LMFDB - Embedded newform 539.2.q.g.214.1

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			214.1
Character	$\chi$	$=$	539.214
Dual form			539.2.q.g.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62629 + 1.80618i) q^{2} +(1.31021 - 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(-1.23113 + 0.261684i) q^{5} +(-1.07716 + 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +O(q^{10})$	\(q+(-1.62629 + 1.80618i) q^{2} +(1.31021 - 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(-1.23113 + 0.261684i) q^{5} +(-1.07716 + 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +(1.52952 - 2.64921i) q^{10} +(-2.39780 + 2.29141i) q^{11} +(-2.80179 - 4.85285i) q^{12} +(-0.982152 - 3.02275i) q^{13} +(-1.46039 + 1.06103i) q^{15} +(-3.37581 + 0.717551i) q^{16} +(3.96405 + 4.40252i) q^{17} +(-0.239584 - 2.27949i) q^{18} +(-0.299183 + 2.84654i) q^{19} +(1.51962 + 4.67691i) q^{20} +(-0.239188 - 8.05735i) q^{22} +(-3.38171 - 5.85730i) q^{23} +(6.50244 + 1.38214i) q^{24} +(-3.12053 + 1.38935i) q^{25} +(7.05689 + 3.14193i) q^{26} +(-1.74754 + 5.37837i) q^{27} +(-3.63693 + 2.64238i) q^{29} +(0.458598 - 4.36326i) q^{30} +(-9.51494 - 2.02246i) q^{31} +(-0.441092 + 0.763993i) q^{32} +(-1.80494 + 4.40098i) q^{33} -14.3984 q^{34} +(2.98090 + 2.16575i) q^{36} +(-4.98335 - 2.21873i) q^{37} +(-4.65480 - 5.16968i) q^{38} +(-3.05013 - 3.38751i) q^{39} +(-5.32953 - 2.37286i) q^{40} +(0.254423 + 0.184849i) q^{41} -0.132562 q^{43} +(9.88300 + 8.38129i) q^{44} +(0.593478 - 1.02793i) q^{45} +(16.0790 + 3.41769i) q^{46} +(-0.979960 + 9.32369i) q^{47} +(-4.00445 + 2.90940i) q^{48} +(2.56548 - 7.89572i) q^{50} +(7.76194 + 3.45584i) q^{51} +(-11.3444 + 5.05084i) q^{52} +(-4.25682 - 0.904816i) q^{53} +(-6.87229 - 11.9032i) q^{54} +(2.35237 - 3.44849i) q^{55} +(1.26852 + 3.90410i) q^{57} +(1.14209 - 10.8662i) q^{58} +(0.726144 + 6.90880i) q^{59} +(4.71928 + 5.24129i) q^{60} +(2.39857 - 0.509832i) q^{61} +(19.1270 - 13.8966i) q^{62} +(-2.79554 - 8.60379i) q^{64} +(2.00016 + 3.46438i) q^{65} +(-5.01360 - 10.4173i) q^{66} +(4.70993 - 8.15784i) q^{67} +(15.4879 - 17.2011i) q^{68} +(-7.84759 - 5.70161i) q^{69} +(-0.0360345 + 0.110903i) q^{71} +(-4.27564 + 0.908815i) q^{72} +(-0.0642883 - 0.611662i) q^{73} +(12.1118 - 5.39252i) q^{74} +(-3.27809 + 3.64069i) q^{75} +11.1830 q^{76} +11.0789 q^{78} +(5.70720 - 6.33849i) q^{79} +(3.96828 - 1.76679i) q^{80} +(0.552066 + 5.25256i) q^{81} +(-0.747637 + 0.158915i) q^{82} +(0.293731 - 0.904010i) q^{83} +(-6.03232 - 4.38274i) q^{85} +(0.215584 - 0.239431i) q^{86} +(-3.22373 + 5.58367i) q^{87} +(-15.2343 + 2.05986i) q^{88} +(-5.02758 - 8.70803i) q^{89} +(0.891464 + 2.74364i) q^{90} +(-21.3786 + 15.5325i) q^{92} +(-13.6464 + 2.90063i) q^{93} +(-15.2466 - 16.9330i) q^{94} +(-0.376561 - 3.58274i) q^{95} +(-0.132253 + 1.25830i) 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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.62629	+	1.80618i	−1.14996	+	1.27716i	−0.194876	+	0.980828i	$0.562430\pi$
$2$	−1.62629	+	1.80618i	−1.14996	+	1.27716i	−0.955085	+	0.296333i	$0.904236\pi$
$3$	1.31021	−	0.583344i	0.756452	−	0.336794i	0.00798646	−	0.999968i	$-0.497458\pi$
$3$	1.31021	−	0.583344i	0.756452	−	0.336794i	0.748465	+	0.663174i	$0.230791\pi$
$4$	−0.408403	−	3.88570i	−0.204202	−	1.94285i
$5$	−1.23113	+	0.261684i	−0.550577	+	0.117029i	−0.474796	−	0.880096i	$-0.657478\pi$
$5$	−1.23113	+	0.261684i	−0.550577	+	0.117029i	−0.0757806	+	0.997125i	$0.524145\pi$
$6$	−1.07716	+	3.31516i	−0.439750	+	1.35341i
$7$		0			0
$7$		0			0
$8$	3.74989	+	2.72445i	1.32579	+	0.963239i
$9$	−0.631025	+	0.700825i	−0.210342	+	0.233608i
$10$	1.52952	−	2.64921i	0.483677	−	0.837754i
$11$	−2.39780	+	2.29141i	−0.722963	+	0.690887i
$11$	−2.39780	+	2.29141i	−0.722963	+	0.690887i
$12$	−2.80179	−	4.85285i	−0.808808	−	1.40090i
$13$	−0.982152	−	3.02275i	−0.272400	−	0.838361i	−0.989896	−	0.141798i	$-0.954712\pi$
$13$	−0.982152	−	3.02275i	−0.272400	−	0.838361i	0.717496	−	0.696563i	$-0.245288\pi$
$14$		0			0
$15$	−1.46039	+	1.06103i	−0.377070	+	0.273957i
$16$	−3.37581	+	0.717551i	−0.843953	+	0.179388i
$17$	3.96405	+	4.40252i	0.961424	+	1.06777i	0.997656	+	0.0684256i	$0.0217976\pi$
$17$	3.96405	+	4.40252i	0.961424	+	1.06777i	−0.0362327	+	0.999343i	$0.511536\pi$
$18$	−0.239584	−	2.27949i	−0.0564705	−	0.537281i
$19$	−0.299183	+	2.84654i	−0.0686373	+	0.653041i	0.905074	+	0.425254i	$0.139815\pi$
$19$	−0.299183	+	2.84654i	−0.0686373	+	0.653041i	−0.973711	+	0.227786i	$0.926851\pi$
$20$	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	$-0.415781\pi$
$24$	6.50244	+	1.38214i	1.32731	+	0.282127i
$25$	−3.12053	+	1.38935i	−0.624106	+	0.277870i
$26$	7.05689	+	3.14193i	1.38397	+	0.616183i
$27$	−1.74754	+	5.37837i	−0.336314	+	1.03507i
$28$		0			0
$29$	−3.63693	+	2.64238i	−0.675361	+	0.490678i	−0.871815	−	0.489834i	$-0.837057\pi$
$29$	−3.63693	+	2.64238i	−0.675361	+	0.490678i	0.196454	+	0.980513i	$0.437057\pi$
$30$	0.458598	−	4.36326i	0.0837281	−	0.796620i
$31$	−9.51494	−	2.02246i	−1.70893	−	0.363245i	−0.753272	−	0.657709i	$-0.771525\pi$
$31$	−9.51494	−	2.02246i	−1.70893	−	0.363245i	−0.955663	+	0.294464i	$0.904859\pi$
$32$	−0.441092	+	0.763993i	−0.0779748	+	0.135056i
$33$	−1.80494	+	4.40098i	−0.314200	+	0.766112i
$34$	−14.3984			−2.46931
$35$		0			0
$36$	2.98090	+	2.16575i	0.496817	+	0.360959i
$37$	−4.98335	−	2.21873i	−0.819257	−	0.364757i	−0.0460730	−	0.998938i	$-0.514671\pi$
$37$	−4.98335	−	2.21873i	−0.819257	−	0.364757i	−0.773184	+	0.634181i	$0.781337\pi$
$38$	−4.65480	−	5.16968i	−0.755108	−	0.838632i
$39$	−3.05013	−	3.38751i	−0.488412	−	0.542437i
$40$	−5.32953	−	2.37286i	−0.842673	−	0.375182i
$41$	0.254423	+	0.184849i	0.0397342	+	0.0288686i	0.607475	−	0.794339i	$-0.292182\pi$
$41$	0.254423	+	0.184849i	0.0397342	+	0.0288686i	−0.567741	+	0.823207i	$0.692182\pi$
$42$		0			0
$43$	−0.132562			−0.0202155			−0.0101078	−	0.999949i	$-0.503217\pi$
$43$	−0.132562			−0.0202155			−0.0101078	+	0.999949i	$0.503217\pi$
$44$	9.88300	+	8.38129i	1.48992	+	1.26353i
$45$	0.593478	−	1.02793i	0.0884704	−	0.153235i
$46$	16.0790	+	3.41769i	2.37072	+	0.503911i
$47$	−0.979960	+	9.32369i	−0.142942	+	1.36000i	0.654252	+	0.756277i	$0.272984\pi$
$47$	−0.979960	+	9.32369i	−0.142942	+	1.36000i	−0.797194	+	0.603724i	$0.793683\pi$
$48$	−4.00445	+	2.90940i	−0.577993	+	0.419936i
$49$		0			0
$50$	2.56548	−	7.89572i	0.362813	−	1.11662i
$51$	7.76194	+	3.45584i	1.08689	+	0.483914i
$52$	−11.3444	+	5.05084i	−1.57318	+	0.700426i
$53$	−4.25682	−	0.904816i	−0.584720	−	0.124286i	−0.0939524	−	0.995577i	$-0.529950\pi$
$53$	−4.25682	−	0.904816i	−0.584720	−	0.124286i	−0.490767	+	0.871291i	$0.663283\pi$
$54$	−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
$58$	1.14209	−	10.8662i	0.149963	−	1.42681i
$59$	0.726144	+	6.90880i	0.0945359	+	0.899449i	0.934298	+	0.356494i	$0.116028\pi$
$59$	0.726144	+	6.90880i	0.0945359	+	0.899449i	−0.839762	+	0.542955i	$0.817305\pi$
$60$	4.71928	+	5.24129i	0.609256	+	0.676647i
$61$	2.39857	−	0.509832i	0.307105	−	0.0652772i	−0.0517812	−	0.998658i	$-0.516490\pi$
$61$	2.39857	−	0.509832i	0.307105	−	0.0652772i	0.358886	+	0.933381i	$0.383157\pi$
$62$	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
$66$	−5.01360	−	10.4173i	−0.617131	−	1.28228i
$67$	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	$-0.0284908\pi$
$68$	15.4879	−	17.2011i	1.87819	−	2.08594i
$69$	−7.84759	−	5.70161i	−0.944739	−	0.686393i
$70$		0			0
$71$	−0.0360345	+	0.110903i	−0.00427651	+	0.0131617i	−0.953172	−	0.302429i	$-0.902203\pi$
$71$	−0.0360345	+	0.110903i	−0.00427651	+	0.0131617i	0.948895	+	0.315590i	$0.102203\pi$
$72$	−4.27564	+	0.908815i	−0.503889	+	0.107105i
$73$	−0.0642883	−	0.611662i	−0.00752438	−	0.0715897i	0.990115	−	0.140256i	$-0.0447924\pi$
$73$	−0.0642883	−	0.611662i	−0.00752438	−	0.0715897i	−0.997640	+	0.0686659i	$0.978126\pi$
$74$	12.1118	−	5.39252i	1.40797	−	0.626867i
$75$	−3.27809	+	3.64069i	−0.378521	+	0.420391i
$76$	11.1830			1.28277
$77$		0			0
$78$	11.0789			1.25443
$79$	5.70720	−	6.33849i	0.642111	−	0.713136i	−0.330960	−	0.943645i	$-0.607372\pi$
$79$	5.70720	−	6.33849i	0.642111	−	0.713136i	0.973070	+	0.230509i	$0.0740391\pi$
$80$	3.96828	−	1.76679i	0.443667	−	0.197533i
$81$	0.552066	+	5.25256i	0.0613407	+	0.583618i
$82$	−0.747637	+	0.158915i	−0.0825627	+	0.0175492i
$83$	0.293731	−	0.904010i	0.0322411	−	0.0992280i	−0.933641	−	0.358210i	$-0.883387\pi$
$83$	0.293731	−	0.904010i	0.0322411	−	0.0992280i	0.965882	+	0.258982i	$0.0833871\pi$
$84$		0			0
$85$	−6.03232	−	4.38274i	−0.654297	−	0.475375i
$86$	0.215584	−	0.239431i	0.0232471	−	0.0258185i
$87$	−3.22373	+	5.58367i	−0.345620	+	0.598632i
$88$	−15.2343	+	2.05986i	−1.62398	+	0.219582i
$89$	−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
$93$	−13.6464	+	2.90063i	−1.41506	+	0.300781i
$94$	−15.2466	−	16.9330i	−1.57256	−	1.74651i
$95$	−0.376561	−	3.58274i	−0.0386344	−	0.367582i
$96$	−0.132253	+	1.25830i	−0.0134980	+	0.128425i
$97$	5.43159	+	16.7167i	0.551495	+	1.69733i	0.705025	+	0.709182i	$0.250936\pi$
$97$	5.43159	+	16.7167i	0.551495	+	1.69733i	−0.153530	+	0.988144i	$0.549064\pi$
$98$		0			0
$99$	−0.0928085	−	3.12637i	−0.00932760	−	0.314212i
$100$	6.67303	+	11.5580i	0.667303	+	1.15580i
$101$	12.2035	+	2.59394i	1.21429	+	0.258106i	0.770158	−	0.637853i	$-0.220177\pi$
$101$	12.2035	+	2.59394i	1.21429	+	0.258106i	0.444137	+	0.895959i	$0.353510\pi$
$102$	−18.8650	+	8.39925i	−1.86792	+	0.831649i
$103$	7.50754	+	3.34257i	0.739740	+	0.329353i	0.741779	−	0.670645i	$-0.233982\pi$
$103$	7.50754	+	3.34257i	0.739740	+	0.329353i	−0.00203908	+	0.999998i	$0.500649\pi$
$104$	4.55239	−	14.0108i	0.446398	−	1.37387i
$105$		0			0
$106$	8.55709	−	6.21709i	0.831138	−	0.603857i
$107$	−1.27405	+	12.1218i	−0.123167	+	1.17185i	0.742011	+	0.670388i	$0.233872\pi$
$107$	−1.27405	+	12.1218i	−0.123167	+	1.17185i	−0.865177	+	0.501466i	$0.832794\pi$
$108$	21.6124	+	4.59386i	2.07965	+	0.442044i
$109$	−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	$0.180178\pi$
$110$	2.40295	+	9.85703i	0.229112	+	0.939831i
$111$	−7.82353			−0.742577
$112$		0			0
$113$	−3.67700	−	2.67149i	−0.345903	−	0.251313i	0.401245	−	0.915971i	$-0.368577\pi$
$113$	−3.67700	−	2.67149i	−0.345903	−	0.251313i	−0.747148	+	0.664658i	$0.768577\pi$
$114$	−9.11447	−	4.05802i	−0.853649	−	0.380069i
$115$	5.69608	+	6.32614i	0.531163	+	0.589916i
$116$	11.7528	+	13.0528i	1.09122	+	1.21193i
$117$	2.73818	+	1.21912i	0.253145	+	0.112707i
$118$	−13.6594	−	9.92416i	−1.25745	−	0.913593i
$119$		0			0
$120$	−8.36702			−0.763801
$121$	0.498853	−	10.9887i	0.0453503	−	0.998971i
$122$	−2.97992	+	5.16138i	−0.269789	+	0.467289i
$123$	0.441179	+	0.0937755i	0.0397798	+	0.00845546i
$124$	−3.97275	+	37.7982i	−0.356763	+	3.39437i
$125$	8.56947	−	6.22608i	0.766477	−	0.556878i
$126$		0			0
$127$	−2.48072	+	7.63488i	−0.220129	+	0.677486i	0.778621	+	0.627494i	$0.215919\pi$
$127$	−2.48072	+	7.63488i	−0.220129	+	0.677486i	−0.998750	+	0.0499916i	$0.984081\pi$
$128$	18.4745	+	8.22538i	1.63293	+	0.727028i
$129$	−0.173684	+	0.0773293i	−0.0152921	+	0.00680846i
$130$	−9.51012	−	2.02144i	−0.834093	−	0.177292i
$131$	−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
$135$	0.744007	−	7.07876i	0.0640340	−	0.609242i
$136$	2.87027	+	27.3088i	0.246124	+	2.34171i
$137$	−3.05397	−	3.39178i	−0.260919	−	0.289779i	0.598424	−	0.801179i	$-0.295794\pi$
$137$	−3.05397	−	3.39178i	−0.260919	−	0.289779i	−0.859343	+	0.511400i	$0.829127\pi$
$138$	23.0606	−	4.90168i	1.96305	−	0.417258i
$139$	3.09475	−	2.24847i	0.262494	−	0.190713i	−0.448752	−	0.893656i	$-0.648131\pi$
$139$	3.09475	−	2.24847i	0.262494	−	0.190713i	0.711246	+	0.702944i	$0.248131\pi$
$140$		0			0
$141$	4.15497	+	12.7877i	0.349911	+	1.07692i
$142$	−0.141708	−	0.245445i	−0.0118918	−	0.0205973i
$143$	9.28137	+	4.99743i	0.776147	+	0.417906i
$144$	1.62734	−	2.81864i	0.135612	−	0.234887i
$145$	3.78605	−	4.20484i	0.314415	−	0.349193i
$146$	1.20932	+	0.878624i	0.100084	+	0.0727155i
$147$		0			0
$148$	−6.58609	+	20.2699i	−0.541374	+	1.66618i
$149$	4.76576	−	1.01299i	0.390427	−	0.0829877i	−0.00851575	−	0.999964i	$-0.502711\pi$
$149$	4.76576	−	1.01299i	0.390427	−	0.0829877i	0.398942	+	0.916976i	$0.369377\pi$
$150$	−1.24461	−	11.8416i	−0.101622	−	0.966865i
$151$	−15.5064	+	6.90389i	−1.26189	+	0.561831i	−0.925091	−	0.379745i	$-0.876012\pi$
$151$	−15.5064	+	6.90389i	−1.26189	+	0.561831i	−0.336802	+	0.941576i	$0.609345\pi$
$152$	−8.87716	+	9.85909i	−0.720033	+	0.799677i
$153$	−5.58681			−0.451667
$154$		0			0
$155$	12.2434			0.983410
$156$	−11.9172	+	13.2354i	−0.954137	+	1.05968i
$157$	2.05075	−	0.913055i	0.163668	−	0.0728697i	−0.323267	−	0.946308i	$-0.604781\pi$
$157$	2.05075	−	0.913055i	0.163668	−	0.0728697i	0.486935	+	0.873438i	$0.338115\pi$
$158$	2.16688	+	20.6165i	0.172387	+	1.64016i
$159$	−6.10516	+	1.29769i	−0.484171	+	0.102914i
$160$	0.343115	−	1.05600i	0.0271256	−	0.0834841i
$161$		0			0
$162$	−10.3849	−	7.54506i	−0.815913	−	0.592796i
$163$	−10.5972	+	11.7694i	−0.830036	+	0.921848i	−0.997953	−	0.0639530i	$-0.979629\pi$
$163$	−10.5972	+	11.7694i	−0.830036	+	0.921848i	0.167917	+	0.985801i	$0.446296\pi$
$164$	0.614361	−	1.06410i	0.0479735	−	0.0830926i
$165$	1.07044	−	5.89049i	0.0833340	−	0.458574i
$166$	1.15511	+	2.00071i	0.0896540	+	0.155285i
$167$	6.40950	+	19.7264i	0.495982	+	1.52647i	0.815421	+	0.578868i	$0.196505\pi$
$167$	6.40950	+	19.7264i	0.495982	+	1.52647i	−0.319440	+	0.947607i	$0.603495\pi$
$168$		0			0
$169$	2.34481	−	1.70361i	0.180370	−	0.131047i
$170$	17.7263	−	3.76784i	1.35955	−	0.288980i
$171$	−1.80613	−	2.00591i	−0.138118	−	0.153396i
$172$	0.0541387	+	0.515096i	0.00412804	+	0.0392757i
$173$	2.25315	−	21.4373i	0.171304	−	1.62985i	−0.484410	−	0.874841i	$-0.660966\pi$
$173$	2.25315	−	21.4373i	0.171304	−	1.62985i	0.655714	−	0.755009i	$-0.272368\pi$
$174$	−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
$178$	23.9046	+	5.08107i	1.79172	+	0.380842i
$179$	4.36822	−	1.94485i	0.326496	−	0.145365i	−0.236942	−	0.971524i	$-0.576145\pi$
$179$	4.36822	−	1.94485i	0.326496	−	0.145365i	0.563438	+	0.826159i	$0.309478\pi$
$180$	−4.23662	−	1.88626i	−0.315779	−	0.140594i
$181$	−2.42666	+	7.46850i	−0.180372	+	0.555129i	−0.999838	−	0.0179992i	$-0.994270\pi$
$181$	−2.42666	+	7.46850i	−0.180372	+	0.555129i	0.819466	+	0.573128i	$0.194270\pi$
$182$		0			0
$183$	2.84523	−	2.06718i	0.210325	−	0.152810i
$184$	3.27689	−	31.1775i	0.241576	−	2.29844i
$185$	6.71574	+	1.42747i	0.493751	+	0.104950i
$186$	16.9539	−	29.3651i	1.24312	−	2.15315i
$187$	−19.5930	−	1.47308i	−1.43278	−	0.107722i
$188$	36.6293			2.67146
$189$		0			0
$190$	7.08347	+	5.14644i	0.513889	+	0.373362i
$191$	−8.06687	−	3.59160i	−0.583698	−	0.259879i	0.0935733	−	0.995612i	$-0.470171\pi$
$191$	−8.06687	−	3.59160i	−0.583698	−	0.259879i	−0.677271	+	0.735733i	$0.736838\pi$
$192$	−8.68173	−	9.64203i	−0.626550	−	0.695854i
$193$	17.1313	+	19.0262i	1.23313	+	1.36954i	0.905285	+	0.424805i	$0.139657\pi$
$193$	17.1313	+	19.0262i	1.23313	+	1.36954i	0.327850	+	0.944730i	$0.393676\pi$
$194$	−39.0267	−	17.3758i	−2.80196	−	1.24751i
$195$	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	$0.630608\pi$
$198$	5.79772	+	4.91676i	0.412026	+	0.349419i
$199$	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	$0.0236979\pi$
$200$	−15.4869	−	3.29183i	−1.09509	−	0.232768i
$201$	1.41218	−	13.4360i	0.0996077	−	0.947704i
$202$	−24.5316	+	17.8232i	−1.72603	+	1.25404i
$203$		0			0
$204$	10.2583	−	31.5719i	0.718227	−	2.21048i
$205$	−0.361599	−	0.160994i	−0.0252552	−	0.0112443i
$206$	−18.2467	+	8.12396i	−1.27131	+	0.566023i
$207$	6.23889	+	1.32612i	0.433633	+	0.0921715i
$208$	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	−0.980255	−	0.197736i	$-0.936641\pi$
$211$	−4.40769	−	13.5655i	−0.303438	−	0.933887i	0.676817	−	0.736151i	$-0.263359\pi$
$212$	−1.77734	+	16.9103i	−0.122068	+	1.16140i
$213$	0.0174817	+	0.166327i	0.00119782	+	0.0113965i
$214$	−19.8221	−	22.0146i	−1.35501	−	1.50489i
$215$	0.163201	−	0.0346894i	0.0111302	−	0.00236580i
$216$	−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
$220$	−14.3605	−	7.73220i	−0.968183	−	0.521305i
$221$	9.41444	−	16.3063i	0.633284	−	1.09688i
$222$	12.7233	−	14.1307i	0.853934	−	0.948390i
$223$	2.39793	+	1.74220i	0.160577	+	0.116666i	0.665172	−	0.746690i	$-0.268358\pi$
$223$	2.39793	+	1.74220i	0.160577	+	0.116666i	−0.504595	+	0.863356i	$0.668358\pi$
$224$		0			0
$225$	0.995444	−	3.06366i	0.0663629	−	0.204244i
$226$	10.8051	−	2.29669i	0.718742	−	0.152773i
$227$	−0.862993	−	8.21083i	−0.0572788	−	0.544972i	−0.985104	−	0.171957i	$-0.944991\pi$
$227$	−0.862993	−	8.21083i	−0.0572788	−	0.544972i	0.927826	−	0.373014i	$-0.121676\pi$
$228$	14.6521	−	6.52352i	0.970357	−	0.432031i
$229$	8.77104	−	9.74122i	0.579607	−	0.643718i	−0.380026	−	0.924976i	$-0.624085\pi$
$229$	8.77104	−	9.74122i	0.579607	−	0.643718i	0.959632	+	0.281258i	$0.0907515\pi$
$230$	−20.6896			−1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	−8.58339	+	9.53282i	−0.562317	+	0.624516i	−0.955517	−	0.294937i	$-0.904701\pi$
$233$	−8.58339	+	9.53282i	−0.562317	+	0.624516i	0.393200	+	0.919453i	$0.371368\pi$
$234$	−6.65502	+	2.96301i	−0.435052	+	0.193698i
$235$	−1.23341	−	11.7351i	−0.0804586	−	0.765513i
$236$	26.5489	−	5.64315i	1.72819	−	0.367338i
$237$	3.78013	−	11.6340i	0.245546	−	0.755712i
$238$		0			0
$239$	4.02979	+	2.92781i	0.260665	+	0.189384i	0.710440	−	0.703758i	$-0.248496\pi$
$239$	4.02979	+	2.92781i	0.260665	+	0.189384i	−0.449775	+	0.893142i	$0.648496\pi$
$240$	4.16864	−	4.62975i	0.269085	−	0.298849i
$241$	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	$0.139704\pi$
$242$	19.0362	+	18.7718i	1.22370	+	1.20670i
$243$	−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
$247$	8.89822	−	1.89138i	0.566180	−	0.120345i
$248$	−30.1699	−	33.5070i	−1.91579	−	2.12770i
$249$	−0.142499	−	1.35579i	−0.00903053	−	0.0859198i
$250$	−2.69103	+	25.6034i	−0.170195	+	1.61930i
$251$	−8.10332	−	24.9395i	−0.511477	−	1.57417i	−0.789601	−	0.613620i	$-0.789713\pi$
$251$	−8.10332	−	24.9395i	−0.511477	−	1.57417i	0.278124	−	0.960545i	$-0.410287\pi$
$252$		0			0
$253$	21.5302	+	6.29571i	1.35359	+	0.395808i
$254$	−9.75558	−	16.8972i	−0.612119	−	1.06022i
$255$	−10.4603	−	2.22340i	−0.655047	−	0.139235i
$256$	−28.3725	+	12.6323i	−1.77328	+	0.789517i
$257$	27.3623	+	12.1825i	1.70681	+	0.759923i	0.998542	+	0.0539837i	$0.0171919\pi$
$257$	27.3623	+	12.1825i	1.70681	+	0.759923i	0.708273	+	0.705939i	$0.249475\pi$
$258$	0.142791	−	0.439465i	0.00888977	−	0.0273599i
$259$		0			0
$260$	12.6446	−	9.18688i	0.784188	−	0.569746i
$261$	0.443147	−	4.21626i	0.0274301	−	0.260980i
$262$	0.241207	+	0.0512701i	0.0149018	+	0.00316747i
$263$	−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	$0.199475\pi$
$264$	−18.7586	+	11.5857i	−1.15451	+	0.713050i
$265$	5.47747			0.336478
$266$		0			0
$267$	−11.6670	−	8.47656i	−0.714008	−	0.518757i
$268$	−33.6225	−	14.9697i	−2.05382	−	0.914419i
$269$	−1.16149	−	1.28996i	−0.0708170	−	0.0786502i	0.706695	−	0.707518i	$-0.250185\pi$
$269$	−1.16149	−	1.28996i	−0.0708170	−	0.0786502i	−0.777512	+	0.628868i	$0.783519\pi$
$270$	11.5755	+	12.8559i	0.704464	+	0.782387i
$271$	−2.26190	−	1.00706i	−0.137401	−	0.0611747i	0.336885	−	0.941546i	$-0.390627\pi$
$271$	−2.26190	−	1.00706i	−0.137401	−	0.0611747i	−0.474285	+	0.880371i	$0.657293\pi$
$272$	−16.5409	−	12.0177i	−1.00294	−	0.728679i
$273$		0			0
$274$	11.0928			0.670141
$275$	4.29882	−	10.4818i	0.259229	−	0.632077i
$276$	−18.9497	+	32.8219i	−1.14064	+	1.97565i
$277$	−5.04304	−	1.07193i	−0.303007	−	0.0644061i	0.0538991	−	0.998546i	$-0.482835\pi$
$277$	−5.04304	−	1.07193i	−0.303007	−	0.0644061i	−0.356906	+	0.934140i	$0.616168\pi$
$278$	−0.971830	+	9.24634i	−0.0582865	+	0.554559i
$279$	7.42156	−	5.39208i	0.444317	−	0.322815i
$280$		0			0
$281$	−6.97467	+	21.4658i	−0.416074	+	1.28054i	0.495213	+	0.868772i	$0.335090\pi$
$281$	−6.97467	+	21.4658i	−0.416074	+	1.28054i	−0.911287	+	0.411772i	$0.864910\pi$
$282$	−29.8540	−	13.2919i	−1.77778	−	0.791519i
$283$	−7.75378	+	3.45221i	−0.460914	+	0.205212i	−0.624039	−	0.781393i	$-0.714509\pi$
$283$	−7.75378	+	3.45221i	−0.460914	+	0.205212i	0.163125	+	0.986605i	$0.447843\pi$
$284$	0.445651	+	0.0947261i	0.0264445	+	0.00562096i
$285$	−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
$289$	−1.89154	+	17.9968i	−0.111267	+	1.05863i
$290$	1.43747	+	13.6766i	0.0844109	+	0.803116i
$291$	16.8681	+	18.7340i	0.988828	+	1.09821i
$292$	−2.35048	+	0.499610i	−0.137551	+	0.0292374i
$293$	−19.9229	+	14.4749i	−1.16391	+	0.845630i	−0.990267	−	0.139178i	$-0.955554\pi$
$293$	−19.9229	+	14.4749i	−1.16391	+	0.845630i	−0.173643	+	0.984809i	$0.555554\pi$
$294$		0			0
$295$	−2.70190	−	8.31559i	−0.157311	−	0.484152i
$296$	−12.6422	−	21.8969i	−0.734811	−	1.27273i
$297$	−8.13382	−	16.9006i	−0.471972	−	0.980670i
$298$	−5.92087	+	10.2552i	−0.342987	+	0.594070i
$299$	−14.3838	+	15.9748i	−0.831837	+	0.923849i
$300$	15.4854	+	11.2508i	0.894050	+	0.649565i
$301$		0			0
$302$	12.7482	−	39.2351i	0.733579	−	2.25772i
$303$	17.5024	−	3.72024i	1.00548	−	0.213722i
$304$	−1.03255	−	9.82405i	−0.0592208	−	0.563448i
$305$	−2.81953	+	1.25533i	−0.161446	+	0.0718803i
$306$	9.08578	−	10.0908i	0.519400	−	0.576852i
$307$	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
$310$	−19.9112	+	22.1137i	−1.13088	+	1.25597i
$311$	−2.01960	+	0.899186i	−0.114521	+	0.0509882i	−0.463198	−	0.886255i	$-0.653298\pi$
$311$	−2.01960	+	0.899186i	−0.114521	+	0.0509882i	0.348676	+	0.937243i	$0.386631\pi$
$312$	−2.20853	−	21.0127i	−0.125033	−	1.18961i
$313$	9.48733	−	2.01659i	0.536256	−	0.113985i	0.0681799	−	0.997673i	$-0.478281\pi$
$313$	9.48733	−	2.01659i	0.536256	−	0.113985i	0.468076	+	0.883688i	$0.344947\pi$
$314$	−1.68598	+	5.18892i	−0.0951455	+	0.292828i
$315$		0			0
$316$	−26.9603	−	19.5878i	−1.51664	−	1.10190i
$317$	4.31950	−	4.79729i	0.242607	−	0.269443i	−0.609528	−	0.792765i	$-0.708641\pi$
$317$	4.31950	−	4.79729i	0.242607	−	0.269443i	0.852135	+	0.523322i	$0.175308\pi$
$318$	7.58490	−	13.1374i	0.425340	−	0.736711i
$319$	2.66582	−	14.6696i	0.149257	−	0.821340i
$320$	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
$324$	20.1844	−	4.29033i	1.12136	−	0.238351i
$325$	7.26450	+	8.06804i	0.402962	+	0.447534i
$326$	−4.02348	−	38.2808i	−0.222840	−	2.12018i
$327$	−0.132838	+	1.26387i	−0.00734597	+	0.0698922i
$328$	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	$0.865060\pi$
$332$	−3.63267	−	0.772147i	−0.199369	−	0.0423771i
$333$	4.69956	−	2.09238i	0.257534	−	0.114662i
$334$	−46.0531	−	20.5042i	−2.51991	−	1.12194i
$335$	−3.66375	+	11.2759i	−0.200172	+	0.616066i
$336$		0			0
$337$	5.18183	−	3.76482i	0.282272	−	0.205083i	−0.437636	−	0.899152i	$-0.644184\pi$
$337$	5.18183	−	3.76482i	0.282272	−	0.205083i	0.719908	+	0.694070i	$0.244184\pi$
$338$	−0.736330	+	7.00571i	−0.0400511	+	0.381060i
$339$	−6.37605	−	1.35527i	−0.346299	−	0.0736082i
$340$	−14.5664	+	25.2297i	−0.789972	+	1.36827i
$341$	27.4492	−	16.9532i	1.48646	−	0.918068i
$342$	6.56033			0.354742
$343$		0			0
$344$	−0.497093	−	0.361159i	−0.0268014	−	0.0194724i
$345$	11.1534	+	4.96581i	0.600479	+	0.267350i
$346$	35.0554	+	38.9329i	1.88459	+	2.09305i
$347$	−11.6830	−	12.9753i	−0.627177	−	0.696551i	0.342893	−	0.939374i	$-0.388593\pi$
$347$	−11.6830	−	12.9753i	−0.627177	−	0.696551i	−0.970070	+	0.242823i	$0.921926\pi$
$348$	23.0130	+	10.2461i	1.23363	+	0.549246i
$349$	17.4949	+	12.7108i	0.936481	+	0.680393i	0.947571	−	0.319545i	$-0.103530\pi$
$349$	17.4949	+	12.7108i	0.936481	+	0.680393i	−0.0110900	+	0.999939i	$0.503530\pi$
$350$		0			0
$351$	17.9738			0.959371
$352$	−0.692976	−	2.84262i	−0.0369358	−	0.151512i
$353$	−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	$0.204037\pi$
$354$	−23.6860	−	5.03461i	−1.25890	−	0.267586i
$355$	0.0153416	−	0.145965i	0.000814245	−	0.00774703i
$356$	−31.7835	+	23.0920i	−1.68452	+	1.22388i
$357$		0			0
$358$	−3.59123	+	11.0527i	−0.189802	+	0.584152i
$359$	−9.75825	−	4.34465i	−0.515021	−	0.229302i	0.132733	−	0.991152i	$-0.457625\pi$
$359$	−9.75825	−	4.34465i	−0.515021	−	0.229302i	−0.647754	+	0.761850i	$0.724291\pi$
$360$	5.02603	−	2.23773i	0.264895	−	0.117939i
$361$	10.5715	+	2.24705i	0.556397	+	0.118266i
$362$	−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
$366$	−0.893472	+	8.50082i	−0.0467025	+	0.444345i
$367$	−1.06794	−	10.1608i	−0.0557460	−	0.530388i	−0.986385	−	0.164450i	$-0.947415\pi$
$367$	−1.06794	−	10.1608i	−0.0557460	−	0.530388i	0.930639	−	0.365938i	$-0.119252\pi$
$368$	15.6189	+	17.3466i	0.814194	+	0.904254i
$369$	−0.290094	+	0.0616615i	−0.0151017	+	0.00320997i
$370$	−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	$0.576595\pi$
$374$	34.5245	−	32.9928i	1.78522	−	1.70602i
$375$	7.59588	−	13.1564i	0.392249	−	0.679396i
$376$	−29.0767	+	32.2929i	−1.49952	+	1.66538i
$377$	11.5593	+	8.39832i	0.595334	+	0.432535i
$378$		0			0
$379$	0.354761	−	1.09184i	0.0182228	−	0.0560841i	−0.941532	−	0.336925i	$-0.890613\pi$
$379$	0.354761	−	1.09184i	0.0182228	−	0.0560841i	0.959754	+	0.280841i	$0.0906132\pi$
$380$	−13.7677	+	2.92641i	−0.706266	+	0.150121i
$381$	1.20349	+	11.4504i	0.0616566	+	0.586623i
$382$	19.6061	−	8.72922i	1.00314	−	0.446626i
$383$	−13.3502	+	14.8269i	−0.682165	+	0.757621i	−0.980431	−	0.196861i	$-0.936925\pi$
$383$	−13.3502	+	14.8269i	−0.682165	+	0.757621i	0.298266	+	0.954483i	$0.403592\pi$
$384$	29.0038			1.48009
$385$		0			0
$386$	−62.2251			−3.16717
$387$	0.0836500	−	0.0929027i	0.00425217	−	0.00472251i
$388$	62.7378	−	27.9327i	3.18503	−	1.41807i
$389$	−0.271774	−	2.58576i	−0.0137795	−	0.131103i	0.985469	−	0.169853i	$-0.0543292\pi$
$389$	−0.271774	−	2.58576i	−0.0137795	−	0.131103i	−0.999249	+	0.0387496i	$0.987663\pi$
$390$	−13.6395	+	2.89916i	−0.690662	+	0.146805i
$391$	12.3816	−	38.1067i	0.626166	−	1.92714i
$392$		0			0
$393$	−0.117725	−	0.0855319i	−0.00593842	−	0.00431451i
$394$	18.2107	−	20.2250i	0.917441	−	1.01892i
$395$	−5.36761	+	9.29697i	−0.270074	+	0.467782i
$396$	−12.1102	+	1.63745i	−0.608562	+	0.0822848i
$397$	−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
$401$	−27.7339	+	5.89502i	−1.38496	+	0.294383i	−0.839322	−	0.543634i	$-0.817048\pi$
$401$	−27.7339	+	5.89502i	−1.38496	+	0.294383i	−0.545643	+	0.838018i	$0.683714\pi$
$402$	21.9712	+	24.4015i	1.09583	+	1.21704i
$403$	3.23171	+	30.7477i	0.160983	+	1.53165i
$404$	5.09530	−	48.4785i	0.253501	−	2.41190i
$405$	−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
$409$	−19.4705	−	4.13859i	−0.962756	−	0.204640i	−0.300386	−	0.953818i	$-0.597116\pi$
$409$	−19.4705	−	4.13859i	−0.962756	−	0.204640i	−0.662369	+	0.749178i	$0.730449\pi$
$410$	0.878850	−	0.391289i	0.0434033	−	0.0193244i
$411$	−5.97993	−	2.66244i	−0.294968	−	0.131328i
$412$	9.92212	−	30.5371i	0.488828	−	1.50446i
$413$		0			0
$414$	−12.5414	+	9.11189i	−0.616379	+	0.447825i
$415$	−0.125055	+	1.18982i	−0.00613869	+	0.0584057i
$416$	2.74258	+	0.582954i	0.134466	+	0.0285817i
$417$	2.74315	−	4.75128i	0.134333	−	0.232671i
$418$	23.0071	+	1.72977i	1.12531	+	0.0846057i
$419$	−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	0.951729	−	0.306939i	$-0.0993049\pi$
$421$	19.5727	+	14.2204i	0.953913	+	0.693058i	0.00218371	+	0.999998i	$0.499305\pi$
$422$	31.6699	+	14.1003i	1.54167	+	0.686394i
$423$	−5.91589	−	6.57027i	−0.287641	−	0.319457i
$424$	−13.4975	−	14.9905i	−0.655496	−	0.728002i
$425$	−18.4866	−	8.23076i	−0.896732	−	0.399251i
$426$	−0.328846	−	0.238921i	−0.0159326	−	0.0115757i
$427$		0			0
$428$	47.6218			2.30188
$429$	15.0758	+	1.13346i	0.727866	+	0.0547239i
$430$	−0.202756	+	0.351184i	−0.00977778	+	0.0169356i
$431$	−18.9761	−	4.03350i	−0.914047	−	0.194287i	−0.273202	−	0.961957i	$-0.588083\pi$
$431$	−18.9761	−	4.03350i	−0.914047	−	0.194287i	−0.640845	+	0.767670i	$0.721416\pi$
$432$	2.04010	−	19.4103i	0.0981546	−	0.933878i
$433$	17.3030	−	12.5714i	0.831530	−	0.604142i	−0.0884616	−	0.996080i	$-0.528195\pi$
$433$	17.3030	−	12.5714i	0.831530	−	0.604142i	0.919992	+	0.391937i	$0.128195\pi$
$434$		0			0
$435$	2.50767	−	7.71780i	0.120233	−	0.370040i
$436$	3.16273	+	1.40814i	0.151467	+	0.0674375i
$437$	17.6848	−	7.87377i	0.845978	−	0.376654i
$438$	2.09701	+	0.445733i	0.100199	+	0.0212980i
$439$	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
$443$	0.174155	−	1.65698i	0.00827437	−	0.0787254i	−0.989605	−	0.143809i	$-0.954065\pi$
$443$	0.174155	−	1.65698i	0.00827437	−	0.0787254i	0.997880	+	0.0650839i	$0.0207315\pi$
$444$	3.19515	+	30.3999i	0.151635	+	1.44271i
$445$	8.46835	+	9.40505i	0.401438	+	0.445842i
$446$	−7.04644	+	1.49777i	−0.333659	+	0.0709213i
$447$	5.65324	−	4.10732i	0.267389	−	0.194270i
$448$		0			0
$449$	−5.31070	−	16.3447i	−0.250627	−	0.771352i	−0.994660	−	0.103208i	$-0.967089\pi$
$449$	−5.31070	−	16.3447i	−0.250627	−	0.771352i	0.744032	−	0.668144i	$-0.232911\pi$
$450$	3.91464	+	6.78035i	0.184538	+	0.319629i
$451$	−1.03362	+	0.139758i	−0.0486713	+	0.00658093i
$452$	−8.87892	+	15.3787i	−0.417629	+	0.723355i
$453$	−16.2893	+	18.0911i	−0.765340	+	0.849996i
$454$	16.2337	+	11.7945i	0.761885	+	0.553542i
$455$		0			0
$456$	−5.87973	+	18.0959i	−0.275343	+	0.847420i
$457$	−9.99729	+	2.12499i	−0.467654	+	0.0994029i	−0.435711	−	0.900087i	$-0.643503\pi$
$457$	−9.99729	+	2.12499i	−0.467654	+	0.0994029i	−0.0319431	+	0.999490i	$0.510170\pi$
$458$	3.33013	+	31.6841i	0.155607	+	1.48050i
$459$	−30.6057	+	13.6265i	−1.42855	+	0.636033i
$460$	22.2552	−	24.7169i	1.03765	−	1.15243i
$461$	−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	$0.749389\pi$
$464$	10.3815	−	11.5299i	0.481951	−	0.535261i
$465$	16.0414	−	7.14209i	0.743902	−	0.331206i
$466$	−3.25889	−	31.0063i	−0.150965	−	1.43634i
$467$	−24.6404	+	5.23748i	−1.14022	+	0.242362i	−0.739056	−	0.673644i	$-0.764728\pi$
$467$	−24.6404	+	5.23748i	−1.14022	+	0.242362i	−0.401166	+	0.916005i	$0.631395\pi$
$468$	3.61884	−	11.1376i	0.167281	−	0.514837i
$469$		0			0
$470$	23.2015	+	16.8569i	1.07021	+	0.777551i
$471$	2.15430	−	2.39259i	0.0992648	−	0.110245i
$472$	−16.0997	+	27.8856i	−0.741050	+	1.28354i
$473$	0.317857	−	0.303754i	0.0146151	−	0.0139666i
$474$	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
$478$	−11.8418	+	2.51704i	−0.541629	+	0.115127i
$479$	−14.1882	−	15.7576i	−0.648277	−	0.719985i	0.325992	−	0.945373i	$-0.394302\pi$
$479$	−14.1882	−	15.7576i	−0.648277	−	0.719985i	−0.974269	+	0.225388i	$0.927635\pi$
$480$	−0.166458	−	1.58374i	−0.00759772	−	0.0722874i
$481$	−1.81227	+	17.2426i	−0.0826322	+	0.786193i
$482$	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
$486$	22.3249	+	4.74530i	1.01268	+	0.215251i
$487$	−15.3656	+	6.84121i	−0.696283	+	0.310005i	−0.724185	−	0.689606i	$-0.757784\pi$
$487$	−15.3656	+	6.84121i	−0.696283	+	0.310005i	0.0279025	+	0.999611i	$0.491117\pi$
$488$	10.3834	+	4.62298i	0.470033	+	0.209272i
$489$	−7.01897	+	21.6022i	−0.317409	+	0.976884i
$490$		0			0
$491$	−3.91406	+	2.84373i	−0.176639	+	0.128336i	−0.672592	−	0.740014i	$-0.734819\pi$
$491$	−3.91406	+	2.84373i	−0.176639	+	0.128336i	0.495953	+	0.868350i	$0.334819\pi$
$492$	0.184204	−	1.75259i	0.00830457	−	0.0790127i
$493$	−26.0501	−	5.53713i	−1.17324	−	0.249380i
$494$	−11.0549	+	19.1477i	−0.497385	+	0.861496i
$495$	0.932382	+	3.82468i	0.0419074	+	0.171906i
$496$	33.5719			1.50742
$497$		0			0
$498$	2.68055	+	1.94753i	0.120118	+	0.0872709i
$499$	27.9395	+	12.4395i	1.25074	+	0.556866i	0.921867	−	0.387507i	$-0.126664\pi$
$499$	27.9395	+	12.4395i	1.25074	+	0.556866i	0.328876	+	0.944373i	$0.393330\pi$
$500$	−27.6925	−	30.7556i	−1.23845	−	1.37543i
$501$	19.9051	+	22.1068i	0.889293	+	0.987660i
$502$	58.2235	+	25.9228i	2.59864	+	1.15699i
$503$	22.8472	+	16.5994i	1.01871	+	0.740133i	0.966017	−	0.258478i	$-0.0832211\pi$
$503$	22.8472	+	16.5994i	1.01871	+	0.740133i	0.0526880	+	0.998611i	$0.483221\pi$
$504$		0			0
$505$	−15.7029			−0.698768
$506$	−46.3855	+	28.6487i	−2.06209	+	1.27359i
$507$	2.07842	−	3.59992i	0.0923057	−	0.159878i
$508$	30.6800	+	6.52123i	1.36120	+	0.289333i
$509$	0.439087	−	4.17764i	0.0194622	−	0.185170i	−0.980472	−	0.196660i	$-0.936991\pi$
$509$	0.439087	−	4.17764i	0.0194622	−	0.185170i	0.999934	+	0.0114893i	$0.00365724\pi$
$510$	21.0273	−	15.2772i	0.931104	−	0.676486i
$511$		0			0
$512$	10.8274	−	33.3234i	0.478509	−	1.47270i
$513$	−14.7869	−	6.58355i	−0.652857	−	0.290671i
$514$	−66.5028	+	29.6090i	−2.93331	+	1.30600i
$515$	−10.1174	−	2.15053i	−0.445827	−	0.0947635i
$516$	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
$520$	−1.93816	+	18.4404i	−0.0849940	+	0.808664i
$521$	2.15819	+	20.5339i	0.0945522	+	0.899604i	0.934266	+	0.356576i	$0.116056\pi$
$521$	2.15819	+	20.5339i	0.0945522	+	0.899604i	−0.839714	+	0.543029i	$0.817278\pi$
$522$	6.89464	+	7.65727i	0.301770	+	0.335150i
$523$	22.1395	−	4.70589i	0.968091	−	0.205774i	0.303376	−	0.952871i	$-0.401886\pi$
$523$	22.1395	−	4.70589i	0.968091	−	0.205774i	0.664715	+	0.747097i	$0.268553\pi$
$524$	−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
$528$	2.93521	−	16.1520i	0.127739	−	0.702926i
$529$	−11.3720	+	19.6969i	−0.494434	+	0.856385i
$530$	−8.90795	+	9.89328i	−0.386937	+	0.429737i
$531$	−5.30007	−	3.85073i	−0.230003	−	0.167107i
$532$		0			0
$533$	0.308871	−	0.950608i	0.0133787	−	0.0411754i
$534$	34.2841	−	7.28730i	1.48362	−	0.315353i
$535$	−1.60356	−	15.2568i	−0.0693278	−	0.659610i
$536$	39.8874	−	17.7590i	1.72287	−	0.767072i
$537$	4.58877	−	5.09635i	0.198020	−	0.219924i
$538$	4.21881			0.181886
$539$		0			0
$540$	−27.8098			−1.19674
$541$	28.5828	−	31.7444i	1.22887	−	1.36480i	0.320163	−	0.947363i	$-0.396262\pi$
$541$	28.5828	−	31.7444i	1.22887	−	1.36480i	0.908707	−	0.417435i	$-0.137071\pi$
$542$	5.49744	−	2.44762i	0.236135	−	0.105134i
$543$	1.17726	+	11.2009i	0.0505212	+	0.480677i
$544$	−5.11201	+	1.08659i	−0.219176	+	0.0465872i
$545$	0.344634	−	1.06067i	0.0147625	−	0.0454343i
$546$		0			0
$547$	−35.9873	−	26.1463i	−1.53870	−	1.11793i	−0.951141	−	0.308756i	$-0.900087\pi$
$547$	−35.9873	−	26.1463i	−1.53870	−	1.11793i	−0.587563	−	0.809178i	$-0.699913\pi$
$548$	−11.9322	+	13.2520i	−0.509717	+	0.566098i
$549$	−1.15626	+	2.00269i	−0.0493478	+	0.0854728i
$550$	11.9409	+	24.8109i	0.509161	+	1.05794i
$551$	−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
$555$	9.63176	−	2.04729i	0.408845	−	0.0869028i
$556$	−10.0008	−	11.1070i	−0.424128	−	0.471041i
$557$	2.61228	+	24.8542i	0.110686	+	1.05311i	0.899035	+	0.437878i	$0.144270\pi$
$557$	2.61228	+	24.8542i	0.110686	+	1.05311i	−0.788349	+	0.615229i	$0.789064\pi$
$558$	−2.33056	+	22.1738i	−0.0986603	+	0.938690i
$559$	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
$563$	−8.81316	−	1.87330i	−0.371431	−	0.0789500i	0.0184146	−	0.999830i	$-0.494138\pi$
$563$	−8.81316	−	1.87330i	−0.371431	−	0.0789500i	−0.389845	+	0.920880i	$0.627471\pi$
$564$	47.9921	−	21.3675i	2.02083	−	0.899733i
$565$	5.22594	+	2.32674i	0.219857	+	0.0978866i
$566$	6.37460	−	19.6190i	0.267944	−	0.824648i
$567$		0			0
$568$	−0.437275	+	0.317699i	−0.0183476	+	0.0133303i
$569$	−3.04950	+	29.0140i	−0.127842	+	1.21633i	0.722977	+	0.690872i	$0.242773\pi$
$569$	−3.04950	+	29.0140i	−0.127842	+	1.21633i	−0.850819	+	0.525459i	$0.823893\pi$
$570$	12.2830	+	2.61083i	0.514478	+	0.109356i
$571$	−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	$0.178591\pi$
$572$	15.6279	−	38.1056i	0.653437	−	1.59327i
$573$	−12.6645			−0.529065
$574$		0			0
$575$	18.6906	+	13.5795i	0.779452	+	0.566305i
$576$	7.79381	+	3.47003i	0.324742	+	0.144584i
$577$	−14.4432	−	16.0408i	−0.601277	−	0.667785i	0.363274	−	0.931682i	$-0.381659\pi$
$577$	−14.4432	−	16.0408i	−0.601277	−	0.667785i	−0.964551	+	0.263897i	$0.914992\pi$
$578$	−29.4292	−	32.6845i	−1.22409	−	1.35949i
$579$	33.5444	+	14.9349i	1.39406	+	0.620675i
$580$	−17.8850	−	12.9942i	−0.742633	−	0.539554i
$581$		0			0
$582$	−61.2694			−2.53970
$583$	12.2803	−	7.58458i	0.508598	−	0.314121i
$584$	1.42537	−	2.46881i	0.0589823	−	0.102160i
$585$	−3.69007	−	0.784349i	−0.152566	−	0.0324288i
$586$	6.25630	−	59.5247i	0.258445	−	2.45894i
$587$	−4.46865	+	3.24666i	−0.184441	+	0.134004i	−0.676174	−	0.736742i	$-0.736363\pi$
$587$	−4.46865	+	3.24666i	−0.184441	+	0.134004i	0.491734	+	0.870746i	$0.336363\pi$
$588$		0			0
$589$	8.60373	−	26.4796i	0.354511	−	1.09107i
$590$	19.4135	+	8.64345i	0.799241	+	0.355845i
$591$	−14.6713	+	6.53210i	−0.603499	+	0.268695i
$592$	18.4149	+	3.91421i	0.756847	+	0.160873i
$593$	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
$597$	1.83651	−	17.4732i	0.0751632	−	0.715130i
$598$	−5.46116	−	51.9595i	−0.223323	−	2.12478i
$599$	−17.7419	−	19.7044i	−0.724916	−	0.805101i	0.262216	−	0.965009i	$-0.415547\pi$
$599$	−17.7419	−	19.7044i	−0.724916	−	0.805101i	−0.987132	+	0.159908i	$0.948880\pi$
$600$	−22.2114	+	4.72117i	−0.906775	+	0.192741i
$601$	30.5565	−	22.2006i	1.24643	−	0.905581i	0.248417	−	0.968653i	$-0.420090\pi$
$601$	30.5565	−	22.2006i	1.24643	−	0.905581i	0.998009	+	0.0630720i	$0.0200898\pi$
$602$		0			0
$603$	2.74513	+	8.44864i	0.111790	+	0.344055i
$604$	33.1593	+	57.4336i	1.34923	+	2.33694i
$605$	2.26141	+	13.6590i	0.0919395	+	0.555318i
$606$	−21.7445	+	37.6626i	−0.883310	+	1.52994i
$607$	−18.5512	+	20.6032i	−0.752971	+	0.836259i	−0.990840	−	0.135038i	$-0.956884\pi$
$607$	−18.5512	+	20.6032i	−0.752971	+	0.836259i	0.237870	+	0.971297i	$0.423551\pi$
$608$	−2.04277	−	1.48416i	−0.0828452	−	0.0601906i
$609$		0			0
$610$	2.31801	−	7.13411i	0.0938536	−	0.288852i
$611$	29.1457	−	6.19511i	1.17911	−	0.250627i
$612$	2.28167	+	21.7087i	0.0922311	+	0.877521i
$613$	33.0945	−	14.7346i	1.33667	−	0.595126i	0.391045	−	0.920372i	$-0.372114\pi$
$613$	33.0945	−	14.7346i	1.33667	−	0.595126i	0.945630	+	0.325246i	$0.105447\pi$
$614$	−7.47102	+	8.29741i	−0.301506	+	0.334856i
$615$	−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	$0.188817\pi$
$618$	−19.1680	+	21.2882i	−0.771051	+	0.856338i
$619$	−32.6497	+	14.5366i	−1.31230	+	0.584274i	−0.939154	−	0.343497i	$-0.888388\pi$
$619$	−32.6497	+	14.5366i	−1.31230	+	0.584274i	−0.373148	+	0.927772i	$0.621722\pi$
$620$	−5.00022	−	47.5739i	−0.200814	−	1.91062i
$621$	37.4124	−	7.95225i	1.50131	−	0.319113i
$622$	1.66037	−	5.11010i	0.0665749	−	0.204897i
$623$		0			0
$624$	12.7274	+	9.24698i	0.509503	+	0.370176i
$625$	2.50740	−	2.78475i	0.100296	−	0.111390i
$626$	−11.7868	+	20.4154i	−0.471096	+	0.815963i
$627$	−11.9875	−	6.45453i	−0.478736	−	0.257769i
$628$	−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	−0.631421	−	0.775440i	$-0.717528\pi$
$631$	−2.23700	+	1.62527i	−0.0890534	+	0.0647011i	0.542368	+	0.840141i	$0.317528\pi$
$632$	38.6703	−	8.21962i	1.53822	−	0.326959i
$633$	−13.6884	−	15.2025i	−0.544064	−	0.604244i
$634$	1.64000	+	15.6036i	0.0651328	+	0.619697i
$635$	1.05616	−	10.0487i	0.0419123	−	0.398769i
$636$	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
$640$	−24.8969	−	5.29200i	−0.984137	−	0.209185i
$641$	35.1591	−	15.6538i	1.38870	−	0.618290i	0.430032	−	0.902813i	$-0.358502\pi$
$641$	35.1591	−	15.6538i	1.38870	−	0.618290i	0.958669	+	0.284524i	$0.0918355\pi$
$642$	−38.8132	−	17.2808i	−1.53184	−	0.682018i
$643$	−8.15130	+	25.0871i	−0.321456	+	0.989339i	0.651559	+	0.758598i	$0.274115\pi$
$643$	−8.15130	+	25.0871i	−0.321456	+	0.989339i	−0.973015	+	0.230741i	$0.925885\pi$
$644$		0			0
$645$	0.193592	−	0.140653i	0.00762267	−	0.00553819i
$646$	4.30777	−	40.9857i	0.169487	−	1.61256i
$647$	26.7241	+	5.68037i	1.05063	+	0.223319i	0.700699	−	0.713457i	$-0.252871\pi$
$647$	26.7241	+	5.68037i	1.05063	+	0.223319i	0.349932	+	0.936775i	$0.386205\pi$
$648$	−12.2402	+	21.2006i	−0.480839	+	0.832838i
$649$	−17.5721	−	14.9020i	−0.689763	−	0.584954i
$650$	−26.3865			−1.03496
$651$		0			0
$652$	50.0601	+	36.3708i	1.96051	+	1.42439i
$653$	−7.73011	−	3.44166i	−0.302502	−	0.134683i	0.249872	−	0.968279i	$-0.419611\pi$
$653$	−7.73011	−	3.44166i	−0.302502	−	0.134683i	−0.552374	+	0.833596i	$0.686278\pi$
$654$	−2.06674	−	2.29535i	−0.0808160	−	0.0897553i
$655$	0.0854490	+	0.0949008i	0.00333877	+	0.00370808i
$656$	−0.991523	−	0.441455i	−0.0387125	−	0.0172359i
$657$	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	$0.532871\pi$
$660$	−23.3258	−	1.75373i	−0.907956	−	0.0682638i
$661$	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	$0.0443922\pi$
$662$	8.60778	+	1.82964i	0.334551	+	0.0711110i
$663$	2.82274	−	26.8566i	0.109626	−	1.04302i
$664$	3.56439	−	2.58968i	0.138325	−	0.100499i
$665$		0			0
$666$	−3.86364	+	11.8911i	−0.149713	+	0.460769i
$667$	27.7763	+	12.3668i	1.07550	+	0.478845i
$668$	74.0331	−	32.9617i	2.86443	−	1.27533i
$669$	4.15809	+	0.883830i	0.160761	+	0.0341708i
$670$	−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	−0.998164	−	0.0605625i	$-0.980711\pi$
$673$	−5.86892	−	18.0627i	−0.226230	−	0.696265i	0.771934	−	0.635702i	$-0.219289\pi$
$674$	−1.62722	+	15.4820i	−0.0626783	+	0.596344i
$675$	−2.01919	−	19.2113i	−0.0777187	−	0.739444i
$676$	−7.57733	−	8.41548i	−0.291436	−	0.323672i
$677$	−31.7134	+	6.74089i	−1.21884	+	0.259073i	−0.772049	−	0.635563i	$-0.780768\pi$
$677$	−31.7134	+	6.74089i	−1.21884	+	0.259073i	−0.446795	+	0.894636i	$0.647435\pi$
$678$	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
$682$	−14.0198	+	77.1490i	−0.536847	+	2.95419i
$683$	−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	$0.260119\pi$
$684$	−7.05674	+	7.83730i	−0.269821	+	0.299667i
$685$	4.64740	+	3.37654i	0.177568	+	0.129011i
$686$		0			0
$687$	5.80944	−	17.8796i	0.221644	−	0.682150i
$688$	0.447504	−	0.0951200i	0.0170609	−	0.00362641i
$689$	1.44581	+	13.7560i	0.0550811	+	0.524061i
$690$	−27.1078	+	12.0692i	−1.03198	+	0.459466i
$691$	−21.0179	+	23.3428i	−0.799559	+	0.888000i	−0.995706	−	0.0925742i	$-0.970490\pi$
$691$	−21.0179	+	23.3428i	−0.799559	+	0.888000i	0.196147	+	0.980575i	$0.437157\pi$
$692$	−84.2192			−3.20153
$693$		0			0
$694$	42.4357			1.61084
$695$	−3.22165	+	3.57800i	−0.122204	+	0.135721i
$696$	−27.3011	+	12.1552i	−1.03484	+	0.460742i
$697$	0.194743	+	1.85286i	0.00737642	+	0.0701819i
$698$	−51.4098	+	10.9275i	−1.94589	+	0.413611i
$699$	−5.68515	+	17.4971i	−0.215032	+	0.661801i
$700$		0			0
$701$	12.9966	+	9.44259i	0.490875	+	0.356642i	0.805521	−	0.592568i	$-0.201886\pi$
$701$	12.9966	+	9.44259i	0.490875	+	0.356642i	−0.314646	+	0.949209i	$0.601886\pi$
$702$	−29.2306	+	32.4639i	−1.10324	+	1.22527i
$703$	7.80663	−	13.5215i	0.294433	−	0.509972i
$704$	26.4180	+	14.2244i	0.995665	+	0.536102i
$705$	−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
$709$	−38.8303	+	8.25363i	−1.45830	+	0.309972i	−0.867739	−	0.497020i	$-0.834428\pi$
$709$	−38.8303	+	8.25363i	−1.45830	+	0.309972i	−0.590563	+	0.806992i	$0.701094\pi$
$710$	0.238689	+	0.265091i	0.00895785	+	0.00994870i
$711$	0.840781	+	7.99950i	0.0315318	+	0.300005i
$712$	4.87174	−	46.3515i	0.182576	−	1.73710i
$713$	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
$717$	6.98780	+	1.48530i	0.260964	+	0.0554696i
$718$	23.7170	−	10.5595i	0.885109	−	0.394076i
$719$	−9.00976	−	4.01140i	−0.336007	−	0.149600i	0.231796	−	0.972764i	$-0.425540\pi$
$719$	−9.00976	−	4.01140i	−0.336007	−	0.149600i	−0.567803	+	0.823164i	$0.692207\pi$
$720$	−1.26587	+	3.89596i	−0.0471763	+	0.145194i
$721$		0			0
$722$	−21.2510	+	15.4397i	−0.790879	+	0.574607i
$723$	0.393806	−	3.74681i	0.0146458	−	0.139346i
$724$	30.0114	+	6.37911i	1.11536	+	0.237078i
$725$	7.67796	−	13.2986i	0.285152	−	0.493898i
$726$	35.8919	+	13.4904i	1.33207	+	0.500675i
$727$	−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
$730$	−1.71875	−	0.765238i	−0.0636139	−	0.0283227i
$731$	−0.525482	−	0.583607i	−0.0194357	−	0.0215855i
$732$	−9.19443	−	10.2114i	−0.339836	−	0.377426i
$733$	37.7226	+	16.7952i	1.39332	+	0.620345i	0.959770	−	0.280786i	$-0.0905951\pi$
$733$	37.7226	+	16.7952i	1.39332	+	0.620345i	0.433547	+	0.901131i	$0.357262\pi$
$734$	20.0889	+	14.5955i	0.741496	+	0.538729i
$735$		0			0
$736$	5.96659			0.219931
$737$	7.39953	+	30.3533i	0.272565	+	1.11808i
$738$	0.360406	−	0.624242i	0.0132667	−	0.0229787i
$739$	−34.6358	−	7.36206i	−1.27410	−	0.270818i	−0.479278	−	0.877663i	$-0.659101\pi$
$739$	−34.6358	−	7.36206i	−1.27410	−	0.270818i	−0.794820	+	0.606846i	$0.792435\pi$
$740$	2.80400	−	26.6783i	0.103077	−	0.980714i
$741$	10.5552	−	7.66883i	0.387756	−	0.281722i
$742$		0			0
$743$	−1.24351	+	3.82713i	−0.0456200	+	0.140404i	−0.971272	−	0.237972i	$-0.923517\pi$
$743$	−1.24351	+	3.82713i	−0.0456200	+	0.140404i	0.925652	+	0.378376i	$0.123517\pi$
$744$	−59.0751	−	26.3019i	−2.16580	−	0.964275i
$745$	−5.60218	+	2.49425i	−0.205248	+	0.0913822i
$746$	−66.2923	−	14.0909i	−2.42713	−	0.515903i
$747$	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
$751$	−2.55248	+	24.2852i	−0.0931413	+	0.886180i	0.843792	+	0.536671i	$0.180318\pi$
$751$	−2.55248	+	24.2852i	−0.0931413	+	0.886180i	−0.936933	+	0.349509i	$0.886348\pi$
$752$	−3.38206	−	32.1782i	−0.123331	−	1.17342i
$753$	−25.1654	−	27.9490i	−0.917077	−	1.01852i
$754$	−33.9676	+	7.22004i	−1.23703	+	0.262938i
$755$	17.2837	−	12.5573i	0.629019	−	0.457009i
$756$		0			0
$757$	−0.407046	−	1.25276i	−0.0147943	−	0.0455323i	0.943387	−	0.331695i	$-0.107620\pi$
$757$	−0.407046	−	1.25276i	−0.0147943	−	0.0455323i	−0.958181	+	0.286162i	$0.907620\pi$
$758$	1.39512	+	2.41641i	0.0506729	+	0.0877680i
$759$	31.8817	−	4.31077i	1.15723	−	0.156471i
$760$	8.34895	−	14.4608i	0.302848	−	0.524548i
$761$	−4.84721	+	5.38337i	−0.175711	+	0.195147i	−0.824567	−	0.565764i	$-0.808581\pi$
$761$	−4.84721	+	5.38337i	−0.175711	+	0.195147i	0.648856	+	0.760911i	$0.275248\pi$
$762$	−22.6387	−	16.4480i	−0.820115	−	0.595848i
$763$		0			0
$764$	−10.6613	+	32.8122i	−0.385714	+	1.18710i
$765$	6.87808	−	1.46198i	0.248677	−	0.0528580i
$766$	−5.06874	−	48.2258i	−0.183141	−	1.74247i
$767$	20.1704	−	8.98044i	0.728311	−	0.324265i
$768$	−29.8051	+	33.1019i	−1.07550	+	1.19446i
$769$	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
$772$	66.9335	−	74.3372i	2.40899	−	2.67546i
$773$	17.4085	−	7.75075i	0.626139	−	0.278775i	−0.0690374	−	0.997614i	$-0.521993\pi$
$773$	17.4085	−	7.75075i	0.626139	−	0.278775i	0.695177	+	0.718839i	$0.255326\pi$
$774$	0.0317597	+	0.302174i	0.00114158	+	0.0108614i
$775$	32.5016	−	6.90843i	1.16749	−	0.248158i
$776$	−25.1761	+	77.4839i	−0.903768	+	2.78151i
$777$		0			0
$778$	5.11232	+	3.71432i	0.183286	+	0.133165i
$779$	−0.602300	+	0.668922i	−0.0215796	+	0.0239666i
$780$	11.2081	−	19.4129i	0.401313	−	0.695095i
$781$	−0.167721	−	0.348492i	−0.00600152	−	0.0124700i
$782$	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
$786$	0.345940	−	0.0735318i	0.0123393	−	0.00262279i
$787$	21.0509	+	23.3793i	0.750382	+	0.833384i	0.990522	−	0.137355i	$-0.0438600\pi$
$787$	21.0509	+	23.3793i	0.750382	+	0.833384i	−0.240140	+	0.970738i	$0.577193\pi$
$788$	4.57317	+	43.5108i	0.162912	+	1.55001i
$789$	−0.500280	+	4.75985i	−0.0178105	+	0.169455i
$790$	−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
$794$	20.8549	+	4.43285i	0.740113	+	0.157316i
$795$	7.17665	−	3.19525i	0.254529	−	0.113324i
$796$	−43.7251	−	19.4677i	−1.54980	−	0.690013i
$797$	−3.87670	+	11.9313i	−0.137320	+	0.422627i	−0.995944	−	0.0899793i	$-0.971320\pi$
$797$	−3.87670	+	11.9313i	−0.137320	+	0.422627i	0.858624	+	0.512606i	$0.171320\pi$
$798$		0			0
$799$	−44.9324	+	32.6453i	−1.58959	+	1.15491i
$800$	0.314987	−	2.99690i	0.0111365	−	0.105956i
$801$	9.27533	+	1.97153i	0.327728	+	0.0696607i
$802$	34.4559	−	59.6794i	1.21668	−	2.10735i
$803$	1.55572	+	1.31933i	0.0549002	+	0.0465582i
$804$	−52.7850			−1.86159
$805$		0			0
$806$	−60.7915	−	44.1676i	−2.14129	−	1.55574i
$807$	−2.27428	−	1.01258i	−0.0800585	−	0.0356444i
$808$	38.6947	+	42.9749i	1.36128	+	1.51185i
$809$	−3.60008	−	3.99830i	−0.126572	−	0.140573i	0.676527	−	0.736417i	$-0.263484\pi$
$809$	−3.60008	−	3.99830i	−0.126572	−	0.140573i	−0.803100	+	0.595845i	$0.796817\pi$
$810$	14.7595	+	6.57137i	0.518597	+	0.230894i
$811$	−11.0835	−	8.05262i	−0.389194	−	0.282766i	0.375931	−	0.926647i	$-0.377323\pi$
$811$	−11.0835	−	8.05262i	−0.389194	−	0.282766i	−0.765125	+	0.643882i	$0.777323\pi$
$812$		0			0
$813$	−3.55103			−0.124540
$814$	−16.6851	+	40.6833i	−0.584813	+	1.42595i
$815$	9.96663	−	17.2627i	0.349116	−	0.604686i
$816$	−28.6826	−	6.09667i	−1.00409	−	0.213426i
$817$	0.0396603	−	0.377343i	0.00138754	−	0.0132016i
$818$	39.1398	−	28.4367i	1.36849	−	0.994266i
$819$		0			0
$820$	−0.477897	+	1.47082i	−0.0166889	+	0.0513631i
$821$	−8.43308	−	3.75465i	−0.294317	−	0.131038i	0.254267	−	0.967134i	$-0.418166\pi$
$821$	−8.43308	−	3.75465i	−0.294317	−	0.131038i	−0.548583	+	0.836096i	$0.684833\pi$
$822$	14.5339	−	6.47092i	0.506929	−	0.225699i
$823$	12.1708	+	2.58698i	0.424246	+	0.0901763i	0.415087	−	0.909782i	$-0.363751\pi$
$823$	12.1708	+	2.58698i	0.424246	+	0.0901763i	0.00915927	+	0.999958i	$0.497084\pi$
$824$	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	0.924071	−	0.382221i	$-0.124841\pi$
$827$	−1.38559	−	4.26441i	−0.0481817	−	0.148288i	−0.972253	+	0.233932i	$0.924841\pi$
$828$	2.60491	−	24.7840i	0.0905267	−	0.861304i
$829$	3.85475	+	36.6755i	0.133881	+	1.27379i	0.830770	+	0.556615i	$0.187900\pi$
$829$	3.85475	+	36.6755i	0.133881	+	1.27379i	−0.696889	+	0.717179i	$0.745433\pi$
$830$	−1.94564	−	2.16086i	−0.0675343	−	0.0750044i
$831$	−7.23276	+	1.53737i	−0.250902	+	0.0533308i
$832$	−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
$836$	−26.8145	+	25.6248i	−0.927398	+	0.886252i
$837$	27.5053	−	47.6405i	0.950721	−	1.64670i
$838$	50.2453	−	55.8031i	1.73570	−	1.92769i
$839$	−7.41389	−	5.38651i	−0.255956	−	0.185963i	0.452406	−	0.891812i	$-0.350566\pi$
$839$	−7.41389	−	5.38651i	−0.255956	−	0.185963i	−0.708362	+	0.705849i	$0.750566\pi$
$840$		0			0
$841$	−2.71643	+	8.36030i	−0.0936699	+	0.288286i
$842$	−57.5153	+	12.2253i	−1.98211	+	0.421310i
$843$	3.38367	+	32.1934i	0.116540	+	1.10880i
$844$	−50.9112	+	22.6671i	−1.75244	+	0.780235i
$845$	−2.44096	+	2.71096i	−0.0839715	+	0.0932598i
$846$	21.4880			0.738774
$847$		0			0
$848$	15.0195			0.515771
$849$	−8.14528	+	9.04625i	−0.279545	+	0.310466i
$850$	44.9308	−	20.0045i	1.54111	−	0.686148i
$851$	3.85649	+	36.6921i	0.132199	+	1.25779i
$852$	0.639156	−	0.135857i	0.0218971	−	0.00465438i
$853$	2.01494	−	6.20135i	0.0689903	−	0.212330i	−0.910617	−	0.413251i	$-0.864393\pi$
$853$	2.01494	−	6.20135i	0.0689903	−	0.212330i	0.979608	+	0.200921i	$0.0643933\pi$
$854$		0			0
$855$	2.74849	+	1.99690i	0.0939965	+	0.0682924i
$856$	−37.8027	+	41.9841i	−1.29207	+	1.43499i
$857$	−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	$0.860038\pi$
$858$	−26.5648	+	25.3862i	−0.906909	+	0.866672i
$859$	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
$863$	−3.54767	+	0.754081i	−0.120764	+	0.0256692i	−0.267897	−	0.963447i	$-0.586329\pi$
$863$	−3.54767	+	0.754081i	−0.120764	+	0.0256692i	0.147133	+	0.989117i	$0.452995\pi$
$864$	−3.33821	−	3.70746i	−0.113568	−	0.126130i
$865$	2.83589	+	26.9817i	0.0964232	+	0.917405i
$866$	−5.43358	+	51.6971i	−0.184641	+	1.75674i
$867$	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
$871$	−29.2850	−	6.22472i	−0.992285	−	0.210917i
$872$	−3.75204	+	1.67052i	−0.127060	+	0.0565708i
$873$	−15.1430	−	6.74208i	−0.512512	−	0.228185i
$874$	−14.5392	+	44.7469i	−0.491794	+	1.51359i
$875$		0			0
$876$	−2.78818	+	2.02573i	−0.0942039	+	0.0684432i
$877$	−2.79171	+	26.5613i	−0.0942692	+	0.896911i	0.840537	+	0.541754i	$0.182239\pi$
$877$	−2.79171	+	26.5613i	−0.0942692	+	0.896911i	−0.934806	+	0.355158i	$0.884427\pi$
$878$	−75.4367	−	16.0346i	−2.54587	−	0.541140i
$879$	−17.6595	+	30.5871i	−0.595639	+	1.03168i
$880$	−5.46668	+	13.3294i	−0.184282	+	0.449333i
$881$	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	0.996848	−	0.0793369i	$-0.0252803\pi$
$883$	36.5331	+	26.5429i	1.22944	+	0.893238i	0.232589	+	0.972575i	$0.425280\pi$
$884$	−67.2062	−	29.9221i	−2.26039	−	1.00639i
$885$	−8.39091	−	9.31905i	−0.282057	−	0.313256i
$886$	2.70957	+	3.00928i	0.0910298	+	0.101099i
$887$	−21.9478	−	9.77179i	−0.736935	−	0.328105i	0.00371735	−	0.999993i	$-0.498817\pi$
$887$	−21.9478	−	9.77179i	−0.736935	−	0.328105i	−0.740652	+	0.671889i	$0.765483\pi$
$888$	−29.3373	−	21.3148i	−0.984497	−	0.715279i
$889$		0			0
$890$	−30.7592			−1.03105
$891$	−13.3595	−	11.3296i	−0.447561	−	0.379555i
$892$	5.79032	−	10.0291i	0.193874	−	0.335800i
$893$	−26.2471	−	5.57898i	−0.878324	−	0.186694i
$894$	−1.77526	+	16.8905i	−0.0593735	+	0.564901i
$895$	−4.86889	+	3.53746i	−0.162749	+	0.118244i
$896$		0			0
$897$	−9.52702	+	29.3212i	−0.318098	+	0.979005i
$898$	38.1581	+	16.9891i	1.27335	+	0.566933i
$899$	39.9493	−	17.7866i	1.33238	−	0.593216i
$900$	−12.3110	−	2.61678i	−0.410367	−	0.0872261i
$901$	−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
$905$	1.03314	−	9.82969i	0.0343428	−	0.326750i
$906$	−6.18464	−	58.8429i	−0.205471	−	1.95492i
$907$	−10.7241	−	11.9104i	−0.356089	−	0.395477i	0.538310	−	0.842747i	$-0.319063\pi$
$907$	−10.7241	−	11.9104i	−0.356089	−	0.395477i	−0.894399	+	0.447270i	$0.852396\pi$
$908$	−31.5523	+	6.70665i	−1.04710	+	0.222568i
$909$	−9.51862	+	6.91568i	−0.315713	+	0.229379i
$910$		0			0
$911$	−5.06922	−	15.6014i	−0.167951	−	0.516899i	0.831291	−	0.555838i	$-0.187602\pi$
$911$	−5.06922	−	15.6014i	−0.167951	−	0.516899i	−0.999242	+	0.0389385i	$0.987602\pi$
$912$	−7.08366	−	12.2693i	−0.234564	−	0.406276i
$913$	1.36715	+	2.84069i	0.0452462	+	0.0940131i
$914$	12.4204	−	21.5127i	0.410830	−	0.711578i
$915$	−2.96189	+	3.28951i	−0.0979170	+	0.108748i
$916$	−41.4336	−	30.1032i	−1.36900	−	0.994639i
$917$		0			0
$918$	25.1618	−	77.4401i	0.830464	−	2.55590i
$919$	−31.6139	+	6.71973i	−1.04284	+	0.221664i	−0.697330	−	0.716750i	$-0.745629\pi$
$919$	−31.6139	+	6.71973i	−1.04284	+	0.221664i	−0.345515	+	0.938413i	$0.612296\pi$
$920$	4.12440	+	39.2410i	0.135977	+	1.29374i
$921$	6.01899	−	2.67983i	0.198333	−	0.0883033i
$922$	35.9670	−	39.9454i	1.18451	−	1.31553i
$923$	0.370623			0.0121992
$924$		0			0
$925$	18.6333			0.612659
$926$	49.3933	−	54.8568i	1.62316	−	1.80271i
$927$	−7.08000	+	3.15222i	−0.232538	+	0.103533i
$928$	−0.414544	−	3.94412i	−0.0136081	−	0.129472i
$929$	8.01622	−	1.70390i	0.263004	−	0.0559032i	−0.0745223	−	0.997219i	$-0.523743\pi$
$929$	8.01622	−	1.70390i	0.263004	−	0.0559032i	0.337526	+	0.941316i	$0.390410\pi$
$930$	−13.1881	+	40.5887i	−0.432454	+	1.33096i
$931$		0			0
$932$	40.5471	+	29.4592i	1.32817	+	0.964969i
$933$	−2.12158	+	2.35625i	−0.0694573	+	0.0771402i
$934$	30.6126	−	53.0226i	1.00168	−	1.73495i
$935$	24.5069	−	3.31363i	0.801463	−	0.108367i
$936$	6.94645	+	12.0316i	0.227052	+	0.393265i
$937$	10.5490	+	32.4666i	0.344622	+	1.06064i	0.961786	+	0.273803i	$0.0882817\pi$
$937$	10.5490	+	32.4666i	0.344622	+	1.06064i	−0.617164	+	0.786835i	$0.711718\pi$
$938$		0			0
$939$	11.2541	−	8.17655i	0.367262	−	0.266831i
$940$	−45.0953	+	9.58530i	−1.47085	+	0.312638i
$941$	0.655327	+	0.727814i	0.0213630	+	0.0237261i	0.753732	−	0.657182i	$-0.228252\pi$
$941$	0.655327	+	0.727814i	0.0213630	+	0.0237261i	−0.732369	+	0.680908i	$0.761585\pi$
$942$	0.817931	+	7.78210i	0.0266496	+	0.253554i
$943$	0.222331	−	2.11534i	0.00724010	−	0.0688850i
$944$	−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	$0.838172\pi$
$948$	−46.7501	−	9.93705i	−1.51837	−	0.322740i
$949$	−1.78576	+	0.795073i	−0.0579683	+	0.0258092i
$950$	21.7079	+	9.66499i	0.704298	+	0.313574i
$951$	2.86099	−	8.80523i	0.0927740	−	0.285529i
$952$		0			0
$953$	−13.5365	+	9.83486i	−0.438491	+	0.318582i	−0.785035	−	0.619451i	$-0.787355\pi$
$953$	−13.5365	+	9.83486i	−0.438491	+	0.318582i	0.346544	+	0.938034i	$0.387355\pi$
$954$	−1.04265	+	9.92016i	−0.0337571	+	0.321177i
$955$	10.8712	+	2.31075i	0.351784	+	0.0747740i
$956$	9.73081	−	16.8543i	0.314717	−	0.545106i
$957$	−5.06464	−	20.7754i	−0.163716	−	0.671573i
$958$	51.5353			1.66503
$959$		0			0
$960$	13.2115	+	9.59870i	0.426399	+	0.309797i
$961$	58.1239	+	25.8784i	1.87496	+	0.834788i
$962$	−28.1959	−	31.3147i	−0.909071	−	1.00963i
$963$	−7.69127	−	8.54202i	−0.247848	−	0.275263i
$964$	−9.37607	−	4.17450i	−0.301983	−	0.134451i
$965$	−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	$0.300710\pi$
$968$	31.8088	−	39.8472i	1.02237	−	1.28074i
$969$	−12.1594	+	21.0607i	−0.390617	+	0.676568i
$970$	52.5938	+	11.1792i	1.68869	+	0.358941i
$971$	3.47471	−	33.0596i	0.111509	−	1.06093i	−0.785482	−	0.618885i	$-0.787585\pi$
$971$	3.47471	−	33.0596i	0.111509	−	1.06093i	0.896991	−	0.442050i	$-0.145748\pi$
$972$	−29.6832	+	21.5661i	−0.952088	+	0.691732i
$973$		0			0
$974$	12.6325	−	38.8788i	0.404771	−	1.24576i
$975$	14.2245	+	6.33315i	0.455548	+	0.202823i
$976$	−7.73128	+	3.44219i	−0.247472	+	0.110182i
$977$	−22.0735	−	4.69186i	−0.706193	−	0.150106i	−0.159204	−	0.987246i	$-0.550893\pi$
$977$	−22.0735	−	4.69186i	−0.706193	−	0.150106i	−0.546989	+	0.837140i	$0.684226\pi$
$978$	−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
$982$	1.22911	−	11.6942i	0.0392225	−	0.373178i
$983$	1.57888	+	15.0220i	0.0503584	+	0.479128i	0.990416	+	0.138114i	$0.0441039\pi$
$983$	1.57888	+	15.0220i	0.0503584	+	0.479128i	−0.940058	+	0.341015i	$0.889229\pi$
$984$	1.39889	+	1.55362i	0.0445948	+	0.0495276i
$985$	13.7858	−	2.93026i	0.439251	−	0.0933657i
$986$	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
$990$	−8.42437	−	4.53599i	−0.267744	−	0.144163i
$991$	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	$-0.173133\pi$
$992$	5.74211	−	6.37726i	0.182312	−	0.202478i
$993$	−4.20116	−	3.05232i	−0.133320	−	0.0968624i
$994$		0			0
$995$	−4.76461	+	14.6639i	−0.151048	+	0.464878i
$996$	−5.20999	+	1.10742i	−0.165085	+	0.0350899i
$997$	−5.19556	−	49.4325i	−0.164545	−	1.56554i	−0.695740	−	0.718293i	$-0.744924\pi$
$997$	−5.19556	−	49.4325i	−0.164545	−	1.56554i	0.531195	−	0.847249i	$-0.321743\pi$
$998$	−67.9056	+	30.2335i	−2.14951	+	0.957025i
$999$	20.6417	−	22.9250i	0.653076	−	0.725314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.214.1		32
7.2	even	3	inner	539.2.q.g.324.4		32
7.3	odd	6		539.2.f.e.148.1		16
7.4	even	3		77.2.f.b.71.1	yes	16
7.5	odd	6		539.2.q.f.324.4		32
7.6	odd	2		539.2.q.f.214.1		32
11.9	even	5	inner	539.2.q.g.361.4		32
21.11	odd	6		693.2.m.i.379.4		16
77.3	odd	30		5929.2.a.bt.1.1		8
77.4	even	15		847.2.f.w.729.4		16
77.9	even	15	inner	539.2.q.g.471.1		32
77.18	odd	30		847.2.f.v.729.1		16
77.20	odd	10		539.2.q.f.361.4		32
77.25	even	15		847.2.a.p.1.1		8
77.31	odd	30		539.2.f.e.295.1		16
77.32	odd	6		847.2.f.x.148.4		16
77.39	odd	30		847.2.f.v.323.1		16
77.46	odd	30		847.2.f.x.372.4		16
77.52	even	30		5929.2.a.bs.1.8		8
77.53	even	15		77.2.f.b.64.1	✓	16
77.60	even	15		847.2.f.w.323.4		16
77.74	odd	30		847.2.a.o.1.8		8
77.75	odd	30		539.2.q.f.471.1		32
231.53	odd	30		693.2.m.i.64.4		16
231.74	even	30		7623.2.a.cw.1.1		8
231.179	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	77.53	even	15
77.2.f.b.71.1	yes	16	7.4	even	3
539.2.f.e.148.1		16	7.3	odd	6
539.2.f.e.295.1		16	77.31	odd	30
539.2.q.f.214.1		32	7.6	odd	2
539.2.q.f.324.4		32	7.5	odd	6
539.2.q.f.361.4		32	77.20	odd	10
539.2.q.f.471.1		32	77.75	odd	30
539.2.q.g.214.1		32	1.1	even	1	trivial
539.2.q.g.324.4		32	7.2	even	3	inner
539.2.q.g.361.4		32	11.9	even	5	inner
539.2.q.g.471.1		32	77.9	even	15	inner
693.2.m.i.64.4		16	231.53	odd	30
693.2.m.i.379.4		16	21.11	odd	6
847.2.a.o.1.8		8	77.74	odd	30
847.2.a.p.1.1		8	77.25	even	15
847.2.f.v.323.1		16	77.39	odd	30
847.2.f.v.729.1		16	77.18	odd	30
847.2.f.w.323.4		16	77.60	even	15
847.2.f.w.729.4		16	77.4	even	15
847.2.f.x.148.4		16	77.32	odd	6
847.2.f.x.372.4		16	77.46	odd	30
5929.2.a.bs.1.8		8	77.52	even	30
5929.2.a.bt.1.1		8	77.3	odd	30
7623.2.a.ct.1.8		8	231.179	odd	30
7623.2.a.cw.1.1		8	231.74	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)

\(f(q)\)	\(=\)	\(q+(-1.62629 + 1.80618i) q^{2} +(1.31021 - 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(-1.23113 + 0.261684i) q^{5} +(-1.07716 + 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +O(q^{10})\)	\(q+(-1.62629 + 1.80618i) q^{2} +(1.31021 - 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(-1.23113 + 0.261684i) q^{5} +(-1.07716 + 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +(1.52952 - 2.64921i) q^{10} +(-2.39780 + 2.29141i) q^{11} +(-2.80179 - 4.85285i) q^{12} +(-0.982152 - 3.02275i) q^{13} +(-1.46039 + 1.06103i) q^{15} +(-3.37581 + 0.717551i) q^{16} +(3.96405 + 4.40252i) q^{17} +(-0.239584 - 2.27949i) q^{18} +(-0.299183 + 2.84654i) q^{19} +(1.51962 + 4.67691i) q^{20} +(-0.239188 - 8.05735i) q^{22} +(-3.38171 - 5.85730i) q^{23} +(6.50244 + 1.38214i) q^{24} +(-3.12053 + 1.38935i) q^{25} +(7.05689 + 3.14193i) q^{26} +(-1.74754 + 5.37837i) q^{27} +(-3.63693 + 2.64238i) q^{29} +(0.458598 - 4.36326i) q^{30} +(-9.51494 - 2.02246i) q^{31} +(-0.441092 + 0.763993i) q^{32} +(-1.80494 + 4.40098i) q^{33} -14.3984 q^{34} +(2.98090 + 2.16575i) q^{36} +(-4.98335 - 2.21873i) q^{37} +(-4.65480 - 5.16968i) q^{38} +(-3.05013 - 3.38751i) q^{39} +(-5.32953 - 2.37286i) q^{40} +(0.254423 + 0.184849i) q^{41} -0.132562 q^{43} +(9.88300 + 8.38129i) q^{44} +(0.593478 - 1.02793i) q^{45} +(16.0790 + 3.41769i) q^{46} +(-0.979960 + 9.32369i) q^{47} +(-4.00445 + 2.90940i) q^{48} +(2.56548 - 7.89572i) q^{50} +(7.76194 + 3.45584i) q^{51} +(-11.3444 + 5.05084i) q^{52} +(-4.25682 - 0.904816i) q^{53} +(-6.87229 - 11.9032i) q^{54} +(2.35237 - 3.44849i) q^{55} +(1.26852 + 3.90410i) q^{57} +(1.14209 - 10.8662i) q^{58} +(0.726144 + 6.90880i) q^{59} +(4.71928 + 5.24129i) q^{60} +(2.39857 - 0.509832i) q^{61} +(19.1270 - 13.8966i) q^{62} +(-2.79554 - 8.60379i) q^{64} +(2.00016 + 3.46438i) q^{65} +(-5.01360 - 10.4173i) q^{66} +(4.70993 - 8.15784i) q^{67} +(15.4879 - 17.2011i) q^{68} +(-7.84759 - 5.70161i) q^{69} +(-0.0360345 + 0.110903i) q^{71} +(-4.27564 + 0.908815i) q^{72} +(-0.0642883 - 0.611662i) q^{73} +(12.1118 - 5.39252i) q^{74} +(-3.27809 + 3.64069i) q^{75} +11.1830 q^{76} +11.0789 q^{78} +(5.70720 - 6.33849i) q^{79} +(3.96828 - 1.76679i) q^{80} +(0.552066 + 5.25256i) q^{81} +(-0.747637 + 0.158915i) q^{82} +(0.293731 - 0.904010i) q^{83} +(-6.03232 - 4.38274i) q^{85} +(0.215584 - 0.239431i) q^{86} +(-3.22373 + 5.58367i) q^{87} +(-15.2343 + 2.05986i) q^{88} +(-5.02758 - 8.70803i) q^{89} +(0.891464 + 2.74364i) q^{90} +(-21.3786 + 15.5325i) q^{92} +(-13.6464 + 2.90063i) q^{93} +(-15.2466 - 16.9330i) q^{94} +(-0.376561 - 3.58274i) q^{95} +(-0.132253 + 1.25830i) 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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