LMFDB - Embedded newform 806.2.k.c.157.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [806,2,Mod(157,806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(806, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("806.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 806 = 2 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	806.k (of order $5$, degree $4$, 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:	$6.43594240292$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	806.157
Dual form			806.2.k.c.729.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(2.64130 - 1.91901i) q^{3} +(0.309017 + 0.951057i) q^{4} -0.940065 q^{5} +3.26482 q^{6} +(0.903176 + 2.77969i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.36678 - 7.28420i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(2.64130 - 1.91901i) q^{3} +(0.309017 + 0.951057i) q^{4} -0.940065 q^{5} +3.26482 q^{6} +(0.903176 + 2.77969i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.36678 - 7.28420i) q^{9} +(-0.760528 - 0.552556i) q^{10} +(1.41950 + 4.36878i) q^{11} +(2.64130 + 1.91901i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.903176 + 2.77969i) q^{14} +(-2.48299 + 1.80400i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.729235 - 2.24435i) q^{17} +(6.19631 - 4.50188i) q^{18} +(1.33644 + 0.970980i) q^{19} +(-0.290496 - 0.894055i) q^{20} +(7.71982 + 5.60878i) q^{21} +(-1.41950 + 4.36878i) q^{22} +(1.76887 - 5.44403i) q^{23} +(1.00889 + 3.10503i) q^{24} -4.11628 q^{25} +1.00000 q^{26} +(-4.70046 - 14.4665i) q^{27} +(-2.36455 + 1.71794i) q^{28} +(2.10338 + 1.52820i) q^{29} -3.06914 q^{30} +(-4.67249 - 3.02785i) q^{31} -1.00000 q^{32} +(12.1331 + 8.81519i) q^{33} +(1.90916 - 1.38709i) q^{34} +(-0.849044 - 2.61309i) q^{35} +7.65906 q^{36} +1.49919 q^{37} +(0.510474 + 1.57108i) q^{38} +(1.00889 - 3.10503i) q^{39} +(0.290496 - 0.894055i) q^{40} +(-2.43906 - 1.77208i) q^{41} +(2.94871 + 9.07519i) q^{42} +(-7.79458 - 5.66309i) q^{43} +(-3.71630 + 2.70005i) q^{44} +(-2.22493 + 6.84762i) q^{45} +(4.63097 - 3.36460i) q^{46} +(-10.0607 + 7.30949i) q^{47} +(-1.00889 + 3.10503i) q^{48} +(-1.24783 + 0.906600i) q^{49} +(-3.33014 - 2.41949i) q^{50} +(-2.38082 - 7.32742i) q^{51} +(0.809017 + 0.587785i) q^{52} +(-2.85905 + 8.79925i) q^{53} +(4.70046 - 14.4665i) q^{54} +(-1.33442 - 4.10693i) q^{55} -2.92274 q^{56} +5.39326 q^{57} +(0.803420 + 2.47267i) q^{58} +(2.30310 - 1.67330i) q^{59} +(-2.48299 - 1.80400i) q^{60} +12.0484 q^{61} +(-2.00040 - 5.19600i) q^{62} +22.3854 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.760528 + 0.552556i) q^{65} +(4.63442 + 14.2633i) q^{66} -8.72548 q^{67} +2.35985 q^{68} +(-5.77506 - 17.7738i) q^{69} +(0.849044 - 2.61309i) q^{70} +(-2.95805 + 9.10393i) q^{71} +(6.19631 + 4.50188i) q^{72} +(-0.682105 - 2.09930i) q^{73} +(1.21287 + 0.881202i) q^{74} +(-10.8723 + 7.89920i) q^{75} +(-0.510474 + 1.57108i) q^{76} +(-10.8618 + 7.89155i) q^{77} +(2.64130 - 1.91901i) q^{78} +(3.45510 - 10.6337i) q^{79} +(0.760528 - 0.552556i) q^{80} +(-21.5878 - 15.6845i) q^{81} +(-0.931639 - 2.86729i) q^{82} +(-6.90269 - 5.01510i) q^{83} +(-2.94871 + 9.07519i) q^{84} +(-0.685528 + 2.10984i) q^{85} +(-2.97727 - 9.16308i) q^{86} +8.48828 q^{87} -4.59361 q^{88} +(-4.46505 - 13.7420i) q^{89} +(-5.82493 + 4.23206i) q^{90} +(2.36455 + 1.71794i) q^{91} +5.72420 q^{92} +(-18.1519 + 0.969133i) q^{93} -12.4357 q^{94} +(-1.25634 - 0.912784i) q^{95} +(-2.64130 + 1.91901i) q^{96} +(1.21072 + 3.72621i) q^{97} -1.54240 q^{98} +35.1827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8}+O(q^{10}) $ 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8} + 3 q^{10} + 3 q^{11} + q^{12} + 7 q^{13} + q^{14} + 6 q^{15} - 7 q^{16} - 2 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} + 15 q^{21} - 3 q^{22} + 18 q^{23} + 4 q^{24} + 54 q^{25} + 28 q^{26} - 26 q^{27} + 4 q^{28} + 27 q^{29} + 14 q^{30} - 33 q^{31} - 28 q^{32} + 3 q^{33} + 2 q^{34} + 8 q^{35} + 30 q^{36} - 6 q^{37} - 27 q^{38} + 4 q^{39} - 2 q^{40} - 22 q^{41} + 5 q^{42} + q^{43} - 12 q^{44} + 28 q^{45} + 27 q^{46} + 7 q^{47} - 4 q^{48} - 30 q^{49} + q^{50} - 52 q^{51} + 7 q^{52} + q^{53} + 26 q^{54} - 18 q^{55} + 6 q^{56} - 112 q^{57} + 23 q^{58} + 27 q^{59} + 6 q^{60} - 6 q^{61} - 17 q^{62} + 54 q^{63} - 7 q^{64} + 3 q^{65} + 17 q^{66} - 24 q^{67} + 8 q^{68} + 6 q^{69} - 8 q^{70} + 28 q^{71} + 15 q^{72} - 8 q^{73} - 9 q^{74} - 62 q^{75} + 27 q^{76} - 62 q^{77} + q^{78} + 40 q^{79} - 3 q^{80} - 24 q^{81} - 18 q^{82} + 3 q^{83} - 5 q^{84} - q^{85} + 4 q^{86} + 42 q^{87} - 18 q^{88} - 5 q^{89} - 23 q^{90} - 4 q^{91} + 18 q^{92} - 69 q^{93} - 12 q^{94} - 17 q^{95} - q^{96} + 29 q^{97} - 30 q^{98} + 88 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8 + 3 * q^10 + 3 * q^11 + q^12 + 7 * q^13 + q^14 + 6 * q^15 - 7 * q^16 - 2 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 + 15 * q^21 - 3 * q^22 + 18 * q^23 + 4 * q^24 + 54 * q^25 + 28 * q^26 - 26 * q^27 + 4 * q^28 + 27 * q^29 + 14 * q^30 - 33 * q^31 - 28 * q^32 + 3 * q^33 + 2 * q^34 + 8 * q^35 + 30 * q^36 - 6 * q^37 - 27 * q^38 + 4 * q^39 - 2 * q^40 - 22 * q^41 + 5 * q^42 + q^43 - 12 * q^44 + 28 * q^45 + 27 * q^46 + 7 * q^47 - 4 * q^48 - 30 * q^49 + q^50 - 52 * q^51 + 7 * q^52 + q^53 + 26 * q^54 - 18 * q^55 + 6 * q^56 - 112 * q^57 + 23 * q^58 + 27 * q^59 + 6 * q^60 - 6 * q^61 - 17 * q^62 + 54 * q^63 - 7 * q^64 + 3 * q^65 + 17 * q^66 - 24 * q^67 + 8 * q^68 + 6 * q^69 - 8 * q^70 + 28 * q^71 + 15 * q^72 - 8 * q^73 - 9 * q^74 - 62 * q^75 + 27 * q^76 - 62 * q^77 + q^78 + 40 * q^79 - 3 * q^80 - 24 * q^81 - 18 * q^82 + 3 * q^83 - 5 * q^84 - q^85 + 4 * q^86 + 42 * q^87 - 18 * q^88 - 5 * q^89 - 23 * q^90 - 4 * q^91 + 18 * q^92 - 69 * q^93 - 12 * q^94 - 17 * q^95 - q^96 + 29 * q^97 - 30 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/806\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	2.64130	−	1.91901i	1.52495	−	1.10794i	0.565990	−	0.824412i	$-0.308494\pi$
$3$	2.64130	−	1.91901i	1.52495	−	1.10794i	0.958963	−	0.283531i	$-0.0915060\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.940065			−0.420410			−0.210205	−	0.977657i	$-0.567413\pi$
$5$	−0.940065			−0.420410			−0.210205	+	0.977657i	$0.567413\pi$
$6$	3.26482			1.33286
$7$	0.903176	+	2.77969i	0.341368	+	1.05062i	0.963499	+	0.267711i	$0.0862671\pi$
$7$	0.903176	+	2.77969i	0.341368	+	1.05062i	−0.622131	+	0.782913i	$0.713733\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.36678	−	7.28420i	0.788927	−	2.42807i
$10$	−0.760528	−	0.552556i	−0.240500	−	0.174734i
$11$	1.41950	+	4.36878i	0.427996	+	1.31724i	0.900096	+	0.435691i	$0.143496\pi$
$11$	1.41950	+	4.36878i	0.427996	+	1.31724i	−0.472100	+	0.881545i	$0.656504\pi$
$12$	2.64130	+	1.91901i	0.762477	+	0.553972i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−0.903176	+	2.77969i	−0.241384	+	0.742903i
$15$	−2.48299	+	1.80400i	−0.641105	+	0.465790i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.729235	−	2.24435i	0.176865	−	0.544336i	−0.822848	−	0.568261i	$-0.807616\pi$
$17$	0.729235	−	2.24435i	0.176865	−	0.544336i	0.999714	+	0.0239252i	$0.00761635\pi$
$18$	6.19631	−	4.50188i	1.46048	−	1.06110i
$19$	1.33644	+	0.970980i	0.306600	+	0.222758i	0.730436	−	0.682981i	$-0.239317\pi$
$19$	1.33644	+	0.970980i	0.306600	+	0.222758i	−0.423836	+	0.905739i	$0.639317\pi$
$20$	−0.290496	−	0.894055i	−0.0649569	−	0.199917i
$21$	7.71982	+	5.60878i	1.68460	+	1.22394i
$22$	−1.41950	+	4.36878i	−0.302639	+	0.931427i
$23$	1.76887	−	5.44403i	0.368836	−	1.13516i	−0.578708	−	0.815535i	$-0.696443\pi$
$23$	1.76887	−	5.44403i	0.368836	−	1.13516i	0.947544	−	0.319625i	$-0.103557\pi$
$24$	1.00889	+	3.10503i	0.205938	+	0.633812i
$25$	−4.11628			−0.823256
$26$	1.00000			0.196116
$27$	−4.70046	−	14.4665i	−0.904604	−	2.78408i
$28$	−2.36455	+	1.71794i	−0.446857	+	0.324661i
$29$	2.10338	+	1.52820i	0.390588	+	0.283779i	0.765696	−	0.643202i	$-0.222395\pi$
$29$	2.10338	+	1.52820i	0.390588	+	0.283779i	−0.375108	+	0.926981i	$0.622395\pi$
$30$	−3.06914			−0.560346
$31$	−4.67249	−	3.02785i	−0.839204	−	0.543817i
$31$	−4.67249	−	3.02785i	−0.839204	−	0.543817i
$32$	−1.00000			−0.176777
$33$	12.1331	+	8.81519i	2.11210	+	1.53453i
$34$	1.90916	−	1.38709i	0.327419	−	0.237884i
$35$	−0.849044	−	2.61309i	−0.143515	−	0.441693i
$36$	7.65906			1.27651
$37$	1.49919			0.246465			0.123233	−	0.992378i	$-0.460674\pi$
$37$	1.49919			0.246465			0.123233	+	0.992378i	$0.460674\pi$
$38$	0.510474	+	1.57108i	0.0828099	+	0.254863i
$39$	1.00889	−	3.10503i	0.161551	−	0.497203i
$40$	0.290496	−	0.894055i	0.0459315	−	0.141362i
$41$	−2.43906	−	1.77208i	−0.380918	−	0.276753i	0.380806	−	0.924655i	$-0.375647\pi$
$41$	−2.43906	−	1.77208i	−0.380918	−	0.276753i	−0.761724	+	0.647902i	$0.775647\pi$
$42$	2.94871	+	9.07519i	0.454996	+	1.40033i
$43$	−7.79458	−	5.66309i	−1.18866	−	0.863614i	−0.195540	−	0.980696i	$-0.562646\pi$
$43$	−7.79458	−	5.66309i	−1.18866	−	0.863614i	−0.993122	+	0.117082i	$0.962646\pi$
$44$	−3.71630	+	2.70005i	−0.560254	+	0.407048i
$45$	−2.22493	+	6.84762i	−0.331672	+	1.02078i
$46$	4.63097	−	3.36460i	0.682800	−	0.496083i
$47$	−10.0607	+	7.30949i	−1.46750	+	1.06620i	−0.486167	+	0.873866i	$0.661605\pi$
$47$	−10.0607	+	7.30949i	−1.46750	+	1.06620i	−0.981330	+	0.192333i	$0.938395\pi$
$48$	−1.00889	+	3.10503i	−0.145620	+	0.448172i
$49$	−1.24783	+	0.906600i	−0.178261	+	0.129514i
$50$	−3.33014	−	2.41949i	−0.470953	−	0.342167i
$51$	−2.38082	−	7.32742i	−0.333382	−	1.02604i
$52$	0.809017	+	0.587785i	0.112190	+	0.0815111i
$53$	−2.85905	+	8.79925i	−0.392721	+	1.20867i	0.538002	+	0.842944i	$0.319179\pi$
$53$	−2.85905	+	8.79925i	−0.392721	+	1.20867i	−0.930722	+	0.365727i	$0.880821\pi$
$54$	4.70046	−	14.4665i	0.639651	−	1.96864i
$55$	−1.33442	−	4.10693i	−0.179934	−	0.553779i
$56$	−2.92274			−0.390567
$57$	5.39326			0.714354
$58$	0.803420	+	2.47267i	0.105494	+	0.324678i
$59$	2.30310	−	1.67330i	0.299838	−	0.217845i	−0.427686	−	0.903928i	$-0.640671\pi$
$59$	2.30310	−	1.67330i	0.299838	−	0.217845i	0.727524	+	0.686082i	$0.240671\pi$
$60$	−2.48299	−	1.80400i	−0.320553	−	0.232895i
$61$	12.0484			1.54265			0.771323	−	0.636444i	$-0.219595\pi$
$61$	12.0484			1.54265			0.771323	+	0.636444i	$0.219595\pi$
$62$	−2.00040	−	5.19600i	−0.254051	−	0.659892i
$63$	22.3854			2.82030
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.760528	+	0.552556i	−0.0943319	+	0.0685362i
$66$	4.63442	+	14.2633i	0.570458	+	1.75569i
$67$	−8.72548			−1.06599			−0.532993	−	0.846119i	$-0.678933\pi$
$67$	−8.72548			−1.06599			−0.532993	+	0.846119i	$0.678933\pi$
$68$	2.35985			0.286174
$69$	−5.77506	−	17.7738i	−0.695235	−	2.13971i
$70$	0.849044	−	2.61309i	0.101480	−	0.312324i
$71$	−2.95805	+	9.10393i	−0.351056	+	1.08044i	0.607206	+	0.794545i	$0.292290\pi$
$71$	−2.95805	+	9.10393i	−0.351056	+	1.08044i	−0.958261	+	0.285893i	$0.907710\pi$
$72$	6.19631	+	4.50188i	0.730242	+	0.530552i
$73$	−0.682105	−	2.09930i	−0.0798344	−	0.245705i	0.903171	−	0.429280i	$-0.141233\pi$
$73$	−0.682105	−	2.09930i	−0.0798344	−	0.245705i	−0.983006	+	0.183576i	$0.941233\pi$
$74$	1.21287	+	0.881202i	0.140993	+	0.102438i
$75$	−10.8723	+	7.89920i	−1.25543	+	0.912121i
$76$	−0.510474	+	1.57108i	−0.0585554	+	0.180215i
$77$	−10.8618	+	7.89155i	−1.23782	+	0.899326i
$78$	2.64130	−	1.91901i	0.299068	−	0.217286i
$79$	3.45510	−	10.6337i	0.388730	−	1.19639i	−0.545009	−	0.838430i	$-0.683474\pi$
$79$	3.45510	−	10.6337i	0.388730	−	1.19639i	0.933738	−	0.357956i	$-0.116526\pi$
$80$	0.760528	−	0.552556i	0.0850297	−	0.0617777i
$81$	−21.5878	−	15.6845i	−2.39865	−	1.74272i
$82$	−0.931639	−	2.86729i	−0.102882	−	0.316639i
$83$	−6.90269	−	5.01510i	−0.757669	−	0.550479i	0.140526	−	0.990077i	$-0.455121\pi$
$83$	−6.90269	−	5.01510i	−0.757669	−	0.550479i	−0.898194	+	0.439599i	$0.855121\pi$
$84$	−2.94871	+	9.07519i	−0.321730	+	0.990184i
$85$	−0.685528	+	2.10984i	−0.0743560	+	0.228844i
$86$	−2.97727	−	9.16308i	−0.321047	−	0.988080i
$87$	8.48828			0.910039
$88$	−4.59361			−0.489680
$89$	−4.46505	−	13.7420i	−0.473294	−	1.45665i	−0.848245	−	0.529604i	$-0.822340\pi$
$89$	−4.46505	−	13.7420i	−0.473294	−	1.45665i	0.374951	−	0.927045i	$-0.377660\pi$
$90$	−5.82493	+	4.23206i	−0.614002	+	0.446098i
$91$	2.36455	+	1.71794i	0.247872	+	0.180089i
$92$	5.72420			0.596789
$93$	−18.1519	+	0.969133i	−1.88226	+	0.100494i
$94$	−12.4357			−1.28264
$95$	−1.25634	−	0.912784i	−0.128898	−	0.0936497i
$96$	−2.64130	+	1.91901i	−0.269576	+	0.195859i
$97$	1.21072	+	3.72621i	0.122930	+	0.378339i	0.993518	−	0.113673i	$-0.0362616\pi$
$97$	1.21072	+	3.72621i	0.122930	+	0.378339i	−0.870588	+	0.492012i	$0.836262\pi$
$98$	−1.54240			−0.155806
$99$	35.1827			3.53599
$100$	−1.27200	−	3.91481i	−0.127200	−	0.391481i
$101$	−5.17953	+	15.9410i	−0.515383	+	1.58618i	0.267202	+	0.963641i	$0.413901\pi$
$101$	−5.17953	+	15.9410i	−0.515383	+	1.58618i	−0.782585	+	0.622544i	$0.786099\pi$
$102$	2.38082	−	7.32742i	0.235737	−	0.725522i
$103$	9.17166	+	6.66360i	0.903710	+	0.656584i	0.939416	−	0.342778i	$-0.111368\pi$
$103$	9.17166	+	6.66360i	0.903710	+	0.656584i	−0.0357061	+	0.999362i	$0.511368\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$	−7.25713	−	5.27261i	−0.708223	−	0.514554i
$106$	−7.48509	+	5.43824i	−0.727016	+	0.528208i
$107$	−2.99605	+	9.22089i	−0.289639	+	0.891417i	0.695331	+	0.718690i	$0.255258\pi$
$107$	−2.99605	+	9.22089i	−0.289639	+	0.891417i	−0.984970	+	0.172727i	$0.944742\pi$
$108$	12.3060	−	8.94080i	1.18414	−	0.860329i
$109$	9.00689	−	6.54389i	0.862704	−	0.626791i	−0.0659155	−	0.997825i	$-0.520997\pi$
$109$	9.00689	−	6.54389i	0.862704	−	0.626791i	0.928619	+	0.371034i	$0.120997\pi$
$110$	1.33442	−	4.10693i	0.127232	−	0.391581i
$111$	3.95981	−	2.87697i	0.375848	−	0.273070i
$112$	−2.36455	−	1.71794i	−0.223429	−	0.162330i
$113$	2.69912	+	8.30702i	0.253911	+	0.781459i	0.994042	+	0.108996i	$0.0347636\pi$
$113$	2.69912	+	8.30702i	0.253911	+	0.781459i	−0.740131	+	0.672463i	$0.765236\pi$
$114$	4.36324	+	3.17008i	0.408655	+	0.296905i
$115$	−1.66286	+	5.11774i	−0.155062	+	0.477232i
$116$	−0.803420	+	2.47267i	−0.0745956	+	0.229582i
$117$	−2.36678	−	7.28420i	−0.218809	−	0.673424i
$118$	2.84679			0.262068
$119$	6.89724			0.632269
$120$	−0.948418	−	2.91893i	−0.0865783	−	0.266461i
$121$	−8.17205	+	5.93734i	−0.742914	+	0.539758i
$122$	9.74740	+	7.08190i	0.882488	+	0.641165i
$123$	−9.84294			−0.887508
$124$	1.43577	−	5.37946i	0.128936	−	0.483089i
$125$	8.56989			0.766514
$126$	18.1102	+	13.1578i	1.61338	+	1.17219i
$127$	−0.615947	+	0.447512i	−0.0546565	+	0.0397103i	−0.614778	−	0.788700i	$-0.710754\pi$
$127$	−0.615947	+	0.447512i	−0.0546565	+	0.0397103i	0.560122	+	0.828410i	$0.310754\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−31.4554			−2.76949
$130$	−0.940065			−0.0824491
$131$	3.34174	+	10.2848i	0.291969	+	0.898589i	0.984223	+	0.176935i	$0.0566181\pi$
$131$	3.34174	+	10.2848i	0.291969	+	0.898589i	−0.692253	+	0.721655i	$0.743382\pi$
$132$	−4.63442	+	14.2633i	−0.403375	+	1.24146i
$133$	−1.49198	+	4.59185i	−0.129371	+	0.398164i
$134$	−7.05906	−	5.12871i	−0.609810	−	0.443053i
$135$	4.41874	+	13.5995i	0.380304	+	1.17046i
$136$	1.90916	+	1.38709i	0.163709	+	0.118942i
$137$	11.9207	−	8.66086i	1.01845	−	0.739948i	0.0524858	−	0.998622i	$-0.483286\pi$
$137$	11.9207	−	8.66086i	1.01845	−	0.739948i	0.965965	+	0.258674i	$0.0832856\pi$
$138$	5.77506	−	17.7738i	0.491606	−	1.51301i
$139$	−3.53850	+	2.57087i	−0.300132	+	0.218058i	−0.727651	−	0.685948i	$-0.759388\pi$
$139$	−3.53850	+	2.57087i	−0.300132	+	0.218058i	0.427519	+	0.904006i	$0.359388\pi$
$140$	2.22283	−	1.61498i	0.187863	−	0.136490i
$141$	−12.5461	+	38.6131i	−1.05658	+	3.25181i
$142$	−7.74427	+	5.62654i	−0.649884	+	0.472169i
$143$	3.71630	+	2.70005i	0.310773	+	0.225790i
$144$	2.36678	+	7.28420i	0.197232	+	0.607017i
$145$	−1.97731	−	1.43660i	−0.164207	−	0.119303i
$146$	0.682105	−	2.09930i	0.0564514	−	0.173740i
$147$	−1.55610	+	4.78920i	−0.128345	+	0.395006i
$148$	0.463275	+	1.42581i	0.0380810	+	0.117201i
$149$	−11.4649			−0.939244			−0.469622	−	0.882868i	$-0.655610\pi$
$149$	−11.4649			−0.939244			−0.469622	+	0.882868i	$0.655610\pi$
$150$	−13.4389			−1.09728
$151$	3.49189	+	10.7469i	0.284166	+	0.874574i	0.986647	+	0.162871i	$0.0520755\pi$
$151$	3.49189	+	10.7469i	0.284166	+	0.874574i	−0.702481	+	0.711702i	$0.747924\pi$
$152$	−1.33644	+	0.970980i	−0.108400	+	0.0787569i
$153$	−14.6224	−	10.6238i	−1.18215	−	0.858882i
$154$	−13.4259			−1.08189
$155$	4.39244	+	2.84637i	0.352809	+	0.228626i
$156$	3.26482			0.261395
$157$	−2.23942	−	1.62703i	−0.178725	−	0.129852i	0.494826	−	0.868992i	$-0.335232\pi$
$157$	−2.23942	−	1.62703i	−0.178725	−	0.129852i	−0.673551	+	0.739141i	$0.735232\pi$
$158$	9.04558	−	6.57200i	0.719628	−	0.522840i
$159$	9.33429	+	28.7280i	0.740257	+	2.27828i
$160$	0.940065			0.0743186
$161$	16.7303			1.31853
$162$	−8.24582	−	25.3780i	−0.647853	−	1.99389i
$163$	−3.56464	+	10.9708i	−0.279204	+	0.859302i	0.708872	+	0.705337i	$0.249204\pi$
$163$	−3.56464	+	10.9708i	−0.279204	+	0.859302i	−0.988076	+	0.153965i	$0.950796\pi$
$164$	0.931639	−	2.86729i	0.0727488	−	0.223898i
$165$	−11.4059	−	8.28685i	−0.887946	−	0.645131i
$166$	−2.63659	−	8.11460i	−0.204639	−	0.629815i
$167$	11.4354	+	8.30832i	0.884899	+	0.642917i	0.934543	−	0.355850i	$-0.115809\pi$
$167$	11.4354	+	8.30832i	0.884899	+	0.642917i	−0.0496439	+	0.998767i	$0.515809\pi$
$168$	−7.71982	+	5.60878i	−0.595597	+	0.432726i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−1.79474	+	1.30395i	−0.137650	+	0.100009i
$171$	10.2359	−	7.43680i	0.782757	−	0.568706i
$172$	2.97727	−	9.16308i	0.227014	−	0.698678i
$173$	4.52476	−	3.28743i	0.344011	−	0.249938i	−0.402341	−	0.915490i	$-0.631803\pi$
$173$	4.52476	−	3.28743i	0.344011	−	0.249938i	0.746352	+	0.665551i	$0.231803\pi$
$174$	6.86716	+	4.98928i	0.520598	+	0.378237i
$175$	−3.71772	−	11.4420i	−0.281033	−	0.864932i
$176$	−3.71630	−	2.70005i	−0.280127	−	0.203524i
$177$	2.87209	−	8.83937i	0.215879	−	0.664408i
$178$	4.46505	−	13.7420i	0.334669	−	1.03001i
$179$	−5.31639	−	16.3622i	−0.397365	−	1.22297i	−0.927104	−	0.374804i	$-0.877710\pi$
$179$	−5.31639	−	16.3622i	−0.397365	−	1.22297i	0.529739	−	0.848161i	$-0.322290\pi$
$180$	−7.20001			−0.536657
$181$	2.61611			0.194454			0.0972268	−	0.995262i	$-0.469003\pi$
$181$	2.61611			0.194454			0.0972268	+	0.995262i	$0.469003\pi$
$182$	0.903176	+	2.77969i	0.0669478	+	0.206044i
$183$	31.8235	−	23.1211i	2.35246	−	1.70916i
$184$	4.63097	+	3.36460i	0.341400	+	0.248041i
$185$	−1.40934			−0.103616
$186$	−15.2548	−	9.88538i	−1.11854	−	0.724831i
$187$	10.8402			0.792717
$188$	−10.0607	−	7.30949i	−0.733748	−	0.533099i
$189$	35.9671	−	26.1316i	2.61622	−	1.90080i
$190$	−0.479879	−	1.47692i	−0.0348141	−	0.107147i
$191$	−27.3678			−1.98027			−0.990133	−	0.140130i	$-0.955248\pi$
$191$	−27.3678			−1.98027			−0.990133	+	0.140130i	$0.955248\pi$
$192$	−3.26482			−0.235618
$193$	−6.69151	−	20.5943i	−0.481665	−	1.48241i	−0.836753	−	0.547580i	$-0.815549\pi$
$193$	−6.69151	−	20.5943i	−0.481665	−	1.48241i	0.355088	−	0.934833i	$-0.384451\pi$
$194$	−1.21072	+	3.72621i	−0.0869245	+	0.267526i
$195$	−0.948418	+	2.91893i	−0.0679176	+	0.209029i
$196$	−1.24783	−	0.906600i	−0.0891306	−	0.0647571i
$197$	−3.53472	−	10.8788i	−0.251838	−	0.775079i	−0.994436	−	0.105341i	$-0.966407\pi$
$197$	−3.53472	−	10.8788i	−0.251838	−	0.775079i	0.742598	−	0.669738i	$-0.233593\pi$
$198$	28.4634	+	20.6799i	2.02281	+	1.46965i
$199$	17.6392	−	12.8156i	1.25041	−	0.908476i	0.252165	−	0.967684i	$-0.418858\pi$
$199$	17.6392	−	12.8156i	1.25041	−	0.908476i	0.998246	+	0.0592082i	$0.0188576\pi$
$200$	1.27200	−	3.91481i	0.0899440	−	0.276819i
$201$	−23.0466	+	16.7443i	−1.62558	+	1.18105i
$202$	−13.5602	+	9.85205i	−0.954092	+	0.693188i
$203$	−2.34819	+	7.22697i	−0.164810	+	0.507234i
$204$	6.23307	−	4.52859i	0.436402	−	0.317065i
$205$	2.29288	+	1.66587i	0.160141	+	0.116350i
$206$	3.50326	+	10.7819i	0.244084	+	0.751213i
$207$	−35.4689	−	25.7697i	−2.46526	−	1.79112i
$208$	−0.309017	+	0.951057i	−0.0214265	+	0.0659439i
$209$	−2.34492	+	7.21692i	−0.162201	+	0.499204i
$210$	−2.77198	−	8.53127i	−0.191285	−	0.588713i
$211$	6.00485			0.413391			0.206695	−	0.978405i	$-0.433729\pi$
$211$	6.00485			0.413391			0.206695	+	0.978405i	$0.433729\pi$
$212$	−9.25208			−0.635436
$213$	9.65750	+	29.7227i	0.661721	+	2.03657i
$214$	−7.84376	+	5.69883i	−0.536188	+	0.389564i
$215$	7.32741	+	5.32368i	0.499725	+	0.363072i
$216$	15.2110			1.03498
$217$	4.19639	−	15.7227i	0.284870	−	1.06733i
$218$	11.1331			0.754031
$219$	−5.83024	−	4.23591i	−0.393971	−	0.286237i
$220$	3.49357	−	2.53823i	0.235536	−	0.171127i
$221$	−0.729235	−	2.24435i	−0.0490537	−	0.150972i
$222$	4.89459			0.328503
$223$	−12.5373			−0.839558			−0.419779	−	0.907626i	$-0.637892\pi$
$223$	−12.5373			−0.839558			−0.419779	+	0.907626i	$0.637892\pi$
$224$	−0.903176	−	2.77969i	−0.0603460	−	0.185726i
$225$	−9.74232	+	29.9838i	−0.649488	+	1.99892i
$226$	−2.69912	+	8.30702i	−0.179543	+	0.552575i
$227$	−1.25645	−	0.912861i	−0.0833932	−	0.0605887i	0.545307	−	0.838236i	$-0.316413\pi$
$227$	−1.25645	−	0.912861i	−0.0833932	−	0.0605887i	−0.628701	+	0.777647i	$0.716413\pi$
$228$	1.66661	+	5.12929i	0.110374	+	0.339696i
$229$	6.01474	+	4.36996i	0.397465	+	0.288775i	0.768508	−	0.639841i	$-0.221000\pi$
$229$	6.01474	+	4.36996i	0.397465	+	0.288775i	−0.371043	+	0.928616i	$0.621000\pi$
$230$	−4.35341	+	3.16294i	−0.287056	+	0.208558i
$231$	−13.5452	+	41.6878i	−0.891209	+	2.74286i
$232$	−2.10338	+	1.52820i	−0.138094	+	0.100331i
$233$	15.3056	−	11.1202i	1.00270	−	0.728506i	0.0400371	−	0.999198i	$-0.487252\pi$
$233$	15.3056	−	11.1202i	1.00270	−	0.728506i	0.962666	+	0.270692i	$0.0872524\pi$
$234$	2.36678	−	7.28420i	0.154721	−	0.476183i
$235$	9.45767	−	6.87140i	0.616950	−	0.448240i
$236$	2.30310	+	1.67330i	0.149919	+	0.108923i
$237$	−11.2803	−	34.7172i	−0.732734	−	2.25512i
$238$	5.57998	+	4.05409i	0.361696	+	0.262788i
$239$	−2.16767	+	6.67140i	−0.140215	+	0.431537i	−0.996365	−	0.0851906i	$-0.972850\pi$
$239$	−2.16767	+	6.67140i	−0.140215	+	0.431537i	0.856150	+	0.516728i	$0.172850\pi$
$240$	0.948418	−	2.91893i	0.0612201	−	0.188416i
$241$	−8.91688	−	27.4433i	−0.574387	−	1.76778i	−0.638257	−	0.769823i	$-0.720344\pi$
$241$	−8.91688	−	27.4433i	−0.574387	−	1.76778i	0.0638702	−	0.997958i	$-0.479656\pi$
$242$	−10.1012			−0.649330
$243$	−41.4856			−2.66130
$244$	3.72317	+	11.4588i	0.238352	+	0.733572i
$245$	1.17304	−	0.852263i	0.0749427	−	0.0544491i
$246$	−7.96311	−	5.78554i	−0.507709	−	0.368872i
$247$	1.65193			0.105110
$248$	4.32353	−	3.50814i	0.274544	−	0.222767i
$249$	−27.8561			−1.76531
$250$	6.93319	+	5.03726i	0.438493	+	0.318584i
$251$	−1.19853	+	0.870786i	−0.0756508	+	0.0549635i	−0.624968	−	0.780651i	$-0.714888\pi$
$251$	−1.19853	+	0.870786i	−0.0756508	+	0.0549635i	0.549317	+	0.835614i	$0.314888\pi$
$252$	6.91748	+	21.2898i	0.435760	+	1.34113i
$253$	26.2947			1.65313
$254$	−0.761353			−0.0477715
$255$	2.23813	+	6.88825i	0.140157	+	0.431359i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.0620153	+	0.190863i	−0.00386841	+	0.0119057i	−0.952972	−	0.303058i	$-0.901992\pi$
$257$	−0.0620153	+	0.190863i	−0.00386841	+	0.0119057i	0.949104	+	0.314964i	$0.101992\pi$
$258$	−25.4479	−	18.4890i	−1.58432	−	1.15107i
$259$	1.35403	+	4.16728i	0.0841355	+	0.258942i
$260$	−0.760528	−	0.552556i	−0.0471660	−	0.0342681i
$261$	16.1099	−	11.7045i	0.997179	−	0.724493i
$262$	−3.34174	+	10.2848i	−0.206454	+	0.635399i
$263$	−16.1955	+	11.7667i	−0.998656	+	0.725566i	−0.961800	−	0.273754i	$-0.911734\pi$
$263$	−16.1955	+	11.7667i	−0.998656	+	0.725566i	−0.0368565	+	0.999321i	$0.511734\pi$
$264$	−12.1331	+	8.81519i	−0.746739	+	0.542538i
$265$	2.68769	−	8.27187i	0.165104	−	0.508137i
$266$	−3.90606	+	2.83792i	−0.239496	+	0.174004i
$267$	−38.1646	−	27.7282i	−2.33564	−	1.69694i
$268$	−2.69632	−	8.29842i	−0.164704	−	0.506907i
$269$	−3.20305	−	2.32715i	−0.195294	−	0.141889i	0.485841	−	0.874047i	$-0.338513\pi$
$269$	−3.20305	−	2.32715i	−0.195294	−	0.141889i	−0.681135	+	0.732158i	$0.738513\pi$
$270$	−4.41874	+	13.5995i	−0.268916	+	0.827637i
$271$	1.54854	−	4.76592i	0.0940672	−	0.289509i	−0.892942	−	0.450171i	$-0.851363\pi$
$271$	1.54854	−	4.76592i	0.0940672	−	0.289509i	0.987009	+	0.160662i	$0.0513629\pi$
$272$	0.729235	+	2.24435i	0.0442164	+	0.136084i
$273$	9.54222			0.577521
$274$	14.7347			0.890158
$275$	−5.84307	−	17.9831i	−0.352350	−	1.08442i
$276$	15.1193	−	10.9848i	0.910075	−	0.661208i
$277$	24.7491	+	17.9813i	1.48703	+	1.08039i	0.975205	+	0.221304i	$0.0710312\pi$
$277$	24.7491	+	17.9813i	1.48703	+	1.08039i	0.511827	+	0.859088i	$0.328969\pi$
$278$	−4.37383			−0.262325
$279$	−33.1142	+	26.8691i	−1.98249	+	1.60861i
$280$	2.74756			0.164198
$281$	−14.1515	−	10.2817i	−0.844209	−	0.613354i	0.0793342	−	0.996848i	$-0.474721\pi$
$281$	−14.1515	−	10.2817i	−0.844209	−	0.613354i	−0.923543	+	0.383494i	$0.874721\pi$
$282$	−32.8462	+	23.8642i	−1.95596	+	1.42109i
$283$	−9.96974	−	30.6837i	−0.592639	−	1.82396i	−0.566142	−	0.824308i	$-0.691565\pi$
$283$	−9.96974	−	30.6837i	−0.592639	−	1.82396i	−0.0264972	−	0.999649i	$-0.508435\pi$
$284$	−9.57244			−0.568020
$285$	−5.07001			−0.300322
$286$	1.41950	+	4.36878i	0.0839369	+	0.258331i
$287$	2.72294	−	8.38034i	0.160730	−	0.494676i
$288$	−2.36678	+	7.28420i	−0.139464	+	0.429226i
$289$	9.24795	+	6.71903i	0.543997	+	0.395237i
$290$	−0.755267	−	2.32447i	−0.0443508	−	0.136498i
$291$	10.3485	+	7.51863i	0.606640	+	0.440750i
$292$	1.78577	−	1.29744i	0.104505	−	0.0759270i
$293$	−0.863101	+	2.65635i	−0.0504229	+	0.155186i	−0.973097	−	0.230394i	$-0.925999\pi$
$293$	−0.863101	+	2.65635i	−0.0504229	+	0.155186i	0.922675	+	0.385580i	$0.125999\pi$
$294$	−4.07394	+	2.95989i	−0.237597	+	0.172624i
$295$	−2.16507	+	1.57301i	−0.126055	+	0.0915843i
$296$	−0.463275	+	1.42581i	−0.0269273	+	0.0828738i
$297$	56.5287	−	41.0705i	3.28013	−	2.38315i
$298$	−9.27532	−	6.73892i	−0.537305	−	0.390375i
$299$	−1.76887	−	5.44403i	−0.102297	−	0.314837i
$300$	−10.8723	−	7.89920i	−0.627713	−	0.456060i
$301$	8.70177	−	26.7813i	0.501562	−	1.54365i
$302$	−3.49189	+	10.7469i	−0.200936	+	0.618417i
$303$	16.9102	+	52.0444i	0.971468	+	2.98987i
$304$	−1.65193			−0.0947447
$305$	−11.3263			−0.648543
$306$	−5.58526	−	17.1896i	−0.319288	−	0.982667i
$307$	13.6804	−	9.93942i	0.780784	−	0.567272i	−0.124431	−	0.992228i	$-0.539710\pi$
$307$	13.6804	−	9.93942i	0.780784	−	0.567272i	0.905214	+	0.424956i	$0.139710\pi$
$308$	−10.8618	−	7.89155i	−0.618908	−	0.449663i
$309$	37.0126			2.10557
$310$	1.88051	+	4.88458i	0.106806	+	0.277425i
$311$	14.3719			0.814958			0.407479	−	0.913215i	$-0.366408\pi$
$311$	14.3719			0.814958			0.407479	+	0.913215i	$0.366408\pi$
$312$	2.64130	+	1.91901i	0.149534	+	0.108643i
$313$	−14.8663	+	10.8010i	−0.840293	+	0.610509i	−0.922453	−	0.386110i	$-0.873818\pi$
$313$	−14.8663	+	10.8010i	−0.840293	+	0.610509i	0.0821594	+	0.996619i	$0.473818\pi$
$314$	−0.855383	−	2.63260i	−0.0482720	−	0.148566i
$315$	−21.0438			−1.18568
$316$	11.1809			0.628978
$317$	−2.28511	−	7.03284i	−0.128344	−	0.395004i	0.866151	−	0.499782i	$-0.166587\pi$
$317$	−2.28511	−	7.03284i	−0.128344	−	0.395004i	−0.994496	+	0.104779i	$0.966587\pi$
$318$	−9.33429	+	28.7280i	−0.523441	+	1.61099i
$319$	−3.69059	+	11.3585i	−0.206634	+	0.635953i
$320$	0.760528	+	0.552556i	0.0425148	+	0.0308888i
$321$	9.78157	+	30.1046i	0.545954	+	1.68027i
$322$	13.5351	+	9.83384i	0.754283	+	0.548018i
$323$	3.15380	−	2.29137i	0.175482	−	0.127495i
$324$	8.24582	−	25.3780i	0.458101	−	1.40989i
$325$	−3.33014	+	2.41949i	−0.184723	+	0.134209i
$326$	−9.33234	+	6.78034i	−0.516871	+	0.375529i
$327$	11.2321	−	34.5687i	0.621134	−	1.91165i
$328$	2.43906	−	1.77208i	0.134675	−	0.0978469i
$329$	−29.4047	−	21.3637i	−1.62113	−	1.17782i
$330$	−4.35666	−	13.4084i	−0.239826	−	0.738109i
$331$	10.2266	+	7.43003i	0.562103	+	0.408391i	0.832228	−	0.554434i	$-0.187065\pi$
$331$	10.2266	+	7.43003i	0.562103	+	0.408391i	−0.270125	+	0.962825i	$0.587065\pi$
$332$	2.63659	−	8.11460i	0.144702	−	0.445346i
$333$	3.54825	−	10.9204i	0.194443	−	0.598434i
$334$	4.36794	+	13.4431i	0.239003	+	0.735576i
$335$	8.20252			0.448151
$336$	−9.54222			−0.520571
$337$	4.83913	+	14.8933i	0.263604	+	0.811291i	0.992012	+	0.126147i	$0.0402609\pi$
$337$	4.83913	+	14.8933i	0.263604	+	0.811291i	−0.728407	+	0.685144i	$0.759739\pi$
$338$	0.809017	−	0.587785i	0.0440047	−	0.0319713i
$339$	23.0705	+	16.7617i	1.25302	+	0.910369i
$340$	−2.21842			−0.120310
$341$	6.59538	−	24.7111i	0.357160	−	1.33818i
$342$	12.6522			0.684154
$343$	12.9047	+	9.37584i	0.696791	+	0.506248i
$344$	7.79458	−	5.66309i	0.420256	−	0.305334i
$345$	5.42893	+	16.7085i	0.292284	+	0.899557i
$346$	5.59291			0.300676
$347$	−6.26216			−0.336170			−0.168085	−	0.985772i	$-0.553758\pi$
$347$	−6.26216			−0.336170			−0.168085	+	0.985772i	$0.553758\pi$
$348$	2.62302	+	8.07283i	0.140609	+	0.432749i
$349$	−0.0440075	+	0.135441i	−0.00235567	+	0.00725000i	−0.952227	−	0.305390i	$-0.901213\pi$
$349$	−0.0440075	+	0.135441i	−0.00235567	+	0.00725000i	0.949872	+	0.312640i	$0.101213\pi$
$350$	3.71772	−	11.4420i	0.198721	−	0.611599i
$351$	−12.3060	−	8.94080i	−0.656844	−	0.477225i
$352$	−1.41950	−	4.36878i	−0.0756597	−	0.232857i
$353$	14.3298	+	10.4112i	0.762699	+	0.554133i	0.899737	−	0.436433i	$-0.143758\pi$
$353$	14.3298	+	10.4112i	0.762699	+	0.554133i	−0.137038	+	0.990566i	$0.543758\pi$
$354$	7.51922	−	5.46303i	0.399642	−	0.290357i
$355$	2.78076	−	8.55829i	0.147587	−	0.454227i
$356$	11.6896	−	8.49302i	0.619550	−	0.450129i
$357$	18.2176	−	13.2359i	0.964180	−	0.700518i
$358$	5.31639	−	16.3622i	0.280980	−	0.864767i
$359$	5.18864	−	3.76977i	0.273846	−	0.198961i	−0.442383	−	0.896826i	$-0.645867\pi$
$359$	5.18864	−	3.76977i	0.273846	−	0.198961i	0.716229	+	0.697866i	$0.245867\pi$
$360$	−5.82493	−	4.23206i	−0.307001	−	0.223049i
$361$	−5.02805	−	15.4748i	−0.264634	−	0.814461i
$362$	2.11647	+	1.53771i	0.111239	+	0.0808202i
$363$	−10.1910	+	31.3646i	−0.534887	+	1.64621i
$364$	−0.903176	+	2.77969i	−0.0473393	+	0.145695i
$365$	0.641223	+	1.97348i	0.0335632	+	0.103297i
$366$	39.3360			2.05613
$367$	10.0213			0.523109			0.261555	−	0.965189i	$-0.415765\pi$
$367$	10.0213			0.523109			0.261555	+	0.965189i	$0.415765\pi$
$368$	1.76887	+	5.44403i	0.0922089	+	0.283790i
$369$	−18.6809	+	13.5725i	−0.972490	+	0.706556i
$370$	−1.14018	−	0.828387i	−0.0592750	−	0.0430658i
$371$	−27.0414			−1.40392
$372$	−6.53095	−	16.9640i	−0.338614	−	0.879543i
$373$	−9.43298			−0.488421			−0.244211	−	0.969722i	$-0.578529\pi$
$373$	−9.43298			−0.488421			−0.244211	+	0.969722i	$0.578529\pi$
$374$	8.76994	+	6.37173i	0.453483	+	0.329474i
$375$	22.6356	−	16.4457i	1.16890	−	0.849255i
$376$	−3.84283	−	11.8270i	−0.198179	−	0.609931i
$377$	2.59992			0.133903
$378$	44.4578			2.28666
$379$	0.478999	+	1.47421i	0.0246045	+	0.0757250i	0.962605	−	0.270910i	$-0.0873244\pi$
$379$	0.478999	+	1.47421i	0.0246045	+	0.0757250i	−0.938000	+	0.346635i	$0.887324\pi$
$380$	0.479879	−	1.47692i	0.0246173	−	0.0757642i
$381$	−0.768118	+	2.36402i	−0.0393519	+	0.121113i
$382$	−22.1410	−	16.0864i	−1.13283	−	0.823052i
$383$	10.6844	+	32.8833i	0.545949	+	1.68026i	0.718724	+	0.695296i	$0.244727\pi$
$383$	10.6844	+	32.8833i	0.545949	+	1.68026i	−0.172775	+	0.984961i	$0.555273\pi$
$384$	−2.64130	−	1.91901i	−0.134788	−	0.0979293i
$385$	10.2108	−	7.41857i	0.520390	−	0.378085i
$386$	6.69151	−	20.5943i	0.340589	−	1.04822i
$387$	−59.6992	+	43.3740i	−3.03468	+	2.20482i
$388$	−3.16970	+	2.30292i	−0.160917	+	0.116913i
$389$	−0.532604	+	1.63919i	−0.0270041	+	0.0831101i	−0.963650	−	0.267167i	$-0.913913\pi$
$389$	−0.532604	+	1.63919i	−0.0270041	+	0.0831101i	0.936646	+	0.350277i	$0.113913\pi$
$390$	−2.48299	+	1.80400i	−0.125731	+	0.0913490i
$391$	−10.9284	−	7.93996i	−0.552674	−	0.401541i
$392$	−0.476628	−	1.46691i	−0.0240733	−	0.0740901i
$393$	28.5633	+	20.7524i	1.44083	+	1.04682i
$394$	3.53472	−	10.8788i	0.178077	−	0.548064i
$395$	−3.24802	+	9.99638i	−0.163426	+	0.502973i
$396$	10.8721	+	33.4607i	0.546341	+	1.68147i
$397$	9.71506			0.487585			0.243792	−	0.969827i	$-0.421608\pi$
$397$	9.71506			0.487585			0.243792	+	0.969827i	$0.421608\pi$
$398$	21.8033			1.09290
$399$	4.87106	+	14.9916i	0.243858	+	0.750518i
$400$	3.33014	−	2.41949i	0.166507	−	0.120974i
$401$	3.98672	+	2.89653i	0.199088	+	0.144646i	0.682863	−	0.730547i	$-0.260735\pi$
$401$	3.98672	+	2.89653i	0.199088	+	0.144646i	−0.483775	+	0.875192i	$0.660735\pi$
$402$	−28.4871			−1.42081
$403$	−5.55985	+	0.296841i	−0.276956	+	0.0147867i
$404$	−16.7613			−0.833907
$405$	20.2940	+	14.7444i	1.00842	+	0.732656i
$406$	−6.14763	+	4.46651i	−0.305102	+	0.221669i
$407$	2.12810	+	6.54963i	0.105486	+	0.324653i
$408$	7.70450			0.381430
$409$	5.45781			0.269871			0.134936	−	0.990854i	$-0.456917\pi$
$409$	5.45781			0.269871			0.134936	+	0.990854i	$0.456917\pi$
$410$	0.875801	+	2.69544i	0.0432527	+	0.133118i
$411$	14.8657	−	45.7518i	0.733269	−	2.25677i
$412$	−3.50326	+	10.7819i	−0.172593	+	0.531187i
$413$	6.73137	+	4.89062i	0.331229	+	0.240652i
$414$	−13.5479	−	41.6962i	−0.665844	−	2.04926i
$415$	6.48898	+	4.71452i	0.318531	+	0.231427i
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$	−4.41269	+	13.5809i	−0.216090	+	0.665058i
$418$	−6.13908	+	4.46030i	−0.300272	+	0.218160i
$419$	15.5399	−	11.2904i	0.759175	−	0.551573i	−0.139482	−	0.990225i	$-0.544544\pi$
$419$	15.5399	−	11.2904i	0.759175	−	0.551573i	0.898657	+	0.438652i	$0.144544\pi$
$420$	2.77198	−	8.53127i	0.135259	−	0.416283i
$421$	12.2829	−	8.92405i	0.598632	−	0.434932i	−0.246761	−	0.969076i	$-0.579366\pi$
$421$	12.2829	−	8.92405i	0.598632	−	0.434932i	0.845393	+	0.534145i	$0.179366\pi$
$422$	4.85802	+	3.52956i	0.236485	+	0.171816i
$423$	29.4324	+	90.5838i	1.43105	+	4.40433i
$424$	−7.48509	−	5.43824i	−0.363508	−	0.264104i
$425$	−3.00173	+	9.23839i	−0.145605	+	0.448128i
$426$	−9.65750	+	29.7227i	−0.467907	+	1.44007i
$427$	10.8819	+	33.4909i	0.526610	+	1.62074i
$428$	−9.69542			−0.468646
$429$	14.9973			0.724077
$430$	2.79882	+	8.61389i	0.134971	+	0.415399i
$431$	10.3794	−	7.54104i	0.499956	−	0.363239i	−0.309044	−	0.951048i	$-0.600009\pi$
$431$	10.3794	−	7.54104i	0.499956	−	0.363239i	0.809000	+	0.587808i	$0.200009\pi$
$432$	12.3060	+	8.94080i	0.592071	+	0.430165i
$433$	38.7781			1.86356			0.931778	−	0.363029i	$-0.118258\pi$
$433$	38.7781			1.86356			0.931778	+	0.363029i	$0.118258\pi$
$434$	12.6366	−	10.2534i	0.606574	−	0.492178i
$435$	−7.97953			−0.382589
$436$	9.00689	+	6.54389i	0.431352	+	0.313395i
$437$	7.65004	−	5.55808i	0.365951	−	0.265879i
$438$	−2.22695	−	6.85385i	−0.106408	−	0.327490i
$439$	−4.39383			−0.209706			−0.104853	−	0.994488i	$-0.533437\pi$
$439$	−4.39383			−0.209706			−0.104853	+	0.994488i	$0.533437\pi$
$440$	4.31829			0.205866
$441$	3.65052	+	11.2351i	0.173834	+	0.535007i
$442$	0.729235	−	2.24435i	0.0346862	−	0.106753i
$443$	−4.97738	+	15.3188i	−0.236482	+	0.727818i	0.760439	+	0.649410i	$0.224984\pi$
$443$	−4.97738	+	15.3188i	−0.236482	+	0.727818i	−0.996921	+	0.0784086i	$0.975016\pi$
$444$	3.95981	+	2.87697i	0.187924	+	0.136535i
$445$	4.19743	+	12.9184i	0.198977	+	0.612389i
$446$	−10.1429	−	7.36923i	−0.480279	−	0.348943i
$447$	−30.2823	+	22.0014i	−1.43230	+	1.04063i
$448$	0.903176	−	2.77969i	0.0426710	−	0.131328i
$449$	−29.6101	+	21.5130i	−1.39739	+	1.01526i	−0.402377	+	0.915474i	$0.631816\pi$
$449$	−29.6101	+	21.5130i	−1.39739	+	1.01526i	−0.995009	+	0.0997865i	$0.968184\pi$
$450$	−25.5057	+	18.5310i	−1.20235	+	0.873560i
$451$	4.27958	−	13.1712i	0.201518	−	0.620208i
$452$	−7.06638	+	5.13402i	−0.332374	+	0.241484i
$453$	29.8467	+	21.6849i	1.40232	+	1.01884i
$454$	−0.479919	−	1.47704i	−0.0225237	−	0.0693209i
$455$	−2.22283	−	1.61498i	−0.104208	−	0.0757113i
$456$	−1.66661	+	5.12929i	−0.0780461	+	0.240201i
$457$	−9.82220	+	30.2296i	−0.459463	+	1.41408i	0.406352	+	0.913717i	$0.366801\pi$
$457$	−9.82220	+	30.2296i	−0.459463	+	1.41408i	−0.865815	+	0.500365i	$0.833199\pi$
$458$	2.29742	+	7.07075i	0.107352	+	0.330394i
$459$	−35.8957			−1.67547
$460$	−5.38111			−0.250896
$461$	2.99041	+	9.20352i	0.139277	+	0.428651i	0.996231	−	0.0867427i	$-0.0276458\pi$
$461$	2.99041	+	9.20352i	0.139277	+	0.428651i	−0.856954	+	0.515393i	$0.827646\pi$
$462$	−35.4618	+	25.7645i	−1.64983	+	1.19867i
$463$	−23.4866	−	17.0640i	−1.09151	−	0.793032i	−0.111860	−	0.993724i	$-0.535681\pi$
$463$	−23.4866	−	17.0640i	−1.09151	−	0.793032i	−0.979654	+	0.200692i	$0.935681\pi$
$464$	−2.59992			−0.120698
$465$	17.0640	−	0.911048i	0.791323	−	0.0422488i
$466$	18.9188			0.876395
$467$	26.2588	+	19.0781i	1.21511	+	0.882830i	0.995685	−	0.0927993i	$-0.0295815\pi$
$467$	26.2588	+	19.0781i	1.21511	+	0.882830i	0.219426	+	0.975629i	$0.429581\pi$
$468$	6.19631	−	4.50188i	0.286425	−	0.208100i
$469$	−7.88064	−	24.2541i	−0.363894	−	1.11995i
$470$	11.6903			0.539234
$471$	−9.03728			−0.416416
$472$	0.879707	+	2.70746i	0.0404918	+	0.124621i
$473$	13.6764	−	42.0916i	0.628841	−	1.93537i
$474$	11.2803	−	34.7172i	0.518121	−	1.59461i
$475$	−5.50116	−	3.99682i	−0.252410	−	0.183387i
$476$	2.13136	+	6.55966i	0.0976909	+	0.300662i
$477$	57.3288	+	41.6518i	2.62490	+	1.90710i
$478$	−5.67504	+	4.12315i	−0.259570	+	0.188589i
$479$	−4.26516	+	13.1268i	−0.194880	+	0.599779i	0.805098	+	0.593142i	$0.202113\pi$
$479$	−4.26516	+	13.1268i	−0.194880	+	0.599779i	−0.999978	+	0.00663710i	$0.997887\pi$
$480$	2.48299	−	1.80400i	0.113332	−	0.0823408i
$481$	1.21287	−	0.881202i	0.0553021	−	0.0401793i
$482$	8.91688	−	27.4433i	0.406153	−	1.25001i
$483$	44.1897	−	32.1057i	2.01070	−	1.46086i
$484$	−8.17205	−	5.93734i	−0.371457	−	0.269879i
$485$	−1.13815	−	3.50288i	−0.0516809	−	0.159057i
$486$	−33.5625	−	24.3846i	−1.52243	−	1.10611i
$487$	−4.16123	+	12.8069i	−0.188563	+	0.580338i	−0.999992	−	0.00411400i	$-0.998690\pi$
$487$	−4.16123	+	12.8069i	−0.188563	+	0.580338i	0.811428	+	0.584452i	$0.198690\pi$
$488$	−3.72317	+	11.4588i	−0.168540	+	0.518713i
$489$	11.6379	+	35.8178i	0.526284	+	1.61974i
$490$	1.44996			0.0655023
$491$	−5.59480			−0.252490			−0.126245	−	0.991999i	$-0.540293\pi$
$491$	−5.59480			−0.252490			−0.126245	+	0.991999i	$0.540293\pi$
$492$	−3.04164	−	9.36119i	−0.137128	−	0.422035i
$493$	4.96367	−	3.60632i	0.223552	−	0.162420i
$494$	1.33644	+	0.970980i	0.0601293	+	0.0436865i
$495$	−33.0740			−1.48657
$496$	5.55985	−	0.296841i	0.249644	−	0.0133286i
$497$	−27.9777			−1.25497
$498$	−22.5361	−	16.3734i	−1.00986	−	0.733710i
$499$	31.1503	−	22.6320i	1.39448	−	1.01315i	0.399122	−	0.916898i	$-0.369315\pi$
$499$	31.1503	−	22.6320i	1.39448	−	1.01315i	0.995357	−	0.0962506i	$-0.0306850\pi$
$500$	2.64824	+	8.15045i	0.118433	+	0.364499i
$501$	46.1481			2.06175
$502$	−1.48147			−0.0661212
$503$	1.88353	+	5.79692i	0.0839826	+	0.258472i	0.984226	−	0.176915i	$-0.0566117\pi$
$503$	1.88353	+	5.79692i	0.0839826	+	0.258472i	−0.900244	+	0.435387i	$0.856612\pi$
$504$	−6.91748	+	21.2898i	−0.308129	+	0.948324i
$505$	4.86909	−	14.9855i	0.216672	−	0.666847i
$506$	21.2729	+	15.4556i	0.945694	+	0.687087i
$507$	−1.00889	−	3.10503i	−0.0448062	−	0.137899i
$508$	−0.615947	−	0.447512i	−0.0273282	−	0.0198551i
$509$	−27.1887	+	19.7538i	−1.20512	+	0.875570i	−0.994778	−	0.102059i	$-0.967457\pi$
$509$	−27.1887	+	19.7538i	−1.20512	+	0.875570i	−0.210340	+	0.977628i	$0.567457\pi$
$510$	−2.23813	+	6.88825i	−0.0991059	+	0.305017i
$511$	5.21935	−	3.79208i	0.230891	−	0.167752i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	7.76483	−	23.8977i	0.342826	−	1.05511i
$514$	−0.162358	+	0.117960i	−0.00716131	+	0.00520299i
$515$	−8.62195	−	6.26421i	−0.379929	−	0.276034i
$516$	−9.72024	−	29.9158i	−0.427910	−	1.31697i
$517$	−46.2147	−	33.5769i	−2.03252	−	1.47671i
$518$	−1.35403	+	4.16728i	−0.0594928	+	0.183100i
$519$	5.64260	−	17.3661i	0.247683	−	0.762289i
$520$	−0.290496	−	0.894055i	−0.0127391	−	0.0392069i
$521$	26.4449			1.15857			0.579287	−	0.815124i	$-0.303331\pi$
$521$	26.4449			1.15857			0.579287	+	0.815124i	$0.303331\pi$
$522$	19.9130			0.871566
$523$	8.09962	+	24.9281i	0.354172	+	1.09003i	0.956488	+	0.291771i	$0.0942445\pi$
$523$	8.09962	+	24.9281i	0.354172	+	1.09003i	−0.602317	+	0.798257i	$0.705755\pi$
$524$	−8.74880	+	6.35637i	−0.382193	+	0.277679i
$525$	−31.7769	−	23.0873i	−1.38686	−	1.00761i
$526$	−20.0187			−0.872857
$527$	−10.2029	+	8.27871i	−0.444445	+	0.360626i
$528$	−14.9973			−0.652674
$529$	−7.90120	−	5.74056i	−0.343530	−	0.249589i
$530$	7.03647	−	5.11230i	0.305645	−	0.222064i
$531$	−6.73773	−	20.7366i	−0.292393	−	0.899892i
$532$	−4.82816			−0.209327
$533$	−3.01485			−0.130588
$534$	−14.5776	−	44.8652i	−0.630834	−	1.94151i
$535$	2.81648	−	8.66824i	0.121767	−	0.374761i
$536$	2.69632	−	8.29842i	0.116463	−	0.358437i
$537$	−45.4414	−	33.0151i	−1.96094	−	1.42471i
$538$	−1.22346	−	3.76541i	−0.0527470	−	0.162339i
$539$	−5.73203	−	4.16456i	−0.246896	−	0.179380i
$540$	−11.5684	+	8.40493i	−0.497825	+	0.361691i
$541$	−0.603243	+	1.85659i	−0.0259354	+	0.0798211i	−0.963186	−	0.268834i	$-0.913362\pi$
$541$	−0.603243	+	1.85659i	−0.0259354	+	0.0798211i	0.937251	+	0.348655i	$0.113362\pi$
$542$	4.05414	−	2.94550i	0.174140	−	0.126520i
$543$	6.90991	−	5.02035i	0.296533	−	0.215444i
$544$	−0.729235	+	2.24435i	−0.0312657	+	0.0962259i
$545$	−8.46706	+	6.15168i	−0.362689	+	0.263509i
$546$	7.71982	+	5.60878i	0.330378	+	0.240033i
$547$	−9.40662	−	28.9506i	−0.402198	−	1.23784i	−0.923212	−	0.384290i	$-0.874446\pi$
$547$	−9.40662	−	28.9506i	−0.402198	−	1.23784i	0.521015	−	0.853548i	$-0.325554\pi$
$548$	11.9207	+	8.66086i	0.509225	+	0.369974i
$549$	28.5160	−	87.7633i	1.21703	−	3.74565i
$550$	5.84307	−	17.9831i	0.249149	−	0.766802i
$551$	1.32719	+	4.08468i	0.0565403	+	0.174013i
$552$	18.6885			0.795434
$553$	32.6790			1.38965
$554$	9.45333	+	29.0944i	0.401634	+	1.23610i
$555$	−3.72247	+	2.70454i	−0.158010	+	0.114801i
$556$	−3.53850	−	2.57087i	−0.150066	−	0.109029i
$557$	19.6453			0.832399			0.416200	−	0.909273i	$-0.363362\pi$
$557$	19.6453			0.832399			0.416200	+	0.909273i	$0.363362\pi$
$558$	−42.5832	+	2.27352i	−1.80269	+	0.0962459i
$559$	−9.63463			−0.407502
$560$	2.22283	+	1.61498i	0.0939315	+	0.0682452i
$561$	28.6323	−	20.8026i	1.20886	−	0.878285i
$562$	−5.40540	−	16.6361i	−0.228013	−	0.701752i
$563$	29.7419			1.25347			0.626735	−	0.779232i	$-0.284391\pi$
$563$	29.7419			1.25347			0.626735	+	0.779232i	$0.284391\pi$
$564$	−40.6002			−1.70958
$565$	−2.53734	−	7.80914i	−0.106747	−	0.328533i
$566$	9.96974	−	30.6837i	0.419059	−	1.28973i
$567$	24.1004	−	74.1733i	1.01212	−	3.11499i
$568$	−7.74427	−	5.62654i	−0.324942	−	0.236084i
$569$	−10.6768	−	32.8599i	−0.447595	−	1.37756i	−0.879612	−	0.475692i	$-0.842198\pi$
$569$	−10.6768	−	32.8599i	−0.447595	−	1.37756i	0.432017	−	0.901866i	$-0.357802\pi$
$570$	−4.10172	−	2.98008i	−0.171802	−	0.124822i
$571$	−11.3357	+	8.23589i	−0.474385	+	0.344661i	−0.799148	−	0.601134i	$-0.794716\pi$
$571$	−11.3357	+	8.23589i	−0.474385	+	0.344661i	0.324763	+	0.945796i	$0.394716\pi$
$572$	−1.41950	+	4.36878i	−0.0593524	+	0.182668i
$573$	−72.2865	+	52.5192i	−3.01981	+	2.19402i
$574$	7.12874	−	5.17934i	0.297548	−	0.216181i
$575$	−7.28118	+	22.4092i	−0.303646	+	0.934526i
$576$	−6.19631	+	4.50188i	−0.258180	+	0.187578i
$577$	−17.7267	−	12.8792i	−0.737972	−	0.536168i	0.154104	−	0.988055i	$-0.450751\pi$
$577$	−17.7267	−	12.8792i	−0.737972	−	0.536168i	−0.892075	+	0.451887i	$0.850751\pi$
$578$	3.53240	+	10.8716i	0.146929	+	0.452199i
$579$	−57.1951	−	41.5547i	−2.37695	−	1.72695i
$580$	0.755267	−	2.32447i	0.0313607	−	0.0965184i
$581$	7.70607	−	23.7169i	0.319702	−	0.983941i
$582$	3.95278	+	12.1654i	0.163848	+	0.504272i
$583$	−42.5004			−1.76019
$584$	2.20734			0.0913403
$585$	2.22493	+	6.84762i	0.0919894	+	0.283114i
$586$	−2.25963	+	1.64172i	−0.0933444	+	0.0678187i
$587$	22.8062	+	16.5697i	0.941312	+	0.683903i	0.948736	−	0.316069i	$-0.102363\pi$
$587$	22.8062	+	16.5697i	0.941312	+	0.683903i	−0.00742425	+	0.999972i	$0.502363\pi$
$588$	−5.03566			−0.207667
$589$	−3.30452	−	8.58343i	−0.136160	−	0.353674i
$590$	−2.67617			−0.110176
$591$	−30.2127	−	21.9508i	−1.24279	−	0.902936i
$592$	−1.21287	+	0.881202i	−0.0498487	+	0.0362172i
$593$	13.2320	+	40.7240i	0.543374	+	1.67233i	0.724824	+	0.688934i	$0.241921\pi$
$593$	13.2320	+	40.7240i	0.543374	+	1.67233i	−0.181450	+	0.983400i	$0.558079\pi$
$594$	69.8733			2.86694
$595$	−6.48385			−0.265812
$596$	−3.54286	−	10.9038i	−0.145121	−	0.446637i
$597$	21.9970	−	67.6998i	0.900277	−	2.77077i
$598$	1.76887	−	5.44403i	0.0723346	−	0.222623i
$599$	20.8539	+	15.1512i	0.852066	+	0.619062i	0.925715	−	0.378222i	$-0.123464\pi$
$599$	20.8539	+	15.1512i	0.852066	+	0.619062i	−0.0736490	+	0.997284i	$0.523464\pi$
$600$	−4.15285	−	12.7812i	−0.169540	−	0.521789i
$601$	17.9002	+	13.0052i	0.730163	+	0.530494i	0.889615	−	0.456711i	$-0.150973\pi$
$601$	17.9002	+	13.0052i	0.730163	+	0.530494i	−0.159452	+	0.987206i	$0.550973\pi$
$602$	22.7815	−	16.5517i	0.928506	−	0.674599i
$603$	−20.6513	+	63.5581i	−0.840985	+	2.58829i
$604$	−9.14189	+	6.64198i	−0.371978	+	0.270258i
$605$	7.68226	−	5.58149i	0.312328	−	0.226920i
$606$	−16.9102	+	52.0444i	−0.686932	+	2.11416i
$607$	−25.1579	+	18.2783i	−1.02113	+	0.741893i	−0.966514	−	0.256614i	$-0.917393\pi$
$607$	−25.1579	+	18.2783i	−1.02113	+	0.741893i	−0.0546148	+	0.998507i	$0.517393\pi$
$608$	−1.33644	−	0.970980i	−0.0541998	−	0.0393784i
$609$	7.66641	+	23.5948i	0.310659	+	0.956109i
$610$	−9.16319	−	6.65744i	−0.371007	−	0.269552i
$611$	−3.84283	+	11.8270i	−0.155464	+	0.478469i
$612$	5.58526	−	17.1896i	0.225771	−	0.694850i
$613$	−7.12688	−	21.9343i	−0.287852	−	0.885917i	−0.985529	−	0.169505i	$-0.945783\pi$
$613$	−7.12688	−	21.9343i	−0.287852	−	0.885917i	0.697677	−	0.716412i	$-0.254217\pi$
$614$	16.9099			0.682430
$615$	9.25300			0.373117
$616$	−4.14883	−	12.7688i	−0.167161	−	0.514469i
$617$	−23.6300	+	17.1682i	−0.951309	+	0.691166i	−0.951116	−	0.308833i	$-0.900061\pi$
$617$	−23.6300	+	17.1682i	−0.951309	+	0.691166i	−0.000192939		1.00000i	$0.500061\pi$
$618$	29.9438	+	21.7555i	1.20452	+	0.875133i
$619$	33.0366			1.32785			0.663927	−	0.747798i	$-0.268889\pi$
$619$	33.0366			1.32785			0.663927	+	0.747798i	$0.268889\pi$
$620$	−1.34972	+	5.05704i	−0.0542061	+	0.203096i
$621$	−87.0708			−3.49403
$622$	11.6271	+	8.44762i	0.466206	+	0.338719i
$623$	34.1658	−	24.8229i	1.36882	−	0.994508i
$624$	1.00889	+	3.10503i	0.0403877	+	0.124301i
$625$	12.5251			0.501005
$626$	−18.3758			−0.734443
$627$	7.65574	+	23.5619i	0.305741	+	0.940973i
$628$	0.855383	−	2.63260i	0.0341335	−	0.105052i
$629$	1.09326	−	3.36471i	0.0435912	−	0.134160i
$630$	−17.0248	−	12.3692i	−0.678283	−	0.492801i
$631$	1.30495	+	4.01622i	0.0519492	+	0.159883i	0.973665	−	0.227982i	$-0.0732127\pi$
$631$	1.30495	+	4.01622i	0.0519492	+	0.159883i	−0.921716	+	0.387865i	$0.873213\pi$
$632$	9.04558	+	6.57200i	0.359814	+	0.261420i
$633$	15.8606	−	11.5234i	0.630401	−	0.458013i
$634$	2.28511	−	7.03284i	0.0907532	−	0.279310i
$635$	0.579030	−	0.420690i	0.0229781	−	0.0166946i
$636$	−24.4375	+	17.7549i	−0.969010	+	0.704027i
$637$	−0.476628	+	1.46691i	−0.0188847	+	0.0581211i
$638$	−9.66210	+	7.01993i	−0.382526	+	0.277921i
$639$	59.3138	+	43.0940i	2.34642	+	1.70477i
$640$	0.290496	+	0.894055i	0.0114829	+	0.0353406i
$641$	4.76869	+	3.46466i	0.188352	+	0.136846i	0.677965	−	0.735094i	$-0.262862\pi$
$641$	4.76869	+	3.46466i	0.188352	+	0.136846i	−0.489613	+	0.871940i	$0.662862\pi$
$642$	−9.78157	+	30.1046i	−0.386048	+	1.18813i
$643$	−1.75630	+	5.40534i	−0.0692617	+	0.213166i	−0.979696	−	0.200488i	$-0.935747\pi$
$643$	−1.75630	+	5.40534i	−0.0692617	+	0.213166i	0.910435	+	0.413653i	$0.135747\pi$
$644$	5.16996	+	15.9115i	0.203725	+	0.627000i
$645$	29.5701			1.16432
$646$	3.89831			0.153377
$647$	1.75679	+	5.40684i	0.0690665	+	0.212565i	0.979632	−	0.200799i	$-0.0643538\pi$
$647$	1.75679	+	5.40684i	0.0690665	+	0.212565i	−0.910566	+	0.413364i	$0.864354\pi$
$648$	21.5878	−	15.6845i	0.848050	−	0.616144i
$649$	10.5795	+	7.68649i	0.415283	+	0.301721i
$650$	−4.11628			−0.161454
$651$	−19.0883	−	49.5814i	−0.748128	−	1.94325i
$652$	−11.5354			−0.451762
$653$	−36.2624	−	26.3461i	−1.41906	−	1.03100i	−0.991927	−	0.126814i	$-0.959525\pi$
$653$	−36.2624	−	26.3461i	−1.41906	−	1.03100i	−0.427129	−	0.904191i	$-0.640475\pi$
$654$	29.4059	−	21.3646i	1.14986	−	0.835423i
$655$	−3.14145	−	9.66840i	−0.122747	−	0.377776i
$656$	3.01485			0.117710
$657$	−16.9061			−0.659571
$658$	−11.2316	−	34.5672i	−0.437853	−	1.34757i
$659$	−9.90978	+	30.4992i	−0.386030	+	1.18808i	0.549700	+	0.835362i	$0.314742\pi$
$659$	−9.90978	+	30.4992i	−0.386030	+	1.18808i	−0.935730	+	0.352716i	$0.885258\pi$
$660$	4.35666	−	13.4084i	0.169583	−	0.521922i
$661$	28.7050	+	20.8554i	1.11649	+	0.811180i	0.983674	−	0.179960i	$-0.0575968\pi$
$661$	28.7050	+	20.8554i	1.11649	+	0.811180i	0.132820	+	0.991140i	$0.457597\pi$
$662$	3.90620	+	12.0220i	0.151819	+	0.467250i
$663$	−6.23307	−	4.52859i	−0.242073	−	0.175876i
$664$	6.90269	−	5.01510i	0.267876	−	0.194624i
$665$	1.40256	−	4.31664i	0.0543890	−	0.167392i
$666$	9.28945	−	6.74918i	0.359959	−	0.261525i
$667$	12.0402	−	8.74769i	0.466197	−	0.338712i
$668$	−4.36794	+	13.4431i	−0.169001	+	0.520131i
$669$	−33.1147	+	24.0592i	−1.28029	+	0.930183i
$670$	6.63597	+	4.82132i	0.256370	+	0.186264i
$671$	17.1028	+	52.6370i	0.660246	+	2.03203i
$672$	−7.71982	−	5.60878i	−0.297798	−	0.216363i
$673$	−3.21682	+	9.90036i	−0.123999	+	0.381631i	−0.993717	−	0.111918i	$-0.964301\pi$
$673$	−3.21682	+	9.90036i	−0.123999	+	0.381631i	0.869718	+	0.493549i	$0.164301\pi$
$674$	−4.83913	+	14.8933i	−0.186396	+	0.573669i
$675$	19.3484	+	59.5482i	0.744720	+	2.29201i
$676$	1.00000			0.0384615
$677$	−15.0820			−0.579649			−0.289825	−	0.957080i	$-0.593597\pi$
$677$	−15.0820			−0.579649			−0.289825	+	0.957080i	$0.593597\pi$
$678$	8.81213	+	27.1210i	0.338428	+	1.04157i
$679$	−9.26421	+	6.73084i	−0.355528	+	0.258306i
$680$	−1.79474	−	1.30395i	−0.0688250	−	0.0500043i
$681$	−5.07044			−0.194300
$682$	19.8606	−	16.1150i	0.760501	−	0.617077i
$683$	34.1225			1.30566			0.652831	−	0.757503i	$-0.273581\pi$
$683$	34.1225			1.30566			0.652831	+	0.757503i	$0.273581\pi$
$684$	10.2359	+	7.43680i	0.391378	+	0.284353i
$685$	−11.2062	+	8.14177i	−0.428167	+	0.311081i
$686$	4.92917	+	15.1704i	0.188197	+	0.579210i
$687$	24.2727			0.926062
$688$	9.63463			0.367317
$689$	2.85905	+	8.79925i	0.108921	+	0.335225i
$690$	−5.42893	+	16.7085i	−0.206676	+	0.636083i
$691$	2.32519	−	7.15619i	0.0884543	−	0.272234i	−0.897038	−	0.441953i	$-0.854286\pi$
$691$	2.32519	−	7.15619i	0.0884543	−	0.272234i	0.985493	+	0.169719i	$0.0542859\pi$
$692$	4.52476	+	3.28743i	0.172005	+	0.124969i
$693$	31.7762	+	97.7970i	1.20708	+	3.71500i
$694$	−5.06619	−	3.68080i	−0.192310	−	0.139721i
$695$	3.32642	−	2.41679i	0.126178	−	0.0916739i
$696$	−2.62302	+	8.07283i	−0.0994254	+	0.306000i
$697$	−5.75583	+	4.18186i	−0.218018	+	0.158399i
$698$	−0.115213	+	0.0837073i	−0.00436088	+	0.00316837i
$699$	19.0869	−	58.7433i	0.721931	−	2.22188i
$700$	9.73313	−	7.07153i	0.367878	−	0.267279i
$701$	−15.8861	−	11.5420i	−0.600012	−	0.435934i	0.245871	−	0.969302i	$-0.420926\pi$
$701$	−15.8861	−	11.5420i	−0.600012	−	0.435934i	−0.845883	+	0.533369i	$0.820926\pi$
$702$	−4.70046	−	14.4665i	−0.177407	−	0.546004i
$703$	2.00358	+	1.45568i	0.0755663	+	0.0549022i
$704$	1.41950	−	4.36878i	0.0534995	−	0.164655i
$705$	11.7942	−	36.2988i	0.444195	−	1.36709i
$706$	5.47350	+	16.8457i	0.205998	+	0.633996i
$707$	−48.9889			−1.84242
$708$	9.29427			0.349300
$709$	−15.2349	−	46.8882i	−0.572158	−	1.76092i	−0.645658	−	0.763627i	$-0.723417\pi$
$709$	−15.2349	−	46.8882i	−0.572158	−	1.76092i	0.0734996	−	0.997295i	$-0.476583\pi$
$710$	7.28011	−	5.28931i	0.273218	−	0.198504i
$711$	−69.2806	−	50.3353i	−2.59823	−	1.88772i
$712$	14.4492			0.541506
$713$	−24.7487	+	20.0813i	−0.926848	+	0.752051i
$714$	22.5182			0.842724
$715$	−3.49357	−	2.53823i	−0.130652	−	0.0949242i
$716$	13.9185	−	10.1124i	0.520158	−	0.377917i
$717$	7.07706	+	21.7809i	0.264298	+	0.813424i
$718$	6.41352			0.239350
$719$	−45.7218			−1.70513			−0.852567	−	0.522617i	$-0.824956\pi$
$719$	−45.7218			−1.70513			−0.852567	+	0.522617i	$0.824956\pi$
$720$	−2.22493	−	6.84762i	−0.0829181	−	0.255196i
$721$	−10.2391	+	31.5128i	−0.381325	+	1.17360i
$722$	5.02805	−	15.4748i	0.187125	−	0.575911i
$723$	−76.2163	−	55.3744i	−2.83451	−	2.05940i
$724$	0.808421	+	2.48807i	0.0300447	+	0.0924682i
$725$	−8.65810	−	6.29048i	−0.321554	−	0.233622i
$726$	−26.6803	+	19.3844i	−0.990198	+	0.719421i
$727$	7.83915	−	24.1264i	0.290738	−	0.894799i	−0.693882	−	0.720089i	$-0.744101\pi$
$727$	7.83915	−	24.1264i	0.290738	−	0.894799i	0.984620	−	0.174710i	$-0.0558989\pi$
$728$	−2.36455	+	1.71794i	−0.0876359	+	0.0636712i
$729$	−44.8122	+	32.5580i	−1.65971	+	1.20585i
$730$	−0.641223	+	1.97348i	−0.0237327	+	0.0730418i
$731$	−18.3941	+	13.3641i	−0.680329	+	0.494288i
$732$	31.8235	+	23.1211i	1.17623	+	0.854582i
$733$	−12.0466	−	37.0756i	−0.444951	−	1.36942i	−0.882537	−	0.470243i	$-0.844166\pi$
$733$	−12.0466	−	37.0756i	−0.444951	−	1.36942i	0.437586	−	0.899177i	$-0.355834\pi$
$734$	8.10743	+	5.89039i	0.299251	+	0.217418i
$735$	1.46284	−	4.50216i	0.0539576	−	0.166065i
$736$	−1.76887	+	5.44403i	−0.0652016	+	0.200670i
$737$	−12.3858	−	38.1197i	−0.456238	−	1.40416i
$738$	−23.0909			−0.849988
$739$	21.9683			0.808117			0.404059	−	0.914733i	$-0.367599\pi$
$739$	21.9683			0.808117			0.404059	+	0.914733i	$0.367599\pi$
$740$	−0.435509	−	1.34036i	−0.0160096	−	0.0492725i
$741$	4.36324	−	3.17008i	0.160287	−	0.116456i
$742$	−21.8770	−	15.8945i	−0.803129	−	0.583507i
$743$	25.3443			0.929794			0.464897	−	0.885365i	$-0.346091\pi$
$743$	25.3443			0.929794			0.464897	+	0.885365i	$0.346091\pi$
$744$	4.68755	−	17.5630i	0.171854	−	0.643890i
$745$	10.7778			0.394867
$746$	−7.63144	−	5.54457i	−0.279407	−	0.203001i
$747$	−52.8681	+	38.4109i	−1.93434	+	1.40538i
$748$	3.34982	+	10.3097i	0.122481	+	0.376959i
$749$	−28.3372			−1.03542
$750$	27.9792			1.02165
$751$	0.0885066	+	0.272395i	0.00322965	+	0.00993985i	0.952658	−	0.304043i	$-0.0983366\pi$
$751$	0.0885066	+	0.272395i	0.00322965	+	0.00993985i	−0.949429	+	0.313983i	$0.898337\pi$
$752$	3.84283	−	11.8270i	0.140133	−	0.431287i
$753$	−1.49463	+	4.60001i	−0.0544674	+	0.167634i
$754$	2.10338	+	1.52820i	0.0766006	+	0.0556536i
$755$	−3.28261	−	10.1028i	−0.119466	−	0.367679i
$756$	35.9671	+	26.1316i	1.30811	+	0.950398i
$757$	23.9397	−	17.3932i	0.870103	−	0.632167i	−0.0605118	−	0.998167i	$-0.519273\pi$
$757$	23.9397	−	17.3932i	0.870103	−	0.632167i	0.930615	+	0.366001i	$0.119273\pi$
$758$	−0.478999	+	1.47421i	−0.0173980	+	0.0535457i
$759$	69.4521	−	50.4599i	2.52095	−	1.83158i
$760$	1.25634	−	0.912784i	0.0455722	−	0.0331102i
$761$	−4.94515	+	15.2196i	−0.179262	+	0.551711i	−0.999802	−	0.0198774i	$-0.993672\pi$
$761$	−4.94515	+	15.2196i	−0.179262	+	0.551711i	0.820541	+	0.571588i	$0.193672\pi$
$762$	−2.01096	+	1.46105i	−0.0728493	+	0.0529281i
$763$	26.3248	+	19.1261i	0.953021	+	0.692410i
$764$	−8.45712	−	26.0283i	−0.305968	−	0.941673i
$765$	13.7460	+	9.98705i	0.496987	+	0.361082i
$766$	−10.6844	+	32.8833i	−0.386044	+	1.18812i
$767$	0.879707	−	2.70746i	0.0317644	−	0.0977607i
$768$	−1.00889	−	3.10503i	−0.0364050	−	0.112043i
$769$	−11.7548			−0.423889			−0.211944	−	0.977282i	$-0.567980\pi$
$769$	−11.7548			−0.423889			−0.211944	+	0.977282i	$0.567980\pi$
$770$	12.6212			0.454837
$771$	0.202469	+	0.623135i	0.00729173	+	0.0224416i
$772$	17.5186	−	12.7280i	0.630508	−	0.458091i
$773$	−0.0811068	−	0.0589276i	−0.00291721	−	0.00211948i	0.586326	−	0.810075i	$-0.300574\pi$
$773$	−0.0811068	−	0.0589276i	−0.00291721	−	0.00211948i	−0.589243	+	0.807956i	$0.700574\pi$
$774$	−73.7922			−2.65241
$775$	19.2333	+	12.4635i	0.690879	+	0.447701i
$776$	−3.91797			−0.140647
$777$	11.5735	+	8.40862i	0.415196	+	0.301658i
$778$	−1.39438	+	1.01307i	−0.0499908	+	0.0363204i
$779$	−1.53900	−	4.73656i	−0.0551405	−	0.169705i
$780$	−3.06914			−0.109893
$781$	−43.9720			−1.57344
$782$	−4.17428	−	12.8471i	−0.149272	−	0.459412i
$783$	12.2208	−	37.6118i	0.436736	−	1.34414i
$784$	0.476628	−	1.46691i	0.0170224	−	0.0523896i
$785$	2.10520	+	1.52952i	0.0751379	+	0.0545908i
$786$	10.9102	+	33.5781i	0.389154	+	1.19769i
$787$	21.2572	+	15.4443i	0.757738	+	0.550529i	0.898216	−	0.439555i	$-0.144864\pi$
$787$	21.2572	+	15.4443i	0.757738	+	0.550529i	−0.140478	+	0.990084i	$0.544864\pi$
$788$	9.25402	−	6.72344i	0.329661	−	0.239513i
$789$	−20.1966	+	62.1587i	−0.719018	+	2.21291i
$790$	−8.50343	+	6.17810i	−0.302538	+	0.219807i
$791$	−20.6532	+	15.0054i	−0.734342	+	0.533531i
$792$	−10.8721	+	33.4607i	−0.386322	+	1.18898i
$793$	9.74740	−	7.08190i	0.346140	−	0.251486i
$794$	7.85965	+	5.71037i	0.278929	+	0.202653i
$795$	−8.77484	−	27.0062i	−0.311211	−	0.957810i
$796$	17.6392	+	12.8156i	0.625205	+	0.454238i
$797$	7.25474	−	22.3278i	0.256976	−	0.790891i	−0.736458	−	0.676483i	$-0.763503\pi$
$797$	7.25474	−	22.3278i	0.256976	−	0.790891i	0.993434	−	0.114407i	$-0.0364969\pi$
$798$	−4.87106	+	14.9916i	−0.172434	+	0.530696i
$799$	9.06851	+	27.9100i	0.320821	+	0.987385i
$800$	4.11628			0.145532
$801$	−110.667			−3.91023
$802$	1.52279	+	4.68668i	0.0537717	+	0.165492i
$803$	8.20314	−	5.95993i	0.289483	−	0.210321i
$804$	−23.0466	−	16.7443i	−0.812790	−	0.590527i
$805$	−15.7276			−0.554325
$806$	−4.67249	−	3.02785i	−0.164581	−	0.106651i
$807$	−12.9261			−0.455019
$808$	−13.5602	−	9.85205i	−0.477046	−	0.346594i
$809$	29.7158	−	21.5898i	1.04475	−	0.759056i	0.0735432	−	0.997292i	$-0.476569\pi$
$809$	29.7158	−	21.5898i	1.04475	−	0.759056i	0.971207	+	0.238236i	$0.0765693\pi$
$810$	7.75160	+	23.8570i	0.272364	+	0.838249i
$811$	−17.8693			−0.627476			−0.313738	−	0.949510i	$-0.601581\pi$
$811$	−17.8693			−0.627476			−0.313738	+	0.949510i	$0.601581\pi$
$812$	−7.59889			−0.266669
$813$	−5.05571	−	15.5599i	−0.177312	−	0.545709i
$814$	−2.12810	+	6.54963i	−0.0745900	+	0.229564i
$815$	3.35099	−	10.3133i	0.117380	−	0.361259i
$816$	6.23307	+	4.52859i	0.218201	+	0.158532i
$817$	−4.91823	−	15.1368i	−0.172067	−	0.529568i
$818$	4.41546	+	3.20802i	0.154383	+	0.112166i
$819$	18.1102	−	13.1578i	0.632821	−	0.459772i
$820$	−0.875801	+	2.69544i	−0.0305843	+	0.0941288i
$821$	33.1053	−	24.0524i	1.15538	−	0.839436i	0.166197	−	0.986093i	$-0.446851\pi$
$821$	33.1053	−	24.0524i	1.15538	−	0.839436i	0.989187	+	0.146657i	$0.0468513\pi$
$822$	38.9188	−	28.2762i	1.35745	−	0.986245i
$823$	−3.91080	+	12.0362i	−0.136322	+	0.419556i	−0.995793	−	0.0916281i	$-0.970793\pi$
$823$	−3.91080	+	12.0362i	−0.136322	+	0.419556i	0.859471	+	0.511184i	$0.170793\pi$
$824$	−9.17166	+	6.66360i	−0.319510	+	0.232137i
$825$	−49.9431	−	36.2858i	−1.73880	−	1.26331i
$826$	2.57115	+	7.91320i	0.0894619	+	0.275335i
$827$	−37.1843	−	27.0160i	−1.29302	−	0.939438i	−0.293163	−	0.956062i	$-0.594708\pi$
$827$	−37.1843	−	27.0160i	−1.29302	−	0.939438i	−0.999862	+	0.0166249i	$0.994708\pi$
$828$	13.5479	−	41.6962i	0.470822	−	1.44904i
$829$	−13.2657	+	40.8277i	−0.460737	+	1.41800i	0.403528	+	0.914967i	$0.367784\pi$
$829$	−13.2657	+	40.8277i	−0.460737	+	1.41800i	−0.864265	+	0.503036i	$0.832216\pi$
$830$	2.47857	+	7.62825i	0.0860324	+	0.264780i
$831$	99.8762			3.46467
$832$	−1.00000			−0.0346688
$833$	1.12477	+	3.46169i	0.0389710	+	0.119941i
$834$	−11.5526	+	8.39344i	−0.400033	+	0.290641i
$835$	−10.7500	−	7.81036i	−0.372020	−	0.270289i
$836$	−7.58831			−0.262447
$837$	−21.8396	+	81.8269i	−0.754886	+	2.82835i
$838$	19.2084			0.663543
$839$	22.9937	+	16.7059i	0.793829	+	0.576751i	0.909097	−	0.416584i	$-0.136773\pi$
$839$	22.9937	+	16.7059i	0.793829	+	0.576751i	−0.115268	+	0.993334i	$0.536773\pi$
$840$	7.25713	−	5.27261i	0.250395	−	0.181922i
$841$	−6.87267	−	21.1519i	−0.236988	−	0.729375i
$842$	15.1825			0.523224
$843$	−57.1091			−1.96694
$844$	1.85560	+	5.71095i	0.0638724	+	0.196579i
$845$	−0.290496	+	0.894055i	−0.00999337	+	0.0307564i
$846$	−29.4324	+	90.5838i	−1.01191	+	3.11433i
$847$	−23.8848	−	17.3533i	−0.820690	−	0.596266i
$848$	−2.85905	−	8.79925i	−0.0981802	−	0.302168i
$849$	−85.2155	−	61.9127i	−2.92459	−	2.12484i
$850$	−7.85864	+	5.70964i	−0.269549	+	0.195839i
$851$	2.65188	−	8.16164i	0.0909052	−	0.279777i
$852$	−25.2837	+	18.3696i	−0.866204	+	0.629334i
$853$	4.08906	−	2.97088i	0.140007	−	0.101721i	−0.515577	−	0.856843i	$-0.672422\pi$
$853$	4.08906	−	2.97088i	0.140007	−	0.101721i	0.655584	+	0.755122i	$0.272422\pi$
$854$	−10.8819	+	33.4909i	−0.372370	+	1.14604i
$855$	−9.62238	+	6.99107i	−0.329078	+	0.239090i
$856$	−7.84376	−	5.69883i	−0.268094	−	0.194782i
$857$	16.4452	+	50.6131i	0.561758	+	1.72891i	0.677394	+	0.735620i	$0.263109\pi$
$857$	16.4452	+	50.6131i	0.561758	+	1.72891i	−0.115637	+	0.993292i	$0.536891\pi$
$858$	12.1331	+	8.81519i	0.414216	+	0.300946i
$859$	6.95456	−	21.4039i	0.237287	−	0.730293i	−0.759523	−	0.650480i	$-0.774568\pi$
$859$	6.95456	−	21.4039i	0.237287	−	0.730293i	0.996810	−	0.0798129i	$-0.0254323\pi$
$860$	−2.79882	+	8.61389i	−0.0954390	+	0.293731i
$861$	−8.88991	−	27.3603i	−0.302967	−	0.932437i
$862$	12.8296			0.436977
$863$	−4.92827			−0.167760			−0.0838802	−	0.996476i	$-0.526731\pi$
$863$	−4.92827			−0.167760			−0.0838802	+	0.996476i	$0.526731\pi$
$864$	4.70046	+	14.4665i	0.159913	+	0.492161i
$865$	−4.25356	+	3.09039i	−0.144626	+	0.105077i
$866$	31.3721	+	22.7932i	1.06607	+	0.774544i
$867$	37.3205			1.26747
$868$	16.2500	−	0.867589i	0.551560	−	0.0294479i
$869$	51.3609			1.74230
$870$	−6.45558	−	4.69025i	−0.218865	−	0.159014i
$871$	−7.05906	+	5.12871i	−0.239187	+	0.173780i
$872$	3.44033	+	10.5882i	0.116504	+	0.358563i
$873$	30.0079			1.01562
$874$	9.45597			0.319853
$875$	7.74012	+	23.8216i	0.261664	+	0.805318i
$876$	2.22695	−	6.85385i	0.0752417	−	0.231570i
$877$	−8.26083	+	25.4242i	−0.278948	+	0.858514i	0.709199	+	0.705008i	$0.249057\pi$
$877$	−8.26083	+	25.4242i	−0.278948	+	0.858514i	−0.988148	+	0.153507i	$0.950943\pi$
$878$	−3.55468	−	2.58263i	−0.119965	−	0.0871595i
$879$	2.81787	+	8.67252i	0.0950445	+	0.292517i
$880$	3.49357	+	2.53823i	0.117768	+	0.0855636i
$881$	−20.1448	+	14.6361i	−0.678696	+	0.493102i	−0.872925	−	0.487855i	$-0.837780\pi$
$881$	−20.1448	+	14.6361i	−0.678696	+	0.493102i	0.194229	+	0.980956i	$0.437780\pi$
$882$	−3.65052	+	11.2351i	−0.122919	+	0.378307i
$883$	−1.48097	+	1.07599i	−0.0498387	+	0.0362099i	−0.612426	−	0.790528i	$-0.709806\pi$
$883$	−1.48097	+	1.07599i	−0.0498387	+	0.0362099i	0.562587	+	0.826738i	$0.309806\pi$
$884$	1.90916	−	1.38709i	0.0642121	−	0.0466528i
$885$	−2.69995	+	8.30958i	−0.0907577	+	0.279324i
$886$	−13.0309	+	9.46754i	−0.437783	+	0.318068i
$887$	9.28260	+	6.74420i	0.311679	+	0.226448i	0.732617	−	0.680641i	$-0.238299\pi$
$887$	9.28260	+	6.74420i	0.311679	+	0.226448i	−0.420937	+	0.907090i	$0.638299\pi$
$888$	1.51251	+	4.65503i	0.0507565	+	0.156213i
$889$	−1.80025	−	1.30796i	−0.0603785	−	0.0438676i
$890$	−4.19743	+	12.9184i	−0.140698	+	0.433025i
$891$	37.8780	−	116.577i	1.26896	−	3.90546i
$892$	−3.87423	−	11.9237i	−0.129719	−	0.399234i
$893$	−20.5428			−0.687439
$894$	−37.4310			−1.25188
$895$	4.99775	+	15.3815i	0.167056	+	0.514146i
$896$	2.36455	−	1.71794i	0.0789939	−	0.0573924i
$897$	−15.1193	−	10.9848i	−0.504819	−	0.366772i
$898$	−36.6001			−1.22136
$899$	−5.20088	−	13.5092i	−0.173459	−	0.450557i
$900$	−31.5268			−1.05089
$901$	17.6637	+	12.8334i	0.588464	+	0.427544i
$902$	11.2041	−	8.14025i	0.373056	−	0.271041i
$903$	−28.4097	−	87.4361i	−0.945416	−	2.90969i
$904$	−8.73452			−0.290506
$905$	−2.45931			−0.0817502
$906$	11.4004	+	35.0868i	0.378753	+	1.16568i
$907$	−15.4232	+	47.4676i	−0.512117	+	1.57614i	0.276349	+	0.961057i	$0.410875\pi$
$907$	−15.4232	+	47.4676i	−0.512117	+	1.57614i	−0.788466	+	0.615078i	$0.789125\pi$
$908$	0.479919	−	1.47704i	0.0159267	−	0.0490173i
$909$	103.858	+	75.4575i	3.44476	+	2.50277i
$910$	−0.849044	−	2.61309i	−0.0281455	−	0.0866230i
$911$	9.01482	+	6.54965i	0.298674	+	0.217000i	0.727022	−	0.686615i	$-0.240904\pi$
$911$	9.01482	+	6.54965i	0.298674	+	0.217000i	−0.428347	+	0.903614i	$0.640904\pi$
$912$	−4.36324	+	3.17008i	−0.144481	+	0.104972i
$913$	12.1115	−	37.2753i	0.400831	−	1.23363i
$914$	−25.7148	+	18.6829i	−0.850571	+	0.617976i
$915$	−29.9162	+	21.7354i	−0.988998	+	0.718549i
$916$	−2.29742	+	7.07075i	−0.0759091	+	0.233624i
$917$	−25.5704	+	18.5780i	−0.844410	+	0.613500i
$918$	−29.0403	−	21.0990i	−0.958472	−	0.696370i
$919$	−9.98286	−	30.7241i	−0.329304	−	1.01349i	−0.969460	−	0.245249i	$-0.921130\pi$
$919$	−9.98286	−	30.7241i	−0.329304	−	1.01349i	0.640156	−	0.768245i	$-0.278870\pi$
$920$	−4.35341	−	3.16294i	−0.143528	−	0.104279i
$921$	17.0602	−	52.5059i	0.562153	−	1.73013i
$922$	−2.99041	+	9.20352i	−0.0984837	+	0.303102i
$923$	2.95805	+	9.10393i	0.0973653	+	0.299660i
$924$	−43.8332			−1.44201
$925$	−6.17108			−0.202904
$926$	−8.97108	−	27.6101i	−0.294808	−	0.907326i
$927$	70.2463	−	51.0369i	2.30719	−	1.67627i
$928$	−2.10338	−	1.52820i	−0.0690468	−	0.0501655i
$929$	9.81420			0.321994			0.160997	−	0.986955i	$-0.448529\pi$
$929$	9.81420			0.321994			0.160997	+	0.986955i	$0.448529\pi$
$930$	14.3405	+	9.29290i	0.470245	+	0.304726i
$931$	−2.54794			−0.0835053
$932$	15.3056	+	11.1202i	0.501352	+	0.364253i
$933$	37.9606	−	27.5800i	1.24277	−	0.902928i
$934$	10.0300	+	30.8690i	0.328190	+	1.01007i
$935$	−10.1905			−0.333266
$936$	7.65906			0.250344
$937$	8.42042	+	25.9154i	0.275083	+	0.846619i	0.989197	+	0.146590i	$0.0468297\pi$
$937$	8.42042	+	25.9154i	0.275083	+	0.846619i	−0.714114	+	0.700029i	$0.753170\pi$
$938$	7.88064	−	24.2541i	0.257312	−	0.791925i
$939$	−18.5390	+	57.0573i	−0.604999	+	1.86199i
$940$	9.45767	+	6.87140i	0.308475	+	0.224120i
$941$	−12.8370	−	39.5083i	−0.418475	−	1.28794i	−0.909105	−	0.416567i	$-0.863233\pi$
$941$	−12.8370	−	39.5083i	−0.418475	−	1.28794i	0.490630	−	0.871368i	$-0.336767\pi$
$942$	−7.31131	−	5.31198i	−0.238215	−	0.173074i
$943$	−13.9617	+	10.1438i	−0.454655	+	0.330326i
$944$	−0.879707	+	2.70746i	−0.0286320	+	0.0881203i
$945$	−33.8114	+	24.5654i	−1.09989	+	0.799113i
$946$	35.8052	−	26.0140i	1.16413	−	0.845789i
$947$	−16.5292	+	50.8718i	−0.537128	+	1.65311i	0.201876	+	0.979411i	$0.435296\pi$
$947$	−16.5292	+	50.8718i	−0.537128	+	1.65311i	−0.739005	+	0.673700i	$0.764704\pi$
$948$	29.5322	−	21.4564i	0.959161	−	0.696871i
$949$	−1.78577	−	1.29744i	−0.0579687	−	0.0421167i
$950$	−2.10125	−	6.46700i	−0.0681737	−	0.209817i
$951$	−19.5318	−	14.1907i	−0.633361	−	0.460164i
$952$	−2.13136	+	6.55966i	−0.0690779	+	0.212600i
$953$	14.0639	−	43.2844i	0.455576	−	1.40212i	−0.414882	−	0.909875i	$-0.636177\pi$
$953$	14.0639	−	43.2844i	0.455576	−	1.40212i	0.870458	−	0.492243i	$-0.163823\pi$
$954$	21.8976	+	67.3940i	0.708962	+	2.18196i
$955$	25.7275			0.832523
$956$	−7.01473			−0.226873
$957$	12.0491	+	37.0834i	0.389493	+	1.19874i
$958$	−11.1663	+	8.11281i	−0.360768	+	0.262113i
$959$	34.8410	+	25.3134i	1.12507	+	0.817414i
$960$	3.06914			0.0990562
$961$	12.6643	+	28.2952i	0.408526	+	0.912747i
$962$	1.49919			0.0483358
$963$	60.0758	+	43.6477i	1.93592	+	1.40653i
$964$	23.3447	−	16.9609i	0.751882	−	0.546274i
$965$	6.29045	+	19.3600i	0.202497	+	0.623221i
$966$	54.6215			1.75742
$967$	−22.3005			−0.717135			−0.358567	−	0.933504i	$-0.616735\pi$
$967$	−22.3005			−0.717135			−0.358567	+	0.933504i	$0.616735\pi$
$968$	−3.12145	−	9.60682i	−0.100327	−	0.308775i
$969$	3.93295	−	12.1044i	0.126345	−	0.388849i
$970$	1.13815	−	3.50288i	0.0365439	−	0.112471i
$971$	−6.79591	−	4.93751i	−0.218091	−	0.158452i	0.473376	−	0.880861i	$-0.343035\pi$
$971$	−6.79591	−	4.93751i	−0.218091	−	0.158452i	−0.691467	+	0.722408i	$0.743035\pi$
$972$	−12.8198	−	39.4551i	−0.411194	−	1.26552i
$973$	−10.3421	−	7.51398i	−0.331553	−	0.240887i
$974$	−10.8942	+	7.91513i	−0.349074	+	0.253617i
$975$	−4.15285	+	12.7812i	−0.132998	+	0.409325i
$976$	−9.74740	+	7.08190i	−0.312007	+	0.226686i
$977$	−29.3661	+	21.3357i	−0.939506	+	0.682591i	−0.948302	−	0.317370i	$-0.897200\pi$
$977$	−29.3661	+	21.3357i	−0.939506	+	0.682591i	0.00879585	+	0.999961i	$0.497200\pi$
$978$	−11.6379	+	35.8178i	−0.372139	+	1.14533i
$979$	53.6976	−	39.0136i	1.71618	−	1.24688i
$980$	1.17304	+	0.852263i	0.0374714	+	0.0272245i
$981$	−26.3497	−	81.0959i	−0.841280	−	2.58919i
$982$	−4.52629	−	3.28854i	−0.144440	−	0.104942i
$983$	11.2527	−	34.6322i	0.358905	−	1.10460i	−0.594805	−	0.803870i	$-0.702771\pi$
$983$	11.2527	−	34.6322i	0.358905	−	1.10460i	0.953710	−	0.300727i	$-0.0972292\pi$
$984$	3.04164	−	9.36119i	0.0969638	−	0.298424i
$985$	3.32287	+	10.2267i	0.105875	+	0.325851i
$986$	6.13543			0.195392
$987$	−118.664			−3.77711
$988$	0.510474	+	1.57108i	0.0162404	+	0.0499827i
$989$	−44.6177	+	32.4167i	−1.41876	+	1.03079i
$990$	−26.7574	−	19.4404i	−0.850407	−	0.617857i
$991$	−7.26567			−0.230802			−0.115401	−	0.993319i	$-0.536815\pi$
$991$	−7.26567			−0.230802			−0.115401	+	0.993319i	$0.536815\pi$
$992$	4.67249	+	3.02785i	0.148352	+	0.0961342i
$993$	41.2697			1.30965
$994$	−22.6345	−	16.4449i	−0.717922	−	0.521601i
$995$	−16.5820	+	12.0475i	−0.525685	+	0.381932i
$996$	−8.60801	−	26.4927i	−0.272755	−	0.839454i
$997$	1.52937			0.0484356			0.0242178	−	0.999707i	$-0.492290\pi$
$997$	1.52937			0.0484356			0.0242178	+	0.999707i	$0.492290\pi$
$998$	38.5039			1.21882
$999$	−7.04688	−	21.6881i	−0.222953	−	0.686180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	806.2.k.c.157.7	✓	28
31.16	even	5	inner	806.2.k.c.729.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
806.2.k.c.157.7	✓	28	1.1	even	1	trivial
806.2.k.c.729.7	yes	28	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(2.64130 - 1.91901i) q^{3} +(0.309017 + 0.951057i) q^{4} -0.940065 q^{5} +3.26482 q^{6} +(0.903176 + 2.77969i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.36678 - 7.28420i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(2.64130 - 1.91901i) q^{3} +(0.309017 + 0.951057i) q^{4} -0.940065 q^{5} +3.26482 q^{6} +(0.903176 + 2.77969i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.36678 - 7.28420i) q^{9} +(-0.760528 - 0.552556i) q^{10} +(1.41950 + 4.36878i) q^{11} +(2.64130 + 1.91901i) q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.903176 + 2.77969i) q^{14} +(-2.48299 + 1.80400i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.729235 - 2.24435i) q^{17} +(6.19631 - 4.50188i) q^{18} +(1.33644 + 0.970980i) q^{19} +(-0.290496 - 0.894055i) q^{20} +(7.71982 + 5.60878i) q^{21} +(-1.41950 + 4.36878i) q^{22} +(1.76887 - 5.44403i) q^{23} +(1.00889 + 3.10503i) q^{24} -4.11628 q^{25} +1.00000 q^{26} +(-4.70046 - 14.4665i) q^{27} +(-2.36455 + 1.71794i) q^{28} +(2.10338 + 1.52820i) q^{29} -3.06914 q^{30} +(-4.67249 - 3.02785i) q^{31} -1.00000 q^{32} +(12.1331 + 8.81519i) q^{33} +(1.90916 - 1.38709i) q^{34} +(-0.849044 - 2.61309i) q^{35} +7.65906 q^{36} +1.49919 q^{37} +(0.510474 + 1.57108i) q^{38} +(1.00889 - 3.10503i) q^{39} +(0.290496 - 0.894055i) q^{40} +(-2.43906 - 1.77208i) q^{41} +(2.94871 + 9.07519i) q^{42} +(-7.79458 - 5.66309i) q^{43} +(-3.71630 + 2.70005i) q^{44} +(-2.22493 + 6.84762i) q^{45} +(4.63097 - 3.36460i) q^{46} +(-10.0607 + 7.30949i) q^{47} +(-1.00889 + 3.10503i) q^{48} +(-1.24783 + 0.906600i) q^{49} +(-3.33014 - 2.41949i) q^{50} +(-2.38082 - 7.32742i) q^{51} +(0.809017 + 0.587785i) q^{52} +(-2.85905 + 8.79925i) q^{53} +(4.70046 - 14.4665i) q^{54} +(-1.33442 - 4.10693i) q^{55} -2.92274 q^{56} +5.39326 q^{57} +(0.803420 + 2.47267i) q^{58} +(2.30310 - 1.67330i) q^{59} +(-2.48299 - 1.80400i) q^{60} +12.0484 q^{61} +(-2.00040 - 5.19600i) q^{62} +22.3854 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.760528 + 0.552556i) q^{65} +(4.63442 + 14.2633i) q^{66} -8.72548 q^{67} +2.35985 q^{68} +(-5.77506 - 17.7738i) q^{69} +(0.849044 - 2.61309i) q^{70} +(-2.95805 + 9.10393i) q^{71} +(6.19631 + 4.50188i) q^{72} +(-0.682105 - 2.09930i) q^{73} +(1.21287 + 0.881202i) q^{74} +(-10.8723 + 7.89920i) q^{75} +(-0.510474 + 1.57108i) q^{76} +(-10.8618 + 7.89155i) q^{77} +(2.64130 - 1.91901i) q^{78} +(3.45510 - 10.6337i) q^{79} +(0.760528 - 0.552556i) q^{80} +(-21.5878 - 15.6845i) q^{81} +(-0.931639 - 2.86729i) q^{82} +(-6.90269 - 5.01510i) q^{83} +(-2.94871 + 9.07519i) q^{84} +(-0.685528 + 2.10984i) q^{85} +(-2.97727 - 9.16308i) q^{86} +8.48828 q^{87} -4.59361 q^{88} +(-4.46505 - 13.7420i) q^{89} +(-5.82493 + 4.23206i) q^{90} +(2.36455 + 1.71794i) q^{91} +5.72420 q^{92} +(-18.1519 + 0.969133i) q^{93} -12.4357 q^{94} +(-1.25634 - 0.912784i) q^{95} +(-2.64130 + 1.91901i) q^{96} +(1.21072 + 3.72621i) q^{97} -1.54240 q^{98} +35.1827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8}+O(q^{10}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8	\( 28 q + 7 q^{2} + q^{3} - 7 q^{4} + 2 q^{5} - 6 q^{6} - q^{7} + 7 q^{8} + 3 q^{10} + 3 q^{11} + q^{12} + 7 q^{13} + q^{14} + 6 q^{15} - 7 q^{16} - 2 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} + 15 q^{21} - 3 q^{22} + 18 q^{23} + 4 q^{24} + 54 q^{25} + 28 q^{26} - 26 q^{27} + 4 q^{28} + 27 q^{29} + 14 q^{30} - 33 q^{31} - 28 q^{32} + 3 q^{33} + 2 q^{34} + 8 q^{35} + 30 q^{36} - 6 q^{37} - 27 q^{38} + 4 q^{39} - 2 q^{40} - 22 q^{41} + 5 q^{42} + q^{43} - 12 q^{44} + 28 q^{45} + 27 q^{46} + 7 q^{47} - 4 q^{48} - 30 q^{49} + q^{50} - 52 q^{51} + 7 q^{52} + q^{53} + 26 q^{54} - 18 q^{55} + 6 q^{56} - 112 q^{57} + 23 q^{58} + 27 q^{59} + 6 q^{60} - 6 q^{61} - 17 q^{62} + 54 q^{63} - 7 q^{64} + 3 q^{65} + 17 q^{66} - 24 q^{67} + 8 q^{68} + 6 q^{69} - 8 q^{70} + 28 q^{71} + 15 q^{72} - 8 q^{73} - 9 q^{74} - 62 q^{75} + 27 q^{76} - 62 q^{77} + q^{78} + 40 q^{79} - 3 q^{80} - 24 q^{81} - 18 q^{82} + 3 q^{83} - 5 q^{84} - q^{85} + 4 q^{86} + 42 q^{87} - 18 q^{88} - 5 q^{89} - 23 q^{90} - 4 q^{91} + 18 q^{92} - 69 q^{93} - 12 q^{94} - 17 q^{95} - q^{96} + 29 q^{97} - 30 q^{98} + 88 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 + q^3 - 7 * q^4 + 2 * q^5 - 6 * q^6 - q^7 + 7 * q^8 + 3 * q^10 + 3 * q^11 + q^12 + 7 * q^13 + q^14 + 6 * q^15 - 7 * q^16 - 2 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 + 15 * q^21 - 3 * q^22 + 18 * q^23 + 4 * q^24 + 54 * q^25 + 28 * q^26 - 26 * q^27 + 4 * q^28 + 27 * q^29 + 14 * q^30 - 33 * q^31 - 28 * q^32 + 3 * q^33 + 2 * q^34 + 8 * q^35 + 30 * q^36 - 6 * q^37 - 27 * q^38 + 4 * q^39 - 2 * q^40 - 22 * q^41 + 5 * q^42 + q^43 - 12 * q^44 + 28 * q^45 + 27 * q^46 + 7 * q^47 - 4 * q^48 - 30 * q^49 + q^50 - 52 * q^51 + 7 * q^52 + q^53 + 26 * q^54 - 18 * q^55 + 6 * q^56 - 112 * q^57 + 23 * q^58 + 27 * q^59 + 6 * q^60 - 6 * q^61 - 17 * q^62 + 54 * q^63 - 7 * q^64 + 3 * q^65 + 17 * q^66 - 24 * q^67 + 8 * q^68 + 6 * q^69 - 8 * q^70 + 28 * q^71 + 15 * q^72 - 8 * q^73 - 9 * q^74 - 62 * q^75 + 27 * q^76 - 62 * q^77 + q^78 + 40 * q^79 - 3 * q^80 - 24 * q^81 - 18 * q^82 + 3 * q^83 - 5 * q^84 - q^85 + 4 * q^86 + 42 * q^87 - 18 * q^88 - 5 * q^89 - 23 * q^90 - 4 * q^91 + 18 * q^92 - 69 * q^93 - 12 * q^94 - 17 * q^95 - q^96 + 29 * q^97 - 30 * q^98 + 88 * q^99

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