LMFDB - Embedded newform 539.2.q.g.471.1

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			471.1
Character	$\chi$	$=$	539.471
Dual form			539.2.q.g.214.1

$q$-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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.62629	−	1.80618i	−1.14996	−	1.27716i	−0.955085	−	0.296333i	$-0.904236\pi$
$2$	−1.62629	−	1.80618i	−1.14996	−	1.27716i	−0.194876	−	0.980828i	$-0.562430\pi$
$3$	1.31021	+	0.583344i	0.756452	+	0.336794i	0.748465	−	0.663174i	$-0.230791\pi$
$3$	1.31021	+	0.583344i	0.756452	+	0.336794i	0.00798646	+	0.999968i	$0.497458\pi$
$4$	−0.408403	+	3.88570i	−0.204202	+	1.94285i
$5$	−1.23113	−	0.261684i	−0.550577	−	0.117029i	−0.0757806	−	0.997125i	$-0.524145\pi$
$5$	−1.23113	−	0.261684i	−0.550577	−	0.117029i	−0.474796	+	0.880096i	$0.657478\pi$
$6$	−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	0.717496	+	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
$16$	−3.37581	−	0.717551i	−0.843953	−	0.179388i
$17$	3.96405	−	4.40252i	0.961424	−	1.06777i	−0.0362327	−	0.999343i	$-0.511536\pi$
$17$	3.96405	−	4.40252i	0.961424	−	1.06777i	0.997656	−	0.0684256i	$-0.0217976\pi$
$18$	−0.239584	+	2.27949i	−0.0564705	+	0.537281i
$19$	−0.299183	−	2.84654i	−0.0686373	−	0.653041i	−0.973711	−	0.227786i	$-0.926851\pi$
$19$	−0.299183	−	2.84654i	−0.0686373	−	0.653041i	0.905074	−	0.425254i	$-0.139815\pi$
$20$	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	0.261506	+	0.965202i	$0.415781\pi$
$23$	−3.38171	+	5.85730i	−0.705136	+	1.22133i	−0.966642	+	0.256130i	$0.917552\pi$
$24$	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	0.196454	−	0.980513i	$-0.437057\pi$
$29$	−3.63693	−	2.64238i	−0.675361	−	0.490678i	−0.871815	+	0.489834i	$0.837057\pi$
$30$	0.458598	+	4.36326i	0.0837281	+	0.796620i
$31$	−9.51494	+	2.02246i	−1.70893	+	0.363245i	−0.955663	−	0.294464i	$-0.904859\pi$
$31$	−9.51494	+	2.02246i	−1.70893	+	0.363245i	−0.753272	+	0.657709i	$0.771525\pi$
$32$	−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	−0.773184	−	0.634181i	$-0.781337\pi$
$37$	−4.98335	+	2.21873i	−0.819257	+	0.364757i	−0.0460730	+	0.998938i	$0.514671\pi$
$38$	−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	−0.567741	−	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	$0.503217\pi$
$44$	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	−0.797194	−	0.603724i	$-0.793683\pi$
$47$	−0.979960	−	9.32369i	−0.142942	−	1.36000i	0.654252	−	0.756277i	$-0.272984\pi$
$48$	−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	−0.490767	−	0.871291i	$-0.663283\pi$
$53$	−4.25682	+	0.904816i	−0.584720	+	0.124286i	−0.0939524	+	0.995577i	$0.529950\pi$
$54$	−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	−0.839762	−	0.542955i	$-0.817305\pi$
$59$	0.726144	−	6.90880i	0.0945359	−	0.899449i	0.934298	−	0.356494i	$-0.116028\pi$
$60$	4.71928	−	5.24129i	0.609256	−	0.676647i
$61$	2.39857	+	0.509832i	0.307105	+	0.0652772i	0.358886	−	0.933381i	$-0.383157\pi$
$61$	2.39857	+	0.509832i	0.307105	+	0.0652772i	−0.0517812	+	0.998658i	$0.516490\pi$
$62$	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	0.995997	+	0.0893871i	$0.0284908\pi$
$67$	4.70993	+	8.15784i	0.575410	+	0.996639i	−0.420587	+	0.907252i	$0.638176\pi$
$68$	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	0.948895	−	0.315590i	$-0.102203\pi$
$71$	−0.0360345	−	0.110903i	−0.00427651	−	0.0131617i	−0.953172	+	0.302429i	$0.902203\pi$
$72$	−4.27564	−	0.908815i	−0.503889	−	0.107105i
$73$	−0.0642883	+	0.611662i	−0.00752438	+	0.0715897i	−0.997640	−	0.0686659i	$-0.978126\pi$
$73$	−0.0642883	+	0.611662i	−0.00752438	+	0.0715897i	0.990115	+	0.140256i	$0.0447924\pi$
$74$	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	0.973070	−	0.230509i	$-0.0740391\pi$
$79$	5.70720	+	6.33849i	0.642111	+	0.713136i	−0.330960	+	0.943645i	$0.607372\pi$
$80$	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	0.965882	−	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
$86$	0.215584	+	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	0.466338	+	0.884607i	$0.345573\pi$
$89$	−5.02758	+	8.70803i	−0.532923	+	0.923049i	−0.999261	+	0.0384427i	$0.987760\pi$
$90$	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	−0.153530	−	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
$101$	12.2035	−	2.59394i	1.21429	−	0.258106i	0.444137	−	0.895959i	$-0.353510\pi$
$101$	12.2035	−	2.59394i	1.21429	−	0.258106i	0.770158	+	0.637853i	$0.220177\pi$
$102$	−18.8650	−	8.39925i	−1.86792	−	0.831649i
$103$	7.50754	−	3.34257i	0.739740	−	0.329353i	−0.00203908	−	0.999998i	$-0.500649\pi$
$103$	7.50754	−	3.34257i	0.739740	−	0.329353i	0.741779	+	0.670645i	$0.233982\pi$
$104$	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	−0.865177	−	0.501466i	$-0.832794\pi$
$107$	−1.27405	−	12.1218i	−0.123167	−	1.17185i	0.742011	−	0.670388i	$-0.233872\pi$
$108$	21.6124	−	4.59386i	2.07965	−	0.442044i
$109$	−0.443044	−	0.767375i	−0.0424359	−	0.0735012i	0.844027	−	0.536300i	$-0.180178\pi$
$109$	−0.443044	−	0.767375i	−0.0424359	−	0.0735012i	−0.886463	+	0.462799i	$0.846845\pi$
$110$	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	−0.747148	−	0.664658i	$-0.768577\pi$
$113$	−3.67700	+	2.67149i	−0.345903	+	0.251313i	0.401245	+	0.915971i	$0.368577\pi$
$114$	−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	−0.998750	−	0.0499916i	$-0.984081\pi$
$127$	−2.48072	−	7.63488i	−0.220129	−	0.677486i	0.778621	−	0.627494i	$-0.215919\pi$
$128$	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	−0.868233	−	0.496157i	$-0.834744\pi$
$131$	−0.0507303	+	0.0878675i	−0.00443233	+	0.00767702i	0.863801	+	0.503834i	$0.168078\pi$
$132$	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	−0.859343	−	0.511400i	$-0.829127\pi$
$137$	−3.05397	+	3.39178i	−0.260919	+	0.289779i	0.598424	+	0.801179i	$0.295794\pi$
$138$	23.0606	+	4.90168i	1.96305	+	0.417258i
$139$	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
$143$	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	0.398942	−	0.916976i	$-0.369377\pi$
$149$	4.76576	+	1.01299i	0.390427	+	0.0829877i	−0.00851575	+	0.999964i	$0.502711\pi$
$150$	−1.24461	+	11.8416i	−0.101622	+	0.966865i
$151$	−15.5064	−	6.90389i	−1.26189	−	0.561831i	−0.336802	−	0.941576i	$-0.609345\pi$
$151$	−15.5064	−	6.90389i	−1.26189	−	0.561831i	−0.925091	+	0.379745i	$0.876012\pi$
$152$	−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	0.486935	−	0.873438i	$-0.338115\pi$
$157$	2.05075	+	0.913055i	0.163668	+	0.0728697i	−0.323267	+	0.946308i	$0.604781\pi$
$158$	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	0.167917	−	0.985801i	$-0.446296\pi$
$163$	−10.5972	−	11.7694i	−0.830036	−	0.921848i	−0.997953	+	0.0639530i	$0.979629\pi$
$164$	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	−0.319440	−	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
$170$	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	0.655714	+	0.755009i	$0.272368\pi$
$173$	2.25315	+	21.4373i	0.171304	+	1.62985i	−0.484410	+	0.874841i	$0.660966\pi$
$174$	−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	0.563438	−	0.826159i	$-0.309478\pi$
$179$	4.36822	+	1.94485i	0.326496	+	0.145365i	−0.236942	+	0.971524i	$0.576145\pi$
$180$	−4.23662	+	1.88626i	−0.315779	+	0.140594i
$181$	−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
$184$	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	−0.677271	−	0.735733i	$-0.736838\pi$
$191$	−8.06687	+	3.59160i	−0.583698	+	0.259879i	0.0935733	+	0.995612i	$0.470171\pi$
$192$	−8.68173	+	9.64203i	−0.626550	+	0.695854i
$193$	17.1313	−	19.0262i	1.23313	−	1.36954i	0.327850	−	0.944730i	$-0.393676\pi$
$193$	17.1313	−	19.0262i	1.23313	−	1.36954i	0.905285	−	0.424805i	$-0.139657\pi$
$194$	−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	0.997230	−	0.0743802i	$-0.0236979\pi$
$199$	6.12514	+	10.6091i	0.434200	+	0.752056i	−0.563030	+	0.826436i	$0.690365\pi$
$200$	−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	0.676817	+	0.736151i	$0.263359\pi$
$211$	−4.40769	+	13.5655i	−0.303438	+	0.933887i	−0.980255	+	0.197736i	$0.936641\pi$
$212$	−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	−0.504595	−	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
$226$	10.8051	+	2.29669i	0.718742	+	0.152773i
$227$	−0.862993	+	8.21083i	−0.0572788	+	0.544972i	0.927826	+	0.373014i	$0.121676\pi$
$227$	−0.862993	+	8.21083i	−0.0572788	+	0.544972i	−0.985104	+	0.171957i	$0.944991\pi$
$228$	14.6521	+	6.52352i	0.970357	+	0.432031i
$229$	8.77104	+	9.74122i	0.579607	+	0.643718i	0.959632	−	0.281258i	$-0.0907515\pi$
$229$	8.77104	+	9.74122i	0.579607	+	0.643718i	−0.380026	+	0.924976i	$0.624085\pi$
$230$	−20.6896			−1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	−8.58339	−	9.53282i	−0.562317	−	0.624516i	0.393200	−	0.919453i	$-0.371368\pi$
$233$	−8.58339	−	9.53282i	−0.562317	−	0.624516i	−0.955517	+	0.294937i	$0.904701\pi$
$234$	−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	−0.449775	−	0.893142i	$-0.648496\pi$
$239$	4.02979	−	2.92781i	0.260665	−	0.189384i	0.710440	+	0.703758i	$0.248496\pi$
$240$	4.16864	+	4.62975i	0.269085	+	0.298849i
$241$	1.31343	+	2.27492i	0.0846053	+	0.146541i	0.905223	−	0.424937i	$-0.139704\pi$
$241$	1.31343	+	2.27492i	0.0846053	+	0.146541i	−0.820618	+	0.571478i	$0.806370\pi$
$242$	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	0.278124	+	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
$255$	−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	0.708273	−	0.705939i	$-0.249475\pi$
$257$	27.3623	−	12.1825i	1.70681	−	0.759923i	0.998542	−	0.0539837i	$-0.0171919\pi$
$258$	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	0.809986	−	0.586449i	$-0.199475\pi$
$263$	−1.66854	−	2.89000i	−0.102887	−	0.178205i	−0.912873	+	0.408244i	$0.866141\pi$
$264$	−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	−0.777512	−	0.628868i	$-0.783519\pi$
$269$	−1.16149	+	1.28996i	−0.0708170	+	0.0786502i	0.706695	+	0.707518i	$0.250185\pi$
$270$	11.5755	−	12.8559i	0.704464	−	0.782387i
$271$	−2.26190	+	1.00706i	−0.137401	+	0.0611747i	−0.474285	−	0.880371i	$-0.657293\pi$
$271$	−2.26190	+	1.00706i	−0.137401	+	0.0611747i	0.336885	+	0.941546i	$0.390627\pi$
$272$	−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	−0.356906	−	0.934140i	$-0.616168\pi$
$277$	−5.04304	+	1.07193i	−0.303007	+	0.0644061i	0.0538991	+	0.998546i	$0.482835\pi$
$278$	−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	−0.911287	−	0.411772i	$-0.864910\pi$
$281$	−6.97467	−	21.4658i	−0.416074	−	1.28054i	0.495213	−	0.868772i	$-0.335090\pi$
$282$	−29.8540	+	13.2919i	−1.77778	+	0.791519i
$283$	−7.75378	−	3.45221i	−0.460914	−	0.205212i	0.163125	−	0.986605i	$-0.447843\pi$
$283$	−7.75378	−	3.45221i	−0.460914	−	0.205212i	−0.624039	+	0.781393i	$0.714509\pi$
$284$	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	−0.173643	−	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
$297$	−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	0.348676	−	0.937243i	$-0.386631\pi$
$311$	−2.01960	−	0.899186i	−0.114521	−	0.0509882i	−0.463198	+	0.886255i	$0.653298\pi$
$312$	−2.20853	+	21.0127i	−0.125033	+	1.18961i
$313$	9.48733	+	2.01659i	0.536256	+	0.113985i	0.468076	−	0.883688i	$-0.344947\pi$
$313$	9.48733	+	2.01659i	0.536256	+	0.113985i	0.0681799	+	0.997673i	$0.478281\pi$
$314$	−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	0.852135	−	0.523322i	$-0.175308\pi$
$317$	4.31950	+	4.79729i	0.242607	+	0.269443i	−0.609528	+	0.792765i	$0.708641\pi$
$318$	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	−0.911481	−	0.411342i	$-0.865060\pi$
$331$	−1.81038	+	3.13567i	−0.0995075	+	0.172352i	0.811973	+	0.583694i	$0.198393\pi$
$332$	−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	0.719908	−	0.694070i	$-0.244184\pi$
$337$	5.18183	+	3.76482i	0.282272	+	0.205083i	−0.437636	+	0.899152i	$0.644184\pi$
$338$	−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	−0.970070	−	0.242823i	$-0.921926\pi$
$347$	−11.6830	+	12.9753i	−0.627177	+	0.696551i	0.342893	+	0.939374i	$0.388593\pi$
$348$	23.0130	−	10.2461i	1.23363	−	0.549246i
$349$	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
$352$	−0.692976	+	2.84262i	−0.0369358	+	0.151512i
$353$	−2.20075	−	3.81181i	−0.117134	−	0.202882i	0.801497	−	0.597999i	$-0.204037\pi$
$353$	−2.20075	−	3.81181i	−0.117134	−	0.202882i	−0.918631	+	0.395117i	$0.870704\pi$
$354$	−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	−0.647754	−	0.761850i	$-0.724291\pi$
$359$	−9.75825	+	4.34465i	−0.515021	+	0.229302i	0.132733	+	0.991152i	$0.457625\pi$
$360$	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	0.930639	+	0.365938i	$0.119252\pi$
$367$	−1.06794	+	10.1608i	−0.0557460	+	0.530388i	−0.986385	+	0.164450i	$0.947415\pi$
$368$	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	−0.238314	−	0.971188i	$-0.576595\pi$
$373$	13.9425	−	24.1492i	0.721917	−	1.25040i	0.960231	−	0.279208i	$-0.0900720\pi$
$374$	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	0.959754	−	0.280841i	$-0.0906132\pi$
$379$	0.354761	+	1.09184i	0.0182228	+	0.0560841i	−0.941532	+	0.336925i	$0.890613\pi$
$380$	−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	0.298266	−	0.954483i	$-0.403592\pi$
$383$	−13.3502	−	14.8269i	−0.682165	−	0.757621i	−0.980431	+	0.196861i	$0.936925\pi$
$384$	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	−0.999249	−	0.0387496i	$-0.987663\pi$
$389$	−0.271774	+	2.58576i	−0.0137795	+	0.131103i	0.985469	+	0.169853i	$0.0543292\pi$
$390$	−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	−0.954849	−	0.297091i	$-0.903984\pi$
$397$	−4.38618	+	7.59709i	−0.220136	+	0.381287i	0.734713	+	0.678378i	$0.237317\pi$
$398$	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	−0.545643	−	0.838018i	$-0.683714\pi$
$401$	−27.7339	−	5.89502i	−1.38496	−	0.294383i	−0.839322	+	0.543634i	$0.817048\pi$
$402$	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	−0.662369	−	0.749178i	$-0.730449\pi$
$409$	−19.4705	+	4.13859i	−0.962756	+	0.204640i	−0.300386	+	0.953818i	$0.597116\pi$
$410$	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	0.00218371	−	0.999998i	$-0.499305\pi$
$421$	19.5727	−	14.2204i	0.953913	−	0.693058i	0.951729	+	0.306939i	$0.0993049\pi$
$422$	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	−0.640845	−	0.767670i	$-0.721416\pi$
$431$	−18.9761	+	4.03350i	−0.914047	+	0.194287i	−0.273202	+	0.961957i	$0.588083\pi$
$432$	2.04010	+	19.4103i	0.0981546	+	0.933878i
$433$	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
$436$	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	−0.187025	−	0.982355i	$-0.559885\pi$
$439$	15.8658	−	27.4803i	0.757232	−	1.31156i	0.944257	−	0.329209i	$-0.106782\pi$
$440$	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	0.997880	−	0.0650839i	$-0.0207315\pi$
$443$	0.174155	+	1.65698i	0.00827437	+	0.0787254i	−0.989605	+	0.143809i	$0.954065\pi$
$444$	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	0.744032	+	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
$451$	−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	−0.0319431	−	0.999490i	$-0.510170\pi$
$457$	−9.99729	−	2.12499i	−0.467654	−	0.0994029i	−0.435711	+	0.900087i	$0.643503\pi$
$458$	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	−0.401166	−	0.916005i	$-0.631395\pi$
$467$	−24.6404	−	5.23748i	−1.14022	−	0.242362i	−0.739056	+	0.673644i	$0.764728\pi$
$468$	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	−0.974269	−	0.225388i	$-0.927635\pi$
$479$	−14.1882	+	15.7576i	−0.648277	+	0.719985i	0.325992	+	0.945373i	$0.394302\pi$
$480$	−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	0.0279025	−	0.999611i	$-0.491117\pi$
$487$	−15.3656	−	6.84121i	−0.696283	−	0.310005i	−0.724185	+	0.689606i	$0.757784\pi$
$488$	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	0.495953	−	0.868350i	$-0.334819\pi$
$491$	−3.91406	−	2.84373i	−0.176639	−	0.128336i	−0.672592	+	0.740014i	$0.734819\pi$
$492$	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	0.328876	−	0.944373i	$-0.393330\pi$
$499$	27.9395	−	12.4395i	1.25074	−	0.556866i	0.921867	+	0.387507i	$0.126664\pi$
$500$	−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	0.0526880	−	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
$506$	−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	0.999934	−	0.0114893i	$-0.00365724\pi$
$509$	0.439087	+	4.17764i	0.0194622	+	0.185170i	−0.980472	+	0.196660i	$0.936991\pi$
$510$	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	−0.839714	−	0.543029i	$-0.817278\pi$
$521$	2.15819	−	20.5339i	0.0945522	−	0.899604i	0.934266	−	0.356576i	$-0.116056\pi$
$522$	6.89464	−	7.65727i	0.301770	−	0.335150i
$523$	22.1395	+	4.70589i	0.968091	+	0.205774i	0.664715	−	0.747097i	$-0.268553\pi$
$523$	22.1395	+	4.70589i	0.968091	+	0.205774i	0.303376	+	0.952871i	$0.401886\pi$
$524$	−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	0.908707	+	0.417435i	$0.137071\pi$
$541$	28.5828	+	31.7444i	1.22887	+	1.36480i	0.320163	+	0.947363i	$0.396262\pi$
$542$	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	−0.587563	+	0.809178i	$0.699913\pi$
$547$	−35.9873	+	26.1463i	−1.53870	+	1.11793i	−0.951141	+	0.308756i	$0.900087\pi$
$548$	−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	−0.788349	−	0.615229i	$-0.789064\pi$
$557$	2.61228	−	24.8542i	0.110686	−	1.05311i	0.899035	−	0.437878i	$-0.144270\pi$
$558$	−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	−0.389845	−	0.920880i	$-0.627471\pi$
$563$	−8.81316	+	1.87330i	−0.371431	+	0.0789500i	0.0184146	+	0.999830i	$0.494138\pi$
$564$	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	−0.850819	−	0.525459i	$-0.823893\pi$
$569$	−3.04950	−	29.0140i	−0.127842	−	1.21633i	0.722977	−	0.690872i	$-0.242773\pi$
$570$	12.2830	−	2.61083i	0.514478	−	0.109356i
$571$	−0.894970	−	1.55013i	−0.0374533	−	0.0648711i	0.846691	−	0.532085i	$-0.178591\pi$
$571$	−0.894970	−	1.55013i	−0.0374533	−	0.0648711i	−0.884144	+	0.467214i	$0.845258\pi$
$572$	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	−0.964551	−	0.263897i	$-0.914992\pi$
$577$	−14.4432	+	16.0408i	−0.601277	+	0.667785i	0.363274	+	0.931682i	$0.381659\pi$
$578$	−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	0.491734	−	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
$590$	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	−0.0545633	−	0.998510i	$-0.517377\pi$
$593$	20.3933	−	35.3223i	0.837454	−	1.45051i	0.892017	−	0.452002i	$-0.149290\pi$
$594$	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	−0.987132	−	0.159908i	$-0.948880\pi$
$599$	−17.7419	+	19.7044i	−0.724916	+	0.805101i	0.262216	+	0.965009i	$0.415547\pi$
$600$	−22.2114	−	4.72117i	−0.906775	−	0.192741i
$601$	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
$605$	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	0.237870	−	0.971297i	$-0.423551\pi$
$607$	−18.5512	−	20.6032i	−0.752971	−	0.836259i	−0.990840	+	0.135038i	$0.956884\pi$
$608$	−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	0.945630	−	0.325246i	$-0.105447\pi$
$613$	33.0945	+	14.7346i	1.33667	+	0.595126i	0.391045	+	0.920372i	$0.372114\pi$
$614$	−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	−0.373148	−	0.927772i	$-0.621722\pi$
$619$	−32.6497	−	14.5366i	−1.31230	−	0.584274i	−0.939154	+	0.343497i	$0.888388\pi$
$620$	−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	0.542368	−	0.840141i	$-0.317528\pi$
$631$	−2.23700	−	1.62527i	−0.0890534	−	0.0647011i	−0.631421	+	0.775440i	$0.717528\pi$
$632$	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	0.958669	−	0.284524i	$-0.0918355\pi$
$641$	35.1591	+	15.6538i	1.38870	+	0.618290i	0.430032	+	0.902813i	$0.358502\pi$
$642$	−38.8132	+	17.2808i	−1.53184	+	0.682018i
$643$	−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
$646$	4.30777	+	40.9857i	0.169487	+	1.61256i
$647$	26.7241	−	5.68037i	1.05063	−	0.223319i	0.349932	−	0.936775i	$-0.386205\pi$
$647$	26.7241	−	5.68037i	1.05063	−	0.223319i	0.700699	+	0.713457i	$0.252871\pi$
$648$	−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	−0.552374	−	0.833596i	$-0.686278\pi$
$653$	−7.73011	+	3.44166i	−0.302502	+	0.134683i	0.249872	+	0.968279i	$0.419611\pi$
$654$	−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	0.990291	−	0.139011i	$-0.0443922\pi$
$661$	9.63501	+	16.6883i	0.374759	+	0.649101i	−0.615532	+	0.788112i	$0.711059\pi$
$662$	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	0.771934	+	0.635702i	$0.219289\pi$
$673$	−5.86892	+	18.0627i	−0.226230	+	0.696265i	−0.998164	+	0.0605625i	$0.980711\pi$
$674$	−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	−0.446795	−	0.894636i	$-0.647435\pi$
$677$	−31.7134	−	6.74089i	−1.21884	−	0.259073i	−0.772049	+	0.635563i	$0.780768\pi$
$678$	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	0.684275	−	0.729224i	$-0.260119\pi$
$683$	−7.56298	−	13.0995i	−0.289389	−	0.501237i	−0.973664	+	0.227987i	$0.926786\pi$
$684$	−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	0.196147	−	0.980575i	$-0.437157\pi$
$691$	−21.0179	−	23.3428i	−0.799559	−	0.888000i	−0.995706	+	0.0925742i	$0.970490\pi$
$692$	−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	−0.314646	−	0.949209i	$-0.601886\pi$
$701$	12.9966	−	9.44259i	0.490875	−	0.356642i	0.805521	+	0.592568i	$0.201886\pi$
$702$	−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	−0.590563	−	0.806992i	$-0.701094\pi$
$709$	−38.8303	−	8.25363i	−1.45830	−	0.309972i	−0.867739	+	0.497020i	$0.834428\pi$
$710$	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	−0.567803	−	0.823164i	$-0.692207\pi$
$719$	−9.00976	+	4.01140i	−0.336007	+	0.149600i	0.231796	+	0.972764i	$0.425540\pi$
$720$	−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	0.433547	−	0.901131i	$-0.357262\pi$
$733$	37.7226	−	16.7952i	1.39332	−	0.620345i	0.959770	+	0.280786i	$0.0905951\pi$
$734$	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	−0.794820	−	0.606846i	$-0.792435\pi$
$739$	−34.6358	+	7.36206i	−1.27410	+	0.270818i	−0.479278	+	0.877663i	$0.659101\pi$
$740$	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	0.925652	−	0.378376i	$-0.123517\pi$
$743$	−1.24351	−	3.82713i	−0.0456200	−	0.140404i	−0.971272	+	0.237972i	$0.923517\pi$
$744$	−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	−0.936933	−	0.349509i	$-0.886348\pi$
$751$	−2.55248	−	24.2852i	−0.0931413	−	0.886180i	0.843792	−	0.536671i	$-0.180318\pi$
$752$	−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	−0.958181	−	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
$759$	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	0.648856	−	0.760911i	$-0.275248\pi$
$761$	−4.84721	−	5.38337i	−0.175711	−	0.195147i	−0.824567	+	0.565764i	$0.808581\pi$
$762$	−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	0.695177	−	0.718839i	$-0.255326\pi$
$773$	17.4085	+	7.75075i	0.626139	+	0.278775i	−0.0690374	+	0.997614i	$0.521993\pi$
$774$	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	−0.240140	−	0.970738i	$-0.577193\pi$
$787$	21.0509	−	23.3793i	0.750382	−	0.833384i	0.990522	+	0.137355i	$0.0438600\pi$
$788$	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	0.858624	−	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
$800$	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	−0.803100	−	0.595845i	$-0.796817\pi$
$809$	−3.60008	+	3.99830i	−0.126572	+	0.140573i	0.676527	+	0.736417i	$0.263484\pi$
$810$	14.7595	−	6.57137i	0.518597	−	0.230894i
$811$	−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
$814$	−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	−0.548583	−	0.836096i	$-0.684833\pi$
$821$	−8.43308	+	3.75465i	−0.294317	+	0.131038i	0.254267	+	0.967134i	$0.418166\pi$
$822$	14.5339	+	6.47092i	0.506929	+	0.225699i
$823$	12.1708	−	2.58698i	0.424246	−	0.0901763i	0.00915927	−	0.999958i	$-0.497084\pi$
$823$	12.1708	−	2.58698i	0.424246	−	0.0901763i	0.415087	+	0.909782i	$0.363751\pi$
$824$	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	$0.124841\pi$
$828$	2.60491	+	24.7840i	0.0905267	+	0.861304i
$829$	3.85475	−	36.6755i	0.133881	−	1.27379i	−0.696889	−	0.717179i	$-0.745433\pi$
$829$	3.85475	−	36.6755i	0.133881	−	1.27379i	0.830770	−	0.556615i	$-0.187900\pi$
$830$	−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	−0.708362	−	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
$842$	−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	0.979608	−	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
$856$	−37.8027	−	41.9841i	−1.29207	−	1.43499i
$857$	−24.0368	−	41.6330i	−0.821082	−	1.42216i	−0.904877	−	0.425673i	$-0.860038\pi$
$857$	−24.0368	−	41.6330i	−0.821082	−	1.42216i	0.0837952	−	0.996483i	$-0.473296\pi$
$858$	−26.5648	−	25.3862i	−0.906909	−	0.866672i
$859$	0.158149	−	0.273922i	0.00539598	−	0.00934610i	−0.863315	−	0.504666i	$-0.831616\pi$
$859$	0.158149	−	0.273922i	0.00539598	−	0.00934610i	0.868711	+	0.495320i	$0.164949\pi$
$860$	−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	0.147133	−	0.989117i	$-0.452995\pi$
$863$	−3.54767	−	0.754081i	−0.120764	−	0.0256692i	−0.267897	+	0.963447i	$0.586329\pi$
$864$	−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	−0.934806	−	0.355158i	$-0.884427\pi$
$877$	−2.79171	−	26.5613i	−0.0942692	−	0.896911i	0.840537	−	0.541754i	$-0.182239\pi$
$878$	−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	0.232589	−	0.972575i	$-0.425280\pi$
$883$	36.5331	−	26.5429i	1.22944	−	0.893238i	0.996848	+	0.0793369i	$0.0252803\pi$
$884$	−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	−0.740652	−	0.671889i	$-0.765483\pi$
$887$	−21.9478	+	9.77179i	−0.736935	+	0.328105i	0.00371735	+	0.999993i	$0.498817\pi$
$888$	−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	−0.894399	−	0.447270i	$-0.852396\pi$
$907$	−10.7241	+	11.9104i	−0.356089	+	0.395477i	0.538310	+	0.842747i	$0.319063\pi$
$908$	−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	−0.999242	−	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
$913$	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	−0.345515	−	0.938413i	$-0.612296\pi$
$919$	−31.6139	−	6.71973i	−1.04284	−	0.221664i	−0.697330	+	0.716750i	$0.745629\pi$
$920$	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	0.337526	−	0.941316i	$-0.390410\pi$
$929$	8.01622	+	1.70390i	0.263004	+	0.0559032i	−0.0745223	+	0.997219i	$0.523743\pi$
$930$	−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	−0.617164	−	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
$940$	−45.0953	−	9.58530i	−1.47085	−	0.312638i
$941$	0.655327	−	0.727814i	0.0213630	−	0.0237261i	−0.732369	−	0.680908i	$-0.761585\pi$
$941$	0.655327	−	0.727814i	0.0213630	−	0.0237261i	0.753732	+	0.657182i	$0.228252\pi$
$942$	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	−0.873526	−	0.486777i	$-0.838172\pi$
$947$	−0.467800	+	0.810253i	−0.0152014	+	0.0263297i	0.858325	+	0.513107i	$0.171506\pi$
$948$	−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	0.346544	−	0.938034i	$-0.387355\pi$
$953$	−13.5365	−	9.83486i	−0.438491	−	0.318582i	−0.785035	+	0.619451i	$0.787355\pi$
$954$	−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	0.896991	+	0.442050i	$0.145748\pi$
$971$	3.47471	+	33.0596i	0.111509	+	1.06093i	−0.785482	+	0.618885i	$0.787585\pi$
$972$	−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	−0.546989	−	0.837140i	$-0.684226\pi$
$977$	−22.0735	+	4.69186i	−0.706193	+	0.150106i	−0.159204	+	0.987246i	$0.550893\pi$
$978$	−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	−0.940058	−	0.341015i	$-0.889229\pi$
$983$	1.57888	−	15.0220i	0.0503584	−	0.479128i	0.990416	−	0.138114i	$-0.0441039\pi$
$984$	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	0.855690	+	0.517488i	$0.173133\pi$
$991$	27.5767	+	47.7643i	0.876003	+	1.51728i	0.0203128	+	0.999794i	$0.493534\pi$
$992$	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	0.531195	+	0.847249i	$0.321743\pi$
$997$	−5.19556	+	49.4325i	−0.164545	+	1.56554i	−0.695740	+	0.718293i	$0.744924\pi$
$998$	−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.471.1		32
7.2	even	3		77.2.f.b.64.1	✓	16
7.3	odd	6		539.2.q.f.361.4		32
7.4	even	3	inner	539.2.q.g.361.4		32
7.5	odd	6		539.2.f.e.295.1		16
7.6	odd	2		539.2.q.f.471.1		32
11.5	even	5	inner	539.2.q.g.324.4		32
21.2	odd	6		693.2.m.i.64.4		16
77.2	odd	30		847.2.f.v.729.1		16
77.5	odd	30		539.2.f.e.148.1		16
77.9	even	15		847.2.f.w.729.4		16
77.16	even	15		77.2.f.b.71.1	yes	16
77.26	odd	30		5929.2.a.bt.1.1		8
77.27	odd	10		539.2.q.f.324.4		32
77.30	odd	30		847.2.f.v.323.1		16
77.37	even	15		847.2.a.p.1.1		8
77.38	odd	30		539.2.q.f.214.1		32
77.40	even	30		5929.2.a.bs.1.8		8
77.51	odd	30		847.2.a.o.1.8		8
77.58	even	15		847.2.f.w.323.4		16
77.60	even	15	inner	539.2.q.g.214.1		32
77.65	odd	6		847.2.f.x.372.4		16
77.72	odd	30		847.2.f.x.148.4		16
231.128	even	30		7623.2.a.cw.1.1		8
231.170	odd	30		693.2.m.i.379.4		16
231.191	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	7.2	even	3
77.2.f.b.71.1	yes	16	77.16	even	15
539.2.f.e.148.1		16	77.5	odd	30
539.2.f.e.295.1		16	7.5	odd	6
539.2.q.f.214.1		32	77.38	odd	30
539.2.q.f.324.4		32	77.27	odd	10
539.2.q.f.361.4		32	7.3	odd	6
539.2.q.f.471.1		32	7.6	odd	2
539.2.q.g.214.1		32	77.60	even	15	inner
539.2.q.g.324.4		32	11.5	even	5	inner
539.2.q.g.361.4		32	7.4	even	3	inner
539.2.q.g.471.1		32	1.1	even	1	trivial
693.2.m.i.64.4		16	21.2	odd	6
693.2.m.i.379.4		16	231.170	odd	30
847.2.a.o.1.8		8	77.51	odd	30
847.2.a.p.1.1		8	77.37	even	15
847.2.f.v.323.1		16	77.30	odd	30
847.2.f.v.729.1		16	77.2	odd	30
847.2.f.w.323.4		16	77.58	even	15
847.2.f.w.729.4		16	77.9	even	15
847.2.f.x.148.4		16	77.72	odd	30
847.2.f.x.372.4		16	77.65	odd	6
5929.2.a.bs.1.8		8	77.40	even	30
5929.2.a.bt.1.1		8	77.26	odd	30
7623.2.a.ct.1.8		8	231.191	odd	30
7623.2.a.cw.1.1		8	231.128	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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