LMFDB - Embedded newform 8015.2.a.m.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25277 q^{2} +3.29965 q^{3} +3.07495 q^{4} +1.00000 q^{5} -7.43334 q^{6} -1.00000 q^{7} -2.42162 q^{8} +7.88769 q^{9} +O(q^{10})$	\(q-2.25277 q^{2} +3.29965 q^{3} +3.07495 q^{4} +1.00000 q^{5} -7.43334 q^{6} -1.00000 q^{7} -2.42162 q^{8} +7.88769 q^{9} -2.25277 q^{10} +4.57213 q^{11} +10.1463 q^{12} -5.96180 q^{13} +2.25277 q^{14} +3.29965 q^{15} -0.694565 q^{16} -3.44576 q^{17} -17.7691 q^{18} -4.11220 q^{19} +3.07495 q^{20} -3.29965 q^{21} -10.2999 q^{22} +1.39772 q^{23} -7.99050 q^{24} +1.00000 q^{25} +13.4305 q^{26} +16.1277 q^{27} -3.07495 q^{28} +5.87991 q^{29} -7.43334 q^{30} +6.25258 q^{31} +6.40793 q^{32} +15.0864 q^{33} +7.76248 q^{34} -1.00000 q^{35} +24.2543 q^{36} -6.59053 q^{37} +9.26383 q^{38} -19.6719 q^{39} -2.42162 q^{40} +9.35930 q^{41} +7.43334 q^{42} -4.84985 q^{43} +14.0591 q^{44} +7.88769 q^{45} -3.14874 q^{46} -4.89393 q^{47} -2.29182 q^{48} +1.00000 q^{49} -2.25277 q^{50} -11.3698 q^{51} -18.3323 q^{52} +13.2081 q^{53} -36.3319 q^{54} +4.57213 q^{55} +2.42162 q^{56} -13.5688 q^{57} -13.2461 q^{58} +11.0758 q^{59} +10.1463 q^{60} +1.01143 q^{61} -14.0856 q^{62} -7.88769 q^{63} -13.0464 q^{64} -5.96180 q^{65} -33.9862 q^{66} +6.62309 q^{67} -10.5955 q^{68} +4.61199 q^{69} +2.25277 q^{70} -16.3206 q^{71} -19.1010 q^{72} -10.5392 q^{73} +14.8469 q^{74} +3.29965 q^{75} -12.6448 q^{76} -4.57213 q^{77} +44.3161 q^{78} +0.249892 q^{79} -0.694565 q^{80} +29.5526 q^{81} -21.0843 q^{82} +2.44702 q^{83} -10.1463 q^{84} -3.44576 q^{85} +10.9256 q^{86} +19.4016 q^{87} -11.0720 q^{88} +13.6034 q^{89} -17.7691 q^{90} +5.96180 q^{91} +4.29793 q^{92} +20.6313 q^{93} +11.0249 q^{94} -4.11220 q^{95} +21.1439 q^{96} +3.03072 q^{97} -2.25277 q^{98} +36.0635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * 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 $

$2$	−2.25277	−1.59295	−0.796473	−	0.604674i	$-0.793303\pi$
$2$	−2.25277	−1.59295	−0.796473	+	0.604674i	$0.793303\pi$
$3$	3.29965	1.90505	0.952527	−	0.304454i	$-0.0984740\pi$
$3$	3.29965	1.90505	0.952527	+	0.304454i	$0.0984740\pi$
$4$	3.07495	1.53748
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.43334	−3.03465
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.42162	−0.856172
$9$	7.88769	2.62923
$10$	−2.25277	−0.712387
$11$	4.57213	1.37855	0.689274	−	0.724501i	$-0.257930\pi$
$11$	4.57213	1.37855	0.689274	+	0.724501i	$0.257930\pi$
$12$	10.1463	2.92898
$13$	−5.96180	−1.65351	−0.826753	−	0.562565i	$-0.809815\pi$
$13$	−5.96180	−1.65351	−0.826753	+	0.562565i	$0.809815\pi$
$14$	2.25277	0.602077
$15$	3.29965	0.851966
$16$	−0.694565	−0.173641
$17$	−3.44576	−0.835719	−0.417859	−	0.908512i	$-0.637220\pi$
$17$	−3.44576	−0.835719	−0.417859	+	0.908512i	$0.637220\pi$
$18$	−17.7691	−4.18822
$19$	−4.11220	−0.943404	−0.471702	−	0.881758i	$-0.656360\pi$
$19$	−4.11220	−0.943404	−0.471702	+	0.881758i	$0.656360\pi$
$20$	3.07495	0.687581
$21$	−3.29965	−0.720043
$22$	−10.2999	−2.19595
$23$	1.39772	0.291445	0.145722	−	0.989326i	$-0.453449\pi$
$23$	1.39772	0.291445	0.145722	+	0.989326i	$0.453449\pi$
$24$	−7.99050	−1.63105
$25$	1.00000	0.200000
$26$	13.4305	2.63395
$27$	16.1277	3.10377
$28$	−3.07495	−0.581112
$29$	5.87991	1.09187	0.545936	−	0.837827i	$-0.316174\pi$
$29$	5.87991	1.09187	0.545936	+	0.837827i	$0.316174\pi$
$30$	−7.43334	−1.35714
$31$	6.25258	1.12300	0.561499	−	0.827478i	$-0.310225\pi$
$31$	6.25258	1.12300	0.561499	+	0.827478i	$0.310225\pi$
$32$	6.40793	1.13277
$33$	15.0864	2.62621
$34$	7.76248	1.33126
$35$	−1.00000	−0.169031
$36$	24.2543	4.04238
$37$	−6.59053	−1.08348	−0.541738	−	0.840547i	$-0.682234\pi$
$37$	−6.59053	−1.08348	−0.541738	+	0.840547i	$0.682234\pi$
$38$	9.26383	1.50279
$39$	−19.6719	−3.15002
$40$	−2.42162	−0.382892
$41$	9.35930	1.46168	0.730839	−	0.682550i	$-0.239129\pi$
$41$	9.35930	1.46168	0.730839	+	0.682550i	$0.239129\pi$
$42$	7.43334	1.14699
$43$	−4.84985	−0.739595	−0.369798	−	0.929112i	$-0.620573\pi$
$43$	−4.84985	−0.739595	−0.369798	+	0.929112i	$0.620573\pi$
$44$	14.0591	2.11949
$45$	7.88769	1.17583
$46$	−3.14874	−0.464256
$47$	−4.89393	−0.713853	−0.356927	−	0.934132i	$-0.616175\pi$
$47$	−4.89393	−0.713853	−0.356927	+	0.934132i	$0.616175\pi$
$48$	−2.29182	−0.330796
$49$	1.00000	0.142857
$50$	−2.25277	−0.318589
$51$	−11.3698	−1.59209
$52$	−18.3323	−2.54223
$53$	13.2081	1.81427	0.907135	−	0.420839i	$-0.138264\pi$
$53$	13.2081	1.81427	0.907135	+	0.420839i	$0.138264\pi$
$54$	−36.3319	−4.94414
$55$	4.57213	0.616506
$56$	2.42162	0.323603
$57$	−13.5688	−1.79724
$58$	−13.2461	−1.73929
$59$	11.0758	1.44194	0.720971	−	0.692965i	$-0.243696\pi$
$59$	11.0758	1.44194	0.720971	+	0.692965i	$0.243696\pi$
$60$	10.1463	1.30988
$61$	1.01143	0.129500	0.0647500	−	0.997902i	$-0.479375\pi$
$61$	1.01143	0.129500	0.0647500	+	0.997902i	$0.479375\pi$
$62$	−14.0856	−1.78887
$63$	−7.88769	−0.993756
$64$	−13.0464	−1.63081
$65$	−5.96180	−0.739470
$66$	−33.9862	−4.18341
$67$	6.62309	0.809140	0.404570	−	0.914507i	$-0.367421\pi$
$67$	6.62309	0.809140	0.404570	+	0.914507i	$0.367421\pi$
$68$	−10.5955	−1.28490
$69$	4.61199	0.555218
$70$	2.25277	0.269257
$71$	−16.3206	−1.93690	−0.968449	−	0.249213i	$-0.919828\pi$
$71$	−16.3206	−1.93690	−0.968449	+	0.249213i	$0.919828\pi$
$72$	−19.1010	−2.25107
$73$	−10.5392	−1.23352	−0.616758	−	0.787153i	$-0.711554\pi$
$73$	−10.5392	−1.23352	−0.616758	+	0.787153i	$0.711554\pi$
$74$	14.8469	1.72592
$75$	3.29965	0.381011
$76$	−12.6448	−1.45046
$77$	−4.57213	−0.521042
$78$	44.3161	5.01781
$79$	0.249892	0.0281150	0.0140575	−	0.999901i	$-0.495525\pi$
$79$	0.249892	0.0281150	0.0140575	+	0.999901i	$0.495525\pi$
$80$	−0.694565	−0.0776548
$81$	29.5526	3.28362
$82$	−21.0843	−2.32837
$83$	2.44702	0.268596	0.134298	−	0.990941i	$-0.457122\pi$
$83$	2.44702	0.268596	0.134298	+	0.990941i	$0.457122\pi$
$84$	−10.1463	−1.10705
$85$	−3.44576	−0.373745
$86$	10.9256	1.17814
$87$	19.4016	2.08007
$88$	−11.0720	−1.18027
$89$	13.6034	1.44196	0.720979	−	0.692957i	$-0.243692\pi$
$89$	13.6034	1.44196	0.720979	+	0.692957i	$0.243692\pi$
$90$	−17.7691	−1.87303
$91$	5.96180	0.624967
$92$	4.29793	0.448090
$93$	20.6313	2.13937
$94$	11.0249	1.13713
$95$	−4.11220	−0.421903
$96$	21.1439	2.15799
$97$	3.03072	0.307723	0.153862	−	0.988092i	$-0.450829\pi$
$97$	3.03072	0.307723	0.153862	+	0.988092i	$0.450829\pi$
$98$	−2.25277	−0.227564
$99$	36.0635	3.62452
$100$	3.07495	0.307495
$101$	11.2867	1.12307	0.561535	−	0.827453i	$-0.310211\pi$
$101$	11.2867	1.12307	0.561535	+	0.827453i	$0.310211\pi$
$102$	25.6135	2.53611
$103$	9.38847	0.925073	0.462537	−	0.886600i	$-0.346939\pi$
$103$	9.38847	0.925073	0.462537	+	0.886600i	$0.346939\pi$
$104$	14.4372	1.41569
$105$	−3.29965	−0.322013
$106$	−29.7547	−2.89004
$107$	−13.4621	−1.30143	−0.650717	−	0.759320i	$-0.725532\pi$
$107$	−13.4621	−1.30143	−0.650717	+	0.759320i	$0.725532\pi$
$108$	49.5919	4.77198
$109$	9.99384	0.957236	0.478618	−	0.878023i	$-0.341138\pi$
$109$	9.99384	0.957236	0.478618	+	0.878023i	$0.341138\pi$
$110$	−10.2999	−0.982060
$111$	−21.7465	−2.06408
$112$	0.694565	0.0656303
$113$	11.9296	1.12224	0.561122	−	0.827733i	$-0.310370\pi$
$113$	11.9296	1.12224	0.561122	+	0.827733i	$0.310370\pi$
$114$	30.5674	2.86290
$115$	1.39772	0.130338
$116$	18.0804	1.67873
$117$	−47.0249	−4.34745
$118$	−24.9511	−2.29694
$119$	3.44576	0.315872
$120$	−7.99050	−0.729429
$121$	9.90435	0.900395
$122$	−2.27851	−0.206287
$123$	30.8824	2.78458
$124$	19.2264	1.72658
$125$	1.00000	0.0894427
$126$	17.7691	1.58300
$127$	−19.0411	−1.68963	−0.844813	−	0.535062i	$-0.820288\pi$
$127$	−19.0411	−1.68963	−0.844813	+	0.535062i	$0.820288\pi$
$128$	16.5747	1.46501
$129$	−16.0028	−1.40897
$130$	13.4305	1.17794
$131$	14.4263	1.26043	0.630215	−	0.776420i	$-0.282967\pi$
$131$	14.4263	1.26043	0.630215	+	0.776420i	$0.282967\pi$
$132$	46.3901	4.03774
$133$	4.11220	0.356573
$134$	−14.9203	−1.28892
$135$	16.1277	1.38805
$136$	8.34432	0.715519
$137$	6.09096	0.520386	0.260193	−	0.965557i	$-0.416214\pi$
$137$	6.09096	0.520386	0.260193	+	0.965557i	$0.416214\pi$
$138$	−10.3897	−0.884433
$139$	5.87488	0.498300	0.249150	−	0.968465i	$-0.419849\pi$
$139$	5.87488	0.498300	0.249150	+	0.968465i	$0.419849\pi$
$140$	−3.07495	−0.259881
$141$	−16.1483	−1.35993
$142$	36.7665	3.08537
$143$	−27.2581	−2.27944
$144$	−5.47852	−0.456543
$145$	5.87991	0.488300
$146$	23.7423	1.96492
$147$	3.29965	0.272151
$148$	−20.2656	−1.66582
$149$	16.7581	1.37288	0.686440	−	0.727187i	$-0.259173\pi$
$149$	16.7581	1.37288	0.686440	+	0.727187i	$0.259173\pi$
$150$	−7.43334	−0.606930
$151$	2.57035	0.209172	0.104586	−	0.994516i	$-0.466648\pi$
$151$	2.57035	0.209172	0.104586	+	0.994516i	$0.466648\pi$
$152$	9.95819	0.807716
$153$	−27.1791	−2.19730
$154$	10.2999	0.829992
$155$	6.25258	0.502220
$156$	−60.4901	−4.84308
$157$	−3.36779	−0.268779	−0.134390	−	0.990929i	$-0.542907\pi$
$157$	−3.36779	−0.268779	−0.134390	+	0.990929i	$0.542907\pi$
$158$	−0.562948	−0.0447858
$159$	43.5821	3.45628
$160$	6.40793	0.506592
$161$	−1.39772	−0.110156
$162$	−66.5751	−5.23064
$163$	21.7140	1.70077	0.850384	−	0.526163i	$-0.176370\pi$
$163$	21.7140	1.70077	0.850384	+	0.526163i	$0.176370\pi$
$164$	28.7794	2.24730
$165$	15.0864	1.17448
$166$	−5.51257	−0.427859
$167$	−9.78287	−0.757021	−0.378511	−	0.925597i	$-0.623564\pi$
$167$	−9.78287	−0.757021	−0.378511	+	0.925597i	$0.623564\pi$
$168$	7.99050	0.616480
$169$	22.5431	1.73408
$170$	7.76248	0.595355
$171$	−32.4358	−2.48043
$172$	−14.9131	−1.13711
$173$	−6.18195	−0.470005	−0.235002	−	0.971995i	$-0.575510\pi$
$173$	−6.18195	−0.470005	−0.235002	+	0.971995i	$0.575510\pi$
$174$	−43.7074	−3.31345
$175$	−1.00000	−0.0755929
$176$	−3.17564	−0.239373
$177$	36.5462	2.74698
$178$	−30.6453	−2.29696
$179$	−4.44369	−0.332137	−0.166069	−	0.986114i	$-0.553107\pi$
$179$	−4.44369	−0.332137	−0.166069	+	0.986114i	$0.553107\pi$
$180$	24.2543	1.80781
$181$	−1.17630	−0.0874334	−0.0437167	−	0.999044i	$-0.513920\pi$
$181$	−1.17630	−0.0874334	−0.0437167	+	0.999044i	$0.513920\pi$
$182$	−13.4305	−0.995538
$183$	3.33736	0.246705
$184$	−3.38475	−0.249527
$185$	−6.59053	−0.484546
$186$	−46.4776	−3.40790
$187$	−15.7544	−1.15208
$188$	−15.0486	−1.09753
$189$	−16.1277	−1.17312
$190$	9.26383	0.672069
$191$	−7.62011	−0.551372	−0.275686	−	0.961248i	$-0.588905\pi$
$191$	−7.62011	−0.551372	−0.275686	+	0.961248i	$0.588905\pi$
$192$	−43.0487	−3.10677
$193$	17.6576	1.27102	0.635512	−	0.772091i	$-0.280789\pi$
$193$	17.6576	1.27102	0.635512	+	0.772091i	$0.280789\pi$
$194$	−6.82751	−0.490186
$195$	−19.6719	−1.40873
$196$	3.07495	0.219640
$197$	22.5754	1.60843	0.804217	−	0.594336i	$-0.202585\pi$
$197$	22.5754	1.60843	0.804217	+	0.594336i	$0.202585\pi$
$198$	−81.2427	−5.77367
$199$	10.4350	0.739719	0.369860	−	0.929088i	$-0.379406\pi$
$199$	10.4350	0.739719	0.369860	+	0.929088i	$0.379406\pi$
$200$	−2.42162	−0.171234
$201$	21.8539	1.54145
$202$	−25.4263	−1.78899
$203$	−5.87991	−0.412689
$204$	−34.9616	−2.44780
$205$	9.35930	0.653682
$206$	−21.1500	−1.47359
$207$	11.0248	0.766276
$208$	4.14086	0.287117
$209$	−18.8015	−1.30053
$210$	7.43334	0.512949
$211$	−20.2968	−1.39729	−0.698643	−	0.715470i	$-0.746212\pi$
$211$	−20.2968	−1.39729	−0.698643	+	0.715470i	$0.746212\pi$
$212$	40.6143	2.78940
$213$	−53.8522	−3.68989
$214$	30.3270	2.07311
$215$	−4.84985	−0.330757
$216$	−39.0551	−2.65736
$217$	−6.25258	−0.424453
$218$	−22.5138	−1.52483
$219$	−34.7756	−2.34992
$220$	14.0591	0.947863
$221$	20.5429	1.38187
$222$	48.9897	3.28797
$223$	−15.4809	−1.03668	−0.518339	−	0.855175i	$-0.673449\pi$
$223$	−15.4809	−1.03668	−0.518339	+	0.855175i	$0.673449\pi$
$224$	−6.40793	−0.428148
$225$	7.88769	0.525846
$226$	−26.8746	−1.78767
$227$	26.1812	1.73771	0.868854	−	0.495068i	$-0.164857\pi$
$227$	26.1812	1.73771	0.868854	+	0.495068i	$0.164857\pi$
$228$	−41.7235	−2.76321
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−3.14874	−0.207622
$231$	−15.0864	−0.992614
$232$	−14.2389	−0.934830
$233$	−14.3776	−0.941908	−0.470954	−	0.882158i	$-0.656090\pi$
$233$	−14.3776	−0.941908	−0.470954	+	0.882158i	$0.656090\pi$
$234$	105.936	6.92525
$235$	−4.89393	−0.319245
$236$	34.0575	2.21695
$237$	0.824556	0.0535607
$238$	−7.76248	−0.503167
$239$	−14.5247	−0.939527	−0.469764	−	0.882792i	$-0.655661\pi$
$239$	−14.5247	−0.939527	−0.469764	+	0.882792i	$0.655661\pi$
$240$	−2.29182	−0.147937
$241$	2.99289	0.192789	0.0963944	−	0.995343i	$-0.469269\pi$
$241$	2.99289	0.192789	0.0963944	+	0.995343i	$0.469269\pi$
$242$	−22.3122	−1.43428
$243$	49.1303	3.15171
$244$	3.11009	0.199103
$245$	1.00000	0.0638877
$246$	−69.5709	−4.43568
$247$	24.5161	1.55992
$248$	−15.1414	−0.961479
$249$	8.07433	0.511690
$250$	−2.25277	−0.142477
$251$	10.5135	0.663606	0.331803	−	0.943349i	$-0.392343\pi$
$251$	10.5135	0.663606	0.331803	+	0.943349i	$0.392343\pi$
$252$	−24.2543	−1.52788
$253$	6.39056	0.401771
$254$	42.8952	2.69148
$255$	−11.3698	−0.712004
$256$	−11.2461	−0.702879
$257$	8.76403	0.546685	0.273343	−	0.961917i	$-0.411871\pi$
$257$	8.76403	0.546685	0.273343	+	0.961917i	$0.411871\pi$
$258$	36.0506	2.24441
$259$	6.59053	0.409516
$260$	−18.3323	−1.13692
$261$	46.3789	2.87078
$262$	−32.4991	−2.00780
$263$	−1.25088	−0.0771323	−0.0385662	−	0.999256i	$-0.512279\pi$
$263$	−1.25088	−0.0771323	−0.0385662	+	0.999256i	$0.512279\pi$
$264$	−36.5336	−2.24849
$265$	13.2081	0.811367
$266$	−9.26383	−0.568002
$267$	44.8865	2.74701
$268$	20.3657	1.24403
$269$	−7.84851	−0.478532	−0.239266	−	0.970954i	$-0.576907\pi$
$269$	−7.84851	−0.478532	−0.239266	+	0.970954i	$0.576907\pi$
$270$	−36.3319	−2.21109
$271$	−30.3470	−1.84345	−0.921723	−	0.387849i	$-0.873218\pi$
$271$	−30.3470	−1.84345	−0.921723	+	0.387849i	$0.873218\pi$
$272$	2.39330	0.145115
$273$	19.6719	1.19060
$274$	−13.7215	−0.828947
$275$	4.57213	0.275710
$276$	14.1817	0.853635
$277$	6.77949	0.407340	0.203670	−	0.979040i	$-0.434713\pi$
$277$	6.77949	0.407340	0.203670	+	0.979040i	$0.434713\pi$
$278$	−13.2347	−0.793766
$279$	49.3185	2.95262
$280$	2.42162	0.144719
$281$	−11.4247	−0.681538	−0.340769	−	0.940147i	$-0.610687\pi$
$281$	−11.4247	−0.681538	−0.340769	+	0.940147i	$0.610687\pi$
$282$	36.3782	2.16629
$283$	32.2328	1.91604	0.958021	−	0.286697i	$-0.0925573\pi$
$283$	32.2328	1.91604	0.958021	+	0.286697i	$0.0925573\pi$
$284$	−50.1851	−2.97794
$285$	−13.5688	−0.803748
$286$	61.4061	3.63102
$287$	−9.35930	−0.552462
$288$	50.5438	2.97832
$289$	−5.12676	−0.301574
$290$	−13.2461	−0.777835
$291$	10.0003	0.586229
$292$	−32.4075	−1.89650
$293$	18.8606	1.10185	0.550925	−	0.834555i	$-0.314275\pi$
$293$	18.8606	1.10185	0.550925	+	0.834555i	$0.314275\pi$
$294$	−7.43334	−0.433521
$295$	11.0758	0.644856
$296$	15.9598	0.927642
$297$	73.7378	4.27870
$298$	−37.7521	−2.18692
$299$	−8.33293	−0.481906
$300$	10.1463	0.585795
$301$	4.84985	0.279541
$302$	−5.79041	−0.333200
$303$	37.2422	2.13951
$304$	2.85619	0.163814
$305$	1.01143	0.0579142
$306$	61.2281	3.50018
$307$	16.7659	0.956878	0.478439	−	0.878121i	$-0.341203\pi$
$307$	16.7659	0.956878	0.478439	+	0.878121i	$0.341203\pi$
$308$	−14.0591	−0.801091
$309$	30.9787	1.76231
$310$	−14.0856	−0.800009
$311$	−32.9882	−1.87059	−0.935294	−	0.353872i	$-0.884865\pi$
$311$	−32.9882	−1.87059	−0.935294	+	0.353872i	$0.884865\pi$
$312$	47.6378	2.69696
$313$	−14.9539	−0.845244	−0.422622	−	0.906306i	$-0.638890\pi$
$313$	−14.9539	−0.845244	−0.422622	+	0.906306i	$0.638890\pi$
$314$	7.58685	0.428150
$315$	−7.88769	−0.444421
$316$	0.768406	0.0432262
$317$	−20.6415	−1.15934	−0.579671	−	0.814851i	$-0.696819\pi$
$317$	−20.6415	−1.15934	−0.579671	+	0.814851i	$0.696819\pi$
$318$	−98.1802	−5.50567
$319$	26.8837	1.50520
$320$	−13.0464	−0.729318
$321$	−44.4203	−2.47930
$322$	3.14874	0.175472
$323$	14.1696	0.788420
$324$	90.8730	5.04850
$325$	−5.96180	−0.330701
$326$	−48.9164	−2.70923
$327$	32.9762	1.82359
$328$	−22.6647	−1.25145
$329$	4.89393	0.269811
$330$	−33.9862	−1.87088
$331$	18.8681	1.03709	0.518543	−	0.855051i	$-0.326474\pi$
$331$	18.8681	1.03709	0.518543	+	0.855051i	$0.326474\pi$
$332$	7.52449	0.412960
$333$	−51.9841	−2.84871
$334$	22.0385	1.20589
$335$	6.62309	0.361858
$336$	2.29182	0.125029
$337$	−1.73161	−0.0943267	−0.0471634	−	0.998887i	$-0.515018\pi$
$337$	−1.73161	−0.0943267	−0.0471634	+	0.998887i	$0.515018\pi$
$338$	−50.7843	−2.76230
$339$	39.3635	2.13793
$340$	−10.5955	−0.574624
$341$	28.5876	1.54811
$342$	73.0702	3.95119
$343$	−1.00000	−0.0539949
$344$	11.7445	0.633221
$345$	4.61199	0.248301
$346$	13.9265	0.748692
$347$	19.4055	1.04174	0.520871	−	0.853635i	$-0.325607\pi$
$347$	19.4055	1.04174	0.520871	+	0.853635i	$0.325607\pi$
$348$	59.6592	3.19807
$349$	28.1966	1.50933	0.754665	−	0.656110i	$-0.227799\pi$
$349$	28.1966	1.50933	0.754665	+	0.656110i	$0.227799\pi$
$350$	2.25277	0.120415
$351$	−96.1500	−5.13211
$352$	29.2979	1.56158
$353$	−13.3871	−0.712525	−0.356263	−	0.934386i	$-0.615949\pi$
$353$	−13.3871	−0.712525	−0.356263	+	0.934386i	$0.615949\pi$
$354$	−82.3299	−4.37579
$355$	−16.3206	−0.866207
$356$	41.8299	2.21698
$357$	11.3698	0.601753
$358$	10.0106	0.529077
$359$	5.80967	0.306623	0.153311	−	0.988178i	$-0.451006\pi$
$359$	5.80967	0.306623	0.153311	+	0.988178i	$0.451006\pi$
$360$	−19.1010	−1.00671
$361$	−2.08980	−0.109990
$362$	2.64992	0.139277
$363$	32.6809	1.71530
$364$	18.3323	0.960872
$365$	−10.5392	−0.551645
$366$	−7.51829	−0.392987
$367$	3.13261	0.163521	0.0817605	−	0.996652i	$-0.473946\pi$
$367$	3.13261	0.163521	0.0817605	+	0.996652i	$0.473946\pi$
$368$	−0.970808	−0.0506069
$369$	73.8233	3.84309
$370$	14.8469	0.771855
$371$	−13.2081	−0.685730
$372$	63.4404	3.28923
$373$	−22.7066	−1.17570	−0.587852	−	0.808969i	$-0.700026\pi$
$373$	−22.7066	−1.17570	−0.587852	+	0.808969i	$0.700026\pi$
$374$	35.4911	1.83520
$375$	3.29965	0.170393
$376$	11.8512	0.611181
$377$	−35.0548	−1.80542
$378$	36.3319	1.86871
$379$	−11.1138	−0.570876	−0.285438	−	0.958397i	$-0.592139\pi$
$379$	−11.1138	−0.570876	−0.285438	+	0.958397i	$0.592139\pi$
$380$	−12.6448	−0.648666
$381$	−62.8290	−3.21883
$382$	17.1663	0.878306
$383$	20.5648	1.05081	0.525407	−	0.850851i	$-0.323913\pi$
$383$	20.5648	1.05081	0.525407	+	0.850851i	$0.323913\pi$
$384$	54.6908	2.79093
$385$	−4.57213	−0.233017
$386$	−39.7785	−2.02467
$387$	−38.2541	−1.94457
$388$	9.31933	0.473117
$389$	11.7614	0.596326	0.298163	−	0.954515i	$-0.403626\pi$
$389$	11.7614	0.596326	0.298163	+	0.954515i	$0.403626\pi$
$390$	44.3161	2.24403
$391$	−4.81621	−0.243566
$392$	−2.42162	−0.122310
$393$	47.6017	2.40119
$394$	−50.8572	−2.56215
$395$	0.249892	0.0125734
$396$	110.894	5.57262
$397$	32.8844	1.65042	0.825209	−	0.564827i	$-0.191057\pi$
$397$	32.8844	1.65042	0.825209	+	0.564827i	$0.191057\pi$
$398$	−23.5077	−1.17833
$399$	13.5688	0.679291
$400$	−0.694565	−0.0347283
$401$	−23.9160	−1.19431	−0.597153	−	0.802127i	$-0.703701\pi$
$401$	−23.9160	−1.19431	−0.597153	+	0.802127i	$0.703701\pi$
$402$	−49.2317	−2.45545
$403$	−37.2767	−1.85688
$404$	34.7061	1.72670
$405$	29.5526	1.46848
$406$	13.2461	0.657391
$407$	−30.1328	−1.49363
$408$	27.5333	1.36310
$409$	−35.3744	−1.74915	−0.874575	−	0.484890i	$-0.838860\pi$
$409$	−35.3744	−1.74915	−0.874575	+	0.484890i	$0.838860\pi$
$410$	−21.0843	−1.04128
$411$	20.0981	0.991364
$412$	28.8691	1.42228
$413$	−11.0758	−0.545003
$414$	−24.8363	−1.22064
$415$	2.44702	0.120120
$416$	−38.2028	−1.87305
$417$	19.3850	0.949289
$418$	42.3554	2.07167
$419$	−3.90832	−0.190934	−0.0954670	−	0.995433i	$-0.530434\pi$
$419$	−3.90832	−0.190934	−0.0954670	+	0.995433i	$0.530434\pi$
$420$	−10.1463	−0.495087
$421$	−18.1129	−0.882771	−0.441385	−	0.897318i	$-0.645513\pi$
$421$	−18.1129	−0.882771	−0.441385	+	0.897318i	$0.645513\pi$
$422$	45.7238	2.22580
$423$	−38.6018	−1.87688
$424$	−31.9850	−1.55333
$425$	−3.44576	−0.167144
$426$	121.316	5.87780
$427$	−1.01143	−0.0489464
$428$	−41.3954	−2.00092
$429$	−89.9422	−4.34245
$430$	10.9256	0.526878
$431$	11.3923	0.548748	0.274374	−	0.961623i	$-0.411529\pi$
$431$	11.3923	0.548748	0.274374	+	0.961623i	$0.411529\pi$
$432$	−11.2017	−0.538943
$433$	−35.5114	−1.70657	−0.853284	−	0.521446i	$-0.825393\pi$
$433$	−35.5114	−1.70657	−0.853284	+	0.521446i	$0.825393\pi$
$434$	14.0856	0.676131
$435$	19.4016	0.930237
$436$	30.7306	1.47173
$437$	−5.74771	−0.274950
$438$	78.3412	3.74329
$439$	−9.36302	−0.446873	−0.223436	−	0.974719i	$-0.571727\pi$
$439$	−9.36302	−0.446873	−0.223436	+	0.974719i	$0.571727\pi$
$440$	−11.0720	−0.527835
$441$	7.88769	0.375604
$442$	−46.2784	−2.20124
$443$	−2.86671	−0.136202	−0.0681008	−	0.997678i	$-0.521694\pi$
$443$	−2.86671	−0.136202	−0.0681008	+	0.997678i	$0.521694\pi$
$444$	−66.8693	−3.17348
$445$	13.6034	0.644863
$446$	34.8749	1.65137
$447$	55.2960	2.61541
$448$	13.0464	0.616386
$449$	−29.2720	−1.38143	−0.690715	−	0.723127i	$-0.742704\pi$
$449$	−29.2720	−1.38143	−0.690715	+	0.723127i	$0.742704\pi$
$450$	−17.7691	−0.837645
$451$	42.7919	2.01499
$452$	36.6830	1.72542
$453$	8.48127	0.398485
$454$	−58.9801	−2.76808
$455$	5.96180	0.279494
$456$	32.8585	1.53874
$457$	−28.6883	−1.34198	−0.670991	−	0.741465i	$-0.734131\pi$
$457$	−28.6883	−1.34198	−0.670991	+	0.741465i	$0.734131\pi$
$458$	2.25277	0.105265
$459$	−55.5721	−2.59388
$460$	4.29793	0.200392
$461$	13.0616	0.608338	0.304169	−	0.952618i	$-0.401621\pi$
$461$	13.0616	0.608338	0.304169	+	0.952618i	$0.401621\pi$
$462$	33.9862	1.58118
$463$	36.6424	1.70292	0.851459	−	0.524421i	$-0.175718\pi$
$463$	36.6424	1.70292	0.851459	+	0.524421i	$0.175718\pi$
$464$	−4.08398	−0.189594
$465$	20.6313	0.956755
$466$	32.3894	1.50041
$467$	15.7324	0.728009	0.364004	−	0.931397i	$-0.381409\pi$
$467$	15.7324	0.728009	0.364004	+	0.931397i	$0.381409\pi$
$468$	−144.599	−6.68410
$469$	−6.62309	−0.305826
$470$	11.0249	0.508540
$471$	−11.1125	−0.512039
$472$	−26.8213	−1.23455
$473$	−22.1741	−1.01957
$474$	−1.85753	−0.0853193
$475$	−4.11220	−0.188681
$476$	10.5955	0.485646
$477$	104.181	4.77014
$478$	32.7208	1.49662
$479$	−18.9931	−0.867818	−0.433909	−	0.900957i	$-0.642866\pi$
$479$	−18.9931	−0.867818	−0.433909	+	0.900957i	$0.642866\pi$
$480$	21.1439	0.965084
$481$	39.2914	1.79154
$482$	−6.74227	−0.307102
$483$	−4.61199	−0.209853
$484$	30.4554	1.38434
$485$	3.03072	0.137618
$486$	−110.679	−5.02050
$487$	−40.5683	−1.83833	−0.919163	−	0.393878i	$-0.871133\pi$
$487$	−40.5683	−1.83833	−0.919163	+	0.393878i	$0.871133\pi$
$488$	−2.44929	−0.110874
$489$	71.6484	3.24005
$490$	−2.25277	−0.101770
$491$	−18.3123	−0.826424	−0.413212	−	0.910635i	$-0.635593\pi$
$491$	−18.3123	−0.826424	−0.413212	+	0.910635i	$0.635593\pi$
$492$	94.9621	4.28122
$493$	−20.2607	−0.912498
$494$	−55.2291	−2.48487
$495$	36.0635	1.62094
$496$	−4.34283	−0.194999
$497$	16.3206	0.732078
$498$	−18.1896	−0.815094
$499$	12.2484	0.548315	0.274158	−	0.961685i	$-0.411601\pi$
$499$	12.2484	0.548315	0.274158	+	0.961685i	$0.411601\pi$
$500$	3.07495	0.137516
$501$	−32.2801	−1.44217
$502$	−23.6844	−1.05709
$503$	−38.2854	−1.70706	−0.853530	−	0.521044i	$-0.825543\pi$
$503$	−38.2854	−1.70706	−0.853530	+	0.521044i	$0.825543\pi$
$504$	19.1010	0.850826
$505$	11.2867	0.502252
$506$	−14.3964	−0.639999
$507$	74.3842	3.30352
$508$	−58.5506	−2.59776
$509$	−10.0215	−0.444195	−0.222098	−	0.975024i	$-0.571290\pi$
$509$	−10.0215	−0.444195	−0.222098	+	0.975024i	$0.571290\pi$
$510$	25.6135	1.13418
$511$	10.5392	0.466225
$512$	−7.81468	−0.345363
$513$	−66.3203	−2.92811
$514$	−19.7433	−0.870840
$515$	9.38847	0.413705
$516$	−49.2079	−2.16626
$517$	−22.3757	−0.984081
$518$	−14.8469	−0.652336
$519$	−20.3983	−0.895384
$520$	14.4372	0.633114
$521$	6.40121	0.280442	0.140221	−	0.990120i	$-0.455219\pi$
$521$	6.40121	0.280442	0.140221	+	0.990120i	$0.455219\pi$
$522$	−104.481	−4.57300
$523$	−19.9474	−0.872238	−0.436119	−	0.899889i	$-0.643647\pi$
$523$	−19.9474	−0.872238	−0.436119	+	0.899889i	$0.643647\pi$
$524$	44.3602	1.93788
$525$	−3.29965	−0.144009
$526$	2.81793	0.122868
$527$	−21.5449	−0.938510
$528$	−10.4785	−0.456018
$529$	−21.0464	−0.915060
$530$	−29.7547	−1.29246
$531$	87.3623	3.79120
$532$	12.6448	0.548223
$533$	−55.7983	−2.41689
$534$	−101.119	−4.37584
$535$	−13.4621	−0.582019
$536$	−16.0386	−0.692763
$537$	−14.6626	−0.632739
$538$	17.6809	0.762276
$539$	4.57213	0.196935
$540$	49.5919	2.13409
$541$	−17.8973	−0.769465	−0.384732	−	0.923028i	$-0.625706\pi$
$541$	−17.8973	−0.769465	−0.384732	+	0.923028i	$0.625706\pi$
$542$	68.3646	2.93651
$543$	−3.88137	−0.166565
$544$	−22.0802	−0.946680
$545$	9.99384	0.428089
$546$	−44.3161	−1.89655
$547$	−38.1341	−1.63050	−0.815248	−	0.579112i	$-0.803399\pi$
$547$	−38.1341	−1.63050	−0.815248	+	0.579112i	$0.803399\pi$
$548$	18.7294	0.800082
$549$	7.97783	0.340486
$550$	−10.2999	−0.439191
$551$	−24.1794	−1.03008
$552$	−11.1685	−0.475362
$553$	−0.249892	−0.0106265
$554$	−15.2726	−0.648870
$555$	−21.7465	−0.923085
$556$	18.0650	0.766125
$557$	−1.17981	−0.0499900	−0.0249950	−	0.999688i	$-0.507957\pi$
$557$	−1.17981	−0.0499900	−0.0249950	+	0.999688i	$0.507957\pi$
$558$	−111.103	−4.70336
$559$	28.9138	1.22293
$560$	0.694565	0.0293507
$561$	−51.9842	−2.19477
$562$	25.7371	1.08565
$563$	21.3838	0.901221	0.450611	−	0.892721i	$-0.351206\pi$
$563$	21.3838	0.901221	0.450611	+	0.892721i	$0.351206\pi$
$564$	−49.6552	−2.09086
$565$	11.9296	0.501882
$566$	−72.6130	−3.05215
$567$	−29.5526	−1.24109
$568$	39.5223	1.65832
$569$	20.2861	0.850439	0.425219	−	0.905090i	$-0.360197\pi$
$569$	20.2861	0.850439	0.425219	+	0.905090i	$0.360197\pi$
$570$	30.5674	1.28033
$571$	33.8456	1.41639	0.708197	−	0.706015i	$-0.249509\pi$
$571$	33.8456	1.41639	0.708197	+	0.706015i	$0.249509\pi$
$572$	−83.8174	−3.50458
$573$	−25.1437	−1.05039
$574$	21.0843	0.880043
$575$	1.39772	0.0582890
$576$	−102.906	−4.28776
$577$	3.26536	0.135939	0.0679693	−	0.997687i	$-0.478348\pi$
$577$	3.26536	0.135939	0.0679693	+	0.997687i	$0.478348\pi$
$578$	11.5494	0.480391
$579$	58.2640	2.42137
$580$	18.0804	0.750750
$581$	−2.44702	−0.101520
$582$	−22.5284	−0.933831
$583$	60.3891	2.50106
$584$	25.5219	1.05610
$585$	−47.0249	−1.94424
$586$	−42.4886	−1.75519
$587$	−20.0689	−0.828331	−0.414165	−	0.910202i	$-0.635926\pi$
$587$	−20.0689	−0.828331	−0.414165	+	0.910202i	$0.635926\pi$
$588$	10.1463	0.418425
$589$	−25.7119	−1.05944
$590$	−24.9511	−1.02722
$591$	74.4911	3.06415
$592$	4.57756	0.188136
$593$	19.8211	0.813956	0.406978	−	0.913438i	$-0.366583\pi$
$593$	19.8211	0.813956	0.406978	+	0.913438i	$0.366583\pi$
$594$	−166.114	−6.81574
$595$	3.44576	0.141262
$596$	51.5305	2.11077
$597$	34.4319	1.40921
$598$	18.7721	0.767650
$599$	31.7468	1.29714	0.648569	−	0.761156i	$-0.275368\pi$
$599$	31.7468	1.29714	0.648569	+	0.761156i	$0.275368\pi$
$600$	−7.99050	−0.326211
$601$	−8.19949	−0.334464	−0.167232	−	0.985918i	$-0.553483\pi$
$601$	−8.19949	−0.334464	−0.167232	+	0.985918i	$0.553483\pi$
$602$	−10.9256	−0.445293
$603$	52.2409	2.12741
$604$	7.90372	0.321598
$605$	9.90435	0.402669
$606$	−83.8980	−3.40812
$607$	38.9985	1.58290	0.791451	−	0.611233i	$-0.209326\pi$
$607$	38.9985	1.58290	0.791451	+	0.611233i	$0.209326\pi$
$608$	−26.3507	−1.06866
$609$	−19.4016	−0.786194
$610$	−2.27851	−0.0922542
$611$	29.1766	1.18036
$612$	−83.5744	−3.37830
$613$	4.90038	0.197924	0.0989622	−	0.995091i	$-0.468448\pi$
$613$	4.90038	0.197924	0.0989622	+	0.995091i	$0.468448\pi$
$614$	−37.7696	−1.52426
$615$	30.8824	1.24530
$616$	11.0720	0.446102
$617$	−22.8985	−0.921858	−0.460929	−	0.887437i	$-0.652484\pi$
$617$	−22.8985	−0.921858	−0.460929	+	0.887437i	$0.652484\pi$
$618$	−69.7877	−2.80727
$619$	36.8021	1.47920	0.739601	−	0.673046i	$-0.235014\pi$
$619$	36.8021	1.47920	0.739601	+	0.673046i	$0.235014\pi$
$620$	19.2264	0.772151
$621$	22.5420	0.904579
$622$	74.3146	2.97974
$623$	−13.6034	−0.545009
$624$	13.6634	0.546973
$625$	1.00000	0.0400000
$626$	33.6876	1.34643
$627$	−62.0384	−2.47758
$628$	−10.3558	−0.413242
$629$	22.7094	0.905482
$630$	17.7691	0.707939
$631$	−13.0621	−0.519996	−0.259998	−	0.965609i	$-0.583722\pi$
$631$	−13.0621	−0.519996	−0.259998	+	0.965609i	$0.583722\pi$
$632$	−0.605143	−0.0240713
$633$	−66.9722	−2.66191
$634$	46.5004	1.84677
$635$	−19.0411	−0.755624
$636$	134.013	5.31396
$637$	−5.96180	−0.236215
$638$	−60.5626	−2.39770
$639$	−128.732	−5.09255
$640$	16.5747	0.655173
$641$	−31.7534	−1.25419	−0.627093	−	0.778945i	$-0.715755\pi$
$641$	−31.7534	−1.25419	−0.627093	+	0.778945i	$0.715755\pi$
$642$	100.069	3.94939
$643$	6.86452	0.270710	0.135355	−	0.990797i	$-0.456782\pi$
$643$	6.86452	0.270710	0.135355	+	0.990797i	$0.456782\pi$
$644$	−4.29793	−0.169362
$645$	−16.0028	−0.630110
$646$	−31.9209	−1.25591
$647$	−38.0896	−1.49746	−0.748728	−	0.662878i	$-0.769335\pi$
$647$	−38.0896	−1.49746	−0.748728	+	0.662878i	$0.769335\pi$
$648$	−71.5652	−2.81135
$649$	50.6398	1.98779
$650$	13.4305	0.526789
$651$	−20.6313	−0.808606
$652$	66.7694	2.61489
$653$	38.0389	1.48858	0.744289	−	0.667857i	$-0.232788\pi$
$653$	38.0389	1.48858	0.744289	+	0.667857i	$0.232788\pi$
$654$	−74.2876	−2.90487
$655$	14.4263	0.563682
$656$	−6.50065	−0.253808
$657$	−83.1297	−3.24320
$658$	−11.0249	−0.429794
$659$	9.63858	0.375466	0.187733	−	0.982220i	$-0.439886\pi$
$659$	9.63858	0.375466	0.187733	+	0.982220i	$0.439886\pi$
$660$	46.3901	1.80573
$661$	−48.2269	−1.87581	−0.937905	−	0.346891i	$-0.887237\pi$
$661$	−48.2269	−1.87581	−0.937905	+	0.346891i	$0.887237\pi$
$662$	−42.5055	−1.65202
$663$	67.7845	2.63253
$664$	−5.92576	−0.229964
$665$	4.11220	0.159464
$666$	117.108	4.53784
$667$	8.21847	0.318220
$668$	−30.0819	−1.16390
$669$	−51.0816	−1.97493
$670$	−14.9203	−0.576421
$671$	4.62438	0.178522
$672$	−21.1439	−0.815645
$673$	−22.7873	−0.878386	−0.439193	−	0.898393i	$-0.644736\pi$
$673$	−22.7873	−0.878386	−0.439193	+	0.898393i	$0.644736\pi$
$674$	3.90091	0.150257
$675$	16.1277	0.620755
$676$	69.3189	2.66611
$677$	13.0824	0.502798	0.251399	−	0.967884i	$-0.419109\pi$
$677$	13.0824	0.502798	0.251399	+	0.967884i	$0.419109\pi$
$678$	−88.6768	−3.40561
$679$	−3.03072	−0.116308
$680$	8.34432	0.319990
$681$	86.3889	3.31043
$682$	−64.4012	−2.46605
$683$	−0.102257	−0.00391274	−0.00195637	−	0.999998i	$-0.500623\pi$
$683$	−0.102257	−0.00391274	−0.00195637	+	0.999998i	$0.500623\pi$
$684$	−99.7385	−3.81360
$685$	6.09096	0.232724
$686$	2.25277	0.0860110
$687$	−3.29965	−0.125890
$688$	3.36854	0.128424
$689$	−78.7440	−2.99991
$690$	−10.3897	−0.395530
$691$	−28.7307	−1.09297	−0.546483	−	0.837470i	$-0.684034\pi$
$691$	−28.7307	−1.09297	−0.546483	+	0.837470i	$0.684034\pi$
$692$	−19.0092	−0.722621
$693$	−36.0635	−1.36994
$694$	−43.7161	−1.65944
$695$	5.87488	0.222847
$696$	−46.9834	−1.78090
$697$	−32.2499	−1.22155
$698$	−63.5204	−2.40428
$699$	−47.4411	−1.79439
$700$	−3.07495	−0.116222
$701$	19.5574	0.738674	0.369337	−	0.929295i	$-0.379585\pi$
$701$	19.5574	0.738674	0.369337	+	0.929295i	$0.379585\pi$
$702$	216.603	8.17517
$703$	27.1016	1.02216
$704$	−59.6500	−2.24814
$705$	−16.1483	−0.608179
$706$	30.1581	1.13501
$707$	−11.2867	−0.424481
$708$	112.378	4.22342
$709$	−5.88946	−0.221183	−0.110592	−	0.993866i	$-0.535275\pi$
$709$	−5.88946	−0.221183	−0.110592	+	0.993866i	$0.535275\pi$
$710$	36.7665	1.37982
$711$	1.97107	0.0739210
$712$	−32.9423	−1.23456
$713$	8.73936	0.327292
$714$	−25.6135	−0.958561
$715$	−27.2581	−1.01940
$716$	−13.6642	−0.510653
$717$	−47.9266	−1.78985
$718$	−13.0878	−0.488434
$719$	−35.2656	−1.31519	−0.657593	−	0.753373i	$-0.728425\pi$
$719$	−35.2656	−1.31519	−0.657593	+	0.753373i	$0.728425\pi$
$720$	−5.47852	−0.204172
$721$	−9.38847	−0.349645
$722$	4.70783	0.175207
$723$	9.87548	0.367273
$724$	−3.61706	−0.134427
$725$	5.87991	0.218374
$726$	−73.6224	−2.73238
$727$	−10.8425	−0.402125	−0.201062	−	0.979578i	$-0.564439\pi$
$727$	−10.8425	−0.402125	−0.201062	+	0.979578i	$0.564439\pi$
$728$	−14.4372	−0.535079
$729$	73.4549	2.72055
$730$	23.7423	0.878741
$731$	16.7114	0.618094
$732$	10.2622	0.379303
$733$	−0.864092	−0.0319160	−0.0159580	−	0.999873i	$-0.505080\pi$
$733$	−0.864092	−0.0319160	−0.0159580	+	0.999873i	$0.505080\pi$
$734$	−7.05704	−0.260480
$735$	3.29965	0.121709
$736$	8.95650	0.330141
$737$	30.2816	1.11544
$738$	−166.307	−6.12183
$739$	−8.08944	−0.297575	−0.148787	−	0.988869i	$-0.547537\pi$
$739$	−8.08944	−0.297575	−0.148787	+	0.988869i	$0.547537\pi$
$740$	−20.2656	−0.744978
$741$	80.8946	2.97174
$742$	29.7547	1.09233
$743$	36.0650	1.32310	0.661548	−	0.749903i	$-0.269900\pi$
$743$	36.0650	1.32310	0.661548	+	0.749903i	$0.269900\pi$
$744$	−49.9613	−1.83167
$745$	16.7581	0.613970
$746$	51.1527	1.87283
$747$	19.3014	0.706201
$748$	−48.4442	−1.77129
$749$	13.4621	0.491896
$750$	−7.43334	−0.271427
$751$	−30.6272	−1.11760	−0.558800	−	0.829302i	$-0.688738\pi$
$751$	−30.6272	−1.11760	−0.558800	+	0.829302i	$0.688738\pi$
$752$	3.39915	0.123954
$753$	34.6909	1.26421
$754$	78.9703	2.87593
$755$	2.57035	0.0935448
$756$	−49.5919	−1.80364
$757$	36.4642	1.32531	0.662656	−	0.748924i	$-0.269429\pi$
$757$	36.4642	1.32531	0.662656	+	0.748924i	$0.269429\pi$
$758$	25.0367	0.909375
$759$	21.0866	0.765395
$760$	9.95819	0.361221
$761$	−2.90772	−0.105405	−0.0527023	−	0.998610i	$-0.516783\pi$
$761$	−2.90772	−0.105405	−0.0527023	+	0.998610i	$0.516783\pi$
$762$	141.539	5.12742
$763$	−9.99384	−0.361801
$764$	−23.4315	−0.847722
$765$	−27.1791	−0.982662
$766$	−46.3277	−1.67389
$767$	−66.0315	−2.38426
$768$	−37.1081	−1.33902
$769$	−12.2217	−0.440725	−0.220363	−	0.975418i	$-0.570724\pi$
$769$	−12.2217	−0.440725	−0.220363	+	0.975418i	$0.570724\pi$
$770$	10.2999	0.371184
$771$	28.9182	1.04147
$772$	54.2964	1.95417
$773$	−31.3115	−1.12619	−0.563097	−	0.826391i	$-0.690390\pi$
$773$	−31.3115	−1.12619	−0.563097	+	0.826391i	$0.690390\pi$
$774$	86.1776	3.09759
$775$	6.25258	0.224599
$776$	−7.33925	−0.263464
$777$	21.7465	0.780150
$778$	−26.4956	−0.949914
$779$	−38.4873	−1.37895
$780$	−60.4901	−2.16589
$781$	−74.6198	−2.67011
$782$	10.8498	0.387988
$783$	94.8293	3.38892
$784$	−0.694565	−0.0248059
$785$	−3.36779	−0.120202
$786$	−107.236	−3.82496
$787$	53.3985	1.90345	0.951725	−	0.306952i	$-0.0993093\pi$
$787$	53.3985	1.90345	0.951725	+	0.306952i	$0.0993093\pi$
$788$	69.4185	2.47293
$789$	−4.12745	−0.146941
$790$	−0.562948	−0.0200288
$791$	−11.9296	−0.424168
$792$	−87.3322	−3.10321
$793$	−6.02993	−0.214129
$794$	−74.0807	−2.62903
$795$	43.5821	1.54570
$796$	32.0872	1.13730
$797$	2.87086	0.101691	0.0508456	−	0.998707i	$-0.483808\pi$
$797$	2.87086	0.101691	0.0508456	+	0.998707i	$0.483808\pi$
$798$	−30.5674	−1.08207
$799$	16.8633	0.596581
$800$	6.40793	0.226555
$801$	107.299	3.79124
$802$	53.8770	1.90246
$803$	−48.1864	−1.70046
$804$	67.1997	2.36995
$805$	−1.39772	−0.0492632
$806$	83.9756	2.95791
$807$	−25.8973	−0.911629
$808$	−27.3321	−0.961542
$809$	2.48352	0.0873158	0.0436579	−	0.999047i	$-0.486099\pi$
$809$	2.48352	0.0873158	0.0436579	+	0.999047i	$0.486099\pi$
$810$	−66.5751	−2.33921
$811$	48.8466	1.71524	0.857618	−	0.514288i	$-0.171944\pi$
$811$	48.8466	1.71524	0.857618	+	0.514288i	$0.171944\pi$
$812$	−18.0804	−0.634499
$813$	−100.134	−3.51186
$814$	67.8820	2.37926
$815$	21.7140	0.760606
$816$	7.89707	0.276453
$817$	19.9436	0.697737
$818$	79.6902	2.78630
$819$	47.0249	1.64318
$820$	28.7794	1.00502
$821$	−35.1864	−1.22801	−0.614007	−	0.789300i	$-0.710444\pi$
$821$	−35.1864	−1.22801	−0.614007	+	0.789300i	$0.710444\pi$
$822$	−45.2762	−1.57919
$823$	−29.8739	−1.04134	−0.520670	−	0.853758i	$-0.674318\pi$
$823$	−29.8739	−1.04134	−0.520670	+	0.853758i	$0.674318\pi$
$824$	−22.7353	−0.792022
$825$	15.0864	0.525242
$826$	24.9511	0.868160
$827$	−3.51177	−0.122116	−0.0610581	−	0.998134i	$-0.519447\pi$
$827$	−3.51177	−0.122116	−0.0610581	+	0.998134i	$0.519447\pi$
$828$	33.9007	1.17813
$829$	34.1705	1.18679	0.593396	−	0.804911i	$-0.297787\pi$
$829$	34.1705	1.18679	0.593396	+	0.804911i	$0.297787\pi$
$830$	−5.51257	−0.191344
$831$	22.3699	0.776005
$832$	77.7803	2.69655
$833$	−3.44576	−0.119388
$834$	−43.6699	−1.51217
$835$	−9.78287	−0.338550
$836$	−57.8138	−1.99953
$837$	100.840	3.48553
$838$	8.80454	0.304148
$839$	−21.6031	−0.745823	−0.372911	−	0.927867i	$-0.621640\pi$
$839$	−21.6031	−0.745823	−0.372911	+	0.927867i	$0.621640\pi$
$840$	7.99050	0.275698
$841$	5.57331	0.192183
$842$	40.8042	1.40621
$843$	−37.6974	−1.29837
$844$	−62.4116	−2.14830
$845$	22.5431	0.775505
$846$	86.9609	2.98978
$847$	−9.90435	−0.340317
$848$	−9.17388	−0.315032
$849$	106.357	3.65016
$850$	7.76248	0.266251
$851$	−9.21172	−0.315774
$852$	−165.593	−5.67313
$853$	33.2547	1.13862	0.569309	−	0.822123i	$-0.307211\pi$
$853$	33.2547	1.13862	0.569309	+	0.822123i	$0.307211\pi$
$854$	2.27851	0.0779690
$855$	−32.4358	−1.10928
$856$	32.6002	1.11425
$857$	12.4960	0.426857	0.213428	−	0.976959i	$-0.431537\pi$
$857$	12.4960	0.426857	0.213428	+	0.976959i	$0.431537\pi$
$858$	202.619	6.91729
$859$	46.1612	1.57500	0.787500	−	0.616314i	$-0.211375\pi$
$859$	46.1612	1.57500	0.787500	+	0.616314i	$0.211375\pi$
$860$	−14.9131	−0.508531
$861$	−30.8824	−1.05247
$862$	−25.6642	−0.874126
$863$	−20.1556	−0.686106	−0.343053	−	0.939316i	$-0.611461\pi$
$863$	−20.1556	−0.686106	−0.343053	+	0.939316i	$0.611461\pi$
$864$	103.345	3.51587
$865$	−6.18195	−0.210192
$866$	79.9989	2.71847
$867$	−16.9165	−0.574514
$868$	−19.2264	−0.652587
$869$	1.14254	0.0387579
$870$	−43.7074	−1.48182
$871$	−39.4856	−1.33792
$872$	−24.2013	−0.819559
$873$	23.9054	0.809075
$874$	12.9482	0.437981
$875$	−1.00000	−0.0338062
$876$	−106.933	−3.61294
$877$	−18.5971	−0.627979	−0.313990	−	0.949426i	$-0.601666\pi$
$877$	−18.5971	−0.627979	−0.313990	+	0.949426i	$0.601666\pi$
$878$	21.0927	0.711844
$879$	62.2335	2.09908
$880$	−3.17564	−0.107051
$881$	−1.62254	−0.0546649	−0.0273324	−	0.999626i	$-0.508701\pi$
$881$	−1.62254	−0.0546649	−0.0273324	+	0.999626i	$0.508701\pi$
$882$	−17.7691	−0.598318
$883$	−26.1989	−0.881662	−0.440831	−	0.897590i	$-0.645316\pi$
$883$	−26.1989	−0.881662	−0.440831	+	0.897590i	$0.645316\pi$
$884$	63.1685	2.12459
$885$	36.5462	1.22849
$886$	6.45803	0.216962
$887$	−19.7895	−0.664466	−0.332233	−	0.943197i	$-0.607802\pi$
$887$	−19.7895	−0.664466	−0.332233	+	0.943197i	$0.607802\pi$
$888$	52.6616	1.76721
$889$	19.0411	0.638619
$890$	−30.6453	−1.02723
$891$	135.118	4.52664
$892$	−47.6031	−1.59387
$893$	20.1248	0.673452
$894$	−124.569	−4.16621
$895$	−4.44369	−0.148536
$896$	−16.5747	−0.553722
$897$	−27.4958	−0.918057
$898$	65.9429	2.20054
$899$	36.7646	1.22617
$900$	24.2543	0.808476
$901$	−45.5119	−1.51622
$902$	−96.4002	−3.20978
$903$	16.0028	0.532540
$904$	−28.8890	−0.960833
$905$	−1.17630	−0.0391014
$906$	−19.1063	−0.634765
$907$	−11.0904	−0.368251	−0.184126	−	0.982903i	$-0.558945\pi$
$907$	−11.0904	−0.368251	−0.184126	+	0.982903i	$0.558945\pi$
$908$	80.5060	2.67169
$909$	89.0262	2.95281
$910$	−13.4305	−0.445218
$911$	50.5933	1.67623	0.838115	−	0.545494i	$-0.183658\pi$
$911$	50.5933	1.67623	0.838115	+	0.545494i	$0.183658\pi$
$912$	9.42444	0.312074
$913$	11.1881	0.370272
$914$	64.6281	2.13771
$915$	3.33736	0.110330
$916$	−3.07495	−0.101599
$917$	−14.4263	−0.476398
$918$	125.191	4.13191
$919$	14.0781	0.464394	0.232197	−	0.972669i	$-0.425409\pi$
$919$	14.0781	0.464394	0.232197	+	0.972669i	$0.425409\pi$
$920$	−3.38475	−0.111592
$921$	55.3215	1.82290
$922$	−29.4247	−0.969050
$923$	97.3001	3.20267
$924$	−46.3901	−1.52612
$925$	−6.59053	−0.216695
$926$	−82.5468	−2.71266
$927$	74.0534	2.43223
$928$	37.6781	1.23684
$929$	−7.95276	−0.260921	−0.130461	−	0.991453i	$-0.541646\pi$
$929$	−7.95276	−0.260921	−0.130461	+	0.991453i	$0.541646\pi$
$930$	−46.4776	−1.52406
$931$	−4.11220	−0.134772
$932$	−44.2105	−1.44816
$933$	−108.849	−3.56357
$934$	−35.4414	−1.15968
$935$	−15.7544	−0.515225
$936$	113.876	3.72216
$937$	21.6529	0.707369	0.353684	−	0.935365i	$-0.384929\pi$
$937$	21.6529	0.707369	0.353684	+	0.935365i	$0.384929\pi$
$938$	14.9203	0.487164
$939$	−49.3426	−1.61023
$940$	−15.0486	−0.490832
$941$	48.3813	1.57719	0.788593	−	0.614916i	$-0.210810\pi$
$941$	48.3813	1.57719	0.788593	+	0.614916i	$0.210810\pi$
$942$	25.0339	0.815650
$943$	13.0817	0.425998
$944$	−7.69284	−0.250381
$945$	−16.1277	−0.524633
$946$	49.9531	1.62412
$947$	−27.9615	−0.908627	−0.454314	−	0.890842i	$-0.650115\pi$
$947$	−27.9615	−0.908627	−0.454314	+	0.890842i	$0.650115\pi$
$948$	2.53547	0.0823483
$949$	62.8324	2.03963
$950$	9.26383	0.300558
$951$	−68.1097	−2.20861
$952$	−8.34432	−0.270441
$953$	−15.4745	−0.501267	−0.250633	−	0.968082i	$-0.580639\pi$
$953$	−15.4745	−0.501267	−0.250633	+	0.968082i	$0.580639\pi$
$954$	−234.696	−7.59857
$955$	−7.62011	−0.246581
$956$	−44.6629	−1.44450
$957$	88.7068	2.86748
$958$	42.7871	1.38239
$959$	−6.09096	−0.196687
$960$	−43.0487	−1.38939
$961$	8.09480	0.261122
$962$	−88.5144	−2.85382
$963$	−106.185	−3.42177
$964$	9.20299	0.296408
$965$	17.6576	0.568419
$966$	10.3897	0.334284
$967$	−3.07661	−0.0989370	−0.0494685	−	0.998776i	$-0.515753\pi$
$967$	−3.07661	−0.0989370	−0.0494685	+	0.998776i	$0.515753\pi$
$968$	−23.9846	−0.770893
$969$	46.7549	1.50198
$970$	−6.82751	−0.219218
$971$	−30.1007	−0.965979	−0.482989	−	0.875626i	$-0.660449\pi$
$971$	−30.1007	−0.965979	−0.482989	+	0.875626i	$0.660449\pi$
$972$	151.073	4.84568
$973$	−5.87488	−0.188340
$974$	91.3909	2.92835
$975$	−19.6719	−0.630004
$976$	−0.702503	−0.0224866
$977$	41.0040	1.31184	0.655918	−	0.754833i	$-0.272282\pi$
$977$	41.0040	1.31184	0.655918	+	0.754833i	$0.272282\pi$
$978$	−161.407	−5.16123
$979$	62.1965	1.98781
$980$	3.07495	0.0982258
$981$	78.8283	2.51679
$982$	41.2534	1.31645
$983$	10.6712	0.340358	0.170179	−	0.985413i	$-0.445565\pi$
$983$	10.6712	0.340358	0.170179	+	0.985413i	$0.445565\pi$
$984$	−74.7855	−2.38408
$985$	22.5754	0.719314
$986$	45.6427	1.45356
$987$	16.1483	0.514005
$988$	75.3860	2.39835
$989$	−6.77874	−0.215551
$990$	−81.2427	−2.58206
$991$	34.3746	1.09195	0.545973	−	0.837803i	$-0.316160\pi$
$991$	34.3746	1.09195	0.545973	+	0.837803i	$0.316160\pi$
$992$	40.0661	1.27210
$993$	62.2583	1.97571
$994$	−36.7665	−1.16616
$995$	10.4350	0.330813
$996$	24.8282	0.786711
$997$	−0.978141	−0.0309780	−0.0154890	−	0.999880i	$-0.504931\pi$
$997$	−0.978141	−0.0309780	−0.0154890	+	0.999880i	$0.504931\pi$
$998$	−27.5929	−0.873437
$999$	−106.290	−3.36287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.9	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.9	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25277 q^{2} +3.29965 q^{3} +3.07495 q^{4} +1.00000 q^{5} -7.43334 q^{6} -1.00000 q^{7} -2.42162 q^{8} +7.88769 q^{9} +O(q^{10})\)	\(q-2.25277 q^{2} +3.29965 q^{3} +3.07495 q^{4} +1.00000 q^{5} -7.43334 q^{6} -1.00000 q^{7} -2.42162 q^{8} +7.88769 q^{9} -2.25277 q^{10} +4.57213 q^{11} +10.1463 q^{12} -5.96180 q^{13} +2.25277 q^{14} +3.29965 q^{15} -0.694565 q^{16} -3.44576 q^{17} -17.7691 q^{18} -4.11220 q^{19} +3.07495 q^{20} -3.29965 q^{21} -10.2999 q^{22} +1.39772 q^{23} -7.99050 q^{24} +1.00000 q^{25} +13.4305 q^{26} +16.1277 q^{27} -3.07495 q^{28} +5.87991 q^{29} -7.43334 q^{30} +6.25258 q^{31} +6.40793 q^{32} +15.0864 q^{33} +7.76248 q^{34} -1.00000 q^{35} +24.2543 q^{36} -6.59053 q^{37} +9.26383 q^{38} -19.6719 q^{39} -2.42162 q^{40} +9.35930 q^{41} +7.43334 q^{42} -4.84985 q^{43} +14.0591 q^{44} +7.88769 q^{45} -3.14874 q^{46} -4.89393 q^{47} -2.29182 q^{48} +1.00000 q^{49} -2.25277 q^{50} -11.3698 q^{51} -18.3323 q^{52} +13.2081 q^{53} -36.3319 q^{54} +4.57213 q^{55} +2.42162 q^{56} -13.5688 q^{57} -13.2461 q^{58} +11.0758 q^{59} +10.1463 q^{60} +1.01143 q^{61} -14.0856 q^{62} -7.88769 q^{63} -13.0464 q^{64} -5.96180 q^{65} -33.9862 q^{66} +6.62309 q^{67} -10.5955 q^{68} +4.61199 q^{69} +2.25277 q^{70} -16.3206 q^{71} -19.1010 q^{72} -10.5392 q^{73} +14.8469 q^{74} +3.29965 q^{75} -12.6448 q^{76} -4.57213 q^{77} +44.3161 q^{78} +0.249892 q^{79} -0.694565 q^{80} +29.5526 q^{81} -21.0843 q^{82} +2.44702 q^{83} -10.1463 q^{84} -3.44576 q^{85} +10.9256 q^{86} +19.4016 q^{87} -11.0720 q^{88} +13.6034 q^{89} -17.7691 q^{90} +5.96180 q^{91} +4.29793 q^{92} +20.6313 q^{93} +11.0249 q^{94} -4.11220 q^{95} +21.1439 q^{96} +3.03072 q^{97} -2.25277 q^{98} +36.0635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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