LMFDB - Embedded newform 360.2.x.a.53.16

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			53.16
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.734068 + 1.20878i) q^{2} +(-0.922287 + 1.77465i) q^{4} +(-2.03368 - 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-2.82218 + 0.187875i) q^{8} +O(q^{10})$	\(q+(0.734068 + 1.20878i) q^{2} +(-0.922287 + 1.77465i) q^{4} +(-2.03368 - 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-2.82218 + 0.187875i) q^{8} +(-0.369193 - 3.14065i) q^{10} +3.92878 q^{11} +(-4.55591 + 4.55591i) q^{13} +(-4.84680 - 1.18425i) q^{14} +(-2.29877 - 3.27348i) q^{16} +(-1.88566 - 1.88566i) q^{17} -4.61555 q^{19} +(3.52534 - 2.75173i) q^{20} +(2.88399 + 4.74902i) q^{22} +(0.741221 - 0.741221i) q^{23} +(3.27172 + 3.78098i) q^{25} +(-8.85143 - 2.16273i) q^{26} +(-2.12638 - 6.72802i) q^{28} +4.35885i q^{29} +9.67119 q^{31} +(2.26945 - 5.18166i) q^{32} +(0.895142 - 3.66355i) q^{34} +(7.39245 - 2.75436i) q^{35} +(5.39704 + 5.39704i) q^{37} +(-3.38813 - 5.57917i) q^{38} +(5.91406 + 2.24139i) q^{40} +6.33584i q^{41} +(-0.206110 + 0.206110i) q^{43} +(-3.62346 + 6.97221i) q^{44} +(1.44008 + 0.351864i) q^{46} +(-3.48081 - 3.48081i) q^{47} -5.44695i q^{49} +(-2.16870 + 6.73028i) q^{50} +(-3.88329 - 12.2870i) q^{52} +(-1.01974 - 1.01974i) q^{53} +(-7.98989 - 3.65216i) q^{55} +(6.57177 - 7.50916i) q^{56} +(-5.26888 + 3.19969i) q^{58} +0.531064i q^{59} +3.00356i q^{61} +(7.09932 + 11.6903i) q^{62} +(7.92941 - 1.06044i) q^{64} +(13.5004 - 5.03014i) q^{65} +(1.28660 + 1.28660i) q^{67} +(5.08552 - 1.60727i) q^{68} +(8.75597 + 6.91393i) q^{70} -7.61692i q^{71} +(-0.509262 - 0.509262i) q^{73} +(-2.56202 + 10.4856i) q^{74} +(4.25686 - 8.19099i) q^{76} +(-9.80109 + 9.80109i) q^{77} +1.31920i q^{79} +(1.63198 + 8.79413i) q^{80} +(-7.65863 + 4.65094i) q^{82} +(9.85533 + 9.85533i) q^{83} +(2.08194 + 5.58774i) q^{85} +(-0.400440 - 0.0978424i) q^{86} +(-11.0877 + 0.738121i) q^{88} -2.91798 q^{89} -22.7312i q^{91} +(0.631790 + 1.99903i) q^{92} +(1.65237 - 6.76268i) q^{94} +(9.38656 + 4.29057i) q^{95} +(-8.11369 + 8.11369i) q^{97} +(6.58416 - 3.99844i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.734068	+	1.20878i	0.519065	+	0.854735i
$2$	0.734068	+	1.20878i	0.519065	+	0.854735i
$3$		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	$0.482308\pi$
$8$	−2.82218	+	0.187875i	−0.997791	+	0.0664240i
$9$		0			0
$10$	−0.369193	−	3.14065i	−0.116749	−	0.993161i
$11$	3.92878			1.18457			0.592286	−	0.805728i	$-0.298226\pi$
$11$	3.92878			1.18457			0.592286	+	0.805728i	$0.298226\pi$
$12$		0			0
$13$	−4.55591	+	4.55591i	−1.26358	+	1.26358i	−0.314237	+	0.949345i	$0.601749\pi$
$13$	−4.55591	+	4.55591i	−1.26358	+	1.26358i	−0.949345	+	0.314237i	$0.898251\pi$
$14$	−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	$-0.677598\pi$
$19$	−4.61555			−1.05888			−0.529440	+	0.848347i	$0.677598\pi$
$20$	3.52534	−	2.75173i	0.788289	−	0.615305i
$21$		0			0
$22$	2.88399	+	4.74902i	0.614870	+	1.01249i
$23$	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
$28$	−2.12638	−	6.72802i	−0.401849	−	1.27148i
$29$			4.35885i			0.809418i	0.914446	+	0.404709i	$0.132627\pi$
$29$			4.35885i			0.809418i	−0.914446	+	0.404709i	$0.867373\pi$
$30$		0			0
$31$	9.67119			1.73700			0.868499	−	0.495691i	$-0.165085\pi$
$31$	9.67119			1.73700			0.868499	+	0.495691i	$0.165085\pi$
$32$	2.26945	−	5.18166i	0.401185	−	0.915997i
$33$		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	0.994260	−	0.106992i	$-0.0341221\pi$
$37$	5.39704	+	5.39704i	0.887267	+	0.887267i	−0.106992	+	0.994260i	$0.534122\pi$
$38$	−3.38813	−	5.57917i	−0.549627	−	0.905061i
$39$		0			0
$40$	5.91406	+	2.24139i	0.935096	+	0.354396i
$41$			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	−0.722648	−	0.691216i	$-0.757075\pi$
$43$	−0.206110	+	0.206110i	−0.0314315	+	0.0314315i	0.691216	+	0.722648i	$0.257075\pi$
$44$	−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
$50$	−2.16870	+	6.73028i	−0.306701	+	0.951806i
$51$		0			0
$52$	−3.88329	−	12.2870i	−0.538516	−	1.70390i
$53$	−1.01974	−	1.01974i	−0.140073	−	0.140073i	0.633593	−	0.773666i	$-0.281579\pi$
$53$	−1.01974	−	1.01974i	−0.140073	−	0.140073i	−0.773666	+	0.633593i	$0.781579\pi$
$54$		0			0
$55$	−7.98989	−	3.65216i	−1.07736	−	0.492457i
$56$	6.57177	−	7.50916i	0.878190	−	1.00345i
$57$		0			0
$58$	−5.26888	+	3.19969i	−0.691837	+	0.420140i
$59$			0.531064i			0.0691386i	0.999402	+	0.0345693i	$0.0110059\pi$
$59$			0.531064i			0.0691386i	−0.999402	+	0.0345693i	$0.988994\pi$
$60$		0			0
$61$			3.00356i			0.384566i	0.981340	+	0.192283i	$0.0615892\pi$
$61$			3.00356i			0.384566i	−0.981340	+	0.192283i	$0.938411\pi$
$62$	7.09932	+	11.6903i	0.901614	+	1.48467i
$63$		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	0.781317	−	0.624134i	$-0.214548\pi$
$67$	1.28660	+	1.28660i	0.157183	+	0.157183i	−0.624134	+	0.781317i	$0.714548\pi$
$68$	5.08552	−	1.60727i	0.616710	−	0.194910i
$69$		0			0
$70$	8.75597	+	6.91393i	1.04654	+	0.826373i
$71$		−	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	$0.976356\pi$
$80$	1.63198	+	8.79413i	0.182461	+	0.983213i
$81$		0			0
$82$	−7.65863	+	4.65094i	−0.845754	+	0.513611i
$83$	9.85533	+	9.85533i	1.08176	+	1.08176i	0.996345	+	0.0854172i	$0.0272223\pi$
$83$	9.85533	+	9.85533i	1.08176	+	1.08176i	0.0854172	+	0.996345i	$0.472778\pi$
$84$		0			0
$85$	2.08194	+	5.58774i	0.225819	+	0.606075i
$86$	−0.400440	−	0.0978424i	−0.0431806	−	0.0105506i
$87$		0			0
$88$	−11.0877	+	0.738121i	−1.18196	+	0.0786840i
$89$	−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
$92$	0.631790	+	1.99903i	0.0658686	+	0.208413i
$93$		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	$0.447937\pi$
$98$	6.58416	−	3.99844i	0.665100	−	0.403903i
$99$		0			0
$100$	−9.72739	+	2.31901i	−0.972739	+	0.231901i
$101$	−11.0269			−1.09721			−0.548607	−	0.836080i	$-0.684842\pi$
$101$	−11.0269			−1.09721			−0.548607	+	0.836080i	$0.684842\pi$
$102$		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	−0.406975	−	0.913439i	$-0.633416\pi$
$107$	5.23891	−	5.23891i	0.506465	−	0.506465i	0.913439	+	0.406975i	$0.133416\pi$
$108$		0			0
$109$	−5.31464			−0.509050			−0.254525	−	0.967066i	$-0.581919\pi$
$109$	−5.31464			−0.509050			−0.254525	+	0.967066i	$0.581919\pi$
$110$	−1.45048	−	12.3389i	−0.138298	−	1.17647i
$111$		0			0
$112$	13.9010	+	2.43158i	1.31352	+	0.229763i
$113$	−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
$118$	−0.641938	+	0.389837i	−0.0590952	+	0.0358874i
$119$	9.40829			0.862457
$120$		0			0
$121$	4.43532			0.403211
$122$	−3.63063	+	2.20482i	−0.328702	+	0.199615i
$123$		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	$0.272162\pi$
$128$	7.10256	+	8.80646i	0.627783	+	0.778388i
$129$		0			0
$130$	15.9905	+	12.6265i	1.40246	+	1.10742i
$131$	0.996979			0.0871065			0.0435532	−	0.999051i	$-0.486132\pi$
$131$	0.996979			0.0871065			0.0435532	+	0.999051i	$0.486132\pi$
$132$		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	$-0.244032\pi$
$139$	16.9830			1.44048			0.720239	+	0.693726i	$0.244032\pi$
$140$	−1.92992	+	15.6593i	−0.163108	+	1.32345i
$141$		0			0
$142$	9.20716	−	5.59134i	0.772648	−	0.469215i
$143$	−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
$148$	−14.5555	+	4.60024i	−1.19645	+	0.378137i
$149$		−	6.48772i		−	0.531495i	−0.964043	−	0.265747i	$-0.914381\pi$
$149$		−	6.48772i		−	0.531495i	0.964043	−	0.265747i	$-0.0856187\pi$
$150$		0			0
$151$	4.21210			0.342776			0.171388	−	0.985204i	$-0.445175\pi$
$151$	4.21210			0.342776			0.171388	+	0.985204i	$0.445175\pi$
$152$	13.0259	−	0.867148i	1.05654	−	0.0703350i
$153$		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	0.708577	−	0.705633i	$-0.249337\pi$
$157$	0.0368875	+	0.0368875i	0.00294395	+	0.00294395i	−0.705633	+	0.708577i	$0.749337\pi$
$158$	−1.59463	+	0.968387i	−0.126862	+	0.0770407i
$159$		0			0
$160$	−9.43216	+	8.42819i	−0.745678	+	0.666307i
$161$			3.69823i			0.291461i
$162$		0			0
$163$	−1.33256	+	1.33256i	−0.104374	+	0.104374i	−0.757365	−	0.652991i	$-0.773514\pi$
$163$	−1.33256	+	1.33256i	−0.104374	+	0.104374i	0.652991	+	0.757365i	$0.273514\pi$
$164$	−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
$170$	−5.22604	+	6.61839i	−0.400819	+	0.507607i
$171$		0			0
$172$	−0.175681	−	0.555867i	−0.0133955	−	0.0423844i
$173$	2.16963	+	2.16963i	0.164954	+	0.164954i	0.784757	−	0.619804i	$-0.212788\pi$
$173$	2.16963	+	2.16963i	0.164954	+	0.164954i	−0.619804	+	0.784757i	$0.712788\pi$
$174$		0			0
$175$	−17.5943	−	1.27045i	−1.33000	−	0.0960371i
$176$	−9.03138	−	12.8608i	−0.680766	−	0.969417i
$177$		0			0
$178$	−2.14200	−	3.52719i	−0.160550	−	0.264374i
$179$		−	14.2973i		−	1.06863i	−0.845285	−	0.534316i	$-0.820569\pi$
$179$		−	14.2973i		−	1.06863i	0.845285	−	0.534316i	$-0.179431\pi$
$180$		0			0
$181$		−	11.0562i		−	0.821800i	−0.911680	−	0.410900i	$-0.865215\pi$
$181$		−	11.0562i		−	0.821800i	0.911680	−	0.410900i	$-0.134785\pi$
$182$	27.4769	−	16.6862i	2.03672	−	1.23687i
$183$		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
$188$	9.38753	−	2.96692i	0.684656	−	0.216385i
$189$		0			0
$190$	1.70403	+	14.4958i	0.123623	+	1.05164i
$191$			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	−0.256698	−	0.966492i	$-0.582634\pi$
$197$	9.96244	−	9.96244i	0.709794	−	0.709794i	0.966492	+	0.256698i	$0.0826344\pi$
$198$		0			0
$199$			15.6722i			1.11097i	0.831525	+	0.555487i	$0.187468\pi$
$199$			15.6722i			1.11097i	−0.831525	+	0.555487i	$0.812532\pi$
$200$	−9.94374	−	10.0559i	−0.703129	−	0.711063i
$201$		0			0
$202$	−8.09448	−	13.3290i	−0.569526	−	0.937828i
$203$	−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
$208$	25.3867	+	4.44065i	1.76025	+	0.307904i
$209$	−18.1335			−1.25432
$210$		0			0
$211$			22.1294i			1.52345i	0.647901	+	0.761725i	$0.275647\pi$
$211$			22.1294i			1.52345i	−0.647901	+	0.761725i	$0.724353\pi$
$212$	2.75019	−	0.869194i	0.188884	−	0.0596965i
$213$		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
$218$	−3.90131	−	6.42422i	−0.264230	−	0.435103i
$219$		0			0
$220$	13.8503	−	10.8109i	0.933786	−	0.728872i
$221$	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	$0.584512\pi$
$227$	−18.4920	+	18.4920i	−1.22735	+	1.22735i	−0.964961	+	0.262393i	$0.915488\pi$
$228$		0			0
$229$	−19.2316			−1.27086			−0.635428	−	0.772160i	$-0.719176\pi$
$229$	−19.2316			−1.27086			−0.635428	+	0.772160i	$0.719176\pi$
$230$	−2.60157	−	2.05426i	−0.171542	−	0.135454i
$231$		0			0
$232$	−0.818920	−	12.3015i	−0.0537647	−	0.807630i
$233$	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
$238$	6.90633	+	11.3725i	0.447671	+	0.737172i
$239$	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	$0.692286\pi$
$242$	3.25583	+	5.36131i	0.209292	+	0.344638i
$243$		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
$248$	−27.2939	+	1.81698i	−1.73316	+	0.115378i
$249$		0			0
$250$	10.6669	−	11.6713i	0.674631	−	0.738155i
$251$	−13.0522			−0.823846			−0.411923	−	0.911219i	$-0.635143\pi$
$251$	−13.0522			−0.823846			−0.411923	+	0.911219i	$0.635143\pi$
$252$		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
$260$	−3.52451	+	28.5977i	−0.218581	+	1.77356i
$261$		0			0
$262$	0.731851	+	1.20513i	0.0452139	+	0.0744529i
$263$	−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
$268$	−3.46988	+	1.09665i	−0.211957	+	0.0669886i
$269$		−	9.89975i		−	0.603599i	−0.953371	−	0.301799i	$-0.902413\pi$
$269$		−	9.89975i		−	0.603599i	0.953371	−	0.301799i	$-0.0975873\pi$
$270$		0			0
$271$	16.6235			1.00981			0.504904	−	0.863176i	$-0.331528\pi$
$271$	16.6235			1.00981			0.504904	+	0.863176i	$0.331528\pi$
$272$	−1.83796	+	10.5074i	−0.111443	+	0.637104i
$273$		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	0.873315	−	0.487156i	$-0.161966\pi$
$277$	6.42695	+	6.42695i	0.386158	+	0.386158i	−0.487156	+	0.873315i	$0.661966\pi$
$278$	12.4667	+	20.5287i	0.747702	+	1.23123i
$279$		0			0
$280$	−20.3453	+	9.16217i	−1.21587	+	0.547544i
$281$			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	$-0.473814\pi$
$283$	18.1481	−	18.1481i	1.07879	−	1.07879i	0.996618	−	0.0821722i	$-0.0261857\pi$
$284$	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
$290$	13.6896	−	1.60925i	0.803882	−	0.0944987i
$291$		0			0
$292$	1.37345	−	0.434077i	0.0803750	−	0.0254024i
$293$	11.4905	+	11.4905i	0.671281	+	0.671281i	0.958011	−	0.286730i	$-0.0925684\pi$
$293$	11.4905	+	11.4905i	0.671281	+	0.671281i	−0.286730	+	0.958011i	$0.592568\pi$
$294$		0			0
$295$	0.493672	−	1.08001i	0.0287427	−	0.0628809i
$296$	−16.2454	−	14.2174i	−0.944244	−	0.826372i
$297$		0			0
$298$	7.84221	−	4.76243i	0.454287	−	0.275880i
$299$			6.75387i			0.390586i
$300$		0			0
$301$		−	1.02836i		−	0.0592738i
$302$	3.09197	+	5.09149i	0.177923	+	0.292982i
$303$		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	$0.00627765\pi$
$307$	17.8635	+	17.8635i	1.01953	+	1.01953i	0.0197205	+	0.999806i	$0.493722\pi$
$308$	−8.35410	−	26.4329i	−0.476019	−	1.50616i
$309$		0			0
$310$	−3.57053	−	30.3739i	−0.202793	−	1.72512i
$311$			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	−0.227445	−	0.973791i	$-0.573037\pi$
$317$	13.2883	−	13.2883i	0.746346	−	0.746346i	0.973791	+	0.227445i	$0.0730371\pi$
$318$		0			0
$319$			17.1250i			0.958813i
$320$	−17.1117	−	5.21451i	−0.956571	−	0.291500i
$321$		0			0
$322$	−4.47034	+	2.71475i	−0.249122	+	0.151287i
$323$	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
$328$	−1.19035	−	17.8809i	−0.0657260	−	0.987307i
$329$	17.3671			0.957479
$330$		0			0
$331$			8.60834i			0.473157i	0.971612	+	0.236579i	$0.0760261\pi$
$331$			8.60834i			0.473157i	−0.971612	+	0.236579i	$0.923974\pi$
$332$	−26.5792	+	8.40033i	−1.45872	+	0.461028i
$333$		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	$0.234063\pi$
$338$	34.4654	−	20.9302i	1.87467	−	1.13845i
$339$		0			0
$340$	−11.8364	−	1.45877i	−0.641921	−	0.0791130i
$341$	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	−0.999900	−	0.0141438i	$-0.995498\pi$
$347$	−18.3626	+	18.3626i	−0.985756	+	0.985756i	0.0141438	+	0.999900i	$0.495498\pi$
$348$		0			0
$349$	31.1787			1.66896			0.834478	−	0.551041i	$-0.185769\pi$
$349$	31.1787			1.66896			0.834478	+	0.551041i	$0.185769\pi$
$350$	−11.3797	−	22.2002i	−0.608272	−	1.18665i
$351$		0			0
$352$	8.91616	−	20.3576i	0.475233	−	1.08506i
$353$	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
$358$	17.2823	−	10.4952i	0.913396	−	0.554689i
$359$	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
$362$	13.3645	−	8.11600i	0.702421	−	0.426567i
$363$		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	$0.209386\pi$
$368$	−4.13027	−	0.722469i	−0.215305	−	0.0376613i
$369$		0			0
$370$	14.9577	−	18.9428i	0.777612	−	0.984787i
$371$	5.08789			0.264150
$372$		0			0
$373$	−7.24984	+	7.24984i	−0.375382	+	0.375382i	−0.869433	−	0.494051i	$-0.835516\pi$
$373$	−7.24984	+	7.24984i	−0.375382	+	0.375382i	0.494051	+	0.869433i	$0.335516\pi$
$374$	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	$-0.230492\pi$
$379$	29.1664			1.49818			0.749088	+	0.662470i	$0.230492\pi$
$380$	−16.2714	+	12.7007i	−0.834704	+	0.651534i
$381$		0			0
$382$	−15.3671	+	9.33214i	−0.786248	+	0.477474i
$383$	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
$388$	−6.91581	−	21.8821i	−0.351097	−	1.11090i
$389$			31.4290i			1.59351i	0.604301	+	0.796756i	$0.293452\pi$
$389$			31.4290i			1.59351i	−0.604301	+	0.796756i	$0.706548\pi$
$390$		0			0
$391$	−2.79539			−0.141369
$392$	1.02335	+	15.3723i	0.0516869	+	0.776418i
$393$		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	0.224782	−	0.974409i	$-0.427833\pi$
$397$	−14.9362	−	14.9362i	−0.749627	−	0.749627i	−0.974409	+	0.224782i	$0.927833\pi$
$398$	−18.9442	+	11.5045i	−0.949588	+	0.576667i
$399$		0			0
$400$	4.85601	−	19.4015i	0.242801	−	0.970076i
$401$		−	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	$-0.0367973\pi$
$410$	19.8987	−	2.33915i	0.982726	−	0.115522i
$411$		0			0
$412$	7.79761	−	2.46443i	0.384161	−	0.121414i
$413$	−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
$418$	−13.3112	−	21.9193i	−0.651073	−	1.07211i
$419$			2.43646i			0.119029i	0.998227	+	0.0595144i	$0.0189552\pi$
$419$			2.43646i			0.119029i	−0.998227	+	0.0595144i	$0.981045\pi$
$420$		0			0
$421$			9.62136i			0.468916i	0.972126	+	0.234458i	$0.0753316\pi$
$421$			9.62136i			0.468916i	−0.972126	+	0.234458i	$0.924668\pi$
$422$	−26.7495	+	16.2445i	−1.30215	+	0.790769i
$423$		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
$428$	4.46546	+	14.1290i	0.215846	+	0.682952i
$429$		0			0
$430$	0.723415	+	0.571226i	0.0348862	+	0.0275470i
$431$		−	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	$0.649381\pi$
$440$	23.2351	+	8.80595i	1.10769	+	0.419807i
$441$		0			0
$442$	12.6126	+	20.7690i	0.599922	+	0.987881i
$443$	−18.0711	−	18.0711i	−0.858585	−	0.858585i	0.132587	−	0.991171i	$-0.457672\pi$
$443$	−18.0711	−	18.0711i	−0.858585	−	0.858585i	−0.991171	+	0.132587i	$0.957672\pi$
$444$		0			0
$445$	5.93425	+	2.71253i	0.281310	+	0.128586i
$446$	1.50792	−	6.17146i	0.0714019	−	0.292227i
$447$		0			0
$448$	−17.1359	+	22.4269i	−0.809597	+	1.05957i
$449$	−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
$452$	−8.82702	−	27.9293i	−0.415188	−	1.31368i
$453$		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	$0.188947\pi$
$458$	−14.1173	−	23.2467i	−0.659657	−	1.08625i
$459$		0			0
$460$	0.573417	−	4.65269i	0.0267357	−	0.216933i
$461$	10.6204			0.494639			0.247320	−	0.968934i	$-0.420450\pi$
$461$	10.6204			0.494639			0.247320	+	0.968934i	$0.420450\pi$
$462$		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	−0.383354	−	0.923602i	$-0.625231\pi$
$467$	11.6749	−	11.6749i	0.540248	−	0.540248i	0.923602	+	0.383354i	$0.125231\pi$
$468$		0			0
$469$	−6.41933			−0.296417
$470$	−9.64693	+	12.2171i	−0.444980	+	0.563533i
$471$		0			0
$472$	−0.0997738	−	1.49876i	−0.00459246	−	0.0689859i
$473$	−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
$478$	19.6534	+	32.3629i	0.898925	+	1.48024i
$479$	−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
$482$	−12.9458	−	21.3176i	−0.589665	−	0.970992i
$483$		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	$0.211091\pi$
$488$	−0.564294	−	8.47658i	−0.0255444	−	0.383717i
$489$		0			0
$490$	−17.1070	+	2.01098i	−0.772815	+	0.0908466i
$491$	−19.3774			−0.874492			−0.437246	−	0.899342i	$-0.644046\pi$
$491$	−19.3774			−0.874492			−0.437246	+	0.899342i	$0.644046\pi$
$492$		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	$-0.339600\pi$
$499$	21.5723			0.965707			0.482853	+	0.875701i	$0.339600\pi$
$500$	21.9382	+	4.32637i	0.981104	+	0.193481i
$501$		0			0
$502$	−9.58119	−	15.7772i	−0.427629	−	0.704170i
$503$	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
$508$	−0.945030	−	2.99014i	−0.0419289	−	0.132666i
$509$		−	9.29371i		−	0.411937i	−0.978559	−	0.205968i	$-0.933966\pi$
$509$		−	9.29371i		−	0.411937i	0.978559	−	0.205968i	$-0.0660344\pi$
$510$		0			0
$511$	2.54090			0.112403
$512$	−22.1790	+	4.48248i	−0.980182	+	0.198100i
$513$		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
$518$	−19.7669	−	32.5498i	−0.868508	−	1.43016i
$519$		0			0
$520$	−37.1555	+	16.7323i	−1.62938	+	0.733762i
$521$			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	−0.191610	−	0.981471i	$-0.561371\pi$
$523$	18.0635	−	18.0635i	0.789861	−	0.789861i	0.981471	+	0.191610i	$0.0613710\pi$
$524$	−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
$530$	−2.82618	+	3.57915i	−0.122761	+	0.155468i
$531$		0			0
$532$	9.81443	+	31.0535i	0.425510	+	1.34634i
$533$	−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
$538$	11.9666	−	7.26710i	0.515917	−	0.313307i
$539$		−	21.3999i		−	0.921758i
$540$		0			0
$541$			29.6103i			1.27305i	0.771258	+	0.636523i	$0.219628\pi$
$541$			29.6103i			1.27305i	−0.771258	+	0.636523i	$0.780372\pi$
$542$	12.2028	+	20.0941i	0.524155	+	0.863117i
$543$		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	0.344816	−	0.938670i	$-0.387941\pi$
$547$	−13.8891	−	13.8891i	−0.593855	−	0.593855i	−0.938670	+	0.344816i	$0.887941\pi$
$548$	−2.78410	+	0.879912i	−0.118931	+	0.0375880i
$549$		0			0
$550$	−8.52035	+	26.4418i	−0.363309	+	1.12748i
$551$		−	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	−0.960317	−	0.278910i	$-0.910027\pi$
$557$	−16.0818	+	16.0818i	−0.681408	+	0.681408i	0.278910	+	0.960317i	$0.410027\pi$
$558$		0			0
$559$		−	1.87804i		−	0.0794326i
$560$	−26.0099	−	17.8673i	−1.09912	−	0.755033i
$561$		0			0
$562$	−32.6696	+	19.8397i	−1.37809	+	0.836886i
$563$	11.6731	+	11.6731i	0.491962	+	0.491962i	0.908924	−	0.416962i	$-0.136905\pi$
$563$	11.6731	+	11.6731i	0.491962	+	0.491962i	−0.416962	+	0.908924i	$0.636905\pi$
$564$		0			0
$565$	30.6874	−	11.4339i	1.29103	−	0.481027i
$566$	35.2589	+	8.61505i	1.48204	+	0.362118i
$567$		0			0
$568$	1.43103	+	21.4963i	0.0600447	+	0.901965i
$569$	−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	$-0.654271\pi$
$571$		−	42.2873i		−	1.76967i	0.465904	−	0.884835i	$-0.345729\pi$
$572$	−15.2566	−	48.2729i	−0.637911	−	2.01839i
$573$		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	$0.152256\pi$
$578$	11.9531	−	7.25887i	0.497181	−	0.301929i
$579$		0			0
$580$	11.9944	+	15.3664i	0.498038	+	0.638055i
$581$	−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	−0.204563	−	0.978853i	$-0.565577\pi$
$587$	18.7596	−	18.7596i	0.774290	−	0.774290i	0.978853	+	0.204563i	$0.0655773\pi$
$588$		0			0
$589$	−44.6379			−1.83927
$590$	1.66789	−	0.196065i	0.0686658	−	0.00807186i
$591$		0			0
$592$	5.26050	−	30.0736i	0.216205	−	1.23602i
$593$	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
$598$	−8.16392	+	4.95780i	−0.333848	+	0.202739i
$599$	−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	$0.556553\pi$
$602$	1.24306	−	0.754888i	0.0506634	−	0.0307669i
$603$		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	$0.298765\pi$
$608$	−10.4747	+	23.9162i	−0.424807	+	0.969931i
$609$		0			0
$610$	9.43313	−	1.10889i	0.381936	−	0.0448977i
$611$	31.7165			1.28311
$612$		0			0
$613$	−0.848748	+	0.848748i	−0.0342806	+	0.0342806i	−0.724039	−	0.689759i	$-0.757717\pi$
$613$	−0.848748	+	0.848748i	−0.0342806	+	0.0342806i	0.689759	+	0.724039i	$0.257717\pi$
$614$	−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	$-0.539890\pi$
$619$	−6.21940			−0.249979			−0.124989	+	0.992158i	$0.539890\pi$
$620$	34.0942	−	26.6125i	1.36926	−	1.06878i
$621$		0			0
$622$	−12.0125	+	7.29494i	−0.481655	+	0.292500i
$623$	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
$628$	−0.0994834	+	0.0314416i	−0.00396982	+	0.00125466i
$629$		−	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	$0.423215\pi$
$632$	−0.247846	−	3.72303i	−0.00985879	−	0.148094i
$633$		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
$638$	−20.7003	+	12.5709i	−0.819531	+	0.497686i
$639$		0			0
$640$	−6.25794	−	24.5120i	−0.247367	−	0.968922i
$641$		−	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	−0.336792	−	0.941579i	$-0.609342\pi$
$643$	15.3358	−	15.3358i	0.604787	−	0.604787i	0.941579	+	0.336792i	$0.109342\pi$
$644$	−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
$650$	−20.7822	−	40.5430i	−0.815143	−	1.59023i
$651$		0			0
$652$	−1.13582	−	3.59382i	−0.0444822	−	0.140745i
$653$	−2.21463	−	2.21463i	−0.0866651	−	0.0866651i	0.662445	−	0.749110i	$-0.269519\pi$
$653$	−2.21463	−	2.21463i	−0.0866651	−	0.0866651i	−0.749110	+	0.662445i	$0.769519\pi$
$654$		0			0
$655$	−2.02754	−	0.926783i	−0.0792225	−	0.0362124i
$656$	20.7402	−	14.5647i	0.809770	−	0.568655i
$657$		0			0
$658$	12.7486	+	20.9930i	0.496993	+	0.818390i
$659$			37.2920i			1.45269i	0.687330	+	0.726345i	$0.258782\pi$
$659$			37.2920i			1.45269i	−0.687330	+	0.726345i	$0.741218\pi$
$660$		0			0
$661$			6.19442i			0.240935i	0.992717	+	0.120467i	$0.0384393\pi$
$661$			6.19442i			0.240935i	−0.992717	+	0.120467i	$0.961561\pi$
$662$	−10.4056	+	6.31911i	−0.404424	+	0.245599i
$663$		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
$668$	40.5326	−	12.8103i	1.56825	−	0.495644i
$669$		0			0
$670$	3.56576	−	4.51577i	0.137757	−	0.174459i
$671$			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	−0.872935	−	0.487837i	$-0.837786\pi$
$677$	−10.0200	+	10.0200i	−0.385098	+	0.385098i	0.487837	+	0.872935i	$0.337786\pi$
$678$		0			0
$679$		−	40.4823i		−	1.55357i
$680$	−6.92542	−	15.3785i	−0.265578	−	0.589737i
$681$		0			0
$682$	27.8917	+	45.9287i	1.06803	+	1.75870i
$683$	−11.5229	−	11.5229i	−0.440911	−	0.440911i	0.451407	−	0.892318i	$-0.350922\pi$
$683$	−11.5229	−	11.5229i	−0.440911	−	0.440911i	−0.892318	+	0.451407i	$0.850922\pi$
$684$		0			0
$685$	−1.13977	−	3.05904i	−0.0435485	−	0.116880i
$686$	1.83920	−	7.52730i	0.0702209	−	0.287394i
$687$		0			0
$688$	1.14850	+	0.200896i	0.0437861	+	0.00765909i
$689$	9.29173			0.353987
$690$		0			0
$691$		−	18.3907i		−	0.699614i	−0.936822	−	0.349807i	$-0.886247\pi$
$691$		−	18.3907i		−	0.699614i	0.936822	−	0.349807i	$-0.113753\pi$
$692$	−5.85134	+	1.84931i	−0.222435	+	0.0703002i
$693$		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
$698$	22.8873	+	37.6881i	0.866297	+	1.42652i
$699$		0			0
$700$	18.4816	−	30.0520i	0.698539	−	1.13586i
$701$	−52.0764			−1.96690			−0.983449	−	0.181186i	$-0.942006\pi$
$701$	−52.0764			−1.96690			−0.983449	+	0.181186i	$0.942006\pi$
$702$		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	$-0.114349\pi$
$709$	49.8546			1.87233			0.936165	+	0.351561i	$0.114349\pi$
$710$	−23.9221	+	2.81211i	−0.897780	+	0.105537i
$711$		0			0
$712$	8.23508	−	0.548217i	0.308622	−	0.0205453i
$713$	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
$718$	9.62164	+	15.8438i	0.359076	+	0.591285i
$719$	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
$722$	1.69078	+	2.78418i	0.0629243	+	0.103616i
$723$		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	$0.138223\pi$
$728$	4.27062	+	64.1514i	0.158280	+	2.37761i
$729$		0			0
$730$	−1.41140	+	1.78743i	−0.0522383	+	0.0661558i
$731$	0.777309			0.0287498
$732$		0			0
$733$	3.40526	−	3.40526i	0.125776	−	0.125776i	−0.641417	−	0.767193i	$-0.721653\pi$
$733$	3.40526	−	3.40526i	0.125776	−	0.125776i	0.767193	+	0.641417i	$0.221653\pi$
$734$	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	$-0.540196\pi$
$739$	−6.84745			−0.251887			−0.125944	+	0.992037i	$0.540196\pi$
$740$	33.8775	+	4.17521i	1.24536	+	0.153484i
$741$		0			0
$742$	3.73486	+	6.15013i	0.137111	+	0.225778i
$743$	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
$748$	19.9799	−	6.31462i	0.730537	−	0.230885i
$749$			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	$0.728903\pi$
$752$	−3.39275	+	19.3959i	−0.123721	+	0.707297i
$753$		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	0.998654	−	0.0518693i	$-0.0165179\pi$
$757$	26.0495	+	26.0495i	0.946785	+	0.946785i	−0.0518693	+	0.998654i	$0.516518\pi$
$758$	21.4101	+	35.2557i	0.777651	+	1.28054i
$759$		0			0
$760$	−27.2967	−	10.3453i	−0.990154	−	0.375262i
$761$		−	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	$-0.251677\pi$
$770$	34.4003	+	27.1633i	1.23970	+	0.978898i
$771$		0			0
$772$	−44.7238	+	14.1349i	−1.60965	+	0.508727i
$773$	−2.76896	−	2.76896i	−0.0995925	−	0.0995925i	0.655555	−	0.755147i	$-0.272435\pi$
$773$	−2.76896	−	2.76896i	−0.0995925	−	0.0995925i	−0.755147	+	0.655555i	$0.772435\pi$
$774$		0			0
$775$	31.6414	+	36.5666i	1.13659	+	1.31351i
$776$	21.3739	−	24.4226i	0.767279	−	0.876722i
$777$		0			0
$778$	−37.9906	+	23.0710i	−1.36203	+	0.827136i
$779$		−	29.2434i		−	1.04775i
$780$		0			0
$781$		−	29.9252i		−	1.07081i
$782$	−2.05200	−	3.37900i	−0.0733795	−	0.120833i
$783$		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	0.250138	−	0.968210i	$-0.419524\pi$
$787$	−20.1445	−	20.1445i	−0.718072	−	0.718072i	−0.968210	+	0.250138i	$0.919524\pi$
$788$	8.49162	+	26.8681i	0.302502	+	0.957136i
$789$		0			0
$790$	4.14316	−	0.487041i	0.147407	−	0.0173281i
$791$		−	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	−0.0257360	−	0.999669i	$-0.508193\pi$
$797$	27.4953	−	27.4953i	0.973933	−	0.973933i	0.999669	+	0.0257360i	$0.00819294\pi$
$798$		0			0
$799$			13.1273i			0.464410i
$800$	27.0168	−	8.37221i	0.955187	−	0.296002i
$801$		0			0
$802$	32.6946	−	19.8549i	1.15449	−	0.701099i
$803$	−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
$808$	31.1198	−	2.07168i	1.09479	−	0.0728814i
$809$	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	$-0.849695\pi$
$811$		−	25.9061i		−	0.909687i	0.890571	−	0.454844i	$-0.150305\pi$
$812$	29.3264	−	9.26858i	1.02916	−	0.325263i
$813$		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
$818$	5.63944	−	3.42473i	0.197178	−	0.119743i
$819$		0			0
$820$	17.4345	+	22.3360i	0.608839	+	0.780006i
$821$	14.0659			0.490904			0.245452	−	0.969409i	$-0.421064\pi$
$821$	14.0659			0.490904			0.245452	+	0.969409i	$0.421064\pi$
$822$		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	−0.803213	−	0.595692i	$-0.796878\pi$
$827$	−5.96783	+	5.96783i	−0.207522	+	0.207522i	0.595692	+	0.803213i	$0.296878\pi$
$828$		0			0
$829$	8.93872			0.310454			0.155227	−	0.987879i	$-0.450389\pi$
$829$	8.93872			0.310454			0.155227	+	0.987879i	$0.450389\pi$
$830$	27.3136	−	34.5907i	0.948070	−	1.20066i
$831$		0			0
$832$	−31.2944	+	40.9569i	−1.08494	+	1.41992i
$833$	−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
$838$	−2.94514	+	1.78853i	−0.101738	+	0.0617836i
$839$	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
$842$	−11.6301	+	7.06274i	−0.400799	+	0.243398i
$843$		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
$848$	−0.993948	+	5.68227i	−0.0341323	+	0.195130i
$849$		0			0
$850$	16.7805	−	8.60161i	0.575566	−	0.295033i
$851$	8.00079			0.274264
$852$		0			0
$853$	−17.2928	+	17.2928i	−0.592094	+	0.592094i	−0.938197	−	0.346103i	$-0.887505\pi$
$853$	−17.2928	+	17.2928i	−0.592094	+	0.592094i	0.346103	+	0.938197i	$0.387505\pi$
$854$	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	$-0.675745\pi$
$859$	−30.7443			−1.04898			−0.524492	+	0.851416i	$0.675745\pi$
$860$	−0.159449	+	1.29377i	−0.00543718	+	0.0441171i
$861$		0			0
$862$	31.9657	−	19.4122i	1.08876	−	0.661182i
$863$	−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
$868$	−20.5647	−	65.0680i	−0.698010	−	2.20855i
$869$			5.18287i			0.175817i
$870$		0			0
$871$	−11.7233			−0.397228
$872$	14.9989	−	0.998490i	0.507926	−	0.0338131i
$873$		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	0.0889274	−	0.996038i	$-0.471656\pi$
$877$	−26.8633	−	26.8633i	−0.907111	−	0.907111i	−0.996038	+	0.0889274i	$0.971656\pi$
$878$	−45.1771	+	27.4352i	−1.52465	+	0.925895i
$879$		0			0
$880$	6.41169	+	34.5502i	0.216138	+	1.16469i
$881$			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	−0.907156	−	0.420794i	$-0.861751\pi$
$883$	−14.4524	+	14.4524i	−0.486362	+	0.486362i	0.420794	+	0.907156i	$0.361751\pi$
$884$	−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
$890$	1.07730	+	9.16437i	0.0361111	+	0.307190i
$891$		0			0
$892$	8.56683	−	2.70754i	0.286839	−	0.0906550i
$893$	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
$898$	−17.9531	−	29.5631i	−0.599103	−	0.986532i
$899$			42.1552i			1.40596i
$900$		0			0
$901$			3.84579i			0.128122i
$902$	−30.0891	+	18.2725i	−1.00186	+	0.608409i
$903$		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	0.392929	−	0.919569i	$-0.371462\pi$
$907$	−15.8605	−	15.8605i	−0.526640	−	0.526640i	−0.919569	+	0.392929i	$0.871462\pi$
$908$	−15.7619	−	49.8717i	−0.523076	−	1.65505i
$909$		0			0
$910$	−71.3907	+	8.39218i	−2.36658	+	0.278198i
$911$			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	$0.843534\pi$
$920$	6.04499	−	2.72226i	0.199298	−	0.0897502i
$921$		0			0
$922$	7.79607	+	12.8377i	0.256750	+	0.422786i
$923$	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
$928$	22.5861	+	9.89217i	0.741424	+	0.324727i
$929$	−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
$932$	11.7031	+	37.0295i	0.383349	+	1.21294i
$933$		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	$0.268627\pi$
$938$	−4.71223	−	7.75955i	−0.153860	−	0.253358i
$939$		0			0
$940$	−21.8493	−	2.69280i	−0.712645	−	0.0878294i
$941$	−28.8111			−0.939216			−0.469608	−	0.882875i	$-0.655605\pi$
$941$	−28.8111			−0.939216			−0.469608	+	0.882875i	$0.655605\pi$
$942$		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	−0.0838038	−	0.996482i	$-0.526707\pi$
$947$	28.0862	−	28.0862i	0.912678	−	0.912678i	0.996482	+	0.0838038i	$0.0267069\pi$
$948$		0			0
$949$	4.64031			0.150631
$950$	10.0098	−	31.0640i	0.324759	−	1.00785i
$951$		0			0
$952$	−26.5519	+	1.76759i	−0.860552	+	0.0572878i
$953$	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
$958$	−3.74901	−	6.17343i	−0.121125	−	0.199454i
$959$	−5.15063			−0.166323
$960$		0			0
$961$	62.5320			2.01716
$962$	−36.0991	−	59.4438i	−1.16388	−	1.91655i
$963$		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	$0.0353168\pi$
$968$	−12.5173	+	0.833287i	−0.402320	+	0.0267828i
$969$		0			0
$970$	28.4778	+	22.4868i	0.914366	+	0.722006i
$971$	−41.1632			−1.32099			−0.660496	−	0.750830i	$-0.729654\pi$
$971$	−41.1632			−1.32099			−0.660496	+	0.750830i	$0.729654\pi$
$972$		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
$980$	−14.9885	−	19.2024i	−0.478791	−	0.613397i
$981$		0			0
$982$	−14.2244	−	23.4230i	−0.453918	−	0.747459i
$983$	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
$988$	17.9235	+	56.7113i	0.570223	+	1.80423i
$989$			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	$0.394629\pi$
$992$	21.9483	−	50.1128i	0.696858	−	1.59108i
$993$		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	0.237898	−	0.971290i	$-0.423542\pi$
$997$	−23.1571	−	23.1571i	−0.733392	−	0.733392i	−0.971290	+	0.237898i	$0.923542\pi$
$998$	15.8355	+	26.0761i	0.501264	+	0.825423i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.734068 + 1.20878i) q^{2} +(-0.922287 + 1.77465i) q^{4} +(-2.03368 - 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-2.82218 + 0.187875i) q^{8} +O(q^{10})\)	\(q+(0.734068 + 1.20878i) q^{2} +(-0.922287 + 1.77465i) q^{4} +(-2.03368 - 0.929591i) q^{5} +(-2.49469 + 2.49469i) q^{7} +(-2.82218 + 0.187875i) q^{8} +(-0.369193 - 3.14065i) q^{10} +3.92878 q^{11} +(-4.55591 + 4.55591i) q^{13} +(-4.84680 - 1.18425i) q^{14} +(-2.29877 - 3.27348i) q^{16} +(-1.88566 - 1.88566i) q^{17} -4.61555 q^{19} +(3.52534 - 2.75173i) q^{20} +(2.88399 + 4.74902i) q^{22} +(0.741221 - 0.741221i) q^{23} +(3.27172 + 3.78098i) q^{25} +(-8.85143 - 2.16273i) q^{26} +(-2.12638 - 6.72802i) q^{28} +4.35885i q^{29} +9.67119 q^{31} +(2.26945 - 5.18166i) q^{32} +(0.895142 - 3.66355i) q^{34} +(7.39245 - 2.75436i) q^{35} +(5.39704 + 5.39704i) q^{37} +(-3.38813 - 5.57917i) q^{38} +(5.91406 + 2.24139i) q^{40} +6.33584i q^{41} +(-0.206110 + 0.206110i) q^{43} +(-3.62346 + 6.97221i) q^{44} +(1.44008 + 0.351864i) q^{46} +(-3.48081 - 3.48081i) q^{47} -5.44695i q^{49} +(-2.16870 + 6.73028i) q^{50} +(-3.88329 - 12.2870i) q^{52} +(-1.01974 - 1.01974i) q^{53} +(-7.98989 - 3.65216i) q^{55} +(6.57177 - 7.50916i) q^{56} +(-5.26888 + 3.19969i) q^{58} +0.531064i q^{59} +3.00356i q^{61} +(7.09932 + 11.6903i) q^{62} +(7.92941 - 1.06044i) q^{64} +(13.5004 - 5.03014i) q^{65} +(1.28660 + 1.28660i) q^{67} +(5.08552 - 1.60727i) q^{68} +(8.75597 + 6.91393i) q^{70} -7.61692i q^{71} +(-0.509262 - 0.509262i) q^{73} +(-2.56202 + 10.4856i) q^{74} +(4.25686 - 8.19099i) q^{76} +(-9.80109 + 9.80109i) q^{77} +1.31920i q^{79} +(1.63198 + 8.79413i) q^{80} +(-7.65863 + 4.65094i) q^{82} +(9.85533 + 9.85533i) q^{83} +(2.08194 + 5.58774i) q^{85} +(-0.400440 - 0.0978424i) q^{86} +(-11.0877 + 0.738121i) q^{88} -2.91798 q^{89} -22.7312i q^{91} +(0.631790 + 1.99903i) q^{92} +(1.65237 - 6.76268i) q^{94} +(9.38656 + 4.29057i) q^{95} +(-8.11369 + 8.11369i) q^{97} +(6.58416 - 3.99844i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

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