LMFDB - Embedded newform 552.2.f.c.277.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$4.40774219157$
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^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.13
Root			$1.26873 + 0.624769i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.624769 - 1.26873i) q^{2} -1.00000i q^{3} +(-1.21933 - 1.58532i) q^{4} +3.50951i q^{5} +(-1.26873 - 0.624769i) q^{6} -4.50530 q^{7} +(-2.77313 + 0.556532i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.624769 - 1.26873i) q^{2} -1.00000i q^{3} +(-1.21933 - 1.58532i) q^{4} +3.50951i q^{5} +(-1.26873 - 0.624769i) q^{6} -4.50530 q^{7} +(-2.77313 + 0.556532i) q^{8} -1.00000 q^{9} +(4.45260 + 2.19263i) q^{10} -4.67738i q^{11} +(-1.58532 + 1.21933i) q^{12} +3.59462i q^{13} +(-2.81477 + 5.71598i) q^{14} +3.50951 q^{15} +(-1.02648 + 3.86605i) q^{16} -5.72933 q^{17} +(-0.624769 + 1.26873i) q^{18} +2.98758i q^{19} +(5.56369 - 4.27924i) q^{20} +4.50530i q^{21} +(-5.93431 - 2.92228i) q^{22} -1.00000 q^{23} +(0.556532 + 2.77313i) q^{24} -7.31663 q^{25} +(4.56059 + 2.24581i) q^{26} +1.00000i q^{27} +(5.49343 + 7.14234i) q^{28} +7.72016i q^{29} +(2.19263 - 4.45260i) q^{30} -0.242892 q^{31} +(4.26364 + 3.71771i) q^{32} -4.67738 q^{33} +(-3.57951 + 7.26895i) q^{34} -15.8114i q^{35} +(1.21933 + 1.58532i) q^{36} -10.8581i q^{37} +(3.79041 + 1.86655i) q^{38} +3.59462 q^{39} +(-1.95315 - 9.73233i) q^{40} +1.48656 q^{41} +(5.71598 + 2.81477i) q^{42} -4.67372i q^{43} +(-7.41515 + 5.70326i) q^{44} -3.50951i q^{45} +(-0.624769 + 1.26873i) q^{46} -9.11719 q^{47} +(3.86605 + 1.02648i) q^{48} +13.2977 q^{49} +(-4.57120 + 9.28279i) q^{50} +5.72933i q^{51} +(5.69863 - 4.38302i) q^{52} -12.0550i q^{53} +(1.26873 + 0.624769i) q^{54} +16.4153 q^{55} +(12.4938 - 2.50734i) q^{56} +2.98758 q^{57} +(9.79476 + 4.82332i) q^{58} +2.22874i q^{59} +(-4.27924 - 5.56369i) q^{60} -1.86693i q^{61} +(-0.151752 + 0.308164i) q^{62} +4.50530 q^{63} +(7.38055 - 3.08667i) q^{64} -12.6154 q^{65} +(-2.92228 + 5.93431i) q^{66} +2.80443i q^{67} +(6.98593 + 9.08283i) q^{68} +1.00000i q^{69} +(-20.0603 - 9.87845i) q^{70} -7.46668 q^{71} +(2.77313 - 0.556532i) q^{72} -2.34874 q^{73} +(-13.7760 - 6.78381i) q^{74} +7.31663i q^{75} +(4.73627 - 3.64283i) q^{76} +21.0730i q^{77} +(2.24581 - 4.56059i) q^{78} -2.09395 q^{79} +(-13.5679 - 3.60245i) q^{80} +1.00000 q^{81} +(0.928754 - 1.88603i) q^{82} +5.94376i q^{83} +(7.14234 - 5.49343i) q^{84} -20.1071i q^{85} +(-5.92966 - 2.92000i) q^{86} +7.72016 q^{87} +(2.60311 + 12.9710i) q^{88} -10.9924 q^{89} +(-4.45260 - 2.19263i) q^{90} -16.1949i q^{91} +(1.21933 + 1.58532i) q^{92} +0.242892i q^{93} +(-5.69614 + 11.5672i) q^{94} -10.4849 q^{95} +(3.71771 - 4.26364i) q^{96} +17.6742 q^{97} +(8.30800 - 16.8711i) q^{98} +4.67738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.624769	−	1.26873i	0.441778	−	0.897124i
$2$	0.624769	−	1.26873i	0.441778	−	0.897124i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.21933	−	1.58532i	−0.609664	−	0.792660i
$5$			3.50951i			1.56950i	0.619813	+	0.784749i	$0.287208\pi$
$5$			3.50951i			1.56950i	−0.619813	+	0.784749i	$0.712792\pi$
$6$	−1.26873	−	0.624769i	−0.517955	−	0.255061i
$7$	−4.50530			−1.70284			−0.851421	−	0.524482i	$-0.824259\pi$
$7$	−4.50530			−1.70284			−0.851421	+	0.524482i	$0.824259\pi$
$8$	−2.77313	+	0.556532i	−0.980451	+	0.196764i
$9$	−1.00000			−0.333333
$10$	4.45260	+	2.19263i	1.40804	+	0.693371i
$11$		−	4.67738i		−	1.41028i	−0.709066	−	0.705142i	$-0.750883\pi$
$11$		−	4.67738i		−	1.41028i	0.709066	−	0.705142i	$-0.249117\pi$
$12$	−1.58532	+	1.21933i	−0.457643	+	0.351989i
$13$			3.59462i			0.996969i	0.866899	+	0.498485i	$0.166110\pi$
$13$			3.59462i			0.996969i	−0.866899	+	0.498485i	$0.833890\pi$
$14$	−2.81477	+	5.71598i	−0.752279	+	1.52766i
$15$	3.50951			0.906150
$16$	−1.02648	+	3.86605i	−0.256621	+	0.966512i
$17$	−5.72933			−1.38957			−0.694784	−	0.719219i	$-0.744500\pi$
$17$	−5.72933			−1.38957			−0.694784	+	0.719219i	$0.744500\pi$
$18$	−0.624769	+	1.26873i	−0.147259	+	0.299041i
$19$			2.98758i			0.685397i	0.939445	+	0.342699i	$0.111341\pi$
$19$			2.98758i			0.685397i	−0.939445	+	0.342699i	$0.888659\pi$
$20$	5.56369	−	4.27924i	1.24408	−	0.956866i
$21$			4.50530i			0.983137i
$22$	−5.93431	−	2.92228i	−1.26520	−	0.623033i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	0.556532	+	2.77313i	0.113602	+	0.566064i
$25$	−7.31663			−1.46333
$26$	4.56059	+	2.24581i	0.894405	+	0.440440i
$27$			1.00000i			0.192450i
$28$	5.49343	+	7.14234i	1.03816	+	1.34978i
$29$			7.72016i			1.43360i	0.697280	+	0.716799i	$0.254393\pi$
$29$			7.72016i			1.43360i	−0.697280	+	0.716799i	$0.745607\pi$
$30$	2.19263	−	4.45260i	0.400318	−	0.812929i
$31$	−0.242892			−0.0436248			−0.0218124	−	0.999762i	$-0.506944\pi$
$31$	−0.242892			−0.0436248			−0.0218124	+	0.999762i	$0.506944\pi$
$32$	4.26364	+	3.71771i	0.753712	+	0.657205i
$33$	−4.67738			−0.814228
$34$	−3.57951	+	7.26895i	−0.613881	+	1.24661i
$35$		−	15.8114i		−	2.67261i
$36$	1.21933	+	1.58532i	0.203221	+	0.264220i
$37$		−	10.8581i		−	1.78506i	−0.450985	−	0.892532i	$-0.648927\pi$
$37$		−	10.8581i		−	1.78506i	0.450985	−	0.892532i	$-0.351073\pi$
$38$	3.79041	+	1.86655i	0.614886	+	0.302794i
$39$	3.59462			0.575600
$40$	−1.95315	−	9.73233i	−0.308820	−	1.53882i
$41$	1.48656			0.232161			0.116080	−	0.993240i	$-0.462967\pi$
$41$	1.48656			0.232161			0.116080	+	0.993240i	$0.462967\pi$
$42$	5.71598	+	2.81477i	0.881996	+	0.434329i
$43$		−	4.67372i		−	0.712735i	−0.934346	−	0.356368i	$-0.884015\pi$
$43$		−	4.67372i		−	0.712735i	0.934346	−	0.356368i	$-0.115985\pi$
$44$	−7.41515	+	5.70326i	−1.11788	+	0.859798i
$45$		−	3.50951i		−	0.523166i
$46$	−0.624769	+	1.26873i	−0.0921172	+	0.187063i
$47$	−9.11719			−1.32988			−0.664939	−	0.746897i	$-0.731543\pi$
$47$	−9.11719			−1.32988			−0.664939	+	0.746897i	$0.731543\pi$
$48$	3.86605	+	1.02648i	0.558016	+	0.148160i
$49$	13.2977			1.89967
$50$	−4.57120	+	9.28279i	−0.646466	+	1.31278i
$51$			5.72933i			0.802267i
$52$	5.69863	−	4.38302i	0.790258	−	0.607816i
$53$		−	12.0550i		−	1.65588i	−0.560813	−	0.827942i	$-0.689511\pi$
$53$		−	12.0550i		−	1.65588i	0.560813	−	0.827942i	$-0.310489\pi$
$54$	1.26873	+	0.624769i	0.172652	+	0.0850203i
$55$	16.4153			2.21344
$56$	12.4938	−	2.50734i	1.66955	−	0.335057i
$57$	2.98758			0.395714
$58$	9.79476	+	4.82332i	1.28611	+	0.633332i
$59$			2.22874i			0.290157i	0.989420	+	0.145078i	$0.0463434\pi$
$59$			2.22874i			0.290157i	−0.989420	+	0.145078i	$0.953657\pi$
$60$	−4.27924	−	5.56369i	−0.552447	−	0.718269i
$61$		−	1.86693i		−	0.239036i	−0.992832	−	0.119518i	$-0.961865\pi$
$61$		−	1.86693i		−	0.239036i	0.992832	−	0.119518i	$-0.0381349\pi$
$62$	−0.151752	+	0.308164i	−0.0192725	+	0.0391368i
$63$	4.50530			0.567614
$64$	7.38055	−	3.08667i	0.922568	−	0.385834i
$65$	−12.6154			−1.56474
$66$	−2.92228	+	5.93431i	−0.359708	+	0.730463i
$67$			2.80443i			0.342615i	0.985218	+	0.171308i	$0.0547992\pi$
$67$			2.80443i			0.342615i	−0.985218	+	0.171308i	$0.945201\pi$
$68$	6.98593	+	9.08283i	0.847168	+	1.10145i
$69$			1.00000i			0.120386i
$70$	−20.0603	−	9.87845i	−2.39766	−	1.18070i
$71$	−7.46668			−0.886131			−0.443066	−	0.896489i	$-0.646109\pi$
$71$	−7.46668			−0.886131			−0.443066	+	0.896489i	$0.646109\pi$
$72$	2.77313	−	0.556532i	0.326817	−	0.0655879i
$73$	−2.34874			−0.274899			−0.137450	−	0.990509i	$-0.543890\pi$
$73$	−2.34874			−0.274899			−0.137450	+	0.990509i	$0.543890\pi$
$74$	−13.7760	−	6.78381i	−1.60142	−	0.788602i
$75$			7.31663i			0.844852i
$76$	4.73627	−	3.64283i	0.543287	−	0.417862i
$77$			21.0730i			2.40149i
$78$	2.24581	−	4.56059i	0.254288	−	0.516385i
$79$	−2.09395			−0.235588			−0.117794	−	0.993038i	$-0.537582\pi$
$79$	−2.09395			−0.235588			−0.117794	+	0.993038i	$0.537582\pi$
$80$	−13.5679	−	3.60245i	−1.51694	−	0.402766i
$81$	1.00000			0.111111
$82$	0.928754	−	1.88603i	0.102564	−	0.208277i
$83$			5.94376i			0.652413i	0.945299	+	0.326206i	$0.105770\pi$
$83$			5.94376i			0.652413i	−0.945299	+	0.326206i	$0.894230\pi$
$84$	7.14234	−	5.49343i	0.779293	−	0.599383i
$85$		−	20.1071i		−	2.18092i
$86$	−5.92966	−	2.92000i	−0.639412	−	0.314871i
$87$	7.72016			0.827688
$88$	2.60311	+	12.9710i	0.277492	+	1.38271i
$89$	−10.9924			−1.16519			−0.582594	−	0.812763i	$-0.697962\pi$
$89$	−10.9924			−1.16519			−0.582594	+	0.812763i	$0.697962\pi$
$90$	−4.45260	−	2.19263i	−0.469345	−	0.231124i
$91$		−	16.1949i		−	1.69768i
$92$	1.21933	+	1.58532i	0.127124	+	0.165281i
$93$			0.242892i			0.0251868i
$94$	−5.69614	+	11.5672i	−0.587512	+	1.19307i
$95$	−10.4849			−1.07573
$96$	3.71771	−	4.26364i	0.379437	−	0.435156i
$97$	17.6742			1.79455			0.897273	−	0.441477i	$-0.145545\pi$
$97$	17.6742			1.79455			0.897273	+	0.441477i	$0.145545\pi$
$98$	8.30800	−	16.8711i	0.839235	−	1.70424i
$99$			4.67738i			0.470094i
$100$	8.92136	+	11.5992i	0.892136	+	1.15992i
$101$			14.6952i			1.46222i	0.682258	+	0.731111i	$0.260998\pi$
$101$			14.6952i			1.46222i	−0.682258	+	0.731111i	$0.739002\pi$
$102$	7.26895	+	3.57951i	0.719733	+	0.354424i
$103$	−8.32561			−0.820347			−0.410173	−	0.912008i	$-0.634532\pi$
$103$	−8.32561			−0.820347			−0.410173	+	0.912008i	$0.634532\pi$
$104$	−2.00052	−	9.96837i	−0.196167	−	0.977479i
$105$	−15.8114			−1.54303
$106$	−15.2945	−	7.53161i	−1.48553	−	0.731534i
$107$		−	4.49423i		−	0.434474i	−0.976119	−	0.217237i	$-0.930296\pi$
$107$		−	4.49423i		−	0.434474i	0.976119	−	0.217237i	$-0.0697044\pi$
$108$	1.58532	−	1.21933i	0.152548	−	0.117330i
$109$			0.346182i			0.0331583i	0.999863	+	0.0165791i	$0.00527754\pi$
$109$			0.346182i			0.0331583i	−0.999863	+	0.0165791i	$0.994722\pi$
$110$	10.2558	−	20.8265i	0.977849	−	1.98573i
$111$	−10.8581			−1.03061
$112$	4.62461	−	17.4177i	0.436985	−	1.64582i
$113$	−9.54965			−0.898355			−0.449178	−	0.893443i	$-0.648283\pi$
$113$	−9.54965			−0.898355			−0.449178	+	0.893443i	$0.648283\pi$
$114$	1.86655	−	3.79041i	0.174818	−	0.355005i
$115$		−	3.50951i		−	0.327263i
$116$	12.2389	−	9.41340i	1.13636	−	0.874012i
$117$		−	3.59462i		−	0.332323i
$118$	2.82765	+	1.39245i	0.260307	+	0.128185i
$119$	25.8123			2.36621
$120$	−9.73233	+	1.95315i	−0.888436	+	0.178297i
$121$	−10.8779			−0.988900
$122$	−2.36862	−	1.16640i	−0.214445	−	0.105601i
$123$		−	1.48656i		−	0.134038i
$124$	0.296165	+	0.385062i	0.0265964	+	0.0345796i
$125$		−	8.13022i		−	0.727189i
$126$	2.81477	−	5.71598i	0.250760	−	0.509220i
$127$	5.87741			0.521536			0.260768	−	0.965402i	$-0.416024\pi$
$127$	5.87741			0.521536			0.260768	+	0.965402i	$0.416024\pi$
$128$	0.694997	−	11.2923i	0.0614296	−	0.998111i
$129$	−4.67372			−0.411498
$130$	−7.88168	+	16.0054i	−0.691269	+	1.40377i
$131$			5.72986i			0.500620i	0.968166	+	0.250310i	$0.0805326\pi$
$131$			5.72986i			0.500620i	−0.968166	+	0.250310i	$0.919467\pi$
$132$	5.70326	+	7.41515i	0.496405	+	0.645406i
$133$		−	13.4599i		−	1.16712i
$134$	3.55805	+	1.75212i	0.307368	+	0.151360i
$135$	−3.50951			−0.302050
$136$	15.8882	−	3.18855i	1.36240	−	0.273416i
$137$	−7.62052			−0.651065			−0.325532	−	0.945531i	$-0.605543\pi$
$137$	−7.62052			−0.651065			−0.325532	+	0.945531i	$0.605543\pi$
$138$	1.26873	+	0.624769i	0.108001	+	0.0531839i
$139$			2.97024i			0.251933i	0.992035	+	0.125966i	$0.0402031\pi$
$139$			2.97024i			0.251933i	−0.992035	+	0.125966i	$0.959797\pi$
$140$	−25.0661	+	19.2792i	−2.11847	+	1.62939i
$141$			9.11719i			0.767806i
$142$	−4.66495	+	9.47316i	−0.391474	+	0.794970i
$143$	16.8134			1.40601
$144$	1.02648	−	3.86605i	0.0855402	−	0.322171i
$145$	−27.0939			−2.25003
$146$	−1.46742	+	2.97990i	−0.121445	+	0.246619i
$147$		−	13.2977i		−	1.09678i
$148$	−17.2136	+	13.2396i	−1.41495	+	1.08829i
$149$			5.94828i			0.487302i	0.969863	+	0.243651i	$0.0783452\pi$
$149$			5.94828i			0.487302i	−0.969863	+	0.243651i	$0.921655\pi$
$150$	9.28279	+	4.57120i	0.757937	+	0.373237i
$151$	16.1249			1.31223			0.656114	−	0.754661i	$-0.272199\pi$
$151$	16.1249			1.31223			0.656114	+	0.754661i	$0.272199\pi$
$152$	−1.66268	−	8.28495i	−0.134861	−	0.671998i
$153$	5.72933			0.463189
$154$	26.7358	+	13.1658i	2.15444	+	1.06093i
$155$		−	0.852432i		−	0.0684690i
$156$	−4.38302	−	5.69863i	−0.350923	−	0.456256i
$157$			14.5867i			1.16415i	0.813137	+	0.582073i	$0.197758\pi$
$157$			14.5867i			1.16415i	−0.813137	+	0.582073i	$0.802242\pi$
$158$	−1.30824	+	2.65665i	−0.104078	+	0.211352i
$159$	−12.0550			−0.956025
$160$	−13.0473	+	14.9633i	−1.03148	+	1.18295i
$161$	4.50530			0.355067
$162$	0.624769	−	1.26873i	0.0490865	−	0.0996805i
$163$		−	5.43118i		−	0.425403i	−0.977117	−	0.212701i	$-0.931774\pi$
$163$		−	5.43118i		−	0.425403i	0.977117	−	0.212701i	$-0.0682262\pi$
$164$	−1.81260	−	2.35667i	−0.141540	−	0.184025i
$165$		−	16.4153i		−	1.27793i
$166$	7.54100	+	3.71348i	0.585295	+	0.288222i
$167$	8.87420			0.686707			0.343353	−	0.939206i	$-0.388437\pi$
$167$	8.87420			0.686707			0.343353	+	0.939206i	$0.388437\pi$
$168$	−2.50734	−	12.4938i	−0.193446	−	0.963917i
$169$	0.0786791			0.00605224
$170$	−25.5104	−	12.5623i	−1.95656	−	0.963485i
$171$		−	2.98758i		−	0.228466i
$172$	−7.40934	+	5.69879i	−0.564957	+	0.434529i
$173$		−	18.5102i		−	1.40731i	−0.710543	−	0.703654i	$-0.751551\pi$
$173$		−	18.5102i		−	1.40731i	0.710543	−	0.703654i	$-0.248449\pi$
$174$	4.82332	−	9.79476i	0.365655	−	0.742539i
$175$	32.9636			2.49181
$176$	18.0830	+	4.80125i	1.36306	+	0.361908i
$177$	2.22874			0.167522
$178$	−6.86769	+	13.9463i	−0.514755	+	1.04532i
$179$			18.8447i			1.40852i	0.709942	+	0.704261i	$0.248721\pi$
$179$			18.8447i			1.40852i	−0.709942	+	0.704261i	$0.751279\pi$
$180$	−5.56369	+	4.27924i	−0.414693	+	0.318955i
$181$			17.3941i			1.29290i	0.762958	+	0.646448i	$0.223746\pi$
$181$			17.3941i			1.29290i	−0.762958	+	0.646448i	$0.776254\pi$
$182$	−20.5468	−	10.1180i	−1.52303	−	0.749999i
$183$	−1.86693			−0.138007
$184$	2.77313	−	0.556532i	0.204438	−	0.0410281i
$185$	38.1066			2.80165
$186$	0.308164	+	0.151752i	0.0225957	+	0.0111270i
$187$			26.7983i			1.95968i
$188$	11.1168	+	14.4537i	0.810779	+	1.05414i
$189$		−	4.50530i		−	0.327712i
$190$	−6.55065	+	13.3025i	−0.475234	+	0.965063i
$191$	−18.5079			−1.33919			−0.669594	−	0.742727i	$-0.733532\pi$
$191$	−18.5079			−1.33919			−0.669594	+	0.742727i	$0.733532\pi$
$192$	−3.08667	−	7.38055i	−0.222761	−	0.532645i
$193$	−10.9554			−0.788586			−0.394293	−	0.918985i	$-0.629011\pi$
$193$	−10.9554			−0.788586			−0.394293	+	0.918985i	$0.629011\pi$
$194$	11.0423	−	22.4237i	0.792791	−	1.60993i
$195$			12.6154i			0.903404i
$196$	−16.2143	−	21.0811i	−1.15816	−	1.50580i
$197$			5.71221i			0.406978i	0.979077	+	0.203489i	$0.0652281\pi$
$197$			5.71221i			0.406978i	−0.979077	+	0.203489i	$0.934772\pi$
$198$	5.93431	+	2.92228i	0.421733	+	0.207678i
$199$	5.04958			0.357955			0.178978	−	0.983853i	$-0.442721\pi$
$199$	5.04958			0.357955			0.178978	+	0.983853i	$0.442721\pi$
$200$	20.2900	−	4.07194i	1.43472	−	0.287929i
$201$	2.80443			0.197809
$202$	18.6441	+	9.18108i	1.31180	+	0.645979i
$203$		−	34.7816i		−	2.44119i
$204$	9.08283	−	6.98593i	0.635925	−	0.489113i
$205$			5.21707i			0.364376i
$206$	−5.20158	+	10.5629i	−0.362412	+	0.735953i
$207$	1.00000			0.0695048
$208$	−13.8970	−	3.68982i	−0.963583	−	0.255843i
$209$	13.9740			0.966604
$210$	−9.87845	+	20.0603i	−0.681678	+	1.38429i
$211$		−	13.3987i		−	0.922405i	−0.887295	−	0.461202i	$-0.847418\pi$
$211$		−	13.3987i		−	0.922405i	0.887295	−	0.461202i	$-0.152582\pi$
$212$	−19.1111	+	14.6990i	−1.31255	+	1.00953i
$213$			7.46668i			0.511608i
$214$	−5.70194	−	2.80786i	−0.389777	−	0.191941i
$215$	16.4024			1.11864
$216$	−0.556532	−	2.77313i	−0.0378672	−	0.188688i
$217$	1.09430			0.0742861
$218$	0.439210	+	0.216284i	0.0297471	+	0.0146486i
$219$			2.34874i			0.158713i
$220$	−20.0156	−	26.0235i	−1.34945	−	1.75450i
$221$		−	20.5948i		−	1.38536i
$222$	−6.78381	+	13.7760i	−0.455300	+	0.924582i
$223$	7.18715			0.481287			0.240644	−	0.970614i	$-0.422641\pi$
$223$	7.18715			0.481287			0.240644	+	0.970614i	$0.422641\pi$
$224$	−19.2090	−	16.7494i	−1.28345	−	1.11912i
$225$	7.31663			0.487775
$226$	−5.96632	+	12.1159i	−0.396874	+	0.805936i
$227$		−	0.490244i		−	0.0325386i	−0.999868	−	0.0162693i	$-0.994821\pi$
$227$		−	0.490244i		−	0.0325386i	0.999868	−	0.0162693i	$-0.00517891\pi$
$228$	−3.64283	−	4.73627i	−0.241253	−	0.313667i
$229$		−	6.36961i		−	0.420916i	−0.977603	−	0.210458i	$-0.932505\pi$
$229$		−	6.36961i		−	0.420916i	0.977603	−	0.210458i	$-0.0674954\pi$
$230$	−4.45260	−	2.19263i	−0.293596	−	0.144578i
$231$	21.0730			1.38650
$232$	−4.29651	−	21.4090i	−0.282080	−	1.40557i
$233$	2.65768			0.174110			0.0870552	−	0.996203i	$-0.472254\pi$
$233$	2.65768			0.174110			0.0870552	+	0.996203i	$0.472254\pi$
$234$	−4.56059	−	2.24581i	−0.298135	−	0.146813i
$235$		−	31.9968i		−	2.08724i
$236$	3.53326	−	2.71756i	0.229996	−	0.176898i
$237$			2.09395i			0.136017i
$238$	16.1268	−	32.7488i	1.04534	−	2.12279i
$239$	−13.9449			−0.902021			−0.451011	−	0.892519i	$-0.648936\pi$
$239$	−13.9449			−0.902021			−0.451011	+	0.892519i	$0.648936\pi$
$240$	−3.60245	+	13.5679i	−0.232537	+	0.875805i
$241$	−1.27865			−0.0823653			−0.0411826	−	0.999152i	$-0.513113\pi$
$241$	−1.27865			−0.0823653			−0.0411826	+	0.999152i	$0.513113\pi$
$242$	−6.79617	+	13.8011i	−0.436875	+	0.887166i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.95968	+	2.27640i	−0.189474	+	0.145732i
$245$			46.6684i			2.98153i
$246$	−1.88603	−	0.928754i	−0.120249	−	0.0592152i
$247$	−10.7392			−0.683320
$248$	0.673573	−	0.135177i	0.0427720	−	0.00858377i
$249$	5.94376			0.376671
$250$	−10.3150	−	5.07951i	−0.652379	−	0.321257i
$251$		−	19.1552i		−	1.20906i	−0.796581	−	0.604532i	$-0.793360\pi$
$251$		−	19.1552i		−	1.20906i	0.796581	−	0.604532i	$-0.206640\pi$
$252$	−5.49343	−	7.14234i	−0.346054	−	0.449925i
$253$			4.67738i			0.294064i
$254$	3.67202	−	7.45681i	0.230403	−	0.467882i
$255$	−20.1071			−1.25916
$256$	−13.8927	−	7.93687i	−0.868292	−	0.496054i
$257$	−15.0389			−0.938101			−0.469051	−	0.883171i	$-0.655404\pi$
$257$	−15.0389			−0.938101			−0.469051	+	0.883171i	$0.655404\pi$
$258$	−2.92000	+	5.92966i	−0.181791	+	0.369165i
$259$			48.9190i			3.03968i
$260$	15.3822	+	19.9994i	0.953966	+	1.24031i
$261$		−	7.72016i		−	0.477866i
$262$	7.26962	+	3.57984i	0.449119	+	0.221163i
$263$	−23.3903			−1.44231			−0.721153	−	0.692775i	$-0.756388\pi$
$263$	−23.3903			−1.44231			−0.721153	+	0.692775i	$0.756388\pi$
$264$	12.9710	−	2.60311i	0.798310	−	0.160210i
$265$	42.3072			2.59891
$266$	−17.0769	−	8.40935i	−1.04705	−	0.515610i
$267$			10.9924i			0.672722i
$268$	4.44592	−	3.41951i	0.271578	−	0.208880i
$269$			13.7026i			0.835459i	0.908571	+	0.417730i	$0.137174\pi$
$269$			13.7026i			0.835459i	−0.908571	+	0.417730i	$0.862826\pi$
$270$	−2.19263	+	4.45260i	−0.133439	+	0.270976i
$271$	−13.6805			−0.831034			−0.415517	−	0.909585i	$-0.636399\pi$
$271$	−13.6805			−0.831034			−0.415517	+	0.909585i	$0.636399\pi$
$272$	5.88106	−	22.1499i	0.356592	−	1.34303i
$273$	−16.1949			−0.980157
$274$	−4.76106	+	9.66834i	−0.287626	+	0.584086i
$275$			34.2227i			2.06370i
$276$	1.58532	−	1.21933i	0.0954251	−	0.0733949i
$277$			7.23978i			0.434996i	0.976061	+	0.217498i	$0.0697896\pi$
$277$			7.23978i			0.434996i	−0.976061	+	0.217498i	$0.930210\pi$
$278$	3.76842	+	1.85572i	0.226015	+	0.111298i
$279$	0.242892			0.0145416
$280$	8.79953	+	43.8470i	0.525872	+	2.62036i
$281$	16.3834			0.977349			0.488674	−	0.872466i	$-0.337481\pi$
$281$	16.3834			0.977349			0.488674	+	0.872466i	$0.337481\pi$
$282$	11.5672	+	5.69614i	0.688817	+	0.339200i
$283$			3.39269i			0.201675i	0.994903	+	0.100837i	$0.0321522\pi$
$283$			3.39269i			0.201675i	−0.994903	+	0.100837i	$0.967848\pi$
$284$	9.10432	+	11.8371i	0.540242	+	0.702401i
$285$			10.4849i			0.621073i
$286$	10.5045	−	21.3316i	0.621145	−	1.26136i
$287$	−6.69738			−0.395334
$288$	−4.26364	−	3.71771i	−0.251237	−	0.219068i
$289$	15.8252			0.930897
$290$	−16.9275	+	34.3748i	−0.994014	+	2.01856i
$291$		−	17.6742i		−	1.03608i
$292$	2.86388	+	3.72350i	0.167596	+	0.217902i
$293$			12.7936i			0.747412i	0.927547	+	0.373706i	$0.121913\pi$
$293$			12.7936i			0.747412i	−0.927547	+	0.373706i	$0.878087\pi$
$294$	−16.8711	−	8.30800i	−0.983945	−	0.484532i
$295$	−7.82176			−0.455401
$296$	6.04288	+	30.1110i	0.351235	+	1.75017i
$297$	4.67738			0.271409
$298$	7.54673	+	3.71630i	0.437171	+	0.215280i
$299$		−	3.59462i		−	0.207882i
$300$	11.5992	−	8.92136i	0.669680	−	0.515075i
$301$			21.0565i			1.21368i
$302$	10.0744	−	20.4581i	0.579714	−	1.17723i
$303$	14.6952			0.844215
$304$	−11.5501	−	3.06670i	−0.662445	−	0.175887i
$305$	6.55200			0.375167
$306$	3.57951	−	7.26895i	0.204627	−	0.415538i
$307$			9.24175i			0.527454i	0.964597	+	0.263727i	$0.0849518\pi$
$307$			9.24175i			0.527454i	−0.964597	+	0.263727i	$0.915048\pi$
$308$	33.4075	−	25.6949i	1.90357	−	1.46410i
$309$			8.32561i			0.473627i
$310$	−1.08150	−	0.532574i	−0.0614252	−	0.0302481i
$311$	6.67351			0.378420			0.189210	−	0.981937i	$-0.439407\pi$
$311$	6.67351			0.378420			0.189210	+	0.981937i	$0.439407\pi$
$312$	−9.96837	+	2.00052i	−0.564348	+	0.113257i
$313$	−11.6994			−0.661288			−0.330644	−	0.943756i	$-0.607266\pi$
$313$	−11.6994			−0.661288			−0.330644	+	0.943756i	$0.607266\pi$
$314$	18.5065	+	9.11332i	1.04438	+	0.514294i
$315$			15.8114i			0.890870i
$316$	2.55321	+	3.31959i	0.143630	+	0.186741i
$317$			0.480609i			0.0269937i	0.999909	+	0.0134968i	$0.00429631\pi$
$317$			0.480609i			0.0269937i	−0.999909	+	0.0134968i	$0.995704\pi$
$318$	−7.53161	+	15.2945i	−0.422351	+	0.857673i
$319$	36.1101			2.02178
$320$	10.8327	+	25.9021i	0.605566	+	1.44797i
$321$	−4.49423			−0.250844
$322$	2.81477	−	5.71598i	0.156861	−	0.318539i
$323$		−	17.1168i		−	0.952406i
$324$	−1.21933	−	1.58532i	−0.0677404	−	0.0880734i
$325$		−	26.3005i		−	1.45889i
$326$	−6.89068	−	3.39323i	−0.381639	−	0.187934i
$327$	0.346182			0.0191439
$328$	−4.12242	+	0.827315i	−0.227622	+	0.0456808i
$329$	41.0757			2.26457
$330$	−20.8265	−	10.2558i	−1.14646	−	0.564562i
$331$		−	5.31594i		−	0.292191i	−0.989271	−	0.146095i	$-0.953329\pi$
$331$		−	5.31594i		−	0.292191i	0.989271	−	0.146095i	$-0.0466706\pi$
$332$	9.42277	−	7.24739i	0.517142	−	0.397752i
$333$			10.8581i			0.595021i
$334$	5.54433	−	11.2589i	0.303372	−	0.616061i
$335$	−9.84215			−0.537734
$336$	−17.4177	−	4.62461i	−0.950213	−	0.252293i
$337$	10.4717			0.570431			0.285216	−	0.958463i	$-0.407935\pi$
$337$	10.4717			0.570431			0.285216	+	0.958463i	$0.407935\pi$
$338$	0.0491563	−	0.0998222i	0.00267375	−	0.00542961i
$339$			9.54965i			0.518666i
$340$	−31.8762	+	24.5172i	−1.72873	+	1.32963i
$341$			1.13610i			0.0615233i
$342$	−3.79041	−	1.86655i	−0.204962	−	0.100931i
$343$	−28.3731			−1.53200
$344$	2.60107	+	12.9608i	0.140240	+	0.698802i
$345$	−3.50951			−0.188945
$346$	−23.4844	−	11.5646i	−1.26253	−	0.621718i
$347$		−	4.97473i		−	0.267057i	−0.991045	−	0.133529i	$-0.957369\pi$
$347$		−	4.97473i		−	0.267057i	0.991045	−	0.133529i	$-0.0426309\pi$
$348$	−9.41340	−	12.2389i	−0.504611	−	0.656075i
$349$		−	17.3790i		−	0.930275i	−0.885239	−	0.465137i	$-0.846005\pi$
$349$		−	17.3790i		−	0.930275i	0.885239	−	0.465137i	$-0.153995\pi$
$350$	20.5946	−	41.8217i	1.10083	−	2.23547i
$351$	−3.59462			−0.191867
$352$	17.3892	−	19.9427i	0.926845	−	1.06295i
$353$	−21.8712			−1.16409			−0.582044	−	0.813157i	$-0.697747\pi$
$353$	−21.8712			−1.16409			−0.582044	+	0.813157i	$0.697747\pi$
$354$	1.39245	−	2.82765i	0.0740076	−	0.150288i
$355$		−	26.2043i		−	1.39078i
$356$	13.4033	+	17.4264i	0.710373	+	0.923599i
$357$		−	25.8123i		−	1.36613i
$358$	23.9088	+	11.7736i	1.26362	+	0.622254i
$359$	−0.0599609			−0.00316461			−0.00158231	−	0.999999i	$-0.500504\pi$
$359$	−0.0599609			−0.00316461			−0.00158231	+	0.999999i	$0.500504\pi$
$360$	1.95315	+	9.73233i	0.102940	+	0.512939i
$361$	10.0744			0.530231
$362$	22.0684	+	10.8673i	1.15989	+	0.571174i
$363$			10.8779i			0.570941i
$364$	−25.6740	+	19.7468i	−1.34568	+	1.03501i
$365$		−	8.24291i		−	0.431454i
$366$	−1.16640	+	2.36862i	−0.0609687	+	0.123810i
$367$	−28.2905			−1.47675			−0.738377	−	0.674388i	$-0.764408\pi$
$367$	−28.2905			−1.47675			−0.738377	+	0.674388i	$0.764408\pi$
$368$	1.02648	−	3.86605i	0.0535091	−	0.201532i
$369$	−1.48656			−0.0773870
$370$	23.8078	−	48.3468i	1.23771	−	2.51343i
$371$			54.3115i			2.81971i
$372$	0.385062	−	0.296165i	0.0199646	−	0.0153555i
$373$			30.1222i			1.55967i	0.625987	+	0.779833i	$0.284696\pi$
$373$			30.1222i			1.55967i	−0.625987	+	0.779833i	$0.715304\pi$
$374$	33.9996	+	16.7427i	1.75808	+	0.865746i
$375$	−8.13022			−0.419843
$376$	25.2832	−	5.07400i	1.30388	−	0.261672i
$377$	−27.7511			−1.42925
$378$	−5.71598	−	2.81477i	−0.293999	−	0.144776i
$379$			28.9567i			1.48741i	0.668510	+	0.743703i	$0.266933\pi$
$379$			28.9567i			1.48741i	−0.668510	+	0.743703i	$0.733067\pi$
$380$	12.7845	+	16.6220i	0.655833	+	0.852689i
$381$		−	5.87741i		−	0.301109i
$382$	−11.5632	+	23.4815i	−0.591624	+	1.20142i
$383$	−22.1401			−1.13131			−0.565654	−	0.824642i	$-0.691376\pi$
$383$	−22.1401			−1.13131			−0.565654	+	0.824642i	$0.691376\pi$
$384$	−11.2923	−	0.694997i	−0.576260	−	0.0354664i
$385$	−73.9558			−3.76914
$386$	−6.84459	+	13.8994i	−0.348380	+	0.707460i
$387$			4.67372i			0.237578i
$388$	−21.5507	−	28.0193i	−1.09407	−	1.42246i
$389$		−	10.9128i		−	0.553302i	−0.960970	−	0.276651i	$-0.910775\pi$
$389$		−	10.9128i		−	0.553302i	0.960970	−	0.276651i	$-0.0892246\pi$
$390$	16.0054	+	7.88168i	0.810466	+	0.399105i
$391$	5.72933			0.289745
$392$	−36.8763	+	7.40059i	−1.86254	+	0.373786i
$393$	5.72986			0.289033
$394$	7.24722	+	3.56881i	0.365110	+	0.179794i
$395$		−	7.34874i		−	0.369755i
$396$	7.41515	−	5.70326i	0.372625	−	0.286599i
$397$		−	1.08875i		−	0.0546430i	−0.999627	−	0.0273215i	$-0.991302\pi$
$397$		−	1.08875i		−	0.0546430i	0.999627	−	0.0273215i	$-0.00869778\pi$
$398$	3.15482	−	6.40653i	0.158137	−	0.321130i
$399$	−13.4599			−0.673839
$400$	7.51039	−	28.2864i	0.375520	−	1.41432i
$401$	37.3995			1.86764			0.933820	−	0.357743i	$-0.116454\pi$
$401$	37.3995			1.86764			0.933820	+	0.357743i	$0.116454\pi$
$402$	1.75212	−	3.55805i	0.0873878	−	0.177459i
$403$		−	0.873107i		−	0.0434926i
$404$	23.2965	−	17.9182i	1.15905	−	0.891464i
$405$			3.50951i			0.174389i
$406$	−44.1283	−	21.7305i	−2.19005	−	1.07847i
$407$	−50.7875			−2.51744
$408$	−3.18855	−	15.8882i	−0.157857	−	0.786583i
$409$	−19.8870			−0.983348			−0.491674	−	0.870779i	$-0.663615\pi$
$409$	−19.8870			−0.983348			−0.491674	+	0.870779i	$0.663615\pi$
$410$	6.61903	+	3.25947i	0.326891	+	0.160974i
$411$			7.62052i			0.375892i
$412$	10.1516	+	13.1988i	0.500136	+	0.650256i
$413$		−	10.0411i		−	0.494091i
$414$	0.624769	−	1.26873i	0.0307057	−	0.0623544i
$415$	−20.8597			−1.02396
$416$	−13.3638	+	15.3262i	−0.655213	+	0.751428i
$417$	2.97024			0.145453
$418$	8.73055	−	17.7292i	0.427025	−	0.867164i
$419$			0.870763i			0.0425395i	0.999774	+	0.0212698i	$0.00677089\pi$
$419$			0.870763i			0.0425395i	−0.999774	+	0.0212698i	$0.993229\pi$
$420$	19.2792	+	25.0661i	0.940730	+	1.22310i
$421$		−	39.3724i		−	1.91890i	−0.281887	−	0.959448i	$-0.590960\pi$
$421$		−	39.3724i		−	1.91890i	0.281887	−	0.959448i	$-0.409040\pi$
$422$	−16.9993	−	8.37110i	−0.827512	−	0.407499i
$423$	9.11719			0.443293
$424$	6.70900	+	33.4302i	0.325818	+	1.62351i
$425$	41.9194			2.03339
$426$	9.47316	+	4.66495i	0.458976	+	0.226018i
$427$			8.41108i			0.407041i
$428$	−7.12480	+	5.47994i	−0.344390	+	0.264883i
$429$		−	16.8134i		−	0.811760i
$430$	10.2477	−	20.8102i	0.494190	−	1.00356i
$431$	28.4360			1.36971			0.684857	−	0.728678i	$-0.259865\pi$
$431$	28.4360			1.36971			0.684857	+	0.728678i	$0.259865\pi$
$432$	−3.86605	−	1.02648i	−0.186005	−	0.0493867i
$433$	17.8457			0.857611			0.428806	−	0.903397i	$-0.358935\pi$
$433$	17.8457			0.857611			0.428806	+	0.903397i	$0.358935\pi$
$434$	0.683687	−	1.38837i	0.0328180	−	0.0666439i
$435$			27.0939i			1.29905i
$436$	0.548810	−	0.422110i	0.0262832	−	0.0202154i
$437$		−	2.98758i		−	0.142915i
$438$	2.97990	+	1.46742i	0.142385	+	0.0701160i
$439$	14.7782			0.705326			0.352663	−	0.935750i	$-0.385276\pi$
$439$	14.7782			0.705326			0.352663	+	0.935750i	$0.385276\pi$
$440$	−45.5218	+	9.13563i	−2.17017	+	0.435524i
$441$	−13.2977			−0.633224
$442$	−26.1291	−	12.8670i	−1.24284	−	0.612020i
$443$		−	10.4043i		−	0.494322i	−0.968974	−	0.247161i	$-0.920502\pi$
$443$		−	10.4043i		−	0.494322i	0.968974	−	0.247161i	$-0.0794977\pi$
$444$	13.2396	+	17.2136i	0.628323	+	0.816921i
$445$		−	38.5778i		−	1.82876i
$446$	4.49031	−	9.11852i	0.212622	−	0.431775i
$447$	5.94828			0.281344
$448$	−33.2516	+	13.9064i	−1.57099	+	0.657015i
$449$	−19.9204			−0.940103			−0.470051	−	0.882639i	$-0.655765\pi$
$449$	−19.9204			−0.940103			−0.470051	+	0.882639i	$0.655765\pi$
$450$	4.57120	−	9.28279i	0.215489	−	0.437595i
$451$		−	6.95319i		−	0.327413i
$452$	11.6441	+	15.1392i	0.547694	+	0.712090i
$453$		−	16.1249i		−	0.757616i
$454$	−0.621985	−	0.306289i	−0.0291912	−	0.0143749i
$455$	56.8359			2.66451
$456$	−8.28495	+	1.66268i	−0.387978	+	0.0778622i
$457$	14.9111			0.697514			0.348757	−	0.937213i	$-0.386604\pi$
$457$	14.9111			0.697514			0.348757	+	0.937213i	$0.386604\pi$
$458$	−8.08128	−	3.97953i	−0.377613	−	0.185951i
$459$		−	5.72933i		−	0.267422i
$460$	−5.56369	+	4.27924i	−0.259408	+	0.199520i
$461$		−	4.39756i		−	0.204815i	−0.994743	−	0.102407i	$-0.967345\pi$
$461$		−	4.39756i		−	0.204815i	0.994743	−	0.102407i	$-0.0326545\pi$
$462$	13.1658	−	26.7358i	0.612526	−	1.24386i
$463$	1.19154			0.0553758			0.0276879	−	0.999617i	$-0.491186\pi$
$463$	1.19154			0.0553758			0.0276879	+	0.999617i	$0.491186\pi$
$464$	−29.8465	−	7.92461i	−1.38559	−	0.367891i
$465$	−0.852432			−0.0395306
$466$	1.66044	−	3.37186i	0.0769182	−	0.156199i
$467$		−	7.88490i		−	0.364869i	−0.983218	−	0.182435i	$-0.941602\pi$
$467$		−	7.88490i		−	0.364869i	0.983218	−	0.182435i	$-0.0583978\pi$
$468$	−5.69863	+	4.38302i	−0.263419	+	0.202605i
$469$		−	12.6348i		−	0.583420i
$470$	−40.5952	−	19.9906i	−1.87252	−	0.922099i
$471$	14.5867			0.672120
$472$	−1.24036	−	6.18058i	−0.0570923	−	0.284484i
$473$	−21.8608			−1.00516
$474$	2.65665	+	1.30824i	0.122024	+	0.0600893i
$475$		−	21.8590i		−	1.00296i
$476$	−31.4737	−	40.9208i	−1.44259	−	1.87560i
$477$			12.0550i			0.551962i
$478$	−8.71235	+	17.6923i	−0.398494	+	0.809225i
$479$	−33.1955			−1.51674			−0.758370	−	0.651824i	$-0.774004\pi$
$479$	−33.1955			−1.51674			−0.758370	+	0.651824i	$0.774004\pi$
$480$	14.9633	+	13.0473i	0.682976	+	0.595527i
$481$	39.0308			1.77965
$482$	−0.798863	+	1.62226i	−0.0363872	+	0.0738919i
$483$		−	4.50530i		−	0.204998i
$484$	13.2637	+	17.2450i	0.602896	+	0.783861i
$485$			62.0278i			2.81654i
$486$	−1.26873	−	0.624769i	−0.0575505	−	0.0283401i
$487$	0.904152			0.0409710			0.0204855	−	0.999790i	$-0.493479\pi$
$487$	0.904152			0.0409710			0.0204855	+	0.999790i	$0.493479\pi$
$488$	1.03901	+	5.17725i	0.0470336	+	0.234363i
$489$	−5.43118			−0.245607
$490$	59.2094	+	29.1570i	2.67481	+	1.31718i
$491$		−	17.7233i		−	0.799844i	−0.916549	−	0.399922i	$-0.869037\pi$
$491$		−	17.7233i		−	0.799844i	0.916549	−	0.399922i	$-0.130963\pi$
$492$	−2.35667	+	1.81260i	−0.106247	+	0.0817182i
$493$		−	44.2313i		−	1.99208i
$494$	−6.70953	+	13.6251i	−0.301876	+	0.613023i
$495$	−16.4153			−0.737813
$496$	0.249325	−	0.939034i	0.0111950	−	0.0421639i
$497$	33.6396			1.50894
$498$	3.71348	−	7.54100i	0.166405	−	0.337920i
$499$		−	23.5382i		−	1.05371i	−0.849954	−	0.526856i	$-0.823371\pi$
$499$		−	23.5382i		−	1.05371i	0.849954	−	0.526856i	$-0.176629\pi$
$500$	−12.8890	+	9.91340i	−0.576414	+	0.443341i
$501$		−	8.87420i		−	0.396470i
$502$	−24.3027	−	11.9676i	−1.08468	−	0.534138i
$503$	20.8077			0.927771			0.463885	−	0.885895i	$-0.346455\pi$
$503$	20.8077			0.927771			0.463885	+	0.885895i	$0.346455\pi$
$504$	−12.4938	+	2.50734i	−0.556518	+	0.111686i
$505$	−51.5727			−2.29496
$506$	5.93431	+	2.92228i	0.263812	+	0.129911i
$507$		−	0.0786791i		−	0.00349426i
$508$	−7.16648	−	9.31757i	−0.317961	−	0.413401i
$509$			22.1593i			0.982192i	0.871106	+	0.491096i	$0.163404\pi$
$509$			22.1593i			0.982192i	−0.871106	+	0.491096i	$0.836596\pi$
$510$	−12.5623	+	25.5104i	−0.556268	+	1.12962i
$511$	10.5818			0.468110
$512$	−18.7494	+	12.6673i	−0.828615	+	0.559819i
$513$	−2.98758			−0.131905
$514$	−9.39585	+	19.0802i	−0.414433	+	0.841593i
$515$		−	29.2188i		−	1.28753i
$516$	5.69879	+	7.40934i	0.250875	+	0.326178i
$517$			42.6446i			1.87551i
$518$	62.0648	+	30.5631i	2.72697	+	1.34287i
$519$	−18.5102			−0.812509
$520$	34.9841	−	7.02084i	1.53415	−	0.307884i
$521$	−8.20700			−0.359555			−0.179778	−	0.983707i	$-0.557538\pi$
$521$	−8.20700			−0.359555			−0.179778	+	0.983707i	$0.557538\pi$
$522$	−9.79476	−	4.82332i	−0.428705	−	0.211111i
$523$		−	25.5120i		−	1.11556i	−0.829988	−	0.557781i	$-0.811653\pi$
$523$		−	25.5120i		−	1.11556i	0.829988	−	0.557781i	$-0.188347\pi$
$524$	9.08367	−	6.98657i	0.396822	−	0.305210i
$525$		−	32.9636i		−	1.43865i
$526$	−14.6135	+	29.6758i	−0.637180	+	1.29393i
$527$	1.39161			0.0606196
$528$	4.80125	−	18.0830i	0.208948	−	0.786961i
$529$	1.00000			0.0434783
$530$	26.4322	−	53.6762i	1.14814	−	2.33154i
$531$		−	2.22874i		−	0.0967189i
$532$	−21.3383	+	16.4121i	−0.925133	+	0.711553i
$533$			5.34361i			0.231457i
$534$	13.9463	+	6.86769i	0.603515	+	0.297194i
$535$	15.7725			0.681906
$536$	−1.56075	−	7.77705i	−0.0674142	−	0.335918i
$537$	18.8447			0.813210
$538$	17.3848	+	8.56093i	0.749511	+	0.369088i
$539$		−	62.1985i		−	2.67908i
$540$	4.27924	+	5.56369i	0.184149	+	0.239423i
$541$			0.637649i			0.0274147i	0.999906	+	0.0137073i	$0.00436331\pi$
$541$			0.637649i			0.0274147i	−0.999906	+	0.0137073i	$0.995637\pi$
$542$	−8.54718	+	17.3569i	−0.367133	+	0.745541i
$543$	17.3941			0.746454
$544$	−24.4278	−	21.3000i	−1.04733	−	0.913230i
$545$	−1.21493			−0.0520418
$546$	−10.1180	+	20.5468i	−0.433012	+	0.879323i
$547$			37.0000i			1.58200i	0.611814	+	0.791002i	$0.290440\pi$
$547$			37.0000i			1.58200i	−0.611814	+	0.791002i	$0.709560\pi$
$548$	9.29190	+	12.0810i	0.396930	+	0.516073i
$549$			1.86693i			0.0796787i
$550$	43.4192	+	21.3813i	1.85140	+	0.911700i
$551$	−23.0646			−0.982584
$552$	−0.556532	−	2.77313i	−0.0236876	−	0.118032i
$553$	9.43389			0.401170
$554$	9.18529	+	4.52319i	0.390245	+	0.192172i
$555$		−	38.1066i		−	1.61754i
$556$	4.70878	−	3.62170i	0.199697	−	0.153594i
$557$		−	36.6371i		−	1.55237i	−0.630508	−	0.776183i	$-0.717153\pi$
$557$		−	36.6371i		−	1.55237i	0.630508	−	0.776183i	$-0.282847\pi$
$558$	0.151752	−	0.308164i	0.00642416	−	0.0130456i
$559$	16.8003			0.710575
$560$	61.1275	+	16.2301i	2.58311	+	0.685847i
$561$	26.7983			1.13142
$562$	10.2358	−	20.7860i	0.431772	−	0.876803i
$563$		−	30.8226i		−	1.29902i	−0.760353	−	0.649510i	$-0.774974\pi$
$563$		−	30.8226i		−	1.29902i	0.760353	−	0.649510i	$-0.225026\pi$
$564$	14.4537	−	11.1168i	0.608609	−	0.468103i
$565$		−	33.5145i		−	1.40997i
$566$	4.30440	+	2.11965i	0.180927	+	0.0890955i
$567$	−4.50530			−0.189205
$568$	20.7061	−	4.15544i	0.868808	−	0.174358i
$569$	−6.92981			−0.290513			−0.145256	−	0.989394i	$-0.546401\pi$
$569$	−6.92981			−0.290513			−0.145256	+	0.989394i	$0.546401\pi$
$570$	13.3025	+	6.55065i	0.557180	+	0.274377i
$571$			35.0797i			1.46804i	0.679128	+	0.734020i	$0.262358\pi$
$571$			35.0797i			1.46804i	−0.679128	+	0.734020i	$0.737642\pi$
$572$	−20.5011	−	26.6547i	−0.857193	−	1.11449i
$573$			18.5079i			0.773181i
$574$	−4.18431	+	8.49713i	−0.174650	+	0.354663i
$575$	7.31663			0.305125
$576$	−7.38055	+	3.08667i	−0.307523	+	0.128611i
$577$	15.1270			0.629745			0.314873	−	0.949134i	$-0.398038\pi$
$577$	15.1270			0.629745			0.314873	+	0.949134i	$0.398038\pi$
$578$	9.88712	−	20.0779i	0.411250	−	0.835130i
$579$			10.9554i			0.455290i
$580$	33.0364	+	42.9526i	1.37176	+	1.78351i
$581$		−	26.7784i		−	1.11096i
$582$	−22.4237	−	11.0423i	−0.929493	−	0.457718i
$583$	−56.3859			−2.33527
$584$	6.51337	−	1.30715i	0.269525	−	0.0540901i
$585$	12.6154			0.521581
$586$	16.2316	+	7.99307i	0.670521	+	0.330191i
$587$			2.09631i			0.0865240i	0.999064	+	0.0432620i	$0.0137750\pi$
$587$			2.09631i			0.0865240i	−0.999064	+	0.0432620i	$0.986225\pi$
$588$	−21.0811	+	16.2143i	−0.869371	+	0.668665i
$589$		−	0.725660i		−	0.0299003i
$590$	−4.88679	+	9.92366i	−0.201186	+	0.408551i
$591$	5.71221			0.234969
$592$	41.9780	+	11.1457i	1.72529	+	0.458084i
$593$	12.5982			0.517345			0.258673	−	0.965965i	$-0.416715\pi$
$593$	12.5982			0.517345			0.258673	+	0.965965i	$0.416715\pi$
$594$	2.92228	−	5.93431i	0.119903	−	0.243488i
$595$			90.5886i			3.71377i
$596$	9.42993	−	7.25290i	0.386265	−	0.297090i
$597$		−	5.04958i		−	0.206666i
$598$	−4.56059	−	2.24581i	−0.186496	−	0.0918380i
$599$	−36.4595			−1.48969			−0.744847	−	0.667235i	$-0.767478\pi$
$599$	−36.4595			−1.48969			−0.744847	+	0.667235i	$0.767478\pi$
$600$	−4.07194	−	20.2900i	−0.166236	−	0.828336i
$601$	−2.37923			−0.0970508			−0.0485254	−	0.998822i	$-0.515452\pi$
$601$	−2.37923			−0.0970508			−0.0485254	+	0.998822i	$0.515452\pi$
$602$	26.7149	+	13.1554i	1.08882	+	0.536176i
$603$		−	2.80443i		−	0.114205i
$604$	−19.6616	−	25.5632i	−0.800018	−	1.04015i
$605$		−	38.1760i		−	1.55208i
$606$	9.18108	−	18.6441i	0.372956	−	0.757365i
$607$	−38.0929			−1.54614			−0.773072	−	0.634318i	$-0.781281\pi$
$607$	−38.0929			−1.54614			−0.773072	+	0.634318i	$0.781281\pi$
$608$	−11.1070	+	12.7380i	−0.450446	+	0.516592i
$609$	−34.7816			−1.40942
$610$	4.09349	−	8.31269i	0.165741	−	0.336571i
$611$		−	32.7729i		−	1.32585i
$612$	−6.98593	−	9.08283i	−0.282389	−	0.367152i
$613$			18.3042i			0.739301i	0.929171	+	0.369651i	$0.120523\pi$
$613$			18.3042i			0.739301i	−0.929171	+	0.369651i	$0.879477\pi$
$614$	11.7252	+	5.77396i	0.473192	+	0.233018i
$615$	5.21707			0.210373
$616$	−11.7278	−	58.4382i	−0.472526	−	2.35454i
$617$	−26.8651			−1.08155			−0.540775	−	0.841168i	$-0.681869\pi$
$617$	−26.8651			−1.08155			−0.540775	+	0.841168i	$0.681869\pi$
$618$	10.5629	+	5.20158i	0.424903	+	0.209238i
$619$		−	23.0068i		−	0.924721i	−0.886692	−	0.462360i	$-0.847003\pi$
$619$		−	23.0068i		−	0.924721i	0.886692	−	0.462360i	$-0.152997\pi$
$620$	−1.35138	+	1.03939i	−0.0542727	+	0.0417431i
$621$		−	1.00000i		−	0.0401286i
$622$	4.16940	−	8.46685i	0.167178	−	0.339490i
$623$	49.5239			1.98413
$624$	−3.68982	+	13.8970i	−0.147711	+	0.556325i
$625$	−8.05008			−0.322003
$626$	−7.30941	+	14.8433i	−0.292143	+	0.593257i
$627$		−	13.9740i		−	0.558069i
$628$	23.1246	−	17.7860i	0.922772	−	0.709737i
$629$			62.2097i			2.48046i
$630$	20.0603	+	9.87845i	0.799221	+	0.393567i
$631$	−14.8837			−0.592510			−0.296255	−	0.955109i	$-0.595738\pi$
$631$	−14.8837			−0.592510			−0.296255	+	0.955109i	$0.595738\pi$
$632$	5.80681	−	1.16535i	0.230983	−	0.0463552i
$633$	−13.3987			−0.532551
$634$	0.609760	+	0.300269i	0.0242167	+	0.0119252i
$635$			20.6268i			0.818549i
$636$	14.6990	+	19.1111i	0.582854	+	0.757803i
$637$			47.8003i			1.89392i
$638$	22.5605	−	45.8138i	0.893178	−	1.81379i
$639$	7.46668			0.295377
$640$	39.6305	+	2.43909i	1.56653	+	0.0964137i
$641$	9.31472			0.367909			0.183955	−	0.982935i	$-0.441110\pi$
$641$	9.31472			0.367909			0.183955	+	0.982935i	$0.441110\pi$
$642$	−2.80786	+	5.70194i	−0.110817	+	0.225038i
$643$		−	7.49904i		−	0.295733i	−0.989007	−	0.147867i	$-0.952759\pi$
$643$		−	7.49904i		−	0.295733i	0.989007	−	0.147867i	$-0.0472407\pi$
$644$	−5.49343	−	7.14234i	−0.216472	−	0.281448i
$645$		−	16.4024i		−	0.645846i
$646$	−21.7165	−	10.6941i	−0.854426	−	0.420752i
$647$	−45.7056			−1.79687			−0.898437	−	0.439103i	$-0.855296\pi$
$647$	−45.7056			−1.79687			−0.898437	+	0.439103i	$0.855296\pi$
$648$	−2.77313	+	0.556532i	−0.108939	+	0.0218626i
$649$	10.4246			0.409203
$650$	−33.3681	−	16.4318i	−1.30881	−	0.644507i
$651$		−	1.09430i		−	0.0428891i
$652$	−8.61016	+	6.62239i	−0.337200	+	0.259353i
$653$		−	10.5867i		−	0.414289i	−0.978310	−	0.207145i	$-0.933583\pi$
$653$		−	10.5867i		−	0.414289i	0.978310	−	0.207145i	$-0.0664171\pi$
$654$	0.216284	−	0.439210i	0.00845738	−	0.0171745i
$655$	−20.1090			−0.785723
$656$	−1.52592	+	5.74710i	−0.0595773	+	0.224386i
$657$	2.34874			0.0916330
$658$	25.6628	−	52.1137i	1.00044	−	2.03160i
$659$			37.0968i			1.44509i	0.691325	+	0.722544i	$0.257027\pi$
$659$			37.0968i			1.44509i	−0.691325	+	0.722544i	$0.742973\pi$
$660$	−26.0235	+	20.0156i	−1.01296	+	0.779107i
$661$		−	15.1351i		−	0.588689i	−0.955699	−	0.294344i	$-0.904899\pi$
$661$		−	15.1351i		−	0.588689i	0.955699	−	0.294344i	$-0.0951013\pi$
$662$	−6.74447	−	3.32124i	−0.262131	−	0.129083i
$663$	−20.5948			−0.799835
$664$	−3.30789	−	16.4829i	−0.128371	−	0.639659i
$665$	47.2377			1.83180
$666$	13.7760	+	6.78381i	0.533808	+	0.262867i
$667$		−	7.72016i		−	0.298926i
$668$	−10.8206	−	14.0685i	−0.418660	−	0.544325i
$669$		−	7.18715i		−	0.277871i
$670$	−6.14907	+	12.4870i	−0.237559	+	0.482414i
$671$	−8.73235			−0.337109
$672$	−16.7494	+	19.2090i	−0.646122	+	0.741002i
$673$	−14.6252			−0.563760			−0.281880	−	0.959450i	$-0.590958\pi$
$673$	−14.6252			−0.563760			−0.281880	+	0.959450i	$0.590958\pi$
$674$	6.54241	−	13.2857i	0.252004	−	0.511748i
$675$		−	7.31663i		−	0.281617i
$676$	−0.0959356	−	0.124732i	−0.00368983	−	0.00479737i
$677$			9.04953i			0.347802i	0.984763	+	0.173901i	$0.0556372\pi$
$677$			9.04953i			0.347802i	−0.984763	+	0.173901i	$0.944363\pi$
$678$	12.1159	+	5.96632i	0.465307	+	0.229135i
$679$	−79.6276			−3.05583
$680$	11.1902	+	55.7597i	0.429126	+	2.13829i
$681$	−0.490244			−0.0187862
$682$	1.44140	+	0.709801i	0.0551940	+	0.0271797i
$683$			38.6237i			1.47789i	0.673764	+	0.738947i	$0.264677\pi$
$683$			38.6237i			1.47789i	−0.673764	+	0.738947i	$0.735323\pi$
$684$	−4.73627	+	3.64283i	−0.181096	+	0.139287i
$685$		−	26.7442i		−	1.02184i
$686$	−17.7266	+	35.9976i	−0.676805	+	1.37440i
$687$	−6.36961			−0.243016
$688$	18.0688	+	4.79749i	0.688867	+	0.182903i
$689$	43.3333			1.65087
$690$	−2.19263	+	4.45260i	−0.0834720	+	0.169508i
$691$		−	28.4576i		−	1.08258i	−0.840837	−	0.541289i	$-0.817937\pi$
$691$		−	28.4576i		−	1.08258i	0.840837	−	0.541289i	$-0.182063\pi$
$692$	−29.3447	+	22.5700i	−1.11552	+	0.857984i
$693$		−	21.0730i		−	0.800497i
$694$	−6.31157	−	3.10806i	−0.239584	−	0.117980i
$695$	−10.4241			−0.395408
$696$	−21.4090	+	4.29651i	−0.811507	+	0.162859i
$697$	−8.51697			−0.322603
$698$	−22.0491	−	10.8578i	−0.834572	−	0.410975i
$699$		−	2.65768i		−	0.100523i
$700$	−40.1934	−	52.2579i	−1.51917	−	1.97516i
$701$		−	9.06773i		−	0.342483i	−0.985229	−	0.171242i	$-0.945222\pi$
$701$		−	9.06773i		−	0.342483i	0.985229	−	0.171242i	$-0.0547779\pi$
$702$	−2.24581	+	4.56059i	−0.0847626	+	0.172128i
$703$	32.4395			1.22348
$704$	−14.4375	−	34.5216i	−0.544136	−	1.30108i
$705$	−31.9968			−1.20507
$706$	−13.6645	+	27.7486i	−0.514269	+	1.04433i
$707$		−	66.2061i		−	2.48994i
$708$	−2.71756	−	3.53326i	−0.102132	−	0.132788i
$709$		−	22.4777i		−	0.844169i	−0.906557	−	0.422084i	$-0.861299\pi$
$709$		−	22.4777i		−	0.844169i	0.906557	−	0.422084i	$-0.138701\pi$
$710$	−33.2461	−	16.3717i	−1.24770	−	0.614418i
$711$	2.09395			0.0785294
$712$	30.4833	−	6.11760i	1.14241	−	0.229267i
$713$	0.242892			0.00909639
$714$	−32.7488	−	16.1268i	−1.22559	−	0.603529i
$715$			59.0068i			2.20673i
$716$	29.8749	−	22.9779i	1.11648	−	0.858724i
$717$			13.9449i			0.520782i
$718$	−0.0374617	+	0.0760739i	−0.00139806	+	0.00283905i
$719$	−39.1309			−1.45934			−0.729668	−	0.683802i	$-0.760325\pi$
$719$	−39.1309			−1.45934			−0.729668	+	0.683802i	$0.760325\pi$
$720$	13.5679	+	3.60245i	0.505647	+	0.134255i
$721$	37.5094			1.39692
$722$	6.29416	−	12.7816i	0.234244	−	0.475683i
$723$			1.27865i			0.0475536i
$724$	27.5753	−	21.2091i	1.02483	−	0.788232i
$725$		−	56.4855i		−	2.09782i
$726$	13.8011	+	6.79617i	0.512205	+	0.252230i
$727$	−51.1605			−1.89744			−0.948719	−	0.316122i	$-0.897619\pi$
$727$	−51.1605			−1.89744			−0.948719	+	0.316122i	$0.897619\pi$
$728$	9.01295	+	44.9105i	0.334042	+	1.66449i
$729$	−1.00000			−0.0370370
$730$	−10.4580	−	5.14992i	−0.387068	−	0.190607i
$731$			26.7773i			0.990394i
$732$	2.27640	+	2.95968i	0.0841381	+	0.109393i
$733$			28.8256i			1.06470i	0.846525	+	0.532349i	$0.178690\pi$
$733$			28.8256i			1.06470i	−0.846525	+	0.532349i	$0.821310\pi$
$734$	−17.6751	+	35.8929i	−0.652398	+	1.32483i
$735$	46.6684			1.72139
$736$	−4.26364	−	3.71771i	−0.157160	−	0.137037i
$737$	13.1174			0.483185
$738$	−0.928754	+	1.88603i	−0.0341879	+	0.0694257i
$739$			10.9839i			0.404050i	0.979380	+	0.202025i	$0.0647522\pi$
$739$			10.9839i			0.404050i	−0.979380	+	0.202025i	$0.935248\pi$
$740$	−46.4644	−	60.4112i	−1.70807	−	2.22076i
$741$			10.7392i			0.394515i
$742$	68.9063	+	33.9321i	2.52963	+	1.24569i
$743$	38.8313			1.42458			0.712292	−	0.701884i	$-0.247657\pi$
$743$	38.8313			1.42458			0.712292	+	0.701884i	$0.247657\pi$
$744$	−0.135177	−	0.673573i	−0.00495584	−	0.0246944i
$745$	−20.8755			−0.764820
$746$	38.2168	+	18.8194i	1.39921	+	0.689027i
$747$		−	5.94376i		−	0.217471i
$748$	42.4838	−	32.6759i	1.55336	−	1.19475i
$749$			20.2478i			0.739840i
$750$	−5.07951	+	10.3150i	−0.185478	+	0.376651i
$751$	25.5363			0.931833			0.465916	−	0.884829i	$-0.345725\pi$
$751$	25.5363			0.931833			0.465916	+	0.884829i	$0.345725\pi$
$752$	9.35864	−	35.2475i	0.341274	−	1.28534i
$753$	−19.1552			−0.698053
$754$	−17.3380	+	35.2085i	−0.631413	+	1.28222i
$755$			56.5906i			2.05954i
$756$	−7.14234	+	5.49343i	−0.259764	+	0.199794i
$757$			51.9440i			1.88794i	0.330033	+	0.943969i	$0.392940\pi$
$757$			51.9440i			1.88794i	−0.330033	+	0.943969i	$0.607060\pi$
$758$	36.7381	+	18.0913i	1.33439	+	0.657104i
$759$	4.67738			0.169778
$760$	29.0761	−	5.83519i	1.05470	−	0.211665i
$761$	16.9023			0.612707			0.306353	−	0.951918i	$-0.400891\pi$
$761$	16.9023			0.612707			0.306353	+	0.951918i	$0.400891\pi$
$762$	−7.45681	−	3.67202i	−0.270132	−	0.133023i
$763$		−	1.55965i		−	0.0564633i
$764$	22.5672	+	29.3410i	0.816454	+	1.06152i
$765$			20.1071i			0.726975i
$766$	−13.8325	+	28.0898i	−0.499788	+	1.01492i
$767$	−8.01147			−0.289277
$768$	−7.93687	+	13.8927i	−0.286397	+	0.501308i
$769$	−19.1318			−0.689910			−0.344955	−	0.938619i	$-0.612106\pi$
$769$	−19.1318			−0.689910			−0.344955	+	0.938619i	$0.612106\pi$
$770$	−46.2053	+	93.8296i	−1.66512	+	3.38138i
$771$			15.0389i			0.541613i
$772$	13.3582	+	17.3678i	0.480772	+	0.625081i
$773$		−	24.2356i		−	0.871693i	−0.900021	−	0.435846i	$-0.856449\pi$
$773$		−	24.2356i		−	0.871693i	0.900021	−	0.435846i	$-0.143551\pi$
$774$	5.92966	+	2.92000i	0.213137	+	0.104957i
$775$	1.77715			0.0638373
$776$	−49.0130	+	9.83626i	−1.75946	+	0.353101i
$777$	48.9190			1.75496
$778$	−13.8454	−	6.81800i	−0.496381	−	0.244437i
$779$			4.44120i			0.159123i
$780$	19.9994	−	15.3822i	0.716093	−	0.550773i
$781$			34.9245i			1.24970i
$782$	3.57951	−	7.26895i	0.128003	−	0.259937i
$783$	−7.72016			−0.275896
$784$	−13.6499	+	51.4096i	−0.487495	+	1.83606i
$785$	−51.1921			−1.82712
$786$	3.57984	−	7.26962i	0.127689	−	0.259299i
$787$			4.87006i			0.173599i	0.996226	+	0.0867994i	$0.0276639\pi$
$787$			4.87006i			0.173599i	−0.996226	+	0.0867994i	$0.972336\pi$
$788$	9.05568	−	6.96505i	0.322595	−	0.248120i
$789$			23.3903i			0.832716i
$790$	−9.32353	−	4.59127i	−0.331716	−	0.163350i
$791$	43.0240			1.52976
$792$	−2.60311	−	12.9710i	−0.0924975	−	0.460905i
$793$	6.71091			0.238312
$794$	−1.38133	−	0.680219i	−0.0490215	−	0.0241401i
$795$		−	42.3072i		−	1.50048i
$796$	−6.15709	−	8.00521i	−0.218232	−	0.283737i
$797$		−	49.3297i		−	1.74735i	−0.486513	−	0.873673i	$-0.661731\pi$
$797$		−	49.3297i		−	1.74735i	0.486513	−	0.873673i	$-0.338269\pi$
$798$	−8.40935	+	17.0769i	−0.297688	+	0.604517i
$799$	52.2354			1.84796
$800$	−31.1955	−	27.2011i	−1.10293	−	0.961705i
$801$	10.9924			0.388396
$802$	23.3660	−	47.4496i	0.825083	−	1.67550i
$803$			10.9859i			0.387686i
$804$	−3.41951	−	4.44592i	−0.120597	−	0.156795i
$805$			15.8114i			0.557277i
$806$	−1.10773	−	0.545490i	−0.0390182	−	0.0192141i
$807$	13.7026			0.482353
$808$	−8.17832	−	40.7516i	−0.287712	−	1.43364i
$809$	−24.1453			−0.848904			−0.424452	−	0.905450i	$-0.639533\pi$
$809$	−24.1453			−0.848904			−0.424452	+	0.905450i	$0.639533\pi$
$810$	4.45260	+	2.19263i	0.156448	+	0.0770412i
$811$		−	42.3569i		−	1.48735i	−0.668541	−	0.743675i	$-0.733081\pi$
$811$		−	42.3569i		−	1.48735i	0.668541	−	0.743675i	$-0.266919\pi$
$812$	−55.1400	+	42.4102i	−1.93503	+	1.48830i
$813$			13.6805i			0.479798i
$814$	−31.7305	+	64.4354i	−1.11215	+	2.25846i
$815$	19.0608			0.667669
$816$	−22.1499	−	5.88106i	−0.775401	−	0.205878i
$817$	13.9631			0.488507
$818$	−12.4248	+	25.2311i	−0.434422	+	0.882185i
$819$			16.1949i			0.565894i
$820$	8.27074	−	6.36132i	0.288827	−	0.222147i
$821$			24.4948i			0.854875i	0.904045	+	0.427438i	$0.140584\pi$
$821$			24.4948i			0.854875i	−0.904045	+	0.427438i	$0.859416\pi$
$822$	9.66834	+	4.76106i	0.337222	+	0.166061i
$823$	−14.3473			−0.500114			−0.250057	−	0.968231i	$-0.580449\pi$
$823$	−14.3473			−0.500114			−0.250057	+	0.968231i	$0.580449\pi$
$824$	23.0880	−	4.63347i	0.804310	−	0.161414i
$825$	34.2227			1.19148
$826$	−12.7394	−	6.27338i	−0.443261	−	0.218279i
$827$			16.2032i			0.563441i	0.959497	+	0.281721i	$0.0909051\pi$
$827$			16.2032i			0.563441i	−0.959497	+	0.281721i	$0.909095\pi$
$828$	−1.21933	−	1.58532i	−0.0423745	−	0.0550937i
$829$			21.8585i			0.759178i	0.925155	+	0.379589i	$0.123935\pi$
$829$			21.8585i			0.759178i	−0.925155	+	0.379589i	$0.876065\pi$
$830$	−13.0325	+	26.4652i	−0.452364	+	0.918620i
$831$	7.23978			0.251145
$832$	11.0954	+	26.5303i	0.384665	+	0.919772i
$833$	−76.1870			−2.63972
$834$	1.85572	−	3.76842i	0.0642582	−	0.130490i
$835$			31.1441i			1.07779i
$836$	−17.0389	−	22.1533i	−0.589304	−	0.766189i
$837$		−	0.242892i		−	0.00839559i
$838$	1.10476	+	0.544026i	0.0381633	+	0.0187931i
$839$	−8.30377			−0.286678			−0.143339	−	0.989674i	$-0.545784\pi$
$839$	−8.30377			−0.286678			−0.143339	+	0.989674i	$0.545784\pi$
$840$	43.8470	−	8.79953i	1.51287	−	0.303612i
$841$	−30.6008			−1.05520
$842$	−49.9528	−	24.5987i	−1.72149	−	0.847727i
$843$		−	16.3834i		−	0.564273i
$844$	−21.2412	+	16.3374i	−0.731154	+	0.562357i
$845$			0.276125i			0.00949898i
$846$	5.69614	−	11.5672i	0.195837	−	0.397689i
$847$	49.0082			1.68394
$848$	46.6053	+	12.3743i	1.60043	+	0.424934i
$849$	3.39269			0.116437
$850$	26.1899	−	53.1842i	0.898308	−	1.82420i
$851$			10.8581i			0.372211i
$852$	11.8371	−	9.10432i	0.405532	−	0.311909i
$853$		−	29.2451i		−	1.00133i	−0.865640	−	0.500667i	$-0.833088\pi$
$853$		−	29.2451i		−	1.00133i	0.865640	−	0.500667i	$-0.166912\pi$
$854$	10.6713	+	5.25498i	0.365166	+	0.179822i
$855$	10.4849			0.358577
$856$	2.50118	+	12.4631i	0.0854886	+	0.425980i
$857$	−17.0825			−0.583527			−0.291763	−	0.956491i	$-0.594242\pi$
$857$	−17.0825			−0.583527			−0.291763	+	0.956491i	$0.594242\pi$
$858$	−21.3316	−	10.5045i	−0.728249	−	0.358618i
$859$		−	6.37910i		−	0.217652i	−0.994061	−	0.108826i	$-0.965291\pi$
$859$		−	6.37910i		−	0.217652i	0.994061	−	0.108826i	$-0.0347091\pi$
$860$	−19.9999	−	26.0031i	−0.681992	−	0.886699i
$861$			6.69738i			0.228246i
$862$	17.7659	−	36.0775i	0.605110	−	1.22880i
$863$	36.7815			1.25206			0.626029	−	0.779800i	$-0.284679\pi$
$863$	36.7815			1.25206			0.626029	+	0.779800i	$0.284679\pi$
$864$	−3.71771	+	4.26364i	−0.126479	+	0.145052i
$865$	64.9618			2.20877
$866$	11.1495	−	22.6413i	0.378874	−	0.769384i
$867$		−	15.8252i		−	0.537453i
$868$	−1.33431	−	1.73482i	−0.0452895	−	0.0588837i
$869$			9.79422i			0.332246i
$870$	34.3748	+	16.9275i	1.16541	+	0.573894i
$871$	−10.0809			−0.341577
$872$	−0.192661	−	0.960010i	−0.00652434	−	0.0325100i
$873$	−17.6742			−0.598182
$874$	−3.79041	−	1.86655i	−0.128213	−	0.0631369i
$875$			36.6291i			1.23829i
$876$	3.72350	−	2.86388i	0.125806	−	0.0967616i
$877$		−	14.9533i		−	0.504937i	−0.967605	−	0.252468i	$-0.918758\pi$
$877$		−	14.9533i		−	0.504937i	0.967605	−	0.252468i	$-0.0812424\pi$
$878$	9.23298	−	18.7495i	0.311598	−	0.632765i
$879$	12.7936			0.431518
$880$	−16.8500	+	63.4623i	−0.568014	+	2.13931i
$881$	−55.1114			−1.85675			−0.928376	−	0.371643i	$-0.878794\pi$
$881$	−55.1114			−1.85675			−0.928376	+	0.371643i	$0.878794\pi$
$882$	−8.30800	+	16.8711i	−0.279745	+	0.568081i
$883$			14.9904i			0.504466i	0.967666	+	0.252233i	$0.0811650\pi$
$883$			14.9904i			0.504466i	−0.967666	+	0.252233i	$0.918835\pi$
$884$	−32.6494	+	25.1118i	−1.09812	+	0.844601i
$885$			7.82176i			0.262926i
$886$	−13.2002	−	6.50027i	−0.443469	−	0.218381i
$887$	30.7222			1.03155			0.515775	−	0.856724i	$-0.327504\pi$
$887$	30.7222			1.03155			0.515775	+	0.856724i	$0.327504\pi$
$888$	30.1110	−	6.04288i	1.01046	−	0.202786i
$889$	−26.4795			−0.888093
$890$	−48.9446	−	24.1022i	−1.64063	−	0.807908i
$891$		−	4.67738i		−	0.156698i
$892$	−8.76349	−	11.3939i	−0.293423	−	0.381497i
$893$		−	27.2383i		−	0.911495i
$894$	3.71630	−	7.54673i	0.124292	−	0.252401i
$895$	−66.1357			−2.21067
$896$	−3.13117	+	50.8754i	−0.104605	+	1.69963i
$897$	−3.59462			−0.120021
$898$	−12.4457	+	25.2735i	−0.415317	+	0.843389i
$899$		−	1.87517i		−	0.0625404i
$900$	−8.92136	−	11.5992i	−0.297379	−	0.386640i
$901$			69.0672i			2.30096i
$902$	−8.82168	−	4.34414i	−0.293730	−	0.144644i
$903$	21.0565			0.700716
$904$	26.4824	−	5.31468i	0.880793	−	0.176764i
$905$	−61.0448			−2.02920
$906$	−20.4581	−	10.0744i	−0.679675	−	0.334698i
$907$			12.9296i			0.429321i	0.976689	+	0.214661i	$0.0688645\pi$
$907$			12.9296i			0.429321i	−0.976689	+	0.214661i	$0.931135\pi$
$908$	−0.777194	+	0.597768i	−0.0257921	+	0.0198376i
$909$		−	14.6952i		−	0.487408i
$910$	35.5093	−	72.1092i	1.17712	−	2.39040i
$911$	31.9145			1.05738			0.528688	−	0.848817i	$-0.322684\pi$
$911$	31.9145			1.05738			0.528688	+	0.848817i	$0.322684\pi$
$912$	−3.06670	+	11.5501i	−0.101548	+	0.382463i
$913$	27.8012			0.920087
$914$	9.31602	−	18.9181i	0.308147	−	0.625757i
$915$		−	6.55200i		−	0.216603i
$916$	−10.0979	+	7.76664i	−0.333643	+	0.256617i
$917$		−	25.8147i		−	0.852478i
$918$	−7.26895	−	3.57951i	−0.239911	−	0.118141i
$919$	−20.7530			−0.684578			−0.342289	−	0.939595i	$-0.611202\pi$
$919$	−20.7530			−0.684578			−0.342289	+	0.939595i	$0.611202\pi$
$920$	1.95315	+	9.73233i	0.0643935	+	0.320865i
$921$	9.24175			0.304526
$922$	−5.57929	−	2.74746i	−0.183744	−	0.0904827i
$923$		−	26.8399i		−	0.883446i
$924$	−25.6949	−	33.4075i	−0.845299	−	1.09902i
$925$			79.4448i			2.61213i
$926$	0.744440	−	1.51174i	0.0244638	−	0.0496789i
$927$	8.32561			0.273449
$928$	−28.7013	+	32.9160i	−0.942167	+	1.08052i
$929$	44.8040			1.46997			0.734986	−	0.678083i	$-0.237189\pi$
$929$	44.8040			1.46997			0.734986	+	0.678083i	$0.237189\pi$
$930$	−0.532574	+	1.08150i	−0.0174638	+	0.0354639i
$931$			39.7279i			1.30203i
$932$	−3.24058	−	4.21327i	−0.106149	−	0.138010i
$933$		−	6.67351i		−	0.218481i
$934$	−10.0038	−	4.92624i	−0.327333	−	0.161191i
$935$	−94.0487			−3.07572
$936$	2.00052	+	9.96837i	0.0653891	+	0.325826i
$937$	53.8510			1.75924			0.879618	−	0.475680i	$-0.157798\pi$
$937$	53.8510			1.75924			0.879618	+	0.475680i	$0.157798\pi$
$938$	−16.0301	−	7.89382i	−0.523400	−	0.257742i
$939$			11.6994i			0.381795i
$940$	−50.7252	+	39.0146i	−1.65447	+	1.27252i
$941$			33.2419i			1.08365i	0.840490	+	0.541827i	$0.182267\pi$
$941$			33.2419i			1.08365i	−0.840490	+	0.541827i	$0.817733\pi$
$942$	9.11332	−	18.5065i	0.296928	−	0.602975i
$943$	−1.48656			−0.0484089
$944$	−8.61640	−	2.28776i	−0.280440	−	0.0744602i
$945$	15.8114			0.514344
$946$	−13.6579	+	27.7353i	−0.444058	+	0.901752i
$947$			26.1384i			0.849383i	0.905338	+	0.424691i	$0.139617\pi$
$947$			26.1384i			0.849383i	−0.905338	+	0.424691i	$0.860383\pi$
$948$	3.31959	−	2.55321i	0.107815	−	0.0829246i
$949$		−	8.44283i		−	0.274066i
$950$	−27.7331	−	13.6568i	−0.899779	−	0.443086i
$951$	0.480609			0.0155848
$952$	−71.5811	+	14.3654i	−2.31996	+	0.465585i
$953$	−38.2227			−1.23815			−0.619077	−	0.785330i	$-0.712493\pi$
$953$	−38.2227			−1.23815			−0.619077	+	0.785330i	$0.712493\pi$
$954$	15.2945	+	7.53161i	0.495178	+	0.243845i
$955$		−	64.9537i		−	2.10185i
$956$	17.0034	+	22.1072i	0.549930	+	0.714996i
$957$		−	36.1101i		−	1.16727i
$958$	−20.7395	+	42.1160i	−0.670063	+	1.36070i
$959$	34.3327			1.10866
$960$	25.9021	−	10.8327i	0.835986	−	0.349624i
$961$	−30.9410			−0.998097
$962$	24.3853	−	49.5194i	0.786212	−	1.59657i
$963$			4.49423i			0.144825i
$964$	1.55910	+	2.02708i	0.0502151	+	0.0652877i
$965$		−	38.4480i		−	1.23768i
$966$	−5.71598	−	2.81477i	−0.183909	−	0.0905638i
$967$	41.8596			1.34611			0.673056	−	0.739591i	$-0.264981\pi$
$967$	41.8596			1.34611			0.673056	+	0.739591i	$0.264981\pi$
$968$	30.1659	−	6.05389i	0.969567	−	0.194579i
$969$	−17.1168			−0.549872
$970$	78.6962	+	38.7530i	2.52678	+	1.24429i
$971$			9.36635i			0.300580i	0.988642	+	0.150290i	$0.0480208\pi$
$971$			9.36635i			0.300580i	−0.988642	+	0.150290i	$0.951979\pi$
$972$	−1.58532	+	1.21933i	−0.0508492	+	0.0391099i
$973$		−	13.3818i		−	0.429002i
$974$	0.564886	−	1.14712i	0.0181001	−	0.0367561i
$975$	−26.3005			−0.842291
$976$	7.21765	+	1.91637i	0.231031	+	0.0613416i
$977$	−7.87379			−0.251905			−0.125952	−	0.992036i	$-0.540199\pi$
$977$	−7.87379			−0.251905			−0.125952	+	0.992036i	$0.540199\pi$
$978$	−3.39323	+	6.89068i	−0.108504	+	0.220340i
$979$			51.4155i			1.64325i
$980$	73.9843	−	56.9040i	2.36334	−	1.81773i
$981$		−	0.346182i		−	0.0110528i
$982$	−22.4861	−	11.0730i	−0.717559	−	0.353354i
$983$	−27.7540			−0.885214			−0.442607	−	0.896716i	$-0.645946\pi$
$983$	−27.7540			−0.885214			−0.442607	+	0.896716i	$0.645946\pi$
$984$	0.827315	+	4.12242i	0.0263738	+	0.131418i
$985$	−20.0470			−0.638752
$986$	−56.1174	−	27.6344i	−1.78714	−	0.880058i
$987$		−	41.0757i		−	1.30745i
$988$	13.0946	+	17.0251i	0.416595	+	0.541641i
$989$			4.67372i			0.148616i
$990$	−10.2558	+	20.8265i	−0.325950	+	0.661910i
$991$	38.8553			1.23428			0.617140	−	0.786853i	$-0.288291\pi$
$991$	38.8553			1.23428			0.617140	+	0.786853i	$0.288291\pi$
$992$	−1.03561	−	0.903004i	−0.0328805	−	0.0286704i
$993$	−5.31594			−0.168696
$994$	21.0170	−	42.6794i	0.666618	−	1.35371i
$995$			17.7215i			0.561810i
$996$	−7.24739	−	9.42277i	−0.229642	−	0.298572i
$997$		−	7.29815i		−	0.231135i	−0.993300	−	0.115567i	$-0.963131\pi$
$997$		−	7.29815i		−	0.231135i	0.993300	−	0.115567i	$-0.0368686\pi$
$998$	−29.8635	−	14.7059i	−0.945311	−	0.465508i
$999$	10.8581			0.343536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.13	✓	18
4.3	odd	2		2208.2.f.c.1105.17		18
8.3	odd	2		2208.2.f.c.1105.2		18
8.5	even	2	inner	552.2.f.c.277.14	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.13	✓	18	1.1	even	1	trivial
552.2.f.c.277.14	yes	18	8.5	even	2	inner
2208.2.f.c.1105.2		18	8.3	odd	2
2208.2.f.c.1105.17		18	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.624769 - 1.26873i) q^{2} -1.00000i q^{3} +(-1.21933 - 1.58532i) q^{4} +3.50951i q^{5} +(-1.26873 - 0.624769i) q^{6} -4.50530 q^{7} +(-2.77313 + 0.556532i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.624769 - 1.26873i) q^{2} -1.00000i q^{3} +(-1.21933 - 1.58532i) q^{4} +3.50951i q^{5} +(-1.26873 - 0.624769i) q^{6} -4.50530 q^{7} +(-2.77313 + 0.556532i) q^{8} -1.00000 q^{9} +(4.45260 + 2.19263i) q^{10} -4.67738i q^{11} +(-1.58532 + 1.21933i) q^{12} +3.59462i q^{13} +(-2.81477 + 5.71598i) q^{14} +3.50951 q^{15} +(-1.02648 + 3.86605i) q^{16} -5.72933 q^{17} +(-0.624769 + 1.26873i) q^{18} +2.98758i q^{19} +(5.56369 - 4.27924i) q^{20} +4.50530i q^{21} +(-5.93431 - 2.92228i) q^{22} -1.00000 q^{23} +(0.556532 + 2.77313i) q^{24} -7.31663 q^{25} +(4.56059 + 2.24581i) q^{26} +1.00000i q^{27} +(5.49343 + 7.14234i) q^{28} +7.72016i q^{29} +(2.19263 - 4.45260i) q^{30} -0.242892 q^{31} +(4.26364 + 3.71771i) q^{32} -4.67738 q^{33} +(-3.57951 + 7.26895i) q^{34} -15.8114i q^{35} +(1.21933 + 1.58532i) q^{36} -10.8581i q^{37} +(3.79041 + 1.86655i) q^{38} +3.59462 q^{39} +(-1.95315 - 9.73233i) q^{40} +1.48656 q^{41} +(5.71598 + 2.81477i) q^{42} -4.67372i q^{43} +(-7.41515 + 5.70326i) q^{44} -3.50951i q^{45} +(-0.624769 + 1.26873i) q^{46} -9.11719 q^{47} +(3.86605 + 1.02648i) q^{48} +13.2977 q^{49} +(-4.57120 + 9.28279i) q^{50} +5.72933i q^{51} +(5.69863 - 4.38302i) q^{52} -12.0550i q^{53} +(1.26873 + 0.624769i) q^{54} +16.4153 q^{55} +(12.4938 - 2.50734i) q^{56} +2.98758 q^{57} +(9.79476 + 4.82332i) q^{58} +2.22874i q^{59} +(-4.27924 - 5.56369i) q^{60} -1.86693i q^{61} +(-0.151752 + 0.308164i) q^{62} +4.50530 q^{63} +(7.38055 - 3.08667i) q^{64} -12.6154 q^{65} +(-2.92228 + 5.93431i) q^{66} +2.80443i q^{67} +(6.98593 + 9.08283i) q^{68} +1.00000i q^{69} +(-20.0603 - 9.87845i) q^{70} -7.46668 q^{71} +(2.77313 - 0.556532i) q^{72} -2.34874 q^{73} +(-13.7760 - 6.78381i) q^{74} +7.31663i q^{75} +(4.73627 - 3.64283i) q^{76} +21.0730i q^{77} +(2.24581 - 4.56059i) q^{78} -2.09395 q^{79} +(-13.5679 - 3.60245i) q^{80} +1.00000 q^{81} +(0.928754 - 1.88603i) q^{82} +5.94376i q^{83} +(7.14234 - 5.49343i) q^{84} -20.1071i q^{85} +(-5.92966 - 2.92000i) q^{86} +7.72016 q^{87} +(2.60311 + 12.9710i) q^{88} -10.9924 q^{89} +(-4.45260 - 2.19263i) q^{90} -16.1949i q^{91} +(1.21933 + 1.58532i) q^{92} +0.242892i q^{93} +(-5.69614 + 11.5672i) q^{94} -10.4849 q^{95} +(3.71771 - 4.26364i) q^{96} +17.6742 q^{97} +(8.30800 - 16.8711i) q^{98} +4.67738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Introduction

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