LMFDB - Embedded newform 462.2.bc.b.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.b.95.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(0.752814 + 1.55989i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.112013 - 0.251585i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.86654 + 2.34862i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(0.752814 + 1.55989i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.112013 - 0.251585i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.86654 + 2.34862i) q^{9} +(-0.238498 + 0.137697i) q^{10} +(-0.877660 + 3.19839i) q^{11} +(-1.06068 - 1.36929i) q^{12} +(0.376661 + 0.518429i) q^{13} +(0.863588 + 2.50084i) q^{14} +(0.308121 - 0.364124i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.638932 + 6.07903i) q^{17} +(2.53086 + 1.61082i) q^{18} +(0.228950 - 1.07712i) q^{19} +(0.161872 + 0.222798i) q^{20} +(-2.87227 - 3.57073i) q^{21} +(3.27261 + 0.538529i) q^{22} +(-1.05359 - 0.608290i) q^{23} +(-1.25092 + 1.19800i) q^{24} +(3.29491 - 3.65936i) q^{25} +(0.476217 - 0.428788i) q^{26} +(-5.06876 - 1.14353i) q^{27} +(2.39687 - 1.12027i) q^{28} +(-2.73094 + 8.40497i) q^{29} +(-0.394337 - 0.268371i) q^{30} +(-4.57176 - 2.03548i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.64987 + 1.03874i) q^{33} +6.11252 q^{34} +(0.439011 + 0.581515i) q^{35} +(1.33745 - 2.68537i) q^{36} +(4.83899 + 5.37424i) q^{37} +(-1.09515 - 0.115105i) q^{38} +(-0.525139 + 0.977832i) q^{39} +(0.204657 - 0.184274i) q^{40} +(0.939549 + 2.89164i) q^{41} +(-3.25093 + 3.22978i) q^{42} -1.12509i q^{43} +(0.193498 - 3.31098i) q^{44} +(0.799953 + 0.206518i) q^{45} +(-0.494828 + 1.11140i) q^{46} +(0.496136 - 2.33414i) q^{47} +(1.32220 + 1.11884i) q^{48} +(6.28611 - 3.07974i) q^{49} +(-3.98373 - 2.89435i) q^{50} +(-9.96364 + 3.57971i) q^{51} +(-0.476217 - 0.428788i) q^{52} +(3.33385 - 7.48795i) q^{53} +(-0.607440 + 5.16052i) q^{54} +(0.902975 - 0.137455i) q^{55} +(-1.36467 - 2.26664i) q^{56} +(1.85256 - 0.453736i) q^{57} +(8.64439 + 1.83742i) q^{58} +(1.83954 + 8.65435i) q^{59} +(-0.225682 + 0.420229i) q^{60} +(-1.80155 - 4.04635i) q^{61} +(-1.54645 + 4.75948i) q^{62} +(3.40767 - 7.16853i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0882380 - 0.152833i) q^{65} +(1.62362 + 5.51034i) q^{66} +(-5.31001 - 9.19720i) q^{67} +(-0.638932 - 6.07903i) q^{68} +(0.155712 - 2.10142i) q^{69} +(0.532441 - 0.497391i) q^{70} +(6.62602 - 9.11993i) q^{71} +(-2.81046 - 1.04942i) q^{72} +(2.37065 + 11.1530i) q^{73} +(4.83899 - 5.37424i) q^{74} +(8.18867 + 2.38489i) q^{75} +1.10119i q^{76} +(0.351220 - 8.76793i) q^{77} +(1.02737 + 0.420051i) q^{78} +(12.3514 - 1.29819i) q^{79} +(-0.204657 - 0.184274i) q^{80} +(-2.03204 - 8.76760i) q^{81} +(2.77758 - 1.23666i) q^{82} +(3.41598 + 2.48186i) q^{83} +(3.55190 + 2.89552i) q^{84} +(1.60096 - 0.520183i) q^{85} +(-1.11893 + 0.117604i) q^{86} +(-15.1668 + 2.06740i) q^{87} +(-3.31306 + 0.153653i) q^{88} +(15.7235 + 9.07797i) q^{89} +(0.121769 - 0.817158i) q^{90} +(-1.28054 - 1.11117i) q^{91} +(1.15704 + 0.375944i) q^{92} +(-0.266553 - 8.66380i) q^{93} +(-2.37321 - 0.249434i) q^{94} +(-0.296633 + 0.0630513i) q^{95} +(0.974501 - 1.43190i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(-3.71994 - 5.92976i) q^{98} +(-5.87362 - 8.03122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	0.752814	+	1.55989i	0.434637	+	0.900606i
$3$	0.752814	+	1.55989i	0.434637	+	0.900606i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	−0.112013	−	0.251585i	−0.0500936	−	0.112512i	0.886765	−	0.462221i	$-0.152947\pi$
$5$	−0.112013	−	0.251585i	−0.0500936	−	0.112512i	−0.936858	+	0.349709i	$0.886281\pi$
$6$	1.47266	−	0.911743i	0.601210	−	0.372218i
$7$	−2.57741	+	0.597448i	−0.974170	+	0.225814i
$7$	−2.57741	+	0.597448i	−0.974170	+	0.225814i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.86654	+	2.34862i	−0.622181	+	0.782874i
$10$	−0.238498	+	0.137697i	−0.0754196	+	0.0435435i
$11$	−0.877660	+	3.19839i	−0.264624	+	0.964352i
$11$	−0.877660	+	3.19839i	−0.264624	+	0.964352i
$12$	−1.06068	−	1.36929i	−0.306193	−	0.395279i
$13$	0.376661	+	0.518429i	0.104467	+	0.143786i	0.858050	−	0.513567i	$-0.171676\pi$
$13$	0.376661	+	0.518429i	0.104467	+	0.143786i	−0.753583	+	0.657353i	$0.771676\pi$
$14$	0.863588	+	2.50084i	0.230804	+	0.668378i
$15$	0.308121	−	0.364124i	0.0795564	−	0.0940165i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−0.638932	+	6.07903i	−0.154964	+	1.47438i	0.590069	+	0.807353i	$0.299101\pi$
$17$	−0.638932	+	6.07903i	−0.154964	+	1.47438i	−0.745032	+	0.667028i	$0.767566\pi$
$18$	2.53086	+	1.61082i	0.596530	+	0.379674i
$19$	0.228950	−	1.07712i	0.0525247	−	0.247109i	−0.944051	−	0.329801i	$-0.893018\pi$
$19$	0.228950	−	1.07712i	0.0525247	−	0.247109i	0.996575	+	0.0826918i	$0.0263517\pi$
$20$	0.161872	+	0.222798i	0.0361957	+	0.0498192i
$21$	−2.87227	−	3.57073i	−0.626780	−	0.779196i
$22$	3.27261	+	0.538529i	0.697723	+	0.114815i
$23$	−1.05359	−	0.608290i	−0.219689	−	0.126837i	0.386117	−	0.922450i	$-0.373816\pi$
$23$	−1.05359	−	0.608290i	−0.219689	−	0.126837i	−0.605806	+	0.795612i	$0.707149\pi$
$24$	−1.25092	+	1.19800i	−0.255342	+	0.244541i
$25$	3.29491	−	3.65936i	0.658981	−	0.731873i
$26$	0.476217	−	0.428788i	0.0933939	−	0.0840922i
$27$	−5.06876	−	1.14353i	−0.975483	−	0.220073i
$28$	2.39687	−	1.12027i	0.452967	−	0.211710i
$29$	−2.73094	+	8.40497i	−0.507123	+	1.56076i	0.290049	+	0.957012i	$0.406328\pi$
$29$	−2.73094	+	8.40497i	−0.507123	+	1.56076i	−0.797172	+	0.603752i	$0.793672\pi$
$30$	−0.394337	−	0.268371i	−0.0719957	−	0.0489977i
$31$	−4.57176	−	2.03548i	−0.821113	−	0.365583i	−0.0472080	−	0.998885i	$-0.515032\pi$
$31$	−4.57176	−	2.03548i	−0.821113	−	0.365583i	−0.773905	+	0.633302i	$0.781699\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−5.64987	+	1.03874i	−0.983516	+	0.180821i
$34$	6.11252			1.04829
$35$	0.439011	+	0.581515i	0.0742065	+	0.0982940i
$36$	1.33745	−	2.68537i	0.222908	−	0.447562i
$37$	4.83899	+	5.37424i	0.795524	+	0.883519i	0.995351	−	0.0963120i	$-0.0307047\pi$
$37$	4.83899	+	5.37424i	0.795524	+	0.883519i	−0.199827	+	0.979831i	$0.564038\pi$
$38$	−1.09515	−	0.115105i	−0.177658	−	0.0186726i
$39$	−0.525139	+	0.977832i	−0.0840896	+	0.156578i
$40$	0.204657	−	0.184274i	0.0323592	−	0.0291363i
$41$	0.939549	+	2.89164i	0.146733	+	0.451598i	0.997230	−	0.0743826i	$-0.0236986\pi$
$41$	0.939549	+	2.89164i	0.146733	+	0.451598i	−0.850497	+	0.525980i	$0.823699\pi$
$42$	−3.25093	+	3.22978i	−0.501629	+	0.498365i
$43$		−	1.12509i		−	0.171575i	−0.996313	−	0.0857877i	$-0.972659\pi$
$43$		−	1.12509i		−	0.171575i	0.996313	−	0.0857877i	$-0.0273407\pi$
$44$	0.193498	−	3.31098i	0.0291709	−	0.499148i
$45$	0.799953	+	0.206518i	0.119250	+	0.0307859i
$46$	−0.494828	+	1.11140i	−0.0729584	+	0.163867i
$47$	0.496136	−	2.33414i	0.0723689	−	0.340469i	−0.927036	−	0.374973i	$-0.877652\pi$
$47$	0.496136	−	2.33414i	0.0723689	−	0.340469i	0.999405	+	0.0345044i	$0.0109853\pi$
$48$	1.32220	+	1.11884i	0.190843	+	0.161490i
$49$	6.28611	−	3.07974i	0.898016	−	0.439963i
$50$	−3.98373	−	2.89435i	−0.563384	−	0.409323i
$51$	−9.96364	+	3.57971i	−1.39519	+	0.501260i
$52$	−0.476217	−	0.428788i	−0.0660395	−	0.0594622i
$53$	3.33385	−	7.48795i	0.457940	−	1.02855i	−0.526071	−	0.850441i	$-0.676335\pi$
$53$	3.33385	−	7.48795i	0.457940	−	1.02855i	0.984011	−	0.178109i	$-0.0569979\pi$
$54$	−0.607440	+	5.16052i	−0.0826622	+	0.702258i
$55$	0.902975	−	0.137455i	0.121757	−	0.0185344i
$56$	−1.36467	−	2.26664i	−0.182362	−	0.302893i
$57$	1.85256	−	0.453736i	0.245377	−	0.0600988i
$58$	8.64439	+	1.83742i	1.13506	+	0.241265i
$59$	1.83954	+	8.65435i	0.239487	+	1.12670i	0.919375	+	0.393383i	$0.128695\pi$
$59$	1.83954	+	8.65435i	0.239487	+	1.12670i	−0.679887	+	0.733317i	$0.737971\pi$
$60$	−0.225682	+	0.420229i	−0.0291354	+	0.0542513i
$61$	−1.80155	−	4.04635i	−0.230665	−	0.518082i	0.760717	−	0.649084i	$-0.224847\pi$
$61$	−1.80155	−	4.04635i	−0.230665	−	0.518082i	−0.991382	+	0.131001i	$0.958181\pi$
$62$	−1.54645	+	4.75948i	−0.196399	+	0.604455i
$63$	3.40767	−	7.16853i	0.429326	−	0.903149i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.0882380	−	0.152833i	0.0109446	−	0.0189566i
$66$	1.62362	+	5.51034i	0.199854	+	0.678276i
$67$	−5.31001	−	9.19720i	−0.648721	−	1.12362i	−0.983429	−	0.181295i	$-0.941971\pi$
$67$	−5.31001	−	9.19720i	−0.648721	−	1.12362i	0.334708	−	0.942322i	$-0.391362\pi$
$68$	−0.638932	−	6.07903i	−0.0774819	−	0.737191i
$69$	0.155712	−	2.10142i	0.0187455	−	0.252981i
$70$	0.532441	−	0.497391i	0.0636388	−	0.0594496i
$71$	6.62602	−	9.11993i	0.786363	−	1.08234i	−0.208188	−	0.978089i	$-0.566757\pi$
$71$	6.62602	−	9.11993i	0.786363	−	1.08234i	0.994551	−	0.104248i	$-0.0332434\pi$
$72$	−2.81046	−	1.04942i	−0.331216	−	0.123676i
$73$	2.37065	+	11.1530i	0.277464	+	1.30536i	0.867277	+	0.497825i	$0.165868\pi$
$73$	2.37065	+	11.1530i	0.277464	+	1.30536i	−0.589813	+	0.807540i	$0.700799\pi$
$74$	4.83899	−	5.37424i	0.562521	−	0.624742i
$75$	8.18867	+	2.38489i	0.945546	+	0.275383i
$76$			1.10119i			0.126315i
$77$	0.351220	−	8.76793i	0.0400252	−	0.999199i
$78$	1.02737	+	0.420051i	0.116326	+	0.0475614i
$79$	12.3514	−	1.29819i	1.38964	−	0.146057i	0.620035	−	0.784574i	$-0.287118\pi$
$79$	12.3514	−	1.29819i	1.38964	−	0.146057i	0.769608	+	0.638517i	$0.220452\pi$
$80$	−0.204657	−	0.184274i	−0.0228814	−	0.0206025i
$81$	−2.03204	−	8.76760i	−0.225782	−	0.974178i
$82$	2.77758	−	1.23666i	0.306733	−	0.136566i
$83$	3.41598	+	2.48186i	0.374953	+	0.272419i	0.759262	−	0.650785i	$-0.225560\pi$
$83$	3.41598	+	2.48186i	0.374953	+	0.272419i	−0.384309	+	0.923205i	$0.625560\pi$
$84$	3.55190	+	2.89552i	0.387544	+	0.315927i
$85$	1.60096	−	0.520183i	0.173648	−	0.0564218i
$86$	−1.11893	+	0.117604i	−0.120657	+	0.0126816i
$87$	−15.1668	+	2.06740i	−1.62605	+	0.221649i
$88$	−3.31306	+	0.153653i	−0.353174	+	0.0163795i
$89$	15.7235	+	9.07797i	1.66669	+	0.962263i	0.969405	+	0.245468i	$0.0789418\pi$
$89$	15.7235	+	9.07797i	1.66669	+	0.962263i	0.697284	+	0.716795i	$0.254392\pi$
$90$	0.121769	−	0.817158i	0.0128355	−	0.0861360i
$91$	−1.28054	−	1.11117i	−0.134238	−	0.116482i
$92$	1.15704	+	0.375944i	0.120629	+	0.0391949i
$93$	−0.266553	−	8.66380i	−0.0276402	−	0.898395i
$94$	−2.37321	−	0.249434i	−0.244778	−	0.0257272i
$95$	−0.296633	+	0.0630513i	−0.0304339	+	0.00646892i
$96$	0.974501	−	1.43190i	0.0994596	−	0.146143i
$97$	−8.14146	+	5.91512i	−0.826640	+	0.600589i	−0.918607	−	0.395173i	$-0.870685\pi$
$97$	−8.14146	+	5.91512i	−0.826640	+	0.600589i	0.0919669	+	0.995762i	$0.470685\pi$
$98$	−3.71994	−	5.92976i	−0.375771	−	0.598996i
$99$	−5.87362	−	8.03122i	−0.590321	−	0.807168i
$100$	−2.46208	+	4.26445i	−0.246208	+	0.426445i
$101$	−4.80806	−	2.14068i	−0.478419	−	0.213006i	0.153336	−	0.988174i	$-0.450998\pi$
$101$	−4.80806	−	2.14068i	−0.478419	−	0.213006i	−0.631755	+	0.775168i	$0.717665\pi$
$102$	4.60159	+	9.53488i	0.455625	+	0.944094i
$103$	−8.86266	−	9.84298i	−0.873264	−	0.969857i	0.126492	−	0.991968i	$-0.459628\pi$
$103$	−8.86266	−	9.84298i	−0.873264	−	0.969857i	−0.999756	+	0.0221102i	$0.992962\pi$
$104$	−0.376661	+	0.518429i	−0.0369346	+	0.0508362i
$105$	−0.576609	+	1.12258i	−0.0562713	+	0.109553i
$106$	−7.79542	−	2.53288i	−0.757158	−	0.246015i
$107$	−6.65818	−	1.41524i	−0.643670	−	0.136816i	−0.125500	−	0.992094i	$-0.540053\pi$
$107$	−6.65818	−	1.41524i	−0.643670	−	0.136816i	−0.518171	+	0.855277i	$0.673387\pi$
$108$	5.19575	+	0.0646911i	0.499961	+	0.00622491i
$109$	4.10671	−	2.37101i	0.393352	−	0.227102i	−0.290260	−	0.956948i	$-0.593742\pi$
$109$	4.10671	−	2.37101i	0.393352	−	0.227102i	0.683611	+	0.729846i	$0.260408\pi$
$110$	−0.231088	−	0.883660i	−0.0220334	−	0.0842537i
$111$	−4.74039	+	11.5941i	−0.449938	+	1.10046i
$112$	−2.11158	+	1.59412i	−0.199526	+	0.150631i
$113$	1.41966	−	0.461276i	0.133550	−	0.0433932i	−0.241479	−	0.970406i	$-0.577633\pi$
$113$	1.41966	−	0.461276i	0.133550	−	0.0433932i	0.375030	+	0.927013i	$0.377633\pi$
$114$	−0.644896	−	1.79498i	−0.0604000	−	0.168115i
$115$	−0.0350211	+	0.333203i	−0.00326573	+	0.0310713i
$116$	0.923771	−	8.78910i	0.0857700	−	0.816047i
$117$	−1.92065	−	0.0830364i	−0.177564	−	0.00767672i
$118$	8.41465	−	2.73409i	0.774632	−	0.251693i
$119$	−1.98511	−	16.0499i	−0.181975	−	1.47129i
$120$	0.441517	+	0.180520i	0.0403048	+	0.0164791i
$121$	−9.45943	−	5.61420i	−0.859948	−	0.510382i
$122$	−3.83587	+	2.21464i	−0.347284	+	0.200504i
$123$	−3.80334	+	3.64246i	−0.342936	+	0.328430i
$124$	4.89506	+	1.04048i	0.439589	+	0.0934376i
$125$	−2.59928	−	0.844559i	−0.232487	−	0.0755396i
$126$	−7.48546	−	2.63969i	−0.666857	−	0.235162i
$127$	0.0509999	−	0.0701953i	0.00452551	−	0.00622883i	−0.806748	−	0.590895i	$-0.798775\pi$
$127$	0.0509999	−	0.0701953i	0.00452551	−	0.00622883i	0.811274	+	0.584666i	$0.198775\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	1.75503	−	0.846987i	0.154522	−	0.0745730i
$130$	−0.161219	−	0.0717792i	−0.0141398	−	0.00629545i
$131$	−5.90912	+	10.2349i	−0.516282	+	0.894227i	0.483539	+	0.875323i	$0.339351\pi$
$131$	−5.90912	+	10.2349i	−0.516282	+	0.894227i	−0.999821	+	0.0189040i	$0.993982\pi$
$132$	5.31044	−	2.19071i	0.462215	−	0.190677i
$133$	0.0534271	+	2.91298i	0.00463272	+	0.252587i
$134$	−8.59177	+	6.24229i	−0.742216	+	0.539251i
$135$	0.280070	+	1.40331i	0.0241046	+	0.120778i
$136$	−5.97894	+	1.27086i	−0.512690	+	0.108976i
$137$	8.55726	+	0.899404i	0.731096	+	0.0768413i	0.462759	−	0.886484i	$-0.346859\pi$
$137$	8.55726	+	0.899404i	0.731096	+	0.0768413i	0.268337	+	0.963325i	$0.413526\pi$
$138$	−2.10618	+	0.0647993i	−0.179290	+	0.00551609i
$139$	8.90966	+	2.89492i	0.755707	+	0.245544i	0.661435	−	0.750002i	$-0.269948\pi$
$139$	8.90966	+	2.89492i	0.755707	+	0.245544i	0.0942720	+	0.995546i	$0.469948\pi$
$140$	−0.550322	−	0.477532i	−0.0465107	−	0.0403588i
$141$	4.01450	−	0.983250i	0.338082	−	0.0828046i
$142$	−9.76258	−	5.63643i	−0.819257	−	0.472998i
$143$	−1.98872	+	0.749704i	−0.166305	+	0.0626934i
$144$	−0.749901	+	2.90476i	−0.0624918	+	0.242064i
$145$	2.42046	−	0.254401i	0.201008	−	0.0211268i
$146$	10.8441	−	3.52348i	0.897468	−	0.291605i
$147$	9.53634	+	7.48720i	0.786544	+	0.617534i
$148$	−5.85061	−	4.25072i	−0.480917	−	0.349407i
$149$	−13.0189	+	5.79639i	−1.06655	+	0.474859i	−0.863521	−	0.504313i	$-0.831746\pi$
$149$	−13.0189	+	5.79639i	−1.06655	+	0.474859i	−0.203030	+	0.979172i	$0.565079\pi$
$150$	1.51587	−	8.39310i	0.123770	−	0.685294i
$151$	−7.77891	−	7.00416i	−0.633039	−	0.569991i	0.288884	−	0.957364i	$-0.406716\pi$
$151$	−7.77891	−	7.00416i	−0.633039	−	0.569991i	−0.921923	+	0.387373i	$0.873382\pi$
$152$	1.09515	−	0.115105i	0.0888288	−	0.00933628i
$153$	−13.0847	−	12.8474i	−1.05784	−	1.03865i
$154$	−8.75661	+	0.567203i	−0.705628	+	0.0457065i
$155$			1.37818i			0.110698i
$156$	0.310361	−	1.06565i	0.0248488	−	0.0853200i
$157$	10.0844	−	11.1999i	0.804826	−	0.893850i	−0.191323	−	0.981527i	$-0.561278\pi$
$157$	10.0844	−	11.1999i	0.804826	−	0.893850i	0.996149	+	0.0876774i	$0.0279445\pi$
$158$	−2.58215	−	12.1481i	−0.205425	−	0.966448i
$159$	14.1902	−	0.436579i	1.12536	−	0.0346230i
$160$	−0.161872	+	0.222798i	−0.0127971	+	0.0176137i
$161$	3.07896	+	0.938351i	0.242656	+	0.0739524i
$162$	−8.50716	+	2.93737i	−0.668386	+	0.230782i
$163$	2.21897	+	21.1121i	0.173803	+	1.65362i	0.639582	+	0.768723i	$0.279108\pi$
$163$	2.21897	+	21.1121i	0.173803	+	1.65362i	−0.465779	+	0.884901i	$0.654226\pi$
$164$	−1.52022	−	2.63310i	−0.118709	−	0.205611i
$165$	0.894187	+	1.30507i	0.0696124	+	0.101599i
$166$	2.11119	−	3.65669i	0.163860	−	0.283815i
$167$	3.23429	−	2.34985i	0.250277	−	0.181837i	−0.455573	−	0.890199i	$-0.650566\pi$
$167$	3.23429	−	2.34985i	0.250277	−	0.181837i	0.705849	+	0.708362i	$0.250566\pi$
$168$	2.50838	−	3.83510i	0.193526	−	0.295885i
$169$	3.89033	−	11.9732i	0.299256	−	0.921015i
$170$	−0.684679	−	1.53781i	−0.0525125	−	0.117945i
$171$	2.10241	+	2.54821i	0.160775	+	0.194867i
$172$	0.233920	+	1.10051i	0.0178363	+	0.0839130i
$173$	0.739743	+	0.157237i	0.0562417	+	0.0119545i	0.235947	−	0.971766i	$-0.424181\pi$
$173$	0.739743	+	0.157237i	0.0562417	+	0.0119545i	−0.179705	+	0.983721i	$0.557514\pi$
$174$	3.64143	+	14.8676i	0.276056	+	1.12711i
$175$	−6.30605	+	11.4002i	−0.476693	+	0.861776i
$176$	0.499121	+	3.27885i	0.0376227	+	0.247153i
$177$	−12.1150	+	9.38460i	−0.910622	+	0.705390i
$178$	7.38469	−	16.5863i	0.553506	−	1.24319i
$179$	−1.35024	−	1.21576i	−0.100922	−	0.0908704i	0.617125	−	0.786865i	$-0.288297\pi$
$179$	−1.35024	−	1.21576i	−0.100922	−	0.0908704i	−0.718047	+	0.695994i	$0.754964\pi$
$180$	−0.825410	−	0.0356854i	−0.0615224	−	0.00265983i
$181$	16.7786	+	12.1904i	1.24714	+	0.906102i	0.998053	−	0.0623784i	$-0.0198686\pi$
$181$	16.7786	+	12.1904i	1.24714	+	0.906102i	0.249090	+	0.968480i	$0.419869\pi$
$182$	−0.971230	+	1.38968i	−0.0719924	+	0.103010i
$183$	4.95565	−	5.85638i	0.366332	−	0.432916i
$184$	0.252941	−	1.19000i	0.0186471	−	0.0877276i
$185$	0.810047	−	1.81940i	0.0595559	−	0.133765i
$186$	−8.58848	+	1.17071i	−0.629738	+	0.0858404i
$187$	−18.8824	−	7.37888i	−1.38081	−	0.539597i
$188$			2.38628i			0.174037i
$189$	13.7475	−	0.0809583i	0.999983	−	0.00588885i
$190$	0.0937124	+	0.288417i	0.00679862	+	0.0209240i
$191$	−8.53554	+	7.68543i	−0.617610	+	0.556098i	−0.917430	−	0.397897i	$-0.869740\pi$
$191$	−8.53554	+	7.68543i	−0.617610	+	0.556098i	0.299820	+	0.953996i	$0.403073\pi$
$192$	−1.52592	−	0.819488i	−0.110124	−	0.0591415i
$193$	4.33302	+	0.455419i	0.311898	+	0.0327818i	0.259184	−	0.965828i	$-0.416546\pi$
$193$	4.33302	+	0.455419i	0.311898	+	0.0327818i	0.0527134	+	0.998610i	$0.483213\pi$
$194$	6.73373	+	7.47856i	0.483453	+	0.536929i
$195$	0.304830	+	0.0225874i	0.0218293	+	0.00161752i
$196$	−5.50843	+	4.31940i	−0.393459	+	0.308528i
$197$	16.6705			1.18773			0.593863	−	0.804566i	$-0.297602\pi$
$197$	16.6705			1.18773			0.593863	+	0.804566i	$0.297602\pi$
$198$	−7.37327	+	6.68094i	−0.523995	+	0.474794i
$199$	2.72284	+	4.71610i	0.193017	+	0.334315i	0.946249	−	0.323440i	$-0.104839\pi$
$199$	2.72284	+	4.71610i	0.193017	+	0.334315i	−0.753232	+	0.657755i	$0.771506\pi$
$200$	4.49844	+	2.00284i	0.318088	+	0.141622i
$201$	10.3492	−	15.2068i	0.729977	−	1.07261i
$202$	−1.62638	+	5.00548i	−0.114432	+	0.352184i
$203$	2.01723	−	23.2947i	0.141582	−	1.63497i
$204$	9.00165	−	5.57305i	0.630242	−	0.390191i
$205$	0.622249	−	0.560276i	0.0434598	−	0.0391314i
$206$	−8.86266	+	9.84298i	−0.617491	+	0.685793i
$207$	3.39521	−	1.33908i	0.235984	−	0.0930727i
$208$	0.554961	+	0.320407i	0.0384796	+	0.0222162i
$209$	3.24412	+	1.67762i	0.224401	+	0.116043i
$210$	1.17671	+	0.456108i	0.0812005	+	0.0314744i
$211$	12.1580	+	16.7340i	0.836989	+	1.15202i	0.986582	+	0.163269i	$0.0522037\pi$
$211$	12.1580	+	16.7340i	0.836989	+	1.15202i	−0.149593	+	0.988748i	$0.547796\pi$
$212$	−1.70417	+	8.01747i	−0.117043	+	0.550642i
$213$	19.2143	+	3.47028i	1.31654	+	0.237779i
$214$	−0.711518	+	6.76964i	−0.0486383	+	0.462763i
$215$	−0.283056	+	0.126025i	−0.0193043	+	0.00859482i
$216$	−0.478767	−	5.17405i	−0.0325760	−	0.352049i
$217$	12.9994	+	2.51488i	0.882457	+	0.170721i
$218$	−2.78729	−	3.83638i	−0.188779	−	0.259832i
$219$	−15.6129	+	12.0941i	−1.05502	+	0.817246i
$220$	−0.854664	+	0.322190i	−0.0576215	+	0.0217220i
$221$	−3.39221	+	1.95849i	−0.228185	+	0.131742i
$222$	12.0261	+	3.50251i	0.807139	+	0.235073i
$223$	1.74306	+	5.36460i	0.116724	+	0.359240i	0.992303	−	0.123836i	$-0.0395196\pi$
$223$	1.74306	+	5.36460i	0.116724	+	0.359240i	−0.875579	+	0.483076i	$0.839520\pi$
$224$	1.80611	+	1.93338i	0.120676	+	0.129179i
$225$	2.44438	+	14.5688i	0.162958	+	0.971256i
$226$	−0.607144	−	1.36367i	−0.0403866	−	0.0907098i
$227$	−23.4975	+	4.99455i	−1.55958	+	0.331500i	−0.905308	−	0.424755i	$-0.860360\pi$
$227$	−23.4975	+	4.99455i	−1.55958	+	0.331500i	−0.654277	+	0.756255i	$0.727027\pi$
$228$	−1.71774	+	0.828989i	−0.113760	+	0.0549011i
$229$	2.70995	+	25.7834i	0.179078	+	1.70382i	0.602692	+	0.797974i	$0.294095\pi$
$229$	2.70995	+	25.7834i	0.179078	+	1.70382i	−0.423614	+	0.905843i	$0.639239\pi$
$230$	0.335038			0.0220918
$231$	13.9415	−	6.05276i	0.917280	−	0.398242i
$232$	−8.83751			−0.580211
$233$	−1.76179	−	16.7624i	−0.115419	−	1.09814i	−0.886924	−	0.461915i	$-0.847162\pi$
$233$	−1.76179	−	16.7624i	−0.115419	−	1.09814i	0.771505	−	0.636223i	$-0.219504\pi$
$234$	0.118181	+	1.91880i	0.00772571	+	0.125436i
$235$	−0.642806	+	0.136633i	−0.0419320	+	0.00891293i
$236$	−3.59868	−	8.08277i	−0.234254	−	0.526143i
$237$	11.3234	+	18.2896i	0.735531	+	1.18804i
$238$	−15.7545	+	3.65191i	−1.02121	+	0.236718i
$239$	4.22887	+	13.0151i	0.273543	+	0.841877i	0.989601	+	0.143837i	$0.0459442\pi$
$239$	4.22887	+	13.0151i	0.273543	+	0.841877i	−0.716059	+	0.698040i	$0.754056\pi$
$240$	0.133380	−	0.457968i	0.00860961	−	0.0295617i
$241$	2.75040	−	1.58794i	0.177169	−	0.102288i	−0.408793	−	0.912627i	$-0.634050\pi$
$241$	2.75040	−	1.58794i	0.177169	−	0.102288i	0.585962	+	0.810339i	$0.300717\pi$
$242$	−4.59467	+	9.99445i	−0.295356	+	0.642468i
$243$	12.1468	−	9.77014i	0.779217	−	0.626755i
$244$	2.60347	+	3.58337i	0.166670	+	0.229401i
$245$	−1.47894	−	1.23652i	−0.0944859	−	0.0789983i
$246$	4.02006	+	3.40176i	0.256310	+	0.216889i
$247$	0.644649	−	0.287016i	0.0410180	−	0.0182624i
$248$	0.523104	−	4.97700i	0.0332171	−	0.316040i
$249$	−1.29984	+	7.19695i	−0.0823737	+	0.456088i
$250$	−0.568233	+	2.67333i	−0.0359382	+	0.169076i
$251$	5.83265	+	8.02796i	0.368154	+	0.506720i	0.952398	−	0.304858i	$-0.0986089\pi$
$251$	5.83265	+	8.02796i	0.368154	+	0.506720i	−0.584244	+	0.811578i	$0.698609\pi$
$252$	−1.84279	+	7.72037i	−0.116085	+	0.486338i
$253$	2.87024	−	2.83592i	0.180451	−	0.178293i
$254$	−0.0751417	−	0.0433831i	−0.00471481	−	0.00272210i
$255$	2.01665	+	2.10573i	0.126288	+	0.131866i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−15.5229	+	13.9769i	−0.968290	+	0.871852i	−0.991791	−	0.127871i	$-0.959186\pi$
$257$	−15.5229	+	13.9769i	−0.968290	+	0.871852i	0.0235005	+	0.999724i	$0.492519\pi$
$258$	−1.02580	−	1.65688i	−0.0638634	−	0.103153i
$259$	−15.6829	−	10.9606i	−0.974487	−	0.681058i
$260$	−0.0545341	+	0.167839i	−0.00338206	+	0.0104089i
$261$	−14.6427	−	22.1022i	−0.906359	−	1.36809i
$262$	10.7965	+	4.80691i	0.667010	+	0.296972i
$263$	9.65220	+	16.7181i	0.595180	+	1.03088i	0.993521	+	0.113645i	$0.0362526\pi$
$263$	9.65220	+	16.7181i	0.595180	+	1.03088i	−0.398341	+	0.917237i	$0.630414\pi$
$264$	−2.73380	−	5.05236i	−0.168254	−	0.310951i
$265$	−2.25729			−0.138664
$266$	2.89144	−	0.357624i	0.177285	−	0.0219273i
$267$	−2.32380	+	31.3610i	−0.142214	+	1.91926i
$268$	7.10618	+	7.89221i	0.434079	+	0.482093i
$269$	21.5198	+	2.26183i	1.31209	+	0.137906i	0.734604	−	0.678496i	$-0.237368\pi$
$269$	21.5198	+	2.26183i	1.31209	+	0.137906i	0.577484	+	0.816402i	$0.304035\pi$
$270$	1.36635	−	0.425221i	0.0831534	−	0.0258781i
$271$	−17.0856	+	15.3840i	−1.03788	+	0.934509i	−0.997905	−	0.0646918i	$-0.979394\pi$
$271$	−17.0856	+	15.3840i	−1.03788	+	0.934509i	−0.0399721	+	0.999201i	$0.512727\pi$
$272$	1.88887	+	5.81335i	0.114530	+	0.352486i
$273$	0.769297	−	2.83402i	0.0465600	−	0.171523i
$274$		−	8.60439i		−	0.519810i
$275$	8.81227	+	13.7501i	0.531400	+	0.829161i
$276$	0.284600	+	2.08787i	0.0171309	+	0.125675i
$277$	12.5072	−	28.0916i	0.751484	−	1.68786i	0.0259608	−	0.999663i	$-0.491735\pi$
$277$	12.5072	−	28.0916i	0.751484	−	1.68786i	0.725523	−	0.688198i	$-0.241598\pi$
$278$	1.94775	−	9.16345i	0.116818	−	0.549587i
$279$	13.3140	−	6.93803i	0.797086	−	0.415369i
$280$	−0.417392	+	0.597223i	−0.0249439	+	0.0356909i
$281$	−5.30840	−	3.85678i	−0.316673	−	0.230076i	0.418082	−	0.908409i	$-0.362703\pi$
$281$	−5.30840	−	3.85678i	−0.316673	−	0.230076i	−0.734754	+	0.678333i	$0.762703\pi$
$282$	−1.39749	−	3.88973i	−0.0832195	−	0.231630i
$283$	15.1591	+	13.6493i	0.901115	+	0.811368i	0.982682	−	0.185300i	$-0.0593257\pi$
$283$	15.1591	+	13.6493i	0.901115	+	0.811368i	−0.0815666	+	0.996668i	$0.525992\pi$
$284$	−4.58508	+	10.2983i	−0.272075	+	0.611089i
$285$	−0.321663	−	0.415250i	−0.0190537	−	0.0245973i
$286$	0.953475	+	1.89946i	0.0563802	+	0.112317i
$287$	−4.14921	−	6.89161i	−0.244920	−	0.406799i
$288$	2.96724	+	0.442163i	0.174846	+	0.0260547i
$289$	−19.9179	−	4.23367i	−1.17164	−	0.249040i
$290$	−0.506014	−	2.38061i	−0.0297142	−	0.139794i
$291$	−15.3560	−	8.24683i	−0.900182	−	0.483438i
$292$	−4.63770	−	10.4164i	−0.271401	−	0.609576i
$293$	−2.75468	+	8.47805i	−0.160930	+	0.495293i	−0.998713	−	0.0507105i	$-0.983851\pi$
$293$	−2.75468	+	8.47805i	−0.160930	+	0.495293i	0.837783	+	0.546003i	$0.183851\pi$
$294$	6.44937	−	10.2667i	0.376135	−	0.598768i
$295$	1.97125	−	1.43220i	0.114770	−	0.0833856i
$296$	−3.61587	+	6.26288i	−0.210168	+	0.364022i
$297$	8.10612	−	15.2082i	0.470365	−	0.882472i
$298$	7.12549	+	12.3417i	0.412768	+	0.714936i
$299$	−0.0814905	−	0.775331i	−0.00471272	−	0.0448385i
$300$	−8.50557	−	0.630249i	−0.491070	−	0.0363875i
$301$	0.672185	+	2.89983i	0.0387441	+	0.167144i
$302$	−6.15267	+	8.46843i	−0.354047	+	0.487303i
$303$	−0.280330	−	9.11160i	−0.0161045	−	0.523448i
$304$	−0.228950	−	1.07712i	−0.0131312	−	0.0617773i
$305$	−0.816203	+	0.906485i	−0.0467356	+	0.0519052i
$306$	−11.4093	+	14.3560i	−0.652225	+	0.820677i
$307$		−	18.1321i		−	1.03485i	−0.855728	−	0.517426i	$-0.826890\pi$
$307$		−	18.1321i		−	1.03485i	0.855728	−	0.517426i	$-0.173110\pi$
$308$	1.47941	+	8.64936i	0.0842973	+	0.492843i
$309$	8.68208	−	21.2347i	0.493906	−	1.20800i
$310$	1.37063	−	0.144059i	0.0778468	−	0.00818203i
$311$	−14.8237	−	13.3473i	−0.840574	−	0.756856i	0.131554	−	0.991309i	$-0.458003\pi$
$311$	−14.8237	−	13.3473i	−0.840574	−	0.756856i	−0.972127	+	0.234453i	$0.924670\pi$
$312$	−1.09225	−	0.197270i	−0.0618365	−	0.0111682i
$313$	−22.4597	+	9.99970i	−1.26950	+	0.565216i	−0.927267	−	0.374400i	$-0.877849\pi$
$313$	−22.4597	+	9.99970i	−1.26950	+	0.565216i	−0.342229	+	0.939616i	$0.611182\pi$
$314$	−12.1927	−	8.85849i	−0.688072	−	0.499913i
$315$	−2.18519	−	0.0543518i	−0.123122	−	0.00306238i
$316$	−11.8116	+	3.83782i	−0.664455	+	0.215894i
$317$	15.7403	−	1.65437i	0.884061	−	0.0929185i	0.348394	−	0.937348i	$-0.386727\pi$
$317$	15.7403	−	1.65437i	0.884061	−	0.0929185i	0.535667	+	0.844430i	$0.320060\pi$
$318$	−1.91747	−	14.0668i	−0.107526	−	0.788828i
$319$	−24.4856	−	16.1113i	−1.37093	−	0.902061i
$320$	0.238498	+	0.137697i	0.0133324	+	0.00769748i
$321$	−2.80475	−	11.4515i	−0.156546	−	0.639159i
$322$	0.611371	−	3.16017i	0.0340704	−	0.176110i
$323$	6.40158	+	2.08000i	0.356194	+	0.115734i
$324$	3.81052	+	8.15352i	0.211696	+	0.452973i
$325$	3.13818	+	0.329836i	0.174075	+	0.0182960i
$326$	20.7645	−	4.41362i	1.15004	−	0.244448i
$327$	6.79012	+	4.62111i	0.375495	+	0.255548i
$328$	−2.45977	+	1.78713i	−0.135818	+	0.0986777i
$329$	0.115777	+	6.31245i	0.00638299	+	0.348016i
$330$	1.20445	−	1.02571i	0.0663028	−	0.0564632i
$331$	2.50319	−	4.33564i	0.137588	−	0.238309i	−0.788995	−	0.614399i	$-0.789399\pi$
$331$	2.50319	−	4.33564i	0.137588	−	0.238309i	0.926583	+	0.376091i	$0.122732\pi$
$332$	−3.85734	−	1.71740i	−0.211699	−	0.0942545i
$333$	−21.6542	+	1.33370i	−1.18664	+	0.0730863i
$334$	−2.67505	−	2.97094i	−0.146372	−	0.162563i
$335$	−1.71909	+	2.36612i	−0.0939237	+	0.129275i
$336$	−4.07629	−	2.09376i	−0.222380	−	0.114224i
$337$	−33.0515	−	10.7391i	−1.80043	−	0.584996i	−0.800534	−	0.599287i	$-0.795451\pi$
$337$	−33.0515	−	10.7391i	−1.80043	−	0.584996i	−0.999898	+	0.0142910i	$0.995451\pi$
$338$	−12.3143	−	2.61747i	−0.669807	−	0.142372i
$339$	1.78828	+	1.86727i	0.0971261	+	0.101416i
$340$	−1.45782	+	0.841674i	−0.0790615	+	0.0456462i
$341$	10.5227	−	12.8358i	0.569837	−	0.695099i
$342$	2.31449	−	2.35725i	0.125153	−	0.127466i
$343$	−14.3619	+	11.6934i	−0.775471	+	0.631383i
$344$	1.07003	−	0.347673i	0.0576921	−	0.0187453i
$345$	−0.546126	+	0.196211i	−0.0294024	+	0.0105636i
$346$	0.0790517	−	0.752127i	0.00424985	−	0.0404346i
$347$	0.595247	−	5.66339i	0.0319545	−	0.304027i	−0.966858	−	0.255314i	$-0.917821\pi$
$347$	0.595247	−	5.66339i	0.0319545	−	0.304027i	0.998813	−	0.0487133i	$-0.0155121\pi$
$348$	14.4055	−	5.17557i	0.772215	−	0.277440i
$349$	1.53551	−	0.498918i	0.0821941	−	0.0267065i	−0.267631	−	0.963521i	$-0.586241\pi$
$349$	1.53551	−	0.498918i	0.0821941	−	0.0267065i	0.349825	+	0.936815i	$0.386241\pi$
$350$	11.9969	+	5.07986i	0.641263	+	0.271530i
$351$	−1.31636	−	3.05852i	−0.0702622	−	0.163252i
$352$	3.20872	−	0.839120i	0.171025	−	0.0447253i
$353$	−3.35330	+	1.93603i	−0.178478	+	0.103044i	−0.586578	−	0.809893i	$-0.699525\pi$
$353$	−3.35330	+	1.93603i	−0.178478	+	0.103044i	0.408099	+	0.912938i	$0.366192\pi$
$354$	10.5996	+	11.0677i	0.563360	+	0.588242i
$355$	−3.03663	−	0.645456i	−0.161168	−	0.0342572i
$356$	−17.2673	−	5.61050i	−0.915167	−	0.297356i
$357$	23.5417	−	15.1792i	1.24596	−	0.803366i
$358$	−1.06796	+	1.46993i	−0.0564436	+	0.0776880i
$359$	8.86611	+	9.84681i	0.467935	+	0.519695i	0.930203	−	0.367046i	$-0.119631\pi$
$359$	8.86611	+	9.84681i	0.467935	+	0.519695i	−0.462268	+	0.886740i	$0.652964\pi$
$360$	0.0507889	+	0.824618i	0.00267681	+	0.0434612i
$361$	16.2496	+	7.23478i	0.855241	+	0.380778i
$362$	10.3697	−	17.9609i	0.545021	−	0.944004i
$363$	1.63637	−	18.9822i	0.0858874	−	0.996305i
$364$	1.48359	+	0.820649i	0.0777611	+	0.0430137i
$365$	2.54039	−	1.84570i	0.132970	−	0.0966084i
$366$	−6.34231	−	4.31634i	−0.331518	−	0.225619i
$367$	−9.16748	+	1.94861i	−0.478539	+	0.101717i	−0.440865	−	0.897574i	$-0.645328\pi$
$367$	−9.16748	+	1.94861i	−0.478539	+	0.101717i	−0.0376739	+	0.999290i	$0.511995\pi$
$368$	−1.20992	−	0.127167i	−0.0630712	−	0.00662905i
$369$	−8.54506	−	3.19071i	−0.444838	−	0.166102i
$370$	−1.89410	−	0.615431i	−0.0984697	−	0.0319947i
$371$	−4.11905	+	21.2913i	−0.213851	+	1.10539i
$372$	2.06203	+	8.41906i	0.106911	+	0.436508i
$373$	−11.2890	−	6.51770i	−0.584522	−	0.337474i	0.178406	−	0.983957i	$-0.442906\pi$
$373$	−11.2890	−	6.51770i	−0.584522	−	0.337474i	−0.762928	+	0.646483i	$0.776239\pi$
$374$	−5.36471	+	19.5502i	−0.277403	+	1.01092i
$375$	−0.639355	−	4.69040i	−0.0330161	−	0.242211i
$376$	2.37321	−	0.249434i	0.122389	−	0.0128636i
$377$	−5.38602	+	1.75002i	−0.277394	+	0.0901308i
$378$	−1.51752	−	13.6637i	−0.0780527	−	0.702786i
$379$	3.50425	+	2.54599i	0.180001	+	0.130778i	0.674137	−	0.738606i	$-0.264516\pi$
$379$	3.50425	+	2.54599i	0.180001	+	0.130778i	−0.494136	+	0.869385i	$0.664516\pi$
$380$	0.277042	−	0.123347i	0.0142119	−	0.00632756i
$381$	0.147891	+	0.0267104i	0.00757667	+	0.00136842i
$382$	8.53554	+	7.68543i	0.436716	+	0.393221i
$383$	−18.5415	+	1.94879i	−0.947428	+	0.0995787i	−0.565623	−	0.824664i	$-0.691364\pi$
$383$	−18.5415	+	1.94879i	−0.947428	+	0.0995787i	−0.381805	+	0.924243i	$0.624697\pi$
$384$	−0.655497	+	1.60322i	−0.0334507	+	0.0818141i
$385$	−2.24522	+	0.893758i	−0.114427	+	0.0455501i
$386$		−	4.35689i		−	0.221760i
$387$	2.64242	+	2.10004i	0.134322	+	0.106751i
$388$	6.73373	−	7.47856i	0.341853	−	0.379666i
$389$	−6.44589	−	30.3255i	−0.326820	−	1.53757i	−0.768179	−	0.640236i	$-0.778837\pi$
$389$	−6.44589	−	30.3255i	−0.326820	−	1.53757i	0.441359	−	0.897331i	$-0.354497\pi$
$390$	−0.00939972	−	0.305521i	−0.000475973	−	0.0154706i
$391$	4.37099	−	6.01615i	0.221050	−	0.304250i
$392$	4.87152	+	5.02676i	0.246049	+	0.253890i
$393$	−20.4138	−	1.51263i	−1.02974	−	0.0763021i
$394$	−1.74254	−	16.5792i	−0.0877881	−	0.835248i
$395$	−1.71012	−	2.96201i	−0.0860454	−	0.149035i
$396$	7.41505	+	6.63453i	0.372620	+	0.333398i
$397$	−0.560544	+	0.970891i	−0.0281329	+	0.0487276i	−0.879749	−	0.475438i	$-0.842289\pi$
$397$	−0.560544	+	0.970891i	−0.0281329	+	0.0487276i	0.851616	+	0.524166i	$0.175623\pi$
$398$	4.40565	−	3.20089i	0.220835	−	0.160446i
$399$	−4.50372	+	2.27627i	−0.225468	+	0.113956i
$400$	1.52165	−	4.68315i	0.0760824	−	0.234158i
$401$	4.70955	+	10.5778i	0.235184	+	0.528232i	0.992125	−	0.125251i	$-0.0399738\pi$
$401$	4.70955	+	10.5778i	0.235184	+	0.528232i	−0.756941	+	0.653483i	$0.773307\pi$
$402$	−16.2053	−	8.70298i	−0.808248	−	0.434065i
$403$	−0.666751	−	3.13682i	−0.0332133	−	0.156256i
$404$	5.14806	+	1.09425i	0.256126	+	0.0544412i
$405$	−1.97818	+	1.49331i	−0.0982965	+	0.0742033i
$406$	−23.3779	+	0.428776i	−1.16023	+	0.0212798i
$407$	−21.4359	+	10.7602i	−1.06254	+	0.533364i
$408$	−6.48344	−	8.36980i	−0.320978	−	0.414367i
$409$	7.37683	−	16.5686i	0.364761	−	0.819266i	−0.634177	−	0.773188i	$-0.718661\pi$
$409$	7.37683	−	16.5686i	0.364761	−	0.819266i	0.998938	−	0.0460783i	$-0.0146724\pi$
$410$	−0.622249	−	0.560276i	−0.0307307	−	0.0276700i
$411$	5.03905	+	14.0255i	0.248558	+	0.691827i
$412$	10.7155	+	7.78523i	0.527913	+	0.383551i
$413$	−9.91177	−	21.2068i	−0.487726	−	1.04352i
$414$	−1.68664	−	3.23664i	−0.0828940	−	0.159072i
$415$	0.241763	−	1.13741i	0.0118677	−	0.0558331i
$416$	0.260642	−	0.585412i	0.0127790	−	0.0287022i
$417$	2.19154	+	16.0775i	0.107320	+	0.787317i
$418$	1.32933	−	3.40171i	0.0650194	−	0.166383i
$419$		−	11.8865i		−	0.580692i	−0.956922	−	0.290346i	$-0.906230\pi$
$419$		−	11.8865i		−	0.580692i	0.956922	−	0.290346i	$-0.0937704\pi$
$420$	0.330610	−	1.21794i	0.0161321	−	0.0594292i
$421$	8.22765	+	25.3221i	0.400991	+	1.23412i	0.924197	+	0.381917i	$0.124736\pi$
$421$	8.22765	+	25.3221i	0.400991	+	1.23412i	−0.523206	+	0.852206i	$0.675264\pi$
$422$	15.3715	−	13.8405i	0.748272	−	0.673747i
$423$	4.55594	+	5.52200i	0.221517	+	0.268489i
$424$	8.15168	+	0.856777i	0.395881	+	0.0416087i
$425$	20.1402	+	22.3679i	0.976941	+	1.08500i
$426$	1.44283	−	19.4718i	0.0699052	−	0.943410i
$427$	7.06083	+	9.35279i	0.341697	+	0.452613i
$428$	6.80693			0.329025
$429$	−2.66660	−	2.53780i	−0.128744	−	0.122526i
$430$	0.154922	+	0.268333i	0.00747100	+	0.0129401i
$431$	4.19913	+	1.86957i	0.202265	+	0.0900543i	0.505369	−	0.862903i	$-0.331356\pi$
$431$	4.19913	+	1.86957i	0.202265	+	0.0900543i	−0.303104	+	0.952957i	$0.598023\pi$
$432$	−5.09566	+	1.01698i	−0.245165	+	0.0489295i
$433$	−5.62756	+	17.3199i	−0.270443	+	0.832339i	0.719946	+	0.694030i	$0.244167\pi$
$433$	−5.62756	+	17.3199i	−0.270443	+	0.832339i	−0.990389	+	0.138309i	$0.955833\pi$
$434$	1.14230	−	13.1911i	0.0548320	−	0.633192i
$435$	2.21899	+	3.58415i	0.106393	+	0.171847i
$436$	−3.52401	+	3.17303i	−0.168770	+	0.151961i
$437$	−0.896423	+	0.995579i	−0.0428817	+	0.0476250i
$438$	13.6599	+	14.2632i	0.652694	+	0.681522i
$439$	19.3916	+	11.1958i	0.925513	+	0.534345i	0.885390	−	0.464850i	$-0.153892\pi$
$439$	19.3916	+	11.1958i	0.925513	+	0.534345i	0.0401231	+	0.999195i	$0.487225\pi$
$440$	0.409762	+	0.816304i	0.0195346	+	0.0389158i
$441$	−4.50016	+	20.5122i	−0.214293	+	0.976769i
$442$	2.30234	+	3.16891i	0.109511	+	0.150729i
$443$	3.23742	−	15.2308i	0.153814	−	0.723639i	−0.831861	−	0.554984i	$-0.812724\pi$
$443$	3.23742	−	15.2308i	0.153814	−	0.723639i	0.985675	−	0.168655i	$-0.0539424\pi$
$444$	2.22625	−	12.3263i	0.105653	−	0.584982i
$445$	0.522645	−	4.97264i	0.0247758	−	0.235726i
$446$	5.15301	−	2.29427i	0.244002	−	0.108637i
$447$	−18.8426	−	15.9445i	−0.891224	−	0.754150i
$448$	1.73400	−	1.99831i	0.0819238	−	0.0944113i
$449$	10.9616	+	15.0873i	0.517309	+	0.712014i	0.985130	−	0.171809i	$-0.0549610\pi$
$449$	10.9616	+	15.0873i	0.517309	+	0.712014i	−0.467822	+	0.883823i	$0.654961\pi$
$450$	14.2335	−	3.95384i	0.670975	−	0.186386i
$451$	−10.0732	+	0.467175i	−0.474328	+	0.0219984i
$452$	−1.29273	+	0.746360i	−0.0608050	+	0.0351058i
$453$	5.06968	−	17.4071i	0.238194	−	0.817857i
$454$	7.42335	+	22.8467i	0.348395	+	1.07225i
$455$	−0.136116	+	0.446630i	−0.00638122	+	0.0209384i
$456$	1.00400	+	1.62167i	0.0470166	+	0.0759418i
$457$	−7.79806	−	17.5147i	−0.364778	−	0.819304i	−0.998937	−	0.0461017i	$-0.985320\pi$
$457$	−7.79806	−	17.5147i	−0.364778	−	0.819304i	0.634159	−	0.773203i	$-0.281347\pi$
$458$	25.3589	−	5.39020i	1.18494	−	0.251868i
$459$	10.1902	−	30.0825i	0.475637	−	1.40413i
$460$	−0.0350211	−	0.333203i	−0.00163287	−	0.0155357i
$461$	23.8811			1.11225			0.556126	−	0.831098i	$-0.312287\pi$
$461$	23.8811			1.11225			0.556126	+	0.831098i	$0.312287\pi$
$462$	−7.47688	−	13.2324i	−0.347856	−	0.615627i
$463$	−9.27277			−0.430942			−0.215471	−	0.976510i	$-0.569129\pi$
$463$	−9.27277			−0.430942			−0.215471	+	0.976510i	$0.569129\pi$
$464$	0.923771	+	8.78910i	0.0428850	+	0.408024i
$465$	−2.14982	+	1.03752i	−0.0996956	+	0.0481137i
$466$	−16.4864	+	3.50429i	−0.763716	+	0.162333i
$467$	−11.7726	−	26.4416i	−0.544769	−	1.22357i	−0.950827	−	0.309723i	$-0.899764\pi$
$467$	−11.7726	−	26.4416i	−0.544769	−	1.22357i	0.406058	−	0.913847i	$-0.366903\pi$
$468$	1.89594	−	0.318103i	0.0876399	−	0.0147043i
$469$	19.1809	+	20.5325i	0.885693	+	0.948104i
$470$	0.203076	+	0.625002i	0.00936718	+	0.0288292i
$471$	25.0624	+	7.29922i	1.15481	+	0.336330i
$472$	−7.66232	+	4.42384i	−0.352687	+	0.203624i
$473$	3.59849	+	0.987450i	0.165459	+	0.0454030i
$474$	17.0058	−	13.1731i	0.781103	−	0.605061i
$475$	−3.18722	−	4.38683i	−0.146240	−	0.201282i
$476$	5.27869	+	15.2864i	0.241949	+	0.700653i
$477$	11.3636	+	21.8065i	0.520303	+	0.998453i
$478$	12.5018	−	5.56615i	0.571818	−	0.254590i
$479$	3.33424	−	31.7232i	0.152345	−	1.44947i	−0.604880	−	0.796317i	$-0.706779\pi$
$479$	3.33424	−	31.7232i	0.152345	−	1.44947i	0.757225	−	0.653154i	$-0.226554\pi$
$480$	−0.469401	−	0.0847782i	−0.0214251	−	0.00386958i
$481$	−0.963505	+	4.53293i	−0.0439320	+	0.206684i
$482$	−1.86674	−	2.56934i	−0.0850275	−	0.117030i
$483$	0.854154	+	5.50925i	0.0388654	+	0.250680i
$484$	10.4200	+	3.52479i	0.473635	+	0.160218i
$485$	2.40010	+	1.38570i	0.108983	+	0.0629213i
$486$	−10.9863	−	11.0590i	−0.498349	−	0.501646i
$487$	12.8020	−	14.2181i	0.580114	−	0.644281i	−0.379637	−	0.925136i	$-0.623951\pi$
$487$	12.8020	−	14.2181i	0.580114	−	0.644281i	0.959750	+	0.280854i	$0.0906177\pi$
$488$	3.29160	−	2.96377i	0.149004	−	0.134164i
$489$	−31.2621	+	19.3548i	−1.41372	+	0.875255i
$490$	−1.07515	+	1.60009i	−0.0485705	+	0.0722846i
$491$	8.01785	−	24.6764i	0.361841	−	1.11363i	−0.590095	−	0.807334i	$-0.700910\pi$
$491$	8.01785	−	24.6764i	0.361841	−	1.11363i	0.951936	−	0.306297i	$-0.0990901\pi$
$492$	2.96292	−	4.35362i	0.133579	−	0.196276i
$493$	−49.3492	−	21.9717i	−2.22258	−	0.989555i
$494$	−0.352828	−	0.611116i	−0.0158745	−	0.0274954i
$495$	−1.36261	+	2.37731i	−0.0612448	+	0.106852i
$496$	−5.00442			−0.224705
$497$	−11.6293	+	27.4645i	−0.521645	+	1.23195i
$498$	7.29339	+	0.540429i	0.326825	+	0.0242172i
$499$	14.2687	+	15.8470i	0.638755	+	0.709410i	0.972408	−	0.233286i	$-0.0749480\pi$
$499$	14.2687	+	15.8470i	0.638755	+	0.709410i	−0.333653	+	0.942696i	$0.608281\pi$
$500$	2.71808	+	0.285681i	0.121556	+	0.0127761i
$501$	6.10033	+	3.27615i	0.272543	+	0.146368i
$502$	7.37430	−	6.63985i	0.329131	−	0.296351i
$503$	−10.3394	−	31.8215i	−0.461013	−	1.41885i	−0.863929	−	0.503614i	$-0.832003\pi$
$503$	−10.3394	−	31.8215i	−0.461013	−	1.41885i	0.402916	−	0.915237i	$-0.367997\pi$
$504$	7.87070	+	1.02569i	0.350589	+	0.0456879i
$505$			1.44942i			0.0644982i
$506$	−3.12041	−	2.55809i	−0.138719	−	0.113721i
$507$	21.6056	−	2.94509i	0.959539	−	0.130796i
$508$	−0.0352910	+	0.0792649i	−0.00156578	+	0.00351681i
$509$	1.20700	−	5.67847i	0.0534991	−	0.251694i	−0.943269	−	0.332031i	$-0.892266\pi$
$509$	1.20700	−	5.67847i	0.0534991	−	0.251694i	0.996768	+	0.0803369i	$0.0255996\pi$
$510$	1.88339	−	2.22572i	0.0833980	−	0.0985563i
$511$	−12.7735	−	27.3297i	−0.565067	−	1.20899i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−2.39222	+	5.19787i	−0.105619	+	0.229492i
$514$	15.5229	+	13.9769i	0.684685	+	0.616493i
$515$	−1.48361	+	3.33225i	−0.0653757	+	0.146836i
$516$	−1.54058	+	1.19337i	−0.0678202	+	0.0525352i
$517$	7.03004	+	3.63541i	0.309181	+	0.159885i
$518$	−9.26124	+	16.7427i	−0.406915	+	0.735631i
$519$	0.311616	+	1.27229i	0.0136784	+	0.0558474i
$520$	0.172619	+	0.0366914i	0.00756987	+	0.00160902i
$521$	1.69719	+	7.98464i	0.0743552	+	0.349814i	0.999560	−	0.0296540i	$-0.00944054\pi$
$521$	1.69719	+	7.98464i	0.0743552	+	0.349814i	−0.925205	+	0.379468i	$0.876107\pi$
$522$	−20.4505	+	16.8728i	−0.895095	+	0.738501i
$523$	2.40958	+	5.41201i	0.105364	+	0.236651i	0.958532	−	0.284985i	$-0.0919886\pi$
$523$	2.40958	+	5.41201i	0.105364	+	0.236651i	−0.853168	+	0.521636i	$0.825322\pi$
$524$	3.65204	−	11.2398i	0.159540	−	0.491013i
$525$	−22.5304	−	1.25453i	−0.983309	−	0.0547522i
$526$	15.6176	−	11.3468i	0.680959	−	0.494746i
$527$	15.2948	−	26.4913i	0.666251	−	1.15398i
$528$	−4.73892	+	3.24694i	−0.206235	+	0.141305i
$529$	−10.7600	−	18.6368i	−0.467825	−	0.810296i
$530$	0.235951	+	2.24492i	0.0102490	+	0.0975131i
$531$	−23.7594	−	11.8333i	−1.03107	−	0.513523i
$532$	−0.657902	−	2.83821i	−0.0285237	−	0.123052i
$533$	−1.14522	+	1.57626i	−0.0496048	+	0.0682752i
$534$	31.4321	−	0.967049i	1.36020	−	0.0418483i
$535$	0.389748	+	1.83362i	0.0168503	+	0.0792743i
$536$	7.10618	−	7.89221i	0.306940	−	0.340891i
$537$	0.879981	−	3.02148i	0.0379740	−	0.130386i
$538$		−	21.6384i		−	0.932897i
$539$	4.33314	+	22.8084i	0.186642	+	0.982428i
$540$	−0.565714	−	1.31442i	−0.0243445	−	0.0565635i
$541$	15.4635	−	1.62528i	0.664829	−	0.0698764i	0.233898	−	0.972261i	$-0.424852\pi$
$541$	15.4635	−	1.62528i	0.664829	−	0.0698764i	0.430931	+	0.902385i	$0.358185\pi$
$542$	17.0856	+	15.3840i	0.733890	+	0.660798i
$543$	−6.38452	+	35.3499i	−0.273986	+	1.51701i
$544$	5.58406	−	2.48618i	0.239415	−	0.106594i
$545$	−1.05651	−	0.767602i	−0.0452561	−	0.0328805i
$546$	−2.89891	−	0.468847i	−0.124062	−	0.0200648i
$547$	−17.7453	+	5.76579i	−0.758734	+	0.246527i	−0.662735	−	0.748854i	$-0.730604\pi$
$547$	−17.7453	+	5.76579i	−0.758734	+	0.246527i	−0.0959986	+	0.995381i	$0.530604\pi$
$548$	−8.55726	+	0.899404i	−0.365548	+	0.0384206i
$549$	12.8660	+	3.32152i	0.549108	+	0.141759i
$550$	12.7536	−	10.2013i	0.543816	−	0.434984i
$551$	8.42794	+	4.86588i	0.359043	+	0.207293i
$552$	2.04669	−	0.501283i	0.0871127	−	0.0213360i
$553$	−31.0591	+	10.7253i	−1.32077	+	0.456086i
$554$	−29.2451	−	9.50230i	−1.24250	−	0.403714i
$555$	3.44788	−	0.106078i	0.146354	−	0.00450278i
$556$	−9.31685	−	0.979240i	−0.395122	−	0.0415290i
$557$	−44.9497	+	9.55435i	−1.90458	+	0.404831i	−0.999779	−	0.0210059i	$-0.993313\pi$
$557$	−44.9497	+	9.55435i	−1.90458	+	0.404831i	−0.904800	+	0.425837i	$0.859980\pi$
$558$	−8.29171	−	12.5158i	−0.351016	−	0.529836i
$559$	0.583282	−	0.423779i	0.0246702	−	0.0179239i
$560$	0.637580	+	0.352679i	0.0269427	+	0.0149034i
$561$	−2.70464	−	35.0094i	−0.114190	−	1.47810i
$562$	−3.28077	+	5.68246i	−0.138391	+	0.239700i
$563$	2.94216	+	1.30993i	0.123997	+	0.0552072i	0.467798	−	0.883836i	$-0.345048\pi$
$563$	2.94216	+	1.30993i	0.123997	+	0.0552072i	−0.343800	+	0.939043i	$0.611714\pi$
$564$	−3.72235	+	1.79643i	−0.156739	+	0.0756432i
$565$	−0.275070	−	0.305496i	−0.0115723	−	0.0128523i
$566$	11.9900	−	16.5028i	0.503977	−	0.693665i
$567$	10.4756	+	21.3837i	0.439933	+	0.898030i
$568$	10.7211	+	3.48350i	0.449848	+	0.146165i
$569$	15.9791	+	3.39647i	0.669880	+	0.142387i	0.530282	−	0.847821i	$-0.322086\pi$
$569$	15.9791	+	3.39647i	0.669880	+	0.142387i	0.139597	+	0.990208i	$0.455419\pi$
$570$	−0.379352	+	0.363306i	−0.0158893	+	0.0152172i
$571$	36.1012	−	20.8430i	1.51079	−	0.872253i	0.510865	−	0.859661i	$-0.329325\pi$
$571$	36.1012	−	20.8430i	1.51079	−	0.872253i	0.999921	−	0.0125921i	$-0.00400830\pi$
$572$	1.78939	−	1.14680i	0.0748181	−	0.0479501i
$573$	−18.4141	−	7.52884i	−0.769261	−	0.314522i
$574$	−6.42014	+	4.84685i	−0.267972	+	0.202303i
$575$	−5.69743	+	1.85121i	−0.237599	+	0.0772007i
$576$	0.129580	−	2.99720i	0.00539915	−	0.124883i
$577$	−4.05864	+	38.6154i	−0.168963	+	1.60758i	0.501176	+	0.865345i	$0.332901\pi$
$577$	−4.05864	+	38.6154i	−0.168963	+	1.60758i	−0.670140	+	0.742235i	$0.733766\pi$
$578$	−2.12850	+	20.2513i	−0.0885338	+	0.842343i
$579$	2.55155	+	7.10190i	0.106039	+	0.295145i
$580$	−2.31467	+	0.752083i	−0.0961116	+	0.0312286i
$581$	−10.2872	−	4.35590i	−0.426784	−	0.180713i
$582$	−6.59652	+	16.1339i	−0.273435	+	0.668770i
$583$	21.0234	+	17.2348i	0.870701	+	0.713794i
$584$	−9.87460	+	5.70110i	−0.408614	+	0.235913i
$585$	0.194246	+	0.492506i	0.00803108	+	0.0203626i
$586$	8.71955	+	1.85340i	0.360201	+	0.0765631i
$587$	−19.6492	−	6.38441i	−0.811009	−	0.263513i	−0.125984	−	0.992032i	$-0.540209\pi$
$587$	−19.6492	−	6.38441i	−0.811009	−	0.263513i	−0.685025	+	0.728520i	$0.740209\pi$
$588$	−10.8846	−	5.34087i	−0.448874	−	0.220254i
$589$	−3.23917	+	4.45833i	−0.133468	+	0.183702i
$590$	−1.63040	−	1.81074i	−0.0671226	−	0.0745472i
$591$	12.5498	+	26.0043i	0.516230	+	1.06967i
$592$	6.60653	+	2.94142i	0.271527	+	0.120892i
$593$	−4.92618	+	8.53239i	−0.202294	+	0.350383i	−0.949267	−	0.314471i	$-0.898173\pi$
$593$	−4.92618	+	8.53239i	−0.202294	+	0.350383i	0.746973	+	0.664854i	$0.231506\pi$
$594$	−15.9723	−	6.47202i	−0.655350	−	0.265550i
$595$	−3.81555	+	2.29721i	−0.156422	+	0.0941766i
$596$	11.5293	−	8.37651i	0.472258	−	0.343115i
$597$	−5.30682	+	7.79769i	−0.217194	+	0.319138i
$598$	−0.762565	+	0.162088i	−0.0311836	+	0.00662828i
$599$	2.87618	+	0.302299i	0.117518	+	0.0123516i	0.163105	−	0.986609i	$-0.447849\pi$
$599$	2.87618	+	0.302299i	0.117518	+	0.0123516i	−0.0455871	+	0.998960i	$0.514516\pi$
$600$	0.262278	+	8.52486i	0.0107074	+	0.348026i
$601$	3.36832	+	1.09443i	0.137396	+	0.0446428i	0.376908	−	0.926251i	$-0.376987\pi$
$601$	3.36832	+	1.09443i	0.137396	+	0.0446428i	−0.239512	+	0.970894i	$0.576987\pi$
$602$	2.81369	−	0.971618i	0.114677	−	0.0396002i
$603$	31.5121	+	4.69577i	1.28327	+	0.191227i
$604$	9.06517	+	5.23378i	0.368856	+	0.212959i
$605$	−0.352871	+	3.00871i	−0.0143462	+	0.122321i
$606$	−9.03238	+	1.23122i	−0.366915	+	0.0500147i
$607$	−11.0904	+	1.16565i	−0.450146	+	0.0473123i	−0.326890	−	0.945063i	$-0.606001\pi$
$607$	−11.0904	+	1.16565i	−0.450146	+	0.0473123i	−0.123257	+	0.992375i	$0.539334\pi$
$608$	−1.04729	+	0.340286i	−0.0424733	+	0.0138004i
$609$	37.8558	−	14.3899i	1.53400	−	0.583108i
$610$	0.986836	+	0.716978i	0.0399558	+	0.0290296i
$611$	1.39696	−	0.621966i	0.0565149	−	0.0251621i
$612$	15.4699	+	9.84616i	0.625335	+	0.398007i
$613$	5.82568	+	5.24547i	0.235297	+	0.211862i	0.778341	−	0.627842i	$-0.216062\pi$
$613$	5.82568	+	5.24547i	0.235297	+	0.211862i	−0.543044	+	0.839704i	$0.682728\pi$
$614$	−18.0327	+	1.89532i	−0.727743	+	0.0764888i
$615$	1.34241	+	0.548860i	0.0541312	+	0.0221322i
$616$	8.44733	−	2.37541i	0.340353	−	0.0957080i
$617$		−	31.5067i		−	1.26841i	−0.773165	−	0.634205i	$-0.781327\pi$
$617$		−	31.5067i		−	1.26841i	0.773165	−	0.634205i	$-0.218673\pi$
$618$	−22.0259	−	6.41488i	−0.886013	−	0.258044i
$619$	8.37604	−	9.30253i	0.336661	−	0.373900i	−0.550915	−	0.834562i	$-0.685721\pi$
$619$	8.37604	−	9.30253i	0.336661	−	0.373900i	0.887576	+	0.460661i	$0.152388\pi$
$620$	−0.286541	−	1.34807i	−0.0115077	−	0.0541397i
$621$	4.64479	+	4.28809i	0.186389	+	0.172075i
$622$	−11.7247	+	16.1376i	−0.470117	+	0.647061i
$623$	−45.9496	−	14.0037i	−1.84093	−	0.561047i
$624$	−0.0820185	+	1.10689i	−0.00328337	+	0.0443109i
$625$	−2.49490	−	23.7374i	−0.0997959	−	0.949495i
$626$	12.2926	+	21.2914i	0.491311	+	0.850975i
$627$	−0.174687	+	6.32343i	−0.00697634	+	0.252533i
$628$	−7.53548	+	13.0518i	−0.300698	+	0.520825i
$629$	−35.7619	+	25.9826i	−1.42592	+	1.03599i
$630$	0.174361	+	2.17890i	0.00694670	+	0.0868096i
$631$	11.8671	−	36.5231i	0.472420	−	1.45396i	−0.376985	−	0.926219i	$-0.623039\pi$
$631$	11.8671	−	36.5231i	0.472420	−	1.45396i	0.849405	−	0.527741i	$-0.176961\pi$
$632$	5.05145	+	11.3457i	0.200936	+	0.451309i
$633$	−16.9506	+	31.5627i	−0.673726	+	1.25451i
$634$	−3.29061	−	15.4811i	−0.130687	−	0.614833i
$635$	−0.0233727	−	0.00496802i	−0.000927517	−	0.000197150i
$636$	−13.7893	+	3.37734i	−0.546782	+	0.133920i
$637$	3.96436	+	2.09889i	0.157074	+	0.0831609i
$638$	−13.4636	+	26.0355i	−0.533030	+	1.03076i
$639$	9.05152	+	32.5847i	0.358072	+	1.28903i
$640$	0.112013	−	0.251585i	0.00442769	−	0.00994475i
$641$	−17.1858	−	15.4741i	−0.678797	−	0.611192i	0.255872	−	0.966711i	$-0.417638\pi$
$641$	−17.1858	−	15.4741i	−0.678797	−	0.611192i	−0.934669	+	0.355519i	$0.884304\pi$
$642$	−11.0956	+	3.98639i	−0.437907	+	0.157330i
$643$	−2.06467	−	1.50007i	−0.0814226	−	0.0591570i	0.546329	−	0.837570i	$-0.316025\pi$
$643$	−2.06467	−	1.50007i	−0.0814226	−	0.0591570i	−0.627752	+	0.778414i	$0.716025\pi$
$644$	−3.20677	−	0.277694i	−0.126364	−	0.0109427i
$645$	−0.409674	−	0.346665i	−0.0161309	−	0.0136499i
$646$	1.39946	−	6.58394i	0.0550610	−	0.259041i
$647$	11.2366	−	25.2378i	0.441756	−	0.992199i	−0.546227	−	0.837637i	$-0.683937\pi$
$647$	11.2366	−	25.2378i	0.441756	−	0.992199i	0.987983	−	0.154563i	$-0.0493968\pi$
$648$	7.71055	−	4.64192i	0.302899	−	0.182352i
$649$	−29.2945	−	1.71201i	−1.14991	−	0.0672022i
$650$		−	3.15547i		−	0.123768i
$651$	5.86319	+	22.1709i	0.229796	+	0.868948i
$652$	−6.55992	−	20.1894i	−0.256906	−	0.790677i
$653$	8.39627	−	7.56003i	0.328571	−	0.295847i	−0.488290	−	0.872682i	$-0.662379\pi$
$653$	8.39627	−	7.56003i	0.328571	−	0.295847i	0.816861	+	0.576835i	$0.195712\pi$
$654$	3.88603	−	7.23596i	0.151956	−	0.282948i
$655$	3.23684	+	0.340205i	0.126474	+	0.0132929i
$656$	2.03445	+	2.25949i	0.0794321	+	0.0882183i
$657$	−30.6192	−	15.2499i	−1.19457	−	0.594954i
$658$	6.26576	−	0.774973i	0.244265	−	0.0302116i
$659$	34.2568			1.33445			0.667227	−	0.744855i	$-0.267481\pi$
$659$	34.2568			1.33445			0.667227	+	0.744855i	$0.267481\pi$
$660$	−1.14599	−	1.09064i	−0.0446074	−	0.0424530i
$661$	−14.5364	−	25.1779i	−0.565402	−	0.979306i	−0.997012	−	0.0772451i	$-0.975388\pi$
$661$	−14.5364	−	25.1779i	−0.565402	−	0.979306i	0.431610	−	0.902060i	$-0.357946\pi$
$662$	−4.57355	−	2.03627i	−0.177756	−	0.0791421i
$663$	−5.60874	−	3.81711i	−0.217825	−	0.148244i
$664$	−1.30479	+	4.01573i	−0.0506356	+	0.155840i
$665$	0.726876	−	0.339732i	0.0281870	−	0.0131742i
$666$	3.58988	+	21.3962i	0.139105	+	0.829085i
$667$	7.98995	−	7.19419i	0.309372	−	0.278560i
$668$	−2.67505	+	2.97094i	−0.103501	+	0.114949i
$669$	−7.05600	+	6.75754i	−0.272801	+	0.261262i
$670$	2.53285	+	1.46234i	0.0978525	+	0.0564952i
$671$	14.5230	−	2.21075i	0.560653	−	0.0853450i
$672$	−1.65620	+	4.27282i	−0.0638895	+	0.164828i
$673$	6.21543	+	8.55481i	0.239587	+	0.329764i	0.911831	−	0.410567i	$-0.134669\pi$
$673$	6.21543	+	8.55481i	0.239587	+	0.329764i	−0.672243	+	0.740330i	$0.734669\pi$
$674$	−7.22544	+	33.9930i	−0.278314	+	1.30936i
$675$	−20.8857	+	14.7806i	−0.803891	+	0.568905i
$676$	−1.31595	+	12.5204i	−0.0506133	+	0.481554i
$677$	−39.3125	+	17.5031i	−1.51090	+	0.672697i	−0.984153	−	0.177323i	$-0.943256\pi$
$677$	−39.3125	+	17.5031i	−1.51090	+	0.672697i	−0.526750	+	0.850020i	$0.676590\pi$
$678$	1.67011	−	1.97367i	0.0641402	−	0.0757982i
$679$	17.4499	−	20.1098i	0.669667	−	0.771743i
$680$	0.989447	+	1.36186i	0.0379436	+	0.0522248i
$681$	−25.4802	−	32.8937i	−0.976404	−	1.26049i
$682$	−13.8654	−	9.12336i	−0.530935	−	0.349351i
$683$	−7.54826	+	4.35799i	−0.288826	+	0.166754i	−0.637412	−	0.770523i	$-0.719995\pi$
$683$	−7.54826	+	4.35799i	−0.288826	+	0.166754i	0.348586	+	0.937277i	$0.386662\pi$
$684$	−2.58627	−	2.05541i	−0.0988886	−	0.0785907i
$685$	−0.732245	−	2.25362i	−0.0279776	−	0.0861063i
$686$	13.1306	+	13.0610i	0.501327	+	0.498670i
$687$	−38.1793	+	23.6374i	−1.45663	+	0.901821i
$688$	−0.457617	−	1.02783i	−0.0174465	−	0.0391855i
$689$	5.13770	−	1.09205i	0.195731	−	0.0416039i
$690$	0.252222	+	0.522625i	0.00960191	+	0.0198960i
$691$	0.153012	+	1.45581i	0.00582086	+	0.0553818i	0.997047	−	0.0767970i	$-0.0244693\pi$
$691$	0.153012	+	1.45581i	0.00582086	+	0.0553818i	−0.991226	+	0.132179i	$0.957803\pi$
$692$	−0.756270			−0.0287491
$693$	19.9370	+	17.1906i	0.757343	+	0.653017i
$694$	−5.69459			−0.216164
$695$	−0.269676	−	2.56580i	−0.0102294	−	0.0973263i
$696$	−6.65300	−	13.7856i	−0.252181	−	0.522541i
$697$	−18.1786	+	3.86399i	−0.688565	+	0.146359i
$698$	−0.656690	−	1.47495i	−0.0248561	−	0.0558276i
$699$	24.8212	−	15.3671i	0.938824	−	0.581239i
$700$	3.79801	−	12.4622i	0.143551	−	0.471027i
$701$	2.37893	+	7.32158i	0.0898508	+	0.276532i	0.985878	−	0.167468i	$-0.0535590\pi$
$701$	2.37893	+	7.32158i	0.0898508	+	0.276532i	−0.896027	+	0.444000i	$0.853559\pi$
$702$	−2.90416	+	1.62885i	−0.109611	+	0.0614771i
$703$	6.89660	−	3.98176i	0.260110	−	0.150175i
$704$	−1.16993	−	3.10343i	−0.0440932	−	0.116965i
$705$	−0.697046	−	0.899850i	−0.0262523	−	0.0338903i
$706$	2.27594	+	3.13256i	0.0856561	+	0.117896i
$707$	13.6713	+	2.64486i	0.514162	+	0.0994704i
$708$	9.89913	−	11.6984i	0.372032	−	0.439652i
$709$	41.7752	−	18.5995i	1.56890	−	0.698519i	0.575996	−	0.817452i	$-0.304614\pi$
$709$	41.7752	−	18.5995i	1.56890	−	0.698519i	0.992902	+	0.118933i	$0.0379475\pi$
$710$	−0.324506	+	3.08746i	−0.0121785	+	0.115870i
$711$	−20.0055	+	31.4319i	−0.750265	+	1.17879i
$712$	−3.77483	+	17.7592i	−0.141468	+	0.665554i
$713$	3.57860	+	4.92552i	0.134020	+	0.184462i
$714$	−17.5568	−	21.8261i	−0.657046	−	0.816822i
$715$	0.411376	+	0.416355i	0.0153846	+	0.0155708i
$716$	1.57351	+	0.908464i	0.0588047	+	0.0339509i
$717$	−17.1186	+	16.3945i	−0.639308	+	0.612265i
$718$	8.86611	−	9.84681i	0.330880	−	0.367480i
$719$	−19.1451	+	17.2383i	−0.713991	+	0.642881i	−0.943862	−	0.330340i	$-0.892836\pi$
$719$	−19.1451	+	17.2383i	−0.713991	+	0.642881i	0.229870	+	0.973221i	$0.426170\pi$
$720$	0.814792	−	0.136707i	0.0303655	−	0.00509476i
$721$	28.7234	+	20.0744i	1.06971	+	0.747611i
$722$	5.49660	−	16.9168i	0.204562	−	0.629578i
$723$	4.54756	+	3.09490i	0.169125	+	0.115101i
$724$	−18.9464	−	8.43550i	−0.704139	−	0.313503i
$725$	21.7586	+	37.6871i	0.808096	+	1.39966i
$726$	−19.0492	+	0.356766i	−0.706983	+	0.0132408i
$727$	48.6736			1.80521			0.902603	−	0.430474i	$-0.141654\pi$
$727$	48.6736			1.80521			0.902603	+	0.430474i	$0.141654\pi$
$728$	0.661076	−	1.56124i	0.0245011	−	0.0578634i
$729$	24.3847	+	11.5926i	0.903135	+	0.429356i
$730$	−2.10113	−	2.33354i	−0.0777664	−	0.0863684i
$731$	6.83948	+	0.718859i	0.252967	+	0.0265880i
$732$	−3.62975	+	6.75874i	−0.134159	+	0.249810i
$733$	31.1698	−	28.0654i	1.15128	−	1.03662i	0.152452	−	0.988311i	$-0.451283\pi$
$733$	31.1698	−	28.0654i	1.15128	−	1.03662i	0.998832	−	0.0483098i	$-0.0153835\pi$
$734$	2.89620	+	8.91357i	0.106901	+	0.329006i
$735$	0.815474	−	3.23786i	0.0300792	−	0.119430i
$736$			1.21658i			0.0448438i
$737$	34.0766	−	8.91147i	1.25523	−	0.328258i
$738$	−2.28003	+	8.83177i	−0.0839292	+	0.325102i
$739$	−7.30858	+	16.4153i	−0.268851	+	0.603848i	−0.996636	−	0.0819568i	$-0.973883\pi$
$739$	−7.30858	+	16.4153i	−0.268851	+	0.603848i	0.727785	+	0.685805i	$0.240550\pi$
$740$	−0.414072	+	1.94806i	−0.0152216	+	0.0716120i
$741$	0.933015	+	0.789514i	0.0342752	+	0.0290035i
$742$	21.6053	+	1.87094i	0.793154	+	0.0686842i
$743$	−16.6041	−	12.0636i	−0.609145	−	0.442570i	0.239968	−	0.970781i	$-0.422863\pi$
$743$	−16.6041	−	12.0636i	−0.609145	−	0.442570i	−0.849113	+	0.528211i	$0.822863\pi$
$744$	8.15740	−	2.93077i	0.299065	−	0.107447i
$745$	2.91657	+	2.62609i	0.106855	+	0.0962124i
$746$	−5.30198	+	11.9084i	−0.194119	+	0.435999i
$747$	−12.2050	+	3.39036i	−0.446558	+	0.124047i
$748$	20.0039	+	3.29177i	0.731415	+	0.120359i
$749$	18.0064	−	0.330257i	0.657940	−	0.0120673i
$750$	−4.59788	+	1.12613i	−0.167891	+	0.0411206i
$751$	5.82008	+	1.23710i	0.212378	+	0.0451422i	0.312872	−	0.949795i	$-0.398709\pi$
$751$	5.82008	+	1.23710i	0.212378	+	0.0451422i	−0.100494	+	0.994938i	$0.532042\pi$
$752$	−0.496136	−	2.33414i	−0.0180922	−	0.0851172i
$753$	−8.13187	+	15.1419i	−0.296342	+	0.551801i
$754$	2.30343	+	5.17359i	0.0838859	+	0.188411i
$755$	−0.890802	+	2.74161i	−0.0324196	+	0.0997773i
$756$	−13.4302	+	2.93745i	−0.488453	+	0.106834i
$757$	29.7626	−	21.6238i	1.08174	−	0.785930i	0.103754	−	0.994603i	$-0.466914\pi$
$757$	29.7626	−	21.6238i	1.08174	−	0.785930i	0.977985	+	0.208673i	$0.0669145\pi$
$758$	2.16574	−	3.75118i	0.0786634	−	0.136249i
$759$	6.58450	+	2.34236i	0.239002	+	0.0850222i
$760$	−0.151630	−	0.262631i	−0.00550020	−	0.00952662i
$761$	−1.46847	−	13.9716i	−0.0532320	−	0.506469i	−0.988357	−	0.152151i	$-0.951380\pi$
$761$	−1.46847	−	13.9716i	−0.0532320	−	0.506469i	0.935125	−	0.354317i	$-0.115287\pi$
$762$	0.0111053	−	0.149873i	0.000402303	−	0.00542931i
$763$	−9.16814	+	8.56462i	−0.331909	+	0.310060i
$764$	6.75112	−	9.29212i	0.244247	−	0.336177i
$765$	−1.76654	+	4.73099i	−0.0638695	+	0.171049i
$766$	3.87623	+	18.2362i	0.140054	+	0.658902i
$767$	−3.79378	+	4.21342i	−0.136986	+	0.152138i
$768$	1.66296	+	0.484323i	0.0600068	+	0.0174765i
$769$			46.4499i			1.67503i	0.546416	+	0.837514i	$0.315992\pi$
$769$			46.4499i			1.67503i	−0.546416	+	0.837514i	$0.684008\pi$
$770$	1.12355	+	2.13949i	0.0404900	+	0.0771020i
$771$	−33.4883	−	13.6921i	−1.20605	−	0.493108i
$772$	−4.33302	+	0.455419i	−0.155949	+	0.0163909i
$773$	8.66828	+	7.80495i	0.311776	+	0.280725i	0.810131	−	0.586248i	$-0.199396\pi$
$773$	8.66828	+	7.80495i	0.311776	+	0.280725i	−0.498355	+	0.866973i	$0.666062\pi$
$774$	1.81232	−	2.84746i	0.0651426	−	0.102350i
$775$	−22.5121	+	10.0230i	−0.808658	+	0.360038i
$776$	−8.14146	−	5.91512i	−0.292261	−	0.212340i
$777$	5.29106	−	32.7149i	0.189816	−	1.17364i
$778$	−29.4856	+	9.58047i	−1.05711	+	0.343476i
$779$	3.32976	−	0.349972i	0.119301	−	0.0125390i
$780$	−0.302864	+	0.0412838i	−0.0108443	+	0.00147820i
$781$	23.3537	+	29.1968i	0.835662	+	1.04474i
$782$	−6.44008	−	3.71818i	−0.230297	−	0.132962i
$783$	23.4539	−	39.4799i	0.838172	−	1.41089i
$784$	4.49001	−	5.37027i	0.160357	−	0.191795i
$785$	−3.94731	−	1.28256i	−0.140885	−	0.0457765i
$786$	0.629480	+	20.4601i	0.0224528	+	0.729788i
$787$	31.0394	+	3.26238i	1.10644	+	0.116291i	0.640082	−	0.768307i	$-0.278900\pi$
$787$	31.0394	+	3.26238i	1.10644	+	0.116291i	0.466355	+	0.884598i	$0.345567\pi$
$788$	−16.3062	+	3.46600i	−0.580886	+	0.123471i
$789$	−18.8122	+	27.6420i	−0.669731	+	0.984082i
$790$	−2.76703	+	2.01037i	−0.0984465	+	0.0715256i
$791$	−3.38346	+	2.03707i	−0.120302	+	0.0724299i
$792$	5.82310	−	8.06793i	0.206915	−	0.286681i
$793$	1.41917	−	2.45808i	0.0503963	−	0.0872889i
$794$	1.02417	+	0.455988i	0.0363463	+	0.0161824i
$795$	−1.69932	−	3.52113i	−0.0602686	−	0.124882i
$796$	−3.64387	−	4.04693i	−0.129154	−	0.143440i
$797$	15.3391	−	21.1125i	0.543339	−	0.747842i	−0.445751	−	0.895157i	$-0.647063\pi$
$797$	15.3391	−	21.1125i	0.543339	−	0.747842i	0.989090	+	0.147315i	$0.0470632\pi$
$798$	2.73457	+	4.24111i	0.0968027	+	0.150134i
$799$	13.8723	+	4.50738i	0.490766	+	0.159460i
$800$	−4.81655	−	1.02379i	−0.170291	−	0.0361964i
$801$	−50.6693	+	19.9841i	−1.79031	+	0.706105i
$802$	10.0276	−	5.78944i	0.354087	−	0.204432i
$803$	−37.7524	−	2.20630i	−1.33225	−	0.0778587i
$804$	−6.96138	+	17.0262i	−0.245509	+	0.600470i
$805$	−0.108808	−	0.879725i	−0.00383497	−	0.0310062i
$806$	−3.04994	+	0.990986i	−0.107430	+	0.0349060i
$807$	12.6722	+	35.2714i	0.446084	+	1.24161i
$808$	0.550141	−	5.23424i	0.0193539	−	0.184140i
$809$	−4.81944	+	45.8539i	−0.169443	+	1.61214i	0.497796	+	0.867294i	$0.334143\pi$
$809$	−4.81944	+	45.8539i	−0.169443	+	1.61214i	−0.667239	+	0.744844i	$0.732524\pi$
$810$	1.69191	+	1.81125i	0.0594476	+	0.0636408i
$811$	13.2059	−	4.29084i	0.463720	−	0.150672i	−0.0678331	−	0.997697i	$-0.521609\pi$
$811$	13.2059	−	4.29084i	0.463720	−	0.150672i	0.531553	+	0.847025i	$0.321609\pi$
$812$	2.87009	+	23.2050i	0.100720	+	0.814337i
$813$	−36.8596	−	15.0705i	−1.29272	−	0.528546i
$814$	12.9419	+	20.1937i	0.453615	+	0.707790i
$815$	5.06292	−	2.92308i	0.177346	−	0.102391i
$816$	−7.64624	+	7.32281i	−0.267672	+	0.256350i
$817$	−1.21187	−	0.257590i	−0.0423978	−	0.00901194i
$818$	−17.2490	−	5.60453i	−0.603096	−	0.195958i
$819$	4.99991	−	0.933467i	0.174711	−	0.0326180i
$820$	−0.492164	+	0.677405i	−0.0171871	+	0.0236560i
$821$	6.39806	+	7.10577i	0.223294	+	0.247993i	0.844374	−	0.535754i	$-0.179973\pi$
$821$	6.39806	+	7.10577i	0.223294	+	0.247993i	−0.621080	+	0.783747i	$0.713306\pi$
$822$	13.4219	−	6.47751i	0.468144	−	0.225929i
$823$	−13.8919	−	6.18509i	−0.484243	−	0.215599i	0.150070	−	0.988675i	$-0.452050\pi$
$823$	−13.8919	−	6.18509i	−0.484243	−	0.215599i	−0.634313	+	0.773077i	$0.718717\pi$
$824$	6.62252	−	11.4705i	0.230706	−	0.399595i
$825$	−14.8147	+	24.0975i	−0.515780	+	0.838966i
$826$	−20.0546	+	12.0742i	−0.697787	+	0.420115i
$827$	14.2074	−	10.3223i	0.494039	−	0.358940i	−0.312697	−	0.949853i	$-0.601232\pi$
$827$	14.2074	−	10.3223i	0.494039	−	0.358940i	0.806735	+	0.590913i	$0.201232\pi$
$828$	−3.04261	+	2.01573i	−0.105738	+	0.0700513i
$829$	0.242717	−	0.0515910i	0.00842990	−	0.00179183i	−0.203695	−	0.979034i	$-0.565295\pi$
$829$	0.242717	−	0.0515910i	0.00842990	−	0.00179183i	0.212125	+	0.977243i	$0.431962\pi$
$830$	−1.15645	−	0.121548i	−0.0401409	−	0.00421898i
$831$	53.2355	−	1.63786i	1.84672	−	0.0568166i
$832$	−0.609450	−	0.198022i	−0.0211289	−	0.00686519i
$833$	14.7054	+	40.1812i	0.509513	+	1.39220i
$834$	15.7603	−	3.86009i	0.545735	−	0.133664i
$835$	−0.953466	−	0.550484i	−0.0329961	−	0.0190503i
$836$	−3.52203	−	0.966468i	−0.121812	−	0.0334260i
$837$	20.8455	+	15.5453i	0.720527	+	0.537325i
$838$	−11.8213	+	1.24247i	−0.408362	+	0.0429205i
$839$	−15.1848	+	4.93383i	−0.524236	+	0.170335i	−0.559167	−	0.829055i	$-0.688879\pi$
$839$	−15.1848	+	4.93383i	−0.524236	+	0.170335i	0.0349307	+	0.999390i	$0.488879\pi$
$840$	−1.24582	−	0.201490i	−0.0429850	−	0.00695206i
$841$	−39.7240	−	28.8612i	−1.36979	−	0.995213i
$842$	24.3234	−	10.8295i	0.838238	−	0.373208i
$843$	2.01993	−	11.1840i	0.0695701	−	0.385197i
$844$	−15.3715	−	13.8405i	−0.529108	−	0.476411i
$845$	−3.44803	+	0.362403i	−0.118616	+	0.0124670i
$846$	5.01552	−	5.10819i	0.172437	−	0.175623i
$847$	27.7350	+	8.81860i	0.952987	+	0.303011i
$848$		−	8.19659i		−	0.281472i
$849$	−9.87952	+	33.9220i	−0.339064	+	1.16420i
$850$	20.1402	−	22.3679i	0.690802	−	0.767213i
$851$	−1.82921	−	8.60575i	−0.0627045	−	0.295001i
$852$	−19.5159	+	0.600431i	−0.668604	+	0.0205704i
$853$	−24.3236	+	33.4786i	−0.832825	+	1.14628i	0.154566	+	0.987982i	$0.450602\pi$
$853$	−24.3236	+	33.4786i	−0.832825	+	1.14628i	−0.987391	+	0.158303i	$0.949398\pi$
$854$	8.56349	−	7.99978i	0.293037	−	0.273747i
$855$	0.405594	−	0.814366i	0.0138710	−	0.0278507i
$856$	−0.711518	−	6.76964i	−0.0243192	−	0.231381i
$857$	−27.7853	−	48.1256i	−0.949128	−	1.64394i	−0.747267	−	0.664524i	$-0.768634\pi$
$857$	−27.7853	−	48.1256i	−0.949128	−	1.64394i	−0.201861	−	0.979414i	$-0.564699\pi$
$858$	−2.24517	+	2.91726i	−0.0766487	+	0.0995936i
$859$	24.3875	−	42.2404i	0.832092	−	1.44123i	−0.0642847	−	0.997932i	$-0.520477\pi$
$859$	24.3875	−	42.2404i	0.832092	−	1.44123i	0.896376	−	0.443294i	$-0.146190\pi$
$860$	0.250669	−	0.182122i	0.00854774	−	0.00621030i
$861$	7.62660	−	11.6604i	0.259914	−	0.397386i
$862$	1.42040	−	4.37155i	0.0483792	−	0.148896i
$863$	−17.0292	−	38.2483i	−0.579682	−	1.30199i	−0.930756	−	0.365640i	$-0.880850\pi$
$863$	−17.0292	−	38.2483i	−0.579682	−	1.30199i	0.351074	−	0.936348i	$-0.385817\pi$
$864$	1.54405	+	4.96144i	0.0525296	+	0.168792i
$865$	−0.0433021	−	0.203721i	−0.00147232	−	0.00692671i
$866$	17.8132	+	3.78632i	0.605318	+	0.128664i
$867$	−8.39037	−	34.2570i	−0.284952	−	1.16343i
$868$	−13.2382	+	0.242803i	−0.449334	+	0.00824127i
$869$	−6.68824	+	40.6441i	−0.226883	+	1.37876i
$870$	3.33256	−	2.58148i	0.112985	−	0.0875205i
$871$	2.76803	−	6.21709i	0.0937910	−	0.210658i
$872$	3.52401	+	3.17303i	0.119338	+	0.107452i
$873$	1.30401	−	30.1620i	0.0441341	−	1.02083i
$874$	1.08383	+	0.787446i	0.0366610	+	0.0266358i
$875$	7.20401	+	0.623840i	0.243540	+	0.0210896i
$876$	12.7572	−	15.0760i	0.431026	−	0.509369i
$877$	9.78033	−	46.0128i	0.330258	−	1.55374i	−0.429213	−	0.903203i	$-0.641209\pi$
$877$	9.78033	−	46.0128i	0.330258	−	1.55374i	0.759472	−	0.650540i	$-0.225458\pi$
$878$	9.10746	−	20.4557i	0.307362	−	0.690346i
$879$	−15.2986	+	2.08537i	−0.516010	+	0.0703379i
$880$	0.769001	−	0.492844i	0.0259230	−	0.0166138i
$881$		−	40.9648i		−	1.38014i	−0.723744	−	0.690069i	$-0.757580\pi$
$881$		−	40.9648i		−	1.38014i	0.723744	−	0.690069i	$-0.242420\pi$
$882$	20.8702	+	2.33140i	0.702736	+	0.0785023i
$883$	8.15181	+	25.0887i	0.274330	+	0.844302i	0.989396	+	0.145245i	$0.0463969\pi$
$883$	8.15181	+	25.0887i	0.274330	+	0.844302i	−0.715065	+	0.699058i	$0.753603\pi$
$884$	2.91089	−	2.62097i	0.0979037	−	0.0881529i
$885$	3.71806	+	1.99676i	0.124981	+	0.0671204i
$886$	−15.4858	−	1.62762i	−0.520256	−	0.0546811i
$887$	−7.98764	−	8.87117i	−0.268199	−	0.297865i	0.593969	−	0.804488i	$-0.297560\pi$
$887$	−7.98764	−	8.87117i	−0.268199	−	0.297865i	−0.862168	+	0.506623i	$0.830894\pi$
$888$	−12.4915	−	0.925601i	−0.419188	−	0.0310611i
$889$	−0.0895097	+	0.211392i	−0.00300206	+	0.00708986i
$890$	−5.00003			−0.167601
$891$	29.8257	+	1.19571i	0.999197	+	0.0400578i
$892$	−2.82034	−	4.88497i	−0.0944318	−	0.163561i
$893$	−2.40056	−	1.06880i	−0.0803318	−	0.0357660i
$894$	−13.8876	+	20.4060i	−0.464471	+	0.682479i
$895$	−0.154623	+	0.475880i	−0.00516847	+	0.0159069i
$896$	−2.16862	−	1.51562i	−0.0724484	−	0.0506333i
$897$	1.14809	−	0.710796i	0.0383335	−	0.0237328i
$898$	13.8589	−	12.4786i	0.462476	−	0.416416i
$899$	29.5934	−	32.8667i	0.986994	−	1.09617i
$900$	−5.41999	−	13.7423i	−0.180666	−	0.458075i
$901$	43.3894	+	25.0509i	1.44551	+	0.834566i
$902$	1.51755	+	9.96917i	0.0505289	+	0.331937i
$903$	−4.01740	+	3.23157i	−0.133691	+	0.107540i
$904$	0.877398	+	1.20764i	0.0291818	+	0.0401653i
$905$	1.18749	−	5.58671i	0.0394735	−	0.185708i
$906$	−17.8417	−	3.22237i	−0.592750	−	0.107056i
$907$	−0.751126	+	7.14648i	−0.0249407	+	0.237295i	0.974949	+	0.222429i	$0.0713987\pi$
$907$	−0.751126	+	7.14648i	−0.0249407	+	0.237295i	−0.999890	+	0.0148656i	$0.995268\pi$
$908$	21.9456	−	9.77081i	0.728291	−	0.324256i
$909$	14.0021	−	7.29662i	0.464420	−	0.242014i
$910$	0.458412	+	0.0886849i	0.0151962	+	0.00293988i
$911$	−27.3013	−	37.5770i	−0.904531	−	1.24498i	−0.969000	−	0.247061i	$-0.920535\pi$
$911$	−27.3013	−	37.5770i	−0.904531	−	1.24498i	0.0644688	−	0.997920i	$-0.479465\pi$
$912$	1.50784	−	1.16801i	0.0499297	−	0.0386767i
$913$	−10.9360	+	8.74743i	−0.361930	+	0.289498i
$914$	−16.6037	+	9.58613i	−0.549200	+	0.317081i
$915$	−2.02847	−	0.590776i	−0.0670592	−	0.0195304i
$916$	−8.01141	−	24.6566i	−0.264704	−	0.814676i
$917$	9.11542	−	29.9099i	0.301018	−	0.987713i
$918$	−30.9829	−	6.98987i	−1.02259	−	0.230700i
$919$	7.05541	+	15.8467i	0.232737	+	0.522735i	0.991727	−	0.128367i	$-0.0409736\pi$
$919$	7.05541	+	15.8467i	0.232737	+	0.522735i	−0.758990	+	0.651102i	$0.774307\pi$
$920$	−0.327717	+	0.0696584i	−0.0108045	+	0.00229657i
$921$	28.2841	−	13.6501i	0.931994	−	0.449785i
$922$	−2.49625	−	23.7502i	−0.0822097	−	0.782173i
$923$	7.22380			0.237774
$924$	−12.3784	+	8.81908i	−0.407218	+	0.290126i
$925$	35.6103			1.17086
$926$	0.969268	+	9.22197i	0.0318521	+	0.303053i
$927$	39.6599	−	2.44269i	1.30260	−	0.0802284i
$928$	8.64439	−	1.83742i	0.283766	−	0.0603163i
$929$	22.8077	+	51.2269i	0.748296	+	1.68070i	0.732446	+	0.680826i	$0.238379\pi$
$929$	22.8077	+	51.2269i	0.748296	+	1.68070i	0.0158503	+	0.999874i	$0.494954\pi$
$930$	1.25655	+	2.02959i	0.0412039	+	0.0665530i
$931$	−1.87806	−	7.47603i	−0.0615508	−	0.245017i
$932$	5.20838	+	16.0298i	0.170606	+	0.525072i
$933$	9.66091	−	33.1714i	0.316284	−	1.08598i
$934$	−25.0662	+	14.4720i	−0.820190	+	0.473537i
$935$	0.258652	+	5.57704i	0.00845882	+	0.182389i
$936$	−0.514540	−	1.85230i	−0.0168183	−	0.0605444i
$937$	−16.3941	−	22.5645i	−0.535572	−	0.737151i	0.452395	−	0.891818i	$-0.350570\pi$
$937$	−16.3941	−	22.5645i	−0.535572	−	0.737151i	−0.987967	+	0.154666i	$0.950570\pi$
$938$	18.4151	−	21.2221i	0.601274	−	0.692926i
$939$	−32.5064	−	27.5068i	−1.06081	−	0.897652i
$940$	0.600351	−	0.267294i	0.0195813	−	0.00871816i
$941$	2.62505	−	24.9757i	0.0855743	−	0.814186i	−0.864599	−	0.502463i	$-0.832427\pi$
$941$	2.62505	−	24.9757i	0.0855743	−	0.814186i	0.950173	−	0.311723i	$-0.100906\pi$
$942$	4.63950	−	25.6881i	0.151163	−	0.836962i
$943$	0.769054	−	3.61812i	0.0250439	−	0.117822i
$944$	5.20054	+	7.15793i	0.169263	+	0.232971i
$945$	−1.56026	−	3.44959i	−0.0507553	−	0.112215i
$946$	0.605896	−	3.68200i	0.0196994	−	0.119712i
$947$	31.8795	+	18.4056i	1.03594	+	0.598102i	0.918682	−	0.394999i	$-0.129255\pi$
$947$	31.8795	+	18.4056i	1.03594	+	0.598102i	0.117262	+	0.993101i	$0.462588\pi$
$948$	−14.8785	−	15.5357i	−0.483232	−	0.504576i
$949$	−4.88913	+	5.42993i	−0.158708	+	0.176263i
$950$	−4.02964	+	3.62831i	−0.130739	+	0.117718i
$951$	14.4301	+	23.3077i	0.467929	+	0.755804i
$952$	14.6509	−	6.84765i	0.474839	−	0.221933i
$953$	−4.53556	+	13.9590i	−0.146921	+	0.452177i	−0.997253	−	0.0740700i	$-0.976401\pi$
$953$	−4.53556	+	13.9590i	−0.146921	+	0.452177i	0.850332	+	0.526247i	$0.176401\pi$
$954$	20.4993	−	13.5807i	0.663688	−	0.439693i
$955$	2.88962	+	1.28654i	0.0935060	+	0.0416316i
$956$	−6.84245	−	11.8515i	−0.221301	−	0.383304i
$957$	6.69890	−	50.3237i	0.216545	−	1.62673i
$958$	−31.8979			−1.03058
$959$	−22.5929	+	2.79438i	−0.729564	+	0.0902352i
$960$	−0.0352480	+	0.475691i	−0.00113762	+	0.0153529i
$961$	−3.98522	−	4.42604i	−0.128556	−	0.142775i
$962$	4.60882	+	0.484406i	0.148594	+	0.0156179i
$963$	15.7516	−	12.9959i	0.507589	−	0.418788i
$964$	−2.36014	+	2.12508i	−0.0760150	+	0.0684442i
$965$	−0.370777	−	1.14113i	−0.0119357	−	0.0367344i
$966$	5.38979	−	1.42535i	0.173414	−	0.0458598i
$967$		−	14.2865i		−	0.459422i	−0.973259	−	0.229711i	$-0.926222\pi$
$967$		−	14.2865i		−	0.459422i	0.973259	−	0.229711i	$-0.0737781\pi$
$968$	2.41630	−	10.7313i	0.0776628	−	0.344918i
$969$	1.57462	+	11.5517i	0.0505841	+	0.371093i
$970$	1.12723	−	2.53179i	0.0361931	−	0.0812910i
$971$	−3.18344	+	14.9769i	−0.102161	+	0.480632i	0.897086	+	0.441855i	$0.145679\pi$
$971$	−3.18344	+	14.9769i	−0.102161	+	0.480632i	−0.999248	+	0.0387768i	$0.987654\pi$
$972$	−9.85002	+	12.0821i	−0.315940	+	0.387533i
$973$	−24.6934	−	2.13836i	−0.791635	−	0.0685526i
$974$	−15.4783	−	11.2457i	−0.495958	−	0.360334i
$975$	1.84796	+	5.14354i	0.0591820	+	0.164725i
$976$	−3.29160	−	2.96377i	−0.105362	−	0.0948679i
$977$	7.51775	−	16.8851i	0.240514	−	0.540203i	−0.752446	−	0.658654i	$-0.771126\pi$
$977$	7.51775	−	16.8851i	0.240514	−	0.540203i	0.992960	+	0.118451i	$0.0377928\pi$
$978$	22.5166	+	29.0677i	0.720000	+	0.929484i
$979$	−42.8348	+	42.3226i	−1.36901	+	1.35264i
$980$	1.70371	+	0.902009i	0.0544229	+	0.0288136i
$981$	−2.09675	+	14.0707i	−0.0669439	+	0.449243i
$982$	−25.3793	−	5.39454i	−0.809887	−	0.172147i
$983$	7.90921	+	37.2099i	0.252265	+	1.18681i	0.903720	+	0.428125i	$0.140826\pi$
$983$	7.90921	+	37.2099i	0.252265	+	1.18681i	−0.651455	+	0.758687i	$0.725841\pi$
$984$	−4.63948	−	2.49161i	−0.147901	−	0.0794296i
$985$	−1.86731	−	4.19405i	−0.0594974	−	0.133633i
$986$	−16.6929	+	51.3755i	−0.531611	+	1.63613i
$987$	−9.75959	+	4.93270i	−0.310651	+	0.157009i
$988$	−0.570887	+	0.414774i	−0.0181623	+	0.0131957i
$989$	−0.684384	+	1.18539i	−0.0217622	+	0.0376932i
$990$	2.50672	+	1.10665i	0.0796688	+	0.0351717i
$991$	11.0674	+	19.1694i	0.351569	+	0.608936i	0.986525	−	0.163613i	$-0.0523149\pi$
$991$	11.0674	+	19.1694i	0.351569	+	0.608936i	−0.634955	+	0.772549i	$0.718982\pi$
$992$	0.523104	+	4.97700i	0.0166086	+	0.158020i
$993$	8.64758	+	0.640772i	0.274423	+	0.0203343i
$994$	28.5297	+	8.69477i	0.904906	+	0.275781i
$995$	0.881505	−	1.21329i	0.0279456	−	0.0384638i
$996$	−0.224899	−	7.30993i	−0.00712620	−	0.231624i
$997$	−7.47016	−	35.1443i	−0.236582	−	1.11303i	−0.922693	−	0.385535i	$-0.874017\pi$
$997$	−7.47016	−	35.1443i	−0.236582	−	1.11303i	0.686111	−	0.727497i	$-0.259316\pi$
$998$	14.2687	−	15.8470i	0.451668	−	0.501628i
$999$	−18.3820	−	32.7743i	−0.581582	−	1.03693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.107.11	yes	128
3.2	odd	2		462.2.bc.a.107.2	yes	128
7.4	even	3	inner	462.2.bc.b.305.12	yes	128
11.7	odd	10		462.2.bc.a.359.8	yes	128
21.11	odd	6		462.2.bc.a.305.8	yes	128
33.29	even	10	inner	462.2.bc.b.359.12	yes	128
77.18	odd	30		462.2.bc.a.95.2	✓	128
231.95	even	30	inner	462.2.bc.b.95.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.2	✓	128	77.18	odd	30
462.2.bc.a.107.2	yes	128	3.2	odd	2
462.2.bc.a.305.8	yes	128	21.11	odd	6
462.2.bc.a.359.8	yes	128	11.7	odd	10
462.2.bc.b.95.11	yes	128	231.95	even	30	inner
462.2.bc.b.107.11	yes	128	1.1	even	1	trivial
462.2.bc.b.305.12	yes	128	7.4	even	3	inner
462.2.bc.b.359.12	yes	128	33.29	even	10	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.752814 + 1.55989i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.112013 - 0.251585i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.86654 + 2.34862i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.752814 + 1.55989i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.112013 - 0.251585i) q^{5} +(1.47266 - 0.911743i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.86654 + 2.34862i) q^{9} +(-0.238498 + 0.137697i) q^{10} +(-0.877660 + 3.19839i) q^{11} +(-1.06068 - 1.36929i) q^{12} +(0.376661 + 0.518429i) q^{13} +(0.863588 + 2.50084i) q^{14} +(0.308121 - 0.364124i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.638932 + 6.07903i) q^{17} +(2.53086 + 1.61082i) q^{18} +(0.228950 - 1.07712i) q^{19} +(0.161872 + 0.222798i) q^{20} +(-2.87227 - 3.57073i) q^{21} +(3.27261 + 0.538529i) q^{22} +(-1.05359 - 0.608290i) q^{23} +(-1.25092 + 1.19800i) q^{24} +(3.29491 - 3.65936i) q^{25} +(0.476217 - 0.428788i) q^{26} +(-5.06876 - 1.14353i) q^{27} +(2.39687 - 1.12027i) q^{28} +(-2.73094 + 8.40497i) q^{29} +(-0.394337 - 0.268371i) q^{30} +(-4.57176 - 2.03548i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.64987 + 1.03874i) q^{33} +6.11252 q^{34} +(0.439011 + 0.581515i) q^{35} +(1.33745 - 2.68537i) q^{36} +(4.83899 + 5.37424i) q^{37} +(-1.09515 - 0.115105i) q^{38} +(-0.525139 + 0.977832i) q^{39} +(0.204657 - 0.184274i) q^{40} +(0.939549 + 2.89164i) q^{41} +(-3.25093 + 3.22978i) q^{42} -1.12509i q^{43} +(0.193498 - 3.31098i) q^{44} +(0.799953 + 0.206518i) q^{45} +(-0.494828 + 1.11140i) q^{46} +(0.496136 - 2.33414i) q^{47} +(1.32220 + 1.11884i) q^{48} +(6.28611 - 3.07974i) q^{49} +(-3.98373 - 2.89435i) q^{50} +(-9.96364 + 3.57971i) q^{51} +(-0.476217 - 0.428788i) q^{52} +(3.33385 - 7.48795i) q^{53} +(-0.607440 + 5.16052i) q^{54} +(0.902975 - 0.137455i) q^{55} +(-1.36467 - 2.26664i) q^{56} +(1.85256 - 0.453736i) q^{57} +(8.64439 + 1.83742i) q^{58} +(1.83954 + 8.65435i) q^{59} +(-0.225682 + 0.420229i) q^{60} +(-1.80155 - 4.04635i) q^{61} +(-1.54645 + 4.75948i) q^{62} +(3.40767 - 7.16853i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0882380 - 0.152833i) q^{65} +(1.62362 + 5.51034i) q^{66} +(-5.31001 - 9.19720i) q^{67} +(-0.638932 - 6.07903i) q^{68} +(0.155712 - 2.10142i) q^{69} +(0.532441 - 0.497391i) q^{70} +(6.62602 - 9.11993i) q^{71} +(-2.81046 - 1.04942i) q^{72} +(2.37065 + 11.1530i) q^{73} +(4.83899 - 5.37424i) q^{74} +(8.18867 + 2.38489i) q^{75} +1.10119i q^{76} +(0.351220 - 8.76793i) q^{77} +(1.02737 + 0.420051i) q^{78} +(12.3514 - 1.29819i) q^{79} +(-0.204657 - 0.184274i) q^{80} +(-2.03204 - 8.76760i) q^{81} +(2.77758 - 1.23666i) q^{82} +(3.41598 + 2.48186i) q^{83} +(3.55190 + 2.89552i) q^{84} +(1.60096 - 0.520183i) q^{85} +(-1.11893 + 0.117604i) q^{86} +(-15.1668 + 2.06740i) q^{87} +(-3.31306 + 0.153653i) q^{88} +(15.7235 + 9.07797i) q^{89} +(0.121769 - 0.817158i) q^{90} +(-1.28054 - 1.11117i) q^{91} +(1.15704 + 0.375944i) q^{92} +(-0.266553 - 8.66380i) q^{93} +(-2.37321 - 0.249434i) q^{94} +(-0.296633 + 0.0630513i) q^{95} +(0.974501 - 1.43190i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(-3.71994 - 5.92976i) q^{98} +(-5.87362 - 8.03122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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