LMFDB - Embedded newform 230.6.a.g.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-20,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 772x^{3} - 255x^{2} + 13416x + 10080 $ x^5 - 772x^3 - 255x^2 + 13416*x + 10080
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.766035$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} +0.233965 q^{3} +16.0000 q^{4} -25.0000 q^{5} -0.935860 q^{6} +203.513 q^{7} -64.0000 q^{8} -242.945 q^{9} +100.000 q^{10} -151.197 q^{11} +3.74344 q^{12} +1152.80 q^{13} -814.051 q^{14} -5.84912 q^{15} +256.000 q^{16} -692.618 q^{17} +971.781 q^{18} -360.416 q^{19} -400.000 q^{20} +47.6148 q^{21} +604.789 q^{22} +529.000 q^{23} -14.9738 q^{24} +625.000 q^{25} -4611.19 q^{26} -113.694 q^{27} +3256.20 q^{28} -3686.27 q^{29} +23.3965 q^{30} +868.793 q^{31} -1024.00 q^{32} -35.3748 q^{33} +2770.47 q^{34} -5087.82 q^{35} -3887.12 q^{36} +4023.42 q^{37} +1441.66 q^{38} +269.714 q^{39} +1600.00 q^{40} -6448.34 q^{41} -190.459 q^{42} +6561.73 q^{43} -2419.16 q^{44} +6073.63 q^{45} -2116.00 q^{46} +12850.0 q^{47} +59.8950 q^{48} +24610.4 q^{49} -2500.00 q^{50} -162.048 q^{51} +18444.8 q^{52} -11515.1 q^{53} +454.777 q^{54} +3779.93 q^{55} -13024.8 q^{56} -84.3247 q^{57} +14745.1 q^{58} +28695.2 q^{59} -93.5860 q^{60} +3672.30 q^{61} -3475.17 q^{62} -49442.5 q^{63} +4096.00 q^{64} -28819.9 q^{65} +141.499 q^{66} +39498.4 q^{67} -11081.9 q^{68} +123.767 q^{69} +20351.3 q^{70} +31887.5 q^{71} +15548.5 q^{72} +2911.70 q^{73} -16093.7 q^{74} +146.228 q^{75} -5766.66 q^{76} -30770.6 q^{77} -1078.86 q^{78} +100421. q^{79} -6400.00 q^{80} +59009.1 q^{81} +25793.4 q^{82} +77129.7 q^{83} +761.838 q^{84} +17315.4 q^{85} -26246.9 q^{86} -862.457 q^{87} +9676.62 q^{88} +106159. q^{89} -24294.5 q^{90} +234609. q^{91} +8464.00 q^{92} +203.267 q^{93} -51399.9 q^{94} +9010.40 q^{95} -239.580 q^{96} -35876.4 q^{97} -98441.8 q^{98} +36732.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18}+ \cdots + 362547 q^{99}+O(q^{100}) $ 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	0.233965	0.0150089	0.00750443	−	0.999972i	$-0.497611\pi$
$3$	0.233965	0.0150089	0.00750443	+	0.999972i	$0.497611\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−0.935860	−0.0106129
$7$	203.513	1.56981	0.784904	−	0.619617i	$-0.212712\pi$
$7$	203.513	1.56981	0.784904	+	0.619617i	$0.212712\pi$
$8$	−64.0000	−0.353553
$9$	−242.945	−0.999775
$10$	100.000	0.316228
$11$	−151.197	−0.376758	−0.188379	−	0.982096i	$-0.560323\pi$
$11$	−151.197	−0.376758	−0.188379	+	0.982096i	$0.560323\pi$
$12$	3.74344	0.00750443
$13$	1152.80	1.89188	0.945942	−	0.324336i	$-0.105141\pi$
$13$	1152.80	1.89188	0.945942	+	0.324336i	$0.105141\pi$
$14$	−814.051	−1.11002
$15$	−5.84912	−0.00671216
$16$	256.000	0.250000
$17$	−692.618	−0.581261	−0.290631	−	0.956835i	$-0.593865\pi$
$17$	−692.618	−0.581261	−0.290631	+	0.956835i	$0.593865\pi$
$18$	971.781	0.706947
$19$	−360.416	−0.229045	−0.114522	−	0.993421i	$-0.536534\pi$
$19$	−360.416	−0.229045	−0.114522	+	0.993421i	$0.536534\pi$
$20$	−400.000	−0.223607
$21$	47.6148	0.0235610
$22$	604.789	0.266408
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−14.9738	−0.00530643
$25$	625.000	0.200000
$26$	−4611.19	−1.33776
$27$	−113.694	−0.0300143
$28$	3256.20	0.784904
$29$	−3686.27	−0.813938	−0.406969	−	0.913442i	$-0.633414\pi$
$29$	−3686.27	−0.813938	−0.406969	+	0.913442i	$0.633414\pi$
$30$	23.3965	0.00474622
$31$	868.793	0.162372	0.0811861	−	0.996699i	$-0.474129\pi$
$31$	868.793	0.162372	0.0811861	+	0.996699i	$0.474129\pi$
$32$	−1024.00	−0.176777
$33$	−35.3748	−0.00565470
$34$	2770.47	0.411014
$35$	−5087.82	−0.702040
$36$	−3887.12	−0.499887
$37$	4023.42	0.483160	0.241580	−	0.970381i	$-0.422334\pi$
$37$	4023.42	0.483160	0.241580	+	0.970381i	$0.422334\pi$
$38$	1441.66	0.161959
$39$	269.714	0.0283950
$40$	1600.00	0.158114
$41$	−6448.34	−0.599085	−0.299542	−	0.954083i	$-0.596834\pi$
$41$	−6448.34	−0.599085	−0.299542	+	0.954083i	$0.596834\pi$
$42$	−190.459	−0.0166602
$43$	6561.73	0.541187	0.270593	−	0.962694i	$-0.412780\pi$
$43$	6561.73	0.541187	0.270593	+	0.962694i	$0.412780\pi$
$44$	−2419.16	−0.188379
$45$	6073.63	0.447113
$46$	−2116.00	−0.147442
$47$	12850.0	0.848512	0.424256	−	0.905542i	$-0.360536\pi$
$47$	12850.0	0.848512	0.424256	+	0.905542i	$0.360536\pi$
$48$	59.8950	0.00375221
$49$	24610.4	1.46430
$50$	−2500.00	−0.141421
$51$	−162.048	−0.00872407
$52$	18444.8	0.945942
$53$	−11515.1	−0.563092	−0.281546	−	0.959548i	$-0.590847\pi$
$53$	−11515.1	−0.563092	−0.281546	+	0.959548i	$0.590847\pi$
$54$	454.777	0.0212233
$55$	3779.93	0.168491
$56$	−13024.8	−0.555011
$57$	−84.3247	−0.00343770
$58$	14745.1	0.575541
$59$	28695.2	1.07320	0.536598	−	0.843838i	$-0.319709\pi$
$59$	28695.2	1.07320	0.536598	+	0.843838i	$0.319709\pi$
$60$	−93.5860	−0.00335608
$61$	3672.30	0.126361	0.0631805	−	0.998002i	$-0.479876\pi$
$61$	3672.30	0.126361	0.0631805	+	0.998002i	$0.479876\pi$
$62$	−3475.17	−0.114815
$63$	−49442.5	−1.56945
$64$	4096.00	0.125000
$65$	−28819.9	−0.846076
$66$	141.499	0.00399848
$67$	39498.4	1.07496	0.537480	−	0.843276i	$-0.319376\pi$
$67$	39498.4	1.07496	0.537480	+	0.843276i	$0.319376\pi$
$68$	−11081.9	−0.290631
$69$	123.767	0.00312956
$70$	20351.3	0.496417
$71$	31887.5	0.750713	0.375357	−	0.926880i	$-0.377520\pi$
$71$	31887.5	0.750713	0.375357	+	0.926880i	$0.377520\pi$
$72$	15548.5	0.353474
$73$	2911.70	0.0639499	0.0319749	−	0.999489i	$-0.489820\pi$
$73$	2911.70	0.0639499	0.0319749	+	0.999489i	$0.489820\pi$
$74$	−16093.7	−0.341645
$75$	146.228	0.00300177
$76$	−5766.66	−0.114522
$77$	−30770.6	−0.591437
$78$	−1078.86	−0.0200783
$79$	100421.	1.81032	0.905159	−	0.425073i	$-0.139752\pi$
$79$	100421.	1.81032	0.905159	+	0.425073i	$0.139752\pi$
$80$	−6400.00	−0.111803
$81$	59009.1	0.999324
$82$	25793.4	0.423617
$83$	77129.7	1.22893	0.614464	−	0.788945i	$-0.289372\pi$
$83$	77129.7	1.22893	0.614464	+	0.788945i	$0.289372\pi$
$84$	761.838	0.0117805
$85$	17315.4	0.259948
$86$	−26246.9	−0.382677
$87$	−862.457	−0.0122163
$88$	9676.62	0.133204
$89$	106159.	1.42063	0.710316	−	0.703883i	$-0.248552\pi$
$89$	106159.	1.42063	0.710316	+	0.703883i	$0.248552\pi$
$90$	−24294.5	−0.316157
$91$	234609.	2.96989
$92$	8464.00	0.104257
$93$	203.267	0.00243702
$94$	−51399.9	−0.599988
$95$	9010.40	0.102432
$96$	−239.580	−0.00265322
$97$	−35876.4	−0.387150	−0.193575	−	0.981085i	$-0.562008\pi$
$97$	−35876.4	−0.387150	−0.193575	+	0.981085i	$0.562008\pi$
$98$	−98441.8	−1.03541
$99$	36732.6	0.376673
$100$	10000.0	0.100000
$101$	149519.	1.45846	0.729228	−	0.684270i	$-0.239879\pi$
$101$	149519.	1.45846	0.729228	+	0.684270i	$0.239879\pi$
$102$	648.193	0.00616885
$103$	185430.	1.72221	0.861105	−	0.508427i	$-0.169773\pi$
$103$	185430.	1.72221	0.861105	+	0.508427i	$0.169773\pi$
$104$	−73779.0	−0.668882
$105$	−1190.37	−0.0105368
$106$	46060.5	0.398166
$107$	−51104.2	−0.431516	−0.215758	−	0.976447i	$-0.569222\pi$
$107$	−51104.2	−0.431516	−0.215758	+	0.976447i	$0.569222\pi$
$108$	−1819.11	−0.0150072
$109$	−199534.	−1.60861	−0.804305	−	0.594216i	$-0.797462\pi$
$109$	−199534.	−1.60861	−0.804305	+	0.594216i	$0.797462\pi$
$110$	−15119.7	−0.119141
$111$	941.338	0.00725167
$112$	52099.3	0.392452
$113$	38000.0	0.279955	0.139977	−	0.990155i	$-0.455297\pi$
$113$	38000.0	0.279955	0.139977	+	0.990155i	$0.455297\pi$
$114$	337.299	0.00243082
$115$	−13225.0	−0.0932505
$116$	−58980.2	−0.406969
$117$	−280067.	−1.89146
$118$	−114781.	−0.758865
$119$	−140957.	−0.912469
$120$	374.344	0.00237311
$121$	−138190.	−0.858054
$122$	−14689.2	−0.0893507
$123$	−1508.69	−0.00899158
$124$	13900.7	0.0811861
$125$	−15625.0	−0.0894427
$126$	197770.	1.10977
$127$	−139632.	−0.768204	−0.384102	−	0.923291i	$-0.625489\pi$
$127$	−139632.	−0.768204	−0.384102	+	0.923291i	$0.625489\pi$
$128$	−16384.0	−0.0883883
$129$	1535.21	0.00812259
$130$	115280.	0.598266
$131$	79990.9	0.407251	0.203626	−	0.979049i	$-0.434727\pi$
$131$	79990.9	0.407251	0.203626	+	0.979049i	$0.434727\pi$
$132$	−565.997	−0.00282735
$133$	−73349.3	−0.359556
$134$	−157994.	−0.760112
$135$	2842.35	0.0134228
$136$	44327.5	0.205507
$137$	58350.3	0.265608	0.132804	−	0.991142i	$-0.457602\pi$
$137$	58350.3	0.265608	0.132804	+	0.991142i	$0.457602\pi$
$138$	−495.070	−0.00221294
$139$	−232905.	−1.02245	−0.511226	−	0.859447i	$-0.670808\pi$
$139$	−232905.	−1.02245	−0.511226	+	0.859447i	$0.670808\pi$
$140$	−81405.1	−0.351020
$141$	3006.45	0.0127352
$142$	−127550.	−0.530834
$143$	−174300.	−0.712782
$144$	−62194.0	−0.249944
$145$	92156.6	0.364004
$146$	−11646.8	−0.0452194
$147$	5757.98	0.0219774
$148$	64374.6	0.241580
$149$	191123.	0.705258	0.352629	−	0.935763i	$-0.385288\pi$
$149$	191123.	0.705258	0.352629	+	0.935763i	$0.385288\pi$
$150$	−584.912	−0.00212257
$151$	89666.2	0.320027	0.160013	−	0.987115i	$-0.448846\pi$
$151$	89666.2	0.320027	0.160013	+	0.987115i	$0.448846\pi$
$152$	23066.6	0.0809795
$153$	168268.	0.581130
$154$	123082.	0.418209
$155$	−21719.8	−0.0726151
$156$	4315.42	0.0141975
$157$	−487729.	−1.57917	−0.789586	−	0.613639i	$-0.789705\pi$
$157$	−487729.	−1.57917	−0.789586	+	0.613639i	$0.789705\pi$
$158$	−401682.	−1.28009
$159$	−2694.14	−0.00845136
$160$	25600.0	0.0790569
$161$	107658.	0.327328
$162$	−236036.	−0.706629
$163$	−159582.	−0.470453	−0.235226	−	0.971941i	$-0.575583\pi$
$163$	−159582.	−0.470453	−0.235226	+	0.971941i	$0.575583\pi$
$164$	−103173.	−0.299542
$165$	884.371	0.00252886
$166$	−308519.	−0.868983
$167$	−145695.	−0.404254	−0.202127	−	0.979359i	$-0.564785\pi$
$167$	−145695.	−0.404254	−0.202127	+	0.979359i	$0.564785\pi$
$168$	−3047.35	−0.00833008
$169$	957648.	2.57922
$170$	−69261.8	−0.183811
$171$	87561.4	0.228993
$172$	104988.	0.270593
$173$	461231.	1.17167	0.585833	−	0.810432i	$-0.300768\pi$
$173$	461231.	1.17167	0.585833	+	0.810432i	$0.300768\pi$
$174$	3449.83	0.00863822
$175$	127195.	0.313962
$176$	−38706.5	−0.0941894
$177$	6713.67	0.0161075
$178$	−424636.	−1.00454
$179$	−105545.	−0.246210	−0.123105	−	0.992394i	$-0.539285\pi$
$179$	−105545.	−0.246210	−0.123105	+	0.992394i	$0.539285\pi$
$180$	97178.1	0.223556
$181$	−176285.	−0.399962	−0.199981	−	0.979800i	$-0.564088\pi$
$181$	−176285.	−0.399962	−0.199981	+	0.979800i	$0.564088\pi$
$182$	−938436.	−2.10003
$183$	859.188	0.00189653
$184$	−33856.0	−0.0737210
$185$	−100585.	−0.216076
$186$	−813.068	−0.00172323
$187$	104722.	0.218995
$188$	205600.	0.424256
$189$	−23138.2	−0.0471167
$190$	−36041.6	−0.0724303
$191$	−572948.	−1.13640	−0.568201	−	0.822890i	$-0.692360\pi$
$191$	−572948.	−1.13640	−0.568201	+	0.822890i	$0.692360\pi$
$192$	958.320	0.00187611
$193$	567106.	1.09590	0.547950	−	0.836511i	$-0.315408\pi$
$193$	567106.	1.09590	0.547950	+	0.836511i	$0.315408\pi$
$194$	143506.	0.273756
$195$	−6742.85	−0.0126986
$196$	393767.	0.732149
$197$	−414063.	−0.760154	−0.380077	−	0.924955i	$-0.624102\pi$
$197$	−414063.	−0.760154	−0.380077	+	0.924955i	$0.624102\pi$
$198$	−146931.	−0.266348
$199$	−945301.	−1.69214	−0.846072	−	0.533068i	$-0.821039\pi$
$199$	−945301.	−1.69214	−0.846072	+	0.533068i	$0.821039\pi$
$200$	−40000.0	−0.0707107
$201$	9241.24	0.0161339
$202$	−598077.	−1.03128
$203$	−750202.	−1.27773
$204$	−2592.77	−0.00436203
$205$	161208.	0.267919
$206$	−741719.	−1.21779
$207$	−128518.	−0.208467
$208$	295116.	0.472971
$209$	54493.9	0.0862943
$210$	4761.48	0.00745065
$211$	383647.	0.593234	0.296617	−	0.954997i	$-0.404142\pi$
$211$	383647.	0.593234	0.296617	+	0.954997i	$0.404142\pi$
$212$	−184242.	−0.281546
$213$	7460.55	0.0112673
$214$	204417.	0.305128
$215$	−164043.	−0.242026
$216$	7276.42	0.0106117
$217$	176810.	0.254893
$218$	798136.	1.13746
$219$	681.236	0.000959815 0
$220$	60478.9	0.0842456
$221$	−798448.	−1.09968
$222$	−3765.35	−0.00512771
$223$	−453010.	−0.610022	−0.305011	−	0.952349i	$-0.598660\pi$
$223$	−453010.	−0.610022	−0.305011	+	0.952349i	$0.598660\pi$
$224$	−208397.	−0.277505
$225$	−151841.	−0.199955
$226$	−152000.	−0.197958
$227$	643854.	0.829322	0.414661	−	0.909976i	$-0.363900\pi$
$227$	643854.	0.829322	0.414661	+	0.909976i	$0.363900\pi$
$228$	−1349.20	−0.00171885
$229$	1.26959e6	1.59984	0.799920	−	0.600107i	$-0.204875\pi$
$229$	1.26959e6	1.59984	0.799920	+	0.600107i	$0.204875\pi$
$230$	52900.0	0.0659380
$231$	−7199.23	−0.00887680
$232$	235921.	0.287771
$233$	1.22552e6	1.47887	0.739434	−	0.673229i	$-0.235093\pi$
$233$	1.22552e6	1.47887	0.739434	+	0.673229i	$0.235093\pi$
$234$	1.12027e6	1.33746
$235$	−321250.	−0.379466
$236$	459123.	0.536598
$237$	23494.9	0.0271708
$238$	563826.	0.645213
$239$	−194741.	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$239$	−194741.	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$240$	−1497.38	−0.00167804
$241$	497293.	0.551531	0.275766	−	0.961225i	$-0.411069\pi$
$241$	497293.	0.551531	0.275766	+	0.961225i	$0.411069\pi$
$242$	552762.	0.606736
$243$	41433.7	0.0450130
$244$	58756.7	0.0631805
$245$	−615261.	−0.654854
$246$	6034.74	0.00635800
$247$	−415486.	−0.433326
$248$	−55602.7	−0.0574073
$249$	18045.6	0.0184448
$250$	62500.0	0.0632456
$251$	989940.	0.991801	0.495901	−	0.868379i	$-0.334838\pi$
$251$	989940.	0.991801	0.495901	+	0.868379i	$0.334838\pi$
$252$	−791079.	−0.784727
$253$	−79983.3	−0.0785594
$254$	558529.	0.543202
$255$	4051.21	0.00390152
$256$	65536.0	0.0625000
$257$	758424.	0.716274	0.358137	−	0.933669i	$-0.383412\pi$
$257$	758424.	0.716274	0.358137	+	0.933669i	$0.383412\pi$
$258$	−6140.86	−0.00574354
$259$	818816.	0.758468
$260$	−461119.	−0.423038
$261$	895561.	0.813755
$262$	−319964.	−0.287970
$263$	199181.	0.177565	0.0887826	−	0.996051i	$-0.471702\pi$
$263$	199181.	0.177565	0.0887826	+	0.996051i	$0.471702\pi$
$264$	2263.99	0.00199924
$265$	287878.	0.251822
$266$	293397.	0.254245
$267$	24837.5	0.0213221
$268$	631975.	0.537480
$269$	−684342.	−0.576624	−0.288312	−	0.957537i	$-0.593094\pi$
$269$	−684342.	−0.576624	−0.288312	+	0.957537i	$0.593094\pi$
$270$	−11369.4	−0.00949136
$271$	642357.	0.531316	0.265658	−	0.964067i	$-0.414411\pi$
$271$	642357.	0.531316	0.265658	+	0.964067i	$0.414411\pi$
$272$	−177310.	−0.145315
$273$	54890.2	0.0445747
$274$	−233401.	−0.187814
$275$	−94498.3	−0.0753515
$276$	1980.28	0.00156478
$277$	−2.49604e6	−1.95457	−0.977286	−	0.211924i	$-0.932027\pi$
$277$	−2.49604e6	−1.95457	−0.977286	+	0.211924i	$0.932027\pi$
$278$	931622.	0.722982
$279$	−211069.	−0.162336
$280$	325620.	0.248208
$281$	−1.14932e6	−0.868314	−0.434157	−	0.900837i	$-0.642954\pi$
$281$	−1.14932e6	−0.868314	−0.434157	+	0.900837i	$0.642954\pi$
$282$	−12025.8	−0.00900514
$283$	−100173.	−0.0743508	−0.0371754	−	0.999309i	$-0.511836\pi$
$283$	−100173.	−0.0743508	−0.0371754	+	0.999309i	$0.511836\pi$
$284$	510199.	0.375357
$285$	2108.12	0.00153738
$286$	697199.	0.504013
$287$	−1.31232e6	−0.940448
$288$	248776.	0.176737
$289$	−940137.	−0.662135
$290$	−368627.	−0.257390
$291$	−8393.81	−0.00581068
$292$	46587.2	0.0319749
$293$	1.22703e6	0.834998	0.417499	−	0.908677i	$-0.362907\pi$
$293$	1.22703e6	0.834998	0.417499	+	0.908677i	$0.362907\pi$
$294$	−23031.9	−0.0155404
$295$	−717380.	−0.479948
$296$	−257499.	−0.170823
$297$	17190.2	0.0113081
$298$	−764494.	−0.498693
$299$	609830.	0.394485
$300$	2339.65	0.00150089
$301$	1.33540e6	0.849559
$302$	−358665.	−0.226293
$303$	34982.2	0.0218898
$304$	−92266.5	−0.0572611
$305$	−91807.4	−0.0565103
$306$	−673073.	−0.410921
$307$	2.32776e6	1.40959	0.704793	−	0.709413i	$-0.251040\pi$
$307$	2.32776e6	1.40959	0.704793	+	0.709413i	$0.251040\pi$
$308$	−492329.	−0.295719
$309$	43384.0	0.0258484
$310$	86879.3	0.0513466
$311$	1.48165e6	0.868652	0.434326	−	0.900756i	$-0.356987\pi$
$311$	1.48165e6	0.868652	0.434326	+	0.900756i	$0.356987\pi$
$312$	−17261.7	−0.0100392
$313$	−1.07449e6	−0.619928	−0.309964	−	0.950748i	$-0.600317\pi$
$313$	−1.07449e6	−0.619928	−0.309964	+	0.950748i	$0.600317\pi$
$314$	1.95092e6	1.11664
$315$	1.23606e6	0.701881
$316$	1.60673e6	0.905159
$317$	−947703.	−0.529693	−0.264846	−	0.964291i	$-0.585321\pi$
$317$	−947703.	−0.529693	−0.264846	+	0.964291i	$0.585321\pi$
$318$	10776.5	0.00597602
$319$	557353.	0.306658
$320$	−102400.	−0.0559017
$321$	−11956.6	−0.00647657
$322$	−430633.	−0.231456
$323$	249631.	0.133135
$324$	944146.	0.499662
$325$	720498.	0.378377
$326$	638330.	0.332660
$327$	−46684.0	−0.0241434
$328$	412694.	0.211808
$329$	2.61514e6	1.33200
$330$	−3537.48	−0.00178817
$331$	1.87583e6	0.941075	0.470537	−	0.882380i	$-0.344060\pi$
$331$	1.87583e6	0.941075	0.470537	+	0.882380i	$0.344060\pi$
$332$	1.23408e6	0.614464
$333$	−977470.	−0.483051
$334$	582781.	0.285851
$335$	−987460.	−0.480737
$336$	12189.4	0.00589026
$337$	−3.58245e6	−1.71832	−0.859162	−	0.511703i	$-0.829015\pi$
$337$	−3.58245e6	−1.71832	−0.859162	+	0.511703i	$0.829015\pi$
$338$	−3.83059e6	−1.82379
$339$	8890.67	0.00420180
$340$	277047.	0.129974
$341$	−131359.	−0.0611750
$342$	−350245.	−0.161922
$343$	1.58810e6	0.728858
$344$	−419951.	−0.191338
$345$	−3094.19	−0.00139958
$346$	−1.84493e6	−0.828492
$347$	−3.93298e6	−1.75347	−0.876735	−	0.480973i	$-0.840283\pi$
$347$	−3.93298e6	−1.75347	−0.876735	+	0.480973i	$0.840283\pi$
$348$	−13799.3	−0.00610814
$349$	1.49068e6	0.655118	0.327559	−	0.944831i	$-0.393774\pi$
$349$	1.49068e6	0.655118	0.327559	+	0.944831i	$0.393774\pi$
$350$	−508782.	−0.222004
$351$	−131066.	−0.0567836
$352$	154826.	0.0666020
$353$	1.78776e6	0.763610	0.381805	−	0.924243i	$-0.375303\pi$
$353$	1.78776e6	0.763610	0.381805	+	0.924243i	$0.375303\pi$
$354$	−26854.7	−0.0113897
$355$	−797186.	−0.335729
$356$	1.69854e6	0.710316
$357$	−32978.9	−0.0136951
$358$	422181.	0.174097
$359$	−4.66089e6	−1.90868	−0.954340	−	0.298724i	$-0.903439\pi$
$359$	−4.66089e6	−1.90868	−0.954340	+	0.298724i	$0.903439\pi$
$360$	−388712.	−0.158078
$361$	−2.34620e6	−0.947539
$362$	705139.	0.282816
$363$	−32331.7	−0.0128784
$364$	3.75374e6	1.48495
$365$	−72792.5	−0.0285993
$366$	−3436.75	−0.00134105
$367$	−2.73126e6	−1.05852	−0.529258	−	0.848461i	$-0.677530\pi$
$367$	−2.73126e6	−1.05852	−0.529258	+	0.848461i	$0.677530\pi$
$368$	135424.	0.0521286
$369$	1.56659e6	0.598950
$370$	402342.	0.152788
$371$	−2.34348e6	−0.883946
$372$	3252.27	0.00121851
$373$	2.46023e6	0.915594	0.457797	−	0.889057i	$-0.348639\pi$
$373$	2.46023e6	0.915594	0.457797	+	0.889057i	$0.348639\pi$
$374$	−418888.	−0.154853
$375$	−3655.70	−0.00134243
$376$	−822399.	−0.299994
$377$	−4.24951e6	−1.53988
$378$	92552.8	0.0333166
$379$	760759.	0.272050	0.136025	−	0.990705i	$-0.456567\pi$
$379$	760759.	0.272050	0.136025	+	0.990705i	$0.456567\pi$
$380$	144166.	0.0512159
$381$	−32669.1	−0.0115299
$382$	2.29179e6	0.803557
$383$	−450971.	−0.157091	−0.0785456	−	0.996911i	$-0.525028\pi$
$383$	−450971.	−0.157091	−0.0785456	+	0.996911i	$0.525028\pi$
$384$	−3833.28	−0.00132661
$385$	769264.	0.264499
$386$	−2.26842e6	−0.774918
$387$	−1.59414e6	−0.541065
$388$	−574022.	−0.193575
$389$	3.98642e6	1.33570	0.667851	−	0.744295i	$-0.267214\pi$
$389$	3.98642e6	1.33570	0.667851	+	0.744295i	$0.267214\pi$
$390$	26971.4	0.00897929
$391$	−366395.	−0.121201
$392$	−1.57507e6	−0.517707
$393$	18715.1	0.00611237
$394$	1.65625e6	0.537510
$395$	−2.51051e6	−0.809599
$396$	587722.	0.188336
$397$	3.80676e6	1.21221	0.606106	−	0.795384i	$-0.292731\pi$
$397$	3.80676e6	1.21221	0.606106	+	0.795384i	$0.292731\pi$
$398$	3.78120e6	1.19653
$399$	−17161.2	−0.00539652
$400$	160000.	0.0500000
$401$	−3.32199e6	−1.03166	−0.515831	−	0.856691i	$-0.672517\pi$
$401$	−3.32199e6	−1.03166	−0.515831	+	0.856691i	$0.672517\pi$
$402$	−36965.0	−0.0114084
$403$	1.00154e6	0.307189
$404$	2.39231e6	0.729228
$405$	−1.47523e6	−0.446911
$406$	3.00081e6	0.903490
$407$	−608329.	−0.182034
$408$	10371.1	0.00308442
$409$	4.28210e6	1.26575	0.632876	−	0.774254i	$-0.281874\pi$
$409$	4.28210e6	1.26575	0.632876	+	0.774254i	$0.281874\pi$
$410$	−644834.	−0.189447
$411$	13651.9	0.00398648
$412$	2.96687e6	0.861105
$413$	5.83984e6	1.68471
$414$	514072.	0.147409
$415$	−1.92824e6	−0.549593
$416$	−1.18046e6	−0.334441
$417$	−54491.7	−0.0153458
$418$	−217976.	−0.0610193
$419$	−6.20611e6	−1.72697	−0.863484	−	0.504376i	$-0.831722\pi$
$419$	−6.20611e6	−1.72697	−0.863484	+	0.504376i	$0.831722\pi$
$420$	−19045.9	−0.00526841
$421$	2.07048e6	0.569333	0.284666	−	0.958627i	$-0.408117\pi$
$421$	2.07048e6	0.569333	0.284666	+	0.958627i	$0.408117\pi$
$422$	−1.53459e6	−0.419480
$423$	−3.12184e6	−0.848321
$424$	736968.	0.199083
$425$	−432886.	−0.116252
$426$	−29842.2	−0.00796722
$427$	747359.	0.198362
$428$	−817667.	−0.215758
$429$	−40780.0	−0.0106980
$430$	656173.	0.171138
$431$	−823282.	−0.213479	−0.106740	−	0.994287i	$-0.534041\pi$
$431$	−823282.	−0.213479	−0.106740	+	0.994287i	$0.534041\pi$
$432$	−29105.7	−0.00750358
$433$	−1.18003e6	−0.302463	−0.151231	−	0.988498i	$-0.548324\pi$
$433$	−1.18003e6	−0.302463	−0.151231	+	0.988498i	$0.548324\pi$
$434$	−707242.	−0.180237
$435$	21561.4	0.00546329
$436$	−3.19255e6	−0.804305
$437$	−190660.	−0.0477591
$438$	−2724.94	−0.000678691 0
$439$	851386.	0.210846	0.105423	−	0.994427i	$-0.466380\pi$
$439$	851386.	0.210846	0.105423	+	0.994427i	$0.466380\pi$
$440$	−241916.	−0.0595706
$441$	−5.97899e6	−1.46397
$442$	3.19379e6	0.777590
$443$	5.36112e6	1.29791	0.648957	−	0.760825i	$-0.275205\pi$
$443$	5.36112e6	1.29791	0.648957	+	0.760825i	$0.275205\pi$
$444$	15061.4	0.00362584
$445$	−2.65397e6	−0.635326
$446$	1.81204e6	0.431351
$447$	44716.2	0.0105851
$448$	833588.	0.196226
$449$	−7.95035e6	−1.86110	−0.930552	−	0.366160i	$-0.880672\pi$
$449$	−7.95035e6	−1.86110	−0.930552	+	0.366160i	$0.880672\pi$
$450$	607363.	0.141389
$451$	974971.	0.225710
$452$	608000.	0.139977
$453$	20978.7	0.00480324
$454$	−2.57542e6	−0.586419
$455$	−5.86522e6	−1.32818
$456$	5396.78	0.00121541
$457$	3.30600e6	0.740477	0.370239	−	0.928937i	$-0.379276\pi$
$457$	3.30600e6	0.740477	0.370239	+	0.928937i	$0.379276\pi$
$458$	−5.07838e6	−1.13126
$459$	78746.6	0.0174462
$460$	−211600.	−0.0466252
$461$	2.00937e6	0.440359	0.220180	−	0.975459i	$-0.429336\pi$
$461$	2.00937e6	0.440359	0.220180	+	0.975459i	$0.429336\pi$
$462$	28796.9	0.00627684
$463$	−2.90957e6	−0.630777	−0.315389	−	0.948963i	$-0.602135\pi$
$463$	−2.90957e6	−0.630777	−0.315389	+	0.948963i	$0.602135\pi$
$464$	−943684.	−0.203485
$465$	−5081.67	−0.00108987
$466$	−4.90207e6	−1.04572
$467$	2.93379e6	0.622496	0.311248	−	0.950329i	$-0.399253\pi$
$467$	2.93379e6	0.622496	0.311248	+	0.950329i	$0.399253\pi$
$468$	−4.48106e6	−0.945729
$469$	8.03843e6	1.68748
$470$	1.28500e6	0.268323
$471$	−114112.	−0.0237016
$472$	−1.83649e6	−0.379432
$473$	−992115.	−0.203896
$474$	−93979.5	−0.0192127
$475$	−225260.	−0.0458089
$476$	−2.25531e6	−0.456234
$477$	2.79755e6	0.562965
$478$	778966.	0.155937
$479$	7.67607e6	1.52862	0.764311	−	0.644848i	$-0.223079\pi$
$479$	7.67607e6	1.52862	0.764311	+	0.644848i	$0.223079\pi$
$480$	5989.50	0.00118655
$481$	4.63818e6	0.914082
$482$	−1.98917e6	−0.389991
$483$	25188.3	0.00491281
$484$	−2.21105e6	−0.429027
$485$	896909.	0.173139
$486$	−165735.	−0.0318290
$487$	−1.04420e7	−1.99508	−0.997542	−	0.0700748i	$-0.977676\pi$
$487$	−1.04420e7	−1.99508	−0.997542	+	0.0700748i	$0.977676\pi$
$488$	−235027.	−0.0446754
$489$	−37336.7	−0.00706096
$490$	2.46104e6	0.463052
$491$	−2.99730e6	−0.561082	−0.280541	−	0.959842i	$-0.590514\pi$
$491$	−2.99730e6	−0.561082	−0.280541	+	0.959842i	$0.590514\pi$
$492$	−24139.0	−0.00449579
$493$	2.55317e6	0.473111
$494$	1.66195e6	0.306408
$495$	−918316.	−0.168453
$496$	222411.	0.0405931
$497$	6.48951e6	1.17848
$498$	−72182.6	−0.0130424
$499$	6.27374e6	1.12791	0.563956	−	0.825805i	$-0.309279\pi$
$499$	6.27374e6	1.12791	0.563956	+	0.825805i	$0.309279\pi$
$500$	−250000.	−0.0447214
$501$	−34087.6	−0.00606739
$502$	−3.95976e6	−0.701309
$503$	−7.83976e6	−1.38160	−0.690801	−	0.723045i	$-0.742742\pi$
$503$	−7.83976e6	−1.38160	−0.690801	+	0.723045i	$0.742742\pi$
$504$	3.16432e6	0.554886
$505$	−3.73798e6	−0.652242
$506$	319933.	0.0555499
$507$	224056.	0.0387112
$508$	−2.23412e6	−0.384102
$509$	−6.50183e6	−1.11235	−0.556175	−	0.831065i	$-0.687732\pi$
$509$	−6.50183e6	−1.11235	−0.556175	+	0.831065i	$0.687732\pi$
$510$	−16204.8	−0.00275879
$511$	592568.	0.100389
$512$	−262144.	−0.0441942
$513$	40977.2	0.00687462
$514$	−3.03370e6	−0.506482
$515$	−4.63574e6	−0.770196
$516$	24563.4	0.00406130
$517$	−1.94288e6	−0.319683
$518$	−3.27527e6	−0.536318
$519$	107912.	0.0175854
$520$	1.84448e6	0.299133
$521$	−2.34251e6	−0.378083	−0.189041	−	0.981969i	$-0.560538\pi$
$521$	−2.34251e6	−0.378083	−0.189041	+	0.981969i	$0.560538\pi$
$522$	−3.58224e6	−0.575412
$523$	−3.35596e6	−0.536491	−0.268245	−	0.963351i	$-0.586444\pi$
$523$	−3.35596e6	−0.536491	−0.268245	+	0.963351i	$0.586444\pi$
$524$	1.27985e6	0.203626
$525$	29759.3	0.00471220
$526$	−796722.	−0.125557
$527$	−601741.	−0.0943807
$528$	−9055.96	−0.00141368
$529$	279841.	0.0434783
$530$	−1.15151e6	−0.178065
$531$	−6.97136e6	−1.07295
$532$	−1.17359e6	−0.179778
$533$	−7.43363e6	−1.13340
$534$	−99349.9	−0.0150770
$535$	1.27761e6	0.192980
$536$	−2.52790e6	−0.380056
$537$	−24693.9	−0.00369533
$538$	2.73737e6	0.407735
$539$	−3.72103e6	−0.551685
$540$	45477.7	0.00671141
$541$	−5.51252e6	−0.809762	−0.404881	−	0.914369i	$-0.632687\pi$
$541$	−5.51252e6	−0.809762	−0.404881	+	0.914369i	$0.632687\pi$
$542$	−2.56943e6	−0.375697
$543$	−41244.5	−0.00600297
$544$	709241.	0.102753
$545$	4.98835e6	0.719392
$546$	−219561.	−0.0315191
$547$	−1.20434e7	−1.72099	−0.860497	−	0.509456i	$-0.829847\pi$
$547$	−1.20434e7	−1.72099	−0.860497	+	0.509456i	$0.829847\pi$
$548$	933605.	0.132804
$549$	−892167.	−0.126333
$550$	377993.	0.0532816
$551$	1.32859e6	0.186428
$552$	−7921.12	−0.00110647
$553$	2.04369e7	2.84185
$554$	9.98415e6	1.38209
$555$	−23533.4	−0.00324305
$556$	−3.72649e6	−0.511226
$557$	1.74232e6	0.237952	0.118976	−	0.992897i	$-0.462039\pi$
$557$	1.74232e6	0.237952	0.118976	+	0.992897i	$0.462039\pi$
$558$	844276.	0.114789
$559$	7.56434e6	1.02386
$560$	−1.30248e6	−0.175510
$561$	24501.2	0.00328686
$562$	4.59730e6	0.613991
$563$	6.67328e6	0.887296	0.443648	−	0.896201i	$-0.353684\pi$
$563$	6.67328e6	0.887296	0.443648	+	0.896201i	$0.353684\pi$
$564$	48103.1	0.00636760
$565$	−950001.	−0.125200
$566$	400693.	0.0525739
$567$	1.20091e7	1.56875
$568$	−2.04080e6	−0.265417
$569$	−1.34670e7	−1.74377	−0.871887	−	0.489706i	$-0.837104\pi$
$569$	−1.34670e7	−1.74377	−0.871887	+	0.489706i	$0.837104\pi$
$570$	−8432.47	−0.00108710
$571$	7.11055e6	0.912669	0.456334	−	0.889808i	$-0.349162\pi$
$571$	7.11055e6	0.912669	0.456334	+	0.889808i	$0.349162\pi$
$572$	−2.78879e6	−0.356391
$573$	−134050.	−0.0170561
$574$	5.24928e6	0.664997
$575$	330625.	0.0417029
$576$	−995104.	−0.124972
$577$	5.30997e6	0.663977	0.331988	−	0.943283i	$-0.392281\pi$
$577$	5.30997e6	0.663977	0.331988	+	0.943283i	$0.392281\pi$
$578$	3.76055e6	0.468200
$579$	132683.	0.0164482
$580$	1.47451e6	0.182002
$581$	1.56969e7	1.92918
$582$	33575.3	0.00410877
$583$	1.74106e6	0.212149
$584$	−186349.	−0.0226097
$585$	7.00166e6	0.845885
$586$	−4.90811e6	−0.590432
$587$	−1.01272e7	−1.21309	−0.606544	−	0.795050i	$-0.707444\pi$
$587$	−1.01272e7	−1.21309	−0.606544	+	0.795050i	$0.707444\pi$
$588$	92127.7	0.0109887
$589$	−313127.	−0.0371905
$590$	2.86952e6	0.339375
$591$	−96876.3	−0.0114090
$592$	1.02999e6	0.120790
$593$	1.40987e7	1.64642	0.823212	−	0.567734i	$-0.192180\pi$
$593$	1.40987e7	1.64642	0.823212	+	0.567734i	$0.192180\pi$
$594$	−68760.9	−0.00799605
$595$	3.52391e6	0.408068
$596$	3.05797e6	0.352629
$597$	−221167.	−0.0253972
$598$	−2.43932e6	−0.278943
$599$	1.33928e6	0.152512	0.0762562	−	0.997088i	$-0.475703\pi$
$599$	1.33928e6	0.152512	0.0762562	+	0.997088i	$0.475703\pi$
$600$	−9358.60	−0.00106129
$601$	−1.45405e7	−1.64207	−0.821036	−	0.570877i	$-0.806603\pi$
$601$	−1.45405e7	−1.64207	−0.821036	+	0.570877i	$0.806603\pi$
$602$	−5.34158e6	−0.600729
$603$	−9.59595e6	−1.07472
$604$	1.43466e6	0.160013
$605$	3.45476e6	0.383733
$606$	−139929.	−0.0154784
$607$	9.58016e6	1.05536	0.527680	−	0.849443i	$-0.323062\pi$
$607$	9.58016e6	1.05536	0.527680	+	0.849443i	$0.323062\pi$
$608$	369066.	0.0404897
$609$	−175521.	−0.0191772
$610$	367230.	0.0399588
$611$	1.48134e7	1.60529
$612$	2.69229e6	0.290565
$613$	3.59833e6	0.386767	0.193383	−	0.981123i	$-0.438054\pi$
$613$	3.59833e6	0.386767	0.193383	+	0.981123i	$0.438054\pi$
$614$	−9.31102e6	−0.996728
$615$	37717.1	0.00402116
$616$	1.96932e6	0.209105
$617$	−1.24752e7	−1.31928	−0.659639	−	0.751583i	$-0.729291\pi$
$617$	−1.24752e7	−1.31928	−0.659639	+	0.751583i	$0.729291\pi$
$618$	−173536.	−0.0182776
$619$	−1.22762e7	−1.28777	−0.643884	−	0.765123i	$-0.722678\pi$
$619$	−1.22762e7	−1.28777	−0.643884	+	0.765123i	$0.722678\pi$
$620$	−347517.	−0.0363075
$621$	−60144.2	−0.00625842
$622$	−5.92661e6	−0.614229
$623$	2.16047e7	2.23012
$624$	69046.8	0.00709875
$625$	390625.	0.0400000
$626$	4.29796e6	0.438355
$627$	12749.7	0.00129518
$628$	−7.80367e6	−0.789586
$629$	−2.78669e6	−0.280842
$630$	−4.94425e6	−0.496305
$631$	574528.	0.0574431	0.0287215	−	0.999587i	$-0.490856\pi$
$631$	574528.	0.0574431	0.0287215	+	0.999587i	$0.490856\pi$
$632$	−6.42691e6	−0.640044
$633$	89760.0	0.00890376
$634$	3.79081e6	0.374549
$635$	3.49081e6	0.343551
$636$	−43106.2	−0.00422568
$637$	2.83708e7	2.77028
$638$	−2.22941e6	−0.216840
$639$	−7.74691e6	−0.750544
$640$	409600.	0.0395285
$641$	1.25521e7	1.20663	0.603313	−	0.797504i	$-0.293847\pi$
$641$	1.25521e7	1.20663	0.603313	+	0.797504i	$0.293847\pi$
$642$	47826.4	0.00457962
$643$	4.31938e6	0.411997	0.205998	−	0.978552i	$-0.433956\pi$
$643$	4.31938e6	0.411997	0.205998	+	0.978552i	$0.433956\pi$
$644$	1.72253e6	0.163664
$645$	−38380.3	−0.00363253
$646$	−998522.	−0.0941405
$647$	−1.07445e7	−1.00908	−0.504539	−	0.863389i	$-0.668338\pi$
$647$	−1.07445e7	−1.00908	−0.504539	+	0.863389i	$0.668338\pi$
$648$	−3.77658e6	−0.353314
$649$	−4.33864e6	−0.404335
$650$	−2.88199e6	−0.267553
$651$	41367.4	0.00382566
$652$	−2.55332e6	−0.235226
$653$	1.54073e7	1.41398	0.706989	−	0.707225i	$-0.250053\pi$
$653$	1.54073e7	1.41398	0.706989	+	0.707225i	$0.250053\pi$
$654$	186736.	0.0170720
$655$	−1.99977e6	−0.182128
$656$	−1.65077e6	−0.149771
$657$	−707384.	−0.0639355
$658$	−1.04605e7	−0.941867
$659$	−3.65055e6	−0.327450	−0.163725	−	0.986506i	$-0.552351\pi$
$659$	−3.65055e6	−0.327450	−0.163725	+	0.986506i	$0.552351\pi$
$660$	14149.9	0.00126443
$661$	1.23719e7	1.10137	0.550685	−	0.834713i	$-0.314367\pi$
$661$	1.23719e7	1.10137	0.550685	+	0.834713i	$0.314367\pi$
$662$	−7.50333e6	−0.665440
$663$	−186809.	−0.0165049
$664$	−4.93630e6	−0.434492
$665$	1.83373e6	0.160798
$666$	3.90988e6	0.341568
$667$	−1.95003e6	−0.169718
$668$	−2.33113e6	−0.202127
$669$	−105988.	−0.00915574
$670$	3.94984e6	0.339932
$671$	−555241.	−0.0476075
$672$	−48757.6	−0.00416504
$673$	8.32824e6	0.708787	0.354393	−	0.935096i	$-0.384687\pi$
$673$	8.32824e6	0.708787	0.354393	+	0.935096i	$0.384687\pi$
$674$	1.43298e7	1.21504
$675$	−71058.8	−0.00600287
$676$	1.53224e7	1.28961
$677$	1.77897e6	0.149175	0.0745876	−	0.997214i	$-0.476236\pi$
$677$	1.77897e6	0.149175	0.0745876	+	0.997214i	$0.476236\pi$
$678$	−35562.7	−0.00297112
$679$	−7.30130e6	−0.607751
$680$	−1.10819e6	−0.0919055
$681$	150639.	0.0124472
$682$	525436.	0.0432573
$683$	−1.18219e7	−0.969695	−0.484847	−	0.874599i	$-0.661125\pi$
$683$	−1.18219e7	−0.969695	−0.484847	+	0.874599i	$0.661125\pi$
$684$	1.40098e6	0.114496
$685$	−1.45876e6	−0.118784
$686$	−6.35241e6	−0.515380
$687$	297041.	0.0240118
$688$	1.67980e6	0.135297
$689$	−1.32746e7	−1.06530
$690$	12376.7	0.000989655 0
$691$	3.20554e6	0.255392	0.127696	−	0.991813i	$-0.459242\pi$
$691$	3.20554e6	0.255392	0.127696	+	0.991813i	$0.459242\pi$
$692$	7.37970e6	0.585833
$693$	7.47556e6	0.591304
$694$	1.57319e7	1.23989
$695$	5.82263e6	0.457254
$696$	55197.2	0.00431911
$697$	4.46624e6	0.348225
$698$	−5.96270e6	−0.463239
$699$	286728.	0.0221961
$700$	2.03513e6	0.156981
$701$	4.59853e6	0.353447	0.176724	−	0.984261i	$-0.443450\pi$
$701$	4.59853e6	0.353447	0.176724	+	0.984261i	$0.443450\pi$
$702$	524265.	0.0401521
$703$	−1.45010e6	−0.110665
$704$	−619304.	−0.0470947
$705$	−75161.1	−0.00569535
$706$	−7.15102e6	−0.539954
$707$	3.04291e7	2.28950
$708$	107419.	0.00805373
$709$	2.34840e7	1.75452	0.877258	−	0.480020i	$-0.159371\pi$
$709$	2.34840e7	1.75452	0.877258	+	0.480020i	$0.159371\pi$
$710$	3.18875e6	0.237396
$711$	−2.43967e7	−1.80991
$712$	−6.79418e6	−0.502269
$713$	459591.	0.0338570
$714$	131916.	0.00968391
$715$	4.35749e6	0.318766
$716$	−1.68872e6	−0.123105
$717$	−45562.7	−0.00330987
$718$	1.86436e7	1.34964
$719$	−2.14856e7	−1.54997	−0.774987	−	0.631977i	$-0.782244\pi$
$719$	−2.14856e7	−1.54997	−0.774987	+	0.631977i	$0.782244\pi$
$720$	1.55485e6	0.111778
$721$	3.77373e7	2.70354
$722$	9.38480e6	0.670011
$723$	116349.	0.00827785
$724$	−2.82056e6	−0.199981
$725$	−2.30392e6	−0.162788
$726$	129327.	0.00910641
$727$	−4.42772e6	−0.310702	−0.155351	−	0.987859i	$-0.549651\pi$
$727$	−4.42772e6	−0.310702	−0.155351	+	0.987859i	$0.549651\pi$
$728$	−1.50150e7	−1.05002
$729$	−1.43295e7	−0.998649
$730$	291170.	0.0202227
$731$	−4.54477e6	−0.314571
$732$	13747.0	0.000948267 0
$733$	−2.64063e7	−1.81530	−0.907650	−	0.419729i	$-0.862125\pi$
$733$	−2.64063e7	−1.81530	−0.907650	+	0.419729i	$0.862125\pi$
$734$	1.09250e7	0.748484
$735$	−143950.	−0.00982861
$736$	−541696.	−0.0368605
$737$	−5.97205e6	−0.405000
$738$	−6.26637e6	−0.423521
$739$	2.19652e7	1.47953	0.739766	−	0.672864i	$-0.234936\pi$
$739$	2.19652e7	1.47953	0.739766	+	0.672864i	$0.234936\pi$
$740$	−1.60937e6	−0.108038
$741$	−97209.2	−0.00650372
$742$	9.37390e6	0.625044
$743$	−128787.	−0.00855857	−0.00427928	−	0.999991i	$-0.501362\pi$
$743$	−128787.	−0.00855857	−0.00427928	+	0.999991i	$0.501362\pi$
$744$	−13009.1	−0.000861617 0
$745$	−4.77809e6	−0.315401
$746$	−9.84091e6	−0.647423
$747$	−1.87383e7	−1.22865
$748$	1.67555e6	0.109497
$749$	−1.04004e7	−0.677398
$750$	14622.8	0.000949243 0
$751$	1.90153e7	1.23028	0.615140	−	0.788418i	$-0.289100\pi$
$751$	1.90153e7	1.23028	0.615140	+	0.788418i	$0.289100\pi$
$752$	3.28960e6	0.212128
$753$	231611.	0.0148858
$754$	1.69981e7	1.08886
$755$	−2.24165e6	−0.143120
$756$	−370211.	−0.0235584
$757$	2.12542e7	1.34804	0.674022	−	0.738711i	$-0.264565\pi$
$757$	2.12542e7	1.34804	0.674022	+	0.738711i	$0.264565\pi$
$758$	−3.04303e6	−0.192368
$759$	−18713.3	−0.00117909
$760$	−576666.	−0.0362151
$761$	2.02918e7	1.27016	0.635081	−	0.772446i	$-0.280967\pi$
$761$	2.02918e7	1.27016	0.635081	+	0.772446i	$0.280967\pi$
$762$	130676.	0.00815285
$763$	−4.06077e7	−2.52521
$764$	−9.16717e6	−0.568201
$765$	−4.20671e6	−0.259889
$766$	1.80388e6	0.111080
$767$	3.30797e7	2.03036
$768$	15333.1	0.000938054 0
$769$	−1.45513e7	−0.887333	−0.443667	−	0.896192i	$-0.646323\pi$
$769$	−1.45513e7	−0.887333	−0.443667	+	0.896192i	$0.646323\pi$
$770$	−3.07706e6	−0.187029
$771$	177445.	0.0107505
$772$	9.07370e6	0.547950
$773$	−2.07604e7	−1.24964	−0.624822	−	0.780767i	$-0.714829\pi$
$773$	−2.07604e7	−1.24964	−0.624822	+	0.780767i	$0.714829\pi$
$774$	6.37656e6	0.382591
$775$	542995.	0.0324745
$776$	2.29609e6	0.136878
$777$	191574.	0.0113837
$778$	−1.59457e7	−0.944484
$779$	2.32408e6	0.137217
$780$	−107886.	−0.00634932
$781$	−4.82129e6	−0.282837
$782$	1.46558e6	0.0857023
$783$	419107.	0.0244298
$784$	6.30027e6	0.366074
$785$	1.21932e7	0.706228
$786$	−74860.2	−0.00432210
$787$	1.86429e7	1.07294	0.536470	−	0.843919i	$-0.319757\pi$
$787$	1.86429e7	1.07294	0.536470	+	0.843919i	$0.319757\pi$
$788$	−6.62502e6	−0.380077
$789$	46601.3	0.00266505
$790$	1.00421e7	0.572473
$791$	7.73349e6	0.439475
$792$	−2.35089e6	−0.133174
$793$	4.23341e6	0.239060
$794$	−1.52270e7	−0.857164
$795$	67353.4	0.00377956
$796$	−1.51248e7	−0.846072
$797$	−2.88725e6	−0.161005	−0.0805024	−	0.996754i	$-0.525652\pi$
$797$	−2.88725e6	−0.161005	−0.0805024	+	0.996754i	$0.525652\pi$
$798$	68644.6	0.00381592
$799$	−8.90013e6	−0.493207
$800$	−640000.	−0.0353553
$801$	−2.57908e7	−1.42031
$802$	1.32879e7	0.729495
$803$	−440241.	−0.0240936
$804$	147860.	0.00806697
$805$	−2.69146e6	−0.146385
$806$	−4.00617e6	−0.217216
$807$	−160112.	−0.00865446
$808$	−9.56923e6	−0.515642
$809$	1.17399e7	0.630659	0.315330	−	0.948982i	$-0.397885\pi$
$809$	1.17399e7	0.630659	0.315330	+	0.948982i	$0.397885\pi$
$810$	5.90091e6	0.316014
$811$	−3.53820e7	−1.88899	−0.944496	−	0.328524i	$-0.893449\pi$
$811$	−3.53820e7	−1.88899	−0.944496	+	0.328524i	$0.893449\pi$
$812$	−1.20032e7	−0.638864
$813$	150289.	0.00797445
$814$	2.43332e6	0.128718
$815$	3.98956e6	0.210393
$816$	−41484.4	−0.00218102
$817$	−2.36495e6	−0.123956
$818$	−1.71284e7	−0.895021
$819$	−5.69971e7	−2.96923
$820$	2.57934e6	0.133959
$821$	−3.04709e7	−1.57771	−0.788855	−	0.614579i	$-0.789326\pi$
$821$	−3.04709e7	−1.57771	−0.788855	+	0.614579i	$0.789326\pi$
$822$	−54607.7	−0.00281887
$823$	7.41573e6	0.381640	0.190820	−	0.981625i	$-0.438885\pi$
$823$	7.41573e6	0.381640	0.190820	+	0.981625i	$0.438885\pi$
$824$	−1.18675e7	−0.608893
$825$	−22109.3	−0.00113094
$826$	−2.33594e7	−1.19127
$827$	−2.84029e7	−1.44411	−0.722053	−	0.691838i	$-0.756801\pi$
$827$	−2.84029e7	−1.44411	−0.722053	+	0.691838i	$0.756801\pi$
$828$	−2.05629e6	−0.104234
$829$	−7.05907e6	−0.356748	−0.178374	−	0.983963i	$-0.557084\pi$
$829$	−7.05907e6	−0.356748	−0.178374	+	0.983963i	$0.557084\pi$
$830$	7.71297e6	0.388621
$831$	−583985.	−0.0293359
$832$	4.72186e6	0.236485
$833$	−1.70456e7	−0.851139
$834$	217967.	0.0108511
$835$	3.64238e6	0.180788
$836$	871902.	0.0431471
$837$	−98776.6	−0.00487350
$838$	2.48244e7	1.22115
$839$	5.57054e6	0.273207	0.136604	−	0.990626i	$-0.456381\pi$
$839$	5.57054e6	0.273207	0.136604	+	0.990626i	$0.456381\pi$
$840$	76183.8	0.00372532
$841$	−6.92260e6	−0.337504
$842$	−8.28192e6	−0.402579
$843$	−268901.	−0.0130324
$844$	6.13836e6	0.296617
$845$	−2.39412e7	−1.15346
$846$	1.24874e7	0.599853
$847$	−2.81235e7	−1.34698
$848$	−2.94787e6	−0.140773
$849$	−23437.0	−0.00111592
$850$	1.73154e6	0.0822028
$851$	2.12839e6	0.100746
$852$	119369.	0.00563367
$853$	9.71741e6	0.457275	0.228638	−	0.973512i	$-0.426573\pi$
$853$	9.71741e6	0.457275	0.228638	+	0.973512i	$0.426573\pi$
$854$	−2.98944e6	−0.140263
$855$	−2.18903e6	−0.102409
$856$	3.27067e6	0.152564
$857$	−8.28472e6	−0.385324	−0.192662	−	0.981265i	$-0.561712\pi$
$857$	−8.28472e6	−0.385324	−0.192662	+	0.981265i	$0.561712\pi$
$858$	163120.	0.00756465
$859$	−2.43156e7	−1.12435	−0.562177	−	0.827017i	$-0.690036\pi$
$859$	−2.43156e7	−1.12435	−0.562177	+	0.827017i	$0.690036\pi$
$860$	−2.62469e6	−0.121013
$861$	−307037.	−0.0141150
$862$	3.29313e6	0.150952
$863$	2.71765e7	1.24213	0.621064	−	0.783760i	$-0.286701\pi$
$863$	2.71765e7	1.24213	0.621064	+	0.783760i	$0.286701\pi$
$864$	116423.	0.00530583
$865$	−1.15308e7	−0.523985
$866$	4.72010e6	0.213873
$867$	−219959.	−0.00993789
$868$	2.82897e6	0.127447
$869$	−1.51833e7	−0.682051
$870$	−86245.7	−0.00386313
$871$	4.55337e7	2.03370
$872$	1.27702e7	0.568730
$873$	8.71600e6	0.387063
$874$	762640.	0.0337708
$875$	−3.17989e6	−0.140408
$876$	10899.8	0.000479907 0
$877$	6.70848e6	0.294527	0.147264	−	0.989097i	$-0.452953\pi$
$877$	6.70848e6	0.294527	0.147264	+	0.989097i	$0.452953\pi$
$878$	−3.40554e6	−0.149091
$879$	287081.	0.0125324
$880$	967662.	0.0421228
$881$	9.51261e6	0.412914	0.206457	−	0.978456i	$-0.433807\pi$
$881$	9.51261e6	0.412914	0.206457	+	0.978456i	$0.433807\pi$
$882$	2.39160e7	1.03518
$883$	−2.23053e7	−0.962732	−0.481366	−	0.876520i	$-0.659859\pi$
$883$	−2.23053e7	−0.962732	−0.481366	+	0.876520i	$0.659859\pi$
$884$	−1.27752e7	−0.549839
$885$	−167842.	−0.00720347
$886$	−2.14445e7	−0.917764
$887$	1.01123e7	0.431559	0.215780	−	0.976442i	$-0.430771\pi$
$887$	1.01123e7	0.431559	0.215780	+	0.976442i	$0.430771\pi$
$888$	−60245.6	−0.00256385
$889$	−2.84170e7	−1.20593
$890$	1.06159e7	0.449243
$891$	−8.92201e6	−0.376503
$892$	−7.24816e6	−0.305011
$893$	−4.63134e6	−0.194347
$894$	−178865.	−0.00748481
$895$	2.63863e6	0.110109
$896$	−3.33435e6	−0.138753
$897$	142679.	0.00592077
$898$	3.18014e7	1.31600
$899$	−3.20260e6	−0.132161
$900$	−2.42945e6	−0.0999775
$901$	7.97559e6	0.327303
$902$	−3.89988e6	−0.159601
$903$	312436.	0.0127509
$904$	−2.43200e6	−0.0989789
$905$	4.40712e6	0.178868
$906$	−83915.0	−0.00339640
$907$	4.17244e7	1.68412	0.842058	−	0.539386i	$-0.181344\pi$
$907$	4.17244e7	1.68412	0.842058	+	0.539386i	$0.181344\pi$
$908$	1.03017e7	0.414661
$909$	−3.63250e7	−1.45813
$910$	2.34609e7	0.939163
$911$	3.58922e6	0.143286	0.0716431	−	0.997430i	$-0.477176\pi$
$911$	3.58922e6	0.143286	0.0716431	+	0.997430i	$0.477176\pi$
$912$	−21587.1	−0.000859424 0
$913$	−1.16618e7	−0.463008
$914$	−1.32240e7	−0.523596
$915$	−21479.7	−0.000848156 0
$916$	2.03135e7	0.799920
$917$	1.62792e7	0.639306
$918$	−314986.	−0.0123363
$919$	−4.74566e7	−1.85356	−0.926782	−	0.375599i	$-0.877437\pi$
$919$	−4.74566e7	−1.85356	−0.926782	+	0.375599i	$0.877437\pi$
$920$	846400.	0.0329690
$921$	544613.	0.0211563
$922$	−8.03747e6	−0.311381
$923$	3.67598e7	1.42026
$924$	−115188.	−0.00443840
$925$	2.51463e6	0.0966319
$926$	1.16383e7	0.446027
$927$	−4.50493e7	−1.72182
$928$	3.77474e6	0.143885
$929$	3.32561e7	1.26425	0.632124	−	0.774867i	$-0.282183\pi$
$929$	3.32561e7	1.26425	0.632124	+	0.774867i	$0.282183\pi$
$930$	20326.7	0.000770654 0
$931$	−8.87000e6	−0.335389
$932$	1.96083e7	0.739434
$933$	346655.	0.0130375
$934$	−1.17352e7	−0.440171
$935$	−2.61805e6	−0.0979374
$936$	1.79243e7	0.668731
$937$	−1.92009e7	−0.714450	−0.357225	−	0.934018i	$-0.616277\pi$
$937$	−1.92009e7	−0.714450	−0.357225	+	0.934018i	$0.616277\pi$
$938$	−3.21537e7	−1.19323
$939$	−251393.	−0.00930441
$940$	−5.13999e6	−0.189733
$941$	3.49771e7	1.28768	0.643842	−	0.765158i	$-0.277339\pi$
$941$	3.49771e7	1.28768	0.643842	+	0.765158i	$0.277339\pi$
$942$	456446.	0.0167595
$943$	−3.41117e6	−0.124918
$944$	7.34597e6	0.268299
$945$	578455.	0.0210712
$946$	3.96846e6	0.144176
$947$	−9.14501e6	−0.331367	−0.165683	−	0.986179i	$-0.552983\pi$
$947$	−9.14501e6	−0.331367	−0.165683	+	0.986179i	$0.552983\pi$
$948$	375918.	0.0135854
$949$	3.35660e6	0.120986
$950$	901040.	0.0323918
$951$	−221729.	−0.00795008
$952$	9.02122e6	0.322606
$953$	4.37224e7	1.55945	0.779725	−	0.626122i	$-0.215359\pi$
$953$	4.37224e7	1.55945	0.779725	+	0.626122i	$0.215359\pi$
$954$	−1.11902e7	−0.398076
$955$	1.43237e7	0.508214
$956$	−3.11586e6	−0.110264
$957$	130401.	0.00460258
$958$	−3.07043e7	−1.08090
$959$	1.18750e7	0.416954
$960$	−23958.0	−0.000839021 0
$961$	−2.78744e7	−0.973635
$962$	−1.85527e7	−0.646353
$963$	1.24155e7	0.431419
$964$	7.95669e6	0.275766
$965$	−1.41776e7	−0.490101
$966$	−100753.	−0.00347388
$967$	−1.07614e7	−0.370087	−0.185044	−	0.982730i	$-0.559243\pi$
$967$	−1.07614e7	−0.370087	−0.185044	+	0.982730i	$0.559243\pi$
$968$	8.84419e6	0.303368
$969$	58404.8	0.00199820
$970$	−3.58764e6	−0.122428
$971$	−3.44853e7	−1.17378	−0.586889	−	0.809668i	$-0.699647\pi$
$971$	−3.44853e7	−1.17378	−0.586889	+	0.809668i	$0.699647\pi$
$972$	662940.	0.0225065
$973$	−4.73992e7	−1.60505
$974$	4.17680e7	1.41074
$975$	168571.	0.00567900
$976$	940108.	0.0315902
$977$	2.92695e7	0.981022	0.490511	−	0.871435i	$-0.336810\pi$
$977$	2.92695e7	0.981022	0.490511	+	0.871435i	$0.336810\pi$
$978$	149347.	0.00499285
$979$	−1.60509e7	−0.535234
$980$	−9.84418e6	−0.327427
$981$	4.84759e7	1.60825
$982$	1.19892e7	0.396745
$983$	−5.73299e7	−1.89233	−0.946166	−	0.323681i	$-0.895080\pi$
$983$	−5.73299e7	−1.89233	−0.946166	+	0.323681i	$0.895080\pi$
$984$	96555.9	0.00317900
$985$	1.03516e7	0.339951
$986$	−1.02127e7	−0.334540
$987$	611850.	0.0199918
$988$	−6.64778e6	−0.216663
$989$	3.47115e6	0.112845
$990$	3.67326e6	0.119114
$991$	−4.26292e7	−1.37887	−0.689435	−	0.724347i	$-0.742141\pi$
$991$	−4.26292e7	−1.37887	−0.689435	+	0.724347i	$0.742141\pi$
$992$	−889644.	−0.0287036
$993$	438879.	0.0141245
$994$	−2.59580e7	−0.833308
$995$	2.36325e7	0.756750
$996$	288730.	0.00922240
$997$	−1.37248e7	−0.437288	−0.218644	−	0.975805i	$-0.570163\pi$
$997$	−1.37248e7	−0.437288	−0.218644	+	0.975805i	$0.570163\pi$
$998$	−2.50949e7	−0.797554
$999$	−457439.	−0.0145017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.g.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.g.1.3	✓	5	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +0.233965 q^{3} +16.0000 q^{4} -25.0000 q^{5} -0.935860 q^{6} +203.513 q^{7} -64.0000 q^{8} -242.945 q^{9} +100.000 q^{10} -151.197 q^{11} +3.74344 q^{12} +1152.80 q^{13} -814.051 q^{14} -5.84912 q^{15} +256.000 q^{16} -692.618 q^{17} +971.781 q^{18} -360.416 q^{19} -400.000 q^{20} +47.6148 q^{21} +604.789 q^{22} +529.000 q^{23} -14.9738 q^{24} +625.000 q^{25} -4611.19 q^{26} -113.694 q^{27} +3256.20 q^{28} -3686.27 q^{29} +23.3965 q^{30} +868.793 q^{31} -1024.00 q^{32} -35.3748 q^{33} +2770.47 q^{34} -5087.82 q^{35} -3887.12 q^{36} +4023.42 q^{37} +1441.66 q^{38} +269.714 q^{39} +1600.00 q^{40} -6448.34 q^{41} -190.459 q^{42} +6561.73 q^{43} -2419.16 q^{44} +6073.63 q^{45} -2116.00 q^{46} +12850.0 q^{47} +59.8950 q^{48} +24610.4 q^{49} -2500.00 q^{50} -162.048 q^{51} +18444.8 q^{52} -11515.1 q^{53} +454.777 q^{54} +3779.93 q^{55} -13024.8 q^{56} -84.3247 q^{57} +14745.1 q^{58} +28695.2 q^{59} -93.5860 q^{60} +3672.30 q^{61} -3475.17 q^{62} -49442.5 q^{63} +4096.00 q^{64} -28819.9 q^{65} +141.499 q^{66} +39498.4 q^{67} -11081.9 q^{68} +123.767 q^{69} +20351.3 q^{70} +31887.5 q^{71} +15548.5 q^{72} +2911.70 q^{73} -16093.7 q^{74} +146.228 q^{75} -5766.66 q^{76} -30770.6 q^{77} -1078.86 q^{78} +100421. q^{79} -6400.00 q^{80} +59009.1 q^{81} +25793.4 q^{82} +77129.7 q^{83} +761.838 q^{84} +17315.4 q^{85} -26246.9 q^{86} -862.457 q^{87} +9676.62 q^{88} +106159. q^{89} -24294.5 q^{90} +234609. q^{91} +8464.00 q^{92} +203.267 q^{93} -51399.9 q^{94} +9010.40 q^{95} -239.580 q^{96} -35876.4 q^{97} -98441.8 q^{98} +36732.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18}+ \cdots + 362547 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more