LMFDB - Embedded newform 1870.4.a.j.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,4,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, 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("1870.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,-20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$110.333571711$
Analytic rank:	$1$
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} - x^{9} - 168 x^{8} + 138 x^{7} + 9025 x^{6} - 8357 x^{5} - 177203 x^{4} + 269951 x^{3} + \cdots + 1239820 $ x^10 - x^9 - 168x^8 + 138x^7 + 9025x^6 - 8357x^5 - 177203x^4 + 269951x^3 + 1064495x^2 - 2545931x + 1239820
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-5.39267$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +5.39267 q^{3} +4.00000 q^{4} -5.00000 q^{5} -10.7853 q^{6} +27.8251 q^{7} -8.00000 q^{8} +2.08092 q^{9} +10.0000 q^{10} -11.0000 q^{11} +21.5707 q^{12} +28.2867 q^{13} -55.6501 q^{14} -26.9634 q^{15} +16.0000 q^{16} +17.0000 q^{17} -4.16185 q^{18} -121.775 q^{19} -20.0000 q^{20} +150.052 q^{21} +22.0000 q^{22} -9.59740 q^{23} -43.1414 q^{24} +25.0000 q^{25} -56.5735 q^{26} -134.380 q^{27} +111.300 q^{28} -199.726 q^{29} +53.9267 q^{30} +119.814 q^{31} -32.0000 q^{32} -59.3194 q^{33} -34.0000 q^{34} -139.125 q^{35} +8.32370 q^{36} -33.4824 q^{37} +243.551 q^{38} +152.541 q^{39} +40.0000 q^{40} -296.335 q^{41} -300.103 q^{42} -5.08455 q^{43} -44.0000 q^{44} -10.4046 q^{45} +19.1948 q^{46} -370.402 q^{47} +86.2828 q^{48} +431.235 q^{49} -50.0000 q^{50} +91.6754 q^{51} +113.147 q^{52} -589.694 q^{53} +268.761 q^{54} +55.0000 q^{55} -222.601 q^{56} -656.695 q^{57} +399.452 q^{58} +388.382 q^{59} -107.853 q^{60} +409.983 q^{61} -239.628 q^{62} +57.9019 q^{63} +64.0000 q^{64} -141.434 q^{65} +118.639 q^{66} -654.061 q^{67} +68.0000 q^{68} -51.7556 q^{69} +278.251 q^{70} -668.591 q^{71} -16.6474 q^{72} -6.05482 q^{73} +66.9647 q^{74} +134.817 q^{75} -487.101 q^{76} -306.076 q^{77} -305.082 q^{78} +1080.05 q^{79} -80.0000 q^{80} -780.855 q^{81} +592.671 q^{82} -170.391 q^{83} +600.206 q^{84} -85.0000 q^{85} +10.1691 q^{86} -1077.06 q^{87} +88.0000 q^{88} -92.4246 q^{89} +20.8092 q^{90} +787.081 q^{91} -38.3896 q^{92} +646.117 q^{93} +740.805 q^{94} +608.877 q^{95} -172.566 q^{96} -917.695 q^{97} -862.470 q^{98} -22.8902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) $ 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * 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
$3$	5.39267	1.03782	0.518910	−	0.854829i	$-0.326338\pi$
$3$	5.39267	1.03782	0.518910	+	0.854829i	$0.326338\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−10.7853	−0.733850
$7$	27.8251	1.50241	0.751206	−	0.660067i	$-0.229472\pi$
$7$	27.8251	1.50241	0.751206	+	0.660067i	$0.229472\pi$
$8$	−8.00000	−0.353553
$9$	2.08092	0.0770713
$10$	10.0000	0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	21.5707	0.518910
$13$	28.2867	0.603487	0.301744	−	0.953389i	$-0.402431\pi$
$13$	28.2867	0.603487	0.301744	+	0.953389i	$0.402431\pi$
$14$	−55.6501	−1.06237
$15$	−26.9634	−0.464127
$16$	16.0000	0.250000
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−4.16185	−0.0544976
$19$	−121.775	−1.47038	−0.735189	−	0.677862i	$-0.762907\pi$
$19$	−121.775	−1.47038	−0.735189	+	0.677862i	$0.762907\pi$
$20$	−20.0000	−0.223607
$21$	150.052	1.55923
$22$	22.0000	0.213201
$23$	−9.59740	−0.0870085	−0.0435043	−	0.999053i	$-0.513852\pi$
$23$	−9.59740	−0.0870085	−0.0435043	+	0.999053i	$0.513852\pi$
$24$	−43.1414	−0.366925
$25$	25.0000	0.200000
$26$	−56.5735	−0.426730
$27$	−134.380	−0.957834
$28$	111.300	0.751206
$29$	−199.726	−1.27890	−0.639452	−	0.768831i	$-0.720839\pi$
$29$	−199.726	−1.27890	−0.639452	+	0.768831i	$0.720839\pi$
$30$	53.9267	0.328188
$31$	119.814	0.694167	0.347084	−	0.937834i	$-0.387172\pi$
$31$	119.814	0.694167	0.347084	+	0.937834i	$0.387172\pi$
$32$	−32.0000	−0.176777
$33$	−59.3194	−0.312915
$34$	−34.0000	−0.171499
$35$	−139.125	−0.671899
$36$	8.32370	0.0385356
$37$	−33.4824	−0.148769	−0.0743847	−	0.997230i	$-0.523699\pi$
$37$	−33.4824	−0.148769	−0.0743847	+	0.997230i	$0.523699\pi$
$38$	243.551	1.03971
$39$	152.541	0.626311
$40$	40.0000	0.158114
$41$	−296.335	−1.12878	−0.564388	−	0.825510i	$-0.690888\pi$
$41$	−296.335	−1.12878	−0.564388	+	0.825510i	$0.690888\pi$
$42$	−300.103	−1.10255
$43$	−5.08455	−0.0180322	−0.00901612	−	0.999959i	$-0.502870\pi$
$43$	−5.08455	−0.0180322	−0.00901612	+	0.999959i	$0.502870\pi$
$44$	−44.0000	−0.150756
$45$	−10.4046	−0.0344673
$46$	19.1948	0.0615243
$47$	−370.402	−1.14955	−0.574774	−	0.818312i	$-0.694910\pi$
$47$	−370.402	−1.14955	−0.574774	+	0.818312i	$0.694910\pi$
$48$	86.2828	0.259455
$49$	431.235	1.25724
$50$	−50.0000	−0.141421
$51$	91.6754	0.251708
$52$	113.147	0.301744
$53$	−589.694	−1.52831	−0.764157	−	0.645030i	$-0.776845\pi$
$53$	−589.694	−1.52831	−0.764157	+	0.645030i	$0.776845\pi$
$54$	268.761	0.677291
$55$	55.0000	0.134840
$56$	−222.601	−0.531183
$57$	−656.695	−1.52599
$58$	399.452	0.904322
$59$	388.382	0.857000	0.428500	−	0.903542i	$-0.359042\pi$
$59$	388.382	0.857000	0.428500	+	0.903542i	$0.359042\pi$
$60$	−107.853	−0.232064
$61$	409.983	0.860540	0.430270	−	0.902700i	$-0.358418\pi$
$61$	409.983	0.860540	0.430270	+	0.902700i	$0.358418\pi$
$62$	−239.628	−0.490851
$63$	57.9019	0.115793
$64$	64.0000	0.125000
$65$	−141.434	−0.269888
$66$	118.639	0.221264
$67$	−654.061	−1.19263	−0.596316	−	0.802750i	$-0.703369\pi$
$67$	−654.061	−1.19263	−0.596316	+	0.802750i	$0.703369\pi$
$68$	68.0000	0.121268
$69$	−51.7556	−0.0902992
$70$	278.251	0.475105
$71$	−668.591	−1.11757	−0.558783	−	0.829314i	$-0.688732\pi$
$71$	−668.591	−1.11757	−0.558783	+	0.829314i	$0.688732\pi$
$72$	−16.6474	−0.0272488
$73$	−6.05482	−0.00970772	−0.00485386	−	0.999988i	$-0.501545\pi$
$73$	−6.05482	−0.00970772	−0.00485386	+	0.999988i	$0.501545\pi$
$74$	66.9647	0.105196
$75$	134.817	0.207564
$76$	−487.101	−0.735189
$77$	−306.076	−0.452995
$78$	−305.082	−0.442869
$79$	1080.05	1.53817	0.769085	−	0.639146i	$-0.220712\pi$
$79$	1080.05	1.53817	0.769085	+	0.639146i	$0.220712\pi$
$80$	−80.0000	−0.111803
$81$	−780.855	−1.07113
$82$	592.671	0.798165
$83$	−170.391	−0.225335	−0.112668	−	0.993633i	$-0.535940\pi$
$83$	−170.391	−0.225335	−0.112668	+	0.993633i	$0.535940\pi$
$84$	600.206	0.779617
$85$	−85.0000	−0.108465
$86$	10.1691	0.0127507
$87$	−1077.06	−1.32727
$88$	88.0000	0.106600
$89$	−92.4246	−0.110079	−0.0550393	−	0.998484i	$-0.517528\pi$
$89$	−92.4246	−0.110079	−0.0550393	+	0.998484i	$0.517528\pi$
$90$	20.8092	0.0243721
$91$	787.081	0.906687
$92$	−38.3896	−0.0435043
$93$	646.117	0.720421
$94$	740.805	0.812853
$95$	608.877	0.657573
$96$	−172.566	−0.183462
$97$	−917.695	−0.960596	−0.480298	−	0.877105i	$-0.659472\pi$
$97$	−917.695	−0.960596	−0.480298	+	0.877105i	$0.659472\pi$
$98$	−862.470	−0.889006
$99$	−22.8902	−0.0232379
$100$	100.000	0.100000
$101$	136.282	0.134263	0.0671317	−	0.997744i	$-0.478615\pi$
$101$	136.282	0.134263	0.0671317	+	0.997744i	$0.478615\pi$
$102$	−183.351	−0.177985
$103$	−425.876	−0.407406	−0.203703	−	0.979033i	$-0.565298\pi$
$103$	−425.876	−0.407406	−0.203703	+	0.979033i	$0.565298\pi$
$104$	−226.294	−0.213365
$105$	−750.258	−0.697311
$106$	1179.39	1.08068
$107$	809.290	0.731187	0.365594	−	0.930775i	$-0.380866\pi$
$107$	809.290	0.731187	0.365594	+	0.930775i	$0.380866\pi$
$108$	−537.522	−0.478917
$109$	−1774.17	−1.55904	−0.779519	−	0.626379i	$-0.784536\pi$
$109$	−1774.17	−1.55904	−0.779519	+	0.626379i	$0.784536\pi$
$110$	−110.000	−0.0953463
$111$	−180.559	−0.154396
$112$	445.201	0.375603
$113$	1649.80	1.37346	0.686728	−	0.726915i	$-0.259046\pi$
$113$	1649.80	1.37346	0.686728	+	0.726915i	$0.259046\pi$
$114$	1313.39	1.07904
$115$	47.9870	0.0389114
$116$	−798.905	−0.639452
$117$	58.8626	0.0465115
$118$	−776.763	−0.605990
$119$	473.026	0.364389
$120$	215.707	0.164094
$121$	121.000	0.0909091
$122$	−819.966	−0.608493
$123$	−1598.04	−1.17147
$124$	479.255	0.347084
$125$	−125.000	−0.0894427
$126$	−115.804	−0.0818779
$127$	291.828	0.203902	0.101951	−	0.994789i	$-0.467491\pi$
$127$	291.828	0.203902	0.101951	+	0.994789i	$0.467491\pi$
$128$	−128.000	−0.0883883
$129$	−27.4193	−0.0187142
$130$	282.867	0.190839
$131$	1207.75	0.805506	0.402753	−	0.915309i	$-0.368053\pi$
$131$	1207.75	0.805506	0.402753	+	0.915309i	$0.368053\pi$
$132$	−237.278	−0.156457
$133$	−3388.41	−2.20911
$134$	1308.12	0.843318
$135$	671.902	0.428357
$136$	−136.000	−0.0857493
$137$	−1252.99	−0.781389	−0.390695	−	0.920520i	$-0.627765\pi$
$137$	−1252.99	−0.781389	−0.390695	+	0.920520i	$0.627765\pi$
$138$	103.511	0.0638512
$139$	−1274.37	−0.777631	−0.388816	−	0.921316i	$-0.627116\pi$
$139$	−1274.37	−0.777631	−0.388816	+	0.921316i	$0.627116\pi$
$140$	−556.501	−0.335950
$141$	−1997.46	−1.19302
$142$	1337.18	0.790238
$143$	−311.154	−0.181958
$144$	33.2948	0.0192678
$145$	998.631	0.571943
$146$	12.1096	0.00686439
$147$	2325.51	1.30479
$148$	−133.929	−0.0743847
$149$	1209.87	0.665210	0.332605	−	0.943066i	$-0.392072\pi$
$149$	1209.87	0.665210	0.332605	+	0.943066i	$0.392072\pi$
$150$	−269.634	−0.146770
$151$	−1076.24	−0.580022	−0.290011	−	0.957023i	$-0.593659\pi$
$151$	−1076.24	−0.580022	−0.290011	+	0.957023i	$0.593659\pi$
$152$	974.203	0.519857
$153$	35.3757	0.0186925
$154$	612.152	0.320315
$155$	−599.069	−0.310441
$156$	610.165	0.313156
$157$	1745.71	0.887405	0.443702	−	0.896174i	$-0.353665\pi$
$157$	1745.71	0.887405	0.443702	+	0.896174i	$0.353665\pi$
$158$	−2160.11	−1.08765
$159$	−3180.03	−1.58612
$160$	160.000	0.0790569
$161$	−267.048	−0.130723
$162$	1561.71	0.757404
$163$	946.502	0.454821	0.227410	−	0.973799i	$-0.426974\pi$
$163$	946.502	0.454821	0.227410	+	0.973799i	$0.426974\pi$
$164$	−1185.34	−0.564388
$165$	296.597	0.139940
$166$	340.782	0.159336
$167$	−2841.15	−1.31649	−0.658247	−	0.752802i	$-0.728702\pi$
$167$	−2841.15	−1.31649	−0.658247	+	0.752802i	$0.728702\pi$
$168$	−1200.41	−0.551273
$169$	−1396.86	−0.635803
$170$	170.000	0.0766965
$171$	−253.405	−0.113324
$172$	−20.3382	−0.00901612
$173$	−1124.52	−0.494197	−0.247098	−	0.968990i	$-0.579477\pi$
$173$	−1124.52	−0.494197	−0.247098	+	0.968990i	$0.579477\pi$
$174$	2154.12	0.938524
$175$	695.627	0.300483
$176$	−176.000	−0.0753778
$177$	2094.41	0.889412
$178$	184.849	0.0778373
$179$	−778.092	−0.324901	−0.162451	−	0.986717i	$-0.551940\pi$
$179$	−778.092	−0.324901	−0.162451	+	0.986717i	$0.551940\pi$
$180$	−41.6185	−0.0172337
$181$	−63.3454	−0.0260134	−0.0130067	−	0.999915i	$-0.504140\pi$
$181$	−63.3454	−0.0260134	−0.0130067	+	0.999915i	$0.504140\pi$
$182$	−1574.16	−0.641124
$183$	2210.90	0.893086
$184$	76.7792	0.0307622
$185$	167.412	0.0665317
$186$	−1292.23	−0.509415
$187$	−187.000	−0.0731272
$188$	−1481.61	−0.574774
$189$	−3739.15	−1.43906
$190$	−1217.75	−0.464974
$191$	3000.97	1.13687	0.568436	−	0.822727i	$-0.307549\pi$
$191$	3000.97	1.13687	0.568436	+	0.822727i	$0.307549\pi$
$192$	345.131	0.129728
$193$	−1434.05	−0.534844	−0.267422	−	0.963580i	$-0.586172\pi$
$193$	−1434.05	−0.534844	−0.267422	+	0.963580i	$0.586172\pi$
$194$	1835.39	0.679244
$195$	−762.706	−0.280095
$196$	1724.94	0.628622
$197$	−3115.69	−1.12682	−0.563411	−	0.826177i	$-0.690511\pi$
$197$	−3115.69	−1.12682	−0.563411	+	0.826177i	$0.690511\pi$
$198$	45.7803	0.0164317
$199$	−2471.73	−0.880483	−0.440241	−	0.897879i	$-0.645107\pi$
$199$	−2471.73	−0.880483	−0.440241	+	0.897879i	$0.645107\pi$
$200$	−200.000	−0.0707107
$201$	−3527.14	−1.23774
$202$	−272.565	−0.0949386
$203$	−5557.40	−1.92144
$204$	366.702	0.125854
$205$	1481.68	0.504804
$206$	851.752	0.288080
$207$	−19.9715	−0.00670586
$208$	452.588	0.150872
$209$	1339.53	0.443336
$210$	1500.52	0.493073
$211$	4787.28	1.56194	0.780972	−	0.624566i	$-0.214724\pi$
$211$	4787.28	1.56194	0.780972	+	0.624566i	$0.214724\pi$
$212$	−2358.78	−0.764157
$213$	−3605.49	−1.15983
$214$	−1618.58	−0.517027
$215$	25.4227	0.00806426
$216$	1075.04	0.338646
$217$	3333.83	1.04293
$218$	3548.35	1.10241
$219$	−32.6517	−0.0100749
$220$	220.000	0.0674200
$221$	480.875	0.146367
$222$	361.119	0.109174
$223$	2662.25	0.799451	0.399725	−	0.916635i	$-0.369106\pi$
$223$	2662.25	0.799451	0.399725	+	0.916635i	$0.369106\pi$
$224$	−890.402	−0.265592
$225$	52.0231	0.0154143
$226$	−3299.61	−0.971180
$227$	2766.77	0.808973	0.404486	−	0.914544i	$-0.367450\pi$
$227$	2766.77	0.808973	0.404486	+	0.914544i	$0.367450\pi$
$228$	−2626.78	−0.762994
$229$	4564.50	1.31717	0.658583	−	0.752508i	$-0.271156\pi$
$229$	4564.50	1.31717	0.658583	+	0.752508i	$0.271156\pi$
$230$	−95.9740	−0.0275145
$231$	−1650.57	−0.470127
$232$	1597.81	0.452161
$233$	−5140.39	−1.44531	−0.722657	−	0.691207i	$-0.757079\pi$
$233$	−5140.39	−1.44531	−0.722657	+	0.691207i	$0.757079\pi$
$234$	−117.725	−0.0328886
$235$	1852.01	0.514093
$236$	1553.53	0.428500
$237$	5824.37	1.59634
$238$	−946.053	−0.257662
$239$	−2378.28	−0.643674	−0.321837	−	0.946795i	$-0.604300\pi$
$239$	−2378.28	−0.643674	−0.321837	+	0.946795i	$0.604300\pi$
$240$	−431.414	−0.116032
$241$	2856.02	0.763370	0.381685	−	0.924292i	$-0.375344\pi$
$241$	2856.02	0.763370	0.381685	+	0.924292i	$0.375344\pi$
$242$	−242.000	−0.0642824
$243$	−582.623	−0.153808
$244$	1639.93	0.430270
$245$	−2156.17	−0.562257
$246$	3196.08	0.828352
$247$	−3444.63	−0.887354
$248$	−958.510	−0.245425
$249$	−918.862	−0.233858
$250$	250.000	0.0632456
$251$	175.676	0.0441775	0.0220887	−	0.999756i	$-0.492968\pi$
$251$	175.676	0.0441775	0.0220887	+	0.999756i	$0.492968\pi$
$252$	231.608	0.0578964
$253$	105.571	0.0262341
$254$	−583.657	−0.144181
$255$	−458.377	−0.112567
$256$	256.000	0.0625000
$257$	980.370	0.237953	0.118976	−	0.992897i	$-0.462039\pi$
$257$	980.370	0.237953	0.118976	+	0.992897i	$0.462039\pi$
$258$	54.8386	0.0132330
$259$	−931.649	−0.223513
$260$	−565.735	−0.134944
$261$	−415.615	−0.0985668
$262$	−2415.49	−0.569579
$263$	−5851.60	−1.37196	−0.685979	−	0.727621i	$-0.740626\pi$
$263$	−5851.60	−1.37196	−0.685979	+	0.727621i	$0.740626\pi$
$264$	474.555	0.110632
$265$	2948.47	0.683483
$266$	6776.82	1.56208
$267$	−498.416	−0.114242
$268$	−2616.25	−0.596316
$269$	−64.3328	−0.0145816	−0.00729079	−	0.999973i	$-0.502321\pi$
$269$	−64.3328	−0.0145816	−0.00729079	+	0.999973i	$0.502321\pi$
$270$	−1343.80	−0.302894
$271$	−4474.40	−1.00295	−0.501477	−	0.865171i	$-0.667210\pi$
$271$	−4474.40	−1.00295	−0.501477	+	0.865171i	$0.667210\pi$
$272$	272.000	0.0606339
$273$	4244.47	0.940978
$274$	2505.98	0.552526
$275$	−275.000	−0.0603023
$276$	−207.023	−0.0451496
$277$	5283.26	1.14599	0.572997	−	0.819557i	$-0.305781\pi$
$277$	5283.26	1.14599	0.572997	+	0.819557i	$0.305781\pi$
$278$	2548.74	0.549868
$279$	249.323	0.0535004
$280$	1113.00	0.237552
$281$	4903.72	1.04104	0.520518	−	0.853851i	$-0.325739\pi$
$281$	4903.72	1.04104	0.520518	+	0.853851i	$0.325739\pi$
$282$	3994.92	0.843596
$283$	3344.50	0.702508	0.351254	−	0.936280i	$-0.385755\pi$
$283$	3344.50	0.702508	0.351254	+	0.936280i	$0.385755\pi$
$284$	−2674.36	−0.558783
$285$	3283.47	0.682443
$286$	622.308	0.128664
$287$	−8245.55	−1.69589
$288$	−66.5896	−0.0136244
$289$	289.000	0.0588235
$290$	−1997.26	−0.404425
$291$	−4948.83	−0.996927
$292$	−24.2193	−0.00485386
$293$	3800.13	0.757700	0.378850	−	0.925458i	$-0.376320\pi$
$293$	3800.13	0.757700	0.378850	+	0.925458i	$0.376320\pi$
$294$	−4651.02	−0.922629
$295$	−1941.91	−0.383262
$296$	267.859	0.0525979
$297$	1478.18	0.288798
$298$	−2419.74	−0.470375
$299$	−271.479	−0.0525085
$300$	539.267	0.103782
$301$	−141.478	−0.0270919
$302$	2152.49	0.410138
$303$	734.926	0.139341
$304$	−1948.41	−0.367594
$305$	−2049.91	−0.384845
$306$	−70.7514	−0.0132176
$307$	−1290.96	−0.239996	−0.119998	−	0.992774i	$-0.538289\pi$
$307$	−1290.96	−0.239996	−0.119998	+	0.992774i	$0.538289\pi$
$308$	−1224.30	−0.226497
$309$	−2296.61	−0.422814
$310$	1198.14	0.219515
$311$	−5757.26	−1.04972	−0.524862	−	0.851187i	$-0.675883\pi$
$311$	−5757.26	−1.04972	−0.524862	+	0.851187i	$0.675883\pi$
$312$	−1220.33	−0.221434
$313$	591.550	0.106826	0.0534128	−	0.998573i	$-0.482990\pi$
$313$	591.550	0.106826	0.0534128	+	0.998573i	$0.482990\pi$
$314$	−3491.41	−0.627490
$315$	−289.509	−0.0517842
$316$	4320.21	0.769085
$317$	−4329.06	−0.767016	−0.383508	−	0.923537i	$-0.625284\pi$
$317$	−4329.06	−0.767016	−0.383508	+	0.923537i	$0.625284\pi$
$318$	6360.05	1.12155
$319$	2196.99	0.385604
$320$	−320.000	−0.0559017
$321$	4364.24	0.758841
$322$	534.097	0.0924349
$323$	−2070.18	−0.356619
$324$	−3123.42	−0.535566
$325$	707.169	0.120697
$326$	−1893.00	−0.321607
$327$	−9567.54	−1.61800
$328$	2370.68	0.399082
$329$	−10306.5	−1.72710
$330$	−593.194	−0.0989523
$331$	−9173.18	−1.52327	−0.761637	−	0.648004i	$-0.775604\pi$
$331$	−9173.18	−1.52327	−0.761637	+	0.648004i	$0.775604\pi$
$332$	−681.563	−0.112668
$333$	−69.6743	−0.0114658
$334$	5682.29	0.930902
$335$	3270.31	0.533361
$336$	2400.82	0.389809
$337$	−9000.07	−1.45479	−0.727396	−	0.686218i	$-0.759270\pi$
$337$	−9000.07	−1.45479	−0.727396	+	0.686218i	$0.759270\pi$
$338$	2793.72	0.449581
$339$	8896.85	1.42540
$340$	−340.000	−0.0542326
$341$	−1317.95	−0.209299
$342$	506.811	0.0801321
$343$	2455.14	0.386487
$344$	40.6764	0.00637536
$345$	258.778	0.0403830
$346$	2249.05	0.349450
$347$	4007.72	0.620016	0.310008	−	0.950734i	$-0.399668\pi$
$347$	4007.72	0.620016	0.310008	+	0.950734i	$0.399668\pi$
$348$	−4308.23	−0.663637
$349$	−1541.42	−0.236420	−0.118210	−	0.992989i	$-0.537716\pi$
$349$	−1541.42	−0.236420	−0.118210	+	0.992989i	$0.537716\pi$
$350$	−1391.25	−0.212473
$351$	−3801.19	−0.578041
$352$	352.000	0.0533002
$353$	4712.82	0.710590	0.355295	−	0.934754i	$-0.384380\pi$
$353$	4712.82	0.710590	0.355295	+	0.934754i	$0.384380\pi$
$354$	−4188.83	−0.628909
$355$	3342.96	0.499791
$356$	−369.698	−0.0550393
$357$	2550.88	0.378170
$358$	1556.18	0.229740
$359$	−7558.07	−1.11114	−0.555571	−	0.831469i	$-0.687500\pi$
$359$	−7558.07	−1.11114	−0.555571	+	0.831469i	$0.687500\pi$
$360$	83.2370	0.0121860
$361$	7970.23	1.16201
$362$	126.691	0.0183943
$363$	652.513	0.0943473
$364$	3148.32	0.453343
$365$	30.2741	0.00434142
$366$	−4421.81	−0.631507
$367$	−4740.32	−0.674231	−0.337115	−	0.941463i	$-0.609451\pi$
$367$	−4740.32	−0.674231	−0.337115	+	0.941463i	$0.609451\pi$
$368$	−153.558	−0.0217521
$369$	−616.651	−0.0869962
$370$	−334.824	−0.0470450
$371$	−16408.3	−2.29616
$372$	2584.47	0.360211
$373$	−6097.89	−0.846480	−0.423240	−	0.906018i	$-0.639107\pi$
$373$	−6097.89	−0.846480	−0.423240	+	0.906018i	$0.639107\pi$
$374$	374.000	0.0517088
$375$	−674.084	−0.0928255
$376$	2963.22	0.406427
$377$	−5649.61	−0.771802
$378$	7478.29	1.01757
$379$	−3017.84	−0.409014	−0.204507	−	0.978865i	$-0.565559\pi$
$379$	−3017.84	−0.409014	−0.204507	+	0.978865i	$0.565559\pi$
$380$	2435.51	0.328786
$381$	1573.74	0.211614
$382$	−6001.94	−0.803890
$383$	−4631.39	−0.617893	−0.308946	−	0.951079i	$-0.599976\pi$
$383$	−4631.39	−0.617893	−0.308946	+	0.951079i	$0.599976\pi$
$384$	−690.262	−0.0917312
$385$	1530.38	0.202585
$386$	2868.09	0.378192
$387$	−10.5806	−0.00138977
$388$	−3670.78	−0.480298
$389$	3377.14	0.440174	0.220087	−	0.975480i	$-0.429366\pi$
$389$	3377.14	0.440174	0.220087	+	0.975480i	$0.429366\pi$
$390$	1525.41	0.198057
$391$	−163.156	−0.0211027
$392$	−3449.88	−0.444503
$393$	6512.98	0.835971
$394$	6231.38	0.796783
$395$	−5400.27	−0.687891
$396$	−91.5607	−0.0116189
$397$	15187.4	1.91998	0.959991	−	0.280032i	$-0.0903452\pi$
$397$	15187.4	1.91998	0.959991	+	0.280032i	$0.0903452\pi$
$398$	4943.45	0.622595
$399$	−18272.6	−2.29266
$400$	400.000	0.0500000
$401$	−450.790	−0.0561381	−0.0280691	−	0.999606i	$-0.508936\pi$
$401$	−450.790	−0.0561381	−0.0280691	+	0.999606i	$0.508936\pi$
$402$	7054.28	0.875213
$403$	3389.14	0.418921
$404$	545.130	0.0671317
$405$	3904.27	0.479024
$406$	11114.8	1.35867
$407$	368.306	0.0448557
$408$	−733.404	−0.0889924
$409$	−4537.30	−0.548546	−0.274273	−	0.961652i	$-0.588437\pi$
$409$	−4537.30	−0.548546	−0.274273	+	0.961652i	$0.588437\pi$
$410$	−2963.35	−0.356950
$411$	−6756.98	−0.810942
$412$	−1703.50	−0.203703
$413$	10806.7	1.28757
$414$	39.9429	0.00474176
$415$	851.954	0.100773
$416$	−905.176	−0.106682
$417$	−6872.26	−0.807041
$418$	−2679.06	−0.313486
$419$	−13750.6	−1.60324	−0.801621	−	0.597832i	$-0.796029\pi$
$419$	−13750.6	−1.60324	−0.801621	+	0.597832i	$0.796029\pi$
$420$	−3001.03	−0.348655
$421$	884.509	0.102395	0.0511975	−	0.998689i	$-0.483696\pi$
$421$	884.509	0.102395	0.0511975	+	0.998689i	$0.483696\pi$
$422$	−9574.56	−1.10446
$423$	−770.780	−0.0885971
$424$	4717.55	0.540341
$425$	425.000	0.0485071
$426$	7210.99	0.820126
$427$	11407.8	1.29289
$428$	3237.16	0.365594
$429$	−1677.95	−0.188840
$430$	−50.8455	−0.00570229
$431$	−14467.6	−1.61689	−0.808446	−	0.588570i	$-0.799691\pi$
$431$	−14467.6	−1.61689	−0.808446	+	0.588570i	$0.799691\pi$
$432$	−2150.09	−0.239459
$433$	−8241.96	−0.914742	−0.457371	−	0.889276i	$-0.651209\pi$
$433$	−8241.96	−0.914742	−0.457371	+	0.889276i	$0.651209\pi$
$434$	−6667.65	−0.737460
$435$	5385.29	0.593575
$436$	−7096.70	−0.779519
$437$	1168.73	0.127935
$438$	65.3034	0.00712401
$439$	−10752.9	−1.16904	−0.584519	−	0.811380i	$-0.698717\pi$
$439$	−10752.9	−1.16904	−0.584519	+	0.811380i	$0.698717\pi$
$440$	−440.000	−0.0476731
$441$	897.367	0.0968974
$442$	−961.749	−0.103497
$443$	−2131.64	−0.228616	−0.114308	−	0.993445i	$-0.536465\pi$
$443$	−2131.64	−0.228616	−0.114308	+	0.993445i	$0.536465\pi$
$444$	−722.238	−0.0771980
$445$	462.123	0.0492286
$446$	−5324.50	−0.565297
$447$	6524.43	0.690369
$448$	1780.80	0.187802
$449$	16904.8	1.77681	0.888406	−	0.459059i	$-0.151814\pi$
$449$	16904.8	1.77681	0.888406	+	0.459059i	$0.151814\pi$
$450$	−104.046	−0.0108995
$451$	3259.69	0.340339
$452$	6599.22	0.686728
$453$	−5803.82	−0.601959
$454$	−5533.53	−0.572030
$455$	−3935.40	−0.405483
$456$	5253.56	0.539518
$457$	−299.117	−0.0306173	−0.0153087	−	0.999883i	$-0.504873\pi$
$457$	−299.117	−0.0306173	−0.0153087	+	0.999883i	$0.504873\pi$
$458$	−9129.01	−0.931377
$459$	−2284.47	−0.232309
$460$	191.948	0.0194557
$461$	−4100.04	−0.414226	−0.207113	−	0.978317i	$-0.566407\pi$
$461$	−4100.04	−0.414226	−0.207113	+	0.978317i	$0.566407\pi$
$462$	3301.13	0.332430
$463$	12374.5	1.24210	0.621050	−	0.783771i	$-0.286706\pi$
$463$	12374.5	1.24210	0.621050	+	0.783771i	$0.286706\pi$
$464$	−3195.62	−0.319726
$465$	−3230.58	−0.322182
$466$	10280.8	1.02199
$467$	−13288.2	−1.31671	−0.658357	−	0.752706i	$-0.728748\pi$
$467$	−13288.2	−1.31671	−0.658357	+	0.752706i	$0.728748\pi$
$468$	235.450	0.0232558
$469$	−18199.3	−1.79183
$470$	−3704.02	−0.363519
$471$	9414.03	0.920967
$472$	−3107.05	−0.302995
$473$	55.9300	0.00543692
$474$	−11648.7	−1.12879
$475$	−3044.38	−0.294076
$476$	1892.11	0.182194
$477$	−1227.11	−0.117789
$478$	4756.56	0.455146
$479$	−9178.39	−0.875514	−0.437757	−	0.899093i	$-0.644227\pi$
$479$	−9178.39	−0.875514	−0.437757	+	0.899093i	$0.644227\pi$
$480$	862.828	0.0820469
$481$	−947.107	−0.0897804
$482$	−5712.03	−0.539784
$483$	−1440.10	−0.135667
$484$	484.000	0.0454545
$485$	4588.48	0.429592
$486$	1165.25	0.108758
$487$	−20100.4	−1.87030	−0.935151	−	0.354249i	$-0.884737\pi$
$487$	−20100.4	−1.87030	−0.935151	+	0.354249i	$0.884737\pi$
$488$	−3279.86	−0.304247
$489$	5104.18	0.472022
$490$	4312.35	0.397576
$491$	4677.77	0.429948	0.214974	−	0.976620i	$-0.431033\pi$
$491$	4677.77	0.429948	0.214974	+	0.976620i	$0.431033\pi$
$492$	−6392.16	−0.585733
$493$	−3395.35	−0.310180
$494$	6889.26	0.627454
$495$	114.451	0.0103923
$496$	1917.02	0.173542
$497$	−18603.6	−1.67905
$498$	1837.72	0.165362
$499$	3212.98	0.288242	0.144121	−	0.989560i	$-0.453965\pi$
$499$	3212.98	0.288242	0.144121	+	0.989560i	$0.453965\pi$
$500$	−500.000	−0.0447214
$501$	−15321.4	−1.36628
$502$	−351.351	−0.0312382
$503$	−16743.2	−1.48418	−0.742090	−	0.670300i	$-0.766165\pi$
$503$	−16743.2	−1.48418	−0.742090	+	0.670300i	$0.766165\pi$
$504$	−463.215	−0.0409390
$505$	−681.412	−0.0600444
$506$	−211.143	−0.0185503
$507$	−7532.81	−0.659850
$508$	1167.31	0.101951
$509$	14285.4	1.24399	0.621993	−	0.783023i	$-0.286323\pi$
$509$	14285.4	1.24399	0.621993	+	0.783023i	$0.286323\pi$
$510$	916.754	0.0795972
$511$	−168.476	−0.0145850
$512$	−512.000	−0.0441942
$513$	16364.2	1.40838
$514$	−1960.74	−0.168258
$515$	2129.38	0.182197
$516$	−109.677	−0.00935711
$517$	4074.43	0.346602
$518$	1863.30	0.158048
$519$	−6064.19	−0.512887
$520$	1131.47	0.0954197
$521$	−791.662	−0.0665707	−0.0332854	−	0.999446i	$-0.510597\pi$
$521$	−791.662	−0.0665707	−0.0332854	+	0.999446i	$0.510597\pi$
$522$	831.231	0.0696973
$523$	−13655.2	−1.14168	−0.570840	−	0.821061i	$-0.693382\pi$
$523$	−13655.2	−1.14168	−0.570840	+	0.821061i	$0.693382\pi$
$524$	4830.99	0.402753
$525$	3751.29	0.311847
$526$	11703.2	0.970121
$527$	2036.83	0.168360
$528$	−949.110	−0.0782287
$529$	−12074.9	−0.992430
$530$	−5896.94	−0.483296
$531$	808.193	0.0660501
$532$	−13553.6	−1.10456
$533$	−8382.36	−0.681201
$534$	996.832	0.0807811
$535$	−4046.45	−0.326997
$536$	5232.49	0.421659
$537$	−4196.00	−0.337189
$538$	128.666	0.0103107
$539$	−4743.58	−0.379073
$540$	2687.61	0.214178
$541$	−6116.04	−0.486043	−0.243022	−	0.970021i	$-0.578139\pi$
$541$	−6116.04	−0.486043	−0.243022	+	0.970021i	$0.578139\pi$
$542$	8948.81	0.709196
$543$	−341.601	−0.0269972
$544$	−544.000	−0.0428746
$545$	8870.87	0.697223
$546$	−8488.94	−0.665372
$547$	4297.07	0.335885	0.167943	−	0.985797i	$-0.446288\pi$
$547$	4297.07	0.335885	0.167943	+	0.985797i	$0.446288\pi$
$548$	−5011.97	−0.390695
$549$	853.143	0.0663229
$550$	550.000	0.0426401
$551$	24321.7	1.88047
$552$	414.045	0.0319256
$553$	30052.6	2.31097
$554$	−10566.5	−0.810340
$555$	902.797	0.0690480
$556$	−5097.48	−0.388816
$557$	−14422.8	−1.09715	−0.548575	−	0.836101i	$-0.684829\pi$
$557$	−14422.8	−1.09715	−0.548575	+	0.836101i	$0.684829\pi$
$558$	−498.647	−0.0378305
$559$	−143.825	−0.0108822
$560$	−2226.01	−0.167975
$561$	−1008.43	−0.0758929
$562$	−9807.43	−0.736124
$563$	23902.4	1.78928	0.894641	−	0.446786i	$-0.147431\pi$
$563$	23902.4	1.78928	0.894641	+	0.446786i	$0.147431\pi$
$564$	−7989.84	−0.596512
$565$	−8249.02	−0.614228
$566$	−6688.99	−0.496748
$567$	−21727.3	−1.60928
$568$	5348.73	0.395119
$569$	−12696.6	−0.935448	−0.467724	−	0.883875i	$-0.654926\pi$
$569$	−12696.6	−0.935448	−0.467724	+	0.883875i	$0.654926\pi$
$570$	−6566.95	−0.482560
$571$	15927.5	1.16733	0.583664	−	0.811995i	$-0.301618\pi$
$571$	15927.5	1.16733	0.583664	+	0.811995i	$0.301618\pi$
$572$	−1244.62	−0.0909791
$573$	16183.3	1.17987
$574$	16491.1	1.19917
$575$	−239.935	−0.0174017
$576$	133.179	0.00963391
$577$	−18957.1	−1.36776	−0.683879	−	0.729596i	$-0.739708\pi$
$577$	−18957.1	−1.36776	−0.683879	+	0.729596i	$0.739708\pi$
$578$	−578.000	−0.0415945
$579$	−7733.34	−0.555072
$580$	3994.52	0.285972
$581$	−4741.14	−0.338547
$582$	9897.66	0.704934
$583$	6486.63	0.460804
$584$	48.4386	0.00343220
$585$	−294.313	−0.0208006
$586$	−7600.26	−0.535775
$587$	−9755.33	−0.685938	−0.342969	−	0.939347i	$-0.611433\pi$
$587$	−9755.33	−0.685938	−0.342969	+	0.939347i	$0.611433\pi$
$588$	9302.03	0.652397
$589$	−14590.4	−1.02069
$590$	3883.82	0.271007
$591$	−16801.9	−1.16944
$592$	−535.718	−0.0371924
$593$	7616.11	0.527414	0.263707	−	0.964603i	$-0.415055\pi$
$593$	7616.11	0.527414	0.263707	+	0.964603i	$0.415055\pi$
$594$	−2956.37	−0.204211
$595$	−2365.13	−0.162960
$596$	4839.47	0.332605
$597$	−13329.2	−0.913783
$598$	542.958	0.0371291
$599$	−19817.9	−1.35182	−0.675909	−	0.736985i	$-0.736249\pi$
$599$	−19817.9	−1.35182	−0.675909	+	0.736985i	$0.736249\pi$
$600$	−1078.53	−0.0733850
$601$	5112.14	0.346969	0.173485	−	0.984837i	$-0.444497\pi$
$601$	5112.14	0.346969	0.173485	+	0.984837i	$0.444497\pi$
$602$	282.956	0.0191568
$603$	−1361.05	−0.0919177
$604$	−4304.97	−0.290011
$605$	−605.000	−0.0406558
$606$	−1469.85	−0.0985292
$607$	8327.35	0.556831	0.278416	−	0.960461i	$-0.410191\pi$
$607$	8327.35	0.556831	0.278416	+	0.960461i	$0.410191\pi$
$608$	3896.81	0.259929
$609$	−29969.2	−1.99411
$610$	4099.83	0.272127
$611$	−10477.5	−0.693737
$612$	141.503	0.00934627
$613$	−20856.8	−1.37423	−0.687113	−	0.726551i	$-0.741122\pi$
$613$	−20856.8	−1.37423	−0.687113	+	0.726551i	$0.741122\pi$
$614$	2581.92	0.169703
$615$	7990.20	0.523896
$616$	2448.61	0.160158
$617$	4513.81	0.294520	0.147260	−	0.989098i	$-0.452955\pi$
$617$	4513.81	0.294520	0.147260	+	0.989098i	$0.452955\pi$
$618$	4593.22	0.298975
$619$	15718.1	1.02062	0.510311	−	0.859990i	$-0.329530\pi$
$619$	15718.1	1.02062	0.510311	+	0.859990i	$0.329530\pi$
$620$	−2396.28	−0.155221
$621$	1289.70	0.0833397
$622$	11514.5	0.742267
$623$	−2571.72	−0.165383
$624$	2440.66	0.156578
$625$	625.000	0.0400000
$626$	−1183.10	−0.0755370
$627$	7223.64	0.460103
$628$	6982.83	0.443702
$629$	−569.200	−0.0360819
$630$	579.019	0.0366169
$631$	9582.34	0.604543	0.302272	−	0.953222i	$-0.402255\pi$
$631$	9582.34	0.604543	0.302272	+	0.953222i	$0.402255\pi$
$632$	−8640.42	−0.543825
$633$	25816.2	1.62102
$634$	8658.12	0.542363
$635$	−1459.14	−0.0911879
$636$	−12720.1	−0.793058
$637$	12198.2	0.758731
$638$	−4393.98	−0.272663
$639$	−1391.29	−0.0861322
$640$	640.000	0.0395285
$641$	15636.2	0.963484	0.481742	−	0.876313i	$-0.340004\pi$
$641$	15636.2	0.963484	0.481742	+	0.876313i	$0.340004\pi$
$642$	−8728.47	−0.536582
$643$	10101.5	0.619538	0.309769	−	0.950812i	$-0.399748\pi$
$643$	10101.5	0.619538	0.309769	+	0.950812i	$0.399748\pi$
$644$	−1068.19	−0.0653613
$645$	137.097	0.00836926
$646$	4140.36	0.252168
$647$	19031.7	1.15643	0.578216	−	0.815884i	$-0.303749\pi$
$647$	19031.7	1.15643	0.578216	+	0.815884i	$0.303749\pi$
$648$	6246.84	0.378702
$649$	−4272.20	−0.258395
$650$	−1414.34	−0.0853460
$651$	17978.2	1.08237
$652$	3786.01	0.227410
$653$	−7566.06	−0.453419	−0.226710	−	0.973962i	$-0.572797\pi$
$653$	−7566.06	−0.453419	−0.226710	+	0.973962i	$0.572797\pi$
$654$	19135.1	1.14410
$655$	−6038.73	−0.360233
$656$	−4741.36	−0.282194
$657$	−12.5996	−0.000748186 0
$658$	20613.0	1.22124
$659$	−12354.8	−0.730310	−0.365155	−	0.930947i	$-0.618984\pi$
$659$	−12354.8	−0.730310	−0.365155	+	0.930947i	$0.618984\pi$
$660$	1186.39	0.0699698
$661$	22156.3	1.30375	0.651877	−	0.758325i	$-0.273982\pi$
$661$	22156.3	1.30375	0.651877	+	0.758325i	$0.273982\pi$
$662$	18346.4	1.07712
$663$	2593.20	0.151903
$664$	1363.13	0.0796681
$665$	16942.0	0.987946
$666$	139.349	0.00810758
$667$	1916.85	0.111276
$668$	−11364.6	−0.658247
$669$	14356.6	0.829686
$670$	−6540.61	−0.377143
$671$	−4509.81	−0.259462
$672$	−4801.65	−0.275636
$673$	24162.0	1.38392	0.691959	−	0.721937i	$-0.256748\pi$
$673$	24162.0	1.38392	0.691959	+	0.721937i	$0.256748\pi$
$674$	18000.1	1.02869
$675$	−3359.51	−0.191567
$676$	−5587.44	−0.317902
$677$	−9435.35	−0.535642	−0.267821	−	0.963469i	$-0.586304\pi$
$677$	−9435.35	−0.535642	−0.267821	+	0.963469i	$0.586304\pi$
$678$	−17793.7	−1.00791
$679$	−25534.9	−1.44321
$680$	680.000	0.0383482
$681$	14920.3	0.839568
$682$	2635.90	0.147997
$683$	30241.4	1.69422	0.847111	−	0.531416i	$-0.178340\pi$
$683$	30241.4	1.69422	0.847111	+	0.531416i	$0.178340\pi$
$684$	−1013.62	−0.0566620
$685$	6264.96	0.349448
$686$	−4910.28	−0.273288
$687$	24614.9	1.36698
$688$	−81.3528	−0.00450806
$689$	−16680.5	−0.922318
$690$	−517.556	−0.0285551
$691$	23024.3	1.26756	0.633782	−	0.773511i	$-0.281501\pi$
$691$	23024.3	1.26756	0.633782	+	0.773511i	$0.281501\pi$
$692$	−4498.10	−0.247098
$693$	−636.921	−0.0349129
$694$	−8015.43	−0.438417
$695$	6371.85	0.347767
$696$	8616.47	0.469262
$697$	−5037.70	−0.273768
$698$	3082.85	0.167174
$699$	−27720.5	−1.49998
$700$	2782.51	0.150241
$701$	3847.14	0.207282	0.103641	−	0.994615i	$-0.466951\pi$
$701$	3847.14	0.207282	0.103641	+	0.994615i	$0.466951\pi$
$702$	7602.37	0.408736
$703$	4077.33	0.218747
$704$	−704.000	−0.0376889
$705$	9987.30	0.533537
$706$	−9425.65	−0.502463
$707$	3792.07	0.201719
$708$	8377.66	0.444706
$709$	14168.1	0.750484	0.375242	−	0.926927i	$-0.377560\pi$
$709$	14168.1	0.750484	0.375242	+	0.926927i	$0.377560\pi$
$710$	−6685.91	−0.353405
$711$	2247.51	0.118549
$712$	739.397	0.0389186
$713$	−1149.90	−0.0603985
$714$	−5101.75	−0.267407
$715$	1555.77	0.0813742
$716$	−3112.37	−0.162451
$717$	−12825.3	−0.668018
$718$	15116.1	0.785696
$719$	−3009.94	−0.156122	−0.0780611	−	0.996949i	$-0.524873\pi$
$719$	−3009.94	−0.156122	−0.0780611	+	0.996949i	$0.524873\pi$
$720$	−166.474	−0.00861683
$721$	−11850.0	−0.612092
$722$	−15940.5	−0.821666
$723$	15401.6	0.792241
$724$	−253.382	−0.0130067
$725$	−4993.16	−0.255781
$726$	−1305.03	−0.0667136
$727$	2707.78	0.138138	0.0690688	−	0.997612i	$-0.477997\pi$
$727$	2707.78	0.138138	0.0690688	+	0.997612i	$0.477997\pi$
$728$	−6296.65	−0.320562
$729$	17941.2	0.911507
$730$	−60.5482	−0.00306985
$731$	−86.4373	−0.00437346
$732$	8843.61	0.446543
$733$	−13258.9	−0.668114	−0.334057	−	0.942553i	$-0.608418\pi$
$733$	−13258.9	−0.668114	−0.334057	+	0.942553i	$0.608418\pi$
$734$	9480.64	0.476753
$735$	−11627.5	−0.583522
$736$	307.117	0.0153811
$737$	7194.68	0.359592
$738$	1233.30	0.0615156
$739$	26600.3	1.32410	0.662049	−	0.749461i	$-0.269687\pi$
$739$	26600.3	1.32410	0.662049	+	0.749461i	$0.269687\pi$
$740$	669.647	0.0332658
$741$	−18575.8	−0.920914
$742$	32816.5	1.62363
$743$	13781.7	0.680489	0.340244	−	0.940337i	$-0.389490\pi$
$743$	13781.7	0.680489	0.340244	+	0.940337i	$0.389490\pi$
$744$	−5168.93	−0.254707
$745$	−6049.34	−0.297491
$746$	12195.8	0.598551
$747$	−354.571	−0.0173669
$748$	−748.000	−0.0365636
$749$	22518.6	1.09854
$750$	1348.17	0.0656375
$751$	19431.3	0.944154	0.472077	−	0.881557i	$-0.343504\pi$
$751$	19431.3	0.944154	0.472077	+	0.881557i	$0.343504\pi$
$752$	−5926.44	−0.287387
$753$	947.362	0.0458483
$754$	11299.2	0.545747
$755$	5381.21	0.259394
$756$	−14956.6	−0.719531
$757$	−9645.51	−0.463107	−0.231553	−	0.972822i	$-0.574381\pi$
$757$	−9645.51	−0.463107	−0.231553	+	0.972822i	$0.574381\pi$
$758$	6035.69	0.289216
$759$	569.312	0.0272262
$760$	−4871.01	−0.232487
$761$	2931.80	0.139655	0.0698276	−	0.997559i	$-0.477755\pi$
$761$	2931.80	0.139655	0.0698276	+	0.997559i	$0.477755\pi$
$762$	−3147.47	−0.149634
$763$	−49366.5	−2.34232
$764$	12003.9	0.568436
$765$	−176.879	−0.00835955
$766$	9262.78	0.436916
$767$	10986.1	0.517188
$768$	1380.52	0.0648638
$769$	−24795.2	−1.16273	−0.581363	−	0.813644i	$-0.697480\pi$
$769$	−24795.2	−1.16273	−0.581363	+	0.813644i	$0.697480\pi$
$770$	−3060.76	−0.143249
$771$	5286.82	0.246952
$772$	−5736.18	−0.267422
$773$	32369.2	1.50613	0.753065	−	0.657946i	$-0.228575\pi$
$773$	32369.2	1.50613	0.753065	+	0.657946i	$0.228575\pi$
$774$	21.1611	0.000982714 0
$775$	2995.34	0.138833
$776$	7341.56	0.339622
$777$	−5024.08	−0.231966
$778$	−6754.27	−0.311250
$779$	36086.3	1.65973
$780$	−3050.82	−0.140047
$781$	7354.50	0.336959
$782$	326.312	0.0149218
$783$	26839.3	1.22498
$784$	6899.76	0.314311
$785$	−8728.53	−0.396860
$786$	−13026.0	−0.591120
$787$	8705.82	0.394319	0.197159	−	0.980371i	$-0.436828\pi$
$787$	8705.82	0.394319	0.197159	+	0.980371i	$0.436828\pi$
$788$	−12462.8	−0.563411
$789$	−31555.8	−1.42385
$790$	10800.5	0.486412
$791$	45905.9	2.06350
$792$	183.121	0.00821583
$793$	11597.1	0.519325
$794$	−30374.7	−1.35763
$795$	15900.1	0.709333
$796$	−9886.91	−0.440241
$797$	23495.4	1.04423	0.522115	−	0.852875i	$-0.325143\pi$
$797$	23495.4	1.04423	0.522115	+	0.852875i	$0.325143\pi$
$798$	36545.2	1.62116
$799$	−6296.84	−0.278806
$800$	−800.000	−0.0353553
$801$	−192.329	−0.00848389
$802$	901.581	0.0396957
$803$	66.6031	0.00292699
$804$	−14108.6	−0.618869
$805$	1335.24	0.0584610
$806$	−6778.28	−0.296222
$807$	−346.926	−0.0151331
$808$	−1090.26	−0.0474693
$809$	6298.70	0.273733	0.136867	−	0.990589i	$-0.456297\pi$
$809$	6298.70	0.273733	0.136867	+	0.990589i	$0.456297\pi$
$810$	−7808.55	−0.338721
$811$	21111.5	0.914088	0.457044	−	0.889444i	$-0.348908\pi$
$811$	21111.5	0.914088	0.457044	+	0.889444i	$0.348908\pi$
$812$	−22229.6	−0.960721
$813$	−24129.0	−1.04089
$814$	−736.612	−0.0317177
$815$	−4732.51	−0.203402
$816$	1466.81	0.0629271
$817$	619.173	0.0265142
$818$	9074.60	0.387880
$819$	1637.86	0.0698795
$820$	5926.71	0.252402
$821$	22565.2	0.959234	0.479617	−	0.877478i	$-0.340776\pi$
$821$	22565.2	0.959234	0.479617	+	0.877478i	$0.340776\pi$
$822$	13514.0	0.573422
$823$	35457.8	1.50180	0.750900	−	0.660416i	$-0.229620\pi$
$823$	35457.8	1.50180	0.750900	+	0.660416i	$0.229620\pi$
$824$	3407.01	0.144040
$825$	−1482.99	−0.0625829
$826$	−21613.5	−0.910447
$827$	15080.6	0.634106	0.317053	−	0.948408i	$-0.397307\pi$
$827$	15080.6	0.634106	0.317053	+	0.948408i	$0.397307\pi$
$828$	−79.8858	−0.00335293
$829$	34814.6	1.45858	0.729290	−	0.684205i	$-0.239851\pi$
$829$	34814.6	1.45858	0.729290	+	0.684205i	$0.239851\pi$
$830$	−1703.91	−0.0712573
$831$	28490.9	1.18934
$832$	1810.35	0.0754359
$833$	7330.99	0.304927
$834$	13744.5	0.570664
$835$	14205.7	0.588754
$836$	5358.12	0.221668
$837$	−16100.6	−0.664897
$838$	27501.1	1.13366
$839$	25309.5	1.04146	0.520728	−	0.853723i	$-0.325661\pi$
$839$	25309.5	1.04146	0.520728	+	0.853723i	$0.325661\pi$
$840$	6002.06	0.246537
$841$	15501.6	0.635597
$842$	−1769.02	−0.0724042
$843$	26444.1	1.08041
$844$	19149.1	0.780972
$845$	6984.30	0.284340
$846$	1541.56	0.0626476
$847$	3366.83	0.136583
$848$	−9435.10	−0.382079
$849$	18035.8	0.729077
$850$	−850.000	−0.0342997
$851$	321.344	0.0129442
$852$	−14422.0	−0.579916
$853$	43334.8	1.73946	0.869728	−	0.493531i	$-0.164294\pi$
$853$	43334.8	1.73946	0.869728	+	0.493531i	$0.164294\pi$
$854$	−22815.6	−0.914208
$855$	1267.03	0.0506800
$856$	−6474.32	−0.258514
$857$	14610.5	0.582365	0.291183	−	0.956668i	$-0.405951\pi$
$857$	14610.5	0.582365	0.291183	+	0.956668i	$0.405951\pi$
$858$	3355.91	0.133530
$859$	−38719.8	−1.53795	−0.768977	−	0.639276i	$-0.779234\pi$
$859$	−38719.8	−1.53795	−0.768977	+	0.639276i	$0.779234\pi$
$860$	101.691	0.00403213
$861$	−44465.6	−1.76003
$862$	28935.2	1.14332
$863$	31015.8	1.22340	0.611698	−	0.791092i	$-0.290487\pi$
$863$	31015.8	1.22340	0.611698	+	0.791092i	$0.290487\pi$
$864$	4300.17	0.169323
$865$	5622.62	0.221011
$866$	16483.9	0.646820
$867$	1558.48	0.0610483
$868$	13335.3	0.521463
$869$	−11880.6	−0.463776
$870$	−10770.6	−0.419721
$871$	−18501.3	−0.719738
$872$	14193.4	0.551203
$873$	−1909.65	−0.0740344
$874$	−2337.45	−0.0904640
$875$	−3478.13	−0.134380
$876$	−130.607	−0.00503743
$877$	7073.98	0.272373	0.136187	−	0.990683i	$-0.456515\pi$
$877$	7073.98	0.272373	0.136187	+	0.990683i	$0.456515\pi$
$878$	21505.8	0.826635
$879$	20492.9	0.786356
$880$	880.000	0.0337100
$881$	23284.1	0.890423	0.445212	−	0.895425i	$-0.353128\pi$
$881$	23284.1	0.890423	0.445212	+	0.895425i	$0.353128\pi$
$882$	−1794.73	−0.0685168
$883$	31682.2	1.20746	0.603732	−	0.797187i	$-0.293680\pi$
$883$	31682.2	1.20746	0.603732	+	0.797187i	$0.293680\pi$
$884$	1923.50	0.0731836
$885$	−10472.1	−0.397757
$886$	4263.27	0.161656
$887$	23289.7	0.881614	0.440807	−	0.897602i	$-0.354692\pi$
$887$	23289.7	0.881614	0.440807	+	0.897602i	$0.354692\pi$
$888$	1444.48	0.0545872
$889$	8120.15	0.306345
$890$	−924.246	−0.0348099
$891$	8589.40	0.322958
$892$	10649.0	0.399725
$893$	45105.9	1.69027
$894$	−13048.9	−0.488164
$895$	3890.46	0.145300
$896$	−3561.61	−0.132796
$897$	−1464.00	−0.0544944
$898$	−33809.7	−1.25640
$899$	−23930.0	−0.887774
$900$	208.092	0.00770713
$901$	−10024.8	−0.370671
$902$	−6519.38	−0.240656
$903$	−762.944	−0.0281165
$904$	−13198.4	−0.485590
$905$	316.727	0.0116335
$906$	11607.6	0.425649
$907$	12889.3	0.471865	0.235932	−	0.971769i	$-0.424186\pi$
$907$	12889.3	0.471865	0.235932	+	0.971769i	$0.424186\pi$
$908$	11067.1	0.404486
$909$	283.593	0.0103479
$910$	7870.81	0.286719
$911$	−5001.12	−0.181882	−0.0909411	−	0.995856i	$-0.528987\pi$
$911$	−5001.12	−0.181882	−0.0909411	+	0.995856i	$0.528987\pi$
$912$	−10507.1	−0.381497
$913$	1874.30	0.0679411
$914$	598.234	0.0216497
$915$	−11054.5	−0.399400
$916$	18258.0	0.658583
$917$	33605.6	1.21020
$918$	4568.93	0.164267
$919$	−35950.1	−1.29041	−0.645204	−	0.764010i	$-0.723228\pi$
$919$	−35950.1	−1.29041	−0.645204	+	0.764010i	$0.723228\pi$
$920$	−383.896	−0.0137573
$921$	−6961.72	−0.249073
$922$	8200.09	0.292902
$923$	−18912.3	−0.674437
$924$	−6602.27	−0.235063
$925$	−837.059	−0.0297539
$926$	−24749.0	−0.878298
$927$	−886.216	−0.0313993
$928$	6391.24	0.226081
$929$	−722.553	−0.0255180	−0.0127590	−	0.999919i	$-0.504061\pi$
$929$	−722.553	−0.0255180	−0.0127590	+	0.999919i	$0.504061\pi$
$930$	6461.17	0.227817
$931$	−52513.8	−1.84862
$932$	−20561.6	−0.722657
$933$	−31047.0	−1.08943
$934$	26576.4	0.931057
$935$	935.000	0.0327035
$936$	−470.901	−0.0164443
$937$	−47672.7	−1.66211	−0.831056	−	0.556189i	$-0.812263\pi$
$937$	−47672.7	−1.66211	−0.831056	+	0.556189i	$0.812263\pi$
$938$	36398.6	1.26701
$939$	3190.04	0.110866
$940$	7408.05	0.257047
$941$	−22836.9	−0.791140	−0.395570	−	0.918436i	$-0.629453\pi$
$941$	−22836.9	−0.791140	−0.395570	+	0.918436i	$0.629453\pi$
$942$	−18828.1	−0.651222
$943$	2844.05	0.0982131
$944$	6214.11	0.214250
$945$	18695.7	0.643568
$946$	−111.860	−0.00384449
$947$	−20889.7	−0.716814	−0.358407	−	0.933565i	$-0.616680\pi$
$947$	−20889.7	−0.716814	−0.358407	+	0.933565i	$0.616680\pi$
$948$	23297.5	0.798172
$949$	−171.271	−0.00585848
$950$	6088.77	0.207943
$951$	−23345.2	−0.796025
$952$	−3784.21	−0.128831
$953$	8799.82	0.299112	0.149556	−	0.988753i	$-0.452216\pi$
$953$	8799.82	0.299112	0.149556	+	0.988753i	$0.452216\pi$
$954$	2454.22	0.0832895
$955$	−15004.9	−0.508425
$956$	−9513.12	−0.321837
$957$	11847.6	0.400188
$958$	18356.8	0.619082
$959$	−34864.6	−1.17397
$960$	−1725.66	−0.0580159
$961$	−15435.7	−0.518132
$962$	1894.21	0.0634843
$963$	1684.07	0.0563535
$964$	11424.1	0.381685
$965$	7170.23	0.239189
$966$	2880.21	0.0959308
$967$	−30990.5	−1.03060	−0.515298	−	0.857011i	$-0.672319\pi$
$967$	−30990.5	−1.03060	−0.515298	+	0.857011i	$0.672319\pi$
$968$	−968.000	−0.0321412
$969$	−11163.8	−0.370107
$970$	−9176.95	−0.303767
$971$	1206.85	0.0398865	0.0199433	−	0.999801i	$-0.493651\pi$
$971$	1206.85	0.0398865	0.0199433	+	0.999801i	$0.493651\pi$
$972$	−2330.49	−0.0769038
$973$	−35459.5	−1.16832
$974$	40200.9	1.32250
$975$	3813.53	0.125262
$976$	6559.72	0.215135
$977$	−13046.2	−0.427209	−0.213605	−	0.976920i	$-0.568520\pi$
$977$	−13046.2	−0.427209	−0.213605	+	0.976920i	$0.568520\pi$
$978$	−10208.4	−0.333770
$979$	1016.67	0.0331899
$980$	−8624.70	−0.281128
$981$	−3691.92	−0.120157
$982$	−9355.53	−0.304019
$983$	−42847.8	−1.39027	−0.695134	−	0.718880i	$-0.744655\pi$
$983$	−42847.8	−1.39027	−0.695134	+	0.718880i	$0.744655\pi$
$984$	12784.3	0.414176
$985$	15578.5	0.503930
$986$	6790.69	0.219330
$987$	−55579.5	−1.79242
$988$	−13778.5	−0.443677
$989$	48.7984	0.00156896
$990$	−228.902	−0.00734846
$991$	−55931.4	−1.79285	−0.896427	−	0.443191i	$-0.853846\pi$
$991$	−55931.4	−1.79285	−0.896427	+	0.443191i	$0.853846\pi$
$992$	−3834.04	−0.122713
$993$	−49468.0	−1.58089
$994$	37207.2	1.18726
$995$	12358.6	0.393764
$996$	−3675.45	−0.116929
$997$	20758.6	0.659410	0.329705	−	0.944084i	$-0.393051\pi$
$997$	20758.6	0.659410	0.329705	+	0.944084i	$0.393051\pi$
$998$	−6425.96	−0.203818
$999$	4499.38	0.142496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.j.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.j.1.8	✓	10	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:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +5.39267 q^{3} +4.00000 q^{4} -5.00000 q^{5} -10.7853 q^{6} +27.8251 q^{7} -8.00000 q^{8} +2.08092 q^{9} +10.0000 q^{10} -11.0000 q^{11} +21.5707 q^{12} +28.2867 q^{13} -55.6501 q^{14} -26.9634 q^{15} +16.0000 q^{16} +17.0000 q^{17} -4.16185 q^{18} -121.775 q^{19} -20.0000 q^{20} +150.052 q^{21} +22.0000 q^{22} -9.59740 q^{23} -43.1414 q^{24} +25.0000 q^{25} -56.5735 q^{26} -134.380 q^{27} +111.300 q^{28} -199.726 q^{29} +53.9267 q^{30} +119.814 q^{31} -32.0000 q^{32} -59.3194 q^{33} -34.0000 q^{34} -139.125 q^{35} +8.32370 q^{36} -33.4824 q^{37} +243.551 q^{38} +152.541 q^{39} +40.0000 q^{40} -296.335 q^{41} -300.103 q^{42} -5.08455 q^{43} -44.0000 q^{44} -10.4046 q^{45} +19.1948 q^{46} -370.402 q^{47} +86.2828 q^{48} +431.235 q^{49} -50.0000 q^{50} +91.6754 q^{51} +113.147 q^{52} -589.694 q^{53} +268.761 q^{54} +55.0000 q^{55} -222.601 q^{56} -656.695 q^{57} +399.452 q^{58} +388.382 q^{59} -107.853 q^{60} +409.983 q^{61} -239.628 q^{62} +57.9019 q^{63} +64.0000 q^{64} -141.434 q^{65} +118.639 q^{66} -654.061 q^{67} +68.0000 q^{68} -51.7556 q^{69} +278.251 q^{70} -668.591 q^{71} -16.6474 q^{72} -6.05482 q^{73} +66.9647 q^{74} +134.817 q^{75} -487.101 q^{76} -306.076 q^{77} -305.082 q^{78} +1080.05 q^{79} -80.0000 q^{80} -780.855 q^{81} +592.671 q^{82} -170.391 q^{83} +600.206 q^{84} -85.0000 q^{85} +10.1691 q^{86} -1077.06 q^{87} +88.0000 q^{88} -92.4246 q^{89} +20.8092 q^{90} +787.081 q^{91} -38.3896 q^{92} +646.117 q^{93} +740.805 q^{94} +608.877 q^{95} -172.566 q^{96} -917.695 q^{97} -862.470 q^{98} -22.8902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) \) 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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