LMFDB - Embedded newform 1849.4.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.36605 q^{2} +6.88924 q^{3} +20.7944 q^{4} -18.7139 q^{5} -36.9680 q^{6} -7.67108 q^{7} -68.6556 q^{8} +20.4617 q^{9} +O(q^{10})$	\(q-5.36605 q^{2} +6.88924 q^{3} +20.7944 q^{4} -18.7139 q^{5} -36.9680 q^{6} -7.67108 q^{7} -68.6556 q^{8} +20.4617 q^{9} +100.419 q^{10} +34.0145 q^{11} +143.258 q^{12} -27.7222 q^{13} +41.1634 q^{14} -128.924 q^{15} +202.054 q^{16} -55.4017 q^{17} -109.798 q^{18} -93.5482 q^{19} -389.145 q^{20} -52.8479 q^{21} -182.524 q^{22} +26.6839 q^{23} -472.985 q^{24} +225.209 q^{25} +148.759 q^{26} -45.0441 q^{27} -159.516 q^{28} +93.8119 q^{29} +691.814 q^{30} -64.7587 q^{31} -534.984 q^{32} +234.334 q^{33} +297.288 q^{34} +143.556 q^{35} +425.489 q^{36} -283.659 q^{37} +501.984 q^{38} -190.985 q^{39} +1284.81 q^{40} +365.879 q^{41} +283.584 q^{42} +707.314 q^{44} -382.917 q^{45} -143.187 q^{46} -333.251 q^{47} +1392.00 q^{48} -284.155 q^{49} -1208.48 q^{50} -381.676 q^{51} -576.469 q^{52} +177.507 q^{53} +241.709 q^{54} -636.544 q^{55} +526.663 q^{56} -644.476 q^{57} -503.399 q^{58} -65.8734 q^{59} -2680.91 q^{60} -34.2444 q^{61} +347.498 q^{62} -156.963 q^{63} +1254.32 q^{64} +518.790 q^{65} -1257.45 q^{66} -1029.37 q^{67} -1152.05 q^{68} +183.832 q^{69} -770.326 q^{70} +1028.31 q^{71} -1404.81 q^{72} -1134.87 q^{73} +1522.12 q^{74} +1551.52 q^{75} -1945.28 q^{76} -260.928 q^{77} +1024.84 q^{78} -243.098 q^{79} -3781.20 q^{80} -862.785 q^{81} -1963.33 q^{82} +82.8780 q^{83} -1098.94 q^{84} +1036.78 q^{85} +646.293 q^{87} -2335.29 q^{88} +409.461 q^{89} +2054.75 q^{90} +212.659 q^{91} +554.877 q^{92} -446.139 q^{93} +1788.24 q^{94} +1750.65 q^{95} -3685.63 q^{96} +672.485 q^{97} +1524.79 q^{98} +695.994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.36605	−1.89718	−0.948592	−	0.316502i	$-0.897492\pi$
$2$	−5.36605	−1.89718	−0.948592	+	0.316502i	$0.897492\pi$
$3$	6.88924	1.32584	0.662918	−	0.748692i	$-0.269318\pi$
$3$	6.88924	1.32584	0.662918	+	0.748692i	$0.269318\pi$
$4$	20.7944	2.59931
$5$	−18.7139	−1.67382	−0.836910	−	0.547341i	$-0.815640\pi$
$5$	−18.7139	−1.67382	−0.836910	+	0.547341i	$0.815640\pi$
$6$	−36.9680	−2.51535
$7$	−7.67108	−0.414199	−0.207100	−	0.978320i	$-0.566402\pi$
$7$	−7.67108	−0.414199	−0.207100	+	0.978320i	$0.566402\pi$
$8$	−68.6556	−3.03418
$9$	20.4617	0.757840
$10$	100.419	3.17554
$11$	34.0145	0.932343	0.466171	−	0.884694i	$-0.345633\pi$
$11$	34.0145	0.932343	0.466171	+	0.884694i	$0.345633\pi$
$12$	143.258	3.44625
$13$	−27.7222	−0.591443	−0.295722	−	0.955274i	$-0.595560\pi$
$13$	−27.7222	−0.591443	−0.295722	+	0.955274i	$0.595560\pi$
$14$	41.1634	0.785812
$15$	−128.924	−2.21921
$16$	202.054	3.15709
$17$	−55.4017	−0.790405	−0.395203	−	0.918594i	$-0.629326\pi$
$17$	−55.4017	−0.790405	−0.395203	+	0.918594i	$0.629326\pi$
$18$	−109.798	−1.43776
$19$	−93.5482	−1.12955	−0.564774	−	0.825245i	$-0.691037\pi$
$19$	−93.5482	−1.12955	−0.564774	+	0.825245i	$0.691037\pi$
$20$	−389.145	−4.35077
$21$	−52.8479	−0.549160
$22$	−182.524	−1.76883
$23$	26.6839	0.241912	0.120956	−	0.992658i	$-0.461404\pi$
$23$	26.6839	0.241912	0.120956	+	0.992658i	$0.461404\pi$
$24$	−472.985	−4.02282
$25$	225.209	1.80167
$26$	148.759	1.12208
$27$	−45.0441	−0.321065
$28$	−159.516	−1.07663
$29$	93.8119	0.600704	0.300352	−	0.953828i	$-0.402896\pi$
$29$	93.8119	0.600704	0.300352	+	0.953828i	$0.402896\pi$
$30$	691.814	4.21025
$31$	−64.7587	−0.375194	−0.187597	−	0.982246i	$-0.560070\pi$
$31$	−64.7587	−0.375194	−0.187597	+	0.982246i	$0.560070\pi$
$32$	−534.984	−2.95540
$33$	234.334	1.23613
$34$	297.288	1.49954
$35$	143.556	0.693295
$36$	425.489	1.96986
$37$	−283.659	−1.26036	−0.630178	−	0.776451i	$-0.717018\pi$
$37$	−283.659	−1.26036	−0.630178	+	0.776451i	$0.717018\pi$
$38$	501.984	2.14296
$39$	−190.985	−0.784157
$40$	1284.81	5.07867
$41$	365.879	1.39368	0.696838	−	0.717228i	$-0.254589\pi$
$41$	365.879	1.39368	0.696838	+	0.717228i	$0.254589\pi$
$42$	283.584	1.04186
$43$	0	0
$43$	0	0
$44$	707.314	2.42344
$45$	−382.917	−1.26849
$46$	−143.187	−0.458951
$47$	−333.251	−1.03425	−0.517124	−	0.855911i	$-0.672997\pi$
$47$	−333.251	−1.03425	−0.517124	+	0.855911i	$0.672997\pi$
$48$	1392.00	4.18578
$49$	−284.155	−0.828439
$50$	−1208.48	−3.41810
$51$	−381.676	−1.04795
$52$	−576.469	−1.53734
$53$	177.507	0.460048	0.230024	−	0.973185i	$-0.426120\pi$
$53$	177.507	0.460048	0.230024	+	0.973185i	$0.426120\pi$
$54$	241.709	0.609119
$55$	−636.544	−1.56057
$56$	526.663	1.25675
$57$	−644.476	−1.49760
$58$	−503.399	−1.13965
$59$	−65.8734	−0.145356	−0.0726779	−	0.997355i	$-0.523154\pi$
$59$	−65.8734	−0.145356	−0.0726779	+	0.997355i	$0.523154\pi$
$60$	−2680.91	−5.76840
$61$	−34.2444	−0.0718779	−0.0359389	−	0.999354i	$-0.511442\pi$
$61$	−34.2444	−0.0718779	−0.0359389	+	0.999354i	$0.511442\pi$
$62$	347.498	0.711812
$63$	−156.963	−0.313897
$64$	1254.32	2.44984
$65$	518.790	0.989969
$66$	−1257.45	−2.34517
$67$	−1029.37	−1.87698	−0.938489	−	0.345309i	$-0.887774\pi$
$67$	−1029.37	−1.87698	−0.938489	+	0.345309i	$0.887774\pi$
$68$	−1152.05	−2.05451
$69$	183.832	0.320735
$70$	−770.326	−1.31531
$71$	1028.31	1.71885	0.859423	−	0.511265i	$-0.170823\pi$
$71$	1028.31	1.71885	0.859423	+	0.511265i	$0.170823\pi$
$72$	−1404.81	−2.29942
$73$	−1134.87	−1.81954	−0.909771	−	0.415111i	$-0.863743\pi$
$73$	−1134.87	−1.81954	−0.909771	+	0.415111i	$0.863743\pi$
$74$	1522.12	2.39113
$75$	1551.52	2.38872
$76$	−1945.28	−2.93604
$77$	−260.928	−0.386176
$78$	1024.84	1.48769
$79$	−243.098	−0.346211	−0.173105	−	0.984903i	$-0.555380\pi$
$79$	−243.098	−0.346211	−0.173105	+	0.984903i	$0.555380\pi$
$80$	−3781.20	−5.28439
$81$	−862.785	−1.18352
$82$	−1963.33	−2.64406
$83$	82.8780	0.109603	0.0548015	−	0.998497i	$-0.482547\pi$
$83$	82.8780	0.109603	0.0548015	+	0.998497i	$0.482547\pi$
$84$	−1098.94	−1.42744
$85$	1036.78	1.32300
$86$	0	0
$87$	646.293	0.796435
$88$	−2335.29	−2.82889
$89$	409.461	0.487672	0.243836	−	0.969816i	$-0.421594\pi$
$89$	409.461	0.487672	0.243836	+	0.969816i	$0.421594\pi$
$90$	2054.75	2.40655
$91$	212.659	0.244975
$92$	554.877	0.628803
$93$	−446.139	−0.497445
$94$	1788.24	1.96216
$95$	1750.65	1.89066
$96$	−3685.63	−3.91837
$97$	672.485	0.703923	0.351961	−	0.936015i	$-0.385515\pi$
$97$	672.485	0.703923	0.351961	+	0.936015i	$0.385515\pi$
$98$	1524.79	1.57170
$99$	695.994	0.706566
$100$	4683.10	4.68310
$101$	−73.9123	−0.0728173	−0.0364087	−	0.999337i	$-0.511592\pi$
$101$	−73.9123	−0.0728173	−0.0364087	+	0.999337i	$0.511592\pi$
$102$	2048.09	1.98815
$103$	865.019	0.827504	0.413752	−	0.910390i	$-0.364218\pi$
$103$	865.019	0.827504	0.413752	+	0.910390i	$0.364218\pi$
$104$	1903.29	1.79454
$105$	988.989	0.919195
$106$	−952.513	−0.872795
$107$	1450.18	1.31023	0.655115	−	0.755529i	$-0.272620\pi$
$107$	1450.18	1.31023	0.655115	+	0.755529i	$0.272620\pi$
$108$	−936.668	−0.834545
$109$	−1243.75	−1.09293	−0.546465	−	0.837482i	$-0.684027\pi$
$109$	−1243.75	−1.09293	−0.546465	+	0.837482i	$0.684027\pi$
$110$	3415.72	2.96069
$111$	−1954.19	−1.67103
$112$	−1549.97	−1.30766
$113$	−176.788	−0.147175	−0.0735875	−	0.997289i	$-0.523445\pi$
$113$	−176.788	−0.147175	−0.0735875	+	0.997289i	$0.523445\pi$
$114$	3458.29	2.84121
$115$	−499.359	−0.404917
$116$	1950.77	1.56141
$117$	−567.243	−0.448219
$118$	353.480	0.275766
$119$	424.991	0.327385
$120$	8851.38	6.73348
$121$	−174.011	−0.130737
$122$	183.757	0.136366
$123$	2520.63	1.84779
$124$	−1346.62	−0.975244
$125$	−1875.30	−1.34185
$126$	842.271	0.595520
$127$	−357.379	−0.249703	−0.124851	−	0.992175i	$-0.539845\pi$
$127$	−357.379	−0.249703	−0.124851	+	0.992175i	$0.539845\pi$
$128$	−2450.86	−1.69240
$129$	0	0
$130$	−2783.85	−1.87815
$131$	−718.745	−0.479367	−0.239683	−	0.970851i	$-0.577044\pi$
$131$	−718.745	−0.479367	−0.239683	+	0.970851i	$0.577044\pi$
$132$	4872.86	3.21309
$133$	717.615	0.467858
$134$	5523.64	3.56097
$135$	842.950	0.537404
$136$	3803.64	2.39823
$137$	−2250.88	−1.40369	−0.701845	−	0.712330i	$-0.747640\pi$
$137$	−2250.88	−1.40369	−0.701845	+	0.712330i	$0.747640\pi$
$138$	−986.450	−0.608494
$139$	2471.22	1.50796	0.753979	−	0.656899i	$-0.228132\pi$
$139$	2471.22	1.50796	0.753979	+	0.656899i	$0.228132\pi$
$140$	2985.16	1.80209
$141$	−2295.85	−1.37124
$142$	−5517.97	−3.26097
$143$	−942.959	−0.551428
$144$	4134.35	2.39257
$145$	−1755.58	−1.00547
$146$	6089.77	3.45200
$147$	−1957.61	−1.09837
$148$	−5898.52	−3.27605
$149$	471.916	0.259469	0.129735	−	0.991549i	$-0.458587\pi$
$149$	471.916	0.259469	0.129735	+	0.991549i	$0.458587\pi$
$150$	−8325.52	−4.53184
$151$	1608.10	0.866656	0.433328	−	0.901236i	$-0.357339\pi$
$151$	1608.10	0.866656	0.433328	+	0.901236i	$0.357339\pi$
$152$	6422.61	3.42725
$153$	−1133.61	−0.599001
$154$	1400.15	0.732646
$155$	1211.89	0.628007
$156$	−3971.43	−2.03826
$157$	3544.70	1.80190	0.900949	−	0.433925i	$-0.142872\pi$
$157$	3544.70	1.80190	0.900949	+	0.433925i	$0.142872\pi$
$158$	1304.47	0.656825
$159$	1222.89	0.609947
$160$	10011.6	4.94680
$161$	−204.694	−0.100200
$162$	4629.74	2.24535
$163$	−2122.66	−1.02000	−0.509998	−	0.860176i	$-0.670354\pi$
$163$	−2122.66	−1.02000	−0.509998	+	0.860176i	$0.670354\pi$
$164$	7608.26	3.62259
$165$	−4385.30	−2.06906
$166$	−444.727	−0.207937
$167$	2606.27	1.20766	0.603829	−	0.797114i	$-0.293641\pi$
$167$	2606.27	1.20766	0.603829	+	0.797114i	$0.293641\pi$
$168$	3628.31	1.66625
$169$	−1428.48	−0.650195
$170$	−5563.41	−2.50997
$171$	−1914.15	−0.856017
$172$	0	0
$173$	−2954.57	−1.29845	−0.649225	−	0.760596i	$-0.724907\pi$
$173$	−2954.57	−1.29845	−0.649225	+	0.760596i	$0.724907\pi$
$174$	−3468.04	−1.51098
$175$	−1727.60	−0.746251
$176$	6872.76	2.94349
$177$	−453.818	−0.192718
$178$	−2197.19	−0.925203
$179$	−2155.05	−0.899864	−0.449932	−	0.893063i	$-0.648552\pi$
$179$	−2155.05	−0.899864	−0.449932	+	0.893063i	$0.648552\pi$
$180$	−7962.55	−3.29719
$181$	4656.42	1.91221	0.956103	−	0.293032i	$-0.0946644\pi$
$181$	4656.42	1.91221	0.956103	+	0.293032i	$0.0946644\pi$
$182$	−1141.14	−0.464763
$183$	−235.918	−0.0952982
$184$	−1832.00	−0.734004
$185$	5308.35	2.10961
$186$	2394.00	0.943745
$187$	−1884.46	−0.736929
$188$	−6929.77	−2.68832
$189$	345.537	0.132985
$190$	−9394.06	−3.58693
$191$	964.904	0.365539	0.182770	−	0.983156i	$-0.441494\pi$
$191$	964.904	0.365539	0.182770	+	0.983156i	$0.441494\pi$
$192$	8641.31	3.24809
$193$	−1092.32	−0.407392	−0.203696	−	0.979034i	$-0.565295\pi$
$193$	−1092.32	−0.407392	−0.203696	+	0.979034i	$0.565295\pi$
$194$	−3608.59	−1.33547
$195$	3574.07	1.31254
$196$	−5908.84	−2.15337
$197$	1916.30	0.693051	0.346525	−	0.938041i	$-0.387361\pi$
$197$	1916.30	0.693051	0.346525	+	0.938041i	$0.387361\pi$
$198$	−3734.74	−1.34049
$199$	−516.956	−0.184151	−0.0920755	−	0.995752i	$-0.529350\pi$
$199$	−516.956	−0.184151	−0.0920755	+	0.995752i	$0.529350\pi$
$200$	−15461.9	−5.46659
$201$	−7091.58	−2.48856
$202$	396.617	0.138148
$203$	−719.638	−0.248811
$204$	−7936.74	−2.72394
$205$	−6847.02	−2.33276
$206$	−4641.73	−1.56993
$207$	545.997	0.183330
$208$	−5601.37	−1.86724
$209$	−3182.00	−1.05313
$210$	−5306.96	−1.74388
$211$	3009.17	0.981801	0.490900	−	0.871216i	$-0.336668\pi$
$211$	3009.17	0.981801	0.490900	+	0.871216i	$0.336668\pi$
$212$	3691.17	1.19580
$213$	7084.29	2.27891
$214$	−7781.75	−2.48575
$215$	0	0
$216$	3092.53	0.974167
$217$	496.769	0.155405
$218$	6674.01	2.07349
$219$	−7818.40	−2.41241
$220$	−13236.6	−4.05641
$221$	1535.86	0.467480
$222$	10486.3	3.17024
$223$	3624.85	1.08851	0.544256	−	0.838919i	$-0.316812\pi$
$223$	3624.85	1.08851	0.544256	+	0.838919i	$0.316812\pi$
$224$	4103.90	1.22412
$225$	4608.15	1.36538
$226$	948.650	0.279218
$227$	−6400.71	−1.87150	−0.935748	−	0.352668i	$-0.885274\pi$
$227$	−6400.71	−1.87150	−0.935748	+	0.352668i	$0.885274\pi$
$228$	−13401.5	−3.89271
$229$	3611.95	1.04229	0.521144	−	0.853469i	$-0.325505\pi$
$229$	3611.95	1.04229	0.521144	+	0.853469i	$0.325505\pi$
$230$	2679.58	0.768202
$231$	−1797.60	−0.512005
$232$	−6440.71	−1.82264
$233$	5269.94	1.48174	0.740870	−	0.671648i	$-0.234413\pi$
$233$	5269.94	1.48174	0.740870	+	0.671648i	$0.234413\pi$
$234$	3043.85	0.850354
$235$	6236.41	1.73114
$236$	−1369.80	−0.377824
$237$	−1674.76	−0.459018
$238$	−2280.52	−0.621110
$239$	419.525	0.113543	0.0567716	−	0.998387i	$-0.481919\pi$
$239$	419.525	0.113543	0.0567716	+	0.998387i	$0.481919\pi$
$240$	−26049.6	−7.00624
$241$	3093.37	0.826812	0.413406	−	0.910547i	$-0.364339\pi$
$241$	3093.37	0.826812	0.413406	+	0.910547i	$0.364339\pi$
$242$	933.751	0.248032
$243$	−4727.74	−1.24809
$244$	−712.094	−0.186833
$245$	5317.63	1.38666
$246$	−13525.8	−3.50559
$247$	2593.36	0.668064
$248$	4446.05	1.13840
$249$	570.967	0.145315
$250$	10062.9	2.54574
$251$	440.557	0.110788	0.0553938	−	0.998465i	$-0.482359\pi$
$251$	440.557	0.110788	0.0553938	+	0.998465i	$0.482359\pi$
$252$	−3263.96	−0.815914
$253$	907.640	0.225545
$254$	1917.71	0.473732
$255$	7142.63	1.75408
$256$	3116.89	0.760960
$257$	−363.978	−0.0883436	−0.0441718	−	0.999024i	$-0.514065\pi$
$257$	−363.978	−0.0883436	−0.0441718	+	0.999024i	$0.514065\pi$
$258$	0	0
$259$	2175.97	0.522039
$260$	10788.0	2.57323
$261$	1919.55	0.455238
$262$	3856.82	0.909446
$263$	−1427.24	−0.334630	−0.167315	−	0.985904i	$-0.553510\pi$
$263$	−1427.24	−0.334630	−0.167315	+	0.985904i	$0.553510\pi$
$264$	−16088.4	−3.75065
$265$	−3321.85	−0.770037
$266$	−3850.76	−0.887613
$267$	2820.88	0.646573
$268$	−21405.2	−4.87884
$269$	−4812.53	−1.09080	−0.545400	−	0.838176i	$-0.683622\pi$
$269$	−4812.53	−1.09080	−0.545400	+	0.838176i	$0.683622\pi$
$270$	−4523.31	−1.01955
$271$	2622.07	0.587747	0.293874	−	0.955844i	$-0.405055\pi$
$271$	2622.07	0.587747	0.293874	+	0.955844i	$0.405055\pi$
$272$	−11194.1	−2.49538
$273$	1465.06	0.324797
$274$	12078.3	2.66306
$275$	7660.38	1.67978
$276$	3822.68	0.833690
$277$	2899.20	0.628866	0.314433	−	0.949280i	$-0.398186\pi$
$277$	2899.20	0.628866	0.314433	+	0.949280i	$0.398186\pi$
$278$	−13260.7	−2.86087
$279$	−1325.07	−0.284337
$280$	−9855.90	−2.10358
$281$	−4854.46	−1.03058	−0.515290	−	0.857016i	$-0.672316\pi$
$281$	−4854.46	−1.03058	−0.515290	+	0.857016i	$0.672316\pi$
$282$	12319.6	2.60150
$283$	−1869.40	−0.392666	−0.196333	−	0.980537i	$-0.562903\pi$
$283$	−1869.40	−0.392666	−0.196333	+	0.980537i	$0.562903\pi$
$284$	21383.2	4.46781
$285$	12060.6	2.50670
$286$	5059.96	1.04616
$287$	−2806.69	−0.577260
$288$	−10946.7	−2.23972
$289$	−1843.65	−0.375259
$290$	9420.54	1.90756
$291$	4632.91	0.933286
$292$	−23599.0	−4.72955
$293$	−2060.41	−0.410820	−0.205410	−	0.978676i	$-0.565853\pi$
$293$	−2060.41	−0.410820	−0.205410	+	0.978676i	$0.565853\pi$
$294$	10504.6	2.08382
$295$	1232.75	0.243299
$296$	19474.8	3.82414
$297$	−1532.16	−0.299342
$298$	−2532.33	−0.492261
$299$	−739.737	−0.143077
$300$	32263.0	6.20902
$301$	0	0
$302$	−8629.12	−1.64421
$303$	−509.200	−0.0965438
$304$	−18901.7	−3.56608
$305$	640.846	0.120311
$306$	6083.01	1.13641
$307$	8944.01	1.66274	0.831371	−	0.555718i	$-0.187557\pi$
$307$	8944.01	1.66274	0.831371	+	0.555718i	$0.187557\pi$
$308$	−5425.86	−1.00379
$309$	5959.33	1.09713
$310$	−6503.04	−1.19144
$311$	2920.61	0.532517	0.266259	−	0.963902i	$-0.414212\pi$
$311$	2920.61	0.532517	0.266259	+	0.963902i	$0.414212\pi$
$312$	13112.2	2.37927
$313$	7676.95	1.38635	0.693174	−	0.720770i	$-0.256212\pi$
$313$	7676.95	1.38635	0.693174	+	0.720770i	$0.256212\pi$
$314$	−19021.0	−3.41853
$315$	2937.39	0.525406
$316$	−5055.09	−0.899908
$317$	−379.325	−0.0672082	−0.0336041	−	0.999435i	$-0.510699\pi$
$317$	−379.325	−0.0672082	−0.0336041	+	0.999435i	$0.510699\pi$
$318$	−6562.09	−1.15718
$319$	3190.97	0.560062
$320$	−23473.2	−4.10059
$321$	9990.67	1.73715
$322$	1098.40	0.190097
$323$	5182.73	0.892801
$324$	−17941.1	−3.07633
$325$	−6243.30	−1.06559
$326$	11390.3	1.93512
$327$	−8568.48	−1.44905
$328$	−25119.7	−4.22866
$329$	2556.39	0.428384
$330$	23531.7	3.92539
$331$	−7582.92	−1.25920	−0.629600	−	0.776920i	$-0.716781\pi$
$331$	−7582.92	−1.25920	−0.629600	+	0.776920i	$0.716781\pi$
$332$	1723.40	0.284892
$333$	−5804.13	−0.955148
$334$	−13985.3	−2.29115
$335$	19263.5	3.14172
$336$	−10678.1	−1.73375
$337$	1081.00	0.174735	0.0873676	−	0.996176i	$-0.472155\pi$
$337$	1081.00	0.174735	0.0873676	+	0.996176i	$0.472155\pi$
$338$	7665.28	1.23354
$339$	−1217.93	−0.195130
$340$	21559.3	3.43887
$341$	−2202.74	−0.349809
$342$	10271.4	1.62402
$343$	4810.95	0.757338
$344$	0	0
$345$	−3440.20	−0.536853
$346$	15854.4	2.46340
$347$	5335.27	0.825396	0.412698	−	0.910868i	$-0.364586\pi$
$347$	5335.27	0.825396	0.412698	+	0.910868i	$0.364586\pi$
$348$	13439.3	2.07018
$349$	9613.43	1.47448	0.737242	−	0.675628i	$-0.236128\pi$
$349$	9613.43	1.47448	0.737242	+	0.675628i	$0.236128\pi$
$350$	9270.36	1.41578
$351$	1248.72	0.189892
$352$	−18197.2	−2.75544
$353$	−6732.69	−1.01514	−0.507571	−	0.861610i	$-0.669456\pi$
$353$	−6732.69	−1.01514	−0.507571	+	0.861610i	$0.669456\pi$
$354$	2435.21	0.365621
$355$	−19243.7	−2.87704
$356$	8514.52	1.26761
$357$	2927.87	0.434059
$358$	11564.1	1.70721
$359$	3450.72	0.507304	0.253652	−	0.967295i	$-0.418368\pi$
$359$	3450.72	0.507304	0.253652	+	0.967295i	$0.418368\pi$
$360$	26289.4	3.84881
$361$	1892.26	0.275880
$362$	−24986.6	−3.62780
$363$	−1198.80	−0.173336
$364$	4422.14	0.636766
$365$	21237.8	3.04558
$366$	1265.95	0.180798
$367$	−7346.47	−1.04491	−0.522456	−	0.852666i	$-0.674984\pi$
$367$	−7346.47	−1.04491	−0.522456	+	0.852666i	$0.674984\pi$
$368$	5391.57	0.763737
$369$	7486.50	1.05618
$370$	−28484.9	−4.00232
$371$	−1361.67	−0.190551
$372$	−9277.21	−1.29301
$373$	4003.91	0.555803	0.277902	−	0.960610i	$-0.410361\pi$
$373$	4003.91	0.555803	0.277902	+	0.960610i	$0.410361\pi$
$374$	10112.1	1.39809
$375$	−12919.4	−1.77908
$376$	22879.5	3.13809
$377$	−2600.67	−0.355283
$378$	−1854.17	−0.252297
$379$	4681.44	0.634485	0.317242	−	0.948345i	$-0.397243\pi$
$379$	4681.44	0.634485	0.317242	+	0.948345i	$0.397243\pi$
$380$	36403.8	4.91441
$381$	−2462.07	−0.331065
$382$	−5177.72	−0.693495
$383$	7676.00	1.02409	0.512043	−	0.858960i	$-0.328889\pi$
$383$	7676.00	1.02409	0.512043	+	0.858960i	$0.328889\pi$
$384$	−16884.6	−2.24385
$385$	4882.98	0.646388
$386$	5861.42	0.772897
$387$	0	0
$388$	13984.0	1.82971
$389$	8384.68	1.09285	0.546427	−	0.837507i	$-0.315988\pi$
$389$	8384.68	1.09285	0.546427	+	0.837507i	$0.315988\pi$
$390$	−19178.6	−2.49012
$391$	−1478.33	−0.191209
$392$	19508.8	2.51363
$393$	−4951.61	−0.635561
$394$	−10283.0	−1.31484
$395$	4549.30	0.579494
$396$	14472.8	1.83658
$397$	−5208.37	−0.658439	−0.329220	−	0.944253i	$-0.606786\pi$
$397$	−5208.37	−0.658439	−0.329220	+	0.944253i	$0.606786\pi$
$398$	2774.01	0.349368
$399$	4943.83	0.620303
$400$	45504.3	5.68803
$401$	6854.49	0.853608	0.426804	−	0.904344i	$-0.359639\pi$
$401$	6854.49	0.853608	0.426804	+	0.904344i	$0.359639\pi$
$402$	38053.7	4.72126
$403$	1795.26	0.221906
$404$	−1536.97	−0.189274
$405$	16146.0	1.98100
$406$	3861.61	0.472041
$407$	−9648.52	−1.17508
$408$	26204.2	3.17966
$409$	−2937.36	−0.355117	−0.177559	−	0.984110i	$-0.556820\pi$
$409$	−2937.36	−0.355117	−0.177559	+	0.984110i	$0.556820\pi$
$410$	36741.4	4.42568
$411$	−15506.8	−1.86106
$412$	17987.6	2.15094
$413$	505.320	0.0602062
$414$	−2929.84	−0.347812
$415$	−1550.97	−0.183456
$416$	14830.9	1.74795
$417$	17024.8	1.99930
$418$	17074.7	1.99797
$419$	2365.57	0.275813	0.137907	−	0.990445i	$-0.455963\pi$
$419$	2365.57	0.275813	0.137907	+	0.990445i	$0.455963\pi$
$420$	20565.5	2.38927
$421$	−4403.66	−0.509789	−0.254895	−	0.966969i	$-0.582041\pi$
$421$	−4403.66	−0.509789	−0.254895	+	0.966969i	$0.582041\pi$
$422$	−16147.4	−1.86266
$423$	−6818.87	−0.783794
$424$	−12186.9	−1.39587
$425$	−12477.0	−1.42405
$426$	−38014.6	−4.32351
$427$	262.692	0.0297718
$428$	30155.8	3.40569
$429$	−6496.27	−0.731103
$430$	0	0
$431$	3628.52	0.405521	0.202761	−	0.979228i	$-0.435009\pi$
$431$	3628.52	0.405521	0.202761	+	0.979228i	$0.435009\pi$
$432$	−9101.33	−1.01363
$433$	−8029.81	−0.891196	−0.445598	−	0.895233i	$-0.647009\pi$
$433$	−8029.81	−0.891196	−0.445598	+	0.895233i	$0.647009\pi$
$434$	−2665.69	−0.294832
$435$	−12094.6	−1.33309
$436$	−25863.0	−2.84086
$437$	−2496.23	−0.273251
$438$	41953.9	4.57679
$439$	9355.83	1.01715	0.508576	−	0.861017i	$-0.330172\pi$
$439$	9355.83	1.01715	0.508576	+	0.861017i	$0.330172\pi$
$440$	43702.3	4.73506
$441$	−5814.28	−0.627824
$442$	−8241.49	−0.886896
$443$	−1434.14	−0.153811	−0.0769054	−	0.997038i	$-0.524504\pi$
$443$	−1434.14	−0.153811	−0.0769054	+	0.997038i	$0.524504\pi$
$444$	−40636.4	−4.34351
$445$	−7662.60	−0.816275
$446$	−19451.1	−2.06511
$447$	3251.15	0.344013
$448$	−9621.98	−1.01472
$449$	−10527.1	−1.10647	−0.553233	−	0.833027i	$-0.686606\pi$
$449$	−10527.1	−1.10647	−0.553233	+	0.833027i	$0.686606\pi$
$450$	−24727.6	−2.59037
$451$	12445.2	1.29938
$452$	−3676.20	−0.382553
$453$	11078.6	1.14904
$454$	34346.5	3.55057
$455$	−3979.68	−0.410045
$456$	44246.9	4.54397
$457$	7798.41	0.798237	0.399119	−	0.916899i	$-0.369316\pi$
$457$	7798.41	0.798237	0.399119	+	0.916899i	$0.369316\pi$
$458$	−19381.9	−1.97741
$459$	2495.52	0.253771
$460$	−10383.9	−1.05250
$461$	2333.99	0.235802	0.117901	−	0.993025i	$-0.462383\pi$
$461$	2333.99	0.235802	0.117901	+	0.993025i	$0.462383\pi$
$462$	9645.99	0.971368
$463$	15037.6	1.50941	0.754705	−	0.656064i	$-0.227780\pi$
$463$	15037.6	1.50941	0.754705	+	0.656064i	$0.227780\pi$
$464$	18955.0	1.89648
$465$	8348.98	0.832634
$466$	−28278.8	−2.81113
$467$	12459.5	1.23460	0.617301	−	0.786727i	$-0.288226\pi$
$467$	12459.5	1.23460	0.617301	+	0.786727i	$0.288226\pi$
$468$	−11795.5	−1.16506
$469$	7896.38	0.777443
$470$	−33464.9	−3.28430
$471$	24420.3	2.38902
$472$	4522.58	0.441035
$473$	0	0
$474$	8986.84	0.870842
$475$	−21067.9	−2.03508
$476$	8837.45	0.850975
$477$	3632.10	0.348642
$478$	−2251.19	−0.215412
$479$	−3023.91	−0.288446	−0.144223	−	0.989545i	$-0.546068\pi$
$479$	−3023.91	−0.288446	−0.144223	+	0.989545i	$0.546068\pi$
$480$	68972.5	6.55864
$481$	7863.65	0.745429
$482$	−16599.2	−1.56861
$483$	−1410.19	−0.132848
$484$	−3618.46	−0.339826
$485$	−12584.8	−1.17824
$486$	25369.3	2.36785
$487$	−3520.21	−0.327548	−0.163774	−	0.986498i	$-0.552367\pi$
$487$	−3520.21	−0.327548	−0.163774	+	0.986498i	$0.552367\pi$
$488$	2351.07	0.218090
$489$	−14623.5	−1.35235
$490$	−28534.7	−2.63074
$491$	4304.06	0.395599	0.197800	−	0.980242i	$-0.436620\pi$
$491$	4304.06	0.395599	0.197800	+	0.980242i	$0.436620\pi$
$492$	52415.1	4.80296
$493$	−5197.34	−0.474800
$494$	−13916.1	−1.26744
$495$	−13024.7	−1.18266
$496$	−13084.7	−1.18452
$497$	−7888.26	−0.711945
$498$	−3063.83	−0.275690
$499$	−20991.8	−1.88321	−0.941603	−	0.336724i	$-0.890681\pi$
$499$	−20991.8	−1.88321	−0.941603	+	0.336724i	$0.890681\pi$
$500$	−38995.8	−3.48789
$501$	17955.2	1.60116
$502$	−2364.05	−0.210185
$503$	12297.0	1.09005	0.545025	−	0.838420i	$-0.316520\pi$
$503$	12297.0	1.09005	0.545025	+	0.838420i	$0.316520\pi$
$504$	10776.4	0.952418
$505$	1383.19	0.121883
$506$	−4870.44	−0.427900
$507$	−9841.13	−0.862051
$508$	−7431.50	−0.649054
$509$	2660.37	0.231667	0.115834	−	0.993269i	$-0.463046\pi$
$509$	2660.37	0.231667	0.115834	+	0.993269i	$0.463046\pi$
$510$	−38327.7	−3.32780
$511$	8705.68	0.753653
$512$	2881.51	0.248723
$513$	4213.80	0.362658
$514$	1953.12	0.167604
$515$	−16187.9	−1.38509
$516$	0	0
$517$	−11335.4	−0.964273
$518$	−11676.3	−0.990403
$519$	−20354.8	−1.72153
$520$	−35617.9	−3.00374
$521$	13650.7	1.14789	0.573943	−	0.818895i	$-0.305413\pi$
$521$	13650.7	1.14789	0.573943	+	0.818895i	$0.305413\pi$
$522$	−10300.4	−0.863669
$523$	−6491.45	−0.542737	−0.271368	−	0.962476i	$-0.587476\pi$
$523$	−6491.45	−0.542737	−0.271368	+	0.962476i	$0.587476\pi$
$524$	−14945.9	−1.24602
$525$	−11901.8	−0.989406
$526$	7658.66	0.634854
$527$	3587.74	0.296555
$528$	47348.1	3.90258
$529$	−11455.0	−0.941479
$530$	17825.2	1.46090
$531$	−1347.88	−0.110156
$532$	14922.4	1.21611
$533$	−10143.0	−0.824281
$534$	−15137.0	−1.22667
$535$	−27138.6	−2.19309
$536$	70672.0	5.69508
$537$	−14846.6	−1.19307
$538$	25824.3	2.06945
$539$	−9665.39	−0.772389
$540$	17528.7	1.39688
$541$	−639.051	−0.0507855	−0.0253927	−	0.999678i	$-0.508084\pi$
$541$	−639.051	−0.0507855	−0.0253927	+	0.999678i	$0.508084\pi$
$542$	−14070.2	−1.11506
$543$	32079.2	2.53527
$544$	29639.0	2.33596
$545$	23275.3	1.82937
$546$	−7861.59	−0.616200
$547$	−19860.2	−1.55239	−0.776197	−	0.630491i	$-0.782854\pi$
$547$	−19860.2	−1.55239	−0.776197	+	0.630491i	$0.782854\pi$
$548$	−46805.8	−3.64862
$549$	−700.698	−0.0544719
$550$	−41106.0	−3.18684
$551$	−8775.93	−0.678525
$552$	−12621.1	−0.973168
$553$	1864.82	0.143400
$554$	−15557.2	−1.19308
$555$	36570.5	2.79699
$556$	51387.7	3.91964
$557$	−17265.6	−1.31341	−0.656704	−	0.754149i	$-0.728050\pi$
$557$	−17265.6	−1.31341	−0.656704	+	0.754149i	$0.728050\pi$
$558$	7110.40	0.539439
$559$	0	0
$560$	29005.9	2.18879
$561$	−12982.5	−0.977046
$562$	26049.2	1.95520
$563$	22382.5	1.67551	0.837754	−	0.546048i	$-0.183868\pi$
$563$	22382.5	1.67551	0.837754	+	0.546048i	$0.183868\pi$
$564$	−47740.8	−3.56428
$565$	3308.38	0.246344
$566$	10031.3	0.744959
$567$	6618.49	0.490213
$568$	−70599.3	−5.21529
$569$	8459.16	0.623245	0.311623	−	0.950206i	$-0.399128\pi$
$569$	8459.16	0.623245	0.311623	+	0.950206i	$0.399128\pi$
$570$	−64718.0	−4.75568
$571$	11099.2	0.813461	0.406731	−	0.913548i	$-0.366669\pi$
$571$	11099.2	0.813461	0.406731	+	0.913548i	$0.366669\pi$
$572$	−19608.3	−1.43333
$573$	6647.46	0.484645
$574$	15060.8	1.09517
$575$	6009.45	0.435846
$576$	25665.5	1.85659
$577$	18536.5	1.33741	0.668704	−	0.743528i	$-0.266849\pi$
$577$	18536.5	1.33741	0.668704	+	0.743528i	$0.266849\pi$
$578$	9893.10	0.711936
$579$	−7525.23	−0.540135
$580$	−36506.4	−2.61353
$581$	−635.764	−0.0453975
$582$	−24860.4	−1.77061
$583$	6037.83	0.428922
$584$	77915.2	5.52081
$585$	10615.3	0.750238
$586$	11056.2	0.779401
$587$	5011.42	0.352374	0.176187	−	0.984357i	$-0.443624\pi$
$587$	5011.42	0.352374	0.176187	+	0.984357i	$0.443624\pi$
$588$	−40707.4	−2.85501
$589$	6058.06	0.423800
$590$	−6614.97	−0.461583
$591$	13201.9	0.918871
$592$	−57314.2	−3.97905
$593$	16120.5	1.11634	0.558169	−	0.829728i	$-0.311504\pi$
$593$	16120.5	1.11634	0.558169	+	0.829728i	$0.311504\pi$
$594$	8221.62	0.567907
$595$	−7953.23	−0.547984
$596$	9813.24	0.674440
$597$	−3561.44	−0.244154
$598$	3969.46	0.271444
$599$	2551.08	0.174014	0.0870070	−	0.996208i	$-0.472270\pi$
$599$	2551.08	0.174014	0.0870070	+	0.996208i	$0.472270\pi$
$600$	−106521.	−7.24780
$601$	16965.0	1.15144	0.575720	−	0.817647i	$-0.304722\pi$
$601$	16965.0	1.15144	0.575720	+	0.817647i	$0.304722\pi$
$602$	0	0
$603$	−21062.6	−1.42245
$604$	33439.5	2.25270
$605$	3256.42	0.218830
$606$	2732.39	0.183161
$607$	−11460.4	−0.766329	−0.383164	−	0.923680i	$-0.625166\pi$
$607$	−11460.4	−0.766329	−0.383164	+	0.923680i	$0.625166\pi$
$608$	50046.8	3.33826
$609$	−4957.76	−0.329883
$610$	−3438.81	−0.228251
$611$	9238.45	0.611699
$612$	−23572.8	−1.55699
$613$	20032.8	1.31993	0.659964	−	0.751297i	$-0.270571\pi$
$613$	20032.8	1.31993	0.659964	+	0.751297i	$0.270571\pi$
$614$	−47994.0	−3.15453
$615$	−47170.8	−3.09286
$616$	17914.2	1.17173
$617$	−9340.25	−0.609440	−0.304720	−	0.952442i	$-0.598563\pi$
$617$	−9340.25	−0.609440	−0.304720	+	0.952442i	$0.598563\pi$
$618$	−31978.0	−2.08146
$619$	7733.12	0.502133	0.251067	−	0.967970i	$-0.419219\pi$
$619$	7733.12	0.502133	0.251067	+	0.967970i	$0.419219\pi$
$620$	25200.5	1.63238
$621$	−1201.95	−0.0776694
$622$	−15672.2	−1.01028
$623$	−3141.01	−0.201993
$624$	−38589.2	−2.47565
$625$	6942.96	0.444350
$626$	−41194.9	−2.63016
$627$	−21921.6	−1.39627
$628$	73710.1	4.68369
$629$	15715.2	0.996192
$630$	−15762.2	−0.996793
$631$	5606.13	0.353687	0.176844	−	0.984239i	$-0.443411\pi$
$631$	5606.13	0.353687	0.176844	+	0.984239i	$0.443411\pi$
$632$	16690.0	1.05046
$633$	20730.9	1.30171
$634$	2035.48	0.127506
$635$	6687.95	0.417958
$636$	25429.4	1.58544
$637$	7877.40	0.489975
$638$	−17122.9	−1.06254
$639$	21041.0	1.30261
$640$	45865.1	2.83278
$641$	29939.2	1.84482	0.922408	−	0.386218i	$-0.126219\pi$
$641$	29939.2	1.84482	0.922408	+	0.386218i	$0.126219\pi$
$642$	−53610.4	−3.29569
$643$	1004.21	0.0615895	0.0307947	−	0.999526i	$-0.490196\pi$
$643$	1004.21	0.0615895	0.0307947	+	0.999526i	$0.490196\pi$
$644$	−4256.50	−0.260450
$645$	0	0
$646$	−27810.8	−1.69381
$647$	16811.4	1.02152	0.510759	−	0.859724i	$-0.329364\pi$
$647$	16811.4	1.02152	0.510759	+	0.859724i	$0.329364\pi$
$648$	59235.0	3.59101
$649$	−2240.65	−0.135521
$650$	33501.8	2.02161
$651$	3422.36	0.206042
$652$	−44139.4	−2.65128
$653$	−21727.1	−1.30207	−0.651033	−	0.759050i	$-0.725664\pi$
$653$	−21727.1	−1.30207	−0.651033	+	0.759050i	$0.725664\pi$
$654$	45978.8	2.74911
$655$	13450.5	0.802373
$656$	73927.2	4.39996
$657$	−23221.3	−1.37892
$658$	−13717.7	−0.812724
$659$	−13323.0	−0.787544	−0.393772	−	0.919208i	$-0.628830\pi$
$659$	−13323.0	−0.787544	−0.393772	+	0.919208i	$0.628830\pi$
$660$	−91190.0	−5.37813
$661$	9236.11	0.543484	0.271742	−	0.962370i	$-0.412400\pi$
$661$	9236.11	0.543484	0.271742	+	0.962370i	$0.412400\pi$
$662$	40690.3	2.38893
$663$	10580.9	0.619802
$664$	−5690.04	−0.332555
$665$	−13429.4	−0.783110
$666$	31145.2	1.81209
$667$	2503.26	0.145318
$668$	54195.9	3.13907
$669$	24972.5	1.44319
$670$	−103369.	−5.96042
$671$	−1164.81	−0.0670148
$672$	28272.8	1.62299
$673$	18824.1	1.07818	0.539091	−	0.842247i	$-0.318768\pi$
$673$	18824.1	1.07818	0.539091	+	0.842247i	$0.318768\pi$
$674$	−5800.69	−0.331505
$675$	−10144.3	−0.578453
$676$	−29704.4	−1.69006
$677$	−2666.38	−0.151370	−0.0756850	−	0.997132i	$-0.524114\pi$
$677$	−2666.38	−0.151370	−0.0756850	+	0.997132i	$0.524114\pi$
$678$	6535.48	0.370197
$679$	−5158.69	−0.291564
$680$	−71180.8	−4.01421
$681$	−44096.0	−2.48130
$682$	11820.0	0.663652
$683$	−27630.7	−1.54796	−0.773982	−	0.633207i	$-0.781738\pi$
$683$	−27630.7	−1.54796	−0.773982	+	0.633207i	$0.781738\pi$
$684$	−39803.7	−2.22505
$685$	42122.6	2.34952
$686$	−25815.8	−1.43681
$687$	24883.6	1.38190
$688$	0	0
$689$	−4920.90	−0.272092
$690$	18460.3	1.01851
$691$	−5981.29	−0.329290	−0.164645	−	0.986353i	$-0.552648\pi$
$691$	−5981.29	−0.329290	−0.164645	+	0.986353i	$0.552648\pi$
$692$	−61438.7	−3.37507
$693$	−5339.03	−0.292659
$694$	−28629.3	−1.56593
$695$	−46246.1	−2.52405
$696$	−44371.6	−2.41653
$697$	−20270.3	−1.10157
$698$	−51586.1	−2.79737
$699$	36305.9	1.96454
$700$	−35924.4	−1.93974
$701$	22443.7	1.20925	0.604626	−	0.796510i	$-0.293323\pi$
$701$	22443.7	1.20925	0.604626	+	0.796510i	$0.293323\pi$
$702$	−6700.71	−0.360259
$703$	26535.7	1.42363
$704$	42665.1	2.28409
$705$	42964.2	2.29521
$706$	36127.9	1.92591
$707$	566.987	0.0301609
$708$	−9436.89	−0.500932
$709$	24042.7	1.27354	0.636771	−	0.771053i	$-0.280270\pi$
$709$	24042.7	1.27354	0.636771	+	0.771053i	$0.280270\pi$
$710$	103262.	5.45827
$711$	−4974.19	−0.262372
$712$	−28111.8	−1.47968
$713$	−1728.01	−0.0907639
$714$	−15711.1	−0.823490
$715$	17646.4	0.922991
$716$	−44813.0	−2.33902
$717$	2890.21	0.150540
$718$	−18516.7	−0.962450
$719$	18299.0	0.949148	0.474574	−	0.880216i	$-0.342602\pi$
$719$	18299.0	0.949148	0.474574	+	0.880216i	$0.342602\pi$
$720$	−77369.8	−4.00472
$721$	−6635.63	−0.342752
$722$	−10154.0	−0.523395
$723$	21311.0	1.09622
$724$	96827.7	4.97041
$725$	21127.3	1.08227
$726$	6432.84	0.328850
$727$	−18731.9	−0.955611	−0.477805	−	0.878466i	$-0.658568\pi$
$727$	−18731.9	−0.955611	−0.477805	+	0.878466i	$0.658568\pi$
$728$	−14600.3	−0.743299
$729$	−9275.39	−0.471238
$730$	−113963.	−5.77803
$731$	0	0
$732$	−4905.79	−0.247709
$733$	−1247.75	−0.0628743	−0.0314371	−	0.999506i	$-0.510008\pi$
$733$	−1247.75	−0.0628743	−0.0314371	+	0.999506i	$0.510008\pi$
$734$	39421.5	1.98239
$735$	36634.5	1.83848
$736$	−14275.4	−0.714945
$737$	−35013.5	−1.74999
$738$	−40172.9	−2.00377
$739$	−5411.92	−0.269392	−0.134696	−	0.990887i	$-0.543006\pi$
$739$	−5411.92	−0.269392	−0.134696	+	0.990887i	$0.543006\pi$
$740$	110384.	5.48352
$741$	17866.3	0.885743
$742$	7306.80	0.361511
$743$	26984.8	1.33240	0.666202	−	0.745771i	$-0.267919\pi$
$743$	26984.8	1.33240	0.666202	+	0.745771i	$0.267919\pi$
$744$	30629.9	1.50934
$745$	−8831.38	−0.434304
$746$	−21485.2	−1.05446
$747$	1695.82	0.0830615
$748$	−39186.4	−1.91550
$749$	−11124.5	−0.542696
$750$	69326.0	3.37524
$751$	3170.51	0.154053	0.0770263	−	0.997029i	$-0.475457\pi$
$751$	3170.51	0.154053	0.0770263	+	0.997029i	$0.475457\pi$
$752$	−67334.5	−3.26521
$753$	3035.10	0.146886
$754$	13955.3	0.674036
$755$	−30093.7	−1.45063
$756$	7185.25	0.345668
$757$	−2249.92	−0.108025	−0.0540123	−	0.998540i	$-0.517201\pi$
$757$	−2249.92	−0.108025	−0.0540123	+	0.998540i	$0.517201\pi$
$758$	−25120.8	−1.20373
$759$	6252.95	0.299035
$760$	−120192.	−5.73660
$761$	40622.1	1.93502	0.967511	−	0.252829i	$-0.0813611\pi$
$761$	40622.1	1.93502	0.967511	+	0.252829i	$0.0813611\pi$
$762$	13211.6	0.628091
$763$	9540.88	0.452691
$764$	20064.7	0.950149
$765$	21214.3	1.00262
$766$	−41189.8	−1.94288
$767$	1826.16	0.0859697
$768$	21473.0	1.00891
$769$	−304.926	−0.0142990	−0.00714948	−	0.999974i	$-0.502276\pi$
$769$	−304.926	−0.0142990	−0.00714948	+	0.999974i	$0.502276\pi$
$770$	−26202.3	−1.22632
$771$	−2507.53	−0.117129
$772$	−22714.1	−1.05894
$773$	26494.3	1.23277	0.616387	−	0.787443i	$-0.288596\pi$
$773$	26494.3	1.23277	0.616387	+	0.787443i	$0.288596\pi$
$774$	0	0
$775$	−14584.2	−0.675976
$776$	−46169.9	−2.13583
$777$	14990.8	0.692137
$778$	−44992.6	−2.07334
$779$	−34227.3	−1.57423
$780$	74320.9	3.41168
$781$	34977.5	1.60255
$782$	7932.80	0.362758
$783$	−4225.67	−0.192865
$784$	−57414.4	−2.61545
$785$	−66335.1	−3.01605
$786$	26570.5	1.20578
$787$	−20599.0	−0.933003	−0.466502	−	0.884520i	$-0.654486\pi$
$787$	−20599.0	−0.933003	−0.466502	+	0.884520i	$0.654486\pi$
$788$	39848.5	1.80145
$789$	−9832.63	−0.443664
$790$	−24411.8	−1.09941
$791$	1356.15	0.0609598
$792$	−47783.9	−2.14385
$793$	949.332	0.0425117
$794$	27948.3	1.24918
$795$	−22885.0	−1.02094
$796$	−10749.8	−0.478665
$797$	20106.9	0.893630	0.446815	−	0.894626i	$-0.352558\pi$
$797$	20106.9	0.893630	0.446815	+	0.894626i	$0.352558\pi$
$798$	−26528.8	−1.17683
$799$	18462.7	0.817475
$800$	−120483.	−5.32465
$801$	8378.26	0.369577
$802$	−36781.5	−1.61945
$803$	−38602.1	−1.69644
$804$	−147465.	−6.46854
$805$	3830.62	0.167716
$806$	−9633.43	−0.420996
$807$	−33154.7	−1.44622
$808$	5074.49	0.220941
$809$	33397.8	1.45143	0.725713	−	0.687997i	$-0.241510\pi$
$809$	33397.8	1.45143	0.725713	+	0.687997i	$0.241510\pi$
$810$	−86640.4	−3.75831
$811$	−11274.9	−0.488182	−0.244091	−	0.969752i	$-0.578490\pi$
$811$	−11274.9	−0.488182	−0.244091	+	0.969752i	$0.578490\pi$
$812$	−14964.5	−0.646737
$813$	18064.1	0.779256
$814$	51774.4	2.22935
$815$	39723.1	1.70729
$816$	−77119.0	−3.30846
$817$	0	0
$818$	15762.0	0.673723
$819$	4351.37	0.185652
$820$	−142380.	−6.06357
$821$	15903.9	0.676067	0.338033	−	0.941134i	$-0.390238\pi$
$821$	15903.9	0.676067	0.338033	+	0.941134i	$0.390238\pi$
$822$	83210.4	3.53077
$823$	25896.6	1.09684	0.548421	−	0.836203i	$-0.315229\pi$
$823$	25896.6	1.09684	0.548421	+	0.836203i	$0.315229\pi$
$824$	−59388.4	−2.51079
$825$	52774.2	2.22711
$826$	−2711.57	−0.114222
$827$	−14494.1	−0.609445	−0.304722	−	0.952441i	$-0.598564\pi$
$827$	−14494.1	−0.609445	−0.304722	+	0.952441i	$0.598564\pi$
$828$	11353.7	0.476532
$829$	−38909.2	−1.63012	−0.815062	−	0.579374i	$-0.803297\pi$
$829$	−38909.2	−1.63012	−0.815062	+	0.579374i	$0.803297\pi$
$830$	8322.57	0.348049
$831$	19973.3	0.833773
$832$	−34772.5	−1.44894
$833$	15742.7	0.654803
$834$	−91356.0	−3.79305
$835$	−48773.3	−2.02140
$836$	−66167.9	−2.73740
$837$	2917.00	0.120462
$838$	−12693.8	−0.523269
$839$	−38057.3	−1.56601	−0.783007	−	0.622013i	$-0.786315\pi$
$839$	−38057.3	−1.56601	−0.783007	+	0.622013i	$0.786315\pi$
$840$	−67899.7	−2.78900
$841$	−15588.3	−0.639154
$842$	23630.3	0.967164
$843$	−33443.5	−1.36638
$844$	62574.1	2.55200
$845$	26732.4	1.08831
$846$	36590.4	1.48700
$847$	1334.85	0.0541512
$848$	35866.0	1.45241
$849$	−12878.8	−0.520610
$850$	66952.0	2.70169
$851$	−7569.11	−0.304895
$852$	147314.	5.92358
$853$	13585.7	0.545330	0.272665	−	0.962109i	$-0.412095\pi$
$853$	13585.7	0.545330	0.272665	+	0.962109i	$0.412095\pi$
$854$	−1409.62	−0.0564825
$855$	35821.2	1.43282
$856$	−99563.3	−3.97547
$857$	−44673.0	−1.78063	−0.890314	−	0.455346i	$-0.849515\pi$
$857$	−44673.0	−1.78063	−0.890314	+	0.455346i	$0.849515\pi$
$858$	34859.3	1.38704
$859$	6056.75	0.240575	0.120287	−	0.992739i	$-0.461618\pi$
$859$	6056.75	0.240575	0.120287	+	0.992739i	$0.461618\pi$
$860$	0	0
$861$	−19336.0	−0.765352
$862$	−19470.8	−0.769349
$863$	33033.4	1.30298	0.651490	−	0.758657i	$-0.274144\pi$
$863$	33033.4	1.30298	0.651490	+	0.758657i	$0.274144\pi$
$864$	24097.9	0.948873
$865$	55291.5	2.17337
$866$	43088.3	1.69076
$867$	−12701.3	−0.497532
$868$	10330.0	0.403945
$869$	−8268.86	−0.322787
$870$	64900.4	2.52911
$871$	28536.4	1.11013
$872$	85390.2	3.31614
$873$	13760.2	0.533461
$874$	13394.9	0.518408
$875$	14385.6	0.555795
$876$	−162579.	−6.27060
$877$	−17049.8	−0.656477	−0.328238	−	0.944595i	$-0.606455\pi$
$877$	−17049.8	−0.656477	−0.328238	+	0.944595i	$0.606455\pi$
$878$	−50203.8	−1.92972
$879$	−14194.7	−0.544680
$880$	−128616.	−4.92687
$881$	−6436.70	−0.246150	−0.123075	−	0.992397i	$-0.539276\pi$
$881$	−6436.70	−0.246150	−0.123075	+	0.992397i	$0.539276\pi$
$882$	31199.7	1.19110
$883$	−17200.0	−0.655523	−0.327761	−	0.944761i	$-0.606294\pi$
$883$	−17200.0	−0.655523	−0.327761	+	0.944761i	$0.606294\pi$
$884$	31937.4	1.21512
$885$	8492.69	0.322575
$886$	7695.68	0.291807
$887$	−11613.9	−0.439635	−0.219818	−	0.975541i	$-0.570546\pi$
$887$	−11613.9	−0.439635	−0.219818	+	0.975541i	$0.570546\pi$
$888$	134166.	5.07019
$889$	2741.48	0.103427
$890$	41117.9	1.54862
$891$	−29347.2	−1.10345
$892$	75376.9	2.82938
$893$	31175.0	1.16823
$894$	−17445.8	−0.652657
$895$	40329.3	1.50621
$896$	18800.8	0.700993
$897$	−5096.23	−0.189697
$898$	56488.8	2.09917
$899$	−6075.14	−0.225381
$900$	95824.0	3.54904
$901$	−9834.22	−0.363624
$902$	−66781.6	−2.46517
$903$	0	0
$904$	12137.5	0.446555
$905$	−87139.7	−3.20069
$906$	−59448.1	−2.17995
$907$	−44569.6	−1.63165	−0.815826	−	0.578297i	$-0.803717\pi$
$907$	−44569.6	−1.63165	−0.815826	+	0.578297i	$0.803717\pi$
$908$	−133099.	−4.86459
$909$	−1512.37	−0.0551838
$910$	21355.2	0.777930
$911$	−44104.8	−1.60401	−0.802007	−	0.597314i	$-0.796234\pi$
$911$	−44104.8	−1.60401	−0.802007	+	0.597314i	$0.796234\pi$
$912$	−130219.	−4.72804
$913$	2819.06	0.102188
$914$	−41846.6	−1.51440
$915$	4414.94	0.159512
$916$	75108.4	2.70923
$917$	5513.55	0.198553
$918$	−13391.1	−0.481451
$919$	−36401.1	−1.30660	−0.653298	−	0.757101i	$-0.726615\pi$
$919$	−36401.1	−1.30660	−0.653298	+	0.757101i	$0.726615\pi$
$920$	34283.8	1.22859
$921$	61617.5	2.20452
$922$	−12524.3	−0.447360
$923$	−28507.1	−1.01660
$924$	−37380.1	−1.33086
$925$	−63882.5	−2.27075
$926$	−80692.5	−2.86363
$927$	17699.7	0.627115
$928$	−50187.8	−1.77532
$929$	−8835.42	−0.312035	−0.156018	−	0.987754i	$-0.549866\pi$
$929$	−8835.42	−0.312035	−0.156018	+	0.987754i	$0.549866\pi$
$930$	−44801.0	−1.57966
$931$	26582.1	0.935762
$932$	109586.	3.85150
$933$	20120.8	0.706030
$934$	−66858.5	−2.34227
$935$	35265.6	1.23349
$936$	38944.4	1.35998
$937$	9205.79	0.320961	0.160480	−	0.987039i	$-0.448696\pi$
$937$	9205.79	0.320961	0.160480	+	0.987039i	$0.448696\pi$
$938$	−42372.3	−1.47495
$939$	52888.4	1.83807
$940$	129683.	4.49977
$941$	−1239.80	−0.0429503	−0.0214752	−	0.999769i	$-0.506836\pi$
$941$	−1239.80	−0.0429503	−0.0214752	+	0.999769i	$0.506836\pi$
$942$	−131041.	−4.53241
$943$	9763.08	0.337147
$944$	−13310.0	−0.458901
$945$	−6466.34	−0.222593
$946$	0	0
$947$	47869.8	1.64262	0.821310	−	0.570482i	$-0.193244\pi$
$947$	47869.8	1.64262	0.821310	+	0.570482i	$0.193244\pi$
$948$	−34825.7	−1.19313
$949$	31461.1	1.07616
$950$	113051.	3.86091
$951$	−2613.26	−0.0891071
$952$	−29178.0	−0.993345
$953$	54491.9	1.85222	0.926109	−	0.377255i	$-0.123132\pi$
$953$	54491.9	1.85222	0.926109	+	0.377255i	$0.123132\pi$
$954$	−19490.0	−0.661438
$955$	−18057.1	−0.611847
$956$	8723.80	0.295134
$957$	21983.3	0.742550
$958$	16226.4	0.547236
$959$	17266.7	0.581407
$960$	−161712.	−5.43671
$961$	−25597.3	−0.859230
$962$	−42196.7	−1.41422
$963$	29673.2	0.992944
$964$	64325.0	2.14914
$965$	20441.5	0.681900
$966$	7567.13	0.252038
$967$	4088.52	0.135965	0.0679823	−	0.997687i	$-0.478344\pi$
$967$	4088.52	0.135965	0.0679823	+	0.997687i	$0.478344\pi$
$968$	11946.8	0.396679
$969$	35705.1	1.18371
$970$	67530.6	2.23534
$971$	38001.5	1.25595	0.627975	−	0.778234i	$-0.283884\pi$
$971$	38001.5	1.25595	0.627975	+	0.778234i	$0.283884\pi$
$972$	−98310.9	−3.24416
$973$	−18956.9	−0.624595
$974$	18889.6	0.621419
$975$	−43011.6	−1.41279
$976$	−6919.21	−0.226925
$977$	−28001.4	−0.916935	−0.458468	−	0.888711i	$-0.651601\pi$
$977$	−28001.4	−0.916935	−0.458468	+	0.888711i	$0.651601\pi$
$978$	78470.3	2.56565
$979$	13927.6	0.454677
$980$	110577.	3.60435
$981$	−25449.2	−0.828266
$982$	−23095.8	−0.750525
$983$	−15493.5	−0.502711	−0.251355	−	0.967895i	$-0.580876\pi$
$983$	−15493.5	−0.502711	−0.251355	+	0.967895i	$0.580876\pi$
$984$	−173055.	−5.60651
$985$	−35861.5	−1.16004
$986$	27889.2	0.900783
$987$	17611.6	0.567967
$988$	53927.6	1.73650
$989$	0	0
$990$	69891.4	2.24373
$991$	37563.1	1.20407	0.602034	−	0.798470i	$-0.294357\pi$
$991$	37563.1	1.20407	0.602034	+	0.798470i	$0.294357\pi$
$992$	34644.9	1.10885
$993$	−52240.6	−1.66949
$994$	42328.7	1.35069
$995$	9674.25	0.308236
$996$	11872.9	0.377719
$997$	58039.6	1.84366	0.921832	−	0.387590i	$-0.126692\pi$
$997$	58039.6	1.84366	0.921832	+	0.387590i	$0.126692\pi$
$998$	112643.	3.57279
$999$	12777.2	0.404656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.4	✓	110
43.42	odd	2	inner	1849.4.a.m.1.107	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.4	✓	110	1.1	even	1	trivial
1849.4.a.m.1.107	yes	110	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.36605 q^{2} +6.88924 q^{3} +20.7944 q^{4} -18.7139 q^{5} -36.9680 q^{6} -7.67108 q^{7} -68.6556 q^{8} +20.4617 q^{9} +O(q^{10})\)	\(q-5.36605 q^{2} +6.88924 q^{3} +20.7944 q^{4} -18.7139 q^{5} -36.9680 q^{6} -7.67108 q^{7} -68.6556 q^{8} +20.4617 q^{9} +100.419 q^{10} +34.0145 q^{11} +143.258 q^{12} -27.7222 q^{13} +41.1634 q^{14} -128.924 q^{15} +202.054 q^{16} -55.4017 q^{17} -109.798 q^{18} -93.5482 q^{19} -389.145 q^{20} -52.8479 q^{21} -182.524 q^{22} +26.6839 q^{23} -472.985 q^{24} +225.209 q^{25} +148.759 q^{26} -45.0441 q^{27} -159.516 q^{28} +93.8119 q^{29} +691.814 q^{30} -64.7587 q^{31} -534.984 q^{32} +234.334 q^{33} +297.288 q^{34} +143.556 q^{35} +425.489 q^{36} -283.659 q^{37} +501.984 q^{38} -190.985 q^{39} +1284.81 q^{40} +365.879 q^{41} +283.584 q^{42} +707.314 q^{44} -382.917 q^{45} -143.187 q^{46} -333.251 q^{47} +1392.00 q^{48} -284.155 q^{49} -1208.48 q^{50} -381.676 q^{51} -576.469 q^{52} +177.507 q^{53} +241.709 q^{54} -636.544 q^{55} +526.663 q^{56} -644.476 q^{57} -503.399 q^{58} -65.8734 q^{59} -2680.91 q^{60} -34.2444 q^{61} +347.498 q^{62} -156.963 q^{63} +1254.32 q^{64} +518.790 q^{65} -1257.45 q^{66} -1029.37 q^{67} -1152.05 q^{68} +183.832 q^{69} -770.326 q^{70} +1028.31 q^{71} -1404.81 q^{72} -1134.87 q^{73} +1522.12 q^{74} +1551.52 q^{75} -1945.28 q^{76} -260.928 q^{77} +1024.84 q^{78} -243.098 q^{79} -3781.20 q^{80} -862.785 q^{81} -1963.33 q^{82} +82.8780 q^{83} -1098.94 q^{84} +1036.78 q^{85} +646.293 q^{87} -2335.29 q^{88} +409.461 q^{89} +2054.75 q^{90} +212.659 q^{91} +554.877 q^{92} -446.139 q^{93} +1788.24 q^{94} +1750.65 q^{95} -3685.63 q^{96} +672.485 q^{97} +1524.79 q^{98} +695.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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