LMFDB - Embedded newform 7942.2.a.ca.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 33 x^{13} + 101 x^{12} + 408 x^{11} - 1314 x^{10} - 2271 x^{9} + 8292 x^{8} + \cdots - 3592 $ x^15 - 3x^14 - 33x^13 + 101x^12 + 408x^11 - 1314x^10 - 2271x^9 + 8292x^8 + 4944x^7 - 26254x^6 + 1401x^5 + 39318x^4 - 19069x^3 - 20118x^2 + 18180x - 3592
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.11596$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.11596 q^{3} +1.00000 q^{4} +1.31280 q^{5} +1.11596 q^{6} +4.27450 q^{7} +1.00000 q^{8} -1.75463 q^{9} +1.31280 q^{10} -1.00000 q^{11} +1.11596 q^{12} +1.28738 q^{13} +4.27450 q^{14} +1.46503 q^{15} +1.00000 q^{16} +4.16533 q^{17} -1.75463 q^{18} +1.31280 q^{20} +4.77018 q^{21} -1.00000 q^{22} -5.17499 q^{23} +1.11596 q^{24} -3.27656 q^{25} +1.28738 q^{26} -5.30599 q^{27} +4.27450 q^{28} -4.44333 q^{29} +1.46503 q^{30} +1.41424 q^{31} +1.00000 q^{32} -1.11596 q^{33} +4.16533 q^{34} +5.61155 q^{35} -1.75463 q^{36} +9.94702 q^{37} +1.43667 q^{39} +1.31280 q^{40} +1.43023 q^{41} +4.77018 q^{42} +7.81236 q^{43} -1.00000 q^{44} -2.30347 q^{45} -5.17499 q^{46} +7.17369 q^{47} +1.11596 q^{48} +11.2714 q^{49} -3.27656 q^{50} +4.64835 q^{51} +1.28738 q^{52} +7.03965 q^{53} -5.30599 q^{54} -1.31280 q^{55} +4.27450 q^{56} -4.44333 q^{58} +1.81150 q^{59} +1.46503 q^{60} -5.39823 q^{61} +1.41424 q^{62} -7.50015 q^{63} +1.00000 q^{64} +1.69007 q^{65} -1.11596 q^{66} +3.85733 q^{67} +4.16533 q^{68} -5.77510 q^{69} +5.61155 q^{70} -4.84903 q^{71} -1.75463 q^{72} +10.5626 q^{73} +9.94702 q^{74} -3.65652 q^{75} -4.27450 q^{77} +1.43667 q^{78} +7.22195 q^{79} +1.31280 q^{80} -0.657405 q^{81} +1.43023 q^{82} +11.8052 q^{83} +4.77018 q^{84} +5.46823 q^{85} +7.81236 q^{86} -4.95859 q^{87} -1.00000 q^{88} -2.08674 q^{89} -2.30347 q^{90} +5.50292 q^{91} -5.17499 q^{92} +1.57824 q^{93} +7.17369 q^{94} +1.11596 q^{96} -9.42699 q^{97} +11.2714 q^{98} +1.75463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 15 q^{8} + 30 q^{9} + 9 q^{10} - 15 q^{11} + 3 q^{12} + 21 q^{15} + 15 q^{16} + 21 q^{17} + 30 q^{18} + 9 q^{20} - 9 q^{21} - 15 q^{22} + 21 q^{23}+ \cdots - 30 q^{99}+O(q^{100}) $ 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 15 * q^8 + 30 * q^9 + 9 * q^10 - 15 * q^11 + 3 * q^12 + 21 * q^15 + 15 * q^16 + 21 * q^17 + 30 * q^18 + 9 * q^20 - 9 * q^21 - 15 * q^22 + 21 * q^23 + 3 * q^24 + 24 * q^25 + 3 * q^27 - 9 * q^29 + 21 * q^30 + 18 * q^31 + 15 * q^32 - 3 * q^33 + 21 * q^34 + 18 * q^35 + 30 * q^36 - 9 * q^37 + 9 * q^40 + 15 * q^41 - 9 * q^42 + 3 * q^43 - 15 * q^44 + 54 * q^45 + 21 * q^46 + 39 * q^47 + 3 * q^48 + 33 * q^49 + 24 * q^50 + 30 * q^51 + 18 * q^53 + 3 * q^54 - 9 * q^55 - 9 * q^58 + 6 * q^59 + 21 * q^60 - 30 * q^61 + 18 * q^62 + 24 * q^63 + 15 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 + 21 * q^68 - 42 * q^69 + 18 * q^70 + 9 * q^71 + 30 * q^72 + 12 * q^73 - 9 * q^74 + 21 * q^75 + 12 * q^79 + 9 * q^80 + 63 * q^81 + 15 * q^82 + 30 * q^83 - 9 * q^84 - 3 * q^85 + 3 * q^86 + 9 * q^87 - 15 * q^88 - 6 * q^89 + 54 * q^90 + 96 * q^91 + 21 * q^92 + 102 * q^93 + 39 * q^94 + 3 * q^96 + 33 * q^98 - 30 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.11596	0.644301	0.322151	−	0.946688i	$-0.395594\pi$
$3$	1.11596	0.644301	0.322151	+	0.946688i	$0.395594\pi$
$4$	1.00000	0.500000
$5$	1.31280	0.587101	0.293550	−	0.955944i	$-0.405163\pi$
$5$	1.31280	0.587101	0.293550	+	0.955944i	$0.405163\pi$
$6$	1.11596	0.455590
$7$	4.27450	1.61561	0.807805	−	0.589450i	$-0.200656\pi$
$7$	4.27450	1.61561	0.807805	+	0.589450i	$0.200656\pi$
$8$	1.00000	0.353553
$9$	−1.75463	−0.584876
$10$	1.31280	0.415143
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.11596	0.322151
$13$	1.28738	0.357056	0.178528	−	0.983935i	$-0.442866\pi$
$13$	1.28738	0.357056	0.178528	+	0.983935i	$0.442866\pi$
$14$	4.27450	1.14241
$15$	1.46503	0.378270
$16$	1.00000	0.250000
$17$	4.16533	1.01024	0.505120	−	0.863049i	$-0.331448\pi$
$17$	4.16533	1.01024	0.505120	+	0.863049i	$0.331448\pi$
$18$	−1.75463	−0.413569
$19$	0	0
$19$	0	0
$20$	1.31280	0.293550
$21$	4.77018	1.04094
$22$	−1.00000	−0.213201
$23$	−5.17499	−1.07906	−0.539530	−	0.841966i	$-0.681398\pi$
$23$	−5.17499	−1.07906	−0.539530	+	0.841966i	$0.681398\pi$
$24$	1.11596	0.227795
$25$	−3.27656	−0.655312
$26$	1.28738	0.252477
$27$	−5.30599	−1.02114
$28$	4.27450	0.807805
$29$	−4.44333	−0.825106	−0.412553	−	0.910934i	$-0.635363\pi$
$29$	−4.44333	−0.825106	−0.412553	+	0.910934i	$0.635363\pi$
$30$	1.46503	0.267477
$31$	1.41424	0.254005	0.127002	−	0.991902i	$-0.459464\pi$
$31$	1.41424	0.254005	0.127002	+	0.991902i	$0.459464\pi$
$32$	1.00000	0.176777
$33$	−1.11596	−0.194264
$34$	4.16533	0.714348
$35$	5.61155	0.948526
$36$	−1.75463	−0.292438
$37$	9.94702	1.63528	0.817640	−	0.575730i	$-0.195282\pi$
$37$	9.94702	1.63528	0.817640	+	0.575730i	$0.195282\pi$
$38$	0	0
$39$	1.43667	0.230052
$40$	1.31280	0.207572
$41$	1.43023	0.223364	0.111682	−	0.993744i	$-0.464376\pi$
$41$	1.43023	0.223364	0.111682	+	0.993744i	$0.464376\pi$
$42$	4.77018	0.736055
$43$	7.81236	1.19137	0.595686	−	0.803217i	$-0.296880\pi$
$43$	7.81236	1.19137	0.595686	+	0.803217i	$0.296880\pi$
$44$	−1.00000	−0.150756
$45$	−2.30347	−0.343381
$46$	−5.17499	−0.763011
$47$	7.17369	1.04639	0.523195	−	0.852213i	$-0.324740\pi$
$47$	7.17369	1.04639	0.523195	+	0.852213i	$0.324740\pi$
$48$	1.11596	0.161075
$49$	11.2714	1.61019
$50$	−3.27656	−0.463376
$51$	4.64835	0.650899
$52$	1.28738	0.178528
$53$	7.03965	0.966970	0.483485	−	0.875353i	$-0.339371\pi$
$53$	7.03965	0.966970	0.483485	+	0.875353i	$0.339371\pi$
$54$	−5.30599	−0.722053
$55$	−1.31280	−0.177018
$56$	4.27450	0.571204
$57$	0	0
$58$	−4.44333	−0.583438
$59$	1.81150	0.235838	0.117919	−	0.993023i	$-0.462378\pi$
$59$	1.81150	0.235838	0.117919	+	0.993023i	$0.462378\pi$
$60$	1.46503	0.189135
$61$	−5.39823	−0.691173	−0.345586	−	0.938387i	$-0.612320\pi$
$61$	−5.39823	−0.691173	−0.345586	+	0.938387i	$0.612320\pi$
$62$	1.41424	0.179608
$63$	−7.50015	−0.944931
$64$	1.00000	0.125000
$65$	1.69007	0.209628
$66$	−1.11596	−0.137366
$67$	3.85733	0.471248	0.235624	−	0.971844i	$-0.424287\pi$
$67$	3.85733	0.471248	0.235624	+	0.971844i	$0.424287\pi$
$68$	4.16533	0.505120
$69$	−5.77510	−0.695240
$70$	5.61155	0.670709
$71$	−4.84903	−0.575474	−0.287737	−	0.957709i	$-0.592903\pi$
$71$	−4.84903	−0.575474	−0.287737	+	0.957709i	$0.592903\pi$
$72$	−1.75463	−0.206785
$73$	10.5626	1.23626	0.618128	−	0.786077i	$-0.287891\pi$
$73$	10.5626	1.23626	0.618128	+	0.786077i	$0.287891\pi$
$74$	9.94702	1.15632
$75$	−3.65652	−0.422219
$76$	0	0
$77$	−4.27450	−0.487125
$78$	1.43667	0.162671
$79$	7.22195	0.812533	0.406266	−	0.913755i	$-0.366830\pi$
$79$	7.22195	0.812533	0.406266	+	0.913755i	$0.366830\pi$
$80$	1.31280	0.146775
$81$	−0.657405	−0.0730450
$82$	1.43023	0.157942
$83$	11.8052	1.29579	0.647896	−	0.761729i	$-0.275649\pi$
$83$	11.8052	1.29579	0.647896	+	0.761729i	$0.275649\pi$
$84$	4.77018	0.520470
$85$	5.46823	0.593113
$86$	7.81236	0.842428
$87$	−4.95859	−0.531617
$88$	−1.00000	−0.106600
$89$	−2.08674	−0.221194	−0.110597	−	0.993865i	$-0.535276\pi$
$89$	−2.08674	−0.221194	−0.110597	+	0.993865i	$0.535276\pi$
$90$	−2.30347	−0.242807
$91$	5.50292	0.576863
$92$	−5.17499	−0.539530
$93$	1.57824	0.163656
$94$	7.17369	0.739909
$95$	0	0
$96$	1.11596	0.113897
$97$	−9.42699	−0.957166	−0.478583	−	0.878042i	$-0.658849\pi$
$97$	−9.42699	−0.957166	−0.478583	+	0.878042i	$0.658849\pi$
$98$	11.2714	1.13858
$99$	1.75463	0.176347
$100$	−3.27656	−0.327656
$101$	19.0888	1.89941	0.949703	−	0.313153i	$-0.101385\pi$
$101$	19.0888	1.89941	0.949703	+	0.313153i	$0.101385\pi$
$102$	4.64835	0.460255
$103$	−9.14040	−0.900630	−0.450315	−	0.892870i	$-0.648688\pi$
$103$	−9.14040	−0.900630	−0.450315	+	0.892870i	$0.648688\pi$
$104$	1.28738	0.126238
$105$	6.26229	0.611137
$106$	7.03965	0.683751
$107$	10.9124	1.05494	0.527469	−	0.849575i	$-0.323141\pi$
$107$	10.9124	1.05494	0.527469	+	0.849575i	$0.323141\pi$
$108$	−5.30599	−0.510569
$109$	−20.1828	−1.93316	−0.966582	−	0.256357i	$-0.917478\pi$
$109$	−20.1828	−1.93316	−0.966582	+	0.256357i	$0.917478\pi$
$110$	−1.31280	−0.125170
$111$	11.1005	1.05361
$112$	4.27450	0.403902
$113$	−1.14974	−0.108158	−0.0540791	−	0.998537i	$-0.517222\pi$
$113$	−1.14974	−0.108158	−0.0540791	+	0.998537i	$0.517222\pi$
$114$	0	0
$115$	−6.79372	−0.633517
$116$	−4.44333	−0.412553
$117$	−2.25888	−0.208833
$118$	1.81150	0.166762
$119$	17.8047	1.63215
$120$	1.46503	0.133739
$121$	1.00000	0.0909091
$122$	−5.39823	−0.488733
$123$	1.59608	0.143914
$124$	1.41424	0.127002
$125$	−10.8655	−0.971836
$126$	−7.50015	−0.668167
$127$	−9.97947	−0.885535	−0.442767	−	0.896637i	$-0.646003\pi$
$127$	−9.97947	−0.885535	−0.442767	+	0.896637i	$0.646003\pi$
$128$	1.00000	0.0883883
$129$	8.71830	0.767603
$130$	1.69007	0.148229
$131$	14.6673	1.28149	0.640746	−	0.767753i	$-0.278625\pi$
$131$	14.6673	1.28149	0.640746	+	0.767753i	$0.278625\pi$
$132$	−1.11596	−0.0971321
$133$	0	0
$134$	3.85733	0.333223
$135$	−6.96569	−0.599511
$136$	4.16533	0.357174
$137$	−12.2599	−1.04743	−0.523715	−	0.851893i	$-0.675454\pi$
$137$	−12.2599	−1.04743	−0.523715	+	0.851893i	$0.675454\pi$
$138$	−5.77510	−0.491609
$139$	−6.46785	−0.548596	−0.274298	−	0.961645i	$-0.588445\pi$
$139$	−6.46785	−0.548596	−0.274298	+	0.961645i	$0.588445\pi$
$140$	5.61155	0.474263
$141$	8.00557	0.674191
$142$	−4.84903	−0.406921
$143$	−1.28738	−0.107656
$144$	−1.75463	−0.146219
$145$	−5.83319	−0.484420
$146$	10.5626	0.874165
$147$	12.5784	1.03745
$148$	9.94702	0.817640
$149$	18.1637	1.48803	0.744013	−	0.668165i	$-0.232920\pi$
$149$	18.1637	1.48803	0.744013	+	0.668165i	$0.232920\pi$
$150$	−3.65652	−0.298554
$151$	−3.66729	−0.298440	−0.149220	−	0.988804i	$-0.547676\pi$
$151$	−3.66729	−0.298440	−0.149220	+	0.988804i	$0.547676\pi$
$152$	0	0
$153$	−7.30860	−0.590865
$154$	−4.27450	−0.344449
$155$	1.85661	0.149126
$156$	1.43667	0.115026
$157$	−9.47377	−0.756089	−0.378045	−	0.925787i	$-0.623403\pi$
$157$	−9.47377	−0.756089	−0.378045	+	0.925787i	$0.623403\pi$
$158$	7.22195	0.574548
$159$	7.85598	0.623020
$160$	1.31280	0.103786
$161$	−22.1205	−1.74334
$162$	−0.657405	−0.0516506
$163$	11.4020	0.893077	0.446539	−	0.894764i	$-0.352657\pi$
$163$	11.4020	0.893077	0.446539	+	0.894764i	$0.352657\pi$
$164$	1.43023	0.111682
$165$	−1.46503	−0.114053
$166$	11.8052	0.916263
$167$	−6.70943	−0.519191	−0.259596	−	0.965717i	$-0.583589\pi$
$167$	−6.70943	−0.519191	−0.259596	+	0.965717i	$0.583589\pi$
$168$	4.77018	0.368028
$169$	−11.3426	−0.872511
$170$	5.46823	0.419394
$171$	0	0
$172$	7.81236	0.595686
$173$	14.7854	1.12411	0.562055	−	0.827100i	$-0.310011\pi$
$173$	14.7854	1.12411	0.562055	+	0.827100i	$0.310011\pi$
$174$	−4.95859	−0.375910
$175$	−14.0057	−1.05873
$176$	−1.00000	−0.0753778
$177$	2.02157	0.151951
$178$	−2.08674	−0.156408
$179$	−12.5066	−0.934788	−0.467394	−	0.884049i	$-0.654807\pi$
$179$	−12.5066	−0.934788	−0.467394	+	0.884049i	$0.654807\pi$
$180$	−2.30347	−0.171691
$181$	−17.5886	−1.30735	−0.653677	−	0.756774i	$-0.726774\pi$
$181$	−17.5886	−1.30735	−0.653677	+	0.756774i	$0.726774\pi$
$182$	5.50292	0.407904
$183$	−6.02423	−0.445324
$184$	−5.17499	−0.381505
$185$	13.0584	0.960074
$186$	1.57824	0.115722
$187$	−4.16533	−0.304599
$188$	7.17369	0.523195
$189$	−22.6804	−1.64976
$190$	0	0
$191$	−19.7063	−1.42590	−0.712949	−	0.701216i	$-0.752641\pi$
$191$	−19.7063	−1.42590	−0.712949	+	0.701216i	$0.752641\pi$
$192$	1.11596	0.0805377
$193$	−12.6093	−0.907635	−0.453817	−	0.891095i	$-0.649938\pi$
$193$	−12.6093	−0.907635	−0.453817	+	0.891095i	$0.649938\pi$
$194$	−9.42699	−0.676818
$195$	1.88606	0.135064
$196$	11.2714	0.805097
$197$	11.4923	0.818795	0.409398	−	0.912356i	$-0.365739\pi$
$197$	11.4923	0.818795	0.409398	+	0.912356i	$0.365739\pi$
$198$	1.75463	0.124696
$199$	−22.2171	−1.57493	−0.787465	−	0.616360i	$-0.788607\pi$
$199$	−22.2171	−1.57493	−0.787465	+	0.616360i	$0.788607\pi$
$200$	−3.27656	−0.231688
$201$	4.30464	0.303626
$202$	19.0888	1.34308
$203$	−18.9930	−1.33305
$204$	4.64835	0.325450
$205$	1.87760	0.131137
$206$	−9.14040	−0.636842
$207$	9.08018	0.631116
$208$	1.28738	0.0892640
$209$	0	0
$210$	6.26229	0.432139
$211$	−25.9989	−1.78984	−0.894918	−	0.446230i	$-0.852766\pi$
$211$	−25.9989	−1.78984	−0.894918	+	0.446230i	$0.852766\pi$
$212$	7.03965	0.483485
$213$	−5.41134	−0.370779
$214$	10.9124	0.745953
$215$	10.2560	0.699456
$216$	−5.30599	−0.361027
$217$	6.04516	0.410372
$218$	−20.1828	−1.36695
$219$	11.7874	0.796522
$220$	−1.31280	−0.0885088
$221$	5.36238	0.360712
$222$	11.1005	0.745017
$223$	9.44727	0.632636	0.316318	−	0.948653i	$-0.397553\pi$
$223$	9.44727	0.632636	0.316318	+	0.948653i	$0.397553\pi$
$224$	4.27450	0.285602
$225$	5.74914	0.383276
$226$	−1.14974	−0.0764794
$227$	−27.4851	−1.82425	−0.912124	−	0.409915i	$-0.865558\pi$
$227$	−27.4851	−1.82425	−0.912124	+	0.409915i	$0.865558\pi$
$228$	0	0
$229$	−9.14706	−0.604454	−0.302227	−	0.953236i	$-0.597730\pi$
$229$	−9.14706	−0.604454	−0.302227	+	0.953236i	$0.597730\pi$
$230$	−6.79372	−0.447964
$231$	−4.77018	−0.313855
$232$	−4.44333	−0.291719
$233$	−6.02154	−0.394484	−0.197242	−	0.980355i	$-0.563199\pi$
$233$	−6.02154	−0.394484	−0.197242	+	0.980355i	$0.563199\pi$
$234$	−2.25888	−0.147667
$235$	9.41760	0.614337
$236$	1.81150	0.117919
$237$	8.05943	0.523516
$238$	17.8047	1.15411
$239$	23.8647	1.54368	0.771840	−	0.635817i	$-0.219337\pi$
$239$	23.8647	1.54368	0.771840	+	0.635817i	$0.219337\pi$
$240$	1.46503	0.0945675
$241$	20.3440	1.31047	0.655236	−	0.755425i	$-0.272569\pi$
$241$	20.3440	1.31047	0.655236	+	0.755425i	$0.272569\pi$
$242$	1.00000	0.0642824
$243$	15.1843	0.974075
$244$	−5.39823	−0.345586
$245$	14.7970	0.945347
$246$	1.59608	0.101763
$247$	0	0
$248$	1.41424	0.0898042
$249$	13.1742	0.834880
$250$	−10.8655	−0.687191
$251$	−1.96033	−0.123735	−0.0618676	−	0.998084i	$-0.519706\pi$
$251$	−1.96033	−0.123735	−0.0618676	+	0.998084i	$0.519706\pi$
$252$	−7.50015	−0.472465
$253$	5.17499	0.325349
$254$	−9.97947	−0.626168
$255$	6.10235	0.382144
$256$	1.00000	0.0625000
$257$	0.599255	0.0373805	0.0186903	−	0.999825i	$-0.494050\pi$
$257$	0.599255	0.0373805	0.0186903	+	0.999825i	$0.494050\pi$
$258$	8.71830	0.542778
$259$	42.5185	2.64197
$260$	1.69007	0.104814
$261$	7.79639	0.482584
$262$	14.6673	0.906151
$263$	15.8684	0.978485	0.489242	−	0.872148i	$-0.337273\pi$
$263$	15.8684	0.978485	0.489242	+	0.872148i	$0.337273\pi$
$264$	−1.11596	−0.0686828
$265$	9.24163	0.567709
$266$	0	0
$267$	−2.32873	−0.142516
$268$	3.85733	0.235624
$269$	10.3445	0.630714	0.315357	−	0.948973i	$-0.397876\pi$
$269$	10.3445	0.630714	0.315357	+	0.948973i	$0.397876\pi$
$270$	−6.96569	−0.423918
$271$	−16.3659	−0.994159	−0.497080	−	0.867705i	$-0.665594\pi$
$271$	−16.3659	−0.994159	−0.497080	+	0.867705i	$0.665594\pi$
$272$	4.16533	0.252560
$273$	6.14106	0.371674
$274$	−12.2599	−0.740645
$275$	3.27656	0.197584
$276$	−5.77510	−0.347620
$277$	−0.767289	−0.0461019	−0.0230510	−	0.999734i	$-0.507338\pi$
$277$	−0.767289	−0.0461019	−0.0230510	+	0.999734i	$0.507338\pi$
$278$	−6.46785	−0.387916
$279$	−2.48146	−0.148561
$280$	5.61155	0.335355
$281$	−26.5207	−1.58209	−0.791047	−	0.611755i	$-0.790464\pi$
$281$	−26.5207	−1.58209	−0.791047	+	0.611755i	$0.790464\pi$
$282$	8.00557	0.476725
$283$	−6.65638	−0.395681	−0.197840	−	0.980234i	$-0.563393\pi$
$283$	−6.65638	−0.395681	−0.197840	+	0.980234i	$0.563393\pi$
$284$	−4.84903	−0.287737
$285$	0	0
$286$	−1.28738	−0.0761246
$287$	6.11352	0.360870
$288$	−1.75463	−0.103392
$289$	0.349959	0.0205858
$290$	−5.83319	−0.342537
$291$	−10.5202	−0.616703
$292$	10.5626	0.618128
$293$	−4.18747	−0.244635	−0.122317	−	0.992491i	$-0.539033\pi$
$293$	−4.18747	−0.244635	−0.122317	+	0.992491i	$0.539033\pi$
$294$	12.5784	0.733588
$295$	2.37814	0.138461
$296$	9.94702	0.578159
$297$	5.30599	0.307885
$298$	18.1637	1.05219
$299$	−6.66220	−0.385285
$300$	−3.65652	−0.211109
$301$	33.3939	1.92479
$302$	−3.66729	−0.211029
$303$	21.3024	1.22379
$304$	0	0
$305$	−7.08679	−0.405788
$306$	−7.30860	−0.417805
$307$	10.0213	0.571944	0.285972	−	0.958238i	$-0.407684\pi$
$307$	10.0213	0.571944	0.285972	+	0.958238i	$0.407684\pi$
$308$	−4.27450	−0.243562
$309$	−10.2003	−0.580278
$310$	1.85661	0.105448
$311$	−11.1459	−0.632026	−0.316013	−	0.948755i	$-0.602344\pi$
$311$	−11.1459	−0.632026	−0.316013	+	0.948755i	$0.602344\pi$
$312$	1.43667	0.0813356
$313$	−2.43390	−0.137572	−0.0687860	−	0.997631i	$-0.521913\pi$
$313$	−2.43390	−0.137572	−0.0687860	+	0.997631i	$0.521913\pi$
$314$	−9.47377	−0.534636
$315$	−9.84618	−0.554770
$316$	7.22195	0.406266
$317$	−11.3922	−0.639851	−0.319926	−	0.947443i	$-0.603658\pi$
$317$	−11.3922	−0.639851	−0.319926	+	0.947443i	$0.603658\pi$
$318$	7.85598	0.440542
$319$	4.44333	0.248779
$320$	1.31280	0.0733876
$321$	12.1778	0.679698
$322$	−22.1205	−1.23273
$323$	0	0
$324$	−0.657405	−0.0365225
$325$	−4.21819	−0.233983
$326$	11.4020	0.631501
$327$	−22.5233	−1.24554
$328$	1.43023	0.0789712
$329$	30.6639	1.69056
$330$	−1.46503	−0.0806474
$331$	5.72063	0.314434	0.157217	−	0.987564i	$-0.449748\pi$
$331$	5.72063	0.314434	0.157217	+	0.987564i	$0.449748\pi$
$332$	11.8052	0.647896
$333$	−17.4533	−0.956435
$334$	−6.70943	−0.367124
$335$	5.06390	0.276670
$336$	4.77018	0.260235
$337$	21.1662	1.15300	0.576499	−	0.817098i	$-0.304418\pi$
$337$	21.1662	1.15300	0.576499	+	0.817098i	$0.304418\pi$
$338$	−11.3426	−0.616958
$339$	−1.28306	−0.0696865
$340$	5.46823	0.296557
$341$	−1.41424	−0.0765853
$342$	0	0
$343$	18.2579	0.985835
$344$	7.81236	0.421214
$345$	−7.58153	−0.408176
$346$	14.7854	0.794866
$347$	−30.3317	−1.62829	−0.814144	−	0.580663i	$-0.802793\pi$
$347$	−30.3317	−1.62829	−0.814144	+	0.580663i	$0.802793\pi$
$348$	−4.95859	−0.265808
$349$	7.30224	0.390880	0.195440	−	0.980716i	$-0.437386\pi$
$349$	7.30224	0.390880	0.195440	+	0.980716i	$0.437386\pi$
$350$	−14.0057	−0.748634
$351$	−6.83084	−0.364603
$352$	−1.00000	−0.0533002
$353$	−0.674177	−0.0358828	−0.0179414	−	0.999839i	$-0.505711\pi$
$353$	−0.674177	−0.0358828	−0.0179414	+	0.999839i	$0.505711\pi$
$354$	2.02157	0.107445
$355$	−6.36579	−0.337861
$356$	−2.08674	−0.110597
$357$	19.8694	1.05160
$358$	−12.5066	−0.660995
$359$	26.7789	1.41334	0.706668	−	0.707545i	$-0.250197\pi$
$359$	26.7789	1.41334	0.706668	+	0.707545i	$0.250197\pi$
$360$	−2.30347	−0.121404
$361$	0	0
$362$	−17.5886	−0.924438
$363$	1.11596	0.0585729
$364$	5.50292	0.288432
$365$	13.8665	0.725807
$366$	−6.02423	−0.314891
$367$	−23.5890	−1.23134	−0.615669	−	0.788005i	$-0.711114\pi$
$367$	−23.5890	−1.23134	−0.615669	+	0.788005i	$0.711114\pi$
$368$	−5.17499	−0.269765
$369$	−2.50952	−0.130640
$370$	13.0584	0.678875
$371$	30.0910	1.56225
$372$	1.57824	0.0818278
$373$	−26.4394	−1.36898	−0.684491	−	0.729021i	$-0.739976\pi$
$373$	−26.4394	−1.36898	−0.684491	+	0.729021i	$0.739976\pi$
$374$	−4.16533	−0.215384
$375$	−12.1254	−0.626155
$376$	7.17369	0.369955
$377$	−5.72027	−0.294609
$378$	−22.6804	−1.16656
$379$	−5.38458	−0.276587	−0.138294	−	0.990391i	$-0.544162\pi$
$379$	−5.38458	−0.276587	−0.138294	+	0.990391i	$0.544162\pi$
$380$	0	0
$381$	−11.1367	−0.570551
$382$	−19.7063	−1.00826
$383$	6.57402	0.335917	0.167958	−	0.985794i	$-0.446283\pi$
$383$	6.57402	0.335917	0.167958	+	0.985794i	$0.446283\pi$
$384$	1.11596	0.0569487
$385$	−5.61155	−0.285991
$386$	−12.6093	−0.641795
$387$	−13.7078	−0.696805
$388$	−9.42699	−0.478583
$389$	29.5322	1.49734	0.748670	−	0.662943i	$-0.230693\pi$
$389$	29.5322	1.49734	0.748670	+	0.662943i	$0.230693\pi$
$390$	1.88606	0.0955044
$391$	−21.5555	−1.09011
$392$	11.2714	0.569290
$393$	16.3682	0.825667
$394$	11.4923	0.578976
$395$	9.48096	0.477039
$396$	1.75463	0.0881733
$397$	−33.3685	−1.67472	−0.837359	−	0.546653i	$-0.815902\pi$
$397$	−33.3685	−1.67472	−0.837359	+	0.546653i	$0.815902\pi$
$398$	−22.2171	−1.11364
$399$	0	0
$400$	−3.27656	−0.163828
$401$	16.0156	0.799780	0.399890	−	0.916563i	$-0.369048\pi$
$401$	16.0156	0.799780	0.399890	+	0.916563i	$0.369048\pi$
$402$	4.30464	0.214696
$403$	1.82067	0.0906939
$404$	19.0888	0.949703
$405$	−0.863039	−0.0428848
$406$	−18.9930	−0.942608
$407$	−9.94702	−0.493055
$408$	4.64835	0.230128
$409$	19.4042	0.959476	0.479738	−	0.877412i	$-0.340732\pi$
$409$	19.4042	0.959476	0.479738	+	0.877412i	$0.340732\pi$
$410$	1.87760	0.0927282
$411$	−13.6815	−0.674861
$412$	−9.14040	−0.450315
$413$	7.74327	0.381022
$414$	9.08018	0.446266
$415$	15.4979	0.760760
$416$	1.28738	0.0631192
$417$	−7.21788	−0.353461
$418$	0	0
$419$	8.09863	0.395644	0.197822	−	0.980238i	$-0.436613\pi$
$419$	8.09863	0.395644	0.197822	+	0.980238i	$0.436613\pi$
$420$	6.26229	0.305568
$421$	−28.8307	−1.40512	−0.702560	−	0.711625i	$-0.747960\pi$
$421$	−28.8307	−1.40512	−0.702560	+	0.711625i	$0.747960\pi$
$422$	−25.9989	−1.26561
$423$	−12.5871	−0.612008
$424$	7.03965	0.341875
$425$	−13.6480	−0.662023
$426$	−5.41134	−0.262180
$427$	−23.0747	−1.11667
$428$	10.9124	0.527469
$429$	−1.43667	−0.0693632
$430$	10.2560	0.494590
$431$	6.21324	0.299281	0.149641	−	0.988740i	$-0.452188\pi$
$431$	6.21324	0.299281	0.149641	+	0.988740i	$0.452188\pi$
$432$	−5.30599	−0.255284
$433$	0.769196	0.0369652	0.0184826	−	0.999829i	$-0.494116\pi$
$433$	0.769196	0.0369652	0.0184826	+	0.999829i	$0.494116\pi$
$434$	6.04516	0.290177
$435$	−6.50963	−0.312113
$436$	−20.1828	−0.966582
$437$	0	0
$438$	11.7874	0.563226
$439$	1.96983	0.0940151	0.0470075	−	0.998895i	$-0.485032\pi$
$439$	1.96983	0.0940151	0.0470075	+	0.998895i	$0.485032\pi$
$440$	−1.31280	−0.0625852
$441$	−19.7770	−0.941763
$442$	5.36238	0.255062
$443$	23.4896	1.11602	0.558012	−	0.829833i	$-0.311564\pi$
$443$	23.4896	1.11602	0.558012	+	0.829833i	$0.311564\pi$
$444$	11.1005	0.526806
$445$	−2.73947	−0.129863
$446$	9.44727	0.447341
$447$	20.2700	0.958737
$448$	4.27450	0.201951
$449$	−33.5468	−1.58317	−0.791587	−	0.611057i	$-0.790745\pi$
$449$	−33.5468	−1.58317	−0.791587	+	0.611057i	$0.790745\pi$
$450$	5.74914	0.271017
$451$	−1.43023	−0.0673469
$452$	−1.14974	−0.0540791
$453$	−4.09256	−0.192285
$454$	−27.4851	−1.28994
$455$	7.22422	0.338677
$456$	0	0
$457$	−25.9818	−1.21538	−0.607688	−	0.794176i	$-0.707903\pi$
$457$	−25.9818	−1.21538	−0.607688	+	0.794176i	$0.707903\pi$
$458$	−9.14706	−0.427414
$459$	−22.1012	−1.03159
$460$	−6.79372	−0.316759
$461$	17.9883	0.837797	0.418898	−	0.908033i	$-0.362416\pi$
$461$	17.9883	0.837797	0.418898	+	0.908033i	$0.362416\pi$
$462$	−4.77018	−0.221929
$463$	33.2333	1.54448	0.772241	−	0.635330i	$-0.219136\pi$
$463$	33.2333	1.54448	0.772241	+	0.635330i	$0.219136\pi$
$464$	−4.44333	−0.206276
$465$	2.07191	0.0960824
$466$	−6.02154	−0.278943
$467$	−29.5798	−1.36879	−0.684394	−	0.729112i	$-0.739933\pi$
$467$	−29.5798	−1.36879	−0.684394	+	0.729112i	$0.739933\pi$
$468$	−2.25888	−0.104417
$469$	16.4882	0.761353
$470$	9.41760	0.434402
$471$	−10.5724	−0.487150
$472$	1.81150	0.0833812
$473$	−7.81236	−0.359212
$474$	8.05943	0.370182
$475$	0	0
$476$	17.8047	0.816077
$477$	−12.3520	−0.565557
$478$	23.8647	1.09155
$479$	−4.73485	−0.216341	−0.108170	−	0.994132i	$-0.534499\pi$
$479$	−4.73485	−0.216341	−0.108170	+	0.994132i	$0.534499\pi$
$480$	1.46503	0.0668693
$481$	12.8056	0.583886
$482$	20.3440	0.926643
$483$	−24.6857	−1.12324
$484$	1.00000	0.0454545
$485$	−12.3757	−0.561953
$486$	15.1843	0.688775
$487$	−40.9597	−1.85606	−0.928031	−	0.372503i	$-0.878500\pi$
$487$	−40.9597	−1.85606	−0.928031	+	0.372503i	$0.878500\pi$
$488$	−5.39823	−0.244366
$489$	12.7243	0.575411
$490$	14.7970	0.668461
$491$	−22.1902	−1.00143	−0.500716	−	0.865612i	$-0.666930\pi$
$491$	−22.1902	−1.00143	−0.500716	+	0.865612i	$0.666930\pi$
$492$	1.59608	0.0719570
$493$	−18.5079	−0.833555
$494$	0	0
$495$	2.30347	0.103533
$496$	1.41424	0.0635012
$497$	−20.7272	−0.929741
$498$	13.1742	0.590350
$499$	−8.03146	−0.359538	−0.179769	−	0.983709i	$-0.557535\pi$
$499$	−8.03146	−0.359538	−0.179769	+	0.983709i	$0.557535\pi$
$500$	−10.8655	−0.485918
$501$	−7.48747	−0.334516
$502$	−1.96033	−0.0874940
$503$	10.5087	0.468561	0.234280	−	0.972169i	$-0.424727\pi$
$503$	10.5087	0.468561	0.234280	+	0.972169i	$0.424727\pi$
$504$	−7.50015	−0.334083
$505$	25.0597	1.11514
$506$	5.17499	0.230056
$507$	−12.6580	−0.562160
$508$	−9.97947	−0.442767
$509$	−17.6769	−0.783515	−0.391757	−	0.920069i	$-0.628133\pi$
$509$	−17.6769	−0.783515	−0.391757	+	0.920069i	$0.628133\pi$
$510$	6.10235	0.270216
$511$	45.1498	1.99731
$512$	1.00000	0.0441942
$513$	0	0
$514$	0.599255	0.0264320
$515$	−11.9995	−0.528761
$516$	8.71830	0.383802
$517$	−7.17369	−0.315498
$518$	42.5185	1.86816
$519$	16.4999	0.724266
$520$	1.69007	0.0741147
$521$	−40.6341	−1.78021	−0.890106	−	0.455754i	$-0.849370\pi$
$521$	−40.6341	−1.78021	−0.890106	+	0.455754i	$0.849370\pi$
$522$	7.79639	0.341239
$523$	−14.8612	−0.649834	−0.324917	−	0.945743i	$-0.605336\pi$
$523$	−14.8612	−0.649834	−0.324917	+	0.945743i	$0.605336\pi$
$524$	14.6673	0.640746
$525$	−15.6298	−0.682141
$526$	15.8684	0.691893
$527$	5.89077	0.256606
$528$	−1.11596	−0.0485661
$529$	3.78053	0.164371
$530$	9.24163	0.401431
$531$	−3.17851	−0.137936
$532$	0	0
$533$	1.84125	0.0797536
$534$	−2.32873	−0.100774
$535$	14.3257	0.619355
$536$	3.85733	0.166611
$537$	−13.9569	−0.602285
$538$	10.3445	0.445982
$539$	−11.2714	−0.485492
$540$	−6.96569	−0.299755
$541$	36.0785	1.55113	0.775567	−	0.631265i	$-0.217464\pi$
$541$	36.0785	1.55113	0.775567	+	0.631265i	$0.217464\pi$
$542$	−16.3659	−0.702977
$543$	−19.6283	−0.842330
$544$	4.16533	0.178587
$545$	−26.4960	−1.13496
$546$	6.14106	0.262813
$547$	41.1739	1.76047	0.880234	−	0.474541i	$-0.157386\pi$
$547$	41.1739	1.76047	0.880234	+	0.474541i	$0.157386\pi$
$548$	−12.2599	−0.523715
$549$	9.47188	0.404250
$550$	3.27656	0.139713
$551$	0	0
$552$	−5.77510	−0.245804
$553$	30.8702	1.31274
$554$	−0.767289	−0.0325990
$555$	14.5727	0.618577
$556$	−6.46785	−0.274298
$557$	3.31512	0.140466	0.0702331	−	0.997531i	$-0.477626\pi$
$557$	3.31512	0.140466	0.0702331	+	0.997531i	$0.477626\pi$
$558$	−2.48146	−0.105049
$559$	10.0575	0.425387
$560$	5.61155	0.237131
$561$	−4.64835	−0.196254
$562$	−26.5207	−1.11871
$563$	−1.44663	−0.0609681	−0.0304841	−	0.999535i	$-0.509705\pi$
$563$	−1.44663	−0.0609681	−0.0304841	+	0.999535i	$0.509705\pi$
$564$	8.00557	0.337095
$565$	−1.50937	−0.0634998
$566$	−6.65638	−0.279788
$567$	−2.81008	−0.118012
$568$	−4.84903	−0.203461
$569$	−5.98659	−0.250971	−0.125486	−	0.992095i	$-0.540049\pi$
$569$	−5.98659	−0.250971	−0.125486	+	0.992095i	$0.540049\pi$
$570$	0	0
$571$	12.2104	0.510990	0.255495	−	0.966810i	$-0.417762\pi$
$571$	12.2104	0.510990	0.255495	+	0.966810i	$0.417762\pi$
$572$	−1.28738	−0.0538282
$573$	−21.9915	−0.918709
$574$	6.11352	0.255173
$575$	16.9562	0.707122
$576$	−1.75463	−0.0731094
$577$	16.2507	0.676524	0.338262	−	0.941052i	$-0.390161\pi$
$577$	16.2507	0.676524	0.338262	+	0.941052i	$0.390161\pi$
$578$	0.349959	0.0145564
$579$	−14.0715	−0.584791
$580$	−5.83319	−0.242210
$581$	50.4614	2.09349
$582$	−10.5202	−0.436075
$583$	−7.03965	−0.291552
$584$	10.5626	0.437083
$585$	−2.96545	−0.122606
$586$	−4.18747	−0.172983
$587$	−26.8913	−1.10992	−0.554962	−	0.831876i	$-0.687267\pi$
$587$	−26.8913	−1.10992	−0.554962	+	0.831876i	$0.687267\pi$
$588$	12.5784	0.518725
$589$	0	0
$590$	2.37814	0.0979064
$591$	12.8250	0.527551
$592$	9.94702	0.408820
$593$	22.3850	0.919243	0.459621	−	0.888115i	$-0.347985\pi$
$593$	22.3850	0.919243	0.459621	+	0.888115i	$0.347985\pi$
$594$	5.30599	0.217707
$595$	23.3740	0.958239
$596$	18.1637	0.744013
$597$	−24.7935	−1.01473
$598$	−6.66220	−0.272438
$599$	−24.9416	−1.01909	−0.509543	−	0.860445i	$-0.670185\pi$
$599$	−24.9416	−1.01909	−0.509543	+	0.860445i	$0.670185\pi$
$600$	−3.65652	−0.149277
$601$	−13.4718	−0.549526	−0.274763	−	0.961512i	$-0.588599\pi$
$601$	−13.4718	−0.549526	−0.274763	+	0.961512i	$0.588599\pi$
$602$	33.3939	1.36103
$603$	−6.76818	−0.275622
$604$	−3.66729	−0.149220
$605$	1.31280	0.0533728
$606$	21.3024	0.865350
$607$	−45.8015	−1.85902	−0.929512	−	0.368792i	$-0.879772\pi$
$607$	−45.8015	−1.85902	−0.929512	+	0.368792i	$0.879772\pi$
$608$	0	0
$609$	−21.1955	−0.858885
$610$	−7.08679	−0.286936
$611$	9.23529	0.373620
$612$	−7.30860	−0.295432
$613$	−15.3049	−0.618158	−0.309079	−	0.951036i	$-0.600021\pi$
$613$	−15.3049	−0.618158	−0.309079	+	0.951036i	$0.600021\pi$
$614$	10.0213	0.404426
$615$	2.09533	0.0844920
$616$	−4.27450	−0.172225
$617$	34.7798	1.40018	0.700091	−	0.714054i	$-0.253143\pi$
$617$	34.7798	1.40018	0.700091	+	0.714054i	$0.253143\pi$
$618$	−10.2003	−0.410318
$619$	−27.7967	−1.11724	−0.558621	−	0.829423i	$-0.688669\pi$
$619$	−27.7967	−1.11724	−0.558621	+	0.829423i	$0.688669\pi$
$620$	1.85661	0.0745632
$621$	27.4584	1.10187
$622$	−11.1459	−0.446910
$623$	−8.91978	−0.357363
$624$	1.43667	0.0575129
$625$	2.11867	0.0847469
$626$	−2.43390	−0.0972781
$627$	0	0
$628$	−9.47377	−0.378045
$629$	41.4326	1.65203
$630$	−9.84618	−0.392281
$631$	−47.1235	−1.87596	−0.937978	−	0.346694i	$-0.887304\pi$
$631$	−47.1235	−1.87596	−0.937978	+	0.346694i	$0.887304\pi$
$632$	7.22195	0.287274
$633$	−29.0138	−1.15319
$634$	−11.3922	−0.452443
$635$	−13.1010	−0.519898
$636$	7.85598	0.311510
$637$	14.5106	0.574929
$638$	4.44333	0.175913
$639$	8.50824	0.336581
$640$	1.31280	0.0518929
$641$	3.90439	0.154214	0.0771071	−	0.997023i	$-0.475432\pi$
$641$	3.90439	0.154214	0.0771071	+	0.997023i	$0.475432\pi$
$642$	12.1778	0.480619
$643$	42.1642	1.66280	0.831398	−	0.555678i	$-0.187541\pi$
$643$	42.1642	1.66280	0.831398	+	0.555678i	$0.187541\pi$
$644$	−22.1205	−0.871670
$645$	11.4454	0.450661
$646$	0	0
$647$	−4.76139	−0.187190	−0.0935948	−	0.995610i	$-0.529836\pi$
$647$	−4.76139	−0.187190	−0.0935948	+	0.995610i	$0.529836\pi$
$648$	−0.657405	−0.0258253
$649$	−1.81150	−0.0711077
$650$	−4.21819	−0.165451
$651$	6.74618	0.264404
$652$	11.4020	0.446539
$653$	26.2632	1.02776	0.513880	−	0.857862i	$-0.328208\pi$
$653$	26.2632	1.02776	0.513880	+	0.857862i	$0.328208\pi$
$654$	−22.5233	−0.880730
$655$	19.2553	0.752365
$656$	1.43023	0.0558411
$657$	−18.5334	−0.723056
$658$	30.6639	1.19540
$659$	−25.0496	−0.975795	−0.487898	−	0.872901i	$-0.662236\pi$
$659$	−25.0496	−0.975795	−0.487898	+	0.872901i	$0.662236\pi$
$660$	−1.46503	−0.0570264
$661$	11.8593	0.461273	0.230636	−	0.973040i	$-0.425919\pi$
$661$	11.8593	0.461273	0.230636	+	0.973040i	$0.425919\pi$
$662$	5.72063	0.222339
$663$	5.98421	0.232408
$664$	11.8052	0.458131
$665$	0	0
$666$	−17.4533	−0.676302
$667$	22.9942	0.890339
$668$	−6.70943	−0.259596
$669$	10.5428	0.407609
$670$	5.06390	0.195635
$671$	5.39823	0.208396
$672$	4.77018	0.184014
$673$	18.7492	0.722728	0.361364	−	0.932425i	$-0.382311\pi$
$673$	18.7492	0.722728	0.361364	+	0.932425i	$0.382311\pi$
$674$	21.1662	0.815293
$675$	17.3854	0.669164
$676$	−11.3426	−0.436256
$677$	29.2640	1.12471	0.562354	−	0.826897i	$-0.309896\pi$
$677$	29.2640	1.12471	0.562354	+	0.826897i	$0.309896\pi$
$678$	−1.28306	−0.0492758
$679$	−40.2957	−1.54641
$680$	5.46823	0.209697
$681$	−30.6723	−1.17537
$682$	−1.41424	−0.0541540
$683$	−4.78541	−0.183109	−0.0915544	−	0.995800i	$-0.529184\pi$
$683$	−4.78541	−0.183109	−0.0915544	+	0.995800i	$0.529184\pi$
$684$	0	0
$685$	−16.0947	−0.614947
$686$	18.2579	0.697091
$687$	−10.2078	−0.389451
$688$	7.81236	0.297843
$689$	9.06273	0.345262
$690$	−7.58153	−0.288624
$691$	−22.4180	−0.852822	−0.426411	−	0.904529i	$-0.640222\pi$
$691$	−22.4180	−0.852822	−0.426411	+	0.904529i	$0.640222\pi$
$692$	14.7854	0.562055
$693$	7.50015	0.284907
$694$	−30.3317	−1.15137
$695$	−8.49098	−0.322081
$696$	−4.95859	−0.187955
$697$	5.95738	0.225652
$698$	7.30224	0.276394
$699$	−6.71982	−0.254167
$700$	−14.0057	−0.529365
$701$	1.85326	0.0699967	0.0349983	−	0.999387i	$-0.488857\pi$
$701$	1.85326	0.0699967	0.0349983	+	0.999387i	$0.488857\pi$
$702$	−6.83084	−0.257813
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	10.5097	0.395818
$706$	−0.674177	−0.0253730
$707$	81.5950	3.06870
$708$	2.02157	0.0759753
$709$	15.7952	0.593200	0.296600	−	0.955002i	$-0.404147\pi$
$709$	15.7952	0.593200	0.296600	+	0.955002i	$0.404147\pi$
$710$	−6.36579	−0.238904
$711$	−12.6718	−0.475231
$712$	−2.08674	−0.0782040
$713$	−7.31867	−0.274086
$714$	19.8694	0.743593
$715$	−1.69007	−0.0632052
$716$	−12.5066	−0.467394
$717$	26.6321	0.994595
$718$	26.7789	0.999380
$719$	14.7250	0.549151	0.274575	−	0.961566i	$-0.411463\pi$
$719$	14.7250	0.549151	0.274575	+	0.961566i	$0.411463\pi$
$720$	−2.30347	−0.0858453
$721$	−39.0707	−1.45507
$722$	0	0
$723$	22.7031	0.844339
$724$	−17.5886	−0.653677
$725$	14.5588	0.540702
$726$	1.11596	0.0414173
$727$	5.85243	0.217055	0.108527	−	0.994093i	$-0.465387\pi$
$727$	5.85243	0.217055	0.108527	+	0.994093i	$0.465387\pi$
$728$	5.50292	0.203952
$729$	18.9174	0.700643
$730$	13.8665	0.513223
$731$	32.5410	1.20357
$732$	−6.02423	−0.222662
$733$	22.3036	0.823801	0.411901	−	0.911229i	$-0.364865\pi$
$733$	22.3036	0.823801	0.411901	+	0.911229i	$0.364865\pi$
$734$	−23.5890	−0.870687
$735$	16.5129	0.609088
$736$	−5.17499	−0.190753
$737$	−3.85733	−0.142087
$738$	−2.50952	−0.0923767
$739$	−9.16658	−0.337198	−0.168599	−	0.985685i	$-0.553924\pi$
$739$	−9.16658	−0.337198	−0.168599	+	0.985685i	$0.553924\pi$
$740$	13.0584	0.480037
$741$	0	0
$742$	30.0910	1.10467
$743$	−12.9197	−0.473977	−0.236988	−	0.971512i	$-0.576160\pi$
$743$	−12.9197	−0.473977	−0.236988	+	0.971512i	$0.576160\pi$
$744$	1.57824	0.0578610
$745$	23.8452	0.873621
$746$	−26.4394	−0.968017
$747$	−20.7138	−0.757877
$748$	−4.16533	−0.152299
$749$	46.6449	1.70437
$750$	−12.1254	−0.442759
$751$	41.9107	1.52934	0.764671	−	0.644421i	$-0.222902\pi$
$751$	41.9107	1.52934	0.764671	+	0.644421i	$0.222902\pi$
$752$	7.17369	0.261597
$753$	−2.18766	−0.0797228
$754$	−5.72027	−0.208320
$755$	−4.81441	−0.175214
$756$	−22.6804	−0.824880
$757$	35.2762	1.28214	0.641068	−	0.767484i	$-0.278492\pi$
$757$	35.2762	1.28214	0.641068	+	0.767484i	$0.278492\pi$
$758$	−5.38458	−0.195577
$759$	5.77510	0.209623
$760$	0	0
$761$	46.1674	1.67357	0.836784	−	0.547533i	$-0.184433\pi$
$761$	46.1674	1.67357	0.836784	+	0.547533i	$0.184433\pi$
$762$	−11.1367	−0.403441
$763$	−86.2715	−3.12324
$764$	−19.7063	−0.712949
$765$	−9.59471	−0.346897
$766$	6.57402	0.237529
$767$	2.33210	0.0842072
$768$	1.11596	0.0402688
$769$	−36.4351	−1.31388	−0.656942	−	0.753941i	$-0.728150\pi$
$769$	−36.4351	−1.31388	−0.656942	+	0.753941i	$0.728150\pi$
$770$	−5.61155	−0.202226
$771$	0.668747	0.0240843
$772$	−12.6093	−0.453817
$773$	−34.2165	−1.23068	−0.615342	−	0.788260i	$-0.710982\pi$
$773$	−34.2165	−1.23068	−0.615342	+	0.788260i	$0.710982\pi$
$774$	−13.7078	−0.492716
$775$	−4.63384	−0.166452
$776$	−9.42699	−0.338409
$777$	47.4491	1.70223
$778$	29.5322	1.05878
$779$	0	0
$780$	1.88606	0.0675318
$781$	4.84903	0.173512
$782$	−21.5555	−0.770824
$783$	23.5763	0.842547
$784$	11.2714	0.402549
$785$	−12.4371	−0.443901
$786$	16.3682	0.583835
$787$	−30.1433	−1.07449	−0.537246	−	0.843425i	$-0.680535\pi$
$787$	−30.1433	−1.07449	−0.537246	+	0.843425i	$0.680535\pi$
$788$	11.4923	0.409398
$789$	17.7085	0.630439
$790$	9.48096	0.337317
$791$	−4.91455	−0.174741
$792$	1.75463	0.0623479
$793$	−6.94960	−0.246787
$794$	−33.3685	−1.18420
$795$	10.3133	0.365776
$796$	−22.2171	−0.787465
$797$	−28.4871	−1.00907	−0.504533	−	0.863392i	$-0.668335\pi$
$797$	−28.4871	−1.00907	−0.504533	+	0.863392i	$0.668335\pi$
$798$	0	0
$799$	29.8808	1.05711
$800$	−3.27656	−0.115844
$801$	3.66145	0.129371
$802$	16.0156	0.565530
$803$	−10.5626	−0.372745
$804$	4.30464	0.151813
$805$	−29.0397	−1.02352
$806$	1.82067	0.0641303
$807$	11.5440	0.406370
$808$	19.0888	0.671541
$809$	29.7117	1.04461	0.522304	−	0.852759i	$-0.325072\pi$
$809$	29.7117	1.04461	0.522304	+	0.852759i	$0.325072\pi$
$810$	−0.863039	−0.0303241
$811$	−44.2541	−1.55397	−0.776985	−	0.629519i	$-0.783252\pi$
$811$	−44.2541	−1.55397	−0.776985	+	0.629519i	$0.783252\pi$
$812$	−18.9930	−0.666524
$813$	−18.2638	−0.640538
$814$	−9.94702	−0.348643
$815$	14.9686	0.524326
$816$	4.64835	0.162725
$817$	0	0
$818$	19.4042	0.678452
$819$	−9.65558	−0.337393
$820$	1.87760	0.0655687
$821$	−25.6177	−0.894065	−0.447032	−	0.894518i	$-0.647519\pi$
$821$	−25.6177	−0.894065	−0.447032	+	0.894518i	$0.647519\pi$
$822$	−13.6815	−0.477199
$823$	49.3509	1.72026	0.860132	−	0.510072i	$-0.170381\pi$
$823$	49.3509	1.72026	0.860132	+	0.510072i	$0.170381\pi$
$824$	−9.14040	−0.318421
$825$	3.65652	0.127304
$826$	7.74327	0.269423
$827$	57.1250	1.98643	0.993216	−	0.116286i	$-0.0370990\pi$
$827$	57.1250	1.98643	0.993216	+	0.116286i	$0.0370990\pi$
$828$	9.08018	0.315558
$829$	47.8205	1.66087	0.830437	−	0.557112i	$-0.188091\pi$
$829$	47.8205	1.66087	0.830437	+	0.557112i	$0.188091\pi$
$830$	15.4979	0.537939
$831$	−0.856266	−0.0297035
$832$	1.28738	0.0446320
$833$	46.9489	1.62668
$834$	−7.21788	−0.249935
$835$	−8.80812	−0.304818
$836$	0	0
$837$	−7.50393	−0.259374
$838$	8.09863	0.279762
$839$	39.6840	1.37004	0.685022	−	0.728522i	$-0.259793\pi$
$839$	39.6840	1.37004	0.685022	+	0.728522i	$0.259793\pi$
$840$	6.26229	0.216069
$841$	−9.25681	−0.319200
$842$	−28.8307	−0.993570
$843$	−29.5961	−1.01935
$844$	−25.9989	−0.894918
$845$	−14.8906	−0.512252
$846$	−12.5871	−0.432755
$847$	4.27450	0.146874
$848$	7.03965	0.241742
$849$	−7.42827	−0.254938
$850$	−13.6480	−0.468121
$851$	−51.4757	−1.76456
$852$	−5.41134	−0.185389
$853$	4.37089	0.149656	0.0748282	−	0.997196i	$-0.476159\pi$
$853$	4.37089	0.149656	0.0748282	+	0.997196i	$0.476159\pi$
$854$	−23.0747	−0.789602
$855$	0	0
$856$	10.9124	0.372977
$857$	−46.3671	−1.58387	−0.791935	−	0.610605i	$-0.790926\pi$
$857$	−46.3671	−1.58387	−0.791935	+	0.610605i	$0.790926\pi$
$858$	−1.43667	−0.0490472
$859$	2.99733	0.102268	0.0511338	−	0.998692i	$-0.483717\pi$
$859$	2.99733	0.102268	0.0511338	+	0.998692i	$0.483717\pi$
$860$	10.2560	0.349728
$861$	6.82246	0.232509
$862$	6.21324	0.211624
$863$	17.9885	0.612337	0.306168	−	0.951977i	$-0.400953\pi$
$863$	17.9885	0.612337	0.306168	+	0.951977i	$0.400953\pi$
$864$	−5.30599	−0.180513
$865$	19.4102	0.659966
$866$	0.769196	0.0261383
$867$	0.390541	0.0132635
$868$	6.04516	0.205186
$869$	−7.22195	−0.244988
$870$	−6.50963	−0.220697
$871$	4.96587	0.168262
$872$	−20.1828	−0.683477
$873$	16.5408	0.559823
$874$	0	0
$875$	−46.4444	−1.57011
$876$	11.7874	0.398261
$877$	−12.1006	−0.408607	−0.204303	−	0.978908i	$-0.565493\pi$
$877$	−12.1006	−0.408607	−0.204303	+	0.978908i	$0.565493\pi$
$878$	1.96983	0.0664787
$879$	−4.67306	−0.157619
$880$	−1.31280	−0.0442544
$881$	31.5643	1.06343	0.531713	−	0.846924i	$-0.321548\pi$
$881$	31.5643	1.06343	0.531713	+	0.846924i	$0.321548\pi$
$882$	−19.7770	−0.665927
$883$	29.3224	0.986778	0.493389	−	0.869809i	$-0.335758\pi$
$883$	29.3224	0.986778	0.493389	+	0.869809i	$0.335758\pi$
$884$	5.36238	0.180356
$885$	2.65391	0.0892103
$886$	23.4896	0.789148
$887$	−13.7873	−0.462934	−0.231467	−	0.972843i	$-0.574352\pi$
$887$	−13.7873	−0.462934	−0.231467	+	0.972843i	$0.574352\pi$
$888$	11.1005	0.372508
$889$	−42.6573	−1.43068
$890$	−2.73947	−0.0918272
$891$	0.657405	0.0220239
$892$	9.44727	0.316318
$893$	0	0
$894$	20.2700	0.677929
$895$	−16.4187	−0.548815
$896$	4.27450	0.142801
$897$	−7.43477	−0.248240
$898$	−33.5468	−1.11947
$899$	−6.28393	−0.209581
$900$	5.74914	0.191638
$901$	29.3224	0.976872
$902$	−1.43023	−0.0476214
$903$	37.2664	1.24015
$904$	−1.14974	−0.0382397
$905$	−23.0903	−0.767548
$906$	−4.09256	−0.135966
$907$	−10.3386	−0.343286	−0.171643	−	0.985159i	$-0.554908\pi$
$907$	−10.3386	−0.343286	−0.171643	+	0.985159i	$0.554908\pi$
$908$	−27.4851	−0.912124
$909$	−33.4937	−1.11092
$910$	7.22422	0.239481
$911$	25.5187	0.845473	0.422736	−	0.906253i	$-0.361070\pi$
$911$	25.5187	0.845473	0.422736	+	0.906253i	$0.361070\pi$
$912$	0	0
$913$	−11.8052	−0.390696
$914$	−25.9818	−0.859401
$915$	−7.90859	−0.261450
$916$	−9.14706	−0.302227
$917$	62.6956	2.07039
$918$	−22.1012	−0.729448
$919$	2.90082	0.0956892	0.0478446	−	0.998855i	$-0.484765\pi$
$919$	2.90082	0.0956892	0.0478446	+	0.998855i	$0.484765\pi$
$920$	−6.79372	−0.223982
$921$	11.1834	0.368505
$922$	17.9883	0.592412
$923$	−6.24256	−0.205476
$924$	−4.77018	−0.156928
$925$	−32.5920	−1.07162
$926$	33.2333	1.09211
$927$	16.0380	0.526757
$928$	−4.44333	−0.145859
$929$	−8.91763	−0.292578	−0.146289	−	0.989242i	$-0.546733\pi$
$929$	−8.91763	−0.292578	−0.146289	+	0.989242i	$0.546733\pi$
$930$	2.07191	0.0679405
$931$	0	0
$932$	−6.02154	−0.197242
$933$	−12.4384	−0.407215
$934$	−29.5798	−0.967879
$935$	−5.46823	−0.178830
$936$	−2.25888	−0.0738337
$937$	−48.6800	−1.59031	−0.795154	−	0.606408i	$-0.792610\pi$
$937$	−48.6800	−1.59031	−0.795154	+	0.606408i	$0.792610\pi$
$938$	16.4882	0.538358
$939$	−2.71614	−0.0886379
$940$	9.41760	0.307168
$941$	−47.0318	−1.53319	−0.766596	−	0.642130i	$-0.778051\pi$
$941$	−47.0318	−1.53319	−0.766596	+	0.642130i	$0.778051\pi$
$942$	−10.5724	−0.344467
$943$	−7.40142	−0.241024
$944$	1.81150	0.0589594
$945$	−29.7748	−0.968576
$946$	−7.81236	−0.254002
$947$	−15.3933	−0.500217	−0.250108	−	0.968218i	$-0.580466\pi$
$947$	−15.3933	−0.500217	−0.250108	+	0.968218i	$0.580466\pi$
$948$	8.05943	0.261758
$949$	13.5981	0.441413
$950$	0	0
$951$	−12.7133	−0.412257
$952$	17.8047	0.577054
$953$	−11.4276	−0.370177	−0.185088	−	0.982722i	$-0.559257\pi$
$953$	−11.4276	−0.370177	−0.185088	+	0.982722i	$0.559257\pi$
$954$	−12.3520	−0.399909
$955$	−25.8704	−0.837146
$956$	23.8647	0.771840
$957$	4.95859	0.160289
$958$	−4.73485	−0.152976
$959$	−52.4048	−1.69224
$960$	1.46503	0.0472838
$961$	−28.9999	−0.935482
$962$	12.8056	0.412870
$963$	−19.1471	−0.617007
$964$	20.3440	0.655236
$965$	−16.5534	−0.532873
$966$	−24.6857	−0.794248
$967$	−33.1958	−1.06750	−0.533752	−	0.845641i	$-0.679219\pi$
$967$	−33.1958	−1.06750	−0.533752	+	0.845641i	$0.679219\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−12.3757	−0.397361
$971$	−15.9611	−0.512215	−0.256108	−	0.966648i	$-0.582440\pi$
$971$	−15.9611	−0.512215	−0.256108	+	0.966648i	$0.582440\pi$
$972$	15.1843	0.487037
$973$	−27.6468	−0.886317
$974$	−40.9597	−1.31243
$975$	−4.70735	−0.150756
$976$	−5.39823	−0.172793
$977$	34.6293	1.10789	0.553944	−	0.832554i	$-0.313122\pi$
$977$	34.6293	1.10789	0.553944	+	0.832554i	$0.313122\pi$
$978$	12.7243	0.406877
$979$	2.08674	0.0666926
$980$	14.7970	0.472673
$981$	35.4133	1.13066
$982$	−22.1902	−0.708119
$983$	30.5391	0.974047	0.487023	−	0.873389i	$-0.338083\pi$
$983$	30.5391	0.974047	0.487023	+	0.873389i	$0.338083\pi$
$984$	1.59608	0.0508813
$985$	15.0871	0.480716
$986$	−18.5079	−0.589413
$987$	34.2198	1.08923
$988$	0	0
$989$	−40.4289	−1.28556
$990$	2.30347	0.0732091
$991$	46.7100	1.48379	0.741896	−	0.670515i	$-0.233927\pi$
$991$	46.7100	1.48379	0.741896	+	0.670515i	$0.233927\pi$
$992$	1.41424	0.0449021
$993$	6.38401	0.202590
$994$	−20.7272	−0.657426
$995$	−29.1666	−0.924643
$996$	13.1742	0.417440
$997$	3.24383	0.102733	0.0513666	−	0.998680i	$-0.483642\pi$
$997$	3.24383	0.102733	0.0513666	+	0.998680i	$0.483642\pi$
$998$	−8.03146	−0.254232
$999$	−52.7787	−1.66985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.ca.1.9		15
19.6	even	9		418.2.j.d.397.3	yes	30
19.16	even	9		418.2.j.d.199.3	✓	30
19.18	odd	2		7942.2.a.by.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.d.199.3	✓	30	19.16	even	9
418.2.j.d.397.3	yes	30	19.6	even	9
7942.2.a.by.1.7		15	19.18	odd	2
7942.2.a.ca.1.9		15	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.11596 q^{3} +1.00000 q^{4} +1.31280 q^{5} +1.11596 q^{6} +4.27450 q^{7} +1.00000 q^{8} -1.75463 q^{9} +1.31280 q^{10} -1.00000 q^{11} +1.11596 q^{12} +1.28738 q^{13} +4.27450 q^{14} +1.46503 q^{15} +1.00000 q^{16} +4.16533 q^{17} -1.75463 q^{18} +1.31280 q^{20} +4.77018 q^{21} -1.00000 q^{22} -5.17499 q^{23} +1.11596 q^{24} -3.27656 q^{25} +1.28738 q^{26} -5.30599 q^{27} +4.27450 q^{28} -4.44333 q^{29} +1.46503 q^{30} +1.41424 q^{31} +1.00000 q^{32} -1.11596 q^{33} +4.16533 q^{34} +5.61155 q^{35} -1.75463 q^{36} +9.94702 q^{37} +1.43667 q^{39} +1.31280 q^{40} +1.43023 q^{41} +4.77018 q^{42} +7.81236 q^{43} -1.00000 q^{44} -2.30347 q^{45} -5.17499 q^{46} +7.17369 q^{47} +1.11596 q^{48} +11.2714 q^{49} -3.27656 q^{50} +4.64835 q^{51} +1.28738 q^{52} +7.03965 q^{53} -5.30599 q^{54} -1.31280 q^{55} +4.27450 q^{56} -4.44333 q^{58} +1.81150 q^{59} +1.46503 q^{60} -5.39823 q^{61} +1.41424 q^{62} -7.50015 q^{63} +1.00000 q^{64} +1.69007 q^{65} -1.11596 q^{66} +3.85733 q^{67} +4.16533 q^{68} -5.77510 q^{69} +5.61155 q^{70} -4.84903 q^{71} -1.75463 q^{72} +10.5626 q^{73} +9.94702 q^{74} -3.65652 q^{75} -4.27450 q^{77} +1.43667 q^{78} +7.22195 q^{79} +1.31280 q^{80} -0.657405 q^{81} +1.43023 q^{82} +11.8052 q^{83} +4.77018 q^{84} +5.46823 q^{85} +7.81236 q^{86} -4.95859 q^{87} -1.00000 q^{88} -2.08674 q^{89} -2.30347 q^{90} +5.50292 q^{91} -5.17499 q^{92} +1.57824 q^{93} +7.17369 q^{94} +1.11596 q^{96} -9.42699 q^{97} +11.2714 q^{98} +1.75463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 15 q^{8} + 30 q^{9} + 9 q^{10} - 15 q^{11} + 3 q^{12} + 21 q^{15} + 15 q^{16} + 21 q^{17} + 30 q^{18} + 9 q^{20} - 9 q^{21} - 15 q^{22} + 21 q^{23}+ \cdots - 30 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 15 * q^8 + 30 * q^9 + 9 * q^10 - 15 * q^11 + 3 * q^12 + 21 * q^15 + 15 * q^16 + 21 * q^17 + 30 * q^18 + 9 * q^20 - 9 * q^21 - 15 * q^22 + 21 * q^23 + 3 * q^24 + 24 * q^25 + 3 * q^27 - 9 * q^29 + 21 * q^30 + 18 * q^31 + 15 * q^32 - 3 * q^33 + 21 * q^34 + 18 * q^35 + 30 * q^36 - 9 * q^37 + 9 * q^40 + 15 * q^41 - 9 * q^42 + 3 * q^43 - 15 * q^44 + 54 * q^45 + 21 * q^46 + 39 * q^47 + 3 * q^48 + 33 * q^49 + 24 * q^50 + 30 * q^51 + 18 * q^53 + 3 * q^54 - 9 * q^55 - 9 * q^58 + 6 * q^59 + 21 * q^60 - 30 * q^61 + 18 * q^62 + 24 * q^63 + 15 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 + 21 * q^68 - 42 * q^69 + 18 * q^70 + 9 * q^71 + 30 * q^72 + 12 * q^73 - 9 * q^74 + 21 * q^75 + 12 * q^79 + 9 * q^80 + 63 * q^81 + 15 * q^82 + 30 * q^83 - 9 * q^84 - 3 * q^85 + 3 * q^86 + 9 * q^87 - 15 * q^88 - 6 * q^89 + 54 * q^90 + 96 * q^91 + 21 * q^92 + 102 * q^93 + 39 * q^94 + 3 * q^96 + 33 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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