LMFDB - Embedded newform 462.2.bc.a.107.2

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			107.2
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.a.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-1.63004 - 0.585637i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.112013 + 0.251585i) q^{5} +(0.412043 - 1.68233i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.31406 + 1.90922i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-1.63004 - 0.585637i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.112013 + 0.251585i) q^{5} +(0.412043 - 1.68233i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.31406 + 1.90922i) q^{9} +(-0.238498 + 0.137697i) q^{10} +(0.877660 - 3.19839i) q^{11} +(1.71618 + 0.233935i) q^{12} +(0.376661 + 0.518429i) q^{13} +(-0.863588 - 2.50084i) q^{14} +(-0.0352480 - 0.475691i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.638932 - 6.07903i) q^{17} +(-1.65688 + 2.50095i) q^{18} +(0.228950 - 1.07712i) q^{19} +(-0.161872 - 0.222798i) q^{20} +(4.55117 + 0.535564i) q^{21} +(3.27261 + 0.538529i) q^{22} +(1.05359 + 0.608290i) q^{23} +(-0.0532635 + 1.73123i) q^{24} +(3.29491 - 3.65936i) q^{25} +(-0.476217 + 0.428788i) q^{26} +(-2.65390 - 4.46731i) q^{27} +(2.39687 - 1.12027i) q^{28} +(2.73094 - 8.40497i) q^{29} +(0.469401 - 0.0847782i) q^{30} +(-4.57176 - 2.03548i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.30372 + 4.69952i) q^{33} +6.11252 q^{34} +(-0.439011 - 0.581515i) q^{35} +(-2.66044 - 1.38638i) q^{36} +(4.83899 + 5.37424i) q^{37} +(1.09515 + 0.115105i) q^{38} +(-0.310361 - 1.06565i) q^{39} +(0.204657 - 0.184274i) q^{40} +(-0.939549 - 2.89164i) q^{41} +(-0.0569028 + 4.58222i) q^{42} -1.12509i q^{43} +(-0.193498 + 3.31098i) q^{44} +(-0.221127 + 0.796039i) q^{45} +(-0.494828 + 1.11140i) q^{46} +(-0.496136 + 2.33414i) q^{47} +(-1.72732 + 0.127991i) q^{48} +(6.28611 - 3.07974i) q^{49} +(3.98373 + 2.89435i) q^{50} +(-4.60159 + 9.53488i) q^{51} +(-0.476217 - 0.428788i) q^{52} +(-3.33385 + 7.48795i) q^{53} +(4.16543 - 3.10632i) q^{54} +(0.902975 - 0.137455i) q^{55} +(1.36467 + 2.26664i) q^{56} +(-1.00400 + 1.62167i) q^{57} +(8.64439 + 1.83742i) q^{58} +(-1.83954 - 8.65435i) q^{59} +(0.133380 + 0.457968i) q^{60} +(-1.80155 - 4.04635i) q^{61} +(1.54645 - 4.75948i) q^{62} +(-7.10495 - 3.53832i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0882380 + 0.152833i) q^{65} +(-5.01910 - 2.79438i) q^{66} +(-5.31001 - 9.19720i) q^{67} +(0.638932 + 6.07903i) q^{68} +(-1.36116 - 1.60856i) q^{69} +(0.532441 - 0.497391i) q^{70} +(-6.62602 + 9.11993i) q^{71} +(1.10069 - 2.79078i) q^{72} +(2.37065 + 11.1530i) q^{73} +(-4.83899 + 5.37424i) q^{74} +(-7.51388 + 4.03529i) 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} +(1.70974 + 8.83611i) q^{81} +(2.77758 - 1.23666i) q^{82} +(-3.41598 - 2.48186i) q^{83} +(-4.56307 + 0.422382i) q^{84} +(1.60096 - 0.520183i) q^{85} +(1.11893 - 0.117604i) q^{86} +(-9.37380 + 12.1011i) q^{87} +(-3.31306 + 0.153653i) q^{88} +(-15.7235 - 9.07797i) q^{89} +(-0.814792 - 0.136707i) q^{90} +(-1.28054 - 1.11117i) q^{91} +(-1.15704 - 0.375944i) q^{92} +(6.26010 + 5.99530i) q^{93} +(-2.37321 - 0.249434i) q^{94} +(0.296633 - 0.0630513i) q^{95} +(-0.307844 - 1.70447i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(3.71994 + 5.92976i) q^{98} +(8.13740 - 5.72562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 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} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * 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 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * 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
$3$	−1.63004	−	0.585637i	−0.941104	−	0.338117i
$3$	−1.63004	−	0.585637i	−0.941104	−	0.338117i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	0.112013	+	0.251585i	0.0500936	+	0.112512i	0.936858	−	0.349709i	$-0.113719\pi$
$5$	0.112013	+	0.251585i	0.0500936	+	0.112512i	−0.886765	+	0.462221i	$0.847053\pi$
$6$	0.412043	−	1.68233i	0.168216	−	0.686807i
$7$	−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
$9$	2.31406	+	1.90922i	0.771353	+	0.636407i
$10$	−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
$12$	1.71618	+	0.233935i	0.495419	+	0.0675311i
$13$	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
$15$	−0.0352480	−	0.475691i	−0.00910099	−	0.122823i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.638932	−	6.07903i	0.154964	−	1.47438i	−0.590069	−	0.807353i	$-0.700899\pi$
$17$	0.638932	−	6.07903i	0.154964	−	1.47438i	0.745032	−	0.667028i	$-0.232434\pi$
$18$	−1.65688	+	2.50095i	−0.390530	+	0.589480i
$19$	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
$21$	4.55117	+	0.535564i	0.993147	+	0.116870i
$22$	3.27261	+	0.538529i	0.697723	+	0.114815i
$23$	1.05359	+	0.608290i	0.219689	+	0.126837i	0.605806	−	0.795612i	$-0.292851\pi$
$23$	1.05359	+	0.608290i	0.219689	+	0.126837i	−0.386117	+	0.922450i	$0.626184\pi$
$24$	−0.0532635	+	1.73123i	−0.0108724	+	0.353386i
$25$	3.29491	−	3.65936i	0.658981	−	0.731873i
$26$	−0.476217	+	0.428788i	−0.0933939	+	0.0840922i
$27$	−2.65390	−	4.46731i	−0.510743	−	0.859733i
$28$	2.39687	−	1.12027i	0.452967	−	0.211710i
$29$	2.73094	−	8.40497i	0.507123	−	1.56076i	−0.290049	−	0.957012i	$-0.593672\pi$
$29$	2.73094	−	8.40497i	0.507123	−	1.56076i	0.797172	−	0.603752i	$-0.206328\pi$
$30$	0.469401	−	0.0847782i	0.0857005	−	0.0154783i
$31$	−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
$33$	−3.30372	+	4.69952i	−0.575103	+	0.818081i
$34$	6.11252			1.04829
$35$	−0.439011	−	0.581515i	−0.0742065	−	0.0982940i
$36$	−2.66044	−	1.38638i	−0.443407	−	0.231063i
$37$	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
$39$	−0.310361	−	1.06565i	−0.0496975	−	0.170640i
$40$	0.204657	−	0.184274i	0.0323592	−	0.0291363i
$41$	−0.939549	−	2.89164i	−0.146733	−	0.451598i	0.850497	−	0.525980i	$-0.176301\pi$
$41$	−0.939549	−	2.89164i	−0.146733	−	0.451598i	−0.997230	+	0.0743826i	$0.976301\pi$
$42$	−0.0569028	+	4.58222i	−0.00878029	+	0.707052i
$43$		−	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
$45$	−0.221127	+	0.796039i	−0.0329636	+	0.118666i
$46$	−0.494828	+	1.11140i	−0.0729584	+	0.163867i
$47$	−0.496136	+	2.33414i	−0.0723689	+	0.340469i	−0.999405	−	0.0345044i	$-0.989015\pi$
$47$	−0.496136	+	2.33414i	−0.0723689	+	0.340469i	0.927036	+	0.374973i	$0.122348\pi$
$48$	−1.72732	+	0.127991i	−0.249316	+	0.0184739i
$49$	6.28611	−	3.07974i	0.898016	−	0.439963i
$50$	3.98373	+	2.89435i	0.563384	+	0.409323i
$51$	−4.60159	+	9.53488i	−0.644351	+	1.33515i
$52$	−0.476217	−	0.428788i	−0.0660395	−	0.0594622i
$53$	−3.33385	+	7.48795i	−0.457940	+	1.02855i	0.526071	+	0.850441i	$0.323665\pi$
$53$	−3.33385	+	7.48795i	−0.457940	+	1.02855i	−0.984011	+	0.178109i	$0.943002\pi$
$54$	4.16543	−	3.10632i	0.566843	−	0.422717i
$55$	0.902975	−	0.137455i	0.121757	−	0.0185344i
$56$	1.36467	+	2.26664i	0.182362	+	0.302893i
$57$	−1.00400	+	1.62167i	−0.132983	+	0.214796i
$58$	8.64439	+	1.83742i	1.13506	+	0.241265i
$59$	−1.83954	−	8.65435i	−0.239487	−	1.12670i	−0.919375	−	0.393383i	$-0.871305\pi$
$59$	−1.83954	−	8.65435i	−0.239487	−	1.12670i	0.679887	−	0.733317i	$-0.262029\pi$
$60$	0.133380	+	0.457968i	0.0172192	+	0.0591234i
$61$	−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
$63$	−7.10495	−	3.53832i	−0.895139	−	0.445787i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.0882380	+	0.152833i	−0.0109446	+	0.0189566i
$66$	−5.01910	−	2.79438i	−0.617809	−	0.343965i
$67$	−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
$69$	−1.36116	−	1.60856i	−0.163864	−	0.193648i
$70$	0.532441	−	0.497391i	0.0636388	−	0.0594496i
$71$	−6.62602	+	9.11993i	−0.786363	+	1.08234i	0.208188	+	0.978089i	$0.433243\pi$
$71$	−6.62602	+	9.11993i	−0.786363	+	1.08234i	−0.994551	+	0.104248i	$0.966757\pi$
$72$	1.10069	−	2.79078i	0.129718	−	0.328897i
$73$	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
$75$	−7.51388	+	4.03529i	−0.867629	+	0.465955i
$76$			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
$81$	1.70974	+	8.83611i	0.189971	+	0.981790i
$82$	2.77758	−	1.23666i	0.306733	−	0.136566i
$83$	−3.41598	−	2.48186i	−0.374953	−	0.272419i	0.384309	−	0.923205i	$-0.374440\pi$
$83$	−3.41598	−	2.48186i	−0.374953	−	0.272419i	−0.759262	+	0.650785i	$0.774440\pi$
$84$	−4.56307	+	0.422382i	−0.497872	+	0.0460856i
$85$	1.60096	−	0.520183i	0.173648	−	0.0564218i
$86$	1.11893	−	0.117604i	0.120657	−	0.0126816i
$87$	−9.37380	+	12.1011i	−1.00498	+	1.29737i
$88$	−3.31306	+	0.153653i	−0.353174	+	0.0163795i
$89$	−15.7235	−	9.07797i	−1.66669	−	0.962263i	−0.969405	−	0.245468i	$-0.921058\pi$
$89$	−15.7235	−	9.07797i	−1.66669	−	0.962263i	−0.697284	−	0.716795i	$-0.745608\pi$
$90$	−0.814792	−	0.136707i	−0.0858866	−	0.0144102i
$91$	−1.28054	−	1.11117i	−0.134238	−	0.116482i
$92$	−1.15704	−	0.375944i	−0.120629	−	0.0391949i
$93$	6.26010	+	5.99530i	0.649142	+	0.621684i
$94$	−2.37321	−	0.249434i	−0.244778	−	0.0257272i
$95$	0.296633	−	0.0630513i	0.0304339	−	0.00646892i
$96$	−0.307844	−	1.70447i	−0.0314192	−	0.173962i
$97$	−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
$99$	8.13740	−	5.72562i	0.817839	−	0.575447i
$100$	−2.46208	+	4.26445i	−0.246208	+	0.426445i
$101$	4.80806	+	2.14068i	0.478419	+	0.213006i	0.631755	−	0.775168i	$-0.282335\pi$
$101$	4.80806	+	2.14068i	0.478419	+	0.213006i	−0.153336	+	0.988174i	$0.549002\pi$
$102$	−9.96364	−	3.57971i	−0.986548	−	0.354444i
$103$	−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
$105$	0.375049	+	1.20499i	0.0366011	+	0.117595i
$106$	−7.79542	−	2.53288i	−0.757158	−	0.246015i
$107$	6.65818	+	1.41524i	0.643670	+	0.136816i	0.518171	−	0.855277i	$-0.326613\pi$
$107$	6.65818	+	1.41524i	0.643670	+	0.136816i	0.125500	+	0.992094i	$0.459947\pi$
$108$	3.52471	+	3.81791i	0.339165	+	0.367378i
$109$	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	−0.375030	−	0.927013i	$-0.622367\pi$
$113$	−1.41966	+	0.461276i	−0.133550	+	0.0433932i	0.241479	+	0.970406i	$0.422367\pi$
$114$	−1.71774	−	0.828989i	−0.160881	−	0.0776419i
$115$	−0.0350211	+	0.333203i	−0.00326573	+	0.0310713i
$116$	−0.923771	+	8.78910i	−0.0857700	+	0.816047i
$117$	−0.118181	+	1.91880i	−0.0109258	+	0.177394i
$118$	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
$123$	−0.161945	+	5.26371i	−0.0146021	+	0.474613i
$124$	4.89506	+	1.04048i	0.439589	+	0.0934376i
$125$	2.59928	+	0.844559i	0.232487	+	0.0755396i
$126$	2.77627	−	7.43588i	0.247330	−	0.662441i
$127$	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
$129$	−0.658897	+	1.83395i	−0.0580126	+	0.161470i
$130$	−0.161219	−	0.0717792i	−0.0141398	−	0.00629545i
$131$	5.90912	−	10.2349i	0.516282	−	0.894227i	−0.483539	−	0.875323i	$-0.660649\pi$
$131$	5.90912	−	10.2349i	0.516282	−	0.894227i	0.999821	−	0.0189040i	$-0.00601769\pi$
$132$	2.25444	−	5.28370i	0.196224	−	0.459887i
$133$	0.0534271	+	2.91298i	0.00463272	+	0.252587i
$134$	8.59177	−	6.24229i	0.742216	−	0.539251i
$135$	0.826635	−	1.16807i	0.0711454	−	0.100532i
$136$	−5.97894	+	1.27086i	−0.512690	+	0.108976i
$137$	−8.55726	−	0.899404i	−0.731096	−	0.0768413i	−0.268337	−	0.963325i	$-0.586474\pi$
$137$	−8.55726	−	0.899404i	−0.731096	−	0.0768413i	−0.462759	+	0.886484i	$0.653141\pi$
$138$	1.45747	−	1.52184i	0.124068	−	0.129548i
$139$	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
$141$	2.17568	−	3.51418i	0.183225	−	0.295947i
$142$	−9.76258	−	5.63643i	−0.819257	−	0.472998i
$143$	1.98872	−	0.749704i	0.166305	−	0.0626934i
$144$	2.89055	+	0.802948i	0.240879	+	0.0669123i
$145$	2.42046	−	0.254401i	0.201008	−	0.0211268i
$146$	−10.8441	+	3.52348i	−0.897468	+	0.291605i
$147$	−12.0502	+	1.33872i	−0.993885	+	0.110416i
$148$	−5.85061	−	4.25072i	−0.480917	−	0.349407i
$149$	13.0189	−	5.79639i	1.06655	−	0.474859i	0.203030	−	0.979172i	$-0.434921\pi$
$149$	13.0189	−	5.79639i	1.06655	−	0.474859i	0.863521	+	0.504313i	$0.168254\pi$
$150$	−4.79860	−	7.05092i	−0.391804	−	0.575705i
$151$	−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
$156$	0.525139	+	0.977832i	0.0420448	+	0.0782892i
$157$	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
$159$	9.81953	−	10.2532i	0.778739	−	0.813135i
$160$	−0.161872	+	0.222798i	−0.0127971	+	0.0176137i
$161$	−3.07896	−	0.938351i	−0.242656	−	0.0739524i
$162$	−8.60898	+	2.62400i	−0.676386	+	0.206161i
$163$	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
$165$	−1.55238	−	0.304759i	−0.120853	−	0.0237254i
$166$	2.11119	−	3.65669i	0.163860	−	0.283815i
$167$	−3.23429	+	2.34985i	−0.250277	+	0.181837i	−0.705849	−	0.708362i	$-0.749434\pi$
$167$	−3.23429	+	2.34985i	−0.250277	+	0.181837i	0.455573	+	0.890199i	$0.349434\pi$
$168$	−0.897038	−	4.49392i	−0.0692080	−	0.346714i
$169$	3.89033	−	11.9732i	0.299256	−	0.921015i
$170$	0.684679	+	1.53781i	0.0525125	+	0.117945i
$171$	2.58627	−	2.05541i	0.197777	−	0.157181i
$172$	0.233920	+	1.10051i	0.0178363	+	0.0839130i
$173$	−0.739743	−	0.157237i	−0.0562417	−	0.0119545i	0.179705	−	0.983721i	$-0.442486\pi$
$173$	−0.739743	−	0.157237i	−0.0562417	−	0.0119545i	−0.235947	+	0.971766i	$0.575819\pi$
$174$	−13.0146	−	8.05754i	−0.986637	−	0.610841i
$175$	−6.30605	+	11.4002i	−0.476693	+	0.861776i
$176$	−0.499121	−	3.27885i	−0.0376227	−	0.247153i
$177$	−2.06978	+	15.1842i	−0.155574	+	1.14132i
$178$	7.38469	−	16.5863i	0.553506	−	1.24319i
$179$	1.35024	+	1.21576i	0.100922	+	0.0908704i	0.718047	−	0.695994i	$-0.245036\pi$
$179$	1.35024	+	1.21576i	0.100922	+	0.0908704i	−0.617125	+	0.786865i	$0.711703\pi$
$180$	0.0507889	−	0.824618i	0.00378558	−	0.0614634i
$181$	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
$183$	0.566910	+	7.65077i	0.0419072	+	0.565561i
$184$	0.252941	−	1.19000i	0.0186471	−	0.0877276i
$185$	−0.810047	+	1.81940i	−0.0595559	+	0.133765i
$186$	−5.30810	+	6.85249i	−0.389209	+	0.502449i
$187$	−18.8824	−	7.37888i	−1.38081	−	0.539597i
$188$		−	2.38628i		−	0.174037i
$189$	9.50917	+	9.92852i	0.691691	+	0.722194i
$190$	0.0937124	+	0.288417i	0.00679862	+	0.0209240i
$191$	8.53554	−	7.68543i	0.617610	−	0.556098i	−0.299820	−	0.953996i	$-0.596927\pi$
$191$	8.53554	−	7.68543i	0.617610	−	0.556098i	0.917430	+	0.397897i	$0.130260\pi$
$192$	1.66296	−	0.484323i	0.120014	−	0.0349530i
$193$	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
$195$	0.233336	−	0.197448i	0.0167095	−	0.0141395i
$196$	−5.50843	+	4.31940i	−0.393459	+	0.308528i
$197$	−16.6705			−1.18773			−0.593863	−	0.804566i	$-0.702398\pi$
$197$	−16.6705			−1.18773			−0.593863	+	0.804566i	$0.702398\pi$
$198$	6.54485	+	7.49433i	0.465122	+	0.532599i
$199$	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
$201$	3.26930	+	18.1015i	0.230599	+	1.27678i
$202$	−1.62638	+	5.00548i	−0.114432	+	0.352184i
$203$	−2.01723	+	23.2947i	−0.141582	+	1.63497i
$204$	2.51862	−	10.2832i	0.176339	−	0.719971i
$205$	0.622249	−	0.560276i	0.0434598	−	0.0391314i
$206$	8.86266	−	9.84298i	0.617491	−	0.685793i
$207$	1.27671	+	3.41916i	0.0887374	+	0.237648i
$208$	0.554961	+	0.320407i	0.0384796	+	0.0222162i
$209$	−3.24412	−	1.67762i	−0.224401	−	0.116043i
$210$	−1.15919	+	0.498951i	−0.0799917	+	0.0344309i
$211$	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
$213$	16.1416	−	10.9854i	1.10601	−	0.752708i
$214$	−0.711518	+	6.76964i	−0.0486383	+	0.462763i
$215$	0.283056	−	0.126025i	0.0193043	−	0.00859482i
$216$	−3.42856	+	3.90448i	−0.233284	+	0.265666i
$217$	12.9994	+	2.51488i	0.882457	+	0.170721i
$218$	2.78729	+	3.83638i	0.188779	+	0.259832i
$219$	2.66737	−	19.5682i	0.180244	−	1.32230i
$220$	−0.854664	+	0.322190i	−0.0576215	+	0.0217220i
$221$	3.39221	−	1.95849i	0.228185	−	0.131742i
$222$	11.0351	−	5.92633i	0.740627	−	0.397750i
$223$	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
$225$	14.6111	−	2.17728i	0.974076	−	0.145152i
$226$	−0.607144	−	1.36367i	−0.0403866	−	0.0907098i
$227$	23.4975	−	4.99455i	1.55958	−	0.331500i	0.654277	−	0.756255i	$-0.272973\pi$
$227$	23.4975	−	4.99455i	1.55958	−	0.331500i	0.905308	+	0.424755i	$0.139640\pi$
$228$	0.644896	−	1.79498i	0.0427093	−	0.118875i
$229$	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
$231$	5.70732	−	14.0864i	0.375514	−	0.926817i
$232$	−8.83751			−0.580211
$233$	1.76179	+	16.7624i	0.115419	+	1.09814i	0.886924	+	0.461915i	$0.152838\pi$
$233$	1.76179	+	16.7624i	0.115419	+	1.09814i	−0.771505	+	0.636223i	$0.780496\pi$
$234$	−1.92065	+	0.0830364i	−0.125557	+	0.00542826i
$235$	−0.642806	+	0.136633i	−0.0419320	+	0.00891293i
$236$	3.59868	+	8.08277i	0.234254	+	0.526143i
$237$	−20.8936	−	5.11735i	−1.35718	−	0.332407i
$238$	−15.7545	+	3.65191i	−1.02121	+	0.236718i
$239$	−4.22887	−	13.0151i	−0.273543	−	0.841877i	−0.989601	−	0.143837i	$-0.954056\pi$
$239$	−4.22887	−	13.0151i	−0.273543	−	0.841877i	0.716059	−	0.698040i	$-0.245944\pi$
$240$	−0.225682	−	0.420229i	−0.0145677	−	0.0271257i
$241$	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
$243$	2.38780	−	15.4045i	0.153177	−	0.988199i
$244$	2.60347	+	3.58337i	0.166670	+	0.229401i
$245$	1.47894	+	1.23652i	0.0944859	+	0.0789983i
$246$	−5.25181	+	0.389150i	−0.334843	+	0.0248113i
$247$	0.644649	−	0.287016i	0.0410180	−	0.0182624i
$248$	−0.523104	+	4.97700i	−0.0332171	+	0.316040i
$249$	4.11472	+	6.04605i	0.260760	+	0.383153i
$250$	−0.568233	+	2.67333i	−0.0359382	+	0.169076i
$251$	−5.83265	−	8.02796i	−0.368154	−	0.506720i	0.584244	−	0.811578i	$-0.301391\pi$
$251$	−5.83265	−	8.02796i	−0.368154	−	0.506720i	−0.952398	+	0.304858i	$0.901391\pi$
$252$	7.68535	+	1.98380i	0.484131	+	0.124968i
$253$	2.87024	−	2.83592i	0.180451	−	0.178293i
$254$	0.0751417	+	0.0433831i	0.00471481	+	0.00272210i
$255$	−2.91426	−	0.0896610i	−0.182498	−	0.00561479i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	15.5229	−	13.9769i	0.968290	−	0.871852i	−0.0235005	−	0.999724i	$-0.507481\pi$
$257$	15.5229	−	13.9769i	0.968290	−	0.871852i	0.991791	+	0.127871i	$0.0408145\pi$
$258$	−1.89278	−	0.463587i	−0.117839	−	0.0288617i
$259$	−15.6829	−	10.9606i	−0.974487	−	0.681058i
$260$	0.0545341	−	0.167839i	0.00338206	−	0.0104089i
$261$	22.3665	−	14.2356i	1.38445	−	0.881163i
$262$	10.7965	+	4.80691i	0.667010	+	0.296972i
$263$	−9.65220	−	16.7181i	−0.595180	−	1.03088i	−0.993521	−	0.113645i	$-0.963747\pi$
$263$	−9.65220	−	16.7181i	−0.595180	−	1.03088i	0.398341	−	0.917237i	$-0.369586\pi$
$264$	5.49041	+	1.68979i	0.337911	+	0.103999i
$265$	−2.25729			−0.138664
$266$	−2.89144	+	0.357624i	−0.177285	+	0.0219273i
$267$	20.3136	+	24.0057i	1.24317	+	1.46913i
$268$	7.10618	+	7.89221i	0.434079	+	0.482093i
$269$	−21.5198	−	2.26183i	−1.31209	−	0.137906i	−0.577484	−	0.816402i	$-0.695965\pi$
$269$	−21.5198	−	2.26183i	−1.31209	−	0.137906i	−0.734604	+	0.678496i	$0.762632\pi$
$270$	1.24808	+	0.700009i	0.0759559	+	0.0426012i
$271$	−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
$273$	1.43660	+	2.56119i	0.0869468	+	0.155010i
$274$		−	8.60439i		−	0.519810i
$275$	−8.81227	−	13.7501i	−0.531400	−	0.829161i
$276$	1.66585	+	1.29041i	0.100272	+	0.0776734i
$277$	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
$279$	−6.69315	−	13.4387i	−0.400708	−	0.804556i
$280$	−0.417392	+	0.597223i	−0.0249439	+	0.0356909i
$281$	5.30840	+	3.85678i	0.316673	+	0.230076i	0.734754	−	0.678333i	$-0.237297\pi$
$281$	5.30840	+	3.85678i	0.316673	+	0.230076i	−0.418082	+	0.908409i	$0.637297\pi$
$282$	3.72235	+	1.79643i	0.221663	+	0.106976i
$283$	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
$285$	−0.520449	−	0.0709430i	−0.0308287	−	0.00420230i
$286$	0.953475	+	1.89946i	0.0563802	+	0.112317i
$287$	4.14921	+	6.89161i	0.244920	+	0.406799i
$288$	−0.496405	+	2.95865i	−0.0292509	+	0.174340i
$289$	−19.9179	−	4.23367i	−1.17164	−	0.249040i
$290$	0.506014	+	2.38061i	0.0297142	+	0.139794i
$291$	16.7350	−	4.87394i	0.981024	−	0.285715i
$292$	−4.63770	−	10.4164i	−0.271401	−	0.609576i
$293$	2.75468	−	8.47805i	0.160930	−	0.495293i	−0.837783	−	0.546003i	$-0.816149\pi$
$293$	2.75468	−	8.47805i	0.160930	−	0.495293i	0.998713	+	0.0507105i	$0.0161486\pi$
$294$	−2.59098	−	11.8443i	−0.151109	−	0.690772i
$295$	1.97125	−	1.43220i	0.114770	−	0.0833856i
$296$	3.61587	−	6.26288i	0.210168	−	0.364022i
$297$	−16.6174	+	4.56743i	−0.964240	+	0.265029i
$298$	7.12549	+	12.3417i	0.412768	+	0.714936i
$299$	0.0814905	+	0.775331i	0.00471272	+	0.0448385i
$300$	6.51070	−	5.50933i	0.375896	−	0.318082i
$301$	0.672185	+	2.89983i	0.0387441	+	0.167144i
$302$	6.15267	−	8.46843i	0.354047	−	0.487303i
$303$	−6.58366	−	6.30517i	−0.378221	−	0.362223i
$304$	−0.228950	−	1.07712i	−0.0131312	−	0.0617773i
$305$	0.816203	−	0.906485i	0.0467356	−	0.0519052i
$306$	14.1447	+	11.6701i	0.808600	+	0.667138i
$307$		−	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	0.972127	−	0.234453i	$-0.0753299\pi$
$311$	14.8237	+	13.3473i	0.840574	+	0.756856i	−0.131554	+	0.991309i	$0.541997\pi$
$312$	−0.917583	+	0.624474i	−0.0519479	+	0.0353539i
$313$	−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
$315$	0.0943435	−	2.18383i	0.00531565	−	0.123045i
$316$	−11.8116	+	3.83782i	−0.664455	+	0.215894i
$317$	−15.7403	+	1.65437i	−0.884061	+	0.0929185i	−0.535667	−	0.844430i	$-0.679940\pi$
$317$	−15.7403	+	1.65437i	−0.884061	+	0.0929185i	−0.348394	+	0.937348i	$0.613273\pi$
$318$	11.2235	+	8.69398i	0.629382	+	0.487534i
$319$	−24.4856	−	16.1113i	−1.37093	−	0.902061i
$320$	−0.238498	−	0.137697i	−0.0133324	−	0.00769748i
$321$	−10.0243	−	6.20617i	−0.559501	−	0.346395i
$322$	0.611371	−	3.16017i	0.0340704	−	0.176110i
$323$	−6.40158	−	2.08000i	−0.356194	−	0.115734i
$324$	−3.50951	−	8.28754i	−0.194973	−	0.460419i
$325$	3.13818	+	0.329836i	0.174075	+	0.0182960i
$326$	−20.7645	+	4.41362i	−1.15004	+	0.244448i
$327$	−8.08266	+	1.45980i	−0.446972	+	0.0807273i
$328$	−2.45977	+	1.78713i	−0.135818	+	0.0986777i
$329$	−0.115777	−	6.31245i	−0.00638299	−	0.348016i
$330$	0.140821	−	1.57574i	0.00775193	−	0.0867414i
$331$	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
$333$	0.937088	+	21.6750i	0.0513521	+	1.18778i
$334$	−2.67505	−	2.97094i	−0.146372	−	0.162563i
$335$	1.71909	−	2.36612i	0.0939237	−	0.129275i
$336$	4.37554	−	1.36187i	0.238705	−	0.0742959i
$337$	−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
$339$	2.58424	+	0.0795074i	0.140357	+	0.00431825i
$340$	−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
$345$	0.252222	−	0.522625i	0.0135792	−	0.0281372i
$346$	0.0790517	−	0.752127i	0.00424985	−	0.0404346i
$347$	−0.595247	+	5.66339i	−0.0319545	+	0.304027i	0.966858	+	0.255314i	$0.0821787\pi$
$347$	−0.595247	+	5.66339i	−0.0319545	+	0.304027i	−0.998813	+	0.0487133i	$0.984488\pi$
$348$	6.65300	−	13.7856i	0.356638	−	0.738985i
$349$	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	−0.408099	−	0.912938i	$-0.633808\pi$
$353$	3.35330	−	1.93603i	0.178478	−	0.103044i	0.586578	+	0.809893i	$0.300475\pi$
$354$	−15.3174	−	0.471259i	−0.814111	−	0.0250471i
$355$	−3.03663	−	0.645456i	−0.161168	−	0.0342572i
$356$	17.2673	+	5.61050i	0.915167	+	0.297356i
$357$	6.16360	−	27.3245i	0.326212	−	1.44617i
$358$	−1.06796	+	1.46993i	−0.0564436	+	0.0776880i
$359$	−8.86611	−	9.84681i	−0.467935	−	0.519695i	0.462268	−	0.886740i	$-0.347036\pi$
$359$	−8.86611	−	9.84681i	−0.467935	−	0.519695i	−0.930203	+	0.367046i	$0.880369\pi$
$360$	0.825410	−	0.0356854i	0.0435029	−	0.00188079i
$361$	16.2496	+	7.23478i	0.855241	+	0.380778i
$362$	−10.3697	+	17.9609i	−0.545021	+	0.944004i
$363$	12.1314	+	14.6912i	0.636731	+	0.771086i
$364$	1.48359	+	0.820649i	0.0777611	+	0.0430137i
$365$	−2.54039	+	1.84570i	−0.132970	+	0.0966084i
$366$	−7.54960	+	1.36353i	−0.394624	+	0.0712727i
$367$	−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
$369$	3.34660	−	8.48522i	0.174217	−	0.441723i
$370$	−1.89410	−	0.615431i	−0.0984697	−	0.0319947i
$371$	4.11905	−	21.2913i	0.213851	−	1.10539i
$372$	−7.36980	−	4.56274i	−0.382106	−	0.236567i
$373$	−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
$375$	−3.74233	−	2.89890i	−0.193253	−	0.149699i
$376$	2.37321	−	0.249434i	0.122389	−	0.0128636i
$377$	5.38602	−	1.75002i	0.277394	−	0.0901308i
$378$	−8.88016	+	10.4949i	−0.456746	+	0.539799i
$379$	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
$381$	−0.124241	+	0.0845538i	−0.00636505	+	0.00433182i
$382$	8.53554	+	7.68543i	0.436716	+	0.393221i
$383$	18.5415	−	1.94879i	0.947428	−	0.0995787i	0.381805	−	0.924243i	$-0.375303\pi$
$383$	18.5415	−	1.94879i	0.947428	−	0.0995787i	0.565623	+	0.824664i	$0.308636\pi$
$384$	0.655497	+	1.60322i	0.0334507	+	0.0818141i
$385$	−2.24522	+	0.893758i	−0.114427	+	0.0455501i
$386$			4.35689i			0.221760i
$387$	2.14806	−	2.60354i	0.109192	−	0.132345i
$388$	6.73373	−	7.47856i	0.341853	−	0.379666i
$389$	6.44589	+	30.3255i	0.326820	+	1.53757i	0.768179	+	0.640236i	$0.221163\pi$
$389$	6.44589	+	30.3255i	0.326820	+	1.53757i	−0.441359	+	0.897331i	$0.645503\pi$
$390$	0.220756	+	0.211419i	0.0111784	+	0.0107056i
$391$	4.37099	−	6.01615i	0.221050	−	0.304250i
$392$	−4.87152	−	5.02676i	−0.246049	−	0.253890i
$393$	−15.6260	+	13.2227i	−0.788229	+	0.666996i
$394$	−1.74254	−	16.5792i	−0.0877881	−	0.835248i
$395$	1.71012	+	2.96201i	0.0860454	+	0.149035i
$396$	−6.76915	+	7.29236i	−0.340163	+	0.366455i
$397$	−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
$399$	1.61886	−	4.77956i	0.0810443	−	0.239277i
$400$	1.52165	−	4.68315i	0.0760824	−	0.234158i
$401$	−4.70955	−	10.5778i	−0.235184	−	0.528232i	0.756941	−	0.653483i	$-0.226693\pi$
$401$	−4.70955	−	10.5778i	−0.235184	−	0.528232i	−0.992125	+	0.125251i	$0.960026\pi$
$402$	−17.6606	+	5.14352i	−0.880833	+	0.256536i
$403$	−0.666751	−	3.13682i	−0.0332133	−	0.156256i
$404$	−5.14806	−	1.09425i	−0.256126	−	0.0544412i
$405$	−2.03151	+	1.41990i	−0.100947	+	0.0705554i
$406$	−23.3779	+	0.428776i	−1.16023	+	0.0212798i
$407$	21.4359	−	10.7602i	1.06254	−	0.533364i
$408$	10.4902	+	1.42993i	0.519341	+	0.0707921i
$409$	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
$411$	13.4219	+	6.47751i	0.662056	+	0.319512i
$412$	10.7155	+	7.78523i	0.527913	+	0.383551i
$413$	9.91177	+	21.2068i	0.487726	+	1.04352i
$414$	−3.26697	+	1.62711i	−0.160563	+	0.0799683i
$415$	0.241763	−	1.13741i	0.0118677	−	0.0558331i
$416$	−0.260642	+	0.585412i	−0.0127790	+	0.0287022i
$417$	−12.8277	−	9.93666i	−0.628176	−	0.486600i
$418$	1.32933	−	3.40171i	0.0650194	−	0.166383i
$419$			11.8865i			0.580692i	0.956922	+	0.290346i	$0.0937704\pi$
$419$			11.8865i			0.580692i	−0.956922	+	0.290346i	$0.906230\pi$
$420$	−0.617386	−	1.10069i	−0.0301254	−	0.0537079i
$421$	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
$423$	−5.60447	+	4.45410i	−0.272499	+	0.216566i
$424$	8.15168	+	0.856777i	0.395881	+	0.0416087i
$425$	−20.1402	−	22.3679i	−0.976941	−	1.08500i
$426$	12.6125	+	14.9049i	0.611077	+	0.722146i
$427$	7.06083	+	9.35279i	0.341697	+	0.452613i
$428$	−6.80693			−0.329025
$429$	−3.68075	+	0.0573812i	−0.177708	+	0.00277039i
$430$	0.154922	+	0.268333i	0.00747100	+	0.0129401i
$431$	−4.19913	−	1.86957i	−0.202265	−	0.0900543i	0.303104	−	0.952957i	$-0.401977\pi$
$431$	−4.19913	−	1.86957i	−0.202265	−	0.0900543i	−0.505369	+	0.862903i	$0.668644\pi$
$432$	−4.24147	−	3.00165i	−0.204068	−	0.144417i
$433$	−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
$435$	−4.09443	−	1.00283i	−0.196313	−	0.0480819i
$436$	−3.52401	+	3.17303i	−0.168770	+	0.151961i
$437$	0.896423	−	0.995579i	0.0428817	−	0.0476250i
$438$	19.7399	+	0.607321i	0.943207	+	0.0290189i
$439$	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
$441$	20.4263	+	4.87489i	0.972683	+	0.232137i
$442$	2.30234	+	3.16891i	0.109511	+	0.150729i
$443$	−3.23742	+	15.2308i	−0.153814	+	0.723639i	0.831861	+	0.554984i	$0.187276\pi$
$443$	−3.23742	+	15.2308i	−0.153814	+	0.723639i	−0.985675	+	0.168655i	$0.946058\pi$
$444$	7.04735	+	10.3552i	0.334452	+	0.491434i
$445$	0.522645	−	4.97264i	0.0247758	−	0.235726i
$446$	−5.15301	+	2.29427i	−0.244002	+	0.108637i
$447$	−24.6159	+	1.82400i	−1.16429	+	0.0862723i
$448$	1.73400	−	1.99831i	0.0819238	−	0.0944113i
$449$	−10.9616	−	15.0873i	−0.517309	−	0.712014i	0.467822	−	0.883823i	$-0.345039\pi$
$449$	−10.9616	−	15.0873i	−0.517309	−	0.712014i	−0.985130	+	0.171809i	$0.945039\pi$
$450$	3.69263	+	14.3035i	0.174072	+	0.674274i
$451$	−10.0732	+	0.467175i	−0.474328	+	0.0219984i
$452$	1.29273	−	0.746360i	0.0608050	−	0.0351058i
$453$	8.57804	+	15.9727i	0.403031	+	0.750462i
$454$	7.42335	+	22.8467i	0.348395	+	1.07225i
$455$	0.136116	−	0.446630i	0.00638122	−	0.0209384i
$456$	1.85256	+	0.453736i	0.0867539	+	0.0212482i
$457$	−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
$459$	−28.8526	+	13.2788i	−1.34672	+	0.619803i
$460$	−0.0350211	−	0.333203i	−0.00163287	−	0.0155357i
$461$	−23.8811			−1.11225			−0.556126	−	0.831098i	$-0.687713\pi$
$461$	−23.8811			−1.11225			−0.556126	+	0.831098i	$0.687713\pi$
$462$	14.6058	+	4.20363i	0.679523	+	0.195571i
$463$	−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
$465$	−0.807115	+	2.24649i	−0.0374291	+	0.104179i
$466$	−16.4864	+	3.50429i	−0.763716	+	0.162333i
$467$	11.7726	+	26.4416i	0.544769	+	1.22357i	0.950827	+	0.309723i	$0.100236\pi$
$467$	11.7726	+	26.4416i	0.544769	+	1.22357i	−0.406058	+	0.913847i	$0.633097\pi$
$468$	−0.283344	−	1.90145i	−0.0130976	−	0.0878943i
$469$	19.1809	+	20.5325i	0.885693	+	0.948104i
$470$	−0.203076	−	0.625002i	−0.00936718	−	0.0288292i
$471$	−22.9971	+	12.3505i	−1.05965	+	0.569080i
$472$	−7.66232	+	4.42384i	−0.352687	+	0.203624i
$473$	−3.59849	−	0.987450i	−0.165459	−	0.0454030i
$474$	2.90534	−	21.3140i	0.133447	−	0.978986i
$475$	−3.18722	−	4.38683i	−0.146240	−	0.201282i
$476$	−5.27869	−	15.2864i	−0.241949	−	0.700653i
$477$	−22.0109	+	10.9625i	−1.00781	+	0.501939i
$478$	12.5018	−	5.56615i	0.571818	−	0.254590i
$479$	−3.33424	+	31.7232i	−0.152345	+	1.44947i	0.604880	+	0.796317i	$0.293221\pi$
$479$	−3.33424	+	31.7232i	−0.152345	+	1.44947i	−0.757225	+	0.653154i	$0.773446\pi$
$480$	0.394337	−	0.268371i	0.0179989	−	0.0122494i
$481$	−0.963505	+	4.53293i	−0.0439320	+	0.206684i
$482$	1.86674	+	2.56934i	0.0850275	+	0.117030i
$483$	4.46929	+	3.33270i	0.203360	+	0.151643i
$484$	10.4200	+	3.52479i	0.473635	+	0.160218i
$485$	−2.40010	−	1.38570i	−0.108983	−	0.0629213i
$486$	15.5697	+	0.764509i	0.706256	+	0.0346788i
$487$	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
$489$	8.74699	−	35.7130i	0.395553	−	1.61500i
$490$	−1.07515	+	1.60009i	−0.0485705	+	0.0722846i
$491$	−8.01785	+	24.6764i	−0.361841	+	1.11363i	0.590095	+	0.807334i	$0.299090\pi$
$491$	−8.01785	+	24.6764i	−0.361841	+	1.11363i	−0.951936	+	0.306297i	$0.900910\pi$
$492$	−0.935982	−	5.18236i	−0.0421973	−	0.233639i
$493$	−49.3492	−	21.9717i	−2.22258	−	0.989555i
$494$	0.352828	+	0.611116i	0.0158745	+	0.0274954i
$495$	2.35197	+	1.40590i	0.105713	+	0.0631906i
$496$	−5.00442			−0.224705
$497$	11.6293	−	27.4645i	0.521645	−	1.23195i
$498$	−5.58282	+	4.72417i	−0.250172	+	0.211695i
$499$	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
$501$	6.64817	−	1.93623i	0.297018	−	0.0865042i
$502$	7.37430	−	6.63985i	0.329131	−	0.296351i
$503$	10.3394	+	31.8215i	0.461013	+	1.41885i	0.863929	+	0.503614i	$0.167997\pi$
$503$	10.3394	+	31.8215i	0.461013	+	1.41885i	−0.402916	+	0.915237i	$0.632003\pi$
$504$	−1.16960	+	7.85061i	−0.0520980	+	0.349694i
$505$			1.44942i			0.0644982i
$506$	3.12041	+	2.55809i	0.138719	+	0.113721i
$507$	−13.3533	+	17.2385i	−0.593042	+	0.765587i
$508$	−0.0352910	+	0.0792649i	−0.00156578	+	0.00351681i
$509$	−1.20700	+	5.67847i	−0.0534991	+	0.251694i	−0.996768	−	0.0803369i	$-0.974400\pi$
$509$	−1.20700	+	5.67847i	−0.0534991	+	0.251694i	0.943269	+	0.332031i	$0.107734\pi$
$510$	−0.215454	−	2.90767i	−0.00954045	−	0.128754i
$511$	−12.7735	−	27.3297i	−0.565067	−	1.20899i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−5.41945	+	1.83579i	−0.239275	+	0.0810521i
$514$	15.5229	+	13.9769i	0.684685	+	0.616493i
$515$	1.48361	−	3.33225i	0.0653757	−	0.146836i
$516$	0.263199	−	1.93087i	0.0115867	−	0.0850016i
$517$	7.03004	+	3.63541i	0.309181	+	0.159885i
$518$	9.26124	−	16.7427i	0.406915	−	0.735631i
$519$	1.11373	+	0.689524i	0.0488872	+	0.0302667i
$520$	0.172619	+	0.0366914i	0.00756987	+	0.00160902i
$521$	−1.69719	−	7.98464i	−0.0743552	−	0.349814i	0.925205	−	0.379468i	$-0.123893\pi$
$521$	−1.69719	−	7.98464i	−0.0743552	−	0.349814i	−0.999560	+	0.0296540i	$0.990559\pi$
$522$	16.4956	+	20.7560i	0.721992	+	0.908464i
$523$	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
$525$	16.9555	−	14.8898i	0.739999	−	0.649842i
$526$	15.6176	−	11.3468i	0.680959	−	0.494746i
$527$	−15.2948	+	26.4913i	−0.666251	+	1.15398i
$528$	−1.10663	+	5.63696i	−0.0481599	+	0.245317i
$529$	−10.7600	−	18.6368i	−0.467825	−	0.810296i
$530$	−0.235951	−	2.24492i	−0.0102490	−	0.0975131i
$531$	12.2663	−	23.5388i	0.532311	−	1.02150i
$532$	−0.657902	−	2.83821i	−0.0285237	−	0.123052i
$533$	1.14522	−	1.57626i	0.0496048	−	0.0682752i
$534$	−21.7509	+	22.7116i	−0.941252	+	0.982825i
$535$	0.389748	+	1.83362i	0.0168503	+	0.0792743i
$536$	−7.10618	+	7.89221i	−0.306940	+	0.340891i
$537$	−1.48895	−	2.77249i	−0.0642530	−	0.119642i
$538$		−	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
$543$	−20.2106	−	29.6969i	−0.867322	−	1.27442i
$544$	5.58406	−	2.48618i	0.239415	−	0.106594i
$545$	1.05651	+	0.767602i	0.0452561	+	0.0328805i
$546$	−2.39699	+	1.69644i	−0.102582	+	0.0726011i
$547$	−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
$549$	3.55649	−	12.8031i	0.151787	−	0.546421i
$550$	12.7536	−	10.2013i	0.543816	−	0.434984i
$551$	−8.42794	−	4.86588i	−0.359043	−	0.207293i
$552$	−1.10921	+	1.79161i	−0.0472111	+	0.0762559i
$553$	−31.0591	+	10.7253i	−1.32077	+	0.456086i
$554$	29.2451	+	9.50230i	1.24250	+	0.403714i
$555$	2.38591	−	2.49129i	0.101276	−	0.105750i
$556$	−9.31685	−	0.979240i	−0.395122	−	0.0415290i
$557$	44.9497	−	9.55435i	1.90458	−	0.404831i	0.904800	−	0.425837i	$-0.140020\pi$
$557$	44.9497	−	9.55435i	1.90458	−	0.404831i	0.999779	+	0.0210059i	$0.00668688\pi$
$558$	12.6655	−	8.06121i	0.536173	−	0.341258i
$559$	0.583282	−	0.423779i	0.0246702	−	0.0179239i
$560$	−0.637580	−	0.352679i	−0.0269427	−	0.0149034i
$561$	26.4577	+	23.0861i	1.11704	+	0.974694i
$562$	−3.28077	+	5.68246i	−0.138391	+	0.239700i
$563$	−2.94216	−	1.30993i	−0.123997	−	0.0552072i	0.343800	−	0.939043i	$-0.388286\pi$
$563$	−2.94216	−	1.30993i	−0.123997	−	0.0552072i	−0.467798	+	0.883836i	$0.654952\pi$
$564$	−1.39749	+	3.88973i	−0.0588451	+	0.163787i
$565$	−0.275070	−	0.305496i	−0.0115723	−	0.0128523i
$566$	−11.9900	+	16.5028i	−0.503977	+	0.693665i
$567$	−9.68583	−	21.7528i	−0.406766	−	0.913532i
$568$	10.7211	+	3.48350i	0.449848	+	0.146165i
$569$	−15.9791	−	3.39647i	−0.669880	−	0.142387i	−0.139597	−	0.990208i	$-0.544581\pi$
$569$	−15.9791	−	3.39647i	−0.669880	−	0.142387i	−0.530282	+	0.847821i	$0.677914\pi$
$570$	0.0161527	−	0.525013i	0.000676561	−	0.0219904i
$571$	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
$576$	−2.99433	−	0.184423i	−0.124764	−	0.00768429i
$577$	−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
$579$	−6.79629	−	3.27993i	−0.282444	−	0.136309i
$580$	−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
$585$	−0.495979	+	0.185198i	−0.0205062	+	0.00765699i
$586$	8.71955	+	1.85340i	0.360201	+	0.0765631i
$587$	19.6492	+	6.38441i	0.811009	+	0.263513i	0.685025	−	0.728520i	$-0.259791\pi$
$587$	19.6492	+	6.38441i	0.811009	+	0.263513i	0.125984	+	0.992032i	$0.459791\pi$
$588$	11.5086	−	3.81485i	0.474605	−	0.157322i
$589$	−3.23917	+	4.45833i	−0.133468	+	0.183702i
$590$	1.63040	+	1.81074i	0.0671226	+	0.0745472i
$591$	27.1736	+	9.76287i	1.11777	+	0.401591i
$592$	6.60653	+	2.94142i	0.271527	+	0.120892i
$593$	4.92618	−	8.53239i	0.202294	−	0.350383i	−0.746973	−	0.664854i	$-0.768494\pi$
$593$	4.92618	−	8.53239i	0.202294	−	0.350383i	0.949267	+	0.314471i	$0.101827\pi$
$594$	−6.27941	−	16.0490i	−0.257647	−	0.658497i
$595$	−3.81555	+	2.29721i	−0.156422	+	0.0941766i
$596$	−11.5293	+	8.37651i	−0.472258	+	0.343115i
$597$	−1.67642	−	9.28202i	−0.0686113	−	0.379888i
$598$	−0.762565	+	0.162088i	−0.0311836	+	0.00662828i
$599$	−2.87618	−	0.302299i	−0.117518	−	0.0123516i	0.0455871	−	0.998960i	$-0.485484\pi$
$599$	−2.87618	−	0.302299i	−0.117518	−	0.0123516i	−0.163105	+	0.986609i	$0.552151\pi$
$600$	6.15971	+	5.89915i	0.251469	+	0.240832i
$601$	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
$603$	5.27183	−	31.4209i	0.214685	−	1.27956i
$604$	9.06517	+	5.23378i	0.368856	+	0.212959i
$605$	0.352871	−	3.00871i	0.0143462	−	0.122321i
$606$	5.58245	−	7.20666i	0.226772	−	0.292751i
$607$	−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
$609$	16.9304	−	36.7899i	0.686054	−	1.49080i
$610$	0.986836	+	0.716978i	0.0399558	+	0.0290296i
$611$	−1.39696	+	0.621966i	−0.0565149	+	0.0251621i
$612$	−10.1277	+	15.2871i	−0.409388	+	0.617944i
$613$	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	$0.218673\pi$
$617$			31.5067i			1.26841i	−0.773165	+	0.634205i	$0.781327\pi$
$618$	−20.2109	+	10.8541i	−0.813001	+	0.436618i
$619$	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
$621$	−0.0787020	−	6.32105i	−0.00315820	−	0.253655i
$622$	−11.7247	+	16.1376i	−0.470117	+	0.647061i
$623$	45.9496	+	14.0037i	1.84093	+	0.561047i
$624$	−0.716966	−	0.847281i	−0.0287016	−	0.0339184i
$625$	−2.49490	−	23.7374i	−0.0997959	−	0.949495i
$626$	−12.2926	−	21.2914i	−0.491311	−	0.850975i
$627$	4.30558	+	4.63446i	0.171948	+	0.185083i
$628$	−7.53548	+	13.0518i	−0.300698	+	0.520825i
$629$	35.7619	−	25.9826i	1.42592	−	1.03599i
$630$	2.18173	−	0.134446i	0.0869222	−	0.00535645i
$631$	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
$633$	−10.0179	−	34.3972i	−0.398177	−	1.36717i
$634$	−3.29061	−	15.4811i	−0.130687	−	0.614833i
$635$	0.0233727	+	0.00496802i	0.000927517	+	0.000197150i
$636$	−7.47318	+	12.0708i	−0.296331	+	0.478637i
$637$	3.96436	+	2.09889i	0.157074	+	0.0831609i
$638$	13.4636	−	26.0355i	0.533030	−	1.03076i
$639$	−32.7450	+	8.45352i	−1.29537	+	0.334416i
$640$	0.112013	−	0.251585i	0.00442769	−	0.00994475i
$641$	17.1858	+	15.4741i	0.678797	+	0.611192i	0.934669	−	0.355519i	$-0.115696\pi$
$641$	17.1858	+	15.4741i	0.678797	+	0.611192i	−0.255872	+	0.966711i	$0.582362\pi$
$642$	5.12435	−	10.6181i	0.202242	−	0.419063i
$643$	−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
$645$	−0.535198	+	0.0396573i	−0.0210734	+	0.00156150i
$646$	1.39946	−	6.58394i	0.0550610	−	0.259041i
$647$	−11.2366	+	25.2378i	−0.441756	+	0.992199i	0.546227	+	0.837637i	$0.316063\pi$
$647$	−11.2366	+	25.2378i	−0.441756	+	0.992199i	−0.987983	+	0.154563i	$0.950603\pi$
$648$	7.87530	−	4.35657i	0.309371	−	0.171142i
$649$	−29.2945	−	1.71201i	−1.14991	−	0.0672022i
$650$			3.15547i			0.123768i
$651$	−19.7167	−	11.7123i	−0.772760	−	0.459041i
$652$	−6.55992	−	20.1894i	−0.256906	−	0.790677i
$653$	−8.39627	+	7.56003i	−0.328571	+	0.295847i	−0.816861	−	0.576835i	$-0.804288\pi$
$653$	−8.39627	+	7.56003i	−0.328571	+	0.295847i	0.488290	+	0.872682i	$0.337621\pi$
$654$	−2.29667	−	7.88579i	−0.0898070	−	0.308359i
$655$	3.23684	+	0.340205i	0.126474	+	0.0132929i
$656$	−2.03445	−	2.25949i	−0.0794321	−	0.0882183i
$657$	−15.8078	+	30.3349i	−0.616721	+	1.18348i
$658$	6.26576	−	0.774973i	0.244265	−	0.0302116i
$659$	−34.2568			−1.33445			−0.667227	−	0.744855i	$-0.732519\pi$
$659$	−34.2568			−1.33445			−0.667227	+	0.744855i	$0.732519\pi$
$660$	1.58182	−	0.0246599i	0.0615724	−	0.000959885i
$661$	−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
$663$	−6.67640	+	1.20582i	−0.259290	+	0.0468301i
$664$	−1.30479	+	4.01573i	−0.0506356	+	0.155840i
$665$	−0.726876	+	0.339732i	−0.0281870	+	0.0131742i
$666$	−21.4583	+	3.19761i	−0.831493	+	0.123905i
$667$	7.98995	−	7.19419i	0.309372	−	0.278560i
$668$	2.67505	−	2.97094i	0.103501	−	0.114949i
$669$	0.300442	−	9.76531i	0.0116158	−	0.377549i
$670$	2.53285	+	1.46234i	0.0978525	+	0.0564952i
$671$	−14.5230	+	2.21075i	−0.560653	+	0.0853450i
$672$	1.81177	+	4.20921i	0.0698907	+	0.162374i
$673$	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
$675$	−25.0918	−	5.00777i	−0.965785	−	0.192749i
$676$	−1.31595	+	12.5204i	−0.0506133	+	0.481554i
$677$	39.3125	−	17.5031i	1.51090	−	0.672697i	0.526750	−	0.850020i	$-0.323410\pi$
$677$	39.3125	−	17.5031i	1.51090	−	0.672697i	0.984153	+	0.177323i	$0.0567438\pi$
$678$	0.191055	+	2.57840i	0.00733742	+	0.0990227i
$679$	17.4499	−	20.1098i	0.669667	−	0.771743i
$680$	−0.989447	−	1.36186i	−0.0379436	−	0.0522248i
$681$	−41.2269	−	5.61969i	−1.57982	−	0.215347i
$682$	−13.8654	−	9.12336i	−0.530935	−	0.349351i
$683$	7.54826	−	4.35799i	0.288826	−	0.166754i	−0.348586	−	0.937277i	$-0.613338\pi$
$683$	7.54826	−	4.35799i	0.288826	−	0.166754i	0.637412	+	0.770523i	$0.280005\pi$
$684$	−2.10241	+	2.54821i	−0.0803877	+	0.0974334i
$685$	−0.732245	−	2.25362i	−0.0279776	−	0.0861063i
$686$	−13.1306	−	13.0610i	−0.501327	−	0.498670i
$687$	10.6824	−	43.6151i	0.407559	−	1.66402i
$688$	−0.457617	−	1.02783i	−0.0174465	−	0.0391855i
$689$	−5.13770	+	1.09205i	−0.195731	+	0.0416039i
$690$	0.546126	+	0.196211i	0.0207907	+	0.00746962i
$691$	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
$693$	−17.5527	+	19.6190i	−0.666771	+	0.745263i
$694$	−5.69459			−0.216164
$695$	0.269676	+	2.56580i	0.0102294	+	0.0973263i
$696$	14.4055	+	5.17557i	0.546039	+	0.196179i
$697$	−18.1786	+	3.86399i	−0.688565	+	0.146359i
$698$	0.656690	+	1.47495i	0.0248561	+	0.0558276i
$699$	6.94485	−	28.3551i	0.262678	−	1.07249i
$700$	3.79801	−	12.4622i	0.143551	−	0.471027i
$701$	−2.37893	−	7.32158i	−0.0898508	−	0.276532i	0.896027	−	0.444000i	$-0.146441\pi$
$701$	−2.37893	−	7.32158i	−0.0898508	−	0.276532i	−0.985878	+	0.167468i	$0.946441\pi$
$702$	3.17936	+	0.989448i	0.119997	+	0.0373443i
$703$	6.89660	−	3.98176i	0.260110	−	0.150175i
$704$	1.16993	+	3.10343i	0.0440932	+	0.116965i
$705$	1.12782	+	0.153734i	0.0424760	+	0.00578996i
$706$	2.27594	+	3.13256i	0.0856561	+	0.117896i
$707$	−13.6713	−	2.64486i	−0.514162	−	0.0994704i
$708$	−1.13243	−	15.2828i	−0.0425592	−	0.574361i
$709$	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
$711$	31.0604	+	20.5775i	1.16486	+	0.771717i
$712$	−3.77483	+	17.7592i	−0.141468	+	0.665554i
$713$	−3.57860	−	4.92552i	−0.134020	−	0.184462i
$714$	27.8191	+	3.27364i	1.04110	+	0.122513i
$715$	0.411376	+	0.416355i	0.0153846	+	0.0155708i
$716$	−1.57351	−	0.908464i	−0.0588047	−	0.0339509i
$717$	−0.728905	+	23.6917i	−0.0272215	+	0.884784i
$718$	8.86611	−	9.84681i	0.330880	−	0.367480i
$719$	19.1451	−	17.2383i	0.713991	−	0.642881i	−0.229870	−	0.973221i	$-0.573830\pi$
$719$	19.1451	−	17.2383i	0.713991	−	0.642881i	0.943862	+	0.330340i	$0.107164\pi$
$720$	0.121769	+	0.817158i	0.00453805	+	0.0304537i
$721$	28.7234	+	20.0744i	1.06971	+	0.747611i
$722$	−5.49660	+	16.9168i	−0.204562	+	0.629578i
$723$	−5.41321	+	0.977676i	−0.201319	+	0.0363601i
$724$	−18.9464	−	8.43550i	−0.704139	−	0.313503i
$725$	−21.7586	−	37.6871i	−0.808096	−	1.39966i
$726$	−13.3426	+	13.6005i	−0.495191	+	0.504764i
$727$	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
$729$	−12.9136	+	23.7116i	−0.478283	+	0.878206i
$730$	−2.10113	−	2.33354i	−0.0777664	−	0.0863684i
$731$	−6.83948	−	0.718859i	−0.252967	−	0.0265880i
$732$	−2.14521	−	7.36571i	−0.0792891	−	0.272245i
$733$	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
$735$	−1.68658	−	2.88170i	−0.0622104	−	0.106293i
$736$			1.21658i			0.0448438i
$737$	−34.0766	+	8.91147i	−1.25523	+	0.328258i
$738$	8.78856	+	2.44132i	0.323511	+	0.0898662i
$739$	−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
$741$	−1.21889	+	0.0903178i	−0.0447770	+	0.00331791i
$742$	21.6053	+	1.87094i	0.793154	+	0.0686842i
$743$	16.6041	+	12.0636i	0.609145	+	0.442570i	0.849113	−	0.528211i	$-0.177137\pi$
$743$	16.6041	+	12.0636i	0.609145	+	0.442570i	−0.239968	+	0.970781i	$0.577137\pi$
$744$	3.76739	−	7.80636i	0.138119	−	0.286195i
$745$	2.91657	+	2.62609i	0.106855	+	0.0962124i
$746$	5.30198	−	11.9084i	0.194119	−	0.435999i
$747$	−3.16637	−	12.2650i	−0.115852	−	0.448754i
$748$	20.0039	+	3.29177i	0.731415	+	0.120359i
$749$	−18.0064	+	0.330257i	−0.657940	+	0.0120673i
$750$	2.49184	−	4.02485i	0.0909891	−	0.146967i
$751$	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
$753$	4.80599	+	16.5017i	0.175140	+	0.601356i
$754$	2.30343	+	5.17359i	0.0838859	+	0.188411i
$755$	0.890802	−	2.74161i	0.0324196	−	0.0997773i
$756$	−11.3656	−	7.73449i	−0.413364	−	0.281301i
$757$	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
$759$	−6.33943	+	2.94174i	−0.230107	+	0.106779i
$760$	−0.151630	−	0.262631i	−0.00550020	−	0.00952662i
$761$	1.46847	+	13.9716i	0.0532320	+	0.506469i	0.988357	+	0.152151i	$0.0486201\pi$
$761$	1.46847	+	13.9716i	0.0532320	+	0.506469i	−0.935125	+	0.354317i	$0.884713\pi$
$762$	−0.0970773	−	0.114722i	−0.00351674	−	0.00415594i
$763$	−9.16814	+	8.56462i	−0.331909	+	0.310060i
$764$	−6.75112	+	9.29212i	−0.244247	+	0.336177i
$765$	4.69786	+	1.85285i	0.169851	+	0.0669900i
$766$	3.87623	+	18.2362i	0.140054	+	0.658902i
$767$	3.79378	−	4.21342i	0.136986	−	0.152138i
$768$	−1.52592	+	0.819488i	−0.0550620	+	0.0295707i
$769$			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	0.498355	−	0.866973i	$-0.333938\pi$
$773$	−8.66828	−	7.80495i	−0.311776	−	0.280725i	−0.810131	+	0.586248i	$0.800604\pi$
$774$	2.81381	+	1.86414i	0.101140	+	0.0670053i
$775$	−22.5121	+	10.0230i	−0.808658	+	0.360038i
$776$	8.14146	+	5.91512i	0.292261	+	0.212340i
$777$	19.1448	+	27.0507i	0.686816	+	0.970437i
$778$	−29.4856	+	9.58047i	−1.05711	+	0.343476i
$779$	−3.32976	+	0.349972i	−0.119301	+	0.0125390i
$780$	−0.187185	+	0.241646i	−0.00670230	+	0.00865233i
$781$	23.3537	+	29.1968i	0.835662	+	1.04474i
$782$	6.44008	+	3.71818i	0.230297	+	0.132962i
$783$	−44.7952	+	10.1060i	−1.60085	+	0.361159i
$784$	4.49001	−	5.37027i	0.160357	−	0.191795i
$785$	3.94731	+	1.28256i	0.140885	+	0.0457765i
$786$	−14.7836	−	14.1583i	−0.527314	−	0.505009i
$787$	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
$789$	5.94274	+	32.9038i	0.211567	+	1.17141i
$790$	−2.76703	+	2.01037i	−0.0984465	+	0.0715256i
$791$	3.38346	−	2.03707i	0.120302	−	0.0724299i
$792$	−7.95998	−	5.96981i	−0.282846	−	0.212128i
$793$	1.41917	−	2.45808i	0.0503963	−	0.0872889i
$794$	−1.02417	−	0.455988i	−0.0363463	−	0.0161824i
$795$	3.67947	+	1.32195i	0.130497	+	0.0468847i
$796$	−3.64387	−	4.04693i	−0.129154	−	0.143440i
$797$	−15.3391	+	21.1125i	−0.543339	+	0.747842i	−0.989090	−	0.147315i	$-0.952937\pi$
$797$	−15.3391	+	21.1125i	−0.543339	+	0.747842i	0.445751	+	0.895157i	$0.352937\pi$
$798$	4.92259	+	1.11039i	0.174258	+	0.0393074i
$799$	13.8723	+	4.50738i	0.490766	+	0.159460i
$800$	4.81655	+	1.02379i	0.170291	+	0.0361964i
$801$	−19.0533	−	51.0266i	−0.673214	−	1.80294i
$802$	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
$807$	33.7536	+	16.2897i	1.18818	+	0.573424i
$808$	0.550141	−	5.23424i	0.0193539	−	0.184140i
$809$	4.81944	−	45.8539i	0.169443	−	1.61214i	−0.497796	−	0.867294i	$-0.665857\pi$
$809$	4.81944	−	45.8539i	0.169443	−	1.61214i	0.667239	−	0.744844i	$-0.267476\pi$
$810$	−1.62447	−	1.87197i	−0.0570782	−	0.0657742i
$811$	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
$816$	−0.325574	+	10.5822i	−0.0113974	+	0.370450i
$817$	−1.21187	−	0.257590i	−0.0423978	−	0.00901194i
$818$	17.2490	+	5.60453i	0.603096	+	0.195958i
$819$	−0.841785	−	5.01616i	−0.0294143	−	0.175279i
$820$	−0.492164	+	0.677405i	−0.0171871	+	0.0236560i
$821$	−6.39806	−	7.10577i	−0.223294	−	0.247993i	0.621080	−	0.783747i	$-0.286694\pi$
$821$	−6.39806	−	7.10577i	−0.223294	−	0.247993i	−0.844374	+	0.535754i	$0.820027\pi$
$822$	−5.03905	+	14.0255i	−0.175757	+	0.489196i
$823$	−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
$825$	6.31181	+	27.5740i	0.219749	+	0.960002i
$826$	−20.0546	+	12.0742i	−0.697787	+	0.420115i
$827$	−14.2074	+	10.3223i	−0.494039	+	0.358940i	−0.806735	−	0.590913i	$-0.798768\pi$
$827$	−14.2074	+	10.3223i	−0.494039	+	0.358940i	0.312697	+	0.949853i	$0.398768\pi$
$828$	−1.95969	−	3.07900i	−0.0681040	−	0.107003i
$829$	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
$831$	−36.8387	+	38.4658i	−1.27792	+	1.33436i
$832$	−0.609450	−	0.198022i	−0.0211289	−	0.00686519i
$833$	−14.7054	−	40.1812i	−0.509513	−	1.39220i
$834$	8.54136	−	13.7961i	0.295763	−	0.477720i
$835$	−0.953466	−	0.550484i	−0.0329961	−	0.0190503i
$836$	3.52203	+	0.966468i	0.121812	+	0.0334260i
$837$	3.03988	+	25.8254i	0.105074	+	0.892657i
$838$	−11.8213	+	1.24247i	−0.408362	+	0.0429205i
$839$	15.1848	−	4.93383i	0.524236	−	0.170335i	−0.0349307	−	0.999390i	$-0.511121\pi$
$839$	15.1848	−	4.93383i	0.524236	−	0.170335i	0.559167	+	0.829055i	$0.311121\pi$
$840$	1.03012	−	0.729057i	0.0355426	−	0.0251549i
$841$	−39.7240	−	28.8612i	−1.36979	−	0.995213i
$842$	−24.3234	+	10.8295i	−0.838238	+	0.373208i
$843$	−6.39423	−	9.39550i	−0.220229	−	0.323598i
$844$	−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
$849$	−16.7164	−	31.1267i	−0.573706	−	1.06826i
$850$	20.1402	−	22.3679i	0.690802	−	0.767213i
$851$	1.82921	+	8.60575i	0.0627045	+	0.295001i
$852$	−13.5049	+	14.1014i	−0.462670	+	0.483106i
$853$	−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
$855$	0.806805	+	0.420434i	0.0275921	+	0.0143785i
$856$	−0.711518	−	6.76964i	−0.0243192	−	0.231381i
$857$	27.7853	+	48.1256i	0.949128	+	1.64394i	0.747267	+	0.664524i	$0.231366\pi$
$857$	27.7853	+	48.1256i	0.949128	+	1.64394i	0.201861	+	0.979414i	$0.435301\pi$
$858$	−0.441810	−	3.65458i	−0.0150831	−	0.124765i
$859$	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
$861$	−2.72740	−	13.6635i	−0.0929494	−	0.465651i
$862$	1.42040	−	4.37155i	0.0483792	−	0.148896i
$863$	17.0292	+	38.2483i	0.579682	+	1.30199i	0.930756	+	0.365640i	$0.119150\pi$
$863$	17.0292	+	38.2483i	0.579682	+	1.30199i	−0.351074	+	0.936348i	$0.614183\pi$
$864$	2.54185	−	4.53200i	0.0864755	−	0.154182i
$865$	−0.0433021	−	0.203721i	−0.00147232	−	0.00692671i
$866$	−17.8132	−	3.78632i	−0.605318	−	0.128664i
$867$	29.9875	+	18.5657i	1.01843	+	0.630524i
$868$	−13.2382	+	0.242803i	−0.449334	+	0.00824127i
$869$	6.68824	−	40.6441i	0.226883	−	1.37876i
$870$	0.569349	−	4.17683i	0.0193027	−	0.141608i
$871$	2.76803	−	6.21709i	0.0937910	−	0.210658i
$872$	−3.52401	−	3.17303i	−0.119338	−	0.107452i
$873$	−30.1331	−	1.85592i	−1.01985	−	0.0628134i
$874$	1.08383	+	0.787446i	0.0366610	+	0.0266358i
$875$	−7.20401	−	0.623840i	−0.243540	−	0.0210896i
$876$	1.45938	+	19.6952i	0.0493080	+	0.665439i
$877$	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
$879$	−9.45530	+	12.2063i	−0.318919	+	0.411709i
$880$	0.769001	−	0.492844i	0.0259230	−	0.0166138i
$881$			40.9648i			1.38014i	0.723744	+	0.690069i	$0.242420\pi$
$881$			40.9648i			1.38014i	−0.723744	+	0.690069i	$0.757580\pi$
$882$	−2.71305	+	20.8240i	−0.0913530	+	0.701181i
$883$	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
$885$	−4.05196	+	1.18010i	−0.136205	+	0.0396687i
$886$	−15.4858	−	1.62762i	−0.520256	−	0.0546811i
$887$	7.98764	+	8.87117i	0.268199	+	0.297865i	0.862168	−	0.506623i	$-0.169106\pi$
$887$	7.98764	+	8.87117i	0.268199	+	0.297865i	−0.593969	+	0.804488i	$0.702440\pi$
$888$	−9.56179	+	8.09115i	−0.320873	+	0.271521i
$889$	−0.0895097	+	0.211392i	−0.00300206	+	0.00708986i
$890$	5.00003			0.167601
$891$	29.7619	+	2.28667i	0.997061	+	0.0766062i
$892$	−2.82034	−	4.88497i	−0.0944318	−	0.163561i
$893$	2.40056	+	1.06880i	0.0803318	+	0.0357660i
$894$	−4.38707	−	24.2904i	−0.146726	−	0.812393i
$895$	−0.154623	+	0.475880i	−0.00516847	+	0.0159069i
$896$	2.16862	+	1.51562i	0.0724484	+	0.0506333i
$897$	0.321229	−	1.31154i	0.0107255	−	0.0437912i
$898$	13.8589	−	12.4786i	0.462476	−	0.416416i
$899$	−29.5934	+	32.8667i	−0.986994	+	1.09617i
$900$	−13.8392	+	5.16753i	−0.461306	+	0.172251i
$901$	43.3894	+	25.0509i	1.44551	+	0.834566i
$902$	−1.51755	−	9.96917i	−0.0505289	−	0.331937i
$903$	0.602560	−	5.12050i	0.0200519	−	0.170400i
$904$	0.877398	+	1.20764i	0.0291818	+	0.0401653i
$905$	−1.18749	+	5.58671i	−0.0394735	+	0.185708i
$906$	−14.9885	+	10.2006i	−0.497960	+	0.338894i
$907$	−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
$909$	7.03908	+	14.1333i	0.233472	+	0.468772i
$910$	0.458412	+	0.0886849i	0.0151962	+	0.00293988i
$911$	27.3013	+	37.5770i	0.904531	+	1.24498i	0.969000	+	0.247061i	$0.0794647\pi$
$911$	27.3013	+	37.5770i	0.904531	+	1.24498i	−0.0644688	+	0.997920i	$0.520535\pi$
$912$	−0.257606	+	1.88984i	−0.00853018	+	0.0625787i
$913$	−10.9360	+	8.74743i	−0.361930	+	0.289498i
$914$	16.6037	−	9.58613i	0.549200	−	0.317081i
$915$	−1.86131	+	0.999609i	−0.0615331	+	0.0330460i
$916$	−8.01141	−	24.6566i	−0.264704	−	0.814676i
$917$	−9.11542	+	29.9099i	−0.301018	+	0.987713i
$918$	−16.2220	−	27.3065i	−0.535406	−	0.901248i
$919$	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
$921$	−10.6188	+	29.5560i	−0.349902	+	0.973904i
$922$	−2.49625	−	23.7502i	−0.0822097	−	0.782173i
$923$	−7.22380			−0.237774
$924$	−2.65388	+	14.9652i	−0.0873063	+	0.492319i
$925$	35.6103			1.17086
$926$	−0.969268	−	9.22197i	−0.0318521	−	0.303053i
$927$	−1.71629	−	39.6980i	−0.0563703	−	1.30385i
$928$	8.64439	−	1.83742i	0.283766	−	0.0603163i
$929$	−22.8077	−	51.2269i	−0.748296	−	1.68070i	−0.732446	−	0.680826i	$-0.761621\pi$
$929$	−22.8077	−	51.2269i	−0.748296	−	1.68070i	−0.0158503	−	0.999874i	$-0.505046\pi$
$930$	−2.31855	−	0.567871i	−0.0760284	−	0.0186212i
$931$	−1.87806	−	7.47603i	−0.0615508	−	0.245017i
$932$	−5.20838	−	16.0298i	−0.170606	−	0.525072i
$933$	−16.3465	−	30.4379i	−0.535161	−	0.996493i
$934$	−25.0662	+	14.4720i	−0.820190	+	0.473537i
$935$	−0.258652	−	5.57704i	−0.00845882	−	0.182389i
$936$	1.86141	−	0.480547i	0.0608421	−	0.0157072i
$937$	−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
$939$	42.4664	−	3.14669i	1.38584	−	0.102688i
$940$	0.600351	−	0.267294i	0.0195813	−	0.00871816i
$941$	−2.62505	+	24.9757i	−0.0855743	+	0.814186i	0.864599	+	0.502463i	$0.167573\pi$
$941$	−2.62505	+	24.9757i	−0.0855743	+	0.814186i	−0.950173	+	0.311723i	$0.899094\pi$
$942$	−14.6867	−	21.5802i	−0.478518	−	0.703119i
$943$	0.769054	−	3.61812i	0.0250439	−	0.117822i
$944$	−5.20054	−	7.15793i	−0.169263	−	0.232971i
$945$	−1.43272	+	3.50448i	−0.0466062	+	0.114001i
$946$	0.605896	−	3.68200i	0.0196994	−	0.119712i
$947$	−31.8795	−	18.4056i	−1.03594	−	0.598102i	−0.117262	−	0.993101i	$-0.537412\pi$
$947$	−31.8795	−	18.4056i	−1.03594	−	0.598102i	−0.918682	+	0.394999i	$0.870745\pi$
$948$	21.5010	+	0.661504i	0.698319	+	0.0214846i
$949$	−4.88913	+	5.42993i	−0.158708	+	0.176263i
$950$	4.02964	−	3.62831i	0.130739	−	0.117718i
$951$	26.6261	+	6.52138i	0.863410	+	0.211470i
$952$	14.6509	−	6.84765i	0.474839	−	0.221933i
$953$	4.53556	−	13.9590i	0.146921	−	0.452177i	−0.850332	−	0.526247i	$-0.823599\pi$
$953$	4.53556	−	13.9590i	0.146921	−	0.452177i	0.997253	+	0.0740700i	$0.0235988\pi$
$954$	−13.2032	−	20.7444i	−0.427470	−	0.671626i
$955$	2.88962	+	1.28654i	0.0935060	+	0.0416316i
$956$	6.84245	+	11.8515i	0.221301	+	0.383304i
$957$	30.4771	+	40.6017i	0.985183	+	1.31247i
$958$	−31.8979			−1.03058
$959$	22.5929	−	2.79438i	0.729564	−	0.0902352i
$960$	0.308121	+	0.364124i	0.00994455	+	0.0117521i
$961$	−3.98522	−	4.42604i	−0.128556	−	0.142775i
$962$	−4.60882	−	0.484406i	−0.148594	−	0.0156179i
$963$	12.7054	+	15.9869i	0.409426	+	0.515170i
$964$	−2.36014	+	2.12508i	−0.0760150	+	0.0684442i
$965$	0.370777	+	1.14113i	0.0119357	+	0.0367344i
$966$	−2.84727	+	4.79317i	−0.0916095	+	0.154218i
$967$		−	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
$969$	9.21671	+	7.13949i	0.296083	+	0.229353i
$970$	1.12723	−	2.53179i	0.0361931	−	0.0812910i
$971$	3.18344	−	14.9769i	0.102161	−	0.480632i	−0.897086	−	0.441855i	$-0.854321\pi$
$971$	3.18344	−	14.9769i	0.102161	−	0.480632i	0.999248	−	0.0387768i	$-0.0123461\pi$
$972$	0.867156	+	15.5643i	0.0278140	+	0.499226i
$973$	−24.6934	−	2.13836i	−0.791635	−	0.0685526i
$974$	15.4783	+	11.2457i	0.495958	+	0.360334i
$975$	−4.92220	−	2.37548i	−0.157636	−	0.0760762i
$976$	−3.29160	−	2.96377i	−0.105362	−	0.0948679i
$977$	−7.51775	+	16.8851i	−0.240514	+	0.540203i	−0.992960	−	0.118451i	$-0.962207\pi$
$977$	−7.51775	+	16.8851i	−0.240514	+	0.540203i	0.752446	+	0.658654i	$0.228874\pi$
$978$	36.4317	+	4.96605i	1.16496	+	0.158797i
$979$	−42.8348	+	42.3226i	−1.36901	+	1.35264i
$980$	−1.70371	−	0.902009i	−0.0544229	−	0.0288136i
$981$	14.0300	+	2.35396i	0.447942	+	0.0751563i
$982$	−25.3793	−	5.39454i	−0.809887	−	0.172147i
$983$	−7.90921	−	37.2099i	−0.252265	−	1.18681i	−0.903720	−	0.428125i	$-0.859174\pi$
$983$	−7.90921	−	37.2099i	−0.252265	−	1.18681i	0.651455	−	0.758687i	$-0.274159\pi$
$984$	5.05613	−	1.47256i	0.161184	−	0.0469435i
$985$	−1.86731	−	4.19405i	−0.0594974	−	0.133633i
$986$	16.6929	−	51.3755i	0.531611	−	1.63613i
$987$	−3.50808	+	10.3573i	−0.111663	+	0.329678i
$988$	−0.570887	+	0.414774i	−0.0181623	+	0.0131957i
$989$	0.684384	−	1.18539i	0.0217622	−	0.0376932i
$990$	−1.15235	+	2.48604i	−0.0366241	+	0.0790116i
$991$	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
$993$	−6.61940	+	5.60132i	−0.210060	+	0.177752i
$994$	28.5297	+	8.69477i	0.904906	+	0.275781i
$995$	−0.881505	+	1.21329i	−0.0279456	+	0.0384638i
$996$	−5.28185	−	5.05843i	−0.167362	−	0.160282i
$997$	−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
$999$	11.1662	−	35.8799i	0.353282	−	1.13519i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.63004 - 0.585637i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.112013 + 0.251585i) q^{5} +(0.412043 - 1.68233i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.31406 + 1.90922i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.63004 - 0.585637i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.112013 + 0.251585i) q^{5} +(0.412043 - 1.68233i) q^{6} +(-2.57741 + 0.597448i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.31406 + 1.90922i) q^{9} +(-0.238498 + 0.137697i) q^{10} +(0.877660 - 3.19839i) q^{11} +(1.71618 + 0.233935i) q^{12} +(0.376661 + 0.518429i) q^{13} +(-0.863588 - 2.50084i) q^{14} +(-0.0352480 - 0.475691i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.638932 - 6.07903i) q^{17} +(-1.65688 + 2.50095i) q^{18} +(0.228950 - 1.07712i) q^{19} +(-0.161872 - 0.222798i) q^{20} +(4.55117 + 0.535564i) q^{21} +(3.27261 + 0.538529i) q^{22} +(1.05359 + 0.608290i) q^{23} +(-0.0532635 + 1.73123i) q^{24} +(3.29491 - 3.65936i) q^{25} +(-0.476217 + 0.428788i) q^{26} +(-2.65390 - 4.46731i) q^{27} +(2.39687 - 1.12027i) q^{28} +(2.73094 - 8.40497i) q^{29} +(0.469401 - 0.0847782i) q^{30} +(-4.57176 - 2.03548i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.30372 + 4.69952i) q^{33} +6.11252 q^{34} +(-0.439011 - 0.581515i) q^{35} +(-2.66044 - 1.38638i) q^{36} +(4.83899 + 5.37424i) q^{37} +(1.09515 + 0.115105i) q^{38} +(-0.310361 - 1.06565i) q^{39} +(0.204657 - 0.184274i) q^{40} +(-0.939549 - 2.89164i) q^{41} +(-0.0569028 + 4.58222i) q^{42} -1.12509i q^{43} +(-0.193498 + 3.31098i) q^{44} +(-0.221127 + 0.796039i) q^{45} +(-0.494828 + 1.11140i) q^{46} +(-0.496136 + 2.33414i) q^{47} +(-1.72732 + 0.127991i) q^{48} +(6.28611 - 3.07974i) q^{49} +(3.98373 + 2.89435i) q^{50} +(-4.60159 + 9.53488i) q^{51} +(-0.476217 - 0.428788i) q^{52} +(-3.33385 + 7.48795i) q^{53} +(4.16543 - 3.10632i) q^{54} +(0.902975 - 0.137455i) q^{55} +(1.36467 + 2.26664i) q^{56} +(-1.00400 + 1.62167i) q^{57} +(8.64439 + 1.83742i) q^{58} +(-1.83954 - 8.65435i) q^{59} +(0.133380 + 0.457968i) q^{60} +(-1.80155 - 4.04635i) q^{61} +(1.54645 - 4.75948i) q^{62} +(-7.10495 - 3.53832i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0882380 + 0.152833i) q^{65} +(-5.01910 - 2.79438i) q^{66} +(-5.31001 - 9.19720i) q^{67} +(0.638932 + 6.07903i) q^{68} +(-1.36116 - 1.60856i) q^{69} +(0.532441 - 0.497391i) q^{70} +(-6.62602 + 9.11993i) q^{71} +(1.10069 - 2.79078i) q^{72} +(2.37065 + 11.1530i) q^{73} +(-4.83899 + 5.37424i) q^{74} +(-7.51388 + 4.03529i) 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} +(1.70974 + 8.83611i) q^{81} +(2.77758 - 1.23666i) q^{82} +(-3.41598 - 2.48186i) q^{83} +(-4.56307 + 0.422382i) q^{84} +(1.60096 - 0.520183i) q^{85} +(1.11893 - 0.117604i) q^{86} +(-9.37380 + 12.1011i) q^{87} +(-3.31306 + 0.153653i) q^{88} +(-15.7235 - 9.07797i) q^{89} +(-0.814792 - 0.136707i) q^{90} +(-1.28054 - 1.11117i) q^{91} +(-1.15704 - 0.375944i) q^{92} +(6.26010 + 5.99530i) q^{93} +(-2.37321 - 0.249434i) q^{94} +(0.296633 - 0.0630513i) q^{95} +(-0.307844 - 1.70447i) q^{96} +(-8.14146 + 5.91512i) q^{97} +(3.71994 + 5.92976i) q^{98} +(8.13740 - 5.72562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * 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 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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