LMFDB - Embedded newform 6034.2.a.q.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.603112 q^{3} +1.00000 q^{4} -3.65115 q^{5} +0.603112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.63626 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.603112 q^{3} +1.00000 q^{4} -3.65115 q^{5} +0.603112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.63626 q^{9} -3.65115 q^{10} -2.59249 q^{11} +0.603112 q^{12} -4.90247 q^{13} +1.00000 q^{14} -2.20205 q^{15} +1.00000 q^{16} +1.46539 q^{17} -2.63626 q^{18} -0.547176 q^{19} -3.65115 q^{20} +0.603112 q^{21} -2.59249 q^{22} +2.99477 q^{23} +0.603112 q^{24} +8.33092 q^{25} -4.90247 q^{26} -3.39929 q^{27} +1.00000 q^{28} +5.75124 q^{29} -2.20205 q^{30} -6.65065 q^{31} +1.00000 q^{32} -1.56356 q^{33} +1.46539 q^{34} -3.65115 q^{35} -2.63626 q^{36} +0.927920 q^{37} -0.547176 q^{38} -2.95674 q^{39} -3.65115 q^{40} +0.244169 q^{41} +0.603112 q^{42} +5.49672 q^{43} -2.59249 q^{44} +9.62538 q^{45} +2.99477 q^{46} -0.969314 q^{47} +0.603112 q^{48} +1.00000 q^{49} +8.33092 q^{50} +0.883794 q^{51} -4.90247 q^{52} +0.688843 q^{53} -3.39929 q^{54} +9.46556 q^{55} +1.00000 q^{56} -0.330008 q^{57} +5.75124 q^{58} +3.68712 q^{59} -2.20205 q^{60} +10.2419 q^{61} -6.65065 q^{62} -2.63626 q^{63} +1.00000 q^{64} +17.8997 q^{65} -1.56356 q^{66} +4.90369 q^{67} +1.46539 q^{68} +1.80618 q^{69} -3.65115 q^{70} +7.66025 q^{71} -2.63626 q^{72} +8.06712 q^{73} +0.927920 q^{74} +5.02447 q^{75} -0.547176 q^{76} -2.59249 q^{77} -2.95674 q^{78} -12.9803 q^{79} -3.65115 q^{80} +5.85862 q^{81} +0.244169 q^{82} -0.0485866 q^{83} +0.603112 q^{84} -5.35037 q^{85} +5.49672 q^{86} +3.46864 q^{87} -2.59249 q^{88} -14.6910 q^{89} +9.62538 q^{90} -4.90247 q^{91} +2.99477 q^{92} -4.01109 q^{93} -0.969314 q^{94} +1.99782 q^{95} +0.603112 q^{96} +11.9974 q^{97} +1.00000 q^{98} +6.83446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.603112	0.348207	0.174103	−	0.984727i	$-0.444297\pi$
$3$	0.603112	0.348207	0.174103	+	0.984727i	$0.444297\pi$
$4$	1.00000	0.500000
$5$	−3.65115	−1.63285	−0.816423	−	0.577455i	$-0.804046\pi$
$5$	−3.65115	−1.63285	−0.816423	+	0.577455i	$0.804046\pi$
$6$	0.603112	0.246219
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.63626	−0.878752
$10$	−3.65115	−1.15460
$11$	−2.59249	−0.781664	−0.390832	−	0.920462i	$-0.627813\pi$
$11$	−2.59249	−0.781664	−0.390832	+	0.920462i	$0.627813\pi$
$12$	0.603112	0.174103
$13$	−4.90247	−1.35970	−0.679850	−	0.733351i	$-0.737955\pi$
$13$	−4.90247	−1.35970	−0.679850	+	0.733351i	$0.737955\pi$
$14$	1.00000	0.267261
$15$	−2.20205	−0.568568
$16$	1.00000	0.250000
$17$	1.46539	0.355410	0.177705	−	0.984084i	$-0.443133\pi$
$17$	1.46539	0.355410	0.177705	+	0.984084i	$0.443133\pi$
$18$	−2.63626	−0.621372
$19$	−0.547176	−0.125531	−0.0627654	−	0.998028i	$-0.519992\pi$
$19$	−0.547176	−0.125531	−0.0627654	+	0.998028i	$0.519992\pi$
$20$	−3.65115	−0.816423
$21$	0.603112	0.131610
$22$	−2.59249	−0.552720
$23$	2.99477	0.624454	0.312227	−	0.950008i	$-0.398925\pi$
$23$	2.99477	0.624454	0.312227	+	0.950008i	$0.398925\pi$
$24$	0.603112	0.123110
$25$	8.33092	1.66618
$26$	−4.90247	−0.961453
$27$	−3.39929	−0.654194
$28$	1.00000	0.188982
$29$	5.75124	1.06798	0.533989	−	0.845491i	$-0.320692\pi$
$29$	5.75124	1.06798	0.533989	+	0.845491i	$0.320692\pi$
$30$	−2.20205	−0.402038
$31$	−6.65065	−1.19449	−0.597246	−	0.802058i	$-0.703738\pi$
$31$	−6.65065	−1.19449	−0.597246	+	0.802058i	$0.703738\pi$
$32$	1.00000	0.176777
$33$	−1.56356	−0.272181
$34$	1.46539	0.251313
$35$	−3.65115	−0.617158
$36$	−2.63626	−0.439376
$37$	0.927920	0.152549	0.0762746	−	0.997087i	$-0.475697\pi$
$37$	0.927920	0.152549	0.0762746	+	0.997087i	$0.475697\pi$
$38$	−0.547176	−0.0887636
$39$	−2.95674	−0.473457
$40$	−3.65115	−0.577298
$41$	0.244169	0.0381328	0.0190664	−	0.999818i	$-0.493931\pi$
$41$	0.244169	0.0381328	0.0190664	+	0.999818i	$0.493931\pi$
$42$	0.603112	0.0930621
$43$	5.49672	0.838242	0.419121	−	0.907930i	$-0.362338\pi$
$43$	5.49672	0.838242	0.419121	+	0.907930i	$0.362338\pi$
$44$	−2.59249	−0.390832
$45$	9.62538	1.43487
$46$	2.99477	0.441555
$47$	−0.969314	−0.141389	−0.0706945	−	0.997498i	$-0.522522\pi$
$47$	−0.969314	−0.141389	−0.0706945	+	0.997498i	$0.522522\pi$
$48$	0.603112	0.0870516
$49$	1.00000	0.142857
$50$	8.33092	1.17817
$51$	0.883794	0.123756
$52$	−4.90247	−0.679850
$53$	0.688843	0.0946198	0.0473099	−	0.998880i	$-0.484935\pi$
$53$	0.688843	0.0946198	0.0473099	+	0.998880i	$0.484935\pi$
$54$	−3.39929	−0.462585
$55$	9.46556	1.27634
$56$	1.00000	0.133631
$57$	−0.330008	−0.0437106
$58$	5.75124	0.755175
$59$	3.68712	0.480023	0.240011	−	0.970770i	$-0.422849\pi$
$59$	3.68712	0.480023	0.240011	+	0.970770i	$0.422849\pi$
$60$	−2.20205	−0.284284
$61$	10.2419	1.31134	0.655670	−	0.755047i	$-0.272386\pi$
$61$	10.2419	1.31134	0.655670	+	0.755047i	$0.272386\pi$
$62$	−6.65065	−0.844634
$63$	−2.63626	−0.332137
$64$	1.00000	0.125000
$65$	17.8997	2.22018
$66$	−1.56356	−0.192461
$67$	4.90369	0.599081	0.299540	−	0.954084i	$-0.403167\pi$
$67$	4.90369	0.599081	0.299540	+	0.954084i	$0.403167\pi$
$68$	1.46539	0.177705
$69$	1.80618	0.217439
$70$	−3.65115	−0.436396
$71$	7.66025	0.909105	0.454552	−	0.890720i	$-0.349799\pi$
$71$	7.66025	0.909105	0.454552	+	0.890720i	$0.349799\pi$
$72$	−2.63626	−0.310686
$73$	8.06712	0.944185	0.472092	−	0.881549i	$-0.343499\pi$
$73$	8.06712	0.944185	0.472092	+	0.881549i	$0.343499\pi$
$74$	0.927920	0.107869
$75$	5.02447	0.580176
$76$	−0.547176	−0.0627654
$77$	−2.59249	−0.295441
$78$	−2.95674	−0.334784
$79$	−12.9803	−1.46040	−0.730201	−	0.683232i	$-0.760574\pi$
$79$	−12.9803	−1.46040	−0.730201	+	0.683232i	$0.760574\pi$
$80$	−3.65115	−0.408211
$81$	5.85862	0.650958
$82$	0.244169	0.0269640
$83$	−0.0485866	−0.00533307	−0.00266654	−	0.999996i	$-0.500849\pi$
$83$	−0.0485866	−0.00533307	−0.00266654	+	0.999996i	$0.500849\pi$
$84$	0.603112	0.0658049
$85$	−5.35037	−0.580329
$86$	5.49672	0.592727
$87$	3.46864	0.371877
$88$	−2.59249	−0.276360
$89$	−14.6910	−1.55724	−0.778620	−	0.627495i	$-0.784080\pi$
$89$	−14.6910	−1.55724	−0.778620	+	0.627495i	$0.784080\pi$
$90$	9.62538	1.01460
$91$	−4.90247	−0.513918
$92$	2.99477	0.312227
$93$	−4.01109	−0.415930
$94$	−0.969314	−0.0999771
$95$	1.99782	0.204972
$96$	0.603112	0.0615548
$97$	11.9974	1.21815	0.609073	−	0.793114i	$-0.291541\pi$
$97$	11.9974	1.21815	0.609073	+	0.793114i	$0.291541\pi$
$98$	1.00000	0.101015
$99$	6.83446	0.686889
$100$	8.33092	0.833092
$101$	1.45851	0.145128	0.0725638	−	0.997364i	$-0.476882\pi$
$101$	1.45851	0.145128	0.0725638	+	0.997364i	$0.476882\pi$
$102$	0.883794	0.0875087
$103$	−7.36858	−0.726048	−0.363024	−	0.931780i	$-0.618256\pi$
$103$	−7.36858	−0.726048	−0.363024	+	0.931780i	$0.618256\pi$
$104$	−4.90247	−0.480727
$105$	−2.20205	−0.214898
$106$	0.688843	0.0669063
$107$	12.2316	1.18248	0.591238	−	0.806497i	$-0.298640\pi$
$107$	12.2316	1.18248	0.591238	+	0.806497i	$0.298640\pi$
$108$	−3.39929	−0.327097
$109$	−1.28684	−0.123257	−0.0616286	−	0.998099i	$-0.519629\pi$
$109$	−1.28684	−0.123257	−0.0616286	+	0.998099i	$0.519629\pi$
$110$	9.46556	0.902506
$111$	0.559639	0.0531186
$112$	1.00000	0.0944911
$113$	9.73322	0.915624	0.457812	−	0.889049i	$-0.348633\pi$
$113$	9.73322	0.915624	0.457812	+	0.889049i	$0.348633\pi$
$114$	−0.330008	−0.0309081
$115$	−10.9344	−1.01964
$116$	5.75124	0.533989
$117$	12.9242	1.19484
$118$	3.68712	0.339427
$119$	1.46539	0.134332
$120$	−2.20205	−0.201019
$121$	−4.27902	−0.389002
$122$	10.2419	0.927258
$123$	0.147261	0.0132781
$124$	−6.65065	−0.597246
$125$	−12.1617	−1.08778
$126$	−2.63626	−0.234856
$127$	0.892974	0.0792386	0.0396193	−	0.999215i	$-0.487385\pi$
$127$	0.892974	0.0792386	0.0396193	+	0.999215i	$0.487385\pi$
$128$	1.00000	0.0883883
$129$	3.31514	0.291881
$130$	17.8997	1.56990
$131$	−0.212205	−0.0185405	−0.00927023	−	0.999957i	$-0.502951\pi$
$131$	−0.212205	−0.0185405	−0.00927023	+	0.999957i	$0.502951\pi$
$132$	−1.56356	−0.136090
$133$	−0.547176	−0.0474462
$134$	4.90369	0.423614
$135$	12.4113	1.06820
$136$	1.46539	0.125656
$137$	2.17513	0.185834	0.0929170	−	0.995674i	$-0.470381\pi$
$137$	2.17513	0.185834	0.0929170	+	0.995674i	$0.470381\pi$
$138$	1.80618	0.153753
$139$	11.8669	1.00654	0.503269	−	0.864130i	$-0.332131\pi$
$139$	11.8669	1.00654	0.503269	+	0.864130i	$0.332131\pi$
$140$	−3.65115	−0.308579
$141$	−0.584604	−0.0492326
$142$	7.66025	0.642834
$143$	12.7096	1.06283
$144$	−2.63626	−0.219688
$145$	−20.9987	−1.74384
$146$	8.06712	0.667640
$147$	0.603112	0.0497438
$148$	0.927920	0.0762746
$149$	12.1089	0.991999	0.496000	−	0.868323i	$-0.334802\pi$
$149$	12.1089	0.991999	0.496000	+	0.868323i	$0.334802\pi$
$150$	5.02447	0.410247
$151$	13.3576	1.08702	0.543512	−	0.839401i	$-0.317094\pi$
$151$	13.3576	1.08702	0.543512	+	0.839401i	$0.317094\pi$
$152$	−0.547176	−0.0443818
$153$	−3.86315	−0.312317
$154$	−2.59249	−0.208908
$155$	24.2826	1.95042
$156$	−2.95674	−0.236728
$157$	−1.82471	−0.145627	−0.0728137	−	0.997346i	$-0.523198\pi$
$157$	−1.82471	−0.145627	−0.0728137	+	0.997346i	$0.523198\pi$
$158$	−12.9803	−1.03266
$159$	0.415449	0.0329473
$160$	−3.65115	−0.288649
$161$	2.99477	0.236021
$162$	5.85862	0.460296
$163$	14.0009	1.09664	0.548319	−	0.836270i	$-0.315268\pi$
$163$	14.0009	1.09664	0.548319	+	0.836270i	$0.315268\pi$
$164$	0.244169	0.0190664
$165$	5.70879	0.444429
$166$	−0.0485866	−0.00377105
$167$	5.09348	0.394145	0.197073	−	0.980389i	$-0.436856\pi$
$167$	5.09348	0.394145	0.197073	+	0.980389i	$0.436856\pi$
$168$	0.603112	0.0465311
$169$	11.0342	0.848784
$170$	−5.35037	−0.410355
$171$	1.44250	0.110310
$172$	5.49672	0.419121
$173$	20.5568	1.56291	0.781454	−	0.623963i	$-0.214478\pi$
$173$	20.5568	1.56291	0.781454	+	0.623963i	$0.214478\pi$
$174$	3.46864	0.262957
$175$	8.33092	0.629758
$176$	−2.59249	−0.195416
$177$	2.22375	0.167147
$178$	−14.6910	−1.10114
$179$	−11.9519	−0.893329	−0.446665	−	0.894701i	$-0.647388\pi$
$179$	−11.9519	−0.893329	−0.446665	+	0.894701i	$0.647388\pi$
$180$	9.62538	0.717433
$181$	−11.9012	−0.884610	−0.442305	−	0.896865i	$-0.645839\pi$
$181$	−11.9012	−0.884610	−0.442305	+	0.896865i	$0.645839\pi$
$182$	−4.90247	−0.363395
$183$	6.17701	0.456617
$184$	2.99477	0.220778
$185$	−3.38798	−0.249089
$186$	−4.01109	−0.294107
$187$	−3.79901	−0.277811
$188$	−0.969314	−0.0706945
$189$	−3.39929	−0.247262
$190$	1.99782	0.144937
$191$	−16.2983	−1.17930	−0.589652	−	0.807658i	$-0.700735\pi$
$191$	−16.2983	−1.17930	−0.589652	+	0.807658i	$0.700735\pi$
$192$	0.603112	0.0435258
$193$	8.22901	0.592337	0.296168	−	0.955136i	$-0.404291\pi$
$193$	8.22901	0.592337	0.296168	+	0.955136i	$0.404291\pi$
$194$	11.9974	0.861360
$195$	10.7955	0.773081
$196$	1.00000	0.0714286
$197$	−17.5777	−1.25236	−0.626180	−	0.779678i	$-0.715383\pi$
$197$	−17.5777	−1.25236	−0.626180	+	0.779678i	$0.715383\pi$
$198$	6.83446	0.485704
$199$	6.22172	0.441046	0.220523	−	0.975382i	$-0.429224\pi$
$199$	6.22172	0.441046	0.220523	+	0.975382i	$0.429224\pi$
$200$	8.33092	0.589085
$201$	2.95747	0.208604
$202$	1.45851	0.102621
$203$	5.75124	0.403658
$204$	0.883794	0.0618780
$205$	−0.891500	−0.0622650
$206$	−7.36858	−0.513393
$207$	−7.89499	−0.548740
$208$	−4.90247	−0.339925
$209$	1.41855	0.0981228
$210$	−2.20205	−0.151956
$211$	4.29207	0.295478	0.147739	−	0.989026i	$-0.452800\pi$
$211$	4.29207	0.295478	0.147739	+	0.989026i	$0.452800\pi$
$212$	0.688843	0.0473099
$213$	4.61999	0.316556
$214$	12.2316	0.836136
$215$	−20.0694	−1.36872
$216$	−3.39929	−0.231292
$217$	−6.65065	−0.451476
$218$	−1.28684	−0.0871559
$219$	4.86537	0.328771
$220$	9.46556	0.638168
$221$	−7.18403	−0.483250
$222$	0.559639	0.0375605
$223$	−25.2931	−1.69375	−0.846875	−	0.531792i	$-0.821519\pi$
$223$	−25.2931	−1.69375	−0.846875	+	0.531792i	$0.821519\pi$
$224$	1.00000	0.0668153
$225$	−21.9624	−1.46416
$226$	9.73322	0.647444
$227$	13.7499	0.912614	0.456307	−	0.889822i	$-0.349172\pi$
$227$	13.7499	0.912614	0.456307	+	0.889822i	$0.349172\pi$
$228$	−0.330008	−0.0218553
$229$	−3.41534	−0.225692	−0.112846	−	0.993612i	$-0.535997\pi$
$229$	−3.41534	−0.225692	−0.112846	+	0.993612i	$0.535997\pi$
$230$	−10.9344	−0.720992
$231$	−1.56356	−0.102875
$232$	5.75124	0.377587
$233$	−24.0682	−1.57676	−0.788380	−	0.615188i	$-0.789080\pi$
$233$	−24.0682	−1.57676	−0.788380	+	0.615188i	$0.789080\pi$
$234$	12.9242	0.844879
$235$	3.53911	0.230866
$236$	3.68712	0.240011
$237$	−7.82859	−0.508522
$238$	1.46539	0.0949872
$239$	10.1952	0.659474	0.329737	−	0.944073i	$-0.393040\pi$
$239$	10.1952	0.659474	0.329737	+	0.944073i	$0.393040\pi$
$240$	−2.20205	−0.142142
$241$	−2.54260	−0.163783	−0.0818915	−	0.996641i	$-0.526096\pi$
$241$	−2.54260	−0.163783	−0.0818915	+	0.996641i	$0.526096\pi$
$242$	−4.27902	−0.275066
$243$	13.7313	0.880862
$244$	10.2419	0.655670
$245$	−3.65115	−0.233264
$246$	0.147261	0.00938904
$247$	2.68251	0.170684
$248$	−6.65065	−0.422317
$249$	−0.0293031	−0.00185701
$250$	−12.1617	−0.769173
$251$	0.293428	0.0185210	0.00926050	−	0.999957i	$-0.497052\pi$
$251$	0.293428	0.0185210	0.00926050	+	0.999957i	$0.497052\pi$
$252$	−2.63626	−0.166069
$253$	−7.76391	−0.488113
$254$	0.892974	0.0560301
$255$	−3.22687	−0.202074
$256$	1.00000	0.0625000
$257$	−18.0476	−1.12578	−0.562888	−	0.826533i	$-0.690310\pi$
$257$	−18.0476	−1.12578	−0.562888	+	0.826533i	$0.690310\pi$
$258$	3.31514	0.206391
$259$	0.927920	0.0576582
$260$	17.8997	1.11009
$261$	−15.1617	−0.938488
$262$	−0.212205	−0.0131101
$263$	−1.45731	−0.0898614	−0.0449307	−	0.998990i	$-0.514307\pi$
$263$	−1.45731	−0.0898614	−0.0449307	+	0.998990i	$0.514307\pi$
$264$	−1.56356	−0.0962303
$265$	−2.51507	−0.154500
$266$	−0.547176	−0.0335495
$267$	−8.86030	−0.542241
$268$	4.90369	0.299540
$269$	8.50710	0.518687	0.259344	−	0.965785i	$-0.416494\pi$
$269$	8.50710	0.518687	0.259344	+	0.965785i	$0.416494\pi$
$270$	12.4113	0.755330
$271$	5.80043	0.352351	0.176175	−	0.984359i	$-0.443627\pi$
$271$	5.80043	0.352351	0.176175	+	0.984359i	$0.443627\pi$
$272$	1.46539	0.0888524
$273$	−2.95674	−0.178950
$274$	2.17513	0.131404
$275$	−21.5978	−1.30240
$276$	1.80618	0.108719
$277$	2.52701	0.151833	0.0759167	−	0.997114i	$-0.475812\pi$
$277$	2.52701	0.151833	0.0759167	+	0.997114i	$0.475812\pi$
$278$	11.8669	0.711730
$279$	17.5328	1.04966
$280$	−3.65115	−0.218198
$281$	10.9032	0.650429	0.325214	−	0.945640i	$-0.394564\pi$
$281$	10.9032	0.650429	0.325214	+	0.945640i	$0.394564\pi$
$282$	−0.584604	−0.0348127
$283$	6.27043	0.372739	0.186369	−	0.982480i	$-0.440328\pi$
$283$	6.27043	0.372739	0.186369	+	0.982480i	$0.440328\pi$
$284$	7.66025	0.454552
$285$	1.20491	0.0713727
$286$	12.7096	0.751533
$287$	0.244169	0.0144129
$288$	−2.63626	−0.155343
$289$	−14.8526	−0.873684
$290$	−20.9987	−1.23308
$291$	7.23574	0.424167
$292$	8.06712	0.472092
$293$	4.12075	0.240737	0.120368	−	0.992729i	$-0.461592\pi$
$293$	4.12075	0.240737	0.120368	+	0.992729i	$0.461592\pi$
$294$	0.603112	0.0351742
$295$	−13.4623	−0.783803
$296$	0.927920	0.0539343
$297$	8.81261	0.511360
$298$	12.1089	0.701449
$299$	−14.6818	−0.849070
$300$	5.02447	0.290088
$301$	5.49672	0.316826
$302$	13.3576	0.768643
$303$	0.879646	0.0505344
$304$	−0.547176	−0.0313827
$305$	−37.3947	−2.14122
$306$	−3.86315	−0.220841
$307$	7.16274	0.408799	0.204399	−	0.978888i	$-0.434476\pi$
$307$	7.16274	0.408799	0.204399	+	0.978888i	$0.434476\pi$
$308$	−2.59249	−0.147721
$309$	−4.44408	−0.252815
$310$	24.2826	1.37916
$311$	17.4381	0.988821	0.494411	−	0.869228i	$-0.335384\pi$
$311$	17.4381	0.988821	0.494411	+	0.869228i	$0.335384\pi$
$312$	−2.95674	−0.167392
$313$	2.83622	0.160313	0.0801563	−	0.996782i	$-0.474458\pi$
$313$	2.83622	0.160313	0.0801563	+	0.996782i	$0.474458\pi$
$314$	−1.82471	−0.102974
$315$	9.62538	0.542329
$316$	−12.9803	−0.730201
$317$	18.0306	1.01270	0.506349	−	0.862328i	$-0.330995\pi$
$317$	18.0306	1.01270	0.506349	+	0.862328i	$0.330995\pi$
$318$	0.415449	0.0232972
$319$	−14.9100	−0.834800
$320$	−3.65115	−0.204106
$321$	7.37703	0.411746
$322$	2.99477	0.166892
$323$	−0.801827	−0.0446148
$324$	5.85862	0.325479
$325$	−40.8421	−2.26551
$326$	14.0009	0.775440
$327$	−0.776109	−0.0429189
$328$	0.244169	0.0134820
$329$	−0.969314	−0.0534400
$330$	5.70879	0.314259
$331$	−10.4035	−0.571828	−0.285914	−	0.958255i	$-0.592297\pi$
$331$	−10.4035	−0.571828	−0.285914	+	0.958255i	$0.592297\pi$
$332$	−0.0485866	−0.00266654
$333$	−2.44624	−0.134053
$334$	5.09348	0.278703
$335$	−17.9041	−0.978206
$336$	0.603112	0.0329024
$337$	−3.22829	−0.175856	−0.0879281	−	0.996127i	$-0.528025\pi$
$337$	−3.22829	−0.175856	−0.0879281	+	0.996127i	$0.528025\pi$
$338$	11.0342	0.600181
$339$	5.87022	0.318826
$340$	−5.35037	−0.290164
$341$	17.2417	0.933692
$342$	1.44250	0.0780012
$343$	1.00000	0.0539949
$344$	5.49672	0.296363
$345$	−6.59465	−0.355044
$346$	20.5568	1.10514
$347$	5.10002	0.273784	0.136892	−	0.990586i	$-0.456289\pi$
$347$	5.10002	0.273784	0.136892	+	0.990586i	$0.456289\pi$
$348$	3.46864	0.185939
$349$	−17.1577	−0.918429	−0.459214	−	0.888325i	$-0.651869\pi$
$349$	−17.1577	−0.918429	−0.459214	+	0.888325i	$0.651869\pi$
$350$	8.33092	0.445306
$351$	16.6649	0.889507
$352$	−2.59249	−0.138180
$353$	29.3122	1.56013	0.780064	−	0.625699i	$-0.215186\pi$
$353$	29.3122	1.56013	0.780064	+	0.625699i	$0.215186\pi$
$354$	2.22375	0.118191
$355$	−27.9688	−1.48443
$356$	−14.6910	−0.778620
$357$	0.883794	0.0467754
$358$	−11.9519	−0.631679
$359$	29.2845	1.54558	0.772789	−	0.634663i	$-0.218861\pi$
$359$	29.2845	1.54558	0.772789	+	0.634663i	$0.218861\pi$
$360$	9.62538	0.507302
$361$	−18.7006	−0.984242
$362$	−11.9012	−0.625514
$363$	−2.58072	−0.135453
$364$	−4.90247	−0.256959
$365$	−29.4543	−1.54171
$366$	6.17701	0.322877
$367$	−21.6854	−1.13197	−0.565984	−	0.824416i	$-0.691504\pi$
$367$	−21.6854	−1.13197	−0.565984	+	0.824416i	$0.691504\pi$
$368$	2.99477	0.156113
$369$	−0.643693	−0.0335093
$370$	−3.38798	−0.176133
$371$	0.688843	0.0357629
$372$	−4.01109	−0.207965
$373$	21.3814	1.10709	0.553543	−	0.832821i	$-0.313275\pi$
$373$	21.3814	1.10709	0.553543	+	0.832821i	$0.313275\pi$
$374$	−3.79901	−0.196442
$375$	−7.33486	−0.378771
$376$	−0.969314	−0.0499886
$377$	−28.1953	−1.45213
$378$	−3.39929	−0.174841
$379$	17.9526	0.922163	0.461082	−	0.887358i	$-0.347462\pi$
$379$	17.9526	0.922163	0.461082	+	0.887358i	$0.347462\pi$
$380$	1.99782	0.102486
$381$	0.538563	0.0275914
$382$	−16.2983	−0.833893
$383$	16.2767	0.831703	0.415851	−	0.909433i	$-0.363484\pi$
$383$	16.2767	0.831703	0.415851	+	0.909433i	$0.363484\pi$
$384$	0.603112	0.0307774
$385$	9.46556	0.482410
$386$	8.22901	0.418845
$387$	−14.4908	−0.736607
$388$	11.9974	0.609073
$389$	27.2876	1.38354	0.691769	−	0.722119i	$-0.256832\pi$
$389$	27.2876	1.38354	0.691769	+	0.722119i	$0.256832\pi$
$390$	10.7955	0.546651
$391$	4.38852	0.221937
$392$	1.00000	0.0505076
$393$	−0.127983	−0.00645591
$394$	−17.5777	−0.885553
$395$	47.3932	2.38461
$396$	6.83446	0.343444
$397$	−17.6557	−0.886116	−0.443058	−	0.896493i	$-0.646106\pi$
$397$	−17.6557	−0.886116	−0.443058	+	0.896493i	$0.646106\pi$
$398$	6.22172	0.311866
$399$	−0.330008	−0.0165211
$400$	8.33092	0.416546
$401$	−7.50189	−0.374627	−0.187313	−	0.982300i	$-0.559978\pi$
$401$	−7.50189	−0.374627	−0.187313	+	0.982300i	$0.559978\pi$
$402$	2.95747	0.147505
$403$	32.6046	1.62415
$404$	1.45851	0.0725638
$405$	−21.3907	−1.06291
$406$	5.75124	0.285429
$407$	−2.40562	−0.119242
$408$	0.883794	0.0437543
$409$	15.3140	0.757228	0.378614	−	0.925555i	$-0.376401\pi$
$409$	15.3140	0.757228	0.378614	+	0.925555i	$0.376401\pi$
$410$	−0.891500	−0.0440280
$411$	1.31185	0.0647086
$412$	−7.36858	−0.363024
$413$	3.68712	0.181431
$414$	−7.89499	−0.388018
$415$	0.177397	0.00870809
$416$	−4.90247	−0.240363
$417$	7.15707	0.350483
$418$	1.41855	0.0693833
$419$	−2.53590	−0.123887	−0.0619434	−	0.998080i	$-0.519730\pi$
$419$	−2.53590	−0.123887	−0.0619434	+	0.998080i	$0.519730\pi$
$420$	−2.20205	−0.107449
$421$	−9.50517	−0.463254	−0.231627	−	0.972805i	$-0.574405\pi$
$421$	−9.50517	−0.463254	−0.231627	+	0.972805i	$0.574405\pi$
$422$	4.29207	0.208935
$423$	2.55536	0.124246
$424$	0.688843	0.0334532
$425$	12.2081	0.592178
$426$	4.61999	0.223839
$427$	10.2419	0.495640
$428$	12.2316	0.591238
$429$	7.66529	0.370084
$430$	−20.0694	−0.967831
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−3.39929	−0.163548
$433$	−9.36334	−0.449973	−0.224987	−	0.974362i	$-0.572234\pi$
$433$	−9.36334	−0.449973	−0.224987	+	0.974362i	$0.572234\pi$
$434$	−6.65065	−0.319242
$435$	−12.6645	−0.607218
$436$	−1.28684	−0.0616286
$437$	−1.63867	−0.0783881
$438$	4.86537	0.232476
$439$	−8.18480	−0.390639	−0.195320	−	0.980740i	$-0.562574\pi$
$439$	−8.18480	−0.390639	−0.195320	+	0.980740i	$0.562574\pi$
$440$	9.46556	0.451253
$441$	−2.63626	−0.125536
$442$	−7.18403	−0.341710
$443$	−3.69384	−0.175500	−0.0877498	−	0.996143i	$-0.527968\pi$
$443$	−3.69384	−0.175500	−0.0877498	+	0.996143i	$0.527968\pi$
$444$	0.559639	0.0265593
$445$	53.6390	2.54273
$446$	−25.2931	−1.19766
$447$	7.30301	0.345421
$448$	1.00000	0.0472456
$449$	7.89193	0.372443	0.186222	−	0.982508i	$-0.440376\pi$
$449$	7.89193	0.372443	0.186222	+	0.982508i	$0.440376\pi$
$450$	−21.9624	−1.03532
$451$	−0.633006	−0.0298071
$452$	9.73322	0.457812
$453$	8.05611	0.378509
$454$	13.7499	0.645315
$455$	17.8997	0.839149
$456$	−0.330008	−0.0154540
$457$	−12.5130	−0.585333	−0.292666	−	0.956215i	$-0.594543\pi$
$457$	−12.5130	−0.585333	−0.292666	+	0.956215i	$0.594543\pi$
$458$	−3.41534	−0.159589
$459$	−4.98129	−0.232507
$460$	−10.9344	−0.509818
$461$	−32.1472	−1.49724	−0.748622	−	0.662997i	$-0.769284\pi$
$461$	−32.1472	−1.49724	−0.748622	+	0.662997i	$0.769284\pi$
$462$	−1.56356	−0.0727433
$463$	28.6003	1.32917	0.664584	−	0.747214i	$-0.268609\pi$
$463$	28.6003	1.32917	0.664584	+	0.747214i	$0.268609\pi$
$464$	5.75124	0.266995
$465$	14.6451	0.679150
$466$	−24.0682	−1.11494
$467$	−20.8547	−0.965039	−0.482520	−	0.875885i	$-0.660278\pi$
$467$	−20.8547	−0.965039	−0.482520	+	0.875885i	$0.660278\pi$
$468$	12.9242	0.597420
$469$	4.90369	0.226431
$470$	3.53911	0.163247
$471$	−1.10050	−0.0507084
$472$	3.68712	0.169714
$473$	−14.2502	−0.655223
$474$	−7.82859	−0.359579
$475$	−4.55848	−0.209157
$476$	1.46539	0.0671661
$477$	−1.81597	−0.0831474
$478$	10.1952	0.466319
$479$	19.8706	0.907911	0.453956	−	0.891024i	$-0.350012\pi$
$479$	19.8706	0.907911	0.453956	+	0.891024i	$0.350012\pi$
$480$	−2.20205	−0.100509
$481$	−4.54910	−0.207421
$482$	−2.54260	−0.115812
$483$	1.80618	0.0821842
$484$	−4.27902	−0.194501
$485$	−43.8042	−1.98905
$486$	13.7313	0.622863
$487$	3.70908	0.168074	0.0840372	−	0.996463i	$-0.473219\pi$
$487$	3.70908	0.168074	0.0840372	+	0.996463i	$0.473219\pi$
$488$	10.2419	0.463629
$489$	8.44412	0.381856
$490$	−3.65115	−0.164942
$491$	22.8010	1.02899	0.514497	−	0.857492i	$-0.327979\pi$
$491$	22.8010	1.02899	0.514497	+	0.857492i	$0.327979\pi$
$492$	0.147261	0.00663905
$493$	8.42782	0.379570
$494$	2.68251	0.120692
$495$	−24.9537	−1.12158
$496$	−6.65065	−0.298623
$497$	7.66025	0.343609
$498$	−0.0293031	−0.00131311
$499$	4.66366	0.208774	0.104387	−	0.994537i	$-0.466712\pi$
$499$	4.66366	0.208774	0.104387	+	0.994537i	$0.466712\pi$
$500$	−12.1617	−0.543888
$501$	3.07194	0.137244
$502$	0.293428	0.0130963
$503$	−20.8163	−0.928154	−0.464077	−	0.885795i	$-0.653614\pi$
$503$	−20.8163	−0.928154	−0.464077	+	0.885795i	$0.653614\pi$
$504$	−2.63626	−0.117428
$505$	−5.32526	−0.236971
$506$	−7.76391	−0.345148
$507$	6.65485	0.295552
$508$	0.892974	0.0396193
$509$	−38.4763	−1.70543	−0.852716	−	0.522374i	$-0.825046\pi$
$509$	−38.4763	−1.70543	−0.852716	+	0.522374i	$0.825046\pi$
$510$	−3.22687	−0.142888
$511$	8.06712	0.356868
$512$	1.00000	0.0441942
$513$	1.86001	0.0821214
$514$	−18.0476	−0.796044
$515$	26.9038	1.18552
$516$	3.31514	0.145941
$517$	2.51293	0.110519
$518$	0.927920	0.0407705
$519$	12.3981	0.544215
$520$	17.8997	0.784952
$521$	6.06032	0.265508	0.132754	−	0.991149i	$-0.457618\pi$
$521$	6.06032	0.265508	0.132754	+	0.991149i	$0.457618\pi$
$522$	−15.1617	−0.663611
$523$	−29.4721	−1.28872	−0.644362	−	0.764720i	$-0.722877\pi$
$523$	−29.4721	−1.28872	−0.644362	+	0.764720i	$0.722877\pi$
$524$	−0.212205	−0.00927023
$525$	5.02447	0.219286
$526$	−1.45731	−0.0635416
$527$	−9.74581	−0.424534
$528$	−1.56356	−0.0680451
$529$	−14.0313	−0.610058
$530$	−2.51507	−0.109248
$531$	−9.72020	−0.421821
$532$	−0.547176	−0.0237231
$533$	−1.19703	−0.0518492
$534$	−8.86030	−0.383423
$535$	−44.6595	−1.93080
$536$	4.90369	0.211807
$537$	−7.20835	−0.311063
$538$	8.50710	0.366767
$539$	−2.59249	−0.111666
$540$	12.4113	0.534099
$541$	19.0078	0.817207	0.408604	−	0.912712i	$-0.366016\pi$
$541$	19.0078	0.817207	0.408604	+	0.912712i	$0.366016\pi$
$542$	5.80043	0.249150
$543$	−7.17776	−0.308027
$544$	1.46539	0.0628281
$545$	4.69846	0.201260
$546$	−2.95674	−0.126537
$547$	−18.4152	−0.787379	−0.393689	−	0.919243i	$-0.628801\pi$
$547$	−18.4152	−0.787379	−0.393689	+	0.919243i	$0.628801\pi$
$548$	2.17513	0.0929170
$549$	−27.0003	−1.15234
$550$	−21.5978	−0.920933
$551$	−3.14694	−0.134064
$552$	1.80618	0.0768763
$553$	−12.9803	−0.551980
$554$	2.52701	0.107362
$555$	−2.04333	−0.0867345
$556$	11.8669	0.503269
$557$	23.1013	0.978834	0.489417	−	0.872050i	$-0.337210\pi$
$557$	23.1013	0.978834	0.489417	+	0.872050i	$0.337210\pi$
$558$	17.5328	0.742224
$559$	−26.9475	−1.13976
$560$	−3.65115	−0.154289
$561$	−2.29122	−0.0967356
$562$	10.9032	0.459923
$563$	26.0331	1.09717	0.548583	−	0.836096i	$-0.315168\pi$
$563$	26.0331	1.09717	0.548583	+	0.836096i	$0.315168\pi$
$564$	−0.584604	−0.0246163
$565$	−35.5375	−1.49507
$566$	6.27043	0.263566
$567$	5.85862	0.246039
$568$	7.66025	0.321417
$569$	−45.4758	−1.90644	−0.953222	−	0.302270i	$-0.902256\pi$
$569$	−45.4758	−1.90644	−0.953222	+	0.302270i	$0.902256\pi$
$570$	1.20491	0.0504681
$571$	30.7344	1.28620	0.643098	−	0.765784i	$-0.277649\pi$
$571$	30.7344	1.28620	0.643098	+	0.765784i	$0.277649\pi$
$572$	12.7096	0.531414
$573$	−9.82969	−0.410641
$574$	0.244169	0.0101914
$575$	24.9492	1.04045
$576$	−2.63626	−0.109844
$577$	10.4807	0.436317	0.218158	−	0.975913i	$-0.429995\pi$
$577$	10.4807	0.436317	0.218158	+	0.975913i	$0.429995\pi$
$578$	−14.8526	−0.617788
$579$	4.96301	0.206256
$580$	−20.9987	−0.871922
$581$	−0.0485866	−0.00201571
$582$	7.23574	0.299931
$583$	−1.78582	−0.0739609
$584$	8.06712	0.333820
$585$	−47.1881	−1.95099
$586$	4.12075	0.170227
$587$	26.0575	1.07551	0.537754	−	0.843102i	$-0.319273\pi$
$587$	26.0575	1.07551	0.537754	+	0.843102i	$0.319273\pi$
$588$	0.603112	0.0248719
$589$	3.63908	0.149946
$590$	−13.4623	−0.554232
$591$	−10.6013	−0.436080
$592$	0.927920	0.0381373
$593$	34.2460	1.40631	0.703157	−	0.711035i	$-0.251773\pi$
$593$	34.2460	1.40631	0.703157	+	0.711035i	$0.251773\pi$
$594$	8.81261	0.361586
$595$	−5.35037	−0.219344
$596$	12.1089	0.496000
$597$	3.75239	0.153575
$598$	−14.6818	−0.600383
$599$	31.3253	1.27992	0.639959	−	0.768409i	$-0.278951\pi$
$599$	31.3253	1.27992	0.639959	+	0.768409i	$0.278951\pi$
$600$	5.02447	0.205123
$601$	−18.9653	−0.773613	−0.386806	−	0.922161i	$-0.626422\pi$
$601$	−18.9653	−0.773613	−0.386806	+	0.922161i	$0.626422\pi$
$602$	5.49672	0.224030
$603$	−12.9274	−0.526444
$604$	13.3576	0.543512
$605$	15.6233	0.635179
$606$	0.879646	0.0357332
$607$	−45.3747	−1.84170	−0.920851	−	0.389914i	$-0.872505\pi$
$607$	−45.3747	−1.84170	−0.920851	+	0.389914i	$0.872505\pi$
$608$	−0.547176	−0.0221909
$609$	3.46864	0.140556
$610$	−37.3947	−1.51407
$611$	4.75203	0.192247
$612$	−3.86315	−0.156158
$613$	9.06764	0.366239	0.183119	−	0.983091i	$-0.441381\pi$
$613$	9.06764	0.366239	0.183119	+	0.983091i	$0.441381\pi$
$614$	7.16274	0.289065
$615$	−0.537674	−0.0216811
$616$	−2.59249	−0.104454
$617$	20.1346	0.810590	0.405295	−	0.914186i	$-0.367169\pi$
$617$	20.1346	0.810590	0.405295	+	0.914186i	$0.367169\pi$
$618$	−4.44408	−0.178767
$619$	0.718386	0.0288744	0.0144372	−	0.999896i	$-0.495404\pi$
$619$	0.718386	0.0288744	0.0144372	+	0.999896i	$0.495404\pi$
$620$	24.2826	0.975211
$621$	−10.1801	−0.408514
$622$	17.4381	0.699202
$623$	−14.6910	−0.588582
$624$	−2.95674	−0.118364
$625$	2.74963	0.109985
$626$	2.83622	0.113358
$627$	0.855541	0.0341670
$628$	−1.82471	−0.0728137
$629$	1.35977	0.0542174
$630$	9.62538	0.383484
$631$	20.6541	0.822227	0.411113	−	0.911584i	$-0.365140\pi$
$631$	20.6541	0.822227	0.411113	+	0.911584i	$0.365140\pi$
$632$	−12.9803	−0.516330
$633$	2.58860	0.102887
$634$	18.0306	0.716086
$635$	−3.26038	−0.129384
$636$	0.415449	0.0164736
$637$	−4.90247	−0.194243
$638$	−14.9100	−0.590293
$639$	−20.1944	−0.798878
$640$	−3.65115	−0.144325
$641$	−4.06113	−0.160405	−0.0802025	−	0.996779i	$-0.525557\pi$
$641$	−4.06113	−0.160405	−0.0802025	+	0.996779i	$0.525557\pi$
$642$	7.37703	0.291148
$643$	−9.95561	−0.392611	−0.196305	−	0.980543i	$-0.562894\pi$
$643$	−9.95561	−0.392611	−0.196305	+	0.980543i	$0.562894\pi$
$644$	2.99477	0.118011
$645$	−12.1041	−0.476597
$646$	−0.801827	−0.0315474
$647$	21.0721	0.828429	0.414215	−	0.910179i	$-0.364056\pi$
$647$	21.0721	0.828429	0.414215	+	0.910179i	$0.364056\pi$
$648$	5.85862	0.230148
$649$	−9.55882	−0.375216
$650$	−40.8421	−1.60196
$651$	−4.01109	−0.157207
$652$	14.0009	0.548319
$653$	37.8614	1.48163	0.740816	−	0.671708i	$-0.234439\pi$
$653$	37.8614	1.48163	0.740816	+	0.671708i	$0.234439\pi$
$654$	−0.776109	−0.0303483
$655$	0.774794	0.0302737
$656$	0.244169	0.00953321
$657$	−21.2670	−0.829705
$658$	−0.969314	−0.0377878
$659$	20.6864	0.805827	0.402914	−	0.915238i	$-0.367997\pi$
$659$	20.6864	0.805827	0.402914	+	0.915238i	$0.367997\pi$
$660$	5.70879	0.222214
$661$	27.3589	1.06414	0.532068	−	0.846701i	$-0.321415\pi$
$661$	27.3589	1.06414	0.532068	+	0.846701i	$0.321415\pi$
$662$	−10.4035	−0.404343
$663$	−4.33277	−0.168271
$664$	−0.0485866	−0.00188553
$665$	1.99782	0.0774722
$666$	−2.44624	−0.0947897
$667$	17.2237	0.666903
$668$	5.09348	0.197073
$669$	−15.2545	−0.589775
$670$	−17.9041	−0.691696
$671$	−26.5520	−1.02503
$672$	0.603112	0.0232655
$673$	49.1731	1.89548	0.947742	−	0.319037i	$-0.103360\pi$
$673$	49.1731	1.89548	0.947742	+	0.319037i	$0.103360\pi$
$674$	−3.22829	−0.124349
$675$	−28.3192	−1.09001
$676$	11.0342	0.424392
$677$	28.3584	1.08990	0.544952	−	0.838467i	$-0.316548\pi$
$677$	28.3584	1.08990	0.544952	+	0.838467i	$0.316548\pi$
$678$	5.87022	0.225444
$679$	11.9974	0.460416
$680$	−5.35037	−0.205177
$681$	8.29273	0.317778
$682$	17.2417	0.660220
$683$	6.62417	0.253467	0.126733	−	0.991937i	$-0.459551\pi$
$683$	6.62417	0.253467	0.126733	+	0.991937i	$0.459551\pi$
$684$	1.44250	0.0551552
$685$	−7.94173	−0.303438
$686$	1.00000	0.0381802
$687$	−2.05983	−0.0785876
$688$	5.49672	0.209560
$689$	−3.37703	−0.128655
$690$	−6.59465	−0.251054
$691$	22.6936	0.863306	0.431653	−	0.902040i	$-0.357930\pi$
$691$	22.6936	0.863306	0.431653	+	0.902040i	$0.357930\pi$
$692$	20.5568	0.781454
$693$	6.83446	0.259620
$694$	5.10002	0.193594
$695$	−43.3279	−1.64352
$696$	3.46864	0.131478
$697$	0.357804	0.0135528
$698$	−17.1577	−0.649427
$699$	−14.5158	−0.549038
$700$	8.33092	0.314879
$701$	−0.726945	−0.0274563	−0.0137282	−	0.999906i	$-0.504370\pi$
$701$	−0.726945	−0.0274563	−0.0137282	+	0.999906i	$0.504370\pi$
$702$	16.6649	0.628977
$703$	−0.507736	−0.0191496
$704$	−2.59249	−0.0977080
$705$	2.13448	0.0803892
$706$	29.3122	1.10318
$707$	1.45851	0.0548530
$708$	2.22375	0.0835735
$709$	−47.7556	−1.79350	−0.896750	−	0.442538i	$-0.854078\pi$
$709$	−47.7556	−1.79350	−0.896750	+	0.442538i	$0.854078\pi$
$710$	−27.9688	−1.04965
$711$	34.2195	1.28333
$712$	−14.6910	−0.550568
$713$	−19.9172	−0.745905
$714$	0.883794	0.0330752
$715$	−46.4046	−1.73543
$716$	−11.9519	−0.446665
$717$	6.14886	0.229633
$718$	29.2845	1.09289
$719$	−38.5419	−1.43737	−0.718685	−	0.695336i	$-0.755256\pi$
$719$	−38.5419	−1.43737	−0.718685	+	0.695336i	$0.755256\pi$
$720$	9.62538	0.358717
$721$	−7.36858	−0.274420
$722$	−18.7006	−0.695964
$723$	−1.53347	−0.0570303
$724$	−11.9012	−0.442305
$725$	47.9131	1.77945
$726$	−2.58072	−0.0957797
$727$	12.3287	0.457248	0.228624	−	0.973515i	$-0.426577\pi$
$727$	12.3287	0.457248	0.228624	+	0.973515i	$0.426577\pi$
$728$	−4.90247	−0.181698
$729$	−9.29436	−0.344236
$730$	−29.4543	−1.09015
$731$	8.05485	0.297919
$732$	6.17701	0.228309
$733$	21.4674	0.792916	0.396458	−	0.918053i	$-0.370239\pi$
$733$	21.4674	0.792916	0.396458	+	0.918053i	$0.370239\pi$
$734$	−21.6854	−0.800423
$735$	−2.20205	−0.0812239
$736$	2.99477	0.110389
$737$	−12.7127	−0.468280
$738$	−0.643693	−0.0236947
$739$	−9.53769	−0.350850	−0.175425	−	0.984493i	$-0.556130\pi$
$739$	−9.53769	−0.350850	−0.175425	+	0.984493i	$0.556130\pi$
$740$	−3.38798	−0.124545
$741$	1.61785	0.0594333
$742$	0.688843	0.0252882
$743$	−10.7012	−0.392587	−0.196294	−	0.980545i	$-0.562891\pi$
$743$	−10.7012	−0.392587	−0.196294	+	0.980545i	$0.562891\pi$
$744$	−4.01109	−0.147054
$745$	−44.2114	−1.61978
$746$	21.3814	0.782828
$747$	0.128087	0.00468645
$748$	−3.79901	−0.138905
$749$	12.2316	0.446934
$750$	−7.33486	−0.267831
$751$	−47.2945	−1.72580	−0.862901	−	0.505373i	$-0.831355\pi$
$751$	−47.2945	−1.72580	−0.862901	+	0.505373i	$0.831355\pi$
$752$	−0.969314	−0.0353472
$753$	0.176970	0.00644914
$754$	−28.1953	−1.02681
$755$	−48.7706	−1.77494
$756$	−3.39929	−0.123631
$757$	−13.3327	−0.484584	−0.242292	−	0.970203i	$-0.577899\pi$
$757$	−13.3327	−0.484584	−0.242292	+	0.970203i	$0.577899\pi$
$758$	17.9526	0.652068
$759$	−4.68250	−0.169964
$760$	1.99782	0.0724686
$761$	41.2998	1.49712	0.748559	−	0.663069i	$-0.230746\pi$
$761$	41.2998	1.49712	0.748559	+	0.663069i	$0.230746\pi$
$762$	0.538563	0.0195101
$763$	−1.28684	−0.0465868
$764$	−16.2983	−0.589652
$765$	14.1049	0.509965
$766$	16.2767	0.588103
$767$	−18.0760	−0.652687
$768$	0.603112	0.0217629
$769$	−11.2266	−0.404842	−0.202421	−	0.979299i	$-0.564881\pi$
$769$	−11.2266	−0.404842	−0.202421	+	0.979299i	$0.564881\pi$
$770$	9.46556	0.341115
$771$	−10.8847	−0.392003
$772$	8.22901	0.296168
$773$	−2.22079	−0.0798761	−0.0399380	−	0.999202i	$-0.512716\pi$
$773$	−2.22079	−0.0798761	−0.0399380	+	0.999202i	$0.512716\pi$
$774$	−14.4908	−0.520860
$775$	−55.4061	−1.99024
$776$	11.9974	0.430680
$777$	0.559639	0.0200770
$778$	27.2876	0.978310
$779$	−0.133604	−0.00478684
$780$	10.7955	0.386541
$781$	−19.8591	−0.710614
$782$	4.38852	0.156933
$783$	−19.5501	−0.698665
$784$	1.00000	0.0357143
$785$	6.66228	0.237787
$786$	−0.127983	−0.00456502
$787$	0.431393	0.0153775	0.00768874	−	0.999970i	$-0.497553\pi$
$787$	0.431393	0.0153775	0.00768874	+	0.999970i	$0.497553\pi$
$788$	−17.5777	−0.626180
$789$	−0.878918	−0.0312903
$790$	47.3932	1.68617
$791$	9.73322	0.346073
$792$	6.83446	0.242852
$793$	−50.2106	−1.78303
$794$	−17.6557	−0.626579
$795$	−1.51687	−0.0537978
$796$	6.22172	0.220523
$797$	18.2519	0.646516	0.323258	−	0.946311i	$-0.395222\pi$
$797$	18.2519	0.646516	0.323258	+	0.946311i	$0.395222\pi$
$798$	−0.330008	−0.0116822
$799$	−1.42042	−0.0502510
$800$	8.33092	0.294543
$801$	38.7292	1.36843
$802$	−7.50189	−0.264901
$803$	−20.9139	−0.738035
$804$	2.95747	0.104302
$805$	−10.9344	−0.385386
$806$	32.6046	1.14845
$807$	5.13073	0.180610
$808$	1.45851	0.0513103
$809$	−9.06263	−0.318625	−0.159312	−	0.987228i	$-0.550928\pi$
$809$	−9.06263	−0.318625	−0.159312	+	0.987228i	$0.550928\pi$
$810$	−21.3907	−0.751593
$811$	18.1269	0.636522	0.318261	−	0.948003i	$-0.396901\pi$
$811$	18.1269	0.636522	0.318261	+	0.948003i	$0.396901\pi$
$812$	5.75124	0.201829
$813$	3.49830	0.122691
$814$	−2.40562	−0.0843170
$815$	−51.1195	−1.79064
$816$	0.883794	0.0309390
$817$	−3.00767	−0.105225
$818$	15.3140	0.535441
$819$	12.9242	0.451607
$820$	−0.891500	−0.0311325
$821$	46.4255	1.62026	0.810130	−	0.586250i	$-0.199396\pi$
$821$	46.4255	1.62026	0.810130	+	0.586250i	$0.199396\pi$
$822$	1.31185	0.0457559
$823$	−41.9074	−1.46080	−0.730400	−	0.683019i	$-0.760666\pi$
$823$	−41.9074	−1.46080	−0.730400	+	0.683019i	$0.760666\pi$
$824$	−7.36858	−0.256697
$825$	−13.0259	−0.453503
$826$	3.68712	0.128291
$827$	22.9798	0.799087	0.399543	−	0.916714i	$-0.369169\pi$
$827$	22.9798	0.799087	0.399543	+	0.916714i	$0.369169\pi$
$828$	−7.89499	−0.274370
$829$	−47.2171	−1.63992	−0.819958	−	0.572423i	$-0.806004\pi$
$829$	−47.2171	−1.63992	−0.819958	+	0.572423i	$0.806004\pi$
$830$	0.177397	0.00615755
$831$	1.52407	0.0528694
$832$	−4.90247	−0.169963
$833$	1.46539	0.0507728
$834$	7.15707	0.247829
$835$	−18.5971	−0.643579
$836$	1.41855	0.0490614
$837$	22.6075	0.781430
$838$	−2.53590	−0.0876011
$839$	−36.1482	−1.24797	−0.623987	−	0.781435i	$-0.714488\pi$
$839$	−36.1482	−1.24797	−0.623987	+	0.781435i	$0.714488\pi$
$840$	−2.20205	−0.0759780
$841$	4.07674	0.140577
$842$	−9.50517	−0.327570
$843$	6.57583	0.226484
$844$	4.29207	0.147739
$845$	−40.2875	−1.38593
$846$	2.55536	0.0878551
$847$	−4.27902	−0.147029
$848$	0.688843	0.0236550
$849$	3.78177	0.129790
$850$	12.2081	0.418733
$851$	2.77891	0.0952599
$852$	4.61999	0.158278
$853$	−46.0166	−1.57558	−0.787790	−	0.615944i	$-0.788775\pi$
$853$	−46.0166	−1.57558	−0.787790	+	0.615944i	$0.788775\pi$
$854$	10.2419	0.350470
$855$	−5.26677	−0.180120
$856$	12.2316	0.418068
$857$	11.2060	0.382789	0.191394	−	0.981513i	$-0.438699\pi$
$857$	11.2060	0.382789	0.191394	+	0.981513i	$0.438699\pi$
$858$	7.66529	0.261689
$859$	−1.75281	−0.0598050	−0.0299025	−	0.999553i	$-0.509520\pi$
$859$	−1.75281	−0.0598050	−0.0299025	+	0.999553i	$0.509520\pi$
$860$	−20.0694	−0.684360
$861$	0.147261	0.00501865
$862$	1.00000	0.0340601
$863$	33.4225	1.13771	0.568857	−	0.822436i	$-0.307386\pi$
$863$	33.4225	1.13771	0.568857	+	0.822436i	$0.307386\pi$
$864$	−3.39929	−0.115646
$865$	−75.0562	−2.55199
$866$	−9.36334	−0.318179
$867$	−8.95779	−0.304223
$868$	−6.65065	−0.225738
$869$	33.6513	1.14154
$870$	−12.6645	−0.429368
$871$	−24.0402	−0.814570
$872$	−1.28684	−0.0435780
$873$	−31.6281	−1.07045
$874$	−1.63867	−0.0554288
$875$	−12.1617	−0.411141
$876$	4.86537	0.164386
$877$	31.5904	1.06673	0.533367	−	0.845884i	$-0.320927\pi$
$877$	31.5904	1.06673	0.533367	+	0.845884i	$0.320927\pi$
$878$	−8.18480	−0.276223
$879$	2.48527	0.0838261
$880$	9.46556	0.319084
$881$	−24.7168	−0.832730	−0.416365	−	0.909198i	$-0.636696\pi$
$881$	−24.7168	−0.832730	−0.416365	+	0.909198i	$0.636696\pi$
$882$	−2.63626	−0.0887674
$883$	−8.70175	−0.292837	−0.146419	−	0.989223i	$-0.546775\pi$
$883$	−8.70175	−0.292837	−0.146419	+	0.989223i	$0.546775\pi$
$884$	−7.18403	−0.241625
$885$	−8.11924	−0.272925
$886$	−3.69384	−0.124097
$887$	−54.1672	−1.81876	−0.909378	−	0.415971i	$-0.863442\pi$
$887$	−54.1672	−1.81876	−0.909378	+	0.415971i	$0.863442\pi$
$888$	0.559639	0.0187803
$889$	0.892974	0.0299494
$890$	53.6390	1.79798
$891$	−15.1884	−0.508830
$892$	−25.2931	−0.846875
$893$	0.530385	0.0177487
$894$	7.30301	0.244249
$895$	43.6383	1.45867
$896$	1.00000	0.0334077
$897$	−8.85476	−0.295652
$898$	7.89193	0.263357
$899$	−38.2495	−1.27569
$900$	−21.9624	−0.732081
$901$	1.00942	0.0336288
$902$	−0.633006	−0.0210768
$903$	3.31514	0.110321
$904$	9.73322	0.323722
$905$	43.4532	1.44443
$906$	8.05611	0.267646
$907$	−1.48372	−0.0492663	−0.0246331	−	0.999697i	$-0.507842\pi$
$907$	−1.48372	−0.0492663	−0.0246331	+	0.999697i	$0.507842\pi$
$908$	13.7499	0.456307
$909$	−3.84502	−0.127531
$910$	17.8997	0.593368
$911$	28.2045	0.934456	0.467228	−	0.884137i	$-0.345253\pi$
$911$	28.2045	0.934456	0.467228	+	0.884137i	$0.345253\pi$
$912$	−0.330008	−0.0109277
$913$	0.125960	0.00416867
$914$	−12.5130	−0.413893
$915$	−22.5532	−0.745586
$916$	−3.41534	−0.112846
$917$	−0.212205	−0.00700763
$918$	−4.98129	−0.164407
$919$	−38.9638	−1.28530	−0.642648	−	0.766162i	$-0.722164\pi$
$919$	−38.9638	−1.28530	−0.642648	+	0.766162i	$0.722164\pi$
$920$	−10.9344	−0.360496
$921$	4.31993	0.142347
$922$	−32.1472	−1.05871
$923$	−37.5541	−1.23611
$924$	−1.56356	−0.0514373
$925$	7.73043	0.254175
$926$	28.6003	0.939864
$927$	19.4255	0.638016
$928$	5.75124	0.188794
$929$	22.9317	0.752366	0.376183	−	0.926545i	$-0.377236\pi$
$929$	22.9317	0.752366	0.376183	+	0.926545i	$0.377236\pi$
$930$	14.6451	0.480231
$931$	−0.547176	−0.0179330
$932$	−24.0682	−0.788380
$933$	10.5171	0.344314
$934$	−20.8547	−0.682386
$935$	13.8708	0.453622
$936$	12.9242	0.422440
$937$	−21.3754	−0.698304	−0.349152	−	0.937066i	$-0.613530\pi$
$937$	−21.3754	−0.698304	−0.349152	+	0.937066i	$0.613530\pi$
$938$	4.90369	0.160111
$939$	1.71056	0.0558219
$940$	3.53911	0.115433
$941$	6.63815	0.216398	0.108199	−	0.994129i	$-0.465492\pi$
$941$	6.63815	0.216398	0.108199	+	0.994129i	$0.465492\pi$
$942$	−1.10050	−0.0358563
$943$	0.731232	0.0238122
$944$	3.68712	0.120006
$945$	12.4113	0.403741
$946$	−14.2502	−0.463313
$947$	40.0717	1.30216	0.651078	−	0.759011i	$-0.274317\pi$
$947$	40.0717	1.30216	0.651078	+	0.759011i	$0.274317\pi$
$948$	−7.82859	−0.254261
$949$	−39.5488	−1.28381
$950$	−4.55848	−0.147897
$951$	10.8745	0.352628
$952$	1.46539	0.0474936
$953$	−10.4419	−0.338247	−0.169123	−	0.985595i	$-0.554094\pi$
$953$	−10.4419	−0.338247	−0.169123	+	0.985595i	$0.554094\pi$
$954$	−1.81597	−0.0587941
$955$	59.5076	1.92562
$956$	10.1952	0.329737
$957$	−8.99240	−0.290683
$958$	19.8706	0.641990
$959$	2.17513	0.0702386
$960$	−2.20205	−0.0710709
$961$	13.2312	0.426812
$962$	−4.54910	−0.146669
$963$	−32.2457	−1.03910
$964$	−2.54260	−0.0818915
$965$	−30.0454	−0.967195
$966$	1.80618	0.0581130
$967$	48.8016	1.56935	0.784677	−	0.619905i	$-0.212829\pi$
$967$	48.8016	1.56935	0.784677	+	0.619905i	$0.212829\pi$
$968$	−4.27902	−0.137533
$969$	−0.483591	−0.0155352
$970$	−43.8042	−1.40647
$971$	−4.41651	−0.141733	−0.0708663	−	0.997486i	$-0.522576\pi$
$971$	−4.41651	−0.141733	−0.0708663	+	0.997486i	$0.522576\pi$
$972$	13.7313	0.440431
$973$	11.8669	0.380435
$974$	3.70908	0.118847
$975$	−24.6323	−0.788866
$976$	10.2419	0.327835
$977$	−17.7876	−0.569077	−0.284539	−	0.958665i	$-0.591840\pi$
$977$	−17.7876	−0.569077	−0.284539	+	0.958665i	$0.591840\pi$
$978$	8.44412	0.270013
$979$	38.0862	1.21724
$980$	−3.65115	−0.116632
$981$	3.39245	0.108312
$982$	22.8010	0.727608
$983$	2.11006	0.0673006	0.0336503	−	0.999434i	$-0.489287\pi$
$983$	2.11006	0.0673006	0.0336503	+	0.999434i	$0.489287\pi$
$984$	0.147261	0.00469452
$985$	64.1789	2.04491
$986$	8.42782	0.268396
$987$	−0.584604	−0.0186082
$988$	2.68251	0.0853421
$989$	16.4614	0.523443
$990$	−24.9537	−0.793079
$991$	−59.7186	−1.89702	−0.948512	−	0.316742i	$-0.897411\pi$
$991$	−59.7186	−1.89702	−0.948512	+	0.316742i	$0.897411\pi$
$992$	−6.65065	−0.211158
$993$	−6.27447	−0.199114
$994$	7.66025	0.242968
$995$	−22.7164	−0.720160
$996$	−0.0293031	−0.000928506 0
$997$	−3.04126	−0.0963178	−0.0481589	−	0.998840i	$-0.515335\pi$
$997$	−3.04126	−0.0963178	−0.0481589	+	0.998840i	$0.515335\pi$
$998$	4.66366	0.147625
$999$	−3.15427	−0.0997967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.19	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.19	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.603112 q^{3} +1.00000 q^{4} -3.65115 q^{5} +0.603112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.63626 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.603112 q^{3} +1.00000 q^{4} -3.65115 q^{5} +0.603112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.63626 q^{9} -3.65115 q^{10} -2.59249 q^{11} +0.603112 q^{12} -4.90247 q^{13} +1.00000 q^{14} -2.20205 q^{15} +1.00000 q^{16} +1.46539 q^{17} -2.63626 q^{18} -0.547176 q^{19} -3.65115 q^{20} +0.603112 q^{21} -2.59249 q^{22} +2.99477 q^{23} +0.603112 q^{24} +8.33092 q^{25} -4.90247 q^{26} -3.39929 q^{27} +1.00000 q^{28} +5.75124 q^{29} -2.20205 q^{30} -6.65065 q^{31} +1.00000 q^{32} -1.56356 q^{33} +1.46539 q^{34} -3.65115 q^{35} -2.63626 q^{36} +0.927920 q^{37} -0.547176 q^{38} -2.95674 q^{39} -3.65115 q^{40} +0.244169 q^{41} +0.603112 q^{42} +5.49672 q^{43} -2.59249 q^{44} +9.62538 q^{45} +2.99477 q^{46} -0.969314 q^{47} +0.603112 q^{48} +1.00000 q^{49} +8.33092 q^{50} +0.883794 q^{51} -4.90247 q^{52} +0.688843 q^{53} -3.39929 q^{54} +9.46556 q^{55} +1.00000 q^{56} -0.330008 q^{57} +5.75124 q^{58} +3.68712 q^{59} -2.20205 q^{60} +10.2419 q^{61} -6.65065 q^{62} -2.63626 q^{63} +1.00000 q^{64} +17.8997 q^{65} -1.56356 q^{66} +4.90369 q^{67} +1.46539 q^{68} +1.80618 q^{69} -3.65115 q^{70} +7.66025 q^{71} -2.63626 q^{72} +8.06712 q^{73} +0.927920 q^{74} +5.02447 q^{75} -0.547176 q^{76} -2.59249 q^{77} -2.95674 q^{78} -12.9803 q^{79} -3.65115 q^{80} +5.85862 q^{81} +0.244169 q^{82} -0.0485866 q^{83} +0.603112 q^{84} -5.35037 q^{85} +5.49672 q^{86} +3.46864 q^{87} -2.59249 q^{88} -14.6910 q^{89} +9.62538 q^{90} -4.90247 q^{91} +2.99477 q^{92} -4.01109 q^{93} -0.969314 q^{94} +1.99782 q^{95} +0.603112 q^{96} +11.9974 q^{97} +1.00000 q^{98} +6.83446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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