LMFDB - Embedded newform 360.2.x.a.53.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.21
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20878 + 0.734068i) q^{2} +(0.922287 + 1.77465i) q^{4} +(2.03368 + 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-0.187875 + 2.82218i) q^{8} +O(q^{10})$	\(q+(1.20878 + 0.734068i) q^{2} +(0.922287 + 1.77465i) q^{4} +(2.03368 + 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-0.187875 + 2.82218i) q^{8} +(1.77589 + 2.61653i) q^{10} -3.92878 q^{11} +(4.55591 - 4.55591i) q^{13} +(-4.84680 + 1.18425i) q^{14} +(-2.29877 + 3.27348i) q^{16} +(-1.88566 - 1.88566i) q^{17} +4.61555 q^{19} +(0.225939 + 4.46642i) q^{20} +(-4.74902 - 2.88399i) q^{22} +(0.741221 - 0.741221i) q^{23} +(3.27172 + 3.78098i) q^{25} +(8.85143 - 2.16273i) q^{26} +(-6.72802 - 2.12638i) q^{28} -4.35885i q^{29} +9.67119 q^{31} +(-5.18166 + 2.26945i) q^{32} +(-0.895142 - 3.66355i) q^{34} +(-7.39245 + 2.75436i) q^{35} +(-5.39704 - 5.39704i) q^{37} +(5.57917 + 3.38813i) q^{38} +(-3.00555 + 5.56477i) q^{40} +6.33584i q^{41} +(0.206110 - 0.206110i) q^{43} +(-3.62346 - 6.97221i) q^{44} +(1.44008 - 0.351864i) q^{46} +(-3.48081 - 3.48081i) q^{47} -5.44695i q^{49} +(1.17928 + 6.97204i) q^{50} +(12.2870 + 3.88329i) q^{52} +(1.01974 + 1.01974i) q^{53} +(-7.98989 - 3.65216i) q^{55} +(-6.57177 - 7.50916i) q^{56} +(3.19969 - 5.26888i) q^{58} -0.531064i q^{59} -3.00356i q^{61} +(11.6903 + 7.09932i) q^{62} +(-7.92941 - 1.06044i) q^{64} +(13.5004 - 5.03014i) q^{65} +(-1.28660 - 1.28660i) q^{67} +(1.60727 - 5.08552i) q^{68} +(-10.9577 - 2.09715i) q^{70} -7.61692i q^{71} +(-0.509262 - 0.509262i) q^{73} +(-2.56202 - 10.4856i) q^{74} +(4.25686 + 8.19099i) q^{76} +(9.80109 - 9.80109i) q^{77} +1.31920i q^{79} +(-7.71797 + 4.52029i) q^{80} +(-4.65094 + 7.65863i) q^{82} +(-9.85533 - 9.85533i) q^{83} +(-2.08194 - 5.58774i) q^{85} +(0.400440 - 0.0978424i) q^{86} +(0.738121 - 11.0877i) q^{88} -2.91798 q^{89} +22.7312i q^{91} +(1.99903 + 0.631790i) q^{92} +(-1.65237 - 6.76268i) q^{94} +(9.38656 + 4.29057i) q^{95} +(-8.11369 + 8.11369i) q^{97} +(3.99844 - 6.58416i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	1.20878	+	0.734068i	0.854735	+	0.519065i
$2$	1.20878	+	0.734068i	0.854735	+	0.519065i
$3$		0			0
$3$		0			0
$4$	0.922287	+	1.77465i	0.461144	+	0.887326i
$5$	2.03368	+	0.929591i	0.909490	+	0.415726i
$5$	2.03368	+	0.929591i	0.909490	+	0.415726i
$6$		0			0
$7$	−2.49469	+	2.49469i	−0.942904	+	0.942904i	−0.998456	−	0.0555517i	$-0.982308\pi$
$7$	−2.49469	+	2.49469i	−0.942904	+	0.942904i	0.0555517	+	0.998456i	$0.482308\pi$
$8$	−0.187875	+	2.82218i	−0.0664240	+	0.997791i
$9$		0			0
$10$	1.77589	+	2.61653i	0.561584	+	0.827420i
$11$	−3.92878			−1.18457			−0.592286	−	0.805728i	$-0.701774\pi$
$11$	−3.92878			−1.18457			−0.592286	+	0.805728i	$0.701774\pi$
$12$		0			0
$13$	4.55591	−	4.55591i	1.26358	−	1.26358i	0.314237	−	0.949345i	$-0.398251\pi$
$13$	4.55591	−	4.55591i	1.26358	−	1.26358i	0.949345	−	0.314237i	$-0.101749\pi$
$14$	−4.84680	+	1.18425i	−1.29536	+	0.316505i
$15$		0			0
$16$	−2.29877	+	3.27348i	−0.574693	+	0.818369i
$17$	−1.88566	−	1.88566i	−0.457341	−	0.457341i	0.440441	−	0.897782i	$-0.354822\pi$
$17$	−1.88566	−	1.88566i	−0.457341	−	0.457341i	−0.897782	+	0.440441i	$0.854822\pi$
$18$		0			0
$19$	4.61555			1.05888			0.529440	−	0.848347i	$-0.322402\pi$
$19$	4.61555			1.05888			0.529440	+	0.848347i	$0.322402\pi$
$20$	0.225939	+	4.46642i	0.0505214	+	0.998723i
$21$		0			0
$22$	−4.74902	−	2.88399i	−1.01249	−	0.614870i
$23$	0.741221	−	0.741221i	0.154555	−	0.154555i	−0.625594	−	0.780149i	$-0.715143\pi$
$23$	0.741221	−	0.741221i	0.154555	−	0.154555i	0.780149	+	0.625594i	$0.215143\pi$
$24$		0			0
$25$	3.27172	+	3.78098i	0.654344	+	0.756197i
$26$	8.85143	−	2.16273i	1.73591	−	0.424147i
$27$		0			0
$28$	−6.72802	−	2.12638i	−1.27148	−	0.401849i
$29$		−	4.35885i		−	0.809418i	−0.914446	−	0.404709i	$-0.867373\pi$
$29$		−	4.35885i		−	0.809418i	0.914446	−	0.404709i	$-0.132627\pi$
$30$		0			0
$31$	9.67119			1.73700			0.868499	−	0.495691i	$-0.165085\pi$
$31$	9.67119			1.73700			0.868499	+	0.495691i	$0.165085\pi$
$32$	−5.18166	+	2.26945i	−0.915997	+	0.401185i
$33$		0			0
$34$	−0.895142	−	3.66355i	−0.153516	−	0.628294i
$35$	−7.39245	+	2.75436i	−1.24955	+	0.465572i
$36$		0			0
$37$	−5.39704	−	5.39704i	−0.887267	−	0.887267i	0.106992	−	0.994260i	$-0.465878\pi$
$37$	−5.39704	−	5.39704i	−0.887267	−	0.887267i	−0.994260	+	0.106992i	$0.965878\pi$
$38$	5.57917	+	3.38813i	0.905061	+	0.549627i
$39$		0			0
$40$	−3.00555	+	5.56477i	−0.475220	+	0.879867i
$41$			6.33584i			0.989492i	0.869038	+	0.494746i	$0.164739\pi$
$41$			6.33584i			0.989492i	−0.869038	+	0.494746i	$0.835261\pi$
$42$		0			0
$43$	0.206110	−	0.206110i	0.0314315	−	0.0314315i	−0.691216	−	0.722648i	$-0.742925\pi$
$43$	0.206110	−	0.206110i	0.0314315	−	0.0314315i	0.722648	+	0.691216i	$0.242925\pi$
$44$	−3.62346	−	6.97221i	−0.546258	−	1.05110i
$45$		0			0
$46$	1.44008	−	0.351864i	0.212328	−	0.0518796i
$47$	−3.48081	−	3.48081i	−0.507729	−	0.507729i	0.406100	−	0.913829i	$-0.366888\pi$
$47$	−3.48081	−	3.48081i	−0.507729	−	0.507729i	−0.913829	+	0.406100i	$0.866888\pi$
$48$		0			0
$49$		−	5.44695i		−	0.778136i
$50$	1.17928	+	6.97204i	0.166776	+	0.985995i
$51$		0			0
$52$	12.2870	+	3.88329i	1.70390	+	0.538516i
$53$	1.01974	+	1.01974i	0.140073	+	0.140073i	0.773666	−	0.633593i	$-0.218421\pi$
$53$	1.01974	+	1.01974i	0.140073	+	0.140073i	−0.633593	+	0.773666i	$0.718421\pi$
$54$		0			0
$55$	−7.98989	−	3.65216i	−1.07736	−	0.492457i
$56$	−6.57177	−	7.50916i	−0.878190	−	1.00345i
$57$		0			0
$58$	3.19969	−	5.26888i	0.420140	−	0.691837i
$59$		−	0.531064i		−	0.0691386i	−0.999402	−	0.0345693i	$-0.988994\pi$
$59$		−	0.531064i		−	0.0691386i	0.999402	−	0.0345693i	$-0.0110059\pi$
$60$		0			0
$61$		−	3.00356i		−	0.384566i	−0.981340	−	0.192283i	$-0.938411\pi$
$61$		−	3.00356i		−	0.384566i	0.981340	−	0.192283i	$-0.0615892\pi$
$62$	11.6903	+	7.09932i	1.48467	+	0.901614i
$63$		0			0
$64$	−7.92941	−	1.06044i	−0.991176	−	0.132555i
$65$	13.5004	−	5.03014i	1.67452	−	0.623912i
$66$		0			0
$67$	−1.28660	−	1.28660i	−0.157183	−	0.157183i	0.624134	−	0.781317i	$-0.285452\pi$
$67$	−1.28660	−	1.28660i	−0.157183	−	0.157183i	−0.781317	+	0.624134i	$0.785452\pi$
$68$	1.60727	−	5.08552i	0.194910	−	0.616710i
$69$		0			0
$70$	−10.9577	−	2.09715i	−1.30970	−	0.250657i
$71$		−	7.61692i		−	0.903962i	−0.892028	−	0.451981i	$-0.850718\pi$
$71$		−	7.61692i		−	0.903962i	0.892028	−	0.451981i	$-0.149282\pi$
$72$		0			0
$73$	−0.509262	−	0.509262i	−0.0596047	−	0.0596047i	0.676676	−	0.736281i	$-0.263420\pi$
$73$	−0.509262	−	0.509262i	−0.0596047	−	0.0596047i	−0.736281	+	0.676676i	$0.763420\pi$
$74$	−2.56202	−	10.4856i	−0.297829	−	1.21893i
$75$		0			0
$76$	4.25686	+	8.19099i	0.488296	+	0.939571i
$77$	9.80109	−	9.80109i	1.11694	−	1.11694i
$78$		0			0
$79$			1.31920i			0.148422i	0.997243	+	0.0742111i	$0.0236439\pi$
$79$			1.31920i			0.148422i	−0.997243	+	0.0742111i	$0.976356\pi$
$80$	−7.71797	+	4.52029i	−0.862895	+	0.505384i
$81$		0			0
$82$	−4.65094	+	7.65863i	−0.513611	+	0.845754i
$83$	−9.85533	−	9.85533i	−1.08176	−	1.08176i	−0.996345	−	0.0854172i	$-0.972778\pi$
$83$	−9.85533	−	9.85533i	−1.08176	−	1.08176i	−0.0854172	−	0.996345i	$-0.527222\pi$
$84$		0			0
$85$	−2.08194	−	5.58774i	−0.225819	−	0.606075i
$86$	0.400440	−	0.0978424i	0.0431806	−	0.0105506i
$87$		0			0
$88$	0.738121	−	11.0877i	0.0786840	−	1.18196i
$89$	−2.91798			−0.309306			−0.154653	−	0.987969i	$-0.549426\pi$
$89$	−2.91798			−0.309306			−0.154653	+	0.987969i	$0.549426\pi$
$90$		0			0
$91$			22.7312i			2.38287i
$92$	1.99903	+	0.631790i	0.208413	+	0.0658686i
$93$		0			0
$94$	−1.65237	−	6.76268i	−0.170429	−	0.697517i
$95$	9.38656	+	4.29057i	0.963041	+	0.440204i
$96$		0			0
$97$	−8.11369	+	8.11369i	−0.823820	+	0.823820i	−0.986654	−	0.162834i	$-0.947937\pi$
$97$	−8.11369	+	8.11369i	−0.823820	+	0.823820i	0.162834	+	0.986654i	$0.447937\pi$
$98$	3.99844	−	6.58416i	0.403903	−	0.665100i
$99$		0			0
$100$	−3.69246	+	9.29332i	−0.369246	+	0.929332i
$101$	11.0269			1.09721			0.548607	−	0.836080i	$-0.315158\pi$
$101$	11.0269			1.09721			0.548607	+	0.836080i	$0.315158\pi$
$102$		0			0
$103$	−2.89128	−	2.89128i	−0.284887	−	0.284887i	0.550168	−	0.835054i	$-0.314564\pi$
$103$	−2.89128	−	2.89128i	−0.284887	−	0.284887i	−0.835054	+	0.550168i	$0.814564\pi$
$104$	12.0017	+	13.7135i	1.17686	+	1.34472i
$105$		0			0
$106$	0.484082	+	1.98121i	0.0470182	+	0.192432i
$107$	−5.23891	+	5.23891i	−0.506465	+	0.506465i	−0.913439	−	0.406975i	$-0.866584\pi$
$107$	−5.23891	+	5.23891i	−0.506465	+	0.506465i	0.406975	+	0.913439i	$0.366584\pi$
$108$		0			0
$109$	5.31464			0.509050			0.254525	−	0.967066i	$-0.418081\pi$
$109$	5.31464			0.509050			0.254525	+	0.967066i	$0.418081\pi$
$110$	−6.97706	−	10.2798i	−0.665237	−	0.980138i
$111$		0			0
$112$	−2.43158	−	13.9010i	−0.229763	−	1.31352i
$113$	−10.3559	+	10.3559i	−0.974204	+	0.974204i	−0.999676	−	0.0254720i	$-0.991891\pi$
$113$	−10.3559	+	10.3559i	−0.974204	+	0.974204i	0.0254720	+	0.999676i	$0.491891\pi$
$114$		0			0
$115$	2.19644	−	0.818375i	0.204819	−	0.0763138i
$116$	7.73543	−	4.02011i	0.718217	−	0.373258i
$117$		0			0
$118$	0.389837	−	0.641938i	0.0358874	−	0.0590952i
$119$	9.40829			0.862457
$120$		0			0
$121$	4.43532			0.403211
$122$	2.20482	−	3.63063i	0.199615	−	0.328702i
$123$		0			0
$124$	8.91962	+	17.1630i	0.801005	+	1.54128i
$125$	3.13887	+	10.7307i	0.280749	+	0.959781i
$126$		0			0
$127$	−1.10872	+	1.10872i	−0.0983826	+	0.0983826i	−0.754585	−	0.656202i	$-0.772162\pi$
$127$	−1.10872	+	1.10872i	−0.0983826	+	0.0983826i	0.656202	+	0.754585i	$0.272162\pi$
$128$	−8.80646	−	7.10256i	−0.778388	−	0.627783i
$129$		0			0
$130$	20.0114	+	3.82990i	1.75512	+	0.335904i
$131$	−0.996979			−0.0871065			−0.0435532	−	0.999051i	$-0.513868\pi$
$131$	−0.996979			−0.0871065			−0.0435532	+	0.999051i	$0.513868\pi$
$132$		0			0
$133$	−11.5144	+	11.5144i	−0.998422	+	0.998422i
$134$	−0.610761	−	2.49967i	−0.0527617	−	0.215938i
$135$		0			0
$136$	5.67595	−	4.96741i	0.486709	−	0.425952i
$137$	1.03232	+	1.03232i	0.0881970	+	0.0881970i	0.749829	−	0.661632i	$-0.230136\pi$
$137$	1.03232	+	1.03232i	0.0881970	+	0.0881970i	−0.661632	+	0.749829i	$0.730136\pi$
$138$		0			0
$139$	−16.9830			−1.44048			−0.720239	−	0.693726i	$-0.755968\pi$
$139$	−16.9830			−1.44048			−0.720239	+	0.693726i	$0.755968\pi$
$140$	−11.7060	−	10.5787i	−0.989337	−	0.894063i
$141$		0			0
$142$	5.59134	−	9.20716i	0.469215	−	0.772648i
$143$	−17.8992	+	17.8992i	−1.49680	+	1.49680i
$144$		0			0
$145$	4.05194	−	8.86451i	0.336496	−	0.736157i
$146$	−0.241752	−	0.989419i	−0.0200075	−	0.0818849i
$147$		0			0
$148$	4.60024	−	14.5555i	0.378137	−	1.19645i
$149$			6.48772i			0.531495i	0.964043	+	0.265747i	$0.0856187\pi$
$149$			6.48772i			0.531495i	−0.964043	+	0.265747i	$0.914381\pi$
$150$		0			0
$151$	4.21210			0.342776			0.171388	−	0.985204i	$-0.445175\pi$
$151$	4.21210			0.342776			0.171388	+	0.985204i	$0.445175\pi$
$152$	−0.867148	+	13.0259i	−0.0703350	+	1.05654i
$153$		0			0
$154$	19.0420	−	4.65267i	1.53445	−	0.374923i
$155$	19.6681	+	8.99025i	1.57978	+	0.722114i
$156$		0			0
$157$	−0.0368875	−	0.0368875i	−0.00294395	−	0.00294395i	0.705633	−	0.708577i	$-0.250663\pi$
$157$	−0.0368875	−	0.0368875i	−0.00294395	−	0.00294395i	−0.708577	+	0.705633i	$0.750663\pi$
$158$	−0.968387	+	1.59463i	−0.0770407	+	0.126862i
$159$		0			0
$160$	−12.6475	−	0.201492i	−0.999873	−	0.0159293i
$161$			3.69823i			0.291461i
$162$		0			0
$163$	1.33256	−	1.33256i	0.104374	−	0.104374i	−0.652991	−	0.757365i	$-0.726486\pi$
$163$	1.33256	−	1.33256i	0.104374	−	0.104374i	0.757365	+	0.652991i	$0.226486\pi$
$164$	−11.2439	+	5.84347i	−0.878002	+	0.456298i
$165$		0			0
$166$	−4.67841	−	19.1474i	−0.363115	−	1.48612i
$167$	−15.0291	−	15.0291i	−1.16299	−	1.16299i	−0.983818	−	0.179169i	$-0.942659\pi$
$167$	−15.0291	−	15.0291i	−1.16299	−	1.16299i	−0.179169	−	0.983818i	$-0.557341\pi$
$168$		0			0
$169$		−	28.5126i		−	2.19328i
$170$	1.58517	−	8.28262i	0.121577	−	0.635248i
$171$		0			0
$172$	0.555867	+	0.175681i	0.0423844	+	0.0133955i
$173$	−2.16963	−	2.16963i	−0.164954	−	0.164954i	0.619804	−	0.784757i	$-0.287212\pi$
$173$	−2.16963	−	2.16963i	−0.164954	−	0.164954i	−0.784757	+	0.619804i	$0.787212\pi$
$174$		0			0
$175$	−17.5943	−	1.27045i	−1.33000	−	0.0960371i
$176$	9.03138	−	12.8608i	0.680766	−	0.969417i
$177$		0			0
$178$	−3.52719	−	2.14200i	−0.264374	−	0.160550i
$179$			14.2973i			1.06863i	0.845285	+	0.534316i	$0.179431\pi$
$179$			14.2973i			1.06863i	−0.845285	+	0.534316i	$0.820569\pi$
$180$		0			0
$181$			11.0562i			0.821800i	0.911680	+	0.410900i	$0.134785\pi$
$181$			11.0562i			0.821800i	−0.911680	+	0.410900i	$0.865215\pi$
$182$	−16.6862	+	27.4769i	−1.23687	+	2.03672i
$183$		0			0
$184$	1.95260	+	2.23112i	0.143948	+	0.164480i
$185$	−5.95882	−	15.9929i	−0.438101	−	1.17582i
$186$		0			0
$187$	7.40836	+	7.40836i	0.541753	+	0.541753i
$188$	2.96692	−	9.38753i	0.216385	−	0.684656i
$189$		0			0
$190$	8.19669	+	12.0767i	0.594650	+	0.876138i
$191$			12.7129i			0.919873i	0.887952	+	0.459937i	$0.152128\pi$
$191$			12.7129i			0.919873i	−0.887952	+	0.459937i	$0.847872\pi$
$192$		0			0
$193$	16.5832	+	16.5832i	1.19368	+	1.19368i	0.976025	+	0.217659i	$0.0698420\pi$
$193$	16.5832	+	16.5832i	1.19368	+	1.19368i	0.217659	+	0.976025i	$0.430158\pi$
$194$	−15.7636	+	3.85164i	−1.13176	+	0.276532i
$195$		0			0
$196$	9.66644	−	5.02366i	0.690460	−	0.358833i
$197$	−9.96244	+	9.96244i	−0.709794	+	0.709794i	−0.966492	−	0.256698i	$-0.917366\pi$
$197$	−9.96244	+	9.96244i	−0.709794	+	0.709794i	0.256698	+	0.966492i	$0.417366\pi$
$198$		0			0
$199$			15.6722i			1.11097i	0.831525	+	0.555487i	$0.187468\pi$
$199$			15.6722i			1.11097i	−0.831525	+	0.555487i	$0.812532\pi$
$200$	−11.2853	+	8.52303i	−0.797991	+	0.602670i
$201$		0			0
$202$	13.3290	+	8.09448i	0.937828	+	0.569526i
$203$	10.8740	+	10.8740i	0.763203	+	0.763203i
$204$		0			0
$205$	−5.88974	+	12.8851i	−0.411357	+	0.899933i
$206$	−1.37252	−	5.61732i	−0.0956280	−	0.391377i
$207$		0			0
$208$	4.44065	+	25.3867i	0.307904	+	1.76025i
$209$	−18.1335			−1.25432
$210$		0			0
$211$		−	22.1294i		−	1.52345i	−0.647901	−	0.761725i	$-0.724353\pi$
$211$		−	22.1294i		−	1.52345i	0.647901	−	0.761725i	$-0.275647\pi$
$212$	−0.869194	+	2.75019i	−0.0596965	+	0.188884i
$213$		0			0
$214$	−10.1784	+	2.48696i	−0.695781	+	0.170005i
$215$	0.610761	−	0.227564i	0.0416535	−	0.0155198i
$216$		0			0
$217$	−24.1266	+	24.1266i	−1.63782	+	1.63782i
$218$	6.42422	+	3.90131i	0.435103	+	0.264230i
$219$		0			0
$220$	−0.887663	−	17.5476i	−0.0598462	−	1.18306i
$221$	−17.1818			−1.15577
$222$		0			0
$223$	−3.17650	−	3.17650i	−0.212714	−	0.212714i	0.592705	−	0.805420i	$-0.298060\pi$
$223$	−3.17650	−	3.17650i	−0.212714	−	0.212714i	−0.805420	+	0.592705i	$0.798060\pi$
$224$	7.26507	−	18.5882i	0.485418	−	1.24198i
$225$		0			0
$226$	−20.1200	+	4.91605i	−1.33836	+	0.327011i
$227$	18.4920	−	18.4920i	1.22735	−	1.22735i	0.262393	−	0.964961i	$-0.415488\pi$
$227$	18.4920	−	18.4920i	1.22735	−	1.22735i	0.964961	−	0.262393i	$-0.0845116\pi$
$228$		0			0
$229$	19.2316			1.27086			0.635428	−	0.772160i	$-0.280824\pi$
$229$	19.2316			1.27086			0.635428	+	0.772160i	$0.280824\pi$
$230$	3.25575	+	0.623103i	0.214678	+	0.0410862i
$231$		0			0
$232$	12.3015	+	0.818920i	0.807630	+	0.0537647i
$233$	13.7302	−	13.7302i	0.899495	−	0.899495i	−0.0958959	−	0.995391i	$-0.530572\pi$
$233$	13.7302	−	13.7302i	0.899495	−	0.899495i	0.995391	+	0.0958959i	$0.0305716\pi$
$234$		0			0
$235$	−3.84313	−	10.3146i	−0.250698	−	0.672850i
$236$	0.942453	−	0.489793i	0.0613485	−	0.0318828i
$237$		0			0
$238$	11.3725	+	6.90633i	0.737172	+	0.447671i
$239$	26.7732			1.73182			0.865908	−	0.500203i	$-0.166741\pi$
$239$	26.7732			1.73182			0.865908	+	0.500203i	$0.166741\pi$
$240$		0			0
$241$	−17.6357			−1.13601			−0.568007	−	0.823023i	$-0.692286\pi$
$241$	−17.6357			−1.13601			−0.568007	+	0.823023i	$0.692286\pi$
$242$	5.36131	+	3.25583i	0.344638	+	0.209292i
$243$		0			0
$244$	5.33027	−	2.77014i	0.341235	−	0.177340i
$245$	5.06344	−	11.0774i	0.323491	−	0.707707i
$246$		0			0
$247$	21.0280	−	21.0280i	1.33798	−	1.33798i
$248$	−1.81698	+	27.2939i	−0.115378	+	1.73316i
$249$		0			0
$250$	−4.08286	+	15.2752i	−0.258222	+	0.966085i
$251$	13.0522			0.823846			0.411923	−	0.911219i	$-0.364857\pi$
$251$	13.0522			0.823846			0.411923	+	0.911219i	$0.364857\pi$
$252$		0			0
$253$	−2.91209	+	2.91209i	−0.183082	+	0.183082i
$254$	−2.15406	+	0.526318i	−0.135158	+	0.0330241i
$255$		0			0
$256$	−5.43128	−	15.0500i	−0.339455	−	0.940622i
$257$	9.03127	+	9.03127i	0.563355	+	0.563355i	0.930259	−	0.366904i	$-0.119582\pi$
$257$	9.03127	+	9.03127i	0.563355	+	0.563355i	−0.366904	+	0.930259i	$0.619582\pi$
$258$		0			0
$259$	26.9279			1.67322
$260$	21.3780	+	19.3193i	1.32581	+	1.19813i
$261$		0			0
$262$	−1.20513	−	0.731851i	−0.0744529	−	0.0452139i
$263$	−2.83442	+	2.83442i	−0.174778	+	0.174778i	−0.789075	−	0.614297i	$-0.789440\pi$
$263$	−2.83442	+	2.83442i	−0.174778	+	0.174778i	0.614297	+	0.789075i	$0.289440\pi$
$264$		0			0
$265$	1.12589	+	3.02178i	0.0691629	+	0.185627i
$266$	−22.3706	+	5.46598i	−1.37163	+	0.335140i
$267$		0			0
$268$	1.09665	−	3.46988i	0.0669886	−	0.211957i
$269$			9.89975i			0.603599i	0.953371	+	0.301799i	$0.0975873\pi$
$269$			9.89975i			0.603599i	−0.953371	+	0.301799i	$0.902413\pi$
$270$		0			0
$271$	16.6235			1.00981			0.504904	−	0.863176i	$-0.331528\pi$
$271$	16.6235			1.00981			0.504904	+	0.863176i	$0.331528\pi$
$272$	10.5074	−	1.83796i	0.637104	−	0.111443i
$273$		0			0
$274$	0.490052	+	2.00564i	0.0296051	+	0.121165i
$275$	−12.8539	−	14.8547i	−0.775118	−	0.895769i
$276$		0			0
$277$	−6.42695	−	6.42695i	−0.386158	−	0.386158i	0.487156	−	0.873315i	$-0.338034\pi$
$277$	−6.42695	−	6.42695i	−0.386158	−	0.386158i	−0.873315	+	0.487156i	$0.838034\pi$
$278$	−20.5287	−	12.4667i	−1.23123	−	0.747702i
$279$		0			0
$280$	−6.38445	−	21.3803i	−0.381544	−	1.27772i
$281$			27.0270i			1.61230i	0.591714	+	0.806148i	$0.298451\pi$
$281$			27.0270i			1.61230i	−0.591714	+	0.806148i	$0.701549\pi$
$282$		0			0
$283$	−18.1481	+	18.1481i	−1.07879	+	1.07879i	−0.0821722	+	0.996618i	$0.526186\pi$
$283$	−18.1481	+	18.1481i	−1.07879	+	1.07879i	−0.996618	+	0.0821722i	$0.973814\pi$
$284$	13.5174	−	7.02498i	0.802108	−	0.416856i
$285$		0			0
$286$	−34.7753	+	8.49690i	−2.05631	+	0.502432i
$287$	−15.8060	−	15.8060i	−0.932996	−	0.932996i
$288$		0			0
$289$		−	9.88854i		−	0.581679i
$290$	11.4051	−	7.74081i	0.669728	−	0.454556i
$291$		0			0
$292$	0.434077	−	1.37345i	0.0254024	−	0.0803750i
$293$	−11.4905	−	11.4905i	−0.671281	−	0.671281i	0.286730	−	0.958011i	$-0.407432\pi$
$293$	−11.4905	−	11.4905i	−0.671281	−	0.671281i	−0.958011	+	0.286730i	$0.907432\pi$
$294$		0			0
$295$	0.493672	−	1.08001i	0.0287427	−	0.0628809i
$296$	16.2454	−	14.2174i	0.944244	−	0.826372i
$297$		0			0
$298$	−4.76243	+	7.84221i	−0.275880	+	0.454287i
$299$		−	6.75387i		−	0.390586i
$300$		0			0
$301$			1.02836i			0.0592738i
$302$	5.09149	+	3.09197i	0.292982	+	0.177923i
$303$		0			0
$304$	−10.6101	+	15.1089i	−0.608531	+	0.866554i
$305$	2.79208	−	6.10828i	0.159874	−	0.349759i
$306$		0			0
$307$	−17.8635	−	17.8635i	−1.01953	−	1.01953i	−0.999806	−	0.0197205i	$-0.993722\pi$
$307$	−17.8635	−	17.8635i	−1.01953	−	1.01953i	−0.0197205	−	0.999806i	$-0.506278\pi$
$308$	26.4329	+	8.35410i	1.50616	+	0.476019i
$309$		0			0
$310$	17.1749	+	25.3050i	0.975471	+	1.43723i
$311$			9.93768i			0.563514i	0.959486	+	0.281757i	$0.0909173\pi$
$311$			9.93768i			0.563514i	−0.959486	+	0.281757i	$0.909083\pi$
$312$		0			0
$313$	5.20616	+	5.20616i	0.294269	+	0.294269i	0.838764	−	0.544495i	$-0.183279\pi$
$313$	5.20616	+	5.20616i	0.294269	+	0.294269i	−0.544495	+	0.838764i	$0.683279\pi$
$314$	−0.0175109	−	0.0716668i	−0.000988195	−	0.00404439i
$315$		0			0
$316$	−2.34113	+	1.21669i	−0.131699	+	0.0684439i
$317$	−13.2883	+	13.2883i	−0.746346	+	0.746346i	−0.973791	−	0.227445i	$-0.926963\pi$
$317$	−13.2883	+	13.2883i	−0.746346	+	0.746346i	0.227445	+	0.973791i	$0.426963\pi$
$318$		0			0
$319$			17.1250i			0.958813i
$320$	−15.1401	−	9.52769i	−0.846358	−	0.532614i
$321$		0			0
$322$	−2.71475	+	4.47034i	−0.151287	+	0.249122i
$323$	−8.70338	−	8.70338i	−0.484269	−	0.484269i
$324$		0			0
$325$	32.1315	+	2.32015i	1.78233	+	0.128699i
$326$	2.58895	−	0.632577i	0.143389	−	0.0350352i
$327$		0			0
$328$	−17.8809	−	1.19035i	−0.987307	−	0.0657260i
$329$	17.3671			0.957479
$330$		0			0
$331$		−	8.60834i		−	0.473157i	−0.971612	−	0.236579i	$-0.923974\pi$
$331$		−	8.60834i		−	0.473157i	0.971612	−	0.236579i	$-0.0760261\pi$
$332$	8.40033	−	26.5792i	0.461028	−	1.45872i
$333$		0			0
$334$	−7.13446	−	29.1993i	−0.390380	−	1.59771i
$335$	−1.42052	−	3.81255i	−0.0776114	−	0.208302i
$336$		0			0
$337$	1.29928	−	1.29928i	0.0707764	−	0.0707764i	−0.670832	−	0.741609i	$-0.734063\pi$
$337$	1.29928	−	1.29928i	0.0707764	−	0.0707764i	0.741609	+	0.670832i	$0.234063\pi$
$338$	20.9302	−	34.4654i	1.13845	−	1.87467i
$339$		0			0
$340$	7.99613	−	8.84822i	0.433651	−	0.479862i
$341$	−37.9960			−2.05760
$342$		0			0
$343$	−3.87437	−	3.87437i	−0.209196	−	0.209196i
$344$	0.542957	+	0.620403i	0.0292743	+	0.0334499i
$345$		0			0
$346$	−1.02994	−	4.21525i	−0.0553700	−	0.226613i
$347$	18.3626	−	18.3626i	0.985756	−	0.985756i	−0.0141438	−	0.999900i	$-0.504502\pi$
$347$	18.3626	−	18.3626i	0.985756	−	0.985756i	0.999900	+	0.0141438i	$0.00450226\pi$
$348$		0			0
$349$	−31.1787			−1.66896			−0.834478	−	0.551041i	$-0.814231\pi$
$349$	−31.1787			−1.66896			−0.834478	+	0.551041i	$0.814231\pi$
$350$	−20.3350	−	14.4511i	−1.08695	−	0.772445i
$351$		0			0
$352$	20.3576	−	8.91616i	1.08506	−	0.475233i
$353$	9.04629	−	9.04629i	0.481485	−	0.481485i	−0.424120	−	0.905606i	$-0.639417\pi$
$353$	9.04629	−	9.04629i	0.481485	−	0.481485i	0.905606	+	0.424120i	$0.139417\pi$
$354$		0			0
$355$	7.08062	−	15.4904i	0.375800	−	0.822144i
$356$	−2.69122	−	5.17840i	−0.142634	−	0.274455i
$357$		0			0
$358$	−10.4952	+	17.2823i	−0.554689	+	0.913396i
$359$	13.1073			0.691776			0.345888	−	0.938276i	$-0.387578\pi$
$359$	13.1073			0.691776			0.345888	+	0.938276i	$0.387578\pi$
$360$		0			0
$361$	2.30330			0.121226
$362$	−8.11600	+	13.3645i	−0.426567	+	0.702421i
$363$		0			0
$364$	−40.3399	+	20.9647i	−2.11438	+	1.09885i
$365$	−0.562272	−	1.50908i	−0.0294307	−	0.0789890i
$366$		0			0
$367$	3.44746	−	3.44746i	0.179956	−	0.179956i	−0.611381	−	0.791337i	$-0.709386\pi$
$367$	3.44746	−	3.44746i	0.179956	−	0.179956i	0.791337	+	0.611381i	$0.209386\pi$
$368$	0.722469	+	4.13027i	0.0376613	+	0.215305i
$369$		0			0
$370$	4.53699	−	23.7060i	0.235867	−	1.23242i
$371$	−5.08789			−0.264150
$372$		0			0
$373$	7.24984	−	7.24984i	0.375382	−	0.375382i	−0.494051	−	0.869433i	$-0.664484\pi$
$373$	7.24984	−	7.24984i	0.375382	−	0.375382i	0.869433	+	0.494051i	$0.164484\pi$
$374$	3.51682	+	14.3933i	0.181850	+	0.744260i
$375$		0			0
$376$	10.4774	−	9.16952i	0.540333	−	0.472882i
$377$	−19.8585	−	19.8585i	−1.02277	−	1.02277i
$378$		0			0
$379$	−29.1664			−1.49818			−0.749088	−	0.662470i	$-0.769508\pi$
$379$	−29.1664			−1.49818			−0.749088	+	0.662470i	$0.769508\pi$
$380$	1.04283	+	20.6150i	0.0534961	+	1.05753i
$381$		0			0
$382$	−9.33214	+	15.3671i	−0.477474	+	0.786248i
$383$	12.2895	−	12.2895i	0.627965	−	0.627965i	−0.319591	−	0.947556i	$-0.603545\pi$
$383$	12.2895	−	12.2895i	0.627965	−	0.627965i	0.947556	+	0.319591i	$0.103545\pi$
$384$		0			0
$385$	29.0433	−	10.8213i	1.48018	−	0.551504i
$386$	7.87219	+	32.2186i	0.400684	+	1.63988i
$387$		0			0
$388$	−21.8821	−	6.91581i	−1.11090	−	0.351097i
$389$		−	31.4290i		−	1.59351i	−0.604301	−	0.796756i	$-0.706548\pi$
$389$		−	31.4290i		−	1.59351i	0.604301	−	0.796756i	$-0.293452\pi$
$390$		0			0
$391$	−2.79539			−0.141369
$392$	15.3723	+	1.02335i	0.776418	+	0.0516869i
$393$		0			0
$394$	−19.3555	+	4.72926i	−0.975115	+	0.238257i
$395$	−1.22632	+	2.68284i	−0.0617029	+	0.134988i
$396$		0			0
$397$	14.9362	+	14.9362i	0.749627	+	0.749627i	0.974409	−	0.224782i	$-0.0721671\pi$
$397$	14.9362	+	14.9362i	0.749627	+	0.749627i	−0.224782	+	0.974409i	$0.572167\pi$
$398$	−11.5045	+	18.9442i	−0.576667	+	0.949588i
$399$		0			0
$400$	−19.8979	+	2.01828i	−0.994895	+	0.100914i
$401$		−	27.0477i		−	1.35070i	−0.737499	−	0.675349i	$-0.763993\pi$
$401$		−	27.0477i		−	1.35070i	0.737499	−	0.675349i	$-0.236007\pi$
$402$		0			0
$403$	44.0611	−	44.0611i	2.19484	−	2.19484i
$404$	10.1699	+	19.5689i	0.505974	+	0.973587i
$405$		0			0
$406$	5.16197	+	21.1265i	0.256185	+	1.04849i
$407$	21.2038	+	21.2038i	1.05103	+	1.05103i
$408$		0			0
$409$		−	4.66540i		−	0.230689i	−0.993326	−	0.115345i	$-0.963203\pi$
$409$		−	4.66540i		−	0.230689i	0.993326	−	0.115345i	$-0.0367973\pi$
$410$	−16.5779	+	11.2517i	−0.818725	+	0.555683i
$411$		0			0
$412$	2.46443	−	7.79761i	0.121414	−	0.384161i
$413$	1.32484	+	1.32484i	0.0651911	+	0.0651911i
$414$		0			0
$415$	−10.8812	−	29.2040i	−0.534136	−	1.43357i
$416$	−13.2678	+	33.9466i	−0.650506	+	1.66437i
$417$		0			0
$418$	−21.9193	−	13.3112i	−1.07211	−	0.651073i
$419$		−	2.43646i		−	0.119029i	−0.998227	−	0.0595144i	$-0.981045\pi$
$419$		−	2.43646i		−	0.119029i	0.998227	−	0.0595144i	$-0.0189552\pi$
$420$		0			0
$421$		−	9.62136i		−	0.468916i	−0.972126	−	0.234458i	$-0.924668\pi$
$421$		−	9.62136i		−	0.468916i	0.972126	−	0.234458i	$-0.0753316\pi$
$422$	16.2445	−	26.7495i	0.790769	−	1.30215i
$423$		0			0
$424$	−3.06949	+	2.68632i	−0.149068	+	0.130459i
$425$	0.960298	−	13.2990i	0.0465813	−	0.645098i
$426$		0			0
$427$	7.49294	+	7.49294i	0.362609	+	0.362609i
$428$	−14.1290	−	4.46546i	−0.682952	−	0.215846i
$429$		0			0
$430$	0.905322	+	0.173265i	0.0436585	+	0.00835560i
$431$		−	26.4447i		−	1.27380i	−0.770948	−	0.636898i	$-0.780217\pi$
$431$		−	26.4447i		−	1.27380i	0.770948	−	0.636898i	$-0.219783\pi$
$432$		0			0
$433$	5.22850	+	5.22850i	0.251266	+	0.251266i	0.821490	−	0.570224i	$-0.193143\pi$
$433$	5.22850	+	5.22850i	0.251266	+	0.251266i	−0.570224	+	0.821490i	$0.693143\pi$
$434$	−46.8743	+	11.4531i	−2.25004	+	0.549768i
$435$		0			0
$436$	4.90162	+	9.43163i	0.234745	+	0.451693i
$437$	3.42114	−	3.42114i	0.163655	−	0.163655i
$438$		0			0
$439$			37.3742i			1.78377i	0.452258	+	0.891887i	$0.350619\pi$
$439$			37.3742i			1.78377i	−0.452258	+	0.891887i	$0.649381\pi$
$440$	11.8082	−	21.8628i	0.562932	−	1.04227i
$441$		0			0
$442$	−20.7690	−	12.6126i	−0.987881	−	0.599922i
$443$	18.0711	+	18.0711i	0.858585	+	0.858585i	0.991171	−	0.132587i	$-0.0423283\pi$
$443$	18.0711	+	18.0711i	0.858585	+	0.858585i	−0.132587	+	0.991171i	$0.542328\pi$
$444$		0			0
$445$	−5.93425	−	2.71253i	−0.281310	−	0.128586i
$446$	−1.50792	−	6.17146i	−0.0714019	−	0.292227i
$447$		0			0
$448$	22.4269	−	17.1359i	1.05957	−	0.809597i
$449$	−24.4570			−1.15420			−0.577098	−	0.816675i	$-0.695815\pi$
$449$	−24.4570			−1.15420			−0.577098	+	0.816675i	$0.695815\pi$
$450$		0			0
$451$		−	24.8921i		−	1.17212i
$452$	−27.9293	−	8.82702i	−1.31368	−	0.415188i
$453$		0			0
$454$	35.9270	−	8.77830i	1.68614	−	0.411986i
$455$	−21.1307	+	46.2279i	−0.990621	+	2.16720i
$456$		0			0
$457$	5.76322	−	5.76322i	0.269592	−	0.269592i	−0.559344	−	0.828936i	$-0.688947\pi$
$457$	5.76322	−	5.76322i	0.269592	−	0.269592i	0.828936	+	0.559344i	$0.188947\pi$
$458$	23.2467	+	14.1173i	1.08625	+	0.659657i
$459$		0			0
$460$	3.47808	+	3.14314i	0.162166	+	0.146549i
$461$	−10.6204			−0.494639			−0.247320	−	0.968934i	$-0.579550\pi$
$461$	−10.6204			−0.494639			−0.247320	+	0.968934i	$0.579550\pi$
$462$		0			0
$463$	13.7984	+	13.7984i	0.641268	+	0.641268i	0.950867	−	0.309599i	$-0.100195\pi$
$463$	13.7984	+	13.7984i	0.641268	+	0.641268i	−0.309599	+	0.950867i	$0.600195\pi$
$464$	14.2686	+	10.0200i	0.662402	+	0.465167i
$465$		0			0
$466$	26.6757	−	6.51785i	1.23573	−	0.301934i
$467$	−11.6749	+	11.6749i	−0.540248	+	0.540248i	−0.923602	−	0.383354i	$-0.874769\pi$
$467$	−11.6749	+	11.6749i	−0.540248	+	0.540248i	0.383354	+	0.923602i	$0.374769\pi$
$468$		0			0
$469$	6.41933			0.296417
$470$	2.92613	−	15.2892i	0.134972	−	0.705237i
$471$		0			0
$472$	1.49876	+	0.0997738i	0.0689859	+	0.00459246i
$473$	−0.809762	+	0.809762i	−0.0372329	+	0.0372329i
$474$		0			0
$475$	15.1008	+	17.4513i	0.692872	+	0.800721i
$476$	8.67715	+	16.6964i	0.397716	+	0.765280i
$477$		0			0
$478$	32.3629	+	19.6534i	1.48024	+	0.898925i
$479$	−5.10716			−0.233352			−0.116676	−	0.993170i	$-0.537224\pi$
$479$	−5.10716			−0.233352			−0.116676	+	0.993170i	$0.537224\pi$
$480$		0			0
$481$	−49.1768			−2.24227
$482$	−21.3176	−	12.9458i	−0.970992	−	0.589665i
$483$		0			0
$484$	4.09063	+	7.87114i	0.185938	+	0.357779i
$485$	−24.0431	+	8.95824i	−1.09174	+	0.406773i
$486$		0			0
$487$	3.80542	−	3.80542i	0.172440	−	0.172440i	−0.615611	−	0.788050i	$-0.711091\pi$
$487$	3.80542	−	3.80542i	0.172440	−	0.172440i	0.788050	+	0.615611i	$0.211091\pi$
$488$	8.47658	+	0.564294i	0.383717	+	0.0255444i
$489$		0			0
$490$	14.2521	−	9.67317i	0.643845	−	0.436989i
$491$	19.3774			0.874492			0.437246	−	0.899342i	$-0.355954\pi$
$491$	19.3774			0.874492			0.437246	+	0.899342i	$0.355954\pi$
$492$		0			0
$493$	−8.21932	+	8.21932i	−0.370180	+	0.370180i
$494$	40.8542	−	9.98220i	1.83812	−	0.449120i
$495$		0			0
$496$	−22.2319	+	31.6584i	−0.998241	+	1.42150i
$497$	19.0018	+	19.0018i	0.852349	+	0.852349i
$498$		0			0
$499$	−21.5723			−0.965707			−0.482853	−	0.875701i	$-0.660400\pi$
$499$	−21.5723			−0.965707			−0.482853	+	0.875701i	$0.660400\pi$
$500$	−16.1483	+	15.4672i	−0.722173	+	0.691713i
$501$		0			0
$502$	15.7772	+	9.58119i	0.704170	+	0.427629i
$503$	0.650945	−	0.650945i	0.0290242	−	0.0290242i	−0.692446	−	0.721470i	$-0.743467\pi$
$503$	0.650945	−	0.650945i	0.0290242	−	0.0290242i	0.721470	+	0.692446i	$0.243467\pi$
$504$		0			0
$505$	22.4251	+	10.2505i	0.997906	+	0.456140i
$506$	−5.65775	+	1.38240i	−0.251518	+	0.0614551i
$507$		0			0
$508$	−2.99014	−	0.945030i	−0.132666	−	0.0419289i
$509$			9.29371i			0.411937i	0.978559	+	0.205968i	$0.0660344\pi$
$509$			9.29371i			0.411937i	−0.978559	+	0.205968i	$0.933966\pi$
$510$		0			0
$511$	2.54090			0.112403
$512$	4.48248	−	22.1790i	0.198100	−	0.980182i
$513$		0			0
$514$	4.28723	+	17.5464i	0.189101	+	0.773937i
$515$	−3.19224	−	8.56766i	−0.140667	−	0.377536i
$516$		0			0
$517$	13.6753	+	13.6753i	0.601441	+	0.601441i
$518$	32.5498	+	19.7669i	1.43016	+	0.868508i
$519$		0			0
$520$	11.6596	+	39.0456i	0.511305	+	1.71226i
$521$			37.4945i			1.64266i	0.570451	+	0.821331i	$0.306768\pi$
$521$			37.4945i			1.64266i	−0.570451	+	0.821331i	$0.693232\pi$
$522$		0			0
$523$	−18.0635	+	18.0635i	−0.789861	+	0.789861i	−0.981471	−	0.191610i	$-0.938629\pi$
$523$	−18.0635	+	18.0635i	−0.789861	+	0.789861i	0.191610	+	0.981471i	$0.438629\pi$
$524$	−0.919501	−	1.76929i	−0.0401686	−	0.0772918i
$525$		0			0
$526$	−5.50685	+	1.34553i	−0.240110	+	0.0586677i
$527$	−18.2366	−	18.2366i	−0.794400	−	0.794400i
$528$		0			0
$529$			21.9012i			0.952225i
$530$	−0.857243	+	4.47914i	−0.0372363	+	0.194562i
$531$		0			0
$532$	−31.0535	−	9.81443i	−1.34634	−	0.425510i
$533$	28.8655	+	28.8655i	1.25030	+	1.25030i
$534$		0			0
$535$	−15.5243	+	5.78423i	−0.671175	+	0.250074i
$536$	3.87274	−	3.38930i	0.167277	−	0.146395i
$537$		0			0
$538$	−7.26710	+	11.9666i	−0.313307	+	0.515917i
$539$			21.3999i			0.921758i
$540$		0			0
$541$		−	29.6103i		−	1.27305i	−0.771258	−	0.636523i	$-0.780372\pi$
$541$		−	29.6103i		−	1.27305i	0.771258	−	0.636523i	$-0.219628\pi$
$542$	20.0941	+	12.2028i	0.863117	+	0.524155i
$543$		0			0
$544$	14.0503	+	5.49146i	0.602401	+	0.235444i
$545$	10.8083	+	4.94044i	0.462976	+	0.211625i
$546$		0			0
$547$	13.8891	+	13.8891i	0.593855	+	0.593855i	0.938670	−	0.344816i	$-0.112059\pi$
$547$	13.8891	+	13.8891i	0.593855	+	0.593855i	−0.344816	+	0.938670i	$0.612059\pi$
$548$	−0.879912	+	2.78410i	−0.0375880	+	0.118931i
$549$		0			0
$550$	−4.63314	−	27.3916i	−0.197558	−	1.16798i
$551$		−	20.1185i		−	0.857076i
$552$		0			0
$553$	−3.29101	−	3.29101i	−0.139948	−	0.139948i
$554$	−3.05093	−	12.4866i	−0.129622	−	0.530504i
$555$		0			0
$556$	−15.6632	−	30.1389i	−0.664267	−	1.27817i
$557$	16.0818	−	16.0818i	0.681408	−	0.681408i	−0.278910	−	0.960317i	$-0.589973\pi$
$557$	16.0818	−	16.0818i	0.681408	−	0.681408i	0.960317	+	0.278910i	$0.0899730\pi$
$558$		0			0
$559$		−	1.87804i		−	0.0794326i
$560$	7.97721	−	30.5306i	0.337099	−	1.29016i
$561$		0			0
$562$	−19.8397	+	32.6696i	−0.836886	+	1.37809i
$563$	−11.6731	−	11.6731i	−0.491962	−	0.491962i	0.416962	−	0.908924i	$-0.363095\pi$
$563$	−11.6731	−	11.6731i	−0.491962	−	0.491962i	−0.908924	+	0.416962i	$0.863095\pi$
$564$		0			0
$565$	−30.6874	+	11.4339i	−1.29103	+	0.481027i
$566$	−35.2589	+	8.61505i	−1.48204	+	0.362118i
$567$		0			0
$568$	21.4963	+	1.43103i	0.901965	+	0.0600447i
$569$	−26.5009			−1.11098			−0.555488	−	0.831524i	$-0.687469\pi$
$569$	−26.5009			−1.11098			−0.555488	+	0.831524i	$0.687469\pi$
$570$		0			0
$571$			42.2873i			1.76967i	0.465904	+	0.884835i	$0.345729\pi$
$571$			42.2873i			1.76967i	−0.465904	+	0.884835i	$0.654271\pi$
$572$	−48.2729	−	15.2566i	−2.01839	−	0.637911i
$573$		0			0
$574$	−7.50324	−	30.7086i	−0.313179	−	1.28175i
$575$	5.22761	+	0.377476i	0.218006	+	0.0157418i
$576$		0			0
$577$	10.2682	−	10.2682i	0.427473	−	0.427473i	−0.460294	−	0.887767i	$-0.652256\pi$
$577$	10.2682	−	10.2682i	0.427473	−	0.427473i	0.887767	+	0.460294i	$0.152256\pi$
$578$	7.25887	−	11.9531i	0.301929	−	0.497181i
$579$		0			0
$580$	19.4685	−	0.984832i	0.808384	−	0.0408929i
$581$	49.1720			2.04000
$582$		0			0
$583$	−4.00635	−	4.00635i	−0.165926	−	0.165926i
$584$	1.53291	−	1.34155i	0.0634322	−	0.0555138i
$585$		0			0
$586$	−5.45464	−	22.3242i	−0.225329	−	0.922206i
$587$	−18.7596	+	18.7596i	−0.774290	+	0.774290i	−0.978853	−	0.204563i	$-0.934423\pi$
$587$	−18.7596	+	18.7596i	−0.774290	+	0.774290i	0.204563	+	0.978853i	$0.434423\pi$
$588$		0			0
$589$	44.6379			1.83927
$590$	1.38954	−	0.943108i	0.0572066	−	0.0388272i
$591$		0			0
$592$	30.0736	−	5.26050i	1.23602	−	0.216205i
$593$	1.79755	−	1.79755i	0.0738164	−	0.0738164i	−0.669235	−	0.743051i	$-0.733378\pi$
$593$	1.79755	−	1.79755i	0.0738164	−	0.0738164i	0.743051	+	0.669235i	$0.233378\pi$
$594$		0			0
$595$	19.1335	+	8.74586i	0.784396	+	0.358545i
$596$	−11.5134	+	5.98354i	−0.471609	+	0.245095i
$597$		0			0
$598$	4.95780	−	8.16392i	0.202739	−	0.333848i
$599$	−34.7082			−1.41814			−0.709069	−	0.705139i	$-0.750885\pi$
$599$	−34.7082			−1.41814			−0.709069	+	0.705139i	$0.750885\pi$
$600$		0			0
$601$	−8.66540			−0.353469			−0.176735	−	0.984259i	$-0.556553\pi$
$601$	−8.66540			−0.353469			−0.176735	+	0.984259i	$0.556553\pi$
$602$	−0.754888	+	1.24306i	−0.0307669	+	0.0506634i
$603$		0			0
$604$	3.88476	+	7.47500i	0.158069	+	0.304153i
$605$	9.02002	+	4.12303i	0.366716	+	0.167625i
$606$		0			0
$607$	−5.31702	+	5.31702i	−0.215811	+	0.215811i	−0.806731	−	0.590919i	$-0.798765\pi$
$607$	−5.31702	+	5.31702i	−0.215811	+	0.215811i	0.590919	+	0.806731i	$0.298765\pi$
$608$	−23.9162	+	10.4747i	−0.969931	+	0.424807i
$609$		0			0
$610$	7.85890	−	5.33397i	0.318197	−	0.215966i
$611$	−31.7165			−1.28311
$612$		0			0
$613$	0.848748	−	0.848748i	0.0342806	−	0.0342806i	−0.689759	−	0.724039i	$-0.742283\pi$
$613$	0.848748	−	0.848748i	0.0342806	−	0.0342806i	0.724039	+	0.689759i	$0.242283\pi$
$614$	−8.47999	−	34.7061i	−0.342224	−	1.40062i
$615$		0			0
$616$	25.8191	+	29.5018i	1.04028	+	1.18866i
$617$	16.6187	+	16.6187i	0.669043	+	0.669043i	0.957494	−	0.288452i	$-0.0931405\pi$
$617$	16.6187	+	16.6187i	0.669043	+	0.669043i	−0.288452	+	0.957494i	$0.593141\pi$
$618$		0			0
$619$	6.21940			0.249979			0.124989	−	0.992158i	$-0.460110\pi$
$619$	6.21940			0.249979			0.124989	+	0.992158i	$0.460110\pi$
$620$	2.18510	+	43.1957i	0.0877556	+	1.73478i
$621$		0			0
$622$	−7.29494	+	12.0125i	−0.292500	+	0.481655i
$623$	7.27946	−	7.27946i	0.291646	−	0.291646i
$624$		0			0
$625$	−3.59168	+	24.7407i	−0.143667	+	0.989626i
$626$	2.47141	+	10.1148i	0.0987774	+	0.404267i
$627$		0			0
$628$	0.0314416	−	0.0994834i	0.00125466	−	0.00396982i
$629$			20.3540i			0.811567i
$630$		0			0
$631$	12.0019			0.477790			0.238895	−	0.971045i	$-0.423215\pi$
$631$	12.0019			0.477790			0.238895	+	0.971045i	$0.423215\pi$
$632$	−3.72303	−	0.247846i	−0.148094	−	0.00985879i
$633$		0			0
$634$	−25.8172	+	6.30809i	−1.02533	+	0.250526i
$635$	−3.28543	+	1.22412i	−0.130378	+	0.0485778i
$636$		0			0
$637$	−24.8158	−	24.8158i	−0.983239	−	0.983239i
$638$	−12.5709	+	20.7003i	−0.497686	+	0.819531i
$639$		0			0
$640$	−11.3071	−	22.6307i	−0.446951	−	0.894559i
$641$		−	6.27061i		−	0.247674i	−0.992303	−	0.123837i	$-0.960480\pi$
$641$		−	6.27061i		−	0.247674i	0.992303	−	0.123837i	$-0.0395200\pi$
$642$		0			0
$643$	−15.3358	+	15.3358i	−0.604787	+	0.604787i	−0.941579	−	0.336792i	$-0.890658\pi$
$643$	−15.3358	+	15.3358i	−0.604787	+	0.604787i	0.336792	+	0.941579i	$0.390658\pi$
$644$	−6.56307	+	3.41083i	−0.258621	+	0.134406i
$645$		0			0
$646$	−4.13157	−	16.9093i	−0.162555	−	0.665288i
$647$	28.9583	+	28.9583i	1.13847	+	1.13847i	0.988725	+	0.149741i	$0.0478441\pi$
$647$	28.9583	+	28.9583i	1.13847	+	1.13847i	0.149741	+	0.988725i	$0.452156\pi$
$648$		0			0
$649$			2.08643i			0.0818997i
$650$	37.1367	+	26.3913i	1.45662	+	1.03515i
$651$		0			0
$652$	3.59382	+	1.13582i	0.140745	+	0.0444822i
$653$	2.21463	+	2.21463i	0.0866651	+	0.0866651i	0.749110	−	0.662445i	$-0.230481\pi$
$653$	2.21463	+	2.21463i	0.0866651	+	0.0866651i	−0.662445	+	0.749110i	$0.730481\pi$
$654$		0			0
$655$	−2.02754	−	0.926783i	−0.0792225	−	0.0362124i
$656$	−20.7402	−	14.5647i	−0.809770	−	0.568655i
$657$		0			0
$658$	20.9930	+	12.7486i	0.818390	+	0.496993i
$659$		−	37.2920i		−	1.45269i	−0.687330	−	0.726345i	$-0.741218\pi$
$659$		−	37.2920i		−	1.45269i	0.687330	−	0.726345i	$-0.258782\pi$
$660$		0			0
$661$		−	6.19442i		−	0.240935i	−0.992717	−	0.120467i	$-0.961561\pi$
$661$		−	6.19442i		−	0.240935i	0.992717	−	0.120467i	$-0.0384393\pi$
$662$	6.31911	−	10.4056i	0.245599	−	0.404424i
$663$		0			0
$664$	29.6651	−	25.9619i	1.15123	−	1.00752i
$665$	−34.1202	+	12.7129i	−1.32312	+	0.492985i
$666$		0			0
$667$	−3.23087	−	3.23087i	−0.125100	−	0.125100i
$668$	12.8103	−	40.5326i	0.495644	−	1.56825i
$669$		0			0
$670$	1.08157	−	5.65128i	0.0417848	−	0.218328i
$671$			11.8003i			0.455546i
$672$		0			0
$673$	−27.8727	−	27.8727i	−1.07441	−	1.07441i	−0.996999	−	0.0774133i	$-0.975334\pi$
$673$	−27.8727	−	27.8727i	−1.07441	−	1.07441i	−0.0774133	−	0.996999i	$-0.524666\pi$
$674$	2.52431	−	0.616781i	0.0972326	−	0.0237575i
$675$		0			0
$676$	50.5999	−	26.2968i	1.94615	−	1.01142i
$677$	10.0200	−	10.0200i	0.385098	−	0.385098i	−0.487837	−	0.872935i	$-0.662214\pi$
$677$	10.0200	−	10.0200i	0.385098	−	0.385098i	0.872935	+	0.487837i	$0.162214\pi$
$678$		0			0
$679$		−	40.4823i		−	1.55357i
$680$	16.1607	−	4.82582i	0.619736	−	0.185062i
$681$		0			0
$682$	−45.9287	−	27.8917i	−1.75870	−	1.06803i
$683$	11.5229	+	11.5229i	0.440911	+	0.440911i	0.892318	−	0.451407i	$-0.149078\pi$
$683$	11.5229	+	11.5229i	0.440911	+	0.440911i	−0.451407	+	0.892318i	$0.649078\pi$
$684$		0			0
$685$	1.13977	+	3.05904i	0.0435485	+	0.116880i
$686$	−1.83920	−	7.52730i	−0.0702209	−	0.287394i
$687$		0			0
$688$	0.200896	+	1.14850i	0.00765909	+	0.0437861i
$689$	9.29173			0.353987
$690$		0			0
$691$			18.3907i			0.699614i	0.936822	+	0.349807i	$0.113753\pi$
$691$			18.3907i			0.699614i	−0.936822	+	0.349807i	$0.886247\pi$
$692$	1.84931	−	5.85134i	0.0703002	−	0.222435i
$693$		0			0
$694$	35.6757	−	8.71690i	1.35423	−	0.330889i
$695$	−34.5380	−	15.7872i	−1.31010	−	0.598844i
$696$		0			0
$697$	11.9473	−	11.9473i	0.452535	−	0.452535i
$698$	−37.6881	−	22.8873i	−1.42652	−	0.866297i
$699$		0			0
$700$	−13.9724	−	32.3955i	−0.528107	−	1.22443i
$701$	52.0764			1.96690			0.983449	−	0.181186i	$-0.0579937\pi$
$701$	52.0764			1.96690			0.983449	+	0.181186i	$0.0579937\pi$
$702$		0			0
$703$	−24.9103	−	24.9103i	−0.939509	−	0.939509i
$704$	31.1529	+	4.16622i	1.17412	+	0.157020i
$705$		0			0
$706$	17.5755	−	4.29436i	0.661464	−	0.161620i
$707$	−27.5086	+	27.5086i	−1.03457	+	1.03457i
$708$		0			0
$709$	−49.8546			−1.87233			−0.936165	−	0.351561i	$-0.885651\pi$
$709$	−49.8546			−1.87233			−0.936165	+	0.351561i	$0.885651\pi$
$710$	19.9299	−	13.5268i	0.747956	−	0.507651i
$711$		0			0
$712$	0.548217	−	8.23508i	0.0205453	−	0.308622i
$713$	7.16849	−	7.16849i	0.268462	−	0.268462i
$714$		0			0
$715$	−53.0401	+	19.7623i	−1.98359	+	0.739068i
$716$	−25.3727	+	13.1862i	−0.948224	+	0.492792i
$717$		0			0
$718$	15.8438	+	9.62164i	0.591285	+	0.359076i
$719$	21.3548			0.796400			0.398200	−	0.917299i	$-0.369635\pi$
$719$	21.3548			0.796400			0.398200	+	0.917299i	$0.369635\pi$
$720$		0			0
$721$	14.4257			0.537242
$722$	2.78418	+	1.69078i	0.103616	+	0.0629243i
$723$		0			0
$724$	−19.6209	+	10.1970i	−0.729204	+	0.378968i
$725$	16.4807	−	14.2609i	0.612079	−	0.529638i
$726$		0			0
$727$	13.1166	−	13.1166i	0.486469	−	0.486469i	−0.420721	−	0.907190i	$-0.638223\pi$
$727$	13.1166	−	13.1166i	0.486469	−	0.486469i	0.907190	+	0.420721i	$0.138223\pi$
$728$	−64.1514	−	4.27062i	−2.37761	−	0.158280i
$729$		0			0
$730$	0.428109	−	2.23689i	0.0158450	−	0.0827911i
$731$	−0.777309			−0.0287498
$732$		0			0
$733$	−3.40526	+	3.40526i	−0.125776	+	0.125776i	−0.767193	−	0.641417i	$-0.778347\pi$
$733$	−3.40526	+	3.40526i	−0.125776	+	0.125776i	0.641417	+	0.767193i	$0.278347\pi$
$734$	6.69789	−	1.63654i	0.247224	−	0.0604059i
$735$		0			0
$736$	−2.15859	+	5.52291i	−0.0795668	+	0.203577i
$737$	5.05477	+	5.05477i	0.186195	+	0.186195i
$738$		0			0
$739$	6.84745			0.251887			0.125944	−	0.992037i	$-0.459804\pi$
$739$	6.84745			0.251887			0.125944	+	0.992037i	$0.459804\pi$
$740$	22.8861	−	25.3249i	0.841308	−	0.930960i
$741$		0			0
$742$	−6.15013	−	3.73486i	−0.225778	−	0.137111i
$743$	9.83167	−	9.83167i	0.360689	−	0.360689i	−0.503377	−	0.864067i	$-0.667909\pi$
$743$	9.83167	−	9.83167i	0.360689	−	0.360689i	0.864067	+	0.503377i	$0.167909\pi$
$744$		0			0
$745$	−6.03092	+	13.1940i	−0.220956	+	0.483389i
$746$	14.0853	−	3.44157i	0.515700	−	0.126005i
$747$		0			0
$748$	−6.31462	+	19.9799i	−0.230885	+	0.730537i
$749$		−	26.1389i		−	0.955095i
$750$		0			0
$751$	−36.1038			−1.31745			−0.658723	−	0.752385i	$-0.728903\pi$
$751$	−36.1038			−1.31745			−0.658723	+	0.752385i	$0.728903\pi$
$752$	19.3959	−	3.39275i	0.707297	−	0.123721i
$753$		0			0
$754$	−9.42702	−	38.5820i	−0.343312	−	1.40507i
$755$	8.56606	+	3.91553i	0.311751	+	0.142501i
$756$		0			0
$757$	−26.0495	−	26.0495i	−0.946785	−	0.946785i	0.0518693	−	0.998654i	$-0.483482\pi$
$757$	−26.0495	−	26.0495i	−0.946785	−	0.946785i	−0.998654	+	0.0518693i	$0.983482\pi$
$758$	−35.2557	−	21.4101i	−1.28054	−	0.777651i
$759$		0			0
$760$	−13.8723	+	25.6845i	−0.503200	+	0.931674i
$761$		−	29.4006i		−	1.06577i	−0.846188	−	0.532885i	$-0.821108\pi$
$761$		−	29.4006i		−	1.06577i	0.846188	−	0.532885i	$-0.178892\pi$
$762$		0			0
$763$	−13.2584	+	13.2584i	−0.479986	+	0.479986i
$764$	−22.5610	+	11.7249i	−0.816227	+	0.424194i
$765$		0			0
$766$	23.8767	−	5.83395i	0.862698	−	0.210789i
$767$	−2.41948	−	2.41948i	−0.0873623	−	0.0873623i
$768$		0			0
$769$		−	39.4234i		−	1.42164i	−0.703372	−	0.710822i	$-0.748323\pi$
$769$		−	39.4234i		−	1.42164i	0.703372	−	0.710822i	$-0.251677\pi$
$770$	43.0505	+	8.23923i	1.55143	+	0.296921i
$771$		0			0
$772$	−14.1349	+	44.7238i	−0.508727	+	1.60965i
$773$	2.76896	+	2.76896i	0.0995925	+	0.0995925i	0.755147	−	0.655555i	$-0.227565\pi$
$773$	2.76896	+	2.76896i	0.0995925	+	0.0995925i	−0.655555	+	0.755147i	$0.727565\pi$
$774$		0			0
$775$	31.6414	+	36.5666i	1.13659	+	1.31351i
$776$	−21.3739	−	24.4226i	−0.767279	−	0.876722i
$777$		0			0
$778$	23.0710	−	37.9906i	0.827136	−	1.36203i
$779$			29.2434i			1.04775i
$780$		0			0
$781$			29.9252i			1.07081i
$782$	−3.37900	−	2.05200i	−0.120833	−	0.0733795i
$783$		0			0
$784$	17.8305	+	12.5213i	0.636803	+	0.447190i
$785$	−0.0407272	−	0.109308i	−0.00145362	−	0.00390136i
$786$		0			0
$787$	20.1445	+	20.1445i	0.718072	+	0.718072i	0.968210	−	0.250138i	$-0.0804760\pi$
$787$	20.1445	+	20.1445i	0.718072	+	0.718072i	−0.250138	+	0.968210i	$0.580476\pi$
$788$	−26.8681	−	8.49162i	−0.957136	−	0.302502i
$789$		0			0
$790$	−3.45174	+	2.34276i	−0.122807	+	0.0833515i
$791$		−	51.6696i		−	1.83716i
$792$		0			0
$793$	−13.6839	−	13.6839i	−0.485931	−	0.485931i
$794$	7.09036	+	29.0188i	0.251627	+	1.02984i
$795$		0			0
$796$	−27.8127	+	14.4543i	−0.985795	+	0.512318i
$797$	−27.4953	+	27.4953i	−0.973933	+	0.973933i	−0.999669	−	0.0257360i	$-0.991807\pi$
$797$	−27.4953	+	27.4953i	−0.973933	+	0.973933i	0.0257360	+	0.999669i	$0.491807\pi$
$798$		0			0
$799$			13.1273i			0.464410i
$800$	−25.5337	−	12.1668i	−0.902752	−	0.430161i
$801$		0			0
$802$	19.8549	−	32.6946i	0.701099	−	1.15449i
$803$	2.00078	+	2.00078i	0.0706060	+	0.0706060i
$804$		0			0
$805$	−3.43784	+	7.52102i	−0.121168	+	0.265081i
$806$	85.6039	−	20.9162i	3.01527	−	0.736742i
$807$		0			0
$808$	−2.07168	+	31.1198i	−0.0728814	+	1.09479i
$809$	25.2679			0.888372			0.444186	−	0.895935i	$-0.353493\pi$
$809$	25.2679			0.888372			0.444186	+	0.895935i	$0.353493\pi$
$810$		0			0
$811$			25.9061i			0.909687i	0.890571	+	0.454844i	$0.150305\pi$
$811$			25.9061i			0.909687i	−0.890571	+	0.454844i	$0.849695\pi$
$812$	−9.26858	+	29.3264i	−0.325263	+	1.02916i
$813$		0			0
$814$	10.0656	+	41.1957i	0.352800	+	1.44391i
$815$	3.94873	−	1.47126i	0.138318	−	0.0515361i
$816$		0			0
$817$	0.951312	−	0.951312i	0.0332822	−	0.0332822i
$818$	3.42473	−	5.63944i	0.119743	−	0.197178i
$819$		0			0
$820$	−28.2986	+	1.43151i	−0.988229	+	0.0499905i
$821$	−14.0659			−0.490904			−0.245452	−	0.969409i	$-0.578936\pi$
$821$	−14.0659			−0.490904			−0.245452	+	0.969409i	$0.578936\pi$
$822$		0			0
$823$	−18.9660	−	18.9660i	−0.661112	−	0.661112i	0.294530	−	0.955642i	$-0.404837\pi$
$823$	−18.9660	−	18.9660i	−0.661112	−	0.661112i	−0.955642	+	0.294530i	$0.904837\pi$
$824$	8.70293	−	7.61652i	0.303181	−	0.265334i
$825$		0			0
$826$	0.628913	+	2.57396i	0.0218827	+	0.0895595i
$827$	5.96783	−	5.96783i	0.207522	−	0.207522i	−0.595692	−	0.803213i	$-0.703122\pi$
$827$	5.96783	−	5.96783i	0.207522	−	0.207522i	0.803213	+	0.595692i	$0.203122\pi$
$828$		0			0
$829$	−8.93872			−0.310454			−0.155227	−	0.987879i	$-0.549611\pi$
$829$	−8.93872			−0.310454			−0.155227	+	0.987879i	$0.549611\pi$
$830$	8.28483	−	43.2887i	0.287571	−	1.50257i
$831$		0			0
$832$	−40.9569	+	31.2944i	−1.41992	+	1.08494i
$833$	−10.2711	+	10.2711i	−0.355873	+	0.355873i
$834$		0			0
$835$	−16.5935	−	44.5354i	−0.574242	−	1.54121i
$836$	−16.7243	−	32.1806i	−0.578421	−	1.11299i
$837$		0			0
$838$	1.78853	−	2.94514i	0.0617836	−	0.101738i
$839$	7.98961			0.275832			0.137916	−	0.990444i	$-0.455960\pi$
$839$	7.98961			0.275832			0.137916	+	0.990444i	$0.455960\pi$
$840$		0			0
$841$	10.0005			0.344843
$842$	7.06274	−	11.6301i	0.243398	−	0.400799i
$843$		0			0
$844$	39.2719	−	20.4096i	1.35180	−	0.702529i
$845$	26.5051	−	57.9855i	0.911802	−	1.99476i
$846$		0			0
$847$	−11.0647	+	11.0647i	−0.380189	+	0.380189i
$848$	−5.68227	+	0.993948i	−0.195130	+	0.0341323i
$849$		0			0
$850$	10.9232	−	15.3706i	0.374662	−	0.527209i
$851$	−8.00079			−0.274264
$852$		0			0
$853$	17.2928	−	17.2928i	0.592094	−	0.592094i	−0.346103	−	0.938197i	$-0.612495\pi$
$853$	17.2928	−	17.2928i	0.592094	−	0.592094i	0.938197	+	0.346103i	$0.112495\pi$
$854$	3.55697	+	14.5576i	0.121717	+	0.498152i
$855$		0			0
$856$	−13.8009	−	15.7694i	−0.471705	−	0.538987i
$857$	31.0209	+	31.0209i	1.05965	+	1.05965i	0.998104	+	0.0615490i	$0.0196040\pi$
$857$	31.0209	+	31.0209i	1.05965	+	1.05965i	0.0615490	+	0.998104i	$0.480396\pi$
$858$		0			0
$859$	30.7443			1.04898			0.524492	−	0.851416i	$-0.324255\pi$
$859$	30.7443			1.04898			0.524492	+	0.851416i	$0.324255\pi$
$860$	0.967144	+	0.874008i	0.0329793	+	0.0298034i
$861$		0			0
$862$	19.4122	−	31.9657i	0.661182	−	1.08876i
$863$	−26.9037	+	26.9037i	−0.915812	+	0.915812i	−0.996721	−	0.0809092i	$-0.974218\pi$
$863$	−26.9037	+	26.9037i	−0.915812	+	0.915812i	0.0809092	+	0.996721i	$0.474218\pi$
$864$		0			0
$865$	−2.39546	−	6.42919i	−0.0814482	−	0.218599i
$866$	2.48202	+	10.1582i	0.0843425	+	0.345189i
$867$		0			0
$868$	−65.0680	−	20.5647i	−2.20855	−	0.698010i
$869$		−	5.18287i		−	0.175817i
$870$		0			0
$871$	−11.7233			−0.397228
$872$	−0.998490	+	14.9989i	−0.0338131	+	0.507926i
$873$		0			0
$874$	6.64675	−	1.62405i	0.224830	−	0.0549342i
$875$	−34.6002	−	18.9392i	−1.16970	−	0.640262i
$876$		0			0
$877$	26.8633	+	26.8633i	0.907111	+	0.907111i	0.996038	−	0.0889274i	$-0.0283439\pi$
$877$	26.8633	+	26.8633i	0.907111	+	0.907111i	−0.0889274	+	0.996038i	$0.528344\pi$
$878$	−27.4352	+	45.1771i	−0.925895	+	1.52465i
$879$		0			0
$880$	30.3222	−	17.7592i	1.02216	−	0.598663i
$881$			5.85067i			0.197114i	0.995131	+	0.0985571i	$0.0314227\pi$
$881$			5.85067i			0.197114i	−0.995131	+	0.0985571i	$0.968577\pi$
$882$		0			0
$883$	14.4524	−	14.4524i	0.486362	−	0.486362i	−0.420794	−	0.907156i	$-0.638249\pi$
$883$	14.4524	−	14.4524i	0.486362	−	0.486362i	0.907156	+	0.420794i	$0.138249\pi$
$884$	−15.8466	−	30.4917i	−0.532978	−	1.02555i
$885$		0			0
$886$	8.57853	+	35.1094i	0.288201	+	1.17952i
$887$	23.4185	+	23.4185i	0.786317	+	0.786317i	0.980888	−	0.194571i	$-0.0623315\pi$
$887$	23.4185	+	23.4185i	0.786317	+	0.786317i	−0.194571	+	0.980888i	$0.562332\pi$
$888$		0			0
$889$		−	5.53180i		−	0.185531i
$890$	−5.18200	−	7.63499i	−0.173701	−	0.255925i
$891$		0			0
$892$	2.70754	−	8.56683i	0.0906550	−	0.286839i
$893$	−16.0659	−	16.0659i	−0.537623	−	0.537623i
$894$		0			0
$895$	−13.2906	+	29.0762i	−0.444257	+	0.971909i
$896$	39.6881	−	4.25070i	1.32588	−	0.142006i
$897$		0			0
$898$	−29.5631	−	17.9531i	−0.986532	−	0.599103i
$899$		−	42.1552i		−	1.40596i
$900$		0			0
$901$		−	3.84579i		−	0.128122i
$902$	18.2725	−	30.0891i	0.608409	−	1.00186i
$903$		0			0
$904$	−27.2807	−	31.1719i	−0.907342	−	1.03676i
$905$	−10.2777	+	22.4848i	−0.341643	+	0.747419i
$906$		0			0
$907$	15.8605	+	15.8605i	0.526640	+	0.526640i	0.919569	−	0.392929i	$-0.128538\pi$
$907$	15.8605	+	15.8605i	0.526640	+	0.526640i	−0.392929	+	0.919569i	$0.628538\pi$
$908$	49.8717	+	15.7619i	1.65505	+	0.523076i
$909$		0			0
$910$	−59.4768	+	40.3679i	−1.97164	+	1.33818i
$911$			48.6371i			1.61142i	0.592310	+	0.805710i	$0.298216\pi$
$911$			48.6371i			1.61142i	−0.592310	+	0.805710i	$0.701784\pi$
$912$		0			0
$913$	38.7194	+	38.7194i	1.28143	+	1.28143i
$914$	11.1970	−	2.73585i	0.370365	−	0.0904940i
$915$		0			0
$916$	17.7370	+	34.1293i	0.586047	+	1.12766i
$917$	2.48715	−	2.48715i	0.0821330	−	0.0821330i
$918$		0			0
$919$			28.6171i			0.943990i	0.881601	+	0.471995i	$0.156466\pi$
$919$			28.6171i			0.943990i	−0.881601	+	0.471995i	$0.843534\pi$
$920$	1.89694	+	6.35250i	0.0625404	+	0.209436i
$921$		0			0
$922$	−12.8377	−	7.79607i	−0.422786	−	0.256750i
$923$	−34.7020	−	34.7020i	−1.14223	−	1.14223i
$924$		0			0
$925$	2.74851	−	38.0637i	0.0903704	−	1.25153i
$926$	6.55024	+	26.8082i	0.215254	+	0.880973i
$927$		0			0
$928$	9.89217	+	22.5861i	0.324727	+	0.741424i
$929$	−27.8635			−0.914171			−0.457086	−	0.889423i	$-0.651107\pi$
$929$	−27.8635			−0.914171			−0.457086	+	0.889423i	$0.651107\pi$
$930$		0			0
$931$		−	25.1407i		−	0.823953i
$932$	37.0295	+	11.7031i	1.21294	+	0.383349i
$933$		0			0
$934$	−22.6824	+	5.54216i	−0.742192	+	0.181345i
$935$	8.17950	+	21.9530i	0.267498	+	0.717939i
$936$		0			0
$937$	−2.53180	+	2.53180i	−0.0827105	+	0.0827105i	−0.747252	−	0.664541i	$-0.768627\pi$
$937$	−2.53180	+	2.53180i	−0.0827105	+	0.0827105i	0.664541	+	0.747252i	$0.268627\pi$
$938$	7.75955	+	4.71223i	0.253358	+	0.153860i
$939$		0			0
$940$	14.7603	−	16.3332i	0.481429	−	0.532731i
$941$	28.8111			0.939216			0.469608	−	0.882875i	$-0.344395\pi$
$941$	28.8111			0.939216			0.469608	+	0.882875i	$0.344395\pi$
$942$		0			0
$943$	4.69626	+	4.69626i	0.152931	+	0.152931i
$944$	1.73842	+	1.22080i	0.0565809	+	0.0397335i
$945$		0			0
$946$	−1.57324	+	0.384401i	−0.0511505	+	0.0124980i
$947$	−28.0862	+	28.0862i	−0.912678	+	0.912678i	−0.996482	−	0.0838038i	$-0.973293\pi$
$947$	−28.0862	+	28.0862i	−0.912678	+	0.912678i	0.0838038	+	0.996482i	$0.473293\pi$
$948$		0			0
$949$	−4.64031			−0.150631
$950$	5.44304	+	32.1798i	0.176596	+	1.04405i
$951$		0			0
$952$	−1.76759	+	26.5519i	−0.0572878	+	0.860552i
$953$	23.3080	−	23.3080i	0.755020	−	0.755020i	−0.220392	−	0.975411i	$-0.570734\pi$
$953$	23.3080	−	23.3080i	0.755020	−	0.755020i	0.975411	+	0.220392i	$0.0707336\pi$
$954$		0			0
$955$	−11.8178	+	25.8540i	−0.382415	+	0.836616i
$956$	24.6926	+	47.5131i	0.798616	+	1.53668i
$957$		0			0
$958$	−6.17343	−	3.74901i	−0.199454	−	0.121125i
$959$	−5.15063			−0.166323
$960$		0			0
$961$	62.5320			2.01716
$962$	−59.4438	−	36.0991i	−1.91655	−	1.16388i
$963$		0			0
$964$	−16.2652	−	31.2972i	−0.523866	−	1.00802i
$965$	18.3093	+	49.1405i	0.589398	+	1.58189i
$966$		0			0
$967$	27.4623	−	27.4623i	0.883128	−	0.883128i	−0.110723	−	0.993851i	$-0.535317\pi$
$967$	27.4623	−	27.4623i	0.883128	−	0.883128i	0.993851	+	0.110723i	$0.0353168\pi$
$968$	−0.833287	+	12.5173i	−0.0267828	+	0.402320i
$969$		0			0
$970$	−35.6387	−	6.82073i	−1.14429	−	0.219000i
$971$	41.1632			1.32099			0.660496	−	0.750830i	$-0.270346\pi$
$971$	41.1632			1.32099			0.660496	+	0.750830i	$0.270346\pi$
$972$		0			0
$973$	42.3673	−	42.3673i	1.35823	−	1.35823i
$974$	7.39334	−	1.80647i	0.236898	−	0.0578829i
$975$		0			0
$976$	9.83207	+	6.90450i	0.314717	+	0.221008i
$977$	−8.98437	−	8.98437i	−0.287435	−	0.287435i	0.548630	−	0.836065i	$-0.315150\pi$
$977$	−8.98437	−	8.98437i	−0.287435	−	0.287435i	−0.836065	+	0.548630i	$0.815150\pi$
$978$		0			0
$979$	11.4641			0.366395
$980$	24.3284	−	1.23068i	0.777143	−	0.0393125i
$981$		0			0
$982$	23.4230	+	14.2244i	0.747459	+	0.453918i
$983$	37.2602	−	37.2602i	1.18842	−	1.18842i	0.210910	−	0.977505i	$-0.432357\pi$
$983$	37.2602	−	37.2602i	1.18842	−	1.18842i	0.977505	−	0.210910i	$-0.0676428\pi$
$984$		0			0
$985$	−29.5214	+	10.9994i	−0.940631	+	0.350471i
$986$	−15.9689	+	3.90179i	−0.508553	+	0.124258i
$987$		0			0
$988$	56.7113	+	17.9235i	1.80423	+	0.570223i
$989$		−	0.305546i		−	0.00971581i
$990$		0			0
$991$	20.4634			0.650040			0.325020	−	0.945707i	$-0.394629\pi$
$991$	20.4634			0.650040			0.325020	+	0.945707i	$0.394629\pi$
$992$	−50.1128	+	21.9483i	−1.59108	+	0.696858i
$993$		0			0
$994$	9.02035	+	36.9177i	0.286108	+	1.17096i
$995$	−14.5687	+	31.8723i	−0.461860	+	1.01042i
$996$		0			0
$997$	23.1571	+	23.1571i	0.733392	+	0.733392i	0.971290	−	0.237898i	$-0.0764584\pi$
$997$	23.1571	+	23.1571i	0.733392	+	0.733392i	−0.237898	+	0.971290i	$0.576458\pi$
$998$	−26.0761	−	15.8355i	−0.825423	−	0.501264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.21	yes	48
3.2	odd	2	inner	360.2.x.a.53.4	✓	48
4.3	odd	2		1440.2.bj.a.593.21		48
5.2	odd	4	inner	360.2.x.a.197.9	yes	48
8.3	odd	2		1440.2.bj.a.593.4		48
8.5	even	2	inner	360.2.x.a.53.16	yes	48
12.11	even	2		1440.2.bj.a.593.3		48
15.2	even	4	inner	360.2.x.a.197.16	yes	48
20.7	even	4		1440.2.bj.a.17.22		48
24.5	odd	2	inner	360.2.x.a.53.9	yes	48
24.11	even	2		1440.2.bj.a.593.22		48
40.27	even	4		1440.2.bj.a.17.3		48
40.37	odd	4	inner	360.2.x.a.197.4	yes	48
60.47	odd	4		1440.2.bj.a.17.4		48
120.77	even	4	inner	360.2.x.a.197.21	yes	48
120.107	odd	4		1440.2.bj.a.17.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.4	✓	48	3.2	odd	2	inner
360.2.x.a.53.9	yes	48	24.5	odd	2	inner
360.2.x.a.53.16	yes	48	8.5	even	2	inner
360.2.x.a.53.21	yes	48	1.1	even	1	trivial
360.2.x.a.197.4	yes	48	40.37	odd	4	inner
360.2.x.a.197.9	yes	48	5.2	odd	4	inner
360.2.x.a.197.16	yes	48	15.2	even	4	inner
360.2.x.a.197.21	yes	48	120.77	even	4	inner
1440.2.bj.a.17.3		48	40.27	even	4
1440.2.bj.a.17.4		48	60.47	odd	4
1440.2.bj.a.17.21		48	120.107	odd	4
1440.2.bj.a.17.22		48	20.7	even	4
1440.2.bj.a.593.3		48	12.11	even	2
1440.2.bj.a.593.4		48	8.3	odd	2
1440.2.bj.a.593.21		48	4.3	odd	2
1440.2.bj.a.593.22		48	24.11	even	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20878 + 0.734068i) q^{2} +(0.922287 + 1.77465i) q^{4} +(2.03368 + 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-0.187875 + 2.82218i) q^{8} +O(q^{10})\)	\(q+(1.20878 + 0.734068i) q^{2} +(0.922287 + 1.77465i) q^{4} +(2.03368 + 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-0.187875 + 2.82218i) q^{8} +(1.77589 + 2.61653i) q^{10} -3.92878 q^{11} +(4.55591 - 4.55591i) q^{13} +(-4.84680 + 1.18425i) q^{14} +(-2.29877 + 3.27348i) q^{16} +(-1.88566 - 1.88566i) q^{17} +4.61555 q^{19} +(0.225939 + 4.46642i) q^{20} +(-4.74902 - 2.88399i) q^{22} +(0.741221 - 0.741221i) q^{23} +(3.27172 + 3.78098i) q^{25} +(8.85143 - 2.16273i) q^{26} +(-6.72802 - 2.12638i) q^{28} -4.35885i q^{29} +9.67119 q^{31} +(-5.18166 + 2.26945i) q^{32} +(-0.895142 - 3.66355i) q^{34} +(-7.39245 + 2.75436i) q^{35} +(-5.39704 - 5.39704i) q^{37} +(5.57917 + 3.38813i) q^{38} +(-3.00555 + 5.56477i) q^{40} +6.33584i q^{41} +(0.206110 - 0.206110i) q^{43} +(-3.62346 - 6.97221i) q^{44} +(1.44008 - 0.351864i) q^{46} +(-3.48081 - 3.48081i) q^{47} -5.44695i q^{49} +(1.17928 + 6.97204i) q^{50} +(12.2870 + 3.88329i) q^{52} +(1.01974 + 1.01974i) q^{53} +(-7.98989 - 3.65216i) q^{55} +(-6.57177 - 7.50916i) q^{56} +(3.19969 - 5.26888i) q^{58} -0.531064i q^{59} -3.00356i q^{61} +(11.6903 + 7.09932i) q^{62} +(-7.92941 - 1.06044i) q^{64} +(13.5004 - 5.03014i) q^{65} +(-1.28660 - 1.28660i) q^{67} +(1.60727 - 5.08552i) q^{68} +(-10.9577 - 2.09715i) q^{70} -7.61692i q^{71} +(-0.509262 - 0.509262i) q^{73} +(-2.56202 - 10.4856i) q^{74} +(4.25686 + 8.19099i) q^{76} +(9.80109 - 9.80109i) q^{77} +1.31920i q^{79} +(-7.71797 + 4.52029i) q^{80} +(-4.65094 + 7.65863i) q^{82} +(-9.85533 - 9.85533i) q^{83} +(-2.08194 - 5.58774i) q^{85} +(0.400440 - 0.0978424i) q^{86} +(0.738121 - 11.0877i) q^{88} -2.91798 q^{89} +22.7312i q^{91} +(1.99903 + 0.631790i) q^{92} +(-1.65237 - 6.76268i) q^{94} +(9.38656 + 4.29057i) q^{95} +(-8.11369 + 8.11369i) q^{97} +(3.99844 - 6.58416i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more