LMFDB - Embedded newform 2695.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
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			1.4
Root			$-0.568445$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.568445 q^{2} +0.674153 q^{3} -1.67687 q^{4} +1.00000 q^{5} -0.383219 q^{6} +2.09010 q^{8} -2.54552 q^{9} +O(q^{10})$	\(q-0.568445 q^{2} +0.674153 q^{3} -1.67687 q^{4} +1.00000 q^{5} -0.383219 q^{6} +2.09010 q^{8} -2.54552 q^{9} -0.568445 q^{10} -1.00000 q^{11} -1.13047 q^{12} +1.13393 q^{13} +0.674153 q^{15} +2.16563 q^{16} -0.503652 q^{17} +1.44699 q^{18} -5.40761 q^{19} -1.67687 q^{20} +0.568445 q^{22} +0.365925 q^{23} +1.40905 q^{24} +1.00000 q^{25} -0.644578 q^{26} -3.73853 q^{27} +7.02874 q^{29} -0.383219 q^{30} +5.91866 q^{31} -5.41124 q^{32} -0.674153 q^{33} +0.286299 q^{34} +4.26850 q^{36} -1.70697 q^{37} +3.07393 q^{38} +0.764444 q^{39} +2.09010 q^{40} -1.38530 q^{41} +9.60393 q^{43} +1.67687 q^{44} -2.54552 q^{45} -0.208008 q^{46} +1.01427 q^{47} +1.45997 q^{48} -0.568445 q^{50} -0.339539 q^{51} -1.90146 q^{52} -0.0335756 q^{53} +2.12515 q^{54} -1.00000 q^{55} -3.64556 q^{57} -3.99545 q^{58} +6.99424 q^{59} -1.13047 q^{60} +4.73120 q^{61} -3.36443 q^{62} -1.25527 q^{64} +1.13393 q^{65} +0.383219 q^{66} -7.09660 q^{67} +0.844559 q^{68} +0.246689 q^{69} +1.01456 q^{71} -5.32038 q^{72} -8.82857 q^{73} +0.970318 q^{74} +0.674153 q^{75} +9.06787 q^{76} -0.434544 q^{78} +6.44507 q^{79} +2.16563 q^{80} +5.11621 q^{81} +0.787470 q^{82} +4.08099 q^{83} -0.503652 q^{85} -5.45931 q^{86} +4.73845 q^{87} -2.09010 q^{88} +2.62316 q^{89} +1.44699 q^{90} -0.613609 q^{92} +3.99008 q^{93} -0.576559 q^{94} -5.40761 q^{95} -3.64801 q^{96} +17.6494 q^{97} +2.54552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} + 4 q^{12} + 8 q^{13} + 6 q^{16} + 28 q^{17} - 10 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} - 8 q^{23} + 32 q^{24} + 10 q^{25} + 12 q^{26} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 20 q^{34} - 22 q^{36} + 28 q^{37} + 24 q^{38} - 24 q^{39} + 6 q^{40} + 44 q^{41} + 20 q^{43} - 10 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 36 q^{52} - 8 q^{54} - 10 q^{55} + 12 q^{57} - 8 q^{58} + 16 q^{59} + 4 q^{60} + 16 q^{61} + 36 q^{62} - 34 q^{64} + 8 q^{65} - 4 q^{66} + 20 q^{67} + 8 q^{68} + 4 q^{69} - 4 q^{71} + 10 q^{72} + 20 q^{73} - 16 q^{74} + 4 q^{76} + 52 q^{78} - 20 q^{79} + 6 q^{80} + 10 q^{81} - 32 q^{82} + 16 q^{83} + 28 q^{85} - 20 q^{86} + 20 q^{87} - 6 q^{88} + 44 q^{89} - 10 q^{90} - 24 q^{92} + 16 q^{93} + 24 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 + 4 * q^12 + 8 * q^13 + 6 * q^16 + 28 * q^17 - 10 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 - 8 * q^23 + 32 * q^24 + 10 * q^25 + 12 * q^26 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 14 * q^32 + 20 * q^34 - 22 * q^36 + 28 * q^37 + 24 * q^38 - 24 * q^39 + 6 * q^40 + 44 * q^41 + 20 * q^43 - 10 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 36 * q^52 - 8 * q^54 - 10 * q^55 + 12 * q^57 - 8 * q^58 + 16 * q^59 + 4 * q^60 + 16 * q^61 + 36 * q^62 - 34 * q^64 + 8 * q^65 - 4 * q^66 + 20 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^71 + 10 * q^72 + 20 * q^73 - 16 * q^74 + 4 * q^76 + 52 * q^78 - 20 * q^79 + 6 * q^80 + 10 * q^81 - 32 * q^82 + 16 * q^83 + 28 * q^85 - 20 * q^86 + 20 * q^87 - 6 * q^88 + 44 * q^89 - 10 * q^90 - 24 * q^92 + 16 * q^93 + 24 * q^94 + 8 * q^95 - 4 * q^97 - 10 * 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 $

$2$	−0.568445	−0.401951	−0.200976	−	0.979596i	$-0.564411\pi$
$2$	−0.568445	−0.401951	−0.200976	+	0.979596i	$0.564411\pi$
$3$	0.674153	0.389222	0.194611	−	0.980880i	$-0.437655\pi$
$3$	0.674153	0.389222	0.194611	+	0.980880i	$0.437655\pi$
$4$	−1.67687	−0.838435
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.383219	−0.156449
$7$	0	0
$7$	0	0
$8$	2.09010	0.738962
$9$	−2.54552	−0.848506
$10$	−0.568445	−0.179758
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.13047	−0.326338
$13$	1.13393	0.314496	0.157248	−	0.987559i	$-0.449738\pi$
$13$	1.13393	0.314496	0.157248	+	0.987559i	$0.449738\pi$
$14$	0	0
$15$	0.674153	0.174066
$16$	2.16563	0.541408
$17$	−0.503652	−0.122154	−0.0610768	−	0.998133i	$-0.519453\pi$
$17$	−0.503652	−0.122154	−0.0610768	+	0.998133i	$0.519453\pi$
$18$	1.44699	0.341058
$19$	−5.40761	−1.24059	−0.620296	−	0.784368i	$-0.712987\pi$
$19$	−5.40761	−1.24059	−0.620296	+	0.784368i	$0.712987\pi$
$20$	−1.67687	−0.374960
$21$	0	0
$22$	0.568445	0.121193
$23$	0.365925	0.0763006	0.0381503	−	0.999272i	$-0.487853\pi$
$23$	0.365925	0.0763006	0.0381503	+	0.999272i	$0.487853\pi$
$24$	1.40905	0.287620
$25$	1.00000	0.200000
$26$	−0.644578	−0.126412
$27$	−3.73853	−0.719480
$28$	0	0
$29$	7.02874	1.30520	0.652602	−	0.757701i	$-0.273677\pi$
$29$	7.02874	1.30520	0.652602	+	0.757701i	$0.273677\pi$
$30$	−0.383219	−0.0699659
$31$	5.91866	1.06302	0.531512	−	0.847051i	$-0.321624\pi$
$31$	5.91866	1.06302	0.531512	+	0.847051i	$0.321624\pi$
$32$	−5.41124	−0.956581
$33$	−0.674153	−0.117355
$34$	0.286299	0.0490998
$35$	0	0
$36$	4.26850	0.711417
$37$	−1.70697	−0.280624	−0.140312	−	0.990107i	$-0.544811\pi$
$37$	−1.70697	−0.280624	−0.140312	+	0.990107i	$0.544811\pi$
$38$	3.07393	0.498658
$39$	0.764444	0.122409
$40$	2.09010	0.330474
$41$	−1.38530	−0.216348	−0.108174	−	0.994132i	$-0.534500\pi$
$41$	−1.38530	−0.216348	−0.108174	+	0.994132i	$0.534500\pi$
$42$	0	0
$43$	9.60393	1.46459	0.732293	−	0.680990i	$-0.238450\pi$
$43$	9.60393	1.46459	0.732293	+	0.680990i	$0.238450\pi$
$44$	1.67687	0.252798
$45$	−2.54552	−0.379463
$46$	−0.208008	−0.0306691
$47$	1.01427	0.147947	0.0739735	−	0.997260i	$-0.476432\pi$
$47$	1.01427	0.147947	0.0739735	+	0.997260i	$0.476432\pi$
$48$	1.45997	0.210728
$49$	0	0
$50$	−0.568445	−0.0803903
$51$	−0.339539	−0.0475449
$52$	−1.90146	−0.263685
$53$	−0.0335756	−0.00461196	−0.00230598	−	0.999997i	$-0.500734\pi$
$53$	−0.0335756	−0.00461196	−0.00230598	+	0.999997i	$0.500734\pi$
$54$	2.12515	0.289196
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−3.64556	−0.482866
$58$	−3.99545	−0.524629
$59$	6.99424	0.910572	0.455286	−	0.890345i	$-0.349537\pi$
$59$	6.99424	0.910572	0.455286	+	0.890345i	$0.349537\pi$
$60$	−1.13047	−0.145943
$61$	4.73120	0.605769	0.302884	−	0.953027i	$-0.402050\pi$
$61$	4.73120	0.605769	0.302884	+	0.953027i	$0.402050\pi$
$62$	−3.36443	−0.427284
$63$	0	0
$64$	−1.25527	−0.156909
$65$	1.13393	0.140647
$66$	0.383219	0.0471710
$67$	−7.09660	−0.866987	−0.433494	−	0.901157i	$-0.642719\pi$
$67$	−7.09660	−0.866987	−0.433494	+	0.901157i	$0.642719\pi$
$68$	0.844559	0.102418
$69$	0.246689	0.0296979
$70$	0	0
$71$	1.01456	0.120407	0.0602033	−	0.998186i	$-0.480825\pi$
$71$	1.01456	0.120407	0.0602033	+	0.998186i	$0.480825\pi$
$72$	−5.32038	−0.627013
$73$	−8.82857	−1.03331	−0.516653	−	0.856195i	$-0.672822\pi$
$73$	−8.82857	−1.03331	−0.516653	+	0.856195i	$0.672822\pi$
$74$	0.970318	0.112797
$75$	0.674153	0.0778445
$76$	9.06787	1.04016
$77$	0	0
$78$	−0.434544	−0.0492025
$79$	6.44507	0.725128	0.362564	−	0.931959i	$-0.381902\pi$
$79$	6.44507	0.725128	0.362564	+	0.931959i	$0.381902\pi$
$80$	2.16563	0.242125
$81$	5.11621	0.568468
$82$	0.787470	0.0869615
$83$	4.08099	0.447947	0.223973	−	0.974595i	$-0.428097\pi$
$83$	4.08099	0.447947	0.223973	+	0.974595i	$0.428097\pi$
$84$	0	0
$85$	−0.503652	−0.0546287
$86$	−5.45931	−0.588692
$87$	4.73845	0.508015
$88$	−2.09010	−0.222805
$89$	2.62316	0.278054	0.139027	−	0.990289i	$-0.455603\pi$
$89$	2.62316	0.278054	0.139027	+	0.990289i	$0.455603\pi$
$90$	1.44699	0.152526
$91$	0	0
$92$	−0.613609	−0.0639731
$93$	3.99008	0.413753
$94$	−0.576559	−0.0594675
$95$	−5.40761	−0.554809
$96$	−3.64801	−0.372323
$97$	17.6494	1.79203	0.896014	−	0.444027i	$-0.146450\pi$
$97$	17.6494	1.79203	0.896014	+	0.444027i	$0.146450\pi$
$98$	0	0
$99$	2.54552	0.255834
$100$	−1.67687	−0.167687
$101$	2.44549	0.243335	0.121667	−	0.992571i	$-0.461176\pi$
$101$	2.44549	0.243335	0.121667	+	0.992571i	$0.461176\pi$
$102$	0.193009	0.0191107
$103$	3.36481	0.331545	0.165772	−	0.986164i	$-0.446988\pi$
$103$	3.36481	0.331545	0.165772	+	0.986164i	$0.446988\pi$
$104$	2.37003	0.232401
$105$	0	0
$106$	0.0190859	0.00185378
$107$	−14.1642	−1.36931	−0.684653	−	0.728870i	$-0.740046\pi$
$107$	−14.1642	−1.36931	−0.684653	+	0.728870i	$0.740046\pi$
$108$	6.26903	0.603237
$109$	3.13848	0.300612	0.150306	−	0.988640i	$-0.451974\pi$
$109$	3.13848	0.300612	0.150306	+	0.988640i	$0.451974\pi$
$110$	0.568445	0.0541991
$111$	−1.15076	−0.109225
$112$	0	0
$113$	18.2697	1.71866	0.859332	−	0.511417i	$-0.170879\pi$
$113$	18.2697	1.71866	0.859332	+	0.511417i	$0.170879\pi$
$114$	2.07230	0.194089
$115$	0.365925	0.0341227
$116$	−11.7863	−1.09433
$117$	−2.88644	−0.266852
$118$	−3.97584	−0.366006
$119$	0	0
$120$	1.40905	0.128628
$121$	1.00000	0.0909091
$122$	−2.68943	−0.243490
$123$	−0.933907	−0.0842076
$124$	−9.92483	−0.891276
$125$	1.00000	0.0894427
$126$	0	0
$127$	5.43021	0.481853	0.240927	−	0.970543i	$-0.422549\pi$
$127$	5.43021	0.481853	0.240927	+	0.970543i	$0.422549\pi$
$128$	11.5360	1.01965
$129$	6.47452	0.570050
$130$	−0.644578	−0.0565332
$131$	6.91012	0.603740	0.301870	−	0.953349i	$-0.402389\pi$
$131$	6.91012	0.603740	0.301870	+	0.953349i	$0.402389\pi$
$132$	1.13047	0.0983945
$133$	0	0
$134$	4.03403	0.348487
$135$	−3.73853	−0.321761
$136$	−1.05268	−0.0902668
$137$	−14.9978	−1.28135	−0.640674	−	0.767813i	$-0.721345\pi$
$137$	−14.9978	−1.28135	−0.640674	+	0.767813i	$0.721345\pi$
$138$	−0.140229	−0.0119371
$139$	0.0552864	0.00468933	0.00234466	−	0.999997i	$-0.499254\pi$
$139$	0.0552864	0.00468933	0.00234466	+	0.999997i	$0.499254\pi$
$140$	0	0
$141$	0.683776	0.0575843
$142$	−0.576724	−0.0483976
$143$	−1.13393	−0.0948241
$144$	−5.51266	−0.459388
$145$	7.02874	0.583705
$146$	5.01856	0.415339
$147$	0	0
$148$	2.86237	0.235285
$149$	3.62444	0.296926	0.148463	−	0.988918i	$-0.452567\pi$
$149$	3.62444	0.296926	0.148463	+	0.988918i	$0.452567\pi$
$150$	−0.383219	−0.0312897
$151$	12.9617	1.05481	0.527403	−	0.849615i	$-0.323166\pi$
$151$	12.9617	1.05481	0.527403	+	0.849615i	$0.323166\pi$
$152$	−11.3024	−0.916750
$153$	1.28205	0.103648
$154$	0	0
$155$	5.91866	0.475398
$156$	−1.28187	−0.102632
$157$	12.4335	0.992304	0.496152	−	0.868236i	$-0.334746\pi$
$157$	12.4335	0.992304	0.496152	+	0.868236i	$0.334746\pi$
$158$	−3.66367	−0.291466
$159$	−0.0226351	−0.00179508
$160$	−5.41124	−0.427796
$161$	0	0
$162$	−2.90829	−0.228497
$163$	−6.81245	−0.533593	−0.266796	−	0.963753i	$-0.585965\pi$
$163$	−6.81245	−0.533593	−0.266796	+	0.963753i	$0.585965\pi$
$164$	2.32298	0.181394
$165$	−0.674153	−0.0524828
$166$	−2.31982	−0.180053
$167$	20.2324	1.56563	0.782815	−	0.622255i	$-0.213783\pi$
$167$	20.2324	1.56563	0.782815	+	0.622255i	$0.213783\pi$
$168$	0	0
$169$	−11.7142	−0.901092
$170$	0.286299	0.0219581
$171$	13.7652	1.05265
$172$	−16.1045	−1.22796
$173$	7.82703	0.595078	0.297539	−	0.954710i	$-0.403834\pi$
$173$	7.82703	0.595078	0.297539	+	0.954710i	$0.403834\pi$
$174$	−2.69355	−0.204197
$175$	0	0
$176$	−2.16563	−0.163241
$177$	4.71519	0.354415
$178$	−1.49112	−0.111764
$179$	−21.3414	−1.59513	−0.797566	−	0.603232i	$-0.793879\pi$
$179$	−21.3414	−1.59513	−0.797566	+	0.603232i	$0.793879\pi$
$180$	4.26850	0.318155
$181$	20.4739	1.52181	0.760905	−	0.648863i	$-0.224755\pi$
$181$	20.4739	1.52181	0.760905	+	0.648863i	$0.224755\pi$
$182$	0	0
$183$	3.18956	0.235779
$184$	0.764819	0.0563832
$185$	−1.70697	−0.125499
$186$	−2.26814	−0.166308
$187$	0.503652	0.0368307
$188$	−1.70080	−0.124044
$189$	0	0
$190$	3.07393	0.223006
$191$	−4.60135	−0.332942	−0.166471	−	0.986046i	$-0.553237\pi$
$191$	−4.60135	−0.332942	−0.166471	+	0.986046i	$0.553237\pi$
$192$	−0.846246	−0.0610726
$193$	9.71647	0.699407	0.349704	−	0.936860i	$-0.386282\pi$
$193$	9.71647	0.699407	0.349704	+	0.936860i	$0.386282\pi$
$194$	−10.0327	−0.720308
$195$	0.764444	0.0547429
$196$	0	0
$197$	3.69894	0.263538	0.131769	−	0.991280i	$-0.457934\pi$
$197$	3.69894	0.263538	0.131769	+	0.991280i	$0.457934\pi$
$198$	−1.44699	−0.102833
$199$	19.7976	1.40341	0.701706	−	0.712467i	$-0.252422\pi$
$199$	19.7976	1.40341	0.701706	+	0.712467i	$0.252422\pi$
$200$	2.09010	0.147792
$201$	−4.78419	−0.337451
$202$	−1.39012	−0.0978088
$203$	0	0
$204$	0.569362	0.0398633
$205$	−1.38530	−0.0967538
$206$	−1.91271	−0.133265
$207$	−0.931468	−0.0647415
$208$	2.45568	0.170271
$209$	5.40761	0.374052
$210$	0	0
$211$	−7.66398	−0.527610	−0.263805	−	0.964576i	$-0.584978\pi$
$211$	−7.66398	−0.527610	−0.263805	+	0.964576i	$0.584978\pi$
$212$	0.0563019	0.00386683
$213$	0.683972	0.0468650
$214$	8.05157	0.550394
$215$	9.60393	0.654983
$216$	−7.81389	−0.531668
$217$	0	0
$218$	−1.78406	−0.120832
$219$	−5.95181	−0.402186
$220$	1.67687	0.113055
$221$	−0.571107	−0.0384168
$222$	0.654143	0.0439032
$223$	−12.9545	−0.867500	−0.433750	−	0.901033i	$-0.642810\pi$
$223$	−12.9545	−0.867500	−0.433750	+	0.901033i	$0.642810\pi$
$224$	0	0
$225$	−2.54552	−0.169701
$226$	−10.3853	−0.690820
$227$	−15.8645	−1.05296	−0.526481	−	0.850187i	$-0.676489\pi$
$227$	−15.8645	−1.05296	−0.526481	+	0.850187i	$0.676489\pi$
$228$	6.11313	0.404852
$229$	19.9089	1.31562	0.657808	−	0.753186i	$-0.271484\pi$
$229$	19.9089	1.31562	0.657808	+	0.753186i	$0.271484\pi$
$230$	−0.208008	−0.0137157
$231$	0	0
$232$	14.6908	0.964496
$233$	20.7923	1.36215	0.681075	−	0.732214i	$-0.261513\pi$
$233$	20.7923	1.36215	0.681075	+	0.732214i	$0.261513\pi$
$234$	1.64078	0.107261
$235$	1.01427	0.0661639
$236$	−11.7284	−0.763456
$237$	4.34497	0.282236
$238$	0	0
$239$	−11.9214	−0.771131	−0.385566	−	0.922680i	$-0.625994\pi$
$239$	−11.9214	−0.771131	−0.385566	+	0.922680i	$0.625994\pi$
$240$	1.45997	0.0942406
$241$	6.58176	0.423969	0.211984	−	0.977273i	$-0.432007\pi$
$241$	6.58176	0.423969	0.211984	+	0.977273i	$0.432007\pi$
$242$	−0.568445	−0.0365410
$243$	14.6647	0.940741
$244$	−7.93362	−0.507898
$245$	0	0
$246$	0.530875	0.0338474
$247$	−6.13187	−0.390161
$248$	12.3706	0.785533
$249$	2.75121	0.174351
$250$	−0.568445	−0.0359516
$251$	20.0887	1.26799	0.633993	−	0.773339i	$-0.281415\pi$
$251$	20.0887	1.26799	0.633993	+	0.773339i	$0.281415\pi$
$252$	0	0
$253$	−0.365925	−0.0230055
$254$	−3.08678	−0.193682
$255$	−0.339539	−0.0212627
$256$	−4.04706	−0.252941
$257$	5.36471	0.334641	0.167321	−	0.985903i	$-0.446488\pi$
$257$	5.36471	0.334641	0.167321	+	0.985903i	$0.446488\pi$
$258$	−3.68041	−0.229132
$259$	0	0
$260$	−1.90146	−0.117923
$261$	−17.8918	−1.10747
$262$	−3.92803	−0.242674
$263$	13.0523	0.804841	0.402420	−	0.915455i	$-0.368169\pi$
$263$	13.0523	0.804841	0.402420	+	0.915455i	$0.368169\pi$
$264$	−1.40905	−0.0867208
$265$	−0.0335756	−0.00206253
$266$	0	0
$267$	1.76841	0.108225
$268$	11.9001	0.726913
$269$	9.82615	0.599111	0.299555	−	0.954079i	$-0.403162\pi$
$269$	9.82615	0.599111	0.299555	+	0.954079i	$0.403162\pi$
$270$	2.12515	0.129332
$271$	−29.7080	−1.80463	−0.902315	−	0.431078i	$-0.858134\pi$
$271$	−29.7080	−1.80463	−0.902315	+	0.431078i	$0.858134\pi$
$272$	−1.09073	−0.0661350
$273$	0	0
$274$	8.52542	0.515040
$275$	−1.00000	−0.0603023
$276$	−0.413666	−0.0248998
$277$	32.0297	1.92448	0.962240	−	0.272202i	$-0.0877518\pi$
$277$	32.0297	1.92448	0.962240	+	0.272202i	$0.0877518\pi$
$278$	−0.0314273	−0.00188488
$279$	−15.0661	−0.901981
$280$	0	0
$281$	−26.6901	−1.59220	−0.796099	−	0.605166i	$-0.793107\pi$
$281$	−26.6901	−1.59220	−0.796099	+	0.605166i	$0.793107\pi$
$282$	−0.388689	−0.0231461
$283$	7.98722	0.474791	0.237395	−	0.971413i	$-0.423706\pi$
$283$	7.98722	0.474791	0.237395	+	0.971413i	$0.423706\pi$
$284$	−1.70129	−0.100953
$285$	−3.64556	−0.215944
$286$	0.644578	0.0381147
$287$	0	0
$288$	13.7744	0.811665
$289$	−16.7463	−0.985079
$290$	−3.99545	−0.234621
$291$	11.8984	0.697497
$292$	14.8044	0.866360
$293$	7.11083	0.415419	0.207709	−	0.978191i	$-0.433399\pi$
$293$	7.11083	0.415419	0.207709	+	0.978191i	$0.433399\pi$
$294$	0	0
$295$	6.99424	0.407220
$296$	−3.56773	−0.207370
$297$	3.73853	0.216931
$298$	−2.06030	−0.119350
$299$	0.414934	0.0239962
$300$	−1.13047	−0.0652676
$301$	0	0
$302$	−7.36800	−0.423981
$303$	1.64863	0.0947114
$304$	−11.7109	−0.671667
$305$	4.73120	0.270908
$306$	−0.728778	−0.0416615
$307$	−6.50588	−0.371310	−0.185655	−	0.982615i	$-0.559441\pi$
$307$	−6.50588	−0.371310	−0.185655	+	0.982615i	$0.559441\pi$
$308$	0	0
$309$	2.26840	0.129045
$310$	−3.36443	−0.191087
$311$	18.2962	1.03748	0.518742	−	0.854931i	$-0.326400\pi$
$311$	18.2962	1.03748	0.518742	+	0.854931i	$0.326400\pi$
$312$	1.59776	0.0904555
$313$	16.0903	0.909479	0.454740	−	0.890624i	$-0.349732\pi$
$313$	16.0903	0.909479	0.454740	+	0.890624i	$0.349732\pi$
$314$	−7.06778	−0.398858
$315$	0	0
$316$	−10.8076	−0.607972
$317$	9.54356	0.536020	0.268010	−	0.963416i	$-0.413634\pi$
$317$	9.54356	0.536020	0.268010	+	0.963416i	$0.413634\pi$
$318$	0.0128668	0.000721534 0
$319$	−7.02874	−0.393534
$320$	−1.25527	−0.0701719
$321$	−9.54884	−0.532964
$322$	0	0
$323$	2.72356	0.151543
$324$	−8.57922	−0.476624
$325$	1.13393	0.0628992
$326$	3.87251	0.214478
$327$	2.11582	0.117005
$328$	−2.89542	−0.159873
$329$	0	0
$330$	0.383219	0.0210955
$331$	5.60649	0.308160	0.154080	−	0.988058i	$-0.450759\pi$
$331$	5.60649	0.308160	0.154080	+	0.988058i	$0.450759\pi$
$332$	−6.84329	−0.375574
$333$	4.34512	0.238111
$334$	−11.5010	−0.629307
$335$	−7.09660	−0.387729
$336$	0	0
$337$	−20.5663	−1.12032	−0.560159	−	0.828385i	$-0.689260\pi$
$337$	−20.5663	−1.12032	−0.560159	+	0.828385i	$0.689260\pi$
$338$	6.65888	0.362195
$339$	12.3165	0.668943
$340$	0.844559	0.0458026
$341$	−5.91866	−0.320514
$342$	−7.82475	−0.423114
$343$	0	0
$344$	20.0732	1.08227
$345$	0.246689	0.0132813
$346$	−4.44924	−0.239193
$347$	18.2446	0.979420	0.489710	−	0.871885i	$-0.337103\pi$
$347$	18.2446	0.979420	0.489710	+	0.871885i	$0.337103\pi$
$348$	−7.94576	−0.425937
$349$	−14.7931	−0.791858	−0.395929	−	0.918281i	$-0.629577\pi$
$349$	−14.7931	−0.791858	−0.395929	+	0.918281i	$0.629577\pi$
$350$	0	0
$351$	−4.23924	−0.226274
$352$	5.41124	0.288420
$353$	−31.5154	−1.67739	−0.838697	−	0.544598i	$-0.816682\pi$
$353$	−31.5154	−1.67739	−0.838697	+	0.544598i	$0.816682\pi$
$354$	−2.68033	−0.142458
$355$	1.01456	0.0538475
$356$	−4.39869	−0.233130
$357$	0	0
$358$	12.1314	0.641166
$359$	28.4057	1.49919	0.749597	−	0.661894i	$-0.230247\pi$
$359$	28.4057	1.49919	0.749597	+	0.661894i	$0.230247\pi$
$360$	−5.32038	−0.280409
$361$	10.2423	0.539068
$362$	−11.6383	−0.611694
$363$	0.674153	0.0353839
$364$	0	0
$365$	−8.82857	−0.462108
$366$	−1.81309	−0.0947716
$367$	−28.5233	−1.48890	−0.744452	−	0.667676i	$-0.767289\pi$
$367$	−28.5233	−1.48890	−0.744452	+	0.667676i	$0.767289\pi$
$368$	0.792459	0.0413098
$369$	3.52632	0.183573
$370$	0.970318	0.0504444
$371$	0	0
$372$	−6.69085	−0.346905
$373$	−12.4266	−0.643427	−0.321714	−	0.946837i	$-0.604259\pi$
$373$	−12.4266	−0.643427	−0.321714	+	0.946837i	$0.604259\pi$
$374$	−0.286299	−0.0148041
$375$	0.674153	0.0348131
$376$	2.11993	0.109327
$377$	7.97011	0.410482
$378$	0	0
$379$	−21.6828	−1.11377	−0.556885	−	0.830589i	$-0.688004\pi$
$379$	−21.6828	−1.11377	−0.556885	+	0.830589i	$0.688004\pi$
$380$	9.06787	0.465172
$381$	3.66079	0.187548
$382$	2.61562	0.133827
$383$	18.2748	0.933800	0.466900	−	0.884310i	$-0.345371\pi$
$383$	18.2748	0.933800	0.466900	+	0.884310i	$0.345371\pi$
$384$	7.77706	0.396871
$385$	0	0
$386$	−5.52328	−0.281128
$387$	−24.4470	−1.24271
$388$	−29.5958	−1.50250
$389$	−5.27042	−0.267221	−0.133611	−	0.991034i	$-0.542657\pi$
$389$	−5.27042	−0.267221	−0.133611	+	0.991034i	$0.542657\pi$
$390$	−0.434544	−0.0220040
$391$	−0.184299	−0.00932039
$392$	0	0
$393$	4.65848	0.234989
$394$	−2.10264	−0.105930
$395$	6.44507	0.324287
$396$	−4.26850	−0.214500
$397$	−27.7636	−1.39341	−0.696707	−	0.717356i	$-0.745352\pi$
$397$	−27.7636	−1.39341	−0.696707	+	0.717356i	$0.745352\pi$
$398$	−11.2538	−0.564103
$399$	0	0
$400$	2.16563	0.108282
$401$	−29.8814	−1.49220	−0.746102	−	0.665831i	$-0.768077\pi$
$401$	−29.8814	−1.49220	−0.746102	+	0.665831i	$0.768077\pi$
$402$	2.71955	0.135639
$403$	6.71136	0.334317
$404$	−4.10076	−0.204020
$405$	5.11621	0.254227
$406$	0	0
$407$	1.70697	0.0846113
$408$	−0.709669	−0.0351339
$409$	−13.5548	−0.670241	−0.335121	−	0.942175i	$-0.608777\pi$
$409$	−13.5548	−0.670241	−0.335121	+	0.942175i	$0.608777\pi$
$410$	0.787470	0.0388903
$411$	−10.1108	−0.498730
$412$	−5.64235	−0.277979
$413$	0	0
$414$	0.529489	0.0260229
$415$	4.08099	0.200328
$416$	−6.13598	−0.300841
$417$	0.0372715	0.00182519
$418$	−3.07393	−0.150351
$419$	−14.0874	−0.688215	−0.344107	−	0.938930i	$-0.611818\pi$
$419$	−14.0874	−0.688215	−0.344107	+	0.938930i	$0.611818\pi$
$420$	0	0
$421$	−8.19147	−0.399228	−0.199614	−	0.979875i	$-0.563969\pi$
$421$	−8.19147	−0.399228	−0.199614	+	0.979875i	$0.563969\pi$
$422$	4.35655	0.212074
$423$	−2.58185	−0.125534
$424$	−0.0701763	−0.00340806
$425$	−0.503652	−0.0244307
$426$	−0.388800	−0.0188374
$427$	0	0
$428$	23.7515	1.14807
$429$	−0.764444	−0.0369077
$430$	−5.45931	−0.263271
$431$	−2.60824	−0.125635	−0.0628173	−	0.998025i	$-0.520009\pi$
$431$	−2.60824	−0.125635	−0.0628173	+	0.998025i	$0.520009\pi$
$432$	−8.09628	−0.389533
$433$	−35.1789	−1.69059	−0.845296	−	0.534299i	$-0.820576\pi$
$433$	−35.1789	−1.69059	−0.845296	+	0.534299i	$0.820576\pi$
$434$	0	0
$435$	4.73845	0.227191
$436$	−5.26283	−0.252044
$437$	−1.97878	−0.0946579
$438$	3.38328	0.161659
$439$	33.3167	1.59012	0.795059	−	0.606532i	$-0.207440\pi$
$439$	33.3167	1.59012	0.795059	+	0.606532i	$0.207440\pi$
$440$	−2.09010	−0.0996416
$441$	0	0
$442$	0.324643	0.0154417
$443$	3.93942	0.187167	0.0935837	−	0.995611i	$-0.470168\pi$
$443$	3.93942	0.187167	0.0935837	+	0.995611i	$0.470168\pi$
$444$	1.92967	0.0915782
$445$	2.62316	0.124350
$446$	7.36395	0.348693
$447$	2.44343	0.115570
$448$	0	0
$449$	−9.34751	−0.441136	−0.220568	−	0.975372i	$-0.570791\pi$
$449$	−9.34751	−0.441136	−0.220568	+	0.975372i	$0.570791\pi$
$450$	1.44699	0.0682116
$451$	1.38530	0.0652314
$452$	−30.6358	−1.44099
$453$	8.73816	0.410554
$454$	9.01808	0.423240
$455$	0	0
$456$	−7.61958	−0.356820
$457$	6.06419	0.283671	0.141835	−	0.989890i	$-0.454700\pi$
$457$	6.06419	0.283671	0.141835	+	0.989890i	$0.454700\pi$
$458$	−11.3171	−0.528813
$459$	1.88292	0.0878870
$460$	−0.613609	−0.0286096
$461$	20.3944	0.949862	0.474931	−	0.880023i	$-0.342473\pi$
$461$	20.3944	0.949862	0.474931	+	0.880023i	$0.342473\pi$
$462$	0	0
$463$	9.40897	0.437272	0.218636	−	0.975806i	$-0.429839\pi$
$463$	9.40897	0.437272	0.218636	+	0.975806i	$0.429839\pi$
$464$	15.2217	0.706649
$465$	3.99008	0.185036
$466$	−11.8193	−0.547518
$467$	4.45853	0.206316	0.103158	−	0.994665i	$-0.467105\pi$
$467$	4.45853	0.206316	0.103158	+	0.994665i	$0.467105\pi$
$468$	4.84019	0.223738
$469$	0	0
$470$	−0.576559	−0.0265947
$471$	8.38211	0.386227
$472$	14.6186	0.672878
$473$	−9.60393	−0.441589
$474$	−2.46988	−0.113445
$475$	−5.40761	−0.248118
$476$	0	0
$477$	0.0854672	0.00391328
$478$	6.77666	0.309957
$479$	−0.155578	−0.00710856	−0.00355428	−	0.999994i	$-0.501131\pi$
$479$	−0.155578	−0.00710856	−0.00355428	+	0.999994i	$0.501131\pi$
$480$	−3.64801	−0.166508
$481$	−1.93559	−0.0882551
$482$	−3.74137	−0.170415
$483$	0	0
$484$	−1.67687	−0.0762214
$485$	17.6494	0.801419
$486$	−8.33607	−0.378132
$487$	26.6194	1.20624	0.603120	−	0.797650i	$-0.293924\pi$
$487$	26.6194	1.20624	0.603120	+	0.797650i	$0.293924\pi$
$488$	9.88869	0.447640
$489$	−4.59264	−0.207686
$490$	0	0
$491$	−19.6121	−0.885080	−0.442540	−	0.896749i	$-0.645923\pi$
$491$	−19.6121	−0.885080	−0.442540	+	0.896749i	$0.645923\pi$
$492$	1.56604	0.0706026
$493$	−3.54004	−0.159435
$494$	3.48563	0.156826
$495$	2.54552	0.114413
$496$	12.8177	0.575530
$497$	0	0
$498$	−1.56391	−0.0700806
$499$	−23.7632	−1.06379	−0.531894	−	0.846811i	$-0.678520\pi$
$499$	−23.7632	−1.06379	−0.531894	+	0.846811i	$0.678520\pi$
$500$	−1.67687	−0.0749919
$501$	13.6397	0.609378
$502$	−11.4193	−0.509669
$503$	18.2299	0.812829	0.406415	−	0.913689i	$-0.366779\pi$
$503$	18.2299	0.812829	0.406415	+	0.913689i	$0.366779\pi$
$504$	0	0
$505$	2.44549	0.108823
$506$	0.208008	0.00924709
$507$	−7.89716	−0.350725
$508$	−9.10576	−0.404003
$509$	−1.28695	−0.0570432	−0.0285216	−	0.999593i	$-0.509080\pi$
$509$	−1.28695	−0.0570432	−0.0285216	+	0.999593i	$0.509080\pi$
$510$	0.193009	0.00854658
$511$	0	0
$512$	−20.7715	−0.917981
$513$	20.2165	0.892581
$514$	−3.04954	−0.134510
$515$	3.36481	0.148271
$516$	−10.8569	−0.477950
$517$	−1.01427	−0.0446077
$518$	0	0
$519$	5.27662	0.231618
$520$	2.37003	0.103933
$521$	9.45381	0.414179	0.207089	−	0.978322i	$-0.433601\pi$
$521$	9.45381	0.414179	0.207089	+	0.978322i	$0.433601\pi$
$522$	10.1705	0.445151
$523$	20.5157	0.897090	0.448545	−	0.893760i	$-0.351942\pi$
$523$	20.5157	0.897090	0.448545	+	0.893760i	$0.351942\pi$
$524$	−11.5874	−0.506197
$525$	0	0
$526$	−7.41953	−0.323507
$527$	−2.98095	−0.129852
$528$	−1.45997	−0.0635370
$529$	−22.8661	−0.994178
$530$	0.0190859	0.000829037 0
$531$	−17.8040	−0.772626
$532$	0	0
$533$	−1.57084	−0.0680407
$534$	−1.00524	−0.0435012
$535$	−14.1642	−0.612372
$536$	−14.8326	−0.640670
$537$	−14.3874	−0.620861
$538$	−5.58563	−0.240813
$539$	0	0
$540$	6.26903	0.269776
$541$	14.7343	0.633475	0.316738	−	0.948513i	$-0.397412\pi$
$541$	14.7343	0.633475	0.316738	+	0.948513i	$0.397412\pi$
$542$	16.8873	0.725373
$543$	13.8025	0.592323
$544$	2.72538	0.116850
$545$	3.13848	0.134438
$546$	0	0
$547$	−6.09388	−0.260555	−0.130278	−	0.991478i	$-0.541587\pi$
$547$	−6.09388	−0.260555	−0.130278	+	0.991478i	$0.541587\pi$
$548$	25.1494	1.07433
$549$	−12.0434	−0.513998
$550$	0.568445	0.0242386
$551$	−38.0087	−1.61923
$552$	0.515605	0.0219456
$553$	0	0
$554$	−18.2071	−0.773548
$555$	−1.15076	−0.0488470
$556$	−0.0927080	−0.00393170
$557$	−9.19514	−0.389611	−0.194805	−	0.980842i	$-0.562408\pi$
$557$	−9.19514	−0.389611	−0.194805	+	0.980842i	$0.562408\pi$
$558$	8.56423	0.362553
$559$	10.8902	0.460606
$560$	0	0
$561$	0.339539	0.0143353
$562$	15.1719	0.639987
$563$	−25.2794	−1.06540	−0.532699	−	0.846305i	$-0.678822\pi$
$563$	−25.2794	−1.06540	−0.532699	+	0.846305i	$0.678822\pi$
$564$	−1.14660	−0.0482807
$565$	18.2697	0.768610
$566$	−4.54029	−0.190843
$567$	0	0
$568$	2.12054	0.0889759
$569$	18.2740	0.766088	0.383044	−	0.923730i	$-0.374876\pi$
$569$	18.2740	0.766088	0.383044	+	0.923730i	$0.374876\pi$
$570$	2.07230	0.0867991
$571$	23.8395	0.997651	0.498826	−	0.866702i	$-0.333765\pi$
$571$	23.8395	0.997651	0.498826	+	0.866702i	$0.333765\pi$
$572$	1.90146	0.0795039
$573$	−3.10202	−0.129589
$574$	0	0
$575$	0.365925	0.0152601
$576$	3.19532	0.133138
$577$	2.67675	0.111434	0.0557172	−	0.998447i	$-0.482255\pi$
$577$	2.67675	0.111434	0.0557172	+	0.998447i	$0.482255\pi$
$578$	9.51937	0.395954
$579$	6.55039	0.272225
$580$	−11.7863	−0.489399
$581$	0	0
$582$	−6.76359	−0.280360
$583$	0.0335756	0.00139056
$584$	−18.4526	−0.763573
$585$	−2.88644	−0.119340
$586$	−4.04212	−0.166978
$587$	−9.90516	−0.408830	−0.204415	−	0.978884i	$-0.565529\pi$
$587$	−9.90516	−0.408830	−0.204415	+	0.978884i	$0.565529\pi$
$588$	0	0
$589$	−32.0058	−1.31878
$590$	−3.97584	−0.163683
$591$	2.49365	0.102575
$592$	−3.69667	−0.151932
$593$	48.1768	1.97838	0.989191	−	0.146631i	$-0.0468431\pi$
$593$	48.1768	1.97838	0.989191	+	0.146631i	$0.0468431\pi$
$594$	−2.12515	−0.0871959
$595$	0	0
$596$	−6.07772	−0.248953
$597$	13.3466	0.546239
$598$	−0.235867	−0.00964533
$599$	33.2671	1.35926	0.679629	−	0.733556i	$-0.262141\pi$
$599$	33.2671	1.35926	0.679629	+	0.733556i	$0.262141\pi$
$600$	1.40905	0.0575241
$601$	15.9829	0.651954	0.325977	−	0.945378i	$-0.394307\pi$
$601$	15.9829	0.651954	0.325977	+	0.945378i	$0.394307\pi$
$602$	0	0
$603$	18.0645	0.735644
$604$	−21.7351	−0.884387
$605$	1.00000	0.0406558
$606$	−0.937157	−0.0380694
$607$	−30.5652	−1.24060	−0.620302	−	0.784363i	$-0.712990\pi$
$607$	−30.5652	−1.24060	−0.620302	+	0.784363i	$0.712990\pi$
$608$	29.2619	1.18673
$609$	0	0
$610$	−2.68943	−0.108892
$611$	1.15012	0.0465287
$612$	−2.14984	−0.0869021
$613$	38.1825	1.54218	0.771088	−	0.636728i	$-0.219713\pi$
$613$	38.1825	1.54218	0.771088	+	0.636728i	$0.219713\pi$
$614$	3.69824	0.149249
$615$	−0.933907	−0.0376588
$616$	0	0
$617$	0.00117367	4.72501e−5 0	2.36251e−5	−	1.00000i	$-0.499992\pi$
$617$	0.00117367	4.72501e−5 0	2.36251e−5		1.00000i	$0.499992\pi$
$618$	−1.28946	−0.0518697
$619$	−46.6222	−1.87390	−0.936952	−	0.349457i	$-0.886366\pi$
$619$	−46.6222	−1.87390	−0.936952	+	0.349457i	$0.886366\pi$
$620$	−9.92483	−0.398591
$621$	−1.36802	−0.0548968
$622$	−10.4004	−0.417018
$623$	0	0
$624$	1.65550	0.0662732
$625$	1.00000	0.0400000
$626$	−9.14647	−0.365566
$627$	3.64556	0.145590
$628$	−20.8494	−0.831983
$629$	0.859718	0.0342792
$630$	0	0
$631$	−17.2295	−0.685897	−0.342949	−	0.939354i	$-0.611426\pi$
$631$	−17.2295	−0.685897	−0.342949	+	0.939354i	$0.611426\pi$
$632$	13.4708	0.535841
$633$	−5.16670	−0.205358
$634$	−5.42499	−0.215454
$635$	5.43021	0.215491
$636$	0.0379561	0.00150506
$637$	0	0
$638$	3.99545	0.158182
$639$	−2.58259	−0.102166
$640$	11.5360	0.456002
$641$	−47.4149	−1.87278	−0.936388	−	0.350965i	$-0.885853\pi$
$641$	−47.4149	−1.87278	−0.936388	+	0.350965i	$0.885853\pi$
$642$	5.42799	0.214226
$643$	−39.5197	−1.55851	−0.779253	−	0.626709i	$-0.784401\pi$
$643$	−39.5197	−1.55851	−0.779253	+	0.626709i	$0.784401\pi$
$644$	0	0
$645$	6.47452	0.254934
$646$	−1.54819	−0.0609128
$647$	41.5454	1.63332	0.816659	−	0.577121i	$-0.195824\pi$
$647$	41.5454	1.63332	0.816659	+	0.577121i	$0.195824\pi$
$648$	10.6934	0.420076
$649$	−6.99424	−0.274548
$650$	−0.644578	−0.0252824
$651$	0	0
$652$	11.4236	0.447383
$653$	−8.78683	−0.343855	−0.171928	−	0.985110i	$-0.555000\pi$
$653$	−8.78683	−0.343855	−0.171928	+	0.985110i	$0.555000\pi$
$654$	−1.20273	−0.0470303
$655$	6.91012	0.270001
$656$	−3.00006	−0.117133
$657$	22.4733	0.876766
$658$	0	0
$659$	−29.2977	−1.14128	−0.570638	−	0.821202i	$-0.693304\pi$
$659$	−29.2977	−1.14128	−0.570638	+	0.821202i	$0.693304\pi$
$660$	1.13047	0.0440034
$661$	−19.9286	−0.775132	−0.387566	−	0.921842i	$-0.626684\pi$
$661$	−19.9286	−0.775132	−0.387566	+	0.921842i	$0.626684\pi$
$662$	−3.18698	−0.123866
$663$	−0.385014	−0.0149527
$664$	8.52968	0.331016
$665$	0	0
$666$	−2.46996	−0.0957091
$667$	2.57199	0.0995879
$668$	−33.9271	−1.31268
$669$	−8.73335	−0.337651
$670$	4.03403	0.155848
$671$	−4.73120	−0.182646
$672$	0	0
$673$	−3.84472	−0.148203	−0.0741014	−	0.997251i	$-0.523609\pi$
$673$	−3.84472	−0.148203	−0.0741014	+	0.997251i	$0.523609\pi$
$674$	11.6908	0.450314
$675$	−3.73853	−0.143896
$676$	19.6432	0.755507
$677$	47.4390	1.82323	0.911615	−	0.411045i	$-0.134836\pi$
$677$	47.4390	1.82323	0.911615	+	0.411045i	$0.134836\pi$
$678$	−7.00128	−0.268883
$679$	0	0
$680$	−1.05268	−0.0403685
$681$	−10.6951	−0.409837
$682$	3.36443	0.128831
$683$	−35.3639	−1.35316	−0.676580	−	0.736369i	$-0.736539\pi$
$683$	−35.3639	−1.35316	−0.676580	+	0.736369i	$0.736539\pi$
$684$	−23.0824	−0.882578
$685$	−14.9978	−0.573036
$686$	0	0
$687$	13.4216	0.512067
$688$	20.7986	0.792939
$689$	−0.0380724	−0.00145044
$690$	−0.140229	−0.00533844
$691$	−22.0002	−0.836928	−0.418464	−	0.908233i	$-0.637431\pi$
$691$	−22.0002	−0.836928	−0.418464	+	0.908233i	$0.637431\pi$
$692$	−13.1249	−0.498934
$693$	0	0
$694$	−10.3710	−0.393679
$695$	0.0552864	0.00209713
$696$	9.90382	0.375403
$697$	0.697711	0.0264277
$698$	8.40908	0.318288
$699$	14.0172	0.530179
$700$	0	0
$701$	−40.9344	−1.54607	−0.773036	−	0.634362i	$-0.781263\pi$
$701$	−40.9344	−1.54607	−0.773036	+	0.634362i	$0.781263\pi$
$702$	2.40977	0.0909510
$703$	9.23063	0.348140
$704$	1.25527	0.0473099
$705$	0.683776	0.0257525
$706$	17.9148	0.674231
$707$	0	0
$708$	−7.90676	−0.297154
$709$	−22.3925	−0.840969	−0.420485	−	0.907300i	$-0.638140\pi$
$709$	−22.3925	−0.840969	−0.420485	+	0.907300i	$0.638140\pi$
$710$	−0.576724	−0.0216441
$711$	−16.4061	−0.615275
$712$	5.48266	0.205471
$713$	2.16579	0.0811093
$714$	0	0
$715$	−1.13393	−0.0424066
$716$	35.7868	1.33741
$717$	−8.03685	−0.300142
$718$	−16.1471	−0.602603
$719$	−25.9588	−0.968099	−0.484049	−	0.875041i	$-0.660835\pi$
$719$	−25.9588	−0.968099	−0.484049	+	0.875041i	$0.660835\pi$
$720$	−5.51266	−0.205445
$721$	0	0
$722$	−5.82218	−0.216679
$723$	4.43712	0.165018
$724$	−34.3320	−1.27594
$725$	7.02874	0.261041
$726$	−0.383219	−0.0142226
$727$	−39.2963	−1.45742	−0.728710	−	0.684823i	$-0.759880\pi$
$727$	−39.2963	−1.45742	−0.728710	+	0.684823i	$0.759880\pi$
$728$	0	0
$729$	−5.46239	−0.202311
$730$	5.01856	0.185745
$731$	−4.83704	−0.178904
$732$	−5.34847	−0.197685
$733$	21.3131	0.787218	0.393609	−	0.919278i	$-0.371226\pi$
$733$	21.3131	0.787218	0.393609	+	0.919278i	$0.371226\pi$
$734$	16.2139	0.598467
$735$	0	0
$736$	−1.98011	−0.0729878
$737$	7.09660	0.261407
$738$	−2.00452	−0.0737873
$739$	18.2051	0.669687	0.334843	−	0.942274i	$-0.391317\pi$
$739$	18.2051	0.669687	0.334843	+	0.942274i	$0.391317\pi$
$740$	2.86237	0.105223
$741$	−4.13382	−0.151860
$742$	0	0
$743$	−32.2352	−1.18259	−0.591297	−	0.806454i	$-0.701384\pi$
$743$	−32.2352	−1.18259	−0.591297	+	0.806454i	$0.701384\pi$
$744$	8.33967	0.305747
$745$	3.62444	0.132789
$746$	7.06386	0.258626
$747$	−10.3882	−0.380086
$748$	−0.844559	−0.0308801
$749$	0	0
$750$	−0.383219	−0.0139932
$751$	−31.4539	−1.14777	−0.573885	−	0.818936i	$-0.694564\pi$
$751$	−31.4539	−1.14777	−0.573885	+	0.818936i	$0.694564\pi$
$752$	2.19654	0.0800997
$753$	13.5428	0.493529
$754$	−4.53057	−0.164994
$755$	12.9617	0.471724
$756$	0	0
$757$	−41.1684	−1.49629	−0.748146	−	0.663534i	$-0.769056\pi$
$757$	−41.1684	−1.49629	−0.748146	+	0.663534i	$0.769056\pi$
$758$	12.3255	0.447682
$759$	−0.246689	−0.00895426
$760$	−11.3024	−0.409983
$761$	−22.2691	−0.807253	−0.403627	−	0.914924i	$-0.632251\pi$
$761$	−22.2691	−0.807253	−0.403627	+	0.914924i	$0.632251\pi$
$762$	−2.08096	−0.0753852
$763$	0	0
$764$	7.71587	0.279150
$765$	1.28205	0.0463528
$766$	−10.3882	−0.375342
$767$	7.93099	0.286371
$768$	−2.72834	−0.0984504
$769$	−10.5404	−0.380097	−0.190049	−	0.981775i	$-0.560865\pi$
$769$	−10.5404	−0.380097	−0.190049	+	0.981775i	$0.560865\pi$
$770$	0	0
$771$	3.61663	0.130250
$772$	−16.2933	−0.586407
$773$	1.27990	0.0460349	0.0230174	−	0.999735i	$-0.492673\pi$
$773$	1.27990	0.0460349	0.0230174	+	0.999735i	$0.492673\pi$
$774$	13.8968	0.499509
$775$	5.91866	0.212605
$776$	36.8890	1.32424
$777$	0	0
$778$	2.99595	0.107410
$779$	7.49119	0.268400
$780$	−1.28187	−0.0458984
$781$	−1.01456	−0.0363040
$782$	0.104764	0.00374634
$783$	−26.2771	−0.939068
$784$	0	0
$785$	12.4335	0.443772
$786$	−2.64809	−0.0944543
$787$	25.5723	0.911552	0.455776	−	0.890094i	$-0.349362\pi$
$787$	25.5723	0.911552	0.455776	+	0.890094i	$0.349362\pi$
$788$	−6.20264	−0.220960
$789$	8.79926	0.313262
$790$	−3.66367	−0.130348
$791$	0	0
$792$	5.32038	0.189052
$793$	5.36486	0.190512
$794$	15.7821	0.560085
$795$	−0.0226351	−0.000802784 0
$796$	−33.1979	−1.17667
$797$	20.4741	0.725229	0.362615	−	0.931939i	$-0.381884\pi$
$797$	20.4741	0.725229	0.362615	+	0.931939i	$0.381884\pi$
$798$	0	0
$799$	−0.510841	−0.0180722
$800$	−5.41124	−0.191316
$801$	−6.67729	−0.235931
$802$	16.9859	0.599794
$803$	8.82857	0.311553
$804$	8.02247	0.282931
$805$	0	0
$806$	−3.81504	−0.134379
$807$	6.62433	0.233187
$808$	5.11131	0.179815
$809$	0.832183	0.0292580	0.0146290	−	0.999893i	$-0.495343\pi$
$809$	0.832183	0.0292580	0.0146290	+	0.999893i	$0.495343\pi$
$810$	−2.90829	−0.102187
$811$	−49.9094	−1.75256	−0.876278	−	0.481805i	$-0.839981\pi$
$811$	−49.9094	−1.75256	−0.876278	+	0.481805i	$0.839981\pi$
$812$	0	0
$813$	−20.0277	−0.702402
$814$	−0.970318	−0.0340096
$815$	−6.81245	−0.238630
$816$	−0.735316	−0.0257412
$817$	−51.9343	−1.81695
$818$	7.70515	0.269404
$819$	0	0
$820$	2.32298	0.0811218
$821$	53.6558	1.87260	0.936301	−	0.351199i	$-0.114226\pi$
$821$	53.6558	1.87260	0.936301	+	0.351199i	$0.114226\pi$
$822$	5.74744	0.200465
$823$	−6.46470	−0.225345	−0.112673	−	0.993632i	$-0.535941\pi$
$823$	−6.46470	−0.225345	−0.112673	+	0.993632i	$0.535941\pi$
$824$	7.03279	0.244999
$825$	−0.674153	−0.0234710
$826$	0	0
$827$	−20.5318	−0.713961	−0.356981	−	0.934112i	$-0.616194\pi$
$827$	−20.5318	−0.713961	−0.356981	+	0.934112i	$0.616194\pi$
$828$	1.56195	0.0542816
$829$	−18.6169	−0.646591	−0.323295	−	0.946298i	$-0.604791\pi$
$829$	−18.6169	−0.646591	−0.323295	+	0.946298i	$0.604791\pi$
$830$	−2.31982	−0.0805221
$831$	21.5929	0.749051
$832$	−1.42339	−0.0493473
$833$	0	0
$834$	−0.0211868	−0.000733638 0
$835$	20.2324	0.700171
$836$	−9.06787	−0.313619
$837$	−22.1271	−0.764824
$838$	8.00791	0.276629
$839$	0.757528	0.0261528	0.0130764	−	0.999915i	$-0.495838\pi$
$839$	0.757528	0.0261528	0.0130764	+	0.999915i	$0.495838\pi$
$840$	0	0
$841$	20.4032	0.703558
$842$	4.65640	0.160470
$843$	−17.9932	−0.619720
$844$	12.8515	0.442367
$845$	−11.7142	−0.402981
$846$	1.46764	0.0504585
$847$	0	0
$848$	−0.0727124	−0.00249695
$849$	5.38461	0.184799
$850$	0.286299	0.00981996
$851$	−0.624623	−0.0214118
$852$	−1.14693	−0.0392932
$853$	−4.79884	−0.164309	−0.0821546	−	0.996620i	$-0.526180\pi$
$853$	−4.79884	−0.164309	−0.0821546	+	0.996620i	$0.526180\pi$
$854$	0	0
$855$	13.7652	0.470759
$856$	−29.6046	−1.01186
$857$	31.3756	1.07177	0.535885	−	0.844291i	$-0.319978\pi$
$857$	31.3756	1.07177	0.535885	+	0.844291i	$0.319978\pi$
$858$	0.434544	0.0148351
$859$	−53.3634	−1.82074	−0.910368	−	0.413799i	$-0.864202\pi$
$859$	−53.3634	−1.82074	−0.910368	+	0.413799i	$0.864202\pi$
$860$	−16.1045	−0.549160
$861$	0	0
$862$	1.48264	0.0504990
$863$	−27.5763	−0.938710	−0.469355	−	0.883010i	$-0.655513\pi$
$863$	−27.5763	−0.938710	−0.469355	+	0.883010i	$0.655513\pi$
$864$	20.2301	0.688241
$865$	7.82703	0.266127
$866$	19.9973	0.679536
$867$	−11.2896	−0.383415
$868$	0	0
$869$	−6.44507	−0.218634
$870$	−2.69355	−0.0913198
$871$	−8.04706	−0.272664
$872$	6.55974	0.222141
$873$	−44.9269	−1.52055
$874$	1.12483	0.0380479
$875$	0	0
$876$	9.98041	0.337207
$877$	−12.8590	−0.434219	−0.217110	−	0.976147i	$-0.569663\pi$
$877$	−12.8590	−0.434219	−0.217110	+	0.976147i	$0.569663\pi$
$878$	−18.9387	−0.639150
$879$	4.79379	0.161690
$880$	−2.16563	−0.0730035
$881$	27.3881	0.922727	0.461364	−	0.887211i	$-0.347360\pi$
$881$	27.3881	0.922727	0.461364	+	0.887211i	$0.347360\pi$
$882$	0	0
$883$	30.0300	1.01059	0.505295	−	0.862947i	$-0.331384\pi$
$883$	30.0300	1.01059	0.505295	+	0.862947i	$0.331384\pi$
$884$	0.957672	0.0322100
$885$	4.71519	0.158499
$886$	−2.23934	−0.0752322
$887$	−20.8177	−0.698990	−0.349495	−	0.936938i	$-0.613647\pi$
$887$	−20.8177	−0.698990	−0.349495	+	0.936938i	$0.613647\pi$
$888$	−2.40520	−0.0807132
$889$	0	0
$890$	−1.49112	−0.0499825
$891$	−5.11621	−0.171400
$892$	21.7231	0.727343
$893$	−5.48480	−0.183542
$894$	−1.38896	−0.0464536
$895$	−21.3414	−0.713365
$896$	0	0
$897$	0.279729	0.00933988
$898$	5.31355	0.177315
$899$	41.6007	1.38746
$900$	4.26850	0.142283
$901$	0.0169104	0.000563367 0
$902$	−0.787470	−0.0262199
$903$	0	0
$904$	38.1854	1.27003
$905$	20.4739	0.680574
$906$	−4.96716	−0.165023
$907$	51.6770	1.71591	0.857953	−	0.513728i	$-0.171736\pi$
$907$	51.6770	1.71591	0.857953	+	0.513728i	$0.171736\pi$
$908$	26.6027	0.882840
$909$	−6.22503	−0.206471
$910$	0	0
$911$	39.2348	1.29991	0.649953	−	0.759974i	$-0.274788\pi$
$911$	39.2348	1.29991	0.649953	+	0.759974i	$0.274788\pi$
$912$	−7.89495	−0.261428
$913$	−4.08099	−0.135061
$914$	−3.44716	−0.114022
$915$	3.18956	0.105443
$916$	−33.3846	−1.10306
$917$	0	0
$918$	−1.07034	−0.0353263
$919$	−48.8612	−1.61178	−0.805892	−	0.592063i	$-0.798314\pi$
$919$	−48.8612	−1.61178	−0.805892	+	0.592063i	$0.798314\pi$
$920$	0.764819	0.0252153
$921$	−4.38596	−0.144522
$922$	−11.5931	−0.381798
$923$	1.15045	0.0378674
$924$	0	0
$925$	−1.70697	−0.0561248
$926$	−5.34849	−0.175762
$927$	−8.56519	−0.281318
$928$	−38.0342	−1.24853
$929$	52.6633	1.72783	0.863914	−	0.503640i	$-0.168006\pi$
$929$	52.6633	1.72783	0.863914	+	0.503640i	$0.168006\pi$
$930$	−2.26814	−0.0743754
$931$	0	0
$932$	−34.8660	−1.14207
$933$	12.3345	0.403812
$934$	−2.53443	−0.0829292
$935$	0.503652	0.0164712
$936$	−6.03295	−0.197193
$937$	51.8474	1.69378	0.846890	−	0.531769i	$-0.178472\pi$
$937$	51.8474	1.69378	0.846890	+	0.531769i	$0.178472\pi$
$938$	0	0
$939$	10.8473	0.353990
$940$	−1.70080	−0.0554741
$941$	34.8801	1.13706	0.568530	−	0.822663i	$-0.307512\pi$
$941$	34.8801	1.13706	0.568530	+	0.822663i	$0.307512\pi$
$942$	−4.76477	−0.155245
$943$	−0.506917	−0.0165075
$944$	15.1470	0.492991
$945$	0	0
$946$	5.45931	0.177497
$947$	1.40279	0.0455846	0.0227923	−	0.999740i	$-0.492744\pi$
$947$	1.40279	0.0455846	0.0227923	+	0.999740i	$0.492744\pi$
$948$	−7.28595	−0.236637
$949$	−10.0110	−0.324971
$950$	3.07393	0.0997315
$951$	6.43382	0.208631
$952$	0	0
$953$	57.4396	1.86065	0.930326	−	0.366733i	$-0.119524\pi$
$953$	57.4396	1.86065	0.930326	+	0.366733i	$0.119524\pi$
$954$	−0.0485834	−0.00157295
$955$	−4.60135	−0.148896
$956$	19.9906	0.646543
$957$	−4.73845	−0.153172
$958$	0.0884378	0.00285730
$959$	0	0
$960$	−0.846246	−0.0273125
$961$	4.03056	0.130018
$962$	1.10027	0.0354743
$963$	36.0552	1.16186
$964$	−11.0368	−0.355470
$965$	9.71647	0.312784
$966$	0	0
$967$	−19.9908	−0.642859	−0.321430	−	0.946933i	$-0.604163\pi$
$967$	−19.9908	−0.642859	−0.321430	+	0.946933i	$0.604163\pi$
$968$	2.09010	0.0671783
$969$	1.83609	0.0589838
$970$	−10.0327	−0.322131
$971$	−6.66332	−0.213836	−0.106918	−	0.994268i	$-0.534098\pi$
$971$	−6.66332	−0.213836	−0.106918	+	0.994268i	$0.534098\pi$
$972$	−24.5908	−0.788750
$973$	0	0
$974$	−15.1317	−0.484850
$975$	0.764444	0.0244818
$976$	10.2461	0.327968
$977$	−42.2902	−1.35298	−0.676492	−	0.736450i	$-0.736501\pi$
$977$	−42.2902	−1.35298	−0.676492	+	0.736450i	$0.736501\pi$
$978$	2.61066	0.0834798
$979$	−2.62316	−0.0838365
$980$	0	0
$981$	−7.98907	−0.255071
$982$	11.1484	0.355759
$983$	22.4181	0.715027	0.357514	−	0.933908i	$-0.383625\pi$
$983$	22.4181	0.715027	0.357514	+	0.933908i	$0.383625\pi$
$984$	−1.95196	−0.0622262
$985$	3.69894	0.117858
$986$	2.01232	0.0640853
$987$	0	0
$988$	10.2823	0.327125
$989$	3.51432	0.111749
$990$	−1.44699	−0.0459883
$991$	−26.5445	−0.843214	−0.421607	−	0.906779i	$-0.638534\pi$
$991$	−26.5445	−0.843214	−0.421607	+	0.906779i	$0.638534\pi$
$992$	−32.0273	−1.01687
$993$	3.77963	0.119943
$994$	0	0
$995$	19.7976	0.627625
$996$	−4.61343	−0.146182
$997$	−11.3954	−0.360897	−0.180448	−	0.983584i	$-0.557755\pi$
$997$	−11.3954	−0.360897	−0.180448	+	0.983584i	$0.557755\pi$
$998$	13.5081	0.427591
$999$	6.38155	0.201903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.x.1.4	yes	10
7.6	odd	2		2695.2.a.w.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.4	✓	10	7.6	odd	2
2695.2.a.x.1.4	yes	10	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-0.568445 q^{2} +0.674153 q^{3} -1.67687 q^{4} +1.00000 q^{5} -0.383219 q^{6} +2.09010 q^{8} -2.54552 q^{9} +O(q^{10})\)	\(q-0.568445 q^{2} +0.674153 q^{3} -1.67687 q^{4} +1.00000 q^{5} -0.383219 q^{6} +2.09010 q^{8} -2.54552 q^{9} -0.568445 q^{10} -1.00000 q^{11} -1.13047 q^{12} +1.13393 q^{13} +0.674153 q^{15} +2.16563 q^{16} -0.503652 q^{17} +1.44699 q^{18} -5.40761 q^{19} -1.67687 q^{20} +0.568445 q^{22} +0.365925 q^{23} +1.40905 q^{24} +1.00000 q^{25} -0.644578 q^{26} -3.73853 q^{27} +7.02874 q^{29} -0.383219 q^{30} +5.91866 q^{31} -5.41124 q^{32} -0.674153 q^{33} +0.286299 q^{34} +4.26850 q^{36} -1.70697 q^{37} +3.07393 q^{38} +0.764444 q^{39} +2.09010 q^{40} -1.38530 q^{41} +9.60393 q^{43} +1.67687 q^{44} -2.54552 q^{45} -0.208008 q^{46} +1.01427 q^{47} +1.45997 q^{48} -0.568445 q^{50} -0.339539 q^{51} -1.90146 q^{52} -0.0335756 q^{53} +2.12515 q^{54} -1.00000 q^{55} -3.64556 q^{57} -3.99545 q^{58} +6.99424 q^{59} -1.13047 q^{60} +4.73120 q^{61} -3.36443 q^{62} -1.25527 q^{64} +1.13393 q^{65} +0.383219 q^{66} -7.09660 q^{67} +0.844559 q^{68} +0.246689 q^{69} +1.01456 q^{71} -5.32038 q^{72} -8.82857 q^{73} +0.970318 q^{74} +0.674153 q^{75} +9.06787 q^{76} -0.434544 q^{78} +6.44507 q^{79} +2.16563 q^{80} +5.11621 q^{81} +0.787470 q^{82} +4.08099 q^{83} -0.503652 q^{85} -5.45931 q^{86} +4.73845 q^{87} -2.09010 q^{88} +2.62316 q^{89} +1.44699 q^{90} -0.613609 q^{92} +3.99008 q^{93} -0.576559 q^{94} -5.40761 q^{95} -3.64801 q^{96} +17.6494 q^{97} +2.54552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} + 4 q^{12} + 8 q^{13} + 6 q^{16} + 28 q^{17} - 10 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} - 8 q^{23} + 32 q^{24} + 10 q^{25} + 12 q^{26} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 20 q^{34} - 22 q^{36} + 28 q^{37} + 24 q^{38} - 24 q^{39} + 6 q^{40} + 44 q^{41} + 20 q^{43} - 10 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 36 q^{52} - 8 q^{54} - 10 q^{55} + 12 q^{57} - 8 q^{58} + 16 q^{59} + 4 q^{60} + 16 q^{61} + 36 q^{62} - 34 q^{64} + 8 q^{65} - 4 q^{66} + 20 q^{67} + 8 q^{68} + 4 q^{69} - 4 q^{71} + 10 q^{72} + 20 q^{73} - 16 q^{74} + 4 q^{76} + 52 q^{78} - 20 q^{79} + 6 q^{80} + 10 q^{81} - 32 q^{82} + 16 q^{83} + 28 q^{85} - 20 q^{86} + 20 q^{87} - 6 q^{88} + 44 q^{89} - 10 q^{90} - 24 q^{92} + 16 q^{93} + 24 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 + 4 * q^12 + 8 * q^13 + 6 * q^16 + 28 * q^17 - 10 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 - 8 * q^23 + 32 * q^24 + 10 * q^25 + 12 * q^26 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 14 * q^32 + 20 * q^34 - 22 * q^36 + 28 * q^37 + 24 * q^38 - 24 * q^39 + 6 * q^40 + 44 * q^41 + 20 * q^43 - 10 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 36 * q^52 - 8 * q^54 - 10 * q^55 + 12 * q^57 - 8 * q^58 + 16 * q^59 + 4 * q^60 + 16 * q^61 + 36 * q^62 - 34 * q^64 + 8 * q^65 - 4 * q^66 + 20 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^71 + 10 * q^72 + 20 * q^73 - 16 * q^74 + 4 * q^76 + 52 * q^78 - 20 * q^79 + 6 * q^80 + 10 * q^81 - 32 * q^82 + 16 * q^83 + 28 * q^85 - 20 * q^86 + 20 * q^87 - 6 * q^88 + 44 * q^89 - 10 * q^90 - 24 * q^92 + 16 * q^93 + 24 * q^94 + 8 * q^95 - 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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