LMFDB - Embedded newform 4034.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.90524 q^{3} +1.00000 q^{4} -3.49980 q^{5} +1.90524 q^{6} -2.88392 q^{7} -1.00000 q^{8} +0.629935 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.90524 q^{3} +1.00000 q^{4} -3.49980 q^{5} +1.90524 q^{6} -2.88392 q^{7} -1.00000 q^{8} +0.629935 q^{9} +3.49980 q^{10} -2.01105 q^{11} -1.90524 q^{12} -5.40960 q^{13} +2.88392 q^{14} +6.66795 q^{15} +1.00000 q^{16} +4.25855 q^{17} -0.629935 q^{18} +2.92193 q^{19} -3.49980 q^{20} +5.49456 q^{21} +2.01105 q^{22} -2.94949 q^{23} +1.90524 q^{24} +7.24858 q^{25} +5.40960 q^{26} +4.51554 q^{27} -2.88392 q^{28} -3.50412 q^{29} -6.66795 q^{30} -7.26975 q^{31} -1.00000 q^{32} +3.83152 q^{33} -4.25855 q^{34} +10.0931 q^{35} +0.629935 q^{36} +7.06471 q^{37} -2.92193 q^{38} +10.3066 q^{39} +3.49980 q^{40} -2.34033 q^{41} -5.49456 q^{42} +4.99473 q^{43} -2.01105 q^{44} -2.20464 q^{45} +2.94949 q^{46} +8.87354 q^{47} -1.90524 q^{48} +1.31699 q^{49} -7.24858 q^{50} -8.11356 q^{51} -5.40960 q^{52} +7.95720 q^{53} -4.51554 q^{54} +7.03825 q^{55} +2.88392 q^{56} -5.56697 q^{57} +3.50412 q^{58} +11.9249 q^{59} +6.66795 q^{60} -0.563706 q^{61} +7.26975 q^{62} -1.81668 q^{63} +1.00000 q^{64} +18.9325 q^{65} -3.83152 q^{66} -0.351716 q^{67} +4.25855 q^{68} +5.61949 q^{69} -10.0931 q^{70} -4.94089 q^{71} -0.629935 q^{72} -1.76703 q^{73} -7.06471 q^{74} -13.8103 q^{75} +2.92193 q^{76} +5.79970 q^{77} -10.3066 q^{78} -4.78543 q^{79} -3.49980 q^{80} -10.4930 q^{81} +2.34033 q^{82} -7.48468 q^{83} +5.49456 q^{84} -14.9041 q^{85} -4.99473 q^{86} +6.67618 q^{87} +2.01105 q^{88} +12.6204 q^{89} +2.20464 q^{90} +15.6009 q^{91} -2.94949 q^{92} +13.8506 q^{93} -8.87354 q^{94} -10.2262 q^{95} +1.90524 q^{96} +0.00634918 q^{97} -1.31699 q^{98} -1.26683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−1.90524	−1.09999	−0.549995	−	0.835168i	$-0.685370\pi$
$3$	−1.90524	−1.09999	−0.549995	+	0.835168i	$0.685370\pi$
$4$	1.00000	0.500000
$5$	−3.49980	−1.56516	−0.782578	−	0.622552i	$-0.786096\pi$
$5$	−3.49980	−1.56516	−0.782578	+	0.622552i	$0.786096\pi$
$6$	1.90524	0.777810
$7$	−2.88392	−1.09002	−0.545010	−	0.838430i	$-0.683474\pi$
$7$	−2.88392	−1.09002	−0.545010	+	0.838430i	$0.683474\pi$
$8$	−1.00000	−0.353553
$9$	0.629935	0.209978
$10$	3.49980	1.10673
$11$	−2.01105	−0.606353	−0.303177	−	0.952934i	$-0.598047\pi$
$11$	−2.01105	−0.606353	−0.303177	+	0.952934i	$0.598047\pi$
$12$	−1.90524	−0.549995
$13$	−5.40960	−1.50035	−0.750177	−	0.661238i	$-0.770032\pi$
$13$	−5.40960	−1.50035	−0.750177	+	0.661238i	$0.770032\pi$
$14$	2.88392	0.770760
$15$	6.66795	1.72166
$16$	1.00000	0.250000
$17$	4.25855	1.03285	0.516425	−	0.856332i	$-0.327262\pi$
$17$	4.25855	1.03285	0.516425	+	0.856332i	$0.327262\pi$
$18$	−0.629935	−0.148477
$19$	2.92193	0.670336	0.335168	−	0.942158i	$-0.391207\pi$
$19$	2.92193	0.670336	0.335168	+	0.942158i	$0.391207\pi$
$20$	−3.49980	−0.782578
$21$	5.49456	1.19901
$22$	2.01105	0.428757
$23$	−2.94949	−0.615012	−0.307506	−	0.951546i	$-0.599494\pi$
$23$	−2.94949	−0.615012	−0.307506	+	0.951546i	$0.599494\pi$
$24$	1.90524	0.388905
$25$	7.24858	1.44972
$26$	5.40960	1.06091
$27$	4.51554	0.869016
$28$	−2.88392	−0.545010
$29$	−3.50412	−0.650698	−0.325349	−	0.945594i	$-0.605482\pi$
$29$	−3.50412	−0.650698	−0.325349	+	0.945594i	$0.605482\pi$
$30$	−6.66795	−1.21740
$31$	−7.26975	−1.30568	−0.652842	−	0.757494i	$-0.726424\pi$
$31$	−7.26975	−1.30568	−0.652842	+	0.757494i	$0.726424\pi$
$32$	−1.00000	−0.176777
$33$	3.83152	0.666983
$34$	−4.25855	−0.730335
$35$	10.0931	1.70605
$36$	0.629935	0.104989
$37$	7.06471	1.16143	0.580716	−	0.814106i	$-0.302773\pi$
$37$	7.06471	1.16143	0.580716	+	0.814106i	$0.302773\pi$
$38$	−2.92193	−0.473999
$39$	10.3066	1.65037
$40$	3.49980	0.553367
$41$	−2.34033	−0.365498	−0.182749	−	0.983160i	$-0.558500\pi$
$41$	−2.34033	−0.365498	−0.182749	+	0.983160i	$0.558500\pi$
$42$	−5.49456	−0.847828
$43$	4.99473	0.761690	0.380845	−	0.924639i	$-0.375633\pi$
$43$	4.99473	0.761690	0.380845	+	0.924639i	$0.375633\pi$
$44$	−2.01105	−0.303177
$45$	−2.20464	−0.328649
$46$	2.94949	0.434879
$47$	8.87354	1.29434	0.647169	−	0.762346i	$-0.275953\pi$
$47$	8.87354	1.29434	0.647169	+	0.762346i	$0.275953\pi$
$48$	−1.90524	−0.274998
$49$	1.31699	0.188142
$50$	−7.24858	−1.02510
$51$	−8.11356	−1.13613
$52$	−5.40960	−0.750177
$53$	7.95720	1.09301	0.546503	−	0.837457i	$-0.315959\pi$
$53$	7.95720	1.09301	0.546503	+	0.837457i	$0.315959\pi$
$54$	−4.51554	−0.614487
$55$	7.03825	0.949038
$56$	2.88392	0.385380
$57$	−5.56697	−0.737363
$58$	3.50412	0.460113
$59$	11.9249	1.55249	0.776246	−	0.630430i	$-0.217121\pi$
$59$	11.9249	1.55249	0.776246	+	0.630430i	$0.217121\pi$
$60$	6.66795	0.860829
$61$	−0.563706	−0.0721752	−0.0360876	−	0.999349i	$-0.511490\pi$
$61$	−0.563706	−0.0721752	−0.0360876	+	0.999349i	$0.511490\pi$
$62$	7.26975	0.923259
$63$	−1.81668	−0.228880
$64$	1.00000	0.125000
$65$	18.9325	2.34829
$66$	−3.83152	−0.471628
$67$	−0.351716	−0.0429690	−0.0214845	−	0.999769i	$-0.506839\pi$
$67$	−0.351716	−0.0429690	−0.0214845	+	0.999769i	$0.506839\pi$
$68$	4.25855	0.516425
$69$	5.61949	0.676507
$70$	−10.0931	−1.20636
$71$	−4.94089	−0.586376	−0.293188	−	0.956055i	$-0.594716\pi$
$71$	−4.94089	−0.586376	−0.293188	+	0.956055i	$0.594716\pi$
$72$	−0.629935	−0.0742386
$73$	−1.76703	−0.206815	−0.103407	−	0.994639i	$-0.532975\pi$
$73$	−1.76703	−0.206815	−0.103407	+	0.994639i	$0.532975\pi$
$74$	−7.06471	−0.821256
$75$	−13.8103	−1.59467
$76$	2.92193	0.335168
$77$	5.79970	0.660937
$78$	−10.3066	−1.16699
$79$	−4.78543	−0.538403	−0.269202	−	0.963084i	$-0.586760\pi$
$79$	−4.78543	−0.538403	−0.269202	+	0.963084i	$0.586760\pi$
$80$	−3.49980	−0.391289
$81$	−10.4930	−1.16589
$82$	2.34033	0.258446
$83$	−7.48468	−0.821550	−0.410775	−	0.911737i	$-0.634742\pi$
$83$	−7.48468	−0.821550	−0.410775	+	0.911737i	$0.634742\pi$
$84$	5.49456	0.599505
$85$	−14.9041	−1.61657
$86$	−4.99473	−0.538596
$87$	6.67618	0.715762
$88$	2.01105	0.214378
$89$	12.6204	1.33776	0.668879	−	0.743371i	$-0.266774\pi$
$89$	12.6204	1.33776	0.668879	+	0.743371i	$0.266774\pi$
$90$	2.20464	0.232390
$91$	15.6009	1.63541
$92$	−2.94949	−0.307506
$93$	13.8506	1.43624
$94$	−8.87354	−0.915236
$95$	−10.2262	−1.04918
$96$	1.90524	0.194453
$97$	0.00634918	0.000644662 0	0.000322331	−	1.00000i	$-0.499897\pi$
$97$	0.00634918	0.000644662 0	0.000322331		1.00000i	$0.499897\pi$
$98$	−1.31699	−0.133037
$99$	−1.26683	−0.127321
$100$	7.24858	0.724858
$101$	−0.454204	−0.0451950	−0.0225975	−	0.999745i	$-0.507194\pi$
$101$	−0.454204	−0.0451950	−0.0225975	+	0.999745i	$0.507194\pi$
$102$	8.11356	0.803362
$103$	−6.73265	−0.663388	−0.331694	−	0.943387i	$-0.607620\pi$
$103$	−6.73265	−0.663388	−0.331694	+	0.943387i	$0.607620\pi$
$104$	5.40960	0.530455
$105$	−19.2298	−1.87664
$106$	−7.95720	−0.772872
$107$	11.1557	1.07847	0.539233	−	0.842156i	$-0.318714\pi$
$107$	11.1557	1.07847	0.539233	+	0.842156i	$0.318714\pi$
$108$	4.51554	0.434508
$109$	−4.83977	−0.463566	−0.231783	−	0.972768i	$-0.574456\pi$
$109$	−4.83977	−0.463566	−0.231783	+	0.972768i	$0.574456\pi$
$110$	−7.03825	−0.671071
$111$	−13.4600	−1.27756
$112$	−2.88392	−0.272505
$113$	1.84849	0.173891	0.0869457	−	0.996213i	$-0.472289\pi$
$113$	1.84849	0.173891	0.0869457	+	0.996213i	$0.472289\pi$
$114$	5.56697	0.521395
$115$	10.3226	0.962590
$116$	−3.50412	−0.325349
$117$	−3.40770	−0.315042
$118$	−11.9249	−1.09778
$119$	−12.2813	−1.12583
$120$	−6.66795	−0.608698
$121$	−6.95569	−0.632336
$122$	0.563706	0.0510356
$123$	4.45889	0.402044
$124$	−7.26975	−0.652842
$125$	−7.86958	−0.703877
$126$	1.81668	0.161843
$127$	10.9581	0.972375	0.486188	−	0.873854i	$-0.338387\pi$
$127$	10.9581	0.972375	0.486188	+	0.873854i	$0.338387\pi$
$128$	−1.00000	−0.0883883
$129$	−9.51616	−0.837851
$130$	−18.9325	−1.66049
$131$	−10.9162	−0.953752	−0.476876	−	0.878971i	$-0.658231\pi$
$131$	−10.9162	−0.953752	−0.476876	+	0.878971i	$0.658231\pi$
$132$	3.83152	0.333491
$133$	−8.42661	−0.730680
$134$	0.351716	0.0303836
$135$	−15.8035	−1.36015
$136$	−4.25855	−0.365168
$137$	2.33517	0.199507	0.0997537	−	0.995012i	$-0.468195\pi$
$137$	2.33517	0.199507	0.0997537	+	0.995012i	$0.468195\pi$
$138$	−5.61949	−0.478362
$139$	−22.0818	−1.87295	−0.936476	−	0.350730i	$-0.885933\pi$
$139$	−22.0818	−1.87295	−0.936476	+	0.350730i	$0.885933\pi$
$140$	10.0931	0.853026
$141$	−16.9062	−1.42376
$142$	4.94089	0.414630
$143$	10.8790	0.909744
$144$	0.629935	0.0524946
$145$	12.2637	1.01845
$146$	1.76703	0.146240
$147$	−2.50919	−0.206954
$148$	7.06471	0.580716
$149$	16.0944	1.31851	0.659254	−	0.751921i	$-0.270872\pi$
$149$	16.0944	1.31851	0.659254	+	0.751921i	$0.270872\pi$
$150$	13.8103	1.12760
$151$	18.7962	1.52961	0.764805	−	0.644262i	$-0.222835\pi$
$151$	18.7962	1.52961	0.764805	+	0.644262i	$0.222835\pi$
$152$	−2.92193	−0.237000
$153$	2.68261	0.216876
$154$	−5.79970	−0.467353
$155$	25.4426	2.04360
$156$	10.3066	0.825187
$157$	7.37409	0.588517	0.294258	−	0.955726i	$-0.404927\pi$
$157$	7.37409	0.588517	0.294258	+	0.955726i	$0.404927\pi$
$158$	4.78543	0.380708
$159$	−15.1604	−1.20230
$160$	3.49980	0.276683
$161$	8.50610	0.670375
$162$	10.4930	0.824407
$163$	−7.90195	−0.618929	−0.309464	−	0.950911i	$-0.600150\pi$
$163$	−7.90195	−0.618929	−0.309464	+	0.950911i	$0.600150\pi$
$164$	−2.34033	−0.182749
$165$	−13.4096	−1.04393
$166$	7.48468	0.580924
$167$	−5.99110	−0.463605	−0.231803	−	0.972763i	$-0.574462\pi$
$167$	−5.99110	−0.463605	−0.231803	+	0.972763i	$0.574462\pi$
$168$	−5.49456	−0.423914
$169$	16.2638	1.25106
$170$	14.9041	1.14309
$171$	1.84063	0.140756
$172$	4.99473	0.380845
$173$	7.39202	0.562005	0.281002	−	0.959707i	$-0.409333\pi$
$173$	7.39202	0.562005	0.281002	+	0.959707i	$0.409333\pi$
$174$	−6.67618	−0.506120
$175$	−20.9043	−1.58022
$176$	−2.01105	−0.151588
$177$	−22.7198	−1.70773
$178$	−12.6204	−0.945938
$179$	17.7607	1.32750	0.663748	−	0.747957i	$-0.268965\pi$
$179$	17.7607	1.32750	0.663748	+	0.747957i	$0.268965\pi$
$180$	−2.20464	−0.164325
$181$	1.46007	0.108526	0.0542631	−	0.998527i	$-0.482719\pi$
$181$	1.46007	0.108526	0.0542631	+	0.998527i	$0.482719\pi$
$182$	−15.6009	−1.15641
$183$	1.07399	0.0793920
$184$	2.94949	0.217439
$185$	−24.7251	−1.81782
$186$	−13.8506	−1.01558
$187$	−8.56414	−0.626272
$188$	8.87354	0.647169
$189$	−13.0225	−0.947244
$190$	10.2262	0.741883
$191$	−18.3850	−1.33029	−0.665146	−	0.746714i	$-0.731631\pi$
$191$	−18.3850	−1.33029	−0.665146	+	0.746714i	$0.731631\pi$
$192$	−1.90524	−0.137499
$193$	−7.00329	−0.504108	−0.252054	−	0.967713i	$-0.581106\pi$
$193$	−7.00329	−0.504108	−0.252054	+	0.967713i	$0.581106\pi$
$194$	−0.00634918	−0.000455845 0
$195$	−36.0709	−2.58309
$196$	1.31699	0.0940711
$197$	8.71782	0.621119	0.310560	−	0.950554i	$-0.399484\pi$
$197$	8.71782	0.621119	0.310560	+	0.950554i	$0.399484\pi$
$198$	1.26683	0.0900296
$199$	−10.3997	−0.737218	−0.368609	−	0.929584i	$-0.620166\pi$
$199$	−10.3997	−0.737218	−0.368609	+	0.929584i	$0.620166\pi$
$200$	−7.24858	−0.512552
$201$	0.670103	0.0472654
$202$	0.454204	0.0319577
$203$	10.1056	0.709274
$204$	−8.11356	−0.568063
$205$	8.19068	0.572062
$206$	6.73265	0.469086
$207$	−1.85799	−0.129139
$208$	−5.40960	−0.375088
$209$	−5.87613	−0.406461
$210$	19.2298	1.32698
$211$	7.30799	0.503103	0.251551	−	0.967844i	$-0.419059\pi$
$211$	7.30799	0.503103	0.251551	+	0.967844i	$0.419059\pi$
$212$	7.95720	0.546503
$213$	9.41358	0.645008
$214$	−11.1557	−0.762591
$215$	−17.4806	−1.19216
$216$	−4.51554	−0.307244
$217$	20.9654	1.42322
$218$	4.83977	0.327791
$219$	3.36661	0.227494
$220$	7.03825	0.474519
$221$	−23.0371	−1.54964
$222$	13.4600	0.903374
$223$	−8.31783	−0.557003	−0.278502	−	0.960436i	$-0.589838\pi$
$223$	−8.31783	−0.557003	−0.278502	+	0.960436i	$0.589838\pi$
$224$	2.88392	0.192690
$225$	4.56614	0.304409
$226$	−1.84849	−0.122960
$227$	23.6241	1.56798	0.783992	−	0.620771i	$-0.213180\pi$
$227$	23.6241	1.56798	0.783992	+	0.620771i	$0.213180\pi$
$228$	−5.56697	−0.368682
$229$	3.83211	0.253233	0.126616	−	0.991952i	$-0.459588\pi$
$229$	3.83211	0.253233	0.126616	+	0.991952i	$0.459588\pi$
$230$	−10.3226	−0.680654
$231$	−11.0498	−0.727024
$232$	3.50412	0.230057
$233$	5.46717	0.358166	0.179083	−	0.983834i	$-0.442687\pi$
$233$	5.46717	0.358166	0.179083	+	0.983834i	$0.442687\pi$
$234$	3.40770	0.222768
$235$	−31.0556	−2.02584
$236$	11.9249	0.776246
$237$	9.11739	0.592238
$238$	12.2813	0.796080
$239$	27.6306	1.78728	0.893638	−	0.448788i	$-0.148144\pi$
$239$	27.6306	1.78728	0.893638	+	0.448788i	$0.148144\pi$
$240$	6.66795	0.430414
$241$	5.69112	0.366597	0.183299	−	0.983057i	$-0.441322\pi$
$241$	5.69112	0.366597	0.183299	+	0.983057i	$0.441322\pi$
$242$	6.95569	0.447129
$243$	6.44503	0.413449
$244$	−0.563706	−0.0360876
$245$	−4.60921	−0.294472
$246$	−4.45889	−0.284288
$247$	−15.8065	−1.00574
$248$	7.26975	0.461629
$249$	14.2601	0.903697
$250$	7.86958	0.497716
$251$	−7.05503	−0.445310	−0.222655	−	0.974897i	$-0.571472\pi$
$251$	−7.05503	−0.445310	−0.222655	+	0.974897i	$0.571472\pi$
$252$	−1.81668	−0.114440
$253$	5.93156	0.372914
$254$	−10.9581	−0.687573
$255$	28.3958	1.77821
$256$	1.00000	0.0625000
$257$	−7.04580	−0.439505	−0.219752	−	0.975556i	$-0.570525\pi$
$257$	−7.04580	−0.439505	−0.219752	+	0.975556i	$0.570525\pi$
$258$	9.51616	0.592450
$259$	−20.3741	−1.26598
$260$	18.9325	1.17414
$261$	−2.20737	−0.136633
$262$	10.9162	0.674404
$263$	−24.7135	−1.52390	−0.761950	−	0.647636i	$-0.775758\pi$
$263$	−24.7135	−1.52390	−0.761950	+	0.647636i	$0.775758\pi$
$264$	−3.83152	−0.235814
$265$	−27.8486	−1.71073
$266$	8.42661	0.516669
$267$	−24.0449	−1.47152
$268$	−0.351716	−0.0214845
$269$	−22.5693	−1.37607	−0.688036	−	0.725676i	$-0.741527\pi$
$269$	−22.5693	−1.37607	−0.688036	+	0.725676i	$0.741527\pi$
$270$	15.8035	0.961769
$271$	−24.8140	−1.50734	−0.753671	−	0.657252i	$-0.771719\pi$
$271$	−24.8140	−1.50734	−0.753671	+	0.657252i	$0.771719\pi$
$272$	4.25855	0.258213
$273$	−29.7234	−1.79894
$274$	−2.33517	−0.141073
$275$	−14.5772	−0.879040
$276$	5.61949	0.338253
$277$	3.36643	0.202269	0.101135	−	0.994873i	$-0.467753\pi$
$277$	3.36643	0.202269	0.101135	+	0.994873i	$0.467753\pi$
$278$	22.0818	1.32438
$279$	−4.57947	−0.274166
$280$	−10.0931	−0.603180
$281$	−25.0535	−1.49456	−0.747282	−	0.664507i	$-0.768642\pi$
$281$	−25.0535	−1.49456	−0.747282	+	0.664507i	$0.768642\pi$
$282$	16.9062	1.00675
$283$	21.3030	1.26633	0.633166	−	0.774016i	$-0.281755\pi$
$283$	21.3030	1.26633	0.633166	+	0.774016i	$0.281755\pi$
$284$	−4.94089	−0.293188
$285$	19.4833	1.15409
$286$	−10.8790	−0.643286
$287$	6.74932	0.398400
$288$	−0.629935	−0.0371193
$289$	1.13526	0.0667797
$290$	−12.2637	−0.720149
$291$	−0.0120967	−0.000709122 0
$292$	−1.76703	−0.103407
$293$	17.1355	1.00107	0.500533	−	0.865718i	$-0.333138\pi$
$293$	17.1355	1.00107	0.500533	+	0.865718i	$0.333138\pi$
$294$	2.50919	0.146339
$295$	−41.7348	−2.42989
$296$	−7.06471	−0.410628
$297$	−9.08096	−0.526931
$298$	−16.0944	−0.932325
$299$	15.9556	0.922735
$300$	−13.8103	−0.797337
$301$	−14.4044	−0.830257
$302$	−18.7962	−1.08160
$303$	0.865367	0.0497140
$304$	2.92193	0.167584
$305$	1.97286	0.112965
$306$	−2.68261	−0.153355
$307$	9.70104	0.553667	0.276834	−	0.960918i	$-0.410715\pi$
$307$	9.70104	0.553667	0.276834	+	0.960918i	$0.410715\pi$
$308$	5.79970	0.330468
$309$	12.8273	0.729720
$310$	−25.4426	−1.44504
$311$	−32.7922	−1.85948	−0.929739	−	0.368220i	$-0.879967\pi$
$311$	−32.7922	−1.85948	−0.929739	+	0.368220i	$0.879967\pi$
$312$	−10.3066	−0.583495
$313$	30.9671	1.75036	0.875182	−	0.483793i	$-0.160741\pi$
$313$	30.9671	1.75036	0.875182	+	0.483793i	$0.160741\pi$
$314$	−7.37409	−0.416144
$315$	6.35802	0.358234
$316$	−4.78543	−0.269202
$317$	−20.2374	−1.13665	−0.568323	−	0.822805i	$-0.692408\pi$
$317$	−20.2374	−1.13665	−0.568323	+	0.822805i	$0.692408\pi$
$318$	15.1604	0.850151
$319$	7.04694	0.394553
$320$	−3.49980	−0.195645
$321$	−21.2544	−1.18630
$322$	−8.50610	−0.474026
$323$	12.4432	0.692357
$324$	−10.4930	−0.582944
$325$	−39.2119	−2.17509
$326$	7.90195	0.437649
$327$	9.22092	0.509918
$328$	2.34033	0.129223
$329$	−25.5906	−1.41085
$330$	13.4096	0.738172
$331$	−9.70079	−0.533204	−0.266602	−	0.963807i	$-0.585901\pi$
$331$	−9.70079	−0.533204	−0.266602	+	0.963807i	$0.585901\pi$
$332$	−7.48468	−0.410775
$333$	4.45031	0.243875
$334$	5.99110	0.327818
$335$	1.23094	0.0672532
$336$	5.49456	0.299753
$337$	12.1815	0.663566	0.331783	−	0.943356i	$-0.392350\pi$
$337$	12.1815	0.663566	0.331783	+	0.943356i	$0.392350\pi$
$338$	−16.2638	−0.884633
$339$	−3.52182	−0.191279
$340$	−14.9041	−0.808286
$341$	14.6198	0.791706
$342$	−1.84063	−0.0995296
$343$	16.3893	0.884941
$344$	−4.99473	−0.269298
$345$	−19.6671	−1.05884
$346$	−7.39202	−0.397397
$347$	−33.5336	−1.80018	−0.900089	−	0.435705i	$-0.856499\pi$
$347$	−33.5336	−1.80018	−0.900089	+	0.435705i	$0.856499\pi$
$348$	6.67618	0.357881
$349$	−22.3931	−1.19867	−0.599336	−	0.800497i	$-0.704569\pi$
$349$	−22.3931	−1.19867	−0.599336	+	0.800497i	$0.704569\pi$
$350$	20.9043	1.11738
$351$	−24.4273	−1.30383
$352$	2.01105	0.107189
$353$	−14.4526	−0.769232	−0.384616	−	0.923077i	$-0.625666\pi$
$353$	−14.4526	−0.769232	−0.384616	+	0.923077i	$0.625666\pi$
$354$	22.7198	1.20754
$355$	17.2921	0.917771
$356$	12.6204	0.668879
$357$	23.3988	1.23840
$358$	−17.7607	−0.938681
$359$	0.610238	0.0322071	0.0161036	−	0.999870i	$-0.494874\pi$
$359$	0.610238	0.0322071	0.0161036	+	0.999870i	$0.494874\pi$
$360$	2.20464	0.116195
$361$	−10.4623	−0.550649
$362$	−1.46007	−0.0767396
$363$	13.2523	0.695563
$364$	15.6009	0.817707
$365$	6.18424	0.323698
$366$	−1.07399	−0.0561386
$367$	−15.9049	−0.830228	−0.415114	−	0.909769i	$-0.636258\pi$
$367$	−15.9049	−0.830228	−0.415114	+	0.909769i	$0.636258\pi$
$368$	−2.94949	−0.153753
$369$	−1.47426	−0.0767467
$370$	24.7251	1.28539
$371$	−22.9479	−1.19140
$372$	13.8506	0.718120
$373$	−27.7278	−1.43569	−0.717847	−	0.696201i	$-0.754872\pi$
$373$	−27.7278	−1.43569	−0.717847	+	0.696201i	$0.754872\pi$
$374$	8.56414	0.442841
$375$	14.9934	0.774257
$376$	−8.87354	−0.457618
$377$	18.9559	0.976277
$378$	13.0225	0.669803
$379$	1.89031	0.0970989	0.0485494	−	0.998821i	$-0.484540\pi$
$379$	1.89031	0.0970989	0.0485494	+	0.998821i	$0.484540\pi$
$380$	−10.2262	−0.524591
$381$	−20.8778	−1.06960
$382$	18.3850	0.940658
$383$	7.90872	0.404117	0.202058	−	0.979374i	$-0.435237\pi$
$383$	7.90872	0.404117	0.202058	+	0.979374i	$0.435237\pi$
$384$	1.90524	0.0972263
$385$	−20.2978	−1.03447
$386$	7.00329	0.356458
$387$	3.14636	0.159938
$388$	0.00634918	0.000322331 0
$389$	17.3292	0.878624	0.439312	−	0.898335i	$-0.355222\pi$
$389$	17.3292	0.878624	0.439312	+	0.898335i	$0.355222\pi$
$390$	36.0709	1.82652
$391$	−12.5606	−0.635215
$392$	−1.31699	−0.0665183
$393$	20.7979	1.04912
$394$	−8.71782	−0.439198
$395$	16.7480	0.842685
$396$	−1.26683	−0.0636605
$397$	15.0514	0.755408	0.377704	−	0.925926i	$-0.376714\pi$
$397$	15.0514	0.755408	0.377704	+	0.925926i	$0.376714\pi$
$398$	10.3997	0.521292
$399$	16.0547	0.803740
$400$	7.24858	0.362429
$401$	24.8172	1.23931	0.619656	−	0.784874i	$-0.287272\pi$
$401$	24.8172	1.23931	0.619656	+	0.784874i	$0.287272\pi$
$402$	−0.670103	−0.0334217
$403$	39.3264	1.95899
$404$	−0.454204	−0.0225975
$405$	36.7233	1.82480
$406$	−10.1056	−0.501532
$407$	−14.2075	−0.704238
$408$	8.11356	0.401681
$409$	−0.439221	−0.0217181	−0.0108590	−	0.999941i	$-0.503457\pi$
$409$	−0.439221	−0.0217181	−0.0108590	+	0.999941i	$0.503457\pi$
$410$	−8.19068	−0.404509
$411$	−4.44906	−0.219456
$412$	−6.73265	−0.331694
$413$	−34.3905	−1.69225
$414$	1.85799	0.0913151
$415$	26.1949	1.28585
$416$	5.40960	0.265227
$417$	42.0711	2.06023
$418$	5.87613	0.287411
$419$	17.0577	0.833326	0.416663	−	0.909061i	$-0.363200\pi$
$419$	17.0577	0.833326	0.416663	+	0.909061i	$0.363200\pi$
$420$	−19.2298	−0.938320
$421$	6.02590	0.293685	0.146842	−	0.989160i	$-0.453089\pi$
$421$	6.02590	0.293685	0.146842	+	0.989160i	$0.453089\pi$
$422$	−7.30799	−0.355748
$423$	5.58975	0.271783
$424$	−7.95720	−0.386436
$425$	30.8685	1.49734
$426$	−9.41358	−0.456089
$427$	1.62568	0.0786723
$428$	11.1557	0.539233
$429$	−20.7270	−1.00071
$430$	17.4806	0.842987
$431$	8.63924	0.416137	0.208069	−	0.978114i	$-0.433282\pi$
$431$	8.63924	0.416137	0.208069	+	0.978114i	$0.433282\pi$
$432$	4.51554	0.217254
$433$	3.10441	0.149188	0.0745942	−	0.997214i	$-0.476234\pi$
$433$	3.10441	0.149188	0.0745942	+	0.997214i	$0.476234\pi$
$434$	−20.9654	−1.00637
$435$	−23.3653	−1.12028
$436$	−4.83977	−0.231783
$437$	−8.61820	−0.412265
$438$	−3.36661	−0.160863
$439$	−32.3919	−1.54598	−0.772989	−	0.634419i	$-0.781239\pi$
$439$	−32.3919	−1.54598	−0.772989	+	0.634419i	$0.781239\pi$
$440$	−7.03825	−0.335536
$441$	0.829621	0.0395058
$442$	23.0371	1.09576
$443$	27.1351	1.28923	0.644615	−	0.764508i	$-0.277018\pi$
$443$	27.1351	1.28923	0.644615	+	0.764508i	$0.277018\pi$
$444$	−13.4600	−0.638782
$445$	−44.1688	−2.09380
$446$	8.31783	0.393861
$447$	−30.6637	−1.45034
$448$	−2.88392	−0.136252
$449$	13.9609	0.658858	0.329429	−	0.944180i	$-0.393144\pi$
$449$	13.9609	0.658858	0.329429	+	0.944180i	$0.393144\pi$
$450$	−4.56614	−0.215250
$451$	4.70651	0.221621
$452$	1.84849	0.0869457
$453$	−35.8112	−1.68256
$454$	−23.6241	−1.10873
$455$	−54.5998	−2.55968
$456$	5.56697	0.260697
$457$	25.6876	1.20162	0.600808	−	0.799393i	$-0.294846\pi$
$457$	25.6876	1.20162	0.600808	+	0.799393i	$0.294846\pi$
$458$	−3.83211	−0.179063
$459$	19.2297	0.897563
$460$	10.3226	0.481295
$461$	29.2267	1.36122	0.680612	−	0.732644i	$-0.261714\pi$
$461$	29.2267	1.36122	0.680612	+	0.732644i	$0.261714\pi$
$462$	11.0498	0.514084
$463$	−30.4742	−1.41625	−0.708127	−	0.706085i	$-0.750460\pi$
$463$	−30.4742	−1.41625	−0.708127	+	0.706085i	$0.750460\pi$
$464$	−3.50412	−0.162675
$465$	−48.4743	−2.24794
$466$	−5.46717	−0.253262
$467$	7.13236	0.330046	0.165023	−	0.986290i	$-0.447230\pi$
$467$	7.13236	0.330046	0.165023	+	0.986290i	$0.447230\pi$
$468$	−3.40770	−0.157521
$469$	1.01432	0.0468370
$470$	31.0556	1.43249
$471$	−14.0494	−0.647362
$472$	−11.9249	−0.548889
$473$	−10.0446	−0.461853
$474$	−9.11739	−0.418776
$475$	21.1798	0.971798
$476$	−12.2813	−0.562913
$477$	5.01252	0.229507
$478$	−27.6306	−1.26380
$479$	−0.778681	−0.0355788	−0.0177894	−	0.999842i	$-0.505663\pi$
$479$	−0.778681	−0.0355788	−0.0177894	+	0.999842i	$0.505663\pi$
$480$	−6.66795	−0.304349
$481$	−38.2173	−1.74256
$482$	−5.69112	−0.259223
$483$	−16.2062	−0.737405
$484$	−6.95569	−0.316168
$485$	−0.0222209	−0.00100900
$486$	−6.44503	−0.292352
$487$	11.9725	0.542526	0.271263	−	0.962505i	$-0.412559\pi$
$487$	11.9725	0.542526	0.271263	+	0.962505i	$0.412559\pi$
$488$	0.563706	0.0255178
$489$	15.0551	0.680816
$490$	4.60921	0.208223
$491$	42.6438	1.92449	0.962243	−	0.272192i	$-0.0877486\pi$
$491$	42.6438	1.92449	0.962243	+	0.272192i	$0.0877486\pi$
$492$	4.45889	0.201022
$493$	−14.9225	−0.672074
$494$	15.8065	0.711167
$495$	4.43364	0.199277
$496$	−7.26975	−0.326421
$497$	14.2491	0.639161
$498$	−14.2601	−0.639010
$499$	−8.33065	−0.372931	−0.186466	−	0.982461i	$-0.559703\pi$
$499$	−8.33065	−0.372931	−0.186466	+	0.982461i	$0.559703\pi$
$500$	−7.86958	−0.351938
$501$	11.4145	0.509961
$502$	7.05503	0.314882
$503$	26.7657	1.19342	0.596711	−	0.802456i	$-0.296474\pi$
$503$	26.7657	1.19342	0.596711	+	0.802456i	$0.296474\pi$
$504$	1.81668	0.0809215
$505$	1.58962	0.0707372
$506$	−5.93156	−0.263690
$507$	−30.9864	−1.37615
$508$	10.9581	0.486188
$509$	0.135397	0.00600134	0.00300067	−	0.999995i	$-0.499045\pi$
$509$	0.135397	0.00600134	0.00300067	+	0.999995i	$0.499045\pi$
$510$	−28.3958	−1.25739
$511$	5.09596	0.225432
$512$	−1.00000	−0.0441942
$513$	13.1941	0.582533
$514$	7.04580	0.310777
$515$	23.5629	1.03831
$516$	−9.51616	−0.418926
$517$	−17.8451	−0.784827
$518$	20.3741	0.895185
$519$	−14.0836	−0.618200
$520$	−18.9325	−0.830245
$521$	−21.2508	−0.931016	−0.465508	−	0.885044i	$-0.654128\pi$
$521$	−21.2508	−0.931016	−0.465508	+	0.885044i	$0.654128\pi$
$522$	2.20737	0.0966138
$523$	−17.4252	−0.761949	−0.380974	−	0.924586i	$-0.624411\pi$
$523$	−17.4252	−0.761949	−0.380974	+	0.924586i	$0.624411\pi$
$524$	−10.9162	−0.476876
$525$	39.8277	1.73823
$526$	24.7135	1.07756
$527$	−30.9586	−1.34858
$528$	3.83152	0.166746
$529$	−14.3005	−0.621761
$530$	27.8486	1.20967
$531$	7.51192	0.325990
$532$	−8.42661	−0.365340
$533$	12.6603	0.548376
$534$	24.0449	1.04052
$535$	−39.0428	−1.68797
$536$	0.351716	0.0151918
$537$	−33.8383	−1.46023
$538$	22.5693	0.973031
$539$	−2.64854	−0.114081
$540$	−15.8035	−0.680073
$541$	41.7436	1.79470	0.897350	−	0.441320i	$-0.145490\pi$
$541$	41.7436	1.79470	0.897350	+	0.441320i	$0.145490\pi$
$542$	24.8140	1.06585
$543$	−2.78178	−0.119378
$544$	−4.25855	−0.182584
$545$	16.9382	0.725554
$546$	29.7234	1.27204
$547$	11.0958	0.474422	0.237211	−	0.971458i	$-0.423767\pi$
$547$	11.0958	0.474422	0.237211	+	0.971458i	$0.423767\pi$
$548$	2.33517	0.0997537
$549$	−0.355098	−0.0151552
$550$	14.5772	0.621575
$551$	−10.2388	−0.436187
$552$	−5.61949	−0.239181
$553$	13.8008	0.586870
$554$	−3.36643	−0.143026
$555$	47.1071	1.99959
$556$	−22.0818	−0.936476
$557$	29.6460	1.25614	0.628071	−	0.778156i	$-0.283845\pi$
$557$	29.6460	1.25614	0.628071	+	0.778156i	$0.283845\pi$
$558$	4.57947	0.193864
$559$	−27.0195	−1.14280
$560$	10.0931	0.426513
$561$	16.3167	0.688893
$562$	25.0535	1.05682
$563$	−16.3895	−0.690733	−0.345367	−	0.938468i	$-0.612245\pi$
$563$	−16.3895	−0.690733	−0.345367	+	0.938468i	$0.612245\pi$
$564$	−16.9062	−0.711880
$565$	−6.46935	−0.272167
$566$	−21.3030	−0.895432
$567$	30.2609	1.27084
$568$	4.94089	0.207315
$569$	5.16484	0.216522	0.108261	−	0.994123i	$-0.465472\pi$
$569$	5.16484	0.216522	0.108261	+	0.994123i	$0.465472\pi$
$570$	−19.4833	−0.816065
$571$	−35.9197	−1.50319	−0.751596	−	0.659624i	$-0.770715\pi$
$571$	−35.9197	−1.50319	−0.751596	+	0.659624i	$0.770715\pi$
$572$	10.8790	0.454872
$573$	35.0278	1.46331
$574$	−6.74932	−0.281711
$575$	−21.3796	−0.891592
$576$	0.629935	0.0262473
$577$	−25.4219	−1.05833	−0.529165	−	0.848519i	$-0.677495\pi$
$577$	−25.4219	−1.05833	−0.529165	+	0.848519i	$0.677495\pi$
$578$	−1.13526	−0.0472204
$579$	13.3429	0.554514
$580$	12.2637	0.509223
$581$	21.5852	0.895505
$582$	0.0120967	0.000501425 0
$583$	−16.0023	−0.662747
$584$	1.76703	0.0731201
$585$	11.9262	0.493090
$586$	−17.1355	−0.707860
$587$	−10.5916	−0.437160	−0.218580	−	0.975819i	$-0.570142\pi$
$587$	−10.5916	−0.437160	−0.218580	+	0.975819i	$0.570142\pi$
$588$	−2.50919	−0.103477
$589$	−21.2417	−0.875248
$590$	41.7348	1.71819
$591$	−16.6095	−0.683225
$592$	7.06471	0.290358
$593$	47.4552	1.94875	0.974375	−	0.224931i	$-0.0722156\pi$
$593$	47.4552	1.94875	0.974375	+	0.224931i	$0.0722156\pi$
$594$	9.08096	0.372596
$595$	42.9821	1.76210
$596$	16.0944	0.659254
$597$	19.8140	0.810933
$598$	−15.9556	−0.652472
$599$	26.9343	1.10051	0.550253	−	0.834998i	$-0.314531\pi$
$599$	26.9343	1.10051	0.550253	+	0.834998i	$0.314531\pi$
$600$	13.8103	0.563802
$601$	−6.87084	−0.280267	−0.140134	−	0.990133i	$-0.544753\pi$
$601$	−6.87084	−0.280267	−0.140134	+	0.990133i	$0.544753\pi$
$602$	14.4044	0.587080
$603$	−0.221558	−0.00902255
$604$	18.7962	0.764805
$605$	24.3435	0.989705
$606$	−0.865367	−0.0351531
$607$	−24.0567	−0.976431	−0.488216	−	0.872723i	$-0.662352\pi$
$607$	−24.0567	−0.976431	−0.488216	+	0.872723i	$0.662352\pi$
$608$	−2.92193	−0.118500
$609$	−19.2536	−0.780194
$610$	−1.97286	−0.0798787
$611$	−48.0023	−1.94197
$612$	2.68261	0.108438
$613$	−22.4272	−0.905827	−0.452914	−	0.891554i	$-0.649615\pi$
$613$	−22.4272	−0.905827	−0.452914	+	0.891554i	$0.649615\pi$
$614$	−9.70104	−0.391502
$615$	−15.6052	−0.629263
$616$	−5.79970	−0.233676
$617$	22.3168	0.898440	0.449220	−	0.893421i	$-0.351702\pi$
$617$	22.3168	0.898440	0.449220	+	0.893421i	$0.351702\pi$
$618$	−12.8273	−0.515990
$619$	−21.1514	−0.850148	−0.425074	−	0.905159i	$-0.639752\pi$
$619$	−21.1514	−0.850148	−0.425074	+	0.905159i	$0.639752\pi$
$620$	25.4426	1.02180
$621$	−13.3185	−0.534455
$622$	32.7922	1.31485
$623$	−36.3962	−1.45818
$624$	10.3066	0.412593
$625$	−8.70097	−0.348039
$626$	−30.9671	−1.23769
$627$	11.1954	0.447103
$628$	7.37409	0.294258
$629$	30.0854	1.19958
$630$	−6.35802	−0.253310
$631$	−6.83801	−0.272217	−0.136108	−	0.990694i	$-0.543460\pi$
$631$	−6.83801	−0.272217	−0.136108	+	0.990694i	$0.543460\pi$
$632$	4.78543	0.190354
$633$	−13.9235	−0.553408
$634$	20.2374	0.803730
$635$	−38.3512	−1.52192
$636$	−15.1604	−0.601148
$637$	−7.12442	−0.282280
$638$	−7.04694	−0.278991
$639$	−3.11244	−0.123126
$640$	3.49980	0.138342
$641$	35.6626	1.40859	0.704294	−	0.709909i	$-0.251264\pi$
$641$	35.6626	1.40859	0.704294	+	0.709909i	$0.251264\pi$
$642$	21.2544	0.838843
$643$	14.9594	0.589941	0.294971	−	0.955506i	$-0.404690\pi$
$643$	14.9594	0.589941	0.294971	+	0.955506i	$0.404690\pi$
$644$	8.50610	0.335187
$645$	33.3046	1.31137
$646$	−12.4432	−0.489570
$647$	−46.3014	−1.82030	−0.910148	−	0.414284i	$-0.864032\pi$
$647$	−46.3014	−1.82030	−0.910148	+	0.414284i	$0.864032\pi$
$648$	10.4930	0.412203
$649$	−23.9816	−0.941359
$650$	39.2119	1.53802
$651$	−39.9440	−1.56553
$652$	−7.90195	−0.309464
$653$	4.94057	0.193340	0.0966698	−	0.995317i	$-0.469181\pi$
$653$	4.94057	0.193340	0.0966698	+	0.995317i	$0.469181\pi$
$654$	−9.22092	−0.360567
$655$	38.2045	1.49277
$656$	−2.34033	−0.0913745
$657$	−1.11311	−0.0434266
$658$	25.5906	0.997625
$659$	−18.5394	−0.722193	−0.361097	−	0.932528i	$-0.617598\pi$
$659$	−18.5394	−0.722193	−0.361097	+	0.932528i	$0.617598\pi$
$660$	−13.4096	−0.521966
$661$	−2.01326	−0.0783068	−0.0391534	−	0.999233i	$-0.512466\pi$
$661$	−2.01326	−0.0783068	−0.0391534	+	0.999233i	$0.512466\pi$
$662$	9.70079	0.377032
$663$	43.8911	1.70459
$664$	7.48468	0.290462
$665$	29.4914	1.14363
$666$	−4.45031	−0.172446
$667$	10.3354	0.400187
$668$	−5.99110	−0.231803
$669$	15.8475	0.612698
$670$	−1.23094	−0.0475552
$671$	1.13364	0.0437637
$672$	−5.49456	−0.211957
$673$	32.8778	1.26734	0.633672	−	0.773601i	$-0.281547\pi$
$673$	32.8778	1.26734	0.633672	+	0.773601i	$0.281547\pi$
$674$	−12.1815	−0.469212
$675$	32.7313	1.25983
$676$	16.2638	0.625530
$677$	17.1824	0.660373	0.330186	−	0.943916i	$-0.392888\pi$
$677$	17.1824	0.660373	0.330186	+	0.943916i	$0.392888\pi$
$678$	3.52182	0.135255
$679$	−0.0183105	−0.000702694 0
$680$	14.9041	0.571545
$681$	−45.0095	−1.72477
$682$	−14.6198	−0.559821
$683$	−21.6317	−0.827713	−0.413857	−	0.910342i	$-0.635819\pi$
$683$	−21.6317	−0.827713	−0.413857	+	0.910342i	$0.635819\pi$
$684$	1.84063	0.0703781
$685$	−8.17264	−0.312260
$686$	−16.3893	−0.625748
$687$	−7.30108	−0.278554
$688$	4.99473	0.190422
$689$	−43.0453	−1.63989
$690$	19.6671	0.748712
$691$	−16.2513	−0.618229	−0.309115	−	0.951025i	$-0.600033\pi$
$691$	−16.2513	−0.618229	−0.309115	+	0.951025i	$0.600033\pi$
$692$	7.39202	0.281002
$693$	3.65343	0.138782
$694$	33.5336	1.27292
$695$	77.2818	2.93147
$696$	−6.67618	−0.253060
$697$	−9.96641	−0.377505
$698$	22.3931	0.847589
$699$	−10.4163	−0.393979
$700$	−20.9043	−0.790109
$701$	2.84727	0.107540	0.0537700	−	0.998553i	$-0.482876\pi$
$701$	2.84727	0.107540	0.0537700	+	0.998553i	$0.482876\pi$
$702$	24.4273	0.921948
$703$	20.6426	0.778550
$704$	−2.01105	−0.0757942
$705$	59.1683	2.22841
$706$	14.4526	0.543929
$707$	1.30989	0.0492634
$708$	−22.7198	−0.853863
$709$	−3.53594	−0.132795	−0.0663975	−	0.997793i	$-0.521151\pi$
$709$	−3.53594	−0.132795	−0.0663975	+	0.997793i	$0.521151\pi$
$710$	−17.2921	−0.648962
$711$	−3.01451	−0.113053
$712$	−12.6204	−0.472969
$713$	21.4421	0.803011
$714$	−23.3988	−0.875680
$715$	−38.0741	−1.42389
$716$	17.7607	0.663748
$717$	−52.6430	−1.96599
$718$	−0.610238	−0.0227739
$719$	−33.9248	−1.26518	−0.632591	−	0.774486i	$-0.718009\pi$
$719$	−33.9248	−1.26518	−0.632591	+	0.774486i	$0.718009\pi$
$720$	−2.20464	−0.0821623
$721$	19.4164	0.723106
$722$	10.4623	0.389368
$723$	−10.8429	−0.403253
$724$	1.46007	0.0542631
$725$	−25.3999	−0.943328
$726$	−13.2523	−0.491837
$727$	26.1905	0.971353	0.485677	−	0.874138i	$-0.338573\pi$
$727$	26.1905	0.971353	0.485677	+	0.874138i	$0.338573\pi$
$728$	−15.6009	−0.578206
$729$	19.1996	0.711098
$730$	−6.18424	−0.228889
$731$	21.2703	0.786711
$732$	1.07399	0.0396960
$733$	−3.15491	−0.116529	−0.0582646	−	0.998301i	$-0.518557\pi$
$733$	−3.15491	−0.116529	−0.0582646	+	0.998301i	$0.518557\pi$
$734$	15.9049	0.587060
$735$	8.78165	0.323916
$736$	2.94949	0.108720
$737$	0.707317	0.0260544
$738$	1.47426	0.0542681
$739$	−47.5353	−1.74861	−0.874307	−	0.485373i	$-0.838684\pi$
$739$	−47.5353	−1.74861	−0.874307	+	0.485373i	$0.838684\pi$
$740$	−24.7251	−0.908911
$741$	30.1151	1.10631
$742$	22.9479	0.842445
$743$	−30.5413	−1.12045	−0.560226	−	0.828340i	$-0.689286\pi$
$743$	−30.5413	−1.12045	−0.560226	+	0.828340i	$0.689286\pi$
$744$	−13.8506	−0.507788
$745$	−56.3272	−2.06367
$746$	27.7278	1.01519
$747$	−4.71486	−0.172508
$748$	−8.56414	−0.313136
$749$	−32.1723	−1.17555
$750$	−14.9934	−0.547483
$751$	−1.70752	−0.0623083	−0.0311542	−	0.999515i	$-0.509918\pi$
$751$	−1.70752	−0.0623083	−0.0311542	+	0.999515i	$0.509918\pi$
$752$	8.87354	0.323585
$753$	13.4415	0.489836
$754$	−18.9559	−0.690332
$755$	−65.7827	−2.39408
$756$	−13.0225	−0.473622
$757$	33.6539	1.22317	0.611586	−	0.791178i	$-0.290532\pi$
$757$	33.6539	1.22317	0.611586	+	0.791178i	$0.290532\pi$
$758$	−1.89031	−0.0686593
$759$	−11.3010	−0.410202
$760$	10.2262	0.370942
$761$	50.1065	1.81636	0.908180	−	0.418580i	$-0.137472\pi$
$761$	50.1065	1.81636	0.908180	+	0.418580i	$0.137472\pi$
$762$	20.8778	0.756324
$763$	13.9575	0.505296
$764$	−18.3850	−0.665146
$765$	−9.38859	−0.339445
$766$	−7.90872	−0.285754
$767$	−64.5090	−2.32929
$768$	−1.90524	−0.0687494
$769$	28.6000	1.03134	0.515672	−	0.856786i	$-0.327542\pi$
$769$	28.6000	1.03134	0.515672	+	0.856786i	$0.327542\pi$
$770$	20.2978	0.731481
$771$	13.4239	0.483451
$772$	−7.00329	−0.252054
$773$	41.2350	1.48312	0.741559	−	0.670887i	$-0.234087\pi$
$773$	41.2350	1.48312	0.741559	+	0.670887i	$0.234087\pi$
$774$	−3.14636	−0.113093
$775$	−52.6953	−1.89287
$776$	−0.00634918	−0.000227922 0
$777$	38.8175	1.39257
$778$	−17.3292	−0.621281
$779$	−6.83828	−0.245007
$780$	−36.0709	−1.29155
$781$	9.93636	0.355551
$782$	12.5606	0.449165
$783$	−15.8230	−0.565467
$784$	1.31699	0.0470355
$785$	−25.8078	−0.921121
$786$	−20.7979	−0.741838
$787$	17.5280	0.624806	0.312403	−	0.949950i	$-0.398866\pi$
$787$	17.5280	0.624806	0.312403	+	0.949950i	$0.398866\pi$
$788$	8.71782	0.310560
$789$	47.0851	1.67628
$790$	−16.7480	−0.595868
$791$	−5.33090	−0.189545
$792$	1.26683	0.0450148
$793$	3.04943	0.108288
$794$	−15.0514	−0.534154
$795$	53.0582	1.88178
$796$	−10.3997	−0.368609
$797$	−2.37796	−0.0842316	−0.0421158	−	0.999113i	$-0.513410\pi$
$797$	−2.37796	−0.0842316	−0.0421158	+	0.999113i	$0.513410\pi$
$798$	−16.0547	−0.568330
$799$	37.7884	1.33686
$800$	−7.24858	−0.256276
$801$	7.95002	0.280900
$802$	−24.8172	−0.876326
$803$	3.55357	0.125403
$804$	0.670103	0.0236327
$805$	−29.7696	−1.04924
$806$	−39.3264	−1.38521
$807$	42.9999	1.51367
$808$	0.454204	0.0159788
$809$	26.5804	0.934518	0.467259	−	0.884120i	$-0.345242\pi$
$809$	26.5804	0.934518	0.467259	+	0.884120i	$0.345242\pi$
$810$	−36.7233	−1.29033
$811$	42.0330	1.47598	0.737989	−	0.674813i	$-0.235776\pi$
$811$	42.0330	1.47598	0.737989	+	0.674813i	$0.235776\pi$
$812$	10.1056	0.354637
$813$	47.2766	1.65806
$814$	14.2075	0.497971
$815$	27.6552	0.968721
$816$	−8.11356	−0.284031
$817$	14.5943	0.510588
$818$	0.439221	0.0153570
$819$	9.82752	0.343402
$820$	8.19068	0.286031
$821$	39.7124	1.38597	0.692987	−	0.720950i	$-0.256295\pi$
$821$	39.7124	1.38597	0.692987	+	0.720950i	$0.256295\pi$
$822$	4.44906	0.155179
$823$	−26.1260	−0.910697	−0.455348	−	0.890313i	$-0.650485\pi$
$823$	−26.1260	−0.910697	−0.455348	+	0.890313i	$0.650485\pi$
$824$	6.73265	0.234543
$825$	27.7731	0.966936
$826$	34.3905	1.19660
$827$	36.1439	1.25685	0.628423	−	0.777872i	$-0.283701\pi$
$827$	36.1439	1.25685	0.628423	+	0.777872i	$0.283701\pi$
$828$	−1.85799	−0.0645696
$829$	−39.0700	−1.35696	−0.678479	−	0.734620i	$-0.737361\pi$
$829$	−39.0700	−1.35696	−0.678479	+	0.734620i	$0.737361\pi$
$830$	−26.1949	−0.909237
$831$	−6.41386	−0.222494
$832$	−5.40960	−0.187544
$833$	5.60849	0.194323
$834$	−42.0711	−1.45680
$835$	20.9676	0.725615
$836$	−5.87613	−0.203230
$837$	−32.8268	−1.13466
$838$	−17.0577	−0.589250
$839$	−32.1173	−1.10881	−0.554407	−	0.832246i	$-0.687055\pi$
$839$	−32.1173	−1.10881	−0.554407	+	0.832246i	$0.687055\pi$
$840$	19.2298	0.663492
$841$	−16.7212	−0.576592
$842$	−6.02590	−0.207666
$843$	47.7328	1.64401
$844$	7.30799	0.251551
$845$	−56.9199	−1.95811
$846$	−5.58975	−0.192180
$847$	20.0597	0.689258
$848$	7.95720	0.273251
$849$	−40.5873	−1.39295
$850$	−30.8685	−1.05878
$851$	−20.8373	−0.714294
$852$	9.41358	0.322504
$853$	−37.4828	−1.28339	−0.641693	−	0.766961i	$-0.721768\pi$
$853$	−37.4828	−1.28339	−0.641693	+	0.766961i	$0.721768\pi$
$854$	−1.62568	−0.0556297
$855$	−6.44181	−0.220305
$856$	−11.1557	−0.381296
$857$	−1.60560	−0.0548463	−0.0274231	−	0.999624i	$-0.508730\pi$
$857$	−1.60560	−0.0548463	−0.0274231	+	0.999624i	$0.508730\pi$
$858$	20.7270	0.707609
$859$	53.7911	1.83533	0.917663	−	0.397358i	$-0.130073\pi$
$859$	53.7911	1.83533	0.917663	+	0.397358i	$0.130073\pi$
$860$	−17.4806	−0.596082
$861$	−12.8591	−0.438236
$862$	−8.63924	−0.294254
$863$	−29.1249	−0.991422	−0.495711	−	0.868488i	$-0.665092\pi$
$863$	−29.1249	−0.991422	−0.495711	+	0.868488i	$0.665092\pi$
$864$	−4.51554	−0.153622
$865$	−25.8706	−0.879626
$866$	−3.10441	−0.105492
$867$	−2.16293	−0.0734570
$868$	20.9654	0.711611
$869$	9.62372	0.326462
$870$	23.3653	0.792157
$871$	1.90264	0.0644686
$872$	4.83977	0.163895
$873$	0.00399957	0.000135365 0
$874$	8.61820	0.291515
$875$	22.6952	0.767239
$876$	3.36661	0.113747
$877$	26.6573	0.900152	0.450076	−	0.892990i	$-0.351397\pi$
$877$	26.6573	0.900152	0.450076	+	0.892990i	$0.351397\pi$
$878$	32.3919	1.09317
$879$	−32.6472	−1.10116
$880$	7.03825	0.237260
$881$	26.4236	0.890233	0.445116	−	0.895473i	$-0.353162\pi$
$881$	26.4236	0.890233	0.445116	+	0.895473i	$0.353162\pi$
$882$	−0.829621	−0.0279348
$883$	20.9237	0.704139	0.352070	−	0.935974i	$-0.385478\pi$
$883$	20.9237	0.704139	0.352070	+	0.935974i	$0.385478\pi$
$884$	−23.0371	−0.774820
$885$	79.5148	2.67286
$886$	−27.1351	−0.911623
$887$	1.69347	0.0568612	0.0284306	−	0.999596i	$-0.490949\pi$
$887$	1.69347	0.0568612	0.0284306	+	0.999596i	$0.490949\pi$
$888$	13.4600	0.451687
$889$	−31.6023	−1.05991
$890$	44.1688	1.48054
$891$	21.1019	0.706940
$892$	−8.31783	−0.278502
$893$	25.9278	0.867642
$894$	30.6637	1.02555
$895$	−62.1588	−2.07774
$896$	2.88392	0.0963450
$897$	−30.3992	−1.01500
$898$	−13.9609	−0.465883
$899$	25.4740	0.849607
$900$	4.56614	0.152205
$901$	33.8861	1.12891
$902$	−4.70651	−0.156710
$903$	27.4438	0.913274
$904$	−1.84849	−0.0614799
$905$	−5.10995	−0.169861
$906$	35.8112	1.18975
$907$	8.18715	0.271850	0.135925	−	0.990719i	$-0.456599\pi$
$907$	8.18715	0.271850	0.135925	+	0.990719i	$0.456599\pi$
$908$	23.6241	0.783992
$909$	−0.286119	−0.00948997
$910$	54.5998	1.80997
$911$	1.81873	0.0602573	0.0301287	−	0.999546i	$-0.490408\pi$
$911$	1.81873	0.0602573	0.0301287	+	0.999546i	$0.490408\pi$
$912$	−5.56697	−0.184341
$913$	15.0520	0.498150
$914$	−25.6876	−0.849671
$915$	−3.75876	−0.124261
$916$	3.83211	0.126616
$917$	31.4814	1.03961
$918$	−19.2297	−0.634673
$919$	−5.21102	−0.171896	−0.0859478	−	0.996300i	$-0.527392\pi$
$919$	−5.21102	−0.171896	−0.0859478	+	0.996300i	$0.527392\pi$
$920$	−10.3226	−0.340327
$921$	−18.4828	−0.609029
$922$	−29.2267	−0.962531
$923$	26.7283	0.879771
$924$	−11.0498	−0.363512
$925$	51.2091	1.68375
$926$	30.4742	1.00144
$927$	−4.24113	−0.139297
$928$	3.50412	0.115028
$929$	−38.3334	−1.25768	−0.628839	−	0.777536i	$-0.716469\pi$
$929$	−38.3334	−1.25768	−0.628839	+	0.777536i	$0.716469\pi$
$930$	48.4743	1.58953
$931$	3.84816	0.126118
$932$	5.46717	0.179083
$933$	62.4770	2.04541
$934$	−7.13236	−0.233378
$935$	29.9728	0.980214
$936$	3.40770	0.111384
$937$	−36.1764	−1.18183	−0.590915	−	0.806734i	$-0.701233\pi$
$937$	−36.1764	−1.18183	−0.590915	+	0.806734i	$0.701233\pi$
$938$	−1.01432	−0.0331188
$939$	−58.9997	−1.92538
$940$	−31.0556	−1.01292
$941$	−6.72384	−0.219191	−0.109596	−	0.993976i	$-0.534956\pi$
$941$	−6.72384	−0.219191	−0.109596	+	0.993976i	$0.534956\pi$
$942$	14.0494	0.457754
$943$	6.90278	0.224786
$944$	11.9249	0.388123
$945$	45.5760	1.48259
$946$	10.0446	0.326579
$947$	−24.1222	−0.783867	−0.391933	−	0.919994i	$-0.628194\pi$
$947$	−24.1222	−0.783867	−0.391933	+	0.919994i	$0.628194\pi$
$948$	9.11739	0.296119
$949$	9.55891	0.310295
$950$	−21.1798	−0.687165
$951$	38.5571	1.25030
$952$	12.2813	0.398040
$953$	−7.55477	−0.244723	−0.122362	−	0.992486i	$-0.539047\pi$
$953$	−7.55477	−0.244723	−0.122362	+	0.992486i	$0.539047\pi$
$954$	−5.01252	−0.162286
$955$	64.3437	2.08211
$956$	27.6306	0.893638
$957$	−13.4261	−0.434004
$958$	0.778681	0.0251580
$959$	−6.73446	−0.217467
$960$	6.66795	0.215207
$961$	21.8492	0.704813
$962$	38.2173	1.23217
$963$	7.02739	0.226455
$964$	5.69112	0.183299
$965$	24.5101	0.789008
$966$	16.2062	0.521424
$967$	41.4730	1.33368	0.666841	−	0.745200i	$-0.267646\pi$
$967$	41.4730	1.33368	0.666841	+	0.745200i	$0.267646\pi$
$968$	6.95569	0.223564
$969$	−23.7072	−0.761586
$970$	0.0222209	0.000713469 0
$971$	0.792163	0.0254217	0.0127109	−	0.999919i	$-0.495954\pi$
$971$	0.792163	0.0254217	0.0127109	+	0.999919i	$0.495954\pi$
$972$	6.44503	0.206724
$973$	63.6821	2.04155
$974$	−11.9725	−0.383623
$975$	74.7081	2.39257
$976$	−0.563706	−0.0180438
$977$	52.9164	1.69295	0.846473	−	0.532432i	$-0.178722\pi$
$977$	52.9164	1.69295	0.846473	+	0.532432i	$0.178722\pi$
$978$	−15.0551	−0.481409
$979$	−25.3802	−0.811154
$980$	−4.60921	−0.147236
$981$	−3.04874	−0.0973388
$982$	−42.6438	−1.36082
$983$	5.78273	0.184441	0.0922203	−	0.995739i	$-0.470604\pi$
$983$	5.78273	0.184441	0.0922203	+	0.995739i	$0.470604\pi$
$984$	−4.45889	−0.142144
$985$	−30.5106	−0.972149
$986$	14.9225	0.475228
$987$	48.7562	1.55193
$988$	−15.8065	−0.502871
$989$	−14.7319	−0.468448
$990$	−4.43364	−0.140910
$991$	1.51350	0.0480779	0.0240390	−	0.999711i	$-0.492347\pi$
$991$	1.51350	0.0480779	0.0240390	+	0.999711i	$0.492347\pi$
$992$	7.26975	0.230815
$993$	18.4823	0.586519
$994$	−14.2491	−0.451955
$995$	36.3970	1.15386
$996$	14.2601	0.451848
$997$	−20.9144	−0.662365	−0.331182	−	0.943567i	$-0.607448\pi$
$997$	−20.9144	−0.662365	−0.331182	+	0.943567i	$0.607448\pi$
$998$	8.33065	0.263702
$999$	31.9010	1.00930

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.10	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.10	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90524 q^{3} +1.00000 q^{4} -3.49980 q^{5} +1.90524 q^{6} -2.88392 q^{7} -1.00000 q^{8} +0.629935 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.90524 q^{3} +1.00000 q^{4} -3.49980 q^{5} +1.90524 q^{6} -2.88392 q^{7} -1.00000 q^{8} +0.629935 q^{9} +3.49980 q^{10} -2.01105 q^{11} -1.90524 q^{12} -5.40960 q^{13} +2.88392 q^{14} +6.66795 q^{15} +1.00000 q^{16} +4.25855 q^{17} -0.629935 q^{18} +2.92193 q^{19} -3.49980 q^{20} +5.49456 q^{21} +2.01105 q^{22} -2.94949 q^{23} +1.90524 q^{24} +7.24858 q^{25} +5.40960 q^{26} +4.51554 q^{27} -2.88392 q^{28} -3.50412 q^{29} -6.66795 q^{30} -7.26975 q^{31} -1.00000 q^{32} +3.83152 q^{33} -4.25855 q^{34} +10.0931 q^{35} +0.629935 q^{36} +7.06471 q^{37} -2.92193 q^{38} +10.3066 q^{39} +3.49980 q^{40} -2.34033 q^{41} -5.49456 q^{42} +4.99473 q^{43} -2.01105 q^{44} -2.20464 q^{45} +2.94949 q^{46} +8.87354 q^{47} -1.90524 q^{48} +1.31699 q^{49} -7.24858 q^{50} -8.11356 q^{51} -5.40960 q^{52} +7.95720 q^{53} -4.51554 q^{54} +7.03825 q^{55} +2.88392 q^{56} -5.56697 q^{57} +3.50412 q^{58} +11.9249 q^{59} +6.66795 q^{60} -0.563706 q^{61} +7.26975 q^{62} -1.81668 q^{63} +1.00000 q^{64} +18.9325 q^{65} -3.83152 q^{66} -0.351716 q^{67} +4.25855 q^{68} +5.61949 q^{69} -10.0931 q^{70} -4.94089 q^{71} -0.629935 q^{72} -1.76703 q^{73} -7.06471 q^{74} -13.8103 q^{75} +2.92193 q^{76} +5.79970 q^{77} -10.3066 q^{78} -4.78543 q^{79} -3.49980 q^{80} -10.4930 q^{81} +2.34033 q^{82} -7.48468 q^{83} +5.49456 q^{84} -14.9041 q^{85} -4.99473 q^{86} +6.67618 q^{87} +2.01105 q^{88} +12.6204 q^{89} +2.20464 q^{90} +15.6009 q^{91} -2.94949 q^{92} +13.8506 q^{93} -8.87354 q^{94} -10.2262 q^{95} +1.90524 q^{96} +0.00634918 q^{97} -1.31699 q^{98} -1.26683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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