LMFDB - Embedded newform 539.2.q.g.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.4
Character	$\chi$	$=$	539.361
Dual form			539.2.q.g.324.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37734 - 0.505320i) q^{2} +(-0.149915 - 1.42635i) q^{3} +(3.56931 - 1.58916i) q^{4} +(0.842189 - 0.935345i) q^{5} +(-1.07716 - 3.31516i) q^{6} +(3.74989 - 2.72445i) q^{8} +(0.922445 - 0.196072i) q^{9} +O(q^{10})$	\(q+(2.37734 - 0.505320i) q^{2} +(-0.149915 - 1.42635i) q^{3} +(3.56931 - 1.58916i) q^{4} +(0.842189 - 0.935345i) q^{5} +(-1.07716 - 3.31516i) q^{6} +(3.74989 - 2.72445i) q^{8} +(0.922445 - 0.196072i) q^{9} +(1.52952 - 2.64921i) q^{10} +(-0.785524 + 3.22226i) q^{11} +(-2.80179 - 4.85285i) q^{12} +(-0.982152 + 3.02275i) q^{13} +(-1.46039 - 1.06103i) q^{15} +(2.30932 - 2.56476i) q^{16} +(-5.79472 - 1.23171i) q^{17} +(2.09389 - 0.932259i) q^{18} +(2.61477 + 1.16417i) q^{19} +(1.51962 - 4.67691i) q^{20} +(-0.239188 + 8.05735i) q^{22} +(-3.38171 - 5.85730i) q^{23} +(-4.44819 - 4.94021i) q^{24} +(0.357053 + 3.39714i) q^{25} +(-0.807454 + 7.68241i) q^{26} +(-1.74754 - 5.37837i) q^{27} +(-3.63693 - 2.64238i) q^{29} +(-4.00800 - 1.78448i) q^{30} +(6.50898 + 7.22895i) q^{31} +(-0.441092 + 0.763993i) q^{32} +(4.71383 + 0.637365i) q^{33} -14.3984 q^{34} +(2.98090 - 2.16575i) q^{36} +(0.570198 - 5.42507i) q^{37} +(6.80447 + 1.44633i) q^{38} +(4.45874 + 0.947734i) q^{39} +(0.609809 - 5.80194i) q^{40} +(0.254423 - 0.184849i) q^{41} -0.132562 q^{43} +(2.31691 + 12.7496i) q^{44} +(0.593478 - 1.02793i) q^{45} +(-10.9993 - 12.2160i) q^{46} +(8.56453 + 3.81318i) q^{47} +(-4.00445 - 2.90940i) q^{48} +(2.56548 + 7.89572i) q^{50} +(-0.888126 + 8.44995i) q^{51} +(1.29803 + 12.3499i) q^{52} +(2.91201 + 3.23411i) q^{53} +(-6.87229 - 11.9032i) q^{54} +(2.35237 + 3.44849i) q^{55} +(1.26852 - 3.90410i) q^{57} +(-9.98147 - 4.44404i) q^{58} +(-6.34627 + 2.82554i) q^{59} +(-6.89873 - 1.46637i) q^{60} +(-1.64081 + 1.82231i) q^{61} +(19.1270 + 13.8966i) q^{62} +(-2.79554 + 8.60379i) q^{64} +(2.00016 + 3.46438i) q^{65} +(11.5285 - 0.866755i) q^{66} +(4.70993 - 8.15784i) q^{67} +(-22.6406 + 4.81240i) q^{68} +(-7.84759 + 5.70161i) q^{69} +(-0.0360345 - 0.110903i) q^{71} +(2.92488 - 3.24840i) q^{72} +(0.561859 - 0.250156i) q^{73} +(-1.38584 - 13.1854i) q^{74} +(4.79197 - 1.01857i) q^{75} +11.1830 q^{76} +11.0789 q^{78} +(-8.34290 + 1.77334i) q^{79} +(-0.454053 - 4.32003i) q^{80} +(-4.82488 + 2.14818i) q^{81} +(0.511443 - 0.568015i) q^{82} +(0.293731 + 0.904010i) q^{83} +(-6.03232 + 4.38274i) q^{85} +(-0.315145 + 0.0669862i) q^{86} +(-3.22373 + 5.58367i) q^{87} +(5.83327 + 14.2232i) q^{88} +(-5.02758 - 8.70803i) q^{89} +(0.891464 - 2.74364i) q^{90} +(-21.3786 - 15.5325i) q^{92} +(9.33521 - 10.3678i) q^{93} +(22.2877 + 4.73740i) q^{94} +(3.29103 - 1.46526i) q^{95} +(1.15585 + 0.514617i) q^{96} +(5.43159 - 16.7167i) q^{97} +(-0.0928085 + 3.12637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	2.37734	−	0.505320i	1.68103	−	0.357315i	0.734174	−	0.678961i	$-0.237570\pi$
$2$	2.37734	−	0.505320i	1.68103	−	0.357315i	0.946860	+	0.321646i	$0.104236\pi$
$3$	−0.149915	−	1.42635i	−0.0865537	−	0.823503i	−0.948558	−	0.316603i	$-0.897458\pi$
$3$	−0.149915	−	1.42635i	−0.0865537	−	0.823503i	0.862005	−	0.506901i	$-0.169209\pi$
$4$	3.56931	−	1.58916i	1.78466	−	0.794580i
$5$	0.842189	−	0.935345i	0.376638	−	0.418299i	−0.524787	−	0.851233i	$-0.675855\pi$
$5$	0.842189	−	0.935345i	0.376638	−	0.418299i	0.901425	+	0.432934i	$0.142522\pi$
$6$	−1.07716	−	3.31516i	−0.439750	−	1.35341i
$7$		0			0
$7$		0			0
$8$	3.74989	−	2.72445i	1.32579	−	0.963239i
$9$	0.922445	−	0.196072i	0.307482	−	0.0653572i
$10$	1.52952	−	2.64921i	0.483677	−	0.837754i
$11$	−0.785524	+	3.22226i	−0.236844	+	0.971548i
$11$	−0.785524	+	3.22226i	−0.236844	+	0.971548i
$12$	−2.80179	−	4.85285i	−0.808808	−	1.40090i
$13$	−0.982152	+	3.02275i	−0.272400	+	0.838361i	0.717496	+	0.696563i	$0.245288\pi$
$13$	−0.982152	+	3.02275i	−0.272400	+	0.838361i	−0.989896	+	0.141798i	$0.954712\pi$
$14$		0			0
$15$	−1.46039	−	1.06103i	−0.377070	−	0.273957i
$16$	2.30932	−	2.56476i	0.577331	−	0.641191i
$17$	−5.79472	−	1.23171i	−1.40543	−	0.298733i	−0.558086	−	0.829783i	$-0.688464\pi$
$17$	−5.79472	−	1.23171i	−1.40543	−	0.298733i	−0.847340	+	0.531050i	$0.821798\pi$
$18$	2.09389	−	0.932259i	0.493534	−	0.219735i
$19$	2.61477	+	1.16417i	0.599868	+	0.267079i	0.684124	−	0.729366i	$-0.260185\pi$
$19$	2.61477	+	1.16417i	0.599868	+	0.267079i	−0.0842558	+	0.996444i	$0.526851\pi$
$20$	1.51962	−	4.67691i	0.339798	−	1.04579i
$21$		0			0
$22$	−0.239188	+	8.05735i	−0.0509950	+	1.71783i
$23$	−3.38171	−	5.85730i	−0.705136	−	1.22133i	−0.966642	−	0.256130i	$-0.917552\pi$
$23$	−3.38171	−	5.85730i	−0.705136	−	1.22133i	0.261506	−	0.965202i	$-0.415781\pi$
$24$	−4.44819	−	4.94021i	−0.907982	−	1.00842i
$25$	0.357053	+	3.39714i	0.0714107	+	0.679427i
$26$	−0.807454	+	7.68241i	−0.158355	+	1.50665i
$27$	−1.74754	−	5.37837i	−0.336314	−	1.03507i
$28$		0			0
$29$	−3.63693	−	2.64238i	−0.675361	−	0.490678i	0.196454	−	0.980513i	$-0.437057\pi$
$29$	−3.63693	−	2.64238i	−0.675361	−	0.490678i	−0.871815	+	0.489834i	$0.837057\pi$
$30$	−4.00800	−	1.78448i	−0.731757	−	0.325799i
$31$	6.50898	+	7.22895i	1.16905	+	1.29836i	0.946229	+	0.323498i	$0.104859\pi$
$31$	6.50898	+	7.22895i	1.16905	+	1.29836i	0.222818	+	0.974860i	$0.428475\pi$
$32$	−0.441092	+	0.763993i	−0.0779748	+	0.135056i
$33$	4.71383	+	0.637365i	0.820572	+	0.110951i
$34$	−14.3984			−2.46931
$35$		0			0
$36$	2.98090	−	2.16575i	0.496817	−	0.360959i
$37$	0.570198	−	5.42507i	0.0937400	−	0.891876i	−0.842069	−	0.539369i	$-0.818663\pi$
$37$	0.570198	−	5.42507i	0.0937400	−	0.891876i	0.935809	−	0.352507i	$-0.114671\pi$
$38$	6.80447	+	1.44633i	1.10383	+	0.234626i
$39$	4.45874	+	0.947734i	0.713970	+	0.151759i
$40$	0.609809	−	5.80194i	0.0964192	−	0.917368i
$41$	0.254423	−	0.184849i	0.0397342	−	0.0288686i	−0.567741	−	0.823207i	$-0.692182\pi$
$41$	0.254423	−	0.184849i	0.0397342	−	0.0288686i	0.607475	+	0.794339i	$0.292182\pi$
$42$		0			0
$43$	−0.132562			−0.0202155			−0.0101078	−	0.999949i	$-0.503217\pi$
$43$	−0.132562			−0.0202155			−0.0101078	+	0.999949i	$0.503217\pi$
$44$	2.31691	+	12.7496i	0.349287	+	1.92207i
$45$	0.593478	−	1.02793i	0.0884704	−	0.153235i
$46$	−10.9993	−	12.2160i	−1.62176	−	1.80114i
$47$	8.56453	+	3.81318i	1.24927	+	0.556209i	0.921437	−	0.388528i	$-0.127016\pi$
$47$	8.56453	+	3.81318i	1.24927	+	0.556209i	0.327829	+	0.944737i	$0.393683\pi$
$48$	−4.00445	−	2.90940i	−0.577993	−	0.419936i
$49$		0			0
$50$	2.56548	+	7.89572i	0.362813	+	1.11662i
$51$	−0.888126	+	8.44995i	−0.124362	+	1.18323i
$52$	1.29803	+	12.3499i	0.180005	+	1.71263i
$53$	2.91201	+	3.23411i	0.399995	+	0.444239i	0.909171	−	0.416423i	$-0.136717\pi$
$53$	2.91201	+	3.23411i	0.399995	+	0.444239i	−0.509176	+	0.860662i	$0.670050\pi$
$54$	−6.87229	−	11.9032i	−0.935200	−	1.61981i
$55$	2.35237	+	3.44849i	0.317193	+	0.464994i
$56$		0			0
$57$	1.26852	−	3.90410i	0.168019	−	0.517110i
$58$	−9.98147	−	4.44404i	−1.31063	−	0.583531i
$59$	−6.34627	+	2.82554i	−0.826213	+	0.367854i	−0.775882	−	0.630879i	$-0.782695\pi$
$59$	−6.34627	+	2.82554i	−0.826213	+	0.367854i	−0.0503319	+	0.998733i	$0.516028\pi$
$60$	−6.89873	−	1.46637i	−0.890622	−	0.189308i
$61$	−1.64081	+	1.82231i	−0.210084	+	0.233322i	−0.838973	−	0.544173i	$-0.816843\pi$
$61$	−1.64081	+	1.82231i	−0.210084	+	0.233322i	0.628889	+	0.777495i	$0.283510\pi$
$62$	19.1270	+	13.8966i	2.42913	+	1.76487i
$63$		0			0
$64$	−2.79554	+	8.60379i	−0.349443	+	1.07547i
$65$	2.00016	+	3.46438i	0.248089	+	0.429703i
$66$	11.5285	−	0.866755i	1.41905	−	0.106690i
$67$	4.70993	−	8.15784i	0.575410	−	0.996639i	−0.420587	−	0.907252i	$-0.638176\pi$
$67$	4.70993	−	8.15784i	0.575410	−	0.996639i	0.995997	−	0.0893871i	$-0.0284908\pi$
$68$	−22.6406	+	4.81240i	−2.74557	+	0.583589i
$69$	−7.84759	+	5.70161i	−0.944739	+	0.686393i
$70$		0			0
$71$	−0.0360345	−	0.110903i	−0.00427651	−	0.0131617i	0.948895	−	0.315590i	$-0.102203\pi$
$71$	−0.0360345	−	0.110903i	−0.00427651	−	0.0131617i	−0.953172	+	0.302429i	$0.902203\pi$
$72$	2.92488	−	3.24840i	0.344700	−	0.382828i
$73$	0.561859	−	0.250156i	0.0657607	−	0.0292785i	−0.373593	−	0.927593i	$-0.621874\pi$
$73$	0.561859	−	0.250156i	0.0657607	−	0.0292785i	0.439353	+	0.898314i	$0.355208\pi$
$74$	−1.38584	−	13.1854i	−0.161101	−	1.53277i
$75$	4.79197	−	1.01857i	0.553330	−	0.117614i
$76$	11.1830			1.28277
$77$		0			0
$78$	11.0789			1.25443
$79$	−8.34290	+	1.77334i	−0.938649	+	0.199516i	−0.651741	−	0.758442i	$-0.725961\pi$
$79$	−8.34290	+	1.77334i	−0.938649	+	0.199516i	−0.286909	+	0.957958i	$0.592628\pi$
$80$	−0.454053	−	4.32003i	−0.0507647	−	0.482994i
$81$	−4.82488	+	2.14818i	−0.536098	+	0.238686i
$82$	0.511443	−	0.568015i	0.0564794	−	0.0627267i
$83$	0.293731	+	0.904010i	0.0322411	+	0.0992280i	0.965882	−	0.258982i	$-0.0833871\pi$
$83$	0.293731	+	0.904010i	0.0322411	+	0.0992280i	−0.933641	+	0.358210i	$0.883387\pi$
$84$		0			0
$85$	−6.03232	+	4.38274i	−0.654297	+	0.475375i
$86$	−0.315145	+	0.0669862i	−0.0339830	+	0.00722330i
$87$	−3.22373	+	5.58367i	−0.345620	+	0.598632i
$88$	5.83327	+	14.2232i	0.621828	+	1.51620i
$89$	−5.02758	−	8.70803i	−0.532923	−	0.923049i	−0.999261	−	0.0384427i	$-0.987760\pi$
$89$	−5.02758	−	8.70803i	−0.532923	−	0.923049i	0.466338	−	0.884607i	$-0.345573\pi$
$90$	0.891464	−	2.74364i	0.0939686	−	0.289206i
$91$		0			0
$92$	−21.3786	−	15.5325i	−2.22887	−	1.61937i
$93$	9.33521	−	10.3678i	0.968017	−	1.07509i
$94$	22.2877	+	4.73740i	2.29880	+	0.488625i
$95$	3.29103	−	1.46526i	0.337652	−	0.150332i
$96$	1.15585	+	0.514617i	0.117968	+	0.0525228i
$97$	5.43159	−	16.7167i	0.551495	−	1.69733i	−0.153530	−	0.988144i	$-0.549064\pi$
$97$	5.43159	−	16.7167i	0.551495	−	1.69733i	0.705025	−	0.709182i	$-0.250936\pi$
$98$		0			0
$99$	−0.0928085	+	3.12637i	−0.00932760	+	0.314212i
$100$	6.67303	+	11.5580i	0.667303	+	1.15580i
$101$	−8.34817	−	9.27158i	−0.830674	−	0.922557i	0.167318	−	0.985903i	$-0.446490\pi$
$101$	−8.34817	−	9.27158i	−0.830674	−	0.922557i	−0.997992	+	0.0633460i	$0.979823\pi$
$102$	2.15855	+	20.5372i	0.213728	+	2.03349i
$103$	−0.859017	+	8.17301i	−0.0846415	+	0.805310i	0.867043	+	0.498233i	$0.166018\pi$
$103$	−0.859017	+	8.17301i	−0.0846415	+	0.805310i	−0.951685	+	0.307077i	$0.900649\pi$
$104$	4.55239	+	14.0108i	0.446398	+	1.37387i
$105$		0			0
$106$	8.55709	+	6.21709i	0.831138	+	0.603857i
$107$	11.1348	+	4.95752i	1.07644	+	0.479261i	0.866871	−	0.498533i	$-0.166128\pi$
$107$	11.1348	+	4.95752i	1.07644	+	0.479261i	0.209568	+	0.977794i	$0.432794\pi$
$108$	−14.7846	−	16.4200i	−1.42265	−	1.58001i
$109$	−0.443044	+	0.767375i	−0.0424359	+	0.0735012i	−0.886463	−	0.462799i	$-0.846845\pi$
$109$	−0.443044	+	0.767375i	−0.0424359	+	0.0735012i	0.844027	+	0.536300i	$0.180178\pi$
$110$	7.33496	+	7.00953i	0.699361	+	0.668333i
$111$	−7.82353			−0.742577
$112$		0			0
$113$	−3.67700	+	2.67149i	−0.345903	+	0.251313i	−0.747148	−	0.664658i	$-0.768577\pi$
$113$	−3.67700	+	2.67149i	−0.345903	+	0.251313i	0.401245	+	0.915971i	$0.368577\pi$
$114$	1.04288	−	9.92238i	0.0976750	−	0.929316i
$115$	−8.32664	−	1.76988i	−0.776463	−	0.165042i
$116$	−17.1805	−	3.65183i	−1.59517	−	0.339064i
$117$	−0.313305	+	2.98089i	−0.0289650	+	0.275584i
$118$	−13.6594	+	9.92416i	−1.25745	+	0.913593i
$119$		0			0
$120$	−8.36702			−0.763801
$121$	−9.76591	−	5.06232i	−0.887810	−	0.460211i
$122$	−2.97992	+	5.16138i	−0.269789	+	0.467289i
$123$	−0.301802	−	0.335185i	−0.0272125	−	0.0302226i
$124$	34.7205	+	15.4586i	3.11800	+	1.38822i
$125$	8.56947	+	6.22608i	0.766477	+	0.556878i
$126$		0			0
$127$	−2.48072	−	7.63488i	−0.220129	−	0.677486i	−0.998750	−	0.0499916i	$-0.984081\pi$
$127$	−2.48072	−	7.63488i	−0.220129	−	0.677486i	0.778621	−	0.627494i	$-0.215919\pi$
$128$	−2.11387	+	20.1121i	−0.186841	+	1.77767i
$129$	0.0198731	+	0.189080i	0.00174973	+	0.0166475i
$130$	6.50568	+	7.22529i	0.570586	+	0.633700i
$131$	−0.0507303	−	0.0878675i	−0.00443233	−	0.00767702i	0.863801	−	0.503834i	$-0.168078\pi$
$131$	−0.0507303	−	0.0878675i	−0.00443233	−	0.00767702i	−0.868233	+	0.496157i	$0.834744\pi$
$132$	17.8380	−	5.21608i	1.55260	−	0.454001i
$133$		0			0
$134$	7.07480	−	21.7740i	0.611170	−	1.88099i
$135$	−6.50239	−	2.89505i	−0.559636	−	0.249166i
$136$	−25.0853	+	11.1687i	−2.15105	+	0.957707i
$137$	4.46435	+	0.948928i	0.381416	+	0.0810724i	0.394630	−	0.918840i	$-0.370873\pi$
$137$	4.46435	+	0.948928i	0.381416	+	0.0810724i	−0.0132140	+	0.999913i	$0.504206\pi$
$138$	−15.7753	+	17.5202i	−1.34288	+	1.49142i
$139$	3.09475	+	2.24847i	0.262494	+	0.190713i	0.711246	−	0.702944i	$-0.248131\pi$
$139$	3.09475	+	2.24847i	0.262494	+	0.190713i	−0.448752	+	0.893656i	$0.648131\pi$
$140$		0			0
$141$	4.15497	−	12.7877i	0.349911	−	1.07692i
$142$	−0.141708	−	0.245445i	−0.0118918	−	0.0205973i
$143$	−8.96859	−	5.53919i	−0.749991	−	0.463210i
$144$	1.62734	−	2.81864i	0.135612	−	0.234887i
$145$	−5.53452	+	1.17640i	−0.459617	+	0.0976946i
$146$	1.20932	−	0.878624i	0.100084	−	0.0727155i
$147$		0			0
$148$	−6.58609	−	20.2699i	−0.541374	−	1.66618i
$149$	−3.26016	+	3.62078i	−0.267083	+	0.296625i	−0.861736	−	0.507357i	$-0.830623\pi$
$149$	−3.26016	+	3.62078i	−0.267083	+	0.296625i	0.594653	+	0.803982i	$0.297289\pi$
$150$	10.8775	−	4.84296i	0.888141	−	0.395426i
$151$	1.77425	+	16.8809i	0.144387	+	1.37375i	0.791414	+	0.611280i	$0.209345\pi$
$151$	1.77425	+	16.8809i	0.144387	+	1.37375i	−0.647028	+	0.762467i	$0.723988\pi$
$152$	12.9768	−	2.75830i	1.05256	−	0.223728i
$153$	−5.58681			−0.451667
$154$		0			0
$155$	12.2434			0.983410
$156$	17.4207	−	3.70289i	1.39478	−	0.296469i
$157$	−0.234649	−	2.23253i	−0.0187270	−	0.178175i	0.981160	−	0.193196i	$-0.0618853\pi$
$157$	−0.234649	−	2.23253i	−0.0187270	−	0.178175i	−0.999887	+	0.0150205i	$0.995219\pi$
$158$	−18.9378	+	8.43166i	−1.50661	+	0.670787i
$159$	4.17642	−	4.63838i	0.331211	−	0.367847i
$160$	0.343115	+	1.05600i	0.0271256	+	0.0834841i
$161$		0			0
$162$	−10.3849	+	7.54506i	−0.815913	+	0.592796i
$163$	15.4912	−	3.29275i	1.21336	−	0.257908i	0.443592	−	0.896229i	$-0.353704\pi$
$163$	15.4912	−	3.29275i	1.21336	−	0.257908i	0.769770	+	0.638321i	$0.220371\pi$
$164$	0.614361	−	1.06410i	0.0479735	−	0.0830926i
$165$	4.56609	−	3.87228i	0.355470	−	0.301456i
$166$	1.15511	+	2.00071i	0.0896540	+	0.155285i
$167$	6.40950	−	19.7264i	0.495982	−	1.52647i	−0.319440	−	0.947607i	$-0.603495\pi$
$167$	6.40950	−	19.7264i	0.495982	−	1.52647i	0.815421	−	0.578868i	$-0.196505\pi$
$168$		0			0
$169$	2.34481	+	1.70361i	0.180370	+	0.131047i
$170$	−12.1262	+	13.4675i	−0.930037	+	1.03291i
$171$	2.64024	+	0.561200i	0.201904	+	0.0429160i
$172$	−0.473155	+	0.210662i	−0.0360778	+	0.0160628i
$173$	−19.6919	−	8.76738i	−1.49714	−	0.666571i	−0.515429	−	0.856932i	$-0.672368\pi$
$173$	−19.6919	−	8.76738i	−1.49714	−	0.666571i	−0.981714	+	0.190361i	$0.939034\pi$
$174$	−4.84238	+	14.9033i	−0.367100	+	1.12982i
$175$		0			0
$176$	6.45030	+	9.45592i	0.486210	+	0.712767i
$177$	4.98161	+	8.62840i	0.374441	+	0.648550i
$178$	−16.3526	−	18.1614i	−1.22568	−	1.36126i
$179$	−0.499814	−	4.75541i	−0.0373579	−	0.355436i	−0.997193	−	0.0748721i	$-0.976145\pi$
$179$	−0.499814	−	4.75541i	−0.0373579	−	0.355436i	0.959835	−	0.280564i	$-0.0905215\pi$
$180$	0.484756	−	4.61215i	0.0361316	−	0.343769i
$181$	−2.42666	−	7.46850i	−0.180372	−	0.555129i	0.819466	−	0.573128i	$-0.194270\pi$
$181$	−2.42666	−	7.46850i	−0.180372	−	0.555129i	−0.999838	+	0.0179992i	$0.994270\pi$
$182$		0			0
$183$	2.84523	+	2.06718i	0.210325	+	0.152810i
$184$	−28.6390	−	12.7509i	−2.11129	−	0.940009i
$185$	−4.59410	−	5.10227i	−0.337765	−	0.375126i
$186$	16.9539	−	29.3651i	1.24312	−	2.15315i
$187$	8.52077	−	17.7046i	0.623100	−	1.29469i
$188$	36.6293			2.67146
$189$		0			0
$190$	7.08347	−	5.14644i	0.513889	−	0.373362i
$191$	0.923016	−	8.78191i	0.0667871	−	0.635437i	−0.909012	−	0.416769i	$-0.863162\pi$
$191$	0.923016	−	8.78191i	0.0667871	−	0.635437i	0.975799	−	0.218668i	$-0.0701711\pi$
$192$	12.6911	+	2.69758i	0.915902	+	0.194681i
$193$	−25.0428	−	5.32301i	−1.80262	−	0.383159i	−0.820535	−	0.571597i	$-0.806324\pi$
$193$	−25.0428	−	5.32301i	−1.80262	−	0.383159i	−0.982085	+	0.188438i	$0.939657\pi$
$194$	4.46546	−	42.4861i	0.320602	−	3.05032i
$195$	4.64156	−	3.37229i	0.332389	−	0.241495i
$196$		0			0
$197$	−11.1977			−0.797802			−0.398901	−	0.916994i	$-0.630608\pi$
$197$	−11.1977			−0.797802			−0.398901	+	0.916994i	$0.630608\pi$
$198$	1.35918	+	7.47936i	0.0965928	+	0.531535i
$199$	6.12514	−	10.6091i	0.434200	−	0.752056i	−0.563030	−	0.826436i	$-0.690365\pi$
$199$	6.12514	−	10.6091i	0.434200	−	0.752056i	0.997230	+	0.0743802i	$0.0236979\pi$
$200$	10.5942	+	11.7661i	0.749126	+	0.831989i
$201$	−12.3420	−	5.49503i	−0.870540	−	0.387589i
$202$	−24.5316	−	17.8232i	−1.72603	−	1.25404i
$203$		0			0
$204$	10.2583	+	31.5719i	0.718227	+	2.21048i
$205$	0.0413744	−	0.393651i	0.00288972	−	0.0274938i
$206$	2.08780	+	19.8641i	0.145464	+	1.38400i
$207$	−4.26790	−	4.73998i	−0.296639	−	0.329451i
$208$	5.48454	+	9.49949i	0.380284	+	0.658671i
$209$	−5.80521	+	7.51097i	−0.401555	+	0.519545i
$210$		0			0
$211$	−4.40769	+	13.5655i	−0.303438	+	0.933887i	0.676817	+	0.736151i	$0.263359\pi$
$211$	−4.40769	+	13.5655i	−0.303438	+	0.933887i	−0.980255	+	0.197736i	$0.936641\pi$
$212$	15.5334	+	6.91591i	1.06684	+	0.474986i
$213$	−0.152784	+	0.0680239i	−0.0104686	+	0.00466092i
$214$	28.9763	+	6.15910i	1.98078	+	0.421027i
$215$	−0.111642	+	0.123991i	−0.00761394	+	0.00845613i
$216$	−21.2062	−	15.4072i	−1.44290	−	1.04833i
$217$		0			0
$218$	−0.665497	+	2.04819i	−0.0450732	+	0.138721i
$219$	−0.441041	−	0.763905i	−0.0298028	−	0.0516199i
$220$	13.8765	+	8.57044i	0.935555	+	0.577819i
$221$	9.41444	−	16.3063i	0.633284	−	1.09688i
$222$	−18.5992	+	3.95338i	−1.24830	+	0.265334i
$223$	2.39793	−	1.74220i	0.160577	−	0.116666i	−0.504595	−	0.863356i	$-0.668358\pi$
$223$	2.39793	−	1.74220i	0.160577	−	0.116666i	0.665172	+	0.746690i	$0.268358\pi$
$224$		0			0
$225$	0.995444	+	3.06366i	0.0663629	+	0.204244i
$226$	−7.39152	+	8.20911i	−0.491676	+	0.546062i
$227$	7.54228	−	3.35804i	0.500599	−	0.222881i	−0.140873	−	0.990028i	$-0.544991\pi$
$227$	7.54228	−	3.35804i	0.500599	−	0.222881i	0.641472	+	0.767147i	$0.278324\pi$
$228$	−1.67650	−	15.9508i	−0.111029	−	1.05637i
$229$	−12.8217	+	2.72533i	−0.847280	+	0.180095i	−0.611040	−	0.791600i	$-0.709248\pi$
$229$	−12.8217	+	2.72533i	−0.847280	+	0.180095i	−0.236240	+	0.971695i	$0.575915\pi$
$230$	−20.6896			−1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	12.5474	−	2.66702i	0.822005	−	0.174723i	0.222335	−	0.974970i	$-0.428632\pi$
$233$	12.5474	−	2.66702i	0.822005	−	0.174723i	0.599670	+	0.800248i	$0.295299\pi$
$234$	0.761472	+	7.24492i	0.0497790	+	0.473615i
$235$	10.7796	−	4.79938i	0.703183	−	0.313077i
$236$	−18.1616	+	20.1705i	−1.18222	+	1.31299i
$237$	3.78013	+	11.6340i	0.245546	+	0.755712i
$238$		0			0
$239$	4.02979	−	2.92781i	0.260665	−	0.189384i	−0.449775	−	0.893142i	$-0.648496\pi$
$239$	4.02979	−	2.92781i	0.260665	−	0.189384i	0.710440	+	0.703758i	$0.248496\pi$
$240$	−6.09380	+	1.29528i	−0.393353	+	0.0836098i
$241$	1.31343	−	2.27492i	0.0846053	−	0.146541i	−0.820618	−	0.571478i	$-0.806370\pi$
$241$	1.31343	−	2.27492i	0.0846053	−	0.146541i	0.905223	+	0.424937i	$0.139704\pi$
$242$	−25.7750	−	7.09996i	−1.65688	−	0.456403i
$243$	−4.69535	−	8.13258i	−0.301207	−	0.521706i
$244$	−2.96063	+	9.11189i	−0.189535	+	0.583329i
$245$		0			0
$246$	−0.886861	−	0.644342i	−0.0565442	−	0.0410818i
$247$	−6.08709	+	6.76040i	−0.387312	+	0.430154i
$248$	44.1029	+	9.37435i	2.80053	+	0.595272i
$249$	1.24540	−	0.554487i	0.0789240	−	0.0351392i
$250$	23.5187	+	10.4712i	1.48745	+	0.662257i
$251$	−8.10332	+	24.9395i	−0.511477	+	1.57417i	0.278124	+	0.960545i	$0.410287\pi$
$251$	−8.10332	+	24.9395i	−0.511477	+	1.57417i	−0.789601	+	0.613620i	$0.789713\pi$
$252$		0			0
$253$	21.5302	−	6.29571i	1.35359	−	0.395808i
$254$	−9.75558	−	16.8972i	−0.612119	−	1.06022i
$255$	7.15565	+	7.94716i	0.448104	+	0.497670i
$256$	3.24640	+	30.8875i	0.202900	+	1.93047i
$257$	−3.13081	+	29.7877i	−0.195295	+	1.85811i	0.257225	+	0.966352i	$0.417192\pi$
$257$	−3.13081	+	29.7877i	−0.195295	+	1.85811i	−0.452520	+	0.891754i	$0.649475\pi$
$258$	0.142791	+	0.439465i	0.00888977	+	0.0273599i
$259$		0			0
$260$	12.6446	+	9.18688i	0.784188	+	0.569746i
$261$	−3.87296	−	1.72435i	−0.239730	−	0.106735i
$262$	−0.165005	−	0.183256i	−0.0101940	−	0.0113216i
$263$	−1.66854	+	2.89000i	−0.102887	+	0.178205i	−0.912873	−	0.408244i	$-0.866141\pi$
$263$	−1.66854	+	2.89000i	−0.102887	+	0.178205i	0.809986	+	0.586449i	$0.199475\pi$
$264$	19.4128	−	10.4526i	1.19478	−	0.643310i
$265$	5.47747			0.336478
$266$		0			0
$267$	−11.6670	+	8.47656i	−0.714008	+	0.518757i
$268$	3.84710	−	36.6027i	0.234999	−	2.23587i
$269$	1.69788	+	0.360896i	0.103522	+	0.0220042i	0.259381	−	0.965775i	$-0.416481\pi$
$269$	1.69788	+	0.360896i	0.103522	+	0.0220042i	−0.155860	+	0.987779i	$0.549815\pi$
$270$	−16.9213	−	3.59674i	−1.02980	−	0.218890i
$271$	0.258808	−	2.46239i	0.0157215	−	0.149580i	−0.983845	−	0.179022i	$-0.942707\pi$
$271$	0.258808	−	2.46239i	0.0157215	−	0.149580i	0.999566	+	0.0294426i	$0.00937322\pi$
$272$	−16.5409	+	12.0177i	−1.00294	+	0.728679i
$273$		0			0
$274$	11.0928			0.670141
$275$	−11.2269	−	1.51801i	−0.677009	−	0.0915396i
$276$	−18.9497	+	32.8219i	−1.14064	+	1.97565i
$277$	3.44984	+	3.83144i	0.207281	+	0.230209i	0.837817	−	0.545951i	$-0.183832\pi$
$277$	3.44984	+	3.83144i	0.207281	+	0.230209i	−0.630536	+	0.776160i	$0.717165\pi$
$278$	8.49348	+	3.78154i	0.509405	+	0.226802i
$279$	7.42156	+	5.39208i	0.444317	+	0.322815i
$280$		0			0
$281$	−6.97467	−	21.4658i	−0.416074	−	1.28054i	−0.911287	−	0.411772i	$-0.864910\pi$
$281$	−6.97467	−	21.4658i	−0.416074	−	1.28054i	0.495213	−	0.868772i	$-0.335090\pi$
$282$	3.41591	−	32.5002i	0.203415	−	1.93536i
$283$	0.887193	+	8.44107i	0.0527381	+	0.501770i	0.988726	+	0.149737i	$0.0478427\pi$
$283$	0.887193	+	8.44107i	0.0527381	+	0.501770i	−0.935988	+	0.352033i	$0.885491\pi$
$284$	−0.304861	−	0.338582i	−0.0180902	−	0.0200912i
$285$	−2.58335	−	4.47449i	−0.153024	−	0.265046i
$286$	−24.1205	−	8.63654i	−1.42627	−	0.510690i
$287$		0			0
$288$	−0.257085	+	0.791227i	−0.0151489	+	0.0466235i
$289$	16.5314	+	7.36027i	0.972438	+	0.432957i
$290$	−12.5630	+	5.59341i	−0.737724	+	0.328456i
$291$	−24.6582	−	5.24126i	−1.44549	−	0.307248i
$292$	1.60791	−	1.78577i	0.0940960	−	0.104504i
$293$	−19.9229	−	14.4749i	−1.16391	−	0.845630i	−0.173643	−	0.984809i	$-0.555554\pi$
$293$	−19.9229	−	14.4749i	−1.16391	−	0.845630i	−0.990267	+	0.139178i	$0.955554\pi$
$294$		0			0
$295$	−2.70190	+	8.31559i	−0.157311	+	0.484152i
$296$	−12.6422	−	21.8969i	−0.734811	−	1.27273i
$297$	18.7032	−	1.40618i	1.08527	−	0.0815950i
$298$	−5.92087	+	10.2552i	−0.342987	+	0.594070i
$299$	21.0265	−	4.46933i	1.21600	−	0.258468i
$300$	15.4854	−	11.2508i	0.894050	−	0.649565i
$301$		0			0
$302$	12.7482	+	39.2351i	0.733579	+	2.25772i
$303$	−11.9730	+	13.2974i	−0.687831	+	0.763914i
$304$	9.02415	−	4.01781i	0.517571	−	0.230437i
$305$	0.322612	+	3.06945i	0.0184727	+	0.175756i
$306$	−13.2818	+	2.82313i	−0.759268	+	0.161387i
$307$	4.59391			0.262188			0.131094	−	0.991370i	$-0.458151\pi$
$307$	4.59391			0.262188			0.131094	+	0.991370i	$0.458151\pi$
$308$		0			0
$309$	11.7863			0.670502
$310$	29.1066	−	6.18680i	1.65315	−	0.351387i
$311$	0.231085	+	2.19862i	0.0131036	+	0.124672i	0.999118	−	0.0419867i	$-0.0133687\pi$
$311$	0.231085	+	2.19862i	0.0131036	+	0.124672i	−0.986015	+	0.166659i	$0.946702\pi$
$312$	19.3018	−	8.59373i	1.09275	−	0.486524i
$313$	−6.49009	+	7.20797i	−0.366841	+	0.407419i	−0.898100	−	0.439791i	$-0.855053\pi$
$313$	−6.49009	+	7.20797i	−0.366841	+	0.407419i	0.531259	+	0.847210i	$0.321719\pi$
$314$	−1.68598	−	5.18892i	−0.0951455	−	0.292828i
$315$		0			0
$316$	−26.9603	+	19.5878i	−1.51664	+	1.10190i
$317$	−6.31433	+	1.34215i	−0.354648	+	0.0753828i	−0.381791	−	0.924249i	$-0.624692\pi$
$317$	−6.31433	+	1.34215i	−0.354648	+	0.0753828i	0.0271427	+	0.999632i	$0.491359\pi$
$318$	7.58490	−	13.1374i	0.425340	−	0.736711i
$319$	11.3713	−	9.64348i	0.636673	−	0.539931i
$320$	5.69314	+	9.86081i	0.318256	+	0.551236i
$321$	5.40188	−	16.6253i	0.301504	−	0.927933i
$322$		0			0
$323$	−13.7179	−	9.96666i	−0.763286	−	0.554560i
$324$	−13.8077	+	15.3350i	−0.767096	+	0.851946i
$325$	−10.6194	−	2.25722i	−0.589057	−	0.125208i
$326$	35.1639	−	15.6560i	1.94755	−	0.867104i
$327$	1.16096	+	0.516894i	0.0642014	+	0.0285843i
$328$	0.450445	−	1.38633i	0.0248717	−	0.0765471i
$329$		0			0
$330$	8.89842	−	11.5131i	0.489842	−	0.633773i
$331$	−1.81038	−	3.13567i	−0.0995075	−	0.172352i	0.811973	−	0.583694i	$-0.198393\pi$
$331$	−1.81038	−	3.13567i	−0.0995075	−	0.172352i	−0.911481	+	0.411342i	$0.865060\pi$
$332$	2.48503	+	2.75991i	0.136384	+	0.151470i
$333$	−0.537727	−	5.11613i	−0.0294672	−	0.280362i
$334$	5.26942	−	50.1352i	0.288330	−	2.74328i
$335$	−3.66375	−	11.2759i	−0.200172	−	0.616066i
$336$		0			0
$337$	5.18183	+	3.76482i	0.282272	+	0.205083i	0.719908	−	0.694070i	$-0.244184\pi$
$337$	5.18183	+	3.76482i	0.282272	+	0.205083i	−0.437636	+	0.899152i	$0.644184\pi$
$338$	6.43529	+	2.86518i	0.350034	+	0.155845i
$339$	4.36172	+	4.84418i	0.236896	+	0.263100i
$340$	−14.5664	+	25.2297i	−0.789972	+	1.36827i
$341$	−28.4065	+	15.2951i	−1.53830	+	0.828276i
$342$	6.56033			0.354742
$343$		0			0
$344$	−0.497093	+	0.361159i	−0.0268014	+	0.0194724i
$345$	−1.27618	+	12.1420i	−0.0687072	+	0.653705i
$346$	−51.2446	−	10.8924i	−2.75493	−	0.585578i
$347$	17.0785	+	3.63014i	0.916819	+	0.194876i	0.642075	−	0.766641i	$-0.278074\pi$
$347$	17.0785	+	3.63014i	0.916819	+	0.194876i	0.274744	+	0.961517i	$0.411407\pi$
$348$	−2.63316	+	25.0529i	−0.141152	+	1.34298i
$349$	17.4949	−	12.7108i	0.936481	−	0.680393i	−0.0110900	−	0.999939i	$-0.503530\pi$
$349$	17.4949	−	12.7108i	0.936481	−	0.680393i	0.947571	+	0.319545i	$0.103530\pi$
$350$		0			0
$351$	17.9738			0.959371
$352$	−2.11530	−	2.02145i	−0.112746	−	0.107743i
$353$	−2.20075	+	3.81181i	−0.117134	+	0.202882i	−0.918631	−	0.395117i	$-0.870704\pi$
$353$	−2.20075	+	3.81181i	−0.117134	+	0.202882i	0.801497	+	0.597999i	$0.204037\pi$
$354$	16.2031	+	17.9954i	0.861184	+	0.956442i
$355$	−0.134080	−	0.0596964i	−0.00711624	−	0.00316836i
$356$	−31.7835	−	23.0920i	−1.68452	−	1.22388i
$357$		0			0
$358$	−3.59123	−	11.0527i	−0.189802	−	0.584152i
$359$	1.11655	−	10.6232i	0.0589290	−	0.560672i	−0.924729	−	0.380626i	$-0.875709\pi$
$359$	1.11655	−	10.6232i	0.0589290	−	0.560672i	0.983658	−	0.180046i	$-0.0576247\pi$
$360$	−0.575082	−	5.47154i	−0.0303095	−	0.288375i
$361$	−7.23177	−	8.03169i	−0.380619	−	0.422721i
$362$	−9.54298	−	16.5289i	−0.501568	−	0.868741i
$363$	−5.75658	+	14.6885i	−0.302142	+	0.770947i
$364$		0			0
$365$	0.239209	−	0.736211i	0.0125208	−	0.0385350i
$366$	7.80866	+	3.47664i	0.408165	+	0.181727i
$367$	9.33346	−	4.15552i	0.487202	−	0.216916i	−0.148408	−	0.988926i	$-0.547415\pi$
$367$	9.33346	−	4.15552i	0.487202	−	0.216916i	0.635611	+	0.772010i	$0.280748\pi$
$368$	−22.8321	−	4.85310i	−1.19020	−	0.252986i
$369$	0.198448	−	0.220398i	0.0103308	−	0.0114735i
$370$	−13.5000	−	9.80834i	−0.701833	−	0.509911i
$371$		0			0
$372$	16.8442	−	51.8411i	0.873331	−	2.68784i
$373$	13.9425	+	24.1492i	0.721917	+	1.25040i	0.960231	+	0.279208i	$0.0900720\pi$
$373$	13.9425	+	24.1492i	0.721917	+	1.25040i	−0.238314	+	0.971188i	$0.576595\pi$
$374$	11.3103	−	46.3955i	0.584843	−	2.39905i
$375$	7.59588	−	13.1564i	0.392249	−	0.679396i
$376$	42.5049	−	9.03469i	2.19202	−	0.465928i
$377$	11.5593	−	8.39832i	0.595334	−	0.432535i
$378$		0			0
$379$	0.354761	+	1.09184i	0.0182228	+	0.0560841i	0.959754	−	0.280841i	$-0.0906132\pi$
$379$	0.354761	+	1.09184i	0.0182228	+	0.0560841i	−0.941532	+	0.336925i	$0.890613\pi$
$380$	9.41817	−	10.4599i	0.483142	−	0.536583i
$381$	−10.5181	+	4.68296i	−0.538859	+	0.239915i
$382$	−2.24335	−	21.3440i	−0.114780	−	1.09206i
$383$	19.5156	−	4.14818i	0.997202	−	0.211962i	0.319729	−	0.947509i	$-0.396408\pi$
$383$	19.5156	−	4.14818i	0.997202	−	0.211962i	0.677473	+	0.735547i	$0.263075\pi$
$384$	29.0038			1.48009
$385$		0			0
$386$	−62.2251			−3.16717
$387$	−0.122281	+	0.0259917i	−0.00621590	+	0.00132123i
$388$	−7.17850	−	68.2989i	−0.364433	−	3.46735i
$389$	2.37522	−	1.05752i	0.120428	−	0.0536182i	−0.345638	−	0.938368i	$-0.612337\pi$
$389$	2.37522	−	1.05752i	0.120428	−	0.0536182i	0.466066	+	0.884750i	$0.345671\pi$
$390$	9.33049	−	10.3626i	0.472468	−	0.524728i
$391$	12.3816	+	38.1067i	0.626166	+	1.92714i
$392$		0			0
$393$	−0.117725	+	0.0855319i	−0.00593842	+	0.00431451i
$394$	−26.6207	+	5.65841i	−1.34113	+	0.285066i
$395$	−5.36761	+	9.29697i	−0.270074	+	0.467782i
$396$	4.63705	+	11.3065i	0.233020	+	0.568173i
$397$	−4.38618	−	7.59709i	−0.220136	−	0.381287i	0.734713	−	0.678378i	$-0.237317\pi$
$397$	−4.38618	−	7.59709i	−0.220136	−	0.381287i	−0.954849	+	0.297091i	$0.903984\pi$
$398$	9.20059	−	28.3165i	0.461184	−	1.41938i
$399$		0			0
$400$	9.53740	+	6.92932i	0.476870	+	0.346466i
$401$	18.9722	−	21.0708i	0.947426	−	1.05222i	−0.0511402	−	0.998691i	$-0.516286\pi$
$401$	18.9722	−	21.0708i	0.947426	−	1.05222i	0.998566	−	0.0535317i	$-0.0170478\pi$
$402$	−32.1180	−	6.82688i	−1.60190	−	0.340494i
$403$	−28.2441	+	12.5751i	−1.40694	+	0.626410i
$404$	−44.5313	−	19.8266i	−2.21551	−	0.986410i
$405$	−2.05418	+	6.32210i	−0.102073	+	0.314148i
$406$		0			0
$407$	17.0331	+	6.09885i	0.844298	+	0.302309i
$408$	19.6911	+	34.1060i	0.974856	+	1.68850i
$409$	13.3194	+	14.7927i	0.658601	+	0.731451i	0.976223	−	0.216767i	$-0.0695510\pi$
$409$	13.3194	+	14.7927i	0.658601	+	0.731451i	−0.317622	+	0.948217i	$0.602884\pi$
$410$	−0.100559	−	0.956751i	−0.00496624	−	0.0472506i
$411$	0.684227	−	6.50999i	0.0337504	−	0.321114i
$412$	9.92212	+	30.5371i	0.488828	+	1.50446i
$413$		0			0
$414$	−12.5414	−	9.11189i	−0.616379	−	0.447825i
$415$	1.09294	+	0.486607i	0.0536502	+	0.0238866i
$416$	−1.87614	−	2.08367i	−0.0919855	−	0.102160i
$417$	2.74315	−	4.75128i	0.134333	−	0.232671i
$418$	−10.0055	+	20.7896i	−0.489387	+	1.01685i
$419$	−30.8957			−1.50935			−0.754676	−	0.656097i	$-0.772206\pi$
$419$	−30.8957			−1.50935			−0.754676	+	0.656097i	$0.772206\pi$
$420$		0			0
$421$	19.5727	−	14.2204i	0.953913	−	0.693058i	0.00218371	−	0.999998i	$-0.499305\pi$
$421$	19.5727	−	14.2204i	0.953913	−	0.693058i	0.951729	+	0.306939i	$0.0993049\pi$
$422$	−3.62369	+	34.4771i	−0.176398	+	1.67832i
$423$	8.64796	+	1.83818i	0.420478	+	0.0893755i
$424$	19.7309	+	4.19393i	0.958216	+	0.203675i
$425$	2.11525	−	20.1252i	0.102605	−	0.976218i
$426$	−0.328846	+	0.238921i	−0.0159326	+	0.0115757i
$427$		0			0
$428$	47.6218			2.30188
$429$	−6.55629	+	13.6227i	−0.316541	+	0.657712i
$430$	−0.202756	+	0.351184i	−0.00977778	+	0.0169356i
$431$	12.9812	+	14.4171i	0.625281	+	0.694445i	0.969680	−	0.244378i	$-0.0785839\pi$
$431$	12.9812	+	14.4171i	0.625281	+	0.694445i	−0.344399	+	0.938823i	$0.611917\pi$
$432$	−17.8299	−	7.93837i	−0.857840	−	0.381935i
$433$	17.3030	+	12.5714i	0.831530	+	0.604142i	0.919992	−	0.391937i	$-0.128195\pi$
$433$	17.3030	+	12.5714i	0.831530	+	0.604142i	−0.0884616	+	0.996080i	$0.528195\pi$
$434$		0			0
$435$	2.50767	+	7.71780i	0.120233	+	0.370040i
$436$	−0.361881	+	3.44307i	−0.0173310	+	0.164893i
$437$	−2.02350	−	19.2524i	−0.0967974	−	0.920965i
$438$	−1.43452	−	1.59320i	−0.0685441	−	0.0761259i
$439$	15.8658	+	27.4803i	0.757232	+	1.31156i	0.944257	+	0.329209i	$0.106782\pi$
$439$	15.8658	+	27.4803i	0.757232	+	1.31156i	−0.187025	+	0.982355i	$0.559885\pi$
$440$	18.2163	+	6.52252i	0.868430	+	0.310949i
$441$		0			0
$442$	14.1415	−	43.5229i	0.672640	−	2.07017i
$443$	−1.52206	−	0.677666i	−0.0723154	−	0.0321969i	0.370260	−	0.928928i	$-0.379269\pi$
$443$	−1.52206	−	0.677666i	−0.0723154	−	0.0321969i	−0.442576	+	0.896731i	$0.645935\pi$
$444$	−27.9246	+	12.4328i	−1.32524	+	0.590037i
$445$	−12.3792	−	2.63128i	−0.586830	−	0.124735i
$446$	4.82032	−	5.35351i	0.228249	−	0.253496i
$447$	5.65324	+	4.10732i	0.267389	+	0.194270i
$448$		0			0
$449$	−5.31070	+	16.3447i	−0.250627	+	0.771352i	0.744032	+	0.668144i	$0.232911\pi$
$449$	−5.31070	+	16.3447i	−0.250627	+	0.771352i	−0.994660	+	0.103208i	$0.967089\pi$
$450$	3.91464	+	6.78035i	0.184538	+	0.319629i
$451$	0.395777	+	0.965021i	0.0186364	+	0.0454411i
$452$	−8.87892	+	15.3787i	−0.417629	+	0.723355i
$453$	23.8121	−	5.06141i	1.11879	−	0.237806i
$454$	16.2337	−	11.7945i	0.761885	−	0.553542i
$455$		0			0
$456$	−5.87973	−	18.0959i	−0.275343	−	0.847420i
$457$	6.83894	−	7.59541i	0.319912	−	0.355299i	−0.561643	−	0.827380i	$-0.689830\pi$
$457$	6.83894	−	7.59541i	0.319912	−	0.355299i	0.881555	+	0.472081i	$0.156497\pi$
$458$	−29.1043	+	12.9581i	−1.35996	+	0.605491i
$459$	3.50193	+	33.3186i	0.163456	+	1.55518i
$460$	−32.5330	+	6.91511i	−1.51686	+	0.322418i
$461$	−22.1160			−1.03004			−0.515022	−	0.857177i	$-0.672216\pi$
$461$	−22.1160			−1.03004			−0.515022	+	0.857177i	$0.672216\pi$
$462$		0			0
$463$	−30.3717			−1.41149			−0.705747	−	0.708464i	$-0.749389\pi$
$463$	−30.3717			−1.41149			−0.705747	+	0.708464i	$0.749389\pi$
$464$	−15.1759	+	3.22574i	−0.704525	+	0.149751i
$465$	−1.83547	−	17.4633i	−0.0851177	−	0.809841i
$466$	28.4817	−	12.6809i	1.31939	−	0.587429i
$467$	16.8560	−	18.7205i	0.780002	−	0.866280i	−0.213865	−	0.976863i	$-0.568605\pi$
$467$	16.8560	−	18.7205i	0.780002	−	0.866280i	0.993867	+	0.110583i	$0.0352718\pi$
$468$	3.61884	+	11.1376i	0.167281	+	0.514837i
$469$		0			0
$470$	23.2015	−	16.8569i	1.07021	−	0.777551i
$471$	−3.14919	+	0.669382i	−0.145107	+	0.0308435i
$472$	−16.0997	+	27.8856i	−0.741050	+	1.28354i
$473$	0.104131	−	0.427149i	0.00478793	−	0.0196403i
$474$	14.8656	+	25.7479i	0.682798	+	1.18264i
$475$	−3.02123	+	9.29838i	−0.138623	+	0.426639i
$476$		0			0
$477$	3.32028	+	2.41233i	0.152025	+	0.110453i
$478$	8.10070	−	8.99674i	0.370517	−	0.411501i
$479$	20.7406	+	4.40856i	0.947663	+	0.201432i	0.655721	−	0.755004i	$-0.272365\pi$
$479$	20.7406	+	4.40856i	0.947663	+	0.201432i	0.291943	+	0.956436i	$0.405698\pi$
$480$	1.45479	−	0.647713i	0.0664016	−	0.0295639i
$481$	15.8386	+	7.05181i	0.722179	+	0.321535i
$482$	1.97290	−	6.07197i	0.0898633	−	0.276571i
$483$		0			0
$484$	−42.9024	−	2.54942i	−1.95011	−	0.115883i
$485$	−11.0615	−	19.1591i	−0.502276	−	0.869968i
$486$	−15.2720	−	16.9613i	−0.692752	−	0.769379i
$487$	1.75814	+	16.7276i	0.0796691	+	0.758001i	0.959309	+	0.282360i	$0.0911172\pi$
$487$	1.75814	+	16.7276i	0.0796691	+	0.758001i	−0.879639	+	0.475641i	$0.842216\pi$
$488$	−1.18807	+	11.3038i	−0.0537815	+	0.511697i
$489$	−7.01897	−	21.6022i	−0.317409	−	0.976884i
$490$		0			0
$491$	−3.91406	−	2.84373i	−0.176639	−	0.128336i	0.495953	−	0.868350i	$-0.334819\pi$
$491$	−3.91406	−	2.84373i	−0.176639	−	0.128336i	−0.672592	+	0.740014i	$0.734819\pi$
$492$	−1.60989	−	0.716768i	−0.0725793	−	0.0323144i
$493$	17.8204	+	19.7915i	0.802589	+	0.891365i
$494$	−11.0549	+	19.1477i	−0.497385	+	0.861496i
$495$	2.84608	+	2.71980i	0.127922	+	0.122246i
$496$	33.5719			1.50742
$497$		0			0
$498$	2.68055	−	1.94753i	0.120118	−	0.0872709i
$499$	−3.19685	+	30.4160i	−0.143111	+	1.36161i	0.653413	+	0.757001i	$0.273336\pi$
$499$	−3.19685	+	30.4160i	−0.143111	+	1.36161i	−0.796524	+	0.604607i	$0.793330\pi$
$500$	40.4814	+	8.60458i	1.81038	+	0.384809i
$501$	−29.0976	−	6.18489i	−1.29999	−	0.276320i
$502$	−6.66197	+	63.3844i	−0.297338	+	2.82898i
$503$	22.8472	−	16.5994i	1.01871	−	0.740133i	0.0526880	−	0.998611i	$-0.483221\pi$
$503$	22.8472	−	16.5994i	1.01871	−	0.740133i	0.966017	+	0.258478i	$0.0832211\pi$
$504$		0			0
$505$	−15.7029			−0.698768
$506$	48.0032	−	25.8467i	2.13400	−	1.14902i
$507$	2.07842	−	3.59992i	0.0923057	−	0.159878i
$508$	−20.9875	−	23.3090i	−0.931171	−	1.03417i
$509$	−3.83748	−	1.70856i	−0.170093	−	0.0757305i	0.319924	−	0.947443i	$-0.396343\pi$
$509$	−3.83748	−	1.70856i	−0.170093	−	0.0757305i	−0.490017	+	0.871713i	$0.663009\pi$
$510$	21.0273	+	15.2772i	0.931104	+	0.676486i
$511$		0			0
$512$	10.8274	+	33.3234i	0.478509	+	1.47270i
$513$	1.69193	−	16.0976i	0.0747004	−	0.710726i
$514$	7.60929	+	72.3976i	0.335632	+	3.19332i
$515$	6.92113	+	7.68669i	0.304981	+	0.338716i
$516$	0.371411	+	0.643303i	0.0163505	+	0.0283198i
$517$	−19.0147	+	24.6018i	−0.836265	+	1.08199i
$518$		0			0
$519$	−9.55323	+	29.4018i	−0.419340	+	1.29060i
$520$	16.9389	+	7.54169i	0.742820	+	0.330725i
$521$	−18.8619	+	8.39787i	−0.826356	+	0.367918i	−0.775937	−	0.630811i	$-0.782722\pi$
$521$	−18.8619	+	8.39787i	−0.826356	+	0.367918i	−0.0504195	+	0.998728i	$0.516056\pi$
$522$	−10.0787	−	2.14230i	−0.441133	−	0.0937657i
$523$	−15.1451	+	16.8204i	−0.662251	+	0.735504i	−0.976898	−	0.213704i	$-0.931447\pi$
$523$	−15.1451	+	16.8204i	−0.662251	+	0.735504i	0.314647	+	0.949209i	$0.398114\pi$
$524$	−0.320708	−	0.233008i	−0.0140102	−	0.0101790i
$525$		0			0
$526$	−2.50632	+	7.71367i	−0.109281	+	0.336332i
$527$	−28.8138	−	49.9069i	−1.25515	−	2.17398i
$528$	12.5204	−	10.6180i	0.544882	−	0.462088i
$529$	−11.3720	+	19.6969i	−0.494434	+	0.856385i
$530$	13.0218	−	2.76787i	0.565631	−	0.120229i
$531$	−5.30007	+	3.85073i	−0.230003	+	0.167107i
$532$		0			0
$533$	0.308871	+	0.950608i	0.0133787	+	0.0411754i
$534$	−23.4530	+	26.0472i	−1.01491	+	1.12717i
$535$	14.0146	−	6.23969i	0.605903	−	0.269765i
$536$	−4.56394	−	43.4230i	−0.197132	−	1.87559i
$537$	−6.70795	+	1.42582i	−0.289469	+	0.0615286i
$538$	4.21881			0.181886
$539$		0			0
$540$	−27.8098			−1.19674
$541$	−41.7828	+	8.88122i	−1.79638	+	0.381833i	−0.980521	−	0.196412i	$-0.937071\pi$
$541$	−41.7828	+	8.88122i	−1.79638	+	0.381833i	−0.815863	+	0.578245i	$0.803738\pi$
$542$	−0.629021	−	5.98473i	−0.0270188	−	0.257066i
$543$	−10.2889	+	4.58091i	−0.441539	+	0.196586i
$544$	3.49702	−	3.88383i	0.149934	−	0.166518i
$545$	0.344634	+	1.06067i	0.0147625	+	0.0454343i
$546$		0			0
$547$	−35.9873	+	26.1463i	−1.53870	+	1.11793i	−0.587563	+	0.809178i	$0.699913\pi$
$547$	−35.9873	+	26.1463i	−1.53870	+	1.11793i	−0.951141	+	0.308756i	$0.900087\pi$
$548$	17.4427	−	3.70756i	0.745114	−	0.158379i
$549$	−1.15626	+	2.00269i	−0.0493478	+	0.0854728i
$550$	−27.4573	+	2.06435i	−1.17078	+	0.0880242i
$551$	−6.43354	−	11.1432i	−0.274078	−	0.474717i
$552$	−13.8938	+	42.7608i	−0.591360	+	1.82002i
$553$		0			0
$554$	10.1376	+	7.36536i	0.430703	+	0.312924i
$555$	−6.58889	+	7.31770i	−0.279683	+	0.310619i
$556$	14.6193	+	3.10743i	0.619998	+	0.131785i
$557$	−22.8305	+	10.1648i	−0.967360	+	0.430696i	−0.828730	−	0.559648i	$-0.810936\pi$
$557$	−22.8305	+	10.1648i	−0.967360	+	0.430696i	−0.138629	+	0.990344i	$0.544270\pi$
$558$	20.3683	+	9.06856i	0.862259	+	0.383903i
$559$	0.130196	−	0.400702i	0.00550670	−	0.0169479i
$560$		0			0
$561$	−26.5303	−	9.49941i	−1.12011	−	0.401065i
$562$	−27.4283	−	47.5072i	−1.15699	−	2.00397i
$563$	6.02890	+	6.69578i	0.254088	+	0.282193i	0.856671	−	0.515863i	$-0.172529\pi$
$563$	6.02890	+	6.69578i	0.254088	+	0.282193i	−0.602583	+	0.798056i	$0.705862\pi$
$564$	−5.49129	−	52.2461i	−0.231225	−	2.19996i
$565$	−0.597955	+	5.68916i	−0.0251562	+	0.239345i
$566$	6.37460	+	19.6190i	0.267944	+	0.824648i
$567$		0			0
$568$	−0.437275	−	0.317699i	−0.0183476	−	0.0133303i
$569$	26.6516	+	11.8661i	1.11729	+	0.497452i	0.880471	−	0.474101i	$-0.157227\pi$
$569$	26.6516	+	11.8661i	1.11729	+	0.497452i	0.236824	+	0.971553i	$0.423893\pi$
$570$	−8.40254	−	9.33197i	−0.351944	−	0.390873i
$571$	−0.894970	+	1.55013i	−0.0374533	+	0.0648711i	−0.884144	−	0.467214i	$-0.845258\pi$
$571$	−0.894970	+	1.55013i	−0.0374533	+	0.0648711i	0.846691	+	0.532085i	$0.178591\pi$
$572$	−40.8144	−	5.51858i	−1.70653	−	0.230743i
$573$	−12.6645			−0.529065
$574$		0			0
$575$	18.6906	−	13.5795i	0.779452	−	0.566305i
$576$	−0.891772	+	8.48465i	−0.0371572	+	0.353527i
$577$	21.1133	+	4.48777i	0.878958	+	0.186828i	0.625223	−	0.780446i	$-0.285008\pi$
$577$	21.1133	+	4.48777i	0.878958	+	0.186828i	0.253734	+	0.967274i	$0.418341\pi$
$578$	43.0202	+	9.14422i	1.78940	+	0.380349i
$579$	−3.83817	+	36.5178i	−0.159509	+	1.51763i
$580$	−17.8850	+	12.9942i	−0.742633	+	0.539554i
$581$		0			0
$582$	−61.2694			−2.53970
$583$	−12.7086	+	6.84276i	−0.526336	+	0.283398i
$584$	1.42537	−	2.46881i	0.0589823	−	0.102160i
$585$	2.52430	+	2.80352i	0.104367	+	0.115911i
$586$	−54.6780	−	24.3442i	−2.25873	−	1.00565i
$587$	−4.46865	−	3.24666i	−0.184441	−	0.134004i	0.491734	−	0.870746i	$-0.336363\pi$
$587$	−4.46865	−	3.24666i	−0.184441	−	0.134004i	−0.676174	+	0.736742i	$0.736363\pi$
$588$		0			0
$589$	8.60373	+	26.4796i	0.354511	+	1.09107i
$590$	−2.22131	+	21.1343i	−0.0914497	+	0.870086i
$591$	1.67871	+	15.9718i	0.0690527	+	0.656993i
$592$	−12.5972	−	13.9907i	−0.517744	−	0.575013i
$593$	20.3933	+	35.3223i	0.837454	+	1.45051i	0.892017	+	0.452002i	$0.149290\pi$
$593$	20.3933	+	35.3223i	0.837454	+	1.45051i	−0.0545633	+	0.998510i	$0.517377\pi$
$594$	43.7534	−	12.7941i	1.79522	−	0.524948i
$595$		0			0
$596$	−5.88254	+	18.1046i	−0.240958	+	0.741593i
$597$	−16.0505	−	7.14613i	−0.656902	−	0.292472i
$598$	47.7288	−	21.2502i	1.95178	−	0.868986i
$599$	25.9355	+	5.51276i	1.05970	+	0.225245i	0.704615	−	0.709590i	$-0.251120\pi$
$599$	25.9355	+	5.51276i	1.05970	+	0.225245i	0.355081	+	0.934835i	$0.384453\pi$
$600$	15.1943	−	16.8750i	0.620306	−	0.688919i
$601$	30.5565	+	22.2006i	1.24643	+	0.905581i	0.998009	−	0.0630720i	$-0.0200898\pi$
$601$	30.5565	+	22.2006i	1.24643	+	0.905581i	0.248417	+	0.968653i	$0.420090\pi$
$602$		0			0
$603$	2.74513	−	8.44864i	0.111790	−	0.344055i
$604$	33.1593	+	57.4336i	1.34923	+	2.33694i
$605$	−12.9598	+	4.87106i	−0.526889	+	0.198037i
$606$	−21.7445	+	37.6626i	−0.883310	+	1.52994i
$607$	27.1185	−	5.76422i	1.10071	−	0.233962i	0.378474	−	0.925612i	$-0.376449\pi$
$607$	27.1185	−	5.76422i	1.10071	−	0.233962i	0.722233	+	0.691650i	$0.243116\pi$
$608$	−2.04277	+	1.48416i	−0.0828452	+	0.0601906i
$609$		0			0
$610$	2.31801	+	7.13411i	0.0938536	+	0.288852i
$611$	−19.9380	+	22.1433i	−0.806603	+	0.895824i
$612$	−19.9411	+	8.87834i	−0.806071	+	0.358886i
$613$	−3.78669	−	36.0280i	−0.152943	−	1.45516i	−0.754486	−	0.656316i	$-0.772114\pi$
$613$	−3.78669	−	36.0280i	−0.152943	−	1.45516i	0.601543	−	0.798841i	$-0.294553\pi$
$614$	10.9213	−	2.32139i	0.440747	−	0.0936837i
$615$	−0.567687			−0.0228914
$616$		0			0
$617$	41.1920			1.65833			0.829163	−	0.559007i	$-0.188817\pi$
$617$	41.1920			1.65833			0.829163	+	0.559007i	$0.188817\pi$
$618$	28.0202	−	5.95587i	1.12714	−	0.239580i
$619$	3.73580	+	35.5437i	0.150154	+	1.42862i	0.767054	+	0.641582i	$0.221722\pi$
$619$	3.73580	+	35.5437i	0.150154	+	1.42862i	−0.616900	+	0.787042i	$0.711612\pi$
$620$	43.7004	−	19.4567i	1.75505	−	0.781398i
$621$	−25.5930	+	28.4240i	−1.02701	+	1.14061i
$622$	1.66037	+	5.11010i	0.0665749	+	0.204897i
$623$		0			0
$624$	12.7274	−	9.24698i	0.509503	−	0.370176i
$625$	−3.66537	+	0.779098i	−0.146615	+	0.0311639i
$626$	−11.7868	+	20.4154i	−0.471096	+	0.815963i
$627$	11.5836	+	7.15425i	0.462603	+	0.285713i
$628$	−4.38539	−	7.59571i	−0.174996	−	0.303102i
$629$	−9.98623	+	30.7345i	−0.398177	+	1.22546i
$630$		0			0
$631$	−2.23700	−	1.62527i	−0.0890534	−	0.0647011i	0.542368	−	0.840141i	$-0.317528\pi$
$631$	−2.23700	−	1.62527i	−0.0890534	−	0.0647011i	−0.631421	+	0.775440i	$0.717528\pi$
$632$	−26.4535	+	29.3796i	−1.05227	+	1.16866i
$633$	20.0099	+	4.25324i	0.795322	+	0.169051i
$634$	−14.3331	+	6.38151i	−0.569240	+	0.253442i
$635$	−9.23048	−	4.10968i	−0.366301	−	0.163088i
$636$	7.53581	−	23.1928i	0.298814	−	0.919655i
$637$		0			0
$638$	22.1605	−	28.6720i	0.877344	−	1.13514i
$639$	−0.0549848	−	0.0952364i	−0.00217516	−	0.00376749i
$640$	17.0315	+	18.9154i	0.673228	+	0.747696i
$641$	−4.02293	−	38.2756i	−0.158896	−	1.51180i	−0.725739	−	0.687970i	$-0.758502\pi$
$641$	−4.02293	−	38.2756i	−0.158896	−	1.51180i	0.566843	−	0.823826i	$-0.308165\pi$
$642$	4.44104	−	42.2536i	0.175274	−	1.66762i
$643$	−8.15130	−	25.0871i	−0.321456	−	0.989339i	−0.973015	−	0.230741i	$-0.925885\pi$
$643$	−8.15130	−	25.0871i	−0.321456	−	0.989339i	0.651559	−	0.758598i	$-0.274115\pi$
$644$		0			0
$645$	0.193592	+	0.140653i	0.00762267	+	0.00553819i
$646$	−37.6486	−	16.7622i	−1.48126	−	0.659501i
$647$	−18.2814	−	20.3035i	−0.718715	−	0.798214i	0.267522	−	0.963552i	$-0.413795\pi$
$647$	−18.2814	−	20.3035i	−0.718715	−	0.798214i	−0.986237	+	0.165338i	$0.947129\pi$
$648$	−12.2402	+	21.2006i	−0.480839	+	0.832838i
$649$	−4.11948	−	22.6688i	−0.161704	−	0.889830i
$650$	−26.3865			−1.03496
$651$		0			0
$652$	50.0601	−	36.3708i	1.96051	−	1.42439i
$653$	0.884484	−	8.41530i	0.0346125	−	0.329316i	−0.963490	−	0.267744i	$-0.913722\pi$
$653$	0.884484	−	8.41530i	0.0346125	−	0.329316i	0.998103	−	0.0615722i	$-0.0196114\pi$
$654$	3.02120	+	0.642177i	0.118138	+	0.0251111i
$655$	−0.124911	−	0.0265506i	−0.00488068	−	0.00103742i
$656$	0.113451	−	1.07941i	0.00442951	−	0.0421439i
$657$	0.469236	−	0.340920i	0.0183066	−	0.0133005i
$658$		0			0
$659$	−5.29247			−0.206165			−0.103083	−	0.994673i	$-0.532871\pi$
$659$	−5.29247			−0.206165			−0.103083	+	0.994673i	$0.532871\pi$
$660$	10.1441	−	21.0776i	0.394860	−	0.820445i
$661$	9.63501	−	16.6883i	0.374759	−	0.649101i	−0.615532	−	0.788112i	$-0.711059\pi$
$661$	9.63501	−	16.6883i	0.374759	−	0.649101i	0.990291	+	0.139011i	$0.0443922\pi$
$662$	−5.88841	−	6.53974i	−0.228859	−	0.254174i
$663$	−24.6698	−	10.9837i	−0.958097	−	0.426572i
$664$	3.56439	+	2.58968i	0.138325	+	0.100499i
$665$		0			0
$666$	−3.86364	−	11.8911i	−0.149713	−	0.460769i
$667$	−3.17818	+	30.2384i	−0.123060	+	1.17084i
$668$	−8.47092	−	80.5954i	−0.327750	−	3.11833i
$669$	−2.84447	−	3.15910i	−0.109973	−	0.122138i
$670$	−14.4079	−	24.9552i	−0.556625	−	0.964104i
$671$	−4.58304	−	6.71858i	−0.176926	−	0.259368i
$672$		0			0
$673$	−5.86892	+	18.0627i	−0.226230	+	0.696265i	0.771934	+	0.635702i	$0.219289\pi$
$673$	−5.86892	+	18.0627i	−0.226230	+	0.696265i	−0.998164	+	0.0605625i	$0.980711\pi$
$674$	14.2214	+	6.33178i	0.547789	+	0.243891i
$675$	17.6471	−	7.85699i	0.679236	−	0.302416i
$676$	11.0767	+	2.35442i	0.426026	+	0.0905547i
$677$	21.6945	−	24.0942i	0.833786	−	0.926013i	−0.164389	−	0.986396i	$-0.552565\pi$
$677$	21.6945	−	24.0942i	0.833786	−	0.926013i	0.998175	+	0.0603821i	$0.0192319\pi$
$678$	12.8172	+	9.31222i	0.492240	+	0.357633i
$679$		0			0
$680$	−10.6800	+	32.8695i	−0.409558	+	1.26049i
$681$	−5.92044	−	10.2545i	−0.226872	−	0.392954i
$682$	−59.8031	+	50.7160i	−2.28998	+	1.94202i
$683$	−7.56298	+	13.0995i	−0.289389	+	0.501237i	−0.973664	−	0.227987i	$-0.926786\pi$
$683$	−7.56298	+	13.0995i	−0.289389	+	0.501237i	0.684275	+	0.729224i	$0.260119\pi$
$684$	10.3157	−	2.19266i	0.394430	−	0.0838386i
$685$	4.64740	−	3.37654i	0.177568	−	0.129011i
$686$		0			0
$687$	5.80944	+	17.8796i	0.221644	+	0.682150i
$688$	−0.306128	+	0.339990i	−0.0116710	+	0.0129620i
$689$	−12.6359	+	5.62588i	−0.481391	+	0.214329i
$690$	3.10169	+	29.5106i	0.118079	+	1.12345i
$691$	30.7244	−	6.53067i	1.16881	−	0.248438i	0.417681	−	0.908594i	$-0.362843\pi$
$691$	30.7244	−	6.53067i	1.16881	−	0.248438i	0.751129	+	0.660155i	$0.229510\pi$
$692$	−84.2192			−3.20153
$693$		0			0
$694$	42.4357			1.61084
$695$	4.70946	−	1.00103i	0.178640	−	0.0379711i
$696$	3.12381	+	29.7210i	0.118408	+	1.12657i
$697$	−1.70199	+	0.757776i	−0.0644675	+	0.0287028i
$698$	35.1684	−	39.0584i	1.33114	−	1.47838i
$699$	−5.68515	−	17.4971i	−0.215032	−	0.661801i
$700$		0			0
$701$	12.9966	−	9.44259i	0.490875	−	0.356642i	−0.314646	−	0.949209i	$-0.601886\pi$
$701$	12.9966	−	9.44259i	0.490875	−	0.356642i	0.805521	+	0.592568i	$0.201886\pi$
$702$	42.7299	−	9.08252i	1.61274	−	0.342798i
$703$	7.80663	−	13.5215i	0.294433	−	0.509972i
$704$	−25.5277	−	15.7664i	−0.962111	−	0.594220i
$705$	−8.46162	−	14.6560i	−0.318683	−	0.551975i
$706$	−3.30575	+	10.1741i	−0.124414	+	0.382906i
$707$		0			0
$708$	31.4928	+	22.8809i	1.18357	+	0.859916i
$709$	26.5630	−	29.5012i	0.997594	−	1.10794i	0.00343775	−	0.999994i	$-0.498906\pi$
$709$	26.5630	−	29.5012i	0.997594	−	1.10794i	0.994157	−	0.107947i	$-0.0344276\pi$
$710$	−0.348920	−	0.0741653i	−0.0130948	−	0.00278338i
$711$	−7.34816	+	3.27161i	−0.275578	+	0.122695i
$712$	−42.5775	−	18.9567i	−1.59566	−	0.710433i
$713$	20.3306	−	62.5713i	0.761389	−	2.34331i
$714$		0			0
$715$	−12.7343	+	3.72368i	−0.476236	+	0.139258i
$716$	−9.34111	−	16.1793i	−0.349094	−	0.604648i
$717$	−4.78021	−	5.30896i	−0.178520	−	0.198267i
$718$	−2.71371	−	25.8192i	−0.101275	−	0.963565i
$719$	1.03090	−	9.80838i	0.0384462	−	0.365791i	−0.958337	−	0.285641i	$-0.907793\pi$
$719$	1.03090	−	9.80838i	0.0384462	−	0.365791i	0.996783	−	0.0801497i	$-0.0255399\pi$
$720$	−1.26587	−	3.89596i	−0.0471763	−	0.145194i
$721$		0			0
$722$	−21.2510	−	15.4397i	−0.790879	−	0.574607i
$723$	−3.44174	−	1.53236i	−0.128000	−	0.0569891i
$724$	−20.5302	−	22.8011i	−0.762998	−	0.847395i
$725$	7.67796	−	13.2986i	0.285152	−	0.493898i
$726$	−6.26296	+	37.8285i	−0.232440	+	1.40395i
$727$	−31.5764			−1.17111			−0.585553	−	0.810634i	$-0.699122\pi$
$727$	−31.5764			−1.17111			−0.585553	+	0.810634i	$0.699122\pi$
$728$		0			0
$729$	−23.7145	+	17.2296i	−0.878313	+	0.638132i
$730$	0.196661	−	1.87110i	0.00727874	−	0.0692526i
$731$	0.768160	+	0.163277i	0.0284114	+	0.00603904i
$732$	13.4406	+	2.85688i	0.496778	+	0.105594i
$733$	−4.31625	+	41.0664i	−0.159424	+	1.51682i	0.563629	+	0.826028i	$0.309405\pi$
$733$	−4.31625	+	41.0664i	−0.159424	+	1.51682i	−0.723053	+	0.690793i	$0.757262\pi$
$734$	20.0889	−	14.5955i	0.741496	−	0.538729i
$735$		0			0
$736$	5.96659			0.219931
$737$	22.5869	+	21.5848i	0.832000	+	0.795087i
$738$	0.360406	−	0.624242i	0.0132667	−	0.0229787i
$739$	23.6936	+	26.3144i	0.871584	+	0.967992i	0.999718	−	0.0237652i	$-0.00756542\pi$
$739$	23.6936	+	26.3144i	0.871584	+	0.967992i	−0.128134	+	0.991757i	$0.540899\pi$
$740$	−24.5061	−	10.9108i	−0.900862	−	0.401090i
$741$	10.5552	+	7.66883i	0.387756	+	0.281722i
$742$		0			0
$743$	−1.24351	−	3.82713i	−0.0456200	−	0.140404i	0.925652	−	0.378376i	$-0.123517\pi$
$743$	−1.24351	−	3.82713i	−0.0456200	−	0.140404i	−0.971272	+	0.237972i	$0.923517\pi$
$744$	6.75941	−	64.3114i	0.247812	−	2.35777i
$745$	0.641005	+	6.09875i	0.0234846	+	0.223441i
$746$	45.3492	+	50.3654i	1.66035	+	1.84401i
$747$	0.448201	+	0.776307i	0.0163988	+	0.0284036i
$748$	2.27790	−	76.7340i	0.0832882	−	2.80567i
$749$		0			0
$750$	11.4098	−	35.1157i	0.416626	−	1.28224i
$751$	22.3079	+	9.93210i	0.814025	+	0.362427i	0.771150	−	0.636653i	$-0.219682\pi$
$751$	22.3079	+	9.93210i	0.814025	+	0.362427i	0.0428749	+	0.999080i	$0.486348\pi$
$752$	29.5582	−	13.1601i	1.07788	−	0.479901i
$753$	36.7872	+	7.81936i	1.34060	+	0.284953i
$754$	23.2365	−	25.8068i	0.846225	−	0.939828i
$755$	17.2837	+	12.5573i	0.629019	+	0.457009i
$756$		0			0
$757$	−0.407046	+	1.25276i	−0.0147943	+	0.0455323i	−0.958181	−	0.286162i	$-0.907620\pi$
$757$	−0.407046	+	1.25276i	−0.0147943	+	0.0455323i	0.943387	+	0.331695i	$0.107620\pi$
$758$	1.39512	+	2.41641i	0.0506729	+	0.0877680i
$759$	−12.2076	−	29.7657i	−0.443107	−	1.08043i
$760$	8.34895	−	14.4608i	0.302848	−	0.524548i
$761$	7.08574	−	1.50612i	0.256858	−	0.0545968i	−0.0776828	−	0.996978i	$-0.524752\pi$
$761$	7.08574	−	1.50612i	0.256858	−	0.0545968i	0.334541	+	0.942381i	$0.391419\pi$
$762$	−22.6387	+	16.4480i	−0.820115	+	0.595848i
$763$		0			0
$764$	−10.6613	−	32.8122i	−0.385714	−	1.18710i
$765$	−4.70515	+	5.22560i	−0.170115	+	0.188932i
$766$	44.2992	−	19.7233i	1.60059	−	0.712630i
$767$	−2.30791	−	21.9583i	−0.0833338	−	0.792868i
$768$	43.5696	−	9.26101i	1.57218	−	0.334178i
$769$	44.3139			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$769$	44.3139			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$770$		0			0
$771$	42.9570			1.54706
$772$	−97.8447	+	20.7975i	−3.52151	+	0.748520i
$773$	−1.99189	−	18.9516i	−0.0716433	−	0.681640i	−0.970121	−	0.242621i	$-0.921993\pi$
$773$	−1.99189	−	18.9516i	−0.0716433	−	0.681640i	0.898478	−	0.439019i	$-0.144674\pi$
$774$	−0.277570	+	0.123582i	−0.00997704	+	0.00444207i
$775$	−22.2337	+	24.6930i	−0.798657	+	0.886999i
$776$	−25.1761	−	77.4839i	−0.903768	−	2.78151i
$777$		0			0
$778$	5.11232	−	3.71432i	0.183286	−	0.133165i
$779$	0.880453	−	0.187146i	0.0315455	−	0.00670520i
$780$	11.2081	−	19.4129i	0.401313	−	0.695095i
$781$	0.385664	−	0.0289957i	0.0138001	−	0.00103755i
$782$	48.6914	+	84.3360i	1.74120	+	3.01585i
$783$	−7.85604	+	24.1784i	−0.280752	+	0.864066i
$784$		0			0
$785$	−2.28581	−	1.66074i	−0.0815840	−	0.0592742i
$786$	−0.236650	+	0.262827i	−0.00844104	+	0.00937473i
$787$	−30.7725	−	6.54091i	−1.09692	−	0.233158i	−0.376308	−	0.926494i	$-0.622807\pi$
$787$	−30.7725	−	6.54091i	−1.09692	−	0.233158i	−0.720614	+	0.693336i	$0.756140\pi$
$788$	−39.9680	+	17.7949i	−1.42380	+	0.633918i
$789$	4.37229	+	1.94667i	0.155658	+	0.0693033i
$790$	−8.06270	+	24.8144i	−0.286858	+	0.882858i
$791$		0			0
$792$	8.16964	+	11.9764i	0.290295	+	0.425563i
$793$	−3.89685	−	6.74955i	−0.138381	−	0.239683i
$794$	−14.2664	−	15.8445i	−0.506296	−	0.562299i
$795$	−0.821156	−	7.81278i	−0.0291234	−	0.277091i
$796$	5.00305	−	47.6009i	0.177329	−	1.68717i
$797$	−3.87670	−	11.9313i	−0.137320	−	0.422627i	0.858624	−	0.512606i	$-0.171320\pi$
$797$	−3.87670	−	11.9313i	−0.137320	−	0.422627i	−0.995944	+	0.0899793i	$0.971320\pi$
$798$		0			0
$799$	−44.9324	−	32.6453i	−1.58959	−	1.15491i
$800$	−2.75288	−	1.22566i	−0.0973291	−	0.0433337i
$801$	−6.34506	−	7.04691i	−0.224192	−	0.248990i
$802$	34.4559	−	59.6794i	1.21668	−	2.10735i
$803$	0.364713	+	2.00696i	0.0128704	+	0.0708241i
$804$	−52.7850			−1.86159
$805$		0			0
$806$	−60.7915	+	44.1676i	−2.14129	+	1.55574i
$807$	0.260225	−	2.47587i	0.00916035	−	0.0871549i
$808$	−56.5647	−	12.0232i	−1.98994	−	0.422975i
$809$	5.26267	+	1.11861i	0.185026	+	0.0393284i	0.299492	−	0.954099i	$-0.403183\pi$
$809$	5.26267	+	1.11861i	0.185026	+	0.0393284i	−0.114467	+	0.993427i	$0.536516\pi$
$810$	−1.68880	+	16.0678i	−0.0593382	+	0.564565i
$811$	−11.0835	+	8.05262i	−0.389194	+	0.282766i	−0.765125	−	0.643882i	$-0.777323\pi$
$811$	−11.0835	+	8.05262i	−0.389194	+	0.282766i	0.375931	+	0.926647i	$0.377323\pi$
$812$		0			0
$813$	−3.55103			−0.124540
$814$	43.5753	+	5.89189i	1.52731	+	0.206511i
$815$	9.96663	−	17.2627i	0.349116	−	0.604686i
$816$	19.6212	+	21.7915i	0.686878	+	0.762855i
$817$	−0.346619	−	0.154325i	−0.0121266	−	0.00539913i
$818$	39.1398	+	28.4367i	1.36849	+	0.994266i
$819$		0			0
$820$	−0.477897	−	1.47082i	−0.0166889	−	0.0513631i
$821$	0.964918	−	9.18059i	0.0336759	−	0.320405i	−0.964696	−	0.263366i	$-0.915167\pi$
$821$	0.964918	−	9.18059i	0.0336759	−	0.320405i	0.998372	−	0.0570390i	$-0.0181659\pi$
$822$	−1.66298	−	15.8222i	−0.0580032	−	0.551863i
$823$	−8.32577	−	9.24670i	−0.290218	−	0.322320i	0.580351	−	0.814367i	$-0.302916\pi$
$823$	−8.32577	−	9.24670i	−0.290218	−	0.322320i	−0.870569	+	0.492047i	$0.836249\pi$
$824$	19.0457	+	32.9882i	0.663490	+	1.14920i
$825$	−0.482127	+	16.2411i	−0.0167855	+	0.565442i
$826$		0			0
$827$	−1.38559	+	4.26441i	−0.0481817	+	0.148288i	−0.972253	−	0.233932i	$-0.924841\pi$
$827$	−1.38559	+	4.26441i	−0.0481817	+	0.148288i	0.924071	+	0.382221i	$0.124841\pi$
$828$	−22.7660	−	10.1361i	−0.791175	−	0.352254i
$829$	−33.6893	+	14.9995i	−1.17008	+	0.520953i	−0.897428	−	0.441161i	$-0.854567\pi$
$829$	−33.6893	+	14.9995i	−1.17008	+	0.520953i	−0.272650	+	0.962113i	$0.587900\pi$
$830$	2.84418	+	0.604549i	0.0987229	+	0.0209842i
$831$	4.94778	−	5.49507i	0.171637	−	0.190622i
$832$	−23.2615	−	16.9005i	−0.806447	−	0.585918i
$833$		0			0
$834$	4.12050	−	12.6816i	0.142681	−	0.439127i
$835$	−13.0530	−	22.6084i	−0.451717	−	0.782397i
$836$	−8.78449	+	36.0344i	−0.303818	+	1.24628i
$837$	27.5053	−	47.6405i	0.950721	−	1.64670i
$838$	−73.4496	+	15.6122i	−2.53727	+	0.539314i
$839$	−7.41389	+	5.38651i	−0.255956	+	0.185963i	−0.708362	−	0.705849i	$-0.750566\pi$
$839$	−7.41389	+	5.38651i	−0.255956	+	0.185963i	0.452406	+	0.891812i	$0.350566\pi$
$840$		0			0
$841$	−2.71643	−	8.36030i	−0.0936699	−	0.288286i
$842$	39.3451	−	43.6971i	1.35592	−	1.50590i
$843$	−29.5722	+	13.1664i	−1.01852	+	0.453474i
$844$	5.82530	+	55.4240i	0.200515	+	1.90777i
$845$	3.56824	−	0.758452i	0.122751	−	0.0260915i
$846$	21.4880			0.738774
$847$		0			0
$848$	15.0195			0.515771
$849$	11.9069	−	2.53089i	0.408644	−	0.0868600i
$850$	−5.14101	−	48.9134i	−0.176335	−	1.67772i
$851$	−33.7045	+	15.0062i	−1.15538	+	0.514407i
$852$	−0.437233	+	0.485597i	−0.0149794	+	0.0166363i
$853$	2.01494	+	6.20135i	0.0689903	+	0.212330i	0.979608	−	0.200921i	$-0.0643933\pi$
$853$	2.01494	+	6.20135i	0.0689903	+	0.212330i	−0.910617	+	0.413251i	$0.864393\pi$
$854$		0			0
$855$	2.74849	−	1.99690i	0.0939965	−	0.0682924i
$856$	55.2606	−	11.7460i	1.88877	−	0.401470i
$857$	−24.0368	+	41.6330i	−0.821082	+	1.42216i	0.0837952	+	0.996483i	$0.473296\pi$
$857$	−24.0368	+	41.6330i	−0.821082	+	1.42216i	−0.904877	+	0.425673i	$0.860038\pi$
$858$	−8.70270	+	35.6989i	−0.297105	+	1.21874i
$859$	0.158149	+	0.273922i	0.00539598	+	0.00934610i	0.868711	−	0.495320i	$-0.164949\pi$
$859$	0.158149	+	0.273922i	0.00539598	+	0.00934610i	−0.863315	+	0.504666i	$0.831616\pi$
$860$	−0.201444	+	0.619981i	−0.00686918	+	0.0211412i
$861$		0			0
$862$	38.1459	+	27.7146i	1.29925	+	0.943963i
$863$	2.42689	−	2.69533i	0.0826123	−	0.0917502i	−0.700421	−	0.713730i	$-0.747005\pi$
$863$	2.42689	−	2.69533i	0.0826123	−	0.0917502i	0.783034	+	0.621979i	$0.213671\pi$
$864$	4.87986	+	1.03725i	0.166016	+	0.0352878i
$865$	−24.7848	+	11.0349i	−0.842708	+	0.375198i
$866$	47.4878	+	21.1429i	1.61370	+	0.718465i
$867$	8.02000	−	24.6830i	0.272374	−	0.838280i
$868$		0			0
$869$	0.839391	−	28.2760i	0.0284744	−	0.959197i
$870$	9.86154	+	17.0807i	0.334337	+	0.579089i
$871$	20.0333	+	22.2492i	0.678802	+	0.753885i
$872$	0.429311	+	4.08462i	0.0145383	+	0.138323i
$873$	1.73267	−	16.4852i	0.0586419	−	0.557941i
$874$	−14.5392	−	44.7469i	−0.491794	−	1.51359i
$875$		0			0
$876$	−2.78818	−	2.02573i	−0.0942039	−	0.0684432i
$877$	24.3986	+	10.8630i	0.823883	+	0.366816i	0.774979	−	0.631987i	$-0.217761\pi$
$877$	24.3986	+	10.8630i	0.823883	+	0.366816i	0.0489039	+	0.998803i	$0.484427\pi$
$878$	51.6047	+	57.3128i	1.74157	+	1.93421i
$879$	−17.6595	+	30.5871i	−0.595639	+	1.03168i
$880$	14.2769	+	1.93041i	0.481275	+	0.0650740i
$881$	2.91937			0.0983560			0.0491780	−	0.998790i	$-0.484340\pi$
$881$	2.91937			0.0983560			0.0491780	+	0.998790i	$0.484340\pi$
$882$		0			0
$883$	36.5331	−	26.5429i	1.22944	−	0.893238i	0.232589	−	0.972575i	$-0.425280\pi$
$883$	36.5331	−	26.5429i	1.22944	−	0.893238i	0.996848	+	0.0793369i	$0.0252803\pi$
$884$	7.68977	−	73.1633i	0.258635	−	2.46075i
$885$	12.2660	+	2.60722i	0.412317	+	0.0876406i
$886$	−3.96090	−	0.841915i	−0.133069	−	0.0282847i
$887$	2.51128	−	23.8932i	0.0843206	−	0.802257i	−0.867878	−	0.496777i	$-0.834517\pi$
$887$	2.51128	−	23.8932i	0.0843206	−	0.802257i	0.952199	−	0.305479i	$-0.0988167\pi$
$888$	−29.3373	+	21.3148i	−0.984497	+	0.715279i
$889$		0			0
$890$	−30.7592			−1.03105
$891$	−3.13192	−	17.2345i	−0.104923	−	0.577377i
$892$	5.79032	−	10.0291i	0.193874	−	0.335800i
$893$	17.9551	+	19.9411i	0.600844	+	0.667304i
$894$	15.5152	+	6.90781i	0.518906	+	0.231032i
$895$	−4.86889	−	3.53746i	−0.162749	−	0.118244i
$896$		0			0
$897$	−9.52702	−	29.3212i	−0.318098	−	0.979005i
$898$	−4.36607	+	41.5404i	−0.145698	+	1.38622i
$899$	−4.57103	−	43.4904i	−0.152452	−	1.45049i
$900$	8.42170	+	9.35325i	0.280723	+	0.311775i
$901$	−12.8908	−	22.3275i	−0.429455	−	0.743837i
$902$	1.42854	+	2.09419i	0.0475652	+	0.0697289i
$903$		0			0
$904$	−6.50996	+	20.0356i	−0.216518	+	0.666374i
$905$	−9.02933	−	4.02012i	−0.300145	−	0.133633i
$906$	54.0517	−	24.0654i	1.79575	−	0.799519i
$907$	15.6767	+	3.33219i	0.520537	+	0.110644i	0.460685	−	0.887564i	$-0.347604\pi$
$907$	15.6767	+	3.33219i	0.520537	+	0.110644i	0.0598522	+	0.998207i	$0.480937\pi$
$908$	21.5843	−	23.9718i	0.716300	−	0.795532i
$909$	−9.51862	−	6.91568i	−0.315713	−	0.229379i
$910$		0			0
$911$	−5.06922	+	15.6014i	−0.167951	+	0.516899i	−0.999242	−	0.0389385i	$-0.987602\pi$
$911$	−5.06922	+	15.6014i	−0.167951	+	0.516899i	0.831291	+	0.555838i	$0.187602\pi$
$912$	−7.08366	−	12.2693i	−0.234564	−	0.406276i
$913$	−3.14369	+	0.236355i	−0.104041	+	0.00782220i
$914$	12.4204	−	21.5127i	0.410830	−	0.711578i
$915$	4.32974	−	0.920316i	0.143137	−	0.0304247i
$916$	−41.4336	+	30.1032i	−1.36900	+	0.994639i
$917$		0			0
$918$	25.1618	+	77.4401i	0.830464	+	2.55590i
$919$	21.6264	−	24.0185i	0.713389	−	0.792298i	−0.272058	−	0.962281i	$-0.587704\pi$
$919$	21.6264	−	24.0185i	0.713389	−	0.792298i	0.985447	+	0.169982i	$0.0543711\pi$
$920$	−36.0459	+	16.0487i	−1.18840	+	0.529109i
$921$	−0.688697	−	6.55252i	−0.0226933	−	0.215913i
$922$	−52.5772	+	11.1756i	−1.73154	+	0.368050i
$923$	0.370623			0.0121992
$924$		0			0
$925$	18.6333			0.612659
$926$	−72.2040	+	15.3474i	−2.37277	+	0.504348i
$927$	0.810099	+	7.70757i	0.0266071	+	0.253150i
$928$	3.62298	−	1.61306i	0.118930	−	0.0529512i
$929$	−5.48373	+	6.09030i	−0.179915	+	0.199816i	−0.826356	−	0.563148i	$-0.809590\pi$
$929$	−5.48373	+	6.09030i	−0.179915	+	0.199816i	0.646441	+	0.762964i	$0.276257\pi$
$930$	−13.1881	−	40.5887i	−0.432454	−	1.33096i
$931$		0			0
$932$	40.5471	−	29.4592i	1.32817	−	0.964969i
$933$	3.10136	−	0.659215i	0.101534	−	0.0215817i
$934$	30.6126	−	53.0226i	1.00168	−	1.73495i
$935$	−9.38378	−	22.8804i	−0.306883	−	0.748271i
$936$	6.94645	+	12.0316i	0.227052	+	0.393265i
$937$	10.5490	−	32.4666i	0.344622	−	1.06064i	−0.617164	−	0.786835i	$-0.711718\pi$
$937$	10.5490	−	32.4666i	0.344622	−	1.06064i	0.961786	−	0.273803i	$-0.0882817\pi$
$938$		0			0
$939$	11.2541	+	8.17655i	0.367262	+	0.266831i
$940$	30.8487	−	34.2610i	1.00618	−	1.11747i
$941$	−0.957969	−	0.203623i	−0.0312289	−	0.00663791i	0.192271	−	0.981342i	$-0.438415\pi$
$941$	−0.957969	−	0.203623i	−0.0312289	−	0.00663791i	−0.223500	+	0.974704i	$0.571748\pi$
$942$	−7.14846	+	3.18270i	−0.232909	+	0.103698i
$943$	−1.94310	−	0.865126i	−0.0632762	−	0.0281724i
$944$	−7.40874	+	22.8017i	−0.241134	+	0.742134i
$945$		0			0
$946$	0.0317072	−	1.06810i	0.00103089	−	0.0347269i
$947$	−0.467800	−	0.810253i	−0.0152014	−	0.0263297i	0.858325	−	0.513107i	$-0.171506\pi$
$947$	−0.467800	−	0.810253i	−0.0152014	−	0.0263297i	−0.873526	+	0.486777i	$0.838172\pi$
$948$	31.9808	+	35.5183i	1.03869	+	1.15358i
$949$	0.204328	+	1.94405i	0.00663277	+	0.0631066i
$950$	−2.48384	+	23.6321i	−0.0805863	+	0.766727i
$951$	2.86099	+	8.80523i	0.0927740	+	0.285529i
$952$		0			0
$953$	−13.5365	−	9.83486i	−0.438491	−	0.318582i	0.346544	−	0.938034i	$-0.387355\pi$
$953$	−13.5365	−	9.83486i	−0.438491	−	0.318582i	−0.785035	+	0.619451i	$0.787355\pi$
$954$	9.11244	+	4.05712i	0.295026	+	0.131354i
$955$	−7.43677	−	8.25937i	−0.240648	−	0.267267i
$956$	9.73081	−	16.8543i	0.314717	−	0.545106i
$957$	−15.4597	−	14.7738i	−0.499741	−	0.477569i
$958$	51.5353			1.66503
$959$		0			0
$960$	13.2115	−	9.59870i	0.426399	−	0.309797i
$961$	−6.65057	+	63.2760i	−0.214535	+	2.04116i
$962$	41.2172	+	8.76099i	1.32890	+	0.282466i
$963$	11.2432	+	2.38982i	0.362308	+	0.0770110i
$964$	1.07282	−	10.2072i	0.0345531	−	0.328751i
$965$	−26.0696	+	18.9407i	−0.839210	+	0.609722i
$966$		0			0
$967$	36.4439			1.17196			0.585978	−	0.810327i	$-0.300710\pi$
$967$	36.4439			1.17196			0.585978	+	0.810327i	$0.300710\pi$
$968$	−50.4131	+	7.62361i	−1.62034	+	0.245032i
$969$	−12.1594	+	21.0607i	−0.390617	+	0.676568i
$970$	−35.9784	−	39.9580i	−1.15520	−	1.28297i
$971$	−30.3678	−	13.5206i	−0.974550	−	0.433898i	−0.143229	−	0.989690i	$-0.545748\pi$
$971$	−30.3678	−	13.5206i	−0.974550	−	0.433898i	−0.831321	+	0.555792i	$0.812415\pi$
$972$	−29.6832	−	21.5661i	−0.952088	−	0.691732i
$973$		0			0
$974$	12.6325	+	38.8788i	0.404771	+	1.24576i
$975$	−1.62757	+	15.4853i	−0.0521241	+	0.495928i
$976$	0.884619	+	8.41658i	0.0283159	+	0.269408i
$977$	15.1000	+	16.7703i	0.483092	+	0.536528i	0.934582	−	0.355748i	$-0.115774\pi$
$977$	15.1000	+	16.7703i	0.483092	+	0.536528i	−0.451490	+	0.892276i	$0.649107\pi$
$978$	−27.6025	−	47.8089i	−0.882631	−	1.52876i
$979$	32.0088	−	9.35981i	1.02301	−	0.299141i
$980$		0			0
$981$	−0.258223	+	0.794729i	−0.00824443	+	0.0253737i
$982$	−10.7420	−	4.78267i	−0.342793	−	0.152621i
$983$	−13.7989	+	6.14366i	−0.440116	+	0.195952i	−0.614818	−	0.788669i	$-0.710771\pi$
$983$	−13.7989	+	6.14366i	−0.440116	+	0.195952i	0.174702	+	0.984621i	$0.444104\pi$
$984$	−2.04492	−	0.434660i	−0.0651896	−	0.0138565i
$985$	−9.43056	+	10.4737i	−0.300483	+	0.333720i
$986$	52.3661	+	38.0462i	1.66768	+	1.21164i
$987$		0			0
$988$	−10.9834	+	33.8033i	−0.349428	+	1.07543i
$989$	0.448287	+	0.776456i	0.0142547	+	0.0246899i
$990$	8.14047	+	5.02773i	0.258721	+	0.159792i
$991$	27.5767	−	47.7643i	0.876003	−	1.51728i	0.0203128	−	0.999794i	$-0.493534\pi$
$991$	27.5767	−	47.7643i	0.876003	−	1.51728i	0.855690	−	0.517488i	$-0.173133\pi$
$992$	−8.39393	+	1.78418i	−0.266507	+	0.0566479i
$993$	−4.20116	+	3.05232i	−0.133320	+	0.0968624i
$994$		0			0
$995$	−4.76461	−	14.6639i	−0.151048	−	0.464878i
$996$	3.56405	−	3.95828i	0.112931	−	0.125423i
$997$	45.4076	−	20.2168i	1.43807	−	0.640271i	0.468142	−	0.883653i	$-0.344924\pi$
$997$	45.4076	−	20.2168i	1.43807	−	0.640271i	0.969930	+	0.243382i	$0.0782569\pi$
$998$	7.76980	+	73.9247i	0.245949	+	2.34005i
$999$	−30.1745	+	6.41378i	−0.954678	+	0.202923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.361.4		32
7.2	even	3	inner	539.2.q.g.471.1		32
7.3	odd	6		539.2.f.e.295.1		16
7.4	even	3		77.2.f.b.64.1	✓	16
7.5	odd	6		539.2.q.f.471.1		32
7.6	odd	2		539.2.q.f.361.4		32
11.5	even	5	inner	539.2.q.g.214.1		32
21.11	odd	6		693.2.m.i.64.4		16
77.4	even	15		847.2.a.p.1.1		8
77.5	odd	30		539.2.q.f.324.4		32
77.16	even	15	inner	539.2.q.g.324.4		32
77.18	odd	30		847.2.a.o.1.8		8
77.25	even	15		847.2.f.w.323.4		16
77.27	odd	10		539.2.q.f.214.1		32
77.32	odd	6		847.2.f.x.372.4		16
77.38	odd	30		539.2.f.e.148.1		16
77.39	odd	30		847.2.f.x.148.4		16
77.46	odd	30		847.2.f.v.729.1		16
77.53	even	15		847.2.f.w.729.4		16
77.59	odd	30		5929.2.a.bt.1.1		8
77.60	even	15		77.2.f.b.71.1	yes	16
77.73	even	30		5929.2.a.bs.1.8		8
77.74	odd	30		847.2.f.v.323.1		16
231.95	even	30		7623.2.a.cw.1.1		8
231.137	odd	30		693.2.m.i.379.4		16
231.158	odd	30		7623.2.a.ct.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	7.4	even	3
77.2.f.b.71.1	yes	16	77.60	even	15
539.2.f.e.148.1		16	77.38	odd	30
539.2.f.e.295.1		16	7.3	odd	6
539.2.q.f.214.1		32	77.27	odd	10
539.2.q.f.324.4		32	77.5	odd	30
539.2.q.f.361.4		32	7.6	odd	2
539.2.q.f.471.1		32	7.5	odd	6
539.2.q.g.214.1		32	11.5	even	5	inner
539.2.q.g.324.4		32	77.16	even	15	inner
539.2.q.g.361.4		32	1.1	even	1	trivial
539.2.q.g.471.1		32	7.2	even	3	inner
693.2.m.i.64.4		16	21.11	odd	6
693.2.m.i.379.4		16	231.137	odd	30
847.2.a.o.1.8		8	77.18	odd	30
847.2.a.p.1.1		8	77.4	even	15
847.2.f.v.323.1		16	77.74	odd	30
847.2.f.v.729.1		16	77.46	odd	30
847.2.f.w.323.4		16	77.25	even	15
847.2.f.w.729.4		16	77.53	even	15
847.2.f.x.148.4		16	77.39	odd	30
847.2.f.x.372.4		16	77.32	odd	6
5929.2.a.bs.1.8		8	77.73	even	30
5929.2.a.bt.1.1		8	77.59	odd	30
7623.2.a.ct.1.8		8	231.158	odd	30
7623.2.a.cw.1.1		8	231.95	even	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.37734 - 0.505320i) q^{2} +(-0.149915 - 1.42635i) q^{3} +(3.56931 - 1.58916i) q^{4} +(0.842189 - 0.935345i) q^{5} +(-1.07716 - 3.31516i) q^{6} +(3.74989 - 2.72445i) q^{8} +(0.922445 - 0.196072i) q^{9} +O(q^{10})\)	\(q+(2.37734 - 0.505320i) q^{2} +(-0.149915 - 1.42635i) q^{3} +(3.56931 - 1.58916i) q^{4} +(0.842189 - 0.935345i) q^{5} +(-1.07716 - 3.31516i) q^{6} +(3.74989 - 2.72445i) q^{8} +(0.922445 - 0.196072i) q^{9} +(1.52952 - 2.64921i) q^{10} +(-0.785524 + 3.22226i) q^{11} +(-2.80179 - 4.85285i) q^{12} +(-0.982152 + 3.02275i) q^{13} +(-1.46039 - 1.06103i) q^{15} +(2.30932 - 2.56476i) q^{16} +(-5.79472 - 1.23171i) q^{17} +(2.09389 - 0.932259i) q^{18} +(2.61477 + 1.16417i) q^{19} +(1.51962 - 4.67691i) q^{20} +(-0.239188 + 8.05735i) q^{22} +(-3.38171 - 5.85730i) q^{23} +(-4.44819 - 4.94021i) q^{24} +(0.357053 + 3.39714i) q^{25} +(-0.807454 + 7.68241i) q^{26} +(-1.74754 - 5.37837i) q^{27} +(-3.63693 - 2.64238i) q^{29} +(-4.00800 - 1.78448i) q^{30} +(6.50898 + 7.22895i) q^{31} +(-0.441092 + 0.763993i) q^{32} +(4.71383 + 0.637365i) q^{33} -14.3984 q^{34} +(2.98090 - 2.16575i) q^{36} +(0.570198 - 5.42507i) q^{37} +(6.80447 + 1.44633i) q^{38} +(4.45874 + 0.947734i) q^{39} +(0.609809 - 5.80194i) q^{40} +(0.254423 - 0.184849i) q^{41} -0.132562 q^{43} +(2.31691 + 12.7496i) q^{44} +(0.593478 - 1.02793i) q^{45} +(-10.9993 - 12.2160i) q^{46} +(8.56453 + 3.81318i) q^{47} +(-4.00445 - 2.90940i) q^{48} +(2.56548 + 7.89572i) q^{50} +(-0.888126 + 8.44995i) q^{51} +(1.29803 + 12.3499i) q^{52} +(2.91201 + 3.23411i) q^{53} +(-6.87229 - 11.9032i) q^{54} +(2.35237 + 3.44849i) q^{55} +(1.26852 - 3.90410i) q^{57} +(-9.98147 - 4.44404i) q^{58} +(-6.34627 + 2.82554i) q^{59} +(-6.89873 - 1.46637i) q^{60} +(-1.64081 + 1.82231i) q^{61} +(19.1270 + 13.8966i) q^{62} +(-2.79554 + 8.60379i) q^{64} +(2.00016 + 3.46438i) q^{65} +(11.5285 - 0.866755i) q^{66} +(4.70993 - 8.15784i) q^{67} +(-22.6406 + 4.81240i) q^{68} +(-7.84759 + 5.70161i) q^{69} +(-0.0360345 - 0.110903i) q^{71} +(2.92488 - 3.24840i) q^{72} +(0.561859 - 0.250156i) q^{73} +(-1.38584 - 13.1854i) q^{74} +(4.79197 - 1.01857i) q^{75} +11.1830 q^{76} +11.0789 q^{78} +(-8.34290 + 1.77334i) q^{79} +(-0.454053 - 4.32003i) q^{80} +(-4.82488 + 2.14818i) q^{81} +(0.511443 - 0.568015i) q^{82} +(0.293731 + 0.904010i) q^{83} +(-6.03232 + 4.38274i) q^{85} +(-0.315145 + 0.0669862i) q^{86} +(-3.22373 + 5.58367i) q^{87} +(5.83327 + 14.2232i) q^{88} +(-5.02758 - 8.70803i) q^{89} +(0.891464 - 2.74364i) q^{90} +(-21.3786 - 15.5325i) q^{92} +(9.33521 - 10.3678i) q^{93} +(22.2877 + 4.73740i) q^{94} +(3.29103 - 1.46526i) q^{95} +(1.15585 + 0.514617i) q^{96} +(5.43159 - 16.7167i) q^{97} +(-0.0928085 + 3.12637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

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