LMFDB - Embedded newform 6034.2.a.m.1.11

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.235507 q^{3} +1.00000 q^{4} +1.96765 q^{5} -0.235507 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.94454 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.235507 q^{3} +1.00000 q^{4} +1.96765 q^{5} -0.235507 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.94454 q^{9} +1.96765 q^{10} -1.72571 q^{11} -0.235507 q^{12} -2.88399 q^{13} +1.00000 q^{14} -0.463396 q^{15} +1.00000 q^{16} +4.64419 q^{17} -2.94454 q^{18} -0.307017 q^{19} +1.96765 q^{20} -0.235507 q^{21} -1.72571 q^{22} -7.97106 q^{23} -0.235507 q^{24} -1.12834 q^{25} -2.88399 q^{26} +1.39998 q^{27} +1.00000 q^{28} -5.30054 q^{29} -0.463396 q^{30} -10.4527 q^{31} +1.00000 q^{32} +0.406418 q^{33} +4.64419 q^{34} +1.96765 q^{35} -2.94454 q^{36} +4.09908 q^{37} -0.307017 q^{38} +0.679199 q^{39} +1.96765 q^{40} -10.0035 q^{41} -0.235507 q^{42} +6.28292 q^{43} -1.72571 q^{44} -5.79383 q^{45} -7.97106 q^{46} -0.831654 q^{47} -0.235507 q^{48} +1.00000 q^{49} -1.12834 q^{50} -1.09374 q^{51} -2.88399 q^{52} -5.46881 q^{53} +1.39998 q^{54} -3.39560 q^{55} +1.00000 q^{56} +0.0723046 q^{57} -5.30054 q^{58} -4.70985 q^{59} -0.463396 q^{60} -6.46422 q^{61} -10.4527 q^{62} -2.94454 q^{63} +1.00000 q^{64} -5.67468 q^{65} +0.406418 q^{66} +5.35979 q^{67} +4.64419 q^{68} +1.87724 q^{69} +1.96765 q^{70} +10.2101 q^{71} -2.94454 q^{72} +0.780246 q^{73} +4.09908 q^{74} +0.265732 q^{75} -0.307017 q^{76} -1.72571 q^{77} +0.679199 q^{78} +9.92927 q^{79} +1.96765 q^{80} +8.50390 q^{81} -10.0035 q^{82} -9.14440 q^{83} -0.235507 q^{84} +9.13816 q^{85} +6.28292 q^{86} +1.24831 q^{87} -1.72571 q^{88} -0.127349 q^{89} -5.79383 q^{90} -2.88399 q^{91} -7.97106 q^{92} +2.46168 q^{93} -0.831654 q^{94} -0.604102 q^{95} -0.235507 q^{96} +10.1745 q^{97} +1.00000 q^{98} +5.08143 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	−0.235507	−0.135970	−0.0679850	−	0.997686i	$-0.521657\pi$
$3$	−0.235507	−0.135970	−0.0679850	+	0.997686i	$0.521657\pi$
$4$	1.00000	0.500000
$5$	1.96765	0.879961	0.439981	−	0.898007i	$-0.354985\pi$
$5$	1.96765	0.879961	0.439981	+	0.898007i	$0.354985\pi$
$6$	−0.235507	−0.0961453
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.94454	−0.981512
$10$	1.96765	0.622226
$11$	−1.72571	−0.520322	−0.260161	−	0.965565i	$-0.583776\pi$
$11$	−1.72571	−0.520322	−0.260161	+	0.965565i	$0.583776\pi$
$12$	−0.235507	−0.0679850
$13$	−2.88399	−0.799874	−0.399937	−	0.916543i	$-0.630968\pi$
$13$	−2.88399	−0.799874	−0.399937	+	0.916543i	$0.630968\pi$
$14$	1.00000	0.267261
$15$	−0.463396	−0.119648
$16$	1.00000	0.250000
$17$	4.64419	1.12638	0.563191	−	0.826327i	$-0.309574\pi$
$17$	4.64419	1.12638	0.563191	+	0.826327i	$0.309574\pi$
$18$	−2.94454	−0.694034
$19$	−0.307017	−0.0704345	−0.0352172	−	0.999380i	$-0.511212\pi$
$19$	−0.307017	−0.0704345	−0.0352172	+	0.999380i	$0.511212\pi$
$20$	1.96765	0.439981
$21$	−0.235507	−0.0513918
$22$	−1.72571	−0.367923
$23$	−7.97106	−1.66208	−0.831041	−	0.556211i	$-0.812254\pi$
$23$	−7.97106	−1.66208	−0.831041	+	0.556211i	$0.812254\pi$
$24$	−0.235507	−0.0480727
$25$	−1.12834	−0.225668
$26$	−2.88399	−0.565596
$27$	1.39998	0.269426
$28$	1.00000	0.188982
$29$	−5.30054	−0.984285	−0.492142	−	0.870515i	$-0.663786\pi$
$29$	−5.30054	−0.984285	−0.492142	+	0.870515i	$0.663786\pi$
$30$	−0.463396	−0.0846042
$31$	−10.4527	−1.87736	−0.938680	−	0.344789i	$-0.887950\pi$
$31$	−10.4527	−1.87736	−0.938680	+	0.344789i	$0.887950\pi$
$32$	1.00000	0.176777
$33$	0.406418	0.0707482
$34$	4.64419	0.796472
$35$	1.96765	0.332594
$36$	−2.94454	−0.490756
$37$	4.09908	0.673884	0.336942	−	0.941525i	$-0.390607\pi$
$37$	4.09908	0.673884	0.336942	+	0.941525i	$0.390607\pi$
$38$	−0.307017	−0.0498047
$39$	0.679199	0.108759
$40$	1.96765	0.311113
$41$	−10.0035	−1.56228	−0.781142	−	0.624353i	$-0.785363\pi$
$41$	−10.0035	−1.56228	−0.781142	+	0.624353i	$0.785363\pi$
$42$	−0.235507	−0.0363395
$43$	6.28292	0.958137	0.479069	−	0.877778i	$-0.340975\pi$
$43$	6.28292	0.958137	0.479069	+	0.877778i	$0.340975\pi$
$44$	−1.72571	−0.260161
$45$	−5.79383	−0.863693
$46$	−7.97106	−1.17527
$47$	−0.831654	−0.121309	−0.0606546	−	0.998159i	$-0.519319\pi$
$47$	−0.831654	−0.121309	−0.0606546	+	0.998159i	$0.519319\pi$
$48$	−0.235507	−0.0339925
$49$	1.00000	0.142857
$50$	−1.12834	−0.159572
$51$	−1.09374	−0.153154
$52$	−2.88399	−0.399937
$53$	−5.46881	−0.751199	−0.375599	−	0.926782i	$-0.622563\pi$
$53$	−5.46881	−0.751199	−0.375599	+	0.926782i	$0.622563\pi$
$54$	1.39998	0.190513
$55$	−3.39560	−0.457863
$56$	1.00000	0.133631
$57$	0.0723046	0.00957698
$58$	−5.30054	−0.695994
$59$	−4.70985	−0.613171	−0.306585	−	0.951843i	$-0.599186\pi$
$59$	−4.70985	−0.613171	−0.306585	+	0.951843i	$0.599186\pi$
$60$	−0.463396	−0.0598242
$61$	−6.46422	−0.827659	−0.413829	−	0.910354i	$-0.635809\pi$
$61$	−6.46422	−0.827659	−0.413829	+	0.910354i	$0.635809\pi$
$62$	−10.4527	−1.32749
$63$	−2.94454	−0.370977
$64$	1.00000	0.125000
$65$	−5.67468	−0.703858
$66$	0.406418	0.0500265
$67$	5.35979	0.654803	0.327402	−	0.944885i	$-0.393827\pi$
$67$	5.35979	0.654803	0.327402	+	0.944885i	$0.393827\pi$
$68$	4.64419	0.563191
$69$	1.87724	0.225993
$70$	1.96765	0.235180
$71$	10.2101	1.21172	0.605860	−	0.795571i	$-0.292829\pi$
$71$	10.2101	1.21172	0.605860	+	0.795571i	$0.292829\pi$
$72$	−2.94454	−0.347017
$73$	0.780246	0.0913209	0.0456604	−	0.998957i	$-0.485461\pi$
$73$	0.780246	0.0913209	0.0456604	+	0.998957i	$0.485461\pi$
$74$	4.09908	0.476508
$75$	0.265732	0.0306841
$76$	−0.307017	−0.0352172
$77$	−1.72571	−0.196663
$78$	0.679199	0.0769041
$79$	9.92927	1.11713	0.558565	−	0.829461i	$-0.311352\pi$
$79$	9.92927	1.11713	0.558565	+	0.829461i	$0.311352\pi$
$80$	1.96765	0.219990
$81$	8.50390	0.944878
$82$	−10.0035	−1.10470
$83$	−9.14440	−1.00373	−0.501864	−	0.864947i	$-0.667352\pi$
$83$	−9.14440	−1.00373	−0.501864	+	0.864947i	$0.667352\pi$
$84$	−0.235507	−0.0256959
$85$	9.13816	0.991172
$86$	6.28292	0.677505
$87$	1.24831	0.133833
$88$	−1.72571	−0.183962
$89$	−0.127349	−0.0134990	−0.00674950	−	0.999977i	$-0.502148\pi$
$89$	−0.127349	−0.0134990	−0.00674950	+	0.999977i	$0.502148\pi$
$90$	−5.79383	−0.610723
$91$	−2.88399	−0.302324
$92$	−7.97106	−0.831041
$93$	2.46168	0.255265
$94$	−0.831654	−0.0857786
$95$	−0.604102	−0.0619796
$96$	−0.235507	−0.0240363
$97$	10.1745	1.03307	0.516534	−	0.856266i	$-0.327222\pi$
$97$	10.1745	1.03307	0.516534	+	0.856266i	$0.327222\pi$
$98$	1.00000	0.101015
$99$	5.08143	0.510702
$100$	−1.12834	−0.112834
$101$	1.39226	0.138535	0.0692675	−	0.997598i	$-0.477934\pi$
$101$	1.39226	0.138535	0.0692675	+	0.997598i	$0.477934\pi$
$102$	−1.09374	−0.108296
$103$	−16.9870	−1.67378	−0.836891	−	0.547369i	$-0.815629\pi$
$103$	−16.9870	−1.67378	−0.836891	+	0.547369i	$0.815629\pi$
$104$	−2.88399	−0.282798
$105$	−0.463396	−0.0452228
$106$	−5.46881	−0.531178
$107$	−13.5614	−1.31103	−0.655514	−	0.755183i	$-0.727548\pi$
$107$	−13.5614	−1.31103	−0.655514	+	0.755183i	$0.727548\pi$
$108$	1.39998	0.134713
$109$	−19.0825	−1.82777	−0.913885	−	0.405973i	$-0.866933\pi$
$109$	−19.0825	−1.82777	−0.913885	+	0.405973i	$0.866933\pi$
$110$	−3.39560	−0.323758
$111$	−0.965361	−0.0916280
$112$	1.00000	0.0944911
$113$	−18.1595	−1.70830	−0.854152	−	0.520024i	$-0.825923\pi$
$113$	−18.1595	−1.70830	−0.854152	+	0.520024i	$0.825923\pi$
$114$	0.0723046	0.00677195
$115$	−15.6843	−1.46257
$116$	−5.30054	−0.492142
$117$	8.49200	0.785086
$118$	−4.70985	−0.433577
$119$	4.64419	0.425732
$120$	−0.463396	−0.0423021
$121$	−8.02191	−0.729265
$122$	−6.46422	−0.585243
$123$	2.35589	0.212424
$124$	−10.4527	−0.938680
$125$	−12.0585	−1.07854
$126$	−2.94454	−0.262320
$127$	9.57533	0.849673	0.424837	−	0.905270i	$-0.360332\pi$
$127$	9.57533	0.849673	0.424837	+	0.905270i	$0.360332\pi$
$128$	1.00000	0.0883883
$129$	−1.47967	−0.130278
$130$	−5.67468	−0.497703
$131$	21.9596	1.91862	0.959308	−	0.282362i	$-0.0911178\pi$
$131$	21.9596	1.91862	0.959308	+	0.282362i	$0.0911178\pi$
$132$	0.406418	0.0353741
$133$	−0.307017	−0.0266217
$134$	5.35979	0.463016
$135$	2.75468	0.237085
$136$	4.64419	0.398236
$137$	10.5347	0.900039	0.450019	−	0.893019i	$-0.351417\pi$
$137$	10.5347	0.900039	0.450019	+	0.893019i	$0.351417\pi$
$138$	1.87724	0.159801
$139$	6.78086	0.575145	0.287573	−	0.957759i	$-0.407152\pi$
$139$	6.78086	0.575145	0.287573	+	0.957759i	$0.407152\pi$
$140$	1.96765	0.166297
$141$	0.195860	0.0164944
$142$	10.2101	0.856815
$143$	4.97693	0.416192
$144$	−2.94454	−0.245378
$145$	−10.4296	−0.866132
$146$	0.780246	0.0645736
$147$	−0.235507	−0.0194243
$148$	4.09908	0.336942
$149$	5.39150	0.441689	0.220844	−	0.975309i	$-0.429119\pi$
$149$	5.39150	0.441689	0.220844	+	0.975309i	$0.429119\pi$
$150$	0.265732	0.0216970
$151$	23.8616	1.94183	0.970916	−	0.239419i	$-0.0769568\pi$
$151$	23.8616	1.94183	0.970916	+	0.239419i	$0.0769568\pi$
$152$	−0.307017	−0.0249023
$153$	−13.6750	−1.10556
$154$	−1.72571	−0.139062
$155$	−20.5673	−1.65200
$156$	0.679199	0.0543794
$157$	−1.01929	−0.0813484	−0.0406742	−	0.999172i	$-0.512951\pi$
$157$	−1.01929	−0.0813484	−0.0406742	+	0.999172i	$0.512951\pi$
$158$	9.92927	0.789930
$159$	1.28794	0.102141
$160$	1.96765	0.155557
$161$	−7.97106	−0.628208
$162$	8.50390	0.668130
$163$	9.87472	0.773448	0.386724	−	0.922196i	$-0.373607\pi$
$163$	9.87472	0.773448	0.386724	+	0.922196i	$0.373607\pi$
$164$	−10.0035	−0.781142
$165$	0.799689	0.0622557
$166$	−9.14440	−0.709743
$167$	−13.7228	−1.06190	−0.530950	−	0.847403i	$-0.678165\pi$
$167$	−13.7228	−1.06190	−0.530950	+	0.847403i	$0.678165\pi$
$168$	−0.235507	−0.0181698
$169$	−4.68263	−0.360202
$170$	9.13816	0.700865
$171$	0.904022	0.0691323
$172$	6.28292	0.479069
$173$	10.0588	0.764757	0.382379	−	0.924006i	$-0.375105\pi$
$173$	10.0588	0.764757	0.382379	+	0.924006i	$0.375105\pi$
$174$	1.24831	0.0946344
$175$	−1.12834	−0.0852946
$176$	−1.72571	−0.130081
$177$	1.10920	0.0833728
$178$	−0.127349	−0.00954524
$179$	2.39706	0.179165	0.0895824	−	0.995979i	$-0.471447\pi$
$179$	2.39706	0.179165	0.0895824	+	0.995979i	$0.471447\pi$
$180$	−5.79383	−0.431846
$181$	22.4407	1.66801	0.834003	−	0.551761i	$-0.186044\pi$
$181$	22.4407	1.66801	0.834003	+	0.551761i	$0.186044\pi$
$182$	−2.88399	−0.213775
$183$	1.52237	0.112537
$184$	−7.97106	−0.587635
$185$	8.06556	0.592992
$186$	2.46168	0.180499
$187$	−8.01454	−0.586081
$188$	−0.831654	−0.0606546
$189$	1.39998	0.101834
$190$	−0.604102	−0.0438262
$191$	−5.89785	−0.426753	−0.213377	−	0.976970i	$-0.568446\pi$
$191$	−5.89785	−0.426753	−0.213377	+	0.976970i	$0.568446\pi$
$192$	−0.235507	−0.0169963
$193$	−22.5032	−1.61982	−0.809909	−	0.586556i	$-0.800483\pi$
$193$	−22.5032	−1.61982	−0.809909	+	0.586556i	$0.800483\pi$
$194$	10.1745	0.730490
$195$	1.33643	0.0957036
$196$	1.00000	0.0714286
$197$	23.8090	1.69632	0.848160	−	0.529740i	$-0.177711\pi$
$197$	23.8090	1.69632	0.848160	+	0.529740i	$0.177711\pi$
$198$	5.08143	0.361121
$199$	−9.51464	−0.674475	−0.337237	−	0.941420i	$-0.609493\pi$
$199$	−9.51464	−0.674475	−0.337237	+	0.941420i	$0.609493\pi$
$200$	−1.12834	−0.0797858
$201$	−1.26227	−0.0890336
$202$	1.39226	0.0979591
$203$	−5.30054	−0.372025
$204$	−1.09374	−0.0765771
$205$	−19.6834	−1.37475
$206$	−16.9870	−1.18354
$207$	23.4711	1.63135
$208$	−2.88399	−0.199968
$209$	0.529823	0.0366486
$210$	−0.463396	−0.0319774
$211$	−13.7154	−0.944205	−0.472103	−	0.881544i	$-0.656505\pi$
$211$	−13.7154	−0.944205	−0.472103	+	0.881544i	$0.656505\pi$
$212$	−5.46881	−0.375599
$213$	−2.40456	−0.164758
$214$	−13.5614	−0.927036
$215$	12.3626	0.843123
$216$	1.39998	0.0952566
$217$	−10.4527	−0.709575
$218$	−19.0825	−1.29243
$219$	−0.183753	−0.0124169
$220$	−3.39560	−0.228932
$221$	−13.3938	−0.900963
$222$	−0.965361	−0.0647908
$223$	−26.6491	−1.78456	−0.892278	−	0.451487i	$-0.850894\pi$
$223$	−26.6491	−1.78456	−0.892278	+	0.451487i	$0.850894\pi$
$224$	1.00000	0.0668153
$225$	3.32244	0.221496
$226$	−18.1595	−1.20795
$227$	10.8064	0.717247	0.358623	−	0.933482i	$-0.383246\pi$
$227$	10.8064	0.717247	0.358623	+	0.933482i	$0.383246\pi$
$228$	0.0723046	0.00478849
$229$	15.5078	1.02479	0.512393	−	0.858751i	$-0.328759\pi$
$229$	15.5078	1.02479	0.512393	+	0.858751i	$0.328759\pi$
$230$	−15.6843	−1.03419
$231$	0.406418	0.0267403
$232$	−5.30054	−0.347997
$233$	−26.5781	−1.74119	−0.870596	−	0.491998i	$-0.836267\pi$
$233$	−26.5781	−1.74119	−0.870596	+	0.491998i	$0.836267\pi$
$234$	8.49200	0.555139
$235$	−1.63641	−0.106747
$236$	−4.70985	−0.306585
$237$	−2.33841	−0.151896
$238$	4.64419	0.301038
$239$	−12.6822	−0.820341	−0.410170	−	0.912009i	$-0.634531\pi$
$239$	−12.6822	−0.820341	−0.410170	+	0.912009i	$0.634531\pi$
$240$	−0.463396	−0.0299121
$241$	−5.68374	−0.366122	−0.183061	−	0.983102i	$-0.558601\pi$
$241$	−5.68374	−0.366122	−0.183061	+	0.983102i	$0.558601\pi$
$242$	−8.02191	−0.515668
$243$	−6.20267	−0.397901
$244$	−6.46422	−0.413829
$245$	1.96765	0.125709
$246$	2.35589	0.150206
$247$	0.885432	0.0563387
$248$	−10.4527	−0.663747
$249$	2.15357	0.136477
$250$	−12.0585	−0.762643
$251$	−0.347864	−0.0219570	−0.0109785	−	0.999940i	$-0.503495\pi$
$251$	−0.347864	−0.0219570	−0.0109785	+	0.999940i	$0.503495\pi$
$252$	−2.94454	−0.185488
$253$	13.7558	0.864818
$254$	9.57533	0.600810
$255$	−2.15210	−0.134770
$256$	1.00000	0.0625000
$257$	31.2873	1.95165	0.975825	−	0.218554i	$-0.0701340\pi$
$257$	31.2873	1.95165	0.975825	+	0.218554i	$0.0701340\pi$
$258$	−1.47967	−0.0921204
$259$	4.09908	0.254704
$260$	−5.67468	−0.351929
$261$	15.6076	0.966088
$262$	21.9596	1.35667
$263$	15.9622	0.984274	0.492137	−	0.870518i	$-0.336216\pi$
$263$	15.9622	0.984274	0.492137	+	0.870518i	$0.336216\pi$
$264$	0.406418	0.0250133
$265$	−10.7607	−0.661026
$266$	−0.307017	−0.0188244
$267$	0.0299917	0.00183546
$268$	5.35979	0.327402
$269$	−21.1626	−1.29030	−0.645152	−	0.764054i	$-0.723206\pi$
$269$	−21.1626	−1.29030	−0.645152	+	0.764054i	$0.723206\pi$
$270$	2.75468	0.167644
$271$	27.4129	1.66522	0.832608	−	0.553862i	$-0.186847\pi$
$271$	27.4129	1.66522	0.832608	+	0.553862i	$0.186847\pi$
$272$	4.64419	0.281595
$273$	0.679199	0.0411070
$274$	10.5347	0.636423
$275$	1.94719	0.117420
$276$	1.87724	0.112997
$277$	−0.661251	−0.0397307	−0.0198654	−	0.999803i	$-0.506324\pi$
$277$	−0.661251	−0.0397307	−0.0198654	+	0.999803i	$0.506324\pi$
$278$	6.78086	0.406689
$279$	30.7784	1.84265
$280$	1.96765	0.117590
$281$	4.79424	0.286000	0.143000	−	0.989723i	$-0.454325\pi$
$281$	4.79424	0.286000	0.143000	+	0.989723i	$0.454325\pi$
$282$	0.195860	0.0116633
$283$	2.86537	0.170328	0.0851642	−	0.996367i	$-0.472859\pi$
$283$	2.86537	0.170328	0.0851642	+	0.996367i	$0.472859\pi$
$284$	10.2101	0.605860
$285$	0.142270	0.00842737
$286$	4.97693	0.294292
$287$	−10.0035	−0.590488
$288$	−2.94454	−0.173508
$289$	4.56851	0.268736
$290$	−10.4296	−0.612448
$291$	−2.39618	−0.140466
$292$	0.780246	0.0456604
$293$	−5.50172	−0.321414	−0.160707	−	0.987002i	$-0.551377\pi$
$293$	−5.50172	−0.321414	−0.160707	+	0.987002i	$0.551377\pi$
$294$	−0.235507	−0.0137350
$295$	−9.26736	−0.539566
$296$	4.09908	0.238254
$297$	−2.41596	−0.140188
$298$	5.39150	0.312321
$299$	22.9884	1.32946
$300$	0.265732	0.0153421
$301$	6.28292	0.362142
$302$	23.8616	1.37308
$303$	−0.327887	−0.0188366
$304$	−0.307017	−0.0176086
$305$	−12.7193	−0.728307
$306$	−13.6750	−0.781747
$307$	−18.8836	−1.07775	−0.538873	−	0.842387i	$-0.681150\pi$
$307$	−18.8836	−1.07775	−0.538873	+	0.842387i	$0.681150\pi$
$308$	−1.72571	−0.0983316
$309$	4.00057	0.227584
$310$	−20.5673	−1.16814
$311$	27.0763	1.53535	0.767677	−	0.640836i	$-0.221412\pi$
$311$	27.0763	1.53535	0.767677	+	0.640836i	$0.221412\pi$
$312$	0.679199	0.0384521
$313$	−30.4166	−1.71925	−0.859623	−	0.510929i	$-0.829301\pi$
$313$	−30.4166	−1.71925	−0.859623	+	0.510929i	$0.829301\pi$
$314$	−1.01929	−0.0575220
$315$	−5.79383	−0.326445
$316$	9.92927	0.558565
$317$	−18.6378	−1.04681	−0.523403	−	0.852085i	$-0.675338\pi$
$317$	−18.6378	−1.04681	−0.523403	+	0.852085i	$0.675338\pi$
$318$	1.28794	0.0722243
$319$	9.14720	0.512145
$320$	1.96765	0.109995
$321$	3.19380	0.178260
$322$	−7.97106	−0.444210
$323$	−1.42584	−0.0793361
$324$	8.50390	0.472439
$325$	3.25412	0.180506
$326$	9.87472	0.546910
$327$	4.49406	0.248522
$328$	−10.0035	−0.552351
$329$	−0.831654	−0.0458506
$330$	0.799689	0.0440214
$331$	−13.6815	−0.752002	−0.376001	−	0.926619i	$-0.622701\pi$
$331$	−13.6815	−0.752002	−0.376001	+	0.926619i	$0.622701\pi$
$332$	−9.14440	−0.501864
$333$	−12.0699	−0.661425
$334$	−13.7228	−0.750876
$335$	10.5462	0.576201
$336$	−0.235507	−0.0128480
$337$	−2.54284	−0.138518	−0.0692588	−	0.997599i	$-0.522063\pi$
$337$	−2.54284	−0.138518	−0.0692588	+	0.997599i	$0.522063\pi$
$338$	−4.68263	−0.254701
$339$	4.27669	0.232278
$340$	9.13816	0.495586
$341$	18.0384	0.976832
$342$	0.904022	0.0488839
$343$	1.00000	0.0539949
$344$	6.28292	0.338753
$345$	3.69376	0.198865
$346$	10.0588	0.540765
$347$	−16.1827	−0.868734	−0.434367	−	0.900736i	$-0.643028\pi$
$347$	−16.1827	−0.868734	−0.434367	+	0.900736i	$0.643028\pi$
$348$	1.24831	0.0669166
$349$	11.8673	0.635244	0.317622	−	0.948217i	$-0.397116\pi$
$349$	11.8673	0.635244	0.317622	+	0.948217i	$0.397116\pi$
$350$	−1.12834	−0.0603124
$351$	−4.03752	−0.215507
$352$	−1.72571	−0.0919808
$353$	22.6072	1.20326	0.601630	−	0.798775i	$-0.294518\pi$
$353$	22.6072	1.20326	0.601630	+	0.798775i	$0.294518\pi$
$354$	1.10920	0.0589535
$355$	20.0900	1.06627
$356$	−0.127349	−0.00674950
$357$	−1.09374	−0.0578868
$358$	2.39706	0.126689
$359$	6.24708	0.329708	0.164854	−	0.986318i	$-0.447285\pi$
$359$	6.24708	0.329708	0.164854	+	0.986318i	$0.447285\pi$
$360$	−5.79383	−0.305361
$361$	−18.9057	−0.995039
$362$	22.4407	1.17946
$363$	1.88922	0.0991582
$364$	−2.88399	−0.151162
$365$	1.53525	0.0803588
$366$	1.52237	0.0795755
$367$	22.6817	1.18397	0.591987	−	0.805948i	$-0.298344\pi$
$367$	22.6817	1.18397	0.591987	+	0.805948i	$0.298344\pi$
$368$	−7.97106	−0.415520
$369$	29.4557	1.53340
$370$	8.06556	0.419308
$371$	−5.46881	−0.283926
$372$	2.46168	0.127632
$373$	−23.3540	−1.20922	−0.604611	−	0.796521i	$-0.706671\pi$
$373$	−23.3540	−1.20922	−0.604611	+	0.796521i	$0.706671\pi$
$374$	−8.01454	−0.414422
$375$	2.83985	0.146649
$376$	−0.831654	−0.0428893
$377$	15.2867	0.787303
$378$	1.39998	0.0720072
$379$	15.5653	0.799534	0.399767	−	0.916617i	$-0.369091\pi$
$379$	15.5653	0.799534	0.399767	+	0.916617i	$0.369091\pi$
$380$	−0.604102	−0.0309898
$381$	−2.25506	−0.115530
$382$	−5.89785	−0.301760
$383$	−17.4671	−0.892529	−0.446265	−	0.894901i	$-0.647246\pi$
$383$	−17.4671	−0.892529	−0.446265	+	0.894901i	$0.647246\pi$
$384$	−0.235507	−0.0120182
$385$	−3.39560	−0.173056
$386$	−22.5032	−1.14538
$387$	−18.5003	−0.940423
$388$	10.1745	0.516534
$389$	−7.27551	−0.368883	−0.184442	−	0.982843i	$-0.559048\pi$
$389$	−7.27551	−0.368883	−0.184442	+	0.982843i	$0.559048\pi$
$390$	1.33643	0.0676726
$391$	−37.0191	−1.87214
$392$	1.00000	0.0505076
$393$	−5.17163	−0.260874
$394$	23.8090	1.19948
$395$	19.5374	0.983031
$396$	5.08143	0.255351
$397$	39.7889	1.99695	0.998474	−	0.0552320i	$-0.0175898\pi$
$397$	39.7889	1.99695	0.998474	+	0.0552320i	$0.0175898\pi$
$398$	−9.51464	−0.476926
$399$	0.0723046	0.00361976
$400$	−1.12834	−0.0564171
$401$	−1.75772	−0.0877765	−0.0438883	−	0.999036i	$-0.513975\pi$
$401$	−1.75772	−0.0877765	−0.0438883	+	0.999036i	$0.513975\pi$
$402$	−1.26227	−0.0629563
$403$	30.1454	1.50165
$404$	1.39226	0.0692675
$405$	16.7327	0.831456
$406$	−5.30054	−0.263061
$407$	−7.07383	−0.350637
$408$	−1.09374	−0.0541482
$409$	−24.2987	−1.20149	−0.600747	−	0.799439i	$-0.705130\pi$
$409$	−24.2987	−1.20149	−0.600747	+	0.799439i	$0.705130\pi$
$410$	−19.6834	−0.972095
$411$	−2.48099	−0.122378
$412$	−16.9870	−0.836891
$413$	−4.70985	−0.231757
$414$	23.4711	1.15354
$415$	−17.9930	−0.883242
$416$	−2.88399	−0.141399
$417$	−1.59694	−0.0782025
$418$	0.529823	0.0259145
$419$	33.0057	1.61243	0.806216	−	0.591621i	$-0.201512\pi$
$419$	33.0057	1.61243	0.806216	+	0.591621i	$0.201512\pi$
$420$	−0.463396	−0.0226114
$421$	11.7929	0.574752	0.287376	−	0.957818i	$-0.407217\pi$
$421$	11.7929	0.574752	0.287376	+	0.957818i	$0.407217\pi$
$422$	−13.7154	−0.667654
$423$	2.44884	0.119066
$424$	−5.46881	−0.265589
$425$	−5.24024	−0.254189
$426$	−2.40456	−0.116501
$427$	−6.46422	−0.312826
$428$	−13.5614	−0.655514
$429$	−1.17210	−0.0565896
$430$	12.3626	0.596178
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.39998	0.0673566
$433$	17.1768	0.825466	0.412733	−	0.910852i	$-0.364574\pi$
$433$	17.1768	0.825466	0.412733	+	0.910852i	$0.364574\pi$
$434$	−10.4527	−0.501746
$435$	2.45625	0.117768
$436$	−19.0825	−0.913885
$437$	2.44725	0.117068
$438$	−0.183753	−0.00878008
$439$	−6.90312	−0.329468	−0.164734	−	0.986338i	$-0.552677\pi$
$439$	−6.90312	−0.329468	−0.164734	+	0.986338i	$0.552677\pi$
$440$	−3.39560	−0.161879
$441$	−2.94454	−0.140216
$442$	−13.3938	−0.637077
$443$	−24.9097	−1.18349	−0.591747	−	0.806124i	$-0.701561\pi$
$443$	−24.9097	−1.18349	−0.591747	+	0.806124i	$0.701561\pi$
$444$	−0.965361	−0.0458140
$445$	−0.250579	−0.0118786
$446$	−26.6491	−1.26187
$447$	−1.26974	−0.0600564
$448$	1.00000	0.0472456
$449$	−4.67211	−0.220490	−0.110245	−	0.993904i	$-0.535164\pi$
$449$	−4.67211	−0.220490	−0.110245	+	0.993904i	$0.535164\pi$
$450$	3.32244	0.156622
$451$	17.2632	0.812891
$452$	−18.1595	−0.854152
$453$	−5.61958	−0.264031
$454$	10.8064	0.507170
$455$	−5.67468	−0.266033
$456$	0.0723046	0.00338597
$457$	−3.73132	−0.174544	−0.0872720	−	0.996185i	$-0.527815\pi$
$457$	−3.73132	−0.174544	−0.0872720	+	0.996185i	$0.527815\pi$
$458$	15.5078	0.724633
$459$	6.50177	0.303477
$460$	−15.6843	−0.731284
$461$	10.2506	0.477416	0.238708	−	0.971091i	$-0.423276\pi$
$461$	10.2506	0.477416	0.238708	+	0.971091i	$0.423276\pi$
$462$	0.406418	0.0189083
$463$	−12.5998	−0.585561	−0.292781	−	0.956180i	$-0.594581\pi$
$463$	−12.5998	−0.585561	−0.292781	+	0.956180i	$0.594581\pi$
$464$	−5.30054	−0.246071
$465$	4.84374	0.224623
$466$	−26.5781	−1.23121
$467$	−40.9396	−1.89446	−0.947229	−	0.320557i	$-0.896130\pi$
$467$	−40.9396	−1.89446	−0.947229	+	0.320557i	$0.896130\pi$
$468$	8.49200	0.392543
$469$	5.35979	0.247492
$470$	−1.63641	−0.0754818
$471$	0.240050	0.0110609
$472$	−4.70985	−0.216789
$473$	−10.8425	−0.498540
$474$	−2.33841	−0.107407
$475$	0.346420	0.0158948
$476$	4.64419	0.212866
$477$	16.1031	0.737311
$478$	−12.6822	−0.580069
$479$	12.5483	0.573345	0.286672	−	0.958029i	$-0.407451\pi$
$479$	12.5483	0.573345	0.286672	+	0.958029i	$0.407451\pi$
$480$	−0.463396	−0.0211510
$481$	−11.8217	−0.539022
$482$	−5.68374	−0.258887
$483$	1.87724	0.0854175
$484$	−8.02191	−0.364632
$485$	20.0200	0.909060
$486$	−6.20267	−0.281359
$487$	−30.6911	−1.39075	−0.695374	−	0.718648i	$-0.744761\pi$
$487$	−30.6911	−1.39075	−0.695374	+	0.718648i	$0.744761\pi$
$488$	−6.46422	−0.292622
$489$	−2.32557	−0.105166
$490$	1.96765	0.0888895
$491$	14.5681	0.657447	0.328724	−	0.944426i	$-0.393382\pi$
$491$	14.5681	0.657447	0.328724	+	0.944426i	$0.393382\pi$
$492$	2.35589	0.106212
$493$	−24.6167	−1.10868
$494$	0.885432	0.0398375
$495$	9.99848	0.449398
$496$	−10.4527	−0.469340
$497$	10.2101	0.457987
$498$	2.15357	0.0965038
$499$	−27.5857	−1.23490	−0.617452	−	0.786609i	$-0.711835\pi$
$499$	−27.5857	−1.23490	−0.617452	+	0.786609i	$0.711835\pi$
$500$	−12.0585	−0.539270
$501$	3.23181	0.144386
$502$	−0.347864	−0.0155260
$503$	9.50168	0.423659	0.211830	−	0.977307i	$-0.432058\pi$
$503$	9.50168	0.423659	0.211830	+	0.977307i	$0.432058\pi$
$504$	−2.94454	−0.131160
$505$	2.73949	0.121906
$506$	13.7558	0.611519
$507$	1.10279	0.0489767
$508$	9.57533	0.424837
$509$	3.66470	0.162435	0.0812174	−	0.996696i	$-0.474119\pi$
$509$	3.66470	0.162435	0.0812174	+	0.996696i	$0.474119\pi$
$510$	−2.15210	−0.0952966
$511$	0.780246	0.0345160
$512$	1.00000	0.0441942
$513$	−0.429817	−0.0189769
$514$	31.2873	1.38002
$515$	−33.4246	−1.47286
$516$	−1.47967	−0.0651390
$517$	1.43520	0.0631199
$518$	4.09908	0.180103
$519$	−2.36892	−0.103984
$520$	−5.67468	−0.248851
$521$	2.11574	0.0926920	0.0463460	−	0.998925i	$-0.485242\pi$
$521$	2.11574	0.0926920	0.0463460	+	0.998925i	$0.485242\pi$
$522$	15.6076	0.683127
$523$	−8.28083	−0.362095	−0.181048	−	0.983474i	$-0.557949\pi$
$523$	−8.28083	−0.362095	−0.181048	+	0.983474i	$0.557949\pi$
$524$	21.9596	0.959308
$525$	0.265732	0.0115975
$526$	15.9622	0.695987
$527$	−48.5443	−2.11462
$528$	0.406418	0.0176871
$529$	40.5379	1.76252
$530$	−10.7607	−0.467416
$531$	13.8683	0.601834
$532$	−0.307017	−0.0133109
$533$	28.8499	1.24963
$534$	0.0299917	0.00129787
$535$	−26.6841	−1.15365
$536$	5.35979	0.231508
$537$	−0.564525	−0.0243610
$538$	−21.1626	−0.912383
$539$	−1.72571	−0.0743317
$540$	2.75468	0.118542
$541$	−8.59753	−0.369637	−0.184818	−	0.982773i	$-0.559170\pi$
$541$	−8.59753	−0.369637	−0.184818	+	0.982773i	$0.559170\pi$
$542$	27.4129	1.17749
$543$	−5.28495	−0.226799
$544$	4.64419	0.199118
$545$	−37.5477	−1.60837
$546$	0.679199	0.0290670
$547$	11.8745	0.507717	0.253858	−	0.967241i	$-0.418300\pi$
$547$	11.8745	0.507717	0.253858	+	0.967241i	$0.418300\pi$
$548$	10.5347	0.450019
$549$	19.0341	0.812357
$550$	1.94719	0.0830287
$551$	1.62735	0.0693276
$552$	1.87724	0.0799007
$553$	9.92927	0.422235
$554$	−0.661251	−0.0280939
$555$	−1.89950	−0.0806291
$556$	6.78086	0.287573
$557$	−24.1888	−1.02491	−0.512456	−	0.858714i	$-0.671264\pi$
$557$	−24.1888	−1.02491	−0.512456	+	0.858714i	$0.671264\pi$
$558$	30.7784	1.30295
$559$	−18.1199	−0.766388
$560$	1.96765	0.0831485
$561$	1.88748	0.0796895
$562$	4.79424	0.202233
$563$	−40.4786	−1.70597	−0.852985	−	0.521935i	$-0.825210\pi$
$563$	−40.4786	−1.70597	−0.852985	+	0.521935i	$0.825210\pi$
$564$	0.195860	0.00824721
$565$	−35.7316	−1.50324
$566$	2.86537	0.120440
$567$	8.50390	0.357130
$568$	10.2101	0.428408
$569$	−20.5608	−0.861953	−0.430976	−	0.902363i	$-0.641831\pi$
$569$	−20.5608	−0.861953	−0.430976	+	0.902363i	$0.641831\pi$
$570$	0.142270	0.00595905
$571$	−20.0493	−0.839038	−0.419519	−	0.907747i	$-0.637801\pi$
$571$	−20.0493	−0.839038	−0.419519	+	0.907747i	$0.637801\pi$
$572$	4.97693	0.208096
$573$	1.38898	0.0580257
$574$	−10.0035	−0.417538
$575$	8.99409	0.375079
$576$	−2.94454	−0.122689
$577$	16.6877	0.694719	0.347360	−	0.937732i	$-0.387078\pi$
$577$	16.6877	0.694719	0.347360	+	0.937732i	$0.387078\pi$
$578$	4.56851	0.190025
$579$	5.29967	0.220247
$580$	−10.4296	−0.433066
$581$	−9.14440	−0.379373
$582$	−2.39618	−0.0993247
$583$	9.43760	0.390865
$584$	0.780246	0.0322868
$585$	16.7093	0.690845
$586$	−5.50172	−0.227274
$587$	16.1793	0.667790	0.333895	−	0.942610i	$-0.391637\pi$
$587$	16.1793	0.667790	0.333895	+	0.942610i	$0.391637\pi$
$588$	−0.235507	−0.00971215
$589$	3.20915	0.132231
$590$	−9.26736	−0.381531
$591$	−5.60718	−0.230649
$592$	4.09908	0.168471
$593$	−32.8522	−1.34908	−0.674539	−	0.738239i	$-0.735657\pi$
$593$	−32.8522	−1.34908	−0.674539	+	0.738239i	$0.735657\pi$
$594$	−2.41596	−0.0991282
$595$	9.13816	0.374628
$596$	5.39150	0.220844
$597$	2.24076	0.0917084
$598$	22.9884	0.940067
$599$	−5.00596	−0.204538	−0.102269	−	0.994757i	$-0.532610\pi$
$599$	−5.00596	−0.204538	−0.102269	+	0.994757i	$0.532610\pi$
$600$	0.265732	0.0108485
$601$	11.3093	0.461316	0.230658	−	0.973035i	$-0.425912\pi$
$601$	11.3093	0.461316	0.230658	+	0.973035i	$0.425912\pi$
$602$	6.28292	0.256073
$603$	−15.7821	−0.642697
$604$	23.8616	0.970916
$605$	−15.7843	−0.641725
$606$	−0.327887	−0.0133195
$607$	−23.3297	−0.946922	−0.473461	−	0.880815i	$-0.656996\pi$
$607$	−23.3297	−0.946922	−0.473461	+	0.880815i	$0.656996\pi$
$608$	−0.307017	−0.0124512
$609$	1.24831	0.0505842
$610$	−12.7193	−0.514991
$611$	2.39848	0.0970320
$612$	−13.6750	−0.552779
$613$	−19.4503	−0.785589	−0.392794	−	0.919626i	$-0.628492\pi$
$613$	−19.4503	−0.785589	−0.392794	+	0.919626i	$0.628492\pi$
$614$	−18.8836	−0.762082
$615$	4.63558	0.186925
$616$	−1.72571	−0.0695310
$617$	−12.3457	−0.497020	−0.248510	−	0.968629i	$-0.579941\pi$
$617$	−12.3457	−0.497020	−0.248510	+	0.968629i	$0.579941\pi$
$618$	4.00057	0.160926
$619$	6.24945	0.251186	0.125593	−	0.992082i	$-0.459917\pi$
$619$	6.24945	0.251186	0.125593	+	0.992082i	$0.459917\pi$
$620$	−20.5673	−0.826002
$621$	−11.1593	−0.447809
$622$	27.0763	1.08566
$623$	−0.127349	−0.00510214
$624$	0.679199	0.0271897
$625$	−18.0851	−0.723405
$626$	−30.4166	−1.21569
$627$	−0.124777	−0.00498311
$628$	−1.01929	−0.0406742
$629$	19.0369	0.759051
$630$	−5.79383	−0.230832
$631$	25.7222	1.02399	0.511993	−	0.858990i	$-0.328908\pi$
$631$	25.7222	1.02399	0.511993	+	0.858990i	$0.328908\pi$
$632$	9.92927	0.394965
$633$	3.23007	0.128384
$634$	−18.6378	−0.740203
$635$	18.8409	0.747679
$636$	1.28794	0.0510703
$637$	−2.88399	−0.114268
$638$	9.14720	0.362141
$639$	−30.0641	−1.18932
$640$	1.96765	0.0777783
$641$	−30.7824	−1.21583	−0.607916	−	0.794001i	$-0.707994\pi$
$641$	−30.7824	−1.21583	−0.607916	+	0.794001i	$0.707994\pi$
$642$	3.19380	0.126049
$643$	21.6110	0.852256	0.426128	−	0.904663i	$-0.359877\pi$
$643$	21.6110	0.852256	0.426128	+	0.904663i	$0.359877\pi$
$644$	−7.97106	−0.314104
$645$	−2.91148	−0.114640
$646$	−1.42584	−0.0560991
$647$	−21.0508	−0.827593	−0.413797	−	0.910369i	$-0.635798\pi$
$647$	−21.0508	−0.827593	−0.413797	+	0.910369i	$0.635798\pi$
$648$	8.50390	0.334065
$649$	8.12786	0.319046
$650$	3.25412	0.127637
$651$	2.46168	0.0964810
$652$	9.87472	0.386724
$653$	43.1238	1.68756	0.843782	−	0.536686i	$-0.180324\pi$
$653$	43.1238	1.68756	0.843782	+	0.536686i	$0.180324\pi$
$654$	4.49406	0.175732
$655$	43.2088	1.68831
$656$	−10.0035	−0.390571
$657$	−2.29746	−0.0896325
$658$	−0.831654	−0.0324213
$659$	−18.9892	−0.739716	−0.369858	−	0.929088i	$-0.620594\pi$
$659$	−18.9892	−0.739716	−0.369858	+	0.929088i	$0.620594\pi$
$660$	0.799689	0.0311278
$661$	−23.5200	−0.914823	−0.457412	−	0.889255i	$-0.651223\pi$
$661$	−23.5200	−0.914823	−0.457412	+	0.889255i	$0.651223\pi$
$662$	−13.6815	−0.531746
$663$	3.15433	0.122504
$664$	−9.14440	−0.354871
$665$	−0.604102	−0.0234261
$666$	−12.0699	−0.467698
$667$	42.2509	1.63596
$668$	−13.7228	−0.530950
$669$	6.27605	0.242646
$670$	10.5462	0.407436
$671$	11.1554	0.430649
$672$	−0.235507	−0.00908488
$673$	3.61412	0.139314	0.0696570	−	0.997571i	$-0.477810\pi$
$673$	3.61412	0.139314	0.0696570	+	0.997571i	$0.477810\pi$
$674$	−2.54284	−0.0979467
$675$	−1.57966	−0.0608010
$676$	−4.68263	−0.180101
$677$	−10.8696	−0.417753	−0.208876	−	0.977942i	$-0.566981\pi$
$677$	−10.8696	−0.417753	−0.208876	+	0.977942i	$0.566981\pi$
$678$	4.27669	0.164245
$679$	10.1745	0.390463
$680$	9.13816	0.350432
$681$	−2.54499	−0.0975241
$682$	18.0384	0.690724
$683$	8.70358	0.333033	0.166517	−	0.986039i	$-0.446748\pi$
$683$	8.70358	0.333033	0.166517	+	0.986039i	$0.446748\pi$
$684$	0.904022	0.0345661
$685$	20.7286	0.791999
$686$	1.00000	0.0381802
$687$	−3.65220	−0.139340
$688$	6.28292	0.239534
$689$	15.7720	0.600864
$690$	3.69376	0.140619
$691$	9.66750	0.367769	0.183884	−	0.982948i	$-0.441133\pi$
$691$	9.66750	0.367769	0.183884	+	0.982948i	$0.441133\pi$
$692$	10.0588	0.382379
$693$	5.08143	0.193027
$694$	−16.1827	−0.614288
$695$	13.3424	0.506105
$696$	1.24831	0.0473172
$697$	−46.4582	−1.75973
$698$	11.8673	0.449185
$699$	6.25934	0.236750
$700$	−1.12834	−0.0426473
$701$	−22.7529	−0.859365	−0.429683	−	0.902980i	$-0.641375\pi$
$701$	−22.7529	−0.859365	−0.429683	+	0.902980i	$0.641375\pi$
$702$	−4.03752	−0.152386
$703$	−1.25848	−0.0474647
$704$	−1.72571	−0.0650403
$705$	0.385385	0.0145144
$706$	22.6072	0.850833
$707$	1.39226	0.0523613
$708$	1.10920	0.0416864
$709$	30.5146	1.14600	0.572999	−	0.819556i	$-0.305780\pi$
$709$	30.5146	1.14600	0.572999	+	0.819556i	$0.305780\pi$
$710$	20.0900	0.753964
$711$	−29.2371	−1.09648
$712$	−0.127349	−0.00477262
$713$	83.3191	3.12033
$714$	−1.09374	−0.0409322
$715$	9.79287	0.366233
$716$	2.39706	0.0895824
$717$	2.98674	0.111542
$718$	6.24708	0.233139
$719$	26.9359	1.00454	0.502270	−	0.864711i	$-0.332498\pi$
$719$	26.9359	1.00454	0.502270	+	0.864711i	$0.332498\pi$
$720$	−5.79383	−0.215923
$721$	−16.9870	−0.632630
$722$	−18.9057	−0.703599
$723$	1.33856	0.0497816
$724$	22.4407	0.834003
$725$	5.98082	0.222122
$726$	1.88922	0.0701154
$727$	13.4818	0.500013	0.250007	−	0.968244i	$-0.419567\pi$
$727$	13.4818	0.500013	0.250007	+	0.968244i	$0.419567\pi$
$728$	−2.88399	−0.106888
$729$	−24.0509	−0.890776
$730$	1.53525	0.0568223
$731$	29.1791	1.07923
$732$	1.52237	0.0562684
$733$	−7.97943	−0.294727	−0.147363	−	0.989082i	$-0.547079\pi$
$733$	−7.97943	−0.294727	−0.147363	+	0.989082i	$0.547079\pi$
$734$	22.6817	0.837196
$735$	−0.463396	−0.0170926
$736$	−7.97106	−0.293817
$737$	−9.24947	−0.340708
$738$	29.4557	1.08428
$739$	17.4729	0.642752	0.321376	−	0.946952i	$-0.395855\pi$
$739$	17.4729	0.642752	0.321376	+	0.946952i	$0.395855\pi$
$740$	8.06556	0.296496
$741$	−0.208525	−0.00766037
$742$	−5.46881	−0.200766
$743$	3.32720	0.122063	0.0610316	−	0.998136i	$-0.480561\pi$
$743$	3.32720	0.122063	0.0610316	+	0.998136i	$0.480561\pi$
$744$	2.46168	0.0902497
$745$	10.6086	0.388669
$746$	−23.3540	−0.855049
$747$	26.9260	0.985171
$748$	−8.01454	−0.293041
$749$	−13.5614	−0.495522
$750$	2.83985	0.103697
$751$	38.9947	1.42294	0.711468	−	0.702719i	$-0.248031\pi$
$751$	38.9947	1.42294	0.711468	+	0.702719i	$0.248031\pi$
$752$	−0.831654	−0.0303273
$753$	0.0819245	0.00298550
$754$	15.2867	0.556708
$755$	46.9514	1.70874
$756$	1.39998	0.0509168
$757$	−21.4317	−0.778948	−0.389474	−	0.921037i	$-0.627343\pi$
$757$	−21.4317	−0.778948	−0.389474	+	0.921037i	$0.627343\pi$
$758$	15.5653	0.565356
$759$	−3.23958	−0.117589
$760$	−0.604102	−0.0219131
$761$	−16.0928	−0.583363	−0.291682	−	0.956515i	$-0.594215\pi$
$761$	−16.0928	−0.583363	−0.291682	+	0.956515i	$0.594215\pi$
$762$	−2.25506	−0.0816921
$763$	−19.0825	−0.690832
$764$	−5.89785	−0.213377
$765$	−26.9076	−0.972847
$766$	−17.4671	−0.631114
$767$	13.5831	0.490459
$768$	−0.235507	−0.00849813
$769$	−31.6787	−1.14236	−0.571182	−	0.820823i	$-0.693515\pi$
$769$	−31.6787	−1.14236	−0.571182	+	0.820823i	$0.693515\pi$
$770$	−3.39560	−0.122369
$771$	−7.36839	−0.265366
$772$	−22.5032	−0.809909
$773$	0.194052	0.00697956	0.00348978	−	0.999994i	$-0.498889\pi$
$773$	0.194052	0.00697956	0.00348978	+	0.999994i	$0.498889\pi$
$774$	−18.5003	−0.664980
$775$	11.7942	0.423661
$776$	10.1745	0.365245
$777$	−0.965361	−0.0346321
$778$	−7.27551	−0.260840
$779$	3.07124	0.110039
$780$	1.33643	0.0478518
$781$	−17.6198	−0.630484
$782$	−37.0191	−1.32380
$783$	−7.42065	−0.265192
$784$	1.00000	0.0357143
$785$	−2.00561	−0.0715834
$786$	−5.17163	−0.184466
$787$	52.1891	1.86034	0.930170	−	0.367128i	$-0.119659\pi$
$787$	52.1891	1.86034	0.930170	+	0.367128i	$0.119659\pi$
$788$	23.8090	0.848160
$789$	−3.75922	−0.133832
$790$	19.5374	0.695108
$791$	−18.1595	−0.645678
$792$	5.08143	0.180561
$793$	18.6427	0.662022
$794$	39.7889	1.41205
$795$	2.53423	0.0898797
$796$	−9.51464	−0.337237
$797$	−8.15624	−0.288909	−0.144454	−	0.989511i	$-0.546143\pi$
$797$	−8.15624	−0.288909	−0.144454	+	0.989511i	$0.546143\pi$
$798$	0.0723046	0.00255955
$799$	−3.86236	−0.136640
$800$	−1.12834	−0.0398929
$801$	0.374985	0.0132494
$802$	−1.75772	−0.0620674
$803$	−1.34648	−0.0475163
$804$	−1.26227	−0.0445168
$805$	−15.6843	−0.552798
$806$	30.1454	1.06183
$807$	4.98393	0.175443
$808$	1.39226	0.0489796
$809$	31.7454	1.11611	0.558054	−	0.829805i	$-0.311548\pi$
$809$	31.7454	1.11611	0.558054	+	0.829805i	$0.311548\pi$
$810$	16.7327	0.587928
$811$	−43.6346	−1.53222	−0.766109	−	0.642711i	$-0.777810\pi$
$811$	−43.6346	−1.53222	−0.766109	+	0.642711i	$0.777810\pi$
$812$	−5.30054	−0.186012
$813$	−6.45594	−0.226420
$814$	−7.07383	−0.247938
$815$	19.4300	0.680604
$816$	−1.09374	−0.0382885
$817$	−1.92896	−0.0674859
$818$	−24.2987	−0.849584
$819$	8.49200	0.296734
$820$	−19.6834	−0.687375
$821$	−27.7157	−0.967285	−0.483642	−	0.875266i	$-0.660686\pi$
$821$	−27.7157	−0.967285	−0.483642	+	0.875266i	$0.660686\pi$
$822$	−2.48099	−0.0865345
$823$	43.4044	1.51298	0.756491	−	0.654004i	$-0.226912\pi$
$823$	43.4044	1.51298	0.756491	+	0.654004i	$0.226912\pi$
$824$	−16.9870	−0.591772
$825$	−0.458578	−0.0159656
$826$	−4.70985	−0.163877
$827$	34.2379	1.19057	0.595285	−	0.803515i	$-0.297039\pi$
$827$	34.2379	1.19057	0.595285	+	0.803515i	$0.297039\pi$
$828$	23.4711	0.815677
$829$	23.3628	0.811423	0.405711	−	0.914001i	$-0.367024\pi$
$829$	23.3628	0.811423	0.405711	+	0.914001i	$0.367024\pi$
$830$	−17.9930	−0.624546
$831$	0.155729	0.00540219
$832$	−2.88399	−0.0999842
$833$	4.64419	0.160912
$834$	−1.59694	−0.0552975
$835$	−27.0016	−0.934430
$836$	0.529823	0.0183243
$837$	−14.6336	−0.505810
$838$	33.0057	1.14016
$839$	2.64504	0.0913171	0.0456585	−	0.998957i	$-0.485461\pi$
$839$	2.64504	0.0913171	0.0456585	+	0.998957i	$0.485461\pi$
$840$	−0.463396	−0.0159887
$841$	−0.904317	−0.0311834
$842$	11.7929	0.406411
$843$	−1.12908	−0.0388875
$844$	−13.7154	−0.472103
$845$	−9.21379	−0.316964
$846$	2.44884	0.0841927
$847$	−8.02191	−0.275636
$848$	−5.46881	−0.187800
$849$	−0.674815	−0.0231596
$850$	−5.24024	−0.179739
$851$	−32.6740	−1.12005
$852$	−2.40456	−0.0823788
$853$	51.4299	1.76093	0.880463	−	0.474114i	$-0.157232\pi$
$853$	51.4299	1.76093	0.880463	+	0.474114i	$0.157232\pi$
$854$	−6.46422	−0.221201
$855$	1.77880	0.0608337
$856$	−13.5614	−0.463518
$857$	10.4358	0.356481	0.178241	−	0.983987i	$-0.442959\pi$
$857$	10.4358	0.356481	0.178241	+	0.983987i	$0.442959\pi$
$858$	−1.17210	−0.0400149
$859$	−11.1126	−0.379157	−0.189579	−	0.981866i	$-0.560712\pi$
$859$	−11.1126	−0.379157	−0.189579	+	0.981866i	$0.560712\pi$
$860$	12.3626	0.421562
$861$	2.35589	0.0802887
$862$	−1.00000	−0.0340601
$863$	5.88104	0.200193	0.100097	−	0.994978i	$-0.468085\pi$
$863$	5.88104	0.200193	0.100097	+	0.994978i	$0.468085\pi$
$864$	1.39998	0.0476283
$865$	19.7922	0.672957
$866$	17.1768	0.583693
$867$	−1.07592	−0.0365400
$868$	−10.4527	−0.354788
$869$	−17.1351	−0.581267
$870$	2.45625	0.0832746
$871$	−15.4576	−0.523760
$872$	−19.0825	−0.646214
$873$	−29.9593	−1.01397
$874$	2.44725	0.0827795
$875$	−12.0585	−0.407650
$876$	−0.183753	−0.00620845
$877$	−13.1114	−0.442741	−0.221370	−	0.975190i	$-0.571053\pi$
$877$	−13.1114	−0.442741	−0.221370	+	0.975190i	$0.571053\pi$
$878$	−6.90312	−0.232969
$879$	1.29569	0.0437027
$880$	−3.39560	−0.114466
$881$	−36.0536	−1.21468	−0.607339	−	0.794443i	$-0.707763\pi$
$881$	−36.0536	−1.21468	−0.607339	+	0.794443i	$0.707763\pi$
$882$	−2.94454	−0.0991477
$883$	−20.1551	−0.678272	−0.339136	−	0.940737i	$-0.610135\pi$
$883$	−20.1551	−0.678272	−0.339136	+	0.940737i	$0.610135\pi$
$884$	−13.3938	−0.450481
$885$	2.18253	0.0733649
$886$	−24.9097	−0.836856
$887$	46.0063	1.54474	0.772370	−	0.635173i	$-0.219071\pi$
$887$	46.0063	1.54474	0.772370	+	0.635173i	$0.219071\pi$
$888$	−0.965361	−0.0323954
$889$	9.57533	0.321146
$890$	−0.250579	−0.00839944
$891$	−14.6753	−0.491641
$892$	−26.6491	−0.892278
$893$	0.255332	0.00854435
$894$	−1.26974	−0.0424663
$895$	4.71658	0.157658
$896$	1.00000	0.0334077
$897$	−5.41394	−0.180766
$898$	−4.67211	−0.155910
$899$	55.4049	1.84786
$900$	3.32244	0.110748
$901$	−25.3982	−0.846137
$902$	17.2632	0.574801
$903$	−1.47967	−0.0492404
$904$	−18.1595	−0.603977
$905$	44.1555	1.46778
$906$	−5.61958	−0.186698
$907$	43.6017	1.44777	0.723885	−	0.689921i	$-0.242355\pi$
$907$	43.6017	1.44777	0.723885	+	0.689921i	$0.242355\pi$
$908$	10.8064	0.358623
$909$	−4.09956	−0.135974
$910$	−5.67468	−0.188114
$911$	39.7114	1.31570	0.657848	−	0.753150i	$-0.271467\pi$
$911$	39.7114	1.31570	0.657848	+	0.753150i	$0.271467\pi$
$912$	0.0723046	0.00239424
$913$	15.7806	0.522262
$914$	−3.73132	−0.123421
$915$	2.99549	0.0990280
$916$	15.5078	0.512393
$917$	21.9596	0.725169
$918$	6.50177	0.214591
$919$	12.0403	0.397174	0.198587	−	0.980083i	$-0.436365\pi$
$919$	12.0403	0.397174	0.198587	+	0.980083i	$0.436365\pi$
$920$	−15.6843	−0.517096
$921$	4.44723	0.146541
$922$	10.2506	0.337584
$923$	−29.4459	−0.969222
$924$	0.406418	0.0133702
$925$	−4.62516	−0.152074
$926$	−12.5998	−0.414054
$927$	50.0190	1.64284
$928$	−5.30054	−0.173999
$929$	−45.3352	−1.48740	−0.743700	−	0.668513i	$-0.766931\pi$
$929$	−45.3352	−1.48740	−0.743700	+	0.668513i	$0.766931\pi$
$930$	4.84374	0.158832
$931$	−0.307017	−0.0100621
$932$	−26.5781	−0.870596
$933$	−6.37665	−0.208762
$934$	−40.9396	−1.33958
$935$	−15.7698	−0.515729
$936$	8.49200	0.277570
$937$	19.8700	0.649124	0.324562	−	0.945864i	$-0.394783\pi$
$937$	19.8700	0.649124	0.324562	+	0.945864i	$0.394783\pi$
$938$	5.35979	0.175003
$939$	7.16331	0.233766
$940$	−1.63641	−0.0533737
$941$	−42.5772	−1.38798	−0.693988	−	0.719987i	$-0.744148\pi$
$941$	−42.5772	−1.38798	−0.693988	+	0.719987i	$0.744148\pi$
$942$	0.240050	0.00782127
$943$	79.7385	2.59664
$944$	−4.70985	−0.153293
$945$	2.75468	0.0896096
$946$	−10.8425	−0.352521
$947$	−1.81066	−0.0588385	−0.0294193	−	0.999567i	$-0.509366\pi$
$947$	−1.81066	−0.0588385	−0.0294193	+	0.999567i	$0.509366\pi$
$948$	−2.33841	−0.0759481
$949$	−2.25022	−0.0730451
$950$	0.346420	0.0112393
$951$	4.38934	0.142334
$952$	4.64419	0.150519
$953$	25.5902	0.828949	0.414475	−	0.910061i	$-0.363965\pi$
$953$	25.5902	0.828949	0.414475	+	0.910061i	$0.363965\pi$
$954$	16.1031	0.521357
$955$	−11.6049	−0.375526
$956$	−12.6822	−0.410170
$957$	−2.15423	−0.0696364
$958$	12.5483	0.405416
$959$	10.5347	0.340183
$960$	−0.463396	−0.0149560
$961$	78.2589	2.52448
$962$	−11.8217	−0.381146
$963$	39.9320	1.28679
$964$	−5.68374	−0.183061
$965$	−44.2785	−1.42538
$966$	1.87724	0.0603993
$967$	38.1147	1.22569	0.612843	−	0.790205i	$-0.290026\pi$
$967$	38.1147	1.22569	0.612843	+	0.790205i	$0.290026\pi$
$968$	−8.02191	−0.257834
$969$	0.335796	0.0107873
$970$	20.0200	0.642803
$971$	50.2486	1.61255	0.806277	−	0.591538i	$-0.201479\pi$
$971$	50.2486	1.61255	0.806277	+	0.591538i	$0.201479\pi$
$972$	−6.20267	−0.198951
$973$	6.78086	0.217384
$974$	−30.6911	−0.983407
$975$	−0.766369	−0.0245434
$976$	−6.46422	−0.206915
$977$	−50.6240	−1.61961	−0.809803	−	0.586703i	$-0.800426\pi$
$977$	−50.6240	−1.61961	−0.809803	+	0.586703i	$0.800426\pi$
$978$	−2.32557	−0.0743634
$979$	0.219768	0.00702383
$980$	1.96765	0.0628544
$981$	56.1891	1.79398
$982$	14.5681	0.464886
$983$	−29.4469	−0.939209	−0.469604	−	0.882877i	$-0.655603\pi$
$983$	−29.4469	−0.939209	−0.469604	+	0.882877i	$0.655603\pi$
$984$	2.35589	0.0751032
$985$	46.8478	1.49270
$986$	−24.6167	−0.783955
$987$	0.195860	0.00623431
$988$	0.885432	0.0281693
$989$	−50.0816	−1.59250
$990$	9.99848	0.317773
$991$	5.63402	0.178970	0.0894852	−	0.995988i	$-0.471478\pi$
$991$	5.63402	0.178970	0.0894852	+	0.995988i	$0.471478\pi$
$992$	−10.4527	−0.331874
$993$	3.22208	0.102250
$994$	10.2101	0.323846
$995$	−18.7215	−0.593512
$996$	2.15357	0.0682385
$997$	9.88345	0.313012	0.156506	−	0.987677i	$-0.449977\pi$
$997$	9.88345	0.313012	0.156506	+	0.987677i	$0.449977\pi$
$998$	−27.5857	−0.873209
$999$	5.73863	0.181562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.11	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.11	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.235507 q^{3} +1.00000 q^{4} +1.96765 q^{5} -0.235507 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.94454 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.235507 q^{3} +1.00000 q^{4} +1.96765 q^{5} -0.235507 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.94454 q^{9} +1.96765 q^{10} -1.72571 q^{11} -0.235507 q^{12} -2.88399 q^{13} +1.00000 q^{14} -0.463396 q^{15} +1.00000 q^{16} +4.64419 q^{17} -2.94454 q^{18} -0.307017 q^{19} +1.96765 q^{20} -0.235507 q^{21} -1.72571 q^{22} -7.97106 q^{23} -0.235507 q^{24} -1.12834 q^{25} -2.88399 q^{26} +1.39998 q^{27} +1.00000 q^{28} -5.30054 q^{29} -0.463396 q^{30} -10.4527 q^{31} +1.00000 q^{32} +0.406418 q^{33} +4.64419 q^{34} +1.96765 q^{35} -2.94454 q^{36} +4.09908 q^{37} -0.307017 q^{38} +0.679199 q^{39} +1.96765 q^{40} -10.0035 q^{41} -0.235507 q^{42} +6.28292 q^{43} -1.72571 q^{44} -5.79383 q^{45} -7.97106 q^{46} -0.831654 q^{47} -0.235507 q^{48} +1.00000 q^{49} -1.12834 q^{50} -1.09374 q^{51} -2.88399 q^{52} -5.46881 q^{53} +1.39998 q^{54} -3.39560 q^{55} +1.00000 q^{56} +0.0723046 q^{57} -5.30054 q^{58} -4.70985 q^{59} -0.463396 q^{60} -6.46422 q^{61} -10.4527 q^{62} -2.94454 q^{63} +1.00000 q^{64} -5.67468 q^{65} +0.406418 q^{66} +5.35979 q^{67} +4.64419 q^{68} +1.87724 q^{69} +1.96765 q^{70} +10.2101 q^{71} -2.94454 q^{72} +0.780246 q^{73} +4.09908 q^{74} +0.265732 q^{75} -0.307017 q^{76} -1.72571 q^{77} +0.679199 q^{78} +9.92927 q^{79} +1.96765 q^{80} +8.50390 q^{81} -10.0035 q^{82} -9.14440 q^{83} -0.235507 q^{84} +9.13816 q^{85} +6.28292 q^{86} +1.24831 q^{87} -1.72571 q^{88} -0.127349 q^{89} -5.79383 q^{90} -2.88399 q^{91} -7.97106 q^{92} +2.46168 q^{93} -0.831654 q^{94} -0.604102 q^{95} -0.235507 q^{96} +10.1745 q^{97} +1.00000 q^{98} +5.08143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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