LMFDB - Embedded newform 6045.2.a.bi.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.55076$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55076 q^{2} +1.00000 q^{3} +0.404854 q^{4} +1.00000 q^{5} -1.55076 q^{6} -3.31793 q^{7} +2.47369 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.55076 q^{2} +1.00000 q^{3} +0.404854 q^{4} +1.00000 q^{5} -1.55076 q^{6} -3.31793 q^{7} +2.47369 q^{8} +1.00000 q^{9} -1.55076 q^{10} -1.66559 q^{11} +0.404854 q^{12} -1.00000 q^{13} +5.14531 q^{14} +1.00000 q^{15} -4.64580 q^{16} +2.49510 q^{17} -1.55076 q^{18} +4.05977 q^{19} +0.404854 q^{20} -3.31793 q^{21} +2.58293 q^{22} -4.08888 q^{23} +2.47369 q^{24} +1.00000 q^{25} +1.55076 q^{26} +1.00000 q^{27} -1.34328 q^{28} -7.74560 q^{29} -1.55076 q^{30} +1.00000 q^{31} +2.25715 q^{32} -1.66559 q^{33} -3.86931 q^{34} -3.31793 q^{35} +0.404854 q^{36} -2.81862 q^{37} -6.29572 q^{38} -1.00000 q^{39} +2.47369 q^{40} +5.15982 q^{41} +5.14531 q^{42} +5.13332 q^{43} -0.674321 q^{44} +1.00000 q^{45} +6.34086 q^{46} +6.36962 q^{47} -4.64580 q^{48} +4.00865 q^{49} -1.55076 q^{50} +2.49510 q^{51} -0.404854 q^{52} +1.15119 q^{53} -1.55076 q^{54} -1.66559 q^{55} -8.20752 q^{56} +4.05977 q^{57} +12.0116 q^{58} -11.7707 q^{59} +0.404854 q^{60} +4.37024 q^{61} -1.55076 q^{62} -3.31793 q^{63} +5.79131 q^{64} -1.00000 q^{65} +2.58293 q^{66} +0.148698 q^{67} +1.01015 q^{68} -4.08888 q^{69} +5.14531 q^{70} +8.56722 q^{71} +2.47369 q^{72} -4.20895 q^{73} +4.37101 q^{74} +1.00000 q^{75} +1.64361 q^{76} +5.52631 q^{77} +1.55076 q^{78} -4.52909 q^{79} -4.64580 q^{80} +1.00000 q^{81} -8.00164 q^{82} -3.30024 q^{83} -1.34328 q^{84} +2.49510 q^{85} -7.96055 q^{86} -7.74560 q^{87} -4.12015 q^{88} -4.50283 q^{89} -1.55076 q^{90} +3.31793 q^{91} -1.65540 q^{92} +1.00000 q^{93} -9.87775 q^{94} +4.05977 q^{95} +2.25715 q^{96} +6.24763 q^{97} -6.21645 q^{98} -1.66559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * 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 $

$2$	−1.55076	−1.09655	−0.548276	−	0.836297i	$-0.684716\pi$
$2$	−1.55076	−1.09655	−0.548276	+	0.836297i	$0.684716\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.404854	0.202427
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.55076	−0.633095
$7$	−3.31793	−1.25406	−0.627030	−	0.778995i	$-0.715729\pi$
$7$	−3.31793	−1.25406	−0.627030	+	0.778995i	$0.715729\pi$
$8$	2.47369	0.874580
$9$	1.00000	0.333333
$10$	−1.55076	−0.490393
$11$	−1.66559	−0.502194	−0.251097	−	0.967962i	$-0.580791\pi$
$11$	−1.66559	−0.502194	−0.251097	+	0.967962i	$0.580791\pi$
$12$	0.404854	0.116871
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.14531	1.37514
$15$	1.00000	0.258199
$16$	−4.64580	−1.16145
$17$	2.49510	0.605152	0.302576	−	0.953125i	$-0.402153\pi$
$17$	2.49510	0.605152	0.302576	+	0.953125i	$0.402153\pi$
$18$	−1.55076	−0.365517
$19$	4.05977	0.931374	0.465687	−	0.884950i	$-0.345807\pi$
$19$	4.05977	0.931374	0.465687	+	0.884950i	$0.345807\pi$
$20$	0.404854	0.0905281
$21$	−3.31793	−0.724031
$22$	2.58293	0.550682
$23$	−4.08888	−0.852590	−0.426295	−	0.904584i	$-0.640181\pi$
$23$	−4.08888	−0.852590	−0.426295	+	0.904584i	$0.640181\pi$
$24$	2.47369	0.504939
$25$	1.00000	0.200000
$26$	1.55076	0.304129
$27$	1.00000	0.192450
$28$	−1.34328	−0.253856
$29$	−7.74560	−1.43832	−0.719161	−	0.694844i	$-0.755474\pi$
$29$	−7.74560	−1.43832	−0.719161	+	0.694844i	$0.755474\pi$
$30$	−1.55076	−0.283129
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	2.25715	0.399011
$33$	−1.66559	−0.289942
$34$	−3.86931	−0.663580
$35$	−3.31793	−0.560832
$36$	0.404854	0.0674757
$37$	−2.81862	−0.463379	−0.231690	−	0.972790i	$-0.574425\pi$
$37$	−2.81862	−0.463379	−0.231690	+	0.972790i	$0.574425\pi$
$38$	−6.29572	−1.02130
$39$	−1.00000	−0.160128
$40$	2.47369	0.391124
$41$	5.15982	0.805829	0.402914	−	0.915238i	$-0.367997\pi$
$41$	5.15982	0.805829	0.402914	+	0.915238i	$0.367997\pi$
$42$	5.14531	0.793938
$43$	5.13332	0.782825	0.391412	−	0.920215i	$-0.371987\pi$
$43$	5.13332	0.782825	0.391412	+	0.920215i	$0.371987\pi$
$44$	−0.674321	−0.101658
$45$	1.00000	0.149071
$46$	6.34086	0.934909
$47$	6.36962	0.929105	0.464552	−	0.885546i	$-0.346215\pi$
$47$	6.36962	0.929105	0.464552	+	0.885546i	$0.346215\pi$
$48$	−4.64580	−0.670564
$49$	4.00865	0.572664
$50$	−1.55076	−0.219310
$51$	2.49510	0.349384
$52$	−0.404854	−0.0561432
$53$	1.15119	0.158127	0.0790637	−	0.996870i	$-0.474807\pi$
$53$	1.15119	0.158127	0.0790637	+	0.996870i	$0.474807\pi$
$54$	−1.55076	−0.211032
$55$	−1.66559	−0.224588
$56$	−8.20752	−1.09678
$57$	4.05977	0.537729
$58$	12.0116	1.57720
$59$	−11.7707	−1.53242	−0.766209	−	0.642592i	$-0.777859\pi$
$59$	−11.7707	−1.53242	−0.766209	+	0.642592i	$0.777859\pi$
$60$	0.404854	0.0522664
$61$	4.37024	0.559552	0.279776	−	0.960065i	$-0.409740\pi$
$61$	4.37024	0.559552	0.279776	+	0.960065i	$0.409740\pi$
$62$	−1.55076	−0.196947
$63$	−3.31793	−0.418020
$64$	5.79131	0.723914
$65$	−1.00000	−0.124035
$66$	2.58293	0.317936
$67$	0.148698	0.0181664	0.00908319	−	0.999959i	$-0.497109\pi$
$67$	0.148698	0.0181664	0.00908319	+	0.999959i	$0.497109\pi$
$68$	1.01015	0.122499
$69$	−4.08888	−0.492243
$70$	5.14531	0.614982
$71$	8.56722	1.01674	0.508371	−	0.861138i	$-0.330248\pi$
$71$	8.56722	1.01674	0.508371	+	0.861138i	$0.330248\pi$
$72$	2.47369	0.291527
$73$	−4.20895	−0.492620	−0.246310	−	0.969191i	$-0.579218\pi$
$73$	−4.20895	−0.492620	−0.246310	+	0.969191i	$0.579218\pi$
$74$	4.37101	0.508119
$75$	1.00000	0.115470
$76$	1.64361	0.188535
$77$	5.52631	0.629781
$78$	1.55076	0.175589
$79$	−4.52909	−0.509563	−0.254781	−	0.966999i	$-0.582003\pi$
$79$	−4.52909	−0.509563	−0.254781	+	0.966999i	$0.582003\pi$
$80$	−4.64580	−0.519416
$81$	1.00000	0.111111
$82$	−8.00164	−0.883633
$83$	−3.30024	−0.362249	−0.181124	−	0.983460i	$-0.557974\pi$
$83$	−3.30024	−0.362249	−0.181124	+	0.983460i	$0.557974\pi$
$84$	−1.34328	−0.146564
$85$	2.49510	0.270632
$86$	−7.96055	−0.858408
$87$	−7.74560	−0.830416
$88$	−4.12015	−0.439209
$89$	−4.50283	−0.477299	−0.238650	−	0.971106i	$-0.576705\pi$
$89$	−4.50283	−0.477299	−0.238650	+	0.971106i	$0.576705\pi$
$90$	−1.55076	−0.163464
$91$	3.31793	0.347813
$92$	−1.65540	−0.172587
$93$	1.00000	0.103695
$94$	−9.87775	−1.01881
$95$	4.05977	0.416523
$96$	2.25715	0.230369
$97$	6.24763	0.634350	0.317175	−	0.948367i	$-0.397266\pi$
$97$	6.24763	0.634350	0.317175	+	0.948367i	$0.397266\pi$
$98$	−6.21645	−0.627956
$99$	−1.66559	−0.167398
$100$	0.404854	0.0404854
$101$	−0.573038	−0.0570194	−0.0285097	−	0.999594i	$-0.509076\pi$
$101$	−0.573038	−0.0570194	−0.0285097	+	0.999594i	$0.509076\pi$
$102$	−3.86931	−0.383118
$103$	−2.53344	−0.249627	−0.124814	−	0.992180i	$-0.539833\pi$
$103$	−2.53344	−0.249627	−0.124814	+	0.992180i	$0.539833\pi$
$104$	−2.47369	−0.242565
$105$	−3.31793	−0.323797
$106$	−1.78521	−0.173395
$107$	17.9433	1.73465	0.867324	−	0.497744i	$-0.165838\pi$
$107$	17.9433	1.73465	0.867324	+	0.497744i	$0.165838\pi$
$108$	0.404854	0.0389571
$109$	−0.299709	−0.0287070	−0.0143535	−	0.999897i	$-0.504569\pi$
$109$	−0.299709	−0.0287070	−0.0143535	+	0.999897i	$0.504569\pi$
$110$	2.58293	0.246273
$111$	−2.81862	−0.267532
$112$	15.4144	1.45653
$113$	−14.3246	−1.34755	−0.673774	−	0.738937i	$-0.735328\pi$
$113$	−14.3246	−1.34755	−0.673774	+	0.738937i	$0.735328\pi$
$114$	−6.29572	−0.589648
$115$	−4.08888	−0.381290
$116$	−3.13584	−0.291155
$117$	−1.00000	−0.0924500
$118$	18.2536	1.68038
$119$	−8.27858	−0.758896
$120$	2.47369	0.225816
$121$	−8.22581	−0.747801
$122$	−6.77719	−0.613578
$123$	5.15982	0.465245
$124$	0.404854	0.0363570
$125$	1.00000	0.0894427
$126$	5.14531	0.458380
$127$	17.5201	1.55465	0.777327	−	0.629096i	$-0.216575\pi$
$127$	17.5201	1.55465	0.777327	+	0.629096i	$0.216575\pi$
$128$	−13.4952	−1.19282
$129$	5.13332	0.451964
$130$	1.55076	0.136011
$131$	1.81654	0.158712	0.0793560	−	0.996846i	$-0.474714\pi$
$131$	1.81654	0.158712	0.0793560	+	0.996846i	$0.474714\pi$
$132$	−0.674321	−0.0586921
$133$	−13.4700	−1.16800
$134$	−0.230595	−0.0199204
$135$	1.00000	0.0860663
$136$	6.17211	0.529254
$137$	15.6531	1.33733	0.668665	−	0.743563i	$-0.266866\pi$
$137$	15.6531	1.33733	0.668665	+	0.743563i	$0.266866\pi$
$138$	6.34086	0.539770
$139$	1.77491	0.150546	0.0752728	−	0.997163i	$-0.476017\pi$
$139$	1.77491	0.150546	0.0752728	+	0.997163i	$0.476017\pi$
$140$	−1.34328	−0.113528
$141$	6.36962	0.536419
$142$	−13.2857	−1.11491
$143$	1.66559	0.139284
$144$	−4.64580	−0.387150
$145$	−7.74560	−0.643237
$146$	6.52707	0.540184
$147$	4.00865	0.330628
$148$	−1.14113	−0.0938005
$149$	−5.03528	−0.412506	−0.206253	−	0.978499i	$-0.566127\pi$
$149$	−5.03528	−0.412506	−0.206253	+	0.978499i	$0.566127\pi$
$150$	−1.55076	−0.126619
$151$	14.5513	1.18417	0.592085	−	0.805876i	$-0.298305\pi$
$151$	14.5513	1.18417	0.592085	+	0.805876i	$0.298305\pi$
$152$	10.0426	0.814561
$153$	2.49510	0.201717
$154$	−8.56997	−0.690588
$155$	1.00000	0.0803219
$156$	−0.404854	−0.0324143
$157$	5.31445	0.424139	0.212070	−	0.977255i	$-0.431980\pi$
$157$	5.31445	0.424139	0.212070	+	0.977255i	$0.431980\pi$
$158$	7.02353	0.558762
$159$	1.15119	0.0912950
$160$	2.25715	0.178443
$161$	13.5666	1.06920
$162$	−1.55076	−0.121839
$163$	−13.4099	−1.05035	−0.525174	−	0.850995i	$-0.676000\pi$
$163$	−13.4099	−1.05035	−0.525174	+	0.850995i	$0.676000\pi$
$164$	2.08898	0.163122
$165$	−1.66559	−0.129666
$166$	5.11788	0.397224
$167$	3.09033	0.239137	0.119569	−	0.992826i	$-0.461849\pi$
$167$	3.09033	0.239137	0.119569	+	0.992826i	$0.461849\pi$
$168$	−8.20752	−0.633224
$169$	1.00000	0.0769231
$170$	−3.86931	−0.296762
$171$	4.05977	0.310458
$172$	2.07825	0.158465
$173$	10.4768	0.796535	0.398268	−	0.917269i	$-0.369612\pi$
$173$	10.4768	0.796535	0.398268	+	0.917269i	$0.369612\pi$
$174$	12.0116	0.910594
$175$	−3.31793	−0.250812
$176$	7.73800	0.583274
$177$	−11.7707	−0.884742
$178$	6.98281	0.523383
$179$	9.38189	0.701235	0.350618	−	0.936519i	$-0.385972\pi$
$179$	9.38189	0.701235	0.350618	+	0.936519i	$0.385972\pi$
$180$	0.404854	0.0301760
$181$	20.1053	1.49442	0.747209	−	0.664589i	$-0.231393\pi$
$181$	20.1053	1.49442	0.747209	+	0.664589i	$0.231393\pi$
$182$	−5.14531	−0.381396
$183$	4.37024	0.323057
$184$	−10.1146	−0.745658
$185$	−2.81862	−0.207229
$186$	−1.55076	−0.113707
$187$	−4.15582	−0.303904
$188$	2.57877	0.188076
$189$	−3.31793	−0.241344
$190$	−6.29572	−0.456739
$191$	15.5042	1.12185	0.560924	−	0.827867i	$-0.310446\pi$
$191$	15.5042	1.12185	0.560924	+	0.827867i	$0.310446\pi$
$192$	5.79131	0.417952
$193$	4.54091	0.326862	0.163431	−	0.986555i	$-0.447744\pi$
$193$	4.54091	0.326862	0.163431	+	0.986555i	$0.447744\pi$
$194$	−9.68856	−0.695598
$195$	−1.00000	−0.0716115
$196$	1.62292	0.115923
$197$	−13.8141	−0.984210	−0.492105	−	0.870536i	$-0.663772\pi$
$197$	−13.8141	−0.984210	−0.492105	+	0.870536i	$0.663772\pi$
$198$	2.58293	0.183561
$199$	1.25468	0.0889420	0.0444710	−	0.999011i	$-0.485840\pi$
$199$	1.25468	0.0889420	0.0444710	+	0.999011i	$0.485840\pi$
$200$	2.47369	0.174916
$201$	0.148698	0.0104884
$202$	0.888644	0.0625248
$203$	25.6993	1.80374
$204$	1.01015	0.0707249
$205$	5.15982	0.360378
$206$	3.92876	0.273730
$207$	−4.08888	−0.284197
$208$	4.64580	0.322128
$209$	−6.76190	−0.467731
$210$	5.14531	0.355060
$211$	−10.9450	−0.753482	−0.376741	−	0.926319i	$-0.622955\pi$
$211$	−10.9450	−0.753482	−0.376741	+	0.926319i	$0.622955\pi$
$212$	0.466062	0.0320093
$213$	8.56722	0.587016
$214$	−27.8258	−1.90213
$215$	5.13332	0.350090
$216$	2.47369	0.168313
$217$	−3.31793	−0.225236
$218$	0.464777	0.0314787
$219$	−4.20895	−0.284414
$220$	−0.674321	−0.0454627
$221$	−2.49510	−0.167839
$222$	4.37101	0.293363
$223$	−23.5214	−1.57511	−0.787553	−	0.616247i	$-0.788652\pi$
$223$	−23.5214	−1.57511	−0.787553	+	0.616247i	$0.788652\pi$
$224$	−7.48905	−0.500383
$225$	1.00000	0.0666667
$226$	22.2141	1.47766
$227$	12.9536	0.859759	0.429879	−	0.902886i	$-0.358556\pi$
$227$	12.9536	0.859759	0.429879	+	0.902886i	$0.358556\pi$
$228$	1.64361	0.108851
$229$	−11.2474	−0.743251	−0.371625	−	0.928383i	$-0.621199\pi$
$229$	−11.2474	−0.743251	−0.371625	+	0.928383i	$0.621199\pi$
$230$	6.34086	0.418104
$231$	5.52631	0.363604
$232$	−19.1602	−1.25793
$233$	28.1805	1.84617	0.923083	−	0.384601i	$-0.125661\pi$
$233$	28.1805	1.84617	0.923083	+	0.384601i	$0.125661\pi$
$234$	1.55076	0.101376
$235$	6.36962	0.415508
$236$	−4.76543	−0.310203
$237$	−4.52909	−0.294196
$238$	12.8381	0.832169
$239$	−12.5399	−0.811138	−0.405569	−	0.914065i	$-0.632927\pi$
$239$	−12.5399	−0.811138	−0.405569	+	0.914065i	$0.632927\pi$
$240$	−4.64580	−0.299885
$241$	−1.73016	−0.111449	−0.0557247	−	0.998446i	$-0.517747\pi$
$241$	−1.73016	−0.111449	−0.0557247	+	0.998446i	$0.517747\pi$
$242$	12.7563	0.820003
$243$	1.00000	0.0641500
$244$	1.76931	0.113268
$245$	4.00865	0.256103
$246$	−8.00164	−0.510166
$247$	−4.05977	−0.258317
$248$	2.47369	0.157079
$249$	−3.30024	−0.209144
$250$	−1.55076	−0.0980786
$251$	11.5732	0.730497	0.365248	−	0.930910i	$-0.380984\pi$
$251$	11.5732	0.730497	0.365248	+	0.930910i	$0.380984\pi$
$252$	−1.34328	−0.0846185
$253$	6.81039	0.428165
$254$	−27.1694	−1.70476
$255$	2.49510	0.156249
$256$	9.34522	0.584076
$257$	25.6966	1.60291	0.801456	−	0.598054i	$-0.204059\pi$
$257$	25.6966	1.60291	0.801456	+	0.598054i	$0.204059\pi$
$258$	−7.96055	−0.495602
$259$	9.35200	0.581105
$260$	−0.404854	−0.0251080
$261$	−7.74560	−0.479441
$262$	−2.81702	−0.174036
$263$	14.0658	0.867335	0.433667	−	0.901073i	$-0.357219\pi$
$263$	14.0658	0.867335	0.433667	+	0.901073i	$0.357219\pi$
$264$	−4.12015	−0.253578
$265$	1.15119	0.0707168
$266$	20.8887	1.28077
$267$	−4.50283	−0.275569
$268$	0.0602011	0.00367737
$269$	26.5162	1.61672	0.808362	−	0.588686i	$-0.200354\pi$
$269$	26.5162	1.61672	0.808362	+	0.588686i	$0.200354\pi$
$270$	−1.55076	−0.0943762
$271$	−7.75598	−0.471142	−0.235571	−	0.971857i	$-0.575696\pi$
$271$	−7.75598	−0.471142	−0.235571	+	0.971857i	$0.575696\pi$
$272$	−11.5918	−0.702854
$273$	3.31793	0.200810
$274$	−24.2741	−1.46645
$275$	−1.66559	−0.100439
$276$	−1.65540	−0.0996433
$277$	−7.19646	−0.432393	−0.216197	−	0.976350i	$-0.569365\pi$
$277$	−7.19646	−0.432393	−0.216197	+	0.976350i	$0.569365\pi$
$278$	−2.75245	−0.165081
$279$	1.00000	0.0598684
$280$	−8.20752	−0.490493
$281$	−14.8018	−0.883004	−0.441502	−	0.897260i	$-0.645554\pi$
$281$	−14.8018	−0.883004	−0.441502	+	0.897260i	$0.645554\pi$
$282$	−9.87775	−0.588211
$283$	4.75365	0.282575	0.141288	−	0.989969i	$-0.454876\pi$
$283$	4.75365	0.282575	0.141288	+	0.989969i	$0.454876\pi$
$284$	3.46847	0.205816
$285$	4.05977	0.240480
$286$	−2.58293	−0.152732
$287$	−17.1199	−1.01056
$288$	2.25715	0.133004
$289$	−10.7745	−0.633791
$290$	12.0116	0.705343
$291$	6.24763	0.366242
$292$	−1.70401	−0.0997197
$293$	18.1813	1.06216	0.531080	−	0.847321i	$-0.321786\pi$
$293$	18.1813	1.06216	0.531080	+	0.847321i	$0.321786\pi$
$294$	−6.21645	−0.362551
$295$	−11.7707	−0.685318
$296$	−6.97240	−0.405262
$297$	−1.66559	−0.0966473
$298$	7.80851	0.452335
$299$	4.08888	0.236466
$300$	0.404854	0.0233743
$301$	−17.0320	−0.981708
$302$	−22.5656	−1.29850
$303$	−0.573038	−0.0329202
$304$	−18.8609	−1.08174
$305$	4.37024	0.250239
$306$	−3.86931	−0.221193
$307$	20.8888	1.19219	0.596094	−	0.802915i	$-0.296718\pi$
$307$	20.8888	1.19219	0.596094	+	0.802915i	$0.296718\pi$
$308$	2.23735	0.127485
$309$	−2.53344	−0.144122
$310$	−1.55076	−0.0880772
$311$	−8.45476	−0.479425	−0.239713	−	0.970844i	$-0.577053\pi$
$311$	−8.45476	−0.479425	−0.239713	+	0.970844i	$0.577053\pi$
$312$	−2.47369	−0.140045
$313$	7.51009	0.424496	0.212248	−	0.977216i	$-0.431922\pi$
$313$	7.51009	0.424496	0.212248	+	0.977216i	$0.431922\pi$
$314$	−8.24143	−0.465091
$315$	−3.31793	−0.186944
$316$	−1.83362	−0.103149
$317$	−18.8364	−1.05796	−0.528979	−	0.848635i	$-0.677425\pi$
$317$	−18.8364	−1.05796	−0.528979	+	0.848635i	$0.677425\pi$
$318$	−1.78521	−0.100110
$319$	12.9010	0.722317
$320$	5.79131	0.323744
$321$	17.9433	1.00150
$322$	−21.0385	−1.17243
$323$	10.1295	0.563623
$324$	0.404854	0.0224919
$325$	−1.00000	−0.0554700
$326$	20.7956	1.15176
$327$	−0.299709	−0.0165740
$328$	12.7638	0.704762
$329$	−21.1339	−1.16515
$330$	2.58293	0.142186
$331$	−6.94183	−0.381558	−0.190779	−	0.981633i	$-0.561101\pi$
$331$	−6.94183	−0.381558	−0.190779	+	0.981633i	$0.561101\pi$
$332$	−1.33612	−0.0733289
$333$	−2.81862	−0.154460
$334$	−4.79237	−0.262227
$335$	0.148698	0.00812425
$336$	15.4144	0.840926
$337$	8.46476	0.461105	0.230552	−	0.973060i	$-0.425947\pi$
$337$	8.46476	0.461105	0.230552	+	0.973060i	$0.425947\pi$
$338$	−1.55076	−0.0843502
$339$	−14.3246	−0.778008
$340$	1.01015	0.0547833
$341$	−1.66559	−0.0901967
$342$	−6.29572	−0.340433
$343$	9.92509	0.535904
$344$	12.6982	0.684643
$345$	−4.08888	−0.220138
$346$	−16.2470	−0.873443
$347$	11.6458	0.625179	0.312589	−	0.949888i	$-0.398804\pi$
$347$	11.6458	0.625179	0.312589	+	0.949888i	$0.398804\pi$
$348$	−3.13584	−0.168099
$349$	−4.37048	−0.233946	−0.116973	−	0.993135i	$-0.537319\pi$
$349$	−4.37048	−0.233946	−0.116973	+	0.993135i	$0.537319\pi$
$350$	5.14531	0.275028
$351$	−1.00000	−0.0533761
$352$	−3.75948	−0.200381
$353$	−3.41740	−0.181890	−0.0909450	−	0.995856i	$-0.528989\pi$
$353$	−3.41740	−0.181890	−0.0909450	+	0.995856i	$0.528989\pi$
$354$	18.2536	0.970166
$355$	8.56722	0.454701
$356$	−1.82299	−0.0966183
$357$	−8.27858	−0.438149
$358$	−14.5491	−0.768941
$359$	24.5447	1.29542	0.647709	−	0.761888i	$-0.275727\pi$
$359$	24.5447	1.29542	0.647709	+	0.761888i	$0.275727\pi$
$360$	2.47369	0.130375
$361$	−2.51831	−0.132543
$362$	−31.1785	−1.63871
$363$	−8.22581	−0.431743
$364$	1.34328	0.0704069
$365$	−4.20895	−0.220306
$366$	−6.77719	−0.354249
$367$	−9.66042	−0.504270	−0.252135	−	0.967692i	$-0.581133\pi$
$367$	−9.66042	−0.504270	−0.252135	+	0.967692i	$0.581133\pi$
$368$	18.9961	0.990240
$369$	5.15982	0.268610
$370$	4.37101	0.227238
$371$	−3.81955	−0.198301
$372$	0.404854	0.0209907
$373$	−30.3588	−1.57192	−0.785960	−	0.618277i	$-0.787831\pi$
$373$	−30.3588	−1.57192	−0.785960	+	0.618277i	$0.787831\pi$
$374$	6.44468	0.333246
$375$	1.00000	0.0516398
$376$	15.7564	0.812577
$377$	7.74560	0.398919
$378$	5.14531	0.264646
$379$	1.50023	0.0770618	0.0385309	−	0.999257i	$-0.487732\pi$
$379$	1.50023	0.0770618	0.0385309	+	0.999257i	$0.487732\pi$
$380$	1.64361	0.0843156
$381$	17.5201	0.897580
$382$	−24.0433	−1.23016
$383$	12.1613	0.621411	0.310706	−	0.950506i	$-0.399435\pi$
$383$	12.1613	0.621411	0.310706	+	0.950506i	$0.399435\pi$
$384$	−13.4952	−0.688675
$385$	5.52631	0.281647
$386$	−7.04186	−0.358421
$387$	5.13332	0.260942
$388$	2.52938	0.128410
$389$	25.2954	1.28253	0.641263	−	0.767321i	$-0.278411\pi$
$389$	25.2954	1.28253	0.641263	+	0.767321i	$0.278411\pi$
$390$	1.55076	0.0785257
$391$	−10.2022	−0.515946
$392$	9.91614	0.500841
$393$	1.81654	0.0916324
$394$	21.4223	1.07924
$395$	−4.52909	−0.227883
$396$	−0.674321	−0.0338859
$397$	30.2630	1.51886	0.759428	−	0.650591i	$-0.225479\pi$
$397$	30.2630	1.51886	0.759428	+	0.650591i	$0.225479\pi$
$398$	−1.94571	−0.0975296
$399$	−13.4700	−0.674344
$400$	−4.64580	−0.232290
$401$	14.8950	0.743822	0.371911	−	0.928268i	$-0.378703\pi$
$401$	14.8950	0.743822	0.371911	+	0.928268i	$0.378703\pi$
$402$	−0.230595	−0.0115010
$403$	−1.00000	−0.0498135
$404$	−0.231997	−0.0115423
$405$	1.00000	0.0496904
$406$	−39.8535	−1.97790
$407$	4.69467	0.232706
$408$	6.17211	0.305565
$409$	8.50362	0.420477	0.210239	−	0.977650i	$-0.432576\pi$
$409$	8.50362	0.420477	0.210239	+	0.977650i	$0.432576\pi$
$410$	−8.00164	−0.395173
$411$	15.6531	0.772108
$412$	−1.02567	−0.0505313
$413$	39.0544	1.92174
$414$	6.34086	0.311636
$415$	−3.30024	−0.162002
$416$	−2.25715	−0.110666
$417$	1.77491	0.0869176
$418$	10.4861	0.512891
$419$	34.9960	1.70967	0.854834	−	0.518902i	$-0.173659\pi$
$419$	34.9960	1.70967	0.854834	+	0.518902i	$0.173659\pi$
$420$	−1.34328	−0.0655452
$421$	12.1494	0.592124	0.296062	−	0.955169i	$-0.404327\pi$
$421$	12.1494	0.592124	0.296062	+	0.955169i	$0.404327\pi$
$422$	16.9730	0.826232
$423$	6.36962	0.309702
$424$	2.84767	0.138295
$425$	2.49510	0.121030
$426$	−13.2857	−0.643694
$427$	−14.5001	−0.701711
$428$	7.26444	0.351140
$429$	1.66559	0.0804154
$430$	−7.96055	−0.383892
$431$	5.02466	0.242029	0.121015	−	0.992651i	$-0.461385\pi$
$431$	5.02466	0.242029	0.121015	+	0.992651i	$0.461385\pi$
$432$	−4.64580	−0.223521
$433$	20.1247	0.967132	0.483566	−	0.875308i	$-0.339341\pi$
$433$	20.1247	0.967132	0.483566	+	0.875308i	$0.339341\pi$
$434$	5.14531	0.246983
$435$	−7.74560	−0.371373
$436$	−0.121339	−0.00581107
$437$	−16.5999	−0.794080
$438$	6.52707	0.311875
$439$	−27.2116	−1.29874	−0.649370	−	0.760473i	$-0.724967\pi$
$439$	−27.2116	−1.29874	−0.649370	+	0.760473i	$0.724967\pi$
$440$	−4.12015	−0.196420
$441$	4.00865	0.190888
$442$	3.86931	0.184044
$443$	26.9113	1.27859	0.639296	−	0.768961i	$-0.279226\pi$
$443$	26.9113	1.27859	0.639296	+	0.768961i	$0.279226\pi$
$444$	−1.14113	−0.0541557
$445$	−4.50283	−0.213455
$446$	36.4760	1.72719
$447$	−5.03528	−0.238161
$448$	−19.2152	−0.907831
$449$	−19.4893	−0.919756	−0.459878	−	0.887982i	$-0.652107\pi$
$449$	−19.4893	−0.919756	−0.459878	+	0.887982i	$0.652107\pi$
$450$	−1.55076	−0.0731035
$451$	−8.59414	−0.404682
$452$	−5.79939	−0.272780
$453$	14.5513	0.683681
$454$	−20.0879	−0.942770
$455$	3.31793	0.155547
$456$	10.0426	0.470287
$457$	−18.1179	−0.847518	−0.423759	−	0.905775i	$-0.639290\pi$
$457$	−18.1179	−0.847518	−0.423759	+	0.905775i	$0.639290\pi$
$458$	17.4420	0.815013
$459$	2.49510	0.116461
$460$	−1.65540	−0.0771834
$461$	12.5532	0.584662	0.292331	−	0.956317i	$-0.405569\pi$
$461$	12.5532	0.584662	0.292331	+	0.956317i	$0.405569\pi$
$462$	−8.56997	−0.398711
$463$	5.01956	0.233279	0.116639	−	0.993174i	$-0.462788\pi$
$463$	5.01956	0.233279	0.116639	+	0.993174i	$0.462788\pi$
$464$	35.9845	1.67054
$465$	1.00000	0.0463739
$466$	−43.7012	−2.02442
$467$	14.9226	0.690535	0.345267	−	0.938504i	$-0.387788\pi$
$467$	14.9226	0.690535	0.345267	+	0.938504i	$0.387788\pi$
$468$	−0.404854	−0.0187144
$469$	−0.493370	−0.0227817
$470$	−9.87775	−0.455627
$471$	5.31445	0.244877
$472$	−29.1171	−1.34022
$473$	−8.55001	−0.393130
$474$	7.02353	0.322601
$475$	4.05977	0.186275
$476$	−3.35162	−0.153621
$477$	1.15119	0.0527092
$478$	19.4463	0.889455
$479$	−26.3205	−1.20262	−0.601308	−	0.799017i	$-0.705354\pi$
$479$	−26.3205	−1.20262	−0.601308	+	0.799017i	$0.705354\pi$
$480$	2.25715	0.103024
$481$	2.81862	0.128518
$482$	2.68306	0.122210
$483$	13.5666	0.617302
$484$	−3.33025	−0.151375
$485$	6.24763	0.283690
$486$	−1.55076	−0.0703439
$487$	−4.09257	−0.185452	−0.0927261	−	0.995692i	$-0.529558\pi$
$487$	−4.09257	−0.185452	−0.0927261	+	0.995692i	$0.529558\pi$
$488$	10.8106	0.489373
$489$	−13.4099	−0.606419
$490$	−6.21645	−0.280831
$491$	0.341322	0.0154036	0.00770182	−	0.999970i	$-0.497548\pi$
$491$	0.341322	0.0154036	0.00770182	+	0.999970i	$0.497548\pi$
$492$	2.08898	0.0941783
$493$	−19.3261	−0.870403
$494$	6.29572	0.283258
$495$	−1.66559	−0.0748627
$496$	−4.64580	−0.208603
$497$	−28.4254	−1.27505
$498$	5.11788	0.229338
$499$	−0.364219	−0.0163047	−0.00815233	−	0.999967i	$-0.502595\pi$
$499$	−0.364219	−0.0163047	−0.00815233	+	0.999967i	$0.502595\pi$
$500$	0.404854	0.0181056
$501$	3.09033	0.138066
$502$	−17.9473	−0.801028
$503$	36.7878	1.64029	0.820143	−	0.572158i	$-0.193894\pi$
$503$	36.7878	1.64029	0.820143	+	0.572158i	$0.193894\pi$
$504$	−8.20752	−0.365592
$505$	−0.573038	−0.0254999
$506$	−10.5613	−0.469506
$507$	1.00000	0.0444116
$508$	7.09307	0.314704
$509$	−23.3848	−1.03651	−0.518256	−	0.855226i	$-0.673418\pi$
$509$	−23.3848	−1.03651	−0.518256	+	0.855226i	$0.673418\pi$
$510$	−3.86931	−0.171336
$511$	13.9650	0.617775
$512$	12.4983	0.552351
$513$	4.05977	0.179243
$514$	−39.8493	−1.75768
$515$	−2.53344	−0.111637
$516$	2.07825	0.0914897
$517$	−10.6092	−0.466591
$518$	−14.5027	−0.637212
$519$	10.4768	0.459880
$520$	−2.47369	−0.108478
$521$	−4.00096	−0.175285	−0.0876426	−	0.996152i	$-0.527933\pi$
$521$	−4.00096	−0.175285	−0.0876426	+	0.996152i	$0.527933\pi$
$522$	12.0116	0.525732
$523$	−0.839234	−0.0366971	−0.0183486	−	0.999832i	$-0.505841\pi$
$523$	−0.839234	−0.0366971	−0.0183486	+	0.999832i	$0.505841\pi$
$524$	0.735434	0.0321276
$525$	−3.31793	−0.144806
$526$	−21.8127	−0.951078
$527$	2.49510	0.108688
$528$	7.73800	0.336753
$529$	−6.28109	−0.273091
$530$	−1.78521	−0.0775446
$531$	−11.7707	−0.510806
$532$	−5.45339	−0.236434
$533$	−5.15982	−0.223497
$534$	6.98281	0.302176
$535$	17.9433	0.775758
$536$	0.367833	0.0158880
$537$	9.38189	0.404858
$538$	−41.1203	−1.77282
$539$	−6.67676	−0.287589
$540$	0.404854	0.0174221
$541$	−18.5869	−0.799115	−0.399557	−	0.916708i	$-0.630836\pi$
$541$	−18.5869	−0.799115	−0.399557	+	0.916708i	$0.630836\pi$
$542$	12.0277	0.516632
$543$	20.1053	0.862803
$544$	5.63181	0.241462
$545$	−0.299709	−0.0128381
$546$	−5.14531	−0.220199
$547$	1.20197	0.0513927	0.0256963	−	0.999670i	$-0.491820\pi$
$547$	1.20197	0.0513927	0.0256963	+	0.999670i	$0.491820\pi$
$548$	6.33720	0.270712
$549$	4.37024	0.186517
$550$	2.58293	0.110136
$551$	−31.4453	−1.33962
$552$	−10.1146	−0.430506
$553$	15.0272	0.639022
$554$	11.1600	0.474142
$555$	−2.81862	−0.119644
$556$	0.718578	0.0304745
$557$	−33.6159	−1.42435	−0.712175	−	0.702002i	$-0.752290\pi$
$557$	−33.6159	−1.42435	−0.712175	+	0.702002i	$0.752290\pi$
$558$	−1.55076	−0.0656489
$559$	−5.13332	−0.217116
$560$	15.4144	0.651379
$561$	−4.15582	−0.175459
$562$	22.9541	0.968260
$563$	2.35055	0.0990638	0.0495319	−	0.998773i	$-0.484227\pi$
$563$	2.35055	0.0990638	0.0495319	+	0.998773i	$0.484227\pi$
$564$	2.57877	0.108586
$565$	−14.3246	−0.602642
$566$	−7.37177	−0.309859
$567$	−3.31793	−0.139340
$568$	21.1926	0.889222
$569$	−33.2570	−1.39421	−0.697104	−	0.716970i	$-0.745528\pi$
$569$	−33.2570	−1.39421	−0.697104	+	0.716970i	$0.745528\pi$
$570$	−6.29572	−0.263699
$571$	3.37199	0.141114	0.0705568	−	0.997508i	$-0.477522\pi$
$571$	3.37199	0.141114	0.0705568	+	0.997508i	$0.477522\pi$
$572$	0.674321	0.0281948
$573$	15.5042	0.647699
$574$	26.5489	1.10813
$575$	−4.08888	−0.170518
$576$	5.79131	0.241305
$577$	11.2323	0.467607	0.233803	−	0.972284i	$-0.424883\pi$
$577$	11.2323	0.467607	0.233803	+	0.972284i	$0.424883\pi$
$578$	16.7086	0.694986
$579$	4.54091	0.188714
$580$	−3.13584	−0.130209
$581$	10.9500	0.454281
$582$	−9.68856	−0.401604
$583$	−1.91740	−0.0794107
$584$	−10.4116	−0.430836
$585$	−1.00000	−0.0413449
$586$	−28.1948	−1.16472
$587$	15.3010	0.631538	0.315769	−	0.948836i	$-0.397738\pi$
$587$	15.3010	0.631538	0.315769	+	0.948836i	$0.397738\pi$
$588$	1.62292	0.0669280
$589$	4.05977	0.167280
$590$	18.2536	0.751487
$591$	−13.8141	−0.568234
$592$	13.0948	0.538192
$593$	22.7643	0.934816	0.467408	−	0.884042i	$-0.345188\pi$
$593$	22.7643	0.934816	0.467408	+	0.884042i	$0.345188\pi$
$594$	2.58293	0.105979
$595$	−8.27858	−0.339389
$596$	−2.03855	−0.0835024
$597$	1.25468	0.0513507
$598$	−6.34086	−0.259297
$599$	−11.0486	−0.451433	−0.225717	−	0.974193i	$-0.572472\pi$
$599$	−11.0486	−0.451433	−0.225717	+	0.974193i	$0.572472\pi$
$600$	2.47369	0.100988
$601$	5.56911	0.227169	0.113584	−	0.993528i	$-0.463767\pi$
$601$	5.56911	0.227169	0.113584	+	0.993528i	$0.463767\pi$
$602$	26.4125	1.07649
$603$	0.148698	0.00605546
$604$	5.89116	0.239708
$605$	−8.22581	−0.334427
$606$	0.888644	0.0360987
$607$	11.3289	0.459827	0.229913	−	0.973211i	$-0.426156\pi$
$607$	11.3289	0.459827	0.229913	+	0.973211i	$0.426156\pi$
$608$	9.16348	0.371628
$609$	25.6993	1.04139
$610$	−6.77719	−0.274400
$611$	−6.36962	−0.257687
$612$	1.01015	0.0408330
$613$	−26.1373	−1.05568	−0.527838	−	0.849345i	$-0.676997\pi$
$613$	−26.1373	−1.05568	−0.527838	+	0.849345i	$0.676997\pi$
$614$	−32.3935	−1.30730
$615$	5.15982	0.208064
$616$	13.6704	0.550794
$617$	23.8280	0.959277	0.479639	−	0.877466i	$-0.340768\pi$
$617$	23.8280	0.959277	0.479639	+	0.877466i	$0.340768\pi$
$618$	3.92876	0.158038
$619$	31.1759	1.25306	0.626532	−	0.779396i	$-0.284474\pi$
$619$	31.1759	1.25306	0.626532	+	0.779396i	$0.284474\pi$
$620$	0.404854	0.0162593
$621$	−4.08888	−0.164081
$622$	13.1113	0.525715
$623$	14.9401	0.598561
$624$	4.64580	0.185981
$625$	1.00000	0.0400000
$626$	−11.6463	−0.465482
$627$	−6.76190	−0.270044
$628$	2.15158	0.0858573
$629$	−7.03276	−0.280415
$630$	5.14531	0.204994
$631$	35.3813	1.40851	0.704253	−	0.709949i	$-0.251282\pi$
$631$	35.3813	1.40851	0.704253	+	0.709949i	$0.251282\pi$
$632$	−11.2036	−0.445653
$633$	−10.9450	−0.435023
$634$	29.2107	1.16011
$635$	17.5201	0.695263
$636$	0.466062	0.0184806
$637$	−4.00865	−0.158828
$638$	−20.0063	−0.792058
$639$	8.56722	0.338914
$640$	−13.4952	−0.533446
$641$	34.5093	1.36304	0.681518	−	0.731802i	$-0.261320\pi$
$641$	34.5093	1.36304	0.681518	+	0.731802i	$0.261320\pi$
$642$	−27.8258	−1.09820
$643$	32.0023	1.26205	0.631023	−	0.775764i	$-0.282635\pi$
$643$	32.0023	1.26205	0.631023	+	0.775764i	$0.282635\pi$
$644$	5.49249	0.216435
$645$	5.13332	0.202124
$646$	−15.7085	−0.618042
$647$	−7.84053	−0.308243	−0.154121	−	0.988052i	$-0.549255\pi$
$647$	−7.84053	−0.308243	−0.154121	+	0.988052i	$0.549255\pi$
$648$	2.47369	0.0971756
$649$	19.6052	0.769571
$650$	1.55076	0.0608258
$651$	−3.31793	−0.130040
$652$	−5.42907	−0.212619
$653$	40.5625	1.58733	0.793666	−	0.608354i	$-0.208170\pi$
$653$	40.5625	1.58733	0.793666	+	0.608354i	$0.208170\pi$
$654$	0.464777	0.0181742
$655$	1.81654	0.0709781
$656$	−23.9715	−0.935930
$657$	−4.20895	−0.164207
$658$	32.7737	1.27765
$659$	39.0331	1.52051	0.760257	−	0.649622i	$-0.225073\pi$
$659$	39.0331	1.52051	0.760257	+	0.649622i	$0.225073\pi$
$660$	−0.674321	−0.0262479
$661$	2.61576	0.101741	0.0508706	−	0.998705i	$-0.483800\pi$
$661$	2.61576	0.101741	0.0508706	+	0.998705i	$0.483800\pi$
$662$	10.7651	0.418398
$663$	−2.49510	−0.0969018
$664$	−8.16376	−0.316815
$665$	−13.4700	−0.522345
$666$	4.37101	0.169373
$667$	31.6708	1.22630
$668$	1.25113	0.0484079
$669$	−23.5214	−0.909388
$670$	−0.230595	−0.00890867
$671$	−7.27903	−0.281004
$672$	−7.48905	−0.288896
$673$	11.3846	0.438844	0.219422	−	0.975630i	$-0.429583\pi$
$673$	11.3846	0.438844	0.219422	+	0.975630i	$0.429583\pi$
$674$	−13.1268	−0.505626
$675$	1.00000	0.0384900
$676$	0.404854	0.0155713
$677$	−5.12165	−0.196841	−0.0984204	−	0.995145i	$-0.531379\pi$
$677$	−5.12165	−0.196841	−0.0984204	+	0.995145i	$0.531379\pi$
$678$	22.2141	0.853126
$679$	−20.7292	−0.795513
$680$	6.17211	0.236690
$681$	12.9536	0.496382
$682$	2.58293	0.0989054
$683$	19.8233	0.758518	0.379259	−	0.925290i	$-0.376179\pi$
$683$	19.8233	0.758518	0.379259	+	0.925290i	$0.376179\pi$
$684$	1.64361	0.0628451
$685$	15.6531	0.598072
$686$	−15.3914	−0.587647
$687$	−11.2474	−0.429116
$688$	−23.8484	−0.909212
$689$	−1.15119	−0.0438567
$690$	6.34086	0.241392
$691$	35.7956	1.36173	0.680865	−	0.732409i	$-0.261604\pi$
$691$	35.7956	1.36173	0.680865	+	0.732409i	$0.261604\pi$
$692$	4.24157	0.161240
$693$	5.52631	0.209927
$694$	−18.0598	−0.685541
$695$	1.77491	0.0673260
$696$	−19.1602	−0.726265
$697$	12.8743	0.487649
$698$	6.77756	0.256534
$699$	28.1805	1.06588
$700$	−1.34328	−0.0507711
$701$	−12.8582	−0.485646	−0.242823	−	0.970071i	$-0.578073\pi$
$701$	−12.8582	−0.485646	−0.242823	+	0.970071i	$0.578073\pi$
$702$	1.55076	0.0585296
$703$	−11.4430	−0.431579
$704$	−9.64595	−0.363545
$705$	6.36962	0.239894
$706$	5.29957	0.199452
$707$	1.90130	0.0715057
$708$	−4.76543	−0.179096
$709$	11.4025	0.428229	0.214114	−	0.976809i	$-0.431313\pi$
$709$	11.4025	0.428229	0.214114	+	0.976809i	$0.431313\pi$
$710$	−13.2857	−0.498603
$711$	−4.52909	−0.169854
$712$	−11.1386	−0.417436
$713$	−4.08888	−0.153130
$714$	12.8381	0.480453
$715$	1.66559	0.0622895
$716$	3.79830	0.141949
$717$	−12.5399	−0.468311
$718$	−38.0629	−1.42049
$719$	26.1504	0.975245	0.487623	−	0.873054i	$-0.337864\pi$
$719$	26.1504	0.975245	0.487623	+	0.873054i	$0.337864\pi$
$720$	−4.64580	−0.173139
$721$	8.40578	0.313048
$722$	3.90529	0.145340
$723$	−1.73016	−0.0643453
$724$	8.13973	0.302511
$725$	−7.74560	−0.287664
$726$	12.7563	0.473429
$727$	6.71434	0.249021	0.124511	−	0.992218i	$-0.460264\pi$
$727$	6.71434	0.249021	0.124511	+	0.992218i	$0.460264\pi$
$728$	8.20752	0.304191
$729$	1.00000	0.0370370
$730$	6.52707	0.241578
$731$	12.8082	0.473728
$732$	1.76931	0.0653956
$733$	−45.4669	−1.67936	−0.839680	−	0.543081i	$-0.817257\pi$
$733$	−45.4669	−1.67936	−0.839680	+	0.543081i	$0.817257\pi$
$734$	14.9810	0.552959
$735$	4.00865	0.147861
$736$	−9.22919	−0.340192
$737$	−0.247670	−0.00912305
$738$	−8.00164	−0.294544
$739$	9.39847	0.345728	0.172864	−	0.984946i	$-0.444698\pi$
$739$	9.39847	0.345728	0.172864	+	0.984946i	$0.444698\pi$
$740$	−1.14113	−0.0419488
$741$	−4.05977	−0.149139
$742$	5.92320	0.217448
$743$	21.5795	0.791674	0.395837	−	0.918321i	$-0.370455\pi$
$743$	21.5795	0.791674	0.395837	+	0.918321i	$0.370455\pi$
$744$	2.47369	0.0906898
$745$	−5.03528	−0.184478
$746$	47.0792	1.72369
$747$	−3.30024	−0.120750
$748$	−1.68250	−0.0615183
$749$	−59.5347	−2.17535
$750$	−1.55076	−0.0566257
$751$	23.7265	0.865792	0.432896	−	0.901444i	$-0.357492\pi$
$751$	23.7265	0.865792	0.432896	+	0.901444i	$0.357492\pi$
$752$	−29.5920	−1.07911
$753$	11.5732	0.421752
$754$	−12.0116	−0.437435
$755$	14.5513	0.529577
$756$	−1.34328	−0.0488545
$757$	2.86699	0.104203	0.0521013	−	0.998642i	$-0.483408\pi$
$757$	2.86699	0.104203	0.0521013	+	0.998642i	$0.483408\pi$
$758$	−2.32650	−0.0845023
$759$	6.81039	0.247201
$760$	10.0426	0.364283
$761$	−47.5230	−1.72271	−0.861354	−	0.508006i	$-0.830383\pi$
$761$	−47.5230	−1.72271	−0.861354	+	0.508006i	$0.830383\pi$
$762$	−27.1694	−0.984244
$763$	0.994414	0.0360002
$764$	6.27696	0.227092
$765$	2.49510	0.0902107
$766$	−18.8592	−0.681410
$767$	11.7707	0.425016
$768$	9.34522	0.337216
$769$	−3.43665	−0.123929	−0.0619644	−	0.998078i	$-0.519737\pi$
$769$	−3.43665	−0.123929	−0.0619644	+	0.998078i	$0.519737\pi$
$770$	−8.56997	−0.308840
$771$	25.6966	0.925441
$772$	1.83841	0.0661657
$773$	−26.8268	−0.964893	−0.482447	−	0.875925i	$-0.660252\pi$
$773$	−26.8268	−0.964893	−0.482447	+	0.875925i	$0.660252\pi$
$774$	−7.96055	−0.286136
$775$	1.00000	0.0359211
$776$	15.4547	0.554790
$777$	9.35200	0.335501
$778$	−39.2270	−1.40636
$779$	20.9477	0.750528
$780$	−0.404854	−0.0144961
$781$	−14.2695	−0.510602
$782$	15.8211	0.565762
$783$	−7.74560	−0.276805
$784$	−18.6234	−0.665121
$785$	5.31445	0.189681
$786$	−2.81702	−0.100480
$787$	9.27427	0.330592	0.165296	−	0.986244i	$-0.447142\pi$
$787$	9.27427	0.330592	0.165296	+	0.986244i	$0.447142\pi$
$788$	−5.59268	−0.199231
$789$	14.0658	0.500756
$790$	7.02353	0.249886
$791$	47.5281	1.68991
$792$	−4.12015	−0.146403
$793$	−4.37024	−0.155192
$794$	−46.9306	−1.66551
$795$	1.15119	0.0408283
$796$	0.507963	0.0180043
$797$	40.2390	1.42534	0.712669	−	0.701500i	$-0.247486\pi$
$797$	40.2390	1.42534	0.712669	+	0.701500i	$0.247486\pi$
$798$	20.8887	0.739453
$799$	15.8929	0.562249
$800$	2.25715	0.0798021
$801$	−4.50283	−0.159100
$802$	−23.0986	−0.815640
$803$	7.01038	0.247391
$804$	0.0602011	0.00212313
$805$	13.5666	0.478160
$806$	1.55076	0.0546232
$807$	26.5162	0.933416
$808$	−1.41752	−0.0498681
$809$	−1.40572	−0.0494224	−0.0247112	−	0.999695i	$-0.507867\pi$
$809$	−1.40572	−0.0494224	−0.0247112	+	0.999695i	$0.507867\pi$
$810$	−1.55076	−0.0544881
$811$	−11.3893	−0.399932	−0.199966	−	0.979803i	$-0.564083\pi$
$811$	−11.3893	−0.399932	−0.199966	+	0.979803i	$0.564083\pi$
$812$	10.4045	0.365126
$813$	−7.75598	−0.272014
$814$	−7.28031	−0.255175
$815$	−13.4099	−0.469730
$816$	−11.5918	−0.405793
$817$	20.8401	0.729102
$818$	−13.1871	−0.461075
$819$	3.31793	0.115938
$820$	2.08898	0.0729502
$821$	0.361547	0.0126181	0.00630905	−	0.999980i	$-0.497992\pi$
$821$	0.361547	0.0126181	0.00630905	+	0.999980i	$0.497992\pi$
$822$	−24.2741	−0.846657
$823$	21.5461	0.751048	0.375524	−	0.926813i	$-0.377463\pi$
$823$	21.5461	0.751048	0.375524	+	0.926813i	$0.377463\pi$
$824$	−6.26694	−0.218319
$825$	−1.66559	−0.0579884
$826$	−60.5640	−2.10729
$827$	34.9851	1.21655	0.608276	−	0.793726i	$-0.291862\pi$
$827$	34.9851	1.21655	0.608276	+	0.793726i	$0.291862\pi$
$828$	−1.65540	−0.0575291
$829$	14.1417	0.491163	0.245581	−	0.969376i	$-0.421021\pi$
$829$	14.1417	0.491163	0.245581	+	0.969376i	$0.421021\pi$
$830$	5.11788	0.177644
$831$	−7.19646	−0.249642
$832$	−5.79131	−0.200778
$833$	10.0020	0.346549
$834$	−2.75245	−0.0953096
$835$	3.09033	0.106945
$836$	−2.73758	−0.0946813
$837$	1.00000	0.0345651
$838$	−54.2704	−1.87474
$839$	−23.6587	−0.816790	−0.408395	−	0.912805i	$-0.633911\pi$
$839$	−23.6587	−0.816790	−0.408395	+	0.912805i	$0.633911\pi$
$840$	−8.20752	−0.283186
$841$	30.9943	1.06877
$842$	−18.8407	−0.649295
$843$	−14.8018	−0.509802
$844$	−4.43111	−0.152525
$845$	1.00000	0.0344010
$846$	−9.87775	−0.339604
$847$	27.2927	0.937787
$848$	−5.34818	−0.183657
$849$	4.75365	0.163145
$850$	−3.86931	−0.132716
$851$	11.5250	0.395072
$852$	3.46847	0.118828
$853$	15.5965	0.534013	0.267006	−	0.963695i	$-0.413965\pi$
$853$	15.5965	0.534013	0.267006	+	0.963695i	$0.413965\pi$
$854$	22.4862	0.769463
$855$	4.05977	0.138841
$856$	44.3862	1.51709
$857$	30.8366	1.05336	0.526680	−	0.850064i	$-0.323437\pi$
$857$	30.8366	1.05336	0.526680	+	0.850064i	$0.323437\pi$
$858$	−2.58293	−0.0881797
$859$	−1.07964	−0.0368367	−0.0184184	−	0.999830i	$-0.505863\pi$
$859$	−1.07964	−0.0368367	−0.0184184	+	0.999830i	$0.505863\pi$
$860$	2.07825	0.0708677
$861$	−17.1199	−0.583445
$862$	−7.79203	−0.265398
$863$	−19.9324	−0.678507	−0.339254	−	0.940695i	$-0.610175\pi$
$863$	−19.9324	−0.678507	−0.339254	+	0.940695i	$0.610175\pi$
$864$	2.25715	0.0767896
$865$	10.4768	0.356221
$866$	−31.2086	−1.06051
$867$	−10.7745	−0.365920
$868$	−1.34328	−0.0455938
$869$	7.54361	0.255899
$870$	12.0116	0.407230
$871$	−0.148698	−0.00503845
$872$	−0.741387	−0.0251065
$873$	6.24763	0.211450
$874$	25.7424	0.870750
$875$	−3.31793	−0.112166
$876$	−1.70401	−0.0575732
$877$	49.0025	1.65470	0.827349	−	0.561688i	$-0.189848\pi$
$877$	49.0025	1.65470	0.827349	+	0.561688i	$0.189848\pi$
$878$	42.1987	1.42414
$879$	18.1813	0.613239
$880$	7.73800	0.260848
$881$	−56.2950	−1.89663	−0.948314	−	0.317334i	$-0.897212\pi$
$881$	−56.2950	−1.89663	−0.948314	+	0.317334i	$0.897212\pi$
$882$	−6.21645	−0.209319
$883$	9.13454	0.307402	0.153701	−	0.988117i	$-0.450881\pi$
$883$	9.13454	0.307402	0.153701	+	0.988117i	$0.450881\pi$
$884$	−1.01015	−0.0339751
$885$	−11.7707	−0.395669
$886$	−41.7329	−1.40204
$887$	−53.0728	−1.78201	−0.891004	−	0.453995i	$-0.849999\pi$
$887$	−53.0728	−1.78201	−0.891004	+	0.453995i	$0.849999\pi$
$888$	−6.97240	−0.233978
$889$	−58.1303	−1.94963
$890$	6.98281	0.234064
$891$	−1.66559	−0.0557993
$892$	−9.52272	−0.318844
$893$	25.8592	0.865344
$894$	7.80851	0.261156
$895$	9.38189	0.313602
$896$	44.7762	1.49587
$897$	4.08888	0.136524
$898$	30.2232	1.00856
$899$	−7.74560	−0.258330
$900$	0.404854	0.0134951
$901$	2.87233	0.0956911
$902$	13.3274	0.443755
$903$	−17.0320	−0.566790
$904$	−35.4347	−1.17854
$905$	20.1053	0.668324
$906$	−22.5656	−0.749692
$907$	33.7425	1.12040	0.560201	−	0.828357i	$-0.310724\pi$
$907$	33.7425	1.12040	0.560201	+	0.828357i	$0.310724\pi$
$908$	5.24431	0.174038
$909$	−0.573038	−0.0190065
$910$	−5.14531	−0.170565
$911$	−50.8789	−1.68569	−0.842847	−	0.538153i	$-0.819122\pi$
$911$	−50.8789	−1.68569	−0.842847	+	0.538153i	$0.819122\pi$
$912$	−18.8609	−0.624546
$913$	5.49685	0.181919
$914$	28.0965	0.929348
$915$	4.37024	0.144476
$916$	−4.55357	−0.150454
$917$	−6.02715	−0.199034
$918$	−3.86931	−0.127706
$919$	13.5652	0.447476	0.223738	−	0.974649i	$-0.428174\pi$
$919$	13.5652	0.447476	0.223738	+	0.974649i	$0.428174\pi$
$920$	−10.1146	−0.333468
$921$	20.8888	0.688310
$922$	−19.4670	−0.641113
$923$	−8.56722	−0.281993
$924$	2.23735	0.0736034
$925$	−2.81862	−0.0926758
$926$	−7.78412	−0.255802
$927$	−2.53344	−0.0832091
$928$	−17.4829	−0.573906
$929$	−27.5530	−0.903985	−0.451993	−	0.892022i	$-0.649287\pi$
$929$	−27.5530	−0.903985	−0.451993	+	0.892022i	$0.649287\pi$
$930$	−1.55076	−0.0508514
$931$	16.2742	0.533364
$932$	11.4090	0.373714
$933$	−8.45476	−0.276796
$934$	−23.1413	−0.757208
$935$	−4.15582	−0.135910
$936$	−2.47369	−0.0808550
$937$	8.11727	0.265180	0.132590	−	0.991171i	$-0.457671\pi$
$937$	8.11727	0.265180	0.132590	+	0.991171i	$0.457671\pi$
$938$	0.765098	0.0249813
$939$	7.51009	0.245083
$940$	2.57877	0.0841101
$941$	−0.690452	−0.0225081	−0.0112541	−	0.999937i	$-0.503582\pi$
$941$	−0.690452	−0.0225081	−0.0112541	+	0.999937i	$0.503582\pi$
$942$	−8.24143	−0.268520
$943$	−21.0979	−0.687041
$944$	54.6844	1.77983
$945$	−3.31793	−0.107932
$946$	13.2590	0.431088
$947$	49.6391	1.61305	0.806527	−	0.591197i	$-0.201345\pi$
$947$	49.6391	1.61305	0.806527	+	0.591197i	$0.201345\pi$
$948$	−1.83362	−0.0595533
$949$	4.20895	0.136628
$950$	−6.29572	−0.204260
$951$	−18.8364	−0.610813
$952$	−20.4786	−0.663716
$953$	16.6302	0.538705	0.269353	−	0.963042i	$-0.413190\pi$
$953$	16.6302	0.538705	0.269353	+	0.963042i	$0.413190\pi$
$954$	−1.78521	−0.0577984
$955$	15.5042	0.501705
$956$	−5.07682	−0.164196
$957$	12.9010	0.417030
$958$	40.8168	1.31873
$959$	−51.9357	−1.67709
$960$	5.79131	0.186914
$961$	1.00000	0.0322581
$962$	−4.37101	−0.140927
$963$	17.9433	0.578216
$964$	−0.700462	−0.0225604
$965$	4.54091	0.146177
$966$	−21.0385	−0.676904
$967$	−32.1331	−1.03333	−0.516665	−	0.856188i	$-0.672827\pi$
$967$	−32.1331	−1.03333	−0.516665	+	0.856188i	$0.672827\pi$
$968$	−20.3481	−0.654012
$969$	10.1295	0.325408
$970$	−9.68856	−0.311081
$971$	38.6019	1.23879	0.619397	−	0.785078i	$-0.287377\pi$
$971$	38.6019	1.23879	0.619397	+	0.785078i	$0.287377\pi$
$972$	0.404854	0.0129857
$973$	−5.88901	−0.188793
$974$	6.34660	0.203358
$975$	−1.00000	−0.0320256
$976$	−20.3033	−0.649892
$977$	40.3500	1.29091	0.645455	−	0.763798i	$-0.276668\pi$
$977$	40.3500	1.29091	0.645455	+	0.763798i	$0.276668\pi$
$978$	20.7956	0.664970
$979$	7.49987	0.239697
$980$	1.62292	0.0518422
$981$	−0.299709	−0.00956899
$982$	−0.529308	−0.0168909
$983$	−16.6711	−0.531725	−0.265863	−	0.964011i	$-0.585657\pi$
$983$	−16.6711	−0.531725	−0.265863	+	0.964011i	$0.585657\pi$
$984$	12.7638	0.406895
$985$	−13.8141	−0.440152
$986$	29.9701	0.954442
$987$	−21.1339	−0.672701
$988$	−1.64361	−0.0522903
$989$	−20.9895	−0.667428
$990$	2.58293	0.0820908
$991$	−31.8011	−1.01020	−0.505098	−	0.863062i	$-0.668544\pi$
$991$	−31.8011	−1.01020	−0.505098	+	0.863062i	$0.668544\pi$
$992$	2.25715	0.0716644
$993$	−6.94183	−0.220292
$994$	44.0810	1.39816
$995$	1.25468	0.0397761
$996$	−1.33612	−0.0423365
$997$	−10.4195	−0.329988	−0.164994	−	0.986295i	$-0.552760\pi$
$997$	−10.4195	−0.329988	−0.164994	+	0.986295i	$0.552760\pi$
$998$	0.564815	0.0178789
$999$	−2.81862	−0.0891773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.5	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55076 q^{2} +1.00000 q^{3} +0.404854 q^{4} +1.00000 q^{5} -1.55076 q^{6} -3.31793 q^{7} +2.47369 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.55076 q^{2} +1.00000 q^{3} +0.404854 q^{4} +1.00000 q^{5} -1.55076 q^{6} -3.31793 q^{7} +2.47369 q^{8} +1.00000 q^{9} -1.55076 q^{10} -1.66559 q^{11} +0.404854 q^{12} -1.00000 q^{13} +5.14531 q^{14} +1.00000 q^{15} -4.64580 q^{16} +2.49510 q^{17} -1.55076 q^{18} +4.05977 q^{19} +0.404854 q^{20} -3.31793 q^{21} +2.58293 q^{22} -4.08888 q^{23} +2.47369 q^{24} +1.00000 q^{25} +1.55076 q^{26} +1.00000 q^{27} -1.34328 q^{28} -7.74560 q^{29} -1.55076 q^{30} +1.00000 q^{31} +2.25715 q^{32} -1.66559 q^{33} -3.86931 q^{34} -3.31793 q^{35} +0.404854 q^{36} -2.81862 q^{37} -6.29572 q^{38} -1.00000 q^{39} +2.47369 q^{40} +5.15982 q^{41} +5.14531 q^{42} +5.13332 q^{43} -0.674321 q^{44} +1.00000 q^{45} +6.34086 q^{46} +6.36962 q^{47} -4.64580 q^{48} +4.00865 q^{49} -1.55076 q^{50} +2.49510 q^{51} -0.404854 q^{52} +1.15119 q^{53} -1.55076 q^{54} -1.66559 q^{55} -8.20752 q^{56} +4.05977 q^{57} +12.0116 q^{58} -11.7707 q^{59} +0.404854 q^{60} +4.37024 q^{61} -1.55076 q^{62} -3.31793 q^{63} +5.79131 q^{64} -1.00000 q^{65} +2.58293 q^{66} +0.148698 q^{67} +1.01015 q^{68} -4.08888 q^{69} +5.14531 q^{70} +8.56722 q^{71} +2.47369 q^{72} -4.20895 q^{73} +4.37101 q^{74} +1.00000 q^{75} +1.64361 q^{76} +5.52631 q^{77} +1.55076 q^{78} -4.52909 q^{79} -4.64580 q^{80} +1.00000 q^{81} -8.00164 q^{82} -3.30024 q^{83} -1.34328 q^{84} +2.49510 q^{85} -7.96055 q^{86} -7.74560 q^{87} -4.12015 q^{88} -4.50283 q^{89} -1.55076 q^{90} +3.31793 q^{91} -1.65540 q^{92} +1.00000 q^{93} -9.87775 q^{94} +4.05977 q^{95} +2.25715 q^{96} +6.24763 q^{97} -6.21645 q^{98} -1.66559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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