LMFDB - Embedded newform 1849.4.a.i.1.41

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			1.41
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)

$f(q)$	$=$	$q+3.88871 q^{2} -9.09520 q^{3} +7.12206 q^{4} +19.0468 q^{5} -35.3686 q^{6} -18.7927 q^{7} -3.41407 q^{8} +55.7226 q^{9} +O(q^{10})$	\(q+3.88871 q^{2} -9.09520 q^{3} +7.12206 q^{4} +19.0468 q^{5} -35.3686 q^{6} -18.7927 q^{7} -3.41407 q^{8} +55.7226 q^{9} +74.0673 q^{10} +4.37373 q^{11} -64.7765 q^{12} +45.6452 q^{13} -73.0793 q^{14} -173.234 q^{15} -70.2528 q^{16} -62.8152 q^{17} +216.689 q^{18} -33.1127 q^{19} +135.652 q^{20} +170.923 q^{21} +17.0082 q^{22} -32.0896 q^{23} +31.0516 q^{24} +237.779 q^{25} +177.501 q^{26} -261.237 q^{27} -133.843 q^{28} +291.097 q^{29} -673.657 q^{30} -83.9237 q^{31} -245.880 q^{32} -39.7799 q^{33} -244.270 q^{34} -357.940 q^{35} +396.859 q^{36} +90.1795 q^{37} -128.766 q^{38} -415.152 q^{39} -65.0270 q^{40} -422.014 q^{41} +664.670 q^{42} +31.1499 q^{44} +1061.33 q^{45} -124.787 q^{46} -363.055 q^{47} +638.963 q^{48} +10.1649 q^{49} +924.654 q^{50} +571.316 q^{51} +325.087 q^{52} +387.946 q^{53} -1015.88 q^{54} +83.3054 q^{55} +64.1595 q^{56} +301.166 q^{57} +1131.99 q^{58} -248.120 q^{59} -1233.78 q^{60} -64.5638 q^{61} -326.355 q^{62} -1047.18 q^{63} -394.134 q^{64} +869.393 q^{65} -154.692 q^{66} +80.6113 q^{67} -447.373 q^{68} +291.861 q^{69} -1391.92 q^{70} -936.123 q^{71} -190.241 q^{72} +651.084 q^{73} +350.682 q^{74} -2162.65 q^{75} -235.830 q^{76} -82.1941 q^{77} -1614.40 q^{78} +1114.36 q^{79} -1338.09 q^{80} +871.496 q^{81} -1641.09 q^{82} +26.3884 q^{83} +1217.32 q^{84} -1196.43 q^{85} -2647.58 q^{87} -14.9322 q^{88} +347.849 q^{89} +4127.22 q^{90} -857.795 q^{91} -228.544 q^{92} +763.303 q^{93} -1411.82 q^{94} -630.689 q^{95} +2236.33 q^{96} +291.207 q^{97} +39.5283 q^{98} +243.715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.88871	1.37487	0.687433	−	0.726248i	$-0.258737\pi$
$2$	3.88871	1.37487	0.687433	+	0.726248i	$0.258737\pi$
$3$	−9.09520	−1.75037	−0.875186	−	0.483787i	$-0.839261\pi$
$3$	−9.09520	−1.75037	−0.875186	+	0.483787i	$0.839261\pi$
$4$	7.12206	0.890257
$5$	19.0468	1.70359	0.851797	−	0.523872i	$-0.175513\pi$
$5$	19.0468	1.70359	0.851797	+	0.523872i	$0.175513\pi$
$6$	−35.3686	−2.40653
$7$	−18.7927	−1.01471	−0.507355	−	0.861737i	$-0.669377\pi$
$7$	−18.7927	−1.01471	−0.507355	+	0.861737i	$0.669377\pi$
$8$	−3.41407	−0.150882
$9$	55.7226	2.06380
$10$	74.0673	2.34221
$11$	4.37373	0.119884	0.0599422	−	0.998202i	$-0.480908\pi$
$11$	4.37373	0.119884	0.0599422	+	0.998202i	$0.480908\pi$
$12$	−64.7765	−1.55828
$13$	45.6452	0.973822	0.486911	−	0.873452i	$-0.338124\pi$
$13$	45.6452	0.973822	0.486911	+	0.873452i	$0.338124\pi$
$14$	−73.0793	−1.39509
$15$	−173.234	−2.98192
$16$	−70.2528	−1.09770
$17$	−62.8152	−0.896172	−0.448086	−	0.893990i	$-0.647894\pi$
$17$	−62.8152	−0.896172	−0.448086	+	0.893990i	$0.647894\pi$
$18$	216.689	2.83745
$19$	−33.1127	−0.399819	−0.199910	−	0.979814i	$-0.564065\pi$
$19$	−33.1127	−0.399819	−0.199910	+	0.979814i	$0.564065\pi$
$20$	135.652	1.51664
$21$	170.923	1.77612
$22$	17.0082	0.164825
$23$	−32.0896	−0.290919	−0.145459	−	0.989364i	$-0.546466\pi$
$23$	−32.0896	−0.290919	−0.145459	+	0.989364i	$0.546466\pi$
$24$	31.0516	0.264100
$25$	237.779	1.90223
$26$	177.501	1.33888
$27$	−261.237	−1.86204
$28$	−133.843	−0.903352
$29$	291.097	1.86398	0.931988	−	0.362490i	$-0.118073\pi$
$29$	291.097	1.86398	0.931988	+	0.362490i	$0.118073\pi$
$30$	−673.657	−4.09974
$31$	−83.9237	−0.486231	−0.243115	−	0.969997i	$-0.578169\pi$
$31$	−83.9237	−0.486231	−0.243115	+	0.969997i	$0.578169\pi$
$32$	−245.880	−1.35831
$33$	−39.7799	−0.209842
$34$	−244.270	−1.23212
$35$	−357.940	−1.72865
$36$	396.859	1.83731
$37$	90.1795	0.400687	0.200343	−	0.979726i	$-0.435794\pi$
$37$	90.1795	0.400687	0.200343	+	0.979726i	$0.435794\pi$
$38$	−128.766	−0.549698
$39$	−415.152	−1.70455
$40$	−65.0270	−0.257042
$41$	−422.014	−1.60750	−0.803750	−	0.594967i	$-0.797165\pi$
$41$	−422.014	−1.60750	−0.803750	+	0.594967i	$0.797165\pi$
$42$	664.670	2.44192
$43$	0	0
$43$	0	0
$44$	31.1499	0.106728
$45$	1061.33	3.51588
$46$	−124.787	−0.399974
$47$	−363.055	−1.12675	−0.563373	−	0.826203i	$-0.690497\pi$
$47$	−363.055	−1.12675	−0.563373	+	0.826203i	$0.690497\pi$
$48$	638.963	1.92138
$49$	10.1649	0.0296352
$50$	924.654	2.61532
$51$	571.316	1.56863
$52$	325.087	0.866952
$53$	387.946	1.00544	0.502722	−	0.864448i	$-0.332332\pi$
$53$	387.946	1.00544	0.502722	+	0.864448i	$0.332332\pi$
$54$	−1015.88	−2.56006
$55$	83.3054	0.204234
$56$	64.1595	0.153101
$57$	301.166	0.699832
$58$	1131.99	2.56272
$59$	−248.120	−0.547500	−0.273750	−	0.961801i	$-0.588264\pi$
$59$	−248.120	−0.547500	−0.273750	+	0.961801i	$0.588264\pi$
$60$	−1233.78	−2.65468
$61$	−64.5638	−0.135517	−0.0677586	−	0.997702i	$-0.521585\pi$
$61$	−64.5638	−0.135517	−0.0677586	+	0.997702i	$0.521585\pi$
$62$	−326.355	−0.668502
$63$	−1047.18	−2.09416
$64$	−394.134	−0.769792
$65$	869.393	1.65900
$66$	−154.692	−0.288505
$67$	80.6113	0.146989	0.0734943	−	0.997296i	$-0.476585\pi$
$67$	80.6113	0.146989	0.0734943	+	0.997296i	$0.476585\pi$
$68$	−447.373	−0.797823
$69$	291.861	0.509216
$70$	−1391.92	−2.37667
$71$	−936.123	−1.56475	−0.782375	−	0.622807i	$-0.785992\pi$
$71$	−936.123	−1.56475	−0.782375	+	0.622807i	$0.785992\pi$
$72$	−190.241	−0.311390
$73$	651.084	1.04389	0.521943	−	0.852980i	$-0.325207\pi$
$73$	651.084	1.04389	0.521943	+	0.852980i	$0.325207\pi$
$74$	350.682	0.550891
$75$	−2162.65	−3.32962
$76$	−235.830	−0.355942
$77$	−82.1941	−0.121648
$78$	−1614.40	−2.34353
$79$	1114.36	1.58703	0.793516	−	0.608549i	$-0.208248\pi$
$79$	1114.36	1.58703	0.793516	+	0.608549i	$0.208248\pi$
$80$	−1338.09	−1.87003
$81$	871.496	1.19547
$82$	−1641.09	−2.21010
$83$	26.3884	0.0348976	0.0174488	−	0.999848i	$-0.494446\pi$
$83$	26.3884	0.0348976	0.0174488	+	0.999848i	$0.494446\pi$
$84$	1217.32	1.58120
$85$	−1196.43	−1.52671
$86$	0	0
$87$	−2647.58	−3.26265
$88$	−14.9322	−0.0180884
$89$	347.849	0.414292	0.207146	−	0.978310i	$-0.433583\pi$
$89$	347.849	0.414292	0.207146	+	0.978310i	$0.433583\pi$
$90$	4127.22	4.83386
$91$	−857.795	−0.988147
$92$	−228.544	−0.258993
$93$	763.303	0.851084
$94$	−1411.82	−1.54912
$95$	−630.689	−0.681130
$96$	2236.33	2.37754
$97$	291.207	0.304821	0.152410	−	0.988317i	$-0.451296\pi$
$97$	291.207	0.304821	0.152410	+	0.988317i	$0.451296\pi$
$98$	39.5283	0.0407445
$99$	243.715	0.247417
$100$	1693.48	1.69348
$101$	−1176.57	−1.15913	−0.579567	−	0.814924i	$-0.696778\pi$
$101$	−1176.57	−1.15913	−0.579567	+	0.814924i	$0.696778\pi$
$102$	2221.68	2.15666
$103$	457.000	0.437181	0.218590	−	0.975817i	$-0.429854\pi$
$103$	457.000	0.437181	0.218590	+	0.975817i	$0.429854\pi$
$104$	−155.836	−0.146932
$105$	3255.53	3.02579
$106$	1508.61	1.38235
$107$	−731.873	−0.661242	−0.330621	−	0.943764i	$-0.607258\pi$
$107$	−731.873	−0.661242	−0.330621	+	0.943764i	$0.607258\pi$
$108$	−1860.55	−1.65770
$109$	−119.276	−0.104813	−0.0524063	−	0.998626i	$-0.516689\pi$
$109$	−119.276	−0.104813	−0.0524063	+	0.998626i	$0.516689\pi$
$110$	323.950	0.280795
$111$	−820.200	−0.701351
$112$	1320.24	1.11385
$113$	−1149.02	−0.956554	−0.478277	−	0.878209i	$-0.658739\pi$
$113$	−1149.02	−0.956554	−0.478277	+	0.878209i	$0.658739\pi$
$114$	1171.15	0.962176
$115$	−611.202	−0.495608
$116$	2073.21	1.65942
$117$	2543.47	2.00977
$118$	−964.868	−0.752740
$119$	1180.47	0.909354
$120$	591.433	0.449919
$121$	−1311.87	−0.985628
$122$	−251.070	−0.186318
$123$	3838.30	2.81372
$124$	−597.710	−0.432870
$125$	2148.08	1.53704
$126$	−4072.17	−2.87918
$127$	−1354.82	−0.946621	−0.473310	−	0.880896i	$-0.656941\pi$
$127$	−1354.82	−0.946621	−0.473310	+	0.880896i	$0.656941\pi$
$128$	434.370	0.299947
$129$	0	0
$130$	3380.81	2.28090
$131$	−986.023	−0.657628	−0.328814	−	0.944395i	$-0.606649\pi$
$131$	−986.023	−0.657628	−0.328814	+	0.944395i	$0.606649\pi$
$132$	−283.315	−0.186813
$133$	622.276	0.405701
$134$	313.474	0.202090
$135$	−4975.73	−3.17217
$136$	214.456	0.135216
$137$	−876.858	−0.546825	−0.273412	−	0.961897i	$-0.588152\pi$
$137$	−876.858	−0.546825	−0.273412	+	0.961897i	$0.588152\pi$
$138$	1134.96	0.700104
$139$	−1371.22	−0.836731	−0.418365	−	0.908279i	$-0.637397\pi$
$139$	−1371.22	−0.836731	−0.418365	+	0.908279i	$0.637397\pi$
$140$	−2549.27	−1.53895
$141$	3302.06	1.97222
$142$	−3640.31	−2.15132
$143$	199.639	0.116746
$144$	−3914.67	−2.26543
$145$	5544.45	3.17546
$146$	2531.88	1.43520
$147$	−92.4516	−0.0518727
$148$	642.263	0.356714
$149$	−2597.36	−1.42808	−0.714040	−	0.700105i	$-0.753137\pi$
$149$	−2597.36	−1.42808	−0.714040	+	0.700105i	$0.753137\pi$
$150$	−8409.91	−4.57778
$151$	−285.155	−0.153679	−0.0768397	−	0.997043i	$-0.524483\pi$
$151$	−285.155	−0.153679	−0.0768397	+	0.997043i	$0.524483\pi$
$152$	113.049	0.0603256
$153$	−3500.22	−1.84952
$154$	−319.629	−0.167250
$155$	−1598.48	−0.828340
$156$	−2956.73	−1.51749
$157$	−1326.53	−0.674323	−0.337161	−	0.941447i	$-0.609467\pi$
$157$	−1326.53	−0.674323	−0.337161	+	0.941447i	$0.609467\pi$
$158$	4333.43	2.18196
$159$	−3528.45	−1.75990
$160$	−4683.22	−2.31401
$161$	603.049	0.295198
$162$	3388.99	1.64361
$163$	182.755	0.0878191	0.0439095	−	0.999036i	$-0.486019\pi$
$163$	182.755	0.0878191	0.0439095	+	0.999036i	$0.486019\pi$
$164$	−3005.61	−1.43109
$165$	−757.679	−0.357486
$166$	102.617	0.0479795
$167$	−2822.36	−1.30779	−0.653894	−	0.756586i	$-0.726866\pi$
$167$	−2822.36	−1.30779	−0.653894	+	0.756586i	$0.726866\pi$
$168$	−583.544	−0.267984
$169$	−113.520	−0.0516704
$170$	−4652.55	−2.09903
$171$	−1845.12	−0.825147
$172$	0	0
$173$	−2917.04	−1.28196	−0.640978	−	0.767559i	$-0.721471\pi$
$173$	−2917.04	−1.28196	−0.640978	+	0.767559i	$0.721471\pi$
$174$	−10295.7	−4.48571
$175$	−4468.51	−1.93022
$176$	−307.267	−0.131597
$177$	2256.70	0.958329
$178$	1352.68	0.569595
$179$	2240.14	0.935397	0.467699	−	0.883888i	$-0.345083\pi$
$179$	2240.14	0.935397	0.467699	+	0.883888i	$0.345083\pi$
$180$	7558.89	3.13003
$181$	−4100.39	−1.68387	−0.841934	−	0.539581i	$-0.818583\pi$
$181$	−4100.39	−1.68387	−0.841934	+	0.539581i	$0.818583\pi$
$182$	−3335.71	−1.35857
$183$	587.221	0.237205
$184$	109.556	0.0438944
$185$	1717.63	0.682608
$186$	2968.26	1.17013
$187$	−274.737	−0.107437
$188$	−2585.70	−1.00309
$189$	4909.35	1.88943
$190$	−2452.57	−0.936463
$191$	−3114.34	−1.17982	−0.589910	−	0.807469i	$-0.700837\pi$
$191$	−3114.34	−1.17982	−0.589910	+	0.807469i	$0.700837\pi$
$192$	3584.72	1.34742
$193$	1369.02	0.510590	0.255295	−	0.966863i	$-0.417827\pi$
$193$	1369.02	0.510590	0.255295	+	0.966863i	$0.417827\pi$
$194$	1132.42	0.419088
$195$	−7907.30	−2.90386
$196$	72.3949	0.0263830
$197$	−4821.42	−1.74372	−0.871858	−	0.489758i	$-0.837085\pi$
$197$	−4821.42	−1.74372	−0.871858	+	0.489758i	$0.837085\pi$
$198$	947.738	0.340166
$199$	3469.11	1.23577	0.617887	−	0.786267i	$-0.287989\pi$
$199$	3469.11	1.23577	0.617887	+	0.786267i	$0.287989\pi$
$200$	−811.795	−0.287013
$201$	−733.175	−0.257285
$202$	−4575.32	−1.59366
$203$	−5470.49	−1.89139
$204$	4068.95	1.39649
$205$	−8038.00	−2.73853
$206$	1777.14	0.601065
$207$	−1788.11	−0.600398
$208$	−3206.70	−1.06896
$209$	−144.826	−0.0479321
$210$	12659.8	4.16005
$211$	949.908	0.309926	0.154963	−	0.987920i	$-0.450474\pi$
$211$	949.908	0.309926	0.154963	+	0.987920i	$0.450474\pi$
$212$	2762.97	0.895103
$213$	8514.22	2.73889
$214$	−2846.04	−0.909119
$215$	0	0
$216$	891.883	0.280949
$217$	1577.15	0.493383
$218$	−463.830	−0.144103
$219$	−5921.74	−1.82719
$220$	593.305	0.181821
$221$	−2867.21	−0.872712
$222$	−3189.52	−0.964264
$223$	5128.19	1.53995	0.769976	−	0.638073i	$-0.220268\pi$
$223$	5128.19	1.53995	0.769976	+	0.638073i	$0.220268\pi$
$224$	4620.74	1.37829
$225$	13249.7	3.92583
$226$	−4468.20	−1.31513
$227$	−3818.68	−1.11654	−0.558270	−	0.829659i	$-0.688535\pi$
$227$	−3818.68	−1.11654	−0.558270	+	0.829659i	$0.688535\pi$
$228$	2144.92	0.623031
$229$	−2587.09	−0.746548	−0.373274	−	0.927721i	$-0.621765\pi$
$229$	−2587.09	−0.746548	−0.373274	+	0.927721i	$0.621765\pi$
$230$	−2376.79	−0.681394
$231$	747.571	0.212929
$232$	−993.825	−0.281240
$233$	−3660.55	−1.02923	−0.514615	−	0.857421i	$-0.672065\pi$
$233$	−3660.55	−1.02923	−0.514615	+	0.857421i	$0.672065\pi$
$234$	9890.80	2.76317
$235$	−6915.03	−1.91952
$236$	−1767.13	−0.487416
$237$	−10135.3	−2.77789
$238$	4590.49	1.25024
$239$	840.112	0.227374	0.113687	−	0.993517i	$-0.463734\pi$
$239$	840.112	0.227374	0.113687	+	0.993517i	$0.463734\pi$
$240$	12170.2	3.27326
$241$	1237.68	0.330813	0.165406	−	0.986226i	$-0.447106\pi$
$241$	1237.68	0.330813	0.165406	+	0.986226i	$0.447106\pi$
$242$	−5101.48	−1.35511
$243$	−873.016	−0.230469
$244$	−459.827	−0.120645
$245$	193.608	0.0504864
$246$	14926.0	3.86849
$247$	−1511.43	−0.389353
$248$	286.522	0.0733635
$249$	−240.007	−0.0610837
$250$	8353.26	2.11323
$251$	−4783.43	−1.20290	−0.601449	−	0.798911i	$-0.705410\pi$
$251$	−4783.43	−1.20290	−0.601449	+	0.798911i	$0.705410\pi$
$252$	−7458.05	−1.86434
$253$	−140.351	−0.0348766
$254$	−5268.50	−1.30148
$255$	10881.7	2.67232
$256$	4842.20	1.18218
$257$	−3254.28	−0.789869	−0.394935	−	0.918709i	$-0.629233\pi$
$257$	−3254.28	−0.789869	−0.394935	+	0.918709i	$0.629233\pi$
$258$	0	0
$259$	−1694.71	−0.406581
$260$	6191.86	1.47693
$261$	16220.7	3.84687
$262$	−3834.36	−0.904150
$263$	4499.66	1.05498	0.527492	−	0.849560i	$-0.323132\pi$
$263$	4499.66	1.05498	0.527492	+	0.849560i	$0.323132\pi$
$264$	135.811	0.0316614
$265$	7389.12	1.71287
$266$	2419.85	0.557784
$267$	−3163.76	−0.725164
$268$	574.118	0.130858
$269$	4396.09	0.996409	0.498205	−	0.867059i	$-0.333993\pi$
$269$	4396.09	0.996409	0.498205	+	0.867059i	$0.333993\pi$
$270$	−19349.2	−4.36131
$271$	489.737	0.109776	0.0548882	−	0.998493i	$-0.482520\pi$
$271$	489.737	0.109776	0.0548882	+	0.998493i	$0.482520\pi$
$272$	4412.94	0.983728
$273$	7801.81	1.72962
$274$	−3409.84	−0.751811
$275$	1039.98	0.228048
$276$	2078.65	0.453333
$277$	2576.01	0.558762	0.279381	−	0.960180i	$-0.409871\pi$
$277$	2576.01	0.558762	0.279381	+	0.960180i	$0.409871\pi$
$278$	−5332.28	−1.15039
$279$	−4676.45	−1.00348
$280$	1222.03	0.260823
$281$	6339.36	1.34582	0.672908	−	0.739726i	$-0.265045\pi$
$281$	6339.36	1.34582	0.672908	+	0.739726i	$0.265045\pi$
$282$	12840.7	2.71154
$283$	3492.92	0.733684	0.366842	−	0.930283i	$-0.380439\pi$
$283$	3492.92	0.733684	0.366842	+	0.930283i	$0.380439\pi$
$284$	−6667.12	−1.39303
$285$	5736.24	1.19223
$286$	776.340	0.160510
$287$	7930.77	1.63115
$288$	−13701.1	−2.80327
$289$	−967.251	−0.196876
$290$	21560.8	4.36583
$291$	−2648.59	−0.533550
$292$	4637.06	0.929327
$293$	−6042.69	−1.20484	−0.602419	−	0.798180i	$-0.705796\pi$
$293$	−6042.69	−1.20484	−0.602419	+	0.798180i	$0.705796\pi$
$294$	−359.517	−0.0713180
$295$	−4725.89	−0.932719
$296$	−307.879	−0.0604565
$297$	−1142.58	−0.223230
$298$	−10100.4	−1.96342
$299$	−1464.73	−0.283303
$300$	−15402.5	−2.96421
$301$	0	0
$302$	−1108.89	−0.211289
$303$	10701.1	2.02892
$304$	2326.26	0.438882
$305$	−1229.73	−0.230866
$306$	−13611.4	−2.54284
$307$	7899.54	1.46857	0.734285	−	0.678842i	$-0.237518\pi$
$307$	7899.54	1.46857	0.734285	+	0.678842i	$0.237518\pi$
$308$	−585.391	−0.108298
$309$	−4156.51	−0.765228
$310$	−6216.01	−1.13886
$311$	−10690.9	−1.94927	−0.974636	−	0.223798i	$-0.928154\pi$
$311$	−10690.9	−1.94927	−0.974636	+	0.223798i	$0.928154\pi$
$312$	1417.36	0.257186
$313$	1211.51	0.218782	0.109391	−	0.993999i	$-0.465110\pi$
$313$	1211.51	0.218782	0.109391	+	0.993999i	$0.465110\pi$
$314$	−5158.49	−0.927103
$315$	−19945.3	−3.56759
$316$	7936.55	1.41287
$317$	−6471.09	−1.14654	−0.573269	−	0.819367i	$-0.694325\pi$
$317$	−6471.09	−1.14654	−0.573269	+	0.819367i	$0.694325\pi$
$318$	−13721.1	−2.41963
$319$	1273.18	0.223462
$320$	−7506.97	−1.31141
$321$	6656.53	1.15742
$322$	2345.08	0.405858
$323$	2079.98	0.358307
$324$	6206.84	1.06427
$325$	10853.5	1.85244
$326$	710.682	0.120739
$327$	1084.84	0.183461
$328$	1440.79	0.242543
$329$	6822.78	1.14332
$330$	−2946.39	−0.491496
$331$	−1395.83	−0.231788	−0.115894	−	0.993262i	$-0.536973\pi$
$331$	−1395.83	−0.231788	−0.115894	+	0.993262i	$0.536973\pi$
$332$	187.939	0.0310678
$333$	5025.03	0.826937
$334$	−10975.3	−1.79803
$335$	1535.38	0.250409
$336$	−12007.8	−1.94964
$337$	11548.8	1.86678	0.933391	−	0.358860i	$-0.116835\pi$
$337$	11548.8	1.86678	0.933391	+	0.358860i	$0.116835\pi$
$338$	−441.446	−0.0710399
$339$	10450.6	1.67432
$340$	−8521.02	−1.35917
$341$	−367.060	−0.0582915
$342$	−7175.15	−1.13447
$343$	6254.86	0.984638
$344$	0	0
$345$	5559.00	0.867498
$346$	−11343.5	−1.76252
$347$	−3970.96	−0.614330	−0.307165	−	0.951656i	$-0.599380\pi$
$347$	−3970.96	−0.614330	−0.307165	+	0.951656i	$0.599380\pi$
$348$	−18856.2	−2.90460
$349$	1461.92	0.224226	0.112113	−	0.993695i	$-0.464238\pi$
$349$	1461.92	0.224226	0.112113	+	0.993695i	$0.464238\pi$
$350$	−17376.7	−2.65379
$351$	−11924.2	−1.81330
$352$	−1075.41	−0.162840
$353$	−4652.97	−0.701565	−0.350783	−	0.936457i	$-0.614084\pi$
$353$	−4652.97	−0.701565	−0.350783	+	0.936457i	$0.614084\pi$
$354$	8775.66	1.31757
$355$	−17830.1	−2.66570
$356$	2477.40	0.368826
$357$	−10736.6	−1.59171
$358$	8711.26	1.28605
$359$	84.9556	0.0124897	0.00624483	−	0.999981i	$-0.498012\pi$
$359$	84.9556	0.0124897	0.00624483	+	0.999981i	$0.498012\pi$
$360$	−3623.47	−0.530483
$361$	−5762.55	−0.840144
$362$	−15945.2	−2.31509
$363$	11931.7	1.72521
$364$	−6109.26	−0.879704
$365$	12401.1	1.77836
$366$	2283.53	0.326126
$367$	−5121.53	−0.728452	−0.364226	−	0.931311i	$-0.618666\pi$
$367$	−5121.53	−0.728452	−0.364226	+	0.931311i	$0.618666\pi$
$368$	2254.38	0.319341
$369$	−23515.7	−3.31756
$370$	6679.35	0.938495
$371$	−7290.55	−1.02023
$372$	5436.29	0.757683
$373$	898.596	0.124739	0.0623693	−	0.998053i	$-0.480134\pi$
$373$	898.596	0.124739	0.0623693	+	0.998053i	$0.480134\pi$
$374$	−1068.37	−0.147712
$375$	−19537.2	−2.69039
$376$	1239.50	0.170006
$377$	13287.2	1.81518
$378$	19091.0	2.59772
$379$	9099.47	1.23327	0.616634	−	0.787250i	$-0.288496\pi$
$379$	9099.47	1.23327	0.616634	+	0.787250i	$0.288496\pi$
$380$	−4491.81	−0.606381
$381$	12322.3	1.65694
$382$	−12110.8	−1.62209
$383$	6069.35	0.809738	0.404869	−	0.914375i	$-0.367317\pi$
$383$	6069.35	0.809738	0.404869	+	0.914375i	$0.367317\pi$
$384$	−3950.68	−0.525018
$385$	−1565.53	−0.207239
$386$	5323.70	0.701993
$387$	0	0
$388$	2073.99	0.271369
$389$	−8283.52	−1.07967	−0.539834	−	0.841771i	$-0.681513\pi$
$389$	−8283.52	−1.07967	−0.539834	+	0.841771i	$0.681513\pi$
$390$	−30749.2	−3.99242
$391$	2015.71	0.260713
$392$	−34.7036	−0.00447142
$393$	8968.08	1.15109
$394$	−18749.1	−2.39738
$395$	21225.0	2.70366
$396$	1735.75	0.220265
$397$	5831.90	0.737266	0.368633	−	0.929575i	$-0.379826\pi$
$397$	5831.90	0.737266	0.368633	+	0.929575i	$0.379826\pi$
$398$	13490.4	1.69902
$399$	−5659.72	−0.710127
$400$	−16704.7	−2.08808
$401$	−14041.3	−1.74860	−0.874299	−	0.485389i	$-0.838678\pi$
$401$	−14041.3	−1.74860	−0.874299	+	0.485389i	$0.838678\pi$
$402$	−2851.10	−0.353732
$403$	−3830.71	−0.473502
$404$	−8379.56	−1.03193
$405$	16599.2	2.03659
$406$	−21273.1	−2.60041
$407$	394.421	0.0480361
$408$	−1950.51	−0.236679
$409$	−2456.40	−0.296971	−0.148486	−	0.988915i	$-0.547440\pi$
$409$	−2456.40	−0.296971	−0.148486	+	0.988915i	$0.547440\pi$
$410$	−31257.4	−3.76511
$411$	7975.19	0.957147
$412$	3254.78	0.389203
$413$	4662.85	0.555554
$414$	−6953.45	−0.825467
$415$	502.613	0.0594513
$416$	−11223.2	−1.32275
$417$	12471.5	1.46459
$418$	−563.186	−0.0659003
$419$	−9412.48	−1.09745	−0.548723	−	0.836004i	$-0.684886\pi$
$419$	−9412.48	−1.09745	−0.548723	+	0.836004i	$0.684886\pi$
$420$	23186.1	2.69373
$421$	7475.80	0.865435	0.432718	−	0.901529i	$-0.357555\pi$
$421$	7475.80	0.865435	0.432718	+	0.901529i	$0.357555\pi$
$422$	3693.92	0.426107
$423$	−20230.4	−2.32538
$424$	−1324.48	−0.151703
$425$	−14936.2	−1.70473
$426$	33109.3	3.76561
$427$	1213.33	0.137511
$428$	−5212.44	−0.588675
$429$	−1815.76	−0.204349
$430$	0	0
$431$	12819.7	1.43273	0.716363	−	0.697728i	$-0.245806\pi$
$431$	12819.7	1.43273	0.716363	+	0.697728i	$0.245806\pi$
$432$	18352.7	2.04396
$433$	8929.20	0.991017	0.495508	−	0.868603i	$-0.334982\pi$
$433$	8929.20	0.991017	0.495508	+	0.868603i	$0.334982\pi$
$434$	6133.09	0.678335
$435$	−50427.9	−5.55823
$436$	−849.490	−0.0933101
$437$	1062.57	0.116315
$438$	−23027.9	−2.51214
$439$	−9033.45	−0.982103	−0.491051	−	0.871131i	$-0.663387\pi$
$439$	−9033.45	−0.982103	−0.491051	+	0.871131i	$0.663387\pi$
$440$	−284.410	−0.0308153
$441$	566.414	0.0611612
$442$	−11149.7	−1.19986
$443$	7257.25	0.778335	0.389167	−	0.921167i	$-0.372763\pi$
$443$	7257.25	0.778335	0.389167	+	0.921167i	$0.372763\pi$
$444$	−5841.51	−0.624382
$445$	6625.40	0.705785
$446$	19942.1	2.11723
$447$	23623.5	2.49967
$448$	7406.83	0.781115
$449$	−11843.1	−1.24479	−0.622394	−	0.782704i	$-0.713840\pi$
$449$	−11843.1	−1.24479	−0.622394	+	0.782704i	$0.713840\pi$
$450$	51524.1	5.39749
$451$	−1845.77	−0.192714
$452$	−8183.38	−0.851579
$453$	2593.54	0.268996
$454$	−14849.7	−1.53509
$455$	−16338.2	−1.68340
$456$	−1028.20	−0.105592
$457$	−6136.43	−0.628119	−0.314059	−	0.949403i	$-0.601689\pi$
$457$	−6136.43	−0.628119	−0.314059	+	0.949403i	$0.601689\pi$
$458$	−10060.4	−1.02640
$459$	16409.7	1.66871
$460$	−4353.02	−0.441218
$461$	1927.73	0.194758	0.0973788	−	0.995247i	$-0.468954\pi$
$461$	1927.73	0.194758	0.0973788	+	0.995247i	$0.468954\pi$
$462$	2907.09	0.292749
$463$	10705.1	1.07453	0.537264	−	0.843414i	$-0.319458\pi$
$463$	10705.1	1.07453	0.537264	+	0.843414i	$0.319458\pi$
$464$	−20450.3	−2.04609
$465$	14538.5	1.44990
$466$	−14234.8	−1.41505
$467$	13219.7	1.30992	0.654962	−	0.755661i	$-0.272684\pi$
$467$	13219.7	1.30992	0.654962	+	0.755661i	$0.272684\pi$
$468$	18114.7	1.78921
$469$	−1514.90	−0.149151
$470$	−26890.5	−2.63908
$471$	12065.1	1.18032
$472$	847.101	0.0826080
$473$	0	0
$474$	−39413.4	−3.81923
$475$	−7873.51	−0.760550
$476$	8407.34	0.809559
$477$	21617.4	2.07503
$478$	3266.95	0.312608
$479$	−2249.15	−0.214543	−0.107271	−	0.994230i	$-0.534211\pi$
$479$	−2249.15	−0.214543	−0.107271	+	0.994230i	$0.534211\pi$
$480$	42594.8	4.05037
$481$	4116.26	0.390198
$482$	4812.97	0.454823
$483$	−5484.85	−0.516706
$484$	−9343.21	−0.877462
$485$	5546.56	0.519291
$486$	−3394.90	−0.316864
$487$	17135.5	1.59443	0.797213	−	0.603698i	$-0.206307\pi$
$487$	17135.5	1.59443	0.797213	+	0.603698i	$0.206307\pi$
$488$	220.425	0.0204471
$489$	−1662.20	−0.153716
$490$	752.886	0.0694121
$491$	17052.6	1.56736	0.783680	−	0.621165i	$-0.213340\pi$
$491$	17052.6	1.56736	0.783680	+	0.621165i	$0.213340\pi$
$492$	27336.6	2.50494
$493$	−18285.3	−1.67044
$494$	−5877.52	−0.535308
$495$	4641.99	0.421499
$496$	5895.88	0.533735
$497$	17592.3	1.58777
$498$	−933.319	−0.0839820
$499$	−7199.58	−0.645887	−0.322944	−	0.946418i	$-0.604672\pi$
$499$	−7199.58	−0.645887	−0.322944	+	0.946418i	$0.604672\pi$
$500$	15298.8	1.36836
$501$	25669.9	2.28911
$502$	−18601.4	−1.65382
$503$	17120.4	1.51761	0.758807	−	0.651316i	$-0.225783\pi$
$503$	17120.4	1.51761	0.758807	+	0.651316i	$0.225783\pi$
$504$	3575.14	0.315971
$505$	−22409.8	−1.97470
$506$	−545.784	−0.0479507
$507$	1032.49	0.0904424
$508$	−9649.10	−0.842735
$509$	12743.3	1.10970	0.554848	−	0.831952i	$-0.312776\pi$
$509$	12743.3	1.10970	0.554848	+	0.831952i	$0.312776\pi$
$510$	42315.9	3.67408
$511$	−12235.6	−1.05924
$512$	15355.0	1.32539
$513$	8650.27	0.744481
$514$	−12655.0	−1.08596
$515$	8704.38	0.744778
$516$	0	0
$517$	−1587.91	−0.135079
$518$	−6590.25	−0.558994
$519$	26531.1	2.24390
$520$	−2968.17	−0.250313
$521$	15646.4	1.31570	0.657851	−	0.753148i	$-0.271465\pi$
$521$	15646.4	1.31570	0.657851	+	0.753148i	$0.271465\pi$
$522$	63077.4	5.28893
$523$	−11556.5	−0.966213	−0.483106	−	0.875562i	$-0.660492\pi$
$523$	−11556.5	−0.966213	−0.483106	+	0.875562i	$0.660492\pi$
$524$	−7022.51	−0.585458
$525$	40642.0	3.37859
$526$	17497.9	1.45046
$527$	5271.69	0.435746
$528$	2794.65	0.230344
$529$	−11137.3	−0.915366
$530$	28734.1	2.35496
$531$	−13825.9	−1.12993
$532$	4431.88	0.361178
$533$	−19262.9	−1.56542
$534$	−12302.9	−0.997003
$535$	−13939.8	−1.12649
$536$	−275.213	−0.0221779
$537$	−20374.5	−1.63729
$538$	17095.1	1.36993
$539$	44.4584	0.00355280
$540$	−35437.4	−2.82404
$541$	4750.49	0.377523	0.188761	−	0.982023i	$-0.439553\pi$
$541$	4750.49	0.377523	0.188761	+	0.982023i	$0.439553\pi$
$542$	1904.44	0.150928
$543$	37293.9	2.94739
$544$	15445.0	1.21728
$545$	−2271.82	−0.178558
$546$	30339.0	2.37800
$547$	−3938.22	−0.307836	−0.153918	−	0.988084i	$-0.549189\pi$
$547$	−3938.22	−0.307836	−0.153918	+	0.988084i	$0.549189\pi$
$548$	−6245.03	−0.486815
$549$	−3597.66	−0.279680
$550$	4044.19	0.313536
$551$	−9638.99	−0.745254
$552$	−996.433	−0.0768315
$553$	−20941.9	−1.61038
$554$	10017.3	0.768223
$555$	−15622.2	−1.19482
$556$	−9765.92	−0.744905
$557$	−8504.39	−0.646934	−0.323467	−	0.946239i	$-0.604849\pi$
$557$	−8504.39	−0.646934	−0.323467	+	0.946239i	$0.604849\pi$
$558$	−18185.3	−1.37965
$559$	0	0
$560$	25146.3	1.89754
$561$	2498.78	0.188055
$562$	24651.9	1.85032
$563$	−18079.0	−1.35335	−0.676676	−	0.736281i	$-0.736580\pi$
$563$	−18079.0	−1.35335	−0.676676	+	0.736281i	$0.736580\pi$
$564$	23517.4	1.75579
$565$	−21885.1	−1.62958
$566$	13582.9	1.00872
$567$	−16377.7	−1.21305
$568$	3195.99	0.236093
$569$	18686.5	1.37677	0.688383	−	0.725347i	$-0.258321\pi$
$569$	18686.5	1.37677	0.688383	+	0.725347i	$0.258321\pi$
$570$	22306.6	1.63916
$571$	−5322.93	−0.390119	−0.195059	−	0.980791i	$-0.562490\pi$
$571$	−5322.93	−0.390119	−0.195059	+	0.980791i	$0.562490\pi$
$572$	1421.84	0.103934
$573$	28325.5	2.06512
$574$	30840.5	2.24261
$575$	−7630.23	−0.553396
$576$	−21962.1	−1.58870
$577$	8955.95	0.646171	0.323086	−	0.946370i	$-0.395280\pi$
$577$	8955.95	0.646171	0.323086	+	0.946370i	$0.395280\pi$
$578$	−3761.36	−0.270678
$579$	−12451.5	−0.893722
$580$	39487.9	2.82697
$581$	−495.908	−0.0354109
$582$	−10299.6	−0.733559
$583$	1696.77	0.120537
$584$	−2222.85	−0.157504
$585$	48444.8	3.42384
$586$	−23498.2	−1.65649
$587$	15496.4	1.08962	0.544810	−	0.838560i	$-0.316602\pi$
$587$	15496.4	1.08962	0.544810	+	0.838560i	$0.316602\pi$
$588$	−658.446	−0.0461800
$589$	2778.94	0.194404
$590$	−18377.6	−1.28236
$591$	43851.8	3.05215
$592$	−6335.36	−0.439834
$593$	4288.84	0.297001	0.148500	−	0.988912i	$-0.452555\pi$
$593$	4288.84	0.297001	0.148500	+	0.988912i	$0.452555\pi$
$594$	−4443.17	−0.306911
$595$	22484.1	1.54917
$596$	−18498.5	−1.27136
$597$	−31552.3	−2.16306
$598$	−5695.92	−0.389504
$599$	9242.19	0.630427	0.315213	−	0.949021i	$-0.397924\pi$
$599$	9242.19	0.630427	0.315213	+	0.949021i	$0.397924\pi$
$600$	7383.44	0.502379
$601$	2151.32	0.146014	0.0730068	−	0.997331i	$-0.476741\pi$
$601$	2151.32	0.146014	0.0730068	+	0.997331i	$0.476741\pi$
$602$	0	0
$603$	4491.87	0.303355
$604$	−2030.89	−0.136814
$605$	−24986.9	−1.67911
$606$	41613.4	2.78949
$607$	−3764.19	−0.251703	−0.125851	−	0.992049i	$-0.540166\pi$
$607$	−3764.19	−0.251703	−0.125851	+	0.992049i	$0.540166\pi$
$608$	8141.75	0.543078
$609$	49755.1	3.31064
$610$	−4782.07	−0.317410
$611$	−16571.7	−1.09725
$612$	−24928.8	−1.64655
$613$	−22176.0	−1.46114	−0.730571	−	0.682837i	$-0.760746\pi$
$613$	−22176.0	−1.46114	−0.730571	+	0.682837i	$0.760746\pi$
$614$	30719.0	2.01909
$615$	73107.2	4.79344
$616$	280.616	0.0183545
$617$	−8804.57	−0.574487	−0.287244	−	0.957858i	$-0.592739\pi$
$617$	−8804.57	−0.574487	−0.287244	+	0.957858i	$0.592739\pi$
$618$	−16163.5	−1.05209
$619$	−11451.5	−0.743579	−0.371789	−	0.928317i	$-0.621256\pi$
$619$	−11451.5	−0.743579	−0.371789	+	0.928317i	$0.621256\pi$
$620$	−11384.4	−0.737435
$621$	8382.99	0.541704
$622$	−41573.7	−2.67999
$623$	−6537.02	−0.420386
$624$	29165.5	1.87108
$625$	11191.6	0.716262
$626$	4711.23	0.300796
$627$	1317.22	0.0838990
$628$	−9447.62	−0.600320
$629$	−5664.64	−0.359084
$630$	−77561.6	−4.90496
$631$	−1972.40	−0.124437	−0.0622187	−	0.998063i	$-0.519818\pi$
$631$	−1972.40	−0.124437	−0.0622187	+	0.998063i	$0.519818\pi$
$632$	−3804.51	−0.239455
$633$	−8639.60	−0.542486
$634$	−25164.2	−1.57634
$635$	−25804.9	−1.61266
$636$	−25129.8	−1.56676
$637$	463.978	0.0288594
$638$	4951.02	0.307230
$639$	−52163.2	−3.22933
$640$	8273.34	0.510988
$641$	−4829.62	−0.297595	−0.148798	−	0.988868i	$-0.547540\pi$
$641$	−4829.62	−0.297595	−0.148798	+	0.988868i	$0.547540\pi$
$642$	25885.3	1.59130
$643$	7867.97	0.482554	0.241277	−	0.970456i	$-0.422434\pi$
$643$	7867.97	0.482554	0.241277	+	0.970456i	$0.422434\pi$
$644$	4294.95	0.262802
$645$	0	0
$646$	8088.43	0.492624
$647$	−378.715	−0.0230121	−0.0115060	−	0.999934i	$-0.503663\pi$
$647$	−378.715	−0.0230121	−0.0115060	+	0.999934i	$0.503663\pi$
$648$	−2975.35	−0.180375
$649$	−1085.21	−0.0656368
$650$	42206.0	2.54685
$651$	−14344.5	−0.863603
$652$	1301.59	0.0781815
$653$	4432.62	0.265639	0.132819	−	0.991140i	$-0.457597\pi$
$653$	4432.62	0.265639	0.132819	+	0.991140i	$0.457597\pi$
$654$	4218.62	0.252234
$655$	−18780.6	−1.12033
$656$	29647.6	1.76455
$657$	36280.1	2.15437
$658$	26531.8	1.57191
$659$	24352.2	1.43950	0.719748	−	0.694236i	$-0.244257\pi$
$659$	24352.2	1.43950	0.719748	+	0.694236i	$0.244257\pi$
$660$	−5396.23	−0.318254
$661$	−7875.21	−0.463404	−0.231702	−	0.972787i	$-0.574429\pi$
$661$	−7875.21	−0.463404	−0.231702	+	0.972787i	$0.574429\pi$
$662$	−5427.98	−0.318678
$663$	26077.8	1.52757
$664$	−90.0918	−0.00526542
$665$	11852.3	0.691149
$666$	19540.9	1.13693
$667$	−9341.16	−0.542266
$668$	−20101.0	−1.16427
$669$	−46641.9	−2.69549
$670$	5970.66	0.344279
$671$	−282.385	−0.0162464
$672$	−42026.6	−2.41252
$673$	−3508.40	−0.200949	−0.100475	−	0.994940i	$-0.532036\pi$
$673$	−3508.40	−0.200949	−0.100475	+	0.994940i	$0.532036\pi$
$674$	44910.1	2.56658
$675$	−62116.9	−3.54204
$676$	−808.495	−0.0459999
$677$	18304.0	1.03912	0.519558	−	0.854435i	$-0.326097\pi$
$677$	18304.0	1.03912	0.519558	+	0.854435i	$0.326097\pi$
$678$	40639.1	2.30197
$679$	−5472.57	−0.309305
$680$	4084.68	0.230354
$681$	34731.6	1.95436
$682$	−1427.39	−0.0801430
$683$	14143.7	0.792378	0.396189	−	0.918169i	$-0.370332\pi$
$683$	14143.7	0.792378	0.396189	+	0.918169i	$0.370332\pi$
$684$	−13141.1	−0.734593
$685$	−16701.3	−0.931568
$686$	24323.3	1.35375
$687$	23530.0	1.30674
$688$	0	0
$689$	17707.9	0.979123
$690$	21617.3	1.19269
$691$	−2755.08	−0.151676	−0.0758380	−	0.997120i	$-0.524163\pi$
$691$	−2755.08	−0.151676	−0.0758380	+	0.997120i	$0.524163\pi$
$692$	−20775.3	−1.14127
$693$	−4580.07	−0.251057
$694$	−15441.9	−0.844621
$695$	−26117.4	−1.42545
$696$	9039.03	0.492275
$697$	26508.9	1.44060
$698$	5684.98	0.308281
$699$	33293.4	1.80153
$700$	−31825.0	−1.71839
$701$	−27986.8	−1.50792	−0.753958	−	0.656923i	$-0.771858\pi$
$701$	−27986.8	−1.50792	−0.753958	+	0.656923i	$0.771858\pi$
$702$	−46369.8	−2.49304
$703$	−2986.08	−0.160202
$704$	−1723.83	−0.0922861
$705$	62893.5	3.35987
$706$	−18094.0	−0.964559
$707$	22110.8	1.17618
$708$	16072.4	0.853159
$709$	18906.6	1.00148	0.500741	−	0.865597i	$-0.333061\pi$
$709$	18906.6	1.00148	0.500741	+	0.865597i	$0.333061\pi$
$710$	−69336.1	−3.66498
$711$	62095.1	3.27532
$712$	−1187.58	−0.0625092
$713$	2693.08	0.141454
$714$	−41751.4	−2.18838
$715$	3802.49	0.198888
$716$	15954.4	0.832744
$717$	−7640.98	−0.397988
$718$	330.368	0.0171716
$719$	25788.9	1.33764	0.668820	−	0.743424i	$-0.266800\pi$
$719$	25788.9	1.33764	0.668820	+	0.743424i	$0.266800\pi$
$720$	−74561.7	−3.85938
$721$	−8588.26	−0.443611
$722$	−22408.9	−1.15509
$723$	−11256.9	−0.579045
$724$	−29203.2	−1.49907
$725$	69216.8	3.54572
$726$	46399.0	2.37194
$727$	−15335.9	−0.782364	−0.391182	−	0.920313i	$-0.627934\pi$
$727$	−15335.9	−0.782364	−0.391182	+	0.920313i	$0.627934\pi$
$728$	2928.57	0.149094
$729$	−15590.1	−0.792061
$730$	48224.1	2.44500
$731$	0	0
$732$	4182.22	0.211174
$733$	36179.3	1.82308	0.911538	−	0.411217i	$-0.134896\pi$
$733$	36179.3	1.82308	0.911538	+	0.411217i	$0.134896\pi$
$734$	−19916.2	−1.00152
$735$	−1760.90	−0.0883700
$736$	7890.18	0.395157
$737$	352.572	0.0176216
$738$	−91445.7	−4.56120
$739$	−26665.5	−1.32735	−0.663673	−	0.748023i	$-0.731003\pi$
$739$	−26665.5	−1.32735	−0.663673	+	0.748023i	$0.731003\pi$
$740$	12233.0	0.607697
$741$	13746.8	0.681512
$742$	−28350.8	−1.40268
$743$	18545.2	0.915692	0.457846	−	0.889032i	$-0.348621\pi$
$743$	18545.2	0.915692	0.457846	+	0.889032i	$0.348621\pi$
$744$	−2605.97	−0.128413
$745$	−49471.3	−2.43287
$746$	3494.38	0.171499
$747$	1470.43	0.0720216
$748$	−1956.69	−0.0956466
$749$	13753.9	0.670968
$750$	−75974.5	−3.69893
$751$	−19902.5	−0.967048	−0.483524	−	0.875331i	$-0.660643\pi$
$751$	−19902.5	−0.967048	−0.483524	+	0.875331i	$0.660643\pi$
$752$	25505.6	1.23683
$753$	43506.2	2.10552
$754$	51669.9	2.49563
$755$	−5431.28	−0.261808
$756$	34964.7	1.68208
$757$	34693.7	1.66574	0.832869	−	0.553470i	$-0.186697\pi$
$757$	34693.7	1.66574	0.832869	+	0.553470i	$0.186697\pi$
$758$	35385.2	1.69558
$759$	1276.52	0.0610471
$760$	2153.22	0.102770
$761$	−6333.20	−0.301680	−0.150840	−	0.988558i	$-0.548198\pi$
$761$	−6333.20	−0.301680	−0.150840	+	0.988558i	$0.548198\pi$
$762$	47918.0	2.27807
$763$	2241.52	0.106354
$764$	−22180.5	−1.05034
$765$	−66668.0	−3.15083
$766$	23602.0	1.11328
$767$	−11325.5	−0.533168
$768$	−44040.8	−2.06925
$769$	−7479.29	−0.350729	−0.175364	−	0.984504i	$-0.556110\pi$
$769$	−7479.29	−0.350729	−0.175364	+	0.984504i	$0.556110\pi$
$770$	−6087.90	−0.284925
$771$	29598.3	1.38256
$772$	9750.20	0.454556
$773$	18737.7	0.871860	0.435930	−	0.899981i	$-0.356420\pi$
$773$	18737.7	0.871860	0.435930	+	0.899981i	$0.356420\pi$
$774$	0	0
$775$	−19955.3	−0.924925
$776$	−994.202	−0.0459920
$777$	15413.8	0.711667
$778$	−32212.2	−1.48440
$779$	13974.0	0.642710
$780$	−56316.2	−2.58518
$781$	−4094.35	−0.187589
$782$	7838.51	0.358446
$783$	−76045.3	−3.47080
$784$	−714.111	−0.0325306
$785$	−25266.1	−1.14877
$786$	34874.2	1.58260
$787$	−29807.9	−1.35011	−0.675054	−	0.737768i	$-0.735880\pi$
$787$	−29807.9	−1.35011	−0.675054	+	0.737768i	$0.735880\pi$
$788$	−34338.4	−1.55236
$789$	−40925.3	−1.84661
$790$	82537.8	3.71717
$791$	21593.1	0.970624
$792$	−832.062	−0.0373308
$793$	−2947.03	−0.131970
$794$	22678.6	1.01364
$795$	−67205.5	−2.99815
$796$	24707.2	1.10016
$797$	−23158.3	−1.02924	−0.514622	−	0.857417i	$-0.672068\pi$
$797$	−23158.3	−1.02924	−0.514622	+	0.857417i	$0.672068\pi$
$798$	−22009.0	−0.976329
$799$	22805.4	1.00976
$800$	−58465.2	−2.58382
$801$	19383.1	0.855015
$802$	−54602.4	−2.40409
$803$	2847.67	0.125146
$804$	−5221.71	−0.229049
$805$	11486.1	0.502898
$806$	−14896.5	−0.651002
$807$	−39983.3	−1.74409
$808$	4016.88	0.174893
$809$	−18381.5	−0.798836	−0.399418	−	0.916769i	$-0.630788\pi$
$809$	−18381.5	−0.798836	−0.399418	+	0.916769i	$0.630788\pi$
$810$	64549.4	2.80004
$811$	−32529.5	−1.40847	−0.704233	−	0.709969i	$-0.748709\pi$
$811$	−32529.5	−1.40847	−0.704233	+	0.709969i	$0.748709\pi$
$812$	−38961.1	−1.68383
$813$	−4454.25	−0.192149
$814$	1533.79	0.0660432
$815$	3480.90	0.149608
$816$	−40136.6	−1.72189
$817$	0	0
$818$	−9552.23	−0.408296
$819$	−47798.5	−2.03934
$820$	−57247.1	−2.43799
$821$	24119.8	1.02532	0.512660	−	0.858592i	$-0.328660\pi$
$821$	24119.8	1.02532	0.512660	+	0.858592i	$0.328660\pi$
$822$	31013.2	1.31595
$823$	−22679.7	−0.960588	−0.480294	−	0.877108i	$-0.659470\pi$
$823$	−22679.7	−0.960588	−0.480294	+	0.877108i	$0.659470\pi$
$824$	−1560.23	−0.0659627
$825$	−9458.84	−0.399169
$826$	18132.5	0.763812
$827$	7335.57	0.308443	0.154222	−	0.988036i	$-0.450713\pi$
$827$	7335.57	0.308443	0.154222	+	0.988036i	$0.450713\pi$
$828$	−12735.0	−0.534509
$829$	−2389.09	−0.100092	−0.0500461	−	0.998747i	$-0.515937\pi$
$829$	−2389.09	−0.100092	−0.0500461	+	0.998747i	$0.515937\pi$
$830$	1954.52	0.0817376
$831$	−23429.3	−0.978042
$832$	−17990.3	−0.749641
$833$	−638.509	−0.0265583
$834$	48498.2	2.01361
$835$	−53756.8	−2.22794
$836$	−1031.46	−0.0426719
$837$	21924.0	0.905383
$838$	−36602.4	−1.50884
$839$	6893.41	0.283656	0.141828	−	0.989891i	$-0.454702\pi$
$839$	6893.41	0.283656	0.141828	+	0.989891i	$0.454702\pi$
$840$	−11114.6	−0.456537
$841$	60348.3	2.47440
$842$	29071.2	1.18986
$843$	−57657.7	−2.35568
$844$	6765.30	0.275914
$845$	−2162.19	−0.0880254
$846$	−78670.0	−3.19708
$847$	24653.6	1.00013
$848$	−27254.3	−1.10367
$849$	−31768.8	−1.28422
$850$	−58082.4	−2.34377
$851$	−2893.82	−0.116567
$852$	60638.7	2.43832
$853$	−6006.16	−0.241087	−0.120543	−	0.992708i	$-0.538464\pi$
$853$	−6006.16	−0.241087	−0.120543	+	0.992708i	$0.538464\pi$
$854$	4718.28	0.189059
$855$	−35143.6	−1.40572
$856$	2498.67	0.0997695
$857$	9759.72	0.389015	0.194507	−	0.980901i	$-0.437689\pi$
$857$	9759.72	0.389015	0.194507	+	0.980901i	$0.437689\pi$
$858$	−7060.96	−0.280953
$859$	−12026.8	−0.477705	−0.238853	−	0.971056i	$-0.576771\pi$
$859$	−12026.8	−0.477705	−0.238853	+	0.971056i	$0.576771\pi$
$860$	0	0
$861$	−72131.9	−2.85511
$862$	49852.2	1.96981
$863$	−36262.9	−1.43036	−0.715182	−	0.698938i	$-0.753656\pi$
$863$	−36262.9	−1.43036	−0.715182	+	0.698938i	$0.753656\pi$
$864$	64233.1	2.52923
$865$	−55560.2	−2.18393
$866$	34723.1	1.36252
$867$	8797.34	0.344606
$868$	11232.6	0.439237
$869$	4873.92	0.190260
$870$	−196099.	−7.64182
$871$	3679.51	0.143141
$872$	407.217	0.0158143
$873$	16226.8	0.629089
$874$	4132.03	0.159918
$875$	−40368.2	−1.55965
$876$	−42175.0	−1.62667
$877$	−3560.34	−0.137086	−0.0685429	−	0.997648i	$-0.521835\pi$
$877$	−3560.34	−0.137086	−0.0685429	+	0.997648i	$0.521835\pi$
$878$	−35128.5	−1.35026
$879$	54959.4	2.10891
$880$	−5852.43	−0.224188
$881$	45565.8	1.74251	0.871255	−	0.490831i	$-0.163307\pi$
$881$	45565.8	1.74251	0.871255	+	0.490831i	$0.163307\pi$
$882$	2202.62	0.0840884
$883$	−12993.7	−0.495214	−0.247607	−	0.968861i	$-0.579644\pi$
$883$	−12993.7	−0.495214	−0.247607	+	0.968861i	$0.579644\pi$
$884$	−20420.4	−0.776938
$885$	42982.9	1.63260
$886$	28221.3	1.07011
$887$	−33676.4	−1.27480	−0.637398	−	0.770535i	$-0.719989\pi$
$887$	−33676.4	−1.27480	−0.637398	+	0.770535i	$0.719989\pi$
$888$	2800.22	0.105821
$889$	25460.7	0.960545
$890$	25764.3	0.970360
$891$	3811.69	0.143318
$892$	36523.3	1.37095
$893$	12021.7	0.450495
$894$	91864.9	3.43671
$895$	42667.5	1.59354
$896$	−8162.97	−0.304359
$897$	13322.0	0.495886
$898$	−46054.3	−1.71142
$899$	−24429.9	−0.906322
$900$	94364.9	3.49500
$901$	−24368.9	−0.901050
$902$	−7177.68	−0.264956
$903$	0	0
$904$	3922.83	0.144327
$905$	−78099.3	−2.86863
$906$	10085.5	0.369834
$907$	22376.4	0.819180	0.409590	−	0.912270i	$-0.365672\pi$
$907$	22376.4	0.819180	0.409590	+	0.912270i	$0.365672\pi$
$908$	−27196.8	−0.994008
$909$	−65561.2	−2.39222
$910$	−63534.6	−2.31445
$911$	−52260.5	−1.90062	−0.950312	−	0.311298i	$-0.899236\pi$
$911$	−52260.5	−1.90062	−0.950312	+	0.311298i	$0.899236\pi$
$912$	−21157.8	−0.768206
$913$	115.416	0.00418368
$914$	−23862.8	−0.863579
$915$	11184.7	0.404102
$916$	−18425.4	−0.664619
$917$	18530.0	0.667301
$918$	63812.5	2.29425
$919$	−30391.1	−1.09087	−0.545436	−	0.838153i	$-0.683636\pi$
$919$	−30391.1	−1.09087	−0.545436	+	0.838153i	$0.683636\pi$
$920$	2086.69	0.0747783
$921$	−71847.9	−2.57054
$922$	7496.37	0.267766
$923$	−42729.5	−1.52379
$924$	5324.24	0.189561
$925$	21442.8	0.762201
$926$	41628.9	1.47733
$927$	25465.2	0.902253
$928$	−71574.8	−2.53185
$929$	9900.90	0.349664	0.174832	−	0.984598i	$-0.444062\pi$
$929$	9900.90	0.349664	0.174832	+	0.984598i	$0.444062\pi$
$930$	56535.8	1.99342
$931$	−336.587	−0.0118487
$932$	−26070.6	−0.916279
$933$	97235.5	3.41195
$934$	51407.6	1.80097
$935$	−5232.84	−0.183029
$936$	−8683.57	−0.303239
$937$	24469.5	0.853131	0.426566	−	0.904457i	$-0.359723\pi$
$937$	24469.5	0.853131	0.426566	+	0.904457i	$0.359723\pi$
$938$	−5891.01	−0.205062
$939$	−11019.0	−0.382950
$940$	−49249.2	−1.70886
$941$	8819.85	0.305546	0.152773	−	0.988261i	$-0.451180\pi$
$941$	8819.85	0.305546	0.152773	+	0.988261i	$0.451180\pi$
$942$	46917.5	1.62278
$943$	13542.2	0.467652
$944$	17431.1	0.600991
$945$	93507.3	3.21883
$946$	0	0
$947$	46001.3	1.57850	0.789250	−	0.614072i	$-0.210469\pi$
$947$	46001.3	1.57850	0.789250	+	0.614072i	$0.210469\pi$
$948$	−72184.5	−2.47304
$949$	29718.9	1.01656
$950$	−30617.8	−1.04565
$951$	58855.8	2.00687
$952$	−4030.19	−0.137205
$953$	−12737.3	−0.432950	−0.216475	−	0.976288i	$-0.569456\pi$
$953$	−12737.3	−0.432950	−0.216475	+	0.976288i	$0.569456\pi$
$954$	84063.6	2.85289
$955$	−59318.1	−2.00994
$956$	5983.32	0.202421
$957$	−11579.8	−0.391141
$958$	−8746.27	−0.294968
$959$	16478.5	0.554868
$960$	68277.3	2.29546
$961$	−22747.8	−0.763580
$962$	16006.9	0.536470
$963$	−40781.9	−1.36467
$964$	8814.81	0.294508
$965$	26075.3	0.869838
$966$	−21329.0	−0.710402
$967$	28175.8	0.936992	0.468496	−	0.883466i	$-0.344796\pi$
$967$	28175.8	0.936992	0.468496	+	0.883466i	$0.344796\pi$
$968$	4478.82	0.148714
$969$	−18917.8	−0.627170
$970$	21568.9	0.713956
$971$	14012.5	0.463113	0.231557	−	0.972821i	$-0.425618\pi$
$971$	14012.5	0.463113	0.231557	+	0.972821i	$0.425618\pi$
$972$	−6217.67	−0.205177
$973$	25768.9	0.849039
$974$	66635.2	2.19212
$975$	−98714.5	−3.24245
$976$	4535.79	0.148757
$977$	25344.3	0.829924	0.414962	−	0.909839i	$-0.363795\pi$
$977$	25344.3	0.829924	0.414962	+	0.909839i	$0.363795\pi$
$978$	−6463.80	−0.211339
$979$	1521.40	0.0496671
$980$	1378.89	0.0449459
$981$	−6646.37	−0.216312
$982$	66312.6	2.15491
$983$	31795.3	1.03165	0.515825	−	0.856694i	$-0.327486\pi$
$983$	31795.3	1.03165	0.515825	+	0.856694i	$0.327486\pi$
$984$	−13104.2	−0.424540
$985$	−91832.5	−2.97059
$986$	−71106.2	−2.29663
$987$	−62054.5	−2.00123
$988$	−10764.5	−0.346624
$989$	0	0
$990$	18051.3	0.579505
$991$	57046.1	1.82859	0.914294	−	0.405051i	$-0.132746\pi$
$991$	57046.1	1.82859	0.914294	+	0.405051i	$0.132746\pi$
$992$	20635.2	0.660451
$993$	12695.4	0.405715
$994$	68411.2	2.18297
$995$	66075.4	2.10526
$996$	−1709.35	−0.0543802
$997$	14197.2	0.450984	0.225492	−	0.974245i	$-0.427601\pi$
$997$	14197.2	0.450984	0.225492	+	0.974245i	$0.427601\pi$
$998$	−27997.1	−0.888008
$999$	−23558.3	−0.746096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.41	✓	50
43.42	odd	2		1849.4.a.j.1.10	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.41	✓	50	1.1	even	1	trivial
1849.4.a.j.1.10	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)

\(f(q)\)	\(=\)	\(q+3.88871 q^{2} -9.09520 q^{3} +7.12206 q^{4} +19.0468 q^{5} -35.3686 q^{6} -18.7927 q^{7} -3.41407 q^{8} +55.7226 q^{9} +O(q^{10})\)	\(q+3.88871 q^{2} -9.09520 q^{3} +7.12206 q^{4} +19.0468 q^{5} -35.3686 q^{6} -18.7927 q^{7} -3.41407 q^{8} +55.7226 q^{9} +74.0673 q^{10} +4.37373 q^{11} -64.7765 q^{12} +45.6452 q^{13} -73.0793 q^{14} -173.234 q^{15} -70.2528 q^{16} -62.8152 q^{17} +216.689 q^{18} -33.1127 q^{19} +135.652 q^{20} +170.923 q^{21} +17.0082 q^{22} -32.0896 q^{23} +31.0516 q^{24} +237.779 q^{25} +177.501 q^{26} -261.237 q^{27} -133.843 q^{28} +291.097 q^{29} -673.657 q^{30} -83.9237 q^{31} -245.880 q^{32} -39.7799 q^{33} -244.270 q^{34} -357.940 q^{35} +396.859 q^{36} +90.1795 q^{37} -128.766 q^{38} -415.152 q^{39} -65.0270 q^{40} -422.014 q^{41} +664.670 q^{42} +31.1499 q^{44} +1061.33 q^{45} -124.787 q^{46} -363.055 q^{47} +638.963 q^{48} +10.1649 q^{49} +924.654 q^{50} +571.316 q^{51} +325.087 q^{52} +387.946 q^{53} -1015.88 q^{54} +83.3054 q^{55} +64.1595 q^{56} +301.166 q^{57} +1131.99 q^{58} -248.120 q^{59} -1233.78 q^{60} -64.5638 q^{61} -326.355 q^{62} -1047.18 q^{63} -394.134 q^{64} +869.393 q^{65} -154.692 q^{66} +80.6113 q^{67} -447.373 q^{68} +291.861 q^{69} -1391.92 q^{70} -936.123 q^{71} -190.241 q^{72} +651.084 q^{73} +350.682 q^{74} -2162.65 q^{75} -235.830 q^{76} -82.1941 q^{77} -1614.40 q^{78} +1114.36 q^{79} -1338.09 q^{80} +871.496 q^{81} -1641.09 q^{82} +26.3884 q^{83} +1217.32 q^{84} -1196.43 q^{85} -2647.58 q^{87} -14.9322 q^{88} +347.849 q^{89} +4127.22 q^{90} -857.795 q^{91} -228.544 q^{92} +763.303 q^{93} -1411.82 q^{94} -630.689 q^{95} +2236.33 q^{96} +291.207 q^{97} +39.5283 q^{98} +243.715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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

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