LMFDB - Embedded newform 4013.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69142 q^{2} -1.48564 q^{3} +5.24374 q^{4} +2.79908 q^{5} +3.99849 q^{6} -0.286125 q^{7} -8.73026 q^{8} -0.792861 q^{9} +O(q^{10})$	\(q-2.69142 q^{2} -1.48564 q^{3} +5.24374 q^{4} +2.79908 q^{5} +3.99849 q^{6} -0.286125 q^{7} -8.73026 q^{8} -0.792861 q^{9} -7.53350 q^{10} +2.80645 q^{11} -7.79033 q^{12} +4.18635 q^{13} +0.770083 q^{14} -4.15844 q^{15} +13.0093 q^{16} +5.40916 q^{17} +2.13392 q^{18} +0.265499 q^{19} +14.6776 q^{20} +0.425080 q^{21} -7.55334 q^{22} +3.24564 q^{23} +12.9701 q^{24} +2.83485 q^{25} -11.2672 q^{26} +5.63484 q^{27} -1.50037 q^{28} +6.04882 q^{29} +11.1921 q^{30} +3.04205 q^{31} -17.5530 q^{32} -4.16939 q^{33} -14.5583 q^{34} -0.800888 q^{35} -4.15756 q^{36} +6.30060 q^{37} -0.714570 q^{38} -6.21943 q^{39} -24.4367 q^{40} -9.22799 q^{41} -1.14407 q^{42} +3.39398 q^{43} +14.7163 q^{44} -2.21928 q^{45} -8.73539 q^{46} +0.818851 q^{47} -19.3272 q^{48} -6.91813 q^{49} -7.62978 q^{50} -8.03609 q^{51} +21.9521 q^{52} -4.84904 q^{53} -15.1657 q^{54} +7.85548 q^{55} +2.49795 q^{56} -0.394438 q^{57} -16.2799 q^{58} +9.79339 q^{59} -21.8058 q^{60} +6.77090 q^{61} -8.18743 q^{62} +0.226858 q^{63} +21.2239 q^{64} +11.7179 q^{65} +11.2216 q^{66} +2.80376 q^{67} +28.3642 q^{68} -4.82187 q^{69} +2.15552 q^{70} +0.744457 q^{71} +6.92188 q^{72} +3.42551 q^{73} -16.9576 q^{74} -4.21158 q^{75} +1.39221 q^{76} -0.802997 q^{77} +16.7391 q^{78} +7.92259 q^{79} +36.4141 q^{80} -5.99279 q^{81} +24.8364 q^{82} +6.43668 q^{83} +2.22901 q^{84} +15.1407 q^{85} -9.13463 q^{86} -8.98640 q^{87} -24.5011 q^{88} -6.10051 q^{89} +5.97302 q^{90} -1.19782 q^{91} +17.0193 q^{92} -4.51940 q^{93} -2.20387 q^{94} +0.743154 q^{95} +26.0775 q^{96} +3.75807 q^{97} +18.6196 q^{98} -2.22513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.69142	−1.90312	−0.951560	−	0.307462i	$-0.900520\pi$
$2$	−2.69142	−1.90312	−0.951560	+	0.307462i	$0.900520\pi$
$3$	−1.48564	−0.857737	−0.428869	−	0.903367i	$-0.641088\pi$
$3$	−1.48564	−0.857737	−0.428869	+	0.903367i	$0.641088\pi$
$4$	5.24374	2.62187
$5$	2.79908	1.25179	0.625893	−	0.779909i	$-0.284734\pi$
$5$	2.79908	1.25179	0.625893	+	0.779909i	$0.284734\pi$
$6$	3.99849	1.63238
$7$	−0.286125	−0.108145	−0.0540726	−	0.998537i	$-0.517220\pi$
$7$	−0.286125	−0.108145	−0.0540726	+	0.998537i	$0.517220\pi$
$8$	−8.73026	−3.08661
$9$	−0.792861	−0.264287
$10$	−7.53350	−2.38230
$11$	2.80645	0.846177	0.423088	−	0.906088i	$-0.360946\pi$
$11$	2.80645	0.846177	0.423088	+	0.906088i	$0.360946\pi$
$12$	−7.79033	−2.24887
$13$	4.18635	1.16109	0.580543	−	0.814230i	$-0.302840\pi$
$13$	4.18635	1.16109	0.580543	+	0.814230i	$0.302840\pi$
$14$	0.770083	0.205813
$15$	−4.15844	−1.07370
$16$	13.0093	3.25233
$17$	5.40916	1.31191	0.655957	−	0.754798i	$-0.272265\pi$
$17$	5.40916	1.31191	0.655957	+	0.754798i	$0.272265\pi$
$18$	2.13392	0.502970
$19$	0.265499	0.0609097	0.0304549	−	0.999536i	$-0.490304\pi$
$19$	0.265499	0.0609097	0.0304549	+	0.999536i	$0.490304\pi$
$20$	14.6776	3.28202
$21$	0.425080	0.0927602
$22$	−7.55334	−1.61038
$23$	3.24564	0.676764	0.338382	−	0.941009i	$-0.390120\pi$
$23$	3.24564	0.676764	0.338382	+	0.941009i	$0.390120\pi$
$24$	12.9701	2.64750
$25$	2.83485	0.566970
$26$	−11.2672	−2.20969
$27$	5.63484	1.08443
$28$	−1.50037	−0.283543
$29$	6.04882	1.12324	0.561619	−	0.827396i	$-0.310179\pi$
$29$	6.04882	1.12324	0.561619	+	0.827396i	$0.310179\pi$
$30$	11.1921	2.04339
$31$	3.04205	0.546368	0.273184	−	0.961962i	$-0.411923\pi$
$31$	3.04205	0.546368	0.273184	+	0.961962i	$0.411923\pi$
$32$	−17.5530	−3.10296
$33$	−4.16939	−0.725797
$34$	−14.5583	−2.49673
$35$	−0.800888	−0.135375
$36$	−4.15756	−0.692926
$37$	6.30060	1.03581	0.517906	−	0.855437i	$-0.326712\pi$
$37$	6.30060	1.03581	0.517906	+	0.855437i	$0.326712\pi$
$38$	−0.714570	−0.115919
$39$	−6.21943	−0.995906
$40$	−24.4367	−3.86378
$41$	−9.22799	−1.44117	−0.720585	−	0.693367i	$-0.756127\pi$
$41$	−9.22799	−1.44117	−0.720585	+	0.693367i	$0.756127\pi$
$42$	−1.14407	−0.176534
$43$	3.39398	0.517578	0.258789	−	0.965934i	$-0.416677\pi$
$43$	3.39398	0.517578	0.258789	+	0.965934i	$0.416677\pi$
$44$	14.7163	2.21857
$45$	−2.21928	−0.330831
$46$	−8.73539	−1.28796
$47$	0.818851	0.119442	0.0597209	−	0.998215i	$-0.480979\pi$
$47$	0.818851	0.119442	0.0597209	+	0.998215i	$0.480979\pi$
$48$	−19.3272	−2.78964
$49$	−6.91813	−0.988305
$50$	−7.62978	−1.07901
$51$	−8.03609	−1.12528
$52$	21.9521	3.04422
$53$	−4.84904	−0.666067	−0.333034	−	0.942915i	$-0.608072\pi$
$53$	−4.84904	−0.666067	−0.333034	+	0.942915i	$0.608072\pi$
$54$	−15.1657	−2.06379
$55$	7.85548	1.05923
$56$	2.49795	0.333802
$57$	−0.394438	−0.0522445
$58$	−16.2799	−2.13766
$59$	9.79339	1.27499	0.637496	−	0.770454i	$-0.279970\pi$
$59$	9.79339	1.27499	0.637496	+	0.770454i	$0.279970\pi$
$60$	−21.8058	−2.81511
$61$	6.77090	0.866925	0.433462	−	0.901172i	$-0.357292\pi$
$61$	6.77090	0.866925	0.433462	+	0.901172i	$0.357292\pi$
$62$	−8.18743	−1.03980
$63$	0.226858	0.0285814
$64$	21.2239	2.65298
$65$	11.7179	1.45343
$66$	11.2216	1.38128
$67$	2.80376	0.342534	0.171267	−	0.985225i	$-0.445214\pi$
$67$	2.80376	0.342534	0.171267	+	0.985225i	$0.445214\pi$
$68$	28.3642	3.43967
$69$	−4.82187	−0.580485
$70$	2.15552	0.257634
$71$	0.744457	0.0883508	0.0441754	−	0.999024i	$-0.485934\pi$
$71$	0.744457	0.0883508	0.0441754	+	0.999024i	$0.485934\pi$
$72$	6.92188	0.815752
$73$	3.42551	0.400926	0.200463	−	0.979701i	$-0.435755\pi$
$73$	3.42551	0.400926	0.200463	+	0.979701i	$0.435755\pi$
$74$	−16.9576	−1.97128
$75$	−4.21158	−0.486312
$76$	1.39221	0.159697
$77$	−0.802997	−0.0915100
$78$	16.7391	1.89533
$79$	7.92259	0.891361	0.445681	−	0.895192i	$-0.352962\pi$
$79$	7.92259	0.891361	0.445681	+	0.895192i	$0.352962\pi$
$80$	36.4141	4.07122
$81$	−5.99279	−0.665865
$82$	24.8364	2.74272
$83$	6.43668	0.706518	0.353259	−	0.935526i	$-0.385073\pi$
$83$	6.43668	0.706518	0.353259	+	0.935526i	$0.385073\pi$
$84$	2.22901	0.243205
$85$	15.1407	1.64224
$86$	−9.13463	−0.985013
$87$	−8.98640	−0.963443
$88$	−24.5011	−2.61182
$89$	−6.10051	−0.646653	−0.323327	−	0.946287i	$-0.604801\pi$
$89$	−6.10051	−0.646653	−0.323327	+	0.946287i	$0.604801\pi$
$90$	5.97302	0.629611
$91$	−1.19782	−0.125566
$92$	17.0193	1.77439
$93$	−4.51940	−0.468640
$94$	−2.20387	−0.227312
$95$	0.743154	0.0762460
$96$	26.0775	2.66153
$97$	3.75807	0.381574	0.190787	−	0.981631i	$-0.438896\pi$
$97$	3.75807	0.381574	0.190787	+	0.981631i	$0.438896\pi$
$98$	18.6196	1.88086
$99$	−2.22513	−0.223634
$100$	14.8652	1.48652
$101$	−16.3351	−1.62540	−0.812700	−	0.582682i	$-0.802003\pi$
$101$	−16.3351	−1.62540	−0.812700	+	0.582682i	$0.802003\pi$
$102$	21.6285	2.14154
$103$	6.83641	0.673611	0.336806	−	0.941574i	$-0.390653\pi$
$103$	6.83641	0.673611	0.336806	+	0.941574i	$0.390653\pi$
$104$	−36.5480	−3.58382
$105$	1.18983	0.116116
$106$	13.0508	1.26761
$107$	6.33015	0.611959	0.305980	−	0.952038i	$-0.401016\pi$
$107$	6.33015	0.611959	0.305980	+	0.952038i	$0.401016\pi$
$108$	29.5476	2.84322
$109$	−3.30908	−0.316953	−0.158476	−	0.987363i	$-0.550658\pi$
$109$	−3.30908	−0.316953	−0.158476	+	0.987363i	$0.550658\pi$
$110$	−21.1424	−2.01585
$111$	−9.36046	−0.888455
$112$	−3.72229	−0.351724
$113$	3.19554	0.300611	0.150305	−	0.988640i	$-0.451974\pi$
$113$	3.19554	0.300611	0.150305	+	0.988640i	$0.451974\pi$
$114$	1.06160	0.0994277
$115$	9.08482	0.847164
$116$	31.7184	2.94498
$117$	−3.31920	−0.306860
$118$	−26.3581	−2.42646
$119$	−1.54770	−0.141877
$120$	36.3043	3.31411
$121$	−3.12383	−0.283985
$122$	−18.2233	−1.64986
$123$	13.7095	1.23614
$124$	15.9517	1.43251
$125$	−6.06042	−0.542061
$126$	−0.610569	−0.0543938
$127$	9.98372	0.885912	0.442956	−	0.896543i	$-0.353930\pi$
$127$	9.98372	0.885912	0.442956	+	0.896543i	$0.353930\pi$
$128$	−22.0163	−1.94599
$129$	−5.04225	−0.443946
$130$	−31.5379	−2.76606
$131$	−15.0029	−1.31081	−0.655407	−	0.755276i	$-0.727503\pi$
$131$	−15.0029	−1.31081	−0.655407	+	0.755276i	$0.727503\pi$
$132$	−21.8632	−1.90295
$133$	−0.0759661	−0.00658709
$134$	−7.54610	−0.651884
$135$	15.7724	1.35747
$136$	−47.2234	−4.04937
$137$	−11.0626	−0.945141	−0.472571	−	0.881293i	$-0.656674\pi$
$137$	−11.0626	−0.945141	−0.472571	+	0.881293i	$0.656674\pi$
$138$	12.9777	1.10473
$139$	−10.2326	−0.867919	−0.433960	−	0.900932i	$-0.642884\pi$
$139$	−10.2326	−0.867919	−0.433960	+	0.900932i	$0.642884\pi$
$140$	−4.19965	−0.354935
$141$	−1.21652	−0.102450
$142$	−2.00365	−0.168142
$143$	11.7488	0.982484
$144$	−10.3146	−0.859548
$145$	16.9311	1.40605
$146$	−9.21948	−0.763010
$147$	10.2779	0.847706
$148$	33.0387	2.71577
$149$	−17.5245	−1.43566	−0.717831	−	0.696217i	$-0.754865\pi$
$149$	−17.5245	−1.43566	−0.717831	+	0.696217i	$0.754865\pi$
$150$	11.3351	0.925510
$151$	18.6727	1.51957	0.759783	−	0.650177i	$-0.225305\pi$
$151$	18.6727	1.51957	0.759783	+	0.650177i	$0.225305\pi$
$152$	−2.31788	−0.188005
$153$	−4.28871	−0.346722
$154$	2.16120	0.174155
$155$	8.51494	0.683936
$156$	−32.6131	−2.61114
$157$	−2.35498	−0.187948	−0.0939739	−	0.995575i	$-0.529957\pi$
$157$	−2.35498	−0.187948	−0.0939739	+	0.995575i	$0.529957\pi$
$158$	−21.3230	−1.69637
$159$	7.20395	0.571311
$160$	−49.1323	−3.88425
$161$	−0.928661	−0.0731887
$162$	16.1291	1.26722
$163$	−7.15351	−0.560306	−0.280153	−	0.959955i	$-0.590385\pi$
$163$	−7.15351	−0.560306	−0.280153	+	0.959955i	$0.590385\pi$
$164$	−48.3892	−3.77856
$165$	−11.6705	−0.908544
$166$	−17.3238	−1.34459
$167$	14.0437	1.08674	0.543369	−	0.839494i	$-0.317149\pi$
$167$	14.0437	1.08674	0.543369	+	0.839494i	$0.317149\pi$
$168$	−3.71106	−0.286315
$169$	4.52557	0.348120
$170$	−40.7499	−3.12537
$171$	−0.210504	−0.0160976
$172$	17.7972	1.35702
$173$	6.80468	0.517350	0.258675	−	0.965964i	$-0.416714\pi$
$173$	6.80468	0.517350	0.258675	+	0.965964i	$0.416714\pi$
$174$	24.1862	1.83355
$175$	−0.811123	−0.0613151
$176$	36.5100	2.75205
$177$	−14.5495	−1.09361
$178$	16.4190	1.23066
$179$	−16.5332	−1.23575	−0.617873	−	0.786278i	$-0.712005\pi$
$179$	−16.5332	−1.23575	−0.617873	+	0.786278i	$0.712005\pi$
$180$	−11.6373	−0.867396
$181$	2.95404	0.219572	0.109786	−	0.993955i	$-0.464983\pi$
$181$	2.95404	0.219572	0.109786	+	0.993955i	$0.464983\pi$
$182$	3.22384	0.238967
$183$	−10.0591	−0.743594
$184$	−28.3353	−2.08891
$185$	17.6359	1.29662
$186$	12.1636	0.891879
$187$	15.1805	1.11011
$188$	4.29384	0.313161
$189$	−1.61227	−0.117275
$190$	−2.00014	−0.145105
$191$	−16.8899	−1.22211	−0.611054	−	0.791589i	$-0.709254\pi$
$191$	−16.8899	−1.22211	−0.611054	+	0.791589i	$0.709254\pi$
$192$	−31.5311	−2.27556
$193$	−9.76301	−0.702757	−0.351378	−	0.936234i	$-0.614287\pi$
$193$	−9.76301	−0.702757	−0.351378	+	0.936234i	$0.614287\pi$
$194$	−10.1145	−0.726182
$195$	−17.4087	−1.24666
$196$	−36.2769	−2.59121
$197$	−7.54701	−0.537702	−0.268851	−	0.963182i	$-0.586644\pi$
$197$	−7.54701	−0.537702	−0.268851	+	0.963182i	$0.586644\pi$
$198$	5.98875	0.425602
$199$	11.3080	0.801604	0.400802	−	0.916165i	$-0.368732\pi$
$199$	11.3080	0.801604	0.400802	+	0.916165i	$0.368732\pi$
$200$	−24.7490	−1.75002
$201$	−4.16539	−0.293804
$202$	43.9645	3.09333
$203$	−1.73072	−0.121473
$204$	−42.1391	−2.95033
$205$	−25.8299	−1.80404
$206$	−18.3996	−1.28196
$207$	−2.57334	−0.178860
$208$	54.4616	3.77623
$209$	0.745111	0.0515404
$210$	−3.20234	−0.220983
$211$	−6.24109	−0.429655	−0.214827	−	0.976652i	$-0.568919\pi$
$211$	−6.24109	−0.429655	−0.214827	+	0.976652i	$0.568919\pi$
$212$	−25.4271	−1.74634
$213$	−1.10600	−0.0757817
$214$	−17.0371	−1.16463
$215$	9.50003	0.647897
$216$	−49.1936	−3.34720
$217$	−0.870407	−0.0590871
$218$	8.90613	0.603199
$219$	−5.08909	−0.343889
$220$	41.1921	2.77717
$221$	22.6447	1.52324
$222$	25.1929	1.69084
$223$	10.4414	0.699206	0.349603	−	0.936898i	$-0.386316\pi$
$223$	10.4414	0.699206	0.349603	+	0.936898i	$0.386316\pi$
$224$	5.02236	0.335571
$225$	−2.24764	−0.149843
$226$	−8.60053	−0.572099
$227$	−20.2964	−1.34712	−0.673561	−	0.739132i	$-0.735236\pi$
$227$	−20.2964	−1.34712	−0.673561	+	0.739132i	$0.735236\pi$
$228$	−2.06833	−0.136978
$229$	−2.91319	−0.192509	−0.0962545	−	0.995357i	$-0.530686\pi$
$229$	−2.91319	−0.192509	−0.0962545	+	0.995357i	$0.530686\pi$
$230$	−24.4511	−1.61226
$231$	1.19297	0.0784915
$232$	−52.8078	−3.46700
$233$	−6.61000	−0.433035	−0.216518	−	0.976279i	$-0.569470\pi$
$233$	−6.61000	−0.433035	−0.216518	+	0.976279i	$0.569470\pi$
$234$	8.93335	0.583991
$235$	2.29203	0.149516
$236$	51.3540	3.34286
$237$	−11.7702	−0.764553
$238$	4.16550	0.270009
$239$	−25.1970	−1.62986	−0.814930	−	0.579560i	$-0.803225\pi$
$239$	−25.1970	−1.62986	−0.814930	+	0.579560i	$0.803225\pi$
$240$	−54.0984	−3.49204
$241$	−8.40074	−0.541139	−0.270570	−	0.962700i	$-0.587212\pi$
$241$	−8.40074	−0.541139	−0.270570	+	0.962700i	$0.587212\pi$
$242$	8.40754	0.540457
$243$	−8.00137	−0.513288
$244$	35.5048	2.27296
$245$	−19.3644	−1.23715
$246$	−36.8980	−2.35253
$247$	1.11147	0.0707214
$248$	−26.5579	−1.68643
$249$	−9.56262	−0.606007
$250$	16.3111	1.03161
$251$	7.53319	0.475491	0.237745	−	0.971328i	$-0.423592\pi$
$251$	7.53319	0.475491	0.237745	+	0.971328i	$0.423592\pi$
$252$	1.18958	0.0749366
$253$	9.10874	0.572662
$254$	−26.8704	−1.68600
$255$	−22.4936	−1.40861
$256$	16.8074	1.05046
$257$	1.68405	0.105048	0.0525241	−	0.998620i	$-0.483273\pi$
$257$	1.68405	0.105048	0.0525241	+	0.998620i	$0.483273\pi$
$258$	13.5708	0.844882
$259$	−1.80276	−0.112018
$260$	61.4458	3.81071
$261$	−4.79588	−0.296857
$262$	40.3792	2.49464
$263$	6.28335	0.387448	0.193724	−	0.981056i	$-0.437943\pi$
$263$	6.28335	0.387448	0.193724	+	0.981056i	$0.437943\pi$
$264$	36.3998	2.24026
$265$	−13.5729	−0.833774
$266$	0.204457	0.0125360
$267$	9.06319	0.554658
$268$	14.7022	0.898080
$269$	27.2278	1.66011	0.830054	−	0.557682i	$-0.188309\pi$
$269$	27.2278	1.66011	0.830054	+	0.557682i	$0.188309\pi$
$270$	−42.4501	−2.58343
$271$	−2.93617	−0.178360	−0.0891798	−	0.996016i	$-0.528425\pi$
$271$	−2.93617	−0.178360	−0.0891798	+	0.996016i	$0.528425\pi$
$272$	70.3695	4.26678
$273$	1.77954	0.107703
$274$	29.7741	1.79872
$275$	7.95587	0.479757
$276$	−25.2846	−1.52196
$277$	9.99074	0.600285	0.300143	−	0.953894i	$-0.402966\pi$
$277$	9.99074	0.600285	0.300143	+	0.953894i	$0.402966\pi$
$278$	27.5403	1.65176
$279$	−2.41192	−0.144398
$280$	6.99196	0.417849
$281$	21.4887	1.28191	0.640954	−	0.767579i	$-0.278539\pi$
$281$	21.4887	1.28191	0.640954	+	0.767579i	$0.278539\pi$
$282$	3.27417	0.194974
$283$	1.76734	0.105058	0.0525288	−	0.998619i	$-0.483272\pi$
$283$	1.76734	0.105058	0.0525288	+	0.998619i	$0.483272\pi$
$284$	3.90374	0.231644
$285$	−1.10406	−0.0653990
$286$	−31.6209	−1.86979
$287$	2.64036	0.155856
$288$	13.9171	0.820073
$289$	12.2590	0.721117
$290$	−45.5688	−2.67589
$291$	−5.58316	−0.327290
$292$	17.9625	1.05117
$293$	−29.3759	−1.71616	−0.858079	−	0.513517i	$-0.828342\pi$
$293$	−29.3759	−1.71616	−0.858079	+	0.513517i	$0.828342\pi$
$294$	−27.6621	−1.61329
$295$	27.4125	1.59602
$296$	−55.0059	−3.19715
$297$	15.8139	0.917616
$298$	47.1657	2.73224
$299$	13.5874	0.785781
$300$	−22.0844	−1.27505
$301$	−0.971105	−0.0559735
$302$	−50.2562	−2.89192
$303$	24.2681	1.39417
$304$	3.45397	0.198098
$305$	18.9523	1.08521
$306$	11.5427	0.659853
$307$	−16.4452	−0.938577	−0.469289	−	0.883045i	$-0.655490\pi$
$307$	−16.4452	−0.938577	−0.469289	+	0.883045i	$0.655490\pi$
$308$	−4.21070	−0.239927
$309$	−10.1565	−0.577782
$310$	−22.9173	−1.30161
$311$	−2.89813	−0.164338	−0.0821690	−	0.996618i	$-0.526185\pi$
$311$	−2.89813	−0.164338	−0.0821690	+	0.996618i	$0.526185\pi$
$312$	54.2973	3.07398
$313$	−6.23292	−0.352305	−0.176153	−	0.984363i	$-0.556365\pi$
$313$	−6.23292	−0.352305	−0.176153	+	0.984363i	$0.556365\pi$
$314$	6.33824	0.357687
$315$	0.634993	0.0357778
$316$	41.5440	2.33703
$317$	−27.6178	−1.55117	−0.775584	−	0.631244i	$-0.782544\pi$
$317$	−27.6178	−1.55117	−0.775584	+	0.631244i	$0.782544\pi$
$318$	−19.3889	−1.08727
$319$	16.9757	0.950458
$320$	59.4073	3.32097
$321$	−9.40436	−0.524900
$322$	2.49942	0.139287
$323$	1.43613	0.0799083
$324$	−31.4246	−1.74581
$325$	11.8677	0.658301
$326$	19.2531	1.06633
$327$	4.91612	0.271862
$328$	80.5627	4.44833
$329$	−0.234294	−0.0129171
$330$	31.4101	1.72907
$331$	13.5221	0.743240	0.371620	−	0.928385i	$-0.378803\pi$
$331$	13.5221	0.743240	0.371620	+	0.928385i	$0.378803\pi$
$332$	33.7523	1.85240
$333$	−4.99550	−0.273752
$334$	−37.7976	−2.06819
$335$	7.84796	0.428780
$336$	5.53001	0.301687
$337$	−14.9306	−0.813320	−0.406660	−	0.913580i	$-0.633307\pi$
$337$	−14.9306	−0.813320	−0.406660	+	0.913580i	$0.633307\pi$
$338$	−12.1802	−0.662515
$339$	−4.74743	−0.257845
$340$	79.3937	4.30573
$341$	8.53736	0.462324
$342$	0.566555	0.0306358
$343$	3.98233	0.215026
$344$	−29.6304	−1.59756
$345$	−13.4968	−0.726644
$346$	−18.3142	−0.984580
$347$	17.2501	0.926035	0.463018	−	0.886349i	$-0.346767\pi$
$347$	17.2501	0.926035	0.463018	+	0.886349i	$0.346767\pi$
$348$	−47.1223	−2.52602
$349$	20.6513	1.10544	0.552718	−	0.833368i	$-0.313591\pi$
$349$	20.6513	1.10544	0.552718	+	0.833368i	$0.313591\pi$
$350$	2.18307	0.116690
$351$	23.5894	1.25911
$352$	−49.2617	−2.62566
$353$	−3.65390	−0.194478	−0.0972388	−	0.995261i	$-0.531001\pi$
$353$	−3.65390	−0.194478	−0.0972388	+	0.995261i	$0.531001\pi$
$354$	39.1588	2.08127
$355$	2.08379	0.110596
$356$	−31.9895	−1.69544
$357$	2.29933	0.121693
$358$	44.4977	2.35177
$359$	11.3854	0.600900	0.300450	−	0.953798i	$-0.402863\pi$
$359$	11.3854	0.600900	0.300450	+	0.953798i	$0.402863\pi$
$360$	19.3749	1.02115
$361$	−18.9295	−0.996290
$362$	−7.95057	−0.417873
$363$	4.64090	0.243584
$364$	−6.28107	−0.329217
$365$	9.58828	0.501873
$366$	27.0734	1.41515
$367$	−11.2201	−0.585687	−0.292843	−	0.956160i	$-0.594601\pi$
$367$	−11.2201	−0.585687	−0.292843	+	0.956160i	$0.594601\pi$
$368$	42.2236	2.20106
$369$	7.31651	0.380882
$370$	−47.4656	−2.46762
$371$	1.38743	0.0720320
$372$	−23.6986	−1.22871
$373$	20.8830	1.08128	0.540640	−	0.841254i	$-0.318182\pi$
$373$	20.8830	1.08128	0.540640	+	0.841254i	$0.318182\pi$
$374$	−40.8572	−2.11268
$375$	9.00363	0.464946
$376$	−7.14879	−0.368671
$377$	25.3225	1.30418
$378$	4.33930	0.223189
$379$	25.4372	1.30662	0.653310	−	0.757091i	$-0.273380\pi$
$379$	25.4372	1.30662	0.653310	+	0.757091i	$0.273380\pi$
$380$	3.89691	0.199907
$381$	−14.8323	−0.759880
$382$	45.4577	2.32582
$383$	3.92344	0.200478	0.100239	−	0.994963i	$-0.468039\pi$
$383$	3.92344	0.200478	0.100239	+	0.994963i	$0.468039\pi$
$384$	32.7084	1.66915
$385$	−2.24765	−0.114551
$386$	26.2764	1.33743
$387$	−2.69096	−0.136789
$388$	19.7063	1.00044
$389$	22.8749	1.15980	0.579901	−	0.814687i	$-0.303091\pi$
$389$	22.8749	1.15980	0.579901	+	0.814687i	$0.303091\pi$
$390$	46.8541	2.37255
$391$	17.5562	0.887855
$392$	60.3971	3.05051
$393$	22.2890	1.12433
$394$	20.3122	1.02331
$395$	22.1760	1.11579
$396$	−11.6680	−0.586338
$397$	−14.7620	−0.740884	−0.370442	−	0.928856i	$-0.620794\pi$
$397$	−14.7620	−0.740884	−0.370442	+	0.928856i	$0.620794\pi$
$398$	−30.4346	−1.52555
$399$	0.112859	0.00565000
$400$	36.8795	1.84397
$401$	−21.5584	−1.07658	−0.538288	−	0.842761i	$-0.680929\pi$
$401$	−21.5584	−1.07658	−0.538288	+	0.842761i	$0.680929\pi$
$402$	11.2108	0.559145
$403$	12.7351	0.634380
$404$	−85.6569	−4.26159
$405$	−16.7743	−0.833522
$406$	4.65810	0.231177
$407$	17.6823	0.876481
$408$	70.1571	3.47330
$409$	34.8248	1.72197	0.860987	−	0.508627i	$-0.169847\pi$
$409$	34.8248	1.72197	0.860987	+	0.508627i	$0.169847\pi$
$410$	69.5190	3.43330
$411$	16.4351	0.810683
$412$	35.8483	1.76612
$413$	−2.80214	−0.137884
$414$	6.92595	0.340392
$415$	18.0168	0.884410
$416$	−73.4831	−3.60281
$417$	15.2020	0.744447
$418$	−2.00541	−0.0980876
$419$	15.2011	0.742624	0.371312	−	0.928508i	$-0.378908\pi$
$419$	15.2011	0.742624	0.371312	+	0.928508i	$0.378908\pi$
$420$	6.23918	0.304441
$421$	−20.3109	−0.989892	−0.494946	−	0.868924i	$-0.664812\pi$
$421$	−20.3109	−0.989892	−0.494946	+	0.868924i	$0.664812\pi$
$422$	16.7974	0.817685
$423$	−0.649235	−0.0315669
$424$	42.3334	2.05589
$425$	15.3342	0.743816
$426$	2.97670	0.144222
$427$	−1.93733	−0.0937538
$428$	33.1937	1.60448
$429$	−17.4545	−0.842713
$430$	−25.5686	−1.23303
$431$	−12.9096	−0.621832	−0.310916	−	0.950437i	$-0.600636\pi$
$431$	−12.9096	−0.621832	−0.310916	+	0.950437i	$0.600636\pi$
$432$	73.3055	3.52691
$433$	9.69178	0.465757	0.232879	−	0.972506i	$-0.425185\pi$
$433$	9.69178	0.465757	0.232879	+	0.972506i	$0.425185\pi$
$434$	2.34263	0.112450
$435$	−25.1537	−1.20603
$436$	−17.3520	−0.831008
$437$	0.861716	0.0412215
$438$	13.6969	0.654462
$439$	20.8581	0.995503	0.497751	−	0.867320i	$-0.334159\pi$
$439$	20.8581	0.995503	0.497751	+	0.867320i	$0.334159\pi$
$440$	−68.5804	−3.26944
$441$	5.48512	0.261196
$442$	−60.9463	−2.89892
$443$	−14.2882	−0.678851	−0.339425	−	0.940633i	$-0.610233\pi$
$443$	−14.2882	−0.678851	−0.339425	+	0.940633i	$0.610233\pi$
$444$	−49.0838	−2.32941
$445$	−17.0758	−0.809472
$446$	−28.1021	−1.33067
$447$	26.0352	1.23142
$448$	−6.07269	−0.286907
$449$	23.9531	1.13042	0.565209	−	0.824948i	$-0.308796\pi$
$449$	23.9531	1.13042	0.565209	+	0.824948i	$0.308796\pi$
$450$	6.04935	0.285169
$451$	−25.8979	−1.21948
$452$	16.7566	0.788162
$453$	−27.7410	−1.30339
$454$	54.6262	2.56374
$455$	−3.35280	−0.157182
$456$	3.44354	0.161259
$457$	−40.4290	−1.89119	−0.945593	−	0.325351i	$-0.894518\pi$
$457$	−40.4290	−1.89119	−0.945593	+	0.325351i	$0.894518\pi$
$458$	7.84062	0.366368
$459$	30.4798	1.42267
$460$	47.6384	2.22115
$461$	−12.0855	−0.562877	−0.281438	−	0.959579i	$-0.590811\pi$
$461$	−12.0855	−0.562877	−0.281438	+	0.959579i	$0.590811\pi$
$462$	−3.21078	−0.149379
$463$	30.4311	1.41425	0.707127	−	0.707087i	$-0.249991\pi$
$463$	30.4311	1.41425	0.707127	+	0.707087i	$0.249991\pi$
$464$	78.6911	3.65314
$465$	−12.6502	−0.586637
$466$	17.7903	0.824118
$467$	−7.71047	−0.356798	−0.178399	−	0.983958i	$-0.557092\pi$
$467$	−7.71047	−0.356798	−0.178399	+	0.983958i	$0.557092\pi$
$468$	−17.4050	−0.804547
$469$	−0.802227	−0.0370434
$470$	−6.16882	−0.284546
$471$	3.49866	0.161210
$472$	−85.4989	−3.93540
$473$	9.52505	0.437962
$474$	31.6784	1.45504
$475$	0.752651	0.0345340
$476$	−8.11572	−0.371983
$477$	3.84462	0.176033
$478$	67.8157	3.10182
$479$	−24.0535	−1.09903	−0.549516	−	0.835483i	$-0.685188\pi$
$479$	−24.0535	−1.09903	−0.549516	+	0.835483i	$0.685188\pi$
$480$	72.9931	3.33166
$481$	26.3766	1.20267
$482$	22.6099	1.02985
$483$	1.37966	0.0627767
$484$	−16.3806	−0.744571
$485$	10.5191	0.477650
$486$	21.5351	0.976850
$487$	14.7718	0.669372	0.334686	−	0.942330i	$-0.391370\pi$
$487$	14.7718	0.669372	0.334686	+	0.942330i	$0.391370\pi$
$488$	−59.1117	−2.67586
$489$	10.6276	0.480596
$490$	52.1177	2.35444
$491$	−2.40803	−0.108673	−0.0543365	−	0.998523i	$-0.517304\pi$
$491$	−2.40803	−0.108673	−0.0543365	+	0.998523i	$0.517304\pi$
$492$	71.8891	3.24101
$493$	32.7190	1.47359
$494$	−2.99144	−0.134591
$495$	−6.22831	−0.279941
$496$	39.5750	1.77697
$497$	−0.213008	−0.00955471
$498$	25.7370	1.15330
$499$	11.6519	0.521611	0.260805	−	0.965391i	$-0.416012\pi$
$499$	11.6519	0.521611	0.260805	+	0.965391i	$0.416012\pi$
$500$	−31.7793	−1.42121
$501$	−20.8640	−0.932135
$502$	−20.2750	−0.904916
$503$	19.8736	0.886120	0.443060	−	0.896492i	$-0.353893\pi$
$503$	19.8736	0.886120	0.443060	+	0.896492i	$0.353893\pi$
$504$	−1.98053	−0.0882196
$505$	−45.7232	−2.03466
$506$	−24.5154	−1.08984
$507$	−6.72338	−0.298596
$508$	52.3520	2.32275
$509$	−24.7488	−1.09697	−0.548486	−	0.836160i	$-0.684796\pi$
$509$	−24.7488	−1.09697	−0.548486	+	0.836160i	$0.684796\pi$
$510$	60.5398	2.68075
$511$	−0.980125	−0.0433582
$512$	−1.20318	−0.0531735
$513$	1.49605	0.0660521
$514$	−4.53249	−0.199920
$515$	19.1357	0.843218
$516$	−26.4403	−1.16397
$517$	2.29807	0.101069
$518$	4.85199	0.213184
$519$	−10.1093	−0.443751
$520$	−102.301	−4.48618
$521$	−20.2028	−0.885099	−0.442549	−	0.896744i	$-0.645926\pi$
$521$	−20.2028	−0.885099	−0.442549	+	0.896744i	$0.645926\pi$
$522$	12.9077	0.564955
$523$	−9.83082	−0.429872	−0.214936	−	0.976628i	$-0.568954\pi$
$523$	−9.83082	−0.429872	−0.214936	+	0.976628i	$0.568954\pi$
$524$	−78.6715	−3.43678
$525$	1.20504	0.0525923
$526$	−16.9111	−0.737360
$527$	16.4549	0.716787
$528$	−54.2409	−2.36053
$529$	−12.4658	−0.541991
$530$	36.5303	1.58677
$531$	−7.76480	−0.336964
$532$	−0.398346	−0.0172705
$533$	−38.6316	−1.67332
$534$	−24.3929	−1.05558
$535$	17.7186	0.766042
$536$	−24.4776	−1.05727
$537$	24.5624	1.05995
$538$	−73.2815	−3.15939
$539$	−19.4154	−0.836280
$540$	82.7062	3.55911
$541$	36.7405	1.57960	0.789798	−	0.613367i	$-0.210185\pi$
$541$	36.7405	1.57960	0.789798	+	0.613367i	$0.210185\pi$
$542$	7.90246	0.339440
$543$	−4.38866	−0.188335
$544$	−94.9470	−4.07082
$545$	−9.26239	−0.396757
$546$	−4.78948	−0.204971
$547$	−4.70766	−0.201285	−0.100642	−	0.994923i	$-0.532090\pi$
$547$	−4.70766	−0.201285	−0.100642	+	0.994923i	$0.532090\pi$
$548$	−58.0094	−2.47804
$549$	−5.36838	−0.229117
$550$	−21.4126	−0.913036
$551$	1.60596	0.0684161
$552$	42.0962	1.79173
$553$	−2.26685	−0.0963964
$554$	−26.8893	−1.14242
$555$	−26.2007	−1.11216
$556$	−53.6572	−2.27557
$557$	4.25540	0.180307	0.0901535	−	0.995928i	$-0.471264\pi$
$557$	4.25540	0.180307	0.0901535	+	0.995928i	$0.471264\pi$
$558$	6.49149	0.274807
$559$	14.2084	0.600952
$560$	−10.4190	−0.440283
$561$	−22.5529	−0.952183
$562$	−57.8351	−2.43963
$563$	13.6785	0.576479	0.288240	−	0.957558i	$-0.406930\pi$
$563$	13.6785	0.576479	0.288240	+	0.957558i	$0.406930\pi$
$564$	−6.37912	−0.268610
$565$	8.94456	0.376301
$566$	−4.75666	−0.199937
$567$	1.71469	0.0720101
$568$	−6.49930	−0.272705
$569$	2.75673	0.115568	0.0577840	−	0.998329i	$-0.481597\pi$
$569$	2.75673	0.115568	0.0577840	+	0.998329i	$0.481597\pi$
$570$	2.97150	0.124462
$571$	−34.2905	−1.43501	−0.717507	−	0.696551i	$-0.754717\pi$
$571$	−34.2905	−1.43501	−0.717507	+	0.696551i	$0.754717\pi$
$572$	61.6076	2.57594
$573$	25.0923	1.04825
$574$	−7.10632	−0.296612
$575$	9.20092	0.383705
$576$	−16.8276	−0.701149
$577$	45.6606	1.90087	0.950437	−	0.310918i	$-0.100636\pi$
$577$	45.6606	1.90087	0.950437	+	0.310918i	$0.100636\pi$
$578$	−32.9941	−1.37237
$579$	14.5044	0.602781
$580$	88.7825	3.68649
$581$	−1.84170	−0.0764065
$582$	15.0266	0.622873
$583$	−13.6086	−0.563611
$584$	−29.9056	−1.23750
$585$	−9.29070	−0.384123
$586$	79.0629	3.26606
$587$	−24.8654	−1.02631	−0.513153	−	0.858297i	$-0.671523\pi$
$587$	−24.8654	−1.02631	−0.513153	+	0.858297i	$0.671523\pi$
$588$	53.8945	2.22257
$589$	0.807662	0.0332791
$590$	−73.7785	−3.03741
$591$	11.2122	0.461207
$592$	81.9666	3.36881
$593$	−17.4835	−0.717961	−0.358981	−	0.933345i	$-0.616876\pi$
$593$	−17.4835	−0.717961	−0.358981	+	0.933345i	$0.616876\pi$
$594$	−42.5619	−1.74633
$595$	−4.33213	−0.177600
$596$	−91.8938	−3.76412
$597$	−16.7997	−0.687565
$598$	−36.5694	−1.49544
$599$	7.69707	0.314494	0.157247	−	0.987559i	$-0.449738\pi$
$599$	7.69707	0.314494	0.157247	+	0.987559i	$0.449738\pi$
$600$	36.7682	1.50106
$601$	−17.7599	−0.724442	−0.362221	−	0.932092i	$-0.617981\pi$
$601$	−17.7599	−0.724442	−0.362221	+	0.932092i	$0.617981\pi$
$602$	2.61365	0.106524
$603$	−2.22299	−0.0905273
$604$	97.9149	3.98410
$605$	−8.74386	−0.355488
$606$	−65.3157	−2.65327
$607$	41.9612	1.70315	0.851577	−	0.524229i	$-0.175647\pi$
$607$	41.9612	1.70315	0.851577	+	0.524229i	$0.175647\pi$
$608$	−4.66031	−0.189001
$609$	2.57124	0.104192
$610$	−51.0086	−2.06528
$611$	3.42800	0.138682
$612$	−22.4889	−0.909059
$613$	28.2052	1.13920	0.569599	−	0.821923i	$-0.307098\pi$
$613$	28.2052	1.13920	0.569599	+	0.821923i	$0.307098\pi$
$614$	44.2609	1.78623
$615$	38.3740	1.54739
$616$	7.01037	0.282456
$617$	27.3189	1.09982	0.549910	−	0.835224i	$-0.314662\pi$
$617$	27.3189	1.09982	0.549910	+	0.835224i	$0.314662\pi$
$618$	27.3353	1.09959
$619$	−33.5023	−1.34657	−0.673286	−	0.739382i	$-0.735118\pi$
$619$	−33.5023	−1.34657	−0.673286	+	0.739382i	$0.735118\pi$
$620$	44.6501	1.79319
$621$	18.2887	0.733900
$622$	7.80009	0.312755
$623$	1.74551	0.0699324
$624$	−80.9106	−3.23902
$625$	−31.1379	−1.24551
$626$	16.7754	0.670480
$627$	−1.10697	−0.0442081
$628$	−12.3489	−0.492775
$629$	34.0810	1.35890
$630$	−1.70903	−0.0680894
$631$	−31.8477	−1.26784	−0.633919	−	0.773399i	$-0.718555\pi$
$631$	−31.8477	−1.26784	−0.633919	+	0.773399i	$0.718555\pi$
$632$	−69.1663	−2.75129
$633$	9.27204	0.368531
$634$	74.3310	2.95206
$635$	27.9452	1.10897
$636$	37.7757	1.49790
$637$	−28.9618	−1.14751
$638$	−45.6888	−1.80884
$639$	−0.590251	−0.0233500
$640$	−61.6255	−2.43596
$641$	33.3807	1.31846	0.659229	−	0.751942i	$-0.270883\pi$
$641$	33.3807	1.31846	0.659229	+	0.751942i	$0.270883\pi$
$642$	25.3111	0.998948
$643$	13.3337	0.525829	0.262915	−	0.964819i	$-0.415316\pi$
$643$	13.3337	0.525829	0.262915	+	0.964819i	$0.415316\pi$
$644$	−4.86966	−0.191891
$645$	−14.1137	−0.555725
$646$	−3.86522	−0.152075
$647$	−30.2486	−1.18920	−0.594598	−	0.804023i	$-0.702689\pi$
$647$	−30.2486	−1.18920	−0.594598	+	0.804023i	$0.702689\pi$
$648$	52.3186	2.05527
$649$	27.4847	1.07887
$650$	−31.9409	−1.25283
$651$	1.29311	0.0506812
$652$	−37.5112	−1.46905
$653$	13.6521	0.534249	0.267125	−	0.963662i	$-0.413926\pi$
$653$	13.6521	0.534249	0.267125	+	0.963662i	$0.413926\pi$
$654$	−13.2313	−0.517386
$655$	−41.9945	−1.64086
$656$	−120.050	−4.68716
$657$	−2.71595	−0.105959
$658$	0.630584	0.0245827
$659$	−11.7515	−0.457774	−0.228887	−	0.973453i	$-0.573509\pi$
$659$	−11.7515	−0.457774	−0.228887	+	0.973453i	$0.573509\pi$
$660$	−61.1968	−2.38208
$661$	−14.9300	−0.580709	−0.290354	−	0.956919i	$-0.593773\pi$
$661$	−14.9300	−0.580709	−0.290354	+	0.956919i	$0.593773\pi$
$662$	−36.3935	−1.41447
$663$	−33.6419	−1.30654
$664$	−56.1939	−2.18075
$665$	−0.212635	−0.00824564
$666$	13.4450	0.520983
$667$	19.6323	0.760167
$668$	73.6417	2.84928
$669$	−15.5122	−0.599735
$670$	−21.1221	−0.816020
$671$	19.0022	0.733572
$672$	−7.46144	−0.287831
$673$	34.4796	1.32909	0.664545	−	0.747249i	$-0.268626\pi$
$673$	34.4796	1.32909	0.664545	+	0.747249i	$0.268626\pi$
$674$	40.1844	1.54785
$675$	15.9739	0.614837
$676$	23.7309	0.912726
$677$	38.3308	1.47317	0.736586	−	0.676344i	$-0.236437\pi$
$677$	38.3308	1.47317	0.736586	+	0.676344i	$0.236437\pi$
$678$	12.7773	0.490710
$679$	−1.07528	−0.0412654
$680$	−132.182	−5.06895
$681$	30.1533	1.15548
$682$	−22.9776	−0.879858
$683$	−10.1833	−0.389653	−0.194827	−	0.980838i	$-0.562414\pi$
$683$	−10.1833	−0.389653	−0.194827	+	0.980838i	$0.562414\pi$
$684$	−1.10383	−0.0422059
$685$	−30.9651	−1.18312
$686$	−10.7181	−0.409220
$687$	4.32797	0.165122
$688$	44.1534	1.68333
$689$	−20.2998	−0.773361
$690$	36.3256	1.38289
$691$	−40.1813	−1.52857	−0.764284	−	0.644880i	$-0.776907\pi$
$691$	−40.1813	−1.52857	−0.764284	+	0.644880i	$0.776907\pi$
$692$	35.6820	1.35642
$693$	0.636665	0.0241849
$694$	−46.4273	−1.76236
$695$	−28.6419	−1.08645
$696$	78.4536	2.97378
$697$	−49.9156	−1.89069
$698$	−55.5812	−2.10378
$699$	9.82010	0.371430
$700$	−4.25332	−0.160760
$701$	46.4592	1.75474	0.877370	−	0.479814i	$-0.159296\pi$
$701$	46.4592	1.75474	0.877370	+	0.479814i	$0.159296\pi$
$702$	−63.4891	−2.39624
$703$	1.67281	0.0630911
$704$	59.5638	2.24489
$705$	−3.40514	−0.128245
$706$	9.83419	0.370115
$707$	4.67388	0.175779
$708$	−76.2938	−2.86730
$709$	−18.7578	−0.704464	−0.352232	−	0.935913i	$-0.614577\pi$
$709$	−18.7578	−0.704464	−0.352232	+	0.935913i	$0.614577\pi$
$710$	−5.60836	−0.210478
$711$	−6.28151	−0.235575
$712$	53.2591	1.99597
$713$	9.87340	0.369762
$714$	−6.18845	−0.231597
$715$	32.8858	1.22986
$716$	−86.6955	−3.23996
$717$	37.4338	1.39799
$718$	−30.6430	−1.14359
$719$	−45.4287	−1.69420	−0.847102	−	0.531431i	$-0.821654\pi$
$719$	−45.4287	−1.69420	−0.847102	+	0.531431i	$0.821654\pi$
$720$	−28.8713	−1.07597
$721$	−1.95607	−0.0728478
$722$	50.9473	1.89606
$723$	12.4805	0.464155
$724$	15.4902	0.575690
$725$	17.1475	0.636843
$726$	−12.4906	−0.463570
$727$	51.4697	1.90891	0.954454	−	0.298359i	$-0.0964394\pi$
$727$	51.4697	1.90891	0.954454	+	0.298359i	$0.0964394\pi$
$728$	10.4573	0.387573
$729$	29.8656	1.10613
$730$	−25.8061	−0.955126
$731$	18.3586	0.679017
$732$	−52.7476	−1.94961
$733$	51.4983	1.90213	0.951067	−	0.308984i	$-0.0999889\pi$
$733$	51.4983	1.90213	0.951067	+	0.308984i	$0.0999889\pi$
$734$	30.1981	1.11463
$735$	28.7686	1.06115
$736$	−56.9708	−2.09997
$737$	7.86862	0.289844
$738$	−19.6918	−0.724865
$739$	39.7126	1.46085	0.730425	−	0.682993i	$-0.239322\pi$
$739$	39.7126	1.46085	0.730425	+	0.682993i	$0.239322\pi$
$740$	92.4780	3.39956
$741$	−1.65126	−0.0606604
$742$	−3.73417	−0.137086
$743$	18.5360	0.680021	0.340011	−	0.940422i	$-0.389569\pi$
$743$	18.5360	0.680021	0.340011	+	0.940422i	$0.389569\pi$
$744$	39.4555	1.44651
$745$	−49.0525	−1.79714
$746$	−56.2049	−2.05781
$747$	−5.10340	−0.186723
$748$	79.6028	2.91057
$749$	−1.81122	−0.0661804
$750$	−24.2326	−0.884848
$751$	10.9874	0.400936	0.200468	−	0.979700i	$-0.435754\pi$
$751$	10.9874	0.400936	0.200468	+	0.979700i	$0.435754\pi$
$752$	10.6527	0.388464
$753$	−11.1916	−0.407846
$754$	−68.1535	−2.48200
$755$	52.2665	1.90217
$756$	−8.45433	−0.307481
$757$	−30.5194	−1.10925	−0.554624	−	0.832101i	$-0.687138\pi$
$757$	−30.5194	−1.10925	−0.554624	+	0.832101i	$0.687138\pi$
$758$	−68.4621	−2.48665
$759$	−13.5324	−0.491193
$760$	−6.48793	−0.235342
$761$	28.2181	1.02291	0.511453	−	0.859311i	$-0.329107\pi$
$761$	28.2181	1.02291	0.511453	+	0.859311i	$0.329107\pi$
$762$	39.9198	1.44614
$763$	0.946812	0.0342769
$764$	−88.5661	−3.20421
$765$	−12.0044	−0.434022
$766$	−10.5596	−0.381535
$767$	40.9986	1.48037
$768$	−24.9699	−0.901022
$769$	12.5429	0.452307	0.226154	−	0.974092i	$-0.427385\pi$
$769$	12.5429	0.452307	0.226154	+	0.974092i	$0.427385\pi$
$770$	6.04937	0.218004
$771$	−2.50190	−0.0901038
$772$	−51.1947	−1.84254
$773$	4.45713	0.160312	0.0801559	−	0.996782i	$-0.474458\pi$
$773$	4.45713	0.160312	0.0801559	+	0.996782i	$0.474458\pi$
$774$	7.24250	0.260326
$775$	8.62375	0.309774
$776$	−32.8089	−1.17777
$777$	2.67826	0.0960822
$778$	−61.5659	−2.20724
$779$	−2.45002	−0.0877812
$780$	−91.2867	−3.26859
$781$	2.08928	0.0747604
$782$	−47.2511	−1.68970
$783$	34.0842	1.21807
$784$	−90.0002	−3.21429
$785$	−6.59178	−0.235271
$786$	−59.9892	−2.13974
$787$	4.12695	0.147110	0.0735550	−	0.997291i	$-0.476566\pi$
$787$	4.12695	0.147110	0.0735550	+	0.997291i	$0.476566\pi$
$788$	−39.5745	−1.40978
$789$	−9.33482	−0.332329
$790$	−59.6848	−2.12349
$791$	−0.914324	−0.0325096
$792$	19.4259	0.690270
$793$	28.3454	1.00657
$794$	39.7308	1.40999
$795$	20.1644	0.715159
$796$	59.2963	2.10170
$797$	−53.2824	−1.88736	−0.943679	−	0.330862i	$-0.892660\pi$
$797$	−53.2824	−1.88736	−0.943679	+	0.330862i	$0.892660\pi$
$798$	−0.303750	−0.0107526
$799$	4.42930	0.156697
$800$	−49.7602	−1.75929
$801$	4.83686	0.170902
$802$	58.0227	2.04885
$803$	9.61353	0.339254
$804$	−21.8422	−0.770316
$805$	−2.59940	−0.0916167
$806$	−34.2755	−1.20730
$807$	−40.4508	−1.42394
$808$	142.609	5.01698
$809$	−30.8146	−1.08338	−0.541692	−	0.840577i	$-0.682216\pi$
$809$	−30.8146	−1.08338	−0.541692	+	0.840577i	$0.682216\pi$
$810$	45.1467	1.58629
$811$	7.01510	0.246334	0.123167	−	0.992386i	$-0.460695\pi$
$811$	7.01510	0.246334	0.123167	+	0.992386i	$0.460695\pi$
$812$	−9.07545	−0.318486
$813$	4.36210	0.152986
$814$	−47.5906	−1.66805
$815$	−20.0233	−0.701384
$816$	−104.544	−3.65977
$817$	0.901100	0.0315255
$818$	−93.7280	−3.27712
$819$	0.949706	0.0331854
$820$	−135.445	−4.72995
$821$	49.1660	1.71591	0.857953	−	0.513727i	$-0.171736\pi$
$821$	49.1660	1.71591	0.857953	+	0.513727i	$0.171736\pi$
$822$	−44.2337	−1.54283
$823$	46.0047	1.60362	0.801812	−	0.597577i	$-0.203870\pi$
$823$	46.0047	1.60362	0.801812	+	0.597577i	$0.203870\pi$
$824$	−59.6836	−2.07918
$825$	−11.8196	−0.411506
$826$	7.54173	0.262410
$827$	−47.7963	−1.66204	−0.831021	−	0.556242i	$-0.812243\pi$
$827$	−47.7963	−1.66204	−0.831021	+	0.556242i	$0.812243\pi$
$828$	−13.4939	−0.468947
$829$	−4.33283	−0.150485	−0.0752427	−	0.997165i	$-0.523973\pi$
$829$	−4.33283	−0.150485	−0.0752427	+	0.997165i	$0.523973\pi$
$830$	−48.4908	−1.68314
$831$	−14.8427	−0.514887
$832$	88.8507	3.08034
$833$	−37.4213	−1.29657
$834$	−40.9150	−1.41677
$835$	39.3096	1.36036
$836$	3.90717	0.135132
$837$	17.1415	0.592495
$838$	−40.9126	−1.41330
$839$	−15.0066	−0.518087	−0.259043	−	0.965866i	$-0.583407\pi$
$839$	−15.0066	−0.518087	−0.259043	+	0.965866i	$0.583407\pi$
$840$	−10.3876	−0.358405
$841$	7.58826	0.261664
$842$	54.6651	1.88388
$843$	−31.9245	−1.09954
$844$	−32.7267	−1.12650
$845$	12.6674	0.435773
$846$	1.74736	0.0600756
$847$	0.893808	0.0307116
$848$	−63.0827	−2.16627
$849$	−2.62564	−0.0901117
$850$	−41.2707	−1.41557
$851$	20.4495	0.701001
$852$	−5.79956	−0.198690
$853$	40.0903	1.37267	0.686333	−	0.727288i	$-0.259219\pi$
$853$	40.0903	1.37267	0.686333	+	0.727288i	$0.259219\pi$
$854$	5.21416	0.178425
$855$	−0.589218	−0.0201508
$856$	−55.2639	−1.88888
$857$	9.56757	0.326822	0.163411	−	0.986558i	$-0.447750\pi$
$857$	9.56757	0.326822	0.163411	+	0.986558i	$0.447750\pi$
$858$	46.9775	1.60378
$859$	−9.16527	−0.312715	−0.156358	−	0.987701i	$-0.549975\pi$
$859$	−9.16527	−0.312715	−0.156358	+	0.987701i	$0.549975\pi$
$860$	49.8157	1.69870
$861$	−3.92264	−0.133683
$862$	34.7451	1.18342
$863$	−52.8980	−1.80067	−0.900335	−	0.435199i	$-0.856678\pi$
$863$	−52.8980	−1.80067	−0.900335	+	0.435199i	$0.856678\pi$
$864$	−98.9084	−3.36493
$865$	19.0468	0.647612
$866$	−26.0847	−0.886393
$867$	−18.2125	−0.618529
$868$	−4.56419	−0.154919
$869$	22.2344	0.754249
$870$	67.6990	2.29521
$871$	11.7375	0.397712
$872$	28.8891	0.978310
$873$	−2.97963	−0.100845
$874$	−2.31924	−0.0784495
$875$	1.73404	0.0586213
$876$	−26.6859	−0.901631
$877$	32.1519	1.08569	0.542845	−	0.839833i	$-0.317347\pi$
$877$	32.1519	1.08569	0.542845	+	0.839833i	$0.317347\pi$
$878$	−56.1379	−1.89456
$879$	43.6421	1.47201
$880$	102.194	3.44497
$881$	30.2674	1.01974	0.509868	−	0.860253i	$-0.329694\pi$
$881$	30.2674	1.01974	0.509868	+	0.860253i	$0.329694\pi$
$882$	−14.7628	−0.497088
$883$	−4.93612	−0.166114	−0.0830569	−	0.996545i	$-0.526468\pi$
$883$	−4.93612	−0.166114	−0.0830569	+	0.996545i	$0.526468\pi$
$884$	118.743	3.99375
$885$	−40.7252	−1.36896
$886$	38.4554	1.29194
$887$	10.0994	0.339106	0.169553	−	0.985521i	$-0.445768\pi$
$887$	10.0994	0.339106	0.169553	+	0.985521i	$0.445768\pi$
$888$	81.7192	2.74232
$889$	−2.85659	−0.0958071
$890$	45.9582	1.54052
$891$	−16.8185	−0.563440
$892$	54.7518	1.83323
$893$	0.217405	0.00727516
$894$	−70.0715	−2.34354
$895$	−46.2776	−1.54689
$896$	6.29943	0.210449
$897$	−20.1861	−0.673993
$898$	−64.4679	−2.15132
$899$	18.4008	0.613701
$900$	−11.7861	−0.392868
$901$	−26.2292	−0.873823
$902$	69.7021	2.32083
$903$	1.44272	0.0480106
$904$	−27.8979	−0.927869
$905$	8.26860	0.274858
$906$	74.6628	2.48050
$907$	−10.4372	−0.346561	−0.173280	−	0.984873i	$-0.555437\pi$
$907$	−10.4372	−0.346561	−0.173280	+	0.984873i	$0.555437\pi$
$908$	−106.429	−3.53198
$909$	12.9514	0.429572
$910$	9.02379	0.299136
$911$	24.3012	0.805135	0.402568	−	0.915390i	$-0.368118\pi$
$911$	24.3012	0.805135	0.402568	+	0.915390i	$0.368118\pi$
$912$	−5.13136	−0.169916
$913$	18.0642	0.597839
$914$	108.811	3.59916
$915$	−28.1564	−0.930821
$916$	−15.2760	−0.504734
$917$	4.29272	0.141758
$918$	−82.0338	−2.70752
$919$	−13.9309	−0.459539	−0.229769	−	0.973245i	$-0.573797\pi$
$919$	−13.9309	−0.459539	−0.229769	+	0.973245i	$0.573797\pi$
$920$	−79.3129	−2.61487
$921$	24.4317	0.805053
$922$	32.5271	1.07122
$923$	3.11656	0.102583
$924$	6.25561	0.205794
$925$	17.8613	0.587275
$926$	−81.9029	−2.69149
$927$	−5.42032	−0.178027
$928$	−106.175	−3.48537
$929$	−41.6798	−1.36747	−0.683735	−	0.729730i	$-0.739646\pi$
$929$	−41.6798	−1.36747	−0.683735	+	0.729730i	$0.739646\pi$
$930$	34.0469	1.11644
$931$	−1.83676	−0.0601974
$932$	−34.6611	−1.13536
$933$	4.30560	0.140959
$934$	20.7521	0.679030
$935$	42.4915	1.38962
$936$	28.9775	0.947158
$937$	−2.21386	−0.0723235	−0.0361618	−	0.999346i	$-0.511513\pi$
$937$	−2.21386	−0.0723235	−0.0361618	+	0.999346i	$0.511513\pi$
$938$	2.15913	0.0704981
$939$	9.25990	0.302185
$940$	12.0188	0.392010
$941$	−5.21326	−0.169948	−0.0849738	−	0.996383i	$-0.527081\pi$
$941$	−5.21326	−0.169948	−0.0849738	+	0.996383i	$0.527081\pi$
$942$	−9.41636	−0.306802
$943$	−29.9508	−0.975331
$944$	127.405	4.14669
$945$	−4.51288	−0.146804
$946$	−25.6359	−0.833495
$947$	14.2634	0.463499	0.231749	−	0.972776i	$-0.425555\pi$
$947$	14.2634	0.463499	0.231749	+	0.972776i	$0.425555\pi$
$948$	−61.7196	−2.00456
$949$	14.3404	0.465509
$950$	−2.02570	−0.0657224
$951$	41.0302	1.33049
$952$	13.5118	0.437920
$953$	42.0797	1.36310	0.681548	−	0.731773i	$-0.261307\pi$
$953$	42.0797	1.36310	0.681548	+	0.731773i	$0.261307\pi$
$954$	−10.3475	−0.335012
$955$	−47.2761	−1.52982
$956$	−132.127	−4.27328
$957$	−25.2199	−0.815243
$958$	64.7381	2.09159
$959$	3.16529	0.102213
$960$	−88.2582	−2.84852
$961$	−21.7459	−0.701482
$962$	−70.9904	−2.28882
$963$	−5.01893	−0.161733
$964$	−44.0513	−1.41880
$965$	−27.3274	−0.879702
$966$	−3.71324	−0.119472
$967$	3.92952	0.126365	0.0631824	−	0.998002i	$-0.479875\pi$
$967$	3.92952	0.126365	0.0631824	+	0.998002i	$0.479875\pi$
$968$	27.2719	0.876551
$969$	−2.13358	−0.0685403
$970$	−28.3114	−0.909025
$971$	27.7696	0.891169	0.445584	−	0.895240i	$-0.352996\pi$
$971$	27.7696	0.891169	0.445584	+	0.895240i	$0.352996\pi$
$972$	−41.9571	−1.34578
$973$	2.92781	0.0938613
$974$	−39.7570	−1.27390
$975$	−17.6312	−0.564649
$976$	88.0848	2.81953
$977$	14.5624	0.465893	0.232947	−	0.972490i	$-0.425163\pi$
$977$	14.5624	0.465893	0.232947	+	0.972490i	$0.425163\pi$
$978$	−28.6033	−0.914632
$979$	−17.1208	−0.547183
$980$	−101.542	−3.24364
$981$	2.62364	0.0837664
$982$	6.48103	0.206818
$983$	22.4051	0.714612	0.357306	−	0.933987i	$-0.383695\pi$
$983$	22.4051	0.714612	0.357306	+	0.933987i	$0.383695\pi$
$984$	−119.688	−3.81550
$985$	−21.1247	−0.673088
$986$	−88.0607	−2.80442
$987$	0.348078	0.0110794
$988$	5.82828	0.185422
$989$	11.0157	0.350278
$990$	16.7630	0.532763
$991$	22.6964	0.720975	0.360487	−	0.932764i	$-0.382610\pi$
$991$	22.6964	0.720975	0.360487	+	0.932764i	$0.382610\pi$
$992$	−53.3971	−1.69536
$993$	−20.0890	−0.637504
$994$	0.573294	0.0181838
$995$	31.6520	1.00344
$996$	−50.1439	−1.58887
$997$	−5.20588	−0.164872	−0.0824359	−	0.996596i	$-0.526270\pi$
$997$	−5.20588	−0.164872	−0.0824359	+	0.996596i	$0.526270\pi$
$998$	−31.3601	−0.992688
$999$	35.5029	1.12326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.5	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.5	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69142 q^{2} -1.48564 q^{3} +5.24374 q^{4} +2.79908 q^{5} +3.99849 q^{6} -0.286125 q^{7} -8.73026 q^{8} -0.792861 q^{9} +O(q^{10})\)	\(q-2.69142 q^{2} -1.48564 q^{3} +5.24374 q^{4} +2.79908 q^{5} +3.99849 q^{6} -0.286125 q^{7} -8.73026 q^{8} -0.792861 q^{9} -7.53350 q^{10} +2.80645 q^{11} -7.79033 q^{12} +4.18635 q^{13} +0.770083 q^{14} -4.15844 q^{15} +13.0093 q^{16} +5.40916 q^{17} +2.13392 q^{18} +0.265499 q^{19} +14.6776 q^{20} +0.425080 q^{21} -7.55334 q^{22} +3.24564 q^{23} +12.9701 q^{24} +2.83485 q^{25} -11.2672 q^{26} +5.63484 q^{27} -1.50037 q^{28} +6.04882 q^{29} +11.1921 q^{30} +3.04205 q^{31} -17.5530 q^{32} -4.16939 q^{33} -14.5583 q^{34} -0.800888 q^{35} -4.15756 q^{36} +6.30060 q^{37} -0.714570 q^{38} -6.21943 q^{39} -24.4367 q^{40} -9.22799 q^{41} -1.14407 q^{42} +3.39398 q^{43} +14.7163 q^{44} -2.21928 q^{45} -8.73539 q^{46} +0.818851 q^{47} -19.3272 q^{48} -6.91813 q^{49} -7.62978 q^{50} -8.03609 q^{51} +21.9521 q^{52} -4.84904 q^{53} -15.1657 q^{54} +7.85548 q^{55} +2.49795 q^{56} -0.394438 q^{57} -16.2799 q^{58} +9.79339 q^{59} -21.8058 q^{60} +6.77090 q^{61} -8.18743 q^{62} +0.226858 q^{63} +21.2239 q^{64} +11.7179 q^{65} +11.2216 q^{66} +2.80376 q^{67} +28.3642 q^{68} -4.82187 q^{69} +2.15552 q^{70} +0.744457 q^{71} +6.92188 q^{72} +3.42551 q^{73} -16.9576 q^{74} -4.21158 q^{75} +1.39221 q^{76} -0.802997 q^{77} +16.7391 q^{78} +7.92259 q^{79} +36.4141 q^{80} -5.99279 q^{81} +24.8364 q^{82} +6.43668 q^{83} +2.22901 q^{84} +15.1407 q^{85} -9.13463 q^{86} -8.98640 q^{87} -24.5011 q^{88} -6.10051 q^{89} +5.97302 q^{90} -1.19782 q^{91} +17.0193 q^{92} -4.51940 q^{93} -2.20387 q^{94} +0.743154 q^{95} +26.0775 q^{96} +3.75807 q^{97} +18.6196 q^{98} -2.22513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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