LMFDB - Embedded newform 315.2.k.c.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04330 - 1.80705i) q^{2} +(0.853418 + 1.50721i) q^{3} +(-1.17696 + 2.03855i) q^{4} +1.00000 q^{5} +(1.83323 - 3.11464i) q^{6} +(2.35024 - 1.21507i) q^{7} +0.738471 q^{8} +(-1.54336 + 2.57256i) q^{9} +O(q^{10})$	\(q+(-1.04330 - 1.80705i) q^{2} +(0.853418 + 1.50721i) q^{3} +(-1.17696 + 2.03855i) q^{4} +1.00000 q^{5} +(1.83323 - 3.11464i) q^{6} +(2.35024 - 1.21507i) q^{7} +0.738471 q^{8} +(-1.54336 + 2.57256i) q^{9} +(-1.04330 - 1.80705i) q^{10} -0.0154416 q^{11} +(-4.07695 - 0.0341853i) q^{12} +(3.01043 + 5.21422i) q^{13} +(-4.64769 - 2.97931i) q^{14} +(0.853418 + 1.50721i) q^{15} +(1.58346 + 2.74264i) q^{16} +(-0.453816 - 0.786032i) q^{17} +(6.25893 + 0.104970i) q^{18} +(3.94407 - 6.83134i) q^{19} +(-1.17696 + 2.03855i) q^{20} +(3.83709 + 2.50534i) q^{21} +(0.0161102 + 0.0279038i) q^{22} +3.32997 q^{23} +(0.630224 + 1.11303i) q^{24} +1.00000 q^{25} +(6.28157 - 10.8800i) q^{26} +(-5.19451 - 0.130693i) q^{27} +(-0.289151 + 6.22115i) q^{28} +(1.08973 - 1.88747i) q^{29} +(1.83323 - 3.11464i) q^{30} +(-0.610692 + 1.05775i) q^{31} +(4.04253 - 7.00187i) q^{32} +(-0.0131781 - 0.0232737i) q^{33} +(-0.946933 + 1.64014i) q^{34} +(2.35024 - 1.21507i) q^{35} +(-3.42782 - 6.17399i) q^{36} +(-4.79552 + 8.30608i) q^{37} -16.4594 q^{38} +(-5.28976 + 8.98726i) q^{39} +0.738471 q^{40} +(-5.46963 - 9.47367i) q^{41} +(0.524024 - 9.54764i) q^{42} +(0.234772 - 0.406637i) q^{43} +(0.0181741 - 0.0314784i) q^{44} +(-1.54336 + 2.57256i) q^{45} +(-3.47416 - 6.01743i) q^{46} +(2.53419 + 4.38934i) q^{47} +(-2.78237 + 4.72723i) q^{48} +(4.04722 - 5.71139i) q^{49} +(-1.04330 - 1.80705i) q^{50} +(0.797420 - 1.35481i) q^{51} -14.1726 q^{52} +(-1.39434 - 2.41507i) q^{53} +(5.18327 + 9.52309i) q^{54} -0.0154416 q^{55} +(1.73558 - 0.897292i) q^{56} +(13.6622 + 0.114558i) q^{57} -4.54768 q^{58} +(-2.60645 + 4.51450i) q^{59} +(-4.07695 - 0.0341853i) q^{60} +(-4.12820 - 7.15026i) q^{61} +2.54854 q^{62} +(-0.501419 + 7.92140i) q^{63} -10.5365 q^{64} +(3.01043 + 5.21422i) q^{65} +(-0.0283080 + 0.0480951i) q^{66} +(-2.66210 + 4.61089i) q^{67} +2.13648 q^{68} +(2.84186 + 5.01896i) q^{69} +(-4.64769 - 2.97931i) q^{70} +4.77171 q^{71} +(-1.13972 + 1.89976i) q^{72} +(-0.466621 - 0.808211i) q^{73} +20.0127 q^{74} +(0.853418 + 1.50721i) q^{75} +(9.28400 + 16.0804i) q^{76} +(-0.0362914 + 0.0187626i) q^{77} +(21.7592 + 0.182452i) q^{78} +(-3.51232 - 6.08351i) q^{79} +(1.58346 + 2.74264i) q^{80} +(-4.23611 - 7.94074i) q^{81} +(-11.4129 + 19.7678i) q^{82} +(-8.41010 + 14.5667i) q^{83} +(-9.62333 + 4.87343i) q^{84} +(-0.453816 - 0.786032i) q^{85} -0.979752 q^{86} +(3.77481 + 0.0316519i) q^{87} -0.0114032 q^{88} +(-6.33695 + 10.9759i) q^{89} +(6.25893 + 0.104970i) q^{90} +(13.4109 + 8.59677i) q^{91} +(-3.91923 + 6.78830i) q^{92} +(-2.11543 - 0.0177379i) q^{93} +(5.28785 - 9.15882i) q^{94} +(3.94407 - 6.83134i) q^{95} +(14.0032 + 0.117417i) q^{96} +(3.11544 - 5.39610i) q^{97} +(-14.5432 - 1.35483i) q^{98} +(0.0238319 - 0.0397244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.04330	−	1.80705i	−0.737725	−	1.27778i	−0.953517	−	0.301339i	$-0.902567\pi$
$2$	−1.04330	−	1.80705i	−0.737725	−	1.27778i	0.215792	−	0.976439i	$-0.430767\pi$
$3$	0.853418	+	1.50721i	0.492721	+	0.870187i
$3$	0.853418	+	1.50721i	0.492721	+	0.870187i
$4$	−1.17696	+	2.03855i	−0.588478	+	1.01927i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.83323	−	3.11464i	0.748413	−	1.27155i
$7$	2.35024	−	1.21507i	0.888306	−	0.459252i
$7$	2.35024	−	1.21507i	0.888306	−	0.459252i
$8$	0.738471			0.261089
$9$	−1.54336	+	2.57256i	−0.514452	+	0.857519i
$10$	−1.04330	−	1.80705i	−0.329921	−	0.571440i
$11$	−0.0154416			−0.00465582			−0.00232791	−	0.999997i	$-0.500741\pi$
$11$	−0.0154416			−0.00465582			−0.00232791	+	0.999997i	$0.500741\pi$
$12$	−4.07695	−	0.0341853i	−1.17691	−	0.00986845i
$13$	3.01043	+	5.21422i	0.834943	+	1.44616i	0.894077	+	0.447914i	$0.147833\pi$
$13$	3.01043	+	5.21422i	0.834943	+	1.44616i	−0.0591331	+	0.998250i	$0.518834\pi$
$14$	−4.64769	−	2.97931i	−1.24215	−	0.796255i
$15$	0.853418	+	1.50721i	0.220352	+	0.389160i
$16$	1.58346	+	2.74264i	0.395866	+	0.685660i
$17$	−0.453816	−	0.786032i	−0.110067	−	0.190641i	0.805730	−	0.592283i	$-0.201773\pi$
$17$	−0.453816	−	0.786032i	−0.110067	−	0.190641i	−0.915797	+	0.401642i	$0.868440\pi$
$18$	6.25893	+	0.104970i	1.47524	+	0.0247416i
$19$	3.94407	−	6.83134i	0.904833	−	1.56722i	0.0836906	−	0.996492i	$-0.473329\pi$
$19$	3.94407	−	6.83134i	0.904833	−	1.56722i	0.821142	−	0.570724i	$-0.193337\pi$
$20$	−1.17696	+	2.03855i	−0.263175	+	0.455833i
$21$	3.83709	+	2.50534i	0.837323	+	0.546709i
$22$	0.0161102	+	0.0279038i	0.00343472	+	0.00594910i
$23$	3.32997			0.694347			0.347173	−	0.937801i	$-0.387142\pi$
$23$	3.32997			0.694347			0.347173	+	0.937801i	$0.387142\pi$
$24$	0.630224	+	1.11303i	0.128644	+	0.227196i
$25$	1.00000			0.200000
$26$	6.28157	−	10.8800i	1.23192	−	2.13374i
$27$	−5.19451	−	0.130693i	−0.999684	−	0.0251518i
$28$	−0.289151	+	6.22115i	−0.0546444	+	1.17569i
$29$	1.08973	−	1.88747i	0.202358	−	0.350495i	−0.746930	−	0.664903i	$-0.768473\pi$
$29$	1.08973	−	1.88747i	0.202358	−	0.350495i	0.949288	+	0.314408i	$0.101806\pi$
$30$	1.83323	−	3.11464i	0.334701	−	0.568653i
$31$	−0.610692	+	1.05775i	−0.109684	+	0.189978i	−0.915642	−	0.401995i	$-0.868317\pi$
$31$	−0.610692	+	1.05775i	−0.109684	+	0.189978i	0.805958	+	0.591972i	$0.201650\pi$
$32$	4.04253	−	7.00187i	0.714625	−	1.23777i
$33$	−0.0131781	−	0.0232737i	−0.00229402	−	0.00405143i
$34$	−0.946933	+	1.64014i	−0.162398	+	0.281281i
$35$	2.35024	−	1.21507i	0.397262	−	0.205384i
$36$	−3.42782	−	6.17399i	−0.571303	−	1.02900i
$37$	−4.79552	+	8.30608i	−0.788378	+	1.36551i	0.138581	+	0.990351i	$0.455746\pi$
$37$	−4.79552	+	8.30608i	−0.788378	+	1.36551i	−0.926960	+	0.375160i	$0.877588\pi$
$38$	−16.4594			−2.67007
$39$	−5.28976	+	8.98726i	−0.847040	+	1.43911i
$40$	0.738471			0.116762
$41$	−5.46963	−	9.47367i	−0.854212	−	1.47954i	−0.877374	−	0.479808i	$-0.840706\pi$
$41$	−5.46963	−	9.47367i	−0.854212	−	1.47954i	0.0231614	−	0.999732i	$-0.492627\pi$
$42$	0.524024	−	9.54764i	0.0808587	−	1.47323i
$43$	0.234772	−	0.406637i	0.0358024	−	0.0620116i	−0.847569	−	0.530685i	$-0.821935\pi$
$43$	0.234772	−	0.406637i	0.0358024	−	0.0620116i	0.883371	+	0.468674i	$0.155268\pi$
$44$	0.0181741	−	0.0314784i	0.00273984	−	0.00474555i
$45$	−1.54336	+	2.57256i	−0.230070	+	0.383494i
$46$	−3.47416	−	6.01743i	−0.512237	−	0.887221i
$47$	2.53419	+	4.38934i	0.369649	+	0.640252i	0.989511	−	0.144460i	$-0.0461444\pi$
$47$	2.53419	+	4.38934i	0.369649	+	0.640252i	−0.619861	+	0.784711i	$0.712811\pi$
$48$	−2.78237	+	4.72723i	−0.401601	+	0.682316i
$49$	4.04722	−	5.71139i	0.578174	−	0.815913i
$50$	−1.04330	−	1.80705i	−0.147545	−	0.255556i
$51$	0.797420	−	1.35481i	0.111661	−	0.189711i
$52$	−14.1726			−1.96538
$53$	−1.39434	−	2.41507i	−0.191527	−	0.331735i	0.754229	−	0.656611i	$-0.228011\pi$
$53$	−1.39434	−	2.41507i	−0.191527	−	0.331735i	−0.945757	+	0.324876i	$0.894677\pi$
$54$	5.18327	+	9.52309i	0.705354	+	1.29593i
$55$	−0.0154416			−0.00208215
$56$	1.73558	−	0.897292i	0.231927	−	0.119906i
$57$	13.6622	+	0.114558i	1.80960	+	0.0151735i
$58$	−4.54768			−0.597139
$59$	−2.60645	+	4.51450i	−0.339330	+	0.587738i	−0.984307	−	0.176465i	$-0.943534\pi$
$59$	−2.60645	+	4.51450i	−0.339330	+	0.587738i	0.644976	+	0.764202i	$0.276867\pi$
$60$	−4.07695	−	0.0341853i	−0.526332	−	0.00441330i
$61$	−4.12820	−	7.15026i	−0.528562	−	0.915497i	−0.999445	−	0.0333013i	$-0.989398\pi$
$61$	−4.12820	−	7.15026i	−0.528562	−	0.915497i	0.470883	−	0.882196i	$-0.343935\pi$
$62$	2.54854			0.323665
$63$	−0.501419	+	7.92140i	−0.0631729	+	0.998003i
$64$	−10.5365			−1.31706
$65$	3.01043	+	5.21422i	0.373398	+	0.646744i
$66$	−0.0283080	+	0.0480951i	−0.00348448	+	0.00592009i
$67$	−2.66210	+	4.61089i	−0.325227	+	0.563309i	−0.981558	−	0.191163i	$-0.938774\pi$
$67$	−2.66210	+	4.61089i	−0.325227	+	0.563309i	0.656331	+	0.754473i	$0.272107\pi$
$68$	2.13648			0.259087
$69$	2.84186	+	5.01896i	0.342119	+	0.604212i
$70$	−4.64769	−	2.97931i	−0.555506	−	0.356096i
$71$	4.77171			0.566298			0.283149	−	0.959076i	$-0.408621\pi$
$71$	4.77171			0.566298			0.283149	+	0.959076i	$0.408621\pi$
$72$	−1.13972	+	1.89976i	−0.134318	+	0.223889i
$73$	−0.466621	−	0.808211i	−0.0546138	−	0.0945939i	0.837426	−	0.546551i	$-0.184059\pi$
$73$	−0.466621	−	0.808211i	−0.0546138	−	0.0945939i	−0.892040	+	0.451957i	$0.850726\pi$
$74$	20.0127			2.32643
$75$	0.853418	+	1.50721i	0.0985442	+	0.174037i
$76$	9.28400	+	16.0804i	1.06495	+	1.84454i
$77$	−0.0362914	+	0.0187626i	−0.00413579	+	0.00213820i
$78$	21.7592	+	0.182452i	2.46375	+	0.0206586i
$79$	−3.51232	−	6.08351i	−0.395166	−	0.684448i	0.597956	−	0.801529i	$-0.295980\pi$
$79$	−3.51232	−	6.08351i	−0.395166	−	0.684448i	−0.993122	+	0.117081i	$0.962646\pi$
$80$	1.58346	+	2.74264i	0.177037	+	0.306636i
$81$	−4.23611	−	7.94074i	−0.470678	−	0.882305i
$82$	−11.4129	+	19.7678i	−1.26035	+	2.18299i
$83$	−8.41010	+	14.5667i	−0.923128	+	1.59890i	−0.128583	+	0.991699i	$0.541043\pi$
$83$	−8.41010	+	14.5667i	−0.923128	+	1.59890i	−0.794545	+	0.607206i	$0.792290\pi$
$84$	−9.62333	+	4.87343i	−1.04999	+	0.531734i
$85$	−0.453816	−	0.786032i	−0.0492232	−	0.0852571i
$86$	−0.979752			−0.105649
$87$	3.77481	+	0.0316519i	0.404702	+	0.00339344i
$88$	−0.0114032			−0.00121558
$89$	−6.33695	+	10.9759i	−0.671716	+	1.16345i	0.305701	+	0.952127i	$0.401109\pi$
$89$	−6.33695	+	10.9759i	−0.671716	+	1.16345i	−0.977417	+	0.211319i	$0.932224\pi$
$90$	6.25893	+	0.104970i	0.659749	+	0.0110648i
$91$	13.4109	+	8.59677i	1.40584	+	0.901186i
$92$	−3.91923	+	6.78830i	−0.408608	+	0.707729i
$93$	−2.11543	−	0.0177379i	−0.219359	−	0.00183933i
$94$	5.28785	−	9.15882i	0.545400	−	0.944660i
$95$	3.94407	−	6.83134i	0.404653	−	0.700880i
$96$	14.0032	+	0.117417i	1.42920	+	0.0119839i
$97$	3.11544	−	5.39610i	0.316325	−	0.547891i	−0.663393	−	0.748271i	$-0.730884\pi$
$97$	3.11544	−	5.39610i	0.316325	−	0.547891i	0.979718	+	0.200380i	$0.0642177\pi$
$98$	−14.5432	−	1.35483i	−1.46909	−	0.136859i
$99$	0.0238319	−	0.0397244i	0.00239519	−	0.00399245i
$100$	−1.17696	+	2.03855i	−0.117696	+	0.203855i
$101$	−11.8457			−1.17870			−0.589348	−	0.807879i	$-0.700615\pi$
$101$	−11.8457			−1.17870			−0.589348	+	0.807879i	$0.700615\pi$
$102$	−3.28016	−	0.0275042i	−0.324784	−	0.00272332i
$103$	−13.7562			−1.35544			−0.677718	−	0.735322i	$-0.737031\pi$
$103$	−13.7562			−1.35544			−0.677718	+	0.735322i	$0.737031\pi$
$104$	2.22311	+	3.85055i	0.217994	+	0.377577i
$105$	3.83709	+	2.50534i	0.374462	+	0.244496i
$106$	−2.90944	+	5.03929i	−0.282589	+	0.489459i
$107$	−6.15963	+	10.6688i	−0.595474	+	1.03139i	0.398006	+	0.917383i	$0.369702\pi$
$107$	−6.15963	+	10.6688i	−0.595474	+	1.03139i	−0.993480	+	0.114009i	$0.963631\pi$
$108$	6.38013	−	10.4354i	0.613928	−	1.00415i
$109$	−2.57892	−	4.46682i	−0.247015	−	0.427843i	0.715681	−	0.698427i	$-0.246117\pi$
$109$	−2.57892	−	4.46682i	−0.247015	−	0.427843i	−0.962696	+	0.270584i	$0.912783\pi$
$110$	0.0161102	+	0.0279038i	0.00153605	+	0.00266052i
$111$	−16.6116	−	0.139288i	−1.57670	−	0.0132207i
$112$	7.05400	+	4.52183i	0.666541	+	0.427273i
$113$	−6.84910	−	11.8630i	−0.644310	−	1.11598i	−0.984461	−	0.175606i	$-0.943812\pi$
$113$	−6.84910	−	11.8630i	−0.644310	−	1.11598i	0.340151	−	0.940371i	$-0.389522\pi$
$114$	−14.0468	−	24.8078i	−1.31560	−	2.32346i
$115$	3.32997			0.310521
$116$	2.56513	+	4.44294i	0.238167	+	0.412517i
$117$	−18.0600	−	0.302889i	−1.66965	−	0.0280021i
$118$	10.8772			1.00133
$119$	−2.02166	−	1.29594i	−0.185325	−	0.118799i
$120$	0.630224	+	1.11303i	0.0575313	+	0.101605i
$121$	−10.9998			−0.999978
$122$	−8.61392	+	14.9198i	−0.779868	+	1.35077i
$123$	9.61092	−	16.3289i	0.866588	−	1.47232i
$124$	−1.43752	−	2.48985i	−0.129093	−	0.223595i
$125$	1.00000			0.0894427
$126$	14.8375	−	7.35832i	1.32183	−	0.655531i
$127$	11.6693			1.03548			0.517742	−	0.855537i	$-0.326773\pi$
$127$	11.6693			1.03548			0.517742	+	0.855537i	$0.326773\pi$
$128$	2.90763	+	5.03617i	0.257001	+	0.445139i
$129$	0.813245	+	0.00681908i	0.0716023	+	0.000600387i
$130$	6.28157	−	10.8800i	0.550930	−	0.954240i
$131$	16.0399			1.40142			0.700708	−	0.713448i	$-0.252868\pi$
$131$	16.0399			1.40142			0.700708	+	0.713448i	$0.252868\pi$
$132$	0.0629546		0.000527876i	0.00547950		4.59457e-5i
$133$	0.968969	−	20.8476i	0.0840203	−	1.80771i
$134$	11.1095			0.959712
$135$	−5.19451	−	0.130693i	−0.447072	−	0.0112482i
$136$	−0.335130	−	0.580462i	−0.0287371	−	0.0497742i
$137$	5.75280			0.491495			0.245747	−	0.969334i	$-0.420967\pi$
$137$	5.75280			0.491495			0.245747	+	0.969334i	$0.420967\pi$
$138$	6.10460	−	10.3717i	0.519658	−	0.882895i
$139$	1.48176	+	2.56649i	0.125681	+	0.217686i	0.921999	−	0.387192i	$-0.126555\pi$
$139$	1.48176	+	2.56649i	0.125681	+	0.217686i	−0.796318	+	0.604879i	$0.793222\pi$
$140$	−0.289151	+	6.22115i	−0.0244377	+	0.525783i
$141$	−4.45294	+	7.56550i	−0.375005	+	0.637130i
$142$	−4.97834	−	8.62273i	−0.417773	−	0.723603i
$143$	−0.0464859	−	0.0805159i	−0.00388734	−	0.00673308i
$144$	−9.49944	−	0.159317i	−0.791620	−	0.0132764i
$145$	1.08973	−	1.88747i	0.0904973	−	0.156746i
$146$	−0.973652	+	1.68641i	−0.0805800	+	0.139569i
$147$	12.0622	+	1.22580i	0.994876	+	0.101102i
$148$	−11.2882	−	19.5518i	−0.927886	−	1.60715i
$149$	8.08400			0.662267			0.331133	−	0.943584i	$-0.392569\pi$
$149$	8.08400			0.662267			0.331133	+	0.943584i	$0.392569\pi$
$150$	1.83323	−	3.11464i	0.149683	−	0.254309i
$151$	−8.48540			−0.690532			−0.345266	−	0.938505i	$-0.612211\pi$
$151$	−8.48540			−0.690532			−0.345266	+	0.938505i	$0.612211\pi$
$152$	2.91258	−	5.04474i	0.236242	−	0.409182i
$153$	2.72251	+	0.0456599i	0.220102	+	0.00369138i
$154$	0.0717678	+	0.0460054i	0.00578322	+	0.00370722i
$155$	−0.610692	+	1.05775i	−0.0490520	+	0.0849605i
$156$	−12.0951	−	21.3610i	−0.968385	−	1.71025i
$157$	8.60705	−	14.9079i	0.686918	−	1.18978i	−0.285912	−	0.958256i	$-0.592297\pi$
$157$	8.60705	−	14.9079i	0.686918	−	1.18978i	0.972830	−	0.231520i	$-0.0743700\pi$
$158$	−7.32881	+	12.6939i	−0.583049	+	1.00987i
$159$	2.45006	−	4.16263i	0.194302	−	0.330118i
$160$	4.04253	−	7.00187i	0.319590	−	0.553546i
$161$	7.82622	−	4.04614i	0.616792	−	0.318880i
$162$	−9.92979	+	15.9394i	−0.780158	+	1.25232i
$163$	−0.597394	+	1.03472i	−0.0467915	+	0.0810453i	−0.888473	−	0.458930i	$-0.848233\pi$
$163$	−0.597394	+	1.03472i	−0.0467915	+	0.0810453i	0.841681	+	0.539975i	$0.181566\pi$
$164$	25.7500			2.01074
$165$	−0.0131781	−	0.0232737i	−0.00102592	−	0.00181186i
$166$	35.0971			2.72406
$167$	−4.13064	−	7.15448i	−0.319638	−	0.553630i	0.660774	−	0.750585i	$-0.270228\pi$
$167$	−4.13064	−	7.15448i	−0.319638	−	0.553630i	−0.980413	+	0.196955i	$0.936895\pi$
$168$	2.83358	+	1.85012i	0.218616	+	0.142740i
$169$	−11.6254	+	20.1358i	−0.894261	+	1.54891i
$170$	−0.946933	+	1.64014i	−0.0726265	+	0.125793i
$171$	11.4869	+	20.6895i	0.878425	+	1.58217i
$172$	0.552632	+	0.957187i	0.0421378	+	0.0729848i
$173$	−7.01950	−	12.1581i	−0.533683	−	0.924366i	−0.999226	−	0.0393406i	$-0.987474\pi$
$173$	−7.01950	−	12.1581i	−0.533683	−	0.924366i	0.465543	−	0.885025i	$-0.345859\pi$
$174$	−3.88107	−	6.85430i	−0.294223	−	0.519623i
$175$	2.35024	−	1.21507i	0.177661	−	0.0918505i
$176$	−0.0244512	−	0.0423507i	−0.00184308	−	0.00319231i
$177$	−9.02868	−	0.0757057i	−0.678637	−	0.00569039i
$178$	26.4454			1.98217
$179$	−3.95787	−	6.85523i	−0.295825	−	0.512384i	0.679352	−	0.733813i	$-0.262261\pi$
$179$	−3.95787	−	6.85523i	−0.295825	−	0.512384i	−0.975176	+	0.221429i	$0.928928\pi$
$180$	−3.42782	−	6.17399i	−0.255494	−	0.460182i
$181$	5.55480			0.412885			0.206442	−	0.978459i	$-0.433811\pi$
$181$	5.55480			0.412885			0.206442	+	0.978459i	$0.433811\pi$
$182$	1.54324	−	33.2031i	0.114393	−	2.46118i
$183$	7.25385	−	12.3242i	0.536220	−	0.911033i
$184$	2.45909			0.181286
$185$	−4.79552	+	8.30608i	−0.352574	+	0.610675i
$186$	2.17497	+	3.84119i	0.159477	+	0.281650i
$187$	0.00700764	+	0.0121376i	0.000512450	+	0.000887589i
$188$	−11.9305			−0.870122
$189$	−12.3671	+	6.00452i	−0.899576	+	0.436765i
$190$	−16.4594			−1.19409
$191$	−0.671325	−	1.16277i	−0.0485753	−	0.0841350i	0.840715	−	0.541477i	$-0.182135\pi$
$191$	−0.671325	−	1.16277i	−0.0485753	−	0.0841350i	−0.889291	+	0.457342i	$0.848801\pi$
$192$	−8.99200	−	15.8806i	−0.648941	−	1.14609i
$193$	6.22771	−	10.7867i	0.448281	−	0.776445i	−0.549994	−	0.835169i	$-0.685370\pi$
$193$	6.22771	−	10.7867i	0.448281	−	0.776445i	0.998274	+	0.0587239i	$0.0187032\pi$
$194$	−13.0014			−0.933444
$195$	−5.28976	+	8.98726i	−0.378808	+	0.643591i
$196$	6.87954	+	14.9725i	0.491396	+	1.06946i
$197$	13.6680			0.973808			0.486904	−	0.873456i	$-0.338126\pi$
$197$	13.6680			0.973808			0.486904	+	0.873456i	$0.338126\pi$
$198$	−0.0966479	−	0.00162090i	−0.00686846	−	0.000115193i
$199$	−8.61705	−	14.9252i	−0.610846	−	1.05802i	−0.991098	−	0.133134i	$-0.957496\pi$
$199$	−8.61705	−	14.9252i	−0.610846	−	1.05802i	0.380252	−	0.924883i	$-0.375837\pi$
$200$	0.738471			0.0522178
$201$	−9.22145	−	0.0773220i	−0.650431	−	0.00545388i
$202$	12.3587	+	21.4059i	0.869554	+	1.50611i
$203$	0.267722	−	5.76010i	0.0187904	−	0.404280i
$204$	1.82331	+	3.22013i	0.127657	+	0.225454i
$205$	−5.46963	−	9.47367i	−0.382015	−	0.661670i
$206$	14.3518	+	24.8581i	0.999940	+	1.73195i
$207$	−5.13933	+	8.56654i	−0.357208	+	0.595416i
$208$	−9.53381	+	16.5131i	−0.661051	+	1.14497i
$209$	−0.0609028	+	0.105487i	−0.00421274	+	0.00729667i
$210$	0.524024	−	9.54764i	0.0361611	−	0.658850i
$211$	−4.78123	−	8.28134i	−0.329154	−	0.570111i	0.653190	−	0.757194i	$-0.273430\pi$
$211$	−4.78123	−	8.28134i	−0.329154	−	0.570111i	−0.982344	+	0.187083i	$0.940097\pi$
$212$	6.56431			0.450839
$213$	4.07227	+	7.19197i	0.279027	+	0.492786i
$214$	25.7054			1.75719
$215$	0.234772	−	0.406637i	0.0160113	−	0.0277324i
$216$	−3.83599	−	0.0965127i	−0.261006	−	0.00656686i
$217$	−0.150033	+	3.22800i	−0.0101849	+	0.219131i
$218$	−5.38118	+	9.32047i	−0.364459	+	0.631262i
$219$	0.819920	−	1.39304i	0.0554050	−	0.0941327i
$220$	0.0181741	−	0.0314784i	0.00122530	−	0.00212227i
$221$	2.73236	−	4.73259i	0.183799	−	0.318349i
$222$	17.0792	+	30.1633i	1.14628	+	2.02443i
$223$	2.00954	−	3.48062i	0.134569	−	0.233080i	−0.790864	−	0.611992i	$-0.790368\pi$
$223$	2.00954	−	3.48062i	0.134569	−	0.233080i	0.925433	+	0.378912i	$0.123702\pi$
$224$	0.993157	−	21.3680i	0.0663581	−	1.42771i
$225$	−1.54336	+	2.57256i	−0.102890	+	0.171504i
$226$	−14.2914	+	24.7534i	−0.950647	+	1.64657i
$227$	−2.79947			−0.185807			−0.0929036	−	0.995675i	$-0.529615\pi$
$227$	−2.79947			−0.185807			−0.0929036	+	0.995675i	$0.529615\pi$
$228$	−16.3133	+	27.7162i	−1.08038	+	1.83555i
$229$	−20.3143			−1.34241			−0.671205	−	0.741272i	$-0.734223\pi$
$229$	−20.3143			−1.34241			−0.671205	+	0.741272i	$0.734223\pi$
$230$	−3.47416	−	6.01743i	−0.229079	−	0.396777i
$231$	−0.0592509	−	0.0386864i	−0.00389842	−	0.00254538i
$232$	0.804735	−	1.39384i	0.0528335	−	0.0915102i
$233$	−3.25707	+	5.64141i	−0.213378	+	0.369581i	−0.952769	−	0.303694i	$-0.901780\pi$
$233$	−3.25707	+	5.64141i	−0.213378	+	0.369581i	0.739392	+	0.673275i	$0.235113\pi$
$234$	18.2947	+	32.9514i	1.19596	+	2.15410i
$235$	2.53419	+	4.38934i	0.165312	+	0.286329i
$236$	−6.13534	−	10.6267i	−0.399377	−	0.691741i
$237$	6.17164	−	10.4856i	0.400891	−	0.681111i
$238$	−0.232640	+	5.00530i	−0.0150798	+	0.324445i
$239$	14.5402	+	25.1843i	0.940525	+	1.62904i	0.764472	+	0.644657i	$0.223000\pi$
$239$	14.5402	+	25.1843i	0.940525	+	1.62904i	0.176053	+	0.984381i	$0.443667\pi$
$240$	−2.78237	+	4.72723i	−0.179601	+	0.305141i
$241$	−14.0449			−0.904713			−0.452357	−	0.891837i	$-0.649417\pi$
$241$	−14.0449			−0.904713			−0.452357	+	0.891837i	$0.649417\pi$
$242$	11.4761	+	19.8771i	0.737709	+	1.27775i
$243$	8.35319	−	13.1615i	0.535857	−	0.844309i
$244$	19.4348			1.24419
$245$	4.04722	−	5.71139i	0.258567	−	0.364887i
$246$	−39.5342	−	0.331495i	−2.52061	−	0.0211354i
$247$	47.4934			3.02194
$248$	−0.450978	+	0.781117i	−0.0286372	+	0.0496010i
$249$	−29.1324	−	0.244276i	−1.84619	−	0.0154804i
$250$	−1.04330	−	1.80705i	−0.0659842	−	0.114288i
$251$	15.2271			0.961125			0.480562	−	0.876961i	$-0.340433\pi$
$251$	15.2271			0.961125			0.480562	+	0.876961i	$0.340433\pi$
$252$	−15.5580	−	10.3453i	−0.980061	−	0.651693i
$253$	−0.0514201			−0.00323275
$254$	−12.1746	−	21.0870i	−0.763903	−	1.32312i
$255$	0.797420	−	1.35481i	0.0499364	−	0.0848414i
$256$	−4.46937	+	7.74118i	−0.279336	+	0.483824i
$257$	−0.497965			−0.0310622			−0.0155311	−	0.999879i	$-0.504944\pi$
$257$	−0.497965			−0.0310622			−0.0155311	+	0.999879i	$0.504944\pi$
$258$	−0.836138	−	1.47669i	−0.0520557	−	0.0919347i
$259$	−1.17815	+	25.3481i	−0.0732067	+	1.57506i
$260$	−14.1726			−0.878946
$261$	3.17379	+	5.71644i	0.196452	+	0.353839i
$262$	−16.7345	−	28.9850i	−1.03386	−	1.79070i
$263$	17.5939			1.08489			0.542443	−	0.840093i	$-0.317500\pi$
$263$	17.5939			1.08489			0.542443	+	0.840093i	$0.317500\pi$
$264$	−0.00973167	−	0.0171870i	−0.000598943	−	0.00105778i
$265$	−1.39434	−	2.41507i	−0.0856537	−	0.148357i
$266$	−38.6835	+	19.9993i	−2.37184	+	1.22624i
$267$	−21.9511	−	0.184060i	−1.34338	−	0.0112643i
$268$	−6.26634	−	10.8536i	−0.382777	−	0.662990i
$269$	7.14020	+	12.3672i	0.435346	+	0.754041i	0.997324	−	0.0731112i	$-0.0232928\pi$
$269$	7.14020	+	12.3672i	0.435346	+	0.754041i	−0.561978	+	0.827152i	$0.689959\pi$
$270$	5.18327	+	9.52309i	0.315444	+	0.579557i
$271$	−2.92303	+	5.06284i	−0.177562	+	0.307546i	−0.941045	−	0.338282i	$-0.890154\pi$
$271$	−2.92303	+	5.06284i	−0.177562	+	0.307546i	0.763483	+	0.645828i	$0.223488\pi$
$272$	1.43720	−	2.48931i	0.0871431	−	0.150936i
$273$	−1.51206	+	27.5496i	−0.0915143	+	1.66738i
$274$	−6.00190	−	10.3956i	−0.362588	−	0.628021i
$275$	−0.0154416			−0.000931164
$276$	−13.5761	−	0.113836i	−0.817186	−	0.00685213i
$277$	11.6188			0.698106			0.349053	−	0.937103i	$-0.386503\pi$
$277$	11.6188			0.698106			0.349053	+	0.937103i	$0.386503\pi$
$278$	3.09185	−	5.35524i	0.185437	−	0.321186i
$279$	−1.77861	−	3.20353i	−0.106482	−	0.191790i
$280$	1.73558	−	0.897292i	0.103721	−	0.0536234i
$281$	2.00648	−	3.47533i	0.119697	−	0.207321i	−0.799951	−	0.600066i	$-0.795141\pi$
$281$	2.00648	−	3.47533i	0.119697	−	0.207321i	0.919647	+	0.392745i	$0.128474\pi$
$282$	18.3170	+	0.153588i	1.09076	+	0.00914605i
$283$	6.18587	−	10.7142i	0.367712	−	0.636896i	−0.621496	−	0.783418i	$-0.713475\pi$
$283$	6.18587	−	10.7142i	0.367712	−	0.636896i	0.989207	+	0.146522i	$0.0468079\pi$
$284$	−5.61609	+	9.72736i	−0.333254	+	0.577213i
$285$	13.6622	+	0.114558i	0.809278	+	0.00678582i
$286$	−0.0969976	+	0.168005i	−0.00573559	+	0.00993433i
$287$	−24.3661	−	15.6194i	−1.43828	−	0.921984i
$288$	11.7736	+	21.2060i	0.693768	+	1.24958i
$289$	8.08810	−	14.0090i	0.475771	−	0.824059i
$290$	−4.54768			−0.267049
$291$	10.7918	+	0.0904896i	0.632628	+	0.00530460i
$292$	2.19677			0.128556
$293$	12.9308	+	22.3968i	0.755426	+	1.30844i	0.945162	+	0.326601i	$0.105903\pi$
$293$	12.9308	+	22.3968i	0.755426	+	1.30844i	−0.189736	+	0.981835i	$0.560763\pi$
$294$	−10.3695	−	23.0759i	−0.604759	−	1.34582i
$295$	−2.60645	+	4.51450i	−0.151753	+	0.262844i
$296$	−3.54135	+	6.13380i	−0.205837	+	0.356520i
$297$	0.0802115	+	0.00201810i	0.00465434	+	0.000117102i
$298$	−8.43404	−	14.6082i	−0.488571	−	0.846230i
$299$	10.0246	+	17.3632i	0.579740	+	1.00414i
$300$	−4.07695	−	0.0341853i	−0.235383	−	0.00197369i
$301$	0.0576781	−	1.24096i	0.00332451	−	0.0715276i
$302$	8.85283	+	15.3335i	0.509423	+	0.882346i
$303$	−10.1094	−	17.8540i	−0.580768	−	1.02569i
$304$	24.9812			1.43277
$305$	−4.12820	−	7.15026i	−0.236380	−	0.409423i
$306$	−2.75789	−	4.96735i	−0.157658	−	0.283965i
$307$	7.24147			0.413293			0.206646	−	0.978416i	$-0.433745\pi$
$307$	7.24147			0.413293			0.206646	+	0.978416i	$0.433745\pi$
$308$	0.00446496	−	0.0960645i	0.000254414	−	0.00547378i
$309$	−11.7398	−	20.7334i	−0.667852	−	1.17948i
$310$	2.54854			0.144748
$311$	16.7171	−	28.9548i	0.947938	−	1.64188i	0.198180	−	0.980166i	$-0.436497\pi$
$311$	16.7171	−	28.9548i	0.947938	−	1.64188i	0.749758	−	0.661712i	$-0.230170\pi$
$312$	−3.90633	+	6.63682i	−0.221153	+	0.375736i
$313$	10.4560	+	18.1104i	0.591010	+	1.02366i	0.994097	+	0.108497i	$0.0346039\pi$
$313$	10.4560	+	18.1104i	0.591010	+	1.02366i	−0.403087	+	0.915162i	$0.632063\pi$
$314$	−35.9190			−2.02703
$315$	−0.501419	+	7.92140i	−0.0282518	+	0.446320i
$316$	16.5354			0.930186
$317$	−4.83802	−	8.37970i	−0.271730	−	0.470651i	0.697575	−	0.716512i	$-0.254263\pi$
$317$	−4.83802	−	8.37970i	−0.271730	−	0.470651i	−0.969305	+	0.245861i	$0.920929\pi$
$318$	−10.0782	−	0.0845062i	−0.565159	−	0.00473887i
$319$	−0.0168272	+	0.0291456i	−0.000942143	+	0.00163184i
$320$	−10.5365			−0.589005
$321$	−21.3368	−	0.178910i	−1.19091	−	0.00998578i
$322$	−15.4767	−	9.92103i	−0.862482	−	0.552877i
$323$	−7.15953			−0.398367
$324$	21.1733	+	0.710403i	1.17629	+	0.0394669i
$325$	3.01043	+	5.21422i	0.166989	+	0.289233i
$326$	2.49305			0.138077
$327$	4.53153	−	7.69903i	0.250594	−	0.425757i
$328$	−4.03916	−	6.99603i	−0.223025	−	0.386291i
$329$	11.2893	+	7.23678i	0.622399	+	0.398977i
$330$	−0.0283080	+	0.0480951i	−0.00155831	+	0.00264755i
$331$	8.40886	+	14.5646i	0.462193	+	0.800541i	0.999070	−	0.0431190i	$-0.0137295\pi$
$331$	8.40886	+	14.5646i	0.462193	+	0.800541i	−0.536877	+	0.843660i	$0.680396\pi$
$332$	−19.7966	−	34.2887i	−1.08648	−	1.88184i
$333$	−13.9667	−	25.1560i	−0.765370	−	1.37854i
$334$	−8.61900	+	14.9285i	−0.471611	+	0.816854i
$335$	−2.66210	+	4.61089i	−0.145446	+	0.251920i
$336$	−0.795334	+	14.4909i	−0.0433890	+	0.790542i
$337$	−0.286076	−	0.495498i	−0.0155836	−	0.0269915i	0.858128	−	0.513435i	$-0.171627\pi$
$337$	−0.286076	−	0.495498i	−0.0155836	−	0.0269915i	−0.873712	+	0.486444i	$0.838294\pi$
$338$	48.5151			2.63888
$339$	12.0349	−	20.4471i	0.653644	−	1.11054i
$340$	2.13648			0.115867
$341$	0.00943007	−	0.0163334i	0.000510667	−	0.000884501i
$342$	25.4028	−	42.3428i	1.37362	−	2.28964i
$343$	2.57220	−	18.3408i	0.138886	−	0.990308i
$344$	0.173372	−	0.300289i	0.00934760	−	0.0161905i
$345$	2.84186	+	5.01896i	0.153000	+	0.270212i
$346$	−14.6469	+	25.3692i	−0.787423	+	1.36386i
$347$	−3.52555	+	6.10643i	−0.189261	+	0.327810i	−0.945004	−	0.327058i	$-0.893943\pi$
$347$	−3.52555	+	6.10643i	−0.189261	+	0.327810i	0.755743	+	0.654868i	$0.227276\pi$
$348$	−4.50731	+	7.65787i	−0.241617	+	0.410505i
$349$	−2.29666	+	3.97793i	−0.122937	+	0.212934i	−0.920925	−	0.389740i	$-0.872565\pi$
$349$	−2.29666	+	3.97793i	−0.122937	+	0.212934i	0.797988	+	0.602674i	$0.205898\pi$
$350$	−4.64769	−	2.97931i	−0.248430	−	0.159251i
$351$	−14.9563	−	27.4788i	−0.798306	−	1.46671i
$352$	−0.0624231	+	0.108120i	−0.00332716	+	0.00576282i
$353$	−24.1607			−1.28594			−0.642972	−	0.765890i	$-0.722299\pi$
$353$	−24.1607			−1.28594			−0.642972	+	0.765890i	$0.722299\pi$
$354$	9.28283	+	16.3943i	0.493377	+	0.871345i
$355$	4.77171			0.253256
$356$	−14.9166	−	25.8363i	−0.790579	−	1.36932i
$357$	0.227940	−	4.15304i	0.0120639	−	0.219802i
$358$	−8.25849	+	14.3041i	−0.436475	+	0.755997i
$359$	−5.16729	+	8.95001i	−0.272719	+	0.472364i	−0.969557	−	0.244865i	$-0.921256\pi$
$359$	−5.16729	+	8.95001i	−0.272719	+	0.472364i	0.696838	+	0.717229i	$0.254590\pi$
$360$	−1.13972	+	1.89976i	−0.0600687	+	0.100126i
$361$	−21.6114	−	37.4321i	−1.13744	−	1.97011i
$362$	−5.79533	−	10.0378i	−0.304596	−	0.527575i
$363$	−9.38739	−	16.5789i	−0.492710	−	0.870168i
$364$	−33.3089	+	17.2206i	−1.74586	+	0.902606i
$365$	−0.466621	−	0.808211i	−0.0244240	−	0.0423037i
$366$	−29.8385	−	0.250196i	−1.55968	−	0.0130780i
$367$	−29.0352			−1.51562			−0.757812	−	0.652473i	$-0.773732\pi$
$367$	−29.0352			−1.51562			−0.757812	+	0.652473i	$0.773732\pi$
$368$	5.27289	+	9.13291i	0.274868	+	0.476086i
$369$	32.8132	+	0.550317i	1.70818	+	0.0286483i
$370$	20.0127			1.04041
$371$	−6.21150	−	3.98177i	−0.322485	−	0.206723i
$372$	2.52592	−	4.29152i	0.130963	−	0.222505i
$373$	−13.3952			−0.693578			−0.346789	−	0.937943i	$-0.612728\pi$
$373$	−13.3952			−0.693578			−0.346789	+	0.937943i	$0.612728\pi$
$374$	0.0146222	−	0.0253263i	0.000756094	−	0.00130959i
$375$	0.853418	+	1.50721i	0.0440703	+	0.0778319i
$376$	1.87142	+	3.24140i	0.0965113	+	0.167163i
$377$	13.1223			0.675831
$378$	23.7531	+	16.0835i	1.22173	+	0.827246i
$379$	33.0340			1.69684			0.848420	−	0.529323i	$-0.177554\pi$
$379$	33.0340			1.69684			0.848420	+	0.529323i	$0.177554\pi$
$380$	9.28400	+	16.0804i	0.476259	+	0.824905i
$381$	9.95880	+	17.5881i	0.510205	+	0.901065i
$382$	−1.40079	+	2.42624i	−0.0716705	+	0.124137i
$383$	−12.8266			−0.655408			−0.327704	−	0.944780i	$-0.606275\pi$
$383$	−12.8266			−0.655408			−0.327704	+	0.944780i	$0.606275\pi$
$384$	−5.10913	+	8.68037i	−0.260724	+	0.442968i
$385$	−0.0362914	+	0.0187626i	−0.00184958	+	0.000956230i
$386$	−25.9895			−1.32283
$387$	0.683760	+	1.23155i	0.0347575	+	0.0626032i
$388$	7.33347	+	12.7019i	0.372300	+	0.644843i
$389$	7.46719			0.378602			0.189301	−	0.981919i	$-0.439378\pi$
$389$	7.46719			0.378602			0.189301	+	0.981919i	$0.439378\pi$
$390$	21.7592	+	0.182452i	1.10182	+	0.00923880i
$391$	−1.51119	−	2.61746i	−0.0764243	−	0.132371i
$392$	2.98875	−	4.21770i	0.150955	−	0.213026i
$393$	13.6888	+	24.1755i	0.690507	+	1.21949i
$394$	−14.2599	−	24.6988i	−0.718403	−	1.24431i
$395$	−3.51232	−	6.08351i	−0.176724	−	0.306095i
$396$	0.0529310	+	0.0953363i	0.00265988	+	0.00479083i
$397$	−5.56382	+	9.63681i	−0.279240	+	0.483658i	−0.971196	−	0.238282i	$-0.923416\pi$
$397$	−5.56382	+	9.63681i	−0.279240	+	0.483658i	0.691956	+	0.721940i	$0.256749\pi$
$398$	−17.9804	+	31.1429i	−0.901274	+	1.56105i
$399$	32.2486	−	16.3312i	1.61445	−	0.817585i
$400$	1.58346	+	2.74264i	0.0791732	+	0.137132i
$401$	17.9819			0.897973			0.448987	−	0.893538i	$-0.351785\pi$
$401$	17.9819			0.897973			0.448987	+	0.893538i	$0.351785\pi$
$402$	9.48102	+	16.7443i	0.472870	+	0.835129i
$403$	−7.35379			−0.366318
$404$	13.9419	−	24.1481i	0.693636	−	1.20141i
$405$	−4.23611	−	7.94074i	−0.210494	−	0.394579i
$406$	−10.6881	+	5.52574i	−0.530442	+	0.274238i
$407$	0.0740505	−	0.128259i	0.00367055	−	0.00635757i
$408$	0.588871	−	1.00049i	0.0291535	−	0.0495315i
$409$	−17.0901	+	29.6009i	−0.845051	+	1.46367i	0.0405262	+	0.999178i	$0.487097\pi$
$409$	−17.0901	+	29.6009i	−0.845051	+	1.46367i	−0.885577	+	0.464493i	$0.846237\pi$
$410$	−11.4129	+	19.7678i	−0.563645	+	0.976262i
$411$	4.90954	+	8.67067i	0.242170	+	0.427693i
$412$	16.1904	−	28.0426i	0.797644	−	1.38156i
$413$	−0.640345	+	13.7771i	−0.0315093	+	0.677929i
$414$	20.8420	+	0.349547i	1.02433	+	0.0171793i
$415$	−8.41010	+	14.5667i	−0.412835	+	0.715052i
$416$	48.6790			2.38669
$417$	−2.60367	+	4.42361i	−0.127502	+	0.216625i
$418$	0.254160			0.0124314
$419$	−10.7526	−	18.6241i	−0.525299	−	0.909845i	−0.999566	−	0.0294638i	$-0.990620\pi$
$419$	−10.7526	−	18.6241i	−0.525299	−	0.909845i	0.474266	−	0.880381i	$-0.342713\pi$
$420$	−9.62333	+	4.87343i	−0.469570	+	0.237799i
$421$	11.1492	−	19.3110i	0.543379	−	0.941160i	−0.455328	−	0.890324i	$-0.650478\pi$
$421$	11.1492	−	19.3110i	0.543379	−	0.941160i	0.998707	−	0.0508365i	$-0.0161887\pi$
$422$	−9.97654	+	17.2799i	−0.485650	+	0.841171i
$423$	−15.2030	−	0.254973i	−0.739195	−	0.0123972i
$424$	−1.02968	−	1.78346i	−0.0500057	−	0.0866124i
$425$	−0.453816	−	0.786032i	−0.0220133	−	0.0381282i
$426$	8.74765	−	14.8622i	0.423825	−	0.720075i
$427$	−18.3903	−	11.7888i	−0.889969	−	0.570498i
$428$	−14.4992	−	25.1134i	−0.700846	−	1.21390i
$429$	0.0816824	−	0.138778i	0.00394366	−	0.00670025i
$430$	−0.979752			−0.0472478
$431$	7.82668	+	13.5562i	0.376998	+	0.652980i	0.990624	−	0.136617i	$-0.0436230\pi$
$431$	7.82668	+	13.5562i	0.376998	+	0.652980i	−0.613626	+	0.789597i	$0.710290\pi$
$432$	−7.86687	−	14.4536i	−0.378495	−	0.695400i
$433$	−31.0383			−1.49160			−0.745802	−	0.666167i	$-0.767934\pi$
$433$	−31.0383			−1.49160			−0.745802	+	0.666167i	$0.767934\pi$
$434$	5.98968	−	3.09665i	0.287514	−	0.148644i
$435$	3.77481	+	0.0316519i	0.180988	+	0.00151759i
$436$	12.1411			0.581452
$437$	13.1336	−	22.7481i	0.628268	−	1.08819i
$438$	−3.37271	−	0.0282803i	−0.161154	−	0.00135128i
$439$	0.915300	+	1.58535i	0.0436849	+	0.0756644i	0.887041	−	0.461690i	$-0.152757\pi$
$439$	0.915300	+	1.58535i	0.0436849	+	0.0756644i	−0.843356	+	0.537355i	$0.819424\pi$
$440$	−0.0114032			−0.000543625
$441$	8.44658	+	19.2264i	0.402218	+	0.915544i
$442$	−11.4027			−0.542372
$443$	8.90738	+	15.4280i	0.423202	+	0.733008i	0.996251	−	0.0865137i	$-0.0275726\pi$
$443$	8.90738	+	15.4280i	0.423202	+	0.733008i	−0.573048	+	0.819522i	$0.694239\pi$
$444$	19.8350	−	33.6995i	0.941329	−	1.59931i
$445$	−6.33695	+	10.9759i	−0.300400	+	0.520309i
$446$	−8.38622			−0.397099
$447$	6.89903	+	12.1843i	0.326313	+	0.576296i
$448$	−24.7631	+	12.8025i	−1.16995	+	0.604861i
$449$	13.1843			0.622204			0.311102	−	0.950377i	$-0.399302\pi$
$449$	13.1843			0.622204			0.311102	+	0.950377i	$0.399302\pi$
$450$	6.25893	+	0.104970i	0.295049	+	0.00494833i
$451$	0.0844598	+	0.146289i	0.00397706	+	0.00688847i
$452$	32.2444			1.51665
$453$	−7.24159	−	12.7893i	−0.340240	−	0.600892i
$454$	2.92069	+	5.05878i	0.137075	+	0.237420i
$455$	13.4109	+	8.59677i	0.628711	+	0.403023i
$456$	10.0891	+	0.0845975i	0.472467	+	0.00396164i
$457$	12.1505	+	21.0453i	0.568376	+	0.984457i	0.996727	+	0.0808442i	$0.0257616\pi$
$457$	12.1505	+	21.0453i	0.568376	+	0.984457i	−0.428350	+	0.903613i	$0.640905\pi$
$458$	21.1940	+	36.7090i	0.990330	+	1.71530i
$459$	2.25462	+	4.14236i	0.105237	+	0.193349i
$460$	−3.91923	+	6.78830i	−0.182735	+	0.316506i
$461$	3.59092	−	6.21965i	0.167246	−	0.289678i	−0.770205	−	0.637797i	$-0.779846\pi$
$461$	3.59092	−	6.21965i	0.167246	−	0.289678i	0.937450	+	0.348119i	$0.113179\pi$
$462$	−0.00809177	+	0.147431i	−0.000376463	+	0.00685911i
$463$	6.29354	+	10.9007i	0.292486	+	0.506600i	0.974397	−	0.224835i	$-0.0721843\pi$
$463$	6.29354	+	10.9007i	0.292486	+	0.506600i	−0.681911	+	0.731435i	$0.738851\pi$
$464$	6.90220			0.320427
$465$	−2.11543	−	0.0177379i	−0.0981005	−	0.000822575i
$466$	13.5924			0.629656
$467$	−7.03434	+	12.1838i	−0.325511	+	0.563801i	−0.981616	−	0.190869i	$-0.938870\pi$
$467$	−7.03434	+	12.1838i	−0.325511	+	0.563801i	0.656105	+	0.754670i	$0.272203\pi$
$468$	21.8733	−	36.4598i	1.01109	−	1.68535i
$469$	−0.654016	+	14.0713i	−0.0301997	+	0.649752i
$470$	5.28785	−	9.15882i	0.243910	−	0.422465i
$471$	29.8147	+	0.249997i	1.37379	+	0.0115192i
$472$	−1.92478	+	3.33382i	−0.0885954	+	0.153452i
$473$	−0.00362526	+	0.00627913i	−0.000166689	+	0.000288715i
$474$	−25.3868	−	0.212869i	−1.16606	−	0.00977741i
$475$	3.94407	−	6.83134i	0.180967	−	0.313443i
$476$	5.02124	−	2.59597i	0.230148	−	0.118986i
$477$	8.36487	+	0.140289i	0.383001	+	0.00642340i
$478$	30.3395	−	52.5496i	1.38770	−	2.40356i
$479$	−27.6482			−1.26328			−0.631639	−	0.775263i	$-0.717617\pi$
$479$	−27.6482			−1.26328			−0.631639	+	0.775263i	$0.717617\pi$
$480$	14.0032	+	0.117417i	0.639157	+	0.00535935i
$481$	−57.7463			−2.63301
$482$	14.6531	+	25.3799i	0.667430	+	1.15602i
$483$	12.7774	+	8.34269i	0.581392	+	0.379606i
$484$	12.9462	−	22.4235i	0.588465	−	1.01925i
$485$	3.11544	−	5.39610i	0.141465	−	0.245024i
$486$	−32.4983	−	1.36326i	−1.47415	−	0.0618389i
$487$	11.3473	+	19.6541i	0.514196	+	0.890613i	0.999864	+	0.0164702i	$0.00524286\pi$
$487$	11.3473	+	19.6541i	0.514196	+	0.890613i	−0.485669	+	0.874143i	$0.661424\pi$
$488$	−3.04856	−	5.28026i	−0.138002	−	0.239026i
$489$	−2.06936	−	0.0173516i	−0.0935798	−	0.000784669i
$490$	−14.5432	−	1.35483i	−0.656997	−	0.0612050i
$491$	9.71567	+	16.8280i	0.438462	+	0.759439i	0.997571	−	0.0696555i	$-0.0221900\pi$
$491$	9.71567	+	16.8280i	0.438462	+	0.759439i	−0.559109	+	0.829094i	$0.688857\pi$
$492$	21.9755	+	38.8107i	0.990734	+	1.74972i
$493$	−1.97815			−0.0890914
$494$	−49.5500	−	85.8231i	−2.22936	−	3.86136i
$495$	0.0238319	−	0.0397244i	0.00107116	−	0.00178548i
$496$	−3.86804			−0.173680
$497$	11.2147	−	5.79796i	0.503046	−	0.260074i
$498$	29.9525	+	52.8986i	1.34220	+	2.37044i
$499$	18.6400			0.834441			0.417220	−	0.908805i	$-0.363004\pi$
$499$	18.6400			0.834441			0.417220	+	0.908805i	$0.363004\pi$
$500$	−1.17696	+	2.03855i	−0.0526350	+	0.0911666i
$501$	7.25813	−	12.3315i	0.324269	−	0.550930i
$502$	−15.8864	−	27.5161i	−0.709046	−	1.22810i
$503$	23.0793			1.02905			0.514527	−	0.857474i	$-0.327967\pi$
$503$	23.0793			1.02905			0.514527	+	0.857474i	$0.327967\pi$
$504$	−0.370283	+	5.84972i	−0.0164937	+	0.260567i
$505$	−11.8457			−0.527129
$506$	0.0536466	+	0.0929187i	0.00238488	+	0.00413074i
$507$	−40.2701	−	0.337666i	−1.78846	−	0.0149963i
$508$	−13.7343	+	23.7884i	−0.609359	+	1.05544i
$509$	−36.5986			−1.62220			−0.811101	−	0.584906i	$-0.801132\pi$
$509$	−36.5986			−1.62220			−0.811101	+	0.584906i	$0.801132\pi$
$510$	−3.28016	−	0.0275042i	−0.145248	−	0.00121791i
$511$	−2.07870	−	1.33251i	−0.0919563	−	0.0589468i
$512$	30.2821			1.33829
$513$	−21.3803	+	34.9700i	−0.943965	+	1.54396i
$514$	0.519528	+	0.899849i	0.0229154	+	0.0396906i
$515$	−13.7562			−0.606170
$516$	−0.971055	+	1.64981i	−0.0427483	+	0.0726290i
$517$	−0.0391319	−	0.0677785i	−0.00172102	−	0.00298089i
$518$	47.0345	−	24.3168i	2.06658	−	1.06842i
$519$	12.3343	−	20.9558i	0.541415	−	0.919859i
$520$	2.22311	+	3.85055i	0.0974900	+	0.168858i
$521$	−5.46507	−	9.46578i	−0.239429	−	0.414703i	0.721122	−	0.692809i	$-0.243627\pi$
$521$	−5.46507	−	9.46578i	−0.239429	−	0.414703i	−0.960551	+	0.278105i	$0.910294\pi$
$522$	7.01868	−	11.6992i	0.307199	−	0.512058i
$523$	3.42296	−	5.92875i	0.149676	−	0.259246i	−0.781432	−	0.623991i	$-0.785510\pi$
$523$	3.42296	−	5.92875i	0.149676	−	0.259246i	0.931108	+	0.364745i	$0.118844\pi$
$524$	−18.8783	+	32.6982i	−0.824702	+	1.42843i
$525$	3.83709	+	2.50534i	0.167465	+	0.109342i
$526$	−18.3557	−	31.7930i	−0.800347	−	1.38624i
$527$	1.10857			0.0482900
$528$	0.0429643	−	0.0729959i	0.00186978	−	0.00317674i
$529$	−11.9113			−0.517883
$530$	−2.90944	+	5.03929i	−0.126378	+	0.218893i
$531$	−7.59113	−	13.6727i	−0.329427	−	0.593345i
$532$	41.3583	+	26.5119i	1.79311	+	1.14944i
$533$	32.9319	−	57.0397i	1.42644	−	2.47066i
$534$	22.5690	+	39.8588i	0.976656	+	1.72486i
$535$	−6.15963	+	10.6688i	−0.266304	+	0.461252i
$536$	−1.96588	+	3.40500i	−0.0849131	+	0.147074i
$537$	6.95454	−	11.8157i	0.300111	−	0.509885i
$538$	14.8988	−	25.8054i	0.642331	−	1.11255i
$539$	−0.0624956	+	0.0881930i	−0.00269187	+	0.00379874i
$540$	6.38013	−	10.4354i	0.274557	−	0.449069i
$541$	−3.96333	+	6.86468i	−0.170397	+	0.295136i	−0.938559	−	0.345120i	$-0.887838\pi$
$541$	−3.96333	+	6.86468i	−0.170397	+	0.295136i	0.768162	+	0.640256i	$0.221172\pi$
$542$	12.1984			0.523967
$543$	4.74056	+	8.37224i	0.203437	+	0.359287i
$544$	−7.33825			−0.314625
$545$	−2.57892	−	4.46682i	−0.110469	−	0.191337i
$546$	51.3611	−	26.0102i	2.19805	−	1.11313i
$547$	−11.0438	+	19.1285i	−0.472201	+	0.817876i	−0.999494	−	0.0318076i	$-0.989874\pi$
$547$	−11.0438	+	19.1285i	−0.472201	+	0.817876i	0.527293	+	0.849683i	$0.323207\pi$
$548$	−6.77079	+	11.7273i	−0.289234	+	0.500968i
$549$	24.7657	+	0.415352i	1.05698	+	0.0177268i
$550$	0.0161102	+	0.0279038i	0.000686943	+	0.00118982i
$551$	−8.59597	−	14.8887i	−0.366201	−	0.634278i
$552$	2.09863	+	3.70635i	0.0893235	+	0.157753i
$553$	−15.6466	−	10.0300i	−0.665363	−	0.426518i
$554$	−12.1219	−	20.9958i	−0.515010	−	0.892024i
$555$	−16.6116	−	0.139288i	−0.705122	−	0.00591247i
$556$	−6.97587			−0.295843
$557$	4.88781	+	8.46594i	0.207103	+	0.358713i	0.950801	−	0.309803i	$-0.100263\pi$
$557$	4.88781	+	8.46594i	0.207103	+	0.358713i	−0.743698	+	0.668516i	$0.766930\pi$
$558$	−3.93331	+	6.55628i	−0.166510	+	0.277549i
$559$	2.82706			0.119572
$560$	7.05400	+	4.52183i	0.298086	+	0.191082i
$561$	−0.0123134	+	0.0209204i	−0.000519874	+	0.000883261i
$562$	−8.37346			−0.353213
$563$	4.14149	−	7.17327i	0.174543	−	0.302317i	−0.765460	−	0.643483i	$-0.777489\pi$
$563$	4.14149	−	7.17327i	0.174543	−	0.302317i	0.940003	+	0.341166i	$0.110822\pi$
$564$	−10.1817	−	17.9818i	−0.428727	−	0.757169i
$565$	−6.84910	−	11.8630i	−0.288144	−	0.499080i
$566$	−25.8149			−1.08508
$567$	−19.6044	−	13.5155i	−0.823307	−	0.567596i
$568$	3.52377			0.147854
$569$	−10.7242	−	18.5748i	−0.449580	−	0.778695i	0.548779	−	0.835968i	$-0.315093\pi$
$569$	−10.7242	−	18.5748i	−0.449580	−	0.778695i	−0.998359	+	0.0572724i	$0.981760\pi$
$570$	−14.0468	−	24.8078i	−0.588354	−	1.03908i
$571$	3.84066	−	6.65222i	0.160727	−	0.278387i	−0.774403	−	0.632693i	$-0.781950\pi$
$571$	3.84066	−	6.65222i	0.160727	−	0.278387i	0.935130	+	0.354306i	$0.115283\pi$
$572$	0.218847			0.00915046
$573$	1.17961	−	2.00415i	0.0492791	−	0.0837247i
$574$	−2.80390	+	60.3265i	−0.117033	+	2.51798i
$575$	3.32997			0.138869
$576$	16.2615	−	27.1056i	0.677562	−	1.12940i
$577$	2.67530	+	4.63376i	0.111374	+	0.192906i	0.916325	−	0.400436i	$-0.131141\pi$
$577$	2.67530	+	4.63376i	0.111374	+	0.192906i	−0.804950	+	0.593342i	$0.797808\pi$
$578$	−33.7533			−1.40395
$579$	21.5727	+	0.180887i	0.896530	+	0.00751742i
$580$	2.56513	+	4.44294i	0.106511	+	0.184483i
$581$	−2.06617	+	44.4540i	−0.0857191	+	1.84426i
$582$	−11.0956	−	19.5958i	−0.459927	−	0.812271i
$583$	0.0215309	+	0.0372925i	0.000891717	+	0.00154450i
$584$	−0.344586	−	0.596840i	−0.0142591	−	0.0246974i
$585$	−18.0600	−	0.302889i	−0.746691	−	0.0125229i
$586$	26.9815	−	46.7333i	1.11459	−	1.93053i
$587$	−16.6897	+	28.9075i	−0.688859	+	1.19314i	0.283348	+	0.959017i	$0.408555\pi$
$587$	−16.6897	+	28.9075i	−0.688859	+	1.19314i	−0.972207	+	0.234122i	$0.924778\pi$
$588$	−16.6956	+	23.1467i	−0.688513	+	0.954554i
$589$	4.81723	+	8.34369i	0.198491	+	0.343796i
$590$	10.8772			0.447809
$591$	11.6646	+	20.6006i	0.479816	+	0.847395i
$592$	−30.3741			−1.24837
$593$	1.54029	−	2.66786i	0.0632521	−	0.109556i	−0.832665	−	0.553777i	$-0.813186\pi$
$593$	1.54029	−	2.66786i	0.0632521	−	0.109556i	0.895917	+	0.444221i	$0.146519\pi$
$594$	−0.0800380	−	0.147052i	−0.00328400	−	0.00603361i
$595$	−2.02166	−	1.29594i	−0.0828798	−	0.0531285i
$596$	−9.51450	+	16.4796i	−0.389729	+	0.675031i
$597$	15.1414	−	25.7251i	0.619696	−	1.05286i
$598$	20.9175	−	36.2301i	0.855378	−	1.48156i
$599$	−13.2829	+	23.0067i	−0.542725	+	0.940027i	0.456022	+	0.889969i	$0.349274\pi$
$599$	−13.2829	+	23.0067i	−0.542725	+	0.940027i	−0.998746	+	0.0500579i	$0.984059\pi$
$600$	0.630224	+	1.11303i	0.0257288	+	0.0454392i
$601$	−20.2237	+	35.0284i	−0.824941	+	1.42884i	0.0770237	+	0.997029i	$0.475458\pi$
$601$	−20.2237	+	35.0284i	−0.824941	+	1.42884i	−0.901965	+	0.431810i	$0.857875\pi$
$602$	−2.30265	+	1.19046i	−0.0938489	+	0.0485197i
$603$	−7.75321	−	13.9646i	−0.315735	−	0.568684i
$604$	9.98693	−	17.2979i	0.406363	−	0.703841i
$605$	−10.9998			−0.447204
$606$	−21.7160	+	36.8953i	−0.882152	+	1.49877i
$607$	5.75989			0.233787			0.116893	−	0.993144i	$-0.462706\pi$
$607$	5.75989			0.233787			0.116893	+	0.993144i	$0.462706\pi$
$608$	−31.8881	−	55.2317i	−1.29323	−	2.23994i
$609$	8.91016	−	4.51226i	0.361058	−	0.182846i
$610$	−8.61392	+	14.9198i	−0.348768	+	0.604083i
$611$	−15.2580	+	26.4276i	−0.617273	+	1.06915i
$612$	−3.29735	+	5.49623i	−0.133288	+	0.222172i
$613$	−17.6856	−	30.6324i	−0.714315	−	1.23723i	−0.963223	−	0.268702i	$-0.913405\pi$
$613$	−17.6856	−	30.6324i	−0.714315	−	1.23723i	0.248909	−	0.968527i	$-0.419928\pi$
$614$	−7.55504	−	13.0857i	−0.304897	−	0.528096i
$615$	9.61092	−	16.3289i	0.387550	−	0.658444i
$616$	−0.0268001	+	0.0138556i	−0.00107981	+	0.000558259i
$617$	−15.8253	−	27.4103i	−0.637104	−	1.10350i	−0.986065	−	0.166359i	$-0.946799\pi$
$617$	−15.8253	−	27.4103i	−0.637104	−	1.10350i	0.348961	−	0.937137i	$-0.386534\pi$
$618$	−25.2182	+	42.8456i	−1.01443	+	1.72350i
$619$	−3.10618			−0.124848			−0.0624240	−	0.998050i	$-0.519883\pi$
$619$	−3.10618			−0.124848			−0.0624240	+	0.998050i	$0.519883\pi$
$620$	−1.43752	−	2.48985i	−0.0577320	−	0.0999948i
$621$	−17.2976	−	0.435203i	−0.694127	−	0.0174641i
$622$	−69.7638			−2.79727
$623$	−1.55685	+	33.4959i	−0.0623737	+	1.34198i
$624$	−33.0249	−	0.276915i	−1.32206	−	0.0110855i
$625$	1.00000			0.0400000
$626$	21.8176	−	37.7892i	0.872006	−	1.51036i
$627$	−0.210966	−	0.00176896i	−0.00842517	−	7.06453e-5i
$628$	20.2602	+	35.0918i	0.808471	+	1.40031i
$629$	8.70513			0.347096
$630$	14.8375	−	7.35832i	0.591140	−	0.293162i
$631$	48.2486			1.92075			0.960374	−	0.278715i	$-0.0899085\pi$
$631$	48.2486			1.92075			0.960374	+	0.278715i	$0.0899085\pi$
$632$	−2.59374	−	4.49249i	−0.103173	−	0.178702i
$633$	8.40132	−	14.2738i	0.333922	−	0.567331i
$634$	−10.0950	+	17.4851i	−0.400925	+	0.694422i
$635$	11.6693			0.463083
$636$	5.60210	+	9.89378i	0.222138	+	0.392314i
$637$	41.9643	+	3.90935i	1.66269	+	0.154894i
$638$	0.0702234			0.00278017
$639$	−7.36445	+	12.2755i	−0.291333	+	0.485612i
$640$	2.90763	+	5.03617i	0.114934	+	0.199072i
$641$	2.09541			0.0827637			0.0413818	−	0.999143i	$-0.486824\pi$
$641$	2.09541			0.0827637			0.0413818	+	0.999143i	$0.486824\pi$
$642$	21.9375	+	38.7434i	0.865802	+	1.52908i
$643$	−1.93014	−	3.34309i	−0.0761171	−	0.131839i	0.825454	−	0.564469i	$-0.190919\pi$
$643$	−1.93014	−	3.34309i	−0.0761171	−	0.131839i	−0.901572	+	0.432630i	$0.857586\pi$
$644$	−0.962865	+	20.7162i	−0.0379422	+	0.816334i
$645$	0.813245	+	0.00681908i	0.0320215	+	0.000268501i
$646$	7.46955	+	12.9376i	0.293885	+	0.509025i
$647$	−20.6094	−	35.6965i	−0.810238	−	1.40337i	−0.912698	−	0.408636i	$-0.866005\pi$
$647$	−20.6094	−	35.6965i	−0.810238	−	1.40337i	0.102460	−	0.994737i	$-0.467329\pi$
$648$	−3.12824	−	5.86401i	−0.122889	−	0.230360i
$649$	0.0402477	−	0.0697111i	0.00157986	−	0.00273640i
$650$	6.28157	−	10.8800i	0.246384	−	0.426749i
$651$	−4.99330	+	2.52870i	−0.195703	+	0.0991075i
$652$	−1.40621	−	2.43563i	−0.0550716	−	0.0953867i
$653$	−19.7476			−0.772783			−0.386391	−	0.922335i	$-0.626279\pi$
$653$	−19.7476			−0.772783			−0.386391	+	0.922335i	$0.626279\pi$
$654$	−18.6403	−	0.156299i	−0.728893	−	0.00611178i
$655$	16.0399			0.626732
$656$	17.3219	−	30.0024i	0.676307	−	1.17140i
$657$	2.79933	+	0.0469482i	0.109212	+	0.00183162i
$658$	1.29910	−	27.9505i	0.0506443	−	1.08962i
$659$	6.81311	−	11.8007i	0.265401	−	0.459688i	−0.702268	−	0.711913i	$-0.747829\pi$
$659$	6.81311	−	11.8007i	0.265401	−	0.459688i	0.967669	+	0.252225i	$0.0811623\pi$
$660$	0.0629546		0.000527876i	0.00245051		2.05475e-5i
$661$	14.7513	−	25.5499i	0.573757	−	0.993777i	−0.422418	−	0.906401i	$-0.638819\pi$
$661$	14.7513	−	25.5499i	0.573757	−	0.993777i	0.996175	−	0.0873760i	$-0.0278481\pi$
$662$	17.5460	−	30.3905i	0.681943	−	1.18116i
$663$	9.46485	+	0.0793630i	0.367584	+	0.00308220i
$664$	−6.21061	+	10.7571i	−0.241018	+	0.417456i
$665$	0.968969	−	20.8476i	0.0375750	−	0.808434i
$666$	−30.8867	+	51.4838i	−1.19684	+	1.99496i
$667$	3.62878	−	6.28522i	0.140507	−	0.243365i
$668$	19.4463			0.752400
$669$	6.96100	+	0.0583682i	0.269128	+	0.00225664i
$670$	11.1095			0.429196
$671$	0.0637461	+	0.110411i	0.00246089	+	0.00426239i
$672$	33.0536	−	16.7389i	1.27507	−	0.645718i
$673$	−12.4123	+	21.4987i	−0.478458	+	0.828714i	−0.999695	−	0.0246979i	$-0.992138\pi$
$673$	−12.4123	+	21.4987i	−0.478458	+	0.828714i	0.521237	+	0.853412i	$0.325471\pi$
$674$	−0.596927	+	1.03391i	−0.0229928	+	0.0398246i
$675$	−5.19451	−	0.130693i	−0.199937	−	0.00503036i
$676$	−27.3651	−	47.3978i	−1.05251	−	1.82299i
$677$	12.7480	+	22.0802i	0.489945	+	0.848610i	0.999933	−	0.0115717i	$-0.00368345\pi$
$677$	12.7480	+	22.0802i	0.489945	+	0.848610i	−0.509988	+	0.860182i	$0.670350\pi$
$678$	−49.5050	−	0.415100i	−1.90123	−	0.0159418i
$679$	0.765393	−	16.4676i	0.0293731	−	0.631968i
$680$	−0.335130	−	0.580462i	−0.0128516	−	0.0222597i
$681$	−2.38911	−	4.21938i	−0.0915511	−	0.161687i
$682$	−0.0393536			−0.00150693
$683$	19.1745	+	33.2112i	0.733692	+	1.27079i	0.955295	+	0.295655i	$0.0955377\pi$
$683$	19.1745	+	33.2112i	0.733692	+	1.27079i	−0.221603	+	0.975137i	$0.571129\pi$
$684$	−55.6961	−	0.934092i	−2.12960	−	0.0357159i
$685$	5.75280			0.219803
$686$	−35.8263	+	14.4869i	−1.36785	+	0.553111i
$687$	−17.3366	−	30.6180i	−0.661433	−	1.16815i
$688$	1.48701			0.0566918
$689$	8.39514	−	14.5408i	0.319829	−	0.553960i
$690$	6.10460	−	10.3717i	0.232398	−	0.394843i
$691$	−3.32673	−	5.76206i	−0.126555	−	0.219199i	0.795785	−	0.605579i	$-0.207059\pi$
$691$	−3.32673	−	5.76206i	−0.126555	−	0.219199i	−0.922340	+	0.386380i	$0.873725\pi$
$692$	33.0466			1.25624
$693$	0.00774272	−	0.122319i	0.000294121	−	0.00464652i
$694$	14.7128			0.558492
$695$	1.48176	+	2.56649i	0.0562064	+	0.0973524i
$696$	2.78759	+	0.0233740i	0.105663	+	0.000885988i
$697$	−4.96441	+	8.59861i	−0.188040	+	0.325695i
$698$	9.58442			0.362776
$699$	−11.2824	−	0.0946033i	−0.426740	−	0.00357823i
$700$	−0.289151	+	6.22115i	−0.0109289	+	0.235137i
$701$	15.9966			0.604183			0.302091	−	0.953279i	$-0.402315\pi$
$701$	15.9966			0.604183			0.302091	+	0.953279i	$0.402315\pi$
$702$	−34.0516	+	55.6953i	−1.28520	+	2.10208i
$703$	37.8278	+	65.5196i	1.42670	+	2.47112i
$704$	0.162700			0.00613197
$705$	−4.45294	+	7.56550i	−0.167707	+	0.284933i
$706$	25.2069	+	43.6596i	0.948674	+	1.64315i
$707$	−27.8403	+	14.3934i	−1.04704	+	0.541319i
$708$	10.7807	−	18.3163i	0.405163	−	0.688368i
$709$	19.5042	+	33.7822i	0.732494	+	1.26872i	0.955814	+	0.293972i	$0.0949773\pi$
$709$	19.5042	+	33.7822i	0.732494	+	1.26872i	−0.223320	+	0.974745i	$0.571689\pi$
$710$	−4.97834	−	8.62273i	−0.186834	−	0.323605i
$711$	21.0709	+	0.353385i	0.790222	+	0.0132530i
$712$	−4.67965	+	8.10540i	−0.175377	+	0.303763i
$713$	−2.03359	+	3.52228i	−0.0761584	+	0.131910i
$714$	−7.74257	+	3.92097i	−0.289758	+	0.146739i
$715$	−0.0464859	−	0.0805159i	−0.00173847	−	0.00301112i
$716$	18.6329			0.696345
$717$	−25.5492	+	43.4078i	−0.954151	+	1.62109i
$718$	21.5642			0.804768
$719$	22.0049	−	38.1135i	0.820643	−	1.42140i	−0.0845611	−	0.996418i	$-0.526949\pi$
$719$	22.0049	−	38.1135i	0.820643	−	1.42140i	0.905204	−	0.424977i	$-0.139718\pi$
$720$	−9.49944	−	0.159317i	−0.354023	−	0.00593740i
$721$	−32.3303	+	16.7147i	−1.20404	+	0.622487i
$722$	−45.0945	+	78.1059i	−1.67824	+	2.90680i
$723$	−11.9862	−	21.1686i	−0.445771	−	0.787270i
$724$	−6.53775	+	11.3237i	−0.242973	+	0.420842i
$725$	1.08973	−	1.88747i	0.0404716	−	0.0700989i
$726$	−20.1651	+	34.2603i	−0.748397	+	1.27152i
$727$	−9.74378	+	16.8767i	−0.361377	+	0.625923i	−0.988188	−	0.153248i	$-0.951027\pi$
$727$	−9.74378	+	16.8767i	−0.361377	+	0.625923i	0.626811	+	0.779171i	$0.284360\pi$
$728$	9.90352	+	6.34846i	0.367049	+	0.235290i
$729$	26.9658	+	1.35777i	0.998735	+	0.0502877i
$730$	−0.973652	+	1.68641i	−0.0360365	+	0.0624170i
$731$	−0.426173			−0.0157626
$732$	16.5860	+	29.2924i	0.613038	+	1.08268i
$733$	41.3259			1.52641			0.763204	−	0.646157i	$-0.223625\pi$
$733$	41.3259			1.52641			0.763204	+	0.646157i	$0.223625\pi$
$734$	30.2925	+	52.4681i	1.11811	+	1.93663i
$735$	12.0622	+	1.22580i	0.444922	+	0.0452144i
$736$	13.4615	−	23.3160i	0.496198	−	0.859439i
$737$	0.0411070	−	0.0711995i	0.00151420	−	0.00262267i
$738$	−33.2396	−	59.8692i	−1.22356	−	2.20382i
$739$	19.1130	+	33.1047i	0.703084	+	1.21778i	0.967379	+	0.253335i	$0.0815276\pi$
$739$	19.1130	+	33.1047i	0.703084	+	1.21778i	−0.264294	+	0.964442i	$0.585139\pi$
$740$	−11.2882	−	19.5518i	−0.414963	−	0.718738i
$741$	40.5318	+	71.5825i	1.48897	+	2.62965i
$742$	−0.714782	+	15.3787i	−0.0262405	+	0.564569i
$743$	−23.1922	−	40.1701i	−0.850839	−	1.47370i	−0.880452	−	0.474136i	$-0.842761\pi$
$743$	−23.1922	−	40.1701i	−0.850839	−	1.47370i	0.0296124	−	0.999561i	$-0.490573\pi$
$744$	−1.56218	−	0.0130989i	−0.0572723	−	0.000480229i
$745$	8.08400			0.296175
$746$	13.9752	+	24.2058i	0.511670	+	0.886238i
$747$	−24.4939	−	44.1171i	−0.896186	−	1.61416i
$748$	−0.0329907			−0.00120626
$749$	−1.51328	+	32.5586i	−0.0552941	+	1.18966i
$750$	1.83323	−	3.11464i	0.0669401	−	0.113731i
$751$	12.5303			0.457238			0.228619	−	0.973516i	$-0.426579\pi$
$751$	12.5303			0.457238			0.228619	+	0.973516i	$0.426579\pi$
$752$	−8.02559	+	13.9007i	−0.292663	+	0.506907i
$753$	12.9951	+	22.9504i	0.473566	+	0.836359i
$754$	−13.6905	−	23.7126i	−0.498577	−	0.863561i
$755$	−8.48540			−0.308815
$756$	2.31506	−	32.2780i	0.0841978	−	1.17394i
$757$	14.1254			0.513397			0.256698	−	0.966492i	$-0.417365\pi$
$757$	14.1254			0.513397			0.256698	+	0.966492i	$0.417365\pi$
$758$	−34.4644	−	59.6941i	−1.25180	−	2.16819i
$759$	−0.0438828	−	0.0775008i	−0.00159285	−	0.00281310i
$760$	2.91258	−	5.04474i	0.105650	−	0.182992i
$761$	9.94974			0.360678			0.180339	−	0.983605i	$-0.442281\pi$
$761$	9.94974			0.360678			0.180339	+	0.983605i	$0.442281\pi$
$762$	21.3925	−	36.3457i	0.774970	−	1.31667i
$763$	−11.4885	−	7.36451i	−0.415913	−	0.266613i
$764$	3.16048			0.114342
$765$	2.72251	+	0.0456599i	0.0984326	+	0.00165084i
$766$	13.3820	+	23.1783i	0.483511	+	0.837466i
$767$	−31.3861			−1.13329
$768$	−15.4818	−	0.129815i	−0.558652	−	0.00468431i
$769$	−24.1352	−	41.8033i	−0.870336	−	1.50747i	−0.861649	−	0.507505i	$-0.830568\pi$
$769$	−24.1352	−	41.8033i	−0.870336	−	1.50747i	−0.00868735	−	0.999962i	$-0.502765\pi$
$770$	0.0717678	+	0.0460054i	0.00258633	+	0.00165792i
$771$	−0.424972	−	0.750538i	−0.0153050	−	0.0270299i
$772$	14.6595	+	25.3910i	0.527606	+	0.913841i
$773$	7.45682	+	12.9156i	0.268203	+	0.464542i	0.968398	−	0.249410i	$-0.0802368\pi$
$773$	7.45682	+	12.9156i	0.268203	+	0.464542i	−0.700195	+	0.713952i	$0.746903\pi$
$774$	1.51211	−	2.52047i	0.0543515	−	0.0905963i
$775$	−0.610692	+	1.05775i	−0.0219367	+	0.0379955i
$776$	2.30066	−	3.98486i	0.0825889	−	0.143048i
$777$	−39.2104	+	19.8568i	−1.40666	+	0.712360i
$778$	−7.79053	−	13.4936i	−0.279304	−	0.483769i
$779$	−86.2905			−3.09168
$780$	−12.0951	−	21.3610i	−0.433075	−	0.764847i
$781$	−0.0736829			−0.00263658
$782$	−3.15326	+	5.46161i	−0.112760	+	0.195307i
$783$	−5.90730	+	9.66207i	−0.211110	+	0.345294i
$784$	22.0729	+	2.05629i	0.788318	+	0.0734388i
$785$	8.60705	−	14.9079i	0.307199	−	0.532084i
$786$	29.4049	−	49.9587i	1.04884	−	1.78197i
$787$	3.05460	−	5.29072i	0.108885	−	0.188594i	−0.806434	−	0.591324i	$-0.798605\pi$
$787$	3.05460	−	5.29072i	0.108885	−	0.188594i	0.915319	+	0.402730i	$0.131939\pi$
$788$	−16.0867	+	27.8629i	−0.573064	+	0.992576i
$789$	15.0149	+	26.5177i	0.534546	+	0.944053i
$790$	−7.32881	+	12.6939i	−0.260747	+	0.451627i
$791$	−30.5114	−	19.5587i	−1.08486	−	0.695428i
$792$	0.0175991	−	0.0293353i	0.000625358	−	0.00104238i
$793$	24.8554	−	43.0507i	0.882639	−	1.52878i
$794$	23.2189			0.824010
$795$	2.45006	−	4.16263i	0.0868946	−	0.147633i
$796$	40.5675			1.43788
$797$	−10.2256	−	17.7112i	−0.362209	−	0.627364i	0.626115	−	0.779730i	$-0.284644\pi$
$797$	−10.2256	−	17.7112i	−0.362209	−	0.627364i	−0.988324	+	0.152367i	$0.951311\pi$
$798$	−63.1564	−	41.2364i	−2.23571	−	1.45975i
$799$	2.30011	−	3.98391i	0.0813720	−	0.140941i
$800$	4.04253	−	7.00187i	0.142925	−	0.247553i
$801$	−18.4560	−	33.2419i	−0.652112	−	1.17455i
$802$	−18.7605	−	32.4942i	−0.662458	−	1.14741i
$803$	0.00720537	+	0.0124801i	0.000254272	+	0.000440412i
$804$	11.0109	−	18.7073i	0.388323	−	0.659757i
$805$	7.82622	−	4.04614i	0.275838	−	0.142608i
$806$	7.67222	+	13.2887i	0.270242	+	0.468073i
$807$	−12.5464	+	21.3162i	−0.441653	+	0.750364i
$808$	−8.74773			−0.307744
$809$	25.4615	+	44.1006i	0.895178	+	1.55049i	0.833584	+	0.552392i	$0.186285\pi$
$809$	25.4615	+	44.1006i	0.895178	+	1.55049i	0.0615935	+	0.998101i	$0.480382\pi$
$810$	−9.92979	+	15.9394i	−0.348897	+	0.560055i
$811$	28.5592			1.00285			0.501424	−	0.865202i	$-0.332810\pi$
$811$	28.5592			1.00285			0.501424	+	0.865202i	$0.332810\pi$
$812$	11.4271	+	7.32515i	0.401014	+	0.257062i
$813$	−10.1253	−	0.0849011i	−0.355111	−	0.00297761i
$814$	−0.309028			−0.0108314
$815$	−0.597394	+	1.03472i	−0.0209258	+	0.0362446i
$816$	4.97844	+	0.0417443i	0.174280	+	0.00146134i
$817$	−1.85192	−	3.20761i	−0.0647903	−	0.112220i
$818$	71.3205			2.49366
$819$	−42.8134	+	21.2323i	−1.49602	+	0.741917i
$820$	25.7500			0.899230
$821$	−17.0589	−	29.5469i	−0.595359	−	1.03119i	−0.993496	−	0.113867i	$-0.963676\pi$
$821$	−17.0589	−	29.5469i	−0.595359	−	1.03119i	0.398137	−	0.917326i	$-0.369657\pi$
$822$	10.5462	−	17.9179i	0.367841	−	0.624959i
$823$	−20.0631	+	34.7503i	−0.699356	+	1.21132i	0.269335	+	0.963047i	$0.413196\pi$
$823$	−20.0631	+	34.7503i	−0.699356	+	1.21132i	−0.968690	+	0.248273i	$0.920137\pi$
$824$	−10.1585			−0.353889
$825$	−0.0131781	−	0.0232737i	−0.000458804	−	0.000810287i
$826$	25.5641	−	13.2166i	0.889488	−	0.459864i
$827$	−3.36758			−0.117102			−0.0585511	−	0.998284i	$-0.518648\pi$
$827$	−3.36758			−0.117102			−0.0585511	+	0.998284i	$0.518648\pi$
$828$	−11.4145	−	20.5592i	−0.396682	−	0.714481i
$829$	−8.14761	−	14.1121i	−0.282978	−	0.490133i	0.689139	−	0.724630i	$-0.257989\pi$
$829$	−8.14761	−	14.1121i	−0.282978	−	0.490133i	−0.972117	+	0.234497i	$0.924656\pi$
$830$	35.0971			1.21824
$831$	9.91569	+	17.5119i	0.343971	+	0.607483i
$832$	−31.7193	−	54.9394i	−1.09967	−	1.90468i
$833$	−6.32603	−	0.589325i	−0.219184	−	0.0204189i
$834$	10.7101	+	0.0898044i	0.370860	+	0.00310967i
$835$	−4.13064	−	7.15448i	−0.142947	−	0.247591i
$836$	−0.143360	−	0.248306i	−0.00495820	−	0.00858786i
$837$	3.31049	−	5.41468i	0.114427	−	0.187159i
$838$	−22.4364	+	38.8610i	−0.775053	+	1.34243i
$839$	−2.95539	+	5.11888i	−0.102031	+	0.176723i	−0.912521	−	0.409029i	$-0.865868\pi$
$839$	−2.95539	+	5.11888i	−0.102031	+	0.176723i	0.810490	+	0.585752i	$0.199201\pi$
$840$	2.83358	+	1.85012i	0.0977678	+	0.0638351i
$841$	12.1250	+	21.0011i	0.418102	+	0.724174i
$842$	−46.5279			−1.60346
$843$	6.95041	+	0.0582793i	0.239385	+	0.00200725i
$844$	22.5092			0.774799
$845$	−11.6254	+	20.1358i	−0.399926	+	0.692692i
$846$	15.4006	+	27.7386i	0.529482	+	0.953673i
$847$	−25.8520	+	13.3655i	−0.888287	+	0.459242i
$848$	4.41578	−	7.64835i	0.151638	−	0.262645i
$849$	21.4277	+	0.179672i	0.735398	+	0.00616633i
$850$	−0.946933	+	1.64014i	−0.0324795	+	0.0562562i
$851$	−15.9689	+	27.6590i	−0.547408	+	0.948139i
$852$	−19.4540	−	0.163123i	−0.666484	−	0.00558849i
$853$	3.68713	−	6.38630i	0.126245	−	0.218663i	−0.795974	−	0.605331i	$-0.793041\pi$
$853$	3.68713	−	6.38630i	0.126245	−	0.218663i	0.922219	+	0.386668i	$0.126374\pi$
$854$	−2.11624	+	45.5314i	−0.0724164	+	1.55805i
$855$	11.4869	+	20.6895i	0.392844	+	0.707567i
$856$	−4.54871	+	7.87859i	−0.155472	+	0.269285i
$857$	−14.5063			−0.495525			−0.247762	−	0.968821i	$-0.579695\pi$
$857$	−14.5063			−0.495525			−0.247762	+	0.968821i	$0.579695\pi$
$858$	−0.335998	−	0.00281735i	−0.0114708	−	9.61826e-5i
$859$	32.8519			1.12089			0.560447	−	0.828190i	$-0.310629\pi$
$859$	32.8519			1.12089			0.560447	+	0.828190i	$0.310629\pi$
$860$	0.552632	+	0.957187i	0.0188446	+	0.0326398i
$861$	2.74726	−	50.0546i	0.0936263	−	1.70586i
$862$	16.3312	−	28.2864i	0.556242	−	0.963440i
$863$	7.99037	−	13.8397i	0.271995	−	0.471109i	−0.697377	−	0.716704i	$-0.745650\pi$
$863$	7.99037	−	13.8397i	0.271995	−	0.471109i	0.969373	+	0.245595i	$0.0789832\pi$
$864$	−21.9140	+	35.8429i	−0.745531	+	1.21940i
$865$	−7.01950	−	12.1581i	−0.238670	−	0.413389i
$866$	32.3823	+	56.0878i	1.10039	+	1.90594i
$867$	28.0170	+	0.234923i	0.951508	+	0.00797842i
$868$	−6.40384	−	4.10506i	−0.217360	−	0.139335i
$869$	0.0542358	+	0.0939391i	0.00183982	+	0.00318667i
$870$	−3.88107	−	6.85430i	−0.131581	−	0.232382i
$871$	−32.0562			−1.08618
$872$	−1.90445	−	3.29861i	−0.0644930	−	0.111705i
$873$	9.07354	+	16.3427i	0.307093	+	0.553118i
$874$	−54.8094			−1.85396
$875$	2.35024	−	1.21507i	0.0794525	−	0.0410768i
$876$	1.87476	+	3.31099i	0.0633423	+	0.111868i
$877$	−3.22057			−0.108751			−0.0543755	−	0.998521i	$-0.517317\pi$
$877$	−3.22057			−0.108751			−0.0543755	+	0.998521i	$0.517317\pi$
$878$	1.90987	−	3.30799i	0.0644549	−	0.111639i
$879$	−22.7213	+	38.6033i	−0.766370	+	1.30206i
$880$	−0.0244512	−	0.0423507i	−0.000824250	−	0.00142764i
$881$	8.42574			0.283871			0.141935	−	0.989876i	$-0.454668\pi$
$881$	8.42574			0.283871			0.141935	+	0.989876i	$0.454668\pi$
$882$	25.9308	−	35.3224i	0.873135	−	1.18937i
$883$	−54.8523			−1.84593			−0.922964	−	0.384886i	$-0.874241\pi$
$883$	−54.8523			−1.84593			−0.922964	+	0.384886i	$0.874241\pi$
$884$	6.43174	+	11.1401i	0.216323	+	0.374682i
$885$	−9.02868	−	0.0757057i	−0.303496	−	0.00254482i
$886$	18.5862	−	32.1922i	0.624414	−	1.08152i
$887$	22.4721			0.754540			0.377270	−	0.926103i	$-0.376863\pi$
$887$	22.4721			0.754540			0.377270	+	0.926103i	$0.376863\pi$
$888$	−12.2672	−	0.102860i	−0.411659	−	0.00345177i
$889$	27.4256	−	14.1790i	0.919827	−	0.475549i
$890$	26.4454			0.886452
$891$	0.0654122	+	0.122618i	0.00219139	+	0.00410785i
$892$	4.73028	+	8.19308i	0.158381	+	0.274325i
$893$	39.9801			1.33788
$894$	14.8198	−	25.1788i	0.495649	−	0.842104i
$895$	−3.95787	−	6.85523i	−0.132297	−	0.229145i
$896$	12.9529	+	8.30322i	0.432727	+	0.277391i
$897$	−17.6147	+	29.9273i	−0.588139	+	0.999243i
$898$	−13.7552	−	23.8246i	−0.459016	−	0.795038i
$899$	1.33098	+	2.30533i	0.0443907	+	0.0768870i
$900$	−3.42782	−	6.17399i	−0.114261	−	0.205800i
$901$	−1.26555	+	2.19199i	−0.0421615	+	0.0730259i
$902$	0.176234	−	0.305246i	0.00586795	−	0.0101636i
$903$	1.91960	−	0.972122i	0.0638804	−	0.0323502i
$904$	−5.05786	−	8.76047i	−0.168222	−	0.291369i
$905$	5.55480			0.184648
$906$	−15.5557	+	26.4290i	−0.516803	+	0.878044i
$907$	37.9712			1.26081			0.630407	−	0.776265i	$-0.282888\pi$
$907$	37.9712			1.26081			0.630407	+	0.776265i	$0.282888\pi$
$908$	3.29485	−	5.70684i	0.109343	−	0.189388i
$909$	18.2822	−	30.4739i	0.606382	−	1.01075i
$910$	1.54324	−	33.2031i	0.0511579	−	1.10067i
$911$	1.75368	−	3.03747i	0.0581021	−	0.100636i	−0.835511	−	0.549473i	$-0.814828\pi$
$911$	1.75368	−	3.03747i	0.0581021	−	0.100636i	0.893613	+	0.448837i	$0.148162\pi$
$912$	21.3194	+	37.6519i	0.705955	+	1.24678i
$913$	0.129865	−	0.224933i	0.00429792	−	0.00744421i
$914$	25.3533	−	43.9131i	0.838612	−	1.45252i
$915$	7.25385	−	12.3242i	0.239805	−	0.407426i
$916$	23.9091	−	41.4117i	0.789978	−	1.36828i
$917$	37.6976	−	19.4896i	1.24489	−	0.643604i
$918$	5.13321	−	8.39595i	0.169421	−	0.277108i
$919$	−6.42021	+	11.1201i	−0.211783	+	0.366819i	−0.952273	−	0.305249i	$-0.901260\pi$
$919$	−6.42021	+	11.1201i	−0.211783	+	0.366819i	0.740490	+	0.672068i	$0.234594\pi$
$920$	2.45909			0.0810736
$921$	6.18000	+	10.9144i	0.203638	+	0.359642i
$922$	−14.9856			−0.493525
$923$	14.3649	+	24.8808i	0.472827	+	0.818960i
$924$	0.148600	−	0.0752535i	0.00488857	−	0.00247566i
$925$	−4.79552	+	8.30608i	−0.157676	+	0.273102i
$926$	13.1321	−	22.7455i	0.431548	−	0.747464i
$927$	21.2307	−	35.3886i	0.697307	−	1.16231i
$928$	−8.81055	−	15.2603i	−0.289220	−	0.500945i
$929$	25.6091	+	44.3563i	0.840208	+	1.45528i	0.889718	+	0.456510i	$0.150901\pi$
$929$	25.6091	+	44.3563i	0.840208	+	1.45528i	−0.0495099	+	0.998774i	$0.515766\pi$
$930$	2.17497	+	3.84119i	0.0713202	+	0.125958i
$931$	−23.0539	−	50.1741i	−0.755561	−	1.64439i
$932$	−7.66685	−	13.2794i	−0.251136	−	0.434980i
$933$	57.9076	+	0.485557i	1.89581	+	0.0158964i
$934$	29.3558			0.960550
$935$	0.00700764	+	0.0121376i	0.000229174	+	0.000396942i
$936$	−13.3368	−	0.223675i	−0.435927	−	0.00731104i
$937$	32.2456			1.05342			0.526708	−	0.850046i	$-0.323426\pi$
$937$	32.2456			1.05342			0.526708	+	0.850046i	$0.323426\pi$
$938$	26.1099	−	13.4988i	0.852518	−	0.440750i
$939$	−18.3728	+	31.2151i	−0.599572	+	1.01867i
$940$	−11.9305			−0.389130
$941$	23.9064	−	41.4071i	0.779326	−	1.34983i	−0.153005	−	0.988225i	$-0.548895\pi$
$941$	23.9064	−	41.4071i	0.779326	−	1.34983i	0.932331	−	0.361607i	$-0.117772\pi$
$942$	−30.6539	−	54.1374i	−0.998758	−	1.76389i
$943$	−18.2137	−	31.5471i	−0.593120	−	1.02731i
$944$	−16.5088			−0.537317
$945$	−12.3671	+	6.00452i	−0.402303	+	0.195327i
$946$	0.0151289			0.000491884
$947$	−10.0385	−	17.3873i	−0.326209	−	0.565011i	0.655547	−	0.755154i	$-0.272438\pi$
$947$	−10.0385	−	17.3873i	−0.326209	−	0.565011i	−0.981756	+	0.190144i	$0.939105\pi$
$948$	14.1116	+	24.9222i	0.458322	+	0.809436i
$949$	2.80946	−	4.86613i	0.0911989	−	0.157961i
$950$	−16.4594			−0.534014
$951$	8.50110	−	14.4433i	0.275667	−	0.468356i
$952$	−1.49293	−	0.957017i	−0.0483863	−	0.0310171i
$953$	−34.9184			−1.13112			−0.565560	−	0.824707i	$-0.691340\pi$
$953$	−34.9184			−1.13112			−0.565560	+	0.824707i	$0.691340\pi$
$954$	−8.47357	−	15.2621i	−0.274342	−	0.494129i
$955$	−0.671325	−	1.16277i	−0.0217236	−	0.0376263i
$956$	−68.4525			−2.21391
$957$	−0.0582891		0.000488756i	−0.00188422		1.57992e-5i
$958$	28.8454	+	49.9617i	0.931952	+	1.61419i
$959$	13.5204	−	6.99004i	0.436598	−	0.225720i
$960$	−8.99200	−	15.8806i	−0.290215	−	0.512545i
$961$	14.7541	+	25.5549i	0.475939	+	0.824351i
$962$	60.2468	+	104.351i	1.94244	+	3.36440i
$963$	−17.9396	−	32.3118i	−0.578095	−	1.04123i
$964$	16.5302	−	28.6312i	0.532403	−	0.922150i
$965$	6.22771	−	10.7867i	0.200477	−	0.347237i
$966$	1.74498	−	31.7934i	0.0561440	−	1.02293i
$967$	−13.1123	−	22.7112i	−0.421664	−	0.730343i	0.574439	−	0.818548i	$-0.305220\pi$
$967$	−13.1123	−	22.7112i	−0.421664	−	0.730343i	−0.996102	+	0.0882047i	$0.971887\pi$
$968$	−8.12300			−0.261083
$969$	−6.11007	−	10.7909i	−0.196284	−	0.346654i
$970$	−13.0014			−0.417449
$971$	−28.3045	+	49.0249i	−0.908336	+	1.57328i	−0.0919602	+	0.995763i	$0.529313\pi$
$971$	−28.3045	+	49.0249i	−0.908336	+	1.57328i	−0.816376	+	0.577521i	$0.804020\pi$
$972$	16.9989	+	32.5188i	0.545241	+	1.04304i
$973$	6.60094	+	4.23141i	0.211617	+	0.135653i
$974$	23.6773	−	41.0103i	0.758671	−	1.31406i
$975$	−5.28976	+	8.98726i	−0.169408	+	0.287823i
$976$	13.0737	−	22.6443i	0.418480	−	0.724828i
$977$	11.6770	−	20.2252i	0.373582	−	0.647062i	−0.616532	−	0.787330i	$-0.711463\pi$
$977$	11.6770	−	20.2252i	0.373582	−	0.647062i	0.990114	+	0.140268i	$0.0447963\pi$
$978$	2.12761	+	3.75755i	0.0680336	+	0.120153i
$979$	0.0978527	−	0.169486i	0.00312739	−	0.00541679i
$980$	6.87954	+	14.9725i	0.219759	+	0.478279i
$981$	15.4713	+	0.259473i	0.493961	+	0.00828434i
$982$	20.2727	−	35.1134i	0.646929	−	1.12051i
$983$	−40.1678			−1.28115			−0.640576	−	0.767894i	$-0.721305\pi$
$983$	−40.1678			−1.28115			−0.640576	+	0.767894i	$0.721305\pi$
$984$	7.09739	−	12.0584i	0.226256	−	0.384408i
$985$	13.6680			0.435500
$986$	2.06381	+	3.57462i	0.0657250	+	0.113839i
$987$	−1.27286	+	23.1913i	−0.0405156	+	0.738188i
$988$	−55.8977	+	96.8176i	−1.77834	+	3.08018i
$989$	0.781784	−	1.35409i	0.0248593	−	0.0430575i
$990$	−0.0966479	−	0.00162090i	−0.00307167	−	5.15157e-5i
$991$	16.5599	+	28.6826i	0.526042	+	0.911131i	0.999540	+	0.0303363i	$0.00965783\pi$
$991$	16.5599	+	28.6826i	0.526042	+	0.911131i	−0.473498	+	0.880795i	$0.657009\pi$
$992$	4.93748	+	8.55197i	0.156765	+	0.271525i
$993$	−14.7756	+	25.1036i	−0.468889	+	0.796638i
$994$	−22.1775	−	14.2164i	−0.703427	−	0.450918i
$995$	−8.61705	−	14.9252i	−0.273179	−	0.473160i
$996$	34.7855	−	59.1002i	1.10222	−	1.87266i
$997$	16.2256			0.513869			0.256935	−	0.966429i	$-0.417287\pi$
$997$	16.2256			0.513869			0.256935	+	0.966429i	$0.417287\pi$
$998$	−19.4471	−	33.6834i	−0.615588	−	1.06623i
$999$	25.9959	−	42.5193i	0.822474	−	1.34525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.3	✓	36
3.2	odd	2		945.2.k.c.856.16		36
7.4	even	3		315.2.l.c.151.16	yes	36
9.4	even	3		315.2.l.c.121.16	yes	36
9.5	odd	6		945.2.l.c.226.3		36
21.11	odd	6		945.2.l.c.46.3		36
63.4	even	3	inner	315.2.k.c.256.3	yes	36
63.32	odd	6		945.2.k.c.361.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.3	✓	36	1.1	even	1	trivial
315.2.k.c.256.3	yes	36	63.4	even	3	inner
315.2.l.c.121.16	yes	36	9.4	even	3
315.2.l.c.151.16	yes	36	7.4	even	3
945.2.k.c.361.16		36	63.32	odd	6
945.2.k.c.856.16		36	3.2	odd	2
945.2.l.c.46.3		36	21.11	odd	6
945.2.l.c.226.3		36	9.5	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04330 - 1.80705i) q^{2} +(0.853418 + 1.50721i) q^{3} +(-1.17696 + 2.03855i) q^{4} +1.00000 q^{5} +(1.83323 - 3.11464i) q^{6} +(2.35024 - 1.21507i) q^{7} +0.738471 q^{8} +(-1.54336 + 2.57256i) q^{9} +O(q^{10})\)	\(q+(-1.04330 - 1.80705i) q^{2} +(0.853418 + 1.50721i) q^{3} +(-1.17696 + 2.03855i) q^{4} +1.00000 q^{5} +(1.83323 - 3.11464i) q^{6} +(2.35024 - 1.21507i) q^{7} +0.738471 q^{8} +(-1.54336 + 2.57256i) q^{9} +(-1.04330 - 1.80705i) q^{10} -0.0154416 q^{11} +(-4.07695 - 0.0341853i) q^{12} +(3.01043 + 5.21422i) q^{13} +(-4.64769 - 2.97931i) q^{14} +(0.853418 + 1.50721i) q^{15} +(1.58346 + 2.74264i) q^{16} +(-0.453816 - 0.786032i) q^{17} +(6.25893 + 0.104970i) q^{18} +(3.94407 - 6.83134i) q^{19} +(-1.17696 + 2.03855i) q^{20} +(3.83709 + 2.50534i) q^{21} +(0.0161102 + 0.0279038i) q^{22} +3.32997 q^{23} +(0.630224 + 1.11303i) q^{24} +1.00000 q^{25} +(6.28157 - 10.8800i) q^{26} +(-5.19451 - 0.130693i) q^{27} +(-0.289151 + 6.22115i) q^{28} +(1.08973 - 1.88747i) q^{29} +(1.83323 - 3.11464i) q^{30} +(-0.610692 + 1.05775i) q^{31} +(4.04253 - 7.00187i) q^{32} +(-0.0131781 - 0.0232737i) q^{33} +(-0.946933 + 1.64014i) q^{34} +(2.35024 - 1.21507i) q^{35} +(-3.42782 - 6.17399i) q^{36} +(-4.79552 + 8.30608i) q^{37} -16.4594 q^{38} +(-5.28976 + 8.98726i) q^{39} +0.738471 q^{40} +(-5.46963 - 9.47367i) q^{41} +(0.524024 - 9.54764i) q^{42} +(0.234772 - 0.406637i) q^{43} +(0.0181741 - 0.0314784i) q^{44} +(-1.54336 + 2.57256i) q^{45} +(-3.47416 - 6.01743i) q^{46} +(2.53419 + 4.38934i) q^{47} +(-2.78237 + 4.72723i) q^{48} +(4.04722 - 5.71139i) q^{49} +(-1.04330 - 1.80705i) q^{50} +(0.797420 - 1.35481i) q^{51} -14.1726 q^{52} +(-1.39434 - 2.41507i) q^{53} +(5.18327 + 9.52309i) q^{54} -0.0154416 q^{55} +(1.73558 - 0.897292i) q^{56} +(13.6622 + 0.114558i) q^{57} -4.54768 q^{58} +(-2.60645 + 4.51450i) q^{59} +(-4.07695 - 0.0341853i) q^{60} +(-4.12820 - 7.15026i) q^{61} +2.54854 q^{62} +(-0.501419 + 7.92140i) q^{63} -10.5365 q^{64} +(3.01043 + 5.21422i) q^{65} +(-0.0283080 + 0.0480951i) q^{66} +(-2.66210 + 4.61089i) q^{67} +2.13648 q^{68} +(2.84186 + 5.01896i) q^{69} +(-4.64769 - 2.97931i) q^{70} +4.77171 q^{71} +(-1.13972 + 1.89976i) q^{72} +(-0.466621 - 0.808211i) q^{73} +20.0127 q^{74} +(0.853418 + 1.50721i) q^{75} +(9.28400 + 16.0804i) q^{76} +(-0.0362914 + 0.0187626i) q^{77} +(21.7592 + 0.182452i) q^{78} +(-3.51232 - 6.08351i) q^{79} +(1.58346 + 2.74264i) q^{80} +(-4.23611 - 7.94074i) q^{81} +(-11.4129 + 19.7678i) q^{82} +(-8.41010 + 14.5667i) q^{83} +(-9.62333 + 4.87343i) q^{84} +(-0.453816 - 0.786032i) q^{85} -0.979752 q^{86} +(3.77481 + 0.0316519i) q^{87} -0.0114032 q^{88} +(-6.33695 + 10.9759i) q^{89} +(6.25893 + 0.104970i) q^{90} +(13.4109 + 8.59677i) q^{91} +(-3.91923 + 6.78830i) q^{92} +(-2.11543 - 0.0177379i) q^{93} +(5.28785 - 9.15882i) q^{94} +(3.94407 - 6.83134i) q^{95} +(14.0032 + 0.117417i) q^{96} +(3.11544 - 5.39610i) q^{97} +(-14.5432 - 1.35483i) q^{98} +(0.0238319 - 0.0397244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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