LMFDB - Embedded newform 1501.2.a.c.1.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1501,2,Mod(1,1501)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1501.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1501, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1501 = 19 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1501.a (trivial)

Newform invariants

comment:select newform

sage:traces = [31] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$11.9855453434$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	1501.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.45761 q^{2} +2.31684 q^{3} +4.03987 q^{4} +2.67319 q^{5} +5.69389 q^{6} -3.21511 q^{7} +5.01321 q^{8} +2.36773 q^{9} +6.56966 q^{10} -0.0519201 q^{11} +9.35971 q^{12} -0.507406 q^{13} -7.90150 q^{14} +6.19333 q^{15} +4.24080 q^{16} -2.21460 q^{17} +5.81896 q^{18} +1.00000 q^{19} +10.7993 q^{20} -7.44888 q^{21} -0.127600 q^{22} -4.63604 q^{23} +11.6148 q^{24} +2.14592 q^{25} -1.24701 q^{26} -1.46487 q^{27} -12.9886 q^{28} -3.47304 q^{29} +15.2208 q^{30} -2.71551 q^{31} +0.395824 q^{32} -0.120290 q^{33} -5.44264 q^{34} -8.59458 q^{35} +9.56531 q^{36} -8.01848 q^{37} +2.45761 q^{38} -1.17558 q^{39} +13.4012 q^{40} +7.44956 q^{41} -18.3065 q^{42} +11.9248 q^{43} -0.209750 q^{44} +6.32937 q^{45} -11.3936 q^{46} +5.01995 q^{47} +9.82523 q^{48} +3.33693 q^{49} +5.27384 q^{50} -5.13087 q^{51} -2.04985 q^{52} +5.35096 q^{53} -3.60009 q^{54} -0.138792 q^{55} -16.1180 q^{56} +2.31684 q^{57} -8.53539 q^{58} +6.80351 q^{59} +25.0202 q^{60} +2.97690 q^{61} -6.67367 q^{62} -7.61250 q^{63} -7.50881 q^{64} -1.35639 q^{65} -0.295627 q^{66} +3.40356 q^{67} -8.94670 q^{68} -10.7409 q^{69} -21.1222 q^{70} +6.61099 q^{71} +11.8699 q^{72} +0.721070 q^{73} -19.7063 q^{74} +4.97174 q^{75} +4.03987 q^{76} +0.166929 q^{77} -2.88911 q^{78} -1.00000 q^{79} +11.3364 q^{80} -10.4970 q^{81} +18.3082 q^{82} +3.46517 q^{83} -30.0925 q^{84} -5.92004 q^{85} +29.3064 q^{86} -8.04646 q^{87} -0.260286 q^{88} +1.61138 q^{89} +15.5552 q^{90} +1.63136 q^{91} -18.7290 q^{92} -6.29138 q^{93} +12.3371 q^{94} +2.67319 q^{95} +0.917060 q^{96} -0.991429 q^{97} +8.20089 q^{98} -0.122933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 7 q^{2} + 8 q^{3} + 35 q^{4} + q^{5} + 2 q^{6} + 7 q^{7} + 15 q^{8} + 35 q^{9} + 38 q^{11} + 14 q^{12} + 3 q^{13} + 27 q^{14} + 15 q^{15} + 27 q^{16} + 6 q^{17} + 17 q^{18} + 31 q^{19} + 2 q^{20}+ \cdots + 58 q^{99}+O(q^{100}) $ 31 * q + 7 * q^2 + 8 * q^3 + 35 * q^4 + q^5 + 2 * q^6 + 7 * q^7 + 15 * q^8 + 35 * q^9 + 38 * q^11 + 14 * q^12 + 3 * q^13 + 27 * q^14 + 15 * q^15 + 27 * q^16 + 6 * q^17 + 17 * q^18 + 31 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 6 * q^26 + 5 * q^27 + 13 * q^28 + 39 * q^29 - 9 * q^30 + 15 * q^31 + 27 * q^32 + 24 * q^33 - 10 * q^34 + 22 * q^35 + 35 * q^36 + 9 * q^37 + 7 * q^38 + 10 * q^39 - 36 * q^40 + 56 * q^41 + 17 * q^42 + 19 * q^43 + 74 * q^44 - 39 * q^45 + 38 * q^46 + 21 * q^47 + 51 * q^48 + 30 * q^49 + 12 * q^50 + 40 * q^51 + 2 * q^52 + 24 * q^53 + 8 * q^54 - 16 * q^55 + 101 * q^56 + 8 * q^57 - 32 * q^58 + 74 * q^59 + 3 * q^60 - 11 * q^61 - 7 * q^62 + 9 * q^63 + 3 * q^64 + 48 * q^65 + 24 * q^66 + 49 * q^67 - 18 * q^68 - 7 * q^69 - 14 * q^70 + 75 * q^71 + q^72 - 21 * q^73 + 31 * q^74 + 45 * q^75 + 35 * q^76 + 4 * q^77 - 23 * q^78 - 31 * q^79 - q^80 + 19 * q^81 - 20 * q^82 + 34 * q^83 + 22 * q^84 - 10 * q^85 + 62 * q^86 - 6 * q^87 - 3 * q^88 + 36 * q^89 + 9 * q^90 + 38 * q^91 + 5 * q^92 + 34 * q^93 + 50 * q^94 + q^95 - 79 * q^96 + 10 * q^97 + 27 * q^98 + 58 * 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 $

$2$	2.45761	1.73780	0.868898	−	0.494991i	$-0.164829\pi$
$2$	2.45761	1.73780	0.868898	+	0.494991i	$0.164829\pi$
$3$	2.31684	1.33763	0.668813	−	0.743431i	$-0.266803\pi$
$3$	2.31684	1.33763	0.668813	+	0.743431i	$0.266803\pi$
$4$	4.03987	2.01993
$5$	2.67319	1.19548	0.597742	−	0.801688i	$-0.296065\pi$
$5$	2.67319	1.19548	0.597742	+	0.801688i	$0.296065\pi$
$6$	5.69389	2.32452
$7$	−3.21511	−1.21520	−0.607599	−	0.794244i	$-0.707867\pi$
$7$	−3.21511	−1.21520	−0.607599	+	0.794244i	$0.707867\pi$
$8$	5.01321	1.77244
$9$	2.36773	0.789243
$10$	6.56966	2.07751
$11$	−0.0519201	−0.0156545	−0.00782725	−	0.999969i	$-0.502492\pi$
$11$	−0.0519201	−0.0156545	−0.00782725	+	0.999969i	$0.502492\pi$
$12$	9.35971	2.70192
$13$	−0.507406	−0.140729	−0.0703645	−	0.997521i	$-0.522416\pi$
$13$	−0.507406	−0.140729	−0.0703645	+	0.997521i	$0.522416\pi$
$14$	−7.90150	−2.11176
$15$	6.19333	1.59911
$16$	4.24080	1.06020
$17$	−2.21460	−0.537120	−0.268560	−	0.963263i	$-0.586548\pi$
$17$	−2.21460	−0.537120	−0.268560	+	0.963263i	$0.586548\pi$
$18$	5.81896	1.37154
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	10.7993	2.41480
$21$	−7.44888	−1.62548
$22$	−0.127600	−0.0272043
$23$	−4.63604	−0.966680	−0.483340	−	0.875433i	$-0.660577\pi$
$23$	−4.63604	−0.966680	−0.483340	+	0.875433i	$0.660577\pi$
$24$	11.6148	2.37086
$25$	2.14592	0.429184
$26$	−1.24701	−0.244558
$27$	−1.46487	−0.281915
$28$	−12.9886	−2.45462
$29$	−3.47304	−0.644927	−0.322463	−	0.946582i	$-0.604511\pi$
$29$	−3.47304	−0.644927	−0.322463	+	0.946582i	$0.604511\pi$
$30$	15.2208	2.77893
$31$	−2.71551	−0.487719	−0.243860	−	0.969811i	$-0.578414\pi$
$31$	−2.71551	−0.487719	−0.243860	+	0.969811i	$0.578414\pi$
$32$	0.395824	0.0699725
$33$	−0.120290	−0.0209399
$34$	−5.44264	−0.933405
$35$	−8.59458	−1.45275
$36$	9.56531	1.59422
$37$	−8.01848	−1.31823	−0.659115	−	0.752042i	$-0.729069\pi$
$37$	−8.01848	−1.31823	−0.659115	+	0.752042i	$0.729069\pi$
$38$	2.45761	0.398678
$39$	−1.17558	−0.188243
$40$	13.4012	2.11892
$41$	7.44956	1.16343	0.581713	−	0.813394i	$-0.302383\pi$
$41$	7.44956	1.16343	0.581713	+	0.813394i	$0.302383\pi$
$42$	−18.3065	−2.82475
$43$	11.9248	1.81851	0.909254	−	0.416242i	$-0.136653\pi$
$43$	11.9248	1.81851	0.909254	+	0.416242i	$0.136653\pi$
$44$	−0.209750	−0.0316211
$45$	6.32937	0.943527
$46$	−11.3936	−1.67989
$47$	5.01995	0.732235	0.366117	−	0.930569i	$-0.380687\pi$
$47$	5.01995	0.732235	0.366117	+	0.930569i	$0.380687\pi$
$48$	9.82523	1.41815
$49$	3.33693	0.476704
$50$	5.27384	0.745833
$51$	−5.13087	−0.718466
$52$	−2.04985	−0.284263
$53$	5.35096	0.735011	0.367505	−	0.930021i	$-0.380212\pi$
$53$	5.35096	0.735011	0.367505	+	0.930021i	$0.380212\pi$
$54$	−3.60009	−0.489910
$55$	−0.138792	−0.0187147
$56$	−16.1180	−2.15386
$57$	2.31684	0.306872
$58$	−8.53539	−1.12075
$59$	6.80351	0.885742	0.442871	−	0.896585i	$-0.353960\pi$
$59$	6.80351	0.885742	0.442871	+	0.896585i	$0.353960\pi$
$60$	25.0202	3.23010
$61$	2.97690	0.381152	0.190576	−	0.981672i	$-0.438964\pi$
$61$	2.97690	0.381152	0.190576	+	0.981672i	$0.438964\pi$
$62$	−6.67367	−0.847557
$63$	−7.61250	−0.959085
$64$	−7.50881	−0.938601
$65$	−1.35639	−0.168239
$66$	−0.295627	−0.0363892
$67$	3.40356	0.415811	0.207906	−	0.978149i	$-0.433335\pi$
$67$	3.40356	0.415811	0.207906	+	0.978149i	$0.433335\pi$
$68$	−8.94670	−1.08495
$69$	−10.7409	−1.29306
$70$	−21.1222	−2.52458
$71$	6.61099	0.784580	0.392290	−	0.919842i	$-0.371683\pi$
$71$	6.61099	0.784580	0.392290	+	0.919842i	$0.371683\pi$
$72$	11.8699	1.39888
$73$	0.721070	0.0843948	0.0421974	−	0.999109i	$-0.486564\pi$
$73$	0.721070	0.0843948	0.0421974	+	0.999109i	$0.486564\pi$
$74$	−19.7063	−2.29081
$75$	4.97174	0.574087
$76$	4.03987	0.463405
$77$	0.166929	0.0190233
$78$	−2.88911	−0.327127
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	11.3364	1.26745
$81$	−10.4970	−1.16634
$82$	18.3082	2.02180
$83$	3.46517	0.380351	0.190176	−	0.981750i	$-0.439094\pi$
$83$	3.46517	0.380351	0.190176	+	0.981750i	$0.439094\pi$
$84$	−30.0925	−3.28336
$85$	−5.92004	−0.642119
$86$	29.3064	3.16020
$87$	−8.04646	−0.862671
$88$	−0.260286	−0.0277466
$89$	1.61138	0.170806	0.0854032	−	0.996346i	$-0.472782\pi$
$89$	1.61138	0.170806	0.0854032	+	0.996346i	$0.472782\pi$
$90$	15.5552	1.63966
$91$	1.63136	0.171014
$92$	−18.7290	−1.95263
$93$	−6.29138	−0.652386
$94$	12.3371	1.27247
$95$	2.67319	0.274263
$96$	0.917060	0.0935971
$97$	−0.991429	−0.100664	−0.0503322	−	0.998733i	$-0.516028\pi$
$97$	−0.991429	−0.100664	−0.0503322	+	0.998733i	$0.516028\pi$
$98$	8.20089	0.828415
$99$	−0.122933	−0.0123552
$100$	8.66923	0.866923
$101$	4.30167	0.428033	0.214016	−	0.976830i	$-0.431345\pi$
$101$	4.30167	0.428033	0.214016	+	0.976830i	$0.431345\pi$
$102$	−12.6097	−1.24855
$103$	−6.55271	−0.645657	−0.322829	−	0.946457i	$-0.604634\pi$
$103$	−6.55271	−0.645657	−0.322829	+	0.946457i	$0.604634\pi$
$104$	−2.54373	−0.249433
$105$	−19.9122	−1.94324
$106$	13.1506	1.27730
$107$	−11.3752	−1.09968	−0.549839	−	0.835270i	$-0.685311\pi$
$107$	−11.3752	−1.09968	−0.549839	+	0.835270i	$0.685311\pi$
$108$	−5.91789	−0.569449
$109$	17.3611	1.66290	0.831448	−	0.555603i	$-0.187512\pi$
$109$	17.3611	1.66290	0.831448	+	0.555603i	$0.187512\pi$
$110$	−0.341097	−0.0325224
$111$	−18.5775	−1.76330
$112$	−13.6346	−1.28835
$113$	6.24473	0.587454	0.293727	−	0.955889i	$-0.405104\pi$
$113$	6.24473	0.587454	0.293727	+	0.955889i	$0.405104\pi$
$114$	5.69389	0.533282
$115$	−12.3930	−1.15565
$116$	−14.0306	−1.30271
$117$	−1.20140	−0.111069
$118$	16.7204	1.53924
$119$	7.12019	0.652707
$120$	31.0485	2.83432
$121$	−10.9973	−0.999755
$122$	7.31606	0.662365
$123$	17.2594	1.55623
$124$	−10.9703	−0.985161
$125$	−7.62949	−0.682402
$126$	−18.7086	−1.66669
$127$	6.75533	0.599439	0.299719	−	0.954027i	$-0.403107\pi$
$127$	6.75533	0.599439	0.299719	+	0.954027i	$0.403107\pi$
$128$	−19.2454	−1.70107
$129$	27.6277	2.43248
$130$	−3.33348	−0.292366
$131$	2.20452	0.192610	0.0963049	−	0.995352i	$-0.469298\pi$
$131$	2.20452	0.192610	0.0963049	+	0.995352i	$0.469298\pi$
$132$	−0.485957	−0.0422972
$133$	−3.21511	−0.278785
$134$	8.36464	0.722595
$135$	−3.91587	−0.337025
$136$	−11.1023	−0.952011
$137$	2.58163	0.220564	0.110282	−	0.993900i	$-0.464825\pi$
$137$	2.58163	0.220564	0.110282	+	0.993900i	$0.464825\pi$
$138$	−26.3971	−2.24707
$139$	8.56089	0.726125	0.363063	−	0.931765i	$-0.381731\pi$
$139$	8.56089	0.726125	0.363063	+	0.931765i	$0.381731\pi$
$140$	−34.7210	−2.93446
$141$	11.6304	0.979456
$142$	16.2473	1.36344
$143$	0.0263446	0.00220304
$144$	10.0410	0.836754
$145$	−9.28407	−0.771000
$146$	1.77211	0.146661
$147$	7.73112	0.637652
$148$	−32.3936	−2.66274
$149$	−23.0484	−1.88820	−0.944099	−	0.329662i	$-0.893065\pi$
$149$	−23.0484	−1.88820	−0.944099	+	0.329662i	$0.893065\pi$
$150$	12.2186	0.997646
$151$	−5.87919	−0.478442	−0.239221	−	0.970965i	$-0.576892\pi$
$151$	−5.87919	−0.478442	−0.239221	+	0.970965i	$0.576892\pi$
$152$	5.01321	0.406625
$153$	−5.24358	−0.423918
$154$	0.410247	0.0330586
$155$	−7.25905	−0.583061
$156$	−4.74917	−0.380238
$157$	2.69957	0.215449	0.107725	−	0.994181i	$-0.465644\pi$
$157$	2.69957	0.215449	0.107725	+	0.994181i	$0.465644\pi$
$158$	−2.45761	−0.195517
$159$	12.3973	0.983169
$160$	1.05811	0.0836511
$161$	14.9054	1.17471
$162$	−25.7977	−2.02686
$163$	16.3428	1.28007	0.640034	−	0.768346i	$-0.278920\pi$
$163$	16.3428	1.28007	0.640034	+	0.768346i	$0.278920\pi$
$164$	30.0953	2.35004
$165$	−0.321559	−0.0250333
$166$	8.51604	0.660973
$167$	−3.65812	−0.283074	−0.141537	−	0.989933i	$-0.545204\pi$
$167$	−3.65812	−0.283074	−0.141537	+	0.989933i	$0.545204\pi$
$168$	−37.3428	−2.88106
$169$	−12.7425	−0.980195
$170$	−14.5492	−1.11587
$171$	2.36773	0.181065
$172$	48.1744	3.67327
$173$	−3.21750	−0.244622	−0.122311	−	0.992492i	$-0.539031\pi$
$173$	−3.21750	−0.244622	−0.122311	+	0.992492i	$0.539031\pi$
$174$	−19.7751	−1.49915
$175$	−6.89936	−0.521543
$176$	−0.220183	−0.0165969
$177$	15.7626	1.18479
$178$	3.96016	0.296827
$179$	4.80216	0.358930	0.179465	−	0.983764i	$-0.442563\pi$
$179$	4.80216	0.358930	0.179465	+	0.983764i	$0.442563\pi$
$180$	25.5698	1.90586
$181$	7.97855	0.593041	0.296521	−	0.955026i	$-0.404174\pi$
$181$	7.97855	0.593041	0.296521	+	0.955026i	$0.404174\pi$
$182$	4.00927	0.297187
$183$	6.89698	0.509839
$184$	−23.2414	−1.71338
$185$	−21.4349	−1.57592
$186$	−15.4618	−1.13371
$187$	0.114982	0.00840835
$188$	20.2799	1.47907
$189$	4.70972	0.342582
$190$	6.56966	0.476613
$191$	−11.1617	−0.807635	−0.403817	−	0.914840i	$-0.632317\pi$
$191$	−11.1617	−0.807635	−0.403817	+	0.914840i	$0.632317\pi$
$192$	−17.3967	−1.25550
$193$	2.73714	0.197024	0.0985118	−	0.995136i	$-0.468592\pi$
$193$	2.73714	0.197024	0.0985118	+	0.995136i	$0.468592\pi$
$194$	−2.43655	−0.174934
$195$	−3.14253	−0.225041
$196$	13.4808	0.962911
$197$	−15.6690	−1.11637	−0.558185	−	0.829717i	$-0.688502\pi$
$197$	−15.6690	−1.11637	−0.558185	+	0.829717i	$0.688502\pi$
$198$	−0.302121	−0.0214708
$199$	23.5185	1.66718	0.833591	−	0.552382i	$-0.186281\pi$
$199$	23.5185	1.66718	0.833591	+	0.552382i	$0.186281\pi$
$200$	10.7579	0.760701
$201$	7.88549	0.556200
$202$	10.5719	0.743833
$203$	11.1662	0.783713
$204$	−20.7280	−1.45125
$205$	19.9141	1.39086
$206$	−16.1040	−1.12202
$207$	−10.9769	−0.762945
$208$	−2.15180	−0.149201
$209$	−0.0519201	−0.00359139
$210$	−48.9366	−3.37695
$211$	21.1559	1.45643	0.728216	−	0.685347i	$-0.240350\pi$
$211$	21.1559	1.45643	0.728216	+	0.685347i	$0.240350\pi$
$212$	21.6172	1.48467
$213$	15.3166	1.04947
$214$	−27.9558	−1.91102
$215$	31.8771	2.17400
$216$	−7.34370	−0.499676
$217$	8.73065	0.592675
$218$	42.6670	2.88977
$219$	1.67060	0.112889
$220$	−0.560702	−0.0378025
$221$	1.12370	0.0755884
$222$	−45.6563	−3.06425
$223$	−4.59793	−0.307900	−0.153950	−	0.988079i	$-0.549200\pi$
$223$	−4.59793	−0.307900	−0.153950	+	0.988079i	$0.549200\pi$
$224$	−1.27262	−0.0850304
$225$	5.08095	0.338730
$226$	15.3471	1.02088
$227$	1.46643	0.0973305	0.0486653	−	0.998815i	$-0.484503\pi$
$227$	1.46643	0.0973305	0.0486653	+	0.998815i	$0.484503\pi$
$228$	9.35971	0.619862
$229$	3.36093	0.222096	0.111048	−	0.993815i	$-0.464579\pi$
$229$	3.36093	0.222096	0.111048	+	0.993815i	$0.464579\pi$
$230$	−30.4572	−2.00829
$231$	0.386747	0.0254461
$232$	−17.4111	−1.14309
$233$	13.4724	0.882604	0.441302	−	0.897359i	$-0.354517\pi$
$233$	13.4724	0.882604	0.441302	+	0.897359i	$0.354517\pi$
$234$	−2.95257	−0.193016
$235$	13.4192	0.875375
$236$	27.4853	1.78914
$237$	−2.31684	−0.150495
$238$	17.4987	1.13427
$239$	−23.8264	−1.54120	−0.770600	−	0.637320i	$-0.780043\pi$
$239$	−23.8264	−1.54120	−0.770600	+	0.637320i	$0.780043\pi$
$240$	26.2647	1.69538
$241$	−17.0565	−1.09871	−0.549353	−	0.835591i	$-0.685126\pi$
$241$	−17.0565	−1.09871	−0.549353	+	0.835591i	$0.685126\pi$
$242$	−27.0271	−1.73737
$243$	−19.9253	−1.27821
$244$	12.0263	0.769903
$245$	8.92023	0.569893
$246$	42.4170	2.70441
$247$	−0.507406	−0.0322854
$248$	−13.6134	−0.864452
$249$	8.02822	0.508768
$250$	−18.7503	−1.18588
$251$	3.24682	0.204937	0.102469	−	0.994736i	$-0.467326\pi$
$251$	3.24682	0.204937	0.102469	+	0.994736i	$0.467326\pi$
$252$	−30.7535	−1.93729
$253$	0.240704	0.0151329
$254$	16.6020	1.04170
$255$	−13.7158	−0.858915
$256$	−32.2802	−2.01751
$257$	−18.7366	−1.16876	−0.584380	−	0.811480i	$-0.698662\pi$
$257$	−18.7366	−1.16876	−0.584380	+	0.811480i	$0.698662\pi$
$258$	67.8982	4.22716
$259$	25.7803	1.60191
$260$	−5.47963	−0.339832
$261$	−8.22321	−0.509004
$262$	5.41786	0.334716
$263$	4.19718	0.258809	0.129405	−	0.991592i	$-0.458693\pi$
$263$	4.19718	0.258809	0.129405	+	0.991592i	$0.458693\pi$
$264$	−0.603041	−0.0371146
$265$	14.3041	0.878694
$266$	−7.90150	−0.484472
$267$	3.73331	0.228475
$268$	13.7499	0.839911
$269$	−26.2480	−1.60037	−0.800183	−	0.599756i	$-0.795264\pi$
$269$	−26.2480	−1.60037	−0.800183	+	0.599756i	$0.795264\pi$
$270$	−9.62370	−0.585680
$271$	16.4936	1.00191	0.500957	−	0.865472i	$-0.332981\pi$
$271$	16.4936	1.00191	0.500957	+	0.865472i	$0.332981\pi$
$272$	−9.39168	−0.569454
$273$	3.77960	0.228752
$274$	6.34466	0.383295
$275$	−0.111416	−0.00671866
$276$	−43.3920	−2.61189
$277$	−13.3161	−0.800085	−0.400043	−	0.916497i	$-0.631005\pi$
$277$	−13.3161	−0.800085	−0.400043	+	0.916497i	$0.631005\pi$
$278$	21.0394	1.26186
$279$	−6.42958	−0.384929
$280$	−43.0864	−2.57491
$281$	−4.13793	−0.246848	−0.123424	−	0.992354i	$-0.539388\pi$
$281$	−4.13793	−0.246848	−0.123424	+	0.992354i	$0.539388\pi$
$282$	28.5830	1.70209
$283$	28.2557	1.67963	0.839813	−	0.542876i	$-0.182665\pi$
$283$	28.2557	1.67963	0.839813	+	0.542876i	$0.182665\pi$
$284$	26.7075	1.58480
$285$	6.19333	0.366861
$286$	0.0647448	0.00382844
$287$	−23.9512	−1.41379
$288$	0.937204	0.0552253
$289$	−12.0955	−0.711502
$290$	−22.8167	−1.33984
$291$	−2.29698	−0.134651
$292$	2.91303	0.170472
$293$	−14.3157	−0.836335	−0.418167	−	0.908370i	$-0.637327\pi$
$293$	−14.3157	−0.836335	−0.418167	+	0.908370i	$0.637327\pi$
$294$	19.0001	1.10811
$295$	18.1871	1.05889
$296$	−40.1983	−2.33648
$297$	0.0760563	0.00441323
$298$	−56.6441	−3.28130
$299$	2.35235	0.136040
$300$	20.0852	1.15962
$301$	−38.3394	−2.20985
$302$	−14.4488	−0.831434
$303$	9.96627	0.572547
$304$	4.24080	0.243226
$305$	7.95779	0.455662
$306$	−12.8867	−0.736683
$307$	−9.84445	−0.561853	−0.280926	−	0.959729i	$-0.590642\pi$
$307$	−9.84445	−0.561853	−0.280926	+	0.959729i	$0.590642\pi$
$308$	0.674371	0.0384258
$309$	−15.1815	−0.863648
$310$	−17.8399	−1.01324
$311$	10.8094	0.612942	0.306471	−	0.951880i	$-0.400852\pi$
$311$	10.8094	0.612942	0.306471	+	0.951880i	$0.400852\pi$
$312$	−5.89340	−0.333648
$313$	−15.7068	−0.887803	−0.443901	−	0.896076i	$-0.646406\pi$
$313$	−15.7068	−0.887803	−0.443901	+	0.896076i	$0.646406\pi$
$314$	6.63450	0.374406
$315$	−20.3496	−1.14657
$316$	−4.03987	−0.227260
$317$	−11.3879	−0.639608	−0.319804	−	0.947484i	$-0.603617\pi$
$317$	−11.3879	−0.639608	−0.319804	+	0.947484i	$0.603617\pi$
$318$	30.4678	1.70855
$319$	0.180321	0.0100960
$320$	−20.0724	−1.12208
$321$	−26.3544	−1.47096
$322$	36.6316	2.04140
$323$	−2.21460	−0.123224
$324$	−42.4067	−2.35593
$325$	−1.08885	−0.0603986
$326$	40.1643	2.22450
$327$	40.2229	2.22433
$328$	37.3462	2.06210
$329$	−16.1397	−0.889810
$330$	−0.790267	−0.0435028
$331$	−19.2948	−1.06054	−0.530270	−	0.847829i	$-0.677909\pi$
$331$	−19.2948	−1.06054	−0.530270	+	0.847829i	$0.677909\pi$
$332$	13.9988	0.768285
$333$	−18.9856	−1.04040
$334$	−8.99025	−0.491925
$335$	9.09835	0.497096
$336$	−31.5892	−1.72333
$337$	13.0822	0.712633	0.356316	−	0.934365i	$-0.384033\pi$
$337$	13.0822	0.712633	0.356316	+	0.934365i	$0.384033\pi$
$338$	−31.3162	−1.70338
$339$	14.4680	0.785794
$340$	−23.9162	−1.29704
$341$	0.140989	0.00763501
$342$	5.81896	0.314653
$343$	11.7772	0.635907
$344$	59.7813	3.22319
$345$	−28.7125	−1.54583
$346$	−7.90738	−0.425103
$347$	22.4745	1.20650	0.603248	−	0.797554i	$-0.293873\pi$
$347$	22.4745	1.20650	0.603248	+	0.797554i	$0.293873\pi$
$348$	−32.5066	−1.74254
$349$	−0.218518	−0.0116970	−0.00584851	−	0.999983i	$-0.501862\pi$
$349$	−0.218518	−0.0116970	−0.00584851	+	0.999983i	$0.501862\pi$
$350$	−16.9560	−0.906335
$351$	0.743284	0.0396736
$352$	−0.0205513	−0.00109539
$353$	−10.4539	−0.556403	−0.278202	−	0.960523i	$-0.589738\pi$
$353$	−10.4539	−0.556403	−0.278202	+	0.960523i	$0.589738\pi$
$354$	38.7384	2.05893
$355$	17.6724	0.937953
$356$	6.50978	0.345018
$357$	16.4963	0.873078
$358$	11.8019	0.623747
$359$	−22.3142	−1.17770	−0.588849	−	0.808243i	$-0.700419\pi$
$359$	−22.3142	−1.17770	−0.588849	+	0.808243i	$0.700419\pi$
$360$	31.7305	1.67234
$361$	1.00000	0.0526316
$362$	19.6082	1.03058
$363$	−25.4789	−1.33730
$364$	6.59050	0.345436
$365$	1.92755	0.100893
$366$	16.9501	0.885996
$367$	−12.4375	−0.649230	−0.324615	−	0.945846i	$-0.605235\pi$
$367$	−12.4375	−0.649230	−0.324615	+	0.945846i	$0.605235\pi$
$368$	−19.6605	−1.02487
$369$	17.6385	0.918226
$370$	−52.6787	−2.73863
$371$	−17.2039	−0.893183
$372$	−25.4164	−1.31778
$373$	18.6545	0.965892	0.482946	−	0.875650i	$-0.339567\pi$
$373$	18.6545	0.965892	0.482946	+	0.875650i	$0.339567\pi$
$374$	0.282583	0.0146120
$375$	−17.6763	−0.912799
$376$	25.1660	1.29784
$377$	1.76224	0.0907599
$378$	11.5747	0.595337
$379$	−27.0597	−1.38996	−0.694981	−	0.719028i	$-0.744587\pi$
$379$	−27.0597	−1.38996	−0.694981	+	0.719028i	$0.744587\pi$
$380$	10.7993	0.553993
$381$	15.6510	0.801825
$382$	−27.4312	−1.40350
$383$	−27.2221	−1.39099	−0.695493	−	0.718533i	$-0.744814\pi$
$383$	−27.2221	−1.39099	−0.695493	+	0.718533i	$0.744814\pi$
$384$	−44.5884	−2.27539
$385$	0.446232	0.0227421
$386$	6.72683	0.342387
$387$	28.2346	1.43524
$388$	−4.00524	−0.203335
$389$	35.5397	1.80193	0.900967	−	0.433889i	$-0.142859\pi$
$389$	35.5397	1.80193	0.900967	+	0.433889i	$0.142859\pi$
$390$	−7.72313	−0.391076
$391$	10.2670	0.519223
$392$	16.7287	0.844928
$393$	5.10751	0.257640
$394$	−38.5083	−1.94002
$395$	−2.67319	−0.134503
$396$	−0.496632	−0.0249567
$397$	5.82501	0.292349	0.146175	−	0.989259i	$-0.453304\pi$
$397$	5.82501	0.292349	0.146175	+	0.989259i	$0.453304\pi$
$398$	57.7994	2.89722
$399$	−7.44888	−0.372910
$400$	9.10040	0.455020
$401$	37.7905	1.88717	0.943585	−	0.331131i	$-0.107430\pi$
$401$	37.7905	1.88717	0.943585	+	0.331131i	$0.107430\pi$
$402$	19.3795	0.966561
$403$	1.37786	0.0686363
$404$	17.3782	0.864598
$405$	−28.0606	−1.39434
$406$	27.4422	1.36193
$407$	0.416320	0.0206362
$408$	−25.7221	−1.27344
$409$	−28.9234	−1.43017	−0.715085	−	0.699037i	$-0.753612\pi$
$409$	−28.9234	−1.43017	−0.715085	+	0.699037i	$0.753612\pi$
$410$	48.9411	2.41703
$411$	5.98122	0.295032
$412$	−26.4721	−1.30418
$413$	−21.8740	−1.07635
$414$	−26.9769	−1.32584
$415$	9.26303	0.454704
$416$	−0.200844	−0.00984716
$417$	19.8342	0.971284
$418$	−0.127600	−0.00624110
$419$	7.81784	0.381927	0.190963	−	0.981597i	$-0.438839\pi$
$419$	7.81784	0.381927	0.190963	+	0.981597i	$0.438839\pi$
$420$	−80.4428	−3.92521
$421$	−4.35415	−0.212208	−0.106104	−	0.994355i	$-0.533838\pi$
$421$	−4.35415	−0.212208	−0.106104	+	0.994355i	$0.533838\pi$
$422$	51.9931	2.53098
$423$	11.8859	0.577911
$424$	26.8255	1.30276
$425$	−4.75236	−0.230523
$426$	37.6422	1.82377
$427$	−9.57105	−0.463175
$428$	−45.9542	−2.22128
$429$	0.0610360	0.00294685
$430$	78.3416	3.77797
$431$	36.8791	1.77640	0.888202	−	0.459452i	$-0.151954\pi$
$431$	36.8791	1.77640	0.888202	+	0.459452i	$0.151954\pi$
$432$	−6.21222	−0.298886
$433$	29.3538	1.41065	0.705327	−	0.708882i	$-0.250800\pi$
$433$	29.3538	1.41065	0.705327	+	0.708882i	$0.250800\pi$
$434$	21.4566	1.02995
$435$	−21.5097	−1.03131
$436$	70.1367	3.35894
$437$	−4.63604	−0.221772
$438$	4.10569	0.196178
$439$	28.9770	1.38299	0.691497	−	0.722379i	$-0.256951\pi$
$439$	28.9770	1.38299	0.691497	+	0.722379i	$0.256951\pi$
$440$	−0.695794	−0.0331707
$441$	7.90094	0.376235
$442$	2.76163	0.131357
$443$	−6.70184	−0.318414	−0.159207	−	0.987245i	$-0.550894\pi$
$443$	−6.70184	−0.318414	−0.159207	+	0.987245i	$0.550894\pi$
$444$	−75.0506	−3.56175
$445$	4.30753	0.204196
$446$	−11.2999	−0.535068
$447$	−53.3993	−2.52570
$448$	24.1416	1.14059
$449$	14.5287	0.685650	0.342825	−	0.939399i	$-0.388616\pi$
$449$	14.5287	0.685650	0.342825	+	0.939399i	$0.388616\pi$
$450$	12.4870	0.588644
$451$	−0.386782	−0.0182129
$452$	25.2279	1.18662
$453$	−13.6211	−0.639976
$454$	3.60392	0.169141
$455$	4.36094	0.204444
$456$	11.6148	0.543912
$457$	−30.6347	−1.43303	−0.716516	−	0.697570i	$-0.754264\pi$
$457$	−30.6347	−1.43303	−0.716516	+	0.697570i	$0.754264\pi$
$458$	8.25986	0.385958
$459$	3.24411	0.151422
$460$	−50.0660	−2.33434
$461$	31.4270	1.46370	0.731850	−	0.681466i	$-0.238657\pi$
$461$	31.4270	1.46370	0.731850	+	0.681466i	$0.238657\pi$
$462$	0.950475	0.0442201
$463$	−25.5498	−1.18740	−0.593700	−	0.804687i	$-0.702333\pi$
$463$	−25.5498	−1.18740	−0.593700	+	0.804687i	$0.702333\pi$
$464$	−14.7284	−0.683751
$465$	−16.8180	−0.779917
$466$	33.1099	1.53379
$467$	−29.6187	−1.37059	−0.685295	−	0.728265i	$-0.740327\pi$
$467$	−29.6187	−1.37059	−0.685295	+	0.728265i	$0.740327\pi$
$468$	−4.85349	−0.224353
$469$	−10.9428	−0.505292
$470$	32.9793	1.52122
$471$	6.25446	0.288190
$472$	34.1074	1.56992
$473$	−0.619135	−0.0284678
$474$	−5.69389	−0.261529
$475$	2.14592	0.0984615
$476$	28.7646	1.31842
$477$	12.6696	0.580102
$478$	−58.5560	−2.67829
$479$	40.3828	1.84514	0.922568	−	0.385836i	$-0.126087\pi$
$479$	40.3828	1.84514	0.922568	+	0.385836i	$0.126087\pi$
$480$	2.45147	0.111894
$481$	4.06862	0.185513
$482$	−41.9183	−1.90933
$483$	34.5333	1.57132
$484$	−44.4277	−2.01944
$485$	−2.65027	−0.120343
$486$	−48.9688	−2.22127
$487$	−23.3940	−1.06008	−0.530041	−	0.847972i	$-0.677824\pi$
$487$	−23.3940	−1.06008	−0.530041	+	0.847972i	$0.677824\pi$
$488$	14.9238	0.675569
$489$	37.8636	1.71225
$490$	21.9225	0.990357
$491$	7.13883	0.322171	0.161085	−	0.986940i	$-0.448501\pi$
$491$	7.13883	0.322171	0.161085	+	0.986940i	$0.448501\pi$
$492$	69.7258	3.14348
$493$	7.69140	0.346403
$494$	−1.24701	−0.0561055
$495$	−0.328622	−0.0147705
$496$	−11.5159	−0.517080
$497$	−21.2550	−0.953419
$498$	19.7303	0.884135
$499$	11.0481	0.494580	0.247290	−	0.968942i	$-0.420460\pi$
$499$	11.0481	0.494580	0.247290	+	0.968942i	$0.420460\pi$
$500$	−30.8221	−1.37841
$501$	−8.47527	−0.378647
$502$	7.97943	0.356139
$503$	−22.2945	−0.994065	−0.497032	−	0.867732i	$-0.665577\pi$
$503$	−22.2945	−0.994065	−0.497032	+	0.867732i	$0.665577\pi$
$504$	−38.1631	−1.69992
$505$	11.4992	0.511706
$506$	0.591557	0.0262979
$507$	−29.5224	−1.31113
$508$	27.2907	1.21083
$509$	−2.36314	−0.104744	−0.0523721	−	0.998628i	$-0.516678\pi$
$509$	−2.36314	−0.104744	−0.0523721	+	0.998628i	$0.516678\pi$
$510$	−33.7081	−1.49262
$511$	−2.31832	−0.102556
$512$	−40.8414	−1.80495
$513$	−1.46487	−0.0646756
$514$	−46.0474	−2.03106
$515$	−17.5166	−0.771873
$516$	111.612	4.91345
$517$	−0.260636	−0.0114628
$518$	63.3580	2.78379
$519$	−7.45442	−0.327213
$520$	−6.79986	−0.298194
$521$	−31.3372	−1.37291	−0.686453	−	0.727174i	$-0.740833\pi$
$521$	−31.3372	−1.37291	−0.686453	+	0.727174i	$0.740833\pi$
$522$	−20.2095	−0.884545
$523$	−20.2022	−0.883381	−0.441690	−	0.897168i	$-0.645621\pi$
$523$	−20.2022	−0.883381	−0.441690	+	0.897168i	$0.645621\pi$
$524$	8.90597	0.389059
$525$	−15.9847	−0.697629
$526$	10.3150	0.449757
$527$	6.01377	0.261964
$528$	−0.510127	−0.0222004
$529$	−1.50717	−0.0655292
$530$	35.1540	1.52699
$531$	16.1089	0.699065
$532$	−12.9886	−0.563128
$533$	−3.77995	−0.163728
$534$	9.17505	0.397043
$535$	−30.4079	−1.31465
$536$	17.0628	0.736999
$537$	11.1258	0.480114
$538$	−64.5073	−2.78111
$539$	−0.173254	−0.00746257
$540$	−15.8196	−0.680767
$541$	−11.2055	−0.481764	−0.240882	−	0.970554i	$-0.577437\pi$
$541$	−11.2055	−0.481764	−0.240882	+	0.970554i	$0.577437\pi$
$542$	40.5349	1.74112
$543$	18.4850	0.793267
$544$	−0.876594	−0.0375837
$545$	46.4095	1.98797
$546$	9.28881	0.397524
$547$	−18.9734	−0.811244	−0.405622	−	0.914041i	$-0.632945\pi$
$547$	−18.9734	−0.811244	−0.405622	+	0.914041i	$0.632945\pi$
$548$	10.4295	0.445524
$549$	7.04848	0.300822
$550$	−0.273818	−0.0116757
$551$	−3.47304	−0.147956
$552$	−53.8465	−2.29186
$553$	3.21511	0.136720
$554$	−32.7258	−1.39038
$555$	−49.6611	−2.10800
$556$	34.5849	1.46672
$557$	−20.5836	−0.872155	−0.436077	−	0.899909i	$-0.643633\pi$
$557$	−20.5836	−0.872155	−0.436077	+	0.899909i	$0.643633\pi$
$558$	−15.8014	−0.668928
$559$	−6.05069	−0.255917
$560$	−36.4479	−1.54020
$561$	0.266396	0.0112472
$562$	−10.1694	−0.428972
$563$	9.53720	0.401945	0.200973	−	0.979597i	$-0.435590\pi$
$563$	9.53720	0.401945	0.200973	+	0.979597i	$0.435590\pi$
$564$	46.9853	1.97844
$565$	16.6933	0.702293
$566$	69.4416	2.91885
$567$	33.7492	1.41733
$568$	33.1423	1.39062
$569$	41.3833	1.73488	0.867439	−	0.497544i	$-0.165765\pi$
$569$	41.3833	1.73488	0.867439	+	0.497544i	$0.165765\pi$
$570$	15.2208	0.637530
$571$	−8.25211	−0.345340	−0.172670	−	0.984980i	$-0.555239\pi$
$571$	−8.25211	−0.345340	−0.172670	+	0.984980i	$0.555239\pi$
$572$	0.106429	0.00445000
$573$	−25.8599	−1.08031
$574$	−58.8627	−2.45688
$575$	−9.94855	−0.414883
$576$	−17.7788	−0.740784
$577$	18.7136	0.779057	0.389529	−	0.921014i	$-0.372638\pi$
$577$	18.7136	0.779057	0.389529	+	0.921014i	$0.372638\pi$
$578$	−29.7262	−1.23645
$579$	6.34150	0.263544
$580$	−37.5064	−1.55737
$581$	−11.1409	−0.462202
$582$	−5.64509	−0.233996
$583$	−0.277822	−0.0115062
$584$	3.61487	0.149585
$585$	−3.21156	−0.132782
$586$	−35.1826	−1.45338
$587$	−23.9620	−0.989016	−0.494508	−	0.869173i	$-0.664652\pi$
$587$	−23.9620	−0.989016	−0.494508	+	0.869173i	$0.664652\pi$
$588$	31.2327	1.28802
$589$	−2.71551	−0.111890
$590$	44.6968	1.84014
$591$	−36.3025	−1.49328
$592$	−34.0047	−1.39759
$593$	1.08033	0.0443637	0.0221819	−	0.999754i	$-0.492939\pi$
$593$	1.08033	0.0443637	0.0221819	+	0.999754i	$0.492939\pi$
$594$	0.186917	0.00766930
$595$	19.0336	0.780301
$596$	−93.1124	−3.81403
$597$	54.4885	2.23007
$598$	5.78117	0.236410
$599$	−0.874838	−0.0357449	−0.0178725	−	0.999840i	$-0.505689\pi$
$599$	−0.874838	−0.0357449	−0.0178725	+	0.999840i	$0.505689\pi$
$600$	24.9244	1.01753
$601$	−6.52577	−0.266192	−0.133096	−	0.991103i	$-0.542492\pi$
$601$	−6.52577	−0.266192	−0.133096	+	0.991103i	$0.542492\pi$
$602$	−94.2234	−3.84026
$603$	8.05870	0.328176
$604$	−23.7512	−0.966421
$605$	−29.3978	−1.19519
$606$	24.4933	0.994971
$607$	35.0243	1.42159	0.710796	−	0.703398i	$-0.248335\pi$
$607$	35.0243	1.42159	0.710796	+	0.703398i	$0.248335\pi$
$608$	0.395824	0.0160528
$609$	25.8702	1.04832
$610$	19.5572	0.791847
$611$	−2.54715	−0.103047
$612$	−21.1834	−0.856286
$613$	−32.7511	−1.32281	−0.661403	−	0.750031i	$-0.730039\pi$
$613$	−32.7511	−1.32281	−0.661403	+	0.750031i	$0.730039\pi$
$614$	−24.1939	−0.976385
$615$	46.1376	1.86045
$616$	0.836849	0.0337176
$617$	36.0962	1.45318	0.726588	−	0.687073i	$-0.241105\pi$
$617$	36.0962	1.45318	0.726588	+	0.687073i	$0.241105\pi$
$618$	−37.3104	−1.50084
$619$	23.0763	0.927516	0.463758	−	0.885962i	$-0.346501\pi$
$619$	23.0763	0.927516	0.463758	+	0.885962i	$0.346501\pi$
$620$	−29.3256	−1.17774
$621$	6.79119	0.272521
$622$	26.5652	1.06517
$623$	−5.18078	−0.207564
$624$	−4.98538	−0.199575
$625$	−31.1246	−1.24499
$626$	−38.6013	−1.54282
$627$	−0.120290	−0.00480394
$628$	10.9059	0.435193
$629$	17.7577	0.708048
$630$	−50.0115	−1.99251
$631$	7.23320	0.287949	0.143975	−	0.989581i	$-0.454012\pi$
$631$	7.23320	0.287949	0.143975	+	0.989581i	$0.454012\pi$
$632$	−5.01321	−0.199415
$633$	49.0148	1.94816
$634$	−27.9871	−1.11151
$635$	18.0583	0.716620
$636$	50.0834	1.98594
$637$	−1.69318	−0.0670861
$638$	0.443158	0.0175448
$639$	15.6530	0.619224
$640$	−51.4465	−2.03360
$641$	9.39983	0.371271	0.185635	−	0.982619i	$-0.440566\pi$
$641$	9.39983	0.371271	0.185635	+	0.982619i	$0.440566\pi$
$642$	−64.7689	−2.55623
$643$	−7.88554	−0.310975	−0.155488	−	0.987838i	$-0.549695\pi$
$643$	−7.88554	−0.310975	−0.155488	+	0.987838i	$0.549695\pi$
$644$	60.2157	2.37283
$645$	73.8539	2.90800
$646$	−5.44264	−0.214138
$647$	45.9011	1.80456	0.902279	−	0.431153i	$-0.141893\pi$
$647$	45.9011	1.80456	0.902279	+	0.431153i	$0.141893\pi$
$648$	−52.6239	−2.06726
$649$	−0.353239	−0.0138659
$650$	−2.67598	−0.104960
$651$	20.2275	0.792778
$652$	66.0228	2.58565
$653$	12.8801	0.504037	0.252019	−	0.967722i	$-0.418906\pi$
$653$	12.8801	0.504037	0.252019	+	0.967722i	$0.418906\pi$
$654$	98.8524	3.86544
$655$	5.89309	0.230262
$656$	31.5921	1.23346
$657$	1.70730	0.0666080
$658$	−39.6651	−1.54631
$659$	35.3081	1.37541	0.687704	−	0.725991i	$-0.258619\pi$
$659$	35.3081	1.37541	0.687704	+	0.725991i	$0.258619\pi$
$660$	−1.29905	−0.0505656
$661$	41.2223	1.60336	0.801681	−	0.597753i	$-0.203939\pi$
$661$	41.2223	1.60336	0.801681	+	0.597753i	$0.203939\pi$
$662$	−47.4192	−1.84300
$663$	2.60343	0.101109
$664$	17.3716	0.674149
$665$	−8.59458	−0.333284
$666$	−46.6592	−1.80801
$667$	16.1011	0.623438
$668$	−14.7783	−0.571791
$669$	−10.6527	−0.411856
$670$	22.3602	0.863851
$671$	−0.154561	−0.00596675
$672$	−2.94845	−0.113739
$673$	8.06502	0.310884	0.155442	−	0.987845i	$-0.450320\pi$
$673$	8.06502	0.310884	0.155442	+	0.987845i	$0.450320\pi$
$674$	32.1510	1.23841
$675$	−3.14349	−0.120993
$676$	−51.4782	−1.97993
$677$	−27.8269	−1.06948	−0.534738	−	0.845018i	$-0.679590\pi$
$677$	−27.8269	−1.06948	−0.534738	+	0.845018i	$0.679590\pi$
$678$	35.5568	1.36555
$679$	3.18755	0.122327
$680$	−29.6784	−1.13812
$681$	3.39748	0.130192
$682$	0.346498	0.0132681
$683$	7.65929	0.293074	0.146537	−	0.989205i	$-0.453187\pi$
$683$	7.65929	0.293074	0.146537	+	0.989205i	$0.453187\pi$
$684$	9.56531	0.365739
$685$	6.90118	0.263681
$686$	28.9437	1.10508
$687$	7.78671	0.297082
$688$	50.5704	1.92798
$689$	−2.71511	−0.103437
$690$	−70.5643	−2.68634
$691$	−21.3618	−0.812640	−0.406320	−	0.913731i	$-0.633188\pi$
$691$	−21.3618	−0.812640	−0.406320	+	0.913731i	$0.633188\pi$
$692$	−12.9983	−0.494120
$693$	0.395242	0.0150140
$694$	55.2337	2.09664
$695$	22.8848	0.868072
$696$	−40.3386	−1.52903
$697$	−16.4978	−0.624900
$698$	−0.537034	−0.0203270
$699$	31.2133	1.18059
$700$	−27.8725	−1.05348
$701$	−38.3242	−1.44748	−0.723742	−	0.690071i	$-0.757579\pi$
$701$	−38.3242	−1.44748	−0.723742	+	0.690071i	$0.757579\pi$
$702$	1.82670	0.0689445
$703$	−8.01848	−0.302423
$704$	0.389858	0.0146933
$705$	31.0902	1.17092
$706$	−25.6916	−0.966916
$707$	−13.8304	−0.520144
$708$	63.6789	2.39320
$709$	20.1083	0.755182	0.377591	−	0.925972i	$-0.376753\pi$
$709$	20.1083	0.755182	0.377591	+	0.925972i	$0.376753\pi$
$710$	43.4319	1.62997
$711$	−2.36773	−0.0887967
$712$	8.07821	0.302744
$713$	12.5892	0.471469
$714$	40.5416	1.51723
$715$	0.0704239	0.00263370
$716$	19.4001	0.725015
$717$	−55.2018	−2.06155
$718$	−54.8397	−2.04660
$719$	−20.6738	−0.771002	−0.385501	−	0.922707i	$-0.625971\pi$
$719$	−20.6738	−0.771002	−0.385501	+	0.922707i	$0.625971\pi$
$720$	26.8416	1.00033
$721$	21.0677	0.784601
$722$	2.45761	0.0914629
$723$	−39.5171	−1.46966
$724$	32.2323	1.19790
$725$	−7.45286	−0.276792
$726$	−62.6174	−2.32395
$727$	−4.59794	−0.170528	−0.0852640	−	0.996358i	$-0.527173\pi$
$727$	−4.59794	−0.170528	−0.0852640	+	0.996358i	$0.527173\pi$
$728$	8.17837	0.303111
$729$	−14.6726	−0.543428
$730$	4.73718	0.175331
$731$	−26.4086	−0.976757
$732$	27.8629	1.02984
$733$	15.1001	0.557736	0.278868	−	0.960329i	$-0.410041\pi$
$733$	15.1001	0.557736	0.278868	+	0.960329i	$0.410041\pi$
$734$	−30.5665	−1.12823
$735$	20.6667	0.762303
$736$	−1.83506	−0.0676411
$737$	−0.176713	−0.00650932
$738$	43.3487	1.59569
$739$	−43.7633	−1.60986	−0.804929	−	0.593371i	$-0.797797\pi$
$739$	−43.7633	−1.60986	−0.804929	+	0.593371i	$0.797797\pi$
$740$	−86.5941	−3.18326
$741$	−1.17558	−0.0431858
$742$	−42.2806	−1.55217
$743$	11.8241	0.433785	0.216892	−	0.976196i	$-0.430408\pi$
$743$	11.8241	0.433785	0.216892	+	0.976196i	$0.430408\pi$
$744$	−31.5400	−1.15631
$745$	−61.6126	−2.25731
$746$	45.8455	1.67852
$747$	8.20457	0.300190
$748$	0.464514	0.0169843
$749$	36.5724	1.33633
$750$	−43.4415	−1.58626
$751$	−3.27151	−0.119379	−0.0596895	−	0.998217i	$-0.519011\pi$
$751$	−3.27151	−0.119379	−0.0596895	+	0.998217i	$0.519011\pi$
$752$	21.2886	0.776314
$753$	7.52235	0.274130
$754$	4.33090	0.157722
$755$	−15.7162	−0.571970
$756$	19.0267	0.691993
$757$	−34.4153	−1.25085	−0.625423	−	0.780286i	$-0.715074\pi$
$757$	−34.4153	−1.25085	−0.625423	+	0.780286i	$0.715074\pi$
$758$	−66.5022	−2.41547
$759$	0.557671	0.0202422
$760$	13.4012	0.486114
$761$	−3.61827	−0.131162	−0.0655811	−	0.997847i	$-0.520890\pi$
$761$	−3.61827	−0.131162	−0.0655811	+	0.997847i	$0.520890\pi$
$762$	38.4641	1.39341
$763$	−55.8180	−2.02075
$764$	−45.0919	−1.63137
$765$	−14.0171	−0.506788
$766$	−66.9015	−2.41725
$767$	−3.45214	−0.124650
$768$	−74.7878	−2.69867
$769$	45.5169	1.64138	0.820690	−	0.571374i	$-0.193589\pi$
$769$	45.5169	1.64138	0.820690	+	0.571374i	$0.193589\pi$
$770$	1.09667	0.0395211
$771$	−43.4097	−1.56336
$772$	11.0577	0.397975
$773$	−46.5710	−1.67504	−0.837521	−	0.546405i	$-0.815996\pi$
$773$	−46.5710	−1.67504	−0.837521	+	0.546405i	$0.815996\pi$
$774$	69.3897	2.49416
$775$	−5.82725	−0.209321
$776$	−4.97024	−0.178421
$777$	59.7287	2.14276
$778$	87.3428	3.13139
$779$	7.44956	0.266908
$780$	−12.6954	−0.454569
$781$	−0.343243	−0.0122822
$782$	25.2323	0.902304
$783$	5.08755	0.181814
$784$	14.1512	0.505402
$785$	7.21645	0.257566
$786$	12.5523	0.447725
$787$	30.8033	1.09802	0.549010	−	0.835816i	$-0.315005\pi$
$787$	30.8033	1.09802	0.549010	+	0.835816i	$0.315005\pi$
$788$	−63.3007	−2.25499
$789$	9.72417	0.346190
$790$	−6.56966	−0.233738
$791$	−20.0775	−0.713873
$792$	−0.616287	−0.0218988
$793$	−1.51049	−0.0536392
$794$	14.3156	0.508043
$795$	33.1403	1.17536
$796$	95.0116	3.36760
$797$	−33.9711	−1.20332	−0.601659	−	0.798753i	$-0.705493\pi$
$797$	−33.9711	−1.20332	−0.601659	+	0.798753i	$0.705493\pi$
$798$	−18.3065	−0.648042
$799$	−11.1172	−0.393298
$800$	0.849407	0.0300311
$801$	3.81532	0.134808
$802$	92.8746	3.27952
$803$	−0.0374380	−0.00132116
$804$	31.8563	1.12349
$805$	39.8448	1.40434
$806$	3.38626	0.119276
$807$	−60.8122	−2.14069
$808$	21.5652	0.758661
$809$	42.0774	1.47936	0.739681	−	0.672958i	$-0.234976\pi$
$809$	42.0774	1.47936	0.739681	+	0.672958i	$0.234976\pi$
$810$	−68.9620	−2.42308
$811$	−43.7480	−1.53620	−0.768100	−	0.640330i	$-0.778798\pi$
$811$	−43.7480	−1.53620	−0.768100	+	0.640330i	$0.778798\pi$
$812$	45.1100	1.58305
$813$	38.2129	1.34019
$814$	1.02316	0.0358616
$815$	43.6874	1.53030
$816$	−21.7590	−0.761717
$817$	11.9248	0.417194
$818$	−71.0826	−2.48534
$819$	3.86263	0.134971
$820$	80.4502	2.80944
$821$	30.1222	1.05127	0.525637	−	0.850709i	$-0.323827\pi$
$821$	30.1222	1.05127	0.525637	+	0.850709i	$0.323827\pi$
$822$	14.6995	0.512705
$823$	17.5203	0.610718	0.305359	−	0.952237i	$-0.401224\pi$
$823$	17.5203	0.610718	0.305359	+	0.952237i	$0.401224\pi$
$824$	−32.8501	−1.14439
$825$	−0.258133	−0.00898705
$826$	−53.7580	−1.87048
$827$	−36.2190	−1.25946	−0.629729	−	0.776815i	$-0.716834\pi$
$827$	−36.2190	−1.25946	−0.629729	+	0.776815i	$0.716834\pi$
$828$	−44.3451	−1.54110
$829$	−5.74423	−0.199505	−0.0997527	−	0.995012i	$-0.531805\pi$
$829$	−5.74423	−0.199505	−0.0997527	+	0.995012i	$0.531805\pi$
$830$	22.7650	0.790183
$831$	−30.8511	−1.07021
$832$	3.81001	0.132088
$833$	−7.38998	−0.256048
$834$	48.7448	1.68789
$835$	−9.77884	−0.338411
$836$	−0.209750	−0.00725437
$837$	3.97787	0.137495
$838$	19.2132	0.663710
$839$	22.3541	0.771750	0.385875	−	0.922551i	$-0.373900\pi$
$839$	22.3541	0.771750	0.385875	+	0.922551i	$0.373900\pi$
$840$	−99.8242	−3.44426
$841$	−16.9380	−0.584069
$842$	−10.7008	−0.368775
$843$	−9.58690	−0.330191
$844$	85.4671	2.94190
$845$	−34.0632	−1.17181
$846$	29.2109	1.00429
$847$	35.3575	1.21490
$848$	22.6923	0.779258
$849$	65.4638	2.24671
$850$	−11.6795	−0.400602
$851$	37.1740	1.27431
$852$	61.8769	2.11987
$853$	15.3204	0.524561	0.262281	−	0.964992i	$-0.415525\pi$
$853$	15.3204	0.524561	0.262281	+	0.964992i	$0.415525\pi$
$854$	−23.5219	−0.804904
$855$	6.32937	0.216460
$856$	−57.0261	−1.94911
$857$	−13.4432	−0.459210	−0.229605	−	0.973284i	$-0.573744\pi$
$857$	−13.4432	−0.459210	−0.229605	+	0.973284i	$0.573744\pi$
$858$	0.150003	0.00512102
$859$	6.31465	0.215453	0.107727	−	0.994181i	$-0.465643\pi$
$859$	6.31465	0.215453	0.107727	+	0.994181i	$0.465643\pi$
$860$	128.779	4.39133
$861$	−55.4909	−1.89113
$862$	90.6347	3.08703
$863$	−17.1406	−0.583472	−0.291736	−	0.956499i	$-0.594233\pi$
$863$	−17.1406	−0.583472	−0.291736	+	0.956499i	$0.594233\pi$
$864$	−0.579832	−0.0197263
$865$	−8.60098	−0.292442
$866$	72.1404	2.45143
$867$	−28.0234	−0.951723
$868$	35.2707	1.19716
$869$	0.0519201	0.00176127
$870$	−52.8625	−1.79221
$871$	−1.72699	−0.0585167
$872$	87.0350	2.94738
$873$	−2.34743	−0.0794486
$874$	−11.3936	−0.385394
$875$	24.5296	0.829253
$876$	6.74900	0.228028
$877$	5.43293	0.183457	0.0917286	−	0.995784i	$-0.470761\pi$
$877$	5.43293	0.183457	0.0917286	+	0.995784i	$0.470761\pi$
$878$	71.2142	2.40336
$879$	−33.1672	−1.11870
$880$	−0.588589	−0.0198413
$881$	−50.4860	−1.70092	−0.850458	−	0.526043i	$-0.823675\pi$
$881$	−50.4860	−1.70092	−0.850458	+	0.526043i	$0.823675\pi$
$882$	19.4175	0.653820
$883$	7.05801	0.237521	0.118760	−	0.992923i	$-0.462108\pi$
$883$	7.05801	0.237521	0.118760	+	0.992923i	$0.462108\pi$
$884$	4.53961	0.152684
$885$	42.1364	1.41640
$886$	−16.4705	−0.553339
$887$	−32.1284	−1.07877	−0.539384	−	0.842060i	$-0.681343\pi$
$887$	−32.1284	−1.07877	−0.539384	+	0.842060i	$0.681343\pi$
$888$	−93.1329	−3.12533
$889$	−21.7191	−0.728437
$890$	10.5862	0.354852
$891$	0.545008	0.0182585
$892$	−18.5750	−0.621939
$893$	5.01995	0.167986
$894$	−131.235	−4.38915
$895$	12.8371	0.429096
$896$	61.8761	2.06713
$897$	5.45001	0.181971
$898$	35.7059	1.19152
$899$	9.43106	0.314543
$900$	20.5264	0.684212
$901$	−11.8502	−0.394789
$902$	−0.950562	−0.0316503
$903$	−88.8261	−2.95595
$904$	31.3061	1.04123
$905$	21.3281	0.708972
$906$	−33.4755	−1.11215
$907$	20.6841	0.686806	0.343403	−	0.939188i	$-0.388420\pi$
$907$	20.6841	0.686806	0.343403	+	0.939188i	$0.388420\pi$
$908$	5.92419	0.196601
$909$	10.1852	0.337822
$910$	10.7175	0.355282
$911$	−24.8970	−0.824874	−0.412437	−	0.910986i	$-0.635322\pi$
$911$	−24.8970	−0.824874	−0.412437	+	0.910986i	$0.635322\pi$
$912$	9.82523	0.325346
$913$	−0.179912	−0.00595422
$914$	−75.2884	−2.49032
$915$	18.4369	0.609505
$916$	13.5777	0.448620
$917$	−7.08777	−0.234059
$918$	7.97277	0.263140
$919$	53.1858	1.75444	0.877218	−	0.480092i	$-0.159397\pi$
$919$	53.1858	1.75444	0.877218	+	0.480092i	$0.159397\pi$
$920$	−62.1286	−2.04832
$921$	−22.8080	−0.751548
$922$	77.2353	2.54361
$923$	−3.35445	−0.110413
$924$	1.56241	0.0513994
$925$	−17.2070	−0.565763
$926$	−62.7915	−2.06346
$927$	−15.5150	−0.509580
$928$	−1.37471	−0.0451272
$929$	−25.9137	−0.850200	−0.425100	−	0.905146i	$-0.639761\pi$
$929$	−25.9137	−0.850200	−0.425100	+	0.905146i	$0.639761\pi$
$930$	−41.3322	−1.35534
$931$	3.33693	0.109363
$932$	54.4266	1.78280
$933$	25.0435	0.819887
$934$	−72.7914	−2.38181
$935$	0.307369	0.0100521
$936$	−6.02286	−0.196863
$937$	37.6835	1.23107	0.615534	−	0.788111i	$-0.288941\pi$
$937$	37.6835	1.23107	0.615534	+	0.788111i	$0.288941\pi$
$938$	−26.8932	−0.878095
$939$	−36.3902	−1.18755
$940$	54.2120	1.76820
$941$	37.8538	1.23400	0.617000	−	0.786963i	$-0.288348\pi$
$941$	37.8538	1.23400	0.617000	+	0.786963i	$0.288348\pi$
$942$	15.3710	0.500816
$943$	−34.5365	−1.12466
$944$	28.8523	0.939063
$945$	12.5900	0.409551
$946$	−1.52159	−0.0494713
$947$	1.51493	0.0492285	0.0246142	−	0.999697i	$-0.492164\pi$
$947$	1.51493	0.0492285	0.0246142	+	0.999697i	$0.492164\pi$
$948$	−9.35971	−0.303989
$949$	−0.365875	−0.0118768
$950$	5.27384	0.171106
$951$	−26.3839	−0.855556
$952$	35.6950	1.15688
$953$	1.00646	0.0326024	0.0163012	−	0.999867i	$-0.494811\pi$
$953$	1.00646	0.0326024	0.0163012	+	0.999867i	$0.494811\pi$
$954$	31.1370	1.00810
$955$	−29.8374	−0.965515
$956$	−96.2553	−3.11312
$957$	0.417773	0.0135047
$958$	99.2452	3.20647
$959$	−8.30023	−0.268029
$960$	−46.5045	−1.50093
$961$	−23.6260	−0.762130
$962$	9.99910	0.322384
$963$	−26.9333	−0.867913
$964$	−68.9060	−2.21931
$965$	7.31688	0.235539
$966$	84.8695	2.73063
$967$	50.0928	1.61088	0.805438	−	0.592680i	$-0.201930\pi$
$967$	50.0928	1.61088	0.805438	+	0.592680i	$0.201930\pi$
$968$	−55.1318	−1.77200
$969$	−5.13087	−0.164827
$970$	−6.51335	−0.209131
$971$	49.9027	1.60145	0.800727	−	0.599029i	$-0.204447\pi$
$971$	49.9027	1.60145	0.800727	+	0.599029i	$0.204447\pi$
$972$	−80.4957	−2.58190
$973$	−27.5242	−0.882385
$974$	−57.4934	−1.84221
$975$	−2.52269	−0.0807907
$976$	12.6244	0.404097
$977$	52.2542	1.67176	0.835880	−	0.548913i	$-0.184958\pi$
$977$	52.2542	1.67176	0.835880	+	0.548913i	$0.184958\pi$
$978$	93.0542	2.97554
$979$	−0.0836633	−0.00267389
$980$	36.0366	1.15115
$981$	41.1065	1.31243
$982$	17.5445	0.559867
$983$	10.3499	0.330109	0.165055	−	0.986284i	$-0.447220\pi$
$983$	10.3499	0.330109	0.165055	+	0.986284i	$0.447220\pi$
$984$	86.5251	2.75832
$985$	−41.8861	−1.33460
$986$	18.9025	0.601978
$987$	−37.3930	−1.19023
$988$	−2.04985	−0.0652145
$989$	−55.2836	−1.75792
$990$	−0.807626	−0.0256680
$991$	−43.1667	−1.37124	−0.685618	−	0.727962i	$-0.740468\pi$
$991$	−43.1667	−1.37124	−0.685618	+	0.727962i	$0.740468\pi$
$992$	−1.07486	−0.0341270
$993$	−44.7029	−1.41860
$994$	−52.2367	−1.65685
$995$	62.8693	1.99309
$996$	32.4330	1.02768
$997$	−48.5860	−1.53874	−0.769368	−	0.638806i	$-0.779429\pi$
$997$	−48.5860	−1.53874	−0.769368	+	0.638806i	$0.779429\pi$
$998$	27.1519	0.859478
$999$	11.7460	0.371628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1501.2.a.c.1.29	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1501.2.a.c.1.29	✓	31	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1501 = 19 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1501.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45761 q^{2} +2.31684 q^{3} +4.03987 q^{4} +2.67319 q^{5} +5.69389 q^{6} -3.21511 q^{7} +5.01321 q^{8} +2.36773 q^{9} +6.56966 q^{10} -0.0519201 q^{11} +9.35971 q^{12} -0.507406 q^{13} -7.90150 q^{14} +6.19333 q^{15} +4.24080 q^{16} -2.21460 q^{17} +5.81896 q^{18} +1.00000 q^{19} +10.7993 q^{20} -7.44888 q^{21} -0.127600 q^{22} -4.63604 q^{23} +11.6148 q^{24} +2.14592 q^{25} -1.24701 q^{26} -1.46487 q^{27} -12.9886 q^{28} -3.47304 q^{29} +15.2208 q^{30} -2.71551 q^{31} +0.395824 q^{32} -0.120290 q^{33} -5.44264 q^{34} -8.59458 q^{35} +9.56531 q^{36} -8.01848 q^{37} +2.45761 q^{38} -1.17558 q^{39} +13.4012 q^{40} +7.44956 q^{41} -18.3065 q^{42} +11.9248 q^{43} -0.209750 q^{44} +6.32937 q^{45} -11.3936 q^{46} +5.01995 q^{47} +9.82523 q^{48} +3.33693 q^{49} +5.27384 q^{50} -5.13087 q^{51} -2.04985 q^{52} +5.35096 q^{53} -3.60009 q^{54} -0.138792 q^{55} -16.1180 q^{56} +2.31684 q^{57} -8.53539 q^{58} +6.80351 q^{59} +25.0202 q^{60} +2.97690 q^{61} -6.67367 q^{62} -7.61250 q^{63} -7.50881 q^{64} -1.35639 q^{65} -0.295627 q^{66} +3.40356 q^{67} -8.94670 q^{68} -10.7409 q^{69} -21.1222 q^{70} +6.61099 q^{71} +11.8699 q^{72} +0.721070 q^{73} -19.7063 q^{74} +4.97174 q^{75} +4.03987 q^{76} +0.166929 q^{77} -2.88911 q^{78} -1.00000 q^{79} +11.3364 q^{80} -10.4970 q^{81} +18.3082 q^{82} +3.46517 q^{83} -30.0925 q^{84} -5.92004 q^{85} +29.3064 q^{86} -8.04646 q^{87} -0.260286 q^{88} +1.61138 q^{89} +15.5552 q^{90} +1.63136 q^{91} -18.7290 q^{92} -6.29138 q^{93} +12.3371 q^{94} +2.67319 q^{95} +0.917060 q^{96} -0.991429 q^{97} +8.20089 q^{98} -0.122933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 7 q^{2} + 8 q^{3} + 35 q^{4} + q^{5} + 2 q^{6} + 7 q^{7} + 15 q^{8} + 35 q^{9} + 38 q^{11} + 14 q^{12} + 3 q^{13} + 27 q^{14} + 15 q^{15} + 27 q^{16} + 6 q^{17} + 17 q^{18} + 31 q^{19} + 2 q^{20}+ \cdots + 58 q^{99}+O(q^{100}) \) 31 * q + 7 * q^2 + 8 * q^3 + 35 * q^4 + q^5 + 2 * q^6 + 7 * q^7 + 15 * q^8 + 35 * q^9 + 38 * q^11 + 14 * q^12 + 3 * q^13 + 27 * q^14 + 15 * q^15 + 27 * q^16 + 6 * q^17 + 17 * q^18 + 31 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 6 * q^26 + 5 * q^27 + 13 * q^28 + 39 * q^29 - 9 * q^30 + 15 * q^31 + 27 * q^32 + 24 * q^33 - 10 * q^34 + 22 * q^35 + 35 * q^36 + 9 * q^37 + 7 * q^38 + 10 * q^39 - 36 * q^40 + 56 * q^41 + 17 * q^42 + 19 * q^43 + 74 * q^44 - 39 * q^45 + 38 * q^46 + 21 * q^47 + 51 * q^48 + 30 * q^49 + 12 * q^50 + 40 * q^51 + 2 * q^52 + 24 * q^53 + 8 * q^54 - 16 * q^55 + 101 * q^56 + 8 * q^57 - 32 * q^58 + 74 * q^59 + 3 * q^60 - 11 * q^61 - 7 * q^62 + 9 * q^63 + 3 * q^64 + 48 * q^65 + 24 * q^66 + 49 * q^67 - 18 * q^68 - 7 * q^69 - 14 * q^70 + 75 * q^71 + q^72 - 21 * q^73 + 31 * q^74 + 45 * q^75 + 35 * q^76 + 4 * q^77 - 23 * q^78 - 31 * q^79 - q^80 + 19 * q^81 - 20 * q^82 + 34 * q^83 + 22 * q^84 - 10 * q^85 + 62 * q^86 - 6 * q^87 - 3 * q^88 + 36 * q^89 + 9 * q^90 + 38 * q^91 + 5 * q^92 + 34 * q^93 + 50 * q^94 + q^95 - 79 * q^96 + 10 * q^97 + 27 * q^98 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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