LMFDB - Embedded newform 1849.4.a.i.1.17

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:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.53235 q^{2} +8.01322 q^{3} -1.58719 q^{4} +20.7136 q^{5} -20.2923 q^{6} +3.06093 q^{7} +24.2781 q^{8} +37.2117 q^{9} +O(q^{10})$	\(q-2.53235 q^{2} +8.01322 q^{3} -1.58719 q^{4} +20.7136 q^{5} -20.2923 q^{6} +3.06093 q^{7} +24.2781 q^{8} +37.2117 q^{9} -52.4541 q^{10} -50.3240 q^{11} -12.7185 q^{12} -26.3471 q^{13} -7.75136 q^{14} +165.983 q^{15} -48.7833 q^{16} -23.1013 q^{17} -94.2331 q^{18} -135.885 q^{19} -32.8765 q^{20} +24.5279 q^{21} +127.438 q^{22} -91.8712 q^{23} +194.546 q^{24} +304.053 q^{25} +66.7201 q^{26} +81.8285 q^{27} -4.85830 q^{28} -15.5009 q^{29} -420.326 q^{30} -34.9791 q^{31} -70.6888 q^{32} -403.257 q^{33} +58.5007 q^{34} +63.4029 q^{35} -59.0622 q^{36} -221.246 q^{37} +344.110 q^{38} -211.125 q^{39} +502.888 q^{40} +206.730 q^{41} -62.1133 q^{42} +79.8739 q^{44} +770.788 q^{45} +232.650 q^{46} -600.224 q^{47} -390.911 q^{48} -333.631 q^{49} -769.970 q^{50} -185.116 q^{51} +41.8180 q^{52} +408.162 q^{53} -207.218 q^{54} -1042.39 q^{55} +74.3138 q^{56} -1088.88 q^{57} +39.2539 q^{58} -740.433 q^{59} -263.447 q^{60} +51.7496 q^{61} +88.5794 q^{62} +113.902 q^{63} +569.275 q^{64} -545.743 q^{65} +1021.19 q^{66} +334.159 q^{67} +36.6663 q^{68} -736.184 q^{69} -160.559 q^{70} -487.740 q^{71} +903.431 q^{72} -722.667 q^{73} +560.272 q^{74} +2436.45 q^{75} +215.677 q^{76} -154.038 q^{77} +534.643 q^{78} -171.428 q^{79} -1010.48 q^{80} -349.006 q^{81} -523.513 q^{82} -241.764 q^{83} -38.9306 q^{84} -478.511 q^{85} -124.213 q^{87} -1221.77 q^{88} -333.067 q^{89} -1951.91 q^{90} -80.6467 q^{91} +145.817 q^{92} -280.295 q^{93} +1519.98 q^{94} -2814.68 q^{95} -566.445 q^{96} +687.004 q^{97} +844.870 q^{98} -1872.64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * 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 $

$2$	−2.53235	−0.895322	−0.447661	−	0.894203i	$-0.647743\pi$
$2$	−2.53235	−0.895322	−0.447661	+	0.894203i	$0.647743\pi$
$3$	8.01322	1.54214	0.771072	−	0.636747i	$-0.219721\pi$
$3$	8.01322	1.54214	0.771072	+	0.636747i	$0.219721\pi$
$4$	−1.58719	−0.198399
$5$	20.7136	1.85268	0.926340	−	0.376687i	$-0.122937\pi$
$5$	20.7136	1.85268	0.926340	+	0.376687i	$0.122937\pi$
$6$	−20.2923	−1.38072
$7$	3.06093	0.165275	0.0826374	−	0.996580i	$-0.473666\pi$
$7$	3.06093	0.165275	0.0826374	+	0.996580i	$0.473666\pi$
$8$	24.2781	1.07295
$9$	37.2117	1.37821
$10$	−52.4541	−1.65875
$11$	−50.3240	−1.37939	−0.689693	−	0.724102i	$-0.742255\pi$
$11$	−50.3240	−1.37939	−0.689693	+	0.724102i	$0.742255\pi$
$12$	−12.7185	−0.305961
$13$	−26.3471	−0.562105	−0.281053	−	0.959692i	$-0.590684\pi$
$13$	−26.3471	−0.562105	−0.281053	+	0.959692i	$0.590684\pi$
$14$	−7.75136	−0.147974
$15$	165.983	2.85710
$16$	−48.7833	−0.762238
$17$	−23.1013	−0.329582	−0.164791	−	0.986329i	$-0.552695\pi$
$17$	−23.1013	−0.329582	−0.164791	+	0.986329i	$0.552695\pi$
$18$	−94.2331	−1.23394
$19$	−135.885	−1.64075	−0.820375	−	0.571826i	$-0.806235\pi$
$19$	−135.885	−1.64075	−0.820375	+	0.571826i	$0.806235\pi$
$20$	−32.8765	−0.367571
$21$	24.5279	0.254878
$22$	127.438	1.23499
$23$	−91.8712	−0.832890	−0.416445	−	0.909161i	$-0.636724\pi$
$23$	−91.8712	−0.832890	−0.416445	+	0.909161i	$0.636724\pi$
$24$	194.546	1.65465
$25$	304.053	2.43243
$26$	66.7201	0.503265
$27$	81.8285	0.583255
$28$	−4.85830	−0.0327904
$29$	−15.5009	−0.0992570	−0.0496285	−	0.998768i	$-0.515804\pi$
$29$	−15.5009	−0.0992570	−0.0496285	+	0.998768i	$0.515804\pi$
$30$	−420.326	−2.55802
$31$	−34.9791	−0.202659	−0.101330	−	0.994853i	$-0.532310\pi$
$31$	−34.9791	−0.202659	−0.101330	+	0.994853i	$0.532310\pi$
$32$	−70.6888	−0.390504
$33$	−403.257	−2.12721
$34$	58.5007	0.295082
$35$	63.4029	0.306201
$36$	−59.0622	−0.273436
$37$	−221.246	−0.983043	−0.491522	−	0.870865i	$-0.663559\pi$
$37$	−221.246	−0.983043	−0.491522	+	0.870865i	$0.663559\pi$
$38$	344.110	1.46900
$39$	−211.125	−0.866848
$40$	502.888	1.98784
$41$	206.730	0.787459	0.393729	−	0.919226i	$-0.371185\pi$
$41$	206.730	0.787459	0.393729	+	0.919226i	$0.371185\pi$
$42$	−62.1133	−0.228197
$43$	0	0
$43$	0	0
$44$	79.8739	0.273669
$45$	770.788	2.55338
$46$	232.650	0.745704
$47$	−600.224	−1.86280	−0.931400	−	0.363997i	$-0.881412\pi$
$47$	−600.224	−1.86280	−0.931400	+	0.363997i	$0.881412\pi$
$48$	−390.911	−1.17548
$49$	−333.631	−0.972684
$50$	−769.970	−2.17780
$51$	−185.116	−0.508263
$52$	41.8180	0.111521
$53$	408.162	1.05784	0.528919	−	0.848672i	$-0.322598\pi$
$53$	408.162	1.05784	0.528919	+	0.848672i	$0.322598\pi$
$54$	−207.218	−0.522201
$55$	−1042.39	−2.55556
$56$	74.3138	0.177332
$57$	−1088.88	−2.53027
$58$	39.2539	0.0888670
$59$	−740.433	−1.63383	−0.816916	−	0.576756i	$-0.804318\pi$
$59$	−740.433	−1.63383	−0.816916	+	0.576756i	$0.804318\pi$
$60$	−263.447	−0.566847
$61$	51.7496	0.108621	0.0543103	−	0.998524i	$-0.482704\pi$
$61$	51.7496	0.108621	0.0543103	+	0.998524i	$0.482704\pi$
$62$	88.5794	0.181445
$63$	113.902	0.227783
$64$	569.275	1.11187
$65$	−545.743	−1.04140
$66$	1021.19	1.90454
$67$	334.159	0.609314	0.304657	−	0.952462i	$-0.401458\pi$
$67$	334.159	0.609314	0.304657	+	0.952462i	$0.401458\pi$
$68$	36.6663	0.0653888
$69$	−736.184	−1.28444
$70$	−160.559	−0.274149
$71$	−487.740	−0.815269	−0.407634	−	0.913145i	$-0.633646\pi$
$71$	−487.740	−0.815269	−0.407634	+	0.913145i	$0.633646\pi$
$72$	903.431	1.47875
$73$	−722.667	−1.15865	−0.579327	−	0.815095i	$-0.696685\pi$
$73$	−722.667	−1.15865	−0.579327	+	0.815095i	$0.696685\pi$
$74$	560.272	0.880140
$75$	2436.45	3.75115
$76$	215.677	0.325524
$77$	−154.038	−0.227978
$78$	534.643	0.776107
$79$	−171.428	−0.244141	−0.122071	−	0.992521i	$-0.538953\pi$
$79$	−171.428	−0.244141	−0.122071	+	0.992521i	$0.538953\pi$
$80$	−1010.48	−1.41218
$81$	−349.006	−0.478746
$82$	−523.513	−0.705029
$83$	−241.764	−0.319724	−0.159862	−	0.987139i	$-0.551105\pi$
$83$	−241.764	−0.319724	−0.159862	+	0.987139i	$0.551105\pi$
$84$	−38.9306	−0.0505676
$85$	−478.511	−0.610610
$86$	0	0
$87$	−124.213	−0.153069
$88$	−1221.77	−1.48002
$89$	−333.067	−0.396686	−0.198343	−	0.980133i	$-0.563556\pi$
$89$	−333.067	−0.396686	−0.198343	+	0.980133i	$0.563556\pi$
$90$	−1951.91	−2.28610
$91$	−80.6467	−0.0929019
$92$	145.817	0.165245
$93$	−280.295	−0.312530
$94$	1519.98	1.66781
$95$	−2814.68	−3.03979
$96$	−566.445	−0.602214
$97$	687.004	0.719120	0.359560	−	0.933122i	$-0.382927\pi$
$97$	687.004	0.719120	0.359560	+	0.933122i	$0.382927\pi$
$98$	844.870	0.870865
$99$	−1872.64	−1.90108
$100$	−482.592	−0.482592
$101$	918.164	0.904561	0.452281	−	0.891876i	$-0.350611\pi$
$101$	918.164	0.904561	0.452281	+	0.891876i	$0.350611\pi$
$102$	468.779	0.455059
$103$	−348.289	−0.333184	−0.166592	−	0.986026i	$-0.553276\pi$
$103$	−348.289	−0.333184	−0.166592	+	0.986026i	$0.553276\pi$
$104$	−639.659	−0.603112
$105$	508.062	0.472207
$106$	−1033.61	−0.947105
$107$	830.251	0.750125	0.375063	−	0.927000i	$-0.377621\pi$
$107$	830.251	0.750125	0.375063	+	0.927000i	$0.377621\pi$
$108$	−129.878	−0.115717
$109$	−295.829	−0.259957	−0.129979	−	0.991517i	$-0.541491\pi$
$109$	−295.829	−0.259957	−0.129979	+	0.991517i	$0.541491\pi$
$110$	2639.70	2.28805
$111$	−1772.89	−1.51599
$112$	−149.322	−0.125979
$113$	1631.99	1.35862	0.679311	−	0.733850i	$-0.262279\pi$
$113$	1631.99	1.35862	0.679311	+	0.733850i	$0.262279\pi$
$114$	2757.43	2.26541
$115$	−1902.98	−1.54308
$116$	24.6030	0.0196925
$117$	−980.420	−0.774699
$118$	1875.04	1.46281
$119$	−70.7116	−0.0544716
$120$	4029.75	3.06554
$121$	1201.50	0.902706
$122$	−131.048	−0.0972503
$123$	1656.57	1.21438
$124$	55.5186	0.0402074
$125$	3708.84	2.65383
$126$	−288.441	−0.203939
$127$	243.422	0.170080	0.0850401	−	0.996378i	$-0.472898\pi$
$127$	243.422	0.170080	0.0850401	+	0.996378i	$0.472898\pi$
$128$	−876.094	−0.604973
$129$	0	0
$130$	1382.01	0.932389
$131$	−2342.26	−1.56217	−0.781083	−	0.624427i	$-0.785333\pi$
$131$	−2342.26	−1.56217	−0.781083	+	0.624427i	$0.785333\pi$
$132$	640.047	0.422038
$133$	−415.936	−0.271175
$134$	−846.208	−0.545532
$135$	1694.96	1.08059
$136$	−560.857	−0.353626
$137$	1232.79	0.768788	0.384394	−	0.923169i	$-0.374410\pi$
$137$	1232.79	0.768788	0.384394	+	0.923169i	$0.374410\pi$
$138$	1864.28	1.14998
$139$	−310.063	−0.189203	−0.0946014	−	0.995515i	$-0.530158\pi$
$139$	−310.063	−0.189203	−0.0946014	+	0.995515i	$0.530158\pi$
$140$	−100.633	−0.0607502
$141$	−4809.72	−2.87271
$142$	1235.13	0.729928
$143$	1325.89	0.775360
$144$	−1815.31	−1.05052
$145$	−321.080	−0.183892
$146$	1830.05	1.03737
$147$	−2673.46	−1.50002
$148$	351.160	0.195035
$149$	2522.04	1.38667	0.693334	−	0.720616i	$-0.256141\pi$
$149$	2522.04	1.38667	0.693334	+	0.720616i	$0.256141\pi$
$150$	−6169.94	−3.35849
$151$	−999.113	−0.538455	−0.269227	−	0.963077i	$-0.586768\pi$
$151$	−999.113	−0.538455	−0.269227	+	0.963077i	$0.586768\pi$
$152$	−3299.05	−1.76045
$153$	−859.639	−0.454233
$154$	390.079	0.204113
$155$	−724.543	−0.375462
$156$	335.097	0.171982
$157$	−1192.13	−0.606002	−0.303001	−	0.952990i	$-0.597989\pi$
$157$	−1192.13	−0.606002	−0.303001	+	0.952990i	$0.597989\pi$
$158$	434.116	0.218585
$159$	3270.69	1.63134
$160$	−1464.22	−0.723480
$161$	−281.212	−0.137656
$162$	883.806	0.428632
$163$	−114.218	−0.0548847	−0.0274424	−	0.999623i	$-0.508736\pi$
$163$	−114.218	−0.0548847	−0.0274424	+	0.999623i	$0.508736\pi$
$164$	−328.121	−0.156231
$165$	−8352.91	−3.94105
$166$	612.232	0.286256
$167$	3106.64	1.43952	0.719758	−	0.694225i	$-0.244253\pi$
$167$	3106.64	1.43952	0.719758	+	0.694225i	$0.244253\pi$
$168$	595.493	0.273472
$169$	−1502.83	−0.684038
$170$	1211.76	0.546692
$171$	−5056.53	−2.26130
$172$	0	0
$173$	−2342.86	−1.02962	−0.514810	−	0.857304i	$-0.672138\pi$
$173$	−2342.86	−1.02962	−0.514810	+	0.857304i	$0.672138\pi$
$174$	314.550	0.137046
$175$	930.687	0.402019
$176$	2454.97	1.05142
$177$	−5933.25	−2.51961
$178$	843.442	0.355161
$179$	1671.04	0.697762	0.348881	−	0.937167i	$-0.386562\pi$
$179$	1671.04	0.697762	0.348881	+	0.937167i	$0.386562\pi$
$180$	−1223.39	−0.506590
$181$	2195.16	0.901465	0.450732	−	0.892659i	$-0.351163\pi$
$181$	2195.16	0.901465	0.450732	+	0.892659i	$0.351163\pi$
$182$	204.226	0.0831770
$183$	414.681	0.167509
$184$	−2230.46	−0.893652
$185$	−4582.80	−1.82127
$186$	709.806	0.279814
$187$	1162.55	0.454621
$188$	952.672	0.369578
$189$	250.471	0.0963974
$190$	7127.75	2.72159
$191$	79.6602	0.0301781	0.0150890	−	0.999886i	$-0.495197\pi$
$191$	79.6602	0.0301781	0.0150890	+	0.999886i	$0.495197\pi$
$192$	4561.73	1.71466
$193$	1109.31	0.413730	0.206865	−	0.978369i	$-0.433674\pi$
$193$	1109.31	0.413730	0.206865	+	0.978369i	$0.433674\pi$
$194$	−1739.73	−0.643844
$195$	−4373.16	−1.60599
$196$	529.537	0.192980
$197$	2392.69	0.865340	0.432670	−	0.901552i	$-0.357572\pi$
$197$	2392.69	0.865340	0.432670	+	0.901552i	$0.357572\pi$
$198$	4742.18	1.70208
$199$	−210.234	−0.0748899	−0.0374450	−	0.999299i	$-0.511922\pi$
$199$	−210.234	−0.0748899	−0.0374450	+	0.999299i	$0.511922\pi$
$200$	7381.85	2.60988
$201$	2677.69	0.939650
$202$	−2325.11	−0.809873
$203$	−47.4474	−0.0164047
$204$	293.815	0.100839
$205$	4282.12	1.45891
$206$	881.991	0.298307
$207$	−3418.68	−1.14790
$208$	1285.30	0.428458
$209$	6838.29	2.26323
$210$	−1286.59	−0.422777
$211$	−857.579	−0.279802	−0.139901	−	0.990166i	$-0.544678\pi$
$211$	−857.579	−0.279802	−0.139901	+	0.990166i	$0.544678\pi$
$212$	−647.833	−0.209874
$213$	−3908.37	−1.25726
$214$	−2102.49	−0.671603
$215$	0	0
$216$	1986.64	0.625805
$217$	−107.069	−0.0334944
$218$	749.144	0.232745
$219$	−5790.89	−1.78681
$220$	1654.48	0.507022
$221$	608.652	0.185260
$222$	4489.58	1.35730
$223$	3532.28	1.06071	0.530356	−	0.847775i	$-0.322058\pi$
$223$	3532.28	1.06071	0.530356	+	0.847775i	$0.322058\pi$
$224$	−216.374	−0.0645405
$225$	11314.3	3.35240
$226$	−4132.76	−1.21640
$227$	5188.68	1.51711	0.758557	−	0.651607i	$-0.225905\pi$
$227$	5188.68	1.51711	0.758557	+	0.651607i	$0.225905\pi$
$228$	1728.26	0.502005
$229$	3482.36	1.00490	0.502448	−	0.864607i	$-0.332433\pi$
$229$	3482.36	1.00490	0.502448	+	0.864607i	$0.332433\pi$
$230$	4819.02	1.38155
$231$	−1234.34	−0.351575
$232$	−376.334	−0.106498
$233$	−1545.34	−0.434500	−0.217250	−	0.976116i	$-0.569709\pi$
$233$	−1545.34	−0.434500	−0.217250	+	0.976116i	$0.569709\pi$
$234$	2482.77	0.693605
$235$	−12432.8	−3.45117
$236$	1175.21	0.324151
$237$	−1373.69	−0.376501
$238$	179.067	0.0487696
$239$	−2562.59	−0.693558	−0.346779	−	0.937947i	$-0.612725\pi$
$239$	−2562.59	−0.693558	−0.346779	+	0.937947i	$0.612725\pi$
$240$	−8097.17	−2.17779
$241$	4941.93	1.32090	0.660452	−	0.750868i	$-0.270365\pi$
$241$	4941.93	1.32090	0.660452	+	0.750868i	$0.270365\pi$
$242$	−3042.63	−0.808212
$243$	−5006.03	−1.32155
$244$	−82.1366	−0.0215502
$245$	−6910.69	−1.80207
$246$	−4195.03	−1.08726
$247$	3580.19	0.922274
$248$	−849.228	−0.217444
$249$	−1937.31	−0.493060
$250$	−9392.08	−2.37603
$251$	4464.77	1.12276	0.561382	−	0.827557i	$-0.310270\pi$
$251$	4464.77	1.12276	0.561382	+	0.827557i	$0.310270\pi$
$252$	−180.785	−0.0451921
$253$	4623.32	1.14888
$254$	−616.430	−0.152277
$255$	−3834.42	−0.941649
$256$	−2335.62	−0.570220
$257$	5954.45	1.44525	0.722624	−	0.691242i	$-0.242936\pi$
$257$	5954.45	1.44525	0.722624	+	0.691242i	$0.242936\pi$
$258$	0	0
$259$	−677.219	−0.162472
$260$	866.201	0.206613
$261$	−576.816	−0.136797
$262$	5931.41	1.39864
$263$	−46.0385	−0.0107941	−0.00539706	−	0.999985i	$-0.501718\pi$
$263$	−46.0385	−0.0107941	−0.00539706	+	0.999985i	$0.501718\pi$
$264$	−9790.33	−2.28240
$265$	8454.51	1.95984
$266$	1053.30	0.242789
$267$	−2668.94	−0.611747
$268$	−530.375	−0.120887
$269$	924.553	0.209558	0.104779	−	0.994496i	$-0.466587\pi$
$269$	924.553	0.209558	0.104779	+	0.994496i	$0.466587\pi$
$270$	−4292.24	−0.967472
$271$	−5175.61	−1.16013	−0.580067	−	0.814569i	$-0.696974\pi$
$271$	−5175.61	−1.16013	−0.580067	+	0.814569i	$0.696974\pi$
$272$	1126.96	0.251220
$273$	−646.239	−0.143268
$274$	−3121.85	−0.688313
$275$	−15301.2	−3.35526
$276$	1168.47	0.254831
$277$	−6775.52	−1.46968	−0.734840	−	0.678240i	$-0.762743\pi$
$277$	−6775.52	−1.46968	−0.734840	+	0.678240i	$0.762743\pi$
$278$	785.189	0.169397
$279$	−1301.63	−0.279307
$280$	1539.31	0.328540
$281$	2921.27	0.620172	0.310086	−	0.950709i	$-0.399642\pi$
$281$	2921.27	0.620172	0.310086	+	0.950709i	$0.399642\pi$
$282$	12179.9	2.57200
$283$	−5154.70	−1.08274	−0.541369	−	0.840785i	$-0.682094\pi$
$283$	−5154.70	−1.08274	−0.541369	+	0.840785i	$0.682094\pi$
$284$	774.138	0.161749
$285$	−22554.6	−4.68779
$286$	−3357.62	−0.694197
$287$	632.787	0.130147
$288$	−2630.45	−0.538197
$289$	−4379.33	−0.891376
$290$	813.089	0.164642
$291$	5505.11	1.10899
$292$	1147.01	0.229876
$293$	−5833.97	−1.16322	−0.581611	−	0.813467i	$-0.697578\pi$
$293$	−5833.97	−1.16322	−0.581611	+	0.813467i	$0.697578\pi$
$294$	6770.13	1.34300
$295$	−15337.0	−3.02697
$296$	−5371.44	−1.05476
$297$	−4117.93	−0.804534
$298$	−6386.69	−1.24151
$299$	2420.54	0.468172
$300$	−3867.11	−0.744226
$301$	0	0
$302$	2530.11	0.482090
$303$	7357.45	1.39496
$304$	6628.93	1.25064
$305$	1071.92	0.201239
$306$	2176.91	0.406685
$307$	6732.61	1.25163	0.625815	−	0.779971i	$-0.284766\pi$
$307$	6732.61	1.25163	0.625815	+	0.779971i	$0.284766\pi$
$308$	244.489	0.0452306
$309$	−2790.92	−0.513818
$310$	1834.80	0.336160
$311$	8757.73	1.59680	0.798401	−	0.602127i	$-0.205680\pi$
$311$	8757.73	1.59680	0.798401	+	0.602127i	$0.205680\pi$
$312$	−5125.73	−0.930087
$313$	−6736.28	−1.21648	−0.608238	−	0.793754i	$-0.708124\pi$
$313$	−6736.28	−1.21648	−0.608238	+	0.793754i	$0.708124\pi$
$314$	3018.89	0.542567
$315$	2359.33	0.422010
$316$	272.090	0.0484374
$317$	8651.72	1.53290	0.766450	−	0.642304i	$-0.222021\pi$
$317$	8651.72	1.53290	0.766450	+	0.642304i	$0.222021\pi$
$318$	−8282.55	−1.46057
$319$	780.069	0.136914
$320$	11791.7	2.05993
$321$	6652.98	1.15680
$322$	712.127	0.123246
$323$	3139.13	0.540762
$324$	553.941	0.0949830
$325$	−8010.92	−1.36728
$326$	289.239	0.0491395
$327$	−2370.55	−0.400891
$328$	5019.02	0.844906
$329$	−1837.24	−0.307874
$330$	21152.5	3.52850
$331$	−5530.88	−0.918444	−0.459222	−	0.888322i	$-0.651872\pi$
$331$	−5530.88	−0.918444	−0.459222	+	0.888322i	$0.651872\pi$
$332$	383.727	0.0634330
$333$	−8232.93	−1.35484
$334$	−7867.11	−1.28883
$335$	6921.63	1.12886
$336$	−1196.55	−0.194278
$337$	2734.73	0.442049	0.221024	−	0.975268i	$-0.429060\pi$
$337$	2734.73	0.442049	0.221024	+	0.975268i	$0.429060\pi$
$338$	3805.70	0.612434
$339$	13077.5	2.09519
$340$	759.491	0.121145
$341$	1760.29	0.279545
$342$	12804.9	2.02459
$343$	−2071.12	−0.326035
$344$	0	0
$345$	−15249.0	−2.37965
$346$	5932.95	0.921842
$347$	−8367.34	−1.29447	−0.647237	−	0.762289i	$-0.724076\pi$
$347$	−8367.34	−1.29447	−0.647237	+	0.762289i	$0.724076\pi$
$348$	197.149	0.0303687
$349$	2243.31	0.344074	0.172037	−	0.985090i	$-0.444965\pi$
$349$	2243.31	0.344074	0.172037	+	0.985090i	$0.444965\pi$
$350$	−2356.83	−0.359936
$351$	−2155.94	−0.327851
$352$	3557.34	0.538656
$353$	1573.11	0.237190	0.118595	−	0.992943i	$-0.462161\pi$
$353$	1573.11	0.237190	0.118595	+	0.992943i	$0.462161\pi$
$354$	15025.1	2.25586
$355$	−10102.8	−1.51043
$356$	528.642	0.0787022
$357$	−566.627	−0.0840031
$358$	−4231.66	−0.624722
$359$	5107.31	0.750846	0.375423	−	0.926854i	$-0.377497\pi$
$359$	5107.31	0.750846	0.375423	+	0.926854i	$0.377497\pi$
$360$	18713.3	2.73966
$361$	11605.8	1.69206
$362$	−5558.92	−0.807101
$363$	9627.90	1.39210
$364$	128.002	0.0184317
$365$	−14969.0	−2.14662
$366$	−1050.12	−0.149974
$367$	3195.77	0.454545	0.227273	−	0.973831i	$-0.427019\pi$
$367$	3195.77	0.454545	0.227273	+	0.973831i	$0.427019\pi$
$368$	4481.78	0.634861
$369$	7692.77	1.08528
$370$	11605.3	1.63062
$371$	1249.36	0.174834
$372$	444.883	0.0620057
$373$	−12608.7	−1.75027	−0.875136	−	0.483876i	$-0.839228\pi$
$373$	−12608.7	−1.75027	−0.875136	+	0.483876i	$0.839228\pi$
$374$	−2943.99	−0.407032
$375$	29719.7	4.09259
$376$	−14572.3	−1.99870
$377$	408.405	0.0557929
$378$	−634.282	−0.0863067
$379$	1660.61	0.225065	0.112532	−	0.993648i	$-0.464104\pi$
$379$	1660.61	0.225065	0.112532	+	0.993648i	$0.464104\pi$
$380$	4467.44	0.603092
$381$	1950.59	0.262288
$382$	−201.728	−0.0270191
$383$	−10824.1	−1.44409	−0.722043	−	0.691849i	$-0.756797\pi$
$383$	−10824.1	−1.44409	−0.722043	+	0.691849i	$0.756797\pi$
$384$	−7020.33	−0.932955
$385$	−3190.69	−0.422370
$386$	−2809.17	−0.370422
$387$	0	0
$388$	−1090.41	−0.142673
$389$	−6272.78	−0.817590	−0.408795	−	0.912626i	$-0.634051\pi$
$389$	−6272.78	−0.817590	−0.408795	+	0.912626i	$0.634051\pi$
$390$	11074.4	1.43788
$391$	2122.35	0.274505
$392$	−8099.94	−1.04364
$393$	−18769.0	−2.40909
$394$	−6059.13	−0.774758
$395$	−3550.89	−0.452316
$396$	2972.24	0.377174
$397$	−2427.36	−0.306866	−0.153433	−	0.988159i	$-0.549033\pi$
$397$	−2427.36	−0.306866	−0.153433	+	0.988159i	$0.549033\pi$
$398$	532.387	0.0670506
$399$	−3332.99	−0.418191
$400$	−14832.7	−1.85409
$401$	5002.47	0.622971	0.311486	−	0.950251i	$-0.399173\pi$
$401$	5002.47	0.622971	0.311486	+	0.950251i	$0.399173\pi$
$402$	−6780.85	−0.841289
$403$	921.597	0.113916
$404$	−1457.30	−0.179464
$405$	−7229.17	−0.886964
$406$	120.153	0.0146875
$407$	11134.0	1.35600
$408$	−4494.27	−0.545342
$409$	8971.14	1.08458	0.542292	−	0.840190i	$-0.317557\pi$
$409$	8971.14	1.08458	0.542292	+	0.840190i	$0.317557\pi$
$410$	−10843.8	−1.30619
$411$	9878.58	1.18558
$412$	552.803	0.0661035
$413$	−2266.41	−0.270031
$414$	8657.31	1.02774
$415$	−5007.81	−0.592346
$416$	1862.45	0.219505
$417$	−2484.60	−0.291778
$418$	−17317.0	−2.02632
$419$	11112.1	1.29561	0.647806	−	0.761805i	$-0.275687\pi$
$419$	11112.1	1.29561	0.647806	+	0.761805i	$0.275687\pi$
$420$	−806.393	−0.0936856
$421$	−1138.09	−0.131751	−0.0658754	−	0.997828i	$-0.520984\pi$
$421$	−1138.09	−0.131751	−0.0658754	+	0.997828i	$0.520984\pi$
$422$	2171.69	0.250513
$423$	−22335.3	−2.56733
$424$	9909.42	1.13501
$425$	−7024.03	−0.801684
$426$	9897.36	1.12565
$427$	158.402	0.0179522
$428$	−1317.77	−0.148824
$429$	10624.7	1.19572
$430$	0	0
$431$	−7440.65	−0.831563	−0.415781	−	0.909465i	$-0.636492\pi$
$431$	−7440.65	−0.831563	−0.415781	+	0.909465i	$0.636492\pi$
$432$	−3991.86	−0.444580
$433$	−8252.84	−0.915949	−0.457975	−	0.888965i	$-0.651425\pi$
$433$	−8252.84	−0.915949	−0.457975	+	0.888965i	$0.651425\pi$
$434$	271.135	0.0299883
$435$	−2572.89	−0.283587
$436$	469.539	0.0515753
$437$	12484.0	1.36656
$438$	14664.6	1.59977
$439$	−11729.5	−1.27521	−0.637605	−	0.770364i	$-0.720075\pi$
$439$	−11729.5	−1.27521	−0.637605	+	0.770364i	$0.720075\pi$
$440$	−25307.3	−2.74200
$441$	−12415.0	−1.34056
$442$	−1541.32	−0.165867
$443$	1411.13	0.151343	0.0756714	−	0.997133i	$-0.475890\pi$
$443$	1411.13	0.151343	0.0756714	+	0.997133i	$0.475890\pi$
$444$	2813.92	0.300772
$445$	−6899.01	−0.734932
$446$	−8944.97	−0.949679
$447$	20209.7	2.13844
$448$	1742.51	0.183763
$449$	−9517.45	−1.00035	−0.500174	−	0.865925i	$-0.666731\pi$
$449$	−9517.45	−1.00035	−0.500174	+	0.865925i	$0.666731\pi$
$450$	−28651.9	−3.00147
$451$	−10403.5	−1.08621
$452$	−2590.28	−0.269550
$453$	−8006.11	−0.830375
$454$	−13139.6	−1.35830
$455$	−1670.48	−0.172117
$456$	−26436.0	−2.71486
$457$	−11178.2	−1.14419	−0.572093	−	0.820189i	$-0.693868\pi$
$457$	−11178.2	−1.14419	−0.572093	+	0.820189i	$0.693868\pi$
$458$	−8818.57	−0.899705
$459$	−1890.34	−0.192230
$460$	3020.41	0.306146
$461$	−15694.1	−1.58557	−0.792786	−	0.609500i	$-0.791370\pi$
$461$	−15694.1	−1.58557	−0.792786	+	0.609500i	$0.791370\pi$
$462$	3125.79	0.314772
$463$	−2547.36	−0.255693	−0.127847	−	0.991794i	$-0.540807\pi$
$463$	−2547.36	−0.255693	−0.127847	+	0.991794i	$0.540807\pi$
$464$	756.187	0.0756575
$465$	−5805.92	−0.579017
$466$	3913.34	0.389017
$467$	−7822.43	−0.775115	−0.387558	−	0.921845i	$-0.626681\pi$
$467$	−7822.43	−0.775115	−0.387558	+	0.921845i	$0.626681\pi$
$468$	1556.12	0.153700
$469$	1022.84	0.100704
$470$	31484.2	3.08991
$471$	−9552.80	−0.934543
$472$	−17976.3	−1.75302
$473$	0	0
$474$	3478.67	0.337089
$475$	−41316.4	−3.99100
$476$	112.233	0.0108071
$477$	15188.4	1.45792
$478$	6489.39	0.620957
$479$	−14772.7	−1.40915	−0.704573	−	0.709632i	$-0.748861\pi$
$479$	−14772.7	−1.40915	−0.704573	+	0.709632i	$0.748861\pi$
$480$	−11733.1	−1.11571
$481$	5829.19	0.552574
$482$	−12514.7	−1.18263
$483$	−2253.41	−0.212285
$484$	−1907.02	−0.179096
$485$	14230.3	1.33230
$486$	12677.0	1.18321
$487$	5286.95	0.491939	0.245970	−	0.969278i	$-0.420894\pi$
$487$	5286.95	0.491939	0.245970	+	0.969278i	$0.420894\pi$
$488$	1256.38	0.116545
$489$	−915.251	−0.0846402
$490$	17500.3	1.61344
$491$	−17508.4	−1.60925	−0.804624	−	0.593784i	$-0.797633\pi$
$491$	−17508.4	−1.60925	−0.804624	+	0.593784i	$0.797633\pi$
$492$	−2629.30	−0.240931
$493$	358.092	0.0327133
$494$	−9066.29	−0.825732
$495$	−38789.1	−3.52210
$496$	1706.39	0.154474
$497$	−1492.94	−0.134743
$498$	4905.95	0.441447
$499$	−1560.31	−0.139978	−0.0699888	−	0.997548i	$-0.522296\pi$
$499$	−1560.31	−0.139978	−0.0699888	+	0.997548i	$0.522296\pi$
$500$	−5886.65	−0.526518
$501$	24894.2	2.21994
$502$	−11306.4	−1.00523
$503$	7420.52	0.657783	0.328891	−	0.944368i	$-0.393325\pi$
$503$	7420.52	0.657783	0.328891	+	0.944368i	$0.393325\pi$
$504$	2765.34	0.244401
$505$	19018.5	1.67586
$506$	−11707.9	−1.02861
$507$	−12042.5	−1.05489
$508$	−386.358	−0.0337438
$509$	661.902	0.0576390	0.0288195	−	0.999585i	$-0.490825\pi$
$509$	661.902	0.0576390	0.0288195	+	0.999585i	$0.490825\pi$
$510$	9710.09	0.843079
$511$	−2212.03	−0.191496
$512$	12923.4	1.11550
$513$	−11119.3	−0.956976
$514$	−15078.8	−1.29396
$515$	−7214.33	−0.617284
$516$	0	0
$517$	30205.6	2.56952
$518$	1714.96	0.145465
$519$	−18773.9	−1.58782
$520$	−13249.6	−1.11737
$521$	13039.0	1.09645	0.548225	−	0.836331i	$-0.315304\pi$
$521$	13039.0	1.09645	0.548225	+	0.836331i	$0.315304\pi$
$522$	1460.70	0.122477
$523$	−18176.0	−1.51966	−0.759829	−	0.650123i	$-0.774717\pi$
$523$	−18176.0	−1.51966	−0.759829	+	0.650123i	$0.774717\pi$
$524$	3717.62	0.309933
$525$	7457.80	0.619971
$526$	116.586	0.00966421
$527$	808.063	0.0667927
$528$	19672.2	1.62144
$529$	−3726.68	−0.306294
$530$	−21409.8	−1.75468
$531$	−27552.7	−2.25176
$532$	660.172	0.0538009
$533$	−5446.74	−0.442635
$534$	6758.69	0.547710
$535$	17197.5	1.38974
$536$	8112.76	0.653765
$537$	13390.4	1.07605
$538$	−2341.29	−0.187622
$539$	16789.6	1.34171
$540$	−2690.23	−0.214388
$541$	3752.56	0.298216	0.149108	−	0.988821i	$-0.452360\pi$
$541$	3752.56	0.298216	0.149108	+	0.988821i	$0.452360\pi$
$542$	13106.5	1.03869
$543$	17590.3	1.39019
$544$	1633.00	0.128703
$545$	−6127.69	−0.481617
$546$	1636.51	0.128271
$547$	7414.69	0.579578	0.289789	−	0.957090i	$-0.406415\pi$
$547$	7414.69	0.579578	0.289789	+	0.957090i	$0.406415\pi$
$548$	−1956.67	−0.152527
$549$	1925.69	0.149702
$550$	38747.9	3.00403
$551$	2106.35	0.162856
$552$	−17873.2	−1.37814
$553$	−524.729	−0.0403504
$554$	17158.0	1.31584
$555$	−36723.0	−2.80865
$556$	492.130	0.0375377
$557$	−14232.7	−1.08269	−0.541345	−	0.840801i	$-0.682085\pi$
$557$	−14232.7	−1.08269	−0.541345	+	0.840801i	$0.682085\pi$
$558$	3296.19	0.250069
$559$	0	0
$560$	−3093.00	−0.233399
$561$	9315.77	0.701091
$562$	−7397.68	−0.555253
$563$	−20932.3	−1.56695	−0.783475	−	0.621423i	$-0.786555\pi$
$563$	−20932.3	−1.56695	−0.783475	+	0.621423i	$0.786555\pi$
$564$	7633.97	0.569943
$565$	33804.3	2.51709
$566$	13053.5	0.969399
$567$	−1068.28	−0.0791247
$568$	−11841.4	−0.874745
$569$	−3328.84	−0.245259	−0.122629	−	0.992453i	$-0.539133\pi$
$569$	−3328.84	−0.245259	−0.122629	+	0.992453i	$0.539133\pi$
$570$	57116.2	4.19708
$571$	−2268.00	−0.166222	−0.0831110	−	0.996540i	$-0.526486\pi$
$571$	−2268.00	−0.166222	−0.0831110	+	0.996540i	$0.526486\pi$
$572$	−2104.45	−0.153831
$573$	638.335	0.0465389
$574$	−1602.44	−0.116524
$575$	−27933.7	−2.02594
$576$	21183.7	1.53238
$577$	11714.3	0.845190	0.422595	−	0.906319i	$-0.361119\pi$
$577$	11714.3	0.845190	0.422595	+	0.906319i	$0.361119\pi$
$578$	11090.0	0.798068
$579$	8889.16	0.638032
$580$	509.617	0.0364840
$581$	−740.024	−0.0528423
$582$	−13940.9	−0.992900
$583$	−20540.3	−1.45917
$584$	−17545.0	−1.24318
$585$	−20308.0	−1.43527
$586$	14773.7	1.04146
$587$	−13734.5	−0.965730	−0.482865	−	0.875695i	$-0.660404\pi$
$587$	−13734.5	−0.965730	−0.482865	+	0.875695i	$0.660404\pi$
$588$	4243.30	0.297603
$589$	4753.15	0.332513
$590$	38838.7	2.71011
$591$	19173.1	1.33448
$592$	10793.1	0.749313
$593$	−26981.9	−1.86849	−0.934244	−	0.356634i	$-0.883924\pi$
$593$	−26981.9	−1.86849	−0.934244	+	0.356634i	$0.883924\pi$
$594$	10428.1	0.720317
$595$	−1464.69	−0.100918
$596$	−4002.97	−0.275114
$597$	−1684.65	−0.115491
$598$	−6129.66	−0.419164
$599$	2470.79	0.168537	0.0842685	−	0.996443i	$-0.473145\pi$
$599$	2470.79	0.168537	0.0842685	+	0.996443i	$0.473145\pi$
$600$	59152.4	4.02481
$601$	−20621.9	−1.39964	−0.699820	−	0.714319i	$-0.746737\pi$
$601$	−20621.9	−1.39964	−0.699820	+	0.714319i	$0.746737\pi$
$602$	0	0
$603$	12434.6	0.839762
$604$	1585.79	0.106829
$605$	24887.4	1.67243
$606$	−18631.6	−1.24894
$607$	−4220.90	−0.282242	−0.141121	−	0.989992i	$-0.545071\pi$
$607$	−4220.90	−0.282242	−0.141121	+	0.989992i	$0.545071\pi$
$608$	9605.58	0.640720
$609$	−380.206	−0.0252984
$610$	−2714.48	−0.180174
$611$	15814.1	1.04709
$612$	1364.41	0.0901196
$613$	12018.1	0.791852	0.395926	−	0.918282i	$-0.370424\pi$
$613$	12018.1	0.791852	0.395926	+	0.918282i	$0.370424\pi$
$614$	−17049.3	−1.12061
$615$	34313.6	2.24985
$616$	−3739.76	−0.244609
$617$	−5171.02	−0.337403	−0.168701	−	0.985667i	$-0.553957\pi$
$617$	−5171.02	−0.337403	−0.168701	+	0.985667i	$0.553957\pi$
$618$	7067.59	0.460033
$619$	5055.56	0.328272	0.164136	−	0.986438i	$-0.447516\pi$
$619$	5055.56	0.328272	0.164136	+	0.986438i	$0.447516\pi$
$620$	1149.99	0.0744915
$621$	−7517.68	−0.485788
$622$	−22177.6	−1.42965
$623$	−1019.50	−0.0655621
$624$	10299.4	0.660745
$625$	38816.7	2.48427
$626$	17058.6	1.08914
$627$	54796.8	3.49023
$628$	1892.14	0.120230
$629$	5111.07	0.323993
$630$	−5974.65	−0.377835
$631$	20865.9	1.31642	0.658209	−	0.752835i	$-0.271314\pi$
$631$	20865.9	1.31642	0.658209	+	0.752835i	$0.271314\pi$
$632$	−4161.95	−0.261952
$633$	−6871.97	−0.431495
$634$	−21909.2	−1.37244
$635$	5042.14	0.315105
$636$	−5191.23	−0.323657
$637$	8790.20	0.546751
$638$	−1975.41	−0.122582
$639$	−18149.6	−1.12361
$640$	−18147.1	−1.12082
$641$	20942.5	1.29045	0.645226	−	0.763992i	$-0.276763\pi$
$641$	20942.5	1.29045	0.645226	+	0.763992i	$0.276763\pi$
$642$	−16847.7	−1.03571
$643$	−1235.94	−0.0758020	−0.0379010	−	0.999281i	$-0.512067\pi$
$643$	−1235.94	−0.0758020	−0.0379010	+	0.999281i	$0.512067\pi$
$644$	446.337	0.0273108
$645$	0	0
$646$	−7949.39	−0.484155
$647$	16372.8	0.994873	0.497437	−	0.867500i	$-0.334275\pi$
$647$	16372.8	0.994873	0.497437	+	0.867500i	$0.334275\pi$
$648$	−8473.22	−0.513672
$649$	37261.5	2.25369
$650$	20286.5	1.22415
$651$	−857.964	−0.0516533
$652$	181.286	0.0108891
$653$	−3699.21	−0.221686	−0.110843	−	0.993838i	$-0.535355\pi$
$653$	−3699.21	−0.221686	−0.110843	+	0.993838i	$0.535355\pi$
$654$	6003.06	0.358927
$655$	−48516.5	−2.89420
$656$	−10085.0	−0.600231
$657$	−26891.6	−1.59687
$658$	4652.55	0.275646
$659$	−27786.0	−1.64247	−0.821237	−	0.570588i	$-0.806715\pi$
$659$	−27786.0	−1.64247	−0.821237	+	0.570588i	$0.806715\pi$
$660$	13257.7	0.781901
$661$	5798.03	0.341176	0.170588	−	0.985342i	$-0.445433\pi$
$661$	5798.03	0.341176	0.170588	+	0.985342i	$0.445433\pi$
$662$	14006.1	0.822302
$663$	4877.27	0.285697
$664$	−5869.59	−0.343048
$665$	−8615.53	−0.502400
$666$	20848.7	1.21302
$667$	1424.09	0.0826702
$668$	−4930.85	−0.285599
$669$	28304.9	1.63577
$670$	−17528.0	−1.01070
$671$	−2604.24	−0.149830
$672$	−1733.85	−0.0995308
$673$	4577.82	0.262202	0.131101	−	0.991369i	$-0.458149\pi$
$673$	4577.82	0.262202	0.131101	+	0.991369i	$0.458149\pi$
$674$	−6925.30	−0.395776
$675$	24880.2	1.41873
$676$	2385.28	0.135713
$677$	12344.6	0.700801	0.350401	−	0.936600i	$-0.386045\pi$
$677$	12344.6	0.700801	0.350401	+	0.936600i	$0.386045\pi$
$678$	−33116.7	−1.87587
$679$	2102.87	0.118852
$680$	−11617.4	−0.655156
$681$	41578.0	2.33961
$682$	−4457.66	−0.250283
$683$	16504.5	0.924635	0.462318	−	0.886714i	$-0.347018\pi$
$683$	16504.5	0.924635	0.462318	+	0.886714i	$0.347018\pi$
$684$	8025.69	0.448640
$685$	25535.4	1.42432
$686$	5244.81	0.291906
$687$	27905.0	1.54969
$688$	0	0
$689$	−10753.9	−0.594616
$690$	38615.9	2.13055
$691$	11094.6	0.610791	0.305396	−	0.952226i	$-0.401211\pi$
$691$	11094.6	0.610791	0.305396	+	0.952226i	$0.401211\pi$
$692$	3718.58	0.204276
$693$	−5732.02	−0.314201
$694$	21189.1	1.15897
$695$	−6422.52	−0.350533
$696$	−3015.65	−0.164236
$697$	−4775.74	−0.259532
$698$	−5680.86	−0.308057
$699$	−12383.1	−0.670061
$700$	−1477.18	−0.0797603
$701$	3488.71	0.187970	0.0939850	−	0.995574i	$-0.470039\pi$
$701$	3488.71	0.187970	0.0939850	+	0.995574i	$0.470039\pi$
$702$	5459.60	0.293532
$703$	30064.1	1.61293
$704$	−28648.2	−1.53369
$705$	−99626.7	−5.32221
$706$	−3983.66	−0.212361
$707$	2810.44	0.149501
$708$	9417.22	0.499888
$709$	11358.7	0.601669	0.300835	−	0.953676i	$-0.402735\pi$
$709$	11358.7	0.601669	0.300835	+	0.953676i	$0.402735\pi$
$710$	25584.0	1.35232
$711$	−6379.12	−0.336478
$712$	−8086.25	−0.425625
$713$	3213.57	0.168793
$714$	1434.90	0.0752098
$715$	27464.0	1.43650
$716$	−2652.27	−0.138436
$717$	−20534.6	−1.06957
$718$	−12933.5	−0.672249
$719$	−34524.2	−1.79073	−0.895364	−	0.445335i	$-0.853085\pi$
$719$	−34524.2	−1.79073	−0.895364	+	0.445335i	$0.853085\pi$
$720$	−37601.5	−1.94629
$721$	−1066.09	−0.0550670
$722$	−29390.1	−1.51494
$723$	39600.8	2.03703
$724$	−3484.15	−0.178850
$725$	−4713.11	−0.241435
$726$	−24381.2	−1.24638
$727$	16846.5	0.859426	0.429713	−	0.902966i	$-0.358615\pi$
$727$	16846.5	0.859426	0.429713	+	0.902966i	$0.358615\pi$
$728$	−1957.95	−0.0996793
$729$	−30691.3	−1.55928
$730$	37906.9	1.92191
$731$	0	0
$732$	−658.179	−0.0332336
$733$	−13917.8	−0.701317	−0.350658	−	0.936503i	$-0.614042\pi$
$733$	−13917.8	−0.701317	−0.350658	+	0.936503i	$0.614042\pi$
$734$	−8092.82	−0.406964
$735$	−55376.9	−2.77906
$736$	6494.27	0.325247
$737$	−16816.2	−0.840479
$738$	−19480.8	−0.971678
$739$	10001.0	0.497825	0.248912	−	0.968526i	$-0.419927\pi$
$739$	10001.0	0.497825	0.248912	+	0.968526i	$0.419927\pi$
$740$	7273.79	0.361338
$741$	28688.8	1.42228
$742$	−3163.81	−0.156533
$743$	−5356.46	−0.264481	−0.132240	−	0.991218i	$-0.542217\pi$
$743$	−5356.46	−0.264481	−0.132240	+	0.991218i	$0.542217\pi$
$744$	−6805.05	−0.335329
$745$	52240.5	2.56905
$746$	31929.6	1.56706
$747$	−8996.45	−0.440647
$748$	−1845.19	−0.0901964
$749$	2541.34	0.123977
$750$	−75260.8	−3.66418
$751$	30162.2	1.46556	0.732779	−	0.680467i	$-0.238223\pi$
$751$	30162.2	1.46556	0.732779	+	0.680467i	$0.238223\pi$
$752$	29280.9	1.41990
$753$	35777.2	1.73146
$754$	−1034.22	−0.0499526
$755$	−20695.2	−0.997585
$756$	−397.547	−0.0191252
$757$	35857.4	1.72161	0.860805	−	0.508935i	$-0.169961\pi$
$757$	35857.4	1.72161	0.860805	+	0.508935i	$0.169961\pi$
$758$	−4205.24	−0.201505
$759$	37047.7	1.77173
$760$	−68335.1	−3.26155
$761$	3433.69	0.163563	0.0817814	−	0.996650i	$-0.473939\pi$
$761$	3433.69	0.163563	0.0817814	+	0.996650i	$0.473939\pi$
$762$	−4939.59	−0.234832
$763$	−905.514	−0.0429644
$764$	−126.436	−0.00598731
$765$	−17806.2	−0.841549
$766$	27410.4	1.29292
$767$	19508.2	0.918386
$768$	−18715.9	−0.879362
$769$	−2028.54	−0.0951248	−0.0475624	−	0.998868i	$-0.515145\pi$
$769$	−2028.54	−0.0951248	−0.0475624	+	0.998868i	$0.515145\pi$
$770$	8079.94	0.378157
$771$	47714.3	2.22878
$772$	−1760.69	−0.0820839
$773$	39469.4	1.83650	0.918251	−	0.395999i	$-0.129602\pi$
$773$	39469.4	1.83650	0.918251	+	0.395999i	$0.129602\pi$
$774$	0	0
$775$	−10635.5	−0.492953
$776$	16679.2	0.771582
$777$	−5426.70	−0.250556
$778$	15884.9	0.732006
$779$	−28091.6	−1.29202
$780$	6941.06	0.318628
$781$	24545.0	1.12457
$782$	−5374.53	−0.245771
$783$	−1268.42	−0.0578922
$784$	16275.6	0.741417
$785$	−24693.3	−1.12273
$786$	47529.7	2.15691
$787$	−39757.2	−1.80075	−0.900376	−	0.435113i	$-0.856708\pi$
$787$	−39757.2	−1.80075	−0.900376	+	0.435113i	$0.856708\pi$
$788$	−3797.66	−0.171683
$789$	−368.916	−0.0166461
$790$	8992.10	0.404968
$791$	4995.40	0.224546
$792$	−45464.2	−2.03977
$793$	−1363.45	−0.0610562
$794$	6146.94	0.274744
$795$	67747.8	3.02235
$796$	333.682	0.0148581
$797$	9242.68	0.410781	0.205391	−	0.978680i	$-0.434154\pi$
$797$	9242.68	0.410781	0.205391	+	0.978680i	$0.434154\pi$
$798$	8440.30	0.374415
$799$	13866.0	0.613945
$800$	−21493.2	−0.949873
$801$	−12394.0	−0.546716
$802$	−12668.0	−0.557760
$803$	36367.5	1.59823
$804$	−4250.01	−0.186426
$805$	−5824.90	−0.255032
$806$	−2333.81	−0.101991
$807$	7408.65	0.323168
$808$	22291.3	0.970552
$809$	−14493.7	−0.629877	−0.314939	−	0.949112i	$-0.601984\pi$
$809$	−14493.7	−0.629877	−0.314939	+	0.949112i	$0.601984\pi$
$810$	18306.8	0.794118
$811$	36976.4	1.60101	0.800504	−	0.599328i	$-0.204565\pi$
$811$	36976.4	1.60101	0.800504	+	0.599328i	$0.204565\pi$
$812$	75.3082	0.00325468
$813$	−41473.3	−1.78909
$814$	−28195.1	−1.21405
$815$	−2365.86	−0.101684
$816$	9030.56	0.387418
$817$	0	0
$818$	−22718.1	−0.971051
$819$	−3001.00	−0.128038
$820$	−6796.57	−0.289447
$821$	41436.7	1.76145	0.880724	−	0.473629i	$-0.157056\pi$
$821$	41436.7	1.76145	0.880724	+	0.473629i	$0.157056\pi$
$822$	−25016.0	−1.06148
$823$	−29097.3	−1.23241	−0.616203	−	0.787588i	$-0.711330\pi$
$823$	−29097.3	−1.23241	−0.616203	+	0.787588i	$0.711330\pi$
$824$	−8455.82	−0.357491
$825$	−122612.	−5.17429
$826$	5739.36	0.241765
$827$	−16157.9	−0.679402	−0.339701	−	0.940534i	$-0.610326\pi$
$827$	−16157.9	−0.679402	−0.339701	+	0.940534i	$0.610326\pi$
$828$	5426.11	0.227742
$829$	41034.9	1.71918	0.859591	−	0.510983i	$-0.170718\pi$
$829$	41034.9	1.71918	0.859591	+	0.510983i	$0.170718\pi$
$830$	12681.5	0.530340
$831$	−54293.7	−2.26646
$832$	−14998.7	−0.624985
$833$	7707.31	0.320579
$834$	6291.89	0.261235
$835$	64349.7	2.66696
$836$	−10853.7	−0.449023
$837$	−2862.28	−0.118202
$838$	−28139.7	−1.15999
$839$	28367.1	1.16727	0.583636	−	0.812015i	$-0.301629\pi$
$839$	28367.1	1.16727	0.583636	+	0.812015i	$0.301629\pi$
$840$	12334.8	0.506656
$841$	−24148.7	−0.990148
$842$	2882.04	0.117959
$843$	23408.8	0.956395
$844$	1361.15	0.0555125
$845$	−31129.0	−1.26730
$846$	56560.9	2.29859
$847$	3677.72	0.149195
$848$	−19911.5	−0.806324
$849$	−41305.7	−1.66974
$850$	17787.3	0.717765
$851$	20326.1	0.818767
$852$	6203.34	0.249440
$853$	−18754.4	−0.752801	−0.376400	−	0.926457i	$-0.622838\pi$
$853$	−18754.4	−0.752801	−0.376400	+	0.926457i	$0.622838\pi$
$854$	−401.129	−0.0160730
$855$	−104739.	−4.18947
$856$	20157.0	0.804849
$857$	−12782.0	−0.509481	−0.254741	−	0.967009i	$-0.581990\pi$
$857$	−12782.0	−0.509481	−0.254741	+	0.967009i	$0.581990\pi$
$858$	−26905.4	−1.07055
$859$	2156.19	0.0856442	0.0428221	−	0.999083i	$-0.486365\pi$
$859$	2156.19	0.0856442	0.0428221	+	0.999083i	$0.486365\pi$
$860$	0	0
$861$	5070.66	0.200706
$862$	18842.3	0.744516
$863$	20877.3	0.823489	0.411744	−	0.911299i	$-0.364920\pi$
$863$	20877.3	0.823489	0.411744	+	0.911299i	$0.364920\pi$
$864$	−5784.36	−0.227764
$865$	−48529.1	−1.90756
$866$	20899.1	0.820069
$867$	−35092.5	−1.37463
$868$	169.939	0.00664527
$869$	8626.93	0.336765
$870$	6515.46	0.253902
$871$	−8804.12	−0.342498
$872$	−7182.19	−0.278922
$873$	25564.6	0.991099
$874$	−31613.8	−1.22351
$875$	11352.5	0.438611
$876$	9191.27	0.354502
$877$	21747.0	0.837336	0.418668	−	0.908139i	$-0.362497\pi$
$877$	21747.0	0.837336	0.418668	+	0.908139i	$0.362497\pi$
$878$	29703.1	1.14172
$879$	−46748.9	−1.79386
$880$	50851.2	1.94795
$881$	39665.9	1.51689	0.758444	−	0.651738i	$-0.225960\pi$
$881$	39665.9	1.51689	0.758444	+	0.651738i	$0.225960\pi$
$882$	31439.0	1.20024
$883$	−32675.0	−1.24530	−0.622652	−	0.782499i	$-0.713945\pi$
$883$	−32675.0	−1.24530	−0.622652	+	0.782499i	$0.713945\pi$
$884$	−966.050	−0.0367554
$885$	−122899.	−4.66803
$886$	−3573.48	−0.135500
$887$	−1318.70	−0.0499183	−0.0249592	−	0.999688i	$-0.507946\pi$
$887$	−1318.70	−0.0499183	−0.0249592	+	0.999688i	$0.507946\pi$
$888$	−43042.5	−1.62659
$889$	745.098	0.0281100
$890$	17470.7	0.658000
$891$	17563.4	0.660376
$892$	−5606.41	−0.210445
$893$	81561.6	3.05639
$894$	−51178.0	−1.91459
$895$	34613.3	1.29273
$896$	−2681.66	−0.0999867
$897$	19396.3	0.721989
$898$	24101.5	0.895634
$899$	542.209	0.0201153
$900$	−17958.1	−0.665113
$901$	−9429.08	−0.348644
$902$	26345.3	0.972507
$903$	0	0
$904$	39621.6	1.45774
$905$	45469.7	1.67013
$906$	20274.3	0.743453
$907$	−2202.10	−0.0806170	−0.0403085	−	0.999187i	$-0.512834\pi$
$907$	−2202.10	−0.0806170	−0.0403085	+	0.999187i	$0.512834\pi$
$908$	−8235.45	−0.300994
$909$	34166.4	1.24668
$910$	4230.25	0.154100
$911$	−10427.7	−0.379237	−0.189618	−	0.981858i	$-0.560725\pi$
$911$	−10427.7	−0.379237	−0.189618	+	0.981858i	$0.560725\pi$
$912$	53119.1	1.92867
$913$	12166.5	0.441022
$914$	28307.1	1.02441
$915$	8589.53	0.310340
$916$	−5527.19	−0.199371
$917$	−7169.49	−0.258187
$918$	4787.02	0.172108
$919$	−4793.05	−0.172044	−0.0860218	−	0.996293i	$-0.527415\pi$
$919$	−4793.05	−0.172044	−0.0860218	+	0.996293i	$0.527415\pi$
$920$	−46200.9	−1.65565
$921$	53949.9	1.93020
$922$	39743.1	1.41960
$923$	12850.5	0.458267
$924$	1959.14	0.0697522
$925$	−67270.5	−2.39118
$926$	6450.82	0.228928
$927$	−12960.4	−0.459198
$928$	1095.74	0.0387603
$929$	−42938.0	−1.51641	−0.758207	−	0.652014i	$-0.773924\pi$
$929$	−42938.0	−1.51641	−0.758207	+	0.652014i	$0.773924\pi$
$930$	14702.6	0.518407
$931$	45335.5	1.59593
$932$	2452.75	0.0862044
$933$	70177.6	2.46250
$934$	19809.1	0.693977
$935$	24080.6	0.842267
$936$	−23802.8	−0.831216
$937$	−17961.4	−0.626224	−0.313112	−	0.949716i	$-0.601372\pi$
$937$	−17961.4	−0.626224	−0.313112	+	0.949716i	$0.601372\pi$
$938$	−2590.19	−0.0901626
$939$	−53979.3	−1.87598
$940$	19733.3	0.684711
$941$	1417.03	0.0490902	0.0245451	−	0.999699i	$-0.492186\pi$
$941$	1417.03	0.0490902	0.0245451	+	0.999699i	$0.492186\pi$
$942$	24191.0	0.836716
$943$	−18992.5	−0.655867
$944$	36120.7	1.24537
$945$	5188.16	0.178594
$946$	0	0
$947$	−1240.24	−0.0425579	−0.0212789	−	0.999774i	$-0.506774\pi$
$947$	−1240.24	−0.0425579	−0.0212789	+	0.999774i	$0.506774\pi$
$948$	2180.31	0.0746975
$949$	19040.2	0.651286
$950$	104628.	3.57323
$951$	69328.2	2.36395
$952$	−1716.75	−0.0584454
$953$	−39421.9	−1.33998	−0.669989	−	0.742371i	$-0.733701\pi$
$953$	−39421.9	−1.33998	−0.669989	+	0.742371i	$0.733701\pi$
$954$	−38462.4	−1.30531
$955$	1650.05	0.0559103
$956$	4067.33	0.137601
$957$	6250.87	0.211141
$958$	37409.6	1.26164
$959$	3773.47	0.127061
$960$	94489.8	3.17671
$961$	−28567.5	−0.958929
$962$	−14761.5	−0.494731
$963$	30895.0	1.03383
$964$	−7843.81	−0.262067
$965$	22977.8	0.766511
$966$	5706.43	0.190063
$967$	13213.8	0.439428	0.219714	−	0.975564i	$-0.429488\pi$
$967$	13213.8	0.439428	0.219714	+	0.975564i	$0.429488\pi$
$968$	29170.2	0.968561
$969$	25154.6	0.833933
$970$	−36036.2	−1.19284
$971$	16647.1	0.550186	0.275093	−	0.961418i	$-0.411291\pi$
$971$	16647.1	0.550186	0.275093	+	0.961418i	$0.411291\pi$
$972$	7945.55	0.262195
$973$	−949.082	−0.0312705
$974$	−13388.4	−0.440444
$975$	−64193.3	−2.10854
$976$	−2524.51	−0.0827948
$977$	−3092.02	−0.101251	−0.0506256	−	0.998718i	$-0.516122\pi$
$977$	−3092.02	−0.101251	−0.0506256	+	0.998718i	$0.516122\pi$
$978$	2317.74	0.0757802
$979$	16761.2	0.547183
$980$	10968.6	0.357530
$981$	−11008.3	−0.358276
$982$	44337.3	1.44079
$983$	−14697.7	−0.476890	−0.238445	−	0.971156i	$-0.576638\pi$
$983$	−14697.7	−0.476890	−0.238445	+	0.971156i	$0.576638\pi$
$984$	40218.5	1.30297
$985$	49561.2	1.60320
$986$	−906.816	−0.0292889
$987$	−14722.2	−0.474786
$988$	−5682.45	−0.182979
$989$	0	0
$990$	98227.7	3.15341
$991$	−43483.8	−1.39385	−0.696927	−	0.717143i	$-0.745450\pi$
$991$	−43483.8	−1.39385	−0.696927	+	0.717143i	$0.745450\pi$
$992$	2472.63	0.0791392
$993$	−44320.2	−1.41637
$994$	3780.65	0.120639
$995$	−4354.70	−0.138747
$996$	3074.89	0.0978228
$997$	−35710.8	−1.13437	−0.567187	−	0.823589i	$-0.691968\pi$
$997$	−35710.8	−1.13437	−0.567187	+	0.823589i	$0.691968\pi$
$998$	3951.24	0.125325
$999$	−18104.2	−0.573365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.17	✓	50
43.42	odd	2		1849.4.a.j.1.34	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.17	✓	50	1.1	even	1	trivial
1849.4.a.j.1.34	yes	50	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.53235 q^{2} +8.01322 q^{3} -1.58719 q^{4} +20.7136 q^{5} -20.2923 q^{6} +3.06093 q^{7} +24.2781 q^{8} +37.2117 q^{9} +O(q^{10})\)	\(q-2.53235 q^{2} +8.01322 q^{3} -1.58719 q^{4} +20.7136 q^{5} -20.2923 q^{6} +3.06093 q^{7} +24.2781 q^{8} +37.2117 q^{9} -52.4541 q^{10} -50.3240 q^{11} -12.7185 q^{12} -26.3471 q^{13} -7.75136 q^{14} +165.983 q^{15} -48.7833 q^{16} -23.1013 q^{17} -94.2331 q^{18} -135.885 q^{19} -32.8765 q^{20} +24.5279 q^{21} +127.438 q^{22} -91.8712 q^{23} +194.546 q^{24} +304.053 q^{25} +66.7201 q^{26} +81.8285 q^{27} -4.85830 q^{28} -15.5009 q^{29} -420.326 q^{30} -34.9791 q^{31} -70.6888 q^{32} -403.257 q^{33} +58.5007 q^{34} +63.4029 q^{35} -59.0622 q^{36} -221.246 q^{37} +344.110 q^{38} -211.125 q^{39} +502.888 q^{40} +206.730 q^{41} -62.1133 q^{42} +79.8739 q^{44} +770.788 q^{45} +232.650 q^{46} -600.224 q^{47} -390.911 q^{48} -333.631 q^{49} -769.970 q^{50} -185.116 q^{51} +41.8180 q^{52} +408.162 q^{53} -207.218 q^{54} -1042.39 q^{55} +74.3138 q^{56} -1088.88 q^{57} +39.2539 q^{58} -740.433 q^{59} -263.447 q^{60} +51.7496 q^{61} +88.5794 q^{62} +113.902 q^{63} +569.275 q^{64} -545.743 q^{65} +1021.19 q^{66} +334.159 q^{67} +36.6663 q^{68} -736.184 q^{69} -160.559 q^{70} -487.740 q^{71} +903.431 q^{72} -722.667 q^{73} +560.272 q^{74} +2436.45 q^{75} +215.677 q^{76} -154.038 q^{77} +534.643 q^{78} -171.428 q^{79} -1010.48 q^{80} -349.006 q^{81} -523.513 q^{82} -241.764 q^{83} -38.9306 q^{84} -478.511 q^{85} -124.213 q^{87} -1221.77 q^{88} -333.067 q^{89} -1951.91 q^{90} -80.6467 q^{91} +145.817 q^{92} -280.295 q^{93} +1519.98 q^{94} -2814.68 q^{95} -566.445 q^{96} +687.004 q^{97} +844.870 q^{98} -1872.64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more