LMFDB - Embedded newform 650.2.l.c.391.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			391.4
Character	$\chi$	$=$	650.391
Dual form			650.2.l.c.261.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.0956093 + 0.294255i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23331 + 0.110958i) q^{5} +(0.0956093 - 0.294255i) q^{6} +1.22498 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.34961 - 1.70709i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.0956093 + 0.294255i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23331 + 0.110958i) q^{5} +(0.0956093 - 0.294255i) q^{6} +1.22498 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.34961 - 1.70709i) q^{9} +(1.87201 + 1.22294i) q^{10} +(-1.80449 - 1.31104i) q^{11} +(-0.250308 + 0.181860i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.991027 - 0.720023i) q^{14} +(-0.246175 - 0.646555i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.145029 - 0.446353i) q^{17} -2.90427 q^{18} +(-0.370595 + 1.14057i) q^{19} +(-0.795659 - 2.08972i) q^{20} +(0.117119 + 0.360456i) q^{21} +(0.689254 + 2.12130i) q^{22} +(2.81853 + 2.04779i) q^{23} +0.309398 q^{24} +(4.97538 - 0.495607i) q^{25} +1.00000 q^{26} +(1.47789 + 1.07375i) q^{27} +(0.378538 + 1.16502i) q^{28} +(-2.79483 - 8.60161i) q^{29} +(-0.180876 + 0.667772i) q^{30} +(3.16474 - 9.74006i) q^{31} +1.00000 q^{32} +(0.213254 - 0.656328i) q^{33} +(-0.379690 + 0.275861i) q^{34} +(-2.73576 + 0.135921i) q^{35} +(2.34961 + 1.70709i) q^{36} +(6.10922 - 4.43861i) q^{37} +(0.970230 - 0.704913i) q^{38} +(-0.250308 - 0.181860i) q^{39} +(-0.584605 + 2.15830i) q^{40} +(4.09802 - 2.97739i) q^{41} +(0.117119 - 0.360456i) q^{42} +8.10003 q^{43} +(0.689254 - 2.12130i) q^{44} +(-5.05799 + 4.07317i) q^{45} +(-1.07658 - 3.31339i) q^{46} +(-3.94313 - 12.1357i) q^{47} +(-0.250308 - 0.181860i) q^{48} -5.49943 q^{49} +(-4.31647 - 2.52350i) q^{50} +0.145208 q^{51} +(-0.809017 - 0.587785i) q^{52} +(0.861524 + 2.65150i) q^{53} +(-0.564503 - 1.73736i) q^{54} +(4.17546 + 2.72774i) q^{55} +(0.378538 - 1.16502i) q^{56} -0.371052 q^{57} +(-2.79483 + 8.60161i) q^{58} +(1.39916 - 1.01655i) q^{59} +(0.538838 - 0.433923i) q^{60} +(9.87773 + 7.17659i) q^{61} +(-8.28539 + 6.01969i) q^{62} +(2.87821 - 2.09114i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.74157 - 1.40248i) q^{65} +(-0.558306 + 0.405633i) q^{66} +(-4.31838 + 13.2906i) q^{67} +0.469323 q^{68} +(-0.333093 + 1.02516i) q^{69} +(2.29317 + 1.49807i) q^{70} +(-1.01766 - 3.13203i) q^{71} +(-0.897470 - 2.76213i) q^{72} +(-4.44606 - 3.23026i) q^{73} -7.55141 q^{74} +(0.621527 + 1.41665i) q^{75} -1.19927 q^{76} +(-2.21046 - 1.60599i) q^{77} +(0.0956093 + 0.294255i) q^{78} +(-3.63836 - 11.1977i) q^{79} +(1.74157 - 1.40248i) q^{80} +(2.51775 - 7.74885i) q^{81} -5.06543 q^{82} +(-2.85831 + 8.79697i) q^{83} +(-0.306622 + 0.222774i) q^{84} +(-0.274368 + 1.01294i) q^{85} +(-6.55306 - 4.76108i) q^{86} +(2.26386 - 1.64479i) q^{87} +(-1.80449 + 1.31104i) q^{88} +(-8.43382 - 6.12753i) q^{89} +(6.48615 - 0.322252i) q^{90} +(-0.991027 + 0.720023i) q^{91} +(-1.07658 + 3.31339i) q^{92} +3.16864 q^{93} +(-3.94313 + 12.1357i) q^{94} +(0.701099 - 2.58838i) q^{95} +(0.0956093 + 0.294255i) q^{96} +(-0.660841 - 2.03386i) q^{97} +(4.44913 + 3.23249i) q^{98} -6.47790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	0.0956093	+	0.294255i	0.0552000	+	0.169888i	0.974856	−	0.222838i	$-0.0715320\pi$
$3$	0.0956093	+	0.294255i	0.0552000	+	0.169888i	−0.919655	+	0.392726i	$0.871532\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.23331	+	0.110958i	−0.998768	+	0.0496218i
$5$	−2.23331	+	0.110958i	−0.998768	+	0.0496218i
$6$	0.0956093	−	0.294255i	0.0390323	−	0.120129i
$7$	1.22498			0.462998			0.231499	−	0.972835i	$-0.425637\pi$
$7$	1.22498			0.462998			0.231499	+	0.972835i	$0.425637\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.34961	−	1.70709i	0.783202	−	0.569030i
$10$	1.87201	+	1.22294i	0.591981	+	0.386728i
$11$	−1.80449	−	1.31104i	−0.544074	−	0.395293i	0.281522	−	0.959555i	$-0.409161\pi$
$11$	−1.80449	−	1.31104i	−0.544074	−	0.395293i	−0.825596	+	0.564262i	$0.809161\pi$
$12$	−0.250308	+	0.181860i	−0.0722578	+	0.0524984i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−0.991027	−	0.720023i	−0.264863	−	0.192434i
$15$	−0.246175	−	0.646555i	−0.0635622	−	0.166940i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.145029	−	0.446353i	0.0351746	−	0.108256i	−0.931928	−	0.362644i	$-0.881874\pi$
$17$	0.145029	−	0.446353i	0.0351746	−	0.108256i	0.967102	+	0.254388i	$0.0818740\pi$
$18$	−2.90427			−0.684544
$19$	−0.370595	+	1.14057i	−0.0850203	+	0.261665i	−0.984525	−	0.175246i	$-0.943928\pi$
$19$	−0.370595	+	1.14057i	−0.0850203	+	0.261665i	0.899504	+	0.436912i	$0.143928\pi$
$20$	−0.795659	−	2.08972i	−0.177915	−	0.467275i
$21$	0.117119	+	0.360456i	0.0255575	+	0.0786579i
$22$	0.689254	+	2.12130i	0.146949	+	0.452264i
$23$	2.81853	+	2.04779i	0.587705	+	0.426993i	0.841494	−	0.540267i	$-0.181677\pi$
$23$	2.81853	+	2.04779i	0.587705	+	0.426993i	−0.253789	+	0.967260i	$0.581677\pi$
$24$	0.309398			0.0631556
$25$	4.97538	−	0.495607i	0.995075	−	0.0991214i
$26$	1.00000			0.196116
$27$	1.47789	+	1.07375i	0.284420	+	0.206643i
$28$	0.378538	+	1.16502i	0.0715371	+	0.220168i
$29$	−2.79483	−	8.60161i	−0.518988	−	1.59728i	−0.775907	−	0.630847i	$-0.782708\pi$
$29$	−2.79483	−	8.60161i	−0.518988	−	1.59728i	0.256920	−	0.966433i	$-0.417292\pi$
$30$	−0.180876	+	0.667772i	−0.0330232	+	0.121918i
$31$	3.16474	−	9.74006i	0.568404	−	1.74937i	−0.0892121	−	0.996013i	$-0.528435\pi$
$31$	3.16474	−	9.74006i	0.568404	−	1.74937i	0.657616	−	0.753354i	$-0.271565\pi$
$32$	1.00000			0.176777
$33$	0.213254	−	0.656328i	0.0371227	−	0.114252i
$34$	−0.379690	+	0.275861i	−0.0651163	+	0.0473098i
$35$	−2.73576	+	0.135921i	−0.462427	+	0.0229748i
$36$	2.34961	+	1.70709i	0.391601	+	0.284515i
$37$	6.10922	−	4.43861i	1.00435	−	0.729703i	0.0413335	−	0.999145i	$-0.486839\pi$
$37$	6.10922	−	4.43861i	1.00435	−	0.729703i	0.963016	+	0.269442i	$0.0868394\pi$
$38$	0.970230	−	0.704913i	0.157392	−	0.114352i
$39$	−0.250308	−	0.181860i	−0.0400814	−	0.0291209i
$40$	−0.584605	+	2.15830i	−0.0924341	+	0.341256i
$41$	4.09802	−	2.97739i	0.640004	−	0.464990i	−0.219848	−	0.975534i	$-0.570556\pi$
$41$	4.09802	−	2.97739i	0.640004	−	0.464990i	0.859851	+	0.510544i	$0.170556\pi$
$42$	0.117119	−	0.360456i	0.0180719	−	0.0556195i
$43$	8.10003			1.23524			0.617621	−	0.786476i	$-0.288096\pi$
$43$	8.10003			1.23524			0.617621	+	0.786476i	$0.288096\pi$
$44$	0.689254	−	2.12130i	0.103909	−	0.319799i
$45$	−5.05799	+	4.07317i	−0.754001	+	0.607192i
$46$	−1.07658	−	3.31339i	−0.158734	−	0.488532i
$47$	−3.94313	−	12.1357i	−0.575165	−	1.77018i	−0.635617	−	0.772004i	$-0.719254\pi$
$47$	−3.94313	−	12.1357i	−0.575165	−	1.77018i	0.0604522	−	0.998171i	$-0.480746\pi$
$48$	−0.250308	−	0.181860i	−0.0361289	−	0.0262492i
$49$	−5.49943			−0.785633
$50$	−4.31647	−	2.52350i	−0.610442	−	0.356877i
$51$	0.145208			0.0203331
$52$	−0.809017	−	0.587785i	−0.112190	−	0.0815111i
$53$	0.861524	+	2.65150i	0.118339	+	0.364211i	0.992629	−	0.121194i	$-0.0386722\pi$
$53$	0.861524	+	2.65150i	0.118339	+	0.364211i	−0.874289	+	0.485405i	$0.838672\pi$
$54$	−0.564503	−	1.73736i	−0.0768192	−	0.236425i
$55$	4.17546	+	2.72774i	0.563019	+	0.367808i
$56$	0.378538	−	1.16502i	0.0505843	−	0.155683i
$57$	−0.371052			−0.0491470
$58$	−2.79483	+	8.60161i	−0.366980	+	1.12945i
$59$	1.39916	−	1.01655i	0.182155	−	0.132343i	−0.492971	−	0.870046i	$-0.664089\pi$
$59$	1.39916	−	1.01655i	0.182155	−	0.132343i	0.675126	+	0.737702i	$0.264089\pi$
$60$	0.538838	−	0.433923i	0.0695637	−	0.0560193i
$61$	9.87773	+	7.17659i	1.26471	+	0.918869i	0.998979	−	0.0451775i	$-0.0143853\pi$
$61$	9.87773	+	7.17659i	1.26471	+	0.918869i	0.265735	+	0.964046i	$0.414385\pi$
$62$	−8.28539	+	6.01969i	−1.05225	+	0.764501i
$63$	2.87821	−	2.09114i	0.362621	−	0.263459i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.74157	−	1.40248i	0.216015	−	0.173956i
$66$	−0.558306	+	0.405633i	−0.0687227	+	0.0499300i
$67$	−4.31838	+	13.2906i	−0.527574	+	1.62371i	0.231595	+	0.972812i	$0.425606\pi$
$67$	−4.31838	+	13.2906i	−0.527574	+	1.62371i	−0.759169	+	0.650893i	$0.774394\pi$
$68$	0.469323			0.0569138
$69$	−0.333093	+	1.02516i	−0.0400997	+	0.123414i
$70$	2.29317	+	1.49807i	0.274086	+	0.179054i
$71$	−1.01766	−	3.13203i	−0.120774	−	0.371704i	0.872334	−	0.488911i	$-0.162606\pi$
$71$	−1.01766	−	3.13203i	−0.120774	−	0.371704i	−0.993107	+	0.117207i	$0.962606\pi$
$72$	−0.897470	−	2.76213i	−0.105768	−	0.325520i
$73$	−4.44606	−	3.23026i	−0.520373	−	0.378073i	0.296372	−	0.955073i	$-0.404223\pi$
$73$	−4.44606	−	3.23026i	−0.520373	−	0.378073i	−0.816744	+	0.577000i	$0.804223\pi$
$74$	−7.55141			−0.877834
$75$	0.621527	+	1.41665i	0.0717678	+	0.163580i
$76$	−1.19927			−0.137566
$77$	−2.21046	−	1.60599i	−0.251905	−	0.183020i
$78$	0.0956093	+	0.294255i	0.0108256	+	0.0333178i
$79$	−3.63836	−	11.1977i	−0.409347	−	1.25984i	−0.917211	−	0.398403i	$-0.869565\pi$
$79$	−3.63836	−	11.1977i	−0.409347	−	1.25984i	0.507864	−	0.861438i	$-0.330435\pi$
$80$	1.74157	−	1.40248i	0.194713	−	0.156802i
$81$	2.51775	−	7.74885i	0.279750	−	0.860983i
$82$	−5.06543			−0.559384
$83$	−2.85831	+	8.79697i	−0.313740	+	0.965592i	0.662530	+	0.749035i	$0.269483\pi$
$83$	−2.85831	+	8.79697i	−0.313740	+	0.965592i	−0.976270	+	0.216557i	$0.930517\pi$
$84$	−0.306622	+	0.222774i	−0.0334552	+	0.0243066i
$85$	−0.274368	+	1.01294i	−0.0297594	+	0.109868i
$86$	−6.55306	−	4.76108i	−0.706635	−	0.513400i
$87$	2.26386	−	1.64479i	0.242711	−	0.176340i
$88$	−1.80449	+	1.31104i	−0.192359	+	0.139757i
$89$	−8.43382	−	6.12753i	−0.893984	−	0.649517i	0.0429300	−	0.999078i	$-0.486331\pi$
$89$	−8.43382	−	6.12753i	−0.893984	−	0.649517i	−0.936914	+	0.349561i	$0.886331\pi$
$90$	6.48615	−	0.322252i	0.683700	−	0.0339683i
$91$	−0.991027	+	0.720023i	−0.103888	+	0.0754789i
$92$	−1.07658	+	3.31339i	−0.112242	+	0.345444i
$93$	3.16864			0.328573
$94$	−3.94313	+	12.1357i	−0.406703	+	1.25170i
$95$	0.701099	−	2.58838i	0.0719312	−	0.265562i
$96$	0.0956093	+	0.294255i	0.00975808	+	0.0300323i
$97$	−0.660841	−	2.03386i	−0.0670982	−	0.206507i	0.911886	−	0.410444i	$-0.134626\pi$
$97$	−0.660841	−	2.03386i	−0.0670982	−	0.206507i	−0.978984	+	0.203937i	$0.934626\pi$
$98$	4.44913	+	3.23249i	0.449430	+	0.326530i
$99$	−6.47790			−0.651053
$100$	2.00883	+	4.57871i	0.200883	+	0.457871i
$101$	8.82663			0.878283			0.439141	−	0.898418i	$-0.355283\pi$
$101$	8.82663			0.878283			0.439141	+	0.898418i	$0.355283\pi$
$102$	−0.117475	−	0.0853509i	−0.0116318	−	0.00845100i
$103$	4.24168	+	13.0545i	0.417945	+	1.28630i	0.909590	+	0.415507i	$0.136396\pi$
$103$	4.24168	+	13.0545i	0.417945	+	1.28630i	−0.491645	+	0.870796i	$0.663604\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$	−0.301559	−	0.792015i	−0.0294291	−	0.0772927i
$106$	0.861524	−	2.65150i	0.0836786	−	0.257536i
$107$	6.23954			0.603200			0.301600	−	0.953435i	$-0.402479\pi$
$107$	6.23954			0.603200			0.301600	+	0.953435i	$0.402479\pi$
$108$	−0.564503	+	1.73736i	−0.0543194	+	0.167178i
$109$	−3.64797	+	2.65041i	−0.349412	+	0.253863i	−0.748622	−	0.662997i	$-0.769284\pi$
$109$	−3.64797	+	2.65041i	−0.349412	+	0.253863i	0.399210	+	0.916859i	$0.369284\pi$
$110$	−1.77469	−	4.66106i	−0.169210	−	0.444415i
$111$	1.89018	+	1.37330i	0.179408	+	0.130348i
$112$	−0.991027	+	0.720023i	−0.0936432	+	0.0680358i
$113$	7.06235	−	5.13110i	0.664370	−	0.482693i	−0.203766	−	0.979020i	$-0.565318\pi$
$113$	7.06235	−	5.13110i	0.664370	−	0.482693i	0.868136	+	0.496326i	$0.165318\pi$
$114$	0.300187	+	0.218099i	0.0281151	+	0.0204268i
$115$	−6.52189	−	4.26061i	−0.608169	−	0.397304i
$116$	7.31697	−	5.31609i	0.679364	−	0.493587i
$117$	−0.897470	+	2.76213i	−0.0829711	+	0.255359i
$118$	−1.72946			−0.159209
$119$	0.177657	−	0.546771i	0.0162858	−	0.0501225i
$120$	−0.690983	+	0.0343301i	−0.0630778	+	0.00313390i
$121$	−1.86183	−	5.73011i	−0.169257	−	0.520919i
$122$	−3.77296	−	11.6120i	−0.341588	−	1.05130i
$123$	1.26792	+	0.921198i	0.114325	+	0.0830616i
$124$	10.2413			0.919696
$125$	−11.0566	+	1.65890i	−0.988931	+	0.148377i
$126$	−3.55767			−0.316942
$127$	14.2028	+	10.3189i	1.26030	+	0.915658i	0.998772	−	0.0495389i	$-0.0157752\pi$
$127$	14.2028	+	10.3189i	1.26030	+	0.915658i	0.261523	+	0.965197i	$0.415775\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.774438	+	2.38347i	0.0681854	+	0.209853i
$130$	−2.23331	+	0.110958i	−0.195875	+	0.00973164i
$131$	−3.81303	+	11.7353i	−0.333146	+	1.02532i	0.634482	+	0.772937i	$0.281213\pi$
$131$	−3.81303	+	11.7353i	−0.333146	+	1.02532i	−0.967628	+	0.252380i	$0.918787\pi$
$132$	0.690104			0.0600658
$133$	−0.453970	+	1.39718i	−0.0393642	+	0.121150i
$134$	11.3057	−	8.21405i	0.976661	−	0.709585i
$135$	−3.41973	−	2.23403i	−0.294323	−	0.192275i
$136$	−0.379690	−	0.275861i	−0.0325582	−	0.0236549i
$137$	−18.6064	+	13.5183i	−1.58965	+	1.15495i	−0.685213	+	0.728343i	$0.740291\pi$
$137$	−18.6064	+	13.5183i	−1.58965	+	1.15495i	−0.904438	+	0.426606i	$0.859709\pi$
$138$	0.872049	−	0.633581i	0.0742338	−	0.0539340i
$139$	−11.1312	−	8.08727i	−0.944134	−	0.685954i	0.00527818	−	0.999986i	$-0.498320\pi$
$139$	−11.1312	−	8.08727i	−0.944134	−	0.685954i	−0.949412	+	0.314033i	$0.898320\pi$
$140$	−0.974663	−	2.55986i	−0.0823741	−	0.216347i
$141$	3.19400	−	2.32057i	0.268983	−	0.195428i
$142$	−1.01766	+	3.13203i	−0.0854001	+	0.262834i
$143$	2.23047			0.186521
$144$	−0.897470	+	2.76213i	−0.0747891	+	0.230177i
$145$	7.19616	+	18.9000i	0.597608	+	1.56956i
$146$	1.69825	+	5.22666i	0.140548	+	0.432562i
$147$	−0.525797	−	1.61824i	−0.0433670	−	0.133470i
$148$	6.10922	+	4.43861i	0.502175	+	0.364851i
$149$	3.34889			0.274352			0.137176	−	0.990547i	$-0.456197\pi$
$149$	3.34889			0.274352			0.137176	+	0.990547i	$0.456197\pi$
$150$	0.329857	−	1.51141i	0.0269327	−	0.123406i
$151$	17.0121			1.38442			0.692211	−	0.721696i	$-0.256637\pi$
$151$	17.0121			1.38442			0.692211	+	0.721696i	$0.256637\pi$
$152$	0.970230	+	0.704913i	0.0786960	+	0.0571760i
$153$	−0.421203	−	1.29633i	−0.0340523	−	0.104802i
$154$	0.844319	+	2.59855i	0.0680372	+	0.209397i
$155$	−5.98711	+	22.1038i	−0.480897	+	1.77542i
$156$	0.0956093	−	0.294255i	0.00765487	−	0.0235593i
$157$	−13.2755			−1.05950			−0.529749	−	0.848154i	$-0.677714\pi$
$157$	−13.2755			−1.05950			−0.529749	+	0.848154i	$0.677714\pi$
$158$	−3.63836	+	11.1977i	−0.289452	+	0.890842i
$159$	−0.697847	+	0.507016i	−0.0553429	+	0.0402090i
$160$	−2.23331	+	0.110958i	−0.176559	+	0.00877198i
$161$	3.45264	+	2.50849i	0.272106	+	0.197697i
$162$	−6.59156	+	4.78905i	−0.517882	+	0.376263i
$163$	3.28374	−	2.38578i	0.257203	−	0.186869i	−0.451710	−	0.892165i	$-0.649186\pi$
$163$	3.28374	−	2.38578i	0.257203	−	0.186869i	0.708913	+	0.705296i	$0.249186\pi$
$164$	4.09802	+	2.97739i	0.320002	+	0.232495i
$165$	−0.403438	+	1.48945i	−0.0314076	+	0.115953i
$166$	7.48315	−	5.43682i	0.580805	−	0.421979i
$167$	−2.78226	+	8.56290i	−0.215297	+	0.662617i	0.783835	+	0.620969i	$0.213261\pi$
$167$	−2.78226	+	8.56290i	−0.215297	+	0.662617i	−0.999132	+	0.0416480i	$0.986739\pi$
$168$	0.379005			0.0292409
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	0.817358	−	0.658214i	0.0626885	−	0.0504827i
$171$	1.07631	+	3.31254i	0.0823073	+	0.253316i
$172$	2.50305	+	7.70358i	0.190855	+	0.587393i
$173$	−14.6572	−	10.6491i	−1.11437	−	0.809636i	−0.131023	−	0.991379i	$-0.541826\pi$
$173$	−14.6572	−	10.6491i	−1.11437	−	0.809636i	−0.983346	+	0.181743i	$0.941826\pi$
$174$	−2.79828			−0.212137
$175$	6.09472	−	0.607107i	0.460717	−	0.0458929i
$176$	2.23047			0.168128
$177$	0.432897	+	0.314518i	0.0325386	+	0.0236407i
$178$	3.22143	+	9.91455i	0.241457	+	0.743127i
$179$	5.58405	+	17.1860i	0.417372	+	1.28454i	0.910112	+	0.414362i	$0.135995\pi$
$179$	5.58405	+	17.1860i	0.417372	+	1.28454i	−0.492740	+	0.870176i	$0.664005\pi$
$180$	−5.43682	−	3.55176i	−0.405237	−	0.264732i
$181$	−4.72993	+	14.5572i	−0.351573	+	1.08203i	0.606397	+	0.795162i	$0.292614\pi$
$181$	−4.72993	+	14.5572i	−0.351573	+	1.08203i	−0.957970	+	0.286868i	$0.907386\pi$
$182$	1.22498			0.0908013
$183$	−1.16735	+	3.59272i	−0.0862927	+	0.265582i
$184$	2.81853	−	2.04779i	0.207785	−	0.150965i
$185$	−13.1513	+	10.5907i	−0.966904	+	0.778642i
$186$	−2.56348	−	1.86248i	−0.187964	−	0.136564i
$187$	−0.846888	+	0.615300i	−0.0619306	+	0.0449952i
$188$	10.3233	−	7.50028i	0.752901	−	0.547014i
$189$	1.81038	+	1.31532i	0.131686	+	0.0956752i
$190$	−2.08861	+	1.68195i	−0.151524	+	0.122021i
$191$	3.63800	−	2.64316i	0.263236	−	0.191252i	−0.448336	−	0.893865i	$-0.647983\pi$
$191$	3.63800	−	2.64316i	0.263236	−	0.191252i	0.711573	+	0.702613i	$0.247983\pi$
$192$	0.0956093	−	0.294255i	0.00690001	−	0.0212360i
$193$	−10.2591			−0.738468			−0.369234	−	0.929337i	$-0.620380\pi$
$193$	−10.2591			−0.738468			−0.369234	+	0.929337i	$0.620380\pi$
$194$	−0.660841	+	2.03386i	−0.0474456	+	0.146022i
$195$	0.579196	+	0.378376i	0.0414771	+	0.0270961i
$196$	−1.69942	−	5.23027i	−0.121387	−	0.373591i
$197$	1.15856	+	3.56567i	0.0825437	+	0.254043i	0.983808	−	0.179227i	$-0.0573596\pi$
$197$	1.15856	+	3.56567i	0.0825437	+	0.254043i	−0.901264	+	0.433270i	$0.857360\pi$
$198$	5.24073	+	3.80761i	0.372442	+	0.270595i
$199$	4.43219			0.314189			0.157095	−	0.987584i	$-0.449787\pi$
$199$	4.43219			0.314189			0.157095	+	0.987584i	$0.449787\pi$
$200$	1.06613	−	4.88502i	0.0753865	−	0.345423i
$201$	−4.32371			−0.304971
$202$	−7.14089	−	5.18816i	−0.502432	−	0.365038i
$203$	−3.42361	−	10.5368i	−0.240290	−	0.739537i
$204$	0.0448716	+	0.138101i	0.00314164	+	0.00966898i
$205$	−8.82180	+	7.10415i	−0.616142	+	0.496175i
$206$	4.24168	−	13.0545i	0.295532	−	0.909553i
$207$	10.1182			0.703263
$208$	0.309017	−	0.951057i	0.0214265	−	0.0659439i
$209$	2.16407	−	1.57229i	0.149692	−	0.108757i
$210$	−0.221568	+	0.818005i	−0.0152897	+	0.0564477i
$211$	11.8039	+	8.57600i	0.812611	+	0.590396i	0.914586	−	0.404391i	$-0.132516\pi$
$211$	11.8039	+	8.57600i	0.812611	+	0.590396i	−0.101976	+	0.994787i	$0.532516\pi$
$212$	−2.25550	+	1.63872i	−0.154908	+	0.112547i
$213$	0.824319	−	0.598903i	0.0564814	−	0.0410361i
$214$	−5.04790	−	3.66751i	−0.345067	−	0.250706i
$215$	−18.0899	+	0.898761i	−1.23372	+	0.0612950i
$216$	1.47789	−	1.07375i	0.100558	−	0.0730594i
$217$	3.87673	−	11.9313i	0.263169	−	0.809952i
$218$	4.50914			0.305397
$219$	0.525434	−	1.61712i	0.0355055	−	0.109275i
$220$	−1.30394	+	4.81402i	−0.0879119	+	0.324561i
$221$	0.145029	+	0.446353i	0.00975569	+	0.0300249i
$222$	−0.721985	−	2.22204i	−0.0484565	−	0.149134i
$223$	15.0974	+	10.9689i	1.01100	+	0.734533i	0.964418	−	0.264382i	$-0.0851680\pi$
$223$	15.0974	+	10.9689i	1.01100	+	0.734533i	0.0465793	+	0.998915i	$0.485168\pi$
$224$	1.22498			0.0818472
$225$	10.8441	−	9.65789i	0.722942	−	0.643859i
$226$	−8.72955			−0.580681
$227$	7.68611	+	5.58429i	0.510145	+	0.370642i	0.812879	−	0.582433i	$-0.197899\pi$
$227$	7.68611	+	5.58429i	0.510145	+	0.370642i	−0.302733	+	0.953075i	$0.597899\pi$
$228$	−0.114661	−	0.352891i	−0.00759363	−	0.0233708i
$229$	−9.20628	−	28.3340i	−0.608368	−	1.87237i	−0.471727	−	0.881745i	$-0.656369\pi$
$229$	−9.20628	−	28.3340i	−0.608368	−	1.87237i	−0.136641	−	0.990621i	$-0.543631\pi$
$230$	2.77200	+	7.28037i	0.182780	+	0.480054i
$231$	0.261231	−	0.803986i	0.0171877	−	0.0528984i
$232$	−9.04427			−0.593786
$233$	4.91311	−	15.1210i	0.321868	−	0.990609i	−0.650966	−	0.759107i	$-0.725636\pi$
$233$	4.91311	−	15.1210i	0.321868	−	0.990609i	0.972834	−	0.231502i	$-0.0743641\pi$
$234$	2.34961	−	1.70709i	0.153599	−	0.111596i
$235$	10.1528	+	26.6653i	0.662296	+	1.73945i
$236$	1.39916	+	1.01655i	0.0910776	+	0.0661717i
$237$	2.94712	−	2.14121i	0.191436	−	0.139086i
$238$	−0.465112	+	0.337923i	−0.0301487	+	0.0219043i
$239$	−4.21061	−	3.05919i	−0.272362	−	0.197882i	0.443217	−	0.896414i	$-0.353837\pi$
$239$	−4.21061	−	3.05919i	−0.272362	−	0.197882i	−0.715579	+	0.698532i	$0.753837\pi$
$240$	0.579196	+	0.378376i	0.0373869	+	0.0244241i
$241$	−12.5432	+	9.11316i	−0.807978	+	0.587030i	−0.913244	−	0.407414i	$-0.866431\pi$
$241$	−12.5432	+	9.11316i	−0.807978	+	0.587030i	0.105266	+	0.994444i	$0.466431\pi$
$242$	−1.86183	+	5.73011i	−0.119683	+	0.368345i
$243$	8.00117			0.513275
$244$	−3.77296	+	11.6120i	−0.241539	+	0.743380i
$245$	12.2820	−	0.610205i	0.784665	−	0.0389845i
$246$	−0.484303	−	1.49053i	−0.0308780	−	0.0950327i
$247$	−0.370595	−	1.14057i	−0.0235804	−	0.0725729i
$248$	−8.28539	−	6.01969i	−0.526123	−	0.382251i
$249$	−2.86183			−0.181361
$250$	9.92004	+	5.15682i	0.627399	+	0.326146i
$251$	−2.43779			−0.153872			−0.0769359	−	0.997036i	$-0.524514\pi$
$251$	−2.43779			−0.153872			−0.0769359	+	0.997036i	$0.524514\pi$
$252$	2.87821	+	2.09114i	0.181310	+	0.131730i
$253$	−2.40129	−	7.39041i	−0.150968	−	0.464631i
$254$	−5.42499	−	16.6964i	−0.340394	−	1.04763i
$255$	−0.324294	+	0.0161119i	−0.0203081	+	0.00100897i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−27.6786			−1.72654			−0.863272	−	0.504739i	$-0.831589\pi$
$257$	−27.6786			−1.72654			−0.863272	+	0.504739i	$0.831589\pi$
$258$	0.774438	−	2.38347i	0.0482144	−	0.148389i
$259$	7.48365	−	5.43719i	0.465012	−	0.337851i
$260$	1.87201	+	1.22294i	0.116097	+	0.0758436i
$261$	−21.2505	−	15.4394i	−1.31537	−	0.955673i
$262$	9.98264	−	7.25281i	0.616730	−	0.448080i
$263$	20.3593	−	14.7919i	1.25541	−	0.912106i	0.256884	−	0.966442i	$-0.417304\pi$
$263$	20.3593	−	14.7919i	1.25541	−	0.912106i	0.998523	+	0.0543358i	$0.0173042\pi$
$264$	−0.558306	−	0.405633i	−0.0343613	−	0.0249650i
$265$	−2.21826	−	5.82603i	−0.136266	−	0.357890i
$266$	1.18851	−	0.863502i	0.0728721	−	0.0529447i
$267$	0.996706	−	3.06754i	0.0609974	−	0.187731i
$268$	−13.9746			−0.853633
$269$	−0.559263	+	1.72123i	−0.0340988	+	0.104945i	−0.966657	−	0.256074i	$-0.917571\pi$
$269$	−0.559263	+	1.72123i	−0.0340988	+	0.104945i	0.932558	+	0.361019i	$0.117571\pi$
$270$	1.45349	+	3.81744i	0.0884564	+	0.232322i
$271$	−3.96089	−	12.1904i	−0.240607	−	0.740512i	−0.996328	−	0.0856186i	$-0.972713\pi$
$271$	−3.96089	−	12.1904i	−0.240607	−	0.740512i	0.755721	−	0.654894i	$-0.227287\pi$
$272$	0.145029	+	0.446353i	0.00879366	+	0.0270641i
$273$	−0.306622	−	0.222774i	−0.0185576	−	0.0134829i
$274$	22.9988			1.38941
$275$	−9.62778	−	5.62859i	−0.580577	−	0.339417i
$276$	−1.07791			−0.0648827
$277$	−15.6606	−	11.3781i	−0.940955	−	0.683644i	0.00769538	−	0.999970i	$-0.497550\pi$
$277$	−15.6606	−	11.3781i	−0.940955	−	0.683644i	−0.948650	+	0.316327i	$0.897550\pi$
$278$	4.25173	+	13.0855i	0.255002	+	0.784815i
$279$	−9.19126	−	28.2878i	−0.550266	−	1.69355i
$280$	−0.716127	+	2.64386i	−0.0427968	+	0.158001i
$281$	−0.678607	+	2.08854i	−0.0404823	+	0.124592i	−0.969255	−	0.246058i	$-0.920865\pi$
$281$	−0.678607	+	2.08854i	−0.0404823	+	0.124592i	0.928773	+	0.370649i	$0.120865\pi$
$282$	−3.94800			−0.235100
$283$	−2.34557	+	7.21894i	−0.139430	+	0.429121i	−0.996253	−	0.0864898i	$-0.972435\pi$
$283$	−2.34557	+	7.21894i	−0.139430	+	0.429121i	0.856823	+	0.515611i	$0.172435\pi$
$284$	2.66427	−	1.93570i	0.158095	−	0.114863i
$285$	0.828675	−	0.0411711i	0.0490865	−	0.00243876i
$286$	−1.80449	−	1.31104i	−0.106702	−	0.0775233i
$287$	5.01998	−	3.64723i	0.296320	−	0.215289i
$288$	2.34961	−	1.70709i	0.138452	−	0.100591i
$289$	13.5751	+	9.86288i	0.798535	+	0.580169i
$290$	5.28732	−	19.5202i	0.310482	−	1.14627i
$291$	0.535291	−	0.388911i	0.0313793	−	0.0227984i
$292$	1.69825	−	5.22666i	0.0993823	−	0.305867i
$293$	25.2052			1.47250			0.736252	−	0.676708i	$-0.236594\pi$
$293$	25.2052			1.47250			0.736252	+	0.676708i	$0.236594\pi$
$294$	−0.525797	+	1.61824i	−0.0306651	+	0.0943775i
$295$	−3.01197	+	2.42552i	−0.175364	+	0.141219i
$296$	−2.33352	−	7.18182i	−0.135633	−	0.417435i
$297$	−1.25911	−	3.87514i	−0.0730609	−	0.224858i
$298$	−2.70931	−	1.96843i	−0.156946	−	0.114028i
$299$	−3.48390			−0.201479
$300$	−1.15525	+	1.02887i	−0.0666982	+	0.0594021i
$301$	9.92234			0.571914
$302$	−13.7630	−	9.99943i	−0.791974	−	0.575403i
$303$	0.843908	+	2.59728i	0.0484812	+	0.149210i
$304$	−0.370595	−	1.14057i	−0.0212551	−	0.0654164i
$305$	−22.8564	−	14.9316i	−1.30875	−	0.854979i
$306$	−0.421203	+	1.29633i	−0.0240786	+	0.0741062i
$307$	−2.18370			−0.124630			−0.0623151	−	0.998057i	$-0.519848\pi$
$307$	−2.18370			−0.124630			−0.0623151	+	0.998057i	$0.519848\pi$
$308$	0.844319	−	2.59855i	0.0481096	−	0.148066i
$309$	−3.43582	+	2.49627i	−0.195457	+	0.142008i
$310$	17.8359	−	14.3632i	1.01301	−	0.815774i
$311$	3.06685	+	2.22820i	0.173905	+	0.126349i	0.671333	−	0.741156i	$-0.265722\pi$
$311$	3.06685	+	2.22820i	0.173905	+	0.126349i	−0.497428	+	0.867505i	$0.665722\pi$
$312$	−0.250308	+	0.181860i	−0.0141709	+	0.0102958i
$313$	2.21901	−	1.61220i	0.125426	−	0.0911271i	−0.523304	−	0.852146i	$-0.675301\pi$
$313$	2.21901	−	1.61220i	0.125426	−	0.0911271i	0.648729	+	0.761019i	$0.275301\pi$
$314$	10.7401	+	7.80313i	0.606098	+	0.440356i
$315$	−6.19592	+	4.98954i	−0.349101	+	0.281129i
$316$	9.52534	−	6.92056i	0.535842	−	0.389312i
$317$	2.81379	−	8.65994i	0.158038	−	0.486391i	−0.840418	−	0.541939i	$-0.817691\pi$
$317$	2.81379	−	8.65994i	0.158038	−	0.486391i	0.998456	+	0.0555478i	$0.0176905\pi$
$318$	0.862586			0.0483714
$319$	−6.23380	+	19.1857i	−0.349026	+	1.07419i
$320$	1.87201	+	1.22294i	0.104648	+	0.0683645i
$321$	0.596558	+	1.83602i	0.0332966	+	0.102477i
$322$	−1.31879	−	4.05882i	−0.0734933	−	0.226189i
$323$	0.455351	+	0.330832i	0.0253364	+	0.0184080i
$324$	8.14762			0.452645
$325$	−3.73385	+	3.32541i	−0.207117	+	0.184460i
$326$	−4.05893			−0.224803
$327$	−1.12868	−	0.820030i	−0.0624159	−	0.0453478i
$328$	−1.56531	−	4.81751i	−0.0864295	−	0.266003i
$329$	−4.83024	−	14.8660i	−0.266300	−	0.819587i
$330$	1.20186	−	0.967854i	0.0661604	−	0.0532786i
$331$	1.25917	−	3.87534i	0.0692105	−	0.213008i	−0.910469	−	0.413577i	$-0.864279\pi$
$331$	1.25917	−	3.87534i	0.0692105	−	0.213008i	0.979680	+	0.200569i	$0.0642792\pi$
$332$	−9.24968			−0.507642
$333$	6.77717	−	20.8580i	0.371386	−	1.14301i
$334$	7.28404	−	5.29216i	0.398565	−	0.289574i
$335$	8.16960	−	30.1612i	0.446353	−	1.64788i
$336$	−0.306622	−	0.222774i	−0.0167276	−	0.0121533i
$337$	6.89703	−	5.01098i	0.375705	−	0.272966i	−0.383868	−	0.923388i	$-0.625408\pi$
$337$	6.89703	−	5.01098i	0.375705	−	0.272966i	0.759573	+	0.650423i	$0.225408\pi$
$338$	−0.809017	+	0.587785i	−0.0440047	+	0.0319713i
$339$	2.18508	+	1.58755i	0.118677	+	0.0862240i
$340$	−1.04815	+	0.0520750i	−0.0568437	+	0.00282416i
$341$	−18.4803	+	13.4267i	−1.00077	+	0.727099i
$342$	1.07631	−	3.31254i	0.0582001	−	0.179121i
$343$	−15.3115			−0.826744
$344$	2.50305	−	7.70358i	0.134955	−	0.415349i
$345$	0.630153	−	2.32645i	0.0339263	−	0.125252i
$346$	5.59856	+	17.2306i	0.300981	+	0.926323i
$347$	−0.923192	−	2.84129i	−0.0495595	−	0.152529i	0.923214	−	0.384286i	$-0.125552\pi$
$347$	−0.923192	−	2.84129i	−0.0495595	−	0.152529i	−0.972774	+	0.231758i	$0.925552\pi$
$348$	2.26386	+	1.64479i	0.121355	+	0.0881699i
$349$	−21.5606			−1.15411			−0.577057	−	0.816704i	$-0.695799\pi$
$349$	−21.5606			−1.15411			−0.577057	+	0.816704i	$0.695799\pi$
$350$	−5.28758	−	3.09123i	−0.282633	−	0.165233i
$351$	−1.82677			−0.0975058
$352$	−1.80449	−	1.31104i	−0.0961796	−	0.0698786i
$353$	7.88120	+	24.2558i	0.419474	+	1.29101i	0.908188	+	0.418564i	$0.137466\pi$
$353$	7.88120	+	24.2558i	0.419474	+	1.29101i	−0.488714	+	0.872444i	$0.662534\pi$
$354$	−0.165352	−	0.508902i	−0.00878837	−	0.0270478i
$355$	2.62027	+	6.88189i	0.139070	+	0.365253i
$356$	3.22143	−	9.91455i	0.170736	−	0.525470i
$357$	0.177876			0.00941419
$358$	5.58405	−	17.1860i	0.295126	−	0.908306i
$359$	2.33904	−	1.69941i	0.123450	−	0.0896916i	−0.524347	−	0.851505i	$-0.675691\pi$
$359$	2.33904	−	1.69941i	0.123450	−	0.0896916i	0.647797	+	0.761813i	$0.275691\pi$
$360$	2.31081	+	6.06912i	0.121790	+	0.319870i
$361$	14.2078	+	10.3225i	0.747777	+	0.543292i
$362$	12.3831	−	8.99686i	0.650842	−	0.472864i
$363$	1.50811	−	1.09570i	0.0791551	−	0.0575095i
$364$	−0.991027	−	0.720023i	−0.0519439	−	0.0377395i
$365$	10.2879	+	6.72085i	0.538492	+	0.351785i
$366$	3.05615	−	2.22042i	0.159748	−	0.116063i
$367$	−2.29776	+	7.07177i	−0.119942	+	0.369143i	−0.992946	−	0.118570i	$-0.962169\pi$
$367$	−2.29776	+	7.07177i	−0.119942	+	0.369143i	0.873004	+	0.487714i	$0.162169\pi$
$368$	−3.48390			−0.181611
$369$	4.54607	−	13.9914i	0.236659	−	0.728362i
$370$	16.8647	−	0.837888i	0.876753	−	0.0435597i
$371$	1.05535	+	3.24802i	0.0547909	+	0.168629i
$372$	0.979164	+	3.01356i	0.0507673	+	0.156246i
$373$	−23.2987	−	16.9275i	−1.20636	−	0.876474i	−0.211467	−	0.977385i	$-0.567824\pi$
$373$	−23.2987	−	16.9275i	−1.20636	−	0.876474i	−0.994895	+	0.100911i	$0.967824\pi$
$374$	1.04681			0.0541293
$375$	−1.54525	−	3.09485i	−0.0797965	−	0.159817i
$376$	−12.7602			−0.658059
$377$	7.31697	+	5.31609i	0.376843	+	0.273793i
$378$	−0.691503	−	2.12823i	−0.0355671	−	0.109464i
$379$	8.96083	+	27.5786i	0.460287	+	1.41662i	0.864814	+	0.502092i	$0.167436\pi$
$379$	8.96083	+	27.5786i	0.460287	+	1.41662i	−0.404527	+	0.914526i	$0.632564\pi$
$380$	2.67835	−	0.133068i	0.137396	−	0.00682626i
$381$	−1.67848	+	5.16584i	−0.0859912	+	0.264654i
$382$	−4.49681			−0.230077
$383$	−2.00545	+	6.17213i	−0.102474	+	0.315381i	−0.989129	−	0.147049i	$-0.953022\pi$
$383$	−2.00545	+	6.17213i	−0.102474	+	0.315381i	0.886656	+	0.462430i	$0.153022\pi$
$384$	−0.250308	+	0.181860i	−0.0127735	+	0.00928049i
$385$	5.11484	+	3.34141i	0.260676	+	0.170294i
$386$	8.29980	+	6.03016i	0.422449	+	0.306927i
$387$	19.0319	−	13.8275i	0.967444	−	0.702889i
$388$	1.73010	−	1.25699i	0.0878327	−	0.0638142i
$389$	−12.5740	−	9.13556i	−0.637528	−	0.463191i	0.221472	−	0.975167i	$-0.428914\pi$
$389$	−12.5740	−	9.13556i	−0.637528	−	0.463191i	−0.859000	+	0.511976i	$0.828914\pi$
$390$	−0.246175	−	0.646555i	−0.0124656	−	0.0327396i
$391$	1.32280	−	0.961073i	0.0668970	−	0.0486035i
$392$	−1.69942	+	5.23027i	−0.0858336	+	0.264169i
$393$	−3.81773			−0.192579
$394$	1.15856	−	3.56567i	0.0583672	−	0.179636i
$395$	9.36806	+	24.6043i	0.471358	+	1.23798i
$396$	−2.00178	−	6.16085i	−0.100593	−	0.309594i
$397$	−1.01852	−	3.13468i	−0.0511180	−	0.157325i	0.922239	−	0.386621i	$-0.126358\pi$
$397$	−1.01852	−	3.13468i	−0.0511180	−	0.157325i	−0.973357	+	0.229296i	$0.926358\pi$
$398$	−3.58571	−	2.60517i	−0.179736	−	0.130586i
$399$	−0.454530			−0.0227549
$400$	−3.73385	+	3.32541i	−0.186693	+	0.166270i
$401$	5.76859			0.288070			0.144035	−	0.989573i	$-0.453992\pi$
$401$	5.76859			0.288070			0.144035	+	0.989573i	$0.453992\pi$
$402$	3.49795	+	2.54141i	0.174462	+	0.126754i
$403$	3.16474	+	9.74006i	0.157647	+	0.485187i
$404$	2.72758	+	8.39462i	0.135702	+	0.417648i
$405$	−4.76314	+	17.5850i	−0.236682	+	0.873804i
$406$	−3.42361	+	10.5368i	−0.169911	+	0.522931i
$407$	−16.8432			−0.834887
$408$	0.0448716	−	0.138101i	0.00222148	−	0.00683700i
$409$	5.11127	−	3.71355i	0.252736	−	0.183623i	−0.454202	−	0.890898i	$-0.650076\pi$
$409$	5.11127	−	3.71355i	0.252736	−	0.183623i	0.706939	+	0.707275i	$0.250076\pi$
$410$	11.3127	−	0.562049i	0.558695	−	0.0277576i
$411$	−5.75678	−	4.18255i	−0.283961	−	0.206310i
$412$	−11.1049	+	8.06815i	−0.547097	+	0.397489i
$413$	1.71394	−	1.24525i	0.0843374	−	0.0612747i
$414$	−8.18579	−	5.94733i	−0.402310	−	0.292295i
$415$	5.40740	−	19.9635i	0.265439	−	0.979971i
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$	1.31548	−	4.04862i	0.0644192	−	0.198262i
$418$	−2.67494			−0.130835
$419$	−4.57022	+	14.0657i	−0.223270	+	0.687155i	0.775193	+	0.631725i	$0.217653\pi$
$419$	−4.57022	+	14.0657i	−0.223270	+	0.687155i	−0.998463	+	0.0554295i	$0.982347\pi$
$420$	0.660064	−	0.531546i	0.0322078	−	0.0259368i
$421$	−6.10889	−	18.8012i	−0.297729	−	0.916316i	−0.982291	−	0.187361i	$-0.940006\pi$
$421$	−6.10889	−	18.8012i	−0.297729	−	0.916316i	0.684562	−	0.728955i	$-0.259994\pi$
$422$	−4.50867	−	13.8763i	−0.219479	−	0.675486i
$423$	−29.9815	−	21.7829i	−1.45775	−	1.05912i
$424$	2.78795			0.135395
$425$	0.500357	−	2.29265i	0.0242709	−	0.111210i
$426$	−1.01891			−0.0493666
$427$	12.1000	+	8.79116i	0.585559	+	0.425434i
$428$	1.92813	+	5.93416i	0.0931995	+	0.286838i
$429$	0.213254	+	0.656328i	0.0102960	+	0.0316878i
$430$	15.1633	+	9.90586i	0.731240	+	0.477703i
$431$	−7.34169	+	22.5954i	−0.353637	+	1.08838i	0.603159	+	0.797621i	$0.293908\pi$
$431$	−7.34169	+	22.5954i	−0.353637	+	1.08838i	−0.956796	+	0.290761i	$0.906092\pi$
$432$	−1.82677			−0.0878906
$433$	−1.51413	+	4.66001i	−0.0727644	+	0.223946i	−0.980824	−	0.194895i	$-0.937563\pi$
$433$	−1.51413	+	4.66001i	−0.0727644	+	0.223946i	0.908060	+	0.418841i	$0.137563\pi$
$434$	−10.1494	+	7.37397i	−0.487187	+	0.353962i
$435$	−4.87340	+	3.92452i	−0.233662	+	0.188166i
$436$	−3.64797	−	2.65041i	−0.174706	−	0.126931i
$437$	−3.38018	+	2.45585i	−0.161696	+	0.117479i
$438$	−1.37560	+	0.999435i	−0.0657289	+	0.0477548i
$439$	11.6705	+	8.47910i	0.557001	+	0.404685i	0.830360	−	0.557227i	$-0.188135\pi$
$439$	11.6705	+	8.47910i	0.557001	+	0.404685i	−0.273359	+	0.961912i	$0.588135\pi$
$440$	3.88452	−	3.12818i	0.185187	−	0.149130i
$441$	−12.9215	+	9.38802i	−0.615310	+	0.447049i
$442$	0.145029	−	0.446353i	0.00689831	−	0.0212308i
$443$	6.39420			0.303798			0.151899	−	0.988396i	$-0.451461\pi$
$443$	6.39420			0.303798			0.151899	+	0.988396i	$0.451461\pi$
$444$	−0.721985	+	2.22204i	−0.0342639	+	0.105453i
$445$	19.5153	+	12.7489i	0.925112	+	0.604356i
$446$	−5.76670	−	17.7481i	−0.273061	−	0.840395i
$447$	0.320185	+	0.985428i	0.0151442	+	0.0466091i
$448$	−0.991027	−	0.720023i	−0.0468216	−	0.0340179i
$449$	28.8932			1.36355			0.681776	−	0.731561i	$-0.261208\pi$
$449$	28.8932			1.36355			0.681776	+	0.731561i	$0.261208\pi$
$450$	−14.4499	+	1.43938i	−0.681173	+	0.0678529i
$451$	−11.2983			−0.532017
$452$	7.06235	+	5.13110i	0.332185	+	0.241347i
$453$	1.62651	+	5.00588i	0.0764201	+	0.235197i
$454$	−2.93583	−	9.03557i	−0.137786	−	0.424060i
$455$	2.13338	−	1.71800i	0.100014	−	0.0805410i
$456$	−0.114661	+	0.352891i	−0.00536951	+	0.0165256i
$457$	23.0234			1.07699			0.538494	−	0.842630i	$-0.318994\pi$
$457$	23.0234			1.07699			0.538494	+	0.842630i	$0.318994\pi$
$458$	−9.20628	+	28.3340i	−0.430181	+	1.32396i
$459$	0.693607	−	0.503935i	0.0323748	−	0.0235217i
$460$	2.03670	−	7.51929i	0.0949618	−	0.350588i
$461$	8.65285	+	6.28666i	0.403003	+	0.292799i	0.770763	−	0.637122i	$-0.219875\pi$
$461$	8.65285	+	6.28666i	0.403003	+	0.292799i	−0.367760	+	0.929921i	$0.619875\pi$
$462$	−0.683911	+	0.496891i	−0.0318184	+	0.0231174i
$463$	11.4713	−	8.33436i	0.533115	−	0.387331i	−0.288407	−	0.957508i	$-0.593125\pi$
$463$	11.4713	−	8.33436i	0.533115	−	0.387331i	0.821522	+	0.570177i	$0.193125\pi$
$464$	7.31697	+	5.31609i	0.339682	+	0.246793i
$465$	−7.07657	+	0.351585i	−0.328168	+	0.0163044i
$466$	−12.8627	+	9.34529i	−0.595852	+	0.432912i
$467$	9.50526	−	29.2542i	0.439851	−	1.35372i	−0.448182	−	0.893943i	$-0.647928\pi$
$467$	9.50526	−	29.2542i	0.439851	−	1.35372i	0.888033	−	0.459780i	$-0.152072\pi$
$468$	−2.90427			−0.134250
$469$	−5.28991	+	16.2807i	−0.244265	+	0.751772i
$470$	7.45970	−	27.5404i	0.344090	−	1.27034i
$471$	−1.26926	−	3.90638i	−0.0584844	−	0.179996i
$472$	−0.534432	−	1.64481i	−0.0245992	−	0.0757086i
$473$	−14.6164	−	10.6194i	−0.672063	−	0.488283i
$474$	−3.64284			−0.167321
$475$	−1.27857	+	5.85845i	−0.0586649	+	0.268804i
$476$	0.574909			0.0263509
$477$	6.55058	+	4.75928i	0.299931	+	0.217912i
$478$	1.60831	+	4.94987i	0.0735624	+	0.226402i
$479$	−3.61841	−	11.1363i	−0.165329	−	0.508832i	0.833731	−	0.552171i	$-0.186200\pi$
$479$	−3.61841	−	11.1363i	−0.165329	−	0.508832i	−0.999060	+	0.0433392i	$0.986200\pi$
$480$	−0.246175	−	0.646555i	−0.0112363	−	0.0295111i
$481$	−2.33352	+	7.18182i	−0.106399	+	0.327463i
$482$	15.5042			0.706198
$483$	−0.408031	+	1.25579i	−0.0185661	+	0.0571405i
$484$	4.87432	−	3.54140i	0.221560	−	0.160973i
$485$	1.70154	+	4.46892i	0.0772628	+	0.202923i
$486$	−6.47308	−	4.70297i	−0.293625	−	0.213331i
$487$	11.2159	−	8.14880i	0.508239	−	0.369257i	−0.303916	−	0.952699i	$-0.598294\pi$
$487$	11.2159	−	8.14880i	0.508239	−	0.369257i	0.812155	+	0.583441i	$0.198294\pi$
$488$	9.87773	−	7.17659i	0.447144	−	0.324869i
$489$	1.01598	+	0.738156i	0.0459444	+	0.0333805i
$490$	−10.2950	−	6.72549i	−0.465080	−	0.303827i
$491$	−4.23043	+	3.07359i	−0.190917	+	0.138709i	−0.679138	−	0.734011i	$-0.737646\pi$
$491$	−4.23043	+	3.07359i	−0.190917	+	0.138709i	0.488221	+	0.872720i	$0.337646\pi$
$492$	−0.484303	+	1.49053i	−0.0218340	+	0.0671983i
$493$	−4.24468			−0.191171
$494$	−0.370595	+	1.14057i	−0.0166738	+	0.0513168i
$495$	14.4672	−	0.718773i	0.650251	−	0.0323064i
$496$	3.16474	+	9.74006i	0.142101	+	0.437342i
$497$	−1.24661	−	3.83667i	−0.0559180	−	0.172098i
$498$	2.31527	+	1.68214i	0.103750	+	0.0753786i
$499$	−19.4266			−0.869652			−0.434826	−	0.900514i	$-0.643190\pi$
$499$	−19.4266			−0.869652			−0.434826	+	0.900514i	$0.643190\pi$
$500$	−4.99438	−	10.0028i	−0.223356	−	0.447339i
$501$	−2.78569			−0.124455
$502$	1.97221	+	1.43290i	0.0880242	+	0.0639533i
$503$	0.0424557	+	0.130665i	0.00189301	+	0.00582607i	0.951999	−	0.306103i	$-0.0990250\pi$
$503$	0.0424557	+	0.130665i	0.00189301	+	0.00582607i	−0.950106	+	0.311929i	$0.899025\pi$
$504$	−1.09938	−	3.38354i	−0.0489702	−	0.150715i
$505$	−19.7126	+	0.979383i	−0.877201	+	0.0435820i
$506$	−2.40129	+	7.39041i	−0.106750	+	0.328544i
$507$	0.309398			0.0137409
$508$	−5.42499	+	16.6964i	−0.240695	+	0.740783i
$509$	15.1879	−	11.0347i	0.673193	−	0.489103i	−0.197900	−	0.980222i	$-0.563412\pi$
$509$	15.1879	−	11.0347i	0.673193	−	0.489103i	0.871092	+	0.491119i	$0.163412\pi$
$510$	0.271830	+	0.177581i	0.0120368	+	0.00786340i
$511$	−5.44632	−	3.95699i	−0.240931	−	0.175047i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−1.77239	+	1.28771i	−0.0782528	+	0.0568540i
$514$	22.3925	+	16.2691i	0.987689	+	0.717598i
$515$	−10.9215	−	28.6842i	−0.481259	−	1.26398i
$516$	−2.02750	+	1.47307i	−0.0892559	+	0.0648482i
$517$	−8.79504	+	27.0684i	−0.386806	+	1.19047i
$518$	−9.25030			−0.406435
$519$	1.73219	−	5.33112i	0.0760345	−	0.234010i
$520$	−0.795659	−	2.08972i	−0.0348919	−	0.0916403i
$521$	12.8255	+	39.4727i	0.561894	+	1.72933i	0.677005	+	0.735978i	$0.263277\pi$
$521$	12.8255	+	39.4727i	0.561894	+	1.72933i	−0.115112	+	0.993353i	$0.536723\pi$
$522$	8.11696	+	24.9814i	0.355270	+	1.09341i
$523$	−23.4463	−	17.0347i	−1.02523	−	0.744876i	−0.0578844	−	0.998323i	$-0.518435\pi$
$523$	−23.4463	−	17.0347i	−1.02523	−	0.744876i	−0.967349	+	0.253447i	$0.918435\pi$
$524$	−12.3392			−0.539041
$525$	0.761356	+	1.73536i	0.0332283	+	0.0757372i
$526$	−25.1654			−1.09727
$527$	−3.88852	−	2.82518i	−0.169387	−	0.123067i
$528$	0.213254	+	0.656328i	0.00928068	+	0.0285630i
$529$	−3.35668	−	10.3308i	−0.145943	−	0.449165i
$530$	−1.62985	+	6.01722i	−0.0707961	+	0.261371i
$531$	1.55213	−	4.77698i	0.0673569	−	0.207303i
$532$	−1.46908			−0.0636926
$533$	−1.56531	+	4.81751i	−0.0678009	+	0.208670i
$534$	−2.60941	+	1.89585i	−0.112920	+	0.0820413i
$535$	−13.9349	+	0.692326i	−0.602456	+	0.0299319i
$536$	11.3057	+	8.21405i	0.488330	+	0.354793i
$537$	−4.52317	+	3.28627i	−0.195189	+	0.141813i
$538$	1.46417	−	1.06378i	0.0631248	−	0.0458628i
$539$	9.92367	+	7.20997i	0.427443	+	0.310555i
$540$	1.06794	−	3.94271i	0.0459568	−	0.169667i
$541$	36.7182	−	26.6773i	1.57864	−	1.14695i	0.660401	−	0.750913i	$-0.270386\pi$
$541$	36.7182	−	26.6773i	1.57864	−	1.14695i	0.918236	−	0.396034i	$-0.129614\pi$
$542$	−3.96089	+	12.1904i	−0.170135	+	0.523621i
$543$	−4.73576			−0.203231
$544$	0.145029	−	0.446353i	0.00621806	−	0.0191372i
$545$	7.85298	−	6.32396i	0.336385	−	0.270888i
$546$	0.117119	+	0.360456i	0.00501224	+	0.0154261i
$547$	−0.331827	−	1.02126i	−0.0141879	−	0.0436658i	0.943712	−	0.330768i	$-0.107308\pi$
$547$	−0.331827	−	1.02126i	−0.0141879	−	0.0436658i	−0.957900	+	0.287103i	$0.907308\pi$
$548$	−18.6064	−	13.5183i	−0.794825	−	0.577474i
$549$	35.4599			1.51339
$550$	4.48063	+	10.2127i	0.191055	+	0.435471i
$551$	10.8465			0.462077
$552$	0.872049	+	0.633581i	0.0371169	+	0.0269670i
$553$	−4.45690	−	13.7169i	−0.189527	−	0.583303i
$554$	5.98182	+	18.4102i	0.254143	+	0.782172i
$555$	−4.37375	−	2.85727i	−0.185655	−	0.121285i
$556$	4.25173	−	13.0855i	0.180314	−	0.554948i
$557$	17.1416			0.726312			0.363156	−	0.931728i	$-0.381699\pi$
$557$	17.1416			0.726312			0.363156	+	0.931728i	$0.381699\pi$
$558$	−9.19126	+	28.2878i	−0.389097	+	1.19752i
$559$	−6.55306	+	4.76108i	−0.277165	+	0.201372i
$560$	2.13338	−	1.71800i	0.0901518	−	0.0725987i
$561$	−0.262026	−	0.190373i	−0.0110627	−	0.00803755i
$562$	1.77662	−	1.29079i	0.0749420	−	0.0544486i
$563$	10.5261	−	7.64769i	0.443624	−	0.322312i	−0.343449	−	0.939171i	$-0.611595\pi$
$563$	10.5261	−	7.64769i	0.443624	−	0.322312i	0.787073	+	0.616859i	$0.211595\pi$
$564$	3.19400	+	2.32057i	0.134491	+	0.0977138i
$565$	−15.2031	+	12.2430i	−0.639600	+	0.515066i
$566$	6.14079	−	4.46155i	0.258117	−	0.187533i
$567$	3.08419	−	9.49215i	0.129524	−	0.398633i
$568$	−3.29321			−0.138180
$569$	−10.7291	+	33.0209i	−0.449788	+	1.38431i	0.427358	+	0.904083i	$0.359444\pi$
$569$	−10.7291	+	33.0209i	−0.449788	+	1.38431i	−0.877146	+	0.480224i	$0.840556\pi$
$570$	−0.694612	−	0.453775i	−0.0290941	−	0.0190065i
$571$	−1.46315	−	4.50313i	−0.0612311	−	0.188450i	0.915762	−	0.401722i	$-0.131588\pi$
$571$	−1.46315	−	4.50313i	−0.0612311	−	0.188450i	−0.976993	+	0.213272i	$0.931588\pi$
$572$	0.689254	+	2.12130i	0.0288191	+	0.0886962i
$573$	1.12559	+	0.817789i	0.0470222	+	0.0341636i
$574$	−6.20504			−0.258993
$575$	15.0382	+	8.79162i	0.627135	+	0.366636i
$576$	−2.90427			−0.121011
$577$	19.0915	+	13.8708i	0.794790	+	0.577449i	0.909381	−	0.415964i	$-0.136556\pi$
$577$	19.0915	+	13.8708i	0.794790	+	0.577449i	−0.114591	+	0.993413i	$0.536556\pi$
$578$	−5.18522	−	15.9585i	−0.215677	−	0.663785i
$579$	−0.980867	−	3.01880i	−0.0407635	−	0.125457i
$580$	−15.7512	+	12.6844i	−0.654034	+	0.526690i
$581$	−3.50136	+	10.7761i	−0.145261	+	0.447067i
$582$	−0.661656			−0.0274265
$583$	1.92160	−	5.91409i	0.0795847	−	0.244937i
$584$	−4.44606	+	3.23026i	−0.183979	+	0.133669i
$585$	1.69785	−	6.26828i	0.0701975	−	0.259161i
$586$	−20.3914	−	14.8152i	−0.842363	−	0.612012i
$587$	−11.5625	+	8.40065i	−0.477235	+	0.346732i	−0.800254	−	0.599661i	$-0.795302\pi$
$587$	−11.5625	+	8.40065i	−0.477235	+	0.346732i	0.323019	+	0.946392i	$0.395302\pi$
$588$	1.37655	−	1.00013i	0.0567681	−	0.0412445i
$589$	9.93642	+	7.21923i	0.409423	+	0.297463i
$590$	3.86242	−	0.191897i	0.159013	−	0.00790026i
$591$	−0.938448	+	0.681822i	−0.0386026	+	0.0280464i
$592$	−2.33352	+	7.18182i	−0.0959069	+	0.295171i
$593$	19.7583			0.811376			0.405688	−	0.914012i	$-0.367032\pi$
$593$	19.7583			0.811376			0.405688	+	0.914012i	$0.367032\pi$
$594$	−1.25911	+	3.87514i	−0.0516619	+	0.158999i
$595$	−0.336095	+	1.24082i	−0.0137785	+	0.0508688i
$596$	1.03486	+	3.18498i	0.0423897	+	0.130462i
$597$	0.423758	+	1.30419i	0.0173433	+	0.0533771i
$598$	2.81853	+	2.04779i	0.115258	+	0.0837402i
$599$	−2.71473			−0.110921			−0.0554604	−	0.998461i	$-0.517663\pi$
$599$	−2.71473			−0.110921			−0.0554604	+	0.998461i	$0.517663\pi$
$600$	1.53937	−	0.153340i	0.0628446	−	0.00626007i
$601$	−19.2048			−0.783378			−0.391689	−	0.920098i	$-0.628109\pi$
$601$	−19.2048			−0.783378			−0.391689	+	0.920098i	$0.628109\pi$
$602$	−8.02734	−	5.83221i	−0.327170	−	0.237703i
$603$	12.5418	+	38.5995i	0.510740	+	1.57189i
$604$	5.25701	+	16.1794i	0.213905	+	0.658331i
$605$	4.79384	+	12.5905i	0.194897	+	0.511879i
$606$	0.843908	−	2.59728i	0.0342814	−	0.105507i
$607$	30.1203			1.22255			0.611273	−	0.791420i	$-0.290658\pi$
$607$	30.1203			1.22255			0.611273	+	0.791420i	$0.290658\pi$
$608$	−0.370595	+	1.14057i	−0.0150296	+	0.0462564i
$609$	2.77317	−	2.01483i	0.112375	−	0.0816449i
$610$	9.71464	+	25.5145i	0.393334	+	1.03305i
$611$	10.3233	+	7.50028i	0.417634	+	0.303429i
$612$	1.10272	−	0.801176i	0.0445750	−	0.0323856i
$613$	−2.36830	+	1.72067i	−0.0956546	+	0.0694971i	−0.634585	−	0.772853i	$-0.718829\pi$
$613$	−2.36830	+	1.72067i	−0.0956546	+	0.0694971i	0.538930	+	0.842351i	$0.318829\pi$
$614$	1.76665	+	1.28354i	0.0712961	+	0.0517996i
$615$	−2.93388	−	1.91664i	−0.118305	−	0.0772863i
$616$	−2.21046	+	1.60599i	−0.0890619	+	0.0647072i
$617$	−7.36021	+	22.6524i	−0.296311	+	0.911951i	0.686467	+	0.727161i	$0.259161\pi$
$617$	−7.36021	+	22.6524i	−0.296311	+	0.911951i	−0.982778	+	0.184790i	$0.940839\pi$
$618$	4.24691			0.170836
$619$	−10.7791	+	33.1746i	−0.433248	+	1.33340i	0.461623	+	0.887076i	$0.347267\pi$
$619$	−10.7791	+	33.1746i	−0.433248	+	1.33340i	−0.894871	+	0.446325i	$0.852733\pi$
$620$	−22.8720	+	1.13635i	−0.918563	+	0.0456370i
$621$	1.96667	+	6.05280i	0.0789199	+	0.242890i
$622$	−1.17143	−	3.60530i	−0.0469702	−	0.144559i
$623$	−10.3312	−	7.50608i	−0.413912	−	0.300725i
$624$	0.309398			0.0123858
$625$	24.5087	−	4.93166i	0.980350	−	0.197266i
$626$	−2.74284			−0.109626
$627$	0.669559	+	0.486463i	0.0267396	+	0.0194275i
$628$	−4.10235	−	12.6257i	−0.163702	−	0.503821i
$629$	−1.09517	−	3.37059i	−0.0436674	−	0.134394i
$630$	7.94538	−	0.394751i	0.316552	−	0.0157272i
$631$	−13.7104	+	42.1962i	−0.545801	+	1.67980i	0.173275	+	0.984873i	$0.444565\pi$
$631$	−13.7104	+	42.1962i	−0.545801	+	1.67980i	−0.719077	+	0.694931i	$0.755435\pi$
$632$	−11.7740			−0.468343
$633$	−1.39497	+	4.29329i	−0.0554453	+	0.170643i
$634$	−7.36659	+	5.35214i	−0.292565	+	0.212561i
$635$	−32.8643	−	21.4695i	−1.30418	−	0.851992i
$636$	−0.697847	−	0.507016i	−0.0276714	−	0.0201045i
$637$	4.44913	−	3.23249i	0.176281	−	0.128076i
$638$	16.3203	−	11.8574i	0.646127	−	0.469439i
$639$	−7.73776	−	5.62181i	−0.306101	−	0.222395i
$640$	−0.795659	−	2.08972i	−0.0314512	−	0.0826034i
$641$	−34.8319	+	25.3068i	−1.37578	+	0.999560i	−0.378515	+	0.925595i	$0.623565\pi$
$641$	−34.8319	+	25.3068i	−1.37578	+	0.999560i	−0.997261	+	0.0739646i	$0.976435\pi$
$642$	0.596558	−	1.83602i	0.0235443	−	0.0724618i
$643$	−9.29483			−0.366552			−0.183276	−	0.983061i	$-0.558670\pi$
$643$	−9.29483			−0.366552			−0.183276	+	0.983061i	$0.558670\pi$
$644$	−1.31879	+	4.05882i	−0.0519676	+	0.159940i
$645$	−1.99403	−	5.23711i	−0.0785147	−	0.206211i
$646$	−0.173929	−	0.535297i	−0.00684313	−	0.0210610i
$647$	12.6434	+	38.9125i	0.497064	+	1.52981i	0.813715	+	0.581264i	$0.197442\pi$
$647$	12.6434	+	38.9125i	0.497064	+	1.52981i	−0.316651	+	0.948542i	$0.602558\pi$
$648$	−6.59156	−	4.78905i	−0.258941	−	0.188132i
$649$	−3.85750			−0.151420
$650$	4.97538	−	0.495607i	0.195150	−	0.0194393i
$651$	3.88151			0.152128
$652$	3.28374	+	2.38578i	0.128601	+	0.0934343i
$653$	−8.71031	−	26.8076i	−0.340861	−	1.04906i	−0.963762	−	0.266762i	$-0.914046\pi$
$653$	−8.71031	−	26.8076i	−0.340861	−	1.04906i	0.622902	−	0.782300i	$-0.285954\pi$
$654$	0.431116	+	1.32684i	0.0168580	+	0.0518834i
$655$	7.21357	−	26.6317i	0.281857	−	1.04059i
$656$	−1.56531	+	4.81751i	−0.0611149	+	0.188092i
$657$	−15.9608			−0.622691
$658$	−4.83024	+	14.8660i	−0.188302	+	0.579535i
$659$	−18.0047	+	13.0812i	−0.701363	+	0.509570i	−0.880376	−	0.474277i	$-0.842710\pi$
$659$	−18.0047	+	13.0812i	−0.701363	+	0.509570i	0.179013	+	0.983847i	$0.442710\pi$
$660$	−1.54122	+	0.0765724i	−0.0599918	+	0.00298058i
$661$	−19.0462	−	13.8378i	−0.740810	−	0.538230i	0.152155	−	0.988357i	$-0.451379\pi$
$661$	−19.0462	−	13.8378i	−0.740810	−	0.538230i	−0.892965	+	0.450127i	$0.851379\pi$
$662$	−3.29656	+	2.39509i	−0.128125	+	0.0930879i
$663$	−0.117475	+	0.0853509i	−0.00456237	+	0.00331475i
$664$	7.48315	+	5.43682i	0.290402	+	0.210990i
$665$	0.858829	−	3.17070i	0.0333040	−	0.122955i
$666$	−17.7428	+	12.8909i	−0.687521	+	0.499514i
$667$	9.73692	−	29.9672i	0.377015	−	1.16033i
$668$	−9.00357			−0.348358
$669$	−1.78421	+	5.49122i	−0.0689814	+	0.212303i
$670$	−24.3377	+	19.5990i	−0.940246	+	0.757175i
$671$	−8.41548	−	25.9002i	−0.324876	−	0.999865i
$672$	0.117119	+	0.360456i	0.00451797	+	0.0139049i
$673$	−19.3817	−	14.0817i	−0.747111	−	0.542808i	0.147819	−	0.989014i	$-0.452775\pi$
$673$	−19.3817	−	14.0817i	−0.747111	−	0.542808i	−0.894930	+	0.446207i	$0.852775\pi$
$674$	−8.52519			−0.328378
$675$	7.88521	+	4.60985i	0.303502	+	0.177433i
$676$	1.00000			0.0384615
$677$	−4.72228	−	3.43094i	−0.181492	−	0.131862i	0.493330	−	0.869842i	$-0.335780\pi$
$677$	−4.72228	−	3.43094i	−0.181492	−	0.131862i	−0.674822	+	0.737981i	$0.735780\pi$
$678$	−0.834626	−	2.56871i	−0.0320536	−	0.0986509i
$679$	−0.809514	−	2.49143i	−0.0310663	−	0.0956122i
$680$	0.878576	+	0.573955i	0.0336919	+	0.0220102i
$681$	−0.908341	+	2.79559i	−0.0348077	+	0.107127i
$682$	22.8429			0.874701
$683$	4.40955	−	13.5712i	0.168727	−	0.519287i	−0.830565	−	0.556922i	$-0.811982\pi$
$683$	4.40955	−	13.5712i	0.168727	−	0.519287i	0.999292	+	0.0376347i	$0.0119823\pi$
$684$	−2.81781	+	2.04726i	−0.107742	+	0.0782789i
$685$	40.0539	−	32.2552i	1.53038	−	1.23241i
$686$	12.3873	+	8.99988i	0.472948	+	0.343617i
$687$	7.45723	−	5.41799i	0.284511	−	0.206709i
$688$	−6.55306	+	4.76108i	−0.249833	+	0.181514i
$689$	−2.25550	−	1.63872i	−0.0859277	−	0.0624301i
$690$	−1.87726	+	1.51175i	−0.0714660	+	0.0575512i
$691$	25.7029	−	18.6742i	0.977783	−	0.710401i	0.0205707	−	0.999788i	$-0.493452\pi$
$691$	25.7029	−	18.6742i	0.977783	−	0.710401i	0.957212	+	0.289388i	$0.0934517\pi$
$692$	5.59856	−	17.2306i	0.212825	−	0.655010i
$693$	−7.93527			−0.301436
$694$	−0.923192	+	2.84129i	−0.0350439	+	0.107854i
$695$	25.7567	+	16.8263i	0.977009	+	0.638259i
$696$	−0.864716	−	2.66132i	−0.0327770	−	0.100877i
$697$	−0.734634	−	2.26097i	−0.0278262	−	0.0856403i
$698$	17.4429	+	12.6730i	0.660224	+	0.479681i
$699$	4.91917			0.186060
$700$	2.46076	+	5.60882i	0.0930082	+	0.211993i
$701$	9.69653			0.366233			0.183116	−	0.983091i	$-0.441381\pi$
$701$	9.69653			0.366233			0.183116	+	0.983091i	$0.441381\pi$
$702$	1.47789	+	1.07375i	0.0557793	+	0.0405260i
$703$	2.79851	+	8.61294i	0.105548	+	0.324843i
$704$	0.689254	+	2.12130i	0.0259772	+	0.0799497i
$705$	−6.87571	+	5.53697i	−0.258954	+	0.208534i
$706$	7.88120	−	24.2558i	0.296613	−	0.912880i
$707$	10.8124			0.406643
$708$	−0.165352	+	0.508902i	−0.00621431	+	0.0191257i
$709$	5.20410	−	3.78100i	0.195444	−	0.141998i	−0.485759	−	0.874093i	$-0.661457\pi$
$709$	5.20410	−	3.78100i	0.195444	−	0.141998i	0.681204	+	0.732094i	$0.261457\pi$
$710$	1.92523	−	7.10773i	0.0722525	−	0.266748i
$711$	−27.6642	−	20.0992i	−1.03749	−	0.753779i
$712$	−8.43382	+	6.12753i	−0.316071	+	0.229639i
$713$	28.8655	−	20.9720i	1.08102	−	0.785407i
$714$	−0.143905	−	0.104553i	−0.00538550	−	0.00391279i
$715$	−4.98134	+	0.247488i	−0.186292	+	0.00925553i
$716$	−14.6192	+	10.6215i	−0.546347	+	0.396944i
$717$	0.497608	−	1.53148i	0.0185835	−	0.0571942i
$718$	−2.89121			−0.107899
$719$	−10.9198	+	33.6078i	−0.407241	+	1.25336i	0.511769	+	0.859123i	$0.328990\pi$
$719$	−10.9198	+	33.6078i	−0.407241	+	1.25336i	−0.919010	+	0.394235i	$0.871010\pi$
$720$	1.69785	−	6.26828i	0.0632752	−	0.233605i
$721$	5.19596	+	15.9915i	0.193507	+	0.595555i
$722$	−5.42688	−	16.7022i	−0.201968	−	0.621592i
$723$	−3.88084	−	2.81959i	−0.144330	−	0.104862i
$724$	−15.3064			−0.568857
$725$	−18.1684	−	41.4111i	−0.674756	−	1.53797i
$726$	−1.86412			−0.0691841
$727$	−5.94200	−	4.31712i	−0.220377	−	0.160113i	0.472120	−	0.881535i	$-0.343489\pi$
$727$	−5.94200	−	4.31712i	−0.220377	−	0.160113i	−0.692496	+	0.721422i	$0.743489\pi$
$728$	0.378538	+	1.16502i	0.0140296	+	0.0431786i
$729$	−6.78827	−	20.8922i	−0.251417	−	0.773783i
$730$	−4.37265	−	11.4843i	−0.161839	−	0.425055i
$731$	1.17474	−	3.61547i	0.0434492	−	0.133723i
$732$	−3.77761			−0.139625
$733$	−9.95220	+	30.6297i	−0.367593	+	1.13133i	0.580749	+	0.814083i	$0.302760\pi$
$733$	−9.95220	+	30.6297i	−0.367593	+	1.13133i	−0.948341	+	0.317251i	$0.897240\pi$
$734$	6.01561	−	4.37060i	0.222040	−	0.161322i
$735$	1.35382	+	3.55569i	0.0499366	+	0.131154i
$736$	2.81853	+	2.04779i	0.103893	+	0.0754824i
$737$	25.2170	−	18.3212i	0.928879	−	0.674870i
$738$	−11.9018	+	8.64715i	−0.438110	+	0.318306i
$739$	−8.66333	−	6.29427i	−0.318686	−	0.231539i	0.416929	−	0.908939i	$-0.363106\pi$
$739$	−8.66333	−	6.29427i	−0.318686	−	0.231539i	−0.735614	+	0.677401i	$0.763106\pi$
$740$	−14.1363	−	9.23494i	−0.519661	−	0.339483i
$741$	0.300187	−	0.218099i	0.0110277	−	0.00801206i
$742$	1.05535	−	3.24802i	0.0387430	−	0.119239i
$743$	−32.5607			−1.19453			−0.597267	−	0.802042i	$-0.703747\pi$
$743$	−32.5607			−1.19453			−0.597267	+	0.802042i	$0.703747\pi$
$744$	0.979164	−	3.01356i	0.0358979	−	0.110482i
$745$	−7.47912	+	0.371585i	−0.274014	+	0.0136138i
$746$	8.89933	+	27.3893i	0.325827	+	1.00279i
$747$	8.30130	+	25.5488i	0.303729	+	0.934781i
$748$	−0.846888	−	0.615300i	−0.0309653	−	0.0224976i
$749$	7.64329			0.279280
$750$	−0.568972	+	3.41206i	−0.0207759	+	0.124591i
$751$	51.1923			1.86803			0.934016	−	0.357231i	$-0.116279\pi$
$751$	51.1923			1.86803			0.934016	+	0.357231i	$0.116279\pi$
$752$	10.3233	+	7.50028i	0.376450	+	0.273507i
$753$	−0.233075	−	0.717332i	−0.00849373	−	0.0261410i
$754$	−2.79483	−	8.60161i	−0.101782	−	0.313252i
$755$	−37.9932	+	1.88762i	−1.38272	+	0.0686975i
$756$	−0.691503	+	2.12823i	−0.0251497	+	0.0774029i
$757$	−28.5554			−1.03786			−0.518931	−	0.854816i	$-0.673670\pi$
$757$	−28.5554			−1.03786			−0.518931	+	0.854816i	$0.673670\pi$
$758$	8.96083	−	27.5786i	0.325472	−	1.00170i
$759$	1.94508	−	1.41318i	0.0706020	−	0.0512954i
$760$	−2.24504	−	1.46664i	−0.0814362	−	0.0532005i
$761$	27.0345	+	19.6417i	0.980000	+	0.712012i	0.957709	−	0.287740i	$-0.0929039\pi$
$761$	27.0345	+	19.6417i	0.980000	+	0.712012i	0.0222913	+	0.999752i	$0.492904\pi$
$762$	4.39432	−	3.19266i	0.159190	−	0.115658i
$763$	−4.46868	+	3.24668i	−0.161777	+	0.117538i
$764$	3.63800	+	2.64316i	0.131618	+	0.0956261i
$765$	1.08452	+	2.84837i	0.0392108	+	0.102983i
$766$	5.25033	−	3.81459i	0.189702	−	0.137827i
$767$	−0.534432	+	1.64481i	−0.0192972	+	0.0593907i
$768$	0.309398			0.0111644
$769$	−4.07233	+	12.5333i	−0.146852	+	0.451964i	−0.997245	−	0.0741848i	$-0.976365\pi$
$769$	−4.07233	+	12.5333i	−0.146852	+	0.451964i	0.850392	+	0.526149i	$0.176365\pi$
$770$	−2.17396	−	5.70969i	−0.0783440	−	0.205763i
$771$	−2.64633	−	8.14457i	−0.0953053	−	0.293320i
$772$	−3.17024	−	9.75700i	−0.114100	−	0.351162i
$773$	3.92060	+	2.84848i	0.141014	+	0.102453i	0.656056	−	0.754712i	$-0.272224\pi$
$773$	3.92060	+	2.84848i	0.141014	+	0.102453i	−0.515042	+	0.857165i	$0.672224\pi$
$774$	−23.5247			−0.845577
$775$	10.9185	−	50.0289i	0.392205	−	1.79709i
$776$	−2.13852			−0.0767686
$777$	2.31543	+	1.68226i	0.0830655	+	0.0603506i
$778$	4.80285	+	14.7816i	0.172190	+	0.529948i
$779$	1.87722	+	5.77750i	0.0672585	+	0.207000i
$780$	−0.180876	+	0.667772i	−0.00647639	+	0.0239101i
$781$	−2.26986	+	6.98591i	−0.0812220	+	0.249976i
$782$	−1.63507			−0.0584701
$783$	5.10552	−	15.7132i	0.182456	−	0.561543i
$784$	4.44913	−	3.23249i	0.158898	−	0.115446i
$785$	29.6483	−	1.47302i	1.05819	−	0.0525742i
$786$	3.08861	+	2.24401i	0.110167	+	0.0800411i
$787$	20.6249	−	14.9849i	0.735198	−	0.534152i	−0.156006	−	0.987756i	$-0.549862\pi$
$787$	20.6249	−	14.9849i	0.735198	−	0.534152i	0.891204	+	0.453604i	$0.149862\pi$
$788$	−3.03314	+	2.20371i	−0.108051	+	0.0785038i
$789$	6.29912	+	4.57658i	0.224255	+	0.162931i
$790$	6.88312	−	25.4117i	0.244890	−	0.904107i
$791$	8.65122	−	6.28548i	0.307602	−	0.223486i
$792$	−2.00178	+	6.16085i	−0.0711302	+	0.218916i
$793$	−12.2095			−0.433574
$794$	−1.01852	+	3.13468i	−0.0361459	+	0.111246i
$795$	1.50225	−	1.20976i	0.0532795	−	0.0429056i
$796$	1.36962	+	4.21526i	0.0485449	+	0.149406i
$797$	−8.61647	−	26.5188i	−0.305211	−	0.939343i	−0.979598	−	0.200965i	$-0.935592\pi$
$797$	−8.61647	−	26.5188i	−0.305211	−	0.939343i	0.674387	−	0.738378i	$-0.264408\pi$
$798$	0.367722	+	0.267166i	0.0130172	+	0.00945757i
$799$	−5.98867			−0.211864
$800$	4.97538	−	0.495607i	0.175906	−	0.0175223i
$801$	−30.2764			−1.06976
$802$	−4.66689	−	3.39069i	−0.164794	−	0.119730i
$803$	3.78789	+	11.6579i	0.133672	+	0.411399i
$804$	−1.33610	−	4.11209i	−0.0471206	−	0.145022i
$805$	−7.98916	−	5.21914i	−0.281581	−	0.183951i
$806$	3.16474	−	9.74006i	0.111473	−	0.343079i
$807$	−0.559953			−0.0197113
$808$	2.72758	−	8.39462i	0.0959559	−	0.295322i
$809$	28.6470	−	20.8133i	1.00717	−	0.731755i	0.0435598	−	0.999051i	$-0.486130\pi$
$809$	28.6470	−	20.8133i	1.00717	−	0.731755i	0.963615	+	0.267296i	$0.0861301\pi$
$810$	14.1896	−	11.4268i	0.498573	−	0.401498i
$811$	−12.8729	−	9.35272i	−0.452029	−	0.328418i	0.338367	−	0.941014i	$-0.390125\pi$
$811$	−12.8729	−	9.35272i	−0.452029	−	0.328418i	−0.790396	+	0.612596i	$0.790125\pi$
$812$	8.96311	−	6.51208i	0.314544	−	0.228529i
$813$	3.20838	−	2.33103i	0.112523	−	0.0817526i
$814$	13.6264	+	9.90019i	0.477607	+	0.347002i
$815$	−7.06891	+	5.69255i	−0.247613	+	0.199401i
$816$	−0.117475	+	0.0853509i	−0.00411246	+	0.00298788i
$817$	−3.00183	+	9.23867i	−0.105021	+	0.323220i
$818$	−6.31788			−0.220899
$819$	−1.09938	+	3.38354i	−0.0384154	+	0.118230i
$820$	−9.48253	−	6.19473i	−0.331144	−	0.216329i
$821$	2.24524	+	6.91015i	0.0783595	+	0.241166i	0.982561	−	0.185940i	$-0.0595331\pi$
$821$	2.24524	+	6.91015i	0.0783595	+	0.241166i	−0.904202	+	0.427106i	$0.859533\pi$
$822$	2.19889	+	6.76750i	0.0766952	+	0.236044i
$823$	−24.2293	−	17.6036i	−0.844581	−	0.613624i	0.0790658	−	0.996869i	$-0.474806\pi$
$823$	−24.2293	−	17.6036i	−0.844581	−	0.613624i	−0.923646	+	0.383246i	$0.874806\pi$
$824$	13.7264			0.478180
$825$	0.735738	−	3.37117i	0.0256151	−	0.117369i
$826$	−2.11854			−0.0737136
$827$	2.66432	+	1.93574i	0.0926476	+	0.0673124i	0.633145	−	0.774033i	$-0.281764\pi$
$827$	2.66432	+	1.93574i	0.0926476	+	0.0673124i	−0.540497	+	0.841346i	$0.681764\pi$
$828$	3.12669	+	9.62298i	0.108660	+	0.334422i
$829$	3.65549	+	11.2504i	0.126960	+	0.390744i	0.994253	−	0.107055i	$-0.0341420\pi$
$829$	3.65549	+	11.2504i	0.126960	+	0.390744i	−0.867293	+	0.497798i	$0.834142\pi$
$830$	−16.1090	+	12.9724i	−0.559150	+	0.450280i
$831$	1.85076	−	5.69607i	0.0642023	−	0.197594i
$832$	1.00000			0.0346688
$833$	−0.797576	+	2.45469i	−0.0276344	+	0.0850498i
$834$	−3.44397	+	2.50219i	−0.119255	+	0.0866437i
$835$	5.26353	−	19.4324i	0.182152	−	0.672484i
$836$	2.16407	+	1.57229i	0.0748459	+	0.0543787i
$837$	15.1355	−	10.9966i	0.523160	−	0.380098i
$838$	11.9650	−	8.69308i	0.413324	−	0.300298i
$839$	45.3295	+	32.9338i	1.56495	+	1.13700i	0.931802	+	0.362968i	$0.118237\pi$
$839$	45.3295	+	32.9338i	1.56495	+	1.13700i	0.633146	+	0.774033i	$0.281763\pi$
$840$	−0.846438	+	0.0420536i	−0.0292049	+	0.00145099i
$841$	−42.7152	+	31.0344i	−1.47294	+	1.07015i
$842$	−6.10889	+	18.8012i	−0.210526	+	0.647933i
$843$	−0.679444			−0.0234013
$844$	−4.50867	+	13.8763i	−0.155195	+	0.477641i
$845$	−0.584605	+	2.15830i	−0.0201110	+	0.0742476i
$846$	11.4519	+	35.2454i	0.393725	+	1.21176i
$847$	−2.28069	−	7.01925i	−0.0783655	−	0.241184i
$848$	−2.25550	−	1.63872i	−0.0774541	−	0.0562737i
$849$	−2.34847			−0.0805992
$850$	−1.75238	+	1.56069i	−0.0601063	+	0.0535312i
$851$	26.3084			0.901840
$852$	0.824319	+	0.598903i	0.0282407	+	0.0205181i
$853$	3.68247	+	11.3335i	0.126085	+	0.388051i	0.994097	−	0.108492i	$-0.0346023\pi$
$853$	3.68247	+	11.3335i	0.126085	+	0.388051i	−0.868012	+	0.496544i	$0.834602\pi$
$854$	−4.62178	−	14.2244i	−0.158154	−	0.486749i
$855$	−2.77128	−	7.27851i	−0.0947759	−	0.248920i
$856$	1.92813	−	5.93416i	0.0659020	−	0.202825i
$857$	4.63743			0.158412			0.0792058	−	0.996858i	$-0.474762\pi$
$857$	4.63743			0.158412			0.0792058	+	0.996858i	$0.474762\pi$
$858$	0.213254	−	0.656328i	0.00728037	−	0.0224067i
$859$	19.1228	−	13.8936i	0.652463	−	0.474042i	−0.211646	−	0.977346i	$-0.567882\pi$
$859$	19.1228	−	13.8936i	0.652463	−	0.474042i	0.864109	+	0.503304i	$0.167882\pi$
$860$	−6.44486	−	16.9268i	−0.219768	−	0.577198i
$861$	1.55317	+	1.12845i	0.0529320	+	0.0384573i
$862$	19.2208	−	13.9647i	0.654663	−	0.475640i
$863$	−19.1392	+	13.9054i	−0.651505	+	0.473346i	−0.863784	−	0.503863i	$-0.831912\pi$
$863$	−19.1392	+	13.9054i	−0.651505	+	0.473346i	0.212279	+	0.977209i	$0.431912\pi$
$864$	1.47789	+	1.07375i	0.0502788	+	0.0365297i
$865$	33.9158	+	22.1564i	1.15317	+	0.753342i
$866$	3.96404	−	2.88004i	0.134704	−	0.0978679i
$867$	−1.60430	+	4.93752i	−0.0544848	+	0.167687i
$868$	12.5454			0.425817
$869$	−8.11525	+	24.9762i	−0.275291	+	0.847258i
$870$	6.24944	−	0.310491i	0.211876	−	0.0105266i
$871$	−4.31838	−	13.2906i	−0.146323	−	0.450335i
$872$	1.39340	+	4.28845i	0.0471865	+	0.145225i
$873$	−5.02469	−	3.65065i	−0.170060	−	0.123556i
$874$	4.17814			0.141328
$875$	−13.5441	+	2.03212i	−0.457873	+	0.0686980i
$876$	1.70034			0.0574492
$877$	−36.2402	−	26.3300i	−1.22374	−	0.889101i	−0.227338	−	0.973816i	$-0.573002\pi$
$877$	−36.2402	−	26.3300i	−1.22374	−	0.889101i	−0.996405	+	0.0847147i	$0.973002\pi$
$878$	−4.45772	−	13.7195i	−0.150441	−	0.463009i
$879$	2.40985	+	7.41676i	0.0812823	+	0.250161i
$880$	−4.98134	+	0.247488i	−0.167921	+	0.00834282i
$881$	10.5547	−	32.4839i	0.355595	−	1.09441i	−0.600068	−	0.799949i	$-0.704860\pi$
$881$	10.5547	−	32.4839i	0.355595	−	1.09441i	0.955664	−	0.294461i	$-0.0951401\pi$
$882$	15.9719			0.537800
$883$	−12.7057	+	39.1041i	−0.427581	+	1.31596i	0.472920	+	0.881105i	$0.343200\pi$
$883$	−12.7057	+	39.1041i	−0.427581	+	1.31596i	−0.900501	+	0.434854i	$0.856800\pi$
$884$	−0.379690	+	0.275861i	−0.0127704	+	0.00927821i
$885$	−1.00169	−	0.654385i	−0.0336716	−	0.0219969i
$886$	−5.17302	−	3.75842i	−0.173791	−	0.126267i
$887$	−32.1750	+	23.3765i	−1.08033	+	0.784905i	−0.977740	−	0.209818i	$-0.932713\pi$
$887$	−32.1750	+	23.3765i	−1.08033	+	0.784905i	−0.102589	+	0.994724i	$0.532713\pi$
$888$	1.89018	−	1.37330i	0.0634304	−	0.0460849i
$889$	17.3981	+	12.6405i	0.583514	+	0.423948i
$890$	−8.29457	−	21.7849i	−0.278035	−	0.730230i
$891$	−14.7023	+	10.6818i	−0.492545	+	0.357855i
$892$	−5.76670	+	17.7481i	−0.193083	+	0.594249i
$893$	15.3030			0.512094
$894$	0.320185	−	0.985428i	0.0107086	−	0.0329576i
$895$	−14.3779	−	37.7620i	−0.480599	−	1.26225i
$896$	0.378538	+	1.16502i	0.0126461	+	0.0389206i
$897$	−0.333093	−	1.02516i	−0.0111217	−	0.0342289i
$898$	−23.3751	−	16.9830i	−0.780036	−	0.566729i
$899$	−92.6251			−3.08922
$900$	12.5362	+	7.32893i	0.417874	+	0.244298i
$901$	1.30845			0.0435907
$902$	9.14052	+	6.64098i	0.304346	+	0.221120i
$903$	0.948668	+	2.91970i	0.0315697	+	0.0971615i
$904$	−2.69758	−	8.30230i	−0.0897202	−	0.276130i
$905$	8.94817	−	33.0357i	0.297447	−	1.09814i
$906$	1.62651	−	5.00588i	0.0540372	−	0.166309i
$907$	42.5523			1.41293			0.706463	−	0.707750i	$-0.250290\pi$
$907$	42.5523			1.41293			0.706463	+	0.707750i	$0.250290\pi$
$908$	−2.93583	+	9.03557i	−0.0974291	+	0.299856i
$909$	20.7391	−	15.0678i	0.687873	−	0.499769i
$910$	−2.73576	+	0.135921i	−0.0906894	+	0.00450572i
$911$	−11.0236	−	8.00912i	−0.365229	−	0.265354i	0.390001	−	0.920814i	$-0.372475\pi$
$911$	−11.0236	−	8.00912i	−0.365229	−	0.265354i	−0.755230	+	0.655460i	$0.772475\pi$
$912$	0.300187	−	0.218099i	0.00994019	−	0.00722197i
$913$	16.6909	−	12.1267i	0.552390	−	0.401335i
$914$	−18.6263	−	13.5328i	−0.616103	−	0.447625i
$915$	2.20841	−	8.15320i	0.0730078	−	0.269537i
$916$	24.1024	−	17.5114i	0.796364	−	0.578593i
$917$	−4.67087	+	14.3755i	−0.154246	+	0.474720i
$918$	−0.857346			−0.0282966
$919$	15.2382	−	46.8983i	0.502661	−	1.54703i	−0.302007	−	0.953306i	$-0.597657\pi$
$919$	15.2382	−	46.8983i	0.502661	−	1.54703i	0.804668	−	0.593726i	$-0.202343\pi$
$920$	−6.06745	+	4.88608i	−0.200038	+	0.161089i
$921$	−0.208782	−	0.642564i	−0.00687959	−	0.0211732i
$922$	−3.30509	−	10.1720i	−0.108847	−	0.334998i
$923$	2.66427	+	1.93570i	0.0876954	+	0.0637144i
$924$	0.845361			0.0278103
$925$	28.1959	−	25.1115i	0.927075	−	0.825662i
$926$	−14.1793			−0.465960
$927$	32.2515	+	23.4321i	1.05928	+	0.769612i
$928$	−2.79483	−	8.60161i	−0.0917449	−	0.282362i
$929$	5.59115	+	17.2078i	0.183440	+	0.564569i	0.999918	−	0.0128068i	$-0.00407664\pi$
$929$	5.59115	+	17.2078i	0.183440	+	0.564569i	−0.816478	+	0.577376i	$0.804077\pi$
$930$	5.93172	+	3.87506i	0.194509	+	0.127068i
$931$	2.03806	−	6.27251i	0.0667947	−	0.205573i
$932$	15.8992			0.520794
$933$	−0.362439	+	1.11547i	−0.0118657	+	0.0365189i
$934$	−24.8851	+	18.0801i	−0.814266	+	0.591599i
$935$	1.82309	−	1.46813i	0.0596216	−	0.0480129i
$936$	2.34961	+	1.70709i	0.0767993	+	0.0557979i
$937$	13.1023	−	9.51936i	0.428033	−	0.310984i	−0.352829	−	0.935688i	$-0.614780\pi$
$937$	13.1023	−	9.51936i	0.428033	−	0.310984i	0.780862	+	0.624704i	$0.214780\pi$
$938$	13.8492	−	10.0620i	0.452191	−	0.328536i
$939$	0.686556	+	0.498812i	0.0224049	+	0.0162781i
$940$	−22.2228	+	17.8959i	−0.724829	+	0.583701i
$941$	1.74510	−	1.26789i	0.0568886	−	0.0413320i	−0.558978	−	0.829183i	$-0.688806\pi$
$941$	1.74510	−	1.26789i	0.0568886	−	0.0413320i	0.615866	+	0.787851i	$0.288806\pi$
$942$	−1.26926	+	3.90638i	−0.0413547	+	0.127277i
$943$	17.6475			0.574681
$944$	−0.534432	+	1.64481i	−0.0173943	+	0.0535340i
$945$	−4.18909	−	2.73664i	−0.136271	−	0.0890229i
$946$	5.58297	+	17.1826i	0.181518	+	0.558655i
$947$	12.2577	+	37.7253i	0.398322	+	1.22591i	0.926344	+	0.376678i	$0.122934\pi$
$947$	12.2577	+	37.7253i	0.398322	+	1.22591i	−0.528022	+	0.849231i	$0.677066\pi$
$948$	2.94712	+	2.14121i	0.0957181	+	0.0695432i
$949$	5.49564			0.178396
$950$	4.47790	−	3.98806i	0.145282	−	0.129390i
$951$	2.81726			0.0913558
$952$	−0.465112	−	0.337923i	−0.0150744	−	0.0109522i
$953$	5.21275	+	16.0432i	0.168857	+	0.519690i	0.999300	−	0.0374149i	$-0.0119123\pi$
$953$	5.21275	+	16.0432i	0.168857	+	0.519690i	−0.830442	+	0.557104i	$0.811912\pi$
$954$	−2.50210	−	7.70067i	−0.0810085	−	0.249318i
$955$	−7.83151	+	6.30667i	−0.253422	+	0.204079i
$956$	1.60831	−	4.94987i	0.0520165	−	0.160090i
$957$	−6.24149			−0.201759
$958$	−3.61841	+	11.1363i	−0.116906	+	0.359798i
$959$	−22.7924	+	16.5596i	−0.736004	+	0.534738i
$960$	−0.180876	+	0.667772i	−0.00583774	+	0.0215523i
$961$	−59.7737	−	43.4281i	−1.92818	−	1.40091i
$962$	6.10922	−	4.43861i	0.196969	−	0.143107i
$963$	14.6605	−	10.6515i	0.472427	−	0.343238i
$964$	−12.5432	−	9.11316i	−0.403989	−	0.293515i
$965$	22.9118	−	1.13833i	0.737558	−	0.0366441i
$966$	1.06824	−	0.776122i	0.0343701	−	0.0249713i
$967$	9.59361	−	29.5261i	0.308510	−	0.949495i	−0.669835	−	0.742510i	$-0.733635\pi$
$967$	9.59361	−	29.5261i	0.308510	−	0.949495i	0.978344	−	0.206985i	$-0.0663650\pi$
$968$	−6.02500			−0.193651
$969$	−0.0538132	+	0.165620i	−0.00172873	+	0.00532048i
$970$	1.25019	−	4.61557i	0.0401412	−	0.148197i
$971$	−4.57309	−	14.0745i	−0.146758	−	0.451673i	0.850475	−	0.526015i	$-0.176314\pi$
$971$	−4.57309	−	14.0745i	−0.146758	−	0.451673i	−0.997233	+	0.0743417i	$0.976314\pi$
$972$	2.47250	+	7.60957i	0.0793054	+	0.244077i
$973$	−13.6354	−	9.90672i	−0.437132	−	0.317595i
$974$	−13.8636			−0.444217
$975$	−1.33551	−	0.780766i	−0.0427705	−	0.0250045i
$976$	−12.2095			−0.390818
$977$	8.41236	+	6.11194i	0.269135	+	0.195538i	0.714165	−	0.699978i	$-0.246807\pi$
$977$	8.41236	+	6.11194i	0.269135	+	0.195538i	−0.445029	+	0.895516i	$0.646807\pi$
$978$	−0.388071	−	1.19436i	−0.0124092	−	0.0381914i
$979$	7.18532	+	22.1141i	0.229644	+	0.706771i
$980$	4.37567	+	11.4923i	0.139776	+	0.367107i
$981$	−4.04682	+	12.4548i	−0.129205	+	0.397652i
$982$	5.22910			0.166867
$983$	−6.45581	+	19.8689i	−0.205908	+	0.633721i	0.793767	+	0.608223i	$0.208117\pi$
$983$	−6.45581	+	19.8689i	−0.205908	+	0.633721i	−0.999675	+	0.0254981i	$0.991883\pi$
$984$	1.26792	−	0.921198i	0.0404198	−	0.0293667i
$985$	−2.98306	−	7.83471i	−0.0950481	−	0.249635i
$986$	3.43402	+	2.49496i	0.109362	+	0.0794558i
$987$	3.91257	−	2.84265i	0.124538	−	0.0904825i
$988$	0.970230	−	0.704913i	0.0308671	−	0.0224263i
$989$	22.8302	+	16.5871i	0.725958	+	0.527440i
$990$	−12.1267	−	7.92209i	−0.385411	−	0.251781i
$991$	−10.3999	+	7.55598i	−0.330364	+	0.240023i	−0.740585	−	0.671963i	$-0.765452\pi$
$991$	−10.3999	+	7.55598i	−0.330364	+	0.240023i	0.410221	+	0.911986i	$0.365452\pi$
$992$	3.16474	−	9.74006i	0.100481	−	0.309247i
$993$	1.26073			0.0400080
$994$	−1.24661	+	3.83667i	−0.0395400	+	0.121692i
$995$	−9.89846	+	0.491785i	−0.313802	+	0.0155906i
$996$	−0.884355	−	2.72176i	−0.0280219	−	0.0862424i
$997$	8.19325	+	25.2162i	0.259483	+	0.798606i	0.992913	+	0.118841i	$0.0379180\pi$
$997$	8.19325	+	25.2162i	0.259483	+	0.798606i	−0.733431	+	0.679764i	$0.762082\pi$
$998$	15.7164	+	11.4186i	0.497494	+	0.361451i
$999$	13.7947			0.436445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.391.4	yes	24
25.11	even	5	inner	650.2.l.c.261.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.261.4	✓	24	25.11	even	5	inner
650.2.l.c.391.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.0956093 + 0.294255i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23331 + 0.110958i) q^{5} +(0.0956093 - 0.294255i) q^{6} +1.22498 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.34961 - 1.70709i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.0956093 + 0.294255i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23331 + 0.110958i) q^{5} +(0.0956093 - 0.294255i) q^{6} +1.22498 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.34961 - 1.70709i) q^{9} +(1.87201 + 1.22294i) q^{10} +(-1.80449 - 1.31104i) q^{11} +(-0.250308 + 0.181860i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.991027 - 0.720023i) q^{14} +(-0.246175 - 0.646555i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.145029 - 0.446353i) q^{17} -2.90427 q^{18} +(-0.370595 + 1.14057i) q^{19} +(-0.795659 - 2.08972i) q^{20} +(0.117119 + 0.360456i) q^{21} +(0.689254 + 2.12130i) q^{22} +(2.81853 + 2.04779i) q^{23} +0.309398 q^{24} +(4.97538 - 0.495607i) q^{25} +1.00000 q^{26} +(1.47789 + 1.07375i) q^{27} +(0.378538 + 1.16502i) q^{28} +(-2.79483 - 8.60161i) q^{29} +(-0.180876 + 0.667772i) q^{30} +(3.16474 - 9.74006i) q^{31} +1.00000 q^{32} +(0.213254 - 0.656328i) q^{33} +(-0.379690 + 0.275861i) q^{34} +(-2.73576 + 0.135921i) q^{35} +(2.34961 + 1.70709i) q^{36} +(6.10922 - 4.43861i) q^{37} +(0.970230 - 0.704913i) q^{38} +(-0.250308 - 0.181860i) q^{39} +(-0.584605 + 2.15830i) q^{40} +(4.09802 - 2.97739i) q^{41} +(0.117119 - 0.360456i) q^{42} +8.10003 q^{43} +(0.689254 - 2.12130i) q^{44} +(-5.05799 + 4.07317i) q^{45} +(-1.07658 - 3.31339i) q^{46} +(-3.94313 - 12.1357i) q^{47} +(-0.250308 - 0.181860i) q^{48} -5.49943 q^{49} +(-4.31647 - 2.52350i) q^{50} +0.145208 q^{51} +(-0.809017 - 0.587785i) q^{52} +(0.861524 + 2.65150i) q^{53} +(-0.564503 - 1.73736i) q^{54} +(4.17546 + 2.72774i) q^{55} +(0.378538 - 1.16502i) q^{56} -0.371052 q^{57} +(-2.79483 + 8.60161i) q^{58} +(1.39916 - 1.01655i) q^{59} +(0.538838 - 0.433923i) q^{60} +(9.87773 + 7.17659i) q^{61} +(-8.28539 + 6.01969i) q^{62} +(2.87821 - 2.09114i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.74157 - 1.40248i) q^{65} +(-0.558306 + 0.405633i) q^{66} +(-4.31838 + 13.2906i) q^{67} +0.469323 q^{68} +(-0.333093 + 1.02516i) q^{69} +(2.29317 + 1.49807i) q^{70} +(-1.01766 - 3.13203i) q^{71} +(-0.897470 - 2.76213i) q^{72} +(-4.44606 - 3.23026i) q^{73} -7.55141 q^{74} +(0.621527 + 1.41665i) q^{75} -1.19927 q^{76} +(-2.21046 - 1.60599i) q^{77} +(0.0956093 + 0.294255i) q^{78} +(-3.63836 - 11.1977i) q^{79} +(1.74157 - 1.40248i) q^{80} +(2.51775 - 7.74885i) q^{81} -5.06543 q^{82} +(-2.85831 + 8.79697i) q^{83} +(-0.306622 + 0.222774i) q^{84} +(-0.274368 + 1.01294i) q^{85} +(-6.55306 - 4.76108i) q^{86} +(2.26386 - 1.64479i) q^{87} +(-1.80449 + 1.31104i) q^{88} +(-8.43382 - 6.12753i) q^{89} +(6.48615 - 0.322252i) q^{90} +(-0.991027 + 0.720023i) q^{91} +(-1.07658 + 3.31339i) q^{92} +3.16864 q^{93} +(-3.94313 + 12.1357i) q^{94} +(0.701099 - 2.58838i) q^{95} +(0.0956093 + 0.294255i) q^{96} +(-0.660841 - 2.03386i) q^{97} +(4.44913 + 3.23249i) q^{98} -6.47790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Introduction

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