LMFDB - Embedded newform 825.2.p.a.586.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(181,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.p (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:	$6.58765816676$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			586.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.586
Dual form			825.2.p.a.466.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690983 + 2.12663i) q^{2} +1.00000 q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(0.809017 - 2.48990i) q^{7} +(1.80902 - 1.31433i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.690983 + 2.12663i) q^{2} +1.00000 q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(0.809017 - 2.48990i) q^{7} +(1.80902 - 1.31433i) q^{8} +1.00000 q^{9} +(-1.54508 - 4.75528i) q^{10} +(0.809017 + 3.21644i) q^{11} +(-2.42705 - 1.76336i) q^{12} -6.00000 q^{13} +(4.73607 + 3.44095i) q^{14} +(-1.80902 + 1.31433i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.92705 - 5.93085i) q^{17} +(-0.690983 + 2.12663i) q^{18} +(-5.35410 + 3.88998i) q^{19} +6.70820 q^{20} +(0.809017 - 2.48990i) q^{21} +(-7.39919 - 0.502029i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 - 1.31433i) q^{24} +(1.54508 - 4.75528i) q^{25} +(4.14590 - 12.7598i) q^{26} +1.00000 q^{27} +(-6.35410 + 4.61653i) q^{28} +(-5.73607 - 4.16750i) q^{29} +(-1.54508 - 4.75528i) q^{30} +(-6.04508 - 4.39201i) q^{31} +6.70820 q^{32} +(0.809017 + 3.21644i) q^{33} +(11.2812 + 8.19624i) q^{34} +(1.80902 + 5.56758i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-0.927051 + 0.673542i) q^{37} +(-4.57295 - 14.0741i) q^{38} -6.00000 q^{39} +(-1.54508 + 4.75528i) q^{40} +(0.545085 - 1.67760i) q^{41} +(4.73607 + 3.44095i) q^{42} +7.94427 q^{43} +(3.70820 - 9.23305i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(-3.78115 - 11.6372i) q^{46} +8.09017 q^{47} +(-0.309017 - 0.951057i) q^{48} +(0.118034 + 0.0857567i) q^{49} +(9.04508 + 6.57164i) q^{50} +(1.92705 - 5.93085i) q^{51} +(14.5623 + 10.5801i) q^{52} +(-0.309017 - 0.951057i) q^{53} +(-0.690983 + 2.12663i) q^{54} +(-5.69098 - 4.75528i) q^{55} +(-1.80902 - 5.56758i) q^{56} +(-5.35410 + 3.88998i) q^{57} +(12.8262 - 9.31881i) q^{58} +(-9.47214 + 6.88191i) q^{59} +6.70820 q^{60} -5.32624 q^{61} +(13.5172 - 9.82084i) q^{62} +(0.809017 - 2.48990i) q^{63} +(-4.01722 + 12.3637i) q^{64} +(10.8541 - 7.88597i) q^{65} +(-7.39919 - 0.502029i) q^{66} +(-1.80902 - 5.56758i) q^{67} +(-15.1353 + 10.9964i) q^{68} +(-4.42705 + 3.21644i) q^{69} -13.0902 q^{70} +(-6.04508 + 4.39201i) q^{71} +(1.80902 - 1.31433i) q^{72} +(-1.00000 - 3.07768i) q^{73} +(-0.791796 - 2.43690i) q^{74} +(1.54508 - 4.75528i) q^{75} +19.8541 q^{76} +(8.66312 + 0.587785i) q^{77} +(4.14590 - 12.7598i) q^{78} +(-4.00000 - 12.3107i) q^{79} +(1.80902 + 1.31433i) q^{80} +1.00000 q^{81} +(3.19098 + 2.31838i) q^{82} +(-2.64590 + 8.14324i) q^{83} +(-6.35410 + 4.61653i) q^{84} +(4.30902 + 13.2618i) q^{85} +(-5.48936 + 16.8945i) q^{86} +(-5.73607 - 4.16750i) q^{87} +(5.69098 + 4.75528i) q^{88} +(-2.88197 + 2.09387i) q^{89} +(-1.54508 - 4.75528i) q^{90} +(-4.85410 + 14.9394i) q^{91} +16.4164 q^{92} +(-6.04508 - 4.39201i) q^{93} +(-5.59017 + 17.2048i) q^{94} +(4.57295 - 14.0741i) q^{95} +6.70820 q^{96} +(0.781153 + 2.40414i) q^{97} +(-0.263932 + 0.191758i) q^{98} +(0.809017 + 3.21644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + q^{11} - 3 q^{12} - 24 q^{13} + 10 q^{14} - 5 q^{15} + q^{16} + q^{17} - 5 q^{18} - 8 q^{19} + q^{21} - 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} + 4 q^{27} - 12 q^{28} - 14 q^{29} + 5 q^{30} - 13 q^{31} + q^{33} + 25 q^{34} + 5 q^{35} - 3 q^{36} + 3 q^{37} - 25 q^{38} - 24 q^{39} + 5 q^{40} - 9 q^{41} + 10 q^{42} - 4 q^{43} - 12 q^{44} - 5 q^{45} + 5 q^{46} + 10 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} - 25 q^{55} - 5 q^{56} - 8 q^{57} + 20 q^{58} - 20 q^{59} + 10 q^{61} + 25 q^{62} + q^{63} + 13 q^{64} + 30 q^{65} - 5 q^{66} - 5 q^{67} - 27 q^{68} - 11 q^{69} - 30 q^{70} - 13 q^{71} + 5 q^{72} - 4 q^{73} - 30 q^{74} - 5 q^{75} + 66 q^{76} + 19 q^{77} + 30 q^{78} - 16 q^{79} + 5 q^{80} + 4 q^{81} + 15 q^{82} - 24 q^{83} - 12 q^{84} + 15 q^{85} + 25 q^{86} - 14 q^{87} + 25 q^{88} - 16 q^{89} + 5 q^{90} - 6 q^{91} + 12 q^{92} - 13 q^{93} + 25 q^{95} - 17 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + q^11 - 3 * q^12 - 24 * q^13 + 10 * q^14 - 5 * q^15 + q^16 + q^17 - 5 * q^18 - 8 * q^19 + q^21 - 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 + 4 * q^27 - 12 * q^28 - 14 * q^29 + 5 * q^30 - 13 * q^31 + q^33 + 25 * q^34 + 5 * q^35 - 3 * q^36 + 3 * q^37 - 25 * q^38 - 24 * q^39 + 5 * q^40 - 9 * q^41 + 10 * q^42 - 4 * q^43 - 12 * q^44 - 5 * q^45 + 5 * q^46 + 10 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 - 25 * q^55 - 5 * q^56 - 8 * q^57 + 20 * q^58 - 20 * q^59 + 10 * q^61 + 25 * q^62 + q^63 + 13 * q^64 + 30 * q^65 - 5 * q^66 - 5 * q^67 - 27 * q^68 - 11 * q^69 - 30 * q^70 - 13 * q^71 + 5 * q^72 - 4 * q^73 - 30 * q^74 - 5 * q^75 + 66 * q^76 + 19 * q^77 + 30 * q^78 - 16 * q^79 + 5 * q^80 + 4 * q^81 + 15 * q^82 - 24 * q^83 - 12 * q^84 + 15 * q^85 + 25 * q^86 - 14 * q^87 + 25 * q^88 - 16 * q^89 + 5 * q^90 - 6 * q^91 + 12 * q^92 - 13 * q^93 + 25 * q^95 - 17 * q^97 - 10 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.690983	+	2.12663i	−0.488599	+	1.50375i	0.338101	+	0.941110i	$0.390215\pi$
$2$	−0.690983	+	2.12663i	−0.488599	+	1.50375i	−0.826700	+	0.562643i	$0.809785\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.42705	−	1.76336i	−1.21353	−	0.881678i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$	−0.690983	+	2.12663i	−0.282093	+	0.868192i
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	−0.673605	−	0.739091i	$-0.735255\pi$
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	0.979385	−	0.202002i	$-0.0647447\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	1.00000			0.333333
$10$	−1.54508	−	4.75528i	−0.488599	−	1.50375i
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$12$	−2.42705	−	1.76336i	−0.700629	−	0.509037i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$	4.73607	+	3.44095i	1.26577	+	0.919634i
$15$	−1.80902	+	1.31433i	−0.467086	+	0.339358i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.92705	−	5.93085i	0.467379	−	1.43844i	−0.388588	−	0.921412i	$-0.627037\pi$
$17$	1.92705	−	5.93085i	0.467379	−	1.43844i	0.855966	−	0.517031i	$-0.172963\pi$
$18$	−0.690983	+	2.12663i	−0.162866	+	0.501251i
$19$	−5.35410	+	3.88998i	−1.22832	+	0.892423i	−0.996763	−	0.0803992i	$-0.974381\pi$
$19$	−5.35410	+	3.88998i	−1.22832	+	0.892423i	−0.231552	+	0.972822i	$0.574381\pi$
$20$	6.70820			1.50000
$21$	0.809017	−	2.48990i	0.176542	−	0.543340i
$22$	−7.39919	−	0.502029i	−1.57751	−	0.107033i
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	−0.944295	−	0.329101i	$-0.893254\pi$
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	0.0211907	+	0.999775i	$0.493254\pi$
$24$	1.80902	−	1.31433i	0.369264	−	0.268286i
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	4.14590	−	12.7598i	0.813077	−	2.50240i
$27$	1.00000			0.192450
$28$	−6.35410	+	4.61653i	−1.20081	+	0.872441i
$29$	−5.73607	−	4.16750i	−1.06516	−	0.773885i	−0.0901248	−	0.995930i	$-0.528727\pi$
$29$	−5.73607	−	4.16750i	−1.06516	−	0.773885i	−0.975036	+	0.222046i	$0.928727\pi$
$30$	−1.54508	−	4.75528i	−0.282093	−	0.868192i
$31$	−6.04508	−	4.39201i	−1.08573	−	0.788829i	−0.107056	−	0.994253i	$-0.534143\pi$
$31$	−6.04508	−	4.39201i	−1.08573	−	0.788829i	−0.978673	+	0.205424i	$0.934143\pi$
$32$	6.70820			1.18585
$33$	0.809017	+	3.21644i	0.140832	+	0.559910i
$34$	11.2812	+	8.19624i	1.93470	+	1.40564i
$35$	1.80902	+	5.56758i	0.305780	+	0.941093i
$36$	−2.42705	−	1.76336i	−0.404508	−	0.293893i
$37$	−0.927051	+	0.673542i	−0.152406	+	0.110730i	−0.661375	−	0.750055i	$-0.730027\pi$
$37$	−0.927051	+	0.673542i	−0.152406	+	0.110730i	0.508969	+	0.860785i	$0.330027\pi$
$38$	−4.57295	−	14.0741i	−0.741830	−	2.28312i
$39$	−6.00000			−0.960769
$40$	−1.54508	+	4.75528i	−0.244299	+	0.751876i
$41$	0.545085	−	1.67760i	0.0851280	−	0.261997i	−0.899427	−	0.437070i	$-0.856016\pi$
$41$	0.545085	−	1.67760i	0.0851280	−	0.261997i	0.984555	+	0.175073i	$0.0560162\pi$
$42$	4.73607	+	3.44095i	0.730791	+	0.530951i
$43$	7.94427			1.21149			0.605745	−	0.795659i	$-0.292875\pi$
$43$	7.94427			1.21149			0.605745	+	0.795659i	$0.292875\pi$
$44$	3.70820	−	9.23305i	0.559033	−	1.39193i
$45$	−1.80902	+	1.31433i	−0.269672	+	0.195928i
$46$	−3.78115	−	11.6372i	−0.557501	−	1.71581i
$47$	8.09017			1.18007			0.590036	−	0.807377i	$-0.299113\pi$
$47$	8.09017			1.18007			0.590036	+	0.807377i	$0.299113\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	0.118034	+	0.0857567i	0.0168620	+	0.0122510i
$50$	9.04508	+	6.57164i	1.27917	+	0.929370i
$51$	1.92705	−	5.93085i	0.269841	−	0.830486i
$52$	14.5623	+	10.5801i	2.01943	+	1.46720i
$53$	−0.309017	−	0.951057i	−0.0424467	−	0.130638i	0.927587	−	0.373606i	$-0.121879\pi$
$53$	−0.309017	−	0.951057i	−0.0424467	−	0.130638i	−0.970034	+	0.242968i	$0.921879\pi$
$54$	−0.690983	+	2.12663i	−0.0940309	+	0.289397i
$55$	−5.69098	−	4.75528i	−0.767372	−	0.641202i
$56$	−1.80902	−	5.56758i	−0.241740	−	0.743999i
$57$	−5.35410	+	3.88998i	−0.709168	+	0.515241i
$58$	12.8262	−	9.31881i	1.68417	−	1.22362i
$59$	−9.47214	+	6.88191i	−1.23317	+	0.895948i	−0.997123	−	0.0757942i	$-0.975851\pi$
$59$	−9.47214	+	6.88191i	−1.23317	+	0.895948i	−0.236044	+	0.971742i	$0.575851\pi$
$60$	6.70820			0.866025
$61$	−5.32624			−0.681955			−0.340977	−	0.940071i	$-0.610758\pi$
$61$	−5.32624			−0.681955			−0.340977	+	0.940071i	$0.610758\pi$
$62$	13.5172	−	9.82084i	1.71669	−	1.24725i
$63$	0.809017	−	2.48990i	0.101927	−	0.313698i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$	10.8541	−	7.88597i	1.34629	−	0.978134i
$66$	−7.39919	−	0.502029i	−0.910777	−	0.0617954i
$67$	−1.80902	−	5.56758i	−0.221007	−	0.680188i	−0.998672	−	0.0515105i	$-0.983596\pi$
$67$	−1.80902	−	5.56758i	−0.221007	−	0.680188i	0.777666	−	0.628678i	$-0.216404\pi$
$68$	−15.1353	+	10.9964i	−1.83542	+	1.33351i
$69$	−4.42705	+	3.21644i	−0.532954	+	0.387214i
$70$	−13.0902			−1.56457
$71$	−6.04508	+	4.39201i	−0.717420	+	0.521236i	−0.885559	−	0.464527i	$-0.846224\pi$
$71$	−6.04508	+	4.39201i	−0.717420	+	0.521236i	0.168139	+	0.985763i	$0.446224\pi$
$72$	1.80902	−	1.31433i	0.213195	−	0.154895i
$73$	−1.00000	−	3.07768i	−0.117041	−	0.360216i	0.875326	−	0.483533i	$-0.160647\pi$
$73$	−1.00000	−	3.07768i	−0.117041	−	0.360216i	−0.992367	+	0.123317i	$0.960647\pi$
$74$	−0.791796	−	2.43690i	−0.0920444	−	0.283284i
$75$	1.54508	−	4.75528i	0.178411	−	0.549093i
$76$	19.8541			2.27742
$77$	8.66312	+	0.587785i	0.987254	+	0.0669843i
$78$	4.14590	−	12.7598i	0.469431	−	1.44476i
$79$	−4.00000	−	12.3107i	−0.450035	−	1.38507i	−0.876866	−	0.480734i	$-0.840370\pi$
$79$	−4.00000	−	12.3107i	−0.450035	−	1.38507i	0.426831	−	0.904331i	$-0.359630\pi$
$80$	1.80902	+	1.31433i	0.202254	+	0.146946i
$81$	1.00000			0.111111
$82$	3.19098	+	2.31838i	0.352385	+	0.256023i
$83$	−2.64590	+	8.14324i	−0.290425	+	0.893836i	0.694295	+	0.719691i	$0.255716\pi$
$83$	−2.64590	+	8.14324i	−0.290425	+	0.893836i	−0.984720	+	0.174146i	$0.944284\pi$
$84$	−6.35410	+	4.61653i	−0.693289	+	0.503704i
$85$	4.30902	+	13.2618i	0.467379	+	1.43844i
$86$	−5.48936	+	16.8945i	−0.591933	+	1.82178i
$87$	−5.73607	−	4.16750i	−0.614971	−	0.446803i
$88$	5.69098	+	4.75528i	0.606661	+	0.506915i
$89$	−2.88197	+	2.09387i	−0.305488	+	0.221950i	−0.729958	−	0.683492i	$-0.760460\pi$
$89$	−2.88197	+	2.09387i	−0.305488	+	0.221950i	0.424470	+	0.905442i	$0.360460\pi$
$90$	−1.54508	−	4.75528i	−0.162866	−	0.501251i
$91$	−4.85410	+	14.9394i	−0.508848	+	1.56607i
$92$	16.4164			1.71153
$93$	−6.04508	−	4.39201i	−0.626846	−	0.455430i
$94$	−5.59017	+	17.2048i	−0.576582	+	1.77454i
$95$	4.57295	−	14.0741i	0.469175	−	1.44397i
$96$	6.70820			0.684653
$97$	0.781153	+	2.40414i	0.0793141	+	0.244104i	0.982849	−	0.184410i	$-0.0590374\pi$
$97$	0.781153	+	2.40414i	0.0793141	+	0.244104i	−0.903535	+	0.428514i	$0.859037\pi$
$98$	−0.263932	+	0.191758i	−0.0266612	+	0.0193705i
$99$	0.809017	+	3.21644i	0.0813093	+	0.323264i
$100$	−12.1353	+	8.81678i	−1.21353	+	0.881678i
$101$	2.66312	−	1.93487i	0.264990	−	0.192527i	−0.447354	−	0.894357i	$-0.647634\pi$
$101$	2.66312	−	1.93487i	0.264990	−	0.192527i	0.712344	+	0.701830i	$0.247634\pi$
$102$	11.2812	+	8.19624i	1.11700	+	0.811548i
$103$	7.04508	+	5.11855i	0.694173	+	0.504346i	0.878029	−	0.478607i	$-0.158858\pi$
$103$	7.04508	+	5.11855i	0.694173	+	0.504346i	−0.183856	+	0.982953i	$0.558858\pi$
$104$	−10.8541	+	7.88597i	−1.06433	+	0.773283i
$105$	1.80902	+	5.56758i	0.176542	+	0.543340i
$106$	2.23607			0.217186
$107$	3.83688	+	11.8087i	0.370925	+	1.14159i	0.946187	+	0.323621i	$0.104900\pi$
$107$	3.83688	+	11.8087i	0.370925	+	1.14159i	−0.575261	+	0.817970i	$0.695100\pi$
$108$	−2.42705	−	1.76336i	−0.233543	−	0.169679i
$109$	−3.47214	−	2.52265i	−0.332570	−	0.241626i	0.408950	−	0.912557i	$-0.365895\pi$
$109$	−3.47214	−	2.52265i	−0.332570	−	0.241626i	−0.741520	+	0.670930i	$0.765895\pi$
$110$	14.0451	−	8.81678i	1.33915	−	0.840647i
$111$	−0.927051	+	0.673542i	−0.0879918	+	0.0639298i
$112$	−2.61803			−0.247381
$113$	−2.30902	+	7.10642i	−0.217214	+	0.668516i	0.781775	+	0.623561i	$0.214315\pi$
$113$	−2.30902	+	7.10642i	−0.217214	+	0.668516i	−0.998989	+	0.0449554i	$0.985685\pi$
$114$	−4.57295	−	14.0741i	−0.428296	−	1.31816i
$115$	3.78115	−	11.6372i	0.352594	−	1.08517i
$116$	6.57295	+	20.2295i	0.610283	+	1.87826i
$117$	−6.00000			−0.554700
$118$	−8.09017	−	24.8990i	−0.744761	−	2.29214i
$119$	−13.2082	−	9.59632i	−1.21079	−	0.879693i
$120$	−1.54508	+	4.75528i	−0.141046	+	0.434096i
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	3.68034	−	11.3269i	0.333202	−	1.02549i
$123$	0.545085	−	1.67760i	0.0491487	−	0.151264i
$124$	6.92705	+	21.3193i	0.622068	+	1.91453i
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$	4.73607	+	3.44095i	0.421922	+	0.306545i
$127$	7.14590			0.634096			0.317048	−	0.948410i	$-0.397308\pi$
$127$	7.14590			0.634096			0.317048	+	0.948410i	$0.397308\pi$
$128$	−12.6631	−	9.20029i	−1.11927	−	0.813199i
$129$	7.94427			0.699454
$130$	9.27051	+	28.5317i	0.813077	+	2.50240i
$131$	−5.35410	−	16.4782i	−0.467790	−	1.43971i	−0.855439	−	0.517903i	$-0.826713\pi$
$131$	−5.35410	−	16.4782i	−0.467790	−	1.43971i	0.387649	−	0.921807i	$-0.373287\pi$
$132$	3.70820	−	9.23305i	0.322758	−	0.803634i
$133$	5.35410	+	16.4782i	0.464260	+	1.42884i
$134$	13.0902			1.13082
$135$	−1.80902	+	1.31433i	−0.155695	+	0.113119i
$136$	−4.30902	−	13.2618i	−0.369495	−	1.13719i
$137$	6.70820	+	20.6457i	0.573121	+	1.76388i	0.642492	+	0.766293i	$0.277901\pi$
$137$	6.70820	+	20.6457i	0.573121	+	1.76388i	−0.0693711	+	0.997591i	$0.522099\pi$
$138$	−3.78115	−	11.6372i	−0.321873	−	0.990624i
$139$	1.59017	+	4.89404i	0.134876	+	0.415107i	0.995571	−	0.0940150i	$-0.0299702\pi$
$139$	1.59017	+	4.89404i	0.134876	+	0.415107i	−0.860694	+	0.509122i	$0.829970\pi$
$140$	5.42705	−	16.7027i	0.458670	−	1.41164i
$141$	8.09017			0.681315
$142$	−5.16312	−	15.8904i	−0.433279	−	1.33350i
$143$	−4.85410	−	19.2986i	−0.405920	−	1.61383i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	15.8541			1.31661
$146$	7.23607			0.598861
$147$	0.118034	+	0.0857567i	0.00973528	+	0.00707309i
$148$	3.43769			0.282577
$149$	0.545085	+	0.396027i	0.0446551	+	0.0324438i	0.609889	−	0.792487i	$-0.291214\pi$
$149$	0.545085	+	0.396027i	0.0446551	+	0.0324438i	−0.565234	+	0.824931i	$0.691214\pi$
$150$	9.04508	+	6.57164i	0.738528	+	0.536572i
$151$	0.500000	+	1.53884i	0.0406894	+	0.125229i	0.969338	−	0.245732i	$-0.0790283\pi$
$151$	0.500000	+	1.53884i	0.0406894	+	0.125229i	−0.928648	+	0.370961i	$0.879028\pi$
$152$	−4.57295	+	14.0741i	−0.370915	+	1.14156i
$153$	1.92705	−	5.93085i	0.155793	−	0.479481i
$154$	−7.23607	+	18.0171i	−0.583099	+	1.45186i
$155$	16.7082			1.34204
$156$	14.5623	+	10.5801i	1.16592	+	0.847089i
$157$	−2.69098	−	8.28199i	−0.214764	−	0.660975i	−0.999170	−	0.0407279i	$-0.987032\pi$
$157$	−2.69098	−	8.28199i	−0.214764	−	0.660975i	0.784406	−	0.620247i	$-0.212968\pi$
$158$	28.9443			2.30268
$159$	−0.309017	−	0.951057i	−0.0245066	−	0.0754237i
$160$	−12.1353	+	8.81678i	−0.959376	+	0.697028i
$161$	4.42705	+	13.6251i	0.348900	+	1.07381i
$162$	−0.690983	+	2.12663i	−0.0542888	+	0.167084i
$163$	−13.0000			−1.01824			−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000			−1.01824			−0.509119	+	0.860696i	$0.670029\pi$
$164$	−4.28115	+	3.11044i	−0.334302	+	0.242885i
$165$	−5.69098	−	4.75528i	−0.443042	−	0.370198i
$166$	−15.4894	−	11.2537i	−1.20221	−	0.873455i
$167$	−20.4894	−	14.8864i	−1.58551	−	1.15194i	−0.910009	−	0.414588i	$-0.863926\pi$
$167$	−20.4894	−	14.8864i	−1.58551	−	1.15194i	−0.675505	−	0.737356i	$-0.736074\pi$
$168$	−1.80902	−	5.56758i	−0.139569	−	0.429548i
$169$	23.0000			1.76923
$170$	−31.1803			−2.39142
$171$	−5.35410	+	3.88998i	−0.409438	+	0.297474i
$172$	−19.2812	−	14.0086i	−1.47017	−	1.06814i
$173$	−16.3992	−	11.9147i	−1.24681	−	0.905858i	−0.248775	−	0.968561i	$-0.580028\pi$
$173$	−16.3992	−	11.9147i	−1.24681	−	0.905858i	−0.998032	+	0.0627030i	$0.980028\pi$
$174$	12.8262	−	9.31881i	0.972355	−	0.706457i
$175$	−10.5902	−	7.69421i	−0.800542	−	0.581628i
$176$	2.80902	−	1.76336i	0.211738	−	0.132918i
$177$	−9.47214	+	6.88191i	−0.711969	+	0.517276i
$178$	−2.46149	−	7.57570i	−0.184497	−	0.567822i
$179$	8.65248			0.646716			0.323358	−	0.946277i	$-0.395188\pi$
$179$	8.65248			0.646716			0.323358	+	0.946277i	$0.395188\pi$
$180$	6.70820			0.500000
$181$	−3.51722	+	10.8249i	−0.261433	+	0.804608i	0.731061	+	0.682312i	$0.239026\pi$
$181$	−3.51722	+	10.8249i	−0.261433	+	0.804608i	−0.992494	+	0.122296i	$0.960974\pi$
$182$	−28.4164	−	20.6457i	−2.10636	−	1.53036i
$183$	−5.32624			−0.393727
$184$	−3.78115	+	11.6372i	−0.278750	+	0.857905i
$185$	0.791796	−	2.43690i	0.0582140	−	0.179164i
$186$	13.5172	−	9.82084i	0.991131	−	0.720099i
$187$	20.6353	+	1.40008i	1.50900	+	0.102384i
$188$	−19.6353	−	14.2658i	−1.43205	−	1.04044i
$189$	0.809017	−	2.48990i	0.0588473	−	0.181113i
$190$	26.7705	+	19.4499i	1.94214	+	1.41105i
$191$	−11.6353	+	8.45351i	−0.841897	+	0.611674i	−0.922900	−	0.385040i	$-0.874188\pi$
$191$	−11.6353	+	8.45351i	−0.841897	+	0.611674i	0.0810026	+	0.996714i	$0.474188\pi$
$192$	−4.01722	+	12.3637i	−0.289918	+	0.892276i
$193$	2.73607	+	1.98787i	0.196946	+	0.143090i	0.681888	−	0.731457i	$-0.261159\pi$
$193$	2.73607	+	1.98787i	0.196946	+	0.143090i	−0.484942	+	0.874547i	$0.661159\pi$
$194$	−5.65248			−0.405824
$195$	10.8541	−	7.88597i	0.777278	−	0.564726i
$196$	−0.135255	−	0.416272i	−0.00966107	−	0.0297337i
$197$	−2.01722	+	6.20837i	−0.143721	+	0.442328i	−0.996844	−	0.0793815i	$-0.974705\pi$
$197$	−2.01722	+	6.20837i	−0.143721	+	0.442328i	0.853123	+	0.521709i	$0.174705\pi$
$198$	−7.39919	−	0.502029i	−0.525837	−	0.0356776i
$199$	−13.7984			−0.978141			−0.489070	−	0.872244i	$-0.662664\pi$
$199$	−13.7984			−0.978141			−0.489070	+	0.872244i	$0.662664\pi$
$200$	−3.45492	−	10.6331i	−0.244299	−	0.751876i
$201$	−1.80902	−	5.56758i	−0.127598	−	0.392707i
$202$	2.27458	+	7.00042i	0.160039	+	0.492548i
$203$	−15.0172	+	10.9106i	−1.05400	+	0.765777i
$204$	−15.1353	+	10.9964i	−1.05968	+	0.769902i
$205$	1.21885	+	3.75123i	0.0851280	+	0.261997i
$206$	−15.7533	+	11.4454i	−1.09758	+	0.797441i
$207$	−4.42705	+	3.21644i	−0.307701	+	0.223558i
$208$	1.85410	+	5.70634i	0.128559	+	0.395663i
$209$	−16.8435	−	14.0741i	−1.16509	−	0.973525i
$210$	−13.0902			−0.903308
$211$	−3.61803	+	11.1352i	−0.249076	+	0.766576i	0.745864	+	0.666099i	$0.232037\pi$
$211$	−3.61803	+	11.1352i	−0.249076	+	0.766576i	−0.994939	+	0.100478i	$0.967963\pi$
$212$	−0.927051	+	2.85317i	−0.0636701	+	0.195956i
$213$	−6.04508	+	4.39201i	−0.414202	+	0.300936i
$214$	−27.7639			−1.89790
$215$	−14.3713	+	10.4414i	−0.980116	+	0.712096i
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	−15.8262	+	11.4984i	−1.07436	+	0.780565i
$218$	7.76393	−	5.64083i	0.525840	−	0.382045i
$219$	−1.00000	−	3.07768i	−0.0675737	−	0.207971i
$220$	5.42705	+	21.5765i	0.365892	+	1.45469i
$221$	−11.5623	+	35.5851i	−0.777765	+	2.39371i
$222$	−0.791796	−	2.43690i	−0.0531419	−	0.163554i
$223$	−2.92705	−	2.12663i	−0.196010	−	0.142409i	0.485451	−	0.874264i	$-0.338655\pi$
$223$	−2.92705	−	2.12663i	−0.196010	−	0.142409i	−0.681461	+	0.731854i	$0.738655\pi$
$224$	5.42705	−	16.7027i	0.362610	−	1.11600i
$225$	1.54508	−	4.75528i	0.103006	−	0.317019i
$226$	−13.5172	−	9.82084i	−0.899152	−	0.653272i
$227$	2.87132	+	8.83702i	0.190576	+	0.586534i	1.00000		0.000691691i	$-0.000220172\pi$
$227$	2.87132	+	8.83702i	0.190576	+	0.586534i	−0.809423	+	0.587226i	$0.800220\pi$
$228$	19.8541			1.31487
$229$	5.25329	+	16.1680i	0.347147	+	1.06841i	0.960424	+	0.278541i	$0.0898509\pi$
$229$	5.25329	+	16.1680i	0.347147	+	1.06841i	−0.613277	+	0.789868i	$0.710149\pi$
$230$	22.1353	+	16.0822i	1.45956	+	1.06043i
$231$	8.66312	+	0.587785i	0.569991	+	0.0386734i
$232$	−15.8541			−1.04087
$233$	−19.7082	−	14.3188i	−1.29113	−	0.938059i	−0.291300	−	0.956632i	$-0.594088\pi$
$233$	−19.7082	−	14.3188i	−1.29113	−	0.938059i	−0.999828	+	0.0185729i	$0.994088\pi$
$234$	4.14590	−	12.7598i	0.271026	−	0.834132i
$235$	−14.6353	+	10.6331i	−0.954699	+	0.693629i
$236$	35.1246			2.28642
$237$	−4.00000	−	12.3107i	−0.259828	−	0.799668i
$238$	29.5344	−	21.4580i	1.91443	−	1.39092i
$239$	10.5902	+	7.69421i	0.685021	+	0.497697i	0.875020	−	0.484087i	$-0.160848\pi$
$239$	10.5902	+	7.69421i	0.685021	+	0.497697i	−0.189999	+	0.981784i	$0.560848\pi$
$240$	1.80902	+	1.31433i	0.116772	+	0.0848395i
$241$	−14.4443	−	10.4944i	−0.930437	−	0.676002i	0.0156625	−	0.999877i	$-0.495014\pi$
$241$	−14.4443	−	10.4944i	−0.930437	−	0.676002i	−0.946100	+	0.323875i	$0.895014\pi$
$242$	−4.37132	−	24.2052i	−0.280999	−	1.55597i
$243$	1.00000			0.0641500
$244$	12.9271	+	9.39205i	0.827570	+	0.601265i
$245$	−0.326238			−0.0208426
$246$	3.19098	+	2.31838i	0.203450	+	0.147815i
$247$	32.1246	−	23.3399i	2.04404	−	1.48508i
$248$	−16.7082			−1.06097
$249$	−2.64590	+	8.14324i	−0.167677	+	0.516057i
$250$	−25.0000			−1.58114
$251$	0.0278640	−	0.0202444i	0.00175876	−	0.00127782i	−0.586906	−	0.809655i	$-0.699654\pi$
$251$	0.0278640	−	0.0202444i	0.00175876	−	0.00127782i	0.588664	+	0.808378i	$0.299654\pi$
$252$	−6.35410	+	4.61653i	−0.400271	+	0.290814i
$253$	−13.9271	−	11.6372i	−0.875586	−	0.731624i
$254$	−4.93769	+	15.1967i	−0.309818	+	0.953523i
$255$	4.30902	+	13.2618i	0.269841	+	0.830486i
$256$	7.28115	−	5.29007i	0.455072	−	0.330629i
$257$	5.01722	−	15.4414i	0.312966	−	0.963209i	−0.663618	−	0.748072i	$-0.730980\pi$
$257$	5.01722	−	15.4414i	0.312966	−	0.963209i	0.976584	−	0.215138i	$-0.0690200\pi$
$258$	−5.48936	+	16.8945i	−0.341752	+	1.05181i
$259$	0.927051	+	2.85317i	0.0576041	+	0.177287i
$260$	−40.2492			−2.49615
$261$	−5.73607	−	4.16750i	−0.355054	−	0.257962i
$262$	38.7426			2.39353
$263$	18.7082	+	13.5923i	1.15360	+	0.838137i	0.988955	−	0.148216i	$-0.0473530\pi$
$263$	18.7082	+	13.5923i	1.15360	+	0.838137i	0.164642	+	0.986353i	$0.447353\pi$
$264$	5.69098	+	4.75528i	0.350256	+	0.292667i
$265$	1.80902	+	1.31433i	0.111127	+	0.0807385i
$266$	−38.7426			−2.37546
$267$	−2.88197	+	2.09387i	−0.176373	+	0.128143i
$268$	−5.42705	+	16.7027i	−0.331510	+	1.02028i
$269$	−5.45492	+	16.7885i	−0.332592	+	1.02361i	0.635304	+	0.772262i	$0.280875\pi$
$269$	−5.45492	+	16.7885i	−0.332592	+	1.02361i	−0.967896	+	0.251351i	$0.919125\pi$
$270$	−1.54508	−	4.75528i	−0.0940309	−	0.289397i
$271$	−3.07295	−	2.23263i	−0.186668	−	0.135623i	0.490526	−	0.871426i	$-0.336805\pi$
$271$	−3.07295	−	2.23263i	−0.186668	−	0.135623i	−0.677195	+	0.735804i	$0.736805\pi$
$272$	−6.23607			−0.378117
$273$	−4.85410	+	14.9394i	−0.293784	+	0.904173i
$274$	−48.5410			−2.93247
$275$	16.5451	+	1.12257i	0.997706	+	0.0676935i
$276$	16.4164			0.988152
$277$	6.37132	−	19.6089i	0.382816	−	1.17819i	−0.555237	−	0.831692i	$-0.687372\pi$
$277$	6.37132	−	19.6089i	0.382816	−	1.17819i	0.938052	−	0.346493i	$-0.112628\pi$
$278$	−11.5066			−0.690119
$279$	−6.04508	−	4.39201i	−0.361910	−	0.262943i
$280$	10.5902	+	7.69421i	0.632884	+	0.459817i
$281$	4.39919	−	13.5393i	0.262433	−	0.807687i	−0.729840	−	0.683618i	$-0.760405\pi$
$281$	4.39919	−	13.5393i	0.262433	−	0.807687i	0.992274	−	0.124069i	$-0.0395945\pi$
$282$	−5.59017	+	17.2048i	−0.332890	+	1.02453i
$283$	15.2812	−	11.1024i	0.908370	−	0.659970i	−0.0322319	−	0.999480i	$-0.510262\pi$
$283$	15.2812	−	11.1024i	0.908370	−	0.659970i	0.940602	+	0.339511i	$0.110262\pi$
$284$	22.4164			1.33017
$285$	4.57295	−	14.0741i	0.270878	−	0.833677i
$286$	44.3951	+	3.01217i	2.62514	+	0.178113i
$287$	−3.73607	−	2.71441i	−0.220533	−	0.160227i
$288$	6.70820			0.395285
$289$	−17.7082	−	12.8658i	−1.04166	−	0.756810i
$290$	−10.9549	+	33.7158i	−0.643295	+	1.97986i
$291$	0.781153	+	2.40414i	0.0457920	+	0.140933i
$292$	−3.00000	+	9.23305i	−0.175562	+	0.540323i
$293$	−9.03444	+	27.8052i	−0.527798	+	1.62439i	0.230918	+	0.972973i	$0.425827\pi$
$293$	−9.03444	+	27.8052i	−0.527798	+	1.62439i	−0.758716	+	0.651421i	$0.774173\pi$
$294$	−0.263932	+	0.191758i	−0.0153928	+	0.0111835i
$295$	8.09017	−	24.8990i	0.471028	−	1.44967i
$296$	−0.791796	+	2.43690i	−0.0460222	+	0.141642i
$297$	0.809017	+	3.21644i	0.0469439	+	0.186637i
$298$	−1.21885	+	0.885544i	−0.0706059	+	0.0512982i
$299$	26.5623	−	19.2986i	1.53614	−	1.11607i
$300$	−12.1353	+	8.81678i	−0.700629	+	0.509037i
$301$	6.42705	−	19.7804i	0.370449	−	1.14012i
$302$	−3.61803			−0.208194
$303$	2.66312	−	1.93487i	0.152992	−	0.111155i
$304$	5.35410	+	3.88998i	0.307079	+	0.223106i
$305$	9.63525	−	7.00042i	0.551713	−	0.400843i
$306$	11.2812	+	8.19624i	0.644901	+	0.468548i
$307$	1.58359			0.0903804			0.0451902	−	0.998978i	$-0.485611\pi$
$307$	1.58359			0.0903804			0.0451902	+	0.998978i	$0.485611\pi$
$308$	−19.9894	−	16.7027i	−1.13900	−	0.951727i
$309$	7.04508	+	5.11855i	0.400781	+	0.291184i
$310$	−11.5451	+	35.5321i	−0.655717	+	2.01809i
$311$	22.3713	+	16.2537i	1.26856	+	0.921664i	0.999144	−	0.0413598i	$-0.0131690\pi$
$311$	22.3713	+	16.2537i	1.26856	+	0.921664i	0.269417	+	0.963024i	$0.413169\pi$
$312$	−10.8541	+	7.88597i	−0.614493	+	0.446455i
$313$	−8.16312	−	25.1235i	−0.461407	−	1.42006i	−0.863446	−	0.504442i	$-0.831698\pi$
$313$	−8.16312	−	25.1235i	−0.461407	−	1.42006i	0.402039	−	0.915622i	$-0.368302\pi$
$314$	19.4721			1.09888
$315$	1.80902	+	5.56758i	0.101927	+	0.313698i
$316$	−12.0000	+	36.9322i	−0.675053	+	2.07760i
$317$	8.09017	+	5.87785i	0.454389	+	0.330133i	0.791326	−	0.611394i	$-0.209391\pi$
$317$	8.09017	+	5.87785i	0.454389	+	0.330133i	−0.336937	+	0.941527i	$0.609391\pi$
$318$	2.23607			0.125392
$319$	8.76393	−	21.8213i	0.490686	−	1.22176i
$320$	−8.98278	−	27.6462i	−0.502153	−	1.54547i
$321$	3.83688	+	11.8087i	0.214154	+	0.659098i
$322$	−32.0344			−1.78521
$323$	12.7533	+	39.2506i	0.709612	+	2.18396i
$324$	−2.42705	−	1.76336i	−0.134836	−	0.0979642i
$325$	−9.27051	+	28.5317i	−0.514235	+	1.58265i
$326$	8.98278	−	27.6462i	0.497510	−	1.53118i
$327$	−3.47214	−	2.52265i	−0.192010	−	0.139503i
$328$	−1.21885	−	3.75123i	−0.0672996	−	0.207127i
$329$	6.54508	−	20.1437i	0.360842	−	1.11056i
$330$	14.0451	−	8.81678i	0.773156	−	0.485348i
$331$	2.18034	+	6.71040i	0.119842	+	0.368837i	0.992926	−	0.118733i	$-0.0378834\pi$
$331$	2.18034	+	6.71040i	0.119842	+	0.368837i	−0.873084	+	0.487570i	$0.837883\pi$
$332$	20.7812	−	15.0984i	1.14051	−	0.828632i
$333$	−0.927051	+	0.673542i	−0.0508021	+	0.0369099i
$334$	45.8156	−	33.2870i	2.50692	−	1.82138i
$335$	10.5902	+	7.69421i	0.578603	+	0.420380i
$336$	−2.61803			−0.142825
$337$	−9.80902	+	7.12667i	−0.534331	+	0.388214i	−0.821975	−	0.569523i	$-0.807128\pi$
$337$	−9.80902	+	7.12667i	−0.534331	+	0.388214i	0.287644	+	0.957737i	$0.407128\pi$
$338$	−15.8926	+	48.9124i	−0.864444	+	2.66048i
$339$	−2.30902	+	7.10642i	−0.125409	+	0.385968i
$340$	12.9271	−	39.7854i	0.701068	−	2.15766i
$341$	9.23607	−	22.9969i	0.500161	−	1.24535i
$342$	−4.57295	−	14.0741i	−0.247277	−	0.761040i
$343$	15.1353	−	10.9964i	0.817227	−	0.593750i
$344$	14.3713	−	10.4414i	0.774850	−	0.562961i
$345$	3.78115	−	11.6372i	0.203570	−	0.626525i
$346$	36.6697	−	26.6421i	1.97138	−	1.43229i
$347$	−14.5172	+	10.5474i	−0.779325	+	0.566213i	−0.904776	−	0.425887i	$-0.859962\pi$
$347$	−14.5172	+	10.5474i	−0.779325	+	0.566213i	0.125451	+	0.992100i	$0.459962\pi$
$348$	6.57295	+	20.2295i	0.352347	+	1.08441i
$349$	−0.100813	−	0.310271i	−0.00539640	−	0.0166084i	0.948322	−	0.317309i	$-0.102779\pi$
$349$	−0.100813	−	0.310271i	−0.00539640	−	0.0166084i	−0.953718	+	0.300701i	$0.902779\pi$
$350$	23.6803	−	17.2048i	1.26577	−	0.919634i
$351$	−6.00000			−0.320256
$352$	5.42705	+	21.5765i	0.289263	+	1.15003i
$353$	4.50000	−	13.8496i	0.239511	−	0.737139i	−0.756980	−	0.653438i	$-0.773326\pi$
$353$	4.50000	−	13.8496i	0.239511	−	0.737139i	0.996491	−	0.0837006i	$-0.0266739\pi$
$354$	−8.09017	−	24.8990i	−0.429988	−	1.32337i
$355$	5.16312	−	15.8904i	0.274030	−	0.843377i
$356$	10.6869			0.566406
$357$	−13.2082	−	9.59632i	−0.699052	−	0.507891i
$358$	−5.97871	+	18.4006i	−0.315985	+	0.972501i
$359$	8.56231	−	6.22088i	0.451901	−	0.328325i	−0.338445	−	0.940986i	$-0.609901\pi$
$359$	8.56231	−	6.22088i	0.451901	−	0.328325i	0.790346	+	0.612661i	$0.209901\pi$
$360$	−1.54508	+	4.75528i	−0.0814331	+	0.250625i
$361$	7.66312	−	23.5847i	0.403322	−	1.24130i
$362$	−20.5902	−	14.9596i	−1.08220	−	0.786261i
$363$	−9.69098	+	5.20431i	−0.508645	+	0.273155i
$364$	38.1246	−	27.6992i	1.99827	−	1.45183i
$365$	5.85410	+	4.25325i	0.306418	+	0.222625i
$366$	3.68034	−	11.3269i	0.192374	−	0.592068i
$367$	−10.7426			−0.560762			−0.280381	−	0.959889i	$-0.590461\pi$
$367$	−10.7426			−0.560762			−0.280381	+	0.959889i	$0.590461\pi$
$368$	4.42705	+	3.21644i	0.230776	+	0.167669i
$369$	0.545085	−	1.67760i	0.0283760	−	0.0873323i
$370$	4.63525	+	3.36771i	0.240975	+	0.175079i
$371$	−2.61803			−0.135922
$372$	6.92705	+	21.3193i	0.359151	+	1.10535i
$373$	3.20820	−	2.33090i	0.166115	−	0.120689i	−0.501622	−	0.865087i	$-0.667263\pi$
$373$	3.20820	−	2.33090i	0.166115	−	0.120689i	0.667737	+	0.744398i	$0.267263\pi$
$374$	−17.2361	+	42.9161i	−0.891256	+	2.21914i
$375$	3.45492	+	10.6331i	0.178411	+	0.549093i
$376$	14.6353	−	10.6331i	0.754756	−	0.548362i
$377$	34.4164	+	25.0050i	1.77254	+	1.28782i
$378$	4.73607	+	3.44095i	0.243597	+	0.176984i
$379$	−21.7254	+	15.7844i	−1.11596	+	0.810792i	−0.983592	−	0.180408i	$-0.942258\pi$
$379$	−21.7254	+	15.7844i	−1.11596	+	0.810792i	−0.132368	+	0.991201i	$0.542258\pi$
$380$	−35.9164	+	26.0948i	−1.84247	+	1.33863i
$381$	7.14590			0.366095
$382$	−9.93769	−	30.5851i	−0.508457	−	1.56487i
$383$	16.2361	+	11.7962i	0.829624	+	0.602757i	0.919453	−	0.393200i	$-0.128632\pi$
$383$	16.2361	+	11.7962i	0.829624	+	0.602757i	−0.0898287	+	0.995957i	$0.528632\pi$
$384$	−12.6631	−	9.20029i	−0.646212	−	0.469501i
$385$	−16.4443	+	10.3229i	−0.838078	+	0.526102i
$386$	−6.11803	+	4.44501i	−0.311400	+	0.226245i
$387$	7.94427			0.403830
$388$	2.34346	−	7.21242i	0.118971	−	0.366155i
$389$	1.48278	+	4.56352i	0.0751799	+	0.231380i	0.981584	−	0.191032i	$-0.0611835\pi$
$389$	1.48278	+	4.56352i	0.0751799	+	0.231380i	−0.906404	+	0.422412i	$0.861184\pi$
$390$	9.27051	+	28.5317i	0.469431	+	1.44476i
$391$	10.5451	+	32.4544i	0.533288	+	1.64129i
$392$	0.326238			0.0164775
$393$	−5.35410	−	16.4782i	−0.270079	−	0.831217i
$394$	−11.8090	−	8.57975i	−0.594930	−	0.432242i
$395$	23.4164	+	17.0130i	1.17821	+	0.856018i
$396$	3.70820	−	9.23305i	0.186344	−	0.463978i
$397$	6.60739	−	20.3355i	0.331615	−	1.02061i	−0.636750	−	0.771070i	$-0.719722\pi$
$397$	6.60739	−	20.3355i	0.331615	−	1.02061i	0.968365	−	0.249537i	$-0.0802784\pi$
$398$	9.53444	−	29.3440i	0.477918	−	1.47088i
$399$	5.35410	+	16.4782i	0.268040	+	0.824943i
$400$	−5.00000			−0.250000
$401$	13.2812	+	9.64932i	0.663229	+	0.481864i	0.867752	−	0.496998i	$-0.165564\pi$
$401$	13.2812	+	9.64932i	0.663229	+	0.481864i	−0.204523	+	0.978862i	$0.565564\pi$
$402$	13.0902			0.652878
$403$	36.2705	+	26.3521i	1.80676	+	1.31269i
$404$	−9.87539			−0.491319
$405$	−1.80902	+	1.31433i	−0.0898908	+	0.0653095i
$406$	−12.8262	−	39.4751i	−0.636555	−	1.95912i
$407$	−2.91641	−	2.43690i	−0.144561	−	0.120793i
$408$	−4.30902	−	13.2618i	−0.213328	−	0.656556i
$409$	−1.94427			−0.0961381			−0.0480690	−	0.998844i	$-0.515307\pi$
$409$	−1.94427			−0.0961381			−0.0480690	+	0.998844i	$0.515307\pi$
$410$	−8.81966			−0.435572
$411$	6.70820	+	20.6457i	0.330891	+	1.01838i
$412$	−8.07295	−	24.8460i	−0.397726	−	1.22407i
$413$	9.47214	+	29.1522i	0.466093	+	1.43449i
$414$	−3.78115	−	11.6372i	−0.185834	−	0.571937i
$415$	−5.91641	−	18.2088i	−0.290425	−	0.893836i
$416$	−40.2492			−1.97338
$417$	1.59017	+	4.89404i	0.0778710	+	0.239662i
$418$	41.5689	−	26.0948i	2.03320	−	1.27634i
$419$	−7.05573	−	21.7153i	−0.344695	−	1.06086i	−0.961747	−	0.273939i	$-0.911673\pi$
$419$	−7.05573	−	21.7153i	−0.344695	−	1.06086i	0.617052	−	0.786922i	$-0.288327\pi$
$420$	5.42705	−	16.7027i	0.264813	−	0.815011i
$421$	25.9787			1.26613			0.633063	−	0.774101i	$-0.281798\pi$
$421$	25.9787			1.26613			0.633063	+	0.774101i	$0.281798\pi$
$422$	−21.1803	−	15.3884i	−1.03104	−	0.749096i
$423$	8.09017			0.393358
$424$	−1.80902	−	1.31433i	−0.0878536	−	0.0638294i
$425$	−25.2254	−	18.3273i	−1.22361	−	0.889007i
$426$	−5.16312	−	15.8904i	−0.250154	−	0.769895i
$427$	−4.30902	+	13.2618i	−0.208528	+	0.641783i
$428$	11.5106	−	35.4261i	0.556388	−	1.71239i
$429$	−4.85410	−	19.2986i	−0.234358	−	0.931747i
$430$	−12.2746	−	37.7773i	−0.591933	−	1.82178i
$431$	−4.04508	−	2.93893i	−0.194845	−	0.141563i	0.486085	−	0.873911i	$-0.338424\pi$
$431$	−4.04508	−	2.93893i	−0.194845	−	0.141563i	−0.680930	+	0.732348i	$0.738424\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	24.9443			1.19875			0.599373	−	0.800470i	$-0.295417\pi$
$433$	24.9443			1.19875			0.599373	+	0.800470i	$0.295417\pi$
$434$	−13.5172	−	41.6017i	−0.648847	−	1.99695i
$435$	15.8541			0.760146
$436$	3.97871	+	12.2452i	0.190546	+	0.586440i
$437$	11.1910	−	34.4423i	0.535337	−	1.64760i
$438$	7.23607			0.345753
$439$	3.88197	−	2.82041i	0.185276	−	0.134611i	−0.491281	−	0.871001i	$-0.663471\pi$
$439$	3.88197	−	2.82041i	0.185276	−	0.134611i	0.676557	+	0.736390i	$0.263471\pi$
$440$	−16.5451	−	1.12257i	−0.788756	−	0.0535164i
$441$	0.118034	+	0.0857567i	0.00562067	+	0.00408365i
$442$	−67.6869	−	49.1774i	−3.21954	−	2.33913i
$443$	−11.8713	−	36.5362i	−0.564024	−	1.73589i	−0.670835	−	0.741607i	$-0.734064\pi$
$443$	−11.8713	−	36.5362i	−0.564024	−	1.73589i	0.106811	−	0.994279i	$-0.465936\pi$
$444$	3.43769			0.163146
$445$	2.46149	−	7.57570i	0.116686	−	0.359122i
$446$	6.54508	−	4.75528i	0.309919	−	0.225169i
$447$	0.545085	+	0.396027i	0.0257816	+	0.0187315i
$448$	27.5344	+	20.0049i	1.30088	+	0.945145i
$449$	−9.78115	+	7.10642i	−0.461601	+	0.335373i	−0.794159	−	0.607710i	$-0.792088\pi$
$449$	−9.78115	+	7.10642i	−0.461601	+	0.335373i	0.332558	+	0.943083i	$0.392088\pi$
$450$	9.04508	+	6.57164i	0.426389	+	0.309790i
$451$	5.83688	+	0.396027i	0.274848	+	0.0186482i
$452$	18.1353	−	13.1760i	0.853011	−	0.619749i
$453$	0.500000	+	1.53884i	0.0234920	+	0.0723011i
$454$	−20.7771			−0.975117
$455$	−10.8541	−	33.4055i	−0.508848	−	1.56607i
$456$	−4.57295	+	14.0741i	−0.214148	+	0.659080i
$457$	−7.94427	−	5.77185i	−0.371617	−	0.269996i	0.386264	−	0.922388i	$-0.373765\pi$
$457$	−7.94427	−	5.77185i	−0.371617	−	0.269996i	−0.757881	+	0.652392i	$0.773765\pi$
$458$	−38.0132			−1.77624
$459$	1.92705	−	5.93085i	0.0899470	−	0.276829i
$460$	−29.6976	+	21.5765i	−1.38466	+	1.00601i
$461$	−25.8713	+	18.7966i	−1.20495	+	0.875446i	−0.994762	−	0.102216i	$-0.967407\pi$
$461$	−25.8713	+	18.7966i	−1.20495	+	0.875446i	−0.210185	+	0.977662i	$0.567407\pi$
$462$	−7.23607	+	18.0171i	−0.336652	+	0.838230i
$463$	27.6074	+	20.0579i	1.28302	+	0.932172i	0.999640	−	0.0268347i	$-0.00854278\pi$
$463$	27.6074	+	20.0579i	1.28302	+	0.932172i	0.283384	+	0.959006i	$0.408543\pi$
$464$	−2.19098	+	6.74315i	−0.101714	+	0.313043i
$465$	16.7082			0.774824
$466$	44.0689	−	32.0179i	2.04145	−	1.48320i
$467$	−4.80902	+	14.8006i	−0.222535	+	0.684892i	0.775998	+	0.630736i	$0.217247\pi$
$467$	−4.80902	+	14.8006i	−0.222535	+	0.684892i	−0.998532	+	0.0541559i	$0.982753\pi$
$468$	14.5623	+	10.5801i	0.673143	+	0.489067i
$469$	−15.3262			−0.707700
$470$	−12.5000	−	38.4710i	−0.576582	−	1.77454i
$471$	−2.69098	−	8.28199i	−0.123994	−	0.381614i
$472$	−8.09017	+	24.8990i	−0.372380	+	1.14607i
$473$	6.42705	+	25.5523i	0.295516	+	1.17490i
$474$	28.9443			1.32945
$475$	10.2254	+	31.4706i	0.469175	+	1.44397i
$476$	15.1353	+	46.5815i	0.693723	+	2.13506i
$477$	−0.309017	−	0.951057i	−0.0141489	−	0.0435459i
$478$	−23.6803	+	17.2048i	−1.08311	+	0.786928i
$479$	−11.4271	+	8.30224i	−0.522115	+	0.379339i	−0.817400	−	0.576070i	$-0.804585\pi$
$479$	−11.4271	+	8.30224i	−0.522115	+	0.379339i	0.295285	+	0.955409i	$0.404585\pi$
$480$	−12.1353	+	8.81678i	−0.553896	+	0.402429i
$481$	5.56231	−	4.04125i	0.253619	−	0.184265i
$482$	32.2984	−	23.4661i	1.47115	−	1.06885i
$483$	4.42705	+	13.6251i	0.201438	+	0.619962i
$484$	32.6976	+	4.45752i	1.48625	+	0.202615i
$485$	−4.57295	−	3.32244i	−0.207647	−	0.150864i
$486$	−0.690983	+	2.12663i	−0.0313436	+	0.0964658i
$487$	4.66312	−	14.3516i	0.211306	−	0.650333i	−0.788089	−	0.615561i	$-0.788929\pi$
$487$	4.66312	−	14.3516i	0.211306	−	0.650333i	0.999395	−	0.0347722i	$-0.0110706\pi$
$488$	−9.63525	+	7.00042i	−0.436167	+	0.316894i
$489$	−13.0000			−0.587880
$490$	0.225425	−	0.693786i	0.0101837	−	0.0313421i
$491$	20.6631	−	15.0126i	0.932514	−	0.677511i	−0.0140934	−	0.999901i	$-0.504486\pi$
$491$	20.6631	−	15.0126i	0.932514	−	0.677511i	0.946607	+	0.322390i	$0.104486\pi$
$492$	−4.28115	+	3.11044i	−0.193009	+	0.140229i
$493$	−35.7705	+	25.9888i	−1.61102	+	1.17048i
$494$	27.4377	+	84.4445i	1.23448	+	3.79934i
$495$	−5.69098	−	4.75528i	−0.255791	−	0.213734i
$496$	−2.30902	+	7.10642i	−0.103678	+	0.319088i
$497$	6.04508	+	18.6049i	0.271159	+	0.834542i
$498$	−15.4894	−	11.2537i	−0.694095	−	0.504289i
$499$	−2.83688	+	8.73102i	−0.126996	+	0.390854i	−0.994259	−	0.106996i	$-0.965877\pi$
$499$	−2.83688	+	8.73102i	−0.126996	+	0.390854i	0.867263	+	0.497850i	$0.165877\pi$
$500$	10.3647	−	31.8994i	0.463525	−	1.42658i
$501$	−20.4894	−	14.8864i	−0.915397	−	0.665075i
$502$	0.0237987	+	0.0732450i	0.00106219	+	0.00326908i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	−1.80902	−	5.56758i	−0.0805800	−	0.248000i
$505$	−2.27458	+	7.00042i	−0.101217	+	0.311515i
$506$	34.3713	−	21.5765i	1.52799	−	0.959194i
$507$	23.0000			1.02147
$508$	−17.3435	−	12.6008i	−0.769492	−	0.559068i
$509$	2.90983	−	8.95554i	0.128976	−	0.396947i	−0.865629	−	0.500687i	$-0.833081\pi$
$509$	2.90983	−	8.95554i	0.128976	−	0.396947i	0.994604	+	0.103740i	$0.0330809\pi$
$510$	−31.1803			−1.38069
$511$	−8.47214			−0.374785
$512$	−3.45492	−	10.6331i	−0.152687	−	0.469923i
$513$	−5.35410	+	3.88998i	−0.236389	+	0.171747i
$514$	29.3713	+	21.3395i	1.29551	+	0.941246i
$515$	−19.4721			−0.858045
$516$	−19.2812	−	14.0086i	−0.848805	−	0.616693i
$517$	6.54508	+	26.0216i	0.287853	+	1.14443i
$518$	−6.70820			−0.294742
$519$	−16.3992	−	11.9147i	−0.719844	−	0.522998i
$520$	9.27051	−	28.5317i	0.406539	−	1.25120i
$521$	5.23607	+	3.80423i	0.229396	+	0.166666i	0.696546	−	0.717512i	$-0.254719\pi$
$521$	5.23607	+	3.80423i	0.229396	+	0.166666i	−0.467150	+	0.884178i	$0.654719\pi$
$522$	12.8262	−	9.31881i	0.561389	−	0.407873i
$523$	31.7984			1.39045			0.695223	−	0.718794i	$-0.255306\pi$
$523$	31.7984			1.39045			0.695223	+	0.718794i	$0.255306\pi$
$524$	−16.0623	+	49.4347i	−0.701685	+	2.15956i
$525$	−10.5902	−	7.69421i	−0.462193	−	0.335803i
$526$	−41.8328	+	30.3933i	−1.82400	+	1.32521i
$527$	−37.6976	+	27.3889i	−1.64213	+	1.19308i
$528$	2.80902	−	1.76336i	0.122247	−	0.0767402i
$529$	2.14590	−	6.60440i	0.0932999	−	0.287148i
$530$	−4.04508	+	2.93893i	−0.175707	+	0.127659i
$531$	−9.47214	+	6.88191i	−0.411056	+	0.298649i
$532$	16.0623	−	49.4347i	0.696389	−	2.14327i
$533$	−3.27051	+	10.0656i	−0.141662	+	0.435989i
$534$	−2.46149	−	7.57570i	−0.106519	−	0.327832i
$535$	−22.4615	−	16.3192i	−0.971095	−	0.705542i
$536$	−10.5902	−	7.69421i	−0.457426	−	0.332339i
$537$	8.65248			0.373382
$538$	−31.9336	−	23.2011i	−1.37676	−	1.00027i
$539$	−0.180340	+	0.449028i	−0.00776779	+	0.0193410i
$540$	6.70820			0.288675
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	6.87132	−	4.99231i	0.295149	−	0.214438i
$543$	−3.51722	+	10.8249i	−0.150938	+	0.464541i
$544$	12.9271	−	39.7854i	0.554243	−	1.70578i
$545$	9.59675			0.411080
$546$	−28.4164	−	20.6457i	−1.21611	−	0.883556i
$547$	39.7639			1.70018			0.850091	−	0.526635i	$-0.176547\pi$
$547$	39.7639			1.70018			0.850091	+	0.526635i	$0.176547\pi$
$548$	20.1246	−	61.9372i	0.859681	−	2.64583i
$549$	−5.32624			−0.227318
$550$	−13.8197	+	34.4095i	−0.589272	+	1.46723i
$551$	46.9230			1.99899
$552$	−3.78115	+	11.6372i	−0.160937	+	0.495312i
$553$	−33.8885			−1.44109
$554$	37.2984	+	27.0989i	1.58466	+	1.15132i
$555$	0.791796	−	2.43690i	0.0336099	−	0.103441i
$556$	4.77051	−	14.6821i	0.202315	−	0.622661i
$557$	13.2254	−	40.7037i	0.560379	−	1.72467i	−0.120917	−	0.992663i	$-0.538584\pi$
$557$	13.2254	−	40.7037i	0.560379	−	1.72467i	0.681297	−	0.732007i	$-0.261416\pi$
$558$	13.5172	−	9.82084i	0.572230	−	0.415749i
$559$	−47.6656			−2.01604
$560$	4.73607	−	3.44095i	0.200135	−	0.145407i
$561$	20.6353	+	1.40008i	0.871221	+	0.0591116i
$562$	25.7533	+	18.7109i	1.08634	+	0.789270i
$563$	−22.4377			−0.945636			−0.472818	−	0.881160i	$-0.656763\pi$
$563$	−22.4377			−0.945636			−0.472818	+	0.881160i	$0.656763\pi$
$564$	−19.6353	−	14.2658i	−0.826793	−	0.600701i
$565$	−5.16312	−	15.8904i	−0.217214	−	0.668516i
$566$	13.0517	+	40.1689i	0.548602	+	1.68842i
$567$	0.809017	−	2.48990i	0.0339755	−	0.104566i
$568$	−5.16312	+	15.8904i	−0.216640	+	0.666748i
$569$	−7.07295	+	5.13880i	−0.296513	+	0.215430i	−0.726088	−	0.687602i	$-0.758664\pi$
$569$	−7.07295	+	5.13880i	−0.296513	+	0.215430i	0.429575	+	0.903031i	$0.358664\pi$
$570$	26.7705	+	19.4499i	1.12129	+	0.814667i
$571$	6.13525	−	18.8824i	0.256752	−	0.790203i	−0.736727	−	0.676190i	$-0.763630\pi$
$571$	6.13525	−	18.8824i	0.256752	−	0.790203i	0.993479	−	0.114012i	$-0.0363703\pi$
$572$	−22.2492	+	55.3983i	−0.930287	+	2.31632i
$573$	−11.6353	+	8.45351i	−0.486070	+	0.353150i
$574$	8.35410	−	6.06961i	0.348693	−	0.253341i
$575$	8.45492	+	26.0216i	0.352594	+	1.08517i
$576$	−4.01722	+	12.3637i	−0.167384	+	0.515156i
$577$	−8.76393			−0.364847			−0.182424	−	0.983220i	$-0.558394\pi$
$577$	−8.76393			−0.364847			−0.182424	+	0.983220i	$0.558394\pi$
$578$	39.5967	−	28.7687i	1.64701	−	1.19662i
$579$	2.73607	+	1.98787i	0.113707	+	0.0826130i
$580$	−38.4787	−	27.9564i	−1.59774	−	1.16083i
$581$	18.1353	+	13.1760i	0.752377	+	0.546634i
$582$	−5.65248			−0.234303
$583$	2.80902	−	1.76336i	0.116338	−	0.0730307i
$584$	−5.85410	−	4.25325i	−0.242244	−	0.176001i
$585$	10.8541	−	7.88597i	0.448762	−	0.326045i
$586$	−52.8885	−	38.4258i	−2.18481	−	1.58735i
$587$	−0.500000	+	0.363271i	−0.0206372	+	0.0149938i	−0.598056	−	0.801454i	$-0.704060\pi$
$587$	−0.500000	+	0.363271i	−0.0206372	+	0.0149938i	0.577419	+	0.816448i	$0.304060\pi$
$588$	−0.135255	−	0.416272i	−0.00557782	−	0.0171668i
$589$	49.4508			2.03759
$590$	47.3607	+	34.4095i	1.94981	+	1.41662i
$591$	−2.01722	+	6.20837i	−0.0829774	+	0.255378i
$592$	0.927051	+	0.673542i	0.0381016	+	0.0276824i
$593$	−20.7082			−0.850384			−0.425192	−	0.905103i	$-0.639793\pi$
$593$	−20.7082			−0.850384			−0.425192	+	0.905103i	$0.639793\pi$
$594$	−7.39919	−	0.502029i	−0.303592	−	0.0205985i
$595$	36.5066			1.49662
$596$	−0.624612	−	1.92236i	−0.0255851	−	0.0787428i
$597$	−13.7984			−0.564730
$598$	22.6869	+	69.8232i	0.927737	+	2.85528i
$599$	2.32624	+	1.69011i	0.0950475	+	0.0690561i	0.634294	−	0.773092i	$-0.281291\pi$
$599$	2.32624	+	1.69011i	0.0950475	+	0.0690561i	−0.539246	+	0.842148i	$0.681291\pi$
$600$	−3.45492	−	10.6331i	−0.141046	−	0.434096i
$601$	−1.35410	+	4.16750i	−0.0552350	+	0.169996i	−0.974868	−	0.222783i	$-0.928486\pi$
$601$	−1.35410	+	4.16750i	−0.0552350	+	0.169996i	0.919633	+	0.392778i	$0.128486\pi$
$602$	37.6246	+	27.3359i	1.53346	+	1.11413i
$603$	−1.80902	−	5.56758i	−0.0736689	−	0.226729i
$604$	1.50000	−	4.61653i	0.0610341	−	0.187844i
$605$	10.6910	−	22.1518i	0.434650	−	0.900599i
$606$	2.27458	+	7.00042i	0.0923983	+	0.284373i
$607$	0.954915	−	0.693786i	0.0387588	−	0.0281599i	−0.568237	−	0.822865i	$-0.692374\pi$
$607$	0.954915	−	0.693786i	0.0387588	−	0.0281599i	0.606996	+	0.794705i	$0.292374\pi$
$608$	−35.9164	+	26.0948i	−1.45660	+	1.05828i
$609$	−15.0172	+	10.9106i	−0.608529	+	0.442122i
$610$	8.22949	+	25.3278i	0.333202	+	1.02549i
$611$	−48.5410			−1.96376
$612$	−15.1353	+	10.9964i	−0.611806	+	0.444503i
$613$	4.38854	−	13.5065i	0.177252	−	0.545524i	−0.822478	−	0.568798i	$-0.807409\pi$
$613$	4.38854	−	13.5065i	0.177252	−	0.545524i	0.999729	+	0.0232732i	$0.00740877\pi$
$614$	−1.09424	+	3.36771i	−0.0441597	+	0.135910i
$615$	1.21885	+	3.75123i	0.0491487	+	0.151264i
$616$	16.4443	−	10.3229i	0.662559	−	0.415920i
$617$	2.03851	+	6.27388i	0.0820672	+	0.252577i	0.983668	−	0.179992i	$-0.0576072\pi$
$617$	2.03851	+	6.27388i	0.0820672	+	0.252577i	−0.901601	+	0.432569i	$0.857607\pi$
$618$	−15.7533	+	11.4454i	−0.633690	+	0.460403i
$619$	−0.663119	+	0.481784i	−0.0266530	+	0.0193645i	−0.601032	−	0.799225i	$-0.705244\pi$
$619$	−0.663119	+	0.481784i	−0.0266530	+	0.0193645i	0.574379	+	0.818589i	$0.305244\pi$
$620$	−40.5517	−	29.4625i	−1.62859	−	1.18324i
$621$	−4.42705	+	3.21644i	−0.177651	+	0.129071i
$622$	−50.0238	+	36.3444i	−2.00577	+	1.45728i
$623$	2.88197	+	8.86978i	0.115464	+	0.355360i
$624$	1.85410	+	5.70634i	0.0742235	+	0.228436i
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	59.0689			2.36087
$627$	−16.8435	−	14.0741i	−0.672663	−	0.562065i
$628$	−8.07295	+	24.8460i	−0.322146	+	0.991463i
$629$	2.20820	+	6.79615i	0.0880469	+	0.270980i
$630$	−13.0902			−0.521525
$631$	14.2918			0.568947			0.284474	−	0.958684i	$-0.408181\pi$
$631$	14.2918			0.568947			0.284474	+	0.958684i	$0.408181\pi$
$632$	−23.4164	−	17.0130i	−0.931455	−	0.676741i
$633$	−3.61803	+	11.1352i	−0.143804	+	0.442583i
$634$	−18.0902	+	13.1433i	−0.718452	+	0.521986i
$635$	−12.9271	+	9.39205i	−0.512994	+	0.372712i
$636$	−0.927051	+	2.85317i	−0.0367600	+	0.113136i
$637$	−0.708204	−	0.514540i	−0.0280601	−	0.0203868i
$638$	40.3500	+	33.7158i	1.59747	+	1.33482i
$639$	−6.04508	+	4.39201i	−0.239140	+	0.173745i
$640$	35.0000			1.38350
$641$	−0.927051	+	2.85317i	−0.0366163	+	0.112693i	−0.967694	−	0.252127i	$-0.918870\pi$
$641$	−0.927051	+	2.85317i	−0.0366163	+	0.112693i	0.931078	+	0.364821i	$0.118870\pi$
$642$	−27.7639			−1.09575
$643$	−6.61803	−	4.80828i	−0.260990	−	0.189620i	0.449594	−	0.893233i	$-0.351569\pi$
$643$	−6.61803	−	4.80828i	−0.260990	−	0.189620i	−0.710583	+	0.703613i	$0.751569\pi$
$644$	13.2812	−	40.8752i	0.523351	−	1.61071i
$645$	−14.3713	+	10.4414i	−0.565870	+	0.411129i
$646$	−92.2837			−3.63085
$647$	−7.81966	−	24.0664i	−0.307423	−	0.946149i	−0.978762	−	0.204999i	$-0.934281\pi$
$647$	−7.81966	−	24.0664i	−0.307423	−	0.946149i	0.671340	−	0.741150i	$-0.265719\pi$
$648$	1.80902	−	1.31433i	0.0710649	−	0.0516317i
$649$	−29.7984	−	24.8990i	−1.16969	−	0.977371i
$650$	−54.2705	−	39.4298i	−2.12866	−	1.54657i
$651$	−15.8262	+	11.4984i	−0.620279	+	0.450659i
$652$	31.5517	+	22.9236i	1.23566	+	0.897758i
$653$	−6.50000	−	4.72253i	−0.254365	−	0.184807i	0.453294	−	0.891361i	$-0.350249\pi$
$653$	−6.50000	−	4.72253i	−0.254365	−	0.184807i	−0.707659	+	0.706554i	$0.750249\pi$
$654$	7.76393	−	5.64083i	0.303594	−	0.220574i
$655$	31.3435	+	22.7724i	1.22469	+	0.889790i
$656$	−1.76393			−0.0688700
$657$	−1.00000	−	3.07768i	−0.0390137	−	0.120072i
$658$	38.3156	+	27.8379i	1.49370	+	1.08523i
$659$	−19.5902	−	14.2331i	−0.763125	−	0.554443i	0.136742	−	0.990607i	$-0.456337\pi$
$659$	−19.5902	−	14.2331i	−0.763125	−	0.554443i	−0.899867	+	0.436164i	$0.856337\pi$
$660$	5.42705	+	21.5765i	0.211248	+	0.839866i
$661$	−12.9443	+	9.40456i	−0.503474	+	0.365795i	−0.810342	−	0.585957i	$-0.800719\pi$
$661$	−12.9443	+	9.40456i	−0.503474	+	0.365795i	0.306868	+	0.951752i	$0.400719\pi$
$662$	−15.7771			−0.613194
$663$	−11.5623	+	35.5851i	−0.449043	+	1.38201i
$664$	5.91641	+	18.2088i	0.229601	+	0.706640i
$665$	−31.3435	−	22.7724i	−1.21545	−	0.883074i
$666$	−0.791796	−	2.43690i	−0.0306815	−	0.0944279i
$667$	38.7984			1.50228
$668$	23.4787	+	72.2601i	0.908419	+	2.79583i
$669$	−2.92705	−	2.12663i	−0.113166	−	0.0822202i
$670$	−23.6803	+	17.2048i	−0.914851	+	0.664678i
$671$	−4.30902	−	17.1315i	−0.166348	−	0.661355i
$672$	5.42705	−	16.7027i	0.209353	−	0.644322i
$673$	−7.75329	+	23.8622i	−0.298867	+	0.919819i	0.683028	+	0.730393i	$0.260663\pi$
$673$	−7.75329	+	23.8622i	−0.298867	+	0.919819i	−0.981895	+	0.189426i	$0.939337\pi$
$674$	−8.37790	−	25.7845i	−0.322705	−	0.993183i
$675$	1.54508	−	4.75528i	0.0594703	−	0.183031i
$676$	−55.8222	−	40.5572i	−2.14701	−	1.55989i
$677$	5.00000			0.192166			0.0960828	−	0.995373i	$-0.469369\pi$
$677$	5.00000			0.192166			0.0960828	+	0.995373i	$0.469369\pi$
$678$	−13.5172	−	9.82084i	−0.519126	−	0.377167i
$679$	6.61803			0.253977
$680$	25.2254	+	18.3273i	0.967351	+	0.702822i
$681$	2.87132	+	8.83702i	0.110029	+	0.338635i
$682$	42.5238	+	35.5321i	1.62832	+	1.36060i
$683$	−5.75329	−	17.7068i	−0.220143	−	0.677532i	−0.998748	−	0.0500175i	$-0.984072\pi$
$683$	−5.75329	−	17.7068i	−0.220143	−	0.677532i	0.778605	−	0.627515i	$-0.215928\pi$
$684$	19.8541			0.759141
$685$	−39.2705	−	28.5317i	−1.50045	−	1.09014i
$686$	12.9271	+	39.7854i	0.493557	+	1.51901i
$687$	5.25329	+	16.1680i	0.200425	+	0.616846i
$688$	−2.45492	−	7.55545i	−0.0935928	−	0.288049i
$689$	1.85410	+	5.70634i	0.0706357	+	0.217394i
$690$	22.1353	+	16.0822i	0.842675	+	0.612239i
$691$	12.5836			0.478702			0.239351	−	0.970933i	$-0.423065\pi$
$691$	12.5836			0.478702			0.239351	+	0.970933i	$0.423065\pi$
$692$	18.7918	+	57.8352i	0.714357	+	2.19856i
$693$	8.66312	+	0.587785i	0.329085	+	0.0223281i
$694$	−12.3992	−	38.1608i	−0.470667	−	1.44856i
$695$	−9.30902	−	6.76340i	−0.353111	−	0.256550i
$696$	−15.8541			−0.600948
$697$	−8.89919	−	6.46564i	−0.337081	−	0.244903i
$698$	0.729490			0.0276116
$699$	−19.7082	−	14.3188i	−0.745433	−	0.541589i
$700$	12.1353	+	37.3485i	0.458670	+	1.41164i
$701$	−5.40983	−	16.6497i	−0.204326	−	0.628852i	−0.999740	−	0.0227856i	$-0.992746\pi$
$701$	−5.40983	−	16.6497i	−0.204326	−	0.628852i	0.795414	−	0.606067i	$-0.207254\pi$
$702$	4.14590	−	12.7598i	0.156477	−	0.481586i
$703$	2.34346	−	7.21242i	0.0883852	−	0.272022i
$704$	−43.0172	−	2.91868i	−1.62127	−	0.110002i
$705$	−14.6353	+	10.6331i	−0.551196	+	0.400467i
$706$	26.3435	+	19.1396i	0.991449	+	0.720330i
$707$	−2.66312	−	8.19624i	−0.100157	−	0.308251i
$708$	35.1246			1.32006
$709$	−5.72542	−	17.6210i	−0.215023	−	0.661772i	−0.999152	−	0.0411746i	$-0.986890\pi$
$709$	−5.72542	−	17.6210i	−0.215023	−	0.661772i	0.784129	−	0.620598i	$-0.213110\pi$
$710$	30.2254	+	21.9601i	1.13434	+	0.824146i
$711$	−4.00000	−	12.3107i	−0.150012	−	0.461689i
$712$	−2.46149	+	7.57570i	−0.0922483	+	0.283911i
$713$	40.8885			1.53129
$714$	29.5344	−	21.4580i	1.10530	−	0.803047i
$715$	34.1459	+	28.5317i	1.27698	+	1.06702i
$716$	−21.0000	−	15.2574i	−0.784807	−	0.570196i
$717$	10.5902	+	7.69421i	0.395497	+	0.287345i
$718$	7.31308	+	22.5074i	0.272922	+	0.839967i
$719$	−16.8541			−0.628552			−0.314276	−	0.949332i	$-0.601762\pi$
$719$	−16.8541			−0.628552			−0.314276	+	0.949332i	$0.601762\pi$
$720$	1.80902	+	1.31433i	0.0674181	+	0.0489821i
$721$	18.4443	−	13.4005i	0.686901	−	0.499062i
$722$	44.8607	+	32.5932i	1.66954	+	1.21299i
$723$	−14.4443	−	10.4944i	−0.537188	−	0.390290i
$724$	27.6246	−	20.0705i	1.02666	−	0.745913i
$725$	−28.6803	+	20.8375i	−1.06516	+	0.773885i
$726$	−4.37132	−	24.2052i	−0.162235	−	0.898339i
$727$	23.6803	−	17.2048i	0.878255	−	0.638090i	−0.0545341	−	0.998512i	$-0.517367\pi$
$727$	23.6803	−	17.2048i	0.878255	−	0.638090i	0.932789	+	0.360422i	$0.117367\pi$
$728$	10.8541	+	33.4055i	0.402280	+	1.23809i
$729$	1.00000			0.0370370
$730$	−13.0902	+	9.51057i	−0.484489	+	0.352002i
$731$	15.3090	−	47.1163i	0.566224	−	1.74266i
$732$	12.9271	+	9.39205i	0.477798	+	0.347140i
$733$	−13.4377			−0.496333			−0.248166	−	0.968717i	$-0.579828\pi$
$733$	−13.4377			−0.496333			−0.248166	+	0.968717i	$0.579828\pi$
$734$	7.42299	−	22.8456i	0.273987	−	0.843247i
$735$	−0.326238			−0.0120335
$736$	−29.6976	+	21.5765i	−1.09467	+	0.795322i
$737$	16.4443	−	10.3229i	0.605733	−	0.380248i
$738$	3.19098	+	2.31838i	0.117462	+	0.0853409i
$739$	8.54508	−	26.2991i	0.314336	−	0.967427i	−0.661691	−	0.749777i	$-0.730161\pi$
$739$	8.54508	−	26.2991i	0.314336	−	0.967427i	0.976027	−	0.217650i	$-0.0698391\pi$
$740$	−6.21885	+	4.51826i	−0.228609	+	0.166094i
$741$	32.1246	−	23.3399i	1.18013	−	0.857413i
$742$	1.80902	−	5.56758i	0.0664111	−	0.204392i
$743$	−26.4894	−	19.2456i	−0.971800	−	0.706054i	−0.0159391	−	0.999873i	$-0.505074\pi$
$743$	−26.4894	−	19.2456i	−0.971800	−	0.706054i	−0.955861	+	0.293819i	$0.905074\pi$
$744$	−16.7082			−0.612552
$745$	−1.50658			−0.0551967
$746$	2.74013	+	8.43326i	0.100323	+	0.308764i
$747$	−2.64590	+	8.14324i	−0.0968083	+	0.297945i
$748$	−47.6140	−	39.7854i	−1.74094	−	1.45470i
$749$	32.5066			1.18776
$750$	−25.0000			−0.912871
$751$	−6.78115	−	20.8702i	−0.247448	−	0.761566i	−0.995224	−	0.0976154i	$-0.968879\pi$
$751$	−6.78115	−	20.8702i	−0.247448	−	0.761566i	0.747776	−	0.663951i	$-0.231121\pi$
$752$	−2.50000	−	7.69421i	−0.0911656	−	0.280579i
$753$	0.0278640	−	0.0202444i	0.00101542	−	0.000737747i
$754$	−76.9574	+	55.9128i	−2.80262	+	2.03623i
$755$	−2.92705	−	2.12663i	−0.106526	−	0.0773959i
$756$	−6.35410	+	4.61653i	−0.231096	+	0.167901i
$757$	−36.4894	+	26.5111i	−1.32623	+	0.963561i	−0.326396	+	0.945233i	$0.605834\pi$
$757$	−36.4894	+	26.5111i	−1.32623	+	0.963561i	−0.999832	+	0.0183282i	$0.994166\pi$
$758$	−18.5557	−	57.1087i	−0.673974	−	2.07428i
$759$	−13.9271	−	11.6372i	−0.505520	−	0.422403i
$760$	−10.2254	−	31.4706i	−0.370915	−	1.14156i
$761$	9.69756	−	29.8460i	0.351536	−	1.08192i	−0.606454	−	0.795118i	$-0.707409\pi$
$761$	9.69756	−	29.8460i	0.351536	−	1.08192i	0.957991	−	0.286799i	$-0.0925913\pi$
$762$	−4.93769	+	15.1967i	−0.178874	+	0.550517i
$763$	−9.09017	+	6.60440i	−0.329086	+	0.239095i
$764$	43.1459			1.56096
$765$	4.30902	+	13.2618i	0.155793	+	0.479481i
$766$	−36.3050	+	26.3771i	−1.31175	+	0.953043i
$767$	56.8328	−	41.2915i	2.05211	−	1.49095i
$768$	7.28115	−	5.29007i	0.262736	−	0.190889i
$769$	−4.81966	−	14.8334i	−0.173801	−	0.534906i	0.825775	−	0.563999i	$-0.190738\pi$
$769$	−4.81966	−	14.8334i	−0.173801	−	0.534906i	−0.999577	+	0.0290936i	$0.990738\pi$
$770$	−10.5902	−	42.1038i	−0.381643	−	1.51731i
$771$	5.01722	−	15.4414i	0.180691	−	0.556109i
$772$	−3.13525	−	9.64932i	−0.112840	−	0.347287i
$773$	−32.4336	−	23.5644i	−1.16656	−	0.847553i	−0.175964	−	0.984397i	$-0.556304\pi$
$773$	−32.4336	−	23.5644i	−1.16656	−	0.847553i	−0.990593	+	0.136844i	$0.956304\pi$
$774$	−5.48936	+	16.8945i	−0.197311	+	0.607260i
$775$	−30.2254	+	21.9601i	−1.08573	+	0.788829i
$776$	4.57295	+	3.32244i	0.164159	+	0.119269i
$777$	0.927051	+	2.85317i	0.0332578	+	0.102357i
$778$	−10.7295			−0.384671
$779$	3.60739	+	11.1024i	0.129248	+	0.397785i
$780$	−40.2492			−1.44115
$781$	−19.0172	−	15.8904i	−0.680490	−	0.568605i
$782$	−76.3050			−2.72866
$783$	−5.73607	−	4.16750i	−0.204990	−	0.148934i
$784$	0.0450850	−	0.138757i	0.00161018	−	0.00495562i
$785$	15.7533	+	11.4454i	0.562259	+	0.408505i
$786$	38.7426			1.38190
$787$	−0.263932	−	0.812299i	−0.00940816	−	0.0289553i	0.946242	−	0.323459i	$-0.104846\pi$
$787$	−0.263932	−	0.812299i	−0.00940816	−	0.0289553i	−0.955650	+	0.294504i	$0.904846\pi$
$788$	15.8435	−	11.5109i	0.564400	−	0.410060i
$789$	18.7082	+	13.5923i	0.666030	+	0.483899i
$790$	−52.3607	+	38.0423i	−1.86291	+	1.35348i
$791$	15.8262	+	11.4984i	0.562716	+	0.408837i
$792$	5.69098	+	4.75528i	0.202220	+	0.168972i
$793$	31.9574			1.13484
$794$	38.6803	+	28.1029i	1.37271	+	0.997335i
$795$	1.80902	+	1.31433i	0.0641592	+	0.0466144i
$796$	33.4894	+	24.3314i	1.18700	+	0.862405i
$797$	−14.7984	+	10.7516i	−0.524185	+	0.380843i	−0.818178	−	0.574965i	$-0.805016\pi$
$797$	−14.7984	+	10.7516i	−0.524185	+	0.380843i	0.293993	+	0.955808i	$0.405016\pi$
$798$	−38.7426			−1.37147
$799$	15.5902	−	47.9816i	0.551541	−	1.69747i
$800$	10.3647	−	31.8994i	0.366449	−	1.12781i
$801$	−2.88197	+	2.09387i	−0.101829	+	0.0739833i
$802$	−29.6976	+	21.5765i	−1.04866	+	0.761894i
$803$	9.09017	−	5.70634i	0.320785	−	0.201372i
$804$	−5.42705	+	16.7027i	−0.191397	+	0.589060i
$805$	−25.9164	−	18.8294i	−0.913433	−	0.663648i
$806$	−81.1033	+	58.9250i	−2.85674	+	2.07555i
$807$	−5.45492	+	16.7885i	−0.192022	+	0.590983i
$808$	2.27458	−	7.00042i	0.0800193	−	0.246274i
$809$	7.81559	+	24.0539i	0.274782	+	0.845691i	0.989277	+	0.146051i	$0.0466563\pi$
$809$	7.81559	+	24.0539i	0.274782	+	0.845691i	−0.714495	+	0.699640i	$0.753344\pi$
$810$	−1.54508	−	4.75528i	−0.0542888	−	0.167084i
$811$	−22.7533	−	16.5312i	−0.798976	−	0.580490i	0.111638	−	0.993749i	$-0.464390\pi$
$811$	−22.7533	−	16.5312i	−0.798976	−	0.580490i	−0.910614	+	0.413259i	$0.864390\pi$
$812$	55.6869			1.95423
$813$	−3.07295	−	2.23263i	−0.107773	−	0.0783017i
$814$	7.19756	−	4.51826i	0.252274	−	0.158365i
$815$	23.5172	−	17.0863i	0.823772	−	0.598506i
$816$	−6.23607			−0.218306
$817$	−42.5344	+	30.9031i	−1.48809	+	1.08116i
$818$	1.34346	−	4.13474i	0.0469729	−	0.144568i
$819$	−4.85410	+	14.9394i	−0.169616	+	0.522025i
$820$	3.65654	−	11.2537i	0.127692	−	0.392995i
$821$	−21.2812	−	15.4617i	−0.742717	−	0.539616i	0.150844	−	0.988558i	$-0.451801\pi$
$821$	−21.2812	−	15.4617i	−0.742717	−	0.539616i	−0.893561	+	0.448942i	$0.851801\pi$
$822$	−48.5410			−1.69306
$823$	14.8156	−	45.5977i	0.516439	−	1.58944i	−0.264209	−	0.964465i	$-0.585111\pi$
$823$	14.8156	−	45.5977i	0.516439	−	1.58944i	0.780648	−	0.624971i	$-0.214889\pi$
$824$	19.4721			0.678344
$825$	16.5451	+	1.12257i	0.576026	+	0.0390829i
$826$	−68.5410			−2.38485
$827$	4.92705	−	15.1639i	0.171330	−	0.527301i	−0.828117	−	0.560556i	$-0.810587\pi$
$827$	4.92705	−	15.1639i	0.171330	−	0.527301i	0.999447	+	0.0332554i	$0.0105875\pi$
$828$	16.4164			0.570510
$829$	−22.0795	−	16.0417i	−0.766854	−	0.557152i	0.134151	−	0.990961i	$-0.457169\pi$
$829$	−22.0795	−	16.0417i	−0.766854	−	0.557152i	−0.901005	+	0.433809i	$0.857169\pi$
$830$	42.8115			1.48601
$831$	6.37132	−	19.6089i	0.221019	−	0.680226i
$832$	24.1033	−	74.1824i	0.835632	−	2.57181i
$833$	0.736068	−	0.534785i	0.0255032	−	0.0185292i
$834$	−11.5066			−0.398440
$835$	56.6312			1.95980
$836$	16.0623	+	63.8595i	0.555526	+	2.20863i
$837$	−6.04508	−	4.39201i	−0.208949	−	0.151810i
$838$	51.0557			1.76369
$839$	14.7361	+	10.7064i	0.508746	+	0.369625i	0.812348	−	0.583174i	$-0.198189\pi$
$839$	14.7361	+	10.7064i	0.508746	+	0.369625i	−0.303602	+	0.952799i	$0.598189\pi$
$840$	10.5902	+	7.69421i	0.365396	+	0.265475i
$841$	6.57295	+	20.2295i	0.226653	+	0.697567i
$842$	−17.9508	+	55.2470i	−0.618627	+	1.90394i
$843$	4.39919	−	13.5393i	0.151516	−	0.466318i
$844$	28.4164	−	20.6457i	0.978133	−	0.710655i
$845$	−41.6074	+	30.2295i	−1.43134	+	1.03993i
$846$	−5.59017	+	17.2048i	−0.192194	+	0.591512i
$847$	5.11803	+	28.3399i	0.175858	+	0.973772i
$848$	−0.809017	+	0.587785i	−0.0277818	+	0.0201846i
$849$	15.2812	−	11.1024i	0.524448	−	0.381034i
$850$	56.4058	−	40.9812i	1.93470	−	1.40564i
$851$	1.93769	−	5.96361i	0.0664233	−	0.204430i
$852$	22.4164			0.767973
$853$	18.5623	−	13.4863i	0.635561	−	0.461762i	−0.222761	−	0.974873i	$-0.571507\pi$
$853$	18.5623	−	13.4863i	0.635561	−	0.461762i	0.858322	+	0.513111i	$0.171507\pi$
$854$	−25.2254	−	18.3273i	−0.863196	−	0.627149i
$855$	4.57295	−	14.0741i	0.156392	−	0.481324i
$856$	22.4615	+	16.3192i	0.767718	+	0.557780i
$857$	−0.729490			−0.0249189			−0.0124595	−	0.999922i	$-0.503966\pi$
$857$	−0.729490			−0.0249189			−0.0124595	+	0.999922i	$0.503966\pi$
$858$	44.3951	+	3.01217i	1.51562	+	0.102834i
$859$	2.28115	+	1.65735i	0.0778319	+	0.0565482i	0.626021	−	0.779806i	$-0.284682\pi$
$859$	2.28115	+	1.65735i	0.0778319	+	0.0565482i	−0.548189	+	0.836355i	$0.684682\pi$
$860$	53.2918			1.81724
$861$	−3.73607	−	2.71441i	−0.127325	−	0.0925069i
$862$	9.04508	−	6.57164i	0.308077	−	0.223831i
$863$	−2.22542	−	6.84915i	−0.0757543	−	0.233148i	0.906008	−	0.423261i	$-0.139115\pi$
$863$	−2.22542	−	6.84915i	−0.0757543	−	0.233148i	−0.981762	+	0.190113i	$0.939115\pi$
$864$	6.70820			0.228218
$865$	45.3262			1.54114
$866$	−17.2361	+	53.0472i	−0.585705	+	1.80262i
$867$	−17.7082	−	12.8658i	−0.601402	−	0.436944i
$868$	58.6869			1.99196
$869$	36.3607	−	22.8254i	1.23345	−	0.774297i
$870$	−10.9549	+	33.7158i	−0.371406	+	1.14307i
$871$	10.8541	+	33.4055i	0.367777	+	1.13190i
$872$	−9.59675			−0.324987
$873$	0.781153	+	2.40414i	0.0264380	+	0.0813679i
$874$	65.5132	+	47.5981i	2.21602	+	1.61003i
$875$	29.2705			0.989524
$876$	−3.00000	+	9.23305i	−0.101361	+	0.311956i
$877$	8.26393	+	6.00410i	0.279053	+	0.202744i	0.718504	−	0.695522i	$-0.244827\pi$
$877$	8.26393	+	6.00410i	0.279053	+	0.202744i	−0.439451	+	0.898266i	$0.644827\pi$
$878$	3.31559	+	10.2044i	0.111896	+	0.344380i
$879$	−9.03444	+	27.8052i	−0.304724	+	0.937845i
$880$	−2.76393	+	6.88191i	−0.0931721	+	0.231989i
$881$	0.263932	+	0.812299i	0.00889210	+	0.0273671i	0.955404	−	0.295301i	$-0.0954201\pi$
$881$	0.263932	+	0.812299i	0.00889210	+	0.0273671i	−0.946512	+	0.322669i	$0.895420\pi$
$882$	−0.263932	+	0.191758i	−0.00888705	+	0.00645682i
$883$	−12.0000	+	8.71851i	−0.403832	+	0.293401i	−0.771100	−	0.636714i	$-0.780293\pi$
$883$	−12.0000	+	8.71851i	−0.403832	+	0.293401i	0.367268	+	0.930115i	$0.380293\pi$
$884$	90.8115	−	65.9784i	3.05432	−	2.21910i
$885$	8.09017	−	24.8990i	0.271948	−	0.836970i
$886$	85.9017			2.88592
$887$	−41.0238	+	29.8055i	−1.37744	+	1.00077i	−0.380331	+	0.924851i	$0.624190\pi$
$887$	−41.0238	+	29.8055i	−1.37744	+	1.00077i	−0.997114	+	0.0759213i	$0.975810\pi$
$888$	−0.791796	+	2.43690i	−0.0265709	+	0.0817769i
$889$	5.78115	−	17.7926i	0.193894	−	0.596743i
$890$	14.4098	+	10.4694i	0.483019	+	0.350934i
$891$	0.809017	+	3.21644i	0.0271031	+	0.107755i
$892$	3.35410	+	10.3229i	0.112304	+	0.345635i
$893$	−43.3156	+	31.4706i	−1.44950	+	1.05312i
$894$	−1.21885	+	0.885544i	−0.0407643	+	0.0296170i
$895$	−15.6525	+	11.3722i	−0.523205	+	0.380130i
$896$	−33.1525	+	24.0867i	−1.10755	+	0.804680i
$897$	26.5623	−	19.2986i	0.886890	−	0.644363i
$898$	−8.35410	−	25.7113i	−0.278780	−	0.857997i
$899$	16.3713	+	50.3858i	0.546014	+	1.68046i
$900$	−12.1353	+	8.81678i	−0.404508	+	0.293893i
$901$	−6.23607			−0.207754
$902$	−4.87539	+	12.1392i	−0.162333	+	0.404192i
$903$	6.42705	−	19.7804i	0.213879	−	0.658251i
$904$	5.16312	+	15.8904i	0.171723	+	0.528508i
$905$	−7.86475	−	24.2052i	−0.261433	−	0.804608i
$906$	−3.61803			−0.120201
$907$	33.2533	+	24.1599i	1.10416	+	0.802217i	0.981734	−	0.190261i	$-0.0609333\pi$
$907$	33.2533	+	24.1599i	1.10416	+	0.802217i	0.122424	+	0.992478i	$0.460933\pi$
$908$	8.61397	−	26.5111i	0.285865	−	0.879801i
$909$	2.66312	−	1.93487i	0.0883301	−	0.0641756i
$910$	78.5410			2.60361
$911$	−12.0729	+	37.1567i	−0.399995	+	1.23106i	0.525008	+	0.851097i	$0.324062\pi$
$911$	−12.0729	+	37.1567i	−0.399995	+	1.23106i	−0.925003	+	0.379960i	$0.875938\pi$
$912$	5.35410	+	3.88998i	0.177292	+	0.128810i
$913$	−28.3328	−	1.92236i	−0.937679	−	0.0636207i
$914$	17.7639	−	12.9063i	0.587579	−	0.426901i
$915$	9.63525	−	7.00042i	0.318532	−	0.231427i
$916$	15.7599	−	48.5039i	0.520721	−	1.60261i
$917$	−45.3607			−1.49794
$918$	11.2812	+	8.19624i	0.372334	+	0.270516i
$919$	−4.21885	+	12.9843i	−0.139167	+	0.428312i	−0.996215	−	0.0869249i	$-0.972296\pi$
$919$	−4.21885	+	12.9843i	−0.139167	+	0.428312i	0.857048	+	0.515237i	$0.172296\pi$
$920$	−8.45492	−	26.0216i	−0.278750	−	0.857905i
$921$	1.58359			0.0521811
$922$	−22.0967	−	68.0068i	−0.727718	−	2.23968i
$923$	36.2705	−	26.3521i	1.19386	−	0.867389i
$924$	−19.9894	−	16.7027i	−0.657602	−	0.549480i
$925$	1.77051	+	5.44907i	0.0582140	+	0.179164i
$926$	−61.7320	+	44.8509i	−2.02864	+	1.47389i
$927$	7.04508	+	5.11855i	0.231391	+	0.168115i
$928$	−38.4787	−	27.9564i	−1.26313	−	0.917715i
$929$	22.5066	−	16.3520i	0.738417	−	0.536491i	−0.153798	−	0.988102i	$-0.549151\pi$
$929$	22.5066	−	16.3520i	0.738417	−	0.536491i	0.892215	+	0.451611i	$0.149151\pi$
$930$	−11.5451	+	35.5321i	−0.378578	+	1.16514i
$931$	−0.965558			−0.0316449
$932$	22.5836	+	69.5051i	0.739750	+	2.27672i
$933$	22.3713	+	16.2537i	0.732404	+	0.532123i
$934$	−28.1525	−	20.4540i	−0.921177	−	0.669274i
$935$	−39.1697	+	24.5887i	−1.28099	+	0.804137i
$936$	−10.8541	+	7.88597i	−0.354777	+	0.257761i
$937$	−37.4508			−1.22347			−0.611733	−	0.791064i	$-0.709527\pi$
$937$	−37.4508			−1.22347			−0.611733	+	0.791064i	$0.709527\pi$
$938$	10.5902	−	32.5932i	0.345781	−	1.06421i
$939$	−8.16312	−	25.1235i	−0.266393	−	0.819874i
$940$	54.2705			1.77011
$941$	−0.545085	−	1.67760i	−0.0177693	−	0.0546882i	0.941779	−	0.336233i	$-0.109153\pi$
$941$	−0.545085	−	1.67760i	−0.0177693	−	0.0546882i	−0.959548	+	0.281545i	$0.909153\pi$
$942$	19.4721			0.634436
$943$	2.98278	+	9.18005i	0.0971327	+	0.298944i
$944$	9.47214	+	6.88191i	0.308292	+	0.223987i
$945$	1.80902	+	5.56758i	0.0588473	+	0.181113i
$946$	−58.7812	−	3.98825i	−1.91114	−	0.129669i
$947$	−11.9549	+	36.7934i	−0.388483	+	1.19563i	0.545440	+	0.838150i	$0.316363\pi$
$947$	−11.9549	+	36.7934i	−0.388483	+	1.19563i	−0.933922	+	0.357476i	$0.883637\pi$
$948$	−12.0000	+	36.9322i	−0.389742	+	1.19950i
$949$	6.00000	+	18.4661i	0.194768	+	0.599435i
$950$	−73.9919			−2.40061
$951$	8.09017	+	5.87785i	0.262342	+	0.190602i
$952$	−36.5066			−1.18318
$953$	13.9721	+	10.1514i	0.452602	+	0.328835i	0.790622	−	0.612304i	$-0.209757\pi$
$953$	13.9721	+	10.1514i	0.452602	+	0.328835i	−0.338020	+	0.941139i	$0.609757\pi$
$954$	2.23607			0.0723954
$955$	9.93769	−	30.5851i	0.321576	−	0.989710i
$956$	−12.1353	−	37.3485i	−0.392482	−	1.20794i
$957$	8.76393	−	21.8213i	0.283298	−	0.705382i
$958$	−9.75987	−	30.0378i	−0.315327	−	0.970477i
$959$	56.8328			1.83523
$960$	−8.98278	−	27.6462i	−0.289918	−	0.892276i
$961$	7.67376	+	23.6174i	0.247541	+	0.761852i
$962$	4.75078	+	14.6214i	0.153171	+	0.471412i
$963$	3.83688	+	11.8087i	0.123642	+	0.380530i
$964$	16.5517	+	50.9408i	0.533093	+	1.64069i
$965$	−7.56231			−0.243439
$966$	−32.0344			−1.03069
$967$	−9.92705	−	30.5523i	−0.319232	−	0.982496i	−0.973977	−	0.226646i	$-0.927224\pi$
$967$	−9.92705	−	30.5523i	−0.319232	−	0.982496i	0.654745	−	0.755850i	$-0.272776\pi$
$968$	−10.6910	+	22.1518i	−0.343621	+	0.711986i
$969$	12.7533	+	39.2506i	0.409695	+	1.26091i
$970$	10.2254	−	7.42921i	0.328319	−	0.238537i
$971$	4.12461			0.132365			0.0661825	−	0.997808i	$-0.478918\pi$
$971$	4.12461			0.132365			0.0661825	+	0.997808i	$0.478918\pi$
$972$	−2.42705	−	1.76336i	−0.0778477	−	0.0565597i
$973$	13.4721			0.431897
$974$	27.2984	+	19.8334i	0.874696	+	0.635504i
$975$	−9.27051	+	28.5317i	−0.296894	+	0.913746i
$976$	1.64590	+	5.06555i	0.0526839	+	0.162144i
$977$	−0.416408	+	1.28157i	−0.0133221	+	0.0410011i	−0.957497	−	0.288445i	$-0.906862\pi$
$977$	−0.416408	+	1.28157i	−0.0133221	+	0.0410011i	0.944175	+	0.329446i	$0.106862\pi$
$978$	8.98278	−	27.6462i	0.287238	−	0.884026i
$979$	−9.06637	−	7.57570i	−0.289762	−	0.242120i
$980$	0.791796	+	0.575274i	0.0252930	+	0.0183764i
$981$	−3.47214	−	2.52265i	−0.110857	−	0.0805422i
$982$	17.6484	+	54.3162i	0.563183	+	1.73330i
$983$	−8.94427			−0.285278			−0.142639	−	0.989775i	$-0.545559\pi$
$983$	−8.94427			−0.285278			−0.142639	+	0.989775i	$0.545559\pi$
$984$	−1.21885	−	3.75123i	−0.0388554	−	0.119585i
$985$	−4.51064	−	13.8823i	−0.143721	−	0.442328i
$986$	−30.5517	−	94.0283i	−0.972963	−	2.99447i
$987$	6.54508	−	20.1437i	0.208332	−	0.641181i
$988$	−119.125			−3.78986
$989$	−35.1697	+	25.5523i	−1.11833	+	0.812515i
$990$	14.0451	−	8.81678i	0.446382	−	0.280216i
$991$	36.9336	+	26.8339i	1.17324	+	0.852405i	0.991393	−	0.130922i	$-0.0417938\pi$
$991$	36.9336	+	26.8339i	1.17324	+	0.852405i	0.181843	+	0.983328i	$0.441794\pi$
$992$	−40.5517	−	29.4625i	−1.28752	−	0.935436i
$993$	2.18034	+	6.71040i	0.0691910	+	0.212948i
$994$	−43.7426			−1.38743
$995$	24.9615	−	18.1356i	0.791333	−	0.574937i
$996$	20.7812	−	15.0984i	0.658476	−	0.478411i
$997$	−23.1525	−	16.8213i	−0.733246	−	0.532735i	0.157342	−	0.987544i	$-0.449707\pi$
$997$	−23.1525	−	16.8213i	−0.733246	−	0.532735i	−0.890589	+	0.454810i	$0.849707\pi$
$998$	−16.6074	−	12.0660i	−0.525698	−	0.381942i
$999$	−0.927051	+	0.673542i	−0.0293306	+	0.0213099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.p.a.586.1	yes	4
11.4	even	5		825.2.r.a.136.1	yes	4
25.16	even	5		825.2.r.a.91.1	yes	4
275.191	even	5	inner	825.2.p.a.466.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.p.a.466.1	✓	4	275.191	even	5	inner
825.2.p.a.586.1	yes	4	1.1	even	1	trivial
825.2.r.a.91.1	yes	4	25.16	even	5
825.2.r.a.136.1	yes	4	11.4	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.p (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 + 2.12663i) q^{2} +1.00000 q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(0.809017 - 2.48990i) q^{7} +(1.80902 - 1.31433i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.690983 + 2.12663i) q^{2} +1.00000 q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(0.809017 - 2.48990i) q^{7} +(1.80902 - 1.31433i) q^{8} +1.00000 q^{9} +(-1.54508 - 4.75528i) q^{10} +(0.809017 + 3.21644i) q^{11} +(-2.42705 - 1.76336i) q^{12} -6.00000 q^{13} +(4.73607 + 3.44095i) q^{14} +(-1.80902 + 1.31433i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.92705 - 5.93085i) q^{17} +(-0.690983 + 2.12663i) q^{18} +(-5.35410 + 3.88998i) q^{19} +6.70820 q^{20} +(0.809017 - 2.48990i) q^{21} +(-7.39919 - 0.502029i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 - 1.31433i) q^{24} +(1.54508 - 4.75528i) q^{25} +(4.14590 - 12.7598i) q^{26} +1.00000 q^{27} +(-6.35410 + 4.61653i) q^{28} +(-5.73607 - 4.16750i) q^{29} +(-1.54508 - 4.75528i) q^{30} +(-6.04508 - 4.39201i) q^{31} +6.70820 q^{32} +(0.809017 + 3.21644i) q^{33} +(11.2812 + 8.19624i) q^{34} +(1.80902 + 5.56758i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-0.927051 + 0.673542i) q^{37} +(-4.57295 - 14.0741i) q^{38} -6.00000 q^{39} +(-1.54508 + 4.75528i) q^{40} +(0.545085 - 1.67760i) q^{41} +(4.73607 + 3.44095i) q^{42} +7.94427 q^{43} +(3.70820 - 9.23305i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(-3.78115 - 11.6372i) q^{46} +8.09017 q^{47} +(-0.309017 - 0.951057i) q^{48} +(0.118034 + 0.0857567i) q^{49} +(9.04508 + 6.57164i) q^{50} +(1.92705 - 5.93085i) q^{51} +(14.5623 + 10.5801i) q^{52} +(-0.309017 - 0.951057i) q^{53} +(-0.690983 + 2.12663i) q^{54} +(-5.69098 - 4.75528i) q^{55} +(-1.80902 - 5.56758i) q^{56} +(-5.35410 + 3.88998i) q^{57} +(12.8262 - 9.31881i) q^{58} +(-9.47214 + 6.88191i) q^{59} +6.70820 q^{60} -5.32624 q^{61} +(13.5172 - 9.82084i) q^{62} +(0.809017 - 2.48990i) q^{63} +(-4.01722 + 12.3637i) q^{64} +(10.8541 - 7.88597i) q^{65} +(-7.39919 - 0.502029i) q^{66} +(-1.80902 - 5.56758i) q^{67} +(-15.1353 + 10.9964i) q^{68} +(-4.42705 + 3.21644i) q^{69} -13.0902 q^{70} +(-6.04508 + 4.39201i) q^{71} +(1.80902 - 1.31433i) q^{72} +(-1.00000 - 3.07768i) q^{73} +(-0.791796 - 2.43690i) q^{74} +(1.54508 - 4.75528i) q^{75} +19.8541 q^{76} +(8.66312 + 0.587785i) q^{77} +(4.14590 - 12.7598i) q^{78} +(-4.00000 - 12.3107i) q^{79} +(1.80902 + 1.31433i) q^{80} +1.00000 q^{81} +(3.19098 + 2.31838i) q^{82} +(-2.64590 + 8.14324i) q^{83} +(-6.35410 + 4.61653i) q^{84} +(4.30902 + 13.2618i) q^{85} +(-5.48936 + 16.8945i) q^{86} +(-5.73607 - 4.16750i) q^{87} +(5.69098 + 4.75528i) q^{88} +(-2.88197 + 2.09387i) q^{89} +(-1.54508 - 4.75528i) q^{90} +(-4.85410 + 14.9394i) q^{91} +16.4164 q^{92} +(-6.04508 - 4.39201i) q^{93} +(-5.59017 + 17.2048i) q^{94} +(4.57295 - 14.0741i) q^{95} +6.70820 q^{96} +(0.781153 + 2.40414i) q^{97} +(-0.263932 + 0.191758i) q^{98} +(0.809017 + 3.21644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + q^{11} - 3 q^{12} - 24 q^{13} + 10 q^{14} - 5 q^{15} + q^{16} + q^{17} - 5 q^{18} - 8 q^{19} + q^{21} - 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} + 4 q^{27} - 12 q^{28} - 14 q^{29} + 5 q^{30} - 13 q^{31} + q^{33} + 25 q^{34} + 5 q^{35} - 3 q^{36} + 3 q^{37} - 25 q^{38} - 24 q^{39} + 5 q^{40} - 9 q^{41} + 10 q^{42} - 4 q^{43} - 12 q^{44} - 5 q^{45} + 5 q^{46} + 10 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} - 25 q^{55} - 5 q^{56} - 8 q^{57} + 20 q^{58} - 20 q^{59} + 10 q^{61} + 25 q^{62} + q^{63} + 13 q^{64} + 30 q^{65} - 5 q^{66} - 5 q^{67} - 27 q^{68} - 11 q^{69} - 30 q^{70} - 13 q^{71} + 5 q^{72} - 4 q^{73} - 30 q^{74} - 5 q^{75} + 66 q^{76} + 19 q^{77} + 30 q^{78} - 16 q^{79} + 5 q^{80} + 4 q^{81} + 15 q^{82} - 24 q^{83} - 12 q^{84} + 15 q^{85} + 25 q^{86} - 14 q^{87} + 25 q^{88} - 16 q^{89} + 5 q^{90} - 6 q^{91} + 12 q^{92} - 13 q^{93} + 25 q^{95} - 17 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + q^11 - 3 * q^12 - 24 * q^13 + 10 * q^14 - 5 * q^15 + q^16 + q^17 - 5 * q^18 - 8 * q^19 + q^21 - 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 + 4 * q^27 - 12 * q^28 - 14 * q^29 + 5 * q^30 - 13 * q^31 + q^33 + 25 * q^34 + 5 * q^35 - 3 * q^36 + 3 * q^37 - 25 * q^38 - 24 * q^39 + 5 * q^40 - 9 * q^41 + 10 * q^42 - 4 * q^43 - 12 * q^44 - 5 * q^45 + 5 * q^46 + 10 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 - 25 * q^55 - 5 * q^56 - 8 * q^57 + 20 * q^58 - 20 * q^59 + 10 * q^61 + 25 * q^62 + q^63 + 13 * q^64 + 30 * q^65 - 5 * q^66 - 5 * q^67 - 27 * q^68 - 11 * q^69 - 30 * q^70 - 13 * q^71 + 5 * q^72 - 4 * q^73 - 30 * q^74 - 5 * q^75 + 66 * q^76 + 19 * q^77 + 30 * q^78 - 16 * q^79 + 5 * q^80 + 4 * q^81 + 15 * q^82 - 24 * q^83 - 12 * q^84 + 15 * q^85 + 25 * q^86 - 14 * q^87 + 25 * q^88 - 16 * q^89 + 5 * q^90 - 6 * q^91 + 12 * q^92 - 13 * q^93 + 25 * q^95 - 17 * q^97 - 10 * q^98 + q^99

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