LMFDB - Embedded newform 462.2.ba.b.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.2
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.468951 + 0.422245i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.177812 + 2.63977i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.468951 + 0.422245i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.177812 + 2.63977i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.315518 - 0.546493i) q^{10} +(2.37729 + 2.31268i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.166797 - 0.513348i) q^{13} +(-2.54511 - 0.722766i) q^{14} +(-0.510519 + 0.370913i) q^{15} +(0.669131 + 0.743145i) q^{16} +(2.04167 - 0.433971i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(-6.95005 + 3.09436i) q^{19} +(0.600151 - 0.195001i) q^{20} +(-0.452769 + 2.60672i) q^{21} +(-2.75641 + 1.84451i) q^{22} +(-0.183774 + 0.318305i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.481018 + 4.57658i) q^{25} +(0.536810 - 0.0564210i) q^{26} +(0.951057 + 0.309017i) q^{27} +(1.23613 - 2.33923i) q^{28} +(2.24314 + 3.08742i) q^{29} +(-0.256665 - 0.576480i) q^{30} +(1.09511 + 0.986040i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.12253 + 2.54850i) q^{33} +2.08729i q^{34} +(-1.03125 - 1.31300i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.695795 - 6.62004i) q^{37} +(-1.58174 - 7.44152i) q^{38} +(-0.112224 - 0.527971i) q^{39} +(0.0659612 + 0.627579i) q^{40} +(6.44949 + 4.68583i) q^{41} +(-2.45562 - 0.984843i) q^{42} +1.98739i q^{43} +(-1.23111 - 3.07967i) q^{44} +(-0.546493 + 0.315518i) q^{45} +(-0.273141 - 0.245937i) q^{46} +(1.05988 + 2.38054i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-6.93677 - 0.938766i) q^{49} +(-4.37657 - 1.42203i) q^{50} +(2.07585 - 0.218181i) q^{51} +(-0.0564210 + 0.536810i) q^{52} +(7.21741 - 8.01575i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.09135 - 0.0807328i) q^{55} +(2.03110 + 1.69547i) q^{56} +(-7.23542 + 2.35093i) q^{57} +(-3.48633 + 1.55222i) q^{58} +(5.08148 - 11.4132i) q^{59} +(0.617246 - 0.131200i) q^{60} +(-5.41931 - 6.01876i) q^{61} +(-1.19218 + 0.866169i) q^{62} +(-0.722766 + 2.54511i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.294979 + 0.170306i) q^{65} +(-2.93411 + 1.54628i) q^{66} +(3.17371 + 5.49702i) q^{67} +(-2.04167 - 0.433971i) q^{68} +(-0.216039 + 0.297352i) q^{69} +(1.49872 - 0.735721i) q^{70} +(3.59753 - 11.0721i) q^{71} +(0.743145 - 0.669131i) q^{72} +(-3.78099 - 1.68341i) q^{73} +(6.62004 + 0.695795i) q^{74} +(-0.956767 + 4.50123i) q^{75} +7.60777 q^{76} +(-6.52765 + 5.86428i) q^{77} +0.539766 q^{78} +(0.495879 - 2.33293i) q^{79} +(-0.627579 - 0.0659612i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-5.92436 + 5.33432i) q^{82} +(-0.361130 + 1.11144i) q^{83} +(1.47387 - 2.19720i) q^{84} +(-0.774203 + 1.06560i) q^{85} +(-1.94396 - 0.413201i) q^{86} +(1.90813 + 3.30498i) q^{87} +(3.26833 - 0.563911i) q^{88} +(-11.1761 - 6.45254i) q^{89} +(-0.195001 - 0.600151i) q^{90} +(1.38478 - 0.349026i) q^{91} +(0.297352 - 0.216039i) q^{92} +(0.986040 + 1.09511i) q^{93} +(-2.54888 + 0.541781i) q^{94} +(1.95265 - 4.38573i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(9.75842 - 3.17070i) q^{97} +(2.36049 - 6.59000i) q^{98} +(1.84451 + 2.75641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−0.468951	+	0.422245i	−0.209721	+	0.188834i	−0.767296	−	0.641293i	$-0.778398\pi$
$5$	−0.468951	+	0.422245i	−0.209721	+	0.188834i	0.557575	+	0.830126i	$0.311732\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−0.177812	+	2.63977i	−0.0672067	+	0.997739i
$7$	−0.177812	+	2.63977i	−0.0672067	+	0.997739i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	−0.315518	−	0.546493i	−0.0997755	−	0.172816i
$11$	2.37729	+	2.31268i	0.716780	+	0.697299i
$11$	2.37729	+	2.31268i	0.716780	+	0.697299i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−0.166797	−	0.513348i	−0.0462612	−	0.142377i	0.925258	−	0.379339i	$-0.123848\pi$
$13$	−0.166797	−	0.513348i	−0.0462612	−	0.142377i	−0.971519	+	0.236961i	$0.923848\pi$
$14$	−2.54511	−	0.722766i	−0.680211	−	0.193167i
$15$	−0.510519	+	0.370913i	−0.131815	+	0.0957695i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	2.04167	−	0.433971i	0.495179	−	0.105253i	0.0464484	−	0.998921i	$-0.485210\pi$
$17$	2.04167	−	0.433971i	0.495179	−	0.105253i	0.448730	+	0.893667i	$0.351876\pi$
$18$	−0.406737	+	0.913545i	−0.0958687	+	0.215325i
$19$	−6.95005	+	3.09436i	−1.59445	+	0.709895i	−0.995838	−	0.0911442i	$-0.970948\pi$
$19$	−6.95005	+	3.09436i	−1.59445	+	0.709895i	−0.598612	+	0.801039i	$0.704281\pi$
$20$	0.600151	−	0.195001i	0.134198	−	0.0436035i
$21$	−0.452769	+	2.60672i	−0.0988023	+	0.568833i
$22$	−2.75641	+	1.84451i	−0.587668	+	0.393251i
$23$	−0.183774	+	0.318305i	−0.0383195	+	0.0663712i	−0.884549	−	0.466447i	$-0.845534\pi$
$23$	−0.183774	+	0.318305i	−0.0383195	+	0.0663712i	0.846230	+	0.532818i	$0.178867\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.481018	+	4.57658i	−0.0962037	+	0.915317i
$26$	0.536810	−	0.0564210i	0.105277	−	0.0110651i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	1.23613	−	2.33923i	0.233607	−	0.442072i
$29$	2.24314	+	3.08742i	0.416542	+	0.573320i	0.964799	−	0.262990i	$-0.0847085\pi$
$29$	2.24314	+	3.08742i	0.416542	+	0.573320i	−0.548257	+	0.836310i	$0.684708\pi$
$30$	−0.256665	−	0.576480i	−0.0468605	−	0.105250i
$31$	1.09511	+	0.986040i	0.196687	+	0.177098i	0.761589	−	0.648060i	$-0.224419\pi$
$31$	1.09511	+	0.986040i	0.196687	+	0.177098i	−0.564902	+	0.825158i	$0.691086\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.12253	+	2.54850i	0.369485	+	0.443638i
$34$			2.08729i			0.357967i
$35$	−1.03125	−	1.31300i	−0.174312	−	0.221938i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−0.695795	−	6.62004i	−0.114388	−	1.08833i	−0.889636	−	0.456671i	$-0.849042\pi$
$37$	−0.695795	−	6.62004i	−0.114388	−	1.08833i	0.775248	−	0.631657i	$-0.217625\pi$
$38$	−1.58174	−	7.44152i	−0.256593	−	1.20717i
$39$	−0.112224	−	0.527971i	−0.0179702	−	0.0845431i
$40$	0.0659612	+	0.627579i	0.0104294	+	0.0992289i
$41$	6.44949	+	4.68583i	1.00724	+	0.731804i	0.963629	−	0.267245i	$-0.0861133\pi$
$41$	6.44949	+	4.68583i	1.00724	+	0.731804i	0.0436126	+	0.999049i	$0.486113\pi$
$42$	−2.45562	−	0.984843i	−0.378911	−	0.151965i
$43$			1.98739i			0.303074i	0.988452	+	0.151537i	$0.0484222\pi$
$43$			1.98739i			0.303074i	−0.988452	+	0.151537i	$0.951578\pi$
$44$	−1.23111	−	3.07967i	−0.185597	−	0.464278i
$45$	−0.546493	+	0.315518i	−0.0814664	+	0.0470346i
$46$	−0.273141	−	0.245937i	−0.0402724	−	0.0362614i
$47$	1.05988	+	2.38054i	0.154600	+	0.347237i	0.974196	−	0.225705i	$-0.0724686\pi$
$47$	1.05988	+	2.38054i	0.154600	+	0.347237i	−0.819596	+	0.572942i	$0.805802\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−6.93677	−	0.938766i	−0.990967	−	0.134109i
$50$	−4.37657	−	1.42203i	−0.618940	−	0.201106i
$51$	2.07585	−	0.218181i	0.290677	−	0.0305514i
$52$	−0.0564210	+	0.536810i	−0.00782418	+	0.0744421i
$53$	7.21741	−	8.01575i	0.991388	−	1.10105i	−0.00349327	−	0.999994i	$-0.501112\pi$
$53$	7.21741	−	8.01575i	0.991388	−	1.10105i	0.994881	−	0.101054i	$-0.0322214\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.09135	−	0.0807328i	−0.281998	−	0.0108860i
$56$	2.03110	+	1.69547i	0.271418	+	0.226567i
$57$	−7.23542	+	2.35093i	−0.958355	+	0.311388i
$58$	−3.48633	+	1.55222i	−0.457778	+	0.203816i
$59$	5.08148	−	11.4132i	0.661552	−	1.48587i	−0.200837	−	0.979625i	$-0.564366\pi$
$59$	5.08148	−	11.4132i	0.661552	−	1.48587i	0.862389	−	0.506246i	$-0.168967\pi$
$60$	0.617246	−	0.131200i	0.0796861	−	0.0169378i
$61$	−5.41931	−	6.01876i	−0.693872	−	0.770623i	0.288516	−	0.957475i	$-0.406838\pi$
$61$	−5.41931	−	6.01876i	−0.693872	−	0.770623i	−0.982388	+	0.186852i	$0.940172\pi$
$62$	−1.19218	+	0.866169i	−0.151407	+	0.110004i
$63$	−0.722766	+	2.54511i	−0.0910599	+	0.320654i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.294979	+	0.170306i	0.0365876	+	0.0211239i
$66$	−2.93411	+	1.54628i	−0.361164	+	0.190334i
$67$	3.17371	+	5.49702i	0.387730	+	0.671568i	0.992144	−	0.125102i	$-0.0399259\pi$
$67$	3.17371	+	5.49702i	0.387730	+	0.671568i	−0.604414	+	0.796671i	$0.706593\pi$
$68$	−2.04167	−	0.433971i	−0.247589	−	0.0526267i
$69$	−0.216039	+	0.297352i	−0.0260080	+	0.0357970i
$70$	1.49872	−	0.735721i	0.179131	−	0.0879355i
$71$	3.59753	−	11.0721i	0.426949	−	1.31401i	−0.474168	−	0.880435i	$-0.657251\pi$
$71$	3.59753	−	11.0721i	0.426949	−	1.31401i	0.901116	−	0.433578i	$-0.142749\pi$
$72$	0.743145	−	0.669131i	0.0875805	−	0.0788578i
$73$	−3.78099	−	1.68341i	−0.442532	−	0.197028i	0.173360	−	0.984859i	$-0.444538\pi$
$73$	−3.78099	−	1.68341i	−0.442532	−	0.197028i	−0.615892	+	0.787831i	$0.711204\pi$
$74$	6.62004	+	0.695795i	0.769564	+	0.0808845i
$75$	−0.956767	+	4.50123i	−0.110478	+	0.519758i
$76$	7.60777			0.872671
$77$	−6.52765	+	5.86428i	−0.743895	+	0.668297i
$78$	0.539766			0.0611165
$79$	0.495879	−	2.33293i	0.0557907	−	0.262475i	−0.941408	−	0.337269i	$-0.890497\pi$
$79$	0.495879	−	2.33293i	0.0557907	−	0.262475i	0.997199	+	0.0747945i	$0.0238301\pi$
$80$	−0.627579	−	0.0659612i	−0.0701654	−	0.00737469i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−5.92436	+	5.33432i	−0.654236	+	0.589077i
$83$	−0.361130	+	1.11144i	−0.0396392	+	0.121997i	−0.968918	−	0.247382i	$-0.920430\pi$
$83$	−0.361130	+	1.11144i	−0.0396392	+	0.121997i	0.929279	+	0.369379i	$0.120430\pi$
$84$	1.47387	−	2.19720i	0.160813	−	0.239734i
$85$	−0.774203	+	1.06560i	−0.0839741	+	0.115580i
$86$	−1.94396	−	0.413201i	−0.209622	−	0.0445566i
$87$	1.90813	+	3.30498i	0.204573	+	0.354331i
$88$	3.26833	−	0.563911i	0.348406	−	0.0601131i
$89$	−11.1761	−	6.45254i	−1.18467	−	0.683968i	−0.227577	−	0.973760i	$-0.573080\pi$
$89$	−11.1761	−	6.45254i	−1.18467	−	0.683968i	−0.957090	+	0.289792i	$0.906414\pi$
$90$	−0.195001	−	0.600151i	−0.0205549	−	0.0632614i
$91$	1.38478	−	0.349026i	0.145164	−	0.0365879i
$92$	0.297352	−	0.216039i	0.0310011	−	0.0225236i
$93$	0.986040	+	1.09511i	0.102248	+	0.113558i
$94$	−2.54888	+	0.541781i	−0.262897	+	0.0558804i
$95$	1.95265	−	4.38573i	0.200338	−	0.449966i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	9.75842	−	3.17070i	0.990817	−	0.321936i	0.231627	−	0.972805i	$-0.425595\pi$
$97$	9.75842	−	3.17070i	0.990817	−	0.321936i	0.759190	+	0.650869i	$0.225595\pi$
$98$	2.36049	−	6.59000i	0.238445	−	0.665691i
$99$	1.84451	+	2.75641i	0.185380	+	0.277029i
$100$	2.30090	−	3.98527i	0.230090	−	0.398527i
$101$	6.10769	−	6.78328i	0.607738	−	0.674961i	−0.358227	−	0.933635i	$-0.616619\pi$
$101$	6.10769	−	6.78328i	0.607738	−	0.674961i	0.965965	+	0.258673i	$0.0832853\pi$
$102$	−0.218181	+	2.07585i	−0.0216031	+	0.205540i
$103$	7.29982	−	0.767242i	0.719273	−	0.0755986i	0.262182	−	0.965018i	$-0.415558\pi$
$103$	7.29982	−	0.767242i	0.719273	−	0.0755986i	0.457091	+	0.889420i	$0.348891\pi$
$104$	−0.513348	−	0.166797i	−0.0503380	−	0.0163558i
$105$	−0.888350	−	1.41360i	−0.0866941	−	0.137954i
$106$	6.34000	+	8.72626i	0.615795	+	0.847569i
$107$	5.89870	+	13.2487i	0.570249	+	1.28080i	0.936625	+	0.350333i	$0.113932\pi$
$107$	5.89870	+	13.2487i	0.570249	+	1.28080i	−0.366376	+	0.930467i	$0.619402\pi$
$108$	−0.743145	−	0.669131i	−0.0715091	−	0.0643871i
$109$	15.8930	−	9.17583i	1.52227	−	0.878886i	0.522621	−	0.852565i	$-0.324954\pi$
$109$	15.8930	−	9.17583i	1.52227	−	0.878886i	0.999654	−	0.0263203i	$-0.00837899\pi$
$110$	0.513785	−	2.02886i	0.0489875	−	0.193445i
$111$		−	6.65651i		−	0.631808i
$112$	−2.08071	+	1.63421i	−0.196609	+	0.154418i
$113$	−7.57686	−	5.50491i	−0.712771	−	0.517859i	0.171295	−	0.985220i	$-0.445205\pi$
$113$	−7.57686	−	5.50491i	−0.712771	−	0.517859i	−0.884067	+	0.467361i	$0.845205\pi$
$114$	−0.795229	−	7.56610i	−0.0744800	−	0.708630i
$115$	−0.0482221	−	0.226867i	−0.00449673	−	0.0211555i
$116$	−0.793446	−	3.73287i	−0.0736696	−	0.346588i
$117$	−0.0564210	−	0.536810i	−0.00521612	−	0.0496281i
$118$	10.1073	+	7.34337i	0.930451	+	0.676012i
$119$	0.782549	+	5.46671i	0.0717362	+	0.501133i
$120$			0.631036i			0.0576054i
$121$	0.303030	+	10.9958i	0.0275482	+	0.999620i
$122$	7.01397	−	4.04952i	0.635015	−	0.366626i
$123$	5.92436	+	5.33432i	0.534181	+	0.480979i
$124$	−0.599373	−	1.34621i	−0.0538253	−	0.120894i
$125$	−3.56143	−	4.90189i	−0.318544	−	0.438439i
$126$	−2.33923	−	1.23613i	−0.208395	−	0.110123i
$127$	0.278565	+	0.0905114i	0.0247187	+	0.00803159i	0.321350	−	0.946960i	$-0.395863\pi$
$127$	0.278565	+	0.0905114i	0.0247187	+	0.00803159i	−0.296632	+	0.954992i	$0.595863\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	−0.207738	+	1.97650i	−0.0182904	+	0.174021i
$130$	−0.227914	+	0.253124i	−0.0199894	+	0.0222004i
$131$	3.08563	−	5.34447i	0.269593	−	0.466949i	−0.699164	−	0.714962i	$-0.746444\pi$
$131$	3.08563	−	5.34447i	0.269593	−	0.466949i	0.968757	+	0.248013i	$0.0797775\pi$
$132$	−0.902455	−	3.19148i	−0.0785487	−	0.277783i
$133$	−6.93259	−	18.8967i	−0.601132	−	1.63855i
$134$	−6.03675	+	1.96146i	−0.521496	+	0.169444i
$135$	−0.576480	+	0.256665i	−0.0496155	+	0.0220902i
$136$	0.848976	−	1.90683i	0.0727991	−	0.163509i
$137$	9.50423	−	2.02019i	0.812001	−	0.172596i	0.216845	−	0.976206i	$-0.430423\pi$
$137$	9.50423	−	2.02019i	0.812001	−	0.172596i	0.595156	+	0.803610i	$0.297090\pi$
$138$	−0.245937	−	0.273141i	−0.0209356	−	0.0232513i
$139$	−11.4310	+	8.30513i	−0.969567	+	0.704432i	−0.955353	−	0.295467i	$-0.904525\pi$
$139$	−11.4310	+	8.30513i	−0.969567	+	0.704432i	−0.0142140	+	0.999899i	$0.504525\pi$
$140$	0.408043	+	1.61893i	0.0344859	+	0.136825i
$141$	0.805243	+	2.47828i	0.0678137	+	0.208709i
$142$	10.0821	+	5.82093i	0.846075	+	0.488482i
$143$	0.790685	−	1.60613i	0.0661204	−	0.134311i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−2.35558	−	0.500693i	−0.195620	−	0.0415803i
$146$	2.43273	−	3.34837i	0.201334	−	0.277113i
$147$	−6.80064	−	1.65871i	−0.560907	−	0.136808i
$148$	−2.05697	+	6.33072i	−0.169082	+	0.520382i
$149$	3.21028	−	2.89055i	0.262996	−	0.236803i	−0.527074	−	0.849820i	$-0.676711\pi$
$149$	3.21028	−	2.89055i	0.262996	−	0.236803i	0.790070	+	0.613017i	$0.210044\pi$
$150$	−4.20395	−	1.87172i	−0.343251	−	0.152825i
$151$	15.4821	+	1.62723i	1.25991	+	0.132422i	0.710842	−	0.703352i	$-0.248314\pi$
$151$	15.4821	+	1.62723i	1.25991	+	0.132422i	0.549073	+	0.835774i	$0.314981\pi$
$152$	−1.58174	+	7.44152i	−0.128296	+	0.603587i
$153$	2.08729			0.168747
$154$	−4.37896	−	7.60426i	−0.352866	−	0.612769i
$155$	−0.929903			−0.0746916
$156$	−0.112224	+	0.527971i	−0.00898509	+	0.0422715i
$157$	−20.1810	−	2.12111i	−1.61062	−	0.169283i	−0.743974	−	0.668209i	$-0.767061\pi$
$157$	−20.1810	−	2.12111i	−1.61062	−	0.169283i	−0.866644	+	0.498926i	$0.833728\pi$
$158$	2.17885	+	0.970085i	0.173340	+	0.0771758i
$159$	8.01575	−	7.21741i	0.635690	−	0.572378i
$160$	0.195001	−	0.600151i	0.0154162	−	0.0474461i
$161$	−0.807575	−	0.541719i	−0.0636459	−	0.0426934i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−5.40335	−	1.14852i	−0.423223	−	0.0899588i	−0.00862333	−	0.999963i	$-0.502745\pi$
$163$	−5.40335	−	1.14852i	−0.423223	−	0.0899588i	−0.414599	+	0.910004i	$0.636078\pi$
$164$	−3.98600	−	6.90396i	−0.311255	−	0.539109i
$165$	−2.07146	−	0.298896i	−0.161263	−	0.0232690i
$166$	−1.01207	−	0.584321i	−0.0785521	−	0.0453521i
$167$	−2.07399	−	6.38308i	−0.160490	−	0.493937i	0.838186	−	0.545385i	$-0.183617\pi$
$167$	−2.07399	−	6.38308i	−0.160490	−	0.493937i	−0.998676	+	0.0514475i	$0.983617\pi$
$168$	1.84275	+	1.89849i	0.142171	+	0.146472i
$169$	10.2815	−	7.46996i	0.790886	−	0.574612i
$170$	−0.881347	−	0.978835i	−0.0675962	−	0.0750732i
$171$	−7.44152	+	1.58174i	−0.569068	+	0.120959i
$172$	0.808343	−	1.81557i	0.0616356	−	0.138436i
$173$	−5.64049	+	2.51131i	−0.428839	+	0.190931i	−0.609794	−	0.792560i	$-0.708748\pi$
$173$	−5.64049	+	2.51131i	−0.428839	+	0.190931i	0.180955	+	0.983491i	$0.442081\pi$
$174$	−3.62948	+	1.17929i	−0.275151	+	0.0894018i
$175$	−11.9956	−	2.08355i	−0.906782	−	0.157502i
$176$	−0.127937	+	3.31416i	−0.00964362	+	0.249814i
$177$	6.24664	−	10.8195i	0.469527	−	0.813244i
$178$	8.63518	−	9.59034i	0.647234	−	0.718827i
$179$	−1.48936	+	14.1703i	−0.111320	+	1.05914i	0.786141	+	0.618047i	$0.212076\pi$
$179$	−1.48936	+	14.1703i	−0.111320	+	1.05914i	−0.897462	+	0.441093i	$0.854591\pi$
$180$	0.627579	−	0.0659612i	0.0467770	−	0.00491646i
$181$	−13.3729	−	4.34511i	−0.993998	−	0.322969i	−0.233533	−	0.972349i	$-0.575029\pi$
$181$	−13.3729	−	4.34511i	−0.993998	−	0.322969i	−0.760465	+	0.649379i	$0.775029\pi$
$182$	0.0534870	+	1.42709i	0.00396472	+	0.105783i
$183$	−4.76050	−	6.55226i	−0.351906	−	0.484357i
$184$	0.149495	+	0.335771i	0.0110209	+	0.0247534i
$185$	3.12158	+	2.81068i	0.229503	+	0.206645i
$186$	−1.27619	+	0.736807i	−0.0935746	+	0.0540253i
$187$	5.85729	+	3.69006i	0.428328	+	0.269844i
$188$		−	2.60582i		−	0.190049i
$189$	−0.984843	+	2.45562i	−0.0716368	+	0.178620i
$190$	3.88391	+	2.82183i	0.281768	+	0.204717i
$191$	1.15043	+	10.9456i	0.0832421	+	0.791996i	0.953904	+	0.300113i	$0.0970244\pi$
$191$	1.15043	+	10.9456i	0.0832421	+	0.791996i	−0.870661	+	0.491883i	$0.836309\pi$
$192$	−0.207912	−	0.978148i	−0.0150047	−	0.0705917i
$193$	1.27106	+	5.97989i	0.0914932	+	0.430442i	0.999923	+	0.0124044i	$0.00394853\pi$
$193$	1.27106	+	5.97989i	0.0914932	+	0.430442i	−0.908430	+	0.418037i	$0.862718\pi$
$194$	1.07253	+	10.2044i	0.0770029	+	0.732633i
$195$	0.275561	+	0.200207i	0.0197333	+	0.0143371i
$196$	5.95522	+	3.67904i	0.425373	+	0.262789i
$197$			23.9888i			1.70913i	0.519341	+	0.854567i	$0.326177\pi$
$197$			23.9888i			1.70913i	−0.519341	+	0.854567i	$0.673823\pi$
$198$	−3.07967	+	1.23111i	−0.218863	+	0.0874914i
$199$	10.0707	−	5.81433i	0.713894	−	0.412167i	−0.0986075	−	0.995126i	$-0.531439\pi$
$199$	10.0707	−	5.81433i	0.713894	−	0.412167i	0.812501	+	0.582960i	$0.198105\pi$
$200$	3.41980	+	3.07920i	0.241816	+	0.217732i
$201$	2.58173	+	5.79865i	0.182101	+	0.409005i
$202$	5.36519	+	7.38455i	0.377493	+	0.519575i
$203$	−8.54895	+	5.37240i	−0.600018	+	0.377069i
$204$	−1.98513	−	0.645007i	−0.138987	−	0.0451595i
$205$	−5.00306	+	0.525843i	−0.349429	+	0.0367265i
$206$	−0.767242	+	7.29982i	−0.0534563	+	0.508603i
$207$	−0.245937	+	0.273141i	−0.0170938	+	0.0189846i
$208$	0.269883	−	0.467451i	0.0187130	−	0.0324119i
$209$	−23.6785	−	8.71703i	−1.63788	−	0.602970i
$210$	1.56741	−	0.575032i	0.108162	−	0.0396810i
$211$	−6.01095	+	1.95307i	−0.413811	+	0.134455i	−0.508521	−	0.861050i	$-0.669808\pi$
$211$	−6.01095	+	1.95307i	−0.413811	+	0.134455i	0.0947103	+	0.995505i	$0.469808\pi$
$212$	−9.85373	+	4.38716i	−0.676757	+	0.301312i
$213$	4.73517	−	10.6354i	0.324449	−	0.728723i
$214$	−14.1856	+	3.01524i	−0.969707	+	0.206118i
$215$	−0.839165	−	0.931987i	−0.0572306	−	0.0635610i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−2.79764	+	2.71550i	−0.189916	+	0.184340i
$218$	5.67098	+	17.4535i	0.384087	+	1.18210i
$219$	−3.58432	−	2.06941i	−0.242206	−	0.139838i
$220$	1.87771	+	0.924382i	0.126595	+	0.0623218i
$221$	−0.563324	−	0.975705i	−0.0378932	−	0.0656330i
$222$	6.51105	+	1.38397i	0.436993	+	0.0928857i
$223$	−12.4231	+	17.0990i	−0.831915	+	1.14503i	0.155648	+	0.987813i	$0.450253\pi$
$223$	−12.4231	+	17.0990i	−0.831915	+	1.14503i	−0.987564	+	0.157220i	$0.949747\pi$
$224$	−1.16589	−	2.37501i	−0.0778996	−	0.158687i
$225$	−1.42203	+	4.37657i	−0.0948022	+	0.291771i
$226$	6.95994	−	6.26675i	0.462968	−	0.416858i
$227$	9.29186	+	4.13700i	0.616722	+	0.274583i	0.691226	−	0.722638i	$-0.257071\pi$
$227$	9.29186	+	4.13700i	0.616722	+	0.274583i	−0.0745040	+	0.997221i	$0.523737\pi$
$228$	7.56610	+	0.795229i	0.501077	+	0.0526653i
$229$	3.43858	−	16.1772i	0.227228	−	1.06902i	−0.705575	−	0.708635i	$-0.749311\pi$
$229$	3.43858	−	16.1772i	0.227228	−	1.06902i	0.932803	−	0.360387i	$-0.117355\pi$
$230$	0.231935			0.0152934
$231$	−7.10488	+	5.14983i	−0.467467	+	0.338834i
$232$	3.81627			0.250550
$233$	−5.49898	+	25.8707i	−0.360250	+	1.69484i	0.308391	+	0.951260i	$0.400209\pi$
$233$	−5.49898	+	25.8707i	−0.360250	+	1.69484i	−0.668642	+	0.743585i	$0.733124\pi$
$234$	0.536810	+	0.0564210i	0.0350923	+	0.00368835i
$235$	−1.50220	−	0.668824i	−0.0979930	−	0.0436293i
$236$	−9.28432	+	8.35964i	−0.604358	+	0.544166i
$237$	0.737020	−	2.26831i	0.0478746	−	0.147343i
$238$	−5.50995	−	0.371145i	−0.357157	−	0.0240578i
$239$	2.34189	−	3.22333i	0.151484	−	0.208500i	−0.726530	−	0.687135i	$-0.758868\pi$
$239$	2.34189	−	3.22333i	0.151484	−	0.208500i	0.878014	+	0.478635i	$0.158868\pi$
$240$	−0.617246	−	0.131200i	−0.0398431	−	0.00846890i
$241$	−8.62814	−	14.9444i	−0.555787	−	0.962652i	−0.997842	−	0.0656638i	$-0.979084\pi$
$241$	−8.62814	−	14.9444i	−0.555787	−	0.962652i	0.442054	−	0.896988i	$-0.354250\pi$
$242$	−10.8185	−	1.98975i	−0.695442	−	0.127906i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.50274	+	7.70264i	0.160222	+	0.493111i
$245$	3.64939	−	2.48878i	0.233151	−	0.159002i
$246$	−6.44949	+	4.68583i	−0.411205	+	0.298758i
$247$	2.74773	+	3.05167i	0.174834	+	0.194173i
$248$	1.44141	−	0.306382i	0.0915298	−	0.0194553i
$249$	−0.475329	+	1.06761i	−0.0301228	+	0.0676568i
$250$	5.53524	−	2.46445i	0.350079	−	0.155865i
$251$	−0.0280581	+	0.00911663i	−0.00177101	+	0.000575437i	−0.309902	−	0.950768i	$-0.600296\pi$
$251$	−0.0280581	+	0.00911663i	−0.00177101	+	0.000575437i	0.308131	+	0.951344i	$0.400296\pi$
$252$	1.69547	−	2.03110i	0.106805	−	0.127947i
$253$	−1.17302	+	0.331695i	−0.0737472	+	0.0208535i
$254$	−0.146451	+	0.253660i	−0.00918912	+	0.0159160i
$255$	−0.881347	+	0.978835i	−0.0551921	+	0.0612970i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−20.8948	+	2.19613i	−1.30338	+	0.136991i	−0.730649	−	0.682753i	$-0.760783\pi$
$257$	−20.8948	+	2.19613i	−1.30338	+	0.136991i	−0.572731	+	0.819744i	$0.694116\pi$
$258$	−1.89012	−	0.614136i	−0.117674	−	0.0382345i
$259$	17.5991	−	0.659613i	1.09356	−	0.0409863i
$260$	−0.200207	−	0.275561i	−0.0124163	−	0.0170896i
$261$	1.55222	+	3.48633i	0.0960797	+	0.215799i
$262$	4.58615	+	4.12938i	0.283333	+	0.255114i
$263$	−11.9581	+	6.90403i	−0.737370	+	0.425721i	−0.821112	−	0.570767i	$-0.806646\pi$
$263$	−11.9581	+	6.90403i	−0.737370	+	0.425721i	0.0837421	+	0.996487i	$0.473313\pi$
$264$	3.30937	−	0.219187i	0.203678	−	0.0134901i
$265$			6.80651i			0.418121i
$266$	19.9252	−	2.85225i	1.22169	−	0.174883i
$267$	−10.4404	−	7.58542i	−0.638944	−	0.464220i
$268$	−0.663486	−	6.31264i	−0.0405288	−	0.385606i
$269$	−5.72636	−	26.9404i	−0.349142	−	1.64259i	−0.705844	−	0.708367i	$-0.749432\pi$
$269$	−5.72636	−	26.9404i	−0.349142	−	1.64259i	0.356702	−	0.934218i	$-0.383901\pi$
$270$	−0.131200	−	0.617246i	−0.00798456	−	0.0375644i
$271$	1.95426	+	18.5935i	0.118713	+	1.12948i	0.877980	+	0.478697i	$0.158891\pi$
$271$	1.95426	+	18.5935i	0.118713	+	1.12948i	−0.759267	+	0.650779i	$0.774443\pi$
$272$	1.68865	+	1.22688i	0.102389	+	0.0743903i
$273$	1.41368	−	0.202365i	0.0855596	−	0.0122477i
$274$			9.71656i			0.586999i
$275$	−11.7277	+	9.76744i	−0.707207	+	0.588998i
$276$	0.318305	−	0.183774i	0.0191597	−	0.0110619i
$277$	−18.2421	−	16.4252i	−1.09606	−	0.986896i	−0.0960953	−	0.995372i	$-0.530635\pi$
$277$	−18.2421	−	16.4252i	−1.09606	−	0.986896i	−0.999964	+	0.00847580i	$0.997302\pi$
$278$	−5.74699	−	12.9080i	−0.344682	−	0.774168i
$279$	0.866169	+	1.19218i	0.0518562	+	0.0713739i
$280$	−1.66839	+	0.0625312i	−0.0997055	+	0.00373695i
$281$	4.92315	+	1.59963i	0.293690	+	0.0954258i	0.452156	−	0.891939i	$-0.350655\pi$
$281$	4.92315	+	1.59963i	0.293690	+	0.0954258i	−0.158466	+	0.987364i	$0.550655\pi$
$282$	−2.59155	+	0.272383i	−0.154324	+	0.0162201i
$283$	−2.21013	+	21.0280i	−0.131379	+	1.24999i	0.707911	+	0.706302i	$0.249638\pi$
$283$	−2.21013	+	21.0280i	−0.131379	+	1.24999i	−0.839290	+	0.543685i	$0.817029\pi$
$284$	−7.78992	+	8.65159i	−0.462247	+	0.513377i
$285$	2.40039	−	4.15759i	0.142187	−	0.246275i
$286$	1.40664	+	1.10734i	0.0831762	+	0.0654783i
$287$	−13.5163	+	16.1920i	−0.797842	+	0.955782i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	−11.5502	+	5.14247i	−0.679422	+	0.302498i
$290$	0.979503	−	2.20000i	0.0575184	−	0.129188i
$291$	10.0364	−	2.13330i	0.588344	−	0.125056i
$292$	2.76941	+	3.07574i	0.162067	+	0.179994i
$293$	7.13210	−	5.18177i	0.416662	−	0.302722i	−0.359632	−	0.933094i	$-0.617098\pi$
$293$	7.13210	−	5.18177i	0.416662	−	0.302722i	0.776293	+	0.630372i	$0.217098\pi$
$294$	3.03640	−	6.30716i	0.177086	−	0.367841i
$295$	2.43620	+	7.49785i	0.141841	+	0.436542i
$296$	−5.76471	−	3.32825i	−0.335067	−	0.193451i
$297$	1.54628	+	2.93411i	0.0897244	+	0.170254i
$298$	2.15993	+	3.74111i	0.125121	+	0.216716i
$299$	0.194054	+	0.0412475i	0.0112225	+	0.00238541i
$300$	2.70487	−	3.72293i	0.156166	−	0.214943i
$301$	−5.24624	−	0.353382i	−0.302388	−	0.0203686i
$302$	−4.81058	+	14.8054i	−0.276818	+	0.851958i
$303$	6.78328	−	6.10769i	0.389689	−	0.350878i
$304$	−6.95005	−	3.09436i	−0.398612	−	0.177474i
$305$	5.08279	+	0.534222i	0.291039	+	0.0305895i
$306$	−0.433971	+	2.04167i	−0.0248085	+	0.116715i
$307$	16.8380			0.960995			0.480498	−	0.876996i	$-0.340456\pi$
$307$	16.8380			0.960995			0.480498	+	0.876996i	$0.340456\pi$
$308$	8.34852	−	2.70225i	0.475701	−	0.153975i
$309$	7.34003			0.417560
$310$	0.193338	−	0.909583i	0.0109808	−	0.0516608i
$311$	12.8760	+	1.35332i	0.730131	+	0.0767398i	0.462297	−	0.886725i	$-0.347025\pi$
$311$	12.8760	+	1.35332i	0.730131	+	0.0767398i	0.267834	+	0.963465i	$0.413692\pi$
$312$	−0.493101	−	0.219543i	−0.0279164	−	0.0124292i
$313$	10.9411	−	9.85139i	0.618426	−	0.556834i	−0.299244	−	0.954177i	$-0.596734\pi$
$313$	10.9411	−	9.85139i	0.618426	−	0.556834i	0.917670	+	0.397343i	$0.130068\pi$
$314$	6.27062	−	19.2990i	0.353872	−	1.08910i
$315$	−0.735721	−	1.49872i	−0.0414532	−	0.0844432i
$316$	−1.40189	+	1.92954i	−0.0788627	+	0.108545i
$317$	16.9418	+	3.60109i	0.951547	+	0.202257i	0.657433	−	0.753513i	$-0.271642\pi$
$317$	16.9418	+	3.60109i	0.951547	+	0.202257i	0.294114	+	0.955770i	$0.404976\pi$
$318$	5.39313	+	9.34117i	0.302431	+	0.523827i
$319$	−1.80761	+	12.5274i	−0.101207	+	0.701399i
$320$	0.546493	+	0.315518i	0.0305499	+	0.0176380i
$321$	4.48152	+	13.7927i	0.250134	+	0.769834i
$322$	0.697785	−	0.677298i	0.0388860	−	0.0377444i
$323$	−12.8469	+	9.33379i	−0.714819	+	0.519346i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	2.42962	−	0.516431i	0.134771	−	0.0286464i
$326$	2.24684	−	5.04648i	0.124441	−	0.279499i
$327$	16.7651	−	7.46430i	0.927111	−	0.412777i
$328$	7.58183	−	2.46349i	0.418637	−	0.136023i
$329$	−6.47253	+	2.37456i	−0.356842	+	0.130914i
$330$	0.723044	−	1.96405i	0.0398023	−	0.108117i
$331$	14.9592	−	25.9101i	0.822232	−	1.42415i	−0.0817839	−	0.996650i	$-0.526062\pi$
$331$	14.9592	−	25.9101i	0.822232	−	1.42415i	0.904016	−	0.427498i	$-0.140605\pi$
$332$	0.781974	−	0.868470i	0.0429164	−	0.0476635i
$333$	0.695795	−	6.62004i	0.0381293	−	0.362776i
$334$	6.67480	−	0.701550i	0.365229	−	0.0383871i
$335$	−3.80941	−	1.23775i	−0.208130	−	0.0676256i
$336$	−2.24013	+	1.40776i	−0.122209	+	0.0767998i
$337$	−14.1051	−	19.4140i	−0.768354	−	1.05755i	−0.996473	−	0.0839156i	$-0.973257\pi$
$337$	−14.1051	−	19.4140i	−0.768354	−	1.05755i	0.228119	−	0.973633i	$-0.426743\pi$
$338$	5.16907	+	11.6099i	0.281161	+	0.631497i
$339$	−6.95994	−	6.26675i	−0.378012	−	0.340363i
$340$	1.14069	−	0.658576i	0.0618625	−	0.0357163i
$341$	0.322998	+	4.87674i	0.0174913	+	0.264090i
$342$		−	7.60777i		−	0.411381i
$343$	3.71157	−	18.1445i	0.200406	−	0.979713i
$344$	1.60783	+	1.16816i	0.0866884	+	0.0629828i
$345$	−0.0242439	−	0.230665i	−0.00130525	−	0.0124186i
$346$	−1.28371	−	6.03937i	−0.0690125	−	0.324678i
$347$	−2.92923	−	13.7809i	−0.157249	−	0.739799i	−0.984134	−	0.177427i	$-0.943222\pi$
$347$	−2.92923	−	13.7809i	−0.157249	−	0.739799i	0.826885	−	0.562371i	$-0.190111\pi$
$348$	−0.398908	−	3.79536i	−0.0213837	−	0.203453i
$349$	−21.3462	−	15.5089i	−1.14263	−	0.830172i	−0.155150	−	0.987891i	$-0.549586\pi$
$349$	−21.3462	−	15.5089i	−1.14263	−	0.830172i	−0.987484	+	0.157719i	$0.949586\pi$
$350$	4.53204	−	11.3003i	0.242248	−	0.604025i
$351$		−	0.539766i		−	0.0288106i
$352$	−3.21513	−	0.814193i	−0.171367	−	0.0433966i
$353$	5.62755	−	3.24907i	0.299524	−	0.172930i	−0.342705	−	0.939443i	$-0.611343\pi$
$353$	5.62755	−	3.24907i	0.299524	−	0.172930i	0.642229	+	0.766513i	$0.278010\pi$
$354$	9.28432	+	8.35964i	0.493456	+	0.444310i
$355$	2.98806	+	6.71130i	0.158590	+	0.356199i
$356$	7.58542	+	10.4404i	0.402026	+	0.553342i
$357$	0.206835	+	5.51857i	0.0109469	+	0.292073i
$358$	−13.5510	−	4.40299i	−0.716193	−	0.232705i
$359$	−5.08399	+	0.534349i	−0.268323	+	0.0282019i	−0.237734	−	0.971330i	$-0.576405\pi$
$359$	−5.08399	+	0.534349i	−0.268323	+	0.0282019i	−0.0305885	+	0.999532i	$0.509738\pi$
$360$	−0.0659612	+	0.627579i	−0.00347646	+	0.0330763i
$361$	26.0146	−	28.8921i	1.36919	−	1.52064i
$362$	7.03053	−	12.1772i	0.369517	−	0.640022i
$363$	−0.848007	+	10.9673i	−0.0445088	+	0.575632i
$364$	−1.40702	−	0.244390i	−0.0737479	−	0.0128095i
$365$	2.48391	−	0.807072i	0.130014	−	0.0422441i
$366$	7.39884	−	3.29418i	0.386744	−	0.172189i
$367$	−3.15944	+	7.09622i	−0.164921	+	0.370420i	−0.977035	−	0.213080i	$-0.931650\pi$
$367$	−3.15944	+	7.09622i	−0.164921	+	0.370420i	0.812113	+	0.583500i	$0.198317\pi$
$368$	−0.359515	+	0.0764174i	−0.0187410	+	0.00398353i
$369$	5.33432	+	5.92436i	0.277693	+	0.308410i
$370$	−3.39827	+	2.46899i	−0.176668	+	0.128357i
$371$	19.8764	+	20.4776i	1.03193	+	1.06314i
$372$	−0.455372	−	1.40149i	−0.0236099	−	0.0726639i
$373$	23.6459	+	13.6520i	1.22434	+	0.706873i	0.965840	−	0.259138i	$-0.0834384\pi$
$373$	23.6459	+	13.6520i	1.22434	+	0.706873i	0.258500	+	0.966011i	$0.416772\pi$
$374$	−4.82722	+	4.96209i	−0.249610	+	0.256583i
$375$	−3.02954	−	5.24731i	−0.156445	−	0.270970i
$376$	2.54888	+	0.541781i	0.131448	+	0.0279402i
$377$	1.21077	−	1.66649i	0.0623581	−	0.0858285i
$378$	−2.19720	−	1.47387i	−0.113012	−	0.0758079i
$379$	6.32520	−	19.4670i	0.324904	−	0.999950i	−0.646580	−	0.762846i	$-0.723802\pi$
$379$	6.32520	−	19.4670i	0.324904	−	0.999950i	0.971484	−	0.237105i	$-0.0761984\pi$
$380$	−3.56767	+	3.21235i	−0.183018	+	0.164790i
$381$	0.267578	+	0.119134i	0.0137085	+	0.00610340i
$382$	−10.9456	−	1.15043i	−0.560026	−	0.0588611i
$383$	−0.295998	+	1.39256i	−0.0151248	+	0.0711565i	−0.985063	−	0.172196i	$-0.944914\pi$
$383$	−0.295998	+	1.39256i	−0.0151248	+	0.0711565i	0.969938	+	0.243352i	$0.0782471\pi$
$384$	1.00000			0.0510310
$385$	0.584984	−	5.50633i	0.0298135	−	0.280629i
$386$	−6.11348			−0.311168
$387$	−0.413201	+	1.94396i	−0.0210042	+	0.0988169i
$388$	−10.2044	−	1.07253i	−0.518050	−	0.0544492i
$389$	−21.6165	−	9.62428i	−1.09600	−	0.487971i	−0.222568	−	0.974917i	$-0.571444\pi$
$389$	−21.6165	−	9.62428i	−1.09600	−	0.487971i	−0.873432	+	0.486947i	$0.838111\pi$
$390$	−0.253124	+	0.227914i	−0.0128174	+	0.0115409i
$391$	−0.237071	+	0.729628i	−0.0119892	+	0.0368989i
$392$	−4.83681	+	5.06017i	−0.244296	+	0.255577i
$393$	3.62738	−	4.99266i	0.182977	−	0.251846i
$394$	−23.4646	−	4.98756i	−1.18213	−	0.251270i
$395$	0.752524	+	1.30341i	0.0378636	+	0.0655817i
$396$	−0.563911	−	3.26833i	−0.0283376	−	0.164240i
$397$	−12.5369	−	7.23819i	−0.629210	−	0.363274i	0.151236	−	0.988498i	$-0.451675\pi$
$397$	−12.5369	−	7.23819i	−0.629210	−	0.363274i	−0.780446	+	0.625223i	$0.785008\pi$
$398$	3.59345	+	11.0595i	0.180123	+	0.554363i
$399$	−4.91937	−	19.5179i	−0.246277	−	0.977116i
$400$	−3.72293	+	2.70487i	−0.186146	+	0.135243i
$401$	22.9721	+	25.5131i	1.14717	+	1.27406i	0.956280	+	0.292453i	$0.0944714\pi$
$401$	22.9721	+	25.5131i	1.14717	+	1.27406i	0.190892	+	0.981611i	$0.438862\pi$
$402$	−6.20871	+	1.31970i	−0.309662	+	0.0658208i
$403$	0.323521	−	0.726641i	0.0161158	−	0.0361966i
$404$	−8.33866	+	3.71261i	−0.414864	+	0.184709i
$405$	−0.600151	+	0.195001i	−0.0298217	+	0.00968967i
$406$	−3.47758	−	9.47912i	−0.172589	−	0.470441i
$407$	13.6559	−	17.3469i	0.676899	−	0.859855i
$408$	1.04364	−	1.80764i	0.0516680	−	0.0894917i
$409$	−22.9201	+	25.4554i	−1.13333	+	1.25869i	−0.171452	+	0.985192i	$0.554846\pi$
$409$	−22.9201	+	25.4554i	−1.13333	+	1.25869i	−0.961874	+	0.273494i	$0.911821\pi$
$410$	0.525843	−	5.00306i	0.0259695	−	0.247084i
$411$	9.66333	−	1.01566i	0.476657	−	0.0500987i
$412$	−6.98079	−	2.26820i	−0.343919	−	0.111746i
$413$	29.2246	+	15.4433i	1.43805	+	0.759917i
$414$	−0.216039	−	0.297352i	−0.0106177	−	0.0146141i
$415$	−0.299950	−	0.673698i	−0.0147240	−	0.0330705i
$416$	0.401125	+	0.361174i	0.0196668	+	0.0177080i
$417$	−12.2365	+	7.06476i	−0.599225	+	0.345963i
$418$	13.4496	−	21.3487i	0.657841	−	1.04420i
$419$		−	29.7464i		−	1.45321i	−0.687056	−	0.726604i	$-0.741097\pi$
$419$		−	29.7464i		−	1.45321i	0.687056	−	0.726604i	$-0.258903\pi$
$420$	0.236583	+	1.65272i	0.0115441	+	0.0806443i
$421$	20.2866	+	14.7391i	0.988710	+	0.718340i	0.959638	−	0.281237i	$-0.0907448\pi$
$421$	20.2866	+	14.7391i	0.988710	+	0.718340i	0.0290721	+	0.999577i	$0.490745\pi$
$422$	−0.660649	−	6.28566i	−0.0321599	−	0.305981i
$423$	0.541781	+	2.54888i	0.0263423	+	0.123931i
$424$	−2.24259	−	10.5505i	−0.108910	−	0.512380i
$425$	1.00402	+	9.55264i	0.0487023	+	0.463371i
$426$	9.41846	+	6.84291i	0.456326	+	0.331540i
$427$	16.8518	−	13.2355i	0.815514	−	0.640512i
$428$		−	14.5025i		−	0.701005i
$429$	0.954240	−	1.51468i	0.0460711	−	0.0731294i
$430$	1.08609	−	0.627056i	0.0523761	−	0.0302393i
$431$	−3.45718	−	3.11286i	−0.166527	−	0.149941i	0.581654	−	0.813436i	$-0.302406\pi$
$431$	−3.45718	−	3.11286i	−0.166527	−	0.149941i	−0.748181	+	0.663495i	$0.769072\pi$
$432$	0.406737	+	0.913545i	0.0195691	+	0.0439530i
$433$	11.3712	+	15.6512i	0.546467	+	0.752147i	0.989527	−	0.144345i	$-0.0461075\pi$
$433$	11.3712	+	15.6512i	0.546467	+	0.752147i	−0.443061	+	0.896492i	$0.646107\pi$
$434$	−2.07450	−	3.30109i	−0.0995793	−	0.158458i
$435$	−2.29033	−	0.744175i	−0.109813	−	0.0356805i
$436$	−18.2511	+	1.91827i	−0.874071	+	0.0918686i
$437$	0.292284	−	2.78090i	0.0139818	−	0.133028i
$438$	2.76941	−	3.07574i	0.132327	−	0.146964i
$439$	−1.26427	+	2.18978i	−0.0603404	+	0.104513i	−0.894618	−	0.446833i	$-0.852552\pi$
$439$	−1.26427	+	2.18978i	−0.0603404	+	0.104513i	0.834277	+	0.551345i	$0.185885\pi$
$440$	−1.29458	+	1.64448i	−0.0617167	+	0.0783977i
$441$	−6.59000	−	2.36049i	−0.313810	−	0.112404i
$442$	1.07151	−	0.348153i	0.0509663	−	0.0165600i
$443$	−8.79443	+	3.91553i	−0.417836	+	0.186033i	−0.604876	−	0.796320i	$-0.706777\pi$
$443$	−8.79443	+	3.91553i	−0.417836	+	0.186033i	0.187040	+	0.982352i	$0.440111\pi$
$444$	−2.70745	+	6.08102i	−0.128490	+	0.288593i
$445$	7.96561	−	1.69314i	0.377606	−	0.0802627i
$446$	−14.1424	−	15.7067i	−0.669663	−	0.743736i
$447$	3.49484	−	2.53915i	0.165300	−	0.120098i
$448$	2.56552	−	0.646624i	0.121209	−	0.0305501i
$449$	−0.221816	−	0.682679i	−0.0104681	−	0.0322176i	0.945686	−	0.325081i	$-0.105392\pi$
$449$	−0.221816	−	0.682679i	−0.0104681	−	0.0322176i	−0.956154	+	0.292864i	$0.905392\pi$
$450$	−3.98527	−	2.30090i	−0.187867	−	0.108465i
$451$	4.49550	+	26.0552i	0.211685	+	1.22689i
$452$	4.68276	+	8.11078i	0.220258	+	0.381499i
$453$	15.2272	+	3.23664i	0.715436	+	0.152071i
$454$	−5.97849	+	8.22868i	−0.280584	+	0.386191i
$455$	−0.502019	+	0.748393i	−0.0235350	+	0.0350852i
$456$	−2.35093	+	7.23542i	−0.110092	+	0.338830i
$457$	12.4998	−	11.2549i	0.584716	−	0.526480i	−0.322817	−	0.946461i	$-0.604630\pi$
$457$	12.4998	−	11.2549i	0.584716	−	0.526480i	0.907533	+	0.419981i	$0.137963\pi$
$458$	15.1088	+	6.72687i	0.705988	+	0.314326i
$459$	2.07585	+	0.218181i	0.0968925	+	0.0101838i
$460$	−0.0482221	+	0.226867i	−0.00224837	+	0.0105777i
$461$	−18.8133			−0.876221			−0.438111	−	0.898921i	$-0.644352\pi$
$461$	−18.8133			−0.876221			−0.438111	+	0.898921i	$0.644352\pi$
$462$	−3.56011	−	8.02033i	−0.165631	−	0.373139i
$463$	−0.154888			−0.00719823			−0.00359912	−	0.999994i	$-0.501146\pi$
$463$	−0.154888			−0.00719823			−0.00359912	+	0.999994i	$0.501146\pi$
$464$	−0.793446	+	3.73287i	−0.0368348	+	0.173294i
$465$	−0.924809	−	0.0972014i	−0.0428870	−	0.00450761i
$466$	−24.1620	−	10.7576i	−1.11928	−	0.498338i
$467$	14.1621	−	12.7516i	0.655344	−	0.590074i	−0.272902	−	0.962042i	$-0.587983\pi$
$467$	14.1621	−	12.7516i	0.655344	−	0.590074i	0.928246	+	0.371968i	$0.121317\pi$
$468$	−0.166797	+	0.513348i	−0.00771019	+	0.0237295i
$469$	−15.0752	+	7.40042i	−0.696108	+	0.341720i
$470$	0.966534	−	1.33032i	0.0445829	−	0.0613631i
$471$	−19.8487	−	4.21898i	−0.914581	−	0.194400i
$472$	−6.24664	−	10.8195i	−0.287525	−	0.498008i
$473$	−4.59619	+	4.72460i	−0.211333	+	0.217237i
$474$	2.06551	+	1.19252i	0.0948720	+	0.0547744i
$475$	−10.8185	−	33.2959i	−0.496387	−	1.52772i
$476$	1.50862	−	5.31238i	0.0691474	−	0.243493i
$477$	8.72626	−	6.34000i	0.399548	−	0.290289i
$478$	2.66599	+	2.96088i	0.121940	+	0.135428i
$479$	15.9266	−	3.38531i	0.727706	−	0.154679i	0.170861	−	0.985295i	$-0.445345\pi$
$479$	15.9266	−	3.38531i	0.727706	−	0.154679i	0.556845	+	0.830616i	$0.312012\pi$
$480$	0.256665	−	0.576480i	0.0117151	−	0.0263126i
$481$	−3.28233	+	1.46139i	−0.149661	+	0.0666336i
$482$	16.4117	−	5.33248i	0.747532	−	0.242888i
$483$	−0.746526	−	0.623166i	−0.0339681	−	0.0283550i
$484$	4.19557	−	10.1684i	0.190708	−	0.462202i
$485$	−3.23741	+	5.60735i	−0.147003	+	0.254617i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	−3.93492	+	37.4383i	−0.178308	+	1.69649i	0.430032	+	0.902814i	$0.358502\pi$
$487$	−3.93492	+	37.4383i	−0.178308	+	1.69649i	−0.608340	+	0.793677i	$0.708164\pi$
$488$	−8.05467	+	0.846580i	−0.364618	+	0.0383229i
$489$	−5.25369	−	1.70703i	−0.237580	−	0.0771945i
$490$	1.67564	+	4.08709i	0.0756979	+	0.184636i
$491$	−17.2147	−	23.6940i	−0.776889	−	1.06930i	−0.995618	−	0.0935109i	$-0.970191\pi$
$491$	−17.2147	−	23.6940i	−0.776889	−	1.06930i	0.218729	−	0.975786i	$-0.429809\pi$
$492$	−3.24251	−	7.28279i	−0.146184	−	0.328334i
$493$	5.91962	+	5.33005i	0.266606	+	0.240054i
$494$	−3.55626	+	2.05321i	−0.160004	+	0.0923783i
$495$	−2.02886	−	0.513785i	−0.0911907	−	0.0230929i
$496$			1.47361i			0.0661672i
$497$	28.5880	+	11.4654i	1.28235	+	0.514294i
$498$	−0.945451	−	0.686910i	−0.0423667	−	0.0307812i
$499$	1.55745	+	14.8182i	0.0697212	+	0.663353i	0.972445	+	0.233132i	$0.0748975\pi$
$499$	1.55745	+	14.8182i	0.0697212	+	0.663353i	−0.902724	+	0.430220i	$0.858436\pi$
$500$	1.25975	+	5.92667i	0.0563378	+	0.265049i
$501$	−1.39541	−	6.56490i	−0.0623424	−	0.293298i
$502$	−0.00308380	−	0.0293404i	−0.000137637	−	0.00130953i
$503$	−1.49833	−	1.08860i	−0.0668073	−	0.0485383i	0.553880	−	0.832596i	$-0.313146\pi$
$503$	−1.49833	−	1.08860i	−0.0668073	−	0.0485383i	−0.620688	+	0.784058i	$0.713146\pi$
$504$	1.63421	+	2.08071i	0.0727935	+	0.0926822i
$505$			5.75997i			0.256315i
$506$	−0.0805618	−	1.21635i	−0.00358141	−	0.0540734i
$507$	11.0060	−	6.35433i	0.488794	−	0.282206i
$508$	−0.217668	−	0.195989i	−0.00965745	−	0.00869561i
$509$	−1.71187	−	3.84491i	−0.0758771	−	0.170423i	0.871624	−	0.490175i	$-0.163067\pi$
$509$	−1.71187	−	3.84491i	−0.0758771	−	0.170423i	−0.947501	+	0.319752i	$0.896400\pi$
$510$	−0.774203	−	1.06560i	−0.0342823	−	0.0471855i
$511$	5.11611	−	9.68162i	0.226323	−	0.428290i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−7.56610	+	0.795229i	−0.334051	+	0.0351102i
$514$	2.19613	−	20.8948i	0.0968671	−	0.921629i
$515$	−3.09930	+	3.44212i	−0.136571	+	0.151678i
$516$	0.993693	−	1.72113i	0.0437449	−	0.0757684i
$517$	−2.98577	+	8.11040i	−0.131314	+	0.356695i
$518$	−3.01386	+	17.3517i	−0.132421	+	0.762388i
$519$	−5.87210	+	1.90796i	−0.257756	+	0.0837502i
$520$	0.311164	−	0.138539i	0.0136455	−	0.00607535i
$521$	−6.65638	+	14.9505i	−0.291622	+	0.654993i	−0.998636	−	0.0522061i	$-0.983375\pi$
$521$	−6.65638	+	14.9505i	−0.291622	+	0.654993i	0.707015	+	0.707199i	$0.250041\pi$
$522$	−3.73287	+	0.793446i	−0.163383	+	0.0347282i
$523$	9.75152	+	10.8302i	0.426404	+	0.473570i	0.917615	−	0.397471i	$-0.130112\pi$
$523$	9.75152	+	10.8302i	0.426404	+	0.473570i	−0.491210	+	0.871041i	$0.663445\pi$
$524$	−4.99266	+	3.62738i	−0.218105	+	0.158463i
$525$	−11.7121	−	3.32602i	−0.511158	−	0.145159i
$526$	−4.26693	−	13.1323i	−0.186047	−	0.572593i
$527$	2.66377	+	1.53793i	0.116036	+	0.0669932i
$528$	−0.473660	+	3.28263i	−0.0206134	+	0.142858i
$529$	11.4325	+	19.8016i	0.497063	+	0.860939i
$530$	−6.65777	−	1.41515i	−0.289195	−	0.0614703i
$531$	7.34337	−	10.1073i	0.318675	−	0.438619i
$532$	−1.35275	+	20.0828i	−0.0586494	+	0.870698i
$533$	1.32971	−	4.09242i	0.0575960	−	0.177262i
$534$	9.59034	−	8.63518i	0.415015	−	0.373681i
$535$	−8.36040	−	3.72229i	−0.361452	−	0.160929i
$536$	6.31264	+	0.663486i	0.272665	+	0.0286582i
$537$	−2.96240	+	13.9370i	−0.127837	+	0.601426i
$538$	27.5423			1.18743
$539$	−14.3196	−	18.2742i	−0.616791	−	0.787127i
$540$	0.631036			0.0271555
$541$	6.09572	−	28.6781i	0.262075	−	1.23297i	−0.628383	−	0.777904i	$-0.716283\pi$
$541$	6.09572	−	28.6781i	0.262075	−	1.23297i	0.890459	−	0.455064i	$-0.150384\pi$
$542$	−18.5935	−	1.95426i	−0.798660	−	0.0839425i
$543$	−12.8454	−	5.71915i	−0.551250	−	0.245432i
$544$	−1.55116	+	1.39667i	−0.0665053	+	0.0598816i
$545$	−3.57859	+	11.0138i	−0.153290	+	0.471778i
$546$	−0.0959771	+	1.42486i	−0.00410744	+	0.0609783i
$547$	4.90236	−	6.74752i	0.209610	−	0.288503i	−0.691248	−	0.722618i	$-0.742939\pi$
$547$	4.90236	−	6.74752i	0.209610	−	0.288503i	0.900858	+	0.434115i	$0.142939\pi$
$548$	−9.50423	−	2.02019i	−0.406000	−	0.0862981i
$549$	−4.04952	−	7.01397i	−0.172829	−	0.299349i
$550$	−7.11567	−	13.5022i	−0.303413	−	0.575735i
$551$	−25.1436	−	14.5166i	−1.07115	−	0.618430i
$552$	0.113578	+	0.349558i	0.00483422	+	0.0148782i
$553$	6.07021	+	1.72383i	0.258132	+	0.0733046i
$554$	19.8590	−	14.4284i	0.843730	−	0.613005i
$555$	2.81068	+	3.12158i	0.119307	+	0.132504i
$556$	13.8208	−	2.93769i	0.586131	−	0.124586i
$557$	15.6544	−	35.1603i	0.663298	−	1.48979i	−0.197214	−	0.980361i	$-0.563189\pi$
$557$	15.6544	−	35.1603i	0.663298	−	1.48979i	0.860512	−	0.509431i	$-0.170144\pi$
$558$	−1.34621	+	0.599373i	−0.0569898	+	0.0253735i
$559$	1.02022	−	0.331490i	0.0431508	−	0.0140205i
$560$	0.285714	−	1.64493i	0.0120736	−	0.0695112i
$561$	5.43949	+	4.28210i	0.229655	+	0.180790i
$562$	−2.58825	+	4.48298i	−0.109179	+	0.189103i
$563$	−0.334727	+	0.371752i	−0.0141071	+	0.0156675i	−0.750157	−	0.661260i	$-0.770022\pi$
$563$	−0.334727	+	0.371752i	−0.0141071	+	0.0156675i	0.736050	+	0.676927i	$0.236689\pi$
$564$	0.272383	−	2.59155i	0.0114694	−	0.109124i
$565$	5.87760	−	0.617761i	0.247273	−	0.0259894i
$566$	−20.1090	−	6.53381i	−0.845244	−	0.274637i
$567$	−1.23613	+	2.33923i	−0.0519126	+	0.0982383i
$568$	−6.84291	−	9.41846i	−0.287122	−	0.395190i
$569$	−3.62513	−	8.14218i	−0.151973	−	0.341338i	0.821475	−	0.570245i	$-0.193152\pi$
$569$	−3.62513	−	8.14218i	−0.151973	−	0.341338i	−0.973448	+	0.228907i	$0.926485\pi$
$570$	3.56767	+	3.21235i	0.149433	+	0.134550i
$571$	−15.1989	+	8.77510i	−0.636055	+	0.367226i	−0.783093	−	0.621904i	$-0.786359\pi$
$571$	−15.1989	+	8.77510i	−0.636055	+	0.367226i	0.147038	+	0.989131i	$0.453026\pi$
$572$	−1.37560	+	1.14567i	−0.0575166	+	0.0479028i
$573$			11.0059i			0.459778i
$574$	−13.0279	−	16.5874i	−0.543776	−	0.692347i
$575$	−1.36835	−	0.994166i	−0.0570642	−	0.0414596i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	9.00052	+	42.3441i	0.374696	+	1.76281i	0.611494	+	0.791249i	$0.290569\pi$
$577$	9.00052	+	42.3441i	0.374696	+	1.76281i	−0.236797	+	0.971559i	$0.576098\pi$
$578$	−2.62868	−	12.3670i	−0.109339	−	0.514397i
$579$	0.639033	+	6.07999i	0.0265573	+	0.252676i
$580$	1.94827	+	1.41550i	0.0808977	+	0.0587756i
$581$	−2.86974	−	1.15093i	−0.119057	−	0.0477485i
$582$			10.2606i			0.425316i
$583$	35.6957	−	2.36421i	1.47837	−	0.0979156i
$584$	−3.58432	+	2.06941i	−0.148320	+	0.0856326i
$585$	0.253124	+	0.227914i	0.0104654	+	0.00942308i
$586$	3.58569	+	8.05359i	0.148124	+	0.332691i
$587$	20.6568	+	28.4316i	0.852596	+	1.17350i	0.983285	+	0.182075i	$0.0582812\pi$
$587$	20.6568	+	28.4316i	0.852596	+	1.17350i	−0.130688	+	0.991423i	$0.541719\pi$
$588$	5.53803	+	4.28138i	0.228385	+	0.176561i
$589$	−10.6622	−	3.46437i	−0.439329	−	0.142747i
$590$	−7.84052	+	0.824072i	−0.322789	+	0.0339265i
$591$	−2.50752	+	23.8574i	−0.103145	+	0.981363i
$592$	4.45407	−	4.94675i	0.183061	−	0.203310i
$593$	−0.303613	+	0.525873i	−0.0124679	+	0.0215950i	−0.872192	−	0.489164i	$-0.837302\pi$
$593$	−0.303613	+	0.525873i	−0.0124679	+	0.0215950i	0.859724	+	0.510759i	$0.170635\pi$
$594$	−3.19148	+	0.902455i	−0.130948	+	0.0370282i
$595$	−2.67527	−	2.23319i	−0.109675	−	0.0915520i
$596$	−4.10843	+	1.33491i	−0.168288	+	0.0546800i
$597$	10.6233	−	4.72980i	0.434783	−	0.193578i
$598$	−0.0806924	+	0.181238i	−0.00329976	+	0.00741137i
$599$	−39.1664	+	8.32507i	−1.60030	+	0.340153i	−0.919735	−	0.392539i	$-0.871597\pi$
$599$	−39.1664	+	8.32507i	−1.60030	+	0.340153i	−0.680560	+	0.732692i	$0.738263\pi$
$600$	3.07920	+	3.41980i	0.125708	+	0.139613i
$601$	3.95193	−	2.87125i	0.161203	−	0.117121i	−0.504259	−	0.863552i	$-0.668234\pi$
$601$	3.95193	−	2.87125i	0.161203	−	0.117121i	0.665462	+	0.746432i	$0.268234\pi$
$602$	1.43641	−	5.05813i	0.0585439	−	0.206154i
$603$	1.96146	+	6.03675i	0.0798768	+	0.245836i
$604$	−13.4817	−	7.78369i	−0.548564	−	0.316714i
$605$	−4.78504	−	5.02855i	−0.194540	−	0.204440i
$606$	4.56390	+	7.90491i	0.185396	+	0.321115i
$607$	−32.4126	−	6.88952i	−1.31559	−	0.279637i	−0.503918	−	0.863752i	$-0.668108\pi$
$607$	−32.4126	−	6.88952i	−1.31559	−	0.279637i	−0.811671	+	0.584115i	$0.801442\pi$
$608$	4.47174	−	6.15482i	0.181353	−	0.249611i
$609$	−9.06368	+	4.44937i	−0.367279	+	0.180297i
$610$	−1.57932	+	4.86064i	−0.0639447	+	0.196802i
$611$	1.04526	−	0.941156i	0.0422867	−	0.0380751i
$612$	−1.90683	−	0.848976i	−0.0770791	−	0.0343178i
$613$	−4.75335	−	0.499597i	−0.191986	−	0.0201785i	0.00804739	−	0.999968i	$-0.497438\pi$
$613$	−4.75335	−	0.499597i	−0.191986	−	0.0201785i	−0.200033	+	0.979789i	$0.564105\pi$
$614$	−3.50082	+	16.4700i	−0.141281	+	0.664677i
$615$	−5.03062			−0.202854
$616$	0.907444	+	8.72792i	0.0365620	+	0.351658i
$617$	32.6246			1.31342			0.656708	−	0.754145i	$-0.271948\pi$
$617$	32.6246			1.31342			0.656708	+	0.754145i	$0.271948\pi$
$618$	−1.52608	+	7.17964i	−0.0613879	+	0.288807i
$619$	38.7791	+	4.07585i	1.55867	+	0.163822i	0.844269	−	0.535919i	$-0.180035\pi$
$619$	38.7791	+	4.07585i	1.55867	+	0.163822i	0.714396	+	0.699741i	$0.246701\pi$
$620$	0.849509	+	0.378226i	0.0341171	+	0.0151899i
$621$	−0.273141	+	0.245937i	−0.0109608	+	0.00986912i
$622$	−4.00082	+	12.3133i	−0.160418	+	0.493716i
$623$	19.0205	−	28.3551i	0.762039	−	1.13602i
$624$	0.317267	−	0.436680i	0.0127008	−	0.0174812i
$625$	−18.7662	−	3.98888i	−0.750649	−	0.159555i
$626$	7.36134	+	12.7502i	0.294218	+	0.509601i
$627$	−22.6377	−	11.1444i	−0.904061	−	0.445063i
$628$	17.5735	+	10.1461i	0.701260	+	0.404872i
$629$	−4.29349	−	13.2140i	−0.171193	−	0.526877i
$630$	1.61893	−	0.408043i	0.0644998	−	0.0162568i
$631$	4.43841	−	3.22469i	0.176690	−	0.128373i	−0.495925	−	0.868365i	$-0.665171\pi$
$631$	4.43841	−	3.22469i	0.176690	−	0.128373i	0.672615	+	0.739992i	$0.265171\pi$
$632$	−1.59591	−	1.77243i	−0.0634818	−	0.0705036i
$633$	−6.18217	+	1.31406i	−0.245719	+	0.0522292i
$634$	−7.04480	+	15.8229i	−0.279785	+	0.628407i
$635$	−0.168852	+	0.0751776i	−0.00670067	+	0.00298333i
$636$	−10.2583	+	3.33314i	−0.406769	+	0.132167i
$637$	0.675118	+	3.71756i	0.0267491	+	0.147295i
$638$	−11.8778	−	4.37270i	−0.470247	−	0.173117i
$639$	5.82093	−	10.0821i	0.230272	−	0.398844i
$640$	−0.422245	+	0.468951i	−0.0166907	+	0.0185369i
$641$	−3.10879	+	29.5782i	−0.122790	+	1.16827i	0.743503	+	0.668732i	$0.233163\pi$
$641$	−3.10879	+	29.5782i	−0.122790	+	1.16827i	−0.866293	+	0.499536i	$0.833504\pi$
$642$	−14.4231	+	1.51592i	−0.569233	+	0.0598288i
$643$	8.27376	+	2.68831i	0.326285	+	0.106016i	0.467579	−	0.883951i	$-0.345126\pi$
$643$	8.27376	+	2.68831i	0.326285	+	0.106016i	−0.141294	+	0.989968i	$0.545126\pi$
$644$	0.517420	+	0.823355i	0.0203892	+	0.0324447i
$645$	−0.737149	−	1.01460i	−0.0290252	−	0.0399498i
$646$	−6.45882	−	14.5067i	−0.254119	−	0.570760i
$647$	−20.3942	−	18.3631i	−0.801780	−	0.721926i	0.162529	−	0.986704i	$-0.448035\pi$
$647$	−20.3942	−	18.3631i	−0.801780	−	0.721926i	−0.964310	+	0.264778i	$0.914701\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	38.4752	−	15.3806i	1.51028	−	0.603743i
$650$			2.48389i			0.0974263i
$651$	−3.06617	+	2.40820i	−0.120172	+	0.0943846i
$652$	4.46906	+	3.24696i	0.175022	+	0.127161i
$653$	−2.02300	−	19.2475i	−0.0791660	−	0.753214i	−0.960040	−	0.279863i	$-0.909711\pi$
$653$	−2.02300	−	19.2475i	−0.0791660	−	0.753214i	0.880874	−	0.473351i	$-0.156956\pi$
$654$	3.81553	+	17.9506i	0.149199	+	0.701926i
$655$	0.809668	+	3.80919i	0.0316364	+	0.148837i
$656$	0.833302	+	7.92834i	0.0325350	+	0.309550i
$657$	−3.34837	−	2.43273i	−0.130632	−	0.0949100i
$658$	−0.976955	−	6.82479i	−0.0380857	−	0.266058i
$659$		−	15.1714i		−	0.590993i	−0.955344	−	0.295496i	$-0.904515\pi$
$659$		−	15.1714i		−	0.590993i	0.955344	−	0.295496i	$-0.0954850\pi$
$660$	1.77080	+	1.11559i	0.0689282	+	0.0434244i
$661$	−28.3617	+	16.3747i	−1.10314	+	0.636900i	−0.937045	−	0.349209i	$-0.886450\pi$
$661$	−28.3617	+	16.3747i	−1.10314	+	0.636900i	−0.166099	+	0.986109i	$0.553117\pi$
$662$	22.2337	+	20.0193i	0.864138	+	0.778073i
$663$	−0.458249	−	1.02924i	−0.0177969	−	0.0399725i
$664$	0.686910	+	0.945451i	0.0266573	+	0.0366906i
$665$	11.2301	+	5.93439i	0.435485	+	0.230126i
$666$	6.33072	+	2.05697i	0.245310	+	0.0797061i
$667$	−1.39497	+	0.146618i	−0.0540136	+	0.00567706i
$668$	−0.701550	+	6.67480i	−0.0271438	+	0.258256i
$669$	−14.1424	+	15.7067i	−0.546777	+	0.607258i
$670$	2.00272	−	3.46882i	0.0773719	−	0.134012i
$671$	1.03617	−	26.8415i	0.0400008	−	1.03620i
$672$	−0.911251	−	2.48387i	−0.0351523	−	0.0958174i
$673$	−24.0714	+	7.82126i	−0.927883	+	0.301487i	−0.733697	−	0.679477i	$-0.762207\pi$
$673$	−24.0714	+	7.82126i	−0.927883	+	0.301487i	−0.194186	+	0.980965i	$0.562207\pi$
$674$	21.9224	−	9.76048i	0.844419	−	0.375960i
$675$	−1.87172	+	4.20395i	−0.0720425	+	0.161810i
$676$	−12.4309	+	2.64228i	−0.478113	+	0.101626i
$677$	21.0604	+	23.3900i	0.809419	+	0.898950i	0.996517	−	0.0833907i	$-0.0265749\pi$
$677$	21.0604	+	23.3900i	0.809419	+	0.898950i	−0.187098	+	0.982341i	$0.559908\pi$
$678$	7.57686	−	5.50491i	0.290988	−	0.211415i
$679$	6.63476	+	26.3238i	0.254619	+	1.01021i
$680$	0.407022	+	1.25269i	0.0156086	+	0.0480383i
$681$	8.80852	+	5.08560i	0.337543	+	0.194881i
$682$	−4.83733	−	0.697992i	−0.185231	−	0.0267275i
$683$	2.14754	+	3.71964i	0.0821732	+	0.142328i	0.904183	−	0.427145i	$-0.140481\pi$
$683$	2.14754	+	3.71964i	0.0821732	+	0.142328i	−0.822010	+	0.569473i	$0.807147\pi$
$684$	7.44152	+	1.58174i	0.284534	+	0.0604795i
$685$	−3.60400	+	4.96048i	−0.137702	+	0.189530i
$686$	16.9764	+	7.40292i	0.648160	+	0.282645i
$687$	5.11072	−	15.7292i	0.194986	−	0.600106i
$688$	−1.47692	+	1.32982i	−0.0563069	+	0.0506990i
$689$	−5.31871	−	2.36804i	−0.202627	−	0.0902153i
$690$	0.230665	+	0.0242439i	0.00878126	+	0.000922948i
$691$	−2.41476	+	11.3605i	−0.0918617	+	0.432175i	0.908050	+	0.418863i	$0.137571\pi$
$691$	−2.41476	+	11.3605i	−0.0918617	+	0.432175i	−0.999911	+	0.0133129i	$0.995762\pi$
$692$	6.17429			0.234711
$693$	−7.60426	+	4.37896i	−0.288862	+	0.166343i
$694$	14.0888			0.534803
$695$	1.85379	−	8.72139i	0.0703182	−	0.330821i
$696$	3.79536	+	0.398908i	0.143863	+	0.0151206i
$697$	15.2013	+	6.76804i	0.575789	+	0.256358i
$698$	19.6081	−	17.6552i	0.742178	−	0.668260i
$699$	−8.17308	+	25.1542i	−0.309134	+	0.951418i
$700$	10.1111	+	6.78247i	0.382162	+	0.256353i
$701$	26.1041	−	35.9292i	0.985939	−	1.35703i	0.0523713	−	0.998628i	$-0.483322\pi$
$701$	26.1041	−	35.9292i	0.985939	−	1.35703i	0.933568	−	0.358401i	$-0.116678\pi$
$702$	0.527971	+	0.112224i	0.0199270	+	0.00423561i
$703$	25.3206	+	43.8566i	0.954984	+	1.65408i
$704$	1.46487	−	2.97560i	0.0552092	−	0.112147i
$705$	−1.42406	−	0.822183i	−0.0536333	−	0.0309652i
$706$	2.00803	+	6.18009i	0.0755733	+	0.232591i
$707$	16.8203	+	17.3290i	0.632591	+	0.651726i
$708$	−10.1073	+	7.34337i	−0.379855	+	0.275981i
$709$	−6.39346	−	7.10066i	−0.240112	−	0.266671i	0.611030	−	0.791608i	$-0.290756\pi$
$709$	−6.39346	−	7.10066i	−0.240112	−	0.266671i	−0.851141	+	0.524937i	$0.824089\pi$
$710$	−7.18589	+	1.52741i	−0.269682	+	0.0573226i
$711$	0.970085	−	2.17885i	0.0363810	−	0.0817132i
$712$	−11.7894	+	5.24897i	−0.441826	+	0.196713i
$713$	−0.515114	+	0.167371i	−0.0192912	+	0.00626808i
$714$	−5.44098	−	0.945059i	−0.203623	−	0.0353679i
$715$	0.307387	+	1.08706i	0.0114956	+	0.0406537i
$716$	7.12419	−	12.3395i	0.266243	−	0.461147i
$717$	2.66599	−	2.96088i	0.0995632	−	0.110576i
$718$	0.534349	−	5.08399i	0.0199417	−	0.189733i
$719$	−24.5611	+	2.58148i	−0.915975	+	0.0962728i	−0.550772	−	0.834655i	$-0.685667\pi$
$719$	−24.5611	+	2.58148i	−0.915975	+	0.0962728i	−0.365202	+	0.930928i	$0.619000\pi$
$720$	−0.600151	−	0.195001i	−0.0223663	−	0.00726725i
$721$	0.727345	+	19.4063i	0.0270878	+	0.722728i
$722$	22.8520	+	31.4531i	0.850465	+	1.17056i
$723$	−7.01876	−	15.7644i	−0.261031	−	0.586284i
$724$	10.4494	+	9.40869i	0.388349	+	0.349671i
$725$	−15.2089	+	8.78084i	−0.564843	+	0.326112i
$726$	−10.5513	−	3.10970i	−0.391595	−	0.115412i
$727$			3.03975i			0.112738i	0.998410	+	0.0563690i	$0.0179523\pi$
$727$			3.03975i			0.112738i	−0.998410	+	0.0563690i	$0.982048\pi$
$728$	0.531585	−	1.32546i	0.0197019	−	0.0491249i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	0.273001	+	2.59743i	0.0101042	+	0.0961352i
$731$	0.862469	+	4.05760i	0.0318996	+	0.150076i
$732$	1.68388	+	7.92206i	0.0622382	+	0.292808i
$733$	5.43532	+	51.7136i	0.200758	+	1.91009i	0.377809	+	0.925883i	$0.376677\pi$
$733$	5.43532	+	51.7136i	0.200758	+	1.91009i	−0.177051	+	0.984202i	$0.556656\pi$
$734$	−6.28426	−	4.56579i	−0.231956	−	0.168526i
$735$	3.88955	−	2.09368i	0.143468	−	0.0772266i
$736$		−	0.367547i		−	0.0135480i
$737$	−5.16802	+	20.4078i	−0.190367	+	0.751731i
$738$	−6.90396	+	3.98600i	−0.254138	+	0.146727i
$739$	−34.9937	−	31.5084i	−1.28726	−	1.15906i	−0.978120	−	0.208041i	$-0.933291\pi$
$739$	−34.9937	−	31.5084i	−1.28726	−	1.15906i	−0.309143	−	0.951016i	$-0.600042\pi$
$740$	−1.70850	−	3.83734i	−0.0628055	−	0.141064i
$741$	2.41369	+	3.32216i	0.0886692	+	0.122043i
$742$	−24.1626	+	15.1845i	−0.887039	+	0.557441i
$743$	−11.1604	−	3.62623i	−0.409435	−	0.133034i	0.0970554	−	0.995279i	$-0.469058\pi$
$743$	−11.1604	−	3.62623i	−0.409435	−	0.133034i	−0.506491	+	0.862245i	$0.669058\pi$
$744$	1.46554	−	0.154035i	0.0537294	−	0.00564718i
$745$	−0.284943	+	2.71105i	−0.0104395	+	0.0993252i
$746$	−18.2699	+	20.2908i	−0.668910	+	0.742899i
$747$	−0.584321	+	1.01207i	−0.0213792	+	0.0370298i
$748$	−3.85002	−	5.75341i	−0.140771	−	0.210366i
$749$	−36.0224	+	13.2154i	−1.31623	+	0.482881i
$750$	5.76252	−	1.87236i	0.210418	−	0.0683688i
$751$	−13.2583	+	5.90297i	−0.483802	+	0.215402i	−0.634119	−	0.773235i	$-0.718637\pi$
$751$	−13.2583	+	5.90297i	−0.483802	+	0.215402i	0.150317	+	0.988638i	$0.451970\pi$
$752$	−1.05988	+	2.38054i	−0.0386500	+	0.0868092i
$753$	−0.0288573	+	0.00613382i	−0.00105162	+	0.000223529i
$754$	1.37834	+	1.53080i	0.0501961	+	0.0557484i
$755$	−7.94743	+	5.77415i	−0.289237	+	0.210143i
$756$	1.89849	−	1.84275i	0.0690474	−	0.0670202i
$757$	7.31754	+	22.5211i	0.265960	+	0.818542i	0.991471	+	0.130331i	$0.0416039\pi$
$757$	7.31754	+	22.5211i	0.265960	+	0.818542i	−0.725510	+	0.688212i	$0.758396\pi$
$758$	17.7265	+	10.2344i	0.643855	+	0.371730i
$759$	−1.20127	+	0.207264i	−0.0436032	+	0.00752320i
$760$	−2.40039	−	4.15759i	−0.0870712	−	0.150812i
$761$	3.39892	+	0.722464i	0.123211	+	0.0261893i	0.269104	−	0.963111i	$-0.413272\pi$
$761$	3.39892	+	0.722464i	0.123211	+	0.0261893i	−0.145893	+	0.989300i	$0.546606\pi$
$762$	−0.172163	+	0.236962i	−0.00623681	+	0.00858423i
$763$	21.3961	+	43.5855i	0.774591	+	1.57790i
$764$	3.40101	−	10.4672i	0.123044	−	0.378691i
$765$	−0.978835	+	0.881347i	−0.0353899	+	0.0318652i
$766$	−1.30059	−	0.579059i	−0.0469921	−	0.0209223i
$767$	−6.70652	−	0.704883i	−0.242158	−	0.0254519i
$768$	−0.207912	+	0.978148i	−0.00750237	+	0.0352959i
$769$	15.1429			0.546068			0.273034	−	0.962004i	$-0.411973\pi$
$769$	15.1429			0.546068			0.273034	+	0.962004i	$0.411973\pi$
$770$	5.26438	+	1.71703i	0.189715	+	0.0618775i
$771$	−21.0099			−0.756652
$772$	1.27106	−	5.97989i	0.0457466	−	0.215221i
$773$	18.4519	+	1.93937i	0.663668	+	0.0697543i	0.430372	−	0.902652i	$-0.358382\pi$
$773$	18.4519	+	1.93937i	0.663668	+	0.0697543i	0.233296	+	0.972406i	$0.425049\pi$
$774$	−1.81557	−	0.808343i	−0.0652593	−	0.0290553i
$775$	−5.03947	+	4.53756i	−0.181023	+	0.162994i
$776$	3.17070	−	9.75842i	0.113822	−	0.350307i
$777$	17.5716	+	1.18361i	0.630379	+	0.0424617i
$778$	13.9083	−	19.1431i	0.498636	−	0.686314i
$779$	−59.3239	−	12.6097i	−2.12550	−	0.451789i
$780$	−0.170306	−	0.294979i	−0.00609793	−	0.0105619i
$781$	34.1585	−	18.0016i	1.22229	−	0.644148i
$782$	−0.664394	−	0.383588i	−0.0237587	−	0.0137171i
$783$	1.17929	+	3.62948i	0.0421444	+	0.129707i
$784$	−3.94396	−	5.78318i	−0.140856	−	0.206542i
$785$	10.3595	−	7.52663i	0.369747	−	0.268637i
$786$	4.12938	+	4.58615i	0.147290	+	0.163582i
$787$	−41.7802	+	8.88065i	−1.48930	+	0.316561i	−0.879464	−	0.475965i	$-0.842099\pi$
$787$	−41.7802	+	8.88065i	−1.48930	+	0.316561i	−0.609838	+	0.792526i	$0.708765\pi$
$788$	9.75714	−	21.9149i	0.347584	−	0.780686i
$789$	−12.6143	+	5.61625i	−0.449081	+	0.199944i
$790$	−1.43139	+	0.465086i	−0.0509264	+	0.0165470i
$791$	15.8790	−	19.0223i	0.564591	−	0.676356i
$792$	3.31416	+	0.127937i	0.117763	+	0.00454604i
$793$	−2.18579	+	3.78591i	−0.0776199	+	0.134442i
$794$	9.68659	−	10.7580i	0.343764	−	0.381789i
$795$	−0.711474	+	6.76922i	−0.0252334	+	0.240080i
$796$	−11.5649	+	1.21553i	−0.409909	+	0.0430831i
$797$	15.6514	+	5.08546i	0.554402	+	0.180136i	0.572801	−	0.819695i	$-0.305857\pi$
$797$	15.6514	+	5.08546i	0.554402	+	0.180136i	−0.0183987	+	0.999831i	$0.505857\pi$
$798$	20.1142	−	0.753876i	0.712033	−	0.0266869i
$799$	3.19702	+	4.40032i	0.113102	+	0.155672i
$800$	−1.87172	−	4.20395i	−0.0661752	−	0.148632i
$801$	−9.59034	−	8.63518i	−0.338858	−	0.305109i
$802$	−29.7318	+	17.1656i	−1.04986	+	0.606140i
$803$	−5.09534	−	12.7462i	−0.179811	−	0.449803i
$804$		−	6.34742i		−	0.223856i
$805$	0.607451	−	0.0869555i	0.0214098	−	0.00306478i
$806$	0.643498	+	0.467529i	0.0226663	+	0.0164680i
$807$	−2.87895	−	27.3914i	−0.101344	−	0.964223i
$808$	−1.89778	−	8.92834i	−0.0667635	−	0.314098i
$809$	3.53154	+	16.6146i	0.124162	+	0.584138i	0.995606	+	0.0936424i	$0.0298510\pi$
$809$	3.53154	+	16.6146i	0.124162	+	0.584138i	−0.871443	+	0.490496i	$0.836816\pi$
$810$	−0.0659612	−	0.627579i	−0.00231764	−	0.0220509i
$811$	−40.1860	−	29.1968i	−1.41112	−	1.02524i	−0.993159	−	0.116774i	$-0.962745\pi$
$811$	−40.1860	−	29.1968i	−1.41112	−	1.02524i	−0.417961	−	0.908465i	$-0.637255\pi$
$812$	9.99500	−	1.43077i	0.350756	−	0.0502100i
$813$			18.6959i			0.655695i
$814$	14.1286	+	16.9641i	0.495208	+	0.594593i
$815$	3.01886	−	1.74294i	0.105746	−	0.0610525i
$816$	1.55116	+	1.39667i	0.0543013	+	0.0488931i
$817$	−6.14969	−	13.8124i	−0.215150	−	0.483236i
$818$	−20.1337	−	27.7117i	−0.703960	−	0.968917i
$819$	1.42709	−	0.0534870i	0.0498664	−	0.00186899i
$820$	4.78441	+	1.55455i	0.167079	+	0.0542872i
$821$	−29.6360	+	3.11487i	−1.03430	+	0.108710i	−0.606436	−	0.795132i	$-0.707401\pi$
$821$	−29.6360	+	3.11487i	−1.03430	+	0.108710i	−0.427866	+	0.903842i	$0.640735\pi$
$822$	−1.01566	+	9.66333i	−0.0354251	+	0.337047i
$823$	−0.0495371	+	0.0550166i	−0.00172676	+	0.00191776i	−0.744008	−	0.668171i	$-0.767077\pi$
$823$	−0.0495371	+	0.0550166i	−0.00172676	+	0.00191776i	0.742281	+	0.670089i	$0.233744\pi$
$824$	3.67002	−	6.35666i	0.127851	−	0.221445i
$825$	−12.6844	+	8.48805i	−0.441615	+	0.295516i
$826$	−21.1820	+	25.3752i	−0.737016	+	0.882915i
$827$	42.7522	−	13.8910i	1.48664	−	0.483038i	0.550550	−	0.834802i	$-0.314418\pi$
$827$	42.7522	−	13.8910i	1.48664	−	0.483038i	0.936089	+	0.351764i	$0.114418\pi$
$828$	0.335771	−	0.149495i	0.0116689	−	0.00519531i
$829$	13.4458	−	30.1997i	0.466991	−	1.04888i	−0.514521	−	0.857478i	$-0.672030\pi$
$829$	13.4458	−	30.1997i	0.466991	−	1.04888i	0.981512	−	0.191401i	$-0.0613031\pi$
$830$	0.721339	−	0.153325i	0.0250380	−	0.00532200i
$831$	−16.4252	−	18.2421i	−0.569785	−	0.632810i
$832$	−0.436680	+	0.317267i	−0.0151392	+	0.0109992i
$833$	−14.5700	+	1.09370i	−0.504821	+	0.0378945i
$834$	−4.36626	−	13.4380i	−0.151191	−	0.465319i
$835$	3.66782	+	2.11762i	0.126930	+	0.0732832i
$836$	18.0859	+	17.5943i	0.625514	+	0.608513i
$837$	0.736807	+	1.27619i	0.0254678	+	0.0441115i
$838$	29.0964	+	6.18463i	1.00512	+	0.213645i
$839$	30.3726	−	41.8043i	1.04858	−	1.44324i	0.158543	−	0.987352i	$-0.449320\pi$
$839$	30.3726	−	41.8043i	1.04858	−	1.44324i	0.890035	−	0.455892i	$-0.150680\pi$
$840$	−1.66579	−	0.112206i	−0.0574752	−	0.00387147i
$841$	4.46100	−	13.7296i	0.153828	−	0.473433i
$842$	−18.6349	+	16.7789i	−0.642199	+	0.578239i
$843$	4.72897	+	2.10547i	0.162874	+	0.0725164i
$844$	6.28566	+	0.660649i	0.216361	+	0.0227405i
$845$	−1.66737	+	7.84437i	−0.0573593	+	0.269854i
$846$	−2.60582			−0.0895900
$847$	−29.0803	−	1.15526i	−0.999212	−	0.0396953i
$848$	10.7863			0.370401
$849$	−4.39605	+	20.6818i	−0.150872	+	0.709798i
$850$	−9.55264	−	1.00402i	−0.327653	−	0.0344377i
$851$	2.23506	+	0.995114i	0.0766170	+	0.0341121i
$852$	−8.65159	+	7.78992i	−0.296399	+	0.266878i
$853$	1.28184	−	3.94508i	0.0438892	−	0.135077i	−0.926711	−	0.375775i	$-0.877376\pi$
$853$	1.28184	−	3.94508i	0.0438892	−	0.135077i	0.970600	+	0.240698i	$0.0773764\pi$
$854$	9.44263	+	19.2353i	0.323120	+	0.658219i
$855$	2.82183	−	3.88391i	0.0965044	−	0.132827i
$856$	14.1856	+	3.01524i	0.484854	+	0.103059i
$857$	−26.4025	−	45.7305i	−0.901892	−	1.56212i	−0.825036	−	0.565081i	$-0.808845\pi$
$857$	−26.4025	−	45.7305i	−0.901892	−	1.56212i	−0.0768564	−	0.997042i	$-0.524488\pi$
$858$	1.28318	+	1.24831i	0.0438071	+	0.0426165i
$859$	−17.2142	−	9.93859i	−0.587339	−	0.339100i	0.176705	−	0.984264i	$-0.443456\pi$
$859$	−17.2142	−	9.93859i	−0.587339	−	0.339100i	−0.764045	+	0.645163i	$0.776789\pi$
$860$	0.387542	+	1.19273i	0.0132151	+	0.0406718i
$861$	−15.1348	+	14.6904i	−0.515792	+	0.500649i
$862$	3.76363	−	2.73444i	0.128190	−	0.0931353i
$863$	18.5976	+	20.6547i	0.633068	+	0.703094i	0.971270	−	0.237980i	$-0.0764852\pi$
$863$	18.5976	+	20.6547i	0.633068	+	0.703094i	−0.338202	+	0.941074i	$0.609819\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	1.58473	−	3.55935i	0.0538823	−	0.121022i
$866$	−17.6734	+	7.86868i	−0.600565	+	0.267389i
$867$	−12.0244	+	3.90697i	−0.408371	+	0.132688i
$868$	3.66027	−	1.34283i	0.124238	−	0.0455787i
$869$	6.57416	−	4.39924i	0.223013	−	0.149234i
$870$	1.20410	−	2.08556i	0.0408228	−	0.0707072i
$871$	2.29252	−	2.54611i	0.0776792	−	0.0862715i
$872$	1.91827	−	18.2511i	0.0649609	−	0.618061i
$873$	10.2044	−	1.07253i	0.345367	−	0.0362995i
$874$	2.65936	+	0.864078i	0.0899542	+	0.0292279i
$875$	13.5731	−	8.52975i	0.458856	−	0.288358i
$876$	2.43273	+	3.34837i	0.0821944	+	0.113131i
$877$	−20.2665	−	45.5193i	−0.684351	−	1.53708i	−0.836051	−	0.548652i	$-0.815141\pi$
$877$	−20.2665	−	45.5193i	−0.684351	−	1.53708i	0.151700	−	0.988427i	$-0.451525\pi$
$878$	−1.87907	−	1.69193i	−0.0634157	−	0.0570997i
$879$	7.63467	−	4.40788i	0.257511	−	0.148674i
$880$	−1.33939	−	1.60820i	−0.0451509	−	0.0542123i
$881$			45.8113i			1.54342i	0.635974	+	0.771710i	$0.280598\pi$
$881$			45.8113i			1.54342i	−0.635974	+	0.771710i	$0.719402\pi$
$882$	3.67904	−	5.95522i	0.123880	−	0.200523i
$883$	−16.9285	−	12.2993i	−0.569691	−	0.413905i	0.265302	−	0.964165i	$-0.414528\pi$
$883$	−16.9285	−	12.2993i	−0.569691	−	0.413905i	−0.834993	+	0.550261i	$0.814528\pi$
$884$	0.117767	+	1.12048i	0.00396092	+	0.0376857i
$885$	1.63912	+	7.71143i	0.0550983	+	0.259217i
$886$	−2.00150	−	9.41634i	−0.0672418	−	0.316348i
$887$	−4.82498	−	45.9066i	−0.162007	−	1.54139i	−0.709574	−	0.704631i	$-0.751112\pi$
$887$	−4.82498	−	45.9066i	−0.162007	−	1.54139i	0.547567	−	0.836762i	$-0.315554\pi$
$888$	−5.38523	−	3.91260i	−0.180716	−	0.131298i
$889$	−0.288462	+	0.719255i	−0.00967469	+	0.0241230i
$890$			8.14357i			0.272973i
$891$	1.23111	+	3.07967i	0.0412438	+	0.103173i
$892$	18.3039	−	10.5678i	0.612860	−	0.353835i
$893$	−14.7325	−	13.2652i	−0.493003	−	0.443902i
$894$	1.75704	+	3.94639i	0.0587644	+	0.131987i
$895$	−5.28491	−	7.27406i	−0.176655	−	0.243145i
$896$	0.0990929	+	2.64389i	0.00331046	+	0.0883263i
$897$	0.188680	+	0.0613058i	0.00629984	+	0.00204694i
$898$	0.713879	−	0.0750317i	0.0238225	−	0.00250384i
$899$	−0.587837	+	5.59290i	−0.0196055	+	0.186534i
$900$	3.07920	−	3.41980i	0.102640	−	0.113993i
$901$	11.2570	−	19.4977i	0.375025	−	0.649562i
$902$	−26.4205	−	1.01992i	−0.879706	−	0.0339595i
$903$	−5.18057	−	0.899827i	−0.172398	−	0.0299444i
$904$	−8.90714	+	2.89410i	−0.296247	+	0.0962565i
$905$	8.10592	−	3.60899i	0.269450	−	0.119967i
$906$	−6.33182	+	14.2215i	−0.210361	+	0.472478i
$907$	−19.0165	+	4.04209i	−0.631433	+	0.134215i	−0.512500	−	0.858687i	$-0.671281\pi$
$907$	−19.0165	+	4.04209i	−0.631433	+	0.134215i	−0.118933	+	0.992902i	$0.537947\pi$
$908$	−6.80587	−	7.55868i	−0.225861	−	0.250844i
$909$	7.38455	−	5.36519i	0.244930	−	0.177952i
$910$	−0.627663	−	0.646649i	−0.0208068	−	0.0214362i
$911$	−7.89373	−	24.2944i	−0.261531	−	0.804910i	−0.992472	−	0.122469i	$-0.960919\pi$
$911$	−7.89373	−	24.2944i	−0.261531	−	0.804910i	0.730941	−	0.682440i	$-0.239081\pi$
$912$	−6.58852	−	3.80389i	−0.218168	−	0.125959i
$913$	−3.42892	+	1.80705i	−0.113481	+	0.0598046i
$914$	8.41007	+	14.5667i	0.278180	+	0.481822i
$915$	4.99910	+	1.06259i	0.165265	+	0.0351282i
$916$	−9.72117	+	13.3800i	−0.321197	+	0.442089i
$917$	13.5595	+	9.09567i	0.447775	+	0.300366i
$918$	−0.645007	+	1.98513i	−0.0212884	+	0.0655190i
$919$	−18.5550	+	16.7070i	−0.612073	+	0.551113i	−0.915794	−	0.401648i	$-0.868437\pi$
$919$	−18.5550	+	16.7070i	−0.612073	+	0.551113i	0.303721	+	0.952761i	$0.401771\pi$
$920$	−0.211884	−	0.0943366i	−0.00698559	−	0.00311019i
$921$	16.7458	+	1.76005i	0.551791	+	0.0579956i
$922$	3.91150	−	18.4022i	0.128818	−	0.606043i
$923$	−6.28389			−0.206837
$924$	8.58525	−	1.81479i	0.282434	−	0.0597022i
$925$	30.6319			1.00717
$926$	0.0322029	−	0.151503i	0.00105825	−	0.00497869i
$927$	7.29982	+	0.767242i	0.239758	+	0.0251995i
$928$	−3.48633	−	1.55222i	−0.114444	−	0.0509540i
$929$	5.57369	−	5.01857i	0.182867	−	0.164654i	−0.572613	−	0.819826i	$-0.694070\pi$
$929$	5.57369	−	5.01857i	0.182867	−	0.164654i	0.755480	+	0.655172i	$0.227404\pi$
$930$	0.287356	−	0.884391i	0.00942277	−	0.0290003i
$931$	51.1157	−	14.9404i	1.67525	−	0.489651i
$932$	15.5461	−	21.3974i	0.509230	−	0.700895i
$933$	12.6640	+	2.69182i	0.414601	+	0.0881261i
$934$	9.52849	+	16.5038i	0.311782	+	0.540022i
$935$	−4.30489	+	0.742756i	−0.140785	+	0.0242907i
$936$	−0.467451	−	0.269883i	−0.0152791	−	0.00882141i
$937$	−3.74252	−	11.5183i	−0.122263	−	0.376286i	0.871130	−	0.491053i	$-0.163388\pi$
$937$	−3.74252	−	11.5183i	−0.122263	−	0.376286i	−0.993392	+	0.114767i	$0.963388\pi$
$938$	−4.10439	−	16.2844i	−0.134013	−	0.531705i
$939$	11.9109	−	8.65377i	0.388697	−	0.282405i
$940$	1.10030	+	1.22200i	0.0358877	+	0.0398573i
$941$	5.36180	−	1.13969i	0.174790	−	0.0371527i	−0.119685	−	0.992812i	$-0.538189\pi$
$941$	5.36180	−	1.13969i	0.174790	−	0.0371527i	0.294475	+	0.955659i	$0.404855\pi$
$942$	8.25356	−	18.5378i	0.268916	−	0.603994i
$943$	−2.67677	+	1.19177i	−0.0871676	+	0.0388095i
$944$	11.8818	−	3.86064i	0.386720	−	0.125653i
$945$	−0.575032	−	1.56741i	−0.0187058	−	0.0509879i
$946$	−3.66575	−	5.47805i	−0.119184	−	0.178107i
$947$	1.16408	−	2.01625i	0.0378275	−	0.0655192i	−0.846492	−	0.532402i	$-0.821290\pi$
$947$	1.16408	−	2.01625i	0.0378275	−	0.0655192i	0.884319	+	0.466883i	$0.154623\pi$
$948$	−1.59591	+	1.77243i	−0.0518326	+	0.0575660i
$949$	−0.233516	+	2.22175i	−0.00758024	+	0.0721212i
$950$	34.8176	−	3.65948i	1.12963	−	0.118729i
$951$	16.4726	+	5.35227i	0.534160	+	0.173559i
$952$	4.88264	+	2.58016i	0.158247	+	0.0836234i
$953$	11.0937	+	15.2692i	0.359361	+	0.494618i	0.949970	−	0.312340i	$-0.101113\pi$
$953$	11.0937	+	15.2692i	0.359361	+	0.494618i	−0.590610	+	0.806957i	$0.701113\pi$
$954$	4.38716	+	9.85373i	0.142040	+	0.319026i
$955$	−5.16122	−	4.64719i	−0.167013	−	0.150379i
$956$	−3.45047	+	1.99213i	−0.111596	+	0.0644301i
$957$	−3.10718	+	12.2698i	−0.100441	+	0.396627i
$958$			16.2824i			0.526062i
$959$	3.64286	+	25.4482i	0.117634	+	0.821765i
$960$	0.510519	+	0.370913i	0.0164769	+	0.0119712i
$961$	−3.01339	−	28.6705i	−0.0972063	−	0.924856i
$962$	−0.747018	−	3.51445i	−0.0240848	−	0.113310i
$963$	3.01524	+	14.1856i	0.0971648	+	0.457124i
$964$	1.80377	+	17.1618i	0.0580956	+	0.552743i
$965$	−3.12105	−	2.26757i	−0.100470	−	0.0729957i
$966$	0.764759	−	0.600650i	0.0246057	−	0.0193256i
$967$		−	16.7697i		−	0.539277i	−0.962962	−	0.269638i	$-0.913096\pi$
$967$		−	16.7697i		−	0.539277i	0.962962	−	0.269638i	$-0.0869041\pi$
$968$	9.07393	+	6.21803i	0.291647	+	0.199855i
$969$	−13.7521	+	7.93980i	−0.441782	+	0.255063i
$970$	−4.81172	−	4.33249i	−0.154495	−	0.139108i
$971$	−9.71800	−	21.8270i	−0.311866	−	0.700462i	0.687811	−	0.725890i	$-0.258572\pi$
$971$	−9.71800	−	21.8270i	−0.311866	−	0.700462i	−0.999677	+	0.0254282i	$0.991905\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−19.8910	−	31.6520i	−0.637677	−	1.01472i
$974$	−35.8020	−	11.6328i	−1.14717	−	0.372739i
$975$	2.47029	−	0.259638i	0.0791125	−	0.00831506i
$976$	0.846580	−	8.05467i	0.0270984	−	0.257824i
$977$	25.8043	−	28.6586i	0.825553	−	0.916869i	−0.172118	−	0.985076i	$-0.555061\pi$
$977$	25.8043	−	28.6586i	0.825553	−	0.916869i	0.997671	+	0.0682070i	$0.0217278\pi$
$978$	2.76203	−	4.78398i	0.0883200	−	0.152975i
$979$	−11.6463	−	41.1864i	−0.372216	−	1.31632i
$980$	−4.34616	+	0.789273i	−0.138833	+	0.0252124i
$981$	17.4535	−	5.67098i	0.557247	−	0.181060i
$982$	26.7554	−	11.9123i	0.853799	−	0.380136i
$983$	−9.59258	+	21.5453i	−0.305956	+	0.687188i	−0.999446	−	0.0332781i	$-0.989405\pi$
$983$	−9.59258	+	21.5453i	−0.305956	+	0.687188i	0.693490	+	0.720466i	$0.256072\pi$
$984$	7.79780	−	1.65747i	0.248585	−	0.0528383i
$985$	−10.1292	−	11.2496i	−0.322742	−	0.358442i
$986$	−6.44434	+	4.68209i	−0.205230	+	0.149108i
$987$	−6.68528	+	1.68499i	−0.212795	+	0.0536337i
$988$	−1.26895	−	3.90544i	−0.0403708	−	0.124249i
$989$	−0.632596	−	0.365229i	−0.0201154	−	0.0116136i
$990$	0.924382	−	1.87771i	0.0293788	−	0.0596775i
$991$	27.1947	+	47.1026i	0.863868	+	1.49626i	0.868167	+	0.496272i	$0.165298\pi$
$991$	27.1947	+	47.1026i	0.863868	+	1.49626i	−0.00429882	+	0.999991i	$0.501368\pi$
$992$	−1.44141	−	0.306382i	−0.0457649	−	0.00972763i
$993$	17.5856	−	24.2045i	0.558062	−	0.768107i
$994$	−17.1586	+	25.5795i	−0.544239	+	0.811333i
$995$	−2.26760	+	6.97894i	−0.0718876	+	0.221247i
$996$	0.868470	−	0.781974i	0.0275185	−	0.0247778i
$997$	−2.27583	−	1.01326i	−0.0720762	−	0.0320904i	0.370382	−	0.928880i	$-0.379227\pi$
$997$	−2.27583	−	1.01326i	−0.0720762	−	0.0320904i	−0.442458	+	0.896789i	$0.645893\pi$
$998$	−14.8182	−	1.55745i	−0.469061	−	0.0493003i
$999$	1.38397	−	6.51105i	0.0437867	−	0.206000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.2	yes	64
7.3	odd	6		462.2.ba.a.325.3	yes	64
11.2	odd	10		462.2.ba.a.145.3	✓	64
77.24	even	30	inner	462.2.ba.b.409.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.3	✓	64	11.2	odd	10
462.2.ba.a.325.3	yes	64	7.3	odd	6
462.2.ba.b.61.2	yes	64	1.1	even	1	trivial
462.2.ba.b.409.2	yes	64	77.24	even	30	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.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.468951 + 0.422245i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.177812 + 2.63977i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.468951 + 0.422245i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.177812 + 2.63977i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.315518 - 0.546493i) q^{10} +(2.37729 + 2.31268i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.166797 - 0.513348i) q^{13} +(-2.54511 - 0.722766i) q^{14} +(-0.510519 + 0.370913i) q^{15} +(0.669131 + 0.743145i) q^{16} +(2.04167 - 0.433971i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(-6.95005 + 3.09436i) q^{19} +(0.600151 - 0.195001i) q^{20} +(-0.452769 + 2.60672i) q^{21} +(-2.75641 + 1.84451i) q^{22} +(-0.183774 + 0.318305i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.481018 + 4.57658i) q^{25} +(0.536810 - 0.0564210i) q^{26} +(0.951057 + 0.309017i) q^{27} +(1.23613 - 2.33923i) q^{28} +(2.24314 + 3.08742i) q^{29} +(-0.256665 - 0.576480i) q^{30} +(1.09511 + 0.986040i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.12253 + 2.54850i) q^{33} +2.08729i q^{34} +(-1.03125 - 1.31300i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.695795 - 6.62004i) q^{37} +(-1.58174 - 7.44152i) q^{38} +(-0.112224 - 0.527971i) q^{39} +(0.0659612 + 0.627579i) q^{40} +(6.44949 + 4.68583i) q^{41} +(-2.45562 - 0.984843i) q^{42} +1.98739i q^{43} +(-1.23111 - 3.07967i) q^{44} +(-0.546493 + 0.315518i) q^{45} +(-0.273141 - 0.245937i) q^{46} +(1.05988 + 2.38054i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-6.93677 - 0.938766i) q^{49} +(-4.37657 - 1.42203i) q^{50} +(2.07585 - 0.218181i) q^{51} +(-0.0564210 + 0.536810i) q^{52} +(7.21741 - 8.01575i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.09135 - 0.0807328i) q^{55} +(2.03110 + 1.69547i) q^{56} +(-7.23542 + 2.35093i) q^{57} +(-3.48633 + 1.55222i) q^{58} +(5.08148 - 11.4132i) q^{59} +(0.617246 - 0.131200i) q^{60} +(-5.41931 - 6.01876i) q^{61} +(-1.19218 + 0.866169i) q^{62} +(-0.722766 + 2.54511i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.294979 + 0.170306i) q^{65} +(-2.93411 + 1.54628i) q^{66} +(3.17371 + 5.49702i) q^{67} +(-2.04167 - 0.433971i) q^{68} +(-0.216039 + 0.297352i) q^{69} +(1.49872 - 0.735721i) q^{70} +(3.59753 - 11.0721i) q^{71} +(0.743145 - 0.669131i) q^{72} +(-3.78099 - 1.68341i) q^{73} +(6.62004 + 0.695795i) q^{74} +(-0.956767 + 4.50123i) q^{75} +7.60777 q^{76} +(-6.52765 + 5.86428i) q^{77} +0.539766 q^{78} +(0.495879 - 2.33293i) q^{79} +(-0.627579 - 0.0659612i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-5.92436 + 5.33432i) q^{82} +(-0.361130 + 1.11144i) q^{83} +(1.47387 - 2.19720i) q^{84} +(-0.774203 + 1.06560i) q^{85} +(-1.94396 - 0.413201i) q^{86} +(1.90813 + 3.30498i) q^{87} +(3.26833 - 0.563911i) q^{88} +(-11.1761 - 6.45254i) q^{89} +(-0.195001 - 0.600151i) q^{90} +(1.38478 - 0.349026i) q^{91} +(0.297352 - 0.216039i) q^{92} +(0.986040 + 1.09511i) q^{93} +(-2.54888 + 0.541781i) q^{94} +(1.95265 - 4.38573i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(9.75842 - 3.17070i) q^{97} +(2.36049 - 6.59000i) q^{98} +(1.84451 + 2.75641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Introduction

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