LMFDB - Embedded newform 1849.4.a.g.1.1

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:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} +O(q^{10})$	\(q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} -46.2944 q^{10} -9.89891 q^{11} +153.883 q^{12} +35.8596 q^{13} +151.373 q^{14} +56.1761 q^{15} +274.822 q^{16} -29.5381 q^{17} -102.211 q^{18} -35.3382 q^{19} +190.383 q^{20} -183.684 q^{21} +54.9695 q^{22} +19.2208 q^{23} -555.174 q^{24} -55.4995 q^{25} -199.131 q^{26} -57.9088 q^{27} -622.513 q^{28} -23.7734 q^{29} -311.950 q^{30} +189.450 q^{31} -866.992 q^{32} -66.7029 q^{33} +164.028 q^{34} -227.253 q^{35} +420.336 q^{36} +353.505 q^{37} +196.236 q^{38} +241.637 q^{39} -686.856 q^{40} +88.4989 q^{41} +1020.01 q^{42} -226.059 q^{44} +153.447 q^{45} -106.735 q^{46} +127.587 q^{47} +1851.86 q^{48} +400.070 q^{49} +308.193 q^{50} -199.040 q^{51} +818.916 q^{52} +556.861 q^{53} +321.572 q^{54} -82.5242 q^{55} +2245.88 q^{56} -238.124 q^{57} +132.015 q^{58} -342.074 q^{59} +1282.88 q^{60} -98.4467 q^{61} -1052.03 q^{62} -501.739 q^{63} +2615.90 q^{64} +298.951 q^{65} +370.407 q^{66} -603.957 q^{67} -674.554 q^{68} +129.518 q^{69} +1261.95 q^{70} +24.3032 q^{71} -1516.47 q^{72} -370.333 q^{73} -1963.04 q^{74} -373.978 q^{75} -807.009 q^{76} +269.837 q^{77} -1341.83 q^{78} -523.511 q^{79} +2291.11 q^{80} -887.180 q^{81} -491.442 q^{82} +628.389 q^{83} -4194.75 q^{84} -246.251 q^{85} -160.195 q^{87} +815.566 q^{88} -1134.03 q^{89} -852.102 q^{90} -977.509 q^{91} +438.940 q^{92} +1276.59 q^{93} -708.500 q^{94} -294.604 q^{95} -5842.15 q^{96} +1630.97 q^{97} -2221.62 q^{98} -182.201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * 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 $

$2$	−5.55308	−1.96331	−0.981655	−	0.190664i	$-0.938936\pi$
$2$	−5.55308	−1.96331	−0.981655	+	0.190664i	$0.938936\pi$
$3$	6.73841	1.29681	0.648404	−	0.761297i	$-0.275437\pi$
$3$	6.73841	1.29681	0.648404	+	0.761297i	$0.275437\pi$
$4$	22.8367	2.85459
$5$	8.33670	0.745657	0.372829	−	0.927900i	$-0.378388\pi$
$5$	8.33670	0.745657	0.372829	+	0.927900i	$0.378388\pi$
$6$	−37.4189	−2.54604
$7$	−27.2593	−1.47186	−0.735932	−	0.677055i	$-0.763256\pi$
$7$	−27.2593	−1.47186	−0.735932	+	0.677055i	$0.763256\pi$
$8$	−82.3895	−3.64114
$9$	18.4062	0.681710
$10$	−46.2944	−1.46396
$11$	−9.89891	−0.271330	−0.135665	−	0.990755i	$-0.543317\pi$
$11$	−9.89891	−0.271330	−0.135665	+	0.990755i	$0.543317\pi$
$12$	153.883	3.70185
$13$	35.8596	0.765052	0.382526	−	0.923945i	$-0.375054\pi$
$13$	35.8596	0.765052	0.382526	+	0.923945i	$0.375054\pi$
$14$	151.373	2.88973
$15$	56.1761	0.966974
$16$	274.822	4.29409
$17$	−29.5381	−0.421415	−0.210707	−	0.977549i	$-0.567577\pi$
$17$	−29.5381	−0.421415	−0.210707	+	0.977549i	$0.567577\pi$
$18$	−102.211	−1.33841
$19$	−35.3382	−0.426692	−0.213346	−	0.976977i	$-0.568436\pi$
$19$	−35.3382	−0.426692	−0.213346	+	0.976977i	$0.568436\pi$
$20$	190.383	2.12854
$21$	−183.684	−1.90872
$22$	54.9695	0.532706
$23$	19.2208	0.174253	0.0871265	−	0.996197i	$-0.472232\pi$
$23$	19.2208	0.174253	0.0871265	+	0.996197i	$0.472232\pi$
$24$	−555.174	−4.72185
$25$	−55.4995	−0.443996
$26$	−199.131	−1.50203
$27$	−57.9088	−0.412761
$28$	−622.513	−4.20157
$29$	−23.7734	−0.152228	−0.0761138	−	0.997099i	$-0.524251\pi$
$29$	−23.7734	−0.152228	−0.0761138	+	0.997099i	$0.524251\pi$
$30$	−311.950	−1.89847
$31$	189.450	1.09762	0.548809	−	0.835948i	$-0.315082\pi$
$31$	189.450	1.09762	0.548809	+	0.835948i	$0.315082\pi$
$32$	−866.992	−4.78950
$33$	−66.7029	−0.351863
$34$	164.028	0.827368
$35$	−227.253	−1.09751
$36$	420.336	1.94600
$37$	353.505	1.57070	0.785349	−	0.619053i	$-0.212483\pi$
$37$	353.505	1.57070	0.785349	+	0.619053i	$0.212483\pi$
$38$	196.236	0.837729
$39$	241.637	0.992125
$40$	−686.856	−2.71504
$41$	88.4989	0.337103	0.168551	−	0.985693i	$-0.446091\pi$
$41$	88.4989	0.337103	0.168551	+	0.985693i	$0.446091\pi$
$42$	1020.01	3.74742
$43$	0	0
$43$	0	0
$44$	−226.059	−0.774537
$45$	153.447	0.508322
$46$	−106.735	−0.342113
$47$	127.587	0.395967	0.197984	−	0.980205i	$-0.436561\pi$
$47$	127.587	0.395967	0.197984	+	0.980205i	$0.436561\pi$
$48$	1851.86	5.56861
$49$	400.070	1.16638
$50$	308.193	0.871701
$51$	−199.040	−0.546494
$52$	818.916	2.18391
$53$	556.861	1.44322	0.721611	−	0.692299i	$-0.243402\pi$
$53$	556.861	1.44322	0.721611	+	0.692299i	$0.243402\pi$
$54$	321.572	0.810378
$55$	−82.5242	−0.202319
$56$	2245.88	5.35926
$57$	−238.124	−0.553337
$58$	132.015	0.298870
$59$	−342.074	−0.754818	−0.377409	−	0.926047i	$-0.623185\pi$
$59$	−342.074	−0.754818	−0.377409	+	0.926047i	$0.623185\pi$
$60$	1282.88	2.76031
$61$	−98.4467	−0.206636	−0.103318	−	0.994648i	$-0.532946\pi$
$61$	−98.4467	−0.206636	−0.103318	+	0.994648i	$0.532946\pi$
$62$	−1052.03	−2.15496
$63$	−501.739	−1.00338
$64$	2615.90	5.10919
$65$	298.951	0.570466
$66$	370.407	0.690817
$67$	−603.957	−1.10127	−0.550635	−	0.834746i	$-0.685614\pi$
$67$	−603.957	−1.10127	−0.550635	+	0.834746i	$0.685614\pi$
$68$	−674.554	−1.20297
$69$	129.518	0.225973
$70$	1261.95	2.15475
$71$	24.3032	0.0406234	0.0203117	−	0.999794i	$-0.493534\pi$
$71$	24.3032	0.0406234	0.0203117	+	0.999794i	$0.493534\pi$
$72$	−1516.47	−2.48220
$73$	−370.333	−0.593755	−0.296878	−	0.954916i	$-0.595945\pi$
$73$	−370.333	−0.593755	−0.296878	+	0.954916i	$0.595945\pi$
$74$	−1963.04	−3.08377
$75$	−373.978	−0.575777
$76$	−807.009	−1.21803
$77$	269.837	0.399361
$78$	−1341.83	−1.94785
$79$	−523.511	−0.745565	−0.372782	−	0.927919i	$-0.621596\pi$
$79$	−523.511	−0.745565	−0.372782	+	0.927919i	$0.621596\pi$
$80$	2291.11	3.20192
$81$	−887.180	−1.21698
$82$	−491.442	−0.661837
$83$	628.389	0.831020	0.415510	−	0.909589i	$-0.363603\pi$
$83$	628.389	0.831020	0.415510	+	0.909589i	$0.363603\pi$
$84$	−4194.75	−5.44863
$85$	−246.251	−0.314231
$86$	0	0
$87$	−160.195	−0.197410
$88$	815.566	0.987951
$89$	−1134.03	−1.35064	−0.675320	−	0.737525i	$-0.735994\pi$
$89$	−1134.03	−1.35064	−0.675320	+	0.737525i	$0.735994\pi$
$90$	−852.102	−0.997994
$91$	−977.509	−1.12605
$92$	438.940	0.497421
$93$	1276.59	1.42340
$94$	−708.500	−0.777407
$95$	−294.604	−0.318166
$96$	−5842.15	−6.21106
$97$	1630.97	1.70721	0.853606	−	0.520919i	$-0.174411\pi$
$97$	1630.97	1.70721	0.853606	+	0.520919i	$0.174411\pi$
$98$	−2221.62	−2.28997
$99$	−182.201	−0.184969
$100$	−1267.43	−1.26743
$101$	1150.29	1.13325	0.566624	−	0.823976i	$-0.308249\pi$
$101$	1150.29	1.13325	0.566624	+	0.823976i	$0.308249\pi$
$102$	1105.29	1.07294
$103$	−353.790	−0.338446	−0.169223	−	0.985578i	$-0.554126\pi$
$103$	−353.790	−0.338446	−0.169223	+	0.985578i	$0.554126\pi$
$104$	−2954.46	−2.78566
$105$	−1531.32	−1.42325
$106$	−3092.29	−2.83349
$107$	−1944.51	−1.75685	−0.878426	−	0.477878i	$-0.841406\pi$
$107$	−1944.51	−1.75685	−0.878426	+	0.477878i	$0.841406\pi$
$108$	−1322.45	−1.17826
$109$	939.726	0.825775	0.412887	−	0.910782i	$-0.364520\pi$
$109$	939.726	0.825775	0.412887	+	0.910782i	$0.364520\pi$
$110$	458.264	0.397216
$111$	2382.06	2.03689
$112$	−7491.45	−6.32032
$113$	−743.611	−0.619053	−0.309527	−	0.950891i	$-0.600171\pi$
$113$	−743.611	−0.619053	−0.309527	+	0.950891i	$0.600171\pi$
$114$	1322.32	1.08637
$115$	160.238	0.129933
$116$	−542.905	−0.434547
$117$	660.038	0.521543
$118$	1899.56	1.48194
$119$	805.189	0.620266
$120$	−4628.32	−3.52088
$121$	−1233.01	−0.926380
$122$	546.682	0.405691
$123$	596.342	0.437157
$124$	4326.41	3.13325
$125$	−1504.77	−1.07673
$126$	2786.20	1.96996
$127$	1005.97	0.702877	0.351439	−	0.936211i	$-0.385693\pi$
$127$	1005.97	0.702877	0.351439	+	0.936211i	$0.385693\pi$
$128$	−7590.39	−5.24142
$129$	0	0
$130$	−1660.10	−1.12000
$131$	−2899.46	−1.93380	−0.966898	−	0.255163i	$-0.917871\pi$
$131$	−2899.46	−1.93380	−0.966898	+	0.255163i	$0.917871\pi$
$132$	−1523.28	−1.00443
$133$	963.296	0.628033
$134$	3353.82	2.16214
$135$	−482.768	−0.307778
$136$	2433.63	1.53443
$137$	−1446.49	−0.902058	−0.451029	−	0.892509i	$-0.648943\pi$
$137$	−1446.49	−0.902058	−0.451029	+	0.892509i	$0.648943\pi$
$138$	−719.223	−0.443654
$139$	−1641.73	−1.00180	−0.500898	−	0.865506i	$-0.666997\pi$
$139$	−1641.73	−1.00180	−0.500898	+	0.865506i	$0.666997\pi$
$140$	−5189.70	−3.13293
$141$	859.733	0.513493
$142$	−134.958	−0.0797563
$143$	−354.971	−0.207582
$144$	5058.42	2.92732
$145$	−198.191	−0.113510
$146$	2056.49	1.16573
$147$	2695.83	1.51258
$148$	8072.89	4.48370
$149$	−939.333	−0.516464	−0.258232	−	0.966083i	$-0.583140\pi$
$149$	−939.333	−0.516464	−0.258232	+	0.966083i	$0.583140\pi$
$150$	2076.73	1.13043
$151$	−2062.34	−1.11146	−0.555731	−	0.831362i	$-0.687562\pi$
$151$	−2062.34	−1.11146	−0.555731	+	0.831362i	$0.687562\pi$
$152$	2911.50	1.55364
$153$	−543.684	−0.287283
$154$	−1498.43	−0.784071
$155$	1579.38	0.818446
$156$	5518.19	2.83211
$157$	−1914.62	−0.973271	−0.486635	−	0.873605i	$-0.661776\pi$
$157$	−1914.62	−0.973271	−0.486635	+	0.873605i	$0.661776\pi$
$158$	2907.10	1.46378
$159$	3752.36	1.87158
$160$	−7227.85	−3.57133
$161$	−523.946	−0.256477
$162$	4926.58	2.38931
$163$	420.494	0.202059	0.101029	−	0.994883i	$-0.467786\pi$
$163$	420.494	0.202059	0.101029	+	0.994883i	$0.467786\pi$
$164$	2021.02	0.962290
$165$	−556.082	−0.262369
$166$	−3489.49	−1.63155
$167$	546.523	0.253241	0.126620	−	0.991951i	$-0.459587\pi$
$167$	546.523	0.253241	0.126620	+	0.991951i	$0.459587\pi$
$168$	15133.7	6.94993
$169$	−911.087	−0.414696
$170$	1367.45	0.616933
$171$	−650.441	−0.290880
$172$	0	0
$173$	−818.511	−0.359712	−0.179856	−	0.983693i	$-0.557563\pi$
$173$	−818.511	−0.359712	−0.179856	+	0.983693i	$0.557563\pi$
$174$	889.574	0.387577
$175$	1512.88	0.653501
$176$	−2720.44	−1.16512
$177$	−2305.03	−0.978853
$178$	6297.36	2.65172
$179$	−3304.21	−1.37971	−0.689856	−	0.723947i	$-0.742326\pi$
$179$	−3304.21	−1.37971	−0.689856	+	0.723947i	$0.742326\pi$
$180$	3504.22	1.45105
$181$	−2609.51	−1.07162	−0.535811	−	0.844338i	$-0.679994\pi$
$181$	−2609.51	−1.07162	−0.535811	+	0.844338i	$0.679994\pi$
$182$	5428.19	2.21079
$183$	−663.374	−0.267967
$184$	−1583.59	−0.634479
$185$	2947.06	1.17120
$186$	−7089.00	−2.79457
$187$	292.396	0.114343
$188$	2913.67	1.13032
$189$	1578.55	0.607528
$190$	1635.96	0.624658
$191$	−1972.83	−0.747377	−0.373688	−	0.927554i	$-0.621907\pi$
$191$	−1972.83	−0.747377	−0.373688	+	0.927554i	$0.621907\pi$
$192$	17627.0	6.62563
$193$	−3415.93	−1.27401	−0.637005	−	0.770860i	$-0.719827\pi$
$193$	−3415.93	−1.27401	−0.637005	+	0.770860i	$0.719827\pi$
$194$	−9056.89	−3.35179
$195$	2014.45	0.739785
$196$	9136.28	3.32955
$197$	−3185.68	−1.15213	−0.576066	−	0.817403i	$-0.695413\pi$
$197$	−3185.68	−1.15213	−0.576066	+	0.817403i	$0.695413\pi$
$198$	1011.78	0.363151
$199$	−893.918	−0.318433	−0.159216	−	0.987244i	$-0.550897\pi$
$199$	−893.918	−0.318433	−0.159216	+	0.987244i	$0.550897\pi$
$200$	4572.57	1.61665
$201$	−4069.71	−1.42814
$202$	−6387.65	−2.22492
$203$	648.045	0.224058
$204$	−4545.42	−1.56002
$205$	737.789	0.251363
$206$	1964.62	0.664475
$207$	353.782	0.118790
$208$	9855.01	3.28520
$209$	349.810	0.115774
$210$	8503.55	2.79429
$211$	−2830.29	−0.923436	−0.461718	−	0.887027i	$-0.652767\pi$
$211$	−2830.29	−0.923436	−0.461718	+	0.887027i	$0.652767\pi$
$212$	12716.9	4.11980
$213$	163.765	0.0526807
$214$	10798.0	3.44925
$215$	0	0
$216$	4771.08	1.50292
$217$	−5164.26	−1.61554
$218$	−5218.38	−1.62125
$219$	−2495.45	−0.769986
$220$	−1884.58	−0.577539
$221$	−1059.23	−0.322404
$222$	−13227.8	−3.99906
$223$	6086.98	1.82787	0.913934	−	0.405863i	$-0.133029\pi$
$223$	6086.98	1.82787	0.913934	+	0.405863i	$0.133029\pi$
$224$	23633.6	7.04950
$225$	−1021.53	−0.302676
$226$	4129.33	1.21539
$227$	3531.47	1.03256	0.516282	−	0.856418i	$-0.327316\pi$
$227$	3531.47	1.03256	0.516282	+	0.856418i	$0.327316\pi$
$228$	−5437.96	−1.57955
$229$	3675.42	1.06061	0.530303	−	0.847808i	$-0.322078\pi$
$229$	3675.42	1.06061	0.530303	+	0.847808i	$0.322078\pi$
$230$	−889.816	−0.255099
$231$	1818.28	0.517895
$232$	1958.67	0.554281
$233$	2445.98	0.687733	0.343866	−	0.939019i	$-0.388263\pi$
$233$	2445.98	0.687733	0.343866	+	0.939019i	$0.388263\pi$
$234$	−3665.25	−1.02395
$235$	1063.65	0.295256
$236$	−7811.85	−2.15469
$237$	−3527.63	−0.966854
$238$	−4471.28	−1.21777
$239$	−347.223	−0.0939750	−0.0469875	−	0.998895i	$-0.514962\pi$
$239$	−347.223	−0.0939750	−0.0469875	+	0.998895i	$0.514962\pi$
$240$	15438.4	4.15227
$241$	2750.80	0.735248	0.367624	−	0.929975i	$-0.380171\pi$
$241$	2750.80	0.735248	0.367624	+	0.929975i	$0.380171\pi$
$242$	6847.01	1.81877
$243$	−4414.64	−1.16543
$244$	−2248.20	−0.589861
$245$	3335.26	0.869723
$246$	−3311.54	−0.858275
$247$	−1267.22	−0.326441
$248$	−15608.7	−3.99657
$249$	4234.34	1.07767
$250$	8356.11	2.11395
$251$	−3851.45	−0.968531	−0.484265	−	0.874921i	$-0.660913\pi$
$251$	−3851.45	−0.968531	−0.484265	+	0.874921i	$0.660913\pi$
$252$	−11458.1	−2.86425
$253$	−190.265	−0.0472801
$254$	−5586.23	−1.37997
$255$	−1659.34	−0.407497
$256$	21222.8	5.18136
$257$	−3377.80	−0.819849	−0.409924	−	0.912119i	$-0.634445\pi$
$257$	−3377.80	−0.819849	−0.409924	+	0.912119i	$0.634445\pi$
$258$	0	0
$259$	−9636.30	−2.31186
$260$	6827.06	1.62845
$261$	−437.576	−0.103775
$262$	16101.0	3.79664
$263$	−3214.33	−0.753627	−0.376813	−	0.926289i	$-0.622980\pi$
$263$	−3214.33	−0.753627	−0.376813	+	0.926289i	$0.622980\pi$
$264$	5495.62	1.28118
$265$	4642.38	1.07615
$266$	−5349.26	−1.23302
$267$	−7641.55	−1.75152
$268$	−13792.4	−3.14367
$269$	1641.68	0.372099	0.186050	−	0.982540i	$-0.440431\pi$
$269$	1641.68	0.372099	0.186050	+	0.982540i	$0.440431\pi$
$270$	2680.85	0.604264
$271$	1602.70	0.359252	0.179626	−	0.983735i	$-0.442511\pi$
$271$	1602.70	0.359252	0.179626	+	0.983735i	$0.442511\pi$
$272$	−8117.73	−1.80959
$273$	−6586.85	−1.46027
$274$	8032.47	1.77102
$275$	549.384	0.120469
$276$	2957.76	0.645059
$277$	−391.521	−0.0849250	−0.0424625	−	0.999098i	$-0.513520\pi$
$277$	−391.521	−0.0849250	−0.0424625	+	0.999098i	$0.513520\pi$
$278$	9116.65	1.96684
$279$	3487.04	0.748257
$280$	18723.2	3.99617
$281$	−613.407	−0.130223	−0.0651117	−	0.997878i	$-0.520740\pi$
$281$	−613.407	−0.130223	−0.0651117	+	0.997878i	$0.520740\pi$
$282$	−4774.17	−1.00815
$283$	−3189.48	−0.669947	−0.334973	−	0.942228i	$-0.608727\pi$
$283$	−3189.48	−0.669947	−0.334973	+	0.942228i	$0.608727\pi$
$284$	555.005	0.115963
$285$	−1985.16	−0.412600
$286$	1971.18	0.407548
$287$	−2412.42	−0.496169
$288$	−15958.0	−3.26505
$289$	−4040.50	−0.822409
$290$	1100.57	0.222855
$291$	10990.1	2.21393
$292$	−8457.18	−1.69493
$293$	−2370.01	−0.472550	−0.236275	−	0.971686i	$-0.575927\pi$
$293$	−2370.01	−0.472550	−0.236275	+	0.971686i	$0.575927\pi$
$294$	−14970.2	−2.96966
$295$	−2851.77	−0.562835
$296$	−29125.1	−5.71913
$297$	573.234	0.111995
$298$	5216.19	1.01398
$299$	689.252	0.133313
$300$	−8540.43	−1.64361
$301$	0	0
$302$	11452.3	2.18215
$303$	7751.12	1.46960
$304$	−9711.72	−1.83225
$305$	−820.720	−0.154080
$306$	3019.12	0.564025
$307$	−1485.87	−0.276232	−0.138116	−	0.990416i	$-0.544105\pi$
$307$	−1485.87	−0.276232	−0.138116	+	0.990416i	$0.544105\pi$
$308$	6162.20	1.14001
$309$	−2383.98	−0.438899
$310$	−8770.45	−1.60686
$311$	−4799.83	−0.875155	−0.437577	−	0.899181i	$-0.644163\pi$
$311$	−4799.83	−0.875155	−0.437577	+	0.899181i	$0.644163\pi$
$312$	−19908.3	−3.61246
$313$	−1762.85	−0.318345	−0.159172	−	0.987251i	$-0.550883\pi$
$313$	−1762.85	−0.318345	−0.159172	+	0.987251i	$0.550883\pi$
$314$	10632.1	1.91083
$315$	−4182.85	−0.748181
$316$	−11955.3	−2.12828
$317$	−4271.00	−0.756730	−0.378365	−	0.925656i	$-0.623514\pi$
$317$	−4271.00	−0.756730	−0.378365	+	0.925656i	$0.623514\pi$
$318$	−20837.1	−3.67449
$319$	235.330	0.0413040
$320$	21808.0	3.80970
$321$	−13102.9	−2.27830
$322$	2909.52	0.503543
$323$	1043.83	0.179814
$324$	−20260.3	−3.47398
$325$	−1990.19	−0.339680
$326$	−2335.03	−0.396704
$327$	6332.26	1.07087
$328$	−7291.38	−1.22744
$329$	−3477.93	−0.582810
$330$	3087.97	0.515112
$331$	9623.51	1.59805	0.799027	−	0.601295i	$-0.205348\pi$
$331$	9623.51	1.59805	0.799027	+	0.601295i	$0.205348\pi$
$332$	14350.3	2.37222
$333$	6506.67	1.07076
$334$	−3034.89	−0.497191
$335$	−5035.01	−0.821170
$336$	−50480.5	−8.19624
$337$	5650.95	0.913432	0.456716	−	0.889613i	$-0.349026\pi$
$337$	5650.95	0.913432	0.456716	+	0.889613i	$0.349026\pi$
$338$	5059.34	0.814177
$339$	−5010.75	−0.802793
$340$	−5623.56	−0.897000
$341$	−1875.34	−0.297817
$342$	3611.95	0.571088
$343$	−1555.68	−0.244895
$344$	0	0
$345$	1079.75	0.168498
$346$	4545.26	0.706227
$347$	2258.74	0.349439	0.174720	−	0.984618i	$-0.444098\pi$
$347$	2258.74	0.349439	0.174720	+	0.984618i	$0.444098\pi$
$348$	−3658.32	−0.563524
$349$	11373.4	1.74442	0.872212	−	0.489128i	$-0.162685\pi$
$349$	11373.4	1.74442	0.872212	+	0.489128i	$0.162685\pi$
$350$	−8401.13	−1.28303
$351$	−2076.59	−0.315784
$352$	8582.28	1.29954
$353$	6551.13	0.987767	0.493883	−	0.869528i	$-0.335577\pi$
$353$	6551.13	0.987767	0.493883	+	0.869528i	$0.335577\pi$
$354$	12800.0	1.92179
$355$	202.608	0.0302911
$356$	−25897.5	−3.85552
$357$	5425.70	0.804365
$358$	18348.6	2.70880
$359$	−4204.66	−0.618144	−0.309072	−	0.951039i	$-0.600018\pi$
$359$	−4204.66	−0.618144	−0.309072	+	0.951039i	$0.600018\pi$
$360$	−12642.4	−1.85087
$361$	−5610.21	−0.817934
$362$	14490.8	2.10393
$363$	−8308.54	−1.20134
$364$	−22323.1	−3.21442
$365$	−3087.35	−0.442738
$366$	3683.77	0.526103
$367$	4867.39	0.692304	0.346152	−	0.938178i	$-0.387488\pi$
$367$	4867.39	0.692304	0.346152	+	0.938178i	$0.387488\pi$
$368$	5282.30	0.748258
$369$	1628.93	0.229806
$370$	−16365.3	−2.29943
$371$	−15179.6	−2.12423
$372$	29153.1	4.06322
$373$	−1208.88	−0.167810	−0.0839051	−	0.996474i	$-0.526739\pi$
$373$	−1208.88	−0.167810	−0.0839051	+	0.996474i	$0.526739\pi$
$374$	−1623.70	−0.224490
$375$	−10139.8	−1.39631
$376$	−10511.8	−1.44177
$377$	−852.504	−0.116462
$378$	−8765.83	−1.19277
$379$	2664.41	0.361112	0.180556	−	0.983565i	$-0.442210\pi$
$379$	2664.41	0.361112	0.180556	+	0.983565i	$0.442210\pi$
$380$	−6727.79	−0.908233
$381$	6778.64	0.911496
$382$	10955.3	1.46733
$383$	7348.76	0.980428	0.490214	−	0.871602i	$-0.336919\pi$
$383$	7348.76	0.980428	0.490214	+	0.871602i	$0.336919\pi$
$384$	−51147.2	−6.79712
$385$	2249.55	0.297787
$386$	18968.9	2.50128
$387$	0	0
$388$	37245.9	4.87339
$389$	2698.30	0.351695	0.175848	−	0.984417i	$-0.443733\pi$
$389$	2698.30	0.351695	0.175848	+	0.984417i	$0.443733\pi$
$390$	−11186.4	−1.45243
$391$	−567.747	−0.0734328
$392$	−32961.6	−4.24696
$393$	−19537.8	−2.50776
$394$	17690.3	2.26199
$395$	−4364.36	−0.555936
$396$	−4160.87	−0.528009
$397$	7999.63	1.01131	0.505655	−	0.862736i	$-0.331251\pi$
$397$	7999.63	1.01131	0.505655	+	0.862736i	$0.331251\pi$
$398$	4964.00	0.625183
$399$	6491.08	0.814437
$400$	−15252.5	−1.90656
$401$	−1655.91	−0.206215	−0.103107	−	0.994670i	$-0.532878\pi$
$401$	−1655.91	−0.206215	−0.103107	+	0.994670i	$0.532878\pi$
$402$	22599.4	2.80387
$403$	6793.59	0.839734
$404$	26268.8	3.23496
$405$	−7396.15	−0.907451
$406$	−3598.65	−0.439896
$407$	−3499.31	−0.426178
$408$	16398.8	1.98986
$409$	2350.99	0.284227	0.142114	−	0.989850i	$-0.454610\pi$
$409$	2350.99	0.284227	0.142114	+	0.989850i	$0.454610\pi$
$410$	−4097.00	−0.493504
$411$	−9747.04	−1.16980
$412$	−8079.39	−0.966124
$413$	9324.70	1.11099
$414$	−1964.58	−0.233222
$415$	5238.69	0.619656
$416$	−31090.0	−3.66422
$417$	−11062.6	−1.29914
$418$	−1942.52	−0.227301
$419$	12597.8	1.46884	0.734421	−	0.678694i	$-0.237454\pi$
$419$	12597.8	1.46884	0.734421	+	0.678694i	$0.237454\pi$
$420$	−34970.4	−4.06281
$421$	14618.2	1.69228	0.846139	−	0.532963i	$-0.178921\pi$
$421$	14618.2	1.69228	0.846139	+	0.532963i	$0.178921\pi$
$422$	15716.8	1.81299
$423$	2348.39	0.269935
$424$	−45879.5	−5.25497
$425$	1639.35	0.187106
$426$	−909.400	−0.103429
$427$	2683.59	0.304140
$428$	−44406.3	−5.01509
$429$	−2391.94	−0.269194
$430$	0	0
$431$	−16070.2	−1.79599	−0.897995	−	0.440005i	$-0.854977\pi$
$431$	−16070.2	−1.79599	−0.897995	+	0.440005i	$0.854977\pi$
$432$	−15914.6	−1.77243
$433$	4032.84	0.447588	0.223794	−	0.974636i	$-0.428156\pi$
$433$	4032.84	0.447588	0.223794	+	0.974636i	$0.428156\pi$
$434$	28677.6	3.17181
$435$	−1335.49	−0.147200
$436$	21460.3	2.35725
$437$	−679.230	−0.0743523
$438$	13857.5	1.51172
$439$	7459.92	0.811031	0.405516	−	0.914088i	$-0.367092\pi$
$439$	7459.92	0.811031	0.405516	+	0.914088i	$0.367092\pi$
$440$	6799.13	0.736672
$441$	7363.75	0.795136
$442$	5881.97	0.632980
$443$	−4510.98	−0.483799	−0.241899	−	0.970301i	$-0.577770\pi$
$443$	−4510.98	−0.483799	−0.241899	+	0.970301i	$0.577770\pi$
$444$	54398.5	5.81450
$445$	−9454.06	−1.00711
$446$	−33801.5	−3.58867
$447$	−6329.61	−0.669754
$448$	−71307.7	−7.52003
$449$	−6496.35	−0.682810	−0.341405	−	0.939916i	$-0.610903\pi$
$449$	−6496.35	−0.682810	−0.341405	+	0.939916i	$0.610903\pi$
$450$	5672.65	0.594247
$451$	−876.043	−0.0914662
$452$	−16981.6	−1.76714
$453$	−13896.9	−1.44135
$454$	−19610.6	−2.02725
$455$	−8149.20	−0.839649
$456$	19618.9	2.01478
$457$	4452.60	0.455763	0.227881	−	0.973689i	$-0.426820\pi$
$457$	4452.60	0.455763	0.227881	+	0.973689i	$0.426820\pi$
$458$	−20409.9	−2.08230
$459$	1710.52	0.173944
$460$	3659.31	0.370905
$461$	−17062.6	−1.72383	−0.861913	−	0.507057i	$-0.830733\pi$
$461$	−17062.6	−1.72383	−0.861913	+	0.507057i	$0.830733\pi$
$462$	−10097.0	−1.01679
$463$	−18830.6	−1.89013	−0.945067	−	0.326877i	$-0.894004\pi$
$463$	−18830.6	−1.89013	−0.945067	+	0.326877i	$0.894004\pi$
$464$	−6533.44	−0.653679
$465$	10642.5	1.06137
$466$	−13582.8	−1.35023
$467$	2455.43	0.243305	0.121653	−	0.992573i	$-0.461181\pi$
$467$	2455.43	0.243305	0.121653	+	0.992573i	$0.461181\pi$
$468$	15073.1	1.48879
$469$	16463.4	1.62092
$470$	−5906.55	−0.579679
$471$	−12901.5	−1.26214
$472$	28183.3	2.74839
$473$	0	0
$474$	19589.2	1.89824
$475$	1961.25	0.189449
$476$	18387.9	1.77060
$477$	10249.7	0.983858
$478$	1928.16	0.184502
$479$	−11404.1	−1.08782	−0.543912	−	0.839142i	$-0.683057\pi$
$479$	−11404.1	−1.08782	−0.543912	+	0.839142i	$0.683057\pi$
$480$	−48704.2	−4.63132
$481$	12676.6	1.20167
$482$	−15275.4	−1.44352
$483$	−3530.56	−0.332601
$484$	−28157.9	−2.64443
$485$	13596.9	1.27299
$486$	24514.9	2.28810
$487$	−5407.50	−0.503157	−0.251578	−	0.967837i	$-0.580950\pi$
$487$	−5407.50	−0.503157	−0.251578	+	0.967837i	$0.580950\pi$
$488$	8110.97	0.752390
$489$	2833.46	0.262031
$490$	−18521.0	−1.70754
$491$	−14996.5	−1.37838	−0.689190	−	0.724581i	$-0.742033\pi$
$491$	−14996.5	−1.37838	−0.689190	+	0.724581i	$0.742033\pi$
$492$	13618.5	1.24790
$493$	702.221	0.0641510
$494$	7036.95	0.640906
$495$	−1518.95	−0.137923
$496$	52064.9	4.71327
$497$	−662.488	−0.0597921
$498$	−23513.6	−2.11581
$499$	10720.9	0.961791	0.480896	−	0.876778i	$-0.340312\pi$
$499$	10720.9	0.961791	0.480896	+	0.876778i	$0.340312\pi$
$500$	−34364.0	−3.07361
$501$	3682.70	0.328405
$502$	21387.4	1.90153
$503$	−21636.0	−1.91790	−0.958949	−	0.283579i	$-0.908478\pi$
$503$	−21636.0	−1.91790	−0.958949	+	0.283579i	$0.908478\pi$
$504$	41338.0	3.65346
$505$	9589.62	0.845014
$506$	1056.56	0.0928256
$507$	−6139.28	−0.537781
$508$	22973.0	2.00643
$509$	13204.0	1.14982	0.574908	−	0.818218i	$-0.305038\pi$
$509$	13204.0	1.14982	0.574908	+	0.818218i	$0.305038\pi$
$510$	9214.44	0.800043
$511$	10095.0	0.873927
$512$	−57129.0	−4.93119
$513$	2046.39	0.176122
$514$	18757.2	1.60962
$515$	−2949.44	−0.252365
$516$	0	0
$517$	−1262.97	−0.107438
$518$	53511.2	4.53889
$519$	−5515.46	−0.466478
$520$	−24630.4	−2.07714
$521$	−12287.5	−1.03325	−0.516626	−	0.856211i	$-0.672812\pi$
$521$	−12287.5	−1.03325	−0.516626	+	0.856211i	$0.672812\pi$
$522$	2429.90	0.203743
$523$	11431.0	0.955721	0.477860	−	0.878436i	$-0.341413\pi$
$523$	11431.0	0.955721	0.477860	+	0.878436i	$0.341413\pi$
$524$	−66214.2	−5.52019
$525$	10194.4	0.847465
$526$	17849.4	1.47960
$527$	−5595.99	−0.462552
$528$	−18331.4	−1.51093
$529$	−11797.6	−0.969636
$530$	−25779.5	−2.11281
$531$	−6296.27	−0.514567
$532$	21998.5	1.79278
$533$	3173.54	0.257901
$534$	42434.2	3.43878
$535$	−16210.8	−1.31001
$536$	49759.7	4.00987
$537$	−22265.1	−1.78922
$538$	−9116.36	−0.730547
$539$	−3960.26	−0.316475
$540$	−11024.8	−0.878580
$541$	−10071.9	−0.800414	−0.400207	−	0.916425i	$-0.631062\pi$
$541$	−10071.9	−0.800414	−0.400207	+	0.916425i	$0.631062\pi$
$542$	−8899.94	−0.705323
$543$	−17584.0	−1.38969
$544$	25609.4	2.01837
$545$	7834.21	0.615745
$546$	36577.3	2.86697
$547$	3049.29	0.238352	0.119176	−	0.992873i	$-0.461975\pi$
$547$	3049.29	0.238352	0.119176	+	0.992873i	$0.461975\pi$
$548$	−33033.1	−2.57501
$549$	−1812.03	−0.140866
$550$	−3050.78	−0.236519
$551$	840.108	0.0649543
$552$	−10670.9	−0.822797
$553$	14270.6	1.09737
$554$	2174.15	0.166734
$555$	19858.5	1.51882
$556$	−37491.7	−2.85971
$557$	19978.3	1.51976	0.759882	−	0.650061i	$-0.225257\pi$
$557$	19978.3	1.51976	0.759882	+	0.650061i	$0.225257\pi$
$558$	−19363.8	−1.46906
$559$	0	0
$560$	−62454.0	−4.71279
$561$	1970.28	0.148280
$562$	3406.30	0.255669
$563$	−7879.14	−0.589815	−0.294908	−	0.955526i	$-0.595289\pi$
$563$	−7879.14	−0.589815	−0.294908	+	0.955526i	$0.595289\pi$
$564$	19633.5	1.46581
$565$	−6199.26	−0.461601
$566$	17711.4	1.31531
$567$	24183.9	1.79123
$568$	−2002.33	−0.147915
$569$	1060.11	0.0781058	0.0390529	−	0.999237i	$-0.487566\pi$
$569$	1060.11	0.0781058	0.0390529	+	0.999237i	$0.487566\pi$
$570$	11023.8	0.810062
$571$	−157.806	−0.0115656	−0.00578281	−	0.999983i	$-0.501841\pi$
$571$	−157.806	−0.0115656	−0.00578281	+	0.999983i	$0.501841\pi$
$572$	−8106.38	−0.592561
$573$	−13293.7	−0.969204
$574$	13396.4	0.974135
$575$	−1066.74	−0.0773676
$576$	48148.8	3.48298
$577$	22077.3	1.59288	0.796440	−	0.604718i	$-0.206714\pi$
$577$	22077.3	1.59288	0.796440	+	0.604718i	$0.206714\pi$
$578$	22437.2	1.61465
$579$	−23017.9	−1.65214
$580$	−4526.04	−0.324023
$581$	−17129.4	−1.22315
$582$	−61029.1	−4.34662
$583$	−5512.32	−0.391590
$584$	30511.5	2.16194
$585$	5502.54	0.388892
$586$	13160.8	0.927763
$587$	−23019.1	−1.61857	−0.809285	−	0.587416i	$-0.800145\pi$
$587$	−23019.1	−1.61857	−0.809285	+	0.587416i	$0.800145\pi$
$588$	61564.0	4.31778
$589$	−6694.81	−0.468345
$590$	15836.1	1.10502
$591$	−21466.4	−1.49409
$592$	97150.9	6.74473
$593$	3709.24	0.256864	0.128432	−	0.991718i	$-0.459006\pi$
$593$	3709.24	0.256864	0.128432	+	0.991718i	$0.459006\pi$
$594$	−3183.21	−0.219880
$595$	6712.62	0.462505
$596$	−21451.3	−1.47429
$597$	−6023.58	−0.412946
$598$	−3827.47	−0.261734
$599$	20702.0	1.41212	0.706059	−	0.708153i	$-0.250471\pi$
$599$	20702.0	1.41212	0.706059	+	0.708153i	$0.250471\pi$
$600$	30811.9	2.09648
$601$	−19631.3	−1.33241	−0.666205	−	0.745769i	$-0.732082\pi$
$601$	−19631.3	−1.33241	−0.666205	+	0.745769i	$0.732082\pi$
$602$	0	0
$603$	−11116.5	−0.750747
$604$	−47097.0	−3.17277
$605$	−10279.2	−0.690762
$606$	−43042.6	−2.88529
$607$	321.288	0.0214839	0.0107419	−	0.999942i	$-0.496581\pi$
$607$	321.288	0.0214839	0.0107419	+	0.999942i	$0.496581\pi$
$608$	30638.0	2.04364
$609$	4366.79	0.290561
$610$	4557.53	0.302506
$611$	4575.22	0.302935
$612$	−12416.0	−0.820074
$613$	−20803.1	−1.37068	−0.685342	−	0.728222i	$-0.740347\pi$
$613$	−20803.1	−1.37068	−0.685342	+	0.728222i	$0.740347\pi$
$614$	8251.18	0.542330
$615$	4971.52	0.325969
$616$	−22231.8	−1.45413
$617$	−18771.8	−1.22484	−0.612418	−	0.790534i	$-0.709803\pi$
$617$	−18771.8	−1.22484	−0.612418	+	0.790534i	$0.709803\pi$
$618$	13238.4	0.861696
$619$	−22616.6	−1.46856	−0.734281	−	0.678846i	$-0.762481\pi$
$619$	−22616.6	−1.46856	−0.734281	+	0.678846i	$0.762481\pi$
$620$	36067.9	2.33633
$621$	−1113.05	−0.0719248
$622$	26653.8	1.71820
$623$	30912.9	1.98796
$624$	66407.1	4.26028
$625$	−5607.38	−0.358872
$626$	9789.23	0.625010
$627$	2357.16	0.150137
$628$	−43723.7	−2.77829
$629$	−10441.9	−0.661916
$630$	23227.7	1.46891
$631$	−19599.7	−1.23653	−0.618267	−	0.785968i	$-0.712165\pi$
$631$	−19599.7	−1.23653	−0.618267	+	0.785968i	$0.712165\pi$
$632$	43131.8	2.71470
$633$	−19071.6	−1.19752
$634$	23717.2	1.48570
$635$	8386.47	0.524105
$636$	85691.5	5.34259
$637$	14346.4	0.892344
$638$	−1306.81	−0.0810925
$639$	447.329	0.0276934
$640$	−63278.8	−3.90830
$641$	−21787.1	−1.34249	−0.671247	−	0.741234i	$-0.734241\pi$
$641$	−21787.1	−1.34249	−0.671247	+	0.741234i	$0.734241\pi$
$642$	72761.6	4.47301
$643$	−2333.40	−0.143111	−0.0715556	−	0.997437i	$-0.522796\pi$
$643$	−2333.40	−0.143111	−0.0715556	+	0.997437i	$0.522796\pi$
$644$	−11965.2	−0.732136
$645$	0	0
$646$	−5796.45	−0.353031
$647$	13759.4	0.836070	0.418035	−	0.908431i	$-0.362719\pi$
$647$	13759.4	0.836070	0.418035	+	0.908431i	$0.362719\pi$
$648$	73094.3	4.43120
$649$	3386.16	0.204805
$650$	11051.7	0.666897
$651$	−34798.9	−2.09505
$652$	9602.69	0.576795
$653$	25853.4	1.54935	0.774673	−	0.632362i	$-0.217914\pi$
$653$	25853.4	1.54935	0.774673	+	0.632362i	$0.217914\pi$
$654$	−35163.6	−2.10245
$655$	−24172.0	−1.44195
$656$	24321.4	1.44755
$657$	−6816.40	−0.404769
$658$	19313.2	1.14424
$659$	−9669.46	−0.571576	−0.285788	−	0.958293i	$-0.592255\pi$
$659$	−9669.46	−0.571576	−0.285788	+	0.958293i	$0.592255\pi$
$660$	−12699.1	−0.748957
$661$	16074.9	0.945904	0.472952	−	0.881088i	$-0.343188\pi$
$661$	16074.9	0.945904	0.472952	+	0.881088i	$0.343188\pi$
$662$	−53440.1	−3.13748
$663$	−7137.51	−0.418096
$664$	−51772.6	−3.02586
$665$	8030.71	0.468297
$666$	−36132.1	−2.10224
$667$	−456.943	−0.0265261
$668$	12480.8	0.722899
$669$	41016.6	2.37039
$670$	27959.8	1.61221
$671$	974.515	0.0560666
$672$	159253.	9.14184
$673$	22908.2	1.31210	0.656052	−	0.754716i	$-0.272225\pi$
$673$	22908.2	1.31210	0.656052	+	0.754716i	$0.272225\pi$
$674$	−31380.2	−1.79335
$675$	3213.91	0.183264
$676$	−20806.2	−1.18379
$677$	28243.9	1.60340	0.801698	−	0.597729i	$-0.203930\pi$
$677$	28243.9	1.60340	0.801698	+	0.597729i	$0.203930\pi$
$678$	27825.1	1.57613
$679$	−44459.0	−2.51278
$680$	20288.5	1.14416
$681$	23796.5	1.33904
$682$	10413.9	0.584707
$683$	12213.6	0.684248	0.342124	−	0.939655i	$-0.388854\pi$
$683$	12213.6	0.684248	0.342124	+	0.939655i	$0.388854\pi$
$684$	−14853.9	−0.830343
$685$	−12058.9	−0.672626
$686$	8638.84	0.480805
$687$	24766.5	1.37540
$688$	0	0
$689$	19968.8	1.10414
$690$	−5995.94	−0.330814
$691$	31697.9	1.74507	0.872535	−	0.488551i	$-0.162474\pi$
$691$	31697.9	1.74507	0.872535	+	0.488551i	$0.162474\pi$
$692$	−18692.1	−1.02683
$693$	4966.67	0.272249
$694$	−12543.0	−0.686058
$695$	−13686.6	−0.746996
$696$	13198.4	0.718796
$697$	−2614.09	−0.142060
$698$	−63157.4	−3.42485
$699$	16482.0	0.891857
$700$	34549.1	1.86548
$701$	10100.8	0.544224	0.272112	−	0.962266i	$-0.412278\pi$
$701$	10100.8	0.544224	0.272112	+	0.962266i	$0.412278\pi$
$702$	11531.5	0.619981
$703$	−12492.2	−0.670205
$704$	−25894.6	−1.38628
$705$	7167.33	0.382890
$706$	−36379.0	−1.93929
$707$	−31356.1	−1.66799
$708$	−52639.4	−2.79422
$709$	−14326.8	−0.758892	−0.379446	−	0.925214i	$-0.623885\pi$
$709$	−14326.8	−0.758892	−0.379446	+	0.925214i	$0.623885\pi$
$710$	−1125.10	−0.0594709
$711$	−9635.84	−0.508259
$712$	93432.1	4.91786
$713$	3641.38	0.191263
$714$	−30129.3	−1.57922
$715$	−2959.29	−0.154785
$716$	−75457.4	−3.93851
$717$	−2339.73	−0.121867
$718$	23348.8	1.21361
$719$	−13059.9	−0.677402	−0.338701	−	0.940894i	$-0.609987\pi$
$719$	−13059.9	−0.677402	−0.338701	+	0.940894i	$0.609987\pi$
$720$	42170.5	2.18278
$721$	9644.06	0.498146
$722$	31153.9	1.60586
$723$	18536.0	0.953475
$724$	−59592.7	−3.05904
$725$	1319.41	0.0675884
$726$	46138.0	2.35860
$727$	6978.02	0.355984	0.177992	−	0.984032i	$-0.443040\pi$
$727$	6978.02	0.355984	0.177992	+	0.984032i	$0.443040\pi$
$728$	80536.5	4.10011
$729$	−5793.82	−0.294357
$730$	17144.3	0.869232
$731$	0	0
$732$	−15149.3	−0.764937
$733$	11737.8	0.591469	0.295734	−	0.955270i	$-0.404436\pi$
$733$	11737.8	0.591469	0.295734	+	0.955270i	$0.404436\pi$
$734$	−27029.0	−1.35921
$735$	22474.4	1.12786
$736$	−16664.3	−0.834585
$737$	5978.52	0.298808
$738$	−9045.56	−0.451181
$739$	7982.37	0.397343	0.198671	−	0.980066i	$-0.436337\pi$
$739$	7982.37	0.397343	0.198671	+	0.980066i	$0.436337\pi$
$740$	67301.3	3.34330
$741$	−8539.02	−0.423332
$742$	84293.8	4.17052
$743$	−36108.3	−1.78289	−0.891444	−	0.453131i	$-0.850307\pi$
$743$	−36108.3	−1.78289	−0.891444	+	0.453131i	$0.850307\pi$
$744$	−105177.	−5.18279
$745$	−7830.93	−0.385105
$746$	6712.99	0.329464
$747$	11566.2	0.566514
$748$	6677.35	0.326401
$749$	53006.1	2.58585
$750$	56306.9	2.74138
$751$	14327.0	0.696138	0.348069	−	0.937469i	$-0.386838\pi$
$751$	14327.0	0.696138	0.348069	+	0.937469i	$0.386838\pi$
$752$	35063.7	1.70032
$753$	−25952.6	−1.25600
$754$	4734.02	0.228651
$755$	−17193.1	−0.828769
$756$	36049.0	1.73424
$757$	19278.0	0.925589	0.462794	−	0.886466i	$-0.346847\pi$
$757$	19278.0	0.925589	0.462794	+	0.886466i	$0.346847\pi$
$758$	−14795.7	−0.708975
$759$	−1282.08	−0.0613132
$760$	24272.3	1.15849
$761$	−1332.42	−0.0634692	−0.0317346	−	0.999496i	$-0.510103\pi$
$761$	−1332.42	−0.0634692	−0.0317346	+	0.999496i	$0.510103\pi$
$762$	−37642.3	−1.78955
$763$	−25616.3	−1.21543
$764$	−45052.9	−2.13345
$765$	−4532.53	−0.214214
$766$	−40808.3	−1.92489
$767$	−12266.6	−0.577475
$768$	143008.	6.71922
$769$	17605.9	0.825599	0.412800	−	0.910822i	$-0.364551\pi$
$769$	17605.9	0.825599	0.412800	+	0.910822i	$0.364551\pi$
$770$	−12492.0	−0.584648
$771$	−22761.0	−1.06319
$772$	−78008.5	−3.63677
$773$	−16456.0	−0.765694	−0.382847	−	0.923812i	$-0.625056\pi$
$773$	−16456.0	−0.765694	−0.382847	+	0.923812i	$0.625056\pi$
$774$	0	0
$775$	−10514.3	−0.487337
$776$	−134375.	−6.21619
$777$	−64933.3	−2.99803
$778$	−14983.9	−0.690487
$779$	−3127.40	−0.143839
$780$	46003.5	2.11178
$781$	−240.575	−0.0110224
$782$	3152.75	0.144171
$783$	1376.69	0.0628336
$784$	109948.	5.00856
$785$	−15961.6	−0.725726
$786$	108495.	4.92351
$787$	−8543.07	−0.386948	−0.193474	−	0.981105i	$-0.561975\pi$
$787$	−8543.07	−0.386948	−0.193474	+	0.981105i	$0.561975\pi$
$788$	−72750.4	−3.28886
$789$	−21659.5	−0.977309
$790$	24235.6	1.09147
$791$	20270.3	0.911162
$792$	15011.4	0.673496
$793$	−3530.26	−0.158087
$794$	−44422.6	−1.98552
$795$	31282.3	1.39556
$796$	−20414.1	−0.908995
$797$	13935.4	0.619345	0.309672	−	0.950843i	$-0.399781\pi$
$797$	13935.4	0.619345	0.309672	+	0.950843i	$0.399781\pi$
$798$	−36045.5	−1.59899
$799$	−3768.68	−0.166866
$800$	48117.6	2.12652
$801$	−20873.1	−0.920744
$802$	9195.38	0.404863
$803$	3665.89	0.161104
$804$	−92938.8	−4.07674
$805$	−4367.98	−0.191244
$806$	−37725.4	−1.64866
$807$	11062.3	0.482541
$808$	−94771.8	−4.12631
$809$	28901.8	1.25604	0.628019	−	0.778198i	$-0.283866\pi$
$809$	28901.8	1.25604	0.628019	+	0.778198i	$0.283866\pi$
$810$	41071.4	1.78161
$811$	22920.0	0.992391	0.496196	−	0.868211i	$-0.334730\pi$
$811$	22920.0	0.992391	0.496196	+	0.868211i	$0.334730\pi$
$812$	14799.2	0.639595
$813$	10799.7	0.465881
$814$	19432.0	0.836721
$815$	3505.53	0.150667
$816$	−54700.6	−2.34670
$817$	0	0
$818$	−13055.2	−0.558027
$819$	−17992.2	−0.767641
$820$	16848.7	0.717538
$821$	−11385.2	−0.483980	−0.241990	−	0.970279i	$-0.577800\pi$
$821$	−11385.2	−0.483980	−0.241990	+	0.970279i	$0.577800\pi$
$822$	54126.1	2.29667
$823$	18547.7	0.785580	0.392790	−	0.919628i	$-0.371510\pi$
$823$	18547.7	0.785580	0.392790	+	0.919628i	$0.371510\pi$
$824$	29148.6	1.23233
$825$	3701.98	0.156226
$826$	−51780.8	−2.18122
$827$	35248.8	1.48213	0.741065	−	0.671434i	$-0.234321\pi$
$827$	35248.8	1.48213	0.741065	+	0.671434i	$0.234321\pi$
$828$	8079.21	0.339097
$829$	−14809.3	−0.620444	−0.310222	−	0.950664i	$-0.600403\pi$
$829$	−14809.3	−0.620444	−0.310222	+	0.950664i	$0.600403\pi$
$830$	−29090.9	−1.21658
$831$	−2638.23	−0.110131
$832$	93805.4	3.90879
$833$	−11817.3	−0.491532
$834$	61431.7	2.55061
$835$	4556.20	0.188831
$836$	7988.51	0.330489
$837$	−10970.8	−0.453054
$838$	−69956.9	−2.88379
$839$	−3415.56	−0.140546	−0.0702730	−	0.997528i	$-0.522387\pi$
$839$	−3415.56	−0.140546	−0.0702730	+	0.997528i	$0.522387\pi$
$840$	126165.	5.18226
$841$	−23823.8	−0.976827
$842$	−81176.2	−3.32247
$843$	−4133.39	−0.168875
$844$	−64634.5	−2.63603
$845$	−7595.46	−0.309221
$846$	−13040.8	−0.529966
$847$	33611.0	1.36351
$848$	153038.	6.19733
$849$	−21492.0	−0.868792
$850$	−9103.45	−0.367348
$851$	6794.66	0.273699
$852$	3739.85	0.150382
$853$	−14467.2	−0.580712	−0.290356	−	0.956919i	$-0.593774\pi$
$853$	−14467.2	−0.580712	−0.290356	+	0.956919i	$0.593774\pi$
$854$	−14902.2	−0.597122
$855$	−5422.53	−0.216897
$856$	160207.	6.39694
$857$	−1495.92	−0.0596262	−0.0298131	−	0.999555i	$-0.509491\pi$
$857$	−1495.92	−0.0596262	−0.0298131	+	0.999555i	$0.509491\pi$
$858$	13282.6	0.528511
$859$	−14786.2	−0.587309	−0.293655	−	0.955912i	$-0.594872\pi$
$859$	−14786.2	−0.587309	−0.293655	+	0.955912i	$0.594872\pi$
$860$	0	0
$861$	−16255.9	−0.643436
$862$	89238.9	3.52609
$863$	−27686.3	−1.09207	−0.546033	−	0.837763i	$-0.683863\pi$
$863$	−27686.3	−1.09207	−0.546033	+	0.837763i	$0.683863\pi$
$864$	50206.5	1.97692
$865$	−6823.68	−0.268222
$866$	−22394.7	−0.878755
$867$	−27226.5	−1.06651
$868$	−117935.	−4.61171
$869$	5182.19	0.202294
$870$	7416.11	0.289000
$871$	−21657.7	−0.842529
$872$	−77423.6	−3.00676
$873$	30019.8	1.16382
$874$	3771.82	0.145977
$875$	41019.0	1.58479
$876$	−56987.9	−2.19800
$877$	1957.85	0.0753843	0.0376921	−	0.999289i	$-0.487999\pi$
$877$	1957.85	0.0753843	0.0376921	+	0.999289i	$0.487999\pi$
$878$	−41425.6	−1.59231
$879$	−15970.1	−0.612807
$880$	−22679.5	−0.868778
$881$	14947.8	0.571629	0.285815	−	0.958285i	$-0.407736\pi$
$881$	14947.8	0.571629	0.285815	+	0.958285i	$0.407736\pi$
$882$	−40891.5	−1.56110
$883$	−6284.37	−0.239509	−0.119754	−	0.992804i	$-0.538211\pi$
$883$	−6284.37	−0.239509	−0.119754	+	0.992804i	$0.538211\pi$
$884$	−24189.3	−0.920332
$885$	−19216.4	−0.729889
$886$	25049.8	0.949848
$887$	42767.5	1.61893	0.809465	−	0.587168i	$-0.199757\pi$
$887$	42767.5	1.61893	0.809465	+	0.587168i	$0.199757\pi$
$888$	−196257.	−7.41661
$889$	−27422.0	−1.03454
$890$	52499.2	1.97728
$891$	8782.11	0.330204
$892$	139007.	5.21781
$893$	−4508.69	−0.168956
$894$	35148.8	1.31494
$895$	−27546.2	−1.02879
$896$	206909.	7.71466
$897$	4644.46	0.172881
$898$	36074.8	1.34057
$899$	−4503.85	−0.167088
$900$	−23328.4	−0.864016
$901$	−16448.6	−0.608195
$902$	4864.74	0.179577
$903$	0	0
$904$	61265.7	2.25406
$905$	−21754.7	−0.799062
$906$	77170.5	2.82982
$907$	21527.8	0.788112	0.394056	−	0.919086i	$-0.371072\pi$
$907$	21527.8	0.788112	0.394056	+	0.919086i	$0.371072\pi$
$908$	80647.3	2.94755
$909$	21172.4	0.772546
$910$	45253.1	1.64849
$911$	11639.2	0.423299	0.211650	−	0.977346i	$-0.432116\pi$
$911$	11639.2	0.423299	0.211650	+	0.977346i	$0.432116\pi$
$912$	−65441.5	−2.37608
$913$	−6220.36	−0.225481
$914$	−24725.6	−0.894804
$915$	−5530.35	−0.199812
$916$	83934.5	3.02759
$917$	79037.4	2.84629
$918$	−9498.65	−0.341506
$919$	38878.1	1.39551	0.697753	−	0.716338i	$-0.254183\pi$
$919$	38878.1	1.39551	0.697753	+	0.716338i	$0.254183\pi$
$920$	−13201.9	−0.473103
$921$	−10012.4	−0.358220
$922$	94749.9	3.38440
$923$	871.504	0.0310790
$924$	41523.4	1.47838
$925$	−19619.3	−0.697383
$926$	104568.	3.71092
$927$	−6511.91	−0.230722
$928$	20611.3	0.729094
$929$	−21729.0	−0.767391	−0.383695	−	0.923460i	$-0.625349\pi$
$929$	−21729.0	−0.767391	−0.383695	+	0.923460i	$0.625349\pi$
$930$	−59098.9	−2.08379
$931$	−14137.8	−0.497687
$932$	55858.3	1.96320
$933$	−32343.2	−1.13491
$934$	−13635.2	−0.477684
$935$	2437.61	0.0852604
$936$	−54380.2	−1.89901
$937$	2387.68	0.0832466	0.0416233	−	0.999133i	$-0.486747\pi$
$937$	2387.68	0.0832466	0.0416233	+	0.999133i	$0.486747\pi$
$938$	−91422.9	−3.18237
$939$	−11878.8	−0.412832
$940$	24290.3	0.842834
$941$	−32184.8	−1.11498	−0.557489	−	0.830185i	$-0.688235\pi$
$941$	−32184.8	−1.11498	−0.557489	+	0.830185i	$0.688235\pi$
$942$	71643.1	2.47798
$943$	1701.02	0.0587411
$944$	−94009.4	−3.24126
$945$	13159.9	0.453008
$946$	0	0
$947$	−38920.2	−1.33552	−0.667760	−	0.744376i	$-0.732747\pi$
$947$	−38920.2	−1.33552	−0.667760	+	0.744376i	$0.732747\pi$
$948$	−80559.6	−2.75997
$949$	−13280.0	−0.454254
$950$	−10891.0	−0.371948
$951$	−28779.8	−0.981333
$952$	−66339.2	−2.25847
$953$	−22243.3	−0.756067	−0.378034	−	0.925792i	$-0.623400\pi$
$953$	−22243.3	−0.756067	−0.378034	+	0.925792i	$0.623400\pi$
$954$	−56917.3	−1.93162
$955$	−16446.9	−0.557287
$956$	−7929.44	−0.268260
$957$	1585.75	0.0535633
$958$	63328.0	2.13574
$959$	39430.3	1.32771
$960$	146951.	4.94045
$961$	6100.13	0.204764
$962$	−70394.0	−2.35924
$963$	−35791.0	−1.19766
$964$	62819.3	2.09883
$965$	−28477.5	−0.949974
$966$	19605.5	0.652999
$967$	−28555.0	−0.949603	−0.474801	−	0.880093i	$-0.657480\pi$
$967$	−28555.0	−0.949603	−0.474801	+	0.880093i	$0.657480\pi$
$968$	101587.	3.37307
$969$	7033.73	0.233185
$970$	−75504.6	−2.49928
$971$	−20068.7	−0.663269	−0.331634	−	0.943408i	$-0.607600\pi$
$971$	−20068.7	−0.663269	−0.331634	+	0.943408i	$0.607600\pi$
$972$	−100816.	−3.32682
$973$	44752.4	1.47451
$974$	30028.3	0.987853
$975$	−13410.7	−0.440499
$976$	−27055.3	−0.887314
$977$	2742.71	0.0898128	0.0449064	−	0.998991i	$-0.485701\pi$
$977$	2742.71	0.0898128	0.0449064	+	0.998991i	$0.485701\pi$
$978$	−15734.4	−0.514449
$979$	11225.7	0.366469
$980$	76166.4	2.48270
$981$	17296.8	0.562939
$982$	83277.0	2.70619
$983$	−52945.4	−1.71790	−0.858950	−	0.512059i	$-0.828883\pi$
$983$	−52945.4	−1.71790	−0.858950	+	0.512059i	$0.828883\pi$
$984$	−49132.3	−1.59175
$985$	−26558.0	−0.859095
$986$	−3899.49	−0.125948
$987$	−23435.7	−0.755792
$988$	−28939.1	−0.931856
$989$	0	0
$990$	8434.88	0.270786
$991$	7835.58	0.251166	0.125583	−	0.992083i	$-0.459920\pi$
$991$	7835.58	0.251166	0.125583	+	0.992083i	$0.459920\pi$
$992$	−164251.	−5.25704
$993$	64847.2	2.07237
$994$	3678.85	0.117390
$995$	−7452.32	−0.237442
$996$	96698.4	3.07631
$997$	−35826.3	−1.13804	−0.569022	−	0.822322i	$-0.692678\pi$
$997$	−35826.3	−1.13804	−0.569022	+	0.822322i	$0.692678\pi$
$998$	−59534.1	−1.88829
$999$	−20471.0	−0.648323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.1		30
43.8	odd	14		43.4.e.a.21.1	✓	60
43.27	odd	14		43.4.e.a.41.1	yes	60
43.42	odd	2		1849.4.a.h.1.30		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.1	✓	60	43.8	odd	14
43.4.e.a.41.1	yes	60	43.27	odd	14
1849.4.a.g.1.1		30	1.1	even	1	trivial
1849.4.a.h.1.30		30	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)

\(f(q)\)	\(=\)	\(q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} +O(q^{10})\)	\(q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} -46.2944 q^{10} -9.89891 q^{11} +153.883 q^{12} +35.8596 q^{13} +151.373 q^{14} +56.1761 q^{15} +274.822 q^{16} -29.5381 q^{17} -102.211 q^{18} -35.3382 q^{19} +190.383 q^{20} -183.684 q^{21} +54.9695 q^{22} +19.2208 q^{23} -555.174 q^{24} -55.4995 q^{25} -199.131 q^{26} -57.9088 q^{27} -622.513 q^{28} -23.7734 q^{29} -311.950 q^{30} +189.450 q^{31} -866.992 q^{32} -66.7029 q^{33} +164.028 q^{34} -227.253 q^{35} +420.336 q^{36} +353.505 q^{37} +196.236 q^{38} +241.637 q^{39} -686.856 q^{40} +88.4989 q^{41} +1020.01 q^{42} -226.059 q^{44} +153.447 q^{45} -106.735 q^{46} +127.587 q^{47} +1851.86 q^{48} +400.070 q^{49} +308.193 q^{50} -199.040 q^{51} +818.916 q^{52} +556.861 q^{53} +321.572 q^{54} -82.5242 q^{55} +2245.88 q^{56} -238.124 q^{57} +132.015 q^{58} -342.074 q^{59} +1282.88 q^{60} -98.4467 q^{61} -1052.03 q^{62} -501.739 q^{63} +2615.90 q^{64} +298.951 q^{65} +370.407 q^{66} -603.957 q^{67} -674.554 q^{68} +129.518 q^{69} +1261.95 q^{70} +24.3032 q^{71} -1516.47 q^{72} -370.333 q^{73} -1963.04 q^{74} -373.978 q^{75} -807.009 q^{76} +269.837 q^{77} -1341.83 q^{78} -523.511 q^{79} +2291.11 q^{80} -887.180 q^{81} -491.442 q^{82} +628.389 q^{83} -4194.75 q^{84} -246.251 q^{85} -160.195 q^{87} +815.566 q^{88} -1134.03 q^{89} -852.102 q^{90} -977.509 q^{91} +438.940 q^{92} +1276.59 q^{93} -708.500 q^{94} -294.604 q^{95} -5842.15 q^{96} +1630.97 q^{97} -2221.62 q^{98} -182.201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * q^99

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