LMFDB - Embedded newform 420.2.bv.c.233.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(53,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("420.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bv (of order $12$, degree $4$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.2
Character	$\chi$	$=$	420.233
Dual form			420.2.bv.c.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54911 + 0.774760i) q^{3} +(0.626199 + 2.14660i) q^{5} +(1.95049 - 1.78762i) q^{7} +(1.79949 - 2.40038i) q^{9} +O(q^{10})$	\(q+(-1.54911 + 0.774760i) q^{3} +(0.626199 + 2.14660i) q^{5} +(1.95049 - 1.78762i) q^{7} +(1.79949 - 2.40038i) q^{9} +(-2.07693 + 1.19911i) q^{11} +(3.37848 + 3.37848i) q^{13} +(-2.63315 - 2.84016i) q^{15} +(-1.27103 + 4.74353i) q^{17} +(-0.151250 - 0.0873244i) q^{19} +(-1.63655 + 4.28039i) q^{21} +(0.324361 + 1.21053i) q^{23} +(-4.21575 + 2.68839i) q^{25} +(-0.927900 + 5.11263i) q^{27} -4.65176 q^{29} +(1.26323 + 2.18799i) q^{31} +(2.28836 - 3.46668i) q^{33} +(5.05869 + 3.06751i) q^{35} +(2.94674 + 10.9974i) q^{37} +(-7.85116 - 2.61614i) q^{39} -1.78650i q^{41} +(-2.46081 - 2.46081i) q^{43} +(6.27949 + 2.35967i) q^{45} +(7.73263 - 2.07195i) q^{47} +(0.608831 - 6.97347i) q^{49} +(-1.70614 - 8.33300i) q^{51} +(10.8978 + 2.92005i) q^{53} +(-3.87458 - 3.70744i) q^{55} +(0.301959 + 0.0180926i) q^{57} +(2.06606 + 3.57852i) q^{59} +(3.47828 - 6.02455i) q^{61} +(-0.781068 - 7.89873i) q^{63} +(-5.13664 + 9.36784i) q^{65} +(-11.6526 - 3.12231i) q^{67} +(-1.44034 - 1.62395i) q^{69} -15.9938i q^{71} +(1.40215 - 5.23288i) q^{73} +(4.44781 - 7.43081i) q^{75} +(-1.90747 + 6.05161i) q^{77} +(-5.52266 - 3.18851i) q^{79} +(-2.52364 - 8.63894i) q^{81} +(-3.05025 + 3.05025i) q^{83} +(-10.9784 + 0.242015i) q^{85} +(7.20610 - 3.60400i) q^{87} +(-2.58127 + 4.47089i) q^{89} +(12.6291 + 0.550258i) q^{91} +(-3.65205 - 2.41073i) q^{93} +(0.0927374 - 0.379356i) q^{95} +(-2.70738 + 2.70738i) q^{97} +(-0.859088 + 7.14321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) $ 48 * q - 2 * q^3 - 8 * q^7	$ 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) $ 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.54911	+	0.774760i	−0.894380	+	0.447308i
$3$	−1.54911	+	0.774760i	−0.894380	+	0.447308i
$4$		0			0
$5$	0.626199	+	2.14660i	0.280045	+	0.959987i
$5$	0.626199	+	2.14660i	0.280045	+	0.959987i
$6$		0			0
$7$	1.95049	−	1.78762i	0.737216	−	0.675657i
$7$	1.95049	−	1.78762i	0.737216	−	0.675657i
$8$		0			0
$9$	1.79949	−	2.40038i	0.599831	−	0.800126i
$10$		0			0
$11$	−2.07693	+	1.19911i	−0.626217	+	0.361546i	−0.779285	−	0.626669i	$-0.784418\pi$
$11$	−2.07693	+	1.19911i	−0.626217	+	0.361546i	0.153069	+	0.988216i	$0.451084\pi$
$12$		0			0
$13$	3.37848	+	3.37848i	0.937023	+	0.937023i	0.998131	−	0.0611083i	$-0.0194635\pi$
$13$	3.37848	+	3.37848i	0.937023	+	0.937023i	−0.0611083	+	0.998131i	$0.519464\pi$
$14$		0			0
$15$	−2.63315	−	2.84016i	−0.679876	−	0.733327i
$16$		0			0
$17$	−1.27103	+	4.74353i	−0.308269	+	1.15048i	0.621826	+	0.783156i	$0.286391\pi$
$17$	−1.27103	+	4.74353i	−0.308269	+	1.15048i	−0.930095	+	0.367320i	$0.880275\pi$
$18$		0			0
$19$	−0.151250	−	0.0873244i	−0.0346992	−	0.0200336i	0.482550	−	0.875868i	$-0.339711\pi$
$19$	−0.151250	−	0.0873244i	−0.0346992	−	0.0200336i	−0.517249	+	0.855835i	$0.673044\pi$
$20$		0			0
$21$	−1.63655	+	4.28039i	−0.357125	+	0.934057i
$22$		0			0
$23$	0.324361	+	1.21053i	0.0676339	+	0.252413i	0.991462	−	0.130394i	$-0.0416241\pi$
$23$	0.324361	+	1.21053i	0.0676339	+	0.252413i	−0.923828	+	0.382807i	$0.874957\pi$
$24$		0			0
$25$	−4.21575	+	2.68839i	−0.843150	+	0.537678i
$26$		0			0
$27$	−0.927900	+	5.11263i	−0.178574	+	0.983926i
$28$		0			0
$29$	−4.65176			−0.863811			−0.431905	−	0.901919i	$-0.642159\pi$
$29$	−4.65176			−0.863811			−0.431905	+	0.901919i	$0.642159\pi$
$30$		0			0
$31$	1.26323	+	2.18799i	0.226884	+	0.392974i	0.956883	−	0.290474i	$-0.0938130\pi$
$31$	1.26323	+	2.18799i	0.226884	+	0.392974i	−0.729999	+	0.683448i	$0.760480\pi$
$32$		0			0
$33$	2.28836	−	3.46668i	0.398353	−	0.603471i
$34$		0			0
$35$	5.05869	+	3.06751i	0.855075	+	0.518504i
$36$		0			0
$37$	2.94674	+	10.9974i	0.484441	+	1.80796i	0.582566	+	0.812783i	$0.302049\pi$
$37$	2.94674	+	10.9974i	0.484441	+	1.80796i	−0.0981254	+	0.995174i	$0.531285\pi$
$38$		0			0
$39$	−7.85116	−	2.61614i	−1.25719	−	0.418917i
$40$		0			0
$41$		−	1.78650i		−	0.279005i	−0.990222	−	0.139503i	$-0.955450\pi$
$41$		−	1.78650i		−	0.279005i	0.990222	−	0.139503i	$-0.0445504\pi$
$42$		0			0
$43$	−2.46081	−	2.46081i	−0.375271	−	0.375271i	0.494122	−	0.869393i	$-0.335490\pi$
$43$	−2.46081	−	2.46081i	−0.375271	−	0.375271i	−0.869393	+	0.494122i	$0.835490\pi$
$44$		0			0
$45$	6.27949	+	2.35967i	0.936090	+	0.351759i
$46$		0			0
$47$	7.73263	−	2.07195i	1.12792	−	0.302225i	0.353835	−	0.935308i	$-0.384877\pi$
$47$	7.73263	−	2.07195i	1.12792	−	0.302225i	0.774084	+	0.633082i	$0.218211\pi$
$48$		0			0
$49$	0.608831	−	6.97347i	0.0869758	−	0.996210i
$50$		0			0
$51$	−1.70614	−	8.33300i	−0.238907	−	1.16685i
$52$		0			0
$53$	10.8978	+	2.92005i	1.49692	+	0.401100i	0.912069	−	0.410037i	$-0.134484\pi$
$53$	10.8978	+	2.92005i	1.49692	+	0.401100i	0.584856	+	0.811137i	$0.301151\pi$
$54$		0			0
$55$	−3.87458	−	3.70744i	−0.522448	−	0.499911i
$56$		0			0
$57$	0.301959	+	0.0180926i	0.0399954	+	0.00239642i
$58$		0			0
$59$	2.06606	+	3.57852i	0.268978	+	0.465884i	0.968598	−	0.248631i	$-0.0799807\pi$
$59$	2.06606	+	3.57852i	0.268978	+	0.465884i	−0.699620	+	0.714515i	$0.746647\pi$
$60$		0			0
$61$	3.47828	−	6.02455i	0.445348	−	0.771365i	−0.552729	−	0.833361i	$-0.686413\pi$
$61$	3.47828	−	6.02455i	0.445348	−	0.771365i	0.998076	+	0.0619964i	$0.0197467\pi$
$62$		0			0
$63$	−0.781068	−	7.89873i	−0.0984053	−	0.995146i
$64$		0			0
$65$	−5.13664	+	9.36784i	−0.637122	+	1.16194i
$66$		0			0
$67$	−11.6526	−	3.12231i	−1.42359	−	0.381451i	−0.536837	−	0.843686i	$-0.680381\pi$
$67$	−11.6526	−	3.12231i	−1.42359	−	0.381451i	−0.886757	+	0.462235i	$0.847047\pi$
$68$		0			0
$69$	−1.44034	−	1.62395i	−0.173397	−	0.195500i
$70$		0			0
$71$		−	15.9938i		−	1.89811i	−0.315111	−	0.949055i	$-0.602042\pi$
$71$		−	15.9938i		−	1.89811i	0.315111	−	0.949055i	$-0.397958\pi$
$72$		0			0
$73$	1.40215	−	5.23288i	0.164109	−	0.612462i	−0.834043	−	0.551699i	$-0.813980\pi$
$73$	1.40215	−	5.23288i	0.164109	−	0.612462i	0.998152	−	0.0607633i	$-0.0193535\pi$
$74$		0			0
$75$	4.44781	−	7.43081i	0.513589	−	0.858036i
$76$		0			0
$77$	−1.90747	+	6.05161i	−0.217376	+	0.689645i
$78$		0			0
$79$	−5.52266	−	3.18851i	−0.621348	−	0.358735i	0.156046	−	0.987750i	$-0.450125\pi$
$79$	−5.52266	−	3.18851i	−0.621348	−	0.358735i	−0.777394	+	0.629014i	$0.783459\pi$
$80$		0			0
$81$	−2.52364	−	8.63894i	−0.280405	−	0.959882i
$82$		0			0
$83$	−3.05025	+	3.05025i	−0.334808	+	0.334808i	−0.854409	−	0.519601i	$-0.826081\pi$
$83$	−3.05025	+	3.05025i	−0.334808	+	0.334808i	0.519601	+	0.854409i	$0.326081\pi$
$84$		0			0
$85$	−10.9784	+	0.242015i	−1.19077	+	0.0262502i
$86$		0			0
$87$	7.20610	−	3.60400i	0.772575	−	0.386389i
$88$		0			0
$89$	−2.58127	+	4.47089i	−0.273614	+	0.473914i	−0.969785	−	0.243963i	$-0.921553\pi$
$89$	−2.58127	+	4.47089i	−0.273614	+	0.473914i	0.696170	+	0.717877i	$0.254886\pi$
$90$		0			0
$91$	12.6291	+	0.550258i	1.32389	+	0.0576827i
$92$		0			0
$93$	−3.65205	−	2.41073i	−0.378700	−	0.249981i
$94$		0			0
$95$	0.0927374	−	0.379356i	0.00951466	−	0.0389211i
$96$		0			0
$97$	−2.70738	+	2.70738i	−0.274893	+	0.274893i	−0.831066	−	0.556173i	$-0.812269\pi$
$97$	−2.70738	+	2.70738i	−0.274893	+	0.274893i	0.556173	+	0.831066i	$0.312269\pi$
$98$		0			0
$99$	−0.859088	+	7.14321i	−0.0863416	+	0.717919i
$100$		0			0
$101$	−1.03830	+	0.599462i	−0.103315	+	0.0596487i	−0.550767	−	0.834659i	$-0.685665\pi$
$101$	−1.03830	+	0.599462i	−0.103315	+	0.0596487i	0.447452	+	0.894308i	$0.352331\pi$
$102$		0			0
$103$	5.21841	−	1.39827i	0.514185	−	0.137775i	0.00760935	−	0.999971i	$-0.497578\pi$
$103$	5.21841	−	1.39827i	0.514185	−	0.137775i	0.506575	+	0.862196i	$0.330911\pi$
$104$		0			0
$105$	−10.2131	−	0.832646i	−0.996693	−	0.0812579i
$106$		0			0
$107$	9.57801	−	2.56642i	0.925941	−	0.248105i	0.235818	−	0.971797i	$-0.424223\pi$
$107$	9.57801	−	2.56642i	0.925941	−	0.248105i	0.690123	+	0.723692i	$0.257556\pi$
$108$		0			0
$109$	13.1440	−	7.58867i	1.25896	−	0.726863i	0.286090	−	0.958203i	$-0.407644\pi$
$109$	13.1440	−	7.58867i	1.25896	−	0.726863i	0.972873	+	0.231340i	$0.0743110\pi$
$110$		0			0
$111$	−13.0852	−	14.7531i	−1.24199	−	1.40031i
$112$		0			0
$113$	11.3407	−	11.3407i	1.06685	−	1.06685i	0.0692464	−	0.997600i	$-0.477941\pi$
$113$	11.3407	−	11.3407i	1.06685	−	1.06685i	0.997600	−	0.0692464i	$-0.0220595\pi$
$114$		0			0
$115$	−2.39541	+	1.45431i	−0.223373	+	0.135615i
$116$		0			0
$117$	14.1892	−	2.03008i	1.31179	−	0.187681i
$118$		0			0
$119$	6.00051	+	11.5243i	0.550066	+	1.05643i
$120$		0			0
$121$	−2.62425	+	4.54534i	−0.238569	+	0.413213i
$122$		0			0
$123$	1.38411	+	2.76750i	0.124801	+	0.249537i
$124$		0			0
$125$	−8.41079	−	7.36605i	−0.752284	−	0.658839i
$126$		0			0
$127$	−14.7150	+	14.7150i	−1.30574	+	1.30574i	−0.381287	+	0.924457i	$0.624519\pi$
$127$	−14.7150	+	14.7150i	−1.30574	+	1.30574i	−0.924457	+	0.381287i	$0.875481\pi$
$128$		0			0
$129$	5.71861	+	1.90554i	0.503496	+	0.167773i
$130$		0			0
$131$	11.6665	+	6.73566i	1.01931	+	0.588497i	0.913903	−	0.405932i	$-0.133053\pi$
$131$	11.6665	+	6.73566i	1.01931	+	0.588497i	0.105404	+	0.994429i	$0.466386\pi$
$132$		0			0
$133$	−0.451115	+	0.100053i	−0.0391166	+	0.00867565i
$134$		0			0
$135$	−11.5558	+	1.20970i	−0.994565	+	0.104114i
$136$		0			0
$137$	3.44229	−	12.8468i	0.294095	−	1.09758i	−0.647839	−	0.761777i	$-0.724327\pi$
$137$	3.44229	−	12.8468i	0.294095	−	1.09758i	0.941934	−	0.335799i	$-0.109006\pi$
$138$		0			0
$139$		−	4.58221i		−	0.388658i	−0.980936	−	0.194329i	$-0.937747\pi$
$139$		−	4.58221i		−	0.388658i	0.980936	−	0.194329i	$-0.0622530\pi$
$140$		0			0
$141$	−10.3734	+	9.20061i	−0.873601	+	0.774832i
$142$		0			0
$143$	−11.0680	−	2.96567i	−0.925556	−	0.248002i
$144$		0			0
$145$	−2.91293	−	9.98546i	−0.241905	−	0.829247i
$146$		0			0
$147$	4.45962	+	11.2744i	0.367823	+	0.929896i
$148$		0			0
$149$	−3.58754	+	6.21379i	−0.293902	+	0.509054i	−0.974729	−	0.223391i	$-0.928287\pi$
$149$	−3.58754	+	6.21379i	−0.293902	+	0.509054i	0.680827	+	0.732445i	$0.261621\pi$
$150$		0			0
$151$	2.15084	+	3.72536i	0.175033	+	0.303166i	0.940173	−	0.340698i	$-0.110663\pi$
$151$	2.15084	+	3.72536i	0.175033	+	0.303166i	−0.765140	+	0.643864i	$0.777330\pi$
$152$		0			0
$153$	9.09907	+	11.5869i	0.735616	+	0.936745i
$154$		0			0
$155$	−3.90569	+	4.08177i	−0.313712	+	0.327855i
$156$		0			0
$157$	8.58676	+	2.30081i	0.685298	+	0.183625i	0.584636	−	0.811296i	$-0.301237\pi$
$157$	8.58676	+	2.30081i	0.685298	+	0.183625i	0.100662	+	0.994921i	$0.467904\pi$
$158$		0			0
$159$	−19.1442	+	3.91968i	−1.51823	+	0.310851i
$160$		0			0
$161$	2.79663	+	1.78130i	0.220406	+	0.140386i
$162$		0			0
$163$	5.72018	−	1.53272i	0.448039	−	0.120052i	−0.0277426	−	0.999615i	$-0.508832\pi$
$163$	5.72018	−	1.53272i	0.448039	−	0.120052i	0.475782	+	0.879563i	$0.342165\pi$
$164$		0			0
$165$	8.87453	+	2.74136i	0.690881	+	0.213415i
$166$		0			0
$167$	16.1499	+	16.1499i	1.24972	+	1.24972i	0.955844	+	0.293876i	$0.0949452\pi$
$167$	16.1499	+	16.1499i	1.24972	+	1.24972i	0.293876	+	0.955844i	$0.405055\pi$
$168$		0			0
$169$			9.82831i			0.756024i
$170$		0			0
$171$	−0.481785	+	0.205918i	−0.0368431	+	0.0157470i
$172$		0			0
$173$	−6.65674	−	24.8433i	−0.506102	−	1.88880i	−0.455836	−	0.890064i	$-0.650660\pi$
$173$	−6.65674	−	24.8433i	−0.506102	−	1.88880i	−0.0502667	−	0.998736i	$-0.516007\pi$
$174$		0			0
$175$	−3.41696	+	12.7798i	−0.258298	+	0.966065i
$176$		0			0
$177$	−5.97305	−	3.94283i	−0.448962	−	0.296361i
$178$		0			0
$179$	−9.95927	−	17.2500i	−0.744391	−	1.28932i	−0.950479	−	0.310789i	$-0.899407\pi$
$179$	−9.95927	−	17.2500i	−0.744391	−	1.28932i	0.206088	−	0.978533i	$-0.433927\pi$
$180$		0			0
$181$	16.4609			1.22353			0.611765	−	0.791040i	$-0.290460\pi$
$181$	16.4609			1.22353			0.611765	+	0.791040i	$0.290460\pi$
$182$		0			0
$183$	−0.720658	+	12.0275i	−0.0532726	+	0.889101i
$184$		0			0
$185$	−21.7617	+	13.2120i	−1.59995	+	0.971365i
$186$		0			0
$187$	−3.04821	−	11.3761i	−0.222907	−	0.831900i
$188$		0			0
$189$	7.32958	+	11.6309i	0.533149	+	0.846022i
$190$		0			0
$191$	−1.56368	−	0.902790i	−0.113144	−	0.0653236i	0.442360	−	0.896837i	$-0.354141\pi$
$191$	−1.56368	−	0.902790i	−0.113144	−	0.0653236i	−0.555504	+	0.831514i	$0.687475\pi$
$192$		0			0
$193$	1.38263	−	5.16003i	0.0995236	−	0.371427i	−0.898143	−	0.439704i	$-0.855083\pi$
$193$	1.38263	−	5.16003i	0.0995236	−	0.371427i	0.997666	+	0.0682768i	$0.0217501\pi$
$194$		0			0
$195$	0.699398	−	18.4915i	0.0500849	−	1.32420i
$196$		0			0
$197$	−15.1248	−	15.1248i	−1.07760	−	1.07760i	−0.996724	−	0.0808739i	$-0.974229\pi$
$197$	−15.1248	−	15.1248i	−1.07760	−	1.07760i	−0.0808739	−	0.996724i	$-0.525771\pi$
$198$		0			0
$199$	−2.10884	+	1.21754i	−0.149491	+	0.0863090i	−0.572880	−	0.819639i	$-0.694174\pi$
$199$	−2.10884	+	1.21754i	−0.149491	+	0.0863090i	0.423388	+	0.905948i	$0.360841\pi$
$200$		0			0
$201$	20.4702	−	4.19117i	1.44386	−	0.295623i
$202$		0			0
$203$	−9.07322	+	8.31558i	−0.636815	+	0.583640i
$204$		0			0
$205$	3.83490	−	1.11871i	0.267841	−	0.0781339i
$206$		0			0
$207$	3.48942	+	1.39976i	0.242532	+	0.0972897i
$208$		0			0
$209$	0.418847			0.0289723
$210$		0			0
$211$	13.8080			0.950581			0.475291	−	0.879829i	$-0.342343\pi$
$211$	13.8080			0.950581			0.475291	+	0.879829i	$0.342343\pi$
$212$		0			0
$213$	12.3913	+	24.7761i	0.849039	+	1.69763i
$214$		0			0
$215$	3.74141	−	6.82333i	0.255162	−	0.465347i
$216$		0			0
$217$	6.37521	+	2.00946i	0.432778	+	0.136411i
$218$		0			0
$219$	1.88214	+	9.19264i	0.127184	+	0.621181i
$220$		0			0
$221$	−20.3201	+	11.7318i	−1.36688	+	0.789167i
$222$		0			0
$223$	−17.6103	−	17.6103i	−1.17928	−	1.17928i	−0.979929	−	0.199347i	$-0.936118\pi$
$223$	−17.6103	−	17.6103i	−1.17928	−	1.17928i	−0.199347	−	0.979929i	$-0.563882\pi$
$224$		0			0
$225$	−1.13306	+	14.9571i	−0.0755373	+	0.997143i
$226$		0			0
$227$	−1.69379	+	6.32132i	−0.112421	+	0.419561i	−0.999081	−	0.0428611i	$-0.986353\pi$
$227$	−1.69379	+	6.32132i	−0.112421	+	0.419561i	0.886660	+	0.462422i	$0.153019\pi$
$228$		0			0
$229$	−20.8421	−	12.0332i	−1.37729	−	0.795177i	−0.385454	−	0.922727i	$-0.625955\pi$
$229$	−20.8421	−	12.0332i	−1.37729	−	0.795177i	−0.991832	+	0.127550i	$0.959289\pi$
$230$		0			0
$231$	−1.73367	−	10.8525i	−0.114067	−	0.714039i
$232$		0			0
$233$	0.520604	+	1.94292i	0.0341059	+	0.127285i	0.980880	−	0.194614i	$-0.0623455\pi$
$233$	0.520604	+	1.94292i	0.0341059	+	0.127285i	−0.946774	+	0.321899i	$0.895679\pi$
$234$		0			0
$235$	9.28981	+	15.3014i	0.606000	+	0.998152i
$236$		0			0
$237$	11.0256	+	0.660622i	0.716187	+	0.0429120i
$238$		0			0
$239$	10.1453			0.656245			0.328123	−	0.944635i	$-0.393584\pi$
$239$	10.1453			0.656245			0.328123	+	0.944635i	$0.393584\pi$
$240$		0			0
$241$	11.1599	+	19.3295i	0.718871	+	1.24512i	0.961448	+	0.274988i	$0.0886740\pi$
$241$	11.1599	+	19.3295i	0.718871	+	1.24512i	−0.242577	+	0.970132i	$0.577993\pi$
$242$		0			0
$243$	10.6025	+	11.4275i	0.680151	+	0.733072i
$244$		0			0
$245$	15.3505	−	3.05987i	0.980706	−	0.195488i
$246$		0			0
$247$	−0.215973	−	0.806020i	−0.0137420	−	0.0512858i
$248$		0			0
$249$	2.36197	−	7.08839i	0.149684	−	0.449208i
$250$		0			0
$251$			4.37814i			0.276346i	0.990408	+	0.138173i	$0.0441230\pi$
$251$			4.37814i			0.276346i	−0.990408	+	0.138173i	$0.955877\pi$
$252$		0			0
$253$	−2.12524	−	2.12524i	−0.133613	−	0.133613i
$254$		0			0
$255$	16.8192	−	8.88050i	1.05326	−	0.556119i
$256$		0			0
$257$	−2.38623	+	0.639388i	−0.148849	+	0.0398839i	−0.332474	−	0.943112i	$-0.607883\pi$
$257$	−2.38623	+	0.639388i	−0.148849	+	0.0398839i	0.183625	+	0.982996i	$0.441217\pi$
$258$		0			0
$259$	25.4067	+	16.1826i	1.57870	+	1.00554i
$260$		0			0
$261$	−8.37082	+	11.1660i	−0.518141	+	0.691158i
$262$		0			0
$263$	0.293053	+	0.0785232i	0.0180704	+	0.00484195i	0.267843	−	0.963463i	$-0.413689\pi$
$263$	0.293053	+	0.0785232i	0.0180704	+	0.00484195i	−0.249773	+	0.968305i	$0.580356\pi$
$264$		0			0
$265$	0.556004	+	25.2217i	0.0341551	+	1.54935i
$266$		0			0
$267$	0.534809	−	8.92578i	0.0327298	−	0.546249i
$268$		0			0
$269$	−8.59823	−	14.8926i	−0.524244	−	0.908017i	−0.999602	−	0.0282241i	$-0.991015\pi$
$269$	−8.59823	−	14.8926i	−0.524244	−	0.908017i	0.475358	−	0.879792i	$-0.342319\pi$
$270$		0			0
$271$	−4.92042	+	8.52242i	−0.298894	+	0.517700i	−0.975883	−	0.218293i	$-0.929951\pi$
$271$	−4.92042	+	8.52242i	−0.298894	+	0.517700i	0.676989	+	0.735993i	$0.263284\pi$
$272$		0			0
$273$	−19.9903	+	8.93215i	−1.20987	+	0.540598i
$274$		0			0
$275$	5.53211	−	10.6388i	0.333599	−	0.641541i
$276$		0			0
$277$	−13.0075	−	3.48534i	−0.781543	−	0.209414i	−0.154078	−	0.988059i	$-0.549241\pi$
$277$	−13.0075	−	3.48534i	−0.781543	−	0.209414i	−0.627465	+	0.778645i	$0.715907\pi$
$278$		0			0
$279$	7.52518	+	0.905026i	0.450521	+	0.0541825i
$280$		0			0
$281$		−	24.4744i		−	1.46002i	−0.683436	−	0.730011i	$-0.739515\pi$
$281$		−	24.4744i		−	1.46002i	0.683436	−	0.730011i	$-0.260485\pi$
$282$		0			0
$283$	1.75689	−	6.55682i	0.104437	−	0.389763i	−0.893844	−	0.448378i	$-0.852002\pi$
$283$	1.75689	−	6.55682i	0.104437	−	0.389763i	0.998281	+	0.0586154i	$0.0186686\pi$
$284$		0			0
$285$	0.150249	+	0.659513i	0.00889997	+	0.0390662i
$286$		0			0
$287$	−3.19359	−	3.48456i	−0.188512	−	0.205687i
$288$		0			0
$289$	−6.16315	−	3.55830i	−0.362538	−	0.209312i
$290$		0			0
$291$	2.09647	−	6.29161i	0.122897	−	0.368821i
$292$		0			0
$293$	−19.9960	+	19.9960i	−1.16818	+	1.16818i	−0.185541	+	0.982637i	$0.559404\pi$
$293$	−19.9960	+	19.9960i	−1.16818	+	1.16818i	−0.982637	+	0.185541i	$0.940596\pi$
$294$		0			0
$295$	−6.38787	+	6.67586i	−0.371916	+	0.388684i
$296$		0			0
$297$	−4.20345	−	11.7312i	−0.243909	−	0.680714i
$298$		0			0
$299$	−2.99391	+	5.18561i	−0.173142	+	0.299892i
$300$		0			0
$301$	−9.19879	−	0.400796i	−0.530210	−	0.0231015i
$302$		0			0
$303$	1.14400	−	1.73307i	0.0657211	−	0.0995620i
$304$		0			0
$305$	15.1104	+	3.69389i	0.865217	+	0.211511i
$306$		0			0
$307$	−5.61961	+	5.61961i	−0.320728	+	0.320728i	−0.849046	−	0.528318i	$-0.822823\pi$
$307$	−5.61961	+	5.61961i	−0.320728	+	0.320728i	0.528318	+	0.849046i	$0.322823\pi$
$308$		0			0
$309$	−7.00057	+	6.20908i	−0.398249	+	0.353222i
$310$		0			0
$311$	−26.1827	+	15.1166i	−1.48468	+	0.857183i	−0.999848	−	0.0174217i	$-0.994454\pi$
$311$	−26.1827	+	15.1166i	−1.48468	+	0.857183i	−0.484836	+	0.874605i	$0.661121\pi$
$312$		0			0
$313$	−10.3638	+	2.77697i	−0.585796	+	0.156964i	−0.539531	−	0.841966i	$-0.681398\pi$
$313$	−10.3638	+	2.77697i	−0.585796	+	0.156964i	−0.0462649	+	0.998929i	$0.514732\pi$
$314$		0			0
$315$	16.4663	−	6.62281i	0.927770	−	0.373153i
$316$		0			0
$317$	10.2698	−	2.75178i	0.576808	−	0.154555i	0.0413908	−	0.999143i	$-0.486821\pi$
$317$	10.2698	−	2.75178i	0.576808	−	0.154555i	0.535417	+	0.844588i	$0.320154\pi$
$318$		0			0
$319$	9.66136	−	5.57799i	0.540933	−	0.312308i
$320$		0			0
$321$	−12.8490	+	11.3963i	−0.717164	+	0.636081i
$322$		0			0
$323$	0.606469	−	0.606469i	0.0337448	−	0.0337448i
$324$		0			0
$325$	−23.3255	−	5.16016i	−1.29387	−	0.286234i
$326$		0			0
$327$	−14.4821	+	21.9391i	−0.800860	+	1.21324i
$328$		0			0
$329$	11.3786	−	17.8643i	0.627320	−	0.984892i
$330$		0			0
$331$	−0.207490	+	0.359384i	−0.0114047	+	0.0197535i	−0.871671	−	0.490091i	$-0.836964\pi$
$331$	−0.207490	+	0.359384i	−0.0114047	+	0.0197535i	0.860267	+	0.509844i	$0.170297\pi$
$332$		0			0
$333$	31.7005	+	12.7164i	1.73718	+	0.696856i
$334$		0			0
$335$	−0.594516	−	26.9686i	−0.0324819	−	1.47345i
$336$		0			0
$337$	12.7807	−	12.7807i	0.696210	−	0.696210i	−0.267381	−	0.963591i	$-0.586158\pi$
$337$	12.7807	−	12.7807i	0.696210	−	0.696210i	0.963591	+	0.267381i	$0.0861582\pi$
$338$		0			0
$339$	−8.78171	+	26.3544i	−0.476957	+	1.43137i
$340$		0			0
$341$	−5.24729	−	3.02952i	−0.284156	−	0.164058i
$342$		0			0
$343$	−11.2784	−	14.6901i	−0.608976	−	0.793188i
$344$		0			0
$345$	2.58402	−	4.10875i	0.139119	−	0.221208i
$346$		0			0
$347$	−8.40176	+	31.3558i	−0.451030	+	1.68327i	0.248473	+	0.968639i	$0.420071\pi$
$347$	−8.40176	+	31.3558i	−0.451030	+	1.68327i	−0.699504	+	0.714629i	$0.746596\pi$
$348$		0			0
$349$		−	13.1679i		−	0.704860i	−0.935838	−	0.352430i	$-0.885355\pi$
$349$		−	13.1679i		−	0.704860i	0.935838	−	0.352430i	$-0.114645\pi$
$350$		0			0
$351$	−20.4078	+	14.1380i	−1.08929	+	0.754633i
$352$		0			0
$353$	9.54503	+	2.55758i	0.508031	+	0.136126i	0.503725	−	0.863864i	$-0.331963\pi$
$353$	9.54503	+	2.55758i	0.508031	+	0.136126i	0.00430620	+	0.999991i	$0.498629\pi$
$354$		0			0
$355$	34.3321	−	10.0153i	1.82216	−	0.531555i
$356$		0			0
$357$	−18.2240	−	13.2035i	−0.964519	−	0.698804i
$358$		0			0
$359$	5.54047	−	9.59637i	0.292415	−	0.506477i	−0.681966	−	0.731384i	$-0.738875\pi$
$359$	5.54047	−	9.59637i	0.292415	−	0.506477i	0.974380	+	0.224907i	$0.0722079\pi$
$360$		0			0
$361$	−9.48475	−	16.4281i	−0.499197	−	0.864635i
$362$		0			0
$363$	0.543715	−	9.07441i	0.0285376	−	0.476283i
$364$		0			0
$365$	12.1109	−	0.266981i	0.633913	−	0.0139744i
$366$		0			0
$367$	7.58247	+	2.03172i	0.395802	+	0.106055i	0.451230	−	0.892408i	$-0.350986\pi$
$367$	7.58247	+	2.03172i	0.395802	+	0.106055i	−0.0554277	+	0.998463i	$0.517652\pi$
$368$		0			0
$369$	−4.28829	−	3.21481i	−0.223239	−	0.167356i
$370$		0			0
$371$	26.4760	−	13.7855i	1.37456	−	0.715710i
$372$		0			0
$373$	10.5435	−	2.82512i	0.545921	−	0.146279i	0.0246907	−	0.999695i	$-0.492140\pi$
$373$	10.5435	−	2.82512i	0.545921	−	0.146279i	0.521230	+	0.853416i	$0.325473\pi$
$374$		0			0
$375$	18.7362	+	4.89449i	0.967532	+	0.252750i
$376$		0			0
$377$	−15.7159	−	15.7159i	−0.809410	−	0.809410i
$378$		0			0
$379$		−	16.7144i		−	0.858560i	−0.903172	−	0.429280i	$-0.858767\pi$
$379$		−	16.7144i		−	0.858560i	0.903172	−	0.429280i	$-0.141233\pi$
$380$		0			0
$381$	11.3946	−	34.1957i	0.583762	−	1.75190i
$382$		0			0
$383$	−3.30792	−	12.3453i	−0.169027	−	0.630817i	−0.997492	−	0.0707764i	$-0.977452\pi$
$383$	−3.30792	−	12.3453i	−0.169027	−	0.630817i	0.828465	−	0.560040i	$-0.189214\pi$
$384$		0			0
$385$	−14.1848	−	0.305046i	−0.722925	−	0.0155466i
$386$		0			0
$387$	−10.3351	+	1.47867i	−0.525363	+	0.0751648i
$388$		0			0
$389$	−17.5206	−	30.3465i	−0.888327	−	1.53863i	−0.841852	−	0.539709i	$-0.818534\pi$
$389$	−17.5206	−	30.3465i	−0.888327	−	1.53863i	−0.0464754	−	0.998919i	$-0.514799\pi$
$390$		0			0
$391$	−6.15447			−0.311245
$392$		0			0
$393$	−23.2912	−	1.39555i	−1.17489	−	0.0703962i
$394$		0			0
$395$	3.38616	−	13.8516i	0.170376	−	0.696948i
$396$		0			0
$397$	−0.529982	−	1.97792i	−0.0265990	−	0.0992690i	0.951350	−	0.308112i	$-0.0996970\pi$
$397$	−0.529982	−	1.97792i	−0.0265990	−	0.0992690i	−0.977949	+	0.208843i	$0.933030\pi$
$398$		0			0
$399$	0.621311	−	0.504498i	0.0311044	−	0.0252565i
$400$		0			0
$401$	13.0417	+	7.52965i	0.651273	+	0.376013i	0.788944	−	0.614465i	$-0.210628\pi$
$401$	13.0417	+	7.52965i	0.651273	+	0.376013i	−0.137671	+	0.990478i	$0.543962\pi$
$402$		0			0
$403$	−3.12426	+	11.6599i	−0.155630	+	0.580820i
$404$		0			0
$405$	16.9640	−	10.8269i	0.842948	−	0.537994i
$406$		0			0
$407$	−19.3073	−	19.3073i	−0.957025	−	0.957025i
$408$		0			0
$409$	8.10578	−	4.67987i	0.400805	−	0.231405i	−0.286026	−	0.958222i	$-0.592334\pi$
$409$	8.10578	−	4.67987i	0.400805	−	0.231405i	0.686831	+	0.726817i	$0.259001\pi$
$410$		0			0
$411$	4.62070	+	22.5681i	0.227922	+	1.11320i
$412$		0			0
$413$	10.4269	+	3.28654i	0.513073	+	0.161720i
$414$		0			0
$415$	−8.45772	−	4.63759i	−0.415173	−	0.227650i
$416$		0			0
$417$	3.55011	+	7.09836i	0.173850	+	0.347608i
$418$		0			0
$419$	20.7118			1.01184			0.505919	−	0.862581i	$-0.331153\pi$
$419$	20.7118			1.01184			0.505919	+	0.862581i	$0.331153\pi$
$420$		0			0
$421$	18.3198			0.892851			0.446426	−	0.894821i	$-0.352697\pi$
$421$	18.3198			0.892851			0.446426	+	0.894821i	$0.352697\pi$
$422$		0			0
$423$	8.94135	−	22.2897i	0.434743	−	1.08376i
$424$		0			0
$425$	−7.39414	−	23.4146i	−0.358669	−	1.13577i
$426$		0			0
$427$	−3.98526	−	17.9687i	−0.192860	−	0.869565i
$428$		0			0
$429$	19.4433	−	3.98092i	0.938732	−	0.192200i
$430$		0			0
$431$	−0.725507	+	0.418872i	−0.0349464	+	0.0201763i	−0.517371	−	0.855761i	$-0.673089\pi$
$431$	−0.725507	+	0.418872i	−0.0349464	+	0.0201763i	0.482425	+	0.875937i	$0.339756\pi$
$432$		0			0
$433$	11.5356	+	11.5356i	0.554366	+	0.554366i	0.927698	−	0.373332i	$-0.121785\pi$
$433$	11.5356	+	11.5356i	0.554366	+	0.554366i	−0.373332	+	0.927698i	$0.621785\pi$
$434$		0			0
$435$	12.2488	+	13.2118i	0.587284	+	0.633456i
$436$		0			0
$437$	0.0566492	−	0.211418i	0.00270990	−	0.0101135i
$438$		0			0
$439$	27.5755	+	15.9207i	1.31611	+	0.759855i	0.983100	−	0.183069i	$-0.0586032\pi$
$439$	27.5755	+	15.9207i	1.31611	+	0.759855i	0.333008	+	0.942924i	$0.391937\pi$
$440$		0			0
$441$	−15.6434	−	14.0101i	−0.744923	−	0.667150i
$442$		0			0
$443$	8.59035	+	32.0596i	0.408140	+	1.52320i	0.798191	+	0.602405i	$0.205791\pi$
$443$	8.59035	+	32.0596i	0.408140	+	1.52320i	−0.390051	+	0.920793i	$0.627543\pi$
$444$		0			0
$445$	−11.2136	−	2.74128i	−0.531575	−	0.129949i
$446$		0			0
$447$	0.743295	−	12.4053i	0.0351566	−	0.586752i
$448$		0			0
$449$	32.3879			1.52848			0.764239	−	0.644933i	$-0.223115\pi$
$449$	32.3879			1.52848			0.764239	+	0.644933i	$0.223115\pi$
$450$		0			0
$451$	2.14222	+	3.71044i	0.100873	+	0.174718i
$452$		0			0
$453$	−6.21815	−	4.10462i	−0.292154	−	0.192852i
$454$		0			0
$455$	6.72717	+	27.4543i	0.315375	+	1.28708i
$456$		0			0
$457$	−4.93026	−	18.4000i	−0.230628	−	0.860716i	−0.980071	−	0.198647i	$-0.936345\pi$
$457$	−4.93026	−	18.4000i	−0.230628	−	0.860716i	0.749443	−	0.662069i	$-0.230321\pi$
$458$		0			0
$459$	−23.0725	−	10.8998i	−1.07693	−	0.508759i
$460$		0			0
$461$			24.9156i			1.16044i	0.814461	+	0.580218i	$0.197033\pi$
$461$			24.9156i			1.16044i	−0.814461	+	0.580218i	$0.802967\pi$
$462$		0			0
$463$	−12.6420	−	12.6420i	−0.587524	−	0.587524i	0.349436	−	0.936960i	$-0.386373\pi$
$463$	−12.6420	−	12.6420i	−0.587524	−	0.587524i	−0.936960	+	0.349436i	$0.886373\pi$
$464$		0			0
$465$	2.88795	−	9.34908i	0.133926	−	0.433553i
$466$		0			0
$467$	−11.7193	+	3.14017i	−0.542303	+	0.145310i	−0.519563	−	0.854432i	$-0.673905\pi$
$467$	−11.7193	+	3.14017i	−0.542303	+	0.145310i	−0.0227391	+	0.999741i	$0.507239\pi$
$468$		0			0
$469$	−28.3098	+	14.7404i	−1.30723	+	0.680649i
$470$		0			0
$471$	−15.0844	+	3.08846i	−0.695053	+	0.142309i
$472$		0			0
$473$	8.06172	+	2.16013i	0.370678	+	0.0993229i
$474$		0			0
$475$	0.872395	−	0.0384821i	0.0400282	−	0.00176568i
$476$		0			0
$477$	26.6197	−	20.9042i	1.21883	−	0.957137i
$478$		0			0
$479$	3.14571	+	5.44853i	0.143731	+	0.248950i	0.928899	−	0.370333i	$-0.120757\pi$
$479$	3.14571	+	5.44853i	0.143731	+	0.248950i	−0.785168	+	0.619283i	$0.787423\pi$
$480$		0			0
$481$	−27.1989	+	47.1100i	−1.24017	+	2.14803i
$482$		0			0
$483$	−5.71238	−	0.592709i	−0.259922	−	0.0269692i
$484$		0			0
$485$	−7.50702	−	4.11630i	−0.340876	−	0.186911i
$486$		0			0
$487$	−21.0669	−	5.64485i	−0.954632	−	0.255793i	−0.252305	−	0.967648i	$-0.581189\pi$
$487$	−21.0669	−	5.64485i	−0.954632	−	0.255793i	−0.702326	+	0.711855i	$0.747855\pi$
$488$		0			0
$489$	−7.67371	+	6.80612i	−0.347017	+	0.307783i
$490$		0			0
$491$			18.6876i			0.843358i	0.906745	+	0.421679i	$0.138559\pi$
$491$			18.6876i			0.843358i	−0.906745	+	0.421679i	$0.861441\pi$
$492$		0			0
$493$	5.91251	−	22.0658i	0.266286	−	0.993793i
$494$		0			0
$495$	−15.8715	+	2.62895i	−0.713373	+	0.118163i
$496$		0			0
$497$	−28.5908	−	31.1957i	−1.28247	−	1.39932i
$498$		0			0
$499$	9.45427	+	5.45843i	0.423231	+	0.244353i	0.696459	−	0.717597i	$-0.254758\pi$
$499$	9.45427	+	5.45843i	0.423231	+	0.244353i	−0.273228	+	0.961949i	$0.588091\pi$
$500$		0			0
$501$	−37.5304	−	12.5057i	−1.67673	−	0.558715i
$502$		0			0
$503$	8.52544	−	8.52544i	0.380131	−	0.380131i	−0.491018	−	0.871149i	$-0.663375\pi$
$503$	8.52544	−	8.52544i	0.380131	−	0.380131i	0.871149	+	0.491018i	$0.163375\pi$
$504$		0			0
$505$	−1.93698	−	1.85342i	−0.0861946	−	0.0824763i
$506$		0			0
$507$	−7.61458	−	15.2251i	−0.338175	−	0.676172i
$508$		0			0
$509$	−16.6925	+	28.9123i	−0.739883	+	1.28151i	0.212665	+	0.977125i	$0.431786\pi$
$509$	−16.6925	+	28.9123i	−0.739883	+	1.28151i	−0.952548	+	0.304389i	$0.901548\pi$
$510$		0			0
$511$	−6.61952	−	12.7132i	−0.292831	−	0.562398i
$512$		0			0
$513$	0.586802	−	0.692258i	0.0259080	−	0.0305640i
$514$		0			0
$515$	6.26927	+	10.3262i	0.276257	+	0.455027i
$516$		0			0
$517$	−13.5756	+	13.5756i	−0.597054	+	0.597054i
$518$		0			0
$519$	29.5596	+	33.3276i	1.29752	+	1.46292i
$520$		0			0
$521$	14.3052	−	8.25910i	0.626722	−	0.361838i	−0.152760	−	0.988263i	$-0.548816\pi$
$521$	14.3052	−	8.25910i	0.626722	−	0.361838i	0.779481	+	0.626425i	$0.215483\pi$
$522$		0			0
$523$	−1.67830	+	0.449698i	−0.0733868	+	0.0196639i	−0.295326	−	0.955397i	$-0.595428\pi$
$523$	−1.67830	+	0.449698i	−0.0733868	+	0.0196639i	0.221939	+	0.975061i	$0.428761\pi$
$524$		0			0
$525$	−4.60805	−	22.4447i	−0.201112	−	0.979568i
$526$		0			0
$527$	−11.9844	+	3.21120i	−0.522048	+	0.139882i
$528$		0			0
$529$	18.5584	−	10.7147i	0.806887	−	0.465857i
$530$		0			0
$531$	12.3077	+	1.48020i	0.534107	+	0.0642352i
$532$		0			0
$533$	6.03568	−	6.03568i	0.261434	−	0.261434i
$534$		0			0
$535$	11.5068	+	18.9530i	0.497483	+	0.819411i
$536$		0			0
$537$	28.7926	+	19.0061i	1.24249	+	0.820173i
$538$		0			0
$539$	7.09749	+	15.2134i	0.305710	+	0.655289i
$540$		0			0
$541$	−1.62294	+	2.81101i	−0.0697756	+	0.120855i	−0.898802	−	0.438354i	$-0.855562\pi$
$541$	−1.62294	+	2.81101i	−0.0697756	+	0.120855i	0.829027	+	0.559209i	$0.188895\pi$
$542$		0			0
$543$	−25.4998	+	12.7532i	−1.09430	+	0.547294i
$544$		0			0
$545$	24.5205	+	23.4628i	1.05034	+	1.00503i
$546$		0			0
$547$	17.2003	−	17.2003i	0.735434	−	0.735434i	−0.236257	−	0.971691i	$-0.575921\pi$
$547$	17.2003	−	17.2003i	0.735434	−	0.735434i	0.971691	+	0.236257i	$0.0759207\pi$
$548$		0			0
$549$	−8.20207	−	19.1903i	−0.350056	−	0.819023i
$550$		0			0
$551$	0.703580	+	0.406212i	0.0299735	+	0.0173052i
$552$		0			0
$553$	−16.4717	+	3.65326i	−0.700450	+	0.155352i
$554$		0			0
$555$	23.4751	−	37.3269i	0.996465	−	1.58444i
$556$		0			0
$557$	−5.16955	+	19.2930i	−0.219041	+	0.817472i	0.765664	+	0.643241i	$0.222411\pi$
$557$	−5.16955	+	19.2930i	−0.219041	+	0.817472i	−0.984705	+	0.174231i	$0.944256\pi$
$558$		0			0
$559$		−	16.6276i		−	0.703274i
$560$		0			0
$561$	13.5357	+	15.2612i	0.571479	+	0.644327i
$562$		0			0
$563$	−36.1653	−	9.69046i	−1.52419	−	0.408404i	−0.603068	−	0.797690i	$-0.706055\pi$
$563$	−36.1653	−	9.69046i	−1.52419	−	0.408404i	−0.921117	+	0.389285i	$0.872722\pi$
$564$		0			0
$565$	31.4455	+	17.2424i	1.32292	+	0.725394i
$566$		0			0
$567$	−20.3655	−	12.3389i	−0.855270	−	0.518183i
$568$		0			0
$569$	−8.83961	+	15.3107i	−0.370576	+	0.641856i	−0.989654	−	0.143473i	$-0.954173\pi$
$569$	−8.83961	+	15.3107i	−0.370576	+	0.641856i	0.619078	+	0.785329i	$0.287506\pi$
$570$		0			0
$571$	9.16309	+	15.8709i	0.383463	+	0.664178i	0.991555	−	0.129689i	$-0.0413980\pi$
$571$	9.16309	+	15.8709i	0.383463	+	0.664178i	−0.608092	+	0.793867i	$0.708065\pi$
$572$		0			0
$573$	3.12176	+	0.187047i	0.130413	+	0.00781401i
$574$		0			0
$575$	−4.62181	−	4.23129i	−0.192743	−	0.176457i
$576$		0			0
$577$	10.0271	+	2.68675i	0.417433	+	0.111851i	0.461421	−	0.887181i	$-0.347340\pi$
$577$	10.0271	+	2.68675i	0.417433	+	0.111851i	−0.0439883	+	0.999032i	$0.514006\pi$
$578$		0			0
$579$	1.85594	+	9.06466i	0.0771303	+	0.376715i
$580$		0			0
$581$	−0.496798	+	11.4022i	−0.0206107	+	0.473042i
$582$		0			0
$583$	−26.1353	+	7.00294i	−1.08242	+	0.290032i
$584$		0			0
$585$	13.2430	+	29.1873i	0.547532	+	1.20674i
$586$		0			0
$587$	16.5786	+	16.5786i	0.684270	+	0.684270i	0.960959	−	0.276689i	$-0.0892372\pi$
$587$	16.5786	+	16.5786i	0.684270	+	0.684270i	−0.276689	+	0.960959i	$0.589237\pi$
$588$		0			0
$589$		−	0.441244i		−	0.0181812i
$590$		0			0
$591$	35.1481	+	11.7119i	1.44580	+	0.481764i
$592$		0			0
$593$	3.59418	+	13.4136i	0.147595	+	0.550832i	0.999626	+	0.0273412i	$0.00870405\pi$
$593$	3.59418	+	13.4136i	0.147595	+	0.550832i	−0.852031	+	0.523491i	$0.824629\pi$
$594$		0			0
$595$	−20.9806	+	20.0972i	−0.860119	+	0.823904i
$596$		0			0
$597$	2.32352	−	3.51994i	0.0950955	−	0.144062i
$598$		0			0
$599$	1.15232	+	1.99588i	0.0470827	+	0.0815496i	0.888606	−	0.458671i	$-0.151674\pi$
$599$	1.15232	+	1.99588i	0.0470827	+	0.0815496i	−0.841524	+	0.540220i	$0.818341\pi$
$600$		0			0
$601$	−7.55165			−0.308038			−0.154019	−	0.988068i	$-0.549222\pi$
$601$	−7.55165			−0.308038			−0.154019	+	0.988068i	$0.549222\pi$
$602$		0			0
$603$	−28.4635	+	22.3521i	−1.15913	+	0.910249i
$604$		0			0
$605$	−11.4003	−	2.78693i	−0.463489	−	0.113305i
$606$		0			0
$607$	8.51167	+	31.7660i	0.345478	+	1.28934i	0.892053	+	0.451932i	$0.149265\pi$
$607$	8.51167	+	31.7660i	0.345478	+	1.28934i	−0.546574	+	0.837411i	$0.684068\pi$
$608$		0			0
$609$	7.61285	−	19.9113i	0.308488	−	0.806848i
$610$		0			0
$611$	33.1246	+	19.1245i	1.34008	+	0.773695i
$612$		0			0
$613$	−5.32864	+	19.8867i	−0.215222	+	0.803218i	0.770867	+	0.636996i	$0.219823\pi$
$613$	−5.32864	+	19.8867i	−0.215222	+	0.803218i	−0.986088	+	0.166222i	$0.946843\pi$
$614$		0			0
$615$	−5.07397	+	4.70413i	−0.204602	+	0.189689i
$616$		0			0
$617$	21.0456	+	21.0456i	0.847265	+	0.847265i	0.989791	−	0.142526i	$-0.0455224\pi$
$617$	21.0456	+	21.0456i	0.847265	+	0.847265i	−0.142526	+	0.989791i	$0.545522\pi$
$618$		0			0
$619$	−24.1068	+	13.9181i	−0.968933	+	0.559414i	−0.898911	−	0.438132i	$-0.855640\pi$
$619$	−24.1068	+	13.9181i	−0.968933	+	0.559414i	−0.0700222	+	0.997545i	$0.522307\pi$
$620$		0			0
$621$	−6.48998	+	0.535086i	−0.260434	+	0.0214723i
$622$		0			0
$623$	2.95751	+	13.3348i	0.118490	+	0.534246i
$624$		0			0
$625$	10.5451	−	22.6672i	0.421804	−	0.906687i
$626$		0			0
$627$	−0.648841	+	0.324506i	−0.0259122	+	0.0129595i
$628$		0			0
$629$	−55.9118			−2.22935
$630$		0			0
$631$	43.7136			1.74021			0.870105	−	0.492867i	$-0.164051\pi$
$631$	43.7136			1.74021			0.870105	+	0.492867i	$0.164051\pi$
$632$		0			0
$633$	−21.3901	+	10.6979i	−0.850181	+	0.425202i
$634$		0			0
$635$	−40.8016	−	22.3726i	−1.61916	−	0.887831i
$636$		0			0
$637$	25.6167	−	21.5028i	1.01497	−	0.851974i
$638$		0			0
$639$	−38.3911	−	28.7807i	−1.51873	−	1.13855i
$640$		0			0
$641$	−3.97235	+	2.29344i	−0.156898	+	0.0905854i	−0.576394	−	0.817172i	$-0.695540\pi$
$641$	−3.97235	+	2.29344i	−0.156898	+	0.0905854i	0.419495	+	0.907758i	$0.362207\pi$
$642$		0			0
$643$	18.3311	+	18.3311i	0.722906	+	0.722906i	0.969196	−	0.246290i	$-0.0792115\pi$
$643$	18.3311	+	18.3311i	0.722906	+	0.722906i	−0.246290	+	0.969196i	$0.579212\pi$
$644$		0			0
$645$	−0.509426	+	13.4688i	−0.0200586	+	0.530333i
$646$		0			0
$647$	11.2932	−	42.1467i	0.443980	−	1.65696i	−0.274635	−	0.961549i	$-0.588557\pi$
$647$	11.2932	−	42.1467i	0.443980	−	1.65696i	0.718615	−	0.695408i	$-0.244776\pi$
$648$		0			0
$649$	−8.58210	−	4.95488i	−0.336877	−	0.194496i
$650$		0			0
$651$	−11.4328	+	1.82637i	−0.448086	+	0.0715813i
$652$		0			0
$653$	3.76895	+	14.0659i	0.147490	+	0.550442i	0.999632	+	0.0271304i	$0.00863693\pi$
$653$	3.76895	+	14.0659i	0.147490	+	0.550442i	−0.852141	+	0.523312i	$0.824696\pi$
$654$		0			0
$655$	−7.15319	+	29.2611i	−0.279498	+	1.14333i
$656$		0			0
$657$	−10.0377	−	12.7822i	−0.391610	−	0.498682i
$658$		0			0
$659$	19.4487			0.757615			0.378808	−	0.925475i	$-0.376334\pi$
$659$	19.4487			0.757615			0.378808	+	0.925475i	$0.376334\pi$
$660$		0			0
$661$	−15.9402	−	27.6092i	−0.620001	−	1.07387i	−0.989485	−	0.144637i	$-0.953799\pi$
$661$	−15.9402	−	27.6092i	−0.620001	−	1.07387i	0.369483	−	0.929237i	$-0.379535\pi$
$662$		0			0
$663$	22.3887	−	33.9171i	0.869507	−	1.31723i
$664$		0			0
$665$	−0.497260	−	0.905709i	−0.0192829	−	0.0351219i
$666$		0			0
$667$	−1.50885	−	5.63111i	−0.0584229	−	0.218037i
$668$		0			0
$669$	40.9242	+	13.6366i	1.58222	+	0.527222i
$670$		0			0
$671$			16.6834i			0.644055i
$672$		0			0
$673$	13.2491	+	13.2491i	0.510715	+	0.510715i	0.914745	−	0.404031i	$-0.132391\pi$
$673$	13.2491	+	13.2491i	0.510715	+	0.510715i	−0.404031	+	0.914745i	$0.632391\pi$
$674$		0			0
$675$	−9.83296	−	24.0481i	−0.378471	−	0.925613i
$676$		0			0
$677$	−9.15724	+	2.45368i	−0.351941	+	0.0943024i	−0.430459	−	0.902610i	$-0.641648\pi$
$677$	−9.15724	+	2.45368i	−0.351941	+	0.0943024i	0.0785172	+	0.996913i	$0.474981\pi$
$678$		0			0
$679$	−0.440955	+	10.1205i	−0.0169223	+	0.388389i
$680$		0			0
$681$	−2.27363	−	11.1047i	−0.0871257	−	0.425533i
$682$		0			0
$683$	3.24333	+	0.869046i	0.124102	+	0.0332531i	0.320336	−	0.947304i	$-0.396204\pi$
$683$	3.24333	+	0.869046i	0.124102	+	0.0332531i	−0.196233	+	0.980557i	$0.562871\pi$
$684$		0			0
$685$	29.7325	−	0.655444i	1.13602	−	0.0250432i
$686$		0			0
$687$	41.6096	+	2.49314i	1.58751	+	0.0951192i
$688$		0			0
$689$	26.9526	+	46.6833i	1.02681	+	1.77849i
$690$		0			0
$691$	0.681637	−	1.18063i	0.0259307	−	0.0449133i	−0.852769	−	0.522289i	$-0.825078\pi$
$691$	0.681637	−	1.18063i	0.0259307	−	0.0449133i	0.878700	+	0.477375i	$0.158412\pi$
$692$		0			0
$693$	11.0937	+	15.4685i	0.421415	+	0.587599i
$694$		0			0
$695$	9.83616	−	2.86937i	0.373107	−	0.108842i
$696$		0			0
$697$	8.47434	+	2.27069i	0.320989	+	0.0860086i
$698$		0			0
$699$	−2.31177	−	2.60646i	−0.0874391	−	0.0985852i
$700$		0			0
$701$		−	16.8670i		−	0.637057i	−0.947913	−	0.318528i	$-0.896811\pi$
$701$		−	16.8670i		−	0.637057i	0.947913	−	0.318528i	$-0.103189\pi$
$702$		0			0
$703$	0.514644	−	1.92068i	0.0194102	−	0.0724397i
$704$		0			0
$705$	−26.2458	−	16.5062i	−0.988476	−	0.621659i
$706$		0			0
$707$	−0.953582	+	3.02533i	−0.0358631	+	0.113779i
$708$		0			0
$709$	6.24998	+	3.60843i	0.234723	+	0.135517i	0.612749	−	0.790278i	$-0.290064\pi$
$709$	6.24998	+	3.60843i	0.234723	+	0.135517i	−0.378026	+	0.925795i	$0.623397\pi$
$710$		0			0
$711$	−17.5916	+	7.51878i	−0.659738	+	0.281976i
$712$		0			0
$713$	−2.23888	+	2.23888i	−0.0838468	+	0.0838468i
$714$		0			0
$715$	−0.564691	−	25.6157i	−0.0211183	−	0.957974i
$716$		0			0
$717$	−15.7162	+	7.86018i	−0.586933	+	0.293544i
$718$		0			0
$719$	−12.0886	+	20.9381i	−0.450829	+	0.780858i	−0.998438	−	0.0558760i	$-0.982205\pi$
$719$	−12.0886	+	20.9381i	−0.450829	+	0.780858i	0.547609	+	0.836734i	$0.315538\pi$
$720$		0			0
$721$	7.67888	−	12.0558i	0.285977	−	0.448983i
$722$		0			0
$723$	−32.2636	−	21.2973i	−1.19990	−	0.792055i
$724$		0			0
$725$	19.6107	−	12.5058i	0.728322	−	0.464452i
$726$		0			0
$727$	20.9329	−	20.9329i	0.776359	−	0.776359i	−0.202850	−	0.979210i	$-0.565021\pi$
$727$	20.9329	−	20.9329i	0.776359	−	0.776359i	0.979210	+	0.202850i	$0.0650205\pi$
$728$		0			0
$729$	−25.2780	−	9.48802i	−0.936222	−	0.351408i
$730$		0			0
$731$	14.8007	−	8.54519i	0.547424	−	0.316055i
$732$		0			0
$733$	−17.3380	+	4.64570i	−0.640393	+	0.171593i	−0.564381	−	0.825514i	$-0.690885\pi$
$733$	−17.3380	+	4.64570i	−0.640393	+	0.171593i	−0.0760117	+	0.997107i	$0.524219\pi$
$734$		0			0
$735$	−21.4089	+	16.6330i	−0.789681	+	0.613518i
$736$		0			0
$737$	27.9456	−	7.48801i	1.02939	−	0.275824i
$738$		0			0
$739$	19.9418	−	11.5134i	0.733569	−	0.423526i	−0.0861572	−	0.996282i	$-0.527459\pi$
$739$	19.9418	−	11.5134i	0.733569	−	0.423526i	0.819727	+	0.572755i	$0.194125\pi$
$740$		0			0
$741$	0.959038	+	1.08129i	0.0352311	+	0.0397221i
$742$		0			0
$743$	−14.5081	+	14.5081i	−0.532251	+	0.532251i	−0.921242	−	0.388990i	$-0.872824\pi$
$743$	−14.5081	+	14.5081i	−0.532251	+	0.532251i	0.388990	+	0.921242i	$0.372824\pi$
$744$		0			0
$745$	−15.5850	−	3.80992i	−0.570991	−	0.139585i
$746$		0			0
$747$	1.83285	+	12.8107i	0.0670605	+	0.468718i
$748$		0			0
$749$	14.0940	−	22.1276i	0.514985	−	0.808526i
$750$		0			0
$751$	15.6139	−	27.0440i	0.569758	−	0.986850i	−0.426831	−	0.904331i	$-0.640370\pi$
$751$	15.6139	−	27.0440i	0.569758	−	0.986850i	0.996590	−	0.0825187i	$-0.0262964\pi$
$752$		0			0
$753$	−3.39201	−	6.78223i	−0.123612	−	0.247158i
$754$		0			0
$755$	−6.65000	+	6.94980i	−0.242018	+	0.252929i
$756$		0			0
$757$	−8.35485	+	8.35485i	−0.303662	+	0.303662i	−0.842445	−	0.538783i	$-0.818884\pi$
$757$	−8.35485	+	8.35485i	−0.303662	+	0.303662i	0.538783	+	0.842445i	$0.318884\pi$
$758$		0			0
$759$	4.93878	+	1.64568i	0.179266	+	0.0597345i
$760$		0			0
$761$	−16.1307	−	9.31307i	−0.584738	−	0.337598i	0.178276	−	0.983980i	$-0.442948\pi$
$761$	−16.1307	−	9.31307i	−0.584738	−	0.337598i	−0.763014	+	0.646382i	$0.776281\pi$
$762$		0			0
$763$	12.0715	−	38.2980i	0.437018	−	1.38648i
$764$		0			0
$765$	−19.1746	+	26.7877i	−0.693258	+	0.968513i
$766$		0			0
$767$	−5.10982	+	19.0701i	−0.184505	+	0.688582i
$768$		0			0
$769$		−	6.68431i		−	0.241042i	−0.992711	−	0.120521i	$-0.961543\pi$
$769$		−	6.68431i		−	0.241042i	0.992711	−	0.120521i	$-0.0384566\pi$
$770$		0			0
$771$	3.20116	−	2.83924i	0.115287	−	0.102253i
$772$		0			0
$773$	−1.88008	−	0.503766i	−0.0676217	−	0.0181192i	0.224850	−	0.974393i	$-0.427811\pi$
$773$	−1.88008	−	0.503766i	−0.0676217	−	0.0181192i	−0.292471	+	0.956274i	$0.594478\pi$
$774$		0			0
$775$	−11.2076	−	5.82793i	−0.402590	−	0.209346i
$776$		0			0
$777$	−51.8955	−	5.38461i	−1.86174	−	0.193172i
$778$		0			0
$779$	−0.156005	+	0.270209i	−0.00558947	+	0.00968125i
$780$		0			0
$781$	19.1783	+	33.2178i	0.686254	+	1.18863i
$782$		0			0
$783$	4.31637	−	23.7828i	0.154255	−	0.849926i
$784$		0			0
$785$	0.438096	+	19.8731i	0.0156363	+	0.709300i
$786$		0			0
$787$	−33.8914	−	9.08117i	−1.20810	−	0.323709i	−0.402082	−	0.915604i	$-0.631713\pi$
$787$	−33.8914	−	9.08117i	−1.20810	−	0.323709i	−0.806015	+	0.591895i	$0.798380\pi$
$788$		0			0
$789$	−0.514808	+	0.105404i	−0.0183277	+	0.00375249i
$790$		0			0
$791$	1.84708	−	42.3929i	0.0656746	−	1.50732i
$792$		0			0
$793$	32.1052	−	8.60255i	1.14009	−	0.305486i
$794$		0			0
$795$	−20.4020	−	38.6404i	−0.723586	−	1.37043i
$796$		0			0
$797$	9.84195	+	9.84195i	0.348620	+	0.348620i	0.859595	−	0.510975i	$-0.170716\pi$
$797$	9.84195	+	9.84195i	0.348620	+	0.348620i	−0.510975	+	0.859595i	$0.670716\pi$
$798$		0			0
$799$			39.3135i			1.39081i
$800$		0			0
$801$	6.08686	+	14.2414i	0.215069	+	0.503194i
$802$		0			0
$803$	3.36266	+	12.5496i	0.118666	+	0.442867i
$804$		0			0
$805$	−2.07248	+	7.11869i	−0.0730452	+	0.250901i
$806$		0			0
$807$	24.8578	+	16.4087i	0.875036	+	0.577614i
$808$		0			0
$809$	3.50324	+	6.06779i	0.123167	+	0.213332i	0.921015	−	0.389527i	$-0.127361\pi$
$809$	3.50324	+	6.06779i	0.123167	+	0.213332i	−0.797848	+	0.602859i	$0.794028\pi$
$810$		0			0
$811$	−49.1753			−1.72678			−0.863390	−	0.504538i	$-0.831663\pi$
$811$	−49.1753			−1.72678			−0.863390	+	0.504538i	$0.831663\pi$
$812$		0			0
$813$	1.01945	−	17.0143i	0.0357538	−	0.596718i
$814$		0			0
$815$	6.87210	+	11.3191i	0.240719	+	0.396492i
$816$		0			0
$817$	0.157310	+	0.587087i	0.00550357	+	0.0205396i
$818$		0			0
$819$	24.0469	−	29.3246i	0.840267	−	1.02468i
$820$		0			0
$821$	5.37009	+	3.10042i	0.187417	+	0.108206i	0.590773	−	0.806838i	$-0.298823\pi$
$821$	5.37009	+	3.10042i	0.187417	+	0.108206i	−0.403356	+	0.915043i	$0.632156\pi$
$822$		0			0
$823$	3.00839	−	11.2275i	0.104866	−	0.391365i	−0.893464	−	0.449135i	$-0.851732\pi$
$823$	3.00839	−	11.2275i	0.104866	−	0.391365i	0.998330	+	0.0577701i	$0.0183990\pi$
$824$		0			0
$825$	−0.327383	+	20.7667i	−0.0113980	+	0.723003i
$826$		0			0
$827$	−30.1289	−	30.1289i	−1.04769	−	1.04769i	−0.998805	−	0.0488806i	$-0.984435\pi$
$827$	−30.1289	−	30.1289i	−1.04769	−	1.04769i	−0.0488806	−	0.998805i	$-0.515565\pi$
$828$		0			0
$829$	−11.1605	+	6.44350i	−0.387619	+	0.223792i	−0.681128	−	0.732164i	$-0.738510\pi$
$829$	−11.1605	+	6.44350i	−0.387619	+	0.223792i	0.293509	+	0.955956i	$0.405177\pi$
$830$		0			0
$831$	22.8503	−	4.67848i	0.792669	−	0.162295i
$832$		0			0
$833$	32.3050	+	11.7515i	1.11930	+	0.407164i
$834$		0			0
$835$	−24.5543	+	44.7805i	−0.849737	+	1.54969i
$836$		0			0
$837$	−12.3585	+	4.42822i	−0.427173	+	0.153062i
$838$		0			0
$839$	−6.48689			−0.223952			−0.111976	−	0.993711i	$-0.535718\pi$
$839$	−6.48689			−0.223952			−0.111976	+	0.993711i	$0.535718\pi$
$840$		0			0
$841$	−7.36110			−0.253831
$842$		0			0
$843$	18.9618	+	37.9136i	0.653079	+	1.30581i
$844$		0			0
$845$	−21.0974	+	6.15447i	−0.725773	+	0.211720i
$846$		0			0
$847$	3.00676	+	13.5568i	0.103313	+	0.465818i
$848$		0			0
$849$	2.35834	+	11.5184i	0.0809379	+	0.395311i
$850$		0			0
$851$	−12.3569	+	7.13424i	−0.423588	+	0.244559i
$852$		0			0
$853$	−14.9986	−	14.9986i	−0.513542	−	0.513542i	0.402068	−	0.915610i	$-0.368292\pi$
$853$	−14.9986	−	14.9986i	−0.513542	−	0.513542i	−0.915610	+	0.402068i	$0.868292\pi$
$854$		0			0
$855$	−0.743717	−	0.905253i	−0.0254346	−	0.0309590i
$856$		0			0
$857$	−5.49764	+	20.5175i	−0.187796	+	0.700864i	0.806219	+	0.591618i	$0.201510\pi$
$857$	−5.49764	+	20.5175i	−0.187796	+	0.700864i	−0.994015	+	0.109246i	$0.965156\pi$
$858$		0			0
$859$	−29.8226	−	17.2181i	−1.01753	−	0.587474i	−0.104146	−	0.994562i	$-0.533211\pi$
$859$	−29.8226	−	17.2181i	−1.01753	−	0.587474i	−0.913389	+	0.407088i	$0.866544\pi$
$860$		0			0
$861$	7.64693	+	2.92371i	0.260607	+	0.0996397i
$862$		0			0
$863$	−9.18477	−	34.2780i	−0.312653	−	1.16684i	−0.926155	−	0.377144i	$-0.876906\pi$
$863$	−9.18477	−	34.2780i	−0.312653	−	1.16684i	0.613501	−	0.789694i	$-0.289761\pi$
$864$		0			0
$865$	49.1601	−	29.8462i	1.67149	−	1.01480i
$866$		0			0
$867$	12.3042	+	0.737237i	0.417874	+	0.0250379i
$868$		0			0
$869$	15.2935			0.518798
$870$		0			0
$871$	−28.8195	−	49.9168i	−0.976512	−	1.69137i
$872$		0			0
$873$	1.62683	+	11.3707i	0.0550597	+	0.384839i
$874$		0			0
$875$	−29.5729	+	0.667883i	−0.999745	+	0.0225786i
$876$		0			0
$877$	12.2143	+	45.5843i	0.412446	+	1.53927i	0.789896	+	0.613241i	$0.210134\pi$
$877$	12.2143	+	45.5843i	0.412446	+	1.53927i	−0.377450	+	0.926030i	$0.623199\pi$
$878$		0			0
$879$	15.4839	−	46.4681i	0.522260	−	1.56733i
$880$		0			0
$881$		−	24.3717i		−	0.821105i	−0.911837	−	0.410552i	$-0.865336\pi$
$881$		−	24.3717i		−	0.821105i	0.911837	−	0.410552i	$-0.134664\pi$
$882$		0			0
$883$	7.59214	+	7.59214i	0.255496	+	0.255496i	0.823219	−	0.567723i	$-0.192176\pi$
$883$	7.59214	+	7.59214i	0.255496	+	0.255496i	−0.567723	+	0.823219i	$0.692176\pi$
$884$		0			0
$885$	4.72334	−	15.2907i	0.158773	−	0.513992i
$886$		0			0
$887$	40.4184	−	10.8301i	1.35712	−	0.363638i	0.494360	−	0.869258i	$-0.335403\pi$
$887$	40.4184	−	10.8301i	1.35712	−	0.363638i	0.862757	+	0.505619i	$0.168736\pi$
$888$		0			0
$889$	−2.39665	+	55.0062i	−0.0803810	+	1.84485i
$890$		0			0
$891$	15.6005	+	14.9163i	0.522636	+	0.499715i
$892$		0			0
$893$	−1.35049	−	0.361864i	−0.0451925	−	0.0121093i
$894$		0			0
$895$	30.7922	−	32.1804i	1.02927	−	1.07567i
$896$		0			0
$897$	0.620304	−	10.3527i	0.0207113	−	0.345665i
$898$		0			0
$899$	−5.87627	−	10.1780i	−0.195984	−	0.339455i
$900$		0			0
$901$	−27.7027	+	47.9825i	−0.922911	+	1.59853i
$902$		0			0
$903$	14.5605	−	6.50598i	0.484542	−	0.216505i
$904$		0			0
$905$	10.3078	+	35.3349i	0.342643	+	1.17457i
$906$		0			0
$907$	−30.1035	−	8.06620i	−0.999570	−	0.267834i	−0.278304	−	0.960493i	$-0.589772\pi$
$907$	−30.1035	−	8.06620i	−0.999570	−	0.267834i	−0.721265	+	0.692659i	$0.756439\pi$
$908$		0			0
$909$	−0.429476	+	3.57104i	−0.0142448	+	0.118444i
$910$		0			0
$911$		−	3.16590i		−	0.104891i	−0.998624	−	0.0524454i	$-0.983298\pi$
$911$		−	3.16590i		−	0.104891i	0.998624	−	0.0524454i	$-0.0167016\pi$
$912$		0			0
$913$	2.67755	−	9.99274i	0.0886138	−	0.330711i
$914$		0			0
$915$	−26.2695	+	5.98466i	−0.868444	+	0.197847i
$916$		0			0
$917$	34.7962	−	7.71743i	1.14907	−	0.254852i
$918$		0			0
$919$	−20.7512	−	11.9807i	−0.684520	−	0.395208i	0.117036	−	0.993128i	$-0.462661\pi$
$919$	−20.7512	−	11.9807i	−0.684520	−	0.395208i	−0.801556	+	0.597920i	$0.795994\pi$
$920$		0			0
$921$	4.35155	−	13.0593i	0.143389	−	0.430317i
$922$		0			0
$923$	54.0346	−	54.0346i	1.77857	−	1.77857i
$924$		0			0
$925$	−41.9880	−	38.4402i	−1.38056	−	1.26391i
$926$		0			0
$927$	6.03412	−	15.0423i	0.198186	−	0.494055i
$928$		0			0
$929$	−2.59475	+	4.49423i	−0.0851309	+	0.147451i	−0.905447	−	0.424459i	$-0.860464\pi$
$929$	−2.59475	+	4.49423i	−0.0851309	+	0.147451i	0.820316	+	0.571910i	$0.193798\pi$
$930$		0			0
$931$	−0.701040	+	1.00157i	−0.0229757	+	0.0328252i
$932$		0			0
$933$	28.8482	−	43.7026i	0.944448	−	1.43076i
$934$		0			0
$935$	22.5110	−	13.6669i	0.736189	−	0.446957i
$936$		0			0
$937$	−22.7185	+	22.7185i	−0.742180	+	0.742180i	−0.972997	−	0.230817i	$-0.925860\pi$
$937$	−22.7185	+	22.7185i	−0.742180	+	0.742180i	0.230817	+	0.972997i	$0.425860\pi$
$938$		0			0
$939$	13.9032	−	12.3313i	0.453713	−	0.402416i
$940$		0			0
$941$	14.4705	−	8.35457i	0.471726	−	0.272351i	−0.245236	−	0.969463i	$-0.578865\pi$
$941$	14.4705	−	8.35457i	0.471726	−	0.272351i	0.716962	+	0.697112i	$0.245532\pi$
$942$		0			0
$943$	2.16262	−	0.579473i	0.0704246	−	0.0188702i
$944$		0			0
$945$	−20.3770	+	23.0169i	−0.662864	+	0.748739i
$946$		0			0
$947$	−28.6499	+	7.67673i	−0.930998	+	0.249460i	−0.692280	−	0.721629i	$-0.743394\pi$
$947$	−28.6499	+	7.67673i	−0.930998	+	0.249460i	−0.238718	+	0.971089i	$0.576727\pi$
$948$		0			0
$949$	22.4163	−	12.9421i	0.727665	−	0.420117i
$950$		0			0
$951$	−13.7771	+	12.2194i	−0.446752	+	0.396242i
$952$		0			0
$953$	−2.59553	+	2.59553i	−0.0840774	+	0.0840774i	−0.747895	−	0.663817i	$-0.768935\pi$
$953$	−2.59553	+	2.59553i	−0.0840774	+	0.0840774i	0.663817	+	0.747895i	$0.268935\pi$
$954$		0			0
$955$	0.958752	−	3.92191i	0.0310245	−	0.126910i
$956$		0			0
$957$	−10.6449	+	16.1262i	−0.344102	+	0.521285i
$958$		0			0
$959$	−16.2510	−	31.2111i	−0.524774	−	1.00786i
$960$		0			0
$961$	12.3085	−	21.3189i	0.397048	−	0.687707i
$962$		0			0
$963$	11.0752	−	27.6091i	0.356893	−	0.889691i
$964$		0			0
$965$	11.9423	−	0.263264i	0.384436	−	0.00847478i
$966$		0			0
$967$	−25.3567	+	25.3567i	−0.815418	+	0.815418i	−0.985440	−	0.170022i	$-0.945616\pi$
$967$	−25.3567	+	25.3567i	−0.815418	+	0.815418i	0.170022	+	0.985440i	$0.445616\pi$
$968$		0			0
$969$	−0.469620	+	1.40936i	−0.0150864	+	0.0452750i
$970$		0			0
$971$	−11.9980	−	6.92703i	−0.385033	−	0.222299i	0.294973	−	0.955506i	$-0.404689\pi$
$971$	−11.9980	−	6.92703i	−0.385033	−	0.222299i	−0.680006	+	0.733207i	$0.738023\pi$
$972$		0			0
$973$	−8.19125	−	8.93756i	−0.262600	−	0.286525i
$974$		0			0
$975$	40.1317	−	10.0780i	1.28524	−	0.322755i
$976$		0			0
$977$	−3.24035	+	12.0931i	−0.103668	+	0.386894i	−0.998191	−	0.0601286i	$-0.980849\pi$
$977$	−3.24035	+	12.0931i	−0.103668	+	0.386894i	0.894523	+	0.447022i	$0.147516\pi$
$978$		0			0
$979$		−	12.3810i		−	0.395697i
$980$		0			0
$981$	5.43680	−	45.2063i	0.173584	−	1.44332i
$982$		0			0
$983$	3.08717	+	0.827204i	0.0984653	+	0.0263837i	0.307715	−	0.951478i	$-0.400436\pi$
$983$	3.08717	+	0.827204i	0.0984653	+	0.0263837i	−0.209250	+	0.977862i	$0.567102\pi$
$984$		0			0
$985$	22.9957	−	41.9380i	0.732705	−	1.33626i
$986$		0			0
$987$	−3.78610	+	36.4895i	−0.120513	+	1.16147i
$988$		0			0
$989$	2.18070	−	3.77708i	0.0693422	−	0.120104i
$990$		0			0
$991$	−18.1183	−	31.3818i	−0.575547	−	0.996877i	−0.995982	−	0.0895543i	$-0.971456\pi$
$991$	−18.1183	−	31.3818i	−0.575547	−	0.996877i	0.420435	−	0.907323i	$-0.361878\pi$
$992$		0			0
$993$	0.0429895	−	0.717480i	0.00136423	−	0.0227685i
$994$		0			0
$995$	−3.93411	−	3.76440i	−0.124720	−	0.119340i
$996$		0			0
$997$	12.7896	+	3.42696i	0.405051	+	0.108533i	0.455591	−	0.890189i	$-0.349428\pi$
$997$	12.7896	+	3.42696i	0.405051	+	0.108533i	−0.0505407	+	0.998722i	$0.516094\pi$
$998$		0			0
$999$	−58.9598	+	4.86112i	−1.86541	+	0.153799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.c.233.2	yes	48
3.2	odd	2	inner	420.2.bv.c.233.9	yes	48
5.2	odd	4	inner	420.2.bv.c.317.9	yes	48
7.4	even	3	inner	420.2.bv.c.53.11	yes	48
15.2	even	4	inner	420.2.bv.c.317.11	yes	48
21.11	odd	6	inner	420.2.bv.c.53.9	✓	48
35.32	odd	12	inner	420.2.bv.c.137.9	yes	48
105.32	even	12	inner	420.2.bv.c.137.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.9	✓	48	21.11	odd	6	inner
420.2.bv.c.53.11	yes	48	7.4	even	3	inner
420.2.bv.c.137.2	yes	48	105.32	even	12	inner
420.2.bv.c.137.9	yes	48	35.32	odd	12	inner
420.2.bv.c.233.2	yes	48	1.1	even	1	trivial
420.2.bv.c.233.9	yes	48	3.2	odd	2	inner
420.2.bv.c.317.9	yes	48	5.2	odd	4	inner
420.2.bv.c.317.11	yes	48	15.2	even	4	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54911 + 0.774760i) q^{3} +(0.626199 + 2.14660i) q^{5} +(1.95049 - 1.78762i) q^{7} +(1.79949 - 2.40038i) q^{9} +O(q^{10})\)	\(q+(-1.54911 + 0.774760i) q^{3} +(0.626199 + 2.14660i) q^{5} +(1.95049 - 1.78762i) q^{7} +(1.79949 - 2.40038i) q^{9} +(-2.07693 + 1.19911i) q^{11} +(3.37848 + 3.37848i) q^{13} +(-2.63315 - 2.84016i) q^{15} +(-1.27103 + 4.74353i) q^{17} +(-0.151250 - 0.0873244i) q^{19} +(-1.63655 + 4.28039i) q^{21} +(0.324361 + 1.21053i) q^{23} +(-4.21575 + 2.68839i) q^{25} +(-0.927900 + 5.11263i) q^{27} -4.65176 q^{29} +(1.26323 + 2.18799i) q^{31} +(2.28836 - 3.46668i) q^{33} +(5.05869 + 3.06751i) q^{35} +(2.94674 + 10.9974i) q^{37} +(-7.85116 - 2.61614i) q^{39} -1.78650i q^{41} +(-2.46081 - 2.46081i) q^{43} +(6.27949 + 2.35967i) q^{45} +(7.73263 - 2.07195i) q^{47} +(0.608831 - 6.97347i) q^{49} +(-1.70614 - 8.33300i) q^{51} +(10.8978 + 2.92005i) q^{53} +(-3.87458 - 3.70744i) q^{55} +(0.301959 + 0.0180926i) q^{57} +(2.06606 + 3.57852i) q^{59} +(3.47828 - 6.02455i) q^{61} +(-0.781068 - 7.89873i) q^{63} +(-5.13664 + 9.36784i) q^{65} +(-11.6526 - 3.12231i) q^{67} +(-1.44034 - 1.62395i) q^{69} -15.9938i q^{71} +(1.40215 - 5.23288i) q^{73} +(4.44781 - 7.43081i) q^{75} +(-1.90747 + 6.05161i) q^{77} +(-5.52266 - 3.18851i) q^{79} +(-2.52364 - 8.63894i) q^{81} +(-3.05025 + 3.05025i) q^{83} +(-10.9784 + 0.242015i) q^{85} +(7.20610 - 3.60400i) q^{87} +(-2.58127 + 4.47089i) q^{89} +(12.6291 + 0.550258i) q^{91} +(-3.65205 - 2.41073i) q^{93} +(0.0927374 - 0.379356i) q^{95} +(-2.70738 + 2.70738i) q^{97} +(-0.859088 + 7.14321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 48 * q - 2 * q^3 - 8 * q^7	\( 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) \) 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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