LMFDB - Embedded newform 1045.4.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68048 q^{2} +7.90527 q^{3} -0.815035 q^{4} +5.00000 q^{5} +21.1899 q^{6} +31.9517 q^{7} -23.6285 q^{8} +35.4933 q^{9} +O(q^{10})$	\(q+2.68048 q^{2} +7.90527 q^{3} -0.815035 q^{4} +5.00000 q^{5} +21.1899 q^{6} +31.9517 q^{7} -23.6285 q^{8} +35.4933 q^{9} +13.4024 q^{10} -11.0000 q^{11} -6.44307 q^{12} -25.1968 q^{13} +85.6460 q^{14} +39.5263 q^{15} -56.8154 q^{16} +124.931 q^{17} +95.1389 q^{18} +19.0000 q^{19} -4.07518 q^{20} +252.587 q^{21} -29.4853 q^{22} +40.9757 q^{23} -186.790 q^{24} +25.0000 q^{25} -67.5396 q^{26} +67.1416 q^{27} -26.0418 q^{28} +181.865 q^{29} +105.950 q^{30} -254.932 q^{31} +36.7356 q^{32} -86.9580 q^{33} +334.874 q^{34} +159.759 q^{35} -28.9283 q^{36} -118.181 q^{37} +50.9291 q^{38} -199.188 q^{39} -118.143 q^{40} +106.376 q^{41} +677.054 q^{42} +334.822 q^{43} +8.96539 q^{44} +177.466 q^{45} +109.834 q^{46} +359.165 q^{47} -449.141 q^{48} +677.914 q^{49} +67.0120 q^{50} +987.610 q^{51} +20.5363 q^{52} -551.123 q^{53} +179.972 q^{54} -55.0000 q^{55} -754.972 q^{56} +150.200 q^{57} +487.485 q^{58} -489.784 q^{59} -32.2154 q^{60} +257.519 q^{61} -683.339 q^{62} +1134.07 q^{63} +552.992 q^{64} -125.984 q^{65} -233.089 q^{66} +583.828 q^{67} -101.823 q^{68} +323.924 q^{69} +428.230 q^{70} -583.141 q^{71} -838.653 q^{72} +65.7363 q^{73} -316.783 q^{74} +197.632 q^{75} -15.4857 q^{76} -351.469 q^{77} -533.919 q^{78} -775.850 q^{79} -284.077 q^{80} -427.546 q^{81} +285.139 q^{82} -88.6690 q^{83} -205.867 q^{84} +624.653 q^{85} +897.483 q^{86} +1437.69 q^{87} +259.914 q^{88} -668.021 q^{89} +475.695 q^{90} -805.083 q^{91} -33.3966 q^{92} -2015.30 q^{93} +962.735 q^{94} +95.0000 q^{95} +290.404 q^{96} +745.682 q^{97} +1817.13 q^{98} -390.426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	2.68048	0.947692	0.473846	−	0.880608i	$-0.342865\pi$
$2$	2.68048	0.947692	0.473846	+	0.880608i	$0.342865\pi$
$3$	7.90527	1.52137	0.760685	−	0.649121i	$-0.224863\pi$
$3$	7.90527	1.52137	0.760685	+	0.649121i	$0.224863\pi$
$4$	−0.815035	−0.101879
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	21.1899	1.44179
$7$	31.9517	1.72523	0.862616	−	0.505859i	$-0.168824\pi$
$7$	31.9517	1.72523	0.862616	+	0.505859i	$0.168824\pi$
$8$	−23.6285	−1.04424
$9$	35.4933	1.31457
$10$	13.4024	0.423821
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−6.44307	−0.154996
$13$	−25.1968	−0.537565	−0.268783	−	0.963201i	$-0.586621\pi$
$13$	−25.1968	−0.537565	−0.268783	+	0.963201i	$0.586621\pi$
$14$	85.6460	1.63499
$15$	39.5263	0.680377
$16$	−56.8154	−0.887741
$17$	124.931	1.78236	0.891180	−	0.453649i	$-0.149878\pi$
$17$	124.931	1.78236	0.891180	+	0.453649i	$0.149878\pi$
$18$	95.1389	1.24580
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−4.07518	−0.0455619
$21$	252.587	2.62472
$22$	−29.4853	−0.285740
$23$	40.9757	0.371479	0.185740	−	0.982599i	$-0.440532\pi$
$23$	40.9757	0.371479	0.185740	+	0.982599i	$0.440532\pi$
$24$	−186.790	−1.58868
$25$	25.0000	0.200000
$26$	−67.5396	−0.509446
$27$	67.1416	0.478570
$28$	−26.0418	−0.175766
$29$	181.865	1.16453	0.582267	−	0.812998i	$-0.302166\pi$
$29$	181.865	1.16453	0.582267	+	0.812998i	$0.302166\pi$
$30$	105.950	0.644788
$31$	−254.932	−1.47700	−0.738501	−	0.674252i	$-0.764466\pi$
$31$	−254.932	−1.47700	−0.738501	+	0.674252i	$0.764466\pi$
$32$	36.7356	0.202937
$33$	−86.9580	−0.458710
$34$	334.874	1.68913
$35$	159.759	0.771547
$36$	−28.9283	−0.133927
$37$	−118.181	−0.525105	−0.262553	−	0.964918i	$-0.584564\pi$
$37$	−118.181	−0.525105	−0.262553	+	0.964918i	$0.584564\pi$
$38$	50.9291	0.217416
$39$	−199.188	−0.817835
$40$	−118.143	−0.466999
$41$	106.376	0.405199	0.202599	−	0.979262i	$-0.435061\pi$
$41$	106.376	0.405199	0.202599	+	0.979262i	$0.435061\pi$
$42$	677.054	2.48742
$43$	334.822	1.18744	0.593719	−	0.804672i	$-0.297659\pi$
$43$	334.822	1.18744	0.593719	+	0.804672i	$0.297659\pi$
$44$	8.96539	0.0307178
$45$	177.466	0.587892
$46$	109.834	0.352048
$47$	359.165	1.11467	0.557337	−	0.830287i	$-0.311823\pi$
$47$	359.165	1.11467	0.557337	+	0.830287i	$0.311823\pi$
$48$	−449.141	−1.35058
$49$	677.914	1.97643
$50$	67.0120	0.189538
$51$	987.610	2.71163
$52$	20.5363	0.0547668
$53$	−551.123	−1.42835	−0.714175	−	0.699967i	$-0.753198\pi$
$53$	−551.123	−1.42835	−0.714175	+	0.699967i	$0.753198\pi$
$54$	179.972	0.453537
$55$	−55.0000	−0.134840
$56$	−754.972	−1.80156
$57$	150.200	0.349026
$58$	487.485	1.10362
$59$	−489.784	−1.08075	−0.540377	−	0.841423i	$-0.681718\pi$
$59$	−489.784	−1.08075	−0.540377	+	0.841423i	$0.681718\pi$
$60$	−32.2154	−0.0693164
$61$	257.519	0.540524	0.270262	−	0.962787i	$-0.412890\pi$
$61$	257.519	0.540524	0.270262	+	0.962787i	$0.412890\pi$
$62$	−683.339	−1.39974
$63$	1134.07	2.26793
$64$	552.992	1.08006
$65$	−125.984	−0.240406
$66$	−233.089	−0.434716
$67$	583.828	1.06457	0.532283	−	0.846567i	$-0.321334\pi$
$67$	583.828	1.06457	0.532283	+	0.846567i	$0.321334\pi$
$68$	−101.823	−0.181586
$69$	323.924	0.565157
$70$	428.230	0.731189
$71$	−583.141	−0.974734	−0.487367	−	0.873197i	$-0.662043\pi$
$71$	−583.141	−0.974734	−0.487367	+	0.873197i	$0.662043\pi$
$72$	−838.653	−1.37273
$73$	65.7363	0.105395	0.0526976	−	0.998611i	$-0.483218\pi$
$73$	65.7363	0.105395	0.0526976	+	0.998611i	$0.483218\pi$
$74$	−316.783	−0.497638
$75$	197.632	0.304274
$76$	−15.4857	−0.0233727
$77$	−351.469	−0.520177
$78$	−533.919	−0.775056
$79$	−775.850	−1.10494	−0.552468	−	0.833534i	$-0.686314\pi$
$79$	−775.850	−1.10494	−0.552468	+	0.833534i	$0.686314\pi$
$80$	−284.077	−0.397010
$81$	−427.546	−0.586483
$82$	285.139	0.384004
$83$	−88.6690	−0.117261	−0.0586306	−	0.998280i	$-0.518673\pi$
$83$	−88.6690	−0.117261	−0.0586306	+	0.998280i	$0.518673\pi$
$84$	−205.867	−0.267405
$85$	624.653	0.797096
$86$	897.483	1.12533
$87$	1437.69	1.77169
$88$	259.914	0.314851
$89$	−668.021	−0.795618	−0.397809	−	0.917468i	$-0.630229\pi$
$89$	−668.021	−0.795618	−0.397809	+	0.917468i	$0.630229\pi$
$90$	475.695	0.557140
$91$	−805.083	−0.927425
$92$	−33.3966	−0.0378461
$93$	−2015.30	−2.24707
$94$	962.735	1.05637
$95$	95.0000	0.102598
$96$	290.404	0.308742
$97$	745.682	0.780541	0.390271	−	0.920700i	$-0.372381\pi$
$97$	745.682	0.780541	0.390271	+	0.920700i	$0.372381\pi$
$98$	1817.13	1.87304
$99$	−390.426	−0.396356
$100$	−20.3759	−0.0203759
$101$	−1486.56	−1.46454	−0.732268	−	0.681016i	$-0.761538\pi$
$101$	−1486.56	−1.46454	−0.732268	+	0.681016i	$0.761538\pi$
$102$	2647.27	2.56979
$103$	−17.1727	−0.0164279	−0.00821395	−	0.999966i	$-0.502615\pi$
$103$	−17.1727	−0.0164279	−0.00821395	+	0.999966i	$0.502615\pi$
$104$	595.364	0.561349
$105$	1262.94	1.17381
$106$	−1477.27	−1.35364
$107$	1233.48	1.11444	0.557222	−	0.830364i	$-0.311867\pi$
$107$	1233.48	1.11444	0.557222	+	0.830364i	$0.311867\pi$
$108$	−54.7228	−0.0487565
$109$	551.149	0.484317	0.242158	−	0.970237i	$-0.422145\pi$
$109$	551.149	0.484317	0.242158	+	0.970237i	$0.422145\pi$
$110$	−147.426	−0.127787
$111$	−934.255	−0.798879
$112$	−1815.35	−1.53156
$113$	−1352.23	−1.12572	−0.562862	−	0.826551i	$-0.690300\pi$
$113$	−1352.23	−1.12572	−0.562862	+	0.826551i	$0.690300\pi$
$114$	402.608	0.330769
$115$	204.879	0.166131
$116$	−148.226	−0.118642
$117$	−894.319	−0.706665
$118$	−1312.86	−1.02422
$119$	3991.75	3.07499
$120$	−933.949	−0.710479
$121$	121.000	0.0909091
$122$	690.274	0.512250
$123$	840.931	0.616457
$124$	207.778	0.150476
$125$	125.000	0.0894427
$126$	3039.86	2.14930
$127$	−310.122	−0.216684	−0.108342	−	0.994114i	$-0.534554\pi$
$127$	−310.122	−0.216684	−0.108342	+	0.994114i	$0.534554\pi$
$128$	1188.40	0.820630
$129$	2646.86	1.80653
$130$	−337.698	−0.227831
$131$	2630.77	1.75459	0.877296	−	0.479950i	$-0.159345\pi$
$131$	2630.77	1.75459	0.877296	+	0.479950i	$0.159345\pi$
$132$	70.8738	0.0467331
$133$	607.083	0.395795
$134$	1564.94	1.00888
$135$	335.708	0.214023
$136$	−2951.92	−1.86122
$137$	−2044.78	−1.27516	−0.637581	−	0.770384i	$-0.720065\pi$
$137$	−2044.78	−1.27516	−0.637581	+	0.770384i	$0.720065\pi$
$138$	868.271	0.535595
$139$	−59.3707	−0.0362285	−0.0181142	−	0.999836i	$-0.505766\pi$
$139$	−59.3707	−0.0362285	−0.0181142	+	0.999836i	$0.505766\pi$
$140$	−130.209	−0.0786048
$141$	2839.30	1.69583
$142$	−1563.10	−0.923747
$143$	277.165	0.162082
$144$	−2016.57	−1.16699
$145$	909.325	0.520795
$146$	176.205	0.0998822
$147$	5359.09	3.00687
$148$	96.3220	0.0534974
$149$	−1747.88	−0.961017	−0.480509	−	0.876990i	$-0.659548\pi$
$149$	−1747.88	−0.961017	−0.480509	+	0.876990i	$0.659548\pi$
$150$	529.748	0.288358
$151$	−2485.21	−1.33936	−0.669680	−	0.742650i	$-0.733569\pi$
$151$	−2485.21	−1.33936	−0.669680	+	0.742650i	$0.733569\pi$
$152$	−448.942	−0.239566
$153$	4434.20	2.34303
$154$	−942.106	−0.492968
$155$	−1274.66	−0.660536
$156$	162.345	0.0833206
$157$	−1890.71	−0.961116	−0.480558	−	0.876963i	$-0.659566\pi$
$157$	−1890.71	−0.961116	−0.480558	+	0.876963i	$0.659566\pi$
$158$	−2079.65	−1.04714
$159$	−4356.77	−2.17305
$160$	183.678	0.0907563
$161$	1309.25	0.640888
$162$	−1146.03	−0.555805
$163$	1855.90	0.891811	0.445905	−	0.895080i	$-0.352882\pi$
$163$	1855.90	0.891811	0.445905	+	0.895080i	$0.352882\pi$
$164$	−86.7003	−0.0412814
$165$	−434.790	−0.205141
$166$	−237.675	−0.111128
$167$	−1816.07	−0.841506	−0.420753	−	0.907175i	$-0.638234\pi$
$167$	−1816.07	−0.841506	−0.420753	+	0.907175i	$0.638234\pi$
$168$	−5968.26	−2.74084
$169$	−1562.12	−0.711024
$170$	1674.37	0.755402
$171$	674.372	0.301582
$172$	−272.892	−0.120976
$173$	2851.24	1.25304	0.626520	−	0.779405i	$-0.284479\pi$
$173$	2851.24	1.25304	0.626520	+	0.779405i	$0.284479\pi$
$174$	3853.70	1.67901
$175$	798.794	0.345046
$176$	624.970	0.267664
$177$	−3871.87	−1.64422
$178$	−1790.61	−0.754001
$179$	−1722.59	−0.719288	−0.359644	−	0.933090i	$-0.617102\pi$
$179$	−1722.59	−0.719288	−0.359644	+	0.933090i	$0.617102\pi$
$180$	−144.641	−0.0598941
$181$	2808.50	1.15334	0.576668	−	0.816978i	$-0.304353\pi$
$181$	2808.50	1.15334	0.576668	+	0.816978i	$0.304353\pi$
$182$	−2158.01	−0.878913
$183$	2035.76	0.822336
$184$	−968.195	−0.387915
$185$	−590.907	−0.234834
$186$	−5401.98	−2.12953
$187$	−1374.24	−0.537402
$188$	−292.732	−0.113562
$189$	2145.29	0.825645
$190$	254.645	0.0972312
$191$	3103.19	1.17560	0.587798	−	0.809008i	$-0.299995\pi$
$191$	3103.19	1.17560	0.587798	+	0.809008i	$0.299995\pi$
$192$	4371.55	1.64318
$193$	2520.30	0.939977	0.469988	−	0.882673i	$-0.344258\pi$
$193$	2520.30	0.939977	0.469988	+	0.882673i	$0.344258\pi$
$194$	1998.78	0.739713
$195$	−995.939	−0.365747
$196$	−552.524	−0.201357
$197$	−4127.81	−1.49286	−0.746432	−	0.665462i	$-0.768235\pi$
$197$	−4127.81	−1.49286	−0.746432	+	0.665462i	$0.768235\pi$
$198$	−1046.53	−0.375624
$199$	3301.54	1.17608	0.588040	−	0.808832i	$-0.299900\pi$
$199$	3301.54	1.17608	0.588040	+	0.808832i	$0.299900\pi$
$200$	−590.713	−0.208849
$201$	4615.32	1.61960
$202$	−3984.69	−1.38793
$203$	5810.90	2.00909
$204$	−804.937	−0.276259
$205$	531.880	0.181210
$206$	−46.0310	−0.0155686
$207$	1454.36	0.488334
$208$	1431.57	0.477219
$209$	−209.000	−0.0691714
$210$	3385.27	1.11241
$211$	−2737.47	−0.893153	−0.446576	−	0.894746i	$-0.647357\pi$
$211$	−2737.47	−0.893153	−0.446576	+	0.894746i	$0.647357\pi$
$212$	449.185	0.145519
$213$	−4609.88	−1.48293
$214$	3306.33	1.05615
$215$	1674.11	0.531039
$216$	−1586.46	−0.499744
$217$	−8145.51	−2.54817
$218$	1477.34	0.458983
$219$	519.663	0.160345
$220$	44.8269	0.0137374
$221$	−3147.86	−0.958135
$222$	−2504.25	−0.757092
$223$	−4092.53	−1.22895	−0.614475	−	0.788936i	$-0.710632\pi$
$223$	−4092.53	−1.22895	−0.614475	+	0.788936i	$0.710632\pi$
$224$	1173.77	0.350114
$225$	887.332	0.262913
$226$	−3624.61	−1.06684
$227$	−5807.93	−1.69818	−0.849088	−	0.528252i	$-0.822848\pi$
$227$	−5807.93	−1.69818	−0.849088	+	0.528252i	$0.822848\pi$
$228$	−122.418	−0.0355586
$229$	4598.59	1.32700	0.663501	−	0.748175i	$-0.269070\pi$
$229$	4598.59	1.32700	0.663501	+	0.748175i	$0.269070\pi$
$230$	549.172	0.157441
$231$	−2778.46	−0.791382
$232$	−4297.20	−1.21606
$233$	−1196.69	−0.336471	−0.168235	−	0.985747i	$-0.553807\pi$
$233$	−1196.69	−0.336471	−0.168235	+	0.985747i	$0.553807\pi$
$234$	−2397.20	−0.669701
$235$	1795.83	0.498497
$236$	399.191	0.110107
$237$	−6133.30	−1.68102
$238$	10699.8	2.91414
$239$	3874.60	1.04865	0.524324	−	0.851519i	$-0.324318\pi$
$239$	3874.60	1.04865	0.524324	+	0.851519i	$0.324318\pi$
$240$	−2245.71	−0.603999
$241$	1391.23	0.371856	0.185928	−	0.982563i	$-0.440471\pi$
$241$	1391.23	0.371856	0.185928	+	0.982563i	$0.440471\pi$
$242$	324.338	0.0861538
$243$	−5192.69	−1.37083
$244$	−209.887	−0.0550682
$245$	3389.57	0.883885
$246$	2254.10	0.584212
$247$	−478.740	−0.123326
$248$	6023.66	1.54235
$249$	−700.952	−0.178398
$250$	335.060	0.0847642
$251$	−3851.70	−0.968595	−0.484297	−	0.874903i	$-0.660925\pi$
$251$	−3851.70	−0.968595	−0.484297	+	0.874903i	$0.660925\pi$
$252$	−924.309	−0.231055
$253$	−450.733	−0.112005
$254$	−831.275	−0.205350
$255$	4938.05	1.21268
$256$	−1238.46	−0.302358
$257$	1603.63	0.389229	0.194615	−	0.980880i	$-0.437654\pi$
$257$	1603.63	0.389229	0.194615	+	0.980880i	$0.437654\pi$
$258$	7094.84	1.71204
$259$	−3776.10	−0.905929
$260$	102.682	0.0244925
$261$	6454.98	1.53086
$262$	7051.72	1.66281
$263$	−2587.41	−0.606641	−0.303321	−	0.952889i	$-0.598095\pi$
$263$	−2587.41	−0.606641	−0.303321	+	0.952889i	$0.598095\pi$
$264$	2054.69	0.479005
$265$	−2755.61	−0.638778
$266$	1627.27	0.375092
$267$	−5280.88	−1.21043
$268$	−475.840	−0.108457
$269$	−7840.10	−1.77702	−0.888512	−	0.458853i	$-0.848260\pi$
$269$	−7840.10	−1.77702	−0.888512	+	0.458853i	$0.848260\pi$
$270$	899.858	0.202828
$271$	−5267.84	−1.18081	−0.590403	−	0.807109i	$-0.701031\pi$
$271$	−5267.84	−1.18081	−0.590403	+	0.807109i	$0.701031\pi$
$272$	−7097.99	−1.58227
$273$	−6364.40	−1.41096
$274$	−5480.98	−1.20846
$275$	−275.000	−0.0603023
$276$	−264.009	−0.0575779
$277$	−1667.03	−0.361597	−0.180798	−	0.983520i	$-0.557868\pi$
$277$	−1667.03	−0.361597	−0.180798	+	0.983520i	$0.557868\pi$
$278$	−159.142	−0.0343334
$279$	−9048.36	−1.94162
$280$	−3774.86	−0.805683
$281$	5860.48	1.24415	0.622077	−	0.782956i	$-0.286289\pi$
$281$	5860.48	1.24415	0.622077	+	0.782956i	$0.286289\pi$
$282$	7610.68	1.60713
$283$	−5337.68	−1.12117	−0.560586	−	0.828096i	$-0.689424\pi$
$283$	−5337.68	−1.12117	−0.560586	+	0.828096i	$0.689424\pi$
$284$	475.280	0.0993053
$285$	751.000	0.156089
$286$	742.936	0.153604
$287$	3398.90	0.699062
$288$	1303.86	0.266774
$289$	10694.7	2.17681
$290$	2437.43	0.493554
$291$	5894.81	1.18749
$292$	−53.5774	−0.0107376
$293$	3496.53	0.697166	0.348583	−	0.937278i	$-0.386663\pi$
$293$	3496.53	0.697166	0.348583	+	0.937278i	$0.386663\pi$
$294$	14364.9	2.84959
$295$	−2448.92	−0.483327
$296$	2792.45	0.548337
$297$	−738.557	−0.144294
$298$	−4685.14	−0.910748
$299$	−1032.46	−0.199694
$300$	−161.077	−0.0309993
$301$	10698.1	2.04861
$302$	−6661.54	−1.26930
$303$	−11751.6	−2.22810
$304$	−1079.49	−0.203662
$305$	1287.60	0.241729
$306$	11885.8	2.22047
$307$	−4330.70	−0.805102	−0.402551	−	0.915398i	$-0.631876\pi$
$307$	−4330.70	−0.805102	−0.402551	+	0.915398i	$0.631876\pi$
$308$	286.460	0.0529953
$309$	−135.755	−0.0249929
$310$	−3416.70	−0.625985
$311$	3119.43	0.568768	0.284384	−	0.958711i	$-0.408211\pi$
$311$	3119.43	0.568768	0.284384	+	0.958711i	$0.408211\pi$
$312$	4706.51	0.854019
$313$	2108.82	0.380824	0.190412	−	0.981704i	$-0.439018\pi$
$313$	2108.82	0.380824	0.190412	+	0.981704i	$0.439018\pi$
$314$	−5068.01	−0.910842
$315$	5670.36	1.01425
$316$	632.345	0.112570
$317$	−5988.77	−1.06108	−0.530541	−	0.847659i	$-0.678011\pi$
$317$	−5988.77	−1.06108	−0.530541	+	0.847659i	$0.678011\pi$
$318$	−11678.2	−2.05938
$319$	−2000.51	−0.351120
$320$	2764.96	0.483019
$321$	9751.02	1.69548
$322$	3509.40	0.607365
$323$	2373.68	0.408902
$324$	348.465	0.0597506
$325$	−629.921	−0.107513
$326$	4974.70	0.845162
$327$	4356.98	0.736824
$328$	−2513.51	−0.423126
$329$	11476.0	1.92307
$330$	−1165.44	−0.194411
$331$	4373.22	0.726205	0.363102	−	0.931749i	$-0.381718\pi$
$331$	4373.22	0.726205	0.363102	+	0.931749i	$0.381718\pi$
$332$	72.2683	0.0119465
$333$	−4194.64	−0.690285
$334$	−4867.93	−0.797489
$335$	2919.14	0.476088
$336$	−14350.8	−2.33007
$337$	−9017.00	−1.45753	−0.728765	−	0.684764i	$-0.759905\pi$
$337$	−9017.00	−1.45753	−0.728765	+	0.684764i	$0.759905\pi$
$338$	−4187.23	−0.673832
$339$	−10689.7	−1.71264
$340$	−509.114	−0.0812077
$341$	2804.25	0.445333
$342$	1807.64	0.285807
$343$	10701.1	1.68456
$344$	−7911.35	−1.23997
$345$	1619.62	0.252746
$346$	7642.70	1.18750
$347$	11232.4	1.73772	0.868859	−	0.495059i	$-0.164854\pi$
$347$	11232.4	1.73772	0.868859	+	0.495059i	$0.164854\pi$
$348$	−1171.77	−0.180498
$349$	−2135.42	−0.327526	−0.163763	−	0.986500i	$-0.552363\pi$
$349$	−2135.42	−0.327526	−0.163763	+	0.986500i	$0.552363\pi$
$350$	2141.15	0.326998
$351$	−1691.76	−0.257263
$352$	−404.091	−0.0611879
$353$	9167.04	1.38219	0.691094	−	0.722765i	$-0.257129\pi$
$353$	9167.04	1.38219	0.691094	+	0.722765i	$0.257129\pi$
$354$	−10378.5	−1.55822
$355$	−2915.70	−0.435914
$356$	544.460	0.0810571
$357$	31555.9	4.67819
$358$	−4617.37	−0.681663
$359$	−1310.59	−0.192675	−0.0963377	−	0.995349i	$-0.530713\pi$
$359$	−1310.59	−0.192675	−0.0963377	+	0.995349i	$0.530713\pi$
$360$	−4193.27	−0.613901
$361$	361.000	0.0526316
$362$	7528.12	1.09301
$363$	956.537	0.138306
$364$	656.171	0.0944855
$365$	328.681	0.0471342
$366$	5456.80	0.779322
$367$	−12987.7	−1.84728	−0.923640	−	0.383262i	$-0.874801\pi$
$367$	−12987.7	−1.84728	−0.923640	+	0.383262i	$0.874801\pi$
$368$	−2328.05	−0.329778
$369$	3775.63	0.532660
$370$	−1583.91	−0.222551
$371$	−17609.3	−2.46424
$372$	1642.54	0.228930
$373$	−14099.0	−1.95716	−0.978580	−	0.205866i	$-0.933999\pi$
$373$	−14099.0	−1.95716	−0.978580	+	0.205866i	$0.933999\pi$
$374$	−3683.61	−0.509292
$375$	988.159	0.136075
$376$	−8486.54	−1.16399
$377$	−4582.42	−0.626013
$378$	5750.40	0.782457
$379$	5577.34	0.755906	0.377953	−	0.925825i	$-0.376628\pi$
$379$	5577.34	0.755906	0.377953	+	0.925825i	$0.376628\pi$
$380$	−77.4284	−0.0104526
$381$	−2451.60	−0.329656
$382$	8318.03	1.11410
$383$	−159.569	−0.0212887	−0.0106444	−	0.999943i	$-0.503388\pi$
$383$	−159.569	−0.0212887	−0.0106444	+	0.999943i	$0.503388\pi$
$384$	9394.62	1.24848
$385$	−1757.35	−0.232630
$386$	6755.62	0.890809
$387$	11883.9	1.56097
$388$	−607.757	−0.0795211
$389$	−3882.47	−0.506039	−0.253019	−	0.967461i	$-0.581424\pi$
$389$	−3882.47	−0.506039	−0.253019	+	0.967461i	$0.581424\pi$
$390$	−2669.59	−0.346616
$391$	5119.12	0.662110
$392$	−16018.1	−2.06387
$393$	20796.9	2.66938
$394$	−11064.5	−1.41478
$395$	−3879.25	−0.494142
$396$	318.211	0.0403806
$397$	−1903.04	−0.240582	−0.120291	−	0.992739i	$-0.538383\pi$
$397$	−1903.04	−0.240582	−0.120291	+	0.992739i	$0.538383\pi$
$398$	8849.70	1.11456
$399$	4799.16	0.602151
$400$	−1420.39	−0.177548
$401$	−13632.0	−1.69763	−0.848813	−	0.528694i	$-0.822682\pi$
$401$	−13632.0	−1.69763	−0.848813	+	0.528694i	$0.822682\pi$
$402$	12371.3	1.53488
$403$	6423.48	0.793985
$404$	1211.60	0.149206
$405$	−2137.73	−0.262283
$406$	15576.0	1.90400
$407$	1300.00	0.158325
$408$	−23335.8	−2.83160
$409$	−2428.58	−0.293607	−0.146804	−	0.989166i	$-0.546899\pi$
$409$	−2428.58	−0.293607	−0.146804	+	0.989166i	$0.546899\pi$
$410$	1425.69	0.171732
$411$	−16164.5	−1.93999
$412$	13.9963	0.00167367
$413$	−15649.5	−1.86455
$414$	3898.39	0.462790
$415$	−443.345	−0.0524408
$416$	−925.620	−0.109092
$417$	−469.341	−0.0551169
$418$	−560.220	−0.0655532
$419$	9820.40	1.14501	0.572504	−	0.819902i	$-0.305972\pi$
$419$	9820.40	1.14501	0.572504	+	0.819902i	$0.305972\pi$
$420$	−1029.34	−0.119587
$421$	−1198.03	−0.138690	−0.0693452	−	0.997593i	$-0.522091\pi$
$421$	−1198.03	−0.138690	−0.0693452	+	0.997593i	$0.522091\pi$
$422$	−7337.73	−0.846434
$423$	12748.0	1.46531
$424$	13022.2	1.49154
$425$	3123.27	0.356472
$426$	−12356.7	−1.40536
$427$	8228.18	0.932529
$428$	−1005.33	−0.113539
$429$	2191.07	0.246587
$430$	4487.42	0.503261
$431$	6527.12	0.729467	0.364734	−	0.931112i	$-0.381160\pi$
$431$	6527.12	0.729467	0.364734	+	0.931112i	$0.381160\pi$
$432$	−3814.68	−0.424847
$433$	643.566	0.0714268	0.0357134	−	0.999362i	$-0.488630\pi$
$433$	643.566	0.0714268	0.0357134	+	0.999362i	$0.488630\pi$
$434$	−21833.9	−2.41488
$435$	7188.46	0.792322
$436$	−449.206	−0.0493419
$437$	778.538	0.0852232
$438$	1392.95	0.151958
$439$	5557.92	0.604249	0.302124	−	0.953269i	$-0.402304\pi$
$439$	5557.92	0.604249	0.302124	+	0.953269i	$0.402304\pi$
$440$	1299.57	0.140806
$441$	24061.4	2.59814
$442$	−8437.77	−0.908017
$443$	−9886.64	−1.06034	−0.530168	−	0.847893i	$-0.677871\pi$
$443$	−9886.64	−1.06034	−0.530168	+	0.847893i	$0.677871\pi$
$444$	761.451	0.0813894
$445$	−3340.10	−0.355811
$446$	−10969.9	−1.16467
$447$	−13817.4	−1.46206
$448$	17669.1	1.86336
$449$	11846.6	1.24516	0.622580	−	0.782556i	$-0.286085\pi$
$449$	11846.6	1.24516	0.622580	+	0.782556i	$0.286085\pi$
$450$	2378.47	0.249161
$451$	−1170.14	−0.122172
$452$	1102.11	0.114688
$453$	−19646.2	−2.03766
$454$	−15568.0	−1.60935
$455$	−4025.42	−0.414757
$456$	−3549.00	−0.364468
$457$	11041.7	1.13021	0.565107	−	0.825017i	$-0.308835\pi$
$457$	11041.7	1.13021	0.565107	+	0.825017i	$0.308835\pi$
$458$	12326.4	1.25759
$459$	8388.04	0.852985
$460$	−166.983	−0.0169253
$461$	3029.02	0.306020	0.153010	−	0.988225i	$-0.451103\pi$
$461$	3029.02	0.306020	0.153010	+	0.988225i	$0.451103\pi$
$462$	−7447.60	−0.749986
$463$	−15399.4	−1.54572	−0.772860	−	0.634576i	$-0.781175\pi$
$463$	−15399.4	−1.54572	−0.772860	+	0.634576i	$0.781175\pi$
$464$	−10332.7	−1.03380
$465$	−10076.5	−1.00492
$466$	−3207.70	−0.318871
$467$	−15413.4	−1.52730	−0.763650	−	0.645631i	$-0.776595\pi$
$467$	−15413.4	−1.52730	−0.763650	+	0.645631i	$0.776595\pi$
$468$	728.901	0.0719946
$469$	18654.3	1.83662
$470$	4813.67	0.472422
$471$	−14946.6	−1.46221
$472$	11572.9	1.12857
$473$	−3683.04	−0.358026
$474$	−16440.2	−1.59309
$475$	475.000	0.0458831
$476$	−3253.42	−0.313278
$477$	−19561.2	−1.87766
$478$	10385.8	0.993796
$479$	−1062.46	−0.101346	−0.0506731	−	0.998715i	$-0.516137\pi$
$479$	−1062.46	−0.101346	−0.0506731	+	0.998715i	$0.516137\pi$
$480$	1452.02	0.138074
$481$	2977.80	0.282278
$482$	3729.17	0.352405
$483$	10349.9	0.975028
$484$	−98.6193	−0.00926177
$485$	3728.41	0.349069
$486$	−13918.9	−1.29912
$487$	1369.05	0.127387	0.0636936	−	0.997970i	$-0.479712\pi$
$487$	1369.05	0.127387	0.0636936	+	0.997970i	$0.479712\pi$
$488$	−6084.79	−0.564438
$489$	14671.4	1.35677
$490$	9085.67	0.837651
$491$	−4762.30	−0.437718	−0.218859	−	0.975757i	$-0.570233\pi$
$491$	−4762.30	−0.437718	−0.218859	+	0.975757i	$0.570233\pi$
$492$	−685.389	−0.0628043
$493$	22720.5	2.07562
$494$	−1283.25	−0.116875
$495$	−1952.13	−0.177256
$496$	14484.1	1.31120
$497$	−18632.4	−1.68164
$498$	−1878.89	−0.169066
$499$	−13434.7	−1.20525	−0.602627	−	0.798023i	$-0.705879\pi$
$499$	−13434.7	−1.20525	−0.602627	+	0.798023i	$0.705879\pi$
$500$	−101.879	−0.00911237
$501$	−14356.5	−1.28024
$502$	−10324.4	−0.917930
$503$	8416.76	0.746093	0.373047	−	0.927813i	$-0.378313\pi$
$503$	8416.76	0.746093	0.373047	+	0.927813i	$0.378313\pi$
$504$	−26796.4	−2.36827
$505$	−7432.80	−0.654961
$506$	−1208.18	−0.106146
$507$	−12349.0	−1.08173
$508$	252.760	0.0220756
$509$	10518.2	0.915938	0.457969	−	0.888968i	$-0.348577\pi$
$509$	10518.2	0.915938	0.457969	+	0.888968i	$0.348577\pi$
$510$	13236.3	1.14924
$511$	2100.39	0.181831
$512$	−12826.9	−1.10717
$513$	1275.69	0.109792
$514$	4298.50	0.368869
$515$	−85.8634	−0.00734678
$516$	−2157.28	−0.184049
$517$	−3950.82	−0.336087
$518$	−10121.8	−0.858542
$519$	22539.8	1.90634
$520$	2976.82	0.251043
$521$	−20745.1	−1.74445	−0.872226	−	0.489102i	$-0.837324\pi$
$521$	−20745.1	−1.74445	−0.872226	+	0.489102i	$0.837324\pi$
$522$	17302.4	1.45078
$523$	1248.72	0.104403	0.0522014	−	0.998637i	$-0.483376\pi$
$523$	1248.72	0.104403	0.0522014	+	0.998637i	$0.483376\pi$
$524$	−2144.17	−0.178757
$525$	6314.68	0.524943
$526$	−6935.50	−0.574909
$527$	−31848.8	−2.63255
$528$	4940.55	0.407216
$529$	−10488.0	−0.862003
$530$	−7386.37	−0.605365
$531$	−17384.0	−1.42072
$532$	−494.794	−0.0403234
$533$	−2680.34	−0.217821
$534$	−14155.3	−1.14711
$535$	6167.42	0.498394
$536$	−13795.0	−1.11167
$537$	−13617.5	−1.09430
$538$	−21015.2	−1.68407
$539$	−7457.06	−0.595915
$540$	−273.614	−0.0218046
$541$	9109.76	0.723954	0.361977	−	0.932187i	$-0.382102\pi$
$541$	9109.76	0.723954	0.361977	+	0.932187i	$0.382102\pi$
$542$	−14120.3	−1.11904
$543$	22201.9	1.75465
$544$	4589.40	0.361707
$545$	2755.75	0.216593
$546$	−17059.6	−1.33715
$547$	−4974.70	−0.388854	−0.194427	−	0.980917i	$-0.562285\pi$
$547$	−4974.70	−0.388854	−0.194427	+	0.980917i	$0.562285\pi$
$548$	1666.57	0.129913
$549$	9140.19	0.710554
$550$	−737.132	−0.0571480
$551$	3455.43	0.267162
$552$	−7653.84	−0.590161
$553$	−24789.8	−1.90627
$554$	−4468.45	−0.342682
$555$	−4671.28	−0.357270
$556$	48.3892	0.00369094
$557$	17172.4	1.30632	0.653160	−	0.757220i	$-0.273443\pi$
$557$	17172.4	1.30632	0.653160	+	0.757220i	$0.273443\pi$
$558$	−24253.9	−1.84006
$559$	−8436.46	−0.638326
$560$	−9076.76	−0.684934
$561$	−10863.7	−0.817587
$562$	15708.9	1.17907
$563$	−13256.7	−0.992366	−0.496183	−	0.868218i	$-0.665266\pi$
$563$	−13256.7	−0.992366	−0.496183	+	0.868218i	$0.665266\pi$
$564$	−2314.13	−0.172770
$565$	−6761.13	−0.503439
$566$	−14307.5	−1.06253
$567$	−13660.8	−1.01182
$568$	13778.7	1.01786
$569$	2643.60	0.194772	0.0973860	−	0.995247i	$-0.468952\pi$
$569$	2643.60	0.194772	0.0973860	+	0.995247i	$0.468952\pi$
$570$	2013.04	0.147925
$571$	16353.9	1.19858	0.599288	−	0.800533i	$-0.295450\pi$
$571$	16353.9	1.19858	0.599288	+	0.800533i	$0.295450\pi$
$572$	−225.900	−0.0165128
$573$	24531.5	1.78852
$574$	9110.68	0.662496
$575$	1024.39	0.0742959
$576$	19627.5	1.41981
$577$	−17453.0	−1.25923	−0.629616	−	0.776907i	$-0.716788\pi$
$577$	−17453.0	−1.25923	−0.629616	+	0.776907i	$0.716788\pi$
$578$	28666.8	2.06294
$579$	19923.7	1.43005
$580$	−741.132	−0.0530583
$581$	−2833.13	−0.202303
$582$	15800.9	1.12538
$583$	6062.35	0.430664
$584$	−1553.25	−0.110058
$585$	−4471.59	−0.316030
$586$	9372.38	0.660699
$587$	24373.6	1.71381	0.856904	−	0.515476i	$-0.172385\pi$
$587$	24373.6	1.71381	0.856904	+	0.515476i	$0.172385\pi$
$588$	−4367.85	−0.306339
$589$	−4843.70	−0.338848
$590$	−6564.28	−0.458046
$591$	−32631.4	−2.27120
$592$	6714.53	0.466158
$593$	−6078.41	−0.420928	−0.210464	−	0.977602i	$-0.567497\pi$
$593$	−6078.41	−0.420928	−0.210464	+	0.977602i	$0.567497\pi$
$594$	−1979.69	−0.136747
$595$	19958.8	1.37518
$596$	1424.58	0.0979079
$597$	26099.5	1.78925
$598$	−2767.48	−0.189249
$599$	9808.66	0.669066	0.334533	−	0.942384i	$-0.391421\pi$
$599$	9808.66	0.669066	0.334533	+	0.942384i	$0.391421\pi$
$600$	−4669.74	−0.317736
$601$	−15863.8	−1.07670	−0.538351	−	0.842720i	$-0.680953\pi$
$601$	−15863.8	−1.07670	−0.538351	+	0.842720i	$0.680953\pi$
$602$	28676.2	1.94145
$603$	20722.0	1.39944
$604$	2025.53	0.136453
$605$	605.000	0.0406558
$606$	−31500.0	−2.11155
$607$	2159.92	0.144429	0.0722144	−	0.997389i	$-0.476993\pi$
$607$	2159.92	0.144429	0.0722144	+	0.997389i	$0.476993\pi$
$608$	697.975	0.0465570
$609$	45936.8	3.05657
$610$	3451.37	0.229085
$611$	−9049.83	−0.599210
$612$	−3614.03	−0.238707
$613$	5048.77	0.332655	0.166328	−	0.986071i	$-0.446809\pi$
$613$	5048.77	0.332655	0.166328	+	0.986071i	$0.446809\pi$
$614$	−11608.4	−0.762989
$615$	4204.66	0.275688
$616$	8304.69	0.543191
$617$	24148.0	1.57563	0.787815	−	0.615912i	$-0.211212\pi$
$617$	24148.0	1.57563	0.787815	+	0.615912i	$0.211212\pi$
$618$	−363.887	−0.0236856
$619$	17093.0	1.10990	0.554948	−	0.831885i	$-0.312738\pi$
$619$	17093.0	1.10990	0.554948	+	0.831885i	$0.312738\pi$
$620$	1038.89	0.0672950
$621$	2751.17	0.177779
$622$	8361.57	0.539017
$623$	−21344.4	−1.37263
$624$	11316.9	0.726026
$625$	625.000	0.0400000
$626$	5652.66	0.360904
$627$	−1652.20	−0.105235
$628$	1541.00	0.0979179
$629$	−14764.5	−0.935927
$630$	15199.3	0.961196
$631$	9732.75	0.614033	0.307016	−	0.951704i	$-0.400669\pi$
$631$	9732.75	0.614033	0.307016	+	0.951704i	$0.400669\pi$
$632$	18332.2	1.15382
$633$	−21640.4	−1.35882
$634$	−16052.8	−1.00558
$635$	−1550.61	−0.0969040
$636$	3550.93	0.221389
$637$	−17081.3	−1.06246
$638$	−5362.34	−0.332754
$639$	−20697.6	−1.28135
$640$	5942.00	0.366997
$641$	−23050.7	−1.42035	−0.710176	−	0.704024i	$-0.751385\pi$
$641$	−23050.7	−1.42035	−0.710176	+	0.704024i	$0.751385\pi$
$642$	26137.4	1.60679
$643$	−7679.92	−0.471021	−0.235511	−	0.971872i	$-0.575676\pi$
$643$	−7679.92	−0.471021	−0.235511	+	0.971872i	$0.575676\pi$
$644$	−1067.08	−0.0652933
$645$	13234.3	0.807906
$646$	6362.60	0.387513
$647$	−21469.5	−1.30456	−0.652281	−	0.757977i	$-0.726188\pi$
$647$	−21469.5	−1.30456	−0.652281	+	0.757977i	$0.726188\pi$
$648$	10102.3	0.612431
$649$	5387.62	0.325859
$650$	−1688.49	−0.101889
$651$	−64392.5	−3.87671
$652$	−1512.62	−0.0908572
$653$	28051.6	1.68108	0.840539	−	0.541751i	$-0.182238\pi$
$653$	28051.6	1.68108	0.840539	+	0.541751i	$0.182238\pi$
$654$	11678.8	0.698283
$655$	13153.9	0.784677
$656$	−6043.80	−0.359712
$657$	2333.20	0.138549
$658$	30761.1	1.82248
$659$	24591.2	1.45362	0.726811	−	0.686837i	$-0.241002\pi$
$659$	24591.2	1.45362	0.726811	+	0.686837i	$0.241002\pi$
$660$	354.369	0.0208997
$661$	30270.4	1.78121	0.890606	−	0.454776i	$-0.150281\pi$
$661$	30270.4	1.78121	0.890606	+	0.454776i	$0.150281\pi$
$662$	11722.3	0.688219
$663$	−24884.7	−1.45768
$664$	2095.12	0.122449
$665$	3035.42	0.177005
$666$	−11243.7	−0.654178
$667$	7452.05	0.432600
$668$	1480.16	0.0857322
$669$	−32352.5	−1.86969
$670$	7824.69	0.451185
$671$	−2832.71	−0.162974
$672$	9278.93	0.532652
$673$	−30999.0	−1.77552	−0.887759	−	0.460309i	$-0.847739\pi$
$673$	−30999.0	−1.77552	−0.887759	+	0.460309i	$0.847739\pi$
$674$	−24169.9	−1.38129
$675$	1678.54	0.0957141
$676$	1273.18	0.0724387
$677$	−4262.95	−0.242007	−0.121003	−	0.992652i	$-0.538611\pi$
$677$	−4262.95	−0.242007	−0.121003	+	0.992652i	$0.538611\pi$
$678$	−28653.5	−1.62306
$679$	23825.8	1.34662
$680$	−14759.6	−0.832361
$681$	−45913.2	−2.58355
$682$	7516.73	0.422039
$683$	27262.4	1.52733	0.763664	−	0.645613i	$-0.223398\pi$
$683$	27262.4	1.52733	0.763664	+	0.645613i	$0.223398\pi$
$684$	−549.637	−0.0307250
$685$	−10223.9	−0.570270
$686$	28684.1	1.59645
$687$	36353.1	2.01886
$688$	−19023.1	−1.05414
$689$	13886.6	0.767831
$690$	4341.36	0.239525
$691$	−16164.9	−0.889928	−0.444964	−	0.895548i	$-0.646784\pi$
$691$	−16164.9	−0.889928	−0.444964	+	0.895548i	$0.646784\pi$
$692$	−2323.86	−0.127659
$693$	−12474.8	−0.683807
$694$	30108.3	1.64682
$695$	−296.853	−0.0162019
$696$	−33970.5	−1.85007
$697$	13289.6	0.722210
$698$	−5723.95	−0.310394
$699$	−9460.15	−0.511897
$700$	−651.045	−0.0351531
$701$	21256.9	1.14531	0.572654	−	0.819797i	$-0.305914\pi$
$701$	21256.9	1.14531	0.572654	+	0.819797i	$0.305914\pi$
$702$	−4534.72	−0.243806
$703$	−2245.45	−0.120467
$704$	−6082.92	−0.325651
$705$	14196.5	0.758398
$706$	24572.1	1.30989
$707$	−47498.2	−2.52667
$708$	3155.71	0.167513
$709$	7157.44	0.379130	0.189565	−	0.981868i	$-0.439292\pi$
$709$	7157.44	0.379130	0.189565	+	0.981868i	$0.439292\pi$
$710$	−7815.48	−0.413112
$711$	−27537.5	−1.45251
$712$	15784.3	0.830819
$713$	−10446.0	−0.548676
$714$	84584.8	4.43348
$715$	1385.83	0.0724853
$716$	1403.97	0.0732806
$717$	30629.7	1.59538
$718$	−3513.02	−0.182597
$719$	24863.2	1.28963	0.644813	−	0.764341i	$-0.276935\pi$
$719$	24863.2	1.28963	0.644813	+	0.764341i	$0.276935\pi$
$720$	−10082.8	−0.521896
$721$	−548.697	−0.0283419
$722$	967.653	0.0498785
$723$	10998.1	0.565731
$724$	−2289.02	−0.117501
$725$	4546.62	0.232907
$726$	2563.98	0.131072
$727$	7845.69	0.400248	0.200124	−	0.979771i	$-0.435865\pi$
$727$	7845.69	0.400248	0.200124	+	0.979771i	$0.435865\pi$
$728$	19022.9	0.968457
$729$	−29505.9	−1.49905
$730$	881.023	0.0446687
$731$	41829.5	2.11644
$732$	−1659.21	−0.0837791
$733$	11332.7	0.571052	0.285526	−	0.958371i	$-0.407832\pi$
$733$	11332.7	0.571052	0.285526	+	0.958371i	$0.407832\pi$
$734$	−34813.2	−1.75065
$735$	26795.5	1.34472
$736$	1505.27	0.0753870
$737$	−6422.11	−0.320979
$738$	10120.5	0.504798
$739$	−17851.4	−0.888598	−0.444299	−	0.895878i	$-0.646547\pi$
$739$	−17851.4	−0.888598	−0.444299	+	0.895878i	$0.646547\pi$
$740$	481.610	0.0239248
$741$	−3784.57	−0.187624
$742$	−47201.5	−2.33534
$743$	16064.7	0.793210	0.396605	−	0.917989i	$-0.370188\pi$
$743$	16064.7	0.793210	0.396605	+	0.917989i	$0.370188\pi$
$744$	47618.6	2.34648
$745$	−8739.38	−0.429780
$746$	−37792.2	−1.85479
$747$	−3147.15	−0.154148
$748$	1120.05	0.0547502
$749$	39412.0	1.92267
$750$	2648.74	0.128958
$751$	−18179.6	−0.883333	−0.441667	−	0.897179i	$-0.645613\pi$
$751$	−18179.6	−0.883333	−0.441667	+	0.897179i	$0.645613\pi$
$752$	−20406.1	−0.989541
$753$	−30448.7	−1.47359
$754$	−12283.1	−0.593268
$755$	−12426.0	−0.598980
$756$	−1748.49	−0.0841162
$757$	18603.7	0.893214	0.446607	−	0.894730i	$-0.352632\pi$
$757$	18603.7	0.893214	0.446607	+	0.894730i	$0.352632\pi$
$758$	14949.9	0.716367
$759$	−3563.16	−0.170401
$760$	−2244.71	−0.107137
$761$	39448.3	1.87910	0.939552	−	0.342406i	$-0.111242\pi$
$761$	39448.3	1.87910	0.939552	+	0.342406i	$0.111242\pi$
$762$	−6571.45	−0.312413
$763$	17610.2	0.835558
$764$	−2529.21	−0.119769
$765$	22171.0	1.04783
$766$	−427.721	−0.0201752
$767$	12341.0	0.580975
$768$	−9790.35	−0.459999
$769$	15494.6	0.726594	0.363297	−	0.931673i	$-0.381651\pi$
$769$	15494.6	0.726594	0.363297	+	0.931673i	$0.381651\pi$
$770$	−4710.53	−0.220462
$771$	12677.2	0.592161
$772$	−2054.14	−0.0957643
$773$	25862.1	1.20336	0.601679	−	0.798738i	$-0.294499\pi$
$773$	25862.1	1.20336	0.601679	+	0.798738i	$0.294499\pi$
$774$	31854.6	1.47932
$775$	−6373.29	−0.295401
$776$	−17619.4	−0.815074
$777$	−29851.1	−1.37825
$778$	−10406.9	−0.479569
$779$	2021.15	0.0929590
$780$	811.726	0.0372621
$781$	6414.55	0.293893
$782$	13721.7	0.627477
$783$	12210.7	0.557311
$784$	−38516.0	−1.75455
$785$	−9453.55	−0.429824
$786$	55745.8	2.52975
$787$	−19411.5	−0.879218	−0.439609	−	0.898189i	$-0.644883\pi$
$787$	−19411.5	−0.879218	−0.439609	+	0.898189i	$0.644883\pi$
$788$	3364.31	0.152092
$789$	−20454.2	−0.922926
$790$	−10398.2	−0.468295
$791$	−43206.0	−1.94213
$792$	9225.18	0.413892
$793$	−6488.67	−0.290567
$794$	−5101.07	−0.227998
$795$	−21783.9	−0.971817
$796$	−2690.87	−0.119818
$797$	14428.2	0.641245	0.320623	−	0.947207i	$-0.396108\pi$
$797$	14428.2	0.641245	0.320623	+	0.947207i	$0.396108\pi$
$798$	12864.0	0.570654
$799$	44870.8	1.98675
$800$	918.389	0.0405874
$801$	−23710.2	−1.04589
$802$	−36540.2	−1.60883
$803$	−723.099	−0.0317779
$804$	−3761.65	−0.165004
$805$	6546.23	0.286614
$806$	17218.0	0.752454
$807$	−61978.1	−2.70351
$808$	35125.2	1.52933
$809$	−20243.8	−0.879770	−0.439885	−	0.898054i	$-0.644981\pi$
$809$	−20243.8	−0.879770	−0.439885	+	0.898054i	$0.644981\pi$
$810$	−5730.14	−0.248564
$811$	−19509.4	−0.844718	−0.422359	−	0.906429i	$-0.638798\pi$
$811$	−19509.4	−0.844718	−0.422359	+	0.906429i	$0.638798\pi$
$812$	−4736.09	−0.204685
$813$	−41643.7	−1.79644
$814$	3484.61	0.150044
$815$	9279.49	0.398830
$816$	−56111.5	−2.40722
$817$	6361.62	0.272417
$818$	−6509.75	−0.278249
$819$	−28575.0	−1.21916
$820$	−433.501	−0.0184616
$821$	−18097.0	−0.769293	−0.384647	−	0.923064i	$-0.625677\pi$
$821$	−18097.0	−0.769293	−0.384647	+	0.923064i	$0.625677\pi$
$822$	−43328.6	−1.83852
$823$	−42644.2	−1.80618	−0.903089	−	0.429454i	$-0.858706\pi$
$823$	−42644.2	−1.80618	−0.903089	+	0.429454i	$0.858706\pi$
$824$	405.765	0.0171547
$825$	−2173.95	−0.0917420
$826$	−41948.0	−1.76702
$827$	−10983.0	−0.461811	−0.230905	−	0.972976i	$-0.574169\pi$
$827$	−10983.0	−0.461811	−0.230905	+	0.972976i	$0.574169\pi$
$828$	−1185.36	−0.0497512
$829$	−15447.7	−0.647192	−0.323596	−	0.946195i	$-0.604892\pi$
$829$	−15447.7	−0.647192	−0.323596	+	0.946195i	$0.604892\pi$
$830$	−1188.38	−0.0496978
$831$	−13178.3	−0.550122
$832$	−13933.7	−0.580604
$833$	84692.2	3.52270
$834$	−1258.06	−0.0522338
$835$	−9080.34	−0.376333
$836$	170.342	0.00704715
$837$	−17116.5	−0.706850
$838$	26323.4	1.08511
$839$	24868.3	1.02330	0.511651	−	0.859194i	$-0.329034\pi$
$839$	24868.3	1.02330	0.511651	+	0.859194i	$0.329034\pi$
$840$	−29841.3	−1.22574
$841$	8685.87	0.356139
$842$	−3211.31	−0.131436
$843$	46328.7	1.89282
$844$	2231.14	0.0909939
$845$	−7810.59	−0.317979
$846$	34170.6	1.38866
$847$	3866.16	0.156839
$848$	31312.3	1.26801
$849$	−42195.8	−1.70572
$850$	8371.85	0.337826
$851$	−4842.56	−0.195066
$852$	3757.22	0.151080
$853$	−2796.09	−0.112235	−0.0561173	−	0.998424i	$-0.517872\pi$
$853$	−2796.09	−0.112235	−0.0561173	+	0.998424i	$0.517872\pi$
$854$	22055.5	0.883750
$855$	3371.86	0.134872
$856$	−29145.4	−1.16375
$857$	−9712.66	−0.387139	−0.193570	−	0.981087i	$-0.562007\pi$
$857$	−9712.66	−0.387139	−0.193570	+	0.981087i	$0.562007\pi$
$858$	5873.11	0.233688
$859$	−25191.1	−1.00059	−0.500297	−	0.865854i	$-0.666776\pi$
$859$	−25191.1	−1.00059	−0.500297	+	0.865854i	$0.666776\pi$
$860$	−1364.46	−0.0541019
$861$	26869.2	1.06353
$862$	17495.8	0.691311
$863$	−12313.8	−0.485710	−0.242855	−	0.970063i	$-0.578084\pi$
$863$	−12313.8	−0.485710	−0.242855	+	0.970063i	$0.578084\pi$
$864$	2466.48	0.0971197
$865$	14256.2	0.560377
$866$	1725.07	0.0676907
$867$	84544.2	3.31173
$868$	6638.88	0.259606
$869$	8534.35	0.333151
$870$	19268.5	0.750878
$871$	−14710.6	−0.572274
$872$	−13022.8	−0.505744
$873$	26466.7	1.02607
$874$	2086.86	0.0807654
$875$	3993.97	0.154309
$876$	−423.544	−0.0163359
$877$	27910.7	1.07466	0.537330	−	0.843372i	$-0.319433\pi$
$877$	27910.7	1.07466	0.537330	+	0.843372i	$0.319433\pi$
$878$	14897.9	0.572642
$879$	27641.0	1.06065
$880$	3124.85	0.119703
$881$	22184.2	0.848358	0.424179	−	0.905578i	$-0.360563\pi$
$881$	22184.2	0.848358	0.424179	+	0.905578i	$0.360563\pi$
$882$	64496.0	2.46224
$883$	25448.2	0.969877	0.484939	−	0.874548i	$-0.338842\pi$
$883$	25448.2	0.969877	0.484939	+	0.874548i	$0.338842\pi$
$884$	2565.62	0.0976142
$885$	−19359.4	−0.735320
$886$	−26500.9	−1.00487
$887$	−6271.45	−0.237401	−0.118701	−	0.992930i	$-0.537873\pi$
$887$	−6271.45	−0.237401	−0.118701	+	0.992930i	$0.537873\pi$
$888$	22075.1	0.834224
$889$	−9908.93	−0.373830
$890$	−8953.07	−0.337200
$891$	4703.01	0.176831
$892$	3335.56	0.125205
$893$	6824.14	0.255724
$894$	−37037.3	−1.38559
$895$	−8612.96	−0.321675
$896$	37971.4	1.41578
$897$	−8161.86	−0.303809
$898$	31754.6	1.18003
$899$	−46363.2	−1.72002
$900$	−723.207	−0.0267854
$901$	−68852.1	−2.54583
$902$	−3136.53	−0.115782
$903$	84571.7	3.11669
$904$	31951.1	1.17553
$905$	14042.5	0.515788
$906$	−52661.3	−1.93107
$907$	47181.5	1.72727	0.863637	−	0.504115i	$-0.168181\pi$
$907$	47181.5	1.72727	0.863637	+	0.504115i	$0.168181\pi$
$908$	4733.67	0.173009
$909$	−52762.8	−1.92523
$910$	−10790.0	−0.393062
$911$	7347.84	0.267228	0.133614	−	0.991033i	$-0.457342\pi$
$911$	7347.84	0.267228	0.133614	+	0.991033i	$0.457342\pi$
$912$	−8533.68	−0.309845
$913$	975.358	0.0353556
$914$	29597.0	1.07110
$915$	10178.8	0.367760
$916$	−3748.02	−0.135194
$917$	84057.7	3.02708
$918$	22484.0	0.808367
$919$	−12945.8	−0.464681	−0.232341	−	0.972634i	$-0.574638\pi$
$919$	−12945.8	−0.464681	−0.232341	+	0.972634i	$0.574638\pi$
$920$	−4840.97	−0.173481
$921$	−34235.4	−1.22486
$922$	8119.22	0.290013
$923$	14693.3	0.523983
$924$	2264.54	0.0806255
$925$	−2954.53	−0.105021
$926$	−41277.6	−1.46487
$927$	−609.514	−0.0215956
$928$	6680.91	0.236327
$929$	10306.1	0.363974	0.181987	−	0.983301i	$-0.441747\pi$
$929$	10306.1	0.363974	0.181987	+	0.983301i	$0.441747\pi$
$930$	−27009.9	−0.952354
$931$	12880.4	0.453423
$932$	975.344	0.0342795
$933$	24659.9	0.865306
$934$	−41315.4	−1.44741
$935$	−6871.18	−0.240333
$936$	21131.4	0.737929
$937$	−20133.7	−0.701964	−0.350982	−	0.936382i	$-0.614152\pi$
$937$	−20133.7	−0.701964	−0.350982	+	0.936382i	$0.614152\pi$
$938$	50002.5	1.74055
$939$	16670.8	0.579374
$940$	−1463.66	−0.0507866
$941$	−3503.13	−0.121359	−0.0606795	−	0.998157i	$-0.519327\pi$
$941$	−3503.13	−0.121359	−0.0606795	+	0.998157i	$0.519327\pi$
$942$	−40064.0	−1.38573
$943$	4358.83	0.150523
$944$	27827.3	0.959429
$945$	10726.5	0.369240
$946$	−9872.31	−0.339299
$947$	40539.3	1.39108	0.695539	−	0.718489i	$-0.255166\pi$
$947$	40539.3	1.39108	0.695539	+	0.718489i	$0.255166\pi$
$948$	4998.86	0.171261
$949$	−1656.35	−0.0566568
$950$	1273.23	0.0434831
$951$	−47342.8	−1.61430
$952$	−94319.2	−3.21103
$953$	44645.6	1.51754	0.758768	−	0.651360i	$-0.225801\pi$
$953$	44645.6	1.51754	0.758768	+	0.651360i	$0.225801\pi$
$954$	−52433.3	−1.77944
$955$	15515.9	0.525742
$956$	−3157.93	−0.106836
$957$	−15814.6	−0.534183
$958$	−2847.89	−0.0960450
$959$	−65334.2	−2.19995
$960$	21857.8	0.734850
$961$	35199.2	1.18154
$962$	7981.92	0.267513
$963$	43780.4	1.46501
$964$	−1133.91	−0.0378845
$965$	12601.5	0.420370
$966$	27742.8	0.924026
$967$	19248.9	0.640128	0.320064	−	0.947396i	$-0.396296\pi$
$967$	19248.9	0.640128	0.320064	+	0.947396i	$0.396296\pi$
$968$	−2859.05	−0.0949311
$969$	18764.6	0.622090
$970$	9993.92	0.330810
$971$	40938.6	1.35302	0.676510	−	0.736433i	$-0.263491\pi$
$971$	40938.6	1.35302	0.676510	+	0.736433i	$0.263491\pi$
$972$	4232.23	0.139659
$973$	−1897.00	−0.0625025
$974$	3669.71	0.120724
$975$	−4979.70	−0.163567
$976$	−14631.1	−0.479845
$977$	20506.2	0.671495	0.335747	−	0.941952i	$-0.391011\pi$
$977$	20506.2	0.671495	0.335747	+	0.941952i	$0.391011\pi$
$978$	39326.3	1.28580
$979$	7348.23	0.239888
$980$	−2762.62	−0.0900497
$981$	19562.1	0.636666
$982$	−12765.2	−0.414822
$983$	−12730.1	−0.413048	−0.206524	−	0.978442i	$-0.566215\pi$
$983$	−12730.1	−0.413048	−0.206524	+	0.978442i	$0.566215\pi$
$984$	−19870.0	−0.643731
$985$	−20639.0	−0.667629
$986$	60901.8	1.96705
$987$	90720.6	2.92570
$988$	390.190	0.0125644
$989$	13719.6	0.441109
$990$	−5232.64	−0.167984
$991$	7540.11	0.241695	0.120847	−	0.992671i	$-0.461439\pi$
$991$	7540.11	0.241695	0.120847	+	0.992671i	$0.461439\pi$
$992$	−9365.06	−0.299739
$993$	34571.5	1.10483
$994$	−49943.7	−1.59368
$995$	16507.7	0.525959
$996$	571.301	0.0181751
$997$	40062.4	1.27261	0.636303	−	0.771439i	$-0.280463\pi$
$997$	40062.4	1.27261	0.636303	+	0.771439i	$0.280463\pi$
$998$	−36011.5	−1.14221
$999$	−7934.88	−0.251300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.17	✓	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68048 q^{2} +7.90527 q^{3} -0.815035 q^{4} +5.00000 q^{5} +21.1899 q^{6} +31.9517 q^{7} -23.6285 q^{8} +35.4933 q^{9} +O(q^{10})\)	\(q+2.68048 q^{2} +7.90527 q^{3} -0.815035 q^{4} +5.00000 q^{5} +21.1899 q^{6} +31.9517 q^{7} -23.6285 q^{8} +35.4933 q^{9} +13.4024 q^{10} -11.0000 q^{11} -6.44307 q^{12} -25.1968 q^{13} +85.6460 q^{14} +39.5263 q^{15} -56.8154 q^{16} +124.931 q^{17} +95.1389 q^{18} +19.0000 q^{19} -4.07518 q^{20} +252.587 q^{21} -29.4853 q^{22} +40.9757 q^{23} -186.790 q^{24} +25.0000 q^{25} -67.5396 q^{26} +67.1416 q^{27} -26.0418 q^{28} +181.865 q^{29} +105.950 q^{30} -254.932 q^{31} +36.7356 q^{32} -86.9580 q^{33} +334.874 q^{34} +159.759 q^{35} -28.9283 q^{36} -118.181 q^{37} +50.9291 q^{38} -199.188 q^{39} -118.143 q^{40} +106.376 q^{41} +677.054 q^{42} +334.822 q^{43} +8.96539 q^{44} +177.466 q^{45} +109.834 q^{46} +359.165 q^{47} -449.141 q^{48} +677.914 q^{49} +67.0120 q^{50} +987.610 q^{51} +20.5363 q^{52} -551.123 q^{53} +179.972 q^{54} -55.0000 q^{55} -754.972 q^{56} +150.200 q^{57} +487.485 q^{58} -489.784 q^{59} -32.2154 q^{60} +257.519 q^{61} -683.339 q^{62} +1134.07 q^{63} +552.992 q^{64} -125.984 q^{65} -233.089 q^{66} +583.828 q^{67} -101.823 q^{68} +323.924 q^{69} +428.230 q^{70} -583.141 q^{71} -838.653 q^{72} +65.7363 q^{73} -316.783 q^{74} +197.632 q^{75} -15.4857 q^{76} -351.469 q^{77} -533.919 q^{78} -775.850 q^{79} -284.077 q^{80} -427.546 q^{81} +285.139 q^{82} -88.6690 q^{83} -205.867 q^{84} +624.653 q^{85} +897.483 q^{86} +1437.69 q^{87} +259.914 q^{88} -668.021 q^{89} +475.695 q^{90} -805.083 q^{91} -33.3966 q^{92} -2015.30 q^{93} +962.735 q^{94} +95.0000 q^{95} +290.404 q^{96} +745.682 q^{97} +1817.13 q^{98} -390.426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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