LMFDB - Embedded newform 8015.2.a.l.1.23

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:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
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)

$f(q)$	$=$	$q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +O(q^{10})$	\(q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +0.883363 q^{10} +6.34675 q^{11} -2.47987 q^{12} +2.46714 q^{13} +0.883363 q^{14} -2.03323 q^{15} -0.0730644 q^{16} -7.94029 q^{17} -1.00177 q^{18} -0.535203 q^{19} +1.21967 q^{20} -2.03323 q^{21} -5.60648 q^{22} -7.18811 q^{23} +5.78280 q^{24} +1.00000 q^{25} -2.17938 q^{26} -3.79393 q^{27} +1.21967 q^{28} +3.71349 q^{29} +1.79608 q^{30} +7.48378 q^{31} -5.62373 q^{32} +12.9044 q^{33} +7.01416 q^{34} +1.00000 q^{35} -1.38316 q^{36} +10.3832 q^{37} +0.472778 q^{38} +5.01627 q^{39} -2.84414 q^{40} -3.56613 q^{41} +1.79608 q^{42} +0.896867 q^{43} -7.74094 q^{44} -1.13404 q^{45} +6.34971 q^{46} +5.81099 q^{47} -0.148557 q^{48} +1.00000 q^{49} -0.883363 q^{50} -16.1445 q^{51} -3.00910 q^{52} +6.83234 q^{53} +3.35142 q^{54} -6.34675 q^{55} -2.84414 q^{56} -1.08819 q^{57} -3.28036 q^{58} -14.7175 q^{59} +2.47987 q^{60} +9.25738 q^{61} -6.61089 q^{62} -1.13404 q^{63} +5.11392 q^{64} -2.46714 q^{65} -11.3993 q^{66} -1.67234 q^{67} +9.68454 q^{68} -14.6151 q^{69} -0.883363 q^{70} -4.43857 q^{71} +3.22537 q^{72} -4.00883 q^{73} -9.17216 q^{74} +2.03323 q^{75} +0.652771 q^{76} -6.34675 q^{77} -4.43119 q^{78} +4.06403 q^{79} +0.0730644 q^{80} -11.1161 q^{81} +3.15019 q^{82} +14.7447 q^{83} +2.47987 q^{84} +7.94029 q^{85} -0.792259 q^{86} +7.55039 q^{87} +18.0510 q^{88} -0.355306 q^{89} +1.00177 q^{90} -2.46714 q^{91} +8.76712 q^{92} +15.2163 q^{93} -5.13321 q^{94} +0.535203 q^{95} -11.4344 q^{96} +16.5587 q^{97} -0.883363 q^{98} +7.19747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−0.883363	−0.624632	−0.312316	−	0.949978i	$-0.601105\pi$
$2$	−0.883363	−0.624632	−0.312316	+	0.949978i	$0.601105\pi$
$3$	2.03323	1.17389	0.586944	−	0.809627i	$-0.300331\pi$
$3$	2.03323	1.17389	0.586944	+	0.809627i	$0.300331\pi$
$4$	−1.21967	−0.609835
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.79608	−0.733248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.84414	1.00555
$9$	1.13404	0.378014
$10$	0.883363	0.279344
$11$	6.34675	1.91362	0.956808	−	0.290720i	$-0.0938947\pi$
$11$	6.34675	1.91362	0.956808	+	0.290720i	$0.0938947\pi$
$12$	−2.47987	−0.715878
$13$	2.46714	0.684262	0.342131	−	0.939652i	$-0.388851\pi$
$13$	2.46714	0.684262	0.342131	+	0.939652i	$0.388851\pi$
$14$	0.883363	0.236089
$15$	−2.03323	−0.524979
$16$	−0.0730644	−0.0182661
$17$	−7.94029	−1.92580	−0.962902	−	0.269851i	$-0.913025\pi$
$17$	−7.94029	−1.92580	−0.962902	+	0.269851i	$0.913025\pi$
$18$	−1.00177	−0.236119
$19$	−0.535203	−0.122784	−0.0613920	−	0.998114i	$-0.519554\pi$
$19$	−0.535203	−0.122784	−0.0613920	+	0.998114i	$0.519554\pi$
$20$	1.21967	0.272727
$21$	−2.03323	−0.443688
$22$	−5.60648	−1.19531
$23$	−7.18811	−1.49882	−0.749412	−	0.662104i	$-0.769664\pi$
$23$	−7.18811	−1.49882	−0.749412	+	0.662104i	$0.769664\pi$
$24$	5.78280	1.18041
$25$	1.00000	0.200000
$26$	−2.17938	−0.427412
$27$	−3.79393	−0.730142
$28$	1.21967	0.230496
$29$	3.71349	0.689577	0.344789	−	0.938680i	$-0.387951\pi$
$29$	3.71349	0.689577	0.344789	+	0.938680i	$0.387951\pi$
$30$	1.79608	0.327918
$31$	7.48378	1.34413	0.672063	−	0.740494i	$-0.265408\pi$
$31$	7.48378	1.34413	0.672063	+	0.740494i	$0.265408\pi$
$32$	−5.62373	−0.994145
$33$	12.9044	2.24637
$34$	7.01416	1.20292
$35$	1.00000	0.169031
$36$	−1.38316	−0.230526
$37$	10.3832	1.70699	0.853497	−	0.521098i	$-0.174478\pi$
$37$	10.3832	1.70699	0.853497	+	0.521098i	$0.174478\pi$
$38$	0.472778	0.0766947
$39$	5.01627	0.803247
$40$	−2.84414	−0.449698
$41$	−3.56613	−0.556936	−0.278468	−	0.960445i	$-0.589827\pi$
$41$	−3.56613	−0.556936	−0.278468	+	0.960445i	$0.589827\pi$
$42$	1.79608	0.277142
$43$	0.896867	0.136771	0.0683855	−	0.997659i	$-0.478215\pi$
$43$	0.896867	0.136771	0.0683855	+	0.997659i	$0.478215\pi$
$44$	−7.74094	−1.16699
$45$	−1.13404	−0.169053
$46$	6.34971	0.936213
$47$	5.81099	0.847620	0.423810	−	0.905751i	$-0.360693\pi$
$47$	5.81099	0.847620	0.423810	+	0.905751i	$0.360693\pi$
$48$	−0.148557	−0.0214424
$49$	1.00000	0.142857
$50$	−0.883363	−0.124926
$51$	−16.1445	−2.26068
$52$	−3.00910	−0.417287
$53$	6.83234	0.938494	0.469247	−	0.883067i	$-0.344525\pi$
$53$	6.83234	0.938494	0.469247	+	0.883067i	$0.344525\pi$
$54$	3.35142	0.456070
$55$	−6.34675	−0.855795
$56$	−2.84414	−0.380064
$57$	−1.08819	−0.144135
$58$	−3.28036	−0.430732
$59$	−14.7175	−1.91605	−0.958027	−	0.286679i	$-0.907449\pi$
$59$	−14.7175	−1.91605	−0.958027	+	0.286679i	$0.907449\pi$
$60$	2.47987	0.320150
$61$	9.25738	1.18529	0.592643	−	0.805465i	$-0.298085\pi$
$61$	9.25738	1.18529	0.592643	+	0.805465i	$0.298085\pi$
$62$	−6.61089	−0.839584
$63$	−1.13404	−0.142876
$64$	5.11392	0.639240
$65$	−2.46714	−0.306011
$66$	−11.3993	−1.40316
$67$	−1.67234	−0.204309	−0.102155	−	0.994769i	$-0.532574\pi$
$67$	−1.67234	−0.204309	−0.102155	+	0.994769i	$0.532574\pi$
$68$	9.68454	1.17442
$69$	−14.6151	−1.75945
$70$	−0.883363	−0.105582
$71$	−4.43857	−0.526761	−0.263380	−	0.964692i	$-0.584837\pi$
$71$	−4.43857	−0.526761	−0.263380	+	0.964692i	$0.584837\pi$
$72$	3.22537	0.380113
$73$	−4.00883	−0.469198	−0.234599	−	0.972092i	$-0.575378\pi$
$73$	−4.00883	−0.469198	−0.234599	+	0.972092i	$0.575378\pi$
$74$	−9.17216	−1.06624
$75$	2.03323	0.234778
$76$	0.652771	0.0748779
$77$	−6.34675	−0.723279
$78$	−4.43119	−0.501733
$79$	4.06403	0.457239	0.228619	−	0.973516i	$-0.426579\pi$
$79$	4.06403	0.457239	0.228619	+	0.973516i	$0.426579\pi$
$80$	0.0730644	0.00816885
$81$	−11.1161	−1.23512
$82$	3.15019	0.347880
$83$	14.7447	1.61844	0.809222	−	0.587503i	$-0.199889\pi$
$83$	14.7447	1.61844	0.809222	+	0.587503i	$0.199889\pi$
$84$	2.47987	0.270577
$85$	7.94029	0.861246
$86$	−0.792259	−0.0854315
$87$	7.55039	0.809486
$88$	18.0510	1.92425
$89$	−0.355306	−0.0376623	−0.0188312	−	0.999823i	$-0.505994\pi$
$89$	−0.355306	−0.0376623	−0.0188312	+	0.999823i	$0.505994\pi$
$90$	1.00177	0.105596
$91$	−2.46714	−0.258627
$92$	8.76712	0.914035
$93$	15.2163	1.57785
$94$	−5.13321	−0.529450
$95$	0.535203	0.0549106
$96$	−11.4344	−1.16701
$97$	16.5587	1.68128	0.840641	−	0.541593i	$-0.182179\pi$
$97$	16.5587	1.68128	0.840641	+	0.541593i	$0.182179\pi$
$98$	−0.883363	−0.0892331
$99$	7.19747	0.723373
$100$	−1.21967	−0.121967
$101$	−14.5424	−1.44702	−0.723509	−	0.690315i	$-0.757472\pi$
$101$	−14.5424	−1.44702	−0.723509	+	0.690315i	$0.757472\pi$
$102$	14.2614	1.41209
$103$	4.66526	0.459681	0.229841	−	0.973228i	$-0.426179\pi$
$103$	4.66526	0.459681	0.229841	+	0.973228i	$0.426179\pi$
$104$	7.01688	0.688062
$105$	2.03323	0.198423
$106$	−6.03544	−0.586213
$107$	−7.94332	−0.767910	−0.383955	−	0.923352i	$-0.625438\pi$
$107$	−7.94332	−0.767910	−0.383955	+	0.923352i	$0.625438\pi$
$108$	4.62735	0.445266
$109$	−5.47547	−0.524455	−0.262227	−	0.965006i	$-0.584457\pi$
$109$	−5.47547	−0.524455	−0.262227	+	0.965006i	$0.584457\pi$
$110$	5.60648	0.534557
$111$	21.1115	2.00382
$112$	0.0730644	0.00690394
$113$	18.4478	1.73543	0.867713	−	0.497065i	$-0.165589\pi$
$113$	18.4478	1.73543	0.867713	+	0.497065i	$0.165589\pi$
$114$	0.961269	0.0900311
$115$	7.18811	0.670294
$116$	−4.52923	−0.420528
$117$	2.79784	0.258660
$118$	13.0009	1.19683
$119$	7.94029	0.727885
$120$	−5.78280	−0.527895
$121$	29.2812	2.66193
$122$	−8.17762	−0.740367
$123$	−7.25078	−0.653781
$124$	−9.12774	−0.819695
$125$	−1.00000	−0.0894427
$126$	1.00177	0.0892447
$127$	−6.10162	−0.541431	−0.270716	−	0.962659i	$-0.587260\pi$
$127$	−6.10162	−0.541431	−0.270716	+	0.962659i	$0.587260\pi$
$128$	6.73001	0.594855
$129$	1.82354	0.160554
$130$	2.17938	0.191144
$131$	−11.9131	−1.04085	−0.520427	−	0.853906i	$-0.674227\pi$
$131$	−11.9131	−1.04085	−0.520427	+	0.853906i	$0.674227\pi$
$132$	−15.7391	−1.36992
$133$	0.535203	0.0464080
$134$	1.47729	0.127618
$135$	3.79393	0.326530
$136$	−22.5833	−1.93650
$137$	−7.13296	−0.609410	−0.304705	−	0.952447i	$-0.598558\pi$
$137$	−7.13296	−0.609410	−0.304705	+	0.952447i	$0.598558\pi$
$138$	12.9104	1.09901
$139$	7.50424	0.636501	0.318250	−	0.948007i	$-0.396905\pi$
$139$	7.50424	0.636501	0.318250	+	0.948007i	$0.396905\pi$
$140$	−1.21967	−0.103081
$141$	11.8151	0.995011
$142$	3.92086	0.329032
$143$	15.6583	1.30941
$144$	−0.0828581	−0.00690484
$145$	−3.71349	−0.308388
$146$	3.54125	0.293076
$147$	2.03323	0.167698
$148$	−12.6641	−1.04098
$149$	19.8264	1.62424	0.812120	−	0.583490i	$-0.198313\pi$
$149$	19.8264	1.62424	0.812120	+	0.583490i	$0.198313\pi$
$150$	−1.79608	−0.146650
$151$	−21.0775	−1.71526	−0.857630	−	0.514268i	$-0.828064\pi$
$151$	−21.0775	−1.71526	−0.857630	+	0.514268i	$0.828064\pi$
$152$	−1.52219	−0.123466
$153$	−9.00462	−0.727980
$154$	5.60648	0.451783
$155$	−7.48378	−0.601111
$156$	−6.11820	−0.489848
$157$	10.4756	0.836042	0.418021	−	0.908437i	$-0.362724\pi$
$157$	10.4756	0.836042	0.418021	+	0.908437i	$0.362724\pi$
$158$	−3.59001	−0.285606
$159$	13.8917	1.10169
$160$	5.62373	0.444595
$161$	7.18811	0.566502
$162$	9.81953	0.771495
$163$	−0.101106	−0.00791920	−0.00395960	−	0.999992i	$-0.501260\pi$
$163$	−0.101106	−0.00791920	−0.00395960	+	0.999992i	$0.501260\pi$
$164$	4.34950	0.339639
$165$	−12.9044	−1.00461
$166$	−13.0249	−1.01093
$167$	16.4514	1.27305	0.636524	−	0.771257i	$-0.280372\pi$
$167$	16.4514	1.27305	0.636524	+	0.771257i	$0.280372\pi$
$168$	−5.78280	−0.446152
$169$	−6.91322	−0.531786
$170$	−7.01416	−0.537961
$171$	−0.606942	−0.0464140
$172$	−1.09388	−0.0834077
$173$	−17.2459	−1.31118	−0.655591	−	0.755116i	$-0.727580\pi$
$173$	−17.2459	−1.31118	−0.655591	+	0.755116i	$0.727580\pi$
$174$	−6.66973	−0.505631
$175$	−1.00000	−0.0755929
$176$	−0.463722	−0.0349543
$177$	−29.9241	−2.24923
$178$	0.313864	0.0235251
$179$	−17.8538	−1.33445	−0.667227	−	0.744855i	$-0.732519\pi$
$179$	−17.8538	−1.33445	−0.667227	+	0.744855i	$0.732519\pi$
$180$	1.38316	0.103094
$181$	3.50394	0.260446	0.130223	−	0.991485i	$-0.458431\pi$
$181$	3.50394	0.260446	0.130223	+	0.991485i	$0.458431\pi$
$182$	2.17938	0.161546
$183$	18.8224	1.39139
$184$	−20.4440	−1.50715
$185$	−10.3832	−0.763391
$186$	−13.4415	−0.985578
$187$	−50.3950	−3.68525
$188$	−7.08749	−0.516908
$189$	3.79393	0.275968
$190$	−0.472778	−0.0342989
$191$	0.526136	0.0380698	0.0190349	−	0.999819i	$-0.493941\pi$
$191$	0.526136	0.0380698	0.0190349	+	0.999819i	$0.493941\pi$
$192$	10.3978	0.750397
$193$	27.1795	1.95642	0.978212	−	0.207609i	$-0.0665681\pi$
$193$	27.1795	1.95642	0.978212	+	0.207609i	$0.0665681\pi$
$194$	−14.6273	−1.05018
$195$	−5.01627	−0.359223
$196$	−1.21967	−0.0871193
$197$	−4.65848	−0.331903	−0.165951	−	0.986134i	$-0.553069\pi$
$197$	−4.65848	−0.331903	−0.165951	+	0.986134i	$0.553069\pi$
$198$	−6.35798	−0.451842
$199$	−2.75427	−0.195245	−0.0976226	−	0.995224i	$-0.531124\pi$
$199$	−2.75427	−0.195245	−0.0976226	+	0.995224i	$0.531124\pi$
$200$	2.84414	0.201111
$201$	−3.40027	−0.239836
$202$	12.8462	0.903853
$203$	−3.71349	−0.260636
$204$	19.6909	1.37864
$205$	3.56613	0.249069
$206$	−4.12111	−0.287132
$207$	−8.15161	−0.566576
$208$	−0.180260	−0.0124988
$209$	−3.39680	−0.234961
$210$	−1.79608	−0.123942
$211$	−17.3275	−1.19287	−0.596437	−	0.802660i	$-0.703417\pi$
$211$	−17.3275	−1.19287	−0.596437	+	0.802660i	$0.703417\pi$
$212$	−8.33320	−0.572327
$213$	−9.02464	−0.618358
$214$	7.01684	0.479661
$215$	−0.896867	−0.0611658
$216$	−10.7905	−0.734198
$217$	−7.48378	−0.508032
$218$	4.83682	0.327591
$219$	−8.15089	−0.550786
$220$	7.74094	0.521894
$221$	−19.5898	−1.31775
$222$	−18.6492	−1.25165
$223$	2.48021	0.166087	0.0830437	−	0.996546i	$-0.473536\pi$
$223$	2.48021	0.166087	0.0830437	+	0.996546i	$0.473536\pi$
$224$	5.62373	0.375751
$225$	1.13404	0.0756027
$226$	−16.2961	−1.08400
$227$	18.5424	1.23070	0.615351	−	0.788253i	$-0.289014\pi$
$227$	18.5424	1.23070	0.615351	+	0.788253i	$0.289014\pi$
$228$	1.32724	0.0878983
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−6.34971	−0.418687
$231$	−12.9044	−0.849049
$232$	10.5617	0.693407
$233$	19.7062	1.29100	0.645498	−	0.763762i	$-0.276650\pi$
$233$	19.7062	1.29100	0.645498	+	0.763762i	$0.276650\pi$
$234$	−2.47151	−0.161567
$235$	−5.81099	−0.379067
$236$	17.9505	1.16848
$237$	8.26312	0.536747
$238$	−7.01416	−0.454660
$239$	20.1134	1.30102	0.650512	−	0.759496i	$-0.274554\pi$
$239$	20.1134	1.30102	0.650512	+	0.759496i	$0.274554\pi$
$240$	0.148557	0.00958932
$241$	15.2440	0.981950	0.490975	−	0.871174i	$-0.336641\pi$
$241$	15.2440	0.981950	0.490975	+	0.871174i	$0.336641\pi$
$242$	−25.8659	−1.66273
$243$	−11.2198	−0.719750
$244$	−11.2909	−0.722829
$245$	−1.00000	−0.0638877
$246$	6.40507	0.408372
$247$	−1.32042	−0.0840163
$248$	21.2849	1.35159
$249$	29.9795	1.89987
$250$	0.883363	0.0558688
$251$	27.3681	1.72746	0.863730	−	0.503955i	$-0.168122\pi$
$251$	27.3681	1.72746	0.863730	+	0.503955i	$0.168122\pi$
$252$	1.38316	0.0871306
$253$	−45.6211	−2.86817
$254$	5.38994	0.338195
$255$	16.1445	1.01101
$256$	−16.1729	−1.01081
$257$	−3.58806	−0.223817	−0.111909	−	0.993718i	$-0.535696\pi$
$257$	−3.58806	−0.223817	−0.111909	+	0.993718i	$0.535696\pi$
$258$	−1.61085	−0.100287
$259$	−10.3832	−0.645183
$260$	3.00910	0.186616
$261$	4.21125	0.260670
$262$	10.5236	0.650150
$263$	−12.5866	−0.776123	−0.388061	−	0.921634i	$-0.626855\pi$
$263$	−12.5866	−0.776123	−0.388061	+	0.921634i	$0.626855\pi$
$264$	36.7019	2.25885
$265$	−6.83234	−0.419707
$266$	−0.472778	−0.0289879
$267$	−0.722420	−0.0442114
$268$	2.03971	0.124595
$269$	16.0251	0.977068	0.488534	−	0.872545i	$-0.337532\pi$
$269$	16.0251	0.977068	0.488534	+	0.872545i	$0.337532\pi$
$270$	−3.35142	−0.203961
$271$	14.5842	0.885928	0.442964	−	0.896540i	$-0.353927\pi$
$271$	14.5842	0.885928	0.442964	+	0.896540i	$0.353927\pi$
$272$	0.580153	0.0351769
$273$	−5.01627	−0.303599
$274$	6.30099	0.380657
$275$	6.34675	0.382723
$276$	17.8256	1.07298
$277$	−11.8124	−0.709740	−0.354870	−	0.934916i	$-0.615475\pi$
$277$	−11.8124	−0.709740	−0.354870	+	0.934916i	$0.615475\pi$
$278$	−6.62896	−0.397579
$279$	8.48691	0.508098
$280$	2.84414	0.169970
$281$	−28.1359	−1.67845	−0.839223	−	0.543787i	$-0.816990\pi$
$281$	−28.1359	−1.67845	−0.839223	+	0.543787i	$0.816990\pi$
$282$	−10.4370	−0.621515
$283$	−3.46777	−0.206138	−0.103069	−	0.994674i	$-0.532866\pi$
$283$	−3.46777	−0.206138	−0.103069	+	0.994674i	$0.532866\pi$
$284$	5.41359	0.321237
$285$	1.08819	0.0644590
$286$	−13.8320	−0.817902
$287$	3.56613	0.210502
$288$	−6.37754	−0.375800
$289$	46.0483	2.70872
$290$	3.28036	0.192629
$291$	33.6677	1.97364
$292$	4.88945	0.286134
$293$	27.8880	1.62923	0.814617	−	0.580000i	$-0.196947\pi$
$293$	27.8880	1.62923	0.814617	+	0.580000i	$0.196947\pi$
$294$	−1.79608	−0.104750
$295$	14.7175	0.856885
$296$	29.5313	1.71647
$297$	−24.0791	−1.39721
$298$	−17.5139	−1.01455
$299$	−17.7341	−1.02559
$300$	−2.47987	−0.143176
$301$	−0.896867	−0.0516946
$302$	18.6190	1.07141
$303$	−29.5680	−1.69864
$304$	0.0391043	0.00224278
$305$	−9.25738	−0.530076
$306$	7.95434	0.454720
$307$	11.7107	0.668363	0.334181	−	0.942509i	$-0.391540\pi$
$307$	11.7107	0.668363	0.334181	+	0.942509i	$0.391540\pi$
$308$	7.74094	0.441081
$309$	9.48556	0.539615
$310$	6.61089	0.375473
$311$	1.46265	0.0829392	0.0414696	−	0.999140i	$-0.486796\pi$
$311$	1.46265	0.0829392	0.0414696	+	0.999140i	$0.486796\pi$
$312$	14.2670	0.807708
$313$	16.5687	0.936518	0.468259	−	0.883591i	$-0.344881\pi$
$313$	16.5687	0.936518	0.468259	+	0.883591i	$0.344881\pi$
$314$	−9.25374	−0.522219
$315$	1.13404	0.0638960
$316$	−4.95677	−0.278840
$317$	−12.1196	−0.680703	−0.340352	−	0.940298i	$-0.610546\pi$
$317$	−12.1196	−0.680703	−0.340352	+	0.940298i	$0.610546\pi$
$318$	−12.2715	−0.688149
$319$	23.5686	1.31959
$320$	−5.11392	−0.285877
$321$	−16.1506	−0.901440
$322$	−6.34971	−0.353855
$323$	4.24967	0.236458
$324$	13.5579	0.753219
$325$	2.46714	0.136852
$326$	0.0893129	0.00494659
$327$	−11.1329	−0.615651
$328$	−10.1426	−0.560029
$329$	−5.81099	−0.320370
$330$	11.3993	0.627510
$331$	16.3250	0.897302	0.448651	−	0.893707i	$-0.351905\pi$
$331$	16.3250	0.897302	0.448651	+	0.893707i	$0.351905\pi$
$332$	−17.9837	−0.986984
$333$	11.7750	0.645267
$334$	−14.5326	−0.795186
$335$	1.67234	0.0913699
$336$	0.148557	0.00810445
$337$	18.4882	1.00712	0.503558	−	0.863961i	$-0.332024\pi$
$337$	18.4882	1.00712	0.503558	+	0.863961i	$0.332024\pi$
$338$	6.10688	0.332171
$339$	37.5088	2.03720
$340$	−9.68454	−0.525218
$341$	47.4976	2.57214
$342$	0.536150	0.0289917
$343$	−1.00000	−0.0539949
$344$	2.55081	0.137531
$345$	14.6151	0.786851
$346$	15.2344	0.819006
$347$	16.1260	0.865687	0.432843	−	0.901469i	$-0.357510\pi$
$347$	16.1260	0.865687	0.432843	+	0.901469i	$0.357510\pi$
$348$	−9.20898	−0.493653
$349$	18.4447	0.987321	0.493661	−	0.869655i	$-0.335659\pi$
$349$	18.4447	0.987321	0.493661	+	0.869655i	$0.335659\pi$
$350$	0.883363	0.0472177
$351$	−9.36016	−0.499608
$352$	−35.6924	−1.90241
$353$	5.94436	0.316386	0.158193	−	0.987408i	$-0.449433\pi$
$353$	5.94436	0.316386	0.158193	+	0.987408i	$0.449433\pi$
$354$	26.4338	1.40494
$355$	4.43857	0.235575
$356$	0.433356	0.0229678
$357$	16.1445	0.854456
$358$	15.7714	0.833542
$359$	−25.5133	−1.34654	−0.673269	−	0.739398i	$-0.735110\pi$
$359$	−25.5133	−1.34654	−0.673269	+	0.739398i	$0.735110\pi$
$360$	−3.22537	−0.169992
$361$	−18.7136	−0.984924
$362$	−3.09525	−0.162683
$363$	59.5356	3.12481
$364$	3.00910	0.157720
$365$	4.00883	0.209832
$366$	−16.6270	−0.869108
$367$	21.1556	1.10431	0.552157	−	0.833740i	$-0.313805\pi$
$367$	21.1556	1.10431	0.552157	+	0.833740i	$0.313805\pi$
$368$	0.525195	0.0273777
$369$	−4.04414	−0.210529
$370$	9.17216	0.476838
$371$	−6.83234	−0.354717
$372$	−18.5588	−0.962231
$373$	5.42023	0.280649	0.140324	−	0.990106i	$-0.455185\pi$
$373$	5.42023	0.280649	0.140324	+	0.990106i	$0.455185\pi$
$374$	44.5171	2.30192
$375$	−2.03323	−0.104996
$376$	16.5272	0.852327
$377$	9.16169	0.471851
$378$	−3.35142	−0.172378
$379$	−24.1972	−1.24293	−0.621464	−	0.783443i	$-0.713462\pi$
$379$	−24.1972	−1.24293	−0.621464	+	0.783443i	$0.713462\pi$
$380$	−0.652771	−0.0334864
$381$	−12.4060	−0.635580
$382$	−0.464769	−0.0237796
$383$	21.8000	1.11393	0.556964	−	0.830537i	$-0.311966\pi$
$383$	21.8000	1.11393	0.556964	+	0.830537i	$0.311966\pi$
$384$	13.6837	0.698293
$385$	6.34675	0.323460
$386$	−24.0094	−1.22204
$387$	1.01708	0.0517013
$388$	−20.1962	−1.02530
$389$	5.75464	0.291772	0.145886	−	0.989301i	$-0.453397\pi$
$389$	5.75464	0.291772	0.145886	+	0.989301i	$0.453397\pi$
$390$	4.43119	0.224382
$391$	57.0757	2.88644
$392$	2.84414	0.143651
$393$	−24.2221	−1.22185
$394$	4.11512	0.207317
$395$	−4.06403	−0.204483
$396$	−8.77854	−0.441138
$397$	15.9853	0.802281	0.401141	−	0.916016i	$-0.368614\pi$
$397$	15.9853	0.802281	0.401141	+	0.916016i	$0.368614\pi$
$398$	2.43302	0.121956
$399$	1.08819	0.0544778
$400$	−0.0730644	−0.00365322
$401$	−8.19554	−0.409266	−0.204633	−	0.978839i	$-0.565600\pi$
$401$	−8.19554	−0.409266	−0.204633	+	0.978839i	$0.565600\pi$
$402$	3.00367	0.149809
$403$	18.4635	0.919734
$404$	17.7369	0.882442
$405$	11.1161	0.552362
$406$	3.28036	0.162801
$407$	65.8998	3.26653
$408$	−45.9171	−2.27323
$409$	3.00358	0.148517	0.0742587	−	0.997239i	$-0.476341\pi$
$409$	3.00358	0.148517	0.0742587	+	0.997239i	$0.476341\pi$
$410$	−3.15019	−0.155577
$411$	−14.5030	−0.715379
$412$	−5.69008	−0.280330
$413$	14.7175	0.724200
$414$	7.20083	0.353901
$415$	−14.7447	−0.723790
$416$	−13.8745	−0.680255
$417$	15.2579	0.747181
$418$	3.00060	0.146764
$419$	−0.841884	−0.0411287	−0.0205644	−	0.999789i	$-0.506546\pi$
$419$	−0.841884	−0.0411287	−0.0205644	+	0.999789i	$0.506546\pi$
$420$	−2.47987	−0.121006
$421$	17.7951	0.867282	0.433641	−	0.901086i	$-0.357229\pi$
$421$	17.7951	0.867282	0.433641	+	0.901086i	$0.357229\pi$
$422$	15.3065	0.745107
$423$	6.58990	0.320412
$424$	19.4321	0.943707
$425$	−7.94029	−0.385161
$426$	7.97203	0.386246
$427$	−9.25738	−0.447996
$428$	9.68823	0.468298
$429$	31.8370	1.53711
$430$	0.792259	0.0382061
$431$	−6.80837	−0.327948	−0.163974	−	0.986465i	$-0.552431\pi$
$431$	−6.80837	−0.327948	−0.163974	+	0.986465i	$0.552431\pi$
$432$	0.277201	0.0133369
$433$	41.0604	1.97324	0.986620	−	0.163039i	$-0.0521296\pi$
$433$	41.0604	1.97324	0.986620	+	0.163039i	$0.0521296\pi$
$434$	6.61089	0.317333
$435$	−7.55039	−0.362013
$436$	6.67826	0.319831
$437$	3.84709	0.184031
$438$	7.20020	0.344039
$439$	−35.2380	−1.68182	−0.840909	−	0.541177i	$-0.817979\pi$
$439$	−35.2380	−1.68182	−0.840909	+	0.541177i	$0.817979\pi$
$440$	−18.0510	−0.860549
$441$	1.13404	0.0540020
$442$	17.3049	0.823111
$443$	10.2041	0.484810	0.242405	−	0.970175i	$-0.422064\pi$
$443$	10.2041	0.484810	0.242405	+	0.970175i	$0.422064\pi$
$444$	−25.7491	−1.22200
$445$	0.355306	0.0168431
$446$	−2.19093	−0.103743
$447$	40.3117	1.90668
$448$	−5.11392	−0.241610
$449$	15.9792	0.754105	0.377053	−	0.926192i	$-0.376938\pi$
$449$	15.9792	0.754105	0.377053	+	0.926192i	$0.376938\pi$
$450$	−1.00177	−0.0472239
$451$	−22.6333	−1.06576
$452$	−22.5003	−1.05832
$453$	−42.8554	−2.01352
$454$	−16.3797	−0.768736
$455$	2.46714	0.115661
$456$	−3.09497	−0.144935
$457$	−10.3973	−0.486366	−0.243183	−	0.969980i	$-0.578192\pi$
$457$	−10.3973	−0.486366	−0.243183	+	0.969980i	$0.578192\pi$
$458$	−0.883363	−0.0412768
$459$	30.1249	1.40611
$460$	−8.76712	−0.408769
$461$	8.46250	0.394138	0.197069	−	0.980390i	$-0.436858\pi$
$461$	8.46250	0.394138	0.197069	+	0.980390i	$0.436858\pi$
$462$	11.3993	0.530343
$463$	−35.0123	−1.62716	−0.813579	−	0.581454i	$-0.802484\pi$
$463$	−35.0123	−1.62716	−0.813579	+	0.581454i	$0.802484\pi$
$464$	−0.271324	−0.0125959
$465$	−15.2163	−0.705638
$466$	−17.4077	−0.806398
$467$	30.9980	1.43441	0.717207	−	0.696860i	$-0.245420\pi$
$467$	30.9980	1.43441	0.717207	+	0.696860i	$0.245420\pi$
$468$	−3.41244	−0.157740
$469$	1.67234	0.0772217
$470$	5.13321	0.236777
$471$	21.2993	0.981420
$472$	−41.8585	−1.92670
$473$	5.69219	0.261727
$474$	−7.29933	−0.335270
$475$	−0.535203	−0.0245568
$476$	−9.68454	−0.443890
$477$	7.74815	0.354764
$478$	−17.7674	−0.812661
$479$	−32.1527	−1.46910	−0.734548	−	0.678557i	$-0.762606\pi$
$479$	−32.1527	−1.46910	−0.734548	+	0.678557i	$0.762606\pi$
$480$	11.4344	0.521905
$481$	25.6169	1.16803
$482$	−13.4660	−0.613357
$483$	14.6151	0.665010
$484$	−35.7134	−1.62334
$485$	−16.5587	−0.751892
$486$	9.91114	0.449579
$487$	−12.0181	−0.544593	−0.272296	−	0.962213i	$-0.587783\pi$
$487$	−12.0181	−0.544593	−0.272296	+	0.962213i	$0.587783\pi$
$488$	26.3292	1.19187
$489$	−0.205571	−0.00929626
$490$	0.883363	0.0399063
$491$	7.13139	0.321835	0.160917	−	0.986968i	$-0.448555\pi$
$491$	7.13139	0.321835	0.160917	+	0.986968i	$0.448555\pi$
$492$	8.84356	0.398698
$493$	−29.4862	−1.32799
$494$	1.16641	0.0524793
$495$	−7.19747	−0.323502
$496$	−0.546798	−0.0245520
$497$	4.43857	0.199097
$498$	−26.4827	−1.18672
$499$	−3.66662	−0.164140	−0.0820702	−	0.996627i	$-0.526153\pi$
$499$	−3.66662	−0.164140	−0.0820702	+	0.996627i	$0.526153\pi$
$500$	1.21967	0.0545453
$501$	33.4495	1.49442
$502$	−24.1760	−1.07903
$503$	17.7006	0.789229	0.394615	−	0.918847i	$-0.370878\pi$
$503$	17.7006	0.789229	0.394615	+	0.918847i	$0.370878\pi$
$504$	−3.22537	−0.143669
$505$	14.5424	0.647126
$506$	40.3000	1.79155
$507$	−14.0562	−0.624257
$508$	7.44196	0.330184
$509$	17.4283	0.772495	0.386247	−	0.922395i	$-0.373771\pi$
$509$	17.4283	0.772495	0.386247	+	0.922395i	$0.373771\pi$
$510$	−14.2614	−0.631507
$511$	4.00883	0.177340
$512$	0.826505	0.0365267
$513$	2.03052	0.0896497
$514$	3.16956	0.139803
$515$	−4.66526	−0.205576
$516$	−2.22412	−0.0979113
$517$	36.8809	1.62202
$518$	9.17216	0.403002
$519$	−35.0649	−1.53918
$520$	−7.01688	−0.307711
$521$	31.8144	1.39382	0.696908	−	0.717161i	$-0.254559\pi$
$521$	31.8144	1.39382	0.696908	+	0.717161i	$0.254559\pi$
$522$	−3.72006	−0.162823
$523$	28.7279	1.25618	0.628092	−	0.778139i	$-0.283836\pi$
$523$	28.7279	1.25618	0.628092	+	0.778139i	$0.283836\pi$
$524$	14.5301	0.634749
$525$	−2.03323	−0.0887376
$526$	11.1185	0.484791
$527$	−59.4234	−2.58852
$528$	−0.942855	−0.0410325
$529$	28.6689	1.24647
$530$	6.03544	0.262163
$531$	−16.6902	−0.724294
$532$	−0.652771	−0.0283012
$533$	−8.79814	−0.381090
$534$	0.638159	0.0276158
$535$	7.94332	0.343420
$536$	−4.75637	−0.205444
$537$	−36.3009	−1.56650
$538$	−14.1560	−0.610308
$539$	6.34675	0.273374
$540$	−4.62735	−0.199129
$541$	−16.3684	−0.703732	−0.351866	−	0.936050i	$-0.614453\pi$
$541$	−16.3684	−0.703732	−0.351866	+	0.936050i	$0.614453\pi$
$542$	−12.8831	−0.553379
$543$	7.12432	0.305734
$544$	44.6541	1.91453
$545$	5.47547	0.234543
$546$	4.43119	0.189637
$547$	1.47261	0.0629642	0.0314821	−	0.999504i	$-0.489977\pi$
$547$	1.47261	0.0629642	0.0314821	+	0.999504i	$0.489977\pi$
$548$	8.69986	0.371640
$549$	10.4982	0.448054
$550$	−5.60648	−0.239061
$551$	−1.98747	−0.0846690
$552$	−41.5673	−1.76922
$553$	−4.06403	−0.172820
$554$	10.4347	0.443326
$555$	−21.1115	−0.896135
$556$	−9.15269	−0.388161
$557$	−38.1285	−1.61556	−0.807778	−	0.589486i	$-0.799330\pi$
$557$	−38.1285	−1.61556	−0.807778	+	0.589486i	$0.799330\pi$
$558$	−7.49702	−0.317374
$559$	2.21270	0.0935871
$560$	−0.0730644	−0.00308754
$561$	−102.465	−4.32607
$562$	24.8542	1.04841
$563$	34.7247	1.46347	0.731735	−	0.681589i	$-0.238711\pi$
$563$	34.7247	1.46347	0.731735	+	0.681589i	$0.238711\pi$
$564$	−14.4105	−0.606792
$565$	−18.4478	−0.776106
$566$	3.06330	0.128760
$567$	11.1161	0.466831
$568$	−12.6239	−0.529687
$569$	2.03097	0.0851426	0.0425713	−	0.999093i	$-0.486445\pi$
$569$	2.03097	0.0851426	0.0425713	+	0.999093i	$0.486445\pi$
$570$	−0.961269	−0.0402631
$571$	24.6002	1.02949	0.514743	−	0.857344i	$-0.327887\pi$
$571$	24.6002	1.02949	0.514743	+	0.857344i	$0.327887\pi$
$572$	−19.0980	−0.798527
$573$	1.06976	0.0446897
$574$	−3.15019	−0.131486
$575$	−7.18811	−0.299765
$576$	5.79940	0.241642
$577$	−46.4646	−1.93435	−0.967173	−	0.254117i	$-0.918215\pi$
$577$	−46.4646	−1.93435	−0.967173	+	0.254117i	$0.918215\pi$
$578$	−40.6773	−1.69195
$579$	55.2623	2.29662
$580$	4.52923	0.188066
$581$	−14.7447	−0.611714
$582$	−29.7408	−1.23280
$583$	43.3631	1.79592
$584$	−11.4017	−0.471804
$585$	−2.79784	−0.115676
$586$	−24.6352	−1.01767
$587$	26.7098	1.10243	0.551215	−	0.834363i	$-0.314164\pi$
$587$	26.7098	1.10243	0.551215	+	0.834363i	$0.314164\pi$
$588$	−2.47987	−0.102268
$589$	−4.00534	−0.165037
$590$	−13.0009	−0.535238
$591$	−9.47177	−0.389617
$592$	−0.758645	−0.0311801
$593$	−11.9743	−0.491727	−0.245863	−	0.969305i	$-0.579071\pi$
$593$	−11.9743	−0.491727	−0.245863	+	0.969305i	$0.579071\pi$
$594$	21.2706	0.872744
$595$	−7.94029	−0.325520
$596$	−24.1816	−0.990519
$597$	−5.60008	−0.229196
$598$	15.6656	0.640615
$599$	−11.5055	−0.470103	−0.235051	−	0.971983i	$-0.575526\pi$
$599$	−11.5055	−0.470103	−0.235051	+	0.971983i	$0.575526\pi$
$600$	5.78280	0.236082
$601$	18.3865	0.749999	0.375000	−	0.927025i	$-0.377643\pi$
$601$	18.3865	0.749999	0.375000	+	0.927025i	$0.377643\pi$
$602$	0.792259	0.0322901
$603$	−1.89651	−0.0772317
$604$	25.7075	1.04603
$605$	−29.2812	−1.19045
$606$	26.1193	1.06102
$607$	26.4097	1.07193	0.535967	−	0.844239i	$-0.319947\pi$
$607$	26.4097	1.07193	0.535967	+	0.844239i	$0.319947\pi$
$608$	3.00984	0.122065
$609$	−7.55039	−0.305957
$610$	8.17762	0.331102
$611$	14.3365	0.579993
$612$	10.9827	0.443948
$613$	−7.19441	−0.290579	−0.145290	−	0.989389i	$-0.546411\pi$
$613$	−7.19441	−0.290579	−0.145290	+	0.989389i	$0.546411\pi$
$614$	−10.3448	−0.417481
$615$	7.25078	0.292380
$616$	−18.0510	−0.727296
$617$	0.00674299	0.000271462 0	0.000135731	−	1.00000i	$-0.499957\pi$
$617$	0.00674299	0.000271462 0	0.000135731		1.00000i	$0.499957\pi$
$618$	−8.37919	−0.337061
$619$	26.2491	1.05504	0.527520	−	0.849543i	$-0.323122\pi$
$619$	26.2491	1.05504	0.527520	+	0.849543i	$0.323122\pi$
$620$	9.12774	0.366579
$621$	27.2712	1.09435
$622$	−1.29205	−0.0518065
$623$	0.355306	0.0142350
$624$	−0.366511	−0.0146722
$625$	1.00000	0.0400000
$626$	−14.6362	−0.584979
$627$	−6.90648	−0.275818
$628$	−12.7768	−0.509848
$629$	−82.4459	−3.28733
$630$	−1.00177	−0.0399115
$631$	−3.62995	−0.144506	−0.0722529	−	0.997386i	$-0.523019\pi$
$631$	−3.62995	−0.144506	−0.0722529	+	0.997386i	$0.523019\pi$
$632$	11.5587	0.459779
$633$	−35.2309	−1.40030
$634$	10.7060	0.425189
$635$	6.10162	0.242135
$636$	−16.9434	−0.671848
$637$	2.46714	0.0977517
$638$	−20.8196	−0.824255
$639$	−5.03352	−0.199123
$640$	−6.73001	−0.266027
$641$	−1.40605	−0.0555356	−0.0277678	−	0.999614i	$-0.508840\pi$
$641$	−1.40605	−0.0555356	−0.0277678	+	0.999614i	$0.508840\pi$
$642$	14.2669	0.563068
$643$	−13.4476	−0.530320	−0.265160	−	0.964204i	$-0.585425\pi$
$643$	−13.4476	−0.530320	−0.265160	+	0.964204i	$0.585425\pi$
$644$	−8.76712	−0.345473
$645$	−1.82354	−0.0718018
$646$	−3.75400	−0.147699
$647$	24.7870	0.974478	0.487239	−	0.873269i	$-0.338004\pi$
$647$	24.7870	0.974478	0.487239	+	0.873269i	$0.338004\pi$
$648$	−31.6156	−1.24198
$649$	−93.4082	−3.66659
$650$	−2.17938	−0.0854823
$651$	−15.2163	−0.596373
$652$	0.123316	0.00482941
$653$	32.4803	1.27105	0.635526	−	0.772079i	$-0.280783\pi$
$653$	32.4803	1.27105	0.635526	+	0.772079i	$0.280783\pi$
$654$	9.83440	0.384555
$655$	11.9131	0.465484
$656$	0.260557	0.0101731
$657$	−4.54618	−0.177363
$658$	5.13321	0.200113
$659$	25.4356	0.990832	0.495416	−	0.868656i	$-0.335016\pi$
$659$	25.4356	0.990832	0.495416	+	0.868656i	$0.335016\pi$
$660$	15.7391	0.612645
$661$	19.1624	0.745330	0.372665	−	0.927966i	$-0.378444\pi$
$661$	19.1624	0.745330	0.372665	+	0.927966i	$0.378444\pi$
$662$	−14.4209	−0.560483
$663$	−39.8307	−1.54690
$664$	41.9360	1.62743
$665$	−0.535203	−0.0207543
$666$	−10.4016	−0.403054
$667$	−26.6929	−1.03355
$668$	−20.0653	−0.776349
$669$	5.04285	0.194968
$670$	−1.47729	−0.0570725
$671$	58.7542	2.26818
$672$	11.4344	0.441090
$673$	9.58214	0.369364	0.184682	−	0.982798i	$-0.440874\pi$
$673$	9.58214	0.369364	0.184682	+	0.982798i	$0.440874\pi$
$674$	−16.3318	−0.629077
$675$	−3.79393	−0.146028
$676$	8.43185	0.324302
$677$	−13.1672	−0.506058	−0.253029	−	0.967459i	$-0.581427\pi$
$677$	−13.1672	−0.506058	−0.253029	+	0.967459i	$0.581427\pi$
$678$	−33.1338	−1.27250
$679$	−16.5587	−0.635465
$680$	22.5833	0.866029
$681$	37.7010	1.44471
$682$	−41.9577	−1.60664
$683$	26.9407	1.03086	0.515429	−	0.856932i	$-0.327633\pi$
$683$	26.9407	1.03086	0.515429	+	0.856932i	$0.327633\pi$
$684$	0.740269	0.0283049
$685$	7.13296	0.272536
$686$	0.883363	0.0337269
$687$	2.03323	0.0775727
$688$	−0.0655291	−0.00249827
$689$	16.8563	0.642176
$690$	−12.9104	−0.491492
$691$	−8.22149	−0.312760	−0.156380	−	0.987697i	$-0.549983\pi$
$691$	−8.22149	−0.312760	−0.156380	+	0.987697i	$0.549983\pi$
$692$	21.0343	0.799604
$693$	−7.19747	−0.273409
$694$	−14.2451	−0.540735
$695$	−7.50424	−0.284652
$696$	21.4743	0.813983
$697$	28.3161	1.07255
$698$	−16.2933	−0.616712
$699$	40.0673	1.51549
$700$	1.21967	0.0460992
$701$	3.90696	0.147564	0.0737820	−	0.997274i	$-0.476493\pi$
$701$	3.90696	0.147564	0.0737820	+	0.997274i	$0.476493\pi$
$702$	8.26842	0.312071
$703$	−5.55713	−0.209591
$704$	32.4568	1.22326
$705$	−11.8151	−0.444982
$706$	−5.25102	−0.197625
$707$	14.5424	0.546921
$708$	36.4975	1.37166
$709$	−20.9681	−0.787473	−0.393736	−	0.919223i	$-0.628818\pi$
$709$	−20.9681	−0.787473	−0.393736	+	0.919223i	$0.628818\pi$
$710$	−3.92086	−0.147147
$711$	4.60877	0.172843
$712$	−1.01054	−0.0378715
$713$	−53.7942	−2.01461
$714$	−14.2614	−0.533721
$715$	−15.6583	−0.585588
$716$	21.7757	0.813797
$717$	40.8952	1.52726
$718$	22.5375	0.841091
$719$	47.3428	1.76559	0.882794	−	0.469760i	$-0.155660\pi$
$719$	47.3428	1.76559	0.882794	+	0.469760i	$0.155660\pi$
$720$	0.0828581	0.00308794
$721$	−4.66526	−0.173743
$722$	16.5309	0.615215
$723$	30.9946	1.15270
$724$	−4.27365	−0.158829
$725$	3.71349	0.137915
$726$	−52.5915	−1.95185
$727$	−16.4317	−0.609418	−0.304709	−	0.952446i	$-0.598559\pi$
$727$	−16.4317	−0.609418	−0.304709	+	0.952446i	$0.598559\pi$
$728$	−7.01688	−0.260063
$729$	10.5358	0.390214
$730$	−3.54125	−0.131068
$731$	−7.12139	−0.263394
$732$	−22.9571	−0.848520
$733$	13.1146	0.484400	0.242200	−	0.970226i	$-0.422131\pi$
$733$	13.1146	0.484400	0.242200	+	0.970226i	$0.422131\pi$
$734$	−18.6881	−0.689790
$735$	−2.03323	−0.0749970
$736$	40.4240	1.49005
$737$	−10.6139	−0.390970
$738$	3.57244	0.131503
$739$	−19.6675	−0.723480	−0.361740	−	0.932279i	$-0.617817\pi$
$739$	−19.6675	−0.723480	−0.361740	+	0.932279i	$0.617817\pi$
$740$	12.6641	0.465542
$741$	−2.68472	−0.0986258
$742$	6.03544	0.221568
$743$	−20.4652	−0.750796	−0.375398	−	0.926864i	$-0.622494\pi$
$743$	−20.4652	−0.750796	−0.375398	+	0.926864i	$0.622494\pi$
$744$	43.2772	1.58662
$745$	−19.8264	−0.726382
$746$	−4.78803	−0.175302
$747$	16.7211	0.611794
$748$	61.4653	2.24739
$749$	7.94332	0.290243
$750$	1.79608	0.0655837
$751$	0.387677	0.0141465	0.00707327	−	0.999975i	$-0.497748\pi$
$751$	0.387677	0.0141465	0.00707327	+	0.999975i	$0.497748\pi$
$752$	−0.424576	−0.0154827
$753$	55.6458	2.02784
$754$	−8.09310	−0.294733
$755$	21.0775	0.767087
$756$	−4.62735	−0.168295
$757$	8.89702	0.323368	0.161684	−	0.986843i	$-0.448308\pi$
$757$	8.89702	0.323368	0.161684	+	0.986843i	$0.448308\pi$
$758$	21.3749	0.776372
$759$	−92.7584	−3.36692
$760$	1.52219	0.0552156
$761$	−16.8698	−0.611528	−0.305764	−	0.952107i	$-0.598912\pi$
$761$	−16.8698	−0.611528	−0.305764	+	0.952107i	$0.598912\pi$
$762$	10.9590	0.397003
$763$	5.47547	0.198225
$764$	−0.641712	−0.0232163
$765$	9.00462	0.325563
$766$	−19.2573	−0.695794
$767$	−36.3101	−1.31108
$768$	−32.8833	−1.18657
$769$	−54.5340	−1.96655	−0.983273	−	0.182139i	$-0.941698\pi$
$769$	−54.5340	−1.96655	−0.983273	+	0.182139i	$0.941698\pi$
$770$	−5.60648	−0.202044
$771$	−7.29538	−0.262737
$772$	−33.1500	−1.19310
$773$	48.8413	1.75670	0.878349	−	0.478019i	$-0.158645\pi$
$773$	48.8413	1.75670	0.878349	+	0.478019i	$0.158645\pi$
$774$	−0.898454	−0.0322943
$775$	7.48378	0.268825
$776$	47.0952	1.69062
$777$	−21.1115	−0.757373
$778$	−5.08343	−0.182250
$779$	1.90860	0.0683828
$780$	6.11820	0.219067
$781$	−28.1705	−1.00802
$782$	−50.4185	−1.80296
$783$	−14.0887	−0.503490
$784$	−0.0730644	−0.00260944
$785$	−10.4756	−0.373889
$786$	21.3969	0.763204
$787$	13.5692	0.483691	0.241846	−	0.970315i	$-0.422247\pi$
$787$	13.5692	0.483691	0.241846	+	0.970315i	$0.422247\pi$
$788$	5.68180	0.202406
$789$	−25.5915	−0.911081
$790$	3.59001	0.127727
$791$	−18.4478	−0.655929
$792$	20.4706	0.727391
$793$	22.8392	0.811045
$794$	−14.1209	−0.501131
$795$	−13.8917	−0.492690
$796$	3.35931	0.119067
$797$	−4.81564	−0.170579	−0.0852894	−	0.996356i	$-0.527181\pi$
$797$	−4.81564	−0.170579	−0.0852894	+	0.996356i	$0.527181\pi$
$798$	−0.961269	−0.0340285
$799$	−46.1409	−1.63235
$800$	−5.62373	−0.198829
$801$	−0.402931	−0.0142369
$802$	7.23964	0.255640
$803$	−25.4430	−0.897865
$804$	4.14720	0.146261
$805$	−7.18811	−0.253347
$806$	−16.3100	−0.574495
$807$	32.5828	1.14697
$808$	−41.3604	−1.45505
$809$	−36.0292	−1.26672	−0.633359	−	0.773858i	$-0.718324\pi$
$809$	−36.0292	−1.26672	−0.633359	+	0.773858i	$0.718324\pi$
$810$	−9.81953	−0.345023
$811$	11.5956	0.407176	0.203588	−	0.979057i	$-0.434740\pi$
$811$	11.5956	0.407176	0.203588	+	0.979057i	$0.434740\pi$
$812$	4.52923	0.158945
$813$	29.6531	1.03998
$814$	−58.2134	−2.04038
$815$	0.101106	0.00354158
$816$	1.17959	0.0412938
$817$	−0.480006	−0.0167933
$818$	−2.65325	−0.0927687
$819$	−2.79784	−0.0977644
$820$	−4.34950	−0.151891
$821$	−12.4009	−0.432793	−0.216396	−	0.976306i	$-0.569430\pi$
$821$	−12.4009	−0.432793	−0.216396	+	0.976306i	$0.569430\pi$
$822$	12.8114	0.446849
$823$	1.63432	0.0569689	0.0284845	−	0.999594i	$-0.490932\pi$
$823$	1.63432	0.0569689	0.0284845	+	0.999594i	$0.490932\pi$
$824$	13.2686	0.462235
$825$	12.9044	0.449274
$826$	−13.0009	−0.452358
$827$	36.2608	1.26091	0.630456	−	0.776225i	$-0.282868\pi$
$827$	36.2608	1.26091	0.630456	+	0.776225i	$0.282868\pi$
$828$	9.94227	0.345518
$829$	−36.5218	−1.26845	−0.634227	−	0.773147i	$-0.718681\pi$
$829$	−36.5218	−1.26845	−0.634227	+	0.773147i	$0.718681\pi$
$830$	13.0249	0.452102
$831$	−24.0174	−0.833155
$832$	12.6168	0.437408
$833$	−7.94029	−0.275115
$834$	−13.4782	−0.466713
$835$	−16.4514	−0.569324
$836$	4.14297	0.143288
$837$	−28.3929	−0.981403
$838$	0.743689	0.0256903
$839$	7.44914	0.257173	0.128586	−	0.991698i	$-0.458956\pi$
$839$	7.44914	0.257173	0.128586	+	0.991698i	$0.458956\pi$
$840$	5.78280	0.199525
$841$	−15.2100	−0.524483
$842$	−15.7196	−0.541732
$843$	−57.2069	−1.97031
$844$	21.1338	0.727456
$845$	6.91322	0.237822
$846$	−5.82127	−0.200139
$847$	−29.2812	−1.00611
$848$	−0.499201	−0.0171426
$849$	−7.05079	−0.241983
$850$	7.01416	0.240584
$851$	−74.6358	−2.55848
$852$	11.0071	0.377097
$853$	10.7573	0.368322	0.184161	−	0.982896i	$-0.441043\pi$
$853$	10.7573	0.368322	0.184161	+	0.982896i	$0.441043\pi$
$854$	8.17762	0.279832
$855$	0.606942	0.0207570
$856$	−22.5919	−0.772175
$857$	−50.2212	−1.71552	−0.857762	−	0.514046i	$-0.828146\pi$
$857$	−50.2212	−1.71552	−0.857762	+	0.514046i	$0.828146\pi$
$858$	−28.1236	−0.960125
$859$	−7.06714	−0.241128	−0.120564	−	0.992706i	$-0.538470\pi$
$859$	−7.06714	−0.241128	−0.120564	+	0.992706i	$0.538470\pi$
$860$	1.09388	0.0373011
$861$	7.25078	0.247106
$862$	6.01426	0.204847
$863$	−45.8402	−1.56042	−0.780210	−	0.625518i	$-0.784888\pi$
$863$	−45.8402	−1.56042	−0.780210	+	0.625518i	$0.784888\pi$
$864$	21.3361	0.725867
$865$	17.2459	0.586378
$866$	−36.2713	−1.23255
$867$	93.6269	3.17974
$868$	9.12774	0.309816
$869$	25.7934	0.874980
$870$	6.66973	0.226125
$871$	−4.12591	−0.139801
$872$	−15.5730	−0.527368
$873$	18.7782	0.635547
$874$	−3.39838	−0.114952
$875$	1.00000	0.0338062
$876$	9.94140	0.335889
$877$	−23.7509	−0.802010	−0.401005	−	0.916076i	$-0.631339\pi$
$877$	−23.7509	−0.802010	−0.401005	+	0.916076i	$0.631339\pi$
$878$	31.1279	1.05052
$879$	56.7028	1.91254
$880$	0.463722	0.0156321
$881$	−6.36334	−0.214386	−0.107193	−	0.994238i	$-0.534186\pi$
$881$	−6.36334	−0.214386	−0.107193	+	0.994238i	$0.534186\pi$
$882$	−1.00177	−0.0337313
$883$	33.0357	1.11174	0.555870	−	0.831269i	$-0.312385\pi$
$883$	33.0357	1.11174	0.555870	+	0.831269i	$0.312385\pi$
$884$	23.8931	0.803612
$885$	29.9241	1.00589
$886$	−9.01390	−0.302828
$887$	0.411785	0.0138264	0.00691319	−	0.999976i	$-0.497799\pi$
$887$	0.411785	0.0138264	0.00691319	+	0.999976i	$0.497799\pi$
$888$	60.0441	2.01495
$889$	6.10162	0.204642
$890$	−0.313864	−0.0105207
$891$	−70.5509	−2.36354
$892$	−3.02504	−0.101286
$893$	−3.11006	−0.104074
$894$	−35.6098	−1.19097
$895$	17.8538	0.596786
$896$	−6.73001	−0.224834
$897$	−36.0575	−1.20393
$898$	−14.1154	−0.471038
$899$	27.7909	0.926879
$900$	−1.38316	−0.0461052
$901$	−54.2508	−1.80736
$902$	19.9934	0.665709
$903$	−1.82354	−0.0606836
$904$	52.4682	1.74507
$905$	−3.50394	−0.116475
$906$	37.8569	1.25771
$907$	33.2480	1.10398	0.551990	−	0.833851i	$-0.313869\pi$
$907$	33.2480	1.10398	0.551990	+	0.833851i	$0.313869\pi$
$908$	−22.6156	−0.750525
$909$	−16.4916	−0.546993
$910$	−2.17938	−0.0722457
$911$	−14.7819	−0.489745	−0.244873	−	0.969555i	$-0.578746\pi$
$911$	−14.7819	−0.489745	−0.244873	+	0.969555i	$0.578746\pi$
$912$	0.0795082	0.00263278
$913$	93.5810	3.09708
$914$	9.18460	0.303800
$915$	−18.8224	−0.622250
$916$	−1.21967	−0.0402990
$917$	11.9131	0.393406
$918$	−26.6112	−0.878302
$919$	40.9568	1.35104	0.675520	−	0.737342i	$-0.263919\pi$
$919$	40.9568	1.35104	0.675520	+	0.737342i	$0.263919\pi$
$920$	20.4440	0.674017
$921$	23.8105	0.784583
$922$	−7.47546	−0.246191
$923$	−10.9506	−0.360442
$924$	15.7391	0.517780
$925$	10.3832	0.341399
$926$	30.9286	1.01638
$927$	5.29059	0.173766
$928$	−20.8836	−0.685539
$929$	−22.7330	−0.745845	−0.372922	−	0.927863i	$-0.621644\pi$
$929$	−22.7330	−0.745845	−0.372922	+	0.927863i	$0.621644\pi$
$930$	13.4415	0.440764
$931$	−0.535203	−0.0175406
$932$	−24.0351	−0.787295
$933$	2.97391	0.0973614
$934$	−27.3824	−0.895981
$935$	50.3950	1.64809
$936$	7.95743	0.260097
$937$	−32.4556	−1.06028	−0.530140	−	0.847910i	$-0.677861\pi$
$937$	−32.4556	−1.06028	−0.530140	+	0.847910i	$0.677861\pi$
$938$	−1.47729	−0.0482351
$939$	33.6880	1.09937
$940$	7.08749	0.231168
$941$	6.41991	0.209283	0.104642	−	0.994510i	$-0.466630\pi$
$941$	6.41991	0.209283	0.104642	+	0.994510i	$0.466630\pi$
$942$	−18.8150	−0.613026
$943$	25.6337	0.834749
$944$	1.07532	0.0349988
$945$	−3.79393	−0.123417
$946$	−5.02827	−0.163483
$947$	14.0363	0.456118	0.228059	−	0.973647i	$-0.426762\pi$
$947$	14.0363	0.456118	0.228059	+	0.973647i	$0.426762\pi$
$948$	−10.0783	−0.327327
$949$	−9.89035	−0.321054
$950$	0.472778	0.0153389
$951$	−24.6419	−0.799070
$952$	22.5833	0.731928
$953$	−56.8548	−1.84171	−0.920854	−	0.389908i	$-0.872507\pi$
$953$	−56.8548	−1.84171	−0.920854	+	0.389908i	$0.872507\pi$
$954$	−6.84443	−0.221597
$955$	−0.526136	−0.0170254
$956$	−24.5317	−0.793410
$957$	47.9204	1.54905
$958$	28.4025	0.917644
$959$	7.13296	0.230335
$960$	−10.3978	−0.335588
$961$	25.0069	0.806675
$962$	−22.6290	−0.729589
$963$	−9.00805	−0.290280
$964$	−18.5926	−0.598828
$965$	−27.1795	−0.874939
$966$	−12.9104	−0.415387
$967$	−27.3680	−0.880095	−0.440048	−	0.897974i	$-0.645038\pi$
$967$	−27.3680	−0.880095	−0.440048	+	0.897974i	$0.645038\pi$
$968$	83.2798	2.67671
$969$	8.64057	0.277575
$970$	14.6273	0.469656
$971$	−27.4121	−0.879697	−0.439849	−	0.898072i	$-0.644968\pi$
$971$	−27.4121	−0.879697	−0.439849	+	0.898072i	$0.644968\pi$
$972$	13.6844	0.438929
$973$	−7.50424	−0.240575
$974$	10.6164	0.340170
$975$	5.01627	0.160649
$976$	−0.676385	−0.0216506
$977$	5.68835	0.181986	0.0909932	−	0.995852i	$-0.470996\pi$
$977$	5.68835	0.181986	0.0909932	+	0.995852i	$0.470996\pi$
$978$	0.181594	0.00580674
$979$	−2.25504	−0.0720712
$980$	1.21967	0.0389609
$981$	−6.20940	−0.198251
$982$	−6.29960	−0.201028
$983$	−52.1324	−1.66276	−0.831382	−	0.555701i	$-0.812450\pi$
$983$	−52.1324	−1.66276	−0.831382	+	0.555701i	$0.812450\pi$
$984$	−20.6222	−0.657412
$985$	4.65848	0.148431
$986$	26.0470	0.829505
$987$	−11.8151	−0.376079
$988$	1.61048	0.0512361
$989$	−6.44677	−0.204996
$990$	6.35798	0.202070
$991$	11.3188	0.359553	0.179777	−	0.983707i	$-0.442463\pi$
$991$	11.3188	0.359553	0.179777	+	0.983707i	$0.442463\pi$
$992$	−42.0868	−1.33626
$993$	33.1925	1.05333
$994$	−3.92086	−0.124362
$995$	2.75427	0.0873163
$996$	−36.5651	−1.15861
$997$	25.9224	0.820971	0.410485	−	0.911867i	$-0.365359\pi$
$997$	25.9224	0.820971	0.410485	+	0.911867i	$0.365359\pi$
$998$	3.23896	0.102527
$999$	−39.3933	−1.24635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.23	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.23	✓	62	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)

\(f(q)\)	\(=\)	\(q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +O(q^{10})\)	\(q-0.883363 q^{2} +2.03323 q^{3} -1.21967 q^{4} -1.00000 q^{5} -1.79608 q^{6} -1.00000 q^{7} +2.84414 q^{8} +1.13404 q^{9} +0.883363 q^{10} +6.34675 q^{11} -2.47987 q^{12} +2.46714 q^{13} +0.883363 q^{14} -2.03323 q^{15} -0.0730644 q^{16} -7.94029 q^{17} -1.00177 q^{18} -0.535203 q^{19} +1.21967 q^{20} -2.03323 q^{21} -5.60648 q^{22} -7.18811 q^{23} +5.78280 q^{24} +1.00000 q^{25} -2.17938 q^{26} -3.79393 q^{27} +1.21967 q^{28} +3.71349 q^{29} +1.79608 q^{30} +7.48378 q^{31} -5.62373 q^{32} +12.9044 q^{33} +7.01416 q^{34} +1.00000 q^{35} -1.38316 q^{36} +10.3832 q^{37} +0.472778 q^{38} +5.01627 q^{39} -2.84414 q^{40} -3.56613 q^{41} +1.79608 q^{42} +0.896867 q^{43} -7.74094 q^{44} -1.13404 q^{45} +6.34971 q^{46} +5.81099 q^{47} -0.148557 q^{48} +1.00000 q^{49} -0.883363 q^{50} -16.1445 q^{51} -3.00910 q^{52} +6.83234 q^{53} +3.35142 q^{54} -6.34675 q^{55} -2.84414 q^{56} -1.08819 q^{57} -3.28036 q^{58} -14.7175 q^{59} +2.47987 q^{60} +9.25738 q^{61} -6.61089 q^{62} -1.13404 q^{63} +5.11392 q^{64} -2.46714 q^{65} -11.3993 q^{66} -1.67234 q^{67} +9.68454 q^{68} -14.6151 q^{69} -0.883363 q^{70} -4.43857 q^{71} +3.22537 q^{72} -4.00883 q^{73} -9.17216 q^{74} +2.03323 q^{75} +0.652771 q^{76} -6.34675 q^{77} -4.43119 q^{78} +4.06403 q^{79} +0.0730644 q^{80} -11.1161 q^{81} +3.15019 q^{82} +14.7447 q^{83} +2.47987 q^{84} +7.94029 q^{85} -0.792259 q^{86} +7.55039 q^{87} +18.0510 q^{88} -0.355306 q^{89} +1.00177 q^{90} -2.46714 q^{91} +8.76712 q^{92} +15.2163 q^{93} -5.13321 q^{94} +0.535203 q^{95} -11.4344 q^{96} +16.5587 q^{97} -0.883363 q^{98} +7.19747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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