LMFDB - Embedded newform 1849.4.a.g.1.26

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			1.26
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)

$f(q)$	$=$	$q+4.08390 q^{2} +9.96623 q^{3} +8.67820 q^{4} -12.0746 q^{5} +40.7010 q^{6} -17.5242 q^{7} +2.76970 q^{8} +72.3258 q^{9} +O(q^{10})$	\(q+4.08390 q^{2} +9.96623 q^{3} +8.67820 q^{4} -12.0746 q^{5} +40.7010 q^{6} -17.5242 q^{7} +2.76970 q^{8} +72.3258 q^{9} -49.3113 q^{10} +10.8512 q^{11} +86.4890 q^{12} -42.2519 q^{13} -71.5670 q^{14} -120.338 q^{15} -58.1144 q^{16} -5.55908 q^{17} +295.371 q^{18} -154.965 q^{19} -104.786 q^{20} -174.650 q^{21} +44.3151 q^{22} -113.312 q^{23} +27.6035 q^{24} +20.7954 q^{25} -172.552 q^{26} +451.727 q^{27} -152.079 q^{28} +23.0645 q^{29} -491.448 q^{30} +35.0562 q^{31} -259.491 q^{32} +108.145 q^{33} -22.7027 q^{34} +211.597 q^{35} +627.657 q^{36} -124.206 q^{37} -632.859 q^{38} -421.092 q^{39} -33.4429 q^{40} +285.427 q^{41} -713.254 q^{42} +94.1687 q^{44} -873.303 q^{45} -462.754 q^{46} -93.0632 q^{47} -579.182 q^{48} -35.9021 q^{49} +84.9262 q^{50} -55.4031 q^{51} -366.670 q^{52} +199.633 q^{53} +1844.81 q^{54} -131.023 q^{55} -48.5368 q^{56} -1544.41 q^{57} +94.1931 q^{58} +477.324 q^{59} -1044.32 q^{60} -622.675 q^{61} +143.166 q^{62} -1267.45 q^{63} -594.818 q^{64} +510.173 q^{65} +441.655 q^{66} -687.465 q^{67} -48.2428 q^{68} -1129.29 q^{69} +864.142 q^{70} -128.142 q^{71} +200.321 q^{72} +353.979 q^{73} -507.243 q^{74} +207.252 q^{75} -1344.81 q^{76} -190.158 q^{77} -1719.69 q^{78} +518.415 q^{79} +701.707 q^{80} +2549.22 q^{81} +1165.66 q^{82} +616.196 q^{83} -1515.65 q^{84} +67.1235 q^{85} +229.866 q^{87} +30.0545 q^{88} -92.5703 q^{89} -3566.48 q^{90} +740.430 q^{91} -983.344 q^{92} +349.378 q^{93} -380.060 q^{94} +1871.13 q^{95} -2586.15 q^{96} +1189.51 q^{97} -146.620 q^{98} +784.820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.08390	1.44388	0.721938	−	0.691958i	$-0.243252\pi$
$2$	4.08390	1.44388	0.721938	+	0.691958i	$0.243252\pi$
$3$	9.96623	1.91800	0.959001	−	0.283403i	$-0.0914633\pi$
$3$	9.96623	1.91800	0.959001	+	0.283403i	$0.0914633\pi$
$4$	8.67820	1.08478
$5$	−12.0746	−1.07998	−0.539991	−	0.841671i	$-0.681573\pi$
$5$	−12.0746	−1.07998	−0.539991	+	0.841671i	$0.681573\pi$
$6$	40.7010	2.76936
$7$	−17.5242	−0.946218	−0.473109	−	0.881004i	$-0.656868\pi$
$7$	−17.5242	−0.946218	−0.473109	+	0.881004i	$0.656868\pi$
$8$	2.76970	0.122405
$9$	72.3258	2.67873
$10$	−49.3113	−1.55936
$11$	10.8512	0.297432	0.148716	−	0.988880i	$-0.452486\pi$
$11$	10.8512	0.297432	0.148716	+	0.988880i	$0.452486\pi$
$12$	86.4890	2.08060
$13$	−42.2519	−0.901427	−0.450714	−	0.892669i	$-0.648830\pi$
$13$	−42.2519	−0.901427	−0.450714	+	0.892669i	$0.648830\pi$
$14$	−71.5670	−1.36622
$15$	−120.338	−2.07141
$16$	−58.1144	−0.908038
$17$	−5.55908	−0.0793103	−0.0396551	−	0.999213i	$-0.512626\pi$
$17$	−5.55908	−0.0793103	−0.0396551	+	0.999213i	$0.512626\pi$
$18$	295.371	3.86775
$19$	−154.965	−1.87112	−0.935561	−	0.353165i	$-0.885106\pi$
$19$	−154.965	−1.87112	−0.935561	+	0.353165i	$0.885106\pi$
$20$	−104.786	−1.17154
$21$	−174.650	−1.81485
$22$	44.3151	0.429455
$23$	−113.312	−1.02727	−0.513635	−	0.858009i	$-0.671701\pi$
$23$	−113.312	−1.02727	−0.513635	+	0.858009i	$0.671701\pi$
$24$	27.6035	0.234772
$25$	20.7954	0.166363
$26$	−172.552	−1.30155
$27$	451.727	3.21981
$28$	−152.079	−1.02643
$29$	23.0645	0.147689	0.0738444	−	0.997270i	$-0.476473\pi$
$29$	23.0645	0.147689	0.0738444	+	0.997270i	$0.476473\pi$
$30$	−491.448	−2.99086
$31$	35.0562	0.203106	0.101553	−	0.994830i	$-0.467619\pi$
$31$	35.0562	0.203106	0.101553	+	0.994830i	$0.467619\pi$
$32$	−259.491	−1.43350
$33$	108.145	0.570476
$34$	−22.7027	−0.114514
$35$	211.597	1.02190
$36$	627.657	2.90582
$37$	−124.206	−0.551872	−0.275936	−	0.961176i	$-0.588988\pi$
$37$	−124.206	−0.551872	−0.275936	+	0.961176i	$0.588988\pi$
$38$	−632.859	−2.70167
$39$	−421.092	−1.72894
$40$	−33.4429	−0.132195
$41$	285.427	1.08723	0.543613	−	0.839336i	$-0.317056\pi$
$41$	285.427	1.08723	0.543613	+	0.839336i	$0.317056\pi$
$42$	−713.254	−2.62041
$43$	0	0
$43$	0	0
$44$	94.1687	0.322647
$45$	−873.303	−2.89298
$46$	−462.754	−1.48325
$47$	−93.0632	−0.288823	−0.144411	−	0.989518i	$-0.546129\pi$
$47$	−93.0632	−0.288823	−0.144411	+	0.989518i	$0.546129\pi$
$48$	−579.182	−1.74162
$49$	−35.9021	−0.104671
$50$	84.9262	0.240207
$51$	−55.4031	−0.152117
$52$	−366.670	−0.977846
$53$	199.633	0.517390	0.258695	−	0.965959i	$-0.416707\pi$
$53$	199.633	0.517390	0.258695	+	0.965959i	$0.416707\pi$
$54$	1844.81	4.64901
$55$	−131.023	−0.321222
$56$	−48.5368	−0.115821
$57$	−1544.41	−3.58882
$58$	94.1931	0.213244
$59$	477.324	1.05326	0.526630	−	0.850095i	$-0.323455\pi$
$59$	477.324	1.05326	0.526630	+	0.850095i	$0.323455\pi$
$60$	−1044.32	−2.24701
$61$	−622.675	−1.30697	−0.653487	−	0.756938i	$-0.726694\pi$
$61$	−622.675	−1.30697	−0.653487	+	0.756938i	$0.726694\pi$
$62$	143.166	0.293259
$63$	−1267.45	−2.53467
$64$	−594.818	−1.16175
$65$	510.173	0.973526
$66$	441.655	0.823696
$67$	−687.465	−1.25354	−0.626771	−	0.779204i	$-0.715624\pi$
$67$	−687.465	−1.25354	−0.626771	+	0.779204i	$0.715624\pi$
$68$	−48.2428	−0.0860338
$69$	−1129.29	−1.97030
$70$	864.142	1.47550
$71$	−128.142	−0.214193	−0.107097	−	0.994249i	$-0.534155\pi$
$71$	−128.142	−0.214193	−0.107097	+	0.994249i	$0.534155\pi$
$72$	200.321	0.327889
$73$	353.979	0.567535	0.283768	−	0.958893i	$-0.408416\pi$
$73$	353.979	0.567535	0.283768	+	0.958893i	$0.408416\pi$
$74$	−507.243	−0.796835
$75$	207.252	0.319085
$76$	−1344.81	−2.02975
$77$	−190.158	−0.281436
$78$	−1719.69	−2.49637
$79$	518.415	0.738306	0.369153	−	0.929369i	$-0.379648\pi$
$79$	518.415	0.738306	0.369153	+	0.929369i	$0.379648\pi$
$80$	701.707	0.980666
$81$	2549.22	3.49687
$82$	1165.66	1.56982
$83$	616.196	0.814895	0.407447	−	0.913229i	$-0.366419\pi$
$83$	616.196	0.814895	0.407447	+	0.913229i	$0.366419\pi$
$84$	−1515.65	−1.96870
$85$	67.1235	0.0856538
$86$	0	0
$87$	229.866	0.283267
$88$	30.0545	0.0364071
$89$	−92.5703	−0.110252	−0.0551260	−	0.998479i	$-0.517556\pi$
$89$	−92.5703	−0.110252	−0.0551260	+	0.998479i	$0.517556\pi$
$90$	−3566.48	−4.17711
$91$	740.430	0.852947
$92$	−983.344	−1.11436
$93$	349.378	0.389557
$94$	−380.060	−0.417024
$95$	1871.13	2.02078
$96$	−2586.15	−2.74945
$97$	1189.51	1.24512	0.622561	−	0.782572i	$-0.286092\pi$
$97$	1189.51	1.24512	0.622561	+	0.782572i	$0.286092\pi$
$98$	−146.620	−0.151132
$99$	784.820	0.796741
$100$	180.466	0.180466
$101$	−1066.14	−1.05035	−0.525175	−	0.850995i	$-0.676000\pi$
$101$	−1066.14	−1.05035	−0.525175	+	0.850995i	$0.676000\pi$
$102$	−226.260	−0.219638
$103$	−981.152	−0.938600	−0.469300	−	0.883039i	$-0.655494\pi$
$103$	−981.152	−0.938600	−0.469300	+	0.883039i	$0.655494\pi$
$104$	−117.025	−0.110339
$105$	2108.83	1.96001
$106$	815.280	0.747047
$107$	376.257	0.339945	0.169973	−	0.985449i	$-0.445632\pi$
$107$	376.257	0.339945	0.169973	+	0.985449i	$0.445632\pi$
$108$	3920.18	3.49277
$109$	−888.095	−0.780404	−0.390202	−	0.920729i	$-0.627595\pi$
$109$	−888.095	−0.780404	−0.390202	+	0.920729i	$0.627595\pi$
$110$	−535.086	−0.463804
$111$	−1237.86	−1.05849
$112$	1018.41	0.859202
$113$	−750.549	−0.624829	−0.312414	−	0.949946i	$-0.601138\pi$
$113$	−750.549	−0.624829	−0.312414	+	0.949946i	$0.601138\pi$
$114$	−6307.22	−5.18180
$115$	1368.19	1.10943
$116$	200.159	0.160209
$117$	−3055.90	−2.41468
$118$	1949.34	1.52078
$119$	97.4185	0.0750448
$120$	−333.300	−0.253550
$121$	−1213.25	−0.911534
$122$	−2542.94	−1.88711
$123$	2844.63	2.08530
$124$	304.225	0.220324
$125$	1258.23	0.900314
$126$	−5176.14	−3.65974
$127$	2121.42	1.48225	0.741126	−	0.671366i	$-0.234292\pi$
$127$	2121.42	1.48225	0.741126	+	0.671366i	$0.234292\pi$
$128$	−353.248	−0.243929
$129$	0	0
$130$	2083.49	1.40565
$131$	1311.61	0.874776	0.437388	−	0.899273i	$-0.355904\pi$
$131$	1311.61	0.874776	0.437388	+	0.899273i	$0.355904\pi$
$132$	938.508	0.618838
$133$	2715.63	1.77049
$134$	−2807.54	−1.80996
$135$	−5454.41	−3.47734
$136$	−15.3970	−0.00970794
$137$	−425.433	−0.265308	−0.132654	−	0.991162i	$-0.542350\pi$
$137$	−425.433	−0.265308	−0.132654	+	0.991162i	$0.542350\pi$
$138$	−4611.92	−2.84487
$139$	397.085	0.242304	0.121152	−	0.992634i	$-0.461341\pi$
$139$	397.085	0.242304	0.121152	+	0.992634i	$0.461341\pi$
$140$	1836.28	1.10853
$141$	−927.490	−0.553962
$142$	−523.320	−0.309268
$143$	−458.483	−0.268114
$144$	−4203.17	−2.43239
$145$	−278.494	−0.159501
$146$	1445.61	0.819450
$147$	−357.808	−0.200759
$148$	−1077.88	−0.598657
$149$	1144.43	0.629233	0.314616	−	0.949219i	$-0.398124\pi$
$149$	1144.43	0.629233	0.314616	+	0.949219i	$0.398124\pi$
$150$	846.394	0.460718
$151$	−3078.56	−1.65914	−0.829568	−	0.558405i	$-0.811413\pi$
$151$	−3078.56	−1.65914	−0.829568	+	0.558405i	$0.811413\pi$
$152$	−429.205	−0.229034
$153$	−402.065	−0.212451
$154$	−776.587	−0.406358
$155$	−423.289	−0.219351
$156$	−3654.32	−1.87551
$157$	−1786.80	−0.908296	−0.454148	−	0.890926i	$-0.650056\pi$
$157$	−1786.80	−0.908296	−0.454148	+	0.890926i	$0.650056\pi$
$158$	2117.15	1.06602
$159$	1989.59	0.992356
$160$	3133.24	1.54815
$161$	1985.70	0.972021
$162$	10410.7	5.04905
$163$	−1031.07	−0.495460	−0.247730	−	0.968829i	$-0.579685\pi$
$163$	−1031.07	−0.495460	−0.247730	+	0.968829i	$0.579685\pi$
$164$	2477.00	1.17940
$165$	−1305.81	−0.616104
$166$	2516.48	1.17661
$167$	−686.945	−0.318308	−0.159154	−	0.987254i	$-0.550877\pi$
$167$	−686.945	−0.318308	−0.159154	+	0.987254i	$0.550877\pi$
$168$	−483.729	−0.222146
$169$	−411.781	−0.187429
$170$	274.125	0.123673
$171$	−11207.9	−5.01224
$172$	0	0
$173$	−34.4261	−0.0151293	−0.00756464	−	0.999971i	$-0.502408\pi$
$173$	−34.4261	−0.0151293	−0.00756464	+	0.999971i	$0.502408\pi$
$174$	938.750	0.409003
$175$	−364.423	−0.157416
$176$	−630.610	−0.270080
$177$	4757.12	2.02015
$178$	−378.048	−0.159190
$179$	−2239.77	−0.935240	−0.467620	−	0.883930i	$-0.654888\pi$
$179$	−2239.77	−0.935240	−0.467620	+	0.883930i	$0.654888\pi$
$180$	−7578.70	−3.13824
$181$	2397.87	0.984711	0.492355	−	0.870394i	$-0.336136\pi$
$181$	2397.87	0.984711	0.492355	+	0.870394i	$0.336136\pi$
$182$	3023.84	1.23155
$183$	−6205.72	−2.50678
$184$	−313.840	−0.125742
$185$	1499.73	0.596013
$186$	1426.82	0.562472
$187$	−60.3226	−0.0235894
$188$	−807.621	−0.313308
$189$	−7916.16	−3.04664
$190$	7641.51	2.91775
$191$	1546.51	0.585870	0.292935	−	0.956132i	$-0.405368\pi$
$191$	1546.51	0.585870	0.292935	+	0.956132i	$0.405368\pi$
$192$	−5928.09	−2.22825
$193$	−61.7238	−0.0230206	−0.0115103	−	0.999934i	$-0.503664\pi$
$193$	−61.7238	−0.0230206	−0.0115103	+	0.999934i	$0.503664\pi$
$194$	4857.85	1.79780
$195$	5084.50	1.86723
$196$	−311.566	−0.113544
$197$	−810.145	−0.292997	−0.146499	−	0.989211i	$-0.546800\pi$
$197$	−810.145	−0.292997	−0.146499	+	0.989211i	$0.546800\pi$
$198$	3205.12	1.15039
$199$	−2018.24	−0.718940	−0.359470	−	0.933157i	$-0.617043\pi$
$199$	−2018.24	−0.718940	−0.359470	+	0.933157i	$0.617043\pi$
$200$	57.5970	0.0203636
$201$	−6851.44	−2.40429
$202$	−4354.02	−1.51657
$203$	−404.187	−0.139746
$204$	−480.799	−0.165013
$205$	−3446.41	−1.17419
$206$	−4006.92	−1.35522
$207$	−8195.38	−2.75178
$208$	2455.44	0.818530
$209$	−1681.55	−0.556532
$210$	8612.23	2.83000
$211$	−5664.67	−1.84821	−0.924104	−	0.382142i	$-0.875186\pi$
$211$	−5664.67	−1.84821	−0.924104	+	0.382142i	$0.875186\pi$
$212$	1732.45	0.561252
$213$	−1277.10	−0.410823
$214$	1536.59	0.490838
$215$	0	0
$216$	1251.15	0.394120
$217$	−614.332	−0.192183
$218$	−3626.89	−1.12681
$219$	3527.83	1.08853
$220$	−1137.05	−0.348453
$221$	234.881	0.0714925
$222$	−5055.30	−1.52833
$223$	273.146	0.0820233	0.0410116	−	0.999159i	$-0.486942\pi$
$223$	273.146	0.0820233	0.0410116	+	0.999159i	$0.486942\pi$
$224$	4547.37	1.35640
$225$	1504.04	0.445642
$226$	−3065.16	−0.902175
$227$	5004.96	1.46340	0.731698	−	0.681629i	$-0.238728\pi$
$227$	5004.96	1.46340	0.731698	+	0.681629i	$0.238728\pi$
$228$	−13402.7	−3.89306
$229$	−4140.80	−1.19490	−0.597449	−	0.801907i	$-0.703819\pi$
$229$	−4140.80	−1.19490	−0.597449	+	0.801907i	$0.703819\pi$
$230$	5587.56	1.60188
$231$	−1895.16	−0.539795
$232$	63.8818	0.0180778
$233$	−1038.11	−0.291883	−0.145942	−	0.989293i	$-0.546621\pi$
$233$	−1038.11	−0.291883	−0.145942	+	0.989293i	$0.546621\pi$
$234$	−12480.0	−3.48650
$235$	1123.70	0.311924
$236$	4142.31	1.14255
$237$	5166.64	1.41607
$238$	397.847	0.108355
$239$	5177.15	1.40118	0.700591	−	0.713564i	$-0.252920\pi$
$239$	5177.15	1.40118	0.700591	+	0.713564i	$0.252920\pi$
$240$	6993.38	1.88092
$241$	−559.247	−0.149478	−0.0747391	−	0.997203i	$-0.523812\pi$
$241$	−559.247	−0.149478	−0.0747391	+	0.997203i	$0.523812\pi$
$242$	−4954.79	−1.31614
$243$	13209.5	3.48720
$244$	−5403.70	−1.41777
$245$	433.502	0.113043
$246$	11617.2	3.01091
$247$	6547.54	1.68668
$248$	97.0952	0.0248611
$249$	6141.15	1.56297
$250$	5138.47	1.29994
$251$	5354.80	1.34658	0.673290	−	0.739378i	$-0.264880\pi$
$251$	5354.80	1.34658	0.673290	+	0.739378i	$0.264880\pi$
$252$	−10999.2	−2.74954
$253$	−1229.57	−0.305543
$254$	8663.67	2.14019
$255$	668.969	0.164284
$256$	3315.92	0.809550
$257$	6690.27	1.62384	0.811921	−	0.583767i	$-0.198422\pi$
$257$	6690.27	1.62384	0.811921	+	0.583767i	$0.198422\pi$
$258$	0	0
$259$	2176.61	0.522192
$260$	4427.39	1.05606
$261$	1668.16	0.395619
$262$	5356.47	1.26307
$263$	−6104.44	−1.43124	−0.715619	−	0.698491i	$-0.753855\pi$
$263$	−6104.44	−1.43124	−0.715619	+	0.698491i	$0.753855\pi$
$264$	299.530	0.0698288
$265$	−2410.48	−0.558773
$266$	11090.4	2.55637
$267$	−922.577	−0.211464
$268$	−5965.96	−1.35981
$269$	1909.80	0.432873	0.216437	−	0.976297i	$-0.430557\pi$
$269$	1909.80	0.432873	0.216437	+	0.976297i	$0.430557\pi$
$270$	−22275.2	−5.02085
$271$	−5027.56	−1.12695	−0.563473	−	0.826134i	$-0.690535\pi$
$271$	−5027.56	−1.12695	−0.563473	+	0.826134i	$0.690535\pi$
$272$	323.063	0.0720168
$273$	7379.30	1.63595
$274$	−1737.42	−0.383071
$275$	225.655	0.0494817
$276$	−9800.24	−2.13734
$277$	3790.77	0.822257	0.411129	−	0.911577i	$-0.365135\pi$
$277$	3790.77	0.822257	0.411129	+	0.911577i	$0.365135\pi$
$278$	1621.65	0.349857
$279$	2535.47	0.544066
$280$	586.061	0.125085
$281$	−1063.57	−0.225790	−0.112895	−	0.993607i	$-0.536012\pi$
$281$	−1063.57	−0.225790	−0.112895	+	0.993607i	$0.536012\pi$
$282$	−3787.77	−0.799853
$283$	−479.882	−0.100799	−0.0503993	−	0.998729i	$-0.516049\pi$
$283$	−479.882	−0.100799	−0.0503993	+	0.998729i	$0.516049\pi$
$284$	−1112.05	−0.232351
$285$	18648.1	3.87586
$286$	−1872.40	−0.387123
$287$	−5001.89	−1.02875
$288$	−18767.9	−3.83996
$289$	−4882.10	−0.993710
$290$	−1137.34	−0.230300
$291$	11855.0	2.38814
$292$	3071.90	0.615648
$293$	−3136.43	−0.625366	−0.312683	−	0.949858i	$-0.601228\pi$
$293$	−3136.43	−0.625366	−0.312683	+	0.949858i	$0.601228\pi$
$294$	−1461.25	−0.289871
$295$	−5763.49	−1.13750
$296$	−344.012	−0.0675517
$297$	4901.77	0.957676
$298$	4673.75	0.908534
$299$	4787.64	0.926009
$300$	1798.57	0.346135
$301$	0	0
$302$	−12572.5	−2.39559
$303$	−10625.4	−2.01457
$304$	9005.68	1.69905
$305$	7518.54	1.41151
$306$	−1641.99	−0.306753
$307$	−201.648	−0.0374875	−0.0187438	−	0.999824i	$-0.505967\pi$
$307$	−201.648	−0.0374875	−0.0187438	+	0.999824i	$0.505967\pi$
$308$	−1650.23	−0.305295
$309$	−9778.39	−1.80024
$310$	−1728.67	−0.316715
$311$	−4207.08	−0.767078	−0.383539	−	0.923525i	$-0.625295\pi$
$311$	−4207.08	−0.767078	−0.383539	+	0.923525i	$0.625295\pi$
$312$	−1166.30	−0.211630
$313$	−5716.05	−1.03224	−0.516119	−	0.856517i	$-0.672624\pi$
$313$	−5716.05	−1.03224	−0.516119	+	0.856517i	$0.672624\pi$
$314$	−7297.12	−1.31147
$315$	15303.9	2.73740
$316$	4498.91	0.800896
$317$	2299.18	0.407365	0.203682	−	0.979037i	$-0.434709\pi$
$317$	2299.18	0.407365	0.203682	+	0.979037i	$0.434709\pi$
$318$	8125.27	1.43284
$319$	250.277	0.0439274
$320$	7182.18	1.25467
$321$	3749.86	0.652015
$322$	8109.41	1.40348
$323$	861.461	0.148399
$324$	22122.6	3.79332
$325$	−878.643	−0.149964
$326$	−4210.80	−0.715382
$327$	−8850.96	−1.49682
$328$	790.548	0.133081
$329$	1630.86	0.273289
$330$	−5332.79	−0.889577
$331$	8139.78	1.35167	0.675835	−	0.737053i	$-0.263783\pi$
$331$	8139.78	1.35167	0.675835	+	0.737053i	$0.263783\pi$
$332$	5347.47	0.883978
$333$	−8983.27	−1.47832
$334$	−2805.41	−0.459596
$335$	8300.85	1.35380
$336$	10149.7	1.64795
$337$	−4002.03	−0.646898	−0.323449	−	0.946246i	$-0.604842\pi$
$337$	−4002.03	−0.646898	−0.323449	+	0.946246i	$0.604842\pi$
$338$	−1681.67	−0.270624
$339$	−7480.14	−1.19842
$340$	582.511	0.0929151
$341$	380.401	0.0604102
$342$	−45772.0	−7.23704
$343$	6639.96	1.04526
$344$	0	0
$345$	13635.7	2.12789
$346$	−140.592	−0.0218448
$347$	−10974.9	−1.69787	−0.848936	−	0.528495i	$-0.822756\pi$
$347$	−10974.9	−1.69787	−0.848936	+	0.528495i	$0.822756\pi$
$348$	1994.83	0.307281
$349$	5935.40	0.910357	0.455179	−	0.890400i	$-0.349575\pi$
$349$	5935.40	0.910357	0.455179	+	0.890400i	$0.349575\pi$
$350$	−1488.26	−0.227289
$351$	−19086.3	−2.90243
$352$	−2815.78	−0.426369
$353$	10737.2	1.61894	0.809470	−	0.587162i	$-0.199755\pi$
$353$	10737.2	1.61894	0.809470	+	0.587162i	$0.199755\pi$
$354$	19427.6	2.91685
$355$	1547.26	0.231325
$356$	−803.344	−0.119599
$357$	970.895	0.143936
$358$	−9146.97	−1.35037
$359$	366.081	0.0538190	0.0269095	−	0.999638i	$-0.491433\pi$
$359$	366.081	0.0538190	0.0269095	+	0.999638i	$0.491433\pi$
$360$	−2418.79	−0.354115
$361$	17155.0	2.50110
$362$	9792.67	1.42180
$363$	−12091.5	−1.74832
$364$	6425.60	0.925256
$365$	−4274.14	−0.612928
$366$	−25343.5	−3.61947
$367$	−10954.3	−1.55807	−0.779035	−	0.626981i	$-0.784290\pi$
$367$	−10954.3	−1.55807	−0.779035	+	0.626981i	$0.784290\pi$
$368$	6585.06	0.932800
$369$	20643.7	2.91239
$370$	6124.74	0.860568
$371$	−3498.41	−0.489564
$372$	3031.98	0.422582
$373$	1725.26	0.239493	0.119746	−	0.992805i	$-0.461792\pi$
$373$	1725.26	0.239493	0.119746	+	0.992805i	$0.461792\pi$
$374$	−246.351	−0.0340602
$375$	12539.8	1.72680
$376$	−257.757	−0.0353532
$377$	−974.519	−0.133131
$378$	−32328.8	−4.39897
$379$	−3436.37	−0.465738	−0.232869	−	0.972508i	$-0.574811\pi$
$379$	−3436.37	−0.465738	−0.232869	+	0.972508i	$0.574811\pi$
$380$	16238.1	2.19209
$381$	21142.6	2.84296
$382$	6315.77	0.845923
$383$	3013.16	0.401998	0.200999	−	0.979591i	$-0.435581\pi$
$383$	3013.16	0.401998	0.200999	+	0.979591i	$0.435581\pi$
$384$	−3520.55	−0.467857
$385$	2296.08	0.303946
$386$	−252.073	−0.0332389
$387$	0	0
$388$	10322.8	1.35068
$389$	10777.3	1.40471	0.702355	−	0.711826i	$-0.252132\pi$
$389$	10777.3	1.40471	0.702355	+	0.711826i	$0.252132\pi$
$390$	20764.6	2.69604
$391$	629.911	0.0814730
$392$	−99.4380	−0.0128122
$393$	13071.8	1.67782
$394$	−3308.55	−0.423051
$395$	−6259.64	−0.797358
$396$	6810.83	0.864285
$397$	−13939.1	−1.76218	−0.881089	−	0.472950i	$-0.843189\pi$
$397$	−13939.1	−1.76218	−0.881089	+	0.472950i	$0.843189\pi$
$398$	−8242.27	−1.03806
$399$	27064.6	3.39580
$400$	−1208.51	−0.151064
$401$	8901.70	1.10855	0.554276	−	0.832333i	$-0.312995\pi$
$401$	8901.70	1.10855	0.554276	+	0.832333i	$0.312995\pi$
$402$	−27980.6	−3.47150
$403$	−1481.19	−0.183085
$404$	−9252.21	−1.13939
$405$	−30780.8	−3.77656
$406$	−1650.66	−0.201775
$407$	−1347.78	−0.164145
$408$	−153.450	−0.0186199
$409$	10808.1	1.30666	0.653332	−	0.757071i	$-0.273371\pi$
$409$	10808.1	1.30666	0.653332	+	0.757071i	$0.273371\pi$
$410$	−14074.8	−1.69538
$411$	−4239.96	−0.508861
$412$	−8514.63	−1.01817
$413$	−8364.73	−0.996613
$414$	−33469.1	−3.97322
$415$	−7440.30	−0.880073
$416$	10964.0	1.29219
$417$	3957.44	0.464740
$418$	−6867.27	−0.803563
$419$	−10204.7	−1.18981	−0.594906	−	0.803795i	$-0.702811\pi$
$419$	−10204.7	−1.18981	−0.594906	+	0.803795i	$0.702811\pi$
$420$	18300.8	2.12617
$421$	−12883.3	−1.49144	−0.745719	−	0.666260i	$-0.767894\pi$
$421$	−12883.3	−1.49144	−0.745719	+	0.666260i	$0.767894\pi$
$422$	−23133.9	−2.66858
$423$	−6730.87	−0.773679
$424$	552.923	0.0633309
$425$	−115.603	−0.0131943
$426$	−5215.53	−0.593177
$427$	10911.9	1.23668
$428$	3265.23	0.368764
$429$	−4569.34	−0.514242
$430$	0	0
$431$	17111.1	1.91233	0.956166	−	0.292825i	$-0.0945954\pi$
$431$	17111.1	1.91233	0.956166	+	0.292825i	$0.0945954\pi$
$432$	−26251.9	−2.92371
$433$	−263.948	−0.0292945	−0.0146473	−	0.999893i	$-0.504663\pi$
$433$	−263.948	−0.0292945	−0.0146473	+	0.999893i	$0.504663\pi$
$434$	−2508.87	−0.277488
$435$	−2775.54	−0.305924
$436$	−7707.06	−0.846563
$437$	17559.4	1.92215
$438$	14407.3	1.57171
$439$	−8311.79	−0.903644	−0.451822	−	0.892108i	$-0.649226\pi$
$439$	−8311.79	−0.903644	−0.451822	+	0.892108i	$0.649226\pi$
$440$	−362.896	−0.0393190
$441$	−2596.65	−0.280385
$442$	959.231	0.103226
$443$	9465.05	1.01512	0.507560	−	0.861617i	$-0.330548\pi$
$443$	9465.05	1.01512	0.507560	+	0.861617i	$0.330548\pi$
$444$	−10742.4	−1.14823
$445$	1117.75	0.119070
$446$	1115.50	0.118431
$447$	11405.7	1.20687
$448$	10423.7	1.09927
$449$	8512.95	0.894768	0.447384	−	0.894342i	$-0.352356\pi$
$449$	8512.95	0.894768	0.447384	+	0.894342i	$0.352356\pi$
$450$	6142.35	0.643451
$451$	3097.22	0.323376
$452$	−6513.41	−0.677799
$453$	−30681.6	−3.18223
$454$	20439.7	2.11296
$455$	−8940.38	−0.921168
$456$	−4277.56	−0.439288
$457$	2596.30	0.265755	0.132877	−	0.991132i	$-0.457578\pi$
$457$	2596.30	0.265755	0.132877	+	0.991132i	$0.457578\pi$
$458$	−16910.6	−1.72528
$459$	−2511.19	−0.255364
$460$	11873.5	1.20349
$461$	11076.8	1.11908	0.559541	−	0.828803i	$-0.310978\pi$
$461$	11076.8	1.11908	0.559541	+	0.828803i	$0.310978\pi$
$462$	−7739.65	−0.779396
$463$	2142.16	0.215021	0.107510	−	0.994204i	$-0.465712\pi$
$463$	2142.16	0.215021	0.107510	+	0.994204i	$0.465712\pi$
$464$	−1340.38	−0.134107
$465$	−4218.60	−0.420715
$466$	−4239.53	−0.421443
$467$	−15201.8	−1.50633	−0.753164	−	0.657833i	$-0.771473\pi$
$467$	−15201.8	−1.50633	−0.753164	+	0.657833i	$0.771473\pi$
$468$	−26519.7	−2.61939
$469$	12047.3	1.18612
$470$	4589.07	0.450379
$471$	−17807.7	−1.74211
$472$	1322.04	0.128924
$473$	0	0
$474$	21100.0	2.04463
$475$	−3222.55	−0.311286
$476$	845.417	0.0814068
$477$	14438.6	1.38595
$478$	21143.0	2.02313
$479$	−17679.9	−1.68646	−0.843232	−	0.537551i	$-0.819350\pi$
$479$	−17679.9	−1.68646	−0.843232	+	0.537551i	$0.819350\pi$
$480$	31226.6	2.96936
$481$	5247.92	0.497473
$482$	−2283.91	−0.215828
$483$	19790.0	1.86434
$484$	−10528.8	−0.988809
$485$	−14362.9	−1.34471
$486$	53946.2	5.03508
$487$	6063.71	0.564216	0.282108	−	0.959383i	$-0.408966\pi$
$487$	6063.71	0.564216	0.282108	+	0.959383i	$0.408966\pi$
$488$	−1724.62	−0.159980
$489$	−10275.9	−0.950293
$490$	1770.38	0.163220
$491$	1445.56	0.132866	0.0664331	−	0.997791i	$-0.478838\pi$
$491$	1445.56	0.132866	0.0664331	+	0.997791i	$0.478838\pi$
$492$	24686.3	2.26208
$493$	−128.218	−0.0117132
$494$	26739.5	2.43536
$495$	−9476.37	−0.860467
$496$	−2037.27	−0.184428
$497$	2245.59	0.202673
$498$	25079.8	2.25673
$499$	−353.934	−0.0317520	−0.0158760	−	0.999874i	$-0.505054\pi$
$499$	−353.934	−0.0317520	−0.0158760	+	0.999874i	$0.505054\pi$
$500$	10919.1	0.976638
$501$	−6846.25	−0.610515
$502$	21868.4	1.94429
$503$	−8190.74	−0.726058	−0.363029	−	0.931778i	$-0.618257\pi$
$503$	−8190.74	−0.726058	−0.363029	+	0.931778i	$0.618257\pi$
$504$	−3510.46	−0.310255
$505$	12873.2	1.13436
$506$	−5021.43	−0.441166
$507$	−4103.90	−0.359489
$508$	18410.1	1.60791
$509$	5958.42	0.518865	0.259433	−	0.965761i	$-0.416464\pi$
$509$	5958.42	0.518865	0.259433	+	0.965761i	$0.416464\pi$
$510$	2732.00	0.237206
$511$	−6203.20	−0.537012
$512$	16367.8	1.41282
$513$	−70001.7	−6.02466
$514$	27322.3	2.34462
$515$	11847.0	1.01367
$516$	0	0
$517$	−1009.85	−0.0859052
$518$	8889.03	0.753980
$519$	−343.098	−0.0290180
$520$	1413.03	0.119164
$521$	−15740.4	−1.32360	−0.661802	−	0.749679i	$-0.730208\pi$
$521$	−15740.4	−1.32360	−0.661802	+	0.749679i	$0.730208\pi$
$522$	6812.59	0.571224
$523$	−10264.1	−0.858157	−0.429078	−	0.903267i	$-0.641162\pi$
$523$	−10264.1	−0.858157	−0.429078	+	0.903267i	$0.641162\pi$
$524$	11382.4	0.948935
$525$	−3631.92	−0.301924
$526$	−24929.9	−2.06653
$527$	−194.880	−0.0161084
$528$	−6284.81	−0.518014
$529$	672.613	0.0552818
$530$	−9844.16	−0.806798
$531$	34522.8	2.82140
$532$	23566.8	1.92058
$533$	−12059.8	−0.980055
$534$	−3767.71	−0.305327
$535$	−4543.14	−0.367135
$536$	−1904.07	−0.153439
$537$	−22322.0	−1.79379
$538$	7799.44	0.625015
$539$	−389.580	−0.0311325
$540$	−47334.5	−3.77213
$541$	2127.67	0.169087	0.0845433	−	0.996420i	$-0.473057\pi$
$541$	2127.67	0.169087	0.0845433	+	0.996420i	$0.473057\pi$
$542$	−20532.0	−1.62717
$543$	23897.8	1.88868
$544$	1442.53	0.113691
$545$	10723.4	0.842823
$546$	30136.3	2.36211
$547$	−10285.2	−0.803957	−0.401978	−	0.915649i	$-0.631677\pi$
$547$	−10285.2	−0.803957	−0.401978	+	0.915649i	$0.631677\pi$
$548$	−3691.99	−0.287799
$549$	−45035.5	−3.50103
$550$	921.549	0.0714454
$551$	−3574.18	−0.276344
$552$	−3127.80	−0.241174
$553$	−9084.81	−0.698599
$554$	15481.1	1.18724
$555$	14946.7	1.14315
$556$	3445.98	0.262846
$557$	−1090.16	−0.0829295	−0.0414647	−	0.999140i	$-0.513202\pi$
$557$	−1090.16	−0.0829295	−0.0414647	+	0.999140i	$0.513202\pi$
$558$	10354.6	0.785564
$559$	0	0
$560$	−12296.9	−0.927924
$561$	−601.189	−0.0452446
$562$	−4343.50	−0.326013
$563$	−23863.4	−1.78636	−0.893181	−	0.449697i	$-0.851532\pi$
$563$	−23863.4	−1.78636	−0.893181	+	0.449697i	$0.851532\pi$
$564$	−8048.94	−0.600925
$565$	9062.56	0.674805
$566$	−1959.79	−0.145541
$567$	−44673.1	−3.30881
$568$	−354.916	−0.0262182
$569$	−21194.7	−1.56156	−0.780780	−	0.624806i	$-0.785178\pi$
$569$	−21194.7	−1.56156	−0.780780	+	0.624806i	$0.785178\pi$
$570$	76157.0	5.59626
$571$	15839.7	1.16089	0.580447	−	0.814298i	$-0.302878\pi$
$571$	15839.7	1.16089	0.580447	+	0.814298i	$0.302878\pi$
$572$	−3978.80	−0.290843
$573$	15412.8	1.12370
$574$	−20427.2	−1.48539
$575$	−2356.37	−0.170900
$576$	−43020.7	−3.11203
$577$	12403.0	0.894878	0.447439	−	0.894314i	$-0.352336\pi$
$577$	12403.0	0.894878	0.447439	+	0.894314i	$0.352336\pi$
$578$	−19938.0	−1.43479
$579$	−615.153	−0.0441535
$580$	−2416.83	−0.173023
$581$	−10798.3	−0.771069
$582$	48414.4	3.44818
$583$	2166.25	0.153889
$584$	980.415	0.0694689
$585$	36898.7	2.60782
$586$	−12808.8	−0.902950
$587$	−3574.22	−0.251318	−0.125659	−	0.992073i	$-0.540105\pi$
$587$	−3574.22	−0.251318	−0.125659	+	0.992073i	$0.540105\pi$
$588$	−3105.13	−0.217778
$589$	−5432.47	−0.380036
$590$	−23537.5	−1.64241
$591$	−8074.09	−0.561969
$592$	7218.14	0.501121
$593$	17985.4	1.24548	0.622741	−	0.782428i	$-0.286019\pi$
$593$	17985.4	1.24548	0.622741	+	0.782428i	$0.286019\pi$
$594$	20018.3	1.38276
$595$	−1176.29	−0.0810472
$596$	9931.63	0.682576
$597$	−20114.2	−1.37893
$598$	19552.2	1.33704
$599$	24032.3	1.63929	0.819645	−	0.572872i	$-0.194171\pi$
$599$	24032.3	1.63929	0.819645	+	0.572872i	$0.194171\pi$
$600$	574.025	0.0390574
$601$	−20178.7	−1.36956	−0.684780	−	0.728750i	$-0.740102\pi$
$601$	−20178.7	−1.36956	−0.684780	+	0.728750i	$0.740102\pi$
$602$	0	0
$603$	−49721.5	−3.35790
$604$	−26716.4	−1.79979
$605$	14649.5	0.984441
$606$	−43393.2	−2.90879
$607$	15690.3	1.04918	0.524588	−	0.851356i	$-0.324219\pi$
$607$	15690.3	1.04918	0.524588	+	0.851356i	$0.324219\pi$
$608$	40211.9	2.68225
$609$	−4028.23	−0.268033
$610$	30704.9	2.03804
$611$	3932.09	0.260353
$612$	−3489.20	−0.230462
$613$	−12674.1	−0.835078	−0.417539	−	0.908659i	$-0.637107\pi$
$613$	−12674.1	−0.835078	−0.417539	+	0.908659i	$0.637107\pi$
$614$	−823.510	−0.0541273
$615$	−34347.8	−2.25209
$616$	−526.682	−0.0344490
$617$	15349.8	1.00156	0.500779	−	0.865575i	$-0.333047\pi$
$617$	15349.8	1.00156	0.500779	+	0.865575i	$0.333047\pi$
$618$	−39933.9	−2.59932
$619$	−18610.5	−1.20843	−0.604215	−	0.796822i	$-0.706513\pi$
$619$	−18610.5	−1.20843	−0.604215	+	0.796822i	$0.706513\pi$
$620$	−3673.39	−0.237946
$621$	−51186.1	−3.30761
$622$	−17181.3	−1.10757
$623$	1622.22	0.104323
$624$	24471.5	1.56994
$625$	−17792.0	−1.13869
$626$	−23343.8	−1.49042
$627$	−16758.7	−1.06743
$628$	−15506.2	−0.985296
$629$	690.469	0.0437692
$630$	62499.7	3.95246
$631$	−19714.6	−1.24378	−0.621891	−	0.783103i	$-0.713635\pi$
$631$	−19714.6	−1.24378	−0.621891	+	0.783103i	$0.713635\pi$
$632$	1435.85	0.0903721
$633$	−56455.4	−3.54487
$634$	9389.60	0.588184
$635$	−25615.3	−1.60081
$636$	17266.0	1.07648
$637$	1516.93	0.0943531
$638$	1022.11	0.0634257
$639$	−9268.00	−0.573766
$640$	4265.31	0.263440
$641$	−5151.16	−0.317408	−0.158704	−	0.987326i	$-0.550732\pi$
$641$	−5151.16	−0.317408	−0.158704	+	0.987326i	$0.550732\pi$
$642$	15314.0	0.941429
$643$	6790.40	0.416465	0.208233	−	0.978079i	$-0.433229\pi$
$643$	6790.40	0.416465	0.208233	+	0.978079i	$0.433229\pi$
$644$	17232.3	1.05442
$645$	0	0
$646$	3518.12	0.214270
$647$	−27509.5	−1.67157	−0.835787	−	0.549054i	$-0.814988\pi$
$647$	−27509.5	−1.67157	−0.835787	+	0.549054i	$0.814988\pi$
$648$	7060.57	0.428033
$649$	5179.53	0.313273
$650$	−3588.29	−0.216530
$651$	−6122.58	−0.368606
$652$	−8947.87	−0.537463
$653$	803.765	0.0481681	0.0240840	−	0.999710i	$-0.492333\pi$
$653$	803.765	0.0481681	0.0240840	+	0.999710i	$0.492333\pi$
$654$	−36146.4	−2.16122
$655$	−15837.1	−0.944743
$656$	−16587.4	−0.987242
$657$	25601.8	1.52027
$658$	6660.26	0.394596
$659$	21576.5	1.27542	0.637710	−	0.770277i	$-0.279882\pi$
$659$	21576.5	1.27542	0.637710	+	0.770277i	$0.279882\pi$
$660$	−11332.1	−0.668334
$661$	16383.1	0.964040	0.482020	−	0.876160i	$-0.339903\pi$
$661$	16383.1	0.964040	0.482020	+	0.876160i	$0.339903\pi$
$662$	33242.0	1.95164
$663$	2340.88	0.137123
$664$	1706.68	0.0997469
$665$	−32790.1	−1.91210
$666$	−36686.7	−2.13451
$667$	−2613.49	−0.151716
$668$	−5961.44	−0.345292
$669$	2722.23	0.157321
$670$	33899.8	1.95472
$671$	−6756.76	−0.388736
$672$	45320.2	2.60158
$673$	−23121.3	−1.32431	−0.662154	−	0.749368i	$-0.730358\pi$
$673$	−23121.3	−1.32431	−0.662154	+	0.749368i	$0.730358\pi$
$674$	−16343.9	−0.934039
$675$	9393.84	0.535658
$676$	−3573.52	−0.203318
$677$	−25046.5	−1.42189	−0.710943	−	0.703250i	$-0.751731\pi$
$677$	−25046.5	−1.42189	−0.710943	+	0.703250i	$0.751731\pi$
$678$	−30548.1	−1.73037
$679$	−20845.3	−1.17816
$680$	185.912	0.0104844
$681$	49880.6	2.80680
$682$	1553.52	0.0872248
$683$	29270.9	1.63985	0.819925	−	0.572471i	$-0.194015\pi$
$683$	29270.9	1.63985	0.819925	+	0.572471i	$0.194015\pi$
$684$	−97264.7	−5.43715
$685$	5136.92	0.286528
$686$	27116.9	1.50922
$687$	−41268.2	−2.29182
$688$	0	0
$689$	−8434.86	−0.466390
$690$	55686.9	3.07241
$691$	−9696.24	−0.533809	−0.266905	−	0.963723i	$-0.586001\pi$
$691$	−9696.24	−0.533809	−0.266905	+	0.963723i	$0.586001\pi$
$692$	−298.756	−0.0164119
$693$	−13753.4	−0.753891
$694$	−44820.2	−2.45152
$695$	−4794.63	−0.261684
$696$	636.661	0.0346732
$697$	−1586.71	−0.0862282
$698$	24239.6	1.31444
$699$	−10346.0	−0.559833
$700$	−3162.53	−0.170761
$701$	−21478.8	−1.15727	−0.578633	−	0.815588i	$-0.696414\pi$
$701$	−21478.8	−1.15727	−0.578633	+	0.815588i	$0.696414\pi$
$702$	−77946.5	−4.19074
$703$	19247.5	1.03262
$704$	−6454.48	−0.345543
$705$	11199.0	0.598270
$706$	43849.8	2.33755
$707$	18683.3	0.993860
$708$	41283.3	2.19141
$709$	9874.81	0.523069	0.261535	−	0.965194i	$-0.415771\pi$
$709$	9874.81	0.523069	0.261535	+	0.965194i	$0.415771\pi$
$710$	6318.87	0.334004
$711$	37494.7	1.97772
$712$	−256.392	−0.0134954
$713$	−3972.29	−0.208644
$714$	3965.03	0.207826
$715$	5535.98	0.289558
$716$	−19437.1	−1.01453
$717$	51596.7	2.68747
$718$	1495.04	0.0777078
$719$	12872.9	0.667703	0.333852	−	0.942626i	$-0.391652\pi$
$719$	12872.9	0.667703	0.333852	+	0.942626i	$0.391652\pi$
$720$	50751.5	2.62694
$721$	17193.9	0.888120
$722$	70059.4	3.61127
$723$	−5573.58	−0.286700
$724$	20809.2	1.06819
$725$	479.635	0.0245699
$726$	−49380.6	−2.52436
$727$	−14598.6	−0.744749	−0.372375	−	0.928082i	$-0.621456\pi$
$727$	−14598.6	−0.744749	−0.372375	+	0.928082i	$0.621456\pi$
$728$	2050.77	0.104405
$729$	62819.9	3.19158
$730$	−17455.2	−0.884992
$731$	0	0
$732$	−53854.5	−2.71929
$733$	14732.6	0.742376	0.371188	−	0.928558i	$-0.378951\pi$
$733$	14732.6	0.742376	0.371188	+	0.928558i	$0.378951\pi$
$734$	−44736.3	−2.24966
$735$	4320.39	0.216816
$736$	29403.4	1.47259
$737$	−7459.81	−0.372844
$738$	84306.9	4.20512
$739$	20.1557	0.00100330	0.000501650	−	1.00000i	$-0.499840\pi$
$739$	20.1557	0.00100330	0.000501650		1.00000i	$0.499840\pi$
$740$	13015.0	0.646540
$741$	65254.3	3.23506
$742$	−14287.1	−0.706870
$743$	−35216.1	−1.73883	−0.869416	−	0.494081i	$-0.835505\pi$
$743$	−35216.1	−1.73883	−0.869416	+	0.494081i	$0.835505\pi$
$744$	967.673	0.0476836
$745$	−13818.6	−0.679561
$746$	7045.79	0.345797
$747$	44566.8	2.18289
$748$	−523.492	−0.0255892
$749$	−6593.60	−0.321662
$750$	51211.1	2.49329
$751$	6676.95	0.324428	0.162214	−	0.986756i	$-0.448136\pi$
$751$	6676.95	0.324428	0.162214	+	0.986756i	$0.448136\pi$
$752$	5408.32	0.262262
$753$	53367.1	2.58274
$754$	−3979.83	−0.192224
$755$	37172.3	1.79184
$756$	−68698.0	−3.30492
$757$	33881.9	1.62676	0.813380	−	0.581733i	$-0.197625\pi$
$757$	33881.9	1.62676	0.813380	+	0.581733i	$0.197625\pi$
$758$	−14033.8	−0.672467
$759$	−12254.2	−0.586032
$760$	5182.47	0.247353
$761$	−14324.4	−0.682336	−0.341168	−	0.940002i	$-0.610822\pi$
$761$	−14324.4	−0.682336	−0.341168	+	0.940002i	$0.610822\pi$
$762$	86344.1	4.10488
$763$	15563.2	0.738433
$764$	13420.9	0.635537
$765$	4854.76	0.229443
$766$	12305.4	0.580435
$767$	−20167.8	−0.949437
$768$	33047.2	1.55272
$769$	−11554.1	−0.541808	−0.270904	−	0.962606i	$-0.587323\pi$
$769$	−11554.1	−0.541808	−0.270904	+	0.962606i	$0.587323\pi$
$770$	9376.96	0.438860
$771$	66676.7	3.11453
$772$	−535.651	−0.0249722
$773$	−17969.5	−0.836119	−0.418059	−	0.908420i	$-0.637290\pi$
$773$	−17969.5	−0.836119	−0.418059	+	0.908420i	$0.637290\pi$
$774$	0	0
$775$	729.007	0.0337893
$776$	3294.59	0.152409
$777$	21692.6	1.00156
$778$	44013.5	2.02823
$779$	−44231.1	−2.03433
$780$	44124.3	2.02552
$781$	−1390.50	−0.0637079
$782$	2572.49	0.117637
$783$	10418.9	0.475530
$784$	2086.43	0.0950451
$785$	21574.9	0.980944
$786$	53383.8	2.42257
$787$	10528.1	0.476857	0.238429	−	0.971160i	$-0.423368\pi$
$787$	10528.1	0.476857	0.238429	+	0.971160i	$0.423368\pi$
$788$	−7030.60	−0.317836
$789$	−60838.2	−2.74512
$790$	−25563.7	−1.15129
$791$	13152.8	0.591225
$792$	2173.72	0.0975248
$793$	26309.2	1.17814
$794$	−56925.9	−2.54437
$795$	−24023.4	−1.07173
$796$	−17514.7	−0.779888
$797$	−30901.8	−1.37340	−0.686700	−	0.726941i	$-0.740941\pi$
$797$	−30901.8	−1.37340	−0.686700	+	0.726941i	$0.740941\pi$
$798$	110529.	4.90312
$799$	517.346	0.0229066
$800$	−5396.21	−0.238481
$801$	−6695.22	−0.295336
$802$	36353.6	1.60061
$803$	3841.09	0.168803
$804$	−59458.2	−2.60812
$805$	−23976.5	−1.04977
$806$	−6049.03	−0.264352
$807$	19033.6	0.830252
$808$	−2952.90	−0.128568
$809$	−10941.2	−0.475491	−0.237746	−	0.971327i	$-0.576408\pi$
$809$	−10941.2	−0.475491	−0.237746	+	0.971327i	$0.576408\pi$
$810$	−125705.	−5.45288
$811$	−17060.3	−0.738680	−0.369340	−	0.929294i	$-0.620416\pi$
$811$	−17060.3	−0.738680	−0.369340	+	0.929294i	$0.620416\pi$
$812$	−3507.62	−0.151593
$813$	−50105.8	−2.16148
$814$	−5504.18	−0.237004
$815$	12449.8	0.535088
$816$	3219.72	0.138128
$817$	0	0
$818$	44139.1	1.88666
$819$	53552.2	2.28482
$820$	−29908.7	−1.27373
$821$	35934.1	1.52754	0.763768	−	0.645491i	$-0.223347\pi$
$821$	35934.1	1.52754	0.763768	+	0.645491i	$0.223347\pi$
$822$	−17315.6	−0.734732
$823$	27067.0	1.14641	0.573206	−	0.819411i	$-0.305699\pi$
$823$	27067.0	1.14641	0.573206	+	0.819411i	$0.305699\pi$
$824$	−2717.50	−0.114889
$825$	2248.92	0.0949061
$826$	−34160.7	−1.43899
$827$	907.175	0.0381446	0.0190723	−	0.999818i	$-0.493929\pi$
$827$	907.175	0.0381446	0.0190723	+	0.999818i	$0.493929\pi$
$828$	−71121.1	−2.98506
$829$	−12529.3	−0.524924	−0.262462	−	0.964942i	$-0.584534\pi$
$829$	−12529.3	−0.524924	−0.262462	+	0.964942i	$0.584534\pi$
$830$	−30385.4	−1.27071
$831$	37779.7	1.57709
$832$	25132.2	1.04724
$833$	199.583	0.00830147
$834$	16161.8	0.671026
$835$	8294.56	0.343767
$836$	−14592.8	−0.603712
$837$	15835.8	0.653963
$838$	−41674.9	−1.71794
$839$	−45919.6	−1.88953	−0.944767	−	0.327743i	$-0.893712\pi$
$839$	−45919.6	−1.88953	−0.944767	+	0.327743i	$0.893712\pi$
$840$	5840.82	0.239914
$841$	−23857.0	−0.978188
$842$	−52614.2	−2.15345
$843$	−10599.8	−0.433067
$844$	−49159.1	−2.00489
$845$	4972.08	0.202420
$846$	−27488.2	−1.11710
$847$	21261.3	0.862510
$848$	−11601.6	−0.469810
$849$	−4782.61	−0.193332
$850$	−472.111	−0.0190509
$851$	14074.0	0.566921
$852$	−11082.9	−0.445650
$853$	−22276.0	−0.894157	−0.447079	−	0.894495i	$-0.647536\pi$
$853$	−22276.0	−0.894157	−0.447079	+	0.894495i	$0.647536\pi$
$854$	44563.0	1.78561
$855$	135331.	5.41313
$856$	1042.12	0.0416108
$857$	−23199.0	−0.924692	−0.462346	−	0.886699i	$-0.652992\pi$
$857$	−23199.0	−0.924692	−0.462346	+	0.886699i	$0.652992\pi$
$858$	−18660.7	−0.742502
$859$	22495.1	0.893508	0.446754	−	0.894657i	$-0.352580\pi$
$859$	22495.1	0.893508	0.446754	+	0.894657i	$0.352580\pi$
$860$	0	0
$861$	−49850.0	−1.97315
$862$	69880.1	2.76117
$863$	23102.4	0.911258	0.455629	−	0.890170i	$-0.349414\pi$
$863$	23102.4	0.911258	0.455629	+	0.890170i	$0.349414\pi$
$864$	−117219.	−4.61559
$865$	415.680	0.0163394
$866$	−1077.94	−0.0422976
$867$	−48656.1	−1.90594
$868$	−5331.30	−0.208475
$869$	5625.41	0.219596
$870$	−11335.0	−0.441716
$871$	29046.7	1.12998
$872$	−2459.75	−0.0955250
$873$	86032.4	3.33535
$874$	71710.6	2.77534
$875$	−22049.4	−0.851893
$876$	30615.2	1.18081
$877$	−6070.47	−0.233735	−0.116867	−	0.993148i	$-0.537285\pi$
$877$	−6070.47	−0.233735	−0.116867	+	0.993148i	$0.537285\pi$
$878$	−33944.5	−1.30475
$879$	−31258.4	−1.19945
$880$	7614.35	0.291682
$881$	6819.50	0.260789	0.130394	−	0.991462i	$-0.458376\pi$
$881$	6819.50	0.260789	0.130394	+	0.991462i	$0.458376\pi$
$882$	−10604.4	−0.404841
$883$	3950.09	0.150545	0.0752724	−	0.997163i	$-0.476017\pi$
$883$	3950.09	0.150545	0.0752724	+	0.997163i	$0.476017\pi$
$884$	2038.35	0.0775532
$885$	−57440.2	−2.18173
$886$	38654.3	1.46571
$887$	−17839.5	−0.675300	−0.337650	−	0.941272i	$-0.609632\pi$
$887$	−17839.5	−0.675300	−0.337650	+	0.941272i	$0.609632\pi$
$888$	−3428.51	−0.129564
$889$	−37176.3	−1.40253
$890$	4564.76	0.171923
$891$	27662.1	1.04008
$892$	2370.41	0.0889768
$893$	14421.5	0.540423
$894$	46579.7	1.74257
$895$	27044.2	1.01004
$896$	6190.38	0.230811
$897$	47714.8	1.77609
$898$	34766.0	1.29193
$899$	808.555	0.0299965
$900$	13052.4	0.483421
$901$	−1109.78	−0.0410344
$902$	12648.7	0.466915
$903$	0	0
$904$	−2078.79	−0.0764819
$905$	−28953.3	−1.06347
$906$	−125301.	−4.59474
$907$	−29847.0	−1.09267	−0.546335	−	0.837567i	$-0.683977\pi$
$907$	−29847.0	−1.09267	−0.546335	+	0.837567i	$0.683977\pi$
$908$	43434.1	1.58746
$909$	−77109.7	−2.81360
$910$	−36511.6	−1.33005
$911$	11569.8	0.420773	0.210387	−	0.977618i	$-0.432528\pi$
$911$	11569.8	0.420773	0.210387	+	0.977618i	$0.432528\pi$
$912$	89752.7	3.25878
$913$	6686.45	0.242376
$914$	10603.0	0.383717
$915$	74931.5	2.70728
$916$	−35934.7	−1.29620
$917$	−22984.9	−0.827729
$918$	−10255.4	−0.368714
$919$	9492.23	0.340718	0.170359	−	0.985382i	$-0.445507\pi$
$919$	9492.23	0.340718	0.170359	+	0.985382i	$0.445507\pi$
$920$	3789.49	0.135800
$921$	−2009.67	−0.0719012
$922$	45236.4	1.61581
$923$	5414.25	0.193079
$924$	−16446.6	−0.585556
$925$	−2582.90	−0.0918112
$926$	8748.36	0.310463
$927$	−70962.6	−2.51426
$928$	−5985.03	−0.211712
$929$	−2730.58	−0.0964343	−0.0482172	−	0.998837i	$-0.515354\pi$
$929$	−2730.58	−0.0964343	−0.0482172	+	0.998837i	$0.515354\pi$
$930$	−17228.3	−0.607460
$931$	5563.55	0.195852
$932$	−9008.92	−0.316628
$933$	−41928.7	−1.47126
$934$	−62082.5	−2.17495
$935$	728.370	0.0254762
$936$	−8463.92	−0.295568
$937$	−5774.98	−0.201345	−0.100672	−	0.994920i	$-0.532099\pi$
$937$	−5774.98	−0.201345	−0.100672	+	0.994920i	$0.532099\pi$
$938$	49199.9	1.71261
$939$	−56967.5	−1.97983
$940$	9751.68	0.338367
$941$	17886.8	0.619654	0.309827	−	0.950793i	$-0.399729\pi$
$941$	17886.8	0.619654	0.309827	+	0.950793i	$0.399729\pi$
$942$	−72724.7	−2.51539
$943$	−32342.3	−1.11687
$944$	−27739.4	−0.956400
$945$	95584.3	3.29032
$946$	0	0
$947$	−7908.01	−0.271358	−0.135679	−	0.990753i	$-0.543322\pi$
$947$	−7908.01	−0.271358	−0.135679	+	0.990753i	$0.543322\pi$
$948$	44837.1	1.53612
$949$	−14956.3	−0.511592
$950$	−13160.6	−0.449458
$951$	22914.1	0.781326
$952$	269.820	0.00918583
$953$	13077.0	0.444497	0.222249	−	0.974990i	$-0.428660\pi$
$953$	13077.0	0.444497	0.222249	+	0.974990i	$0.428660\pi$
$954$	58965.7	2.00114
$955$	−18673.4	−0.632730
$956$	44928.4	1.51997
$957$	2494.32	0.0842528
$958$	−72202.9	−2.43504
$959$	7455.38	0.251039
$960$	71579.2	2.40647
$961$	−28562.1	−0.958748
$962$	21431.9	0.718289
$963$	27213.1	0.910622
$964$	−4853.26	−0.162150
$965$	745.288	0.0248618
$966$	80820.2	2.69187
$967$	23940.4	0.796146	0.398073	−	0.917354i	$-0.369679\pi$
$967$	23940.4	0.796146	0.398073	+	0.917354i	$0.369679\pi$
$968$	−3360.34	−0.111576
$969$	8585.52	0.284630
$970$	−58656.4	−1.94159
$971$	−19376.2	−0.640382	−0.320191	−	0.947353i	$-0.603747\pi$
$971$	−19376.2	−0.640382	−0.320191	+	0.947353i	$0.603747\pi$
$972$	114635.	3.78283
$973$	−6958.59	−0.229273
$974$	24763.6	0.814657
$975$	−8756.76	−0.287632
$976$	36186.4	1.18678
$977$	12226.1	0.400356	0.200178	−	0.979760i	$-0.435848\pi$
$977$	12226.1	0.400356	0.200178	+	0.979760i	$0.435848\pi$
$978$	−41965.8	−1.37210
$979$	−1004.50	−0.0327925
$980$	3762.02	0.122626
$981$	−64232.1	−2.09049
$982$	5903.52	0.191842
$983$	50942.6	1.65292	0.826459	−	0.562997i	$-0.190352\pi$
$983$	50942.6	1.65292	0.826459	+	0.562997i	$0.190352\pi$
$984$	7878.78	0.255250
$985$	9782.15	0.316432
$986$	−523.627	−0.0169125
$987$	16253.5	0.524169
$988$	56820.9	1.82967
$989$	0	0
$990$	−38700.5	−1.24241
$991$	−23461.4	−0.752044	−0.376022	−	0.926611i	$-0.622708\pi$
$991$	−23461.4	−0.752044	−0.376022	+	0.926611i	$0.622708\pi$
$992$	−9096.77	−0.291152
$993$	81122.9	2.59250
$994$	9170.77	0.292635
$995$	24369.4	0.776443
$996$	53294.1	1.69547
$997$	−42646.2	−1.35468	−0.677341	−	0.735669i	$-0.736868\pi$
$997$	−42646.2	−1.35468	−0.677341	+	0.735669i	$0.736868\pi$
$998$	−1445.43	−0.0458460
$999$	−56107.0	−1.77692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.26		30
43.32	odd	14		43.4.e.a.35.9	yes	60
43.39	odd	14		43.4.e.a.16.9	✓	60
43.42	odd	2		1849.4.a.h.1.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.16.9	✓	60	43.39	odd	14
43.4.e.a.35.9	yes	60	43.32	odd	14
1849.4.a.g.1.26		30	1.1	even	1	trivial
1849.4.a.h.1.5		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)

\(f(q)\)	\(=\)	\(q+4.08390 q^{2} +9.96623 q^{3} +8.67820 q^{4} -12.0746 q^{5} +40.7010 q^{6} -17.5242 q^{7} +2.76970 q^{8} +72.3258 q^{9} +O(q^{10})\)	\(q+4.08390 q^{2} +9.96623 q^{3} +8.67820 q^{4} -12.0746 q^{5} +40.7010 q^{6} -17.5242 q^{7} +2.76970 q^{8} +72.3258 q^{9} -49.3113 q^{10} +10.8512 q^{11} +86.4890 q^{12} -42.2519 q^{13} -71.5670 q^{14} -120.338 q^{15} -58.1144 q^{16} -5.55908 q^{17} +295.371 q^{18} -154.965 q^{19} -104.786 q^{20} -174.650 q^{21} +44.3151 q^{22} -113.312 q^{23} +27.6035 q^{24} +20.7954 q^{25} -172.552 q^{26} +451.727 q^{27} -152.079 q^{28} +23.0645 q^{29} -491.448 q^{30} +35.0562 q^{31} -259.491 q^{32} +108.145 q^{33} -22.7027 q^{34} +211.597 q^{35} +627.657 q^{36} -124.206 q^{37} -632.859 q^{38} -421.092 q^{39} -33.4429 q^{40} +285.427 q^{41} -713.254 q^{42} +94.1687 q^{44} -873.303 q^{45} -462.754 q^{46} -93.0632 q^{47} -579.182 q^{48} -35.9021 q^{49} +84.9262 q^{50} -55.4031 q^{51} -366.670 q^{52} +199.633 q^{53} +1844.81 q^{54} -131.023 q^{55} -48.5368 q^{56} -1544.41 q^{57} +94.1931 q^{58} +477.324 q^{59} -1044.32 q^{60} -622.675 q^{61} +143.166 q^{62} -1267.45 q^{63} -594.818 q^{64} +510.173 q^{65} +441.655 q^{66} -687.465 q^{67} -48.2428 q^{68} -1129.29 q^{69} +864.142 q^{70} -128.142 q^{71} +200.321 q^{72} +353.979 q^{73} -507.243 q^{74} +207.252 q^{75} -1344.81 q^{76} -190.158 q^{77} -1719.69 q^{78} +518.415 q^{79} +701.707 q^{80} +2549.22 q^{81} +1165.66 q^{82} +616.196 q^{83} -1515.65 q^{84} +67.1235 q^{85} +229.866 q^{87} +30.0545 q^{88} -92.5703 q^{89} -3566.48 q^{90} +740.430 q^{91} -983.344 q^{92} +349.378 q^{93} -380.060 q^{94} +1871.13 q^{95} -2586.15 q^{96} +1189.51 q^{97} -146.620 q^{98} +784.820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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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