LMFDB - Embedded newform 8014.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.70222 q^{3} +1.00000 q^{4} -2.93383 q^{5} -2.70222 q^{6} +0.0783633 q^{7} +1.00000 q^{8} +4.30198 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.70222 q^{3} +1.00000 q^{4} -2.93383 q^{5} -2.70222 q^{6} +0.0783633 q^{7} +1.00000 q^{8} +4.30198 q^{9} -2.93383 q^{10} +0.0625037 q^{11} -2.70222 q^{12} +3.81447 q^{13} +0.0783633 q^{14} +7.92785 q^{15} +1.00000 q^{16} +3.22867 q^{17} +4.30198 q^{18} +0.762392 q^{19} -2.93383 q^{20} -0.211755 q^{21} +0.0625037 q^{22} +8.02724 q^{23} -2.70222 q^{24} +3.60736 q^{25} +3.81447 q^{26} -3.51823 q^{27} +0.0783633 q^{28} -3.82920 q^{29} +7.92785 q^{30} -3.85325 q^{31} +1.00000 q^{32} -0.168898 q^{33} +3.22867 q^{34} -0.229905 q^{35} +4.30198 q^{36} -0.720130 q^{37} +0.762392 q^{38} -10.3075 q^{39} -2.93383 q^{40} +7.05531 q^{41} -0.211755 q^{42} +6.19559 q^{43} +0.0625037 q^{44} -12.6213 q^{45} +8.02724 q^{46} -5.87784 q^{47} -2.70222 q^{48} -6.99386 q^{49} +3.60736 q^{50} -8.72457 q^{51} +3.81447 q^{52} -4.52557 q^{53} -3.51823 q^{54} -0.183375 q^{55} +0.0783633 q^{56} -2.06015 q^{57} -3.82920 q^{58} -12.1987 q^{59} +7.92785 q^{60} +7.73371 q^{61} -3.85325 q^{62} +0.337117 q^{63} +1.00000 q^{64} -11.1910 q^{65} -0.168898 q^{66} +11.6457 q^{67} +3.22867 q^{68} -21.6913 q^{69} -0.229905 q^{70} +2.05001 q^{71} +4.30198 q^{72} -2.52486 q^{73} -0.720130 q^{74} -9.74788 q^{75} +0.762392 q^{76} +0.00489799 q^{77} -10.3075 q^{78} -10.8242 q^{79} -2.93383 q^{80} -3.39892 q^{81} +7.05531 q^{82} +5.51801 q^{83} -0.211755 q^{84} -9.47238 q^{85} +6.19559 q^{86} +10.3473 q^{87} +0.0625037 q^{88} -13.8719 q^{89} -12.6213 q^{90} +0.298914 q^{91} +8.02724 q^{92} +10.4123 q^{93} -5.87784 q^{94} -2.23673 q^{95} -2.70222 q^{96} -11.0864 q^{97} -6.99386 q^{98} +0.268889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.70222	−1.56013	−0.780063	−	0.625701i	$-0.784813\pi$
$3$	−2.70222	−1.56013	−0.780063	+	0.625701i	$0.784813\pi$
$4$	1.00000	0.500000
$5$	−2.93383	−1.31205	−0.656025	−	0.754740i	$-0.727763\pi$
$5$	−2.93383	−1.31205	−0.656025	+	0.754740i	$0.727763\pi$
$6$	−2.70222	−1.10318
$7$	0.0783633	0.0296185	0.0148093	−	0.999890i	$-0.495286\pi$
$7$	0.0783633	0.0296185	0.0148093	+	0.999890i	$0.495286\pi$
$8$	1.00000	0.353553
$9$	4.30198	1.43399
$10$	−2.93383	−0.927759
$11$	0.0625037	0.0188456	0.00942278	−	0.999956i	$-0.497001\pi$
$11$	0.0625037	0.0188456	0.00942278	+	0.999956i	$0.497001\pi$
$12$	−2.70222	−0.780063
$13$	3.81447	1.05794	0.528971	−	0.848640i	$-0.322578\pi$
$13$	3.81447	1.05794	0.528971	+	0.848640i	$0.322578\pi$
$14$	0.0783633	0.0209435
$15$	7.92785	2.04696
$16$	1.00000	0.250000
$17$	3.22867	0.783068	0.391534	−	0.920164i	$-0.371945\pi$
$17$	3.22867	0.783068	0.391534	+	0.920164i	$0.371945\pi$
$18$	4.30198	1.01399
$19$	0.762392	0.174905	0.0874523	−	0.996169i	$-0.472127\pi$
$19$	0.762392	0.174905	0.0874523	+	0.996169i	$0.472127\pi$
$20$	−2.93383	−0.656025
$21$	−0.211755	−0.0462086
$22$	0.0625037	0.0133258
$23$	8.02724	1.67379	0.836897	−	0.547360i	$-0.184367\pi$
$23$	8.02724	1.67379	0.836897	+	0.547360i	$0.184367\pi$
$24$	−2.70222	−0.551588
$25$	3.60736	0.721473
$26$	3.81447	0.748078
$27$	−3.51823	−0.677083
$28$	0.0783633	0.0148093
$29$	−3.82920	−0.711065	−0.355532	−	0.934664i	$-0.615700\pi$
$29$	−3.82920	−0.711065	−0.355532	+	0.934664i	$0.615700\pi$
$30$	7.92785	1.44742
$31$	−3.85325	−0.692064	−0.346032	−	0.938223i	$-0.612471\pi$
$31$	−3.85325	−0.692064	−0.346032	+	0.938223i	$0.612471\pi$
$32$	1.00000	0.176777
$33$	−0.168898	−0.0294015
$34$	3.22867	0.553713
$35$	−0.229905	−0.0388610
$36$	4.30198	0.716996
$37$	−0.720130	−0.118389	−0.0591943	−	0.998246i	$-0.518853\pi$
$37$	−0.720130	−0.118389	−0.0591943	+	0.998246i	$0.518853\pi$
$38$	0.762392	0.123676
$39$	−10.3075	−1.65052
$40$	−2.93383	−0.463879
$41$	7.05531	1.10185	0.550927	−	0.834553i	$-0.314274\pi$
$41$	7.05531	1.10185	0.550927	+	0.834553i	$0.314274\pi$
$42$	−0.211755	−0.0326744
$43$	6.19559	0.944819	0.472410	−	0.881379i	$-0.343384\pi$
$43$	6.19559	0.944819	0.472410	+	0.881379i	$0.343384\pi$
$44$	0.0625037	0.00942278
$45$	−12.6213	−1.88147
$46$	8.02724	1.18355
$47$	−5.87784	−0.857371	−0.428686	−	0.903454i	$-0.641023\pi$
$47$	−5.87784	−0.857371	−0.428686	+	0.903454i	$0.641023\pi$
$48$	−2.70222	−0.390031
$49$	−6.99386	−0.999123
$50$	3.60736	0.510158
$51$	−8.72457	−1.22168
$52$	3.81447	0.528971
$53$	−4.52557	−0.621635	−0.310817	−	0.950470i	$-0.600603\pi$
$53$	−4.52557	−0.621635	−0.310817	+	0.950470i	$0.600603\pi$
$54$	−3.51823	−0.478770
$55$	−0.183375	−0.0247263
$56$	0.0783633	0.0104717
$57$	−2.06015	−0.272873
$58$	−3.82920	−0.502799
$59$	−12.1987	−1.58814	−0.794070	−	0.607826i	$-0.792042\pi$
$59$	−12.1987	−1.58814	−0.794070	+	0.607826i	$0.792042\pi$
$60$	7.92785	1.02348
$61$	7.73371	0.990201	0.495100	−	0.868836i	$-0.335131\pi$
$61$	7.73371	0.990201	0.495100	+	0.868836i	$0.335131\pi$
$62$	−3.85325	−0.489363
$63$	0.337117	0.0424728
$64$	1.00000	0.125000
$65$	−11.1910	−1.38807
$66$	−0.168898	−0.0207900
$67$	11.6457	1.42274	0.711372	−	0.702815i	$-0.248074\pi$
$67$	11.6457	1.42274	0.711372	+	0.702815i	$0.248074\pi$
$68$	3.22867	0.391534
$69$	−21.6913	−2.61133
$70$	−0.229905	−0.0274789
$71$	2.05001	0.243291	0.121646	−	0.992574i	$-0.461183\pi$
$71$	2.05001	0.243291	0.121646	+	0.992574i	$0.461183\pi$
$72$	4.30198	0.506993
$73$	−2.52486	−0.295512	−0.147756	−	0.989024i	$-0.547205\pi$
$73$	−2.52486	−0.295512	−0.147756	+	0.989024i	$0.547205\pi$
$74$	−0.720130	−0.0837134
$75$	−9.74788	−1.12559
$76$	0.762392	0.0874523
$77$	0.00489799	0.000558178 0
$78$	−10.3075	−1.16710
$79$	−10.8242	−1.21782	−0.608911	−	0.793238i	$-0.708393\pi$
$79$	−10.8242	−1.21782	−0.608911	+	0.793238i	$0.708393\pi$
$80$	−2.93383	−0.328012
$81$	−3.39892	−0.377658
$82$	7.05531	0.779129
$83$	5.51801	0.605681	0.302840	−	0.953041i	$-0.402065\pi$
$83$	5.51801	0.605681	0.302840	+	0.953041i	$0.402065\pi$
$84$	−0.211755	−0.0231043
$85$	−9.47238	−1.02742
$86$	6.19559	0.668088
$87$	10.3473	1.10935
$88$	0.0625037	0.00666291
$89$	−13.8719	−1.47042	−0.735211	−	0.677839i	$-0.762917\pi$
$89$	−13.8719	−1.47042	−0.735211	+	0.677839i	$0.762917\pi$
$90$	−12.6213	−1.33040
$91$	0.298914	0.0313347
$92$	8.02724	0.836897
$93$	10.4123	1.07971
$94$	−5.87784	−0.606253
$95$	−2.23673	−0.229483
$96$	−2.70222	−0.275794
$97$	−11.0864	−1.12566	−0.562828	−	0.826574i	$-0.690287\pi$
$97$	−11.0864	−1.12566	−0.562828	+	0.826574i	$0.690287\pi$
$98$	−6.99386	−0.706486
$99$	0.268889	0.0270244
$100$	3.60736	0.360736
$101$	8.47015	0.842811	0.421406	−	0.906872i	$-0.361537\pi$
$101$	8.47015	0.842811	0.421406	+	0.906872i	$0.361537\pi$
$102$	−8.72457	−0.863861
$103$	−3.91996	−0.386245	−0.193122	−	0.981175i	$-0.561861\pi$
$103$	−3.91996	−0.386245	−0.193122	+	0.981175i	$0.561861\pi$
$104$	3.81447	0.374039
$105$	0.621252	0.0606280
$106$	−4.52557	−0.439562
$107$	15.3019	1.47929	0.739644	−	0.672998i	$-0.234994\pi$
$107$	15.3019	1.47929	0.739644	+	0.672998i	$0.234994\pi$
$108$	−3.51823	−0.338541
$109$	10.4052	0.996637	0.498319	−	0.866994i	$-0.333951\pi$
$109$	10.4052	0.996637	0.498319	+	0.866994i	$0.333951\pi$
$110$	−0.183375	−0.0174841
$111$	1.94595	0.184701
$112$	0.0783633	0.00740463
$113$	18.5379	1.74390	0.871948	−	0.489598i	$-0.162857\pi$
$113$	18.5379	1.74390	0.871948	+	0.489598i	$0.162857\pi$
$114$	−2.06015	−0.192951
$115$	−23.5506	−2.19610
$116$	−3.82920	−0.355532
$117$	16.4098	1.51708
$118$	−12.1987	−1.12298
$119$	0.253009	0.0231933
$120$	7.92785	0.723710
$121$	−10.9961	−0.999645
$122$	7.73371	0.700178
$123$	−19.0650	−1.71903
$124$	−3.85325	−0.346032
$125$	4.08576	0.365441
$126$	0.337117	0.0300328
$127$	−8.35336	−0.741241	−0.370620	−	0.928784i	$-0.620855\pi$
$127$	−8.35336	−0.741241	−0.370620	+	0.928784i	$0.620855\pi$
$128$	1.00000	0.0883883
$129$	−16.7418	−1.47404
$130$	−11.1910	−0.981516
$131$	−5.11646	−0.447027	−0.223513	−	0.974701i	$-0.571753\pi$
$131$	−5.11646	−0.447027	−0.223513	+	0.974701i	$0.571753\pi$
$132$	−0.168898	−0.0147007
$133$	0.0597435	0.00518042
$134$	11.6457	1.00603
$135$	10.3219	0.888366
$136$	3.22867	0.276856
$137$	10.9652	0.936817	0.468408	−	0.883512i	$-0.344828\pi$
$137$	10.9652	0.936817	0.468408	+	0.883512i	$0.344828\pi$
$138$	−21.6913	−1.84649
$139$	5.16055	0.437712	0.218856	−	0.975757i	$-0.429768\pi$
$139$	5.16055	0.437712	0.218856	+	0.975757i	$0.429768\pi$
$140$	−0.229905	−0.0194305
$141$	15.8832	1.33761
$142$	2.05001	0.172033
$143$	0.238418	0.0199375
$144$	4.30198	0.358498
$145$	11.2342	0.932952
$146$	−2.52486	−0.208959
$147$	18.8989	1.55876
$148$	−0.720130	−0.0591943
$149$	3.60522	0.295351	0.147675	−	0.989036i	$-0.452821\pi$
$149$	3.60522	0.295351	0.147675	+	0.989036i	$0.452821\pi$
$150$	−9.74788	−0.795911
$151$	4.76469	0.387745	0.193873	−	0.981027i	$-0.437895\pi$
$151$	4.76469	0.387745	0.193873	+	0.981027i	$0.437895\pi$
$152$	0.762392	0.0618381
$153$	13.8897	1.12291
$154$	0.00489799	0.000394691 0
$155$	11.3048	0.908022
$156$	−10.3075	−0.825262
$157$	−4.59114	−0.366413	−0.183207	−	0.983074i	$-0.558648\pi$
$157$	−4.59114	−0.366413	−0.183207	+	0.983074i	$0.558648\pi$
$158$	−10.8242	−0.861130
$159$	12.2291	0.969828
$160$	−2.93383	−0.231940
$161$	0.629040	0.0495753
$162$	−3.39892	−0.267044
$163$	−13.2330	−1.03649	−0.518245	−	0.855232i	$-0.673414\pi$
$163$	−13.2330	−1.03649	−0.518245	+	0.855232i	$0.673414\pi$
$164$	7.05531	0.550927
$165$	0.495520	0.0385762
$166$	5.51801	0.428281
$167$	−13.0073	−1.00653	−0.503267	−	0.864131i	$-0.667869\pi$
$167$	−13.0073	−1.00653	−0.503267	+	0.864131i	$0.667869\pi$
$168$	−0.211755	−0.0163372
$169$	1.55016	0.119243
$170$	−9.47238	−0.726498
$171$	3.27979	0.250812
$172$	6.19559	0.472410
$173$	6.61443	0.502886	0.251443	−	0.967872i	$-0.419095\pi$
$173$	6.61443	0.502886	0.251443	+	0.967872i	$0.419095\pi$
$174$	10.3473	0.784429
$175$	0.282685	0.0213690
$176$	0.0625037	0.00471139
$177$	32.9636	2.47770
$178$	−13.8719	−1.03974
$179$	19.6856	1.47137	0.735684	−	0.677325i	$-0.236861\pi$
$179$	19.6856	1.47137	0.735684	+	0.677325i	$0.236861\pi$
$180$	−12.6213	−0.940734
$181$	5.26508	0.391350	0.195675	−	0.980669i	$-0.437310\pi$
$181$	5.26508	0.391350	0.195675	+	0.980669i	$0.437310\pi$
$182$	0.298914	0.0221570
$183$	−20.8982	−1.54484
$184$	8.02724	0.591776
$185$	2.11274	0.155332
$186$	10.4123	0.763468
$187$	0.201804	0.0147574
$188$	−5.87784	−0.428686
$189$	−0.275700	−0.0200542
$190$	−2.23673	−0.162269
$191$	14.1805	1.02607	0.513033	−	0.858369i	$-0.328522\pi$
$191$	14.1805	1.02607	0.513033	+	0.858369i	$0.328522\pi$
$192$	−2.70222	−0.195016
$193$	−5.14652	−0.370455	−0.185227	−	0.982696i	$-0.559302\pi$
$193$	−5.14652	−0.370455	−0.185227	+	0.982696i	$0.559302\pi$
$194$	−11.0864	−0.795960
$195$	30.2405	2.16557
$196$	−6.99386	−0.499561
$197$	−13.7557	−0.980053	−0.490027	−	0.871707i	$-0.663013\pi$
$197$	−13.7557	−0.980053	−0.490027	+	0.871707i	$0.663013\pi$
$198$	0.268889	0.0191091
$199$	−4.68146	−0.331860	−0.165930	−	0.986138i	$-0.553063\pi$
$199$	−4.68146	−0.331860	−0.165930	+	0.986138i	$0.553063\pi$
$200$	3.60736	0.255079
$201$	−31.4691	−2.21966
$202$	8.47015	0.595957
$203$	−0.300069	−0.0210607
$204$	−8.72457	−0.610842
$205$	−20.6991	−1.44569
$206$	−3.91996	−0.273116
$207$	34.5330	2.40021
$208$	3.81447	0.264486
$209$	0.0476523	0.00329618
$210$	0.621252	0.0428705
$211$	22.9549	1.58028	0.790141	−	0.612925i	$-0.210007\pi$
$211$	22.9549	1.58028	0.790141	+	0.612925i	$0.210007\pi$
$212$	−4.52557	−0.310817
$213$	−5.53957	−0.379565
$214$	15.3019	1.04602
$215$	−18.1768	−1.23965
$216$	−3.51823	−0.239385
$217$	−0.301953	−0.0204979
$218$	10.4052	0.704729
$219$	6.82271	0.461036
$220$	−0.183375	−0.0123632
$221$	12.3157	0.828441
$222$	1.94595	0.130603
$223$	28.5867	1.91431	0.957153	−	0.289583i	$-0.0935166\pi$
$223$	28.5867	1.91431	0.957153	+	0.289583i	$0.0935166\pi$
$224$	0.0783633	0.00523587
$225$	15.5188	1.03459
$226$	18.5379	1.23312
$227$	19.5765	1.29934	0.649668	−	0.760218i	$-0.274908\pi$
$227$	19.5765	1.29934	0.649668	+	0.760218i	$0.274908\pi$
$228$	−2.06015	−0.136437
$229$	3.43747	0.227154	0.113577	−	0.993529i	$-0.463769\pi$
$229$	3.43747	0.227154	0.113577	+	0.993529i	$0.463769\pi$
$230$	−23.5506	−1.55288
$231$	−0.0132354	−0.000870828 0
$232$	−3.82920	−0.251399
$233$	−21.7086	−1.42218	−0.711089	−	0.703102i	$-0.751798\pi$
$233$	−21.7086	−1.42218	−0.711089	+	0.703102i	$0.751798\pi$
$234$	16.4098	1.07274
$235$	17.2446	1.12491
$236$	−12.1987	−0.794070
$237$	29.2495	1.89996
$238$	0.253009	0.0164002
$239$	−1.85235	−0.119818	−0.0599092	−	0.998204i	$-0.519081\pi$
$239$	−1.85235	−0.119818	−0.0599092	+	0.998204i	$0.519081\pi$
$240$	7.92785	0.511740
$241$	−13.1121	−0.844623	−0.422312	−	0.906451i	$-0.638781\pi$
$241$	−13.1121	−0.844623	−0.422312	+	0.906451i	$0.638781\pi$
$242$	−10.9961	−0.706856
$243$	19.7393	1.26628
$244$	7.73371	0.495100
$245$	20.5188	1.31090
$246$	−19.0650	−1.21554
$247$	2.90812	0.185039
$248$	−3.85325	−0.244682
$249$	−14.9109	−0.944938
$250$	4.08576	0.258406
$251$	3.53478	0.223114	0.111557	−	0.993758i	$-0.464416\pi$
$251$	3.53478	0.223114	0.111557	+	0.993758i	$0.464416\pi$
$252$	0.337117	0.0212364
$253$	0.501732	0.0315436
$254$	−8.35336	−0.524136
$255$	25.5964	1.60291
$256$	1.00000	0.0625000
$257$	0.595616	0.0371535	0.0185767	−	0.999827i	$-0.494086\pi$
$257$	0.595616	0.0371535	0.0185767	+	0.999827i	$0.494086\pi$
$258$	−16.7418	−1.04230
$259$	−0.0564317	−0.00350650
$260$	−11.1910	−0.694036
$261$	−16.4731	−1.01966
$262$	−5.11646	−0.316096
$263$	−2.68822	−0.165763	−0.0828814	−	0.996559i	$-0.526412\pi$
$263$	−2.68822	−0.165763	−0.0828814	+	0.996559i	$0.526412\pi$
$264$	−0.168898	−0.0103950
$265$	13.2773	0.815615
$266$	0.0597435	0.00366311
$267$	37.4850	2.29404
$268$	11.6457	0.711372
$269$	8.89322	0.542229	0.271114	−	0.962547i	$-0.412608\pi$
$269$	8.89322	0.542229	0.271114	+	0.962547i	$0.412608\pi$
$270$	10.3219	0.628170
$271$	−20.0633	−1.21876	−0.609380	−	0.792878i	$-0.708582\pi$
$271$	−20.0633	−1.21876	−0.609380	+	0.792878i	$0.708582\pi$
$272$	3.22867	0.195767
$273$	−0.807731	−0.0488861
$274$	10.9652	0.662430
$275$	0.225473	0.0135966
$276$	−21.6913	−1.30566
$277$	13.5620	0.814862	0.407431	−	0.913236i	$-0.366425\pi$
$277$	13.5620	0.814862	0.407431	+	0.913236i	$0.366425\pi$
$278$	5.16055	0.309509
$279$	−16.5766	−0.992415
$280$	−0.229905	−0.0137394
$281$	−13.4888	−0.804677	−0.402338	−	0.915491i	$-0.631802\pi$
$281$	−13.4888	−0.804677	−0.402338	+	0.915491i	$0.631802\pi$
$282$	15.8832	0.945831
$283$	4.95721	0.294675	0.147338	−	0.989086i	$-0.452930\pi$
$283$	4.95721	0.294675	0.147338	+	0.989086i	$0.452930\pi$
$284$	2.05001	0.121646
$285$	6.04412	0.358023
$286$	0.238418	0.0140980
$287$	0.552877	0.0326353
$288$	4.30198	0.253496
$289$	−6.57568	−0.386805
$290$	11.2342	0.659697
$291$	29.9580	1.75617
$292$	−2.52486	−0.147756
$293$	26.9327	1.57342	0.786711	−	0.617321i	$-0.211782\pi$
$293$	26.9327	1.57342	0.786711	+	0.617321i	$0.211782\pi$
$294$	18.8989	1.10221
$295$	35.7890	2.08372
$296$	−0.720130	−0.0418567
$297$	−0.219902	−0.0127600
$298$	3.60522	0.208845
$299$	30.6196	1.77078
$300$	−9.74788	−0.562794
$301$	0.485507	0.0279842
$302$	4.76469	0.274177
$303$	−22.8882	−1.31489
$304$	0.762392	0.0437262
$305$	−22.6894	−1.29919
$306$	13.8897	0.794020
$307$	−1.95463	−0.111557	−0.0557784	−	0.998443i	$-0.517764\pi$
$307$	−1.95463	−0.111557	−0.0557784	+	0.998443i	$0.517764\pi$
$308$	0.00489799	0.000279089 0
$309$	10.5926	0.602591
$310$	11.3048	0.642068
$311$	−2.21790	−0.125765	−0.0628827	−	0.998021i	$-0.520029\pi$
$311$	−2.21790	−0.125765	−0.0628827	+	0.998021i	$0.520029\pi$
$312$	−10.3075	−0.583548
$313$	−2.18007	−0.123225	−0.0616123	−	0.998100i	$-0.519624\pi$
$313$	−2.18007	−0.123225	−0.0616123	+	0.998100i	$0.519624\pi$
$314$	−4.59114	−0.259093
$315$	−0.989044	−0.0557263
$316$	−10.8242	−0.608911
$317$	−5.22431	−0.293427	−0.146713	−	0.989179i	$-0.546869\pi$
$317$	−5.22431	−0.293427	−0.146713	+	0.989179i	$0.546869\pi$
$318$	12.2291	0.685772
$319$	−0.239339	−0.0134004
$320$	−2.93383	−0.164006
$321$	−41.3490	−2.30788
$322$	0.629040	0.0350551
$323$	2.46151	0.136962
$324$	−3.39892	−0.188829
$325$	13.7602	0.763277
$326$	−13.2330	−0.732909
$327$	−28.1171	−1.55488
$328$	7.05531	0.389564
$329$	−0.460607	−0.0253941
$330$	0.495520	0.0272775
$331$	26.2751	1.44421	0.722106	−	0.691783i	$-0.243174\pi$
$331$	26.2751	1.44421	0.722106	+	0.691783i	$0.243174\pi$
$332$	5.51801	0.302840
$333$	−3.09798	−0.169768
$334$	−13.0073	−0.711727
$335$	−34.1664	−1.86671
$336$	−0.211755	−0.0115522
$337$	29.6792	1.61673	0.808364	−	0.588683i	$-0.200353\pi$
$337$	29.6792	1.61673	0.808364	+	0.588683i	$0.200353\pi$
$338$	1.55016	0.0843174
$339$	−50.0934	−2.72070
$340$	−9.47238	−0.513712
$341$	−0.240842	−0.0130423
$342$	3.27979	0.177351
$343$	−1.09660	−0.0592111
$344$	6.19559	0.334044
$345$	63.6387	3.42619
$346$	6.61443	0.355594
$347$	0.625633	0.0335857	0.0167929	−	0.999859i	$-0.494654\pi$
$347$	0.625633	0.0335857	0.0167929	+	0.999859i	$0.494654\pi$
$348$	10.3473	0.554675
$349$	−6.36170	−0.340534	−0.170267	−	0.985398i	$-0.554463\pi$
$349$	−6.36170	−0.340534	−0.170267	+	0.985398i	$0.554463\pi$
$350$	0.282685	0.0151101
$351$	−13.4202	−0.716315
$352$	0.0625037	0.00333146
$353$	−3.80053	−0.202282	−0.101141	−	0.994872i	$-0.532249\pi$
$353$	−3.80053	−0.202282	−0.101141	+	0.994872i	$0.532249\pi$
$354$	32.9636	1.75200
$355$	−6.01438	−0.319210
$356$	−13.8719	−0.735211
$357$	−0.683686	−0.0361845
$358$	19.6856	1.04041
$359$	34.0307	1.79607	0.898035	−	0.439924i	$-0.144995\pi$
$359$	34.0307	1.79607	0.898035	+	0.439924i	$0.144995\pi$
$360$	−12.6213	−0.665200
$361$	−18.4188	−0.969408
$362$	5.26508	0.276726
$363$	29.7138	1.55957
$364$	0.298914	0.0156674
$365$	7.40750	0.387726
$366$	−20.8982	−1.09237
$367$	30.4196	1.58789	0.793945	−	0.607990i	$-0.208024\pi$
$367$	30.4196	1.58789	0.793945	+	0.607990i	$0.208024\pi$
$368$	8.02724	0.418449
$369$	30.3518	1.58005
$370$	2.11274	0.109836
$371$	−0.354638	−0.0184119
$372$	10.4123	0.539853
$373$	16.5440	0.856615	0.428308	−	0.903633i	$-0.359110\pi$
$373$	16.5440	0.856615	0.428308	+	0.903633i	$0.359110\pi$
$374$	0.201804	0.0104350
$375$	−11.0406	−0.570135
$376$	−5.87784	−0.303126
$377$	−14.6064	−0.752266
$378$	−0.275700	−0.0141805
$379$	22.6644	1.16419	0.582097	−	0.813119i	$-0.302232\pi$
$379$	22.6644	1.16419	0.582097	+	0.813119i	$0.302232\pi$
$380$	−2.23673	−0.114742
$381$	22.5726	1.15643
$382$	14.1805	0.725538
$383$	11.1513	0.569803	0.284902	−	0.958557i	$-0.408039\pi$
$383$	11.1513	0.569803	0.284902	+	0.958557i	$0.408039\pi$
$384$	−2.70222	−0.137897
$385$	−0.0143699	−0.000732357 0
$386$	−5.14652	−0.261951
$387$	26.6533	1.35486
$388$	−11.0864	−0.562828
$389$	9.60311	0.486897	0.243449	−	0.969914i	$-0.421721\pi$
$389$	9.60311	0.486897	0.243449	+	0.969914i	$0.421721\pi$
$390$	30.2405	1.53129
$391$	25.9173	1.31069
$392$	−6.99386	−0.353243
$393$	13.8258	0.697418
$394$	−13.7557	−0.693002
$395$	31.7565	1.59784
$396$	0.268889	0.0135122
$397$	6.89463	0.346032	0.173016	−	0.984919i	$-0.444649\pi$
$397$	6.89463	0.346032	0.173016	+	0.984919i	$0.444649\pi$
$398$	−4.68146	−0.234661
$399$	−0.161440	−0.00808210
$400$	3.60736	0.180368
$401$	12.0251	0.600505	0.300253	−	0.953860i	$-0.402929\pi$
$401$	12.0251	0.600505	0.300253	+	0.953860i	$0.402929\pi$
$402$	−31.4691	−1.56954
$403$	−14.6981	−0.732164
$404$	8.47015	0.421406
$405$	9.97186	0.495506
$406$	−0.300069	−0.0148922
$407$	−0.0450108	−0.00223110
$408$	−8.72457	−0.431931
$409$	−24.7585	−1.22423	−0.612116	−	0.790768i	$-0.709681\pi$
$409$	−24.7585	−1.22423	−0.612116	+	0.790768i	$0.709681\pi$
$410$	−20.6991	−1.02226
$411$	−29.6302	−1.46155
$412$	−3.91996	−0.193122
$413$	−0.955933	−0.0470384
$414$	34.5330	1.69720
$415$	−16.1889	−0.794683
$416$	3.81447	0.187020
$417$	−13.9449	−0.682886
$418$	0.0476523	0.00233075
$419$	−33.4170	−1.63253	−0.816263	−	0.577681i	$-0.803958\pi$
$419$	−33.4170	−1.63253	−0.816263	+	0.577681i	$0.803958\pi$
$420$	0.621252	0.0303140
$421$	−18.9860	−0.925323	−0.462661	−	0.886535i	$-0.653105\pi$
$421$	−18.9860	−0.925323	−0.462661	+	0.886535i	$0.653105\pi$
$422$	22.9549	1.11743
$423$	−25.2863	−1.22946
$424$	−4.52557	−0.219781
$425$	11.6470	0.564962
$426$	−5.53957	−0.268393
$427$	0.606039	0.0293283
$428$	15.3019	0.739644
$429$	−0.644258	−0.0311051
$430$	−18.1768	−0.876564
$431$	35.3730	1.70386	0.851928	−	0.523659i	$-0.175433\pi$
$431$	35.3730	1.70386	0.851928	+	0.523659i	$0.175433\pi$
$432$	−3.51823	−0.169271
$433$	17.8066	0.855733	0.427866	−	0.903842i	$-0.359265\pi$
$433$	17.8066	0.855733	0.427866	+	0.903842i	$0.359265\pi$
$434$	−0.301953	−0.0144942
$435$	−30.3573	−1.45552
$436$	10.4052	0.498319
$437$	6.11990	0.292754
$438$	6.82271	0.326002
$439$	−32.7123	−1.56127	−0.780637	−	0.624985i	$-0.785105\pi$
$439$	−32.7123	−1.56127	−0.780637	+	0.624985i	$0.785105\pi$
$440$	−0.183375	−0.00874207
$441$	−30.0874	−1.43273
$442$	12.3157	0.585796
$443$	−26.2413	−1.24676	−0.623381	−	0.781919i	$-0.714241\pi$
$443$	−26.2413	−1.24676	−0.623381	+	0.781919i	$0.714241\pi$
$444$	1.94595	0.0923506
$445$	40.6979	1.92926
$446$	28.5867	1.35362
$447$	−9.74208	−0.460784
$448$	0.0783633	0.00370232
$449$	26.3454	1.24332	0.621658	−	0.783289i	$-0.286459\pi$
$449$	26.3454	1.24332	0.621658	+	0.783289i	$0.286459\pi$
$450$	15.5188	0.731563
$451$	0.440983	0.0207651
$452$	18.5379	0.871948
$453$	−12.8752	−0.604931
$454$	19.5765	0.918769
$455$	−0.876963	−0.0411127
$456$	−2.06015	−0.0964753
$457$	−42.4642	−1.98639	−0.993196	−	0.116454i	$-0.962847\pi$
$457$	−42.4642	−1.98639	−0.993196	+	0.116454i	$0.962847\pi$
$458$	3.43747	0.160622
$459$	−11.3592	−0.530202
$460$	−23.5506	−1.09805
$461$	−18.9753	−0.883767	−0.441884	−	0.897072i	$-0.645690\pi$
$461$	−18.9753	−0.883767	−0.441884	+	0.897072i	$0.645690\pi$
$462$	−0.0132354	−0.000615768 0
$463$	−9.65077	−0.448510	−0.224255	−	0.974531i	$-0.571995\pi$
$463$	−9.65077	−0.448510	−0.224255	+	0.974531i	$0.571995\pi$
$464$	−3.82920	−0.177766
$465$	−30.5480	−1.41663
$466$	−21.7086	−1.00563
$467$	−34.1128	−1.57855	−0.789276	−	0.614039i	$-0.789544\pi$
$467$	−34.1128	−1.57855	−0.789276	+	0.614039i	$0.789544\pi$
$468$	16.4098	0.758541
$469$	0.912592	0.0421396
$470$	17.2446	0.795433
$471$	12.4063	0.571650
$472$	−12.1987	−0.561492
$473$	0.387247	0.0178057
$474$	29.2495	1.34347
$475$	2.75022	0.126189
$476$	0.253009	0.0115967
$477$	−19.4689	−0.891420
$478$	−1.85235	−0.0847243
$479$	25.8802	1.18250	0.591249	−	0.806489i	$-0.298635\pi$
$479$	25.8802	1.18250	0.591249	+	0.806489i	$0.298635\pi$
$480$	7.92785	0.361855
$481$	−2.74691	−0.125248
$482$	−13.1121	−0.597239
$483$	−1.69980	−0.0773437
$484$	−10.9961	−0.499822
$485$	32.5257	1.47692
$486$	19.7393	0.895393
$487$	32.9394	1.49263	0.746313	−	0.665596i	$-0.231822\pi$
$487$	32.9394	1.49263	0.746313	+	0.665596i	$0.231822\pi$
$488$	7.73371	0.350089
$489$	35.7585	1.61705
$490$	20.5188	0.926945
$491$	−26.4394	−1.19319	−0.596596	−	0.802542i	$-0.703481\pi$
$491$	−26.4394	−1.19319	−0.596596	+	0.802542i	$0.703481\pi$
$492$	−19.0650	−0.859516
$493$	−12.3632	−0.556812
$494$	2.90812	0.130842
$495$	−0.788876	−0.0354573
$496$	−3.85325	−0.173016
$497$	0.160645	0.00720593
$498$	−14.9109	−0.668172
$499$	−6.80290	−0.304539	−0.152270	−	0.988339i	$-0.548658\pi$
$499$	−6.80290	−0.304539	−0.152270	+	0.988339i	$0.548658\pi$
$500$	4.08576	0.182721
$501$	35.1485	1.57032
$502$	3.53478	0.157765
$503$	22.8609	1.01932	0.509659	−	0.860377i	$-0.329772\pi$
$503$	22.8609	1.01932	0.509659	+	0.860377i	$0.329772\pi$
$504$	0.337117	0.0150164
$505$	−24.8500	−1.10581
$506$	0.501732	0.0223047
$507$	−4.18886	−0.186034
$508$	−8.35336	−0.370620
$509$	−37.0664	−1.64294	−0.821471	−	0.570251i	$-0.806846\pi$
$509$	−37.0664	−1.64294	−0.821471	+	0.570251i	$0.806846\pi$
$510$	25.5964	1.13343
$511$	−0.197856	−0.00875264
$512$	1.00000	0.0441942
$513$	−2.68227	−0.118425
$514$	0.595616	0.0262715
$515$	11.5005	0.506772
$516$	−16.7418	−0.737019
$517$	−0.367387	−0.0161576
$518$	−0.0564317	−0.00247947
$519$	−17.8736	−0.784565
$520$	−11.1910	−0.490758
$521$	44.4519	1.94747	0.973736	−	0.227679i	$-0.0731137\pi$
$521$	44.4519	1.94747	0.973736	+	0.227679i	$0.0731137\pi$
$522$	−16.4731	−0.721010
$523$	17.7770	0.777336	0.388668	−	0.921378i	$-0.372935\pi$
$523$	17.7770	0.777336	0.388668	+	0.921378i	$0.372935\pi$
$524$	−5.11646	−0.223513
$525$	−0.763876	−0.0333383
$526$	−2.68822	−0.117212
$527$	−12.4409	−0.541933
$528$	−0.168898	−0.00735036
$529$	41.4365	1.80159
$530$	13.2773	0.576727
$531$	−52.4787	−2.27738
$532$	0.0597435	0.00259021
$533$	26.9123	1.16570
$534$	37.4850	1.62213
$535$	−44.8931	−1.94090
$536$	11.6457	0.503016
$537$	−53.1946	−2.29552
$538$	8.89322	0.383414
$539$	−0.437142	−0.0188290
$540$	10.3219	0.444183
$541$	21.9406	0.943300	0.471650	−	0.881786i	$-0.343659\pi$
$541$	21.9406	0.943300	0.471650	+	0.881786i	$0.343659\pi$
$542$	−20.0633	−0.861794
$543$	−14.2274	−0.610556
$544$	3.22867	0.138428
$545$	−30.5271	−1.30764
$546$	−0.807731	−0.0345677
$547$	−30.3420	−1.29733	−0.648665	−	0.761074i	$-0.724672\pi$
$547$	−30.3420	−1.29733	−0.648665	+	0.761074i	$0.724672\pi$
$548$	10.9652	0.468408
$549$	33.2703	1.41994
$550$	0.225473	0.00961422
$551$	−2.91935	−0.124369
$552$	−21.6913	−0.923244
$553$	−0.848223	−0.0360701
$554$	13.5620	0.576194
$555$	−5.70908	−0.242337
$556$	5.16055	0.218856
$557$	17.6877	0.749454	0.374727	−	0.927135i	$-0.377736\pi$
$557$	17.6877	0.749454	0.374727	+	0.927135i	$0.377736\pi$
$558$	−16.5766	−0.701743
$559$	23.6329	0.999565
$560$	−0.229905	−0.00971524
$561$	−0.545318	−0.0230233
$562$	−13.4888	−0.568992
$563$	−20.5415	−0.865720	−0.432860	−	0.901461i	$-0.642495\pi$
$563$	−20.5415	−0.865720	−0.432860	+	0.901461i	$0.642495\pi$
$564$	15.8832	0.668803
$565$	−54.3870	−2.28808
$566$	4.95721	0.208367
$567$	−0.266351	−0.0111857
$568$	2.05001	0.0860165
$569$	8.68535	0.364109	0.182054	−	0.983288i	$-0.441725\pi$
$569$	8.68535	0.364109	0.182054	+	0.983288i	$0.441725\pi$
$570$	6.04412	0.253161
$571$	1.14742	0.0480180	0.0240090	−	0.999712i	$-0.492357\pi$
$571$	1.14742	0.0480180	0.0240090	+	0.999712i	$0.492357\pi$
$572$	0.238418	0.00996877
$573$	−38.3188	−1.60079
$574$	0.552877	0.0230767
$575$	28.9572	1.20760
$576$	4.30198	0.179249
$577$	−38.8845	−1.61878	−0.809392	−	0.587268i	$-0.800203\pi$
$577$	−38.8845	−1.61878	−0.809392	+	0.587268i	$0.800203\pi$
$578$	−6.57568	−0.273512
$579$	13.9070	0.577956
$580$	11.2342	0.466476
$581$	0.432409	0.0179394
$582$	29.9580	1.24180
$583$	−0.282865	−0.0117151
$584$	−2.52486	−0.104479
$585$	−48.1434	−1.99049
$586$	26.9327	1.11258
$587$	44.9120	1.85372	0.926858	−	0.375413i	$-0.122499\pi$
$587$	44.9120	1.85372	0.926858	+	0.375413i	$0.122499\pi$
$588$	18.8989	0.779379
$589$	−2.93768	−0.121045
$590$	35.7890	1.47341
$591$	37.1709	1.52901
$592$	−0.720130	−0.0295972
$593$	0.0367011	0.00150714	0.000753568	−	1.00000i	$-0.499760\pi$
$593$	0.0367011	0.00150714	0.000753568		1.00000i	$0.499760\pi$
$594$	−0.219902	−0.00902269
$595$	−0.742286	−0.0304308
$596$	3.60522	0.147675
$597$	12.6503	0.517744
$598$	30.6196	1.25213
$599$	40.0144	1.63495	0.817473	−	0.575967i	$-0.195374\pi$
$599$	40.0144	1.63495	0.817473	+	0.575967i	$0.195374\pi$
$600$	−9.74788	−0.397956
$601$	−7.78625	−0.317608	−0.158804	−	0.987310i	$-0.550764\pi$
$601$	−7.78625	−0.317608	−0.158804	+	0.987310i	$0.550764\pi$
$602$	0.485507	0.0197878
$603$	50.0994	2.04020
$604$	4.76469	0.193873
$605$	32.2607	1.31158
$606$	−22.8882	−0.929769
$607$	−41.0004	−1.66415	−0.832077	−	0.554660i	$-0.812849\pi$
$607$	−41.0004	−1.66415	−0.832077	+	0.554660i	$0.812849\pi$
$608$	0.762392	0.0309191
$609$	0.810851	0.0328573
$610$	−22.6894	−0.918667
$611$	−22.4208	−0.907049
$612$	13.8897	0.561457
$613$	17.8047	0.719127	0.359563	−	0.933121i	$-0.382926\pi$
$613$	17.8047	0.719127	0.359563	+	0.933121i	$0.382926\pi$
$614$	−1.95463	−0.0788825
$615$	55.9334	2.25545
$616$	0.00489799	0.000197346 0
$617$	34.4840	1.38827	0.694136	−	0.719844i	$-0.255787\pi$
$617$	34.4840	1.38827	0.694136	+	0.719844i	$0.255787\pi$
$618$	10.5926	0.426096
$619$	−4.74651	−0.190779	−0.0953893	−	0.995440i	$-0.530410\pi$
$619$	−4.74651	−0.190779	−0.0953893	+	0.995440i	$0.530410\pi$
$620$	11.3048	0.454011
$621$	−28.2416	−1.13330
$622$	−2.21790	−0.0889295
$623$	−1.08705	−0.0435517
$624$	−10.3075	−0.412631
$625$	−30.0237	−1.20095
$626$	−2.18007	−0.0871330
$627$	−0.128767	−0.00514245
$628$	−4.59114	−0.183207
$629$	−2.32506	−0.0927063
$630$	−0.989044	−0.0394045
$631$	36.9682	1.47168	0.735840	−	0.677155i	$-0.236787\pi$
$631$	36.9682	1.47168	0.735840	+	0.677155i	$0.236787\pi$
$632$	−10.8242	−0.430565
$633$	−62.0292	−2.46544
$634$	−5.22431	−0.207484
$635$	24.5073	0.972544
$636$	12.2291	0.484914
$637$	−26.6778	−1.05701
$638$	−0.239339	−0.00947553
$639$	8.81909	0.348878
$640$	−2.93383	−0.115970
$641$	3.71236	0.146629	0.0733147	−	0.997309i	$-0.476642\pi$
$641$	3.71236	0.146629	0.0733147	+	0.997309i	$0.476642\pi$
$642$	−41.3490	−1.63192
$643$	27.2934	1.07635	0.538173	−	0.842834i	$-0.319115\pi$
$643$	27.2934	1.07635	0.538173	+	0.842834i	$0.319115\pi$
$644$	0.629040	0.0247877
$645$	49.1177	1.93401
$646$	2.46151	0.0968469
$647$	−15.0111	−0.590146	−0.295073	−	0.955475i	$-0.595344\pi$
$647$	−15.0111	−0.590146	−0.295073	+	0.955475i	$0.595344\pi$
$648$	−3.39892	−0.133522
$649$	−0.762466	−0.0299294
$650$	13.7602	0.539718
$651$	0.815943	0.0319793
$652$	−13.2330	−0.518245
$653$	−0.378824	−0.0148245	−0.00741226	−	0.999973i	$-0.502359\pi$
$653$	−0.378824	−0.0148245	−0.00741226	+	0.999973i	$0.502359\pi$
$654$	−28.1171	−1.09947
$655$	15.0108	0.586521
$656$	7.05531	0.275464
$657$	−10.8619	−0.423762
$658$	−0.460607	−0.0179563
$659$	30.0102	1.16903	0.584516	−	0.811382i	$-0.301284\pi$
$659$	30.0102	1.16903	0.584516	+	0.811382i	$0.301284\pi$
$660$	0.495520	0.0192881
$661$	14.1061	0.548663	0.274331	−	0.961635i	$-0.411543\pi$
$661$	14.1061	0.548663	0.274331	+	0.961635i	$0.411543\pi$
$662$	26.2751	1.02121
$663$	−33.2796	−1.29247
$664$	5.51801	0.214140
$665$	−0.175277	−0.00679696
$666$	−3.09798	−0.120044
$667$	−30.7379	−1.19018
$668$	−13.0073	−0.503267
$669$	−77.2474	−2.98656
$670$	−34.1664	−1.31996
$671$	0.483386	0.0186609
$672$	−0.211755	−0.00816861
$673$	11.9630	0.461138	0.230569	−	0.973056i	$-0.425941\pi$
$673$	11.9630	0.461138	0.230569	+	0.973056i	$0.425941\pi$
$674$	29.6792	1.14320
$675$	−12.6915	−0.488497
$676$	1.55016	0.0596214
$677$	0.762153	0.0292919	0.0146460	−	0.999893i	$-0.495338\pi$
$677$	0.762153	0.0292919	0.0146460	+	0.999893i	$0.495338\pi$
$678$	−50.0934	−1.92382
$679$	−0.868769	−0.0333403
$680$	−9.47238	−0.363249
$681$	−52.8999	−2.02713
$682$	−0.240842	−0.00922233
$683$	19.7773	0.756756	0.378378	−	0.925651i	$-0.376482\pi$
$683$	19.7773	0.756756	0.378378	+	0.925651i	$0.376482\pi$
$684$	3.27979	0.125406
$685$	−32.1699	−1.22915
$686$	−1.09660	−0.0418686
$687$	−9.28879	−0.354390
$688$	6.19559	0.236205
$689$	−17.2626	−0.657654
$690$	63.6387	2.42268
$691$	39.0332	1.48489	0.742446	−	0.669905i	$-0.233665\pi$
$691$	39.0332	1.48489	0.742446	+	0.669905i	$0.233665\pi$
$692$	6.61443	0.251443
$693$	0.0210711	0.000800423 0
$694$	0.625633	0.0237487
$695$	−15.1402	−0.574300
$696$	10.3473	0.392215
$697$	22.7793	0.862827
$698$	−6.36170	−0.240794
$699$	58.6614	2.21878
$700$	0.282685	0.0106845
$701$	2.17859	0.0822841	0.0411421	−	0.999153i	$-0.486900\pi$
$701$	2.17859	0.0822841	0.0411421	+	0.999153i	$0.486900\pi$
$702$	−13.4202	−0.506511
$703$	−0.549021	−0.0207067
$704$	0.0625037	0.00235570
$705$	−46.5986	−1.75501
$706$	−3.80053	−0.143035
$707$	0.663748	0.0249628
$708$	32.9636	1.23885
$709$	7.54320	0.283291	0.141645	−	0.989917i	$-0.454761\pi$
$709$	7.54320	0.283291	0.141645	+	0.989917i	$0.454761\pi$
$710$	−6.01438	−0.225716
$711$	−46.5656	−1.74635
$712$	−13.8719	−0.519872
$713$	−30.9309	−1.15837
$714$	−0.683686	−0.0255863
$715$	−0.699479	−0.0261590
$716$	19.6856	0.735684
$717$	5.00544	0.186932
$718$	34.0307	1.27001
$719$	31.9207	1.19044	0.595220	−	0.803563i	$-0.297065\pi$
$719$	31.9207	1.19044	0.595220	+	0.803563i	$0.297065\pi$
$720$	−12.6213	−0.470367
$721$	−0.307181	−0.0114400
$722$	−18.4188	−0.685475
$723$	35.4317	1.31772
$724$	5.26508	0.195675
$725$	−13.8133	−0.513014
$726$	29.7138	1.10278
$727$	−29.1932	−1.08272	−0.541358	−	0.840792i	$-0.682090\pi$
$727$	−29.1932	−1.08272	−0.541358	+	0.840792i	$0.682090\pi$
$728$	0.298914	0.0110785
$729$	−43.1431	−1.59789
$730$	7.40750	0.274164
$731$	20.0035	0.739858
$732$	−20.8982	−0.772419
$733$	41.6154	1.53710	0.768550	−	0.639790i	$-0.220979\pi$
$733$	41.6154	1.53710	0.768550	+	0.639790i	$0.220979\pi$
$734$	30.4196	1.12281
$735$	−55.4463	−2.04517
$736$	8.02724	0.295888
$737$	0.727897	0.0268124
$738$	30.3518	1.11727
$739$	−5.36374	−0.197308	−0.0986541	−	0.995122i	$-0.531454\pi$
$739$	−5.36374	−0.197308	−0.0986541	+	0.995122i	$0.531454\pi$
$740$	2.11274	0.0776658
$741$	−7.85836	−0.288684
$742$	−0.354638	−0.0130192
$743$	−44.4961	−1.63240	−0.816202	−	0.577767i	$-0.803924\pi$
$743$	−44.4961	−1.63240	−0.816202	+	0.577767i	$0.803924\pi$
$744$	10.4123	0.381734
$745$	−10.5771	−0.387515
$746$	16.5440	0.605719
$747$	23.7384	0.868541
$748$	0.201804	0.00737868
$749$	1.19911	0.0438144
$750$	−11.0406	−0.403146
$751$	−27.4365	−1.00117	−0.500585	−	0.865687i	$-0.666882\pi$
$751$	−27.4365	−1.00117	−0.500585	+	0.865687i	$0.666882\pi$
$752$	−5.87784	−0.214343
$753$	−9.55175	−0.348085
$754$	−14.6064	−0.531932
$755$	−13.9788	−0.508741
$756$	−0.275700	−0.0100271
$757$	−30.6184	−1.11285	−0.556423	−	0.830899i	$-0.687827\pi$
$757$	−30.6184	−1.11285	−0.556423	+	0.830899i	$0.687827\pi$
$758$	22.6644	0.823210
$759$	−1.35579	−0.0492120
$760$	−2.23673	−0.0811347
$761$	42.5416	1.54213	0.771067	−	0.636754i	$-0.219724\pi$
$761$	42.5416	1.54213	0.771067	+	0.636754i	$0.219724\pi$
$762$	22.5726	0.817718
$763$	0.815385	0.0295189
$764$	14.1805	0.513033
$765$	−40.7500	−1.47332
$766$	11.1513	0.402912
$767$	−46.5317	−1.68016
$768$	−2.70222	−0.0975079
$769$	39.9241	1.43970	0.719851	−	0.694129i	$-0.244210\pi$
$769$	39.9241	1.43970	0.719851	+	0.694129i	$0.244210\pi$
$770$	−0.0143699	−0.000517855 0
$771$	−1.60948	−0.0579641
$772$	−5.14652	−0.185227
$773$	51.4669	1.85113	0.925567	−	0.378583i	$-0.123588\pi$
$773$	51.4669	1.85113	0.925567	+	0.378583i	$0.123588\pi$
$774$	26.6533	0.958033
$775$	−13.9001	−0.499305
$776$	−11.0864	−0.397980
$777$	0.152491	0.00547058
$778$	9.60311	0.344288
$779$	5.37891	0.192719
$780$	30.2405	1.08278
$781$	0.128133	0.00458496
$782$	25.9173	0.926801
$783$	13.4720	0.481450
$784$	−6.99386	−0.249781
$785$	13.4696	0.480752
$786$	13.8258	0.493149
$787$	10.1240	0.360882	0.180441	−	0.983586i	$-0.442247\pi$
$787$	10.1240	0.360882	0.180441	+	0.983586i	$0.442247\pi$
$788$	−13.7557	−0.490027
$789$	7.26415	0.258611
$790$	31.7565	1.12985
$791$	1.45269	0.0516516
$792$	0.268889	0.00955457
$793$	29.5000	1.04758
$794$	6.89463	0.244681
$795$	−35.8780	−1.27246
$796$	−4.68146	−0.165930
$797$	−18.2387	−0.646049	−0.323025	−	0.946391i	$-0.604700\pi$
$797$	−18.2387	−0.646049	−0.323025	+	0.946391i	$0.604700\pi$
$798$	−0.161440	−0.00571491
$799$	−18.9776	−0.671380
$800$	3.60736	0.127540
$801$	−59.6767	−2.10857
$802$	12.0251	0.424621
$803$	−0.157813	−0.00556909
$804$	−31.4691	−1.10983
$805$	−1.84550	−0.0650453
$806$	−14.6981	−0.517718
$807$	−24.0314	−0.845945
$808$	8.47015	0.297979
$809$	−3.87429	−0.136213	−0.0681064	−	0.997678i	$-0.521696\pi$
$809$	−3.87429	−0.136213	−0.0681064	+	0.997678i	$0.521696\pi$
$810$	9.97186	0.350375
$811$	−0.0519324	−0.00182359	−0.000911796	−	1.00000i	$-0.500290\pi$
$811$	−0.0519324	−0.00182359	−0.000911796		1.00000i	$0.500290\pi$
$812$	−0.300069	−0.0105303
$813$	54.2155	1.90142
$814$	−0.0450108	−0.00157763
$815$	38.8234	1.35993
$816$	−8.72457	−0.305421
$817$	4.72347	0.165253
$818$	−24.7585	−0.865662
$819$	1.28592	0.0449337
$820$	−20.6991	−0.722844
$821$	3.48261	0.121544	0.0607719	−	0.998152i	$-0.480644\pi$
$821$	3.48261	0.121544	0.0607719	+	0.998152i	$0.480644\pi$
$822$	−29.6302	−1.03347
$823$	−10.1441	−0.353600	−0.176800	−	0.984247i	$-0.556575\pi$
$823$	−10.1441	−0.353600	−0.176800	+	0.984247i	$0.556575\pi$
$824$	−3.91996	−0.136558
$825$	−0.609278	−0.0212123
$826$	−0.955933	−0.0332612
$827$	38.9623	1.35485	0.677426	−	0.735591i	$-0.263095\pi$
$827$	38.9623	1.35485	0.677426	+	0.735591i	$0.263095\pi$
$828$	34.5330	1.20010
$829$	−21.0883	−0.732428	−0.366214	−	0.930531i	$-0.619346\pi$
$829$	−21.0883	−0.732428	−0.366214	+	0.930531i	$0.619346\pi$
$830$	−16.1889	−0.561925
$831$	−36.6475	−1.27129
$832$	3.81447	0.132243
$833$	−22.5809	−0.782381
$834$	−13.9449	−0.482873
$835$	38.1612	1.32062
$836$	0.0476523	0.00164809
$837$	13.5566	0.468585
$838$	−33.4170	−1.15437
$839$	−40.1931	−1.38762	−0.693810	−	0.720158i	$-0.744069\pi$
$839$	−40.1931	−1.38762	−0.693810	+	0.720158i	$0.744069\pi$
$840$	0.621252	0.0214352
$841$	−14.3372	−0.494387
$842$	−18.9860	−0.654302
$843$	36.4498	1.25540
$844$	22.9549	0.790141
$845$	−4.54790	−0.156453
$846$	−25.2863	−0.869362
$847$	−0.861690	−0.0296080
$848$	−4.52557	−0.155409
$849$	−13.3955	−0.459731
$850$	11.6470	0.399489
$851$	−5.78065	−0.198158
$852$	−5.53957	−0.189783
$853$	−40.3197	−1.38052	−0.690261	−	0.723561i	$-0.742504\pi$
$853$	−40.3197	−1.38052	−0.690261	+	0.723561i	$0.742504\pi$
$854$	0.606039	0.0207382
$855$	−9.62235	−0.329078
$856$	15.3019	0.523008
$857$	−39.2307	−1.34010	−0.670048	−	0.742318i	$-0.733726\pi$
$857$	−39.2307	−1.34010	−0.670048	+	0.742318i	$0.733726\pi$
$858$	−0.644258	−0.0219946
$859$	30.7637	1.04965	0.524823	−	0.851212i	$-0.324132\pi$
$859$	30.7637	1.04965	0.524823	+	0.851212i	$0.324132\pi$
$860$	−18.1768	−0.619825
$861$	−1.49399	−0.0509152
$862$	35.3730	1.20481
$863$	15.8072	0.538085	0.269043	−	0.963128i	$-0.413293\pi$
$863$	15.8072	0.538085	0.269043	+	0.963128i	$0.413293\pi$
$864$	−3.51823	−0.119692
$865$	−19.4056	−0.659811
$866$	17.8066	0.605095
$867$	17.7689	0.603464
$868$	−0.301953	−0.0102490
$869$	−0.676555	−0.0229506
$870$	−30.3573	−1.02921
$871$	44.4220	1.50518
$872$	10.4052	0.352364
$873$	−47.6936	−1.61418
$874$	6.11990	0.207009
$875$	0.320173	0.0108238
$876$	6.82271	0.230518
$877$	−2.96612	−0.100159	−0.0500793	−	0.998745i	$-0.515947\pi$
$877$	−2.96612	−0.100159	−0.0500793	+	0.998745i	$0.515947\pi$
$878$	−32.7123	−1.10399
$879$	−72.7779	−2.45474
$880$	−0.183375	−0.00618158
$881$	−38.9957	−1.31380	−0.656899	−	0.753979i	$-0.728132\pi$
$881$	−38.9957	−1.31380	−0.656899	+	0.753979i	$0.728132\pi$
$882$	−30.0874	−1.01310
$883$	8.11921	0.273233	0.136617	−	0.990624i	$-0.456377\pi$
$883$	8.11921	0.273233	0.136617	+	0.990624i	$0.456377\pi$
$884$	12.3157	0.414221
$885$	−96.7097	−3.25086
$886$	−26.2413	−0.881593
$887$	42.3273	1.42121	0.710605	−	0.703591i	$-0.248421\pi$
$887$	42.3273	1.42121	0.710605	+	0.703591i	$0.248421\pi$
$888$	1.94595	0.0653017
$889$	−0.654596	−0.0219545
$890$	40.6979	1.36420
$891$	−0.212445	−0.00711718
$892$	28.5867	0.957153
$893$	−4.48122	−0.149958
$894$	−9.74208	−0.325824
$895$	−57.7541	−1.93051
$896$	0.0783633	0.00261793
$897$	−82.7409	−2.76264
$898$	26.3454	0.879158
$899$	14.7549	0.492102
$900$	15.5188	0.517293
$901$	−14.6116	−0.486782
$902$	0.440983	0.0146831
$903$	−1.31195	−0.0436588
$904$	18.5379	0.616560
$905$	−15.4469	−0.513471
$906$	−12.8752	−0.427751
$907$	−13.8240	−0.459018	−0.229509	−	0.973307i	$-0.573712\pi$
$907$	−13.8240	−0.459018	−0.229509	+	0.973307i	$0.573712\pi$
$908$	19.5765	0.649668
$909$	36.4384	1.20858
$910$	−0.876963	−0.0290711
$911$	24.1335	0.799578	0.399789	−	0.916607i	$-0.369083\pi$
$911$	24.1335	0.799578	0.399789	+	0.916607i	$0.369083\pi$
$912$	−2.06015	−0.0682183
$913$	0.344896	0.0114144
$914$	−42.4642	−1.40459
$915$	61.3117	2.02690
$916$	3.43747	0.113577
$917$	−0.400942	−0.0132403
$918$	−11.3592	−0.374909
$919$	28.1825	0.929655	0.464827	−	0.885401i	$-0.346116\pi$
$919$	28.1825	0.929655	0.464827	+	0.885401i	$0.346116\pi$
$920$	−23.5506	−0.776439
$921$	5.28184	0.174043
$922$	−18.9753	−0.624918
$923$	7.81969	0.257388
$924$	−0.0132354	−0.000435414 0
$925$	−2.59777	−0.0854142
$926$	−9.65077	−0.317144
$927$	−16.8636	−0.553872
$928$	−3.82920	−0.125700
$929$	32.7110	1.07321	0.536607	−	0.843832i	$-0.319706\pi$
$929$	32.7110	1.07321	0.536607	+	0.843832i	$0.319706\pi$
$930$	−30.5480	−1.00171
$931$	−5.33206	−0.174751
$932$	−21.7086	−0.711089
$933$	5.99324	0.196210
$934$	−34.1128	−1.11620
$935$	−0.592058	−0.0193624
$936$	16.4098	0.536369
$937$	−10.4368	−0.340957	−0.170478	−	0.985361i	$-0.554531\pi$
$937$	−10.4368	−0.340957	−0.170478	+	0.985361i	$0.554531\pi$
$938$	0.912592	0.0297972
$939$	5.89101	0.192246
$940$	17.2446	0.562456
$941$	−11.4779	−0.374168	−0.187084	−	0.982344i	$-0.559904\pi$
$941$	−11.4779	−0.374168	−0.187084	+	0.982344i	$0.559904\pi$
$942$	12.4063	0.404218
$943$	56.6347	1.84428
$944$	−12.1987	−0.397035
$945$	0.808856	0.0263121
$946$	0.387247	0.0125905
$947$	−47.0116	−1.52767	−0.763835	−	0.645411i	$-0.776686\pi$
$947$	−47.0116	−1.52767	−0.763835	+	0.645411i	$0.776686\pi$
$948$	29.2495	0.949978
$949$	−9.63098	−0.312635
$950$	2.75022	0.0892290
$951$	14.1172	0.457783
$952$	0.253009	0.00820008
$953$	4.20283	0.136143	0.0680715	−	0.997680i	$-0.478315\pi$
$953$	4.20283	0.136143	0.0680715	+	0.997680i	$0.478315\pi$
$954$	−19.4689	−0.630329
$955$	−41.6032	−1.34625
$956$	−1.85235	−0.0599092
$957$	0.646746	0.0209063
$958$	25.8802	0.836152
$959$	0.859266	0.0277471
$960$	7.92785	0.255870
$961$	−16.1525	−0.521047
$962$	−2.74691	−0.0885640
$963$	65.8284	2.12129
$964$	−13.1121	−0.422312
$965$	15.0990	0.486055
$966$	−1.69980	−0.0546903
$967$	3.06457	0.0985500	0.0492750	−	0.998785i	$-0.484309\pi$
$967$	3.06457	0.0985500	0.0492750	+	0.998785i	$0.484309\pi$
$968$	−10.9961	−0.353428
$969$	−6.65154	−0.213678
$970$	32.5257	1.04434
$971$	−18.9666	−0.608667	−0.304334	−	0.952566i	$-0.598434\pi$
$971$	−18.9666	−0.608667	−0.304334	+	0.952566i	$0.598434\pi$
$972$	19.7393	0.633138
$973$	0.404397	0.0129644
$974$	32.9394	1.05545
$975$	−37.1830	−1.19081
$976$	7.73371	0.247550
$977$	−21.7865	−0.697012	−0.348506	−	0.937307i	$-0.613311\pi$
$977$	−21.7865	−0.697012	−0.348506	+	0.937307i	$0.613311\pi$
$978$	35.7585	1.14343
$979$	−0.867046	−0.0277109
$980$	20.5188	0.655449
$981$	44.7629	1.42917
$982$	−26.4394	−0.843714
$983$	−7.51988	−0.239847	−0.119923	−	0.992783i	$-0.538265\pi$
$983$	−7.51988	−0.239847	−0.119923	+	0.992783i	$0.538265\pi$
$984$	−19.0650	−0.607770
$985$	40.3569	1.28588
$986$	−12.3632	−0.393726
$987$	1.24466	0.0396179
$988$	2.90812	0.0925195
$989$	49.7335	1.58143
$990$	−0.788876	−0.0250721
$991$	−5.49078	−0.174420	−0.0872102	−	0.996190i	$-0.527795\pi$
$991$	−5.49078	−0.174420	−0.0872102	+	0.996190i	$0.527795\pi$
$992$	−3.85325	−0.122341
$993$	−71.0011	−2.25315
$994$	0.160645	0.00509536
$995$	13.7346	0.435417
$996$	−14.9109	−0.472469
$997$	−19.7846	−0.626583	−0.313292	−	0.949657i	$-0.601432\pi$
$997$	−19.7846	−0.626583	−0.313292	+	0.949657i	$0.601432\pi$
$998$	−6.80290	−0.215342
$999$	2.53358	0.0801589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.9	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.9	✓	88	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.70222 q^{3} +1.00000 q^{4} -2.93383 q^{5} -2.70222 q^{6} +0.0783633 q^{7} +1.00000 q^{8} +4.30198 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.70222 q^{3} +1.00000 q^{4} -2.93383 q^{5} -2.70222 q^{6} +0.0783633 q^{7} +1.00000 q^{8} +4.30198 q^{9} -2.93383 q^{10} +0.0625037 q^{11} -2.70222 q^{12} +3.81447 q^{13} +0.0783633 q^{14} +7.92785 q^{15} +1.00000 q^{16} +3.22867 q^{17} +4.30198 q^{18} +0.762392 q^{19} -2.93383 q^{20} -0.211755 q^{21} +0.0625037 q^{22} +8.02724 q^{23} -2.70222 q^{24} +3.60736 q^{25} +3.81447 q^{26} -3.51823 q^{27} +0.0783633 q^{28} -3.82920 q^{29} +7.92785 q^{30} -3.85325 q^{31} +1.00000 q^{32} -0.168898 q^{33} +3.22867 q^{34} -0.229905 q^{35} +4.30198 q^{36} -0.720130 q^{37} +0.762392 q^{38} -10.3075 q^{39} -2.93383 q^{40} +7.05531 q^{41} -0.211755 q^{42} +6.19559 q^{43} +0.0625037 q^{44} -12.6213 q^{45} +8.02724 q^{46} -5.87784 q^{47} -2.70222 q^{48} -6.99386 q^{49} +3.60736 q^{50} -8.72457 q^{51} +3.81447 q^{52} -4.52557 q^{53} -3.51823 q^{54} -0.183375 q^{55} +0.0783633 q^{56} -2.06015 q^{57} -3.82920 q^{58} -12.1987 q^{59} +7.92785 q^{60} +7.73371 q^{61} -3.85325 q^{62} +0.337117 q^{63} +1.00000 q^{64} -11.1910 q^{65} -0.168898 q^{66} +11.6457 q^{67} +3.22867 q^{68} -21.6913 q^{69} -0.229905 q^{70} +2.05001 q^{71} +4.30198 q^{72} -2.52486 q^{73} -0.720130 q^{74} -9.74788 q^{75} +0.762392 q^{76} +0.00489799 q^{77} -10.3075 q^{78} -10.8242 q^{79} -2.93383 q^{80} -3.39892 q^{81} +7.05531 q^{82} +5.51801 q^{83} -0.211755 q^{84} -9.47238 q^{85} +6.19559 q^{86} +10.3473 q^{87} +0.0625037 q^{88} -13.8719 q^{89} -12.6213 q^{90} +0.298914 q^{91} +8.02724 q^{92} +10.4123 q^{93} -5.87784 q^{94} -2.23673 q^{95} -2.70222 q^{96} -11.0864 q^{97} -6.99386 q^{98} +0.268889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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