LMFDB - Embedded newform 603.2.k.a.365.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(38,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("603.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.k (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$66$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.19
Character	$\chi$	$=$	603.365
Dual form			603.2.k.a.38.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.714188 + 1.23701i) q^{2} +(1.73068 + 0.0688806i) q^{3} +(-0.0201279 - 0.0348626i) q^{4} +(-1.51065 + 2.61653i) q^{5} +(-1.32124 + 2.09167i) q^{6} +0.535303i q^{7} -2.79925 q^{8} +(2.99051 + 0.238421i) q^{9} +O(q^{10})$	\(q+(-0.714188 + 1.23701i) q^{2} +(1.73068 + 0.0688806i) q^{3} +(-0.0201279 - 0.0348626i) q^{4} +(-1.51065 + 2.61653i) q^{5} +(-1.32124 + 2.09167i) q^{6} +0.535303i q^{7} -2.79925 q^{8} +(2.99051 + 0.238421i) q^{9} +(-2.15778 - 3.73738i) q^{10} -1.78908 q^{11} +(-0.0324336 - 0.0617224i) q^{12} +1.04905i q^{13} +(-0.662174 - 0.382307i) q^{14} +(-2.79469 + 4.42432i) q^{15} +(2.03945 - 3.53242i) q^{16} +(-3.23605 + 1.86833i) q^{17} +(-2.43071 + 3.52901i) q^{18} +(0.335495 + 0.581095i) q^{19} +0.121625 q^{20} +(-0.0368720 + 0.926438i) q^{21} +(1.27774 - 2.21311i) q^{22} -0.271857i q^{23} +(-4.84461 - 0.192814i) q^{24} +(-2.06415 - 3.57521i) q^{25} +(-1.29768 - 0.749217i) q^{26} +(5.15920 + 0.618619i) q^{27} +(0.0186620 - 0.0107745i) q^{28} -6.13641i q^{29} +(-3.47699 - 6.61685i) q^{30} +(1.36890 - 0.790333i) q^{31} +(0.113843 + 0.197183i) q^{32} +(-3.09632 - 0.123233i) q^{33} -5.33736i q^{34} +(-1.40063 - 0.808657i) q^{35} +(-0.0518808 - 0.109056i) q^{36} +(1.65647 + 2.86910i) q^{37} -0.958426 q^{38} +(-0.0722591 + 1.81557i) q^{39} +(4.22870 - 7.32432i) q^{40} +(5.93039 + 10.2717i) q^{41} +(-1.11968 - 0.707262i) q^{42} +(-5.72612 + 3.30597i) q^{43} +(0.0360104 + 0.0623719i) q^{44} +(-5.14146 + 7.46459i) q^{45} +(0.336290 + 0.194157i) q^{46} +3.47005i q^{47} +(3.77294 - 5.97302i) q^{48} +6.71345 q^{49} +5.89675 q^{50} +(-5.72925 + 3.01058i) q^{51} +(0.0365725 - 0.0211151i) q^{52} -3.66144 q^{53} +(-4.44987 + 5.94016i) q^{54} +(2.70268 - 4.68118i) q^{55} -1.49845i q^{56} +(0.540609 + 1.02880i) q^{57} +(7.59080 + 4.38255i) q^{58} +(4.08512 + 2.35855i) q^{59} +(0.210494 + 0.00837762i) q^{60} +(-9.59087 - 5.53729i) q^{61} +2.25778i q^{62} +(-0.127627 + 1.60083i) q^{63} +7.83256 q^{64} +(-2.74486 - 1.58475i) q^{65} +(2.36380 - 3.74217i) q^{66} +(4.97082 + 6.50315i) q^{67} +(0.130270 + 0.0752112i) q^{68} +(0.0187257 - 0.470498i) q^{69} +(2.00063 - 1.15507i) q^{70} +(-3.36614 - 1.94344i) q^{71} +(-8.37119 - 0.667399i) q^{72} +(-2.18166 - 3.77875i) q^{73} -4.73213 q^{74} +(-3.32612 - 6.32972i) q^{75} +(0.0135056 - 0.0233924i) q^{76} -0.957699i q^{77} +(-2.19427 - 1.38604i) q^{78} -0.302780i q^{79} +(6.16179 + 10.6725i) q^{80} +(8.88631 + 1.42600i) q^{81} -16.9417 q^{82} +(11.3590 + 6.55813i) q^{83} +(0.0330402 - 0.0173618i) q^{84} -11.2896i q^{85} -9.44434i q^{86} +(0.422680 - 10.6202i) q^{87} +5.00808 q^{88} -0.896935i q^{89} +(-5.56179 - 11.6911i) q^{90} -0.561558 q^{91} +(-0.00947763 + 0.00547191i) q^{92} +(2.42356 - 1.27352i) q^{93} +(-4.29248 - 2.47826i) q^{94} -2.02727 q^{95} +(0.183445 + 0.349102i) q^{96} +(-4.54499 - 2.62405i) q^{97} +(-4.79466 + 8.30460i) q^{98} +(-5.35026 - 0.426554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9	$ 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9} - 6 q^{11} + 6 q^{12} + 4 q^{15} - 57 q^{16} + 9 q^{17} - 4 q^{19} - 30 q^{20} - 6 q^{21} - 11 q^{24} - 57 q^{25} + 36 q^{26} - 24 q^{28} + 45 q^{30} + 15 q^{32} - q^{33} + 15 q^{35} - q^{36} - 4 q^{37} + 14 q^{39} - 12 q^{40} + 3 q^{41} + 42 q^{42} + 3 q^{43} + 6 q^{44} - 9 q^{45} - 24 q^{46} - 21 q^{48} - 120 q^{49} - 24 q^{50} + 18 q^{52} - 60 q^{53} - 16 q^{54} - 9 q^{57} + 12 q^{58} + 12 q^{59} - 13 q^{60} + 18 q^{61} + 24 q^{63} + 84 q^{64} + 18 q^{65} - 30 q^{66} - 14 q^{67} - 39 q^{68} - 18 q^{69} + 45 q^{70} - 30 q^{71} + 39 q^{72} + 14 q^{73} + 30 q^{74} + 24 q^{75} - 7 q^{76} - 21 q^{78} + 18 q^{80} - 3 q^{81} - 24 q^{82} - 63 q^{83} + 129 q^{84} - 18 q^{87} - 30 q^{88} - 35 q^{90} + 42 q^{91} - 12 q^{92} - 28 q^{93} - 6 q^{94} + 24 q^{95} + 120 q^{96} - 39 q^{97} + 21 q^{98} - 72 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9 - 6 * q^11 + 6 * q^12 + 4 * q^15 - 57 * q^16 + 9 * q^17 - 4 * q^19 - 30 * q^20 - 6 * q^21 - 11 * q^24 - 57 * q^25 + 36 * q^26 - 24 * q^28 + 45 * q^30 + 15 * q^32 - q^33 + 15 * q^35 - q^36 - 4 * q^37 + 14 * q^39 - 12 * q^40 + 3 * q^41 + 42 * q^42 + 3 * q^43 + 6 * q^44 - 9 * q^45 - 24 * q^46 - 21 * q^48 - 120 * q^49 - 24 * q^50 + 18 * q^52 - 60 * q^53 - 16 * q^54 - 9 * q^57 + 12 * q^58 + 12 * q^59 - 13 * q^60 + 18 * q^61 + 24 * q^63 + 84 * q^64 + 18 * q^65 - 30 * q^66 - 14 * q^67 - 39 * q^68 - 18 * q^69 + 45 * q^70 - 30 * q^71 + 39 * q^72 + 14 * q^73 + 30 * q^74 + 24 * q^75 - 7 * q^76 - 21 * q^78 + 18 * q^80 - 3 * q^81 - 24 * q^82 - 63 * q^83 + 129 * q^84 - 18 * q^87 - 30 * q^88 - 35 * q^90 + 42 * q^91 - 12 * q^92 - 28 * q^93 - 6 * q^94 + 24 * q^95 + 120 * q^96 - 39 * q^97 + 21 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.714188	+	1.23701i	−0.505007	+	0.874698i	0.494976	+	0.868906i	$0.335177\pi$
$2$	−0.714188	+	1.23701i	−0.505007	+	0.874698i	−0.999983	+	0.00579116i	$0.998157\pi$
$3$	1.73068	+	0.0688806i	0.999209	+	0.0397683i
$3$	1.73068	+	0.0688806i	0.999209	+	0.0397683i
$4$	−0.0201279	−	0.0348626i	−0.0100640	−	0.0174313i
$5$	−1.51065	+	2.61653i	−0.675585	+	1.17015i	0.300713	+	0.953715i	$0.402775\pi$
$5$	−1.51065	+	2.61653i	−0.675585	+	1.17015i	−0.976298	+	0.216432i	$0.930558\pi$
$6$	−1.32124	+	2.09167i	−0.539393	+	0.853922i
$7$			0.535303i			0.202325i	0.994870	+	0.101163i	$0.0322563\pi$
$7$			0.535303i			0.202325i	−0.994870	+	0.101163i	$0.967744\pi$
$8$	−2.79925			−0.989684
$9$	2.99051	+	0.238421i	0.996837	+	0.0794736i
$10$	−2.15778	−	3.73738i	−0.682350	−	1.18186i
$11$	−1.78908			−0.539428			−0.269714	−	0.962941i	$-0.586929\pi$
$11$	−1.78908			−0.539428			−0.269714	+	0.962941i	$0.586929\pi$
$12$	−0.0324336	−	0.0617224i	−0.00936278	−	0.0178177i
$13$			1.04905i			0.290954i	0.989362	+	0.145477i	$0.0464716\pi$
$13$			1.04905i			0.290954i	−0.989362	+	0.145477i	$0.953528\pi$
$14$	−0.662174	−	0.382307i	−0.176974	−	0.102176i
$15$	−2.79469	+	4.42432i	−0.721585	+	1.14235i
$16$	2.03945	−	3.53242i	0.509861	−	0.883106i
$17$	−3.23605	+	1.86833i	−0.784856	+	0.453137i	−0.838149	−	0.545442i	$-0.816362\pi$
$17$	−3.23605	+	1.86833i	−0.784856	+	0.453137i	0.0532923	+	0.998579i	$0.483028\pi$
$18$	−2.43071	+	3.52901i	−0.572925	+	0.831796i
$19$	0.335495	+	0.581095i	0.0769679	+	0.133312i	0.901940	−	0.431861i	$-0.142143\pi$
$19$	0.335495	+	0.581095i	0.0769679	+	0.133312i	−0.824972	+	0.565173i	$0.808809\pi$
$20$	0.121625			0.0271962
$21$	−0.0368720	+	0.926438i	−0.00804613	+	0.202165i
$22$	1.27774	−	2.21311i	0.272415	−	0.471836i
$23$		−	0.271857i		−	0.0566861i	−0.999598	−	0.0283430i	$-0.990977\pi$
$23$		−	0.271857i		−	0.0566861i	0.999598	−	0.0283430i	$-0.00902308\pi$
$24$	−4.84461	−	0.192814i	−0.988901	−	0.0393580i
$25$	−2.06415	−	3.57521i	−0.412830	−	0.715042i
$26$	−1.29768	−	0.749217i	−0.254496	−	0.146934i
$27$	5.15920	+	0.618619i	0.992888	+	0.119053i
$28$	0.0186620	−	0.0107745i	0.00352679	−	0.00203619i
$29$		−	6.13641i		−	1.13950i	−0.821817	−	0.569751i	$-0.807039\pi$
$29$		−	6.13641i		−	1.13950i	0.821817	−	0.569751i	$-0.192961\pi$
$30$	−3.47699	−	6.61685i	−0.634809	−	1.20807i
$31$	1.36890	−	0.790333i	0.245861	−	0.141948i	−0.372006	−	0.928230i	$-0.621330\pi$
$31$	1.36890	−	0.790333i	0.245861	−	0.141948i	0.617868	+	0.786282i	$0.287997\pi$
$32$	0.113843	+	0.197183i	0.0201249	+	0.0348573i
$33$	−3.09632	−	0.123233i	−0.539001	−	0.0214521i
$34$		−	5.33736i		−	0.915349i
$35$	−1.40063	−	0.808657i	−0.236750	−	0.136688i
$36$	−0.0518808	−	0.109056i	−0.00864679	−	0.0181760i
$37$	1.65647	+	2.86910i	0.272323	+	0.471676i	0.969456	−	0.245265i	$-0.0788749\pi$
$37$	1.65647	+	2.86910i	0.272323	+	0.471676i	−0.697134	+	0.716941i	$0.745542\pi$
$38$	−0.958426			−0.155477
$39$	−0.0722591	+	1.81557i	−0.0115707	+	0.290723i
$40$	4.22870	−	7.32432i	0.668616	−	1.15808i
$41$	5.93039	+	10.2717i	0.926172	+	1.60418i	0.789666	+	0.613537i	$0.210254\pi$
$41$	5.93039	+	10.2717i	0.926172	+	1.60418i	0.136506	+	0.990639i	$0.456413\pi$
$42$	−1.11968	−	0.707262i	−0.172770	−	0.109133i
$43$	−5.72612	+	3.30597i	−0.873225	+	0.504156i	−0.868418	−	0.495832i	$-0.834863\pi$
$43$	−5.72612	+	3.30597i	−0.873225	+	0.504156i	−0.00480609	+	0.999988i	$0.501530\pi$
$44$	0.0360104	+	0.0623719i	0.00542877	+	0.00940291i
$45$	−5.14146	+	7.46459i	−0.766444	+	1.11275i
$46$	0.336290	+	0.194157i	0.0495832	+	0.0286269i
$47$			3.47005i			0.506158i	0.967446	+	0.253079i	$0.0814433\pi$
$47$			3.47005i			0.506158i	−0.967446	+	0.253079i	$0.918557\pi$
$48$	3.77294	−	5.97302i	0.544578	−	0.862131i
$49$	6.71345			0.959064
$50$	5.89675			0.833927
$51$	−5.72925	+	3.01058i	−0.802256	+	0.421566i
$52$	0.0365725	−	0.0211151i	0.00507169	−	0.00292814i
$53$	−3.66144			−0.502937			−0.251468	−	0.967866i	$-0.580913\pi$
$53$	−3.66144			−0.502937			−0.251468	+	0.967866i	$0.580913\pi$
$54$	−4.44987	+	5.94016i	−0.605551	+	0.808354i
$55$	2.70268	−	4.68118i	0.364429	−	0.631210i
$56$		−	1.49845i		−	0.200238i
$57$	0.540609	+	1.02880i	0.0716054	+	0.136268i
$58$	7.59080	+	4.38255i	0.996720	+	0.575457i
$59$	4.08512	+	2.35855i	0.531837	+	0.307056i	0.741764	−	0.670661i	$-0.233989\pi$
$59$	4.08512	+	2.35855i	0.531837	+	0.307056i	−0.209927	+	0.977717i	$0.567323\pi$
$60$	0.210494	+	0.00837762i	0.0271747	+	0.00108155i
$61$	−9.59087	−	5.53729i	−1.22799	−	0.708978i	−0.261377	−	0.965237i	$-0.584177\pi$
$61$	−9.59087	−	5.53729i	−1.22799	−	0.708978i	−0.966608	+	0.256259i	$0.917510\pi$
$62$			2.25778i			0.286739i
$63$	−0.127627	+	1.60083i	−0.0160795	+	0.201685i
$64$	7.83256			0.979070
$65$	−2.74486	−	1.58475i	−0.340458	−	0.196564i
$66$	2.36380	−	3.74217i	0.290963	−	0.460629i
$67$	4.97082	+	6.50315i	0.607282	+	0.794486i
$67$	4.97082	+	6.50315i	0.607282	+	0.794486i
$68$	0.130270	+	0.0752112i	0.0157975	+	0.00912070i
$69$	0.0187257	−	0.470498i	0.00225431	−	0.0566412i
$70$	2.00063	−	1.15507i	0.239121	−	0.138057i
$71$	−3.36614	−	1.94344i	−0.399487	−	0.230644i	0.286776	−	0.957998i	$-0.407417\pi$
$71$	−3.36614	−	1.94344i	−0.399487	−	0.230644i	−0.686263	+	0.727354i	$0.740750\pi$
$72$	−8.37119	−	0.667399i	−0.986554	−	0.0786538i
$73$	−2.18166	−	3.77875i	−0.255344	−	0.442269i	0.709645	−	0.704560i	$-0.248855\pi$
$73$	−2.18166	−	3.77875i	−0.255344	−	0.442269i	−0.964989	+	0.262291i	$0.915522\pi$
$74$	−4.73213			−0.550099
$75$	−3.32612	−	6.32972i	−0.384067	−	0.730894i
$76$	0.0135056	−	0.0233924i	0.00154920	−	0.00268330i
$77$		−	0.957699i		−	0.109140i
$78$	−2.19427	−	1.38604i	−0.248452	−	0.156938i
$79$		−	0.302780i		−	0.0340654i	−0.999855	−	0.0170327i	$-0.994578\pi$
$79$		−	0.302780i		−	0.0340654i	0.999855	−	0.0170327i	$-0.00542194\pi$
$80$	6.16179	+	10.6725i	0.688909	+	1.19323i
$81$	8.88631	+	1.42600i	0.987368	+	0.158444i
$82$	−16.9417			−1.87089
$83$	11.3590	+	6.55813i	1.24681	+	0.719849i	0.970473	−	0.241211i	$-0.0775445\pi$
$83$	11.3590	+	6.55813i	1.24681	+	0.719849i	0.276342	+	0.961059i	$0.410878\pi$
$84$	0.0330402	−	0.0173618i	0.00360498	−	0.00189433i
$85$		−	11.2896i		−	1.22453i
$86$		−	9.44434i		−	1.01841i
$87$	0.422680	−	10.6202i	0.0453160	−	1.13860i
$88$	5.00808			0.533863
$89$		−	0.896935i		−	0.0950749i	−0.998869	−	0.0475375i	$-0.984863\pi$
$89$		−	0.896935i		−	0.0950749i	0.998869	−	0.0475375i	$-0.0151373\pi$
$90$	−5.56179	−	11.6911i	−0.586265	−	1.23236i
$91$	−0.561558			−0.0588673
$92$	−0.00947763	+	0.00547191i	−0.000988111	+	0.000570486i
$93$	2.42356	−	1.27352i	0.251312	−	0.132058i
$94$	−4.29248	−	2.47826i	−0.442735	−	0.255613i
$95$	−2.02727			−0.207993
$96$	0.183445	+	0.349102i	0.0187227	+	0.0356300i
$97$	−4.54499	−	2.62405i	−0.461474	−	0.266432i	0.251190	−	0.967938i	$-0.419178\pi$
$97$	−4.54499	−	2.62405i	−0.461474	−	0.266432i	−0.712664	+	0.701506i	$0.752512\pi$
$98$	−4.79466	+	8.30460i	−0.484334	+	0.838891i
$99$	−5.35026	−	0.426554i	−0.537721	−	0.0428703i
$100$	−0.0830939	+	0.143923i	−0.00830939	+	0.0143923i
$101$	2.66618			0.265295			0.132647	−	0.991163i	$-0.457652\pi$
$101$	2.66618			0.265295			0.132647	+	0.991163i	$0.457652\pi$
$102$	0.367641	−	9.23726i	0.0364018	−	0.914625i
$103$	7.74140	+	13.4085i	0.762783	+	1.32118i	0.941411	+	0.337262i	$0.109501\pi$
$103$	7.74140	+	13.4085i	0.762783	+	1.32118i	−0.178628	+	0.983917i	$0.557166\pi$
$104$		−	2.93655i		−	0.287952i
$105$	−2.36835	−	1.49600i	−0.231127	−	0.145995i
$106$	2.61495	−	4.52923i	0.253987	−	0.439918i
$107$		−	6.95278i		−	0.672151i	−0.941835	−	0.336076i	$-0.890900\pi$
$107$		−	6.95278i		−	0.672151i	0.941835	−	0.336076i	$-0.109100\pi$
$108$	−0.0822772	−	0.192314i	−0.00791713	−	0.0185054i
$109$			5.66726i			0.542825i	0.962463	+	0.271413i	$0.0874908\pi$
$109$			5.66726i			0.542825i	−0.962463	+	0.271413i	$0.912509\pi$
$110$	3.86044	+	6.68648i	0.368078	+	0.637531i
$111$	2.66920	+	5.07959i	0.253349	+	0.482133i
$112$	1.89092	+	1.09172i	0.178675	+	0.103158i
$113$	−1.81014	−	3.13525i	−0.170283	−	0.294939i	0.768236	−	0.640167i	$-0.221135\pi$
$113$	−1.81014	−	3.13525i	−0.170283	−	0.294939i	−0.938519	+	0.345228i	$0.887802\pi$
$114$	−1.65873	−	0.0660170i	−0.155354	−	0.00618306i
$115$	0.711321	+	0.410682i	0.0663311	+	0.0382963i
$116$	−0.213931	+	0.123513i	−0.0198630	+	0.0114679i
$117$	−0.250115	+	3.13719i	−0.0231231	+	0.290033i
$118$	−5.83509	+	3.36889i	−0.537163	+	0.310131i
$119$	−1.00012	−	1.73226i	−0.0916811	−	0.158796i
$120$	7.82303	−	12.3848i	0.714141	−	1.13057i
$121$	−7.79920			−0.709018
$122$	13.6994	−	7.90933i	1.24028	−	0.716077i
$123$	9.55609	+	18.1856i	0.861644	+	1.63974i
$124$	−0.0551061	−	0.0318155i	−0.00494867	−	0.00285712i
$125$	−2.63369			−0.235564
$126$	−1.88909	−	1.30117i	−0.168294	−	0.115917i
$127$	7.74700	−	13.4182i	0.687435	−	1.19067i	−0.285230	−	0.958459i	$-0.592070\pi$
$127$	7.74700	−	13.4182i	0.687435	−	1.19067i	0.972665	−	0.232213i	$-0.0745968\pi$
$128$	−5.82160	+	10.0833i	−0.514562	+	0.891247i
$129$	−10.1378	+	5.32717i	−0.892583	+	0.469031i
$130$	3.92069	−	2.26361i	0.343868	−	0.198532i
$131$	14.4825	+	8.36149i	1.26534	+	0.730547i	0.974103	−	0.226103i	$-0.0725986\pi$
$131$	14.4825	+	8.36149i	1.26534	+	0.730547i	0.291241	+	0.956650i	$0.405932\pi$
$132$	0.0580263	+	0.110426i	0.00505054	+	0.00961137i
$133$	−0.311062	+	0.179592i	−0.0269725	+	0.0155726i
$134$	−11.5946	+	1.50448i	−1.00162	+	0.129967i
$135$	−9.41239	+	12.5647i	−0.810090	+	1.08139i
$136$	9.05850	−	5.22993i	0.776760	−	0.448463i
$137$	8.00960	+	13.8730i	0.684307	+	1.18525i	0.973654	+	0.228030i	$0.0732284\pi$
$137$	8.00960	+	13.8730i	0.684307	+	1.18525i	−0.289347	+	0.957224i	$0.593438\pi$
$138$	0.568636	+	0.359187i	0.0484055	+	0.0305761i
$139$	1.95994	+	1.13157i	0.166240	+	0.0959786i	0.580812	−	0.814038i	$-0.302735\pi$
$139$	1.95994	+	1.13157i	0.166240	+	0.0959786i	−0.414572	+	0.910017i	$0.636069\pi$
$140$			0.0651063i			0.00550248i
$141$	−0.239019	+	6.00554i	−0.0201290	+	0.505758i
$142$	4.80811	−	2.77596i	0.403487	−	0.232953i
$143$		−	1.87683i		−	0.156948i
$144$	6.94119	−	10.0775i	0.578432	−	0.839792i
$145$	16.0561	+	9.26999i	1.33339	+	0.769831i
$146$	6.23246			0.515802
$147$	11.6188	+	0.462427i	0.958306	+	0.0381403i
$148$	0.0666827	−	0.115498i	0.00548128	−	0.00949386i
$149$	3.56355	+	2.05742i	0.291937	+	0.168550i	0.638815	−	0.769360i	$-0.279425\pi$
$149$	3.56355	+	2.05742i	0.291937	+	0.168550i	−0.346878	+	0.937910i	$0.612758\pi$
$150$	10.2054	+	0.406172i	0.833267	+	0.0331638i
$151$	−3.66358	+	6.34550i	−0.298138	+	0.516389i	−0.975710	−	0.219067i	$-0.929699\pi$
$151$	−3.66358	+	6.34550i	−0.298138	+	0.516389i	0.677572	+	0.735456i	$0.263032\pi$
$152$	−0.939135	−	1.62663i	−0.0761739	−	0.131937i
$153$	−10.1229	+	4.81573i	−0.818386	+	0.389328i
$154$	1.18468	+	0.683977i	0.0954644	+	0.0551164i
$155$			4.77568i			0.383592i
$156$	0.0647497	−	0.0340244i	0.00518413	−	0.00272413i
$157$	0.208426			0.0166342			0.00831710	−	0.999965i	$-0.497353\pi$
$157$	0.208426			0.0166342			0.00831710	+	0.999965i	$0.497353\pi$
$158$	0.374542	+	0.216242i	0.0297969	+	0.0172033i
$159$	−6.33677	−	0.252202i	−0.502539	−	0.0200009i
$160$	−0.687912			−0.0543842
$161$	0.145526			0.0114690
$162$	−8.11047	+	9.97402i	−0.637219	+	0.783633i
$163$	1.23045	−	2.13120i	0.0963762	−	0.166928i	−0.813806	−	0.581137i	$-0.802608\pi$
$163$	1.23045	−	2.13120i	0.0963762	−	0.166928i	0.910182	+	0.414208i	$0.135941\pi$
$164$	0.238733	−	0.413497i	0.0186419	−	0.0322887i
$165$	4.99992	−	7.91546i	0.389243	−	0.616218i
$166$	−16.2249	+	9.36748i	−1.25930	+	0.727057i
$167$	8.10681	−	4.68047i	0.627323	−	0.362185i	−0.152391	−	0.988320i	$-0.548697\pi$
$167$	8.10681	−	4.68047i	0.627323	−	0.362185i	0.779715	+	0.626135i	$0.215364\pi$
$168$	0.103214	−	2.59333i	0.00796313	−	0.200080i
$169$	11.8995			0.915346
$170$	13.9653	+	8.06290i	1.07109	+	0.618396i
$171$	0.864757	+	1.81776i	0.0661296	+	0.139008i
$172$	0.230509	+	0.133085i	0.0175762	+	0.0101476i
$173$	16.1404	+	9.31865i	1.22713	+	0.708484i	0.966429	−	0.256936i	$-0.0827128\pi$
$173$	16.1404	+	9.31865i	1.22713	+	0.708484i	0.260702	+	0.965419i	$0.416046\pi$
$174$	12.8354	+	8.10765i	0.973047	+	0.614639i
$175$	1.91382	−	1.10494i	0.144671	−	0.0835259i
$176$	−3.64873	+	6.31979i	−0.275033	+	0.476372i
$177$	6.90758	+	4.36328i	0.519206	+	0.327964i
$178$	1.10952	+	0.640580i	0.0831618	+	0.0480135i
$179$	8.17375			0.610935			0.305467	−	0.952203i	$-0.401187\pi$
$179$	8.17375			0.610935			0.305467	+	0.952203i	$0.401187\pi$
$180$	0.363721	+	0.0289980i	0.0271102	+	0.00216138i
$181$	9.32448	−	16.1505i	0.693083	−	1.20045i	−0.277740	−	0.960656i	$-0.589585\pi$
$181$	9.32448	−	16.1505i	0.693083	−	1.20045i	0.970823	−	0.239798i	$-0.0770813\pi$
$182$	0.401058	−	0.694653i	0.0297284	−	0.0514911i
$183$	−16.2173	−	10.2439i	−1.19882	−	0.757252i
$184$			0.760996i			0.0561013i
$185$	−10.0094			−0.735908
$186$	−0.155518	+	3.90750i	−0.0114031	+	0.286512i
$187$	5.78954	−	3.34259i	0.423373	−	0.244435i
$188$	0.120975	−	0.0698448i	0.00882298	−	0.00509395i
$189$	−0.331148	+	2.76173i	−0.0240875	+	0.200886i
$190$	1.44785	−	2.50775i	0.105038	−	0.181931i
$191$	8.15165	−	14.1191i	0.589833	−	1.02162i	−0.404421	−	0.914573i	$-0.632527\pi$
$191$	8.15165	−	14.1191i	0.589833	−	1.02162i	0.994254	−	0.107048i	$-0.0341398\pi$
$192$	13.5557	+	0.539512i	0.978295	+	0.0389359i
$193$	−1.94351	+	3.36627i	−0.139897	+	0.242309i	−0.927458	−	0.373928i	$-0.878011\pi$
$193$	−1.94351	+	3.36627i	−0.139897	+	0.242309i	0.787560	+	0.616238i	$0.211344\pi$
$194$	6.49196	−	3.74813i	0.466095	−	0.269100i
$195$	−4.64132	−	2.93176i	−0.332372	−	0.209948i
$196$	−0.135128	−	0.234048i	−0.00965198	−	0.0167177i
$197$	2.94787	−	5.10585i	0.210027	−	0.363777i	−0.741696	−	0.670736i	$-0.765978\pi$
$197$	2.94787	−	5.10585i	0.210027	−	0.363777i	0.951723	+	0.306959i	$0.0993115\pi$
$198$	4.34874	−	6.31368i	0.309052	−	0.448694i
$199$	8.25264	+	14.2940i	0.585014	+	1.01327i	0.994874	+	0.101126i	$0.0322444\pi$
$199$	8.25264	+	14.2940i	0.585014	+	1.01327i	−0.409860	+	0.912149i	$0.634422\pi$
$200$	5.77807	+	10.0079i	0.408571	+	0.707666i
$201$	8.15496	+	11.5973i	0.575206	+	0.818008i
$202$	−1.90415	+	3.29809i	−0.133976	+	0.232053i
$203$	3.28484			0.230550
$204$	0.220274	+	0.139140i	0.0154223	+	0.00974172i
$205$	−35.8351			−2.50283
$206$	−22.1153			−1.54084
$207$	0.0648164	−	0.812991i	0.00450505	−	0.0565068i
$208$	3.70568	+	2.13948i	0.256943	+	0.148346i
$209$	−0.600228	−	1.03962i	−0.0415186	−	0.0719124i
$210$	3.54202	−	1.86124i	0.244422	−	0.128438i
$211$	−6.40867			−0.441191			−0.220596	−	0.975365i	$-0.570800\pi$
$211$	−6.40867			−0.441191			−0.220596	+	0.975365i	$0.570800\pi$
$212$	0.0736970	+	0.127647i	0.00506153	+	0.00876683i
$213$	−5.69184	−	3.59534i	−0.389999	−	0.246348i
$214$	8.60066	+	4.96559i	0.587929	+	0.339441i
$215$		−	19.9767i		−	1.36240i
$216$	−14.4419	−	1.73167i	−0.982646	−	0.117825i
$217$	0.423068	+	0.732774i	0.0287197	+	0.0497440i
$218$	−7.01045	−	4.04749i	−0.474808	−	0.274130i
$219$	−3.51548	−	6.69008i	−0.237554	−	0.452074i
$220$	−0.217597			−0.0146704
$221$	−1.95997	−	3.39477i	−0.131842	−	0.228357i
$222$	−8.18981	−	0.325952i	−0.549664	−	0.0218765i
$223$	−1.48730	−	2.57609i	−0.0995973	−	0.172508i	0.811921	−	0.583768i	$-0.198422\pi$
$223$	−1.48730	−	2.57609i	−0.0995973	−	0.172508i	−0.911518	+	0.411260i	$0.865089\pi$
$224$	−0.105552	+	0.0609407i	−0.00705252	+	0.00407177i
$225$	−5.32045	−	11.1838i	−0.354697	−	0.745589i
$226$	5.17111			0.343977
$227$		−	21.2154i		−	1.40812i	−0.710143	−	0.704058i	$-0.751370\pi$
$227$		−	21.2154i		−	1.40812i	0.710143	−	0.704058i	$-0.248630\pi$
$228$	0.0249852	−	0.0395546i	0.00165469	−	0.00261957i
$229$			9.98468i			0.659806i	0.944015	+	0.329903i	$0.107016\pi$
$229$			9.98468i			0.659806i	−0.944015	+	0.329903i	$0.892984\pi$
$230$	−1.01603	+	0.586607i	−0.0669953	+	0.0386798i
$231$	0.0659669	−	1.65747i	0.00434031	−	0.109054i
$232$			17.1773i			1.12775i
$233$	−9.62164	+	16.6652i	−0.630335	+	1.09177i	0.357149	+	0.934048i	$0.383749\pi$
$233$	−9.62164	+	16.6652i	−0.630335	+	1.09177i	−0.987483	+	0.157724i	$0.949584\pi$
$234$	−3.70210	−	2.54994i	−0.242014	−	0.166695i
$235$	−9.07948	−	5.24204i	−0.592280	−	0.341953i
$236$		−	0.189890i		−	0.0123608i
$237$	0.0208557	−	0.524015i	0.00135472	−	0.0340385i
$238$	2.85710			0.185198
$239$	−5.39980	−	9.35273i	−0.349284	−	0.604978i	0.636838	−	0.770997i	$-0.280242\pi$
$239$	−5.39980	−	9.35273i	−0.349284	−	0.604978i	−0.986122	+	0.166020i	$0.946908\pi$
$240$	9.92896	+	18.8952i	0.640912	+	1.21968i
$241$	2.99482	+	5.18719i	0.192914	+	0.334136i	0.946215	−	0.323540i	$-0.104873\pi$
$241$	2.99482	+	5.18719i	0.192914	+	0.334136i	−0.753301	+	0.657676i	$0.771540\pi$
$242$	5.57009	−	9.64768i	0.358059	−	0.620176i
$243$	15.2811	+	3.08005i	0.980286	+	0.197585i
$244$			0.445816i			0.0285405i
$245$	−10.1417	+	17.5659i	−0.647929	+	1.12225i
$246$	−29.3206	−	1.16695i	−1.86941	−	0.0744021i
$247$	−0.609596	+	0.351951i	−0.0387877	+	0.0223941i
$248$	−3.83189	+	2.21234i	−0.243325	+	0.140484i
$249$	19.2071	+	12.1325i	1.21720	+	0.768863i
$250$	1.88095	−	3.25790i	0.118962	−	0.206047i
$251$	−15.3231	−	26.5404i	−0.967188	−	1.67522i	−0.703619	−	0.710578i	$-0.748434\pi$
$251$	−15.3231	−	26.5404i	−0.967188	−	1.67522i	−0.263569	−	0.964641i	$-0.584900\pi$
$252$	0.0583778	−	0.0277719i	0.00367746	−	0.00174947i
$253$			0.486374i			0.0305780i
$254$	11.0656	+	19.1662i	0.694319	+	1.20260i
$255$	0.777635	−	19.5387i	0.0486974	−	1.22356i
$256$	−0.482875	−	0.836365i	−0.0301797	−	0.0522728i
$257$	19.3176	−	11.1530i	1.20500	−	0.695707i	0.243337	−	0.969942i	$-0.421758\pi$
$257$	19.3176	−	11.1530i	1.20500	−	0.695707i	0.961663	+	0.274234i	$0.0884244\pi$
$258$	0.650533	−	16.3451i	0.0405004	−	1.01760i
$259$	−1.53583	+	0.886715i	−0.0954321	+	0.0550978i
$260$			0.127591i			0.00791283i
$261$	1.46305	−	18.3510i	0.0905604	−	1.13590i
$262$	−20.6865	+	11.9433i	−1.27802	+	0.737862i
$263$	−23.7757	+	13.7269i	−1.46607	+	0.846438i	−0.999280	−	0.0379284i	$-0.987924\pi$
$263$	−23.7757	+	13.7269i	−1.46607	+	0.846438i	−0.466793	+	0.884366i	$0.654591\pi$
$264$	8.66739	+	0.344960i	0.533441	+	0.0212308i
$265$	5.53116	−	9.58025i	0.339776	−	0.588510i
$266$		−	0.513048i		−	0.0314570i
$267$	0.0617815	−	1.55231i	0.00378096	−	0.0949997i
$268$	0.126664	−	0.304190i	0.00773725	−	0.0185814i
$269$		−	23.6488i		−	1.44190i	−0.692990	−	0.720948i	$-0.743707\pi$
$269$		−	23.6488i		−	1.44190i	0.692990	−	0.720948i	$-0.256293\pi$
$270$	−8.82040	−	20.6167i	−0.536792	−	1.25470i
$271$		−	8.20601i		−	0.498479i	−0.968442	−	0.249240i	$-0.919819\pi$
$271$		−	8.20601i		−	0.498479i	0.968442	−	0.249240i	$-0.0801807\pi$
$272$			15.2414i			0.924148i
$273$	−0.971878	−	0.0386805i	−0.0588207	−	0.00234105i
$274$	−22.8814			−1.38232
$275$	3.69292	+	6.39633i	0.222692	+	0.385713i
$276$	−0.0167797	+	0.00881730i	−0.00101002	+	0.000530739i
$277$	−15.6658	−	27.1339i	−0.941265	−	1.63032i	−0.763062	−	0.646325i	$-0.776305\pi$
$277$	−15.6658	−	27.1339i	−0.941265	−	1.63032i	−0.178203	−	0.983994i	$-0.557028\pi$
$278$	−2.79953	+	1.61631i	−0.167904	+	0.0969397i
$279$	4.28213	−	2.03713i	0.256365	−	0.121960i
$280$	3.92073	+	2.26363i	0.234308	+	0.135278i
$281$	14.5145	−	25.1399i	0.865864	−	1.49972i	−0.000322657	−	1.00000i	$-0.500103\pi$
$281$	14.5145	−	25.1399i	0.865864	−	1.49972i	0.866187	−	0.499721i	$-0.166564\pi$
$282$	−7.25821	−	4.58475i	−0.432220	−	0.273018i
$283$	−12.6363	+	21.8867i	−0.751148	+	1.30103i	0.196118	+	0.980580i	$0.437166\pi$
$283$	−12.6363	+	21.8867i	−0.751148	+	1.30103i	−0.947267	+	0.320447i	$0.896167\pi$
$284$			0.156469i			0.00928476i
$285$	−3.50855	−	0.139640i	−0.207829	−	0.00827153i
$286$	2.32166	+	1.34041i	0.137282	+	0.0792600i
$287$	−5.49849	+	3.17456i	−0.324566	+	0.187388i
$288$	0.293438	+	0.616819i	0.0172910	+	0.0363464i
$289$	−1.51867	+	2.63042i	−0.0893338	+	0.154731i
$290$	−22.9341	+	13.2410i	−1.34674	+	0.777540i
$291$	−7.68519	−	4.85446i	−0.450514	−	0.284573i
$292$	−0.0878246	+	0.152117i	−0.00513954	+	0.00890195i
$293$	−26.2035	−	15.1286i	−1.53082	−	0.883821i	−0.999324	−	0.0367620i	$-0.988296\pi$
$293$	−26.2035	−	15.1286i	−1.53082	−	0.883821i	−0.531499	−	0.847059i	$-0.678371\pi$
$294$	−8.87006	+	14.0424i	−0.517312	+	0.818967i
$295$	−12.3424	+	7.12589i	−0.718603	+	0.414885i
$296$	−4.63688	−	8.03132i	−0.269513	−	0.466811i
$297$	−9.23021	−	1.10676i	−0.535591	−	0.0642206i
$298$	−5.09008	+	2.93876i	−0.294861	+	0.170238i
$299$	0.285191			0.0164930
$300$	−0.153723	+	0.243361i	−0.00887518	+	0.0140505i
$301$	−1.76970	−	3.06521i	−0.102004	−	0.176676i
$302$	−5.23296	−	9.06376i	−0.301123	−	0.521561i
$303$	4.61431	+	0.183648i	0.265085	+	0.0105503i
$304$	2.73690			0.156972
$305$	28.9770	−	16.7299i	1.65922	−	0.957949i
$306$	1.27254	−	15.9614i	0.0727461	−	0.912454i
$307$	8.58328	+	14.8667i	0.489874	+	0.848486i	0.999932	−	0.0116537i	$-0.00370957\pi$
$307$	8.58328	+	14.8667i	0.489874	+	0.848486i	−0.510058	+	0.860140i	$0.670376\pi$
$308$	−0.0333878	+	0.0192765i	−0.00190245	+	0.00109838i
$309$	12.4743	+	23.7391i	0.709639	+	1.35047i
$310$	−5.90756	−	3.41073i	−0.335527	−	0.193716i
$311$	−2.86449	+	4.96144i	−0.162430	+	0.281337i	−0.935740	−	0.352691i	$-0.885267\pi$
$311$	−2.86449	+	4.96144i	−0.162430	+	0.281337i	0.773310	+	0.634029i	$0.218600\pi$
$312$	0.202271	−	5.08223i	0.0114514	−	0.287724i
$313$	−12.0034	+	6.93018i	−0.678473	+	0.391717i	−0.799280	−	0.600959i	$-0.794785\pi$
$313$	−12.0034	+	6.93018i	−0.678473	+	0.391717i	0.120806	+	0.992676i	$0.461452\pi$
$314$	−0.148855	+	0.257825i	−0.00840038	+	0.0145499i
$315$	−3.99581	−	2.75224i	−0.225139	−	0.155071i
$316$	−0.0105557	+	0.00609433i	−0.000593804	+	0.000342833i
$317$	−19.3980	−	11.1995i	−1.08950	−	0.629024i	−0.156058	−	0.987748i	$-0.549879\pi$
$317$	−19.3980	−	11.1995i	−1.08950	−	0.629024i	−0.933444	+	0.358724i	$0.883212\pi$
$318$	4.83762	−	7.65853i	0.271280	−	0.429469i
$319$			10.9785i			0.614679i
$320$	−11.8323	+	20.4941i	−0.661445	+	1.14566i
$321$	0.478912	−	12.0330i	0.0267303	−	0.671619i
$322$	−0.103933	+	0.180017i	−0.00579194	+	0.0100319i
$323$	−2.17136	−	1.25363i	−0.120817	−	0.0697540i
$324$	−0.129149	−	0.338502i	−0.00717493	−	0.0188057i
$325$	3.75056	−	2.16539i	0.208044	−	0.120114i
$326$	1.75754	+	3.04415i	0.0973413	+	0.168600i
$327$	−0.390365	+	9.80822i	−0.0215872	+	0.542396i
$328$	−16.6007	−	28.7532i	−0.916618	−	1.58763i
$329$	−1.85753			−0.102409
$330$	6.22062	+	11.8381i	0.342434	+	0.651664i
$331$			24.8204i			1.36425i	0.731234	+	0.682127i	$0.238945\pi$
$331$			24.8204i			1.36425i	−0.731234	+	0.682127i	$0.761055\pi$
$332$		−	0.528006i		−	0.0289781i
$333$	4.26965	+	8.97500i	0.233975	+	0.491827i
$334$			13.3709i			0.731624i
$335$	−24.5249	+	3.18228i	−1.33994	+	0.173866i
$336$	3.19737	+	2.01967i	0.174431	+	0.110182i
$337$		−	1.26454i		−	0.0688838i	−0.999407	−	0.0344419i	$-0.989035\pi$
$337$		−	1.26454i		−	0.0688838i	0.999407	−	0.0344419i	$-0.0109654\pi$
$338$	−8.49847	+	14.7198i	−0.462256	+	0.800651i
$339$	−2.91681	−	5.55080i	−0.158419	−	0.301478i
$340$	−0.393584	+	0.227236i	−0.0213451	+	0.0123236i
$341$	−2.44907	+	1.41397i	−0.132624	+	0.0765707i
$342$	−2.86618	−	0.228509i	−0.154986	−	0.0123563i
$343$			7.34085i			0.396369i
$344$	16.0288	−	9.25425i	0.864217	−	0.498956i
$345$	1.20278	+	0.759755i	0.0647556	+	0.0409038i
$346$	−23.0545	+	13.3105i	−1.23942	+	0.715579i
$347$	−7.44503	−	12.8952i	−0.399670	−	0.692249i	0.594015	−	0.804454i	$-0.297542\pi$
$347$	−7.44503	−	12.8952i	−0.399670	−	0.692249i	−0.993685	+	0.112205i	$0.964209\pi$
$348$	−0.378754	+	0.199026i	−0.0203033	+	0.0106689i
$349$	−10.0566	−	17.4185i	−0.538316	−	0.932391i	−0.998995	−	0.0448240i	$-0.985727\pi$
$349$	−10.0566	−	17.4185i	−0.538316	−	0.932391i	0.460679	−	0.887567i	$-0.347606\pi$
$350$			3.15655i			0.168725i
$351$	−0.648960	+	5.41224i	−0.0346389	+	0.288884i
$352$	−0.203675	−	0.352775i	−0.0108559	−	0.0188030i
$353$	7.79036	−	13.4933i	0.414639	−	0.718176i	−0.580751	−	0.814081i	$-0.697241\pi$
$353$	7.79036	−	13.4933i	0.414639	−	0.718176i	0.995390	+	0.0959050i	$0.0305745\pi$
$354$	−10.3307	+	5.42855i	−0.549072	+	0.288524i
$355$	10.1701	−	5.87173i	0.539775	−	0.311639i
$356$	−0.0312694	+	0.0180534i	−0.00165728	+	0.000956830i
$357$	−1.61157	−	3.06688i	−0.0852935	−	0.162317i
$358$	−5.83759	+	10.1110i	−0.308526	+	0.534383i
$359$			21.7212i			1.14640i	0.819415	+	0.573200i	$0.194298\pi$
$359$			21.7212i			1.14640i	−0.819415	+	0.573200i	$0.805702\pi$
$360$	14.3922	−	20.8952i	0.758537	−	1.10128i
$361$	9.27489	−	16.0646i	0.488152	−	0.845504i
$362$	13.3188	+	23.0689i	0.700023	+	1.21248i
$363$	−13.4979	−	0.537214i	−0.708457	−	0.0281964i
$364$	0.0113030	+	0.0195773i	0.000592438	+	0.00102613i
$365$	13.1829			0.690027
$366$	24.2540	−	12.7449i	1.26778	−	0.666187i
$367$			10.4104i			0.543418i	0.962379	+	0.271709i	$0.0875888\pi$
$367$			10.4104i			0.543418i	−0.962379	+	0.271709i	$0.912411\pi$
$368$	−0.960314	−	0.554437i	−0.0500598	−	0.0289020i
$369$	15.2859	+	32.1317i	0.795752	+	1.67271i
$370$	7.14861	−	12.3818i	0.371639	−	0.643697i
$371$		−	1.95998i		−	0.101757i
$372$	−0.0931795	−	0.0588582i	−0.00483113	−	0.00305166i
$373$	3.45899	−	1.99705i	0.179100	−	0.103403i	−0.407770	−	0.913085i	$-0.633693\pi$
$373$	3.45899	−	1.99705i	0.179100	−	0.103403i	0.586870	+	0.809681i	$0.300360\pi$
$374$			9.54895i			0.493765i
$375$	−4.55807	−	0.181410i	−0.235378	−	0.00936798i
$376$		−	9.71353i		−	0.500937i
$377$	6.43739			0.331542
$378$	−3.17979	−	2.38203i	−0.163551	−	0.122518i
$379$	−1.60598	+	0.927211i	−0.0824935	+	0.0476276i	−0.540679	−	0.841229i	$-0.681833\pi$
$379$	−1.60598	+	0.927211i	−0.0824935	+	0.0476276i	0.458186	+	0.888856i	$0.348499\pi$
$380$	0.0408047	+	0.0706758i	0.00209324	+	0.00362559i
$381$	14.3318	−	22.6890i	0.734242	−	1.16239i
$382$	11.6436	+	20.1673i	0.595739	+	1.03185i
$383$	31.9196			1.63101			0.815507	−	0.578747i	$-0.196458\pi$
$383$	31.9196			1.63101			0.815507	+	0.578747i	$0.196458\pi$
$384$	−10.7699	+	17.0500i	−0.549598	+	0.870079i
$385$	2.50585	+	1.44675i	0.127710	+	0.0737333i
$386$	−2.77607	−	4.80829i	−0.141298	−	0.244736i
$387$	−17.9122	+	8.52133i	−0.910530	+	0.433163i
$388$			0.211267i			0.0107254i
$389$	−17.8883	−	10.3278i	−0.906974	−	0.523642i	−0.0275180	−	0.999621i	$-0.508760\pi$
$389$	−17.8883	−	10.3278i	−0.906974	−	0.523642i	−0.879456	+	0.475979i	$0.842094\pi$
$390$	6.94139	−	3.64753i	0.351491	−	0.184700i
$391$	0.507919	+	0.879741i	0.0256866	+	0.0444904i
$392$	−18.7926			−0.949171
$393$	24.4887	+	15.4686i	1.23529	+	0.780289i
$394$	4.21066	+	7.29308i	0.212130	+	0.367420i
$395$	0.792232	+	0.457396i	0.0398615	+	0.0230141i
$396$	0.0928188	+	0.195109i	0.00466432	+	0.00980462i
$397$	−14.6629			−0.735911			−0.367955	−	0.929843i	$-0.619942\pi$
$397$	−14.6629			−0.735911			−0.367955	+	0.929843i	$0.619942\pi$
$398$	−23.5757			−1.18174
$399$	−0.550719	+	0.289389i	−0.0275704	+	0.0144876i
$400$	−16.8389			−0.841943
$401$	11.8089	−	20.4536i	0.589707	−	1.02140i	−0.404563	−	0.914510i	$-0.632576\pi$
$401$	11.8089	−	20.4536i	0.589707	−	1.02140i	0.994271	−	0.106893i	$-0.0340902\pi$
$402$	−20.1701	+	1.80513i	−1.00599	+	0.0900316i
$403$	0.829097	+	1.43604i	0.0413003	+	0.0715342i
$404$	−0.0536646	−	0.0929499i	−0.00266992	−	0.00462443i
$405$	−17.1553	+	21.0971i	−0.852454	+	1.04832i
$406$	−2.34599	+	4.06337i	−0.116430	+	0.201662i
$407$	−2.96356	−	5.13304i	−0.146898	−	0.254435i
$408$	16.0376	−	8.42738i	0.793980	−	0.417217i
$409$	9.92018	−	5.72742i	0.490521	−	0.283203i	−0.234269	−	0.972172i	$-0.575270\pi$
$409$	9.92018	−	5.72742i	0.490521	−	0.283203i	0.724791	+	0.688969i	$0.241936\pi$
$410$	25.5930	−	44.3283i	1.26395	−	2.18922i
$411$	12.9065	+	24.5615i	0.636630	+	1.21153i
$412$	0.311636	−	0.539770i	0.0153532	−	0.0265926i
$413$	−1.26254	+	2.18678i	−0.0621253	+	0.107604i
$414$	0.959387	+	0.660807i	0.0471513	+	0.0324769i
$415$	−34.3191	+	19.8141i	−1.68466	+	0.972638i
$416$	−0.206854	+	0.119427i	−0.0101419	+	0.00585540i
$417$	3.31408	+	2.09339i	0.162291	+	0.102514i
$418$	1.71470			0.0838688
$419$		−	4.59334i		−	0.224399i	−0.993686	−	0.112200i	$-0.964210\pi$
$419$		−	4.59334i		−	0.224399i	0.993686	−	0.112200i	$-0.0357896\pi$
$420$	−0.00448456	+	0.112678i	−0.000218824	+	0.00549813i
$421$	13.4373	−	23.2741i	0.654896	−	1.13431i	−0.327024	−	0.945016i	$-0.606046\pi$
$421$	13.4373	−	23.2741i	0.654896	−	1.13431i	0.981920	−	0.189296i	$-0.0606207\pi$
$422$	4.57699	−	7.92759i	0.222805	−	0.385909i
$423$	−0.827331	+	10.3772i	−0.0402262	+	0.504557i
$424$	10.2493			0.497749
$425$	13.3593	+	7.71302i	0.648024	+	0.374137i
$426$	8.51251	−	4.47312i	0.412432	−	0.216723i
$427$	2.96413	−	5.13402i	0.143444	−	0.248453i
$428$	−0.242392	+	0.139945i	−0.0117165	+	0.00676450i
$429$	0.129277	−	3.24819i	0.00624156	−	0.156824i
$430$	24.7114	+	14.2671i	1.19169	+	0.688022i
$431$	−12.1565	−	7.01858i	−0.585560	−	0.338073i	0.177780	−	0.984070i	$-0.443108\pi$
$431$	−12.1565	−	7.01858i	−0.585560	−	0.338073i	−0.763340	+	0.645997i	$0.776442\pi$
$432$	12.7071	−	16.9628i	0.611372	−	0.816124i
$433$	−4.80388	−	2.77352i	−0.230860	−	0.133287i	0.380109	−	0.924942i	$-0.375887\pi$
$433$	−4.80388	−	2.77352i	−0.230860	−	0.133287i	−0.610969	+	0.791655i	$0.709220\pi$
$434$	−1.20860			−0.0580146
$435$	27.1494	+	17.1493i	1.30172	+	0.822248i
$436$	0.197575	−	0.114070i	0.00946213	−	0.00546296i
$437$	0.157975	−	0.0912067i	0.00755695	−	0.00436301i
$438$	10.7864	+	0.429296i	0.515394	+	0.0205126i
$439$	2.51806	−	4.36140i	0.120180	−	0.208158i	−0.799658	−	0.600455i	$-0.794986\pi$
$439$	2.51806	−	4.36140i	0.120180	−	0.208158i	0.919839	+	0.392297i	$0.128319\pi$
$440$	−7.56547	+	13.1038i	−0.360670	+	0.624698i
$441$	20.0766	+	1.60063i	0.956031	+	0.0762203i
$442$	5.59914			0.266324
$443$	25.5292			1.21293			0.606463	−	0.795111i	$-0.292588\pi$
$443$	25.5292			1.21293			0.606463	+	0.795111i	$0.292588\pi$
$444$	0.123362	−	0.195297i	0.00585450	−	0.00926837i
$445$	2.34686	+	1.35496i	0.111252	+	0.0642312i
$446$	4.24886			0.201189
$447$	6.02565	+	3.80619i	0.285003	+	0.180027i
$448$			4.19279i			0.198091i
$449$	21.8882	+	12.6371i	1.03297	+	0.596383i	0.917833	−	0.396967i	$-0.129937\pi$
$449$	21.8882	+	12.6371i	1.03297	+	0.596383i	0.115133	+	0.993350i	$0.463271\pi$
$450$	17.6343	+	1.40591i	0.831289	+	0.0662752i
$451$	−10.6099	−	18.3770i	−0.499603	−	0.865337i
$452$	−0.0728685	+	0.126212i	−0.00342745	+	0.00593651i
$453$	−6.77756	+	10.7297i	−0.318438	+	0.504125i
$454$	26.2437	+	15.1518i	1.23168	+	0.711108i
$455$	0.848320	−	1.46933i	0.0397698	−	0.0688834i
$456$	−1.51330	−	2.87987i	−0.0708668	−	0.134862i
$457$	18.9277			0.885402			0.442701	−	0.896669i	$-0.354020\pi$
$457$	18.9277			0.885402			0.442701	+	0.896669i	$0.354020\pi$
$458$	−12.3511	−	7.13093i	−0.577131	−	0.333207i
$459$	−17.8512	+	7.63721i	−0.833222	+	0.356475i
$460$		−	0.0330646i		−	0.00154165i
$461$	−9.18583	+	5.30344i	−0.427827	+	0.247006i	−0.698420	−	0.715688i	$-0.746113\pi$
$461$	−9.18583	+	5.30344i	−0.427827	+	0.247006i	0.270594	+	0.962694i	$0.412780\pi$
$462$	2.00319	+	1.26535i	0.0931970	+	0.0588693i
$463$			6.29179i			0.292404i	0.989255	+	0.146202i	$0.0467050\pi$
$463$			6.29179i			0.292404i	−0.989255	+	0.146202i	$0.953295\pi$
$464$	−21.6764	−	12.5149i	−1.00630	−	0.580988i
$465$	−0.328952	+	8.26517i	−0.0152548	+	0.383288i
$466$	−13.7433	−	23.8041i	−0.636647	−	1.10270i
$467$	−12.4545	+	7.19058i	−0.576323	+	0.332740i	−0.759671	−	0.650308i	$-0.774640\pi$
$467$	−12.4545	+	7.19058i	−0.576323	+	0.332740i	0.183348	+	0.983048i	$0.441307\pi$
$468$	0.114405	−	0.0544254i	0.00528836	−	0.00251581i
$469$	−3.48115	+	2.66089i	−0.160745	+	0.122869i
$470$	12.9689	−	7.48760i	0.598211	−	0.345377i
$471$	0.360719	+	0.0143565i	0.0166210	+	0.000661513i
$472$	−11.4353	−	6.60216i	−0.526351	−	0.303889i
$473$	10.2445	−	5.91465i	0.471041	−	0.271956i
$474$	0.633317	+	0.400044i	0.0290892	+	0.0183746i
$475$	1.38502	−	2.39893i	0.0635492	−	0.110071i
$476$	−0.0402608	+	0.0697337i	−0.00184535	+	0.00319624i
$477$	−10.9496	−	0.872962i	−0.501346	−	0.0399702i
$478$	15.4259			0.705563
$479$	−20.7158	−	11.9603i	−0.946528	−	0.546478i	−0.0545273	−	0.998512i	$-0.517365\pi$
$479$	−20.7158	−	11.9603i	−0.946528	−	0.546478i	−0.892001	+	0.452034i	$0.850699\pi$
$480$	−1.19056	−	0.0473838i	−0.0543412	−	0.00216277i
$481$	−3.00982	+	1.73772i	−0.137236	+	0.0792332i
$482$	−8.55546			−0.389691
$483$	0.251859	+	0.0100239i	0.0114600	+	0.000456104i
$484$	0.156981	+	0.271900i	0.00713552	+	0.0123591i
$485$	13.7318	−	7.92807i	0.623530	−	0.359995i
$486$	−14.7236	+	16.7032i	−0.667878	+	0.757672i
$487$	−23.9230	+	13.8119i	−1.08405	+	0.625878i	−0.931987	−	0.362492i	$-0.881926\pi$
$487$	−23.9230	+	13.8119i	−1.08405	+	0.625878i	−0.152066	+	0.988370i	$0.548593\pi$
$488$	26.8473	+	15.5003i	1.21532	+	0.701664i
$489$	2.27631	−	3.60367i	0.102938	−	0.162964i
$490$	−14.4861	−	25.0907i	−0.654418	−	1.13348i
$491$	−37.6104	−	21.7144i	−1.69733	−	0.979956i	−0.948274	−	0.317453i	$-0.897172\pi$
$491$	−37.6104	−	21.7144i	−1.69733	−	0.979956i	−0.749060	−	0.662503i	$-0.769494\pi$
$492$	0.441652	−	0.699188i	0.0199112	−	0.0315218i
$493$	11.4648	+	19.8577i	0.516351	+	0.894346i
$494$		−	1.00544i		−	0.0452367i
$495$	9.19848	−	13.3547i	0.413441	−	0.600251i
$496$		−	6.44737i		−	0.289495i
$497$	1.04033	−	1.80190i	0.0466651	−	0.0808264i
$498$	−28.7254	+	15.0945i	−1.28722	+	0.676402i
$499$			9.74701i			0.436336i	0.975911	+	0.218168i	$0.0700081\pi$
$499$			9.74701i			0.436336i	−0.975911	+	0.218168i	$0.929992\pi$
$500$	0.0530106	+	0.0918171i	0.00237071	+	0.00410618i
$501$	14.3527	−	7.54199i	0.641231	−	0.336951i
$502$	43.7744			1.95375
$503$	−10.5382	+	18.2528i	−0.469877	+	0.813851i	−0.999407	−	0.0344403i	$-0.989035\pi$
$503$	−10.5382	+	18.2528i	−0.469877	+	0.813851i	0.529530	+	0.848292i	$0.322368\pi$
$504$	0.357261	−	4.48112i	0.0159137	−	0.199605i
$505$	−4.02768	+	6.97614i	−0.179229	+	0.310434i
$506$	−0.601649	−	0.347362i	−0.0267465	−	0.0154421i
$507$	20.5942	+	0.819645i	0.914622	+	0.0364017i
$508$	−0.623723			−0.0276733
$509$	5.83270	+	3.36751i	0.258530	+	0.149262i	0.623664	−	0.781693i	$-0.285643\pi$
$509$	5.83270	+	3.36751i	0.258530	+	0.149262i	−0.365134	+	0.930955i	$0.618977\pi$
$510$	23.6142	+	14.9162i	1.04565	+	0.660502i
$511$	2.02277	−	1.16785i	0.0894823	−	0.0516626i
$512$	−21.9070			−0.968160
$513$	1.37141	+	3.20553i	0.0605492	+	0.141527i
$514$			31.8614i			1.40535i
$515$	−46.7783			−2.06130
$516$	0.389771	+	0.246205i	0.0171587	+	0.0108386i
$517$		−	6.20819i		−	0.273036i
$518$		−	2.53312i		−	0.111299i
$519$	27.2920	+	17.2394i	1.19798	+	0.756724i
$520$	7.68356	+	4.43610i	0.336946	+	0.194536i
$521$	−19.3648			−0.848387			−0.424194	−	0.905572i	$-0.639442\pi$
$521$	−19.3648			−0.848387			−0.424194	+	0.905572i	$0.639442\pi$
$522$	21.6555	+	14.9159i	0.947834	+	0.652850i
$523$	−8.84925	−	15.3273i	−0.386951	−	0.670218i	0.605087	−	0.796159i	$-0.293138\pi$
$523$	−8.84925	−	15.3273i	−0.386951	−	0.670218i	−0.992038	+	0.125941i	$0.959805\pi$
$524$		−	0.673197i		−	0.0294088i
$525$	3.38832	−	1.78048i	0.147878	−	0.0777065i
$526$		−	39.2144i		−	1.70983i
$527$	−2.95321	+	5.11511i	−0.128644	+	0.222818i
$528$	−6.75010	+	10.6862i	−0.293760	+	0.465057i
$529$	22.9261			0.996787
$530$	7.90057	+	13.6842i	0.343179	+	0.594403i
$531$	11.6543	+	8.02723i	0.505752	+	0.348352i
$532$	0.0125220	+	0.00722960i	0.000542899	+	0.000313443i
$533$	−10.7755	+	6.22126i	−0.466741	+	0.269473i
$534$	1.87610	+	1.18506i	0.0811866	+	0.0512827i
$535$	18.1922	+	10.5032i	0.786516	+	0.454095i
$536$	−13.9146	−	18.2039i	−0.601017	−	0.786291i
$537$	14.1462	+	0.563013i	0.610452	+	0.0242958i
$538$	29.2538	+	16.8897i	1.26122	+	0.728167i
$539$	−12.0109			−0.517346
$540$	0.627488	+	0.0752396i	0.0270028	+	0.00323780i
$541$		−	40.2246i		−	1.72939i	−0.502298	−	0.864694i	$-0.667512\pi$
$541$		−	40.2246i		−	1.72939i	0.502298	−	0.864694i	$-0.332488\pi$
$542$	10.1509	+	5.86063i	0.436019	+	0.251736i
$543$	17.2501	−	27.3090i	0.740274	−	1.17194i
$544$	−0.736805	−	0.425395i	−0.0315903	−	0.0182386i
$545$	−14.8285	−	8.56127i	−0.635185	−	0.366724i
$546$	0.741951	−	1.17460i	0.0317526	−	0.0502681i
$547$			30.3585i			1.29803i	0.760774	+	0.649017i	$0.224820\pi$
$547$			30.3585i			1.29803i	−0.760774	+	0.649017i	$0.775180\pi$
$548$	0.322433	−	0.558471i	0.0137737	−	0.0238567i
$549$	−27.3614	−	18.8460i	−1.16776	−	0.804328i
$550$	−10.5498			−0.449843
$551$	3.56584	−	2.05874i	0.151910	−	0.0877051i
$552$	−0.0524179	+	1.31704i	−0.00223105	+	0.0560570i
$553$	0.162079			0.00689230
$554$	44.7532			1.90138
$555$	−17.3231	−	0.689456i	−0.735326	−	0.0292658i
$556$		−	0.0911046i		−	0.00386370i
$557$	11.8454	+	6.83892i	0.501904	+	0.289774i	0.729499	−	0.683981i	$-0.239753\pi$
$557$	11.8454	+	6.83892i	0.501904	+	0.289774i	−0.227596	+	0.973756i	$0.573086\pi$
$558$	−0.538303	+	6.75193i	−0.0227882	+	0.285832i
$559$	−3.46813	−	6.00697i	−0.146686	−	0.254068i
$560$	−5.71304	+	3.29842i	−0.241420	+	0.139384i
$561$	10.2501	−	5.38617i	0.432759	−	0.227404i
$562$	20.7322	+	35.9092i	0.874535	+	1.51474i
$563$	−16.5552	+	28.6744i	−0.697717	+	1.20848i	0.271539	+	0.962427i	$0.412467\pi$
$563$	−16.5552	+	28.6744i	−0.697717	+	1.20848i	−0.969256	+	0.246054i	$0.920866\pi$
$564$	0.214179	−	0.112546i	0.00901858	−	0.00473905i
$565$	10.9380			0.460163
$566$	−18.0493	−	31.2624i	−0.758670	−	1.31406i
$567$	−0.763342	+	4.75687i	−0.0320573	+	0.199770i
$568$	9.42266	+	5.44017i	0.395366	+	0.228265i
$569$			23.3378i			0.978371i	0.872180	+	0.489186i	$0.162706\pi$
$569$			23.3378i			0.978371i	−0.872180	+	0.489186i	$0.837294\pi$
$570$	2.67850	−	4.24039i	0.112190	−	0.177610i
$571$	−2.05981	−	3.56770i	−0.0862004	−	0.149303i	0.819702	−	0.572791i	$-0.194139\pi$
$571$	−2.05981	−	3.56770i	−0.0862004	−	0.149303i	−0.905902	+	0.423487i	$0.860806\pi$
$572$	−0.0654311	+	0.0377766i	−0.00273581	+	0.00157952i
$573$	15.0804	−	23.8741i	0.629994	−	0.997356i
$574$		−	9.06891i		−	0.378529i
$575$	−0.971945	+	0.561153i	−0.0405329	+	0.0234017i
$576$	23.4234	+	1.86745i	0.975973	+	0.0778102i
$577$	−30.5822	−	17.6567i	−1.27315	−	0.735056i	−0.297574	−	0.954699i	$-0.596178\pi$
$577$	−30.5822	−	17.6567i	−1.27315	−	0.735056i	−0.975580	+	0.219642i	$0.929511\pi$
$578$	−2.16924	−	3.75723i	−0.0902284	−	0.156280i
$579$	−3.59547	+	5.69206i	−0.149423	+	0.236554i
$580$		−	0.746342i		−	0.0309902i
$581$	−3.51059	+	6.08052i	−0.145644	+	0.252262i
$582$	11.4937	−	6.03965i	0.476428	−	0.250352i
$583$	6.55060			0.271298
$584$	6.10702	+	10.5777i	0.252710	+	0.437707i
$585$	−7.83071	−	5.39364i	−0.323760	−	0.222999i
$586$	37.4284	−	21.6093i	1.54615	−	0.892671i
$587$	−4.10208	+	7.10500i	−0.169311	+	0.293255i	−0.938178	−	0.346154i	$-0.887488\pi$
$587$	−4.10208	+	7.10500i	−0.169311	+	0.293255i	0.768867	+	0.639409i	$0.220821\pi$
$588$	−0.217742	−	0.414370i	−0.00897951	−	0.0170883i
$589$	0.918517	+	0.530306i	0.0378468	+	0.0218509i
$590$		−	20.3569i		−	0.838080i
$591$	5.45351	−	8.63355i	0.224327	−	0.355137i
$592$	13.5131			0.555387
$593$	−3.55162	−	6.15158i	−0.145848	−	0.252615i	0.783841	−	0.620961i	$-0.213258\pi$
$593$	−3.55162	−	6.15158i	−0.145848	−	0.252615i	−0.929689	+	0.368346i	$0.879924\pi$
$594$	7.96117	−	10.6274i	0.326651	−	0.436049i
$595$	6.04336			0.247753
$596$		−	0.165646i		−	0.00678512i
$597$	13.2981	+	25.3068i	0.544255	+	1.03574i
$598$	−0.203680	+	0.352784i	−0.00832909	+	0.0144264i
$599$	−0.785168	−	1.35995i	−0.0320811	−	0.0555661i	0.849539	−	0.527526i	$-0.176880\pi$
$599$	−0.785168	−	1.35995i	−0.0320811	−	0.0555661i	−0.881620	+	0.471960i	$0.843547\pi$
$600$	9.31063	+	17.7185i	0.380105	+	0.723354i
$601$	−4.92914	+	8.53753i	−0.201064	+	0.348253i	−0.948872	−	0.315663i	$-0.897773\pi$
$601$	−4.92914	+	8.53753i	−0.201064	+	0.348253i	0.747808	+	0.663916i	$0.231107\pi$
$602$	5.05558			0.206050
$603$	13.3148	+	20.6329i	0.542220	+	0.840236i
$604$	0.294960			0.0120018
$605$	11.7819	−	20.4068i	0.479002	−	0.829655i
$606$	−3.52266	+	5.57678i	−0.143098	+	0.226541i
$607$	−3.11013	−	5.38691i	−0.126236	−	0.218648i	0.795979	−	0.605324i	$-0.206956\pi$
$607$	−3.11013	−	5.38691i	−0.126236	−	0.218648i	−0.922216	+	0.386676i	$0.873623\pi$
$608$	−0.0763879	+	0.132308i	−0.00309794	+	0.00536578i
$609$	5.68500	+	0.226262i	0.230368	+	0.00916859i
$610$			47.7930i			1.93508i
$611$	−3.64024			−0.147269
$612$	0.371641	+	0.255979i	0.0150227	+	0.0103473i
$613$	3.95724	+	6.85414i	0.159831	+	0.276836i	0.934808	−	0.355154i	$-0.115572\pi$
$613$	3.95724	+	6.85414i	0.159831	+	0.276836i	−0.774976	+	0.631990i	$0.782238\pi$
$614$	−24.5203			−0.989558
$615$	−62.0191	−	2.46834i	−2.50085	−	0.0995332i
$616$			2.68084i			0.108014i
$617$	2.61286	+	1.50854i	0.105190	+	0.0607314i	0.551672	−	0.834061i	$-0.313990\pi$
$617$	2.61286	+	1.50854i	0.105190	+	0.0607314i	−0.446482	+	0.894793i	$0.647323\pi$
$618$	−38.2744	−	1.52331i	−1.53962	−	0.0612766i
$619$	13.6793	−	23.6933i	0.549819	−	0.952314i	−0.448468	−	0.893799i	$-0.648030\pi$
$619$	13.6793	−	23.6933i	0.549819	−	0.952314i	0.998287	−	0.0585152i	$-0.0186366\pi$
$620$	0.166492	−	0.0961244i	0.00668649	−	0.00386045i
$621$	0.168176	−	1.40256i	0.00674866	−	0.0562829i
$622$	−4.09156	−	7.08679i	−0.164057	−	0.284154i
$623$	0.480132			0.0192361
$624$	6.26598	+	3.95800i	0.250840	+	0.158447i
$625$	14.2993	−	24.7672i	0.571973	−	0.990686i
$626$		−	19.7978i		−	0.791279i
$627$	−0.967192	−	1.84060i	−0.0386259	−	0.0735066i
$628$	−0.00419518	−	0.00726626i	−0.000167406	−	0.000289955i
$629$	−10.7208	−	6.18968i	−0.427468	−	0.246799i
$630$	6.25830	−	2.97724i	0.249337	−	0.118616i
$631$	−41.8302	+	24.1507i	−1.66523	+	0.961423i	−0.695078	+	0.718934i	$0.744630\pi$
$631$	−41.8302	+	24.1507i	−1.66523	+	0.961423i	−0.970154	+	0.242489i	$0.922036\pi$
$632$			0.847557i			0.0337140i
$633$	−11.0914	−	0.441434i	−0.440842	−	0.0175454i
$634$	27.7077	−	15.9970i	1.10041	−	0.635323i
$635$	23.4061	+	40.5405i	0.928841	+	1.60880i
$636$	0.118754	+	0.225992i	0.00470889	+	0.00896118i
$637$			7.04273i			0.279043i
$638$	−13.5805	−	7.84073i	−0.537659	−	0.310417i
$639$	−9.60311	−	6.61443i	−0.379893	−	0.261663i
$640$	−17.5889	−	30.4648i	−0.695260	−	1.20423i
$641$	21.4721			0.848097			0.424049	−	0.905639i	$-0.360609\pi$
$641$	21.4721			0.848097			0.424049	+	0.905639i	$0.360609\pi$
$642$	14.5430	+	9.18627i	0.573965	+	0.362553i
$643$	14.8531	−	25.7263i	0.585750	−	1.01455i	−0.409032	−	0.912520i	$-0.634134\pi$
$643$	14.8531	−	25.7263i	0.585750	−	1.01455i	0.994782	−	0.102028i	$-0.0325331\pi$
$644$	−0.00292913	−	0.00507340i	−0.000115424	−	0.000199920i
$645$	1.37601	−	34.5733i	0.0541803	−	1.36132i
$646$	3.10151	−	1.79066i	0.122027	−	0.0704525i
$647$	10.5009	+	18.1881i	0.412834	+	0.715050i	0.995198	−	0.0978782i	$-0.0312056\pi$
$647$	10.5009	+	18.1881i	0.412834	+	0.715050i	−0.582364	+	0.812928i	$0.697872\pi$
$648$	−24.8750	−	3.99173i	−0.977183	−	0.156810i
$649$	−7.30860	−	4.21963i	−0.286888	−	0.165635i
$650$			6.18598i			0.242634i
$651$	0.681721	+	1.29734i	0.0267187	+	0.0508468i
$652$	−0.0990654			−0.00387970
$653$	5.35483			0.209551			0.104775	−	0.994496i	$-0.466588\pi$
$653$	5.35483			0.209551			0.104775	+	0.994496i	$0.466588\pi$
$654$	−11.8541	−	7.48779i	−0.463530	−	0.292796i
$655$	−43.7562	+	25.2626i	−1.70969	+	0.987093i
$656$	48.3788			1.88888
$657$	−5.62335	−	11.8205i	−0.219388	−	0.461163i
$658$	1.32662	−	2.29778i	0.0517171	−	0.0895766i
$659$		−	48.4898i		−	1.88890i	−0.328660	−	0.944448i	$-0.606597\pi$
$659$		−	48.4898i		−	1.88890i	0.328660	−	0.944448i	$-0.393403\pi$
$660$	−0.376591	−	0.0149882i	−0.0146588	−	0.000583416i
$661$	−33.2175	−	19.1781i	−1.29201	−	0.745943i	−0.313000	−	0.949753i	$-0.601334\pi$
$661$	−33.2175	−	19.1781i	−1.29201	−	0.745943i	−0.979010	+	0.203811i	$0.934667\pi$
$662$	−30.7031	−	17.7264i	−1.19331	−	0.688957i
$663$	−3.15825	−	6.01026i	−0.122656	−	0.233419i
$664$	−31.7967	−	18.3579i	−1.23395	−	0.712423i
$665$		−	1.08520i		−	0.0420823i
$666$	−14.1515	−	1.12824i	−0.548359	−	0.0437184i
$667$	−1.66823			−0.0645940
$668$	−0.326346	−	0.188416i	−0.0126267	−	0.00729003i
$669$	−2.39661	−	4.56083i	−0.0926582	−	0.176332i
$670$	13.5788	−	32.6102i	0.524597	−	1.25984i
$671$	17.1588	+	9.90666i	0.662409	+	0.382442i
$672$	−0.186875	+	0.0981984i	−0.00720886	+	0.00378808i
$673$	1.43344	−	0.827599i	0.0552552	−	0.0319016i	−0.472118	−	0.881535i	$-0.656510\pi$
$673$	1.43344	−	0.827599i	0.0552552	−	0.0319016i	0.527373	+	0.849634i	$0.323177\pi$
$674$	1.56425	+	0.903118i	0.0602525	+	0.0347868i
$675$	−8.43765	−	19.7221i	−0.324765	−	0.759105i
$676$	−0.239512	−	0.414847i	−0.00921200	−	0.0159556i
$677$	39.5050			1.51830			0.759151	−	0.650915i	$-0.225614\pi$
$677$	39.5050			1.51830			0.759151	+	0.650915i	$0.225614\pi$
$678$	8.94954	+	0.356189i	0.343705	+	0.0136794i
$679$	1.40466	−	2.43295i	0.0539060	−	0.0933679i
$680$			31.6024i			1.21190i
$681$	1.46133	−	36.7171i	0.0559983	−	1.40700i
$682$		−	4.03936i		−	0.154675i
$683$	4.43147	+	7.67553i	0.169565	+	0.293696i	0.938267	−	0.345912i	$-0.112430\pi$
$683$	4.43147	+	7.67553i	0.169565	+	0.293696i	−0.768702	+	0.639607i	$0.779097\pi$
$684$	0.0459660	−	0.0667353i	0.00175755	−	0.00255169i
$685$	−48.3989			−1.84923
$686$	−9.08070	−	5.24274i	−0.346703	−	0.200169i
$687$	−0.687751	+	17.2803i	−0.0262393	+	0.659284i
$688$			26.9694i			1.02820i
$689$		−	3.84102i		−	0.146331i
$690$	−1.79884	+	0.945245i	−0.0684805	+	0.0359849i
$691$	9.49293			0.361128			0.180564	−	0.983563i	$-0.442208\pi$
$691$	9.49293			0.361128			0.180564	+	0.983563i	$0.442208\pi$
$692$		−	0.750260i		−	0.0285206i
$693$	0.228335	−	2.86401i	0.00867374	−	0.108795i
$694$	21.2686			0.807345
$695$	−5.92157	+	3.41882i	−0.224618	+	0.129683i
$696$	−1.18319	+	29.7285i	−0.0448486	+	1.12686i
$697$	−38.3820	−	22.1599i	−1.45382	−	0.839365i
$698$	28.7291			1.08741
$699$	−17.7999	+	28.1793i	−0.673254	+	1.06584i
$700$	−0.0770423	−	0.0444804i	−0.00291193	−	0.00168120i
$701$	6.82744	−	11.8255i	0.257869	−	0.446642i	−0.707802	−	0.706411i	$-0.750313\pi$
$701$	6.82744	−	11.8255i	0.257869	−	0.446642i	0.965671	+	0.259769i	$0.0836465\pi$
$702$	−6.23152	−	4.66813i	−0.235193	−	0.176187i
$703$	−1.11148	+	1.92514i	−0.0419202	+	0.0726079i
$704$	−14.0131			−0.528137
$705$	−15.3526	−	9.69769i	−0.578212	−	0.365236i
$706$	11.1276	+	19.2735i	0.418791	+	0.725368i
$707$			1.42721i			0.0536759i
$708$	0.0130798	−	0.328640i	0.000491568	−	0.0123510i
$709$	−7.07279	+	12.2504i	−0.265624	+	0.460074i	−0.967727	−	0.252001i	$-0.918911\pi$
$709$	−7.07279	+	12.2504i	−0.265624	+	0.460074i	0.702103	+	0.712076i	$0.252245\pi$
$710$			16.7741i			0.629519i
$711$	0.0721890	−	0.905467i	0.00270730	−	0.0339577i
$712$			2.51075i			0.0940942i
$713$	−0.214858	−	0.372144i	−0.00804648	−	0.0139369i
$714$	4.94473	+	0.196799i	0.185052	+	0.00736502i
$715$	4.91078	+	2.83524i	0.183653	+	0.106032i
$716$	−0.164520	−	0.284958i	−0.00614842	−	0.0106494i
$717$	−8.70111	−	16.5585i	−0.324949	−	0.618389i
$718$	−26.8693	−	15.5130i	−1.00275	−	0.578940i
$719$	32.5291	−	18.7807i	1.21313	−	0.700401i	0.249690	−	0.968326i	$-0.419671\pi$
$719$	32.5291	−	18.7807i	1.21313	−	0.700401i	0.963440	+	0.267925i	$0.0863379\pi$
$720$	15.8823	+	33.3854i	0.591900	+	1.24420i
$721$	−7.17761	+	4.14399i	−0.267308	+	0.154330i
$722$	13.2480	+	22.9462i	0.493040	+	0.853971i
$723$	4.82579	+	9.18365i	0.179473	+	0.341544i
$724$	−0.750729			−0.0279006
$725$	−21.9389	+	12.6665i	−0.814792	+	0.470420i
$726$	10.3046	−	16.3134i	0.382439	−	0.605446i
$727$	−22.8067	−	13.1674i	−0.845853	−	0.488353i	0.0133965	−	0.999910i	$-0.495736\pi$
$727$	−22.8067	−	13.1674i	−0.845853	−	0.488353i	−0.859249	+	0.511557i	$0.829069\pi$
$728$	1.57194			0.0582600
$729$	26.2346	+	6.38315i	0.971653	+	0.236413i
$730$	−9.41509	+	16.3074i	−0.348468	+	0.603565i
$731$	12.3533	−	21.3966i	0.456904	−	0.791381i
$732$	−0.0307081	+	0.771566i	−0.00113501	+	0.0285179i
$733$	2.54960	−	1.47201i	0.0941714	−	0.0543699i	−0.452175	−	0.891929i	$-0.649352\pi$
$733$	2.54960	−	1.47201i	0.0941714	−	0.0543699i	0.546346	+	0.837559i	$0.316018\pi$
$734$	−12.8777	−	7.43497i	−0.475326	−	0.274430i
$735$	−18.7620	+	29.7025i	−0.692047	+	1.09559i
$736$	0.0536055	−	0.0309491i	0.00197592	−	0.00114080i
$737$	−8.89319	−	11.6347i	−0.327585	−	0.428568i
$738$	−50.6642	−	4.03924i	−1.86497	−	0.148687i
$739$	12.7675	−	7.37131i	0.469659	−	0.271158i	−0.246438	−	0.969159i	$-0.579260\pi$
$739$	12.7675	−	7.37131i	0.469659	−	0.271158i	0.716097	+	0.698001i	$0.245927\pi$
$740$	0.201469	+	0.348954i	0.00740614	+	0.0128278i
$741$	−1.07926	+	0.567125i	−0.0396476	+	0.0208338i
$742$	2.42451	+	1.39979i	0.0890065	+	0.0513879i
$743$			33.9923i			1.24706i	0.781801	+	0.623528i	$0.214301\pi$
$743$			33.9923i			1.24706i	−0.781801	+	0.623528i	$0.785699\pi$
$744$	−6.78416	+	3.56491i	−0.248719	+	0.130696i
$745$	−10.7666	+	6.21608i	−0.394457	+	0.227740i
$746$			5.70507i			0.208878i
$747$	32.4057	+	22.3204i	1.18566	+	0.816661i
$748$	−0.233063	−	0.134559i	−0.00852161	−	0.00491996i
$749$	3.72184			0.135993
$750$	3.47972	−	5.50882i	0.127062	−	0.201154i
$751$	10.0430	−	17.3950i	0.366475	−	0.634753i	−0.622537	−	0.782591i	$-0.713898\pi$
$751$	10.0430	−	17.3950i	0.366475	−	0.634753i	0.989012	+	0.147837i	$0.0472312\pi$
$752$	12.2577	+	7.07697i	0.446991	+	0.258071i
$753$	−24.6913	−	46.9885i	−0.899802	−	1.71236i
$754$	−4.59750	+	7.96311i	−0.167431	+	0.289999i
$755$	−11.0688	−	19.1717i	−0.402834	−	0.697730i
$756$	0.102946	−	0.0440432i	0.00374412	−	0.00160184i
$757$	42.1628	+	24.3427i	1.53243	+	0.884751i	0.999249	+	0.0387528i	$0.0123385\pi$
$757$	42.1628	+	24.3427i	1.53243	+	0.884751i	0.533185	+	0.845998i	$0.320995\pi$
$758$		−	2.64881i		−	0.0962091i
$759$	−0.0335017	+	0.841757i	−0.00121604	+	0.0305539i
$760$	5.67483			0.205848
$761$	34.5740	+	19.9613i	1.25331	+	0.723596i	0.971764	−	0.235953i	$-0.0758211\pi$
$761$	34.5740	+	19.9613i	1.25331	+	0.723596i	0.281541	+	0.959549i	$0.409154\pi$
$762$	17.8309	+	33.9328i	0.645945	+	1.22926i
$763$	−3.03370			−0.109827
$764$	−0.656303			−0.0237442
$765$	2.69168	−	33.7617i	0.0973178	−	1.22066i
$766$	−22.7966	+	39.4848i	−0.823673	+	1.42664i
$767$	−2.47423	+	4.28549i	−0.0893392	+	0.154740i
$768$	−0.778094	−	1.48074i	−0.0280770	−	0.0534316i
$769$	14.5899	−	8.42347i	0.526124	−	0.303758i	−0.213312	−	0.976984i	$-0.568425\pi$
$769$	14.5899	−	8.42347i	0.526124	−	0.303758i	0.739437	+	0.673226i	$0.235092\pi$
$770$	−3.57929	+	2.06650i	−0.128989	+	0.0744716i
$771$	34.2009	−	17.9717i	1.23171	−	0.647236i
$772$	0.156475			0.00563168
$773$	38.1717	+	22.0385i	1.37294	+	0.792668i	0.991298	−	0.131641i	$-0.0420245\pi$
$773$	38.1717	+	22.0385i	1.37294	+	0.792668i	0.381645	+	0.924309i	$0.375358\pi$
$774$	2.25173	−	28.2434i	0.0809367	−	1.01519i
$775$	−5.65121	−	3.26273i	−0.202998	−	0.117201i
$776$	12.7226	+	7.34538i	0.456714	+	0.263684i
$777$	−2.71912	+	1.42883i	−0.0975478	+	0.0512590i
$778$	25.5513	−	14.7520i	0.916057	−	0.528886i
$779$	−3.97924	+	6.89224i	−0.142571	+	0.246940i
$780$	−0.00878852	+	0.220819i	−0.000314680	+	0.00790657i
$781$	6.02228	+	3.47697i	0.215494	+	0.124416i
$782$	−1.45100			−0.0518876
$783$	3.79610	−	31.6589i	0.135661	−	1.13140i
$784$	13.6917	−	23.7148i	0.488990	−	0.846955i
$785$	−0.314859	+	0.545352i	−0.0112378	+	0.0194645i
$786$	−36.6244	+	19.2452i	−1.30635	+	0.686454i
$787$		−	11.0253i		−	0.393010i	−0.980503	−	0.196505i	$-0.937041\pi$
$787$		−	11.0253i		−	0.393010i	0.980503	−	0.196505i	$-0.0629592\pi$
$788$	−0.237337			−0.00845480
$789$	−42.0937	+	22.1192i	−1.49858	+	0.787465i
$790$	−1.13161	+	0.653333i	−0.0402607	+	0.0232445i
$791$	1.67831	−	0.968971i	0.0596737	−	0.0344526i
$792$	14.9767	+	1.19403i	0.532175	+	0.0424280i
$793$	5.80889	−	10.0613i	0.206280	−	0.357287i
$794$	10.4721	−	18.1382i	0.371640	−	0.643699i
$795$	10.2326	−	16.1994i	0.362912	−	0.574532i
$796$	0.332217	−	0.575416i	0.0117751	−	0.0203951i
$797$	0.884759	−	0.510816i	0.0313398	−	0.0180940i	−0.484248	−	0.874931i	$-0.660907\pi$
$797$	0.884759	−	0.510816i	0.0313398	−	0.0180940i	0.515588	+	0.856837i	$0.327574\pi$
$798$	0.0353391	−	0.887923i	0.00125099	−	0.0314321i
$799$	−6.48320	−	11.2292i	−0.229359	−	0.397261i
$800$	0.469979	−	0.814028i	0.0166163	−	0.0287802i
$801$	0.213848	−	2.68229i	0.00755595	−	0.0947742i
$802$	16.8675	+	29.2154i	0.595612	+	1.03163i
$803$	3.90317	+	6.76048i	0.137740	+	0.238572i
$804$	0.240168	−	0.517731i	0.00847008	−	0.0182590i
$805$	−0.219839	+	0.380772i	−0.00774831	+	0.0134205i
$806$	−2.36852			−0.0834277
$807$	1.62895	−	40.9286i	0.0573417	−	1.44075i
$808$	−7.46331			−0.262558
$809$	48.8081			1.71600			0.858001	−	0.513649i	$-0.171707\pi$
$809$	48.8081			1.71600			0.858001	+	0.513649i	$0.171707\pi$
$810$	−13.8452	−	36.2886i	−0.486471	−	1.27505i
$811$	35.4592	+	20.4724i	1.24514	+	0.718882i	0.970136	−	0.242562i	$-0.0779876\pi$
$811$	35.4592	+	20.4724i	1.24514	+	0.718882i	0.275004	+	0.961443i	$0.411321\pi$
$812$	−0.0661169	−	0.114518i	−0.00232025	−	0.00401879i
$813$	0.565235	−	14.2020i	0.0198237	−	0.498085i
$814$	8.46616			0.296739
$815$	3.71756	+	6.43901i	0.130221	+	0.225549i
$816$	−1.04984	+	26.3781i	−0.0367518	+	0.923417i
$817$	−3.84217	−	2.21828i	−0.134421	−	0.0776077i
$818$			16.3618i			0.572077i
$819$	−1.67935	−	0.133887i	−0.0586811	−	0.00467840i
$820$	0.721285	+	1.24930i	0.0251884	+	0.0436275i
$821$	7.78062	+	4.49214i	0.271545	+	0.156777i	0.629590	−	0.776928i	$-0.283223\pi$
$821$	7.78062	+	4.49214i	0.271545	+	0.156777i	−0.358044	+	0.933705i	$0.616556\pi$
$822$	−39.6005	−	1.57609i	−1.38122	−	0.0549724i
$823$	17.2804			0.602356			0.301178	−	0.953568i	$-0.402620\pi$
$823$	17.2804			0.602356			0.301178	+	0.953568i	$0.402620\pi$
$824$	−21.6701	−	37.5338i	−0.754914	−	1.30755i
$825$	5.95069	+	11.3244i	0.207176	+	0.394264i
$826$	−1.80338	−	3.12354i	−0.0627474	−	0.108682i
$827$	13.0191	−	7.51658i	0.452719	−	0.261377i	−0.256259	−	0.966608i	$-0.582490\pi$
$827$	13.0191	−	7.51658i	0.452719	−	0.261377i	0.708978	+	0.705231i	$0.249157\pi$
$828$	−0.0296476	+	0.0141041i	−0.00103032	+	0.000490153i
$829$	5.74446			0.199513			0.0997567	−	0.995012i	$-0.468194\pi$
$829$	5.74446			0.199513			0.0997567	+	0.995012i	$0.468194\pi$
$830$		−	56.6040i		−	1.96476i
$831$	−25.2434	−	48.0392i	−0.875685	−	1.66646i
$832$			8.21673i			0.284864i
$833$	−21.7250	+	12.5430i	−0.752728	+	0.434588i
$834$	−4.95642	+	2.60448i	−0.171627	+	0.0901857i
$835$			28.2823i			0.978748i
$836$	−0.0241626	+	0.0418509i	−0.000835683	+	0.00144744i
$837$	7.55133	−	3.23066i	0.261012	−	0.111668i
$838$	5.68200	+	3.28051i	0.196282	+	0.113323i
$839$			50.0070i			1.72643i	0.504833	+	0.863217i	$0.331554\pi$
$839$			50.0070i			1.72643i	−0.504833	+	0.863217i	$0.668446\pi$
$840$	6.62961	+	4.18769i	0.228743	+	0.144489i
$841$	−8.65553			−0.298467
$842$	19.1936	+	33.2442i	0.661454	+	1.14567i
$843$	26.8517	−	42.5094i	0.924820	−	1.46410i
$844$	0.128993	+	0.223423i	0.00444013	+	0.00769053i
$845$	−17.9760	+	31.1354i	−0.618394	+	1.07109i
$846$	−12.2458	−	8.43469i	−0.421021	−	0.289991i
$847$		−	4.17493i		−	0.143452i
$848$	−7.46730	+	12.9337i	−0.256428	+	0.444146i
$849$	−23.3769	+	37.0084i	−0.802294	+	1.27013i
$850$	−19.0822	+	11.0171i	−0.654513	+	0.377883i
$851$	0.779984	−	0.450324i	0.0267375	−	0.0154369i
$852$	−0.0107777	+	0.270799i	−0.000369239	+	0.00927741i
$853$	27.2306	−	47.1648i	0.932358	−	1.61489i	0.153078	−	0.988214i	$-0.451081\pi$
$853$	27.2306	−	47.1648i	0.932358	−	1.61489i	0.779279	−	0.626677i	$-0.215585\pi$
$854$	4.23389	+	7.33331i	0.144881	+	0.250941i
$855$	−6.06257	−	0.483343i	−0.207335	−	0.0165300i
$856$			19.4626i			0.665217i
$857$	−3.40945	−	5.90535i	−0.116465	−	0.201723i	0.801900	−	0.597459i	$-0.203823\pi$
$857$	−3.40945	−	5.90535i	−0.116465	−	0.201723i	−0.918364	+	0.395736i	$0.870490\pi$
$858$	3.92572	+	2.47974i	0.134022	+	0.0846568i
$859$	11.6598	+	20.1954i	0.397829	+	0.689060i	0.993458	−	0.114200i	$-0.0364305\pi$
$859$	11.6598	+	20.1954i	0.397829	+	0.689060i	−0.595629	+	0.803260i	$0.703097\pi$
$860$	−0.696440	+	0.402090i	−0.0237484	+	0.0137111i
$861$	−9.73480	+	5.11540i	−0.331761	+	0.174332i
$862$	17.3641	−	10.0252i	0.591423	−	0.341458i
$863$			39.1140i			1.33146i	0.746195	+	0.665728i	$0.231879\pi$
$863$			39.1140i			1.33146i	−0.746195	+	0.665728i	$0.768121\pi$
$864$	0.465360	+	1.08773i	0.0158319	+	0.0370053i
$865$	−48.7650	+	28.1545i	−1.65806	+	0.957282i
$866$	6.86174	−	3.96163i	0.233171	−	0.134622i
$867$	−2.80953	+	4.44781i	−0.0954165	+	0.151056i
$868$	0.0170309	−	0.0294984i	0.000578067	−	0.00100124i
$869$			0.541697i			0.0183758i
$870$	−40.6037	+	21.3363i	−1.37659	+	0.723367i
$871$	−6.82212	+	5.21462i	−0.231159	+	0.176691i
$872$		−	15.8641i		−	0.537225i
$873$	−12.9662	−	8.93088i	−0.438840	−	0.302264i
$874$			0.260555i			0.00881340i
$875$		−	1.40982i		−	0.0476606i
$876$	−0.162474	+	0.257216i	−0.00548949	+	0.00869052i
$877$	−40.7271			−1.37526			−0.687628	−	0.726063i	$-0.741348\pi$
$877$	−40.7271			−1.37526			−0.687628	+	0.726063i	$0.741348\pi$
$878$	3.59673	+	6.22972i	0.121384	+	0.210243i
$879$	−44.3078	−	27.9876i	−1.49446	−	0.944000i
$880$	−11.0239	−	19.0940i	−0.371617	−	0.643659i
$881$	19.3263	−	11.1581i	0.651121	−	0.375925i	−0.137765	−	0.990465i	$-0.543992\pi$
$881$	19.3263	−	11.1581i	0.651121	−	0.375925i	0.788885	+	0.614540i	$0.210658\pi$
$882$	−16.3185	+	23.6919i	−0.549472	+	0.797746i
$883$	8.84899	+	5.10896i	0.297792	+	0.171930i	0.641451	−	0.767164i	$-0.278333\pi$
$883$	8.84899	+	5.10896i	0.297792	+	0.171930i	−0.343659	+	0.939095i	$0.611666\pi$
$884$	−0.0789001	+	0.136659i	−0.00265370	+	0.00459634i
$885$	−21.8516	+	11.4825i	−0.734533	+	0.385980i
$886$	−18.2326	+	31.5798i	−0.612536	+	1.06094i
$887$			10.7419i			0.360679i	0.983604	+	0.180339i	$0.0577196\pi$
$887$			10.7419i			0.360679i	−0.983604	+	0.180339i	$0.942280\pi$
$888$	−7.47176	−	14.2190i	−0.250736	−	0.477160i
$889$	7.18280	+	4.14699i	0.240903	+	0.139086i
$890$	−3.35219	+	1.93539i	−0.112366	+	0.0648744i
$891$	−15.8983	−	2.55123i	−0.532614	−	0.0854693i
$892$	−0.0598726	+	0.103702i	−0.00200468	+	0.00347221i
$893$	−2.01643	+	1.16418i	−0.0674771	+	0.0389579i
$894$	−9.01173	+	4.73545i	−0.301397	+	0.158377i
$895$	−12.3477	+	21.3869i	−0.412738	+	0.714884i
$896$	−5.39763	−	3.11632i	−0.180322	−	0.104109i
$897$	0.493574	+	0.0196441i	0.0164800	+	0.000655899i
$898$	−31.2645	+	18.0506i	−1.04331	+	0.602355i
$899$	−4.84981	−	8.40012i	−0.161750	−	0.280160i
$900$	−0.282808	+	0.410592i	−0.00942692	+	0.0136864i
$901$	11.8486	−	6.84077i	0.394733	−	0.227899i
$902$	30.3100			1.00921
$903$	−2.85165	−	5.42679i	−0.0948969	−	0.180592i
$904$	5.06702	+	8.77634i	0.168527	+	0.291897i
$905$	28.1721	+	48.7955i	0.936472	+	1.62202i
$906$	−8.43227	−	16.0469i	−0.280143	−	0.533123i
$907$	10.0652			0.334211			0.167105	−	0.985939i	$-0.446558\pi$
$907$	10.0652			0.334211			0.167105	+	0.985939i	$0.446558\pi$
$908$	−0.739623	+	0.427022i	−0.0245453	+	0.0141712i
$909$	7.97325	+	0.635673i	0.264456	+	0.0210839i
$910$	1.21172	+	2.09876i	0.0401681	+	0.0695732i
$911$	2.34077	−	1.35144i	0.0775532	−	0.0447754i	−0.460722	−	0.887545i	$-0.652409\pi$
$911$	2.34077	−	1.35144i	0.0775532	−	0.0447754i	0.538275	+	0.842769i	$0.319076\pi$
$912$	4.73670	+	0.188519i	0.156848	+	0.00624250i
$913$	−20.3222	−	11.7330i	−0.672566	−	0.388306i
$914$	−13.5180	+	23.4138i	−0.447134	+	0.774459i
$915$	51.3023	−	26.9581i	1.69600	−	0.891207i
$916$	0.348091	−	0.200971i	0.0115013	−	0.00664026i
$917$	−4.47593	+	7.75254i	−0.147808	+	0.256011i
$918$	3.30179	−	27.5365i	0.108975	−	0.908839i
$919$	−36.3379	+	20.9797i	−1.19868	+	0.692056i	−0.960260	−	0.279108i	$-0.909961\pi$
$919$	−36.3379	+	20.9797i	−1.19868	+	0.692056i	−0.238416	+	0.971163i	$0.576628\pi$
$920$	−1.99117	−	1.14960i	−0.0656468	−	0.0379012i
$921$	13.8309	+	26.3207i	0.455743	+	0.867296i
$922$		−	15.1506i		−	0.498959i
$923$	2.03876	−	3.53124i	0.0671066	−	0.116232i
$924$	−0.0591114	+	0.0310616i	−0.00194462	+	0.00102185i
$925$	6.83841	−	11.8445i	0.224846	−	0.389444i
$926$	−7.78300	−	4.49352i	−0.255765	−	0.147666i
$927$	19.9539	+	41.9440i	0.655372	+	1.37762i
$928$	1.20999	−	0.698590i	0.0397200	−	0.0229323i
$929$	−14.4049	−	24.9500i	−0.472609	−	0.818583i	0.526900	−	0.849928i	$-0.323354\pi$
$929$	−14.4049	−	24.9500i	−0.472609	−	0.818583i	−0.999509	+	0.0313447i	$0.990021\pi$
$930$	−9.98916	−	6.30980i	−0.327558	−	0.206907i
$931$	2.25233	+	3.90115i	0.0738172	+	0.127855i
$932$	0.774654			0.0253746
$933$	−5.29926	+	8.38935i	−0.173490	+	0.274655i
$934$		−	20.5417i		−	0.672145i
$935$			20.1980i			0.660545i
$936$	0.700134	−	8.78178i	0.0228846	−	0.287041i
$937$		−	25.0527i		−	0.818436i	−0.912437	−	0.409218i	$-0.865802\pi$
$937$		−	25.0527i		−	0.818436i	0.912437	−	0.409218i	$-0.134198\pi$
$938$	−0.805351	−	6.20660i	−0.0262956	−	0.202653i
$939$	−21.2514	+	11.1671i	−0.693515	+	0.364425i
$940$			0.422045i			0.0137656i
$941$	−18.1397	+	31.4189i	−0.591337	+	1.02423i	0.402716	+	0.915325i	$0.368066\pi$
$941$	−18.1397	+	31.4189i	−0.591337	+	1.02423i	−0.994053	+	0.108901i	$0.965267\pi$
$942$	−0.275380	+	0.435959i	−0.00897236	+	0.0142043i
$943$	2.79244	−	1.61222i	0.0909345	−	0.0525011i
$944$	16.6628	−	9.62025i	0.542327	−	0.313113i
$945$	−6.72590	−	5.03848i	−0.218794	−	0.163902i
$946$			16.8967i			0.549358i
$947$	−13.2038	+	7.62320i	−0.429065	+	0.247721i	−0.698948	−	0.715172i	$-0.746348\pi$
$947$	−13.2038	+	7.62320i	−0.429065	+	0.247721i	0.269883	+	0.962893i	$0.413015\pi$
$948$	−0.0186883	+	0.00982025i	−0.000606968	+	0.000318947i
$949$	3.96409	−	2.28867i	0.128680	−	0.0742933i
$950$	1.97833	+	3.42657i	0.0641856	+	0.111173i
$951$	−32.8004	−	20.7188i	−1.06362	−	0.671854i
$952$	2.79959	+	4.84904i	0.0907354	+	0.157158i
$953$			10.0252i			0.324750i	0.986729	+	0.162375i	$0.0519154\pi$
$953$			10.0252i			0.324750i	−0.986729	+	0.162375i	$0.948085\pi$
$954$	8.89990	−	12.9213i	0.288145	−	0.418341i
$955$	24.6286	+	42.6581i	0.796964	+	1.38038i
$956$	−0.217373	+	0.376502i	−0.00703035	+	0.0121769i
$957$	−0.756208	+	19.0003i	−0.0244447	+	0.614193i
$958$	29.5899	−	17.0837i	0.956006	−	0.551950i
$959$	−7.42628	+	4.28756i	−0.239807	+	0.138453i
$960$	−21.8896	+	34.6538i	−0.706482	+	1.11845i
$961$	−14.2507	+	24.6830i	−0.459702	+	0.796226i
$962$		−	4.96423i		−	0.160053i
$963$	1.65769	−	20.7924i	0.0534183	−	0.670025i
$964$	0.120559	−	0.208814i	0.00388295	−	0.00672546i
$965$	−5.87195	−	10.1705i	−0.189025	−	0.327401i
$966$	−0.192274	+	0.304392i	−0.00618631	+	0.00979367i
$967$	14.8549	+	25.7295i	0.477702	+	0.827405i	0.999673	−	0.0255585i	$-0.00813640\pi$
$967$	14.8549	+	25.7295i	0.477702	+	0.827405i	−0.521971	+	0.852963i	$0.674803\pi$
$968$	21.8319			0.701704
$969$	−3.67157	−	2.31920i	−0.117948	−	0.0745035i
$970$			22.6485i			0.727200i
$971$	−42.6048	−	24.5979i	−1.36725	−	0.789384i	−0.376677	−	0.926344i	$-0.622933\pi$
$971$	−42.6048	−	24.5979i	−1.36725	−	0.789384i	−0.990577	+	0.136960i	$0.956267\pi$
$972$	−0.200199	−	0.594734i	−0.00642139	−	0.0190761i
$973$	−0.605733	+	1.04916i	−0.0194189	+	0.0336345i
$974$		−	39.4572i		−	1.26429i
$975$	6.64018	−	3.48926i	0.212656	−	0.111746i
$976$	−39.1201	+	22.5860i	−1.25220	+	0.722961i
$977$			19.2527i			0.615949i	0.951395	+	0.307974i	$0.0996511\pi$
$977$			19.2527i			0.615949i	−0.951395	+	0.307974i	$0.900349\pi$
$978$	2.83206	+	5.38952i	0.0905593	+	0.172338i
$979$			1.60469i			0.0512860i
$980$	0.816524			0.0260829
$981$	−1.35119	+	16.9480i	−0.0431403	+	0.541108i
$982$	53.7218	−	31.0163i	1.71433	−	0.989769i
$983$	5.61390	+	9.72356i	0.179056	+	0.310134i	0.941557	−	0.336853i	$-0.109362\pi$
$983$	5.61390	+	9.72356i	0.179056	+	0.310134i	−0.762502	+	0.646986i	$0.776029\pi$
$984$	−26.7499	−	50.9060i	−0.852755	−	1.62282i
$985$	8.90641	+	15.4264i	0.283782	+	0.491524i
$986$	−32.7522			−1.04304
$987$	−3.21478	−	0.127948i	−0.102328	−	0.00407262i
$988$	0.0245398	+	0.0141681i	0.000780715	+	0.000450746i
$989$	0.898752	+	1.55668i	0.0285787	+	0.0494997i
$990$	9.95049	+	20.9164i	0.316247	+	0.664767i
$991$		−	0.420878i		−	0.0133696i	−0.999978	−	0.00668482i	$-0.997872\pi$
$991$		−	0.420878i		−	0.0133696i	0.999978	−	0.00668482i	$-0.00212786\pi$
$992$	0.311680	+	0.179949i	0.00989585	+	0.00571337i
$993$	−1.70965	+	42.9562i	−0.0542540	+	1.36317i
$994$	1.48598	+	2.57379i	0.0471324	+	0.0816357i
$995$	−49.8675			−1.58091
$996$	0.0363694	−	0.913810i	0.00115241	−	0.0289552i
$997$	2.12517	+	3.68091i	0.0673049	+	0.116576i	0.897714	−	0.440578i	$-0.145227\pi$
$997$	2.12517	+	3.68091i	0.0673049	+	0.116576i	−0.830409	+	0.557154i	$0.811893\pi$
$998$	−12.0571	−	6.96119i	−0.381662	−	0.220353i
$999$	6.77120	+	15.8270i	0.214231	+	0.500743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.k.a.365.19	yes	132
9.2	odd	6		603.2.t.a.164.19	yes	132
67.38	odd	6		603.2.t.a.239.19	yes	132
603.38	even	6	inner	603.2.k.a.38.19	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.k.a.38.19	✓	132	603.38	even	6	inner
603.2.k.a.365.19	yes	132	1.1	even	1	trivial
603.2.t.a.164.19	yes	132	9.2	odd	6
603.2.t.a.239.19	yes	132	67.38	odd	6

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.714188 + 1.23701i) q^{2} +(1.73068 + 0.0688806i) q^{3} +(-0.0201279 - 0.0348626i) q^{4} +(-1.51065 + 2.61653i) q^{5} +(-1.32124 + 2.09167i) q^{6} +0.535303i q^{7} -2.79925 q^{8} +(2.99051 + 0.238421i) q^{9} +O(q^{10})\)	\(q+(-0.714188 + 1.23701i) q^{2} +(1.73068 + 0.0688806i) q^{3} +(-0.0201279 - 0.0348626i) q^{4} +(-1.51065 + 2.61653i) q^{5} +(-1.32124 + 2.09167i) q^{6} +0.535303i q^{7} -2.79925 q^{8} +(2.99051 + 0.238421i) q^{9} +(-2.15778 - 3.73738i) q^{10} -1.78908 q^{11} +(-0.0324336 - 0.0617224i) q^{12} +1.04905i q^{13} +(-0.662174 - 0.382307i) q^{14} +(-2.79469 + 4.42432i) q^{15} +(2.03945 - 3.53242i) q^{16} +(-3.23605 + 1.86833i) q^{17} +(-2.43071 + 3.52901i) q^{18} +(0.335495 + 0.581095i) q^{19} +0.121625 q^{20} +(-0.0368720 + 0.926438i) q^{21} +(1.27774 - 2.21311i) q^{22} -0.271857i q^{23} +(-4.84461 - 0.192814i) q^{24} +(-2.06415 - 3.57521i) q^{25} +(-1.29768 - 0.749217i) q^{26} +(5.15920 + 0.618619i) q^{27} +(0.0186620 - 0.0107745i) q^{28} -6.13641i q^{29} +(-3.47699 - 6.61685i) q^{30} +(1.36890 - 0.790333i) q^{31} +(0.113843 + 0.197183i) q^{32} +(-3.09632 - 0.123233i) q^{33} -5.33736i q^{34} +(-1.40063 - 0.808657i) q^{35} +(-0.0518808 - 0.109056i) q^{36} +(1.65647 + 2.86910i) q^{37} -0.958426 q^{38} +(-0.0722591 + 1.81557i) q^{39} +(4.22870 - 7.32432i) q^{40} +(5.93039 + 10.2717i) q^{41} +(-1.11968 - 0.707262i) q^{42} +(-5.72612 + 3.30597i) q^{43} +(0.0360104 + 0.0623719i) q^{44} +(-5.14146 + 7.46459i) q^{45} +(0.336290 + 0.194157i) q^{46} +3.47005i q^{47} +(3.77294 - 5.97302i) q^{48} +6.71345 q^{49} +5.89675 q^{50} +(-5.72925 + 3.01058i) q^{51} +(0.0365725 - 0.0211151i) q^{52} -3.66144 q^{53} +(-4.44987 + 5.94016i) q^{54} +(2.70268 - 4.68118i) q^{55} -1.49845i q^{56} +(0.540609 + 1.02880i) q^{57} +(7.59080 + 4.38255i) q^{58} +(4.08512 + 2.35855i) q^{59} +(0.210494 + 0.00837762i) q^{60} +(-9.59087 - 5.53729i) q^{61} +2.25778i q^{62} +(-0.127627 + 1.60083i) q^{63} +7.83256 q^{64} +(-2.74486 - 1.58475i) q^{65} +(2.36380 - 3.74217i) q^{66} +(4.97082 + 6.50315i) q^{67} +(0.130270 + 0.0752112i) q^{68} +(0.0187257 - 0.470498i) q^{69} +(2.00063 - 1.15507i) q^{70} +(-3.36614 - 1.94344i) q^{71} +(-8.37119 - 0.667399i) q^{72} +(-2.18166 - 3.77875i) q^{73} -4.73213 q^{74} +(-3.32612 - 6.32972i) q^{75} +(0.0135056 - 0.0233924i) q^{76} -0.957699i q^{77} +(-2.19427 - 1.38604i) q^{78} -0.302780i q^{79} +(6.16179 + 10.6725i) q^{80} +(8.88631 + 1.42600i) q^{81} -16.9417 q^{82} +(11.3590 + 6.55813i) q^{83} +(0.0330402 - 0.0173618i) q^{84} -11.2896i q^{85} -9.44434i q^{86} +(0.422680 - 10.6202i) q^{87} +5.00808 q^{88} -0.896935i q^{89} +(-5.56179 - 11.6911i) q^{90} -0.561558 q^{91} +(-0.00947763 + 0.00547191i) q^{92} +(2.42356 - 1.27352i) q^{93} +(-4.29248 - 2.47826i) q^{94} -2.02727 q^{95} +(0.183445 + 0.349102i) q^{96} +(-4.54499 - 2.62405i) q^{97} +(-4.79466 + 8.30460i) q^{98} +(-5.35026 - 0.426554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9} - 6 q^{11} + 6 q^{12} + 4 q^{15} - 57 q^{16} + 9 q^{17} - 4 q^{19} - 30 q^{20} - 6 q^{21} - 11 q^{24} - 57 q^{25} + 36 q^{26} - 24 q^{28} + 45 q^{30} + 15 q^{32} - q^{33} + 15 q^{35} - q^{36} - 4 q^{37} + 14 q^{39} - 12 q^{40} + 3 q^{41} + 42 q^{42} + 3 q^{43} + 6 q^{44} - 9 q^{45} - 24 q^{46} - 21 q^{48} - 120 q^{49} - 24 q^{50} + 18 q^{52} - 60 q^{53} - 16 q^{54} - 9 q^{57} + 12 q^{58} + 12 q^{59} - 13 q^{60} + 18 q^{61} + 24 q^{63} + 84 q^{64} + 18 q^{65} - 30 q^{66} - 14 q^{67} - 39 q^{68} - 18 q^{69} + 45 q^{70} - 30 q^{71} + 39 q^{72} + 14 q^{73} + 30 q^{74} + 24 q^{75} - 7 q^{76} - 21 q^{78} + 18 q^{80} - 3 q^{81} - 24 q^{82} - 63 q^{83} + 129 q^{84} - 18 q^{87} - 30 q^{88} - 35 q^{90} + 42 q^{91} - 12 q^{92} - 28 q^{93} - 6 q^{94} + 24 q^{95} + 120 q^{96} - 39 q^{97} + 21 q^{98} - 72 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9 - 6 * q^11 + 6 * q^12 + 4 * q^15 - 57 * q^16 + 9 * q^17 - 4 * q^19 - 30 * q^20 - 6 * q^21 - 11 * q^24 - 57 * q^25 + 36 * q^26 - 24 * q^28 + 45 * q^30 + 15 * q^32 - q^33 + 15 * q^35 - q^36 - 4 * q^37 + 14 * q^39 - 12 * q^40 + 3 * q^41 + 42 * q^42 + 3 * q^43 + 6 * q^44 - 9 * q^45 - 24 * q^46 - 21 * q^48 - 120 * q^49 - 24 * q^50 + 18 * q^52 - 60 * q^53 - 16 * q^54 - 9 * q^57 + 12 * q^58 + 12 * q^59 - 13 * q^60 + 18 * q^61 + 24 * q^63 + 84 * q^64 + 18 * q^65 - 30 * q^66 - 14 * q^67 - 39 * q^68 - 18 * q^69 + 45 * q^70 - 30 * q^71 + 39 * q^72 + 14 * q^73 + 30 * q^74 + 24 * q^75 - 7 * q^76 - 21 * q^78 + 18 * q^80 - 3 * q^81 - 24 * q^82 - 63 * q^83 + 129 * q^84 - 18 * q^87 - 30 * q^88 - 35 * q^90 + 42 * q^91 - 12 * q^92 - 28 * q^93 - 6 * q^94 + 24 * q^95 + 120 * q^96 - 39 * q^97 + 21 * q^98 - 72 * q^99

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