LMFDB - Embedded newform 1849.4.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 62x^{8} + 1289x^{6} - 11252x^{4} + 39376x^{2} - 35688 $ x^10 - 62x^8 + 1289x^6 - 11252x^4 + 39376x^2 - 35688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.53388$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53388 q^{2} +6.96727 q^{3} -1.57947 q^{4} -11.2250 q^{5} -17.6542 q^{6} -27.5005 q^{7} +24.2732 q^{8} +21.5429 q^{9} +O(q^{10})$	\(q-2.53388 q^{2} +6.96727 q^{3} -1.57947 q^{4} -11.2250 q^{5} -17.6542 q^{6} -27.5005 q^{7} +24.2732 q^{8} +21.5429 q^{9} +28.4428 q^{10} +55.7910 q^{11} -11.0046 q^{12} +72.2909 q^{13} +69.6828 q^{14} -78.2076 q^{15} -48.8696 q^{16} +74.4570 q^{17} -54.5870 q^{18} -99.5863 q^{19} +17.7295 q^{20} -191.603 q^{21} -141.367 q^{22} -33.8775 q^{23} +169.118 q^{24} +1.00051 q^{25} -183.176 q^{26} -38.0213 q^{27} +43.4360 q^{28} -148.450 q^{29} +198.168 q^{30} +219.111 q^{31} -70.3560 q^{32} +388.711 q^{33} -188.665 q^{34} +308.692 q^{35} -34.0262 q^{36} +155.992 q^{37} +252.339 q^{38} +503.670 q^{39} -272.466 q^{40} -125.466 q^{41} +485.499 q^{42} -88.1199 q^{44} -241.819 q^{45} +85.8414 q^{46} -235.906 q^{47} -340.488 q^{48} +413.275 q^{49} -2.53516 q^{50} +518.762 q^{51} -114.181 q^{52} +361.509 q^{53} +96.3414 q^{54} -626.253 q^{55} -667.524 q^{56} -693.845 q^{57} +376.154 q^{58} -267.820 q^{59} +123.526 q^{60} -14.9551 q^{61} -555.200 q^{62} -592.438 q^{63} +569.230 q^{64} -811.465 q^{65} -984.945 q^{66} -635.529 q^{67} -117.602 q^{68} -236.034 q^{69} -782.189 q^{70} +719.260 q^{71} +522.914 q^{72} +238.605 q^{73} -395.264 q^{74} +6.97080 q^{75} +157.293 q^{76} -1534.28 q^{77} -1276.24 q^{78} -253.105 q^{79} +548.561 q^{80} -846.562 q^{81} +317.915 q^{82} +263.739 q^{83} +302.630 q^{84} -835.780 q^{85} -1034.29 q^{87} +1354.22 q^{88} +219.608 q^{89} +612.739 q^{90} -1988.03 q^{91} +53.5083 q^{92} +1526.61 q^{93} +597.757 q^{94} +1117.86 q^{95} -490.190 q^{96} +26.7108 q^{97} -1047.19 q^{98} +1201.90 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.53388	−0.895861	−0.447930	−	0.894068i	$-0.647839\pi$
$2$	−2.53388	−0.895861	−0.447930	+	0.894068i	$0.647839\pi$
$3$	6.96727	1.34085	0.670426	−	0.741976i	$-0.266111\pi$
$3$	6.96727	1.34085	0.670426	+	0.741976i	$0.266111\pi$
$4$	−1.57947	−0.197433
$5$	−11.2250	−1.00399	−0.501997	−	0.864869i	$-0.667401\pi$
$5$	−11.2250	−1.00399	−0.501997	+	0.864869i	$0.667401\pi$
$6$	−17.6542	−1.20122
$7$	−27.5005	−1.48488	−0.742442	−	0.669910i	$-0.766333\pi$
$7$	−27.5005	−1.48488	−0.742442	+	0.669910i	$0.766333\pi$
$8$	24.2732	1.07273
$9$	21.5429	0.797884
$10$	28.4428	0.899439
$11$	55.7910	1.52924	0.764618	−	0.644483i	$-0.222927\pi$
$11$	55.7910	1.52924	0.764618	+	0.644483i	$0.222927\pi$
$12$	−11.0046	−0.264729
$13$	72.2909	1.54230	0.771150	−	0.636654i	$-0.219682\pi$
$13$	72.2909	1.54230	0.771150	+	0.636654i	$0.219682\pi$
$14$	69.6828	1.33025
$15$	−78.2076	−1.34621
$16$	−48.8696	−0.763587
$17$	74.4570	1.06226	0.531132	−	0.847289i	$-0.321767\pi$
$17$	74.4570	1.06226	0.531132	+	0.847289i	$0.321767\pi$
$18$	−54.5870	−0.714793
$19$	−99.5863	−1.20246	−0.601228	−	0.799077i	$-0.705322\pi$
$19$	−99.5863	−1.20246	−0.601228	+	0.799077i	$0.705322\pi$
$20$	17.7295	0.198222
$21$	−191.603	−1.99101
$22$	−141.367	−1.36998
$23$	−33.8775	−0.307128	−0.153564	−	0.988139i	$-0.549075\pi$
$23$	−33.8775	−0.307128	−0.153564	+	0.988139i	$0.549075\pi$
$24$	169.118	1.43838
$25$	1.00051	0.00800405
$26$	−183.176	−1.38169
$27$	−38.0213	−0.271008
$28$	43.4360	0.293166
$29$	−148.450	−0.950568	−0.475284	−	0.879832i	$-0.657655\pi$
$29$	−148.450	−0.950568	−0.475284	+	0.879832i	$0.657655\pi$
$30$	198.168	1.20601
$31$	219.111	1.26947	0.634734	−	0.772731i	$-0.281110\pi$
$31$	219.111	1.26947	0.634734	+	0.772731i	$0.281110\pi$
$32$	−70.3560	−0.388666
$33$	388.711	2.05048
$34$	−188.665	−0.951641
$35$	308.692	1.49082
$36$	−34.0262	−0.157529
$37$	155.992	0.693105	0.346553	−	0.938031i	$-0.387352\pi$
$37$	155.992	0.693105	0.346553	+	0.938031i	$0.387352\pi$
$38$	252.339	1.07723
$39$	503.670	2.06799
$40$	−272.466	−1.07702
$41$	−125.466	−0.477915	−0.238957	−	0.971030i	$-0.576806\pi$
$41$	−125.466	−0.477915	−0.238957	+	0.971030i	$0.576806\pi$
$42$	485.499	1.78367
$43$	0	0
$43$	0	0
$44$	−88.1199	−0.301922
$45$	−241.819	−0.801071
$46$	85.8414	0.275144
$47$	−235.906	−0.732137	−0.366069	−	0.930588i	$-0.619296\pi$
$47$	−235.906	−0.732137	−0.366069	+	0.930588i	$0.619296\pi$
$48$	−340.488	−1.02386
$49$	413.275	1.20488
$50$	−2.53516	−0.00717052
$51$	518.762	1.42434
$52$	−114.181	−0.304501
$53$	361.509	0.936925	0.468462	−	0.883483i	$-0.344808\pi$
$53$	361.509	0.936925	0.468462	+	0.883483i	$0.344808\pi$
$54$	96.3414	0.242785
$55$	−626.253	−1.53534
$56$	−667.524	−1.59289
$57$	−693.845	−1.61232
$58$	376.154	0.851577
$59$	−267.820	−0.590969	−0.295485	−	0.955347i	$-0.595481\pi$
$59$	−267.820	−0.590969	−0.295485	+	0.955347i	$0.595481\pi$
$60$	123.526	0.265786
$61$	−14.9551	−0.0313903	−0.0156951	−	0.999877i	$-0.504996\pi$
$61$	−14.9551	−0.0313903	−0.0156951	+	0.999877i	$0.504996\pi$
$62$	−555.200	−1.13727
$63$	−592.438	−1.18477
$64$	569.230	1.11178
$65$	−811.465	−1.54846
$66$	−984.945	−1.83695
$67$	−635.529	−1.15884	−0.579420	−	0.815029i	$-0.696721\pi$
$67$	−635.529	−1.15884	−0.579420	+	0.815029i	$0.696721\pi$
$68$	−117.602	−0.209726
$69$	−236.034	−0.411813
$70$	−782.189	−1.33556
$71$	719.260	1.20226	0.601130	−	0.799151i	$-0.294717\pi$
$71$	719.260	1.20226	0.601130	+	0.799151i	$0.294717\pi$
$72$	522.914	0.855917
$73$	238.605	0.382555	0.191278	−	0.981536i	$-0.438737\pi$
$73$	238.605	0.382555	0.191278	+	0.981536i	$0.438737\pi$
$74$	−395.264	−0.620926
$75$	6.97080	0.0107322
$76$	157.293	0.237405
$77$	−1534.28	−2.27074
$78$	−1276.24	−1.85264
$79$	−253.105	−0.360462	−0.180231	−	0.983624i	$-0.557685\pi$
$79$	−253.105	−0.360462	−0.180231	+	0.983624i	$0.557685\pi$
$80$	548.561	0.766637
$81$	−846.562	−1.16127
$82$	317.915	0.428145
$83$	263.739	0.348785	0.174392	−	0.984676i	$-0.444204\pi$
$83$	263.739	0.348785	0.174392	+	0.984676i	$0.444204\pi$
$84$	302.630	0.393092
$85$	−835.780	−1.06651
$86$	0	0
$87$	−1034.29	−1.27457
$88$	1354.22	1.64046
$89$	219.608	0.261555	0.130777	−	0.991412i	$-0.458253\pi$
$89$	219.608	0.261555	0.130777	+	0.991412i	$0.458253\pi$
$90$	612.739	0.717648
$91$	−1988.03	−2.29014
$92$	53.5083	0.0606372
$93$	1526.61	1.70217
$94$	597.757	0.655893
$95$	1117.86	1.20726
$96$	−490.190	−0.521143
$97$	26.7108	0.0279595	0.0139797	−	0.999902i	$-0.495550\pi$
$97$	26.7108	0.0279595	0.0139797	+	0.999902i	$0.495550\pi$
$98$	−1047.19	−1.07941
$99$	1201.90	1.22015
$100$	−1.58027	−0.00158027
$101$	−1092.82	−1.07663	−0.538315	−	0.842744i	$-0.680939\pi$
$101$	−1092.82	−1.07663	−0.538315	+	0.842744i	$0.680939\pi$
$102$	−1314.48	−1.27601
$103$	−1805.75	−1.72743	−0.863715	−	0.503980i	$-0.831869\pi$
$103$	−1805.75	−1.72743	−0.863715	+	0.503980i	$0.831869\pi$
$104$	1754.73	1.65448
$105$	2150.74	1.99896
$106$	−916.018	−0.839354
$107$	319.584	0.288742	0.144371	−	0.989524i	$-0.453884\pi$
$107$	319.584	0.288742	0.144371	+	0.989524i	$0.453884\pi$
$108$	60.0534	0.0535059
$109$	1918.77	1.68610	0.843050	−	0.537836i	$-0.180758\pi$
$109$	1918.77	1.68610	0.843050	+	0.537836i	$0.180758\pi$
$110$	1586.85	1.37546
$111$	1086.84	0.929351
$112$	1343.94	1.13384
$113$	−196.909	−0.163926	−0.0819630	−	0.996635i	$-0.526119\pi$
$113$	−196.909	−0.163926	−0.0819630	+	0.996635i	$0.526119\pi$
$114$	1758.12	1.44441
$115$	380.274	0.308355
$116$	234.472	0.187674
$117$	1557.35	1.23058
$118$	678.623	0.529426
$119$	−2047.60	−1.57734
$120$	−1898.35	−1.44412
$121$	1781.63	1.33857
$122$	37.8944	0.0281213
$123$	−874.156	−0.640813
$124$	−346.078	−0.250635
$125$	1391.89	0.995958
$126$	1501.17	1.06139
$127$	1747.85	1.22124	0.610618	−	0.791925i	$-0.290921\pi$
$127$	1747.85	1.22124	0.610618	+	0.791925i	$0.290921\pi$
$128$	−879.511	−0.607332
$129$	0	0
$130$	2056.15	1.38720
$131$	−1357.17	−0.905164	−0.452582	−	0.891723i	$-0.649497\pi$
$131$	−1357.17	−0.905164	−0.452582	+	0.891723i	$0.649497\pi$
$132$	−613.955	−0.404833
$133$	2738.67	1.78551
$134$	1610.35	1.03816
$135$	426.789	0.272090
$136$	1807.31	1.13953
$137$	1874.35	1.16888	0.584440	−	0.811437i	$-0.301314\pi$
$137$	1874.35	1.16888	0.584440	+	0.811437i	$0.301314\pi$
$138$	598.080	0.368927
$139$	877.905	0.535704	0.267852	−	0.963460i	$-0.413686\pi$
$139$	877.905	0.535704	0.267852	+	0.963460i	$0.413686\pi$
$140$	−487.569	−0.294336
$141$	−1643.62	−0.981687
$142$	−1822.52	−1.07706
$143$	4033.18	2.35854
$144$	−1052.79	−0.609254
$145$	1666.35	0.954365
$146$	−604.595	−0.342716
$147$	2879.40	1.61557
$148$	−246.384	−0.136842
$149$	−3019.95	−1.66043	−0.830214	−	0.557444i	$-0.811782\pi$
$149$	−3019.95	−1.66043	−0.830214	+	0.557444i	$0.811782\pi$
$150$	−17.6632	−0.00961460
$151$	2466.37	1.32921	0.664604	−	0.747196i	$-0.268600\pi$
$151$	2466.37	1.32921	0.664604	+	0.747196i	$0.268600\pi$
$152$	−2417.28	−1.28992
$153$	1604.02	0.847563
$154$	3887.67	2.03427
$155$	−2459.52	−1.27454
$156$	−795.530	−0.408291
$157$	593.199	0.301544	0.150772	−	0.988569i	$-0.451824\pi$
$157$	593.199	0.301544	0.150772	+	0.988569i	$0.451824\pi$
$158$	641.337	0.322924
$159$	2518.73	1.25628
$160$	789.746	0.390218
$161$	931.646	0.456050
$162$	2145.09	1.04033
$163$	−442.582	−0.212673	−0.106337	−	0.994330i	$-0.533912\pi$
$163$	−442.582	−0.212673	−0.106337	+	0.994330i	$0.533912\pi$
$164$	198.169	0.0943562
$165$	−4363.28	−2.05867
$166$	−668.283	−0.312463
$167$	1349.88	0.625492	0.312746	−	0.949837i	$-0.398751\pi$
$167$	1349.88	0.625492	0.312746	+	0.949837i	$0.398751\pi$
$168$	−4650.82	−2.13582
$169$	3028.97	1.37869
$170$	2117.76	0.955442
$171$	−2145.37	−0.959420
$172$	0	0
$173$	−228.274	−0.100320	−0.0501599	−	0.998741i	$-0.515973\pi$
$173$	−228.274	−0.100320	−0.0501599	+	0.998741i	$0.515973\pi$
$174$	2620.77	1.14184
$175$	−27.5144	−0.0118851
$176$	−2726.48	−1.16771
$177$	−1865.97	−0.792402
$178$	−556.459	−0.234317
$179$	−2428.07	−1.01387	−0.506934	−	0.861985i	$-0.669221\pi$
$179$	−2428.07	−1.01387	−0.506934	+	0.861985i	$0.669221\pi$
$180$	381.944	0.158158
$181$	643.510	0.264264	0.132132	−	0.991232i	$-0.457818\pi$
$181$	643.510	0.264264	0.132132	+	0.991232i	$0.457818\pi$
$182$	5037.43	2.05164
$183$	−104.196	−0.0420897
$184$	−822.314	−0.329466
$185$	−1751.01	−0.695873
$186$	−3868.23	−1.52491
$187$	4154.03	1.62445
$188$	372.606	0.144548
$189$	1045.60	0.402415
$190$	−2832.51	−1.08154
$191$	1578.92	0.598150	0.299075	−	0.954230i	$-0.403322\pi$
$191$	1578.92	0.598150	0.299075	+	0.954230i	$0.403322\pi$
$192$	3965.98	1.49073
$193$	4299.60	1.60358	0.801792	−	0.597603i	$-0.203880\pi$
$193$	4299.60	1.60358	0.801792	+	0.597603i	$0.203880\pi$
$194$	−67.6819	−0.0250478
$195$	−5653.70	−2.07625
$196$	−652.753	−0.237884
$197$	−1860.60	−0.672906	−0.336453	−	0.941700i	$-0.609227\pi$
$197$	−1860.60	−0.672906	−0.336453	+	0.941700i	$0.609227\pi$
$198$	−3045.46	−1.09309
$199$	5206.08	1.85452	0.927259	−	0.374420i	$-0.122158\pi$
$199$	5206.08	1.85452	0.927259	+	0.374420i	$0.122158\pi$
$200$	24.2855	0.00858622
$201$	−4427.91	−1.55383
$202$	2769.07	0.964511
$203$	4082.44	1.41148
$204$	−819.367	−0.281212
$205$	1408.36	0.479823
$206$	4575.54	1.54754
$207$	−729.818	−0.245052
$208$	−3532.83	−1.17768
$209$	−5556.01	−1.83884
$210$	−5449.72	−1.79079
$211$	3395.46	1.10783	0.553917	−	0.832572i	$-0.313132\pi$
$211$	3395.46	1.10783	0.553917	+	0.832572i	$0.313132\pi$
$212$	−570.990	−0.184980
$213$	5011.28	1.61205
$214$	−809.788	−0.258673
$215$	0	0
$216$	−922.899	−0.290719
$217$	−6025.65	−1.88501
$218$	−4861.93	−1.51051
$219$	1662.42	0.512950
$220$	989.145	0.303128
$221$	5382.57	1.63833
$222$	−2753.91	−0.832570
$223$	4443.72	1.33441	0.667205	−	0.744875i	$-0.267491\pi$
$223$	4443.72	1.33441	0.667205	+	0.744875i	$0.267491\pi$
$224$	1934.82	0.577124
$225$	21.5538	0.00638630
$226$	498.943	0.146855
$227$	2972.54	0.869139	0.434570	−	0.900638i	$-0.356900\pi$
$227$	2972.54	0.869139	0.434570	+	0.900638i	$0.356900\pi$
$228$	1095.90	0.318325
$229$	−4526.22	−1.30612	−0.653059	−	0.757307i	$-0.726515\pi$
$229$	−4526.22	−1.30612	−0.653059	+	0.757307i	$0.726515\pi$
$230$	−963.569	−0.276243
$231$	−10689.7	−3.04473
$232$	−3603.35	−1.01971
$233$	354.229	0.0995979	0.0497989	−	0.998759i	$-0.484142\pi$
$233$	354.229	0.0995979	0.0497989	+	0.998759i	$0.484142\pi$
$234$	−3946.14	−1.10242
$235$	2648.04	0.735061
$236$	423.012	0.116677
$237$	−1763.45	−0.483327
$238$	5188.37	1.41308
$239$	4811.20	1.30214	0.651069	−	0.759019i	$-0.274321\pi$
$239$	4811.20	1.30214	0.651069	+	0.759019i	$0.274321\pi$
$240$	3821.97	1.02795
$241$	−1230.75	−0.328960	−0.164480	−	0.986380i	$-0.552595\pi$
$241$	−1230.75	−0.328960	−0.164480	+	0.986380i	$0.552595\pi$
$242$	−4514.43	−1.19917
$243$	−4871.65	−1.28608
$244$	23.6211	0.00619748
$245$	−4639.01	−1.20970
$246$	2215.00	0.574079
$247$	−7199.18	−1.85455
$248$	5318.52	1.36180
$249$	1837.54	0.467669
$250$	−3526.89	−0.892240
$251$	4009.31	1.00823	0.504115	−	0.863637i	$-0.331819\pi$
$251$	4009.31	1.00823	0.504115	+	0.863637i	$0.331819\pi$
$252$	935.736	0.233912
$253$	−1890.06	−0.469671
$254$	−4428.85	−1.09406
$255$	−5823.11	−1.43003
$256$	−2325.27	−0.567692
$257$	3561.46	0.864427	0.432213	−	0.901771i	$-0.357733\pi$
$257$	3561.46	0.864427	0.432213	+	0.901771i	$0.357733\pi$
$258$	0	0
$259$	−4289.84	−1.02918
$260$	1281.68	0.305717
$261$	−3198.04	−0.758443
$262$	3438.90	0.810901
$263$	4242.89	0.994783	0.497391	−	0.867526i	$-0.334291\pi$
$263$	4242.89	0.994783	0.497391	+	0.867526i	$0.334291\pi$
$264$	9435.25	2.19962
$265$	−4057.93	−0.940667
$266$	−6939.45	−1.59957
$267$	1530.07	0.350706
$268$	1003.80	0.228793
$269$	495.125	0.112224	0.0561120	−	0.998424i	$-0.482130\pi$
$269$	495.125	0.112224	0.0561120	+	0.998424i	$0.482130\pi$
$270$	−1081.43	−0.243755
$271$	933.897	0.209337	0.104668	−	0.994507i	$-0.466622\pi$
$271$	933.897	0.209337	0.104668	+	0.994507i	$0.466622\pi$
$272$	−3638.68	−0.811131
$273$	−13851.2	−3.07073
$274$	−4749.37	−1.04715
$275$	55.8192	0.0122401
$276$	372.807	0.0813056
$277$	3263.49	0.707884	0.353942	−	0.935267i	$-0.384841\pi$
$277$	3263.49	0.707884	0.353942	+	0.935267i	$0.384841\pi$
$278$	−2224.50	−0.479917
$279$	4720.28	1.01289
$280$	7492.95	1.59925
$281$	−9337.44	−1.98230	−0.991148	−	0.132764i	$-0.957615\pi$
$281$	−9337.44	−1.98230	−0.991148	+	0.132764i	$0.957615\pi$
$282$	4164.74	0.879455
$283$	5422.52	1.13899	0.569497	−	0.821993i	$-0.307138\pi$
$283$	5422.52	1.13899	0.569497	+	0.821993i	$0.307138\pi$
$284$	−1136.05	−0.237366
$285$	7788.40	1.61876
$286$	−10219.6	−2.11292
$287$	3450.37	0.709648
$288$	−1515.67	−0.310110
$289$	630.852	0.128405
$290$	−4222.33	−0.854978
$291$	186.101	0.0374895
$292$	−376.868	−0.0755291
$293$	2457.76	0.490048	0.245024	−	0.969517i	$-0.421204\pi$
$293$	2457.76	0.490048	0.245024	+	0.969517i	$0.421204\pi$
$294$	−7296.04	−1.44733
$295$	3006.28	0.593330
$296$	3786.42	0.743517
$297$	−2121.25	−0.414435
$298$	7652.18	1.48751
$299$	−2449.03	−0.473683
$300$	−11.0101	−0.00211890
$301$	0	0
$302$	−6249.48	−1.19079
$303$	−7613.97	−1.44360
$304$	4866.74	0.918180
$305$	167.871	0.0315156
$306$	−4064.39	−0.759299
$307$	2014.25	0.374460	0.187230	−	0.982316i	$-0.440049\pi$
$307$	2014.25	0.374460	0.187230	+	0.982316i	$0.440049\pi$
$308$	2423.34	0.448320
$309$	−12581.1	−2.31623
$310$	6232.12	1.14181
$311$	8681.57	1.58291	0.791457	−	0.611224i	$-0.209323\pi$
$311$	8681.57	1.58291	0.791457	+	0.611224i	$0.209323\pi$
$312$	12225.7	2.21841
$313$	10875.8	1.96401	0.982005	−	0.188855i	$-0.0604775\pi$
$313$	10875.8	1.96401	0.982005	+	0.188855i	$0.0604775\pi$
$314$	−1503.09	−0.270142
$315$	6650.12	1.18950
$316$	399.770	0.0711672
$317$	1108.39	0.196384	0.0981919	−	0.995168i	$-0.468694\pi$
$317$	1108.39	0.196384	0.0981919	+	0.995168i	$0.468694\pi$
$318$	−6382.15	−1.12545
$319$	−8282.17	−1.45364
$320$	−6389.60	−1.11622
$321$	2226.63	0.387160
$322$	−2360.68	−0.408557
$323$	−7414.90	−1.27733
$324$	1337.12	0.229272
$325$	72.3275	0.0123446
$326$	1121.45	0.190526
$327$	13368.6	2.26081
$328$	−3045.46	−0.512675
$329$	6487.52	1.08714
$330$	11056.0	1.84428
$331$	−8433.77	−1.40049	−0.700245	−	0.713903i	$-0.746926\pi$
$331$	−8433.77	−1.40049	−0.700245	+	0.713903i	$0.746926\pi$
$332$	−416.567	−0.0688617
$333$	3360.51	0.553017
$334$	−3420.44	−0.560354
$335$	7133.81	1.16347
$336$	9363.56	1.52031
$337$	−3079.96	−0.497853	−0.248926	−	0.968522i	$-0.580078\pi$
$337$	−3079.96	−0.497853	−0.248926	+	0.968522i	$0.580078\pi$
$338$	−7675.05	−1.23511
$339$	−1371.92	−0.219800
$340$	1320.09	0.210564
$341$	12224.4	1.94132
$342$	5436.12	0.859507
$343$	−1932.59	−0.304228
$344$	0	0
$345$	2649.48	0.413458
$346$	578.418	0.0898727
$347$	−4167.29	−0.644702	−0.322351	−	0.946620i	$-0.604473\pi$
$347$	−4167.29	−0.644702	−0.322351	+	0.946620i	$0.604473\pi$
$348$	1633.63	0.251643
$349$	−4059.98	−0.622709	−0.311355	−	0.950294i	$-0.600783\pi$
$349$	−4059.98	−0.622709	−0.311355	+	0.950294i	$0.600783\pi$
$350$	69.7181	0.0106474
$351$	−2748.60	−0.417975
$352$	−3925.23	−0.594362
$353$	4048.24	0.610386	0.305193	−	0.952291i	$-0.401279\pi$
$353$	4048.24	0.610386	0.305193	+	0.952291i	$0.401279\pi$
$354$	4728.15	0.709882
$355$	−8073.69	−1.20706
$356$	−346.863	−0.0516396
$357$	−14266.2	−2.11498
$358$	6152.43	0.908285
$359$	4447.81	0.653890	0.326945	−	0.945043i	$-0.393981\pi$
$359$	4447.81	0.653890	0.326945	+	0.945043i	$0.393981\pi$
$360$	−5869.71	−0.859335
$361$	3058.43	0.445901
$362$	−1630.57	−0.236743
$363$	12413.1	1.79482
$364$	3140.03	0.452149
$365$	−2678.33	−0.384083
$366$	264.021	0.0377065
$367$	−11899.3	−1.69247	−0.846235	−	0.532811i	$-0.821136\pi$
$367$	−11899.3	−1.69247	−0.846235	+	0.532811i	$0.821136\pi$
$368$	1655.58	0.234519
$369$	−2702.90	−0.381320
$370$	4436.84	0.623406
$371$	−9941.65	−1.39123
$372$	−2411.22	−0.336064
$373$	−2158.10	−0.299577	−0.149789	−	0.988718i	$-0.547859\pi$
$373$	−2158.10	−0.299577	−0.149789	+	0.988718i	$0.547859\pi$
$374$	−10525.8	−1.45528
$375$	9697.70	1.33543
$376$	−5726.19	−0.785388
$377$	−10731.6	−1.46606
$378$	−2649.43	−0.360508
$379$	2688.13	0.364327	0.182163	−	0.983268i	$-0.441690\pi$
$379$	2688.13	0.364327	0.182163	+	0.983268i	$0.441690\pi$
$380$	−1765.61	−0.238353
$381$	12177.8	1.63750
$382$	−4000.79	−0.535859
$383$	3873.25	0.516746	0.258373	−	0.966045i	$-0.416814\pi$
$383$	3873.25	0.516746	0.258373	+	0.966045i	$0.416814\pi$
$384$	−6127.79	−0.814343
$385$	17222.2	2.27981
$386$	−10894.6	−1.43659
$387$	0	0
$388$	−42.1888	−0.00552013
$389$	8448.18	1.10113	0.550565	−	0.834792i	$-0.314412\pi$
$389$	8448.18	1.10113	0.550565	+	0.834792i	$0.314412\pi$
$390$	14325.8	1.86004
$391$	−2522.42	−0.326251
$392$	10031.5	1.29252
$393$	−9455.77	−1.21369
$394$	4714.54	0.602830
$395$	2841.10	0.361902
$396$	−1898.35	−0.240899
$397$	3942.16	0.498366	0.249183	−	0.968456i	$-0.419838\pi$
$397$	3942.16	0.498366	0.249183	+	0.968456i	$0.419838\pi$
$398$	−13191.6	−1.66139
$399$	19081.0	2.39410
$400$	−48.8943	−0.00611179
$401$	−12231.4	−1.52321	−0.761605	−	0.648042i	$-0.775588\pi$
$401$	−12231.4	−1.52321	−0.761605	+	0.648042i	$0.775588\pi$
$402$	11219.8	1.39202
$403$	15839.7	1.95790
$404$	1726.07	0.212562
$405$	9502.66	1.16590
$406$	−10344.4	−1.26449
$407$	8702.93	1.05992
$408$	12592.0	1.52794
$409$	6260.56	0.756883	0.378441	−	0.925625i	$-0.376460\pi$
$409$	6260.56	0.756883	0.378441	+	0.925625i	$0.376460\pi$
$410$	−3568.60	−0.429855
$411$	13059.1	1.56729
$412$	2852.11	0.341052
$413$	7365.17	0.877521
$414$	1849.27	0.219533
$415$	−2960.47	−0.350178
$416$	−5086.10	−0.599439
$417$	6116.60	0.718300
$418$	14078.3	1.64735
$419$	8949.73	1.04349	0.521746	−	0.853101i	$-0.325281\pi$
$419$	8949.73	1.04349	0.521746	+	0.853101i	$0.325281\pi$
$420$	−3397.03	−0.394662
$421$	−10707.1	−1.23951	−0.619754	−	0.784796i	$-0.712768\pi$
$421$	−10707.1	−1.23951	−0.619754	+	0.784796i	$0.712768\pi$
$422$	−8603.67	−0.992465
$423$	−5082.09	−0.584160
$424$	8774.97	1.00507
$425$	74.4948	0.00850242
$426$	−12698.0	−1.44417
$427$	411.273	0.0466109
$428$	−504.772	−0.0570072
$429$	28100.2	3.16245
$430$	0	0
$431$	15681.5	1.75256	0.876280	−	0.481802i	$-0.160018\pi$
$431$	15681.5	1.75256	0.876280	+	0.481802i	$0.160018\pi$
$432$	1858.09	0.206938
$433$	5532.63	0.614045	0.307022	−	0.951702i	$-0.400667\pi$
$433$	5532.63	0.614045	0.307022	+	0.951702i	$0.400667\pi$
$434$	15268.3	1.68871
$435$	11609.9	1.27966
$436$	−3030.63	−0.332892
$437$	3373.73	0.369308
$438$	−4212.37	−0.459532
$439$	−2670.49	−0.290332	−0.145166	−	0.989407i	$-0.546372\pi$
$439$	−2670.49	−0.290332	−0.145166	+	0.989407i	$0.546372\pi$
$440$	−15201.2	−1.64702
$441$	8903.12	0.961357
$442$	−13638.8	−1.46771
$443$	11374.6	1.21992	0.609961	−	0.792431i	$-0.291185\pi$
$443$	11374.6	1.21992	0.609961	+	0.792431i	$0.291185\pi$
$444$	−1716.62	−0.183485
$445$	−2465.09	−0.262599
$446$	−11259.8	−1.19544
$447$	−21040.8	−2.22639
$448$	−15654.1	−1.65086
$449$	−6667.85	−0.700835	−0.350418	−	0.936594i	$-0.613960\pi$
$449$	−6667.85	−0.700835	−0.350418	+	0.936594i	$0.613960\pi$
$450$	−54.6146	−0.00572124
$451$	−6999.87	−0.730844
$452$	311.011	0.0323644
$453$	17183.9	1.78227
$454$	−7532.06	−0.778628
$455$	22315.7	2.29928
$456$	−16841.8	−1.72959
$457$	6905.54	0.706843	0.353422	−	0.935464i	$-0.385018\pi$
$457$	6905.54	0.706843	0.353422	+	0.935464i	$0.385018\pi$
$458$	11468.9	1.17010
$459$	−2830.96	−0.287882
$460$	−600.630	−0.0608794
$461$	−2982.06	−0.301276	−0.150638	−	0.988589i	$-0.548133\pi$
$461$	−2982.06	−0.301276	−0.150638	+	0.988589i	$0.548133\pi$
$462$	27086.4	2.72765
$463$	−3665.70	−0.367948	−0.183974	−	0.982931i	$-0.558896\pi$
$463$	−3665.70	−0.367948	−0.183974	+	0.982931i	$0.558896\pi$
$464$	7254.69	0.725841
$465$	−17136.1	−1.70897
$466$	−897.572	−0.0892258
$467$	−7126.34	−0.706140	−0.353070	−	0.935597i	$-0.614862\pi$
$467$	−7126.34	−0.706140	−0.353070	+	0.935597i	$0.614862\pi$
$468$	−2459.79	−0.242956
$469$	17477.3	1.72074
$470$	−6709.82	−0.658513
$471$	4132.98	0.404326
$472$	−6500.84	−0.633953
$473$	0	0
$474$	4468.37	0.432993
$475$	−99.6368	−0.00962452
$476$	3234.12	0.311419
$477$	7787.93	0.747557
$478$	−12191.0	−1.16653
$479$	6707.60	0.639829	0.319915	−	0.947446i	$-0.396346\pi$
$479$	6707.60	0.639829	0.319915	+	0.947446i	$0.396346\pi$
$480$	5502.38	0.523225
$481$	11276.8	1.06898
$482$	3118.56	0.294702
$483$	6491.03	0.611495
$484$	−2814.02	−0.264277
$485$	−299.828	−0.0280712
$486$	12344.2	1.15215
$487$	11143.5	1.03688	0.518441	−	0.855113i	$-0.326513\pi$
$487$	11143.5	1.03688	0.518441	+	0.855113i	$0.326513\pi$
$488$	−363.008	−0.0336734
$489$	−3083.59	−0.285163
$490$	11754.7	1.08372
$491$	3816.90	0.350824	0.175412	−	0.984495i	$-0.443874\pi$
$491$	3816.90	0.350824	0.175412	+	0.984495i	$0.443874\pi$
$492$	1380.70	0.126518
$493$	−11053.1	−1.00975
$494$	18241.9	1.66142
$495$	−13491.3	−1.22503
$496$	−10707.9	−0.969349
$497$	−19780.0	−1.78522
$498$	−4656.11	−0.418966
$499$	9047.84	0.811697	0.405849	−	0.913940i	$-0.366976\pi$
$499$	9047.84	0.811697	0.405849	+	0.913940i	$0.366976\pi$
$500$	−2198.45	−0.196635
$501$	9405.01	0.838692
$502$	−10159.1	−0.903234
$503$	12445.6	1.10323	0.551613	−	0.834100i	$-0.314013\pi$
$503$	12445.6	1.10323	0.551613	+	0.834100i	$0.314013\pi$
$504$	−14380.4	−1.27094
$505$	12266.9	1.08093
$506$	4789.17	0.420760
$507$	21103.7	1.84861
$508$	−2760.68	−0.241113
$509$	−2100.56	−0.182919	−0.0914596	−	0.995809i	$-0.529153\pi$
$509$	−2100.56	−0.182919	−0.0914596	+	0.995809i	$0.529153\pi$
$510$	14755.0	1.28111
$511$	−6561.73	−0.568051
$512$	12928.0	1.11591
$513$	3786.41	0.325875
$514$	−9024.30	−0.774406
$515$	20269.5	1.73433
$516$	0	0
$517$	−13161.4	−1.11961
$518$	10869.9	0.922003
$519$	−1590.45	−0.134514
$520$	−19696.8	−1.66108
$521$	19471.1	1.63733	0.818663	−	0.574275i	$-0.194716\pi$
$521$	19471.1	1.63733	0.818663	+	0.574275i	$0.194716\pi$
$522$	8103.44	0.679459
$523$	−8828.69	−0.738149	−0.369074	−	0.929400i	$-0.620325\pi$
$523$	−8828.69	−0.738149	−0.369074	+	0.929400i	$0.620325\pi$
$524$	2143.60	0.178709
$525$	−191.700	−0.0159362
$526$	−10751.0	−0.891187
$527$	16314.4	1.34851
$528$	−18996.1	−1.56572
$529$	−11019.3	−0.905672
$530$	10282.3	0.842707
$531$	−5769.61	−0.471525
$532$	−4325.63	−0.352519
$533$	−9070.05	−0.737087
$534$	−3877.00	−0.314184
$535$	−3587.33	−0.289895
$536$	−15426.3	−1.24313
$537$	−16917.0	−1.35945
$538$	−1254.59	−0.100537
$539$	23057.0	1.84255
$540$	−674.099	−0.0537196
$541$	−9798.65	−0.778701	−0.389350	−	0.921090i	$-0.627300\pi$
$541$	−9798.65	−0.778701	−0.389350	+	0.921090i	$0.627300\pi$
$542$	−2366.38	−0.187537
$543$	4483.51	0.354338
$544$	−5238.50	−0.412866
$545$	−21538.2	−1.69283
$546$	35097.1	2.75095
$547$	−18347.0	−1.43412	−0.717059	−	0.697013i	$-0.754512\pi$
$547$	−18347.0	−1.43412	−0.717059	+	0.697013i	$0.754512\pi$
$548$	−2960.47	−0.230776
$549$	−322.176	−0.0250458
$550$	−141.439	−0.0109654
$551$	14783.6	1.14302
$552$	−5729.29	−0.441766
$553$	6960.50	0.535245
$554$	−8269.27	−0.634166
$555$	−12199.7	−0.933063
$556$	−1386.62	−0.105766
$557$	−10028.8	−0.762900	−0.381450	−	0.924389i	$-0.624575\pi$
$557$	−10028.8	−0.762900	−0.381450	+	0.924389i	$0.624575\pi$
$558$	−11960.6	−0.907406
$559$	0	0
$560$	−15085.7	−1.13837
$561$	28942.2	2.17815
$562$	23659.9	1.77586
$563$	−12595.3	−0.942858	−0.471429	−	0.881904i	$-0.656262\pi$
$563$	−12595.3	−0.942858	−0.471429	+	0.881904i	$0.656262\pi$
$564$	2596.04	0.193818
$565$	2210.30	0.164581
$566$	−13740.0	−1.02038
$567$	23280.8	1.72435
$568$	17458.7	1.28970
$569$	2559.96	0.188610	0.0943050	−	0.995543i	$-0.469937\pi$
$569$	2559.96	0.188610	0.0943050	+	0.995543i	$0.469937\pi$
$570$	−19734.9	−1.45018
$571$	−17578.9	−1.28836	−0.644180	−	0.764874i	$-0.722801\pi$
$571$	−17578.9	−1.28836	−0.644180	+	0.764874i	$0.722801\pi$
$572$	−6370.27	−0.465654
$573$	11000.8	0.802030
$574$	−8742.82	−0.635746
$575$	−33.8946	−0.00245827
$576$	12262.8	0.887069
$577$	−7195.12	−0.519128	−0.259564	−	0.965726i	$-0.583579\pi$
$577$	−7195.12	−0.519128	−0.259564	+	0.965726i	$0.583579\pi$
$578$	−1598.50	−0.115033
$579$	29956.5	2.15017
$580$	−2631.94	−0.188423
$581$	−7252.95	−0.517905
$582$	−471.558	−0.0335854
$583$	20168.9	1.43278
$584$	5791.69	0.410380
$585$	−17481.3	−1.23549
$586$	−6227.67	−0.439015
$587$	11525.7	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$587$	11525.7	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$588$	−4547.91	−0.318967
$589$	−21820.5	−1.52648
$590$	−7617.54	−0.531541
$591$	−12963.3	−0.902267
$592$	−7623.25	−0.529246
$593$	−23277.3	−1.61195	−0.805974	−	0.591951i	$-0.798358\pi$
$593$	−23277.3	−1.61195	−0.805974	+	0.591951i	$0.798358\pi$
$594$	5374.98	0.371276
$595$	22984.3	1.58364
$596$	4769.91	0.327824
$597$	36272.2	2.48663
$598$	6205.55	0.424354
$599$	16139.3	1.10089	0.550446	−	0.834871i	$-0.314458\pi$
$599$	16139.3	1.10089	0.550446	+	0.834871i	$0.314458\pi$
$600$	169.204	0.0115128
$601$	18531.7	1.25778	0.628890	−	0.777495i	$-0.283510\pi$
$601$	18531.7	1.25778	0.628890	+	0.777495i	$0.283510\pi$
$602$	0	0
$603$	−13691.1	−0.924620
$604$	−3895.55	−0.262430
$605$	−19998.8	−1.34391
$606$	19292.9	1.29327
$607$	−17387.6	−1.16267	−0.581334	−	0.813665i	$-0.697469\pi$
$607$	−17387.6	−1.16267	−0.581334	+	0.813665i	$0.697469\pi$
$608$	7006.50	0.467354
$609$	28443.5	1.89259
$610$	−425.365	−0.0282336
$611$	−17053.9	−1.12917
$612$	−2533.49	−0.167337
$613$	−1554.15	−0.102401	−0.0512003	−	0.998688i	$-0.516305\pi$
$613$	−1554.15	−0.102401	−0.0512003	+	0.998688i	$0.516305\pi$
$614$	−5103.85	−0.335464
$615$	9812.39	0.643372
$616$	−37241.8	−2.43590
$617$	5368.25	0.350272	0.175136	−	0.984544i	$-0.443964\pi$
$617$	5368.25	0.350272	0.175136	+	0.984544i	$0.443964\pi$
$618$	31879.0	2.07502
$619$	7116.61	0.462101	0.231051	−	0.972942i	$-0.425784\pi$
$619$	7116.61	0.462101	0.231051	+	0.972942i	$0.425784\pi$
$620$	3884.73	0.251636
$621$	1288.07	0.0832341
$622$	−21998.0	−1.41807
$623$	−6039.31	−0.388378
$624$	−24614.1	−1.57909
$625$	−15749.1	−1.00794
$626$	−27557.9	−1.75948
$627$	−38710.3	−2.46561
$628$	−936.938	−0.0595349
$629$	11614.7	0.736261
$630$	−16850.6	−1.06562
$631$	4994.94	0.315127	0.157564	−	0.987509i	$-0.449636\pi$
$631$	4994.94	0.315127	0.157564	+	0.987509i	$0.449636\pi$
$632$	−6143.66	−0.386680
$633$	23657.1	1.48544
$634$	−2808.54	−0.175933
$635$	−19619.7	−1.22611
$636$	−3978.24	−0.248031
$637$	29876.0	1.85829
$638$	20986.0	1.30226
$639$	15494.9	0.959264
$640$	9872.51	0.609758
$641$	7631.07	0.470217	0.235108	−	0.971969i	$-0.424455\pi$
$641$	7631.07	0.470217	0.235108	+	0.971969i	$0.424455\pi$
$642$	−5642.01	−0.346842
$643$	−28956.7	−1.77596	−0.887979	−	0.459884i	$-0.847891\pi$
$643$	−28956.7	−1.77596	−0.887979	+	0.459884i	$0.847891\pi$
$644$	−1471.50	−0.0900393
$645$	0	0
$646$	18788.5	1.14431
$647$	−2044.04	−0.124203	−0.0621016	−	0.998070i	$-0.519780\pi$
$647$	−2044.04	−0.124203	−0.0621016	+	0.998070i	$0.519780\pi$
$648$	−20548.8	−1.24573
$649$	−14941.9	−0.903732
$650$	−183.269	−0.0110591
$651$	−41982.3	−2.52752
$652$	699.044	0.0419887
$653$	10129.7	0.607056	0.303528	−	0.952823i	$-0.401835\pi$
$653$	10129.7	0.607056	0.303528	+	0.952823i	$0.401835\pi$
$654$	−33874.4	−2.02537
$655$	15234.2	0.908779
$656$	6131.47	0.364929
$657$	5140.22	0.305235
$658$	−16438.6	−0.973926
$659$	−21314.3	−1.25992	−0.629961	−	0.776626i	$-0.716929\pi$
$659$	−21314.3	−1.25992	−0.629961	+	0.776626i	$0.716929\pi$
$660$	6891.64	0.406450
$661$	−23058.5	−1.35684	−0.678420	−	0.734674i	$-0.737335\pi$
$661$	−23058.5	−1.35684	−0.678420	+	0.734674i	$0.737335\pi$
$662$	21370.1	1.25464
$663$	37501.8	2.19676
$664$	6401.79	0.374153
$665$	−30741.5	−1.79264
$666$	−8515.12	−0.495427
$667$	5029.11	0.291946
$668$	−2132.10	−0.123493
$669$	30960.6	1.78924
$670$	−18076.2	−1.04231
$671$	−834.360	−0.0480032
$672$	13480.4	0.773838
$673$	11219.9	0.642636	0.321318	−	0.946971i	$-0.395874\pi$
$673$	11219.9	0.642636	0.321318	+	0.946971i	$0.395874\pi$
$674$	7804.25	0.446007
$675$	−38.0406	−0.00216916
$676$	−4784.16	−0.272199
$677$	3663.69	0.207987	0.103993	−	0.994578i	$-0.466838\pi$
$677$	3663.69	0.207987	0.103993	+	0.994578i	$0.466838\pi$
$678$	3476.27	0.196911
$679$	−734.559	−0.0415166
$680$	−20287.0	−1.14408
$681$	20710.5	1.16539
$682$	−30975.2	−1.73915
$683$	−395.314	−0.0221468	−0.0110734	−	0.999939i	$-0.503525\pi$
$683$	−395.314	−0.0221468	−0.0110734	+	0.999939i	$0.503525\pi$
$684$	3388.54	0.189421
$685$	−21039.6	−1.17355
$686$	4896.95	0.272546
$687$	−31535.4	−1.75131
$688$	0	0
$689$	26133.8	1.44502
$690$	−6713.45	−0.370401
$691$	−3049.47	−0.167883	−0.0839415	−	0.996471i	$-0.526751\pi$
$691$	−3049.47	−0.167883	−0.0839415	+	0.996471i	$0.526751\pi$
$692$	360.551	0.0198065
$693$	−33052.7	−1.81179
$694$	10559.4	0.577564
$695$	−9854.47	−0.537844
$696$	−25105.5	−1.36727
$697$	−9341.83	−0.507671
$698$	10287.5	0.557861
$699$	2468.01	0.133546
$700$	43.4580	0.00234651
$701$	−3175.59	−0.171099	−0.0855494	−	0.996334i	$-0.527265\pi$
$701$	−3175.59	−0.171099	−0.0855494	+	0.996334i	$0.527265\pi$
$702$	6964.61	0.374448
$703$	−15534.6	−0.833428
$704$	31757.9	1.70017
$705$	18449.6	0.985608
$706$	−10257.7	−0.546821
$707$	30053.0	1.59867
$708$	2947.24	0.156446
$709$	−16013.8	−0.848254	−0.424127	−	0.905603i	$-0.639419\pi$
$709$	−16013.8	−0.848254	−0.424127	+	0.905603i	$0.639419\pi$
$710$	20457.7	1.08136
$711$	−5452.60	−0.287607
$712$	5330.58	0.280578
$713$	−7422.93	−0.389889
$714$	36148.8	1.89473
$715$	−45272.4	−2.36796
$716$	3835.05	0.200171
$717$	33521.0	1.74597
$718$	−11270.2	−0.585794
$719$	795.023	0.0412369	0.0206185	−	0.999787i	$-0.493436\pi$
$719$	795.023	0.0412369	0.0206185	+	0.999787i	$0.493436\pi$
$720$	11817.6	0.611687
$721$	49658.8	2.56504
$722$	−7749.69	−0.399465
$723$	−8574.94	−0.441087
$724$	−1016.40	−0.0521744
$725$	−148.525	−0.00760840
$726$	−31453.3	−1.60791
$727$	7150.37	0.364777	0.182388	−	0.983227i	$-0.441617\pi$
$727$	7150.37	0.364777	0.182388	+	0.983227i	$0.441617\pi$
$728$	−48255.9	−2.45671
$729$	−11084.9	−0.563173
$730$	6786.57	0.344085
$731$	0	0
$732$	164.575	0.00830990
$733$	−25772.3	−1.29866	−0.649331	−	0.760506i	$-0.724951\pi$
$733$	−25772.3	−1.29866	−0.649331	+	0.760506i	$0.724951\pi$
$734$	30151.3	1.51622
$735$	−32321.2	−1.62202
$736$	2383.48	0.119370
$737$	−35456.8	−1.77214
$738$	6848.81	0.341610
$739$	−16503.9	−0.821526	−0.410763	−	0.911742i	$-0.634738\pi$
$739$	−16503.9	−0.821526	−0.410763	+	0.911742i	$0.634738\pi$
$740$	2765.65	0.137388
$741$	−50158.7	−2.48667
$742$	25190.9	1.24634
$743$	−11050.1	−0.545611	−0.272806	−	0.962069i	$-0.587952\pi$
$743$	−11050.1	−0.545611	−0.272806	+	0.962069i	$0.587952\pi$
$744$	37055.6	1.82597
$745$	33898.9	1.66706
$746$	5468.37	0.268380
$747$	5681.70	0.278290
$748$	−6561.15	−0.320721
$749$	−8788.72	−0.428749
$750$	−24572.8	−1.19636
$751$	31117.4	1.51197	0.755985	−	0.654589i	$-0.227158\pi$
$751$	31117.4	1.51197	0.755985	+	0.654589i	$0.227158\pi$
$752$	11528.6	0.559050
$753$	27934.0	1.35189
$754$	27192.5	1.31339
$755$	−27685.0	−1.33452
$756$	−1651.50	−0.0794502
$757$	6688.49	0.321132	0.160566	−	0.987025i	$-0.448668\pi$
$757$	6688.49	0.321132	0.160566	+	0.987025i	$0.448668\pi$
$758$	−6811.39	−0.326386
$759$	−13168.5	−0.629760
$760$	27133.9	1.29507
$761$	9190.90	0.437805	0.218903	−	0.975747i	$-0.429752\pi$
$761$	9190.90	0.437805	0.218903	+	0.975747i	$0.429752\pi$
$762$	−30857.0	−1.46697
$763$	−52767.0	−2.50366
$764$	−2493.85	−0.118095
$765$	−18005.1	−0.850948
$766$	−9814.33	−0.462932
$767$	−19360.9	−0.911451
$768$	−16200.8	−0.761191
$769$	13144.3	0.616377	0.308188	−	0.951325i	$-0.400277\pi$
$769$	13144.3	0.616377	0.308188	+	0.951325i	$0.400277\pi$
$770$	−43639.1	−2.04239
$771$	24813.7	1.15907
$772$	−6791.06	−0.316601
$773$	−25782.2	−1.19964	−0.599819	−	0.800136i	$-0.704761\pi$
$773$	−25782.2	−1.19964	−0.599819	+	0.800136i	$0.704761\pi$
$774$	0	0
$775$	219.222	0.0101609
$776$	648.356	0.0299931
$777$	−29888.5	−1.37998
$778$	−21406.7	−0.986460
$779$	12494.7	0.574671
$780$	8929.82	0.409922
$781$	40128.2	1.83854
$782$	6391.49	0.292275
$783$	5644.27	0.257611
$784$	−20196.6	−0.920033
$785$	−6658.66	−0.302749
$786$	23959.8	1.08730
$787$	20130.5	0.911783	0.455891	−	0.890035i	$-0.349321\pi$
$787$	20130.5	0.911783	0.455891	+	0.890035i	$0.349321\pi$
$788$	2938.76	0.132854
$789$	29561.4	1.33386
$790$	−7199.00	−0.324214
$791$	5415.08	0.243411
$792$	29173.9	1.30890
$793$	−1081.12	−0.0484132
$794$	−9988.94	−0.446466
$795$	−28272.7	−1.26130
$796$	−8222.82	−0.366143
$797$	5870.40	0.260904	0.130452	−	0.991455i	$-0.458357\pi$
$797$	5870.40	0.260904	0.130452	+	0.991455i	$0.458357\pi$
$798$	−48349.0	−2.14478
$799$	−17564.9	−0.777723
$800$	−70.3917	−0.00311090
$801$	4730.98	0.208690
$802$	30992.9	1.36458
$803$	13312.0	0.585018
$804$	6993.72	0.306778
$805$	−10457.7	−0.457871
$806$	−40135.9	−1.75400
$807$	3449.67	0.150476
$808$	−26526.2	−1.15494
$809$	−8490.02	−0.368966	−0.184483	−	0.982836i	$-0.559061\pi$
$809$	−8490.02	−0.368966	−0.184483	+	0.982836i	$0.559061\pi$
$810$	−24078.6	−1.04449
$811$	−40540.6	−1.75533	−0.877666	−	0.479273i	$-0.840900\pi$
$811$	−40540.6	−1.75533	−0.877666	+	0.479273i	$0.840900\pi$
$812$	−6448.08	−0.278674
$813$	6506.72	0.280689
$814$	−22052.2	−0.949543
$815$	4967.99	0.213523
$816$	−25351.7	−1.08761
$817$	0	0
$818$	−15863.5	−0.678062
$819$	−42827.9	−1.82726
$820$	−2224.45	−0.0947330
$821$	10950.8	0.465510	0.232755	−	0.972535i	$-0.425226\pi$
$821$	10950.8	0.465510	0.232755	+	0.972535i	$0.425226\pi$
$822$	−33090.2	−1.40408
$823$	26953.9	1.14162	0.570811	−	0.821081i	$-0.306629\pi$
$823$	26953.9	1.14162	0.570811	+	0.821081i	$0.306629\pi$
$824$	−43831.2	−1.85307
$825$	388.908	0.0164121
$826$	−18662.4	−0.786137
$827$	−11696.4	−0.491804	−0.245902	−	0.969295i	$-0.579084\pi$
$827$	−11696.4	−0.491804	−0.245902	+	0.969295i	$0.579084\pi$
$828$	1152.72	0.0483815
$829$	29330.2	1.22880	0.614402	−	0.788993i	$-0.289397\pi$
$829$	29330.2	1.22880	0.614402	+	0.788993i	$0.289397\pi$
$830$	7501.47	0.313711
$831$	22737.6	0.949168
$832$	41150.2	1.71469
$833$	30771.2	1.27990
$834$	−15498.7	−0.643497
$835$	−15152.4	−0.627990
$836$	8775.53	0.363048
$837$	−8330.89	−0.344036
$838$	−22677.5	−0.934823
$839$	41062.2	1.68966	0.844830	−	0.535034i	$-0.179701\pi$
$839$	41062.2	1.68966	0.844830	+	0.535034i	$0.179701\pi$
$840$	52205.4	2.14435
$841$	−2351.60	−0.0964206
$842$	27130.5	1.11043
$843$	−65056.5	−2.65796
$844$	−5363.01	−0.218723
$845$	−34000.2	−1.38419
$846$	12877.4	0.523326
$847$	−48995.6	−1.98762
$848$	−17666.8	−0.715424
$849$	37780.2	1.52722
$850$	−188.761	−0.00761698
$851$	−5284.61	−0.212872
$852$	−7915.14	−0.318273
$853$	31541.8	1.26609	0.633043	−	0.774116i	$-0.281805\pi$
$853$	31541.8	1.26609	0.633043	+	0.774116i	$0.281805\pi$
$854$	−1042.11	−0.0417569
$855$	24081.8	0.963252
$856$	7757.33	0.309743
$857$	12164.9	0.484884	0.242442	−	0.970166i	$-0.422052\pi$
$857$	12164.9	0.484884	0.242442	+	0.970166i	$0.422052\pi$
$858$	−71202.6	−2.83312
$859$	−25139.0	−0.998522	−0.499261	−	0.866452i	$-0.666395\pi$
$859$	−25139.0	−0.998522	−0.499261	+	0.866452i	$0.666395\pi$
$860$	0	0
$861$	24039.7	0.951533
$862$	−39735.1	−1.57005
$863$	−12077.7	−0.476396	−0.238198	−	0.971217i	$-0.576557\pi$
$863$	−12077.7	−0.476396	−0.238198	+	0.971217i	$0.576557\pi$
$864$	2675.03	0.105332
$865$	2562.37	0.100721
$866$	−14019.0	−0.550099
$867$	4395.32	0.172172
$868$	9517.31	0.372164
$869$	−14121.0	−0.551232
$870$	−29418.1	−1.14640
$871$	−45943.0	−1.78728
$872$	46574.7	1.80874
$873$	575.427	0.0223084
$874$	−8548.62	−0.330848
$875$	−38277.7	−1.47888
$876$	−2625.74	−0.101273
$877$	21545.7	0.829585	0.414793	−	0.909916i	$-0.363854\pi$
$877$	21545.7	0.829585	0.414793	+	0.909916i	$0.363854\pi$
$878$	6766.70	0.260097
$879$	17123.9	0.657081
$880$	30604.7	1.17237
$881$	26871.1	1.02760	0.513798	−	0.857911i	$-0.328238\pi$
$881$	26871.1	1.02760	0.513798	+	0.857911i	$0.328238\pi$
$882$	−22559.4	−0.861242
$883$	45588.3	1.73745	0.868725	−	0.495295i	$-0.164940\pi$
$883$	45588.3	1.73745	0.868725	+	0.495295i	$0.164940\pi$
$884$	−8501.58	−0.323460
$885$	20945.5	0.795567
$886$	−28822.0	−1.09288
$887$	4931.59	0.186682	0.0933408	−	0.995634i	$-0.470245\pi$
$887$	4931.59	0.186682	0.0933408	+	0.995634i	$0.470245\pi$
$888$	26381.0	0.996946
$889$	−48066.8	−1.81340
$890$	6246.25	0.235252
$891$	−47230.5	−1.77585
$892$	−7018.70	−0.263457
$893$	23493.0	0.880363
$894$	53314.8	1.99453
$895$	27255.1	1.01792
$896$	24186.9	0.901818
$897$	−17063.1	−0.635139
$898$	16895.5	0.627851
$899$	−32527.0	−1.20672
$900$	−34.0434	−0.00126087
$901$	26916.9	0.995261
$902$	17736.8	0.654735
$903$	0	0
$904$	−4779.61	−0.175849
$905$	−7223.39	−0.265319
$906$	−43541.8	−1.59667
$907$	52939.1	1.93805	0.969026	−	0.246960i	$-0.0794316\pi$
$907$	52939.1	1.93805	0.969026	+	0.246960i	$0.0794316\pi$
$908$	−4695.03	−0.171597
$909$	−23542.5	−0.859026
$910$	−56545.1	−2.05984
$911$	33446.4	1.21639	0.608194	−	0.793788i	$-0.291894\pi$
$911$	33446.4	1.21639	0.608194	+	0.793788i	$0.291894\pi$
$912$	33907.9	1.23114
$913$	14714.3	0.533375
$914$	−17497.8	−0.633233
$915$	1169.60	0.0422578
$916$	7149.00	0.257871
$917$	37322.8	1.34406
$918$	7173.30	0.257902
$919$	45444.1	1.63119	0.815595	−	0.578623i	$-0.196410\pi$
$919$	45444.1	1.63119	0.815595	+	0.578623i	$0.196410\pi$
$920$	9230.47	0.330782
$921$	14033.8	0.502095
$922$	7556.18	0.269902
$923$	51995.9	1.85424
$924$	16884.0	0.601130
$925$	156.071	0.00554765
$926$	9288.45	0.329630
$927$	−38900.9	−1.37829
$928$	10444.4	0.369453
$929$	35100.6	1.23963	0.619813	−	0.784749i	$-0.287208\pi$
$929$	35100.6	1.23963	0.619813	+	0.784749i	$0.287208\pi$
$930$	43420.9	1.53100
$931$	−41156.5	−1.44882
$932$	−559.492	−0.0196639
$933$	60486.8	2.12245
$934$	18057.3	0.632603
$935$	−46629.0	−1.63094
$936$	37801.9	1.32008
$937$	−31216.6	−1.08837	−0.544184	−	0.838966i	$-0.683161\pi$
$937$	−31216.6	−1.08837	−0.544184	+	0.838966i	$0.683161\pi$
$938$	−44285.4	−1.54155
$939$	75774.5	2.63345
$940$	−4182.49	−0.145125
$941$	45184.0	1.56531	0.782654	−	0.622457i	$-0.213865\pi$
$941$	45184.0	1.56531	0.782654	+	0.622457i	$0.213865\pi$
$942$	−10472.5	−0.362220
$943$	4250.47	0.146781
$944$	13088.2	0.451256
$945$	−11736.9	−0.404023
$946$	0	0
$947$	4627.83	0.158801	0.0794004	−	0.996843i	$-0.474699\pi$
$947$	4627.83	0.158801	0.0794004	+	0.996843i	$0.474699\pi$
$948$	2785.31	0.0954247
$949$	17248.9	0.590015
$950$	252.467	0.00862223
$951$	7722.49	0.263321
$952$	−49701.8	−1.69207
$953$	11981.7	0.407268	0.203634	−	0.979047i	$-0.434725\pi$
$953$	11981.7	0.407268	0.203634	+	0.979047i	$0.434725\pi$
$954$	−19733.7	−0.669707
$955$	−17723.4	−0.600539
$956$	−7599.13	−0.257085
$957$	−57704.1	−1.94912
$958$	−16996.2	−0.573198
$959$	−51545.5	−1.73565
$960$	−44518.1	−1.49668
$961$	18218.6	0.611548
$962$	−28574.0	−0.957653
$963$	6884.76	0.230383
$964$	1943.92	0.0649476
$965$	−48262.9	−1.60999
$966$	−16447.5	−0.547814
$967$	2830.54	0.0941302	0.0470651	−	0.998892i	$-0.485013\pi$
$967$	2830.54	0.0941302	0.0470651	+	0.998892i	$0.485013\pi$
$968$	43245.9	1.43592
$969$	−51661.6	−1.71270
$970$	759.729	0.0251478
$971$	−55053.0	−1.81950	−0.909750	−	0.415156i	$-0.863727\pi$
$971$	−55053.0	−1.81950	−0.909750	+	0.415156i	$0.863727\pi$
$972$	7694.61	0.253914
$973$	−24142.8	−0.795459
$974$	−28236.3	−0.928902
$975$	503.925	0.0165523
$976$	730.850	0.0239692
$977$	−37066.7	−1.21379	−0.606893	−	0.794784i	$-0.707584\pi$
$977$	−37066.7	−1.21379	−0.606893	+	0.794784i	$0.707584\pi$
$978$	7813.44	0.255467
$979$	12252.1	0.399979
$980$	7327.15	0.238834
$981$	41335.8	1.34531
$982$	−9671.56	−0.314289
$983$	−42666.6	−1.38439	−0.692194	−	0.721711i	$-0.743356\pi$
$983$	−42666.6	−1.38439	−0.692194	+	0.721711i	$0.743356\pi$
$984$	−21218.5	−0.687421
$985$	20885.3	0.675594
$986$	28007.3	0.904599
$987$	45200.3	1.45769
$988$	11370.9	0.366149
$989$	0	0
$990$	34185.3	1.09745
$991$	8498.14	0.272404	0.136202	−	0.990681i	$-0.456510\pi$
$991$	8498.14	0.272404	0.136202	+	0.990681i	$0.456510\pi$
$992$	−15415.8	−0.493399
$993$	−58760.4	−1.87785
$994$	50120.0	1.59931
$995$	−58438.2	−1.86193
$996$	−2902.33	−0.0923333
$997$	−59152.1	−1.87900	−0.939502	−	0.342545i	$-0.888711\pi$
$997$	−59152.1	−1.87900	−0.939502	+	0.342545i	$0.888711\pi$
$998$	−22926.1	−0.727168
$999$	−5931.02	−0.187837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.e.1.4	✓	10
43.42	odd	2	inner	1849.4.a.e.1.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.e.1.4	✓	10	1.1	even	1	trivial
1849.4.a.e.1.7	yes	10	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53388 q^{2} +6.96727 q^{3} -1.57947 q^{4} -11.2250 q^{5} -17.6542 q^{6} -27.5005 q^{7} +24.2732 q^{8} +21.5429 q^{9} +O(q^{10})\)	\(q-2.53388 q^{2} +6.96727 q^{3} -1.57947 q^{4} -11.2250 q^{5} -17.6542 q^{6} -27.5005 q^{7} +24.2732 q^{8} +21.5429 q^{9} +28.4428 q^{10} +55.7910 q^{11} -11.0046 q^{12} +72.2909 q^{13} +69.6828 q^{14} -78.2076 q^{15} -48.8696 q^{16} +74.4570 q^{17} -54.5870 q^{18} -99.5863 q^{19} +17.7295 q^{20} -191.603 q^{21} -141.367 q^{22} -33.8775 q^{23} +169.118 q^{24} +1.00051 q^{25} -183.176 q^{26} -38.0213 q^{27} +43.4360 q^{28} -148.450 q^{29} +198.168 q^{30} +219.111 q^{31} -70.3560 q^{32} +388.711 q^{33} -188.665 q^{34} +308.692 q^{35} -34.0262 q^{36} +155.992 q^{37} +252.339 q^{38} +503.670 q^{39} -272.466 q^{40} -125.466 q^{41} +485.499 q^{42} -88.1199 q^{44} -241.819 q^{45} +85.8414 q^{46} -235.906 q^{47} -340.488 q^{48} +413.275 q^{49} -2.53516 q^{50} +518.762 q^{51} -114.181 q^{52} +361.509 q^{53} +96.3414 q^{54} -626.253 q^{55} -667.524 q^{56} -693.845 q^{57} +376.154 q^{58} -267.820 q^{59} +123.526 q^{60} -14.9551 q^{61} -555.200 q^{62} -592.438 q^{63} +569.230 q^{64} -811.465 q^{65} -984.945 q^{66} -635.529 q^{67} -117.602 q^{68} -236.034 q^{69} -782.189 q^{70} +719.260 q^{71} +522.914 q^{72} +238.605 q^{73} -395.264 q^{74} +6.97080 q^{75} +157.293 q^{76} -1534.28 q^{77} -1276.24 q^{78} -253.105 q^{79} +548.561 q^{80} -846.562 q^{81} +317.915 q^{82} +263.739 q^{83} +302.630 q^{84} -835.780 q^{85} -1034.29 q^{87} +1354.22 q^{88} +219.608 q^{89} +612.739 q^{90} -1988.03 q^{91} +53.5083 q^{92} +1526.61 q^{93} +597.757 q^{94} +1117.86 q^{95} -490.190 q^{96} +26.7108 q^{97} -1047.19 q^{98} +1201.90 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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