LMFDB - Embedded newform 2442.4.a.n.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2442,4,Mod(1,2442)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2442, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2442.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2442 = 2 \cdot 3 \cdot 11 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2442.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-24,-36,48,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$144.082664234$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 849 x^{10} + 1205 x^{9} + 248360 x^{8} - 397682 x^{7} - 29936318 x^{6} + \cdots - 37088275010 $ x^12 - 2x^11 - 849x^10 + 1205x^9 + 248360x^8 - 397682x^7 - 29936318x^6 + 69190668x^5 + 1339839809x^4 - 4379648628x^3 - 15280838921x^2 + 65348896151*x - 37088275010
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$4.07363$ of defining polynomial
Character	$\chi$	$=$	2442.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +3.07363 q^{5} +6.00000 q^{6} +8.18892 q^{7} -8.00000 q^{8} +9.00000 q^{9} -6.14725 q^{10} +11.0000 q^{11} -12.0000 q^{12} -51.2106 q^{13} -16.3778 q^{14} -9.22088 q^{15} +16.0000 q^{16} -38.5247 q^{17} -18.0000 q^{18} +107.074 q^{19} +12.2945 q^{20} -24.5668 q^{21} -22.0000 q^{22} +41.5980 q^{23} +24.0000 q^{24} -115.553 q^{25} +102.421 q^{26} -27.0000 q^{27} +32.7557 q^{28} +182.883 q^{29} +18.4418 q^{30} -142.745 q^{31} -32.0000 q^{32} -33.0000 q^{33} +77.0495 q^{34} +25.1697 q^{35} +36.0000 q^{36} -37.0000 q^{37} -214.149 q^{38} +153.632 q^{39} -24.5890 q^{40} +142.251 q^{41} +49.1335 q^{42} +452.690 q^{43} +44.0000 q^{44} +27.6626 q^{45} -83.1960 q^{46} -600.587 q^{47} -48.0000 q^{48} -275.942 q^{49} +231.106 q^{50} +115.574 q^{51} -204.842 q^{52} -194.604 q^{53} +54.0000 q^{54} +33.8099 q^{55} -65.5113 q^{56} -321.223 q^{57} -365.765 q^{58} +520.322 q^{59} -36.8835 q^{60} -72.1506 q^{61} +285.490 q^{62} +73.7003 q^{63} +64.0000 q^{64} -157.402 q^{65} +66.0000 q^{66} +284.421 q^{67} -154.099 q^{68} -124.794 q^{69} -50.3394 q^{70} -433.853 q^{71} -72.0000 q^{72} -262.908 q^{73} +74.0000 q^{74} +346.658 q^{75} +428.298 q^{76} +90.0781 q^{77} -307.264 q^{78} -388.494 q^{79} +49.1780 q^{80} +81.0000 q^{81} -284.501 q^{82} -249.994 q^{83} -98.2670 q^{84} -118.411 q^{85} -905.379 q^{86} -548.648 q^{87} -88.0000 q^{88} -1411.38 q^{89} -55.3253 q^{90} -419.359 q^{91} +166.392 q^{92} +428.234 q^{93} +1201.17 q^{94} +329.107 q^{95} +96.0000 q^{96} +19.5161 q^{97} +551.883 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} - 10 q^{5} + 72 q^{6} - 25 q^{7} - 96 q^{8} + 108 q^{9} + 20 q^{10} + 132 q^{11} - 144 q^{12} + 12 q^{13} + 50 q^{14} + 30 q^{15} + 192 q^{16} - 10 q^{17} - 216 q^{18}+ \cdots + 1188 q^{99}+O(q^{100}) $ 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 - 10 * q^5 + 72 * q^6 - 25 * q^7 - 96 * q^8 + 108 * q^9 + 20 * q^10 + 132 * q^11 - 144 * q^12 + 12 * q^13 + 50 * q^14 + 30 * q^15 + 192 * q^16 - 10 * q^17 - 216 * q^18 - 9 * q^19 - 40 * q^20 + 75 * q^21 - 264 * q^22 - 201 * q^23 + 288 * q^24 + 210 * q^25 - 24 * q^26 - 324 * q^27 - 100 * q^28 - 84 * q^29 - 60 * q^30 + 10 * q^31 - 384 * q^32 - 396 * q^33 + 20 * q^34 - 565 * q^35 + 432 * q^36 - 444 * q^37 + 18 * q^38 - 36 * q^39 + 80 * q^40 + 215 * q^41 - 150 * q^42 - 434 * q^43 + 528 * q^44 - 90 * q^45 + 402 * q^46 - 256 * q^47 - 576 * q^48 + 519 * q^49 - 420 * q^50 + 30 * q^51 + 48 * q^52 - 448 * q^53 + 648 * q^54 - 110 * q^55 + 200 * q^56 + 27 * q^57 + 168 * q^58 - 588 * q^59 + 120 * q^60 + 735 * q^61 - 20 * q^62 - 225 * q^63 + 768 * q^64 - 859 * q^65 + 792 * q^66 - 288 * q^67 - 40 * q^68 + 603 * q^69 + 1130 * q^70 + 1019 * q^71 - 864 * q^72 - 309 * q^73 + 888 * q^74 - 630 * q^75 - 36 * q^76 - 275 * q^77 + 72 * q^78 + 1116 * q^79 - 160 * q^80 + 972 * q^81 - 430 * q^82 - 662 * q^83 + 300 * q^84 + 1093 * q^85 + 868 * q^86 + 252 * q^87 - 1056 * q^88 + 1603 * q^89 + 180 * q^90 + 1502 * q^91 - 804 * q^92 - 30 * q^93 + 512 * q^94 - 2017 * q^95 + 1152 * q^96 + 349 * q^97 - 1038 * q^98 + 1188 * 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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	3.07363	0.274913	0.137457	−	0.990508i	$-0.456107\pi$
$5$	3.07363	0.274913	0.137457	+	0.990508i	$0.456107\pi$
$6$	6.00000	0.408248
$7$	8.18892	0.442160	0.221080	−	0.975256i	$-0.429042\pi$
$7$	8.18892	0.442160	0.221080	+	0.975256i	$0.429042\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−6.14725	−0.194393
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−12.0000	−0.288675
$13$	−51.2106	−1.09256	−0.546279	−	0.837603i	$-0.683956\pi$
$13$	−51.2106	−1.09256	−0.546279	+	0.837603i	$0.683956\pi$
$14$	−16.3778	−0.312654
$15$	−9.22088	−0.158721
$16$	16.0000	0.250000
$17$	−38.5247	−0.549625	−0.274812	−	0.961498i	$-0.588616\pi$
$17$	−38.5247	−0.549625	−0.274812	+	0.961498i	$0.588616\pi$
$18$	−18.0000	−0.235702
$19$	107.074	1.29287	0.646436	−	0.762968i	$-0.276259\pi$
$19$	107.074	1.29287	0.646436	+	0.762968i	$0.276259\pi$
$20$	12.2945	0.137457
$21$	−24.5668	−0.255281
$22$	−22.0000	−0.213201
$23$	41.5980	0.377121	0.188561	−	0.982062i	$-0.439618\pi$
$23$	41.5980	0.377121	0.188561	+	0.982062i	$0.439618\pi$
$24$	24.0000	0.204124
$25$	−115.553	−0.924423
$26$	102.421	0.772556
$27$	−27.0000	−0.192450
$28$	32.7557	0.221080
$29$	182.883	1.17105	0.585525	−	0.810654i	$-0.300888\pi$
$29$	182.883	1.17105	0.585525	+	0.810654i	$0.300888\pi$
$30$	18.4418	0.112233
$31$	−142.745	−0.827023	−0.413512	−	0.910499i	$-0.635698\pi$
$31$	−142.745	−0.827023	−0.413512	+	0.910499i	$0.635698\pi$
$32$	−32.0000	−0.176777
$33$	−33.0000	−0.174078
$34$	77.0495	0.388643
$35$	25.1697	0.121556
$36$	36.0000	0.166667
$37$	−37.0000	−0.164399
$37$	−37.0000	−0.164399
$38$	−214.149	−0.914198
$39$	153.632	0.630789
$40$	−24.5890	−0.0971966
$41$	142.251	0.541849	0.270924	−	0.962601i	$-0.412671\pi$
$41$	142.251	0.541849	0.270924	+	0.962601i	$0.412671\pi$
$42$	49.1335	0.180511
$43$	452.690	1.60545	0.802727	−	0.596347i	$-0.203382\pi$
$43$	452.690	1.60545	0.802727	+	0.596347i	$0.203382\pi$
$44$	44.0000	0.150756
$45$	27.6626	0.0916378
$46$	−83.1960	−0.266665
$47$	−600.587	−1.86393	−0.931965	−	0.362549i	$-0.881906\pi$
$47$	−600.587	−1.86393	−0.931965	+	0.362549i	$0.881906\pi$
$48$	−48.0000	−0.144338
$49$	−275.942	−0.804494
$50$	231.106	0.653665
$51$	115.574	0.317326
$52$	−204.842	−0.546279
$53$	−194.604	−0.504356	−0.252178	−	0.967681i	$-0.581147\pi$
$53$	−194.604	−0.504356	−0.252178	+	0.967681i	$0.581147\pi$
$54$	54.0000	0.136083
$55$	33.8099	0.0828895
$56$	−65.5113	−0.156327
$57$	−321.223	−0.746440
$58$	−365.765	−0.828057
$59$	520.322	1.14814	0.574070	−	0.818806i	$-0.305364\pi$
$59$	520.322	1.14814	0.574070	+	0.818806i	$0.305364\pi$
$60$	−36.8835	−0.0793607
$61$	−72.1506	−0.151442	−0.0757208	−	0.997129i	$-0.524126\pi$
$61$	−72.1506	−0.151442	−0.0757208	+	0.997129i	$0.524126\pi$
$62$	285.490	0.584794
$63$	73.7003	0.147387
$64$	64.0000	0.125000
$65$	−157.402	−0.300359
$66$	66.0000	0.123091
$67$	284.421	0.518621	0.259310	−	0.965794i	$-0.416505\pi$
$67$	284.421	0.518621	0.259310	+	0.965794i	$0.416505\pi$
$68$	−154.099	−0.274812
$69$	−124.794	−0.217731
$70$	−50.3394	−0.0859529
$71$	−433.853	−0.725196	−0.362598	−	0.931946i	$-0.618110\pi$
$71$	−433.853	−0.725196	−0.362598	+	0.931946i	$0.618110\pi$
$72$	−72.0000	−0.117851
$73$	−262.908	−0.421522	−0.210761	−	0.977538i	$-0.567594\pi$
$73$	−262.908	−0.421522	−0.210761	+	0.977538i	$0.567594\pi$
$74$	74.0000	0.116248
$75$	346.658	0.533716
$76$	428.298	0.646436
$77$	90.0781	0.133316
$78$	−307.264	−0.446035
$79$	−388.494	−0.553279	−0.276639	−	0.960974i	$-0.589221\pi$
$79$	−388.494	−0.553279	−0.276639	+	0.960974i	$0.589221\pi$
$80$	49.1780	0.0687284
$81$	81.0000	0.111111
$82$	−284.501	−0.383145
$83$	−249.994	−0.330607	−0.165303	−	0.986243i	$-0.552860\pi$
$83$	−249.994	−0.330607	−0.165303	+	0.986243i	$0.552860\pi$
$84$	−98.2670	−0.127641
$85$	−118.411	−0.151099
$86$	−905.379	−1.13523
$87$	−548.648	−0.676106
$88$	−88.0000	−0.106600
$89$	−1411.38	−1.68097	−0.840485	−	0.541835i	$-0.817730\pi$
$89$	−1411.38	−1.68097	−0.840485	+	0.541835i	$0.817730\pi$
$90$	−55.3253	−0.0647977
$91$	−419.359	−0.483086
$92$	166.392	0.188561
$93$	428.234	0.477482
$94$	1201.17	1.31800
$95$	329.107	0.355428
$96$	96.0000	0.102062
$97$	19.5161	0.0204285	0.0102142	−	0.999948i	$-0.496749\pi$
$97$	19.5161	0.0204285	0.0102142	+	0.999948i	$0.496749\pi$
$98$	551.883	0.568864
$99$	99.0000	0.100504
$100$	−462.211	−0.462211
$101$	−61.6445	−0.0607312	−0.0303656	−	0.999539i	$-0.509667\pi$
$101$	−61.6445	−0.0607312	−0.0303656	+	0.999539i	$0.509667\pi$
$102$	−231.148	−0.224383
$103$	242.265	0.231758	0.115879	−	0.993263i	$-0.463032\pi$
$103$	242.265	0.231758	0.115879	+	0.993263i	$0.463032\pi$
$104$	409.685	0.386278
$105$	−75.5090	−0.0701803
$106$	389.208	0.356634
$107$	473.833	0.428104	0.214052	−	0.976822i	$-0.431334\pi$
$107$	473.833	0.428104	0.214052	+	0.976822i	$0.431334\pi$
$108$	−108.000	−0.0962250
$109$	1325.05	1.16438	0.582188	−	0.813054i	$-0.302197\pi$
$109$	1325.05	1.16438	0.582188	+	0.813054i	$0.302197\pi$
$110$	−67.6198	−0.0586118
$111$	111.000	0.0949158
$112$	131.023	0.110540
$113$	−102.180	−0.0850648	−0.0425324	−	0.999095i	$-0.513543\pi$
$113$	−102.180	−0.0850648	−0.0425324	+	0.999095i	$0.513543\pi$
$114$	642.447	0.527813
$115$	127.857	0.103676
$116$	731.530	0.585525
$117$	−460.895	−0.364186
$118$	−1040.64	−0.811857
$119$	−315.476	−0.243022
$120$	73.7670	0.0561165
$121$	121.000	0.0909091
$122$	144.301	0.107085
$123$	−426.752	−0.312837
$124$	−570.979	−0.413512
$125$	−739.369	−0.529050
$126$	−147.401	−0.104218
$127$	517.102	0.361302	0.180651	−	0.983547i	$-0.442180\pi$
$127$	517.102	0.361302	0.180651	+	0.983547i	$0.442180\pi$
$128$	−128.000	−0.0883883
$129$	−1358.07	−0.926909
$130$	314.805	0.212386
$131$	2508.62	1.67312	0.836561	−	0.547874i	$-0.184563\pi$
$131$	2508.62	1.67312	0.836561	+	0.547874i	$0.184563\pi$
$132$	−132.000	−0.0870388
$133$	876.824	0.571656
$134$	−568.843	−0.366720
$135$	−82.9879	−0.0529071
$136$	308.198	0.194322
$137$	−2427.16	−1.51363	−0.756813	−	0.653632i	$-0.773244\pi$
$137$	−2427.16	−1.51363	−0.756813	+	0.653632i	$0.773244\pi$
$138$	249.588	0.153959
$139$	−852.922	−0.520459	−0.260230	−	0.965547i	$-0.583798\pi$
$139$	−852.922	−0.520459	−0.260230	+	0.965547i	$0.583798\pi$
$140$	100.679	0.0607779
$141$	1801.76	1.07614
$142$	867.707	0.512791
$143$	−563.317	−0.329419
$144$	144.000	0.0833333
$145$	562.113	0.321937
$146$	525.817	0.298061
$147$	827.825	0.464475
$148$	−148.000	−0.0821995
$149$	−918.974	−0.505270	−0.252635	−	0.967562i	$-0.581297\pi$
$149$	−918.974	−0.505270	−0.252635	+	0.967562i	$0.581297\pi$
$150$	−693.317	−0.377394
$151$	−298.176	−0.160697	−0.0803485	−	0.996767i	$-0.525603\pi$
$151$	−298.176	−0.160697	−0.0803485	+	0.996767i	$0.525603\pi$
$152$	−856.596	−0.457099
$153$	−346.723	−0.183208
$154$	−180.156	−0.0942688
$155$	−438.744	−0.227360
$156$	614.527	0.315395
$157$	1534.87	0.780229	0.390114	−	0.920766i	$-0.372436\pi$
$157$	1534.87	0.780229	0.390114	+	0.920766i	$0.372436\pi$
$158$	776.988	0.391227
$159$	583.811	0.291190
$160$	−98.3560	−0.0485983
$161$	340.643	0.166748
$162$	−162.000	−0.0785674
$163$	1885.38	0.905980	0.452990	−	0.891516i	$-0.350357\pi$
$163$	1885.38	0.905980	0.452990	+	0.891516i	$0.350357\pi$
$164$	569.002	0.270924
$165$	−101.430	−0.0478563
$166$	499.987	0.233774
$167$	−836.534	−0.387622	−0.193811	−	0.981039i	$-0.562085\pi$
$167$	−836.534	−0.387622	−0.193811	+	0.981039i	$0.562085\pi$
$168$	196.534	0.0902555
$169$	425.526	0.193685
$170$	236.821	0.106843
$171$	963.670	0.430957
$172$	1810.76	0.802727
$173$	3301.99	1.45113	0.725565	−	0.688154i	$-0.241579\pi$
$173$	3301.99	1.45113	0.725565	+	0.688154i	$0.241579\pi$
$174$	1097.30	0.478079
$175$	−946.253	−0.408743
$176$	176.000	0.0753778
$177$	−1560.97	−0.662878
$178$	2822.77	1.18862
$179$	989.749	0.413281	0.206641	−	0.978417i	$-0.433747\pi$
$179$	989.749	0.413281	0.206641	+	0.978417i	$0.433747\pi$
$180$	110.651	0.0458189
$181$	3921.76	1.61051	0.805254	−	0.592930i	$-0.202029\pi$
$181$	3921.76	1.61051	0.805254	+	0.592930i	$0.202029\pi$
$182$	838.719	0.341593
$183$	216.452	0.0874349
$184$	−332.784	−0.133332
$185$	−113.724	−0.0451955
$186$	−856.469	−0.337631
$187$	−423.772	−0.165718
$188$	−2402.35	−0.931965
$189$	−221.101	−0.0850937
$190$	−658.214	−0.251325
$191$	1158.72	0.438965	0.219483	−	0.975616i	$-0.429563\pi$
$191$	1158.72	0.438965	0.219483	+	0.975616i	$0.429563\pi$
$192$	−192.000	−0.0721688
$193$	−2360.03	−0.880201	−0.440100	−	0.897949i	$-0.645057\pi$
$193$	−2360.03	−0.880201	−0.440100	+	0.897949i	$0.645057\pi$
$194$	−39.0323	−0.0144451
$195$	472.207	0.173412
$196$	−1103.77	−0.402247
$197$	−4004.70	−1.44834	−0.724170	−	0.689621i	$-0.757777\pi$
$197$	−4004.70	−1.44834	−0.724170	+	0.689621i	$0.757777\pi$
$198$	−198.000	−0.0710669
$199$	2980.05	1.06156	0.530778	−	0.847511i	$-0.321900\pi$
$199$	2980.05	1.06156	0.530778	+	0.847511i	$0.321900\pi$
$200$	924.423	0.326833
$201$	−853.264	−0.299426
$202$	123.289	0.0429435
$203$	1497.61	0.517792
$204$	462.297	0.158663
$205$	437.225	0.148962
$206$	−484.529	−0.163877
$207$	374.382	0.125707
$208$	−819.370	−0.273140
$209$	1177.82	0.389816
$210$	151.018	0.0496249
$211$	−655.330	−0.213814	−0.106907	−	0.994269i	$-0.534095\pi$
$211$	−655.330	−0.213814	−0.106907	+	0.994269i	$0.534095\pi$
$212$	−778.415	−0.252178
$213$	1301.56	0.418692
$214$	−947.665	−0.302715
$215$	1391.40	0.441361
$216$	216.000	0.0680414
$217$	−1168.93	−0.365677
$218$	−2650.10	−0.823338
$219$	788.725	0.243366
$220$	135.240	0.0414448
$221$	1972.87	0.600497
$222$	−222.000	−0.0671156
$223$	−2030.02	−0.609598	−0.304799	−	0.952417i	$-0.598589\pi$
$223$	−2030.02	−0.609598	−0.304799	+	0.952417i	$0.598589\pi$
$224$	−262.045	−0.0781636
$225$	−1039.98	−0.308141
$226$	204.361	0.0601499
$227$	−5127.11	−1.49911	−0.749556	−	0.661941i	$-0.769733\pi$
$227$	−5127.11	−1.49911	−0.749556	+	0.661941i	$0.769733\pi$
$228$	−1284.89	−0.373220
$229$	−5277.52	−1.52292	−0.761460	−	0.648212i	$-0.775517\pi$
$229$	−5277.52	−1.52292	−0.761460	+	0.648212i	$0.775517\pi$
$230$	−255.714	−0.0733098
$231$	−270.234	−0.0769702
$232$	−1463.06	−0.414029
$233$	−5012.75	−1.40942	−0.704712	−	0.709493i	$-0.748924\pi$
$233$	−5012.75	−1.40942	−0.704712	+	0.709493i	$0.748924\pi$
$234$	921.791	0.257519
$235$	−1845.98	−0.512419
$236$	2081.29	0.574070
$237$	1165.48	0.319436
$238$	630.952	0.171843
$239$	4511.89	1.22113	0.610564	−	0.791967i	$-0.290943\pi$
$239$	4511.89	1.22113	0.610564	+	0.791967i	$0.290943\pi$
$240$	−147.534	−0.0396803
$241$	4363.49	1.16629	0.583147	−	0.812367i	$-0.301821\pi$
$241$	4363.49	1.16629	0.583147	+	0.812367i	$0.301821\pi$
$242$	−242.000	−0.0642824
$243$	−243.000	−0.0641500
$244$	−288.602	−0.0757208
$245$	−848.141	−0.221166
$246$	853.503	0.221209
$247$	−5483.35	−1.41254
$248$	1141.96	0.292397
$249$	749.981	0.190876
$250$	1478.74	0.374095
$251$	3805.21	0.956904	0.478452	−	0.878114i	$-0.341198\pi$
$251$	3805.21	0.956904	0.478452	+	0.878114i	$0.341198\pi$
$252$	294.801	0.0736933
$253$	457.578	0.113706
$254$	−1034.20	−0.255479
$255$	355.232	0.0872372
$256$	256.000	0.0625000
$257$	−2570.55	−0.623917	−0.311958	−	0.950096i	$-0.600985\pi$
$257$	−2570.55	−0.623917	−0.311958	+	0.950096i	$0.600985\pi$
$258$	2716.14	0.655424
$259$	−302.990	−0.0726907
$260$	−629.609	−0.150180
$261$	1645.94	0.390350
$262$	−5017.24	−1.18308
$263$	2568.18	0.602133	0.301067	−	0.953603i	$-0.402657\pi$
$263$	2568.18	0.602133	0.301067	+	0.953603i	$0.402657\pi$
$264$	264.000	0.0615457
$265$	−598.139	−0.138654
$266$	−1753.65	−0.404222
$267$	4234.15	0.970508
$268$	1137.69	0.259310
$269$	659.031	0.149375	0.0746874	−	0.997207i	$-0.476204\pi$
$269$	659.031	0.149375	0.0746874	+	0.997207i	$0.476204\pi$
$270$	165.976	0.0374110
$271$	−5893.87	−1.32113	−0.660566	−	0.750768i	$-0.729684\pi$
$271$	−5893.87	−1.32113	−0.660566	+	0.750768i	$0.729684\pi$
$272$	−616.396	−0.137406
$273$	1258.08	0.278910
$274$	4854.33	1.07029
$275$	−1271.08	−0.278724
$276$	−499.176	−0.108865
$277$	−758.047	−0.164428	−0.0822141	−	0.996615i	$-0.526199\pi$
$277$	−758.047	−0.164428	−0.0822141	+	0.996615i	$0.526199\pi$
$278$	1705.84	0.368020
$279$	−1284.70	−0.275674
$280$	−201.357	−0.0429765
$281$	−8423.49	−1.78827	−0.894134	−	0.447800i	$-0.852208\pi$
$281$	−8423.49	−1.78827	−0.894134	+	0.447800i	$0.852208\pi$
$282$	−3603.52	−0.760946
$283$	−4328.87	−0.909275	−0.454638	−	0.890676i	$-0.650231\pi$
$283$	−4328.87	−0.909275	−0.454638	+	0.890676i	$0.650231\pi$
$284$	−1735.41	−0.362598
$285$	−987.321	−0.205206
$286$	1126.63	0.232934
$287$	1164.88	0.239584
$288$	−288.000	−0.0589256
$289$	−3428.84	−0.697913
$290$	−1124.23	−0.227644
$291$	−58.5484	−0.0117944
$292$	−1051.63	−0.210761
$293$	−8785.59	−1.75174	−0.875869	−	0.482548i	$-0.839711\pi$
$293$	−8785.59	−1.75174	−0.875869	+	0.482548i	$0.839711\pi$
$294$	−1655.65	−0.328434
$295$	1599.28	0.315639
$296$	296.000	0.0581238
$297$	−297.000	−0.0580259
$298$	1837.95	0.357280
$299$	−2130.26	−0.412027
$300$	1386.63	0.266858
$301$	3707.04	0.709868
$302$	596.353	0.113630
$303$	184.933	0.0350632
$304$	1713.19	0.323218
$305$	−221.764	−0.0416334
$306$	693.445	0.129548
$307$	2466.05	0.458453	0.229226	−	0.973373i	$-0.426380\pi$
$307$	2466.05	0.458453	0.229226	+	0.973373i	$0.426380\pi$
$308$	360.312	0.0666581
$309$	−726.794	−0.133805
$310$	877.488	0.160768
$311$	8340.19	1.52067	0.760336	−	0.649530i	$-0.225034\pi$
$311$	8340.19	1.52067	0.760336	+	0.649530i	$0.225034\pi$
$312$	−1229.05	−0.223018
$313$	7650.77	1.38162	0.690810	−	0.723036i	$-0.257254\pi$
$313$	7650.77	1.38162	0.690810	+	0.723036i	$0.257254\pi$
$314$	−3069.74	−0.551705
$315$	226.527	0.0405186
$316$	−1553.98	−0.276639
$317$	−2797.81	−0.495711	−0.247856	−	0.968797i	$-0.579726\pi$
$317$	−2797.81	−0.495711	−0.247856	+	0.968797i	$0.579726\pi$
$318$	−1167.62	−0.205903
$319$	2011.71	0.353085
$320$	196.712	0.0343642
$321$	−1421.50	−0.247166
$322$	−681.286	−0.117909
$323$	−4125.01	−0.710594
$324$	324.000	0.0555556
$325$	5917.53	1.00999
$326$	−3770.77	−0.640624
$327$	−3975.16	−0.672253
$328$	−1138.00	−0.191572
$329$	−4918.16	−0.824155
$330$	202.859	0.0338395
$331$	5279.51	0.876701	0.438351	−	0.898804i	$-0.355563\pi$
$331$	5279.51	0.876701	0.438351	+	0.898804i	$0.355563\pi$
$332$	−999.975	−0.165303
$333$	−333.000	−0.0547997
$334$	1673.07	0.274090
$335$	874.205	0.142576
$336$	−393.068	−0.0638203
$337$	−8993.90	−1.45379	−0.726897	−	0.686746i	$-0.759038\pi$
$337$	−8993.90	−1.45379	−0.726897	+	0.686746i	$0.759038\pi$
$338$	−851.051	−0.136956
$339$	306.541	0.0491122
$340$	−473.643	−0.0755496
$341$	−1570.19	−0.249357
$342$	−1927.34	−0.304733
$343$	−5068.46	−0.797875
$344$	−3621.52	−0.567614
$345$	−383.570	−0.0598572
$346$	−6603.98	−1.02610
$347$	−6719.14	−1.03949	−0.519744	−	0.854322i	$-0.673973\pi$
$347$	−6719.14	−1.03949	−0.519744	+	0.854322i	$0.673973\pi$
$348$	−2194.59	−0.338053
$349$	8423.73	1.29201	0.646006	−	0.763333i	$-0.276438\pi$
$349$	8423.73	1.29201	0.646006	+	0.763333i	$0.276438\pi$
$350$	1892.51	0.289025
$351$	1382.69	0.210263
$352$	−352.000	−0.0533002
$353$	177.391	0.0267467	0.0133734	−	0.999911i	$-0.495743\pi$
$353$	177.391	0.0267467	0.0133734	+	0.999911i	$0.495743\pi$
$354$	3121.93	0.468726
$355$	−1333.50	−0.199366
$356$	−5645.53	−0.840485
$357$	946.428	0.140309
$358$	−1979.50	−0.292234
$359$	−7598.01	−1.11701	−0.558507	−	0.829500i	$-0.688626\pi$
$359$	−7598.01	−1.11701	−0.558507	+	0.829500i	$0.688626\pi$
$360$	−221.301	−0.0323989
$361$	4605.94	0.671517
$362$	−7843.51	−1.13880
$363$	−363.000	−0.0524864
$364$	−1677.44	−0.241543
$365$	−808.082	−0.115882
$366$	−432.904	−0.0618258
$367$	12598.1	1.79187	0.895933	−	0.444188i	$-0.146508\pi$
$367$	12598.1	1.79187	0.895933	+	0.444188i	$0.146508\pi$
$368$	665.568	0.0942803
$369$	1280.25	0.180616
$370$	227.448	0.0319580
$371$	−1593.59	−0.223006
$372$	1712.94	0.238741
$373$	−7416.15	−1.02947	−0.514737	−	0.857348i	$-0.672110\pi$
$373$	−7416.15	−1.02947	−0.514737	+	0.857348i	$0.672110\pi$
$374$	847.544	0.117180
$375$	2218.11	0.305447
$376$	4804.70	0.658999
$377$	−9365.53	−1.27944
$378$	442.202	0.0601704
$379$	−4963.72	−0.672743	−0.336371	−	0.941729i	$-0.609200\pi$
$379$	−4963.72	−0.672743	−0.336371	+	0.941729i	$0.609200\pi$
$380$	1316.43	0.177714
$381$	−1551.31	−0.208598
$382$	−2317.45	−0.310395
$383$	−13935.6	−1.85920	−0.929602	−	0.368564i	$-0.879850\pi$
$383$	−13935.6	−1.85920	−0.929602	+	0.368564i	$0.879850\pi$
$384$	384.000	0.0510310
$385$	276.866	0.0366504
$386$	4720.06	0.622396
$387$	4074.21	0.535151
$388$	78.0646	0.0102142
$389$	4763.57	0.620881	0.310440	−	0.950593i	$-0.399523\pi$
$389$	4763.57	0.620881	0.310440	+	0.950593i	$0.399523\pi$
$390$	−944.414	−0.122621
$391$	−1602.55	−0.207275
$392$	2207.53	0.284432
$393$	−7525.86	−0.965978
$394$	8009.40	1.02413
$395$	−1194.09	−0.152104
$396$	396.000	0.0502519
$397$	8796.08	1.11200	0.555999	−	0.831183i	$-0.312336\pi$
$397$	8796.08	1.11200	0.555999	+	0.831183i	$0.312336\pi$
$398$	−5960.09	−0.750634
$399$	−2630.47	−0.330046
$400$	−1848.85	−0.231106
$401$	−6638.46	−0.826706	−0.413353	−	0.910571i	$-0.635642\pi$
$401$	−6638.46	−0.826706	−0.413353	+	0.910571i	$0.635642\pi$
$402$	1706.53	0.211726
$403$	7310.05	0.903572
$404$	−246.578	−0.0303656
$405$	248.964	0.0305459
$406$	−2995.22	−0.366134
$407$	−407.000	−0.0495682
$408$	−924.594	−0.112192
$409$	868.442	0.104992	0.0524960	−	0.998621i	$-0.483282\pi$
$409$	868.442	0.104992	0.0524960	+	0.998621i	$0.483282\pi$
$410$	−874.450	−0.105332
$411$	7281.49	0.873892
$412$	969.058	0.115879
$413$	4260.88	0.507661
$414$	−748.764	−0.0888883
$415$	−768.387	−0.0908883
$416$	1638.74	0.193139
$417$	2558.76	0.300487
$418$	−2355.64	−0.275641
$419$	−8289.12	−0.966467	−0.483234	−	0.875491i	$-0.660538\pi$
$419$	−8289.12	−0.966467	−0.483234	+	0.875491i	$0.660538\pi$
$420$	−302.036	−0.0350901
$421$	−5622.66	−0.650906	−0.325453	−	0.945558i	$-0.605517\pi$
$421$	−5622.66	−0.650906	−0.325453	+	0.945558i	$0.605517\pi$
$422$	1310.66	0.151189
$423$	−5405.29	−0.621310
$424$	1556.83	0.178317
$425$	4451.64	0.508085
$426$	−2603.12	−0.296060
$427$	−590.836	−0.0669614
$428$	1895.33	0.214052
$429$	1689.95	0.190190
$430$	−2782.80	−0.312089
$431$	−15296.5	−1.70953	−0.854764	−	0.519016i	$-0.826298\pi$
$431$	−15296.5	−1.70953	−0.854764	+	0.519016i	$0.826298\pi$
$432$	−432.000	−0.0481125
$433$	7436.26	0.825321	0.412660	−	0.910885i	$-0.364600\pi$
$433$	7436.26	0.825321	0.412660	+	0.910885i	$0.364600\pi$
$434$	2337.85	0.258572
$435$	−1686.34	−0.185871
$436$	5300.21	0.582188
$437$	4454.08	0.487569
$438$	−1577.45	−0.172086
$439$	−11640.5	−1.26554	−0.632769	−	0.774340i	$-0.718082\pi$
$439$	−11640.5	−1.26554	−0.632769	+	0.774340i	$0.718082\pi$
$440$	−270.479	−0.0293059
$441$	−2483.47	−0.268165
$442$	−3945.75	−0.424616
$443$	−3470.66	−0.372226	−0.186113	−	0.982528i	$-0.559589\pi$
$443$	−3470.66	−0.372226	−0.186113	+	0.982528i	$0.559589\pi$
$444$	444.000	0.0474579
$445$	−4338.06	−0.462121
$446$	4060.05	0.431051
$447$	2756.92	0.291718
$448$	524.091	0.0552700
$449$	3597.29	0.378099	0.189050	−	0.981968i	$-0.439459\pi$
$449$	3597.29	0.378099	0.189050	+	0.981968i	$0.439459\pi$
$450$	2079.95	0.217888
$451$	1564.76	0.163374
$452$	−408.721	−0.0425324
$453$	894.529	0.0927784
$454$	10254.2	1.06003
$455$	−1288.95	−0.132807
$456$	2569.79	0.263906
$457$	−4089.05	−0.418551	−0.209275	−	0.977857i	$-0.567111\pi$
$457$	−4089.05	−0.418551	−0.209275	+	0.977857i	$0.567111\pi$
$458$	10555.0	1.07687
$459$	1040.17	0.105775
$460$	511.427	0.0518378
$461$	−10004.1	−1.01071	−0.505353	−	0.862913i	$-0.668638\pi$
$461$	−10004.1	−1.01071	−0.505353	+	0.862913i	$0.668638\pi$
$462$	540.469	0.0544261
$463$	2114.41	0.212235	0.106117	−	0.994354i	$-0.466158\pi$
$463$	2114.41	0.212235	0.106117	+	0.994354i	$0.466158\pi$
$464$	2926.12	0.292763
$465$	1316.23	0.131266
$466$	10025.5	0.996614
$467$	−17113.2	−1.69573	−0.847866	−	0.530211i	$-0.822113\pi$
$467$	−17113.2	−1.69573	−0.847866	+	0.530211i	$0.822113\pi$
$468$	−1843.58	−0.182093
$469$	2329.10	0.229313
$470$	3691.96	0.362335
$471$	−4604.61	−0.450465
$472$	−4162.58	−0.405929
$473$	4979.59	0.484063
$474$	−2330.97	−0.225875
$475$	−12372.8	−1.19516
$476$	−1261.90	−0.121511
$477$	−1751.43	−0.168119
$478$	−9023.77	−0.863468
$479$	−12132.7	−1.15732	−0.578659	−	0.815570i	$-0.696424\pi$
$479$	−12132.7	−1.15732	−0.578659	+	0.815570i	$0.696424\pi$
$480$	295.068	0.0280582
$481$	1894.79	0.179616
$482$	−8726.97	−0.824695
$483$	−1021.93	−0.0962719
$484$	484.000	0.0454545
$485$	59.9853	0.00561607
$486$	486.000	0.0453609
$487$	−19366.3	−1.80199	−0.900997	−	0.433825i	$-0.857164\pi$
$487$	−19366.3	−1.80199	−0.900997	+	0.433825i	$0.857164\pi$
$488$	577.205	0.0535427
$489$	−5656.15	−0.523068
$490$	1696.28	0.156388
$491$	−12743.2	−1.17127	−0.585635	−	0.810575i	$-0.699155\pi$
$491$	−12743.2	−1.17127	−0.585635	+	0.810575i	$0.699155\pi$
$492$	−1707.01	−0.156418
$493$	−7045.50	−0.643638
$494$	10966.7	0.998816
$495$	304.289	0.0276298
$496$	−2283.92	−0.206756
$497$	−3552.79	−0.320653
$498$	−1499.96	−0.134970
$499$	−11982.8	−1.07500	−0.537499	−	0.843264i	$-0.680631\pi$
$499$	−11982.8	−1.07500	−0.537499	+	0.843264i	$0.680631\pi$
$500$	−2957.48	−0.264525
$501$	2509.60	0.223794
$502$	−7610.42	−0.676633
$503$	−10130.4	−0.897996	−0.448998	−	0.893533i	$-0.648219\pi$
$503$	−10130.4	−0.897996	−0.448998	+	0.893533i	$0.648219\pi$
$504$	−589.602	−0.0521091
$505$	−189.472	−0.0166958
$506$	−915.156	−0.0804025
$507$	−1276.58	−0.111824
$508$	2068.41	0.180651
$509$	2447.72	0.213150	0.106575	−	0.994305i	$-0.466012\pi$
$509$	2447.72	0.213150	0.106575	+	0.994305i	$0.466012\pi$
$510$	−710.464	−0.0616860
$511$	−2152.94	−0.186380
$512$	−512.000	−0.0441942
$513$	−2891.01	−0.248813
$514$	5141.10	0.441176
$515$	744.631	0.0637133
$516$	−5432.28	−0.463455
$517$	−6606.46	−0.561996
$518$	605.980	0.0514001
$519$	−9905.96	−0.837810
$520$	1259.22	0.106193
$521$	6697.04	0.563153	0.281577	−	0.959539i	$-0.409143\pi$
$521$	6697.04	0.563153	0.281577	+	0.959539i	$0.409143\pi$
$522$	−3291.89	−0.276019
$523$	−10744.5	−0.898328	−0.449164	−	0.893449i	$-0.648278\pi$
$523$	−10744.5	−0.898328	−0.449164	+	0.893449i	$0.648278\pi$
$524$	10034.5	0.836561
$525$	2838.76	0.235988
$526$	−5136.37	−0.425772
$527$	5499.20	0.454552
$528$	−528.000	−0.0435194
$529$	−10436.6	−0.857780
$530$	1196.28	0.0980434
$531$	4682.90	0.382713
$532$	3507.30	0.285828
$533$	−7284.74	−0.592002
$534$	−8468.30	−0.686253
$535$	1456.38	0.117692
$536$	−2275.37	−0.183360
$537$	−2969.25	−0.238608
$538$	−1318.06	−0.105624
$539$	−3035.36	−0.242564
$540$	−331.952	−0.0264536
$541$	10113.2	0.803694	0.401847	−	0.915707i	$-0.368368\pi$
$541$	10113.2	0.803694	0.401847	+	0.915707i	$0.368368\pi$
$542$	11787.7	0.934182
$543$	−11765.3	−0.929827
$544$	1232.79	0.0971608
$545$	4072.71	0.320103
$546$	−2516.16	−0.197219
$547$	2413.40	0.188646	0.0943231	−	0.995542i	$-0.469931\pi$
$547$	2413.40	0.188646	0.0943231	+	0.995542i	$0.469931\pi$
$548$	−9708.66	−0.756813
$549$	−649.356	−0.0504805
$550$	2542.16	0.197088
$551$	19582.1	1.51402
$552$	998.352	0.0769795
$553$	−3181.35	−0.244638
$554$	1516.09	0.116268
$555$	341.173	0.0260936
$556$	−3411.69	−0.260230
$557$	−2425.44	−0.184505	−0.0922524	−	0.995736i	$-0.529407\pi$
$557$	−2425.44	−0.184505	−0.0922524	+	0.995736i	$0.529407\pi$
$558$	2569.41	0.194931
$559$	−23182.5	−1.75405
$560$	402.715	0.0303889
$561$	1271.32	0.0956774
$562$	16847.0	1.26450
$563$	−17183.0	−1.28628	−0.643141	−	0.765748i	$-0.722369\pi$
$563$	−17183.0	−1.28628	−0.643141	+	0.765748i	$0.722369\pi$
$564$	7207.05	0.538070
$565$	−314.064	−0.0233855
$566$	8657.75	0.642955
$567$	663.302	0.0491289
$568$	3470.83	0.256396
$569$	−6320.15	−0.465649	−0.232825	−	0.972519i	$-0.574797\pi$
$569$	−6320.15	−0.465649	−0.232825	+	0.972519i	$0.574797\pi$
$570$	1974.64	0.145103
$571$	−500.896	−0.0367108	−0.0183554	−	0.999832i	$-0.505843\pi$
$571$	−500.896	−0.0367108	−0.0183554	+	0.999832i	$0.505843\pi$
$572$	−2253.27	−0.164709
$573$	−3476.17	−0.253437
$574$	−2329.76	−0.169411
$575$	−4806.77	−0.348619
$576$	576.000	0.0416667
$577$	−10608.2	−0.765383	−0.382692	−	0.923876i	$-0.625003\pi$
$577$	−10608.2	−0.765383	−0.382692	+	0.923876i	$0.625003\pi$
$578$	6857.69	0.493499
$579$	7080.09	0.508184
$580$	2248.45	0.160969
$581$	−2047.18	−0.146181
$582$	117.097	0.00833990
$583$	−2140.64	−0.152069
$584$	2103.27	0.149031
$585$	−1416.62	−0.100120
$586$	17571.2	1.23867
$587$	4.95996	0.000348755 0	0.000174378	−	1.00000i	$-0.499944\pi$
$587$	4.95996	0.000348755 0	0.000174378		1.00000i	$0.499944\pi$
$588$	3311.30	0.232238
$589$	−15284.3	−1.06924
$590$	−3198.55	−0.223190
$591$	12014.1	0.836200
$592$	−592.000	−0.0410997
$593$	15786.1	1.09318	0.546592	−	0.837399i	$-0.315925\pi$
$593$	15786.1	1.09318	0.546592	+	0.837399i	$0.315925\pi$
$594$	594.000	0.0410305
$595$	−969.655	−0.0668101
$596$	−3675.90	−0.252635
$597$	−8940.14	−0.612890
$598$	4260.52	0.291347
$599$	4694.49	0.320219	0.160110	−	0.987099i	$-0.448815\pi$
$599$	4694.49	0.320219	0.160110	+	0.987099i	$0.448815\pi$
$600$	−2773.27	−0.188697
$601$	12784.0	0.867668	0.433834	−	0.900993i	$-0.357160\pi$
$601$	12784.0	0.867668	0.433834	+	0.900993i	$0.357160\pi$
$602$	−7414.08	−0.501952
$603$	2559.79	0.172874
$604$	−1192.71	−0.0803485
$605$	371.909	0.0249921
$606$	−369.867	−0.0247934
$607$	28949.0	1.93576	0.967879	−	0.251416i	$-0.0808961\pi$
$607$	28949.0	1.93576	0.967879	+	0.251416i	$0.0808961\pi$
$608$	−3426.38	−0.228550
$609$	−4492.83	−0.298947
$610$	443.528	0.0294392
$611$	30756.4	2.03645
$612$	−1386.89	−0.0916041
$613$	16031.7	1.05630	0.528150	−	0.849151i	$-0.322886\pi$
$613$	16031.7	1.05630	0.528150	+	0.849151i	$0.322886\pi$
$614$	−4932.10	−0.324175
$615$	−1311.67	−0.0860030
$616$	−720.625	−0.0471344
$617$	15815.1	1.03191	0.515957	−	0.856615i	$-0.327437\pi$
$617$	15815.1	1.03191	0.515957	+	0.856615i	$0.327437\pi$
$618$	1453.59	0.0946147
$619$	−11831.8	−0.768271	−0.384135	−	0.923277i	$-0.625500\pi$
$619$	−11831.8	−0.768271	−0.384135	+	0.923277i	$0.625500\pi$
$620$	−1754.98	−0.113680
$621$	−1123.15	−0.0725770
$622$	−16680.4	−1.07528
$623$	−11557.7	−0.743258
$624$	2458.11	0.157697
$625$	12171.6	0.778980
$626$	−15301.5	−0.976953
$627$	−3533.46	−0.225060
$628$	6139.48	0.390114
$629$	1425.42	0.0903577
$630$	−453.054	−0.0286510
$631$	−17812.8	−1.12380	−0.561899	−	0.827206i	$-0.689929\pi$
$631$	−17812.8	−1.12380	−0.561899	+	0.827206i	$0.689929\pi$
$632$	3107.95	0.195614
$633$	1965.99	0.123446
$634$	5595.61	0.350521
$635$	1589.38	0.0993269
$636$	2335.25	0.145595
$637$	14131.1	0.878958
$638$	−4023.42	−0.249669
$639$	−3904.68	−0.241732
$640$	−393.424	−0.0242991
$641$	−12948.8	−0.797891	−0.398945	−	0.916975i	$-0.630624\pi$
$641$	−12948.8	−0.797891	−0.398945	+	0.916975i	$0.630624\pi$
$642$	2843.00	0.174773
$643$	−22805.5	−1.39870	−0.699349	−	0.714781i	$-0.746527\pi$
$643$	−22805.5	−1.39870	−0.699349	+	0.714781i	$0.746527\pi$
$644$	1362.57	0.0833739
$645$	−4174.20	−0.254820
$646$	8250.03	0.502466
$647$	−1321.81	−0.0803177	−0.0401588	−	0.999193i	$-0.512786\pi$
$647$	−1321.81	−0.0803177	−0.0401588	+	0.999193i	$0.512786\pi$
$648$	−648.000	−0.0392837
$649$	5723.55	0.346177
$650$	−11835.1	−0.714168
$651$	3506.78	0.211124
$652$	7541.54	0.452990
$653$	−18001.0	−1.07876	−0.539382	−	0.842061i	$-0.681342\pi$
$653$	−18001.0	−1.07876	−0.539382	+	0.842061i	$0.681342\pi$
$654$	7950.31	0.475354
$655$	7710.56	0.459964
$656$	2276.01	0.135462
$657$	−2366.18	−0.140507
$658$	9836.32	0.582766
$659$	−14021.0	−0.828804	−0.414402	−	0.910094i	$-0.636009\pi$
$659$	−14021.0	−0.828804	−0.414402	+	0.910094i	$0.636009\pi$
$660$	−405.719	−0.0239281
$661$	−10779.2	−0.634287	−0.317144	−	0.948378i	$-0.602724\pi$
$661$	−10779.2	−0.634287	−0.317144	+	0.948378i	$0.602724\pi$
$662$	−10559.0	−0.619921
$663$	−5918.62	−0.346697
$664$	1999.95	0.116887
$665$	2695.03	0.157156
$666$	666.000	0.0387492
$667$	7607.55	0.441628
$668$	−3346.13	−0.193811
$669$	6090.07	0.351952
$670$	−1748.41	−0.100816
$671$	−793.657	−0.0456614
$672$	786.136	0.0451278
$673$	8704.75	0.498579	0.249289	−	0.968429i	$-0.419803\pi$
$673$	8704.75	0.498579	0.249289	+	0.968429i	$0.419803\pi$
$674$	17987.8	1.02799
$675$	3119.93	0.177905
$676$	1702.10	0.0968424
$677$	11295.9	0.641265	0.320633	−	0.947204i	$-0.396105\pi$
$677$	11295.9	0.641265	0.320633	+	0.947204i	$0.396105\pi$
$678$	−613.082	−0.0347275
$679$	159.816	0.00903267
$680$	947.285	0.0534217
$681$	15381.3	0.865512
$682$	3140.39	0.176322
$683$	−7481.67	−0.419148	−0.209574	−	0.977793i	$-0.567208\pi$
$683$	−7481.67	−0.419148	−0.209574	+	0.977793i	$0.567208\pi$
$684$	3854.68	0.215479
$685$	−7460.20	−0.416116
$686$	10136.9	0.564183
$687$	15832.6	0.879258
$688$	7243.03	0.401363
$689$	9965.78	0.551039
$690$	767.141	0.0423254
$691$	−8279.75	−0.455827	−0.227914	−	0.973681i	$-0.573190\pi$
$691$	−8279.75	−0.455827	−0.227914	+	0.973681i	$0.573190\pi$
$692$	13208.0	0.725565
$693$	810.703	0.0444388
$694$	13438.3	0.735029
$695$	−2621.56	−0.143081
$696$	4389.18	0.239040
$697$	−5480.16	−0.297813
$698$	−16847.5	−0.913590
$699$	15038.2	0.813732
$700$	−3785.01	−0.204371
$701$	486.188	0.0261955	0.0130978	−	0.999914i	$-0.495831\pi$
$701$	486.188	0.0261955	0.0130978	+	0.999914i	$0.495831\pi$
$702$	−2765.37	−0.148678
$703$	−3961.75	−0.212547
$704$	704.000	0.0376889
$705$	5537.94	0.295845
$706$	−354.783	−0.0189128
$707$	−504.801	−0.0268529
$708$	−6243.87	−0.331439
$709$	2200.07	0.116538	0.0582689	−	0.998301i	$-0.481442\pi$
$709$	2200.07	0.116538	0.0582689	+	0.998301i	$0.481442\pi$
$710$	2667.01	0.140973
$711$	−3496.45	−0.184426
$712$	11291.1	0.594312
$713$	−5937.90	−0.311888
$714$	−1892.86	−0.0992134
$715$	−1731.42	−0.0905617
$716$	3959.00	0.206641
$717$	−13535.7	−0.705019
$718$	15196.0	0.789848
$719$	11192.3	0.580532	0.290266	−	0.956946i	$-0.406256\pi$
$719$	11192.3	0.580532	0.290266	+	0.956946i	$0.406256\pi$
$720$	442.602	0.0229095
$721$	1983.89	0.102474
$722$	−9211.88	−0.474835
$723$	−13090.5	−0.673360
$724$	15687.0	0.805254
$725$	−21132.6	−1.08255
$726$	726.000	0.0371135
$727$	19784.7	1.00932	0.504660	−	0.863318i	$-0.331618\pi$
$727$	19784.7	1.00932	0.504660	+	0.863318i	$0.331618\pi$
$728$	3354.88	0.170797
$729$	729.000	0.0370370
$730$	1616.16	0.0819410
$731$	−17439.7	−0.882397
$732$	865.807	0.0437174
$733$	38236.7	1.92675	0.963373	−	0.268166i	$-0.0864176\pi$
$733$	38236.7	1.92675	0.963373	+	0.268166i	$0.0864176\pi$
$734$	−25196.2	−1.26704
$735$	2544.42	0.127690
$736$	−1331.14	−0.0666662
$737$	3128.63	0.156370
$738$	−2560.51	−0.127715
$739$	−23571.1	−1.17331	−0.586656	−	0.809836i	$-0.699556\pi$
$739$	−23571.1	−1.17331	−0.586656	+	0.809836i	$0.699556\pi$
$740$	−454.897	−0.0225978
$741$	16450.0	0.815529
$742$	3187.19	0.157689
$743$	−23302.1	−1.15056	−0.575282	−	0.817955i	$-0.695108\pi$
$743$	−23302.1	−1.15056	−0.575282	+	0.817955i	$0.695108\pi$
$744$	−3425.87	−0.168815
$745$	−2824.58	−0.138906
$746$	14832.3	0.727947
$747$	−2249.94	−0.110202
$748$	−1695.09	−0.0828590
$749$	3880.18	0.189291
$750$	−4436.22	−0.215984
$751$	−16972.8	−0.824698	−0.412349	−	0.911026i	$-0.635291\pi$
$751$	−16972.8	−0.824698	−0.412349	+	0.911026i	$0.635291\pi$
$752$	−9609.40	−0.465982
$753$	−11415.6	−0.552469
$754$	18731.1	0.904701
$755$	−916.482	−0.0441778
$756$	−884.403	−0.0425469
$757$	−26187.0	−1.25731	−0.628654	−	0.777685i	$-0.716394\pi$
$757$	−26187.0	−1.25731	−0.628654	+	0.777685i	$0.716394\pi$
$758$	9927.45	0.475701
$759$	−1372.73	−0.0656484
$760$	−2632.85	−0.125663
$761$	5055.31	0.240808	0.120404	−	0.992725i	$-0.461581\pi$
$761$	5055.31	0.240808	0.120404	+	0.992725i	$0.461581\pi$
$762$	3102.61	0.147501
$763$	10850.7	0.514840
$764$	4634.90	0.219483
$765$	−1065.70	−0.0503664
$766$	27871.2	1.31466
$767$	−26646.0	−1.25441
$768$	−768.000	−0.0360844
$769$	−12297.1	−0.576651	−0.288325	−	0.957532i	$-0.593098\pi$
$769$	−12297.1	−0.576651	−0.288325	+	0.957532i	$0.593098\pi$
$770$	−553.733	−0.0259158
$771$	7711.65	0.360218
$772$	−9440.13	−0.440100
$773$	17375.8	0.808493	0.404246	−	0.914650i	$-0.367534\pi$
$773$	17375.8	0.808493	0.404246	+	0.914650i	$0.367534\pi$
$774$	−8148.41	−0.378409
$775$	16494.6	0.764519
$776$	−156.129	−0.00722256
$777$	908.970	0.0419680
$778$	−9527.14	−0.439029
$779$	15231.4	0.700541
$780$	1888.83	0.0867062
$781$	−4772.39	−0.218655
$782$	3205.10	0.146566
$783$	−4937.83	−0.225369
$784$	−4415.07	−0.201124
$785$	4717.61	0.214495
$786$	15051.7	0.683049
$787$	−1443.69	−0.0653900	−0.0326950	−	0.999465i	$-0.510409\pi$
$787$	−1443.69	−0.0653900	−0.0326950	+	0.999465i	$0.510409\pi$
$788$	−16018.8	−0.724170
$789$	−7704.55	−0.347642
$790$	2388.17	0.107554
$791$	−836.747	−0.0376122
$792$	−792.000	−0.0355335
$793$	3694.88	0.165459
$794$	−17592.2	−0.786301
$795$	1794.42	0.0800521
$796$	11920.2	0.530778
$797$	−17895.1	−0.795330	−0.397665	−	0.917531i	$-0.630179\pi$
$797$	−17895.1	−0.795330	−0.397665	+	0.917531i	$0.630179\pi$
$798$	5260.94	0.233378
$799$	23137.5	1.02446
$800$	3697.69	0.163416
$801$	−12702.4	−0.560323
$802$	13276.9	0.584569
$803$	−2891.99	−0.127094
$804$	−3413.06	−0.149713
$805$	1047.01	0.0458412
$806$	−14620.1	−0.638922
$807$	−1977.09	−0.0862415
$808$	493.156	0.0214717
$809$	−36322.9	−1.57855	−0.789274	−	0.614041i	$-0.789543\pi$
$809$	−36322.9	−1.57855	−0.789274	+	0.614041i	$0.789543\pi$
$810$	−497.927	−0.0215992
$811$	−14521.2	−0.628742	−0.314371	−	0.949300i	$-0.601794\pi$
$811$	−14521.2	−0.628742	−0.314371	+	0.949300i	$0.601794\pi$
$812$	5990.44	0.258896
$813$	17681.6	0.762756
$814$	814.000	0.0350500
$815$	5794.97	0.249066
$816$	1849.19	0.0793315
$817$	48471.5	2.07565
$818$	−1736.88	−0.0742405
$819$	−3774.24	−0.161029
$820$	1748.90	0.0744808
$821$	3236.72	0.137591	0.0687956	−	0.997631i	$-0.478084\pi$
$821$	3236.72	0.137591	0.0687956	+	0.997631i	$0.478084\pi$
$822$	−14563.0	−0.617935
$823$	41242.3	1.74680	0.873400	−	0.487003i	$-0.161910\pi$
$823$	41242.3	1.74680	0.873400	+	0.487003i	$0.161910\pi$
$824$	−1938.12	−0.0819387
$825$	3813.24	0.160921
$826$	−8521.76	−0.358971
$827$	22725.4	0.955552	0.477776	−	0.878482i	$-0.341443\pi$
$827$	22725.4	0.955552	0.477776	+	0.878482i	$0.341443\pi$
$828$	1497.53	0.0628535
$829$	5236.53	0.219387	0.109694	−	0.993965i	$-0.465013\pi$
$829$	5236.53	0.219387	0.109694	+	0.993965i	$0.465013\pi$
$830$	1536.77	0.0642677
$831$	2274.14	0.0949327
$832$	−3277.48	−0.136570
$833$	10630.6	0.442170
$834$	−5117.53	−0.212477
$835$	−2571.19	−0.106563
$836$	4711.28	0.194908
$837$	3854.11	0.159161
$838$	16578.2	0.683396
$839$	12610.4	0.518901	0.259451	−	0.965756i	$-0.416459\pi$
$839$	12610.4	0.518901	0.259451	+	0.965756i	$0.416459\pi$
$840$	604.072	0.0248125
$841$	9057.05	0.371358
$842$	11245.3	0.460260
$843$	25270.5	1.03246
$844$	−2621.32	−0.106907
$845$	1307.91	0.0532466
$846$	10810.6	0.439332
$847$	990.859	0.0401964
$848$	−3113.66	−0.126089
$849$	12986.6	0.524970
$850$	−8903.28	−0.359271
$851$	−1539.13	−0.0619983
$852$	5206.24	0.209346
$853$	−42846.1	−1.71984	−0.859920	−	0.510430i	$-0.829486\pi$
$853$	−42846.1	−1.71984	−0.859920	+	0.510430i	$0.829486\pi$
$854$	1181.67	0.0473489
$855$	2961.96	0.118476
$856$	−3790.66	−0.151358
$857$	25052.1	0.998556	0.499278	−	0.866442i	$-0.333599\pi$
$857$	25052.1	0.998556	0.499278	+	0.866442i	$0.333599\pi$
$858$	−3379.90	−0.134485
$859$	31951.0	1.26910	0.634549	−	0.772883i	$-0.281186\pi$
$859$	31951.0	1.26910	0.634549	+	0.772883i	$0.281186\pi$
$860$	5565.59	0.220680
$861$	−3494.63	−0.138324
$862$	30593.0	1.20882
$863$	−16653.0	−0.656865	−0.328432	−	0.944528i	$-0.606520\pi$
$863$	−16653.0	−0.656865	−0.328432	+	0.944528i	$0.606520\pi$
$864$	864.000	0.0340207
$865$	10149.1	0.398935
$866$	−14872.5	−0.583590
$867$	10286.5	0.402940
$868$	−4675.70	−0.182838
$869$	−4273.44	−0.166820
$870$	3372.68	0.131430
$871$	−14565.4	−0.566624
$872$	−10600.4	−0.411669
$873$	175.645	0.00680950
$874$	−8908.17	−0.344764
$875$	−6054.64	−0.233925
$876$	3154.90	0.121683
$877$	36657.6	1.41145	0.705724	−	0.708486i	$-0.250622\pi$
$877$	36657.6	1.41145	0.705724	+	0.708486i	$0.250622\pi$
$878$	23281.0	0.894871
$879$	26356.8	1.01137
$880$	540.958	0.0207224
$881$	−19122.6	−0.731280	−0.365640	−	0.930756i	$-0.619150\pi$
$881$	−19122.6	−0.731280	−0.365640	+	0.930756i	$0.619150\pi$
$882$	4966.95	0.189621
$883$	580.239	0.0221139	0.0110570	−	0.999939i	$-0.496480\pi$
$883$	580.239	0.0221139	0.0110570	+	0.999939i	$0.496480\pi$
$884$	7891.50	0.300249
$885$	−4797.83	−0.182234
$886$	6941.32	0.263203
$887$	−17085.6	−0.646764	−0.323382	−	0.946269i	$-0.604820\pi$
$887$	−17085.6	−0.646764	−0.323382	+	0.946269i	$0.604820\pi$
$888$	−888.000	−0.0335578
$889$	4234.51	0.159753
$890$	8676.13	0.326769
$891$	891.000	0.0335013
$892$	−8120.09	−0.304799
$893$	−64307.6	−2.40982
$894$	−5513.84	−0.206276
$895$	3042.12	0.113617
$896$	−1048.18	−0.0390818
$897$	6390.78	0.237884
$898$	−7194.58	−0.267357
$899$	−26105.5	−0.968486
$900$	−4159.90	−0.154070
$901$	7497.06	0.277207
$902$	−3129.51	−0.115523
$903$	−11121.1	−0.409842
$904$	817.443	0.0300749
$905$	12054.0	0.442750
$906$	−1789.06	−0.0656043
$907$	16559.8	0.606241	0.303120	−	0.952952i	$-0.401972\pi$
$907$	16559.8	0.606241	0.303120	+	0.952952i	$0.401972\pi$
$908$	−20508.4	−0.749556
$909$	−554.800	−0.0202437
$910$	2577.91	0.0939086
$911$	−25847.7	−0.940035	−0.470018	−	0.882657i	$-0.655752\pi$
$911$	−25847.7	−0.940035	−0.470018	+	0.882657i	$0.655752\pi$
$912$	−5139.57	−0.186610
$913$	−2749.93	−0.0996817
$914$	8178.10	0.295960
$915$	665.292	0.0240370
$916$	−21110.1	−0.761460
$917$	20542.9	0.739788
$918$	−2080.34	−0.0747945
$919$	10191.6	0.365823	0.182911	−	0.983129i	$-0.441448\pi$
$919$	10191.6	0.365823	0.182911	+	0.983129i	$0.441448\pi$
$920$	−1022.85	−0.0366549
$921$	−7398.15	−0.264688
$922$	20008.1	0.714677
$923$	22217.9	0.792319
$924$	−1080.94	−0.0384851
$925$	4275.45	0.151974
$926$	−4228.81	−0.150073
$927$	2180.38	0.0772526
$928$	−5852.24	−0.207014
$929$	30519.6	1.07784	0.538921	−	0.842357i	$-0.318832\pi$
$929$	30519.6	1.07784	0.538921	+	0.842357i	$0.318832\pi$
$930$	−2632.46	−0.0928193
$931$	−29546.3	−1.04011
$932$	−20051.0	−0.704712
$933$	−25020.6	−0.877960
$934$	34226.5	1.19906
$935$	−1302.52	−0.0455581
$936$	3687.16	0.128759
$937$	13066.4	0.455560	0.227780	−	0.973713i	$-0.426853\pi$
$937$	13066.4	0.455560	0.227780	+	0.973713i	$0.426853\pi$
$938$	−4658.21	−0.162149
$939$	−22952.3	−0.797679
$940$	−7383.93	−0.256210
$941$	24407.7	0.845556	0.422778	−	0.906233i	$-0.361055\pi$
$941$	24407.7	0.845556	0.422778	+	0.906233i	$0.361055\pi$
$942$	9209.21	0.318527
$943$	5917.34	0.204343
$944$	8325.16	0.287035
$945$	−679.581	−0.0233934
$946$	−9959.17	−0.342284
$947$	−40157.2	−1.37797	−0.688983	−	0.724778i	$-0.741942\pi$
$947$	−40157.2	−1.37797	−0.688983	+	0.724778i	$0.741942\pi$
$948$	4661.93	0.159718
$949$	13463.7	0.460538
$950$	24745.5	0.845106
$951$	8393.42	0.286199
$952$	2523.81	0.0859213
$953$	−51933.4	−1.76526	−0.882628	−	0.470072i	$-0.844228\pi$
$953$	−51933.4	−1.76526	−0.882628	+	0.470072i	$0.844228\pi$
$954$	3502.87	0.118878
$955$	3561.49	0.120678
$956$	18047.5	0.610564
$957$	−6035.13	−0.203854
$958$	24265.3	0.818347
$959$	−19875.9	−0.669265
$960$	−590.136	−0.0198402
$961$	−9414.93	−0.316033
$962$	−3789.58	−0.127007
$963$	4264.49	0.142701
$964$	17453.9	0.583147
$965$	−7253.85	−0.241979
$966$	2043.86	0.0680745
$967$	−3374.25	−0.112212	−0.0561058	−	0.998425i	$-0.517868\pi$
$967$	−3374.25	−0.112212	−0.0561058	+	0.998425i	$0.517868\pi$
$968$	−968.000	−0.0321412
$969$	12375.0	0.410262
$970$	−119.971	−0.00397116
$971$	4992.23	0.164993	0.0824965	−	0.996591i	$-0.473711\pi$
$971$	4992.23	0.164993	0.0824965	+	0.996591i	$0.473711\pi$
$972$	−972.000	−0.0320750
$973$	−6984.51	−0.230126
$974$	38732.6	1.27420
$975$	−17752.6	−0.583116
$976$	−1154.41	−0.0378604
$977$	−47053.7	−1.54082	−0.770411	−	0.637548i	$-0.779949\pi$
$977$	−47053.7	−1.54082	−0.770411	+	0.637548i	$0.779949\pi$
$978$	11312.3	0.369865
$979$	−15525.2	−0.506831
$980$	−3392.57	−0.110583
$981$	11925.5	0.388125
$982$	25486.4	0.828213
$983$	3656.90	0.118654	0.0593271	−	0.998239i	$-0.481105\pi$
$983$	3656.90	0.118654	0.0593271	+	0.998239i	$0.481105\pi$
$984$	3414.01	0.110604
$985$	−12309.0	−0.398168
$986$	14091.0	0.455121
$987$	14754.5	0.475826
$988$	−21933.4	−0.706269
$989$	18831.0	0.605451
$990$	−608.578	−0.0195373
$991$	52490.5	1.68256	0.841280	−	0.540600i	$-0.181803\pi$
$991$	52490.5	1.68256	0.841280	+	0.540600i	$0.181803\pi$
$992$	4567.83	0.146198
$993$	−15838.5	−0.506164
$994$	7105.58	0.226736
$995$	9159.55	0.291836
$996$	2999.92	0.0954380
$997$	54753.8	1.73929	0.869644	−	0.493680i	$-0.164348\pi$
$997$	54753.8	1.73929	0.869644	+	0.493680i	$0.164348\pi$
$998$	23965.6	0.760139
$999$	999.000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2442.4.a.n.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2442.4.a.n.1.8	✓	12	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:	\( N \)	\(=\)	\( 2442 = 2 \cdot 3 \cdot 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2442.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +3.07363 q^{5} +6.00000 q^{6} +8.18892 q^{7} -8.00000 q^{8} +9.00000 q^{9} -6.14725 q^{10} +11.0000 q^{11} -12.0000 q^{12} -51.2106 q^{13} -16.3778 q^{14} -9.22088 q^{15} +16.0000 q^{16} -38.5247 q^{17} -18.0000 q^{18} +107.074 q^{19} +12.2945 q^{20} -24.5668 q^{21} -22.0000 q^{22} +41.5980 q^{23} +24.0000 q^{24} -115.553 q^{25} +102.421 q^{26} -27.0000 q^{27} +32.7557 q^{28} +182.883 q^{29} +18.4418 q^{30} -142.745 q^{31} -32.0000 q^{32} -33.0000 q^{33} +77.0495 q^{34} +25.1697 q^{35} +36.0000 q^{36} -37.0000 q^{37} -214.149 q^{38} +153.632 q^{39} -24.5890 q^{40} +142.251 q^{41} +49.1335 q^{42} +452.690 q^{43} +44.0000 q^{44} +27.6626 q^{45} -83.1960 q^{46} -600.587 q^{47} -48.0000 q^{48} -275.942 q^{49} +231.106 q^{50} +115.574 q^{51} -204.842 q^{52} -194.604 q^{53} +54.0000 q^{54} +33.8099 q^{55} -65.5113 q^{56} -321.223 q^{57} -365.765 q^{58} +520.322 q^{59} -36.8835 q^{60} -72.1506 q^{61} +285.490 q^{62} +73.7003 q^{63} +64.0000 q^{64} -157.402 q^{65} +66.0000 q^{66} +284.421 q^{67} -154.099 q^{68} -124.794 q^{69} -50.3394 q^{70} -433.853 q^{71} -72.0000 q^{72} -262.908 q^{73} +74.0000 q^{74} +346.658 q^{75} +428.298 q^{76} +90.0781 q^{77} -307.264 q^{78} -388.494 q^{79} +49.1780 q^{80} +81.0000 q^{81} -284.501 q^{82} -249.994 q^{83} -98.2670 q^{84} -118.411 q^{85} -905.379 q^{86} -548.648 q^{87} -88.0000 q^{88} -1411.38 q^{89} -55.3253 q^{90} -419.359 q^{91} +166.392 q^{92} +428.234 q^{93} +1201.17 q^{94} +329.107 q^{95} +96.0000 q^{96} +19.5161 q^{97} +551.883 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} - 10 q^{5} + 72 q^{6} - 25 q^{7} - 96 q^{8} + 108 q^{9} + 20 q^{10} + 132 q^{11} - 144 q^{12} + 12 q^{13} + 50 q^{14} + 30 q^{15} + 192 q^{16} - 10 q^{17} - 216 q^{18}+ \cdots + 1188 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 - 10 * q^5 + 72 * q^6 - 25 * q^7 - 96 * q^8 + 108 * q^9 + 20 * q^10 + 132 * q^11 - 144 * q^12 + 12 * q^13 + 50 * q^14 + 30 * q^15 + 192 * q^16 - 10 * q^17 - 216 * q^18 - 9 * q^19 - 40 * q^20 + 75 * q^21 - 264 * q^22 - 201 * q^23 + 288 * q^24 + 210 * q^25 - 24 * q^26 - 324 * q^27 - 100 * q^28 - 84 * q^29 - 60 * q^30 + 10 * q^31 - 384 * q^32 - 396 * q^33 + 20 * q^34 - 565 * q^35 + 432 * q^36 - 444 * q^37 + 18 * q^38 - 36 * q^39 + 80 * q^40 + 215 * q^41 - 150 * q^42 - 434 * q^43 + 528 * q^44 - 90 * q^45 + 402 * q^46 - 256 * q^47 - 576 * q^48 + 519 * q^49 - 420 * q^50 + 30 * q^51 + 48 * q^52 - 448 * q^53 + 648 * q^54 - 110 * q^55 + 200 * q^56 + 27 * q^57 + 168 * q^58 - 588 * q^59 + 120 * q^60 + 735 * q^61 - 20 * q^62 - 225 * q^63 + 768 * q^64 - 859 * q^65 + 792 * q^66 - 288 * q^67 - 40 * q^68 + 603 * q^69 + 1130 * q^70 + 1019 * q^71 - 864 * q^72 - 309 * q^73 + 888 * q^74 - 630 * q^75 - 36 * q^76 - 275 * q^77 + 72 * q^78 + 1116 * q^79 - 160 * q^80 + 972 * q^81 - 430 * q^82 - 662 * q^83 + 300 * q^84 + 1093 * q^85 + 868 * q^86 + 252 * q^87 - 1056 * q^88 + 1603 * q^89 + 180 * q^90 + 1502 * q^91 - 804 * q^92 - 30 * q^93 + 512 * q^94 - 2017 * q^95 + 1152 * q^96 + 349 * q^97 - 1038 * q^98 + 1188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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