LMFDB - Embedded newform 1764.2.b.i.1567.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.1
Root			$-1.33790 - 0.458297i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.i.1567.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +O(q^{10})$	\(q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +(1.12403 - 3.28134i) q^{10} +1.26539i q^{11} -2.99744i q^{13} +(0.992338 + 3.87495i) q^{16} -1.83319i q^{17} +4.15985 q^{19} +(-3.00766 + 3.87495i) q^{20} +(0.579927 - 1.69296i) q^{22} -6.73842i q^{23} -1.01532 q^{25} +(-1.37372 + 4.01027i) q^{26} +9.42323 q^{29} -9.43978 q^{31} +(0.448237 - 5.63907i) q^{32} +(-0.840146 + 2.45262i) q^{34} +7.51143 q^{37} +(-5.56545 - 1.90645i) q^{38} +(5.79982 - 3.80588i) q^{40} -1.08966i q^{41} -6.27176i q^{43} +(-1.55176 + 1.99923i) q^{44} +(-3.08820 + 9.01530i) q^{46} +7.35158 q^{47} +(1.35840 + 0.465320i) q^{50} +(3.67579 - 4.73574i) q^{52} +0.0716524 q^{53} -3.10353 q^{55} +(-12.6073 - 4.31864i) q^{58} +3.36690 q^{59} +11.1024i q^{61} +(12.6294 + 4.32623i) q^{62} +(-3.18406 + 7.33906i) q^{64} +7.35158 q^{65} -2.80766i q^{67} +(2.24806 - 2.89631i) q^{68} +2.92285i q^{71} +8.10495i q^{73} +(-10.0495 - 3.44247i) q^{74} +(6.57226 + 5.10126i) q^{76} +1.78368i q^{79} +(-9.50377 + 2.43382i) q^{80} +(-0.499388 + 1.45785i) q^{82} +5.33626 q^{83} +4.49611 q^{85} +(-2.87433 + 8.39096i) q^{86} +(2.99234 - 1.96359i) q^{88} +8.57161i q^{89} +(8.26338 - 10.6462i) q^{92} +(-9.83564 - 3.36921i) q^{94} +10.2025i q^{95} +7.10394i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} - 8 q^{10} + 10 q^{16} + 12 q^{19} - 22 q^{20} - 6 q^{22} - 4 q^{25} + 6 q^{26} + 16 q^{29} - 12 q^{31} + 12 q^{32} - 28 q^{34} - 12 q^{37} + 2 q^{38} + 4 q^{40} - 4 q^{44} - 12 q^{46} + 8 q^{47} - 2 q^{50} + 4 q^{52} - 8 q^{53} - 8 q^{55} - 14 q^{58} - 28 q^{59} + 48 q^{62} + 2 q^{64} + 8 q^{65} - 16 q^{68} - 38 q^{74} + 44 q^{76} - 6 q^{80} - 4 q^{82} - 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} - 32 q^{94}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 - 8 * q^10 + 10 * q^16 + 12 * q^19 - 22 * q^20 - 6 * q^22 - 4 * q^25 + 6 * q^26 + 16 * q^29 - 12 * q^31 + 12 * q^32 - 28 * q^34 - 12 * q^37 + 2 * q^38 + 4 * q^40 - 4 * q^44 - 12 * q^46 + 8 * q^47 - 2 * q^50 + 4 * q^52 - 8 * q^53 - 8 * q^55 - 14 * q^58 - 28 * q^59 + 48 * q^62 + 2 * q^64 + 8 * q^65 - 16 * q^68 - 38 * q^74 + 44 * q^76 - 6 * q^80 - 4 * q^82 - 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 - 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.33790	−	0.458297i	−0.946035	−	0.324065i
$2$	−1.33790	−	0.458297i	−0.946035	−	0.324065i
$3$		0			0
$3$		0			0
$4$	1.57993	+	1.22631i	0.789963	+	0.613154i
$5$			2.45262i			1.09684i	0.836202	+	0.548422i	$0.184771\pi$
$5$			2.45262i			1.09684i	−0.836202	+	0.548422i	$0.815229\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.55176	−	2.36475i	−0.548631	−	0.836065i
$9$		0			0
$10$	1.12403	−	3.28134i	0.355449	−	1.03765i
$11$			1.26539i			0.381531i	0.981636	+	0.190765i	$0.0610970\pi$
$11$			1.26539i			0.381531i	−0.981636	+	0.190765i	$0.938903\pi$
$12$		0			0
$13$		−	2.99744i		−	0.831342i	−0.909515	−	0.415671i	$-0.863547\pi$
$13$		−	2.99744i		−	0.831342i	0.909515	−	0.415671i	$-0.136453\pi$
$14$		0			0
$15$		0			0
$16$	0.992338	+	3.87495i	0.248084	+	0.968738i
$17$		−	1.83319i		−	0.444614i	−0.974977	−	0.222307i	$-0.928641\pi$
$17$		−	1.83319i		−	0.444614i	0.974977	−	0.222307i	$-0.0713587\pi$
$18$		0			0
$19$	4.15985			0.954336			0.477168	−	0.878812i	$-0.341663\pi$
$19$	4.15985			0.954336			0.477168	+	0.878812i	$0.341663\pi$
$20$	−3.00766	+	3.87495i	−0.672534	+	0.866466i
$21$		0			0
$22$	0.579927	−	1.69296i	0.123641	−	0.360941i
$23$		−	6.73842i		−	1.40506i	−0.711655	−	0.702529i	$-0.752054\pi$
$23$		−	6.73842i		−	1.40506i	0.711655	−	0.702529i	$-0.247946\pi$
$24$		0			0
$25$	−1.01532			−0.203065
$26$	−1.37372	+	4.01027i	−0.269409	+	0.786478i
$27$		0			0
$28$		0			0
$29$	9.42323			1.74985			0.874925	−	0.484258i	$-0.160910\pi$
$29$	9.42323			1.74985			0.874925	+	0.484258i	$0.160910\pi$
$30$		0			0
$31$	−9.43978			−1.69543			−0.847717	−	0.530448i	$-0.822024\pi$
$31$	−9.43978			−1.69543			−0.847717	+	0.530448i	$0.822024\pi$
$32$	0.448237	−	5.63907i	0.0792379	−	0.996856i
$33$		0			0
$34$	−0.840146	+	2.45262i	−0.144084	+	0.420620i
$35$		0			0
$36$		0			0
$37$	7.51143			1.23487			0.617436	−	0.786621i	$-0.288171\pi$
$37$	7.51143			1.23487			0.617436	+	0.786621i	$0.288171\pi$
$38$	−5.56545	−	1.90645i	−0.902835	−	0.309267i
$39$		0			0
$40$	5.79982	−	3.80588i	0.917032	−	0.601762i
$41$		−	1.08966i		−	0.170176i	−0.996373	−	0.0850880i	$-0.972883\pi$
$41$		−	1.08966i		−	0.170176i	0.996373	−	0.0850880i	$-0.0271171\pi$
$42$		0			0
$43$		−	6.27176i		−	0.956435i	−0.878241	−	0.478218i	$-0.841283\pi$
$43$		−	6.27176i		−	0.956435i	0.878241	−	0.478218i	$-0.158717\pi$
$44$	−1.55176	+	1.99923i	−0.233937	+	0.301395i
$45$		0			0
$46$	−3.08820	+	9.01530i	−0.455330	+	1.32923i
$47$	7.35158			1.07234			0.536169	−	0.844111i	$-0.319871\pi$
$47$	7.35158			1.07234			0.536169	+	0.844111i	$0.319871\pi$
$48$		0			0
$49$		0			0
$50$	1.35840	+	0.465320i	0.192106	+	0.0658063i
$51$		0			0
$52$	3.67579	−	4.73574i	0.509740	−	0.656730i
$53$	0.0716524			0.00984222			0.00492111	−	0.999988i	$-0.498434\pi$
$53$	0.0716524			0.00984222			0.00492111	+	0.999988i	$0.498434\pi$
$54$		0			0
$55$	−3.10353			−0.418479
$56$		0			0
$57$		0			0
$58$	−12.6073	−	4.31864i	−1.65542	−	0.567066i
$59$	3.36690			0.438334			0.219167	−	0.975687i	$-0.429666\pi$
$59$	3.36690			0.438334			0.219167	+	0.975687i	$0.429666\pi$
$60$		0			0
$61$			11.1024i			1.42152i	0.703436	+	0.710758i	$0.251648\pi$
$61$			11.1024i			1.42152i	−0.703436	+	0.710758i	$0.748352\pi$
$62$	12.6294	+	4.32623i	1.60394	+	0.549432i
$63$		0			0
$64$	−3.18406	+	7.33906i	−0.398008	+	0.917382i
$65$	7.35158			0.911851
$66$		0			0
$67$		−	2.80766i		−	0.343011i	−0.985183	−	0.171505i	$-0.945137\pi$
$67$		−	2.80766i		−	0.343011i	0.985183	−	0.171505i	$-0.0548631\pi$
$68$	2.24806	−	2.89631i	0.272617	−	0.351229i
$69$		0			0
$70$		0			0
$71$			2.92285i			0.346878i	0.984845	+	0.173439i	$0.0554880\pi$
$71$			2.92285i			0.346878i	−0.984845	+	0.173439i	$0.944512\pi$
$72$		0			0
$73$			8.10495i			0.948613i	0.880360	+	0.474307i	$0.157301\pi$
$73$			8.10495i			0.948613i	−0.880360	+	0.474307i	$0.842699\pi$
$74$	−10.0495	−	3.44247i	−1.16823	−	0.400179i
$75$		0			0
$76$	6.57226	+	5.10126i	0.753890	+	0.585155i
$77$		0			0
$78$		0			0
$79$			1.78368i			0.200680i	0.994953	+	0.100340i	$0.0319930\pi$
$79$			1.78368i			0.200680i	−0.994953	+	0.100340i	$0.968007\pi$
$80$	−9.50377	+	2.43382i	−1.06255	+	0.272110i
$81$		0			0
$82$	−0.499388	+	1.45785i	−0.0551481	+	0.160992i
$83$	5.33626			0.585730			0.292865	−	0.956154i	$-0.405391\pi$
$83$	5.33626			0.585730			0.292865	+	0.956154i	$0.405391\pi$
$84$		0			0
$85$	4.49611			0.487672
$86$	−2.87433	+	8.39096i	−0.309947	+	0.904821i
$87$		0			0
$88$	2.99234	−	1.96359i	0.318984	−	0.209320i
$89$			8.57161i			0.908589i	0.890852	+	0.454294i	$0.150109\pi$
$89$			8.57161i			0.908589i	−0.890852	+	0.454294i	$0.849891\pi$
$90$		0			0
$91$		0			0
$92$	8.26338	−	10.6462i	0.861517	−	1.10994i
$93$		0			0
$94$	−9.83564	−	3.36921i	−1.01447	−	0.347508i
$95$			10.2025i			1.04676i
$96$		0			0
$97$			7.10394i			0.721296i	0.932702	+	0.360648i	$0.117444\pi$
$97$			7.10394i			0.721296i	−0.932702	+	0.360648i	$0.882556\pi$
$98$		0			0
$99$		0			0
$100$	−1.60414	−	1.24510i	−0.160414	−	0.124510i
$101$		−	0.933313i		−	0.0928682i	−0.998921	−	0.0464341i	$-0.985214\pi$
$101$		−	0.933313i		−	0.0928682i	0.998921	−	0.0464341i	$-0.0147857\pi$
$102$		0			0
$103$	−4.12921			−0.406863			−0.203431	−	0.979089i	$-0.565209\pi$
$103$	−4.12921			−0.406863			−0.203431	+	0.979089i	$0.565209\pi$
$104$	−7.08820	+	4.65132i	−0.695055	+	0.456100i
$105$		0			0
$106$	−0.0958634	−	0.0328381i	−0.00931108	−	0.00318952i
$107$			13.8424i			1.33819i	0.743176	+	0.669096i	$0.233318\pi$
$107$			13.8424i			1.33819i	−0.743176	+	0.669096i	$0.766682\pi$
$108$		0			0
$109$	−0.984676			−0.0943148			−0.0471574	−	0.998887i	$-0.515016\pi$
$109$	−0.984676			−0.0943148			−0.0471574	+	0.998887i	$0.515016\pi$
$110$	4.15219	+	1.42234i	0.395896	+	0.135615i
$111$		0			0
$112$		0			0
$113$	−5.03187			−0.473359			−0.236679	−	0.971588i	$-0.576059\pi$
$113$	−5.03187			−0.473359			−0.236679	+	0.971588i	$0.576059\pi$
$114$		0			0
$115$	16.5268			1.54113
$116$	14.8880	+	11.5558i	1.38232	+	1.07293i
$117$		0			0
$118$	−4.50457	−	1.54304i	−0.414679	−	0.142049i
$119$		0			0
$120$		0			0
$121$	9.39878			0.854434
$122$	5.08820	−	14.8538i	0.460664	−	1.34480i
$123$		0			0
$124$	−14.9142	−	11.5761i	−1.33933	−	1.03956i
$125$			9.77288i			0.874113i
$126$		0			0
$127$		−	6.38337i		−	0.566433i	−0.959056	−	0.283216i	$-0.908599\pi$
$127$		−	6.38337i		−	0.566433i	0.959056	−	0.283216i	$-0.0914015\pi$
$128$	7.62342	−	8.35964i	0.673821	−	0.738895i
$129$		0			0
$130$	−9.83564	−	3.36921i	−0.862643	−	0.295499i
$131$	−3.87202			−0.338300			−0.169150	−	0.985590i	$-0.554102\pi$
$131$	−3.87202			−0.338300			−0.169150	+	0.985590i	$0.554102\pi$
$132$		0			0
$133$		0			0
$134$	−1.28674	+	3.75636i	−0.111158	+	0.324500i
$135$		0			0
$136$	−4.33503	+	2.84468i	−0.371726	+	0.243929i
$137$	14.7032			1.25618			0.628088	−	0.778142i	$-0.283838\pi$
$137$	14.7032			1.25618			0.628088	+	0.778142i	$0.283838\pi$
$138$		0			0
$139$	2.01655			0.171041			0.0855207	−	0.996336i	$-0.472745\pi$
$139$	2.01655			0.171041			0.0855207	+	0.996336i	$0.472745\pi$
$140$		0			0
$141$		0			0
$142$	1.33953	−	3.91046i	0.112411	−	0.328159i
$143$	3.79295			0.317182
$144$		0			0
$145$			23.1116i			1.91931i
$146$	3.71448	−	10.8436i	0.307413	−	0.897421i
$147$		0			0
$148$	11.8675	+	9.21133i	0.975504	+	0.757167i
$149$	0.496110			0.0406429			0.0203215	−	0.999793i	$-0.493531\pi$
$149$	0.496110			0.0406429			0.0203215	+	0.999793i	$0.493531\pi$
$150$		0			0
$151$		−	13.2370i		−	1.07721i	−0.842558	−	0.538605i	$-0.818951\pi$
$151$		−	13.2370i		−	1.07721i	0.842558	−	0.538605i	$-0.181049\pi$
$152$	−6.45511	−	9.83701i	−0.523578	−	0.797886i
$153$		0			0
$154$		0			0
$155$		−	23.1522i		−	1.85963i
$156$		0			0
$157$			5.06158i			0.403958i	0.979390	+	0.201979i	$0.0647372\pi$
$157$			5.06158i			0.403958i	−0.979390	+	0.201979i	$0.935263\pi$
$158$	0.817456	−	2.38638i	0.0650333	−	0.189850i
$159$		0			0
$160$	13.8305	+	1.09935i	1.09339	+	0.0869115i
$161$		0			0
$162$		0			0
$163$		−	12.0357i		−	0.942710i	−0.881944	−	0.471355i	$-0.843765\pi$
$163$		−	12.0357i		−	0.942710i	0.881944	−	0.471355i	$-0.156235\pi$
$164$	1.33626	−	1.72158i	0.104344	−	0.134433i
$165$		0			0
$166$	−7.13935	−	2.44559i	−0.554121	−	0.189815i
$167$	7.46424			0.577600			0.288800	−	0.957389i	$-0.406744\pi$
$167$	7.46424			0.577600			0.288800	+	0.957389i	$0.406744\pi$
$168$		0			0
$169$	4.01532			0.308871
$170$	−6.01532	−	2.06056i	−0.461354	−	0.158037i
$171$		0			0
$172$	7.69111	−	9.90893i	0.586442	−	0.755549i
$173$			4.36398i			0.331787i	0.986144	+	0.165894i	$0.0530508\pi$
$173$			4.36398i			0.331787i	−0.986144	+	0.165894i	$0.946949\pi$
$174$		0			0
$175$		0			0
$176$	−4.90334	+	1.25570i	−0.369603	+	0.0946518i
$177$		0			0
$178$	3.92835	−	11.4679i	0.294442	−	0.859557i
$179$		−	24.5667i		−	1.83620i	−0.396343	−	0.918102i	$-0.629721\pi$
$179$		−	24.5667i		−	1.83620i	0.396343	−	0.918102i	$-0.370279\pi$
$180$		0			0
$181$		−	11.7182i		−	0.871011i	−0.900186	−	0.435505i	$-0.856570\pi$
$181$		−	11.7182i		−	0.871011i	0.900186	−	0.435505i	$-0.143430\pi$
$182$		0			0
$183$		0			0
$184$	−15.9347	+	10.4564i	−1.17472	+	0.770858i
$185$			18.4227i			1.35446i
$186$		0			0
$187$	2.31971			0.169634
$188$	11.6150	+	9.01530i	0.847108	+	0.657508i
$189$		0			0
$190$	4.67579	−	13.6499i	0.339217	−	0.990268i
$191$		−	15.8919i		−	1.14990i	−0.818190	−	0.574948i	$-0.805022\pi$
$191$		−	15.8919i		−	1.14990i	0.818190	−	0.574948i	$-0.194978\pi$
$192$		0			0
$193$	19.7338			1.42047			0.710235	−	0.703964i	$-0.248589\pi$
$193$	19.7338			1.42047			0.710235	+	0.703964i	$0.248589\pi$
$194$	3.25572	−	9.50433i	0.233747	−	0.682371i
$195$		0			0
$196$		0			0
$197$	−0.998775			−0.0711598			−0.0355799	−	0.999367i	$-0.511328\pi$
$197$	−0.998775			−0.0711598			−0.0355799	+	0.999367i	$0.511328\pi$
$198$		0			0
$199$	2.70316			0.191622			0.0958110	−	0.995400i	$-0.469456\pi$
$199$	2.70316			0.191622			0.0958110	+	0.995400i	$0.469456\pi$
$200$	1.57554	+	2.40099i	0.111408	+	0.169775i
$201$		0			0
$202$	−0.427735	+	1.24868i	−0.0300953	+	0.0878565i
$203$		0			0
$204$		0			0
$205$	2.67251			0.186656
$206$	5.52444	+	1.89240i	0.384906	+	0.131850i
$207$		0			0
$208$	11.6150	−	2.97448i	0.805353	−	0.206243i
$209$			5.26385i			0.364108i
$210$		0			0
$211$			18.1798i			1.25155i	0.780004	+	0.625774i	$0.215217\pi$
$211$			18.1798i			1.25155i	−0.780004	+	0.625774i	$0.784783\pi$
$212$	0.113206	+	0.0878679i	0.00777499	+	0.00603479i
$213$		0			0
$214$	6.34392	−	18.5196i	0.433661	−	1.26598i
$215$	15.3822			1.04906
$216$		0			0
$217$		0			0
$218$	1.31739	+	0.451274i	0.0892251	+	0.0305642i
$219$		0			0
$220$	−4.90334	−	3.80588i	−0.330583	−	0.256592i
$221$	−5.49489			−0.369626
$222$		0			0
$223$	11.5996			0.776769			0.388385	−	0.921497i	$-0.373033\pi$
$223$	11.5996			0.776769			0.388385	+	0.921497i	$0.373033\pi$
$224$		0			0
$225$		0			0
$226$	6.73212	+	2.30609i	0.447814	+	0.153399i
$227$	−10.1611			−0.674414			−0.337207	−	0.941430i	$-0.609482\pi$
$227$	−10.1611			−0.674414			−0.337207	+	0.941430i	$0.609482\pi$
$228$		0			0
$229$		−	23.0970i		−	1.52629i	−0.646228	−	0.763145i	$-0.723654\pi$
$229$		−	23.0970i		−	1.52629i	0.646228	−	0.763145i	$-0.276346\pi$
$230$	−22.1111	−	7.57417i	−1.45796	−	0.499426i
$231$		0			0
$232$	−14.6226	−	22.2836i	−0.960022	−	1.46299i
$233$	6.85547			0.449117			0.224558	−	0.974461i	$-0.427906\pi$
$233$	6.85547			0.449117			0.224558	+	0.974461i	$0.427906\pi$
$234$		0			0
$235$			18.0306i			1.17619i
$236$	5.31946	+	4.12886i	0.346268	+	0.268766i
$237$		0			0
$238$		0			0
$239$			22.2257i			1.43766i	0.695184	+	0.718832i	$0.255323\pi$
$239$			22.2257i			1.43766i	−0.695184	+	0.718832i	$0.744677\pi$
$240$		0			0
$241$			15.4273i			0.993762i	0.867819	+	0.496881i	$0.165522\pi$
$241$			15.4273i			0.993762i	−0.867819	+	0.496881i	$0.834478\pi$
$242$	−12.5746	−	4.30744i	−0.808325	−	0.276892i
$243$		0			0
$244$	−13.6150	+	17.5410i	−0.871608	+	1.12295i
$245$		0			0
$246$		0			0
$247$		−	12.4689i		−	0.793379i
$248$	14.6483	+	22.3227i	0.930168	+	1.41749i
$249$		0			0
$250$	4.47889	−	13.0751i	0.283270	−	0.826941i
$251$	−22.2954			−1.40727			−0.703636	−	0.710561i	$-0.748441\pi$
$251$	−22.2954			−1.40727			−0.703636	+	0.710561i	$0.748441\pi$
$252$		0			0
$253$	8.52676			0.536073
$254$	−2.92548	+	8.54029i	−0.183561	+	0.535865i
$255$		0			0
$256$	−14.0305	+	7.69053i	−0.876908	+	0.480658i
$257$			2.86976i			0.179011i	0.995986	+	0.0895055i	$0.0285287\pi$
$257$			2.86976i			0.179011i	−0.995986	+	0.0895055i	$0.971471\pi$
$258$		0			0
$259$		0			0
$260$	11.6150	+	9.01530i	0.720329	+	0.559105i
$261$		0			0
$262$	5.18036	+	1.77454i	0.320043	+	0.109631i
$263$		−	10.3714i		−	0.639526i	−0.947498	−	0.319763i	$-0.896397\pi$
$263$		−	10.3714i		−	0.639526i	0.947498	−	0.319763i	$-0.103603\pi$
$264$		0			0
$265$			0.175736i			0.0107954i
$266$		0			0
$267$		0			0
$268$	3.44306	−	4.43590i	0.210318	−	0.270966i
$269$		−	5.17319i		−	0.315415i	−0.987486	−	0.157707i	$-0.949590\pi$
$269$		−	5.17319i		−	0.315415i	0.987486	−	0.157707i	$-0.0504103\pi$
$270$		0			0
$271$	24.2391			1.47242			0.736209	−	0.676755i	$-0.236614\pi$
$271$	24.2391			1.47242			0.736209	+	0.676755i	$0.236614\pi$
$272$	7.10353	−	1.81914i	0.430714	−	0.110302i
$273$		0			0
$274$	−19.6713	−	6.73842i	−1.18839	−	0.407083i
$275$		−	1.28479i		−	0.0774755i
$276$		0			0
$277$	−3.01532			−0.181173			−0.0905866	−	0.995889i	$-0.528874\pi$
$277$	−3.01532			−0.181173			−0.0905866	+	0.995889i	$0.528874\pi$
$278$	−2.69793	−	0.924179i	−0.161811	−	0.0554286i
$279$		0			0
$280$		0			0
$281$	6.91922			0.412766			0.206383	−	0.978471i	$-0.433831\pi$
$281$	6.91922			0.412766			0.206383	+	0.978471i	$0.433831\pi$
$282$		0			0
$283$	20.5740			1.22299			0.611497	−	0.791246i	$-0.290567\pi$
$283$	20.5740			1.22299			0.611497	+	0.791246i	$0.290567\pi$
$284$	−3.58431	+	4.61789i	−0.212690	+	0.274021i
$285$		0			0
$286$	−5.07457	−	1.73830i	−0.300066	−	0.102788i
$287$		0			0
$288$		0			0
$289$	13.6394			0.802319
$290$	10.5920	−	30.9209i	0.621982	−	1.81574i
$291$		0			0
$292$	−9.93917	+	12.8052i	−0.581646	+	0.749370i
$293$		−	28.3113i		−	1.65396i	−0.562229	−	0.826982i	$-0.690056\pi$
$293$		−	28.3113i		−	1.65396i	0.562229	−	0.826982i	$-0.309944\pi$
$294$		0			0
$295$			8.25772i			0.480783i
$296$	−11.6560	−	17.7626i	−0.677489	−	1.03243i
$297$		0			0
$298$	−0.663744	−	0.227366i	−0.0384496	−	0.0131710i
$299$	−20.1980			−1.16808
$300$		0			0
$301$		0			0
$302$	−6.06647	+	17.7097i	−0.349086	+	1.01908i
$303$		0			0
$304$	4.12798	+	16.1192i	0.236756	+	0.924502i
$305$	−27.2299			−1.55918
$306$		0			0
$307$	−8.65596			−0.494022			−0.247011	−	0.969013i	$-0.579448\pi$
$307$	−8.65596			−0.494022			−0.247011	+	0.969013i	$0.579448\pi$
$308$		0			0
$309$		0			0
$310$	−10.6106	+	30.9752i	−0.602640	+	1.75927i
$311$	−9.34258			−0.529769			−0.264884	−	0.964280i	$-0.585334\pi$
$311$	−9.34258			−0.529769			−0.264884	+	0.964280i	$0.585334\pi$
$312$		0			0
$313$			7.37547i			0.416886i	0.978035	+	0.208443i	$0.0668396\pi$
$313$			7.37547i			0.416886i	−0.978035	+	0.208443i	$0.933160\pi$
$314$	2.31971	−	6.77186i	0.130909	−	0.382158i
$315$		0			0
$316$	−2.18734	+	2.81809i	−0.123048	+	0.158530i
$317$	3.63028			0.203897			0.101949	−	0.994790i	$-0.467492\pi$
$317$	3.63028			0.203897			0.101949	+	0.994790i	$0.467492\pi$
$318$		0			0
$319$			11.9241i			0.667622i
$320$	−17.9999	−	7.80929i	−1.00622	−	0.436552i
$321$		0			0
$322$		0			0
$323$		−	7.62580i		−	0.424311i
$324$		0			0
$325$			3.04338i			0.168816i
$326$	−5.51594	+	16.1025i	−0.305499	+	0.891836i
$327$		0			0
$328$	−2.57677	+	1.69089i	−0.142278	+	0.0933638i
$329$		0			0
$330$		0			0
$331$			0.628347i			0.0345371i	0.999851	+	0.0172685i	$0.00549702\pi$
$331$			0.628347i			0.0345371i	−0.999851	+	0.0172685i	$0.994503\pi$
$332$	8.43090	+	6.54389i	0.462705	+	0.359143i
$333$		0			0
$334$	−9.98637	−	3.42084i	−0.546430	−	0.187180i
$335$	6.88612			0.376229
$336$		0			0
$337$	−22.3119			−1.21541			−0.607704	−	0.794164i	$-0.707909\pi$
$337$	−22.3119			−1.21541			−0.607704	+	0.794164i	$0.707909\pi$
$338$	−5.37208	−	1.84021i	−0.292203	−	0.100094i
$339$		0			0
$340$	7.10353	+	5.51362i	0.385243	+	0.299018i
$341$		−	11.9450i		−	0.646860i
$342$		0			0
$343$		0			0
$344$	−14.8311	+	9.73229i	−0.799642	+	0.524730i
$345$		0			0
$346$	2.00000	−	5.83854i	0.107521	−	0.313882i
$347$			6.89477i			0.370130i	0.982726	+	0.185065i	$0.0592496\pi$
$347$			6.89477i			0.370130i	−0.982726	+	0.185065i	$0.940750\pi$
$348$		0			0
$349$		−	13.4768i		−	0.721399i	−0.932682	−	0.360699i	$-0.882538\pi$
$349$		−	13.4768i		−	0.721399i	0.932682	−	0.360699i	$-0.117462\pi$
$350$		0			0
$351$		0			0
$352$	7.13564	+	0.567197i	0.380331	+	0.0302317i
$353$			28.5846i			1.52140i	0.649101	+	0.760702i	$0.275145\pi$
$353$			28.5846i			1.52140i	−0.649101	+	0.760702i	$0.724855\pi$
$354$		0			0
$355$	−7.16862			−0.380471
$356$	−10.5114	+	13.5425i	−0.557105	+	0.717752i
$357$		0			0
$358$	−11.2589	+	32.8677i	−0.595050	+	1.73711i
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	−1.69562			−0.0892430
$362$	−5.37044	+	15.6778i	−0.282264	+	0.824006i
$363$		0			0
$364$		0			0
$365$	−19.8783			−1.04048
$366$		0			0
$367$	−12.9437			−0.675654			−0.337827	−	0.941208i	$-0.609692\pi$
$367$	−12.9437			−0.675654			−0.337827	+	0.941208i	$0.609692\pi$
$368$	26.1111	−	6.68679i	1.36113	−	0.348573i
$369$		0			0
$370$	8.44306	−	24.6476i	0.438934	−	1.28137i
$371$		0			0
$372$		0			0
$373$	3.07907			0.159428			0.0797141	−	0.996818i	$-0.474599\pi$
$373$	3.07907			0.159428			0.0797141	+	0.996818i	$0.474599\pi$
$374$	−3.10353	−	1.06312i	−0.160479	−	0.0549724i
$375$		0			0
$376$	−11.4079	−	17.3846i	−0.588318	−	0.896544i
$377$		−	28.2456i		−	1.45472i
$378$		0			0
$379$			5.21020i			0.267630i	0.991006	+	0.133815i	$0.0427228\pi$
$379$			5.21020i			0.267630i	−0.991006	+	0.133815i	$0.957277\pi$
$380$	−12.5114	+	16.1192i	−0.641823	+	0.826900i
$381$		0			0
$382$	−7.28321	+	21.2617i	−0.372641	+	1.08784i
$383$	−38.8706			−1.98619			−0.993096	−	0.117301i	$-0.962576\pi$
$383$	−38.8706			−1.98619			−0.993096	+	0.117301i	$0.962576\pi$
$384$		0			0
$385$		0			0
$386$	−26.4018	−	9.04395i	−1.34381	−	0.460325i
$387$		0			0
$388$	−8.71162	+	11.2237i	−0.442265	+	0.569797i
$389$	3.73503			0.189374			0.0946869	−	0.995507i	$-0.469815\pi$
$389$	3.73503			0.189374			0.0946869	+	0.995507i	$0.469815\pi$
$390$		0			0
$391$	−12.3528			−0.624708
$392$		0			0
$393$		0			0
$394$	1.33626	+	0.457736i	0.0673196	+	0.0230604i
$395$	−4.37468			−0.220114
$396$		0			0
$397$			6.70976i			0.336753i	0.985723	+	0.168377i	$0.0538525\pi$
$397$			6.70976i			0.336753i	−0.985723	+	0.168377i	$0.946148\pi$
$398$	−3.61655	−	1.23885i	−0.181281	−	0.0620980i
$399$		0			0
$400$	−1.00754	−	3.93433i	−0.0503772	−	0.196717i
$401$	−5.84769			−0.292020			−0.146010	−	0.989283i	$-0.546643\pi$
$401$	−5.84769			−0.292020			−0.146010	+	0.989283i	$0.546643\pi$
$402$		0			0
$403$			28.2952i			1.40949i
$404$	1.14453	−	1.47457i	0.0569425	−	0.0733625i
$405$		0			0
$406$		0			0
$407$			9.50492i			0.471142i
$408$		0			0
$409$		−	30.8651i		−	1.52618i	−0.646293	−	0.763089i	$-0.723682\pi$
$409$		−	30.8651i		−	1.52618i	0.646293	−	0.763089i	$-0.276318\pi$
$410$	−3.57554	−	1.22481i	−0.176583	−	0.0604889i
$411$		0			0
$412$	−6.52384	−	5.06368i	−0.321407	−	0.249469i
$413$		0			0
$414$		0			0
$415$			13.0878i			0.642454i
$416$	−16.9028	−	1.34357i	−0.828728	−	0.0658738i
$417$		0			0
$418$	2.41241	−	7.04249i	0.117995	−	0.344459i
$419$	−29.0866			−1.42097			−0.710487	−	0.703710i	$-0.751525\pi$
$419$	−29.0866			−1.42097			−0.710487	+	0.703710i	$0.751525\pi$
$420$		0			0
$421$	13.8642			0.675702			0.337851	−	0.941200i	$-0.390300\pi$
$421$	13.8642			0.675702			0.337851	+	0.941200i	$0.390300\pi$
$422$	8.33175	−	24.3227i	0.405583	−	1.18401i
$423$		0			0
$424$	−0.111188	−	0.169440i	−0.00539974	−	0.00822873i
$425$			1.86128i			0.0902854i
$426$		0			0
$427$		0			0
$428$	−16.9750	+	21.8699i	−0.820517	+	1.05712i
$429$		0			0
$430$	−20.5798	−	7.04964i	−0.992447	−	0.339964i
$431$			31.8995i			1.53655i	0.640123	+	0.768273i	$0.278883\pi$
$431$			31.8995i			1.53655i	−0.640123	+	0.768273i	$0.721117\pi$
$432$		0			0
$433$		−	9.82239i		−	0.472034i	−0.971749	−	0.236017i	$-0.924158\pi$
$433$		−	9.82239i		−	0.472034i	0.971749	−	0.236017i	$-0.0758421\pi$
$434$		0			0
$435$		0			0
$436$	−1.55572	−	1.20752i	−0.0745053	−	0.0578295i
$437$		−	28.0308i		−	1.34090i
$438$		0			0
$439$	−17.0398			−0.813264			−0.406632	−	0.913592i	$-0.633297\pi$
$439$	−17.0398			−0.813264			−0.406632	+	0.913592i	$0.633297\pi$
$440$	4.81594	+	7.33906i	0.229591	+	0.349876i
$441$		0			0
$442$	7.35158	+	2.51829i	0.349679	+	0.119783i
$443$			8.42931i			0.400489i	0.979746	+	0.200244i	$0.0641736\pi$
$443$			8.42931i			0.400489i	−0.979746	+	0.200244i	$0.935826\pi$
$444$		0			0
$445$	−21.0229			−0.996580
$446$	−15.5191	−	5.31608i	−0.734851	−	0.251724i
$447$		0			0
$448$		0			0
$449$	−9.64064			−0.454970			−0.227485	−	0.973782i	$-0.573050\pi$
$449$	−9.64064			−0.454970			−0.227485	+	0.973782i	$0.573050\pi$
$450$		0			0
$451$	1.37885			0.0649274
$452$	−7.94999	−	6.17063i	−0.373936	−	0.290242i
$453$		0			0
$454$	13.5945	+	4.65680i	0.638020	+	0.218554i
$455$		0			0
$456$		0			0
$457$	−29.0457			−1.35870			−0.679351	−	0.733813i	$-0.737739\pi$
$457$	−29.0457			−1.35870			−0.679351	+	0.733813i	$0.737739\pi$
$458$	−10.5853	+	30.9013i	−0.494617	+	1.44392i
$459$		0			0
$460$	26.1111	+	20.2669i	1.21743	+	0.944949i
$461$			23.9796i			1.11684i	0.829559	+	0.558420i	$0.188592\pi$
$461$			23.9796i			1.11684i	−0.829559	+	0.558420i	$0.811408\pi$
$462$		0			0
$463$		−	28.4975i		−	1.32439i	−0.749331	−	0.662196i	$-0.769625\pi$
$463$		−	28.4975i		−	1.32439i	0.749331	−	0.662196i	$-0.230375\pi$
$464$	9.35103	+	36.5146i	0.434111	+	1.69515i
$465$		0			0
$466$	−9.17190	−	3.14184i	−0.424880	−	0.145543i
$467$	18.5815			0.859849			0.429925	−	0.902865i	$-0.358540\pi$
$467$	18.5815			0.859849			0.429925	+	0.902865i	$0.358540\pi$
$468$		0			0
$469$		0			0
$470$	8.26338	−	24.1231i	0.381161	−	1.11271i
$471$		0			0
$472$	−5.22464	−	7.96188i	−0.240483	−	0.366475i
$473$	7.93625			0.364909
$474$		0			0
$475$	−4.22360			−0.193792
$476$		0			0
$477$		0			0
$478$	10.1860	−	29.7357i	0.465897	−	1.36008i
$479$	28.3414			1.29495			0.647475	−	0.762087i	$-0.275825\pi$
$479$	28.3414			1.29495			0.647475	+	0.762087i	$0.275825\pi$
$480$		0			0
$481$		−	22.5151i		−	1.02660i
$482$	7.07031	−	20.6402i	0.322044	−	0.940134i
$483$		0			0
$484$	14.8494	+	11.5258i	0.674972	+	0.523900i
$485$	−17.4232			−0.791148
$486$		0			0
$487$		−	41.5113i		−	1.88106i	−0.339718	−	0.940528i	$-0.610331\pi$
$487$		−	41.5113i		−	1.88106i	0.339718	−	0.940528i	$-0.389669\pi$
$488$	26.2544	−	17.2283i	1.18848	−	0.779888i
$489$		0			0
$490$		0			0
$491$			1.72728i			0.0779509i	0.999240	+	0.0389755i	$0.0124094\pi$
$491$			1.72728i			0.0779509i	−0.999240	+	0.0389755i	$0.987591\pi$
$492$		0			0
$493$		−	17.2746i		−	0.778008i
$494$	−5.71448	+	16.6821i	−0.257107	+	0.750564i
$495$		0			0
$496$	−9.36745	−	36.5787i	−0.420611	−	1.64243i
$497$		0			0
$498$		0			0
$499$			42.2870i			1.89303i	0.322663	+	0.946514i	$0.395422\pi$
$499$			42.2870i			1.89303i	−0.322663	+	0.946514i	$0.604578\pi$
$500$	−11.9846	+	15.4404i	−0.535966	+	0.690517i
$501$		0			0
$502$	29.8289	+	10.2179i	1.33133	+	0.456048i
$503$	−4.23770			−0.188950			−0.0944748	−	0.995527i	$-0.530117\pi$
$503$	−4.23770			−0.188950			−0.0944748	+	0.995527i	$0.530117\pi$
$504$		0			0
$505$	2.28906			0.101862
$506$	−11.4079	−	3.90779i	−0.507143	−	0.173723i
$507$		0			0
$508$	7.82798	−	10.0853i	0.347311	−	0.447461i
$509$		−	41.7756i		−	1.85167i	−0.377924	−	0.925836i	$-0.623362\pi$
$509$		−	41.7756i		−	1.85167i	0.377924	−	0.925836i	$-0.376638\pi$
$510$		0			0
$511$		0			0
$512$	22.2959	−	3.85896i	0.985350	−	0.170544i
$513$		0			0
$514$	1.31521	−	3.83944i	0.0580112	−	0.169351i
$515$		−	10.1274i		−	0.446265i
$516$		0			0
$517$			9.30265i			0.409130i
$518$		0			0
$519$		0			0
$520$	−11.4079	−	17.3846i	−0.500270	−	0.762367i
$521$		−	34.9506i		−	1.53121i	−0.643309	−	0.765607i	$-0.722439\pi$
$521$		−	34.9506i		−	1.53121i	0.643309	−	0.765607i	$-0.277561\pi$
$522$		0			0
$523$	−12.2701			−0.536532			−0.268266	−	0.963345i	$-0.586451\pi$
$523$	−12.2701			−0.536532			−0.268266	+	0.963345i	$0.586451\pi$
$524$	−6.11751	−	4.74829i	−0.267245	−	0.207430i
$525$		0			0
$526$	−4.75317	+	13.8758i	−0.207248	+	0.605014i
$527$			17.3049i			0.753814i
$528$		0			0
$529$	−22.4063			−0.974188
$530$	0.0805393	−	0.235116i	0.00349840	−	0.0102128i
$531$		0			0
$532$		0			0
$533$	−3.26619			−0.141474
$534$		0			0
$535$	−33.9500			−1.46779
$536$	−6.63942	+	4.35683i	−0.286779	+	0.188186i
$537$		0			0
$538$	−2.37086	+	6.92118i	−0.102215	+	0.298393i
$539$		0			0
$540$		0			0
$541$	−0.935765			−0.0402317			−0.0201158	−	0.999798i	$-0.506404\pi$
$541$	−0.935765			−0.0402317			−0.0201158	+	0.999798i	$0.506404\pi$
$542$	−32.4293	−	11.1087i	−1.39296	−	0.477159i
$543$		0			0
$544$	−10.3375	−	0.821704i	−0.443216	−	0.0352303i
$545$		−	2.41503i		−	0.103449i
$546$		0			0
$547$			7.13048i			0.304877i	0.988313	+	0.152439i	$0.0487127\pi$
$547$			7.13048i			0.304877i	−0.988313	+	0.152439i	$0.951287\pi$
$548$	23.2299	+	18.0306i	0.992333	+	0.770229i
$549$		0			0
$550$	−0.588814	+	1.71891i	−0.0251071	+	0.0732945i
$551$	39.1993			1.66995
$552$		0			0
$553$		0			0
$554$	4.03419	+	1.38192i	0.171396	+	0.0587120i
$555$		0			0
$556$	3.18600	+	2.47291i	0.135116	+	0.104875i
$557$	−9.95244			−0.421698			−0.210849	−	0.977519i	$-0.567623\pi$
$557$	−9.95244			−0.421698			−0.210849	+	0.977519i	$0.567623\pi$
$558$		0			0
$559$	−18.7993			−0.795124
$560$		0			0
$561$		0			0
$562$	−9.25719	−	3.17106i	−0.390491	−	0.133763i
$563$	1.68906			0.0711855			0.0355927	−	0.999366i	$-0.488668\pi$
$563$	1.68906			0.0711855			0.0355927	+	0.999366i	$0.488668\pi$
$564$		0			0
$565$		−	12.3413i		−	0.519200i
$566$	−27.5258	−	9.42899i	−1.15700	−	0.396330i
$567$		0			0
$568$	6.91180	−	4.53557i	0.290013	−	0.190308i
$569$	13.9387			0.584341			0.292170	−	0.956366i	$-0.405623\pi$
$569$	13.9387			0.584341			0.292170	+	0.956366i	$0.405623\pi$
$570$		0			0
$571$		−	18.6589i		−	0.780853i	−0.920634	−	0.390426i	$-0.872328\pi$
$571$		−	18.6589i		−	0.780853i	0.920634	−	0.390426i	$-0.127672\pi$
$572$	5.99258	+	4.65132i	0.250562	+	0.194482i
$573$		0			0
$574$		0			0
$575$			6.84168i			0.285318i
$576$		0			0
$577$			34.0165i			1.41612i	0.706150	+	0.708062i	$0.250430\pi$
$577$			34.0165i			1.41612i	−0.706150	+	0.708062i	$0.749570\pi$
$578$	−18.2481	−	6.25091i	−0.759021	−	0.260004i
$579$		0			0
$580$	−28.3419	+	36.5146i	−1.17683	+	1.51619i
$581$		0			0
$582$		0			0
$583$			0.0906685i			0.00375511i
$584$	19.1662	−	12.5770i	0.793102	−	0.520439i
$585$		0			0
$586$	−12.9750	+	37.8775i	−0.535992	+	1.56471i
$587$	41.9153			1.73003			0.865015	−	0.501746i	$-0.167309\pi$
$587$	41.9153			1.73003			0.865015	+	0.501746i	$0.167309\pi$
$588$		0			0
$589$	−39.2681			−1.61801
$590$	3.78449	−	11.0480i	0.155805	−	0.454838i
$591$		0			0
$592$	7.45388	+	29.1065i	0.306353	+	1.19627i
$593$			24.4051i			1.00220i	0.865391	+	0.501098i	$0.167070\pi$
$593$			24.4051i			1.00220i	−0.865391	+	0.501098i	$0.832930\pi$
$594$		0			0
$595$		0			0
$596$	0.783818	+	0.608384i	0.0321064	+	0.0249204i
$597$		0			0
$598$	27.0229	+	9.25671i	1.10505	+	0.378535i
$599$			20.7846i			0.849236i	0.905373	+	0.424618i	$0.139592\pi$
$599$			20.7846i			0.849236i	−0.905373	+	0.424618i	$0.860408\pi$
$600$		0			0
$601$			10.6623i			0.434924i	0.976069	+	0.217462i	$0.0697778\pi$
$601$			10.6623i			0.434924i	−0.976069	+	0.217462i	$0.930222\pi$
$602$		0			0
$603$		0			0
$604$	16.2326	−	20.9135i	0.660496	−	0.850957i
$605$			23.0516i			0.937180i
$606$		0			0
$607$	−40.0429			−1.62529			−0.812646	−	0.582757i	$-0.801974\pi$
$607$	−40.0429			−1.62529			−0.812646	+	0.582757i	$0.801974\pi$
$608$	1.86460	−	23.4577i	0.0756196	−	0.951335i
$609$		0			0
$610$	36.4308	+	12.4794i	1.47504	+	0.505276i
$611$		−	22.0360i		−	0.891479i
$612$		0			0
$613$	22.4961			0.908609			0.454305	−	0.890846i	$-0.349888\pi$
$613$	22.4961			0.908609			0.454305	+	0.890846i	$0.349888\pi$
$614$	11.5808	+	3.96701i	0.467362	+	0.160095i
$615$		0			0
$616$		0			0
$617$	18.0820			0.727954			0.363977	−	0.931408i	$-0.381419\pi$
$617$	18.0820			0.727954			0.363977	+	0.931408i	$0.381419\pi$
$618$		0			0
$619$	−32.0929			−1.28992			−0.644962	−	0.764215i	$-0.723127\pi$
$619$	−32.0929			−1.28992			−0.644962	+	0.764215i	$0.723127\pi$
$620$	28.3917	−	36.5787i	1.14024	−	1.46904i
$621$		0			0
$622$	12.4994	+	4.28168i	0.501180	+	0.171680i
$623$		0			0
$624$		0			0
$625$	−29.0457			−1.16183
$626$	3.38016	−	9.86760i	0.135098	−	0.394389i
$627$		0			0
$628$	−6.20705	+	7.99692i	−0.247688	+	0.319112i
$629$		−	13.7699i		−	0.549041i
$630$		0			0
$631$		−	2.95509i		−	0.117640i	−0.998269	−	0.0588201i	$-0.981266\pi$
$631$		−	2.95509i		−	0.117640i	0.998269	−	0.0588201i	$-0.0187338\pi$
$632$	4.21796	−	2.76785i	0.167781	−	0.110099i
$633$		0			0
$634$	−4.85694	−	1.66375i	−0.192894	−	0.0660760i
$635$	15.6560			0.621288
$636$		0			0
$637$		0			0
$638$	5.46479	−	15.9532i	0.216353	−	0.631593i
$639$		0			0
$640$	20.5030	+	18.6973i	0.810451	+	0.739076i
$641$	41.4917			1.63882			0.819412	−	0.573205i	$-0.194300\pi$
$641$	41.4917			1.63882			0.819412	+	0.573205i	$0.194300\pi$
$642$		0			0
$643$	16.7686			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$643$	16.7686			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$644$		0			0
$645$		0			0
$646$	−3.49489	+	10.2025i	−0.137504	+	0.401413i
$647$	18.6236			0.732169			0.366085	−	0.930582i	$-0.380698\pi$
$647$	18.6236			0.732169			0.366085	+	0.930582i	$0.380698\pi$
$648$		0			0
$649$			4.26046i			0.167238i
$650$	1.39477	−	4.07172i	0.0547075	−	0.159706i
$651$		0			0
$652$	14.7595	−	19.0155i	0.578026	−	0.744706i
$653$	−25.6609			−1.00419			−0.502095	−	0.864813i	$-0.667437\pi$
$653$	−25.6609			−1.00419			−0.502095	+	0.864813i	$0.667437\pi$
$654$		0			0
$655$		−	9.49658i		−	0.371062i
$656$	4.22238	−	1.08131i	0.164856	−	0.0422180i
$657$		0			0
$658$		0			0
$659$			27.7044i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$659$			27.7044i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$660$		0			0
$661$		−	34.1182i		−	1.32704i	−0.748157	−	0.663522i	$-0.769061\pi$
$661$		−	34.1182i		−	1.32704i	0.748157	−	0.663522i	$-0.230939\pi$
$662$	0.287970	−	0.840662i	0.0111923	−	0.0326732i
$663$		0			0
$664$	−8.28060	−	12.6189i	−0.321350	−	0.489708i
$665$		0			0
$666$		0			0
$667$		−	63.4977i		−	2.45864i
$668$	11.7929	+	9.15345i	0.456283	+	0.354158i
$669$		0			0
$670$	−9.21290	−	3.15589i	−0.355926	−	0.121923i
$671$	−14.0489			−0.542352
$672$		0			0
$673$	−17.7032			−0.682407			−0.341203	−	0.939990i	$-0.610834\pi$
$673$	−17.7032			−0.682407			−0.341203	+	0.939990i	$0.610834\pi$
$674$	29.8510	+	10.2255i	1.14982	+	0.393872i
$675$		0			0
$676$	6.34392	+	4.92402i	0.243997	+	0.189386i
$677$		−	41.0852i		−	1.57903i	−0.613730	−	0.789516i	$-0.710332\pi$
$677$		−	41.0852i		−	1.57903i	0.613730	−	0.789516i	$-0.289668\pi$
$678$		0			0
$679$		0			0
$680$	−6.97690	−	10.6322i	−0.267552	−	0.407725i
$681$		0			0
$682$	−5.47438	+	15.9812i	−0.209625	+	0.611952i
$683$			21.2282i			0.812275i	0.913812	+	0.406137i	$0.133125\pi$
$683$			21.2282i			0.812275i	−0.913812	+	0.406137i	$0.866875\pi$
$684$		0			0
$685$			36.0612i			1.37783i
$686$		0			0
$687$		0			0
$688$	24.3028	−	6.22371i	0.926535	−	0.237277i
$689$		−	0.214774i		−	0.00818224i
$690$		0			0
$691$	38.9757			1.48270			0.741352	−	0.671116i	$-0.234185\pi$
$691$	38.9757			1.48270			0.741352	+	0.671116i	$0.234185\pi$
$692$	−5.35158	+	6.89477i	−0.203437	+	0.262100i
$693$		0			0
$694$	3.15985	−	9.22447i	0.119946	−	0.350156i
$695$			4.94582i			0.187606i
$696$		0			0
$697$	−1.99755			−0.0756626
$698$	−6.17640	+	18.0306i	−0.233780	+	0.682468i
$699$		0			0
$700$		0			0
$701$	−4.28115			−0.161697			−0.0808485	−	0.996726i	$-0.525763\pi$
$701$	−4.28115			−0.161697			−0.0808485	+	0.996726i	$0.525763\pi$
$702$		0			0
$703$	31.2465			1.17848
$704$	−9.28680	−	4.02910i	−0.350009	−	0.151852i
$705$		0			0
$706$	13.1002	−	38.2432i	0.493034	−	1.43930i
$707$		0			0
$708$		0			0
$709$	−43.7591			−1.64341			−0.821704	−	0.569914i	$-0.806976\pi$
$709$	−43.7591			−1.64341			−0.821704	+	0.569914i	$0.806976\pi$
$710$	9.59087	+	3.28536i	0.359939	+	0.123297i
$711$		0			0
$712$	20.2697	−	13.3011i	0.759639	−	0.498480i
$713$			63.6092i			2.38218i
$714$		0			0
$715$			9.30265i			0.347899i
$716$	30.1264	−	38.8137i	1.12588	−	1.45053i
$717$		0			0
$718$	3.17518	−	9.26921i	0.118497	−	0.345924i
$719$	−41.5314			−1.54886			−0.774429	−	0.632660i	$-0.781963\pi$
$719$	−41.5314			−1.54886			−0.774429	+	0.632660i	$0.781963\pi$
$720$		0			0
$721$		0			0
$722$	2.26856	+	0.777097i	0.0844270	+	0.0289205i
$723$		0			0
$724$	14.3702	−	18.5140i	0.534064	−	0.688067i
$725$	−9.56764			−0.355333
$726$		0			0
$727$	−7.19963			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$727$	−7.19963			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$728$		0			0
$729$		0			0
$730$	26.5951	+	9.11019i	0.984330	+	0.337183i
$731$	−11.4973			−0.425244
$732$		0			0
$733$		−	24.1585i		−	0.892315i	−0.894954	−	0.446158i	$-0.852792\pi$
$733$		−	24.1585i		−	0.892315i	0.894954	−	0.446158i	$-0.147208\pi$
$734$	17.3173	+	5.93205i	0.639192	+	0.218956i
$735$		0			0
$736$	−37.9984	−	3.02041i	−1.40064	−	0.111334i
$737$	3.55280			0.130869
$738$		0			0
$739$			9.43033i			0.346900i	0.984843	+	0.173450i	$0.0554915\pi$
$739$			9.43033i			0.346900i	−0.984843	+	0.173450i	$0.944508\pi$
$740$	−22.5919	+	29.1065i	−0.830493	+	1.06997i
$741$		0			0
$742$		0			0
$743$		−	2.32851i		−	0.0854248i	−0.999087	−	0.0427124i	$-0.986400\pi$
$743$		−	2.32851i		−	0.0854248i	0.999087	−	0.0427124i	$-0.0135999\pi$
$744$		0			0
$745$			1.21677i			0.0445789i
$746$	−4.11947	−	1.41113i	−0.150825	−	0.0516651i
$747$		0			0
$748$	3.66497	+	2.84468i	0.134005	+	0.104012i
$749$		0			0
$750$		0			0
$751$			31.1577i			1.13696i	0.822696	+	0.568481i	$0.192469\pi$
$751$			31.1577i			1.13696i	−0.822696	+	0.568481i	$0.807531\pi$
$752$	7.29525	+	28.4870i	0.266030	+	1.03882i
$753$		0			0
$754$	−12.9449	+	37.7897i	−0.471425	+	1.37622i
$755$	32.4652			1.18153
$756$		0			0
$757$	−0.559856			−0.0203483			−0.0101742	−	0.999948i	$-0.503239\pi$
$757$	−0.559856			−0.0203483			−0.0101742	+	0.999948i	$0.503239\pi$
$758$	2.38782	−	6.97070i	0.0867296	−	0.253187i
$759$		0			0
$760$	24.1264	−	15.8319i	0.875156	−	0.574283i
$761$			45.7488i			1.65839i	0.558958	+	0.829196i	$0.311201\pi$
$761$			45.7488i			1.65839i	−0.558958	+	0.829196i	$0.688799\pi$
$762$		0			0
$763$		0			0
$764$	19.4883	−	25.1080i	0.705063	−	0.908376i
$765$		0			0
$766$	52.0047	+	17.8143i	1.87901	+	0.643656i
$767$		−	10.0921i		−	0.364405i
$768$		0			0
$769$			8.33377i			0.300524i	0.988646	+	0.150262i	$0.0480117\pi$
$769$			8.33377i			0.300524i	−0.988646	+	0.150262i	$0.951988\pi$
$770$		0			0
$771$		0			0
$772$	31.1780	+	24.1997i	1.12212	+	0.870967i
$773$		−	30.6774i		−	1.10339i	−0.834046	−	0.551695i	$-0.813981\pi$
$773$		−	30.6774i		−	1.10339i	0.834046	−	0.551695i	$-0.186019\pi$
$774$		0			0
$775$	9.58444			0.344283
$776$	16.7990	−	11.0236i	0.603050	−	0.395725i
$777$		0			0
$778$	−4.99708	−	1.71176i	−0.179154	−	0.0613695i
$779$		−	4.53282i		−	0.162405i
$780$		0			0
$781$	−3.69855			−0.132345
$782$	16.5268	+	5.66126i	0.590996	+	0.202446i
$783$		0			0
$784$		0			0
$785$	−12.4141			−0.443078
$786$		0			0
$787$	−22.1584			−0.789861			−0.394931	−	0.918711i	$-0.629231\pi$
$787$	−22.1584			−0.789861			−0.394931	+	0.918711i	$0.629231\pi$
$788$	−1.57799	−	1.22481i	−0.0562136	−	0.0436319i
$789$		0			0
$790$	5.85287	+	2.00491i	0.208236	+	0.0713314i
$791$		0			0
$792$		0			0
$793$	33.2788			1.18177
$794$	3.07506	−	8.97695i	0.109130	−	0.318580i
$795$		0			0
$796$	4.27080	+	3.31491i	0.151374	+	0.117494i
$797$			24.1705i			0.856164i	0.903740	+	0.428082i	$0.140811\pi$
$797$			24.1705i			0.856164i	−0.903740	+	0.428082i	$0.859189\pi$
$798$		0			0
$799$		−	13.4768i		−	0.476776i
$800$	−0.455106	+	5.72548i	−0.0160904	+	0.202426i
$801$		0			0
$802$	7.82360	+	2.67998i	0.276261	+	0.0946334i
$803$	−10.2560			−0.361925
$804$		0			0
$805$		0			0
$806$	12.9676	−	37.8560i	0.456765	−	1.33342i
$807$		0			0
$808$	−2.20705	+	1.44828i	−0.0776438	+	0.0509503i
$809$	−15.2209			−0.535139			−0.267569	−	0.963539i	$-0.586220\pi$
$809$	−15.2209			−0.535139			−0.267569	+	0.963539i	$0.586220\pi$
$810$		0			0
$811$	48.4574			1.70157			0.850785	−	0.525515i	$-0.176127\pi$
$811$	48.4574			1.70157			0.850785	+	0.525515i	$0.176127\pi$
$812$		0			0
$813$		0			0
$814$	4.35608	−	12.7166i	0.152681	−	0.445716i
$815$	29.5190			1.03400
$816$		0			0
$817$		−	26.0896i		−	0.912760i
$818$	−14.1454	+	41.2942i	−0.494581	+	1.44382i
$819$		0			0
$820$	4.22238	+	3.27732i	0.147452	+	0.114449i
$821$	−51.5293			−1.79839			−0.899193	−	0.437552i	$-0.855846\pi$
$821$	−51.5293			−1.79839			−0.899193	+	0.437552i	$0.855846\pi$
$822$		0			0
$823$			2.19716i			0.0765881i	0.999267	+	0.0382941i	$0.0121924\pi$
$823$			2.19716i			0.0765881i	−0.999267	+	0.0382941i	$0.987808\pi$
$824$	6.40755	+	9.76453i	0.223217	+	0.340164i
$825$		0			0
$826$		0			0
$827$		−	10.2864i		−	0.357693i	−0.983877	−	0.178846i	$-0.942763\pi$
$827$		−	10.2864i		−	0.357693i	0.983877	−	0.178846i	$-0.0572365\pi$
$828$		0			0
$829$			0.765044i			0.0265711i	0.999912	+	0.0132855i	$0.00422904\pi$
$829$			0.765044i			0.0265711i	−0.999912	+	0.0132855i	$0.995771\pi$
$830$	5.99810	−	17.5101i	0.208197	−	0.607784i
$831$		0			0
$832$	21.9984	+	9.54406i	0.762658	+	0.330881i
$833$		0			0
$834$		0			0
$835$			18.3069i			0.633537i
$836$	−6.45511	+	8.31651i	−0.223255	+	0.287632i
$837$		0			0
$838$	38.9148	+	13.3303i	1.34429	+	0.460488i
$839$	3.50389			0.120968			0.0604839	−	0.998169i	$-0.480736\pi$
$839$	3.50389			0.120968			0.0604839	+	0.998169i	$0.480736\pi$
$840$		0			0
$841$	59.7973			2.06198
$842$	−18.5489	−	6.35395i	−0.639237	−	0.218971i
$843$		0			0
$844$	−22.2940	+	28.7227i	−0.767392	+	0.988678i
$845$			9.84805i			0.338783i
$846$		0			0
$847$		0			0
$848$	0.0711034	+	0.277650i	0.00244170	+	0.00953453i
$849$		0			0
$850$	0.853021	−	2.49020i	0.0292584	−	0.0854132i
$851$		−	50.6152i		−	1.73507i
$852$		0			0
$853$			25.3974i			0.869589i	0.900530	+	0.434795i	$0.143179\pi$
$853$			25.3974i			0.869589i	−0.900530	+	0.434795i	$0.856821\pi$
$854$		0			0
$855$		0			0
$856$	32.7337	−	21.4801i	1.11881	−	0.734173i
$857$			28.9379i			0.988499i	0.869320	+	0.494249i	$0.164557\pi$
$857$			28.9379i			0.988499i	−0.869320	+	0.494249i	$0.835443\pi$
$858$		0			0
$859$	−4.68807			−0.159955			−0.0799775	−	0.996797i	$-0.525485\pi$
$859$	−4.68807			−0.159955			−0.0799775	+	0.996797i	$0.525485\pi$
$860$	24.3028	+	18.8633i	0.828718	+	0.643235i
$861$		0			0
$862$	14.6195	−	42.6782i	0.497941	−	1.45363i
$863$		−	43.4651i		−	1.47957i	−0.672844	−	0.739784i	$-0.734928\pi$
$863$		−	43.4651i		−	1.47957i	0.672844	−	0.739784i	$-0.265072\pi$
$864$		0			0
$865$	−10.7032			−0.363918
$866$	−4.50158	+	13.1413i	−0.152970	+	0.446560i
$867$		0			0
$868$		0			0
$869$	−2.25706			−0.0765655
$870$		0			0
$871$	−8.41582			−0.285159
$872$	1.52798	+	2.32851i	0.0517440	+	0.0788533i
$873$		0			0
$874$	−12.8465	+	37.5023i	−0.434538	+	1.26854i
$875$		0			0
$876$		0			0
$877$	−46.0126			−1.55374			−0.776868	−	0.629663i	$-0.783193\pi$
$877$	−46.0126			−1.55374			−0.776868	+	0.629663i	$0.783193\pi$
$878$	22.7974	+	7.80929i	0.769376	+	0.263551i
$879$		0			0
$880$	−3.07975	−	12.0260i	−0.103818	−	0.405397i
$881$		−	40.8047i		−	1.37475i	−0.726304	−	0.687373i	$-0.758764\pi$
$881$		−	40.8047i		−	1.37475i	0.726304	−	0.687373i	$-0.241236\pi$
$882$		0			0
$883$		−	6.06234i		−	0.204014i	−0.994784	−	0.102007i	$-0.967474\pi$
$883$		−	6.06234i		−	0.204014i	0.994784	−	0.102007i	$-0.0325264\pi$
$884$	−8.68152	−	6.73842i	−0.291991	−	0.226638i
$885$		0			0
$886$	3.86313	−	11.2775i	0.129784	−	0.378876i
$887$	44.2552			1.48595			0.742973	−	0.669322i	$-0.233415\pi$
$887$	44.2552			1.48595			0.742973	+	0.669322i	$0.233415\pi$
$888$		0			0
$889$		0			0
$890$	28.1264	+	9.63473i	0.942799	+	0.322957i
$891$		0			0
$892$	18.3266	+	14.2247i	0.613619	+	0.476279i
$893$	30.5815			1.02337
$894$		0			0
$895$	60.2528			2.01403
$896$		0			0
$897$		0			0
$898$	12.8982	+	4.41828i	0.430417	+	0.147440i
$899$	−88.9533			−2.96676
$900$		0			0
$901$		−	0.131352i		−	0.00437599i
$902$	−1.84475	−	0.631922i	−0.0614236	−	0.0210407i
$903$		0			0
$904$	7.80827	+	11.8991i	0.259699	+	0.395759i
$905$	28.7404			0.955362
$906$		0			0
$907$		−	6.40312i		−	0.212612i	−0.994333	−	0.106306i	$-0.966098\pi$
$907$		−	6.40312i		−	0.212612i	0.994333	−	0.106306i	$-0.0339023\pi$
$908$	−16.0538	−	12.4606i	−0.532763	−	0.413520i
$909$		0			0
$910$		0			0
$911$		−	48.9687i		−	1.62241i	−0.584765	−	0.811203i	$-0.698813\pi$
$911$		−	48.9687i		−	1.62241i	0.584765	−	0.811203i	$-0.301187\pi$
$912$		0			0
$913$			6.75247i			0.223474i
$914$	38.8602	+	13.3116i	1.28538	+	0.440308i
$915$		0			0
$916$	28.3240	−	36.4915i	0.935850	−	1.20571i
$917$		0			0
$918$		0			0
$919$			24.5577i			0.810085i	0.914298	+	0.405042i	$0.132743\pi$
$919$			24.5577i			0.810085i	−0.914298	+	0.405042i	$0.867257\pi$
$920$	−25.6456	−	39.0816i	−0.845511	−	1.28848i
$921$		0			0
$922$	10.9898	−	32.0821i	0.361929	−	1.05657i
$923$	8.76108			0.288374
$924$		0			0
$925$	−7.62654			−0.250759
$926$	−13.0603	+	38.1267i	−0.429189	+	1.25292i
$927$		0			0
$928$	4.22384	−	53.1382i	0.138654	−	1.74435i
$929$		−	9.83435i		−	0.322655i	−0.986901	−	0.161327i	$-0.948423\pi$
$929$		−	9.83435i		−	0.322655i	0.986901	−	0.161327i	$-0.0515775\pi$
$930$		0			0
$931$		0			0
$932$	10.8311	+	8.40692i	0.354786	+	0.275378i
$933$		0			0
$934$	−24.8601	−	8.51585i	−0.813447	−	0.278647i
$935$			5.68935i			0.186062i
$936$		0			0
$937$		−	38.1447i		−	1.24613i	−0.782168	−	0.623067i	$-0.785886\pi$
$937$		−	38.1447i		−	1.24613i	0.782168	−	0.623067i	$-0.214114\pi$
$938$		0			0
$939$		0			0
$940$	−22.1111	+	28.4870i	−0.721184	+	0.929145i
$941$		−	34.3856i		−	1.12094i	−0.828176	−	0.560469i	$-0.810621\pi$
$941$		−	34.3856i		−	1.12094i	0.828176	−	0.560469i	$-0.189379\pi$
$942$		0			0
$943$	−7.34258			−0.239107
$944$	3.34111	+	13.0466i	0.108744	+	0.424631i
$945$		0			0
$946$	−10.6179	−	3.63716i	−0.345217	−	0.118254i
$947$			16.4695i			0.535187i	0.963532	+	0.267594i	$0.0862285\pi$
$947$			16.4695i			0.535187i	−0.963532	+	0.267594i	$0.913772\pi$
$948$		0			0
$949$	24.2942			0.788622
$950$	5.65073	+	1.93567i	0.183334	+	0.0628013i
$951$		0			0
$952$		0			0
$953$	52.4540			1.69915			0.849576	−	0.527466i	$-0.176858\pi$
$953$	52.4540			1.69915			0.849576	+	0.527466i	$0.176858\pi$
$954$		0			0
$955$	38.9767			1.26126
$956$	−27.2556	+	35.1150i	−0.881509	+	1.13570i
$957$		0			0
$958$	−37.9178	−	12.9888i	−1.22507	−	0.419648i
$959$		0			0
$960$		0			0
$961$	58.1095			1.87450
$962$	−10.3186	+	30.1229i	−0.332686	+	0.971200i
$963$		0			0
$964$	−18.9187	+	24.3741i	−0.609329	+	0.785036i
$965$			48.3995i			1.55803i
$966$		0			0
$967$			16.3573i			0.526016i	0.964794	+	0.263008i	$0.0847146\pi$
$967$			16.3573i			0.526016i	−0.964794	+	0.263008i	$0.915285\pi$
$968$	−14.5847	−	22.2257i	−0.468769	−	0.714362i
$969$		0			0
$970$	23.3105	+	7.98502i	0.748454	+	0.256384i
$971$	−23.3182			−0.748318			−0.374159	−	0.927365i	$-0.622069\pi$
$971$	−23.3182			−0.748318			−0.374159	+	0.927365i	$0.622069\pi$
$972$		0			0
$973$		0			0
$974$	−19.0245	+	55.5377i	−0.609585	+	1.77954i
$975$		0			0
$976$	−43.0213	+	11.0173i	−1.37708	+	0.352656i
$977$	−39.9844			−1.27922			−0.639608	−	0.768701i	$-0.720903\pi$
$977$	−39.9844			−1.27922			−0.639608	+	0.768701i	$0.720903\pi$
$978$		0			0
$979$	−10.8465			−0.346655
$980$		0			0
$981$		0			0
$982$	0.791607	−	2.31092i	0.0252612	−	0.0737443i
$983$	21.5255			0.686558			0.343279	−	0.939233i	$-0.388462\pi$
$983$	21.5255			0.686558			0.343279	+	0.939233i	$0.388462\pi$
$984$		0			0
$985$		−	2.44961i		−	0.0780511i
$986$	−7.91689	+	23.1116i	−0.252125	+	0.736022i
$987$		0			0
$988$	15.2908	−	19.7000i	0.486464	−	0.626741i
$989$	−42.2618			−1.34385
$990$		0			0
$991$			11.1967i			0.355676i	0.984060	+	0.177838i	$0.0569103\pi$
$991$			11.1967i			0.355676i	−0.984060	+	0.177838i	$0.943090\pi$
$992$	−4.23126	+	53.2316i	−0.134343	+	1.69010i
$993$		0			0
$994$		0			0
$995$			6.62982i			0.210179i
$996$		0			0
$997$		−	56.7766i		−	1.79813i	−0.437813	−	0.899066i	$-0.644247\pi$
$997$		−	56.7766i		−	1.79813i	0.437813	−	0.899066i	$-0.355753\pi$
$998$	19.3800	−	56.5756i	0.613464	−	1.79087i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.i.1567.1		8
3.2	odd	2		588.2.b.b.391.8		8
4.3	odd	2		1764.2.b.j.1567.2		8
7.4	even	3		252.2.bf.g.19.4		8
7.5	odd	6		252.2.bf.f.199.3		8
7.6	odd	2		1764.2.b.j.1567.1		8
12.11	even	2		588.2.b.a.391.7		8
21.2	odd	6		588.2.o.b.31.2		8
21.5	even	6		84.2.o.b.31.2	yes	8
21.11	odd	6		84.2.o.a.19.1	✓	8
21.17	even	6		588.2.o.d.19.1		8
21.20	even	2		588.2.b.a.391.8		8
28.11	odd	6		252.2.bf.f.19.3		8
28.19	even	6		252.2.bf.g.199.4		8
28.27	even	2	inner	1764.2.b.i.1567.2		8
84.11	even	6		84.2.o.b.19.2	yes	8
84.23	even	6		588.2.o.d.31.1		8
84.47	odd	6		84.2.o.a.31.1	yes	8
84.59	odd	6		588.2.o.b.19.2		8
84.83	odd	2		588.2.b.b.391.7		8
168.5	even	6		1344.2.bl.i.703.1		8
168.11	even	6		1344.2.bl.i.1279.1		8
168.53	odd	6		1344.2.bl.j.1279.1		8
168.131	odd	6		1344.2.bl.j.703.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.1	✓	8	21.11	odd	6
84.2.o.a.31.1	yes	8	84.47	odd	6
84.2.o.b.19.2	yes	8	84.11	even	6
84.2.o.b.31.2	yes	8	21.5	even	6
252.2.bf.f.19.3		8	28.11	odd	6
252.2.bf.f.199.3		8	7.5	odd	6
252.2.bf.g.19.4		8	7.4	even	3
252.2.bf.g.199.4		8	28.19	even	6
588.2.b.a.391.7		8	12.11	even	2
588.2.b.a.391.8		8	21.20	even	2
588.2.b.b.391.7		8	84.83	odd	2
588.2.b.b.391.8		8	3.2	odd	2
588.2.o.b.19.2		8	84.59	odd	6
588.2.o.b.31.2		8	21.2	odd	6
588.2.o.d.19.1		8	21.17	even	6
588.2.o.d.31.1		8	84.23	even	6
1344.2.bl.i.703.1		8	168.5	even	6
1344.2.bl.i.1279.1		8	168.11	even	6
1344.2.bl.j.703.1		8	168.131	odd	6
1344.2.bl.j.1279.1		8	168.53	odd	6
1764.2.b.i.1567.1		8	1.1	even	1	trivial
1764.2.b.i.1567.2		8	28.27	even	2	inner
1764.2.b.j.1567.1		8	7.6	odd	2
1764.2.b.j.1567.2		8	4.3	odd	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +O(q^{10})\)	\(q+(-1.33790 - 0.458297i) q^{2} +(1.57993 + 1.22631i) q^{4} +2.45262i q^{5} +(-1.55176 - 2.36475i) q^{8} +(1.12403 - 3.28134i) q^{10} +1.26539i q^{11} -2.99744i q^{13} +(0.992338 + 3.87495i) q^{16} -1.83319i q^{17} +4.15985 q^{19} +(-3.00766 + 3.87495i) q^{20} +(0.579927 - 1.69296i) q^{22} -6.73842i q^{23} -1.01532 q^{25} +(-1.37372 + 4.01027i) q^{26} +9.42323 q^{29} -9.43978 q^{31} +(0.448237 - 5.63907i) q^{32} +(-0.840146 + 2.45262i) q^{34} +7.51143 q^{37} +(-5.56545 - 1.90645i) q^{38} +(5.79982 - 3.80588i) q^{40} -1.08966i q^{41} -6.27176i q^{43} +(-1.55176 + 1.99923i) q^{44} +(-3.08820 + 9.01530i) q^{46} +7.35158 q^{47} +(1.35840 + 0.465320i) q^{50} +(3.67579 - 4.73574i) q^{52} +0.0716524 q^{53} -3.10353 q^{55} +(-12.6073 - 4.31864i) q^{58} +3.36690 q^{59} +11.1024i q^{61} +(12.6294 + 4.32623i) q^{62} +(-3.18406 + 7.33906i) q^{64} +7.35158 q^{65} -2.80766i q^{67} +(2.24806 - 2.89631i) q^{68} +2.92285i q^{71} +8.10495i q^{73} +(-10.0495 - 3.44247i) q^{74} +(6.57226 + 5.10126i) q^{76} +1.78368i q^{79} +(-9.50377 + 2.43382i) q^{80} +(-0.499388 + 1.45785i) q^{82} +5.33626 q^{83} +4.49611 q^{85} +(-2.87433 + 8.39096i) q^{86} +(2.99234 - 1.96359i) q^{88} +8.57161i q^{89} +(8.26338 - 10.6462i) q^{92} +(-9.83564 - 3.36921i) q^{94} +10.2025i q^{95} +7.10394i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} - 8 q^{10} + 10 q^{16} + 12 q^{19} - 22 q^{20} - 6 q^{22} - 4 q^{25} + 6 q^{26} + 16 q^{29} - 12 q^{31} + 12 q^{32} - 28 q^{34} - 12 q^{37} + 2 q^{38} + 4 q^{40} - 4 q^{44} - 12 q^{46} + 8 q^{47} - 2 q^{50} + 4 q^{52} - 8 q^{53} - 8 q^{55} - 14 q^{58} - 28 q^{59} + 48 q^{62} + 2 q^{64} + 8 q^{65} - 16 q^{68} - 38 q^{74} + 44 q^{76} - 6 q^{80} - 4 q^{82} - 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} - 32 q^{94}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 - 8 * q^10 + 10 * q^16 + 12 * q^19 - 22 * q^20 - 6 * q^22 - 4 * q^25 + 6 * q^26 + 16 * q^29 - 12 * q^31 + 12 * q^32 - 28 * q^34 - 12 * q^37 + 2 * q^38 + 4 * q^40 - 4 * q^44 - 12 * q^46 + 8 * q^47 - 2 * q^50 + 4 * q^52 - 8 * q^53 - 8 * q^55 - 14 * q^58 - 28 * q^59 + 48 * q^62 + 2 * q^64 + 8 * q^65 - 16 * q^68 - 38 * q^74 + 44 * q^76 - 6 * q^80 - 4 * q^82 - 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 - 32 * q^94

Introduction

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