LMFDB - Embedded newform 650.2.l.c.261.1

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			261.1
Character	$\chi$	$=$	650.261
Dual form			650.2.l.c.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.854221 + 2.62902i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.249965 + 2.22205i) q^{5} +(-0.854221 - 2.62902i) q^{6} -2.02551 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.75502 - 2.72818i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.854221 + 2.62902i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.249965 + 2.22205i) q^{5} +(-0.854221 - 2.62902i) q^{6} -2.02551 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.75502 - 2.72818i) q^{9} +(-1.50832 - 1.65075i) q^{10} +(-0.678057 + 0.492637i) q^{11} +(2.23638 + 1.62483i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(1.63867 - 1.19056i) q^{14} +(-6.05535 - 1.24096i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.775855 + 2.38784i) q^{17} +4.64146 q^{18} +(-2.17367 - 6.68988i) q^{19} +(2.19054 + 0.448921i) q^{20} +(1.73023 - 5.32511i) q^{21} +(0.258995 - 0.797103i) q^{22} +(-3.18667 + 2.31525i) q^{23} -2.76432 q^{24} +(-4.87503 + 1.11087i) q^{25} +1.00000 q^{26} +(3.67093 - 2.66708i) q^{27} +(-0.625916 + 1.92637i) q^{28} +(-0.164166 + 0.505250i) q^{29} +(5.62830 - 2.55529i) q^{30} +(0.270530 + 0.832606i) q^{31} +1.00000 q^{32} +(-0.715944 - 2.20345i) q^{33} +(-2.03121 - 1.47576i) q^{34} +(-0.506306 - 4.50079i) q^{35} +(-3.75502 + 2.72818i) q^{36} +(4.29668 + 3.12172i) q^{37} +(5.69075 + 4.13457i) q^{38} +(2.23638 - 1.62483i) q^{39} +(-2.03605 + 0.924383i) q^{40} +(6.74330 + 4.89930i) q^{41} +(1.73023 + 5.32511i) q^{42} +1.54613 q^{43} +(0.258995 + 0.797103i) q^{44} +(5.12354 - 9.02580i) q^{45} +(1.21720 - 3.74616i) q^{46} +(2.31549 - 7.12636i) q^{47} +(2.23638 - 1.62483i) q^{48} -2.89732 q^{49} +(3.29103 - 3.76419i) q^{50} -6.94043 q^{51} +(-0.809017 + 0.587785i) q^{52} +(0.363519 - 1.11880i) q^{53} +(-1.40217 + 4.31543i) q^{54} +(-1.26416 - 1.38354i) q^{55} +(-0.625916 - 1.92637i) q^{56} +19.4446 q^{57} +(-0.164166 - 0.505250i) q^{58} +(-8.91212 - 6.47503i) q^{59} +(-3.05143 + 5.37551i) q^{60} +(3.75862 - 2.73080i) q^{61} +(-0.708257 - 0.514579i) q^{62} +(7.60582 + 5.52595i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.10386 - 1.94460i) q^{65} +(1.87436 + 1.36181i) q^{66} +(-0.877030 - 2.69922i) q^{67} +2.51072 q^{68} +(-3.36473 - 10.3556i) q^{69} +(3.05511 + 3.34361i) q^{70} +(-0.0249146 + 0.0766793i) q^{71} +(1.43429 - 4.41429i) q^{72} +(-9.67564 + 7.02977i) q^{73} -5.31099 q^{74} +(1.24385 - 13.7655i) q^{75} -7.03415 q^{76} +(1.37341 - 0.997840i) q^{77} +(-0.854221 + 2.62902i) q^{78} +(-1.07116 + 3.29670i) q^{79} +(1.10386 - 1.94460i) q^{80} +(-0.426827 - 1.31364i) q^{81} -8.33518 q^{82} +(1.88248 + 5.79368i) q^{83} +(-4.52981 - 3.29110i) q^{84} +(-5.11196 + 2.32086i) q^{85} +(-1.25085 + 0.908795i) q^{86} +(-1.18808 - 0.863191i) q^{87} +(-0.678057 - 0.492637i) q^{88} +(4.60134 - 3.34307i) q^{89} +(1.16020 + 10.3136i) q^{90} +(1.63867 + 1.19056i) q^{91} +(1.21720 + 3.74616i) q^{92} -2.42003 q^{93} +(2.31549 + 7.12636i) q^{94} +(14.3219 - 6.50225i) q^{95} +(-0.854221 + 2.62902i) q^{96} +(-0.286595 + 0.882048i) q^{97} +(2.34398 - 1.70300i) q^{98} +3.89012 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 $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	−0.854221	+	2.62902i	−0.493185	+	1.51787i	0.326581	+	0.945169i	$0.394103\pi$
$3$	−0.854221	+	2.62902i	−0.493185	+	1.51787i	−0.819766	+	0.572698i	$0.805897\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.249965	+	2.22205i	0.111788	+	0.993732i
$5$	0.249965	+	2.22205i	0.111788	+	0.993732i
$6$	−0.854221	−	2.62902i	−0.348734	−	1.07329i
$7$	−2.02551			−0.765570			−0.382785	−	0.923837i	$-0.625035\pi$
$7$	−2.02551			−0.765570			−0.382785	+	0.923837i	$0.625035\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−3.75502	−	2.72818i	−1.25167	−	0.909394i
$10$	−1.50832	−	1.65075i	−0.476971	−	0.522014i
$11$	−0.678057	+	0.492637i	−0.204442	+	0.148536i	−0.685295	−	0.728265i	$-0.740327\pi$
$11$	−0.678057	+	0.492637i	−0.204442	+	0.148536i	0.480854	+	0.876801i	$0.340327\pi$
$12$	2.23638	+	1.62483i	0.645588	+	0.469047i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	1.63867	−	1.19056i	0.437953	−	0.318192i
$15$	−6.05535	−	1.24096i	−1.56349	−	0.320415i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.775855	+	2.38784i	0.188172	+	0.579135i	0.999989	−	0.00477800i	$-0.00152089\pi$
$17$	0.775855	+	2.38784i	0.188172	+	0.579135i	−0.811816	+	0.583913i	$0.801521\pi$
$18$	4.64146			1.09400
$19$	−2.17367	−	6.68988i	−0.498675	−	1.53476i	−0.811151	−	0.584837i	$-0.801158\pi$
$19$	−2.17367	−	6.68988i	−0.498675	−	1.53476i	0.312476	−	0.949926i	$-0.398842\pi$
$20$	2.19054	+	0.448921i	0.489820	+	0.100382i
$21$	1.73023	−	5.32511i	0.377568	−	1.16203i
$22$	0.258995	−	0.797103i	0.0552178	−	0.169943i
$23$	−3.18667	+	2.31525i	−0.664467	+	0.482764i	−0.868169	−	0.496269i	$-0.834703\pi$
$23$	−3.18667	+	2.31525i	−0.664467	+	0.482764i	0.203701	+	0.979033i	$0.434703\pi$
$24$	−2.76432			−0.564264
$25$	−4.87503	+	1.11087i	−0.975007	+	0.222174i
$26$	1.00000			0.196116
$27$	3.67093	−	2.66708i	0.706470	−	0.513280i
$28$	−0.625916	+	1.92637i	−0.118287	+	0.364050i
$29$	−0.164166	+	0.505250i	−0.0304848	+	0.0938226i	−0.965141	−	0.261730i	$-0.915707\pi$
$29$	−0.164166	+	0.505250i	−0.0304848	+	0.0938226i	0.934656	+	0.355552i	$0.115707\pi$
$30$	5.62830	−	2.55529i	1.02758	−	0.466530i
$31$	0.270530	+	0.832606i	0.0485886	+	0.149540i	0.972407	−	0.233290i	$-0.0749492\pi$
$31$	0.270530	+	0.832606i	0.0485886	+	0.149540i	−0.923818	+	0.382831i	$0.874949\pi$
$32$	1.00000			0.176777
$33$	−0.715944	−	2.20345i	−0.124630	−	0.383571i
$34$	−2.03121	−	1.47576i	−0.348350	−	0.253091i
$35$	−0.506306	−	4.50079i	−0.0855814	−	0.760772i
$36$	−3.75502	+	2.72818i	−0.625836	+	0.454697i
$37$	4.29668	+	3.12172i	0.706370	+	0.513208i	0.882001	−	0.471248i	$-0.156196\pi$
$37$	4.29668	+	3.12172i	0.706370	+	0.513208i	−0.175631	+	0.984456i	$0.556196\pi$
$38$	5.69075	+	4.13457i	0.923161	+	0.670716i
$39$	2.23638	−	1.62483i	0.358108	−	0.260180i
$40$	−2.03605	+	0.924383i	−0.321928	+	0.146158i
$41$	6.74330	+	4.89930i	1.05313	+	0.765142i	0.972805	−	0.231627i	$-0.0744050\pi$
$41$	6.74330	+	4.89930i	1.05313	+	0.765142i	0.0803225	+	0.996769i	$0.474405\pi$
$42$	1.73023	+	5.32511i	0.266981	+	0.821682i
$43$	1.54613			0.235783			0.117892	−	0.993026i	$-0.462386\pi$
$43$	1.54613			0.235783			0.117892	+	0.993026i	$0.462386\pi$
$44$	0.258995	+	0.797103i	0.0390449	+	0.120168i
$45$	5.12354	−	9.02580i	0.763772	−	1.34549i
$46$	1.21720	−	3.74616i	0.179466	−	0.552341i
$47$	2.31549	−	7.12636i	0.337750	−	1.03949i	−0.627602	−	0.778534i	$-0.715964\pi$
$47$	2.31549	−	7.12636i	0.337750	−	1.03949i	0.965352	−	0.260952i	$-0.0840364\pi$
$48$	2.23638	−	1.62483i	0.322794	−	0.234523i
$49$	−2.89732			−0.413902
$50$	3.29103	−	3.76419i	0.465422	−	0.532336i
$51$	−6.94043			−0.971854
$52$	−0.809017	+	0.587785i	−0.112190	+	0.0815111i
$53$	0.363519	−	1.11880i	0.0499332	−	0.153679i	−0.922981	−	0.384846i	$-0.874255\pi$
$53$	0.363519	−	1.11880i	0.0499332	−	0.153679i	0.972914	+	0.231167i	$0.0742545\pi$
$54$	−1.40217	+	4.31543i	−0.190811	+	0.587256i
$55$	−1.26416	−	1.38354i	−0.170459	−	0.186556i
$56$	−0.625916	−	1.92637i	−0.0836416	−	0.257422i
$57$	19.4446			2.57551
$58$	−0.164166	−	0.505250i	−0.0215560	−	0.0663426i
$59$	−8.91212	−	6.47503i	−1.16026	−	0.842977i	−0.170448	−	0.985367i	$-0.554521\pi$
$59$	−8.91212	−	6.47503i	−1.16026	−	0.842977i	−0.989811	+	0.142389i	$0.954521\pi$
$60$	−3.05143	+	5.37551i	−0.393938	+	0.693975i
$61$	3.75862	−	2.73080i	0.481242	−	0.349643i	−0.320564	−	0.947227i	$-0.603873\pi$
$61$	3.75862	−	2.73080i	0.481242	−	0.349643i	0.801806	+	0.597584i	$0.203873\pi$
$62$	−0.708257	−	0.514579i	−0.0899487	−	0.0653516i
$63$	7.60582	+	5.52595i	0.958243	+	0.696205i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.10386	−	1.94460i	0.136917	−	0.241198i
$66$	1.87436	+	1.36181i	0.230718	+	0.167627i
$67$	−0.877030	−	2.69922i	−0.107146	−	0.329762i	0.883082	−	0.469219i	$-0.155464\pi$
$67$	−0.877030	−	2.69922i	−0.107146	−	0.329762i	−0.990228	+	0.139457i	$0.955464\pi$
$68$	2.51072			0.304469
$69$	−3.36473	−	10.3556i	−0.405066	−	1.24666i
$70$	3.05511	+	3.34361i	0.365155	+	0.399638i
$71$	−0.0249146	+	0.0766793i	−0.00295682	+	0.00910016i	−0.952524	−	0.304463i	$-0.901523\pi$
$71$	−0.0249146	+	0.0766793i	−0.00295682	+	0.00910016i	0.949567	+	0.313564i	$0.101523\pi$
$72$	1.43429	−	4.41429i	0.169033	−	0.520229i
$73$	−9.67564	+	7.02977i	−1.13245	+	0.822772i	−0.986049	−	0.166454i	$-0.946768\pi$
$73$	−9.67564	+	7.02977i	−1.13245	+	0.822772i	−0.146399	+	0.989226i	$0.546768\pi$
$74$	−5.31099			−0.617390
$75$	1.24385	−	13.7655i	0.143628	−	1.58950i
$76$	−7.03415			−0.806873
$77$	1.37341	−	0.997840i	0.156514	−	0.113714i
$78$	−0.854221	+	2.62902i	−0.0967215	+	0.297678i
$79$	−1.07116	+	3.29670i	−0.120515	+	0.370908i	−0.993057	−	0.117631i	$-0.962470\pi$
$79$	−1.07116	+	3.29670i	−0.120515	+	0.370908i	0.872542	+	0.488539i	$0.162470\pi$
$80$	1.10386	−	1.94460i	0.123416	−	0.217413i
$81$	−0.426827	−	1.31364i	−0.0474252	−	0.145960i
$82$	−8.33518			−0.920467
$83$	1.88248	+	5.79368i	0.206629	+	0.635939i	0.999643	+	0.0267349i	$0.00851101\pi$
$83$	1.88248	+	5.79368i	0.206629	+	0.635939i	−0.793013	+	0.609204i	$0.791489\pi$
$84$	−4.52981	−	3.29110i	−0.494243	−	0.359088i
$85$	−5.11196	+	2.32086i	−0.554470	+	0.251733i
$86$	−1.25085	+	0.908795i	−0.134883	+	0.0979979i
$87$	−1.18808	−	0.863191i	−0.127376	−	0.0925437i
$88$	−0.678057	−	0.492637i	−0.0722811	−	0.0525153i
$89$	4.60134	−	3.34307i	0.487741	−	0.354365i	−0.316574	−	0.948568i	$-0.602532\pi$
$89$	4.60134	−	3.34307i	0.487741	−	0.354365i	0.804315	+	0.594203i	$0.202532\pi$
$90$	1.16020	+	10.3136i	0.122296	+	1.08715i
$91$	1.63867	+	1.19056i	0.171779	+	0.124805i
$92$	1.21720	+	3.74616i	0.126902	+	0.390564i
$93$	−2.42003			−0.250946
$94$	2.31549	+	7.12636i	0.238825	+	0.735028i
$95$	14.3219	−	6.50225i	1.46940	−	0.667117i
$96$	−0.854221	+	2.62902i	−0.0871836	+	0.268324i
$97$	−0.286595	+	0.882048i	−0.0290993	+	0.0895585i	−0.964551	−	0.263895i	$-0.914993\pi$
$97$	−0.286595	+	0.882048i	−0.0290993	+	0.0895585i	0.935452	+	0.353454i	$0.114993\pi$
$98$	2.34398	−	1.70300i	0.236778	−	0.172029i
$99$	3.89012			0.390972
$100$	−0.449968	+	4.97971i	−0.0449968	+	0.497971i
$101$	−13.7306			−1.36625			−0.683124	−	0.730303i	$-0.739379\pi$
$101$	−13.7306			−1.36625			−0.683124	+	0.730303i	$0.739379\pi$
$102$	5.61492	−	4.07948i	0.555960	−	0.403929i
$103$	2.19733	−	6.76267i	0.216509	−	0.666346i	−0.782534	−	0.622608i	$-0.786073\pi$
$103$	2.19733	−	6.76267i	0.216509	−	0.666346i	0.999043	−	0.0437383i	$-0.0139268\pi$
$104$	0.309017	−	0.951057i	0.0303016	−	0.0932588i
$105$	12.2652	+	2.51358i	1.19696	+	0.245300i
$106$	0.363519	+	1.11880i	0.0353081	+	0.108667i
$107$	−13.5568			−1.31059			−0.655295	−	0.755373i	$-0.727456\pi$
$107$	−13.5568			−1.31059			−0.655295	+	0.755373i	$0.727456\pi$
$108$	−1.40217	−	4.31543i	−0.134924	−	0.415253i
$109$	−0.468065	−	0.340069i	−0.0448325	−	0.0325727i	0.565143	−	0.824993i	$-0.308821\pi$
$109$	−0.468065	−	0.340069i	−0.0448325	−	0.0325727i	−0.609976	+	0.792420i	$0.708821\pi$
$110$	1.83595	+	0.376252i	0.175050	+	0.0358742i
$111$	−11.8774	+	8.62943i	−1.12735	+	0.819069i
$112$	1.63867	+	1.19056i	0.154840	+	0.112498i
$113$	13.9675	+	10.1480i	1.31395	+	0.954639i	0.999986	+	0.00520346i	$0.00165632\pi$
$113$	13.9675	+	10.1480i	1.31395	+	0.954639i	0.313962	+	0.949436i	$0.398344\pi$
$114$	−15.7310	+	11.4293i	−1.47335	+	1.07045i
$115$	−5.94117	−	6.50222i	−0.554017	−	0.606335i
$116$	0.429791	+	0.312262i	0.0399051	+	0.0289928i
$117$	1.43429	+	4.41429i	0.132600	+	0.408101i
$118$	11.0160			1.01410
$119$	−1.57150	−	4.83658i	−0.144059	−	0.443368i
$120$	−0.690983	−	6.14246i	−0.0630778	−	0.560727i
$121$	−3.18212	+	9.79355i	−0.289283	+	0.890323i
$122$	−1.43567	+	4.41852i	−0.129979	+	0.400034i
$123$	−18.6406	+	13.5432i	−1.68077	+	1.22115i
$124$	0.875454			0.0786181
$125$	−3.68700	−	10.5549i	−0.329775	−	0.944059i
$126$	−9.40131			−0.837535
$127$	−14.3306	+	10.4118i	−1.27164	+	0.923900i	−0.999267	−	0.0382922i	$-0.987808\pi$
$127$	−14.3306	+	10.4118i	−1.27164	+	0.923900i	−0.272372	+	0.962192i	$0.587808\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.32074	+	4.06482i	−0.116285	+	0.357888i
$130$	0.249965	+	2.22205i	0.0219234	+	0.194887i
$131$	6.46210	+	19.8883i	0.564597	+	1.73765i	0.669147	+	0.743130i	$0.266660\pi$
$131$	6.46210	+	19.8883i	0.564597	+	1.73765i	−0.104551	+	0.994520i	$0.533340\pi$
$132$	−2.31684			−0.201655
$133$	4.40279	+	13.5504i	0.381770	+	1.17497i
$134$	2.29609	+	1.66821i	0.198352	+	0.144111i
$135$	6.84400	+	7.49031i	0.589038	+	0.644663i
$136$	−2.03121	+	1.47576i	−0.174175	+	0.126546i
$137$	−8.54208	−	6.20619i	−0.729800	−	0.530230i	0.159701	−	0.987166i	$-0.448947\pi$
$137$	−8.54208	−	6.20619i	−0.729800	−	0.530230i	−0.889500	+	0.456935i	$0.848947\pi$
$138$	8.80898	+	6.40010i	0.749870	+	0.544813i
$139$	−14.4847	+	10.5238i	−1.22858	+	0.892615i	−0.996783	−	0.0801495i	$-0.974460\pi$
$139$	−14.4847	+	10.5238i	−1.22858	+	0.892615i	−0.231796	+	0.972764i	$0.574460\pi$
$140$	−4.43696	−	0.909293i	−0.374991	−	0.0768493i
$141$	16.7574	+	12.1750i	1.41123	+	1.02532i
$142$	−0.0249146	−	0.0766793i	−0.00209079	−	0.00643478i
$143$	0.838124			0.0700875
$144$	1.43429	+	4.41429i	0.119524	+	0.367857i
$145$	−1.16373	−	0.238490i	−0.0966423	−	0.0198055i
$146$	3.69577	−	11.3744i	0.305864	−	0.941352i
$147$	2.47495	−	7.61711i	0.204130	−	0.628249i
$148$	4.29668	−	3.12172i	0.353185	−	0.256604i
$149$	16.8958			1.38415			0.692077	−	0.721823i	$-0.256696\pi$
$149$	16.8958			1.38415			0.692077	+	0.721823i	$0.256696\pi$
$150$	7.08486	+	11.8677i	0.578477	+	0.968990i
$151$	−19.9285			−1.62176			−0.810879	−	0.585213i	$-0.801011\pi$
$151$	−19.9285			−1.62176			−0.810879	+	0.585213i	$0.801011\pi$
$152$	5.69075	−	4.13457i	0.461581	−	0.335358i
$153$	3.60110	−	11.0830i	0.291131	−	0.896010i
$154$	−0.524596	+	1.61454i	−0.0422731	+	0.130103i
$155$	−1.78247	+	0.809255i	−0.143172	+	0.0650009i
$156$	−0.854221	−	2.62902i	−0.0683925	−	0.210490i
$157$	−17.0592			−1.36147			−0.680735	−	0.732530i	$-0.738339\pi$
$157$	−17.0592			−1.36147			−0.680735	+	0.732530i	$0.738339\pi$
$158$	−1.07116	−	3.29670i	−0.0852173	−	0.262272i
$159$	2.63082	+	1.91140i	0.208638	+	0.151584i
$160$	0.249965	+	2.22205i	0.0197615	+	0.175669i
$161$	6.45463	−	4.68956i	0.508696	−	0.369589i
$162$	1.11745	+	0.811873i	0.0877949	+	0.0637867i
$163$	−9.06077	−	6.58303i	−0.709694	−	0.515623i	0.173381	−	0.984855i	$-0.444531\pi$
$163$	−9.06077	−	6.58303i	−0.709694	−	0.515623i	−0.883075	+	0.469232i	$0.844531\pi$
$164$	6.74330	−	4.89930i	0.526564	−	0.382571i
$165$	4.71722	−	2.14165i	0.367235	−	0.166727i
$166$	−4.92840	−	3.58069i	−0.382518	−	0.277916i
$167$	−7.69354	−	23.6783i	−0.595344	−	1.83228i	−0.553008	−	0.833176i	$-0.686520\pi$
$167$	−7.69354	−	23.6783i	−0.595344	−	1.83228i	−0.0423360	−	0.999103i	$-0.513480\pi$
$168$	5.59915			0.431984
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	2.77149	−	4.88235i	0.212564	−	0.374459i
$171$	−10.0890	+	31.0508i	−0.771526	+	2.37451i
$172$	0.477782	−	1.47046i	0.0364305	−	0.112122i
$173$	−17.6130	+	12.7966i	−1.33909	+	0.972906i	−0.339613	+	0.940565i	$0.610296\pi$
$173$	−17.6130	+	12.7966i	−1.33909	+	0.972906i	−0.999477	+	0.0323401i	$0.989704\pi$
$174$	1.46855			0.111330
$175$	9.87442	−	2.25008i	0.746436	−	0.170090i
$176$	0.838124			0.0631760
$177$	24.6359	−	17.8991i	1.85175	−	1.34538i
$178$	−1.75756	+	5.40920i	−0.131734	+	0.405437i
$179$	0.366211	−	1.12708i	0.0273719	−	0.0842421i	−0.936437	−	0.350835i	$-0.885898\pi$
$179$	0.366211	−	1.12708i	0.0273719	−	0.0842421i	0.963809	+	0.266593i	$0.0858979\pi$
$180$	−7.00078	−	7.66190i	−0.521808	−	0.571084i
$181$	−2.38733	−	7.34745i	−0.177449	−	0.546132i	0.822288	−	0.569072i	$-0.192697\pi$
$181$	−2.38733	−	7.34745i	−0.177449	−	0.546132i	−0.999737	+	0.0229400i	$0.992697\pi$
$182$	−2.02551			−0.150141
$183$	3.96864	+	12.2142i	0.293370	+	0.902900i
$184$	−3.18667	−	2.31525i	−0.234925	−	0.170683i
$185$	−5.86261	+	10.3278i	−0.431028	+	0.759313i
$186$	1.95785	−	1.42246i	0.143556	−	0.104300i
$187$	−1.70241	−	1.23687i	−0.124492	−	0.0904491i
$188$	−6.06204	−	4.40433i	−0.442120	−	0.321219i
$189$	−7.43549	+	5.40220i	−0.540852	+	0.392952i
$190$	−7.76475	+	13.6786i	−0.563314	+	0.992353i
$191$	11.1187	+	8.07819i	0.804519	+	0.584517i	0.912236	−	0.409664i	$-0.134354\pi$
$191$	11.1187	+	8.07819i	0.804519	+	0.584517i	−0.107717	+	0.994182i	$0.534354\pi$
$192$	−0.854221	−	2.62902i	−0.0616481	−	0.189733i
$193$	23.7331			1.70834			0.854172	−	0.519991i	$-0.174065\pi$
$193$	23.7331			1.70834			0.854172	+	0.519991i	$0.174065\pi$
$194$	−0.286595	−	0.882048i	−0.0205763	−	0.0633274i
$195$	4.16947	+	4.56321i	0.298582	+	0.326778i
$196$	−0.895320	+	2.75551i	−0.0639514	+	0.196822i
$197$	−4.32219	+	13.3023i	−0.307944	+	0.947753i	0.670619	+	0.741802i	$0.266029\pi$
$197$	−4.32219	+	13.3023i	−0.307944	+	0.947753i	−0.978562	+	0.205951i	$0.933971\pi$
$198$	−3.14717	+	2.28655i	−0.223660	+	0.162498i
$199$	11.7182			0.830683			0.415342	−	0.909666i	$-0.363662\pi$
$199$	11.7182			0.830683			0.415342	+	0.909666i	$0.363662\pi$
$200$	−2.56297	−	4.29316i	−0.181229	−	0.303572i
$201$	7.84549			0.553378
$202$	11.1083	−	8.07065i	0.781577	−	0.567849i
$203$	0.332519	−	1.02339i	0.0233382	−	0.0718277i
$204$	−2.14471	+	6.60074i	−0.150160	+	0.462144i
$205$	−9.20090	+	16.2086i	−0.642619	+	1.13206i
$206$	2.19733	+	6.76267i	0.153095	+	0.471178i
$207$	18.2824			1.27072
$208$	0.309017	+	0.951057i	0.0214265	+	0.0659439i
$209$	4.76955	+	3.46528i	0.329917	+	0.239699i
$210$	−11.4002	+	5.17576i	−0.786687	+	0.357161i
$211$	−8.56615	+	6.22367i	−0.589718	+	0.428455i	−0.842215	−	0.539143i	$-0.818748\pi$
$211$	−8.56615	+	6.22367i	−0.589718	+	0.428455i	0.252496	+	0.967598i	$0.418748\pi$
$212$	−0.951706	−	0.691455i	−0.0653635	−	0.0474893i
$213$	−0.180309	−	0.131002i	−0.0123546	−	0.00897612i
$214$	10.9677	−	7.96852i	0.749738	−	0.544716i
$215$	0.386480	+	3.43559i	0.0263577	+	0.234305i
$216$	3.67093	+	2.66708i	0.249775	+	0.181472i
$217$	−0.547961	−	1.68645i	−0.0371980	−	0.114484i
$218$	0.578560			0.0391851
$219$	−10.2163	−	31.4425i	−0.690352	−	2.12469i
$220$	−1.70647	+	0.774748i	−0.115050	+	0.0522335i
$221$	0.775855	−	2.38784i	0.0521896	−	0.160623i
$222$	4.53676	−	13.9627i	0.304487	−	0.937116i
$223$	−20.1959	+	14.6732i	−1.35242	+	0.982590i	−0.353532	+	0.935422i	$0.615019\pi$
$223$	−20.1959	+	14.6732i	−1.35242	+	0.982590i	−0.998887	+	0.0471673i	$0.984981\pi$
$224$	−2.02551			−0.135335
$225$	21.3365	+	9.12864i	1.42243	+	0.608576i
$226$	−17.2647			−1.14843
$227$	−9.99882	+	7.26457i	−0.663645	+	0.482166i	−0.867892	−	0.496753i	$-0.834525\pi$
$227$	−9.99882	+	7.26457i	−0.663645	+	0.482166i	0.204247	+	0.978919i	$0.434525\pi$
$228$	6.00872	−	18.4929i	0.397937	−	1.22473i
$229$	3.00404	−	9.24549i	0.198513	−	0.610959i	−0.801405	−	0.598122i	$-0.795914\pi$
$229$	3.00404	−	9.24549i	0.198513	−	0.610959i	0.999918	−	0.0128371i	$-0.00408627\pi$
$230$	8.62842	+	1.76828i	0.568941	+	0.116597i
$231$	1.45015	+	4.46310i	0.0954128	+	0.293650i
$232$	−0.531251			−0.0348783
$233$	−4.64165	−	14.2855i	−0.304085	−	0.935876i	−0.980017	−	0.198913i	$-0.936259\pi$
$233$	−4.64165	−	14.2855i	−0.304085	−	0.935876i	0.675932	−	0.736964i	$-0.263741\pi$
$234$	−3.75502	−	2.72818i	−0.245473	−	0.178347i
$235$	16.4139	+	3.36381i	1.07073	+	0.219431i
$236$	−8.91212	+	6.47503i	−0.580129	+	0.421489i
$237$	−7.75210	−	5.63223i	−0.503553	−	0.365853i
$238$	4.11424	+	2.98917i	0.266687	+	0.193759i
$239$	21.8452	−	15.8715i	1.41305	−	1.02664i	0.420178	−	0.907442i	$-0.361968\pi$
$239$	21.8452	−	15.8715i	1.41305	−	1.02664i	0.992870	−	0.119198i	$-0.0380324\pi$
$240$	4.16947	+	4.56321i	0.269138	+	0.294554i
$241$	14.5749	+	10.5893i	0.938852	+	0.682116i	0.948144	−	0.317841i	$-0.102958\pi$
$241$	14.5749	+	10.5893i	0.938852	+	0.682116i	−0.00929196	+	0.999957i	$0.502958\pi$
$242$	−3.18212	−	9.79355i	−0.204554	−	0.629553i
$243$	17.4307			1.11818
$244$	−1.43567	−	4.41852i	−0.0919091	−	0.282867i
$245$	−0.724228	−	6.43799i	−0.0462692	−	0.411308i
$246$	7.12009	−	21.9134i	0.453960	−	1.39715i
$247$	−2.17367	+	6.68988i	−0.138307	+	0.425667i
$248$	−0.708257	+	0.514579i	−0.0449744	+	0.0326758i
$249$	−16.8398			−1.06718
$250$	9.18686	+	6.37193i	0.581028	+	0.402996i
$251$	−3.52051			−0.222213			−0.111106	−	0.993809i	$-0.535439\pi$
$251$	−3.52051			−0.222213			−0.111106	+	0.993809i	$0.535439\pi$
$252$	7.60582	−	5.52595i	0.479122	−	0.348102i
$253$	1.02017	−	3.13975i	0.0641372	−	0.197394i
$254$	5.47382	−	16.8467i	0.343458	−	1.05705i
$255$	−1.73486	−	15.4220i	−0.108641	−	0.965763i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	12.5009			0.779783			0.389892	−	0.920861i	$-0.372512\pi$
$257$	12.5009			0.779783			0.389892	+	0.920861i	$0.372512\pi$
$258$	−1.32074	−	4.06482i	−0.0822258	−	0.253065i
$259$	−8.70296	−	6.32307i	−0.540776	−	0.392897i
$260$	−1.50832	−	1.65075i	−0.0935418	−	0.102375i
$261$	1.99486	−	1.44935i	0.123479	−	0.0897125i
$262$	−16.9180	−	12.2916i	−1.04520	−	0.759381i
$263$	1.33892	+	0.972781i	0.0825612	+	0.0599843i	0.628300	−	0.777971i	$-0.283751\pi$
$263$	1.33892	+	0.972781i	0.0825612	+	0.0599843i	−0.545739	+	0.837955i	$0.683751\pi$
$264$	1.87436	−	1.36181i	0.115359	−	0.0838133i
$265$	2.57690	+	0.528099i	0.158297	+	0.0324409i
$266$	−11.5267	−	8.37461i	−0.706745	−	0.513480i
$267$	4.85845	+	14.9528i	0.297332	+	0.915094i
$268$	−2.83813			−0.173366
$269$	1.37196	+	4.22246i	0.0836500	+	0.257448i	0.984130	−	0.177449i	$-0.0567846\pi$
$269$	1.37196	+	4.22246i	0.0836500	+	0.257448i	−0.900480	+	0.434898i	$0.856785\pi$
$270$	−9.93961	−	2.03699i	−0.604905	−	0.123967i
$271$	−1.72235	+	5.30085i	−0.104625	+	0.322004i	−0.989642	−	0.143555i	$-0.954147\pi$
$271$	−1.72235	+	5.30085i	−0.104625	+	0.322004i	0.885017	+	0.465559i	$0.154147\pi$
$272$	0.775855	−	2.38784i	0.0470431	−	0.144784i
$273$	−4.52981	+	3.29110i	−0.274156	+	0.199186i
$274$	10.5586			0.637868
$275$	2.75829	−	3.15486i	0.166331	−	0.190245i
$276$	−10.8885			−0.655410
$277$	−17.1381	+	12.4516i	−1.02973	+	0.748144i	−0.968255	−	0.249965i	$-0.919581\pi$
$277$	−17.1381	+	12.4516i	−1.02973	+	0.748144i	−0.0614766	+	0.998109i	$0.519581\pi$
$278$	5.53268	−	17.0278i	0.331828	−	1.02126i
$279$	1.25565	−	3.86451i	0.0751741	−	0.231362i
$280$	4.12404	−	1.87234i	0.246459	−	0.111894i
$281$	−7.15478	−	22.0201i	−0.426818	−	1.31361i	−0.901242	−	0.433315i	$-0.857344\pi$
$281$	−7.15478	−	22.0201i	−0.426818	−	1.31361i	0.474424	−	0.880296i	$-0.342656\pi$
$282$	−20.7133			−1.23346
$283$	−0.941971	−	2.89909i	−0.0559944	−	0.172333i	0.919148	−	0.393913i	$-0.128879\pi$
$283$	−0.941971	−	2.89909i	−0.0559944	−	0.172333i	−0.975142	+	0.221580i	$0.928879\pi$
$284$	0.0652273	+	0.0473904i	0.00387053	+	0.00281210i
$285$	4.86048	+	43.2070i	0.287910	+	2.55936i
$286$	−0.678057	+	0.492637i	−0.0400943	+	0.0291302i
$287$	−13.6586	−	9.92356i	−0.806243	−	0.585770i
$288$	−3.75502	−	2.72818i	−0.221267	−	0.160760i
$289$	8.65348	−	6.28712i	0.509028	−	0.369831i
$290$	1.08166	−	0.491079i	0.0635170	−	0.0288372i
$291$	−2.07411	−	1.50693i	−0.121587	−	0.0883378i
$292$	3.69577	+	11.3744i	0.216278	+	0.665637i
$293$	−27.9838			−1.63483			−0.817417	−	0.576046i	$-0.804595\pi$
$293$	−27.9838			−1.63483			−0.817417	+	0.576046i	$0.804595\pi$
$294$	2.47495	+	7.61711i	0.144342	+	0.444239i
$295$	12.1601	−	21.4217i	0.707991	−	1.24722i
$296$	−1.64119	+	5.05105i	−0.0953920	+	0.293586i
$297$	−1.17519	+	3.61687i	−0.0681915	+	0.209872i
$298$	−13.6690	+	9.93108i	−0.791822	+	0.575292i
$299$	3.93894			0.227795
$300$	−12.7074	−	5.43675i	−0.733662	−	0.313891i
$301$	−3.13171			−0.180509
$302$	16.1225	−	11.7137i	0.927746	−	0.674047i
$303$	11.7290	−	36.0981i	0.673813	−	2.07378i
$304$	−2.17367	+	6.68988i	−0.124669	+	0.383691i
$305$	7.00750	+	7.66925i	0.401248	+	0.439140i
$306$	3.60110	+	11.0830i	0.205861	+	0.633575i
$307$	21.4232			1.22269			0.611343	−	0.791365i	$-0.290629\pi$
$307$	21.4232			1.22269			0.611343	+	0.791365i	$0.290629\pi$
$308$	−0.524596	−	1.61454i	−0.0298916	−	0.0919969i
$309$	15.9022	+	11.5536i	0.904646	+	0.657264i
$310$	0.966382	−	1.70241i	0.0548868	−	0.0966905i
$311$	−11.9937	+	8.71394i	−0.680101	+	0.494122i	−0.873391	−	0.487019i	$-0.838084\pi$
$311$	−11.9937	+	8.71394i	−0.680101	+	0.494122i	0.193290	+	0.981142i	$0.438084\pi$
$312$	2.23638	+	1.62483i	0.126610	+	0.0919876i
$313$	−6.90729	−	5.01844i	−0.390423	−	0.283659i	0.375206	−	0.926942i	$-0.377572\pi$
$313$	−6.90729	−	5.01844i	−0.390423	−	0.283659i	−0.765629	+	0.643283i	$0.777572\pi$
$314$	13.8011	−	10.0271i	0.778844	−	0.565863i
$315$	−10.3778	+	18.2818i	−0.584721	+	1.03006i
$316$	2.80434	+	2.03748i	0.157757	+	0.114617i
$317$	−5.70362	−	17.5539i	−0.320347	−	0.985928i	−0.973497	−	0.228699i	$-0.926553\pi$
$317$	−5.70362	−	17.5539i	−0.320347	−	0.985928i	0.653150	−	0.757229i	$-0.273447\pi$
$318$	−3.25187			−0.182356
$319$	−0.137591	−	0.423462i	−0.00770363	−	0.0237093i
$320$	−1.50832	−	1.65075i	−0.0843174	−	0.0922799i
$321$	11.5806	−	35.6413i	0.646363	−	1.98930i
$322$	−2.46545	+	7.58787i	−0.137394	+	0.422856i
$323$	14.2879	−	10.3807i	0.794998	−	0.577600i
$324$	−1.38124			−0.0767356
$325$	4.59694	+	1.96676i	0.254992	+	0.109096i
$326$	11.1997			0.620295
$327$	1.29388	−	0.940060i	0.0715518	−	0.0519854i
$328$	−2.57571	+	7.92723i	−0.142220	+	0.437708i
$329$	−4.69005	+	14.4345i	−0.258571	+	0.795799i
$330$	−2.55748	+	4.50534i	−0.140785	+	0.248011i
$331$	2.21147	+	6.80622i	0.121554	+	0.374104i	0.993257	−	0.115929i	$-0.0369847\pi$
$331$	2.21147	+	6.80622i	0.121554	+	0.374104i	−0.871704	+	0.490033i	$0.836985\pi$
$332$	6.09184			0.334333
$333$	−7.61750	−	23.4442i	−0.417436	−	1.28474i
$334$	20.1419	+	14.6340i	1.10212	+	0.800736i
$335$	5.77858	−	2.62352i	0.315718	−	0.143338i
$336$	−4.52981	+	3.29110i	−0.247121	+	0.179544i
$337$	21.5493	+	15.6565i	1.17387	+	0.852864i	0.991467	−	0.130360i	$-0.0416133\pi$
$337$	21.5493	+	15.6565i	1.17387	+	0.852864i	0.182400	+	0.983224i	$0.441613\pi$
$338$	−0.809017	−	0.587785i	−0.0440047	−	0.0319713i
$339$	−38.6105	+	28.0522i	−2.09704	+	1.52359i
$340$	0.627592	+	5.57895i	0.0340359	+	0.302561i
$341$	−0.593607	−	0.431281i	−0.0321456	−	0.0233552i
$342$	−10.0890	−	31.0508i	−0.545551	−	1.67903i
$343$	20.0471			1.08244
$344$	0.477782	+	1.47046i	0.0257603	+	0.0792820i
$345$	22.1696	−	10.0651i	1.19357	−	0.541889i
$346$	6.72756	−	20.7053i	0.361676	−	1.11312i
$347$	−4.73777	+	14.5814i	−0.254337	+	0.782768i	0.739623	+	0.673022i	$0.235004\pi$
$347$	−4.73777	+	14.5814i	−0.254337	+	0.782768i	−0.993960	+	0.109747i	$0.964996\pi$
$348$	−1.18808	+	0.863191i	−0.0636878	+	0.0462719i
$349$	−18.8610			−1.00961			−0.504804	−	0.863234i	$-0.668435\pi$
$349$	−18.8610			−1.00961			−0.504804	+	0.863234i	$0.668435\pi$
$350$	−6.66601	+	7.62439i	−0.356313	+	0.407541i
$351$	−4.53751			−0.242195
$352$	−0.678057	+	0.492637i	−0.0361405	+	0.0262576i
$353$	−4.03837	+	12.4288i	−0.214941	+	0.661519i	0.784217	+	0.620486i	$0.213065\pi$
$353$	−4.03837	+	12.4288i	−0.214941	+	0.661519i	−0.999158	+	0.0410327i	$0.986935\pi$
$354$	−9.41009	+	28.9613i	−0.500141	+	1.53927i
$355$	−0.176613	−	0.0361944i	−0.00937366	−	0.00192100i
$356$	−1.75756	−	5.40920i	−0.0931503	−	0.286687i
$357$	14.0579			0.744022
$358$	0.366211	+	1.12708i	0.0193549	+	0.0595682i
$359$	15.7290	+	11.4278i	0.830147	+	0.603137i	0.919601	−	0.392854i	$-0.128512\pi$
$359$	15.7290	+	11.4278i	0.830147	+	0.603137i	−0.0894540	+	0.995991i	$0.528512\pi$
$360$	10.1673	+	2.08365i	0.535864	+	0.109818i
$361$	−24.6583	+	17.9153i	−1.29780	+	0.942909i
$362$	6.25011	+	4.54097i	0.328499	+	0.238668i
$363$	−23.0292	−	16.7317i	−1.20872	−	0.878188i
$364$	1.63867	−	1.19056i	0.0858897	−	0.0624025i
$365$	−18.0391	−	19.7426i	−0.944209	−	1.03337i
$366$	−10.3900	−	7.54880i	−0.543095	−	0.394582i
$367$	−8.98231	−	27.6447i	−0.468873	−	1.44304i	−0.854046	−	0.520198i	$-0.825858\pi$
$367$	−8.98231	−	27.6447i	−0.468873	−	1.44304i	0.385173	−	0.922845i	$-0.374142\pi$
$368$	3.93894			0.205332
$369$	−11.9551	−	36.7939i	−0.622356	−	1.91541i
$370$	−1.32756	−	11.8013i	−0.0690166	−	0.613520i
$371$	−0.736312	+	2.26613i	−0.0382274	+	0.117652i
$372$	−0.747832	+	2.30159i	−0.0387733	+	0.119332i
$373$	18.4913	−	13.4347i	0.957441	−	0.695622i	0.00488628	−	0.999988i	$-0.498445\pi$
$373$	18.4913	−	13.4347i	0.957441	−	0.695622i	0.952555	+	0.304366i	$0.0984446\pi$
$374$	2.10429			0.108810
$375$	30.8986	−	0.676987i	1.59560	−	0.0349594i
$376$	7.49310			0.386427
$377$	0.429791	−	0.312262i	0.0221354	−	0.0160823i
$378$	2.84010	−	8.74094i	0.146079	−	0.449586i
$379$	3.53509	−	10.8799i	0.181585	−	0.558862i	−0.818288	−	0.574809i	$-0.805076\pi$
$379$	3.53509	−	10.8799i	0.181585	−	0.558862i	0.999873	+	0.0159473i	$0.00507639\pi$
$380$	−1.75829	−	15.6303i	−0.0901985	−	0.801815i
$381$	−15.1314	−	46.5696i	−0.775204	−	2.38583i
$382$	−13.7434			−0.703175
$383$	8.64776	+	26.6151i	0.441880	+	1.35997i	0.885869	+	0.463935i	$0.153563\pi$
$383$	8.64776	+	26.6151i	0.441880	+	1.35997i	−0.443989	+	0.896032i	$0.646437\pi$
$384$	2.23638	+	1.62483i	0.114125	+	0.0829165i
$385$	2.56056	+	2.80236i	0.130498	+	0.142822i
$386$	−19.2004	+	13.9499i	−0.977277	+	0.710033i
$387$	−5.80576	−	4.21813i	−0.295124	−	0.214420i
$388$	0.750315	+	0.545136i	0.0380915	+	0.0276751i
$389$	−5.02263	+	3.64915i	−0.254657	+	0.185019i	−0.707788	−	0.706425i	$-0.750307\pi$
$389$	−5.02263	+	3.64915i	−0.254657	+	0.185019i	0.453131	+	0.891444i	$0.350307\pi$
$390$	−6.05535	−	1.24096i	−0.306625	−	0.0628385i
$391$	−8.00084	−	5.81295i	−0.404620	−	0.293973i
$392$	−0.895320	−	2.75551i	−0.0452205	−	0.139174i
$393$	−57.8069			−2.91597
$394$	−4.32219	−	13.3023i	−0.217749	−	0.670162i
$395$	−7.59320	−	1.55612i	−0.382056	−	0.0782970i
$396$	1.20211	−	3.69972i	0.0604084	−	0.185918i
$397$	−5.46318	+	16.8139i	−0.274189	+	0.843868i	0.715244	+	0.698875i	$0.246316\pi$
$397$	−5.46318	+	16.8139i	−0.274189	+	0.843868i	−0.989433	+	0.144992i	$0.953684\pi$
$398$	−9.48025	+	6.88780i	−0.475202	+	0.345254i
$399$	−39.3853			−1.97173
$400$	4.59694	+	1.96676i	0.229847	+	0.0983380i
$401$	30.7896			1.53756			0.768781	−	0.639513i	$-0.220864\pi$
$401$	30.7896			1.53756			0.768781	+	0.639513i	$0.220864\pi$
$402$	−6.34714	+	4.61146i	−0.316566	+	0.229999i
$403$	0.270530	−	0.832606i	0.0134761	−	0.0414751i
$404$	−4.24299	+	13.0586i	−0.211097	+	0.649689i
$405$	2.81228	−	1.27679i	0.139743	−	0.0634444i
$406$	0.332519	+	1.02339i	0.0165026	+	0.0507899i
$407$	−4.45127			−0.220641
$408$	−2.14471	−	6.60074i	−0.106179	−	0.326785i
$409$	21.9393	+	15.9398i	1.08483	+	0.788173i	0.978518	−	0.206160i	$-0.0660967\pi$
$409$	21.9393	+	15.9398i	1.08483	+	0.788173i	0.106309	+	0.994333i	$0.466097\pi$
$410$	−2.08350	−	18.5212i	−0.102897	−	0.914697i
$411$	23.6130	−	17.1559i	1.16475	−	0.846237i
$412$	−5.75267	−	4.17956i	−0.283414	−	0.205912i
$413$	18.0516	+	13.1152i	0.888259	+	0.645358i
$414$	−14.7908	+	10.7462i	−0.726929	+	0.528145i
$415$	−12.4033	+	5.63119i	−0.608855	+	0.276424i
$416$	−0.809017	−	0.587785i	−0.0396653	−	0.0288185i
$417$	−15.2941	−	47.0703i	−0.748954	−	2.30504i
$418$	−5.89549			−0.288358
$419$	3.54622	+	10.9142i	0.173244	+	0.533191i	0.999549	−	0.0300322i	$-0.00956098\pi$
$419$	3.54622	+	10.9142i	0.173244	+	0.533191i	−0.826305	+	0.563224i	$0.809561\pi$
$420$	6.18070	−	10.8881i	0.301587	−	0.531286i
$421$	5.89358	−	18.1386i	0.287235	−	0.884019i	−0.698484	−	0.715625i	$-0.746142\pi$
$421$	5.89358	−	18.1386i	0.287235	−	0.884019i	0.985720	−	0.168394i	$-0.0538581\pi$
$422$	3.27198	−	10.0701i	0.159277	−	0.490206i
$423$	−28.1367	+	20.4425i	−1.36805	+	0.993949i
$424$	1.17637			0.0571298
$425$	−6.43489	−	10.7789i	−0.312138	−	0.522854i
$426$	0.222874			0.0107983
$427$	−7.61312	+	5.53125i	−0.368425	+	0.267676i
$428$	−4.18930	+	12.8933i	−0.202497	+	0.623223i
$429$	−0.715944	+	2.20345i	−0.0345661	+	0.106383i
$430$	−2.33206	−	2.55229i	−0.112462	−	0.123082i
$431$	0.748920	+	2.30494i	0.0360742	+	0.111025i	0.967472	−	0.252978i	$-0.0814099\pi$
$431$	0.748920	+	2.30494i	0.0360742	+	0.111025i	−0.931398	+	0.364003i	$0.881410\pi$
$432$	−4.53751			−0.218311
$433$	−3.01796	−	9.28833i	−0.145034	−	0.446369i	0.851981	−	0.523572i	$-0.175401\pi$
$433$	−3.01796	−	9.28833i	−0.145034	−	0.446369i	−0.997015	+	0.0772035i	$0.975401\pi$
$434$	1.43458	+	1.04228i	0.0688621	+	0.0500312i
$435$	1.62108	−	2.85574i	0.0777247	−	0.136922i
$436$	−0.468065	+	0.340069i	−0.0224163	+	0.0162864i
$437$	22.4155	+	16.2858i	1.07228	+	0.779057i
$438$	26.7466	+	19.4325i	1.27800	+	0.928522i
$439$	0.225307	−	0.163695i	0.0107533	−	0.00781273i	−0.582396	−	0.812905i	$-0.697885\pi$
$439$	0.225307	−	0.163695i	0.0107533	−	0.00781273i	0.593149	+	0.805093i	$0.297885\pi$
$440$	0.925175	−	1.62982i	0.0441060	−	0.0776986i
$441$	10.8795	+	7.90440i	0.518070	+	0.376400i
$442$	0.775855	+	2.38784i	0.0369036	+	0.113578i
$443$	15.0116			0.713221			0.356611	−	0.934253i	$-0.383932\pi$
$443$	15.0116			0.713221			0.356611	+	0.934253i	$0.383932\pi$
$444$	4.53676	+	13.9627i	0.215305	+	0.662641i
$445$	8.57866	+	9.38878i	0.406667	+	0.445071i
$446$	7.71416	−	23.7417i	0.365276	−	1.12420i
$447$	−14.4327	+	44.4194i	−0.682644	+	2.10096i
$448$	1.63867	−	1.19056i	0.0774199	−	0.0562489i
$449$	12.0884			0.570486			0.285243	−	0.958455i	$-0.407926\pi$
$449$	12.0884			0.570486			0.285243	+	0.958455i	$0.407926\pi$
$450$	−22.6273	+	5.15606i	−1.06666	+	0.243059i
$451$	−6.98592			−0.328954
$452$	13.9675	−	10.1480i	0.656974	−	0.477320i
$453$	17.0234	−	52.3925i	0.799827	−	2.46161i
$454$	3.81921	−	11.7543i	0.179244	−	0.551658i
$455$	−2.23588	+	3.93881i	−0.104820	+	0.184654i
$456$	6.00872	+	18.4929i	0.281384	+	0.866012i
$457$	10.3713			0.485149			0.242574	−	0.970133i	$-0.422008\pi$
$457$	10.3713			0.485149			0.242574	+	0.970133i	$0.422008\pi$
$458$	3.00404	+	9.24549i	0.140370	+	0.432013i
$459$	9.21666	+	6.69630i	0.430197	+	0.312556i
$460$	−8.01990	+	3.64109i	−0.373930	+	0.169767i
$461$	25.4049	−	18.4577i	1.18322	−	0.859662i	0.190692	−	0.981650i	$-0.438927\pi$
$461$	25.4049	−	18.4577i	1.18322	−	0.859662i	0.992532	+	0.121988i	$0.0389269\pi$
$462$	−3.79654	−	2.75835i	−0.176631	−	0.128330i
$463$	5.77877	+	4.19852i	0.268562	+	0.195122i	0.713913	−	0.700234i	$-0.246921\pi$
$463$	5.77877	+	4.19852i	0.268562	+	0.195122i	−0.445351	+	0.895356i	$0.646921\pi$
$464$	0.429791	−	0.312262i	0.0199526	−	0.0144964i
$465$	−0.604924	−	5.37744i	−0.0280527	−	0.249373i
$466$	12.1520	+	8.82895i	0.562931	+	0.408993i
$467$	6.04203	+	18.5955i	0.279592	+	0.860496i	0.987968	+	0.154660i	$0.0494283\pi$
$467$	6.04203	+	18.5955i	0.279592	+	0.860496i	−0.708376	+	0.705836i	$0.750572\pi$
$468$	4.64146			0.214551
$469$	1.77643	+	5.46729i	0.0820280	+	0.252456i
$470$	−15.2563	+	6.92649i	−0.703723	+	0.319495i
$471$	14.5723	−	44.8489i	0.671456	−	2.06653i
$472$	3.40413	−	10.4768i	0.156688	−	0.482235i
$473$	−1.04837	+	0.761683i	−0.0482040	+	0.0350222i
$474$	9.58212			0.440122
$475$	18.0283	+	30.1987i	0.827196	+	1.38561i
$476$	−5.08548			−0.233093
$477$	−4.41731	+	3.20936i	−0.202255	+	0.146947i
$478$	−8.34412	+	25.6806i	−0.381651	+	1.17460i
$479$	−8.74888	+	26.9263i	−0.399747	+	1.23029i	0.525456	+	0.850821i	$0.323895\pi$
$479$	−8.74888	+	26.9263i	−0.399747	+	1.23029i	−0.925203	+	0.379473i	$0.876105\pi$
$480$	−6.05535	−	1.24096i	−0.276388	−	0.0566419i
$481$	−1.64119	−	5.05105i	−0.0748316	−	0.230308i
$482$	−18.0156			−0.820587
$483$	6.81529	+	20.9753i	0.310106	+	0.954409i
$484$	8.33089	+	6.05275i	0.378677	+	0.275125i
$485$	−2.03160	−	0.416348i	−0.0922501	−	0.0189054i
$486$	−14.1018	+	10.2455i	−0.639669	+	0.464746i
$487$	1.07196	+	0.778825i	0.0485752	+	0.0352920i	0.611808	−	0.791006i	$-0.290443\pi$
$487$	1.07196	+	0.778825i	0.0485752	+	0.0352920i	−0.563233	+	0.826298i	$0.690443\pi$
$488$	3.75862	+	2.73080i	0.170145	+	0.123617i
$489$	25.0469	−	18.1976i	1.13266	−	0.822924i
$490$	4.37007	+	4.78275i	0.197420	+	0.216063i
$491$	29.2489	+	21.2506i	1.31998	+	0.959025i	0.999932	+	0.0116251i	$0.00370045\pi$
$491$	29.2489	+	21.2506i	1.31998	+	0.959025i	0.320052	+	0.947400i	$0.396300\pi$
$492$	7.12009	+	21.9134i	0.320998	+	0.987932i
$493$	−1.33382			−0.0600723
$494$	−2.17367	−	6.68988i	−0.0977981	−	0.300992i
$495$	0.972393	+	8.64405i	0.0437058	+	0.388521i
$496$	0.270530	−	0.832606i	0.0121472	−	0.0373851i
$497$	0.0504648	−	0.155315i	0.00226365	−	0.00696681i
$498$	13.6237	−	9.89817i	0.610491	−	0.443548i
$499$	−17.2940			−0.774188			−0.387094	−	0.922040i	$-0.626521\pi$
$499$	−17.2940			−0.774188			−0.387094	+	0.922040i	$0.626521\pi$
$500$	−11.1777	+	0.244902i	−0.499880	+	0.0109523i
$501$	68.8227			3.07477
$502$	2.84815	−	2.06930i	0.127119	−	0.0923575i
$503$	−10.6515	+	32.7820i	−0.474928	+	1.46168i	0.371127	+	0.928582i	$0.378972\pi$
$503$	−10.6515	+	32.7820i	−0.474928	+	1.46168i	−0.846055	+	0.533096i	$0.821028\pi$
$504$	−2.90516	+	8.94118i	−0.129406	+	0.398272i
$505$	−3.43217	−	30.5102i	−0.152730	−	1.35768i
$506$	1.02017	+	3.13975i	0.0453519	+	0.139579i
$507$	−2.76432			−0.122768
$508$	5.47382	+	16.8467i	0.242861	+	0.747451i
$509$	−8.05294	−	5.85080i	−0.356940	−	0.259332i	0.394834	−	0.918752i	$-0.370802\pi$
$509$	−8.05294	−	5.85080i	−0.356940	−	0.259332i	−0.751775	+	0.659420i	$0.770802\pi$
$510$	10.4684	+	11.4569i	0.463546	+	0.507321i
$511$	19.5981	−	14.2388i	0.866969	−	0.629890i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−25.8218	−	18.7607i	−1.14006	−	0.828304i
$514$	−10.1134	+	7.34783i	−0.446084	+	0.324099i
$515$	15.5763	+	3.19214i	0.686372	+	0.140663i
$516$	3.45775	+	2.51220i	0.152219	+	0.110593i
$517$	1.94067	+	5.97277i	0.0853506	+	0.262682i
$518$	10.7575			0.472655
$519$	−18.5971	−	57.2360i	−0.816323	−	2.51238i
$520$	2.19054	+	0.448921i	0.0960616	+	0.0196865i
$521$	−7.62597	+	23.4703i	−0.334100	+	1.02825i	0.633064	+	0.774100i	$0.281797\pi$
$521$	−7.62597	+	23.4703i	−0.334100	+	1.02825i	−0.967164	+	0.254154i	$0.918203\pi$
$522$	−0.761968	+	2.34510i	−0.0333504	+	0.102642i
$523$	21.1110	−	15.3380i	0.923119	−	0.670685i	−0.0211794	−	0.999776i	$-0.506742\pi$
$523$	21.1110	−	15.3380i	0.923119	−	0.670685i	0.944298	+	0.329090i	$0.106742\pi$
$524$	20.9118			0.913536
$525$	−2.51944	+	27.8822i	−0.109957	+	1.21688i
$526$	−1.65499			−0.0721612
$527$	−1.77823	+	1.29196i	−0.0774611	+	0.0562788i
$528$	−0.715944	+	2.20345i	−0.0311574	+	0.0958928i
$529$	−2.31291	+	7.11839i	−0.100561	+	0.309495i
$530$	−2.39516	+	1.08742i	−0.104039	+	0.0472345i
$531$	15.8001	+	48.6277i	0.685666	+	2.11026i
$532$	14.2477			0.617717
$533$	−2.57571	−	7.92723i	−0.111567	−	0.343366i
$534$	−12.7196	−	9.24131i	−0.550430	−	0.399911i
$535$	−3.38874	−	30.1240i	−0.146508	−	1.30238i
$536$	2.29609	−	1.66821i	0.0991762	−	0.0720557i
$537$	2.65030	+	1.92556i	0.114369	+	0.0830939i
$538$	−3.59184	−	2.60963i	−0.154855	−	0.112509i
$539$	1.96454	−	1.42733i	0.0846189	−	0.0614793i
$540$	9.23862	−	4.19440i	0.397567	−	0.180498i
$541$	−3.30658	−	2.40237i	−0.142161	−	0.103286i	0.514432	−	0.857531i	$-0.328003\pi$
$541$	−3.30658	−	2.40237i	−0.142161	−	0.103286i	−0.656593	+	0.754245i	$0.728003\pi$
$542$	−1.72235	−	5.30085i	−0.0739813	−	0.227691i
$543$	21.3559			0.916471
$544$	0.775855	+	2.38784i	0.0332645	+	0.102378i
$545$	0.638652	−	1.12507i	0.0273568	−	0.0481927i
$546$	1.73023	−	5.32511i	0.0740471	−	0.227894i
$547$	−9.99279	+	30.7546i	−0.427261	+	1.31497i	0.473552	+	0.880766i	$0.342972\pi$
$547$	−9.99279	+	30.7546i	−0.427261	+	1.31497i	−0.900813	+	0.434207i	$0.857028\pi$
$548$	−8.54208	+	6.20619i	−0.364900	+	0.265115i
$549$	−21.5638			−0.920321
$550$	−0.377129	+	4.17362i	−0.0160808	+	0.177964i
$551$	3.73690			0.159197
$552$	8.80898	−	6.40010i	0.374935	−	0.272406i
$553$	2.16965	−	6.67750i	0.0922630	−	0.283956i
$554$	6.54619	−	20.1471i	0.278121	−	0.855968i
$555$	−22.1440	−	24.2351i	−0.939960	−	1.02872i
$556$	5.53268	+	17.0278i	0.234638	+	0.722141i
$557$	−42.0715			−1.78263			−0.891314	−	0.453387i	$-0.850215\pi$
$557$	−42.0715			−1.78263			−0.891314	+	0.453387i	$0.850215\pi$
$558$	1.25565	+	3.86451i	0.0531561	+	0.163598i
$559$	−1.25085	−	0.908795i	−0.0529053	−	0.0384379i
$560$	−2.23588	+	3.93881i	−0.0944834	+	0.166445i
$561$	4.70600	−	3.41911i	0.198688	−	0.144355i
$562$	18.7315	+	13.6092i	0.790139	+	0.574069i
$563$	28.1101	+	20.4232i	1.18470	+	0.860734i	0.992694	−	0.120660i	$-0.0385012\pi$
$563$	28.1101	+	20.4232i	1.18470	+	0.860734i	0.192005	+	0.981394i	$0.438501\pi$
$564$	16.7574	−	12.1750i	0.705615	−	0.512659i
$565$	−19.0579	+	33.5731i	−0.801772	+	1.41243i
$566$	2.46611	+	1.79174i	0.103658	+	0.0753123i
$567$	0.864541	+	2.66078i	0.0363073	+	0.111742i
$568$	−0.0806254			−0.00338297
$569$	2.01729	+	6.20859i	0.0845693	+	0.260277i	0.984395	−	0.175972i	$-0.0563067\pi$
$569$	2.01729	+	6.20859i	0.0845693	+	0.260277i	−0.899826	+	0.436249i	$0.856307\pi$
$570$	−29.3287	−	32.0983i	−1.22844	−	1.34445i
$571$	4.64617	−	14.2995i	0.194436	−	0.598414i	−0.805546	−	0.592533i	$-0.798128\pi$
$571$	4.64617	−	14.2995i	0.194436	−	0.598414i	0.999983	−	0.00588081i	$-0.00187193\pi$
$572$	0.258995	−	0.797103i	0.0108291	−	0.0333286i
$573$	−30.7356	+	22.3307i	−1.28400	+	0.932878i
$574$	16.8830			0.704682
$575$	12.9632	−	14.8269i	0.540603	−	0.618325i
$576$	4.64146			0.193394
$577$	−16.3693	+	11.8930i	−0.681462	+	0.495111i	−0.873842	−	0.486209i	$-0.838379\pi$
$577$	−16.3693	+	11.8930i	−0.681462	+	0.495111i	0.192380	+	0.981320i	$0.438379\pi$
$578$	−3.30534	+	10.1728i	−0.137484	+	0.423132i
$579$	−20.2733	+	62.3948i	−0.842529	+	2.59304i
$580$	−0.586429	+	1.03307i	−0.0243501	+	0.0428960i
$581$	−3.81298	−	11.7351i	−0.158189	−	0.486856i
$582$	2.56374			0.106271
$583$	0.304674	+	0.937691i	0.0126183	+	0.0388352i
$584$	−9.67564	−	7.02977i	−0.400381	−	0.290894i
$585$	−9.45026	+	4.29048i	−0.390720	+	0.177390i
$586$	22.6394	−	16.4485i	0.935225	−	0.679481i
$587$	27.7355	+	20.1510i	1.14477	+	0.831721i	0.987776	−	0.155879i	$-0.0498211\pi$
$587$	27.7355	+	20.1510i	1.14477	+	0.831721i	0.156990	+	0.987600i	$0.449821\pi$
$588$	−6.47950	−	4.70764i	−0.267210	−	0.194140i
$589$	4.98199	−	3.61963i	0.205279	−	0.149144i
$590$	2.75361	+	24.4781i	0.113364	+	1.00775i
$591$	−31.2801	−	22.7263i	−1.28669	−	0.934835i
$592$	−1.64119	−	5.05105i	−0.0674523	−	0.207597i
$593$	−29.4137			−1.20788			−0.603938	−	0.797032i	$-0.706402\pi$
$593$	−29.4137			−1.20788			−0.603938	+	0.797032i	$0.706402\pi$
$594$	−1.17519	−	3.61687i	−0.0482187	−	0.148402i
$595$	10.3543	−	4.70093i	0.424485	−	0.192719i
$596$	5.22108	−	16.0688i	0.213864	−	0.658205i
$597$	−10.0100	+	30.8075i	−0.409680	+	1.26087i
$598$	−3.18667	+	2.31525i	−0.130313	+	0.0946777i
$599$	−31.9214			−1.30427			−0.652136	−	0.758102i	$-0.726127\pi$
$599$	−31.9214			−1.30427			−0.652136	+	0.758102i	$0.726127\pi$
$600$	13.4762	−	3.07080i	0.550162	−	0.125365i
$601$	−14.1350			−0.576578			−0.288289	−	0.957543i	$-0.593086\pi$
$601$	−14.1350			−0.576578			−0.288289	+	0.957543i	$0.593086\pi$
$602$	2.53361	−	1.84077i	0.103262	−	0.0750243i
$603$	−4.07070	+	12.5283i	−0.165772	+	0.510193i
$604$	−6.15825	+	18.9531i	−0.250576	+	0.771192i
$605$	−22.5572	−	4.62279i	−0.917081	−	0.187943i
$606$	11.7290	+	36.0981i	0.476458	+	1.46639i
$607$	−28.9665			−1.17572			−0.587858	−	0.808964i	$-0.700028\pi$
$607$	−28.9665			−1.17572			−0.587858	+	0.808964i	$0.700028\pi$
$608$	−2.17367	−	6.68988i	−0.0881541	−	0.271310i
$609$	2.40647	+	1.74840i	0.0975149	+	0.0708487i
$610$	−10.1771	−	2.08565i	−0.412057	−	0.0844454i
$611$	−6.06204	+	4.40433i	−0.245244	+	0.178180i
$612$	−9.42779	−	6.84969i	−0.381096	−	0.276882i
$613$	9.65239	+	7.01287i	0.389857	+	0.283247i	0.765397	−	0.643559i	$-0.222543\pi$
$613$	9.65239	+	7.01287i	0.389857	+	0.283247i	−0.375540	+	0.926806i	$0.622543\pi$
$614$	−17.3317	+	12.5922i	−0.699452	+	0.508182i
$615$	−34.7532	−	38.0352i	−1.40139	−	1.53373i
$616$	1.37341	+	0.997840i	0.0553362	+	0.0402041i
$617$	3.81161	+	11.7309i	0.153450	+	0.472270i	0.998001	−	0.0632057i	$-0.0201324\pi$
$617$	3.81161	+	11.7309i	0.153450	+	0.472270i	−0.844551	+	0.535475i	$0.820132\pi$
$618$	−19.6562			−0.790689
$619$	7.76581	+	23.9007i	0.312134	+	0.960650i	0.976918	+	0.213615i	$0.0685237\pi$
$619$	7.76581	+	23.9007i	0.312134	+	0.960650i	−0.664784	+	0.747036i	$0.731476\pi$
$620$	0.218833	+	1.94530i	0.00878854	+	0.0781253i
$621$	−5.52306	+	16.9982i	−0.221633	+	0.682116i
$622$	4.58119	−	14.0995i	0.183689	−	0.565337i
$623$	−9.32006	+	6.77142i	−0.373400	+	0.271291i
$624$	−2.76432			−0.110661
$625$	22.5319	−	10.8311i	0.901277	−	0.433243i
$626$	8.53788			0.341242
$627$	−13.1846	+	9.57915i	−0.526541	+	0.382554i
$628$	−5.27157	+	16.2242i	−0.210359	+	0.647417i
$629$	−4.12056	+	12.6818i	−0.164297	+	0.505655i
$630$	−2.35000	−	20.8902i	−0.0936262	−	0.832286i
$631$	−13.4493	−	41.3926i	−0.535407	−	1.64781i	−0.742769	−	0.669548i	$-0.766488\pi$
$631$	−13.4493	−	41.3926i	−0.535407	−	1.64781i	0.207363	−	0.978264i	$-0.433512\pi$
$632$	−3.46636			−0.137884
$633$	−9.04479	−	27.8370i	−0.359498	−	1.10642i
$634$	14.9323	+	10.8489i	0.593036	+	0.430866i
$635$	−26.7178	−	29.2409i	−1.06026	−	1.16039i
$636$	2.63082	−	1.91140i	0.104319	−	0.0757920i
$637$	2.34398	+	1.70300i	0.0928718	+	0.0674753i
$638$	0.360218	+	0.261714i	0.0142612	+	0.0103614i
$639$	0.302750	−	0.219961i	0.0119766	−	0.00870151i
$640$	2.19054	+	0.448921i	0.0865887	+	0.0177452i
$641$	30.3645	+	22.0611i	1.19933	+	0.871361i	0.994218	−	0.107378i	$-0.0342455\pi$
$641$	30.3645	+	22.0611i	1.19933	+	0.871361i	0.205108	+	0.978739i	$0.434245\pi$
$642$	11.5806	+	35.6413i	0.457048	+	1.40665i
$643$	7.73316			0.304966			0.152483	−	0.988306i	$-0.451273\pi$
$643$	7.73316			0.304966			0.152483	+	0.988306i	$0.451273\pi$
$644$	−2.46545	−	7.58787i	−0.0971523	−	0.299004i
$645$	−9.36239	−	1.91869i	−0.368644	−	0.0755485i
$646$	−5.45748	+	16.7964i	−0.214722	+	0.660845i
$647$	0.707148	−	2.17638i	0.0278009	−	0.0855623i	−0.936193	−	0.351485i	$-0.885677\pi$
$647$	0.707148	−	2.17638i	0.0278009	−	0.0855623i	0.963994	+	0.265923i	$0.0856767\pi$
$648$	1.11745	−	0.811873i	0.0438975	−	0.0318934i
$649$	9.23276			0.362417
$650$	−4.87503	+	1.11087i	−0.191215	+	0.0435719i
$651$	4.90180			0.192117
$652$	−9.06077	+	6.58303i	−0.354847	+	0.257812i
$653$	5.83797	−	17.9674i	0.228457	−	0.703119i	−0.769465	−	0.638689i	$-0.779477\pi$
$653$	5.83797	−	17.9674i	0.228457	−	0.703119i	0.997922	−	0.0644302i	$-0.0205230\pi$
$654$	−0.494219	+	1.52105i	−0.0193255	+	0.0594777i
$655$	−42.5776	+	19.3305i	−1.66364	+	0.755306i
$656$	−2.57571	−	7.92723i	−0.100565	−	0.309506i
$657$	55.5107			2.16568
$658$	−4.69005	−	14.4345i	−0.182837	−	0.562715i
$659$	−12.3432	−	8.96785i	−0.480822	−	0.349338i	0.320822	−	0.947140i	$-0.396041\pi$
$659$	−12.3432	−	8.96785i	−0.480822	−	0.349338i	−0.801644	+	0.597802i	$0.796041\pi$
$660$	−0.579129	−	5.14814i	−0.0225426	−	0.200391i
$661$	−28.8355	+	20.9502i	−1.12157	+	0.814869i	−0.984446	−	0.175685i	$-0.943786\pi$
$661$	−28.8355	+	20.9502i	−1.12157	+	0.814869i	−0.137124	+	0.990554i	$0.543786\pi$
$662$	−5.78972	−	4.20648i	−0.225024	−	0.163489i
$663$	5.61492	+	4.07948i	0.218066	+	0.158434i
$664$	−4.92840	+	3.58069i	−0.191259	+	0.138958i
$665$	−29.0092	+	13.1704i	−1.12493	+	0.510725i
$666$	19.9429	+	14.4893i	0.772770	+	0.561450i
$667$	−0.646639	−	1.99015i	−0.0250380	−	0.0770590i
$668$	−24.8968			−0.963286
$669$	−21.3244	−	65.6297i	−0.824448	−	2.53739i
$670$	−3.13291	+	5.51904i	−0.121035	+	0.213219i
$671$	−1.20327	+	3.70327i	−0.0464516	+	0.142963i
$672$	1.73023	−	5.32511i	0.0667452	−	0.205421i
$673$	−4.17723	+	3.03494i	−0.161020	+	0.116988i	−0.665378	−	0.746507i	$-0.731729\pi$
$673$	−4.17723	+	3.03494i	−0.161020	+	0.116988i	0.504357	+	0.863495i	$0.331729\pi$
$674$	−26.6364			−1.02600
$675$	−14.9331	+	17.0801i	−0.574776	+	0.657411i
$676$	1.00000			0.0384615
$677$	−6.82968	+	4.96205i	−0.262486	+	0.190707i	−0.711242	−	0.702947i	$-0.751867\pi$
$677$	−6.82968	+	4.96205i	−0.262486	+	0.190707i	0.448756	+	0.893654i	$0.351867\pi$
$678$	14.7479	−	45.3894i	0.566390	−	1.74317i
$679$	0.580500	−	1.78660i	0.0222776	−	0.0685633i
$680$	−3.78696	−	4.14457i	−0.145223	−	0.158937i
$681$	−10.5575	−	32.4927i	−0.404565	−	1.24512i
$682$	0.733739			0.0280963
$683$	4.40593	+	13.5601i	0.168588	+	0.518861i	0.999283	−	0.0378674i	$-0.0120565\pi$
$683$	4.40593	+	13.5601i	0.168588	+	0.518861i	−0.830695	+	0.556728i	$0.812056\pi$
$684$	26.4134	+	19.1904i	1.00994	+	0.733765i
$685$	11.6553	−	20.5323i	0.445324	−	0.784498i
$686$	−16.2184	+	11.7834i	−0.619223	+	0.449892i
$687$	21.7405	+	15.7954i	0.829452	+	0.602632i
$688$	−1.25085	−	0.908795i	−0.0476882	−	0.0346475i
$689$	−0.951706	+	0.691455i	−0.0362571	+	0.0263423i
$690$	−12.0194	+	21.1738i	−0.457571	+	0.806073i
$691$	−36.0330	−	26.1795i	−1.37076	−	0.995916i	−0.997677	−	0.0681182i	$-0.978300\pi$
$691$	−36.0330	−	26.1795i	−1.37076	−	0.995916i	−0.373084	−	0.927798i	$-0.621700\pi$
$692$	6.72756	+	20.7053i	0.255743	+	0.787097i
$693$	−7.87946			−0.299316
$694$	−4.73777	−	14.5814i	−0.179843	−	0.553501i
$695$	−27.0051	−	29.5553i	−1.02436	−	1.12110i
$696$	0.453806	−	1.39667i	0.0172015	−	0.0529407i
$697$	−6.46689	+	19.9030i	−0.244951	+	0.753881i
$698$	15.2589	−	11.0862i	0.577557	−	0.419620i
$699$	41.5220			1.57051
$700$	0.911413	−	10.0864i	0.0344482	−	0.381232i
$701$	0.939009			0.0354659			0.0177329	−	0.999843i	$-0.494355\pi$
$701$	0.939009			0.0354659			0.0177329	+	0.999843i	$0.494355\pi$
$702$	3.67093	−	2.66708i	0.138550	−	0.100663i
$703$	11.5443	−	35.5299i	0.435403	−	1.34003i
$704$	0.258995	−	0.797103i	0.00976123	−	0.0300420i
$705$	−22.8647	+	40.2792i	−0.861133	+	1.51700i
$706$	−4.03837	−	12.4288i	−0.151986	−	0.467765i
$707$	27.8115			1.04596
$708$	−9.41009	−	28.9613i	−0.353653	−	1.08843i
$709$	−1.48529	−	1.07912i	−0.0557811	−	0.0405273i	0.559545	−	0.828800i	$-0.310976\pi$
$709$	−1.48529	−	1.07912i	−0.0557811	−	0.0405273i	−0.615326	+	0.788272i	$0.710976\pi$
$710$	0.164158	−	0.0745287i	0.00616073	−	0.00279701i
$711$	13.0162	−	9.45686i	0.488147	−	0.354660i
$712$	4.60134	+	3.34307i	0.172443	+	0.125287i
$713$	−2.78979	−	2.02690i	−0.104478	−	0.0759079i
$714$	−11.3731	+	8.26302i	−0.425626	+	0.309236i
$715$	0.209502	+	1.86236i	0.00783492	+	0.0696482i
$716$	−0.958754	−	0.696576i	−0.0358303	−	0.0260323i
$717$	23.0658	+	70.9893i	0.861409	+	2.65114i
$718$	−19.4422			−0.725575
$719$	15.3697	+	47.3032i	0.573195	+	1.76411i	0.642246	+	0.766498i	$0.278003\pi$
$719$	15.3697	+	47.3032i	0.573195	+	1.76411i	−0.0690517	+	0.997613i	$0.521997\pi$
$720$	−9.45026	+	4.29048i	−0.352190	+	0.159897i
$721$	−4.45070	+	13.6978i	−0.165753	+	0.510135i
$722$	9.41862	−	28.9875i	0.350525	−	1.07880i
$723$	−40.2897	+	29.2722i	−1.49839	+	1.08864i
$724$	−7.72557			−0.287118
$725$	0.239046	−	2.64548i	0.00887794	−	0.0982506i
$726$	28.4657			1.05646
$727$	19.1575	−	13.9187i	0.710511	−	0.516216i	−0.172828	−	0.984952i	$-0.555290\pi$
$727$	19.1575	−	13.9187i	0.710511	−	0.516216i	0.883338	+	0.468736i	$0.155290\pi$
$728$	−0.625916	+	1.92637i	−0.0231980	+	0.0713961i
$729$	−13.6092	+	41.8849i	−0.504045	+	1.55129i
$730$	26.1983	+	5.36899i	0.969644	+	0.198715i
$731$	1.19958	+	3.69191i	0.0443679	+	0.136550i
$732$	12.8428			0.474683
$733$	−1.92928	−	5.93773i	−0.0712597	−	0.219315i	0.909084	−	0.416614i	$-0.136783\pi$
$733$	−1.92928	−	5.93773i	−0.0712597	−	0.219315i	−0.980343	+	0.197299i	$0.936783\pi$
$734$	23.5160	+	17.0854i	0.867992	+	0.630633i
$735$	17.5443	+	3.59546i	0.647130	+	0.132620i
$736$	−3.18667	+	2.31525i	−0.117462	+	0.0853414i
$737$	1.92441	+	1.39817i	0.0708866	+	0.0515021i
$738$	31.2988	+	22.7399i	1.15212	+	0.837067i
$739$	36.3763	−	26.4289i	1.33812	−	0.972203i	0.338612	−	0.940926i	$-0.390043\pi$
$739$	36.3763	−	26.4289i	1.33812	−	0.972203i	0.999511	−	0.0312770i	$-0.00995739\pi$
$740$	8.01065	+	8.76713i	0.294477	+	0.322286i
$741$	−15.7310	−	11.4293i	−0.577894	−	0.419865i
$742$	−0.736312	−	2.26613i	−0.0270309	−	0.0831924i
$743$	36.3786			1.33460			0.667301	−	0.744788i	$-0.267449\pi$
$743$	36.3786			1.33460			0.667301	+	0.744788i	$0.267449\pi$
$744$	−0.747832	−	2.30159i	−0.0274168	−	0.0843803i
$745$	4.22335	+	37.5433i	0.154732	+	1.37548i
$746$	−7.06303	+	21.7378i	−0.258596	+	0.795877i
$747$	8.73746	−	26.8911i	0.319687	−	0.983895i
$748$	−1.70241	+	1.23687i	−0.0622462	+	0.0452245i
$749$	27.4595			1.00335
$750$	−24.5996	+	18.7094i	−0.898250	+	0.683172i
$751$	−6.85352			−0.250088			−0.125044	−	0.992151i	$-0.539907\pi$
$751$	−6.85352			−0.250088			−0.125044	+	0.992151i	$0.539907\pi$
$752$	−6.06204	+	4.40433i	−0.221060	+	0.160609i
$753$	3.00730	−	9.25550i	0.109592	−	0.337289i
$754$	−0.164166	+	0.505250i	−0.00597856	+	0.0184001i
$755$	−4.98143	−	44.2822i	−0.181293	−	1.61159i
$756$	2.84010	+	8.74094i	0.103294	+	0.317905i
$757$	−21.7143			−0.789221			−0.394611	−	0.918848i	$-0.629121\pi$
$757$	−21.7143			−0.789221			−0.394611	+	0.918848i	$0.629121\pi$
$758$	3.53509	+	10.8799i	0.128400	+	0.395175i
$759$	7.38302	+	5.36408i	0.267987	+	0.194704i
$760$	10.6097	+	11.6116i	0.384855	+	0.421199i
$761$	15.1949	−	11.0398i	0.550816	−	0.400191i	−0.277270	−	0.960792i	$-0.589430\pi$
$761$	15.1949	−	11.0398i	0.550816	−	0.400191i	0.828086	+	0.560601i	$0.189430\pi$
$762$	39.6145	+	28.7816i	1.43508	+	1.04265i
$763$	0.948070	+	0.688813i	0.0343224	+	0.0249367i
$764$	11.1187	−	8.07819i	0.402259	−	0.292259i
$765$	25.5272	+	5.23145i	0.922939	+	0.189144i
$766$	−22.6401	−	16.4490i	−0.818021	−	0.594327i
$767$	3.40413	+	10.4768i	0.122916	+	0.378296i
$768$	−2.76432			−0.0997488
$769$	0.854125	+	2.62873i	0.0308005	+	0.0947943i	0.965275	−	0.261236i	$-0.0841300\pi$
$769$	0.854125	+	2.62873i	0.0308005	+	0.0947943i	−0.934474	+	0.356030i	$0.884130\pi$
$770$	−3.71872	−	0.762101i	−0.134013	−	0.0274642i
$771$	−10.6785	+	32.8651i	−0.384577	+	1.18361i
$772$	7.33392	−	22.5715i	0.263954	−	0.812365i
$773$	−26.0593	+	18.9332i	−0.937287	+	0.680979i	−0.947766	−	0.318967i	$-0.896664\pi$
$773$	−26.0593	+	18.9332i	−0.937287	+	0.680979i	0.0104794	+	0.999945i	$0.496664\pi$
$774$	7.17632			0.257947
$775$	−2.24376	−	3.75846i	−0.0805983	−	0.135008i
$776$	−0.927441			−0.0332932
$777$	24.0578	−	17.4790i	0.863067	−	0.627055i
$778$	1.91847	−	5.90445i	0.0687806	−	0.211685i
$779$	18.1180	−	55.7613i	0.649143	−	1.99786i
$780$	5.62830	−	2.55529i	0.201526	−	0.0914940i
$781$	−0.0208815	−	0.0642668i	−0.000747200	−	0.00229965i
$782$	9.88958			0.353651
$783$	0.744904	+	2.29258i	0.0266207	+	0.0819301i
$784$	2.34398	+	1.70300i	0.0837135	+	0.0608214i
$785$	−4.26419	−	37.9063i	−0.152196	−	1.35294i
$786$	46.7668	−	33.9780i	1.66811	−	1.21196i
$787$	5.21101	+	3.78602i	0.185752	+	0.134957i	0.676775	−	0.736190i	$-0.263377\pi$
$787$	5.21101	+	3.78602i	0.185752	+	0.134957i	−0.491023	+	0.871147i	$0.663377\pi$
$788$	11.3157	+	8.22130i	0.403103	+	0.292872i
$789$	−3.70120	+	2.68908i	−0.131766	+	0.0957337i
$790$	7.05770	−	3.20424i	0.251102	−	0.114002i
$791$	−28.2912	−	20.5548i	−1.00592	−	0.730843i
$792$	1.20211	+	3.69972i	0.0427152	+	0.131464i
$793$	−4.64591			−0.164981
$794$	−5.46318	−	16.8139i	−0.193881	−	0.596704i
$795$	−3.58962	+	6.32360i	−0.127311	+	0.224275i
$796$	3.62113	−	11.1447i	0.128348	−	0.395013i
$797$	8.93578	−	27.5015i	0.316522	−	0.974153i	−0.658602	−	0.752491i	$-0.728852\pi$
$797$	8.93578	−	27.5015i	0.316522	−	0.974153i	0.975124	−	0.221662i	$-0.0711481\pi$
$798$	31.8634	−	23.1501i	1.12795	−	0.819504i
$799$	18.8131			0.665558
$800$	−4.87503	+	1.11087i	−0.172359	+	0.0392752i
$801$	−26.3986			−0.932750
$802$	−24.9093	+	18.0977i	−0.879579	+	0.639052i
$803$	3.09751	−	9.53316i	0.109309	−	0.336418i
$804$	2.42439	−	7.46151i	0.0855016	−	0.263147i
$805$	12.0339	+	13.1703i	0.424139	+	0.464192i
$806$	0.270530	+	0.832606i	0.00952902	+	0.0293273i
$807$	−12.2729			−0.432027
$808$	−4.24299	−	13.0586i	−0.149268	−	0.459400i
$809$	25.3010	+	18.3823i	0.889537	+	0.646287i	0.935757	−	0.352645i	$-0.114718\pi$
$809$	25.3010	+	18.3823i	0.889537	+	0.646287i	−0.0462201	+	0.998931i	$0.514718\pi$
$810$	−1.52470	+	2.68597i	−0.0535725	+	0.0943752i
$811$	14.2276	−	10.3370i	0.499599	−	0.362980i	−0.309265	−	0.950976i	$-0.600083\pi$
$811$	14.2276	−	10.3370i	0.499599	−	0.362980i	0.808864	+	0.587996i	$0.200083\pi$
$812$	−0.870546	−	0.632488i	−0.0305502	−	0.0221960i
$813$	−12.4648	−	9.05620i	−0.437159	−	0.317615i
$814$	3.60115	−	2.61639i	0.126220	−	0.0917044i
$815$	12.3630	−	21.7790i	0.433056	−	0.762886i
$816$	5.61492	+	4.07948i	0.196562	+	0.142810i
$817$	−3.36079	−	10.3434i	−0.117579	−	0.361871i
$818$	−27.1184			−0.948174
$819$	−2.90516	−	8.94118i	−0.101515	−	0.312430i
$820$	12.5721	+	13.7593i	0.439036	+	0.480496i
$821$	−13.9175	+	42.8338i	−0.485726	+	1.49491i	0.345202	+	0.938529i	$0.387811\pi$
$821$	−13.9175	+	42.8338i	−0.485726	+	1.49491i	−0.830927	+	0.556381i	$0.812189\pi$
$822$	−9.01938	+	27.7588i	−0.314587	+	0.968199i
$823$	30.5288	−	22.1805i	1.06417	−	0.773162i	0.0893115	−	0.996004i	$-0.471533\pi$
$823$	30.5288	−	22.1805i	1.06417	−	0.773162i	0.974855	+	0.222842i	$0.0715333\pi$
$824$	7.11070			0.247713
$825$	5.93800	+	9.94656i	0.206734	+	0.346295i
$826$	−22.3130			−0.776367
$827$	3.68487	−	2.67721i	0.128135	−	0.0930959i	−0.521871	−	0.853024i	$-0.674766\pi$
$827$	3.68487	−	2.67721i	0.128135	−	0.0930959i	0.650007	+	0.759928i	$0.274766\pi$
$828$	5.64959	−	17.3876i	0.196337	−	0.604262i
$829$	−4.17950	+	12.8632i	−0.145160	+	0.446757i	−0.997032	−	0.0769941i	$-0.975468\pi$
$829$	−4.17950	+	12.8632i	−0.145160	+	0.446757i	0.851871	+	0.523751i	$0.175468\pi$
$830$	6.72456	−	11.8462i	0.233413	−	0.411188i
$831$	−18.0958	−	55.6930i	−0.627735	−	1.93197i
$832$	1.00000			0.0346688
$833$	−2.24790	−	6.91832i	−0.0778850	−	0.239705i
$834$	40.0404	+	29.0911i	1.38649	+	1.00734i
$835$	50.6912	−	23.0142i	1.75424	−	0.796439i
$836$	4.76955	−	3.46528i	0.164958	−	0.119849i
$837$	3.21373	+	2.33491i	0.111083	+	0.0807063i
$838$	−9.28414	−	6.74532i	−0.320715	−	0.233013i
$839$	10.7307	−	7.79629i	0.370464	−	0.269158i	−0.386939	−	0.922105i	$-0.626468\pi$
$839$	10.7307	−	7.79629i	0.370464	−	0.269158i	0.757403	+	0.652947i	$0.226468\pi$
$840$	1.39959	+	12.4416i	0.0482905	+	0.429276i
$841$	23.2332	+	16.8799i	0.801144	+	0.582065i
$842$	5.89358	+	18.1386i	0.203106	+	0.625096i
$843$	64.0032			2.20439
$844$	3.27198	+	10.0701i	0.112626	+	0.346628i
$845$	−2.03605	+	0.924383i	−0.0700424	+	0.0317997i
$846$	10.7473	−	33.0767i	0.369499	−	1.13720i
$847$	6.44540	−	19.8369i	0.221467	−	0.681604i
$848$	−0.951706	+	0.691455i	−0.0326817	+	0.0237447i
$849$	8.42643			0.289194
$850$	11.5416	+	4.93798i	0.395874	+	0.169371i
$851$	−20.9197			−0.717118
$852$	−0.180309	+	0.131002i	−0.00617729	+	0.00448806i
$853$	14.8979	−	45.8511i	0.510095	−	1.56991i	−0.281939	−	0.959432i	$-0.590977\pi$
$853$	14.8979	−	45.8511i	0.510095	−	1.56991i	0.792033	−	0.610478i	$-0.209023\pi$
$854$	2.90795	−	8.94976i	0.0995081	−	0.306254i
$855$	−71.5184	−	14.6567i	−2.44588	−	0.501249i
$856$	−4.18930	−	12.8933i	−0.143187	−	0.440685i
$857$	−50.6440			−1.72997			−0.864983	−	0.501801i	$-0.832671\pi$
$857$	−50.6440			−1.72997			−0.864983	+	0.501801i	$0.832671\pi$
$858$	−0.715944	−	2.20345i	−0.0244419	−	0.0752245i
$859$	−7.12503	−	5.17664i	−0.243103	−	0.176625i	0.459562	−	0.888146i	$-0.348007\pi$
$859$	−7.12503	−	5.17664i	−0.243103	−	0.176625i	−0.702665	+	0.711521i	$0.748007\pi$
$860$	3.38687	+	0.694093i	0.115491	+	0.0236684i
$861$	37.7568	−	27.4319i	1.28675	−	0.934877i
$862$	−1.96070	−	1.42453i	−0.0667816	−	0.0485197i
$863$	3.11182	+	2.26087i	0.105928	+	0.0769609i	0.639488	−	0.768801i	$-0.279146\pi$
$863$	3.11182	+	2.26087i	0.105928	+	0.0769609i	−0.533560	+	0.845762i	$0.679146\pi$
$864$	3.67093	−	2.66708i	0.124887	−	0.0907360i
$865$	−32.8373	−	35.9383i	−1.11650	−	1.22194i
$866$	7.90112	+	5.74050i	0.268491	+	0.195070i
$867$	9.13700	+	28.1208i	0.310309	+	0.955033i
$868$	−1.77324			−0.0601877
$869$	−0.897769	−	2.76305i	−0.0304547	−	0.0937300i
$870$	0.367086	+	3.26319i	0.0124454	+	0.110633i
$871$	−0.877030	+	2.69922i	−0.0297170	+	0.0914596i
$872$	0.178785	−	0.550244i	0.00605442	−	0.0186336i
$873$	3.48256	−	2.53023i	0.117867	−	0.0856352i
$874$	−27.7071			−0.937208
$875$	7.46805	+	21.3790i	0.252466	+	0.722744i
$876$	−33.0606			−1.11701
$877$	1.78067	−	1.29373i	0.0601290	−	0.0436863i	−0.557315	−	0.830301i	$-0.688168\pi$
$877$	1.78067	−	1.29373i	0.0601290	−	0.0436863i	0.617444	+	0.786615i	$0.288168\pi$
$878$	−0.0860595	+	0.264864i	−0.00290437	+	0.00893872i
$879$	23.9044	−	73.5702i	0.806276	−	2.48146i
$880$	0.209502	+	1.86236i	0.00706230	+	0.0627800i
$881$	13.7188	+	42.2221i	0.462197	+	1.42250i	0.862473	+	0.506103i	$0.168914\pi$
$881$	13.7188	+	42.2221i	0.462197	+	1.42250i	−0.400276	+	0.916395i	$0.631086\pi$
$882$	−13.4478			−0.452810
$883$	−13.2663	−	40.8295i	−0.446446	−	1.37402i	−0.880890	−	0.473321i	$-0.843055\pi$
$883$	−13.2663	−	40.8295i	−0.446446	−	1.37402i	0.434443	−	0.900699i	$-0.356945\pi$
$884$	−2.03121	−	1.47576i	−0.0683171	−	0.0496353i
$885$	45.9308	+	50.2682i	1.54395	+	1.68975i
$886$	−12.1446	+	8.82358i	−0.408006	+	0.296434i
$887$	6.54869	+	4.75790i	0.219884	+	0.159755i	0.692274	−	0.721635i	$-0.256609\pi$
$887$	6.54869	+	4.75790i	0.219884	+	0.159755i	−0.472391	+	0.881389i	$0.656609\pi$
$888$	−11.8774	−	8.62943i	−0.398579	−	0.289585i
$889$	29.0268	−	21.0892i	0.973529	−	0.707310i
$890$	−12.4589	−	2.55327i	−0.417622	−	0.0855859i
$891$	0.936559	+	0.680450i	0.0313759	+	0.0227959i
$892$	7.71416	+	23.7417i	0.258289	+	0.794932i
$893$	−52.7076			−1.76379
$894$	−14.4327	−	44.4194i	−0.482703	−	1.48561i
$895$	2.59598	+	0.532010i	0.0867740	+	0.0177831i
$896$	−0.625916	+	1.92637i	−0.0209104	+	0.0643556i
$897$	−3.36473	+	10.3556i	−0.112345	+	0.345763i
$898$	−9.77970	+	7.10537i	−0.326353	+	0.237109i
$899$	−0.465086			−0.0155115
$900$	15.2752	−	17.4713i	0.509173	−	0.582377i
$901$	2.95354			0.0983968
$902$	5.65172	−	4.10622i	0.188182	−	0.136722i
$903$	2.67517	−	8.23333i	0.0890242	−	0.273988i
$904$	−5.33509	+	16.4197i	−0.177443	+	0.546112i
$905$	15.7297	−	7.14138i	0.522872	−	0.237388i
$906$	17.0234	+	52.3925i	0.565563	+	1.74062i
$907$	−45.8754			−1.52327			−0.761634	−	0.648007i	$-0.775603\pi$
$907$	−45.8754			−1.52327			−0.761634	+	0.648007i	$0.775603\pi$
$908$	3.81921	+	11.7543i	0.126745	+	0.390081i
$909$	51.5587	+	37.4596i	1.71009	+	1.24246i
$910$	−0.506306	−	4.50079i	−0.0167839	−	0.149200i
$911$	16.2929	−	11.8375i	0.539807	−	0.392193i	−0.284206	−	0.958763i	$-0.591730\pi$
$911$	16.2929	−	11.8375i	0.539807	−	0.392193i	0.824014	+	0.566570i	$0.191730\pi$
$912$	−15.7310	−	11.4293i	−0.520907	−	0.378461i
$913$	−4.13061	−	3.00106i	−0.136703	−	0.0993207i
$914$	−8.39055	+	6.09609i	−0.277535	+	0.201641i
$915$	−26.1486	+	11.8716i	−0.864446	+	0.392464i
$916$	−7.86468	−	5.71403i	−0.259856	−	0.188797i
$917$	−13.0890	−	40.2839i	−0.432238	−	1.33029i
$918$	−11.3924			−0.376006
$919$	2.08207	+	6.40796i	0.0686813	+	0.211379i	0.979506	−	0.201413i	$-0.0645534\pi$
$919$	2.08207	+	6.40796i	0.0686813	+	0.211379i	−0.910825	+	0.412793i	$0.864553\pi$
$920$	4.34806	−	7.65969i	0.143351	−	0.252532i
$921$	−18.3002	+	56.3221i	−0.603011	+	1.85588i
$922$	−9.70380	+	29.8652i	−0.319578	+	0.983559i
$923$	0.0652273	−	0.0473904i	0.00214698	−	0.00155987i
$924$	4.69278			0.154381
$925$	−24.4143	−	10.4454i	−0.802737	−	0.343444i
$926$	−7.14295			−0.234732
$927$	−26.7008	+	19.3993i	−0.876969	+	0.637155i
$928$	−0.164166	+	0.505250i	−0.00538900	+	0.0165856i
$929$	−2.49999	+	7.69419i	−0.0820221	+	0.252438i	−0.983655	−	0.180064i	$-0.942369\pi$
$929$	−2.49999	+	7.69419i	−0.0820221	+	0.252438i	0.901633	+	0.432503i	$0.142369\pi$
$930$	3.65017	+	3.99488i	0.119694	+	0.130997i
$931$	6.29782	+	19.3827i	0.206403	+	0.635242i
$932$	−15.0207			−0.492019
$933$	−12.6639	−	38.9754i	−0.414597	−	1.27600i
$934$	−15.8183	−	11.4926i	−0.517589	−	0.376050i
$935$	2.32285	−	4.09202i	0.0759654	−	0.133823i
$936$	−3.75502	+	2.72818i	−0.122737	+	0.0891734i
$937$	−33.0198	−	23.9903i	−1.07871	−	0.783729i	−0.101252	−	0.994861i	$-0.532285\pi$
$937$	−33.0198	−	23.9903i	−1.07871	−	0.783729i	−0.977458	+	0.211132i	$0.932285\pi$
$938$	−4.65076	−	3.37897i	−0.151853	−	0.110327i
$939$	19.0939	−	13.8726i	0.623107	−	0.452714i
$940$	8.27136	−	14.5711i	0.269782	−	0.475257i
$941$	−35.5408	−	25.8219i	−1.15860	−	0.841771i	−0.168998	−	0.985616i	$-0.554053\pi$
$941$	−35.5408	−	25.8219i	−1.15860	−	0.841771i	−0.989600	+	0.143846i	$0.954053\pi$
$942$	14.5723	+	44.8489i	0.474791	+	1.46126i
$943$	−32.8318			−1.06915
$944$	3.40413	+	10.4768i	0.110795	+	0.340991i
$945$	−13.8626	−	15.1717i	−0.450950	−	0.493535i
$946$	0.400440	−	1.23243i	0.0130194	−	0.0400697i
$947$	10.2827	−	31.6469i	0.334143	−	1.02839i	−0.632999	−	0.774153i	$-0.718176\pi$
$947$	10.2827	−	31.6469i	0.334143	−	1.02839i	0.967142	−	0.254235i	$-0.0818237\pi$
$948$	−7.75210	+	5.63223i	−0.251777	+	0.182926i
$949$	11.9598			0.388230
$950$	−32.3356	−	13.8345i	−1.04910	−	0.448850i
$951$	51.0219			1.65450
$952$	4.11424	−	2.98917i	0.133343	−	0.0968796i
$953$	−12.2335	+	37.6507i	−0.396280	+	1.21963i	0.531679	+	0.846946i	$0.321561\pi$
$953$	−12.2335	+	37.6507i	−0.396280	+	1.21963i	−0.927960	+	0.372680i	$0.878439\pi$
$954$	1.68726	−	5.19285i	0.0546271	−	0.168125i
$955$	−15.1709	+	26.7255i	−0.490918	+	0.864818i
$956$	−8.34412	−	25.6806i	−0.269868	−	0.830569i
$957$	1.23083			0.0397869
$958$	−8.74888	−	26.9263i	−0.282664	−	0.869949i
$959$	17.3021	+	12.5707i	0.558713	+	0.405929i
$960$	5.62830	−	2.55529i	0.181653	−	0.0824716i
$961$	24.4595	−	17.7709i	0.789015	−	0.573253i
$962$	4.29668	+	3.12172i	0.138531	+	0.100648i
$963$	50.9062	+	36.9855i	1.64043	+	1.19184i
$964$	14.5749	−	10.5893i	0.469426	−	0.341058i
$965$	5.93243	+	52.7361i	0.190972	+	1.69764i
$966$	−17.8427	−	12.9634i	−0.574078	−	0.417092i
$967$	1.71845	+	5.28884i	0.0552616	+	0.170078i	0.974878	−	0.222740i	$-0.0715002\pi$
$967$	1.71845	+	5.28884i	0.0552616	+	0.170078i	−0.919616	+	0.392818i	$0.871500\pi$
$968$	−10.2975			−0.330976
$969$	15.0862	+	46.4306i	0.484639	+	1.49157i
$970$	1.88832	−	0.857310i	0.0606303	−	0.0275266i
$971$	−0.391531	+	1.20501i	−0.0125648	+	0.0386706i	−0.957142	−	0.289618i	$-0.906472\pi$
$971$	−0.391531	+	1.20501i	−0.0125648	+	0.0386706i	0.944578	+	0.328288i	$0.106472\pi$
$972$	5.38639	−	16.5776i	0.172769	−	0.531727i
$973$	29.3389	−	21.3160i	0.940563	−	0.683359i
$974$	−1.32502			−0.0424563
$975$	−9.09746	+	10.4054i	−0.291352	+	0.333240i
$976$	−4.64591			−0.148712
$977$	35.3400	−	25.6760i	1.13063	−	0.821447i	0.144840	−	0.989455i	$-0.453733\pi$
$977$	35.3400	−	25.6760i	1.13063	−	0.821447i	0.985786	+	0.168008i	$0.0537333\pi$
$978$	−9.56705	+	29.4443i	−0.305920	+	0.941526i
$979$	−1.47305	+	4.53358i	−0.0470789	+	0.144894i
$980$	−6.34669	−	1.30067i	−0.202738	−	0.0415483i
$981$	0.829823	+	2.55393i	0.0264942	+	0.0815408i
$982$	−36.1536			−1.15371
$983$	−14.6463	−	45.0766i	−0.467144	−	1.43772i	−0.856266	−	0.516535i	$-0.827222\pi$
$983$	−14.6463	−	45.0766i	−0.467144	−	1.43772i	0.389122	−	0.921186i	$-0.372778\pi$
$984$	−18.6406	−	13.5432i	−0.594242	−	0.431742i
$985$	−30.6389	−	6.27902i	−0.976237	−	0.200066i
$986$	1.07908	−	0.784001i	0.0343651	−	0.0249677i
$987$	−33.9423	−	24.6605i	−1.08039	−	0.784953i
$988$	5.69075	+	4.13457i	0.181047	+	0.131538i
$989$	−4.92702	+	3.57969i	−0.156670	+	0.113828i
$990$	−5.86753	−	6.42162i	−0.186482	−	0.204093i
$991$	15.5461	+	11.2949i	0.493838	+	0.358794i	0.806658	−	0.591018i	$-0.201274\pi$
$991$	15.5461	+	11.2949i	0.493838	+	0.358794i	−0.312820	+	0.949812i	$0.601274\pi$
$992$	0.270530	+	0.832606i	0.00858934	+	0.0264353i
$993$	−19.7828			−0.627788
$994$	0.0504648	+	0.155315i	0.00160065	+	0.00492628i
$995$	2.92915	+	26.0385i	0.0928602	+	0.825477i
$996$	−5.20378	+	16.0156i	−0.164888	+	0.507473i
$997$	4.41677	−	13.5934i	0.139880	−	0.430508i	−0.856437	−	0.516252i	$-0.827327\pi$
$997$	4.41677	−	13.5934i	0.139880	−	0.430508i	0.996317	+	0.0857442i	$0.0273268\pi$
$998$	13.9912	−	10.1652i	0.442883	−	0.321773i
$999$	24.0987			0.762449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.261.1	✓	24
25.16	even	5	inner	650.2.l.c.391.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.261.1	✓	24	1.1	even	1	trivial
650.2.l.c.391.1	yes	24	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.854221 + 2.62902i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.249965 + 2.22205i) q^{5} +(-0.854221 - 2.62902i) q^{6} -2.02551 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.75502 - 2.72818i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.854221 + 2.62902i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.249965 + 2.22205i) q^{5} +(-0.854221 - 2.62902i) q^{6} -2.02551 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.75502 - 2.72818i) q^{9} +(-1.50832 - 1.65075i) q^{10} +(-0.678057 + 0.492637i) q^{11} +(2.23638 + 1.62483i) q^{12} +(-0.809017 - 0.587785i) q^{13} +(1.63867 - 1.19056i) q^{14} +(-6.05535 - 1.24096i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.775855 + 2.38784i) q^{17} +4.64146 q^{18} +(-2.17367 - 6.68988i) q^{19} +(2.19054 + 0.448921i) q^{20} +(1.73023 - 5.32511i) q^{21} +(0.258995 - 0.797103i) q^{22} +(-3.18667 + 2.31525i) q^{23} -2.76432 q^{24} +(-4.87503 + 1.11087i) q^{25} +1.00000 q^{26} +(3.67093 - 2.66708i) q^{27} +(-0.625916 + 1.92637i) q^{28} +(-0.164166 + 0.505250i) q^{29} +(5.62830 - 2.55529i) q^{30} +(0.270530 + 0.832606i) q^{31} +1.00000 q^{32} +(-0.715944 - 2.20345i) q^{33} +(-2.03121 - 1.47576i) q^{34} +(-0.506306 - 4.50079i) q^{35} +(-3.75502 + 2.72818i) q^{36} +(4.29668 + 3.12172i) q^{37} +(5.69075 + 4.13457i) q^{38} +(2.23638 - 1.62483i) q^{39} +(-2.03605 + 0.924383i) q^{40} +(6.74330 + 4.89930i) q^{41} +(1.73023 + 5.32511i) q^{42} +1.54613 q^{43} +(0.258995 + 0.797103i) q^{44} +(5.12354 - 9.02580i) q^{45} +(1.21720 - 3.74616i) q^{46} +(2.31549 - 7.12636i) q^{47} +(2.23638 - 1.62483i) q^{48} -2.89732 q^{49} +(3.29103 - 3.76419i) q^{50} -6.94043 q^{51} +(-0.809017 + 0.587785i) q^{52} +(0.363519 - 1.11880i) q^{53} +(-1.40217 + 4.31543i) q^{54} +(-1.26416 - 1.38354i) q^{55} +(-0.625916 - 1.92637i) q^{56} +19.4446 q^{57} +(-0.164166 - 0.505250i) q^{58} +(-8.91212 - 6.47503i) q^{59} +(-3.05143 + 5.37551i) q^{60} +(3.75862 - 2.73080i) q^{61} +(-0.708257 - 0.514579i) q^{62} +(7.60582 + 5.52595i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.10386 - 1.94460i) q^{65} +(1.87436 + 1.36181i) q^{66} +(-0.877030 - 2.69922i) q^{67} +2.51072 q^{68} +(-3.36473 - 10.3556i) q^{69} +(3.05511 + 3.34361i) q^{70} +(-0.0249146 + 0.0766793i) q^{71} +(1.43429 - 4.41429i) q^{72} +(-9.67564 + 7.02977i) q^{73} -5.31099 q^{74} +(1.24385 - 13.7655i) q^{75} -7.03415 q^{76} +(1.37341 - 0.997840i) q^{77} +(-0.854221 + 2.62902i) q^{78} +(-1.07116 + 3.29670i) q^{79} +(1.10386 - 1.94460i) q^{80} +(-0.426827 - 1.31364i) q^{81} -8.33518 q^{82} +(1.88248 + 5.79368i) q^{83} +(-4.52981 - 3.29110i) q^{84} +(-5.11196 + 2.32086i) q^{85} +(-1.25085 + 0.908795i) q^{86} +(-1.18808 - 0.863191i) q^{87} +(-0.678057 - 0.492637i) q^{88} +(4.60134 - 3.34307i) q^{89} +(1.16020 + 10.3136i) q^{90} +(1.63867 + 1.19056i) q^{91} +(1.21720 + 3.74616i) q^{92} -2.42003 q^{93} +(2.31549 + 7.12636i) q^{94} +(14.3219 - 6.50225i) q^{95} +(-0.854221 + 2.62902i) q^{96} +(-0.286595 + 0.882048i) q^{97} +(2.34398 - 1.70300i) q^{98} +3.89012 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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