LMFDB - Embedded newform 4011.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43265 q^{2} -1.00000 q^{3} +3.91781 q^{4} +2.62505 q^{5} +2.43265 q^{6} -1.00000 q^{7} -4.66537 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.43265 q^{2} -1.00000 q^{3} +3.91781 q^{4} +2.62505 q^{5} +2.43265 q^{6} -1.00000 q^{7} -4.66537 q^{8} +1.00000 q^{9} -6.38585 q^{10} +1.51843 q^{11} -3.91781 q^{12} +1.98499 q^{13} +2.43265 q^{14} -2.62505 q^{15} +3.51361 q^{16} +7.90506 q^{17} -2.43265 q^{18} +4.57675 q^{19} +10.2845 q^{20} +1.00000 q^{21} -3.69381 q^{22} -0.139284 q^{23} +4.66537 q^{24} +1.89091 q^{25} -4.82879 q^{26} -1.00000 q^{27} -3.91781 q^{28} +2.55748 q^{29} +6.38585 q^{30} +9.18022 q^{31} +0.783327 q^{32} -1.51843 q^{33} -19.2303 q^{34} -2.62505 q^{35} +3.91781 q^{36} -4.66028 q^{37} -11.1336 q^{38} -1.98499 q^{39} -12.2468 q^{40} -4.07600 q^{41} -2.43265 q^{42} +10.0844 q^{43} +5.94891 q^{44} +2.62505 q^{45} +0.338829 q^{46} +1.84268 q^{47} -3.51361 q^{48} +1.00000 q^{49} -4.59993 q^{50} -7.90506 q^{51} +7.77680 q^{52} -6.21470 q^{53} +2.43265 q^{54} +3.98595 q^{55} +4.66537 q^{56} -4.57675 q^{57} -6.22147 q^{58} -9.34253 q^{59} -10.2845 q^{60} +13.8815 q^{61} -22.3323 q^{62} -1.00000 q^{63} -8.93279 q^{64} +5.21070 q^{65} +3.69381 q^{66} +1.59891 q^{67} +30.9705 q^{68} +0.139284 q^{69} +6.38585 q^{70} +1.24462 q^{71} -4.66537 q^{72} +5.03666 q^{73} +11.3369 q^{74} -1.89091 q^{75} +17.9308 q^{76} -1.51843 q^{77} +4.82879 q^{78} -0.556046 q^{79} +9.22343 q^{80} +1.00000 q^{81} +9.91549 q^{82} -9.10581 q^{83} +3.91781 q^{84} +20.7512 q^{85} -24.5319 q^{86} -2.55748 q^{87} -7.08402 q^{88} +11.7232 q^{89} -6.38585 q^{90} -1.98499 q^{91} -0.545686 q^{92} -9.18022 q^{93} -4.48260 q^{94} +12.0142 q^{95} -0.783327 q^{96} +8.59339 q^{97} -2.43265 q^{98} +1.51843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	−2.43265	−1.72015	−0.860073	−	0.510170i	$-0.829582\pi$
$2$	−2.43265	−1.72015	−0.860073	+	0.510170i	$0.829582\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.91781	1.95890
$5$	2.62505	1.17396	0.586980	−	0.809601i	$-0.300317\pi$
$5$	2.62505	1.17396	0.586980	+	0.809601i	$0.300317\pi$
$6$	2.43265	0.993127
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.66537	−1.64946
$9$	1.00000	0.333333
$10$	−6.38585	−2.01938
$11$	1.51843	0.457823	0.228911	−	0.973447i	$-0.426483\pi$
$11$	1.51843	0.457823	0.228911	+	0.973447i	$0.426483\pi$
$12$	−3.91781	−1.13097
$13$	1.98499	0.550536	0.275268	−	0.961368i	$-0.411233\pi$
$13$	1.98499	0.550536	0.275268	+	0.961368i	$0.411233\pi$
$14$	2.43265	0.650154
$15$	−2.62505	−0.677786
$16$	3.51361	0.878404
$17$	7.90506	1.91726	0.958629	−	0.284657i	$-0.0918797\pi$
$17$	7.90506	1.91726	0.958629	+	0.284657i	$0.0918797\pi$
$18$	−2.43265	−0.573382
$19$	4.57675	1.04998	0.524989	−	0.851109i	$-0.324069\pi$
$19$	4.57675	1.04998	0.524989	+	0.851109i	$0.324069\pi$
$20$	10.2845	2.29968
$21$	1.00000	0.218218
$22$	−3.69381	−0.787523
$23$	−0.139284	−0.0290426	−0.0145213	−	0.999895i	$-0.504622\pi$
$23$	−0.139284	−0.0290426	−0.0145213	+	0.999895i	$0.504622\pi$
$24$	4.66537	0.952315
$25$	1.89091	0.378182
$26$	−4.82879	−0.947003
$27$	−1.00000	−0.192450
$28$	−3.91781	−0.740396
$29$	2.55748	0.474913	0.237456	−	0.971398i	$-0.423686\pi$
$29$	2.55748	0.474913	0.237456	+	0.971398i	$0.423686\pi$
$30$	6.38585	1.16589
$31$	9.18022	1.64882	0.824408	−	0.565996i	$-0.191508\pi$
$31$	9.18022	1.64882	0.824408	+	0.565996i	$0.191508\pi$
$32$	0.783327	0.138474
$33$	−1.51843	−0.264324
$34$	−19.2303	−3.29797
$35$	−2.62505	−0.443715
$36$	3.91781	0.652968
$37$	−4.66028	−0.766145	−0.383073	−	0.923718i	$-0.625134\pi$
$37$	−4.66028	−0.766145	−0.383073	+	0.923718i	$0.625134\pi$
$38$	−11.1336	−1.80612
$39$	−1.98499	−0.317852
$40$	−12.2468	−1.93640
$41$	−4.07600	−0.636564	−0.318282	−	0.947996i	$-0.603106\pi$
$41$	−4.07600	−0.636564	−0.318282	+	0.947996i	$0.603106\pi$
$42$	−2.43265	−0.375367
$43$	10.0844	1.53786	0.768929	−	0.639334i	$-0.220790\pi$
$43$	10.0844	1.53786	0.768929	+	0.639334i	$0.220790\pi$
$44$	5.94891	0.896832
$45$	2.62505	0.391320
$46$	0.338829	0.0499576
$47$	1.84268	0.268782	0.134391	−	0.990928i	$-0.457092\pi$
$47$	1.84268	0.268782	0.134391	+	0.990928i	$0.457092\pi$
$48$	−3.51361	−0.507147
$49$	1.00000	0.142857
$50$	−4.59993	−0.650528
$51$	−7.90506	−1.10693
$52$	7.77680	1.07845
$53$	−6.21470	−0.853655	−0.426828	−	0.904333i	$-0.640369\pi$
$53$	−6.21470	−0.853655	−0.426828	+	0.904333i	$0.640369\pi$
$54$	2.43265	0.331042
$55$	3.98595	0.537466
$56$	4.66537	0.623436
$57$	−4.57675	−0.606205
$58$	−6.22147	−0.816920
$59$	−9.34253	−1.21629	−0.608147	−	0.793824i	$-0.708087\pi$
$59$	−9.34253	−1.21629	−0.608147	+	0.793824i	$0.708087\pi$
$60$	−10.2845	−1.32772
$61$	13.8815	1.77735	0.888675	−	0.458538i	$-0.151627\pi$
$61$	13.8815	1.77735	0.888675	+	0.458538i	$0.151627\pi$
$62$	−22.3323	−2.83620
$63$	−1.00000	−0.125988
$64$	−8.93279	−1.11660
$65$	5.21070	0.646307
$66$	3.69381	0.454676
$67$	1.59891	0.195339	0.0976693	−	0.995219i	$-0.468861\pi$
$67$	1.59891	0.195339	0.0976693	+	0.995219i	$0.468861\pi$
$68$	30.9705	3.75573
$69$	0.139284	0.0167678
$70$	6.38585	0.763255
$71$	1.24462	0.147709	0.0738546	−	0.997269i	$-0.476470\pi$
$71$	1.24462	0.147709	0.0738546	+	0.997269i	$0.476470\pi$
$72$	−4.66537	−0.549819
$73$	5.03666	0.589497	0.294749	−	0.955575i	$-0.404764\pi$
$73$	5.03666	0.589497	0.294749	+	0.955575i	$0.404764\pi$
$74$	11.3369	1.31788
$75$	−1.89091	−0.218343
$76$	17.9308	2.05681
$77$	−1.51843	−0.173041
$78$	4.82879	0.546752
$79$	−0.556046	−0.0625601	−0.0312800	−	0.999511i	$-0.509958\pi$
$79$	−0.556046	−0.0625601	−0.0312800	+	0.999511i	$0.509958\pi$
$80$	9.22343	1.03121
$81$	1.00000	0.111111
$82$	9.91549	1.09498
$83$	−9.10581	−0.999493	−0.499746	−	0.866172i	$-0.666573\pi$
$83$	−9.10581	−0.999493	−0.499746	+	0.866172i	$0.666573\pi$
$84$	3.91781	0.427468
$85$	20.7512	2.25079
$86$	−24.5319	−2.64534
$87$	−2.55748	−0.274191
$88$	−7.08402	−0.755159
$89$	11.7232	1.24266	0.621331	−	0.783548i	$-0.286592\pi$
$89$	11.7232	1.24266	0.621331	+	0.783548i	$0.286592\pi$
$90$	−6.38585	−0.673128
$91$	−1.98499	−0.208083
$92$	−0.545686	−0.0568917
$93$	−9.18022	−0.951944
$94$	−4.48260	−0.462345
$95$	12.0142	1.23263
$96$	−0.783327	−0.0799480
$97$	8.59339	0.872527	0.436263	−	0.899819i	$-0.356302\pi$
$97$	8.59339	0.872527	0.436263	+	0.899819i	$0.356302\pi$
$98$	−2.43265	−0.245735
$99$	1.51843	0.152608
$100$	7.40822	0.740822
$101$	−1.15323	−0.114751	−0.0573755	−	0.998353i	$-0.518273\pi$
$101$	−1.15323	−0.114751	−0.0573755	+	0.998353i	$0.518273\pi$
$102$	19.2303	1.90408
$103$	−2.91095	−0.286825	−0.143412	−	0.989663i	$-0.545808\pi$
$103$	−2.91095	−0.286825	−0.143412	+	0.989663i	$0.545808\pi$
$104$	−9.26070	−0.908086
$105$	2.62505	0.256179
$106$	15.1182	1.46841
$107$	−9.59617	−0.927697	−0.463848	−	0.885915i	$-0.653532\pi$
$107$	−9.59617	−0.927697	−0.463848	+	0.885915i	$0.653532\pi$
$108$	−3.91781	−0.376991
$109$	12.7182	1.21818	0.609090	−	0.793101i	$-0.291535\pi$
$109$	12.7182	1.21818	0.609090	+	0.793101i	$0.291535\pi$
$110$	−9.69645	−0.924520
$111$	4.66028	0.442334
$112$	−3.51361	−0.332005
$113$	10.6701	1.00376	0.501879	−	0.864938i	$-0.332642\pi$
$113$	10.6701	1.00376	0.501879	+	0.864938i	$0.332642\pi$
$114$	11.1336	1.04276
$115$	−0.365627	−0.0340949
$116$	10.0197	0.930309
$117$	1.98499	0.183512
$118$	22.7272	2.09220
$119$	−7.90506	−0.724656
$120$	12.2468	1.11798
$121$	−8.69438	−0.790398
$122$	−33.7690	−3.05730
$123$	4.07600	0.367520
$124$	35.9663	3.22987
$125$	−8.16153	−0.729990
$126$	2.43265	0.216718
$127$	−21.9832	−1.95070	−0.975348	−	0.220673i	$-0.929175\pi$
$127$	−21.9832	−1.95070	−0.975348	+	0.220673i	$0.929175\pi$
$128$	20.1638	1.78224
$129$	−10.0844	−0.887883
$130$	−12.6758	−1.11174
$131$	2.23782	0.195519	0.0977595	−	0.995210i	$-0.468832\pi$
$131$	2.23782	0.195519	0.0977595	+	0.995210i	$0.468832\pi$
$132$	−5.94891	−0.517786
$133$	−4.57675	−0.396854
$134$	−3.88961	−0.336011
$135$	−2.62505	−0.225929
$136$	−36.8800	−3.16244
$137$	−20.7556	−1.77327	−0.886635	−	0.462469i	$-0.846964\pi$
$137$	−20.7556	−1.77327	−0.886635	+	0.462469i	$0.846964\pi$
$138$	−0.338829	−0.0288430
$139$	22.4273	1.90226	0.951131	−	0.308786i	$-0.0999228\pi$
$139$	22.4273	1.90226	0.951131	+	0.308786i	$0.0999228\pi$
$140$	−10.2845	−0.869196
$141$	−1.84268	−0.155181
$142$	−3.02773	−0.254082
$143$	3.01406	0.252048
$144$	3.51361	0.292801
$145$	6.71353	0.557528
$146$	−12.2525	−1.01402
$147$	−1.00000	−0.0824786
$148$	−18.2581	−1.50081
$149$	1.37833	0.112917	0.0564587	−	0.998405i	$-0.482019\pi$
$149$	1.37833	0.112917	0.0564587	+	0.998405i	$0.482019\pi$
$150$	4.59993	0.375583
$151$	−2.31255	−0.188192	−0.0940961	−	0.995563i	$-0.529996\pi$
$151$	−2.31255	−0.188192	−0.0940961	+	0.995563i	$0.529996\pi$
$152$	−21.3522	−1.73189
$153$	7.90506	0.639086
$154$	3.69381	0.297656
$155$	24.0986	1.93564
$156$	−7.77680	−0.622642
$157$	8.80896	0.703032	0.351516	−	0.936182i	$-0.385666\pi$
$157$	8.80896	0.703032	0.351516	+	0.936182i	$0.385666\pi$
$158$	1.35267	0.107613
$159$	6.21470	0.492858
$160$	2.05628	0.162563
$161$	0.139284	0.0109771
$162$	−2.43265	−0.191127
$163$	−4.84311	−0.379341	−0.189671	−	0.981848i	$-0.560742\pi$
$163$	−4.84311	−0.379341	−0.189671	+	0.981848i	$0.560742\pi$
$164$	−15.9690	−1.24697
$165$	−3.98595	−0.310306
$166$	22.1513	1.71927
$167$	−5.61425	−0.434443	−0.217222	−	0.976122i	$-0.569699\pi$
$167$	−5.61425	−0.434443	−0.217222	+	0.976122i	$0.569699\pi$
$168$	−4.66537	−0.359941
$169$	−9.05983	−0.696910
$170$	−50.4805	−3.87168
$171$	4.57675	0.349993
$172$	39.5088	3.01252
$173$	−11.5682	−0.879515	−0.439758	−	0.898117i	$-0.644936\pi$
$173$	−11.5682	−0.879515	−0.439758	+	0.898117i	$0.644936\pi$
$174$	6.22147	0.471649
$175$	−1.89091	−0.142939
$176$	5.33517	0.402153
$177$	9.34253	0.702228
$178$	−28.5186	−2.13756
$179$	−19.4962	−1.45722	−0.728609	−	0.684930i	$-0.759833\pi$
$179$	−19.4962	−1.45722	−0.728609	+	0.684930i	$0.759833\pi$
$180$	10.2845	0.766559
$181$	−3.74976	−0.278717	−0.139359	−	0.990242i	$-0.544504\pi$
$181$	−3.74976	−0.278717	−0.139359	+	0.990242i	$0.544504\pi$
$182$	4.82879	0.357933
$183$	−13.8815	−1.02615
$184$	0.649809	0.0479046
$185$	−12.2335	−0.899424
$186$	22.3323	1.63748
$187$	12.0033	0.877765
$188$	7.21926	0.526519
$189$	1.00000	0.0727393
$190$	−29.2264	−2.12031
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	8.93279	0.644669
$193$	−14.0721	−1.01293	−0.506466	−	0.862260i	$-0.669048\pi$
$193$	−14.0721	−1.01293	−0.506466	+	0.862260i	$0.669048\pi$
$194$	−20.9048	−1.50087
$195$	−5.21070	−0.373146
$196$	3.91781	0.279844
$197$	−21.9079	−1.56088	−0.780438	−	0.625234i	$-0.785004\pi$
$197$	−21.9079	−1.56088	−0.780438	+	0.625234i	$0.785004\pi$
$198$	−3.69381	−0.262508
$199$	−14.3854	−1.01975	−0.509876	−	0.860248i	$-0.670309\pi$
$199$	−14.3854	−1.01975	−0.509876	+	0.860248i	$0.670309\pi$
$200$	−8.82179	−0.623795
$201$	−1.59891	−0.112779
$202$	2.80542	0.197388
$203$	−2.55748	−0.179500
$204$	−30.9705	−2.16837
$205$	−10.6997	−0.747300
$206$	7.08135	0.493381
$207$	−0.139284	−0.00968088
$208$	6.97448	0.483593
$209$	6.94945	0.480704
$210$	−6.38585	−0.440666
$211$	−26.4869	−1.82344	−0.911718	−	0.410816i	$-0.865244\pi$
$211$	−26.4869	−1.82344	−0.911718	+	0.410816i	$0.865244\pi$
$212$	−24.3480	−1.67223
$213$	−1.24462	−0.0852800
$214$	23.3442	1.59577
$215$	26.4721	1.80538
$216$	4.66537	0.317438
$217$	−9.18022	−0.623194
$218$	−30.9389	−2.09545
$219$	−5.03666	−0.340346
$220$	15.6162	1.05284
$221$	15.6914	1.05552
$222$	−11.3369	−0.760880
$223$	−26.4017	−1.76799	−0.883996	−	0.467495i	$-0.845157\pi$
$223$	−26.4017	−1.76799	−0.883996	+	0.467495i	$0.845157\pi$
$224$	−0.783327	−0.0523382
$225$	1.89091	0.126061
$226$	−25.9566	−1.72661
$227$	6.38419	0.423733	0.211867	−	0.977299i	$-0.432046\pi$
$227$	6.38419	0.423733	0.211867	+	0.977299i	$0.432046\pi$
$228$	−17.9308	−1.18750
$229$	26.0092	1.71874	0.859369	−	0.511357i	$-0.170857\pi$
$229$	26.0092	1.71874	0.859369	+	0.511357i	$0.170857\pi$
$230$	0.889444	0.0586482
$231$	1.51843	0.0999051
$232$	−11.9316	−0.783348
$233$	−19.5941	−1.28365	−0.641826	−	0.766851i	$-0.721823\pi$
$233$	−19.5941	−1.28365	−0.641826	+	0.766851i	$0.721823\pi$
$234$	−4.82879	−0.315668
$235$	4.83713	0.315539
$236$	−36.6023	−2.38260
$237$	0.556046	0.0361191
$238$	19.2303	1.24651
$239$	2.33421	0.150987	0.0754937	−	0.997146i	$-0.475947\pi$
$239$	2.33421	0.150987	0.0754937	+	0.997146i	$0.475947\pi$
$240$	−9.22343	−0.595370
$241$	22.2299	1.43196	0.715978	−	0.698123i	$-0.245981\pi$
$241$	22.2299	1.43196	0.715978	+	0.698123i	$0.245981\pi$
$242$	21.1504	1.35960
$243$	−1.00000	−0.0641500
$244$	54.3853	3.48166
$245$	2.62505	0.167709
$246$	−9.91549	−0.632189
$247$	9.08478	0.578051
$248$	−42.8291	−2.71965
$249$	9.10581	0.577057
$250$	19.8542	1.25569
$251$	29.9861	1.89271	0.946354	−	0.323132i	$-0.104736\pi$
$251$	29.9861	1.89271	0.946354	+	0.323132i	$0.104736\pi$
$252$	−3.91781	−0.246799
$253$	−0.211492	−0.0132964
$254$	53.4776	3.35548
$255$	−20.7512	−1.29949
$256$	−31.1859	−1.94912
$257$	−11.0810	−0.691213	−0.345607	−	0.938380i	$-0.612327\pi$
$257$	−11.0810	−0.691213	−0.345607	+	0.938380i	$0.612327\pi$
$258$	24.5319	1.52729
$259$	4.66028	0.289576
$260$	20.4145	1.26605
$261$	2.55748	0.158304
$262$	−5.44384	−0.336321
$263$	1.68799	0.104086	0.0520431	−	0.998645i	$-0.483427\pi$
$263$	1.68799	0.104086	0.0520431	+	0.998645i	$0.483427\pi$
$264$	7.08402	0.435991
$265$	−16.3139	−1.00216
$266$	11.1336	0.682648
$267$	−11.7232	−0.717451
$268$	6.26424	0.382650
$269$	13.7884	0.840696	0.420348	−	0.907363i	$-0.361908\pi$
$269$	13.7884	0.840696	0.420348	+	0.907363i	$0.361908\pi$
$270$	6.38585	0.388631
$271$	10.4535	0.635002	0.317501	−	0.948258i	$-0.397156\pi$
$271$	10.4535	0.635002	0.317501	+	0.948258i	$0.397156\pi$
$272$	27.7753	1.68413
$273$	1.98499	0.120137
$274$	50.4912	3.05029
$275$	2.87121	0.173140
$276$	0.545686	0.0328465
$277$	21.2841	1.27884	0.639419	−	0.768858i	$-0.279175\pi$
$277$	21.2841	1.27884	0.639419	+	0.768858i	$0.279175\pi$
$278$	−54.5580	−3.27217
$279$	9.18022	0.549605
$280$	12.2468	0.731889
$281$	23.8142	1.42063	0.710317	−	0.703882i	$-0.248552\pi$
$281$	23.8142	1.42063	0.710317	+	0.703882i	$0.248552\pi$
$282$	4.48260	0.266935
$283$	−13.7658	−0.818292	−0.409146	−	0.912469i	$-0.634173\pi$
$283$	−13.7658	−0.818292	−0.409146	+	0.912469i	$0.634173\pi$
$284$	4.87619	0.289348
$285$	−12.0142	−0.711660
$286$	−7.33216	−0.433560
$287$	4.07600	0.240598
$288$	0.783327	0.0461580
$289$	45.4900	2.67588
$290$	−16.3317	−0.959031
$291$	−8.59339	−0.503754
$292$	19.7327	1.15477
$293$	−16.8549	−0.984673	−0.492337	−	0.870405i	$-0.663857\pi$
$293$	−16.8549	−0.984673	−0.492337	+	0.870405i	$0.663857\pi$
$294$	2.43265	0.141875
$295$	−24.5246	−1.42788
$296$	21.7419	1.26372
$297$	−1.51843	−0.0881081
$298$	−3.35301	−0.194234
$299$	−0.276476	−0.0159890
$300$	−7.40822	−0.427714
$301$	−10.0844	−0.581256
$302$	5.62563	0.323718
$303$	1.15323	0.0662515
$304$	16.0809	0.922304
$305$	36.4398	2.08654
$306$	−19.2303	−1.09932
$307$	−27.4323	−1.56564	−0.782821	−	0.622247i	$-0.786220\pi$
$307$	−27.4323	−1.56564	−0.782821	+	0.622247i	$0.786220\pi$
$308$	−5.94891	−0.338970
$309$	2.91095	0.165598
$310$	−58.6235	−3.32959
$311$	−26.7482	−1.51675	−0.758376	−	0.651817i	$-0.774007\pi$
$311$	−26.7482	−1.51675	−0.758376	+	0.651817i	$0.774007\pi$
$312$	9.26070	0.524284
$313$	16.2904	0.920787	0.460394	−	0.887715i	$-0.347708\pi$
$313$	16.2904	0.920787	0.460394	+	0.887715i	$0.347708\pi$
$314$	−21.4292	−1.20932
$315$	−2.62505	−0.147905
$316$	−2.17848	−0.122549
$317$	15.7275	0.883346	0.441673	−	0.897176i	$-0.354385\pi$
$317$	15.7275	0.883346	0.441673	+	0.897176i	$0.354385\pi$
$318$	−15.1182	−0.847788
$319$	3.88335	0.217426
$320$	−23.4491	−1.31084
$321$	9.59617	0.535606
$322$	−0.338829	−0.0188822
$323$	36.1795	2.01308
$324$	3.91781	0.217656
$325$	3.75343	0.208203
$326$	11.7816	0.652523
$327$	−12.7182	−0.703317
$328$	19.0160	1.04998
$329$	−1.84268	−0.101590
$330$	9.69645	0.533772
$331$	−3.51226	−0.193051	−0.0965256	−	0.995331i	$-0.530773\pi$
$331$	−3.51226	−0.193051	−0.0965256	+	0.995331i	$0.530773\pi$
$332$	−35.6748	−1.95791
$333$	−4.66028	−0.255382
$334$	13.6575	0.747306
$335$	4.19724	0.229320
$336$	3.51361	0.191683
$337$	26.5009	1.44360	0.721798	−	0.692103i	$-0.243316\pi$
$337$	26.5009	1.44360	0.721798	+	0.692103i	$0.243316\pi$
$338$	22.0394	1.19879
$339$	−10.6701	−0.579520
$340$	81.2993	4.40907
$341$	13.9395	0.754866
$342$	−11.1336	−0.602039
$343$	−1.00000	−0.0539949
$344$	−47.0475	−2.53663
$345$	0.365627	0.0196847
$346$	28.1415	1.51289
$347$	−35.2280	−1.89114	−0.945569	−	0.325421i	$-0.894494\pi$
$347$	−35.2280	−1.89114	−0.945569	+	0.325421i	$0.894494\pi$
$348$	−10.0197	−0.537114
$349$	11.9758	0.641047	0.320524	−	0.947241i	$-0.396141\pi$
$349$	11.9758	0.641047	0.320524	+	0.947241i	$0.396141\pi$
$350$	4.59993	0.245877
$351$	−1.98499	−0.105951
$352$	1.18942	0.0633965
$353$	−4.63523	−0.246708	−0.123354	−	0.992363i	$-0.539365\pi$
$353$	−4.63523	−0.246708	−0.123354	+	0.992363i	$0.539365\pi$
$354$	−22.7272	−1.20793
$355$	3.26720	0.173405
$356$	45.9294	2.43426
$357$	7.90506	0.418380
$358$	47.4276	2.50663
$359$	−30.2968	−1.59900	−0.799501	−	0.600665i	$-0.794903\pi$
$359$	−30.2968	−1.59900	−0.799501	+	0.600665i	$0.794903\pi$
$360$	−12.2468	−0.645466
$361$	1.94661	0.102453
$362$	9.12187	0.479435
$363$	8.69438	0.456337
$364$	−7.77680	−0.407615
$365$	13.2215	0.692046
$366$	33.7690	1.76513
$367$	20.2652	1.05783	0.528917	−	0.848674i	$-0.322598\pi$
$367$	20.2652	1.05783	0.528917	+	0.848674i	$0.322598\pi$
$368$	−0.489389	−0.0255112
$369$	−4.07600	−0.212188
$370$	29.7599	1.54714
$371$	6.21470	0.322651
$372$	−35.9663	−1.86477
$373$	11.3900	0.589752	0.294876	−	0.955536i	$-0.404722\pi$
$373$	11.3900	0.589752	0.294876	+	0.955536i	$0.404722\pi$
$374$	−29.1998	−1.50988
$375$	8.16153	0.421460
$376$	−8.59677	−0.443345
$377$	5.07657	0.261457
$378$	−2.43265	−0.125122
$379$	−11.3941	−0.585275	−0.292637	−	0.956223i	$-0.594533\pi$
$379$	−11.3941	−0.585275	−0.292637	+	0.956223i	$0.594533\pi$
$380$	47.0694	2.41461
$381$	21.9832	1.12623
$382$	−2.43265	−0.124465
$383$	30.2283	1.54460	0.772298	−	0.635260i	$-0.219107\pi$
$383$	30.2283	1.54460	0.772298	+	0.635260i	$0.219107\pi$
$384$	−20.1638	−1.02898
$385$	−3.98595	−0.203143
$386$	34.2325	1.74239
$387$	10.0844	0.512619
$388$	33.6673	1.70920
$389$	8.17074	0.414273	0.207136	−	0.978312i	$-0.433586\pi$
$389$	8.17074	0.414273	0.207136	+	0.978312i	$0.433586\pi$
$390$	12.6758	0.641865
$391$	−1.10104	−0.0556822
$392$	−4.66537	−0.235637
$393$	−2.23782	−0.112883
$394$	53.2944	2.68493
$395$	−1.45965	−0.0734430
$396$	5.94891	0.298944
$397$	36.7281	1.84333	0.921666	−	0.387985i	$-0.126829\pi$
$397$	36.7281	1.84333	0.921666	+	0.387985i	$0.126829\pi$
$398$	34.9946	1.75412
$399$	4.57675	0.229124
$400$	6.64393	0.332196
$401$	32.1320	1.60459	0.802297	−	0.596925i	$-0.203611\pi$
$401$	32.1320	1.60459	0.802297	+	0.596925i	$0.203611\pi$
$402$	3.88961	0.193996
$403$	18.2226	0.907733
$404$	−4.51815	−0.224786
$405$	2.62505	0.130440
$406$	6.22147	0.308767
$407$	−7.07629	−0.350759
$408$	36.8800	1.82583
$409$	−9.96762	−0.492867	−0.246433	−	0.969160i	$-0.579259\pi$
$409$	−9.96762	−0.492867	−0.246433	+	0.969160i	$0.579259\pi$
$410$	26.0287	1.28547
$411$	20.7556	1.02380
$412$	−11.4046	−0.561862
$413$	9.34253	0.459716
$414$	0.338829	0.0166525
$415$	−23.9032	−1.17336
$416$	1.55489	0.0762349
$417$	−22.4273	−1.09827
$418$	−16.9056	−0.826881
$419$	−22.7684	−1.11231	−0.556155	−	0.831078i	$-0.687724\pi$
$419$	−22.7684	−1.11231	−0.556155	+	0.831078i	$0.687724\pi$
$420$	10.2845	0.501830
$421$	−16.1754	−0.788339	−0.394169	−	0.919038i	$-0.628968\pi$
$421$	−16.1754	−0.788339	−0.394169	+	0.919038i	$0.628968\pi$
$422$	64.4336	3.13658
$423$	1.84268	0.0895940
$424$	28.9939	1.40807
$425$	14.9478	0.725073
$426$	3.02773	0.146694
$427$	−13.8815	−0.671775
$428$	−37.5960	−1.81727
$429$	−3.01406	−0.145520
$430$	−64.3975	−3.10552
$431$	−17.1445	−0.825824	−0.412912	−	0.910771i	$-0.635488\pi$
$431$	−17.1445	−0.825824	−0.412912	+	0.910771i	$0.635488\pi$
$432$	−3.51361	−0.169049
$433$	−9.09579	−0.437116	−0.218558	−	0.975824i	$-0.570135\pi$
$433$	−9.09579	−0.437116	−0.218558	+	0.975824i	$0.570135\pi$
$434$	22.3323	1.07198
$435$	−6.71353	−0.321889
$436$	49.8274	2.38630
$437$	−0.637466	−0.0304941
$438$	12.2525	0.585446
$439$	−1.70448	−0.0813505	−0.0406752	−	0.999172i	$-0.512951\pi$
$439$	−1.70448	−0.0813505	−0.0406752	+	0.999172i	$0.512951\pi$
$440$	−18.5959	−0.886527
$441$	1.00000	0.0476190
$442$	−38.1719	−1.81565
$443$	30.8075	1.46371	0.731853	−	0.681462i	$-0.238656\pi$
$443$	30.8075	1.46371	0.731853	+	0.681462i	$0.238656\pi$
$444$	18.2581	0.866491
$445$	30.7742	1.45883
$446$	64.2263	3.04121
$447$	−1.37833	−0.0651929
$448$	8.93279	0.422035
$449$	18.8179	0.888073	0.444036	−	0.896009i	$-0.353546\pi$
$449$	18.8179	0.888073	0.444036	+	0.896009i	$0.353546\pi$
$450$	−4.59993	−0.216843
$451$	−6.18910	−0.291433
$452$	41.8034	1.96627
$453$	2.31255	0.108653
$454$	−15.5305	−0.728884
$455$	−5.21070	−0.244281
$456$	21.3522	0.999909
$457$	36.9318	1.72760	0.863798	−	0.503838i	$-0.168079\pi$
$457$	36.9318	1.72760	0.863798	+	0.503838i	$0.168079\pi$
$458$	−63.2714	−2.95648
$459$	−7.90506	−0.368977
$460$	−1.43246	−0.0667886
$461$	22.0000	1.02464	0.512322	−	0.858794i	$-0.328785\pi$
$461$	22.0000	1.02464	0.512322	+	0.858794i	$0.328785\pi$
$462$	−3.69381	−0.171852
$463$	−8.61994	−0.400602	−0.200301	−	0.979734i	$-0.564192\pi$
$463$	−8.61994	−0.400602	−0.200301	+	0.979734i	$0.564192\pi$
$464$	8.98601	0.417165
$465$	−24.0986	−1.11754
$466$	47.6656	2.20807
$467$	3.92294	0.181532	0.0907661	−	0.995872i	$-0.471068\pi$
$467$	3.92294	0.181532	0.0907661	+	0.995872i	$0.471068\pi$
$468$	7.77680	0.359483
$469$	−1.59891	−0.0738310
$470$	−11.7671	−0.542774
$471$	−8.80896	−0.405896
$472$	43.5864	2.00622
$473$	15.3124	0.704066
$474$	−1.35267	−0.0621301
$475$	8.65421	0.397083
$476$	−30.9705	−1.41953
$477$	−6.21470	−0.284552
$478$	−5.67833	−0.259721
$479$	8.38666	0.383196	0.191598	−	0.981473i	$-0.438633\pi$
$479$	8.38666	0.383196	0.191598	+	0.981473i	$0.438633\pi$
$480$	−2.05628	−0.0938557
$481$	−9.25059	−0.421791
$482$	−54.0778	−2.46318
$483$	−0.139284	−0.00633762
$484$	−34.0629	−1.54831
$485$	22.5581	1.02431
$486$	2.43265	0.110347
$487$	−14.1909	−0.643053	−0.321526	−	0.946901i	$-0.604196\pi$
$487$	−14.1909	−0.643053	−0.321526	+	0.946901i	$0.604196\pi$
$488$	−64.7625	−2.93166
$489$	4.84311	0.219013
$490$	−6.38585	−0.288483
$491$	−19.2938	−0.870717	−0.435358	−	0.900257i	$-0.643378\pi$
$491$	−19.2938	−0.870717	−0.435358	+	0.900257i	$0.643378\pi$
$492$	15.9690	0.719937
$493$	20.2171	0.910531
$494$	−22.1001	−0.994332
$495$	3.98595	0.179155
$496$	32.2557	1.44833
$497$	−1.24462	−0.0558289
$498$	−22.1513	−0.992623
$499$	18.5240	0.829248	0.414624	−	0.909993i	$-0.363913\pi$
$499$	18.5240	0.829248	0.414624	+	0.909993i	$0.363913\pi$
$500$	−31.9753	−1.42998
$501$	5.61425	0.250826
$502$	−72.9459	−3.25574
$503$	4.60549	0.205349	0.102674	−	0.994715i	$-0.467260\pi$
$503$	4.60549	0.205349	0.102674	+	0.994715i	$0.467260\pi$
$504$	4.66537	0.207812
$505$	−3.02730	−0.134713
$506$	0.514487	0.0228717
$507$	9.05983	0.402361
$508$	−86.1261	−3.82123
$509$	−4.70062	−0.208352	−0.104176	−	0.994559i	$-0.533220\pi$
$509$	−4.70062	−0.208352	−0.104176	+	0.994559i	$0.533220\pi$
$510$	50.4805	2.23532
$511$	−5.03666	−0.222809
$512$	35.5369	1.57053
$513$	−4.57675	−0.202068
$514$	26.9562	1.18899
$515$	−7.64141	−0.336721
$516$	−39.5088	−1.73928
$517$	2.79797	0.123055
$518$	−11.3369	−0.498113
$519$	11.5682	0.507788
$520$	−24.3098	−1.06606
$521$	−20.4912	−0.897734	−0.448867	−	0.893599i	$-0.648172\pi$
$521$	−20.4912	−0.897734	−0.448867	+	0.893599i	$0.648172\pi$
$522$	−6.22147	−0.272307
$523$	14.0484	0.614295	0.307148	−	0.951662i	$-0.400626\pi$
$523$	14.0484	0.614295	0.307148	+	0.951662i	$0.400626\pi$
$524$	8.76734	0.383003
$525$	1.89091	0.0825261
$526$	−4.10631	−0.179043
$527$	72.5702	3.16121
$528$	−5.33517	−0.232183
$529$	−22.9806	−0.999157
$530$	39.6862	1.72386
$531$	−9.34253	−0.405431
$532$	−17.9308	−0.777400
$533$	−8.09080	−0.350451
$534$	28.5186	1.23412
$535$	−25.1905	−1.08908
$536$	−7.45953	−0.322203
$537$	19.4962	0.841325
$538$	−33.5425	−1.44612
$539$	1.51843	0.0654033
$540$	−10.2845	−0.442573
$541$	3.27584	0.140839	0.0704197	−	0.997517i	$-0.477566\pi$
$541$	3.27584	0.140839	0.0704197	+	0.997517i	$0.477566\pi$
$542$	−25.4297	−1.09230
$543$	3.74976	0.160918
$544$	6.19225	0.265490
$545$	33.3859	1.43009
$546$	−4.82879	−0.206653
$547$	8.44756	0.361192	0.180596	−	0.983557i	$-0.442197\pi$
$547$	8.44756	0.361192	0.180596	+	0.983557i	$0.442197\pi$
$548$	−81.3165	−3.47367
$549$	13.8815	0.592450
$550$	−6.98466	−0.297827
$551$	11.7050	0.498648
$552$	−0.649809	−0.0276577
$553$	0.556046	0.0236455
$554$	−51.7769	−2.19979
$555$	12.2335	0.519283
$556$	87.8661	3.72635
$557$	−13.9633	−0.591642	−0.295821	−	0.955243i	$-0.595593\pi$
$557$	−13.9633	−0.591642	−0.295821	+	0.955243i	$0.595593\pi$
$558$	−22.3323	−0.945402
$559$	20.0174	0.846646
$560$	−9.22343	−0.389761
$561$	−12.0033	−0.506778
$562$	−57.9316	−2.44370
$563$	−40.7885	−1.71903	−0.859515	−	0.511111i	$-0.829234\pi$
$563$	−40.7885	−1.71903	−0.859515	+	0.511111i	$0.829234\pi$
$564$	−7.21926	−0.303986
$565$	28.0096	1.17837
$566$	33.4874	1.40758
$567$	−1.00000	−0.0419961
$568$	−5.80662	−0.243640
$569$	22.8653	0.958565	0.479282	−	0.877661i	$-0.340897\pi$
$569$	22.8653	0.958565	0.479282	+	0.877661i	$0.340897\pi$
$570$	29.2264	1.22416
$571$	7.67949	0.321377	0.160688	−	0.987005i	$-0.448629\pi$
$571$	7.67949	0.321377	0.160688	+	0.987005i	$0.448629\pi$
$572$	11.8085	0.493738
$573$	−1.00000	−0.0417756
$574$	−9.91549	−0.413865
$575$	−0.263373	−0.0109834
$576$	−8.93279	−0.372200
$577$	3.82347	0.159173	0.0795865	−	0.996828i	$-0.474640\pi$
$577$	3.82347	0.159173	0.0795865	+	0.996828i	$0.474640\pi$
$578$	−110.661	−4.60291
$579$	14.0721	0.584816
$580$	26.3023	1.09215
$581$	9.10581	0.377773
$582$	20.9048	0.866530
$583$	−9.43657	−0.390823
$584$	−23.4979	−0.972350
$585$	5.21070	0.215436
$586$	41.0021	1.69378
$587$	−7.92655	−0.327164	−0.163582	−	0.986530i	$-0.552305\pi$
$587$	−7.92655	−0.327164	−0.163582	+	0.986530i	$0.552305\pi$
$588$	−3.91781	−0.161568
$589$	42.0155	1.73122
$590$	59.6600	2.45616
$591$	21.9079	0.901172
$592$	−16.3744	−0.672985
$593$	4.07289	0.167253	0.0836267	−	0.996497i	$-0.473350\pi$
$593$	4.07289	0.167253	0.0836267	+	0.996497i	$0.473350\pi$
$594$	3.69381	0.151559
$595$	−20.7512	−0.850717
$596$	5.40004	0.221194
$597$	14.3854	0.588754
$598$	0.672571	0.0275035
$599$	25.9437	1.06003	0.530015	−	0.847988i	$-0.322186\pi$
$599$	25.9437	1.06003	0.530015	+	0.847988i	$0.322186\pi$
$600$	8.82179	0.360148
$601$	3.00798	0.122698	0.0613490	−	0.998116i	$-0.480460\pi$
$601$	3.00798	0.122698	0.0613490	+	0.998116i	$0.480460\pi$
$602$	24.5319	0.999845
$603$	1.59891	0.0651128
$604$	−9.06011	−0.368651
$605$	−22.8232	−0.927896
$606$	−2.80542	−0.113962
$607$	−31.7868	−1.29019	−0.645093	−	0.764104i	$-0.723181\pi$
$607$	−31.7868	−1.29019	−0.645093	+	0.764104i	$0.723181\pi$
$608$	3.58509	0.145395
$609$	2.55748	0.103634
$610$	−88.6455	−3.58915
$611$	3.65769	0.147974
$612$	30.9705	1.25191
$613$	−16.9918	−0.686292	−0.343146	−	0.939282i	$-0.611492\pi$
$613$	−16.9918	−0.686292	−0.343146	+	0.939282i	$0.611492\pi$
$614$	66.7333	2.69314
$615$	10.6997	0.431454
$616$	7.08402	0.285423
$617$	−19.2031	−0.773089	−0.386545	−	0.922271i	$-0.626331\pi$
$617$	−19.2031	−0.773089	−0.386545	+	0.922271i	$0.626331\pi$
$618$	−7.08135	−0.284853
$619$	3.66223	0.147197	0.0735987	−	0.997288i	$-0.476552\pi$
$619$	3.66223	0.147197	0.0735987	+	0.997288i	$0.476552\pi$
$620$	94.4136	3.79174
$621$	0.139284	0.00558926
$622$	65.0692	2.60904
$623$	−11.7232	−0.469682
$624$	−6.97448	−0.279203
$625$	−30.8790	−1.23516
$626$	−39.6289	−1.58389
$627$	−6.94945	−0.277534
$628$	34.5118	1.37717
$629$	−36.8398	−1.46890
$630$	6.38585	0.254418
$631$	−10.4004	−0.414035	−0.207017	−	0.978337i	$-0.566376\pi$
$631$	−10.4004	−0.414035	−0.207017	+	0.978337i	$0.566376\pi$
$632$	2.59416	0.103190
$633$	26.4869	1.05276
$634$	−38.2596	−1.51948
$635$	−57.7072	−2.29004
$636$	24.3480	0.965462
$637$	1.98499	0.0786480
$638$	−9.44685	−0.374004
$639$	1.24462	0.0492364
$640$	52.9309	2.09228
$641$	36.1913	1.42947	0.714735	−	0.699396i	$-0.246547\pi$
$641$	36.1913	1.42947	0.714735	+	0.699396i	$0.246547\pi$
$642$	−23.3442	−0.921321
$643$	−28.6785	−1.13097	−0.565484	−	0.824759i	$-0.691311\pi$
$643$	−28.6785	−1.13097	−0.565484	+	0.824759i	$0.691311\pi$
$644$	0.545686	0.0215031
$645$	−26.4721	−1.04234
$646$	−88.0121	−3.46279
$647$	13.8354	0.543926	0.271963	−	0.962308i	$-0.412327\pi$
$647$	13.8354	0.543926	0.271963	+	0.962308i	$0.412327\pi$
$648$	−4.66537	−0.183273
$649$	−14.1859	−0.556847
$650$	−9.13080	−0.358139
$651$	9.18022	0.359801
$652$	−18.9744	−0.743094
$653$	−4.96017	−0.194106	−0.0970531	−	0.995279i	$-0.530942\pi$
$653$	−4.96017	−0.194106	−0.0970531	+	0.995279i	$0.530942\pi$
$654$	30.9389	1.20981
$655$	5.87439	0.229531
$656$	−14.3215	−0.559160
$657$	5.03666	0.196499
$658$	4.48260	0.174750
$659$	−10.1359	−0.394839	−0.197420	−	0.980319i	$-0.563256\pi$
$659$	−10.1359	−0.394839	−0.197420	+	0.980319i	$0.563256\pi$
$660$	−15.6162	−0.607860
$661$	18.5483	0.721446	0.360723	−	0.932673i	$-0.382530\pi$
$661$	18.5483	0.721446	0.360723	+	0.932673i	$0.382530\pi$
$662$	8.54411	0.332076
$663$	−15.6914	−0.609405
$664$	42.4820	1.64862
$665$	−12.0142	−0.465891
$666$	11.3369	0.439294
$667$	−0.356215	−0.0137927
$668$	−21.9955	−0.851033
$669$	26.4017	1.02075
$670$	−10.2104	−0.394463
$671$	21.0781	0.813711
$672$	0.783327	0.0302175
$673$	−2.52481	−0.0973243	−0.0486621	−	0.998815i	$-0.515496\pi$
$673$	−2.52481	−0.0973243	−0.0486621	+	0.998815i	$0.515496\pi$
$674$	−64.4676	−2.48320
$675$	−1.89091	−0.0727811
$676$	−35.4947	−1.36518
$677$	13.4027	0.515106	0.257553	−	0.966264i	$-0.417084\pi$
$677$	13.4027	0.515106	0.257553	+	0.966264i	$0.417084\pi$
$678$	25.9566	0.996859
$679$	−8.59339	−0.329784
$680$	−96.8121	−3.71257
$681$	−6.38419	−0.244643
$682$	−33.9100	−1.29848
$683$	31.3941	1.20126	0.600630	−	0.799527i	$-0.294916\pi$
$683$	31.3941	1.20126	0.600630	+	0.799527i	$0.294916\pi$
$684$	17.9308	0.685602
$685$	−54.4846	−2.08175
$686$	2.43265	0.0928792
$687$	−26.0092	−0.992313
$688$	35.4327	1.35086
$689$	−12.3361	−0.469968
$690$	−0.889444	−0.0338606
$691$	33.1874	1.26251	0.631254	−	0.775576i	$-0.282541\pi$
$691$	33.1874	1.26251	0.631254	+	0.775576i	$0.282541\pi$
$692$	−45.3221	−1.72289
$693$	−1.51843	−0.0576803
$694$	85.6976	3.25304
$695$	58.8730	2.23318
$696$	11.9316	0.452266
$697$	−32.2210	−1.22046
$698$	−29.1329	−1.10270
$699$	19.5941	0.741116
$700$	−7.40822	−0.280005
$701$	−24.0661	−0.908963	−0.454481	−	0.890756i	$-0.650175\pi$
$701$	−24.0661	−0.908963	−0.454481	+	0.890756i	$0.650175\pi$
$702$	4.82879	0.182251
$703$	−21.3289	−0.804436
$704$	−13.5638	−0.511205
$705$	−4.83713	−0.182177
$706$	11.2759	0.424375
$707$	1.15323	0.0433718
$708$	36.6023	1.37560
$709$	−17.2887	−0.649292	−0.324646	−	0.945836i	$-0.605245\pi$
$709$	−17.2887	−0.649292	−0.324646	+	0.945836i	$0.605245\pi$
$710$	−7.94796	−0.298282
$711$	−0.556046	−0.0208534
$712$	−54.6933	−2.04972
$713$	−1.27865	−0.0478859
$714$	−19.2303	−0.719675
$715$	7.91206	0.295894
$716$	−76.3826	−2.85455
$717$	−2.33421	−0.0871726
$718$	73.7016	2.75052
$719$	15.6789	0.584724	0.292362	−	0.956308i	$-0.405559\pi$
$719$	15.6789	0.584724	0.292362	+	0.956308i	$0.405559\pi$
$720$	9.22343	0.343737
$721$	2.91095	0.108410
$722$	−4.73543	−0.176235
$723$	−22.2299	−0.826740
$724$	−14.6908	−0.545981
$725$	4.83597	0.179603
$726$	−21.1504	−0.784966
$727$	50.0750	1.85718	0.928590	−	0.371108i	$-0.121022\pi$
$727$	50.0750	1.85718	0.928590	+	0.371108i	$0.121022\pi$
$728$	9.26070	0.343224
$729$	1.00000	0.0370370
$730$	−32.1634	−1.19042
$731$	79.7179	2.94847
$732$	−54.3853	−2.01014
$733$	38.9516	1.43871	0.719355	−	0.694642i	$-0.244437\pi$
$733$	38.9516	1.43871	0.719355	+	0.694642i	$0.244437\pi$
$734$	−49.2982	−1.81963
$735$	−2.62505	−0.0968266
$736$	−0.109105	−0.00402165
$737$	2.42783	0.0894305
$738$	9.91549	0.364994
$739$	−21.9861	−0.808772	−0.404386	−	0.914588i	$-0.632515\pi$
$739$	−21.9861	−0.808772	−0.404386	+	0.914588i	$0.632515\pi$
$740$	−47.9285	−1.76189
$741$	−9.08478	−0.333738
$742$	−15.1182	−0.555008
$743$	8.62261	0.316333	0.158166	−	0.987412i	$-0.449442\pi$
$743$	8.62261	0.316333	0.158166	+	0.987412i	$0.449442\pi$
$744$	42.8291	1.57019
$745$	3.61820	0.132560
$746$	−27.7079	−1.01446
$747$	−9.10581	−0.333164
$748$	47.0265	1.71946
$749$	9.59617	0.350636
$750$	−19.8542	−0.724972
$751$	21.8638	0.797821	0.398911	−	0.916990i	$-0.369388\pi$
$751$	21.8638	0.797821	0.398911	+	0.916990i	$0.369388\pi$
$752$	6.47446	0.236099
$753$	−29.9861	−1.09276
$754$	−12.3495	−0.449744
$755$	−6.07056	−0.220930
$756$	3.91781	0.142489
$757$	10.7749	0.391621	0.195810	−	0.980642i	$-0.437266\pi$
$757$	10.7749	0.391621	0.195810	+	0.980642i	$0.437266\pi$
$758$	27.7179	1.00676
$759$	0.211492	0.00767667
$760$	−56.0507	−2.03317
$761$	21.2796	0.771386	0.385693	−	0.922627i	$-0.373962\pi$
$761$	21.2796	0.771386	0.385693	+	0.922627i	$0.373962\pi$
$762$	−53.4776	−1.93729
$763$	−12.7182	−0.460429
$764$	3.91781	0.141741
$765$	20.7512	0.750262
$766$	−73.5351	−2.65693
$767$	−18.5448	−0.669614
$768$	31.1859	1.12532
$769$	−15.9123	−0.573812	−0.286906	−	0.957959i	$-0.592627\pi$
$769$	−15.9123	−0.573812	−0.286906	+	0.957959i	$0.592627\pi$
$770$	9.69645	0.349436
$771$	11.0810	0.399072
$772$	−55.1318	−1.98424
$773$	−18.1754	−0.653722	−0.326861	−	0.945072i	$-0.605991\pi$
$773$	−18.1754	−0.653722	−0.326861	+	0.945072i	$0.605991\pi$
$774$	−24.5319	−0.881780
$775$	17.3590	0.623552
$776$	−40.0913	−1.43920
$777$	−4.66028	−0.167187
$778$	−19.8766	−0.712610
$779$	−18.6548	−0.668378
$780$	−20.4145	−0.730957
$781$	1.88987	0.0676247
$782$	2.67846	0.0957816
$783$	−2.55748	−0.0913970
$784$	3.51361	0.125486
$785$	23.1240	0.825331
$786$	5.44384	0.194175
$787$	8.03972	0.286585	0.143293	−	0.989680i	$-0.454231\pi$
$787$	8.03972	0.286585	0.143293	+	0.989680i	$0.454231\pi$
$788$	−85.8311	−3.05761
$789$	−1.68799	−0.0600942
$790$	3.55083	0.126333
$791$	−10.6701	−0.379385
$792$	−7.08402	−0.251720
$793$	27.5547	0.978495
$794$	−89.3468	−3.17080
$795$	16.3139	0.578596
$796$	−56.3592	−1.99760
$797$	−6.29492	−0.222977	−0.111489	−	0.993766i	$-0.535562\pi$
$797$	−6.29492	−0.222977	−0.111489	+	0.993766i	$0.535562\pi$
$798$	−11.1336	−0.394127
$799$	14.5665	0.515325
$800$	1.48120	0.0523683
$801$	11.7232	0.414220
$802$	−78.1660	−2.76014
$803$	7.64781	0.269885
$804$	−6.26424	−0.220923
$805$	0.365627	0.0128867
$806$	−44.3293	−1.56143
$807$	−13.7884	−0.485376
$808$	5.38026	0.189277
$809$	24.5904	0.864551	0.432275	−	0.901742i	$-0.357711\pi$
$809$	24.5904	0.864551	0.432275	+	0.901742i	$0.357711\pi$
$810$	−6.38585	−0.224376
$811$	−23.7039	−0.832356	−0.416178	−	0.909283i	$-0.636631\pi$
$811$	−23.7039	−0.832356	−0.416178	+	0.909283i	$0.636631\pi$
$812$	−10.0197	−0.351624
$813$	−10.4535	−0.366619
$814$	17.2142	0.603357
$815$	−12.7134	−0.445332
$816$	−27.7753	−0.972331
$817$	46.1538	1.61472
$818$	24.2478	0.847803
$819$	−1.98499	−0.0693610
$820$	−41.9194	−1.46389
$821$	−6.75502	−0.235752	−0.117876	−	0.993028i	$-0.537608\pi$
$821$	−6.75502	−0.235752	−0.117876	+	0.993028i	$0.537608\pi$
$822$	−50.4912	−1.76108
$823$	19.4502	0.677990	0.338995	−	0.940788i	$-0.389913\pi$
$823$	19.4502	0.677990	0.338995	+	0.940788i	$0.389913\pi$
$824$	13.5807	0.473105
$825$	−2.87121	−0.0999626
$826$	−22.7272	−0.790779
$827$	−47.7621	−1.66085	−0.830426	−	0.557130i	$-0.811903\pi$
$827$	−47.7621	−1.66085	−0.830426	+	0.557130i	$0.811903\pi$
$828$	−0.545686	−0.0189639
$829$	−18.4691	−0.641460	−0.320730	−	0.947171i	$-0.603928\pi$
$829$	−18.4691	−0.641460	−0.320730	+	0.947171i	$0.603928\pi$
$830$	58.1483	2.01836
$831$	−21.2841	−0.738338
$832$	−17.7315	−0.614728
$833$	7.90506	0.273894
$834$	54.5580	1.88919
$835$	−14.7377	−0.510019
$836$	27.2266	0.941653
$837$	−9.18022	−0.317315
$838$	55.3877	1.91334
$839$	−5.96938	−0.206086	−0.103043	−	0.994677i	$-0.532858\pi$
$839$	−5.96938	−0.206086	−0.103043	+	0.994677i	$0.532858\pi$
$840$	−12.2468	−0.422556
$841$	−22.4593	−0.774458
$842$	39.3491	1.35606
$843$	−23.8142	−0.820203
$844$	−103.771	−3.57194
$845$	−23.7825	−0.818144
$846$	−4.48260	−0.154115
$847$	8.69438	0.298742
$848$	−21.8361	−0.749854
$849$	13.7658	0.472441
$850$	−36.3627	−1.24723
$851$	0.649100	0.0222509
$852$	−4.87619	−0.167055
$853$	−21.8854	−0.749342	−0.374671	−	0.927158i	$-0.622244\pi$
$853$	−21.8854	−0.749342	−0.374671	+	0.927158i	$0.622244\pi$
$854$	33.7690	1.15555
$855$	12.0142	0.410877
$856$	44.7697	1.53020
$857$	−39.9519	−1.36473	−0.682365	−	0.731011i	$-0.739049\pi$
$857$	−39.9519	−1.36473	−0.682365	+	0.731011i	$0.739049\pi$
$858$	7.33216	0.250316
$859$	−48.4197	−1.65206	−0.826029	−	0.563627i	$-0.809405\pi$
$859$	−48.4197	−1.65206	−0.826029	+	0.563627i	$0.809405\pi$
$860$	103.713	3.53657
$861$	−4.07600	−0.138910
$862$	41.7068	1.42054
$863$	25.0578	0.852977	0.426489	−	0.904493i	$-0.359750\pi$
$863$	25.0578	0.852977	0.426489	+	0.904493i	$0.359750\pi$
$864$	−0.783327	−0.0266493
$865$	−30.3672	−1.03252
$866$	22.1269	0.751903
$867$	−45.4900	−1.54492
$868$	−35.9663	−1.22078
$869$	−0.844315	−0.0286414
$870$	16.3317	0.553697
$871$	3.17382	0.107541
$872$	−59.3350	−2.00934
$873$	8.59339	0.290842
$874$	1.55073	0.0524543
$875$	8.16153	0.275910
$876$	−19.7327	−0.666706
$877$	−14.0618	−0.474835	−0.237417	−	0.971408i	$-0.576301\pi$
$877$	−14.0618	−0.474835	−0.237417	+	0.971408i	$0.576301\pi$
$878$	4.14642	0.139935
$879$	16.8549	0.568501
$880$	14.0051	0.472112
$881$	20.4327	0.688396	0.344198	−	0.938897i	$-0.388151\pi$
$881$	20.4327	0.688396	0.344198	+	0.938897i	$0.388151\pi$
$882$	−2.43265	−0.0819118
$883$	18.9795	0.638711	0.319355	−	0.947635i	$-0.396534\pi$
$883$	18.9795	0.638711	0.319355	+	0.947635i	$0.396534\pi$
$884$	61.4761	2.06766
$885$	24.5246	0.824387
$886$	−74.9439	−2.51779
$887$	43.4132	1.45767	0.728837	−	0.684687i	$-0.240061\pi$
$887$	43.4132	1.45767	0.728837	+	0.684687i	$0.240061\pi$
$888$	−21.7419	−0.729611
$889$	21.9832	0.737294
$890$	−74.8629	−2.50941
$891$	1.51843	0.0508692
$892$	−103.437	−3.46333
$893$	8.43347	0.282215
$894$	3.35301	0.112141
$895$	−51.1787	−1.71072
$896$	−20.1638	−0.673624
$897$	0.276476	0.00923126
$898$	−45.7775	−1.52762
$899$	23.4782	0.783043
$900$	7.40822	0.246941
$901$	−49.1276	−1.63668
$902$	15.0560	0.501308
$903$	10.0844	0.335588
$904$	−49.7799	−1.65566
$905$	−9.84332	−0.327203
$906$	−5.62563	−0.186899
$907$	47.8093	1.58748	0.793740	−	0.608257i	$-0.208131\pi$
$907$	47.8093	1.58748	0.793740	+	0.608257i	$0.208131\pi$
$908$	25.0120	0.830054
$909$	−1.15323	−0.0382503
$910$	12.6758	0.420200
$911$	17.9851	0.595874	0.297937	−	0.954586i	$-0.403701\pi$
$911$	17.9851	0.595874	0.297937	+	0.954586i	$0.403701\pi$
$912$	−16.0809	−0.532493
$913$	−13.8265	−0.457591
$914$	−89.8423	−2.97172
$915$	−36.4398	−1.20466
$916$	101.899	3.36684
$917$	−2.23782	−0.0738992
$918$	19.2303	0.634694
$919$	42.7245	1.40935	0.704676	−	0.709529i	$-0.251092\pi$
$919$	42.7245	1.40935	0.704676	+	0.709529i	$0.251092\pi$
$920$	1.70578	0.0562381
$921$	27.4323	0.903924
$922$	−53.5185	−1.76254
$923$	2.47055	0.0813193
$924$	5.94891	0.195705
$925$	−8.81217	−0.289742
$926$	20.9693	0.689095
$927$	−2.91095	−0.0956083
$928$	2.00335	0.0657630
$929$	20.9384	0.686965	0.343483	−	0.939159i	$-0.388393\pi$
$929$	20.9384	0.686965	0.343483	+	0.939159i	$0.388393\pi$
$930$	58.6235	1.92234
$931$	4.57675	0.149997
$932$	−76.7659	−2.51455
$933$	26.7482	0.875697
$934$	−9.54317	−0.312262
$935$	31.5092	1.03046
$936$	−9.26070	−0.302695
$937$	−39.2109	−1.28096	−0.640482	−	0.767973i	$-0.721266\pi$
$937$	−39.2109	−1.28096	−0.640482	+	0.767973i	$0.721266\pi$
$938$	3.88961	0.127000
$939$	−16.2904	−0.531617
$940$	18.9509	0.618112
$941$	27.8709	0.908565	0.454282	−	0.890858i	$-0.349896\pi$
$941$	27.8709	0.908565	0.454282	+	0.890858i	$0.349896\pi$
$942$	21.4292	0.698200
$943$	0.567719	0.0184875
$944$	−32.8261	−1.06840
$945$	2.62505	0.0853930
$946$	−37.2499	−1.21110
$947$	−5.05801	−0.164363	−0.0821817	−	0.996617i	$-0.526189\pi$
$947$	−5.05801	−0.164363	−0.0821817	+	0.996617i	$0.526189\pi$
$948$	2.17848	0.0707538
$949$	9.99771	0.324539
$950$	−21.0527	−0.683040
$951$	−15.7275	−0.510000
$952$	36.8800	1.19529
$953$	−13.8455	−0.448500	−0.224250	−	0.974532i	$-0.571993\pi$
$953$	−13.8455	−0.448500	−0.224250	+	0.974532i	$0.571993\pi$
$954$	15.1182	0.489471
$955$	2.62505	0.0849448
$956$	9.14499	0.295770
$957$	−3.88335	−0.125531
$958$	−20.4019	−0.659154
$959$	20.7556	0.670233
$960$	23.4491	0.756815
$961$	53.2764	1.71859
$962$	22.5035	0.725542
$963$	−9.59617	−0.309232
$964$	87.0927	2.80507
$965$	−36.9400	−1.18914
$966$	0.338829	0.0109016
$967$	23.9184	0.769163	0.384582	−	0.923091i	$-0.374346\pi$
$967$	23.9184	0.769163	0.384582	+	0.923091i	$0.374346\pi$
$968$	40.5625	1.30373
$969$	−36.1795	−1.16225
$970$	−54.8761	−1.76197
$971$	−15.4958	−0.497284	−0.248642	−	0.968595i	$-0.579984\pi$
$971$	−15.4958	−0.497284	−0.248642	+	0.968595i	$0.579984\pi$
$972$	−3.91781	−0.125664
$973$	−22.4273	−0.718988
$974$	34.5217	1.10615
$975$	−3.75343	−0.120206
$976$	48.7744	1.56123
$977$	−31.6313	−1.01198	−0.505988	−	0.862541i	$-0.668872\pi$
$977$	−31.6313	−1.01198	−0.505988	+	0.862541i	$0.668872\pi$
$978$	−11.7816	−0.376734
$979$	17.8009	0.568919
$980$	10.2845	0.328525
$981$	12.7182	0.406060
$982$	46.9352	1.49776
$983$	−5.84139	−0.186311	−0.0931557	−	0.995652i	$-0.529695\pi$
$983$	−5.84139	−0.186311	−0.0931557	+	0.995652i	$0.529695\pi$
$984$	−19.0160	−0.606209
$985$	−57.5095	−1.83241
$986$	−49.1811	−1.56625
$987$	1.84268	0.0586531
$988$	35.5924	1.13235
$989$	−1.40459	−0.0446634
$990$	−9.69645	−0.308173
$991$	36.1434	1.14813	0.574067	−	0.818808i	$-0.305365\pi$
$991$	36.1434	1.14813	0.574067	+	0.818808i	$0.305365\pi$
$992$	7.19111	0.228318
$993$	3.51226	0.111458
$994$	3.02773	0.0960338
$995$	−37.7624	−1.19715
$996$	35.6748	1.13040
$997$	15.3470	0.486045	0.243023	−	0.970021i	$-0.421861\pi$
$997$	15.3470	0.486045	0.243023	+	0.970021i	$0.421861\pi$
$998$	−45.0625	−1.42643
$999$	4.66028	0.147445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.4	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43265 q^{2} -1.00000 q^{3} +3.91781 q^{4} +2.62505 q^{5} +2.43265 q^{6} -1.00000 q^{7} -4.66537 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.43265 q^{2} -1.00000 q^{3} +3.91781 q^{4} +2.62505 q^{5} +2.43265 q^{6} -1.00000 q^{7} -4.66537 q^{8} +1.00000 q^{9} -6.38585 q^{10} +1.51843 q^{11} -3.91781 q^{12} +1.98499 q^{13} +2.43265 q^{14} -2.62505 q^{15} +3.51361 q^{16} +7.90506 q^{17} -2.43265 q^{18} +4.57675 q^{19} +10.2845 q^{20} +1.00000 q^{21} -3.69381 q^{22} -0.139284 q^{23} +4.66537 q^{24} +1.89091 q^{25} -4.82879 q^{26} -1.00000 q^{27} -3.91781 q^{28} +2.55748 q^{29} +6.38585 q^{30} +9.18022 q^{31} +0.783327 q^{32} -1.51843 q^{33} -19.2303 q^{34} -2.62505 q^{35} +3.91781 q^{36} -4.66028 q^{37} -11.1336 q^{38} -1.98499 q^{39} -12.2468 q^{40} -4.07600 q^{41} -2.43265 q^{42} +10.0844 q^{43} +5.94891 q^{44} +2.62505 q^{45} +0.338829 q^{46} +1.84268 q^{47} -3.51361 q^{48} +1.00000 q^{49} -4.59993 q^{50} -7.90506 q^{51} +7.77680 q^{52} -6.21470 q^{53} +2.43265 q^{54} +3.98595 q^{55} +4.66537 q^{56} -4.57675 q^{57} -6.22147 q^{58} -9.34253 q^{59} -10.2845 q^{60} +13.8815 q^{61} -22.3323 q^{62} -1.00000 q^{63} -8.93279 q^{64} +5.21070 q^{65} +3.69381 q^{66} +1.59891 q^{67} +30.9705 q^{68} +0.139284 q^{69} +6.38585 q^{70} +1.24462 q^{71} -4.66537 q^{72} +5.03666 q^{73} +11.3369 q^{74} -1.89091 q^{75} +17.9308 q^{76} -1.51843 q^{77} +4.82879 q^{78} -0.556046 q^{79} +9.22343 q^{80} +1.00000 q^{81} +9.91549 q^{82} -9.10581 q^{83} +3.91781 q^{84} +20.7512 q^{85} -24.5319 q^{86} -2.55748 q^{87} -7.08402 q^{88} +11.7232 q^{89} -6.38585 q^{90} -1.98499 q^{91} -0.545686 q^{92} -9.18022 q^{93} -4.48260 q^{94} +12.0142 q^{95} -0.783327 q^{96} +8.59339 q^{97} -2.43265 q^{98} +1.51843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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