$90$	−0.406158	−0.0428128
$91$	0	0
$92$	7.66426	0.799055
$93$	−2.82726	−0.293173
$94$	−1.14170	−0.117757
$95$	0.235061	0.0241168
$96$	2.82726	0.288556
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−7.00000	−0.707107
$99$	−6.97123	−0.700635
$100$	−4.99338	−0.499338
$101$	10.3168	1.02656	0.513278	−	0.858223i	$-0.328431\pi$
$101$	10.3168	1.02656	0.513278	+	0.858223i	$0.328431\pi$
$102$	13.2277	1.30974
$103$	−3.78444	−0.372892	−0.186446	−	0.982465i	$-0.559697\pi$
$103$	−3.78444	−0.372892	−0.186446	+	0.982465i	$0.559697\pi$
$104$	0.459934	0.0451002
$105$	0	0
$106$	−2.48177	−0.241051
$107$	5.72842	0.553787	0.276894	−	0.960901i	$-0.410695\pi$
$107$	5.72842	0.553787	0.276894	+	0.960901i	$0.410695\pi$
$108$	5.63581	0.542306
$109$	−7.58437	−0.726451	−0.363226	−	0.931701i	$-0.618325\pi$
$109$	−7.58437	−0.726451	−0.363226	+	0.931701i	$0.618325\pi$
$110$	0.113557	0.0108272
$111$	0	0
$112$	0	0
$113$	6.27247	0.590065	0.295032	−	0.955487i	$-0.404670\pi$
$113$	6.27247	0.590065	0.295032	+	0.955487i	$0.404670\pi$
$114$	−8.17047	−0.765234
$115$	−0.623405	−0.0581328
$116$	7.25212	0.673342
$117$	2.29662	0.212323
$118$	1.07270	0.0987499
$119$	0	0
$120$	−0.229967	−0.0209930
$121$	−9.05092	−0.822811
$122$	−5.26849	−0.476986
$123$	27.5136	2.48082
$124$	−1.00000	−0.0898027
$125$	0.812854	0.0727038
$126$	0	0
$127$	6.05754	0.537520	0.268760	−	0.963207i	$-0.413386\pi$
$127$	6.05754	0.537520	0.268760	+	0.963207i	$0.413386\pi$
$128$	1.00000	0.0883883
$129$	3.94712	0.347524
$130$	−0.0374106	−0.00328113
$131$	−11.0075	−0.961727	−0.480864	−	0.876795i	$-0.659677\pi$
$131$	−11.0075	−0.961727	−0.480864	+	0.876795i	$0.659677\pi$
$132$	−3.94712	−0.343552
$133$	0	0
$134$	10.5005	0.907103
$135$	−0.458412	−0.0394538
$136$	4.67863	0.401189
$137$	−14.7752	−1.26233	−0.631164	−	0.775650i	$-0.717422\pi$
$137$	−14.7752	−1.26233	−0.631164	+	0.775650i	$0.717422\pi$
$138$	21.6688	1.84457
$139$	−2.91987	−0.247660	−0.123830	−	0.992303i	$-0.539518\pi$
$139$	−2.91987	−0.247660	−0.123830	+	0.992303i	$0.539518\pi$
$140$	0	0
$141$	−3.22787	−0.271836
$142$	−7.54007	−0.632748
$143$	−0.642110	−0.0536960
$144$	4.99338	0.416115
$145$	−0.589881	−0.0489870
$146$	5.32226	0.440473
$147$	−19.7908	−1.63232
$148$	0	0
$149$	14.6654	1.20143	0.600717	−	0.799462i	$-0.294882\pi$
$149$	14.6654	1.20143	0.600717	+	0.799462i	$0.294882\pi$
$150$	−14.1176	−1.15270
$151$	9.49184	0.772435	0.386217	−	0.922408i	$-0.373781\pi$
$151$	9.49184	0.772435	0.386217	+	0.922408i	$0.373781\pi$
$152$	−2.88989	−0.234401
$153$	23.3622	1.88872
$154$	0	0
$155$	0.0813392	0.00653332
$156$	1.30035	0.104111
$157$	−15.7483	−1.25685	−0.628425	−	0.777870i	$-0.716300\pi$
$157$	−15.7483	−1.25685	−0.628425	+	0.777870i	$0.716300\pi$
$158$	−6.38916	−0.508294
$159$	−7.01661	−0.556453
$160$	−0.0813392	−0.00643043
$161$	0	0
$162$	0.953731	0.0749322
$163$	16.6795	1.30644	0.653220	−	0.757168i	$-0.273417\pi$
$163$	16.6795	1.30644	0.653220	+	0.757168i	$0.273417\pi$
$164$	9.73155	0.759907
$165$	0.321055	0.0249941
$166$	−2.44670	−0.189901
$167$	12.3737	0.957503	0.478751	−	0.877951i	$-0.341090\pi$
$167$	12.3737	0.957503	0.478751	+	0.877951i	$0.341090\pi$
$168$	0	0
$169$	−12.7885	−0.983728
$170$	−0.380556	−0.0291873
$171$	−14.4303	−1.10352
$172$	1.39609	0.106451
$173$	0.0775757	0.00589797	0.00294899	−	0.999996i	$-0.499061\pi$
$173$	0.0775757	0.00589797	0.00294899	+	0.999996i	$0.499061\pi$
$174$	20.5036	1.55437
$175$	0	0
$176$	−1.39609	−0.105234
$177$	3.03279	0.227959
$178$	10.7721	0.807400
$179$	−11.7114	−0.875353	−0.437676	−	0.899133i	$-0.644198\pi$
$179$	−11.7114	−0.875353	−0.437676	+	0.899133i	$0.644198\pi$
$180$	−0.406158	−0.0302732
$181$	−11.6614	−0.866786	−0.433393	−	0.901205i	$-0.642684\pi$
$181$	−11.6614	−0.866786	−0.433393	+	0.901205i	$0.642684\pi$
$182$	0	0
$183$	−14.8954	−1.10110
$184$	7.66426	0.565017
$185$	0	0
$186$	−2.82726	−0.207305
$187$	−6.53180	−0.477653
$188$	−1.14170	−0.0832668
$189$	0	0
$190$	0.235061	0.0170531
$191$	18.8491	1.36387	0.681936	−	0.731412i	$-0.261138\pi$
$191$	18.8491	1.36387	0.681936	+	0.731412i	$0.261138\pi$
$192$	2.82726	0.204040
$193$	−7.83669	−0.564097	−0.282049	−	0.959400i	$-0.591014\pi$
$193$	−7.83669	−0.564097	−0.282049	+	0.959400i	$0.591014\pi$
$194$	−1.00000	−0.0717958
$195$	−0.105769	−0.00757431
$196$	−7.00000	−0.500000
$197$	−19.4071	−1.38270	−0.691350	−	0.722520i	$-0.742984\pi$
$197$	−19.4071	−1.38270	−0.691350	+	0.722520i	$0.742984\pi$
$198$	−6.97123	−0.495424
$199$	−10.3176	−0.731398	−0.365699	−	0.930733i	$-0.619170\pi$
$199$	−10.3176	−0.731398	−0.365699	+	0.930733i	$0.619170\pi$
$200$	−4.99338	−0.353086
$201$	29.6876	2.09400
$202$	10.3168	0.725884
$203$	0	0
$204$	13.2277	0.926124
$205$	−0.791556	−0.0552847
$206$	−3.78444	−0.263674
$207$	38.2706	2.65999
$208$	0.459934	0.0318907
$209$	4.03456	0.279076
$210$	0	0
$211$	4.39409	0.302502	0.151251	−	0.988495i	$-0.451670\pi$
$211$	4.39409	0.302502	0.151251	+	0.988495i	$0.451670\pi$
$212$	−2.48177	−0.170449
$213$	−21.3177	−1.46067
$214$	5.72842	0.391587
$215$	−0.113557	−0.00774453
$216$	5.63581	0.383468
$217$	0	0
$218$	−7.58437	−0.513679
$219$	15.0474	1.01681
$220$	0.113557	0.00765602
$221$	2.15186	0.144750
$222$	0	0
$223$	−0.104699	−0.00701117	−0.00350558	−	0.999994i	$-0.501116\pi$
$223$	−0.104699	−0.00701117	−0.00350558	+	0.999994i	$0.501116\pi$
$224$	0	0
$225$	−24.9339	−1.66226
$226$	6.27247	0.417239
$227$	11.8717	0.787952	0.393976	−	0.919121i	$-0.371099\pi$
$227$	11.8717	0.787952	0.393976	+	0.919121i	$0.371099\pi$
$228$	−8.17047	−0.541102
$229$	−19.0069	−1.25601	−0.628007	−	0.778208i	$-0.716129\pi$
$229$	−19.0069	−1.25601	−0.628007	+	0.778208i	$0.716129\pi$
$230$	−0.623405	−0.0411061
$231$	0	0
$232$	7.25212	0.476125
$233$	14.8095	0.970201	0.485100	−	0.874459i	$-0.338783\pi$
$233$	14.8095	0.970201	0.485100	+	0.874459i	$0.338783\pi$
$234$	2.29662	0.150135
$235$	0.0928646	0.00605782
$236$	1.07270	0.0698267
$237$	−18.0638	−1.17337
$238$	0	0
$239$	20.0977	1.30001	0.650007	−	0.759928i	$-0.274766\pi$
$239$	20.0977	1.30001	0.650007	+	0.759928i	$0.274766\pi$
$240$	−0.229967	−0.0148443
$241$	−4.88651	−0.314768	−0.157384	−	0.987538i	$-0.550306\pi$
$241$	−4.88651	−0.314768	−0.157384	+	0.987538i	$0.550306\pi$
$242$	−9.05092	−0.581815
$243$	−14.2110	−0.911635
$244$	−5.26849	−0.337280
$245$	0.569374	0.0363760
$246$	27.5136	1.75420
$247$	−1.32916	−0.0845723
$248$	−1.00000	−0.0635001
$249$	−6.91745	−0.438376
$250$	0.812854	0.0514094
$251$	−20.2088	−1.27557	−0.637783	−	0.770216i	$-0.720148\pi$
$251$	−20.2088	−1.27557	−0.637783	+	0.770216i	$0.720148\pi$
$252$	0	0
$253$	−10.7000	−0.672705
$254$	6.05754	0.380084
$255$	−1.07593	−0.0673773
$256$	1.00000	0.0625000
$257$	3.25275	0.202901	0.101451	−	0.994841i	$-0.467652\pi$
$257$	3.25275	0.202901	0.101451	+	0.994841i	$0.467652\pi$
$258$	3.94712	0.245737
$259$	0	0
$260$	−0.0374106	−0.00232011
$261$	36.2126	2.24150
$262$	−11.0075	−0.680044
$263$	−25.9459	−1.59989	−0.799946	−	0.600073i	$-0.795138\pi$
$263$	−25.9459	−1.59989	−0.799946	+	0.600073i	$0.795138\pi$
$264$	−3.94712	−0.242928
$265$	0.201865	0.0124005
$266$	0	0
$267$	30.4554	1.86384
$268$	10.5005	0.641419
$269$	0.479359	0.0292271	0.0146135	−	0.999893i	$-0.495348\pi$
$269$	0.479359	0.0292271	0.0146135	+	0.999893i	$0.495348\pi$
$270$	−0.458412	−0.0278981
$271$	−9.58616	−0.582317	−0.291159	−	0.956675i	$-0.594041\pi$
$271$	−9.58616	−0.582317	−0.291159	+	0.956675i	$0.594041\pi$
$272$	4.67863	0.283684
$273$	0	0
$274$	−14.7752	−0.892600
$275$	6.97123	0.420381
$276$	21.6688	1.30431
$277$	−15.5136	−0.932122	−0.466061	−	0.884753i	$-0.654327\pi$
$277$	−15.5136	−0.932122	−0.466061	+	0.884753i	$0.654327\pi$
$278$	−2.91987	−0.175122
$279$	−4.99338	−0.298946
$280$	0	0
$281$	−17.9511	−1.07088	−0.535438	−	0.844575i	$-0.679853\pi$
$281$	−17.9511	−1.07088	−0.535438	+	0.844575i	$0.679853\pi$
$282$	−3.22787	−0.192217
$283$	4.80479	0.285615	0.142808	−	0.989750i	$-0.454387\pi$
$283$	4.80479	0.285615	0.142808	+	0.989750i	$0.454387\pi$
$284$	−7.54007	−0.447421
$285$	0.664579	0.0393663
$286$	−0.642110	−0.0379688
$287$	0	0
$288$	4.99338	0.294238
$289$	4.88958	0.287622
$290$	−0.589881	−0.0346390
$291$	−2.82726	−0.165737
$292$	5.32226	0.311462
$293$	−4.13058	−0.241311	−0.120655	−	0.992694i	$-0.538500\pi$
$293$	−4.13058	−0.241311	−0.120655	+	0.992694i	$0.538500\pi$
$294$	−19.7908	−1.15422
$295$	−0.0872524	−0.00508003
$296$	0	0
$297$	−7.86812	−0.456554
$298$	14.6654	0.849542
$299$	3.52505	0.203859
$300$	−14.1176	−0.815079
$301$	0	0
$302$	9.49184	0.546194
$303$	29.1681	1.67566
$304$	−2.88989	−0.165747
$305$	0.428534	0.0245378
$306$	23.3622	1.33553
$307$	−2.30523	−0.131566	−0.0657832	−	0.997834i	$-0.520955\pi$
$307$	−2.30523	−0.131566	−0.0657832	+	0.997834i	$0.520955\pi$
$308$	0	0
$309$	−10.6996	−0.608678
$310$	0.0813392	0.00461975
$311$	−4.79908	−0.272131	−0.136066	−	0.990700i	$-0.543446\pi$
$311$	−4.79908	−0.272131	−0.136066	+	0.990700i	$0.543446\pi$
$312$	1.30035	0.0736179
$313$	−8.73402	−0.493676	−0.246838	−	0.969057i	$-0.579392\pi$
$313$	−8.73402	−0.493676	−0.246838	+	0.969057i	$0.579392\pi$
$314$	−15.7483	−0.888728
$315$	0	0
$316$	−6.38916	−0.359418
$317$	26.1000	1.46592	0.732962	−	0.680269i	$-0.238137\pi$
$317$	26.1000	1.46592	0.732962	+	0.680269i	$0.238137\pi$
$318$	−7.01661	−0.393472
$319$	−10.1246	−0.566871
$320$	−0.0813392	−0.00454700
$321$	16.1957	0.903957
$322$	0	0
$323$	−13.5207	−0.752314
$324$	0.953731	0.0529851
$325$	−2.29662	−0.127394
$326$	16.6795	0.923793
$327$	−21.4430	−1.18580
$328$	9.73155	0.537335
$329$	0	0
$330$	0.321055	0.0176735
$331$	−1.34176	−0.0737498	−0.0368749	−	0.999320i	$-0.511740\pi$
$331$	−1.34176	−0.0737498	−0.0368749	+	0.999320i	$0.511740\pi$
$332$	−2.44670	−0.134280
$333$	0	0
$334$	12.3737	0.677057
$335$	−0.854100	−0.0466645
$336$	0	0
$337$	−22.4914	−1.22519	−0.612594	−	0.790398i	$-0.709874\pi$
$337$	−22.4914	−1.22519	−0.612594	+	0.790398i	$0.709874\pi$
$338$	−12.7885	−0.695601
$339$	17.7339	0.963173
$340$	−0.380556	−0.0206385
$341$	1.39609	0.0756027
$342$	−14.4303	−0.780303
$343$	0	0
$344$	1.39609	0.0752723
$345$	−1.76253	−0.0948912
$346$	0.0775757	0.00417050
$347$	1.90442	0.102235	0.0511173	−	0.998693i	$-0.483722\pi$
$347$	1.90442	0.102235	0.0511173	+	0.998693i	$0.483722\pi$
$348$	20.5036	1.09911
$349$	25.7239	1.37697	0.688483	−	0.725252i	$-0.258277\pi$
$349$	25.7239	1.37697	0.688483	+	0.725252i	$0.258277\pi$
$350$	0	0
$351$	2.59210	0.138356
$352$	−1.39609	−0.0744120
$353$	−26.7681	−1.42472	−0.712362	−	0.701812i	$-0.752375\pi$
$353$	−26.7681	−1.42472	−0.712362	+	0.701812i	$0.752375\pi$
$354$	3.03279	0.161191
$355$	0.613303	0.0325507
$356$	10.7721	0.570918
$357$	0	0
$358$	−11.7114	−0.618968
$359$	−23.2865	−1.22901	−0.614507	−	0.788911i	$-0.710645\pi$
$359$	−23.2865	−1.22901	−0.614507	+	0.788911i	$0.710645\pi$
$360$	−0.406158	−0.0214064
$361$	−10.6485	−0.560449
$362$	−11.6614	−0.612910
$363$	−25.5893	−1.34309
$364$	0	0
$365$	−0.432908	−0.0226595
$366$	−14.8954	−0.778593
$367$	19.4226	1.01385	0.506925	−	0.861990i	$-0.330782\pi$
$367$	19.4226	1.01385	0.506925	+	0.861990i	$0.330782\pi$
$368$	7.66426	0.399527
$369$	48.5934	2.52967
$370$	0	0
$371$	0	0
$372$	−2.82726	−0.146586
$373$	−4.76839	−0.246898	−0.123449	−	0.992351i	$-0.539395\pi$
$373$	−4.76839	−0.246898	−0.123449	+	0.992351i	$0.539395\pi$
$374$	−6.53180	−0.337752
$375$	2.29815	0.118676
$376$	−1.14170	−0.0588785
$377$	3.33549	0.171787
$378$	0	0
$379$	9.87700	0.507347	0.253674	−	0.967290i	$-0.418361\pi$
$379$	9.87700	0.507347	0.253674	+	0.967290i	$0.418361\pi$
$380$	0.235061	0.0120584
$381$	17.1262	0.877403
$382$	18.8491	0.964404
$383$	−0.877828	−0.0448549	−0.0224274	−	0.999748i	$-0.507139\pi$
$383$	−0.877828	−0.0448549	−0.0224274	+	0.999748i	$0.507139\pi$
$384$	2.82726	0.144278
$385$	0	0
$386$	−7.83669	−0.398877
$387$	6.97123	0.354368
$388$	−1.00000	−0.0507673
$389$	−28.5435	−1.44721	−0.723607	−	0.690212i	$-0.757517\pi$
$389$	−28.5435	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$390$	−0.105769	−0.00535584
$391$	35.8583	1.81343
$392$	−7.00000	−0.353553
$393$	−31.1210	−1.56984
$394$	−19.4071	−0.977716
$395$	0.519689	0.0261484
$396$	−6.97123	−0.350318
$397$	25.2631	1.26792	0.633958	−	0.773367i	$-0.281429\pi$
$397$	25.2631	1.26792	0.633958	+	0.773367i	$0.281429\pi$
$398$	−10.3176	−0.517177
$399$	0	0
$400$	−4.99338	−0.249669
$401$	−16.2444	−0.811206	−0.405603	−	0.914049i	$-0.632939\pi$
$401$	−16.2444	−0.811206	−0.405603	+	0.914049i	$0.632939\pi$
$402$	29.6876	1.48068
$403$	−0.459934	−0.0229109
$404$	10.3168	0.513278
$405$	−0.0775757	−0.00385477
$406$	0	0
$407$	0	0
$408$	13.2277	0.654868
$409$	3.07969	0.152281	0.0761405	−	0.997097i	$-0.475740\pi$
$409$	3.07969	0.152281	0.0761405	+	0.997097i	$0.475740\pi$
$410$	−0.791556	−0.0390922
$411$	−41.7732	−2.06052
$412$	−3.78444	−0.186446
$413$	0	0
$414$	38.2706	1.88090
$415$	0.199013	0.00976915
$416$	0.459934	0.0225501
$417$	−8.25522	−0.404260
$418$	4.03456	0.197337
$419$	4.42720	0.216283	0.108142	−	0.994136i	$-0.465510\pi$
$419$	4.42720	0.216283	0.108142	+	0.994136i	$0.465510\pi$
$420$	0	0
$421$	6.87961	0.335292	0.167646	−	0.985847i	$-0.446383\pi$
$421$	6.87961	0.335292	0.167646	+	0.985847i	$0.446383\pi$
$422$	4.39409	0.213901
$423$	−5.70093	−0.277189
$424$	−2.48177	−0.120526
$425$	−23.3622	−1.13323
$426$	−21.3177	−1.03285
$427$	0	0
$428$	5.72842	0.276894
$429$	−1.81541	−0.0876489
$430$	−0.113557	−0.00547621
$431$	−1.39110	−0.0670068	−0.0335034	−	0.999439i	$-0.510666\pi$
$431$	−1.39110	−0.0670068	−0.0335034	+	0.999439i	$0.510666\pi$
$432$	5.63581	0.271153
$433$	37.2436	1.78981	0.894907	−	0.446252i	$-0.147241\pi$
$433$	37.2436	1.78981	0.894907	+	0.446252i	$0.147241\pi$
$434$	0	0
$435$	−1.66775	−0.0799623
$436$	−7.58437	−0.363226
$437$	−22.1489	−1.05953
$438$	15.0474	0.718993
$439$	1.53765	0.0733882	0.0366941	−	0.999327i	$-0.488317\pi$
$439$	1.53765	0.0733882	0.0366941	+	0.999327i	$0.488317\pi$
$440$	0.113557	0.00541362
$441$	−34.9537	−1.66446
$442$	2.15186	0.102353
$443$	−23.3876	−1.11118	−0.555590	−	0.831457i	$-0.687507\pi$
$443$	−23.3876	−1.11118	−0.555590	+	0.831457i	$0.687507\pi$
$444$	0	0
$445$	−0.876190	−0.0415354
$446$	−0.104699	−0.00495764
$447$	41.4628	1.96112
$448$	0	0
$449$	16.1563	0.762465	0.381232	−	0.924479i	$-0.375500\pi$
$449$	16.1563	0.762465	0.381232	+	0.924479i	$0.375500\pi$
$450$	−24.9339	−1.17539
$451$	−13.5862	−0.639747
$452$	6.27247	0.295032
$453$	26.8359	1.26086
$454$	11.8717	0.557166
$455$	0	0
$456$	−8.17047	−0.382617
$457$	−32.7376	−1.53140	−0.765701	−	0.643197i	$-0.777608\pi$
$457$	−32.7376	−1.53140	−0.765701	+	0.643197i	$0.777608\pi$
$458$	−19.0069	−0.888136
$459$	26.3679	1.23075
$460$	−0.623405	−0.0290664
$461$	−34.6413	−1.61341	−0.806704	−	0.590956i	$-0.798751\pi$
$461$	−34.6413	−1.61341	−0.806704	+	0.590956i	$0.798751\pi$
$462$	0	0
$463$	36.7043	1.70579	0.852896	−	0.522081i	$-0.174844\pi$
$463$	36.7043	1.70579	0.852896	+	0.522081i	$0.174844\pi$
$464$	7.25212	0.336671
$465$	0.229967	0.0106645
$466$	14.8095	0.686035
$467$	−15.9766	−0.739308	−0.369654	−	0.929170i	$-0.620524\pi$
$467$	−15.9766	−0.739308	−0.369654	+	0.929170i	$0.620524\pi$
$468$	2.29662	0.106162
$469$	0	0
$470$	0.0928646	0.00428353
$471$	−44.5245	−2.05158
$472$	1.07270	0.0493749
$473$	−1.94908	−0.0896186
$474$	−18.0638	−0.829698
$475$	14.4303	0.662109
$476$	0	0
$477$	−12.3924	−0.567411
$478$	20.0977	0.919249
$479$	−15.0186	−0.686219	−0.343110	−	0.939295i	$-0.611480\pi$
$479$	−15.0186	−0.686219	−0.343110	+	0.939295i	$0.611480\pi$
$480$	−0.229967	−0.0104965
$481$	0	0
$482$	−4.88651	−0.222574
$483$	0	0
$484$	−9.05092	−0.411406
$485$	0.0813392	0.00369342
$486$	−14.2110	−0.644623
$487$	−29.9115	−1.35542	−0.677710	−	0.735329i	$-0.737028\pi$
$487$	−29.9115	−1.35542	−0.677710	+	0.735329i	$0.737028\pi$
$488$	−5.26849	−0.238493
$489$	47.1573	2.13253
$490$	0.569374	0.0257217
$491$	8.34925	0.376796	0.188398	−	0.982093i	$-0.439670\pi$
$491$	8.34925	0.376796	0.188398	+	0.982093i	$0.439670\pi$
$492$	27.5136	1.24041
$493$	33.9300	1.52813
$494$	−1.32916	−0.0598016
$495$	0.567034	0.0254863
$496$	−1.00000	−0.0449013
$497$	0	0
$498$	−6.91745	−0.309979
$499$	8.35175	0.373876	0.186938	−	0.982372i	$-0.440144\pi$
$499$	8.35175	0.373876	0.186938	+	0.982372i	$0.440144\pi$
$500$	0.812854	0.0363519
$501$	34.9835	1.56295
$502$	−20.2088	−0.901961
$503$	22.0946	0.985150	0.492575	−	0.870270i	$-0.336056\pi$
$503$	22.0946	0.985150	0.492575	+	0.870270i	$0.336056\pi$
$504$	0	0
$505$	−0.839156	−0.0373420
$506$	−10.7000	−0.475674
$507$	−36.1563	−1.60576
$508$	6.05754	0.268760
$509$	17.9929	0.797520	0.398760	−	0.917055i	$-0.369441\pi$
$509$	17.9929	0.797520	0.398760	+	0.917055i	$0.369441\pi$
$510$	−1.07593	−0.0476430
$511$	0	0
$512$	1.00000	0.0441942
$513$	−16.2869	−0.719083
$514$	3.25275	0.143473
$515$	0.307823	0.0135643
$516$	3.94712	0.173762
$517$	1.59391	0.0701003
$518$	0	0
$519$	0.219327	0.00962737
$520$	−0.0374106	−0.00164056
$521$	−17.8774	−0.783224	−0.391612	−	0.920130i	$-0.628082\pi$
$521$	−17.8774	−0.783224	−0.391612	+	0.920130i	$0.628082\pi$
$522$	36.2126	1.58498
$523$	−27.6311	−1.20822	−0.604112	−	0.796900i	$-0.706472\pi$
$523$	−27.6311	−1.20822	−0.604112	+	0.796900i	$0.706472\pi$
$524$	−11.0075	−0.480864
$525$	0	0
$526$	−25.9459	−1.13129
$527$	−4.67863	−0.203804
$528$	−3.94712	−0.171776
$529$	35.7409	1.55395
$530$	0.201865	0.00876847
$531$	5.35639	0.232448
$532$	0	0
$533$	4.47587	0.193871
$534$	30.4554	1.31793
$535$	−0.465945	−0.0201446
$536$	10.5005	0.453552
$537$	−33.1112	−1.42885
$538$	0.479359	0.0206666
$539$	9.77265	0.420938
$540$	−0.458412	−0.0197269
$541$	−5.82839	−0.250582	−0.125291	−	0.992120i	$-0.539986\pi$
$541$	−5.82839	−0.250582	−0.125291	+	0.992120i	$0.539986\pi$
$542$	−9.58616	−0.411761
$543$	−32.9698	−1.41487
$544$	4.67863	0.200595
$545$	0.616907	0.0264254
$546$	0	0
$547$	21.1665	0.905013	0.452507	−	0.891761i	$-0.350530\pi$
$547$	21.1665	0.905013	0.452507	+	0.891761i	$0.350530\pi$
$548$	−14.7752	−0.631164
$549$	−26.3076	−1.12278
$550$	6.97123	0.297254
$551$	−20.9578	−0.892834
$552$	21.6688	0.922287
$553$	0	0
$554$	−15.5136	−0.659110
$555$	0	0
$556$	−2.91987	−0.123830
$557$	18.3659	0.778188	0.389094	−	0.921198i	$-0.372788\pi$
$557$	18.3659	0.778188	0.389094	+	0.921198i	$0.372788\pi$
$558$	−4.99338	−0.211387
$559$	0.642110	0.0271584
$560$	0	0
$561$	−18.4671	−0.779681
$562$	−17.9511	−0.757223
$563$	−17.4668	−0.736138	−0.368069	−	0.929799i	$-0.619981\pi$
$563$	−17.4668	−0.736138	−0.368069	+	0.929799i	$0.619981\pi$
$564$	−3.22787	−0.135918
$565$	−0.510198	−0.0214642
$566$	4.80479	0.201960
$567$	0	0
$568$	−7.54007	−0.316374
$569$	−11.2227	−0.470479	−0.235240	−	0.971937i	$-0.575588\pi$
$569$	−11.2227	−0.470479	−0.235240	+	0.971937i	$0.575588\pi$
$570$	0.664579	0.0278361
$571$	−0.323017	−0.0135178	−0.00675891	−	0.999977i	$-0.502151\pi$
$571$	−0.323017	−0.0135178	−0.00675891	+	0.999977i	$0.502151\pi$
$572$	−0.642110	−0.0268480
$573$	53.2912	2.22627
$574$	0	0
$575$	−38.2706	−1.59599
$576$	4.99338	0.208058
$577$	−15.8591	−0.660222	−0.330111	−	0.943942i	$-0.607086\pi$
$577$	−15.8591	−0.660222	−0.330111	+	0.943942i	$0.607086\pi$
$578$	4.88958	0.203380
$579$	−22.1563	−0.920786
$580$	−0.589881	−0.0244935
$581$	0	0
$582$	−2.82726	−0.117194
$583$	3.46479	0.143497
$584$	5.32226	0.220237
$585$	−0.186806	−0.00772346
$586$	−4.13058	−0.170633
$587$	−11.1410	−0.459840	−0.229920	−	0.973210i	$-0.573846\pi$
$587$	−11.1410	−0.459840	−0.229920	+	0.973210i	$0.573846\pi$
$588$	−19.7908	−0.816159
$589$	2.88989	0.119076
$590$	−0.0872524	−0.00359212
$591$	−54.8689	−2.25700
$592$	0	0
$593$	−8.50120	−0.349102	−0.174551	−	0.984648i	$-0.555847\pi$
$593$	−8.50120	−0.349102	−0.174551	+	0.984648i	$0.555847\pi$
$594$	−7.86812	−0.322833
$595$	0	0
$596$	14.6654	0.600717
$597$	−29.1706	−1.19387
$598$	3.52505	0.144150
$599$	−23.8745	−0.975487	−0.487744	−	0.872987i	$-0.662180\pi$
$599$	−23.8745	−0.975487	−0.487744	+	0.872987i	$0.662180\pi$
$600$	−14.1176	−0.576348
$601$	−33.8545	−1.38096	−0.690478	−	0.723354i	$-0.742600\pi$
$601$	−33.8545	−1.38096	−0.690478	+	0.723354i	$0.742600\pi$
$602$	0	0
$603$	52.4329	2.13523
$604$	9.49184	0.386217
$605$	0.736195	0.0299306
$606$	29.1681	1.18487
$607$	25.0450	1.01654	0.508272	−	0.861196i	$-0.330284\pi$
$607$	25.0450	1.01654	0.508272	+	0.861196i	$0.330284\pi$
$608$	−2.88989	−0.117201
$609$	0	0
$610$	0.428534	0.0173508
$611$	−0.525104	−0.0212435
$612$	23.3622	0.944361
$613$	35.4070	1.43008	0.715038	−	0.699085i	$-0.246409\pi$
$613$	35.4070	1.43008	0.715038	+	0.699085i	$0.246409\pi$
$614$	−2.30523	−0.0930314
$615$	−2.23793	−0.0902422
$616$	0	0
$617$	−17.5815	−0.707805	−0.353902	−	0.935282i	$-0.615145\pi$
$617$	−17.5815	−0.707805	−0.353902	+	0.935282i	$0.615145\pi$
$618$	−10.6996	−0.430400
$619$	−18.5831	−0.746916	−0.373458	−	0.927647i	$-0.621828\pi$
$619$	−18.5831	−0.746916	−0.373458	+	0.927647i	$0.621828\pi$
$620$	0.0813392	0.00326666
$621$	43.1943	1.73333
$622$	−4.79908	−0.192426
$623$	0	0
$624$	1.30035	0.0520557
$625$	24.9008	0.996032
$626$	−8.73402	−0.349082
$627$	11.4067	0.455541
$628$	−15.7483	−0.628425
$629$	0	0
$630$	0	0
$631$	−47.8984	−1.90680	−0.953402	−	0.301704i	$-0.902445\pi$
$631$	−47.8984	−1.90680	−0.953402	+	0.301704i	$0.902445\pi$
$632$	−6.38916	−0.254147
$633$	12.4232	0.493779
$634$	26.1000	1.03657
$635$	−0.492715	−0.0195528
$636$	−7.01661	−0.278227
$637$	−3.21953	−0.127563
$638$	−10.1246	−0.400838
$639$	−37.6504	−1.48943
$640$	−0.0813392	−0.00321521
$641$	33.6305	1.32832	0.664162	−	0.747589i	$-0.268789\pi$
$641$	33.6305	1.32832	0.664162	+	0.747589i	$0.268789\pi$
$642$	16.1957	0.639194
$643$	37.4673	1.47757	0.738783	−	0.673943i	$-0.235401\pi$
$643$	37.4673	1.47757	0.738783	+	0.673943i	$0.235401\pi$
$644$	0	0
$645$	−0.321055	−0.0126415
$646$	−13.5207	−0.531966
$647$	7.04755	0.277068	0.138534	−	0.990358i	$-0.455761\pi$
$647$	7.04755	0.277068	0.138534	+	0.990358i	$0.455761\pi$
$648$	0.953731	0.0374661
$649$	−1.49759	−0.0587854
$650$	−2.29662	−0.0900810
$651$	0	0
$652$	16.6795	0.653220
$653$	−13.3668	−0.523084	−0.261542	−	0.965192i	$-0.584231\pi$
$653$	−13.3668	−0.523084	−0.261542	+	0.965192i	$0.584231\pi$
$654$	−21.4430	−0.838487
$655$	0.895339	0.0349838
$656$	9.73155	0.379953
$657$	26.5761	1.03683
$658$	0	0
$659$	−16.6004	−0.646662	−0.323331	−	0.946286i	$-0.604803\pi$
$659$	−16.6004	−0.646662	−0.323331	+	0.946286i	$0.604803\pi$
$660$	0.321055	0.0124971
$661$	26.8795	1.04549	0.522745	−	0.852489i	$-0.324908\pi$
$661$	26.8795	1.04549	0.522745	+	0.852489i	$0.324908\pi$
$662$	−1.34176	−0.0521490
$663$	6.08386	0.236277
$664$	−2.44670	−0.0949504
$665$	0	0
$666$	0	0
$667$	55.5822	2.15215
$668$	12.3737	0.478751
$669$	−0.296011	−0.0114445
$670$	−0.854100	−0.0329968
$671$	7.35530	0.283948
$672$	0	0
$673$	−46.1339	−1.77833	−0.889166	−	0.457585i	$-0.848715\pi$
$673$	−46.1339	−1.77833	−0.889166	+	0.457585i	$0.848715\pi$
$674$	−22.4914	−0.866338
$675$	−28.1418	−1.08318
$676$	−12.7885	−0.491864
$677$	24.4398	0.939299	0.469649	−	0.882853i	$-0.344380\pi$
$677$	24.4398	0.939299	0.469649	+	0.882853i	$0.344380\pi$
$678$	17.7339	0.681066
$679$	0	0
$680$	−0.380556	−0.0145937
$681$	33.5643	1.28619
$682$	1.39609	0.0534592
$683$	−26.5910	−1.01748	−0.508739	−	0.860921i	$-0.669888\pi$
$683$	−26.5910	−1.01748	−0.508739	+	0.860921i	$0.669888\pi$
$684$	−14.4303	−0.551758
$685$	1.20180	0.0459184
$686$	0	0
$687$	−53.7375	−2.05021
$688$	1.39609	0.0532256
$689$	−1.14145	−0.0434858
$690$	−1.76253	−0.0670982
$691$	−41.3940	−1.57470	−0.787350	−	0.616506i	$-0.788548\pi$
$691$	−41.3940	−1.57470	−0.787350	+	0.616506i	$0.788548\pi$
$692$	0.0775757	0.00294899
$693$	0	0
$694$	1.90442	0.0722908
$695$	0.237500	0.00900887
$696$	20.5036	0.777187
$697$	45.5303	1.72458
$698$	25.7239	0.973663
$699$	41.8702	1.58368
$700$	0	0
$701$	−7.65273	−0.289040	−0.144520	−	0.989502i	$-0.546164\pi$
$701$	−7.65273	−0.289040	−0.144520	+	0.989502i	$0.546164\pi$
$702$	2.59210	0.0978324
$703$	0	0
$704$	−1.39609	−0.0526172
$705$	0.262552	0.00988829
$706$	−26.7681	−1.00743
$707$	0	0
$708$	3.03279	0.113979
$709$	−30.3480	−1.13974	−0.569872	−	0.821733i	$-0.693007\pi$
$709$	−30.3480	−1.13974	−0.569872	+	0.821733i	$0.693007\pi$
$710$	0.613303	0.0230168
$711$	−31.9035	−1.19648
$712$	10.7721	0.403700
$713$	−7.66426	−0.287029
$714$	0	0
$715$	0.0522287	0.00195324
$716$	−11.7114	−0.437676
$717$	56.8215	2.12204
$718$	−23.2865	−0.869044
$719$	31.5767	1.17761	0.588805	−	0.808275i	$-0.299598\pi$
$719$	31.5767	1.17761	0.588805	+	0.808275i	$0.299598\pi$
$720$	−0.406158	−0.0151366
$721$	0	0
$722$	−10.6485	−0.396297
$723$	−13.8154	−0.513801
$724$	−11.6614	−0.433393
$725$	−36.2126	−1.34490
$726$	−25.5893	−0.949708
$727$	23.2392	0.861896	0.430948	−	0.902377i	$-0.358179\pi$
$727$	23.2392	0.861896	0.430948	+	0.902377i	$0.358179\pi$
$728$	0	0
$729$	−43.0393	−1.59405
$730$	−0.432908	−0.0160227
$731$	6.53180	0.241588
$732$	−14.8954	−0.550549
$733$	14.5572	0.537681	0.268840	−	0.963185i	$-0.413360\pi$
$733$	14.5572	0.537681	0.268840	+	0.963185i	$0.413360\pi$
$734$	19.4226	0.716901
$735$	1.60977	0.0593772
$736$	7.66426	0.282509
$737$	−14.6596	−0.539995
$738$	48.5934	1.78875
$739$	4.77591	0.175685	0.0878424	−	0.996134i	$-0.472003\pi$
$739$	4.77591	0.175685	0.0878424	+	0.996134i	$0.472003\pi$
$740$	0	0
$741$	−3.75787	−0.138049
$742$	0	0
$743$	53.0623	1.94667	0.973334	−	0.229391i	$-0.0736734\pi$
$743$	53.0623	1.94667	0.973334	+	0.229391i	$0.0736734\pi$
$744$	−2.82726	−0.103652
$745$	−1.19287	−0.0437033
$746$	−4.76839	−0.174583
$747$	−12.2173	−0.447008
$748$	−6.53180	−0.238826
$749$	0	0
$750$	2.29815	0.0839164
$751$	−38.7341	−1.41343	−0.706714	−	0.707499i	$-0.749823\pi$
$751$	−38.7341	−1.41343	−0.706714	+	0.707499i	$0.749823\pi$
$752$	−1.14170	−0.0416334
$753$	−57.1354	−2.08213
$754$	3.33549	0.121472
$755$	−0.772058	−0.0280981
$756$	0	0
$757$	17.4367	0.633748	0.316874	−	0.948468i	$-0.397367\pi$
$757$	17.4367	0.633748	0.316874	+	0.948468i	$0.397367\pi$
$758$	9.87700	0.358749
$759$	−30.2517	−1.09807
$760$	0.235061	0.00852657
$761$	−20.6384	−0.748140	−0.374070	−	0.927400i	$-0.622038\pi$
$761$	−20.6384	−0.748140	−0.374070	+	0.927400i	$0.622038\pi$
$762$	17.1262	0.620418
$763$	0	0
$764$	18.8491	0.681936
$765$	−1.90026	−0.0687041
$766$	−0.877828	−0.0317172
$767$	0.493370	0.0178146
$768$	2.82726	0.102020
$769$	−25.6258	−0.924091	−0.462046	−	0.886856i	$-0.652884\pi$
$769$	−25.6258	−0.924091	−0.462046	+	0.886856i	$0.652884\pi$
$770$	0	0
$771$	9.19636	0.331199
$772$	−7.83669	−0.282049
$773$	6.77994	0.243858	0.121929	−	0.992539i	$-0.461092\pi$
$773$	6.77994	0.243858	0.121929	+	0.992539i	$0.461092\pi$
$774$	6.97123	0.250576
$775$	4.99338	0.179368
$776$	−1.00000	−0.0358979
$777$	0	0
$778$	−28.5435	−1.02333
$779$	−28.1231	−1.00762
$780$	−0.105769	−0.00378715
$781$	10.5266	0.376673
$782$	35.8583	1.28229
$783$	40.8716	1.46063
$784$	−7.00000	−0.250000
$785$	1.28095	0.0457192
$786$	−31.1210	−1.11005
$787$	−23.3627	−0.832789	−0.416394	−	0.909184i	$-0.636706\pi$
$787$	−23.3627	−0.832789	−0.416394	+	0.909184i	$0.636706\pi$
$788$	−19.4071	−0.691350
$789$	−73.3557	−2.61153
$790$	0.519689	0.0184897
$791$	0	0
$792$	−6.97123	−0.247712
$793$	−2.42315	−0.0860487
$794$	25.2631	0.896553
$795$	0.570725	0.0202415
$796$	−10.3176	−0.365699
$797$	15.9332	0.564384	0.282192	−	0.959358i	$-0.408939\pi$
$797$	15.9332	0.564384	0.282192	+	0.959358i	$0.408939\pi$
$798$	0	0
$799$	−5.34157	−0.188971
$800$	−4.99338	−0.176543
$801$	53.7890	1.90054
$802$	−16.2444	−0.573610
$803$	−7.43037	−0.262212
$804$	29.6876	1.04700
$805$	0	0
$806$	−0.459934	−0.0162005
$807$	1.35527	0.0477078
$808$	10.3168	0.362942
$809$	−33.1492	−1.16547	−0.582733	−	0.812664i	$-0.698017\pi$
$809$	−33.1492	−1.16547	−0.582733	+	0.812664i	$0.698017\pi$
$810$	−0.0775757	−0.00272573
$811$	24.6262	0.864743	0.432372	−	0.901695i	$-0.357677\pi$
$811$	24.6262	0.864743	0.432372	+	0.901695i	$0.357677\pi$
$812$	0	0
$813$	−27.1025	−0.950527
$814$	0	0
$815$	−1.35670	−0.0475231
$816$	13.2277	0.463062
$817$	−4.03456	−0.141151
$818$	3.07969	0.107679
$819$	0	0
$820$	−0.791556	−0.0276423
$821$	9.27959	0.323860	0.161930	−	0.986802i	$-0.448228\pi$
$821$	9.27959	0.323860	0.161930	+	0.986802i	$0.448228\pi$
$822$	−41.7732	−1.45701
$823$	−23.4885	−0.818759	−0.409380	−	0.912364i	$-0.634255\pi$
$823$	−23.4885	−0.818759	−0.409380	+	0.912364i	$0.634255\pi$
$824$	−3.78444	−0.131837
$825$	19.7095	0.686195
$826$	0	0
$827$	5.74030	0.199610	0.0998049	−	0.995007i	$-0.468178\pi$
$827$	5.74030	0.199610	0.0998049	+	0.995007i	$0.468178\pi$
$828$	38.2706	1.33000
$829$	21.4125	0.743687	0.371844	−	0.928295i	$-0.378726\pi$
$829$	21.4125	0.743687	0.371844	+	0.928295i	$0.378726\pi$
$830$	0.199013	0.00690783
$831$	−43.8609	−1.52152
$832$	0.459934	0.0159453
$833$	−32.7504	−1.13473
$834$	−8.25522	−0.285855
$835$	−1.00646	−0.0348301
$836$	4.03456	0.139538
$837$	−5.63581	−0.194802
$838$	4.42720	0.152935
$839$	5.54233	0.191343	0.0956713	−	0.995413i	$-0.469500\pi$
$839$	5.54233	0.191343	0.0956713	+	0.995413i	$0.469500\pi$
$840$	0	0
$841$	23.5932	0.813560
$842$	6.87961	0.237087
$843$	−50.7525	−1.74801
$844$	4.39409	0.151251
$845$	1.04020	0.0357841
$846$	−5.70093	−0.196002
$847$	0	0
$848$	−2.48177	−0.0852244
$849$	13.5844	0.466214
$850$	−23.3622	−0.801317
$851$	0	0
$852$	−21.3177	−0.730333
$853$	−37.5163	−1.28453	−0.642267	−	0.766481i	$-0.722006\pi$
$853$	−37.5163	−1.28453	−0.642267	+	0.766481i	$0.722006\pi$
$854$	0	0
$855$	1.17375	0.0401415
$856$	5.72842	0.195793
$857$	15.0054	0.512576	0.256288	−	0.966600i	$-0.417500\pi$
$857$	15.0054	0.512576	0.256288	+	0.966600i	$0.417500\pi$
$858$	−1.81541	−0.0619771
$859$	0.193753	0.00661078	0.00330539	−	0.999995i	$-0.498948\pi$
$859$	0.193753	0.00661078	0.00330539	+	0.999995i	$0.498948\pi$
$860$	−0.113557	−0.00387226
$861$	0	0
$862$	−1.39110	−0.0473809
$863$	34.6694	1.18016	0.590080	−	0.807345i	$-0.299096\pi$
$863$	34.6694	1.18016	0.590080	+	0.807345i	$0.299096\pi$
$864$	5.63581	0.191734
$865$	−0.00630995	−0.000214545 0
$866$	37.2436	1.26559
$867$	13.8241	0.469491
$868$	0	0
$869$	8.91987	0.302586
$870$	−1.66775	−0.0565419
$871$	4.82952	0.163642
$872$	−7.58437	−0.256839
$873$	−4.99338	−0.169000
$874$	−22.1489	−0.749197
$875$	0	0
$876$	15.0474	0.508405
$877$	−19.5742	−0.660973	−0.330487	−	0.943811i	$-0.607213\pi$
$877$	−19.5742	−0.660973	−0.330487	+	0.943811i	$0.607213\pi$
$878$	1.53765	0.0518933
$879$	−11.6782	−0.393896
$880$	0.113557	0.00382801
$881$	−4.70825	−0.158625	−0.0793125	−	0.996850i	$-0.525273\pi$
$881$	−4.70825	−0.158625	−0.0793125	+	0.996850i	$0.525273\pi$
$882$	−34.9537	−1.17695
$883$	19.1821	0.645528	0.322764	−	0.946480i	$-0.395388\pi$
$883$	19.1821	0.645528	0.322764	+	0.946480i	$0.395388\pi$
$884$	2.15186	0.0723748
$885$	−0.246685	−0.00829222
$886$	−23.3876	−0.785722
$887$	−20.4288	−0.685932	−0.342966	−	0.939348i	$-0.611432\pi$
$887$	−20.4288	−0.685932	−0.342966	+	0.939348i	$0.611432\pi$
$888$	0	0
$889$	0	0
$890$	−0.876190	−0.0293700
$891$	−1.33150	−0.0446069
$892$	−0.104699	−0.00350558
$893$	3.29938	0.110409
$894$	41.4628	1.38672
$895$	0.952598	0.0318418
$896$	0	0
$897$	9.96623	0.332763
$898$	16.1563	0.539144
$899$	−7.25212	−0.241872
$900$	−24.9339	−0.831129
$901$	−11.6113	−0.386828
$902$	−13.5862	−0.452370
$903$	0	0
$904$	6.27247	0.208619
$905$	0.948530	0.0315302
$906$	26.8359	0.891562
$907$	49.7666	1.65247	0.826236	−	0.563324i	$-0.190478\pi$
$907$	49.7666	1.65247	0.826236	+	0.563324i	$0.190478\pi$
$908$	11.8717	0.393976
$909$	51.5155	1.70866
$910$	0	0
$911$	−11.3102	−0.374722	−0.187361	−	0.982291i	$-0.559993\pi$
$911$	−11.3102	−0.374722	−0.187361	+	0.982291i	$0.559993\pi$
$912$	−8.17047	−0.270551
$913$	3.41582	0.113047
$914$	−32.7376	−1.08286
$915$	1.21158	0.0400535
$916$	−19.0069	−0.628007
$917$	0	0
$918$	26.3679	0.870269
$919$	26.4219	0.871580	0.435790	−	0.900048i	$-0.356469\pi$
$919$	26.4219	0.871580	0.435790	+	0.900048i	$0.356469\pi$
$920$	−0.623405	−0.0205531
$921$	−6.51747	−0.214758
$922$	−34.6413	−1.14085
$923$	−3.46793	−0.114148
$924$	0	0
$925$	0	0
$926$	36.7043	1.20618
$927$	−18.8971	−0.620664
$928$	7.25212	0.238063
$929$	23.5176	0.771587	0.385794	−	0.922585i	$-0.373928\pi$
$929$	23.5176	0.771587	0.385794	+	0.922585i	$0.373928\pi$
$930$	0.229967	0.00754091
$931$	20.2292	0.662987
$932$	14.8095	0.485100
$933$	−13.5682	−0.444204
$934$	−15.9766	−0.522770
$935$	0.531292	0.0173751
$936$	2.29662	0.0750675
$937$	26.3629	0.861237	0.430619	−	0.902534i	$-0.358295\pi$
$937$	26.3629	0.861237	0.430619	+	0.902534i	$0.358295\pi$
$938$	0	0
$939$	−24.6933	−0.805836
$940$	0.0928646	0.00302891
$941$	29.4809	0.961051	0.480526	−	0.876981i	$-0.340446\pi$
$941$	29.4809	0.961051	0.480526	+	0.876981i	$0.340446\pi$
$942$	−44.5245	−1.45069
$943$	74.5852	2.42883
$944$	1.07270	0.0349134
$945$	0	0
$946$	−1.94908	−0.0633700
$947$	33.8662	1.10050	0.550251	−	0.834999i	$-0.314532\pi$
$947$	33.8662	1.10050	0.550251	+	0.834999i	$0.314532\pi$
$948$	−18.0638	−0.586685
$949$	2.44789	0.0794618
$950$	14.4303	0.468182
$951$	73.7916	2.39285
$952$	0	0
$953$	15.4786	0.501401	0.250701	−	0.968065i	$-0.419339\pi$
$953$	15.4786	0.501401	0.250701	+	0.968065i	$0.419339\pi$
$954$	−12.3924	−0.401220
$955$	−1.53317	−0.0496122
$956$	20.0977	0.650007
$957$	−28.6250	−0.925313
$958$	−15.0186	−0.485230
$959$	0	0
$960$	−0.229967	−0.00742215
$961$	1.00000	0.0322581
$962$	0	0
$963$	28.6042	0.921757
$964$	−4.88651	−0.157384
$965$	0.637430	0.0205196
$966$	0	0
$967$	−19.7298	−0.634467	−0.317233	−	0.948348i	$-0.602754\pi$
$967$	−19.7298	−0.634467	−0.317233	+	0.948348i	$0.602754\pi$
$968$	−9.05092	−0.290908
$969$	−38.2266	−1.22801
$970$	0.0813392	0.00261164
$971$	−43.8832	−1.40828	−0.704139	−	0.710062i	$-0.748667\pi$
$971$	−43.8832	−1.40828	−0.704139	+	0.710062i	$0.748667\pi$
$972$	−14.2110	−0.455818
$973$	0	0
$974$	−29.9115	−0.958427
$975$	−6.49315	−0.207947
$976$	−5.26849	−0.168640
$977$	−0.686921	−0.0219765	−0.0109883	−	0.999940i	$-0.503498\pi$
$977$	−0.686921	−0.0219765	−0.0109883	+	0.999940i	$0.503498\pi$
$978$	47.1573	1.50792
$979$	−15.0388	−0.480642
$980$	0.569374	0.0181880
$981$	−37.8717	−1.20915
$982$	8.34925	0.266435
$983$	49.5436	1.58019	0.790097	−	0.612982i	$-0.210030\pi$
$983$	49.5436	1.58019	0.790097	+	0.612982i	$0.210030\pi$
$984$	27.5136	0.877102
$985$	1.57856	0.0502971
$986$	33.9300	1.08055
$987$	0	0
$988$	−1.32916	−0.0422861
$989$	10.7000	0.340241
$990$	0.567034	0.0180215
$991$	−11.2686	−0.357960	−0.178980	−	0.983853i	$-0.557280\pi$
$991$	−11.2686	−0.357960	−0.178980	+	0.983853i	$0.557280\pi$
$992$	−1.00000	−0.0317500
$993$	−3.79350	−0.120383
$994$	0	0
$995$	0.839229	0.0266053
$996$	−6.91745	−0.219188
$997$	28.0867	0.889515	0.444758	−	0.895651i	$-0.353290\pi$
$997$	28.0867	0.889515	0.444758	+	0.895651i	$0.353290\pi$
$998$	8.35175	0.264370
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.d.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.d.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.82726 q^{3} +1.00000 q^{4} -0.0813392 q^{5} +2.82726 q^{6} +1.00000 q^{8} +4.99338 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.82726 q^{3} +1.00000 q^{4} -0.0813392 q^{5} +2.82726 q^{6} +1.00000 q^{8} +4.99338 q^{9} -0.0813392 q^{10} -1.39609 q^{11} +2.82726 q^{12} +0.459934 q^{13} -0.229967 q^{15} +1.00000 q^{16} +4.67863 q^{17} +4.99338 q^{18} -2.88989 q^{19} -0.0813392 q^{20} -1.39609 q^{22} +7.66426 q^{23} +2.82726 q^{24} -4.99338 q^{25} +0.459934 q^{26} +5.63581 q^{27} +7.25212 q^{29} -0.229967 q^{30} -1.00000 q^{31} +1.00000 q^{32} -3.94712 q^{33} +4.67863 q^{34} +4.99338 q^{36} -2.88989 q^{38} +1.30035 q^{39} -0.0813392 q^{40} +9.73155 q^{41} +1.39609 q^{43} -1.39609 q^{44} -0.406158 q^{45} +7.66426 q^{46} -1.14170 q^{47} +2.82726 q^{48} -7.00000 q^{49} -4.99338 q^{50} +13.2277 q^{51} +0.459934 q^{52} -2.48177 q^{53} +5.63581 q^{54} +0.113557 q^{55} -8.17047 q^{57} +7.25212 q^{58} +1.07270 q^{59} -0.229967 q^{60} -5.26849 q^{61} -1.00000 q^{62} +1.00000 q^{64} -0.0374106 q^{65} -3.94712 q^{66} +10.5005 q^{67} +4.67863 q^{68} +21.6688 q^{69} -7.54007 q^{71} +4.99338 q^{72} +5.32226 q^{73} -14.1176 q^{75} -2.88989 q^{76} +1.30035 q^{78} -6.38916 q^{79} -0.0813392 q^{80} +0.953731 q^{81} +9.73155 q^{82} -2.44670 q^{83} -0.380556 q^{85} +1.39609 q^{86} +20.5036 q^{87} -1.39609 q^{88} +10.7721 q^{89} -0.406158 q^{90} +7.66426 q^{92} -2.82726 q^{93} -1.14170 q^{94} +0.235061 q^{95} +2.82726 q^{96} -1.00000 q^{97} -7.00000 q^{98} -6.97123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} - 4 q^{5} + 5 q^{8} + q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^4 - 4 * q^5 + 5 * q^8 + q^9	\( 5 q + 5 q^{2} + 5 q^{4} - 4 q^{5} + 5 q^{8} + q^{9} - 4 q^{10} + 4 q^{11} + 5 q^{16} + 14 q^{17} + q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - q^{25} + 6 q^{27} + 12 q^{29} - 5 q^{31} + 5 q^{32} + 14 q^{34} + q^{36} - 10 q^{38} + 20 q^{39} - 4 q^{40} + 2 q^{41} - 4 q^{43} + 4 q^{44} + 2 q^{45} + 40 q^{47} - 35 q^{49} - q^{50} + 6 q^{51} + 30 q^{53} + 6 q^{54} - 12 q^{55} + 4 q^{57} + 12 q^{58} + 22 q^{59} - 16 q^{61} - 5 q^{62} + 5 q^{64} + 12 q^{65} + 4 q^{67} + 14 q^{68} + 34 q^{69} - 40 q^{71} + q^{72} + 18 q^{73} - 6 q^{75} - 10 q^{76} + 20 q^{78} + 20 q^{79} - 4 q^{80} + 9 q^{81} + 2 q^{82} + 38 q^{83} - 38 q^{85} - 4 q^{86} + 20 q^{87} + 4 q^{88} + 18 q^{89} + 2 q^{90} + 40 q^{94} + 8 q^{95} - 5 q^{97} - 35 q^{98} - 34 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^4 - 4 * q^5 + 5 * q^8 + q^9 - 4 * q^10 + 4 * q^11 + 5 * q^16 + 14 * q^17 + q^18 - 10 * q^19 - 4 * q^20 + 4 * q^22 - q^25 + 6 * q^27 + 12 * q^29 - 5 * q^31 + 5 * q^32 + 14 * q^34 + q^36 - 10 * q^38 + 20 * q^39 - 4 * q^40 + 2 * q^41 - 4 * q^43 + 4 * q^44 + 2 * q^45 + 40 * q^47 - 35 * q^49 - q^50 + 6 * q^51 + 30 * q^53 + 6 * q^54 - 12 * q^55 + 4 * q^57 + 12 * q^58 + 22 * q^59 - 16 * q^61 - 5 * q^62 + 5 * q^64 + 12 * q^65 + 4 * q^67 + 14 * q^68 + 34 * q^69 - 40 * q^71 + q^72 + 18 * q^73 - 6 * q^75 - 10 * q^76 + 20 * q^78 + 20 * q^79 - 4 * q^80 + 9 * q^81 + 2 * q^82 + 38 * q^83 - 38 * q^85 - 4 * q^86 + 20 * q^87 + 4 * q^88 + 18 * q^89 + 2 * q^90 + 40 * q^94 + 8 * q^95 - 5 * q^97 - 35 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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