LMFDB - Embedded newform 722.4.a.k.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,4,Mod(1,722)] 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("722.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,6,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$42.5993790241$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.253788.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 63x + 15 $ x^3 - x^2 - 63*x + 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$8.33908$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +6.33908 q^{3} +4.00000 q^{4} +5.93108 q^{5} +12.6782 q^{6} +0.660916 q^{7} +8.00000 q^{8} +13.1840 q^{9} +11.8622 q^{10} +50.1496 q^{11} +25.3563 q^{12} -2.62650 q^{13} +1.32183 q^{14} +37.5976 q^{15} +16.0000 q^{16} +57.8105 q^{17} +26.3680 q^{18} +23.7243 q^{20} +4.18960 q^{21} +100.299 q^{22} +37.9656 q^{23} +50.7127 q^{24} -89.8223 q^{25} -5.25300 q^{26} -87.5809 q^{27} +2.64366 q^{28} -309.828 q^{29} +75.1952 q^{30} +282.420 q^{31} +32.0000 q^{32} +317.902 q^{33} +115.621 q^{34} +3.91994 q^{35} +52.7360 q^{36} +21.0744 q^{37} -16.6496 q^{39} +47.4486 q^{40} +344.092 q^{41} +8.37920 q^{42} +265.350 q^{43} +200.598 q^{44} +78.1953 q^{45} +75.9312 q^{46} -139.793 q^{47} +101.425 q^{48} -342.563 q^{49} -179.645 q^{50} +366.466 q^{51} -10.5060 q^{52} +133.787 q^{53} -175.162 q^{54} +297.441 q^{55} +5.28733 q^{56} -619.656 q^{58} -455.822 q^{59} +150.390 q^{60} +108.437 q^{61} +564.840 q^{62} +8.71351 q^{63} +64.0000 q^{64} -15.5780 q^{65} +635.805 q^{66} -26.3960 q^{67} +231.242 q^{68} +240.667 q^{69} +7.83989 q^{70} +1119.05 q^{71} +105.472 q^{72} -470.449 q^{73} +42.1489 q^{74} -569.391 q^{75} +33.1446 q^{77} -33.2992 q^{78} -381.892 q^{79} +94.8973 q^{80} -911.150 q^{81} +688.184 q^{82} +1322.28 q^{83} +16.7584 q^{84} +342.879 q^{85} +530.701 q^{86} -1964.03 q^{87} +401.197 q^{88} -405.489 q^{89} +156.391 q^{90} -1.73590 q^{91} +151.862 q^{92} +1790.28 q^{93} -279.587 q^{94} +202.851 q^{96} -1374.15 q^{97} -685.126 q^{98} +661.171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20}+ \cdots + 3184 q^{99}+O(q^{100}) $ 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	6.33908	1.21996	0.609979	−	0.792418i	$-0.291178\pi$
$3$	6.33908	1.21996	0.609979	+	0.792418i	$0.291178\pi$
$4$	4.00000	0.500000
$5$	5.93108	0.530492	0.265246	−	0.964181i	$-0.414547\pi$
$5$	5.93108	0.530492	0.265246	+	0.964181i	$0.414547\pi$
$6$	12.6782	0.862640
$7$	0.660916	0.0356861	0.0178430	−	0.999841i	$-0.494320\pi$
$7$	0.660916	0.0356861	0.0178430	+	0.999841i	$0.494320\pi$
$8$	8.00000	0.353553
$9$	13.1840	0.488296
$10$	11.8622	0.375114
$11$	50.1496	1.37461	0.687303	−	0.726371i	$-0.258794\pi$
$11$	50.1496	1.37461	0.687303	+	0.726371i	$0.258794\pi$
$12$	25.3563	0.609979
$13$	−2.62650	−0.0560354	−0.0280177	−	0.999607i	$-0.508919\pi$
$13$	−2.62650	−0.0560354	−0.0280177	+	0.999607i	$0.508919\pi$
$14$	1.32183	0.0252339
$15$	37.5976	0.647177
$16$	16.0000	0.250000
$17$	57.8105	0.824771	0.412385	−	0.911009i	$-0.364696\pi$
$17$	57.8105	0.824771	0.412385	+	0.911009i	$0.364696\pi$
$18$	26.3680	0.345277
$19$	0	0
$19$	0	0
$20$	23.7243	0.265246
$21$	4.18960	0.0435355
$22$	100.299	0.971993
$23$	37.9656	0.344190	0.172095	−	0.985080i	$-0.444946\pi$
$23$	37.9656	0.344190	0.172095	+	0.985080i	$0.444946\pi$
$24$	50.7127	0.431320
$25$	−89.8223	−0.718578
$26$	−5.25300	−0.0396230
$27$	−87.5809	−0.624257
$28$	2.64366	0.0178430
$29$	−309.828	−1.98392	−0.991959	−	0.126563i	$-0.959606\pi$
$29$	−309.828	−1.98392	−0.991959	+	0.126563i	$0.959606\pi$
$30$	75.1952	0.457623
$31$	282.420	1.63626	0.818131	−	0.575032i	$-0.195010\pi$
$31$	282.420	1.63626	0.818131	+	0.575032i	$0.195010\pi$
$32$	32.0000	0.176777
$33$	317.902	1.67696
$34$	115.621	0.583201
$35$	3.91994	0.0189312
$36$	52.7360	0.244148
$37$	21.0744	0.0936383	0.0468192	−	0.998903i	$-0.485092\pi$
$37$	21.0744	0.0936383	0.0468192	+	0.998903i	$0.485092\pi$
$38$	0	0
$39$	−16.6496	−0.0683608
$40$	47.4486	0.187557
$41$	344.092	1.31069	0.655343	−	0.755331i	$-0.272524\pi$
$41$	344.092	1.31069	0.655343	+	0.755331i	$0.272524\pi$
$42$	8.37920	0.0307843
$43$	265.350	0.941059	0.470530	−	0.882384i	$-0.344063\pi$
$43$	265.350	0.941059	0.470530	+	0.882384i	$0.344063\pi$
$44$	200.598	0.687303
$45$	78.1953	0.259037
$46$	75.9312	0.243379
$47$	−139.793	−0.433850	−0.216925	−	0.976188i	$-0.569603\pi$
$47$	−139.793	−0.433850	−0.216925	+	0.976188i	$0.569603\pi$
$48$	101.425	0.304989
$49$	−342.563	−0.998727
$50$	−179.645	−0.508112
$51$	366.466	1.00619
$52$	−10.5060	−0.0280177
$53$	133.787	0.346737	0.173369	−	0.984857i	$-0.444535\pi$
$53$	133.787	0.346737	0.173369	+	0.984857i	$0.444535\pi$
$54$	−175.162	−0.441416
$55$	297.441	0.729217
$56$	5.28733	0.0126169
$57$	0	0
$58$	−619.656	−1.40284
$59$	−455.822	−1.00581	−0.502907	−	0.864341i	$-0.667736\pi$
$59$	−455.822	−1.00581	−0.502907	+	0.864341i	$0.667736\pi$
$60$	150.390	0.323589
$61$	108.437	0.227605	0.113802	−	0.993503i	$-0.463697\pi$
$61$	108.437	0.227605	0.113802	+	0.993503i	$0.463697\pi$
$62$	564.840	1.15701
$63$	8.71351	0.0174254
$64$	64.0000	0.125000
$65$	−15.5780	−0.0297263
$66$	635.805	1.18579
$67$	−26.3960	−0.0481312	−0.0240656	−	0.999710i	$-0.507661\pi$
$67$	−26.3960	−0.0481312	−0.0240656	+	0.999710i	$0.507661\pi$
$68$	231.242	0.412385
$69$	240.667	0.419897
$70$	7.83989	0.0133864
$71$	1119.05	1.87052	0.935261	−	0.353958i	$-0.115164\pi$
$71$	1119.05	1.87052	0.935261	+	0.353958i	$0.115164\pi$
$72$	105.472	0.172639
$73$	−470.449	−0.754272	−0.377136	−	0.926158i	$-0.623091\pi$
$73$	−470.449	−0.754272	−0.377136	+	0.926158i	$0.623091\pi$
$74$	42.1489	0.0662123
$75$	−569.391	−0.876635
$76$	0	0
$77$	33.1446	0.0490543
$78$	−33.2992	−0.0483384
$79$	−381.892	−0.543877	−0.271938	−	0.962315i	$-0.587665\pi$
$79$	−381.892	−0.543877	−0.271938	+	0.962315i	$0.587665\pi$
$80$	94.8973	0.132623
$81$	−911.150	−1.24986
$82$	688.184	0.926795
$83$	1322.28	1.74866	0.874330	−	0.485332i	$-0.161301\pi$
$83$	1322.28	1.74866	0.874330	+	0.485332i	$0.161301\pi$
$84$	16.7584	0.0217678
$85$	342.879	0.437534
$86$	530.701	0.665430
$87$	−1964.03	−2.42029
$88$	401.197	0.485997
$89$	−405.489	−0.482941	−0.241470	−	0.970408i	$-0.577630\pi$
$89$	−405.489	−0.482941	−0.241470	+	0.970408i	$0.577630\pi$
$90$	156.391	0.183167
$91$	−1.73590	−0.00199968
$92$	151.862	0.172095
$93$	1790.28	1.99617
$94$	−279.587	−0.306779
$95$	0	0
$96$	202.851	0.215660
$97$	−1374.15	−1.43839	−0.719194	−	0.694809i	$-0.755489\pi$
$97$	−1374.15	−1.43839	−0.719194	+	0.694809i	$0.755489\pi$
$98$	−685.126	−0.706206
$99$	661.171	0.671214
$100$	−359.289	−0.359289
$101$	79.8833	0.0786999	0.0393499	−	0.999225i	$-0.487471\pi$
$101$	79.8833	0.0786999	0.0393499	+	0.999225i	$0.487471\pi$
$102$	732.931	0.711480
$103$	−1799.73	−1.72168	−0.860838	−	0.508880i	$-0.830060\pi$
$103$	−1799.73	−1.72168	−0.860838	+	0.508880i	$0.830060\pi$
$104$	−21.0120	−0.0198115
$105$	24.8489	0.0230952
$106$	267.574	0.245180
$107$	−69.2556	−0.0625718	−0.0312859	−	0.999510i	$-0.509960\pi$
$107$	−69.2556	−0.0625718	−0.0312859	+	0.999510i	$0.509960\pi$
$108$	−350.323	−0.312129
$109$	−637.099	−0.559844	−0.279922	−	0.960023i	$-0.590309\pi$
$109$	−637.099	−0.559844	−0.279922	+	0.960023i	$0.590309\pi$
$110$	594.882	0.515634
$111$	133.593	0.114235
$112$	10.5747	0.00892152
$113$	−235.498	−0.196051	−0.0980256	−	0.995184i	$-0.531253\pi$
$113$	−235.498	−0.196051	−0.0980256	+	0.995184i	$0.531253\pi$
$114$	0	0
$115$	225.177	0.182590
$116$	−1239.31	−0.991959
$117$	−34.6277	−0.0273618
$118$	−911.644	−0.711218
$119$	38.2079	0.0294329
$120$	300.781	0.228812
$121$	1183.98	0.889541
$122$	216.873	0.160941
$123$	2181.23	1.59898
$124$	1129.68	0.818131
$125$	−1274.13	−0.911692
$126$	17.4270	0.0123216
$127$	−898.317	−0.627659	−0.313830	−	0.949479i	$-0.601612\pi$
$127$	−898.317	−0.627659	−0.313830	+	0.949479i	$0.601612\pi$
$128$	128.000	0.0883883
$129$	1682.08	1.14805
$130$	−31.1560	−0.0210197
$131$	654.434	0.436475	0.218237	−	0.975896i	$-0.429969\pi$
$131$	654.434	0.436475	0.218237	+	0.975896i	$0.429969\pi$
$132$	1271.61	0.838480
$133$	0	0
$134$	−52.7921	−0.0340339
$135$	−519.449	−0.331163
$136$	462.484	0.291600
$137$	2041.59	1.27317	0.636586	−	0.771205i	$-0.280346\pi$
$137$	2041.59	1.27317	0.636586	+	0.771205i	$0.280346\pi$
$138$	481.334	0.296912
$139$	1839.74	1.12263	0.561313	−	0.827603i	$-0.310296\pi$
$139$	1839.74	1.12263	0.561313	+	0.827603i	$0.310296\pi$
$140$	15.6798	0.00946559
$141$	−886.162	−0.529279
$142$	2238.11	1.32266
$143$	−131.718	−0.0770266
$144$	210.944	0.122074
$145$	−1837.61	−1.05245
$146$	−940.898	−0.533351
$147$	−2171.54	−1.21840
$148$	84.2978	0.0468192
$149$	−333.258	−0.183232	−0.0916159	−	0.995794i	$-0.529203\pi$
$149$	−333.258	−0.183232	−0.0916159	+	0.995794i	$0.529203\pi$
$150$	−1138.78	−0.619875
$151$	−3042.43	−1.63966	−0.819832	−	0.572604i	$-0.805933\pi$
$151$	−3042.43	−1.63966	−0.819832	+	0.572604i	$0.805933\pi$
$152$	0	0
$153$	762.173	0.402732
$154$	66.2893	0.0346866
$155$	1675.05	0.868023
$156$	−66.5984	−0.0341804
$157$	1968.78	1.00080	0.500400	−	0.865794i	$-0.333186\pi$
$157$	1968.78	1.00080	0.500400	+	0.865794i	$0.333186\pi$
$158$	−763.785	−0.384579
$159$	848.088	0.423005
$160$	189.795	0.0937786
$161$	25.0921	0.0122828
$162$	−1822.30	−0.883787
$163$	−1135.59	−0.545682	−0.272841	−	0.962059i	$-0.587963\pi$
$163$	−1135.59	−0.545682	−0.272841	+	0.962059i	$0.587963\pi$
$164$	1376.37	0.655343
$165$	1885.50	0.889614
$166$	2644.55	1.23649
$167$	−790.323	−0.366210	−0.183105	−	0.983093i	$-0.558615\pi$
$167$	−790.323	−0.366210	−0.183105	+	0.983093i	$0.558615\pi$
$168$	33.5168	0.0153921
$169$	−2190.10	−0.996860
$170$	685.757	0.309383
$171$	0	0
$172$	1061.40	0.470530
$173$	−3484.01	−1.53112	−0.765561	−	0.643363i	$-0.777539\pi$
$173$	−3484.01	−1.53112	−0.765561	+	0.643363i	$0.777539\pi$
$174$	−3928.05	−1.71141
$175$	−59.3650	−0.0256433
$176$	802.393	0.343651
$177$	−2889.50	−1.22705
$178$	−810.977	−0.341491
$179$	2185.23	0.912466	0.456233	−	0.889860i	$-0.349198\pi$
$179$	2185.23	0.912466	0.456233	+	0.889860i	$0.349198\pi$
$180$	312.781	0.129518
$181$	−1055.89	−0.433612	−0.216806	−	0.976215i	$-0.569564\pi$
$181$	−1055.89	−0.433612	−0.216806	+	0.976215i	$0.569564\pi$
$182$	−3.47179	−0.00141399
$183$	687.390	0.277668
$184$	303.725	0.121690
$185$	124.994	0.0496744
$186$	3580.57	1.41150
$187$	2899.17	1.13373
$188$	−559.174	−0.216925
$189$	−57.8836	−0.0222773
$190$	0	0
$191$	2658.51	1.00714	0.503568	−	0.863955i	$-0.332020\pi$
$191$	2658.51	1.00714	0.503568	+	0.863955i	$0.332020\pi$
$192$	405.701	0.152495
$193$	4580.49	1.70835	0.854173	−	0.519988i	$-0.174064\pi$
$193$	4580.49	1.70835	0.854173	+	0.519988i	$0.174064\pi$
$194$	−2748.30	−1.01709
$195$	−98.7501	−0.0362648
$196$	−1370.25	−0.499363
$197$	−4882.92	−1.76596	−0.882978	−	0.469414i	$-0.844465\pi$
$197$	−4882.92	−1.76596	−0.882978	+	0.469414i	$0.844465\pi$
$198$	1322.34	0.474620
$199$	−2357.92	−0.839943	−0.419972	−	0.907537i	$-0.637960\pi$
$199$	−2357.92	−0.839943	−0.419972	+	0.907537i	$0.637960\pi$
$200$	−718.578	−0.254056
$201$	−167.327	−0.0587180
$202$	159.767	0.0556492
$203$	−204.770	−0.0707983
$204$	1465.86	0.503093
$205$	2040.84	0.695308
$206$	−3599.46	−1.21741
$207$	500.538	0.168067
$208$	−42.0240	−0.0140088
$209$	0	0
$210$	49.6977	0.0163308
$211$	3215.26	1.04904	0.524520	−	0.851398i	$-0.324245\pi$
$211$	3215.26	1.04904	0.524520	+	0.851398i	$0.324245\pi$
$212$	535.149	0.173369
$213$	7093.77	2.28196
$214$	−138.511	−0.0442450
$215$	1573.81	0.499224
$216$	−700.647	−0.220708
$217$	186.656	0.0583918
$218$	−1274.20	−0.395870
$219$	−2982.21	−0.920180
$220$	1189.76	0.364609
$221$	−151.839	−0.0462163
$222$	267.185	0.0807762
$223$	−3464.65	−1.04040	−0.520202	−	0.854043i	$-0.674143\pi$
$223$	−3464.65	−1.04040	−0.520202	+	0.854043i	$0.674143\pi$
$224$	21.1493	0.00630847
$225$	−1184.22	−0.350879
$226$	−470.996	−0.138629
$227$	−4831.61	−1.41271	−0.706354	−	0.707858i	$-0.749662\pi$
$227$	−4831.61	−1.41271	−0.706354	+	0.707858i	$0.749662\pi$
$228$	0	0
$229$	−4645.49	−1.34054	−0.670268	−	0.742119i	$-0.733821\pi$
$229$	−4645.49	−1.34054	−0.670268	+	0.742119i	$0.733821\pi$
$230$	450.354	0.129111
$231$	210.107	0.0598442
$232$	−2478.62	−0.701421
$233$	−828.510	−0.232951	−0.116475	−	0.993194i	$-0.537160\pi$
$233$	−828.510	−0.232951	−0.116475	+	0.993194i	$0.537160\pi$
$234$	−69.2555	−0.0193477
$235$	−829.126	−0.230154
$236$	−1823.29	−0.502907
$237$	−2420.85	−0.663506
$238$	76.4157	0.0208122
$239$	2735.22	0.740279	0.370139	−	0.928976i	$-0.379310\pi$
$239$	2735.22	0.740279	0.370139	+	0.928976i	$0.379310\pi$
$240$	601.562	0.161794
$241$	−4084.82	−1.09181	−0.545906	−	0.837847i	$-0.683814\pi$
$241$	−4084.82	−1.09181	−0.545906	+	0.837847i	$0.683814\pi$
$242$	2367.96	0.629001
$243$	−3411.17	−0.900522
$244$	433.747	0.113802
$245$	−2031.77	−0.529816
$246$	4362.45	1.13065
$247$	0	0
$248$	2259.36	0.578506
$249$	8382.03	2.13329
$250$	−2548.26	−0.644663
$251$	−2536.74	−0.637920	−0.318960	−	0.947768i	$-0.603334\pi$
$251$	−2536.74	−0.637920	−0.318960	+	0.947768i	$0.603334\pi$
$252$	34.8540	0.00871269
$253$	1903.96	0.473126
$254$	−1796.63	−0.443822
$255$	2173.54	0.533773
$256$	256.000	0.0625000
$257$	6602.55	1.60255	0.801276	−	0.598295i	$-0.204155\pi$
$257$	6602.55	1.60255	0.801276	+	0.598295i	$0.204155\pi$
$258$	3364.16	0.811796
$259$	13.9284	0.00334159
$260$	−62.3119	−0.0148632
$261$	−4084.77	−0.968739
$262$	1308.87	0.308634
$263$	3904.55	0.915456	0.457728	−	0.889092i	$-0.348663\pi$
$263$	3904.55	0.915456	0.457728	+	0.889092i	$0.348663\pi$
$264$	2543.22	0.592895
$265$	793.502	0.183941
$266$	0	0
$267$	−2570.43	−0.589167
$268$	−105.584	−0.0240656
$269$	1596.72	0.361909	0.180955	−	0.983491i	$-0.442081\pi$
$269$	1596.72	0.361909	0.180955	+	0.983491i	$0.442081\pi$
$270$	−1038.90	−0.234168
$271$	4011.39	0.899168	0.449584	−	0.893238i	$-0.351572\pi$
$271$	4011.39	0.899168	0.449584	+	0.893238i	$0.351572\pi$
$272$	924.968	0.206193
$273$	−11.0040	−0.00243953
$274$	4083.18	0.900269
$275$	−4504.55	−0.987762
$276$	962.668	0.209949
$277$	4850.78	1.05218	0.526092	−	0.850427i	$-0.323657\pi$
$277$	4850.78	1.05218	0.526092	+	0.850427i	$0.323657\pi$
$278$	3679.49	0.793817
$279$	3723.42	0.798980
$280$	31.3595	0.00669318
$281$	−6298.99	−1.33725	−0.668623	−	0.743602i	$-0.733116\pi$
$281$	−6298.99	−1.33725	−0.668623	+	0.743602i	$0.733116\pi$
$282$	−1772.32	−0.374257
$283$	5757.01	1.20925	0.604627	−	0.796509i	$-0.293322\pi$
$283$	5757.01	1.20925	0.604627	+	0.796509i	$0.293322\pi$
$284$	4476.21	0.935261
$285$	0	0
$286$	−263.436	−0.0544660
$287$	227.416	0.0467733
$288$	421.888	0.0863193
$289$	−1570.95	−0.319753
$290$	−3675.23	−0.744196
$291$	−8710.84	−1.75477
$292$	−1881.80	−0.377136
$293$	−5424.24	−1.08153	−0.540763	−	0.841175i	$-0.681865\pi$
$293$	−5424.24	−1.08153	−0.540763	+	0.841175i	$0.681865\pi$
$294$	−4343.07	−0.861542
$295$	−2703.52	−0.533576
$296$	168.596	0.0331061
$297$	−4392.14	−0.858108
$298$	−666.515	−0.129564
$299$	−99.7166	−0.0192868
$300$	−2277.56	−0.438318
$301$	175.374	0.0335827
$302$	−6084.86	−1.15942
$303$	506.387	0.0960105
$304$	0	0
$305$	643.147	0.120743
$306$	1524.35	0.284775
$307$	−5629.86	−1.04662	−0.523311	−	0.852142i	$-0.675303\pi$
$307$	−5629.86	−1.04662	−0.523311	+	0.852142i	$0.675303\pi$
$308$	132.579	0.0245272
$309$	−11408.6	−2.10037
$310$	3350.11	0.613785
$311$	3054.01	0.556839	0.278420	−	0.960460i	$-0.410189\pi$
$311$	3054.01	0.556839	0.278420	+	0.960460i	$0.410189\pi$
$312$	−133.197	−0.0241692
$313$	−3300.94	−0.596103	−0.298051	−	0.954550i	$-0.596337\pi$
$313$	−3300.94	−0.596103	−0.298051	+	0.954550i	$0.596337\pi$
$314$	3937.56	0.707673
$315$	51.6805	0.00924402
$316$	−1527.57	−0.271938
$317$	3170.25	0.561699	0.280850	−	0.959752i	$-0.409384\pi$
$317$	3170.25	0.561699	0.280850	+	0.959752i	$0.409384\pi$
$318$	1696.18	0.299110
$319$	−15537.7	−2.72710
$320$	379.589	0.0663115
$321$	−439.017	−0.0763350
$322$	50.1841	0.00868525
$323$	0	0
$324$	−3644.60	−0.624932
$325$	235.918	0.0402658
$326$	−2271.18	−0.385855
$327$	−4038.62	−0.682986
$328$	2752.74	0.463397
$329$	−92.3917	−0.0154824
$330$	3771.01	0.629052
$331$	−1414.75	−0.234929	−0.117465	−	0.993077i	$-0.537477\pi$
$331$	−1414.75	−0.234929	−0.117465	+	0.993077i	$0.537477\pi$
$332$	5289.11	0.874330
$333$	277.845	0.0457232
$334$	−1580.65	−0.258949
$335$	−156.557	−0.0255332
$336$	67.0336	0.0108839
$337$	2159.77	0.349111	0.174555	−	0.984647i	$-0.444151\pi$
$337$	2159.77	0.349111	0.174555	+	0.984647i	$0.444151\pi$
$338$	−4380.20	−0.704886
$339$	−1492.84	−0.239174
$340$	1371.51	0.218767
$341$	14163.2	2.24922
$342$	0	0
$343$	−453.100	−0.0713267
$344$	2122.80	0.332715
$345$	1427.42	0.222752
$346$	−6968.01	−1.08267
$347$	−5468.76	−0.846048	−0.423024	−	0.906119i	$-0.639031\pi$
$347$	−5468.76	−0.846048	−0.423024	+	0.906119i	$0.639031\pi$
$348$	−7856.10	−1.21015
$349$	−3235.26	−0.496216	−0.248108	−	0.968732i	$-0.579809\pi$
$349$	−3235.26	−0.496216	−0.248108	+	0.968732i	$0.579809\pi$
$350$	−118.730	−0.0181325
$351$	230.031	0.0349805
$352$	1604.79	0.242998
$353$	−6191.72	−0.933576	−0.466788	−	0.884369i	$-0.654589\pi$
$353$	−6191.72	−0.933576	−0.466788	+	0.884369i	$0.654589\pi$
$354$	−5778.99	−0.867655
$355$	6637.19	0.992297
$356$	−1621.95	−0.241470
$357$	242.203	0.0359068
$358$	4370.45	0.645211
$359$	−6407.07	−0.941929	−0.470964	−	0.882152i	$-0.656094\pi$
$359$	−6407.07	−0.941929	−0.470964	+	0.882152i	$0.656094\pi$
$360$	625.562	0.0915834
$361$	0	0
$362$	−2111.78	−0.306610
$363$	7505.35	1.08520
$364$	−6.94358	−0.000999842 0
$365$	−2790.27	−0.400135
$366$	1374.78	0.196341
$367$	8368.94	1.19034	0.595171	−	0.803599i	$-0.297084\pi$
$367$	8368.94	1.19034	0.595171	+	0.803599i	$0.297084\pi$
$368$	607.449	0.0860475
$369$	4536.50	0.640003
$370$	249.988	0.0351251
$371$	88.4221	0.0123737
$372$	7161.13	0.998085
$373$	−10254.9	−1.42354	−0.711769	−	0.702414i	$-0.752106\pi$
$373$	−10254.9	−1.42354	−0.711769	+	0.702414i	$0.752106\pi$
$374$	5798.34	0.801672
$375$	−8076.80	−1.11223
$376$	−1118.35	−0.153389
$377$	813.763	0.111170
$378$	−115.767	−0.0157524
$379$	−6607.19	−0.895484	−0.447742	−	0.894163i	$-0.647772\pi$
$379$	−6607.19	−0.895484	−0.447742	+	0.894163i	$0.647772\pi$
$380$	0	0
$381$	−5694.50	−0.765717
$382$	5317.02	0.712153
$383$	9.95746	0.00132847	0.000664233	−	1.00000i	$-0.499789\pi$
$383$	9.95746	0.00132847	0.000664233		1.00000i	$0.499789\pi$
$384$	811.403	0.107830
$385$	196.583	0.0260229
$386$	9160.98	1.20798
$387$	3498.38	0.459515
$388$	−5496.59	−0.719194
$389$	−12381.5	−1.61380	−0.806898	−	0.590691i	$-0.798855\pi$
$389$	−12381.5	−1.61380	−0.806898	+	0.590691i	$0.798855\pi$
$390$	−197.500	−0.0256431
$391$	2194.81	0.283878
$392$	−2740.51	−0.353103
$393$	4148.52	0.532481
$394$	−9765.83	−1.24872
$395$	−2265.03	−0.288522
$396$	2644.69	0.335607
$397$	603.931	0.0763487	0.0381744	−	0.999271i	$-0.487846\pi$
$397$	603.931	0.0763487	0.0381744	+	0.999271i	$0.487846\pi$
$398$	−4715.84	−0.593930
$399$	0	0
$400$	−1437.16	−0.179645
$401$	−10340.3	−1.28770	−0.643851	−	0.765151i	$-0.722664\pi$
$401$	−10340.3	−1.28770	−0.643851	+	0.765151i	$0.722664\pi$
$402$	−334.653	−0.0415199
$403$	−741.776	−0.0916885
$404$	319.533	0.0393499
$405$	−5404.10	−0.663042
$406$	−409.540	−0.0500619
$407$	1056.87	0.128716
$408$	2931.72	0.355740
$409$	161.420	0.0195152	0.00975760	−	0.999952i	$-0.496894\pi$
$409$	161.420	0.0195152	0.00975760	+	0.999952i	$0.496894\pi$
$410$	4081.67	0.491657
$411$	12941.8	1.55322
$412$	−7198.92	−0.860838
$413$	−301.260	−0.0358936
$414$	1001.08	0.118841
$415$	7842.53	0.927650
$416$	−84.0480	−0.00990575
$417$	11662.3	1.36956
$418$	0	0
$419$	7483.41	0.872526	0.436263	−	0.899819i	$-0.356302\pi$
$419$	7483.41	0.872526	0.436263	+	0.899819i	$0.356302\pi$
$420$	99.3954	0.0115476
$421$	−6049.53	−0.700323	−0.350162	−	0.936689i	$-0.613873\pi$
$421$	−6049.53	−0.700323	−0.350162	+	0.936689i	$0.613873\pi$
$422$	6430.52	0.741783
$423$	−1843.03	−0.211847
$424$	1070.30	0.122590
$425$	−5192.67	−0.592663
$426$	14187.5	1.61359
$427$	71.6675	0.00812233
$428$	−277.022	−0.0312859
$429$	−834.970	−0.0939691
$430$	3147.63	0.353005
$431$	−10909.7	−1.21926	−0.609631	−	0.792685i	$-0.708682\pi$
$431$	−10909.7	−1.21926	−0.609631	+	0.792685i	$0.708682\pi$
$432$	−1401.29	−0.156064
$433$	7648.96	0.848927	0.424464	−	0.905445i	$-0.360463\pi$
$433$	7648.96	0.848927	0.424464	+	0.905445i	$0.360463\pi$
$434$	373.312	0.0412892
$435$	−11648.8	−1.28395
$436$	−2548.40	−0.279922
$437$	0	0
$438$	−5964.43	−0.650665
$439$	11415.9	1.24112	0.620558	−	0.784161i	$-0.286906\pi$
$439$	11415.9	1.24112	0.620558	+	0.784161i	$0.286906\pi$
$440$	2379.53	0.257817
$441$	−4516.35	−0.487674
$442$	−303.678	−0.0326799
$443$	−3152.65	−0.338120	−0.169060	−	0.985606i	$-0.554073\pi$
$443$	−3152.65	−0.338120	−0.169060	+	0.985606i	$0.554073\pi$
$444$	534.371	0.0571174
$445$	−2404.98	−0.256196
$446$	−6929.30	−0.735677
$447$	−2112.55	−0.223535
$448$	42.2986	0.00446076
$449$	−5217.04	−0.548346	−0.274173	−	0.961680i	$-0.588404\pi$
$449$	−5217.04	−0.548346	−0.274173	+	0.961680i	$0.588404\pi$
$450$	−2368.43	−0.248109
$451$	17256.1	1.80168
$452$	−941.992	−0.0980256
$453$	−19286.2	−2.00032
$454$	−9663.21	−0.998936
$455$	−10.2957	−0.00106082
$456$	0	0
$457$	15868.7	1.62430	0.812151	−	0.583447i	$-0.198297\pi$
$457$	15868.7	1.62430	0.812151	+	0.583447i	$0.198297\pi$
$458$	−9290.98	−0.947902
$459$	−5063.09	−0.514869
$460$	900.707	0.0912950
$461$	−4341.17	−0.438586	−0.219293	−	0.975659i	$-0.570375\pi$
$461$	−4341.17	−0.438586	−0.219293	+	0.975659i	$0.570375\pi$
$462$	420.213	0.0423162
$463$	−1394.23	−0.139946	−0.0699732	−	0.997549i	$-0.522291\pi$
$463$	−1394.23	−0.139946	−0.0699732	+	0.997549i	$0.522291\pi$
$464$	−4957.25	−0.495979
$465$	10618.3	1.05895
$466$	−1657.02	−0.164721
$467$	6138.35	0.608242	0.304121	−	0.952633i	$-0.401637\pi$
$467$	6138.35	0.608242	0.304121	+	0.952633i	$0.401637\pi$
$468$	−138.511	−0.0136809
$469$	−17.4456	−0.00171761
$470$	−1658.25	−0.162743
$471$	12480.3	1.22093
$472$	−3646.58	−0.355609
$473$	13307.2	1.29359
$474$	−4841.70	−0.469170
$475$	0	0
$476$	152.831	0.0147164
$477$	1763.85	0.169310
$478$	5470.44	0.523456
$479$	7132.94	0.680402	0.340201	−	0.940353i	$-0.389505\pi$
$479$	7132.94	0.680402	0.340201	+	0.940353i	$0.389505\pi$
$480$	1203.12	0.114406
$481$	−55.3520	−0.00524706
$482$	−8169.65	−0.772027
$483$	159.061	0.0149845
$484$	4735.92	0.444771
$485$	−8150.18	−0.763053
$486$	−6822.35	−0.636765
$487$	14396.6	1.33957	0.669787	−	0.742553i	$-0.266385\pi$
$487$	14396.6	1.33957	0.669787	+	0.742553i	$0.266385\pi$
$488$	867.494	0.0804705
$489$	−7198.59	−0.665708
$490$	−4063.54	−0.374637
$491$	7655.81	0.703670	0.351835	−	0.936062i	$-0.385558\pi$
$491$	7655.81	0.703670	0.351835	+	0.936062i	$0.385558\pi$
$492$	8724.91	0.799490
$493$	−17911.3	−1.63628
$494$	0	0
$495$	3921.46	0.356074
$496$	4518.72	0.409065
$497$	739.600	0.0667517
$498$	16764.1	1.50846
$499$	18638.1	1.67206	0.836028	−	0.548687i	$-0.184872\pi$
$499$	18638.1	1.67206	0.836028	+	0.548687i	$0.184872\pi$
$500$	−5096.51	−0.455846
$501$	−5009.92	−0.446760
$502$	−5073.49	−0.451077
$503$	−7479.57	−0.663017	−0.331509	−	0.943452i	$-0.607558\pi$
$503$	−7479.57	−0.663017	−0.331509	+	0.943452i	$0.607558\pi$
$504$	69.7080	0.00616080
$505$	473.794	0.0417496
$506$	3807.92	0.334550
$507$	−13883.2	−1.21613
$508$	−3593.27	−0.313830
$509$	18710.4	1.62932	0.814659	−	0.579940i	$-0.196924\pi$
$509$	18710.4	1.62932	0.814659	+	0.579940i	$0.196924\pi$
$510$	4347.07	0.377434
$511$	−310.927	−0.0269170
$512$	512.000	0.0441942
$513$	0	0
$514$	13205.1	1.13318
$515$	−10674.3	−0.913335
$516$	6728.31	0.574026
$517$	−7010.58	−0.596373
$518$	27.8569	0.00236286
$519$	−22085.4	−1.86790
$520$	−124.624	−0.0105098
$521$	13796.0	1.16010	0.580050	−	0.814581i	$-0.303033\pi$
$521$	13796.0	1.16010	0.580050	+	0.814581i	$0.303033\pi$
$522$	−8169.54	−0.685002
$523$	−12444.3	−1.04044	−0.520221	−	0.854032i	$-0.674150\pi$
$523$	−12444.3	−1.04044	−0.520221	+	0.854032i	$0.674150\pi$
$524$	2617.74	0.218237
$525$	−376.320	−0.0312837
$526$	7809.10	0.647325
$527$	16326.8	1.34954
$528$	5086.44	0.419240
$529$	−10725.6	−0.881533
$530$	1587.00	0.130066
$531$	−6009.55	−0.491135
$532$	0	0
$533$	−903.757	−0.0734448
$534$	−5140.85	−0.416604
$535$	−410.760	−0.0331938
$536$	−211.168	−0.0170169
$537$	13852.3	1.11317
$538$	3193.43	0.255908
$539$	−17179.4	−1.37286
$540$	−2077.80	−0.165582
$541$	17766.9	1.41194	0.705968	−	0.708243i	$-0.250512\pi$
$541$	17766.9	1.41194	0.705968	+	0.708243i	$0.250512\pi$
$542$	8022.78	0.635808
$543$	−6693.39	−0.528988
$544$	1849.94	0.145800
$545$	−3778.68	−0.296993
$546$	−22.0080	−0.00172501
$547$	7190.99	0.562092	0.281046	−	0.959694i	$-0.409319\pi$
$547$	7190.99	0.562092	0.281046	+	0.959694i	$0.409319\pi$
$548$	8166.35	0.636586
$549$	1429.63	0.111139
$550$	−9009.10	−0.698453
$551$	0	0
$552$	1925.34	0.148456
$553$	−252.399	−0.0194088
$554$	9701.56	0.744007
$555$	792.349	0.0606006
$556$	7358.98	0.561313
$557$	18489.1	1.40648	0.703238	−	0.710955i	$-0.251737\pi$
$557$	18489.1	1.40648	0.703238	+	0.710955i	$0.251737\pi$
$558$	7446.84	0.564964
$559$	−696.943	−0.0527326
$560$	62.7191	0.00473280
$561$	18378.1	1.38311
$562$	−12598.0	−0.945576
$563$	−4932.37	−0.369227	−0.184613	−	0.982811i	$-0.559103\pi$
$563$	−4932.37	−0.369227	−0.184613	+	0.982811i	$0.559103\pi$
$564$	−3544.65	−0.264639
$565$	−1396.76	−0.104004
$566$	11514.0	0.855071
$567$	−602.194	−0.0446027
$568$	8952.42	0.661330
$569$	15002.9	1.10537	0.552683	−	0.833392i	$-0.313604\pi$
$569$	15002.9	1.10537	0.552683	+	0.833392i	$0.313604\pi$
$570$	0	0
$571$	−13385.3	−0.981013	−0.490507	−	0.871438i	$-0.663188\pi$
$571$	−13385.3	−0.981013	−0.490507	+	0.871438i	$0.663188\pi$
$572$	−526.871	−0.0385133
$573$	16852.5	1.22866
$574$	454.832	0.0330737
$575$	−3410.16	−0.247328
$576$	843.775	0.0610370
$577$	4891.89	0.352950	0.176475	−	0.984305i	$-0.443531\pi$
$577$	4891.89	0.352950	0.176475	+	0.984305i	$0.443531\pi$
$578$	−3141.89	−0.226100
$579$	29036.1	2.08411
$580$	−7350.45	−0.526226
$581$	873.914	0.0624029
$582$	−17421.7	−1.24081
$583$	6709.37	0.476627
$584$	−3763.59	−0.266675
$585$	−205.380	−0.0145152
$586$	−10848.5	−0.764755
$587$	−12382.4	−0.870659	−0.435330	−	0.900271i	$-0.643368\pi$
$587$	−12382.4	−0.870659	−0.435330	+	0.900271i	$0.643368\pi$
$588$	−8686.15	−0.609202
$589$	0	0
$590$	−5407.03	−0.377295
$591$	−30953.2	−2.15439
$592$	337.191	0.0234096
$593$	22526.1	1.55993	0.779964	−	0.625824i	$-0.215237\pi$
$593$	22526.1	1.55993	0.779964	+	0.625824i	$0.215237\pi$
$594$	−8784.29	−0.606774
$595$	226.614	0.0156139
$596$	−1333.03	−0.0916159
$597$	−14947.1	−1.02469
$598$	−199.433	−0.0136378
$599$	8740.27	0.596190	0.298095	−	0.954536i	$-0.403649\pi$
$599$	8740.27	0.596190	0.298095	+	0.954536i	$0.403649\pi$
$600$	−4555.13	−0.309937
$601$	6198.75	0.420719	0.210360	−	0.977624i	$-0.432537\pi$
$601$	6198.75	0.420719	0.210360	+	0.977624i	$0.432537\pi$
$602$	350.749	0.0237466
$603$	−348.005	−0.0235023
$604$	−12169.7	−0.819832
$605$	7022.28	0.471894
$606$	1012.77	0.0678897
$607$	−9848.40	−0.658541	−0.329271	−	0.944236i	$-0.606803\pi$
$607$	−9848.40	−0.658541	−0.329271	+	0.944236i	$0.606803\pi$
$608$	0	0
$609$	−1298.06	−0.0863709
$610$	1286.29	0.0853779
$611$	367.167	0.0243110
$612$	3048.69	0.201366
$613$	9663.78	0.636731	0.318366	−	0.947968i	$-0.396866\pi$
$613$	9663.78	0.636731	0.318366	+	0.947968i	$0.396866\pi$
$614$	−11259.7	−0.740074
$615$	12937.0	0.848246
$616$	265.157	0.0173433
$617$	5193.66	0.338880	0.169440	−	0.985541i	$-0.445804\pi$
$617$	5193.66	0.338880	0.169440	+	0.985541i	$0.445804\pi$
$618$	−22817.3	−1.48519
$619$	5299.50	0.344112	0.172056	−	0.985087i	$-0.444959\pi$
$619$	5299.50	0.344112	0.172056	+	0.985087i	$0.444959\pi$
$620$	6700.22	0.434012
$621$	−3325.06	−0.214863
$622$	6108.02	0.393745
$623$	−267.994	−0.0172343
$624$	−266.394	−0.0170902
$625$	3670.84	0.234933
$626$	−6601.88	−0.421508
$627$	0	0
$628$	7875.12	0.500400
$629$	1218.32	0.0772301
$630$	103.361	0.00653651
$631$	−14278.4	−0.900814	−0.450407	−	0.892823i	$-0.648721\pi$
$631$	−14278.4	−0.900814	−0.450407	+	0.892823i	$0.648721\pi$
$632$	−3055.14	−0.192289
$633$	20381.8	1.27978
$634$	6340.49	0.397181
$635$	−5327.99	−0.332968
$636$	3392.35	0.211502
$637$	899.742	0.0559640
$638$	−31075.5	−1.92835
$639$	14753.6	0.913369
$640$	759.178	0.0468893
$641$	12871.8	0.793147	0.396574	−	0.918003i	$-0.370199\pi$
$641$	12871.8	0.793147	0.396574	+	0.918003i	$0.370199\pi$
$642$	−878.034	−0.0539770
$643$	17071.4	1.04701	0.523506	−	0.852022i	$-0.324624\pi$
$643$	17071.4	1.04701	0.523506	+	0.852022i	$0.324624\pi$
$644$	100.368	0.00614140
$645$	9976.54	0.609032
$646$	0	0
$647$	−6628.94	−0.402798	−0.201399	−	0.979509i	$-0.564549\pi$
$647$	−6628.94	−0.402798	−0.201399	+	0.979509i	$0.564549\pi$
$648$	−7289.20	−0.441893
$649$	−22859.3	−1.38260
$650$	471.837	0.0284722
$651$	1183.23	0.0712355
$652$	−4542.35	−0.272841
$653$	30340.7	1.81826	0.909129	−	0.416515i	$-0.136749\pi$
$653$	30340.7	1.81826	0.909129	+	0.416515i	$0.136749\pi$
$654$	−8077.25	−0.482944
$655$	3881.50	0.231546
$656$	5505.47	0.327671
$657$	−6202.39	−0.368308
$658$	−184.783	−0.0109477
$659$	−2856.07	−0.168826	−0.0844132	−	0.996431i	$-0.526902\pi$
$659$	−2856.07	−0.168826	−0.0844132	+	0.996431i	$0.526902\pi$
$660$	7542.02	0.444807
$661$	21281.0	1.25224	0.626122	−	0.779725i	$-0.284641\pi$
$661$	21281.0	1.25224	0.626122	+	0.779725i	$0.284641\pi$
$662$	−2829.49	−0.166120
$663$	−962.522	−0.0563820
$664$	10578.2	0.618245
$665$	0	0
$666$	555.690	0.0323312
$667$	−11762.8	−0.682845
$668$	−3161.29	−0.183105
$669$	−21962.7	−1.26925
$670$	−313.114	−0.0180547
$671$	5438.06	0.312867
$672$	134.067	0.00769606
$673$	14334.7	0.821046	0.410523	−	0.911850i	$-0.365346\pi$
$673$	14334.7	0.821046	0.410523	+	0.911850i	$0.365346\pi$
$674$	4319.54	0.246858
$675$	7866.71	0.448578
$676$	−8760.41	−0.498430
$677$	−3300.00	−0.187340	−0.0936700	−	0.995603i	$-0.529860\pi$
$677$	−3300.00	−0.187340	−0.0936700	+	0.995603i	$0.529860\pi$
$678$	−2985.68	−0.169122
$679$	−908.196	−0.0513304
$680$	2743.03	0.154692
$681$	−30628.0	−1.72344
$682$	28326.5	1.59044
$683$	1847.09	0.103480	0.0517400	−	0.998661i	$-0.483523\pi$
$683$	1847.09	0.103480	0.0517400	+	0.998661i	$0.483523\pi$
$684$	0	0
$685$	12108.8	0.675408
$686$	−906.199	−0.0504356
$687$	−29448.2	−1.63540
$688$	4245.61	0.235265
$689$	−351.392	−0.0194296
$690$	2854.83	0.157509
$691$	34144.6	1.87977	0.939886	−	0.341489i	$-0.110931\pi$
$691$	34144.6	1.87977	0.939886	+	0.341489i	$0.110931\pi$
$692$	−13936.0	−0.765561
$693$	436.979	0.0239530
$694$	−10937.5	−0.598246
$695$	10911.7	0.595544
$696$	−15712.2	−0.855703
$697$	19892.1	1.08102
$698$	−6470.52	−0.350878
$699$	−5252.00	−0.284190
$700$	−237.460	−0.0128216
$701$	6732.11	0.362722	0.181361	−	0.983417i	$-0.441950\pi$
$701$	6732.11	0.362722	0.181361	+	0.983417i	$0.441950\pi$
$702$	460.062	0.0247349
$703$	0	0
$704$	3209.57	0.171826
$705$	−5255.90	−0.280778
$706$	−12383.4	−0.660138
$707$	52.7962	0.00280849
$708$	−11558.0	−0.613525
$709$	30919.0	1.63778	0.818892	−	0.573947i	$-0.194589\pi$
$709$	30919.0	1.63778	0.818892	+	0.573947i	$0.194589\pi$
$710$	13274.4	0.701660
$711$	−5034.87	−0.265573
$712$	−3243.91	−0.170745
$713$	10722.2	0.563185
$714$	484.406	0.0253900
$715$	−781.229	−0.0408620
$716$	8740.91	0.456233
$717$	17338.8	0.903108
$718$	−12814.1	−0.666044
$719$	−7461.12	−0.387000	−0.193500	−	0.981100i	$-0.561984\pi$
$719$	−7461.12	−0.387000	−0.193500	+	0.981100i	$0.561984\pi$
$720$	1251.12	0.0647592
$721$	−1189.47	−0.0614399
$722$	0	0
$723$	−25894.0	−1.33196
$724$	−4223.57	−0.216806
$725$	27829.5	1.42560
$726$	15010.7	0.767354
$727$	−10947.7	−0.558498	−0.279249	−	0.960219i	$-0.590085\pi$
$727$	−10947.7	−0.558498	−0.279249	+	0.960219i	$0.590085\pi$
$728$	−13.8872	−0.000706995 0
$729$	2977.33	0.151264
$730$	−5580.54	−0.282938
$731$	15340.0	0.776158
$732$	2749.56	0.138834
$733$	−36104.8	−1.81932	−0.909661	−	0.415352i	$-0.863659\pi$
$733$	−36104.8	−1.81932	−0.909661	+	0.415352i	$0.863659\pi$
$734$	16737.9	0.841698
$735$	−12879.6	−0.646353
$736$	1214.90	0.0608448
$737$	−1323.75	−0.0661614
$738$	9073.01	0.452550
$739$	22783.4	1.13410	0.567052	−	0.823682i	$-0.308084\pi$
$739$	22783.4	1.13410	0.567052	+	0.823682i	$0.308084\pi$
$740$	499.977	0.0248372
$741$	0	0
$742$	176.844	0.00874953
$743$	−22636.0	−1.11768	−0.558839	−	0.829276i	$-0.688753\pi$
$743$	−22636.0	−1.11768	−0.558839	+	0.829276i	$0.688753\pi$
$744$	14322.3	0.705752
$745$	−1976.58	−0.0972029
$746$	−20509.8	−1.00659
$747$	17432.9	0.853863
$748$	11596.7	0.566867
$749$	−45.7721	−0.00223294
$750$	−16153.6	−0.786462
$751$	2859.24	0.138928	0.0694642	−	0.997584i	$-0.477871\pi$
$751$	2859.24	0.138928	0.0694642	+	0.997584i	$0.477871\pi$
$752$	−2236.69	−0.108463
$753$	−16080.6	−0.778235
$754$	1627.53	0.0786087
$755$	−18044.9	−0.869828
$756$	−231.534	−0.0111387
$757$	20091.1	0.964630	0.482315	−	0.875998i	$-0.339796\pi$
$757$	20091.1	0.964630	0.482315	+	0.875998i	$0.339796\pi$
$758$	−13214.4	−0.633203
$759$	12069.3	0.577193
$760$	0	0
$761$	−9968.77	−0.474859	−0.237430	−	0.971405i	$-0.576305\pi$
$761$	−9968.77	−0.474859	−0.237430	+	0.971405i	$0.576305\pi$
$762$	−11389.0	−0.541444
$763$	−421.069	−0.0199787
$764$	10634.0	0.503568
$765$	4520.51	0.213646
$766$	19.9149	0.000939368 0
$767$	1197.22	0.0563611
$768$	1622.81	0.0762473
$769$	20062.4	0.940791	0.470396	−	0.882456i	$-0.344111\pi$
$769$	20062.4	0.940791	0.470396	+	0.882456i	$0.344111\pi$
$770$	393.167	0.0184010
$771$	41854.1	1.95504
$772$	18322.0	0.854173
$773$	−588.965	−0.0274044	−0.0137022	−	0.999906i	$-0.504362\pi$
$773$	−588.965	−0.0274044	−0.0137022	+	0.999906i	$0.504362\pi$
$774$	6996.75	0.324926
$775$	−25367.6	−1.17578
$776$	−10993.2	−0.508547
$777$	88.2935	0.00407659
$778$	−24763.0	−1.14113
$779$	0	0
$780$	−395.000	−0.0181324
$781$	56120.0	2.57123
$782$	4389.62	0.200732
$783$	27135.0	1.23847
$784$	−5481.01	−0.249682
$785$	11677.0	0.530917
$786$	8297.03	0.376521
$787$	14959.0	0.677550	0.338775	−	0.940867i	$-0.389987\pi$
$787$	14959.0	0.677550	0.338775	+	0.940867i	$0.389987\pi$
$788$	−19531.7	−0.882978
$789$	24751.3	1.11682
$790$	−4530.07	−0.204016
$791$	−155.644	−0.00699630
$792$	5289.37	0.237310
$793$	−284.809	−0.0127539
$794$	1207.86	0.0539867
$795$	5030.08	0.224401
$796$	−9431.69	−0.419972
$797$	18464.2	0.820622	0.410311	−	0.911946i	$-0.365420\pi$
$797$	18464.2	0.820622	0.410311	+	0.911946i	$0.365420\pi$
$798$	0	0
$799$	−8081.53	−0.357827
$800$	−2874.31	−0.127028
$801$	−5345.96	−0.235818
$802$	−20680.5	−0.910543
$803$	−23592.8	−1.03683
$804$	−669.307	−0.0293590
$805$	148.823	0.00651592
$806$	−1483.55	−0.0648336
$807$	10121.7	0.441514
$808$	639.067	0.0278246
$809$	13632.5	0.592449	0.296225	−	0.955118i	$-0.404272\pi$
$809$	13632.5	0.592449	0.296225	+	0.955118i	$0.404272\pi$
$810$	−10808.2	−0.468842
$811$	−22906.1	−0.991791	−0.495896	−	0.868382i	$-0.665160\pi$
$811$	−22906.1	−0.991791	−0.495896	+	0.868382i	$0.665160\pi$
$812$	−819.081	−0.0353991
$813$	25428.5	1.09695
$814$	2113.75	0.0910158
$815$	−6735.26	−0.289480
$816$	5863.45	0.251546
$817$	0	0
$818$	322.840	0.0137993
$819$	−22.8860	−0.000976437 0
$820$	8163.34	0.347654
$821$	−42145.6	−1.79158	−0.895792	−	0.444474i	$-0.853391\pi$
$821$	−42145.6	−1.79158	−0.895792	+	0.444474i	$0.853391\pi$
$822$	25883.6	1.09829
$823$	−28338.2	−1.20025	−0.600126	−	0.799906i	$-0.704883\pi$
$823$	−28338.2	−1.20025	−0.600126	+	0.799906i	$0.704883\pi$
$824$	−14397.8	−0.608704
$825$	−28554.7	−1.20503
$826$	−602.520	−0.0253806
$827$	−13589.8	−0.571418	−0.285709	−	0.958316i	$-0.592229\pi$
$827$	−13589.8	−0.571418	−0.285709	+	0.958316i	$0.592229\pi$
$828$	2002.15	0.0840333
$829$	25202.9	1.05589	0.527946	−	0.849278i	$-0.322962\pi$
$829$	25202.9	1.05589	0.527946	+	0.849278i	$0.322962\pi$
$830$	15685.1	0.655947
$831$	30749.5	1.28362
$832$	−168.096	−0.00700442
$833$	−19803.7	−0.823720
$834$	23324.6	0.968423
$835$	−4687.47	−0.194271
$836$	0	0
$837$	−24734.6	−1.02145
$838$	14966.8	0.616969
$839$	3754.65	0.154499	0.0772497	−	0.997012i	$-0.475386\pi$
$839$	3754.65	0.154499	0.0772497	+	0.997012i	$0.475386\pi$
$840$	198.791	0.00816540
$841$	71604.3	2.93593
$842$	−12099.1	−0.495203
$843$	−39929.8	−1.63138
$844$	12861.0	0.524520
$845$	−12989.7	−0.528826
$846$	−3686.07	−0.149799
$847$	782.511	0.0317443
$848$	2140.60	0.0866844
$849$	36494.2	1.47524
$850$	−10385.3	−0.419076
$851$	800.104	0.0322294
$852$	28375.1	1.14098
$853$	23488.3	0.942818	0.471409	−	0.881915i	$-0.343746\pi$
$853$	23488.3	0.942818	0.471409	+	0.881915i	$0.343746\pi$
$854$	143.335	0.00574336
$855$	0	0
$856$	−554.044	−0.0221225
$857$	−3302.78	−0.131646	−0.0658231	−	0.997831i	$-0.520967\pi$
$857$	−3302.78	−0.131646	−0.0658231	+	0.997831i	$0.520967\pi$
$858$	−1669.94	−0.0664462
$859$	−8822.77	−0.350441	−0.175221	−	0.984529i	$-0.556064\pi$
$859$	−8822.77	−0.350441	−0.175221	+	0.984529i	$0.556064\pi$
$860$	6295.26	0.249612
$861$	1441.61	0.0570614
$862$	−21819.4	−0.862148
$863$	20731.7	0.817745	0.408873	−	0.912591i	$-0.365922\pi$
$863$	20731.7	0.817745	0.408873	+	0.912591i	$0.365922\pi$
$864$	−2802.59	−0.110354
$865$	−20663.9	−0.812248
$866$	15297.9	0.600282
$867$	−9958.37	−0.390085
$868$	746.623	0.0291959
$869$	−19151.7	−0.747616
$870$	−23297.6	−0.907887
$871$	69.3292	0.00269705
$872$	−5096.79	−0.197935
$873$	−18116.8	−0.702359
$874$	0	0
$875$	−842.091	−0.0325347
$876$	−11928.9	−0.460090
$877$	11032.5	0.424790	0.212395	−	0.977184i	$-0.431874\pi$
$877$	11032.5	0.424790	0.212395	+	0.977184i	$0.431874\pi$
$878$	22831.7	0.877602
$879$	−34384.7	−1.31942
$880$	4759.06	0.182304
$881$	−23834.2	−0.911457	−0.455728	−	0.890119i	$-0.650621\pi$
$881$	−23834.2	−0.911457	−0.455728	+	0.890119i	$0.650621\pi$
$882$	−9032.70	−0.344838
$883$	−45242.6	−1.72428	−0.862138	−	0.506674i	$-0.830875\pi$
$883$	−45242.6	−1.72428	−0.862138	+	0.506674i	$0.830875\pi$
$884$	−607.357	−0.0231082
$885$	−17137.8	−0.650940
$886$	−6305.31	−0.239087
$887$	3636.94	0.137674	0.0688369	−	0.997628i	$-0.478071\pi$
$887$	3636.94	0.137674	0.0688369	+	0.997628i	$0.478071\pi$
$888$	1068.74	0.0403881
$889$	−593.712	−0.0223987
$890$	−4809.97	−0.181158
$891$	−45693.8	−1.71807
$892$	−13858.6	−0.520202
$893$	0	0
$894$	−4225.10	−0.158063
$895$	12960.8	0.484056
$896$	84.5972	0.00315424
$897$	−632.112	−0.0235291
$898$	−10434.1	−0.387739
$899$	−87501.6	−3.24621
$900$	−4736.87	−0.175439
$901$	7734.30	0.285979
$902$	34512.1	1.27398
$903$	1111.71	0.0409695
$904$	−1883.98	−0.0693146
$905$	−6262.58	−0.230028
$906$	−38572.4	−1.41444
$907$	45706.7	1.67328	0.836641	−	0.547751i	$-0.184516\pi$
$907$	45706.7	1.67328	0.836641	+	0.547751i	$0.184516\pi$
$908$	−19326.4	−0.706354
$909$	1053.18	0.0384288
$910$	−20.5915	−0.000750110 0
$911$	38271.0	1.39185	0.695924	−	0.718115i	$-0.254995\pi$
$911$	38271.0	1.39185	0.695924	+	0.718115i	$0.254995\pi$
$912$	0	0
$913$	66311.6	2.40372
$914$	31737.4	1.14855
$915$	4076.96	0.147301
$916$	−18582.0	−0.670268
$917$	432.526	0.0155761
$918$	−10126.2	−0.364067
$919$	15748.1	0.565267	0.282634	−	0.959228i	$-0.408792\pi$
$919$	15748.1	0.565267	0.282634	+	0.959228i	$0.408792\pi$
$920$	1801.41	0.0645553
$921$	−35688.2	−1.27683
$922$	−8682.33	−0.310127
$923$	−2939.19	−0.104815
$924$	840.427	0.0299221
$925$	−1892.96	−0.0672865
$926$	−2788.45	−0.0989570
$927$	−23727.6	−0.840687
$928$	−9914.49	−0.350710
$929$	14334.7	0.506251	0.253125	−	0.967433i	$-0.418541\pi$
$929$	14334.7	0.506251	0.253125	+	0.967433i	$0.418541\pi$
$930$	21236.6	0.748792
$931$	0	0
$932$	−3314.04	−0.116475
$933$	19359.6	0.679320
$934$	12276.7	0.430092
$935$	17195.2	0.601437
$936$	−277.022	−0.00967387
$937$	18841.8	0.656922	0.328461	−	0.944517i	$-0.393470\pi$
$937$	18841.8	0.656922	0.328461	+	0.944517i	$0.393470\pi$
$938$	−34.8911	−0.00121454
$939$	−20924.9	−0.727220
$940$	−3316.50	−0.115077
$941$	−15020.7	−0.520362	−0.260181	−	0.965560i	$-0.583782\pi$
$941$	−15020.7	−0.520362	−0.260181	+	0.965560i	$0.583782\pi$
$942$	24960.5	0.863331
$943$	13063.6	0.451125
$944$	−7293.16	−0.251453
$945$	−343.312	−0.0118179
$946$	26614.4	0.914703
$947$	−22458.4	−0.770643	−0.385321	−	0.922782i	$-0.625909\pi$
$947$	−22458.4	−0.770643	−0.385321	+	0.922782i	$0.625909\pi$
$948$	−9683.39	−0.331753
$949$	1235.63	0.0422659
$950$	0	0
$951$	20096.5	0.685249
$952$	305.663	0.0104061
$953$	14962.3	0.508579	0.254289	−	0.967128i	$-0.418158\pi$
$953$	14962.3	0.508579	0.254289	+	0.967128i	$0.418158\pi$
$954$	3527.70	0.119721
$955$	15767.8	0.534278
$956$	10940.9	0.370139
$957$	−98495.0	−3.32695
$958$	14265.9	0.481117
$959$	1349.32	0.0454346
$960$	2406.25	0.0808972
$961$	49970.0	1.67735
$962$	−110.704	−0.00371023
$963$	−913.064	−0.0305536
$964$	−16339.3	−0.545906
$965$	27167.2	0.906264
$966$	318.121	0.0105956
$967$	−41031.3	−1.36451	−0.682253	−	0.731116i	$-0.739000\pi$
$967$	−41031.3	−1.36451	−0.682253	+	0.731116i	$0.739000\pi$
$968$	9471.84	0.314500
$969$	0	0
$970$	−16300.4	−0.539560
$971$	−4024.22	−0.133000	−0.0665002	−	0.997786i	$-0.521183\pi$
$971$	−4024.22	−0.133000	−0.0665002	+	0.997786i	$0.521183\pi$
$972$	−13644.7	−0.450261
$973$	1215.92	0.0400622
$974$	28793.2	0.947222
$975$	1495.51	0.0491226
$976$	1734.99	0.0569012
$977$	42051.2	1.37701	0.688505	−	0.725232i	$-0.258267\pi$
$977$	42051.2	1.37701	0.688505	+	0.725232i	$0.258267\pi$
$978$	−14397.2	−0.470727
$979$	−20335.1	−0.663853
$980$	−8127.08	−0.264908
$981$	−8399.51	−0.273370
$982$	15311.6	0.497570
$983$	−43004.4	−1.39535	−0.697674	−	0.716415i	$-0.745782\pi$
$983$	−43004.4	−1.39535	−0.697674	+	0.716415i	$0.745782\pi$
$984$	17449.8	0.565325
$985$	−28961.0	−0.936825
$986$	−35822.6	−1.15702
$987$	−585.679	−0.0188879
$988$	0	0
$989$	10074.2	0.323903
$990$	7842.92	0.251782
$991$	−6614.91	−0.212038	−0.106019	−	0.994364i	$-0.533810\pi$
$991$	−6614.91	−0.212038	−0.106019	+	0.994364i	$0.533810\pi$
$992$	9037.44	0.289253
$993$	−8968.20	−0.286604
$994$	1479.20	0.0472005
$995$	−13985.0	−0.445583
$996$	33528.1	1.06665
$997$	−46602.8	−1.48037	−0.740184	−	0.672405i	$-0.765261\pi$
$997$	−46602.8	−1.48037	−0.740184	+	0.672405i	$0.765261\pi$
$998$	37276.2	1.18232
$999$	−1845.72	−0.0584544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.k.1.3		3
19.8	odd	6		38.4.c.c.7.3	✓	6
19.12	odd	6		38.4.c.c.11.3	yes	6
19.18	odd	2		722.4.a.j.1.1		3
57.8	even	6		342.4.g.f.235.2		6
57.50	even	6		342.4.g.f.163.2		6
76.27	even	6		304.4.i.e.273.1		6
76.31	even	6		304.4.i.e.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.3	✓	6	19.8	odd	6
38.4.c.c.11.3	yes	6	19.12	odd	6
304.4.i.e.49.1		6	76.31	even	6
304.4.i.e.273.1		6	76.27	even	6
342.4.g.f.163.2		6	57.50	even	6
342.4.g.f.235.2		6	57.8	even	6
722.4.a.j.1.1		3	19.18	odd	2
722.4.a.k.1.3		3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +6.33908 q^{3} +4.00000 q^{4} +5.93108 q^{5} +12.6782 q^{6} +0.660916 q^{7} +8.00000 q^{8} +13.1840 q^{9} +11.8622 q^{10} +50.1496 q^{11} +25.3563 q^{12} -2.62650 q^{13} +1.32183 q^{14} +37.5976 q^{15} +16.0000 q^{16} +57.8105 q^{17} +26.3680 q^{18} +23.7243 q^{20} +4.18960 q^{21} +100.299 q^{22} +37.9656 q^{23} +50.7127 q^{24} -89.8223 q^{25} -5.25300 q^{26} -87.5809 q^{27} +2.64366 q^{28} -309.828 q^{29} +75.1952 q^{30} +282.420 q^{31} +32.0000 q^{32} +317.902 q^{33} +115.621 q^{34} +3.91994 q^{35} +52.7360 q^{36} +21.0744 q^{37} -16.6496 q^{39} +47.4486 q^{40} +344.092 q^{41} +8.37920 q^{42} +265.350 q^{43} +200.598 q^{44} +78.1953 q^{45} +75.9312 q^{46} -139.793 q^{47} +101.425 q^{48} -342.563 q^{49} -179.645 q^{50} +366.466 q^{51} -10.5060 q^{52} +133.787 q^{53} -175.162 q^{54} +297.441 q^{55} +5.28733 q^{56} -619.656 q^{58} -455.822 q^{59} +150.390 q^{60} +108.437 q^{61} +564.840 q^{62} +8.71351 q^{63} +64.0000 q^{64} -15.5780 q^{65} +635.805 q^{66} -26.3960 q^{67} +231.242 q^{68} +240.667 q^{69} +7.83989 q^{70} +1119.05 q^{71} +105.472 q^{72} -470.449 q^{73} +42.1489 q^{74} -569.391 q^{75} +33.1446 q^{77} -33.2992 q^{78} -381.892 q^{79} +94.8973 q^{80} -911.150 q^{81} +688.184 q^{82} +1322.28 q^{83} +16.7584 q^{84} +342.879 q^{85} +530.701 q^{86} -1964.03 q^{87} +401.197 q^{88} -405.489 q^{89} +156.391 q^{90} -1.73590 q^{91} +151.862 q^{92} +1790.28 q^{93} -279.587 q^{94} +202.851 q^{96} -1374.15 q^{97} -685.126 q^{98} +661.171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20}+ \cdots + 3184 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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