LMFDB - Embedded newform 672.2.bi.c.17.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.19
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11142 + 1.32844i) q^{3} +(-0.337879 + 0.195075i) q^{5} +(-1.39526 + 2.24795i) q^{7} +(-0.529502 + 2.95290i) q^{9} +O(q^{10})$	\(q+(1.11142 + 1.32844i) q^{3} +(-0.337879 + 0.195075i) q^{5} +(-1.39526 + 2.24795i) q^{7} +(-0.529502 + 2.95290i) q^{9} +(-0.748582 + 1.29658i) q^{11} -3.28768 q^{13} +(-0.634670 - 0.232043i) q^{15} +(-1.68169 + 2.91278i) q^{17} +(-2.56203 - 4.43756i) q^{19} +(-4.53697 + 0.644892i) q^{21} +(4.72764 - 2.72950i) q^{23} +(-2.42389 + 4.19830i) q^{25} +(-4.51125 + 2.57850i) q^{27} +4.13801 q^{29} +(3.60237 + 2.07983i) q^{31} +(-2.55442 + 0.446598i) q^{33} +(0.0329110 - 1.03171i) q^{35} +(-7.46581 + 4.31038i) q^{37} +(-3.65399 - 4.36748i) q^{39} +11.1607 q^{41} +4.79323i q^{43} +(-0.397129 - 1.10102i) q^{45} +(2.51067 + 4.34861i) q^{47} +(-3.10652 - 6.27292i) q^{49} +(-5.73852 + 1.00329i) q^{51} +(0.499243 - 0.864715i) q^{53} -0.584118i q^{55} +(3.04755 - 8.33548i) q^{57} +(1.36034 + 0.785391i) q^{59} +(-3.40889 - 5.90437i) q^{61} +(-5.89917 - 5.31035i) q^{63} +(1.11084 - 0.641343i) q^{65} +(3.05467 + 1.76361i) q^{67} +(8.88036 + 3.24676i) q^{69} +14.3360i q^{71} +(2.76107 + 1.59410i) q^{73} +(-8.27115 + 1.44608i) q^{75} +(-1.87018 - 3.49184i) q^{77} +(0.239413 + 0.414676i) q^{79} +(-8.43926 - 3.12713i) q^{81} -17.4548i q^{83} -1.31222i q^{85} +(4.59906 + 5.49710i) q^{87} +(2.54840 + 4.41396i) q^{89} +(4.58716 - 7.39053i) q^{91} +(1.24081 + 7.09709i) q^{93} +(1.73131 + 0.999573i) q^{95} -9.00074i q^{97} +(-3.43230 - 2.89703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.11142	+	1.32844i	0.641677	+	0.766975i
$3$	1.11142	+	1.32844i	0.641677	+	0.766975i
$4$		0			0
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	−0.573646	−	0.819103i	$-0.694471\pi$
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	0.422542	+	0.906344i	$0.361138\pi$
$6$		0			0
$7$	−1.39526	+	2.24795i	−0.527357	+	0.849644i
$7$	−1.39526	+	2.24795i	−0.527357	+	0.849644i
$8$		0			0
$9$	−0.529502	+	2.95290i	−0.176501	+	0.984301i
$10$		0			0
$11$	−0.748582	+	1.29658i	−0.225706	+	0.390934i	−0.956531	−	0.291631i	$-0.905802\pi$
$11$	−0.748582	+	1.29658i	−0.225706	+	0.390934i	0.730825	+	0.682565i	$0.239136\pi$
$12$		0			0
$13$	−3.28768			−0.911838			−0.455919	−	0.890021i	$-0.650689\pi$
$13$	−3.28768			−0.911838			−0.455919	+	0.890021i	$0.650689\pi$
$14$		0			0
$15$	−0.634670	−	0.232043i	−0.163871	−	0.0599132i
$16$		0			0
$17$	−1.68169	+	2.91278i	−0.407871	+	0.706453i	−0.994651	−	0.103293i	$-0.967062\pi$
$17$	−1.68169	+	2.91278i	−0.407871	+	0.706453i	0.586780	+	0.809746i	$0.300395\pi$
$18$		0			0
$19$	−2.56203	−	4.43756i	−0.587769	−	1.01805i	−0.994524	−	0.104509i	$-0.966673\pi$
$19$	−2.56203	−	4.43756i	−0.587769	−	1.01805i	0.406755	−	0.913537i	$-0.366660\pi$
$20$		0			0
$21$	−4.53697	+	0.644892i	−0.990048	+	0.140727i
$22$		0			0
$23$	4.72764	−	2.72950i	0.985780	−	0.569141i	0.0817700	−	0.996651i	$-0.473943\pi$
$23$	4.72764	−	2.72950i	0.985780	−	0.569141i	0.904010	+	0.427511i	$0.140609\pi$
$24$		0			0
$25$	−2.42389	+	4.19830i	−0.484778	+	0.839661i
$26$		0			0
$27$	−4.51125	+	2.57850i	−0.868190	+	0.496232i
$28$		0			0
$29$	4.13801			0.768410			0.384205	−	0.923248i	$-0.374476\pi$
$29$	4.13801			0.768410			0.384205	+	0.923248i	$0.374476\pi$
$30$		0			0
$31$	3.60237	+	2.07983i	0.647005	+	0.373549i	0.787308	−	0.616560i	$-0.211474\pi$
$31$	3.60237	+	2.07983i	0.647005	+	0.373549i	−0.140303	+	0.990109i	$0.544808\pi$
$32$		0			0
$33$	−2.55442	+	0.446598i	−0.444667	+	0.0777428i
$34$		0			0
$35$	0.0329110	−	1.03171i	0.00556298	−	0.174391i
$36$		0			0
$37$	−7.46581	+	4.31038i	−1.22737	+	0.708623i	−0.966479	−	0.256745i	$-0.917350\pi$
$37$	−7.46581	+	4.31038i	−1.22737	+	0.708623i	−0.260892	+	0.965368i	$0.584017\pi$
$38$		0			0
$39$	−3.65399	−	4.36748i	−0.585106	−	0.699357i
$40$		0			0
$41$	11.1607			1.74301			0.871505	−	0.490387i	$-0.163145\pi$
$41$	11.1607			1.74301			0.871505	+	0.490387i	$0.163145\pi$
$42$		0			0
$43$			4.79323i			0.730961i	0.930819	+	0.365480i	$0.119095\pi$
$43$			4.79323i			0.730961i	−0.930819	+	0.365480i	$0.880905\pi$
$44$		0			0
$45$	−0.397129	−	1.10102i	−0.0592005	−	0.164130i
$46$		0			0
$47$	2.51067	+	4.34861i	0.366219	+	0.634310i	0.988971	−	0.148109i	$-0.0473187\pi$
$47$	2.51067	+	4.34861i	0.366219	+	0.634310i	−0.622752	+	0.782419i	$0.713985\pi$
$48$		0			0
$49$	−3.10652	−	6.27292i	−0.443788	−	0.896132i
$50$		0			0
$51$	−5.73852	+	1.00329i	−0.803553	+	0.140488i
$52$		0			0
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	−0.829699	−	0.558212i	$-0.811488\pi$
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	0.898275	+	0.439434i	$0.144821\pi$
$54$		0			0
$55$		−	0.584118i		−	0.0787624i
$56$		0			0
$57$	3.04755	−	8.33548i	0.403657	−	1.10406i
$58$		0			0
$59$	1.36034	+	0.785391i	0.177101	+	0.102249i	0.585930	−	0.810362i	$-0.300729\pi$
$59$	1.36034	+	0.785391i	0.177101	+	0.102249i	−0.408829	+	0.912611i	$0.634063\pi$
$60$		0			0
$61$	−3.40889	−	5.90437i	−0.436464	−	0.755977i	0.560950	−	0.827850i	$-0.310436\pi$
$61$	−3.40889	−	5.90437i	−0.436464	−	0.755977i	−0.997414	+	0.0718723i	$0.977103\pi$
$62$		0			0
$63$	−5.89917	−	5.31035i	−0.743226	−	0.669041i
$64$		0			0
$65$	1.11084	−	0.641343i	0.137783	−	0.0795488i
$66$		0			0
$67$	3.05467	+	1.76361i	0.373187	+	0.215460i	0.674850	−	0.737955i	$-0.264208\pi$
$67$	3.05467	+	1.76361i	0.373187	+	0.215460i	−0.301663	+	0.953415i	$0.597542\pi$
$68$		0			0
$69$	8.88036	+	3.24676i	1.06907	+	0.390864i
$70$		0			0
$71$			14.3360i			1.70137i	0.525677	+	0.850684i	$0.323812\pi$
$71$			14.3360i			1.70137i	−0.525677	+	0.850684i	$0.676188\pi$
$72$		0			0
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	0.652800	−	0.757531i	$-0.273594\pi$
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	−0.329641	+	0.944106i	$0.606928\pi$
$74$		0			0
$75$	−8.27115	+	1.44608i	−0.955070	+	0.166978i
$76$		0			0
$77$	−1.87018	−	3.49184i	−0.213127	−	0.397932i
$78$		0			0
$79$	0.239413	+	0.414676i	0.0269361	+	0.0466547i	0.879179	−	0.476491i	$-0.158092\pi$
$79$	0.239413	+	0.414676i	0.0269361	+	0.0466547i	−0.852243	+	0.523146i	$0.824758\pi$
$80$		0			0
$81$	−8.43926	−	3.12713i	−0.937695	−	0.347459i
$82$		0			0
$83$		−	17.4548i		−	1.91591i	−0.286911	−	0.957957i	$-0.592628\pi$
$83$		−	17.4548i		−	1.91591i	0.286911	−	0.957957i	$-0.407372\pi$
$84$		0			0
$85$		−	1.31222i		−	0.142331i
$86$		0			0
$87$	4.59906	+	5.49710i	0.493071	+	0.589351i
$88$		0			0
$89$	2.54840	+	4.41396i	0.270130	+	0.467879i	0.968895	−	0.247473i	$-0.0796000\pi$
$89$	2.54840	+	4.41396i	0.270130	+	0.467879i	−0.698765	+	0.715351i	$0.746267\pi$
$90$		0			0
$91$	4.58716	−	7.39053i	0.480865	−	0.774738i
$92$		0			0
$93$	1.24081	+	7.09709i	0.128666	+	0.735934i
$94$		0			0
$95$	1.73131	+	0.999573i	0.177629	+	0.102554i
$96$		0			0
$97$		−	9.00074i		−	0.913887i	−0.889496	−	0.456943i	$-0.848944\pi$
$97$		−	9.00074i		−	0.913887i	0.889496	−	0.456943i	$-0.151056\pi$
$98$		0			0
$99$	−3.43230	−	2.89703i	−0.344959	−	0.291163i
$100$		0			0
$101$	4.63907	+	2.67837i	0.461605	+	0.266508i	0.712719	−	0.701450i	$-0.247464\pi$
$101$	4.63907	+	2.67837i	0.461605	+	0.266508i	−0.251114	+	0.967958i	$0.580797\pi$
$102$		0			0
$103$	−7.70831	+	4.45039i	−0.759522	+	0.438510i	−0.829124	−	0.559065i	$-0.811160\pi$
$103$	−7.70831	+	4.45039i	−0.759522	+	0.438510i	0.0696021	+	0.997575i	$0.477827\pi$
$104$		0			0
$105$	1.40715	−	1.10294i	0.137323	−	0.107636i
$106$		0			0
$107$	7.85256	+	13.6010i	0.759135	+	1.31486i	0.943292	+	0.331964i	$0.107711\pi$
$107$	7.85256	+	13.6010i	0.759135	+	1.31486i	−0.184157	+	0.982897i	$0.558955\pi$
$108$		0			0
$109$	15.1582	+	8.75159i	1.45189	+	0.838250i	0.998589	−	0.0531069i	$-0.0169124\pi$
$109$	15.1582	+	8.75159i	1.45189	+	0.838250i	0.453303	+	0.891357i	$0.350246\pi$
$110$		0			0
$111$	−14.0237	−	5.12723i	−1.33107	−	0.486655i
$112$		0			0
$113$		−	0.0726142i		−	0.00683097i	−0.999994	−	0.00341549i	$-0.998913\pi$
$113$		−	0.0726142i		−	0.00683097i	0.999994	−	0.00341549i	$-0.00108718\pi$
$114$		0			0
$115$	−1.06491	+	1.84448i	−0.0993037	+	0.171999i
$116$		0			0
$117$	1.74083	−	9.70819i	0.160940	−	0.897523i
$118$		0			0
$119$	−4.20138	−	7.84443i	−0.385139	−	0.719098i
$120$		0			0
$121$	4.37925	+	7.58508i	0.398114	+	0.689553i
$122$		0			0
$123$	12.4042	+	14.8263i	1.11845	+	1.33684i
$124$		0			0
$125$		−	3.84211i		−	0.343649i
$126$		0			0
$127$	8.81577			0.782273			0.391137	−	0.920333i	$-0.372082\pi$
$127$	8.81577			0.782273			0.391137	+	0.920333i	$0.372082\pi$
$128$		0			0
$129$	−6.36751	+	5.32728i	−0.560628	+	0.469041i
$130$		0			0
$131$	4.36183	−	2.51830i	0.381095	−	0.220025i	−0.297200	−	0.954815i	$-0.596053\pi$
$131$	4.36183	−	2.51830i	0.381095	−	0.220025i	0.678294	+	0.734790i	$0.262719\pi$
$132$		0			0
$133$	13.5501	+	0.432239i	1.17494	+	0.0374799i
$134$		0			0
$135$	1.02126	−	1.75125i	0.0878959	−	0.150724i
$136$		0			0
$137$	−6.34787	−	3.66494i	−0.542335	−	0.313117i	0.203690	−	0.979035i	$-0.434707\pi$
$137$	−6.34787	−	3.66494i	−0.542335	−	0.313117i	−0.746025	+	0.665918i	$0.768040\pi$
$138$		0			0
$139$	15.7497			1.33587			0.667935	−	0.744220i	$-0.267178\pi$
$139$	15.7497			1.33587			0.667935	+	0.744220i	$0.267178\pi$
$140$		0			0
$141$	−2.98646	+	8.16840i	−0.251505	+	0.687903i
$142$		0			0
$143$	2.46110	−	4.26275i	0.205807	−	0.356469i
$144$		0			0
$145$	−1.39815	+	0.807222i	−0.116110	+	0.0670361i
$146$		0			0
$147$	4.88056	−	11.0987i	0.402542	−	0.915402i
$148$		0			0
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	−0.954078	−	0.299559i	$-0.903161\pi$
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	0.217613	−	0.976035i	$-0.430173\pi$
$150$		0			0
$151$	7.89149	−	13.6685i	0.642201	−	1.11232i	−0.342740	−	0.939430i	$-0.611355\pi$
$151$	7.89149	−	13.6685i	0.642201	−	1.11232i	0.984940	−	0.172894i	$-0.0553117\pi$
$152$		0			0
$153$	−7.71069	−	6.50820i	−0.623373	−	0.526157i
$154$		0			0
$155$	−1.62289			−0.130354
$156$		0			0
$157$	2.53274	−	4.38683i	0.202134	−	0.350107i	−0.747082	−	0.664732i	$-0.768546\pi$
$157$	2.53274	−	4.38683i	0.202134	−	0.350107i	0.949216	+	0.314625i	$0.101879\pi$
$158$		0			0
$159$	1.70359	−	0.297845i	0.135103	−	0.0236206i
$160$		0			0
$161$	−0.460494	+	14.4358i	−0.0362920	+	1.13770i
$162$		0			0
$163$	−10.8745	+	6.27840i	−0.851757	+	0.491762i	−0.861243	−	0.508193i	$-0.830314\pi$
$163$	−10.8745	+	6.27840i	−0.851757	+	0.491762i	0.00948597	+	0.999955i	$0.496980\pi$
$164$		0			0
$165$	0.775965	−	0.649199i	0.0604088	−	0.0505400i
$166$		0			0
$167$	7.43145			0.575063			0.287531	−	0.957771i	$-0.407165\pi$
$167$	7.43145			0.575063			0.287531	+	0.957771i	$0.407165\pi$
$168$		0			0
$169$	−2.19116			−0.168551
$170$		0			0
$171$	14.4603	−	5.21571i	1.10580	−	0.398856i
$172$		0			0
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.951069	−	0.308978i	$-0.900013\pi$
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.207952	+	0.978139i	$0.566680\pi$
$174$		0			0
$175$	−6.05561	−	11.3065i	−0.457761	−	0.854690i
$176$		0			0
$177$	0.468558	+	2.68002i	0.0352190	+	0.201443i
$178$		0			0
$179$	8.11784	−	14.0605i	0.606756	−	1.05093i	−0.385016	−	0.922910i	$-0.625804\pi$
$179$	8.11784	−	14.0605i	0.606756	−	1.05093i	0.991771	−	0.128022i	$-0.0408627\pi$
$180$		0			0
$181$	6.19340			0.460351			0.230176	−	0.973149i	$-0.426070\pi$
$181$	6.19340			0.460351			0.230176	+	0.973149i	$0.426070\pi$
$182$		0			0
$183$	4.05490	−	11.0907i	0.299747	−	0.819850i
$184$		0			0
$185$	1.68169	−	2.91278i	0.123641	−	0.214152i
$186$		0			0
$187$	−2.51777	−	4.36091i	−0.184118	−	0.318901i
$188$		0			0
$189$	0.498031	−	13.7387i	0.0362264	−	0.999344i
$190$		0			0
$191$	7.28788	−	4.20766i	0.527333	−	0.304456i	−0.212597	−	0.977140i	$-0.568192\pi$
$191$	7.28788	−	4.20766i	0.527333	−	0.304456i	0.739930	+	0.672684i	$0.234859\pi$
$192$		0			0
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	−0.526370	−	0.850256i	$-0.676447\pi$
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	0.999528	+	0.0307215i	$0.00978048\pi$
$194$		0			0
$195$	2.08659	+	0.762882i	0.149424	+	0.0546311i
$196$		0			0
$197$	17.6119			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$197$	17.6119			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$198$		0			0
$199$	−17.2688	−	9.97017i	−1.22416	−	0.706767i	−0.258354	−	0.966050i	$-0.583180\pi$
$199$	−17.2688	−	9.97017i	−1.22416	−	0.706767i	−0.965801	+	0.259284i	$0.916514\pi$
$200$		0			0
$201$	1.05216	+	6.01805i	0.0742135	+	0.424480i
$202$		0			0
$203$	−5.77359	+	9.30203i	−0.405227	+	0.652874i
$204$		0			0
$205$	−3.77097	+	2.17717i	−0.263376	+	0.152060i
$206$		0			0
$207$	5.55666	+	15.4055i	0.386214	+	1.07076i
$208$		0			0
$209$	7.67154			0.530652
$210$		0			0
$211$			14.5159i			0.999314i	0.866223	+	0.499657i	$0.166541\pi$
$211$			14.5159i			0.999314i	−0.866223	+	0.499657i	$0.833459\pi$
$212$		0			0
$213$	−19.0445	+	15.9333i	−1.30491	+	1.09173i
$214$		0			0
$215$	−0.935038	−	1.61953i	−0.0637691	−	0.110451i
$216$		0			0
$217$	−9.70158	+	5.19604i	−0.658586	+	0.352730i
$218$		0			0
$219$	0.951031	+	5.43963i	0.0642647	+	0.367576i
$220$		0			0
$221$	5.52887	−	9.57629i	0.371912	−	0.644171i
$222$		0			0
$223$			2.77897i			0.186093i	0.995662	+	0.0930467i	$0.0296606\pi$
$223$			2.77897i			0.186093i	−0.995662	+	0.0930467i	$0.970339\pi$
$224$		0			0
$225$	−11.1137	−	9.38052i	−0.740915	−	0.625368i
$226$		0			0
$227$	−14.0438	−	8.10819i	−0.932119	−	0.538159i	−0.0446379	−	0.999003i	$-0.514213\pi$
$227$	−14.0438	−	8.10819i	−0.932119	−	0.538159i	−0.887481	+	0.460844i	$0.847547\pi$
$228$		0			0
$229$	−10.3150	−	17.8661i	−0.681633	−	1.18062i	−0.974482	−	0.224464i	$-0.927937\pi$
$229$	−10.3150	−	17.8661i	−0.681633	−	1.18062i	0.292849	−	0.956159i	$-0.405397\pi$
$230$		0			0
$231$	2.56014	−	6.36531i	0.168445	−	0.418807i
$232$		0			0
$233$	−1.80462	+	1.04190i	−0.118225	+	0.0682572i	−0.557946	−	0.829877i	$-0.688411\pi$
$233$	−1.80462	+	1.04190i	−0.118225	+	0.0682572i	0.439721	+	0.898134i	$0.355077\pi$
$234$		0			0
$235$	−1.69661	−	0.979538i	−0.110675	−	0.0638980i
$236$		0			0
$237$	−0.284784	+	0.778925i	−0.0184987	+	0.0505966i
$238$		0			0
$239$		−	0.851762i		−	0.0550959i	−0.999620	−	0.0275480i	$-0.991230\pi$
$239$		−	0.851762i		−	0.0550959i	0.999620	−	0.0275480i	$-0.00876990\pi$
$240$		0			0
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	0.857294	−	0.514827i	$-0.172144\pi$
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	−0.0172066	+	0.999852i	$0.505477\pi$
$242$		0			0
$243$	−5.22533	−	14.6866i	−0.335205	−	0.942145i
$244$		0			0
$245$	2.27332	+	1.51349i	0.145237	+	0.0966932i
$246$		0			0
$247$	8.42312	+	14.5893i	0.535950	+	0.928293i
$248$		0			0
$249$	23.1877	−	19.3996i	1.46946	−	1.22940i
$250$		0			0
$251$			11.8022i			0.744948i	0.928043	+	0.372474i	$0.121490\pi$
$251$			11.8022i			0.744948i	−0.928043	+	0.372474i	$0.878510\pi$
$252$		0			0
$253$			8.17302i			0.513834i
$254$		0			0
$255$	1.74321	−	1.45843i	0.109164	−	0.0913304i
$256$		0			0
$257$	−8.86901	−	15.3616i	−0.553233	−	0.958228i	−0.998039	−	0.0626011i	$-0.980060\pi$
$257$	−8.86901	−	15.3616i	−0.553233	−	0.958228i	0.444805	−	0.895627i	$-0.353273\pi$
$258$		0			0
$259$	0.727204	−	22.7968i	0.0451863	−	1.41653i
$260$		0			0
$261$	−2.19109	+	12.2191i	−0.135625	+	0.756346i
$262$		0			0
$263$	−6.27815	−	3.62469i	−0.387128	−	0.223508i	0.293787	−	0.955871i	$-0.405084\pi$
$263$	−6.27815	−	3.62469i	−0.387128	−	0.223508i	−0.680915	+	0.732363i	$0.738418\pi$
$264$		0			0
$265$			0.389559i			0.0239304i
$266$		0			0
$267$	−3.03134	+	8.29114i	−0.185515	+	0.507410i
$268$		0			0
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	0.587463	−	0.809251i	$-0.300127\pi$
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	−0.407100	+	0.913383i	$0.633460\pi$
$270$		0			0
$271$	−3.96989	+	2.29201i	−0.241153	+	0.139230i	−0.615707	−	0.787975i	$-0.711129\pi$
$271$	−3.96989	+	2.29201i	−0.241153	+	0.139230i	0.374553	+	0.927205i	$0.377796\pi$
$272$		0			0
$273$	14.9161	−	2.12020i	0.902764	−	0.128320i
$274$		0			0
$275$	−3.62896	−	6.28555i	−0.218835	−	0.379033i
$276$		0			0
$277$	10.6940	+	6.17421i	0.642543	+	0.370972i	0.785593	−	0.618743i	$-0.212358\pi$
$277$	10.6940	+	6.17421i	0.642543	+	0.370972i	−0.143050	+	0.989715i	$0.545691\pi$
$278$		0			0
$279$	−8.04900	+	9.53617i	−0.481881	+	0.570916i
$280$		0			0
$281$			7.91565i			0.472208i	0.971728	+	0.236104i	$0.0758706\pi$
$281$			7.91565i			0.472208i	−0.971728	+	0.236104i	$0.924129\pi$
$282$		0			0
$283$	−11.3552	+	19.6678i	−0.674999	+	1.16913i	0.301471	+	0.953475i	$0.402522\pi$
$283$	−11.3552	+	19.6678i	−0.674999	+	1.16913i	−0.976469	+	0.215656i	$0.930811\pi$
$284$		0			0
$285$	0.596338	+	3.41089i	0.0353240	+	0.202043i
$286$		0			0
$287$	−15.5720	+	25.0887i	−0.919189	+	1.48094i
$288$		0			0
$289$	2.84381	+	4.92562i	0.167283	+	0.289742i
$290$		0			0
$291$	11.9569	−	10.0036i	0.700928	−	0.586420i
$292$		0			0
$293$			12.8246i			0.749220i	0.927183	+	0.374610i	$0.122223\pi$
$293$			12.8246i			0.749220i	−0.927183	+	0.374610i	$0.877777\pi$
$294$		0			0
$295$	−0.612840			−0.0356809
$296$		0			0
$297$	0.0338081	−	7.77942i	0.00196175	−	0.451408i
$298$		0			0
$299$	−15.5430	+	8.97373i	−0.898872	+	0.518964i
$300$		0			0
$301$	−10.7749	−	6.68778i	−0.621056	−	0.385477i
$302$		0			0
$303$	1.59789	+	9.13951i	0.0917966	+	0.525051i
$304$		0			0
$305$	2.30359	+	1.32998i	0.131903	+	0.0761542i
$306$		0			0
$307$	−12.3622			−0.705549			−0.352774	−	0.935708i	$-0.614762\pi$
$307$	−12.3622			−0.705549			−0.352774	+	0.935708i	$0.614762\pi$
$308$		0			0
$309$	−14.4792	−	5.29377i	−0.823694	−	0.301152i
$310$		0			0
$311$	−0.720819	+	1.24850i	−0.0408739	+	0.0707957i	−0.885739	−	0.464184i	$-0.846348\pi$
$311$	−0.720819	+	1.24850i	−0.0408739	+	0.0707957i	0.844865	+	0.534980i	$0.179681\pi$
$312$		0			0
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.956092	−	0.293067i	$-0.905324\pi$
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.224242	+	0.974533i	$0.571991\pi$
$314$		0			0
$315$	3.02912	+	0.643477i	0.170672	+	0.0362558i
$316$		0			0
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	0.944639	+	0.328111i	$0.106412\pi$
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	−0.188167	+	0.982137i	$0.560255\pi$
$318$		0			0
$319$	−3.09764	+	5.36527i	−0.173435	+	0.300398i
$320$		0			0
$321$	−9.34067	+	25.5481i	−0.521345	+	1.42595i
$322$		0			0
$323$	17.2342			0.958935
$324$		0			0
$325$	7.96898	−	13.8027i	0.442039	−	0.765635i
$326$		0			0
$327$	5.22113	+	29.8634i	0.288729	+	1.65145i
$328$		0			0
$329$	−13.2785	−	0.423575i	−0.732066	−	0.0233524i
$330$		0			0
$331$	−15.2782	+	8.82087i	−0.839766	+	0.484839i	−0.857185	−	0.515009i	$-0.827788\pi$
$331$	−15.2782	+	8.82087i	−0.839766	+	0.484839i	0.0174189	+	0.999848i	$0.494455\pi$
$332$		0			0
$333$	−8.77498	−	24.3281i	−0.480866	−	1.33317i
$334$		0			0
$335$	−1.37615			−0.0751868
$336$		0			0
$337$	11.0396			0.601365			0.300682	−	0.953724i	$-0.402786\pi$
$337$	11.0396			0.601365			0.300682	+	0.953724i	$0.402786\pi$
$338$		0			0
$339$	0.0964636	−	0.0807047i	0.00523918	−	0.00438328i
$340$		0			0
$341$	−5.39334	+	3.11385i	−0.292066	+	0.168624i
$342$		0			0
$343$	18.4356	+	1.76905i	0.995428	+	0.0955198i
$344$		0			0
$345$	−3.63385	+	0.635319i	−0.195640	+	0.0342045i
$346$		0			0
$347$	−10.8299	+	18.7579i	−0.581377	+	1.00697i	0.413940	+	0.910304i	$0.364152\pi$
$347$	−10.8299	+	18.7579i	−0.581377	+	1.00697i	−0.995316	+	0.0966701i	$0.969181\pi$
$348$		0			0
$349$	−6.46130			−0.345865			−0.172933	−	0.984934i	$-0.555324\pi$
$349$	−6.46130			−0.345865			−0.172933	+	0.984934i	$0.555324\pi$
$350$		0			0
$351$	14.8315	−	8.47727i	0.791649	−	0.452483i
$352$		0			0
$353$	14.9846	−	25.9541i	0.797549	−	1.38140i	−0.123659	−	0.992325i	$-0.539463\pi$
$353$	14.9846	−	25.9541i	0.797549	−	1.38140i	0.921208	−	0.389071i	$-0.127204\pi$
$354$		0			0
$355$	−2.79659	−	4.84383i	−0.148428	−	0.257084i
$356$		0			0
$357$	5.75137	−	14.2997i	0.304395	−	0.756821i
$358$		0			0
$359$	−9.44412	+	5.45257i	−0.498442	+	0.287775i	−0.728070	−	0.685503i	$-0.759582\pi$
$359$	−9.44412	+	5.45257i	−0.498442	+	0.287775i	0.229628	+	0.973278i	$0.426249\pi$
$360$		0			0
$361$	−3.62795	+	6.28380i	−0.190945	+	0.330726i
$362$		0			0
$363$	−5.20915	+	14.2478i	−0.273409	+	0.747814i
$364$		0			0
$365$	−1.24388			−0.0651075
$366$		0			0
$367$	2.43552	+	1.40615i	0.127133	+	0.0734002i	0.562218	−	0.826989i	$-0.309948\pi$
$367$	2.43552	+	1.40615i	0.127133	+	0.0734002i	−0.435085	+	0.900389i	$0.643282\pi$
$368$		0			0
$369$	−5.90961	+	32.9565i	−0.307642	+	1.71564i
$370$		0			0
$371$	1.24726	+	2.32877i	0.0647545	+	0.120904i
$372$		0			0
$373$	−26.9266	+	15.5461i	−1.39421	+	0.804947i	−0.993778	−	0.111380i	$-0.964473\pi$
$373$	−26.9266	+	15.5461i	−1.39421	+	0.804947i	−0.400431	+	0.916327i	$0.631140\pi$
$374$		0			0
$375$	5.10401	−	4.27019i	0.263570	−	0.220511i
$376$		0			0
$377$	−13.6045			−0.700665
$378$		0			0
$379$		−	17.6950i		−	0.908931i	−0.890764	−	0.454465i	$-0.849830\pi$
$379$		−	17.6950i		−	0.908931i	0.890764	−	0.454465i	$-0.150170\pi$
$380$		0			0
$381$	9.79800	+	11.7112i	0.501967	+	0.599984i
$382$		0			0
$383$	−17.4953	−	30.3028i	−0.893968	−	1.54840i	−0.835076	−	0.550134i	$-0.814577\pi$
$383$	−17.4953	−	30.3028i	−0.893968	−	1.54840i	−0.0588917	−	0.998264i	$-0.518757\pi$
$384$		0			0
$385$	1.31306	+	0.814994i	0.0669200	+	0.0415359i
$386$		0			0
$387$	−14.1539	−	2.53802i	−0.719485	−	0.129015i
$388$		0			0
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	0.469971	+	0.882682i	$0.344264\pi$
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	−0.999410	+	0.0343338i	$0.989069\pi$
$390$		0			0
$391$			18.3608i			0.928543i
$392$		0			0
$393$	8.19322	+	2.99554i	0.413293	+	0.151105i
$394$		0			0
$395$	−0.161786	−	0.0934070i	−0.00814032	−	0.00469982i
$396$		0			0
$397$	−2.44443	−	4.23387i	−0.122682	−	0.212492i	0.798142	−	0.602469i	$-0.205816\pi$
$397$	−2.44443	−	4.23387i	−0.122682	−	0.212492i	−0.920825	+	0.389977i	$0.872483\pi$
$398$		0			0
$399$	14.4856	+	18.4808i	0.725186	+	0.925200i
$400$		0			0
$401$	6.62355	−	3.82411i	0.330764	−	0.190967i	−0.325416	−	0.945571i	$-0.605504\pi$
$401$	6.62355	−	3.82411i	0.330764	−	0.190967i	0.656180	+	0.754604i	$0.272171\pi$
$402$		0			0
$403$	−11.8434	−	6.83782i	−0.589964	−	0.340616i
$404$		0			0
$405$	3.46148	−	0.589691i	0.172002	−	0.0293020i
$406$		0			0
$407$		−	12.9067i		−	0.639762i
$408$		0			0
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	0.326061	−	0.945349i	$-0.394279\pi$
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	−0.655666	+	0.755051i	$0.727612\pi$
$410$		0			0
$411$	−2.18648	−	12.5060i	−0.107851	−	0.616877i
$412$		0			0
$413$	−3.66354	+	1.96214i	−0.180271	+	0.0965507i
$414$		0			0
$415$	3.40499	+	5.89762i	0.167145	+	0.289503i
$416$		0			0
$417$	17.5045	+	20.9225i	0.857197	+	1.02458i
$418$		0			0
$419$		−	4.38235i		−	0.214092i	−0.994254	−	0.107046i	$-0.965861\pi$
$419$		−	4.38235i		−	0.214092i	0.994254	−	0.107046i	$-0.0341392\pi$
$420$		0			0
$421$			11.9400i			0.581921i	0.956735	+	0.290961i	$0.0939749\pi$
$421$			11.9400i			0.581921i	−0.956735	+	0.290961i	$0.906025\pi$
$422$		0			0
$423$	−14.1704	+	5.11117i	−0.688990	+	0.248514i
$424$		0			0
$425$	−8.15249	−	14.1205i	−0.395454	−	0.684946i
$426$		0			0
$427$	18.0290	+	0.575113i	0.872484	+	0.0278317i
$428$		0			0
$429$	8.39811	−	1.46827i	0.405464	−	0.0708888i
$430$		0			0
$431$	0.588922	+	0.340014i	0.0283674	+	0.0163779i	0.514117	−	0.857720i	$-0.328120\pi$
$431$	0.588922	+	0.340014i	0.0283674	+	0.0163779i	−0.485749	+	0.874098i	$0.661453\pi$
$432$		0			0
$433$		−	0.238499i		−	0.0114615i	−0.999984	−	0.00573077i	$-0.998176\pi$
$433$		−	0.238499i		−	0.0114615i	0.999984	−	0.00573077i	$-0.00182417\pi$
$434$		0			0
$435$	−2.62627	−	0.960196i	−0.125920	−	0.0460379i
$436$		0			0
$437$	−24.2247	−	13.9861i	−1.15882	−	0.669046i
$438$		0			0
$439$	−3.29894	+	1.90465i	−0.157450	+	0.0909038i	−0.576655	−	0.816988i	$-0.695642\pi$
$439$	−3.29894	+	1.90465i	−0.157450	+	0.0909038i	0.419205	+	0.907892i	$0.362309\pi$
$440$		0			0
$441$	20.1682	−	5.85172i	0.960392	−	0.278653i
$442$		0			0
$443$	3.02001	+	5.23080i	0.143485	+	0.248523i	0.928807	−	0.370565i	$-0.120836\pi$
$443$	3.02001	+	5.23080i	0.143485	+	0.248523i	−0.785322	+	0.619088i	$0.787503\pi$
$444$		0			0
$445$	−1.72210	−	0.994257i	−0.0816355	−	0.0471323i
$446$		0			0
$447$	10.6933	−	29.2477i	0.505776	−	1.38337i
$448$		0			0
$449$			28.1482i			1.32839i	0.747558	+	0.664197i	$0.231226\pi$
$449$			28.1482i			1.32839i	−0.747558	+	0.664197i	$0.768774\pi$
$450$		0			0
$451$	−8.35470	+	14.4708i	−0.393408	+	0.681402i
$452$		0			0
$453$	26.9285	−	4.70801i	1.26521	−	0.221201i
$454$		0			0
$455$	−0.108201	+	3.39194i	−0.00507254	+	0.159017i
$456$		0			0
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	0.682612	−	0.730781i	$-0.260844\pi$
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	−0.974181	+	0.225768i	$0.927511\pi$
$458$		0			0
$459$	0.0759502	−	17.4765i	0.00354505	−	0.815734i
$460$		0			0
$461$		−	31.6209i		−	1.47273i	−0.676583	−	0.736367i	$-0.736540\pi$
$461$		−	31.6209i		−	1.47273i	0.676583	−	0.736367i	$-0.263460\pi$
$462$		0			0
$463$	−23.5095			−1.09258			−0.546290	−	0.837596i	$-0.683960\pi$
$463$	−23.5095			−1.09258			−0.546290	+	0.837596i	$0.683960\pi$
$464$		0			0
$465$	−1.80371	−	2.15591i	−0.0836449	−	0.0999779i
$466$		0			0
$467$	−12.7642	+	7.36942i	−0.590657	+	0.341016i	−0.765357	−	0.643606i	$-0.777438\pi$
$467$	−12.7642	+	7.36942i	−0.590657	+	0.341016i	0.174700	+	0.984622i	$0.444104\pi$
$468$		0			0
$469$	−8.22655	+	4.40603i	−0.379867	+	0.203452i
$470$		0			0
$471$	8.64256	−	1.51101i	0.398228	−	0.0696237i
$472$		0			0
$473$	−6.21481	−	3.58812i	−0.285757	−	0.164982i
$474$		0			0
$475$	24.8403			1.13975
$476$		0			0
$477$	2.28907	+	1.93208i	0.104809	+	0.0884641i
$478$		0			0
$479$	17.3034	−	29.9703i	0.790611	−	1.36938i	−0.134979	−	0.990848i	$-0.543097\pi$
$479$	17.3034	−	29.9703i	0.790611	−	1.36938i	0.925589	−	0.378529i	$-0.123570\pi$
$480$		0			0
$481$	24.5452	−	14.1712i	1.11916	−	0.646150i
$482$		0			0
$483$	−19.6889	+	15.4325i	−0.895877	+	0.702203i
$484$		0			0
$485$	1.75582	+	3.04117i	0.0797276	+	0.138092i
$486$		0			0
$487$	12.0284	−	20.8338i	0.545058	−	0.944068i	−0.453545	−	0.891233i	$-0.649841\pi$
$487$	12.0284	−	20.8338i	0.545058	−	0.944068i	0.998603	−	0.0528351i	$-0.0168258\pi$
$488$		0			0
$489$	−20.4266	−	7.46820i	−0.923723	−	0.337724i
$490$		0			0
$491$	15.3708			0.693675			0.346837	−	0.937925i	$-0.387256\pi$
$491$	15.3708			0.693675			0.346837	+	0.937925i	$0.387256\pi$
$492$		0			0
$493$	−6.95887	+	12.0531i	−0.313412	+	0.542845i
$494$		0			0
$495$	1.72484	+	0.309291i	0.0775259	+	0.0139016i
$496$		0			0
$497$	−32.2265	−	20.0024i	−1.44556	−	0.897229i
$498$		0			0
$499$	22.8684	−	13.2031i	1.02373	−	0.591051i	0.108548	−	0.994091i	$-0.465380\pi$
$499$	22.8684	−	13.2031i	1.02373	−	0.591051i	0.915182	+	0.403040i	$0.132047\pi$
$500$		0			0
$501$	8.25944	+	9.87223i	0.369005	+	0.441059i
$502$		0			0
$503$	28.3616			1.26458			0.632291	−	0.774731i	$-0.282115\pi$
$503$	28.3616			1.26458			0.632291	+	0.774731i	$0.282115\pi$
$504$		0			0
$505$	−2.08993			−0.0930006
$506$		0			0
$507$	−2.43530	−	2.91083i	−0.108155	−	0.129274i
$508$		0			0
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	−0.848472	−	0.529240i	$-0.822477\pi$
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	0.0340991	+	0.999418i	$0.489144\pi$
$510$		0			0
$511$	−7.43586	+	3.98255i	−0.328943	+	0.176178i
$512$		0			0
$513$	23.0002	+	13.4128i	1.01548	+	0.592188i
$514$		0			0
$515$	1.73632	−	3.00739i	0.0765113	−	0.132522i
$516$		0			0
$517$	−7.51778			−0.330631
$518$		0			0
$519$	−28.6352	−	10.4694i	−1.25695	−	0.459554i
$520$		0			0
$521$	−5.91179	+	10.2395i	−0.259000	+	0.448601i	−0.965974	−	0.258638i	$-0.916726\pi$
$521$	−5.91179	+	10.2395i	−0.259000	+	0.448601i	0.706974	+	0.707239i	$0.250060\pi$
$522$		0			0
$523$	3.37960	+	5.85364i	0.147780	+	0.255962i	0.930407	−	0.366529i	$-0.119454\pi$
$523$	3.37960	+	5.85364i	0.147780	+	0.255962i	−0.782627	+	0.622491i	$0.786121\pi$
$524$		0			0
$525$	8.28967	−	20.6107i	0.361791	−	0.899526i
$526$		0			0
$527$	−12.1162	+	6.99528i	−0.527789	+	0.304719i
$528$		0			0
$529$	3.40036	−	5.88960i	0.147842	−	0.256070i
$530$		0			0
$531$	−3.03948	+	3.60108i	−0.131902	+	0.156273i
$532$		0			0
$533$	−36.6928			−1.58934
$534$		0			0
$535$	−5.30643	−	3.06367i	−0.229417	−	0.132454i
$536$		0			0
$537$	27.7008	−	4.84304i	1.19538	−	0.208993i
$538$		0			0
$539$	10.4588	+	0.667940i	0.450494	+	0.0287702i
$540$		0			0
$541$	15.3128	−	8.84087i	0.658351	−	0.380099i	−0.133298	−	0.991076i	$-0.542557\pi$
$541$	15.3128	−	8.84087i	0.658351	−	0.380099i	0.791648	+	0.610977i	$0.209223\pi$
$542$		0			0
$543$	6.88345	+	8.22755i	0.295397	+	0.353078i
$544$		0			0
$545$	−6.82885			−0.292516
$546$		0			0
$547$		−	1.49834i		−	0.0640644i	−0.999487	−	0.0320322i	$-0.989802\pi$
$547$		−	1.49834i		−	0.0640644i	0.999487	−	0.0320322i	$-0.0101979\pi$
$548$		0			0
$549$	19.2400	−	6.93974i	0.821145	−	0.296181i
$550$		0			0
$551$	−10.6017	−	18.3627i	−0.451647	−	0.782276i
$552$		0			0
$553$	−1.26621	−	0.0403914i	−0.0538448	−	0.00171762i
$554$		0			0
$555$	5.73852	−	1.00329i	0.243586	−	0.0425871i
$556$		0			0
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	−0.833246	−	0.552902i	$-0.813520\pi$
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	0.895450	+	0.445161i	$0.146854\pi$
$558$		0			0
$559$		−	15.7586i		−	0.666518i
$560$		0			0
$561$	2.99491	−	8.19150i	0.126445	−	0.345845i
$562$		0			0
$563$	14.3950	+	8.31096i	0.606677	+	0.350265i	0.771664	−	0.636031i	$-0.219425\pi$
$563$	14.3950	+	8.31096i	0.606677	+	0.350265i	−0.164987	+	0.986296i	$0.552758\pi$
$564$		0			0
$565$	0.0141652	+	0.0245348i	0.000595934	+	0.00103219i
$566$		0			0
$567$	18.8046	−	14.6078i	0.789717	−	0.613471i
$568$		0			0
$569$	19.2204	−	11.0969i	0.805763	−	0.465207i	−0.0397194	−	0.999211i	$-0.512646\pi$
$569$	19.2204	−	11.0969i	0.805763	−	0.465207i	0.845482	+	0.534003i	$0.179313\pi$
$570$		0			0
$571$	5.22532	+	3.01684i	0.218673	+	0.126251i	0.605336	−	0.795970i	$-0.293039\pi$
$571$	5.22532	+	3.01684i	0.218673	+	0.126251i	−0.386663	+	0.922221i	$0.626372\pi$
$572$		0			0
$573$	13.6895	+	5.00504i	0.571887	+	0.209089i
$574$		0			0
$575$			26.4641i			1.10363i
$576$		0			0
$577$	−17.4549	−	10.0776i	−0.726659	−	0.419537i	0.0905396	−	0.995893i	$-0.471141\pi$
$577$	−17.4549	−	10.0776i	−0.726659	−	0.419537i	−0.817199	+	0.576356i	$0.804474\pi$
$578$		0			0
$579$	22.4304	−	3.92160i	0.932177	−	0.162976i
$580$		0			0
$581$	39.2375	+	24.3539i	1.62784	+	1.01037i
$582$		0			0
$583$	0.747449	+	1.29462i	0.0309562	+	0.0536177i
$584$		0			0
$585$	1.30563	+	3.61979i	0.0539812	+	0.149660i
$586$		0			0
$587$		−	0.369829i		−	0.0152645i	−0.999971	−	0.00763224i	$-0.997571\pi$
$587$		−	0.369829i		−	0.0152645i	0.999971	−	0.00763224i	$-0.00242944\pi$
$588$		0			0
$589$		−	21.3143i		−	0.878241i
$590$		0			0
$591$	19.5742	+	23.3963i	0.805174	+	0.962396i
$592$		0			0
$593$	4.89233	+	8.47376i	0.200904	+	0.347976i	0.948820	−	0.315818i	$-0.102279\pi$
$593$	4.89233	+	8.47376i	0.200904	+	0.347976i	−0.747916	+	0.663793i	$0.768945\pi$
$594$		0			0
$595$	2.94981	+	1.83089i	0.120930	+	0.0750592i
$596$		0			0
$597$	−5.94813	−	34.0216i	−0.243441	−	1.39241i
$598$		0			0
$599$	−31.2524	−	18.0436i	−1.27694	−	0.737240i	−0.300653	−	0.953734i	$-0.597205\pi$
$599$	−31.2524	−	18.0436i	−1.27694	−	0.737240i	−0.976284	+	0.216494i	$0.930538\pi$
$600$		0			0
$601$			9.75944i			0.398096i	0.979990	+	0.199048i	$0.0637849\pi$
$601$			9.75944i			0.398096i	−0.979990	+	0.199048i	$0.936215\pi$
$602$		0			0
$603$	−6.82523	+	8.08629i	−0.277945	+	0.329299i
$604$		0			0
$605$	−2.95932	−	1.70856i	−0.120313	−	0.0694629i
$606$		0			0
$607$	7.33740	−	4.23625i	0.297816	−	0.171944i	−0.343645	−	0.939099i	$-0.611662\pi$
$607$	7.33740	−	4.23625i	0.297816	−	0.171944i	0.641461	+	0.767155i	$0.278328\pi$
$608$		0			0
$609$	−18.7741	+	2.66857i	−0.760763	+	0.108136i
$610$		0			0
$611$	−8.25429	−	14.2968i	−0.333933	−	0.578388i
$612$		0			0
$613$	10.1968	+	5.88712i	0.411844	+	0.237779i	0.691582	−	0.722298i	$-0.256914\pi$
$613$	10.1968	+	5.88712i	0.411844	+	0.237779i	−0.279737	+	0.960077i	$0.590247\pi$
$614$		0			0
$615$	−7.08336	−	2.58976i	−0.285629	−	0.104429i
$616$		0			0
$617$			17.5244i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$617$			17.5244i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$618$		0			0
$619$	12.8081	−	22.1843i	0.514801	−	0.891661i	−0.485052	−	0.874485i	$-0.661199\pi$
$619$	12.8081	−	22.1843i	0.514801	−	0.891661i	0.999852	−	0.0171755i	$-0.00546739\pi$
$620$		0			0
$621$	−14.2895	+	24.5037i	−0.573419	+	0.983298i
$622$		0			0
$623$	−13.4780	−	0.429940i	−0.539985	−	0.0172252i
$624$		0			0
$625$	−11.3700	−	19.6933i	−0.454798	−	0.787734i
$626$		0			0
$627$	8.52629	+	10.1912i	0.340507	+	0.406997i
$628$		0			0
$629$		−	28.9950i		−	1.15611i
$630$		0			0
$631$	7.24555			0.288441			0.144220	−	0.989546i	$-0.453933\pi$
$631$	7.24555			0.288441			0.144220	+	0.989546i	$0.453933\pi$
$632$		0			0
$633$	−19.2835	+	16.1332i	−0.766449	+	0.641237i
$634$		0			0
$635$	−2.97867	+	1.71973i	−0.118205	+	0.0682456i
$636$		0			0
$637$	10.2132	+	20.6234i	0.404663	+	0.817127i
$638$		0			0
$639$	−42.3328	−	7.59093i	−1.67466	−	0.300293i
$640$		0			0
$641$	−11.9401	−	6.89362i	−0.471606	−	0.272282i	0.245306	−	0.969446i	$-0.421112\pi$
$641$	−11.9401	−	6.89362i	−0.471606	−	0.272282i	−0.716912	+	0.697164i	$0.754445\pi$
$642$		0			0
$643$	20.7470			0.818184			0.409092	−	0.912493i	$-0.365846\pi$
$643$	20.7470			0.818184			0.409092	+	0.912493i	$0.365846\pi$
$644$		0			0
$645$	1.11223	−	3.04212i	0.0437942	−	0.119783i
$646$		0			0
$647$	−16.1242	+	27.9279i	−0.633907	+	1.09796i	0.352838	+	0.935684i	$0.385217\pi$
$647$	−16.1242	+	27.9279i	−0.633907	+	1.09796i	−0.986746	+	0.162275i	$0.948117\pi$
$648$		0			0
$649$	−2.03665	+	1.17586i	−0.0799454	+	0.0461565i
$650$		0			0
$651$	−17.6851	−	7.11299i	−0.693135	−	0.278780i
$652$		0			0
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	0.992389	−	0.123141i	$-0.0392966\pi$
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	−0.602838	+	0.797864i	$0.705963\pi$
$654$		0			0
$655$	−0.982514	+	1.70176i	−0.0383900	+	0.0664934i
$656$		0			0
$657$	−6.16923	+	7.30909i	−0.240684	+	0.285155i
$658$		0			0
$659$	−11.4275			−0.445153			−0.222576	−	0.974915i	$-0.571447\pi$
$659$	−11.4275			−0.445153			−0.222576	+	0.974915i	$0.571447\pi$
$660$		0			0
$661$	2.31268	−	4.00568i	0.0899529	−	0.155803i	−0.817538	−	0.575875i	$-0.804662\pi$
$661$	2.31268	−	4.00568i	0.0899529	−	0.155803i	0.907491	+	0.420071i	$0.137995\pi$
$662$		0			0
$663$	18.8664	−	3.29848i	0.732710	−	0.128102i
$664$		0			0
$665$	−4.66261	+	2.49723i	−0.180808	+	0.0968385i
$666$		0			0
$667$	19.5630	−	11.2947i	0.757483	−	0.437333i
$668$		0			0
$669$	−3.69169	+	3.08859i	−0.142729	+	0.119412i
$670$		0			0
$671$	10.2073			0.394050
$672$		0			0
$673$	19.2606			0.742441			0.371220	−	0.928545i	$-0.378939\pi$
$673$	19.2606			0.742441			0.371220	+	0.928545i	$0.378939\pi$
$674$		0			0
$675$	0.109470	−	25.1896i	0.00421350	−	0.969548i
$676$		0			0
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.398630	−	0.917112i	$-0.369486\pi$
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.993557	+	0.113332i	$0.0361524\pi$
$678$		0			0
$679$	20.2332	+	12.5583i	0.776478	+	0.481945i
$680$		0			0
$681$	−4.83728	−	27.6679i	−0.185365	−	1.06024i
$682$		0			0
$683$	6.73357	−	11.6629i	0.257653	−	0.446268i	−0.707960	−	0.706253i	$-0.750384\pi$
$683$	6.73357	−	11.6629i	0.257653	−	0.446268i	0.965613	+	0.259985i	$0.0837176\pi$
$684$		0			0
$685$	2.85975			0.109265
$686$		0			0
$687$	12.2697	−	33.5595i	0.468120	−	1.28037i
$688$		0			0
$689$	−1.64135	+	2.84291i	−0.0625305	+	0.108306i
$690$		0			0
$691$	15.2232	+	26.3674i	0.579118	+	1.00306i	0.995581	+	0.0939090i	$0.0299363\pi$
$691$	15.2232	+	26.3674i	0.579118	+	1.00306i	−0.416463	+	0.909153i	$0.636730\pi$
$692$		0			0
$693$	11.3013	−	3.67353i	0.429301	−	0.139546i
$694$		0			0
$695$	−5.32149	+	3.07236i	−0.201856	+	0.116541i
$696$		0			0
$697$	−18.7689	+	32.5087i	−0.710923	+	1.23135i
$698$		0			0
$699$	−3.38979	−	1.23935i	−0.128214	−	0.0468764i
$700$		0			0
$701$	37.2839			1.40819			0.704096	−	0.710105i	$-0.251353\pi$
$701$	37.2839			1.40819			0.704096	+	0.710105i	$0.251353\pi$
$702$		0			0
$703$	38.2552	+	22.0866i	1.44282	+	0.833013i
$704$		0			0
$705$	−0.584385	−	3.34252i	−0.0220092	−	0.125886i
$706$		0			0
$707$	−12.4935	+	6.69137i	−0.469867	+	0.251655i
$708$		0			0
$709$	39.5076	−	22.8097i	1.48374	−	0.856637i	0.483910	−	0.875118i	$-0.339216\pi$
$709$	39.5076	−	22.8097i	1.48374	−	0.856637i	0.999829	+	0.0184810i	$0.00588302\pi$
$710$		0			0
$711$	−1.35127	+	0.487392i	−0.0506765	+	0.0182786i
$712$		0			0
$713$	22.7076			0.850406
$714$		0			0
$715$			1.92039i			0.0718186i
$716$		0			0
$717$	1.13151	−	0.946663i	0.0422572	−	0.0353538i
$718$		0			0
$719$	8.37315	+	14.5027i	0.312266	+	0.540860i	0.978853	−	0.204567i	$-0.0655787\pi$
$719$	8.37315	+	14.5027i	0.312266	+	0.540860i	−0.666587	+	0.745428i	$0.732245\pi$
$720$		0			0
$721$	0.750825	−	23.5373i	0.0279622	−	0.876575i
$722$		0			0
$723$	4.49211	+	25.6936i	0.167063	+	0.955555i
$724$		0			0
$725$	−10.0301	+	17.3726i	−0.372508	+	0.645204i
$726$		0			0
$727$		−	14.7144i		−	0.545726i	−0.962053	−	0.272863i	$-0.912029\pi$
$727$		−	14.7144i		−	0.545726i	0.962053	−	0.272863i	$-0.0879705\pi$
$728$		0			0
$729$	13.7027	−	23.2645i	0.507508	−	0.861647i
$730$		0			0
$731$	−13.9616	−	8.06075i	−0.516389	−	0.298137i
$732$		0			0
$733$	17.1186	+	29.6503i	0.632290	+	1.09516i	0.987082	+	0.160213i	$0.0512181\pi$
$733$	17.1186	+	29.6503i	0.632290	+	1.09516i	−0.354793	+	0.934945i	$0.615449\pi$
$734$		0			0
$735$	0.516028	+	4.70208i	0.0190340	+	0.173439i
$736$		0			0
$737$	−4.57334	+	2.64042i	−0.168461	+	0.0972610i
$738$		0			0
$739$	1.92964	+	1.11408i	0.0709829	+	0.0409820i	0.535071	−	0.844807i	$-0.320285\pi$
$739$	1.92964	+	1.11408i	0.0709829	+	0.0409820i	−0.464089	+	0.885789i	$0.653618\pi$
$740$		0			0
$741$	−10.0194	+	27.4044i	−0.368070	+	1.00673i
$742$		0			0
$743$			14.7964i			0.542829i	0.962463	+	0.271414i	$0.0874914\pi$
$743$			14.7964i			0.542829i	−0.962463	+	0.271414i	$0.912509\pi$
$744$		0			0
$745$	6.07486	+	3.50732i	0.222566	+	0.128498i
$746$		0			0
$747$	51.5423	+	9.24236i	1.88584	+	0.338160i
$748$		0			0
$749$	−41.5307	−	1.32480i	−1.51750	−	0.0484073i
$750$		0			0
$751$	−18.2439	−	31.5994i	−0.665729	−	1.15308i	−0.979087	−	0.203442i	$-0.934787\pi$
$751$	−18.2439	−	31.5994i	−0.665729	−	1.15308i	0.313358	−	0.949635i	$-0.398546\pi$
$752$		0			0
$753$	−15.6785	+	13.1172i	−0.571356	+	0.478016i
$754$		0			0
$755$			6.15772i			0.224103i
$756$		0			0
$757$			19.9557i			0.725302i	0.931925	+	0.362651i	$0.118128\pi$
$757$			19.9557i			0.725302i	−0.931925	+	0.362651i	$0.881872\pi$
$758$		0			0
$759$	−10.8574	+	9.08364i	−0.394097	+	0.329715i
$760$		0			0
$761$	−18.2013	−	31.5257i	−0.659798	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$761$	−18.2013	−	31.5257i	−0.659798	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$762$		0			0
$763$	−40.8227	+	21.8641i	−1.47788	+	0.791533i
$764$		0			0
$765$	3.87487	+	0.694825i	0.140096	+	0.0251215i
$766$		0			0
$767$	−4.47235	−	2.58211i	−0.161487	−	0.0932347i
$768$		0			0
$769$		−	33.7570i		−	1.21731i	−0.793436	−	0.608654i	$-0.791710\pi$
$769$		−	33.7570i		−	1.21731i	0.793436	−	0.608654i	$-0.208290\pi$
$770$		0			0
$771$	10.5497	−	28.8551i	0.379940	−	1.03919i
$772$		0			0
$773$	35.3297	+	20.3976i	1.27072	+	0.733651i	0.975124	−	0.221662i	$-0.0711481\pi$
$773$	35.3297	+	20.3976i	1.27072	+	0.733651i	0.295597	+	0.955313i	$0.404481\pi$
$774$		0			0
$775$	−17.4635	+	10.0826i	−0.627308	+	0.362176i
$776$		0			0
$777$	31.0924	−	24.3707i	1.11543	−	0.874295i
$778$		0			0
$779$	−28.5940	−	49.5263i	−1.02449	−	1.77446i
$780$		0			0
$781$	−18.5878	−	10.7317i	−0.665123	−	0.384009i
$782$		0			0
$783$	−18.6676	+	10.6698i	−0.667126	+	0.381309i
$784$		0			0
$785$			1.97629i			0.0705368i
$786$		0			0
$787$	5.80545	−	10.0553i	0.206942	−	0.358434i	−0.743808	−	0.668394i	$-0.766982\pi$
$787$	5.80545	−	10.0553i	0.206942	−	0.358434i	0.950750	+	0.309960i	$0.100316\pi$
$788$		0			0
$789$	−2.16246	−	12.3687i	−0.0769858	−	0.440337i
$790$		0			0
$791$	0.163233	+	0.101315i	0.00580389	+	0.00360236i
$792$		0			0
$793$	11.2073	+	19.4117i	0.397984	+	0.689329i
$794$		0			0
$795$	−0.517505	+	0.432963i	−0.0183540	+	0.0153556i
$796$		0			0
$797$			9.90792i			0.350956i	0.984483	+	0.175478i	$0.0561472\pi$
$797$			9.90792i			0.350956i	−0.984483	+	0.175478i	$0.943853\pi$
$798$		0			0
$799$	−16.8887			−0.597481
$800$		0			0
$801$	−14.3834	+	5.18797i	−0.508211	+	0.183308i
$802$		0			0
$803$	−4.13377	+	2.38664i	−0.145878	+	0.0842225i
$804$		0			0
$805$	−2.66047	−	4.96740i	−0.0937694	−	0.175078i
$806$		0			0
$807$	1.01892	+	5.82793i	0.0358677	+	0.205153i
$808$		0			0
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	0.730708	−	0.682690i	$-0.239190\pi$
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	−0.225873	+	0.974157i	$0.572523\pi$
$810$		0			0
$811$	−49.5706			−1.74066			−0.870330	−	0.492470i	$-0.836094\pi$
$811$	−49.5706			−1.74066			−0.870330	+	0.492470i	$0.836094\pi$
$812$		0			0
$813$	−7.45700	−	2.72637i	−0.261528	−	0.0956179i
$814$		0			0
$815$	2.44952	−	4.24268i	0.0858028	−	0.148615i
$816$		0			0
$817$	21.2702	−	12.2804i	0.744151	−	0.429636i
$818$		0			0
$819$	19.3946	+	17.4587i	0.677702	+	0.610057i
$820$		0			0
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.797004	−	0.603973i	$-0.793583\pi$
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.124554	−	0.992213i	$-0.539750\pi$
$822$		0			0
$823$	−12.3351	+	21.3650i	−0.429975	+	0.744739i	−0.996871	−	0.0790510i	$-0.974811\pi$
$823$	−12.3351	+	21.3650i	−0.429975	+	0.744739i	0.566896	+	0.823790i	$0.308144\pi$
$824$		0			0
$825$	4.31668	−	11.8067i	0.150287	−	0.411057i
$826$		0			0
$827$	23.0662			0.802091			0.401045	−	0.916058i	$-0.368647\pi$
$827$	23.0662			0.802091			0.401045	+	0.916058i	$0.368647\pi$
$828$		0			0
$829$	12.2068	−	21.1429i	0.423961	−	0.734322i	−0.572362	−	0.820001i	$-0.693973\pi$
$829$	12.2068	−	21.1429i	0.423961	−	0.734322i	0.996323	+	0.0856795i	$0.0273061\pi$
$830$		0			0
$831$	3.68349	+	21.0685i	0.127779	+	0.730859i
$832$		0			0
$833$	23.4959	+	1.50053i	0.814083	+	0.0519904i
$834$		0			0
$835$	−2.51093	+	1.44969i	−0.0868944	+	0.0501685i
$836$		0			0
$837$	−21.6140	−	0.0939312i	−0.747090	−	0.00324674i
$838$		0			0
$839$	48.3464			1.66910			0.834551	−	0.550931i	$-0.185727\pi$
$839$	48.3464			1.66910			0.834551	+	0.550931i	$0.185727\pi$
$840$		0			0
$841$	−11.8768			−0.409546
$842$		0			0
$843$	−10.5155	+	8.79760i	−0.362172	+	0.303005i
$844$		0			0
$845$	0.740348	−	0.427440i	0.0254688	−	0.0147044i
$846$		0			0
$847$	−23.1610	−	0.738822i	−0.795823	−	0.0253862i
$848$		0			0
$849$	−38.7479	+	6.77445i	−1.32983	+	0.232498i
$850$		0			0
$851$	−23.5304	+	40.7559i	−0.806612	+	1.39709i
$852$		0			0
$853$	−34.6867			−1.18765			−0.593825	−	0.804595i	$-0.702383\pi$
$853$	−34.6867			−1.18765			−0.593825	+	0.804595i	$0.702383\pi$
$854$		0			0
$855$	−3.86837	+	4.58312i	−0.132296	+	0.156739i
$856$		0			0
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	−0.621786	−	0.783187i	$-0.713593\pi$
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	0.989153	+	0.146889i	$0.0469262\pi$
$858$		0			0
$859$	−0.332259	−	0.575490i	−0.0113365	−	0.0196355i	0.860301	−	0.509786i	$-0.170275\pi$
$859$	−0.332259	−	0.575490i	−0.0113365	−	0.0196355i	−0.871638	+	0.490150i	$0.836942\pi$
$860$		0			0
$861$	−50.6358	+	7.19745i	−1.72566	+	0.245289i
$862$		0			0
$863$	14.2150	−	8.20702i	0.483883	−	0.279370i	−0.238150	−	0.971228i	$-0.576541\pi$
$863$	14.2150	−	8.20702i	0.483883	−	0.279370i	0.722033	+	0.691858i	$0.243208\pi$
$864$		0			0
$865$	3.43388	−	5.94765i	0.116755	−	0.202226i
$866$		0			0
$867$	−3.38273	+	9.25225i	−0.114884	+	0.314223i
$868$		0			0
$869$	−0.716882			−0.0243186
$870$		0			0
$871$	−10.0428	−	5.79819i	−0.340286	−	0.196464i
$872$		0			0
$873$	26.5783	+	4.76591i	0.899539	+	0.161302i
$874$		0			0
$875$	8.63685	+	5.36073i	0.291979	+	0.181226i
$876$		0			0
$877$	11.1473	−	6.43591i	0.376419	−	0.217325i	−0.299840	−	0.953989i	$-0.596933\pi$
$877$	11.1473	−	6.43591i	0.376419	−	0.217325i	0.676259	+	0.736664i	$0.263600\pi$
$878$		0			0
$879$	−17.0367	+	14.2535i	−0.574633	+	0.480757i
$880$		0			0
$881$	42.1373			1.41964			0.709821	−	0.704382i	$-0.248776\pi$
$881$	42.1373			1.41964			0.709821	+	0.704382i	$0.248776\pi$
$882$		0			0
$883$		−	14.3108i		−	0.481596i	−0.970575	−	0.240798i	$-0.922591\pi$
$883$		−	14.3108i		−	0.481596i	0.970575	−	0.240798i	$-0.0774091\pi$
$884$		0			0
$885$	−0.681121	−	0.814120i	−0.0228956	−	0.0273664i
$886$		0			0
$887$	3.93855	+	6.82176i	0.132243	+	0.229052i	0.924541	−	0.381082i	$-0.124449\pi$
$887$	3.93855	+	6.82176i	0.132243	+	0.229052i	−0.792298	+	0.610135i	$0.791115\pi$
$888$		0			0
$889$	−12.3003	+	19.8174i	−0.412538	+	0.664653i
$890$		0			0
$891$	10.3721	−	8.60127i	0.347477	−	0.288153i
$892$		0			0
$893$	12.8648	−	22.2825i	0.430505	−	0.745656i
$894$		0			0
$895$			6.33434i			0.211734i
$896$		0			0
$897$	−29.1958	−	10.6743i	−0.974818	−	0.356405i
$898$		0			0
$899$	14.9067	+	8.60636i	0.497165	+	0.287038i
$900$		0			0
$901$	1.67915	+	2.90837i	0.0559406	+	0.0968919i
$902$		0			0
$903$	−3.09112	−	21.7467i	−0.102866	−	0.723686i
$904$		0			0
$905$	−2.09262	+	1.20818i	−0.0695611	+	0.0401611i
$906$		0			0
$907$	−24.8886	−	14.3694i	−0.826413	−	0.477130i	0.0262101	−	0.999656i	$-0.491656\pi$
$907$	−24.8886	−	14.3694i	−0.826413	−	0.477130i	−0.852623	+	0.522527i	$0.824989\pi$
$908$		0			0
$909$	−10.3654	+	12.2805i	−0.343797	+	0.407319i
$910$		0			0
$911$		−	4.32207i		−	0.143197i	−0.997434	−	0.0715983i	$-0.977190\pi$
$911$		−	4.32207i		−	0.143197i	0.997434	−	0.0715983i	$-0.0228100\pi$
$912$		0			0
$913$	22.6316	+	13.0664i	0.748996	+	0.432433i
$914$		0			0
$915$	0.793454	+	4.53834i	0.0262308	+	0.150033i
$916$		0			0
$917$	−0.424862	+	13.3188i	−0.0140302	+	0.439826i
$918$		0			0
$919$	−18.1008	−	31.3515i	−0.597089	−	1.03419i	−0.993248	−	0.116007i	$-0.962990\pi$
$919$	−18.1008	−	31.3515i	−0.597089	−	1.03419i	0.396159	−	0.918182i	$-0.370343\pi$
$920$		0			0
$921$	−13.7396	−	16.4225i	−0.452735	−	0.541138i
$922$		0			0
$923$		−	47.1321i		−	1.55137i
$924$		0			0
$925$		−	41.7916i		−	1.37410i
$926$		0			0
$927$	−9.06001	−	25.1184i	−0.297570	−	0.824995i
$928$		0			0
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	0.859881	−	0.510494i	$-0.170537\pi$
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	−0.872041	+	0.489432i	$0.837204\pi$
$930$		0			0
$931$	−19.8775	+	29.8567i	−0.651458	+	0.978515i
$932$		0			0
$933$	−2.45968	+	0.430035i	−0.0805264	+	0.0140787i
$934$		0			0
$935$	1.70141	+	0.982307i	0.0556419	+	0.0321249i
$936$		0			0
$937$			49.0746i			1.60320i	0.597863	+	0.801598i	$0.296017\pi$
$937$			49.0746i			1.60320i	−0.597863	+	0.801598i	$0.703983\pi$
$938$		0			0
$939$	−39.2250	−	14.3411i	−1.28006	−	0.468005i
$940$		0			0
$941$	−26.9660	−	15.5688i	−0.879065	−	0.507529i	−0.00871528	−	0.999962i	$-0.502774\pi$
$941$	−26.9660	−	15.5688i	−0.879065	−	0.507529i	−0.870350	+	0.492433i	$0.836108\pi$
$942$		0			0
$943$	52.7638	−	30.4632i	1.71822	−	0.992017i
$944$		0			0
$945$	2.51180	+	4.73918i	0.0817088	+	0.154165i
$946$		0			0
$947$	11.6780	+	20.2270i	0.379485	+	0.657288i	0.990987	−	0.133955i	$-0.0427678\pi$
$947$	11.6780	+	20.2270i	0.379485	+	0.657288i	−0.611502	+	0.791243i	$0.709434\pi$
$948$		0			0
$949$	−9.07751	−	5.24090i	−0.294669	−	0.170127i
$950$		0			0
$951$	−16.0210	+	43.8197i	−0.519517	+	1.42095i
$952$		0			0
$953$			37.3593i			1.21019i	0.796155	+	0.605093i	$0.206864\pi$
$953$			37.3593i			1.21019i	−0.796155	+	0.605093i	$0.793136\pi$
$954$		0			0
$955$	−1.64162	+	2.84336i	−0.0531215	+	0.0920091i
$956$		0			0
$957$	−10.5702	+	1.84803i	−0.341686	+	0.0597383i
$958$		0			0
$959$	17.0955	−	9.15612i	0.552042	−	0.295667i
$960$		0			0
$961$	−6.84861	−	11.8621i	−0.220923	−	0.382650i
$962$		0			0
$963$	−44.3204	+	15.9861i	−1.42821	+	0.515144i
$964$		0			0
$965$			5.12916i			0.165114i
$966$		0			0
$967$	32.9761			1.06044			0.530220	−	0.847860i	$-0.322109\pi$
$967$	32.9761			1.06044			0.530220	+	0.847860i	$0.322109\pi$
$968$		0			0
$969$	19.1544	+	22.8946i	0.615327	+	0.735479i
$970$		0			0
$971$	14.3859	−	8.30570i	0.461665	−	0.266543i	−0.251079	−	0.967967i	$-0.580785\pi$
$971$	14.3859	−	8.30570i	0.461665	−	0.266543i	0.712744	+	0.701424i	$0.247452\pi$
$972$		0			0
$973$	−21.9748	+	35.4044i	−0.704481	+	1.13501i
$974$		0			0
$975$	27.1929	−	4.75423i	0.870869	−	0.152257i
$976$		0			0
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	0.489702	−	0.871890i	$-0.337106\pi$
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	−0.510228	+	0.860039i	$0.670439\pi$
$978$		0			0
$979$	−7.63074			−0.243880
$980$		0			0
$981$	−33.8689	+	40.1267i	−1.08135	+	1.28115i
$982$		0			0
$983$	5.11340	−	8.85666i	0.163092	−	0.282484i	−0.772884	−	0.634547i	$-0.781187\pi$
$983$	5.11340	−	8.85666i	0.163092	−	0.282484i	0.935976	+	0.352064i	$0.114520\pi$
$984$		0			0
$985$	−5.95069	+	3.43563i	−0.189605	+	0.109468i
$986$		0			0
$987$	−14.1952	−	18.1104i	−0.451839	−	0.576461i
$988$		0			0
$989$	13.0831	+	22.6606i	0.416019	+	0.720567i
$990$		0			0
$991$	−22.7297	+	39.3690i	−0.722032	+	1.25060i	0.238152	+	0.971228i	$0.423459\pi$
$991$	−22.7297	+	39.3690i	−0.722032	+	1.25060i	−0.960184	+	0.279369i	$0.909875\pi$
$992$		0			0
$993$	−28.6984	−	10.4925i	−0.910718	−	0.332969i
$994$		0			0
$995$	7.77971			0.246633
$996$		0			0
$997$	−13.6051	+	23.5647i	−0.430877	+	0.746300i	−0.996949	−	0.0780552i	$-0.975129\pi$
$997$	−13.6051	+	23.5647i	−0.430877	+	0.746300i	0.566072	+	0.824356i	$0.308462\pi$
$998$		0			0
$999$	22.5658	−	38.6958i	0.713950	−	1.22428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.19		48
3.2	odd	2	inner	672.2.bi.c.17.2		48
4.3	odd	2		168.2.ba.c.101.24	yes	48
7.5	odd	6	inner	672.2.bi.c.593.23		48
8.3	odd	2		168.2.ba.c.101.16	yes	48
8.5	even	2	inner	672.2.bi.c.17.6		48
12.11	even	2		168.2.ba.c.101.1	yes	48
21.5	even	6	inner	672.2.bi.c.593.6		48
24.5	odd	2	inner	672.2.bi.c.17.23		48
24.11	even	2		168.2.ba.c.101.9	yes	48
28.19	even	6		168.2.ba.c.5.9	yes	48
56.5	odd	6	inner	672.2.bi.c.593.2		48
56.19	even	6		168.2.ba.c.5.1	✓	48
84.47	odd	6		168.2.ba.c.5.16	yes	48
168.5	even	6	inner	672.2.bi.c.593.19		48
168.131	odd	6		168.2.ba.c.5.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.1	✓	48	56.19	even	6
168.2.ba.c.5.9	yes	48	28.19	even	6
168.2.ba.c.5.16	yes	48	84.47	odd	6
168.2.ba.c.5.24	yes	48	168.131	odd	6
168.2.ba.c.101.1	yes	48	12.11	even	2
168.2.ba.c.101.9	yes	48	24.11	even	2
168.2.ba.c.101.16	yes	48	8.3	odd	2
168.2.ba.c.101.24	yes	48	4.3	odd	2
672.2.bi.c.17.2		48	3.2	odd	2	inner
672.2.bi.c.17.6		48	8.5	even	2	inner
672.2.bi.c.17.19		48	1.1	even	1	trivial
672.2.bi.c.17.23		48	24.5	odd	2	inner
672.2.bi.c.593.2		48	56.5	odd	6	inner
672.2.bi.c.593.6		48	21.5	even	6	inner
672.2.bi.c.593.19		48	168.5	even	6	inner
672.2.bi.c.593.23		48	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11142 + 1.32844i) q^{3} +(-0.337879 + 0.195075i) q^{5} +(-1.39526 + 2.24795i) q^{7} +(-0.529502 + 2.95290i) q^{9} +O(q^{10})\)	\(q+(1.11142 + 1.32844i) q^{3} +(-0.337879 + 0.195075i) q^{5} +(-1.39526 + 2.24795i) q^{7} +(-0.529502 + 2.95290i) q^{9} +(-0.748582 + 1.29658i) q^{11} -3.28768 q^{13} +(-0.634670 - 0.232043i) q^{15} +(-1.68169 + 2.91278i) q^{17} +(-2.56203 - 4.43756i) q^{19} +(-4.53697 + 0.644892i) q^{21} +(4.72764 - 2.72950i) q^{23} +(-2.42389 + 4.19830i) q^{25} +(-4.51125 + 2.57850i) q^{27} +4.13801 q^{29} +(3.60237 + 2.07983i) q^{31} +(-2.55442 + 0.446598i) q^{33} +(0.0329110 - 1.03171i) q^{35} +(-7.46581 + 4.31038i) q^{37} +(-3.65399 - 4.36748i) q^{39} +11.1607 q^{41} +4.79323i q^{43} +(-0.397129 - 1.10102i) q^{45} +(2.51067 + 4.34861i) q^{47} +(-3.10652 - 6.27292i) q^{49} +(-5.73852 + 1.00329i) q^{51} +(0.499243 - 0.864715i) q^{53} -0.584118i q^{55} +(3.04755 - 8.33548i) q^{57} +(1.36034 + 0.785391i) q^{59} +(-3.40889 - 5.90437i) q^{61} +(-5.89917 - 5.31035i) q^{63} +(1.11084 - 0.641343i) q^{65} +(3.05467 + 1.76361i) q^{67} +(8.88036 + 3.24676i) q^{69} +14.3360i q^{71} +(2.76107 + 1.59410i) q^{73} +(-8.27115 + 1.44608i) q^{75} +(-1.87018 - 3.49184i) q^{77} +(0.239413 + 0.414676i) q^{79} +(-8.43926 - 3.12713i) q^{81} -17.4548i q^{83} -1.31222i q^{85} +(4.59906 + 5.49710i) q^{87} +(2.54840 + 4.41396i) q^{89} +(4.58716 - 7.39053i) q^{91} +(1.24081 + 7.09709i) q^{93} +(1.73131 + 0.999573i) q^{95} -9.00074i q^{97} +(-3.43230 - 2.89703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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