LMFDB - Embedded newform 504.2.cs.a.85.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.11
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.870602 + 1.11447i) q^{2} +(-0.119319 + 1.72794i) q^{3} +(-0.484104 - 1.94053i) q^{4} +(-0.525102 - 0.303168i) q^{5} +(-1.82186 - 1.63732i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.58413 + 1.14991i) q^{8} +(-2.97153 - 0.412353i) q^{9} +O(q^{10})$	\(q+(-0.870602 + 1.11447i) q^{2} +(-0.119319 + 1.72794i) q^{3} +(-0.484104 - 1.94053i) q^{4} +(-0.525102 - 0.303168i) q^{5} +(-1.82186 - 1.63732i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.58413 + 1.14991i) q^{8} +(-2.97153 - 0.412353i) q^{9} +(0.795028 - 0.321274i) q^{10} +(-2.85135 + 1.64622i) q^{11} +(3.41087 - 0.604957i) q^{12} +(-0.689592 - 0.398136i) q^{13} +(-1.40046 - 0.196727i) q^{14} +(0.586510 - 0.871169i) q^{15} +(-3.53129 + 1.87883i) q^{16} -5.18403 q^{17} +(3.04657 - 2.95269i) q^{18} -2.27020i q^{19} +(-0.334102 + 1.16574i) q^{20} +(-1.55610 + 0.760634i) q^{21} +(0.647713 - 4.61096i) q^{22} +(-0.744707 + 1.28987i) q^{23} +(-2.29530 + 4.32800i) q^{24} +(-2.31618 - 4.01174i) q^{25} +(1.04407 - 0.421914i) q^{26} +(1.06708 - 5.08540i) q^{27} +(1.43849 - 1.38951i) q^{28} +(-3.66721 + 2.11726i) q^{29} +(0.460279 + 1.41209i) q^{30} +(-2.19936 + 3.80940i) q^{31} +(0.980438 - 5.57124i) q^{32} +(-2.50435 - 5.12337i) q^{33} +(4.51323 - 5.77746i) q^{34} -0.606336i q^{35} +(0.638345 + 5.96595i) q^{36} -3.68415i q^{37} +(2.53008 + 1.97644i) q^{38} +(0.770236 - 1.14407i) q^{39} +(-1.00832 - 1.38724i) q^{40} +(-1.14467 + 1.98263i) q^{41} +(0.507034 - 2.39644i) q^{42} +(8.20769 - 4.73871i) q^{43} +(4.57489 + 4.73617i) q^{44} +(1.43534 + 1.11740i) q^{45} +(-0.789183 - 1.95292i) q^{46} +(1.15951 + 2.00832i) q^{47} +(-2.82515 - 6.32602i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.48745 + 0.911308i) q^{50} +(0.618556 - 8.95767i) q^{51} +(-0.438760 + 1.53091i) q^{52} +4.61422i q^{53} +(4.73855 + 5.61660i) q^{54} +1.99633 q^{55} +(0.296216 + 2.81287i) q^{56} +(3.92276 + 0.270879i) q^{57} +(0.833045 - 5.93030i) q^{58} +(-0.551717 - 0.318534i) q^{59} +(-1.97446 - 0.716402i) q^{60} +(-0.523563 + 0.302279i) q^{61} +(-2.33071 - 5.76760i) q^{62} +(-1.12865 - 2.77959i) q^{63} +(5.35543 + 5.94301i) q^{64} +(0.241404 + 0.418125i) q^{65} +(7.89015 + 1.66938i) q^{66} +(-11.0479 - 6.37851i) q^{67} +(2.50961 + 10.0597i) q^{68} +(-2.13995 - 1.44071i) q^{69} +(0.675746 + 0.527877i) q^{70} +8.02356 q^{71} +(-7.20464 - 4.48255i) q^{72} -10.1005 q^{73} +(4.10588 + 3.20742i) q^{74} +(7.20839 - 3.52353i) q^{75} +(-4.40539 + 1.09901i) q^{76} +(-2.85135 - 1.64622i) q^{77} +(0.604462 + 1.85443i) q^{78} +(4.73344 + 8.19857i) q^{79} +(2.42389 + 0.0839942i) q^{80} +(8.65993 + 2.45063i) q^{81} +(-1.21304 - 3.00179i) q^{82} +(-4.59066 + 2.65042i) q^{83} +(2.22934 + 2.65142i) q^{84} +(2.72215 + 1.57163i) q^{85} +(-1.86446 + 13.2728i) q^{86} +(-3.22093 - 6.58933i) q^{87} +(-9.26124 + 0.975277i) q^{88} -15.5471 q^{89} +(-2.49492 + 0.626842i) q^{90} -0.796273i q^{91} +(2.86354 + 0.820693i) q^{92} +(-6.31997 - 4.25488i) q^{93} +(-3.24769 - 0.456212i) q^{94} +(-0.688253 + 1.19209i) q^{95} +(9.50977 + 2.35889i) q^{96} +(6.35467 + 11.0066i) q^{97} +(-0.529862 - 1.31120i) q^{98} +(9.15167 - 3.71604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.870602	+	1.11447i	−0.615609	+	0.788052i
$2$	−0.870602	+	1.11447i	−0.615609	+	0.788052i
$3$	−0.119319	+	1.72794i	−0.0688891	+	0.997624i
$3$	−0.119319	+	1.72794i	−0.0688891	+	0.997624i
$4$	−0.484104	−	1.94053i	−0.242052	−	0.970263i
$5$	−0.525102	−	0.303168i	−0.234833	−	0.135581i	0.377967	−	0.925819i	$-0.376623\pi$
$5$	−0.525102	−	0.303168i	−0.234833	−	0.135581i	−0.612800	+	0.790238i	$0.709957\pi$
$6$	−1.82186	−	1.63732i	−0.743771	−	0.668434i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	2.58413	+	1.14991i	0.913627	+	0.406553i
$9$	−2.97153	−	0.412353i	−0.990509	−	0.137451i
$10$	0.795028	−	0.321274i	0.251410	−	0.101596i
$11$	−2.85135	+	1.64622i	−0.859713	+	0.496355i	−0.863916	−	0.503636i	$-0.831995\pi$
$11$	−2.85135	+	1.64622i	−0.859713	+	0.496355i	0.00420321	+	0.999991i	$0.498662\pi$
$12$	3.41087	−	0.604957i	0.984633	−	0.174636i
$13$	−0.689592	−	0.398136i	−0.191258	−	0.110423i	0.401313	−	0.915941i	$-0.368554\pi$
$13$	−0.689592	−	0.398136i	−0.191258	−	0.110423i	−0.592572	+	0.805518i	$0.701887\pi$
$14$	−1.40046	−	0.196727i	−0.374290	−	0.0525774i
$15$	0.586510	−	0.871169i	0.151436	−	0.224935i
$16$	−3.53129	+	1.87883i	−0.882822	+	0.469708i
$17$	−5.18403			−1.25731			−0.628656	−	0.777684i	$-0.716395\pi$
$17$	−5.18403			−1.25731			−0.628656	+	0.777684i	$0.716395\pi$
$18$	3.04657	−	2.95269i	0.718084	−	0.695956i
$19$		−	2.27020i		−	0.520820i	−0.965498	−	0.260410i	$-0.916142\pi$
$19$		−	2.27020i		−	0.520820i	0.965498	−	0.260410i	$-0.0838578\pi$
$20$	−0.334102	+	1.16574i	−0.0747074	+	0.260667i
$21$	−1.55610	+	0.760634i	−0.339568	+	0.165984i
$22$	0.647713	−	4.61096i	0.138093	−	0.983059i
$23$	−0.744707	+	1.28987i	−0.155282	+	0.268956i	−0.933162	−	0.359457i	$-0.882962\pi$
$23$	−0.744707	+	1.28987i	−0.155282	+	0.268956i	0.777880	+	0.628413i	$0.216295\pi$
$24$	−2.29530	+	4.32800i	−0.468526	+	0.883450i
$25$	−2.31618	−	4.01174i	−0.463236	−	0.802348i
$26$	1.04407	−	0.421914i	0.204760	−	0.0827442i
$27$	1.06708	−	5.08540i	0.205360	−	0.978687i
$28$	1.43849	−	1.38951i	0.271850	−	0.262593i
$29$	−3.66721	+	2.11726i	−0.680983	+	0.393166i	−0.800225	−	0.599699i	$-0.795287\pi$
$29$	−3.66721	+	2.11726i	−0.680983	+	0.393166i	0.119242	+	0.992865i	$0.461954\pi$
$30$	0.460279	+	1.41209i	0.0840350	+	0.257812i
$31$	−2.19936	+	3.80940i	−0.395016	+	0.684188i	−0.993103	−	0.117243i	$-0.962594\pi$
$31$	−2.19936	+	3.80940i	−0.395016	+	0.684188i	0.598087	+	0.801431i	$0.295928\pi$
$32$	0.980438	−	5.57124i	0.173319	−	0.984866i
$33$	−2.50435	−	5.12337i	−0.435951	−	0.891864i
$34$	4.51323	−	5.77746i	0.774012	−	0.990827i
$35$		−	0.606336i		−	0.102489i
$36$	0.638345	+	5.96595i	0.106391	+	0.994324i
$37$		−	3.68415i		−	0.605670i	−0.953043	−	0.302835i	$-0.902067\pi$
$37$		−	3.68415i		−	0.605670i	0.953043	−	0.302835i	$-0.0979331\pi$
$38$	2.53008	+	1.97644i	0.410433	+	0.320621i
$39$	0.770236	−	1.14407i	0.123336	−	0.183197i
$40$	−1.00832	−	1.38724i	−0.159429	−	0.219342i
$41$	−1.14467	+	1.98263i	−0.178768	+	0.309635i	−0.941459	−	0.337128i	$-0.890544\pi$
$41$	−1.14467	+	1.98263i	−0.178768	+	0.309635i	0.762691	+	0.646763i	$0.223878\pi$
$42$	0.507034	−	2.39644i	0.0782370	−	0.369778i
$43$	8.20769	−	4.73871i	1.25166	−	0.722647i	0.280222	−	0.959935i	$-0.409592\pi$
$43$	8.20769	−	4.73871i	1.25166	−	0.722647i	0.971439	+	0.237288i	$0.0762585\pi$
$44$	4.57489	+	4.73617i	0.689691	+	0.714004i
$45$	1.43534	+	1.11740i	0.213968	+	0.166572i
$46$	−0.789183	−	1.95292i	−0.116359	−	0.287942i
$47$	1.15951	+	2.00832i	0.169131	+	0.292944i	0.938115	−	0.346325i	$-0.112570\pi$
$47$	1.15951	+	2.00832i	0.169131	+	0.292944i	−0.768983	+	0.639269i	$0.779237\pi$
$48$	−2.82515	−	6.32602i	−0.407775	−	0.913082i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	6.48745	+	0.911308i	0.917464	+	0.128878i
$51$	0.618556	−	8.95767i	0.0866151	−	1.25432i
$52$	−0.438760	+	1.53091i	−0.0608451	+	0.212299i
$53$			4.61422i			0.633812i	0.948457	+	0.316906i	$0.102644\pi$
$53$			4.61422i			0.633812i	−0.948457	+	0.316906i	$0.897356\pi$
$54$	4.73855	+	5.61660i	0.644835	+	0.764322i
$55$	1.99633			0.269185
$56$	0.296216	+	2.81287i	0.0395835	+	0.375886i
$57$	3.92276	+	0.270879i	0.519583	+	0.0358789i
$58$	0.833045	−	5.93030i	0.109384	−	0.778687i
$59$	−0.551717	−	0.318534i	−0.0718275	−	0.0414696i	0.463656	−	0.886015i	$-0.346537\pi$
$59$	−0.551717	−	0.318534i	−0.0718275	−	0.0414696i	−0.535484	+	0.844546i	$0.679871\pi$
$60$	−1.97446	−	0.716402i	−0.254902	−	0.0924871i
$61$	−0.523563	+	0.302279i	−0.0670354	+	0.0387029i	−0.533143	−	0.846025i	$-0.678989\pi$
$61$	−0.523563	+	0.302279i	−0.0670354	+	0.0387029i	0.466108	+	0.884728i	$0.345656\pi$
$62$	−2.33071	−	5.76760i	−0.296000	−	0.732486i
$63$	−1.12865	−	2.77959i	−0.142197	−	0.350196i
$64$	5.35543	+	5.94301i	0.669429	+	0.742876i
$65$	0.241404	+	0.418125i	0.0299425	+	0.0518620i
$66$	7.89015	+	1.66938i	0.971211	+	0.205487i
$67$	−11.0479	−	6.37851i	−1.34972	−	0.779259i	−0.361508	−	0.932369i	$-0.617738\pi$
$67$	−11.0479	−	6.37851i	−1.34972	−	0.779259i	−0.988209	+	0.153110i	$0.951071\pi$
$68$	2.50961	+	10.0597i	0.304335	+	1.21992i
$69$	−2.13995	−	1.44071i	−0.257620	−	0.173441i
$70$	0.675746	+	0.527877i	0.0807670	+	0.0630934i
$71$	8.02356			0.952222			0.476111	−	0.879385i	$-0.342046\pi$
$71$	8.02356			0.952222			0.476111	+	0.879385i	$0.342046\pi$
$72$	−7.20464	−	4.48255i	−0.849074	−	0.528273i
$73$	−10.1005			−1.18217			−0.591086	−	0.806609i	$-0.701301\pi$
$73$	−10.1005			−1.18217			−0.591086	+	0.806609i	$0.701301\pi$
$74$	4.10588	+	3.20742i	0.477299	+	0.372856i
$75$	7.20839	−	3.52353i	0.832353	−	0.406862i
$76$	−4.40539	+	1.09901i	−0.505333	+	0.126065i
$77$	−2.85135	−	1.64622i	−0.324941	−	0.187605i
$78$	0.604462	+	1.85443i	0.0684419	+	0.209973i
$79$	4.73344	+	8.19857i	0.532554	+	0.922411i	0.999277	+	0.0380074i	$0.0121011\pi$
$79$	4.73344	+	8.19857i	0.532554	+	0.922411i	−0.466723	+	0.884403i	$0.654566\pi$
$80$	2.42389	+	0.0839942i	0.270999	+	0.00939083i
$81$	8.65993	+	2.45063i	0.962214	+	0.272293i
$82$	−1.21304	−	3.00179i	−0.133957	−	0.331492i
$83$	−4.59066	+	2.65042i	−0.503890	+	0.290921i	−0.730318	−	0.683107i	$-0.760628\pi$
$83$	−4.59066	+	2.65042i	−0.503890	+	0.290921i	0.226429	+	0.974028i	$0.427295\pi$
$84$	2.22934	+	2.65142i	0.243241	+	0.289294i
$85$	2.72215	+	1.57163i	0.295258	+	0.170467i
$86$	−1.86446	+	13.2728i	−0.201050	+	1.43124i
$87$	−3.22093	−	6.58933i	−0.345320	−	0.706450i
$88$	−9.26124	+	0.975277i	−0.987252	+	0.103965i
$89$	−15.5471			−1.64799			−0.823997	−	0.566594i	$-0.808261\pi$
$89$	−15.5471			−1.64799			−0.823997	+	0.566594i	$0.808261\pi$
$90$	−2.49492	+	0.626842i	−0.262988	+	0.0660750i
$91$		−	0.796273i		−	0.0834720i
$92$	2.86354	+	0.820693i	0.298545	+	0.0855631i
$93$	−6.31997	−	4.25488i	−0.655350	−	0.441211i
$94$	−3.24769	−	0.456212i	−0.334974	−	0.0470547i
$95$	−0.688253	+	1.19209i	−0.0706132	+	0.122306i
$96$	9.50977	+	2.35889i	0.970586	+	0.240753i
$97$	6.35467	+	11.0066i	0.645219	+	1.11755i	0.984251	+	0.176778i	$0.0565674\pi$
$97$	6.35467	+	11.0066i	0.645219	+	1.11755i	−0.339031	+	0.940775i	$0.610099\pi$
$98$	−0.529862	−	1.31120i	−0.0535241	−	0.132451i
$99$	9.15167	−	3.71604i	0.919778	−	0.373476i
$100$	−6.66362	+	6.43670i	−0.666362	+	0.643670i
$101$	−14.6490	+	8.45761i	−1.45763	+	0.841564i	−0.998895	−	0.0470082i	$-0.985031\pi$
$101$	−14.6490	+	8.45761i	−1.45763	+	0.841564i	−0.458737	+	0.888572i	$0.651698\pi$
$102$	9.44457	+	8.48793i	0.935152	+	0.840431i
$103$	−5.12761	+	8.88128i	−0.505238	+	0.875098i	0.494743	+	0.869039i	$0.335262\pi$
$103$	−5.12761	+	8.88128i	−0.505238	+	0.875098i	−0.999982	+	0.00605918i	$0.998071\pi$
$104$	−1.32418	−	1.82180i	−0.129846	−	0.178642i
$105$	1.04771	+	0.0723477i	0.102246	+	0.00706041i
$106$	−5.14242	−	4.01715i	−0.499476	−	0.390180i
$107$		−	5.42861i		−	0.524804i	−0.964959	−	0.262402i	$-0.915485\pi$
$107$		−	5.42861i		−	0.524804i	0.964959	−	0.262402i	$-0.0845146\pi$
$108$	−10.3849	+	0.391165i	−0.999291	+	0.0376399i
$109$			1.28839i			0.123406i	0.998095	+	0.0617028i	$0.0196531\pi$
$109$			1.28839i			0.123406i	−0.998095	+	0.0617028i	$0.980347\pi$
$110$	−1.73801	+	2.22486i	−0.165713	+	0.212132i
$111$	6.36597	+	0.439590i	0.604231	+	0.0417241i
$112$	−3.39276	−	2.11877i	−0.320586	−	0.200205i
$113$	2.01794	−	3.49518i	0.189832	−	0.328799i	−0.755362	−	0.655308i	$-0.772539\pi$
$113$	2.01794	−	3.49518i	0.189832	−	0.328799i	0.945194	+	0.326509i	$0.105872\pi$
$114$	−3.71706	+	4.13599i	−0.348134	+	0.387371i
$115$	0.782095	−	0.451543i	0.0729307	−	0.0421066i
$116$	5.88391	+	6.09134i	0.546308	+	0.565567i
$117$	1.88497	+	1.46743i	0.174265	+	0.135664i
$118$	0.835324	−	0.337558i	0.0768978	−	0.0310747i
$119$	−2.59201	−	4.48950i	−0.237610	−	0.411552i
$120$	2.51738	−	1.57678i	0.229804	−	0.143940i
$121$	−0.0798868	+	0.138368i	−0.00726244	+	0.0125789i
$122$	0.118933	−	0.846662i	0.0107677	−	0.0766532i
$123$	−3.28928	−	2.21449i	−0.296584	−	0.199674i
$124$	8.45696	+	2.42377i	0.759457	+	0.217661i
$125$			5.84044i			0.522385i
$126$	4.08039	+	1.16206i	0.363510	+	0.103525i
$127$	−17.1893			−1.52531			−0.762653	−	0.646808i	$-0.776104\pi$
$127$	−17.1893			−1.52531			−0.762653	+	0.646808i	$0.776104\pi$
$128$	−11.2858	+	0.794494i	−0.997531	+	0.0702240i
$129$	7.20886	+	14.7478i	0.634704	+	1.29847i
$130$	−0.676156	−	0.0949814i	−0.0593028	−	0.00833042i
$131$	14.6568	+	8.46212i	1.28057	+	0.739339i	0.976953	−	0.213455i	$-0.0684716\pi$
$131$	14.6568	+	8.46212i	1.28057	+	0.739339i	0.303619	+	0.952793i	$0.401805\pi$
$132$	−8.72967	+	7.34000i	−0.759820	+	0.638865i
$133$	1.96605	−	1.13510i	0.170478	−	0.0984258i
$134$	16.7270	−	6.75946i	1.44499	−	0.583928i
$135$	−2.10206	+	2.34685i	−0.180916	+	0.201985i
$136$	−13.3962	−	5.96115i	−1.14871	−	0.511164i
$137$	−1.13578	−	1.96722i	−0.0970360	−	0.168071i	0.813420	−	0.581676i	$-0.197603\pi$
$137$	−1.13578	−	1.96722i	−0.0970360	−	0.168071i	−0.910457	+	0.413605i	$0.864270\pi$
$138$	3.46869	−	1.13064i	0.295274	−	0.0962461i
$139$	7.22596	+	4.17191i	0.612898	+	0.353857i	0.774099	−	0.633065i	$-0.218203\pi$
$139$	7.22596	+	4.17191i	0.612898	+	0.353857i	−0.161201	+	0.986922i	$0.551537\pi$
$140$	−1.17661	+	0.293529i	−0.0994418	+	0.0248078i
$141$	−3.60861	+	1.76392i	−0.303900	+	0.148549i
$142$	−6.98533	+	8.94205i	−0.586196	+	0.750400i
$143$	2.62169			0.219237
$144$	11.2681	−	4.12686i	0.939004	−	0.343905i
$145$	2.56755			0.213223
$146$	8.79350	−	11.2567i	0.727755	−	0.931613i
$147$	−1.43678	−	0.967302i	−0.118503	−	0.0797817i
$148$	−7.14918	+	1.78351i	−0.587659	+	0.146603i
$149$	14.8688	+	8.58449i	1.21810	+	0.703269i	0.964511	−	0.264044i	$-0.0850564\pi$
$149$	14.8688	+	8.58449i	1.21810	+	0.703269i	0.253587	+	0.967313i	$0.418390\pi$
$150$	−2.34876	+	11.1012i	−0.191776	+	0.906406i
$151$	8.98525	+	15.5629i	0.731209	+	1.26649i	0.956367	+	0.292169i	$0.0943769\pi$
$151$	8.98525	+	15.5629i	0.731209	+	1.26649i	−0.225158	+	0.974322i	$0.572290\pi$
$152$	2.61052	−	5.86649i	0.211741	−	0.475835i
$153$	15.4045	+	2.13765i	1.24538	+	0.172819i
$154$	4.31706	−	1.74454i	0.347879	−	0.140579i
$155$	2.30978	−	1.33355i	0.185526	−	0.107113i
$156$	−2.59296	−	0.940817i	−0.207603	−	0.0753256i
$157$	18.1116	+	10.4567i	1.44546	+	0.834537i	0.998206	−	0.0598696i	$-0.0190685\pi$
$157$	18.1116	+	10.4567i	1.44546	+	0.834537i	0.447255	+	0.894407i	$0.352402\pi$
$158$	−13.2580	−	1.86239i	−1.05475	−	0.148164i
$159$	−7.97307	−	0.550566i	−0.632306	−	0.0436627i
$160$	−2.20385	+	2.62824i	−0.174230	+	0.207780i
$161$	−1.48941			−0.117382
$162$	−10.2705	+	7.51774i	−0.806928	+	0.590649i
$163$			8.68114i			0.679959i	0.940433	+	0.339980i	$0.110420\pi$
$163$			8.68114i			0.679959i	−0.940433	+	0.339980i	$0.889580\pi$
$164$	4.40149	+	1.26147i	0.343698	+	0.0985041i
$165$	−0.238201	+	3.44953i	−0.0185439	+	0.268546i
$166$	1.04282	−	7.42362i	0.0809382	−	0.576185i
$167$	11.0383	−	19.1188i	0.854167	−	1.47946i	−0.0232487	−	0.999730i	$-0.507401\pi$
$167$	11.0383	−	19.1188i	0.854167	−	1.47946i	0.877416	−	0.479731i	$-0.159266\pi$
$168$	−4.89581	+	0.176212i	−0.377720	+	0.0135950i
$169$	−6.18298	−	10.7092i	−0.475613	−	0.823787i
$170$	−4.12145	+	1.66549i	−0.316101	+	0.127738i
$171$	−0.936125	+	6.74597i	−0.0715872	+	0.515877i
$172$	−13.1690	−	13.6332i	−1.00412	−	1.03952i
$173$	−17.7453	+	10.2453i	−1.34915	+	0.778934i	−0.988130	−	0.153623i	$-0.950906\pi$
$173$	−17.7453	+	10.2453i	−1.34915	+	0.778934i	−0.361024	+	0.932557i	$0.617573\pi$
$174$	10.1478	+	2.14705i	0.769301	+	0.162767i
$175$	2.31618	−	4.01174i	0.175087	−	0.303259i
$176$	6.97594	−	11.1705i	0.525831	−	0.842008i
$177$	0.616237	−	0.915325i	0.0463192	−	0.0688000i
$178$	13.5354	−	17.3269i	1.01452	−	1.29870i
$179$			10.5570i			0.789069i	0.918881	+	0.394534i	$0.129094\pi$
$179$			10.5570i			0.789069i	−0.918881	+	0.394534i	$0.870906\pi$
$180$	1.47349	−	3.32626i	0.109827	−	0.247925i
$181$			12.1890i			0.906004i	0.891509	+	0.453002i	$0.149647\pi$
$181$			12.1890i			0.906004i	−0.891509	+	0.453002i	$0.850353\pi$
$182$	0.887425	+	0.693237i	0.0657803	+	0.0513861i
$183$	−0.459848	−	0.940751i	−0.0339929	−	0.0695423i
$184$	−3.40765	+	2.47685i	−0.251215	+	0.182596i
$185$	−1.11691	+	1.93455i	−0.0821172	+	0.142231i
$186$	10.2441	−	3.33913i	0.751137	−	0.244837i
$187$	14.7815	−	8.53408i	1.08093	−	0.624074i
$188$	3.33589	−	3.22229i	0.243295	−	0.235010i
$189$	4.93763	−	1.61858i	0.359160	−	0.117735i
$190$	−0.729357	−	1.80487i	−0.0529131	−	0.130939i
$191$	−7.33203	−	12.6994i	−0.530527	−	0.918900i	−0.999366	−	0.0356157i	$-0.988661\pi$
$191$	−7.33203	−	12.6994i	−0.530527	−	0.918900i	0.468839	−	0.883284i	$-0.344673\pi$
$192$	−10.9081	+	8.54473i	−0.787228	+	0.616663i
$193$	10.2707	−	17.7894i	0.739302	−	1.28051i	−0.213507	−	0.976941i	$-0.568489\pi$
$193$	10.2707	−	17.7894i	0.739302	−	1.28051i	0.952810	−	0.303568i	$-0.0981779\pi$
$194$	−17.7990	−	2.50027i	−1.27789	−	0.179509i
$195$	−0.751297	+	0.367241i	−0.0538015	+	0.0262987i
$196$	1.92260	+	0.551017i	0.137328	+	0.0393584i
$197$		−	20.4368i		−	1.45606i	−0.685546	−	0.728030i	$-0.740436\pi$
$197$		−	20.4368i		−	1.45606i	0.685546	−	0.728030i	$-0.259564\pi$
$198$	−3.82604	+	13.4345i	−0.271905	+	0.954748i
$199$	−14.6436			−1.03806			−0.519029	−	0.854757i	$-0.673706\pi$
$199$	−14.6436			−1.03806			−0.519029	+	0.854757i	$0.673706\pi$
$200$	−1.37218	−	13.0302i	−0.0970277	−	0.921377i
$201$	12.3399	−	18.3290i	0.870389	−	1.29283i
$202$	3.32768	−	23.6892i	0.234135	−	1.66676i
$203$	−3.66721	−	2.11726i	−0.257388	−	0.148603i
$204$	−17.6820	+	3.13612i	−1.23799	+	0.219572i
$205$	1.20214	−	0.694056i	0.0839611	−	0.0484750i
$206$	−5.43384	−	13.4466i	−0.378594	−	0.936872i
$207$	2.74480	−	3.52580i	0.190777	−	0.245060i
$208$	3.18318	+	0.110306i	0.220714	+	0.00764832i
$209$	3.73726	+	6.47313i	0.258512	+	0.447756i
$210$	−0.992768	+	1.10466i	−0.0685075	+	0.0762287i
$211$	−6.43316	−	3.71419i	−0.442877	−	0.255695i	0.261940	−	0.965084i	$-0.415638\pi$
$211$	−6.43316	−	3.71419i	−0.442877	−	0.255695i	−0.704817	+	0.709389i	$0.748971\pi$
$212$	8.95401	−	2.23376i	0.614964	−	0.153415i
$213$	−0.957368	+	13.8642i	−0.0655978	+	0.949960i
$214$	6.05005	+	4.72616i	0.413573	+	0.323074i
$215$	−5.74651			−0.391908
$216$	8.60521	−	11.9143i	0.585510	−	0.810665i
$217$	−4.39871			−0.298604
$218$	−1.43588	−	1.12168i	−0.0972500	−	0.0759695i
$219$	1.20518	−	17.4530i	0.0814388	−	1.17936i
$220$	−0.966431	−	3.87393i	−0.0651568	−	0.261181i
$221$	3.57487	+	2.06395i	0.240472	+	0.138836i
$222$	−6.03214	+	6.71200i	−0.404851	+	0.450480i
$223$	14.3357	+	24.8302i	0.959989	+	1.66275i	0.722514	+	0.691357i	$0.242987\pi$
$223$	14.3357	+	24.8302i	0.959989	+	1.66275i	0.237476	+	0.971394i	$0.423680\pi$
$224$	5.31506	−	1.93654i	0.355127	−	0.129390i
$225$	5.22833	+	12.8761i	0.348555	+	0.858404i
$226$	2.13846	+	5.29185i	0.142248	+	0.352009i
$227$	−12.3836	+	7.14966i	−0.821927	+	0.474540i	−0.851080	−	0.525035i	$-0.824052\pi$
$227$	−12.3836	+	7.14966i	−0.821927	+	0.474540i	0.0291537	+	0.999575i	$0.490719\pi$
$228$	−1.37338	−	7.74336i	−0.0909540	−	0.512817i
$229$	−3.00168	−	1.73302i	−0.198356	−	0.114521i	0.397532	−	0.917588i	$-0.369867\pi$
$229$	−3.00168	−	1.73302i	−0.198356	−	0.114521i	−0.595889	+	0.803067i	$0.703200\pi$
$230$	−0.177661	+	1.26474i	−0.0117146	+	0.0833943i
$231$	3.18479	−	4.73052i	0.209544	−	0.311245i
$232$	−11.9112	+	1.25434i	−0.782008	+	0.0823511i
$233$	−22.2112			−1.45510			−0.727551	−	0.686053i	$-0.759342\pi$
$233$	−22.2112			−1.45510			−0.727551	+	0.686053i	$0.759342\pi$
$234$	−3.27647	+	0.823202i	−0.214189	+	0.0538144i
$235$		−	1.40610i		−	0.0917240i
$236$	−0.351036	+	1.22483i	−0.0228505	+	0.0797294i
$237$	−14.7314	+	7.20084i	−0.956907	+	0.467745i
$238$	7.26005	+	1.01984i	0.470599	+	0.0661062i
$239$	12.6930	−	21.9850i	0.821043	−	1.42209i	−0.0838627	−	0.996477i	$-0.526726\pi$
$239$	12.6930	−	21.9850i	0.821043	−	1.42209i	0.904906	−	0.425611i	$-0.139941\pi$
$240$	−0.434354	+	4.17830i	−0.0280374	+	0.269708i
$241$	2.16022	+	3.74160i	0.139152	+	0.241018i	0.927176	−	0.374627i	$-0.122229\pi$
$241$	2.16022	+	3.74160i	0.139152	+	0.241018i	−0.788024	+	0.615644i	$0.788896\pi$
$242$	−0.0846579	−	0.209495i	−0.00544201	−	0.0134669i
$243$	−5.26784	+	14.6714i	−0.337932	+	0.941171i
$244$	0.840040	+	0.869654i	0.0537780	+	0.0556739i
$245$	0.525102	−	0.303168i	0.0335476	−	0.0193687i
$246$	5.33164	−	1.73788i	0.339933	−	0.110803i
$247$	−0.903850	+	1.56551i	−0.0575106	+	0.0996113i
$248$	−10.0639	+	7.31492i	−0.639056	+	0.464498i
$249$	−4.03199	−	8.24860i	−0.255517	−	0.522734i
$250$	−6.50902	−	5.08470i	−0.411667	−	0.321585i
$251$			2.43491i			0.153690i	0.997043	+	0.0768450i	$0.0244846\pi$
$251$			2.43491i			0.153690i	−0.997043	+	0.0768450i	$0.975515\pi$
$252$	−4.84749	+	3.53580i	−0.305363	+	0.222734i
$253$		−	4.90382i		−	0.308300i
$254$	14.9651	−	19.1571i	0.938992	−	1.20202i
$255$	−3.04048	+	4.51617i	−0.190403	+	0.282813i
$256$	8.93998	−	13.2694i	0.558749	−	0.829337i
$257$	−0.283514	+	0.491061i	−0.0176851	+	0.0306315i	−0.874733	−	0.484606i	$-0.838963\pi$
$257$	−0.283514	+	0.491061i	−0.0176851	+	0.0306315i	0.857047	+	0.515238i	$0.172296\pi$
$258$	−22.7121	−	4.80538i	−1.41399	−	0.299170i
$259$	3.19056	−	1.84207i	0.198252	−	0.114461i
$260$	0.694517	−	0.670867i	0.0430721	−	0.0416054i
$261$	11.7703	−	4.77932i	0.728561	−	0.295832i
$262$	−22.1911	+	8.96750i	−1.37097	+	0.554014i
$263$	12.1263	+	21.0034i	0.747741	+	1.29512i	0.948903	+	0.315567i	$0.102195\pi$
$263$	12.1263	+	21.0034i	0.747741	+	1.29512i	−0.201163	+	0.979558i	$0.564472\pi$
$264$	−0.580169	−	16.1192i	−0.0357069	−	0.992069i
$265$	1.39888	−	2.42294i	0.0859327	−	0.148840i
$266$	−0.446610	+	3.17934i	−0.0273834	+	0.194938i
$267$	1.85508	−	26.8645i	0.113529	−	1.64408i
$268$	−7.02934	+	24.5266i	−0.429385	+	1.49820i
$269$		−	13.4736i		−	0.821500i	−0.911748	−	0.410750i	$-0.865267\pi$
$269$		−	13.4736i		−	0.821500i	0.911748	−	0.410750i	$-0.134733\pi$
$270$	−0.785450	−	4.38586i	−0.0478010	−	0.266915i
$271$	17.4828			1.06200			0.531001	−	0.847371i	$-0.321816\pi$
$271$	17.4828			1.06200			0.531001	+	0.847371i	$0.321816\pi$
$272$	18.3063	−	9.73992i	1.10998	−	0.590569i
$273$	1.37591	+	0.0950108i	0.0832737	+	0.00575032i
$274$	3.18123	+	0.446876i	0.192185	+	0.0269967i
$275$	13.2084	+	7.62590i	0.796499	+	0.459859i
$276$	−1.75978	+	4.85009i	−0.105926	+	0.291941i
$277$	13.8854	−	8.01675i	0.834293	−	0.481680i	−0.0210270	−	0.999779i	$-0.506694\pi$
$277$	13.8854	−	8.01675i	0.834293	−	0.481680i	0.855320	+	0.518099i	$0.173360\pi$
$278$	−10.9404	+	4.42107i	−0.656163	+	0.265158i
$279$	8.10626	−	10.4128i	0.485309	−	0.623399i
$280$	0.697229	−	1.56685i	0.0416674	−	0.0936372i
$281$	−8.61518	−	14.9219i	−0.513939	−	0.890168i	−0.999869	−	0.0161703i	$-0.994853\pi$
$281$	−8.61518	−	14.9219i	−0.513939	−	0.890168i	0.485931	−	0.873997i	$-0.338481\pi$
$282$	1.17582	−	5.55737i	0.0700190	−	0.330937i
$283$	−0.602805	−	0.348029i	−0.0358330	−	0.0206882i	0.481976	−	0.876184i	$-0.339919\pi$
$283$	−0.602805	−	0.348029i	−0.0358330	−	0.0206882i	−0.517809	+	0.855496i	$0.673252\pi$
$284$	−3.88424	−	15.5699i	−0.230487	−	0.923906i
$285$	−1.97773	−	1.33150i	−0.117151	−	0.0788710i
$286$	−2.28245	+	2.92180i	−0.134964	+	0.172770i
$287$	−2.28934			−0.135136
$288$	−5.21071	+	16.1508i	−0.307044	+	0.951695i
$289$	9.87416			0.580833
$290$	−2.23531	+	2.86146i	−0.131262	+	0.168031i
$291$	−19.7770	+	9.66717i	−1.15935	+	0.566699i
$292$	4.88968	+	19.6003i	0.286147	+	1.14702i
$293$	−15.4114	−	8.89779i	−0.900345	−	0.519814i	−0.0230330	−	0.999735i	$-0.507332\pi$
$293$	−15.4114	−	8.89779i	−0.900345	−	0.519814i	−0.877312	+	0.479920i	$0.840666\pi$
$294$	2.32889	−	0.759115i	0.135824	−	0.0442725i
$295$	0.193139	+	0.334526i	0.0112450	+	0.0194769i
$296$	4.23642	−	9.52030i	0.246237	−	0.553356i
$297$	5.32911	+	16.2569i	0.309226	+	0.943321i
$298$	−22.5120	+	9.09718i	−1.30408	+	0.526986i
$299$	1.02709	−	0.592990i	0.0593980	−	0.0342935i
$300$	−10.3271	−	12.2823i	−0.596236	−	0.709120i
$301$	8.20769	+	4.73871i	0.473084	+	0.273135i
$302$	−25.1670	−	3.53528i	−1.44820	−	0.203432i
$303$	−12.8663	−	26.3217i	−0.739150	−	1.51214i
$304$	4.26533	+	8.01674i	0.244633	+	0.459791i
$305$	0.366566			0.0209895
$306$	−15.7935	+	15.3068i	−0.902856	+	0.875034i
$307$			28.4587i			1.62422i	0.583503	+	0.812111i	$0.301682\pi$
$307$			28.4587i			1.62422i	−0.583503	+	0.812111i	$0.698318\pi$
$308$	−1.81420	+	6.33005i	−0.103373	+	0.360688i
$309$	−14.7345	−	9.91989i	−0.838214	−	0.564323i
$310$	−0.524690	+	3.73518i	−0.0298004	+	0.212144i
$311$	7.49019	−	12.9734i	0.424730	−	0.735654i	−0.571665	−	0.820487i	$-0.693702\pi$
$311$	7.49019	−	12.9734i	0.424730	−	0.735654i	0.996395	+	0.0848333i	$0.0270358\pi$
$312$	3.30596	−	2.07071i	0.187163	−	0.117231i
$313$	−12.8899	−	22.3259i	−0.728579	−	1.26194i	−0.957484	−	0.288487i	$-0.906848\pi$
$313$	−12.8899	−	22.3259i	−0.728579	−	1.26194i	0.228905	−	0.973449i	$-0.426486\pi$
$314$	−27.4217	+	11.0812i	−1.54750	+	0.625350i
$315$	−0.250024	+	1.80174i	−0.0140873	+	0.101517i
$316$	13.6181	−	13.1543i	0.766076	−	0.739989i
$317$	28.3840	−	16.3875i	1.59420	−	0.920414i	0.601630	−	0.798775i	$-0.294518\pi$
$317$	28.3840	−	16.3875i	1.59420	−	0.920414i	0.992574	−	0.121640i	$-0.0388153\pi$
$318$	7.55497	−	8.40646i	0.423661	−	0.471411i
$319$	6.97098	−	12.0741i	0.390300	−	0.676020i
$320$	−1.01042	−	4.74428i	−0.0564842	−	0.265214i
$321$	9.38029	+	0.647739i	0.523557	+	0.0361533i
$322$	1.29669	−	1.65991i	0.0722615	−	0.0925033i
$323$			11.7688i			0.654833i
$324$	0.563218	−	17.9912i	0.0312899	−	0.999510i
$325$			3.68862i			0.204608i
$326$	−9.67490	−	7.55782i	−0.535843	−	0.418589i
$327$	−2.22626	−	0.153730i	−0.123112	−	0.00850130i
$328$	−5.23782	+	3.80710i	−0.289210	+	0.210212i
$329$	−1.15951	+	2.00832i	−0.0639257	+	0.110723i
$330$	−3.63703	−	3.26864i	−0.200212	−	0.179933i
$331$	−21.2921	+	12.2930i	−1.17032	+	0.675685i	−0.953755	−	0.300584i	$-0.902819\pi$
$331$	−21.2921	+	12.2930i	−1.17032	+	0.675685i	−0.216565	+	0.976268i	$0.569485\pi$
$332$	7.36556	+	7.62521i	0.404237	+	0.418488i
$333$	−1.51917	+	10.9475i	−0.0832499	+	0.599921i
$334$	11.6975	+	28.9468i	0.640059	+	1.58390i
$335$	3.86752	+	6.69874i	0.211305	+	0.365992i
$336$	4.06592	−	5.60966i	0.221814	−	0.306032i
$337$	8.04333	−	13.9315i	0.438148	−	0.758895i	−0.559399	−	0.828899i	$-0.688968\pi$
$337$	8.04333	−	13.9315i	0.438148	−	0.758895i	0.997547	+	0.0700039i	$0.0223012\pi$
$338$	17.3181	+	2.43271i	0.941979	+	0.132322i
$339$	5.79867	+	3.90392i	0.314940	+	0.212032i
$340$	1.73199	−	6.04323i	0.0939305	−	0.327740i
$341$		−	14.4825i		−	0.784274i
$342$	−6.70321	−	6.91634i	−0.362468	−	0.373993i
$343$	−1.00000			−0.0539949
$344$	26.6588	−	2.80737i	1.43735	−	0.151363i
$345$	0.686917	+	1.40529i	0.0369824	+	0.0756581i
$346$	4.03104	−	28.6963i	0.216710	−	1.54272i
$347$	−8.66037	−	5.00007i	−0.464913	−	0.268418i	0.249195	−	0.968453i	$-0.419834\pi$
$347$	−8.66037	−	5.00007i	−0.464913	−	0.268418i	−0.714108	+	0.700036i	$0.753167\pi$
$348$	−11.2275	+	9.44021i	−0.601858	+	0.506049i
$349$	−16.4985	+	9.52541i	−0.883144	+	0.509884i	−0.871694	−	0.490051i	$-0.836978\pi$
$349$	−16.4985	+	9.52541i	−0.883144	+	0.509884i	−0.0114505	+	0.999934i	$0.503645\pi$
$350$	2.45451	+	6.07395i	0.131199	+	0.324666i
$351$	−2.76053	+	3.08201i	−0.147346	+	0.164506i
$352$	6.37595	+	17.4996i	0.339839	+	0.932729i
$353$	0.431651	+	0.747642i	0.0229745	+	0.0397930i	0.877284	−	0.479972i	$-0.159353\pi$
$353$	0.431651	+	0.747642i	0.0229745	+	0.0397930i	−0.854310	+	0.519765i	$0.826020\pi$
$354$	0.483608	+	1.48366i	0.0257035	+	0.0788559i
$355$	−4.21319	−	2.43249i	−0.223613	−	0.129103i
$356$	7.52643	+	30.1696i	0.398900	+	1.59899i
$357$	8.06685	−	3.94315i	0.426943	−	0.208694i
$358$	−11.7655	−	9.19097i	−0.621827	−	0.485758i
$359$	−4.43145			−0.233883			−0.116941	−	0.993139i	$-0.537309\pi$
$359$	−4.43145			−0.233883			−0.116941	+	0.993139i	$0.537309\pi$
$360$	2.42421	+	4.53801i	0.127767	+	0.239174i
$361$	13.8462			0.728746
$362$	−13.5844	−	10.6118i	−0.713978	−	0.557744i
$363$	−0.229559	−	0.154549i	−0.0120487	−	0.00811173i
$364$	−1.54519	+	0.385478i	−0.0809899	+	0.0202046i
$365$	5.30379	+	3.06214i	0.277613	+	0.160280i
$366$	1.44879	+	0.306532i	0.0757293	+	0.0160227i
$367$	−4.32793	−	7.49620i	−0.225916	−	0.391298i	0.730678	−	0.682723i	$-0.239204\pi$
$367$	−4.32793	−	7.49620i	−0.225916	−	0.391298i	−0.956594	+	0.291424i	$0.905871\pi$
$368$	0.206325	−	5.95408i	0.0107554	−	0.310378i
$369$	4.21897	−	5.41943i	0.219631	−	0.282124i
$370$	−1.18362	−	2.92900i	−0.0615335	−	0.152271i
$371$	−3.99603	+	2.30711i	−0.207464	+	0.119779i
$372$	−5.19720	+	14.3239i	−0.269462	+	0.742658i
$373$	16.7063	+	9.64536i	0.865017	+	0.499418i	0.865689	−	0.500582i	$-0.166881\pi$
$373$	16.7063	+	9.64536i	0.865017	+	0.499418i	−0.000671858		1.00000i	$0.500214\pi$
$374$	−3.35776	+	23.9033i	−0.173626	+	1.23601i
$375$	−10.0919	−	0.696879i	−0.521144	−	0.0359867i
$376$	0.686929	+	6.52309i	0.0354257	+	0.336403i
$377$	3.37184			0.173658
$378$	−2.49484	+	6.91200i	−0.128321	+	0.355515i
$379$			24.0914i			1.23749i	0.785592	+	0.618745i	$0.212359\pi$
$379$			24.0914i			1.23749i	−0.785592	+	0.618745i	$0.787641\pi$
$380$	2.64647	+	0.758478i	0.135761	+	0.0389091i
$381$	2.05102	−	29.7021i	0.105077	−	1.52168i
$382$	20.5365	+	2.88481i	1.05074	+	0.147600i
$383$	−12.4706	+	21.5997i	−0.637219	+	1.10370i	0.348822	+	0.937189i	$0.386582\pi$
$383$	−12.4706	+	21.5997i	−0.637219	+	1.10370i	−0.986040	+	0.166506i	$0.946751\pi$
$384$	−0.0262207	−	19.5959i	−0.00133807	−	0.999999i
$385$	0.998165	+	1.72887i	0.0508712	+	0.0881115i
$386$	10.8841	+	26.9339i	0.553987	+	1.37090i
$387$	−26.3434	+	10.6967i	−1.33911	+	0.543746i
$388$	18.2823	−	17.6598i	0.928144	−	0.896538i
$389$	29.7971	−	17.2034i	1.51078	−	0.872246i	0.510854	−	0.859667i	$-0.329329\pi$
$389$	29.7971	−	17.2034i	1.51078	−	0.872246i	0.999921	−	0.0125790i	$-0.00400411\pi$
$390$	0.244800	−	1.15702i	0.0123959	−	0.0585880i
$391$	3.86058	−	6.68672i	0.195238	−	0.338162i
$392$	−2.28791	+	1.66297i	−0.115557	+	0.0839925i
$393$	−16.3708	+	24.3164i	−0.825800	+	1.22660i
$394$	22.7762	+	17.7923i	1.14745	+	0.896363i
$395$		−	5.74012i		−	0.288817i
$396$	−11.6414	−	15.9601i	−0.585004	−	0.802026i
$397$		−	31.2914i		−	1.57047i	−0.619197	−	0.785236i	$-0.712542\pi$
$397$		−	31.2914i		−	1.57047i	0.619197	−	0.785236i	$-0.287458\pi$
$398$	12.7487	−	16.3199i	0.639037	−	0.818043i
$399$	1.72679	+	3.53265i	0.0864478	+	0.176854i
$400$	15.7165	+	9.81489i	0.785824	+	0.490745i
$401$	−2.67878	+	4.63978i	−0.133772	+	0.231700i	−0.925128	−	0.379656i	$-0.876042\pi$
$401$	−2.67878	+	4.63978i	−0.133772	+	0.231700i	0.791356	+	0.611356i	$0.209376\pi$
$402$	9.68405	+	29.7098i	0.482996	+	1.48179i
$403$	3.03332	−	1.75129i	0.151100	−	0.0872379i
$404$	23.5039	+	24.3324i	1.16936	+	1.21058i
$405$	−3.80440	−	3.91225i	−0.189042	−	0.194401i
$406$	5.55231	−	2.24371i	0.275557	−	0.111354i
$407$	6.06493	+	10.5048i	0.300628	+	0.520702i
$408$	11.8989	−	22.4365i	0.589084	−	1.11077i
$409$	2.39877	−	4.15479i	0.118611	−	0.205441i	−0.800606	−	0.599191i	$-0.795489\pi$
$409$	2.39877	−	4.15479i	0.118611	−	0.205441i	0.919218	+	0.393750i	$0.128822\pi$
$410$	−0.273079	+	1.94400i	−0.0134864	+	0.0960073i
$411$	3.53476	−	1.72782i	0.174357	−	0.0852272i
$412$	19.7166	+	5.65080i	0.971370	+	0.278395i
$413$		−	0.637068i		−	0.0313481i
$414$	1.53979	+	6.12857i	0.0756763	+	0.301203i
$415$	3.21409			0.157773
$416$	−2.89422	+	3.45154i	−0.141901	+	0.169226i
$417$	−8.07099	+	11.9882i	−0.395238	+	0.587065i
$418$	−10.4678	−	1.47044i	−0.511997	−	0.0719215i
$419$	16.7148	+	9.65028i	0.816570	+	0.471447i	0.849232	−	0.528020i	$-0.177065\pi$
$419$	16.7148	+	9.65028i	0.816570	+	0.471447i	−0.0326623	+	0.999466i	$0.510399\pi$
$420$	−0.366807	−	2.06813i	−0.0178984	−	0.100915i
$421$	−21.1852	+	12.2313i	−1.03250	+	0.596116i	−0.917701	−	0.397273i	$-0.869957\pi$
$421$	−21.1852	+	12.2313i	−1.03250	+	0.596116i	−0.114802	+	0.993388i	$0.536623\pi$
$422$	9.74009	−	3.93601i	0.474140	−	0.191602i
$423$	−2.61737	−	6.44592i	−0.127261	−	0.313411i
$424$	−5.30592	+	11.9237i	−0.257678	+	0.579067i
$425$	12.0071	+	20.7970i	0.582432	+	1.00880i
$426$	−14.6178	−	13.1372i	−0.708235	−	0.636498i
$427$	−0.523563	−	0.302279i	−0.0253370	−	0.0146283i
$428$	−10.5344	+	2.62801i	−0.509198	+	0.127030i
$429$	−0.312818	+	4.53011i	−0.0151030	+	0.218716i
$430$	5.00292	−	6.40433i	0.241262	−	0.308844i
$431$	15.2619			0.735138			0.367569	−	0.929996i	$-0.380190\pi$
$431$	15.2619			0.735138			0.367569	+	0.929996i	$0.380190\pi$
$432$	5.78645	+	19.9629i	0.278401	+	0.960465i
$433$	−5.86115			−0.281669			−0.140834	−	0.990033i	$-0.544979\pi$
$433$	−5.86115			−0.281669			−0.140834	+	0.990033i	$0.544979\pi$
$434$	3.82953	−	4.90225i	0.183823	−	0.235316i
$435$	−0.306358	+	4.43656i	−0.0146888	+	0.212717i
$436$	2.50016	−	0.623715i	0.119736	−	0.0298705i
$437$	2.92827	+	1.69064i	0.140078	+	0.0808741i
$438$	18.4017	+	16.5378i	0.879265	+	0.790205i
$439$	3.03650	+	5.25938i	0.144924	+	0.251016i	0.929345	−	0.369213i	$-0.120373\pi$
$439$	3.03650	+	5.25938i	0.144924	+	0.251016i	−0.784420	+	0.620230i	$0.787039\pi$
$440$	5.15877	+	2.29559i	0.245935	+	0.109438i
$441$	1.84287	−	2.36724i	0.0877558	−	0.112726i
$442$	−5.41250	+	2.18722i	−0.257447	+	0.104035i
$443$	4.22313	−	2.43823i	0.200647	−	0.115844i	−0.396310	−	0.918117i	$-0.629710\pi$
$443$	4.22313	−	2.43823i	0.200647	−	0.115844i	0.596957	+	0.802273i	$0.296376\pi$
$444$	−2.22875	−	12.5661i	−0.105772	−	0.596362i
$445$	8.16384	+	4.71340i	0.387003	+	0.223436i
$446$	−40.1532	−	5.64043i	−1.90131	−	0.267082i
$447$	−16.6076	+	24.6680i	−0.785512	+	1.16676i
$448$	−2.46908	+	7.60944i	−0.116653	+	0.359512i
$449$	−22.9531			−1.08322			−0.541611	−	0.840629i	$-0.682186\pi$
$449$	−22.9531			−1.08322			−0.541611	+	0.840629i	$0.682186\pi$
$450$	−18.9018	−	5.38309i	−0.891041	−	0.253761i
$451$		−	7.53755i		−	0.354929i
$452$	−7.75938	−	2.22384i	−0.364971	−	0.104601i
$453$	−27.9638	+	13.6690i	−1.31385	+	0.642224i
$454$	2.81306	−	20.0257i	0.132023	−	0.939852i
$455$	−0.241404	+	0.418125i	−0.0113172	+	0.0196020i
$456$	9.82544	+	5.21080i	0.460118	+	0.244018i
$457$	−5.89505	−	10.2105i	−0.275759	−	0.477628i	0.694567	−	0.719428i	$-0.255596\pi$
$457$	−5.89505	−	10.2105i	−0.275759	−	0.477628i	−0.970326	+	0.241799i	$0.922262\pi$
$458$	4.54467	−	1.83652i	0.212359	−	0.0858150i
$459$	−5.53178	+	26.3629i	−0.258201	+	1.23051i
$460$	−1.25485	−	1.29908i	−0.0585075	−	0.0605700i
$461$	−10.4070	+	6.00849i	−0.484703	+	0.279843i	−0.722374	−	0.691502i	$-0.756949\pi$
$461$	−10.4070	+	6.00849i	−0.484703	+	0.279843i	0.237671	+	0.971346i	$0.423616\pi$
$462$	2.49935	+	7.66776i	0.116280	+	0.356737i
$463$	−16.7203	+	28.9605i	−0.777060	+	1.34591i	0.156569	+	0.987667i	$0.449957\pi$
$463$	−16.7203	+	28.9605i	−0.777060	+	1.34591i	−0.933629	+	0.358241i	$0.883377\pi$
$464$	8.97198	−	14.3667i	0.416514	−	0.666959i
$465$	2.02869	+	4.15026i	0.0940781	+	0.192464i
$466$	19.3371	−	24.7538i	0.895774	−	1.14670i
$467$		−	26.0344i		−	1.20473i	−0.798222	−	0.602364i	$-0.794226\pi$
$467$		−	26.0344i		−	1.20473i	0.798222	−	0.602364i	$-0.205774\pi$
$468$	1.93506	−	4.36822i	0.0894483	−	0.201921i
$469$		−	12.7570i		−	0.589065i
$470$	1.56706	+	1.22416i	0.0722832	+	0.0564661i
$471$	−20.2296	+	30.0479i	−0.932131	+	1.38454i
$472$	−1.05942	−	1.45756i	−0.0487639	−	0.0670895i
$473$	−15.6020	+	27.0234i	−0.717380	+	1.24254i
$474$	4.80003	−	22.6868i	0.220473	−	1.04204i
$475$	−9.10746	+	5.25819i	−0.417879	+	0.241262i
$476$	−7.45719	+	7.20326i	−0.341800	+	0.330161i
$477$	1.90269	−	13.7113i	0.0871180	−	0.627796i
$478$	13.4511	+	33.2862i	0.615238	+	1.52248i
$479$	4.06426	+	7.03950i	0.185701	+	0.321643i	0.943812	−	0.330482i	$-0.107211\pi$
$479$	4.06426	+	7.03950i	0.185701	+	0.321643i	−0.758112	+	0.652125i	$0.773878\pi$
$480$	−4.27846	−	4.12172i	−0.195284	−	0.188130i
$481$	−1.46679	+	2.54056i	−0.0668799	+	0.115839i
$482$	−6.05061	−	0.849944i	−0.275598	−	0.0387139i
$483$	0.177716	−	2.57361i	0.00808636	−	0.117103i
$484$	0.307180	+	0.0880380i	0.0139627	+	0.00400173i
$485$		−	7.70614i		−	0.349918i
$486$	−11.7647	−	18.6438i	−0.533657	−	0.845701i
$487$	−9.21859			−0.417734			−0.208867	−	0.977944i	$-0.566978\pi$
$487$	−9.21859			−0.417734			−0.208867	+	0.977944i	$0.566978\pi$
$488$	−1.70055	+	0.179080i	−0.0769801	+	0.00810657i
$489$	−15.0005	−	1.03583i	−0.678344	−	0.0468418i
$490$	−0.119282	+	0.849152i	−0.00538863	+	0.0383608i
$491$	−2.83465	−	1.63659i	−0.127926	−	0.0738582i	0.434671	−	0.900589i	$-0.356865\pi$
$491$	−2.83465	−	1.63659i	−0.127926	−	0.0738582i	−0.562597	+	0.826731i	$0.690198\pi$
$492$	−2.70492	+	7.45497i	−0.121947	+	0.336096i
$493$	19.0109	−	10.9760i	0.856208	−	0.494332i
$494$	−0.957831	−	2.37026i	−0.0430948	−	0.106643i
$495$	−5.93215	−	0.823193i	−0.266630	−	0.0369998i
$496$	0.609343	−	17.5843i	0.0273603	−	0.789559i
$497$	4.01178	+	6.94861i	0.179953	+	0.311688i
$498$	12.7031	+	2.68770i	0.569240	+	0.120439i
$499$	−18.7508	−	10.8258i	−0.839401	−	0.484628i	0.0176595	−	0.999844i	$-0.494379\pi$
$499$	−18.7508	−	10.8258i	−0.839401	−	0.484628i	−0.857061	+	0.515216i	$0.827712\pi$
$500$	11.3335	−	2.82738i	0.506851	−	0.126444i
$501$	31.7191	+	21.3547i	1.41710	+	0.954057i
$502$	−2.71364	−	2.11983i	−0.121116	−	0.0946128i
$503$	−26.1829			−1.16744			−0.583720	−	0.811955i	$-0.698403\pi$
$503$	−26.1829			−1.16744			−0.583720	+	0.811955i	$0.698403\pi$
$504$	0.279683	−	8.48067i	0.0124581	−	0.377759i
$505$	10.2563			0.456400
$506$	5.46518	+	4.26928i	0.242957	+	0.189792i
$507$	19.2426	−	9.40597i	0.854594	−	0.417734i
$508$	8.32142	+	33.3564i	0.369203	+	1.47995i
$509$	−21.8532	−	12.6170i	−0.968627	−	0.559237i	−0.0698098	−	0.997560i	$-0.522239\pi$
$509$	−21.8532	−	12.6170i	−0.968627	−	0.559237i	−0.898817	+	0.438323i	$0.855573\pi$
$510$	−2.38610	−	7.32033i	−0.105658	−	0.324149i
$511$	−5.05024	−	8.74727i	−0.223410	−	0.386957i
$512$	7.00522	+	21.5157i	0.309590	+	0.950870i
$513$	−11.5449	−	2.42249i	−0.509720	−	0.106955i
$514$	−0.300447	−	0.743488i	−0.0132521	−	0.0327939i
$515$	5.38504	−	3.10905i	0.237293	−	0.137001i
$516$	25.1286	−	21.1284i	1.10623	−	0.930128i
$517$	−6.61231	−	3.81762i	−0.290809	−	0.167899i
$518$	−0.724770	+	5.15951i	−0.0318446	+	0.226696i
$519$	−15.5858	−	31.8853i	−0.684142	−	1.39961i
$520$	0.143016	+	1.35808i	0.00627165	+	0.0595557i
$521$	−4.59663			−0.201382			−0.100691	−	0.994918i	$-0.532105\pi$
$521$	−4.59663			−0.201382			−0.100691	+	0.994918i	$0.532105\pi$
$522$	−4.92079	+	17.2785i	−0.215377	+	0.756261i
$523$		−	4.21715i		−	0.184403i	−0.995740	−	0.0922014i	$-0.970610\pi$
$523$		−	4.21715i		−	0.184403i	0.995740	−	0.0922014i	$-0.0293904\pi$
$524$	9.32555	−	32.5385i	0.407388	−	1.42145i
$525$	6.65566	+	4.48089i	0.290477	+	0.195562i
$526$	−33.9649	−	4.77114i	−1.48094	−	0.208032i
$527$	11.4015	−	19.7480i	0.496659	−	0.860238i
$528$	18.4695	+	13.3868i	0.803783	+	0.582587i
$529$	10.3908	+	17.9974i	0.451775	+	0.782497i
$530$	1.48243	+	3.66843i	0.0643926	+	0.159347i
$531$	1.50809	+	1.17403i	0.0654457	+	0.0509488i
$532$	−3.15447	−	3.26567i	−0.136764	−	0.141585i
$533$	1.57871	−	0.911471i	0.0683817	−	0.0394802i
$534$	28.3247	+	25.4557i	1.22573	+	1.10158i
$535$	−1.64578	+	2.85058i	−0.0711533	+	0.123241i
$536$	−21.2145	−	29.1869i	−0.916328	−	1.26068i
$537$	−18.2419	−	1.25966i	−0.787194	−	0.0543583i
$538$	15.0160	+	11.7301i	0.647384	+	0.505722i
$539$		−	3.29245i		−	0.141816i
$540$	5.57175	+	2.94298i	0.239770	+	0.126646i
$541$			1.09875i			0.0472390i	0.999721	+	0.0236195i	$0.00751902\pi$
$541$			1.09875i			0.0472390i	−0.999721	+	0.0236195i	$0.992481\pi$
$542$	−15.2205	+	19.4841i	−0.653777	+	0.836912i
$543$	−21.0619	−	1.45439i	−0.903852	−	0.0624138i
$544$	−5.08262	+	28.8815i	−0.217915	+	1.23828i
$545$	0.390599	−	0.676538i	0.0167314	−	0.0289797i
$546$	−1.30376	+	1.45070i	−0.0557956	+	0.0620841i
$547$	8.29357	−	4.78829i	0.354607	−	0.204733i	−0.312105	−	0.950048i	$-0.601034\pi$
$547$	8.29357	−	4.78829i	0.354607	−	0.204733i	0.666713	+	0.745315i	$0.267701\pi$
$548$	−3.26762	+	3.15635i	−0.139586	+	0.134832i
$549$	1.68043	−	0.682338i	0.0717189	−	0.0291215i
$550$	−19.9982	+	8.08134i	−0.852725	+	0.344590i
$551$	4.80662	+	8.32531i	0.204769	+	0.354670i
$552$	−3.87323	−	6.18373i	−0.164856	−	0.263197i
$553$	−4.73344	+	8.19857i	−0.201287	+	0.348639i
$554$	−3.15422	+	22.4543i	−0.134010	+	0.953993i
$555$	−3.20951	−	2.16079i	−0.136236	−	0.0917203i
$556$	4.59759	−	16.0418i	0.194981	−	0.680324i
$557$		−	10.8727i		−	0.460692i	−0.973109	−	0.230346i	$-0.926014\pi$
$557$		−	10.8727i		−	0.460692i	0.973109	−	0.230346i	$-0.0739859\pi$
$558$	4.54748	+	18.0996i	0.192510	+	0.766219i
$559$	−7.54662			−0.319188
$560$	1.13920	+	2.14115i	0.0481401	+	0.0904800i
$561$	12.9826	+	26.5597i	0.548127	+	1.12135i
$562$	24.1305	+	3.38967i	1.01788	+	0.142985i
$563$	−9.13155	−	5.27210i	−0.384849	−	0.222193i	0.295077	−	0.955473i	$-0.404655\pi$
$563$	−9.13155	−	5.27210i	−0.384849	−	0.222193i	−0.679926	+	0.733281i	$0.737988\pi$
$564$	5.16988	+	6.14868i	0.217691	+	0.258906i
$565$	−2.11925	+	1.22355i	−0.0891576	+	0.0514752i
$566$	0.912673	−	0.368815i	0.0383625	−	0.0155024i
$567$	2.20765	+	8.72504i	0.0927127	+	0.366417i
$568$	20.7339	+	9.22634i	0.869976	+	0.387129i
$569$	3.04979	+	5.28239i	0.127854	+	0.221449i	0.922845	−	0.385172i	$-0.125858\pi$
$569$	3.04979	+	5.28239i	0.127854	+	0.221449i	−0.794991	+	0.606621i	$0.792524\pi$
$570$	3.20573	−	1.04493i	0.134273	−	0.0437671i
$571$	−27.1733	−	15.6885i	−1.13717	−	0.656543i	−0.191438	−	0.981505i	$-0.561315\pi$
$571$	−27.1733	−	15.6885i	−1.13717	−	0.656543i	−0.945727	+	0.324962i	$0.894648\pi$
$572$	−1.26917	−	5.08745i	−0.0530666	−	0.212717i
$573$	22.8187	−	11.1540i	0.953264	−	0.465964i
$574$	1.99311	−	2.55141i	0.0831907	−	0.106494i
$575$	6.89949			0.287729
$576$	−13.4632	−	19.8681i	−0.560966	−	0.827839i
$577$	13.8053			0.574724			0.287362	−	0.957822i	$-0.407222\pi$
$577$	13.8053			0.574724			0.287362	+	0.957822i	$0.407222\pi$
$578$	−8.59647	+	11.0045i	−0.357566	+	0.457727i
$579$	29.5135	+	19.8698i	1.22654	+	0.825759i
$580$	−1.24296	−	4.98239i	−0.0516110	−	0.206883i
$581$	−4.59066	−	2.65042i	−0.190452	−	0.109958i
$582$	6.44407	−	30.4572i	0.267115	−	1.26249i
$583$	−7.59604	−	13.1567i	−0.314596	−	0.544896i
$584$	−26.1009	−	11.6146i	−1.08006	−	0.480616i
$585$	−0.544924	−	1.34201i	−0.0225298	−	0.0554854i
$586$	23.3336	−	9.42919i	0.963901	−	0.389516i
$587$	−10.6711	+	6.16099i	−0.440445	+	0.254291i	−0.703786	−	0.710412i	$-0.748509\pi$
$587$	−10.6711	+	6.16099i	−0.440445	+	0.254291i	0.263341	+	0.964703i	$0.415175\pi$
$588$	−1.18153	+	3.25638i	−0.0487253	+	0.134291i
$589$	8.64811	+	4.99299i	0.356339	+	0.205732i
$590$	−0.540968	−	0.0759911i	−0.0222713	−	0.00312850i
$591$	35.3134	+	2.43850i	1.45260	+	0.100307i
$592$	6.92189	+	13.0098i	0.284488	+	0.534698i
$593$	17.3712			0.713348			0.356674	−	0.934229i	$-0.383911\pi$
$593$	17.3712			0.713348			0.356674	+	0.934229i	$0.383911\pi$
$594$	−22.7574	−	8.21414i	−0.933748	−	0.337030i
$595$			3.14326i			0.128861i
$596$	9.46040	−	33.0090i	0.387513	−	1.35210i
$597$	1.74727	−	25.3032i	0.0715109	−	1.03559i
$598$	−0.233314	+	1.66092i	−0.00954091	+	0.0679201i
$599$	−2.45847	+	4.25819i	−0.100450	+	0.173985i	−0.911870	−	0.410479i	$-0.865362\pi$
$599$	−2.45847	+	4.25819i	−0.100450	+	0.173985i	0.811420	+	0.584464i	$0.198695\pi$
$600$	22.6791	−	0.816276i	0.925872	−	0.0333243i
$601$	−6.29257	−	10.8991i	−0.256679	−	0.444582i	0.708671	−	0.705539i	$-0.249295\pi$
$601$	−6.29257	−	10.8991i	−0.256679	−	0.444582i	−0.965350	+	0.260958i	$0.915962\pi$
$602$	−12.4268	+	5.02172i	−0.506479	+	0.204670i
$603$	30.1989	+	23.5096i	1.22980	+	0.957383i
$604$	25.8504	−	24.9702i	1.05184	−	1.01602i
$605$	0.0838975	−	0.0484382i	0.00341092	−	0.00196929i
$606$	40.5363	+	8.57659i	1.64667	+	0.348400i
$607$	5.02612	−	8.70550i	0.204004	−	0.353345i	−0.745811	−	0.666158i	$-0.767938\pi$
$607$	5.02612	−	8.70550i	0.204004	−	0.353345i	0.949815	+	0.312812i	$0.101271\pi$
$608$	−12.6478	−	2.22579i	−0.512938	−	0.0902678i
$609$	4.09607	−	6.08407i	0.165981	−	0.246539i
$610$	−0.319133	+	0.408528i	−0.0129213	+	0.0165408i
$611$		−	1.84657i		−	0.0747041i
$612$	−3.30920	−	30.9276i	−0.133766	−	1.25018i
$613$		−	47.2218i		−	1.90727i	−0.300965	−	0.953635i	$-0.597309\pi$
$613$		−	47.2218i		−	1.90727i	0.300965	−	0.953635i	$-0.402691\pi$
$614$	−31.7164	−	24.7762i	−1.27997	−	0.999885i
$615$	1.05585	+	2.16004i	0.0425758	+	0.0871010i
$616$	−5.47524	−	7.53283i	−0.220604	−	0.303507i
$617$	15.8651	−	27.4792i	0.638705	−	1.10627i	−0.347012	−	0.937861i	$-0.612804\pi$
$617$	15.8651	−	27.4792i	0.638705	−	1.10627i	0.985717	−	0.168409i	$-0.0538629\pi$
$618$	23.8833	−	7.78489i	0.960727	−	0.313154i
$619$	−15.3256	+	8.84825i	−0.615989	+	0.355641i	−0.775306	−	0.631586i	$-0.782404\pi$
$619$	−15.3256	+	8.84825i	−0.615989	+	0.355641i	0.159317	+	0.987227i	$0.449071\pi$
$620$	−3.70596	−	3.83661i	−0.148835	−	0.154082i
$621$	5.76485	+	5.16353i	0.231335	+	0.207205i
$622$	7.93753	+	19.6423i	0.318266	+	0.787584i
$623$	−7.77357	−	13.4642i	−0.311442	−	0.539433i
$624$	−0.570416	+	5.48717i	−0.0228349	+	0.219663i
$625$	−9.81026	+	16.9919i	−0.392410	+	0.679674i
$626$	36.1036	+	5.07157i	1.44299	+	0.202701i
$627$	−11.6311	+	5.68538i	−0.464501	+	0.227052i
$628$	11.5237	−	40.2081i	0.459844	−	1.60448i
$629$			19.0987i			0.761516i
$630$	−1.79032	−	1.84725i	−0.0713282	−	0.0735961i
$631$	−22.2249			−0.884760			−0.442380	−	0.896828i	$-0.645866\pi$
$631$	−22.2249			−0.884760			−0.442380	+	0.896828i	$0.645866\pi$
$632$	2.80425	+	26.6292i	0.111547	+	1.05925i
$633$	7.18548	−	10.6729i	0.285597	−	0.424210i
$634$	−6.44772	+	45.9002i	−0.256072	+	1.82293i
$635$	9.02616	+	5.21126i	0.358192	+	0.206802i
$636$	2.79141	+	15.7385i	0.110686	+	0.624072i
$637$	0.689592	−	0.398136i	0.0273226	−	0.0157747i
$638$	7.38731	+	18.2807i	0.292466	+	0.723740i
$639$	−23.8422	−	3.30854i	−0.943184	−	0.130884i
$640$	6.16705	+	3.00430i	0.243774	+	0.118755i
$641$	16.4058	+	28.4156i	0.647988	+	1.12235i	0.983603	+	0.180349i	$0.0577227\pi$
$641$	16.4058	+	28.4156i	0.647988	+	1.12235i	−0.335614	+	0.941999i	$0.608944\pi$
$642$	−8.88839	+	9.89017i	−0.350797	+	0.390334i
$643$	−22.4156	−	12.9416i	−0.883983	−	0.510368i	−0.0120135	−	0.999928i	$-0.503824\pi$
$643$	−22.4156	−	12.9416i	−0.883983	−	0.510368i	−0.871970	+	0.489560i	$0.837157\pi$
$644$	0.721030	+	2.89025i	0.0284126	+	0.113892i
$645$	0.685670	−	9.92959i	0.0269982	−	0.390977i
$646$	−13.1160	−	10.2459i	−0.516043	−	0.403121i
$647$	38.8162			1.52602			0.763011	−	0.646386i	$-0.223720\pi$
$647$	38.8162			1.52602			0.763011	+	0.646386i	$0.223720\pi$
$648$	19.5604	+	16.2909i	0.768404	+	0.639965i
$649$	2.09752			0.0823347
$650$	−4.11087	−	3.21132i	−0.161242	−	0.125958i
$651$	0.524852	−	7.60070i	0.0205706	−	0.297895i
$652$	16.8460	−	4.20257i	0.659740	−	0.164585i
$653$	14.3737	+	8.29867i	0.562487	+	0.324752i	0.754143	−	0.656710i	$-0.228052\pi$
$653$	14.3737	+	8.29867i	0.562487	+	0.324752i	−0.191656	+	0.981462i	$0.561386\pi$
$654$	2.10951	−	2.34727i	0.0824885	−	0.0917855i
$655$	−5.13089	−	8.88696i	−0.200480	−	0.347242i
$656$	0.317137	−	9.15188i	0.0123821	−	0.357321i
$657$	30.0138	+	4.16496i	1.17095	+	0.162491i
$658$	−1.22876	−	3.04069i	−0.0479019	−	0.118539i
$659$	18.7055	−	10.7996i	0.728664	−	0.420694i	−0.0892691	−	0.996008i	$-0.528453\pi$
$659$	18.7055	−	10.7996i	0.728664	−	0.420694i	0.817933	+	0.575313i	$0.195120\pi$
$660$	6.80922	−	1.20770i	0.265049	−	0.0470095i
$661$	−9.50113	−	5.48548i	−0.369551	−	0.213360i	0.303711	−	0.952764i	$-0.401774\pi$
$661$	−9.50113	−	5.48548i	−0.369551	−	0.213360i	−0.673262	+	0.739404i	$0.735108\pi$
$662$	4.83673	−	34.4318i	0.187985	−	1.33823i
$663$	−3.99292	+	5.93087i	−0.155072	+	0.230336i
$664$	−14.9106	+	1.57019i	−0.578642	+	0.0609353i
$665$	−1.37651			−0.0533786
$666$	−10.8781	−	11.2240i	−0.421520	−	0.434922i
$667$		−	6.30696i		−	0.244207i
$668$	−42.4443	−	12.1646i	−1.64222	−	0.470661i
$669$	−44.6154	+	21.8084i	−1.72493	+	0.843163i
$670$	−10.8326	−	1.52169i	−0.418502	−	0.0587880i
$671$	0.995239	−	1.72381i	0.0384208	−	0.0665468i
$672$	2.71202	+	9.41514i	0.104619	+	0.363197i
$673$	−9.35614	−	16.2053i	−0.360653	−	0.624669i	0.627416	−	0.778685i	$-0.284113\pi$
$673$	−9.35614	−	16.2053i	−0.360653	−	0.624669i	−0.988068	+	0.154016i	$0.950779\pi$
$674$	8.52370	+	21.0928i	0.328321	+	0.812466i
$675$	−22.8729	+	7.49786i	−0.880377	+	0.288593i
$676$	−17.7883	+	17.1826i	−0.684167	+	0.660869i
$677$	−2.90835	+	1.67914i	−0.111777	+	0.0645346i	−0.554846	−	0.831953i	$-0.687223\pi$
$677$	−2.90835	+	1.67914i	−0.111777	+	0.0645346i	0.443069	+	0.896487i	$0.353890\pi$
$678$	−9.39915	+	3.06370i	−0.360972	+	0.117661i
$679$	−6.35467	+	11.0066i	−0.243870	+	0.422395i
$680$	5.22714	+	7.19151i	0.200452	+	0.275782i
$681$	−10.8766	−	22.2511i	−0.416790	−	0.852665i
$682$	16.1404	+	12.6085i	0.618049	+	0.482806i
$683$			4.61293i			0.176509i	0.996098	+	0.0882545i	$0.0281289\pi$
$683$			4.61293i			0.176509i	−0.996098	+	0.0882545i	$0.971871\pi$
$684$	13.5439	−	1.44917i	0.517864	−	0.0554105i
$685$			1.37733i			0.0526249i
$686$	0.870602	−	1.11447i	0.0332397	−	0.0425508i
$687$	3.35270	−	4.97992i	0.127914	−	0.189996i
$688$	−20.0805	+	32.1546i	−0.765561	+	1.22588i
$689$	1.83709	−	3.18193i	0.0699875	−	0.121222i
$690$	−2.16419	−	0.457895i	−0.0823892	−	0.0174318i
$691$	23.9993	−	13.8560i	0.912975	−	0.527106i	0.0315879	−	0.999501i	$-0.489944\pi$
$691$	23.9993	−	13.8560i	0.912975	−	0.527106i	0.881387	+	0.472395i	$0.156610\pi$
$692$	28.4718	+	29.4755i	1.08234	+	1.12049i
$693$	7.79402	+	6.06756i	0.296070	+	0.230488i
$694$	13.1122	−	5.29868i	0.497731	−	0.201135i
$695$	−2.52958	−	4.38136i	−0.0959524	−	0.166194i
$696$	−0.746174	−	20.7314i	−0.0282836	−	0.785823i
$697$	5.93401	−	10.2780i	0.224767	−	0.389308i
$698$	3.74781	−	26.6800i	0.141857	−	1.00985i
$699$	2.65023	−	38.3795i	0.100241	−	1.45165i
$700$	−8.90616	−	2.55251i	−0.336621	−	0.0964758i
$701$			3.52486i			0.133132i	0.997782	+	0.0665660i	$0.0212043\pi$
$701$			3.52486i			0.133132i	−0.997782	+	0.0665660i	$0.978796\pi$
$702$	−1.03149	−	5.75975i	−0.0389312	−	0.217388i
$703$	−8.36376			−0.315445
$704$	−25.0537	−	8.12932i	−0.944247	−	0.306385i
$705$	2.42965	+	0.167775i	0.0915061	+	0.00631879i
$706$	−1.20902	−	0.169835i	−0.0455022	−	0.00639181i
$707$	−14.6490	−	8.45761i	−0.550933	−	0.318081i
$708$	−2.07454	−	0.752713i	−0.0779658	−	0.0282887i
$709$	−22.9608	+	13.2564i	−0.862311	+	0.497856i	−0.864786	−	0.502141i	$-0.832546\pi$
$709$	−22.9608	+	13.2564i	−0.862311	+	0.497856i	0.00247446	+	0.999997i	$0.499212\pi$
$710$	6.37896	−	2.57776i	0.239398	−	0.0967417i
$711$	−10.6848	−	26.3141i	−0.400713	−	0.986856i
$712$	−40.1758	−	17.8777i	−1.50565	−	0.669997i
$713$	−3.27575	−	5.67377i	−0.122678	−	0.212484i
$714$	−2.62848	+	12.4232i	−0.0983683	+	0.464927i
$715$	−1.37665	−	0.794812i	−0.0514840	−	0.0297243i
$716$	20.4862	−	5.11069i	0.765604	−	0.190996i
$717$	36.4741	+	24.5560i	1.36215	+	0.917059i
$718$	3.85803	−	4.93873i	0.143980	−	0.184312i
$719$	−27.6792			−1.03226			−0.516130	−	0.856510i	$-0.672628\pi$
$719$	−27.6792			−1.03226			−0.516130	+	0.856510i	$0.672628\pi$
$720$	−7.16801	−	1.24909i	−0.267136	−	0.0465508i
$721$	−10.2552			−0.381924
$722$	−12.0545	+	15.4312i	−0.448623	+	0.574290i
$723$	−6.72301	+	3.28627i	−0.250031	+	0.122218i
$724$	23.6532	−	5.90076i	0.879063	−	0.219300i
$725$	16.9878	+	9.80792i	0.630912	+	0.364257i
$726$	0.372096	−	0.121287i	0.0138098	−	0.00450137i
$727$	−6.33043	−	10.9646i	−0.234783	−	0.406655i	0.724427	−	0.689352i	$-0.242104\pi$
$727$	−6.33043	−	10.9646i	−0.234783	−	0.406655i	−0.959209	+	0.282696i	$0.908771\pi$
$728$	0.915639	−	2.05767i	0.0339358	−	0.0762623i
$729$	−24.7227	−	10.8531i	−0.915655	−	0.401966i
$730$	−8.03017	+	3.24502i	−0.297210	+	0.120104i
$731$	−42.5489	+	24.5656i	−1.57373	+	0.908593i
$732$	−1.60294	+	1.34777i	−0.0592463	+	0.0498150i
$733$	−39.2840	−	22.6806i	−1.45099	−	0.837729i	−0.452451	−	0.891789i	$-0.649450\pi$
$733$	−39.2840	−	22.6806i	−1.45099	−	0.837729i	−0.998538	+	0.0540602i	$0.982784\pi$
$734$	12.1222	+	1.70284i	0.447440	+	0.0628530i
$735$	0.461200	+	0.943517i	0.0170116	+	0.0348022i
$736$	6.45604	+	5.41358i	0.237973	+	0.199547i
$737$	42.0019			1.54716
$738$	2.36677	+	9.42009i	0.0871220	+	0.346758i
$739$		−	18.4580i		−	0.678987i	−0.940608	−	0.339493i	$-0.889744\pi$
$739$		−	18.4580i		−	0.678987i	0.940608	−	0.339493i	$-0.110256\pi$
$740$	4.29476	+	1.23088i	0.157878	+	0.0452480i
$741$	−2.59726	−	1.74859i	−0.0954128	−	0.0642361i
$742$	0.907740	−	6.46204i	0.0333242	−	0.237229i
$743$	−13.0026	+	22.5211i	−0.477018	+	0.826220i	−0.999653	−	0.0263365i	$-0.991616\pi$
$743$	−13.0026	+	22.5211i	−0.477018	+	0.826220i	0.522635	+	0.852557i	$0.324949\pi$
$744$	−11.4389	−	18.2625i	−0.419370	−	0.669537i
$745$	−5.20508	−	9.01547i	−0.190700	−	0.330301i
$746$	−25.2940	+	10.2214i	−0.926080	+	0.374233i
$747$	14.7342	−	5.98281i	0.539095	−	0.218900i
$748$	−23.7164	−	24.5524i	−0.867156	−	0.897726i
$749$	4.70132	−	2.71431i	0.171782	−	0.0991786i
$750$	9.56270	−	10.6405i	0.349180	−	0.388535i
$751$	16.8322	−	29.1543i	0.614217	−	1.06386i	−0.376304	−	0.926496i	$-0.622805\pi$
$751$	16.8322	−	29.1543i	0.614217	−	1.06386i	0.990521	−	0.137359i	$-0.0438615\pi$
$752$	−7.86786	−	4.91345i	−0.286911	−	0.179175i
$753$	−4.20736	−	0.290532i	−0.153325	−	0.0105876i
$754$	−2.93553	+	3.75782i	−0.106906	+	0.136852i
$755$		−	10.8962i		−	0.396552i
$756$	−5.53123	−	8.79804i	−0.201169	−	0.319982i
$757$			23.2769i			0.846013i	0.906127	+	0.423006i	$0.139025\pi$
$757$			23.2769i			0.846013i	−0.906127	+	0.423006i	$0.860975\pi$
$758$	−26.8492	−	20.9740i	−0.975207	−	0.761810i
$759$	8.47349	+	0.585121i	0.307568	+	0.0212386i
$760$	−3.14932	+	2.28908i	−0.114238	+	0.0830338i
$761$	14.3383	−	24.8347i	0.519763	−	0.900256i	−0.479973	−	0.877283i	$-0.659354\pi$
$761$	14.3383	−	24.8347i	0.519763	−	0.900256i	0.999736	−	0.0229729i	$-0.00731314\pi$
$762$	31.3165	+	28.1445i	1.13448	+	1.01957i
$763$	−1.11578	+	0.644196i	−0.0403940	+	0.0233215i
$764$	−21.0941	+	20.3758i	−0.763160	+	0.737172i
$765$	−7.44086	−	5.79263i	−0.269025	−	0.209433i
$766$	−13.2154	−	32.7030i	−0.477492	−	1.18161i
$767$	0.253640	+	0.439317i	0.00915841	+	0.0158628i
$768$	21.8619	+	17.0310i	0.788875	+	0.614554i
$769$	−11.5424	+	19.9920i	−0.416229	+	0.720931i	−0.995557	−	0.0941645i	$-0.969982\pi$
$769$	−11.5424	+	19.9920i	−0.416229	+	0.720931i	0.579327	+	0.815095i	$0.303315\pi$
$770$	−2.79579	−	0.392732i	−0.100753	−	0.0141531i
$771$	−0.814693	−	0.548488i	−0.0293405	−	0.0197533i
$772$	−39.4929	−	11.3187i	−1.42138	−	0.407368i
$773$		−	20.0109i		−	0.719743i	−0.933002	−	0.359872i	$-0.882820\pi$
$773$		−	20.0109i		−	0.719743i	0.933002	−	0.359872i	$-0.117180\pi$
$774$	11.0134	−	38.6716i	0.395868	−	1.39002i
$775$	20.3764			0.731942
$776$	3.76471	+	35.7498i	0.135145	+	1.28334i
$777$	2.80229	+	5.73288i	0.100531	+	0.205666i
$778$	−6.76873	+	48.1854i	−0.242671	+	1.72753i
$779$	4.50097	+	2.59864i	0.161264	+	0.0931059i
$780$	1.07635	+	1.28013i	0.0385394	+	0.0458360i
$781$	−22.8780	+	13.2086i	−0.818637	+	0.472641i
$782$	4.09115	+	10.1240i	0.146299	+	0.362033i
$783$	6.85394	+	20.9085i	0.244940	+	0.747210i
$784$	0.138527	−	3.99760i	0.00494741	−	0.142771i
$785$	−6.34029	−	10.9817i	−0.226295	−	0.391954i
$786$	−12.8474	−	39.4147i	−0.458253	−	1.40588i
$787$	−26.4080	−	15.2466i	−0.941342	−	0.543484i	−0.0509611	−	0.998701i	$-0.516228\pi$
$787$	−26.4080	−	15.2466i	−0.941342	−	0.543484i	−0.890381	+	0.455217i	$0.849562\pi$
$788$	−39.6581	+	9.89351i	−1.41276	+	0.352442i
$789$	−37.7394	+	18.4474i	−1.34356	+	0.656744i
$790$	6.39721	+	4.99736i	0.227602	+	0.177798i
$791$	4.03589			0.143500
$792$	27.9222	+	0.920841i	0.992172	+	0.0327207i
$793$	0.481393			0.0170948
$794$	34.8735	+	27.2424i	1.23761	+	0.966796i
$795$	4.01977	+	2.70628i	0.142566	+	0.0959820i
$796$	7.08902	+	28.4163i	0.251264	+	1.00719i
$797$	12.4839	+	7.20758i	0.442202	+	0.255306i	0.704531	−	0.709673i	$-0.251157\pi$
$797$	12.4839	+	7.20758i	0.442202	+	0.255306i	−0.262329	+	0.964978i	$0.584491\pi$
$798$	−5.44040	−	1.15107i	−0.192588	−	0.0407474i
$799$	−6.01092	−	10.4112i	−0.212651	−	0.368322i
$800$	−24.6212	+	8.97073i	−0.870492	+	0.317163i
$801$	46.1987	+	6.41091i	1.63235	+	0.226518i
$802$	−2.83876	−	7.02483i	−0.100240	−	0.248055i
$803$	28.8000	−	16.6277i	1.01633	−	0.586778i
$804$	−41.5417	−	15.0728i	−1.46506	−	0.531575i
$805$	0.782095	+	0.451543i	0.0275652	+	0.0159148i
$806$	−0.689050	+	4.90523i	−0.0242708	+	0.172779i
$807$	23.2815	+	1.60766i	0.819548	+	0.0565924i
$808$	−47.5804	+	5.01056i	−1.67387	+	0.176271i
$809$	−7.69470			−0.270531			−0.135266	−	0.990809i	$-0.543189\pi$
$809$	−7.69470			−0.270531			−0.135266	+	0.990809i	$0.543189\pi$
$810$	7.67221	−	0.833888i	0.269574	−	0.0292998i
$811$			51.2894i			1.80102i	0.434839	+	0.900508i	$0.356805\pi$
$811$			51.2894i			1.80102i	−0.434839	+	0.900508i	$0.643195\pi$
$812$	−2.33330	+	8.14129i	−0.0818827	+	0.285703i
$813$	−2.08603	+	30.2091i	−0.0731604	+	1.05948i
$814$	−16.9874	−	2.38627i	−0.595409	−	0.0836387i
$815$	2.63184	−	4.55849i	0.0921895	−	0.159677i
$816$	14.6457	+	32.7943i	0.512701	+	1.14803i
$817$	−10.7578	−	18.6331i	−0.376369	−	0.651891i
$818$	2.54203	+	6.29053i	0.0888800	+	0.219943i
$819$	−0.328345	+	2.36614i	−0.0114733	+	0.0826798i
$820$	−1.92879	−	1.99679i	−0.0673564	−	0.0697309i
$821$	−26.1081	+	15.0735i	−0.911179	+	0.526069i	−0.880810	−	0.473469i	$-0.843001\pi$
$821$	−26.1081	+	15.0735i	−0.911179	+	0.526069i	−0.0303685	+	0.999539i	$0.509668\pi$
$822$	−1.15176	+	5.44364i	−0.0401721	+	0.189869i
$823$	16.2473	−	28.1412i	0.566347	−	0.980942i	−0.430576	−	0.902554i	$-0.641690\pi$
$823$	16.2473	−	28.1412i	0.566347	−	0.980942i	0.996923	−	0.0783873i	$-0.0249771\pi$
$824$	−23.4630	+	17.0541i	−0.817373	+	0.594107i
$825$	−14.7531	+	21.9134i	−0.513637	+	0.762928i
$826$	0.709996	+	0.554633i	0.0247039	+	0.0192982i
$827$			24.4009i			0.848502i	0.905545	+	0.424251i	$0.139463\pi$
$827$			24.4009i			0.848502i	−0.905545	+	0.424251i	$0.860537\pi$
$828$	−8.17067	−	3.61950i	−0.283951	−	0.125786i
$829$			3.83739i			0.133278i	0.997777	+	0.0666391i	$0.0212276\pi$
$829$			3.83739i			0.133278i	−0.997777	+	0.0666391i	$0.978772\pi$
$830$	−2.79819	+	3.58201i	−0.0971266	+	0.124334i
$831$	12.1956	+	24.9497i	0.423061	+	0.865494i
$832$	−1.32694	−	6.23044i	−0.0460033	−	0.216002i
$833$	2.59201	−	4.48950i	0.0898080	−	0.155552i
$834$	−6.33392	−	19.4319i	−0.219326	−	0.672870i
$835$	−11.5924	+	6.69290i	−0.401173	+	0.231617i
$836$	10.7521	−	10.3859i	0.371868	−	0.359205i
$837$	17.0254	+	15.2496i	0.588485	+	0.527102i
$838$	−25.3069	+	10.2266i	−0.874212	+	0.353273i
$839$	−9.13245	−	15.8179i	−0.315287	−	0.546094i	0.664211	−	0.747545i	$-0.268768\pi$
$839$	−9.13245	−	15.8179i	−0.315287	−	0.546094i	−0.979499	+	0.201451i	$0.935434\pi$
$840$	2.62422	+	1.39172i	0.0905443	+	0.0480190i
$841$	−5.53439	+	9.58585i	−0.190841	+	0.330546i
$842$	4.81243	−	34.2589i	0.165847	−	1.18064i
$843$	26.8121	−	13.1060i	0.923458	−	0.451395i
$844$	−4.09316	+	14.2818i	−0.140893	+	0.491599i
$845$			7.49792i			0.257936i
$846$	9.46249	+	2.69484i	0.325327	+	0.0926506i
$847$	−0.159774			−0.00548989
$848$	−8.66934	−	16.2941i	−0.297706	−	0.559543i
$849$	0.673299	−	1.00008i	0.0231076	−	0.0343227i
$850$	−33.6311	−	4.72425i	−1.15354	−	0.162040i
$851$	4.75207	+	2.74361i	0.162899	+	0.0940497i
$852$	27.3673	−	4.85391i	0.937589	−	0.166292i
$853$	−15.6393	+	9.02935i	−0.535479	+	0.309159i	−0.743245	−	0.669020i	$-0.766714\pi$
$853$	−15.6393	+	9.02935i	−0.535479	+	0.309159i	0.207766	+	0.978179i	$0.433381\pi$
$854$	0.792698	−	0.320332i	0.0271256	−	0.0109615i
$855$	2.53672	−	3.25852i	0.0867541	−	0.111439i
$856$	6.24239	−	14.0282i	0.213361	−	0.479475i
$857$	−14.6620	−	25.3954i	−0.500845	−	0.867489i	−1.00000		0.000975934i	$-0.999689\pi$
$857$	−14.6620	−	25.3954i	−0.500845	−	0.867489i	0.499155	−	0.866513i	$-0.333644\pi$
$858$	−4.77635	−	4.29255i	−0.163062	−	0.146545i
$859$	46.5183	+	26.8574i	1.58718	+	0.916361i	0.993768	+	0.111465i	$0.0355542\pi$
$859$	46.5183	+	26.8574i	1.58718	+	0.916361i	0.593415	+	0.804896i	$0.297779\pi$
$860$	2.78190	+	11.1512i	0.0948622	+	0.380254i
$861$	0.273163	−	3.95584i	0.00930938	−	0.134815i
$862$	−13.2870	+	17.0089i	−0.452557	+	0.579327i
$863$	10.7114			0.364619			0.182309	−	0.983241i	$-0.441643\pi$
$863$	10.7114			0.364619			0.182309	+	0.983241i	$0.441643\pi$
$864$	−27.2858	−	10.9309i	−0.928282	−	0.371876i
$865$	12.4242			0.422434
$866$	5.10273	−	6.53210i	0.173398	−	0.221970i
$867$	−1.17818	+	17.0619i	−0.0400131	+	0.579453i
$868$	2.12943	+	8.53582i	0.0722777	+	0.289725i
$869$	−26.9934	−	15.5846i	−0.915687	−	0.528672i
$870$	−4.67771	−	4.20390i	−0.158589	−	0.142526i
$871$	5.07903	+	8.79715i	0.172097	+	0.298080i
$872$	−1.48153	+	3.32937i	−0.0501709	+	0.112747i
$873$	−14.3445	−	35.3268i	−0.485487	−	1.19563i
$874$	−4.43352	+	1.79161i	−0.149966	+	0.0606019i
$875$	−5.05797	+	2.92022i	−0.170991	+	0.0987215i
$876$	−34.4514	+	6.11036i	−1.16401	+	0.206450i
$877$	−5.43539	−	3.13812i	−0.183540	−	0.105967i	0.405415	−	0.914133i	$-0.367127\pi$
$877$	−5.43539	−	3.13812i	−0.183540	−	0.105967i	−0.588955	+	0.808166i	$0.700460\pi$
$878$	−8.50502	−	1.19472i	−0.287031	−	0.0403199i
$879$	17.2137	−	25.5683i	0.580604	−	0.862397i
$880$	−7.04962	+	3.75077i	−0.237643	+	0.126438i
$881$	53.4782			1.80173			0.900864	−	0.434102i	$-0.142934\pi$
$881$	53.4782			1.80173			0.900864	+	0.434102i	$0.142934\pi$
$882$	1.03382	+	4.11476i	0.0348105	+	0.138551i
$883$		−	28.7678i		−	0.968114i	−0.875036	−	0.484057i	$-0.839163\pi$
$883$		−	28.7678i		−	0.968114i	0.875036	−	0.484057i	$-0.160837\pi$
$884$	2.27454	−	7.93629i	0.0765012	−	0.266926i
$885$	−0.601085	+	0.293816i	−0.0202052	+	0.00987651i
$886$	−0.959328	+	6.82929i	−0.0322293	+	0.229435i
$887$	18.1961	−	31.5165i	0.610965	−	1.05822i	−0.380113	−	0.924940i	$-0.624115\pi$
$887$	18.1961	−	31.5165i	0.610965	−	1.05822i	0.991078	−	0.133282i	$-0.0425516\pi$
$888$	15.9450	+	8.45622i	0.535079	+	0.283772i
$889$	−8.59467	−	14.8864i	−0.288256	−	0.499274i
$890$	−12.3604	+	4.99489i	−0.414322	+	0.167429i
$891$	−28.7267	+	7.26859i	−0.962382	+	0.243507i
$892$	41.2436	−	39.8392i	1.38094	−	1.33391i
$893$	4.55930	−	2.63232i	0.152571	−	0.0880871i
$894$	−13.0332	−	39.9847i	−0.435896	−	1.33729i
$895$	3.20055	−	5.54352i	0.106983	−	0.185299i
$896$	−6.33094	−	9.37652i	−0.211502	−	0.313248i
$897$	0.902096	+	1.84550i	0.0301201	+	0.0616194i
$898$	19.9830	−	25.5806i	0.666841	−	0.853636i
$899$		−	18.6265i		−	0.621228i
$900$	22.4553	−	16.3791i	0.748510	−	0.545969i
$901$		−	23.9202i		−	0.796899i
$902$	8.40040	+	6.56221i	0.279703	+	0.218498i
$903$	−9.16753	+	13.6169i	−0.305076	+	0.453144i
$904$	9.23375	−	6.71155i	0.307110	−	0.223223i
$905$	3.69533	−	6.40049i	0.122837	−	0.212760i
$906$	9.11165	−	43.0652i	0.302714	−	1.43074i
$907$	15.4111	−	8.89759i	0.511716	−	0.295440i	−0.221823	−	0.975087i	$-0.571201\pi$
$907$	15.4111	−	8.89759i	0.511716	−	0.295440i	0.733539	+	0.679647i	$0.237867\pi$
$908$	19.8690	+	20.5695i	0.659377	+	0.682622i
$909$	47.0174	−	19.0914i	1.55947	−	0.633223i
$910$	−0.255822	−	0.633059i	−0.00848041	−	0.0209857i
$911$	25.7258	+	44.5584i	0.852335	+	1.47629i	0.879096	+	0.476645i	$0.158147\pi$
$911$	25.7258	+	44.5584i	0.852335	+	1.47629i	−0.0267612	+	0.999642i	$0.508519\pi$
$912$	−14.3613	+	6.41366i	−0.475552	+	0.212378i
$913$	8.72636	−	15.1145i	0.288800	−	0.500217i
$914$	16.5116	+	2.31943i	0.546155	+	0.0767199i
$915$	−0.0437384	+	0.633402i	−0.00144595	+	0.0209396i
$916$	−1.90985	+	6.66380i	−0.0631031	+	0.220178i
$917$			16.9242i			0.558888i
$918$	−24.5648	−	29.1166i	−0.810758	−	0.960991i
$919$	51.3998			1.69552			0.847762	−	0.530377i	$-0.177950\pi$
$919$	51.3998			1.69552			0.847762	+	0.530377i	$0.177950\pi$
$920$	2.54026	−	0.267508i	0.0837500	−	0.00881949i
$921$	−49.1748	−	3.39567i	−1.62036	−	0.111891i
$922$	2.36406	−	16.8293i	0.0778562	−	0.554245i
$923$	−5.53299	−	3.19447i	−0.182121	−	0.105147i
$924$	−10.7215	−	3.89011i	−0.352710	−	0.127975i
$925$	−14.7798	+	8.53314i	−0.485958	+	0.280568i
$926$	−17.7189	−	43.8474i	−0.582280	−	1.44092i
$927$	18.8990	−	24.2766i	0.620726	−	0.797347i
$928$	8.20032	+	22.5067i	0.269189	+	0.738820i
$929$	24.0865	+	41.7191i	0.790254	+	1.36876i	0.925810	+	0.377990i	$0.123385\pi$
$929$	24.0865	+	41.7191i	0.790254	+	1.36876i	−0.135556	+	0.990770i	$0.543282\pi$
$930$	−6.39154	−	1.35231i	−0.209587	−	0.0443440i
$931$	1.96605	+	1.13510i	0.0644348	+	0.0372014i
$932$	10.7525	+	43.1014i	0.352210	+	1.41183i
$933$	21.5235	+	14.4905i	0.704647	+	0.474399i
$934$	29.0146	+	22.6656i	0.949388	+	0.741641i
$935$	−10.3490			−0.338450
$936$	3.18360	+	5.95956i	0.104059	+	0.194794i
$937$	−52.7168			−1.72218			−0.861092	−	0.508450i	$-0.830219\pi$
$937$	−52.7168			−1.72218			−0.861092	+	0.508450i	$0.830219\pi$
$938$	14.2174	+	11.1063i	0.464214	+	0.362633i
$939$	40.1158	−	19.6090i	1.30913	−	0.639915i
$940$	−2.72858	+	0.680699i	−0.0889964	+	0.0222020i
$941$	0.340550	+	0.196617i	0.0111016	+	0.00640953i	0.505541	−	0.862803i	$-0.331293\pi$
$941$	0.340550	+	0.196617i	0.0111016	+	0.00640953i	−0.494439	+	0.869212i	$0.664626\pi$
$942$	−15.8757	−	48.7052i	−0.517258	−	1.58690i
$943$	−1.70489	−	2.95296i	−0.0555189	−	0.0961615i
$944$	2.54674	+	0.0882514i	0.0828895	+	0.00287234i
$945$	−3.08346	−	0.647009i	−0.100305	−	0.0210472i
$946$	−16.5338	−	40.9146i	−0.537559	−	1.33025i
$947$	29.0638	−	16.7800i	0.944447	−	0.545277i	0.0530957	−	0.998589i	$-0.483091\pi$
$947$	29.0638	−	16.7800i	0.944447	−	0.545277i	0.891352	+	0.453312i	$0.149758\pi$
$948$	21.1049	+	25.1007i	0.685457	+	0.815233i
$949$	6.96521	+	4.02137i	0.226100	+	0.130539i
$950$	2.06885	−	14.7278i	0.0671225	−	0.477834i
$951$	24.9298	+	51.0011i	0.808404	+	1.65382i
$952$	−1.53559	−	14.5820i	−0.0497689	−	0.472606i
$953$	−58.0608			−1.88077			−0.940386	−	0.340109i	$-0.889536\pi$
$953$	−58.0608			−1.88077			−0.940386	+	0.340109i	$0.889536\pi$
$954$	13.6244	+	14.0576i	0.441105	+	0.455130i
$955$			8.89134i			0.287717i
$956$	−48.8071	−	13.9881i	−1.57854	−	0.452409i
$957$	20.0315	+	13.4861i	0.647526	+	0.435943i
$958$	−11.3837	−	1.59910i	−0.367790	−	0.0516645i
$959$	1.13578	−	1.96722i	0.0366762	−	0.0635250i
$960$	8.31838	−	1.17986i	0.268475	−	0.0380797i
$961$	5.82565	+	10.0903i	0.187924	+	0.325494i
$962$	−1.55439	−	3.84652i	−0.0501156	−	0.124017i
$963$	−2.23850	+	16.1313i	−0.0721348	+	0.519823i
$964$	6.21491	−	6.00328i	0.200169	−	0.193353i
$965$	−10.7864	+	6.22751i	−0.347225	+	0.200471i
$966$	2.71350	+	2.43865i	0.0873055	+	0.0784623i
$967$	−15.1198	+	26.1883i	−0.486220	+	0.842157i	−0.999875	−	0.0158396i	$-0.994958\pi$
$967$	−15.1198	+	26.1883i	−0.486220	+	0.842157i	0.513655	+	0.857997i	$0.328291\pi$
$968$	−0.365548	+	0.265698i	−0.0117492	+	0.00853987i
$969$	−20.3357	−	1.40425i	−0.653278	−	0.0451109i
$970$	8.58829	+	6.70898i	0.275753	+	0.215412i
$971$		−	13.7262i		−	0.440496i	−0.975444	−	0.220248i	$-0.929313\pi$
$971$		−	13.7262i		−	0.440496i	0.975444	−	0.220248i	$-0.0706867\pi$
$972$	31.0204	+	3.11990i	0.994980	+	0.100071i
$973$			8.34382i			0.267491i
$974$	8.02573	−	10.2739i	0.257161	−	0.329196i
$975$	−6.37370	−	0.440124i	−0.204122	−	0.0140953i
$976$	1.28092	−	2.05112i	0.0410012	−	0.0656548i
$977$	−23.9997	+	41.5686i	−0.767817	+	1.32990i	0.170927	+	0.985284i	$0.445324\pi$
$977$	−23.9997	+	41.5686i	−0.767817	+	1.32990i	−0.938744	+	0.344614i	$0.888010\pi$
$978$	14.2138	−	15.8158i	0.454508	−	0.505734i
$979$	44.3303	−	25.5941i	1.41680	−	0.817991i
$980$	−0.842510	−	0.872210i	−0.0269130	−	0.0278617i
$981$	0.531272	−	3.82849i	0.0169622	−	0.122234i
$982$	4.29179	−	1.73433i	0.136956	−	0.0553447i
$983$	9.45552	+	16.3774i	0.301584	+	0.522359i	0.976495	−	0.215540i	$-0.0691512\pi$
$983$	9.45552	+	16.3774i	0.301584	+	0.522359i	−0.674911	+	0.737899i	$0.735818\pi$
$984$	−5.95346	−	9.50488i	−0.189789	−	0.303004i
$985$	−6.19577	+	10.7314i	−0.197414	+	0.341931i
$986$	−4.31853	+	30.7429i	−0.137530	+	0.979052i
$987$	−3.33191	−	2.24319i	−0.106056	−	0.0714014i
$988$	3.47548	+	0.996074i	0.110570	+	0.0316893i
$989$			14.1158i			0.448857i
$990$	6.08197	−	5.89455i	0.193298	−	0.187341i
$991$	1.31697			0.0418349			0.0209175	−	0.999781i	$-0.493341\pi$
$991$	1.31697			0.0418349			0.0209175	+	0.999781i	$0.493341\pi$
$992$	19.0668	+	15.9880i	0.605370	+	0.507620i
$993$	−18.7010	−	38.2582i	−0.593457	−	1.21409i
$994$	−11.2367	−	1.57845i	−0.356407	−	0.0500654i
$995$	7.68939	+	4.43947i	0.243770	+	0.140741i
$996$	−14.0547	+	11.8174i	−0.445341	+	0.374448i
$997$	2.88256	−	1.66425i	0.0912916	−	0.0527072i	−0.453659	−	0.891175i	$-0.649882\pi$
$997$	2.88256	−	1.66425i	0.0912916	−	0.0527072i	0.544951	+	0.838468i	$0.316548\pi$
$998$	28.3895	−	11.4723i	0.898655	−	0.363150i
$999$	−18.7354	−	3.93128i	−0.592761	−	0.124380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.11	✓	72
8.5	even	2	inner	504.2.cs.a.85.35	yes	72
9.7	even	3	inner	504.2.cs.a.421.35	yes	72
72.61	even	6	inner	504.2.cs.a.421.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.11	✓	72	1.1	even	1	trivial
504.2.cs.a.85.35	yes	72	8.5	even	2	inner
504.2.cs.a.421.11	yes	72	72.61	even	6	inner
504.2.cs.a.421.35	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.870602 + 1.11447i) q^{2} +(-0.119319 + 1.72794i) q^{3} +(-0.484104 - 1.94053i) q^{4} +(-0.525102 - 0.303168i) q^{5} +(-1.82186 - 1.63732i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.58413 + 1.14991i) q^{8} +(-2.97153 - 0.412353i) q^{9} +O(q^{10})\)	\(q+(-0.870602 + 1.11447i) q^{2} +(-0.119319 + 1.72794i) q^{3} +(-0.484104 - 1.94053i) q^{4} +(-0.525102 - 0.303168i) q^{5} +(-1.82186 - 1.63732i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.58413 + 1.14991i) q^{8} +(-2.97153 - 0.412353i) q^{9} +(0.795028 - 0.321274i) q^{10} +(-2.85135 + 1.64622i) q^{11} +(3.41087 - 0.604957i) q^{12} +(-0.689592 - 0.398136i) q^{13} +(-1.40046 - 0.196727i) q^{14} +(0.586510 - 0.871169i) q^{15} +(-3.53129 + 1.87883i) q^{16} -5.18403 q^{17} +(3.04657 - 2.95269i) q^{18} -2.27020i q^{19} +(-0.334102 + 1.16574i) q^{20} +(-1.55610 + 0.760634i) q^{21} +(0.647713 - 4.61096i) q^{22} +(-0.744707 + 1.28987i) q^{23} +(-2.29530 + 4.32800i) q^{24} +(-2.31618 - 4.01174i) q^{25} +(1.04407 - 0.421914i) q^{26} +(1.06708 - 5.08540i) q^{27} +(1.43849 - 1.38951i) q^{28} +(-3.66721 + 2.11726i) q^{29} +(0.460279 + 1.41209i) q^{30} +(-2.19936 + 3.80940i) q^{31} +(0.980438 - 5.57124i) q^{32} +(-2.50435 - 5.12337i) q^{33} +(4.51323 - 5.77746i) q^{34} -0.606336i q^{35} +(0.638345 + 5.96595i) q^{36} -3.68415i q^{37} +(2.53008 + 1.97644i) q^{38} +(0.770236 - 1.14407i) q^{39} +(-1.00832 - 1.38724i) q^{40} +(-1.14467 + 1.98263i) q^{41} +(0.507034 - 2.39644i) q^{42} +(8.20769 - 4.73871i) q^{43} +(4.57489 + 4.73617i) q^{44} +(1.43534 + 1.11740i) q^{45} +(-0.789183 - 1.95292i) q^{46} +(1.15951 + 2.00832i) q^{47} +(-2.82515 - 6.32602i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.48745 + 0.911308i) q^{50} +(0.618556 - 8.95767i) q^{51} +(-0.438760 + 1.53091i) q^{52} +4.61422i q^{53} +(4.73855 + 5.61660i) q^{54} +1.99633 q^{55} +(0.296216 + 2.81287i) q^{56} +(3.92276 + 0.270879i) q^{57} +(0.833045 - 5.93030i) q^{58} +(-0.551717 - 0.318534i) q^{59} +(-1.97446 - 0.716402i) q^{60} +(-0.523563 + 0.302279i) q^{61} +(-2.33071 - 5.76760i) q^{62} +(-1.12865 - 2.77959i) q^{63} +(5.35543 + 5.94301i) q^{64} +(0.241404 + 0.418125i) q^{65} +(7.89015 + 1.66938i) q^{66} +(-11.0479 - 6.37851i) q^{67} +(2.50961 + 10.0597i) q^{68} +(-2.13995 - 1.44071i) q^{69} +(0.675746 + 0.527877i) q^{70} +8.02356 q^{71} +(-7.20464 - 4.48255i) q^{72} -10.1005 q^{73} +(4.10588 + 3.20742i) q^{74} +(7.20839 - 3.52353i) q^{75} +(-4.40539 + 1.09901i) q^{76} +(-2.85135 - 1.64622i) q^{77} +(0.604462 + 1.85443i) q^{78} +(4.73344 + 8.19857i) q^{79} +(2.42389 + 0.0839942i) q^{80} +(8.65993 + 2.45063i) q^{81} +(-1.21304 - 3.00179i) q^{82} +(-4.59066 + 2.65042i) q^{83} +(2.22934 + 2.65142i) q^{84} +(2.72215 + 1.57163i) q^{85} +(-1.86446 + 13.2728i) q^{86} +(-3.22093 - 6.58933i) q^{87} +(-9.26124 + 0.975277i) q^{88} -15.5471 q^{89} +(-2.49492 + 0.626842i) q^{90} -0.796273i q^{91} +(2.86354 + 0.820693i) q^{92} +(-6.31997 - 4.25488i) q^{93} +(-3.24769 - 0.456212i) q^{94} +(-0.688253 + 1.19209i) q^{95} +(9.50977 + 2.35889i) q^{96} +(6.35467 + 11.0066i) q^{97} +(-0.529862 - 1.31120i) q^{98} +(9.15167 - 3.71604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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