LMFDB - Embedded newform 63.3.n.b.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.6
Character	$\chi$	$=$	63.32
Dual form			63.3.n.b.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.444866 - 0.256844i) q^{2} +(2.83879 + 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} -7.02462i q^{5} +(-1.01370 - 1.16073i) q^{6} +(5.34652 + 4.51827i) q^{7} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +O(q^{10})$	\(q+(-0.444866 - 0.256844i) q^{2} +(2.83879 + 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} -7.02462i q^{5} +(-1.01370 - 1.16073i) q^{6} +(5.34652 + 4.51827i) q^{7} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +(-1.80423 + 3.12502i) q^{10} -3.64877i q^{11} +(-2.16392 - 10.9975i) q^{12} +(-3.79085 + 6.56594i) q^{13} +(-1.21800 - 3.38324i) q^{14} +(6.81519 - 19.9414i) q^{15} +(-6.45157 + 11.1744i) q^{16} +(-17.5124 - 10.1108i) q^{17} +(-1.75155 - 4.27854i) q^{18} +(13.6978 + 23.7253i) q^{19} +(-22.7287 + 13.1224i) q^{20} +(10.7941 + 18.0135i) q^{21} +(-0.937164 + 1.62322i) q^{22} +3.94936i q^{23} +(-3.85547 + 11.2812i) q^{24} -24.3452 q^{25} +(3.37284 - 1.94731i) q^{26} +(14.8609 + 22.5422i) q^{27} +(4.63159 - 25.7395i) q^{28} +(-23.7260 + 13.6982i) q^{29} +(-8.15368 + 7.12083i) q^{30} +(-2.42502 - 4.20026i) q^{31} +(19.5063 - 11.2620i) q^{32} +(3.53999 - 10.3581i) q^{33} +(5.19377 + 8.99588i) q^{34} +(31.7391 - 37.5572i) q^{35} +(4.52670 - 33.3190i) q^{36} +(-18.7209 - 32.4256i) q^{37} -14.0728i q^{38} +(-17.1316 + 14.9615i) q^{39} +27.9155 q^{40} +(61.1213 + 35.2884i) q^{41} +(-0.175260 - 10.7860i) q^{42} +(-9.41887 - 16.3140i) q^{43} +(-11.8059 + 6.81613i) q^{44} +(38.6938 - 49.9975i) q^{45} +(1.01437 - 1.75694i) q^{46} +(20.7612 + 11.9865i) q^{47} +(-29.1559 + 25.4627i) q^{48} +(8.17049 + 48.3140i) q^{49} +(10.8304 + 6.25292i) q^{50} +(-39.9046 - 45.6926i) q^{51} +28.3262 q^{52} +(-23.1126 - 13.3441i) q^{53} +(-0.821297 - 13.8452i) q^{54} -25.6312 q^{55} +(-17.9554 + 21.2468i) q^{56} +(15.8672 + 80.6406i) q^{57} +14.0732 q^{58} +(-45.7350 + 26.4051i) q^{59} +(-77.2533 + 15.2007i) q^{60} +(53.4719 - 92.6160i) q^{61} +2.49140i q^{62} +(13.1657 + 61.6090i) q^{63} +40.0422 q^{64} +(46.1232 + 26.6293i) q^{65} +(-4.23524 + 3.69875i) q^{66} +(-51.0777 - 88.4692i) q^{67} +75.5502i q^{68} +(-3.83161 + 11.2114i) q^{69} +(-23.7660 + 8.55596i) q^{70} -138.410i q^{71} +(-21.8898 + 28.2845i) q^{72} +(-34.7679 + 60.2198i) q^{73} +19.2334i q^{74} +(-69.1111 - 23.6194i) q^{75} +(51.1767 - 88.6406i) q^{76} +(16.4861 - 19.5082i) q^{77} +(11.4641 - 2.25573i) q^{78} +(-11.6077 + 20.1052i) q^{79} +(78.4962 + 45.3198i) q^{80} +(20.3169 + 78.4106i) q^{81} +(-18.1272 - 31.3973i) q^{82} +(-25.9282 + 14.9697i) q^{83} +(38.1202 - 68.5755i) q^{84} +(-71.0243 + 123.018i) q^{85} +9.67670i q^{86} +(-80.6431 + 15.8677i) q^{87} +14.5000 q^{88} +(-135.658 + 78.3225i) q^{89} +(-30.0551 + 12.3040i) q^{90} +(-49.9345 + 17.9769i) q^{91} +(12.7785 - 7.37765i) q^{92} +(-2.80909 - 14.2764i) q^{93} +(-6.15730 - 10.6648i) q^{94} +(166.661 - 96.2218i) q^{95} +(66.3007 - 13.0457i) q^{96} +(2.93155 + 5.07760i) q^{97} +(8.77437 - 23.5918i) q^{98} +(20.0986 - 25.9700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.444866	−	0.256844i	−0.222433	−	0.128422i	0.384643	−	0.923065i	$-0.374324\pi$
$2$	−0.444866	−	0.256844i	−0.222433	−	0.128422i	−0.607076	+	0.794643i	$0.707658\pi$
$3$	2.83879	+	0.970187i	0.946264	+	0.323396i
$3$	2.83879	+	0.970187i	0.946264	+	0.323396i
$4$	−1.86806	−	3.23558i	−0.467016	−	0.808895i
$5$		−	7.02462i		−	1.40492i	−0.711722	−	0.702462i	$-0.752084\pi$
$5$		−	7.02462i		−	1.40492i	0.711722	−	0.702462i	$-0.247916\pi$
$6$	−1.01370	−	1.16073i	−0.168949	−	0.193455i
$7$	5.34652	+	4.51827i	0.763788	+	0.645467i
$7$	5.34652	+	4.51827i	0.763788	+	0.645467i
$8$			3.97395i			0.496744i
$9$	7.11748	+	5.50832i	0.790831	+	0.612035i
$10$	−1.80423	+	3.12502i	−0.180423	+	0.312502i
$11$		−	3.64877i		−	0.331707i	−0.986150	−	0.165853i	$-0.946962\pi$
$11$		−	3.64877i		−	0.331707i	0.986150	−	0.165853i	$-0.0530378\pi$
$12$	−2.16392	−	10.9975i	−0.180327	−	0.916459i
$13$	−3.79085	+	6.56594i	−0.291604	+	0.505073i	−0.974189	−	0.225733i	$-0.927522\pi$
$13$	−3.79085	+	6.56594i	−0.291604	+	0.505073i	0.682585	+	0.730806i	$0.260856\pi$
$14$	−1.21800	−	3.38324i	−0.0869998	−	0.241660i
$15$	6.81519	−	19.9414i	0.454346	−	1.32943i
$16$	−6.45157	+	11.1744i	−0.403223	+	0.698403i
$17$	−17.5124	−	10.1108i	−1.03014	−	0.594751i	−0.113114	−	0.993582i	$-0.536083\pi$
$17$	−17.5124	−	10.1108i	−1.03014	−	0.594751i	−0.917024	+	0.398831i	$0.869416\pi$
$18$	−1.75155	−	4.27854i	−0.0973083	−	0.237697i
$19$	13.6978	+	23.7253i	0.720937	+	1.24870i	0.960625	+	0.277849i	$0.0896216\pi$
$19$	13.6978	+	23.7253i	0.720937	+	1.24870i	−0.239688	+	0.970850i	$0.577045\pi$
$20$	−22.7287	+	13.1224i	−1.13644	+	0.656121i
$21$	10.7941	+	18.0135i	0.514004	+	0.857788i
$22$	−0.937164	+	1.62322i	−0.0425984	+	0.0737825i
$23$			3.94936i			0.171711i	0.996308	+	0.0858556i	$0.0273624\pi$
$23$			3.94936i			0.171711i	−0.996308	+	0.0858556i	$0.972638\pi$
$24$	−3.85547	+	11.2812i	−0.160645	+	0.470051i
$25$	−24.3452			−0.973810
$26$	3.37284	−	1.94731i	0.129725	−	0.0748966i
$27$	14.8609	+	22.5422i	0.550405	+	0.834898i
$28$	4.63159	−	25.7395i	0.165414	−	0.919268i
$29$	−23.7260	+	13.6982i	−0.818139	+	0.472353i	−0.849774	−	0.527147i	$-0.823262\pi$
$29$	−23.7260	+	13.6982i	−0.818139	+	0.472353i	0.0316352	+	0.999499i	$0.489929\pi$
$30$	−8.15368	+	7.12083i	−0.271789	+	0.237361i
$31$	−2.42502	−	4.20026i	−0.0782264	−	0.135492i	0.824258	−	0.566214i	$-0.191592\pi$
$31$	−2.42502	−	4.20026i	−0.0782264	−	0.135492i	−0.902485	+	0.430722i	$0.858259\pi$
$32$	19.5063	−	11.2620i	0.609573	−	0.351937i
$33$	3.53999	−	10.3581i	0.107272	−	0.313882i
$34$	5.19377	+	8.99588i	0.152758	+	0.264585i
$35$	31.7391	−	37.5572i	0.906832	−	1.07306i
$36$	4.52670	−	33.3190i	0.125742	−	0.925529i
$37$	−18.7209	−	32.4256i	−0.505971	−	0.876367i	−0.999976	−	0.00690796i	$-0.997801\pi$
$37$	−18.7209	−	32.4256i	−0.505971	−	0.876367i	0.494006	−	0.869459i	$-0.335532\pi$
$38$		−	14.0728i		−	0.370336i
$39$	−17.1316	+	14.9615i	−0.439272	+	0.383629i
$40$	27.9155			0.697887
$41$	61.1213	+	35.2884i	1.49076	+	0.860693i	0.999944	−	0.0105682i	$-0.00336403\pi$
$41$	61.1213	+	35.2884i	1.49076	+	0.860693i	0.490820	+	0.871261i	$0.336697\pi$
$42$	−0.175260	−	10.7860i	−0.00417285	−	0.256810i
$43$	−9.41887	−	16.3140i	−0.219043	−	0.379394i	0.735472	−	0.677555i	$-0.236960\pi$
$43$	−9.41887	−	16.3140i	−0.219043	−	0.379394i	−0.954516	+	0.298160i	$0.903627\pi$
$44$	−11.8059	+	6.81613i	−0.268316	+	0.154912i
$45$	38.6938	−	49.9975i	0.859862	−	1.11106i
$46$	1.01437	−	1.75694i	0.0220515	−	0.0381943i
$47$	20.7612	+	11.9865i	0.441727	+	0.255031i	0.704330	−	0.709873i	$-0.251248\pi$
$47$	20.7612	+	11.9865i	0.441727	+	0.255031i	−0.262603	+	0.964904i	$0.584581\pi$
$48$	−29.1559	+	25.4627i	−0.607416	+	0.530473i
$49$	8.17049	+	48.3140i	0.166745	+	0.986000i
$50$	10.8304	+	6.25292i	0.216608	+	0.125058i
$51$	−39.9046	−	45.6926i	−0.782443	−	0.895934i
$52$	28.3262			0.544734
$53$	−23.1126	−	13.3441i	−0.436087	−	0.251775i	0.265850	−	0.964015i	$-0.414348\pi$
$53$	−23.1126	−	13.3441i	−0.436087	−	0.251775i	−0.701936	+	0.712240i	$0.747681\pi$
$54$	−0.821297	−	13.8452i	−0.0152092	−	0.256393i
$55$	−25.6312			−0.466022
$56$	−17.9554	+	21.2468i	−0.320632	+	0.379407i
$57$	15.8672	+	80.6406i	0.278373	+	1.41475i
$58$	14.0732			0.242642
$59$	−45.7350	+	26.4051i	−0.775170	+	0.447545i	−0.834716	−	0.550681i	$-0.814368\pi$
$59$	−45.7350	+	26.4051i	−0.775170	+	0.447545i	0.0595458	+	0.998226i	$0.481035\pi$
$60$	−77.2533	+	15.2007i	−1.28755	+	0.253346i
$61$	53.4719	−	92.6160i	0.876588	−	1.51829i	0.0215264	−	0.999768i	$-0.493147\pi$
$61$	53.4719	−	92.6160i	0.876588	−	1.51829i	0.855062	−	0.518527i	$-0.173519\pi$
$62$			2.49140i			0.0401839i
$63$	13.1657	+	61.6090i	0.208979	+	0.977920i
$64$	40.0422			0.625660
$65$	46.1232	+	26.6293i	0.709588	+	0.409681i
$66$	−4.23524	+	3.69875i	−0.0641702	+	0.0560416i
$67$	−51.0777	−	88.4692i	−0.762354	−	1.32044i	−0.941634	−	0.336637i	$-0.890710\pi$
$67$	−51.0777	−	88.4692i	−0.762354	−	1.32044i	0.179281	−	0.983798i	$-0.442623\pi$
$68$			75.5502i			1.11103i
$69$	−3.83161	+	11.2114i	−0.0555307	+	0.162484i
$70$	−23.7660	+	8.55596i	−0.339514	+	0.122228i
$71$		−	138.410i		−	1.94944i	−0.223427	−	0.974721i	$-0.571725\pi$
$71$		−	138.410i		−	1.94944i	0.223427	−	0.974721i	$-0.428275\pi$
$72$	−21.8898	+	28.2845i	−0.304025	+	0.392840i
$73$	−34.7679	+	60.2198i	−0.476273	+	0.824929i	−0.999630	−	0.0271843i	$-0.991346\pi$
$73$	−34.7679	+	60.2198i	−0.476273	+	0.824929i	0.523358	+	0.852113i	$0.324679\pi$
$74$			19.2334i			0.259911i
$75$	−69.1111	−	23.6194i	−0.921481	−	0.314926i
$76$	51.1767	−	88.6406i	0.673378	−	1.16632i
$77$	16.4861	−	19.5082i	0.214106	−	0.253354i
$78$	11.4641	−	2.25573i	0.146975	−	0.0289196i
$79$	−11.6077	+	20.1052i	−0.146933	+	0.254496i	−0.930093	−	0.367325i	$-0.880274\pi$
$79$	−11.6077	+	20.1052i	−0.146933	+	0.254496i	0.783159	+	0.621821i	$0.213607\pi$
$80$	78.4962	+	45.3198i	0.981202	+	0.566497i
$81$	20.3169	+	78.4106i	0.250826	+	0.968032i
$82$	−18.1272	−	31.3973i	−0.221064	−	0.382893i
$83$	−25.9282	+	14.9697i	−0.312388	+	0.180357i	−0.647995	−	0.761645i	$-0.724392\pi$
$83$	−25.9282	+	14.9697i	−0.312388	+	0.180357i	0.335606	+	0.942002i	$0.391059\pi$
$84$	38.1202	−	68.5755i	0.453812	−	0.816376i
$85$	−71.0243	+	123.018i	−0.835579	+	1.44727i
$86$			9.67670i			0.112520i
$87$	−80.6431	+	15.8677i	−0.926932	+	0.182388i
$88$	14.5000			0.164773
$89$	−135.658	+	78.3225i	−1.52425	+	0.880028i	−0.524665	+	0.851309i	$0.675809\pi$
$89$	−135.658	+	78.3225i	−1.52425	+	0.880028i	−0.999588	+	0.0287188i	$0.990857\pi$
$90$	−30.0551	+	12.3040i	−0.333946	+	0.136711i
$91$	−49.9345	+	17.9769i	−0.548731	+	0.197548i
$92$	12.7785	−	7.37765i	0.138896	−	0.0801918i
$93$	−2.80909	−	14.2764i	−0.0302053	−	0.153509i
$94$	−6.15730	−	10.6648i	−0.0655032	−	0.113455i
$95$	166.661	−	96.2218i	1.75433	−	1.01286i
$96$	66.3007	−	13.0457i	0.690632	−	0.135892i
$97$	2.93155	+	5.07760i	0.0302222	+	0.0523464i	0.880741	−	0.473598i	$-0.157045\pi$
$97$	2.93155	+	5.07760i	0.0302222	+	0.0523464i	−0.850519	+	0.525945i	$0.823712\pi$
$98$	8.77437	−	23.5918i	0.0895344	−	0.240733i
$99$	20.0986	−	25.9700i	0.203016	−	0.262324i
$100$	45.4784	+	78.7710i	0.454784	+	0.787710i
$101$			19.4750i			0.192822i	0.995342	+	0.0964111i	$0.0307363\pi$
$101$			19.4750i			0.192822i	−0.995342	+	0.0964111i	$0.969264\pi$
$102$	6.01636	+	30.5764i	0.0589839	+	0.299768i
$103$	26.0917			0.253317			0.126659	−	0.991946i	$-0.459575\pi$
$103$	26.0917			0.253317			0.126659	+	0.991946i	$0.459575\pi$
$104$	−26.0927	−	15.0646i	−0.250892	−	0.144852i
$105$	126.538	−	75.8243i	1.20513	−	0.722136i
$106$	6.85468	+	11.8727i	0.0646668	+	0.112006i
$107$	−25.2215	+	14.5616i	−0.235715	+	0.136090i	−0.613206	−	0.789923i	$-0.710120\pi$
$107$	−25.2215	+	14.5616i	−0.235715	+	0.136090i	0.377491	+	0.926013i	$0.376787\pi$
$108$	45.1761	−	90.1941i	0.418297	−	0.835130i
$109$	50.9986	−	88.3322i	0.467877	−	0.810387i	−0.531449	−	0.847090i	$-0.678352\pi$
$109$	50.9986	−	88.3322i	0.467877	−	0.810387i	0.999326	+	0.0367034i	$0.0116857\pi$
$110$	11.4025	+	6.58322i	0.103659	+	0.0598474i
$111$	−21.6859	−	110.212i	−0.195369	−	0.992903i
$112$	−84.9825	+	30.5944i	−0.758773	+	0.273165i
$113$	−122.755	−	70.8728i	−1.08633	−	0.627193i	−0.153734	−	0.988112i	$-0.549130\pi$
$113$	−122.755	−	70.8728i	−1.08633	−	0.627193i	−0.932597	+	0.360919i	$0.882463\pi$
$114$	13.6532	−	39.9497i	0.119765	−	0.350436i
$115$	27.7427			0.241241
$116$	88.6434	+	51.1783i	0.764168	+	0.441192i
$117$	−63.1486	+	25.8518i	−0.539731	+	0.220955i
$118$	27.1280			0.229898
$119$	−47.9470	−	133.183i	−0.402916	−	1.11918i
$120$	79.2462	+	27.0832i	0.660385	+	0.225694i
$121$	107.686			0.889971
$122$	−47.5757	+	27.4678i	−0.389964	+	0.225146i
$123$	139.274	+	159.476i	1.13231	+	1.29655i
$124$	−9.06018	+	15.6927i	−0.0730660	+	0.126554i
$125$		−	4.59944i		−	0.0367955i
$126$	9.96692	−	30.7893i	0.0791025	−	0.244359i
$127$	−39.8045			−0.313421			−0.156711	−	0.987645i	$-0.550089\pi$
$127$	−39.8045			−0.313421			−0.156711	+	0.987645i	$0.550089\pi$
$128$	−95.8388	−	55.3326i	−0.748741	−	0.432286i
$129$	−10.9106	−	55.4500i	−0.0845784	−	0.429845i
$130$	−13.6791	−	23.6929i	−0.105224	−	0.182253i
$131$		−	69.5184i		−	0.530674i	−0.964156	−	0.265337i	$-0.914517\pi$
$131$		−	69.5184i		−	0.530674i	0.964156	−	0.265337i	$-0.0854833\pi$
$132$	−40.1274	+	7.89567i	−0.303995	+	0.0598157i
$133$	−33.9617	+	188.738i	−0.255351	+	1.41908i
$134$			52.4759i			0.391611i
$135$	158.351	−	104.392i	1.17297	−	0.773277i
$136$	40.1797	−	69.5932i	0.295439	−	0.511715i
$137$			75.7533i			0.552944i	0.961022	+	0.276472i	$0.0891653\pi$
$137$			75.7533i			0.552944i	−0.961022	+	0.276472i	$0.910835\pi$
$138$	4.58414	−	4.00345i	0.0332184	−	0.0290105i
$139$	37.4261	−	64.8239i	0.269253	−	0.466359i	−0.699416	−	0.714714i	$-0.746557\pi$
$139$	37.4261	−	64.8239i	0.269253	−	0.466359i	0.968669	+	0.248355i	$0.0798900\pi$
$140$	−180.810	−	32.5351i	−1.29150	−	0.232394i
$141$	47.3076	+	54.1693i	0.335515	+	0.384180i
$142$	−35.5498	+	61.5741i	−0.250351	+	0.433620i
$143$	23.9576	+	13.8319i	0.167536	+	0.0967269i
$144$	−107.471	+	43.9965i	−0.746328	+	0.305532i
$145$	96.2248	+	166.666i	0.663620	+	1.14942i
$146$	30.9342	−	17.8598i	0.211878	−	0.122328i
$147$	−23.6793	+	145.080i	−0.161083	+	0.986941i
$148$	−69.9437	+	121.146i	−0.472592	+	0.818554i
$149$		−	21.6822i		−	0.145518i	−0.997350	−	0.0727591i	$-0.976820\pi$
$149$		−	21.6822i		−	0.145518i	0.997350	−	0.0727591i	$-0.0231804\pi$
$150$	24.6787	+	28.2582i	0.164525	+	0.188388i
$151$	−171.507			−1.13580			−0.567902	−	0.823096i	$-0.692245\pi$
$151$	−171.507			−1.13580			−0.567902	+	0.823096i	$0.692245\pi$
$152$	−94.2831	+	54.4344i	−0.620284	+	0.358121i
$153$	−68.9505	−	168.427i	−0.450657	−	1.10083i
$154$	−12.3447	+	4.44419i	−0.0801603	+	0.0288584i
$155$	−29.5052	+	17.0348i	−0.190356	+	0.109902i
$156$	80.4121	+	27.4817i	0.515462	+	0.176165i
$157$	40.2266	+	69.6745i	0.256220	+	0.443787i	0.965226	−	0.261416i	$-0.0841894\pi$
$157$	40.2266	+	69.6745i	0.256220	+	0.443787i	−0.709006	+	0.705202i	$0.750856\pi$
$158$	10.3278	−	5.96275i	0.0653657	−	0.0377389i
$159$	−52.6656	−	60.3046i	−0.331230	−	0.379274i
$160$	−79.1112	−	137.025i	−0.494445	−	0.856403i
$161$	−17.8443	+	21.1153i	−0.110834	+	0.131151i
$162$	11.1010	−	40.1005i	0.0685244	−	0.247534i
$163$	−67.6792	−	117.224i	−0.415210	−	0.719165i	0.580240	−	0.814445i	$-0.302959\pi$
$163$	−67.6792	−	117.224i	−0.415210	−	0.719165i	−0.995450	+	0.0952804i	$0.969625\pi$
$164$		−	263.684i		−	1.60783i
$165$	−72.7617	−	24.8671i	−0.440980	−	0.150710i
$166$	15.3795			0.0926473
$167$	97.2491	+	56.1468i	0.582330	+	0.336208i	0.762059	−	0.647508i	$-0.224189\pi$
$167$	97.2491	+	56.1468i	0.582330	+	0.336208i	−0.179729	+	0.983716i	$0.557522\pi$
$168$	−71.5849	+	42.8952i	−0.426101	+	0.255328i
$169$	55.7589	+	96.5773i	0.329934	+	0.571463i
$170$	63.1926	−	36.4843i	0.371721	−	0.214613i
$171$	−33.1926	+	244.316i	−0.194109	+	1.42875i
$172$	−35.1901	+	60.9510i	−0.204593	+	0.354366i
$173$	157.656	+	91.0227i	0.911306	+	0.526143i	0.880851	−	0.473393i	$-0.156971\pi$
$173$	157.656	+	91.0227i	0.911306	+	0.526143i	0.0304551	+	0.999536i	$0.490304\pi$
$174$	39.9509	+	13.6536i	0.229603	+	0.0784692i
$175$	−130.162	−	109.998i	−0.743784	−	0.628562i
$176$	40.7730	+	23.5403i	0.231665	+	0.133752i
$177$	−155.450	+	30.5871i	−0.878249	+	0.172809i
$178$	80.4665			0.452059
$179$	182.206	+	105.197i	1.01791	+	0.587691i	0.913498	−	0.406843i	$-0.133370\pi$
$179$	182.206	+	105.197i	1.01791	+	0.587691i	0.104413	+	0.994534i	$0.466704\pi$
$180$	−234.053	−	31.7984i	−1.30030	−	0.176658i
$181$	104.037			0.574791			0.287396	−	0.957812i	$-0.407211\pi$
$181$	104.037			0.574791			0.287396	+	0.957812i	$0.407211\pi$
$182$	26.8314	+	4.82808i	0.147426	+	0.0265279i
$183$	241.650	−	211.040i	1.32049	−	1.15322i
$184$	−15.6946			−0.0852965
$185$	−227.777	+	131.507i	−1.23123	+	0.710850i
$186$	−2.41713	+	7.07258i	−0.0129953	+	0.0380246i
$187$	−36.8919	+	63.8986i	−0.197283	+	0.341704i
$188$		−	89.5660i		−	0.476415i
$189$	−22.3977	+	187.668i	−0.118506	+	0.992953i
$190$	−98.8559			−0.520294
$191$	77.7538	+	44.8912i	0.407088	+	0.235032i	0.689538	−	0.724250i	$-0.257814\pi$
$191$	77.7538	+	44.8912i	0.407088	+	0.235032i	−0.282450	+	0.959282i	$0.591147\pi$
$192$	113.672	+	38.8485i	0.592040	+	0.202336i
$193$	40.0598	+	69.3855i	0.207564	+	0.359511i	0.950946	−	0.309355i	$-0.100113\pi$
$193$	40.0598	+	69.3855i	0.207564	+	0.359511i	−0.743383	+	0.668866i	$0.766780\pi$
$194$		−	3.01180i		−	0.0155248i
$195$	105.099	+	120.343i	0.538969	+	0.617144i
$196$	141.061	−	116.690i	0.719698	−	0.595356i
$197$			49.3712i			0.250615i	0.992118	+	0.125308i	$0.0399918\pi$
$197$			49.3712i			0.250615i	−0.992118	+	0.125308i	$0.960008\pi$
$198$	−15.6114	+	6.39100i	−0.0788456	+	0.0322778i
$199$	1.01765	−	1.76262i	0.00511381	−	0.00885737i	−0.863457	−	0.504422i	$-0.831706\pi$
$199$	1.01765	−	1.76262i	0.00511381	−	0.00885737i	0.868571	+	0.495565i	$0.165039\pi$
$200$		−	96.7468i		−	0.483734i
$201$	−59.1673	−	300.700i	−0.294365	−	1.49602i
$202$	5.00204	−	8.66379i	0.0247626	−	0.0428900i
$203$	−188.744	−	33.9628i	−0.929773	−	0.167304i
$204$	−73.2978	+	214.471i	−0.359303	+	1.05133i
$205$	247.888	−	429.354i	1.20921	−	2.09441i
$206$	−11.6073	−	6.70148i	−0.0563462	−	0.0325315i
$207$	−21.7543	+	28.1095i	−0.105093	+	0.135794i
$208$	−48.9138	−	84.7213i	−0.235163	−	0.407314i
$209$	86.5682	−	49.9802i	0.414202	−	0.239139i
$210$	−75.7676	+	1.23113i	−0.360798	+	0.00586253i
$211$	144.840	−	250.871i	0.686446	−	1.18896i	−0.286534	−	0.958070i	$-0.592503\pi$
$211$	144.840	−	250.871i	0.686446	−	1.18896i	0.972980	−	0.230890i	$-0.0741637\pi$
$212$			99.7102i			0.470331i
$213$	134.284	−	392.918i	0.630441	−	1.84469i
$214$	14.9603			0.0699078
$215$	−114.599	+	66.1639i	−0.533020	+	0.307739i
$216$	−89.5817	+	59.0566i	−0.414730	+	0.273410i
$217$	6.01248	−	33.4136i	0.0277073	−	0.153980i
$218$	−45.3751	+	26.1973i	−0.208143	+	0.120171i
$219$	−157.123	+	137.220i	−0.717458	+	0.626576i
$220$	47.8807	+	82.9319i	0.217640	+	0.376963i
$221$	132.773	−	76.6568i	0.600785	−	0.346863i
$222$	−18.6600	+	54.5996i	−0.0840540	+	0.245944i
$223$	67.9693	+	117.726i	0.304795	+	0.527921i	0.977216	−	0.212249i	$-0.0680787\pi$
$223$	67.9693	+	117.726i	0.304795	+	0.527921i	−0.672421	+	0.740169i	$0.734745\pi$
$224$	155.176	+	27.9225i	0.692748	+	0.124654i
$225$	−173.277	−	134.101i	−0.770118	−	0.596006i
$226$	36.4065	+	63.0579i	0.161091	+	0.279017i
$227$			49.8026i			0.219395i	0.993965	+	0.109697i	$0.0349882\pi$
$227$			49.8026i			0.219395i	−0.993965	+	0.109697i	$0.965012\pi$
$228$	231.278	−	201.981i	1.01438	−	0.885883i
$229$	142.498			0.622261			0.311131	−	0.950367i	$-0.399292\pi$
$229$	142.498			0.622261			0.311131	+	0.950367i	$0.399292\pi$
$230$	−12.3418	−	7.12555i	−0.0536600	−	0.0309806i
$231$	65.7273	−	39.3851i	0.284534	−	0.170498i
$232$	−54.4361	−	94.2861i	−0.234638	−	0.406405i
$233$	−72.6863	+	41.9654i	−0.311958	+	0.180109i	−0.647802	−	0.761808i	$-0.724312\pi$
$233$	−72.6863	+	41.9654i	−0.311958	+	0.180109i	0.335844	+	0.941918i	$0.390978\pi$
$234$	34.7325	+	4.71874i	0.148430	+	0.0201656i
$235$	84.2004	−	145.839i	0.358300	−	0.620593i
$236$	170.872	+	98.6529i	0.724033	+	0.418021i
$237$	−52.4577	+	45.8128i	−0.221341	+	0.193303i
$238$	−12.8772	+	71.5635i	−0.0541059	+	0.300687i
$239$	222.986	+	128.741i	0.932995	+	0.538665i	0.887758	−	0.460311i	$-0.152262\pi$
$239$	222.986	+	128.741i	0.932995	+	0.538665i	0.0452374	+	0.998976i	$0.485596\pi$
$240$	178.866	+	204.809i	0.745273	+	0.853372i
$241$	−127.978			−0.531030			−0.265515	−	0.964107i	$-0.585542\pi$
$241$	−127.978			−0.531030			−0.265515	+	0.964107i	$0.585542\pi$
$242$	−47.9061	−	27.6586i	−0.197959	−	0.114292i
$243$	−18.3974	+	242.303i	−0.0757096	+	0.997130i
$244$	−399.555			−1.63752
$245$	339.387	−	57.3946i	1.38525	−	0.234264i
$246$	−20.9982	−	106.717i	−0.0853585	−	0.433809i
$247$	−207.705			−0.840912
$248$	16.6916	−	9.63691i	0.0673049	−	0.0388585i
$249$	−88.1282	+	17.3405i	−0.353928	+	0.0696407i
$250$	−1.18134	+	2.04613i	−0.00472535	+	0.00818454i
$251$			277.115i			1.10404i	0.833830	+	0.552022i	$0.186144\pi$
$251$			277.115i			1.10404i	−0.833830	+	0.552022i	$0.813856\pi$
$252$	174.746	−	157.688i	0.693438	−	0.625746i
$253$	14.4103			0.0569577
$254$	17.7077	+	10.2235i	0.0697153	+	0.0402502i
$255$	−320.973	+	280.315i	−1.25872	+	1.09927i
$256$	−51.6609	−	89.4792i	−0.201800	−	0.349528i
$257$		−	190.409i		−	0.740891i	−0.928854	−	0.370445i	$-0.879205\pi$
$257$		−	190.409i		−	0.740891i	0.928854	−	0.370445i	$-0.120795\pi$
$258$	−9.38821	+	27.4701i	−0.0363884	+	0.106473i
$259$	46.4158	−	257.950i	0.179211	−	0.995946i
$260$		−	198.981i		−	0.765310i
$261$	−244.324	−	33.1937i	−0.936106	−	0.127179i
$262$	−17.8554	+	30.9264i	−0.0681502	+	0.118040i
$263$			50.8092i			0.193191i	0.995324	+	0.0965954i	$0.0307953\pi$
$263$			50.8092i			0.193191i	−0.995324	+	0.0965954i	$0.969205\pi$
$264$	41.1626	+	14.0677i	0.155919	+	0.0532869i
$265$	−93.7369	+	162.357i	−0.353724	+	0.612669i
$266$	63.5846	−	75.2403i	0.239040	−	0.282858i
$267$	−461.094	+	90.7271i	−1.72694	+	0.339802i
$268$	−190.833	+	330.532i	−0.712062	+	1.23333i
$269$	15.6224	+	9.01962i	0.0580760	+	0.0335302i	0.528757	−	0.848773i	$-0.322658\pi$
$269$	15.6224	+	9.01962i	0.0580760	+	0.0335302i	−0.470681	+	0.882304i	$0.655992\pi$
$270$	−97.2574	+	5.76930i	−0.360212	+	0.0213678i
$271$	−85.9218	−	148.821i	−0.317055	−	0.549155i	0.662818	−	0.748781i	$-0.269361\pi$
$271$	−85.9218	−	148.821i	−0.317055	−	0.549155i	−0.979872	+	0.199626i	$0.936027\pi$
$272$	225.964	−	130.461i	0.830751	−	0.479634i
$273$	−159.195	+	2.58672i	−0.583131	+	0.00947516i
$274$	19.4568	−	33.7001i	0.0710101	−	0.122993i
$275$			88.8302i			0.323019i
$276$	43.4331	−	8.54611i	0.157366	−	0.0309642i
$277$	−226.589			−0.818011			−0.409006	−	0.912532i	$-0.634124\pi$
$277$	−226.589			−0.818011			−0.409006	+	0.912532i	$0.634124\pi$
$278$	−33.2992	+	19.2253i	−0.119781	+	0.0691558i
$279$	5.87633	−	43.2530i	0.0210621	−	0.155029i
$280$	149.251	+	126.130i	0.533038	+	0.450463i
$281$	−360.913	+	208.373i	−1.28439	+	0.741541i	−0.977647	−	0.210252i	$-0.932571\pi$
$281$	−360.913	+	208.373i	−1.28439	+	0.741541i	−0.306740	+	0.951793i	$0.599238\pi$
$282$	−7.13249	−	36.2488i	−0.0252925	−	0.128542i
$283$	62.1546	+	107.655i	0.219627	+	0.380406i	0.954694	−	0.297589i	$-0.0961825\pi$
$283$	62.1546	+	107.655i	0.219627	+	0.380406i	−0.735067	+	0.677995i	$0.762849\pi$
$284$	−447.838	+	258.559i	−1.57689	+	0.910420i
$285$	566.469	−	111.461i	1.98761	−	0.391092i
$286$	−7.10530	−	12.3067i	−0.0248437	−	0.0430305i
$287$	167.344	+	464.833i	0.583079	+	1.61963i
$288$	200.870	+	27.2901i	0.697467	+	0.0947574i
$289$	59.9552	+	103.845i	0.207457	+	0.359327i
$290$		−	98.8590i		−	0.340893i
$291$	3.39585	+	17.2584i	0.0116696	+	0.0593072i
$292$	259.795			0.889708
$293$	−362.584	−	209.338i	−1.23749	−	0.714464i	−0.268908	−	0.963166i	$-0.586663\pi$
$293$	−362.584	−	209.338i	−1.23749	−	0.714464i	−0.968580	+	0.248702i	$0.919996\pi$
$294$	47.7971	−	58.4595i	0.162575	−	0.198842i
$295$	185.486	+	321.271i	0.628766	+	1.08905i
$296$	128.858	−	74.3960i	0.435330	−	0.251338i
$297$	82.2515	−	54.2242i	0.276941	−	0.182573i
$298$	−5.56894	+	9.64568i	−0.0186877	+	0.0323681i
$299$	−25.9313	−	14.9714i	−0.0867267	−	0.0500717i
$300$	52.6813	+	267.737i	0.175604	+	0.892456i
$301$	23.3527	−	129.780i	0.0775837	−	0.431162i
$302$	76.2975	+	44.0504i	0.252641	+	0.145862i
$303$	−18.8944	+	55.2856i	−0.0623578	+	0.182461i
$304$	−353.489			−1.16279
$305$	−650.592	−	375.619i	−2.13309	−	1.23154i
$306$	−12.5856	+	92.6369i	−0.0411294	+	0.302735i
$307$	457.334			1.48969			0.744843	−	0.667239i	$-0.232524\pi$
$307$	457.334			1.48969			0.744843	+	0.667239i	$0.232524\pi$
$308$	−93.9175	−	16.8996i	−0.304927	−	0.0548689i
$309$	74.0689	+	25.3138i	0.239705	+	0.0819217i
$310$	17.5012			0.0564554
$311$	301.499	−	174.070i	0.969449	−	0.559712i	0.0703809	−	0.997520i	$-0.477579\pi$
$311$	301.499	−	174.070i	0.969449	−	0.559712i	0.899068	+	0.437808i	$0.144245\pi$
$312$	−59.4563	−	68.0802i	−0.190565	−	0.218206i
$313$	67.8539	−	117.526i	0.216785	−	0.375483i	−0.737038	−	0.675851i	$-0.763776\pi$
$313$	67.8539	−	117.526i	0.216785	−	0.375483i	0.953823	+	0.300368i	$0.0971094\pi$
$314$		−	41.3278i		−	0.131617i
$315$	432.779	−	92.4837i	1.37390	−	0.293599i
$316$	86.7359			0.274481
$317$	−353.028	−	203.821i	−1.11365	−	0.642967i	−0.173879	−	0.984767i	$-0.555630\pi$
$317$	−353.028	−	203.821i	−1.11365	−	0.642967i	−0.939773	+	0.341800i	$0.888964\pi$
$318$	7.94032	+	40.3543i	0.0249695	+	0.126900i
$319$	49.9817	+	86.5709i	0.156683	+	0.271382i
$320$		−	281.281i		−	0.879005i
$321$	−85.7261	+	16.8679i	−0.267060	+	0.0525480i
$322$	13.3616	−	4.81031i	0.0414958	−	0.0149388i
$323$		−	553.981i		−	1.71511i
$324$	215.750	−	212.213i	0.665896	−	0.654978i
$325$	92.2892	−	159.850i	0.283967	−	0.491845i
$326$			69.5319i			0.213288i
$327$	230.473	−	201.278i	0.704811	−	0.615530i
$328$	−140.234	+	242.893i	−0.427544	+	0.740528i
$329$	56.8419	+	157.891i	0.172772	+	0.479910i
$330$	25.9823	+	29.7509i	0.0787342	+	0.0901543i
$331$	−92.1997	+	159.695i	−0.278549	+	0.482461i	−0.971024	−	0.238981i	$-0.923187\pi$
$331$	−92.1997	+	159.695i	−0.278549	+	0.482461i	0.692475	+	0.721442i	$0.256520\pi$
$332$	96.8711	+	55.9285i	0.291780	+	0.168459i
$333$	45.3646	−	333.909i	0.136230	−	1.00273i
$334$	−28.8419	−	49.9557i	−0.0863530	−	0.149568i
$335$	−621.462	+	358.801i	−1.85511	+	1.07105i
$336$	−270.930	+	4.40228i	−0.806339	+	0.0131020i
$337$	121.608	−	210.631i	0.360855	−	0.625019i	−0.627247	−	0.778820i	$-0.715818\pi$
$337$	121.608	−	210.631i	0.360855	−	0.625019i	0.988102	+	0.153802i	$0.0491516\pi$
$338$		−	57.2853i		−	0.169483i
$339$	−279.717	−	320.289i	−0.825124	−	0.944805i
$340$	530.711			1.56091
$341$	−15.3258	+	8.84834i	−0.0449436	+	0.0259482i
$342$	77.5173	−	100.163i	0.226659	−	0.292873i
$343$	−174.612	+	295.228i	−0.509073	+	0.860723i
$344$	64.8308	−	37.4301i	0.188462	−	0.108808i
$345$	78.7558	+	26.9156i	0.228278	+	0.0780163i
$346$	−46.7572	−	80.9859i	−0.135137	−	0.234063i
$347$	291.677	−	168.400i	0.840568	−	0.485302i	−0.0168893	−	0.999857i	$-0.505376\pi$
$347$	291.677	−	168.400i	0.840568	−	0.485302i	0.857457	+	0.514555i	$0.172043\pi$
$348$	201.988	+	231.285i	0.580424	+	0.664613i
$349$	239.411	+	414.673i	0.685992	+	1.18817i	0.973124	+	0.230282i	$0.0739650\pi$
$349$	239.411	+	414.673i	0.685992	+	1.18817i	−0.287132	+	0.957891i	$0.592702\pi$
$350$	29.6524	+	82.3659i	0.0847212	+	0.235331i
$351$	−204.347	+	12.1218i	−0.582184	+	0.0345351i
$352$	−41.0924	−	71.1742i	−0.116740	−	0.202199i
$353$			213.029i			0.603481i	0.953390	+	0.301740i	$0.0975676\pi$
$353$			213.029i			0.603481i	−0.953390	+	0.301740i	$0.902432\pi$
$354$	77.0106	+	26.3192i	0.217544	+	0.0743480i
$355$	−972.279			−2.73882
$356$	506.837	+	292.623i	1.42370	+	0.821973i
$357$	−6.89917	−	424.596i	−0.0193254	−	1.18934i
$358$	−54.0382	−	93.5970i	−0.150945	−	0.261444i
$359$	439.984	−	254.025i	1.22558	−	0.707590i	0.259479	−	0.965749i	$-0.416449\pi$
$359$	439.984	−	254.025i	1.22558	−	0.707590i	0.966103	+	0.258159i	$0.0831157\pi$
$360$	198.688	+	153.767i	0.551910	+	0.427131i
$361$	−194.760	+	337.333i	−0.539500	+	0.934441i
$362$	−46.2826	−	26.7213i	−0.127853	−	0.0738157i
$363$	305.699	+	104.476i	0.842147	+	0.287813i
$364$	151.446	+	127.985i	0.416062	+	0.351608i
$365$	423.021	+	244.231i	1.15896	+	0.669127i
$366$	−161.706	+	31.8181i	−0.441821	+	0.0869348i
$367$	39.9770			0.108929			0.0544646	−	0.998516i	$-0.482655\pi$
$367$	39.9770			0.108929			0.0544646	+	0.998516i	$0.482655\pi$
$368$	−44.1319	−	25.4795i	−0.119924	−	0.0692379i
$369$	240.650	+	587.840i	0.652167	+	1.59306i
$370$	135.107			0.365155
$371$	−63.2798	−	175.773i	−0.170566	−	0.473782i
$372$	−40.9448	+	35.7582i	−0.110067	+	0.0961242i
$373$	69.3676			0.185972			0.0929860	−	0.995667i	$-0.470359\pi$
$373$	69.3676			0.185972			0.0929860	+	0.995667i	$0.470359\pi$
$374$	32.8239	−	18.9509i	0.0877645	−	0.0506708i
$375$	4.46231	−	13.0568i	0.0118995	−	0.0348183i
$376$	−47.6337	+	82.5039i	−0.126685	+	0.219425i
$377$		−	207.712i		−	0.550960i
$378$	58.1654	−	77.7346i	0.153877	−	0.205647i
$379$	−140.172			−0.369847			−0.184924	−	0.982753i	$-0.559204\pi$
$379$	−140.172			−0.369847			−0.184924	+	0.982753i	$0.559204\pi$
$380$	−622.667	−	359.497i	−1.63860	−	0.946044i
$381$	−112.997	−	38.6178i	−0.296579	−	0.101359i
$382$	−23.0600	−	39.9411i	−0.0603666	−	0.104558i
$383$		−	523.686i		−	1.36733i	−0.729798	−	0.683663i	$-0.760386\pi$
$383$		−	523.686i		−	1.36733i	0.729798	−	0.683663i	$-0.239614\pi$
$384$	−218.383	−	250.059i	−0.568707	−	0.651196i
$385$	−137.038	−	115.809i	−0.355942	−	0.300802i
$386$		−	41.1564i		−	0.106623i
$387$	22.8239	−	167.996i	0.0589764	−	0.434099i
$388$	10.9526	−	18.9705i	0.0282285	−	0.0488931i
$389$			147.180i			0.378356i	0.981943	+	0.189178i	$0.0605823\pi$
$389$			147.180i			0.378356i	−0.981943	+	0.189178i	$0.939418\pi$
$390$	−15.8456	−	80.5306i	−0.0406298	−	0.206489i
$391$	39.9310	−	69.1626i	0.102125	−	0.176886i
$392$	−191.997	+	32.4691i	−0.489789	+	0.0828294i
$393$	67.4458	−	197.348i	0.171618	−	0.502158i
$394$	12.6807	−	21.9636i	0.0321845	−	0.0557452i
$395$	141.231	+	81.5399i	0.357547	+	0.206430i
$396$	−121.574	−	16.5169i	−0.307004	−	0.0417094i
$397$	91.5634	+	158.592i	0.230638	+	0.399477i	0.957996	−	0.286781i	$-0.0925853\pi$
$397$	91.5634	+	158.592i	0.230638	+	0.399477i	−0.727358	+	0.686258i	$0.759252\pi$
$398$	−0.905434	+	0.522753i	−0.00227496	+	0.00131345i
$399$	−279.521	+	502.839i	−0.700555	+	1.26025i
$400$	157.065	−	272.044i	0.392662	−	0.680111i
$401$			614.031i			1.53125i	0.643288	+	0.765624i	$0.277570\pi$
$401$			614.031i			1.53125i	−0.643288	+	0.765624i	$0.722430\pi$
$402$	−50.9115	+	148.968i	−0.126645	+	0.370568i
$403$	36.7715			0.0912445
$404$	63.0130	−	36.3806i	0.155973	−	0.0900510i
$405$	550.804	−	142.719i	1.36001	−	0.352391i
$406$	75.2427	+	63.5866i	0.185327	+	0.156617i
$407$	−118.313	+	68.3083i	−0.290697	+	0.167834i
$408$	181.580	−	158.579i	0.445049	−	0.388674i
$409$	−238.533	−	413.151i	−0.583210	−	1.01015i	−0.995096	−	0.0989139i	$-0.968463\pi$
$409$	−238.533	−	413.151i	−0.583210	−	1.01015i	0.411886	−	0.911235i	$-0.364870\pi$
$410$	−220.554	+	127.337i	−0.537936	+	0.310577i
$411$	−73.4948	+	215.048i	−0.178820	+	0.523231i
$412$	−48.7409	−	84.4217i	−0.118303	−	0.204907i
$413$	−363.829	−	65.4677i	−0.880941	−	0.158517i
$414$	16.8975	−	6.91750i	0.0408152	−	0.0167089i
$415$	105.156	+	182.136i	0.253388	+	0.438881i
$416$			170.770i			0.410505i
$417$	169.136	−	147.711i	0.405602	−	0.354224i
$418$	−51.3483			−0.122843
$419$	−212.402	−	122.630i	−0.506926	−	0.292674i	0.224643	−	0.974441i	$-0.427878\pi$
$419$	−212.402	−	122.630i	−0.506926	−	0.292674i	−0.731569	+	0.681767i	$0.761212\pi$
$420$	−481.717	−	267.780i	−1.14695	−	0.637571i
$421$	−247.132	−	428.045i	−0.587012	−	1.01673i	−0.994621	−	0.103578i	$-0.966971\pi$
$421$	−247.132	−	428.045i	−0.587012	−	1.01673i	0.407609	−	0.913156i	$-0.366363\pi$
$422$	−128.869	+	74.4026i	−0.305377	+	0.176309i
$423$	81.7419	+	199.673i	0.193243	+	0.472039i
$424$	53.0287	−	91.8483i	0.125068	−	0.216623i
$425$	426.343	+	246.149i	1.00316	+	0.579174i
$426$	−160.657	+	140.306i	−0.377129	+	0.329357i
$427$	704.352	−	253.573i	1.64954	−	0.593847i
$428$	94.2307	+	54.4041i	0.220165	+	0.127112i
$429$	54.5912	+	62.5094i	0.127252	+	0.145710i
$430$	67.9751			0.158082
$431$	−274.768	−	158.637i	−0.637513	−	0.368068i	0.146143	−	0.989263i	$-0.453314\pi$
$431$	−274.768	−	158.637i	−0.637513	−	0.368068i	−0.783656	+	0.621195i	$0.786647\pi$
$432$	−347.773	+	20.6299i	−0.805031	+	0.0477544i
$433$	−671.335			−1.55043			−0.775213	−	0.631699i	$-0.782358\pi$
$433$	−671.335			−1.55043			−0.775213	+	0.631699i	$0.782358\pi$
$434$	−11.2568	+	13.3203i	−0.0259374	+	0.0306920i
$435$	111.465	+	566.487i	0.256241	+	1.30227i
$436$	−381.074			−0.874024
$437$	−93.6997	+	54.0975i	−0.214416	+	0.123793i
$438$	105.143	−	20.6885i	0.240053	−	0.0472339i
$439$	−148.977	+	258.036i	−0.339356	+	0.587782i	−0.984312	−	0.176438i	$-0.943543\pi$
$439$	−148.977	+	258.036i	−0.339356	+	0.587782i	0.644956	+	0.764220i	$0.276876\pi$
$440$		−	101.857i		−	0.231494i
$441$	−207.975	+	388.879i	−0.471600	+	0.881813i
$442$	−78.7553			−0.178179
$443$	718.262	+	414.689i	1.62136	+	0.936092i	0.986557	+	0.163418i	$0.0522519\pi$
$443$	718.262	+	414.689i	1.62136	+	0.936092i	0.634802	+	0.772674i	$0.281081\pi$
$444$	−316.090	+	276.050i	−0.711914	+	0.621734i
$445$	550.185	+	952.949i	1.23637	+	2.14146i
$446$		−	69.8300i		−	0.156569i
$447$	21.0358	−	61.5512i	0.0470599	−	0.137699i
$448$	214.087	+	180.922i	0.477872	+	0.403843i
$449$			190.382i			0.424012i	0.977268	+	0.212006i	$0.0679997\pi$
$449$			190.382i			0.424012i	−0.977268	+	0.212006i	$0.932000\pi$
$450$	42.6419	+	104.162i	0.0947597	+	0.231471i
$451$	128.759	−	223.018i	0.285497	−	0.494496i
$452$			529.580i			1.17164i
$453$	−486.871	−	166.393i	−1.07477	−	0.367314i
$454$	12.7915	−	22.1555i	0.0281751	−	0.0488007i
$455$	126.281	+	350.771i	0.277540	+	0.770925i
$456$	−320.462	+	63.0556i	−0.702767	+	0.138280i
$457$	139.987	−	242.465i	0.306318	−	0.530558i	−0.671236	−	0.741243i	$-0.734236\pi$
$457$	139.987	−	242.465i	0.306318	−	0.530558i	0.977554	+	0.210686i	$0.0675697\pi$
$458$	−63.3925	−	36.5997i	−0.138411	−	0.0799119i
$459$	−32.3307	−	545.023i	−0.0704373	−	1.18741i
$460$	−51.8252	−	89.7638i	−0.112663	−	0.195139i
$461$	132.923	−	76.7433i	0.288337	−	0.166471i	−0.348855	−	0.937177i	$-0.613429\pi$
$461$	132.923	−	76.7433i	0.288337	−	0.166471i	0.637192	+	0.770705i	$0.280096\pi$
$462$	−39.3557	+	0.639482i	−0.0851855	+	0.00138416i
$463$	−251.599	+	435.782i	−0.543410	+	0.941215i	0.455295	+	0.890341i	$0.349534\pi$
$463$	−251.599	+	435.782i	−0.543410	+	0.941215i	−0.998705	+	0.0508737i	$0.983799\pi$
$464$		−	353.500i		−	0.761854i
$465$	−100.286	+	19.7328i	−0.215669	+	0.0424361i
$466$	43.1142			0.0925198
$467$	153.150	−	88.4210i	0.327943	−	0.189338i	−0.326984	−	0.945030i	$-0.606032\pi$
$467$	153.150	−	88.4210i	0.327943	−	0.189338i	0.654928	+	0.755692i	$0.272699\pi$
$468$	201.611	+	156.030i	0.430793	+	0.333396i
$469$	126.640	−	703.785i	0.270021	−	1.50061i
$470$	−74.9159	+	43.2527i	−0.159395	+	0.0920270i
$471$	46.5976	+	236.819i	0.0989334	+	0.502800i
$472$	−104.933	−	181.749i	−0.222315	−	0.385061i
$473$	−59.5259	+	34.3673i	−0.125848	+	0.0726581i
$474$	35.1034	−	6.90712i	0.0740578	−	0.0145720i
$475$	−333.476	−	577.598i	−0.702055	−	1.21600i
$476$	−341.356	+	403.930i	−0.717134	+	0.848593i
$477$	−91.0000	−	222.288i	−0.190776	−	0.466012i
$478$	−66.1326	−	114.545i	−0.138353	−	0.239634i
$479$		−	472.862i		−	0.987186i	−0.869693	−	0.493593i	$-0.835683\pi$
$479$		−	472.862i		−	0.987186i	0.869693	−	0.493593i	$-0.164317\pi$
$480$	−91.6407	−	465.737i	−0.190918	−	0.970285i
$481$	283.873			0.590172
$482$	56.9332	+	32.8704i	0.118119	+	0.0681959i
$483$	−71.1419	+	42.6297i	−0.147292	+	0.0882603i
$484$	−201.165	−	348.428i	−0.415630	−	0.719893i
$485$	35.6682	−	20.5930i	0.0735426	−	0.0424599i
$486$	70.4183	−	103.067i	0.144894	−	0.212072i
$487$	−49.3289	+	85.4401i	−0.101291	+	0.175442i	−0.912217	−	0.409708i	$-0.865631\pi$
$487$	−49.3289	+	85.4401i	−0.101291	+	0.175442i	0.810926	+	0.585149i	$0.198964\pi$
$488$	368.051	+	212.495i	0.754203	+	0.435440i
$489$	−78.3982	−	398.436i	−0.160324	−	0.814797i
$490$	−165.723	−	61.6366i	−0.338211	−	0.125789i
$491$	807.412	+	466.160i	1.64442	+	0.949409i	0.979234	+	0.202735i	$0.0649829\pi$
$491$	807.412	+	466.160i	1.64442	+	0.949409i	0.665190	+	0.746674i	$0.268350\pi$
$492$	255.823	−	748.543i	0.519965	−	1.52143i
$493$	553.998			1.12373
$494$	92.4011	+	53.3478i	0.187047	+	0.107991i
$495$	−182.430	−	141.185i	−0.368545	−	0.285222i
$496$	62.5807			0.126171
$497$	625.375	−	740.013i	1.25830	−	1.48896i
$498$	43.6591	+	14.9209i	0.0876688	+	0.0299617i
$499$	475.724			0.953354			0.476677	−	0.879079i	$-0.341841\pi$
$499$	475.724			0.953354			0.476677	+	0.879079i	$0.341841\pi$
$500$	−14.8818	+	8.59204i	−0.0297637	+	0.0171841i
$501$	221.597	+	253.739i	0.442310	+	0.506465i
$502$	71.1753	−	123.279i	0.141783	−	0.245576i
$503$		−	779.244i		−	1.54919i	−0.632456	−	0.774596i	$-0.717953\pi$
$503$		−	779.244i		−	1.54919i	0.632456	−	0.774596i	$-0.282047\pi$
$504$	−244.831	+	52.3197i	−0.485776	+	0.103809i
$505$	136.805			0.270900
$506$	−6.41066	−	3.70120i	−0.0126693	−	0.00731462i
$507$	64.5899	+	328.259i	0.127396	+	0.647454i
$508$	74.3573	+	128.791i	0.146373	+	0.253525i
$509$		−	426.079i		−	0.837091i	−0.908196	−	0.418545i	$-0.862540\pi$
$509$		−	426.079i		−	0.837091i	0.908196	−	0.418545i	$-0.137460\pi$
$510$	214.787	−	42.2626i	0.421151	−	0.0828679i
$511$	−457.977	+	164.875i	−0.896236	+	0.322652i
$512$			495.735i			0.968233i
$513$	−331.259	+	661.359i	−0.645729	+	1.28920i
$514$	−48.9053	+	84.7065i	−0.0951466	+	0.164799i
$515$		−	183.284i		−	0.355891i
$516$	−159.031	+	138.886i	−0.308200	+	0.269159i
$517$	43.7359	−	75.7528i	0.0845956	−	0.146524i
$518$	−86.9016	+	102.832i	−0.167764	+	0.198517i
$519$	359.243	+	411.350i	0.692184	+	0.792582i
$520$	−105.823	+	183.291i	−0.203507	+	0.352484i
$521$	418.449	+	241.592i	0.803166	+	0.463708i	0.844577	−	0.535434i	$-0.179852\pi$
$521$	418.449	+	241.592i	0.803166	+	0.463708i	−0.0414112	+	0.999142i	$0.513185\pi$
$522$	100.166	+	77.5197i	0.191888	+	0.148505i
$523$	−107.843	−	186.789i	−0.206200	−	0.357149i	0.744314	−	0.667829i	$-0.232776\pi$
$523$	−107.843	−	186.789i	−0.206200	−	0.357149i	−0.950514	+	0.310680i	$0.899443\pi$
$524$	−224.932	+	129.865i	−0.429260	+	0.247833i
$525$	−262.785	−	438.544i	−0.500542	−	0.835322i
$526$	13.0500	−	22.6033i	0.0248099	−	0.0429720i
$527$			98.0752i			0.186101i
$528$	92.9075	+	106.383i	0.175961	+	0.201484i
$529$	513.403			0.970515
$530$	83.4008	−	48.1515i	0.157360	−	0.0908519i
$531$	−470.966	−	63.9851i	−0.886941	−	0.120499i
$532$	674.119	−	242.689i	1.26714	−	0.456182i
$533$	−463.404	+	267.546i	−0.869425	+	0.501963i
$534$	228.428	+	78.0675i	0.427767	+	0.146194i
$535$	102.290	+	177.171i	0.191196	+	0.331161i
$536$	351.572	−	202.980i	0.655918	−	0.378694i
$537$	415.185	+	475.406i	0.773156	+	0.885299i
$538$	−4.63327	−	8.02505i	−0.00861202	−	0.0149165i
$539$	176.287	−	29.8123i	0.327063	−	0.0553103i
$540$	−633.579	−	317.344i	−1.17329	−	0.587675i
$541$	−436.156	−	755.444i	−0.806203	−	1.39638i	−0.915476	−	0.402372i	$-0.868186\pi$
$541$	−436.156	−	755.444i	−0.806203	−	1.39638i	0.109273	−	0.994012i	$-0.465148\pi$
$542$			88.2739i			0.162867i
$543$	295.340	+	100.936i	0.543904	+	0.185885i
$544$	−455.469			−0.837260
$545$	−620.500	−	358.246i	−1.13853	−	0.657331i
$546$	71.4847	+	39.7374i	0.130924	+	0.0727791i
$547$	−151.008	−	261.554i	−0.276067	−	0.478161i	0.694337	−	0.719650i	$-0.255698\pi$
$547$	−151.008	−	261.554i	−0.276067	−	0.478161i	−0.970404	+	0.241489i	$0.922364\pi$
$548$	245.106	−	141.512i	0.447273	−	0.258233i
$549$	890.743	−	364.652i	1.62248	−	0.664211i
$550$	22.8155	−	39.5176i	0.0414827	−	0.0718501i
$551$	−649.989	−	375.271i	−1.17965	−	0.681073i
$552$	−44.5536	−	15.2266i	−0.0807130	−	0.0275845i
$553$	−152.902	+	55.0459i	−0.276495	+	0.0995404i
$554$	100.802	+	58.1980i	0.181953	+	0.105051i
$555$	−774.198	+	152.335i	−1.39495	+	0.274478i
$556$	−279.657			−0.502981
$557$	−35.2462	−	20.3494i	−0.0632787	−	0.0365340i	0.468027	−	0.883714i	$-0.344965\pi$
$557$	−35.2462	−	20.3494i	−0.0632787	−	0.0365340i	−0.531306	+	0.847180i	$0.678298\pi$
$558$	−13.7234	+	17.7325i	−0.0245940	+	0.0317787i
$559$	142.822			0.255496
$560$	214.914	+	596.970i	0.383775	+	1.06602i
$561$	−166.722	+	145.603i	−0.297187	+	0.259542i
$562$	214.077			0.380920
$563$	−482.957	+	278.835i	−0.857828	+	0.495267i	−0.863284	−	0.504718i	$-0.831596\pi$
$563$	−482.957	+	278.835i	−0.857828	+	0.495267i	0.00545641	+	0.999985i	$0.498263\pi$
$564$	86.8957	−	254.259i	0.154070	−	0.450814i
$565$	−497.855	+	862.309i	−0.881159	+	1.52621i
$566$		−	63.8560i		−	0.112820i
$567$	−245.655	+	511.021i	−0.433255	+	0.901272i
$568$	550.036			0.968373
$569$	321.583	+	185.666i	0.565173	+	0.326303i	0.755219	−	0.655472i	$-0.227530\pi$
$569$	321.583	+	185.666i	0.565173	+	0.326303i	−0.190046	+	0.981775i	$0.560864\pi$
$570$	−280.631	−	95.9086i	−0.492335	−	0.168261i
$571$	−202.140	−	350.117i	−0.354011	−	0.613164i	0.632938	−	0.774203i	$-0.281849\pi$
$571$	−202.140	−	350.117i	−0.354011	−	0.613164i	−0.986948	+	0.161039i	$0.948516\pi$
$572$		−	103.356i		−	0.180692i
$573$	177.174	+	202.872i	0.309204	+	0.354053i
$574$	44.9438	−	249.770i	0.0782993	−	0.435139i
$575$		−	96.1481i		−	0.167214i
$576$	285.000	+	220.565i	0.494791	+	0.382926i
$577$	−416.462	+	721.333i	−0.721770	+	1.25014i	0.238519	+	0.971138i	$0.423338\pi$
$577$	−416.462	+	721.333i	−0.721770	+	1.25014i	−0.960290	+	0.279005i	$0.909995\pi$
$578$		−	61.5964i		−	0.106568i
$579$	46.4044	+	235.837i	0.0801457	+	0.407317i
$580$	359.508	−	622.686i	0.619841	−	1.07360i
$581$	−206.263	−	37.1151i	−0.355013	−	0.0638814i
$582$	2.92201	−	8.54988i	0.00502064	−	0.0146905i
$583$	−48.6895	+	84.3326i	−0.0835154	+	0.144653i
$584$	−239.311	−	138.166i	−0.409778	−	0.236586i
$585$	181.599	+	443.595i	0.310425	+	0.758281i
$586$	107.534	+	186.255i	0.183506	+	0.317841i
$587$	464.128	−	267.964i	0.790677	−	0.456498i	−0.0495236	−	0.998773i	$-0.515770\pi$
$587$	464.128	−	267.964i	0.790677	−	0.456498i	0.840201	+	0.542275i	$0.182437\pi$
$588$	513.653	−	194.403i	0.873560	−	0.330617i
$589$	66.4349	−	115.069i	0.112793	−	0.195363i
$590$		−	190.564i		−	0.322989i
$591$	−47.8993	+	140.155i	−0.0810479	+	0.237148i
$592$	483.117			0.816076
$593$	−522.472	+	301.649i	−0.881065	+	0.508683i	−0.871010	−	0.491266i	$-0.836534\pi$
$593$	−522.472	+	301.649i	−0.881065	+	0.508683i	−0.0100559	+	0.999949i	$0.503201\pi$
$594$	−50.5181	+	2.99673i	−0.0850472	+	0.00504499i
$595$	−935.559	+	336.809i	−1.57237	+	0.566066i
$596$	−70.1545	+	40.5037i	−0.117709	+	0.0679592i
$597$	4.59896	−	4.01639i	0.00770344	−	0.00672763i
$598$	7.69063	+	13.3206i	0.0128606	+	0.0222752i
$599$	−688.601	+	397.564i	−1.14958	+	0.663712i	−0.948786	−	0.315920i	$-0.897687\pi$
$599$	−688.601	+	397.564i	−1.14958	+	0.663712i	−0.200798	+	0.979633i	$0.564353\pi$
$600$	93.8624	−	274.644i	0.156437	−	0.457740i
$601$	284.164	+	492.186i	0.472818	+	0.818945i	0.999516	−	0.0311074i	$-0.00990340\pi$
$601$	284.164	+	492.186i	0.472818	+	0.818945i	−0.526698	+	0.850053i	$0.676570\pi$
$602$	−43.7220	+	51.7367i	−0.0726278	+	0.0859413i
$603$	123.772	−	911.029i	0.205260	−	1.51083i
$604$	320.385	+	554.923i	0.530439	+	0.918747i
$605$		−	756.456i		−	1.25034i
$606$	22.6052	−	19.7418i	0.0373024	−	0.0325772i
$607$	−238.174			−0.392380			−0.196190	−	0.980566i	$-0.562857\pi$
$607$	−238.174			−0.392380			−0.196190	+	0.980566i	$0.562857\pi$
$608$	534.388	+	308.529i	0.878927	+	0.507449i
$609$	−502.855	−	279.530i	−0.825705	−	0.458998i
$610$	192.951	+	334.201i	0.316313	+	0.547870i
$611$	−157.405	+	90.8779i	−0.257619	+	0.148736i
$612$	−416.154	+	537.727i	−0.679991	+	0.878638i
$613$	−352.492	+	610.534i	−0.575028	+	0.995977i	0.421011	+	0.907056i	$0.361675\pi$
$613$	−352.492	+	610.534i	−0.575028	+	0.995977i	−0.996039	+	0.0889215i	$0.971658\pi$
$614$	−203.452	−	117.463i	−0.331356	−	0.191308i
$615$	1120.25	−	978.349i	1.82155	−	1.59081i
$616$	77.5247	+	65.5151i	0.125852	+	0.106356i
$617$	−722.505	−	417.138i	−1.17100	−	0.676075i	−0.217082	−	0.976153i	$-0.569654\pi$
$617$	−722.505	−	417.138i	−1.17100	−	0.676075i	−0.953915	+	0.300078i	$0.902987\pi$
$618$	−26.4490	−	30.2854i	−0.0427978	−	0.0490055i
$619$	134.623			0.217485			0.108743	−	0.994070i	$-0.465318\pi$
$619$	134.623			0.217485			0.108743	+	0.994070i	$0.465318\pi$
$620$	110.235	+	63.6443i	0.177799	+	0.102652i
$621$	−89.0274	+	58.6912i	−0.143361	+	0.0945107i
$622$	−178.835			−0.287517
$623$	−1079.18	−	194.189i	−1.73223	−	0.311700i
$624$	−56.6608	−	287.962i	−0.0908025	−	0.461477i
$625$	−640.940			−1.02550
$626$	−60.3718	+	34.8557i	−0.0964406	+	0.0556800i
$627$	294.239	−	57.8960i	0.469281	−	0.0923380i
$628$	150.292	−	260.313i	0.239318	−	0.414511i
$629$			757.131i			1.20371i
$630$	−216.283	−	70.0138i	−0.343306	−	0.111133i
$631$	951.730			1.50829			0.754144	−	0.656709i	$-0.228052\pi$
$631$	951.730			1.50829			0.754144	+	0.656709i	$0.228052\pi$
$632$	−79.8970	−	46.1286i	−0.126419	−	0.0729882i
$633$	654.562	−	571.647i	1.03406	−	0.903076i
$634$	104.700	+	181.346i	0.165142	+	0.286035i
$635$			279.611i			0.440333i
$636$	−96.7375	+	283.056i	−0.152103	+	0.445057i
$637$	−348.200	−	129.504i	−0.546625	−	0.203303i
$638$		−	51.3500i		−	0.0804858i
$639$	762.408	−	985.132i	1.19313	−	1.54168i
$640$	−388.690	+	673.231i	−0.607328	+	1.05192i
$641$			34.8141i			0.0543122i	0.999631	+	0.0271561i	$0.00864512\pi$
$641$			34.8141i			0.0543122i	−0.999631	+	0.0271561i	$0.991355\pi$
$642$	42.4691	+	14.5142i	0.0661512	+	0.0226079i
$643$	−504.419	+	873.680i	−0.784478	+	1.35876i	0.144833	+	0.989456i	$0.453736\pi$
$643$	−504.419	+	873.680i	−0.784478	+	1.35876i	−0.929311	+	0.369299i	$0.879598\pi$
$644$	101.654	+	18.2918i	0.157849	+	0.0284034i
$645$	−389.515	+	76.6429i	−0.603899	+	0.118826i
$646$	−142.287	+	246.448i	−0.220258	+	0.381498i
$647$	762.764	+	440.382i	1.17892	+	0.680653i	0.955766	−	0.294129i	$-0.0950297\pi$
$647$	762.764	+	440.382i	1.17892	+	0.680653i	0.223159	+	0.974782i	$0.428363\pi$
$648$	−311.600	+	80.7384i	−0.480864	+	0.124596i
$649$	96.3463	+	166.877i	0.148453	+	0.257129i
$650$	−82.1127	+	47.4078i	−0.126327	+	0.0729350i
$651$	49.4857	−	89.0211i	0.0760148	−	0.136745i
$652$	−252.858	+	437.963i	−0.387819	+	0.671722i
$653$		−	785.935i		−	1.20358i	−0.798656	−	0.601788i	$-0.794455\pi$
$653$		−	785.935i		−	1.20358i	0.798656	−	0.601788i	$-0.205545\pi$
$654$	−154.227	+	30.3464i	−0.235821	+	0.0464013i
$655$	−488.340			−0.745557
$656$	−788.657	+	455.331i	−1.20222	+	0.694102i
$657$	−579.170	+	237.100i	−0.881537	+	0.360883i
$658$	15.2661	−	84.8397i	0.0232008	−	0.128936i
$659$	692.308	−	399.704i	1.05054	−	0.606531i	0.127741	−	0.991808i	$-0.459227\pi$
$659$	692.308	−	399.704i	1.05054	−	0.606531i	0.922801	+	0.385276i	$0.125894\pi$
$660$	55.4640	+	281.880i	0.0840364	+	0.427090i
$661$	−163.861	−	283.816i	−0.247899	−	0.429374i	0.715044	−	0.699080i	$-0.246407\pi$
$661$	−163.861	−	283.816i	−0.247899	−	0.429374i	−0.962943	+	0.269706i	$0.913073\pi$
$662$	82.0331	−	47.3618i	0.123917	−	0.0715436i
$663$	451.288	−	88.7976i	0.680675	−	0.133933i
$664$	−59.4887	−	103.037i	−0.0895914	−	0.155177i
$665$	1325.81	+	238.568i	1.99370	+	0.358749i
$666$	−105.944	+	136.893i	−0.159074	+	0.205545i
$667$	−54.0992	−	93.7026i	−0.0811083	−	0.140484i
$668$		−	419.543i		−	0.628058i
$669$	78.7342	+	400.143i	0.117689	+	0.598122i
$670$	368.623			0.550184
$671$	−337.935	−	195.107i	−0.503628	−	0.290770i
$672$	413.421	+	229.815i	0.615210	+	0.341987i
$673$	287.229	+	497.495i	0.426789	+	0.739221i	0.996586	−	0.0825652i	$-0.0263113\pi$
$673$	287.229	+	497.495i	0.426789	+	0.739221i	−0.569796	+	0.821786i	$0.692978\pi$
$674$	−108.199	+	62.4685i	−0.160532	+	0.0926833i
$675$	−361.793	−	548.796i	−0.535990	−	0.813031i
$676$	208.322	−	360.825i	0.308169	−	0.533764i
$677$	194.813	+	112.476i	0.287760	+	0.166138i	0.636931	−	0.770921i	$-0.280204\pi$
$677$	194.813	+	112.476i	0.287760	+	0.166138i	−0.349171	+	0.937059i	$0.613537\pi$
$678$	42.1725	+	214.329i	0.0622013	+	0.316120i
$679$	−7.26836	+	40.3930i	−0.0107045	+	0.0594890i
$680$	−488.866	−	282.247i	−0.718920	−	0.415069i
$681$	−48.3178	+	141.379i	−0.0709513	+	0.207605i
$682$	9.09057			0.0133293
$683$	−322.171	−	186.006i	−0.471700	−	0.272336i	0.245251	−	0.969460i	$-0.421130\pi$
$683$	−322.171	−	186.006i	−0.471700	−	0.272336i	−0.716951	+	0.697123i	$0.754463\pi$
$684$	852.510	−	349.000i	1.24636	−	0.510234i
$685$	532.138			0.776844
$686$	153.506	−	86.4891i	0.223770	−	0.126077i
$687$	404.522	+	138.249i	0.588823	+	0.201236i
$688$	243.066			0.353293
$689$	175.233	−	101.171i	0.254329	−	0.146837i
$690$	−28.1227	−	32.2018i	−0.0407575	−	0.0466693i
$691$	486.666	−	842.930i	0.704292	−	1.21987i	−0.262654	−	0.964890i	$-0.584598\pi$
$691$	486.666	−	842.930i	0.704292	−	1.21987i	0.966946	−	0.254980i	$-0.0820687\pi$
$692$		−	680.145i		−	0.982868i
$693$	224.797	−	48.0385i	0.324383	−	0.0693196i
$694$	−173.010			−0.249294
$695$	−455.363	−	262.904i	−0.655199	−	0.378279i
$696$	−63.0576	−	320.472i	−0.0906000	−	0.460448i
$697$	−713.586	−	1235.97i	−1.02380	−	1.77327i
$698$		−	245.965i		−	0.352386i
$699$	−247.055	+	48.6119i	−0.353441	+	0.0695449i
$700$	−112.757	+	626.634i	−0.161082	+	0.895192i
$701$			495.876i			0.707384i	0.935362	+	0.353692i	$0.115074\pi$
$701$			495.876i			0.707384i	−0.935362	+	0.353692i	$0.884926\pi$
$702$	94.0204	+	47.0926i	0.133932	+	0.0670834i
$703$	512.871	−	888.318i	0.729546	−	1.26361i
$704$		−	146.105i		−	0.207536i
$705$	380.519	−	332.318i	0.539743	−	0.471372i
$706$	54.7151	−	94.7693i	0.0775001	−	0.134234i
$707$	−87.9934	+	104.124i	−0.124460	+	0.147275i
$708$	389.358	+	445.832i	0.549940	+	0.629707i
$709$	−49.0475	+	84.9528i	−0.0691785	+	0.119821i	−0.898540	−	0.438892i	$-0.855371\pi$
$709$	−49.0475	+	84.9528i	−0.0691785	+	0.119821i	0.829361	+	0.558712i	$0.188704\pi$
$710$	432.534	+	249.724i	0.609203	+	0.351724i
$711$	−193.363	+	79.1591i	−0.271960	+	0.111335i
$712$	−311.250	−	539.100i	−0.437148	−	0.757163i
$713$	16.5883	−	9.57727i	0.0232655	−	0.0134324i
$714$	−105.986	+	190.661i	−0.148439	+	0.267032i
$715$	97.1641	−	168.293i	0.135894	−	0.235375i
$716$		−	786.056i		−	1.09784i
$717$	508.107	+	581.806i	0.708658	+	0.811445i
$718$	−260.979			−0.363480
$719$	256.458	−	148.066i	0.356687	−	0.205933i	−0.310939	−	0.950430i	$-0.600644\pi$
$719$	256.458	−	148.066i	0.356687	−	0.205933i	0.667627	+	0.744496i	$0.267310\pi$
$720$	309.059	+	754.944i	0.429248	+	1.04853i
$721$	139.500	+	117.889i	0.193481	+	0.163508i
$722$	173.284	−	100.046i	0.240005	−	0.138567i
$723$	−363.304	−	124.163i	−0.502495	−	0.171733i
$724$	−194.348	−	336.621i	−0.268436	−	0.464946i
$725$	577.616	−	333.487i	0.796712	−	0.459982i
$726$	−109.161	−	124.995i	−0.150360	−	0.172169i
$727$	12.9897	+	22.4988i	0.0178675	+	0.0309475i	0.874821	−	0.484446i	$-0.160979\pi$
$727$	12.9897	+	22.4988i	0.0178675	+	0.0309475i	−0.856953	+	0.515394i	$0.827646\pi$
$728$	−71.4391	−	198.437i	−0.0981307	−	0.272579i
$729$	−287.305	+	669.998i	−0.394109	+	0.919064i
$730$	−125.459	−	217.301i	−0.171861	−	0.297672i
$731$			380.928i			0.521105i
$732$	−1134.25	−	387.643i	−1.54953	−	0.529567i
$733$	675.530			0.921596			0.460798	−	0.887505i	$-0.347563\pi$
$733$	675.530			0.921596			0.460798	+	0.887505i	$0.347563\pi$
$734$	−17.7844	−	10.2678i	−0.0242295	−	0.0139889i
$735$	1019.13	+	166.338i	1.38658	+	0.226310i
$736$	44.4776	+	77.0375i	0.0604316	+	0.104671i
$737$	−322.804	+	186.371i	−0.437997	+	0.252878i
$738$	43.9260	−	323.320i	0.0595203	−	0.438102i
$739$	8.89120	−	15.4000i	0.0120314	−	0.0208390i	−0.859947	−	0.510383i	$-0.829504\pi$
$739$	8.89120	−	15.4000i	0.0120314	−	0.0208390i	0.871978	+	0.489544i	$0.162837\pi$
$740$	851.004	+	491.327i	1.15001	+	0.663956i
$741$	−589.632	−	201.513i	−0.795725	−	0.271947i
$742$	−16.9952	+	94.4486i	−0.0229045	+	0.127289i
$743$	−748.369	−	432.071i	−1.00723	−	0.581522i	−0.0968479	−	0.995299i	$-0.530876\pi$
$743$	−748.369	−	432.071i	−1.00723	−	0.581522i	−0.910378	+	0.413777i	$0.864209\pi$
$744$	56.7336	−	11.1632i	0.0762549	−	0.0150043i
$745$	−152.309			−0.204442
$746$	−30.8593	−	17.8166i	−0.0413663	−	0.0238829i
$747$	−267.001	−	36.2746i	−0.357431	−	0.0485604i
$748$	275.665			0.368537
$749$	−200.641	−	36.1035i	−0.267878	−	0.0482022i
$750$	−5.33870	+	4.66243i	−0.00711827	+	0.00621658i
$751$	517.624			0.689247			0.344623	−	0.938741i	$-0.388007\pi$
$751$	517.624			0.689247			0.344623	+	0.938741i	$0.388007\pi$
$752$	−267.884	+	154.663i	−0.356229	+	0.205669i
$753$	−268.853	+	786.672i	−0.357043	+	1.04472i
$754$	−53.3495	+	92.4040i	−0.0707553	+	0.122552i
$755$			1204.77i			1.59572i
$756$	649.056	−	278.107i	0.858539	−	0.367866i
$757$	−314.752			−0.415789			−0.207895	−	0.978151i	$-0.566661\pi$
$757$	−314.752			−0.415789			−0.207895	+	0.978151i	$0.566661\pi$
$758$	62.3578	+	36.0023i	0.0822663	+	0.0474965i
$759$	40.9079	+	13.9807i	0.0538970	+	0.0184199i
$760$	382.381	+	662.303i	0.503132	+	0.871451i
$761$			590.863i			0.776429i	0.921569	+	0.388215i	$0.126908\pi$
$761$			590.863i			0.776429i	−0.921569	+	0.388215i	$0.873092\pi$
$762$	40.3497	+	46.2023i	0.0529524	+	0.0606329i
$763$	671.773	−	241.844i	0.880437	−	0.316965i
$764$		−	335.438i		−	0.439055i
$765$	−1183.13	+	484.351i	−1.54658	+	0.633138i
$766$	−134.505	+	232.970i	−0.175594	+	0.304139i
$767$		−	400.392i		−	0.522023i
$768$	−59.8429	−	304.134i	−0.0779204	−	0.396007i
$769$	−292.620	+	506.833i	−0.380521	+	0.659081i	−0.991137	−	0.132846i	$-0.957589\pi$
$769$	−292.620	+	506.833i	−0.380521	+	0.659081i	0.610616	+	0.791927i	$0.290922\pi$
$770$	31.2187	+	86.7167i	0.0405438	+	0.112619i
$771$	184.732	−	540.531i	0.239601	−	0.701078i
$772$	149.668	−	259.233i	0.193871	−	0.335794i
$773$	−856.704	−	494.618i	−1.10828	−	0.639869i	−0.169900	−	0.985461i	$-0.554345\pi$
$773$	−856.704	−	494.618i	−1.10828	−	0.639869i	−0.938385	+	0.345593i	$0.887678\pi$
$774$	−53.3023	+	68.8737i	−0.0688661	+	0.0889841i
$775$	59.0377	+	102.256i	0.0761777	+	0.131944i
$776$	−20.1781	+	11.6498i	−0.0260027	+	0.0150127i
$777$	382.024	−	687.234i	0.491666	−	0.884471i
$778$	37.8024	−	65.4756i	0.0485892	−	0.0841589i
$779$			1933.49i			2.48202i
$780$	193.048	−	564.864i	0.247498	−	0.724185i
$781$	−505.028			−0.646642
$782$	−35.5279	+	20.5121i	−0.0454322	+	0.0262303i
$783$	−661.380	−	331.269i	−0.844674	−	0.423077i
$784$	−592.594	−	220.400i	−0.755860	−	0.281123i
$785$	489.437	−	282.576i	0.623486	−	0.359970i
$786$	−80.6920	+	70.4705i	−0.102662	+	0.0896571i
$787$	614.287	+	1063.98i	0.780543	+	1.35194i	0.931626	+	0.363419i	$0.118391\pi$
$787$	614.287	+	1063.98i	0.780543	+	1.35194i	−0.151083	+	0.988521i	$0.548276\pi$
$788$	159.745	−	92.2286i	0.202722	−	0.117041i
$789$	−49.2944	+	144.237i	−0.0624770	+	0.182809i
$790$	−41.8860	−	72.5487i	−0.0530203	−	0.0918338i
$791$	−336.091	−	933.565i	−0.424894	−	1.18023i
$792$	103.204	+	79.8708i	0.130308	+	0.100847i
$793$	405.408	+	702.187i	0.511233	+	0.885481i
$794$		−	94.0699i		−	0.118476i
$795$	−423.616	+	369.956i	−0.532851	+	0.465353i
$796$	−7.60412			−0.00955291
$797$	631.278	+	364.468i	0.792068	+	0.457300i	0.840690	−	0.541517i	$-0.182150\pi$
$797$	631.278	+	364.468i	0.792068	+	0.457300i	−0.0486223	+	0.998817i	$0.515483\pi$
$798$	253.501	−	151.903i	0.317670	−	0.190354i
$799$	−242.385	−	419.823i	−0.303360	−	0.525436i
$800$	−474.886	+	274.176i	−0.593608	+	0.342720i
$801$	−1396.97	−	189.792i	−1.74403	−	0.236943i
$802$	157.710	−	273.162i	0.196646	−	0.340601i
$803$	219.728	+	126.860i	0.273634	+	0.157983i
$804$	−862.412	+	753.168i	−1.07265	+	0.936776i
$805$	148.327	+	125.349i	0.184257	+	0.155713i
$806$	−16.3584	−	9.44454i	−0.0202958	−	0.0117178i
$807$	35.5982	+	40.7615i	0.0441117	+	0.0505099i
$808$	−77.3928			−0.0957832
$809$	1007.55	+	581.707i	1.24542	+	0.719044i	0.970193	−	0.242335i	$-0.0779131\pi$
$809$	1007.55	+	581.707i	1.24542	+	0.719044i	0.275229	+	0.961379i	$0.411246\pi$
$810$	−281.691	−	77.9800i	−0.347766	−	0.0962716i
$811$	−224.013			−0.276219			−0.138109	−	0.990417i	$-0.544103\pi$
$811$	−224.013			−0.276219			−0.138109	+	0.990417i	$0.544103\pi$
$812$	242.696	+	674.141i	0.298887	+	0.830222i
$813$	−99.5300	−	505.832i	−0.122423	−	0.622179i
$814$	70.1783			0.0862141
$815$	−823.453	+	475.421i	−1.01037	+	0.583338i
$816$	768.037	−	151.123i	0.941221	−	0.185199i
$817$	258.035	−	446.931i	0.315833	−	0.547039i
$818$			245.063i			0.299588i
$819$	−454.430	−	147.105i	−0.554860	−	0.179616i
$820$	−1852.28			−2.25888
$821$	1162.89	+	671.396i	1.41643	+	0.817778i	0.995983	−	0.0895378i	$-0.0285390\pi$
$821$	1162.89	+	671.396i	1.41643	+	0.817778i	0.420450	+	0.907316i	$0.361872\pi$
$822$	87.9291	−	76.7909i	0.106970	−	0.0934195i
$823$	−665.079	−	1151.95i	−0.808115	−	1.39970i	−0.914168	−	0.405336i	$-0.867154\pi$
$823$	−665.079	−	1151.95i	−0.808115	−	1.39970i	0.106052	−	0.994361i	$-0.466179\pi$
$824$			103.687i			0.125834i
$825$	−86.1819	+	252.170i	−0.104463	+	0.305661i
$826$	145.040	+	122.571i	0.175593	+	0.148392i
$827$		−	863.204i		−	1.04378i	−0.853014	−	0.521889i	$-0.825228\pi$
$827$		−	863.204i		−	1.04378i	0.853014	−	0.521889i	$-0.174772\pi$
$828$	131.589	+	17.8776i	0.158924	+	0.0215913i
$829$	288.804	−	500.224i	0.348377	−	0.603406i	−0.637585	−	0.770380i	$-0.720066\pi$
$829$	288.804	−	500.224i	0.348377	−	0.603406i	0.985961	+	0.166974i	$0.0533997\pi$
$830$		−	108.035i		−	0.130162i
$831$	−643.239	−	219.834i	−0.774055	−	0.264541i
$832$	−151.794	+	262.915i	−0.182445	+	0.316004i
$833$	345.407	−	928.702i	0.414654	−	1.11489i
$834$	−113.182	+	22.2702i	−0.135709	+	0.0267029i
$835$	394.410	−	683.138i	0.472347	−	0.818129i
$836$	−323.429	−	186.732i	−0.386877	−	0.223364i
$837$	58.6452	−	117.085i	0.0700659	−	0.139887i
$838$	62.9937	+	109.108i	0.0751715	+	0.130201i
$839$	−264.845	+	152.908i	−0.315667	+	0.182251i	−0.649460	−	0.760396i	$-0.725005\pi$
$839$	−264.845	+	152.908i	−0.315667	+	0.182251i	0.333792	+	0.942647i	$0.391672\pi$
$840$	301.322	+	502.857i	0.358717	+	0.598639i
$841$	−45.2169	+	78.3179i	−0.0537656	+	0.0931248i
$842$			253.897i			0.301541i
$843$	−1226.72	+	241.375i	−1.45518	+	0.286329i
$844$	−1082.28			−1.28232
$845$	678.418	−	391.685i	0.802862	−	0.463533i
$846$	14.9204	−	109.823i	0.0176364	−	0.129814i
$847$	575.748	+	486.556i	0.679749	+	0.574447i
$848$	298.225	−	172.180i	0.351680	−	0.203043i
$849$	71.9985	+	365.911i	0.0848039	+	0.430991i
$850$	−126.444	−	219.007i	−0.148757	−	0.257655i
$851$	128.060	−	73.9356i	0.150482	−	0.0868808i
$852$	−1522.17	+	299.509i	−1.78658	+	0.351537i
$853$	−42.0979	−	72.9157i	−0.0493528	−	0.0854815i	0.840294	−	0.542131i	$-0.182383\pi$
$853$	−42.0979	−	72.9157i	−0.0493528	−	0.0854815i	−0.889646	+	0.456650i	$0.849049\pi$
$854$	−378.471	−	68.1025i	−0.443175	−	0.0797453i
$855$	1716.23	+	233.165i	2.00728	+	0.272708i
$856$	−57.8672	−	100.229i	−0.0676019	−	0.117090i
$857$			237.222i			0.276805i	0.990376	+	0.138402i	$0.0441967\pi$
$857$			237.222i			0.276805i	−0.990376	+	0.138402i	$0.955803\pi$
$858$	−8.23063	−	41.8297i	−0.00959280	−	0.0487526i
$859$	1162.19			1.35296			0.676479	−	0.736462i	$-0.263505\pi$
$859$	1162.19			1.35296			0.676479	+	0.736462i	$0.263505\pi$
$860$	428.157	+	247.197i	0.497857	+	0.287438i
$861$	24.0794	+	1481.92i	0.0279667	+	1.72116i
$862$	81.4900	+	141.145i	0.0945360	+	0.163741i
$863$	−582.552	+	336.337i	−0.675032	+	0.389730i	−0.797980	−	0.602683i	$-0.794098\pi$
$863$	−582.552	+	336.337i	−0.675032	+	0.389730i	0.122949	+	0.992413i	$0.460765\pi$
$864$	543.753	+	272.353i	0.629344	+	0.315223i
$865$	639.400	−	1107.47i	0.739191	−	1.28032i
$866$	298.654	+	172.428i	0.344866	+	0.199109i
$867$	69.4508	+	352.963i	0.0801047	+	0.407109i
$868$	−119.344	+	42.9649i	−0.137493	+	0.0494987i
$869$	73.3592	+	42.3540i	0.0844180	+	0.0487387i
$870$	95.9117	−	280.640i	0.110243	−	0.322575i
$871$	774.512			0.889221
$872$	351.028	+	202.666i	0.402555	+	0.232415i
$873$	−7.10376	+	52.2876i	−0.00813718	+	0.0598941i
$874$	55.5784			0.0635909
$875$	20.7815	−	24.5910i	0.0237503	−	0.0281040i
$876$	737.503	+	252.049i	0.841898	+	0.287727i
$877$	−751.329			−0.856703			−0.428352	−	0.903612i	$-0.640905\pi$
$877$	−751.329			−0.856703			−0.428352	+	0.903612i	$0.640905\pi$
$878$	132.550	−	76.5278i	0.150968	−	0.0871615i
$879$	−826.204	−	946.041i	−0.939936	−	1.07627i
$880$	165.362	−	286.415i	0.187911	−	0.325471i
$881$			696.005i			0.790017i	0.918677	+	0.395009i	$0.129258\pi$
$881$			696.005i			0.790017i	−0.918677	+	0.395009i	$0.870742\pi$
$882$	192.403	−	119.582i	0.218143	−	0.135581i
$883$	−1217.46			−1.37878			−0.689390	−	0.724390i	$-0.742121\pi$
$883$	−1217.46			−1.37878			−0.689390	+	0.724390i	$0.742121\pi$
$884$	−496.058	−	286.399i	−0.561152	−	0.323981i
$885$	214.863	+	1091.98i	0.242783	+	1.23387i
$886$	−213.020	−	368.962i	−0.240429	−	0.416436i
$887$			582.814i			0.657063i	0.944493	+	0.328531i	$0.106554\pi$
$887$			582.814i			0.657063i	−0.944493	+	0.328531i	$0.893446\pi$
$888$	437.978	−	86.1787i	0.493218	−	0.0970481i
$889$	−212.816	−	179.847i	−0.239388	−	0.202303i
$890$		−	565.246i		−	0.635108i
$891$	286.102	−	74.1318i	0.321103	−	0.0832007i
$892$	253.942	−	439.840i	0.284688	−	0.493094i
$893$			656.754i			0.735446i
$894$	−25.1672	+	21.9792i	−0.0281512	+	0.0245852i
$895$	738.967	−	1279.93i	0.825661	−	1.43009i
$896$	−262.396	−	728.862i	−0.292853	−	0.813462i
$897$	−59.0884	−	67.6589i	−0.0658733	−	0.0754280i
$898$	48.8983	−	84.6943i	0.0544524	−	0.0943144i
$899$	115.072	+	66.4370i	0.128000	+	0.0739010i
$900$	−110.204	+	811.160i	−0.122449	+	0.901289i
$901$	269.837	+	467.372i	0.299487	+	0.518726i
$902$	−114.561	+	66.1421i	−0.127008	+	0.0733282i
$903$	192.204	−	345.761i	0.212851	−	0.382903i
$904$	281.645	−	487.824i	0.311554	−	0.539628i
$905$		−	730.821i		−	0.807537i
$906$	173.856	+	199.073i	0.191894	+	0.219727i
$907$	199.160			0.219581			0.109791	−	0.993955i	$-0.464982\pi$
$907$	199.160			0.219581			0.109791	+	0.993955i	$0.464982\pi$
$908$	161.140	−	93.0344i	0.177467	−	0.102461i
$909$	−107.275	+	138.613i	−0.118014	+	0.152490i
$910$	33.9154	−	188.481i	0.0372696	−	0.207122i
$911$	−351.011	+	202.656i	−0.385303	+	0.222455i	−0.680123	−	0.733098i	$-0.738074\pi$
$911$	−351.011	+	202.656i	−0.385303	+	0.222455i	0.294820	+	0.955553i	$0.404740\pi$
$912$	−1003.48	−	342.950i	−1.10031	−	0.376042i
$913$	54.6209	+	94.6062i	0.0598257	+	0.103621i
$914$	−124.551	+	71.9096i	−0.136270	+	0.0786757i
$915$	−1482.47	−	1697.50i	−1.62019	−	1.85519i
$916$	−266.195	−	461.063i	−0.290606	−	0.503344i
$917$	314.103	−	371.681i	0.342533	−	0.405323i
$918$	−125.603	+	250.766i	−0.136822	+	0.273166i
$919$	471.303	+	816.321i	0.512843	+	0.888271i	0.999889	+	0.0148944i	$0.00474119\pi$
$919$	471.303	+	816.321i	0.512843	+	0.888271i	−0.487046	+	0.873377i	$0.661925\pi$
$920$			110.248i			0.119835i
$921$	1298.28	+	443.699i	1.40964	+	0.481758i
$922$	−78.8442			−0.0855143
$923$	908.795	+	524.693i	0.984609	+	0.568465i
$924$	−250.217	−	139.092i	−0.270797	−	0.150532i
$925$	455.765	+	789.408i	0.492719	+	0.853414i
$926$	223.856	−	129.243i	0.241745	−	0.139572i
$927$	185.707	+	143.721i	0.200331	+	0.155039i
$928$	−308.539	+	534.405i	−0.332477	+	0.575867i
$929$	−1200.05	−	692.847i	−1.29176	−	0.745799i	−0.312795	−	0.949821i	$-0.601265\pi$
$929$	−1200.05	−	692.847i	−1.29176	−	0.745799i	−0.978966	+	0.204022i	$0.934599\pi$
$930$	49.6821	+	16.9794i	0.0534217	+	0.0182574i
$931$	−1034.35	+	855.643i	−1.11101	+	0.919058i
$932$	271.565	+	156.788i	0.291379	+	0.168228i
$933$	1024.77	−	201.639i	1.09836	−	0.216119i
$934$	−90.8415			−0.0972607
$935$	448.863	+	259.151i	0.480068	+	0.277167i
$936$	−102.734	−	250.949i	−0.109758	−	0.268108i
$937$	−93.8449			−0.100155			−0.0500773	−	0.998745i	$-0.515947\pi$
$937$	−93.8449			−0.100155			−0.0500773	+	0.998745i	$0.515947\pi$
$938$	−237.100	+	280.564i	−0.252772	+	0.299108i
$939$	306.645	−	267.802i	0.326566	−	0.285199i
$940$	−629.167			−0.669326
$941$	462.418	−	266.977i	0.491411	−	0.283716i	−0.233749	−	0.972297i	$-0.575099\pi$
$941$	462.418	−	266.977i	0.491411	−	0.283716i	0.725160	+	0.688581i	$0.241766\pi$
$942$	40.0957	−	117.321i	0.0425644	−	0.124545i
$943$	−139.367	+	241.390i	−0.147791	+	0.255981i
$944$		−	681.418i		−	0.721841i
$945$	1318.30	+	157.335i	1.39502	+	0.166492i
$946$	35.3081			0.0373236
$947$	−1333.62	−	769.968i	−1.40826	−	0.813060i	−0.413041	−	0.910713i	$-0.635533\pi$
$947$	−1333.62	−	769.968i	−1.40826	−	0.813060i	−0.995221	+	0.0976527i	$0.968867\pi$
$948$	246.225	+	84.1500i	0.259731	+	0.0887658i
$949$	−263.600	−	456.569i	−0.277766	−	0.481105i
$950$			342.605i			0.360637i
$951$	−804.428	−	921.107i	−0.845876	−	0.968567i
$952$	529.262	−	190.539i	0.555948	−	0.200146i
$953$			923.067i			0.968591i	0.874905	+	0.484295i	$0.160924\pi$
$953$			923.067i			0.968591i	−0.874905	+	0.484295i	$0.839076\pi$
$954$	−16.6103	+	122.261i	−0.0174112	+	0.128156i
$955$	315.343	−	546.191i	0.330202	−	0.571927i
$956$		−	961.984i		−	1.00626i
$957$	57.8978	+	294.248i	0.0604992	+	0.307469i
$958$	−121.452	+	210.360i	−0.126776	+	0.219583i
$959$	−342.274	+	405.016i	−0.356907	+	0.422332i
$960$	272.896	−	798.499i	0.284266	−	0.831770i
$961$	468.739	−	811.879i	0.487761	−	0.844827i
$962$	−126.285	−	72.9109i	−0.131274	−	0.0757910i
$963$	−259.724	−	35.2859i	−0.269703	−	0.0366416i
$964$	239.072	+	414.084i	0.248000	+	0.429548i
$965$	487.407	−	281.404i	0.505085	−	0.291611i
$966$	42.5978	−	0.692163i	0.0440971	−	0.000716524i
$967$	−580.540	+	1005.53i	−0.600352	+	1.03984i	0.392416	+	0.919788i	$0.371639\pi$
$967$	−580.540	+	1005.53i	−0.600352	+	1.03984i	−0.992768	+	0.120052i	$0.961694\pi$
$968$			427.941i			0.442087i
$969$	537.465	−	1572.64i	0.554659	−	1.62295i
$970$	−21.1568			−0.0218111
$971$	751.650	−	433.966i	0.774099	−	0.446926i	−0.0602357	−	0.998184i	$-0.519185\pi$
$971$	751.650	−	433.966i	0.774099	−	0.446926i	0.834335	+	0.551258i	$0.185852\pi$
$972$	818.357	−	393.110i	0.841931	−	0.404434i
$973$	492.991	−	177.481i	0.506671	−	0.182406i
$974$	43.8895	−	25.3396i	0.0450611	−	0.0260160i
$975$	417.074	−	364.242i	0.427768	−	0.373581i
$976$	689.955	+	1195.04i	0.706921	+	1.22442i
$977$	1386.29	−	800.376i	1.41893	−	0.819218i	0.422722	−	0.906260i	$-0.361075\pi$
$977$	1386.29	−	800.376i	1.41893	−	0.819218i	0.996205	+	0.0870419i	$0.0277414\pi$
$978$	−67.4590	+	197.387i	−0.0689764	+	0.201827i
$979$	285.781	+	494.987i	0.291911	+	0.505605i
$980$	−819.702	−	990.898i	−0.836430	−	1.01112i
$981$	849.543	−	347.786i	0.865997	−	0.354522i
$982$	−239.460	−	414.757i	−0.243850	−	0.422360i
$983$			1363.25i			1.38683i	0.720541	+	0.693413i	$0.243894\pi$
$983$			1363.25i			1.38683i	−0.720541	+	0.693413i	$0.756106\pi$
$984$	−633.748	+	553.469i	−0.644053	+	0.562469i
$985$	346.814			0.352095
$986$	−246.455	−	142.291i	−0.249955	−	0.144311i
$987$	8.17908	+	503.366i	0.00828680	+	0.509996i
$988$	388.006	+	672.047i	0.392719	+	0.680209i
$989$	64.4296	−	37.1985i	0.0651463	−	0.0376122i
$990$	44.8943	+	109.664i	0.0453478	+	0.110772i
$991$	−470.682	+	815.244i	−0.474956	+	0.822648i	−0.999589	−	0.0286806i	$-0.990869\pi$
$991$	−470.682	+	815.244i	−0.474956	+	0.822648i	0.524632	+	0.851329i	$0.324203\pi$
$992$	−94.6065	−	54.6211i	−0.0953695	−	0.0550616i
$993$	−416.669	+	363.889i	−0.419607	+	0.366454i
$994$	−468.276	+	168.583i	−0.471103	+	0.169601i
$995$	−12.3817	−	7.14858i	−0.0124439	−	0.00718450i
$996$	220.736	+	252.753i	0.221622	+	0.253768i
$997$	−1346.49			−1.35054			−0.675272	−	0.737569i	$-0.735974\pi$
$997$	−1346.49			−1.35054			−0.675272	+	0.737569i	$0.735974\pi$
$998$	−211.633	−	122.187i	−0.212058	−	0.122431i
$999$	452.735	−	903.885i	0.453188	−	0.904790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.32.6	yes	22
3.2	odd	2		189.3.n.b.179.6		22
7.2	even	3		63.3.j.b.23.6	yes	22
7.3	odd	6		441.3.r.f.50.6		22
7.4	even	3		441.3.r.g.50.6		22
7.5	odd	6		441.3.j.f.275.6		22
7.6	odd	2		441.3.n.f.410.6		22
9.2	odd	6		63.3.j.b.11.6	✓	22
9.7	even	3		189.3.j.b.116.6		22
21.2	odd	6		189.3.j.b.44.6		22
63.2	odd	6	inner	63.3.n.b.2.6	yes	22
63.11	odd	6		441.3.r.g.344.6		22
63.16	even	3		189.3.n.b.170.6		22
63.20	even	6		441.3.j.f.263.6		22
63.38	even	6		441.3.r.f.344.6		22
63.47	even	6		441.3.n.f.128.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.6	✓	22	9.2	odd	6
63.3.j.b.23.6	yes	22	7.2	even	3
63.3.n.b.2.6	yes	22	63.2	odd	6	inner
63.3.n.b.32.6	yes	22	1.1	even	1	trivial
189.3.j.b.44.6		22	21.2	odd	6
189.3.j.b.116.6		22	9.7	even	3
189.3.n.b.170.6		22	63.16	even	3
189.3.n.b.179.6		22	3.2	odd	2
441.3.j.f.263.6		22	63.20	even	6
441.3.j.f.275.6		22	7.5	odd	6
441.3.n.f.128.6		22	63.47	even	6
441.3.n.f.410.6		22	7.6	odd	2
441.3.r.f.50.6		22	7.3	odd	6
441.3.r.f.344.6		22	63.38	even	6
441.3.r.g.50.6		22	7.4	even	3
441.3.r.g.344.6		22	63.11	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.444866 - 0.256844i) q^{2} +(2.83879 + 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} -7.02462i q^{5} +(-1.01370 - 1.16073i) q^{6} +(5.34652 + 4.51827i) q^{7} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +O(q^{10})\)	\(q+(-0.444866 - 0.256844i) q^{2} +(2.83879 + 0.970187i) q^{3} +(-1.86806 - 3.23558i) q^{4} -7.02462i q^{5} +(-1.01370 - 1.16073i) q^{6} +(5.34652 + 4.51827i) q^{7} +3.97395i q^{8} +(7.11748 + 5.50832i) q^{9} +(-1.80423 + 3.12502i) q^{10} -3.64877i q^{11} +(-2.16392 - 10.9975i) q^{12} +(-3.79085 + 6.56594i) q^{13} +(-1.21800 - 3.38324i) q^{14} +(6.81519 - 19.9414i) q^{15} +(-6.45157 + 11.1744i) q^{16} +(-17.5124 - 10.1108i) q^{17} +(-1.75155 - 4.27854i) q^{18} +(13.6978 + 23.7253i) q^{19} +(-22.7287 + 13.1224i) q^{20} +(10.7941 + 18.0135i) q^{21} +(-0.937164 + 1.62322i) q^{22} +3.94936i q^{23} +(-3.85547 + 11.2812i) q^{24} -24.3452 q^{25} +(3.37284 - 1.94731i) q^{26} +(14.8609 + 22.5422i) q^{27} +(4.63159 - 25.7395i) q^{28} +(-23.7260 + 13.6982i) q^{29} +(-8.15368 + 7.12083i) q^{30} +(-2.42502 - 4.20026i) q^{31} +(19.5063 - 11.2620i) q^{32} +(3.53999 - 10.3581i) q^{33} +(5.19377 + 8.99588i) q^{34} +(31.7391 - 37.5572i) q^{35} +(4.52670 - 33.3190i) q^{36} +(-18.7209 - 32.4256i) q^{37} -14.0728i q^{38} +(-17.1316 + 14.9615i) q^{39} +27.9155 q^{40} +(61.1213 + 35.2884i) q^{41} +(-0.175260 - 10.7860i) q^{42} +(-9.41887 - 16.3140i) q^{43} +(-11.8059 + 6.81613i) q^{44} +(38.6938 - 49.9975i) q^{45} +(1.01437 - 1.75694i) q^{46} +(20.7612 + 11.9865i) q^{47} +(-29.1559 + 25.4627i) q^{48} +(8.17049 + 48.3140i) q^{49} +(10.8304 + 6.25292i) q^{50} +(-39.9046 - 45.6926i) q^{51} +28.3262 q^{52} +(-23.1126 - 13.3441i) q^{53} +(-0.821297 - 13.8452i) q^{54} -25.6312 q^{55} +(-17.9554 + 21.2468i) q^{56} +(15.8672 + 80.6406i) q^{57} +14.0732 q^{58} +(-45.7350 + 26.4051i) q^{59} +(-77.2533 + 15.2007i) q^{60} +(53.4719 - 92.6160i) q^{61} +2.49140i q^{62} +(13.1657 + 61.6090i) q^{63} +40.0422 q^{64} +(46.1232 + 26.6293i) q^{65} +(-4.23524 + 3.69875i) q^{66} +(-51.0777 - 88.4692i) q^{67} +75.5502i q^{68} +(-3.83161 + 11.2114i) q^{69} +(-23.7660 + 8.55596i) q^{70} -138.410i q^{71} +(-21.8898 + 28.2845i) q^{72} +(-34.7679 + 60.2198i) q^{73} +19.2334i q^{74} +(-69.1111 - 23.6194i) q^{75} +(51.1767 - 88.6406i) q^{76} +(16.4861 - 19.5082i) q^{77} +(11.4641 - 2.25573i) q^{78} +(-11.6077 + 20.1052i) q^{79} +(78.4962 + 45.3198i) q^{80} +(20.3169 + 78.4106i) q^{81} +(-18.1272 - 31.3973i) q^{82} +(-25.9282 + 14.9697i) q^{83} +(38.1202 - 68.5755i) q^{84} +(-71.0243 + 123.018i) q^{85} +9.67670i q^{86} +(-80.6431 + 15.8677i) q^{87} +14.5000 q^{88} +(-135.658 + 78.3225i) q^{89} +(-30.0551 + 12.3040i) q^{90} +(-49.9345 + 17.9769i) q^{91} +(12.7785 - 7.37765i) q^{92} +(-2.80909 - 14.2764i) q^{93} +(-6.15730 - 10.6648i) q^{94} +(166.661 - 96.2218i) q^{95} +(66.3007 - 13.0457i) q^{96} +(2.93155 + 5.07760i) q^{97} +(8.77437 - 23.5918i) q^{98} +(20.0986 - 25.9700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

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