LMFDB - Embedded newform 288.2.bf.a.11.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.44
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39370 - 0.240021i) q^{2} +(0.677899 - 1.59388i) q^{3} +(1.88478 - 0.669032i) q^{4} +(0.183643 + 1.39490i) q^{5} +(0.562222 - 2.38409i) q^{6} +(0.489046 + 1.82515i) q^{7} +(2.46623 - 1.38481i) q^{8} +(-2.08090 - 2.16098i) q^{9} +O(q^{10})$	\(q+(1.39370 - 0.240021i) q^{2} +(0.677899 - 1.59388i) q^{3} +(1.88478 - 0.669032i) q^{4} +(0.183643 + 1.39490i) q^{5} +(0.562222 - 2.38409i) q^{6} +(0.489046 + 1.82515i) q^{7} +(2.46623 - 1.38481i) q^{8} +(-2.08090 - 2.16098i) q^{9} +(0.590748 + 1.90000i) q^{10} +(-1.62332 + 1.24562i) q^{11} +(0.211335 - 3.45765i) q^{12} +(1.42212 - 1.85334i) q^{13} +(1.11965 + 2.42632i) q^{14} +(2.34780 + 0.652901i) q^{15} +(3.10479 - 2.52196i) q^{16} -2.43543 q^{17} +(-3.41883 - 2.51229i) q^{18} +(-7.41946 + 3.07324i) q^{19} +(1.27936 + 2.50623i) q^{20} +(3.24059 + 0.457784i) q^{21} +(-1.96344 + 2.12564i) q^{22} +(-6.65621 - 1.78352i) q^{23} +(-0.535370 - 4.86964i) q^{24} +(2.91760 - 0.781767i) q^{25} +(1.53716 - 2.92434i) q^{26} +(-4.85499 + 1.85178i) q^{27} +(2.14282 + 3.11281i) q^{28} +(1.88325 + 0.247935i) q^{29} +(3.42883 + 0.346425i) q^{30} +(5.12880 - 2.96111i) q^{31} +(3.72182 - 4.26006i) q^{32} +(0.884917 + 3.43178i) q^{33} +(-3.39425 + 0.584553i) q^{34} +(-2.45609 + 1.01735i) q^{35} +(-5.36781 - 2.68078i) q^{36} +(-0.701864 + 1.69445i) q^{37} +(-9.60284 + 6.06399i) q^{38} +(-1.98995 - 3.52307i) q^{39} +(2.38459 + 3.18584i) q^{40} +(-2.28020 + 8.50981i) q^{41} +(4.62627 - 0.139795i) q^{42} +(1.75369 + 2.28545i) q^{43} +(-2.22624 + 3.43377i) q^{44} +(2.63222 - 3.29951i) q^{45} +(-9.70481 - 0.888066i) q^{46} +(8.82446 + 5.09480i) q^{47} +(-1.91496 - 6.65830i) q^{48} +(2.97019 - 1.71484i) q^{49} +(3.87860 - 1.78983i) q^{50} +(-1.65097 + 3.88178i) q^{51} +(1.44044 - 4.44459i) q^{52} +(-0.0950263 + 0.229414i) q^{53} +(-6.32191 + 3.74612i) q^{54} +(-2.03563 - 2.03563i) q^{55} +(3.73359 + 3.82399i) q^{56} +(-0.131271 + 13.9091i) q^{57} +(2.68419 - 0.106473i) q^{58} +(-5.79345 + 0.762722i) q^{59} +(4.86190 - 0.340180i) q^{60} +(-0.474891 + 3.60715i) q^{61} +(6.43726 - 5.35791i) q^{62} +(2.92644 - 4.85477i) q^{63} +(4.16458 - 6.83054i) q^{64} +(2.84640 + 1.64337i) q^{65} +(2.05700 + 4.57046i) q^{66} +(3.74657 - 4.88263i) q^{67} +(-4.59024 + 1.62938i) q^{68} +(-7.35496 + 9.40014i) q^{69} +(-3.17886 + 2.00739i) q^{70} +(-8.45963 - 8.45963i) q^{71} +(-8.12454 - 2.44781i) q^{72} +(7.58174 - 7.58174i) q^{73} +(-0.571482 + 2.53001i) q^{74} +(0.731793 - 5.18026i) q^{75} +(-11.9280 + 10.7562i) q^{76} +(-3.06731 - 2.35363i) q^{77} +(-3.61900 - 4.43246i) q^{78} +(0.353898 - 0.612970i) q^{79} +(4.08806 + 3.86775i) q^{80} +(-0.339671 + 8.99359i) q^{81} +(-1.13537 + 12.4074i) q^{82} +(-11.7142 - 1.54221i) q^{83} +(6.41406 - 1.30523i) q^{84} +(-0.447248 - 3.39719i) q^{85} +(2.99266 + 2.76430i) q^{86} +(1.67183 - 2.83360i) q^{87} +(-2.27853 + 5.31998i) q^{88} +(0.251664 - 0.251664i) q^{89} +(2.87656 - 5.23030i) q^{90} +(4.07810 + 1.68920i) q^{91} +(-13.7387 + 1.09166i) q^{92} +(-1.24285 - 10.1820i) q^{93} +(13.5215 + 4.98256i) q^{94} +(-5.64941 - 9.78506i) q^{95} +(-4.26700 - 8.82002i) q^{96} +(6.37184 - 11.0363i) q^{97} +(3.72795 - 3.10287i) q^{98} +(6.06973 + 0.915952i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.39370	−	0.240021i	0.985492	−	0.169720i
$2$	1.39370	−	0.240021i	0.985492	−	0.169720i
$3$	0.677899	−	1.59388i	0.391385	−	0.920227i
$3$	0.677899	−	1.59388i	0.391385	−	0.920227i
$4$	1.88478	−	0.669032i	0.942390	−	0.334516i
$5$	0.183643	+	1.39490i	0.0821275	+	0.623820i	0.982167	+	0.188012i	$0.0602042\pi$
$5$	0.183643	+	1.39490i	0.0821275	+	0.623820i	−0.900039	+	0.435809i	$0.856462\pi$
$6$	0.562222	−	2.38409i	0.229526	−	0.973302i
$7$	0.489046	+	1.82515i	0.184842	+	0.689840i	0.994664	+	0.103165i	$0.0328969\pi$
$7$	0.489046	+	1.82515i	0.184842	+	0.689840i	−0.809822	+	0.586675i	$0.800436\pi$
$8$	2.46623	−	1.38481i	0.871944	−	0.489606i
$9$	−2.08090	−	2.16098i	−0.693635	−	0.720327i
$10$	0.590748	+	1.90000i	0.186811	+	0.600831i
$11$	−1.62332	+	1.24562i	−0.489450	+	0.375568i	−0.823800	−	0.566881i	$-0.808150\pi$
$11$	−1.62332	+	1.24562i	−0.489450	+	0.375568i	0.334350	+	0.942449i	$0.391483\pi$
$12$	0.211335	−	3.45765i	0.0610072	−	0.998137i
$13$	1.42212	−	1.85334i	0.394425	−	0.514025i	−0.553357	−	0.832944i	$-0.686653\pi$
$13$	1.42212	−	1.85334i	0.394425	−	0.514025i	0.947782	+	0.318920i	$0.103320\pi$
$14$	1.11965	+	2.42632i	0.299240	+	0.648461i
$15$	2.34780	+	0.652901i	0.606200	+	0.168578i
$16$	3.10479	−	2.52196i	0.776198	−	0.630489i
$17$	−2.43543			−0.590678			−0.295339	−	0.955393i	$-0.595433\pi$
$17$	−2.43543			−0.590678			−0.295339	+	0.955393i	$0.595433\pi$
$18$	−3.41883	−	2.51229i	−0.805826	−	0.592153i
$19$	−7.41946	+	3.07324i	−1.70214	+	0.705050i	−0.999976	−	0.00696315i	$-0.997784\pi$
$19$	−7.41946	+	3.07324i	−1.70214	+	0.705050i	−0.702166	+	0.712013i	$0.747784\pi$
$20$	1.27936	+	2.50623i	0.286074	+	0.560409i
$21$	3.24059	+	0.457784i	0.707154	+	0.0998967i
$22$	−1.96344	+	2.12564i	−0.418607	+	0.453189i
$23$	−6.65621	−	1.78352i	−1.38791	−	0.371891i	−0.513925	−	0.857835i	$-0.671809\pi$
$23$	−6.65621	−	1.78352i	−1.38791	−	0.371891i	−0.873990	+	0.485944i	$0.838476\pi$
$24$	−0.535370	−	4.86964i	−0.109282	−	0.994011i
$25$	2.91760	−	0.781767i	0.583519	−	0.156353i
$26$	1.53716	−	2.92434i	0.301462	−	0.573509i
$27$	−4.85499	+	1.85178i	−0.934343	+	0.356376i
$28$	2.14282	+	3.11281i	0.404956	+	0.588266i
$29$	1.88325	+	0.247935i	0.349711	+	0.0460404i	0.303336	−	0.952884i	$-0.401900\pi$
$29$	1.88325	+	0.247935i	0.349711	+	0.0460404i	0.0463755	+	0.998924i	$0.485233\pi$
$30$	3.42883	+	0.346425i	0.626016	+	0.0632482i
$31$	5.12880	−	2.96111i	0.921159	−	0.531831i	0.0371544	−	0.999310i	$-0.488171\pi$
$31$	5.12880	−	2.96111i	0.921159	−	0.531831i	0.884005	+	0.467478i	$0.154837\pi$
$32$	3.72182	−	4.26006i	0.657931	−	0.753079i
$33$	0.884917	+	3.43178i	0.154044	+	0.597396i
$34$	−3.39425	+	0.584553i	−0.582108	+	0.100250i
$35$	−2.45609	+	1.01735i	−0.415156	+	0.171963i
$36$	−5.36781	−	2.68078i	−0.894635	−	0.446797i
$37$	−0.701864	+	1.69445i	−0.115386	+	0.278566i	−0.971013	−	0.239027i	$-0.923172\pi$
$37$	−0.701864	+	1.69445i	−0.115386	+	0.278566i	0.855627	+	0.517592i	$0.173172\pi$
$38$	−9.60284	+	6.06399i	−1.55779	+	0.983709i
$39$	−1.98995	−	3.52307i	−0.318647	−	0.564142i
$40$	2.38459	+	3.18584i	0.377036	+	0.503726i
$41$	−2.28020	+	8.50981i	−0.356107	+	1.32901i	0.522979	+	0.852345i	$0.324820\pi$
$41$	−2.28020	+	8.50981i	−0.356107	+	1.32901i	−0.879086	+	0.476663i	$0.841846\pi$
$42$	4.62627	−	0.139795i	0.713849	−	0.0215709i
$43$	1.75369	+	2.28545i	0.267434	+	0.348527i	0.907695	−	0.419630i	$-0.137840\pi$
$43$	1.75369	+	2.28545i	0.267434	+	0.348527i	−0.640261	+	0.768158i	$0.721174\pi$
$44$	−2.22624	+	3.43377i	−0.335619	+	0.517660i
$45$	2.63222	−	3.29951i	0.392388	−	0.491862i
$46$	−9.70481	−	0.888066i	−1.43090	−	0.130938i
$47$	8.82446	+	5.09480i	1.28718	+	0.743153i	0.978150	−	0.207899i	$-0.0666627\pi$
$47$	8.82446	+	5.09480i	1.28718	+	0.743153i	0.309029	+	0.951053i	$0.399996\pi$
$48$	−1.91496	−	6.65830i	−0.276400	−	0.961043i
$49$	2.97019	−	1.71484i	0.424313	−	0.244977i
$50$	3.87860	−	1.78983i	0.548517	−	0.253120i
$51$	−1.65097	+	3.88178i	−0.231183	+	0.543558i
$52$	1.44044	−	4.44459i	0.199753	−	0.616353i
$53$	−0.0950263	+	0.229414i	−0.0130529	+	0.0315124i	−0.930272	−	0.366872i	$-0.880429\pi$
$53$	−0.0950263	+	0.229414i	−0.0130529	+	0.0315124i	0.917219	+	0.398384i	$0.130429\pi$
$54$	−6.32191	+	3.74612i	−0.860303	+	0.509783i
$55$	−2.03563	−	2.03563i	−0.274484	−	0.274484i
$56$	3.73359	+	3.82399i	0.498921	+	0.511002i
$57$	−0.131271	+	13.9091i	−0.0173873	+	1.84230i
$58$	2.68419	−	0.106473i	0.352452	−	0.0139807i
$59$	−5.79345	+	0.762722i	−0.754242	+	0.0992979i	−0.497836	−	0.867271i	$-0.665872\pi$
$59$	−5.79345	+	0.762722i	−0.754242	+	0.0992979i	−0.256406	+	0.966569i	$0.582539\pi$
$60$	4.86190	−	0.340180i	0.627669	−	0.0439170i
$61$	−0.474891	+	3.60715i	−0.0608036	+	0.461849i	0.933775	+	0.357861i	$0.116494\pi$
$61$	−0.474891	+	3.60715i	−0.0608036	+	0.461849i	−0.994579	+	0.103988i	$0.966840\pi$
$62$	6.43726	−	5.35791i	0.817533	−	0.680455i
$63$	2.92644	−	4.85477i	0.368697	−	0.611644i
$64$	4.16458	−	6.83054i	0.520573	−	0.853817i
$65$	2.84640	+	1.64337i	0.353052	+	0.203835i
$66$	2.05700	+	4.57046i	0.253200	+	0.562585i
$67$	3.74657	−	4.88263i	0.457717	−	0.596508i	−0.506297	−	0.862359i	$-0.668986\pi$
$67$	3.74657	−	4.88263i	0.457717	−	0.596508i	0.964014	+	0.265851i	$0.0856528\pi$
$68$	−4.59024	+	1.62938i	−0.556649	+	0.197591i
$69$	−7.35496	+	9.40014i	−0.885433	+	1.13164i
$70$	−3.17886	+	2.00739i	−0.379947	+	0.239929i
$71$	−8.45963	−	8.45963i	−1.00397	−	1.00397i	−0.999992	−	0.00398084i	$-0.998733\pi$
$71$	−8.45963	−	8.45963i	−1.00397	−	1.00397i	−0.00398084	−	0.999992i	$-0.501267\pi$
$72$	−8.12454	−	2.44781i	−0.957487	−	0.288477i
$73$	7.58174	−	7.58174i	0.887376	−	0.887376i	−0.106894	−	0.994270i	$-0.534091\pi$
$73$	7.58174	−	7.58174i	0.887376	−	0.887376i	0.994270	+	0.106894i	$0.0340907\pi$
$74$	−0.571482	+	2.53001i	−0.0664335	+	0.294108i
$75$	0.731793	−	5.18026i	0.0845002	−	0.598164i
$76$	−11.9280	+	10.7562i	−1.36823	+	1.23383i
$77$	−3.06731	−	2.35363i	−0.349553	−	0.268221i
$78$	−3.61900	−	4.43246i	−0.409771	−	0.501877i
$79$	0.353898	−	0.612970i	0.0398167	−	0.0689645i	−0.845430	−	0.534086i	$-0.820656\pi$
$79$	0.353898	−	0.612970i	0.0398167	−	0.0689645i	0.885247	+	0.465121i	$0.153989\pi$
$80$	4.08806	+	3.86775i	0.457059	+	0.432428i
$81$	−0.339671	+	8.99359i	−0.0377412	+	0.999288i
$82$	−1.13537	+	12.4074i	−0.125381	+	1.37017i
$83$	−11.7142	−	1.54221i	−1.28580	−	0.169279i	−0.543538	−	0.839384i	$-0.682916\pi$
$83$	−11.7142	−	1.54221i	−1.28580	−	0.169279i	−0.742266	+	0.670105i	$0.766249\pi$
$84$	6.41406	−	1.30523i	0.699832	−	0.142413i
$85$	−0.447248	−	3.39719i	−0.0485109	−	0.368477i
$86$	2.99266	+	2.76430i	0.322707	+	0.298082i
$87$	1.67183	−	2.83360i	0.179240	−	0.303794i
$88$	−2.27853	+	5.31998i	−0.242893	+	0.567111i
$89$	0.251664	−	0.251664i	0.0266763	−	0.0266763i	−0.693643	−	0.720319i	$-0.743995\pi$
$89$	0.251664	−	0.251664i	0.0266763	−	0.0266763i	0.720319	+	0.693643i	$0.243995\pi$
$90$	2.87656	−	5.23030i	0.303216	−	0.551322i
$91$	4.07810	+	1.68920i	0.427501	+	0.177077i
$92$	−13.7387	+	1.09166i	−1.43236	+	0.113814i
$93$	−1.24285	−	10.1820i	−0.128877	−	1.05583i
$94$	13.5215	+	4.98256i	1.39463	+	0.513911i
$95$	−5.64941	−	9.78506i	−0.579617	−	1.00393i
$96$	−4.26700	−	8.82002i	−0.435499	−	0.900189i
$97$	6.37184	−	11.0363i	0.646962	−	1.12057i	−0.336882	−	0.941547i	$-0.609372\pi$
$97$	6.37184	−	11.0363i	0.646962	−	1.12057i	0.983845	−	0.179025i	$-0.0572942\pi$
$98$	3.72795	−	3.10287i	0.376579	−	0.313437i
$99$	6.06973	+	0.915952i	0.610031	+	0.0920566i
$100$	4.97600	−	3.42542i	0.497600	−	0.342542i
$101$	2.08007	−	1.59609i	0.206975	−	0.158817i	−0.500073	−	0.865983i	$-0.666693\pi$
$101$	2.08007	−	1.59609i	0.206975	−	0.158817i	0.707047	+	0.707166i	$0.250027\pi$
$102$	−1.36925	+	5.80629i	−0.135576	+	0.574908i
$103$	11.4897	+	3.07865i	1.13211	+	0.303348i	0.775775	−	0.631010i	$-0.217359\pi$
$103$	11.4897	+	3.07865i	1.13211	+	0.303348i	0.356336	+	0.934358i	$0.384026\pi$
$104$	0.940741	−	6.54014i	0.0922472	−	0.641314i
$105$	−0.0434552	+	4.60438i	−0.00424080	+	0.449341i
$106$	−0.0773738	+	0.342542i	−0.00751521	+	0.0332706i
$107$	−12.8146	−	5.30797i	−1.23883	−	0.513141i	−0.335482	−	0.942047i	$-0.608899\pi$
$107$	−12.8146	−	5.30797i	−1.23883	−	0.513141i	−0.903349	+	0.428906i	$0.858899\pi$
$108$	−7.91168	+	6.73835i	−0.761302	+	0.648398i
$109$	−5.41896	−	13.0825i	−0.519043	−	1.25308i	−0.938492	−	0.345301i	$-0.887777\pi$
$109$	−5.41896	−	13.0825i	−0.519043	−	1.25308i	0.419449	−	0.907779i	$-0.362223\pi$
$110$	−3.32564	−	2.34846i	−0.317087	−	0.223916i
$111$	2.22495	+	2.26735i	0.211183	+	0.215207i
$112$	6.12132	+	4.43334i	0.578411	+	0.418912i
$113$	0.766183	+	1.32707i	0.0720764	+	0.124840i	0.899811	−	0.436280i	$-0.143704\pi$
$113$	0.766183	+	1.32707i	0.0720764	+	0.124840i	−0.827735	+	0.561120i	$0.810371\pi$
$114$	3.15551	+	19.4165i	0.295541	+	1.81853i
$115$	1.26548	−	9.61230i	0.118007	−	0.896352i
$116$	3.71539	−	0.792653i	0.344966	−	0.0735960i
$117$	−6.96433	+	0.783457i	−0.643853	+	0.0724306i
$118$	−7.89124	+	2.45355i	−0.726447	+	0.225867i
$119$	−1.19104	−	4.44501i	−0.109182	−	0.407473i
$120$	6.69436	−	1.64106i	0.611109	−	0.149808i
$121$	−1.76340	+	6.58111i	−0.160309	+	0.598283i
$122$	0.203938	+	5.14126i	0.0184637	+	0.465468i
$123$	12.0179	+	9.40315i	1.08361	+	0.847853i
$124$	7.68558	−	9.01237i	0.690185	−	0.809335i
$125$	4.31835	+	10.4254i	0.386245	+	0.932478i
$126$	2.91333	−	7.46849i	0.259540	−	0.665346i
$127$			12.6029i			1.11833i	0.829057	+	0.559164i	$0.188878\pi$
$127$			12.6029i			1.11833i	−0.829057	+	0.559164i	$0.811122\pi$
$128$	4.16469	−	10.5193i	0.368111	−	0.929782i
$129$	4.83155	−	1.24586i	0.425394	−	0.109692i
$130$	4.36146	+	1.60716i	0.382525	+	0.140957i
$131$	5.89699	+	4.52492i	0.515223	+	0.395344i	0.833386	−	0.552692i	$-0.186399\pi$
$131$	5.89699	+	4.52492i	0.515223	+	0.395344i	−0.318163	+	0.948036i	$0.603066\pi$
$132$	3.96384	+	5.87612i	0.345008	+	0.511450i
$133$	−9.23757	−	12.0386i	−0.800999	−	1.04388i
$134$	4.04966	−	7.70416i	0.349837	−	0.665538i
$135$	−3.47465	−	6.43218i	−0.299050	−	0.553593i
$136$	−6.00632	+	3.37261i	−0.515038	+	0.289199i
$137$	6.88430	−	1.84464i	0.588165	−	0.157598i	0.0475507	−	0.998869i	$-0.484858\pi$
$137$	6.88430	−	1.84464i	0.588165	−	0.157598i	0.540615	+	0.841270i	$0.318192\pi$
$138$	−7.99436	+	14.8663i	−0.680525	+	1.26550i
$139$	−19.0925	+	2.51358i	−1.61941	+	0.213199i	−0.885028	−	0.465538i	$-0.845861\pi$
$139$	−19.0925	+	2.51358i	−1.61941	+	0.213199i	−0.734381	+	0.678738i	$0.762527\pi$
$140$	−3.94856	+	3.56068i	−0.333714	+	0.300932i
$141$	14.1026	−	10.6114i	1.18765	−	0.893638i
$142$	−13.8206	−	9.75967i	−1.15980	−	0.819013i
$143$			4.77999i			0.399723i
$144$	−11.9107	−	1.46145i	−0.992556	−	0.121787i
$145$			2.67249i			0.221938i
$146$	8.74687	−	12.3864i	0.723896	−	1.02511i
$147$	−0.719758	−	5.89661i	−0.0593647	−	0.486344i
$148$	−0.189218	+	3.66323i	−0.0155537	+	0.301116i
$149$	17.8522	−	2.35029i	1.46251	−	0.192543i	0.643114	−	0.765771i	$-0.277642\pi$
$149$	17.8522	−	2.35029i	1.46251	−	0.192543i	0.819396	+	0.573228i	$0.194309\pi$
$150$	−0.223471	−	7.39535i	−0.0182463	−	0.603828i
$151$	13.6877	−	3.66761i	1.11389	−	0.298465i	0.345481	−	0.938426i	$-0.387716\pi$
$151$	13.6877	−	3.66761i	1.11389	−	0.298465i	0.768408	+	0.639960i	$0.221049\pi$
$152$	−14.0422	+	17.8539i	−1.13898	+	1.44814i
$153$	5.06789	+	5.26291i	0.409715	+	0.425481i
$154$	−4.83982	−	2.54403i	−0.390004	−	0.205004i
$155$	5.07233	+	6.61039i	0.407420	+	0.530960i
$156$	−6.10766	−	5.30887i	−0.489005	−	0.425050i
$157$	5.99063	+	4.59677i	0.478104	+	0.366862i	0.819520	−	0.573050i	$-0.194240\pi$
$157$	5.99063	+	4.59677i	0.478104	+	0.366862i	−0.341416	+	0.939912i	$0.610907\pi$
$158$	0.346102	−	0.939237i	0.0275344	−	0.0747217i
$159$	0.301240	+	0.306980i	0.0238899	+	0.0243451i
$160$	6.62585	+	4.40925i	0.523820	+	0.348582i
$161$		−	13.0208i		−	1.02618i
$162$	1.68525	+	12.6159i	0.132406	+	0.991196i
$163$	−5.33350	−	12.8762i	−0.417752	−	1.00854i	−0.982997	−	0.183619i	$-0.941219\pi$
$163$	−5.33350	−	12.8762i	−0.417752	−	1.00854i	0.565246	−	0.824923i	$-0.308781\pi$
$164$	1.39566	+	17.5646i	0.108983	+	1.37157i
$165$	−4.62450	+	1.86460i	−0.360017	+	0.145159i
$166$	−16.6963	+	0.662288i	−1.29588	+	0.0514035i
$167$	−2.00465	+	7.48145i	−0.155124	+	0.578932i	0.843970	+	0.536390i	$0.180212\pi$
$167$	−2.00465	+	7.48145i	−0.155124	+	0.578932i	−0.999095	+	0.0425421i	$0.986454\pi$
$168$	8.62598	−	3.35861i	0.665509	−	0.259122i
$169$	1.95219	+	7.28569i	0.150169	+	0.560437i
$170$	−1.43872	−	4.62730i	−0.110345	−	0.354898i
$171$	22.0804	+	9.63819i	1.68853	+	0.737051i
$172$	4.83435	+	3.13429i	0.368616	+	0.238988i
$173$	1.79838	−	13.6600i	0.136728	−	1.03855i	−0.776215	−	0.630468i	$-0.782863\pi$
$173$	1.79838	−	13.6600i	0.136728	−	1.03855i	0.912943	−	0.408086i	$-0.133804\pi$
$174$	1.64991	−	4.35046i	0.125079	−	0.329807i
$175$	2.85368	+	4.94272i	0.215718	+	0.373634i
$176$	−1.89868	+	7.96133i	−0.143118	+	0.600108i
$177$	−2.71169	+	9.75110i	−0.203823	+	0.732938i
$178$	0.290338	−	0.411147i	0.0217618	−	0.0308168i
$179$	−0.702535	−	1.69607i	−0.0525099	−	0.126770i	0.895448	−	0.445167i	$-0.146856\pi$
$179$	−0.702535	−	1.69607i	−0.0525099	−	0.126770i	−0.947958	+	0.318397i	$0.896856\pi$
$180$	2.75367	−	7.97989i	0.205247	−	0.594786i
$181$	−9.16779	−	3.79742i	−0.681437	−	0.282260i	0.0149906	−	0.999888i	$-0.495228\pi$
$181$	−9.16779	−	3.79742i	−0.681437	−	0.282260i	−0.696427	+	0.717627i	$0.745228\pi$
$182$	6.08908	+	1.37541i	0.451353	+	0.101952i
$183$	5.42744	+	3.20221i	0.401208	+	0.236714i
$184$	−18.8856	+	4.81902i	−1.39226	+	0.355263i
$185$	−2.49249	−	0.667860i	−0.183251	−	0.0491020i
$186$	−4.17605	−	13.8923i	−0.306203	−	1.01864i
$187$	3.95348	−	3.03361i	0.289107	−	0.221840i
$188$	20.0407	+	3.69874i	1.46162	+	0.269758i
$189$	−5.75409	−	7.95545i	−0.418548	−	0.578674i
$190$	−10.2222	−	12.2814i	−0.741595	−	0.890989i
$191$	13.1754	−	22.8204i	0.953338	−	1.65123i	0.215211	−	0.976567i	$-0.430956\pi$
$191$	13.1754	−	22.8204i	0.953338	−	1.65123i	0.738127	−	0.674662i	$-0.235711\pi$
$192$	−8.06389	−	11.2683i	−0.581961	−	0.813217i
$193$	−8.88327	−	15.3863i	−0.639432	−	1.10753i	−0.985558	−	0.169340i	$-0.945836\pi$
$193$	−8.88327	−	15.3863i	−0.639432	−	1.10753i	0.346126	−	0.938188i	$-0.387497\pi$
$194$	6.23146	−	16.9107i	0.447393	−	1.21412i
$195$	4.54890	−	3.42278i	0.325754	−	0.245110i
$196$	4.45087	−	5.21925i	0.317919	−	0.372803i
$197$	−4.46253	−	1.84844i	−0.317942	−	0.131696i	0.218005	−	0.975948i	$-0.430045\pi$
$197$	−4.46253	−	1.84844i	−0.317942	−	0.131696i	−0.535947	+	0.844252i	$0.680045\pi$
$198$	8.67921	−	0.180302i	0.616805	−	0.0128135i
$199$	−11.7416	+	11.7416i	−0.832339	+	0.832339i	−0.987836	−	0.155497i	$-0.950302\pi$
$199$	−11.7416	+	11.7416i	−0.832339	+	0.832339i	0.155497	+	0.987836i	$0.450302\pi$
$200$	6.11286	−	5.96834i	0.432245	−	0.422026i
$201$	−5.24253	−	9.28152i	−0.369779	−	0.654668i
$202$	2.51589	−	2.72373i	0.177018	−	0.191641i
$203$	0.468480	+	3.55846i	0.0328809	+	0.249755i
$204$	−0.514691	+	8.42085i	−0.0360356	+	0.589578i
$205$	−12.2891	−	1.61789i	−0.858308	−	0.112998i
$206$	16.7521	+	1.53294i	1.16717	+	0.106805i
$207$	9.99677	+	18.0953i	0.694823	+	1.25771i
$208$	−0.258661	−	9.34077i	−0.0179349	−	0.647666i
$209$	8.21608	−	14.2307i	0.568318	−	0.984356i
$210$	1.04458	+	6.42753i	0.0720830	+	0.443542i
$211$	2.18426	+	1.67604i	0.150371	+	0.115383i	0.681207	−	0.732091i	$-0.261455\pi$
$211$	2.18426	+	1.67604i	0.150371	+	0.115383i	−0.530836	+	0.847474i	$0.678122\pi$
$212$	−0.0256186	+	0.495970i	−0.00175949	+	0.0340634i
$213$	−19.2184	+	7.74885i	−1.31682	+	0.530942i
$214$	−19.1336	−	4.32194i	−1.30795	−	0.295441i
$215$	−2.86593	+	2.86593i	−0.195455	+	0.195455i
$216$	−9.40914	+	11.2902i	−0.640211	+	0.768199i
$217$	7.91268	+	7.91268i	0.537148	+	0.537148i
$218$	−10.6925	−	16.9324i	−0.724186	−	1.14681i
$219$	−6.94473	−	17.2240i	−0.469281	−	1.16389i
$220$	−5.19861	−	2.47481i	−0.350490	−	0.166852i
$221$	−3.46347	+	4.51368i	−0.232978	+	0.303623i
$222$	3.64512	+	2.62597i	0.244645	+	0.176243i
$223$	16.4398	+	9.49150i	1.10089	+	0.635598i	0.936454	−	0.350791i	$-0.114087\pi$
$223$	16.4398	+	9.49150i	1.10089	+	0.635598i	0.164433	+	0.986388i	$0.447420\pi$
$224$	9.59536	+	4.70949i	0.641117	+	0.314666i
$225$	−7.76062	−	4.67808i	−0.517375	−	0.311872i
$226$	1.38635	+	1.66563i	0.0922187	+	0.110796i
$227$	−1.53896	+	11.6896i	−0.102144	+	0.775863i	0.861327	+	0.508051i	$0.169634\pi$
$227$	−1.53896	+	11.6896i	−0.102144	+	0.775863i	−0.963471	+	0.267812i	$0.913699\pi$
$228$	9.05820	+	26.3034i	0.599894	+	1.74198i
$229$	0.0526766	−	0.00693501i	0.00348097	−	0.000458278i	−0.128786	−	0.991672i	$-0.541108\pi$
$229$	0.0526766	−	0.00693501i	0.00348097	−	0.000458278i	0.132266	+	0.991214i	$0.457775\pi$
$230$	−0.543451	−	13.7004i	−0.0358341	−	0.903376i
$231$	−5.83073	+	3.29340i	−0.383634	+	0.216690i
$232$	4.98788	−	1.99649i	0.327470	−	0.131076i
$233$	11.6368	+	11.6368i	0.762353	+	0.762353i	0.976747	−	0.214394i	$-0.0687776\pi$
$233$	11.6368	+	11.6368i	0.762353	+	0.762353i	−0.214394	+	0.976747i	$0.568778\pi$
$234$	−9.51812	+	2.76348i	−0.622219	+	0.180655i
$235$	−5.48622	+	13.2449i	−0.357881	+	0.864002i
$236$	−10.4091	+	5.31356i	−0.677574	+	0.345883i
$237$	−0.737093	−	0.979604i	−0.0478793	−	0.0636321i
$238$	−2.72684	−	5.90912i	−0.176755	−	0.383031i
$239$	25.0656	−	14.4717i	1.62136	−	0.936094i	0.634806	−	0.772672i	$-0.281080\pi$
$239$	25.0656	−	14.4717i	1.62136	−	0.936094i	0.986556	−	0.163422i	$-0.0522532\pi$
$240$	8.93602	−	3.89393i	0.576818	−	0.251352i
$241$	−10.0975	−	5.82980i	−0.650438	−	0.375531i	0.138186	−	0.990406i	$-0.455873\pi$
$241$	−10.0975	−	5.82980i	−0.650438	−	0.375531i	−0.788624	+	0.614876i	$0.789206\pi$
$242$	−0.878047	+	9.59532i	−0.0564430	+	0.616811i
$243$	14.1044	+	6.63814i	0.904800	+	0.425837i
$244$	1.51824	+	7.11641i	0.0971951	+	0.455582i
$245$	2.93749	+	3.82821i	0.187669	+	0.244576i
$246$	19.0062	+	10.2206i	1.21179	+	0.651642i
$247$	−4.85559	+	18.1213i	−0.308954	+	1.15303i
$248$	8.54820	−	14.4052i	0.542812	−	0.914732i
$249$	−10.3992	+	17.6256i	−0.659021	+	1.11698i
$250$	8.52079	+	13.4934i	0.538902	+	0.853396i
$251$	−0.0941454	+	0.227287i	−0.00594241	+	0.0143462i	−0.926823	−	0.375499i	$-0.877471\pi$
$251$	−0.0941454	+	0.227287i	−0.00594241	+	0.0143462i	0.920880	+	0.389845i	$0.127471\pi$
$252$	2.26771	−	11.1081i	0.142852	−	0.699742i
$253$	13.0267	−	5.39586i	0.818985	−	0.339235i
$254$	3.02496	+	17.5646i	0.189803	+	1.10210i
$255$	−5.71790	−	1.59009i	−0.358069	−	0.0995754i
$256$	3.27948	−	15.6603i	0.204967	−	0.978769i
$257$	−25.5643	+	14.7596i	−1.59466	+	0.920676i	−0.602165	+	0.798372i	$0.705695\pi$
$257$	−25.5643	+	14.7596i	−1.59466	+	0.920676i	−0.992493	+	0.122304i	$0.960972\pi$
$258$	6.43468	−	2.89602i	0.400606	−	0.180298i
$259$	−3.43586	−	0.452339i	−0.213494	−	0.0281070i
$260$	6.46430	+	1.19306i	0.400899	+	0.0739903i
$261$	−3.38309	−	4.58560i	−0.209408	−	0.283842i
$262$	9.30469	+	4.89097i	0.574846	+	0.302165i
$263$	5.63138	−	1.50892i	0.347246	−	0.0930443i	−0.0809806	−	0.996716i	$-0.525805\pi$
$263$	5.63138	−	1.50892i	0.347246	−	0.0930443i	0.428227	+	0.903671i	$0.359139\pi$
$264$	6.93479	+	7.23812i	0.426807	+	0.445475i
$265$	−0.337461	−	0.0904225i	−0.0207301	−	0.00555461i
$266$	−15.7639	−	14.5610i	−0.966547	−	0.892792i
$267$	−0.230519	−	0.571724i	−0.0141075	−	0.0349889i
$268$	3.79483	−	11.7093i	0.231806	−	0.715257i
$269$	9.53560	−	3.94978i	0.581396	−	0.240822i	−0.0725482	−	0.997365i	$-0.523113\pi$
$269$	9.53560	−	3.94978i	0.581396	−	0.240822i	0.653944	+	0.756543i	$0.273113\pi$
$270$	−6.38646	−	8.13051i	−0.388667	−	0.494807i
$271$	−29.3045			−1.78012			−0.890060	−	0.455843i	$-0.849338\pi$
$271$	−29.3045			−1.78012			−0.890060	+	0.455843i	$0.849338\pi$
$272$	−7.56150	+	6.14204i	−0.458483	+	0.372416i
$273$	5.45693	−	5.35489i	0.330269	−	0.324093i
$274$	9.15187	−	4.22324i	0.552885	−	0.255136i
$275$	−3.76241	+	4.90327i	−0.226882	+	0.295678i
$276$	−7.57349	+	22.6379i	−0.455871	+	1.36264i
$277$	−26.0799	+	20.0118i	−1.56699	+	1.20239i	−0.687827	+	0.725874i	$0.741435\pi$
$277$	−26.0799	+	20.0118i	−1.56699	+	1.20239i	−0.879164	+	0.476520i	$0.841898\pi$
$278$	−26.0059	+	8.08577i	−1.55973	+	0.484953i
$279$	−17.0714	−	4.92144i	−1.02204	−	0.294639i
$280$	−4.64846	+	5.91024i	−0.277798	+	0.353205i
$281$	−0.939472	−	3.50616i	−0.0560442	−	0.209160i	0.932226	−	0.361878i	$-0.117864\pi$
$281$	−0.939472	−	3.50616i	−0.0560442	−	0.209160i	−0.988270	+	0.152718i	$0.951197\pi$
$282$	17.1078	−	18.1739i	1.01875	−	1.08224i
$283$	4.27968	+	32.5074i	0.254401	+	1.93237i	0.349582	+	0.936906i	$0.386324\pi$
$283$	4.27968	+	32.5074i	0.254401	+	1.93237i	−0.0951812	+	0.995460i	$0.530343\pi$
$284$	−21.6043	−	10.2848i	−1.28198	−	0.610289i
$285$	−19.4259	+	2.37119i	−1.15069	+	0.140457i
$286$	1.14730	+	6.66185i	0.0678410	+	0.393924i
$287$	−16.6468			−0.982627
$288$	−16.9506	+	0.821997i	−0.998826	+	0.0484366i
$289$	−11.0687			−0.651100
$290$	0.641453	+	3.72464i	0.0376674	+	0.218718i
$291$	−13.2711	−	17.6375i	−0.777968	−	1.03393i
$292$	9.21749	−	19.3623i	0.539413	−	1.13310i
$293$	1.43403	+	10.8926i	0.0837772	+	0.636351i	0.980892	+	0.194553i	$0.0623257\pi$
$293$	1.43403	+	10.8926i	0.0837772	+	0.636351i	−0.897115	+	0.441798i	$0.854341\pi$
$294$	−2.41843	−	8.04533i	−0.141046	−	0.469213i
$295$	−2.12785	−	7.94123i	−0.123888	−	0.462357i
$296$	0.615538	+	5.15085i	0.0357774	+	0.299387i
$297$	5.57458	−	9.05350i	0.323470	−	0.525337i
$298$	24.3164	−	7.56049i	1.40861	−	0.437967i
$299$	−12.7714	+	9.79984i	−0.738589	+	0.566740i
$300$	−2.08649	−	10.2532i	−0.120463	−	0.591971i
$301$	−3.31364	+	4.31842i	−0.190995	+	0.248910i
$302$	18.1962	−	8.39686i	1.04707	−	0.483185i
$303$	−1.13390	−	4.39737i	−0.0651411	−	0.252623i
$304$	−15.2853	+	28.2533i	−0.876673	+	1.62044i
$305$	−5.11885			−0.293104
$306$	8.32631	+	6.11850i	0.475983	+	0.349771i
$307$	4.11369	−	1.70395i	0.234781	−	0.0972494i	−0.262191	−	0.965016i	$-0.584445\pi$
$307$	4.11369	−	1.70395i	0.234781	−	0.0972494i	0.496972	+	0.867767i	$0.334445\pi$
$308$	−7.35586	−	2.38395i	−0.419139	−	0.135838i
$309$	12.6958	−	16.2261i	0.722241	−	0.923073i
$310$	8.65592	+	7.99542i	0.491623	+	0.454109i
$311$	6.17183	+	1.65374i	0.349972	+	0.0937747i	0.429523	−	0.903056i	$-0.358682\pi$
$311$	6.17183	+	1.65374i	0.349972	+	0.0937747i	−0.0795505	+	0.996831i	$0.525349\pi$
$312$	−9.78647	−	5.93299i	−0.554050	−	0.335889i
$313$	−0.683314	+	0.183093i	−0.0386232	+	0.0103490i	−0.278079	−	0.960558i	$-0.589698\pi$
$313$	−0.683314	+	0.183093i	−0.0386232	+	0.0103490i	0.239456	+	0.970907i	$0.423031\pi$
$314$	9.45243	+	4.96863i	0.533432	+	0.280396i
$315$	7.30936	+	3.19057i	0.411836	+	0.179768i
$316$	0.256924	−	1.39208i	0.0144531	−	0.0783108i
$317$	12.8941	+	1.69754i	0.724206	+	0.0953435i	0.483612	−	0.875282i	$-0.339325\pi$
$317$	12.8941	+	1.69754i	0.724206	+	0.0953435i	0.240594	+	0.970626i	$0.422658\pi$
$318$	0.493518	+	0.355533i	0.0276751	+	0.0199373i
$319$	−3.36596	+	1.94334i	−0.188457	+	0.108806i
$320$	10.2927	+	4.55482i	0.575382	+	0.254622i
$321$	−17.1472	+	16.8266i	−0.957066	+	0.939170i
$322$	−3.12525	−	18.1470i	−0.174164	−	1.01129i
$323$	18.0696	−	7.48466i	1.00542	−	0.416457i
$324$	5.37679	+	17.1782i	0.298711	+	0.954344i
$325$	2.70029	−	6.51907i	0.149785	−	0.361613i
$326$	−10.5238	−	16.6654i	−0.582861	−	0.923009i
$327$	−24.5255	−	0.231467i	−1.35626	−	0.0128002i
$328$	6.16101	+	24.1448i	0.340185	+	1.33317i
$329$	−4.98319	+	18.5975i	−0.274732	+	1.02531i
$330$	−5.99761	+	3.70866i	−0.330157	+	0.204155i
$331$	−9.37610	−	12.2192i	−0.515357	−	0.671627i	0.461097	−	0.887350i	$-0.347456\pi$
$331$	−9.37610	−	12.2192i	−0.515357	−	0.671627i	−0.976455	+	0.215723i	$0.930789\pi$
$332$	−23.1105	+	4.93047i	−1.26836	+	0.270595i
$333$	5.12218	−	2.00927i	0.280694	−	0.110107i
$334$	−0.998169	+	10.9080i	−0.0546174	+	0.596861i
$335$	7.49883	+	4.32945i	0.409705	+	0.236543i
$336$	11.2159	−	6.75129i	0.611875	−	0.368313i
$337$	−16.8932	+	9.75332i	−0.920234	+	0.531297i	−0.883710	−	0.468036i	$-0.844962\pi$
$337$	−16.8932	+	9.75332i	−0.920234	+	0.531297i	−0.0365240	+	0.999333i	$0.511629\pi$
$338$	4.46948	+	9.68547i	0.243108	+	0.526820i
$339$	2.63458	−	0.321585i	0.143091	−	0.0174661i
$340$	−3.11579	−	6.10373i	−0.168978	−	0.331021i
$341$	−4.63727	+	11.1954i	−0.251122	+	0.606262i
$342$	33.0868	+	8.13296i	1.78913	+	0.439780i
$343$	13.9351	+	13.9351i	0.752424	+	0.752424i
$344$	7.48991	+	3.20791i	0.403829	+	0.172959i
$345$	−14.4630	−	8.53320i	−0.778661	−	0.459412i
$346$	−0.772298	−	19.4696i	−0.0415190	−	1.04669i
$347$	−10.6250	+	1.39881i	−0.570379	+	0.0750918i	−0.410199	−	0.911996i	$-0.634541\pi$
$347$	−10.6250	+	1.39881i	−0.570379	+	0.0750918i	−0.160180	+	0.987088i	$0.551207\pi$
$348$	1.25527	−	6.45923i	0.0672895	−	0.346251i
$349$	−2.73395	+	20.7664i	−0.146345	+	1.11160i	0.747832	+	0.663888i	$0.231095\pi$
$349$	−2.73395	+	20.7664i	−0.146345	+	1.11160i	−0.894177	+	0.447713i	$0.852239\pi$
$350$	5.16351	+	6.20370i	0.276001	+	0.331602i
$351$	−3.47238	+	11.6314i	−0.185342	+	0.620839i
$352$	−0.735302	+	11.5514i	−0.0391917	+	0.615692i
$353$	−14.7391	−	8.50962i	−0.784483	−	0.452922i	0.0535337	−	0.998566i	$-0.482952\pi$
$353$	−14.7391	−	8.50962i	−0.784483	−	0.452922i	−0.838017	+	0.545645i	$0.816285\pi$
$354$	−1.43880	+	14.2409i	−0.0764715	+	0.756897i
$355$	10.2468	−	13.3539i	0.543845	−	0.708752i
$356$	0.305960	−	0.642702i	0.0162158	−	0.0340631i
$357$	−7.89221	−	1.11490i	−0.417700	−	0.0590067i
$358$	−1.38621	−	2.19518i	−0.0732636	−	0.116019i
$359$	−0.817007	−	0.817007i	−0.0431200	−	0.0431200i	0.685218	−	0.728338i	$-0.259707\pi$
$359$	−0.817007	−	0.817007i	−0.0431200	−	0.0431200i	−0.728338	+	0.685218i	$0.759707\pi$
$360$	1.92245	−	11.7825i	0.101322	−	0.620991i
$361$	32.1686	−	32.1686i	1.69308	−	1.69308i
$362$	−13.6886	−	3.09200i	−0.719456	−	0.162512i
$363$	9.29409	+	7.27198i	0.487813	+	0.381680i
$364$	8.81646	+	0.455400i	0.462108	+	0.0238695i
$365$	11.9681	+	9.18348i	0.626441	+	0.480685i
$366$	8.33280	+	3.16021i	0.435563	+	0.165187i
$367$	−1.94461	+	3.36816i	−0.101508	+	0.175816i	−0.912306	−	0.409509i	$-0.865700\pi$
$367$	−1.94461	+	3.36816i	−0.101508	+	0.175816i	0.810798	+	0.585326i	$0.199033\pi$
$368$	−25.1641	+	11.2492i	−1.31177	+	0.586404i
$369$	23.1344	−	12.7806i	1.20433	−	0.665333i
$370$	−3.63407	−	0.332546i	−0.188926	−	0.0172882i
$371$	−0.465186	−	0.0612429i	−0.0241512	−	0.00317957i
$372$	−9.15459	−	18.3594i	−0.474643	−	0.951889i
$373$	−2.58839	−	19.6608i	−0.134022	−	1.01800i	−0.917824	−	0.396987i	$-0.870056\pi$
$373$	−2.58839	−	19.6608i	−0.134022	−	1.01800i	0.783803	−	0.621010i	$-0.213277\pi$
$374$	4.78182	−	5.17685i	0.247262	−	0.267689i
$375$	19.5443	+	0.184455i	1.00926	+	0.00952523i
$376$	28.8185	+	0.344729i	1.48620	+	0.0177780i
$377$	3.13772	−	3.13772i	0.161601	−	0.161601i
$378$	−9.92892	−	9.70638i	−0.510689	−	0.499242i
$379$	15.9789	+	6.61869i	0.820783	+	0.339979i	0.753247	−	0.657737i	$-0.228486\pi$
$379$	15.9789	+	6.61869i	0.820783	+	0.339979i	0.0675356	+	0.997717i	$0.478486\pi$
$380$	−17.1944	−	14.6631i	−0.882055	−	0.752199i
$381$	20.0875	+	8.54351i	1.02912	+	0.437697i
$382$	12.8851	−	34.9671i	0.659260	−	1.78907i
$383$	14.1781	+	24.5572i	0.724468	+	1.25482i	0.959193	+	0.282753i	$0.0912478\pi$
$383$	14.1781	+	24.5572i	0.724468	+	1.25482i	−0.234725	+	0.972062i	$0.575419\pi$
$384$	−13.9432	−	13.7690i	−0.711537	−	0.702648i
$385$	2.71980	−	4.71083i	0.138614	−	0.240086i
$386$	−16.0736	−	19.3116i	−0.818125	−	0.982936i
$387$	1.28955	−	8.54548i	0.0655517	−	0.434391i
$388$	4.62585	−	25.0641i	0.234842	−	1.27243i
$389$	−20.7463	+	15.9192i	−1.05188	+	0.807134i	−0.981706	−	0.190401i	$-0.939021\pi$
$389$	−20.7463	+	15.9192i	−1.05188	+	0.807134i	−0.0701713	+	0.997535i	$0.522355\pi$
$390$	5.51825	−	5.86214i	0.279428	−	0.296841i
$391$	16.2107	+	4.34364i	0.819810	+	0.219668i
$392$	4.95044	−	8.34235i	0.250035	−	0.421352i
$393$	11.2097	−	6.33166i	0.565457	−	0.319390i
$394$	−6.66307	−	1.50507i	−0.335681	−	0.0758241i
$395$	0.920026	+	0.381087i	0.0462915	+	0.0191746i
$396$	12.0529	−	2.33448i	0.605682	−	0.117312i
$397$	13.7375	+	33.1654i	0.689468	+	1.66452i	0.745850	+	0.666113i	$0.232043\pi$
$397$	13.7375	+	33.1654i	0.689468	+	1.66452i	−0.0563826	+	0.998409i	$0.517957\pi$
$398$	−13.5460	+	19.1824i	−0.678999	+	0.961529i
$399$	−25.4503	+	6.56259i	−1.27411	+	0.328541i
$400$	7.08695	−	9.78527i	0.354347	−	0.489264i
$401$	−13.1884	−	22.8429i	−0.658595	−	1.14072i	−0.980980	−	0.194111i	$-0.937818\pi$
$401$	−13.1884	−	22.8429i	−0.658595	−	1.14072i	0.322385	−	0.946609i	$-0.395516\pi$
$402$	−9.53425	−	11.6773i	−0.475525	−	0.582411i
$403$	1.80581	−	13.7165i	0.0899537	−	0.683266i
$404$	2.85264	−	4.39992i	0.141924	−	0.218904i
$405$	−12.6076	+	1.17780i	−0.626475	+	0.0585253i
$406$	1.50702	+	4.84697i	0.0747923	+	0.240551i
$407$	−0.971286	−	3.62489i	−0.0481448	−	0.179679i
$408$	1.30385	+	11.8596i	0.0645504	+	0.587140i
$409$	8.22630	−	30.7010i	0.406764	−	1.51807i	−0.394014	−	0.919104i	$-0.628914\pi$
$409$	8.22630	−	30.7010i	0.406764	−	1.51807i	0.800778	−	0.598961i	$-0.204419\pi$
$410$	−17.5156	+	0.694789i	−0.865034	+	0.0343132i
$411$	1.72672	−	12.2232i	0.0851730	−	0.602927i
$412$	23.7152	−	1.88438i	1.16836	−	0.0928368i
$413$	−4.22534	−	10.2009i	−0.207915	−	0.501952i
$414$	18.2757	+	22.8199i	0.898202	+	1.12154i
$415$		−	16.6235i		−	0.816013i
$416$	−2.60247	−	12.9561i	−0.127597	−	0.635226i
$417$	−8.93648	+	32.1352i	−0.437621	+	1.57367i
$418$	8.03507	−	21.8053i	0.393008	−	1.06653i
$419$	17.6188	+	13.5194i	0.860735	+	0.660465i	0.941774	−	0.336246i	$-0.109157\pi$
$419$	17.6188	+	13.5194i	0.860735	+	0.660465i	−0.0810392	+	0.996711i	$0.525824\pi$
$420$	2.99857	+	8.70731i	0.146315	+	0.424873i
$421$	12.7334	+	16.5945i	0.620588	+	0.808767i	0.992851	−	0.119361i	$-0.0380845\pi$
$421$	12.7334	+	16.5945i	0.620588	+	0.808767i	−0.372262	+	0.928128i	$0.621418\pi$
$422$	3.44648	+	1.81162i	0.167772	+	0.0881885i
$423$	−7.35309	−	29.6713i	−0.357519	−	1.44267i
$424$	0.0833386	+	0.697381i	0.00404728	+	0.0338678i
$425$	−7.10559	+	1.90394i	−0.344672	+	0.0923545i
$426$	−24.9247	+	15.4124i	−1.20761	+	0.746731i
$427$	−6.81582	+	0.897320i	−0.329841	+	0.0434244i
$428$	−27.7038	−	1.43100i	−1.33912	−	0.0691699i
$429$	7.61872	+	3.24035i	0.367835	+	0.156446i
$430$	−3.30635	+	4.68212i	−0.159447	+	0.225792i
$431$		−	25.8563i		−	1.24545i	−0.782439	−	0.622727i	$-0.786025\pi$
$431$		−	25.8563i		−	1.24545i	0.782439	−	0.622727i	$-0.213975\pi$
$432$	−10.4036	+	17.9935i	−0.500544	+	0.865711i
$433$			27.0878i			1.30176i	0.759181	+	0.650879i	$0.225600\pi$
$433$			27.0878i			1.30176i	−0.759181	+	0.650879i	$0.774400\pi$
$434$	12.9271	+	9.12867i	0.620520	+	0.438190i
$435$	4.25963	+	1.81168i	0.204233	+	0.0868634i
$436$	−18.9662	−	21.0322i	−0.908316	−	1.00726i
$437$	54.8667	−	7.22334i	2.62463	−	0.345539i
$438$	−13.8130	−	22.3382i	−0.660009	−	1.06736i
$439$	−6.04765	+	1.62046i	−0.288639	+	0.0773405i	−0.400233	−	0.916413i	$-0.631071\pi$
$439$	−6.04765	+	1.62046i	−0.288639	+	0.0773405i	0.111595	+	0.993754i	$0.464404\pi$
$440$	−7.83929	−	2.20136i	−0.373724	−	0.104946i
$441$	−9.88642	−	2.85010i	−0.470782	−	0.135719i
$442$	−3.74365	+	7.12201i	−0.178067	+	0.338759i
$443$	−1.71155	−	2.23054i	−0.0813183	−	0.105976i	0.750923	−	0.660390i	$-0.229609\pi$
$443$	−1.71155	−	2.23054i	−0.0813183	−	0.105976i	−0.832241	+	0.554414i	$0.812942\pi$
$444$	5.71048	+	2.78489i	0.271007	+	0.132165i
$445$	0.397263	+	0.304831i	0.0188321	+	0.0144504i
$446$	25.1902	+	9.28239i	1.19279	+	0.439534i
$447$	8.35593	−	30.0475i	0.395222	−	1.42120i
$448$	14.5034	+	4.26052i	0.685221	+	0.201291i
$449$		−	31.2741i		−	1.47592i	−0.674846	−	0.737959i	$-0.735790\pi$
$449$		−	31.2741i		−	1.47592i	0.674846	−	0.737959i	$-0.264210\pi$
$450$	−11.9388	−	4.65712i	−0.562800	−	0.219539i
$451$	−6.89848	−	16.6544i	−0.324837	−	0.784225i
$452$	2.33194	+	1.98863i	0.109685	+	0.0935373i
$453$	3.43316	−	24.3028i	0.161304	−	1.14185i
$454$	0.660893	+	16.6611i	0.0310172	+	0.781943i
$455$	−1.60737	+	5.99877i	−0.0753545	+	0.281227i
$456$	18.9377	+	34.4848i	0.886841	+	1.61490i
$457$	2.60374	+	9.71728i	0.121798	+	0.454555i	0.999705	−	0.0242748i	$-0.00772766\pi$
$457$	2.60374	+	9.71728i	0.121798	+	0.454555i	−0.877908	+	0.478830i	$0.841061\pi$
$458$	0.0717506	−	0.0223088i	0.00335269	−	0.00104242i
$459$	11.8240	−	4.50989i	0.551895	−	0.210503i
$460$	−4.04578	−	18.9637i	−0.188635	−	0.884188i
$461$	−3.06818	+	23.3051i	−0.142899	+	1.08543i	0.758263	+	0.651948i	$0.226048\pi$
$461$	−3.06818	+	23.3051i	−0.142899	+	1.08543i	−0.901163	+	0.433481i	$0.857285\pi$
$462$	−7.33579	+	5.98950i	−0.341292	+	0.278657i
$463$	−5.92320	−	10.2593i	−0.275274	−	0.476789i	0.694930	−	0.719077i	$-0.255435\pi$
$463$	−5.92320	−	10.2593i	−0.275274	−	0.476789i	−0.970204	+	0.242288i	$0.922102\pi$
$464$	6.47239	−	3.97970i	0.300473	−	0.184753i
$465$	13.9747	−	3.60351i	0.648061	−	0.167109i
$466$	19.0113	+	13.4251i	0.880680	+	0.621907i
$467$	1.37856	+	3.32815i	0.0637923	+	0.154008i	0.952561	−	0.304348i	$-0.0984385\pi$
$467$	1.37856	+	3.32815i	0.0637923	+	0.154008i	−0.888769	+	0.458356i	$0.848438\pi$
$468$	−12.6021	+	6.13600i	−0.582531	+	0.283637i
$469$	10.7438	+	4.45021i	0.496101	+	0.205492i
$470$	−4.46707	+	19.7762i	−0.206051	+	0.912207i
$471$	11.3877	−	6.43219i	0.524719	−	0.296380i
$472$	−13.2317	+	9.90389i	−0.609040	+	0.455863i
$473$	−5.69359	−	1.52559i	−0.261791	−	0.0701468i
$474$	−1.26241	−	1.18835i	−0.0579844	−	0.0545829i
$475$	−19.2444	+	14.7668i	−0.882995	+	0.677546i
$476$	−5.21869	−	7.58102i	−0.239198	−	0.347476i
$477$	0.693500	−	0.272038i	0.0317532	−	0.0124558i
$478$	31.4604	−	26.1854i	1.43897	−	1.19769i
$479$	12.0894	−	20.9395i	0.552381	−	0.956752i	−0.445721	−	0.895172i	$-0.647053\pi$
$479$	12.0894	−	20.9395i	0.552381	−	0.956752i	0.998102	−	0.0615801i	$-0.0196140\pi$
$480$	11.5195	−	7.57179i	0.525790	−	0.345603i
$481$	2.14226	+	3.71050i	0.0976786	+	0.169184i
$482$	−15.4721	−	5.70137i	−0.704737	−	0.259690i
$483$	−20.7535	−	8.82677i	−0.944319	−	0.401632i
$484$	1.07934	+	13.5837i	0.0490611	+	0.617442i
$485$	16.5648	+	6.86136i	0.752168	+	0.311558i
$486$	21.2506	+	5.86620i	0.963946	+	0.266096i
$487$	−5.63800	+	5.63800i	−0.255482	+	0.255482i	−0.823214	−	0.567732i	$-0.807821\pi$
$487$	−5.63800	+	5.63800i	−0.255482	+	0.255482i	0.567732	+	0.823214i	$0.307821\pi$
$488$	3.82405	+	9.55371i	0.173106	+	0.432476i
$489$	−24.1387	−	0.227816i	−1.09159	−	0.0103022i
$490$	5.01282	+	4.63031i	0.226456	+	0.209176i
$491$	−1.17008	−	8.88765i	−0.0528050	−	0.401094i	−0.997352	−	0.0727190i	$-0.976832\pi$
$491$	−1.17008	−	8.88765i	−0.0528050	−	0.401094i	0.944547	−	0.328375i	$-0.106501\pi$
$492$	28.9420	+	9.68254i	1.30481	+	0.436522i
$493$	−4.58653	−	0.603828i	−0.206567	−	0.0271950i
$494$	−2.41773	+	26.4211i	−0.108779	+	1.18874i
$495$	−0.163004	+	8.63490i	−0.00732647	+	0.388110i
$496$	8.45606	−	22.1282i	0.379688	−	0.993587i
$497$	11.3029	−	19.5772i	0.507004	−	0.878157i
$498$	−10.2628	+	27.0608i	−0.459886	+	1.21262i
$499$	12.8546	+	9.86365i	0.575449	+	0.441558i	0.855040	−	0.518562i	$-0.173532\pi$
$499$	12.8546	+	9.86365i	0.575449	+	0.441558i	−0.279591	+	0.960119i	$0.590199\pi$
$500$	15.1141	+	16.7605i	0.675922	+	0.749553i
$501$	10.5656	+	8.26684i	0.472035	+	0.369335i
$502$	−0.0766565	+	0.339366i	−0.00342135	+	0.0151467i
$503$	−5.54544	+	5.54544i	−0.247259	+	0.247259i	−0.819845	−	0.572586i	$-0.805940\pi$
$503$	−5.54544	+	5.54544i	−0.247259	+	0.247259i	0.572586	+	0.819845i	$0.305940\pi$
$504$	0.494330	−	16.0256i	0.0220192	−	0.713835i
$505$	2.60839	+	2.60839i	0.116072	+	0.116072i
$506$	16.8602	−	10.6469i	0.749528	−	0.473311i
$507$	12.9359	+	1.82740i	0.574503	+	0.0811577i
$508$	8.43176	+	23.7537i	0.374099	+	1.05390i
$509$	−0.735612	+	0.958668i	−0.0326054	+	0.0424922i	−0.809372	−	0.587297i	$-0.800192\pi$
$509$	−0.735612	+	0.958668i	−0.0326054	+	0.0424922i	0.776766	+	0.629789i	$0.216859\pi$
$510$	−8.35067	−	0.843692i	−0.369774	−	0.0373593i
$511$	17.5456	+	10.1300i	0.776172	+	0.448123i
$512$	0.811799	−	22.6128i	0.0358768	−	0.999356i
$513$	30.3304	−	28.6598i	1.33912	−	1.26536i
$514$	−32.0863	+	26.7063i	−1.41527	+	1.17796i
$515$	−2.18443	+	16.5924i	−0.0962573	+	0.731147i
$516$	8.27289	−	5.58063i	0.364194	−	0.245674i
$517$	−20.6711	+	2.72140i	−0.909114	+	0.119687i
$518$	−4.89711	+	0.194253i	−0.215167	+	0.00853499i
$519$	−20.5533	−	12.1265i	−0.902192	−	0.532296i
$520$	9.29563	+	0.111195i	0.407640	+	0.00487622i
$521$	−23.8022	−	23.8022i	−1.04279	−	1.04279i	−0.999043	−	0.0437498i	$-0.986070\pi$
$521$	−23.8022	−	23.8022i	−1.04279	−	1.04279i	−0.0437498	−	0.999043i	$-0.513930\pi$
$522$	−5.81564	−	5.57893i	−0.254544	−	0.244183i
$523$	5.58541	−	13.4844i	0.244233	−	0.589630i	−0.753462	−	0.657491i	$-0.771618\pi$
$523$	5.58541	−	13.4844i	0.244233	−	0.589630i	0.997695	+	0.0678614i	$0.0216176\pi$
$524$	14.1419	+	4.58321i	0.617790	+	0.200218i
$525$	9.81260	−	1.19776i	0.428257	−	0.0522743i
$526$	7.48627	−	3.45463i	0.326417	−	0.150629i
$527$	−12.4908	+	7.21157i	−0.544108	+	0.314141i
$528$	11.4023	+	8.42325i	0.496221	+	0.366575i
$529$	21.2055	+	12.2430i	0.921979	+	0.532305i
$530$	−0.492022	−	0.0450238i	−0.0213721	−	0.00195571i
$531$	13.7038	+	10.9324i	0.594696	+	0.474424i
$532$	−25.4650	−	16.5100i	−1.10405	−	0.715798i
$533$	12.5289	+	16.3279i	0.542686	+	0.707242i
$534$	−0.458499	−	0.741481i	−0.0198412	−	0.0320870i
$535$	5.05081	−	18.8499i	0.218365	−	0.814951i
$536$	2.47838	−	17.2300i	0.107050	−	0.744223i
$537$	−3.17958	−	0.0300083i	−0.137209	−	0.00129495i
$538$	12.3417	−	7.79353i	0.532089	−	0.336003i
$539$	−2.68554	+	6.48346i	−0.115674	+	0.279262i
$540$	−10.8523	−	9.79859i	−0.467007	−	0.421664i
$541$	13.6258	−	5.64398i	0.585818	−	0.242654i	−0.0700324	−	0.997545i	$-0.522310\pi$
$541$	13.6258	−	5.64398i	0.585818	−	0.242654i	0.655850	+	0.754891i	$0.272310\pi$
$542$	−40.8416	+	7.03368i	−1.75430	+	0.302122i
$543$	−12.2675	+	12.0381i	−0.526448	+	0.516604i
$544$	−9.06421	+	10.3751i	−0.388625	+	0.444827i
$545$	17.2537	−	9.96145i	0.739069	−	0.426702i
$546$	6.32002	−	8.77287i	0.270472	−	0.375444i
$547$	7.49904	+	0.987267i	0.320636	+	0.0422125i	0.289126	−	0.957291i	$-0.406635\pi$
$547$	7.49904	+	0.987267i	0.320636	+	0.0422125i	0.0315095	+	0.999503i	$0.489969\pi$
$548$	11.7413	−	8.08256i	0.501562	−	0.345270i
$549$	8.78319	−	6.47992i	0.374858	−	0.276556i
$550$	−4.06677	+	7.73672i	−0.173408	+	0.329895i
$551$	−14.7347	+	3.94815i	−0.627719	+	0.168197i
$552$	−5.12159	+	33.3682i	−0.217989	+	1.42024i
$553$	1.29183	+	0.346145i	0.0549343	+	0.0147196i
$554$	−31.5443	+	34.1501i	−1.34019	+	1.45090i
$555$	−2.75414	+	3.51998i	−0.116907	+	0.149415i
$556$	−34.3036	+	17.5111i	−1.45480	+	0.742635i
$557$	−30.8241	+	12.7678i	−1.30606	+	0.540988i	−0.923732	−	0.383038i	$-0.874878\pi$
$557$	−30.8241	+	12.7678i	−1.30606	+	0.540988i	−0.382328	+	0.924027i	$0.624878\pi$
$558$	−24.9737	−	2.76149i	−1.05722	−	0.116903i
$559$	6.72967			0.284635
$560$	−5.05996	+	9.35281i	−0.213822	+	0.395228i
$561$	−2.15515	−	8.35785i	−0.0909905	−	0.352869i
$562$	−2.15089	−	4.66103i	−0.0907298	−	0.196614i
$563$	2.05276	−	2.67521i	0.0865134	−	0.112747i	−0.748091	−	0.663596i	$-0.769029\pi$
$563$	2.05276	−	2.67521i	0.0865134	−	0.112747i	0.834605	+	0.550849i	$0.185696\pi$
$564$	19.4810	−	29.4352i	0.820296	−	1.23944i
$565$	−1.71043	+	1.31246i	−0.0719583	+	0.0552155i
$566$	13.7670	+	44.2783i	0.578672	+	1.86115i
$567$	−16.5807	+	3.77833i	−0.696325	+	0.158675i
$568$	−32.5784	−	9.14838i	−1.36696	−	0.383858i
$569$	5.10434	+	19.0496i	0.213985	+	0.798602i	0.986521	+	0.163632i	$0.0523210\pi$
$569$	5.10434	+	19.0496i	0.213985	+	0.798602i	−0.772537	+	0.634970i	$0.781012\pi$
$570$	−26.5047	+	7.96735i	−1.11016	+	0.333715i
$571$	−1.70374	−	12.9412i	−0.0712994	−	0.541573i	−0.989399	−	0.145223i	$-0.953610\pi$
$571$	−1.70374	−	12.9412i	−0.0712994	−	0.541573i	0.918100	−	0.396350i	$-0.129723\pi$
$572$	3.19796	+	9.00923i	0.133714	+	0.376695i
$573$	−27.4415	−	36.4700i	−1.14638	−	1.52355i
$574$	−23.2005	+	3.99556i	−0.968371	+	0.166772i
$575$	−20.8144			−0.868021
$576$	−23.4268	+	5.21412i	−0.976115	+	0.217255i
$577$	−7.81056			−0.325158			−0.162579	−	0.986696i	$-0.551981\pi$
$577$	−7.81056			−0.325158			−0.162579	+	0.986696i	$0.551981\pi$
$578$	−15.4264	+	2.65672i	−0.641654	+	0.110505i
$579$	−30.5458	+	3.72852i	−1.26944	+	0.154952i
$580$	1.78798	+	5.03706i	0.0742419	+	0.209152i
$581$	−2.91405	−	22.1344i	−0.120895	−	0.918289i
$582$	−22.7293	−	21.3959i	−0.942160	−	0.886890i
$583$	−0.131504	−	0.490779i	−0.00544633	−	0.0203260i
$584$	8.19902	−	29.1976i	0.339278	−	1.20821i
$585$	−2.37180	−	9.57070i	−0.0980617	−	0.395700i
$586$	4.61305	+	14.8367i	0.190563	+	0.612900i
$587$	22.8785	−	17.5553i	0.944295	−	0.724583i	−0.0170716	−	0.999854i	$-0.505434\pi$
$587$	22.8785	−	17.5553i	0.944295	−	0.724583i	0.961367	+	0.275271i	$0.0887677\pi$
$588$	−5.30161	−	10.6323i	−0.218635	−	0.438468i
$589$	−28.9527	+	37.7319i	−1.19298	+	1.55472i
$590$	−4.87163	−	10.5569i	−0.200562	−	0.434622i
$591$	−5.97134	+	5.85968i	−0.245628	+	0.241035i
$592$	2.09418	+	7.03098i	0.0860704	+	0.288972i
$593$	−3.63338			−0.149205			−0.0746025	−	0.997213i	$-0.523769\pi$
$593$	−3.63338			−0.149205			−0.0746025	+	0.997213i	$0.523769\pi$
$594$	5.59625	−	13.9558i	0.229617	−	0.572615i
$595$	5.98164	−	2.47767i	0.245223	−	0.101575i
$596$	32.0751	−	16.3735i	1.31385	−	0.670684i
$597$	10.7551	+	26.6743i	0.440176	+	1.09171i
$598$	−15.4473	+	16.7234i	−0.631687	+	0.683871i
$599$	−14.2380	−	3.81505i	−0.581748	−	0.155879i	−0.0440689	−	0.999028i	$-0.514032\pi$
$599$	−14.2380	−	3.81505i	−0.581748	−	0.155879i	−0.537679	+	0.843150i	$0.680699\pi$
$600$	−5.36892	−	13.7891i	−0.219185	−	0.562938i
$601$	2.95269	−	0.791171i	0.120443	−	0.0322726i	−0.198094	−	0.980183i	$-0.563475\pi$
$601$	2.95269	−	0.791171i	0.120443	−	0.0322726i	0.318537	+	0.947910i	$0.396809\pi$
$602$	−3.58170	+	6.81391i	−0.145979	+	0.277714i
$603$	−18.3475	+	2.06402i	−0.747169	+	0.0840533i
$604$	23.3445	−	16.0701i	0.949876	−	0.653884i
$605$	−9.50385	−	1.25121i	−0.386387	−	0.0508688i
$606$	−2.63578	−	5.85644i	−0.107071	−	0.237902i
$607$	−36.1165	+	20.8519i	−1.46592	+	0.846351i	−0.999274	−	0.0380925i	$-0.987872\pi$
$607$	−36.1165	+	20.8519i	−1.46592	+	0.846351i	−0.466648	+	0.884443i	$0.654539\pi$
$608$	−14.5217	+	43.0454i	−0.588933	+	1.74572i
$609$	5.98934	+	1.66558i	0.242700	+	0.0674926i
$610$	−7.13412	+	1.22863i	−0.288852	+	0.0497457i
$611$	21.9918	−	9.10932i	0.889695	−	0.368524i
$612$	13.0729	+	6.52885i	0.528441	+	0.263913i
$613$	−2.40339	+	5.80229i	−0.0970720	+	0.234352i	−0.964955	−	0.262417i	$-0.915480\pi$
$613$	−2.40339	+	5.80229i	−0.0970720	+	0.234352i	0.867883	+	0.496769i	$0.165480\pi$
$614$	5.32426	−	3.36216i	0.214870	−	0.135686i
$615$	−10.9095	+	18.4906i	−0.439914	+	0.745613i
$616$	−10.8240	−	1.55694i	−0.436113	−	0.0627310i
$617$	−6.40693	+	23.9110i	−0.257933	+	0.962620i	0.708502	+	0.705709i	$0.249371\pi$
$617$	−6.40693	+	23.9110i	−0.257933	+	0.962620i	−0.966435	+	0.256911i	$0.917295\pi$
$618$	13.7995	−	25.6616i	0.555099	−	1.03226i
$619$	−17.9806	−	23.4327i	−0.722699	−	0.941840i	0.277120	−	0.960835i	$-0.410620\pi$
$619$	−17.9806	−	23.4327i	−0.722699	−	0.941840i	−0.999820	+	0.0189951i	$0.993953\pi$
$620$	13.9828	+	9.06559i	0.561563	+	0.364083i
$621$	35.6185	−	3.66687i	1.42932	−	0.147146i
$622$	8.99858	+	0.823440i	0.360810	+	0.0330169i
$623$	0.582398	+	0.336248i	0.0233333	+	0.0134715i
$624$	−15.0634	−	5.91983i	−0.603019	−	0.236983i
$625$	−0.670208	+	0.386945i	−0.0268083	+	0.0154778i
$626$	−0.908386	+	0.419186i	−0.0363064	+	0.0167540i
$627$	−17.1123	−	22.7424i	−0.683400	−	0.908245i
$628$	14.3664	+	4.65598i	0.573282	+	0.185794i
$629$	1.70934	−	4.12671i	0.0681557	−	0.164543i
$630$	10.9528	+	2.69228i	0.436371	+	0.107263i
$631$	−7.09696	−	7.09696i	−0.282526	−	0.282526i	0.551590	−	0.834115i	$-0.314021\pi$
$631$	−7.09696	−	7.09696i	−0.282526	−	0.282526i	−0.834115	+	0.551590i	$0.814021\pi$
$632$	0.0239458	−	2.00181i	0.000952512	−	0.0796277i
$633$	4.15211	−	2.34526i	0.165032	−	0.0932156i
$634$	18.3779	−	0.728995i	0.729881	−	0.0289521i
$635$	−17.5799	+	2.31443i	−0.697636	+	0.0918455i
$636$	0.773150	+	0.377051i	0.0306574	+	0.0149510i
$637$	1.04578	−	7.94349i	0.0414353	−	0.314732i
$638$	−4.22468	+	3.51632i	−0.167257	+	0.139212i
$639$	−0.677408	+	35.8848i	−0.0267978	+	1.41958i
$640$	15.4382	+	3.87756i	0.610249	+	0.153274i
$641$	31.5504	+	18.2156i	1.24616	+	0.719473i	0.970342	−	0.241735i	$-0.0777166\pi$
$641$	31.5504	+	18.2156i	1.24616	+	0.719473i	0.275822	+	0.961209i	$0.411050\pi$
$642$	−19.8593	+	27.5669i	−0.783785	+	1.08798i
$643$	−1.44675	+	1.88545i	−0.0570544	+	0.0743547i	−0.821009	−	0.570915i	$-0.806588\pi$
$643$	−1.44675	+	1.88545i	−0.0570544	+	0.0743547i	0.763955	+	0.645270i	$0.223255\pi$
$644$	−8.71131	−	24.5413i	−0.343274	−	0.967062i
$645$	2.62513	+	6.51076i	0.103365	+	0.256361i
$646$	23.3870	−	14.7684i	0.920150	−	0.581055i
$647$	26.9732	+	26.9732i	1.06043	+	1.06043i	0.998053	+	0.0623730i	$0.0198668\pi$
$647$	26.9732	+	26.9732i	1.06043	+	1.06043i	0.0623730	+	0.998053i	$0.480133\pi$
$648$	11.6167	+	22.6506i	0.456349	+	0.889801i
$649$	8.45456	−	8.45456i	0.331871	−	0.331871i
$650$	2.19867	−	9.73373i	0.0862389	−	0.381788i
$651$	17.9759	−	7.24786i	0.704529	−	0.284066i
$652$	−18.6671	−	20.7005i	−0.731058	−	0.810695i
$653$	−29.0712	−	22.3071i	−1.13764	−	0.872944i	−0.144460	−	0.989511i	$-0.546144\pi$
$653$	−29.0712	−	22.3071i	−1.13764	−	0.872944i	−0.993183	+	0.116567i	$0.962811\pi$
$654$	−34.2367	+	5.56403i	−1.33876	+	0.217571i
$655$	−5.22889	+	9.05671i	−0.204310	+	0.353875i
$656$	14.3818	+	32.1717i	0.561516	+	1.25610i
$657$	−32.1609	−	0.607111i	−1.25472	−	0.0236857i
$658$	−2.48127	+	27.1153i	−0.0967298	+	1.05707i
$659$	−9.40886	−	1.23870i	−0.366517	−	0.0482529i	−0.0549814	−	0.998487i	$-0.517510\pi$
$659$	−9.40886	−	1.23870i	−0.366517	−	0.0482529i	−0.311536	+	0.950235i	$0.600843\pi$
$660$	−7.46869	+	6.60829i	−0.290718	+	0.257227i
$661$	−4.13426	−	31.4028i	−0.160804	−	1.22143i	−0.861421	−	0.507891i	$-0.830425\pi$
$661$	−4.13426	−	31.4028i	−0.160804	−	1.22143i	0.700617	−	0.713538i	$-0.252908\pi$
$662$	−16.0003	−	14.7794i	−0.621869	−	0.574416i
$663$	4.84638	+	8.58017i	0.188218	+	0.333226i
$664$	−31.0257	+	12.4186i	−1.20403	+	0.481935i
$665$	15.0963	−	15.0963i	0.585411	−	0.585411i
$666$	6.65650	−	4.02975i	0.257934	−	0.156149i
$667$	−12.0931	−	5.00914i	−0.468248	−	0.193955i
$668$	1.22701	+	15.4421i	0.0474743	+	0.597471i
$669$	26.2728	−	19.7687i	1.01577	−	0.764303i
$670$	11.4903	+	4.23407i	0.443907	+	0.163576i
$671$	−3.72224	−	6.44710i	−0.143695	−	0.248888i
$672$	14.0111	−	12.1013i	0.540488	−	0.466817i
$673$	−5.21641	+	9.03509i	−0.201078	+	0.348277i	−0.948876	−	0.315649i	$-0.897778\pi$
$673$	−5.21641	+	9.03509i	−0.201078	+	0.348277i	0.747798	+	0.663926i	$0.231111\pi$
$674$	−21.2031	+	17.6479i	−0.816711	+	0.679771i
$675$	−12.7172	+	9.19823i	−0.489486	+	0.354040i
$676$	8.55381	+	12.4258i	0.328993	+	0.477917i
$677$	10.1458	−	7.78517i	0.389936	−	0.299208i	−0.395124	−	0.918628i	$-0.629299\pi$
$677$	10.1458	−	7.78517i	0.389936	−	0.299208i	0.785060	+	0.619419i	$0.212632\pi$
$678$	3.59462	−	1.08055i	0.138051	−	0.0414981i
$679$	23.2591	+	6.23225i	0.892601	+	0.239172i
$680$	−5.80749	−	7.75889i	−0.222707	−	0.297540i
$681$	17.5885	+	10.3773i	0.673992	+	0.397658i
$682$	−3.77583	+	16.7160i	−0.144584	+	0.640087i
$683$	43.1914	+	17.8904i	1.65267	+	0.684559i	0.997483	−	0.0709064i	$-0.0225892\pi$
$683$	43.1914	+	17.8904i	1.65267	+	0.684559i	0.655189	+	0.755465i	$0.272589\pi$
$684$	48.0650	+	3.39337i	1.83781	+	0.129749i
$685$	3.83735	+	9.26418i	0.146618	+	0.353966i
$686$	22.7660	+	16.0766i	0.869209	+	0.613806i
$687$	0.0246559	−	0.0886614i	0.000940680	−	0.00338264i
$688$	11.2086	+	2.67312i	0.427325	+	0.101912i
$689$	0.290044	+	0.502370i	0.0110498	+	0.0191388i
$690$	−22.2052	−	8.42128i	−0.845336	−	0.320593i
$691$	3.82015	−	29.0169i	0.145325	−	1.10386i	−0.750950	−	0.660359i	$-0.770404\pi$
$691$	3.82015	−	29.0169i	0.145325	−	1.10386i	0.896276	−	0.443497i	$-0.146262\pi$
$692$	−5.74946	−	26.9494i	−0.218562	−	1.02446i
$693$	1.29663	+	11.5261i	0.0492550	+	0.437840i
$694$	−14.4723	+	4.49972i	−0.549359	+	0.170807i
$695$	−7.01241	−	26.1707i	−0.265996	−	0.992710i
$696$	0.199116	−	9.30350i	0.00754748	−	0.352648i
$697$	5.55325	−	20.7250i	0.210344	−	0.785016i
$698$	1.17407	+	29.5983i	0.0444393	+	1.12031i
$699$	26.4363	−	10.6591i	0.999912	−	0.403164i
$700$	8.68539	+	7.40673i	0.328277	+	0.279948i
$701$	10.7323	+	25.9101i	0.405354	+	0.978611i	0.986344	+	0.164700i	$0.0526655\pi$
$701$	10.7323	+	25.9101i	0.405354	+	0.978611i	−0.580990	+	0.813911i	$0.697334\pi$
$702$	−2.04767	+	17.0441i	−0.0772842	+	0.643288i
$703$		−	14.7289i		−	0.555511i
$704$	1.74779	+	16.2756i	0.0658722	+	0.613411i
$705$	17.3917	+	17.7231i	0.655008	+	0.667490i
$706$	−22.5843	−	8.32214i	−0.849972	−	0.313208i
$707$	3.93035	+	3.01587i	0.147816	+	0.113423i
$708$	1.41287	+	20.1929i	0.0530987	+	0.758895i
$709$	22.1169	+	28.8233i	0.830617	+	1.08248i	0.995367	+	0.0961453i	$0.0306514\pi$
$709$	22.1169	+	28.8233i	0.830617	+	1.08248i	−0.164751	+	0.986335i	$0.552682\pi$
$710$	11.0757	−	21.0708i	0.415665	−	0.790771i
$711$	−2.06105	+	0.510765i	−0.0772952	+	0.0191552i
$712$	0.272153	−	0.969168i	0.0101994	−	0.0363211i
$713$	−39.4195	+	10.5624i	−1.47627	+	0.395566i
$714$	−11.2669	+	0.340461i	−0.421655	+	0.0127414i
$715$	−6.66763	+	0.877809i	−0.249355	+	0.0328282i
$716$	−2.45885	−	2.72670i	−0.0918915	−	0.101902i
$717$	−6.07409	−	49.7620i	−0.226841	−	1.85839i
$718$	−1.33476	−	0.942561i	−0.0498127	−	0.0351761i
$719$			7.09333i			0.264536i	0.991214	+	0.132268i	$0.0422260\pi$
$719$			7.09333i			0.264536i	−0.991214	+	0.132268i	$0.957774\pi$
$720$	−0.148731	−	16.8826i	−0.00554290	−	0.629179i
$721$			22.4759i			0.837047i
$722$	37.1121	−	52.5544i	1.38117	−	1.95587i
$723$	−16.1371	+	12.1422i	−0.600145	+	0.451573i
$724$	−19.8199	−	1.02376i	−0.736600	−	0.0380479i
$725$	5.68840	−	0.748892i	0.211262	−	0.0278131i
$726$	14.6986	+	7.90416i	0.545515	+	0.293351i
$727$	−25.0031	+	6.69956i	−0.927313	+	0.248473i	−0.690709	−	0.723133i	$-0.742701\pi$
$727$	−25.0031	+	6.69956i	−0.927313	+	0.248473i	−0.236605	+	0.971606i	$0.576035\pi$
$728$	12.3968	−	1.48144i	0.459455	−	0.0549059i
$729$	20.1418	−	17.9808i	0.745992	−	0.665955i
$730$	18.8842	+	9.92638i	0.698935	+	0.367392i
$731$	−4.27097	−	5.56604i	−0.157968	−	0.205867i
$732$	12.3719	+	2.40432i	0.457279	+	0.0888664i
$733$	18.4661	+	14.1695i	0.682061	+	0.523364i	0.890679	−	0.454634i	$-0.150230\pi$
$733$	18.4661	+	14.1695i	0.682061	+	0.523364i	−0.208618	+	0.977997i	$0.566896\pi$
$734$	−1.90176	+	5.16093i	−0.0701954	+	0.190493i
$735$	8.09303	−	2.08686i	0.298516	−	0.0769751i
$736$	−32.3711	+	21.7179i	−1.19321	+	0.800531i
$737$			12.5929i			0.463865i
$738$	29.1747	−	23.3651i	1.07394	−	0.860080i
$739$	−11.4867	−	27.7313i	−0.422544	−	1.02011i	−0.981594	−	0.190977i	$-0.938834\pi$
$739$	−11.4867	−	27.7313i	−0.422544	−	1.02011i	0.559051	−	0.829133i	$-0.311166\pi$
$740$	−5.14461	+	0.408784i	−0.189120	+	0.0150272i
$741$	25.5916	+	20.0237i	0.940131	+	0.735588i
$742$	−0.663028	+	0.0263002i	−0.0243405	+	0.000965511i
$743$	−11.2843	+	42.1135i	−0.413980	+	1.54500i	0.372889	+	0.927876i	$0.378367\pi$
$743$	−11.2843	+	42.1135i	−0.413980	+	1.54500i	−0.786870	+	0.617119i	$0.788300\pi$
$744$	−17.1653	−	23.3901i	−0.629312	−	0.857522i
$745$	6.55685	+	24.4705i	0.240225	+	0.896530i
$746$	−8.32643	−	26.7799i	−0.304852	−	0.980482i
$747$	21.0435	+	28.5234i	0.769943	+	1.04362i
$748$	5.42186	−	8.36269i	0.198243	−	0.305770i
$749$	3.42090	−	25.9843i	0.124997	−	0.949445i
$750$	27.2831	−	4.43395i	0.996236	−	0.161905i
$751$	−17.2507	−	29.8791i	−0.629486	−	1.09030i	−0.987655	−	0.156645i	$-0.949932\pi$
$751$	−17.2507	−	29.8791i	−0.629486	−	1.09030i	0.358169	−	0.933657i	$-0.383401\pi$
$752$	40.2470	−	6.43659i	1.46766	−	0.234718i
$753$	0.298447	+	0.304134i	0.0108760	+	0.0110833i
$754$	3.61991	−	5.12615i	0.131829	−	0.186683i
$755$	7.62960	+	18.4195i	0.277670	+	0.670354i
$756$	−16.1676	−	11.1446i	−0.588011	−	0.405325i
$757$	−22.0802	−	9.14594i	−0.802520	−	0.332415i	−0.0565548	−	0.998399i	$-0.518012\pi$
$757$	−22.0802	−	9.14594i	−0.802520	−	0.332415i	−0.745965	+	0.665985i	$0.768012\pi$
$758$	23.8584	+	5.38917i	0.866577	+	0.195744i
$759$	0.230480	−	24.4209i	0.00836590	−	0.886423i
$760$	−27.4832	−	16.3088i	−0.996922	−	0.591584i
$761$	−32.4442	−	8.69339i	−1.17610	−	0.315135i	−0.382722	−	0.923864i	$-0.625013\pi$
$761$	−32.4442	−	8.69339i	−1.17610	−	0.315135i	−0.793379	+	0.608728i	$0.791680\pi$
$762$	30.0466	+	7.08564i	1.08847	+	0.256686i
$763$	21.2274	−	16.2884i	0.768484	−	0.589678i
$764$	9.56511	−	51.8263i	0.346054	−	1.87501i
$765$	−6.41057	+	8.03572i	−0.231775	+	0.290532i
$766$	25.6542	+	30.8223i	0.926925	+	1.11365i
$767$	−6.82539	+	11.8219i	−0.246451	+	0.426865i
$768$	−22.7375	−	15.8432i	−0.820468	−	0.571692i
$769$	−7.39426	−	12.8072i	−0.266644	−	0.461841i	0.701349	−	0.712818i	$-0.252581\pi$
$769$	−7.39426	−	12.8072i	−0.266644	−	0.461841i	−0.967993	+	0.250977i	$0.919248\pi$
$770$	2.65988	−	7.21828i	0.0958554	−	0.260129i
$771$	6.19493	+	50.7519i	0.223105	+	1.82779i
$772$	−27.0369	−	23.0566i	−0.973080	−	0.829824i
$773$	−21.4021	−	8.86506i	−0.769781	−	0.318854i	−0.0369976	−	0.999315i	$-0.511779\pi$
$773$	−21.4021	−	8.86506i	−0.769781	−	0.318854i	−0.732784	+	0.680461i	$0.761779\pi$
$774$	−0.253844	−	12.2193i	−0.00912423	−	0.439214i
$775$	12.6489	−	12.6489i	0.454360	−	0.454360i
$776$	0.431137	−	36.0420i	0.0154769	−	1.29383i
$777$	−3.05014	+	5.16970i	−0.109423	+	0.185462i
$778$	−25.0931	+	27.1660i	−0.899630	+	0.973949i
$779$	−9.23487	−	70.1458i	−0.330873	−	2.51323i
$780$	6.28373	−	9.49454i	0.224994	−	0.339959i
$781$	24.2701	+	3.19523i	0.868454	+	0.114334i
$782$	23.6354	+	2.16282i	0.845199	+	0.0773423i
$783$	−9.60229	+	2.28366i	−0.343158	+	0.0816113i
$784$	4.89707	−	12.8149i	0.174895	−	0.457675i
$785$	−5.31192	+	9.20051i	−0.189591	+	0.328380i
$786$	14.1033	−	11.5150i	0.503047	−	0.410726i
$787$	24.0192	+	18.4306i	0.856194	+	0.656980i	0.940624	−	0.339449i	$-0.110241\pi$
$787$	24.0192	+	18.4306i	0.856194	+	0.656980i	−0.0844310	+	0.996429i	$0.526907\pi$
$788$	−9.64755	−	0.498329i	−0.343680	−	0.0177522i
$789$	1.41247	−	9.99865i	0.0502852	−	0.355961i
$790$	1.37371	+	0.310295i	0.0488742	+	0.0110398i
$791$	−2.04739	+	2.04739i	−0.0727969	+	0.0727969i
$792$	16.2378	−	6.14650i	0.576984	−	0.218406i
$793$	6.00994	+	6.00994i	0.213419	+	0.213419i
$794$	27.1064	+	42.9252i	0.961968	+	1.52336i
$795$	−0.372887	+	0.476575i	−0.0132250	+	0.0169024i
$796$	−14.2748	+	29.9858i	−0.505958	+	1.06282i
$797$	14.5911	−	19.0155i	0.516843	−	0.673563i	−0.459901	−	0.887970i	$-0.652115\pi$
$797$	14.5911	−	19.0155i	0.516843	−	0.673563i	0.976744	+	0.214407i	$0.0687818\pi$
$798$	−33.8948	+	15.2549i	−1.19986	+	0.540016i
$799$	−21.4913	−	12.4080i	−0.760308	−	0.438964i
$800$	7.52839	−	15.3387i	0.266169	−	0.542305i
$801$	−1.06753	−	0.0201521i	−0.0377193	−	0.000712038i
$802$	−23.8633	−	28.6706i	−0.842643	−	1.01239i
$803$	−2.86365	+	21.7516i	−0.101056	+	0.767596i
$804$	−16.0906	−	13.9862i	−0.567473	−	0.493256i
$805$	18.1627	−	2.39117i	0.640152	−	0.0842776i
$806$	−0.775488	−	19.5500i	−0.0273154	−	0.688620i
$807$	0.168712	−	17.8762i	0.00593894	−	0.629271i
$808$	2.91964	−	6.81685i	0.102713	−	0.239816i
$809$	22.2499	+	22.2499i	0.782266	+	0.782266i	0.980213	−	0.197947i	$-0.0634273\pi$
$809$	22.2499	+	22.2499i	0.782266	+	0.782266i	−0.197947	+	0.980213i	$0.563427\pi$
$810$	−17.2884	+	4.66757i	−0.607454	+	0.164002i
$811$	4.32863	−	10.4502i	0.151999	−	0.366957i	−0.829478	−	0.558540i	$-0.811362\pi$
$811$	4.32863	−	10.4502i	0.151999	−	0.366957i	0.981477	+	0.191582i	$0.0613619\pi$
$812$	3.26371	+	6.39349i	0.114534	+	0.224368i
$813$	−19.8655	+	46.7078i	−0.696713	+	1.63811i
$814$	−2.22373	−	4.81886i	−0.0779415	−	0.168901i
$815$	16.9816	−	9.80434i	0.594840	−	0.343431i
$816$	4.66374	+	16.2158i	0.163264	+	0.567667i
$817$	−20.0351	−	11.5673i	−0.700941	−	0.404688i
$818$	4.09610	−	44.7623i	0.143217	−	1.56508i
$819$	−4.83580	−	12.3278i	−0.168977	−	0.430767i
$820$	−24.2447	+	5.17243i	−0.846661	+	0.180629i
$821$	1.70485	+	2.22180i	0.0594997	+	0.0775415i	0.822155	−	0.569263i	$-0.192771\pi$
$821$	1.70485	+	2.22180i	0.0594997	+	0.0775415i	−0.762656	+	0.646805i	$0.776105\pi$
$822$	−0.527297	−	17.4499i	−0.0183916	−	0.608636i
$823$	−0.343922	+	1.28354i	−0.0119884	+	0.0447412i	−0.971661	−	0.236379i	$-0.924039\pi$
$823$	−0.343922	+	1.28354i	−0.0119884	+	0.0447412i	0.959673	+	0.281120i	$0.0907060\pi$
$824$	32.5995	−	8.31840i	1.13566	−	0.289785i
$825$	5.26468	+	9.32075i	0.183293	+	0.324507i
$826$	−8.33726	−	13.2028i	−0.290090	−	0.459383i
$827$	10.4122	−	25.1373i	0.362068	−	0.874109i	−0.632930	−	0.774209i	$-0.718148\pi$
$827$	10.4122	−	25.1373i	0.362068	−	0.874109i	0.994998	−	0.0998998i	$-0.0318522\pi$
$828$	30.9480	+	27.4175i	1.07552	+	0.952823i
$829$	−4.97111	+	2.05910i	−0.172654	+	0.0715156i	−0.467336	−	0.884080i	$-0.654786\pi$
$829$	−4.97111	+	2.05910i	−0.172654	+	0.0715156i	0.294682	+	0.955595i	$0.404786\pi$
$830$	−3.98997	−	23.1681i	−0.138494	−	0.804175i
$831$	14.2169	+	55.1343i	0.493178	+	1.91259i
$832$	−6.73679	−	17.4322i	−0.233556	−	0.604354i
$833$	−7.23368	+	4.17637i	−0.250632	+	0.144703i
$834$	−4.74164	+	46.9316i	−0.164189	+	1.62511i
$835$	−10.8040	−	1.42238i	−0.373889	−	0.0492235i
$836$	5.96474	−	32.3185i	0.206295	−	1.11776i
$837$	−19.4169	+	23.8736i	−0.671146	+	0.825192i
$838$	27.8002	+	14.6130i	0.960342	+	0.504799i
$839$	44.0688	−	11.8082i	1.52142	−	0.407664i	0.601213	−	0.799089i	$-0.294684\pi$
$839$	44.0688	−	11.8082i	1.52142	−	0.407664i	0.920210	+	0.391425i	$0.128018\pi$
$840$	6.26903	+	11.4156i	0.216302	+	0.393877i
$841$	−24.5267	−	6.57190i	−0.845748	−	0.226617i
$842$	21.7295	+	20.0714i	0.748849	+	0.691707i
$843$	−6.22526	−	0.879417i	−0.214409	−	0.0302887i
$844$	5.23817	+	1.69763i	0.180305	+	0.0584348i
$845$	−9.80433	+	4.06109i	−0.337279	+	0.139706i
$846$	−17.3697	−	39.5879i	−0.597182	−	1.36106i
$847$	−12.8739			−0.442351
$848$	0.283535	+	0.951935i	0.00973662	+	0.0326896i
$849$	54.7141	+	15.2155i	1.87778	+	0.522193i
$850$	−9.44605	+	4.35900i	−0.323997	+	0.149512i
$851$	7.69384	−	10.0268i	0.263741	−	0.343714i
$852$	−31.0382	+	27.4626i	−1.06335	+	0.940853i
$853$	−5.16310	+	3.96179i	−0.176781	+	0.135649i	−0.693362	−	0.720589i	$-0.743871\pi$
$853$	−5.16310	+	3.96179i	−0.176781	+	0.135649i	0.516581	+	0.856238i	$0.327205\pi$
$854$	−9.28382	+	2.88653i	−0.317686	+	0.0987751i
$855$	−9.38945	+	32.5700i	−0.321112	+	1.11387i
$856$	−38.9542	+	4.65512i	−1.33143	+	0.159109i
$857$	2.00733	+	7.49146i	0.0685691	+	0.255903i	0.991698	−	0.128586i	$-0.0410440\pi$
$857$	2.00733	+	7.49146i	0.0685691	+	0.255903i	−0.923129	+	0.384490i	$0.874377\pi$
$858$	11.3959	+	2.68741i	0.389051	+	0.0917468i
$859$	−6.33316	−	48.1051i	−0.216085	−	1.64133i	−0.664347	−	0.747424i	$-0.731290\pi$
$859$	−6.33316	−	48.1051i	−0.216085	−	1.64133i	0.448263	−	0.893902i	$-0.352043\pi$
$860$	−3.48425	+	7.31904i	−0.118812	+	0.249577i
$861$	−11.2848	+	26.5329i	−0.384586	+	0.904239i
$862$	−6.20604	−	36.0358i	−0.211379	−	1.22739i
$863$	1.63134			0.0555313			0.0277657	−	0.999614i	$-0.491161\pi$
$863$	1.63134			0.0555313			0.0277657	+	0.999614i	$0.491161\pi$
$864$	−10.1807	+	27.5745i	−0.346353	+	0.938104i
$865$	19.3847			0.659100
$866$	6.50164	+	37.7522i	0.220935	+	1.28287i
$867$	−7.50346	+	17.6422i	−0.254831	+	0.599159i
$868$	20.2075	+	9.61982i	0.685887	+	0.326518i
$869$	0.189036	+	1.43587i	0.00641260	+	0.0487085i
$870$	6.37147	+	1.50253i	0.216013	+	0.0509406i
$871$	−3.72111	−	13.8874i	−0.126085	−	0.470556i
$872$	−31.4813	−	24.7603i	−1.06609	−	0.838489i
$873$	−37.1085	+	9.19617i	−1.25593	+	0.311243i
$874$	74.7338	−	23.2363i	2.52791	−	0.785979i
$875$	−16.9160	+	12.9801i	−0.571866	+	0.438808i
$876$	−24.6127	−	27.8173i	−0.831587	−	0.939859i
$877$	−6.33200	+	8.25202i	−0.213816	+	0.278651i	−0.887932	−	0.459975i	$-0.847858\pi$
$877$	−6.33200	+	8.25202i	−0.213816	+	0.278651i	0.674115	+	0.738626i	$0.264525\pi$
$878$	−8.03964	+	3.70999i	−0.271325	+	0.125206i
$879$	18.3336	+	5.09839i	0.618376	+	0.171964i
$880$	−11.4540	−	1.18644i	−0.386113	−	0.0399949i
$881$	−27.9243			−0.940795			−0.470397	−	0.882455i	$-0.655889\pi$
$881$	−27.9243			−0.940795			−0.470397	+	0.882455i	$0.655889\pi$
$882$	−14.4627	−	1.59923i	−0.486986	−	0.0538490i
$883$	−43.4627	+	18.0028i	−1.46264	+	0.605843i	−0.965166	−	0.261638i	$-0.915737\pi$
$883$	−43.4627	+	18.0028i	−1.46264	+	0.605843i	−0.497469	+	0.867482i	$0.665737\pi$
$884$	−3.50808	+	10.8245i	−0.117990	+	0.364066i
$885$	−14.0998	−	1.99183i	−0.473961	−	0.0669545i
$886$	−2.92076	−	2.69788i	−0.0981248	−	0.0906372i
$887$	−5.80423	−	1.55524i	−0.194887	−	0.0522198i	0.160055	−	0.987108i	$-0.448833\pi$
$887$	−5.80423	−	1.55524i	−0.194887	−	0.0522198i	−0.354942	+	0.934888i	$0.615499\pi$
$888$	8.62711	+	2.51066i	0.289507	+	0.0842524i
$889$	−23.0022	+	6.16341i	−0.771468	+	0.206714i
$890$	0.626829	+	0.329490i	0.0210114	+	0.0110445i
$891$	−10.6512	−	15.0226i	−0.356828	−	0.503275i
$892$	37.3354	+	6.89067i	1.25008	+	0.230717i
$893$	−81.1303	−	10.6810i	−2.71492	−	0.357426i
$894$	4.43360	−	43.8827i	0.148282	−	1.46766i
$895$	2.23684	−	1.29144i	0.0747693	−	0.0431681i
$896$	21.2359	+	2.45676i	0.709443	+	0.0820745i
$897$	6.96204	+	26.9994i	0.232456	+	0.901483i
$898$	−7.50644	−	43.5867i	−0.250493	−	1.45451i
$899$	10.3930	−	4.30492i	0.346625	−	0.143577i
$900$	−17.7569	−	3.62505i	−0.591895	−	0.120835i
$901$	0.231430	−	0.558721i	0.00771004	−	0.0186137i
$902$	−13.6118	−	21.5554i	−0.453223	−	0.717716i
$903$	4.63673	+	8.20900i	0.154301	+	0.273178i
$904$	3.72733	+	2.21183i	0.123969	+	0.0735645i
$905$	3.61345	−	13.4856i	0.120115	−	0.448275i
$906$	−1.04840	−	34.6948i	−0.0348306	−	1.15266i
$907$	18.8445	+	24.5586i	0.625721	+	0.815455i	0.993425	−	0.114488i	$-0.0365227\pi$
$907$	18.8445	+	24.5586i	0.625721	+	0.815455i	−0.367704	+	0.929943i	$0.619856\pi$
$908$	4.92009	+	23.0619i	0.163279	+	0.765335i
$909$	−7.77756	−	1.17367i	−0.257965	−	0.0389282i
$910$	−0.800352	+	8.74627i	−0.0265314	+	0.289936i
$911$	−11.0798	−	6.39693i	−0.367090	−	0.211940i	0.305096	−	0.952322i	$-0.401311\pi$
$911$	−11.0798	−	6.39693i	−0.367090	−	0.211940i	−0.672186	+	0.740382i	$0.734645\pi$
$912$	34.6705	+	43.5159i	1.14806	+	1.44095i
$913$	20.9370	−	12.0880i	0.692912	−	0.400053i
$914$	5.96117	+	12.9180i	0.197178	+	0.427289i
$915$	−3.47006	+	8.15882i	−0.114717	+	0.269722i
$916$	0.0946441	−	0.0483133i	0.00312713	−	0.00159632i
$917$	−5.37474	+	12.9758i	−0.177489	+	0.428497i
$918$	15.3966	−	9.12341i	0.508162	−	0.301117i
$919$	15.3396	+	15.3396i	0.506006	+	0.506006i	0.913298	−	0.407292i	$-0.133527\pi$
$919$	15.3396	+	15.3396i	0.506006	+	0.506006i	−0.407292	+	0.913298i	$0.633527\pi$
$920$	−10.1903	−	25.4586i	−0.335963	−	0.839345i
$921$	0.0727829	−	7.71184i	0.00239828	−	0.254114i
$922$	1.31760	+	33.2167i	0.0433929	+	1.09393i
$923$	−27.7092	+	3.64798i	−0.912059	+	0.120075i
$924$	−8.78626	+	10.1083i	−0.289047	+	0.332538i
$925$	−0.723089	+	5.49241i	−0.0237750	+	0.180589i
$926$	−10.7176	−	12.8766i	−0.352202	−	0.423152i
$927$	−17.2560	−	31.2353i	−0.566762	−	1.02590i
$928$	8.06534	−	7.10000i	0.264758	−	0.233069i
$929$	25.1555	+	14.5235i	0.825324	+	0.476501i	0.852249	−	0.523136i	$-0.175238\pi$
$929$	25.1555	+	14.5235i	0.825324	+	0.476501i	−0.0269247	+	0.999637i	$0.508571\pi$
$930$	18.6116	−	8.37641i	0.610298	−	0.274673i
$931$	−16.7671	+	21.8513i	−0.549519	+	0.716147i
$932$	29.7182	+	14.1474i	0.973453	+	0.463415i
$933$	6.81973	−	8.71608i	0.223268	−	0.285352i
$934$	2.72012	+	4.30754i	0.0890052	+	0.140947i
$935$	4.95762	+	4.95762i	0.162132	+	0.162132i
$936$	−16.0907	+	11.5765i	−0.525941	+	0.378389i
$937$	−12.3300	+	12.3300i	−0.402803	+	0.402803i	−0.879220	−	0.476416i	$-0.841936\pi$
$937$	−12.3300	+	12.3300i	−0.402803	+	0.402803i	0.476416	+	0.879220i	$0.341936\pi$
$938$	16.0417	+	3.62352i	0.523779	+	0.118312i
$939$	−0.171389	+	1.21324i	−0.00559308	+	0.0395926i
$940$	−1.47905	+	28.6342i	−0.0482414	+	0.933944i
$941$	−17.6701	−	13.5588i	−0.576029	−	0.442003i	0.279215	−	0.960229i	$-0.409926\pi$
$941$	−17.6701	−	13.5588i	−0.576029	−	0.442003i	−0.855244	+	0.518226i	$0.826593\pi$
$942$	14.3272	−	11.6978i	0.466805	−	0.381135i
$943$	30.3549	−	52.5762i	0.988492	−	1.71212i
$944$	−16.0639	+	16.9789i	−0.522835	+	0.552616i
$945$	10.0404	−	9.48736i	0.326614	−	0.308624i
$946$	−8.30131	−	0.759634i	−0.269899	−	0.0246978i
$947$	14.1256	+	1.85967i	0.459021	+	0.0604313i	0.356491	−	0.934299i	$-0.383973\pi$
$947$	14.1256	+	1.85967i	0.459021	+	0.0604313i	0.102530	+	0.994730i	$0.467306\pi$
$948$	−2.04464	−	1.35320i	−0.0664070	−	0.0439499i
$949$	−3.26942	−	24.8337i	−0.106130	−	0.806136i
$950$	−23.2766	+	25.1995i	−0.755192	+	0.817579i
$951$	11.4466	−	19.4009i	0.371181	−	0.629117i
$952$	−9.09288	−	9.31305i	−0.294702	−	0.301838i
$953$	14.1164	−	14.1164i	0.457276	−	0.457276i	−0.440484	−	0.897760i	$-0.645193\pi$
$953$	14.1164	−	14.1164i	0.457276	−	0.457276i	0.897760	+	0.440484i	$0.145193\pi$
$954$	0.901233	−	0.545593i	0.0291785	−	0.0176642i
$955$	34.2519	+	14.1876i	1.10837	+	0.459100i
$956$	37.5612	−	44.0456i	1.21482	−	1.42454i
$957$	0.815664	+	6.68232i	0.0263667	+	0.216009i
$958$	11.8231	−	32.0851i	0.381987	−	1.03662i
$959$	6.73348	+	11.6627i	0.217435	+	0.376609i
$960$	14.2373	−	13.3177i	0.459506	−	0.429826i
$961$	2.03637	−	3.52709i	0.0656893	−	0.113777i
$962$	3.87626	+	4.65713i	0.124976	+	0.150152i
$963$	15.1955	+	38.7374i	0.489668	+	1.24830i
$964$	−22.9319	−	4.23234i	−0.738588	−	0.136314i
$965$	19.8310	−	15.2169i	0.638384	−	0.489849i
$966$	−31.0427	−	7.32056i	−0.998784	−	0.235535i
$967$	54.4238	+	14.5828i	1.75015	+	0.468951i	0.984658	−	0.174494i	$-0.0558289\pi$
$967$	54.4238	+	14.5828i	1.75015	+	0.468951i	0.765492	+	0.643445i	$0.222496\pi$
$968$	4.76465	+	18.6725i	0.153142	+	0.600157i
$969$	0.319702	−	33.8746i	0.0102703	−	1.08821i
$970$	24.7332	+	5.58676i	0.794134	+	0.179380i
$971$	−30.1234	−	12.4775i	−0.966706	−	0.400423i	−0.157221	−	0.987563i	$-0.550253\pi$
$971$	−30.1234	−	12.4775i	−0.966706	−	0.400423i	−0.809485	+	0.587141i	$0.800253\pi$
$972$	31.0249	+	3.07512i	0.995124	+	0.0986346i
$973$	−13.9248	−	33.6174i	−0.446408	−	1.07772i
$974$	−6.50443	+	9.21090i	−0.208415	+	0.295136i
$975$	−8.56009	−	8.72321i	−0.274142	−	0.279366i
$976$	7.62265	+	12.3971i	0.243995	+	0.396822i
$977$	−22.7901	−	39.4736i	−0.729119	−	1.26287i	−0.957256	−	0.289242i	$-0.906597\pi$
$977$	−22.7901	−	39.4736i	−0.729119	−	1.26287i	0.228137	−	0.973629i	$-0.426737\pi$
$978$	−33.6967	+	5.47628i	−1.07750	+	0.175112i
$979$	−0.0950541	+	0.722007i	−0.00303794	+	0.0230755i
$980$	8.09772	+	5.25006i	0.258672	+	0.167707i
$981$	−16.9948	+	38.9338i	−0.542601	+	1.24306i
$982$	−3.76396	−	12.1058i	−0.120113	−	0.386313i
$983$	−7.10983	−	26.5342i	−0.226768	−	0.846311i	−0.981688	−	0.190494i	$-0.938991\pi$
$983$	−7.10983	−	26.5342i	−0.226768	−	0.846311i	0.754920	−	0.655817i	$-0.227676\pi$
$984$	42.6604	+	6.54783i	1.35996	+	0.208737i
$985$	1.75889	−	6.56425i	0.0560428	−	0.209154i
$986$	−6.53716	+	0.259308i	−0.208185	+	0.00825806i
$987$	26.2641	+	20.5498i	0.835995	+	0.654109i
$988$	2.97202	+	37.4033i	0.0945524	+	1.18996i
$989$	−7.59674	−	18.3401i	−0.241562	−	0.583183i
$990$	1.84538	+	12.0736i	0.0586499	+	0.383723i
$991$		−	13.4151i		−	0.426145i	−0.977036	−	0.213073i	$-0.931653\pi$
$991$		−	13.4151i		−	0.426145i	0.977036	−	0.213073i	$-0.0683471\pi$
$992$	6.47394	−	32.8697i	0.205548	−	1.04361i
$993$	−25.8319	+	6.66101i	−0.819752	+	0.211381i
$994$	11.0539	−	29.9976i	0.350608	−	0.951466i
$995$	−18.5347	−	14.2221i	−0.587588	−	0.450872i
$996$	−7.80805	+	40.1778i	−0.247407	+	1.27308i
$997$	−28.6958	−	37.3971i	−0.908804	−	1.18438i	−0.982344	−	0.187085i	$-0.940096\pi$
$997$	−28.6958	−	37.3971i	−0.908804	−	1.18438i	0.0735394	−	0.997292i	$-0.476571\pi$
$998$	20.2828	+	10.6616i	0.642042	+	0.337486i
$999$	0.269784	−	9.52622i	0.00853560	−	0.301396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.44	✓	368
3.2	odd	2		864.2.bn.a.683.3		368
9.4	even	3		864.2.bn.a.395.17		368
9.5	odd	6	inner	288.2.bf.a.203.30	yes	368
32.3	odd	8	inner	288.2.bf.a.227.30	yes	368
96.35	even	8		864.2.bn.a.35.17		368
288.67	odd	24		864.2.bn.a.611.3		368
288.131	even	24	inner	288.2.bf.a.131.44	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.44	✓	368	1.1	even	1	trivial
288.2.bf.a.131.44	yes	368	288.131	even	24	inner
288.2.bf.a.203.30	yes	368	9.5	odd	6	inner
288.2.bf.a.227.30	yes	368	32.3	odd	8	inner
864.2.bn.a.35.17		368	96.35	even	8
864.2.bn.a.395.17		368	9.4	even	3
864.2.bn.a.611.3		368	288.67	odd	24
864.2.bn.a.683.3		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39370 - 0.240021i) q^{2} +(0.677899 - 1.59388i) q^{3} +(1.88478 - 0.669032i) q^{4} +(0.183643 + 1.39490i) q^{5} +(0.562222 - 2.38409i) q^{6} +(0.489046 + 1.82515i) q^{7} +(2.46623 - 1.38481i) q^{8} +(-2.08090 - 2.16098i) q^{9} +O(q^{10})\)	\(q+(1.39370 - 0.240021i) q^{2} +(0.677899 - 1.59388i) q^{3} +(1.88478 - 0.669032i) q^{4} +(0.183643 + 1.39490i) q^{5} +(0.562222 - 2.38409i) q^{6} +(0.489046 + 1.82515i) q^{7} +(2.46623 - 1.38481i) q^{8} +(-2.08090 - 2.16098i) q^{9} +(0.590748 + 1.90000i) q^{10} +(-1.62332 + 1.24562i) q^{11} +(0.211335 - 3.45765i) q^{12} +(1.42212 - 1.85334i) q^{13} +(1.11965 + 2.42632i) q^{14} +(2.34780 + 0.652901i) q^{15} +(3.10479 - 2.52196i) q^{16} -2.43543 q^{17} +(-3.41883 - 2.51229i) q^{18} +(-7.41946 + 3.07324i) q^{19} +(1.27936 + 2.50623i) q^{20} +(3.24059 + 0.457784i) q^{21} +(-1.96344 + 2.12564i) q^{22} +(-6.65621 - 1.78352i) q^{23} +(-0.535370 - 4.86964i) q^{24} +(2.91760 - 0.781767i) q^{25} +(1.53716 - 2.92434i) q^{26} +(-4.85499 + 1.85178i) q^{27} +(2.14282 + 3.11281i) q^{28} +(1.88325 + 0.247935i) q^{29} +(3.42883 + 0.346425i) q^{30} +(5.12880 - 2.96111i) q^{31} +(3.72182 - 4.26006i) q^{32} +(0.884917 + 3.43178i) q^{33} +(-3.39425 + 0.584553i) q^{34} +(-2.45609 + 1.01735i) q^{35} +(-5.36781 - 2.68078i) q^{36} +(-0.701864 + 1.69445i) q^{37} +(-9.60284 + 6.06399i) q^{38} +(-1.98995 - 3.52307i) q^{39} +(2.38459 + 3.18584i) q^{40} +(-2.28020 + 8.50981i) q^{41} +(4.62627 - 0.139795i) q^{42} +(1.75369 + 2.28545i) q^{43} +(-2.22624 + 3.43377i) q^{44} +(2.63222 - 3.29951i) q^{45} +(-9.70481 - 0.888066i) q^{46} +(8.82446 + 5.09480i) q^{47} +(-1.91496 - 6.65830i) q^{48} +(2.97019 - 1.71484i) q^{49} +(3.87860 - 1.78983i) q^{50} +(-1.65097 + 3.88178i) q^{51} +(1.44044 - 4.44459i) q^{52} +(-0.0950263 + 0.229414i) q^{53} +(-6.32191 + 3.74612i) q^{54} +(-2.03563 - 2.03563i) q^{55} +(3.73359 + 3.82399i) q^{56} +(-0.131271 + 13.9091i) q^{57} +(2.68419 - 0.106473i) q^{58} +(-5.79345 + 0.762722i) q^{59} +(4.86190 - 0.340180i) q^{60} +(-0.474891 + 3.60715i) q^{61} +(6.43726 - 5.35791i) q^{62} +(2.92644 - 4.85477i) q^{63} +(4.16458 - 6.83054i) q^{64} +(2.84640 + 1.64337i) q^{65} +(2.05700 + 4.57046i) q^{66} +(3.74657 - 4.88263i) q^{67} +(-4.59024 + 1.62938i) q^{68} +(-7.35496 + 9.40014i) q^{69} +(-3.17886 + 2.00739i) q^{70} +(-8.45963 - 8.45963i) q^{71} +(-8.12454 - 2.44781i) q^{72} +(7.58174 - 7.58174i) q^{73} +(-0.571482 + 2.53001i) q^{74} +(0.731793 - 5.18026i) q^{75} +(-11.9280 + 10.7562i) q^{76} +(-3.06731 - 2.35363i) q^{77} +(-3.61900 - 4.43246i) q^{78} +(0.353898 - 0.612970i) q^{79} +(4.08806 + 3.86775i) q^{80} +(-0.339671 + 8.99359i) q^{81} +(-1.13537 + 12.4074i) q^{82} +(-11.7142 - 1.54221i) q^{83} +(6.41406 - 1.30523i) q^{84} +(-0.447248 - 3.39719i) q^{85} +(2.99266 + 2.76430i) q^{86} +(1.67183 - 2.83360i) q^{87} +(-2.27853 + 5.31998i) q^{88} +(0.251664 - 0.251664i) q^{89} +(2.87656 - 5.23030i) q^{90} +(4.07810 + 1.68920i) q^{91} +(-13.7387 + 1.09166i) q^{92} +(-1.24285 - 10.1820i) q^{93} +(13.5215 + 4.98256i) q^{94} +(-5.64941 - 9.78506i) q^{95} +(-4.26700 - 8.82002i) q^{96} +(6.37184 - 11.0363i) q^{97} +(3.72795 - 3.10287i) q^{98} +(6.06973 + 0.915952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

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