LMFDB - Embedded newform 1849.4.a.j.1.35

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			1.35
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)

$f(q)$	$=$	$q+3.04766 q^{2} +1.42990 q^{3} +1.28824 q^{4} -10.9474 q^{5} +4.35784 q^{6} -8.62569 q^{7} -20.4552 q^{8} -24.9554 q^{9} +O(q^{10})$	\(q+3.04766 q^{2} +1.42990 q^{3} +1.28824 q^{4} -10.9474 q^{5} +4.35784 q^{6} -8.62569 q^{7} -20.4552 q^{8} -24.9554 q^{9} -33.3638 q^{10} +42.2441 q^{11} +1.84205 q^{12} +78.4327 q^{13} -26.2882 q^{14} -15.6536 q^{15} -72.6463 q^{16} +75.8963 q^{17} -76.0556 q^{18} +107.684 q^{19} -14.1028 q^{20} -12.3339 q^{21} +128.746 q^{22} -27.7883 q^{23} -29.2488 q^{24} -5.15536 q^{25} +239.036 q^{26} -74.2909 q^{27} -11.1119 q^{28} +12.6364 q^{29} -47.7069 q^{30} -188.821 q^{31} -57.7599 q^{32} +60.4047 q^{33} +231.306 q^{34} +94.4285 q^{35} -32.1484 q^{36} +84.0627 q^{37} +328.185 q^{38} +112.151 q^{39} +223.930 q^{40} -215.325 q^{41} -37.5894 q^{42} +54.4203 q^{44} +273.196 q^{45} -84.6893 q^{46} -598.204 q^{47} -103.877 q^{48} -268.598 q^{49} -15.7118 q^{50} +108.524 q^{51} +101.040 q^{52} +368.465 q^{53} -226.413 q^{54} -462.461 q^{55} +176.440 q^{56} +153.977 q^{57} +38.5114 q^{58} -62.2843 q^{59} -20.1655 q^{60} +186.541 q^{61} -575.462 q^{62} +215.257 q^{63} +405.138 q^{64} -858.631 q^{65} +184.093 q^{66} -717.716 q^{67} +97.7723 q^{68} -39.7344 q^{69} +287.786 q^{70} -474.895 q^{71} +510.467 q^{72} +1229.76 q^{73} +256.195 q^{74} -7.37163 q^{75} +138.723 q^{76} -364.384 q^{77} +341.798 q^{78} -1134.35 q^{79} +795.285 q^{80} +567.567 q^{81} -656.237 q^{82} -632.780 q^{83} -15.8889 q^{84} -830.864 q^{85} +18.0687 q^{87} -864.110 q^{88} -6.66926 q^{89} +832.607 q^{90} -676.536 q^{91} -35.7979 q^{92} -269.994 q^{93} -1823.12 q^{94} -1178.86 q^{95} -82.5908 q^{96} -1024.36 q^{97} -818.594 q^{98} -1054.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.04766	1.07751	0.538755	−	0.842462i	$-0.318895\pi$
$2$	3.04766	1.07751	0.538755	+	0.842462i	$0.318895\pi$
$3$	1.42990	0.275184	0.137592	−	0.990489i	$-0.456064\pi$
$3$	1.42990	0.275184	0.137592	+	0.990489i	$0.456064\pi$
$4$	1.28824	0.161029
$5$	−10.9474	−0.979161	−0.489581	−	0.871958i	$-0.662850\pi$
$5$	−10.9474	−0.979161	−0.489581	+	0.871958i	$0.662850\pi$
$6$	4.35784	0.296514
$7$	−8.62569	−0.465743	−0.232872	−	0.972507i	$-0.574812\pi$
$7$	−8.62569	−0.465743	−0.232872	+	0.972507i	$0.574812\pi$
$8$	−20.4552	−0.904000
$9$	−24.9554	−0.924274
$10$	−33.3638	−1.05506
$11$	42.2441	1.15792	0.578958	−	0.815358i	$-0.303460\pi$
$11$	42.2441	1.15792	0.578958	+	0.815358i	$0.303460\pi$
$12$	1.84205	0.0443127
$13$	78.4327	1.67333	0.836666	−	0.547713i	$-0.184501\pi$
$13$	78.4327	1.67333	0.836666	+	0.547713i	$0.184501\pi$
$14$	−26.2882	−0.501843
$15$	−15.6536	−0.269450
$16$	−72.6463	−1.13510
$17$	75.8963	1.08280	0.541398	−	0.840766i	$-0.317895\pi$
$17$	75.8963	1.08280	0.541398	+	0.840766i	$0.317895\pi$
$18$	−76.0556	−0.995915
$19$	107.684	1.30023	0.650117	−	0.759834i	$-0.274720\pi$
$19$	107.684	1.30023	0.650117	+	0.759834i	$0.274720\pi$
$20$	−14.1028	−0.157674
$21$	−12.3339	−0.128165
$22$	128.746	1.24767
$23$	−27.7883	−0.251924	−0.125962	−	0.992035i	$-0.540202\pi$
$23$	−27.7883	−0.251924	−0.125962	+	0.992035i	$0.540202\pi$
$24$	−29.2488	−0.248766
$25$	−5.15536	−0.0412428
$26$	239.036	1.80303
$27$	−74.2909	−0.529529
$28$	−11.1119	−0.0749984
$29$	12.6364	0.0809143	0.0404572	−	0.999181i	$-0.487119\pi$
$29$	12.6364	0.0809143	0.0404572	+	0.999181i	$0.487119\pi$
$30$	−47.7069	−0.290335
$31$	−188.821	−1.09397	−0.546987	−	0.837141i	$-0.684225\pi$
$31$	−188.821	−1.09397	−0.546987	+	0.837141i	$0.684225\pi$
$32$	−57.7599	−0.319082
$33$	60.4047	0.318640
$34$	231.306	1.16673
$35$	94.4285	0.456038
$36$	−32.1484	−0.148835
$37$	84.0627	0.373509	0.186754	−	0.982407i	$-0.440203\pi$
$37$	84.0627	0.373509	0.186754	+	0.982407i	$0.440203\pi$
$38$	328.185	1.40102
$39$	112.151	0.460474
$40$	223.930	0.885162
$41$	−215.325	−0.820197	−0.410099	−	0.912041i	$-0.634506\pi$
$41$	−215.325	−0.820197	−0.410099	+	0.912041i	$0.634506\pi$
$42$	−37.5894	−0.138099
$43$	0	0
$43$	0	0
$44$	54.4203	0.186458
$45$	273.196	0.905013
$46$	−84.6893	−0.271451
$47$	−598.204	−1.85653	−0.928266	−	0.371916i	$-0.878701\pi$
$47$	−598.204	−1.85653	−0.928266	+	0.371916i	$0.878701\pi$
$48$	−103.877	−0.312361
$49$	−268.598	−0.783083
$50$	−15.7118	−0.0444396
$51$	108.524	0.297968
$52$	101.040	0.269456
$53$	368.465	0.954955	0.477477	−	0.878644i	$-0.341551\pi$
$53$	368.465	0.954955	0.477477	+	0.878644i	$0.341551\pi$
$54$	−226.413	−0.570574
$55$	−462.461	−1.13379
$56$	176.440	0.421032
$57$	153.977	0.357804
$58$	38.5114	0.0871860
$59$	−62.2843	−0.137436	−0.0687180	−	0.997636i	$-0.521891\pi$
$59$	−62.2843	−0.137436	−0.0687180	+	0.997636i	$0.521891\pi$
$60$	−20.1655	−0.0433893
$61$	186.541	0.391543	0.195772	−	0.980649i	$-0.437279\pi$
$61$	186.541	0.391543	0.195772	+	0.980649i	$0.437279\pi$
$62$	−575.462	−1.17877
$63$	215.257	0.430474
$64$	405.138	0.791285
$65$	−858.631	−1.63846
$66$	184.093	0.343338
$67$	−717.716	−1.30870	−0.654350	−	0.756192i	$-0.727058\pi$
$67$	−717.716	−1.30870	−0.654350	+	0.756192i	$0.727058\pi$
$68$	97.7723	0.174362
$69$	−39.7344	−0.0693256
$70$	287.786	0.491386
$71$	−474.895	−0.793798	−0.396899	−	0.917862i	$-0.629914\pi$
$71$	−474.895	−0.793798	−0.396899	+	0.917862i	$0.629914\pi$
$72$	510.467	0.835543
$73$	1229.76	1.97168	0.985842	−	0.167678i	$-0.0536268\pi$
$73$	1229.76	1.97168	0.985842	+	0.167678i	$0.0536268\pi$
$74$	256.195	0.402460
$75$	−7.37163	−0.0113494
$76$	138.723	0.209376
$77$	−364.384	−0.539291
$78$	341.798	0.496166
$79$	−1134.35	−1.61549	−0.807747	−	0.589529i	$-0.799313\pi$
$79$	−1134.35	−1.61549	−0.807747	+	0.589529i	$0.799313\pi$
$80$	795.285	1.11145
$81$	567.567	0.778556
$82$	−656.237	−0.883771
$83$	−632.780	−0.836826	−0.418413	−	0.908257i	$-0.637414\pi$
$83$	−632.780	−0.836826	−0.418413	+	0.908257i	$0.637414\pi$
$84$	−15.8889	−0.0206384
$85$	−830.864	−1.06023
$86$	0	0
$87$	18.0687	0.0222663
$88$	−864.110	−1.04676
$89$	−6.66926	−0.00794315	−0.00397158	−	0.999992i	$-0.501264\pi$
$89$	−6.66926	−0.00794315	−0.00397158	+	0.999992i	$0.501264\pi$
$90$	832.607	0.975162
$91$	−676.536	−0.779344
$92$	−35.7979	−0.0405672
$93$	−269.994	−0.301044
$94$	−1823.12	−2.00043
$95$	−1178.86	−1.27314
$96$	−82.5908	−0.0878061
$97$	−1024.36	−1.07224	−0.536122	−	0.844140i	$-0.680111\pi$
$97$	−1024.36	−1.07224	−0.536122	+	0.844140i	$0.680111\pi$
$98$	−818.594	−0.843781
$99$	−1054.22	−1.07023
$100$	−6.64131	−0.00664131
$101$	1296.35	1.27714	0.638572	−	0.769562i	$-0.279526\pi$
$101$	1296.35	1.27714	0.638572	+	0.769562i	$0.279526\pi$
$102$	330.744	0.321064
$103$	30.1268	0.0288202	0.0144101	−	0.999896i	$-0.495413\pi$
$103$	30.1268	0.0288202	0.0144101	+	0.999896i	$0.495413\pi$
$104$	−1604.36	−1.51269
$105$	135.023	0.125494
$106$	1122.96	1.02897
$107$	−1362.61	−1.23111	−0.615554	−	0.788095i	$-0.711068\pi$
$107$	−1362.61	−1.23111	−0.615554	+	0.788095i	$0.711068\pi$
$108$	−95.7042	−0.0852698
$109$	−397.621	−0.349406	−0.174703	−	0.984621i	$-0.555896\pi$
$109$	−397.621	−0.349406	−0.174703	+	0.984621i	$0.555896\pi$
$110$	−1409.42	−1.22167
$111$	120.201	0.102784
$112$	626.624	0.528665
$113$	−348.680	−0.290275	−0.145137	−	0.989412i	$-0.546362\pi$
$113$	−348.680	−0.290275	−0.145137	+	0.989412i	$0.546362\pi$
$114$	469.271	0.385537
$115$	304.208	0.246675
$116$	16.2786	0.0130296
$117$	−1957.32	−1.54662
$118$	−189.821	−0.148089
$119$	−654.657	−0.504305
$120$	320.197	0.243582
$121$	453.562	0.340768
$122$	568.514	0.421892
$123$	−307.893	−0.225705
$124$	−243.246	−0.176162
$125$	1424.86	1.01954
$126$	656.031	0.463841
$127$	296.445	0.207128	0.103564	−	0.994623i	$-0.466975\pi$
$127$	296.445	0.207128	0.103564	+	0.994623i	$0.466975\pi$
$128$	1696.80	1.17170
$129$	0	0
$130$	−2616.82	−1.76546
$131$	−1527.08	−1.01848	−0.509241	−	0.860624i	$-0.670074\pi$
$131$	−1527.08	−1.01848	−0.509241	+	0.860624i	$0.670074\pi$
$132$	77.8155	0.0513104
$133$	−928.850	−0.605575
$134$	−2187.35	−1.41014
$135$	813.289	0.518495
$136$	−1552.47	−0.978848
$137$	−1851.19	−1.15444	−0.577220	−	0.816589i	$-0.695862\pi$
$137$	−1851.19	−1.15444	−0.577220	+	0.816589i	$0.695862\pi$
$138$	−121.097	−0.0746990
$139$	−624.022	−0.380783	−0.190392	−	0.981708i	$-0.560976\pi$
$139$	−624.022	−0.380783	−0.190392	+	0.981708i	$0.560976\pi$
$140$	121.646	0.0734355
$141$	−855.371	−0.510888
$142$	−1447.32	−0.855326
$143$	3313.32	1.93758
$144$	1812.92	1.04914
$145$	−138.335	−0.0792282
$146$	3747.90	2.12451
$147$	−384.067	−0.215492
$148$	108.293	0.0601459
$149$	−2279.84	−1.25350	−0.626750	−	0.779220i	$-0.715615\pi$
$149$	−2279.84	−1.25350	−0.626750	+	0.779220i	$0.715615\pi$
$150$	−22.4662	−0.0122291
$151$	−2948.04	−1.58880	−0.794398	−	0.607398i	$-0.792213\pi$
$151$	−2948.04	−1.58880	−0.794398	+	0.607398i	$0.792213\pi$
$152$	−2202.70	−1.17541
$153$	−1894.02	−1.00080
$154$	−1110.52	−0.581092
$155$	2067.09	1.07118
$156$	144.477	0.0741499
$157$	−1507.11	−0.766115	−0.383058	−	0.923724i	$-0.625129\pi$
$157$	−1507.11	−0.766115	−0.383058	+	0.923724i	$0.625129\pi$
$158$	−3457.11	−1.74071
$159$	526.868	0.262788
$160$	632.319	0.312432
$161$	239.693	0.117332
$162$	1729.75	0.838902
$163$	2880.27	1.38405	0.692026	−	0.721873i	$-0.256719\pi$
$163$	2880.27	1.38405	0.692026	+	0.721873i	$0.256719\pi$
$164$	−277.389	−0.132076
$165$	−661.272	−0.312000
$166$	−1928.50	−0.901689
$167$	2282.83	1.05779	0.528895	−	0.848688i	$-0.322607\pi$
$167$	2282.83	1.05779	0.528895	+	0.848688i	$0.322607\pi$
$168$	252.291	0.115861
$169$	3954.69	1.80004
$170$	−2532.19	−1.14241
$171$	−2687.30	−1.20177
$172$	0	0
$173$	−1889.09	−0.830201	−0.415100	−	0.909776i	$-0.636254\pi$
$173$	−1889.09	−0.830201	−0.415100	+	0.909776i	$0.636254\pi$
$174$	55.0673	0.0239922
$175$	44.4685	0.0192086
$176$	−3068.88	−1.31435
$177$	−89.0602	−0.0378202
$178$	−20.3257	−0.00855883
$179$	1064.35	0.444433	0.222216	−	0.974997i	$-0.428671\pi$
$179$	1064.35	0.444433	0.222216	+	0.974997i	$0.428671\pi$
$180$	351.940	0.145734
$181$	1113.89	0.457429	0.228715	−	0.973494i	$-0.426548\pi$
$181$	1113.89	0.457429	0.228715	+	0.973494i	$0.426548\pi$
$182$	−2061.85	−0.839751
$183$	266.735	0.107746
$184$	568.415	0.227740
$185$	−920.264	−0.365725
$186$	−822.851	−0.324378
$187$	3206.17	1.25379
$188$	−770.628	−0.298956
$189$	640.810	0.246625
$190$	−3592.76	−1.37182
$191$	600.424	0.227461	0.113731	−	0.993512i	$-0.463720\pi$
$191$	600.424	0.227461	0.113731	+	0.993512i	$0.463720\pi$
$192$	579.306	0.217749
$193$	−4418.79	−1.64804	−0.824019	−	0.566562i	$-0.808273\pi$
$193$	−4418.79	−1.64804	−0.824019	+	0.566562i	$0.808273\pi$
$194$	−3121.89	−1.15535
$195$	−1227.76	−0.450879
$196$	−346.017	−0.126099
$197$	2202.16	0.796434	0.398217	−	0.917291i	$-0.369629\pi$
$197$	2202.16	0.796434	0.398217	+	0.917291i	$0.369629\pi$
$198$	−3212.90	−1.15319
$199$	2962.08	1.05516	0.527579	−	0.849506i	$-0.323100\pi$
$199$	2962.08	1.05516	0.527579	+	0.849506i	$0.323100\pi$
$200$	105.454	0.0372835
$201$	−1026.26	−0.360133
$202$	3950.83	1.37614
$203$	−108.997	−0.0376853
$204$	139.804	0.0479817
$205$	2357.24	0.803106
$206$	91.8163	0.0310541
$207$	693.468	0.232847
$208$	−5697.85	−1.89940
$209$	4549.02	1.50556
$210$	411.505	0.135221
$211$	−3121.62	−1.01849	−0.509244	−	0.860622i	$-0.670075\pi$
$211$	−3121.62	−1.01849	−0.509244	+	0.860622i	$0.670075\pi$
$212$	474.670	0.153776
$213$	−679.051	−0.218440
$214$	−4152.77	−1.32653
$215$	0	0
$216$	1519.63	0.478694
$217$	1628.71	0.509511
$218$	−1211.82	−0.376488
$219$	1758.44	0.542576
$220$	−595.759	−0.182573
$221$	5952.75	1.81188
$222$	366.332	0.110750
$223$	1921.29	0.576946	0.288473	−	0.957488i	$-0.406852\pi$
$223$	1921.29	0.576946	0.288473	+	0.957488i	$0.406852\pi$
$224$	498.219	0.148610
$225$	128.654	0.0381197
$226$	−1062.66	−0.312774
$227$	548.261	0.160306	0.0801528	−	0.996783i	$-0.474459\pi$
$227$	548.261	0.160306	0.0801528	+	0.996783i	$0.474459\pi$
$228$	198.359	0.0576169
$229$	2286.66	0.659854	0.329927	−	0.944006i	$-0.392976\pi$
$229$	2286.66	0.659854	0.329927	+	0.944006i	$0.392976\pi$
$230$	927.124	0.265795
$231$	−521.032	−0.148404
$232$	−258.479	−0.0731465
$233$	−4993.15	−1.40392	−0.701958	−	0.712218i	$-0.747691\pi$
$233$	−4993.15	−1.40392	−0.701958	+	0.712218i	$0.747691\pi$
$234$	−5965.25	−1.66650
$235$	6548.75	1.81785
$236$	−80.2368	−0.0221312
$237$	−1622.00	−0.444558
$238$	−1995.17	−0.543394
$239$	−3806.31	−1.03017	−0.515083	−	0.857140i	$-0.672239\pi$
$239$	−3806.31	−1.03017	−0.515083	+	0.857140i	$0.672239\pi$
$240$	1137.18	0.305852
$241$	6268.95	1.67559	0.837797	−	0.545981i	$-0.183843\pi$
$241$	6268.95	1.67559	0.837797	+	0.545981i	$0.183843\pi$
$242$	1382.30	0.367181
$243$	2817.42	0.743775
$244$	240.309	0.0630500
$245$	2940.43	0.766765
$246$	−938.352	−0.243200
$247$	8445.96	2.17572
$248$	3862.36	0.988953
$249$	−904.810	−0.230281
$250$	4342.48	1.09857
$251$	938.494	0.236005	0.118002	−	0.993013i	$-0.462351\pi$
$251$	938.494	0.236005	0.118002	+	0.993013i	$0.462351\pi$
$252$	277.302	0.0693190
$253$	−1173.89	−0.291707
$254$	903.464	0.223183
$255$	−1188.05	−0.291759
$256$	1930.17	0.471234
$257$	7223.21	1.75320	0.876598	−	0.481223i	$-0.159807\pi$
$257$	7223.21	1.75320	0.876598	+	0.481223i	$0.159807\pi$
$258$	0	0
$259$	−725.098	−0.173959
$260$	−1106.12	−0.263841
$261$	−315.346	−0.0747870
$262$	−4654.01	−1.09743
$263$	−6840.18	−1.60374	−0.801870	−	0.597498i	$-0.796162\pi$
$263$	−6840.18	−1.60374	−0.801870	+	0.597498i	$0.796162\pi$
$264$	−1235.59	−0.288050
$265$	−4033.72	−0.935055
$266$	−2830.82	−0.652514
$267$	−9.53637	−0.00218583
$268$	−924.587	−0.210739
$269$	−3969.81	−0.899790	−0.449895	−	0.893081i	$-0.648539\pi$
$269$	−3969.81	−0.899790	−0.449895	+	0.893081i	$0.648539\pi$
$270$	2478.63	0.558684
$271$	−7439.71	−1.66764	−0.833820	−	0.552037i	$-0.813851\pi$
$271$	−7439.71	−1.66764	−0.833820	+	0.552037i	$0.813851\pi$
$272$	−5513.59	−1.22908
$273$	−967.378	−0.214463
$274$	−5641.81	−1.24392
$275$	−217.783	−0.0477557
$276$	−51.1873	−0.0111635
$277$	627.394	0.136088	0.0680442	−	0.997682i	$-0.478324\pi$
$277$	627.394	0.136088	0.0680442	+	0.997682i	$0.478324\pi$
$278$	−1901.81	−0.410298
$279$	4712.10	1.01113
$280$	−1931.55	−0.412258
$281$	8656.81	1.83780	0.918900	−	0.394489i	$-0.129079\pi$
$281$	8656.81	1.83780	0.918900	+	0.394489i	$0.129079\pi$
$282$	−2606.88	−0.550487
$283$	−5735.35	−1.20470	−0.602352	−	0.798231i	$-0.705769\pi$
$283$	−5735.35	−1.20470	−0.602352	+	0.798231i	$0.705769\pi$
$284$	−611.776	−0.127825
$285$	−1685.65	−0.350347
$286$	10097.9	2.08776
$287$	1857.32	0.382001
$288$	1441.42	0.294919
$289$	847.243	0.172449
$290$	−421.598	−0.0853692
$291$	−1464.73	−0.295064
$292$	1584.22	0.317499
$293$	−2132.59	−0.425212	−0.212606	−	0.977138i	$-0.568195\pi$
$293$	−2132.59	−0.425212	−0.212606	+	0.977138i	$0.568195\pi$
$294$	−1170.51	−0.232195
$295$	681.848	0.134572
$296$	−1719.52	−0.337652
$297$	−3138.35	−0.613150
$298$	−6948.17	−1.35066
$299$	−2179.51	−0.421553
$300$	−9.49640	−0.00182758
$301$	0	0
$302$	−8984.63	−1.71194
$303$	1853.65	0.351449
$304$	−7822.86	−1.47589
$305$	−2042.13	−0.383384
$306$	−5772.33	−1.07837
$307$	−2974.73	−0.553020	−0.276510	−	0.961011i	$-0.589178\pi$
$307$	−2974.73	−0.553020	−0.276510	+	0.961011i	$0.589178\pi$
$308$	−469.413	−0.0868418
$309$	43.0783	0.00793087
$310$	6299.78	1.15421
$311$	−8271.14	−1.50808	−0.754040	−	0.656828i	$-0.771898\pi$
$311$	−8271.14	−1.50808	−0.754040	+	0.656828i	$0.771898\pi$
$312$	−2294.07	−0.416269
$313$	−4256.50	−0.768664	−0.384332	−	0.923195i	$-0.625568\pi$
$313$	−4256.50	−0.768664	−0.384332	+	0.923195i	$0.625568\pi$
$314$	−4593.15	−0.825498
$315$	−2356.50	−0.421504
$316$	−1461.31	−0.260142
$317$	−5331.95	−0.944708	−0.472354	−	0.881409i	$-0.656596\pi$
$317$	−5331.95	−0.944708	−0.472354	+	0.881409i	$0.656596\pi$
$318$	1605.71	0.283157
$319$	533.812	0.0936919
$320$	−4435.19	−0.774796
$321$	−1948.39	−0.338781
$322$	730.503	0.126427
$323$	8172.83	1.40789
$324$	731.160	0.125370
$325$	−404.349	−0.0690130
$326$	8778.09	1.49133
$327$	−568.558	−0.0961509
$328$	4404.51	0.741458
$329$	5159.92	0.864668
$330$	−2015.33	−0.336183
$331$	−4689.05	−0.778650	−0.389325	−	0.921100i	$-0.627292\pi$
$331$	−4689.05	−0.778650	−0.389325	+	0.921100i	$0.627292\pi$
$332$	−815.169	−0.134754
$333$	−2097.82	−0.345224
$334$	6957.29	1.13978
$335$	7857.09	1.28143
$336$	896.009	0.145480
$337$	11172.1	1.80588	0.902938	−	0.429770i	$-0.141405\pi$
$337$	11172.1	1.80588	0.902938	+	0.429770i	$0.141405\pi$
$338$	12052.6	1.93957
$339$	−498.576	−0.0798789
$340$	−1070.35	−0.170729
$341$	−7976.56	−1.26673
$342$	−8189.98	−1.29492
$343$	5275.45	0.830459
$344$	0	0
$345$	434.987	0.0678809
$346$	−5757.30	−0.894550
$347$	−7176.25	−1.11020	−0.555102	−	0.831782i	$-0.687321\pi$
$347$	−7176.25	−1.11020	−0.555102	+	0.831782i	$0.687321\pi$
$348$	23.2768	0.00358553
$349$	8305.35	1.27385	0.636927	−	0.770924i	$-0.280205\pi$
$349$	8305.35	1.27385	0.636927	+	0.770924i	$0.280205\pi$
$350$	135.525	0.0206975
$351$	−5826.84	−0.886079
$352$	−2440.02	−0.369469
$353$	5746.60	0.866461	0.433231	−	0.901283i	$-0.357374\pi$
$353$	5746.60	0.866461	0.433231	+	0.901283i	$0.357374\pi$
$354$	−271.425	−0.0407516
$355$	5198.84	0.777256
$356$	−8.59158	−0.00127908
$357$	−936.093	−0.138777
$358$	3243.78	0.478881
$359$	1277.28	0.187778	0.0938891	−	0.995583i	$-0.470070\pi$
$359$	1277.28	0.187778	0.0938891	+	0.995583i	$0.470070\pi$
$360$	−5588.27	−0.818132
$361$	4736.88	0.690608
$362$	3394.75	0.492885
$363$	648.548	0.0937739
$364$	−871.538	−0.125497
$365$	−13462.7	−1.93060
$366$	812.917	0.116098
$367$	−3186.62	−0.453243	−0.226622	−	0.973983i	$-0.572768\pi$
$367$	−3186.62	−0.453243	−0.226622	+	0.973983i	$0.572768\pi$
$368$	2018.72	0.285959
$369$	5373.52	0.758087
$370$	−2804.65	−0.394073
$371$	−3178.27	−0.444764
$372$	−347.816	−0.0484770
$373$	−10717.8	−1.48779	−0.743894	−	0.668298i	$-0.767023\pi$
$373$	−10717.8	−1.48779	−0.743894	+	0.668298i	$0.767023\pi$
$374$	9771.31	1.35097
$375$	2037.40	0.280562
$376$	12236.4	1.67831
$377$	991.105	0.135397
$378$	1952.97	0.265741
$379$	1001.31	0.135709	0.0678544	−	0.997695i	$-0.478385\pi$
$379$	1001.31	0.135709	0.0678544	+	0.997695i	$0.478385\pi$
$380$	−1518.65	−0.205013
$381$	423.886	0.0569983
$382$	1829.89	0.245092
$383$	2126.29	0.283677	0.141838	−	0.989890i	$-0.454699\pi$
$383$	2126.29	0.283677	0.141838	+	0.989890i	$0.454699\pi$
$384$	2426.25	0.322433
$385$	3989.04	0.528053
$386$	−13467.0	−1.77578
$387$	0	0
$388$	−1319.61	−0.172663
$389$	11830.9	1.54203	0.771014	−	0.636819i	$-0.219750\pi$
$389$	11830.9	1.54203	0.771014	+	0.636819i	$0.219750\pi$
$390$	−3741.78	−0.485827
$391$	−2109.03	−0.272783
$392$	5494.21	0.707907
$393$	−2183.56	−0.280270
$394$	6711.44	0.858166
$395$	12418.1	1.58183
$396$	−1358.08	−0.172339
$397$	−4635.30	−0.585992	−0.292996	−	0.956114i	$-0.594652\pi$
$397$	−4635.30	−0.585992	−0.292996	+	0.956114i	$0.594652\pi$
$398$	9027.43	1.13694
$399$	−1328.16	−0.166645
$400$	374.518	0.0468147
$401$	−12934.8	−1.61081	−0.805406	−	0.592724i	$-0.798052\pi$
$401$	−12934.8	−1.61081	−0.805406	+	0.592724i	$0.798052\pi$
$402$	−3127.69	−0.388048
$403$	−14809.7	−1.83058
$404$	1670.00	0.205658
$405$	−6213.36	−0.762332
$406$	−332.187	−0.0406063
$407$	3551.15	0.432491
$408$	−2219.88	−0.269363
$409$	−1367.64	−0.165343	−0.0826717	−	0.996577i	$-0.526345\pi$
$409$	−1367.64	−0.165343	−0.0826717	+	0.996577i	$0.526345\pi$
$410$	7184.06	0.865355
$411$	−2647.02	−0.317683
$412$	38.8104	0.00464091
$413$	537.245	0.0640099
$414$	2113.45	0.250895
$415$	6927.26	0.819388
$416$	−4530.27	−0.533930
$417$	−892.288	−0.104785
$418$	13863.9	1.62226
$419$	11334.8	1.32158	0.660790	−	0.750571i	$-0.270221\pi$
$419$	11334.8	1.32158	0.660790	+	0.750571i	$0.270221\pi$
$420$	173.942	0.0202083
$421$	−16468.4	−1.90646	−0.953231	−	0.302242i	$-0.902265\pi$
$421$	−16468.4	−1.90646	−0.953231	+	0.302242i	$0.902265\pi$
$422$	−9513.63	−1.09743
$423$	14928.4	1.71594
$424$	−7537.03	−0.863279
$425$	−391.272	−0.0446576
$426$	−2069.52	−0.235372
$427$	−1609.05	−0.182359
$428$	−1755.36	−0.198245
$429$	4737.71	0.533190
$430$	0	0
$431$	10893.5	1.21745	0.608726	−	0.793380i	$-0.291681\pi$
$431$	10893.5	1.21745	0.608726	+	0.793380i	$0.291681\pi$
$432$	5396.96	0.601068
$433$	7492.45	0.831557	0.415779	−	0.909466i	$-0.363509\pi$
$433$	7492.45	0.831557	0.415779	+	0.909466i	$0.363509\pi$
$434$	4963.75	0.549004
$435$	−197.805	−0.0218023
$436$	−512.230	−0.0562646
$437$	−2992.36	−0.327561
$438$	5359.12	0.584631
$439$	4521.53	0.491574	0.245787	−	0.969324i	$-0.420954\pi$
$439$	4521.53	0.491574	0.245787	+	0.969324i	$0.420954\pi$
$440$	9459.72	1.02494
$441$	6702.96	0.723783
$442$	18142.0	1.95232
$443$	−8805.39	−0.944372	−0.472186	−	0.881499i	$-0.656535\pi$
$443$	−8805.39	−0.944372	−0.472186	+	0.881499i	$0.656535\pi$
$444$	154.847	0.0165512
$445$	73.0108	0.00777763
$446$	5855.43	0.621665
$447$	−3259.94	−0.344943
$448$	−3494.59	−0.368536
$449$	−10437.9	−1.09709	−0.548545	−	0.836121i	$-0.684818\pi$
$449$	−10437.9	−1.09709	−0.548545	+	0.836121i	$0.684818\pi$
$450$	392.094	0.0410744
$451$	−9096.20	−0.949719
$452$	−449.181	−0.0467427
$453$	−4215.40	−0.437211
$454$	1670.91	0.172731
$455$	7406.28	0.763103
$456$	−3149.64	−0.323454
$457$	3984.75	0.407875	0.203938	−	0.978984i	$-0.434626\pi$
$457$	3984.75	0.407875	0.203938	+	0.978984i	$0.434626\pi$
$458$	6968.96	0.711000
$459$	−5638.40	−0.573373
$460$	391.892	0.0397219
$461$	−5737.15	−0.579622	−0.289811	−	0.957084i	$-0.593592\pi$
$461$	−5737.15	−0.579622	−0.289811	+	0.957084i	$0.593592\pi$
$462$	−1587.93	−0.159907
$463$	−1479.27	−0.148483	−0.0742415	−	0.997240i	$-0.523654\pi$
$463$	−1479.27	−0.148483	−0.0742415	+	0.997240i	$0.523654\pi$
$464$	−917.986	−0.0918457
$465$	2955.73	0.294771
$466$	−15217.4	−1.51273
$467$	−7229.61	−0.716373	−0.358187	−	0.933650i	$-0.616605\pi$
$467$	−7229.61	−0.716373	−0.358187	+	0.933650i	$0.616605\pi$
$468$	−2521.49	−0.249051
$469$	6190.79	0.609518
$470$	19958.4	1.95875
$471$	−2155.01	−0.210823
$472$	1274.04	0.124242
$473$	0	0
$474$	−4943.31	−0.479016
$475$	−555.150	−0.0536254
$476$	−843.353	−0.0812080
$477$	−9195.20	−0.882640
$478$	−11600.3	−1.11002
$479$	11043.4	1.05342	0.526708	−	0.850046i	$-0.323426\pi$
$479$	11043.4	1.05342	0.526708	+	0.850046i	$0.323426\pi$
$480$	904.151	0.0859764
$481$	6593.27	0.625004
$482$	19105.6	1.80547
$483$	342.737	0.0322879
$484$	584.295	0.0548737
$485$	11214.0	1.04990
$486$	8586.53	0.801426
$487$	4969.09	0.462364	0.231182	−	0.972911i	$-0.425741\pi$
$487$	4969.09	0.462364	0.231182	+	0.972911i	$0.425741\pi$
$488$	−3815.73	−0.353955
$489$	4118.50	0.380869
$490$	8961.44	0.826197
$491$	−7549.09	−0.693861	−0.346931	−	0.937891i	$-0.612776\pi$
$491$	−7549.09	−0.693861	−0.346931	+	0.937891i	$0.612776\pi$
$492$	−396.638	−0.0363452
$493$	959.053	0.0876138
$494$	25740.4	2.34437
$495$	11540.9	1.04793
$496$	13717.1	1.24177
$497$	4096.29	0.369706
$498$	−2757.55	−0.248130
$499$	−2644.30	−0.237225	−0.118612	−	0.992941i	$-0.537845\pi$
$499$	−2644.30	−0.237225	−0.118612	+	0.992941i	$0.537845\pi$
$500$	1835.55	0.164177
$501$	3264.22	0.291087
$502$	2860.21	0.254298
$503$	−18851.7	−1.67109	−0.835544	−	0.549424i	$-0.814847\pi$
$503$	−18851.7	−1.67109	−0.835544	+	0.549424i	$0.814847\pi$
$504$	−4403.13	−0.389149
$505$	−14191.6	−1.25053
$506$	−3577.62	−0.314318
$507$	5654.81	0.495343
$508$	381.891	0.0333537
$509$	−7646.38	−0.665855	−0.332927	−	0.942952i	$-0.608036\pi$
$509$	−7646.38	−0.665855	−0.332927	+	0.942952i	$0.608036\pi$
$510$	−3620.77	−0.314374
$511$	−10607.6	−0.918298
$512$	−7691.90	−0.663940
$513$	−7999.96	−0.688512
$514$	22013.9	1.88909
$515$	−329.809	−0.0282197
$516$	0	0
$517$	−25270.6	−2.14971
$518$	−2209.85	−0.187443
$519$	−2701.20	−0.228458
$520$	17563.5	1.48117
$521$	15427.5	1.29729	0.648646	−	0.761090i	$-0.275336\pi$
$521$	15427.5	1.29729	0.648646	+	0.761090i	$0.275336\pi$
$522$	−961.066	−0.0805838
$523$	14469.9	1.20980	0.604899	−	0.796302i	$-0.293214\pi$
$523$	14469.9	1.20980	0.604899	+	0.796302i	$0.293214\pi$
$524$	−1967.23	−0.164006
$525$	63.5854	0.00528589
$526$	−20846.6	−1.72805
$527$	−14330.8	−1.18455
$528$	−4388.18	−0.361688
$529$	−11394.8	−0.936534
$530$	−12293.4	−1.00753
$531$	1554.33	0.127028
$532$	−1196.58	−0.0975154
$533$	−16888.5	−1.37246
$534$	−29.0636	−0.00235525
$535$	14917.0	1.20545
$536$	14681.0	1.18306
$537$	1521.92	0.122301
$538$	−12098.6	−0.969534
$539$	−11346.7	−0.906744
$540$	1047.71	0.0834929
$541$	−2852.57	−0.226694	−0.113347	−	0.993555i	$-0.536157\pi$
$541$	−2852.57	−0.226694	−0.113347	+	0.993555i	$0.536157\pi$
$542$	−22673.7	−1.79690
$543$	1592.75	0.125877
$544$	−4383.76	−0.345501
$545$	4352.90	0.342125
$546$	−2948.24	−0.231086
$547$	1910.22	0.149315	0.0746574	−	0.997209i	$-0.476214\pi$
$547$	1910.22	0.149315	0.0746574	+	0.997209i	$0.476214\pi$
$548$	−2384.77	−0.185899
$549$	−4655.21	−0.361893
$550$	−663.730	−0.0514573
$551$	1360.74	0.105208
$552$	812.775	0.0626703
$553$	9784.53	0.752406
$554$	1912.09	0.146637
$555$	−1315.88	−0.100642
$556$	−803.888	−0.0613173
$557$	−1503.15	−0.114345	−0.0571726	−	0.998364i	$-0.518209\pi$
$557$	−1503.15	−0.114345	−0.0571726	+	0.998364i	$0.518209\pi$
$558$	14360.9	1.08951
$559$	0	0
$560$	−6859.88	−0.517648
$561$	4584.49	0.345022
$562$	26383.0	1.98025
$563$	−7608.15	−0.569530	−0.284765	−	0.958597i	$-0.591916\pi$
$563$	−7608.15	−0.569530	−0.284765	+	0.958597i	$0.591916\pi$
$564$	−1101.92	−0.0822680
$565$	3817.12	0.284226
$566$	−17479.4	−1.29808
$567$	−4895.66	−0.362607
$568$	9714.06	0.717593
$569$	5914.01	0.435726	0.217863	−	0.975979i	$-0.430091\pi$
$569$	5914.01	0.435726	0.217863	+	0.975979i	$0.430091\pi$
$570$	−5137.28	−0.377503
$571$	7673.35	0.562381	0.281191	−	0.959652i	$-0.409271\pi$
$571$	7673.35	0.562381	0.281191	+	0.959652i	$0.409271\pi$
$572$	4268.34	0.312007
$573$	858.545	0.0625938
$574$	5660.49	0.411611
$575$	143.259	0.0103901
$576$	−10110.4	−0.731364
$577$	14776.8	1.06615	0.533074	−	0.846069i	$-0.321037\pi$
$577$	14776.8	1.06615	0.533074	+	0.846069i	$0.321037\pi$
$578$	2582.11	0.185816
$579$	−6318.42	−0.453514
$580$	−178.208	−0.0127581
$581$	5458.16	0.389746
$582$	−4463.99	−0.317935
$583$	15565.5	1.10576
$584$	−25155.0	−1.78240
$585$	21427.5	1.51439
$586$	−6499.41	−0.458171
$587$	−7695.08	−0.541073	−0.270537	−	0.962710i	$-0.587201\pi$
$587$	−7695.08	−0.541073	−0.270537	+	0.962710i	$0.587201\pi$
$588$	−494.769	−0.0347006
$589$	−20333.0	−1.42242
$590$	2078.04	0.145003
$591$	3148.87	0.219166
$592$	−6106.85	−0.423969
$593$	−20083.7	−1.39079	−0.695395	−	0.718628i	$-0.744771\pi$
$593$	−20083.7	−1.39079	−0.695395	+	0.718628i	$0.744771\pi$
$594$	−9564.63	−0.660676
$595$	7166.77	0.493796
$596$	−2936.97	−0.201851
$597$	4235.48	0.290363
$598$	−6642.41	−0.454228
$599$	−15219.6	−1.03815	−0.519077	−	0.854727i	$-0.673724\pi$
$599$	−15219.6	−1.03815	−0.519077	+	0.854727i	$0.673724\pi$
$600$	150.788	0.0102598
$601$	2102.90	0.142727	0.0713636	−	0.997450i	$-0.477265\pi$
$601$	2102.90	0.142727	0.0713636	+	0.997450i	$0.477265\pi$
$602$	0	0
$603$	17910.9	1.20960
$604$	−3797.77	−0.255843
$605$	−4965.31	−0.333667
$606$	5649.28	0.378691
$607$	11150.6	0.745617	0.372808	−	0.927908i	$-0.378395\pi$
$607$	11150.6	0.745617	0.372808	+	0.927908i	$0.378395\pi$
$608$	−6219.83	−0.414881
$609$	−155.855	−0.0103704
$610$	−6223.73	−0.413101
$611$	−46918.8	−3.10660
$612$	−2439.95	−0.161158
$613$	6496.14	0.428021	0.214010	−	0.976831i	$-0.431347\pi$
$613$	6496.14	0.428021	0.214010	+	0.976831i	$0.431347\pi$
$614$	−9065.98	−0.595885
$615$	3370.61	0.221002
$616$	7453.54	0.487519
$617$	−5614.43	−0.366335	−0.183167	−	0.983082i	$-0.558635\pi$
$617$	−5614.43	−0.366335	−0.183167	+	0.983082i	$0.558635\pi$
$618$	131.288	0.00854559
$619$	4482.99	0.291093	0.145546	−	0.989351i	$-0.453506\pi$
$619$	4482.99	0.291093	0.145546	+	0.989351i	$0.453506\pi$
$620$	2662.90	0.172491
$621$	2064.42	0.133401
$622$	−25207.6	−1.62497
$623$	57.5270	0.00369947
$624$	−8147.35	−0.522684
$625$	−14954.0	−0.957056
$626$	−12972.4	−0.828243
$627$	6504.63	0.414306
$628$	−1941.51	−0.123367
$629$	6380.04	0.404434
$630$	−7181.81	−0.454175
$631$	−22320.4	−1.40818	−0.704088	−	0.710112i	$-0.748644\pi$
$631$	−22320.4	−1.40818	−0.704088	+	0.710112i	$0.748644\pi$
$632$	23203.3	1.46041
$633$	−4463.59	−0.280272
$634$	−16250.0	−1.01793
$635$	−3245.29	−0.202812
$636$	678.730	0.0423167
$637$	−21066.8	−1.31036
$638$	1626.88	0.100954
$639$	11851.2	0.733686
$640$	−18575.5	−1.14728
$641$	6797.76	0.418869	0.209435	−	0.977823i	$-0.432838\pi$
$641$	6797.76	0.418869	0.209435	+	0.977823i	$0.432838\pi$
$642$	−5938.04	−0.365040
$643$	−6933.22	−0.425225	−0.212612	−	0.977137i	$-0.568197\pi$
$643$	−6933.22	−0.425225	−0.212612	+	0.977137i	$0.568197\pi$
$644$	308.781	0.0188939
$645$	0	0
$646$	24908.0	1.51702
$647$	−14748.6	−0.896180	−0.448090	−	0.893989i	$-0.647896\pi$
$647$	−14748.6	−0.896180	−0.448090	+	0.893989i	$0.647896\pi$
$648$	−11609.7	−0.703814
$649$	−2631.14	−0.159139
$650$	−1232.32	−0.0743623
$651$	2328.89	0.140209
$652$	3710.47	0.222873
$653$	−10205.7	−0.611605	−0.305803	−	0.952095i	$-0.598925\pi$
$653$	−10205.7	−0.611605	−0.305803	+	0.952095i	$0.598925\pi$
$654$	−1732.77	−0.103604
$655$	16717.4	0.997259
$656$	15642.6	0.931005
$657$	−30689.2	−1.82238
$658$	15725.7	0.931689
$659$	25166.3	1.48762	0.743809	−	0.668392i	$-0.233017\pi$
$659$	25166.3	1.48762	0.743809	+	0.668392i	$0.233017\pi$
$660$	−851.874	−0.0502412
$661$	18594.5	1.09416	0.547080	−	0.837080i	$-0.315739\pi$
$661$	18594.5	1.09416	0.547080	+	0.837080i	$0.315739\pi$
$662$	−14290.6	−0.839004
$663$	8511.83	0.498600
$664$	12943.6	0.756491
$665$	10168.5	0.592956
$666$	−6393.43	−0.371983
$667$	−351.143	−0.0203843
$668$	2940.82	0.170335
$669$	2747.24	0.158766
$670$	23945.7	1.38075
$671$	7880.26	0.453374
$672$	712.402	0.0408951
$673$	−25367.1	−1.45294	−0.726471	−	0.687197i	$-0.758841\pi$
$673$	−25367.1	−1.45294	−0.726471	+	0.687197i	$0.758841\pi$
$674$	34048.6	1.94585
$675$	382.996	0.0218393
$676$	5094.58	0.289860
$677$	8839.77	0.501831	0.250916	−	0.968009i	$-0.419268\pi$
$677$	8839.77	0.501831	0.250916	+	0.968009i	$0.419268\pi$
$678$	−1519.49	−0.0860704
$679$	8835.78	0.499391
$680$	16995.5	0.958450
$681$	783.957	0.0441135
$682$	−24309.8	−1.36492
$683$	11252.9	0.630426	0.315213	−	0.949021i	$-0.397924\pi$
$683$	11252.9	0.630426	0.315213	+	0.949021i	$0.397924\pi$
$684$	−3461.88	−0.193521
$685$	20265.7	1.13038
$686$	16077.8	0.894828
$687$	3269.69	0.181581
$688$	0	0
$689$	28899.7	1.59796
$690$	1325.69	0.0731424
$691$	19933.8	1.09742	0.548711	−	0.836012i	$-0.315119\pi$
$691$	19933.8	1.09742	0.548711	+	0.836012i	$0.315119\pi$
$692$	−2433.59	−0.133687
$693$	9093.35	0.498453
$694$	−21870.8	−1.19626
$695$	6831.40	0.372848
$696$	−369.599	−0.0201287
$697$	−16342.4	−0.888107
$698$	25311.9	1.37259
$699$	−7139.70	−0.386335
$700$	57.2859	0.00309315
$701$	13753.9	0.741052	0.370526	−	0.928822i	$-0.379177\pi$
$701$	13753.9	0.741052	0.370526	+	0.928822i	$0.379177\pi$
$702$	−17758.2	−0.954760
$703$	9052.22	0.485649
$704$	17114.7	0.916241
$705$	9364.05	0.500242
$706$	17513.7	0.933621
$707$	−11181.9	−0.594821
$708$	−114.730	−0.00609016
$709$	−22572.7	−1.19568	−0.597840	−	0.801616i	$-0.703974\pi$
$709$	−22572.7	−1.19568	−0.597840	+	0.801616i	$0.703974\pi$
$710$	15844.3	0.837502
$711$	28308.1	1.49316
$712$	136.421	0.00718061
$713$	5247.01	0.275599
$714$	−2852.89	−0.149533
$715$	−36272.1	−1.89720
$716$	1371.14	0.0715667
$717$	−5442.63	−0.283485
$718$	3892.72	0.202333
$719$	−12405.4	−0.643456	−0.321728	−	0.946832i	$-0.604264\pi$
$719$	−12405.4	−0.643456	−0.321728	+	0.946832i	$0.604264\pi$
$720$	−19846.7	−1.02728
$721$	−259.865	−0.0134228
$722$	14436.4	0.744138
$723$	8963.95	0.461097
$724$	1434.95	0.0736595
$725$	−65.1450	−0.00333714
$726$	1976.55	0.101042
$727$	20179.9	1.02948	0.514740	−	0.857346i	$-0.327888\pi$
$727$	20179.9	1.02948	0.514740	+	0.857346i	$0.327888\pi$
$728$	13838.7	0.704526
$729$	−11295.7	−0.573881
$730$	−41029.6	−2.08024
$731$	0	0
$732$	343.617	0.0173504
$733$	−36311.8	−1.82975	−0.914875	−	0.403736i	$-0.867711\pi$
$733$	−36311.8	−1.82975	−0.914875	+	0.403736i	$0.867711\pi$
$734$	−9711.74	−0.488374
$735$	4204.52	0.211001
$736$	1605.05	0.0803844
$737$	−30319.2	−1.51536
$738$	16376.7	0.816847
$739$	−6848.62	−0.340907	−0.170454	−	0.985366i	$-0.554523\pi$
$739$	−6848.62	−0.340907	−0.170454	+	0.985366i	$0.554523\pi$
$740$	−1185.52	−0.0588925
$741$	12076.9	0.598724
$742$	−9686.28	−0.479238
$743$	−10685.7	−0.527616	−0.263808	−	0.964575i	$-0.584978\pi$
$743$	−10685.7	−0.527616	−0.263808	+	0.964575i	$0.584978\pi$
$744$	5522.78	0.272144
$745$	24958.2	1.22738
$746$	−32664.1	−1.60311
$747$	15791.3	0.773457
$748$	4130.30	0.201897
$749$	11753.4	0.573380
$750$	6209.31	0.302309
$751$	−17077.6	−0.829786	−0.414893	−	0.909870i	$-0.636181\pi$
$751$	−17077.6	−0.829786	−0.414893	+	0.909870i	$0.636181\pi$
$752$	43457.3	2.10735
$753$	1341.95	0.0649447
$754$	3020.55	0.145891
$755$	32273.3	1.55569
$756$	825.514	0.0397138
$757$	13129.5	0.630381	0.315190	−	0.949028i	$-0.397932\pi$
$757$	13129.5	0.630381	0.315190	+	0.949028i	$0.397932\pi$
$758$	3051.64	0.146228
$759$	−1678.54	−0.0802731
$760$	24113.7	1.15092
$761$	−3098.58	−0.147600	−0.0737999	−	0.997273i	$-0.523513\pi$
$761$	−3098.58	−0.147600	−0.0737999	+	0.997273i	$0.523513\pi$
$762$	1291.86	0.0614163
$763$	3429.76	0.162733
$764$	773.487	0.0366280
$765$	20734.5	0.979946
$766$	6480.20	0.305665
$767$	−4885.13	−0.229976
$768$	2759.95	0.129676
$769$	38020.8	1.78292	0.891460	−	0.453099i	$-0.149682\pi$
$769$	38020.8	1.78292	0.891460	+	0.453099i	$0.149682\pi$
$770$	12157.3	0.568983
$771$	10328.5	0.482451
$772$	−5692.44	−0.265383
$773$	−703.368	−0.0327275	−0.0163638	−	0.999866i	$-0.505209\pi$
$773$	−703.368	−0.0327275	−0.0163638	+	0.999866i	$0.505209\pi$
$774$	0	0
$775$	973.438	0.0451186
$776$	20953.4	0.969309
$777$	−1036.82	−0.0478708
$778$	36056.5	1.66155
$779$	−23187.1	−1.06645
$780$	−1581.64	−0.0726048
$781$	−20061.5	−0.919151
$782$	−6427.60	−0.293927
$783$	−938.767	−0.0428465
$784$	19512.6	0.888877
$785$	16498.8	0.750151
$786$	−6654.76	−0.301994
$787$	24681.7	1.11792	0.558962	−	0.829193i	$-0.311200\pi$
$787$	24681.7	1.11792	0.558962	+	0.829193i	$0.311200\pi$
$788$	2836.90	0.128249
$789$	−9780.77	−0.441324
$790$	37846.2	1.70444
$791$	3007.60	0.135193
$792$	21564.2	0.967488
$793$	14630.9	0.655183
$794$	−14126.8	−0.631413
$795$	−5767.81	−0.257312
$796$	3815.86	0.169912
$797$	−23603.5	−1.04903	−0.524516	−	0.851401i	$-0.675754\pi$
$797$	−23603.5	−1.04903	−0.524516	+	0.851401i	$0.675754\pi$
$798$	−4047.78	−0.179561
$799$	−45401.5	−2.01025
$800$	297.773	0.0131598
$801$	166.434	0.00734165
$802$	−39421.0	−1.73567
$803$	51950.2	2.28304
$804$	−1322.06	−0.0579921
$805$	−2624.01	−0.114887
$806$	−45135.0	−1.97247
$807$	−5676.42	−0.247608
$808$	−26517.0	−1.15454
$809$	22689.9	0.986075	0.493038	−	0.870008i	$-0.335887\pi$
$809$	22689.9	0.986075	0.493038	+	0.870008i	$0.335887\pi$
$810$	−18936.2	−0.821421
$811$	−22849.7	−0.989347	−0.494674	−	0.869079i	$-0.664712\pi$
$811$	−22849.7	−0.989347	−0.494674	+	0.869079i	$0.664712\pi$
$812$	−140.414	−0.00606844
$813$	−10638.0	−0.458908
$814$	10822.7	0.466014
$815$	−31531.4	−1.35521
$816$	−7883.86	−0.338224
$817$	0	0
$818$	−4168.10	−0.178159
$819$	16883.2	0.720327
$820$	3036.68	0.129324
$821$	−12956.1	−0.550758	−0.275379	−	0.961336i	$-0.588803\pi$
$821$	−12956.1	−0.550758	−0.275379	+	0.961336i	$0.588803\pi$
$822$	−8067.22	−0.342307
$823$	41910.8	1.77511	0.887557	−	0.460699i	$-0.152401\pi$
$823$	41910.8	1.77511	0.887557	+	0.460699i	$0.152401\pi$
$824$	−616.250	−0.0260535
$825$	−311.408	−0.0131416
$826$	1637.34	0.0689713
$827$	11697.3	0.491846	0.245923	−	0.969289i	$-0.420909\pi$
$827$	11697.3	0.491846	0.245923	+	0.969289i	$0.420909\pi$
$828$	893.350	0.0374952
$829$	−8944.81	−0.374748	−0.187374	−	0.982289i	$-0.559998\pi$
$829$	−8944.81	−0.374748	−0.187374	+	0.982289i	$0.559998\pi$
$830$	21112.0	0.882899
$831$	897.110	0.0374493
$832$	31776.1	1.32408
$833$	−20385.5	−0.847920
$834$	−2719.39	−0.112907
$835$	−24991.0	−1.03575
$836$	5860.21	0.242440
$837$	14027.7	0.579292
$838$	34544.7	1.42402
$839$	−8980.83	−0.369550	−0.184775	−	0.982781i	$-0.559156\pi$
$839$	−8980.83	−0.369550	−0.184775	+	0.982781i	$0.559156\pi$
$840$	−2761.92	−0.113447
$841$	−24229.3	−0.993453
$842$	−50190.1	−2.05423
$843$	12378.4	0.505733
$844$	−4021.38	−0.164007
$845$	−43293.5	−1.76253
$846$	45496.7	1.84895
$847$	−3912.29	−0.158710
$848$	−26767.7	−1.08397
$849$	−8200.96	−0.331515
$850$	−1192.47	−0.0481191
$851$	−2335.96	−0.0940959
$852$	−874.778	−0.0351753
$853$	28833.8	1.15739	0.578694	−	0.815545i	$-0.303563\pi$
$853$	28833.8	1.15739	0.578694	+	0.815545i	$0.303563\pi$
$854$	−4903.83	−0.196493
$855$	29418.8	1.17673
$856$	27872.4	1.11292
$857$	−42317.7	−1.68675	−0.843375	−	0.537325i	$-0.819435\pi$
$857$	−42317.7	−1.68675	−0.843375	+	0.537325i	$0.819435\pi$
$858$	14438.9	0.574518
$859$	46572.9	1.84988	0.924939	−	0.380115i	$-0.124116\pi$
$859$	46572.9	1.84988	0.924939	+	0.380115i	$0.124116\pi$
$860$	0	0
$861$	2655.78	0.105121
$862$	33199.7	1.31182
$863$	10911.3	0.430388	0.215194	−	0.976571i	$-0.430962\pi$
$863$	10911.3	0.430388	0.215194	+	0.976571i	$0.430962\pi$
$864$	4291.04	0.168963
$865$	20680.5	0.812901
$866$	22834.4	0.896012
$867$	1211.47	0.0474552
$868$	2098.16	0.0820463
$869$	−47919.5	−1.87061
$870$	−602.842	−0.0234922
$871$	−56292.4	−2.18989
$872$	8133.42	0.315863
$873$	25563.2	0.991047
$874$	−9119.70	−0.352950
$875$	−12290.4	−0.474846
$876$	2265.28	0.0873707
$877$	−12978.3	−0.499710	−0.249855	−	0.968283i	$-0.580383\pi$
$877$	−12978.3	−0.499710	−0.249855	+	0.968283i	$0.580383\pi$
$878$	13780.1	0.529676
$879$	−3049.39	−0.117012
$880$	33596.1	1.28696
$881$	16494.3	0.630768	0.315384	−	0.948964i	$-0.397867\pi$
$881$	16494.3	0.630768	0.315384	+	0.948964i	$0.397867\pi$
$882$	20428.3	0.779884
$883$	−27803.5	−1.05964	−0.529821	−	0.848110i	$-0.677741\pi$
$883$	−27803.5	−1.05964	−0.529821	+	0.848110i	$0.677741\pi$
$884$	7668.55	0.291766
$885$	974.973	0.0370321
$886$	−26835.9	−1.01757
$887$	−26424.1	−1.00026	−0.500132	−	0.865949i	$-0.666715\pi$
$887$	−26424.1	−1.00026	−0.500132	+	0.865949i	$0.666715\pi$
$888$	−2458.73	−0.0929164
$889$	−2557.04	−0.0964684
$890$	222.512	0.00838048
$891$	23976.4	0.901502
$892$	2475.07	0.0929053
$893$	−64417.1	−2.41393
$894$	−9935.18	−0.371680
$895$	−11651.8	−0.435171
$896$	−14636.1	−0.545711
$897$	−3116.48	−0.116005
$898$	−31811.1	−1.18213
$899$	−2386.01	−0.0885182
$900$	165.737	0.00613839
$901$	27965.1	1.03402
$902$	−27722.1	−1.02333
$903$	0	0
$904$	7132.30	0.262408
$905$	−12194.1	−0.447897
$906$	−12847.1	−0.471100
$907$	12059.4	0.441484	0.220742	−	0.975332i	$-0.429152\pi$
$907$	12059.4	0.441484	0.220742	+	0.975332i	$0.429152\pi$
$908$	706.289	0.0258139
$909$	−32350.9	−1.18043
$910$	22571.8	0.822252
$911$	11271.8	0.409937	0.204969	−	0.978769i	$-0.434291\pi$
$911$	11271.8	0.409937	0.204969	+	0.978769i	$0.434291\pi$
$912$	−11185.9	−0.406142
$913$	−26731.2	−0.968974
$914$	12144.2	0.439490
$915$	−2920.04	−0.105501
$916$	2945.75	0.106256
$917$	13172.1	0.474351
$918$	−17183.9	−0.617815
$919$	48925.3	1.75614	0.878072	−	0.478529i	$-0.158830\pi$
$919$	48925.3	1.75614	0.878072	+	0.478529i	$0.158830\pi$
$920$	−6222.64	−0.222994
$921$	−4253.57	−0.152182
$922$	−17484.9	−0.624549
$923$	−37247.3	−1.32829
$924$	−671.212	−0.0238975
$925$	−433.373	−0.0154046
$926$	−4508.32	−0.159992
$927$	−751.827	−0.0266378
$928$	−729.876	−0.0258183
$929$	13417.4	0.473854	0.236927	−	0.971527i	$-0.423860\pi$
$929$	13417.4	0.473854	0.236927	+	0.971527i	$0.423860\pi$
$930$	9008.05	0.317619
$931$	−28923.7	−1.01819
$932$	−6432.36	−0.226072
$933$	−11826.9	−0.415000
$934$	−22033.4	−0.771900
$935$	−35099.1	−1.22766
$936$	40037.3	1.39814
$937$	16627.3	0.579713	0.289856	−	0.957070i	$-0.406392\pi$
$937$	16627.3	0.579713	0.289856	+	0.957070i	$0.406392\pi$
$938$	18867.4	0.656763
$939$	−6086.36	−0.211524
$940$	8436.34	0.292727
$941$	2488.17	0.0861976	0.0430988	−	0.999071i	$-0.486277\pi$
$941$	2488.17	0.0861976	0.0430988	+	0.999071i	$0.486277\pi$
$942$	−6567.73	−0.227164
$943$	5983.51	0.206628
$944$	4524.72	0.156003
$945$	−7015.18	−0.241485
$946$	0	0
$947$	20531.0	0.704507	0.352254	−	0.935905i	$-0.385415\pi$
$947$	20531.0	0.704507	0.352254	+	0.935905i	$0.385415\pi$
$948$	−2089.52	−0.0715870
$949$	96453.7	3.29928
$950$	−1691.91	−0.0577819
$951$	−7624.15	−0.259969
$952$	13391.1	0.455892
$953$	34038.9	1.15701	0.578504	−	0.815680i	$-0.303637\pi$
$953$	34038.9	1.15701	0.578504	+	0.815680i	$0.303637\pi$
$954$	−28023.8	−0.951054
$955$	−6573.05	−0.222722
$956$	−4903.42	−0.165887
$957$	763.296	0.0257825
$958$	33656.6	1.13507
$959$	15967.8	0.537672
$960$	−6341.87	−0.213211
$961$	5862.28	0.196780
$962$	20094.0	0.673449
$963$	34004.5	1.13788
$964$	8075.88	0.269820
$965$	48374.1	1.61370
$966$	1044.55	0.0347906
$967$	−28484.3	−0.947254	−0.473627	−	0.880726i	$-0.657055\pi$
$967$	−28484.3	−0.947254	−0.473627	+	0.880726i	$0.657055\pi$
$968$	−9277.70	−0.308054
$969$	11686.3	0.387429
$970$	34176.5	1.13128
$971$	15621.7	0.516295	0.258148	−	0.966105i	$-0.416888\pi$
$971$	15621.7	0.516295	0.258148	+	0.966105i	$0.416888\pi$
$972$	3629.50	0.119770
$973$	5382.62	0.177347
$974$	15144.1	0.498202
$975$	−578.177	−0.0189913
$976$	−13551.5	−0.444441
$977$	−10336.9	−0.338491	−0.169245	−	0.985574i	$-0.554133\pi$
$977$	−10336.9	−0.338491	−0.169245	+	0.985574i	$0.554133\pi$
$978$	12551.8	0.410390
$979$	−281.737	−0.00919750
$980$	3787.97	0.123472
$981$	9922.80	0.322947
$982$	−23007.1	−0.747643
$983$	19360.5	0.628182	0.314091	−	0.949393i	$-0.398300\pi$
$983$	19360.5	0.628182	0.314091	+	0.949393i	$0.398300\pi$
$984$	6298.00	0.204037
$985$	−24107.8	−0.779838
$986$	2922.87	0.0944048
$987$	7378.16	0.237943
$988$	10880.4	0.350356
$989$	0	0
$990$	35172.7	1.12915
$991$	−32122.8	−1.02968	−0.514840	−	0.857286i	$-0.672149\pi$
$991$	−32122.8	−1.02968	−0.514840	+	0.857286i	$0.672149\pi$
$992$	10906.3	0.349067
$993$	−6704.86	−0.214272
$994$	12484.1	0.398362
$995$	−32427.0	−1.03317
$996$	−1165.61	−0.0370821
$997$	2315.90	0.0735661	0.0367831	−	0.999323i	$-0.488289\pi$
$997$	2315.90	0.0735661	0.0367831	+	0.999323i	$0.488289\pi$
$998$	−8058.93	−0.255612
$999$	−6245.09	−0.197784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.35	yes	50
43.42	odd	2		1849.4.a.i.1.16	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.16	✓	50	43.42	odd	2
1849.4.a.j.1.35	yes	50	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+3.04766 q^{2} +1.42990 q^{3} +1.28824 q^{4} -10.9474 q^{5} +4.35784 q^{6} -8.62569 q^{7} -20.4552 q^{8} -24.9554 q^{9} +O(q^{10})\)	\(q+3.04766 q^{2} +1.42990 q^{3} +1.28824 q^{4} -10.9474 q^{5} +4.35784 q^{6} -8.62569 q^{7} -20.4552 q^{8} -24.9554 q^{9} -33.3638 q^{10} +42.2441 q^{11} +1.84205 q^{12} +78.4327 q^{13} -26.2882 q^{14} -15.6536 q^{15} -72.6463 q^{16} +75.8963 q^{17} -76.0556 q^{18} +107.684 q^{19} -14.1028 q^{20} -12.3339 q^{21} +128.746 q^{22} -27.7883 q^{23} -29.2488 q^{24} -5.15536 q^{25} +239.036 q^{26} -74.2909 q^{27} -11.1119 q^{28} +12.6364 q^{29} -47.7069 q^{30} -188.821 q^{31} -57.7599 q^{32} +60.4047 q^{33} +231.306 q^{34} +94.4285 q^{35} -32.1484 q^{36} +84.0627 q^{37} +328.185 q^{38} +112.151 q^{39} +223.930 q^{40} -215.325 q^{41} -37.5894 q^{42} +54.4203 q^{44} +273.196 q^{45} -84.6893 q^{46} -598.204 q^{47} -103.877 q^{48} -268.598 q^{49} -15.7118 q^{50} +108.524 q^{51} +101.040 q^{52} +368.465 q^{53} -226.413 q^{54} -462.461 q^{55} +176.440 q^{56} +153.977 q^{57} +38.5114 q^{58} -62.2843 q^{59} -20.1655 q^{60} +186.541 q^{61} -575.462 q^{62} +215.257 q^{63} +405.138 q^{64} -858.631 q^{65} +184.093 q^{66} -717.716 q^{67} +97.7723 q^{68} -39.7344 q^{69} +287.786 q^{70} -474.895 q^{71} +510.467 q^{72} +1229.76 q^{73} +256.195 q^{74} -7.37163 q^{75} +138.723 q^{76} -364.384 q^{77} +341.798 q^{78} -1134.35 q^{79} +795.285 q^{80} +567.567 q^{81} -656.237 q^{82} -632.780 q^{83} -15.8889 q^{84} -830.864 q^{85} +18.0687 q^{87} -864.110 q^{88} -6.66926 q^{89} +832.607 q^{90} -676.536 q^{91} -35.7979 q^{92} -269.994 q^{93} -1823.12 q^{94} -1178.86 q^{95} -82.5908 q^{96} -1024.36 q^{97} -818.594 q^{98} -1054.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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