LMFDB - Embedded newform 1849.4.a.g.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.92929 q^{2} -5.16200 q^{3} -4.27784 q^{4} +3.37495 q^{5} +9.95900 q^{6} +15.9770 q^{7} +23.6875 q^{8} -0.353756 q^{9} +O(q^{10})$	\(q-1.92929 q^{2} -5.16200 q^{3} -4.27784 q^{4} +3.37495 q^{5} +9.95900 q^{6} +15.9770 q^{7} +23.6875 q^{8} -0.353756 q^{9} -6.51127 q^{10} -69.8468 q^{11} +22.0822 q^{12} +8.18001 q^{13} -30.8244 q^{14} -17.4215 q^{15} -11.4774 q^{16} +67.4044 q^{17} +0.682498 q^{18} +11.3922 q^{19} -14.4375 q^{20} -82.4735 q^{21} +134.755 q^{22} +140.537 q^{23} -122.275 q^{24} -113.610 q^{25} -15.7816 q^{26} +141.200 q^{27} -68.3472 q^{28} -166.815 q^{29} +33.6112 q^{30} -27.6648 q^{31} -167.357 q^{32} +360.549 q^{33} -130.043 q^{34} +53.9218 q^{35} +1.51331 q^{36} +32.5950 q^{37} -21.9788 q^{38} -42.2252 q^{39} +79.9443 q^{40} -225.052 q^{41} +159.115 q^{42} +298.793 q^{44} -1.19391 q^{45} -271.137 q^{46} -203.633 q^{47} +59.2466 q^{48} -87.7339 q^{49} +219.186 q^{50} -347.941 q^{51} -34.9928 q^{52} -15.9463 q^{53} -272.416 q^{54} -235.730 q^{55} +378.457 q^{56} -58.8063 q^{57} +321.835 q^{58} +453.727 q^{59} +74.5264 q^{60} +19.9304 q^{61} +53.3734 q^{62} -5.65197 q^{63} +414.700 q^{64} +27.6072 q^{65} -695.605 q^{66} +402.232 q^{67} -288.345 q^{68} -725.452 q^{69} -104.031 q^{70} +876.680 q^{71} -8.37959 q^{72} -963.643 q^{73} -62.8852 q^{74} +586.453 q^{75} -48.7338 q^{76} -1115.95 q^{77} +81.4648 q^{78} +986.472 q^{79} -38.7359 q^{80} -719.323 q^{81} +434.190 q^{82} +1113.48 q^{83} +352.808 q^{84} +227.487 q^{85} +861.100 q^{87} -1654.50 q^{88} +11.0971 q^{89} +2.30340 q^{90} +130.692 q^{91} -601.194 q^{92} +142.805 q^{93} +392.868 q^{94} +38.4480 q^{95} +863.896 q^{96} +1185.25 q^{97} +169.264 q^{98} +24.7087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.92929	−0.682107	−0.341054	−	0.940044i	$-0.610784\pi$
$2$	−1.92929	−0.682107	−0.341054	+	0.940044i	$0.610784\pi$
$3$	−5.16200	−0.993427	−0.496714	−	0.867914i	$-0.665460\pi$
$3$	−5.16200	−0.993427	−0.496714	+	0.867914i	$0.665460\pi$
$4$	−4.27784	−0.534729
$5$	3.37495	0.301865	0.150933	−	0.988544i	$-0.451772\pi$
$5$	3.37495	0.301865	0.150933	+	0.988544i	$0.451772\pi$
$6$	9.95900	0.677624
$7$	15.9770	0.862680	0.431340	−	0.902190i	$-0.358041\pi$
$7$	15.9770	0.862680	0.431340	+	0.902190i	$0.358041\pi$
$8$	23.6875	1.04685
$9$	−0.353756	−0.0131021
$10$	−6.51127	−0.205904
$11$	−69.8468	−1.91451	−0.957255	−	0.289245i	$-0.906596\pi$
$11$	−69.8468	−1.91451	−0.957255	+	0.289245i	$0.906596\pi$
$12$	22.0822	0.531215
$13$	8.18001	0.174518	0.0872588	−	0.996186i	$-0.472189\pi$
$13$	8.18001	0.174518	0.0872588	+	0.996186i	$0.472189\pi$
$14$	−30.8244	−0.588440
$15$	−17.4215	−0.299881
$16$	−11.4774	−0.179335
$17$	67.4044	0.961645	0.480822	−	0.876818i	$-0.340338\pi$
$17$	67.4044	0.961645	0.480822	+	0.876818i	$0.340338\pi$
$18$	0.682498	0.00893701
$19$	11.3922	0.137555	0.0687774	−	0.997632i	$-0.478090\pi$
$19$	11.3922	0.137555	0.0687774	+	0.997632i	$0.478090\pi$
$20$	−14.4375	−0.161416
$21$	−82.4735	−0.857010
$22$	134.755	1.30590
$23$	140.537	1.27409	0.637043	−	0.770828i	$-0.280157\pi$
$23$	140.537	1.27409	0.637043	+	0.770828i	$0.280157\pi$
$24$	−122.275	−1.03997
$25$	−113.610	−0.908877
$26$	−15.7816	−0.119040
$27$	141.200	1.00644
$28$	−68.3472	−0.461300
$29$	−166.815	−1.06817	−0.534083	−	0.845432i	$-0.679343\pi$
$29$	−166.815	−1.06817	−0.534083	+	0.845432i	$0.679343\pi$
$30$	33.6112	0.204551
$31$	−27.6648	−0.160282	−0.0801409	−	0.996784i	$-0.525537\pi$
$31$	−27.6648	−0.160282	−0.0801409	+	0.996784i	$0.525537\pi$
$32$	−167.357	−0.924525
$33$	360.549	1.90193
$34$	−130.043	−0.655945
$35$	53.9218	0.260413
$36$	1.51331	0.00700606
$37$	32.5950	0.144827	0.0724133	−	0.997375i	$-0.476930\pi$
$37$	32.5950	0.144827	0.0724133	+	0.997375i	$0.476930\pi$
$38$	−21.9788	−0.0938271
$39$	−42.2252	−0.173370
$40$	79.9443	0.316008
$41$	−225.052	−0.857248	−0.428624	−	0.903483i	$-0.641002\pi$
$41$	−225.052	−0.857248	−0.428624	+	0.903483i	$0.641002\pi$
$42$	159.115	0.584573
$43$	0	0
$43$	0	0
$44$	298.793	1.02374
$45$	−1.19391	−0.00395506
$46$	−271.137	−0.869064
$47$	−203.633	−0.631978	−0.315989	−	0.948763i	$-0.602336\pi$
$47$	−203.633	−0.631978	−0.315989	+	0.948763i	$0.602336\pi$
$48$	59.2466	0.178156
$49$	−87.7339	−0.255784
$50$	219.186	0.619952
$51$	−347.941	−0.955324
$52$	−34.9928	−0.0933196
$53$	−15.9463	−0.0413281	−0.0206640	−	0.999786i	$-0.506578\pi$
$53$	−15.9463	−0.0413281	−0.0206640	+	0.999786i	$0.506578\pi$
$54$	−272.416	−0.686503
$55$	−235.730	−0.577924
$56$	378.457	0.903096
$57$	−58.8063	−0.136651
$58$	321.835	0.728604
$59$	453.727	1.00119	0.500596	−	0.865681i	$-0.333114\pi$
$59$	453.727	1.00119	0.500596	+	0.865681i	$0.333114\pi$
$60$	74.5264	0.160355
$61$	19.9304	0.0418332	0.0209166	−	0.999781i	$-0.493342\pi$
$61$	19.9304	0.0418332	0.0209166	+	0.999781i	$0.493342\pi$
$62$	53.3734	0.109329
$63$	−5.65197	−0.0113029
$64$	414.700	0.809960
$65$	27.6072	0.0526807
$66$	−695.605	−1.29732
$67$	402.232	0.733440	0.366720	−	0.930331i	$-0.380481\pi$
$67$	402.232	0.733440	0.366720	+	0.930331i	$0.380481\pi$
$68$	−288.345	−0.514220
$69$	−725.452	−1.26571
$70$	−104.031	−0.177630
$71$	876.680	1.46539	0.732695	−	0.680557i	$-0.238262\pi$
$71$	876.680	1.46539	0.732695	+	0.680557i	$0.238262\pi$
$72$	−8.37959	−0.0137159
$73$	−963.643	−1.54501	−0.772506	−	0.635008i	$-0.780997\pi$
$73$	−963.643	−1.54501	−0.772506	+	0.635008i	$0.780997\pi$
$74$	−62.8852	−0.0987873
$75$	586.453	0.902904
$76$	−48.7338	−0.0735546
$77$	−1115.95	−1.65161
$78$	81.4648	0.118257
$79$	986.472	1.40490	0.702448	−	0.711735i	$-0.252090\pi$
$79$	986.472	1.40490	0.702448	+	0.711735i	$0.252090\pi$
$80$	−38.7359	−0.0541350
$81$	−719.323	−0.986726
$82$	434.190	0.584736
$83$	1113.48	1.47253	0.736264	−	0.676695i	$-0.236588\pi$
$83$	1113.48	1.47253	0.736264	+	0.676695i	$0.236588\pi$
$84$	352.808	0.458268
$85$	227.487	0.290287
$86$	0	0
$87$	861.100	1.06114
$88$	−1654.50	−2.00421
$89$	11.0971	0.0132167	0.00660837	−	0.999978i	$-0.497896\pi$
$89$	11.0971	0.0132167	0.00660837	+	0.999978i	$0.497896\pi$
$90$	2.30340	0.00269777
$91$	130.692	0.150553
$92$	−601.194	−0.681291
$93$	142.805	0.159228
$94$	392.868	0.431077
$95$	38.4480	0.0415230
$96$	863.896	0.918448
$97$	1185.25	1.24066	0.620331	−	0.784340i	$-0.286998\pi$
$97$	1185.25	1.24066	0.620331	+	0.784340i	$0.286998\pi$
$98$	169.264	0.174472
$99$	24.7087	0.0250840
$100$	486.003	0.486003
$101$	1000.40	0.985583	0.492792	−	0.870147i	$-0.335977\pi$
$101$	1000.40	0.985583	0.492792	+	0.870147i	$0.335977\pi$
$102$	671.280	0.651634
$103$	−1261.17	−1.20647	−0.603236	−	0.797563i	$-0.706122\pi$
$103$	−1261.17	−1.20647	−0.603236	+	0.797563i	$0.706122\pi$
$104$	193.764	0.182694
$105$	−278.344	−0.258701
$106$	30.7650	0.0281902
$107$	−1089.40	−0.984262	−0.492131	−	0.870521i	$-0.663782\pi$
$107$	−1089.40	−0.984262	−0.492131	+	0.870521i	$0.663782\pi$
$108$	−604.031	−0.538175
$109$	1059.84	0.931321	0.465660	−	0.884963i	$-0.345817\pi$
$109$	1059.84	0.931321	0.465660	+	0.884963i	$0.345817\pi$
$110$	454.792	0.394206
$111$	−168.255	−0.143875
$112$	−183.376	−0.154709
$113$	−739.804	−0.615884	−0.307942	−	0.951405i	$-0.599640\pi$
$113$	−739.804	−0.615884	−0.307942	+	0.951405i	$0.599640\pi$
$114$	113.455	0.0932105
$115$	474.306	0.384602
$116$	713.608	0.571179
$117$	−2.89373	−0.00228654
$118$	−875.373	−0.682920
$119$	1076.92	0.829592
$120$	−412.672	−0.313931
$121$	3547.58	2.66535
$122$	−38.4516	−0.0285348
$123$	1161.72	0.851614
$124$	118.345	0.0857074
$125$	−805.297	−0.576223
$126$	10.9043	0.00770978
$127$	2017.17	1.40941	0.704703	−	0.709503i	$-0.251080\pi$
$127$	2017.17	1.40941	0.704703	+	0.709503i	$0.251080\pi$
$128$	538.778	0.372045
$129$	0	0
$130$	−53.2623	−0.0359339
$131$	−2020.38	−1.34749	−0.673747	−	0.738962i	$-0.735316\pi$
$131$	−2020.38	−1.34749	−0.673747	+	0.738962i	$0.735316\pi$
$132$	−1542.37	−1.01702
$133$	182.013	0.118666
$134$	−776.023	−0.500285
$135$	476.544	0.303810
$136$	1596.64	1.00670
$137$	1668.69	1.04063	0.520314	−	0.853975i	$-0.325815\pi$
$137$	1668.69	1.04063	0.520314	+	0.853975i	$0.325815\pi$
$138$	1399.61	0.863352
$139$	1024.13	0.624935	0.312467	−	0.949928i	$-0.398844\pi$
$139$	1024.13	0.624935	0.312467	+	0.949928i	$0.398844\pi$
$140$	−230.669	−0.139250
$141$	1051.16	0.627825
$142$	−1691.37	−0.999554
$143$	−571.348	−0.334116
$144$	4.06021	0.00234966
$145$	−562.994	−0.322442
$146$	1859.15	1.05386
$147$	452.882	0.254103
$148$	−139.436	−0.0774430
$149$	878.792	0.483177	0.241589	−	0.970379i	$-0.422332\pi$
$149$	878.792	0.483177	0.241589	+	0.970379i	$0.422332\pi$
$150$	−1131.44	−0.615877
$151$	3139.46	1.69196	0.845979	−	0.533217i	$-0.179017\pi$
$151$	3139.46	1.69196	0.845979	+	0.533217i	$0.179017\pi$
$152$	269.852	0.143999
$153$	−23.8447	−0.0125995
$154$	2152.99	1.12657
$155$	−93.3673	−0.0483835
$156$	180.633	0.0927063
$157$	2759.99	1.40300	0.701500	−	0.712670i	$-0.252514\pi$
$157$	2759.99	1.40300	0.701500	+	0.712670i	$0.252514\pi$
$158$	−1903.19	−0.958290
$159$	82.3146	0.0410564
$160$	−564.822	−0.279082
$161$	2245.37	1.09913
$162$	1387.78	0.673053
$163$	−1611.72	−0.774476	−0.387238	−	0.921980i	$-0.626571\pi$
$163$	−1611.72	−0.774476	−0.387238	+	0.921980i	$0.626571\pi$
$164$	962.734	0.458396
$165$	1216.84	0.574125
$166$	−2148.22	−1.00442
$167$	−4137.77	−1.91731	−0.958654	−	0.284576i	$-0.908147\pi$
$167$	−4137.77	−1.91731	−0.958654	+	0.284576i	$0.908147\pi$
$168$	−1953.59	−0.897161
$169$	−2130.09	−0.969544
$170$	−438.888	−0.198007
$171$	−4.03004	−0.00180225
$172$	0	0
$173$	2407.99	1.05825	0.529123	−	0.848545i	$-0.322521\pi$
$173$	2407.99	1.05825	0.529123	+	0.848545i	$0.322521\pi$
$174$	−1661.31	−0.723815
$175$	−1815.15	−0.784070
$176$	801.663	0.343339
$177$	−2342.14	−0.994611
$178$	−21.4095	−0.00901524
$179$	−466.200	−0.194667	−0.0973335	−	0.995252i	$-0.531031\pi$
$179$	−466.200	−0.194667	−0.0973335	+	0.995252i	$0.531031\pi$
$180$	5.10735	0.00211488
$181$	−1962.00	−0.805713	−0.402857	−	0.915263i	$-0.631983\pi$
$181$	−1962.00	−0.805713	−0.402857	+	0.915263i	$0.631983\pi$
$182$	−252.144	−0.102693
$183$	−102.881	−0.0415583
$184$	3328.97	1.33378
$185$	110.007	0.0437181
$186$	−275.513	−0.108611
$187$	−4707.98	−1.84108
$188$	871.110	0.337937
$189$	2255.96	0.868238
$190$	−74.1774	−0.0283231
$191$	−1153.86	−0.437122	−0.218561	−	0.975823i	$-0.570136\pi$
$191$	−1153.86	−0.437122	−0.218561	+	0.975823i	$0.570136\pi$
$192$	−2140.68	−0.804637
$193$	−1488.51	−0.555158	−0.277579	−	0.960703i	$-0.589532\pi$
$193$	−1488.51	−0.555158	−0.277579	+	0.960703i	$0.589532\pi$
$194$	−2286.70	−0.846265
$195$	−142.508	−0.0523345
$196$	375.311	0.136775
$197$	−1195.20	−0.432258	−0.216129	−	0.976365i	$-0.569343\pi$
$197$	−1195.20	−0.432258	−0.216129	+	0.976365i	$0.569343\pi$
$198$	−47.6703	−0.0171100
$199$	−4676.00	−1.66569	−0.832847	−	0.553504i	$-0.813290\pi$
$199$	−4676.00	−1.66569	−0.832847	+	0.553504i	$0.813290\pi$
$200$	−2691.13	−0.951459
$201$	−2076.32	−0.728620
$202$	−1930.07	−0.672274
$203$	−2665.21	−0.921485
$204$	1488.44	0.510840
$205$	−759.539	−0.258773
$206$	2433.16	0.822943
$207$	−49.7157	−0.0166932
$208$	−93.8857	−0.0312971
$209$	−795.706	−0.263350
$210$	537.007	0.176462
$211$	−2421.64	−0.790107	−0.395053	−	0.918658i	$-0.629274\pi$
$211$	−2421.64	−0.790107	−0.395053	+	0.918658i	$0.629274\pi$
$212$	68.2155	0.0220993
$213$	−4525.42	−1.45576
$214$	2101.77	0.671373
$215$	0	0
$216$	3344.68	1.05360
$217$	−442.001	−0.138272
$218$	−2044.73	−0.635261
$219$	4974.32	1.53486
$220$	1008.41	0.309033
$221$	551.369	0.167824
$222$	324.613	0.0981380
$223$	−4896.75	−1.47045	−0.735226	−	0.677822i	$-0.762924\pi$
$223$	−4896.75	−1.47045	−0.735226	+	0.677822i	$0.762924\pi$
$224$	−2673.87	−0.797568
$225$	40.1901	0.0119082
$226$	1427.30	0.420099
$227$	−3993.62	−1.16769	−0.583845	−	0.811865i	$-0.698452\pi$
$227$	−3993.62	−1.16769	−0.583845	+	0.811865i	$0.698452\pi$
$228$	251.564	0.0730711
$229$	3473.20	1.00225	0.501126	−	0.865374i	$-0.332919\pi$
$229$	3473.20	1.00225	0.501126	+	0.865374i	$0.332919\pi$
$230$	−915.074	−0.262340
$231$	5760.51	1.64075
$232$	−3951.44	−1.11821
$233$	2122.93	0.596900	0.298450	−	0.954425i	$-0.403530\pi$
$233$	2122.93	0.596900	0.298450	+	0.954425i	$0.403530\pi$
$234$	5.58284	0.00155967
$235$	−687.253	−0.190772
$236$	−1940.97	−0.535366
$237$	−5092.17	−1.39566
$238$	−2077.70	−0.565871
$239$	−6742.16	−1.82475	−0.912373	−	0.409360i	$-0.865752\pi$
$239$	−6742.16	−1.82475	−0.912373	+	0.409360i	$0.865752\pi$
$240$	199.955	0.0537792
$241$	4998.98	1.33615	0.668075	−	0.744094i	$-0.267118\pi$
$241$	4998.98	1.33615	0.668075	+	0.744094i	$0.267118\pi$
$242$	−6844.31	−1.81805
$243$	−99.2547	−0.0262024
$244$	−85.2590	−0.0223695
$245$	−296.098	−0.0772122
$246$	−2241.29	−0.580892
$247$	93.1880	0.0240057
$248$	−655.309	−0.167791
$249$	−5747.76	−1.46285
$250$	1553.65	0.393046
$251$	4848.72	1.21932	0.609658	−	0.792665i	$-0.291307\pi$
$251$	4848.72	1.21932	0.609658	+	0.792665i	$0.291307\pi$
$252$	24.1782	0.00604398
$253$	−9816.06	−2.43925
$254$	−3891.70	−0.961366
$255$	−1174.29	−0.288379
$256$	−4357.06	−1.06373
$257$	501.910	0.121822	0.0609111	−	0.998143i	$-0.480599\pi$
$257$	501.910	0.121822	0.0609111	+	0.998143i	$0.480599\pi$
$258$	0	0
$259$	520.772	0.124939
$260$	−118.099	−0.0281699
$261$	59.0118	0.0139952
$262$	3897.91	0.919136
$263$	−1969.28	−0.461715	−0.230857	−	0.972988i	$-0.574153\pi$
$263$	−1969.28	−0.461715	−0.230857	+	0.972988i	$0.574153\pi$
$264$	8540.52	1.99103
$265$	−53.8179	−0.0124755
$266$	−351.156	−0.0809428
$267$	−57.2832	−0.0131299
$268$	−1720.68	−0.392192
$269$	3839.22	0.870190	0.435095	−	0.900385i	$-0.356715\pi$
$269$	3839.22	0.870190	0.435095	+	0.900385i	$0.356715\pi$
$270$	−919.392	−0.207231
$271$	−6439.13	−1.44335	−0.721677	−	0.692230i	$-0.756629\pi$
$271$	−6439.13	−1.44335	−0.721677	+	0.692230i	$0.756629\pi$
$272$	−773.630	−0.172457
$273$	−674.635	−0.149563
$274$	−3219.40	−0.709821
$275$	7935.28	1.74006
$276$	3103.36	0.676813
$277$	−2305.14	−0.500009	−0.250004	−	0.968245i	$-0.580432\pi$
$277$	−2305.14	−0.500009	−0.250004	+	0.968245i	$0.580432\pi$
$278$	−1975.85	−0.426273
$279$	9.78656	0.00210002
$280$	1277.27	0.272613
$281$	−7575.90	−1.60833	−0.804164	−	0.594408i	$-0.797387\pi$
$281$	−7575.90	−1.60833	−0.804164	+	0.594408i	$0.797387\pi$
$282$	−2027.99	−0.428244
$283$	2188.15	0.459619	0.229809	−	0.973236i	$-0.426190\pi$
$283$	2188.15	0.459619	0.229809	+	0.973236i	$0.426190\pi$
$284$	−3750.29	−0.783588
$285$	−198.469	−0.0412501
$286$	1102.30	0.227903
$287$	−3595.66	−0.739531
$288$	59.2034	0.0121132
$289$	−369.649	−0.0752389
$290$	1086.18	0.219940
$291$	−6118.28	−1.23251
$292$	4122.30	0.826163
$293$	−7599.80	−1.51531	−0.757654	−	0.652656i	$-0.773655\pi$
$293$	−7599.80	−1.51531	−0.757654	+	0.652656i	$0.773655\pi$
$294$	−873.742	−0.173325
$295$	1531.31	0.302225
$296$	772.094	0.151612
$297$	−9862.38	−1.92685
$298$	−1695.45	−0.329579
$299$	1149.59	0.222350
$300$	−2508.75	−0.482809
$301$	0	0
$302$	−6056.93	−1.15410
$303$	−5164.08	−0.979105
$304$	−130.753	−0.0246684
$305$	67.2642	0.0126280
$306$	46.0033	0.00859424
$307$	−1884.59	−0.350355	−0.175178	−	0.984537i	$-0.556050\pi$
$307$	−1884.59	−0.350355	−0.175178	+	0.984537i	$0.556050\pi$
$308$	4773.83	0.883164
$309$	6510.15	1.19854
$310$	180.133	0.0330027
$311$	5212.18	0.950339	0.475170	−	0.879894i	$-0.342387\pi$
$311$	5212.18	0.950339	0.475170	+	0.879894i	$0.342387\pi$
$312$	−1000.21	−0.181493
$313$	7615.08	1.37517	0.687587	−	0.726102i	$-0.258670\pi$
$313$	7615.08	1.37517	0.687587	+	0.726102i	$0.258670\pi$
$314$	−5324.82	−0.956996
$315$	−19.0751	−0.00341195
$316$	−4219.96	−0.751239
$317$	5652.02	1.00142	0.500709	−	0.865616i	$-0.333073\pi$
$317$	5652.02	1.00142	0.500709	+	0.865616i	$0.333073\pi$
$318$	−158.809	−0.0280049
$319$	11651.5	2.04501
$320$	1399.59	0.244499
$321$	5623.47	0.977793
$322$	−4331.97	−0.749724
$323$	767.882	0.132279
$324$	3077.15	0.527632
$325$	−929.329	−0.158615
$326$	3109.47	0.528276
$327$	−5470.88	−0.925200
$328$	−5330.92	−0.897411
$329$	−3253.46	−0.545195
$330$	−2347.63	−0.391615
$331$	3192.18	0.530085	0.265042	−	0.964237i	$-0.414614\pi$
$331$	3192.18	0.530085	0.265042	+	0.964237i	$0.414614\pi$
$332$	−4763.26	−0.787404
$333$	−11.5307	−0.00189753
$334$	7982.96	1.30781
$335$	1357.52	0.221400
$336$	946.586	0.153692
$337$	409.642	0.0662155	0.0331077	−	0.999452i	$-0.489460\pi$
$337$	409.642	0.0662155	0.0331077	+	0.999452i	$0.489460\pi$
$338$	4109.56	0.661333
$339$	3818.87	0.611836
$340$	−973.151	−0.155225
$341$	1932.30	0.306861
$342$	7.77512	0.00122933
$343$	−6881.86	−1.08334
$344$	0	0
$345$	−2448.37	−0.382074
$346$	−4645.72	−0.721837
$347$	−4000.50	−0.618899	−0.309449	−	0.950916i	$-0.600145\pi$
$347$	−4000.50	−0.618899	−0.309449	+	0.950916i	$0.600145\pi$
$348$	−3683.64	−0.567425
$349$	−3180.70	−0.487848	−0.243924	−	0.969794i	$-0.578435\pi$
$349$	−3180.70	−0.487848	−0.243924	+	0.969794i	$0.578435\pi$
$350$	3501.95	0.534820
$351$	1155.02	0.175642
$352$	11689.3	1.77001
$353$	5857.43	0.883171	0.441585	−	0.897219i	$-0.354416\pi$
$353$	5857.43	0.883171	0.441585	+	0.897219i	$0.354416\pi$
$354$	4518.67	0.678432
$355$	2958.75	0.442350
$356$	−47.4716	−0.00706738
$357$	−5559.08	−0.824139
$358$	899.435	0.132784
$359$	−4592.75	−0.675198	−0.337599	−	0.941290i	$-0.609615\pi$
$359$	−4592.75	−0.675198	−0.337599	+	0.941290i	$0.609615\pi$
$360$	−28.2807	−0.00414035
$361$	−6729.22	−0.981079
$362$	3785.26	0.549583
$363$	−18312.6	−2.64783
$364$	−559.081	−0.0805050
$365$	−3252.25	−0.466385
$366$	198.487	0.0283472
$367$	−4201.58	−0.597604	−0.298802	−	0.954315i	$-0.596587\pi$
$367$	−4201.58	−0.597604	−0.298802	+	0.954315i	$0.596587\pi$
$368$	−1613.01	−0.228488
$369$	79.6133	0.0112317
$370$	−212.235	−0.0298204
$371$	−254.774	−0.0356529
$372$	−610.898	−0.0851441
$373$	−4230.27	−0.587226	−0.293613	−	0.955924i	$-0.594858\pi$
$373$	−4230.27	−0.587226	−0.293613	+	0.955924i	$0.594858\pi$
$374$	9083.07	1.25581
$375$	4156.94	0.572436
$376$	−4823.57	−0.661587
$377$	−1364.55	−0.186414
$378$	−4352.41	−0.592232
$379$	1777.38	0.240892	0.120446	−	0.992720i	$-0.461568\pi$
$379$	1777.38	0.240892	0.120446	+	0.992720i	$0.461568\pi$
$380$	−164.474	−0.0222036
$381$	−10412.6	−1.40014
$382$	2226.13	0.298164
$383$	6157.25	0.821464	0.410732	−	0.911756i	$-0.365273\pi$
$383$	6157.25	0.821464	0.410732	+	0.911756i	$0.365273\pi$
$384$	−2781.17	−0.369599
$385$	−3766.27	−0.498563
$386$	2871.77	0.378677
$387$	0	0
$388$	−5070.32	−0.663419
$389$	1595.98	0.208019	0.104010	−	0.994576i	$-0.466833\pi$
$389$	1595.98	0.208019	0.104010	+	0.994576i	$0.466833\pi$
$390$	274.940	0.0356978
$391$	9472.81	1.22522
$392$	−2078.20	−0.267767
$393$	10429.2	1.33864
$394$	2305.90	0.294846
$395$	3329.30	0.424089
$396$	−105.700	−0.0134132
$397$	6611.68	0.835846	0.417923	−	0.908482i	$-0.362758\pi$
$397$	6611.68	0.835846	0.417923	+	0.908482i	$0.362758\pi$
$398$	9021.37	1.13618
$399$	−939.552	−0.117886
$400$	1303.95	0.162994
$401$	2529.14	0.314961	0.157480	−	0.987522i	$-0.449663\pi$
$401$	2529.14	0.314961	0.157480	+	0.987522i	$0.449663\pi$
$402$	4005.83	0.496997
$403$	−226.298	−0.0279720
$404$	−4279.56	−0.527020
$405$	−2427.68	−0.297858
$406$	5141.98	0.628552
$407$	−2276.66	−0.277272
$408$	−8241.87	−1.00008
$409$	10821.3	1.30826	0.654128	−	0.756384i	$-0.273036\pi$
$409$	10821.3	1.30826	0.654128	+	0.756384i	$0.273036\pi$
$410$	1465.37	0.176511
$411$	−8613.80	−1.03379
$412$	5395.07	0.645136
$413$	7249.23	0.863707
$414$	95.9162	0.0113865
$415$	3757.93	0.444505
$416$	−1368.98	−0.161346
$417$	−5286.58	−0.620827
$418$	1535.15	0.179633
$419$	4479.11	0.522240	0.261120	−	0.965306i	$-0.415908\pi$
$419$	4479.11	0.522240	0.261120	+	0.965306i	$0.415908\pi$
$420$	1190.71	0.138335
$421$	−7401.58	−0.856843	−0.428421	−	0.903579i	$-0.640930\pi$
$421$	−7401.58	−0.856843	−0.428421	+	0.903579i	$0.640930\pi$
$422$	4672.05	0.538938
$423$	72.0365	0.00828022
$424$	−377.727	−0.0432643
$425$	−7657.79	−0.874017
$426$	8730.86	0.992984
$427$	318.429	0.0360887
$428$	4660.27	0.526314
$429$	2949.30	0.331920
$430$	0	0
$431$	−8995.30	−1.00531	−0.502655	−	0.864487i	$-0.667643\pi$
$431$	−8995.30	−1.00531	−0.502655	+	0.864487i	$0.667643\pi$
$432$	−1620.62	−0.180491
$433$	3439.01	0.381682	0.190841	−	0.981621i	$-0.438879\pi$
$433$	3439.01	0.381682	0.190841	+	0.981621i	$0.438879\pi$
$434$	852.749	0.0943163
$435$	2906.17	0.320323
$436$	−4533.81	−0.498005
$437$	1601.02	0.175257
$438$	−9596.92	−1.04694
$439$	3495.75	0.380052	0.190026	−	0.981779i	$-0.439143\pi$
$439$	3495.75	0.380052	0.190026	+	0.981779i	$0.439143\pi$
$440$	−5583.86	−0.605000
$441$	31.0364	0.00335130
$442$	−1063.75	−0.114474
$443$	6848.31	0.734477	0.367238	−	0.930127i	$-0.380303\pi$
$443$	6848.31	0.734477	0.367238	+	0.930127i	$0.380303\pi$
$444$	719.768	0.0769340
$445$	37.4522	0.00398967
$446$	9447.27	1.00301
$447$	−4536.32	−0.480002
$448$	6625.68	0.698736
$449$	−7538.92	−0.792391	−0.396196	−	0.918166i	$-0.629670\pi$
$449$	−7538.92	−0.792391	−0.396196	+	0.918166i	$0.629670\pi$
$450$	−77.5384	−0.00812265
$451$	15719.2	1.64121
$452$	3164.76	0.329331
$453$	−16205.9	−1.68084
$454$	7704.85	0.796490
$455$	441.081	0.0454466
$456$	−1392.98	−0.143053
$457$	1423.34	0.145692	0.0728458	−	0.997343i	$-0.476792\pi$
$457$	1423.34	0.145692	0.0728458	+	0.997343i	$0.476792\pi$
$458$	−6700.82	−0.683643
$459$	9517.51	0.967841
$460$	−2029.00	−0.205658
$461$	−13736.8	−1.38782	−0.693910	−	0.720062i	$-0.744113\pi$
$461$	−13736.8	−1.38782	−0.693910	+	0.720062i	$0.744113\pi$
$462$	−11113.7	−1.11917
$463$	−13465.8	−1.35164	−0.675819	−	0.737068i	$-0.736210\pi$
$463$	−13465.8	−1.35164	−0.675819	+	0.737068i	$0.736210\pi$
$464$	1914.61	0.191560
$465$	481.962	0.0480655
$466$	−4095.75	−0.407150
$467$	−16270.0	−1.61218	−0.806088	−	0.591796i	$-0.798419\pi$
$467$	−16270.0	−1.61218	−0.806088	+	0.591796i	$0.798419\pi$
$468$	12.3789	0.00122268
$469$	6426.49	0.632724
$470$	1325.91	0.130127
$471$	−14247.1	−1.39378
$472$	10747.7	1.04810
$473$	0	0
$474$	9824.28	0.951992
$475$	−1294.26	−0.125020
$476$	−4606.90	−0.443607
$477$	5.64108	0.000541483 0
$478$	13007.6	1.24467
$479$	−16819.6	−1.60440	−0.802198	−	0.597058i	$-0.796336\pi$
$479$	−16819.6	−1.60440	−0.802198	+	0.597058i	$0.796336\pi$
$480$	2915.61	0.277247
$481$	266.627	0.0252748
$482$	−9644.48	−0.911399
$483$	−11590.6	−1.09190
$484$	−15176.0	−1.42524
$485$	4000.18	0.374513
$486$	191.491	0.0178729
$487$	8286.88	0.771077	0.385539	−	0.922692i	$-0.374016\pi$
$487$	8286.88	0.771077	0.385539	+	0.922692i	$0.374016\pi$
$488$	472.102	0.0437931
$489$	8319.69	0.769385
$490$	571.259	0.0526670
$491$	−10993.9	−1.01048	−0.505241	−	0.862978i	$-0.668596\pi$
$491$	−10993.9	−1.01048	−0.505241	+	0.862978i	$0.668596\pi$
$492$	−4969.63	−0.455383
$493$	−11244.1	−1.02720
$494$	−179.787	−0.0163745
$495$	83.3908	0.00757199
$496$	317.521	0.0287442
$497$	14006.8	1.26416
$498$	11089.1	0.997820
$499$	−11949.6	−1.07202	−0.536008	−	0.844213i	$-0.680068\pi$
$499$	−11949.6	−1.07202	−0.536008	+	0.844213i	$0.680068\pi$
$500$	3444.93	0.308124
$501$	21359.2	1.90471
$502$	−9354.59	−0.831704
$503$	−20094.8	−1.78128	−0.890639	−	0.454710i	$-0.849743\pi$
$503$	−20094.8	−1.78128	−0.890639	+	0.454710i	$0.849743\pi$
$504$	−133.881	−0.0118324
$505$	3376.32	0.297513
$506$	18938.0	1.66383
$507$	10995.5	0.963171
$508$	−8629.10	−0.753651
$509$	6860.23	0.597396	0.298698	−	0.954348i	$-0.403448\pi$
$509$	6860.23	0.597396	0.298698	+	0.954348i	$0.403448\pi$
$510$	2265.54	0.196706
$511$	−15396.2	−1.33285
$512$	4095.81	0.353537
$513$	1608.57	0.138441
$514$	−968.331	−0.0830958
$515$	−4256.38	−0.364192
$516$	0	0
$517$	14223.1	1.20993
$518$	−1004.72	−0.0852218
$519$	−12430.1	−1.05129
$520$	653.946	0.0551489
$521$	425.093	0.0357460	0.0178730	−	0.999840i	$-0.494311\pi$
$521$	425.093	0.0357460	0.0178730	+	0.999840i	$0.494311\pi$
$522$	−113.851	−0.00954621
$523$	−6960.22	−0.581930	−0.290965	−	0.956734i	$-0.593976\pi$
$523$	−6960.22	−0.581930	−0.290965	+	0.956734i	$0.593976\pi$
$524$	8642.87	0.720545
$525$	9369.79	0.778917
$526$	3799.31	0.314939
$527$	−1864.73	−0.154134
$528$	−4138.19	−0.341082
$529$	7583.64	0.623296
$530$	103.830	0.00850963
$531$	−160.509	−0.0131177
$532$	−778.622	−0.0634540
$533$	−1840.93	−0.149605
$534$	110.516	0.00895599
$535$	−3676.67	−0.297114
$536$	9527.89	0.767802
$537$	2406.52	0.193388
$538$	−7406.96	−0.593563
$539$	6127.93	0.489701
$540$	−2038.58	−0.162456
$541$	−5384.62	−0.427916	−0.213958	−	0.976843i	$-0.568636\pi$
$541$	−5384.62	−0.427916	−0.213958	+	0.976843i	$0.568636\pi$
$542$	12423.0	0.984523
$543$	10127.8	0.800418
$544$	−11280.6	−0.889064
$545$	3576.90	0.281133
$546$	1301.57	0.102018
$547$	−10869.3	−0.849614	−0.424807	−	0.905284i	$-0.639658\pi$
$547$	−10869.3	−0.849614	−0.424807	+	0.905284i	$0.639658\pi$
$548$	−7138.40	−0.556455
$549$	−7.05050	−0.000548102 0
$550$	−15309.5	−1.18690
$551$	−1900.39	−0.146931
$552$	−17184.2	−1.32501
$553$	15760.9	1.21198
$554$	4447.29	0.341060
$555$	−567.854	−0.0434307
$556$	−4381.08	−0.334171
$557$	−8454.09	−0.643108	−0.321554	−	0.946891i	$-0.604205\pi$
$557$	−8454.09	−0.643108	−0.321554	+	0.946891i	$0.604205\pi$
$558$	−18.8811	−0.00143244
$559$	0	0
$560$	−618.885	−0.0467012
$561$	24302.6	1.82898
$562$	14616.1	1.09705
$563$	−5629.33	−0.421400	−0.210700	−	0.977551i	$-0.567574\pi$
$563$	−5629.33	−0.421400	−0.210700	+	0.977551i	$0.567574\pi$
$564$	−4496.67	−0.335716
$565$	−2496.80	−0.185914
$566$	−4221.58	−0.313509
$567$	−11492.7	−0.851229
$568$	20766.4	1.53405
$569$	−2100.00	−0.154721	−0.0773606	−	0.997003i	$-0.524649\pi$
$569$	−2100.00	−0.154721	−0.0773606	+	0.997003i	$0.524649\pi$
$570$	382.904	0.0281370
$571$	−25603.4	−1.87648	−0.938241	−	0.345984i	$-0.887545\pi$
$571$	−25603.4	−1.87648	−0.938241	+	0.345984i	$0.887545\pi$
$572$	2444.13	0.178661
$573$	5956.22	0.434249
$574$	6937.08	0.504439
$575$	−15966.4	−1.15799
$576$	−146.702	−0.0106121
$577$	−15173.0	−1.09473	−0.547365	−	0.836894i	$-0.684369\pi$
$577$	−15173.0	−1.09473	−0.547365	+	0.836894i	$0.684369\pi$
$578$	713.160	0.0513210
$579$	7683.70	0.551509
$580$	2408.39	0.172419
$581$	17790.1	1.27032
$582$	11803.9	0.840703
$583$	1113.80	0.0791230
$584$	−22826.3	−1.61740
$585$	−9.76619	−0.000690226 0
$586$	14662.2	1.03360
$587$	−1687.84	−0.118679	−0.0593397	−	0.998238i	$-0.518900\pi$
$587$	−1687.84	−0.118679	−0.0593397	+	0.998238i	$0.518900\pi$
$588$	−1937.36	−0.135876
$589$	−315.161	−0.0220475
$590$	−2954.34	−0.206150
$591$	6169.64	0.429416
$592$	−374.107	−0.0259725
$593$	−4751.03	−0.329007	−0.164504	−	0.986376i	$-0.552602\pi$
$593$	−4751.03	−0.329007	−0.164504	+	0.986376i	$0.552602\pi$
$594$	19027.4	1.31432
$595$	3634.57	0.250425
$596$	−3759.33	−0.258369
$597$	24137.5	1.65475
$598$	−2217.90	−0.151667
$599$	17759.3	1.21140	0.605699	−	0.795694i	$-0.292894\pi$
$599$	17759.3	1.21140	0.605699	+	0.795694i	$0.292894\pi$
$600$	13891.6	0.945205
$601$	333.783	0.0226544	0.0113272	−	0.999936i	$-0.496394\pi$
$601$	333.783	0.0226544	0.0113272	+	0.999936i	$0.496394\pi$
$602$	0	0
$603$	−142.292	−0.00960958
$604$	−13430.1	−0.904739
$605$	11972.9	0.804576
$606$	9963.02	0.667855
$607$	7180.35	0.480134	0.240067	−	0.970756i	$-0.422831\pi$
$607$	7180.35	0.480134	0.240067	+	0.970756i	$0.422831\pi$
$608$	−1906.56	−0.127173
$609$	13757.8	0.915428
$610$	−129.772	−0.00861365
$611$	−1665.72	−0.110291
$612$	102.004	0.00673734
$613$	−3342.98	−0.220264	−0.110132	−	0.993917i	$-0.535127\pi$
$613$	−3342.98	−0.220264	−0.110132	+	0.993917i	$0.535127\pi$
$614$	3635.92	0.238980
$615$	3920.74	0.257073
$616$	−26434.0	−1.72899
$617$	22329.5	1.45697	0.728487	−	0.685059i	$-0.240224\pi$
$617$	22329.5	1.45697	0.728487	+	0.685059i	$0.240224\pi$
$618$	−12560.0	−0.817534
$619$	8711.99	0.565694	0.282847	−	0.959165i	$-0.408721\pi$
$619$	8711.99	0.565694	0.282847	+	0.959165i	$0.408721\pi$
$620$	399.410	0.0258721
$621$	19843.8	1.28230
$622$	−10055.8	−0.648234
$623$	177.299	0.0114018
$624$	484.638	0.0310914
$625$	11483.4	0.734936
$626$	−14691.7	−0.938017
$627$	4107.44	0.261619
$628$	−11806.8	−0.750225
$629$	2197.04	0.139272
$630$	36.8015	0.00232731
$631$	−19946.1	−1.25839	−0.629194	−	0.777248i	$-0.716615\pi$
$631$	−19946.1	−1.25839	−0.629194	+	0.777248i	$0.716615\pi$
$632$	23367.1	1.47072
$633$	12500.5	0.784913
$634$	−10904.4	−0.683074
$635$	6807.84	0.425450
$636$	−352.128	−0.0219541
$637$	−717.664	−0.0446388
$638$	−22479.2	−1.39492
$639$	−310.130	−0.0191996
$640$	1818.35	0.112307
$641$	−3937.29	−0.242611	−0.121306	−	0.992615i	$-0.538708\pi$
$641$	−3937.29	−0.242611	−0.121306	+	0.992615i	$0.538708\pi$
$642$	−10849.3	−0.666960
$643$	16927.4	1.03818	0.519092	−	0.854718i	$-0.326270\pi$
$643$	16927.4	1.03818	0.519092	+	0.854718i	$0.326270\pi$
$644$	−9605.31	−0.587736
$645$	0	0
$646$	−1481.47	−0.0902284
$647$	−6597.35	−0.400879	−0.200439	−	0.979706i	$-0.564237\pi$
$647$	−6597.35	−0.400879	−0.200439	+	0.979706i	$0.564237\pi$
$648$	−17039.0	−1.03295
$649$	−31691.4	−1.91679
$650$	1792.95	0.108193
$651$	2281.61	0.137363
$652$	6894.66	0.414135
$653$	9943.15	0.595874	0.297937	−	0.954586i	$-0.403702\pi$
$653$	9943.15	0.595874	0.297937	+	0.954586i	$0.403702\pi$
$654$	10554.9	0.631086
$655$	−6818.70	−0.406761
$656$	2583.02	0.153735
$657$	340.894	0.0202428
$658$	6276.87	0.371881
$659$	−13660.7	−0.807504	−0.403752	−	0.914868i	$-0.632294\pi$
$659$	−13660.7	−0.807504	−0.403752	+	0.914868i	$0.632294\pi$
$660$	−5205.43	−0.307002
$661$	10630.4	0.625526	0.312763	−	0.949831i	$-0.398745\pi$
$661$	10630.4	0.625526	0.312763	+	0.949831i	$0.398745\pi$
$662$	−6158.65	−0.361575
$663$	−2846.17	−0.166721
$664$	26375.5	1.54152
$665$	614.286	0.0358210
$666$	22.2460	0.00129432
$667$	−23443.7	−1.36093
$668$	17700.7	1.02524
$669$	25277.0	1.46079
$670$	−2619.04	−0.151019
$671$	−1392.08	−0.0800902
$672$	13802.5	0.792326
$673$	−34132.6	−1.95500	−0.977499	−	0.210938i	$-0.932348\pi$
$673$	−34132.6	−1.95500	−0.977499	+	0.210938i	$0.932348\pi$
$674$	−790.319	−0.0451661
$675$	−16041.7	−0.914734
$676$	9112.16	0.518443
$677$	9361.83	0.531469	0.265734	−	0.964046i	$-0.414386\pi$
$677$	9361.83	0.531469	0.265734	+	0.964046i	$0.414386\pi$
$678$	−7367.71	−0.417338
$679$	18936.9	1.07029
$680$	5388.60	0.303887
$681$	20615.1	1.16002
$682$	−3727.96	−0.209312
$683$	−597.134	−0.0334534	−0.0167267	−	0.999860i	$-0.505325\pi$
$683$	−597.134	−0.0334534	−0.0167267	+	0.999860i	$0.505325\pi$
$684$	17.2399	0.000963717 0
$685$	5631.77	0.314129
$686$	13277.1	0.738954
$687$	−17928.7	−0.995664
$688$	0	0
$689$	−130.441	−0.00721247
$690$	4723.61	0.260616
$691$	35607.4	1.96031	0.980153	−	0.198244i	$-0.0635240\pi$
$691$	35607.4	1.96031	0.980153	+	0.198244i	$0.0635240\pi$
$692$	−10301.0	−0.565875
$693$	394.772	0.0216395
$694$	7718.12	0.422155
$695$	3456.41	0.188646
$696$	20397.3	1.11086
$697$	−15169.5	−0.824369
$698$	6136.50	0.332765
$699$	−10958.6	−0.592977
$700$	7764.90	0.419265
$701$	−7080.78	−0.381508	−0.190754	−	0.981638i	$-0.561093\pi$
$701$	−7080.78	−0.381508	−0.190754	+	0.981638i	$0.561093\pi$
$702$	−2228.37	−0.119807
$703$	371.327	0.0199216
$704$	−28965.5	−1.55068
$705$	3547.60	0.189518
$706$	−11300.7	−0.602417
$707$	15983.5	0.850242
$708$	10019.3	0.531848
$709$	11050.6	0.585349	0.292674	−	0.956212i	$-0.405455\pi$
$709$	11050.6	0.585349	0.292674	+	0.956212i	$0.405455\pi$
$710$	−5708.30	−0.301730
$711$	−348.970	−0.0184070
$712$	262.863	0.0138360
$713$	−3887.92	−0.204213
$714$	10725.1	0.562151
$715$	−1928.27	−0.100858
$716$	1994.33	0.104094
$717$	34803.1	1.81275
$718$	8860.76	0.460558
$719$	16357.2	0.848428	0.424214	−	0.905562i	$-0.360550\pi$
$719$	16357.2	0.848428	0.424214	+	0.905562i	$0.360550\pi$
$720$	13.7030	0.000709280 0
$721$	−20149.7	−1.04080
$722$	12982.6	0.669201
$723$	−25804.7	−1.32737
$724$	8393.10	0.430839
$725$	18951.8	0.970832
$726$	35330.4	1.80611
$727$	−1844.85	−0.0941153	−0.0470576	−	0.998892i	$-0.514984\pi$
$727$	−1844.85	−0.0941153	−0.0470576	+	0.998892i	$0.514984\pi$
$728$	3095.78	0.157606
$729$	19934.1	1.01276
$730$	6274.54	0.318125
$731$	0	0
$732$	440.107	0.0222224
$733$	18675.8	0.941074	0.470537	−	0.882380i	$-0.344060\pi$
$733$	18675.8	0.941074	0.470537	+	0.882380i	$0.344060\pi$
$734$	8106.07	0.407630
$735$	1528.46	0.0767047
$736$	−23519.8	−1.17792
$737$	−28094.6	−1.40418
$738$	−153.597	−0.00766124
$739$	−32923.7	−1.63886	−0.819431	−	0.573178i	$-0.805710\pi$
$739$	−32923.7	−1.63886	−0.819431	+	0.573178i	$0.805710\pi$
$740$	−470.590	−0.0233773
$741$	−481.037	−0.0238479
$742$	491.534	0.0243191
$743$	18918.9	0.934143	0.467071	−	0.884220i	$-0.345309\pi$
$743$	18918.9	0.934143	0.467071	+	0.884220i	$0.345309\pi$
$744$	3382.71	0.166688
$745$	2965.88	0.145854
$746$	8161.43	0.400551
$747$	−393.898	−0.0192931
$748$	20140.0	0.984479
$749$	−17405.4	−0.849103
$750$	−8019.95	−0.390463
$751$	5346.38	0.259777	0.129888	−	0.991529i	$-0.458538\pi$
$751$	5346.38	0.259777	0.129888	+	0.991529i	$0.458538\pi$
$752$	2337.19	0.113336
$753$	−25029.1	−1.21130
$754$	2632.62	0.127154
$755$	10595.5	0.510743
$756$	−9650.63	−0.464272
$757$	−15569.2	−0.747519	−0.373759	−	0.927526i	$-0.621931\pi$
$757$	−15569.2	−0.747519	−0.373759	+	0.927526i	$0.621931\pi$
$758$	−3429.09	−0.164314
$759$	50670.5	2.42322
$760$	910.738	0.0434684
$761$	−23299.3	−1.10985	−0.554927	−	0.831899i	$-0.687254\pi$
$761$	−23299.3	−1.10985	−0.554927	+	0.831899i	$0.687254\pi$
$762$	20089.0	0.955047
$763$	16933.1	0.803432
$764$	4936.02	0.233742
$765$	−80.4747	−0.00380336
$766$	−11879.1	−0.560327
$767$	3711.50	0.174725
$768$	22491.1	1.05674
$769$	−21311.1	−0.999345	−0.499672	−	0.866214i	$-0.666546\pi$
$769$	−21311.1	−0.999345	−0.499672	+	0.866214i	$0.666546\pi$
$770$	7266.23	0.340074
$771$	−2590.86	−0.121021
$772$	6367.61	0.296859
$773$	−7289.12	−0.339161	−0.169580	−	0.985516i	$-0.554241\pi$
$773$	−7289.12	−0.339161	−0.169580	+	0.985516i	$0.554241\pi$
$774$	0	0
$775$	3142.98	0.145677
$776$	28075.7	1.29879
$777$	−2688.22	−0.124118
$778$	−3079.12	−0.141892
$779$	−2563.83	−0.117919
$780$	609.627	0.0279848
$781$	−61233.3	−2.80551
$782$	−18275.8	−0.835731
$783$	−23554.3	−1.07505
$784$	1006.96	0.0458710
$785$	9314.83	0.423517
$786$	−20121.0	−0.913095
$787$	36120.3	1.63602	0.818011	−	0.575202i	$-0.195077\pi$
$787$	36120.3	1.63602	0.818011	+	0.575202i	$0.195077\pi$
$788$	5112.88	0.231141
$789$	10165.4	0.458680
$790$	−6423.19	−0.289274
$791$	−11819.9	−0.531311
$792$	585.288	0.0262592
$793$	163.031	0.00730063
$794$	−12755.9	−0.570137
$795$	277.808	0.0123935
$796$	20003.2	0.890695
$797$	−13904.3	−0.617960	−0.308980	−	0.951069i	$-0.599988\pi$
$797$	−13904.3	−0.617960	−0.308980	+	0.951069i	$0.599988\pi$
$798$	1812.67	0.0804108
$799$	−13725.8	−0.607739
$800$	19013.4	0.840280
$801$	−3.92566	−0.000173167 0
$802$	−4879.45	−0.214837
$803$	67307.4	2.95794
$804$	8882.17	0.389614
$805$	7578.01	0.331788
$806$	436.595	0.0190799
$807$	−19818.0	−0.864470
$808$	23697.1	1.03176
$809$	−8897.79	−0.386687	−0.193343	−	0.981131i	$-0.561933\pi$
$809$	−8897.79	−0.386687	−0.193343	+	0.981131i	$0.561933\pi$
$810$	4683.71	0.203171
$811$	−1198.53	−0.0518941	−0.0259470	−	0.999663i	$-0.508260\pi$
$811$	−1198.53	−0.0518941	−0.0259470	+	0.999663i	$0.508260\pi$
$812$	11401.3	0.492745
$813$	33238.8	1.43387
$814$	4392.33	0.189129
$815$	−5439.48	−0.233787
$816$	3993.48	0.171323
$817$	0	0
$818$	−20877.4	−0.892372
$819$	−46.2332	−0.00197255
$820$	3249.18	0.138374
$821$	7870.63	0.334576	0.167288	−	0.985908i	$-0.446499\pi$
$821$	7870.63	0.334576	0.167288	+	0.985908i	$0.446499\pi$
$822$	16618.5	0.705155
$823$	−4023.28	−0.170404	−0.0852021	−	0.996364i	$-0.527154\pi$
$823$	−4023.28	−0.170404	−0.0852021	+	0.996364i	$0.527154\pi$
$824$	−29873.9	−1.26300
$825$	−40961.9	−1.72862
$826$	−13985.9	−0.589141
$827$	5733.09	0.241063	0.120531	−	0.992710i	$-0.461540\pi$
$827$	5733.09	0.241063	0.120531	+	0.992710i	$0.461540\pi$
$828$	212.676	0.00892632
$829$	−10598.5	−0.444032	−0.222016	−	0.975043i	$-0.571264\pi$
$829$	−10598.5	−0.444032	−0.222016	+	0.975043i	$0.571264\pi$
$830$	−7250.14	−0.303200
$831$	11899.1	0.496723
$832$	3392.25	0.141352
$833$	−5913.65	−0.245973
$834$	10199.4	0.423471
$835$	−13964.8	−0.578768
$836$	3403.90	0.140821
$837$	−3906.27	−0.161315
$838$	−8641.50	−0.356224
$839$	−36445.2	−1.49968	−0.749839	−	0.661621i	$-0.769869\pi$
$839$	−36445.2	−1.49968	−0.749839	+	0.661621i	$0.769869\pi$
$840$	−6593.29	−0.270822
$841$	3438.30	0.140978
$842$	14279.8	0.584459
$843$	39106.8	1.59776
$844$	10359.4	0.422493
$845$	−7188.95	−0.292671
$846$	−138.979	−0.00564800
$847$	56679.9	2.29934
$848$	183.022	0.00741157
$849$	−11295.2	−0.456598
$850$	14774.1	0.596174
$851$	4580.80	0.184521
$852$	19359.0	0.778437
$853$	−20345.4	−0.816663	−0.408331	−	0.912834i	$-0.633889\pi$
$853$	−20345.4	−0.816663	−0.408331	+	0.912834i	$0.633889\pi$
$854$	−614.343	−0.0246164
$855$	−13.6012	−0.000544037 0
$856$	−25805.1	−1.03038
$857$	−12713.8	−0.506764	−0.253382	−	0.967366i	$-0.581543\pi$
$857$	−12713.8	−0.506764	−0.253382	+	0.967366i	$0.581543\pi$
$858$	−5690.06	−0.226405
$859$	45841.5	1.82083	0.910415	−	0.413696i	$-0.135762\pi$
$859$	45841.5	1.82083	0.910415	+	0.413696i	$0.135762\pi$
$860$	0	0
$861$	18560.8	0.734670
$862$	17354.6	0.685729
$863$	−26896.8	−1.06092	−0.530461	−	0.847709i	$-0.677981\pi$
$863$	−26896.8	−1.06092	−0.530461	+	0.847709i	$0.677981\pi$
$864$	−23630.8	−0.930482
$865$	8126.87	0.319447
$866$	−6634.85	−0.260348
$867$	1908.13	0.0747444
$868$	1890.81	0.0739380
$869$	−68901.9	−2.68969
$870$	−5606.85	−0.218494
$871$	3290.27	0.127998
$872$	25104.9	0.974954
$873$	−419.290	−0.0162552
$874$	−3088.83	−0.119544
$875$	−12866.3	−0.497096
$876$	−21279.3	−0.820733
$877$	−10926.5	−0.420709	−0.210354	−	0.977625i	$-0.567462\pi$
$877$	−10926.5	−0.420709	−0.210354	+	0.977625i	$0.567462\pi$
$878$	−6744.32	−0.259237
$879$	39230.2	1.50535
$880$	2705.58	0.103642
$881$	42249.6	1.61569	0.807847	−	0.589392i	$-0.200633\pi$
$881$	42249.6	1.61569	0.807847	+	0.589392i	$0.200633\pi$
$882$	−59.8782	−0.00228594
$883$	17976.5	0.685118	0.342559	−	0.939496i	$-0.388706\pi$
$883$	17976.5	0.685118	0.342559	+	0.939496i	$0.388706\pi$
$884$	−2358.66	−0.0897404
$885$	−7904.62	−0.300238
$886$	−13212.4	−0.500992
$887$	−28007.5	−1.06020	−0.530100	−	0.847935i	$-0.677846\pi$
$887$	−28007.5	−1.06020	−0.530100	+	0.847935i	$0.677846\pi$
$888$	−3985.55	−0.150615
$889$	32228.4	1.21587
$890$	−72.2562	−0.00272139
$891$	50242.5	1.88910
$892$	20947.5	0.786294
$893$	−2319.82	−0.0869316
$894$	8751.89	0.327413
$895$	−1573.40	−0.0587632
$896$	8608.09	0.320955
$897$	−5934.21	−0.220889
$898$	14544.8	0.540496
$899$	4614.90	0.171208
$900$	−171.926	−0.00636765
$901$	−1074.85	−0.0397429
$902$	−30326.8	−1.11948
$903$	0	0
$904$	−17524.1	−0.644739
$905$	−6621.65	−0.243217
$906$	31265.9	1.14651
$907$	−17738.3	−0.649384	−0.324692	−	0.945820i	$-0.605261\pi$
$907$	−17738.3	−0.649384	−0.324692	+	0.945820i	$0.605261\pi$
$908$	17084.0	0.624398
$909$	−353.898	−0.0129132
$910$	−850.974	−0.0309995
$911$	−33998.3	−1.23646	−0.618230	−	0.785997i	$-0.712150\pi$
$911$	−33998.3	−1.23646	−0.618230	+	0.785997i	$0.712150\pi$
$912$	674.947	0.0245063
$913$	−77772.7	−2.81917
$914$	−2746.04	−0.0993773
$915$	−347.218	−0.0125450
$916$	−14857.8	−0.535933
$917$	−32279.8	−1.16246
$918$	−18362.0	−0.660172
$919$	−16.9598	−0.000608763 0	−0.000304381	−	1.00000i	$-0.500097\pi$
$919$	−16.9598	−0.000608763 0	−0.000304381		1.00000i	$0.500097\pi$
$920$	11235.1	0.402621
$921$	9728.24	0.348053
$922$	26502.2	0.946642
$923$	7171.25	0.255736
$924$	−24642.5	−0.877359
$925$	−3703.11	−0.131630
$926$	25979.4	0.921962
$927$	446.145	0.0158073
$928$	27917.7	0.987545
$929$	7100.88	0.250778	0.125389	−	0.992108i	$-0.459982\pi$
$929$	7100.88	0.250778	0.125389	+	0.992108i	$0.459982\pi$
$930$	−929.845	−0.0327858
$931$	−999.478	−0.0351843
$932$	−9081.54	−0.319180
$933$	−26905.3	−0.944093
$934$	31389.6	1.09968
$935$	−15889.2	−0.555757
$936$	−68.5452	−0.00239366
$937$	−8580.08	−0.299145	−0.149573	−	0.988751i	$-0.547790\pi$
$937$	−8580.08	−0.299145	−0.149573	+	0.988751i	$0.547790\pi$
$938$	−12398.6	−0.431586
$939$	−39309.0	−1.36614
$940$	2939.96	0.102011
$941$	41589.9	1.44080	0.720400	−	0.693559i	$-0.243958\pi$
$941$	41589.9	1.44080	0.720400	+	0.693559i	$0.243958\pi$
$942$	27486.7	0.950706
$943$	−31628.1	−1.09221
$944$	−5207.63	−0.179549
$945$	7613.76	0.262091
$946$	0	0
$947$	−15370.6	−0.527431	−0.263715	−	0.964601i	$-0.584948\pi$
$947$	−15370.6	−0.527431	−0.263715	+	0.964601i	$0.584948\pi$
$948$	21783.5	0.746301
$949$	−7882.61	−0.269632
$950$	2497.00	0.0852774
$951$	−29175.7	−0.994835
$952$	25509.6	0.868458
$953$	−37789.1	−1.28448	−0.642240	−	0.766504i	$-0.721995\pi$
$953$	−37789.1	−1.28448	−0.642240	+	0.766504i	$0.721995\pi$
$954$	−10.8833	−0.000369350 0
$955$	−3894.22	−0.131952
$956$	28841.9	0.975745
$957$	−60145.1	−2.03157
$958$	32449.9	1.09437
$959$	26660.8	0.897729
$960$	−7224.70	−0.242892
$961$	−29025.7	−0.974310
$962$	−514.402	−0.0172401
$963$	385.381	0.0128959
$964$	−21384.8	−0.714479
$965$	−5023.66	−0.167583
$966$	22361.6	0.744796
$967$	22769.9	0.757219	0.378610	−	0.925557i	$-0.376402\pi$
$967$	22769.9	0.757219	0.378610	+	0.925557i	$0.376402\pi$
$968$	84033.4	2.79022
$969$	−3963.80	−0.131409
$970$	−7717.50	−0.255458
$971$	−55134.9	−1.82221	−0.911103	−	0.412179i	$-0.864768\pi$
$971$	−55134.9	−1.82221	−0.911103	+	0.412179i	$0.864768\pi$
$972$	424.595	0.0140112
$973$	16362.6	0.539119
$974$	−15987.8	−0.525957
$975$	4797.20	0.157573
$976$	−228.750	−0.00750217
$977$	3131.11	0.102531	0.0512656	−	0.998685i	$-0.483674\pi$
$977$	3131.11	0.102531	0.0512656	+	0.998685i	$0.483674\pi$
$978$	−16051.1	−0.524803
$979$	−775.097	−0.0253036
$980$	1266.66	0.0412876
$981$	−374.923	−0.0122022
$982$	21210.4	0.689257
$983$	12288.8	0.398731	0.199365	−	0.979925i	$-0.436112\pi$
$983$	12288.8	0.398731	0.199365	+	0.979925i	$0.436112\pi$
$984$	27518.2	0.891512
$985$	−4033.76	−0.130483
$986$	21693.1	0.700658
$987$	16794.4	0.541611
$988$	−398.643	−0.0128366
$989$	0	0
$990$	−160.885	−0.00516491
$991$	20551.7	0.658777	0.329388	−	0.944195i	$-0.393157\pi$
$991$	20551.7	0.658777	0.329388	+	0.944195i	$0.393157\pi$
$992$	4629.89	0.148184
$993$	−16478.0	−0.526601
$994$	−27023.1	−0.862295
$995$	−15781.3	−0.502815
$996$	24588.0	0.782229
$997$	29608.1	0.940521	0.470260	−	0.882528i	$-0.344160\pi$
$997$	29608.1	0.940521	0.470260	+	0.882528i	$0.344160\pi$
$998$	23054.2	0.731231
$999$	4602.41	0.145760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.12		30
43.2	odd	14		43.4.e.a.4.7	✓	60
43.22	odd	14		43.4.e.a.11.7	yes	60
43.42	odd	2		1849.4.a.h.1.19		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.7	✓	60	43.2	odd	14
43.4.e.a.11.7	yes	60	43.22	odd	14
1849.4.a.g.1.12		30	1.1	even	1	trivial
1849.4.a.h.1.19		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)

\(f(q)\)	\(=\)	\(q-1.92929 q^{2} -5.16200 q^{3} -4.27784 q^{4} +3.37495 q^{5} +9.95900 q^{6} +15.9770 q^{7} +23.6875 q^{8} -0.353756 q^{9} +O(q^{10})\)	\(q-1.92929 q^{2} -5.16200 q^{3} -4.27784 q^{4} +3.37495 q^{5} +9.95900 q^{6} +15.9770 q^{7} +23.6875 q^{8} -0.353756 q^{9} -6.51127 q^{10} -69.8468 q^{11} +22.0822 q^{12} +8.18001 q^{13} -30.8244 q^{14} -17.4215 q^{15} -11.4774 q^{16} +67.4044 q^{17} +0.682498 q^{18} +11.3922 q^{19} -14.4375 q^{20} -82.4735 q^{21} +134.755 q^{22} +140.537 q^{23} -122.275 q^{24} -113.610 q^{25} -15.7816 q^{26} +141.200 q^{27} -68.3472 q^{28} -166.815 q^{29} +33.6112 q^{30} -27.6648 q^{31} -167.357 q^{32} +360.549 q^{33} -130.043 q^{34} +53.9218 q^{35} +1.51331 q^{36} +32.5950 q^{37} -21.9788 q^{38} -42.2252 q^{39} +79.9443 q^{40} -225.052 q^{41} +159.115 q^{42} +298.793 q^{44} -1.19391 q^{45} -271.137 q^{46} -203.633 q^{47} +59.2466 q^{48} -87.7339 q^{49} +219.186 q^{50} -347.941 q^{51} -34.9928 q^{52} -15.9463 q^{53} -272.416 q^{54} -235.730 q^{55} +378.457 q^{56} -58.8063 q^{57} +321.835 q^{58} +453.727 q^{59} +74.5264 q^{60} +19.9304 q^{61} +53.3734 q^{62} -5.65197 q^{63} +414.700 q^{64} +27.6072 q^{65} -695.605 q^{66} +402.232 q^{67} -288.345 q^{68} -725.452 q^{69} -104.031 q^{70} +876.680 q^{71} -8.37959 q^{72} -963.643 q^{73} -62.8852 q^{74} +586.453 q^{75} -48.7338 q^{76} -1115.95 q^{77} +81.4648 q^{78} +986.472 q^{79} -38.7359 q^{80} -719.323 q^{81} +434.190 q^{82} +1113.48 q^{83} +352.808 q^{84} +227.487 q^{85} +861.100 q^{87} -1654.50 q^{88} +11.0971 q^{89} +2.30340 q^{90} +130.692 q^{91} -601.194 q^{92} +142.805 q^{93} +392.868 q^{94} +38.4480 q^{95} +863.896 q^{96} +1185.25 q^{97} +169.264 q^{98} +24.7087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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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