LMFDB - Embedded newform 600.2.bp.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(53,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 10, 7]))

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

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

chi := DirichletCharacter("600.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bp (of order $20$, degree $8$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	16.0.6879707136000000000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{12} + 81x^{8} - 729x^{4} + 6561 $ x^16 - 9x^12 + 81x^8 - 729*x^4 + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			53.1
Root			$-1.54327 + 0.786335i$ of defining polynomial
Character	$\chi$	$=$	600.53
Dual form			600.2.bp.a.317.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642040 - 1.26007i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-2.04641 - 0.901229i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(3.64268 - 3.64268i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +O(q^{10})$	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-2.04641 - 0.901229i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(3.64268 - 3.64268i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(0.178260 + 3.15725i) q^{10} +(2.04352 - 6.28930i) q^{11} +(3.08654 + 1.57267i) q^{12} +(-6.92880 - 2.25130i) q^{14} +(-0.987277 + 3.74503i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(3.00000 + 3.00000i) q^{18} +(3.86392 - 2.25170i) q^{20} +(-7.21863 - 5.24464i) q^{21} +(-9.23700 + 1.46300i) q^{22} -4.89898i q^{24} +(3.37557 + 3.68856i) q^{25} +(2.35900 + 4.62981i) q^{27} +(1.61175 + 10.1762i) q^{28} +(-3.14375 + 4.32700i) q^{29} +(5.35289 - 1.16042i) q^{30} +(-1.54886 + 1.12531i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-11.3130 - 1.79180i) q^{33} +(-10.7373 + 4.17153i) q^{35} +(1.85410 - 5.70634i) q^{36} +(-5.31809 - 3.42314i) q^{40} +(-1.97399 + 12.4633i) q^{42} +(7.77400 + 10.7000i) q^{44} +(6.67423 + 0.674235i) q^{45} +(-6.17307 + 3.14534i) q^{48} -19.5383i q^{49} +(2.48061 - 6.62167i) q^{50} +(1.93658 + 12.2271i) q^{53} +(4.31932 - 5.94504i) q^{54} +(-9.84997 + 11.0288i) q^{55} +(11.7880 - 8.56446i) q^{56} +(7.47075 + 1.18325i) q^{58} +(3.92149 - 1.27417i) q^{59} +(-4.89898 - 6.00000i) q^{60} +(2.41240 + 1.22918i) q^{62} +(-7.01624 + 13.7702i) q^{63} +(7.60845 + 2.47214i) q^{64} +(5.00558 + 15.4056i) q^{66} +(12.1502 + 10.8515i) q^{70} +(-8.38081 + 1.32739i) q^{72} +(14.9936 - 7.63962i) q^{73} +(5.39551 - 6.77411i) q^{75} +(-15.4661 - 30.3538i) q^{77} +(-2.92068 + 4.01997i) q^{79} +(-0.898979 + 8.89898i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-14.5755 - 2.30854i) q^{83} +(16.9720 - 5.51454i) q^{84} +(8.25412 + 4.20569i) q^{87} +(8.49157 - 16.6656i) q^{88} +(-3.43554 - 8.84291i) q^{90} +(2.34477 + 2.34477i) q^{93} +(7.92672 + 5.75910i) q^{96} +(1.07668 - 0.170529i) q^{97} +(-24.6197 + 12.5444i) q^{98} +19.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8}+O(q^{10}) $ 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8	$ 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 8 q^{10} + 24 q^{11} - 12 q^{15} + 16 q^{16} + 48 q^{18} + 8 q^{20} - 36 q^{21} - 16 q^{22} + 32 q^{28} - 12 q^{30} - 64 q^{32} + 12 q^{33} - 8 q^{35} - 24 q^{36} + 24 q^{42} + 48 q^{45} + 4 q^{50} + 28 q^{55} + 24 q^{56} - 8 q^{58} - 80 q^{59} + 12 q^{63} - 36 q^{66} - 32 q^{70} - 24 q^{72} - 28 q^{73} + 24 q^{75} + 12 q^{77} + 64 q^{80} + 36 q^{81} - 24 q^{83} - 36 q^{87} + 32 q^{88} - 24 q^{93} - 16 q^{97} - 72 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 8 * q^10 + 24 * q^11 - 12 * q^15 + 16 * q^16 + 48 * q^18 + 8 * q^20 - 36 * q^21 - 16 * q^22 + 32 * q^28 - 12 * q^30 - 64 * q^32 + 12 * q^33 - 8 * q^35 - 24 * q^36 + 24 * q^42 + 48 * q^45 + 4 * q^50 + 28 * q^55 + 24 * q^56 - 8 * q^58 - 80 * q^59 + 12 * q^63 - 36 * q^66 - 32 * q^70 - 24 * q^72 - 28 * q^73 + 24 * q^75 + 12 * q^77 + 64 * q^80 + 36 * q^81 - 24 * q^83 - 36 * q^87 + 32 * q^88 - 24 * q^93 - 16 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−0.642040	−	1.26007i	−0.453990	−	0.891007i
$2$	−0.642040	−	1.26007i	−0.453990	−	0.891007i
$3$	−0.270952	−	1.71073i	−0.156434	−	0.987688i
$3$	−0.270952	−	1.71073i	−0.156434	−	0.987688i
$4$	−1.17557	+	1.61803i	−0.587785	+	0.809017i
$5$	−2.04641	−	0.901229i	−0.915182	−	0.403042i
$5$	−2.04641	−	0.901229i	−0.915182	−	0.403042i
$6$	−1.98168	+	1.43977i	−0.809017	+	0.587785i
$7$	3.64268	−	3.64268i	1.37681	−	1.37681i	0.526842	−	0.849963i	$-0.323376\pi$
$7$	3.64268	−	3.64268i	1.37681	−	1.37681i	0.849963	−	0.526842i	$-0.176624\pi$
$8$	2.79360	+	0.442463i	0.987688	+	0.156434i
$9$	−2.85317	+	0.927051i	−0.951057	+	0.309017i
$10$	0.178260	+	3.15725i	0.0563708	+	0.998410i
$11$	2.04352	−	6.28930i	0.616144	−	1.89630i	0.233748	−	0.972297i	$-0.424901\pi$
$11$	2.04352	−	6.28930i	0.616144	−	1.89630i	0.382396	−	0.923999i	$-0.375099\pi$
$12$	3.08654	+	1.57267i	0.891007	+	0.453990i
$13$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$13$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$14$	−6.92880	−	2.25130i	−1.85180	−	0.601686i
$15$	−0.987277	+	3.74503i	−0.254914	+	0.966964i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$17$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	3.86392	−	2.25170i	0.863998	−	0.503495i
$21$	−7.21863	−	5.24464i	−1.57523	−	1.14447i
$22$	−9.23700	+	1.46300i	−1.96934	+	0.311912i
$23$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$23$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$24$		−	4.89898i		−	1.00000i
$25$	3.37557	+	3.68856i	0.675114	+	0.737713i
$26$		0			0
$27$	2.35900	+	4.62981i	0.453990	+	0.891007i
$28$	1.61175	+	10.1762i	0.304593	+	1.92312i
$29$	−3.14375	+	4.32700i	−0.583780	+	0.803504i	−0.994103	−	0.108436i	$-0.965416\pi$
$29$	−3.14375	+	4.32700i	−0.583780	+	0.803504i	0.410323	+	0.911940i	$0.365416\pi$
$30$	5.35289	−	1.16042i	0.977299	−	0.211862i
$31$	−1.54886	+	1.12531i	−0.278183	+	0.202112i	−0.718125	−	0.695915i	$-0.754999\pi$
$31$	−1.54886	+	1.12531i	−0.278183	+	0.202112i	0.439941	+	0.898027i	$0.354999\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	−11.3130	−	1.79180i	−1.96934	−	0.311912i
$34$		0			0
$35$	−10.7373	+	4.17153i	−1.81494	+	0.705117i
$36$	1.85410	−	5.70634i	0.309017	−	0.951057i
$37$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$37$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$38$		0			0
$39$		0			0
$40$	−5.31809	−	3.42314i	−0.840864	−	0.541246i
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$	−1.97399	+	12.4633i	−0.304593	+	1.92312i
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$	7.77400	+	10.7000i	1.17198	+	1.61309i
$45$	6.67423	+	0.674235i	0.994936	+	0.100509i
$46$		0			0
$47$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$47$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$48$	−6.17307	+	3.14534i	−0.891007	+	0.453990i
$49$		−	19.5383i		−	2.79119i
$50$	2.48061	−	6.62167i	0.350812	−	0.936446i
$51$		0			0
$52$		0			0
$53$	1.93658	+	12.2271i	0.266010	+	1.67952i	0.652939	+	0.757411i	$0.273536\pi$
$53$	1.93658	+	12.2271i	0.266010	+	1.67952i	−0.386929	+	0.922110i	$0.626464\pi$
$54$	4.31932	−	5.94504i	0.587785	−	0.809017i
$55$	−9.84997	+	11.0288i	−1.32817	+	1.48712i
$56$	11.7880	−	8.56446i	1.57523	−	1.14447i
$57$		0			0
$58$	7.47075	+	1.18325i	0.980958	+	0.155368i
$59$	3.92149	−	1.27417i	0.510534	−	0.165883i	−0.0424110	−	0.999100i	$-0.513504\pi$
$59$	3.92149	−	1.27417i	0.510534	−	0.165883i	0.552945	+	0.833218i	$0.313504\pi$
$60$	−4.89898	−	6.00000i	−0.632456	−	0.774597i
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$	2.41240	+	1.22918i	0.306376	+	0.156106i
$63$	−7.01624	+	13.7702i	−0.883963	+	1.73488i
$64$	7.60845	+	2.47214i	0.951057	+	0.309017i
$65$		0			0
$66$	5.00558	+	15.4056i	0.616144	+	1.89630i
$67$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$67$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$68$		0			0
$69$		0			0
$70$	12.1502	+	10.8515i	1.45223	+	1.29700i
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	−8.38081	+	1.32739i	−0.987688	+	0.156434i
$73$	14.9936	−	7.63962i	1.75487	−	0.894149i	0.798493	−	0.602004i	$-0.205631\pi$
$73$	14.9936	−	7.63962i	1.75487	−	0.894149i	0.956374	−	0.292145i	$-0.0943690\pi$
$74$		0			0
$75$	5.39551	−	6.77411i	0.623019	−	0.782206i
$76$		0			0
$77$	−15.4661	−	30.3538i	−1.76252	−	3.45914i
$78$		0			0
$79$	−2.92068	+	4.01997i	−0.328602	+	0.452282i	−0.941069	−	0.338214i	$-0.890177\pi$
$79$	−2.92068	+	4.01997i	−0.328602	+	0.452282i	0.612467	+	0.790496i	$0.290177\pi$
$80$	−0.898979	+	8.89898i	−0.100509	+	0.994936i
$81$	7.28115	−	5.29007i	0.809017	−	0.587785i
$82$		0			0
$83$	−14.5755	−	2.30854i	−1.59987	−	0.253395i	−0.708179	−	0.706033i	$-0.750483\pi$
$83$	−14.5755	−	2.30854i	−1.59987	−	0.253395i	−0.891695	+	0.452638i	$0.850483\pi$
$84$	16.9720	−	5.51454i	1.85180	−	0.601686i
$85$		0			0
$86$		0			0
$87$	8.25412	+	4.20569i	0.884935	+	0.450897i
$88$	8.49157	−	16.6656i	0.905204	−	1.77656i
$89$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$89$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$90$	−3.43554	−	8.84291i	−0.362137	−	0.932125i
$91$		0			0
$92$		0			0
$93$	2.34477	+	2.34477i	0.243141	+	0.243141i
$94$		0			0
$95$		0			0
$96$	7.92672	+	5.75910i	0.809017	+	0.587785i
$97$	1.07668	−	0.170529i	0.109320	−	0.0173146i	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	1.07668	−	0.170529i	0.109320	−	0.0173146i	0.210855	+	0.977517i	$0.432375\pi$
$98$	−24.6197	+	12.5444i	−2.48696	+	1.26717i
$99$			19.8389i			1.99388i
$100$	−9.93645	+	1.12562i	−0.993645	+	0.112562i
$101$	−12.0751			−1.20152			−0.600758	−	0.799431i	$-0.705135\pi$
$101$	−12.0751			−1.20152			−0.600758	+	0.799431i	$0.705135\pi$
$102$		0			0
$103$	1.80346	+	11.3866i	0.177700	+	1.12195i	0.901766	+	0.432224i	$0.142271\pi$
$103$	1.80346	+	11.3866i	0.177700	+	1.12195i	−0.724066	+	0.689730i	$0.757729\pi$
$104$		0			0
$105$	10.0456	+	17.2383i	0.980354	+	1.68229i
$106$	14.1637	−	10.2905i	1.37570	−	0.999503i
$107$	9.17588	−	9.17588i	0.887066	−	0.887066i	−0.107174	−	0.994240i	$-0.534180\pi$
$107$	9.17588	−	9.17588i	0.887066	−	0.887066i	0.994240	+	0.107174i	$0.0341803\pi$
$108$	−10.2644	−	1.62571i	−0.987688	−	0.156434i
$109$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$109$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$110$	20.2212	+	5.33076i	1.92801	+	0.508268i
$111$		0			0
$112$	−18.3602	−	9.35499i	−1.73488	−	0.883963i
$113$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$113$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$114$		0			0
$115$		0			0
$116$	−3.30554	−	10.1734i	−0.306911	−	0.944576i
$117$		0			0
$118$	−4.12330	−	4.12330i	−0.379580	−	0.379580i
$119$		0			0
$120$	−4.41510	+	10.0253i	−0.403042	+	0.915182i
$121$	−26.4802	−	19.2390i	−2.40729	−	1.74900i
$122$		0			0
$123$		0			0
$124$		−	3.82899i		−	0.343853i
$125$	−3.58356	−	10.5905i	−0.320523	−	0.947241i
$126$	21.8561			1.94710
$127$	−2.55268	−	5.00992i	−0.226514	−	0.444559i	0.749578	−	0.661916i	$-0.230256\pi$
$127$	−2.55268	−	5.00992i	−0.226514	−	0.444559i	−0.976092	+	0.217357i	$0.930256\pi$
$128$	−1.76985	−	11.1744i	−0.156434	−	0.987688i
$129$		0			0
$130$		0			0
$131$	14.9260	−	10.8443i	1.30409	−	0.947474i	0.304100	−	0.952640i	$-0.401644\pi$
$131$	14.9260	−	10.8443i	1.30409	−	0.947474i	0.999987	+	0.00516600i	$0.00164440\pi$
$132$	16.1984	−	16.1984i	1.40989	−	1.40989i
$133$		0			0
$134$		0			0
$135$	−0.654969	−	11.6005i	−0.0563708	−	0.998410i
$136$		0			0
$137$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$137$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	5.87280	−	22.2773i	0.496342	−	1.88277i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	7.05342	+	9.70820i	0.587785	+	0.809017i
$145$	10.3330	−	6.02157i	0.858110	−	0.500064i
$146$	−19.2530	−	13.9881i	−1.59339	−	1.15766i
$147$	−33.4247	+	5.29395i	−2.75682	+	0.436638i
$148$		0			0
$149$			20.3217i			1.66482i	0.554163	+	0.832408i	$0.313039\pi$
$149$			20.3217i			1.66482i	−0.554163	+	0.832408i	$0.686961\pi$
$150$	−12.0000	−	2.44949i	−0.979796	−	0.200000i
$151$	12.7797			1.04000			0.519999	−	0.854167i	$-0.325932\pi$
$151$	12.7797			1.04000			0.519999	+	0.854167i	$0.325932\pi$
$152$		0			0
$153$		0			0
$154$	−28.3182	+	38.9767i	−2.28195	+	3.14083i
$155$	4.18376	−	0.906971i	0.336048	−	0.0728496i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	6.94066	+	1.09929i	0.552169	+	0.0874550i
$159$	20.3925	−	6.62592i	1.61723	−	0.525470i
$160$	11.7905	−	4.58072i	0.932125	−	0.362137i
$161$		0			0
$162$	−11.3407	−	5.77836i	−0.891007	−	0.453990i
$163$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$163$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$164$		0			0
$165$	21.5361	+	13.8623i	1.67659	+	1.07918i
$166$	6.44915	+	19.8484i	0.500551	+	1.54054i
$167$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$167$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$168$	−17.8454	−	17.8454i	−1.37681	−	1.37681i
$169$	−7.64121	−	10.5172i	−0.587785	−	0.809017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	23.3430	−	11.8939i	1.77474	−	0.904273i	0.846379	−	0.532581i	$-0.178778\pi$
$173$	23.3430	−	11.8939i	1.77474	−	0.904273i	0.928356	−	0.371692i	$-0.121222\pi$
$174$		−	13.1010i		−	0.993186i
$175$	25.7324	+	1.14013i	1.94519	+	0.0861859i
$176$	−26.4519			−1.99388
$177$	−3.24229	−	6.36335i	−0.243705	−	0.478299i
$178$		0			0
$179$	4.33849	−	5.97142i	0.324274	−	0.446325i	−0.615492	−	0.788143i	$-0.711043\pi$
$179$	4.33849	−	5.97142i	0.324274	−	0.446325i	0.939766	+	0.341818i	$0.111043\pi$
$180$	−8.93697	+	10.0065i	−0.666122	+	0.745843i
$181$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$181$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	1.44915	−	4.46001i	0.106257	−	0.327024i
$187$		0			0
$188$		0			0
$189$	25.4580	+	8.27181i	1.85180	+	0.601686i
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	2.16762	−	13.6858i	0.156434	−	0.987688i
$193$	17.0746	+	17.0746i	1.22906	+	1.22906i	0.964321	+	0.264737i	$0.0852853\pi$
$193$	17.0746	+	17.0746i	1.22906	+	1.22906i	0.264737	+	0.964321i	$0.414715\pi$
$194$	−0.906150	−	1.24721i	−0.0650578	−	0.0895444i
$195$		0			0
$196$	31.6136	+	22.9687i	2.25812	+	1.64062i
$197$	11.1659	−	1.76850i	0.795537	−	0.126001i	0.254581	−	0.967051i	$-0.418062\pi$
$197$	11.1659	−	1.76850i	0.795537	−	0.126001i	0.540956	+	0.841051i	$0.318062\pi$
$198$	24.9985	−	12.7374i	1.77656	−	0.905204i
$199$		−	27.6223i		−	1.95809i	−0.203642	−	0.979045i	$-0.565278\pi$
$199$		−	27.6223i		−	1.95809i	0.203642	−	0.979045i	$-0.434722\pi$
$200$	7.79796	+	11.7980i	0.551399	+	0.834242i
$201$		0			0
$202$	7.75269	+	15.2155i	0.545477	+	1.07056i
$203$	4.31021	+	27.2136i	0.302517	+	1.91002i
$204$		0			0
$205$		0			0
$206$	13.1901	−	9.58313i	0.918995	−	0.667689i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	15.2718	−	23.7259i	1.05386	−	1.63724i
$211$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$211$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$212$	−22.0604	−	11.2404i	−1.51512	−	0.771991i
$213$		0			0
$214$	−17.4536	−	5.67101i	−1.19310	−	0.387662i
$215$		0			0
$216$	4.54160	+	13.9776i	0.309017	+	0.951057i
$217$	−1.54285	+	9.74116i	−0.104735	+	0.661273i
$218$		0			0
$219$	−17.1318	−	23.5800i	−1.15766	−	1.59339i
$220$	−6.26564	−	28.9027i	−0.422429	−	1.94862i
$221$		0			0
$222$		0			0
$223$	−14.6962	+	7.48807i	−0.984128	+	0.501438i	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−14.6962	+	7.48807i	−0.984128	+	0.501438i	−0.113584	+	0.993528i	$0.536233\pi$
$224$			29.1415i			1.94710i
$225$	−13.0506	−	7.39477i	−0.870038	−	0.492985i
$226$		0			0
$227$	13.6703	+	26.8294i	0.907327	+	1.78073i	0.487471	+	0.873139i	$0.337919\pi$
$227$	13.6703	+	26.8294i	0.907327	+	1.78073i	0.419856	+	0.907591i	$0.362081\pi$
$228$		0			0
$229$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$229$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$230$		0			0
$231$	−47.7365	+	34.6826i	−3.14083	+	2.28195i
$232$	−10.6969	+	10.6969i	−0.702288	+	0.702288i
$233$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$233$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$234$		0			0
$235$		0			0
$236$	−2.54834	+	7.84297i	−0.165883	+	0.510534i
$237$	7.66844	+	3.90727i	0.498119	+	0.253804i
$238$		0			0
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$	15.4673	−	0.873292i	0.998410	−	0.0563708i
$241$	−5.53211	−	17.0261i	−0.356355	−	1.09675i	−0.955220	−	0.295897i	$-0.904381\pi$
$241$	−5.53211	−	17.0261i	−0.356355	−	1.09675i	0.598865	−	0.800850i	$-0.295619\pi$
$242$	−7.24120	+	45.7191i	−0.465482	+	2.93894i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$		0			0
$245$	−17.6085	+	39.9833i	−1.12496	+	2.55444i
$246$		0			0
$247$		0			0
$248$	−4.82481	+	2.45836i	−0.306376	+	0.156106i
$249$			25.5603i			1.61982i
$250$	−11.0440	+	11.3150i	−0.698483	+	0.715626i
$251$	−10.4644			−0.660504			−0.330252	−	0.943893i	$-0.607134\pi$
$251$	−10.4644			−0.660504			−0.330252	+	0.943893i	$0.607134\pi$
$252$	−14.0325	−	27.5403i	−0.883963	−	1.73488i
$253$		0			0
$254$	−4.67395	+	6.43314i	−0.293270	+	0.403651i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$257$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.95830	−	15.2601i	0.306911	−	0.944576i
$262$	−23.2477	−	11.8453i	−1.43625	−	0.731805i
$263$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$263$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$264$	−30.8112	−	10.0112i	−1.89630	−	0.616144i
$265$	7.05637	−	26.7669i	0.433470	−	1.64428i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.17243	−	4.36648i	−0.193426	−	0.266229i	0.701277	−	0.712888i	$-0.252613\pi$
$269$	−3.17243	−	4.36648i	−0.193426	−	0.266229i	−0.894704	+	0.446660i	$0.852613\pi$
$270$	−14.1969	+	8.27327i	−0.863998	+	0.503495i
$271$	2.75117	+	1.99884i	0.167122	+	0.121421i	0.668202	−	0.743980i	$-0.267064\pi$
$271$	2.75117	+	1.99884i	0.167122	+	0.121421i	−0.501081	+	0.865401i	$0.667064\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	30.0965	−	13.6923i	1.81489	−	0.825679i
$276$		0			0
$277$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$277$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$278$		0			0
$279$	3.37594	−	4.64658i	0.202112	−	0.278183i
$280$	−31.8416	+	6.90273i	−1.90290	+	0.412517i
$281$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$281$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$282$		0			0
$283$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$283$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	7.70447	−	15.1209i	0.453990	−	0.891007i
$289$	−16.1680	−	5.25329i	−0.951057	−	0.309017i
$290$	−14.2218	−	9.15428i	−0.835135	−	0.537558i
$291$	−0.583458	−	1.79570i	−0.0342029	−	0.105266i
$292$	−5.26486	+	33.2410i	−0.308103	+	1.94528i
$293$	−16.3230	−	16.3230i	−0.953598	−	0.953598i	0.0453720	−	0.998970i	$-0.485553\pi$
$293$	−16.3230	−	16.3230i	−0.953598	−	0.953598i	−0.998970	+	0.0453720i	$0.985553\pi$
$294$	28.1307	+	38.7186i	1.64062	+	2.25812i
$295$	−9.17328	−	0.926689i	−0.534089	−	0.0539539i
$296$		0			0
$297$	33.9389	−	5.37540i	1.96934	−	0.311912i
$298$	25.6068	−	13.0473i	1.48336	−	0.755811i
$299$		0			0
$300$	4.61794	+	16.6936i	0.266617	+	0.963803i
$301$		0			0
$302$	−8.20508	−	16.1034i	−0.472149	−	0.926645i
$303$	3.27178	+	20.6572i	0.187959	+	1.18672i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	67.2950	+	10.6585i	3.83449	+	0.607323i
$309$	18.9907	−	6.17045i	1.08034	−	0.351025i
$310$	−3.82899	−	4.68954i	−0.217472	−	0.266348i
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$		0			0
$313$	−11.7339	+	23.0290i	−0.663237	+	1.30168i	0.276907	+	0.960897i	$0.410691\pi$
$313$	−11.7339	+	23.0290i	−0.663237	+	1.30168i	−0.940144	+	0.340779i	$0.889309\pi$
$314$		0			0
$315$	26.7682	−	21.8561i	1.50821	−	1.23145i
$316$	−3.07099	−	9.45153i	−0.172757	−	0.531690i
$317$	−4.08093	+	25.7660i	−0.229208	+	1.44716i	0.557676	+	0.830059i	$0.311693\pi$
$317$	−4.08093	+	25.7660i	−0.229208	+	1.44716i	−0.786884	+	0.617102i	$0.788307\pi$
$318$	−21.4419	−	21.4419i	−1.20240	−	1.20240i
$319$	20.7895	+	28.6143i	1.16399	+	1.60209i
$320$	−13.3420	−	11.9160i	−0.745843	−	0.666122i
$321$	−18.1836	−	13.2112i	−1.01491	−	0.737377i
$322$		0			0
$323$		0			0
$324$			18.0000i			1.00000i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	3.64050	−	36.0373i	0.200403	−	1.98379i
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$	20.8699	−	20.8699i	1.14538	−	1.14538i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−11.0291	+	33.9440i	−0.601686	+	1.85180i
$337$	23.4578	+	11.9524i	1.27783	+	0.651087i	0.955347	−	0.295488i	$-0.0954822\pi$
$337$	23.4578	+	11.9524i	1.27783	+	0.651087i	0.322484	+	0.946575i	$0.395482\pi$
$338$	−8.34651	+	16.3810i	−0.453990	+	0.891007i
$339$		0			0
$340$		0			0
$341$	3.91230	+	12.0408i	0.211863	+	0.652048i
$342$		0			0
$343$	−45.6731	−	45.6731i	−2.46611	−	2.46611i
$344$		0			0
$345$		0			0
$346$	−29.9743	−	21.7776i	−1.61143	−	1.17077i
$347$	19.1677	−	3.03587i	1.02898	−	0.162974i	0.380954	−	0.924594i	$-0.375596\pi$
$347$	19.1677	−	3.03587i	1.02898	−	0.162974i	0.648024	+	0.761620i	$0.275596\pi$
$348$	−16.5082	+	8.41137i	−0.884935	+	0.450897i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−15.0846	−	33.1568i	−0.806305	−	1.77230i
$351$		0			0
$352$	16.9831	+	33.3313i	0.905204	+	1.77656i
$353$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$353$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$354$	−5.93661	+	8.17105i	−0.315527	+	0.434286i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−10.3099	−	1.63293i	−0.544896	−	0.0863030i
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	18.3468	+	4.83665i	0.966964	+	0.254914i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$		0			0
$363$	−25.7377	+	50.5132i	−1.35088	+	2.65125i
$364$		0			0
$365$	−37.5680	+	2.12111i	−1.96640	+	0.111024i
$366$		0			0
$367$	5.75144	−	36.3131i	0.300223	−	1.89553i	−0.127862	−	0.991792i	$-0.540812\pi$
$367$	5.75144	−	36.3131i	0.300223	−	1.89553i	0.428085	−	0.903739i	$-0.359188\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	51.5938	+	37.4851i	2.67862	+	1.94613i
$372$	−6.55035	+	1.03747i	−0.339620	+	0.0537905i
$373$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$373$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$374$		0			0
$375$	−17.1464	+	9.00000i	−0.885438	+	0.464758i
$376$		0			0
$377$		0			0
$378$	−5.92197	−	37.3898i	−0.304593	−	1.92312i
$379$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$379$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$380$		0			0
$381$	−7.87895	+	5.72439i	−0.403651	+	0.293270i
$382$		0			0
$383$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$383$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$384$	−18.6368	+	6.05547i	−0.951057	+	0.309017i
$385$	4.29410	+	76.0548i	0.218847	+	3.87611i
$386$	10.5527	−	32.4779i	0.537118	−	1.65308i
$387$		0			0
$388$	−0.989790	+	1.94257i	−0.0502490	+	0.0986192i
$389$	15.8949	+	5.16458i	0.805906	+	0.261855i	0.682863	−	0.730547i	$-0.260735\pi$
$389$	15.8949	+	5.16458i	0.805906	+	0.261855i	0.123043	+	0.992401i	$0.460735\pi$
$390$		0			0
$391$		0			0
$392$	8.64498	−	54.5823i	0.436638	−	2.75682i
$393$	−22.5959	−	22.5959i	−1.13981	−	1.13981i
$394$	−9.39739	−	12.9344i	−0.473434	−	0.651626i
$395$	9.59983	−	5.59430i	0.483020	−	0.281480i
$396$	−32.1000	−	23.3220i	−1.61309	−	1.17198i
$397$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$397$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$398$	−34.8061	+	17.7346i	−1.74467	+	0.888955i
$399$		0			0
$400$	9.85970	−	17.4008i	0.492985	−	0.870038i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	14.1951	−	19.5379i	0.706234	−	0.972047i
$405$	−19.6678	+	4.26365i	−0.977299	+	0.211862i
$406$	31.5238	−	22.9034i	1.56450	−	1.13668i
$407$		0			0
$408$		0			0
$409$	−2.47311	+	0.803561i	−0.122287	+	0.0397335i	−0.369521	−	0.929222i	$-0.620478\pi$
$409$	−2.47311	+	0.803561i	−0.122287	+	0.0397335i	0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$	−20.5440	−	10.4677i	−1.01213	−	0.515706i
$413$	9.64335	−	18.9261i	0.474518	−	0.931294i
$414$		0			0
$415$	27.7470	+	17.8601i	1.36205	+	0.876719i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.67427	−	13.3155i	−0.472619	−	0.650504i	0.504447	−	0.863443i	$-0.331697\pi$
$419$	−9.67427	−	13.3155i	−0.472619	−	0.650504i	−0.977066	+	0.212939i	$0.931697\pi$
$420$	−39.7015	−	4.01067i	−1.93724	−	0.195701i
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$		0			0
$423$		0			0
$424$			35.0145i			1.70046i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.05999	+	25.6338i	0.196247	+	1.23906i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	14.6969	−	14.6969i	0.707107	−	0.707107i
$433$	−29.8942	−	4.73477i	−1.43662	−	0.227539i	−0.610941	−	0.791676i	$-0.709209\pi$
$433$	−29.8942	−	4.73477i	−1.43662	−	0.227539i	−0.825681	+	0.564137i	$0.809209\pi$
$434$	13.2651	−	4.31011i	0.636747	−	0.206892i
$435$	−13.1010	−	16.0454i	−0.628146	−	0.769318i
$436$		0			0
$437$		0			0
$438$	−18.7132	+	36.7266i	−0.894149	+	1.75487i
$439$	−32.1482	−	10.4456i	−1.53435	−	0.498540i	−0.584539	−	0.811366i	$-0.698725\pi$
$439$	−32.1482	−	10.4456i	−1.53435	−	0.498540i	−0.949811	+	0.312825i	$0.898725\pi$
$440$	−32.3968	+	26.4519i	−1.54446	+	1.26104i
$441$	18.1130	+	55.7461i	0.862524	+	2.65458i
$442$		0			0
$443$	6.07940	+	6.07940i	0.288841	+	0.288841i	0.836622	−	0.547781i	$-0.184527\pi$
$443$	6.07940	+	6.07940i	0.288841	+	0.288841i	−0.547781	+	0.836622i	$0.684527\pi$
$444$		0			0
$445$		0			0
$446$	18.8710	+	13.7106i	0.893570	+	0.649217i
$447$	34.7648	−	5.50621i	1.64432	−	0.260435i
$448$	36.7204	−	18.7100i	1.73488	−	0.883963i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−0.938977	+	21.1924i	−0.0442638	+	0.999020i
$451$		0			0
$452$		0			0
$453$	−3.46269	−	21.8626i	−0.162691	−	1.02719i
$454$	25.0302	−	34.4511i	1.17472	−	1.61687i
$455$		0			0
$456$		0			0
$457$	0.147398	−	0.147398i	0.00689497	−	0.00689497i	−0.703651	−	0.710546i	$-0.748448\pi$
$457$	0.147398	−	0.147398i	0.00689497	−	0.00689497i	0.710546	+	0.703651i	$0.248448\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.6731	−	32.8483i	0.497094	−	1.52990i	−0.316574	−	0.948568i	$-0.602533\pi$
$461$	10.6731	−	32.8483i	0.497094	−	1.52990i	0.813668	−	0.581330i	$-0.197467\pi$
$462$	74.3514	+	37.8839i	3.45914	+	1.76252i
$463$	−2.66217	+	5.22480i	−0.123722	+	0.242817i	−0.944557	−	0.328348i	$-0.893508\pi$
$463$	−2.66217	+	5.22480i	−0.123722	+	0.242817i	0.820835	+	0.571165i	$0.193508\pi$
$464$	20.3468	+	6.61107i	0.944576	+	0.306911i
$465$	−2.68518	−	6.91152i	−0.124522	−	0.320514i
$466$		0			0
$467$	−0.662709	+	4.18418i	−0.0306665	+	0.193621i	−0.998266	−	0.0588709i	$-0.981250\pi$
$467$	−0.662709	+	4.18418i	−0.0306665	+	0.193621i	0.967599	+	0.252492i	$0.0812500\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	11.5189	−	1.82441i	0.530198	−	0.0839752i
$473$		0			0
$474$		−	12.1714i		−	0.559052i
$475$		0			0
$476$		0			0
$477$	−16.8605	−	33.0907i	−0.771991	−	1.51512i
$478$		0			0
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$	−11.0310	−	18.9292i	−0.503495	−	0.863998i
$481$		0			0
$482$	−17.9023	+	17.9023i	−0.815427	+	0.815427i
$483$		0			0
$484$	62.2586	−	20.2290i	2.82994	−	0.919502i
$485$	−2.35701	−	0.621362i	−0.107026	−	0.0282146i
$486$	−6.81241	+	20.9664i	−0.309017	+	0.951057i
$487$	35.8124	+	18.2473i	1.62281	+	0.826865i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$	35.8124	+	18.2473i	1.62281	+	0.826865i	0.623842	+	0.781551i	$0.285571\pi$
$488$		0			0
$489$		0			0
$490$	61.6873	−	3.48290i	2.78675	−	0.157341i
$491$	8.74821	+	26.9242i	0.394801	+	1.21507i	0.929116	+	0.369787i	$0.120569\pi$
$491$	8.74821	+	26.9242i	0.394801	+	1.21507i	−0.534315	+	0.845285i	$0.679431\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	17.8794	−	40.5985i	0.803619	−	1.82477i
$496$	6.19544	+	4.50125i	0.278183	+	0.202112i
$497$		0			0
$498$	32.2078	−	16.4107i	1.44327	−	0.735381i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	21.3485	+	6.65153i	0.954733	+	0.297465i
$501$		0			0
$502$	6.71853	+	13.1859i	0.299863	+	0.588513i
$503$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$503$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$504$	−25.6934	+	35.3639i	−1.14447	+	1.57523i
$505$	24.7106	+	10.8824i	1.09961	+	0.484261i
$506$		0			0
$507$	−15.9217	+	15.9217i	−0.707107	+	0.707107i
$508$	11.1071	+	1.75919i	0.492797	+	0.0780514i
$509$	−21.8409	+	7.09653i	−0.968079	+	0.314548i	−0.750040	−	0.661392i	$-0.769966\pi$
$509$	−21.8409	+	7.09653i	−0.968079	+	0.314548i	−0.218039	+	0.975940i	$0.569966\pi$
$510$		0			0
$511$	26.7882	−	82.4456i	1.18504	−	3.64718i
$512$	20.1612	+	10.2726i	0.891007	+	0.453990i
$513$		0			0
$514$		0			0
$515$	6.57132	−	24.9269i	0.289567	−	1.09841i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−26.6720	−	36.7108i	−1.17077	−	1.61143i
$520$		0			0
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$	−22.4123	+	3.54975i	−0.980958	+	0.155368i
$523$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$523$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$524$			36.8990i			1.61194i
$525$	−5.02181	−	44.3301i	−0.219170	−	1.93472i
$526$		0			0
$527$		0			0
$528$	7.16719	+	45.2519i	0.311912	+	1.96934i
$529$	13.5191	−	18.6074i	0.587785	−	0.809017i
$530$	−38.2588	+	8.29387i	−1.66185	+	0.360263i
$531$	−10.0074	+	7.27084i	−0.434286	+	0.315527i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−27.0472	+	10.5080i	−1.16935	+	0.454302i
$536$		0			0
$537$	−11.3910	−	5.80400i	−0.491558	−	0.250461i
$538$	−3.46525	+	6.80094i	−0.149398	+	0.293210i
$539$	−122.882	−	39.9269i	−5.29291	−	1.71977i
$540$	19.5399	+	12.5774i	0.840864	+	0.541246i
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$	0.752328	−	4.75001i	0.0323153	−	0.204031i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$547$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$548$		0			0
$549$		0			0
$550$	−36.5765	−	29.1328i	−1.55963	−	1.24223i
$551$		0			0
$552$		0			0
$553$	4.00437	+	25.2826i	0.170283	+	1.07513i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	31.6397	−	31.6397i	1.34062	−	1.34062i	0.445170	−	0.895446i	$-0.353143\pi$
$557$	31.6397	−	31.6397i	1.34062	−	1.34062i	0.895446	−	0.445170i	$-0.146857\pi$
$558$	−8.02251	−	1.27064i	−0.339620	−	0.0537905i
$559$		0			0
$560$	29.1415	+	35.6909i	1.23145	+	1.50821i
$561$		0			0
$562$		0			0
$563$	21.5431	−	42.2807i	0.907934	−	1.78192i	0.444864	−	0.895598i	$-0.353252\pi$
$563$	21.5431	−	42.2807i	0.907934	−	1.78192i	0.463070	−	0.886322i	$-0.346748\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7.25290	−	45.7930i	0.304593	−	1.92312i
$568$		0			0
$569$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$569$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$570$		0			0
$571$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$571$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	−10.4815	−	20.5711i	−0.436350	−	0.856386i	−0.999548	−	0.0300636i	$-0.990429\pi$
$577$	−10.4815	−	20.5711i	−0.436350	−	0.856386i	0.563198	−	0.826322i	$-0.309571\pi$
$578$	3.76094	+	23.7456i	0.156434	+	0.987688i
$579$	24.5836	−	33.8364i	1.02166	−	1.40619i
$580$	−2.40408	+	23.7980i	−0.0998241	+	0.988156i
$581$	−61.5034	+	44.6848i	−2.55159	+	1.85384i
$582$	−1.88811	+	1.88811i	−0.0782646	+	0.0782646i
$583$	80.8573	+	12.8065i	3.34877	+	0.530393i
$584$	45.2664	−	14.7079i	1.87314	−	0.608619i
$585$		0			0
$586$	−10.0882	+	31.0481i	−0.416738	+	1.28259i
$587$	27.1376	+	13.8273i	1.12009	+	0.570715i	0.913144	−	0.407638i	$-0.133647\pi$
$587$	27.1376	+	13.8273i	1.12009	+	0.570715i	0.206947	+	0.978352i	$0.433647\pi$
$588$	30.7273	−	60.3057i	1.26717	−	2.48696i
$589$		0			0
$590$	4.72191	+	12.1540i	0.194398	+	0.500371i
$591$	−6.05085	−	18.6226i	−0.248899	−	0.766032i
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$	−28.5635	−	39.3143i	−1.17198	−	1.61309i
$595$		0			0
$596$	−32.8812	−	23.8896i	−1.34687	−	0.978555i
$597$	−47.2541	+	7.48432i	−1.93398	+	0.306313i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	18.0702	−	16.5369i	0.737713	−	0.675114i
$601$	−45.9740			−1.87532			−0.937660	−	0.347554i	$-0.887012\pi$
$601$	−45.9740			−1.87532			−0.937660	+	0.347554i	$0.887012\pi$
$602$		0			0
$603$		0			0
$604$	−15.0234	+	20.6780i	−0.611295	+	0.841376i
$605$	36.8505	+	63.2355i	1.49819	+	2.57089i
$606$	23.9290	−	17.3854i	0.972047	−	0.706234i
$607$	−28.0148	+	28.0148i	−1.13709	+	1.13709i	−0.148117	+	0.988970i	$0.547321\pi$
$607$	−28.0148	+	28.0148i	−1.13709	+	1.13709i	−0.988970	+	0.148117i	$0.952679\pi$
$608$		0			0
$609$	45.3872	−	14.7472i	1.83918	−	0.597586i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$613$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$614$		0			0
$615$		0			0
$616$	−29.7756	−	91.6398i	−1.19969	−	3.69227i
$617$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$617$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$618$	−19.9680	−	19.9680i	−0.803231	−	0.803231i
$619$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$619$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$620$	−3.45080	+	7.83568i	−0.138587	+	0.314688i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.21102	+	24.9020i	−0.0884409	+	0.996081i
$626$	36.5518			1.46090
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−44.7265	−	19.6974i	−1.78195	−	0.784762i
$631$	−3.96336	+	2.87955i	−0.157779	+	0.114633i	−0.663873	−	0.747845i	$-0.731089\pi$
$631$	−3.96336	+	2.87955i	−0.157779	+	0.114633i	0.506095	+	0.862478i	$0.331089\pi$
$632$	−9.93792	+	9.93792i	−0.395309	+	0.395309i
$633$		0			0
$634$	35.0871	−	11.4005i	1.39349	−	0.452772i
$635$	0.708744	+	12.5529i	0.0281256	+	0.498147i
$636$	−13.2518	+	40.7850i	−0.525470	+	1.61723i
$637$		0			0
$638$	22.7084	−	44.5678i	0.899036	−	1.76446i
$639$		0			0
$640$	−6.44887	+	24.4625i	−0.254914	+	0.966964i
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$	−4.97245	+	31.3948i	−0.196247	+	1.23906i
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$647$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$648$	22.6813	−	11.5567i	0.891007	−	0.453990i
$649$		−	27.2672i		−	1.07033i
$650$		0			0
$651$	17.0825			0.669516
$652$		0			0
$653$	−7.67795	−	48.4766i	−0.300461	−	1.89704i	−0.425622	−	0.904901i	$-0.639945\pi$
$653$	−7.67795	−	48.4766i	−0.300461	−	1.89704i	0.125160	−	0.992137i	$-0.460055\pi$
$654$		0			0
$655$	−40.3178	+	8.74024i	−1.57535	+	0.341509i
$656$		0			0
$657$	−35.6969	+	35.6969i	−1.39267	+	1.39267i
$658$		0			0
$659$	29.5109	−	9.58867i	1.14958	−	0.373522i	0.328596	−	0.944471i	$-0.393425\pi$
$659$	29.5109	−	9.58867i	1.14958	−	0.373522i	0.820985	+	0.570949i	$0.193425\pi$
$660$	−47.7470	+	18.5501i	−1.85855	+	0.722060i
$661$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$661$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$662$		0			0
$663$		0			0
$664$	−39.6969	−	12.8983i	−1.54054	−	0.500551i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	16.7920	+	23.1122i	0.649217	+	0.893570i
$670$		0			0
$671$		0			0
$672$	49.8531	−	7.89595i	1.92312	−	0.304593i
$673$	29.7512	−	15.1590i	1.14682	−	0.584336i	0.225928	−	0.974144i	$-0.427459\pi$
$673$	29.7512	−	15.1590i	1.14682	−	0.584336i	0.920896	+	0.389808i	$0.127459\pi$
$674$		−	37.2325i		−	1.43414i
$675$	−9.11435	+	24.3296i	−0.350812	+	0.936446i
$676$	26.0000			1.00000
$677$	14.9047	+	29.2522i	0.572835	+	1.12425i	0.977726	+	0.209887i	$0.0673095\pi$
$677$	14.9047	+	29.2522i	0.572835	+	1.12425i	−0.404891	+	0.914365i	$0.632690\pi$
$678$		0			0
$679$	3.30082	−	4.54319i	0.126674	−	0.174352i
$680$		0			0
$681$	42.1938	−	30.6556i	1.61687	−	1.17472i
$682$	12.6605	−	12.6605i	0.484795	−	0.484795i
$683$	−47.0834	−	7.45728i	−1.80160	−	0.285345i	−0.836639	−	0.547755i	$-0.815483\pi$
$683$	−47.0834	−	7.45728i	−1.80160	−	0.285345i	−0.964956	+	0.262410i	$0.915483\pi$
$684$		0			0
$685$		0			0
$686$	−28.2275	+	86.8754i	−1.07773	+	3.31692i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$	−8.19668	+	51.7518i	−0.311591	+	1.96731i
$693$	72.2668	+	72.2668i	2.74519	+	2.74519i
$694$	−16.1319	−	22.2036i	−0.612358	−	0.842838i
$695$		0			0
$696$	21.1979	+	15.4012i	0.803504	+	0.583780i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−32.0951	+	40.2956i	−1.21308	+	1.52303i
$701$	−52.9444			−1.99968			−0.999841	−	0.0178345i	$-0.994323\pi$
$701$	−52.9444			−1.99968			−0.999841	+	0.0178345i	$0.994323\pi$
$702$		0			0
$703$		0			0
$704$	31.0960	−	42.8000i	1.17198	−	1.61309i
$705$		0			0
$706$		0			0
$707$	−43.9857	+	43.9857i	−1.65425	+	1.65425i
$708$	14.1077	+	2.23443i	0.530198	+	0.0839752i
$709$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$709$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$710$		0			0
$711$	4.60648	−	14.1773i	0.172757	−	0.531690i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	4.56176	+	14.0397i	0.170481	+	0.524687i
$717$		0			0
$718$		0			0
$719$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$719$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$720$	−5.68487	−	26.2237i	−0.211862	−	0.977299i
$721$	48.0472	+	34.9083i	1.78937	+	1.30005i
$722$	26.5392	−	4.20340i	0.987688	−	0.156434i
$723$	−27.6280	+	14.0772i	−1.02750	+	0.523536i
$724$		0			0
$725$	−26.5724	+	3.01018i	−0.986874	+	0.111795i
$726$	80.1749			2.97557
$727$	17.9414	+	35.2120i	0.665410	+	1.30594i	0.938941	+	0.344077i	$0.111808\pi$
$727$	17.9414	+	35.2120i	0.665410	+	1.30594i	−0.273532	+	0.961863i	$0.588192\pi$
$728$		0			0
$729$	−15.8702	+	21.8435i	−0.587785	+	0.809017i
$730$	26.7929	+	45.9767i	0.991651	+	1.70167i
$731$		0			0
$732$		0			0
$733$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$733$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$734$	−49.4499	+	16.0672i	−1.82523	+	0.593053i
$735$	73.1716	+	19.2897i	2.69898	+	0.711512i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$		0			0
$741$		0			0
$742$	14.1087	−	89.0789i	0.517947	−	3.27019i
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$	5.51288	+	7.58783i	0.202112	+	0.278183i
$745$	18.3145	−	41.5865i	0.670991	−	1.52361i
$746$		0			0
$747$	43.7266	−	6.92562i	1.59987	−	0.253395i
$748$		0			0
$749$		−	66.8497i		−	2.44263i
$750$	22.3493	+	15.8274i	0.816083	+	0.577935i
$751$	−37.7191			−1.37639			−0.688194	−	0.725526i	$-0.741596\pi$
$751$	−37.7191			−1.37639			−0.688194	+	0.725526i	$0.741596\pi$
$752$		0			0
$753$	2.83534	+	17.9016i	0.103326	+	0.652372i
$754$		0			0
$755$	−26.1525	−	11.5174i	−0.951787	−	0.419163i
$756$	−43.3118	+	31.4679i	−1.57523	+	1.14447i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$761$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$762$	12.2718	+	6.25277i	0.444559	+	0.226514i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	19.5959	+	19.5959i	0.707107	+	0.707107i
$769$	29.2893	+	40.3133i	1.05620	+	1.45373i	0.883309	+	0.468792i	$0.155311\pi$
$769$	29.2893	+	40.3133i	1.05620	+	1.45373i	0.172890	+	0.984941i	$0.444689\pi$
$770$	93.0776	−	54.2411i	3.35429	−	1.95471i
$771$		0			0
$772$	−47.6997	+	7.55490i	−1.71675	+	0.271907i
$773$	38.5807	−	19.6578i	1.38765	−	0.707044i	0.408993	−	0.912538i	$-0.365880\pi$
$773$	38.5807	−	19.6578i	1.38765	−	0.707044i	0.978658	+	0.205494i	$0.0658802\pi$
$774$		0			0
$775$	−9.37907	−	1.91449i	−0.336906	−	0.0687707i
$776$	3.08327			0.110683
$777$		0			0
$778$	−3.69743	−	23.3447i	−0.132559	−	0.836947i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−27.4493	−	4.34754i	−0.980958	−	0.155368i
$784$	−74.3281	+	24.1507i	−2.65458	+	0.862524i
$785$		0			0
$786$	−13.9650	+	42.9800i	−0.498117	+	1.53305i
$787$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$787$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$788$	−10.2648	+	20.1458i	−0.365668	+	0.717664i
$789$		0			0
$790$	−13.2127	−	8.50472i	−0.470087	−	0.302584i
$791$		0			0
$792$	−8.77798	+	55.4220i	−0.311912	+	1.96934i
$793$		0			0
$794$		0			0
$795$	−47.7028	−	4.81896i	−1.69184	−	0.170911i
$796$	44.6938	+	32.4719i	1.58413	+	1.15094i
$797$	0.132179	−	0.0209351i	0.00468203	−	0.000741560i	−0.154093	−	0.988056i	$-0.549246\pi$
$797$	0.132179	−	0.0209351i	0.00468203	−	0.000741560i	0.158775	+	0.987315i	$0.449246\pi$
$798$		0			0
$799$		0			0
$800$	−28.2565	−	1.25197i	−0.999020	−	0.0442638i
$801$		0			0
$802$		0			0
$803$	−17.4082	−	109.911i	−0.614321	−	3.87867i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.61027	+	6.61027i	−0.232692	+	0.232692i
$808$	−33.7330	−	5.34279i	−1.18672	−	0.187959i
$809$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$809$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$810$	18.0000	+	22.0454i	0.632456	+	0.774597i
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$	−49.0995	−	25.0174i	−1.72305	−	0.877940i
$813$	2.67404	−	5.24809i	0.0937826	−	0.184059i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	2.60038	+	2.60038i	0.0909201	+	0.0909201i
$819$		0			0
$820$		0			0
$821$	30.9974	+	22.5210i	1.08182	+	0.785987i	0.977999	−	0.208609i	$-0.0668936\pi$
$821$	30.9974	+	22.5210i	1.08182	+	0.785987i	0.103819	+	0.994596i	$0.466894\pi$
$822$		0			0
$823$	45.8322	−	23.3527i	1.59761	−	0.814024i	0.597687	−	0.801730i	$-0.296087\pi$
$823$	45.8322	−	23.3527i	1.59761	−	0.814024i	0.999924	−	0.0122940i	$-0.00391341\pi$
$824$			32.6076i			1.13594i
$825$	−31.5786	−	47.7770i	−1.09943	−	1.66338i
$826$	−30.0397			−1.04522
$827$	11.2783	+	22.1349i	0.392185	+	0.769707i	0.999697	−	0.0246037i	$-0.00783240\pi$
$827$	11.2783	+	22.1349i	0.392185	+	0.769707i	−0.607512	+	0.794310i	$0.707832\pi$
$828$		0			0
$829$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$829$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$830$	4.69040	−	46.4301i	0.162806	−	1.61161i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.86374	−	4.51630i	−0.306376	−	0.156106i
$838$	−10.5672	+	20.7394i	−0.365039	+	0.716429i
$839$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$839$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$840$	20.4362	+	52.6019i	0.705117	+	1.81494i
$841$	0.121715	+	0.374599i	0.00419706	+	0.0129172i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.15861	+	28.4090i	0.211862	+	0.977299i
$846$		0			0
$847$	−166.540	+	26.3774i	−5.72239	+	0.906338i
$848$	44.1209	−	22.4807i	1.51512	−	0.771991i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$853$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$854$		0			0
$855$		0			0
$856$	29.6938	−	21.5738i	1.01491	−	0.737377i
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$859$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$863$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$864$	−27.9552	−	9.08321i	−0.951057	−	0.309017i
$865$	−58.4884	+	3.30229i	−1.98866	+	0.112281i
$866$	13.2271	+	40.7088i	0.449475	+	1.38334i
$867$	−4.60619	+	29.0823i	−0.156434	+	0.987688i
$868$	−13.9478	−	13.9478i	−0.473419	−	0.473419i
$869$	19.3144	+	26.5839i	0.655195	+	0.901798i
$870$	−11.8070	+	26.8100i	−0.400295	+	0.908945i
$871$		0			0
$872$		0			0
$873$	−2.91386	+	1.48469i	−0.0986192	+	0.0502490i
$874$		0			0
$875$	−51.6315	−	25.5240i	−1.74546	−	0.862868i
$876$	58.2929			1.96953
$877$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$877$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$878$	7.47821	+	47.2156i	0.252377	+	1.59345i
$879$	−23.5014	+	32.3469i	−0.792682	+	1.09103i
$880$	54.1313	+	23.8392i	1.82477	+	0.803619i
$881$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$881$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$882$	58.6149	−	58.6149i	1.97367	−	1.97367i
$883$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$883$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$884$		0			0
$885$	0.900210	+	15.9441i	0.0302602	+	0.535954i
$886$	3.75728	−	11.5637i	0.126228	−	0.388491i
$887$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$887$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$888$		0			0
$889$	−27.5482	−	8.95095i	−0.923937	−	0.300205i
$890$		0			0
$891$	−18.3917	−	56.6037i	−0.616144	−	1.89630i
$892$	5.16043	−	32.5817i	0.172784	−	1.09091i
$893$		0			0
$894$	−29.2586	−	40.2710i	−0.978555	−	1.34687i
$895$	−14.2599	+	8.30999i	−0.476657	+	0.277772i
$896$	−47.1519	−	34.2579i	−1.57523	−	1.14447i
$897$		0			0
$898$		0			0
$899$		−	10.2396i		−	0.341510i
$900$	27.3069	−	12.4232i	0.910229	−	0.414106i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−25.3253	+	18.3999i	−0.841376	+	0.611295i
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	−59.4812	−	9.42090i	−1.97395	−	0.312644i
$909$	34.4523	−	11.1942i	1.14271	−	0.371289i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	−44.3045	+	86.9525i	−1.46626	+	2.87771i
$914$	−0.280367	−	0.0910968i	−0.00927372	−	0.00301321i
$915$		0			0
$916$		0			0
$917$	14.8680	−	93.8730i	0.490986	−	3.09996i
$918$		0			0
$919$	20.1568	+	27.7435i	0.664913	+	0.915174i	0.999632	−	0.0271443i	$-0.00864136\pi$
$919$	20.1568	+	27.7435i	0.664913	+	0.915174i	−0.334719	+	0.942318i	$0.608641\pi$
$920$		0			0
$921$		0			0
$922$	−48.2438	+	7.64106i	−1.58882	+	0.251645i
$923$		0			0
$924$		−	118.011i		−	3.88228i
$925$		0			0
$926$	8.29286			0.272520
$927$	−15.7015	−	30.8160i	−0.515706	−	1.01213i
$928$	−4.73300	−	29.8830i	−0.155368	−	0.980958i
$929$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$929$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$930$	−6.98504	+	7.82099i	−0.229048	+	0.256461i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	5.69786	−	1.85135i	0.186440	−	0.0605779i
$935$		0			0
$936$		0			0
$937$	−25.3294	−	12.9060i	−0.827476	−	0.421620i	−0.0116601	−	0.999932i	$-0.503712\pi$
$937$	−25.3294	−	12.9060i	−0.827476	−	0.421620i	−0.815816	+	0.578312i	$0.803712\pi$
$938$		0			0
$939$	42.5756	+	13.8337i	1.38940	+	0.451444i
$940$		0			0
$941$	−12.8336	−	39.4977i	−0.418363	−	1.28759i	−0.909208	−	0.416341i	$-0.863312\pi$
$941$	−12.8336	−	39.4977i	−0.418363	−	1.28759i	0.490846	−	0.871246i	$-0.336688\pi$
$942$		0			0
$943$		0			0
$944$	−9.69445	−	13.3433i	−0.315527	−	0.434286i
$945$	−44.6427	−	39.8710i	−1.45223	−	1.29700i
$946$		0			0
$947$	52.2169	−	8.27034i	1.69682	−	0.268750i	0.768316	−	0.640071i	$-0.221095\pi$
$947$	52.2169	−	8.27034i	1.69682	−	0.268750i	0.928505	+	0.371321i	$0.121095\pi$
$948$	−15.3369	+	7.81453i	−0.498119	+	0.253804i
$949$		0			0
$950$		0			0
$951$	45.1842			1.46520
$952$		0			0
$953$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$953$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$954$	−30.8715	+	42.4910i	−0.999503	+	1.37570i
$955$		0			0
$956$		0			0
$957$	43.3183	−	43.3183i	1.40028	−	1.40028i
$958$		0			0
$959$		0			0
$960$	−16.7699	+	26.0532i	−0.541246	+	0.840864i
$961$	−8.44689	+	25.9969i	−0.272480	+	0.838608i
$962$		0			0
$963$	−17.6738	+	34.6868i	−0.569531	+	1.11777i
$964$	34.0522	+	11.0642i	1.09675	+	0.356355i
$965$	−19.5535	−	50.3298i	−0.629449	−	1.62017i
$966$		0			0
$967$	−9.69941	+	61.2397i	−0.311912	+	1.96934i	−0.0787703	+	0.996893i	$0.525099\pi$
$967$	−9.69941	+	61.2397i	−0.311912	+	1.96934i	−0.233142	+	0.972443i	$0.574901\pi$
$968$	−65.4626	−	65.4626i	−2.10405	−	2.10405i
$969$		0			0
$970$	0.730332	+	3.36895i	0.0234496	+	0.108170i
$971$	49.2832	+	35.8063i	1.58157	+	1.14908i	0.914864	+	0.403763i	$0.132298\pi$
$971$	49.2832	+	35.8063i	1.58157	+	1.14908i	0.666710	+	0.745318i	$0.267702\pi$
$972$	30.7931	−	4.87714i	0.987688	−	0.156434i
$973$		0			0
$974$		−	56.8417i		−	1.82133i
$975$		0			0
$976$		0			0
$977$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$977$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$978$		0			0
$979$		0			0
$980$	−43.9944	−	75.4944i	−1.40535	−	2.41158i
$981$		0			0
$982$	28.3098	−	28.3098i	0.903402	−	0.903402i
$983$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$983$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$984$		0			0
$985$	−24.4438	−	6.44395i	−0.778845	−	0.205321i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−62.6363	+	3.53648i	−1.99071	+	0.112397i
$991$	18.9491	+	58.3195i	0.601939	+	1.85258i	0.516599	+	0.856227i	$0.327198\pi$
$991$	18.9491	+	58.3195i	0.601939	+	1.85258i	0.0853402	+	0.996352i	$0.472802\pi$
$992$	1.69419	−	10.6967i	0.0537905	−	0.339620i
$993$		0			0
$994$		0			0
$995$	−24.8940	+	56.5264i	−0.789193	+	1.79201i
$996$	−41.3574	−	30.0479i	−1.31046	−	0.952104i
$997$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$997$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bp.a.53.1	✓	16
3.2	odd	2		600.2.bp.b.53.2	yes	16
8.5	even	2		600.2.bp.b.53.2	yes	16
24.5	odd	2	CM	600.2.bp.a.53.1	✓	16
25.17	odd	20	inner	600.2.bp.a.317.1	yes	16
75.17	even	20		600.2.bp.b.317.2	yes	16
200.117	odd	20		600.2.bp.b.317.2	yes	16
600.317	even	20	inner	600.2.bp.a.317.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.53.1	✓	16	1.1	even	1	trivial
600.2.bp.a.53.1	✓	16	24.5	odd	2	CM
600.2.bp.a.317.1	yes	16	25.17	odd	20	inner
600.2.bp.a.317.1	yes	16	600.317	even	20	inner
600.2.bp.b.53.2	yes	16	3.2	odd	2
600.2.bp.b.53.2	yes	16	8.5	even	2
600.2.bp.b.317.2	yes	16	75.17	even	20
600.2.bp.b.317.2	yes	16	200.117	odd	20

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-2.04641 - 0.901229i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(3.64268 - 3.64268i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +O(q^{10})\)	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-2.04641 - 0.901229i) q^{5} +(-1.98168 + 1.43977i) q^{6} +(3.64268 - 3.64268i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(0.178260 + 3.15725i) q^{10} +(2.04352 - 6.28930i) q^{11} +(3.08654 + 1.57267i) q^{12} +(-6.92880 - 2.25130i) q^{14} +(-0.987277 + 3.74503i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(3.00000 + 3.00000i) q^{18} +(3.86392 - 2.25170i) q^{20} +(-7.21863 - 5.24464i) q^{21} +(-9.23700 + 1.46300i) q^{22} -4.89898i q^{24} +(3.37557 + 3.68856i) q^{25} +(2.35900 + 4.62981i) q^{27} +(1.61175 + 10.1762i) q^{28} +(-3.14375 + 4.32700i) q^{29} +(5.35289 - 1.16042i) q^{30} +(-1.54886 + 1.12531i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-11.3130 - 1.79180i) q^{33} +(-10.7373 + 4.17153i) q^{35} +(1.85410 - 5.70634i) q^{36} +(-5.31809 - 3.42314i) q^{40} +(-1.97399 + 12.4633i) q^{42} +(7.77400 + 10.7000i) q^{44} +(6.67423 + 0.674235i) q^{45} +(-6.17307 + 3.14534i) q^{48} -19.5383i q^{49} +(2.48061 - 6.62167i) q^{50} +(1.93658 + 12.2271i) q^{53} +(4.31932 - 5.94504i) q^{54} +(-9.84997 + 11.0288i) q^{55} +(11.7880 - 8.56446i) q^{56} +(7.47075 + 1.18325i) q^{58} +(3.92149 - 1.27417i) q^{59} +(-4.89898 - 6.00000i) q^{60} +(2.41240 + 1.22918i) q^{62} +(-7.01624 + 13.7702i) q^{63} +(7.60845 + 2.47214i) q^{64} +(5.00558 + 15.4056i) q^{66} +(12.1502 + 10.8515i) q^{70} +(-8.38081 + 1.32739i) q^{72} +(14.9936 - 7.63962i) q^{73} +(5.39551 - 6.77411i) q^{75} +(-15.4661 - 30.3538i) q^{77} +(-2.92068 + 4.01997i) q^{79} +(-0.898979 + 8.89898i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-14.5755 - 2.30854i) q^{83} +(16.9720 - 5.51454i) q^{84} +(8.25412 + 4.20569i) q^{87} +(8.49157 - 16.6656i) q^{88} +(-3.43554 - 8.84291i) q^{90} +(2.34477 + 2.34477i) q^{93} +(7.92672 + 5.75910i) q^{96} +(1.07668 - 0.170529i) q^{97} +(-24.6197 + 12.5444i) q^{98} +19.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8}+O(q^{10}) \) 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8	\( 16 q - 4 q^{2} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 8 q^{10} + 24 q^{11} - 12 q^{15} + 16 q^{16} + 48 q^{18} + 8 q^{20} - 36 q^{21} - 16 q^{22} + 32 q^{28} - 12 q^{30} - 64 q^{32} + 12 q^{33} - 8 q^{35} - 24 q^{36} + 24 q^{42} + 48 q^{45} + 4 q^{50} + 28 q^{55} + 24 q^{56} - 8 q^{58} - 80 q^{59} + 12 q^{63} - 36 q^{66} - 32 q^{70} - 24 q^{72} - 28 q^{73} + 24 q^{75} + 12 q^{77} + 64 q^{80} + 36 q^{81} - 24 q^{83} - 36 q^{87} + 32 q^{88} - 24 q^{93} - 16 q^{97} - 72 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 8 * q^10 + 24 * q^11 - 12 * q^15 + 16 * q^16 + 48 * q^18 + 8 * q^20 - 36 * q^21 - 16 * q^22 + 32 * q^28 - 12 * q^30 - 64 * q^32 + 12 * q^33 - 8 * q^35 - 24 * q^36 + 24 * q^42 + 48 * q^45 + 4 * q^50 + 28 * q^55 + 24 * q^56 - 8 * q^58 - 80 * q^59 + 12 * q^63 - 36 * q^66 - 32 * q^70 - 24 * q^72 - 28 * q^73 + 24 * q^75 + 12 * q^77 + 64 * q^80 + 36 * q^81 - 24 * q^83 - 36 * q^87 + 32 * q^88 - 24 * q^93 - 16 * q^97 - 72 * q^98

Introduction

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