LMFDB - Embedded newform 1849.4.a.m.1.10

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			1.10
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)

$f(q)$	$=$	$q-4.92230 q^{2} +9.67693 q^{3} +16.2290 q^{4} -12.1144 q^{5} -47.6328 q^{6} -16.5271 q^{7} -40.5059 q^{8} +66.6431 q^{9} +O(q^{10})$	\(q-4.92230 q^{2} +9.67693 q^{3} +16.2290 q^{4} -12.1144 q^{5} -47.6328 q^{6} -16.5271 q^{7} -40.5059 q^{8} +66.6431 q^{9} +59.6309 q^{10} +7.85742 q^{11} +157.047 q^{12} +53.3816 q^{13} +81.3513 q^{14} -117.231 q^{15} +69.5496 q^{16} +59.2079 q^{17} -328.037 q^{18} +4.09232 q^{19} -196.606 q^{20} -159.931 q^{21} -38.6766 q^{22} +218.357 q^{23} -391.973 q^{24} +21.7595 q^{25} -262.760 q^{26} +383.623 q^{27} -268.219 q^{28} -26.5928 q^{29} +577.044 q^{30} +45.3669 q^{31} -18.2974 q^{32} +76.0357 q^{33} -291.439 q^{34} +200.216 q^{35} +1081.55 q^{36} +138.338 q^{37} -20.1436 q^{38} +516.570 q^{39} +490.706 q^{40} -121.495 q^{41} +787.231 q^{42} +127.518 q^{44} -807.343 q^{45} -1074.82 q^{46} +390.739 q^{47} +673.027 q^{48} -69.8557 q^{49} -107.107 q^{50} +572.951 q^{51} +866.333 q^{52} -572.056 q^{53} -1888.31 q^{54} -95.1882 q^{55} +669.443 q^{56} +39.6011 q^{57} +130.898 q^{58} -407.304 q^{59} -1902.54 q^{60} +10.5166 q^{61} -223.310 q^{62} -1101.41 q^{63} -466.332 q^{64} -646.688 q^{65} -374.271 q^{66} -334.448 q^{67} +960.889 q^{68} +2113.03 q^{69} -985.524 q^{70} -920.309 q^{71} -2699.43 q^{72} +399.265 q^{73} -680.942 q^{74} +210.566 q^{75} +66.4145 q^{76} -129.860 q^{77} -2542.72 q^{78} -453.255 q^{79} -842.555 q^{80} +1912.93 q^{81} +598.033 q^{82} -798.013 q^{83} -2595.54 q^{84} -717.271 q^{85} -257.337 q^{87} -318.271 q^{88} -115.021 q^{89} +3973.99 q^{90} -882.242 q^{91} +3543.73 q^{92} +439.013 q^{93} -1923.34 q^{94} -49.5762 q^{95} -177.063 q^{96} +544.143 q^{97} +343.851 q^{98} +523.642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.92230	−1.74030	−0.870148	−	0.492790i	$-0.835977\pi$
$2$	−4.92230	−1.74030	−0.870148	+	0.492790i	$0.835977\pi$
$3$	9.67693	1.86233	0.931163	−	0.364602i	$-0.118795\pi$
$3$	9.67693	1.86233	0.931163	+	0.364602i	$0.118795\pi$
$4$	16.2290	2.02863
$5$	−12.1144	−1.08355	−0.541774	−	0.840524i	$-0.682247\pi$
$5$	−12.1144	−1.08355	−0.541774	+	0.840524i	$0.682247\pi$
$6$	−47.6328	−3.24100
$7$	−16.5271	−0.892378	−0.446189	−	0.894939i	$-0.647219\pi$
$7$	−16.5271	−0.892378	−0.446189	+	0.894939i	$0.647219\pi$
$8$	−40.5059	−1.79012
$9$	66.6431	2.46826
$10$	59.6309	1.88569
$11$	7.85742	0.215373	0.107686	−	0.994185i	$-0.465656\pi$
$11$	7.85742	0.215373	0.107686	+	0.994185i	$0.465656\pi$
$12$	157.047	3.77797
$13$	53.3816	1.13888	0.569438	−	0.822034i	$-0.307161\pi$
$13$	53.3816	1.13888	0.569438	+	0.822034i	$0.307161\pi$
$14$	81.3513	1.55300
$15$	−117.231	−2.01792
$16$	69.5496	1.08671
$17$	59.2079	0.844708	0.422354	−	0.906431i	$-0.361204\pi$
$17$	59.2079	0.844708	0.422354	+	0.906431i	$0.361204\pi$
$18$	−328.037	−4.29551
$19$	4.09232	0.0494128	0.0247064	−	0.999695i	$-0.492135\pi$
$19$	4.09232	0.0494128	0.0247064	+	0.999695i	$0.492135\pi$
$20$	−196.606	−2.19812
$21$	−159.931	−1.66190
$22$	−38.6766	−0.374812
$23$	218.357	1.97959	0.989795	−	0.142499i	$-0.0455139\pi$
$23$	218.357	1.97959	0.989795	+	0.142499i	$0.0455139\pi$
$24$	−391.973	−3.33379
$25$	21.7595	0.174076
$26$	−262.760	−1.98198
$27$	383.623	2.73438
$28$	−268.219	−1.81031
$29$	−26.5928	−0.170281	−0.0851407	−	0.996369i	$-0.527134\pi$
$29$	−26.5928	−0.170281	−0.0851407	+	0.996369i	$0.527134\pi$
$30$	577.044	3.51178
$31$	45.3669	0.262843	0.131422	−	0.991327i	$-0.458046\pi$
$31$	45.3669	0.262843	0.131422	+	0.991327i	$0.458046\pi$
$32$	−18.2974	−0.101080
$33$	76.0357	0.401095
$34$	−291.439	−1.47004
$35$	200.216	0.966935
$36$	1081.55	5.00719
$37$	138.338	0.614666	0.307333	−	0.951602i	$-0.400563\pi$
$37$	138.338	0.614666	0.307333	+	0.951602i	$0.400563\pi$
$38$	−20.1436	−0.0859929
$39$	516.570	2.12096
$40$	490.706	1.93968
$41$	−121.495	−0.462787	−0.231393	−	0.972860i	$-0.574328\pi$
$41$	−121.495	−0.462787	−0.231393	+	0.972860i	$0.574328\pi$
$42$	787.231	2.89220
$43$	0	0
$43$	0	0
$44$	127.518	0.436912
$45$	−807.343	−2.67448
$46$	−1074.82	−3.44507
$47$	390.739	1.21266	0.606331	−	0.795212i	$-0.292641\pi$
$47$	390.739	1.21266	0.606331	+	0.795212i	$0.292641\pi$
$48$	673.027	2.02382
$49$	−69.8557	−0.203661
$50$	−107.107	−0.302944
$51$	572.951	1.57312
$52$	866.333	2.31036
$53$	−572.056	−1.48260	−0.741301	−	0.671172i	$-0.765791\pi$
$53$	−572.056	−1.48260	−0.741301	+	0.671172i	$0.765791\pi$
$54$	−1888.31	−4.75864
$55$	−95.1882	−0.233367
$56$	669.443	1.59747
$57$	39.6011	0.0920228
$58$	130.898	0.296340
$59$	−407.304	−0.898755	−0.449377	−	0.893342i	$-0.648354\pi$
$59$	−407.304	−0.898755	−0.449377	+	0.893342i	$0.648354\pi$
$60$	−1902.54	−4.09362
$61$	10.5166	0.0220740	0.0110370	−	0.999939i	$-0.496487\pi$
$61$	10.5166	0.0220740	0.0110370	+	0.999939i	$0.496487\pi$
$62$	−223.310	−0.457425
$63$	−1101.41	−2.20262
$64$	−466.332	−0.910804
$65$	−646.688	−1.23403
$66$	−374.271	−0.698023
$67$	−334.448	−0.609841	−0.304920	−	0.952378i	$-0.598630\pi$
$67$	−334.448	−0.609841	−0.304920	+	0.952378i	$0.598630\pi$
$68$	960.889	1.71360
$69$	2113.03	3.68664
$70$	−985.524	−1.68275
$71$	−920.309	−1.53832	−0.769159	−	0.639057i	$-0.779325\pi$
$71$	−920.309	−1.53832	−0.769159	+	0.639057i	$0.779325\pi$
$72$	−2699.43	−4.41849
$73$	399.265	0.640143	0.320072	−	0.947393i	$-0.396293\pi$
$73$	399.265	0.640143	0.320072	+	0.947393i	$0.396293\pi$
$74$	−680.942	−1.06970
$75$	210.566	0.324187
$76$	66.4145	0.100240
$77$	−129.860	−0.192194
$78$	−2542.72	−3.69110
$79$	−453.255	−0.645508	−0.322754	−	0.946483i	$-0.604609\pi$
$79$	−453.255	−0.645508	−0.322754	+	0.946483i	$0.604609\pi$
$80$	−842.555	−1.17751
$81$	1912.93	2.62405
$82$	598.033	0.805386
$83$	−798.013	−1.05534	−0.527671	−	0.849449i	$-0.676934\pi$
$83$	−798.013	−1.05534	−0.527671	+	0.849449i	$0.676934\pi$
$84$	−2595.54	−3.37138
$85$	−717.271	−0.915282
$86$	0	0
$87$	−257.337	−0.317120
$88$	−318.271	−0.385544
$89$	−115.021	−0.136991	−0.0684954	−	0.997651i	$-0.521820\pi$
$89$	−115.021	−0.136991	−0.0684954	+	0.997651i	$0.521820\pi$
$90$	3973.99	4.65439
$91$	−882.242	−1.01631
$92$	3543.73	4.01586
$93$	439.013	0.489500
$94$	−1923.34	−2.11039
$95$	−49.5762	−0.0535411
$96$	−177.063	−0.188244
$97$	544.143	0.569581	0.284790	−	0.958590i	$-0.408076\pi$
$97$	544.143	0.569581	0.284790	+	0.958590i	$0.408076\pi$
$98$	343.851	0.354430
$99$	523.642	0.531596
$100$	353.136	0.353136
$101$	330.276	0.325383	0.162691	−	0.986677i	$-0.447982\pi$
$101$	330.276	0.325383	0.162691	+	0.986677i	$0.447982\pi$
$102$	−2820.24	−2.73770
$103$	1138.26	1.08890	0.544448	−	0.838794i	$-0.316739\pi$
$103$	1138.26	1.08890	0.544448	+	0.838794i	$0.316739\pi$
$104$	−2162.27	−2.03873
$105$	1937.48	1.80075
$106$	2815.83	2.58017
$107$	1758.37	1.58868	0.794338	−	0.607476i	$-0.207818\pi$
$107$	1758.37	1.58868	0.794338	+	0.607476i	$0.207818\pi$
$108$	6225.84	5.54705
$109$	239.960	0.210862	0.105431	−	0.994427i	$-0.466378\pi$
$109$	239.960	0.210862	0.105431	+	0.994427i	$0.466378\pi$
$110$	468.545	0.406127
$111$	1338.69	1.14471
$112$	−1149.45	−0.969759
$113$	−126.505	−0.105315	−0.0526575	−	0.998613i	$-0.516769\pi$
$113$	−126.505	−0.105315	−0.0526575	+	0.998613i	$0.516769\pi$
$114$	−194.929	−0.160147
$115$	−2645.27	−2.14498
$116$	−431.576	−0.345438
$117$	3557.51	2.81105
$118$	2004.88	1.56410
$119$	−978.534	−0.753799
$120$	4748.53	3.61233
$121$	−1269.26	−0.953615
$122$	−51.7660	−0.0384153
$123$	−1175.69	−0.861860
$124$	736.262	0.533212
$125$	1250.70	0.894928
$126$	5421.50	3.83322
$127$	1035.64	0.723605	0.361803	−	0.932255i	$-0.382161\pi$
$127$	1035.64	0.723605	0.361803	+	0.932255i	$0.382161\pi$
$128$	2441.80	1.68615
$129$	0	0
$130$	3183.19	2.14757
$131$	2756.93	1.83873	0.919366	−	0.393402i	$-0.128702\pi$
$131$	2756.93	1.83873	0.919366	+	0.393402i	$0.128702\pi$
$132$	1233.99	0.813673
$133$	−67.6341	−0.0440949
$134$	1646.25	1.06130
$135$	−4647.38	−2.96283
$136$	−2398.27	−1.51213
$137$	1771.62	1.10481	0.552407	−	0.833574i	$-0.313709\pi$
$137$	1771.62	1.10481	0.552407	+	0.833574i	$0.313709\pi$
$138$	−10400.9	−6.41585
$139$	−32.5237	−0.0198462	−0.00992311	−	0.999951i	$-0.503159\pi$
$139$	−32.5237	−0.0198462	−0.00992311	+	0.999951i	$0.503159\pi$
$140$	3249.32	1.96155
$141$	3781.16	2.25837
$142$	4530.04	2.67713
$143$	419.442	0.245283
$144$	4635.00	2.68229
$145$	322.157	0.184508
$146$	−1965.30	−1.11404
$147$	−675.989	−0.379283
$148$	2245.10	1.24693
$149$	1215.47	0.668292	0.334146	−	0.942521i	$-0.391552\pi$
$149$	1215.47	0.668292	0.334146	+	0.942521i	$0.391552\pi$
$150$	−1036.47	−0.564181
$151$	−2690.52	−1.45001	−0.725003	−	0.688745i	$-0.758162\pi$
$151$	−2690.52	−1.45001	−0.725003	+	0.688745i	$0.758162\pi$
$152$	−165.763	−0.0884550
$153$	3945.80	2.08496
$154$	639.211	0.334475
$155$	−549.595	−0.284803
$156$	8383.45	4.30265
$157$	86.2491	0.0438435	0.0219217	−	0.999760i	$-0.493022\pi$
$157$	86.2491	0.0438435	0.0219217	+	0.999760i	$0.493022\pi$
$158$	2231.06	1.12338
$159$	−5535.75	−2.76109
$160$	221.663	0.109525
$161$	−3608.80	−1.76654
$162$	−9416.04	−4.56663
$163$	−2734.65	−1.31407	−0.657037	−	0.753858i	$-0.728191\pi$
$163$	−2734.65	−1.31407	−0.657037	+	0.753858i	$0.728191\pi$
$164$	−1971.74	−0.938824
$165$	−921.130	−0.434605
$166$	3928.06	1.83661
$167$	2755.25	1.27669	0.638346	−	0.769750i	$-0.279619\pi$
$167$	2755.25	1.27669	0.638346	+	0.769750i	$0.279619\pi$
$168$	6478.16	2.97501
$169$	652.597	0.297040
$170$	3530.62	1.59286
$171$	272.725	0.121964
$172$	0	0
$173$	3274.62	1.43910	0.719552	−	0.694438i	$-0.244347\pi$
$173$	3274.62	1.43910	0.719552	+	0.694438i	$0.244347\pi$
$174$	1266.69	0.551882
$175$	−359.621	−0.155342
$176$	546.481	0.234048
$177$	−3941.46	−1.67377
$178$	566.167	0.238405
$179$	1797.98	0.750767	0.375384	−	0.926870i	$-0.377511\pi$
$179$	1797.98	0.750767	0.375384	+	0.926870i	$0.377511\pi$
$180$	−13102.4	−5.42553
$181$	2329.20	0.956510	0.478255	−	0.878221i	$-0.341269\pi$
$181$	2329.20	0.956510	0.478255	+	0.878221i	$0.341269\pi$
$182$	4342.66	1.76868
$183$	101.769	0.0411091
$184$	−8844.73	−3.54371
$185$	−1675.89	−0.666021
$186$	−2160.95	−0.851875
$187$	465.222	0.181927
$188$	6341.32	2.46005
$189$	−6340.17	−2.44010
$190$	244.029	0.0931774
$191$	4696.41	1.77916	0.889582	−	0.456775i	$-0.150996\pi$
$191$	4696.41	1.77916	0.889582	+	0.456775i	$0.150996\pi$
$192$	−4512.66	−1.69622
$193$	2337.64	0.871849	0.435925	−	0.899983i	$-0.356421\pi$
$193$	2337.64	0.871849	0.435925	+	0.899983i	$0.356421\pi$
$194$	−2678.43	−0.991239
$195$	−6257.96	−2.29816
$196$	−1133.69	−0.413153
$197$	−303.203	−0.109656	−0.0548282	−	0.998496i	$-0.517461\pi$
$197$	−303.203	−0.109656	−0.0548282	+	0.998496i	$0.517461\pi$
$198$	−2577.53	−0.925135
$199$	−361.372	−0.128729	−0.0643643	−	0.997926i	$-0.520502\pi$
$199$	−361.372	−0.128729	−0.0643643	+	0.997926i	$0.520502\pi$
$200$	−881.388	−0.311618
$201$	−3236.43	−1.13572
$202$	−1625.72	−0.566263
$203$	439.502	0.151956
$204$	9298.46	3.19128
$205$	1471.84	0.501452
$206$	−5602.87	−1.89500
$207$	14552.0	4.88614
$208$	3712.67	1.23763
$209$	32.1551	0.0106422
$210$	−9536.86	−3.13384
$211$	−4038.02	−1.31748	−0.658742	−	0.752369i	$-0.728911\pi$
$211$	−4038.02	−1.31748	−0.658742	+	0.752369i	$0.728911\pi$
$212$	−9283.93	−3.00765
$213$	−8905.77	−2.86485
$214$	−8655.24	−2.76477
$215$	0	0
$216$	−15539.0	−4.89488
$217$	−749.783	−0.234556
$218$	−1181.16	−0.366963
$219$	3863.66	1.19216
$220$	−1544.81	−0.473415
$221$	3160.62	0.962018
$222$	−6589.43	−1.99213
$223$	−5039.34	−1.51327	−0.756635	−	0.653837i	$-0.773158\pi$
$223$	−5039.34	−1.51327	−0.756635	+	0.653837i	$0.773158\pi$
$224$	302.403	0.0902015
$225$	1450.12	0.429666
$226$	622.696	0.183279
$227$	583.798	0.170696	0.0853481	−	0.996351i	$-0.472800\pi$
$227$	583.798	0.170696	0.0853481	+	0.996351i	$0.472800\pi$
$228$	642.689	0.186680
$229$	2179.01	0.628789	0.314395	−	0.949292i	$-0.398198\pi$
$229$	2179.01	0.628789	0.314395	+	0.949292i	$0.398198\pi$
$230$	13020.8	3.73290
$231$	−1256.65	−0.357928
$232$	1077.17	0.304825
$233$	3784.35	1.06404	0.532019	−	0.846732i	$-0.321433\pi$
$233$	3784.35	1.06404	0.532019	+	0.846732i	$0.321433\pi$
$234$	−17511.2	−4.89205
$235$	−4733.58	−1.31398
$236$	−6610.16	−1.82324
$237$	−4386.12	−1.20215
$238$	4816.64	1.31183
$239$	4516.01	1.22225	0.611123	−	0.791536i	$-0.290718\pi$
$239$	4516.01	1.22225	0.611123	+	0.791536i	$0.290718\pi$
$240$	−8153.35	−2.19290
$241$	1703.65	0.455360	0.227680	−	0.973736i	$-0.426886\pi$
$241$	1703.65	0.455360	0.227680	+	0.973736i	$0.426886\pi$
$242$	6247.68	1.65957
$243$	8153.51	2.15246
$244$	170.675	0.0447801
$245$	846.262	0.220676
$246$	5787.12	1.49989
$247$	218.455	0.0562751
$248$	−1837.63	−0.470522
$249$	−7722.32	−1.96539
$250$	−6156.32	−1.55744
$251$	4010.92	1.00863	0.504317	−	0.863519i	$-0.331744\pi$
$251$	4010.92	1.00863	0.504317	+	0.863519i	$0.331744\pi$
$252$	−17874.9	−4.46831
$253$	1715.72	0.426350
$254$	−5097.71	−1.25929
$255$	−6940.98	−1.70455
$256$	−8288.64	−2.02359
$257$	1186.69	0.288029	0.144015	−	0.989576i	$-0.453999\pi$
$257$	1186.69	0.288029	0.144015	+	0.989576i	$0.453999\pi$
$258$	0	0
$259$	−2286.33	−0.548515
$260$	−10495.1	−2.50339
$261$	−1772.23	−0.420299
$262$	−13570.4	−3.19994
$263$	7528.95	1.76523	0.882614	−	0.470098i	$-0.155781\pi$
$263$	7528.95	1.76523	0.882614	+	0.470098i	$0.155781\pi$
$264$	−3079.89	−0.718008
$265$	6930.14	1.60647
$266$	332.916	0.0767382
$267$	−1113.05	−0.255122
$268$	−5427.77	−1.23714
$269$	−6829.44	−1.54795	−0.773975	−	0.633217i	$-0.781734\pi$
$269$	−6829.44	−1.54795	−0.773975	+	0.633217i	$0.781734\pi$
$270$	22875.8	5.15621
$271$	1760.55	0.394635	0.197317	−	0.980340i	$-0.436777\pi$
$271$	1760.55	0.394635	0.197317	+	0.980340i	$0.436777\pi$
$272$	4117.89	0.917955
$273$	−8537.40	−1.89270
$274$	−8720.44	−1.92270
$275$	170.974	0.0374913
$276$	34292.4	7.47884
$277$	7850.33	1.70282	0.851409	−	0.524502i	$-0.175748\pi$
$277$	7850.33	1.70282	0.851409	+	0.524502i	$0.175748\pi$
$278$	160.092	0.0345383
$279$	3023.39	0.648766
$280$	−8109.93	−1.73093
$281$	6541.87	1.38881	0.694404	−	0.719585i	$-0.255668\pi$
$281$	6541.87	1.38881	0.694404	+	0.719585i	$0.255668\pi$
$282$	−18612.0	−3.93024
$283$	−764.199	−0.160519	−0.0802596	−	0.996774i	$-0.525575\pi$
$283$	−764.199	−0.160519	−0.0802596	+	0.996774i	$0.525575\pi$
$284$	−14935.7	−3.12068
$285$	−479.745	−0.0997111
$286$	−2064.62	−0.426865
$287$	2007.95	0.412981
$288$	−1219.40	−0.249492
$289$	−1407.42	−0.286469
$290$	−1585.75	−0.321099
$291$	5265.63	1.06075
$292$	6479.69	1.29861
$293$	−420.429	−0.0838285	−0.0419142	−	0.999121i	$-0.513346\pi$
$293$	−420.429	−0.0838285	−0.0419142	+	0.999121i	$0.513346\pi$
$294$	3327.42	0.660065
$295$	4934.26	0.973844
$296$	−5603.51	−1.10033
$297$	3014.29	0.588912
$298$	−5982.93	−1.16303
$299$	11656.2	2.25451
$300$	3417.28	0.657656
$301$	0	0
$302$	13243.5	2.52344
$303$	3196.06	0.605969
$304$	284.620	0.0536975
$305$	−127.403	−0.0239183
$306$	−19422.4	−3.62845
$307$	−4809.79	−0.894167	−0.447084	−	0.894492i	$-0.647537\pi$
$307$	−4809.79	−0.894167	−0.447084	+	0.894492i	$0.647537\pi$
$308$	−2107.51	−0.389891
$309$	11014.9	2.02788
$310$	2705.27	0.495642
$311$	−1738.02	−0.316894	−0.158447	−	0.987367i	$-0.550649\pi$
$311$	−1738.02	−0.316894	−0.158447	+	0.987367i	$0.550649\pi$
$312$	−20924.1	−3.79678
$313$	−9474.21	−1.71091	−0.855453	−	0.517880i	$-0.826721\pi$
$313$	−9474.21	−1.71091	−0.855453	+	0.517880i	$0.826721\pi$
$314$	−424.544	−0.0763007
$315$	13343.0	2.38665
$316$	−7355.89	−1.30950
$317$	462.521	0.0819489	0.0409744	−	0.999160i	$-0.486954\pi$
$317$	462.521	0.0819489	0.0409744	+	0.999160i	$0.486954\pi$
$318$	27248.6	4.80512
$319$	−208.951	−0.0366740
$320$	5649.35	0.986900
$321$	17015.7	2.95863
$322$	17763.6	3.07431
$323$	242.298	0.0417394
$324$	31045.1	5.32323
$325$	1161.56	0.198251
$326$	13460.8	2.28688
$327$	2322.08	0.392695
$328$	4921.24	0.828445
$329$	−6457.77	−1.08215
$330$	4534.08	0.756342
$331$	9367.65	1.55557	0.777783	−	0.628532i	$-0.216344\pi$
$331$	9367.65	1.55557	0.777783	+	0.628532i	$0.216344\pi$
$332$	−12951.0	−2.14090
$333$	9219.28	1.51716
$334$	−13562.2	−2.22182
$335$	4051.65	0.660792
$336$	−11123.2	−1.80601
$337$	−6256.71	−1.01135	−0.505675	−	0.862724i	$-0.668756\pi$
$337$	−6256.71	−1.01135	−0.505675	+	0.862724i	$0.668756\pi$
$338$	−3212.28	−0.516938
$339$	−1224.18	−0.196131
$340$	−11640.6	−1.85677
$341$	356.467	0.0566093
$342$	−1342.43	−0.212253
$343$	6823.30	1.07412
$344$	0	0
$345$	−25598.1	−3.99465
$346$	−16118.7	−2.50447
$347$	2200.58	0.340442	0.170221	−	0.985406i	$-0.445552\pi$
$347$	2200.58	0.340442	0.170221	+	0.985406i	$0.445552\pi$
$348$	−4176.33	−0.643319
$349$	5741.53	0.880622	0.440311	−	0.897845i	$-0.354868\pi$
$349$	5741.53	0.880622	0.440311	+	0.897845i	$0.354868\pi$
$350$	1770.17	0.270341
$351$	20478.4	3.11412
$352$	−143.770	−0.0217699
$353$	−2123.27	−0.320142	−0.160071	−	0.987105i	$-0.551172\pi$
$353$	−2123.27	−0.320142	−0.160071	+	0.987105i	$0.551172\pi$
$354$	19401.0	2.91286
$355$	11149.0	1.66684
$356$	−1866.68	−0.277904
$357$	−9469.21	−1.40382
$358$	−8850.20	−1.30656
$359$	−594.823	−0.0874472	−0.0437236	−	0.999044i	$-0.513922\pi$
$359$	−594.823	−0.0874472	−0.0437236	+	0.999044i	$0.513922\pi$
$360$	32702.1	4.78765
$361$	−6842.25	−0.997558
$362$	−11465.0	−1.66461
$363$	−12282.6	−1.77594
$364$	−14318.0	−2.06172
$365$	−4836.87	−0.693626
$366$	−500.936	−0.0715419
$367$	6190.68	0.880519	0.440260	−	0.897870i	$-0.354886\pi$
$367$	6190.68	0.880519	0.440260	+	0.897870i	$0.354886\pi$
$368$	15186.6	2.15125
$369$	−8096.77	−1.14228
$370$	8249.23	1.15907
$371$	9454.41	1.32304
$372$	7124.76	0.993015
$373$	−5291.39	−0.734524	−0.367262	−	0.930117i	$-0.619705\pi$
$373$	−5291.39	−0.734524	−0.367262	+	0.930117i	$0.619705\pi$
$374$	−2289.96	−0.316607
$375$	12102.9	1.66665
$376$	−15827.2	−2.17082
$377$	−1419.57	−0.193930
$378$	31208.2	4.24650
$379$	−12814.1	−1.73672	−0.868359	−	0.495936i	$-0.834825\pi$
$379$	−12814.1	−1.73672	−0.868359	+	0.495936i	$0.834825\pi$
$380$	−804.574	−0.108615
$381$	10021.8	1.34759
$382$	−23117.2	−3.09627
$383$	−9124.54	−1.21734	−0.608672	−	0.793422i	$-0.708297\pi$
$383$	−9124.54	−1.21734	−0.608672	+	0.793422i	$0.708297\pi$
$384$	23629.2	3.14016
$385$	1573.18	0.208251
$386$	−11506.6	−1.51728
$387$	0	0
$388$	8830.92	1.15547
$389$	−3769.65	−0.491333	−0.245667	−	0.969354i	$-0.579007\pi$
$389$	−3769.65	−0.491333	−0.245667	+	0.969354i	$0.579007\pi$
$390$	30803.6	3.99948
$391$	12928.5	1.67218
$392$	2829.56	0.364578
$393$	26678.6	3.42432
$394$	1492.46	0.190835
$395$	5490.92	0.699439
$396$	8498.22	1.07841
$397$	1434.36	0.181332	0.0906658	−	0.995881i	$-0.471100\pi$
$397$	1434.36	0.181332	0.0906658	+	0.995881i	$0.471100\pi$
$398$	1778.78	0.224026
$399$	−654.491	−0.0821191
$400$	1513.37	0.189171
$401$	−10674.5	−1.32933	−0.664663	−	0.747143i	$-0.731425\pi$
$401$	−10674.5	−1.32933	−0.664663	+	0.747143i	$0.731425\pi$
$402$	15930.7	1.97649
$403$	2421.76	0.299346
$404$	5360.06	0.660082
$405$	−23174.1	−2.84329
$406$	−2163.36	−0.264448
$407$	1086.98	0.132382
$408$	−23207.9	−2.81608
$409$	−15646.4	−1.89160	−0.945800	−	0.324749i	$-0.894720\pi$
$409$	−15646.4	−1.89160	−0.945800	+	0.324749i	$0.894720\pi$
$410$	−7244.83	−0.872674
$411$	17143.8	2.05752
$412$	18472.9	2.20897
$413$	6731.55	0.802029
$414$	−71629.2	−8.50334
$415$	9667.48	1.14351
$416$	−976.746	−0.115118
$417$	−314.730	−0.0369602
$418$	−158.277	−0.0185205
$419$	8138.71	0.948930	0.474465	−	0.880274i	$-0.342642\pi$
$419$	8138.71	0.948930	0.474465	+	0.880274i	$0.342642\pi$
$420$	31443.4	3.65305
$421$	12341.3	1.42869	0.714344	−	0.699794i	$-0.246725\pi$
$421$	12341.3	1.42869	0.714344	+	0.699794i	$0.246725\pi$
$422$	19876.4	2.29281
$423$	26040.0	2.99317
$424$	23171.6	2.65404
$425$	1288.34	0.147044
$426$	43836.9	4.98569
$427$	−173.809	−0.0196984
$428$	28536.7	3.22284
$429$	4058.91	0.456797
$430$	0	0
$431$	−4911.01	−0.548852	−0.274426	−	0.961608i	$-0.588488\pi$
$431$	−4911.01	−0.548852	−0.274426	+	0.961608i	$0.588488\pi$
$432$	26680.9	2.97149
$433$	7904.54	0.877293	0.438647	−	0.898660i	$-0.355458\pi$
$433$	7904.54	0.877293	0.438647	+	0.898660i	$0.355458\pi$
$434$	3690.66	0.408196
$435$	3117.49	0.343615
$436$	3894.32	0.427762
$437$	893.587	0.0978171
$438$	−19018.1	−2.07470
$439$	2621.30	0.284984	0.142492	−	0.989796i	$-0.454488\pi$
$439$	2621.30	0.284984	0.142492	+	0.989796i	$0.454488\pi$
$440$	3855.68	0.417755
$441$	−4655.40	−0.502688
$442$	−15557.5	−1.67420
$443$	−3062.03	−0.328401	−0.164200	−	0.986427i	$-0.552504\pi$
$443$	−3062.03	−0.328401	−0.164200	+	0.986427i	$0.552504\pi$
$444$	21725.7	2.32219
$445$	1393.41	0.148436
$446$	24805.2	2.63354
$447$	11762.1	1.24458
$448$	7707.10	0.812782
$449$	3287.56	0.345544	0.172772	−	0.984962i	$-0.444728\pi$
$449$	3287.56	0.345544	0.172772	+	0.984962i	$0.444728\pi$
$450$	−7137.93	−0.747746
$451$	−954.633	−0.0996717
$452$	−2053.06	−0.213645
$453$	−26035.9	−2.70039
$454$	−2873.63	−0.297062
$455$	10687.9	1.10122
$456$	−1604.08	−0.164732
$457$	−9817.31	−1.00489	−0.502445	−	0.864609i	$-0.667566\pi$
$457$	−9817.31	−1.00489	−0.502445	+	0.864609i	$0.667566\pi$
$458$	−10725.7	−1.09428
$459$	22713.5	2.30975
$460$	−42930.2	−4.35137
$461$	−4828.27	−0.487798	−0.243899	−	0.969801i	$-0.578427\pi$
$461$	−4828.27	−0.487798	−0.243899	+	0.969801i	$0.578427\pi$
$462$	6185.60	0.622901
$463$	7617.57	0.764619	0.382310	−	0.924034i	$-0.375129\pi$
$463$	7617.57	0.764619	0.382310	+	0.924034i	$0.375129\pi$
$464$	−1849.52	−0.185047
$465$	−5318.39	−0.530397
$466$	−18627.7	−1.85174
$467$	−11061.3	−1.09605	−0.548024	−	0.836462i	$-0.684620\pi$
$467$	−11061.3	−1.09605	−0.548024	+	0.836462i	$0.684620\pi$
$468$	57735.1	5.70257
$469$	5527.45	0.544209
$470$	23300.1	2.28671
$471$	834.627	0.0816509
$472$	16498.2	1.60888
$473$	0	0
$474$	21589.8	2.09209
$475$	89.0470	0.00860159
$476$	−15880.7	−1.52918
$477$	−38123.6	−3.65945
$478$	−22229.2	−2.12707
$479$	−2618.44	−0.249770	−0.124885	−	0.992171i	$-0.539856\pi$
$479$	−2618.44	−0.249770	−0.124885	+	0.992171i	$0.539856\pi$
$480$	2145.02	0.203971
$481$	7384.72	0.700029
$482$	−8385.88	−0.792462
$483$	−34922.1	−3.28988
$484$	−20598.9	−1.93453
$485$	−6591.98	−0.617168
$486$	−40134.0	−3.74592
$487$	5793.31	0.539055	0.269528	−	0.962993i	$-0.413132\pi$
$487$	5793.31	0.539055	0.269528	+	0.962993i	$0.413132\pi$
$488$	−425.985	−0.0395152
$489$	−26463.0	−2.44724
$490$	−4165.56	−0.384042
$491$	−14178.8	−1.30321	−0.651607	−	0.758557i	$-0.725905\pi$
$491$	−14178.8	−1.30321	−0.651607	+	0.758557i	$0.725905\pi$
$492$	−19080.4	−1.74840
$493$	−1574.51	−0.143838
$494$	−1075.30	−0.0979353
$495$	−6343.63	−0.576010
$496$	3155.25	0.285635
$497$	15210.0	1.37276
$498$	38011.6	3.42036
$499$	−3755.15	−0.336881	−0.168440	−	0.985712i	$-0.553873\pi$
$499$	−3755.15	−0.336881	−0.168440	+	0.985712i	$0.553873\pi$
$500$	20297.7	1.81548
$501$	26662.4	2.37762
$502$	−19743.0	−1.75532
$503$	3405.28	0.301857	0.150928	−	0.988545i	$-0.451774\pi$
$503$	3405.28	0.301857	0.150928	+	0.988545i	$0.451774\pi$
$504$	44613.8	3.94297
$505$	−4001.11	−0.352568
$506$	−8445.30	−0.741975
$507$	6315.14	0.553186
$508$	16807.4	1.46793
$509$	8489.02	0.739232	0.369616	−	0.929185i	$-0.379489\pi$
$509$	8489.02	0.739232	0.369616	+	0.929185i	$0.379489\pi$
$510$	34165.6	2.96643
$511$	−6598.68	−0.571250
$512$	21264.8	1.83551
$513$	1569.91	0.135113
$514$	−5841.23	−0.501256
$515$	−13789.4	−1.17987
$516$	0	0
$517$	3070.20	0.261175
$518$	11254.0	0.954579
$519$	31688.3	2.68008
$520$	26194.7	2.20906
$521$	13626.1	1.14582	0.572909	−	0.819619i	$-0.305815\pi$
$521$	13626.1	1.14582	0.572909	+	0.819619i	$0.305815\pi$
$522$	8723.43	0.731445
$523$	−7776.31	−0.650161	−0.325081	−	0.945686i	$-0.605391\pi$
$523$	−7776.31	−0.650161	−0.325081	+	0.945686i	$0.605391\pi$
$524$	44742.3	3.73011
$525$	−3480.03	−0.289297
$526$	−37059.8	−3.07202
$527$	2686.08	0.222026
$528$	5288.26	0.435875
$529$	35512.7	2.91878
$530$	−34112.2	−2.79574
$531$	−27144.0	−2.21836
$532$	−1097.64	−0.0894523
$533$	−6485.57	−0.527057
$534$	5478.76	0.443987
$535$	−21301.7	−1.72141
$536$	13547.1	1.09169
$537$	17398.9	1.39817
$538$	33616.6	2.69389
$539$	−548.885	−0.0438630
$540$	−75422.5	−6.01050
$541$	−21705.1	−1.72491	−0.862454	−	0.506135i	$-0.831074\pi$
$541$	−21705.1	−1.72491	−0.862454	+	0.506135i	$0.831074\pi$
$542$	−8665.97	−0.686781
$543$	22539.6	1.78133
$544$	−1083.35	−0.0853830
$545$	−2906.98	−0.228479
$546$	42023.7	3.29386
$547$	−7157.45	−0.559471	−0.279735	−	0.960077i	$-0.590247\pi$
$547$	−7157.45	−0.559471	−0.279735	+	0.960077i	$0.590247\pi$
$548$	28751.7	2.24126
$549$	700.860	0.0544845
$550$	−841.584	−0.0652459
$551$	−108.826	−0.00841408
$552$	−85589.9	−6.59954
$553$	7490.97	0.576037
$554$	−38641.7	−2.96341
$555$	−16217.5	−1.24035
$556$	−527.829	−0.0402607
$557$	−16739.4	−1.27338	−0.636689	−	0.771121i	$-0.719696\pi$
$557$	−16739.4	−1.27338	−0.636689	+	0.771121i	$0.719696\pi$
$558$	−14882.0	−1.12904
$559$	0	0
$560$	13925.0	1.05078
$561$	4501.92	0.338808
$562$	−32201.0	−2.41694
$563$	−13913.1	−1.04150	−0.520752	−	0.853708i	$-0.674348\pi$
$563$	−13913.1	−1.04150	−0.520752	+	0.853708i	$0.674348\pi$
$564$	61364.6	4.58141
$565$	1532.54	0.114114
$566$	3761.62	0.279351
$567$	−31615.2	−2.34165
$568$	37277.9	2.75378
$569$	23027.2	1.69658	0.848288	−	0.529535i	$-0.177633\pi$
$569$	23027.2	1.69658	0.848288	+	0.529535i	$0.177633\pi$
$570$	2361.45	0.173527
$571$	22191.3	1.62641	0.813203	−	0.581981i	$-0.197722\pi$
$571$	22191.3	1.62641	0.813203	+	0.581981i	$0.197722\pi$
$572$	6807.14	0.497589
$573$	45446.9	3.31339
$574$	−9883.73	−0.718709
$575$	4751.34	0.344600
$576$	−31077.8	−2.24810
$577$	−431.840	−0.0311573	−0.0155786	−	0.999879i	$-0.504959\pi$
$577$	−431.840	−0.0311573	−0.0155786	+	0.999879i	$0.504959\pi$
$578$	6927.74	0.498540
$579$	22621.2	1.62367
$580$	5228.30	0.374299
$581$	13188.8	0.941764
$582$	−25919.0	−1.84601
$583$	−4494.88	−0.319312
$584$	−16172.6	−1.14593
$585$	−43097.3	−3.04590
$586$	2069.48	0.145886
$587$	−20958.0	−1.47365	−0.736823	−	0.676085i	$-0.763675\pi$
$587$	−20958.0	−1.47365	−0.736823	+	0.676085i	$0.763675\pi$
$588$	−10970.7	−0.769426
$589$	185.656	0.0129878
$590$	−24287.9	−1.69478
$591$	−2934.07	−0.204216
$592$	9621.37	0.667966
$593$	14753.4	1.02167	0.510835	−	0.859679i	$-0.329336\pi$
$593$	14753.4	1.02167	0.510835	+	0.859679i	$0.329336\pi$
$594$	−14837.2	−1.02488
$595$	11854.4	0.816777
$596$	19726.0	1.35572
$597$	−3496.97	−0.239735
$598$	−57375.6	−3.92351
$599$	11559.2	0.788475	0.394238	−	0.919009i	$-0.371009\pi$
$599$	11559.2	0.788475	0.394238	+	0.919009i	$0.371009\pi$
$600$	−8529.14	−0.580334
$601$	24817.2	1.68438	0.842192	−	0.539177i	$-0.181265\pi$
$601$	24817.2	1.68438	0.842192	+	0.539177i	$0.181265\pi$
$602$	0	0
$603$	−22288.6	−1.50525
$604$	−43664.5	−2.94153
$605$	15376.4	1.03329
$606$	−15732.0	−1.05457
$607$	7427.73	0.496676	0.248338	−	0.968673i	$-0.420116\pi$
$607$	7427.73	0.496676	0.248338	+	0.968673i	$0.420116\pi$
$608$	−74.8789	−0.00499464
$609$	4253.03	0.282991
$610$	627.116	0.0416249
$611$	20858.3	1.38107
$612$	64036.5	4.22961
$613$	1659.30	0.109329	0.0546643	−	0.998505i	$-0.482591\pi$
$613$	1659.30	0.109329	0.0546643	+	0.998505i	$0.482591\pi$
$614$	23675.3	1.55612
$615$	14242.9	0.933867
$616$	5260.10	0.344051
$617$	−3193.39	−0.208365	−0.104182	−	0.994558i	$-0.533223\pi$
$617$	−3193.39	−0.208365	−0.104182	+	0.994558i	$0.533223\pi$
$618$	−54218.6	−3.52911
$619$	19842.5	1.28843	0.644213	−	0.764846i	$-0.277185\pi$
$619$	19842.5	1.28843	0.644213	+	0.764846i	$0.277185\pi$
$620$	−8919.40	−0.577761
$621$	83766.8	5.41296
$622$	8555.07	0.551490
$623$	1900.96	0.122248
$624$	35927.3	2.30488
$625$	−17871.5	−1.14377
$626$	46634.9	2.97748
$627$	311.163	0.0198192
$628$	1399.74	0.0889423
$629$	8190.72	0.519214
$630$	−65678.4	−4.15347
$631$	388.456	0.0245074	0.0122537	−	0.999925i	$-0.496099\pi$
$631$	388.456	0.0245074	0.0122537	+	0.999925i	$0.496099\pi$
$632$	18359.5	1.15554
$633$	−39075.7	−2.45359
$634$	−2276.67	−0.142615
$635$	−12546.1	−0.784061
$636$	−89839.9	−5.60123
$637$	−3729.01	−0.231945
$638$	1028.52	0.0638236
$639$	−61332.2	−3.79697
$640$	−29581.1	−1.82702
$641$	11219.2	0.691314	0.345657	−	0.938361i	$-0.387656\pi$
$641$	11219.2	0.691314	0.345657	+	0.938361i	$0.387656\pi$
$642$	−83756.2	−5.14890
$643$	−6657.71	−0.408327	−0.204164	−	0.978937i	$-0.565447\pi$
$643$	−6657.71	−0.408327	−0.204164	+	0.978937i	$0.565447\pi$
$644$	−58567.4	−3.58366
$645$	0	0
$646$	−1192.66	−0.0726389
$647$	−10250.9	−0.622884	−0.311442	−	0.950265i	$-0.600812\pi$
$647$	−10250.9	−0.622884	−0.311442	+	0.950265i	$0.600812\pi$
$648$	−77485.0	−4.69738
$649$	−3200.36	−0.193567
$650$	−5717.54	−0.345016
$651$	−7255.60	−0.436819
$652$	−44380.7	−2.66577
$653$	−588.091	−0.0352431	−0.0176216	−	0.999845i	$-0.505609\pi$
$653$	−588.091	−0.0352431	−0.0176216	+	0.999845i	$0.505609\pi$
$654$	−11430.0	−0.683405
$655$	−33398.6	−1.99236
$656$	−8449.90	−0.502916
$657$	26608.2	1.58004
$658$	31787.1	1.88327
$659$	−8335.00	−0.492694	−0.246347	−	0.969182i	$-0.579230\pi$
$659$	−8335.00	−0.492694	−0.246347	+	0.969182i	$0.579230\pi$
$660$	−14949.1	−0.881654
$661$	29410.1	1.73059	0.865294	−	0.501264i	$-0.167132\pi$
$661$	29410.1	1.73059	0.865294	+	0.501264i	$0.167132\pi$
$662$	−46110.4	−2.70715
$663$	30585.1	1.79159
$664$	32324.2	1.88919
$665$	819.349	0.0477789
$666$	−45380.1	−2.64030
$667$	−5806.73	−0.337088
$668$	44715.1	2.58994
$669$	−48765.4	−2.81820
$670$	−19943.4	−1.14997
$671$	82.6335	0.00475414
$672$	2926.33	0.167985
$673$	9059.55	0.518900	0.259450	−	0.965757i	$-0.416459\pi$
$673$	9059.55	0.518900	0.259450	+	0.965757i	$0.416459\pi$
$674$	30797.4	1.76005
$675$	8347.46	0.475991
$676$	10591.0	0.602585
$677$	−10236.5	−0.581122	−0.290561	−	0.956856i	$-0.593842\pi$
$677$	−10236.5	−0.581122	−0.290561	+	0.956856i	$0.593842\pi$
$678$	6025.79	0.341326
$679$	−8993.09	−0.508281
$680$	29053.7	1.63847
$681$	5649.38	0.317892
$682$	−1754.64	−0.0985169
$683$	13541.5	0.758638	0.379319	−	0.925266i	$-0.376158\pi$
$683$	13541.5	0.758638	0.379319	+	0.925266i	$0.376158\pi$
$684$	4426.06	0.247419
$685$	−21462.1	−1.19712
$686$	−33586.3	−1.86929
$687$	21086.1	1.17101
$688$	0	0
$689$	−30537.3	−1.68850
$690$	126002.	6.95188
$691$	−16796.7	−0.924711	−0.462355	−	0.886695i	$-0.652996\pi$
$691$	−16796.7	−0.924711	−0.462355	+	0.886695i	$0.652996\pi$
$692$	53144.0	2.91941
$693$	−8654.28	−0.474385
$694$	−10831.9	−0.592469
$695$	394.006	0.0215043
$696$	10423.7	0.567683
$697$	−7193.44	−0.390920
$698$	−28261.6	−1.53254
$699$	36620.9	1.98159
$700$	−5836.31	−0.315131
$701$	12884.0	0.694185	0.347092	−	0.937831i	$-0.387169\pi$
$701$	12884.0	0.694185	0.347092	+	0.937831i	$0.387169\pi$
$702$	−100801.	−5.41950
$703$	566.124	0.0303724
$704$	−3664.16	−0.196162
$705$	−45806.6	−2.44706
$706$	10451.4	0.557142
$707$	−5458.50	−0.290365
$708$	−63966.1	−3.39547
$709$	15061.5	0.797807	0.398903	−	0.916993i	$-0.369391\pi$
$709$	15061.5	0.797807	0.398903	+	0.916993i	$0.369391\pi$
$710$	−54878.9	−2.90080
$711$	−30206.3	−1.59328
$712$	4659.02	0.245230
$713$	9906.18	0.520322
$714$	46610.3	2.44306
$715$	−5081.30	−0.265776
$716$	29179.5	1.52303
$717$	43701.2	2.27622
$718$	2927.90	0.152184
$719$	12135.9	0.629475	0.314737	−	0.949179i	$-0.398084\pi$
$719$	12135.9	0.629475	0.314737	+	0.949179i	$0.398084\pi$
$720$	−56150.4	−2.90639
$721$	−18812.2	−0.971708
$722$	33679.6	1.73605
$723$	16486.1	0.848030
$724$	37800.8	1.94041
$725$	−578.647	−0.0296420
$726$	60458.4	3.09067
$727$	−151.089	−0.00770783	−0.00385392	−	0.999993i	$-0.501227\pi$
$727$	−151.089	−0.00770783	−0.00385392	+	0.999993i	$0.501227\pi$
$728$	35736.0	1.81932
$729$	27251.8	1.38453
$730$	23808.5	1.20711
$731$	0	0
$732$	1651.61	0.0833951
$733$	−10320.6	−0.520054	−0.260027	−	0.965601i	$-0.583732\pi$
$733$	−10320.6	−0.520054	−0.260027	+	0.965601i	$0.583732\pi$
$734$	−30472.4	−1.53236
$735$	8189.22	0.410972
$736$	−3995.37	−0.200097
$737$	−2627.90	−0.131343
$738$	39854.7	1.98790
$739$	15944.6	0.793683	0.396841	−	0.917887i	$-0.370106\pi$
$739$	15944.6	0.793683	0.396841	+	0.917887i	$0.370106\pi$
$740$	−27198.1	−1.35111
$741$	2113.97	0.104803
$742$	−46537.5	−2.30249
$743$	1087.42	0.0536927	0.0268463	−	0.999640i	$-0.491454\pi$
$743$	1087.42	0.0536927	0.0268463	+	0.999640i	$0.491454\pi$
$744$	−17782.6	−0.876265
$745$	−14724.8	−0.724127
$746$	26045.8	1.27829
$747$	−53182.0	−2.60486
$748$	7550.10	0.369063
$749$	−29060.8	−1.41770
$750$	−59574.3	−2.90046
$751$	−9093.18	−0.441831	−0.220915	−	0.975293i	$-0.570904\pi$
$751$	−9093.18	−0.441831	−0.220915	+	0.975293i	$0.570904\pi$
$752$	27175.8	1.31782
$753$	38813.4	1.87841
$754$	6987.54	0.337495
$755$	32594.1	1.57115
$756$	−102895.	−4.95007
$757$	22045.2	1.05845	0.529225	−	0.848481i	$-0.322483\pi$
$757$	22045.2	1.05845	0.529225	+	0.848481i	$0.322483\pi$
$758$	63074.9	3.02240
$759$	16602.9	0.794003
$760$	2008.13	0.0958452
$761$	3992.94	0.190202	0.0951012	−	0.995468i	$-0.469683\pi$
$761$	3992.94	0.190202	0.0951012	+	0.995468i	$0.469683\pi$
$762$	−49330.2	−2.34520
$763$	−3965.84	−0.188169
$764$	76218.3	3.60927
$765$	−47801.1	−2.25915
$766$	44913.8	2.11854
$767$	−21742.6	−1.02357
$768$	−80208.7	−3.76859
$769$	−3082.39	−0.144543	−0.0722716	−	0.997385i	$-0.523025\pi$
$769$	−3082.39	−0.144543	−0.0722716	+	0.997385i	$0.523025\pi$
$770$	−7743.68	−0.362419
$771$	11483.5	0.536405
$772$	37937.7	1.76866
$773$	−20908.0	−0.972845	−0.486423	−	0.873724i	$-0.661698\pi$
$773$	−20908.0	−0.972845	−0.486423	+	0.873724i	$0.661698\pi$
$774$	0	0
$775$	987.163	0.0457548
$776$	−22041.0	−1.01962
$777$	−22124.6	−1.02151
$778$	18555.3	0.855065
$779$	−497.195	−0.0228676
$780$	−101561.	−4.66212
$781$	−7231.25	−0.331312
$782$	−63637.8	−2.91008
$783$	−10201.6	−0.465615
$784$	−4858.44	−0.221321
$785$	−1044.86	−0.0475065
$786$	−131320.	−5.95933
$787$	−23077.4	−1.04526	−0.522630	−	0.852560i	$-0.675049\pi$
$787$	−23077.4	−1.04526	−0.522630	+	0.852560i	$0.675049\pi$
$788$	−4920.69	−0.222452
$789$	72857.2	3.28743
$790$	−27028.0	−1.21723
$791$	2090.76	0.0939809
$792$	−21210.6	−0.951623
$793$	561.394	0.0251396
$794$	−7060.37	−0.315571
$795$	67062.5	2.99177
$796$	−5864.72	−0.261143
$797$	1617.17	0.0718736	0.0359368	−	0.999354i	$-0.488558\pi$
$797$	1617.17	0.0718736	0.0359368	+	0.999354i	$0.488558\pi$
$798$	3221.60	0.142912
$799$	23134.9	1.02435
$800$	−398.143	−0.0175956
$801$	−7665.34	−0.338129
$802$	52543.2	2.31342
$803$	3137.19	0.137869
$804$	−52524.2	−2.30396
$805$	43718.6	1.91413
$806$	−11920.6	−0.520951
$807$	−66088.0	−2.88279
$808$	−13378.1	−0.582476
$809$	20958.4	0.910826	0.455413	−	0.890280i	$-0.349492\pi$
$809$	20958.4	0.910826	0.455413	+	0.890280i	$0.349492\pi$
$810$	114070.	4.94816
$811$	−6257.79	−0.270950	−0.135475	−	0.990781i	$-0.543256\pi$
$811$	−6257.79	−0.270950	−0.135475	+	0.990781i	$0.543256\pi$
$812$	7132.69	0.308262
$813$	17036.8	0.734939
$814$	−5350.45	−0.230385
$815$	33128.7	1.42386
$816$	39848.6	1.70953
$817$	0	0
$818$	77016.3	3.29195
$819$	−58795.3	−2.50852
$820$	23886.5	1.01726
$821$	−10551.1	−0.448523	−0.224261	−	0.974529i	$-0.571997\pi$
$821$	−10551.1	−0.448523	−0.224261	+	0.974529i	$0.571997\pi$
$822$	−84387.1	−3.58070
$823$	15088.1	0.639051	0.319525	−	0.947578i	$-0.396477\pi$
$823$	15088.1	0.639051	0.319525	+	0.947578i	$0.396477\pi$
$824$	−46106.3	−1.94926
$825$	1654.50	0.0698210
$826$	−33134.7	−1.39577
$827$	28806.9	1.21126	0.605632	−	0.795745i	$-0.292920\pi$
$827$	28806.9	1.21126	0.605632	+	0.795745i	$0.292920\pi$
$828$	236165.	9.91219
$829$	4253.71	0.178212	0.0891059	−	0.996022i	$-0.471599\pi$
$829$	4253.71	0.178212	0.0891059	+	0.996022i	$0.471599\pi$
$830$	−47586.2	−1.99005
$831$	75967.2	3.17121
$832$	−24893.5	−1.03729
$833$	−4136.01	−0.172034
$834$	1549.19	0.0643216
$835$	−33378.3	−1.38336
$836$	521.846	0.0215890
$837$	17403.8	0.718714
$838$	−40061.2	−1.65142
$839$	6016.63	0.247577	0.123789	−	0.992309i	$-0.460496\pi$
$839$	6016.63	0.247577	0.123789	+	0.992309i	$0.460496\pi$
$840$	−78479.3	−3.22356
$841$	−23681.8	−0.971004
$842$	−60747.6	−2.48634
$843$	63305.2	2.58642
$844$	−65533.3	−2.67269
$845$	−7905.85	−0.321857
$846$	−128177.	−5.20900
$847$	20977.2	0.850985
$848$	−39786.3	−1.61116
$849$	−7395.11	−0.298939
$850$	−6341.58	−0.255899
$851$	30207.1	1.21679
$852$	−144532.	−5.81173
$853$	20442.6	0.820563	0.410282	−	0.911959i	$-0.365430\pi$
$853$	20442.6	0.820563	0.410282	+	0.911959i	$0.365430\pi$
$854$	855.541	0.0342810
$855$	−3303.91	−0.132154
$856$	−71224.4	−2.84392
$857$	2745.26	0.109424	0.0547120	−	0.998502i	$-0.482576\pi$
$857$	2745.26	0.109424	0.0547120	+	0.998502i	$0.482576\pi$
$858$	−19979.2	−0.794962
$859$	−4762.66	−0.189173	−0.0945866	−	0.995517i	$-0.530153\pi$
$859$	−4762.66	−0.189173	−0.0945866	+	0.995517i	$0.530153\pi$
$860$	0	0
$861$	19430.8	0.769105
$862$	24173.5	0.955165
$863$	30578.2	1.20613	0.603067	−	0.797690i	$-0.293945\pi$
$863$	30578.2	1.20613	0.603067	+	0.797690i	$0.293945\pi$
$864$	−7019.31	−0.276391
$865$	−39670.2	−1.55934
$866$	−38908.5	−1.52675
$867$	−13619.5	−0.533498
$868$	−12168.3	−0.475827
$869$	−3561.41	−0.139025
$870$	−15345.2	−0.597991
$871$	−17853.4	−0.694533
$872$	−9719.78	−0.377469
$873$	36263.3	1.40587
$874$	−4398.50	−0.170231
$875$	−20670.4	−0.798614
$876$	62703.6	2.41844
$877$	36096.8	1.38985	0.694927	−	0.719081i	$-0.255437\pi$
$877$	36096.8	1.38985	0.694927	+	0.719081i	$0.255437\pi$
$878$	−12902.8	−0.495957
$879$	−4068.47	−0.156116
$880$	−6620.30	−0.253603
$881$	−34598.1	−1.32309	−0.661543	−	0.749907i	$-0.730098\pi$
$881$	−34598.1	−1.32309	−0.661543	+	0.749907i	$0.730098\pi$
$882$	22915.3	0.874827
$883$	26271.0	1.00123	0.500617	−	0.865669i	$-0.333107\pi$
$883$	26271.0	1.00123	0.500617	+	0.865669i	$0.333107\pi$
$884$	51293.8	1.95158
$885$	47748.5	1.81362
$886$	15072.2	0.571514
$887$	32276.4	1.22180	0.610900	−	0.791708i	$-0.290808\pi$
$887$	32276.4	1.22180	0.610900	+	0.791708i	$0.290808\pi$
$888$	−54224.8	−2.04917
$889$	−17116.0	−0.645730
$890$	−6858.79	−0.258323
$891$	15030.7	0.565149
$892$	−81783.7	−3.06987
$893$	1599.03	0.0599211
$894$	−57896.4	−2.16594
$895$	−21781.5	−0.813492
$896$	−40355.9	−1.50468
$897$	112797.	4.19863
$898$	−16182.3	−0.601349
$899$	−1206.43	−0.0447573
$900$	23534.1	0.871633
$901$	−33870.3	−1.25237
$902$	4698.99	0.173458
$903$	0	0
$904$	5124.20	0.188527
$905$	−28217.0	−1.03642
$906$	128157.	4.69947
$907$	−14422.4	−0.527989	−0.263995	−	0.964524i	$-0.585040\pi$
$907$	−14422.4	−0.527989	−0.263995	+	0.964524i	$0.585040\pi$
$908$	9474.49	0.346280
$909$	22010.6	0.803130
$910$	−52608.9	−1.91645
$911$	9836.24	0.357727	0.178863	−	0.983874i	$-0.442758\pi$
$911$	9836.24	0.357727	0.178863	+	0.983874i	$0.442758\pi$
$912$	2754.24	0.100002
$913$	−6270.32	−0.227292
$914$	48323.8	1.74881
$915$	−1232.87	−0.0445436
$916$	35363.2	1.27558
$917$	−45564.0	−1.64085
$918$	−111803.	−4.01966
$919$	−30639.2	−1.09978	−0.549888	−	0.835239i	$-0.685329\pi$
$919$	−30639.2	−1.09978	−0.549888	+	0.835239i	$0.685329\pi$
$920$	107149.	3.83978
$921$	−46544.1	−1.66523
$922$	23766.2	0.848913
$923$	−49127.6	−1.75195
$924$	−20394.2	−0.726104
$925$	3010.17	0.106999
$926$	−37496.0	−1.33066
$927$	75857.3	2.68768
$928$	486.580	0.0172120
$929$	−11915.3	−0.420807	−0.210403	−	0.977615i	$-0.567478\pi$
$929$	−11915.3	−0.420807	−0.210403	+	0.977615i	$0.567478\pi$
$930$	26178.7	0.923047
$931$	−285.872	−0.0100635
$932$	61416.4	2.15854
$933$	−16818.7	−0.590161
$934$	54446.9	1.90745
$935$	−5635.90	−0.197127
$936$	−144100.	−5.03212
$937$	−46592.0	−1.62443	−0.812217	−	0.583355i	$-0.801739\pi$
$937$	−46592.0	−1.62443	−0.812217	+	0.583355i	$0.801739\pi$
$938$	−27207.8	−0.947084
$939$	−91681.3	−3.18627
$940$	−76821.5	−2.66558
$941$	49528.8	1.71583	0.857913	−	0.513794i	$-0.171761\pi$
$941$	49528.8	1.71583	0.857913	+	0.513794i	$0.171761\pi$
$942$	−4108.29	−0.142097
$943$	−26529.2	−0.916128
$944$	−28327.9	−0.976688
$945$	76807.6	2.64397
$946$	0	0
$947$	23584.0	0.809270	0.404635	−	0.914478i	$-0.367399\pi$
$947$	23584.0	0.809270	0.404635	+	0.914478i	$0.367399\pi$
$948$	−71182.5	−2.43871
$949$	21313.4	0.729044
$950$	−438.316	−0.0149693
$951$	4475.79	0.152616
$952$	39636.4	1.34939
$953$	40561.5	1.37872	0.689358	−	0.724421i	$-0.257893\pi$
$953$	40561.5	1.37872	0.689358	+	0.724421i	$0.257893\pi$
$954$	187656.	6.36853
$955$	−56894.4	−1.92781
$956$	73290.6	2.47949
$957$	−2022.00	−0.0682990
$958$	12888.8	0.434673
$959$	−29279.7	−0.985912
$960$	54668.3	1.83793
$961$	−27732.8	−0.930913
$962$	−36349.8	−1.21826
$963$	117183.	3.92127
$964$	27648.6	0.923758
$965$	−28319.2	−0.944691
$966$	171897.	5.72537
$967$	−47112.8	−1.56675	−0.783375	−	0.621550i	$-0.786503\pi$
$967$	−47112.8	−1.56675	−0.783375	+	0.621550i	$0.786503\pi$
$968$	51412.5	1.70709
$969$	2344.70	0.0777324
$970$	32447.7	1.07406
$971$	−43186.7	−1.42732	−0.713659	−	0.700493i	$-0.752964\pi$
$971$	−43186.7	−1.42732	−0.713659	+	0.700493i	$0.752964\pi$
$972$	132324.	4.36655
$973$	537.522	0.0177103
$974$	−28516.4	−0.938116
$975$	11240.3	0.369209
$976$	731.427	0.0239881
$977$	4194.95	0.137368	0.0686840	−	0.997638i	$-0.478120\pi$
$977$	4194.95	0.137368	0.0686840	+	0.997638i	$0.478120\pi$
$978$	130259.	4.25892
$979$	−903.767	−0.0295041
$980$	13734.0	0.447671
$981$	15991.7	0.520463
$982$	69792.1	2.26798
$983$	−15244.0	−0.494618	−0.247309	−	0.968937i	$-0.579546\pi$
$983$	−15244.0	−0.494618	−0.247309	+	0.968937i	$0.579546\pi$
$984$	47622.5	1.54284
$985$	3673.13	0.118818
$986$	7750.19	0.250321
$987$	−62491.5	−2.01532
$988$	3545.31	0.114161
$989$	0	0
$990$	31225.3	1.00243
$991$	7237.20	0.231985	0.115993	−	0.993250i	$-0.462995\pi$
$991$	7237.20	0.231985	0.115993	+	0.993250i	$0.462995\pi$
$992$	−830.097	−0.0265682
$993$	90650.1	2.89697
$994$	−74868.3	−2.38901
$995$	4377.82	0.139484
$996$	−125326.	−3.98705
$997$	8259.08	0.262355	0.131177	−	0.991359i	$-0.458124\pi$
$997$	8259.08	0.262355	0.131177	+	0.991359i	$0.458124\pi$
$998$	18484.0	0.586272
$999$	53069.7	1.68073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.10	✓	110
43.42	odd	2	inner	1849.4.a.m.1.101	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.10	✓	110	1.1	even	1	trivial
1849.4.a.m.1.101	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)

\(f(q)\)	\(=\)	\(q-4.92230 q^{2} +9.67693 q^{3} +16.2290 q^{4} -12.1144 q^{5} -47.6328 q^{6} -16.5271 q^{7} -40.5059 q^{8} +66.6431 q^{9} +O(q^{10})\)	\(q-4.92230 q^{2} +9.67693 q^{3} +16.2290 q^{4} -12.1144 q^{5} -47.6328 q^{6} -16.5271 q^{7} -40.5059 q^{8} +66.6431 q^{9} +59.6309 q^{10} +7.85742 q^{11} +157.047 q^{12} +53.3816 q^{13} +81.3513 q^{14} -117.231 q^{15} +69.5496 q^{16} +59.2079 q^{17} -328.037 q^{18} +4.09232 q^{19} -196.606 q^{20} -159.931 q^{21} -38.6766 q^{22} +218.357 q^{23} -391.973 q^{24} +21.7595 q^{25} -262.760 q^{26} +383.623 q^{27} -268.219 q^{28} -26.5928 q^{29} +577.044 q^{30} +45.3669 q^{31} -18.2974 q^{32} +76.0357 q^{33} -291.439 q^{34} +200.216 q^{35} +1081.55 q^{36} +138.338 q^{37} -20.1436 q^{38} +516.570 q^{39} +490.706 q^{40} -121.495 q^{41} +787.231 q^{42} +127.518 q^{44} -807.343 q^{45} -1074.82 q^{46} +390.739 q^{47} +673.027 q^{48} -69.8557 q^{49} -107.107 q^{50} +572.951 q^{51} +866.333 q^{52} -572.056 q^{53} -1888.31 q^{54} -95.1882 q^{55} +669.443 q^{56} +39.6011 q^{57} +130.898 q^{58} -407.304 q^{59} -1902.54 q^{60} +10.5166 q^{61} -223.310 q^{62} -1101.41 q^{63} -466.332 q^{64} -646.688 q^{65} -374.271 q^{66} -334.448 q^{67} +960.889 q^{68} +2113.03 q^{69} -985.524 q^{70} -920.309 q^{71} -2699.43 q^{72} +399.265 q^{73} -680.942 q^{74} +210.566 q^{75} +66.4145 q^{76} -129.860 q^{77} -2542.72 q^{78} -453.255 q^{79} -842.555 q^{80} +1912.93 q^{81} +598.033 q^{82} -798.013 q^{83} -2595.54 q^{84} -717.271 q^{85} -257.337 q^{87} -318.271 q^{88} -115.021 q^{89} +3973.99 q^{90} -882.242 q^{91} +3543.73 q^{92} +439.013 q^{93} -1923.34 q^{94} -49.5762 q^{95} -177.063 q^{96} +544.143 q^{97} +343.851 q^{98} +523.642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more