LMFDB - Embedded newform 130.4.a.g.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(1,130)] 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("130.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,4,12,8,10,24,4,16,38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{10}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 10 $ x^2 - 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.16228$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +9.16228 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.3246 q^{6} -10.6491 q^{7} +8.00000 q^{8} +56.9473 q^{9} +10.0000 q^{10} -59.4342 q^{11} +36.6491 q^{12} -13.0000 q^{13} -21.2982 q^{14} +45.8114 q^{15} +16.0000 q^{16} +58.2719 q^{17} +113.895 q^{18} -95.0569 q^{19} +20.0000 q^{20} -97.5701 q^{21} -118.868 q^{22} -186.355 q^{23} +73.2982 q^{24} +25.0000 q^{25} -26.0000 q^{26} +274.386 q^{27} -42.5964 q^{28} +257.737 q^{29} +91.6228 q^{30} +173.653 q^{31} +32.0000 q^{32} -544.552 q^{33} +116.544 q^{34} -53.2456 q^{35} +227.789 q^{36} -88.2719 q^{37} -190.114 q^{38} -119.110 q^{39} +40.0000 q^{40} +174.272 q^{41} -195.140 q^{42} +481.179 q^{43} -237.737 q^{44} +284.737 q^{45} -372.710 q^{46} -303.737 q^{47} +146.596 q^{48} -229.596 q^{49} +50.0000 q^{50} +533.903 q^{51} -52.0000 q^{52} -403.570 q^{53} +548.772 q^{54} -297.171 q^{55} -85.1929 q^{56} -870.938 q^{57} +515.473 q^{58} +9.98649 q^{59} +183.246 q^{60} -245.088 q^{61} +347.307 q^{62} -606.438 q^{63} +64.0000 q^{64} -65.0000 q^{65} -1089.10 q^{66} +312.325 q^{67} +233.088 q^{68} -1707.44 q^{69} -106.491 q^{70} +25.0484 q^{71} +455.579 q^{72} -232.483 q^{73} -176.544 q^{74} +229.057 q^{75} -380.228 q^{76} +632.921 q^{77} -238.219 q^{78} -827.623 q^{79} +80.0000 q^{80} +976.421 q^{81} +348.544 q^{82} -466.228 q^{83} -390.280 q^{84} +291.359 q^{85} +962.359 q^{86} +2361.45 q^{87} -475.473 q^{88} +1297.72 q^{89} +569.473 q^{90} +138.438 q^{91} -745.421 q^{92} +1591.06 q^{93} -607.473 q^{94} -475.285 q^{95} +293.193 q^{96} +1001.77 q^{97} -459.193 q^{98} -3384.62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 12 q^{3} + 8 q^{4} + 10 q^{5} + 24 q^{6} + 4 q^{7} + 16 q^{8} + 38 q^{9} + 20 q^{10} - 24 q^{11} + 48 q^{12} - 26 q^{13} + 8 q^{14} + 60 q^{15} + 32 q^{16} + 28 q^{17} + 76 q^{18} - 32 q^{19}+ \cdots - 4056 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 12 * q^3 + 8 * q^4 + 10 * q^5 + 24 * q^6 + 4 * q^7 + 16 * q^8 + 38 * q^9 + 20 * q^10 - 24 * q^11 + 48 * q^12 - 26 * q^13 + 8 * q^14 + 60 * q^15 + 32 * q^16 + 28 * q^17 + 76 * q^18 - 32 * q^19 + 40 * q^20 - 56 * q^21 - 48 * q^22 - 164 * q^23 + 96 * q^24 + 50 * q^25 - 52 * q^26 + 144 * q^27 + 16 * q^28 + 136 * q^29 + 120 * q^30 + 88 * q^31 + 64 * q^32 - 444 * q^33 + 56 * q^34 + 20 * q^35 + 152 * q^36 - 88 * q^37 - 64 * q^38 - 156 * q^39 + 80 * q^40 + 260 * q^41 - 112 * q^42 + 20 * q^43 - 96 * q^44 + 190 * q^45 - 328 * q^46 - 228 * q^47 + 192 * q^48 - 358 * q^49 + 100 * q^50 + 448 * q^51 - 104 * q^52 - 668 * q^53 + 288 * q^54 - 120 * q^55 + 32 * q^56 - 692 * q^57 + 272 * q^58 - 720 * q^59 + 240 * q^60 - 136 * q^61 + 176 * q^62 - 884 * q^63 + 128 * q^64 - 130 * q^65 - 888 * q^66 + 612 * q^67 + 112 * q^68 - 1644 * q^69 + 40 * q^70 + 360 * q^71 + 304 * q^72 - 680 * q^73 - 176 * q^74 + 300 * q^75 - 128 * q^76 + 1152 * q^77 - 312 * q^78 - 1592 * q^79 + 160 * q^80 + 1118 * q^81 + 520 * q^82 - 300 * q^83 - 224 * q^84 + 140 * q^85 + 40 * q^86 + 2016 * q^87 - 192 * q^88 + 268 * q^89 + 380 * q^90 - 52 * q^91 - 656 * q^92 + 1348 * q^93 - 456 * q^94 - 160 * q^95 + 384 * q^96 + 2636 * q^97 - 716 * q^98 - 4056 * 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
$3$	9.16228	1.76328	0.881641	−	0.471921i	$-0.156439\pi$
$3$	9.16228	1.76328	0.881641	+	0.471921i	$0.156439\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	18.3246	1.24683
$7$	−10.6491	−0.574998	−0.287499	−	0.957781i	$-0.592824\pi$
$7$	−10.6491	−0.574998	−0.287499	+	0.957781i	$0.592824\pi$
$8$	8.00000	0.353553
$9$	56.9473	2.10916
$10$	10.0000	0.316228
$11$	−59.4342	−1.62910	−0.814549	−	0.580095i	$-0.803015\pi$
$11$	−59.4342	−1.62910	−0.814549	+	0.580095i	$0.803015\pi$
$12$	36.6491	0.881641
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−21.2982	−0.406585
$15$	45.8114	0.788563
$16$	16.0000	0.250000
$17$	58.2719	0.831353	0.415677	−	0.909512i	$-0.363545\pi$
$17$	58.2719	0.831353	0.415677	+	0.909512i	$0.363545\pi$
$18$	113.895	1.49140
$19$	−95.0569	−1.14777	−0.573883	−	0.818937i	$-0.694564\pi$
$19$	−95.0569	−1.14777	−0.573883	+	0.818937i	$0.694564\pi$
$20$	20.0000	0.223607
$21$	−97.5701	−1.01388
$22$	−118.868	−1.15195
$23$	−186.355	−1.68947	−0.844733	−	0.535187i	$-0.820241\pi$
$23$	−186.355	−1.68947	−0.844733	+	0.535187i	$0.820241\pi$
$24$	73.2982	0.623414
$25$	25.0000	0.200000
$26$	−26.0000	−0.196116
$27$	274.386	1.95576
$28$	−42.5964	−0.287499
$29$	257.737	1.65036	0.825181	−	0.564868i	$-0.191073\pi$
$29$	257.737	1.65036	0.825181	+	0.564868i	$0.191073\pi$
$30$	91.6228	0.557598
$31$	173.653	1.00610	0.503049	−	0.864258i	$-0.332211\pi$
$31$	173.653	1.00610	0.503049	+	0.864258i	$0.332211\pi$
$32$	32.0000	0.176777
$33$	−544.552	−2.87256
$34$	116.544	0.587856
$35$	−53.2456	−0.257147
$36$	227.789	1.05458
$37$	−88.2719	−0.392211	−0.196106	−	0.980583i	$-0.562830\pi$
$37$	−88.2719	−0.392211	−0.196106	+	0.980583i	$0.562830\pi$
$38$	−190.114	−0.811593
$39$	−119.110	−0.489046
$40$	40.0000	0.158114
$41$	174.272	0.663822	0.331911	−	0.943311i	$-0.392307\pi$
$41$	174.272	0.663822	0.331911	+	0.943311i	$0.392307\pi$
$42$	−195.140	−0.716924
$43$	481.179	1.70649	0.853246	−	0.521508i	$-0.174630\pi$
$43$	481.179	1.70649	0.853246	+	0.521508i	$0.174630\pi$
$44$	−237.737	−0.814549
$45$	284.737	0.943245
$46$	−372.710	−1.19463
$47$	−303.737	−0.942650	−0.471325	−	0.881960i	$-0.656224\pi$
$47$	−303.737	−0.942650	−0.471325	+	0.881960i	$0.656224\pi$
$48$	146.596	0.440820
$49$	−229.596	−0.669377
$50$	50.0000	0.141421
$51$	533.903	1.46591
$52$	−52.0000	−0.138675
$53$	−403.570	−1.04594	−0.522968	−	0.852352i	$-0.675175\pi$
$53$	−403.570	−1.04594	−0.522968	+	0.852352i	$0.675175\pi$
$54$	548.772	1.38293
$55$	−297.171	−0.728555
$56$	−85.1929	−0.203292
$57$	−870.938	−2.02383
$58$	515.473	1.16698
$59$	9.98649	0.0220361	0.0110180	−	0.999939i	$-0.496493\pi$
$59$	9.98649	0.0220361	0.0110180	+	0.999939i	$0.496493\pi$
$60$	183.246	0.394282
$61$	−245.088	−0.514430	−0.257215	−	0.966354i	$-0.582805\pi$
$61$	−245.088	−0.514430	−0.257215	+	0.966354i	$0.582805\pi$
$62$	347.307	0.711419
$63$	−606.438	−1.21276
$64$	64.0000	0.125000
$65$	−65.0000	−0.124035
$66$	−1089.10	−2.03120
$67$	312.325	0.569500	0.284750	−	0.958602i	$-0.408089\pi$
$67$	312.325	0.569500	0.284750	+	0.958602i	$0.408089\pi$
$68$	233.088	0.415677
$69$	−1707.44	−2.97901
$70$	−106.491	−0.181830
$71$	25.0484	0.0418690	0.0209345	−	0.999781i	$-0.493336\pi$
$71$	25.0484	0.0418690	0.0209345	+	0.999781i	$0.493336\pi$
$72$	455.579	0.745701
$73$	−232.483	−0.372740	−0.186370	−	0.982480i	$-0.559672\pi$
$73$	−232.483	−0.372740	−0.186370	+	0.982480i	$0.559672\pi$
$74$	−176.544	−0.277335
$75$	229.057	0.352656
$76$	−380.228	−0.573883
$77$	632.921	0.936728
$78$	−238.219	−0.345808
$79$	−827.623	−1.17867	−0.589334	−	0.807889i	$-0.700610\pi$
$79$	−827.623	−1.17867	−0.589334	+	0.807889i	$0.700610\pi$
$80$	80.0000	0.111803
$81$	976.421	1.33940
$82$	348.544	0.469393
$83$	−466.228	−0.616568	−0.308284	−	0.951294i	$-0.599755\pi$
$83$	−466.228	−0.616568	−0.308284	+	0.951294i	$0.599755\pi$
$84$	−390.280	−0.506942
$85$	291.359	0.371793
$86$	962.359	1.20667
$87$	2361.45	2.91005
$88$	−475.473	−0.575973
$89$	1297.72	1.54559	0.772797	−	0.634653i	$-0.218857\pi$
$89$	1297.72	1.54559	0.772797	+	0.634653i	$0.218857\pi$
$90$	569.473	0.666975
$91$	138.438	0.159476
$92$	−745.421	−0.844733
$93$	1591.06	1.77404
$94$	−607.473	−0.666554
$95$	−475.285	−0.513297
$96$	293.193	0.311707
$97$	1001.77	1.04860	0.524302	−	0.851532i	$-0.324326\pi$
$97$	1001.77	1.04860	0.524302	+	0.851532i	$0.324326\pi$
$98$	−459.193	−0.473321
$99$	−3384.62	−3.43603
$100$	100.000	0.100000
$101$	793.667	0.781909	0.390954	−	0.920410i	$-0.372145\pi$
$101$	793.667	0.781909	0.390954	+	0.920410i	$0.372145\pi$
$102$	1067.81	1.03655
$103$	−991.310	−0.948318	−0.474159	−	0.880439i	$-0.657248\pi$
$103$	−991.310	−0.948318	−0.474159	+	0.880439i	$0.657248\pi$
$104$	−104.000	−0.0980581
$105$	−487.851	−0.453422
$106$	−807.140	−0.739589
$107$	1629.60	1.47233	0.736166	−	0.676801i	$-0.236634\pi$
$107$	1629.60	1.47233	0.736166	+	0.676801i	$0.236634\pi$
$108$	1097.54	0.977881
$109$	−480.491	−0.422227	−0.211113	−	0.977462i	$-0.567709\pi$
$109$	−480.491	−0.422227	−0.211113	+	0.977462i	$0.567709\pi$
$110$	−594.342	−0.515166
$111$	−808.772	−0.691578
$112$	−170.386	−0.143749
$113$	785.167	0.653649	0.326824	−	0.945085i	$-0.394021\pi$
$113$	785.167	0.653649	0.326824	+	0.945085i	$0.394021\pi$
$114$	−1741.88	−1.43107
$115$	−931.776	−0.755553
$116$	1030.95	0.825181
$117$	−740.315	−0.584976
$118$	19.9730	0.0155819
$119$	−620.544	−0.478027
$120$	366.491	0.278799
$121$	2201.42	1.65396
$122$	−490.175	−0.363757
$123$	1596.73	1.17050
$124$	694.614	0.503049
$125$	125.000	0.0894427
$126$	−1212.88	−0.857553
$127$	2562.75	1.79061	0.895304	−	0.445455i	$-0.146958\pi$
$127$	2562.75	1.79061	0.895304	+	0.445455i	$0.146958\pi$
$128$	128.000	0.0883883
$129$	4408.70	3.00903
$130$	−130.000	−0.0877058
$131$	−700.772	−0.467379	−0.233690	−	0.972311i	$-0.575080\pi$
$131$	−700.772	−0.467379	−0.233690	+	0.972311i	$0.575080\pi$
$132$	−2178.21	−1.43628
$133$	1012.27	0.659963
$134$	624.649	0.402697
$135$	1371.93	0.874643
$136$	466.175	0.293928
$137$	339.685	0.211834	0.105917	−	0.994375i	$-0.466222\pi$
$137$	339.685	0.211834	0.105917	+	0.994375i	$0.466222\pi$
$138$	−3414.88	−2.10647
$139$	−562.763	−0.343402	−0.171701	−	0.985149i	$-0.554926\pi$
$139$	−562.763	−0.343402	−0.171701	+	0.985149i	$0.554926\pi$
$140$	−212.982	−0.128573
$141$	−2782.92	−1.66216
$142$	50.0968	0.0296058
$143$	772.644	0.451830
$144$	911.157	0.527290
$145$	1288.68	0.738064
$146$	−464.965	−0.263567
$147$	−2103.63	−1.18030
$148$	−353.088	−0.196106
$149$	−860.893	−0.473336	−0.236668	−	0.971591i	$-0.576055\pi$
$149$	−860.893	−0.473336	−0.236668	+	0.971591i	$0.576055\pi$
$150$	458.114	0.249366
$151$	−1172.15	−0.631712	−0.315856	−	0.948807i	$-0.602292\pi$
$151$	−1172.15	−0.631712	−0.315856	+	0.948807i	$0.602292\pi$
$152$	−760.456	−0.405797
$153$	3318.43	1.75346
$154$	1265.84	0.662367
$155$	868.267	0.449941
$156$	−476.438	−0.244523
$157$	240.070	0.122036	0.0610180	−	0.998137i	$-0.480565\pi$
$157$	240.070	0.122036	0.0610180	+	0.998137i	$0.480565\pi$
$158$	−1655.25	−0.833445
$159$	−3697.62	−1.84428
$160$	160.000	0.0790569
$161$	1984.52	0.971440
$162$	1952.84	0.947097
$163$	1008.04	0.484393	0.242196	−	0.970227i	$-0.422132\pi$
$163$	1008.04	0.484393	0.242196	+	0.970227i	$0.422132\pi$
$164$	697.088	0.331911
$165$	−2722.76	−1.28465
$166$	−932.456	−0.435979
$167$	1175.77	0.544814	0.272407	−	0.962182i	$-0.412180\pi$
$167$	1175.77	0.544814	0.272407	+	0.962182i	$0.412180\pi$
$168$	−780.561	−0.358462
$169$	169.000	0.0769231
$170$	582.719	0.262897
$171$	−5413.24	−2.42082
$172$	1924.72	0.853246
$173$	510.167	0.224204	0.112102	−	0.993697i	$-0.464242\pi$
$173$	510.167	0.224204	0.112102	+	0.993697i	$0.464242\pi$
$174$	4722.91	2.05772
$175$	−266.228	−0.115000
$176$	−950.947	−0.407274
$177$	91.4990	0.0388558
$178$	2595.44	1.09290
$179$	2693.68	1.12478	0.562389	−	0.826873i	$-0.309882\pi$
$179$	2693.68	1.12478	0.562389	+	0.826873i	$0.309882\pi$
$180$	1138.95	0.471623
$181$	−4193.93	−1.72228	−0.861139	−	0.508370i	$-0.830248\pi$
$181$	−4193.93	−1.72228	−0.861139	+	0.508370i	$0.830248\pi$
$182$	276.877	0.112766
$183$	−2245.56	−0.907085
$184$	−1490.84	−0.597317
$185$	−441.359	−0.175402
$186$	3182.12	1.25443
$187$	−3463.34	−1.35436
$188$	−1214.95	−0.471325
$189$	−2921.96	−1.12456
$190$	−950.569	−0.362956
$191$	−180.194	−0.0682636	−0.0341318	−	0.999417i	$-0.510867\pi$
$191$	−180.194	−0.0682636	−0.0341318	+	0.999417i	$0.510867\pi$
$192$	586.386	0.220410
$193$	−4986.96	−1.85995	−0.929973	−	0.367629i	$-0.880170\pi$
$193$	−4986.96	−1.85995	−0.929973	+	0.367629i	$0.880170\pi$
$194$	2003.54	0.741475
$195$	−595.548	−0.218708
$196$	−918.386	−0.334689
$197$	3947.77	1.42775	0.713875	−	0.700273i	$-0.246938\pi$
$197$	3947.77	1.42775	0.713875	+	0.700273i	$0.246938\pi$
$198$	−6769.23	−2.42964
$199$	−3419.67	−1.21816	−0.609080	−	0.793109i	$-0.708461\pi$
$199$	−3419.67	−1.21816	−0.609080	+	0.793109i	$0.708461\pi$
$200$	200.000	0.0707107
$201$	2861.60	1.00419
$202$	1587.33	0.552893
$203$	−2744.67	−0.948955
$204$	2135.61	0.732955
$205$	871.359	0.296870
$206$	−1982.62	−0.670562
$207$	−10612.4	−3.56336
$208$	−208.000	−0.0693375
$209$	5649.63	1.86982
$210$	−975.701	−0.320618
$211$	2061.21	0.672509	0.336254	−	0.941771i	$-0.390840\pi$
$211$	2061.21	0.672509	0.336254	+	0.941771i	$0.390840\pi$
$212$	−1614.28	−0.522968
$213$	229.500	0.0738268
$214$	3259.20	1.04110
$215$	2405.90	0.763167
$216$	2195.09	0.691466
$217$	−1849.25	−0.578505
$218$	−960.982	−0.298559
$219$	−2130.07	−0.657246
$220$	−1188.68	−0.364277
$221$	−757.535	−0.230576
$222$	−1617.54	−0.489020
$223$	−4838.61	−1.45299	−0.726496	−	0.687170i	$-0.758853\pi$
$223$	−4838.61	−1.45299	−0.726496	+	0.687170i	$0.758853\pi$
$224$	−340.772	−0.101646
$225$	1423.68	0.421832
$226$	1570.33	0.462200
$227$	4544.22	1.32868	0.664340	−	0.747430i	$-0.268713\pi$
$227$	4544.22	1.32868	0.664340	+	0.747430i	$0.268713\pi$
$228$	−3483.75	−1.01192
$229$	1231.44	0.355354	0.177677	−	0.984089i	$-0.443142\pi$
$229$	1231.44	0.355354	0.177677	+	0.984089i	$0.443142\pi$
$230$	−1863.55	−0.534256
$231$	5799.00	1.65171
$232$	2061.89	0.583491
$233$	6276.45	1.76474	0.882369	−	0.470557i	$-0.155947\pi$
$233$	6276.45	1.76474	0.882369	+	0.470557i	$0.155947\pi$
$234$	−1480.63	−0.413640
$235$	−1518.68	−0.421566
$236$	39.9459	0.0110180
$237$	−7582.91	−2.07832
$238$	−1241.09	−0.338016
$239$	1087.40	0.294301	0.147151	−	0.989114i	$-0.452990\pi$
$239$	1087.40	0.294301	0.147151	+	0.989114i	$0.452990\pi$
$240$	732.982	0.197141
$241$	−4092.46	−1.09385	−0.546927	−	0.837181i	$-0.684202\pi$
$241$	−4092.46	−1.09385	−0.546927	+	0.837181i	$0.684202\pi$
$242$	4402.84	1.16953
$243$	1537.82	0.405972
$244$	−980.350	−0.257215
$245$	−1147.98	−0.299355
$246$	3193.45	0.827672
$247$	1235.74	0.318333
$248$	1389.23	0.355710
$249$	−4271.71	−1.08718
$250$	250.000	0.0632456
$251$	−7261.62	−1.82609	−0.913046	−	0.407856i	$-0.866276\pi$
$251$	−7261.62	−1.82609	−0.913046	+	0.407856i	$0.866276\pi$
$252$	−2425.75	−0.606381
$253$	11075.9	2.75231
$254$	5125.50	1.26615
$255$	2669.52	0.655575
$256$	256.000	0.0625000
$257$	1307.67	0.317393	0.158697	−	0.987327i	$-0.449271\pi$
$257$	1307.67	0.317393	0.158697	+	0.987327i	$0.449271\pi$
$258$	8817.40	2.12770
$259$	940.017	0.225521
$260$	−260.000	−0.0620174
$261$	14677.4	3.48088
$262$	−1401.54	−0.330487
$263$	5854.52	1.37264	0.686321	−	0.727298i	$-0.259224\pi$
$263$	5854.52	1.37264	0.686321	+	0.727298i	$0.259224\pi$
$264$	−4356.42	−1.01560
$265$	−2017.85	−0.467757
$266$	2024.54	0.466664
$267$	11890.1	2.72532
$268$	1249.30	0.284750
$269$	1854.91	0.420432	0.210216	−	0.977655i	$-0.432583\pi$
$269$	1854.91	0.420432	0.210216	+	0.977655i	$0.432583\pi$
$270$	2743.86	0.618466
$271$	2584.18	0.579253	0.289626	−	0.957140i	$-0.406469\pi$
$271$	2584.18	0.579253	0.289626	+	0.957140i	$0.406469\pi$
$272$	932.350	0.207838
$273$	1268.41	0.281201
$274$	679.371	0.149789
$275$	−1485.85	−0.325820
$276$	−6829.75	−1.48950
$277$	−7177.57	−1.55689	−0.778445	−	0.627713i	$-0.783991\pi$
$277$	−7177.57	−1.55689	−0.778445	+	0.627713i	$0.783991\pi$
$278$	−1125.53	−0.242822
$279$	9889.10	2.12202
$280$	−425.964	−0.0909152
$281$	−3841.18	−0.815464	−0.407732	−	0.913102i	$-0.633680\pi$
$281$	−3841.18	−0.815464	−0.407732	+	0.913102i	$0.633680\pi$
$282$	−5565.84	−1.17532
$283$	−6120.73	−1.28565	−0.642826	−	0.766012i	$-0.722238\pi$
$283$	−6120.73	−1.28565	−0.642826	+	0.766012i	$0.722238\pi$
$284$	100.194	0.0209345
$285$	−4354.69	−0.905086
$286$	1545.29	0.319492
$287$	−1855.84	−0.381696
$288$	1822.31	0.372850
$289$	−1517.39	−0.308851
$290$	2577.37	0.521890
$291$	9178.52	1.84898
$292$	−929.930	−0.186370
$293$	3922.74	0.782147	0.391074	−	0.920359i	$-0.372104\pi$
$293$	3922.74	0.782147	0.391074	+	0.920359i	$0.372104\pi$
$294$	−4207.25	−0.834599
$295$	49.9324	0.00985484
$296$	−706.175	−0.138668
$297$	−16307.9	−3.18613
$298$	−1721.79	−0.334699
$299$	2422.62	0.468574
$300$	916.228	0.176328
$301$	−5124.13	−0.981229
$302$	−2344.31	−0.446688
$303$	7271.80	1.37873
$304$	−1520.91	−0.286942
$305$	−1225.44	−0.230060
$306$	6636.86	1.23988
$307$	6318.56	1.17466	0.587328	−	0.809349i	$-0.300180\pi$
$307$	6318.56	1.17466	0.587328	+	0.809349i	$0.300180\pi$
$308$	2531.68	0.468364
$309$	−9082.66	−1.67215
$310$	1736.53	0.318156
$311$	496.850	0.0905909	0.0452955	−	0.998974i	$-0.485577\pi$
$311$	496.850	0.0905909	0.0452955	+	0.998974i	$0.485577\pi$
$312$	−952.877	−0.172904
$313$	3554.43	0.641879	0.320940	−	0.947100i	$-0.396001\pi$
$313$	3554.43	0.641879	0.320940	+	0.947100i	$0.396001\pi$
$314$	480.140	0.0862925
$315$	−3032.19	−0.542364
$316$	−3310.49	−0.589334
$317$	−9393.59	−1.66434	−0.832171	−	0.554519i	$-0.812902\pi$
$317$	−9393.59	−1.66434	−0.832171	+	0.554519i	$0.812902\pi$
$318$	−7395.24	−1.30410
$319$	−15318.4	−2.68860
$320$	320.000	0.0559017
$321$	14930.9	2.59613
$322$	3969.03	0.686912
$323$	−5539.15	−0.954199
$324$	3905.68	0.669699
$325$	−325.000	−0.0554700
$326$	2016.09	0.342517
$327$	−4402.39	−0.744504
$328$	1394.18	0.234696
$329$	3234.53	0.542022
$330$	−5445.52	−0.908382
$331$	−8593.86	−1.42707	−0.713536	−	0.700618i	$-0.752908\pi$
$331$	−8593.86	−1.42707	−0.713536	+	0.700618i	$0.752908\pi$
$332$	−1864.91	−0.308284
$333$	−5026.85	−0.827236
$334$	2351.54	0.385241
$335$	1561.62	0.254688
$336$	−1561.12	−0.253471
$337$	3533.25	0.571122	0.285561	−	0.958360i	$-0.407820\pi$
$337$	3533.25	0.571122	0.285561	+	0.958360i	$0.407820\pi$
$338$	338.000	0.0543928
$339$	7193.92	1.15257
$340$	1165.44	0.185896
$341$	−10320.9	−1.63903
$342$	−10826.5	−1.71178
$343$	6097.64	0.959889
$344$	3849.43	0.603336
$345$	−8537.19	−1.33225
$346$	1020.33	0.158536
$347$	6949.13	1.07507	0.537535	−	0.843242i	$-0.319356\pi$
$347$	6949.13	1.07507	0.537535	+	0.843242i	$0.319356\pi$
$348$	9445.82	1.45503
$349$	3478.53	0.533529	0.266764	−	0.963762i	$-0.414045\pi$
$349$	3478.53	0.533529	0.266764	+	0.963762i	$0.414045\pi$
$350$	−532.456	−0.0813170
$351$	−3567.02	−0.542431
$352$	−1901.89	−0.287987
$353$	−9083.23	−1.36955	−0.684776	−	0.728754i	$-0.740100\pi$
$353$	−9083.23	−1.36955	−0.684776	+	0.728754i	$0.740100\pi$
$354$	182.998	0.0274752
$355$	125.242	0.0187244
$356$	5190.87	0.772797
$357$	−5685.59	−0.842895
$358$	5387.37	0.795338
$359$	−10489.1	−1.54205	−0.771024	−	0.636806i	$-0.780255\pi$
$359$	−10489.1	−1.54205	−0.771024	+	0.636806i	$0.780255\pi$
$360$	2277.89	0.333488
$361$	2176.82	0.317367
$362$	−8387.85	−1.21783
$363$	20170.0	2.91640
$364$	553.754	0.0797379
$365$	−1162.41	−0.166694
$366$	−4491.12	−0.641406
$367$	−5707.20	−0.811753	−0.405877	−	0.913928i	$-0.633034\pi$
$367$	−5707.20	−0.811753	−0.405877	+	0.913928i	$0.633034\pi$
$368$	−2981.68	−0.422367
$369$	9924.32	1.40011
$370$	−882.719	−0.124028
$371$	4297.66	0.601411
$372$	6364.24	0.887018
$373$	−5006.69	−0.695005	−0.347502	−	0.937679i	$-0.612970\pi$
$373$	−5006.69	−0.695005	−0.347502	+	0.937679i	$0.612970\pi$
$374$	−6926.68	−0.957674
$375$	1145.28	0.157713
$376$	−2429.89	−0.333277
$377$	−3350.58	−0.457728
$378$	−5843.93	−0.795183
$379$	−520.522	−0.0705472	−0.0352736	−	0.999378i	$-0.511230\pi$
$379$	−520.522	−0.0705472	−0.0352736	+	0.999378i	$0.511230\pi$
$380$	−1901.14	−0.256648
$381$	23480.6	3.15735
$382$	−360.387	−0.0482697
$383$	−11192.5	−1.49324	−0.746621	−	0.665249i	$-0.768325\pi$
$383$	−11192.5	−1.49324	−0.746621	+	0.665249i	$0.768325\pi$
$384$	1172.77	0.155854
$385$	3164.60	0.418917
$386$	−9973.92	−1.31518
$387$	27401.9	3.59927
$388$	4007.09	0.524302
$389$	−3479.85	−0.453562	−0.226781	−	0.973946i	$-0.572820\pi$
$389$	−3479.85	−0.453562	−0.226781	+	0.973946i	$0.572820\pi$
$390$	−1191.10	−0.154650
$391$	−10859.3	−1.40454
$392$	−1836.77	−0.236661
$393$	−6420.66	−0.824121
$394$	7895.54	1.00957
$395$	−4138.11	−0.527117
$396$	−13538.5	−1.71801
$397$	562.658	0.0711309	0.0355655	−	0.999367i	$-0.488677\pi$
$397$	562.658	0.0711309	0.0355655	+	0.999367i	$0.488677\pi$
$398$	−6839.33	−0.861369
$399$	9274.72	1.16370
$400$	400.000	0.0500000
$401$	15097.0	1.88007	0.940036	−	0.341076i	$-0.110791\pi$
$401$	15097.0	1.88007	0.940036	+	0.341076i	$0.110791\pi$
$402$	5723.21	0.710069
$403$	−2257.49	−0.279042
$404$	3174.67	0.390954
$405$	4882.10	0.598997
$406$	−5489.33	−0.671012
$407$	5246.37	0.638950
$408$	4271.23	0.518277
$409$	1990.99	0.240705	0.120352	−	0.992731i	$-0.461598\pi$
$409$	1990.99	0.240705	0.120352	+	0.992731i	$0.461598\pi$
$410$	1742.72	0.209919
$411$	3112.29	0.373523
$412$	−3965.24	−0.474159
$413$	−106.347	−0.0126707
$414$	−21224.9	−2.51967
$415$	−2331.14	−0.275738
$416$	−416.000	−0.0490290
$417$	−5156.19	−0.605515
$418$	11299.3	1.32216
$419$	13151.0	1.53334	0.766670	−	0.642041i	$-0.221912\pi$
$419$	13151.0	1.53334	0.766670	+	0.642041i	$0.221912\pi$
$420$	−1951.40	−0.226711
$421$	−12795.8	−1.48130	−0.740652	−	0.671889i	$-0.765483\pi$
$421$	−12795.8	−1.48130	−0.740652	+	0.671889i	$0.765483\pi$
$422$	4122.41	0.475536
$423$	−17297.0	−1.98820
$424$	−3228.56	−0.369794
$425$	1456.80	0.166271
$426$	459.001	0.0522034
$427$	2609.96	0.295796
$428$	6518.40	0.736166
$429$	7079.18	0.796704
$430$	4811.79	0.539640
$431$	−3751.97	−0.419318	−0.209659	−	0.977775i	$-0.567235\pi$
$431$	−3751.97	−0.419318	−0.209659	+	0.977775i	$0.567235\pi$
$432$	4390.17	0.488940
$433$	2135.29	0.236987	0.118493	−	0.992955i	$-0.462194\pi$
$433$	2135.29	0.236987	0.118493	+	0.992955i	$0.462194\pi$
$434$	−3698.51	−0.409065
$435$	11807.3	1.30141
$436$	−1921.96	−0.211113
$437$	17714.4	1.93911
$438$	−4260.14	−0.464743
$439$	−6983.59	−0.759245	−0.379623	−	0.925141i	$-0.623946\pi$
$439$	−6983.59	−0.759245	−0.379623	+	0.925141i	$0.623946\pi$
$440$	−2377.37	−0.257583
$441$	−13074.9	−1.41182
$442$	−1515.07	−0.163042
$443$	−7418.03	−0.795579	−0.397789	−	0.917477i	$-0.630223\pi$
$443$	−7418.03	−0.795579	−0.397789	+	0.917477i	$0.630223\pi$
$444$	−3235.09	−0.345789
$445$	6488.59	0.691211
$446$	−9677.22	−1.02742
$447$	−7887.74	−0.834625
$448$	−681.543	−0.0718747
$449$	−15399.2	−1.61856	−0.809278	−	0.587426i	$-0.800141\pi$
$449$	−15399.2	−1.61856	−0.809278	+	0.587426i	$0.800141\pi$
$450$	2847.37	0.298280
$451$	−10357.7	−1.08143
$452$	3140.67	0.326824
$453$	−10739.6	−1.11389
$454$	9088.44	0.939519
$455$	692.192	0.0713197
$456$	−6967.50	−0.715534
$457$	2888.53	0.295667	0.147833	−	0.989012i	$-0.452770\pi$
$457$	2888.53	0.295667	0.147833	+	0.989012i	$0.452770\pi$
$458$	2462.89	0.251274
$459$	15989.0	1.62593
$460$	−3727.10	−0.377776
$461$	5682.27	0.574077	0.287039	−	0.957919i	$-0.407329\pi$
$461$	5682.27	0.574077	0.287039	+	0.957919i	$0.407329\pi$
$462$	11598.0	1.16794
$463$	71.9859	0.00722563	0.00361282	−	0.999993i	$-0.498850\pi$
$463$	71.9859	0.00722563	0.00361282	+	0.999993i	$0.498850\pi$
$464$	4123.79	0.412590
$465$	7955.30	0.793373
$466$	12552.9	1.24786
$467$	−16031.2	−1.58852	−0.794258	−	0.607581i	$-0.792140\pi$
$467$	−16031.2	−1.58852	−0.794258	+	0.607581i	$0.792140\pi$
$468$	−2961.26	−0.292488
$469$	−3325.98	−0.327461
$470$	−3037.37	−0.298092
$471$	2199.59	0.215184
$472$	79.8919	0.00779094
$473$	−28598.5	−2.78004
$474$	−15165.8	−1.46960
$475$	−2376.42	−0.229553
$476$	−2482.18	−0.239013
$477$	−22982.2	−2.20605
$478$	2174.80	0.208103
$479$	1148.19	0.109524	0.0547622	−	0.998499i	$-0.482560\pi$
$479$	1148.19	0.109524	0.0547622	+	0.998499i	$0.482560\pi$
$480$	1465.96	0.139400
$481$	1147.53	0.108780
$482$	−8184.92	−0.773471
$483$	18182.7	1.71292
$484$	8805.68	0.826980
$485$	5008.86	0.468950
$486$	3075.64	0.287066
$487$	17950.9	1.67030	0.835148	−	0.550025i	$-0.185382\pi$
$487$	17950.9	1.67030	0.835148	+	0.550025i	$0.185382\pi$
$488$	−1960.70	−0.181879
$489$	9235.97	0.854120
$490$	−2295.96	−0.211676
$491$	−18219.7	−1.67463	−0.837316	−	0.546719i	$-0.815877\pi$
$491$	−18219.7	−1.67463	−0.837316	+	0.546719i	$0.815877\pi$
$492$	6386.91	0.585252
$493$	15018.8	1.37203
$494$	2471.48	0.225095
$495$	−16923.1	−1.53664
$496$	2778.45	0.251525
$497$	−266.743	−0.0240746
$498$	−8543.42	−0.768754
$499$	3287.03	0.294885	0.147443	−	0.989071i	$-0.452896\pi$
$499$	3287.03	0.294885	0.147443	+	0.989071i	$0.452896\pi$
$500$	500.000	0.0447214
$501$	10772.7	0.960660
$502$	−14523.2	−1.29124
$503$	10961.2	0.971639	0.485820	−	0.874059i	$-0.338521\pi$
$503$	10961.2	0.971639	0.485820	+	0.874059i	$0.338521\pi$
$504$	−4851.51	−0.428776
$505$	3968.33	0.349680
$506$	22151.7	1.94617
$507$	1548.42	0.135637
$508$	10251.0	0.895304
$509$	12986.3	1.13086	0.565429	−	0.824797i	$-0.308711\pi$
$509$	12986.3	1.13086	0.565429	+	0.824797i	$0.308711\pi$
$510$	5339.03	0.463561
$511$	2475.73	0.214325
$512$	512.000	0.0441942
$513$	−26082.3	−2.24476
$514$	2615.34	0.224431
$515$	−4956.55	−0.424101
$516$	17634.8	1.50451
$517$	18052.3	1.53567
$518$	1880.03	0.159467
$519$	4674.29	0.395334
$520$	−520.000	−0.0438529
$521$	−1424.49	−0.119785	−0.0598925	−	0.998205i	$-0.519076\pi$
$521$	−1424.49	−0.119785	−0.0598925	+	0.998205i	$0.519076\pi$
$522$	29354.8	2.46135
$523$	9087.18	0.759761	0.379880	−	0.925036i	$-0.375965\pi$
$523$	9087.18	0.759761	0.379880	+	0.925036i	$0.375965\pi$
$524$	−2803.09	−0.233690
$525$	−2439.25	−0.202777
$526$	11709.0	0.970605
$527$	10119.1	0.836424
$528$	−8712.84	−0.718139
$529$	22561.2	1.85430
$530$	−4035.70	−0.330754
$531$	568.704	0.0464777
$532$	4049.09	0.329982
$533$	−2265.53	−0.184111
$534$	23780.1	1.92709
$535$	8148.00	0.658447
$536$	2498.60	0.201349
$537$	24680.3	1.98330
$538$	3709.83	0.297290
$539$	13645.9	1.09048
$540$	5487.72	0.437322
$541$	1506.21	0.119699	0.0598493	−	0.998207i	$-0.480938\pi$
$541$	1506.21	0.119699	0.0598493	+	0.998207i	$0.480938\pi$
$542$	5168.35	0.409594
$543$	−38425.9	−3.03686
$544$	1864.70	0.146964
$545$	−2402.46	−0.188825
$546$	2536.82	0.198839
$547$	−1897.52	−0.148322	−0.0741608	−	0.997246i	$-0.523628\pi$
$547$	−1897.52	−0.148322	−0.0741608	+	0.997246i	$0.523628\pi$
$548$	1358.74	0.105917
$549$	−13957.1	−1.08502
$550$	−2971.71	−0.230389
$551$	−24499.7	−1.89423
$552$	−13659.5	−1.05324
$553$	8813.45	0.677732
$554$	−14355.1	−1.10089
$555$	−4043.86	−0.309283
$556$	−2251.05	−0.171701
$557$	2287.55	0.174015	0.0870076	−	0.996208i	$-0.472270\pi$
$557$	2287.55	0.174015	0.0870076	+	0.996208i	$0.472270\pi$
$558$	19778.2	1.50050
$559$	−6255.33	−0.473296
$560$	−851.929	−0.0642867
$561$	−31732.1	−2.38811
$562$	−7682.36	−0.576620
$563$	739.713	0.0553733	0.0276867	−	0.999617i	$-0.491186\pi$
$563$	739.713	0.0553733	0.0276867	+	0.999617i	$0.491186\pi$
$564$	−11131.7	−0.831078
$565$	3925.84	0.292321
$566$	−12241.5	−0.909093
$567$	−10398.0	−0.770151
$568$	200.387	0.0148029
$569$	−4683.37	−0.345057	−0.172528	−	0.985005i	$-0.555194\pi$
$569$	−4683.37	−0.345057	−0.172528	+	0.985005i	$0.555194\pi$
$570$	−8709.38	−0.639993
$571$	−8385.89	−0.614604	−0.307302	−	0.951612i	$-0.599426\pi$
$571$	−8385.89	−0.614604	−0.307302	+	0.951612i	$0.599426\pi$
$572$	3090.58	0.225915
$573$	−1650.98	−0.120368
$574$	−3711.68	−0.269900
$575$	−4658.88	−0.337893
$576$	3644.63	0.263645
$577$	−389.573	−0.0281077	−0.0140538	−	0.999901i	$-0.504474\pi$
$577$	−389.573	−0.0281077	−0.0140538	+	0.999901i	$0.504474\pi$
$578$	−3034.77	−0.218391
$579$	−45691.9	−3.27961
$580$	5154.73	0.369032
$581$	4964.91	0.354525
$582$	18357.0	1.30743
$583$	23985.9	1.70393
$584$	−1859.86	−0.131784
$585$	−3701.58	−0.261609
$586$	7845.49	0.553062
$587$	19046.3	1.33922	0.669612	−	0.742711i	$-0.266460\pi$
$587$	19046.3	1.33922	0.669612	+	0.742711i	$0.266460\pi$
$588$	−8414.51	−0.590150
$589$	−16507.0	−1.15477
$590$	99.8649	0.00696843
$591$	36170.5	2.51753
$592$	−1412.35	−0.0980528
$593$	5956.37	0.412477	0.206239	−	0.978502i	$-0.433878\pi$
$593$	5956.37	0.412477	0.206239	+	0.978502i	$0.433878\pi$
$594$	−32615.8	−2.25293
$595$	−3102.72	−0.213780
$596$	−3443.57	−0.236668
$597$	−31331.9	−2.14796
$598$	4845.23	0.331332
$599$	888.898	0.0606334	0.0303167	−	0.999540i	$-0.490348\pi$
$599$	888.898	0.0606334	0.0303167	+	0.999540i	$0.490348\pi$
$600$	1832.46	0.124683
$601$	−3005.76	−0.204006	−0.102003	−	0.994784i	$-0.532525\pi$
$601$	−3005.76	−0.204006	−0.102003	+	0.994784i	$0.532525\pi$
$602$	−10248.3	−0.693834
$603$	17786.1	1.20117
$604$	−4688.62	−0.315856
$605$	11007.1	0.739673
$606$	14543.6	0.974906
$607$	−13705.8	−0.916476	−0.458238	−	0.888829i	$-0.651519\pi$
$607$	−13705.8	−0.916476	−0.458238	+	0.888829i	$0.651519\pi$
$608$	−3041.82	−0.202898
$609$	−25147.4	−1.67327
$610$	−2450.88	−0.162677
$611$	3948.58	0.261444
$612$	13273.7	0.876729
$613$	6959.76	0.458568	0.229284	−	0.973360i	$-0.426362\pi$
$613$	6959.76	0.458568	0.229284	+	0.973360i	$0.426362\pi$
$614$	12637.1	0.830607
$615$	7983.64	0.523466
$616$	5063.37	0.331183
$617$	−20675.0	−1.34902	−0.674508	−	0.738268i	$-0.735644\pi$
$617$	−20675.0	−1.34902	−0.674508	+	0.738268i	$0.735644\pi$
$618$	−18165.3	−1.18239
$619$	−13759.8	−0.893460	−0.446730	−	0.894669i	$-0.647411\pi$
$619$	−13759.8	−0.893460	−0.446730	+	0.894669i	$0.647411\pi$
$620$	3473.07	0.224971
$621$	−51133.2	−3.30419
$622$	993.700	0.0640574
$623$	−13819.5	−0.888713
$624$	−1905.75	−0.122262
$625$	625.000	0.0400000
$626$	7108.86	0.453877
$627$	51763.5	3.29702
$628$	960.279	0.0610180
$629$	−5143.77	−0.326066
$630$	−6064.38	−0.383509
$631$	16760.2	1.05739	0.528694	−	0.848813i	$-0.322682\pi$
$631$	16760.2	1.05739	0.528694	+	0.848813i	$0.322682\pi$
$632$	−6620.98	−0.416722
$633$	18885.4	1.18582
$634$	−18787.2	−1.17687
$635$	12813.7	0.800784
$636$	−14790.5	−0.922140
$637$	2984.75	0.185652
$638$	−30636.7	−1.90113
$639$	1426.44	0.0883084
$640$	640.000	0.0395285
$641$	−2993.27	−0.184442	−0.0922208	−	0.995739i	$-0.529397\pi$
$641$	−2993.27	−0.184442	−0.0922208	+	0.995739i	$0.529397\pi$
$642$	29861.7	1.83574
$643$	24260.3	1.48792	0.743959	−	0.668225i	$-0.232946\pi$
$643$	24260.3	1.48792	0.743959	+	0.668225i	$0.232946\pi$
$644$	7938.07	0.485720
$645$	22043.5	1.34568
$646$	−11078.3	−0.674721
$647$	−1342.40	−0.0815691	−0.0407846	−	0.999168i	$-0.512986\pi$
$647$	−1342.40	−0.0815691	−0.0407846	+	0.999168i	$0.512986\pi$
$648$	7811.37	0.473548
$649$	−593.538	−0.0358990
$650$	−650.000	−0.0392232
$651$	−16943.4	−1.02007
$652$	4032.17	0.242196
$653$	13960.3	0.836611	0.418306	−	0.908306i	$-0.362624\pi$
$653$	13960.3	0.836611	0.418306	+	0.908306i	$0.362624\pi$
$654$	−8804.79	−0.526444
$655$	−3503.86	−0.209018
$656$	2788.35	0.165955
$657$	−13239.3	−0.786169
$658$	6469.05	0.383267
$659$	−26385.2	−1.55967	−0.779836	−	0.625984i	$-0.784697\pi$
$659$	−26385.2	−1.55967	−0.779836	+	0.625984i	$0.784697\pi$
$660$	−10891.0	−0.642323
$661$	−4699.23	−0.276519	−0.138259	−	0.990396i	$-0.544151\pi$
$661$	−4699.23	−0.276519	−0.138259	+	0.990396i	$0.544151\pi$
$662$	−17187.7	−1.00909
$663$	−6940.74	−0.406570
$664$	−3729.82	−0.217990
$665$	5061.36	0.295145
$666$	−10053.7	−0.584944
$667$	−48030.6	−2.78823
$668$	4703.08	0.272407
$669$	−44332.7	−2.56204
$670$	3123.25	0.180092
$671$	14566.6	0.838057
$672$	−3122.24	−0.179231
$673$	−9771.47	−0.559677	−0.279838	−	0.960047i	$-0.590281\pi$
$673$	−9771.47	−0.559677	−0.279838	+	0.960047i	$0.590281\pi$
$674$	7066.49	0.403844
$675$	6859.64	0.391152
$676$	676.000	0.0384615
$677$	32576.0	1.84933	0.924666	−	0.380778i	$-0.124344\pi$
$677$	32576.0	1.84933	0.924666	+	0.380778i	$0.124344\pi$
$678$	14387.8	0.814988
$679$	−10668.0	−0.602945
$680$	2330.88	0.131449
$681$	41635.4	2.34284
$682$	−20641.9	−1.15897
$683$	−10007.9	−0.560677	−0.280338	−	0.959901i	$-0.590447\pi$
$683$	−10007.9	−0.560677	−0.280338	+	0.959901i	$0.590447\pi$
$684$	−21653.0	−1.21041
$685$	1698.43	0.0947351
$686$	12195.3	0.678744
$687$	11282.8	0.626590
$688$	7698.87	0.426623
$689$	5246.41	0.290091
$690$	−17074.4	−0.942044
$691$	15066.7	0.829472	0.414736	−	0.909942i	$-0.363874\pi$
$691$	15066.7	0.829472	0.414736	+	0.909942i	$0.363874\pi$
$692$	2040.67	0.112102
$693$	36043.2	1.97571
$694$	13898.3	0.760189
$695$	−2813.81	−0.153574
$696$	18891.6	1.02886
$697$	10155.2	0.551871
$698$	6957.06	0.377262
$699$	57506.6	3.11173
$700$	−1064.91	−0.0574998
$701$	20020.1	1.07867	0.539335	−	0.842091i	$-0.318676\pi$
$701$	20020.1	1.07867	0.539335	+	0.842091i	$0.318676\pi$
$702$	−7134.03	−0.383556
$703$	8390.86	0.450167
$704$	−3803.79	−0.203637
$705$	−13914.6	−0.743339
$706$	−18166.5	−0.968419
$707$	−8451.85	−0.449596
$708$	365.996	0.0194279
$709$	23129.3	1.22516	0.612581	−	0.790408i	$-0.290131\pi$
$709$	23129.3	1.22516	0.612581	+	0.790408i	$0.290131\pi$
$710$	250.484	0.0132401
$711$	−47130.9	−2.48600
$712$	10381.7	0.546450
$713$	−32361.2	−1.69977
$714$	−11371.2	−0.596017
$715$	3863.22	0.202065
$716$	10774.7	0.562389
$717$	9963.06	0.518936
$718$	−20978.3	−1.09039
$719$	9310.55	0.482927	0.241464	−	0.970410i	$-0.422373\pi$
$719$	9310.55	0.482927	0.241464	+	0.970410i	$0.422373\pi$
$720$	4555.79	0.235811
$721$	10556.6	0.545281
$722$	4353.64	0.224413
$723$	−37496.3	−1.92877
$724$	−16775.7	−0.861139
$725$	6443.42	0.330072
$726$	40340.0	2.06220
$727$	−9388.78	−0.478969	−0.239485	−	0.970900i	$-0.576978\pi$
$727$	−9388.78	−0.478969	−0.239485	+	0.970900i	$0.576978\pi$
$728$	1107.51	0.0563832
$729$	−12273.4	−0.623554
$730$	−2324.83	−0.117871
$731$	28039.2	1.41870
$732$	−8982.24	−0.453543
$733$	−19170.2	−0.965985	−0.482993	−	0.875624i	$-0.660450\pi$
$733$	−19170.2	−0.965985	−0.482993	+	0.875624i	$0.660450\pi$
$734$	−11414.4	−0.573996
$735$	−10518.1	−0.527846
$736$	−5963.37	−0.298658
$737$	−18562.7	−0.927772
$738$	19848.6	0.990025
$739$	36531.3	1.81844	0.909220	−	0.416316i	$-0.136679\pi$
$739$	36531.3	1.81844	0.909220	+	0.416316i	$0.136679\pi$
$740$	−1765.44	−0.0877011
$741$	11322.2	0.561311
$742$	8595.33	0.425262
$743$	−24160.8	−1.19296	−0.596482	−	0.802627i	$-0.703435\pi$
$743$	−24160.8	−1.19296	−0.596482	+	0.802627i	$0.703435\pi$
$744$	12728.5	0.627216
$745$	−4304.46	−0.211682
$746$	−10013.4	−0.491443
$747$	−26550.4	−1.30044
$748$	−13853.4	−0.677178
$749$	−17353.8	−0.846587
$750$	2290.57	0.111520
$751$	−30100.0	−1.46254	−0.731269	−	0.682089i	$-0.761072\pi$
$751$	−30100.0	−1.46254	−0.731269	+	0.682089i	$0.761072\pi$
$752$	−4859.79	−0.235662
$753$	−66532.9	−3.21991
$754$	−6701.15	−0.323663
$755$	−5860.77	−0.282510
$756$	−11687.9	−0.562279
$757$	−7982.97	−0.383284	−0.191642	−	0.981465i	$-0.561381\pi$
$757$	−7982.97	−0.383284	−0.191642	+	0.981465i	$0.561381\pi$
$758$	−1041.04	−0.0498844
$759$	101480.	4.85309
$760$	−3802.28	−0.181478
$761$	6407.73	0.305230	0.152615	−	0.988286i	$-0.451231\pi$
$761$	6407.73	0.305230	0.152615	+	0.988286i	$0.451231\pi$
$762$	46961.2	2.23258
$763$	5116.80	0.242779
$764$	−720.774	−0.0341318
$765$	16592.1	0.784170
$766$	−22385.1	−1.05588
$767$	−129.824	−0.00611171
$768$	2345.54	0.110205
$769$	−9036.84	−0.423767	−0.211884	−	0.977295i	$-0.567960\pi$
$769$	−9036.84	−0.423767	−0.211884	+	0.977295i	$0.567960\pi$
$770$	6329.21	0.296219
$771$	11981.2	0.559654
$772$	−19947.8	−0.929973
$773$	−780.756	−0.0363284	−0.0181642	−	0.999835i	$-0.505782\pi$
$773$	−780.756	−0.0363284	−0.0181642	+	0.999835i	$0.505782\pi$
$774$	54803.8	2.54507
$775$	4341.33	0.201220
$776$	8014.18	0.370737
$777$	8612.70	0.397656
$778$	−6959.71	−0.320717
$779$	−16565.8	−0.761912
$780$	−2382.19	−0.109354
$781$	−1488.73	−0.0682087
$782$	−21718.5	−0.993163
$783$	70719.3	3.22771
$784$	−3673.54	−0.167344
$785$	1200.35	0.0545762
$786$	−12841.3	−0.582742
$787$	10966.2	0.496701	0.248351	−	0.968670i	$-0.420111\pi$
$787$	10966.2	0.496701	0.248351	+	0.968670i	$0.420111\pi$
$788$	15791.1	0.713875
$789$	53640.7	2.42036
$790$	−8276.23	−0.372728
$791$	−8361.33	−0.375847
$792$	−27076.9	−1.21482
$793$	3186.14	0.142677
$794$	1125.32	0.0502972
$795$	−18488.1	−0.824787
$796$	−13678.7	−0.609080
$797$	21136.3	0.939381	0.469690	−	0.882831i	$-0.344366\pi$
$797$	21136.3	0.939381	0.469690	+	0.882831i	$0.344366\pi$
$798$	18549.4	0.822861
$799$	−17699.3	−0.783675
$800$	800.000	0.0353553
$801$	73901.6	3.25991
$802$	30194.0	1.32941
$803$	13817.4	0.607230
$804$	11446.4	0.502095
$805$	9922.58	0.434441
$806$	−4514.99	−0.197312
$807$	16995.2	0.741339
$808$	6349.34	0.276447
$809$	−25615.0	−1.11320	−0.556598	−	0.830782i	$-0.687894\pi$
$809$	−25615.0	−1.11320	−0.556598	+	0.830782i	$0.687894\pi$
$810$	9764.21	0.423555
$811$	17070.8	0.739134	0.369567	−	0.929204i	$-0.379506\pi$
$811$	17070.8	0.739134	0.369567	+	0.929204i	$0.379506\pi$
$812$	−10978.7	−0.474477
$813$	23676.9	1.02139
$814$	10492.7	0.451806
$815$	5040.21	0.216627
$816$	8542.45	0.366477
$817$	−45739.4	−1.95865
$818$	3981.98	0.170204
$819$	7883.70	0.336360
$820$	3485.44	0.148435
$821$	−28147.4	−1.19653	−0.598264	−	0.801299i	$-0.704143\pi$
$821$	−28147.4	−1.19653	−0.598264	+	0.801299i	$0.704143\pi$
$822$	6224.58	0.264121
$823$	−1728.81	−0.0732230	−0.0366115	−	0.999330i	$-0.511656\pi$
$823$	−1728.81	−0.0732230	−0.0366115	+	0.999330i	$0.511656\pi$
$824$	−7930.48	−0.335281
$825$	−13613.8	−0.574511
$826$	−212.694	−0.00895955
$827$	−3827.22	−0.160926	−0.0804628	−	0.996758i	$-0.525640\pi$
$827$	−3827.22	−0.160926	−0.0804628	+	0.996758i	$0.525640\pi$
$828$	−42449.7	−1.78168
$829$	−21716.2	−0.909811	−0.454906	−	0.890540i	$-0.650327\pi$
$829$	−21716.2	−0.909811	−0.454906	+	0.890540i	$0.650327\pi$
$830$	−4662.28	−0.194976
$831$	−65762.9	−2.74523
$832$	−832.000	−0.0346688
$833$	−13379.0	−0.556489
$834$	−10312.4	−0.428164
$835$	5878.85	0.243648
$836$	22598.5	0.934912
$837$	47648.0	1.96769
$838$	26302.0	1.08424
$839$	45771.4	1.88344	0.941719	−	0.336400i	$-0.109209\pi$
$839$	45771.4	1.88344	0.941719	+	0.336400i	$0.109209\pi$
$840$	−3902.80	−0.160309
$841$	42039.2	1.72369
$842$	−25591.6	−1.04744
$843$	−35193.9	−1.43789
$844$	8244.83	0.336254
$845$	845.000	0.0344010
$846$	−34594.0	−1.40587
$847$	−23443.2	−0.951023
$848$	−6457.12	−0.261484
$849$	−56079.8	−2.26696
$850$	2913.59	0.117571
$851$	16449.9	0.662628
$852$	918.001	0.0369134
$853$	2372.68	0.0952390	0.0476195	−	0.998866i	$-0.484837\pi$
$853$	2372.68	0.0952390	0.0476195	+	0.998866i	$0.484837\pi$
$854$	5219.93	0.209160
$855$	−27066.2	−1.08262
$856$	13036.8	0.520548
$857$	22869.2	0.911550	0.455775	−	0.890095i	$-0.349362\pi$
$857$	22869.2	0.911550	0.455775	+	0.890095i	$0.349362\pi$
$858$	14158.4	0.563355
$859$	18742.3	0.744448	0.372224	−	0.928143i	$-0.378595\pi$
$859$	18742.3	0.744448	0.372224	+	0.928143i	$0.378595\pi$
$860$	9623.59	0.381583
$861$	−17003.7	−0.673038
$862$	−7503.93	−0.296502
$863$	−20662.7	−0.815026	−0.407513	−	0.913199i	$-0.633604\pi$
$863$	−20662.7	−0.815026	−0.407513	+	0.913199i	$0.633604\pi$
$864$	8780.34	0.345733
$865$	2550.83	0.100267
$866$	4270.57	0.167575
$867$	−13902.7	−0.544592
$868$	−7397.02	−0.289252
$869$	49189.1	1.92017
$870$	23614.5	0.920239
$871$	−4060.22	−0.157951
$872$	−3843.93	−0.149280
$873$	57048.3	2.21167
$874$	35428.7	1.37116
$875$	−1331.14	−0.0514294
$876$	−8520.28	−0.328623
$877$	−754.683	−0.0290580	−0.0145290	−	0.999894i	$-0.504625\pi$
$877$	−754.683	−0.0290580	−0.0145290	+	0.999894i	$0.504625\pi$
$878$	−13967.2	−0.536868
$879$	35941.3	1.37915
$880$	−4754.73	−0.182139
$881$	−18017.4	−0.689014	−0.344507	−	0.938784i	$-0.611954\pi$
$881$	−18017.4	−0.689014	−0.344507	+	0.938784i	$0.611954\pi$
$882$	−26149.8	−0.998311
$883$	−22201.1	−0.846122	−0.423061	−	0.906101i	$-0.639044\pi$
$883$	−22201.1	−0.846122	−0.423061	+	0.906101i	$0.639044\pi$
$884$	−3030.14	−0.115288
$885$	457.495	0.0173769
$886$	−14836.1	−0.562559
$887$	541.862	0.0205118	0.0102559	−	0.999947i	$-0.496735\pi$
$887$	541.862	0.0205118	0.0102559	+	0.999947i	$0.496735\pi$
$888$	−6470.17	−0.244510
$889$	−27291.0	−1.02960
$890$	12977.2	0.488760
$891$	−58032.7	−2.18201
$892$	−19354.4	−0.726496
$893$	28872.3	1.08194
$894$	−15775.5	−0.590169
$895$	13468.4	0.503016
$896$	−1363.09	−0.0508231
$897$	22196.7	0.826227
$898$	−30798.3	−1.14449
$899$	44756.8	1.66043
$900$	5694.73	0.210916
$901$	−23516.8	−0.869543
$902$	−20715.4	−0.764687
$903$	−46948.7	−1.73018
$904$	6281.34	0.231100
$905$	−20969.6	−0.770226
$906$	−21479.2	−0.787637
$907$	−12289.5	−0.449907	−0.224954	−	0.974369i	$-0.572223\pi$
$907$	−12289.5	−0.449907	−0.224954	+	0.974369i	$0.572223\pi$
$908$	18176.9	0.664340
$909$	45197.2	1.64917
$910$	1384.38	0.0504307
$911$	−26203.0	−0.952957	−0.476479	−	0.879186i	$-0.658087\pi$
$911$	−26203.0	−0.952957	−0.476479	+	0.879186i	$0.658087\pi$
$912$	−13935.0	−0.505959
$913$	27709.9	1.00445
$914$	5777.06	0.209068
$915$	−11227.8	−0.405661
$916$	4925.78	0.177677
$917$	7462.59	0.268742
$918$	31978.0	1.14971
$919$	−19000.1	−0.681996	−0.340998	−	0.940064i	$-0.610765\pi$
$919$	−19000.1	−0.681996	−0.340998	+	0.940064i	$0.610765\pi$
$920$	−7454.21	−0.267128
$921$	57892.4	2.07125
$922$	11364.5	0.405934
$923$	−325.629	−0.0116124
$924$	23196.0	0.825857
$925$	−2206.80	−0.0784422
$926$	143.972	0.00510930
$927$	−56452.5	−2.00015
$928$	8247.57	0.291746
$929$	8393.16	0.296416	0.148208	−	0.988956i	$-0.452649\pi$
$929$	8393.16	0.296416	0.148208	+	0.988956i	$0.452649\pi$
$930$	15910.6	0.560999
$931$	21824.7	0.768289
$932$	25105.8	0.882369
$933$	4552.28	0.159737
$934$	−32062.5	−1.12325
$935$	−17316.7	−0.605686
$936$	−5922.52	−0.206820
$937$	29471.0	1.02751	0.513755	−	0.857937i	$-0.328254\pi$
$937$	29471.0	1.02751	0.513755	+	0.857937i	$0.328254\pi$
$938$	−6651.96	−0.231550
$939$	32566.7	1.13181
$940$	−6074.73	−0.210783
$941$	30380.3	1.05246	0.526232	−	0.850341i	$-0.323604\pi$
$941$	30380.3	1.05246	0.526232	+	0.850341i	$0.323604\pi$
$942$	4399.17	0.152158
$943$	−32476.5	−1.12151
$944$	159.784	0.00550902
$945$	−14609.8	−0.502918
$946$	−57197.0	−1.96579
$947$	−10544.9	−0.361841	−0.180921	−	0.983498i	$-0.557908\pi$
$947$	−10544.9	−0.361841	−0.180921	+	0.983498i	$0.557908\pi$
$948$	−30331.6	−1.03916
$949$	3022.27	0.103379
$950$	−4752.85	−0.162319
$951$	−86066.7	−2.93470
$952$	−4964.35	−0.169008
$953$	−25902.0	−0.880429	−0.440214	−	0.897893i	$-0.645098\pi$
$953$	−25902.0	−0.880429	−0.440214	+	0.897893i	$0.645098\pi$
$954$	−45964.5	−1.55991
$955$	−900.968	−0.0305284
$956$	4349.60	0.147151
$957$	−140351.	−4.74076
$958$	2296.38	0.0774455
$959$	−3617.35	−0.121804
$960$	2931.93	0.0985704
$961$	364.498	0.0122352
$962$	2295.07	0.0769189
$963$	92801.4	3.10538
$964$	−16369.8	−0.546927
$965$	−24934.8	−0.831793
$966$	36365.4	1.21122
$967$	−18253.9	−0.607038	−0.303519	−	0.952825i	$-0.598162\pi$
$967$	−18253.9	−0.607038	−0.303519	+	0.952825i	$0.598162\pi$
$968$	17611.4	0.584763
$969$	−50751.2	−1.68252
$970$	10017.7	0.331598
$971$	46566.4	1.53902	0.769509	−	0.638636i	$-0.220501\pi$
$971$	46566.4	1.53902	0.769509	+	0.638636i	$0.220501\pi$
$972$	6151.29	0.202986
$973$	5992.93	0.197456
$974$	35901.9	1.18108
$975$	−2977.74	−0.0978092
$976$	−3921.40	−0.128608
$977$	34790.8	1.13926	0.569629	−	0.821902i	$-0.307087\pi$
$977$	34790.8	1.13926	0.569629	+	0.821902i	$0.307087\pi$
$978$	18471.9	0.603954
$979$	−77128.8	−2.51792
$980$	−4591.93	−0.149677
$981$	−27362.7	−0.890544
$982$	−36439.5	−1.18414
$983$	−4550.46	−0.147647	−0.0738236	−	0.997271i	$-0.523520\pi$
$983$	−4550.46	−0.147647	−0.0738236	+	0.997271i	$0.523520\pi$
$984$	12773.8	0.413836
$985$	19738.8	0.638509
$986$	30037.6	0.970175
$987$	29635.6	0.955737
$988$	4942.96	0.159167
$989$	−89670.3	−2.88306
$990$	−33846.2	−1.08657
$991$	−21441.0	−0.687281	−0.343641	−	0.939101i	$-0.611660\pi$
$991$	−21441.0	−0.687281	−0.343641	+	0.939101i	$0.611660\pi$
$992$	5556.91	0.177855
$993$	−78739.3	−2.51633
$994$	−533.486	−0.0170233
$995$	−17098.3	−0.544778
$996$	−17086.8	−0.543591
$997$	−10815.2	−0.343553	−0.171776	−	0.985136i	$-0.554951\pi$
$997$	−10815.2	−0.343553	−0.171776	+	0.985136i	$0.554951\pi$
$998$	6574.07	0.208515
$999$	−24220.5	−0.767071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.a.g.1.2	✓	2
3.2	odd	2		1170.4.a.r.1.1		2
4.3	odd	2		1040.4.a.g.1.1		2
5.2	odd	4		650.4.b.o.599.3		4
5.3	odd	4		650.4.b.o.599.2		4
5.4	even	2		650.4.a.j.1.1		2
13.12	even	2		1690.4.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.a.g.1.2	✓	2	1.1	even	1	trivial
650.4.a.j.1.1		2	5.4	even	2
650.4.b.o.599.2		4	5.3	odd	4
650.4.b.o.599.3		4	5.2	odd	4
1040.4.a.g.1.1		2	4.3	odd	2
1170.4.a.r.1.1		2	3.2	odd	2
1690.4.a.p.1.2		2	13.12	even	2

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +9.16228 q^{3} +4.00000 q^{4} +5.00000 q^{5} +18.3246 q^{6} -10.6491 q^{7} +8.00000 q^{8} +56.9473 q^{9} +10.0000 q^{10} -59.4342 q^{11} +36.6491 q^{12} -13.0000 q^{13} -21.2982 q^{14} +45.8114 q^{15} +16.0000 q^{16} +58.2719 q^{17} +113.895 q^{18} -95.0569 q^{19} +20.0000 q^{20} -97.5701 q^{21} -118.868 q^{22} -186.355 q^{23} +73.2982 q^{24} +25.0000 q^{25} -26.0000 q^{26} +274.386 q^{27} -42.5964 q^{28} +257.737 q^{29} +91.6228 q^{30} +173.653 q^{31} +32.0000 q^{32} -544.552 q^{33} +116.544 q^{34} -53.2456 q^{35} +227.789 q^{36} -88.2719 q^{37} -190.114 q^{38} -119.110 q^{39} +40.0000 q^{40} +174.272 q^{41} -195.140 q^{42} +481.179 q^{43} -237.737 q^{44} +284.737 q^{45} -372.710 q^{46} -303.737 q^{47} +146.596 q^{48} -229.596 q^{49} +50.0000 q^{50} +533.903 q^{51} -52.0000 q^{52} -403.570 q^{53} +548.772 q^{54} -297.171 q^{55} -85.1929 q^{56} -870.938 q^{57} +515.473 q^{58} +9.98649 q^{59} +183.246 q^{60} -245.088 q^{61} +347.307 q^{62} -606.438 q^{63} +64.0000 q^{64} -65.0000 q^{65} -1089.10 q^{66} +312.325 q^{67} +233.088 q^{68} -1707.44 q^{69} -106.491 q^{70} +25.0484 q^{71} +455.579 q^{72} -232.483 q^{73} -176.544 q^{74} +229.057 q^{75} -380.228 q^{76} +632.921 q^{77} -238.219 q^{78} -827.623 q^{79} +80.0000 q^{80} +976.421 q^{81} +348.544 q^{82} -466.228 q^{83} -390.280 q^{84} +291.359 q^{85} +962.359 q^{86} +2361.45 q^{87} -475.473 q^{88} +1297.72 q^{89} +569.473 q^{90} +138.438 q^{91} -745.421 q^{92} +1591.06 q^{93} -607.473 q^{94} -475.285 q^{95} +293.193 q^{96} +1001.77 q^{97} -459.193 q^{98} -3384.62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 12 q^{3} + 8 q^{4} + 10 q^{5} + 24 q^{6} + 4 q^{7} + 16 q^{8} + 38 q^{9} + 20 q^{10} - 24 q^{11} + 48 q^{12} - 26 q^{13} + 8 q^{14} + 60 q^{15} + 32 q^{16} + 28 q^{17} + 76 q^{18} - 32 q^{19}+ \cdots - 4056 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 12 * q^3 + 8 * q^4 + 10 * q^5 + 24 * q^6 + 4 * q^7 + 16 * q^8 + 38 * q^9 + 20 * q^10 - 24 * q^11 + 48 * q^12 - 26 * q^13 + 8 * q^14 + 60 * q^15 + 32 * q^16 + 28 * q^17 + 76 * q^18 - 32 * q^19 + 40 * q^20 - 56 * q^21 - 48 * q^22 - 164 * q^23 + 96 * q^24 + 50 * q^25 - 52 * q^26 + 144 * q^27 + 16 * q^28 + 136 * q^29 + 120 * q^30 + 88 * q^31 + 64 * q^32 - 444 * q^33 + 56 * q^34 + 20 * q^35 + 152 * q^36 - 88 * q^37 - 64 * q^38 - 156 * q^39 + 80 * q^40 + 260 * q^41 - 112 * q^42 + 20 * q^43 - 96 * q^44 + 190 * q^45 - 328 * q^46 - 228 * q^47 + 192 * q^48 - 358 * q^49 + 100 * q^50 + 448 * q^51 - 104 * q^52 - 668 * q^53 + 288 * q^54 - 120 * q^55 + 32 * q^56 - 692 * q^57 + 272 * q^58 - 720 * q^59 + 240 * q^60 - 136 * q^61 + 176 * q^62 - 884 * q^63 + 128 * q^64 - 130 * q^65 - 888 * q^66 + 612 * q^67 + 112 * q^68 - 1644 * q^69 + 40 * q^70 + 360 * q^71 + 304 * q^72 - 680 * q^73 - 176 * q^74 + 300 * q^75 - 128 * q^76 + 1152 * q^77 - 312 * q^78 - 1592 * q^79 + 160 * q^80 + 1118 * q^81 + 520 * q^82 - 300 * q^83 - 224 * q^84 + 140 * q^85 + 40 * q^86 + 2016 * q^87 - 192 * q^88 + 268 * q^89 + 380 * q^90 - 52 * q^91 - 656 * q^92 + 1348 * q^93 - 456 * q^94 - 160 * q^95 + 384 * q^96 + 2636 * q^97 - 716 * q^98 - 4056 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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