LMFDB - Embedded newform 567.2.e.f.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.f.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.247934 - 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} +1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(0.446284 + 0.772987i) q^{11} -1.19671 q^{13} +(1.29396 - 0.216492i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(-0.124991 - 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} +6.47721 q^{20} +0.442596 q^{22} +(-1.23886 + 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(-0.296705 + 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} -4.14255 q^{29} +(-1.79257 - 3.10483i) q^{31} +(2.50249 + 4.33444i) q^{32} -0.123959 q^{34} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(-0.696267 - 1.20597i) q^{38} +(3.43695 - 5.95298i) q^{40} +4.78186 q^{41} +9.97857 q^{43} +(-0.782834 + 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +(5.08653 - 8.81013i) q^{47} +(-1.33611 + 6.87130i) q^{49} -4.28189 q^{50} +(-1.04958 - 1.81793i) q^{52} +(-4.94465 - 8.56438i) q^{53} +3.29588 q^{55} +(3.13268 + 3.80050i) q^{56} +(-1.02708 + 1.77895i) q^{58} +(-0.906186 - 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(-2.20948 + 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +(0.219249 - 0.379751i) q^{68} +(1.69671 - 4.53761i) q^{70} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(1.17306 + 2.03181i) q^{74} +4.92604 q^{76} +(-0.827091 + 2.21194i) q^{77} +(0.899562 - 1.55809i) q^{79} +(4.77293 + 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} -12.3231 q^{83} -0.923082 q^{85} +(2.47403 - 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(-1.20370 + 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} -4.34620 q^{92} +(-2.52225 - 4.36867i) q^{94} +(-5.18489 - 8.98049i) q^{95} -11.0442 q^{97} +(2.61951 + 2.27740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29}+ \cdots + 59 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8 - 7 * q^10 + 4 * q^11 + 16 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + q^19 - 10 * q^20 + 2 * q^22 + 3 * q^23 - q^25 + 11 * q^26 - 2 * q^28 - 14 * q^29 - 3 * q^31 - 2 * q^32 - 6 * q^34 + 5 * q^35 + 20 * q^38 - 3 * q^40 - 10 * q^41 + 14 * q^43 - 10 * q^44 + 3 * q^46 + 27 * q^47 - 17 * q^49 - 38 * q^50 - 10 * q^52 - 21 * q^53 + 4 * q^55 + 27 * q^56 - 10 * q^58 + 30 * q^59 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 - 2 * q^67 + 27 * q^68 - 11 * q^70 - 6 * q^71 + 15 * q^73 - 36 * q^74 - 10 * q^76 + 20 * q^77 - 4 * q^79 + 20 * q^80 - 5 * q^82 - 18 * q^83 + 12 * q^85 - 8 * q^86 - 18 * q^88 + 28 * q^89 - 4 * q^91 - 54 * q^92 - 3 * q^94 - 14 * q^95 + 24 * q^97 + 59 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.247934	−	0.429435i	0.175316	−	0.303656i	−0.764955	−	0.644084i	$-0.777239\pi$
$2$	0.247934	−	0.429435i	0.175316	−	0.303656i	0.940271	+	0.340428i	$0.110572\pi$
$3$		0			0
$3$		0			0
$4$	0.877057	+	1.51911i	0.438529	+	0.759554i
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	−0.0757082	−	0.997130i	$-0.524122\pi$
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	0.901394	−	0.433000i	$-0.142545\pi$
$6$		0			0
$7$	1.68284	+	2.04158i	0.636053	+	0.771645i
$7$	1.68284	+	2.04158i	0.636053	+	0.771645i
$8$	1.86155			0.658156
$9$		0			0
$10$	−0.915516	−	1.58572i	−0.289512	−	0.501449i
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	0.925429	−	0.378921i	$-0.123705\pi$
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	−0.790869	+	0.611985i	$0.790371\pi$
$12$		0			0
$13$	−1.19671			−0.331908			−0.165954	−	0.986134i	$-0.553070\pi$
$13$	−1.19671			−0.331908			−0.165954	+	0.986134i	$0.553070\pi$
$14$	1.29396	−	0.216492i	0.345825	−	0.0578598i
$15$		0			0
$16$	−1.29257	+	2.23880i	−0.323143	+	0.559701i
$17$	−0.124991	−	0.216492i	−0.0303149	−	0.0525069i	0.850470	−	0.526024i	$-0.176318\pi$
$17$	−0.124991	−	0.216492i	−0.0303149	−	0.0525069i	−0.880785	+	0.473517i	$0.842984\pi$
$18$		0			0
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	−0.658796	−	0.752321i	$-0.728934\pi$
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	0.980928	+	0.194374i	$0.0622675\pi$
$20$	6.47721			1.44835
$21$		0			0
$22$	0.442596			0.0943618
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	−0.965792	−	0.259318i	$-0.916502\pi$
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	0.707472	+	0.706741i	$0.249835\pi$
$24$		0			0
$25$	−4.31757	−	7.47825i	−0.863514	−	1.49565i
$26$	−0.296705	+	0.513909i	−0.0581887	+	0.100786i
$27$		0			0
$28$	−1.62544	+	4.34700i	−0.307178	+	0.821505i
$29$	−4.14255			−0.769252			−0.384626	−	0.923072i	$-0.625670\pi$
$29$	−4.14255			−0.769252			−0.384626	+	0.923072i	$0.625670\pi$
$30$		0			0
$31$	−1.79257	−	3.10483i	−0.321956	−	0.557644i	0.658936	−	0.752199i	$-0.271007\pi$
$31$	−1.79257	−	3.10483i	−0.321956	−	0.557644i	−0.980892	+	0.194555i	$0.937674\pi$
$32$	2.50249	+	4.33444i	0.442382	+	0.766229i
$33$		0			0
$34$	−0.123959			−0.0212587
$35$	9.63571	−	1.61215i	1.62873	−	0.272502i
$36$		0			0
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$	−0.696267	−	1.20597i	−0.112949	−	0.195634i
$39$		0			0
$40$	3.43695	−	5.95298i	0.543430	−	0.941249i
$41$	4.78186			0.746801			0.373400	−	0.927670i	$-0.378192\pi$
$41$	4.78186			0.746801			0.373400	+	0.927670i	$0.378192\pi$
$42$		0			0
$43$	9.97857			1.52172			0.760859	−	0.648917i	$-0.224778\pi$
$43$	9.97857			1.52172			0.760859	+	0.648917i	$0.224778\pi$
$44$	−0.782834	+	1.35591i	−0.118017	+	0.204411i
$45$		0			0
$46$	0.614310	+	1.06402i	0.0905751	+	0.156881i
$47$	5.08653	−	8.81013i	0.741947	−	1.28509i	−0.209661	−	0.977774i	$-0.567236\pi$
$47$	5.08653	−	8.81013i	0.741947	−	1.28509i	0.951608	−	0.307316i	$-0.0994308\pi$
$48$		0			0
$49$	−1.33611	+	6.87130i	−0.190872	+	0.981615i
$50$	−4.28189			−0.605551
$51$		0			0
$52$	−1.04958	−	1.81793i	−0.145551	−	0.252102i
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	−0.975222	−	0.221227i	$-0.928994\pi$
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	0.296023	−	0.955181i	$-0.404339\pi$
$54$		0			0
$55$	3.29588			0.444416
$56$	3.13268	+	3.80050i	0.418622	+	0.507863i
$57$		0			0
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	−0.906186	−	1.56956i	−0.117975	−	0.204339i	0.800990	−	0.598678i	$-0.204307\pi$
$59$	−0.906186	−	1.56956i	−0.117975	−	0.204339i	−0.918965	+	0.394339i	$0.870974\pi$
$60$		0			0
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	0.279631	+	0.960108i	$0.409788\pi$
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	−0.971293	+	0.237886i	$0.923545\pi$
$62$	−1.77776			−0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	−2.20948	+	3.82692i	−0.274052	+	0.474671i
$66$		0			0
$67$	−0.514685	−	0.891460i	−0.0628787	−	0.108909i	0.832872	−	0.553465i	$-0.186695\pi$
$67$	−0.514685	−	0.891460i	−0.0628787	−	0.108909i	−0.895751	+	0.444556i	$0.853361\pi$
$68$	0.219249	−	0.379751i	0.0265879	−	0.0460516i
$69$		0			0
$70$	1.69671	−	4.53761i	0.202796	−	0.542349i
$71$	−4.94533			−0.586903			−0.293451	−	0.955974i	$-0.594804\pi$
$71$	−4.94533			−0.586903			−0.293451	+	0.955974i	$0.594804\pi$
$72$		0			0
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	0.807480	−	0.589894i	$-0.200831\pi$
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	−0.914604	+	0.404351i	$0.867497\pi$
$74$	1.17306	+	2.03181i	0.136366	+	0.236193i
$75$		0			0
$76$	4.92604			0.565055
$77$	−0.827091	+	2.21194i	−0.0942557	+	0.252074i
$78$		0			0
$79$	0.899562	−	1.55809i	0.101209	−	0.175298i	−0.810974	−	0.585082i	$-0.801062\pi$
$79$	0.899562	−	1.55809i	0.101209	−	0.175298i	0.912183	+	0.409783i	$0.134396\pi$
$80$	4.77293	+	8.26696i	0.533630	+	0.924274i
$81$		0			0
$82$	1.18559	−	2.05350i	0.130926	−	0.226771i
$83$	−12.3231			−1.35264			−0.676319	−	0.736609i	$-0.736426\pi$
$83$	−12.3231			−1.35264			−0.676319	+	0.736609i	$0.736426\pi$
$84$		0			0
$85$	−0.923082			−0.100122
$86$	2.47403	−	4.28514i	0.266781	−	0.462079i
$87$		0			0
$88$	0.830779	+	1.43895i	0.0885613	+	0.153393i
$89$	−1.20370	+	2.08488i	−0.127592	+	0.220997i	−0.922743	−	0.385415i	$-0.874058\pi$
$89$	−1.20370	+	2.08488i	−0.127592	+	0.220997i	0.795151	+	0.606412i	$0.207392\pi$
$90$		0			0
$91$	−2.01387	−	2.44318i	−0.211111	−	0.256115i
$92$	−4.34620			−0.453122
$93$		0			0
$94$	−2.52225	−	4.36867i	−0.260150	−	0.450593i
$95$	−5.18489	−	8.98049i	−0.531958	−	0.921379i
$96$		0			0
$97$	−11.0442			−1.12137			−0.560684	−	0.828030i	$-0.689462\pi$
$97$	−11.0442			−1.12137			−0.560684	+	0.828030i	$0.689462\pi$
$98$	2.61951	+	2.27740i	0.264610	+	0.230052i
$99$		0			0
$100$	7.57351	−	13.1177i	0.757351	−	1.31177i
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	0.923420	−	0.383791i	$-0.125382\pi$
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	−0.794083	+	0.607810i	$0.792048\pi$
$102$		0			0
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	−0.999695	−	0.0247032i	$-0.992136\pi$
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	0.521241	+	0.853409i	$0.325469\pi$
$104$	−2.22773			−0.218447
$105$		0			0
$106$	−4.90379			−0.476298
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	0.472613	+	0.881270i	$0.343311\pi$
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	−0.999509	+	0.0313403i	$0.990022\pi$
$108$		0			0
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$	0.817161	−	1.41536i	0.0779132	−	0.134950i
$111$		0			0
$112$	−6.74589	+	1.12865i	−0.637427	+	0.106648i
$113$	−15.8264			−1.48882			−0.744409	−	0.667724i	$-0.767269\pi$
$113$	−15.8264			−1.48882			−0.744409	+	0.667724i	$0.767269\pi$
$114$		0			0
$115$	4.57458	+	7.92341i	0.426582	+	0.738861i
$116$	−3.63325	−	6.29298i	−0.337339	−	0.584289i
$117$		0			0
$118$	−0.898698			−0.0827318
$119$	0.231645	−	0.619501i	0.0212348	−	0.0567895i
$120$		0			0
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	2.67871	+	4.63966i	0.242519	+	0.420055i
$123$		0			0
$124$	3.14438	−	5.44623i	0.282374	−	0.489086i
$125$	−13.4230			−1.20059
$126$		0			0
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	−5.67155	+	9.82342i	−0.501299	+	0.868275i
$129$		0			0
$130$	1.09561	+	1.89765i	0.0960912	+	0.166435i
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	−0.324965	−	0.945726i	$-0.605353\pi$
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	0.981505	−	0.191435i	$-0.0613140\pi$
$132$		0			0
$133$	7.32814	−	1.22607i	0.635430	−	0.106313i
$134$	−0.510432			−0.0440946
$135$		0			0
$136$	−0.232677	−	0.403009i	−0.0199519	−	0.0345577i
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	0.876271	−	0.481819i	$-0.160024\pi$
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	−0.855403	+	0.517963i	$0.826691\pi$
$138$		0			0
$139$	9.86974			0.837141			0.418570	−	0.908184i	$-0.362531\pi$
$139$	9.86974			0.837141			0.418570	+	0.908184i	$0.362531\pi$
$140$	10.9001	+	13.2237i	0.921226	+	1.11761i
$141$		0			0
$142$	−1.22612	+	2.12370i	−0.102893	+	0.178217i
$143$	−0.534073	−	0.925042i	−0.0446614	−	0.0773559i
$144$		0			0
$145$	−7.64835	+	13.2473i	−0.635161	+	1.10013i
$146$	−0.907699			−0.0751217
$147$		0			0
$148$	−8.29934			−0.682202
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	0.00962096	+	0.999954i	$0.496938\pi$
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	−0.870796	+	0.491645i	$0.836396\pi$
$150$		0			0
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	2.61387	−	4.52735i	0.212013	−	0.367217i
$153$		0			0
$154$	0.744818	+	0.903596i	0.0600192	+	0.0728139i
$155$	−13.2384			−1.06334
$156$		0			0
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	0.979125	+	0.203259i	$0.0651534\pi$
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	−0.313535	+	0.949577i	$0.601513\pi$
$158$	−0.446064	−	0.772606i	−0.0354870	−	0.0614652i
$159$		0			0
$160$	18.4813			1.46108
$161$	−6.46555	+	1.08175i	−0.509557	+	0.0852537i
$162$		0			0
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	−0.966698	−	0.255921i	$-0.917621\pi$
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	0.704983	+	0.709224i	$0.250954\pi$
$164$	4.19396	+	7.26416i	0.327494	+	0.567236i
$165$		0			0
$166$	−3.05532	+	5.29197i	−0.237139	+	0.410737i
$167$	−17.6310			−1.36433			−0.682163	−	0.731200i	$-0.738961\pi$
$167$	−17.6310			−1.36433			−0.682163	+	0.731200i	$0.738961\pi$
$168$		0			0
$169$	−11.5679			−0.889837
$170$	−0.228863	+	0.396403i	−0.0175530	+	0.0304027i
$171$		0			0
$172$	8.75178	+	15.1585i	0.667317	+	1.15583i
$173$	1.94342	−	3.36611i	0.147756	−	0.255920i	−0.782642	−	0.622472i	$-0.786128\pi$
$173$	1.94342	−	3.36611i	0.147756	−	0.255920i	0.930398	+	0.366552i	$0.119462\pi$
$174$		0			0
$175$	8.00168	−	21.3994i	0.604870	−	1.61764i
$176$	−2.30742			−0.173928
$177$		0			0
$178$	0.596879	+	1.03382i	0.0447380	+	0.0774884i
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	0.969915	−	0.243445i	$-0.0782775\pi$
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	−0.695787	+	0.718248i	$0.744944\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$	−1.54849	+	0.259078i	−0.114782	+	0.0192041i
$183$		0			0
$184$	−2.30619	+	3.99444i	−0.170015	+	0.294474i
$185$	8.73545	+	15.1302i	0.642243	+	1.11240i
$186$		0			0
$187$	0.111563	−	0.193234i	0.00815833	−	0.0141306i
$188$	17.8447			1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	11.9230	−	20.6512i	0.862715	−	1.49427i	−0.00658302	−	0.999978i	$-0.502095\pi$
$191$	11.9230	−	20.6512i	0.862715	−	1.49427i	0.869298	−	0.494288i	$-0.164571\pi$
$192$		0			0
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$194$	−2.73823	+	4.74276i	−0.196594	+	0.340510i
$195$		0			0
$196$	−11.6101	+	3.99684i	−0.829292	+	0.285489i
$197$	−15.4682			−1.10206			−0.551032	−	0.834484i	$-0.685766\pi$
$197$	−15.4682			−1.10206			−0.551032	+	0.834484i	$0.685766\pi$
$198$		0			0
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	0.998326	+	0.0578402i	$0.0184214\pi$
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	−0.449072	+	0.893496i	$0.648245\pi$
$200$	−8.03736	−	13.9211i	−0.568327	−	0.984371i
$201$		0			0
$202$	1.28908			0.0906994
$203$	−6.97125	−	8.45735i	−0.489286	−	0.593590i
$204$		0			0
$205$	8.82870	−	15.2917i	0.616623	−	1.06802i
$206$	2.40783	+	4.17048i	0.167761	+	0.290571i
$207$		0			0
$208$	1.54684	−	2.67920i	0.107254	−	0.185769i
$209$	2.50658			0.173384
$210$		0			0
$211$	−1.54380			−0.106279			−0.0531397	−	0.998587i	$-0.516923\pi$
$211$	−1.54380			−0.106279			−0.0531397	+	0.998587i	$0.516923\pi$
$212$	8.67347	−	15.0229i	0.595697	−	1.03178i
$213$		0			0
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	18.4233	−	31.9101i	1.25646	−	2.17625i
$216$		0			0
$217$	3.32215	−	8.88461i	0.225522	−	0.603127i
$218$	−1.05220			−0.0712637
$219$		0			0
$220$	2.89068	+	5.00680i	0.194889	+	0.337558i
$221$	0.149579	+	0.259078i	0.0100617	+	0.0174275i
$222$		0			0
$223$	5.44342			0.364518			0.182259	−	0.983251i	$-0.441659\pi$
$223$	5.44342			0.364518			0.182259	+	0.983251i	$0.441659\pi$
$224$	−4.63783	+	12.4032i	−0.309878	+	0.828725i
$225$		0			0
$226$	−3.92389	+	6.79638i	−0.261014	+	0.452089i
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	0.999234	+	0.0391399i	$0.0124618\pi$
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	−0.465721	+	0.884932i	$0.654205\pi$
$228$		0			0
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	−0.653021	−	0.757340i	$-0.726499\pi$
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	0.982386	+	0.186863i	$0.0598319\pi$
$230$	4.53678			0.299146
$231$		0			0
$232$	−7.71155			−0.506288
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	−0.456985	−	0.889474i	$-0.651071\pi$
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	0.998800	−	0.0489765i	$-0.0155959\pi$
$234$		0			0
$235$	−18.7824	−	32.5321i	−1.22523	−	2.12216i
$236$	1.58955	−	2.75319i	0.103471	−	0.179217i
$237$		0			0
$238$	−0.208602	−	0.253072i	−0.0135217	−	0.0164042i
$239$	22.0239			1.42461			0.712303	−	0.701872i	$-0.247652\pi$
$239$	22.0239			1.42461			0.712303	+	0.701872i	$0.247652\pi$
$240$		0			0
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	−0.998984	−	0.0450623i	$-0.985651\pi$
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	0.460467	−	0.887677i	$-0.347682\pi$
$242$	−2.52975	−	4.38166i	−0.162619	−	0.281664i
$243$		0			0
$244$	−18.9516			−1.21325
$245$	19.5067	+	16.9591i	1.24624	+	1.08348i
$246$		0			0
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	−3.33696	−	5.77978i	−0.211897	−	0.367017i
$249$		0			0
$250$	−3.32803	+	5.76432i	−0.210483	+	0.364568i
$251$	−8.53099			−0.538471			−0.269236	−	0.963074i	$-0.586771\pi$
$251$	−8.53099			−0.538471			−0.269236	+	0.963074i	$0.586771\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$	−0.314743	+	0.545151i	−0.0197488	+	0.0342058i
$255$		0			0
$256$	0.123861	+	0.214533i	0.00774131	+	0.0134083i
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	−0.465264	−	0.885172i	$-0.654041\pi$
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	0.999213	−	0.0396557i	$-0.0126261\pi$
$258$		0			0
$259$	−12.3464	+	2.06567i	−0.767167	+	0.128354i
$260$	−7.75135			−0.480718
$261$		0			0
$262$	−3.72617	−	6.45392i	−0.230204	−	0.398725i
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	−0.986796	−	0.161967i	$-0.948216\pi$
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	0.353130	−	0.935574i	$-0.385117\pi$
$264$		0			0
$265$	−36.5170			−2.24322
$266$	1.29038	−	3.45094i	0.0791183	−	0.211591i
$267$		0			0
$268$	0.902816	−	1.56372i	0.0551483	−	0.0955196i
$269$	9.92267	+	17.1866i	0.604996	+	1.04788i	0.992052	+	0.125827i	$0.0401585\pi$
$269$	9.92267	+	17.1866i	0.604996	+	1.04788i	−0.387057	+	0.922056i	$0.626508\pi$
$270$		0			0
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	−0.657946	−	0.753065i	$-0.728574\pi$
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	0.981147	+	0.193265i	$0.0619077\pi$
$272$	0.646243			0.0391842
$273$		0			0
$274$	0.242228			0.0146335
$275$	3.85373	−	6.67485i	0.232388	−	0.402509i
$276$		0			0
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	2.44705	−	4.23841i	0.146764	−	0.254203i
$279$		0			0
$280$	17.9373	−	3.00109i	1.07196	−	0.179349i
$281$	13.6747			0.815762			0.407881	−	0.913035i	$-0.366268\pi$
$281$	13.6747			0.815762			0.407881	+	0.913035i	$0.366268\pi$
$282$		0			0
$283$	−3.16089	−	5.47483i	−0.187896	−	0.325445i	0.756653	−	0.653817i	$-0.226833\pi$
$283$	−3.16089	−	5.47483i	−0.187896	−	0.325445i	−0.944548	+	0.328372i	$0.893500\pi$
$284$	−4.33734	−	7.51249i	−0.257374	−	0.445784i
$285$		0			0
$286$	−0.529660			−0.0313194
$287$	8.04710	+	9.76255i	0.475005	+	0.576265i
$288$		0			0
$289$	8.46875	−	14.6683i	0.498162	−	0.862842i
$290$	3.79257	+	6.56893i	0.222708	+	0.385741i
$291$		0			0
$292$	1.60547	−	2.78076i	0.0939533	−	0.162732i
$293$	2.63016			0.153655			0.0768277	−	0.997044i	$-0.475521\pi$
$293$	2.63016			0.153655			0.0768277	+	0.997044i	$0.475521\pi$
$294$		0			0
$295$	−6.69233			−0.389642
$296$	−4.40382	+	7.62764i	−0.255967	+	0.443348i
$297$		0			0
$298$	5.21256	+	9.02841i	0.301955	+	0.523002i
$299$	1.48255	−	2.56786i	0.0857384	−	0.148503i
$300$		0			0
$301$	16.7923	+	20.3721i	0.967894	+	1.17423i
$302$	−0.743000			−0.0427548
$303$		0			0
$304$	3.62990	+	6.28717i	0.208189	+	0.360594i
$305$	19.9475	+	34.5501i	1.14219	+	1.97833i
$306$		0			0
$307$	−2.79496			−0.159517			−0.0797583	−	0.996814i	$-0.525415\pi$
$307$	−2.79496			−0.159517			−0.0797583	+	0.996814i	$0.525415\pi$
$308$	−4.08558	+	0.683556i	−0.232797	+	0.0389492i
$309$		0			0
$310$	−3.28226	+	5.68504i	−0.186420	+	0.322889i
$311$	7.55013	+	13.0772i	0.428129	+	0.741541i	0.996707	−	0.0810885i	$-0.0258396\pi$
$311$	7.55013	+	13.0772i	0.428129	+	0.741541i	−0.568578	+	0.822629i	$0.692506\pi$
$312$		0			0
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	−0.240910	−	0.970548i	$-0.577446\pi$
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	0.960974	−	0.276640i	$-0.0892209\pi$
$314$	8.27090			0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	−16.2605	+	28.1639i	−0.913278	+	1.58184i	−0.103875	+	0.994590i	$0.533124\pi$
$317$	−16.2605	+	28.1639i	−0.913278	+	1.58184i	−0.809403	+	0.587253i	$0.800209\pi$
$318$		0			0
$319$	−1.84875	−	3.20214i	−0.103510	−	0.179285i
$320$	−4.96372	+	8.59741i	−0.277480	+	0.480610i
$321$		0			0
$322$	−1.13849	+	3.04473i	−0.0634456	+	0.169676i
$323$	−0.702021			−0.0390615
$324$		0			0
$325$	5.16688	+	8.94931i	0.286607	+	0.496418i
$326$	1.65687	+	2.86978i	0.0917654	+	0.158942i
$327$		0			0
$328$	8.90165			0.491511
$329$	26.5464	−	4.44147i	1.46355	−	0.244866i
$330$		0			0
$331$	−9.04741	+	15.6706i	−0.497291	+	0.861333i	−0.999995	−	0.00312545i	$-0.999005\pi$
$331$	−9.04741	+	15.6706i	−0.497291	+	0.861333i	0.502704	+	0.864458i	$0.332338\pi$
$332$	−10.8081	−	18.7201i	−0.593170	−	1.02740i
$333$		0			0
$334$	−4.37132	+	7.57135i	−0.239188	+	0.414286i
$335$	−3.80103			−0.207672
$336$		0			0
$337$	25.0173			1.36278			0.681389	−	0.731921i	$-0.261376\pi$
$337$	25.0173			1.36278			0.681389	+	0.731921i	$0.261376\pi$
$338$	−2.86807	+	4.96765i	−0.156003	+	0.270204i
$339$		0			0
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	1.59999	−	2.77127i	0.0866446	−	0.150073i
$342$		0			0
$343$	−16.2768	+	8.83553i	−0.878863	+	0.477074i
$344$	18.5756			1.00153
$345$		0			0
$346$	−0.963682	−	1.66915i	−0.0518078	−	0.0897338i
$347$	−5.37444	−	9.30881i	−0.288515	−	0.499723i	0.684940	−	0.728599i	$-0.259828\pi$
$347$	−5.37444	−	9.30881i	−0.288515	−	0.499723i	−0.973456	+	0.228876i	$0.926495\pi$
$348$		0			0
$349$	3.28602			0.175896			0.0879482	−	0.996125i	$-0.471969\pi$
$349$	3.28602			0.175896			0.0879482	+	0.996125i	$0.471969\pi$
$350$	−7.20574	−	8.74183i	−0.385163	−	0.467270i
$351$		0			0
$352$	−2.23365	+	3.86879i	−0.119054	+	0.206207i
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	0.550631	−	0.834748i	$-0.314387\pi$
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	−0.998229	+	0.0594866i	$0.981054\pi$
$354$		0			0
$355$	−9.13051	+	15.8145i	−0.484597	+	0.839347i
$356$	−4.22287			−0.223812
$357$		0			0
$358$	3.63728			0.192236
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	−0.360382	−	0.932805i	$-0.617354\pi$
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	0.988024	−	0.154303i	$-0.0493131\pi$
$360$		0			0
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$	2.79088	−	4.83395i	0.146686	−	0.254067i
$363$		0			0
$364$	1.94518	−	5.20210i	0.101955	−	0.272664i
$365$	−6.75936			−0.353801
$366$		0			0
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	0.874889	−	0.484323i	$-0.160934\pi$
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	−0.856881	+	0.515515i	$0.827601\pi$
$368$	−3.20263	−	5.54712i	−0.166949	−	0.289164i
$369$		0			0
$370$	8.66327			0.450382
$371$	9.16383	−	24.5074i	0.475762	−	1.27236i
$372$		0			0
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	−0.0553208	−	0.0958184i	−0.00286057	−	0.00495465i
$375$		0			0
$376$	9.46882	−	16.4005i	0.488317	−	0.845790i
$377$	4.95744			0.255321
$378$		0			0
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	9.09489	−	15.7528i	0.466558	−	0.808102i
$381$		0			0
$382$	−5.91222	−	10.2403i	−0.302495	−	0.523937i
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	−0.851997	−	0.523546i	$-0.824609\pi$
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	0.879403	+	0.476078i	$0.157942\pi$
$384$		0			0
$385$	5.54643	+	6.72880i	0.282672	+	0.342932i
$386$	−2.94276			−0.149782
$387$		0			0
$388$	−9.68640	−	16.7773i	−0.491752	−	0.851740i
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	0.992529	+	0.122006i	$0.0389326\pi$
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	−0.390605	+	0.920559i	$0.627734\pi$
$390$		0			0
$391$	0.619387			0.0313237
$392$	−2.48722	+	12.7913i	−0.125624	+	0.646056i
$393$		0			0
$394$	−3.83510	+	6.64258i	−0.193209	+	0.334648i
$395$	−3.32170	−	5.75336i	−0.167133	−	0.289483i
$396$		0			0
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	0.865622	+	0.500697i	$0.166923\pi$
$398$	7.68415			0.385172
$399$		0			0
$400$	22.3231			1.11616
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	0.378465	+	0.925616i	$0.376452\pi$
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	−0.990839	+	0.135048i	$0.956881\pi$
$402$		0			0
$403$	2.14519	+	3.71558i	0.106860	+	0.185086i
$404$	−2.28004	+	3.94914i	−0.113436	+	0.196477i
$405$		0			0
$406$	−5.36029	+	0.896827i	−0.266027	+	0.0445088i
$407$	−4.22306			−0.209329
$408$		0			0
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	−0.980001	−	0.198992i	$-0.936233\pi$
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	0.317669	−	0.948202i	$-0.397100\pi$
$410$	−4.37787	−	7.58269i	−0.216208	−	0.374483i
$411$		0			0
$412$	−17.0352			−0.839263
$413$	1.67942	−	4.49137i	0.0826388	−	0.221006i
$414$		0			0
$415$	−22.7520	+	39.4077i	−1.11685	+	1.93445i
$416$	−2.99476	−	5.18708i	−0.146830	−	0.254317i
$417$		0			0
$418$	0.621466	−	1.07641i	0.0303969	−	0.0526490i
$419$	21.0525			1.02848			0.514240	−	0.857646i	$-0.328074\pi$
$419$	21.0525			1.02848			0.514240	+	0.857646i	$0.328074\pi$
$420$		0			0
$421$	14.8907			0.725727			0.362863	−	0.931842i	$-0.381799\pi$
$421$	14.8907			0.725727			0.362863	+	0.931842i	$0.381799\pi$
$422$	−0.382760	+	0.662959i	−0.0186325	+	0.0322724i
$423$		0			0
$424$	−9.20469	−	15.9430i	−0.447019	−	0.774260i
$425$	−1.07932	+	1.86944i	−0.0523547	+	0.0906809i
$426$		0			0
$427$	−28.1931	+	4.71698i	−1.36436	+	0.228270i
$428$	−19.1207			−0.924236
$429$		0			0
$430$	−9.13554	−	15.8232i	−0.440555	−	0.763064i
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	0.608463	−	0.793582i	$-0.291786\pi$
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	−0.991494	+	0.130154i	$0.958453\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$	−2.99169	−	3.62944i	−0.143605	−	0.174219i
$435$		0			0
$436$	1.86105	−	3.22344i	0.0891282	−	0.154375i
$437$	3.47905	+	6.02590i	0.166426	+	0.288258i
$438$		0			0
$439$	7.77236	−	13.4621i	0.370954	−	0.642512i	−0.618758	−	0.785582i	$-0.712364\pi$
$439$	7.77236	−	13.4621i	0.370954	−	0.642512i	0.989713	+	0.143070i	$0.0456973\pi$
$440$	6.13543			0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	−0.895027	+	1.55023i	−0.0425240	+	0.0736537i	−0.886504	−	0.462721i	$-0.846873\pi$
$443$	−0.895027	+	1.55023i	−0.0425240	+	0.0736537i	0.843980	+	0.536375i	$0.180207\pi$
$444$		0			0
$445$	4.44477	+	7.69857i	0.210702	+	0.364947i
$446$	1.34961	−	2.33759i	0.0639058	−	0.110688i
$447$		0			0
$448$	−4.52428	−	5.48875i	−0.213752	−	0.259319i
$449$	13.5666			0.640250			0.320125	−	0.947375i	$-0.396275\pi$
$449$	13.5666			0.640250			0.320125	+	0.947375i	$0.396275\pi$
$450$		0			0
$451$	2.13407	+	3.69631i	0.100489	+	0.174053i
$452$	−13.8806	−	24.0419i	−0.652890	−	1.13084i
$453$		0			0
$454$	7.97176			0.374133
$455$	−11.5312	+	1.92927i	−0.540589	+	0.0904457i
$456$		0			0
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	−0.894506	−	0.447057i	$-0.852472\pi$
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	0.834415	+	0.551136i	$0.185806\pi$
$458$	−2.47151	−	4.28078i	−0.115486	−	0.200028i
$459$		0			0
$460$	−8.02434	+	13.8986i	−0.374137	+	0.648024i
$461$	−36.1869			−1.68539			−0.842695	−	0.538391i	$-0.819033\pi$
$461$	−36.1869			−1.68539			−0.842695	+	0.538391i	$0.819033\pi$
$462$		0			0
$463$	−16.3845			−0.761451			−0.380726	−	0.924688i	$-0.624326\pi$
$463$	−16.3845			−0.761451			−0.380726	+	0.924688i	$0.624326\pi$
$464$	5.35455	−	9.27436i	0.248579	−	0.430551i
$465$		0			0
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	−4.35022	+	7.53480i	−0.201304	+	0.348669i	−0.948949	−	0.315430i	$-0.897851\pi$
$467$	−4.35022	+	7.53480i	−0.201304	+	0.348669i	0.747645	+	0.664099i	$0.231185\pi$
$468$		0			0
$469$	0.953856	−	2.55095i	0.0440450	−	0.117792i
$470$	−18.6272			−0.859209
$471$		0			0
$472$	−1.68691	−	2.92181i	−0.0776462	−	0.134487i
$473$	4.45328	+	7.71330i	0.204762	+	0.354658i
$474$		0			0
$475$	−24.2498			−1.11266
$476$	1.14425	−	0.191445i	0.0524468	−	0.00877485i
$477$		0			0
$478$	5.46047	−	9.45782i	0.249756	−	0.432591i
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	0.994427	−	0.105432i	$-0.0336224\pi$
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	−0.588520	+	0.808483i	$0.700289\pi$
$480$		0			0
$481$	2.83103	−	4.90349i	0.129084	−	0.223580i
$482$	−8.29095			−0.377643
$483$		0			0
$484$	17.8978			0.813536
$485$	−20.3908	+	35.3179i	−0.925898	+	1.60370i
$486$		0			0
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	0.990677	−	0.136229i	$-0.0434983\pi$
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	−0.613316	+	0.789837i	$0.710165\pi$
$488$	−10.0562	+	17.4178i	−0.455222	+	0.788467i
$489$		0			0
$490$	12.1192	−	4.17210i	0.547490	−	0.188476i
$491$	6.42042			0.289749			0.144875	−	0.989450i	$-0.453722\pi$
$491$	6.42042			0.289749			0.144875	+	0.989450i	$0.453722\pi$
$492$		0			0
$493$	0.517784	+	0.896827i	0.0233198	+	0.0403911i
$494$	0.833230	+	1.44320i	0.0374888	+	0.0649325i
$495$		0			0
$496$	9.26814			0.416152
$497$	−8.32220	−	10.0963i	−0.373302	−	0.452881i
$498$		0			0
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	−11.7728	−	20.3911i	−0.526495	−	0.911916i
$501$		0			0
$502$	−2.11512	+	3.66350i	−0.0944026	+	0.163510i
$503$	−17.7223			−0.790200			−0.395100	−	0.918638i	$-0.629290\pi$
$503$	−17.7223			−0.790200			−0.395100	+	0.918638i	$0.629290\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$	−0.548314	+	0.949708i	−0.0243755	+	0.0422197i
$507$		0			0
$508$	−1.11339	−	1.92845i	−0.0493988	−	0.0855612i
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	0.283362	+	0.959013i	$0.408550\pi$
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	−0.972211	+	0.234107i	$0.924783\pi$
$510$		0			0
$511$	1.69624	−	4.53635i	0.0750372	−	0.200676i
$512$	−22.5634			−0.997169
$513$		0			0
$514$	−4.24456	−	7.35180i	−0.187220	−	0.324274i
$515$	17.9303	+	31.0563i	0.790105	+	1.36850i
$516$		0			0
$517$	9.08016			0.399345
$518$	−2.17402	+	5.81411i	−0.0955210	+	0.255457i
$519$		0			0
$520$	−4.11304	+	7.12399i	−0.180369	+	0.312408i
$521$	−2.37986	−	4.12203i	−0.104263	−	0.180590i	0.809174	−	0.587570i	$-0.199915\pi$
$521$	−2.37986	−	4.12203i	−0.104263	−	0.180590i	−0.913437	+	0.406980i	$0.866582\pi$
$522$		0			0
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.0287402	−	0.999587i	$-0.490850\pi$
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.851298	−	0.524683i	$-0.175816\pi$
$524$	26.3624			1.15165
$525$		0			0
$526$	−10.1914			−0.444367
$527$	−0.448113	+	0.776154i	−0.0195201	+	0.0338098i
$528$		0			0
$529$	8.43046	+	14.6020i	0.366542	+	0.634869i
$530$	−9.05381	+	15.6817i	−0.393272	+	0.681168i
$531$		0			0
$532$	8.28972	+	10.0569i	0.359405	+	0.436022i
$533$	−5.72250			−0.247869
$534$		0			0
$535$	20.1255	+	34.8584i	0.870101	+	1.50706i
$536$	−0.958109	−	1.65949i	−0.0413840	−	0.0716792i
$537$		0			0
$538$	9.84067			0.424261
$539$	−5.90771	+	2.03376i	−0.254463	+	0.0876003i
$540$		0			0
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$	−2.63830	−	4.56966i	−0.113325	−	0.196284i
$543$		0			0
$544$	0.625580	−	1.08354i	0.0268215	−	0.0464563i
$545$	−7.83538			−0.335631
$546$		0			0
$547$	12.3550			0.528263			0.264131	−	0.964487i	$-0.414915\pi$
$547$	12.3550			0.528263			0.264131	+	0.964487i	$0.414915\pi$
$548$	−0.428436	+	0.742073i	−0.0183019	+	0.0316998i
$549$		0			0
$550$	−1.91094	−	3.30985i	−0.0814828	−	0.141132i
$551$	−5.81671	+	10.0748i	−0.247800	+	0.429203i
$552$		0			0
$553$	4.69478	−	0.785481i	0.199642	−	0.0334020i
$554$	12.3379			0.524186
$555$		0			0
$556$	8.65633	+	14.9932i	0.367110	+	0.635853i
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	0.938810	−	0.344436i	$-0.111930\pi$
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	−0.767695	+	0.640815i	$0.778597\pi$
$558$		0			0
$559$	−11.9415			−0.505070
$560$	−8.84559	+	23.6563i	−0.373794	+	0.999661i
$561$		0			0
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	−22.6064	−	39.1554i	−0.952744	−	1.65020i	−0.739448	−	0.673214i	$-0.764913\pi$
$563$	−22.6064	−	39.1554i	−0.952744	−	1.65020i	−0.213296	−	0.976988i	$-0.568420\pi$
$564$		0			0
$565$	−29.2200	+	50.6106i	−1.22930	+	2.12920i
$566$	−3.13477			−0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	−11.2149	+	19.4248i	−0.470155	+	0.814332i	−0.999418	−	0.0341263i	$-0.989135\pi$
$569$	−11.2149	+	19.4248i	−0.470155	+	0.814332i	0.529263	+	0.848458i	$0.322468\pi$
$570$		0			0
$571$	10.9134	+	18.9026i	0.456713	+	0.791050i	0.998785	−	0.0492820i	$-0.0156933\pi$
$571$	10.9134	+	18.9026i	0.456713	+	0.791050i	−0.542072	+	0.840332i	$0.682360\pi$
$572$	0.936826	−	1.62263i	0.0391706	−	0.0678455i
$573$		0			0
$574$	6.18753	−	1.03523i	0.258262	−	0.0432098i
$575$	21.3954			0.892251
$576$		0			0
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	−0.977807	−	0.209508i	$-0.932814\pi$
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	0.307465	−	0.951559i	$-0.400519\pi$
$578$	−4.19939	−	7.27355i	−0.174671	−	0.302540i
$579$		0			0
$580$	−26.8322			−1.11414
$581$	−20.7378	−	25.1586i	−0.860350	−	1.04376i
$582$		0			0
$583$	4.41343	−	7.64429i	0.182786	−	0.316594i
$584$	−1.70380	−	2.95107i	−0.0705039	−	0.122116i
$585$		0			0
$586$	0.652105	−	1.12948i	0.0269382	−	0.0466584i
$587$	19.4461			0.802625			0.401313	−	0.915941i	$-0.368554\pi$
$587$	19.4461			0.802625			0.401313	+	0.915941i	$0.368554\pi$
$588$		0			0
$589$	−10.0681			−0.414848
$590$	−1.65926	+	2.87392i	−0.0683105	+	0.118317i
$591$		0			0
$592$	−6.11563	−	10.5926i	−0.251351	−	0.435352i
$593$	−14.4202	+	24.9766i	−0.592168	+	1.02566i	0.401772	+	0.915740i	$0.368394\pi$
$593$	−14.4202	+	24.9766i	−0.592168	+	1.02566i	−0.993940	+	0.109925i	$0.964939\pi$
$594$		0			0
$595$	−1.55340	−	1.88455i	−0.0636831	−	0.0772589i
$596$	−36.8784			−1.51060
$597$		0			0
$598$	−0.735152	−	1.27332i	−0.0300626	−	0.0520699i
$599$	23.4994	+	40.7022i	0.960161	+	1.66305i	0.722089	+	0.691800i	$0.243182\pi$
$599$	23.4994	+	40.7022i	0.960161	+	1.66305i	0.238072	+	0.971247i	$0.423484\pi$
$600$		0			0
$601$	15.6169			0.637025			0.318512	−	0.947919i	$-0.396817\pi$
$601$	15.6169			0.637025			0.318512	+	0.947919i	$0.396817\pi$
$602$	12.9119	−	2.16028i	0.526248	−	0.0880463i
$603$		0			0
$604$	1.31417	−	2.27620i	0.0534727	−	0.0926174i
$605$	−18.8383	−	32.6289i	−0.765885	−	1.32655i
$606$		0			0
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	−0.413802	−	0.910367i	$-0.635800\pi$
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	0.995302	−	0.0968200i	$-0.0308671\pi$
$608$	14.0554			0.570021
$609$		0			0
$610$	19.7827			0.800977
$611$	−6.08711	+	10.5432i	−0.246258	+	0.426531i
$612$		0			0
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$	−0.692965	+	1.20025i	−0.0279658	+	0.0484382i
$615$		0			0
$616$	−1.53967	+	4.11762i	−0.0620350	+	0.165904i
$617$	−4.12801			−0.166188			−0.0830938	−	0.996542i	$-0.526480\pi$
$617$	−4.12801			−0.166188			−0.0830938	+	0.996542i	$0.526480\pi$
$618$		0			0
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	0.542315	−	0.840175i	$-0.317548\pi$
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	−0.998771	+	0.0495708i	$0.984215\pi$
$620$	−11.6109	−	20.1106i	−0.466304	−	0.807662i
$621$		0			0
$622$	7.48774			0.300231
$623$	−6.28209	+	1.05105i	−0.251686	+	0.0421095i
$624$		0			0
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	−6.31698	−	10.9413i	−0.252477	−	0.437304i
$627$		0			0
$628$	−14.6290	+	25.3382i	−0.583761	+	1.01110i
$629$	1.18276			0.0471597
$630$		0			0
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	1.67458	−	2.90045i	0.0666110	−	0.115374i
$633$		0			0
$634$	8.06304	+	13.9656i	0.320224	+	0.554645i
$635$	−2.34380	+	4.05958i	−0.0930107	+	0.161099i
$636$		0			0
$637$	1.59893	−	8.22297i	0.0633520	−	0.325806i
$638$	−1.83348			−0.0725881
$639$		0			0
$640$	20.9427	+	36.2737i	0.827831	+	1.43385i
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	0.997295	+	0.0735002i	$0.0234169\pi$
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	−0.434995	+	0.900433i	$0.643250\pi$
$642$		0			0
$643$	17.0425			0.672091			0.336045	−	0.941846i	$-0.390910\pi$
$643$	17.0425			0.672091			0.336045	+	0.941846i	$0.390910\pi$
$644$	−7.31395	−	8.87311i	−0.288210	−	0.349650i
$645$		0			0
$646$	−0.174055	+	0.301472i	−0.00684810	+	0.0118613i
$647$	1.68809	+	2.92386i	0.0663657	+	0.114949i	0.897299	−	0.441423i	$-0.145526\pi$
$647$	1.68809	+	2.92386i	0.0663657	+	0.114949i	−0.830933	+	0.556372i	$0.812193\pi$
$648$		0			0
$649$	0.808833	−	1.40094i	0.0317495	−	0.0549917i
$650$	5.12419			0.200987
$651$		0			0
$652$	−11.7222			−0.459077
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	−0.628836	−	0.777538i	$-0.716468\pi$
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	0.987786	+	0.155819i	$0.0498017\pi$
$654$		0			0
$655$	−27.7477	−	48.0604i	−1.08419	−	1.87787i
$656$	−6.18090	+	10.7056i	−0.241324	+	0.417985i
$657$		0			0
$658$	4.67444	−	12.5011i	0.182229	−	0.487345i
$659$	27.8495			1.08486			0.542432	−	0.840100i	$-0.317504\pi$
$659$	27.8495			1.08486			0.542432	+	0.840100i	$0.317504\pi$
$660$		0			0
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	−0.943495	−	0.331387i	$-0.892484\pi$
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	0.184758	−	0.982784i	$-0.440850\pi$
$662$	4.48633	+	7.77054i	0.174366	+	0.302011i
$663$		0			0
$664$	−22.9400			−0.890247
$665$	9.60906	−	25.6981i	0.372624	−	0.996529i
$666$		0			0
$667$	5.13203	−	8.88894i	0.198713	−	0.344181i
$668$	−15.4634	−	26.7834i	−0.598296	−	1.03628i
$669$		0			0
$670$	−0.942405	+	1.63229i	−0.0364083	+	0.0630610i
$671$	−9.64340			−0.372280
$672$		0			0
$673$	−49.2309			−1.89771			−0.948856	−	0.315711i	$-0.897757\pi$
$673$	−49.2309			−1.89771			−0.948856	+	0.315711i	$0.897757\pi$
$674$	6.20264	−	10.7433i	0.238917	−	0.413816i
$675$		0			0
$676$	−10.1457	−	17.5729i	−0.390219	−	0.675879i
$677$	11.6958	−	20.2577i	0.449505	−	0.778565i	−0.548849	−	0.835922i	$-0.684934\pi$
$677$	11.6958	−	20.2577i	0.449505	−	0.778565i	0.998354	+	0.0573564i	$0.0182671\pi$
$678$		0			0
$679$	−18.5856	−	22.5476i	−0.713250	−	0.865299i
$680$	−1.71836			−0.0658961
$681$		0			0
$682$	−0.793387	−	1.37419i	−0.0303803	−	0.0526203i
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	−0.995455	−	0.0952356i	$-0.969640\pi$
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	0.415251	−	0.909707i	$-0.363694\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$	−0.241286	+	9.18044i	−0.00921233	+	0.350511i
$687$		0			0
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	5.91731	+	10.2491i	0.225432	+	0.390459i
$690$		0			0
$691$	2.05665	−	3.56223i	0.0782387	−	0.135513i	−0.824251	−	0.566224i	$-0.808404\pi$
$691$	2.05665	−	3.56223i	0.0782387	−	0.135513i	0.902490	+	0.430711i	$0.141737\pi$
$692$	6.81797			0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	18.2224	−	31.5621i	0.691215	−	1.19722i
$696$		0			0
$697$	−0.597691	−	1.03523i	−0.0226392	−	0.0392122i
$698$	0.814716	−	1.41113i	0.0308375	−	0.0534120i
$699$		0			0
$700$	39.5259	−	6.61305i	1.49394	−	0.249950i
$701$	29.1835			1.10225			0.551123	−	0.834424i	$-0.314200\pi$
$701$	29.1835			1.10225			0.551123	+	0.834424i	$0.314200\pi$
$702$		0			0
$703$	6.64347	+	11.5068i	0.250563	+	0.433988i
$704$	−1.19983	−	2.07816i	−0.0452202	−	0.0783236i
$705$		0			0
$706$	−8.34010			−0.313884
$707$	−2.40894	+	6.44236i	−0.0905974	+	0.242290i
$708$		0			0
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	−0.123999	−	0.992282i	$-0.539572\pi$
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	0.921341	−	0.388755i	$-0.127095\pi$
$710$	4.52753	+	7.84192i	0.169915	+	0.294302i
$711$		0			0
$712$	−2.24075	+	3.88109i	−0.0839757	+	0.145450i
$713$	8.88298			0.332670
$714$		0			0
$715$	−3.94421			−0.147505
$716$	−6.43336	+	11.1429i	−0.240426	+	0.416430i
$717$		0			0
$718$	−5.89692	−	10.2138i	−0.220071	−	0.381175i
$719$	−5.57126	+	9.64970i	−0.207773	+	0.359873i	−0.951013	−	0.309152i	$-0.899955\pi$
$719$	−5.57126	+	9.64970i	−0.207773	+	0.359873i	0.743240	+	0.669025i	$0.233288\pi$
$720$		0			0
$721$	−25.3421	+	4.23997i	−0.943789	+	0.157905i
$722$	5.51088			0.205094
$723$		0			0
$724$	9.87264	+	17.0999i	0.366914	+	0.635513i
$725$	17.8858	+	30.9790i	0.664260	+	1.15053i
$726$		0			0
$727$	28.6820			1.06376			0.531878	−	0.846821i	$-0.321487\pi$
$727$	28.6820			1.06376			0.531878	+	0.846821i	$0.321487\pi$
$728$	−3.74892	−	4.54810i	−0.138944	−	0.168564i
$729$		0			0
$730$	−1.67588	+	2.90270i	−0.0620269	+	0.107434i
$731$	−1.24724	−	2.16028i	−0.0461307	−	0.0799007i
$732$		0			0
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	−0.536419	−	0.843952i	$-0.680223\pi$
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	0.999093	+	0.0425768i	$0.0135567\pi$
$734$	0.342141			0.0126287
$735$		0			0
$736$	−12.4009			−0.457104
$737$	0.459391	−	0.795689i	0.0169219	−	0.0293096i
$738$		0			0
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	0.999974	+	0.00717223i	$0.00228301\pi$
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	−0.493776	+	0.869589i	$0.664384\pi$
$740$	−15.3230	+	26.5402i	−0.563284	+	0.975637i
$741$		0			0
$742$	−8.25228	−	10.0115i	−0.302951	−	0.367533i
$743$	14.0122			0.514057			0.257028	−	0.966404i	$-0.417257\pi$
$743$	14.0122			0.514057			0.257028	+	0.966404i	$0.417257\pi$
$744$		0			0
$745$	38.8163	+	67.2318i	1.42212	+	2.46318i
$746$	−0.932261	−	1.61472i	−0.0341325	−	0.0591192i
$747$		0			0
$748$	0.391390			0.0143106
$749$	−28.4447	+	4.75906i	−1.03935	+	0.173892i
$750$		0			0
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	13.1494	+	22.7755i	0.479511	+	0.830537i
$753$		0			0
$754$	1.22912	−	2.12889i	0.0447618	−	0.0775298i
$755$	−5.53289			−0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	8.15047	−	14.1170i	0.296038	−	0.512753i
$759$		0			0
$760$	−9.65191	−	16.7176i	−0.350112	−	0.606411i
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	−0.666266	−	0.745714i	$-0.732109\pi$
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	0.978940	+	0.204146i	$0.0654419\pi$
$762$		0			0
$763$	1.96627	−	5.25850i	0.0711836	−	0.190370i
$764$	41.8285			1.51330
$765$		0			0
$766$	−0.265952	−	0.460642i	−0.00960922	−	0.0166437i
$767$	1.08444	+	1.87831i	0.0391570	+	0.0678218i
$768$		0			0
$769$	21.3454			0.769734			0.384867	−	0.922972i	$-0.374247\pi$
$769$	21.3454			0.769734			0.384867	+	0.922972i	$0.374247\pi$
$770$	4.26473	−	0.713530i	0.153690	−	0.0257138i
$771$		0			0
$772$	5.20495	−	9.01523i	0.187330	−	0.324465i
$773$	−6.57357	−	11.3858i	−0.236435	−	0.409517i	0.723254	−	0.690582i	$-0.242646\pi$
$773$	−6.57357	−	11.3858i	−0.236435	−	0.409517i	−0.959689	+	0.281065i	$0.909312\pi$
$774$		0			0
$775$	−15.4791	+	26.8106i	−0.556027	+	0.963066i
$776$	−20.5593			−0.738036
$777$		0			0
$778$	11.7737			0.422108
$779$	6.71439	−	11.6297i	0.240568	−	0.416676i
$780$		0			0
$781$	−2.20702	−	3.82268i	−0.0789735	−	0.136786i
$782$	0.153567	−	0.265986i	0.00549155	−	0.00951164i
$783$		0			0
$784$	−13.6565	−	11.8729i	−0.487732	−	0.424034i
$785$	61.5909			2.19827
$786$		0			0
$787$	14.0650	+	24.3614i	0.501364	+	0.868389i	0.999999	+	0.00157623i	$0.000501728\pi$
$787$	14.0650	+	24.3614i	0.501364	+	0.868389i	−0.498634	+	0.866812i	$0.666165\pi$
$788$	−13.5665	−	23.4979i	−0.483287	−	0.837077i
$789$		0			0
$790$	−3.29425			−0.117204
$791$	−26.6332	−	32.3108i	−0.946968	−	1.14884i
$792$		0			0
$793$	6.46470	−	11.1972i	0.229568	−	0.397624i
$794$	0.00795814	+	0.0137839i	0.000282424	+	0.000489172i
$795$		0			0
$796$	−13.5912	+	23.5406i	−0.481727	+	0.834376i
$797$	−25.7365			−0.911635			−0.455817	−	0.890073i	$-0.650653\pi$
$797$	−25.7365			−0.911635			−0.455817	+	0.890073i	$0.650653\pi$
$798$		0			0
$799$	−2.54309			−0.0899681
$800$	21.6094	−	37.4285i	0.764007	−	1.32330i
$801$		0			0
$802$	6.08073	+	10.5321i	0.214718	+	0.371902i
$803$	0.816934	−	1.41497i	0.0288290	−	0.0499333i
$804$		0			0
$805$	−8.47799	+	22.6732i	−0.298810	+	0.799125i
$806$	2.12747			0.0749368
$807$		0			0
$808$	2.41968	+	4.19100i	0.0851240	+	0.147439i
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	0.997474	+	0.0710338i	$0.0226298\pi$
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	−0.437220	+	0.899355i	$0.644037\pi$
$810$		0			0
$811$	43.3860			1.52349			0.761744	−	0.647878i	$-0.224343\pi$
$811$	43.3860			1.52349			0.761744	+	0.647878i	$0.224343\pi$
$812$	6.73345	−	18.0077i	0.236298	−	0.631945i
$813$		0			0
$814$	−1.04704	+	1.81353i	−0.0366987	+	0.0635641i
$815$	12.3382	+	21.3704i	0.432188	+	0.748571i
$816$		0			0
$817$	14.0113	−	24.2682i	0.490193	−	0.849039i
$818$	−13.2842			−0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	8.19677	−	14.1972i	0.286069	−	0.495487i	−0.686799	−	0.726848i	$-0.740985\pi$
$821$	8.19677	−	14.1972i	0.286069	−	0.495487i	0.972868	+	0.231361i	$0.0743179\pi$
$822$		0			0
$823$	13.1890	+	22.8440i	0.459739	+	0.796292i	0.998947	−	0.0458812i	$-0.0146096\pi$
$823$	13.1890	+	22.8440i	0.459739	+	0.796292i	−0.539208	+	0.842173i	$0.681276\pi$
$824$	−9.03925	+	15.6564i	−0.314897	+	0.545418i
$825$		0			0
$826$	−1.51236	−	1.83476i	−0.0526219	−	0.0638396i
$827$	36.7225			1.27697			0.638484	−	0.769635i	$-0.279562\pi$
$827$	36.7225			1.27697			0.638484	+	0.769635i	$0.279562\pi$
$828$		0			0
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	0.996160	−	0.0875485i	$-0.0279033\pi$
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	−0.573899	+	0.818926i	$0.694570\pi$
$830$	11.2820	+	19.5410i	0.391604	+	0.678279i
$831$		0			0
$832$	3.21734			0.111541
$833$	1.65458	−	0.569599i	0.0573278	−	0.0197354i
$834$		0			0
$835$	−32.5519	+	56.3815i	−1.12650	+	1.95116i
$836$	2.19841	+	3.80776i	0.0760337	+	0.131694i
$837$		0			0
$838$	5.21962	−	9.04065i	0.180309	−	0.312304i
$839$	25.6810			0.886606			0.443303	−	0.896372i	$-0.353807\pi$
$839$	25.6810			0.886606			0.443303	+	0.896372i	$0.353807\pi$
$840$		0			0
$841$	−11.8393			−0.408251
$842$	3.69190	−	6.39456i	0.127231	−	0.220371i
$843$		0			0
$844$	−1.35400	−	2.34519i	−0.0466065	−	0.0807249i
$845$	−21.3577	+	36.9926i	−0.734726	+	1.27258i
$846$		0			0
$847$	26.6254	−	4.45468i	0.914859	−	0.153065i
$848$	25.5653			0.877915
$849$		0			0
$850$	0.535200	+	0.926994i	0.0183572	+	0.0317956i
$851$	−5.86148	−	10.1524i	−0.200929	−	0.348019i
$852$		0			0
$853$	−28.9743			−0.992061			−0.496031	−	0.868305i	$-0.665210\pi$
$853$	−28.9743			−0.992061			−0.496031	+	0.868305i	$0.665210\pi$
$854$	−4.96440	+	13.2766i	−0.169878	+	0.454316i
$855$		0			0
$856$	−10.1459	+	17.5732i	−0.346780	+	0.600640i
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	0.997180	−	0.0750458i	$-0.0239103\pi$
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	−0.563582	+	0.826060i	$0.690577\pi$
$858$		0			0
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	−0.810721	−	0.585433i	$-0.800925\pi$
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	0.912360	+	0.409388i	$0.134258\pi$
$860$	64.6333			2.20398
$861$		0			0
$862$	−7.88621			−0.268605
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	−0.692154	−	0.721750i	$-0.743338\pi$
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	0.971131	+	0.238548i	$0.0766715\pi$
$864$		0			0
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$	−4.05764	+	7.02804i	−0.137884	+	0.238822i
$867$		0			0
$868$	16.4104	−	2.74562i	0.557005	−	0.0931923i
$869$	1.60584			0.0544744
$870$		0			0
$871$	0.615929	+	1.06682i	0.0208700	+	0.0361478i
$872$	−1.97503	−	3.42086i	−0.0668830	−	0.115845i
$873$		0			0
$874$	3.45030			0.116708
$875$	−22.5888	−	27.4042i	−0.763642	−	0.926432i
$876$		0			0
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	−3.85407	−	6.67544i	−0.130068	−	0.225285i
$879$		0			0
$880$	−4.26017	+	7.37883i	−0.143610	+	0.248740i
$881$	26.2582			0.884661			0.442331	−	0.896852i	$-0.354152\pi$
$881$	26.2582			0.884661			0.442331	+	0.896852i	$0.354152\pi$
$882$		0			0
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	−0.262378	+	0.454452i	−0.00882473	+	0.0152849i
$885$		0			0
$886$	0.443815	+	0.768711i	0.0149103	+	0.0258253i
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	−0.701064	−	0.713099i	$-0.747291\pi$
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	0.968093	+	0.250590i	$0.0806245\pi$
$888$		0			0
$889$	−2.13630	−	2.59171i	−0.0716493	−	0.0869232i
$890$	4.40804			0.147758
$891$		0			0
$892$	4.77419	+	8.26914i	0.159852	+	0.276871i
$893$	−14.2844	−	24.7413i	−0.478009	−	0.827935i
$894$		0			0
$895$	27.0857			0.905374
$896$	−29.5996	+	4.95230i	−0.988853	+	0.165445i
$897$		0			0
$898$	3.36364	−	5.82599i	0.112246	−	0.194416i
$899$	7.42583	+	12.8619i	0.247665	+	0.428969i
$900$		0			0
$901$	−1.23608	+	2.14095i	−0.0411797	+	0.0713253i
$902$	2.11643			0.0704695
$903$		0			0
$904$	−29.4615			−0.979875
$905$	20.7829	−	35.9970i	0.690846	−	1.19658i
$906$		0			0
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	−14.0999	+	24.4217i	−0.467922	+	0.810464i
$909$		0			0
$910$	−2.03047	+	5.43021i	−0.0673095	+	0.180010i
$911$	−29.8869			−0.990199			−0.495099	−	0.868836i	$-0.664868\pi$
$911$	−29.8869			−0.990199			−0.495099	+	0.868836i	$0.664868\pi$
$912$		0			0
$913$	−5.49961	−	9.52561i	−0.182011	−	0.315252i
$914$	0.636986	+	1.10329i	0.0210696	+	0.0364937i
$915$		0			0
$916$	17.4857			0.577744
$917$	39.2176	−	6.56148i	1.29508	−	0.216679i
$918$		0			0
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	−0.602292	−	0.798276i	$-0.705746\pi$
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	0.992473	+	0.122462i	$0.0390791\pi$
$920$	8.51579	+	14.7498i	0.280757	+	0.486286i
$921$		0			0
$922$	−8.97196	+	15.5399i	−0.295476	+	0.511779i
$923$	5.91813			0.194798
$924$		0			0
$925$	40.8559			1.34333
$926$	−4.06227	+	7.03606i	−0.133495	+	0.231219i
$927$		0			0
$928$	−10.3667	−	17.9557i	−0.340304	−	0.589423i
$929$	−6.30880	+	10.9272i	−0.206985	+	0.358509i	−0.950763	−	0.309918i	$-0.899698\pi$
$929$	−6.30880	+	10.9272i	−0.206985	+	0.358509i	0.743778	+	0.668426i	$0.233032\pi$
$930$		0			0
$931$	14.8352	+	12.8977i	0.486204	+	0.422705i
$932$	29.0146			0.950405
$933$		0			0
$934$	2.15714	+	3.73627i	0.0705836	+	0.122254i
$935$	−0.411957	−	0.713530i	−0.0134724	−	0.0233349i
$936$		0			0
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$	−0.858974	−	1.04209i	−0.0280465	−	0.0340254i
$939$		0			0
$940$	32.9465	−	57.0651i	1.07460	−	1.86126i
$941$	−25.4699	−	44.1151i	−0.830294	−	1.43811i	−0.897805	−	0.440392i	$-0.854839\pi$
$941$	−25.4699	−	44.1151i	−0.830294	−	1.43811i	0.0675118	−	0.997718i	$-0.478494\pi$
$942$		0			0
$943$	−5.92404	+	10.2607i	−0.192913	+	0.334136i
$944$	4.68525			0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	−13.8399	+	23.9714i	−0.449737	+	0.778967i	−0.998369	−	0.0570968i	$-0.981816\pi$
$947$	−13.8399	+	23.9714i	−0.449737	+	0.778967i	0.548632	+	0.836064i	$0.315149\pi$
$948$		0			0
$949$	1.09530	+	1.89712i	0.0355551	+	0.0615832i
$950$	−6.01236	+	10.4137i	−0.195067	+	0.337866i
$951$		0			0
$952$	0.431217	−	1.15323i	0.0139758	−	0.0373764i
$953$	−27.4017			−0.887628			−0.443814	−	0.896119i	$-0.646375\pi$
$953$	−27.4017			−0.887628			−0.443814	+	0.896119i	$0.646375\pi$
$954$		0			0
$955$	−44.0265	−	76.2561i	−1.42466	−	2.46759i
$956$	19.3162	+	33.4567i	0.624731	+	1.08207i
$957$		0			0
$958$	8.81029			0.284648
$959$	−0.452657	+	1.21057i	−0.0146171	+	0.0390913i
$960$		0			0
$961$	9.07336	−	15.7155i	0.292689	−	0.506952i
$962$	−1.40382	−	2.43149i	−0.0452610	−	0.0783943i
$963$		0			0
$964$	14.6645	−	25.3996i	0.472310	−	0.818066i
$965$	−21.9138			−0.705431
$966$		0			0
$967$	−18.1814			−0.584674			−0.292337	−	0.956315i	$-0.594433\pi$
$967$	−18.1814			−0.584674			−0.292337	+	0.956315i	$0.594433\pi$
$968$	9.49698	−	16.4492i	0.305244	−	0.528699i
$969$		0			0
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	19.7416	−	34.1935i	0.633538	−	1.09732i	−0.353285	−	0.935516i	$-0.614935\pi$
$971$	19.7416	−	34.1935i	0.633538	−	1.09732i	0.986823	−	0.161804i	$-0.0517313\pi$
$972$		0			0
$973$	16.6092	+	20.1499i	0.532466	+	0.645975i
$974$	8.25881			0.264629
$975$		0			0
$976$	−13.9651	−	24.1883i	−0.447012	−	0.774248i
$977$	−5.95782	−	10.3193i	−0.190608	−	0.330142i	0.754844	−	0.655904i	$-0.227712\pi$
$977$	−5.95782	−	10.3193i	−0.190608	−	0.330142i	−0.945452	+	0.325762i	$0.894379\pi$
$978$		0			0
$979$	−2.14878			−0.0686752
$980$	−8.65423	+	44.5069i	−0.276449	+	1.42172i
$981$		0			0
$982$	1.59184	−	2.75715i	0.0507977	−	0.0879842i
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	0.974910	−	0.222601i	$-0.0714546\pi$
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	−0.680233	+	0.732996i	$0.738121\pi$
$984$		0			0
$985$	−28.5588	+	49.4653i	−0.909959	+	1.57609i
$986$	0.513505			0.0163533
$987$		0			0
$988$	−5.89504			−0.187546
$989$	−12.3620	+	21.4117i	−0.393090	+	0.680851i
$990$		0			0
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	0.747399	−	0.664376i	$-0.231302\pi$
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	−0.949066	+	0.315079i	$0.897969\pi$
$992$	8.97181	−	15.5396i	0.284855	−	0.493384i
$993$		0			0
$994$	−6.39905	+	1.07062i	−0.202966	+	0.0339581i
$995$	57.2215			1.81405
$996$		0			0
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	−0.979464	−	0.201617i	$-0.935380\pi$
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	0.315127	−	0.949050i	$-0.397953\pi$
$998$	2.76345	+	4.78644i	0.0874755	+	0.151512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.f.163.3		10
3.2	odd	2		567.2.e.e.163.3		10
7.2	even	3		3969.2.a.z.1.3		5
7.4	even	3	inner	567.2.e.f.487.3		10
7.5	odd	6		3969.2.a.ba.1.3		5
9.2	odd	6		189.2.h.b.37.3		10
9.4	even	3		63.2.g.b.16.3	yes	10
9.5	odd	6		189.2.g.b.100.3		10
9.7	even	3		63.2.h.b.58.3	yes	10
21.2	odd	6		3969.2.a.bc.1.3		5
21.5	even	6		3969.2.a.bb.1.3		5
21.11	odd	6		567.2.e.e.487.3		10
36.7	odd	6		1008.2.q.i.625.3		10
36.11	even	6		3024.2.q.i.2305.1		10
36.23	even	6		3024.2.t.i.289.5		10
36.31	odd	6		1008.2.t.i.961.1		10
63.2	odd	6		1323.2.f.e.442.3		10
63.4	even	3		63.2.h.b.25.3	yes	10
63.5	even	6		1323.2.f.f.883.3		10
63.11	odd	6		189.2.g.b.172.3		10
63.13	odd	6		441.2.g.f.79.3		10
63.16	even	3		441.2.f.e.148.3		10
63.20	even	6		1323.2.h.f.226.3		10
63.23	odd	6		1323.2.f.e.883.3		10
63.25	even	3		63.2.g.b.4.3	✓	10
63.31	odd	6		441.2.h.f.214.3		10
63.32	odd	6		189.2.h.b.46.3		10
63.34	odd	6		441.2.h.f.373.3		10
63.38	even	6		1323.2.g.f.361.3		10
63.40	odd	6		441.2.f.f.295.3		10
63.41	even	6		1323.2.g.f.667.3		10
63.47	even	6		1323.2.f.f.442.3		10
63.52	odd	6		441.2.g.f.67.3		10
63.58	even	3		441.2.f.e.295.3		10
63.59	even	6		1323.2.h.f.802.3		10
63.61	odd	6		441.2.f.f.148.3		10
252.11	even	6		3024.2.t.i.1873.5		10
252.67	odd	6		1008.2.q.i.529.3		10
252.95	even	6		3024.2.q.i.2881.1		10
252.151	odd	6		1008.2.t.i.193.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	63.25	even	3
63.2.g.b.16.3	yes	10	9.4	even	3
63.2.h.b.25.3	yes	10	63.4	even	3
63.2.h.b.58.3	yes	10	9.7	even	3
189.2.g.b.100.3		10	9.5	odd	6
189.2.g.b.172.3		10	63.11	odd	6
189.2.h.b.37.3		10	9.2	odd	6
189.2.h.b.46.3		10	63.32	odd	6
441.2.f.e.148.3		10	63.16	even	3
441.2.f.e.295.3		10	63.58	even	3
441.2.f.f.148.3		10	63.61	odd	6
441.2.f.f.295.3		10	63.40	odd	6
441.2.g.f.67.3		10	63.52	odd	6
441.2.g.f.79.3		10	63.13	odd	6
441.2.h.f.214.3		10	63.31	odd	6
441.2.h.f.373.3		10	63.34	odd	6
567.2.e.e.163.3		10	3.2	odd	2
567.2.e.e.487.3		10	21.11	odd	6
567.2.e.f.163.3		10	1.1	even	1	trivial
567.2.e.f.487.3		10	7.4	even	3	inner
1008.2.q.i.529.3		10	252.67	odd	6
1008.2.q.i.625.3		10	36.7	odd	6
1008.2.t.i.193.1		10	252.151	odd	6
1008.2.t.i.961.1		10	36.31	odd	6
1323.2.f.e.442.3		10	63.2	odd	6
1323.2.f.e.883.3		10	63.23	odd	6
1323.2.f.f.442.3		10	63.47	even	6
1323.2.f.f.883.3		10	63.5	even	6
1323.2.g.f.361.3		10	63.38	even	6
1323.2.g.f.667.3		10	63.41	even	6
1323.2.h.f.226.3		10	63.20	even	6
1323.2.h.f.802.3		10	63.59	even	6
3024.2.q.i.2305.1		10	36.11	even	6
3024.2.q.i.2881.1		10	252.95	even	6
3024.2.t.i.289.5		10	36.23	even	6
3024.2.t.i.1873.5		10	252.11	even	6
3969.2.a.z.1.3		5	7.2	even	3
3969.2.a.ba.1.3		5	7.5	odd	6
3969.2.a.bb.1.3		5	21.5	even	6
3969.2.a.bc.1.3		5	21.2	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247934 - 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} +1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(0.446284 + 0.772987i) q^{11} -1.19671 q^{13} +(1.29396 - 0.216492i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(-0.124991 - 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} +6.47721 q^{20} +0.442596 q^{22} +(-1.23886 + 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(-0.296705 + 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} -4.14255 q^{29} +(-1.79257 - 3.10483i) q^{31} +(2.50249 + 4.33444i) q^{32} -0.123959 q^{34} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(-0.696267 - 1.20597i) q^{38} +(3.43695 - 5.95298i) q^{40} +4.78186 q^{41} +9.97857 q^{43} +(-0.782834 + 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +(5.08653 - 8.81013i) q^{47} +(-1.33611 + 6.87130i) q^{49} -4.28189 q^{50} +(-1.04958 - 1.81793i) q^{52} +(-4.94465 - 8.56438i) q^{53} +3.29588 q^{55} +(3.13268 + 3.80050i) q^{56} +(-1.02708 + 1.77895i) q^{58} +(-0.906186 - 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(-2.20948 + 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +(0.219249 - 0.379751i) q^{68} +(1.69671 - 4.53761i) q^{70} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(1.17306 + 2.03181i) q^{74} +4.92604 q^{76} +(-0.827091 + 2.21194i) q^{77} +(0.899562 - 1.55809i) q^{79} +(4.77293 + 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} -12.3231 q^{83} -0.923082 q^{85} +(2.47403 - 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(-1.20370 + 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} -4.34620 q^{92} +(-2.52225 - 4.36867i) q^{94} +(-5.18489 - 8.98049i) q^{95} -11.0442 q^{97} +(2.61951 + 2.27740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29}+ \cdots + 59 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 5 * q^7 - 6 * q^8 - 7 * q^10 + 4 * q^11 + 16 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + q^19 - 10 * q^20 + 2 * q^22 + 3 * q^23 - q^25 + 11 * q^26 - 2 * q^28 - 14 * q^29 - 3 * q^31 - 2 * q^32 - 6 * q^34 + 5 * q^35 + 20 * q^38 - 3 * q^40 - 10 * q^41 + 14 * q^43 - 10 * q^44 + 3 * q^46 + 27 * q^47 - 17 * q^49 - 38 * q^50 - 10 * q^52 - 21 * q^53 + 4 * q^55 + 27 * q^56 - 10 * q^58 + 30 * q^59 - 14 * q^61 - 12 * q^62 - 50 * q^64 - 11 * q^65 - 2 * q^67 + 27 * q^68 - 11 * q^70 - 6 * q^71 + 15 * q^73 - 36 * q^74 - 10 * q^76 + 20 * q^77 - 4 * q^79 + 20 * q^80 - 5 * q^82 - 18 * q^83 + 12 * q^85 - 8 * q^86 - 18 * q^88 + 28 * q^89 - 4 * q^91 - 54 * q^92 - 3 * q^94 - 14 * q^95 + 24 * q^97 + 59 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more