LMFDB - Embedded newform 25.2.d.a.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	25.d (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:	$0.199626005053$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	25.6
Dual form			25.2.d.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} +0.618034 q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.618034 + 1.90211i) q^{9} +3.61803 q^{10} +(-1.61803 - 4.97980i) q^{11} +(0.190983 - 0.587785i) q^{12} +(0.572949 - 1.76336i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.690983 - 2.12663i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(4.23607 + 3.07768i) q^{17} +3.23607 q^{18} +(-0.690983 - 0.502029i) q^{19} +(-0.427051 - 1.31433i) q^{20} +(-0.500000 + 0.363271i) q^{21} +(-6.85410 + 4.97980i) q^{22} +(1.16312 + 3.57971i) q^{23} +2.23607 q^{24} +(-4.04508 - 2.93893i) q^{25} -3.00000 q^{26} +(-1.54508 - 4.75528i) q^{27} +(-0.309017 + 0.224514i) q^{28} +(2.92705 - 2.12663i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(2.42705 + 1.76336i) q^{31} +3.38197 q^{32} +(4.23607 + 3.07768i) q^{33} +(2.61803 - 8.05748i) q^{34} +(-0.427051 + 1.31433i) q^{35} +(-0.381966 - 1.17557i) q^{36} +(-0.0729490 + 0.224514i) q^{37} +(-0.427051 + 1.31433i) q^{38} +(0.572949 + 1.76336i) q^{39} +(4.04508 - 2.93893i) q^{40} +(-0.236068 + 0.726543i) q^{41} +(0.809017 + 0.587785i) q^{42} -4.85410 q^{43} +(2.61803 + 1.90211i) q^{44} +(-3.61803 - 2.62866i) q^{45} +(4.92705 - 3.57971i) q^{46} +(-0.500000 + 0.363271i) q^{47} +(-1.50000 - 4.61653i) q^{48} -6.61803 q^{49} +(-2.50000 + 7.69421i) q^{50} -5.23607 q^{51} +(0.354102 + 1.08981i) q^{52} +(2.80902 - 2.04087i) q^{53} +(-6.54508 + 4.75528i) q^{54} +11.7082 q^{55} +(-1.11803 - 0.812299i) q^{56} +0.854102 q^{57} +(-4.73607 - 3.44095i) q^{58} +(-3.35410 + 10.3229i) q^{59} +(1.11803 + 0.812299i) q^{60} +(2.69098 + 8.28199i) q^{61} +(1.50000 - 4.61653i) q^{62} +(-0.381966 + 1.17557i) q^{63} +(1.30902 + 4.02874i) q^{64} +(3.35410 + 2.43690i) q^{65} +(2.61803 - 8.05748i) q^{66} +(-3.85410 - 2.80017i) q^{67} -3.23607 q^{68} +(-3.04508 - 2.21238i) q^{69} +2.23607 q^{70} +(5.35410 - 3.88998i) q^{71} +(3.61803 - 2.62866i) q^{72} +(-2.78115 - 8.55951i) q^{73} +0.381966 q^{74} +5.00000 q^{75} +0.527864 q^{76} +(-1.00000 - 3.07768i) q^{77} +(2.42705 - 1.76336i) q^{78} +(6.54508 - 4.75528i) q^{79} +(-8.78115 - 6.37988i) q^{80} +(-0.809017 - 0.587785i) q^{81} +1.23607 q^{82} +(5.04508 + 3.66547i) q^{83} +(0.118034 - 0.363271i) q^{84} +(-9.47214 + 6.88191i) q^{85} +(2.42705 + 7.46969i) q^{86} +(-1.11803 + 3.44095i) q^{87} +(-3.61803 + 11.1352i) q^{88} +(-2.76393 - 8.50651i) q^{89} +(-2.23607 + 6.88191i) q^{90} +(0.354102 - 1.08981i) q^{91} +(-1.88197 - 1.36733i) q^{92} -3.00000 q^{93} +(0.809017 + 0.587785i) q^{94} +(1.54508 - 1.12257i) q^{95} +(-2.73607 + 1.98787i) q^{96} +(3.11803 - 2.26538i) q^{97} +(3.30902 + 10.1841i) q^{98} +10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 + 9 * q^13 + q^14 - 5 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 - 5 * q^19 + 5 * q^20 - 2 * q^21 - 14 * q^22 - 11 * q^23 - 5 * q^25 - 12 * q^26 + 5 * q^27 + q^28 + 5 * q^29 - 5 * q^30 + 3 * q^31 + 18 * q^32 + 8 * q^33 + 6 * q^34 + 5 * q^35 - 6 * q^36 - 7 * q^37 + 5 * q^38 + 9 * q^39 + 5 * q^40 + 8 * q^41 + q^42 - 6 * q^43 + 6 * q^44 - 10 * q^45 + 13 * q^46 - 2 * q^47 - 6 * q^48 - 22 * q^49 - 10 * q^50 - 12 * q^51 - 12 * q^52 + 9 * q^53 - 15 * q^54 + 20 * q^55 - 10 * q^57 - 10 * q^58 + 13 * q^61 + 6 * q^62 - 6 * q^63 + 3 * q^64 + 6 * q^66 - 2 * q^67 - 4 * q^68 - q^69 + 8 * q^71 + 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^75 + 20 * q^76 - 4 * q^77 + 3 * q^78 + 15 * q^79 - 15 * q^80 - q^81 - 4 * q^82 + 9 * q^83 - 4 * q^84 - 20 * q^85 + 3 * q^86 - 10 * q^88 - 20 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^93 + q^94 - 5 * q^95 - 2 * q^96 + 8 * q^97 + 11 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	−0.796305	−	0.604896i	$-0.793215\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	0.329218	+	0.944254i	$0.393215\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	0.618034			0.233595			0.116797	−	0.993156i	$-0.462737\pi$
$7$	0.618034			0.233595			0.116797	+	0.993156i	$0.462737\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$	3.61803			1.14412
$11$	−1.61803	−	4.97980i	−0.487856	−	1.50147i	−0.827802	−	0.561020i	$-0.810409\pi$
$11$	−1.61803	−	4.97980i	−0.487856	−	1.50147i	0.339946	−	0.940445i	$-0.389591\pi$
$12$	0.190983	−	0.587785i	0.0551320	−	0.169679i
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	−0.839628	−	0.543161i	$-0.817227\pi$
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	0.998536	+	0.0540944i	$0.0172272\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.690983	−	2.12663i	−0.178411	−	0.549093i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.967786	−	0.251774i	$-0.0810139\pi$
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.0596113	+	0.998222i	$0.481014\pi$
$18$	3.23607			0.762749
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	0.505696	−	0.862712i	$-0.331236\pi$
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	−0.664219	+	0.747538i	$0.731236\pi$
$20$	−0.427051	−	1.31433i	−0.0954915	−	0.293893i
$21$	−0.500000	+	0.363271i	−0.109109	+	0.0792723i
$22$	−6.85410	+	4.97980i	−1.46130	+	1.06170i
$23$	1.16312	+	3.57971i	0.242527	+	0.746422i	0.996033	+	0.0889808i	$0.0283610\pi$
$23$	1.16312	+	3.57971i	0.242527	+	0.746422i	−0.753506	+	0.657441i	$0.771639\pi$
$24$	2.23607			0.456435
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	−3.00000			−0.588348
$27$	−1.54508	−	4.75528i	−0.297352	−	0.915155i
$28$	−0.309017	+	0.224514i	−0.0583987	+	0.0424292i
$29$	2.92705	−	2.12663i	0.543540	−	0.394905i	−0.281858	−	0.959456i	$-0.590951\pi$
$29$	2.92705	−	2.12663i	0.543540	−	0.394905i	0.825398	+	0.564551i	$0.190951\pi$
$30$	−2.92705	+	2.12663i	−0.534404	+	0.388267i
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$	3.38197			0.597853
$33$	4.23607	+	3.07768i	0.737405	+	0.535756i
$34$	2.61803	−	8.05748i	0.448989	−	1.38185i
$35$	−0.427051	+	1.31433i	−0.0721848	+	0.222162i
$36$	−0.381966	−	1.17557i	−0.0636610	−	0.195928i
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	−0.956874	−	0.290504i	$-0.906177\pi$
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	0.944881	+	0.327414i	$0.106177\pi$
$38$	−0.427051	+	1.31433i	−0.0692768	+	0.213212i
$39$	0.572949	+	1.76336i	0.0917453	+	0.282363i
$40$	4.04508	−	2.93893i	0.639584	−	0.464685i
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	−0.967797	−	0.251733i	$-0.918999\pi$
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	0.930929	+	0.365200i	$0.118999\pi$
$42$	0.809017	+	0.587785i	0.124834	+	0.0906972i
$43$	−4.85410			−0.740244			−0.370122	−	0.928983i	$-0.620684\pi$
$43$	−4.85410			−0.740244			−0.370122	+	0.928983i	$0.620684\pi$
$44$	2.61803	+	1.90211i	0.394683	+	0.286754i
$45$	−3.61803	−	2.62866i	−0.539345	−	0.391857i
$46$	4.92705	−	3.57971i	0.726454	−	0.527800i
$47$	−0.500000	+	0.363271i	−0.0729325	+	0.0529886i	−0.623654	−	0.781700i	$-0.714353\pi$
$47$	−0.500000	+	0.363271i	−0.0729325	+	0.0529886i	0.550722	+	0.834689i	$0.314353\pi$
$48$	−1.50000	−	4.61653i	−0.216506	−	0.666338i
$49$	−6.61803			−0.945433
$50$	−2.50000	+	7.69421i	−0.353553	+	1.08813i
$51$	−5.23607			−0.733196
$52$	0.354102	+	1.08981i	0.0491051	+	0.151130i
$53$	2.80902	−	2.04087i	0.385848	−	0.280335i	−0.377904	−	0.925845i	$-0.623355\pi$
$53$	2.80902	−	2.04087i	0.385848	−	0.280335i	0.763752	+	0.645510i	$0.223355\pi$
$54$	−6.54508	+	4.75528i	−0.890673	+	0.647112i
$55$	11.7082			1.57873
$56$	−1.11803	−	0.812299i	−0.149404	−	0.108548i
$57$	0.854102			0.113129
$58$	−4.73607	−	3.44095i	−0.621876	−	0.451820i
$59$	−3.35410	+	10.3229i	−0.436667	+	1.34392i	0.454702	+	0.890644i	$0.349746\pi$
$59$	−3.35410	+	10.3229i	−0.436667	+	1.34392i	−0.891369	+	0.453279i	$0.850254\pi$
$60$	1.11803	+	0.812299i	0.144338	+	0.104867i
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	0.961827	+	0.273659i	$0.0882338\pi$
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	−0.617282	+	0.786742i	$0.711766\pi$
$62$	1.50000	−	4.61653i	0.190500	−	0.586299i
$63$	−0.381966	+	1.17557i	−0.0481232	+	0.148108i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	3.35410	+	2.43690i	0.416025	+	0.302260i
$66$	2.61803	−	8.05748i	0.322258	−	0.991807i
$67$	−3.85410	−	2.80017i	−0.470853	−	0.342095i	0.326920	−	0.945052i	$-0.393989\pi$
$67$	−3.85410	−	2.80017i	−0.470853	−	0.342095i	−0.797774	+	0.602957i	$0.793989\pi$
$68$	−3.23607			−0.392431
$69$	−3.04508	−	2.21238i	−0.366585	−	0.266340i
$70$	2.23607			0.267261
$71$	5.35410	−	3.88998i	0.635415	−	0.461656i	−0.222857	−	0.974851i	$-0.571538\pi$
$71$	5.35410	−	3.88998i	0.635415	−	0.461656i	0.858272	+	0.513195i	$0.171538\pi$
$72$	3.61803	−	2.62866i	0.426389	−	0.309790i
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	−0.971210	−	0.238224i	$-0.923435\pi$
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	0.645701	−	0.763590i	$-0.276565\pi$
$74$	0.381966			0.0444026
$75$	5.00000			0.577350
$76$	0.527864			0.0605502
$77$	−1.00000	−	3.07768i	−0.113961	−	0.350735i
$78$	2.42705	−	1.76336i	0.274809	−	0.199661i
$79$	6.54508	−	4.75528i	0.736380	−	0.535011i	−0.155196	−	0.987884i	$-0.549601\pi$
$79$	6.54508	−	4.75528i	0.736380	−	0.535011i	0.891575	+	0.452873i	$0.149601\pi$
$80$	−8.78115	−	6.37988i	−0.981763	−	0.713292i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.23607			0.136501
$83$	5.04508	+	3.66547i	0.553770	+	0.402337i	0.829174	−	0.558991i	$-0.188811\pi$
$83$	5.04508	+	3.66547i	0.553770	+	0.402337i	−0.275404	+	0.961329i	$0.588811\pi$
$84$	0.118034	−	0.363271i	0.0128786	−	0.0396361i
$85$	−9.47214	+	6.88191i	−1.02740	+	0.746448i
$86$	2.42705	+	7.46969i	0.261716	+	0.805478i
$87$	−1.11803	+	3.44095i	−0.119866	+	0.368909i
$88$	−3.61803	+	11.1352i	−0.385684	+	1.18701i
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	−0.983894	−	0.178754i	$-0.942793\pi$
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	0.690918	−	0.722934i	$-0.257207\pi$
$90$	−2.23607	+	6.88191i	−0.235702	+	0.725417i
$91$	0.354102	−	1.08981i	0.0371200	−	0.114244i
$92$	−1.88197	−	1.36733i	−0.196209	−	0.142554i
$93$	−3.00000			−0.311086
$94$	0.809017	+	0.587785i	0.0834437	+	0.0606254i
$95$	1.54508	−	1.12257i	0.158522	−	0.115173i
$96$	−2.73607	+	1.98787i	−0.279249	+	0.202886i
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	−0.418130	−	0.908387i	$-0.637314\pi$
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	0.734718	+	0.678372i	$0.237314\pi$
$98$	3.30902	+	10.1841i	0.334261	+	1.02875i
$99$	10.4721			1.05249
$100$	3.09017			0.309017
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	2.61803	+	8.05748i	0.259224	+	0.797809i
$103$	−6.92705	+	5.03280i	−0.682543	+	0.495896i	−0.874200	−	0.485566i	$-0.838614\pi$
$103$	−6.92705	+	5.03280i	−0.682543	+	0.495896i	0.191658	+	0.981462i	$0.438614\pi$
$104$	−3.35410	+	2.43690i	−0.328897	+	0.238957i
$105$	−0.427051	−	1.31433i	−0.0416759	−	0.128265i
$106$	−4.54508	−	3.30220i	−0.441458	−	0.320738i
$107$	−16.4164			−1.58703			−0.793517	−	0.608548i	$-0.791752\pi$
$107$	−16.4164			−1.58703			−0.793517	+	0.608548i	$0.791752\pi$
$108$	2.50000	+	1.81636i	0.240563	+	0.174779i
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	−0.686904	−	0.726748i	$-0.741031\pi$
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	0.982889	−	0.184199i	$-0.0589691\pi$
$110$	−5.85410	−	18.0171i	−0.558167	−	1.71786i
$111$	−0.0729490	−	0.224514i	−0.00692401	−	0.0213099i
$112$	−0.927051	+	2.85317i	−0.0875981	+	0.269599i
$113$	5.20820	−	16.0292i	0.489947	−	1.50790i	−0.334740	−	0.942311i	$-0.608648\pi$
$113$	5.20820	−	16.0292i	0.489947	−	1.50790i	0.824687	−	0.565590i	$-0.191352\pi$
$114$	−0.427051	−	1.31433i	−0.0399970	−	0.123098i
$115$	−8.41641			−0.784834
$116$	−0.690983	+	2.12663i	−0.0641562	+	0.197452i
$117$	3.00000	+	2.17963i	0.277350	+	0.201507i
$118$	17.5623			1.61674
$119$	2.61803	+	1.90211i	0.239995	+	0.174366i
$120$	−1.54508	+	4.75528i	−0.141046	+	0.434096i
$121$	−13.2812	+	9.64932i	−1.20738	+	0.877211i
$122$	11.3992	−	8.28199i	1.03203	−	0.749817i
$123$	−0.236068	−	0.726543i	−0.0212855	−	0.0655101i
$124$	−1.85410			−0.166503
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$	2.00000			0.178174
$127$	6.14590	+	18.9151i	0.545360	+	1.67845i	0.720132	+	0.693837i	$0.244081\pi$
$127$	6.14590	+	18.9151i	0.545360	+	1.67845i	−0.174772	+	0.984609i	$0.555919\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	3.92705	−	2.85317i	0.345758	−	0.251208i
$130$	2.07295	−	6.37988i	0.181810	−	0.559553i
$131$	−5.50000	−	3.99598i	−0.480537	−	0.349131i	0.320996	−	0.947080i	$-0.395982\pi$
$131$	−5.50000	−	3.99598i	−0.480537	−	0.349131i	−0.801534	+	0.597950i	$0.795982\pi$
$132$	−3.23607			−0.281664
$133$	−0.427051	−	0.310271i	−0.0370300	−	0.0269039i
$134$	−2.38197	+	7.33094i	−0.205771	+	0.633297i
$135$	11.1803			0.962250
$136$	−3.61803	−	11.1352i	−0.310244	−	0.954832i
$137$	−3.69098	+	11.3597i	−0.315342	+	0.970523i	0.660271	+	0.751027i	$0.270441\pi$
$137$	−3.69098	+	11.3597i	−0.315342	+	0.970523i	−0.975613	+	0.219496i	$0.929559\pi$
$138$	−1.88197	+	5.79210i	−0.160204	+	0.493056i
$139$	1.54508	+	4.75528i	0.131052	+	0.403338i	0.994955	−	0.100321i	$-0.0319869\pi$
$139$	1.54508	+	4.75528i	0.131052	+	0.403338i	−0.863903	+	0.503659i	$0.831987\pi$
$140$	−0.263932	−	0.812299i	−0.0223063	−	0.0686518i
$141$	0.190983	−	0.587785i	0.0160837	−	0.0495004i
$142$	−8.66312	−	6.29412i	−0.726993	−	0.528191i
$143$	−9.70820			−0.811841
$144$	−7.85410	−	5.70634i	−0.654508	−	0.475528i
$145$	2.50000	+	7.69421i	0.207614	+	0.638969i
$146$	−11.7812	+	8.55951i	−0.975015	+	0.708390i
$147$	5.35410	−	3.88998i	0.441599	−	0.320840i
$148$	−0.0450850	−	0.138757i	−0.00370596	−	0.0114058i
$149$	−3.94427			−0.323127			−0.161564	−	0.986862i	$-0.551654\pi$
$149$	−3.94427			−0.323127			−0.161564	+	0.986862i	$0.551654\pi$
$150$	−2.50000	−	7.69421i	−0.204124	−	0.628230i
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	0.590170	+	1.81636i	0.0478691	+	0.147326i
$153$	−8.47214	+	6.15537i	−0.684932	+	0.497632i
$154$	−4.23607	+	3.07768i	−0.341352	+	0.248007i
$155$	−5.42705	+	3.94298i	−0.435911	+	0.316708i
$156$	−0.927051	−	0.673542i	−0.0742235	−	0.0539265i
$157$	13.1803			1.05191			0.525953	−	0.850514i	$-0.323709\pi$
$157$	13.1803			1.05191			0.525953	+	0.850514i	$0.323709\pi$
$158$	−10.5902	−	7.69421i	−0.842509	−	0.612118i
$159$	−1.07295	+	3.30220i	−0.0850904	+	0.261881i
$160$	−2.33688	+	7.19218i	−0.184747	+	0.568592i
$161$	0.718847	+	2.21238i	0.0566531	+	0.174360i
$162$	−0.500000	+	1.53884i	−0.0392837	+	0.120903i
$163$	3.39919	−	10.4616i	0.266245	−	0.819417i	−0.725159	−	0.688581i	$-0.758234\pi$
$163$	3.39919	−	10.4616i	0.266245	−	0.819417i	0.991404	−	0.130836i	$-0.0417662\pi$
$164$	−0.145898	−	0.449028i	−0.0113927	−	0.0350632i
$165$	−9.47214	+	6.88191i	−0.737405	+	0.535756i
$166$	3.11803	−	9.59632i	0.242006	−	0.744819i
$167$	−11.7812	−	8.55951i	−0.911653	−	0.662355i	0.0297794	−	0.999556i	$-0.490520\pi$
$167$	−11.7812	−	8.55951i	−0.911653	−	0.662355i	−0.941432	+	0.337202i	$0.890520\pi$
$168$	1.38197			0.106621
$169$	7.73607	+	5.62058i	0.595082	+	0.432352i
$170$	15.3262	+	11.1352i	1.17547	+	0.854028i
$171$	1.38197	−	1.00406i	0.105682	−	0.0767822i
$172$	2.42705	−	1.76336i	0.185061	−	0.134455i
$173$	5.83688	+	17.9641i	0.443770	+	1.36578i	0.883827	+	0.467813i	$0.154958\pi$
$173$	5.83688	+	17.9641i	0.443770	+	1.36578i	−0.440057	+	0.897970i	$0.645042\pi$
$174$	5.85410			0.443798
$175$	−2.50000	−	1.81636i	−0.188982	−	0.137304i
$176$	25.4164			1.91583
$177$	−3.35410	−	10.3229i	−0.252110	−	0.775914i
$178$	−11.7082	+	8.50651i	−0.877567	+	0.637590i
$179$	0.427051	−	0.310271i	0.0319193	−	0.0231907i	−0.571711	−	0.820455i	$-0.693720\pi$
$179$	0.427051	−	0.310271i	0.0319193	−	0.0231907i	0.603631	+	0.797264i	$0.293720\pi$
$180$	2.76393			0.206011
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	0.578977	−	0.815344i	$-0.303452\pi$
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	−0.596524	+	0.802595i	$0.703452\pi$
$182$	−1.85410			−0.137435
$183$	−7.04508	−	5.11855i	−0.520788	−	0.378374i
$184$	2.60081	−	8.00448i	0.191734	−	0.590098i
$185$	−0.427051	−	0.310271i	−0.0313974	−	0.0228116i
$186$	1.50000	+	4.61653i	0.109985	+	0.338500i
$187$	8.47214	−	26.0746i	0.619544	−	1.90676i
$188$	0.118034	−	0.363271i	0.00860851	−	0.0264943i
$189$	−0.954915	−	2.93893i	−0.0694598	−	0.213775i
$190$	−2.50000	−	1.81636i	−0.181369	−	0.131772i
$191$	−0.562306	+	1.73060i	−0.0406870	+	0.125222i	−0.969337	−	0.245736i	$-0.920970\pi$
$191$	−0.562306	+	1.73060i	−0.0406870	+	0.125222i	0.928650	+	0.370958i	$0.120970\pi$
$192$	−3.42705	−	2.48990i	−0.247326	−	0.179693i
$193$	7.70820			0.554849			0.277424	−	0.960747i	$-0.410519\pi$
$193$	7.70820			0.554849			0.277424	+	0.960747i	$0.410519\pi$
$194$	−5.04508	−	3.66547i	−0.362216	−	0.263165i
$195$	−4.14590			−0.296894
$196$	3.30902	−	2.40414i	0.236358	−	0.171724i
$197$	−3.00000	+	2.17963i	−0.213741	+	0.155292i	−0.689505	−	0.724281i	$-0.742172\pi$
$197$	−3.00000	+	2.17963i	−0.213741	+	0.155292i	0.475764	+	0.879573i	$0.342172\pi$
$198$	−5.23607	−	16.1150i	−0.372111	−	1.14524i
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$	3.45492	+	10.6331i	0.244299	+	0.751876i
$201$	4.76393			0.336022
$202$	−0.736068	−	2.26538i	−0.0517896	−	0.159392i
$203$	1.80902	−	1.31433i	0.126968	−	0.0922477i
$204$	2.61803	−	1.90211i	0.183299	−	0.133175i
$205$	−1.38197	−	1.00406i	−0.0965207	−	0.0701264i
$206$	11.2082	+	8.14324i	0.780913	+	0.567366i
$207$	−7.52786			−0.523223
$208$	7.28115	+	5.29007i	0.504857	+	0.366800i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$	−1.80902	+	1.31433i	−0.124834	+	0.0906972i
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	−0.999973	−	0.00735149i	$-0.997660\pi$
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	0.804674	−	0.593717i	$-0.202340\pi$
$212$	−0.663119	+	2.04087i	−0.0455432	+	0.140168i
$213$	−2.04508	+	6.29412i	−0.140127	+	0.431266i
$214$	8.20820	+	25.2623i	0.561101	+	1.72689i
$215$	3.35410	−	10.3229i	0.228748	−	0.704014i
$216$	−3.45492	+	10.6331i	−0.235077	+	0.723493i
$217$	1.50000	+	1.08981i	0.101827	+	0.0739814i
$218$	−16.1803			−1.09587
$219$	7.28115	+	5.29007i	0.492015	+	0.357470i
$220$	−5.85410	+	4.25325i	−0.394683	+	0.286754i
$221$	7.85410	−	5.70634i	0.528324	−	0.383850i
$222$	−0.309017	+	0.224514i	−0.0207399	+	0.0150684i
$223$	−0.0557281	−	0.171513i	−0.00373183	−	0.0114854i	0.949173	−	0.314754i	$-0.101922\pi$
$223$	−0.0557281	−	0.171513i	−0.00373183	−	0.0114854i	−0.952905	+	0.303269i	$0.901922\pi$
$224$	2.09017			0.139655
$225$	8.09017	−	5.87785i	0.539345	−	0.391857i
$226$	−27.2705			−1.81401
$227$	4.56231	+	14.0413i	0.302811	+	0.931956i	0.980485	+	0.196594i	$0.0629880\pi$
$227$	4.56231	+	14.0413i	0.302811	+	0.931956i	−0.677674	+	0.735362i	$0.737012\pi$
$228$	−0.427051	+	0.310271i	−0.0282821	+	0.0205482i
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.989847	−	0.142134i	$-0.954604\pi$
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.170702	+	0.985323i	$0.554604\pi$
$230$	4.20820	+	12.9515i	0.277481	+	0.853998i
$231$	2.61803	+	1.90211i	0.172254	+	0.125150i
$232$	−8.09017			−0.531146
$233$	2.38197	+	1.73060i	0.156048	+	0.113375i	0.663069	−	0.748558i	$-0.269254\pi$
$233$	2.38197	+	1.73060i	0.156048	+	0.113375i	−0.507021	+	0.861933i	$0.669254\pi$
$234$	1.85410	−	5.70634i	0.121206	−	0.373035i
$235$	−0.427051	−	1.31433i	−0.0278577	−	0.0857373i
$236$	−2.07295	−	6.37988i	−0.134937	−	0.415295i
$237$	−2.50000	+	7.69421i	−0.162392	+	0.499793i
$238$	1.61803	−	4.97980i	0.104882	−	0.322792i
$239$	−6.34346	−	19.5232i	−0.410324	−	1.26285i	−0.916367	−	0.400340i	$-0.868892\pi$
$239$	−6.34346	−	19.5232i	−0.410324	−	1.26285i	0.506043	−	0.862508i	$-0.331108\pi$
$240$	10.8541			0.700629
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	−0.922740	−	0.385423i	$-0.874055\pi$
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	0.973058	+	0.230559i	$0.0740554\pi$
$242$	21.4894	+	15.6129i	1.38139	+	1.00364i
$243$	16.0000			1.02640
$244$	−4.35410	−	3.16344i	−0.278743	−	0.202519i
$245$	4.57295	−	14.0741i	0.292155	−	0.899161i
$246$	−1.00000	+	0.726543i	−0.0637577	+	0.0463227i
$247$	−1.28115	+	0.930812i	−0.0815178	+	0.0592262i
$248$	−2.07295	−	6.37988i	−0.131632	−	0.405123i
$249$	−6.23607			−0.395195
$250$	−14.6353	−	10.6331i	−0.925615	−	0.672499i
$251$	−29.1803			−1.84185			−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803			−1.84185			−0.920923	+	0.389744i	$0.872564\pi$
$252$	−0.236068	−	0.726543i	−0.0148709	−	0.0457679i
$253$	15.9443	−	11.5842i	1.00241	−	0.728292i
$254$	26.0344	−	18.9151i	1.63355	−	1.18684i
$255$	3.61803	−	11.1352i	0.226570	−	0.697311i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	22.8541			1.42560			0.712800	−	0.701367i	$-0.247427\pi$
$257$	22.8541			1.42560			0.712800	+	0.701367i	$0.247427\pi$
$258$	−6.35410	−	4.61653i	−0.395589	−	0.287412i
$259$	−0.0450850	+	0.138757i	−0.00280144	+	0.00862196i
$260$	−2.56231			−0.158907
$261$	2.23607	+	6.88191i	0.138409	+	0.425980i
$262$	−3.39919	+	10.4616i	−0.210002	+	0.646321i
$263$	−3.37132	+	10.3759i	−0.207885	+	0.639803i	0.791698	+	0.610913i	$0.209197\pi$
$263$	−3.37132	+	10.3759i	−0.207885	+	0.639803i	−0.999583	+	0.0288905i	$0.990803\pi$
$264$	−3.61803	−	11.1352i	−0.222675	−	0.685322i
$265$	2.39919	+	7.38394i	0.147381	+	0.453592i
$266$	−0.263932	+	0.812299i	−0.0161827	+	0.0498053i
$267$	7.23607	+	5.25731i	0.442840	+	0.321742i
$268$	2.94427			0.179850
$269$	10.3262	+	7.50245i	0.629602	+	0.457433i	0.856262	−	0.516541i	$-0.172781\pi$
$269$	10.3262	+	7.50245i	0.629602	+	0.457433i	−0.226660	+	0.973974i	$0.572781\pi$
$270$	−5.59017	−	17.2048i	−0.340207	−	1.04705i
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	−0.373593	−	0.927593i	$-0.621874\pi$
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	0.766747	+	0.641950i	$0.221874\pi$
$272$	−20.5623	+	14.9394i	−1.24677	+	0.905834i
$273$	0.354102	+	1.08981i	0.0214312	+	0.0659585i
$274$	19.3262			1.16754
$275$	−8.09017	+	24.8990i	−0.487856	+	1.50147i
$276$	2.32624			0.140023
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	−0.866666	−	0.498889i	$-0.833742\pi$
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	0.407908	−	0.913023i	$-0.366258\pi$
$278$	6.54508	−	4.75528i	0.392548	−	0.285203i
$279$	−4.85410	+	3.52671i	−0.290607	+	0.211139i
$280$	2.50000	−	1.81636i	0.149404	−	0.108548i
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	0.317047	−	0.948410i	$-0.397309\pi$
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	−0.804018	+	0.594605i	$0.797309\pi$
$282$	−1.00000			−0.0595491
$283$	24.1525	+	17.5478i	1.43572	+	1.04311i	0.988916	+	0.148474i	$0.0474362\pi$
$283$	24.1525	+	17.5478i	1.43572	+	1.04311i	0.446799	+	0.894634i	$0.352564\pi$
$284$	−1.26393	+	3.88998i	−0.0750006	+	0.230828i
$285$	−0.590170	+	1.81636i	−0.0349587	+	0.107592i
$286$	4.85410	+	14.9394i	0.287029	+	0.883385i
$287$	−0.145898	+	0.449028i	−0.00861209	+	0.0265053i
$288$	−2.09017	+	6.43288i	−0.123164	+	0.379061i
$289$	3.21885	+	9.90659i	0.189344	+	0.582741i
$290$	10.5902	−	7.69421i	0.621876	−	0.451820i
$291$	−1.19098	+	3.66547i	−0.0698167	+	0.214874i
$292$	4.50000	+	3.26944i	0.263343	+	0.191330i
$293$	−19.5279			−1.14083			−0.570415	−	0.821357i	$-0.693218\pi$
$293$	−19.5279			−1.14083			−0.570415	+	0.821357i	$0.693218\pi$
$294$	−8.66312	−	6.29412i	−0.505243	−	0.367081i
$295$	−19.6353	−	14.2658i	−1.14321	−	0.830590i
$296$	0.427051	−	0.310271i	0.0248218	−	0.0180341i
$297$	−21.1803	+	15.3884i	−1.22901	+	0.892927i
$298$	1.97214	+	6.06961i	0.114243	+	0.351603i
$299$	6.97871			0.403589
$300$	−2.50000	+	1.81636i	−0.144338	+	0.104867i
$301$	−3.00000			−0.172917
$302$	−7.28115	−	22.4091i	−0.418983	−	1.28950i
$303$	−1.19098	+	0.865300i	−0.0684202	+	0.0497102i
$304$	3.35410	−	2.43690i	0.192371	−	0.139766i
$305$	−19.4721			−1.11497
$306$	13.7082	+	9.95959i	0.783646	+	0.569352i
$307$	9.23607			0.527130			0.263565	−	0.964642i	$-0.415102\pi$
$307$	9.23607			0.527130			0.263565	+	0.964642i	$0.415102\pi$
$308$	1.61803	+	1.17557i	0.0921960	+	0.0669843i
$309$	2.64590	−	8.14324i	0.150520	−	0.463253i
$310$	8.78115	+	6.37988i	0.498736	+	0.362353i
$311$	2.62868	+	8.09024i	0.149059	+	0.458755i	0.997511	−	0.0705172i	$-0.0224650\pi$
$311$	2.62868	+	8.09024i	0.149059	+	0.458755i	−0.848452	+	0.529272i	$0.822465\pi$
$312$	1.28115	−	3.94298i	0.0725310	−	0.223227i
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	0.691138	+	0.722723i	$0.257110\pi$
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	−0.983948	+	0.178454i	$0.942890\pi$
$314$	−6.59017	−	20.2825i	−0.371905	−	1.14461i
$315$	−2.23607	−	1.62460i	−0.125988	−	0.0915358i
$316$	−1.54508	+	4.75528i	−0.0869178	+	0.267506i
$317$	−6.19098	−	4.49801i	−0.347720	−	0.252634i	0.400192	−	0.916431i	$-0.368944\pi$
$317$	−6.19098	−	4.49801i	−0.347720	−	0.252634i	−0.747912	+	0.663798i	$0.768944\pi$
$318$	5.61803			0.315044
$319$	−15.3262	−	11.1352i	−0.858105	−	0.623449i
$320$	−9.47214			−0.529508
$321$	13.2812	−	9.64932i	0.741282	−	0.538573i
$322$	3.04508	−	2.21238i	0.169696	−	0.123291i
$323$	−1.38197	−	4.25325i	−0.0768946	−	0.236657i
$324$	0.618034			0.0343352
$325$	−7.50000	+	5.44907i	−0.416025	+	0.302260i
$326$	−17.7984			−0.985761
$327$	3.09017	+	9.51057i	0.170887	+	0.525935i
$328$	1.38197	−	1.00406i	0.0763063	−	0.0554398i
$329$	−0.309017	+	0.224514i	−0.0170367	+	0.0123779i
$330$	15.3262	+	11.1352i	0.843682	+	0.612971i
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.967967	−	0.251078i	$-0.0807850\pi$
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.0603290	+	0.998179i	$0.480785\pi$
$332$	−3.85410			−0.211521
$333$	−0.381966	−	0.277515i	−0.0209316	−	0.0152077i
$334$	−7.28115	+	22.4091i	−0.398407	+	1.22617i
$335$	8.61803	−	6.26137i	0.470853	−	0.342095i
$336$	−0.927051	−	2.85317i	−0.0505748	−	0.155653i
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	−0.862936	−	0.505314i	$-0.831377\pi$
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	0.995146	+	0.0984135i	$0.0313768\pi$
$338$	4.78115	−	14.7149i	0.260060	−	0.800384i
$339$	5.20820	+	16.0292i	0.282871	+	0.870587i
$340$	2.23607	−	6.88191i	0.121268	−	0.373224i
$341$	4.85410	−	14.9394i	0.262864	−	0.809013i
$342$	−2.23607	−	1.62460i	−0.120913	−	0.0878482i
$343$	−8.41641			−0.454443
$344$	8.78115	+	6.37988i	0.473448	+	0.343980i
$345$	6.80902	−	4.94704i	0.366585	−	0.266340i
$346$	24.7254	−	17.9641i	1.32925	−	0.965755i
$347$	16.1074	−	11.7027i	0.864690	−	0.628234i	−0.0644668	−	0.997920i	$-0.520535\pi$
$347$	16.1074	−	11.7027i	0.864690	−	0.628234i	0.929157	+	0.369686i	$0.120535\pi$
$348$	−0.690983	−	2.12663i	−0.0370406	−	0.113999i
$349$	21.7082			1.16201			0.581007	−	0.813899i	$-0.302659\pi$
$349$	21.7082			1.16201			0.581007	+	0.813899i	$0.302659\pi$
$350$	−1.54508	+	4.75528i	−0.0825883	+	0.254181i
$351$	−9.27051			−0.494823
$352$	−5.47214	−	16.8415i	−0.291666	−	0.897655i
$353$	−10.4443	+	7.58821i	−0.555893	+	0.403880i	−0.829953	−	0.557833i	$-0.811633\pi$
$353$	−10.4443	+	7.58821i	−0.555893	+	0.403880i	0.274061	+	0.961712i	$0.411633\pi$
$354$	−14.2082	+	10.3229i	−0.755158	+	0.548654i
$355$	4.57295	+	14.0741i	0.242707	+	0.746975i
$356$	4.47214	+	3.24920i	0.237023	+	0.172207i
$357$	−3.23607			−0.171271
$358$	−0.690983	−	0.502029i	−0.0365196	−	0.0265330i
$359$	4.24671	−	13.0700i	0.224133	−	0.689810i	−0.774246	−	0.632885i	$-0.781870\pi$
$359$	4.24671	−	13.0700i	0.224133	−	0.689810i	0.998378	−	0.0569247i	$-0.0181295\pi$
$360$	3.09017	+	9.51057i	0.162866	+	0.501251i
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$	−0.145898	+	0.449028i	−0.00766823	+	0.0236004i
$363$	5.07295	−	15.6129i	0.266261	−	0.819466i
$364$	0.218847	+	0.673542i	0.0114707	+	0.0353032i
$365$	20.1246			1.05337
$366$	−4.35410	+	13.4005i	−0.227593	+	0.700458i
$367$	20.6803	+	15.0251i	1.07950	+	0.784306i	0.977597	−	0.210488i	$-0.0675051\pi$
$367$	20.6803	+	15.0251i	1.07950	+	0.784306i	0.101908	+	0.994794i	$0.467505\pi$
$368$	−18.2705			−0.952416
$369$	−1.23607	−	0.898056i	−0.0643471	−	0.0467509i
$370$	−0.263932	+	0.812299i	−0.0137212	+	0.0422294i
$371$	1.73607	−	1.26133i	0.0901322	−	0.0654848i
$372$	1.50000	−	1.08981i	0.0777714	−	0.0565042i
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	−0.874234	−	0.485505i	$-0.838636\pi$
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	0.421897	−	0.906644i	$-0.361364\pi$
$374$	−44.3607			−2.29384
$375$	−3.45492	+	10.6331i	−0.178411	+	0.549093i
$376$	1.38197			0.0712695
$377$	−2.07295	−	6.37988i	−0.106762	−	0.328581i
$378$	−4.04508	+	2.93893i	−0.208057	+	0.151162i
$379$	−11.8090	+	8.57975i	−0.606588	+	0.440712i	−0.848211	−	0.529658i	$-0.822320\pi$
$379$	−11.8090	+	8.57975i	−0.606588	+	0.440712i	0.241623	+	0.970370i	$0.422320\pi$
$380$	−0.364745	+	1.12257i	−0.0187110	+	0.0575866i
$381$	−16.0902	−	11.6902i	−0.824324	−	0.598907i
$382$	2.94427			0.150642
$383$	−26.9894	−	19.6089i	−1.37909	−	1.00197i	−0.996964	−	0.0778591i	$-0.975192\pi$
$383$	−26.9894	−	19.6089i	−1.37909	−	1.00197i	−0.382127	−	0.924110i	$-0.624808\pi$
$384$	−4.20820	+	12.9515i	−0.214749	+	0.660929i
$385$	7.23607			0.368784
$386$	−3.85410	−	11.8617i	−0.196169	−	0.603745i
$387$	3.00000	−	9.23305i	0.152499	−	0.469342i
$388$	−0.736068	+	2.26538i	−0.0373682	+	0.115007i
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	0.997119	+	0.0758507i	$0.0241672\pi$
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	−0.762102	+	0.647456i	$0.775833\pi$
$390$	2.07295	+	6.37988i	0.104968	+	0.323058i
$391$	−6.09017	+	18.7436i	−0.307993	+	0.947905i
$392$	11.9721	+	8.69827i	0.604684	+	0.439329i
$393$	6.79837			0.342933
$394$	4.85410	+	3.52671i	0.244546	+	0.177673i
$395$	5.59017	+	17.2048i	0.281272	+	0.865666i
$396$	−5.23607	+	3.80423i	−0.263122	+	0.191170i
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.992047	−	0.125870i	$-0.959828\pi$
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.186850	+	0.982388i	$0.559828\pi$
$398$	8.78115	+	27.0256i	0.440159	+	1.35467i
$399$	0.527864			0.0264263
$400$	19.6353	−	14.2658i	0.981763	−	0.713292i
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$	−2.38197	−	7.33094i	−0.118802	−	0.365634i
$403$	4.50000	−	3.26944i	0.224161	−	0.162862i
$404$	−0.736068	+	0.534785i	−0.0366208	+	0.0266065i
$405$	1.80902	−	1.31433i	0.0898908	−	0.0653095i
$406$	−2.92705	−	2.12663i	−0.145267	−	0.105543i
$407$	1.23607			0.0612696
$408$	9.47214	+	6.88191i	0.468941	+	0.340705i
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	−0.938229	−	0.346016i	$-0.887534\pi$
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	0.962426	+	0.271544i	$0.0875344\pi$
$410$	−0.854102	+	2.62866i	−0.0421811	+	0.129820i
$411$	−3.69098	−	11.3597i	−0.182063	−	0.560332i
$412$	1.63525	−	5.03280i	0.0805632	−	0.247948i
$413$	−2.07295	+	6.37988i	−0.102003	+	0.313933i
$414$	3.76393	+	11.5842i	0.184987	+	0.569332i
$415$	−11.2812	+	8.19624i	−0.553770	+	0.402337i
$416$	1.93769	−	5.96361i	0.0950033	−	0.292390i
$417$	−4.04508	−	2.93893i	−0.198089	−	0.143920i
$418$	7.23607			0.353928
$419$	7.66312	+	5.56758i	0.374368	+	0.271994i	0.759020	−	0.651068i	$-0.225679\pi$
$419$	7.66312	+	5.56758i	0.374368	+	0.271994i	−0.384652	+	0.923062i	$0.625679\pi$
$420$	0.690983	+	0.502029i	0.0337165	+	0.0244965i
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.998841	−	0.0481252i	$-0.984675\pi$
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.262889	+	0.964826i	$0.584675\pi$
$422$	−12.0172	+	8.73102i	−0.584989	+	0.425020i
$423$	−0.381966	−	1.17557i	−0.0185718	−	0.0571582i
$424$	−7.76393			−0.377050
$425$	−8.09017	−	24.8990i	−0.392431	−	1.20778i
$426$	10.7082			0.518814
$427$	1.66312	+	5.11855i	0.0804840	+	0.247704i
$428$	8.20820	−	5.96361i	0.396759	−	0.288262i
$429$	7.85410	−	5.70634i	0.379200	−	0.275505i
$430$	−17.5623			−0.846930
$431$	24.1353	+	17.5353i	1.16255	+	0.844645i	0.990099	−	0.140372i	$-0.0448299\pi$
$431$	24.1353	+	17.5353i	1.16255	+	0.844645i	0.172456	+	0.985017i	$0.444830\pi$
$432$	24.2705			1.16772
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.0729839	−	0.997333i	$-0.523252\pi$
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.971073	+	0.238781i	$0.923252\pi$
$434$	0.927051	−	2.85317i	0.0444999	−	0.136957i
$435$	−6.54508	−	4.75528i	−0.313813	−	0.227998i
$436$	1.90983	+	5.87785i	0.0914643	+	0.281498i
$437$	0.993422	−	3.05744i	0.0475218	−	0.146257i
$438$	4.50000	−	13.8496i	0.215018	−	0.661758i
$439$	−12.6631	−	38.9731i	−0.604378	−	1.86008i	−0.501013	−	0.865440i	$-0.667039\pi$
$439$	−12.6631	−	38.9731i	−0.604378	−	1.86008i	−0.103365	−	0.994644i	$-0.532961\pi$
$440$	−21.1803	−	15.3884i	−1.00973	−	0.733614i
$441$	4.09017	−	12.5882i	0.194770	−	0.599440i
$442$	−12.7082	−	9.23305i	−0.604468	−	0.439171i
$443$	29.9443			1.42270			0.711348	−	0.702840i	$-0.248085\pi$
$443$	29.9443			1.42270			0.711348	+	0.702840i	$0.248085\pi$
$444$	0.118034	+	0.0857567i	0.00560165	+	0.00406983i
$445$	20.0000			0.948091
$446$	−0.236068	+	0.171513i	−0.0111781	+	0.00812140i
$447$	3.19098	−	2.31838i	0.150928	−	0.109656i
$448$	0.809017	+	2.48990i	0.0382225	+	0.117637i
$449$	4.67376			0.220568			0.110284	−	0.993900i	$-0.464824\pi$
$449$	4.67376			0.220568			0.110284	+	0.993900i	$0.464824\pi$
$450$	−13.0902	−	9.51057i	−0.617077	−	0.448332i
$451$	4.00000			0.188353
$452$	3.21885	+	9.90659i	0.151402	+	0.465967i
$453$	−11.7812	+	8.55951i	−0.553527	+	0.402161i
$454$	19.3262	−	14.0413i	0.907025	−	0.658992i
$455$	2.07295	+	1.50609i	0.0971813	+	0.0706064i
$456$	−1.54508	−	1.12257i	−0.0723552	−	0.0525692i
$457$	−21.4164			−1.00182			−0.500909	−	0.865500i	$-0.667001\pi$
$457$	−21.4164			−1.00182			−0.500909	+	0.865500i	$0.667001\pi$
$458$	28.4164	+	20.6457i	1.32781	+	0.964712i
$459$	8.09017	−	24.8990i	0.377617	−	1.16218i
$460$	4.20820	−	3.05744i	0.196209	−	0.142554i
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	0.956782	−	0.290807i	$-0.0939238\pi$
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	−0.944985	+	0.327114i	$0.893924\pi$
$462$	1.61803	−	4.97980i	0.0752778	−	0.231681i
$463$	−7.45492	+	22.9439i	−0.346459	+	1.06629i	0.614339	+	0.789042i	$0.289423\pi$
$463$	−7.45492	+	22.9439i	−0.346459	+	1.06629i	−0.960798	+	0.277250i	$0.910577\pi$
$464$	5.42705	+	16.7027i	0.251945	+	0.775405i
$465$	2.07295	−	6.37988i	0.0961307	−	0.295860i
$466$	1.47214	−	4.53077i	0.0681954	−	0.209884i
$467$	−22.2082	−	16.1352i	−1.02767	−	0.746648i	−0.0598315	−	0.998208i	$-0.519056\pi$
$467$	−22.2082	−	16.1352i	−1.02767	−	0.746648i	−0.967842	+	0.251560i	$0.919056\pi$
$468$	−2.29180			−0.105938
$469$	−2.38197	−	1.73060i	−0.109989	−	0.0799117i
$470$	−1.80902	+	1.31433i	−0.0834437	+	0.0606254i
$471$	−10.6631	+	7.74721i	−0.491331	+	0.356973i
$472$	19.6353	−	14.2658i	0.903786	−	0.656639i
$473$	7.85410	+	24.1724i	0.361132	+	1.11145i
$474$	13.0902			0.601251
$475$	1.31966	+	4.06150i	0.0605502	+	0.186354i
$476$	−2.00000			−0.0916698
$477$	2.14590	+	6.60440i	0.0982539	+	0.302394i
$478$	−26.8713	+	19.5232i	−1.22907	+	0.892969i
$479$	8.78115	−	6.37988i	0.401221	−	0.291504i	−0.368817	−	0.929502i	$-0.620237\pi$
$479$	8.78115	−	6.37988i	0.401221	−	0.291504i	0.770038	+	0.637998i	$0.220237\pi$
$480$	−2.33688	−	7.19218i	−0.106664	−	0.328277i
$481$	0.354102	+	0.257270i	0.0161457	+	0.0117305i
$482$	−4.09017			−0.186302
$483$	−1.88197	−	1.36733i	−0.0856324	−	0.0622156i
$484$	3.13525	−	9.64932i	0.142512	−	0.438606i
$485$	2.66312	+	8.19624i	0.120926	+	0.372172i
$486$	−8.00000	−	24.6215i	−0.362887	−	1.11685i
$487$	−11.2533	+	34.6341i	−0.509935	+	1.56942i	0.282377	+	0.959303i	$0.408877\pi$
$487$	−11.2533	+	34.6341i	−0.509935	+	1.56942i	−0.792312	+	0.610116i	$0.791123\pi$
$488$	6.01722	−	18.5191i	0.272387	−	0.838320i
$489$	3.39919	+	10.4616i	0.153717	+	0.473091i
$490$	−23.9443			−1.08169
$491$	−13.3647	+	41.1325i	−0.603143	+	1.85628i	−0.0940550	+	0.995567i	$0.529983\pi$
$491$	−13.3647	+	41.1325i	−0.603143	+	1.85628i	−0.509088	+	0.860715i	$0.670017\pi$
$492$	0.381966	+	0.277515i	0.0172204	+	0.0125113i
$493$	18.9443			0.853207
$494$	2.07295	+	1.50609i	0.0932664	+	0.0677620i
$495$	−7.23607	+	22.2703i	−0.325237	+	1.00098i
$496$	−11.7812	+	8.55951i	−0.528989	+	0.384333i
$497$	3.30902	−	2.40414i	0.148430	−	0.107840i
$498$	3.11803	+	9.59632i	0.139722	+	0.430021i
$499$	7.56231			0.338535			0.169268	−	0.985570i	$-0.445860\pi$
$499$	7.56231			0.338535			0.169268	+	0.985570i	$0.445860\pi$
$500$	−2.13525	+	6.57164i	−0.0954915	+	0.293893i
$501$	14.5623			0.650596
$502$	14.5902	+	44.9039i	0.651191	+	2.00416i
$503$	30.2705	−	21.9928i	1.34970	−	0.980611i	0.350669	−	0.936500i	$-0.385954\pi$
$503$	30.2705	−	21.9928i	1.34970	−	0.980611i	0.999027	−	0.0441115i	$-0.0140457\pi$
$504$	2.23607	−	1.62460i	0.0996024	−	0.0723654i
$505$	−1.01722	+	3.13068i	−0.0452657	+	0.139314i
$506$	−25.7984	−	18.7436i	−1.14688	−	0.833255i
$507$	−9.56231			−0.424677
$508$	−9.94427	−	7.22494i	−0.441206	−	0.320555i
$509$	−6.28115	+	19.3314i	−0.278407	+	0.856849i	0.709891	+	0.704312i	$0.248744\pi$
$509$	−6.28115	+	19.3314i	−0.278407	+	0.856849i	−0.988298	+	0.152537i	$0.951256\pi$
$510$	−18.9443			−0.838866
$511$	−1.71885	−	5.29007i	−0.0760373	−	0.234019i
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	−1.31966	+	4.06150i	−0.0582644	+	0.179319i
$514$	−11.4271	−	35.1688i	−0.504026	−	1.55123i
$515$	−5.91641	−	18.2088i	−0.260708	−	0.802377i
$516$	−0.927051	+	2.85317i	−0.0408111	+	0.125604i
$517$	2.61803	+	1.90211i	0.115141	+	0.0836548i
$518$	0.236068			0.0103722
$519$	−15.2812	−	11.1024i	−0.670768	−	0.487342i
$520$	−2.86475	−	8.81678i	−0.125627	−	0.386641i
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.970412	−	0.241453i	$-0.922376\pi$
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.0702381	+	0.997530i	$0.522376\pi$
$522$	9.47214	−	6.88191i	0.414584	−	0.301213i
$523$	−4.06231	−	12.5025i	−0.177632	−	0.546696i	0.822112	−	0.569326i	$-0.192796\pi$
$523$	−4.06231	−	12.5025i	−0.177632	−	0.546696i	−0.999744	+	0.0226305i	$0.992796\pi$
$524$	4.20163			0.183549
$525$	3.09017			0.134866
$526$	17.6525			0.769685
$527$	4.85410	+	14.9394i	0.211448	+	0.650770i
$528$	−20.5623	+	14.9394i	−0.894860	+	0.650153i
$529$	7.14590	−	5.19180i	0.310691	−	0.225730i
$530$	10.1631	−	7.38394i	0.441458	−	0.320738i
$531$	−17.5623	−	12.7598i	−0.762139	−	0.553727i
$532$	0.326238			0.0141442
$533$	1.14590	+	0.832544i	0.0496344	+	0.0360615i
$534$	4.47214	−	13.7638i	0.193528	−	0.595619i
$535$	11.3435	−	34.9116i	0.490420	−	1.50936i
$536$	3.29180	+	10.1311i	0.142184	+	0.437597i
$537$	−0.163119	+	0.502029i	−0.00703910	+	0.0216641i
$538$	6.38197	−	19.6417i	0.275146	−	0.846813i
$539$	10.7082	+	32.9565i	0.461235	+	1.41954i
$540$	−5.59017	+	4.06150i	−0.240563	+	0.174779i
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	−0.592462	−	0.805599i	$-0.701844\pi$
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	0.952831	−	0.303503i	$-0.0981561\pi$
$542$	−10.4721	−	7.60845i	−0.449817	−	0.326811i
$543$	0.291796			0.0125222
$544$	14.3262	+	10.4086i	0.614232	+	0.446266i
$545$	18.0902	+	13.1433i	0.774898	+	0.562996i
$546$	1.50000	−	1.08981i	0.0641941	−	0.0466397i
$547$	17.2254	−	12.5150i	0.736506	−	0.535103i	−0.155109	−	0.987897i	$-0.549573\pi$
$547$	17.2254	−	12.5150i	0.736506	−	0.535103i	0.891615	+	0.452794i	$0.149573\pi$
$548$	−2.28115	−	7.02067i	−0.0974460	−	0.299908i
$549$	−17.4164			−0.743314
$550$	42.3607			1.80627
$551$	−3.09017			−0.131646
$552$	2.60081	+	8.00448i	0.110698	+	0.340693i
$553$	4.04508	−	2.93893i	0.172015	−	0.124976i
$554$	−32.3435	+	23.4989i	−1.37414	+	0.998373i
$555$	0.527864			0.0224066
$556$	−2.50000	−	1.81636i	−0.106024	−	0.0770307i
$557$	4.76393			0.201854			0.100927	−	0.994894i	$-0.467819\pi$
$557$	4.76393			0.201854			0.100927	+	0.994894i	$0.467819\pi$
$558$	7.85410	+	5.70634i	0.332491	+	0.241569i
$559$	−2.78115	+	8.55951i	−0.117630	+	0.362029i
$560$	−5.42705	−	3.94298i	−0.229335	−	0.166621i
$561$	8.47214	+	26.0746i	0.357694	+	1.10087i
$562$	−5.04508	+	15.5272i	−0.212814	+	0.654974i
$563$	2.28115	−	7.02067i	0.0961391	−	0.295886i	−0.891410	−	0.453198i	$-0.850283\pi$
$563$	2.28115	−	7.02067i	0.0961391	−	0.295886i	0.987549	+	0.157312i	$0.0502830\pi$
$564$	0.118034	+	0.363271i	0.00497013	+	0.0152965i
$565$	30.4894	+	22.1518i	1.28270	+	0.931934i
$566$	14.9271	−	45.9407i	0.627431	−	1.93103i
$567$	−0.500000	−	0.363271i	−0.0209980	−	0.0152560i
$568$	−14.7984			−0.620926
$569$	−16.6074	−	12.0660i	−0.696218	−	0.505832i	0.182480	−	0.983210i	$-0.441587\pi$
$569$	−16.6074	−	12.0660i	−0.696218	−	0.505832i	−0.878698	+	0.477377i	$0.841587\pi$
$570$	3.09017			0.129433
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	−0.441695	−	0.897165i	$-0.645623\pi$
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	0.716764	+	0.697316i	$0.245623\pi$
$572$	4.85410	−	3.52671i	0.202960	−	0.147459i
$573$	−0.562306	−	1.73060i	−0.0234907	−	0.0722968i
$574$	0.763932			0.0318859
$575$	5.81559	−	17.8986i	0.242527	−	0.746422i
$576$	−8.47214			−0.353006
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	−0.893571	−	0.448923i	$-0.851808\pi$
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	0.459044	−	0.888414i	$-0.348192\pi$
$578$	13.6353	−	9.90659i	0.567152	−	0.412060i
$579$	−6.23607	+	4.53077i	−0.259162	+	0.188292i
$580$	−4.04508	−	2.93893i	−0.167963	−	0.122032i
$581$	3.11803	+	2.26538i	0.129358	+	0.0939840i
$582$	6.23607			0.258493
$583$	−14.7082	−	10.6861i	−0.609152	−	0.442575i
$584$	−6.21885	+	19.1396i	−0.257338	+	0.792004i
$585$	−6.70820	+	4.87380i	−0.277350	+	0.201507i
$586$	9.76393	+	30.0503i	0.403344	+	1.24137i
$587$	1.63525	−	5.03280i	0.0674942	−	0.207726i	−0.911621	−	0.411032i	$-0.865169\pi$
$587$	1.63525	−	5.03280i	0.0674942	−	0.207726i	0.979115	+	0.203306i	$0.0651686\pi$
$588$	−1.26393	+	3.88998i	−0.0521237	+	0.160420i
$589$	−0.791796	−	2.43690i	−0.0326254	−	0.100411i
$590$	−12.1353	+	37.3485i	−0.499601	+	1.53761i
$591$	1.14590	−	3.52671i	0.0471359	−	0.145070i
$592$	−0.927051	−	0.673542i	−0.0381016	−	0.0276824i
$593$	−10.9098			−0.448013			−0.224007	−	0.974588i	$-0.571914\pi$
$593$	−10.9098			−0.448013			−0.224007	+	0.974588i	$0.571914\pi$
$594$	34.2705	+	24.8990i	1.40614	+	1.02162i
$595$	−5.85410	+	4.25325i	−0.239995	+	0.174366i
$596$	1.97214	−	1.43284i	0.0807818	−	0.0586914i
$597$	14.2082	−	10.3229i	0.581503	−	0.422487i
$598$	−3.48936	−	10.7391i	−0.142690	−	0.439156i
$599$	−9.47214			−0.387021			−0.193510	−	0.981098i	$-0.561987\pi$
$599$	−9.47214			−0.387021			−0.193510	+	0.981098i	$0.561987\pi$
$600$	−9.04508	−	6.57164i	−0.369264	−	0.268286i
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	1.50000	+	4.61653i	0.0611354	+	0.188156i
$603$	7.70820	−	5.60034i	0.313902	−	0.228063i
$604$	−7.28115	+	5.29007i	−0.296266	+	0.215250i
$605$	−11.3435	−	34.9116i	−0.461177	−	1.41936i
$606$	1.92705	+	1.40008i	0.0782811	+	0.0568745i
$607$	−35.5623			−1.44343			−0.721715	−	0.692191i	$-0.756646\pi$
$607$	−35.5623			−1.44343			−0.721715	+	0.692191i	$0.756646\pi$
$608$	−2.33688	−	1.69784i	−0.0947730	−	0.0688566i
$609$	−0.690983	+	2.12663i	−0.0280000	+	0.0861753i
$610$	9.73607	+	29.9645i	0.394202	+	1.21323i
$611$	0.354102	+	1.08981i	0.0143254	+	0.0440891i
$612$	2.00000	−	6.15537i	0.0808452	−	0.248816i
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	−0.999977	−	0.00685287i	$-0.997819\pi$
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	0.813026	+	0.582227i	$0.197819\pi$
$614$	−4.61803	−	14.2128i	−0.186369	−	0.573584i
$615$	1.70820			0.0688814
$616$	−2.23607	+	6.88191i	−0.0900937	+	0.277280i
$617$	−11.5172	−	8.36775i	−0.463666	−	0.336873i	0.331302	−	0.943525i	$-0.392512\pi$
$617$	−11.5172	−	8.36775i	−0.463666	−	0.336873i	−0.794968	+	0.606652i	$0.792512\pi$
$618$	−13.8541			−0.557294
$619$	−24.6976	−	17.9438i	−0.992679	−	0.721223i	−0.0321727	−	0.999482i	$-0.510243\pi$
$619$	−24.6976	−	17.9438i	−0.992679	−	0.721223i	−0.960506	+	0.278259i	$0.910243\pi$
$620$	1.28115	−	3.94298i	0.0514523	−	0.158354i
$621$	15.2254	−	11.0619i	0.610975	−	0.443900i
$622$	11.1353	−	8.09024i	0.446483	−	0.324389i
$623$	−1.70820	−	5.25731i	−0.0684377	−	0.210630i
$624$	−9.00000			−0.360288
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	27.1246			1.08412
$627$	−1.38197	−	4.25325i	−0.0551904	−	0.169859i
$628$	−6.59017	+	4.78804i	−0.262976	+	0.191064i
$629$	−1.00000	+	0.726543i	−0.0398726	+	0.0289691i
$630$	−1.38197	+	4.25325i	−0.0550588	+	0.169454i
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	0.740290	−	0.672288i	$-0.234688\pi$
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	−0.410622	+	0.911806i	$0.634688\pi$
$632$	−18.0902			−0.719588
$633$	7.42705	+	5.39607i	0.295199	+	0.214474i
$634$	−3.82624	+	11.7759i	−0.151959	+	0.467683i
$635$	−44.4721			−1.76482
$636$	−0.663119	−	2.04087i	−0.0262944	−	0.0809258i
$637$	−3.79180	+	11.6699i	−0.150236	+	0.462380i
$638$	−9.47214	+	29.1522i	−0.375005	+	1.15415i
$639$	4.09017	+	12.5882i	0.161805	+	0.497983i
$640$	9.40983	+	28.9605i	0.371956	+	1.14476i
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	−0.957489	−	0.288470i	$-0.906854\pi$
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	0.944183	+	0.329421i	$0.106854\pi$
$642$	−21.4894	−	15.6129i	−0.848117	−	0.616193i
$643$	−30.8328			−1.21593			−0.607964	−	0.793965i	$-0.708013\pi$
$643$	−30.8328			−1.21593			−0.607964	+	0.793965i	$0.708013\pi$
$644$	−1.16312	−	0.845055i	−0.0458333	−	0.0332998i
$645$	3.35410	+	10.3229i	0.132068	+	0.406462i
$646$	−5.85410	+	4.25325i	−0.230327	+	0.167342i
$647$	29.5623	−	21.4783i	1.16221	−	0.844398i	0.172158	−	0.985069i	$-0.444926\pi$
$647$	29.5623	−	21.4783i	1.16221	−	0.844398i	0.990056	+	0.140671i	$0.0449261\pi$
$648$	0.690983	+	2.12663i	0.0271444	+	0.0835418i
$649$	56.8328			2.23088
$650$	12.1353	+	8.81678i	0.475984	+	0.345823i
$651$	−1.85410			−0.0726680
$652$	2.10081	+	6.46564i	0.0822742	+	0.253214i
$653$	−15.4443	+	11.2209i	−0.604381	+	0.439109i	−0.847431	−	0.530905i	$-0.821852\pi$
$653$	−15.4443	+	11.2209i	−0.604381	+	0.439109i	0.243050	+	0.970014i	$0.421852\pi$
$654$	13.0902	−	9.51057i	0.511866	−	0.371893i
$655$	12.2984	−	8.93529i	0.480537	−	0.349131i
$656$	−3.00000	−	2.17963i	−0.117130	−	0.0851002i
$657$	18.0000			0.702247
$658$	0.500000	+	0.363271i	0.0194920	+	0.0141618i
$659$	4.79837	−	14.7679i	0.186918	−	0.575275i	−0.813058	−	0.582183i	$-0.802199\pi$
$659$	4.79837	−	14.7679i	0.186918	−	0.575275i	0.999976	+	0.00690786i	$0.00219886\pi$
$660$	2.23607	−	6.88191i	0.0870388	−	0.267878i
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	0.996902	+	0.0786563i	$0.0250630\pi$
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	−0.760277	+	0.649598i	$0.774937\pi$
$662$	11.5623	−	35.5851i	0.449382	−	1.38305i
$663$	−3.00000	+	9.23305i	−0.116510	+	0.358582i
$664$	−4.30902	−	13.2618i	−0.167222	−	0.514657i
$665$	0.954915	−	0.693786i	0.0370300	−	0.0269039i
$666$	−0.236068	+	0.726543i	−0.00914745	+	0.0281530i
$667$	11.0172	+	8.00448i	0.426588	+	0.309935i
$668$	9.00000			0.348220
$669$	0.145898	+	0.106001i	0.00564074	+	0.00409824i
$670$	−13.9443	−	10.1311i	−0.538714	−	0.391399i
$671$	36.8885	−	26.8011i	1.42407	−	1.03464i
$672$	−1.69098	+	1.22857i	−0.0652311	+	0.0473932i
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	0.997022	−	0.0771122i	$-0.0245700\pi$
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	−0.851934	+	0.523650i	$0.824570\pi$
$674$	−12.7082			−0.489502
$675$	−7.72542	+	23.7764i	−0.297352	+	0.915155i
$676$	−5.90983			−0.227301
$677$	3.28115	+	10.0984i	0.126105	+	0.388111i	0.994101	−	0.108460i	$-0.0345921\pi$
$677$	3.28115	+	10.0984i	0.126105	+	0.388111i	−0.867996	+	0.496571i	$0.834592\pi$
$678$	22.0623	−	16.0292i	0.847298	−	0.615598i
$679$	1.92705	−	1.40008i	0.0739534	−	0.0537303i
$680$	26.1803			1.00397
$681$	−11.9443	−	8.67802i	−0.457705	−	0.332543i
$682$	−25.4164			−0.973245
$683$	10.8992	+	7.91872i	0.417046	+	0.303002i	0.776448	−	0.630181i	$-0.217019\pi$
$683$	10.8992	+	7.91872i	0.417046	+	0.303002i	−0.359402	+	0.933183i	$0.617019\pi$
$684$	−0.326238	+	1.00406i	−0.0124740	+	0.0383911i
$685$	−21.6074	−	15.6987i	−0.825576	−	0.599816i
$686$	4.20820	+	12.9515i	0.160670	+	0.494491i
$687$	6.70820	−	20.6457i	0.255934	−	0.787684i
$688$	7.28115	−	22.4091i	0.277591	−	0.854338i
$689$	−1.98936	−	6.12261i	−0.0757885	−	0.233253i
$690$	−11.0172	−	8.00448i	−0.419418	−	0.304725i
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	−0.475286	−	0.879831i	$-0.657656\pi$
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	0.901667	−	0.432432i	$-0.142344\pi$
$692$	−9.44427	−	6.86167i	−0.359017	−	0.260841i
$693$	6.47214			0.245856
$694$	−26.0623	−	18.9354i	−0.989312	−	0.718777i
$695$	−11.1803			−0.424094
$696$	6.54508	−	4.75528i	0.248091	−	0.180249i
$697$	−3.23607	+	2.35114i	−0.122575	+	0.0890558i
$698$	−10.8541	−	33.4055i	−0.410834	−	1.26442i
$699$	−2.94427			−0.111363
$700$	1.90983			0.0721848
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$	4.63525	+	14.2658i	0.174946	+	0.538430i
$703$	0.163119	−	0.118513i	0.00615215	−	0.00446980i
$704$	17.9443	−	13.0373i	0.676300	−	0.491361i
$705$	1.11803	+	0.812299i	0.0421076	+	0.0305930i
$706$	16.8992	+	12.2780i	0.636009	+	0.462088i
$707$	0.909830			0.0342177
$708$	5.42705	+	3.94298i	0.203961	+	0.148186i
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	0.544089	+	0.839027i	$0.316875\pi$
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	−0.933345	+	0.358980i	$0.883125\pi$
$710$	19.3713	−	14.0741i	0.726993	−	0.528191i
$711$	5.00000	+	15.3884i	0.187515	+	0.577111i
$712$	−6.18034	+	19.0211i	−0.231618	+	0.712847i
$713$	−3.48936	+	10.7391i	−0.130677	+	0.402184i
$714$	1.61803	+	4.97980i	0.0605534	+	0.186364i
$715$	6.70820	−	20.6457i	0.250873	−	0.772106i
$716$	−0.100813	+	0.310271i	−0.00376756	+	0.0115954i
$717$	16.6074	+	12.0660i	0.620214	+	0.450612i
$718$	−22.2361			−0.829843
$719$	18.8435	+	13.6906i	0.702742	+	0.510572i	0.880824	−	0.473443i	$-0.156989\pi$
$719$	18.8435	+	13.6906i	0.702742	+	0.510572i	−0.178082	+	0.984016i	$0.556989\pi$
$720$	17.5623	−	12.7598i	0.654508	−	0.475528i
$721$	−4.28115	+	3.11044i	−0.159438	+	0.115839i
$722$	−23.9164	+	17.3763i	−0.890077	+	0.646678i
$723$	0.781153	+	2.40414i	0.0290514	+	0.0894110i
$724$	0.180340			0.00670228
$725$	−18.0902			−0.671852
$726$	−26.5623			−0.985820
$727$	7.59017	+	23.3601i	0.281504	+	0.866380i	0.987425	+	0.158089i	$0.0505333\pi$
$727$	7.59017	+	23.3601i	0.281504	+	0.866380i	−0.705921	+	0.708291i	$0.749467\pi$
$728$	−2.07295	+	1.50609i	−0.0768286	+	0.0558192i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	−10.0623	−	30.9686i	−0.372423	−	1.14620i
$731$	−20.5623	−	14.9394i	−0.760524	−	0.552553i
$732$	5.38197			0.198923
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	0.844812	−	0.535063i	$-0.179712\pi$
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	−0.247814	+	0.968808i	$0.579712\pi$
$734$	12.7812	−	39.3363i	0.471761	−	1.45193i
$735$	4.57295	+	14.0741i	0.168676	+	0.519131i
$736$	3.93363	+	12.1065i	0.144995	+	0.446250i
$737$	−7.70820	+	23.7234i	−0.283935	+	0.873863i
$738$	−0.763932	+	2.35114i	−0.0281207	+	0.0865467i
$739$	4.93769	+	15.1967i	0.181636	+	0.559018i	0.999874	−	0.0158612i	$-0.00504898\pi$
$739$	4.93769	+	15.1967i	0.181636	+	0.559018i	−0.818238	+	0.574879i	$0.805049\pi$
$740$	0.326238			0.0119927
$741$	0.489357	−	1.50609i	0.0179770	−	0.0553274i
$742$	−2.80902	−	2.04087i	−0.103122	−	0.0749227i
$743$	28.3607			1.04045			0.520226	−	0.854029i	$-0.325848\pi$
$743$	28.3607			1.04045			0.520226	+	0.854029i	$0.325848\pi$
$744$	5.42705	+	3.94298i	0.198965	+	0.144557i
$745$	2.72542	−	8.38800i	0.0998518	−	0.307312i
$746$	−37.0066	+	26.8869i	−1.35491	+	0.984398i
$747$	−10.0902	+	7.33094i	−0.369180	+	0.268225i
$748$	5.23607	+	16.1150i	0.191450	+	0.589221i
$749$	−10.1459			−0.370723
$750$	18.0902			0.660560
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	−0.927051	−	2.85317i	−0.0338061	−	0.104044i
$753$	23.6074	−	17.1518i	0.860301	−	0.625045i
$754$	−8.78115	+	6.37988i	−0.319791	+	0.232342i
$755$	−10.0623	+	30.9686i	−0.366205	+	1.12706i
$756$	1.54508	+	1.12257i	0.0561942	+	0.0408275i
$757$	30.4164			1.10550			0.552752	−	0.833346i	$-0.313578\pi$
$757$	30.4164			1.10550			0.552752	+	0.833346i	$0.313578\pi$
$758$	19.1074	+	13.8823i	0.694012	+	0.504229i
$759$	−6.09017	+	18.7436i	−0.221059	+	0.680350i
$760$	−4.27051			−0.154908
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	−0.999640	−	0.0268287i	$-0.991459\pi$
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	0.792956	−	0.609279i	$-0.208541\pi$
$762$	−9.94427	+	30.6053i	−0.360243	+	1.10871i
$763$	1.90983	−	5.87785i	0.0691405	−	0.212793i
$764$	−0.347524	−	1.06957i	−0.0125730	−	0.0386957i
$765$	−7.23607	−	22.2703i	−0.261621	−	0.805185i
$766$	−16.6803	+	51.3368i	−0.602685	+	1.85487i
$767$	16.2812	+	11.8290i	0.587878	+	0.427119i
$768$	13.5623			0.489388
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	0.374624	−	0.927177i	$-0.377772\pi$
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	−0.766033	+	0.642802i	$0.777772\pi$
$770$	−3.61803	−	11.1352i	−0.130385	−	0.401283i
$771$	−18.4894	+	13.4333i	−0.665878	+	0.483789i
$772$	−3.85410	+	2.80017i	−0.138712	+	0.100780i
$773$	−11.1738	−	34.3893i	−0.401892	−	1.23690i	−0.923462	−	0.383689i	$-0.874654\pi$
$773$	−11.1738	−	34.3893i	−0.401892	−	1.23690i	0.521570	−	0.853208i	$-0.325346\pi$
$774$	−15.7082			−0.564620
$775$	−4.63525	−	14.2658i	−0.166503	−	0.512444i
$776$	−8.61803			−0.309369
$777$	−0.0450850	−	0.138757i	−0.00161741	−	0.00497789i
$778$	19.6353	−	14.2658i	0.703958	−	0.511455i
$779$	0.527864	−	0.383516i	0.0189127	−	0.0137409i
$780$	2.07295	−	1.50609i	0.0742235	−	0.0539265i
$781$	−28.0344	−	20.3682i	−1.00315	−	0.728832i
$782$	31.8885			1.14033
$783$	−14.6353	−	10.6331i	−0.523021	−	0.379997i
$784$	9.92705	−	30.5523i	0.354538	−	1.09115i
$785$	−9.10739	+	28.0297i	−0.325057	+	1.00042i
$786$	−3.39919	−	10.4616i	−0.121245	−	0.373154i
$787$	−3.65248	+	11.2412i	−0.130197	+	0.400704i	−0.994812	−	0.101730i	$-0.967562\pi$
$787$	−3.65248	+	11.2412i	−0.130197	+	0.400704i	0.864615	+	0.502434i	$0.167562\pi$
$788$	0.708204	−	2.17963i	0.0252287	−	0.0776460i
$789$	−3.37132	−	10.3759i	−0.120022	−	0.369391i
$790$	23.6803	−	17.2048i	0.842509	−	0.612118i
$791$	3.21885	−	9.90659i	0.114449	−	0.352238i
$792$	−18.9443	−	13.7638i	−0.673155	−	0.489076i
$793$	16.1459			0.573358
$794$	38.0066	+	27.6134i	1.34880	+	0.979963i
$795$	−6.28115	−	4.56352i	−0.222770	−	0.161852i
$796$	8.78115	−	6.37988i	0.311240	−	0.226129i
$797$	−7.89919	+	5.73910i	−0.279804	+	0.203289i	−0.718832	−	0.695184i	$-0.755323\pi$
$797$	−7.89919	+	5.73910i	−0.279804	+	0.203289i	0.439028	+	0.898473i	$0.355323\pi$
$798$	−0.263932	−	0.812299i	−0.00934309	−	0.0287551i
$799$	−3.23607			−0.114484
$800$	−13.6803	−	9.93935i	−0.483673	−	0.351409i
$801$	17.8885			0.632061
$802$	−13.2984	−	40.9282i	−0.469582	−	1.44522i
$803$	−38.1246	+	27.6992i	−1.34539	+	0.977482i
$804$	−2.38197	+	1.73060i	−0.0840055	+	0.0610335i
$805$	−5.20163			−0.183333
$806$	−7.28115	−	5.29007i	−0.256468	−	0.186335i
$807$	−12.7639			−0.449312
$808$	−2.66312	−	1.93487i	−0.0936882	−	0.0680685i
$809$	9.57295	−	29.4625i	0.336567	−	1.03585i	−0.629378	−	0.777099i	$-0.716690\pi$
$809$	9.57295	−	29.4625i	0.336567	−	1.03585i	0.965945	−	0.258747i	$-0.0833097\pi$
$810$	−2.92705	−	2.12663i	−0.102846	−	0.0747221i
$811$	−4.54508	−	13.9883i	−0.159600	−	0.491197i	0.838998	−	0.544134i	$-0.183142\pi$
$811$	−4.54508	−	13.9883i	−0.159600	−	0.491197i	−0.998598	+	0.0529372i	$0.983142\pi$
$812$	−0.427051	+	1.31433i	−0.0149866	+	0.0461239i
$813$	−2.47214	+	7.60845i	−0.0867016	+	0.266840i
$814$	−0.618034	−	1.90211i	−0.0216621	−	0.0666690i
$815$	19.8992	+	14.4576i	0.697038	+	0.506428i
$816$	7.85410	−	24.1724i	0.274949	−	0.846205i
$817$	3.35410	+	2.43690i	0.117345	+	0.0852563i
$818$	−2.56231			−0.0895889
$819$	1.85410	+	1.34708i	0.0647876	+	0.0470709i
$820$	1.05573			0.0368676
$821$	32.9164	−	23.9152i	1.14879	−	0.834645i	0.160471	−	0.987041i	$-0.448699\pi$
$821$	32.9164	−	23.9152i	1.14879	−	0.834645i	0.988320	+	0.152395i	$0.0486987\pi$
$822$	−15.6353	+	11.3597i	−0.545342	+	0.396214i
$823$	14.7426	+	45.3732i	0.513896	+	1.58161i	0.785281	+	0.619139i	$0.212518\pi$
$823$	14.7426	+	45.3732i	0.513896	+	1.58161i	−0.271385	+	0.962471i	$0.587482\pi$
$824$	19.1459			0.666979
$825$	−8.09017	−	24.8990i	−0.281664	−	0.866871i
$826$	10.8541			0.377663
$827$	−0.298374	−	0.918300i	−0.0103755	−	0.0319324i	0.945735	−	0.324940i	$-0.105344\pi$
$827$	−0.298374	−	0.918300i	−0.0103755	−	0.0319324i	−0.956110	+	0.293007i	$0.905344\pi$
$828$	3.76393	−	2.73466i	0.130806	−	0.0950359i
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.0437695	−	0.999042i	$-0.486063\pi$
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.963671	+	0.267094i	$0.0860633\pi$
$830$	18.2533	+	13.2618i	0.633581	+	0.460323i
$831$	19.9894	+	14.5231i	0.693423	+	0.503801i
$832$	7.85410			0.272292
$833$	−28.0344	−	20.3682i	−0.971336	−	0.705717i
$834$	−2.50000	+	7.69421i	−0.0865679	+	0.266429i
$835$	26.3435	−	19.1396i	0.911653	−	0.662355i
$836$	−0.854102	−	2.62866i	−0.0295397	−	0.0909140i
$837$	4.63525	−	14.2658i	0.160218	−	0.493100i
$838$	4.73607	−	14.5761i	0.163605	−	0.503524i
$839$	3.35410	+	10.3229i	0.115796	+	0.356385i	0.992112	−	0.125352i	$-0.0400061\pi$
$839$	3.35410	+	10.3229i	0.115796	+	0.356385i	−0.876316	+	0.481737i	$0.840006\pi$
$840$	−0.954915	+	2.93893i	−0.0329477	+	0.101403i
$841$	−4.91641	+	15.1311i	−0.169531	+	0.521764i
$842$	41.8885	+	30.4338i	1.44357	+	1.04882i
$843$	10.0902			0.347524
$844$	4.59017	+	3.33495i	0.158000	+	0.114794i
$845$	−17.2984	+	12.5680i	−0.595082	+	0.432352i
$846$	−1.61803	+	1.17557i	−0.0556292	+	0.0404169i
$847$	−8.20820	+	5.96361i	−0.282037	+	0.204912i
$848$	5.20820	+	16.0292i	0.178850	+	0.550445i
$849$	−29.8541			−1.02459
$850$	−34.2705	+	24.8990i	−1.17547	+	0.854028i
$851$	−0.888544			−0.0304589
$852$	−1.26393	−	3.88998i	−0.0433016	−	0.133269i
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	−0.355275	−	0.934762i	$-0.615613\pi$
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	0.779225	+	0.626744i	$0.215613\pi$
$854$	7.04508	−	5.11855i	0.241078	−	0.175153i
$855$	1.18034	+	3.63271i	0.0403668	+	0.124236i
$856$	29.6976	+	21.5765i	1.01504	+	0.737471i
$857$	19.6869			0.672492			0.336246	−	0.941774i	$-0.390843\pi$
$857$	19.6869			0.672492			0.336246	+	0.941774i	$0.390843\pi$
$858$	−12.7082	−	9.23305i	−0.433851	−	0.315211i
$859$	−0.489357	+	1.50609i	−0.0166966	+	0.0513870i	−0.959058	−	0.283211i	$-0.908600\pi$
$859$	−0.489357	+	1.50609i	−0.0166966	+	0.0513870i	0.942361	+	0.334598i	$0.108600\pi$
$860$	2.07295	+	6.37988i	0.0706870	+	0.217552i
$861$	−0.145898	−	0.449028i	−0.00497219	−	0.0153028i
$862$	14.9164	−	45.9080i	0.508055	−	1.56363i
$863$	−6.62461	+	20.3885i	−0.225504	+	0.694031i	0.772736	+	0.634728i	$0.218888\pi$
$863$	−6.62461	+	20.3885i	−0.225504	+	0.694031i	−0.998240	+	0.0593032i	$0.981112\pi$
$864$	−5.22542	−	16.0822i	−0.177773	−	0.547128i
$865$	−42.2361			−1.43607
$866$	−13.4271	+	41.3242i	−0.456270	+	1.40425i
$867$	−8.42705	−	6.12261i	−0.286198	−	0.207935i
$868$	−1.14590			−0.0388943
$869$	−34.2705	−	24.8990i	−1.16255	−	0.844640i
$870$	−4.04508	+	12.4495i	−0.137141	+	0.422077i
$871$	−7.14590	+	5.19180i	−0.242130	+	0.175917i
$872$	−18.0902	+	13.1433i	−0.612610	+	0.445088i
$873$	2.38197	+	7.33094i	0.0806173	+	0.248115i
$874$	−5.20163			−0.175948
$875$	5.59017	−	4.06150i	0.188982	−	0.137304i
$876$	−5.56231			−0.187933
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	−0.939131	−	0.343559i	$-0.888368\pi$
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	0.557834	−	0.829952i	$-0.311632\pi$
$878$	−53.6418	+	38.9731i	−1.81032	+	1.31528i
$879$	15.7984	−	11.4782i	0.532866	−	0.387150i
$880$	−17.5623	+	54.0512i	−0.592025	+	1.82207i
$881$	32.6525	+	23.7234i	1.10009	+	0.799262i	0.981075	−	0.193630i	$-0.0620262\pi$
$881$	32.6525	+	23.7234i	1.10009	+	0.799262i	0.119015	+	0.992892i	$0.462026\pi$
$882$	−21.4164			−0.721128
$883$	16.6525	+	12.0987i	0.560400	+	0.407155i	0.831605	−	0.555367i	$-0.187422\pi$
$883$	16.6525	+	12.0987i	0.560400	+	0.407155i	−0.271205	+	0.962522i	$0.587422\pi$
$884$	−1.85410	+	5.70634i	−0.0623602	+	0.191925i
$885$	24.2705			0.815844
$886$	−14.9721	−	46.0795i	−0.502999	−	1.54807i
$887$	9.23607	−	28.4257i	0.310117	−	0.954441i	−0.667601	−	0.744519i	$-0.732679\pi$
$887$	9.23607	−	28.4257i	0.310117	−	0.954441i	0.977718	−	0.209922i	$-0.0673211\pi$
$888$	−0.163119	+	0.502029i	−0.00547391	+	0.0168470i
$889$	3.79837	+	11.6902i	0.127393	+	0.392076i
$890$	−10.0000	−	30.7768i	−0.335201	−	1.03164i
$891$	−1.61803	+	4.97980i	−0.0542062	+	0.166829i
$892$	0.0901699	+	0.0655123i	0.00301911	+	0.00219351i
$893$	0.527864			0.0176643
$894$	−5.16312	−	3.75123i	−0.172681	−	0.125460i
$895$	0.364745	+	1.12257i	0.0121921	+	0.0375234i
$896$	6.80902	−	4.94704i	0.227473	−	0.165269i
$897$	−5.64590	+	4.10199i	−0.188511	+	0.136961i
$898$	−2.33688	−	7.19218i	−0.0779827	−	0.240006i
$899$	10.8541			0.362005
$900$	−1.90983	+	5.87785i	−0.0636610	+	0.195928i
$901$	18.1803			0.605675
$902$	−2.00000	−	6.15537i	−0.0665927	−	0.204951i
$903$	2.42705	−	1.76336i	0.0807672	−	0.0586808i
$904$	−30.4894	+	22.1518i	−1.01406	+	0.736758i
$905$	0.527864	−	0.383516i	0.0175468	−	0.0127485i
$906$	19.0623	+	13.8496i	0.633303	+	0.460121i
$907$	−33.2492			−1.10402			−0.552011	−	0.833837i	$-0.686139\pi$
$907$	−33.2492			−1.10402			−0.552011	+	0.833837i	$0.686139\pi$
$908$	−7.38197	−	5.36331i	−0.244979	−	0.177988i
$909$	−0.909830	+	2.80017i	−0.0301772	+	0.0928757i
$910$	1.28115	−	3.94298i	0.0424698	−	0.130709i
$911$	−12.4336	−	38.2668i	−0.411944	−	1.26783i	−0.914955	−	0.403555i	$-0.867774\pi$
$911$	−12.4336	−	38.2668i	−0.411944	−	1.26783i	0.503011	−	0.864280i	$-0.332226\pi$
$912$	−1.28115	+	3.94298i	−0.0424232	+	0.130565i
$913$	10.0902	−	31.0543i	0.333936	−	1.02775i
$914$	10.7082	+	32.9565i	0.354196	+	1.09010i
$915$	15.7533	−	11.4454i	0.520788	−	0.378374i
$916$	4.14590	−	12.7598i	0.136984	−	0.421594i
$917$	−3.39919	−	2.46965i	−0.112251	−	0.0815552i
$918$	−42.3607			−1.39811
$919$	43.0517	+	31.2789i	1.42014	+	1.03179i	0.991748	+	0.128203i	$0.0409209\pi$
$919$	43.0517	+	31.2789i	1.42014	+	1.03179i	0.428395	+	0.903591i	$0.359079\pi$
$920$	15.2254	+	11.0619i	0.501967	+	0.364701i
$921$	−7.47214	+	5.42882i	−0.246215	+	0.178886i
$922$	1.07295	−	0.779543i	0.0353357	−	0.0256729i
$923$	−3.79180	−	11.6699i	−0.124808	−	0.384121i
$924$	−2.00000			−0.0657952
$925$	0.954915	−	0.693786i	0.0313974	−	0.0228116i
$926$	39.0344			1.28275
$927$	−5.29180	−	16.2865i	−0.173805	−	0.534918i
$928$	9.89919	−	7.19218i	0.324957	−	0.236095i
$929$	−33.6803	+	24.4702i	−1.10502	+	0.802841i	−0.981872	−	0.189548i	$-0.939298\pi$
$929$	−33.6803	+	24.4702i	−1.10502	+	0.802841i	−0.123145	+	0.992389i	$0.539298\pi$
$930$	−10.8541			−0.355920
$931$	4.57295	+	3.32244i	0.149872	+	0.108889i
$932$	−1.81966			−0.0596049
$933$	−6.88197	−	5.00004i	−0.225305	−	0.163694i
$934$	−13.7254	+	42.2425i	−0.449110	+	1.38222i
$935$	49.5967	+	36.0341i	1.62199	+	1.17844i
$936$	−2.56231	−	7.88597i	−0.0837516	−	0.257761i
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	−0.820811	−	0.571200i	$-0.806478\pi$
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	0.999793	+	0.0203504i	$0.00647819\pi$
$938$	−1.47214	+	4.53077i	−0.0480669	+	0.147935i
$939$	−5.18034	−	15.9434i	−0.169054	−	0.520295i
$940$	0.690983	+	0.502029i	0.0225374	+	0.0163744i
$941$	−14.3435	+	44.1446i	−0.467583	+	1.43907i	0.388121	+	0.921608i	$0.373124\pi$
$941$	−14.3435	+	44.1446i	−0.467583	+	1.43907i	−0.855704	+	0.517465i	$0.826876\pi$
$942$	17.2533	+	12.5352i	0.562143	+	0.408420i
$943$	−2.87539			−0.0936355
$944$	−42.6246	−	30.9686i	−1.38731	−	1.00794i
$945$	6.90983			0.224777
$946$	33.2705	−	24.1724i	1.08172	−	0.785914i
$947$	−2.14590	+	1.55909i	−0.0697323	+	0.0506635i	−0.622105	−	0.782934i	$-0.713722\pi$
$947$	−2.14590	+	1.55909i	−0.0697323	+	0.0506635i	0.552373	+	0.833597i	$0.313722\pi$
$948$	−1.54508	−	4.75528i	−0.0501820	−	0.154444i
$949$	−16.6869			−0.541680
$950$	5.59017	−	4.06150i	0.181369	−	0.131772i
$951$	7.65248			0.248149
$952$	−2.23607	−	6.88191i	−0.0724714	−	0.223044i
$953$	6.26393	−	4.55101i	0.202909	−	0.147422i	−0.481691	−	0.876341i	$-0.659977\pi$
$953$	6.26393	−	4.55101i	0.202909	−	0.147422i	0.684599	+	0.728919i	$0.259977\pi$
$954$	9.09017	−	6.60440i	0.294305	−	0.213825i
$955$	−3.29180	−	2.39163i	−0.106520	−	0.0773913i
$956$	10.2639	+	7.45718i	0.331959	+	0.241183i
$957$	18.9443			0.612381
$958$	−14.2082	−	10.3229i	−0.459046	−	0.333517i
$959$	−2.28115	+	7.02067i	−0.0736623	+	0.226709i
$960$	7.66312	−	5.56758i	0.247326	−	0.179693i
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	0.218847	−	0.673542i	0.00705591	−	0.0217159i
$963$	10.1459	−	31.2259i	0.326947	−	1.00624i
$964$	0.482779	+	1.48584i	0.0155493	+	0.0478557i
$965$	−5.32624	+	16.3925i	−0.171458	+	0.527692i
$966$	−1.16312	+	3.57971i	−0.0374227	+	0.115175i
$967$	−3.32624	−	2.41665i	−0.106965	−	0.0777143i	0.533017	−	0.846104i	$-0.321058\pi$
$967$	−3.32624	−	2.41665i	−0.106965	−	0.0777143i	−0.639982	+	0.768390i	$0.721058\pi$
$968$	36.7082			1.17985
$969$	3.61803	+	2.62866i	0.116228	+	0.0844446i
$970$	11.2812	−	8.19624i	0.362216	−	0.263165i
$971$	−4.54508	+	3.30220i	−0.145859	+	0.105973i	−0.658321	−	0.752737i	$-0.728733\pi$
$971$	−4.54508	+	3.30220i	−0.145859	+	0.105973i	0.512463	+	0.858709i	$0.328733\pi$
$972$	−8.00000	+	5.81234i	−0.256600	+	0.186431i
$973$	0.954915	+	2.93893i	0.0306132	+	0.0942177i
$974$	58.9230			1.88801
$975$	2.86475	−	8.81678i	0.0917453	−	0.282363i
$976$	−42.2705			−1.35305
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	0.938782	−	0.344513i	$-0.111956\pi$
$977$	−0.725425	−	2.23263i	−0.0232084	−	0.0714281i	−0.961990	+	0.273085i	$0.911956\pi$
$978$	14.3992	−	10.4616i	0.460435	−	0.334526i
$979$	−37.8885	+	27.5276i	−1.21092	+	0.879787i
$980$	2.82624	+	8.69827i	0.0902809	+	0.277856i
$981$	16.1803	+	11.7557i	0.516598	+	0.375331i
$982$	69.9787			2.23311
$983$	−7.78115	−	5.65334i	−0.248180	−	0.180313i	0.456740	−	0.889600i	$-0.349017\pi$
$983$	−7.78115	−	5.65334i	−0.248180	−	0.180313i	−0.704920	+	0.709287i	$0.749017\pi$
$984$	−0.527864	+	1.62460i	−0.0168277	+	0.0517903i
$985$	−2.56231	−	7.88597i	−0.0816419	−	0.251268i
$986$	−9.47214	−	29.1522i	−0.301654	−	0.928396i
$987$	0.118034	−	0.363271i	0.00375706	−	0.0115631i
$988$	0.302439	−	0.930812i	0.00962187	−	0.0296131i
$989$	−5.64590	−	17.3763i	−0.179529	−	0.552534i
$990$	37.8885			1.20418
$991$	−4.74671	+	14.6089i	−0.150784	+	0.464066i	−0.997709	−	0.0676459i	$-0.978451\pi$
$991$	−4.74671	+	14.6089i	−0.150784	+	0.464066i	0.846925	+	0.531712i	$0.178451\pi$
$992$	8.20820	+	5.96361i	0.260611	+	0.189345i
$993$	−23.1246			−0.733837
$994$	−5.35410	−	3.88998i	−0.169822	−	0.123383i
$995$	12.1353	−	37.3485i	0.384713	−	1.18403i
$996$	3.11803	−	2.26538i	0.0987987	−	0.0717814i
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	−0.859056	−	0.511882i	$-0.828949\pi$
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	0.221366	+	0.975191i	$0.428949\pi$
$998$	−3.78115	−	11.6372i	−0.119690	−	0.368369i
$999$	1.18034			0.0373443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.2.d.a.6.1	✓	4
3.2	odd	2		225.2.h.b.181.1		4
4.3	odd	2		400.2.u.b.81.1		4
5.2	odd	4		125.2.e.a.99.2		8
5.3	odd	4		125.2.e.a.99.1		8
5.4	even	2		125.2.d.a.26.1		4
25.2	odd	20		625.2.b.a.624.1		4
25.3	odd	20		125.2.e.a.24.2		8
25.4	even	10		125.2.d.a.101.1		4
25.6	even	5		625.2.d.h.376.1		4
25.8	odd	20		625.2.e.c.249.2		8
25.9	even	10		625.2.d.b.251.1		4
25.11	even	5		625.2.a.b.1.1		2
25.12	odd	20		625.2.e.c.374.2		8
25.13	odd	20		625.2.e.c.374.1		8
25.14	even	10		625.2.a.c.1.2		2
25.16	even	5		625.2.d.h.251.1		4
25.17	odd	20		625.2.e.c.249.1		8
25.19	even	10		625.2.d.b.376.1		4
25.21	even	5	inner	25.2.d.a.21.1	yes	4
25.22	odd	20		125.2.e.a.24.1		8
25.23	odd	20		625.2.b.a.624.4		4
75.11	odd	10		5625.2.a.f.1.2		2
75.14	odd	10		5625.2.a.d.1.1		2
75.71	odd	10		225.2.h.b.46.1		4
100.11	odd	10		10000.2.a.c.1.1		2
100.39	odd	10		10000.2.a.l.1.2		2
100.71	odd	10		400.2.u.b.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	1.1	even	1	trivial
25.2.d.a.21.1	yes	4	25.21	even	5	inner
125.2.d.a.26.1		4	5.4	even	2
125.2.d.a.101.1		4	25.4	even	10
125.2.e.a.24.1		8	25.22	odd	20
125.2.e.a.24.2		8	25.3	odd	20
125.2.e.a.99.1		8	5.3	odd	4
125.2.e.a.99.2		8	5.2	odd	4
225.2.h.b.46.1		4	75.71	odd	10
225.2.h.b.181.1		4	3.2	odd	2
400.2.u.b.81.1		4	4.3	odd	2
400.2.u.b.321.1		4	100.71	odd	10
625.2.a.b.1.1		2	25.11	even	5
625.2.a.c.1.2		2	25.14	even	10
625.2.b.a.624.1		4	25.2	odd	20
625.2.b.a.624.4		4	25.23	odd	20
625.2.d.b.251.1		4	25.9	even	10
625.2.d.b.376.1		4	25.19	even	10
625.2.d.h.251.1		4	25.16	even	5
625.2.d.h.376.1		4	25.6	even	5
625.2.e.c.249.1		8	25.17	odd	20
625.2.e.c.249.2		8	25.8	odd	20
625.2.e.c.374.1		8	25.13	odd	20
625.2.e.c.374.2		8	25.12	odd	20
5625.2.a.d.1.1		2	75.14	odd	10
5625.2.a.f.1.2		2	75.11	odd	10
10000.2.a.c.1.1		2	100.11	odd	10
10000.2.a.l.1.2		2	100.39	odd	10

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(1.30902 + 0.951057i) q^{6} +0.618034 q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.618034 + 1.90211i) q^{9} +3.61803 q^{10} +(-1.61803 - 4.97980i) q^{11} +(0.190983 - 0.587785i) q^{12} +(0.572949 - 1.76336i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.690983 - 2.12663i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(4.23607 + 3.07768i) q^{17} +3.23607 q^{18} +(-0.690983 - 0.502029i) q^{19} +(-0.427051 - 1.31433i) q^{20} +(-0.500000 + 0.363271i) q^{21} +(-6.85410 + 4.97980i) q^{22} +(1.16312 + 3.57971i) q^{23} +2.23607 q^{24} +(-4.04508 - 2.93893i) q^{25} -3.00000 q^{26} +(-1.54508 - 4.75528i) q^{27} +(-0.309017 + 0.224514i) q^{28} +(2.92705 - 2.12663i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(2.42705 + 1.76336i) q^{31} +3.38197 q^{32} +(4.23607 + 3.07768i) q^{33} +(2.61803 - 8.05748i) q^{34} +(-0.427051 + 1.31433i) q^{35} +(-0.381966 - 1.17557i) q^{36} +(-0.0729490 + 0.224514i) q^{37} +(-0.427051 + 1.31433i) q^{38} +(0.572949 + 1.76336i) q^{39} +(4.04508 - 2.93893i) q^{40} +(-0.236068 + 0.726543i) q^{41} +(0.809017 + 0.587785i) q^{42} -4.85410 q^{43} +(2.61803 + 1.90211i) q^{44} +(-3.61803 - 2.62866i) q^{45} +(4.92705 - 3.57971i) q^{46} +(-0.500000 + 0.363271i) q^{47} +(-1.50000 - 4.61653i) q^{48} -6.61803 q^{49} +(-2.50000 + 7.69421i) q^{50} -5.23607 q^{51} +(0.354102 + 1.08981i) q^{52} +(2.80902 - 2.04087i) q^{53} +(-6.54508 + 4.75528i) q^{54} +11.7082 q^{55} +(-1.11803 - 0.812299i) q^{56} +0.854102 q^{57} +(-4.73607 - 3.44095i) q^{58} +(-3.35410 + 10.3229i) q^{59} +(1.11803 + 0.812299i) q^{60} +(2.69098 + 8.28199i) q^{61} +(1.50000 - 4.61653i) q^{62} +(-0.381966 + 1.17557i) q^{63} +(1.30902 + 4.02874i) q^{64} +(3.35410 + 2.43690i) q^{65} +(2.61803 - 8.05748i) q^{66} +(-3.85410 - 2.80017i) q^{67} -3.23607 q^{68} +(-3.04508 - 2.21238i) q^{69} +2.23607 q^{70} +(5.35410 - 3.88998i) q^{71} +(3.61803 - 2.62866i) q^{72} +(-2.78115 - 8.55951i) q^{73} +0.381966 q^{74} +5.00000 q^{75} +0.527864 q^{76} +(-1.00000 - 3.07768i) q^{77} +(2.42705 - 1.76336i) q^{78} +(6.54508 - 4.75528i) q^{79} +(-8.78115 - 6.37988i) q^{80} +(-0.809017 - 0.587785i) q^{81} +1.23607 q^{82} +(5.04508 + 3.66547i) q^{83} +(0.118034 - 0.363271i) q^{84} +(-9.47214 + 6.88191i) q^{85} +(2.42705 + 7.46969i) q^{86} +(-1.11803 + 3.44095i) q^{87} +(-3.61803 + 11.1352i) q^{88} +(-2.76393 - 8.50651i) q^{89} +(-2.23607 + 6.88191i) q^{90} +(0.354102 - 1.08981i) q^{91} +(-1.88197 - 1.36733i) q^{92} -3.00000 q^{93} +(0.809017 + 0.587785i) q^{94} +(1.54508 - 1.12257i) q^{95} +(-2.73607 + 1.98787i) q^{96} +(3.11803 - 2.26538i) q^{97} +(3.30902 + 10.1841i) q^{98} +10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 + 9 * q^13 + q^14 - 5 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 - 5 * q^19 + 5 * q^20 - 2 * q^21 - 14 * q^22 - 11 * q^23 - 5 * q^25 - 12 * q^26 + 5 * q^27 + q^28 + 5 * q^29 - 5 * q^30 + 3 * q^31 + 18 * q^32 + 8 * q^33 + 6 * q^34 + 5 * q^35 - 6 * q^36 - 7 * q^37 + 5 * q^38 + 9 * q^39 + 5 * q^40 + 8 * q^41 + q^42 - 6 * q^43 + 6 * q^44 - 10 * q^45 + 13 * q^46 - 2 * q^47 - 6 * q^48 - 22 * q^49 - 10 * q^50 - 12 * q^51 - 12 * q^52 + 9 * q^53 - 15 * q^54 + 20 * q^55 - 10 * q^57 - 10 * q^58 + 13 * q^61 + 6 * q^62 - 6 * q^63 + 3 * q^64 + 6 * q^66 - 2 * q^67 - 4 * q^68 - q^69 + 8 * q^71 + 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^75 + 20 * q^76 - 4 * q^77 + 3 * q^78 + 15 * q^79 - 15 * q^80 - q^81 - 4 * q^82 + 9 * q^83 - 4 * q^84 - 20 * q^85 + 3 * q^86 - 10 * q^88 - 20 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^93 + q^94 - 5 * q^95 - 2 * q^96 + 8 * q^97 + 11 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more