LMFDB - Embedded newform 483.2.j.a.229.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.9
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.676219 + 1.17124i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.0854570 + 0.148016i) q^{4} +(-1.08513 + 1.87949i) q^{5} -1.35244i q^{6} +(-2.39455 + 1.12522i) q^{7} -2.93602 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.46757 - 2.54190i) q^{10} +(-0.712709 + 0.411483i) q^{11} +(-0.148016 - 0.0854570i) q^{12} -5.68513i q^{13} +(0.301337 - 3.56550i) q^{14} -2.17025i q^{15} +(1.81448 - 3.14277i) q^{16} +(3.43225 + 5.94483i) q^{17} +(0.676219 + 1.17124i) q^{18} +(-0.737450 + 1.27730i) q^{19} -0.370927 q^{20} +(1.51114 - 2.17174i) q^{21} -1.11301i q^{22} +(-1.07484 - 4.67383i) q^{23} +(2.54267 - 1.46801i) q^{24} +(0.145000 + 0.251147i) q^{25} +(6.65867 + 3.84439i) q^{26} +1.00000i q^{27} +(-0.371181 - 0.258274i) q^{28} -4.14924 q^{29} +(2.54190 + 1.46757i) q^{30} +(1.58212 - 0.913437i) q^{31} +(-0.482054 - 0.834943i) q^{32} +(0.411483 - 0.712709i) q^{33} -9.28381 q^{34} +(0.483555 - 5.72155i) q^{35} +0.170914 q^{36} +(-3.57428 - 2.06361i) q^{37} +(-0.997355 - 1.72747i) q^{38} +(2.84256 + 4.92346i) q^{39} +(3.18596 - 5.51824i) q^{40} +11.2151i q^{41} +(1.52178 + 3.23848i) q^{42} -11.7103i q^{43} +(-0.121812 - 0.0703281i) q^{44} +(1.08513 + 1.87949i) q^{45} +(6.20103 + 1.90163i) q^{46} +(-4.23255 - 2.44366i) q^{47} +3.62896i q^{48} +(4.46777 - 5.38878i) q^{49} -0.392206 q^{50} +(-5.94483 - 3.43225i) q^{51} +(0.841489 - 0.485834i) q^{52} +(-1.80578 + 1.04257i) q^{53} +(-1.17124 - 0.676219i) q^{54} -1.78604i q^{55} +(7.03047 - 3.30366i) q^{56} -1.47490i q^{57} +(2.80579 - 4.85977i) q^{58} +(3.87817 - 2.23906i) q^{59} +(0.321232 - 0.185463i) q^{60} +(0.202743 - 0.351161i) q^{61} +2.47073i q^{62} +(-0.222811 + 2.63635i) q^{63} +8.56182 q^{64} +(10.6852 + 6.16908i) q^{65} +(0.556504 + 0.963894i) q^{66} +(-11.5166 + 6.64914i) q^{67} +(-0.586620 + 1.01606i) q^{68} +(3.26776 + 3.51024i) q^{69} +(6.37435 + 4.43538i) q^{70} -12.9089 q^{71} +(-1.46801 + 2.54267i) q^{72} +(-6.24915 + 3.60795i) q^{73} +(4.83399 - 2.79090i) q^{74} +(-0.251147 - 0.145000i) q^{75} -0.252081 q^{76} +(1.24361 - 1.78727i) q^{77} -7.68878 q^{78} +(2.49808 + 1.44227i) q^{79} +(3.93788 + 6.82061i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.1356 - 7.58387i) q^{82} -14.5815 q^{83} +(0.450590 + 0.0380815i) q^{84} -14.8977 q^{85} +(13.7156 + 7.91872i) q^{86} +(3.59334 - 2.07462i) q^{87} +(2.09253 - 1.20812i) q^{88} +(0.557067 - 0.964869i) q^{89} -2.93513 q^{90} +(6.39700 + 13.6133i) q^{91} +(0.599949 - 0.558506i) q^{92} +(-0.913437 + 1.58212i) q^{93} +(5.72426 - 3.30490i) q^{94} +(-1.60045 - 2.77207i) q^{95} +(0.834943 + 0.482054i) q^{96} -3.12154 q^{97} +(3.29039 + 8.87685i) q^{98} +0.822965i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.676219	+	1.17124i	−0.478159	+	0.828195i	−0.999686	−	0.0250391i	$-0.992029\pi$
$2$	−0.676219	+	1.17124i	−0.478159	+	0.828195i	0.521528	+	0.853234i	$0.325362\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.0854570	+	0.148016i	0.0427285	+	0.0740080i
$5$	−1.08513	+	1.87949i	−0.485283	+	0.840536i	−0.999857	−	0.0169107i	$-0.994617\pi$
$5$	−1.08513	+	1.87949i	−0.485283	+	0.840536i	0.514574	+	0.857446i	$0.327950\pi$
$6$		−	1.35244i		−	0.552130i
$7$	−2.39455	+	1.12522i	−0.905056	+	0.425292i
$7$	−2.39455	+	1.12522i	−0.905056	+	0.425292i
$8$	−2.93602			−1.03804
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.46757	−	2.54190i	−0.464085	−	0.803819i
$11$	−0.712709	+	0.411483i	−0.214890	+	0.124067i	−0.603582	−	0.797301i	$-0.706260\pi$
$11$	−0.712709	+	0.411483i	−0.214890	+	0.124067i	0.388692	+	0.921368i	$0.372927\pi$
$12$	−0.148016	−	0.0854570i	−0.0427285	−	0.0246693i
$13$		−	5.68513i		−	1.57677i	−0.615182	−	0.788385i	$-0.710917\pi$
$13$		−	5.68513i		−	1.57677i	0.615182	−	0.788385i	$-0.289083\pi$
$14$	0.301337	−	3.56550i	0.0805358	−	0.952920i
$15$		−	2.17025i		−	0.560357i
$16$	1.81448	−	3.14277i	0.453620	−	0.785693i
$17$	3.43225	+	5.94483i	0.832443	+	1.44183i	0.896095	+	0.443862i	$0.146392\pi$
$17$	3.43225	+	5.94483i	0.832443	+	1.44183i	−0.0636518	+	0.997972i	$0.520275\pi$
$18$	0.676219	+	1.17124i	0.159386	+	0.276065i
$19$	−0.737450	+	1.27730i	−0.169183	+	0.293033i	−0.938133	−	0.346276i	$-0.887446\pi$
$19$	−0.737450	+	1.27730i	−0.169183	+	0.293033i	0.768950	+	0.639309i	$0.220779\pi$
$20$	−0.370927			−0.0829418
$21$	1.51114	−	2.17174i	0.329757	−	0.473913i
$22$		−	1.11301i		−	0.237294i
$23$	−1.07484	−	4.67383i	−0.224121	−	0.974561i
$23$	−1.07484	−	4.67383i	−0.224121	−	0.974561i
$24$	2.54267	−	1.46801i	0.519021	−	0.299657i
$25$	0.145000	+	0.251147i	0.0290000	+	0.0502294i
$26$	6.65867	+	3.84439i	1.30587	+	0.753946i
$27$			1.00000i			0.192450i
$28$	−0.371181	−	0.258274i	−0.0701467	−	0.0488093i
$29$	−4.14924			−0.770494			−0.385247	−	0.922814i	$-0.625884\pi$
$29$	−4.14924			−0.770494			−0.385247	+	0.922814i	$0.625884\pi$
$30$	2.54190	+	1.46757i	0.464085	+	0.267940i
$31$	1.58212	−	0.913437i	0.284157	−	0.164058i	−0.351147	−	0.936320i	$-0.614208\pi$
$31$	1.58212	−	0.913437i	0.284157	−	0.164058i	0.635304	+	0.772262i	$0.280875\pi$
$32$	−0.482054	−	0.834943i	−0.0852160	−	0.147598i
$33$	0.411483	−	0.712709i	0.0716299	−	0.124067i
$34$	−9.28381			−1.59216
$35$	0.483555	−	5.72155i	0.0817358	−	0.967119i
$36$	0.170914			0.0284857
$37$	−3.57428	−	2.06361i	−0.587608	−	0.339256i	0.176543	−	0.984293i	$-0.443508\pi$
$37$	−3.57428	−	2.06361i	−0.587608	−	0.339256i	−0.764151	+	0.645037i	$0.776842\pi$
$38$	−0.997355	−	1.72747i	−0.161792	−	0.280233i
$39$	2.84256	+	4.92346i	0.455174	+	0.788385i
$40$	3.18596	−	5.51824i	0.503744	−	0.872511i
$41$			11.2151i			1.75151i	0.482759	+	0.875753i	$0.339635\pi$
$41$			11.2151i			1.75151i	−0.482759	+	0.875753i	$0.660365\pi$
$42$	1.52178	+	3.23848i	0.234816	+	0.499709i
$43$		−	11.7103i		−	1.78580i	−0.450251	−	0.892902i	$-0.648665\pi$
$43$		−	11.7103i		−	1.78580i	0.450251	−	0.892902i	$-0.351335\pi$
$44$	−0.121812	−	0.0703281i	−0.0183638	−	0.0106024i
$45$	1.08513	+	1.87949i	0.161761	+	0.280179i
$46$	6.20103	+	1.90163i	0.914292	+	0.280379i
$47$	−4.23255	−	2.44366i	−0.617381	−	0.356445i	0.158468	−	0.987364i	$-0.449345\pi$
$47$	−4.23255	−	2.44366i	−0.617381	−	0.356445i	−0.775849	+	0.630919i	$0.782678\pi$
$48$			3.62896i			0.523795i
$49$	4.46777	−	5.38878i	0.638254	−	0.769826i
$50$	−0.392206			−0.0554664
$51$	−5.94483	−	3.43225i	−0.832443	−	0.480611i
$52$	0.841489	−	0.485834i	0.116694	−	0.0673731i
$53$	−1.80578	+	1.04257i	−0.248043	+	0.143208i	−0.618868	−	0.785495i	$-0.712408\pi$
$53$	−1.80578	+	1.04257i	−0.248043	+	0.143208i	0.370825	+	0.928703i	$0.379075\pi$
$54$	−1.17124	−	0.676219i	−0.159386	−	0.0920217i
$55$		−	1.78604i		−	0.240830i
$56$	7.03047	−	3.30366i	0.939486	−	0.441471i
$57$		−	1.47490i		−	0.195355i
$58$	2.80579	−	4.85977i	0.368418	−	0.638119i
$59$	3.87817	−	2.23906i	0.504895	−	0.291501i	−0.225838	−	0.974165i	$-0.572512\pi$
$59$	3.87817	−	2.23906i	0.504895	−	0.291501i	0.730733	+	0.682664i	$0.239179\pi$
$60$	0.321232	−	0.185463i	0.0414709	−	0.0239432i
$61$	0.202743	−	0.351161i	0.0259586	−	0.0449616i	−0.852754	−	0.522312i	$-0.825070\pi$
$61$	0.202743	−	0.351161i	0.0259586	−	0.0449616i	0.878713	+	0.477351i	$0.158403\pi$
$62$			2.47073i			0.313783i
$63$	−0.222811	+	2.63635i	−0.0280715	+	0.332149i
$64$	8.56182			1.07023
$65$	10.6852	+	6.16908i	1.32533	+	0.765181i
$66$	0.556504	+	0.963894i	0.0685009	+	0.118647i
$67$	−11.5166	+	6.64914i	−1.40698	+	0.812322i	−0.995096	−	0.0989136i	$-0.968463\pi$
$67$	−11.5166	+	6.64914i	−1.40698	+	0.812322i	−0.411886	+	0.911235i	$0.635130\pi$
$68$	−0.586620	+	1.01606i	−0.0711381	+	0.123215i
$69$	3.26776	+	3.51024i	0.393392	+	0.422583i
$70$	6.37435	+	4.43538i	0.761881	+	0.530130i
$71$	−12.9089			−1.53201			−0.766005	−	0.642835i	$-0.777758\pi$
$71$	−12.9089			−1.53201			−0.766005	+	0.642835i	$0.777758\pi$
$72$	−1.46801	+	2.54267i	−0.173007	+	0.299657i
$73$	−6.24915	+	3.60795i	−0.731408	+	0.422279i	−0.818937	−	0.573883i	$-0.805436\pi$
$73$	−6.24915	+	3.60795i	−0.731408	+	0.422279i	0.0875290	+	0.996162i	$0.472103\pi$
$74$	4.83399	−	2.79090i	0.561940	−	0.324436i
$75$	−0.251147	−	0.145000i	−0.0290000	−	0.0167431i
$76$	−0.252081			−0.0289157
$77$	1.24361	−	1.78727i	0.141723	−	0.203678i
$78$	−7.68878			−0.870582
$79$	2.49808	+	1.44227i	0.281056	+	0.162268i	0.633901	−	0.773414i	$-0.281452\pi$
$79$	2.49808	+	1.44227i	0.281056	+	0.162268i	−0.352845	+	0.935682i	$0.614786\pi$
$80$	3.93788	+	6.82061i	0.440269	+	0.762568i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−13.1356	−	7.58387i	−1.45059	−	0.837498i
$83$	−14.5815			−1.60053			−0.800264	−	0.599648i	$-0.795307\pi$
$83$	−14.5815			−1.60053			−0.800264	+	0.599648i	$0.795307\pi$
$84$	0.450590	+	0.0380815i	0.0491634	+	0.00415503i
$85$	−14.8977			−1.61588
$86$	13.7156	+	7.91872i	1.47899	+	0.853898i
$87$	3.59334	−	2.07462i	0.385247	−	0.222422i
$88$	2.09253	−	1.20812i	0.223064	−	0.128786i
$89$	0.557067	−	0.964869i	0.0590490	−	0.102276i	−0.834990	−	0.550265i	$-0.814527\pi$
$89$	0.557067	−	0.964869i	0.0590490	−	0.102276i	0.894039	+	0.447990i	$0.147860\pi$
$90$	−2.93513			−0.309390
$91$	6.39700	+	13.6133i	0.670588	+	1.42707i
$92$	0.599949	−	0.558506i	0.0625490	−	0.0582283i
$93$	−0.913437	+	1.58212i	−0.0947190	+	0.164058i
$94$	5.72426	−	3.30490i	0.590412	−	0.340875i
$95$	−1.60045	−	2.77207i	−0.164203	−	0.284408i
$96$	0.834943	+	0.482054i	0.0852160	+	0.0491995i
$97$	−3.12154			−0.316944			−0.158472	−	0.987363i	$-0.550657\pi$
$97$	−3.12154			−0.316944			−0.158472	+	0.987363i	$0.550657\pi$
$98$	3.29039	+	8.87685i	0.332380	+	0.896698i
$99$			0.822965i			0.0827111i
$100$	−0.0247825	+	0.0429246i	−0.00247825	+	0.00429246i
$101$	−0.743462	+	0.429238i	−0.0739773	+	0.0427108i	−0.536532	−	0.843880i	$-0.680266\pi$
$101$	−0.743462	+	0.429238i	−0.0739773	+	0.0427108i	0.462555	+	0.886591i	$0.346933\pi$
$102$	8.04001	−	4.64190i	0.796080	−	0.459617i
$103$	−7.16724	+	12.4140i	−0.706209	+	1.22319i	0.260045	+	0.965597i	$0.416263\pi$
$103$	−7.16724	+	12.4140i	−0.706209	+	1.22319i	−0.966253	+	0.257593i	$0.917071\pi$
$104$			16.6917i			1.63675i
$105$	2.44201	+	5.19679i	0.238315	+	0.507155i
$106$		−	2.82002i		−	0.273904i
$107$	11.4950	+	6.63666i	1.11127	+	0.641590i	0.939157	−	0.343488i	$-0.111609\pi$
$107$	11.4950	+	6.63666i	1.11127	+	0.641590i	0.172109	+	0.985078i	$0.444942\pi$
$108$	−0.148016	+	0.0854570i	−0.0142428	+	0.00822311i
$109$	4.95161	−	2.85881i	0.474278	−	0.273824i	−0.243751	−	0.969838i	$-0.578378\pi$
$109$	4.95161	−	2.85881i	0.474278	−	0.273824i	0.718029	+	0.696013i	$0.245045\pi$
$110$	2.09189	+	1.20776i	0.199454	+	0.115155i
$111$	4.12722			0.391739
$112$	−0.808571	+	9.56722i	−0.0764027	+	0.904017i
$113$		−	10.6223i		−	0.999260i	−0.866239	−	0.499630i	$-0.833469\pi$
$113$		−	10.6223i		−	0.999260i	0.866239	−	0.499630i	$-0.166531\pi$
$114$	1.72747	+	0.997355i	0.161792	+	0.0934109i
$115$	9.95079	+	3.05154i	0.927916	+	0.284557i
$116$	−0.354581	−	0.614153i	−0.0329221	−	0.0570227i
$117$	−4.92346	−	2.84256i	−0.455174	−	0.262795i
$118$			6.05639i			0.557536i
$119$	−14.9079	−	10.3732i	−1.36661	−	0.950910i
$120$			6.37192i			0.581674i
$121$	−5.16136	+	8.93975i	−0.469215	+	0.812704i
$122$	0.274197	+	0.474923i	0.0248246	+	0.0429975i
$123$	−5.60756	−	9.71258i	−0.505616	−	0.875753i
$124$	0.270406	+	0.156119i	0.0242832	+	0.0140199i
$125$	−11.4806			−1.02686
$126$	−2.93715	−	2.04372i	−0.261662	−	0.182069i
$127$	−15.4082			−1.36726			−0.683629	−	0.729830i	$-0.739599\pi$
$127$	−15.4082			−1.36726			−0.683629	+	0.729830i	$0.739599\pi$
$128$	−4.82555	+	8.35810i	−0.426522	+	0.738759i
$129$	5.85515	+	10.1414i	0.515517	+	0.892902i
$130$	−14.4510	+	8.34330i	−1.26744	+	0.731755i
$131$	9.76438	+	5.63747i	0.853118	+	0.492548i	0.861702	−	0.507415i	$-0.169399\pi$
$131$	9.76438	+	5.63747i	0.853118	+	0.492548i	−0.00858390	+	0.999963i	$0.502732\pi$
$132$	0.140656			0.0122426
$133$	0.328623	−	3.88836i	0.0284953	−	0.337163i
$134$		−	17.9851i		−	1.55367i
$135$	−1.87949	−	1.08513i	−0.161761	−	0.0933928i
$136$	−10.0772	−	17.4542i	−0.864111	−	1.49668i
$137$	−7.20777	+	4.16141i	−0.615802	+	0.355533i	−0.775233	−	0.631676i	$-0.782367\pi$
$137$	−7.20777	+	4.16141i	−0.615802	+	0.355533i	0.159431	+	0.987209i	$0.449034\pi$
$138$	−6.32106	+	1.45366i	−0.538085	+	0.123744i
$139$			16.9024i			1.43365i	0.697255	+	0.716824i	$0.254405\pi$
$139$			16.9024i			1.43365i	−0.697255	+	0.716824i	$0.745595\pi$
$140$	0.888204	−	0.417373i	0.0750670	−	0.0352745i
$141$	4.88733			0.411587
$142$	8.72927	−	15.1195i	0.732544	−	1.26880i
$143$	2.33933	+	4.05184i	0.195625	+	0.338832i
$144$	−1.81448	−	3.14277i	−0.151207	−	0.261898i
$145$	4.50245	−	7.79847i	0.373908	−	0.647627i
$146$		−	9.75905i		−	0.807665i
$147$	−1.17481	+	6.90071i	−0.0968971	+	0.569161i
$148$		−	0.705400i		−	0.0579836i
$149$	−3.47028	−	2.00357i	−0.284297	−	0.164139i	0.351070	−	0.936349i	$-0.385818\pi$
$149$	−3.47028	−	2.00357i	−0.284297	−	0.164139i	−0.635367	+	0.772210i	$0.719151\pi$
$150$	0.339661	−	0.196103i	0.0277332	−	0.0160118i
$151$	−0.822931	−	1.42536i	−0.0669692	−	0.115994i	0.830597	−	0.556875i	$-0.188000\pi$
$151$	−0.822931	−	1.42536i	−0.0669692	−	0.115994i	−0.897566	+	0.440881i	$0.854666\pi$
$152$	2.16517	−	3.75019i	0.175619	−	0.304181i
$153$	6.86450			0.554962
$154$	1.25238	+	2.66516i	0.100919	+	0.214765i
$155$			3.96478i			0.318459i
$156$	−0.485834	+	0.841489i	−0.0388978	+	0.0673731i
$157$	7.16304	+	12.4067i	0.571673	+	0.990166i	0.996394	+	0.0848420i	$0.0270386\pi$
$157$	7.16304	+	12.4067i	0.571673	+	0.990166i	−0.424722	+	0.905324i	$0.639628\pi$
$158$	−3.37850	+	1.95058i	−0.268779	+	0.155180i
$159$	1.04257	−	1.80578i	0.0826811	−	0.143208i
$160$	2.09236			0.165416
$161$	7.83285	+	9.98231i	0.617315	+	0.786716i
$162$	1.35244			0.106257
$163$	5.78407	−	10.0183i	0.453044	−	0.784695i	−0.545530	−	0.838091i	$-0.683671\pi$
$163$	5.78407	−	10.0183i	0.453044	−	0.784695i	0.998573	+	0.0533968i	$0.0170048\pi$
$164$	−1.66002	+	0.958411i	−0.129625	+	0.0748393i
$165$	0.893021	+	1.54676i	0.0695216	+	0.120415i
$166$	9.86029	−	17.0785i	0.765307	−	1.32555i
$167$			1.01316i			0.0784010i	0.999231	+	0.0392005i	$0.0124811\pi$
$167$			1.01316i			0.0784010i	−0.999231	+	0.0392005i	$0.987519\pi$
$168$	−4.43673	+	6.37629i	−0.342301	+	0.491942i
$169$	−19.3207			−1.48620
$170$	10.0741	−	17.4489i	0.772649	−	1.33827i
$171$	0.737450	+	1.27730i	0.0563942	+	0.0976777i
$172$	1.73331	−	1.00073i	0.132164	−	0.0763048i
$173$	9.19994	+	5.31159i	0.699458	+	0.403832i	0.807146	−	0.590352i	$-0.201011\pi$
$173$	9.19994	+	5.31159i	0.699458	+	0.403832i	−0.107687	+	0.994185i	$0.534345\pi$
$174$			5.61158i			0.425413i
$175$	−0.629805	−	0.438229i	−0.0476088	−	0.0331270i
$176$			2.98651i			0.225116i
$177$	−2.23906	+	3.87817i	−0.168298	+	0.291501i
$178$	0.753399	+	1.30492i	0.0564696	+	0.0978082i
$179$	−4.63096	−	8.02106i	−0.346134	−	0.599522i	0.639425	−	0.768854i	$-0.279173\pi$
$179$	−4.63096	−	8.02106i	−0.346134	−	0.599522i	−0.985559	+	0.169331i	$0.945839\pi$
$180$	−0.185463	+	0.321232i	−0.0138236	+	0.0239432i
$181$	24.6578			1.83280			0.916399	−	0.400266i	$-0.131082\pi$
$181$	24.6578			1.83280			0.916399	+	0.400266i	$0.131082\pi$
$182$	−20.2703	−	1.71314i	−1.50254	−	0.126986i
$183$			0.405486i			0.0299744i
$184$	3.15577	+	13.7225i	0.232646	+	1.01164i
$185$	7.75709	−	4.47856i	0.570313	−	0.329270i
$186$	−1.23537	−	2.13972i	−0.0905814	−	0.156892i
$187$	−4.89239	−	2.82462i	−0.357767	−	0.206557i
$188$		−	0.835313i		−	0.0609215i
$189$	−1.12522	−	2.39455i	−0.0818475	−	0.174178i
$190$	4.32903			0.314061
$191$	−16.5016	−	9.52721i	−1.19401	−	0.689365i	−0.234800	−	0.972044i	$-0.575444\pi$
$191$	−16.5016	−	9.52721i	−1.19401	−	0.689365i	−0.959215	+	0.282679i	$0.908777\pi$
$192$	−7.41475	+	4.28091i	−0.535114	+	0.308948i
$193$	10.9654	+	18.9926i	0.789305	+	1.36712i	0.926393	+	0.376558i	$0.122893\pi$
$193$	10.9654	+	18.9926i	0.789305	+	1.36712i	−0.137088	+	0.990559i	$0.543774\pi$
$194$	2.11084	−	3.65608i	0.151549	−	0.262491i
$195$	−12.3382			−0.883554
$196$	1.17943	+	0.200792i	0.0842449	+	0.0143423i
$197$	12.4475			0.886848			0.443424	−	0.896312i	$-0.353764\pi$
$197$	12.4475			0.886848			0.443424	+	0.896312i	$0.353764\pi$
$198$	−0.963894	−	0.556504i	−0.0685009	−	0.0395490i
$199$	1.15317	+	1.99734i	0.0817459	+	0.141588i	0.904000	−	0.427533i	$-0.140617\pi$
$199$	1.15317	+	1.99734i	0.0817459	+	0.141588i	−0.822254	+	0.569121i	$0.807284\pi$
$200$	−0.425723	−	0.737374i	−0.0301032	−	0.0521402i
$201$	6.64914	−	11.5166i	0.468994	−	0.812322i
$202$		−	1.16104i		−	0.0816902i
$203$	9.93557	−	4.66879i	0.697340	−	0.327685i
$204$		−	1.17324i		−	0.0821432i
$205$	−21.0788	−	12.1698i	−1.47220	−	0.849977i
$206$	−9.69324	−	16.7892i	−0.675360	−	1.16976i
$207$	−4.58508	−	1.40607i	−0.318685	−	0.0977289i
$208$	−17.8671	−	10.3155i	−1.23886	−	0.715255i
$209$		−	1.21379i		−	0.0839597i
$210$	−7.73804	−	0.653978i	−0.533976	−	0.0451288i
$211$	5.25033			0.361447			0.180724	−	0.983534i	$-0.442156\pi$
$211$	5.25033			0.361447			0.180724	+	0.983534i	$0.442156\pi$
$212$	−0.308633	−	0.178190i	−0.0211970	−	0.0122381i
$213$	11.1795	−	6.45447i	0.766005	−	0.442253i
$214$	−15.5463	+	8.97566i	−1.06272	+	0.613563i
$215$	22.0095	+	12.7072i	1.50103	+	0.866621i
$216$		−	2.93602i		−	0.199771i
$217$	−2.76066	+	3.96750i	−0.187406	+	0.269332i
$218$			7.73272i			0.523726i
$219$	3.60795	−	6.24915i	0.243803	−	0.422279i
$220$	0.264363	−	0.152630i	0.0178233	−	0.0102903i
$221$	33.7971	−	19.5128i	2.27344	−	1.31257i
$222$	−2.79090	+	4.83399i	−0.187313	+	0.324436i
$223$		−	10.3402i		−	0.692429i	−0.938155	−	0.346214i	$-0.887467\pi$
$223$		−	10.3402i		−	0.692429i	0.938155	−	0.346214i	$-0.112533\pi$
$224$	2.09380	+	1.45690i	0.139898	+	0.0973432i
$225$	0.290000			0.0193333
$226$	12.4413	+	7.18298i	0.827582	+	0.477805i
$227$	−11.0138	−	19.0764i	−0.731011	−	1.26615i	−0.956452	−	0.291891i	$-0.905716\pi$
$227$	−11.0138	−	19.0764i	−0.731011	−	1.26615i	0.225441	−	0.974257i	$-0.427618\pi$
$228$	0.218309	−	0.126041i	0.0144579	−	0.00834725i
$229$	0.0144844	−	0.0250878i	0.000957158	−	0.00165785i	−0.865546	−	0.500829i	$-0.833029\pi$
$229$	0.0144844	−	0.0250878i	0.000957158	−	0.00165785i	0.866504	+	0.499171i	$0.166362\pi$
$230$	−10.3030	+	9.59130i	−0.679360	+	0.632432i
$231$	−0.183365	+	2.16963i	−0.0120645	+	0.142751i
$232$	12.1823			0.799804
$233$	−0.353325	+	0.611978i	−0.0231471	+	0.0400920i	−0.877367	−	0.479820i	$-0.840702\pi$
$233$	−0.353325	+	0.611978i	−0.0231471	+	0.0400920i	0.854220	+	0.519912i	$0.174035\pi$
$234$	6.65867	−	3.84439i	0.435291	−	0.251315i
$235$	9.18571	−	5.30337i	0.599209	−	0.345954i
$236$	0.662834	+	0.382688i	0.0431469	+	0.0249108i
$237$	−2.88454			−0.187371
$238$	22.2306	−	10.4463i	1.44099	−	0.677133i
$239$	−2.85318			−0.184557			−0.0922786	−	0.995733i	$-0.529415\pi$
$239$	−2.85318			−0.184557			−0.0922786	+	0.995733i	$0.529415\pi$
$240$	−6.82061	−	3.93788i	−0.440269	−	0.254189i
$241$	2.99570	+	5.18870i	0.192970	+	0.334234i	0.946233	−	0.323486i	$-0.104855\pi$
$241$	2.99570	+	5.18870i	0.192970	+	0.334234i	−0.753263	+	0.657719i	$0.771521\pi$
$242$	−6.98042	−	12.0904i	−0.448718	−	0.777203i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	0.0693032			0.00443668
$245$	5.28009	+	14.2447i	0.337332	+	0.910059i
$246$	15.1677			0.967060
$247$	7.26162	+	4.19250i	0.462046	+	0.266762i
$248$	−4.64514	+	2.68187i	−0.294967	+	0.170299i
$249$	12.6280	−	7.29075i	0.800264	−	0.462033i
$250$	7.76342	−	13.4466i	0.491002	−	0.850440i
$251$	−20.0859			−1.26781			−0.633906	−	0.773410i	$-0.718549\pi$
$251$	−20.0859			−1.26781			−0.633906	+	0.773410i	$0.718549\pi$
$252$	−0.409263	+	0.192315i	−0.0257811	+	0.0121147i
$253$	2.68925	+	2.88880i	0.169072	+	0.181617i
$254$	10.4193	−	18.0468i	0.653766	−	1.13236i
$255$	12.9018	−	7.44886i	0.807942	−	0.466465i
$256$	2.03556	+	3.52570i	0.127223	+	0.220356i
$257$	−5.24200	−	3.02647i	−0.326987	−	0.188786i	0.327516	−	0.944846i	$-0.393789\pi$
$257$	−5.24200	−	3.02647i	−0.326987	−	0.188786i	−0.654503	+	0.756060i	$0.727122\pi$
$258$	−15.8374			−0.985996
$259$	10.8808	+	0.919589i	0.676101	+	0.0571405i
$260$			2.10877i			0.130780i
$261$	−2.07462	+	3.59334i	−0.128416	+	0.222422i
$262$	−13.2057	+	7.62432i	−0.815851	+	0.471032i
$263$	−8.19958	+	4.73403i	−0.505608	+	0.291913i	−0.731026	−	0.682349i	$-0.760958\pi$
$263$	−8.19958	+	4.73403i	−0.505608	+	0.291913i	0.225419	+	0.974262i	$0.427625\pi$
$264$	−1.20812	+	2.09253i	−0.0743548	+	0.128786i
$265$		−	4.52528i		−	0.277986i
$266$	4.33200	+	3.01428i	0.265612	+	0.184817i
$267$			1.11413i			0.0681839i
$268$	−1.96836	−	1.13643i	−0.120237	−	0.0694186i
$269$	−1.90103	+	1.09756i	−0.115908	+	0.0669195i	−0.556833	−	0.830624i	$-0.687984\pi$
$269$	−1.90103	+	1.09756i	−0.115908	+	0.0669195i	0.440925	+	0.897544i	$0.354650\pi$
$270$	2.54190	−	1.46757i	0.154695	−	0.0893132i
$271$	11.8469	+	6.83980i	0.719647	+	0.415488i	0.814623	−	0.579991i	$-0.196944\pi$
$271$	11.8469	+	6.83980i	0.719647	+	0.415488i	−0.0949758	+	0.995480i	$0.530277\pi$
$272$	24.9110			1.51045
$273$	−12.3466	−	8.59100i	−0.747252	−	0.519951i
$274$		−	11.2561i		−	0.680005i
$275$	−0.206685	−	0.119330i	−0.0124636	−	0.00719586i
$276$	−0.240318	+	0.783655i	−0.0144654	+	0.0471705i
$277$	−9.41317	−	16.3041i	−0.565583	−	0.979618i	−0.996995	−	0.0774630i	$-0.975318\pi$
$277$	−9.41317	−	16.3041i	−0.565583	−	0.979618i	0.431413	−	0.902155i	$-0.358015\pi$
$278$	−19.7969	−	11.4297i	−1.18734	−	0.685511i
$279$		−	1.82687i		−	0.109372i
$280$	−1.41973	+	16.7986i	−0.0848451	+	1.00391i
$281$		−	20.7825i		−	1.23978i	−0.784688	−	0.619891i	$-0.787177\pi$
$281$		−	20.7825i		−	1.23978i	0.784688	−	0.619891i	$-0.212823\pi$
$282$	−3.30490	+	5.72426i	−0.196804	+	0.340875i
$283$	−13.4873	−	23.3607i	−0.801737	−	1.38865i	−0.918472	−	0.395486i	$-0.870576\pi$
$283$	−13.4873	−	23.3607i	−0.801737	−	1.38865i	0.116735	−	0.993163i	$-0.462757\pi$
$284$	−1.10316	−	1.91073i	−0.0654605	−	0.113381i
$285$	2.77207	+	1.60045i	0.164203	+	0.0948027i
$286$	−6.32759			−0.374158
$287$	−12.6194	−	26.8552i	−0.744902	−	1.58521i
$288$	−0.964109			−0.0568107
$289$	−15.0607	+	26.0859i	−0.885924	+	1.53447i
$290$	6.08928	+	10.5469i	0.357575	+	0.619337i
$291$	2.70333	−	1.56077i	0.158472	−	0.0914938i
$292$	−1.06807	−	0.616649i	−0.0625040	−	0.0360867i
$293$	19.9128			1.16332			0.581660	−	0.813432i	$-0.302404\pi$
$293$	19.9128			1.16332			0.581660	+	0.813432i	$0.302404\pi$
$294$	−7.28799	−	6.04238i	−0.425044	−	0.352399i
$295$			9.71868i			0.565843i
$296$	10.4942	+	6.05881i	0.609961	+	0.352161i
$297$	−0.411483	−	0.712709i	−0.0238766	−	0.0413555i
$298$	4.69334	−	2.70970i	0.271878	−	0.156969i
$299$	−26.5713	+	6.11063i	−1.53666	+	0.353387i
$300$		−	0.0495650i		−	0.00286164i
$301$	13.1766	+	28.0409i	0.759488	+	1.61625i
$302$	2.22592			0.128088
$303$	0.429238	−	0.743462i	0.0246591	−	0.0427108i
$304$	2.67618	+	4.63528i	0.153489	+	0.265851i
$305$	0.440003	+	0.762108i	0.0251945	+	0.0436382i
$306$	−4.64190	+	8.04001i	−0.265360	+	0.459617i
$307$			23.5216i			1.34245i	0.741254	+	0.671225i	$0.234232\pi$
$307$			23.5216i			1.34245i	−0.741254	+	0.671225i	$0.765768\pi$
$308$	0.370820	+	0.0313397i	0.0211294	+	0.00178575i
$309$		−	14.3345i		−	0.815460i
$310$	−4.64373	−	2.68106i	−0.263746	−	0.152274i
$311$	2.71839	−	1.56946i	0.154146	−	0.0889960i	−0.420943	−	0.907087i	$-0.638301\pi$
$311$	2.71839	−	1.56946i	0.154146	−	0.0889960i	0.575089	+	0.818091i	$0.304968\pi$
$312$	−8.34583	−	14.4554i	−0.472490	−	0.818376i
$313$	−11.1092	+	19.2417i	−0.627930	+	1.08761i	0.360036	+	0.932938i	$0.382764\pi$
$313$	−11.1092	+	19.2417i	−0.627930	+	1.08761i	−0.987966	+	0.154669i	$0.950569\pi$
$314$	−19.3751			−1.09340
$315$	−4.71323	−	3.27955i	−0.265561	−	0.184782i
$316$			0.493008i			0.0277339i
$317$	5.83159	−	10.1006i	0.327535	−	0.567307i	−0.654487	−	0.756073i	$-0.727116\pi$
$317$	5.83159	−	10.1006i	0.327535	−	0.567307i	0.982022	+	0.188766i	$0.0604489\pi$
$318$	1.41001	+	2.44221i	0.0790693	+	0.136952i
$319$	2.95720	−	1.70734i	0.165571	−	0.0955926i
$320$	−9.29066	+	16.0919i	−0.519364	+	0.899564i
$321$	−13.2733			−0.740844
$322$	−16.9884	+	2.42396i	−0.946729	+	0.135082i
$323$	−10.1245			−0.563340
$324$	0.0854570	−	0.148016i	0.00474761	−	0.00822311i
$325$	1.42780	−	0.824342i	0.0792003	−	0.0457263i
$326$	7.82260	+	13.5491i	0.433254	+	0.750417i
$327$	−2.85881	+	4.95161i	−0.158093	+	0.273824i
$328$		−	32.9279i		−	1.81814i
$329$	12.8847	+	1.08895i	0.710358	+	0.0600357i
$330$	−2.41551			−0.132969
$331$	1.18995	−	2.06106i	0.0654056	−	0.113286i	−0.831468	−	0.555572i	$-0.812499\pi$
$331$	1.18995	−	2.06106i	0.0654056	−	0.113286i	0.896874	+	0.442286i	$0.145833\pi$
$332$	−1.24609	−	2.15830i	−0.0683882	−	0.118452i
$333$	−3.57428	+	2.06361i	−0.195869	+	0.113085i
$334$	−1.18666	−	0.685121i	−0.0649313	−	0.0374881i
$335$		−	28.8606i		−	1.57682i
$336$	−4.08337	−	8.68974i	−0.222766	−	0.474064i
$337$			6.18288i			0.336803i	0.985718	+	0.168402i	$0.0538605\pi$
$337$			6.18288i			0.336803i	−0.985718	+	0.168402i	$0.946139\pi$
$338$	13.0650	−	22.6292i	0.710642	−	1.23087i
$339$	5.31114	+	9.19916i	0.288461	+	0.499630i
$340$	−1.27311	−	2.20510i	−0.0690443	−	0.119588i
$341$	−0.751727	+	1.30203i	−0.0407083	+	0.0705088i
$342$	−1.99471			−0.107862
$343$	−4.63478	+	17.9309i	−0.250254	+	0.968180i
$344$			34.3817i			1.85374i
$345$	−10.1434	+	2.33268i	−0.546102	+	0.125588i
$346$	−12.4423	+	7.18358i	−0.668904	+	0.386192i
$347$	6.68290	+	11.5751i	0.358757	+	0.621385i	0.987753	−	0.156023i	$-0.0498675\pi$
$347$	6.68290	+	11.5751i	0.358757	+	0.621385i	−0.628997	+	0.777408i	$0.716534\pi$
$348$	0.614153	+	0.354581i	0.0329221	+	0.0190076i
$349$		−	11.6248i		−	0.622261i	−0.950367	−	0.311130i	$-0.899292\pi$
$349$		−	11.6248i		−	0.622261i	0.950367	−	0.311130i	$-0.100708\pi$
$350$	0.939159	−	0.441317i	0.0502002	−	0.0235894i
$351$	5.68513			0.303450
$352$	0.687129	+	0.396714i	0.0366241	+	0.0211449i
$353$	−18.7557	+	10.8286i	−0.998267	+	0.576350i	−0.907735	−	0.419544i	$-0.862190\pi$
$353$	−18.7557	+	10.8286i	−0.998267	+	0.576350i	−0.0905318	+	0.995894i	$0.528857\pi$
$354$	−3.02819	−	5.24499i	−0.160947	−	0.278768i
$355$	14.0078	−	24.2623i	0.743459	−	1.28771i
$356$	0.190421			0.0100923
$357$	18.0973	+	1.52948i	0.957808	+	0.0809489i
$358$	12.5262			0.662029
$359$	15.8606	+	9.15710i	0.837089	+	0.483293i	0.856274	−	0.516523i	$-0.172774\pi$
$359$	15.8606	+	9.15710i	0.837089	+	0.483293i	−0.0191849	+	0.999816i	$0.506107\pi$
$360$	−3.18596	−	5.51824i	−0.167915	−	0.290837i
$361$	8.41233	+	14.5706i	0.442754	+	0.766873i
$362$	−16.6740	+	28.8803i	−0.876368	+	1.51791i
$363$		−	10.3227i		−	0.541803i
$364$	−1.46832	+	2.11021i	−0.0769610	+	0.110605i
$365$		−	15.6603i		−	0.819699i
$366$	−0.474923	−	0.274197i	−0.0248246	−	0.0143325i
$367$	2.56064	+	4.43516i	0.133664	+	0.231514i	0.925086	−	0.379756i	$-0.123992\pi$
$367$	2.56064	+	4.43516i	0.133664	+	0.231514i	−0.791422	+	0.611270i	$0.790659\pi$
$368$	−16.6391	−	5.10259i	−0.867372	−	0.265991i
$369$	9.71258	+	5.60756i	0.505616	+	0.291918i
$370$			12.1139i			0.629774i
$371$	3.15093	−	4.52838i	0.163588	−	0.235102i
$372$	−0.312239			−0.0161888
$373$	27.7819	+	16.0399i	1.43849	+	0.830515i	0.997745	−	0.0671162i	$-0.0213798\pi$
$373$	27.7819	+	16.0399i	1.43849	+	0.830515i	0.440748	+	0.897631i	$0.354713\pi$
$374$	6.61665	−	3.82012i	0.342139	−	0.197534i
$375$	9.94253	−	5.74032i	0.513430	−	0.296429i
$376$	12.4269	+	7.17466i	0.640867	+	0.370005i
$377$			23.5889i			1.21489i
$378$	3.56550	+	0.301337i	0.183390	+	0.0154991i
$379$		−	5.91889i		−	0.304033i	−0.988378	−	0.152016i	$-0.951423\pi$
$379$		−	5.91889i		−	0.304033i	0.988378	−	0.152016i	$-0.0485766\pi$
$380$	0.273540	−	0.473785i	0.0140323	−	0.0243047i
$381$	13.3439	−	7.70410i	0.683629	−	0.394693i
$382$	22.3174	−	12.8850i	1.14186	−	0.659251i
$383$	10.2575	−	17.7665i	0.524133	−	0.907826i	−0.475472	−	0.879731i	$-0.657723\pi$
$383$	10.2575	−	17.7665i	0.524133	−	0.907826i	0.999605	−	0.0280947i	$-0.00894400\pi$
$384$		−	9.65110i		−	0.492506i
$385$	2.00969	+	4.27678i	0.102423	+	0.217965i
$386$	−29.6600			−1.50965
$387$	−10.1414	−	5.85515i	−0.515517	−	0.297634i
$388$	−0.266757	−	0.462037i	−0.0135425	−	0.0234564i
$389$	−29.1632	+	16.8374i	−1.47863	+	0.853690i	−0.999708	−	0.0241655i	$-0.992307\pi$
$389$	−29.1632	+	16.8374i	−1.47863	+	0.853690i	−0.478926	+	0.877855i	$0.658974\pi$
$390$	8.34330	−	14.4510i	0.422479	−	0.731755i
$391$	24.0960	−	22.4315i	1.21859	−	1.13441i
$392$	−13.1175	+	15.8216i	−0.662534	+	0.799112i
$393$	−11.2749			−0.568745
$394$	−8.41723	+	14.5791i	−0.424054	+	0.734483i
$395$	−5.42147	+	3.13009i	−0.272784	+	0.157492i
$396$	−0.121812	+	0.0703281i	−0.00612128	+	0.00353412i
$397$	−11.8578	−	6.84611i	−0.595126	−	0.343596i	0.171996	−	0.985098i	$-0.444979\pi$
$397$	−11.8578	−	6.84611i	−0.595126	−	0.343596i	−0.767122	+	0.641501i	$0.778312\pi$
$398$	−3.11917			−0.156350
$399$	1.65958	+	3.53173i	0.0830831	+	0.176808i
$400$	1.05240			0.0526199
$401$	−17.3766	−	10.0324i	−0.867746	−	0.500993i	−0.00114750	−	0.999999i	$-0.500365\pi$
$401$	−17.3766	−	10.0324i	−0.867746	−	0.500993i	−0.866599	+	0.499006i	$0.833699\pi$
$402$	8.99254	+	15.5755i	0.448507	+	0.776837i
$403$	−5.19301	−	8.99455i	−0.258682	−	0.448050i
$404$	−0.127068	−	0.0733629i	−0.00632188	−	0.00364994i
$405$	2.17025			0.107841
$406$	−1.25032	+	14.7941i	−0.0620523	+	0.734219i
$407$	3.39656			0.168361
$408$	17.4542	+	10.0772i	0.864111	+	0.498895i
$409$	−21.4043	+	12.3578i	−1.05838	+	0.611053i	−0.924982	−	0.380010i	$-0.875921\pi$
$409$	−21.4043	+	12.3578i	−1.05838	+	0.611053i	−0.133393	+	0.991063i	$0.542587\pi$
$410$	28.5077	−	16.4589i	1.40789	−	0.812848i
$411$	4.16141	−	7.20777i	0.205267	−	0.355533i
$412$	−2.44996			−0.120701
$413$	−6.76706	+	9.72535i	−0.332985	+	0.478553i
$414$	4.74737	−	4.41944i	0.233321	−	0.217204i
$415$	15.8228	−	27.4059i	0.776710	−	1.34530i
$416$	−4.74676	+	2.74054i	−0.232729	+	0.134366i
$417$	−8.45122	−	14.6380i	−0.413858	−	0.716824i
$418$	1.42165	+	0.820789i	0.0695350	+	0.0401461i
$419$	−20.9228			−1.02215			−0.511073	−	0.859537i	$-0.670752\pi$
$419$	−20.9228			−1.02215			−0.511073	+	0.859537i	$0.670752\pi$
$420$	−0.560521	+	0.805558i	−0.0273506	+	0.0393072i
$421$		−	14.5139i		−	0.707365i	−0.935366	−	0.353682i	$-0.884929\pi$
$421$		−	14.5139i		−	0.707365i	0.935366	−	0.353682i	$-0.115071\pi$
$422$	−3.55037	+	6.14942i	−0.172829	+	0.299349i
$423$	−4.23255	+	2.44366i	−0.205794	+	0.118815i
$424$	5.30182	−	3.06101i	0.257479	−	0.148656i
$425$	−0.995352	+	1.72400i	−0.0482817	+	0.0836263i
$426$			17.4585i			0.845869i
$427$	−0.0903465	+	1.06900i	−0.00437217	+	0.0517327i
$428$			2.26860i			0.109657i
$429$	−4.05184	−	2.33933i	−0.195625	−	0.112944i
$430$	−29.7664	+	17.1856i	−1.43546	+	0.828765i
$431$	12.4659	−	7.19716i	0.600459	−	0.346675i	−0.168763	−	0.985657i	$-0.553977\pi$
$431$	12.4659	−	7.19716i	0.600459	−	0.346675i	0.769222	+	0.638981i	$0.220644\pi$
$432$	3.14277	+	1.81448i	0.151207	+	0.0872992i
$433$	26.3437			1.26600			0.632999	−	0.774153i	$-0.281824\pi$
$433$	26.3437			1.26600			0.632999	+	0.774153i	$0.281824\pi$
$434$	−2.78011	−	5.91630i	−0.133450	−	0.283992i
$435$			9.00489i			0.431752i
$436$	0.846299	+	0.488611i	0.0405304	+	0.0234002i
$437$	6.76254	+	2.07382i	0.323496	+	0.0992042i
$438$	4.87953	+	8.45159i	0.233153	+	0.403832i
$439$	−1.16736	−	0.673978i	−0.0557152	−	0.0321672i	0.471884	−	0.881661i	$-0.343574\pi$
$439$	−1.16736	−	0.673978i	−0.0557152	−	0.0321672i	−0.527599	+	0.849494i	$0.676908\pi$
$440$			5.24387i			0.249991i
$441$	−2.43294	−	6.56360i	−0.115854	−	0.312552i
$442$			52.7796i			2.51047i
$443$	−5.37981	+	9.31811i	−0.255603	+	0.442717i	−0.965059	−	0.262033i	$-0.915607\pi$
$443$	−5.37981	+	9.31811i	−0.255603	+	0.442717i	0.709456	+	0.704749i	$0.248941\pi$
$444$	0.352700	+	0.610895i	0.0167384	+	0.0289918i
$445$	1.20898	+	2.09401i	0.0573110	+	0.0992656i
$446$	12.1109	+	6.99221i	0.573466	+	0.331091i
$447$	4.00714			0.189531
$448$	−20.5017	+	9.63390i	−0.968616	+	0.455159i
$449$	1.70559			0.0804918			0.0402459	−	0.999190i	$-0.487186\pi$
$449$	1.70559			0.0804918			0.0402459	+	0.999190i	$0.487186\pi$
$450$	−0.196103	+	0.339661i	−0.00924439	+	0.0160118i
$451$	−4.61482	−	7.99311i	−0.217304	−	0.376381i
$452$	1.57227	−	0.907748i	0.0739532	−	0.0426969i
$453$	1.42536	+	0.822931i	0.0669692	+	0.0386647i
$454$	29.7909			1.39816
$455$	−32.5278	−	2.74907i	−1.52492	−	0.128879i
$456$			4.33035i			0.202787i
$457$	18.6354	+	10.7592i	0.871729	+	0.503293i	0.867922	−	0.496700i	$-0.165455\pi$
$457$	18.6354	+	10.7592i	0.871729	+	0.503293i	0.00380635	+	0.999993i	$0.498788\pi$
$458$	0.0195893	+	0.0339296i	0.000915347	+	0.00158543i
$459$	−5.94483	+	3.43225i	−0.277481	+	0.160204i
$460$	0.398689	+	1.73365i	0.0185890	+	0.0808318i
$461$			33.7176i			1.57039i	0.619251	+	0.785193i	$0.287436\pi$
$461$			33.7176i			1.57039i	−0.619251	+	0.785193i	$0.712564\pi$
$462$	−2.41717	−	1.68191i	−0.112457	−	0.0782494i
$463$	−36.4966			−1.69614			−0.848070	−	0.529884i	$-0.822235\pi$
$463$	−36.4966			−1.69614			−0.848070	+	0.529884i	$0.822235\pi$
$464$	−7.52871	+	13.0401i	−0.349511	+	0.605372i
$465$	−1.98239	−	3.43360i	−0.0919311	−	0.159229i
$466$	−0.477850	−	0.827661i	−0.0221360	−	0.0383407i
$467$	−15.9429	+	27.6138i	−0.737747	+	1.27782i	0.215760	+	0.976446i	$0.430777\pi$
$467$	−15.9429	+	27.6138i	−0.737747	+	1.27782i	−0.953507	+	0.301369i	$0.902556\pi$
$468$		−	0.971668i		−	0.0449154i
$469$	20.0955	−	28.8804i	0.927924	−	1.33358i
$470$			14.3449i			0.661683i
$471$	−12.4067	−	7.16304i	−0.571673	−	0.330055i
$472$	−11.3864	+	6.57395i	−0.524102	+	0.302591i
$473$	4.81858	+	8.34603i	0.221559	+	0.383751i
$474$	1.95058	−	3.37850i	0.0895930	−	0.155180i
$475$	−0.427721			−0.0196252
$476$	0.261410	−	3.09307i	0.0119817	−	0.141771i
$477$			2.08514i			0.0954719i
$478$	1.92938	−	3.34178i	0.0882476	−	0.152849i
$479$	18.3441	+	31.7730i	0.838164	+	1.45174i	0.891428	+	0.453163i	$0.149704\pi$
$479$	18.3441	+	31.7730i	0.838164	+	1.45174i	−0.0532633	+	0.998581i	$0.516962\pi$
$480$	−1.81204	+	1.04618i	−0.0827078	+	0.0477514i
$481$	−11.7319	+	20.3202i	−0.534928	+	0.926523i
$482$	−8.10299			−0.369081
$483$	−11.7746	−	4.72851i	−0.535763	−	0.215155i
$484$	−1.76430			−0.0801954
$485$	3.38726	−	5.86691i	0.153808	−	0.266403i
$486$	−1.17124	+	0.676219i	−0.0531287	+	0.0306739i
$487$	21.7262	+	37.6309i	0.984508	+	1.70522i	0.644102	+	0.764940i	$0.277231\pi$
$487$	21.7262	+	37.6309i	0.984508	+	1.70522i	0.340407	+	0.940278i	$0.389435\pi$
$488$	−0.595258	+	1.03102i	−0.0269461	+	0.0466720i
$489$			11.5681i			0.523130i
$490$	−20.2545	−	3.44823i	−0.915005	−	0.155775i
$491$	24.4796			1.10475			0.552374	−	0.833597i	$-0.313722\pi$
$491$	24.4796			1.10475			0.552374	+	0.833597i	$0.313722\pi$
$492$	0.958411	−	1.66002i	0.0432085	−	0.0748393i
$493$	−14.2412	−	24.6665i	−0.641392	−	1.11092i
$494$	−9.82089	+	5.67009i	−0.441863	+	0.255109i
$495$	−1.54676	−	0.893021i	−0.0695216	−	0.0401383i
$496$		−	6.62965i		−	0.297680i
$497$	30.9112	−	14.5254i	1.38656	−	0.651552i
$498$			19.7206i			0.883700i
$499$	−0.373947	+	0.647696i	−0.0167402	+	0.0289948i	−0.874274	−	0.485433i	$-0.838662\pi$
$499$	−0.373947	+	0.647696i	−0.0167402	+	0.0289948i	0.857534	+	0.514427i	$0.171995\pi$
$500$	−0.981101	−	1.69932i	−0.0438762	−	0.0759958i
$501$	−0.506582	−	0.877426i	−0.0226324	−	0.0392005i
$502$	13.5825	−	23.5255i	0.606215	−	1.05000i
$503$	17.9564			0.800636			0.400318	−	0.916376i	$-0.368900\pi$
$503$	17.9564			0.800636			0.400318	+	0.916376i	$0.368900\pi$
$504$	0.654177	−	7.74040i	0.0291394	−	0.344785i
$505$		−	1.86311i		−	0.0829074i
$506$	−5.20201	+	1.19631i	−0.231258	+	0.0531825i
$507$	16.7322	−	9.66033i	0.743102	−	0.429030i
$508$	−1.31674	−	2.28066i	−0.0584209	−	0.101188i
$509$	12.6221	+	7.28735i	0.559463	+	0.323006i	0.752930	−	0.658101i	$-0.228640\pi$
$509$	12.6221	+	7.28735i	0.559463	+	0.323006i	−0.193467	+	0.981107i	$0.561973\pi$
$510$			20.1482i			0.892178i
$511$	10.9042	−	15.6711i	0.482374	−	0.693248i
$512$	−24.8081			−1.09638
$513$	−1.27730	−	0.737450i	−0.0563942	−	0.0325592i
$514$	7.08947	−	4.09311i	0.312703	−	0.180539i
$515$	−15.5547	−	26.9416i	−0.685423	−	1.18719i
$516$	−1.00073	+	1.73331i	−0.0440546	+	0.0763048i
$517$	4.02210			0.176892
$518$	−8.43487	+	12.1223i	−0.370607	+	0.532621i
$519$	−10.6232			−0.466305
$520$	−31.3719	−	18.1126i	−1.37575	−	0.794289i
$521$	−0.829982	−	1.43757i	−0.0363622	−	0.0629811i	0.847272	−	0.531160i	$-0.178244\pi$
$521$	−0.829982	−	1.43757i	−0.0363622	−	0.0629811i	−0.883634	+	0.468179i	$0.844910\pi$
$522$	−2.80579	−	4.85977i	−0.122806	−	0.212706i
$523$	10.1696	−	17.6143i	0.444688	−	0.770222i	−0.553343	−	0.832954i	$-0.686648\pi$
$523$	10.1696	−	17.6143i	0.444688	−	0.770222i	0.998030	+	0.0627321i	$0.0199814\pi$
$524$			1.92704i			0.0841833i
$525$	0.764541	+	0.0646150i	0.0333673	+	0.00282003i
$526$		−	12.8050i		−	0.558322i
$527$	10.8605	+	6.27029i	0.473089	+	0.273138i
$528$	−1.49325	−	2.58639i	−0.0649855	−	0.112558i
$529$	−20.6894	+	10.0473i	−0.899540	+	0.436839i
$530$	5.30021	+	3.06008i	0.230226	+	0.132921i
$531$		−	4.47813i		−	0.194334i
$532$	0.603622	−	0.283646i	0.0261703	−	0.0122976i
$533$	63.7594			2.76172
$534$	−1.30492	−	0.753399i	−0.0564696	−	0.0326027i
$535$	−24.9471	+	14.4032i	−1.07856	+	0.622706i
$536$	33.8132	−	19.5220i	1.46051	−	0.843224i
$537$	8.02106	+	4.63096i	0.346134	+	0.199841i
$538$		−	2.96876i		−	0.127993i
$539$	−0.966831	+	5.67904i	−0.0416444	+	0.244614i
$540$		−	0.370927i		−	0.0159621i
$541$	−10.9203	+	18.9146i	−0.469502	+	0.813201i	−0.999392	−	0.0348652i	$-0.988900\pi$
$541$	−10.9203	+	18.9146i	−0.469502	+	0.813201i	0.529890	+	0.848066i	$0.322233\pi$
$542$	−16.0222	+	9.25040i	−0.688211	+	0.397339i
$543$	−21.3543	+	12.3289i	−0.916399	+	0.529083i
$544$	3.30906	−	5.73147i	0.141875	−	0.245735i
$545$			12.4087i			0.531530i
$546$	18.4112	−	8.65154i	0.787926	−	0.370252i
$547$	36.5267			1.56177			0.780885	−	0.624675i	$-0.214769\pi$
$547$	36.5267			1.56177			0.780885	+	0.624675i	$0.214769\pi$
$548$	−1.23191	−	0.711243i	−0.0526246	−	0.0303828i
$549$	−0.202743	−	0.351161i	−0.00865286	−	0.0149872i
$550$	0.279529	−	0.161386i	0.0119191	−	0.00688152i
$551$	3.05986	−	5.29983i	0.130354	−	0.225780i
$552$	−9.59422	−	10.3061i	−0.408357	−	0.438658i
$553$	−7.60465	−	0.642705i	−0.323383	−	0.0273306i
$554$	25.4614			1.08175
$555$	−4.47856	+	7.75709i	−0.190104	+	0.329270i
$556$	−2.50183	+	1.44443i	−0.106101	+	0.0612576i
$557$	17.6903	−	10.2135i	0.749561	−	0.432759i	−0.0759740	−	0.997110i	$-0.524207\pi$
$557$	17.6903	−	10.2135i	0.749561	−	0.432759i	0.825535	+	0.564350i	$0.190873\pi$
$558$	2.13972	+	1.23537i	0.0905814	+	0.0522972i
$559$	−66.5745			−2.81580
$560$	−17.1041	−	11.9013i	−0.722782	−	0.502924i
$561$	5.64925			0.238511
$562$	24.3414	+	14.0535i	1.02678	+	0.592813i
$563$	−7.89938	−	13.6821i	−0.332919	−	0.576633i	0.650164	−	0.759794i	$-0.274700\pi$
$563$	−7.89938	−	13.6821i	−0.332919	−	0.576633i	−0.983083	+	0.183161i	$0.941367\pi$
$564$	0.417657	+	0.723402i	0.0175865	+	0.0304607i
$565$	19.9645	+	11.5265i	0.839913	+	0.484924i
$566$	36.4815			1.53343
$567$	2.17174	+	1.51114i	0.0912046	+	0.0634617i
$568$	37.9010			1.59029
$569$	−18.9049	−	10.9148i	−0.792536	−	0.457571i	0.0483183	−	0.998832i	$-0.484614\pi$
$569$	−18.9049	−	10.9148i	−0.792536	−	0.457571i	−0.840855	+	0.541261i	$0.817947\pi$
$570$	−3.74905	+	2.16451i	−0.157030	+	0.0906615i
$571$	−19.2670	+	11.1238i	−0.806300	+	0.465518i	−0.845669	−	0.533707i	$-0.820798\pi$
$571$	−19.2670	+	11.1238i	−0.806300	+	0.465518i	0.0393693	+	0.999225i	$0.487465\pi$
$572$	−0.399824	+	0.692516i	−0.0167175	+	0.0289556i
$573$	19.0544			0.796010
$574$	39.9875	+	3.37953i	1.66905	+	0.141059i
$575$	1.01797	−	0.947649i	0.0424522	−	0.0395197i
$576$	4.28091	−	7.41475i	0.178371	−	0.308948i
$577$	−8.46234	+	4.88573i	−0.352292	+	0.203396i	−0.665694	−	0.746225i	$-0.731864\pi$
$577$	−8.46234	+	4.88573i	−0.352292	+	0.203396i	0.313402	+	0.949620i	$0.398531\pi$
$578$	−20.3687	−	35.2795i	−0.847224	−	1.46744i
$579$	−18.9926	−	10.9654i	−0.789305	−	0.455706i
$580$	1.53906			0.0639061
$581$	34.9162	−	16.4074i	1.44857	−	0.680692i
$582$			4.22168i			0.174994i
$583$	0.857997	−	1.48610i	0.0355346	−	0.0615478i
$584$	18.3477	−	10.5930i	0.759232	−	0.438343i
$585$	10.6852	−	6.16908i	0.441777	−	0.255060i
$586$	−13.4654	+	23.3228i	−0.556251	+	0.963455i
$587$		−	27.0020i		−	1.11449i	−0.830348	−	0.557245i	$-0.811858\pi$
$587$		−	27.0020i		−	1.11449i	0.830348	−	0.557245i	$-0.188142\pi$
$588$	−1.12181	+	0.415823i	−0.0462627	+	0.0171483i
$589$			2.69446i			0.111023i
$590$	−11.3830	−	6.57195i	−0.468629	−	0.270563i
$591$	−10.7799	+	6.22375i	−0.443424	+	0.256011i
$592$	−12.9709	+	7.48876i	−0.533101	+	0.307786i
$593$	5.50082	+	3.17590i	0.225892	+	0.130419i	0.608675	−	0.793419i	$-0.291701\pi$
$593$	5.50082	+	3.17590i	0.225892	+	0.130419i	−0.382784	+	0.923838i	$0.625035\pi$
$594$	1.11301			0.0456673
$595$	35.6734	−	16.7632i	1.46247	−	0.687222i
$596$		−	0.684876i		−	0.0280536i
$597$	−1.99734	−	1.15317i	−0.0817459	−	0.0471960i
$598$	10.8110	−	35.2536i	0.442094	−	1.44163i
$599$	12.4662	+	21.5920i	0.509353	+	0.882226i	0.999941	+	0.0108340i	$0.00344862\pi$
$599$	12.4662	+	21.5920i	0.509353	+	0.882226i	−0.490588	+	0.871392i	$0.663218\pi$
$600$	0.737374	+	0.425723i	0.0301032	+	0.0173801i
$601$		−	36.9718i		−	1.50811i	−0.656811	−	0.754055i	$-0.728095\pi$
$601$		−	36.9718i		−	1.50811i	0.656811	−	0.754055i	$-0.271905\pi$
$602$	−41.7531	−	3.52875i	−1.70173	−	0.143821i
$603$			13.2983i			0.541548i
$604$	0.140650	−	0.243614i	0.00572299	−	0.00991250i
$605$	−11.2015	−	19.4015i	−0.455404	−	0.788784i
$606$	0.580518	+	1.00549i	0.0235819	+	0.0408451i
$607$	−20.8840	−	12.0574i	−0.847656	−	0.489395i	0.0122032	−	0.999926i	$-0.496116\pi$
$607$	−20.8840	−	12.0574i	−0.847656	−	0.489395i	−0.859859	+	0.510531i	$0.829449\pi$
$608$	1.42197			0.0576683
$609$	−6.27006	+	9.01107i	−0.254076	+	0.365147i
$610$	−1.19015			−0.0481879
$611$	−13.8925	+	24.0626i	−0.562032	+	0.973468i
$612$	0.586620	+	1.01606i	0.0237127	+	0.0410716i
$613$	−20.5349	+	11.8558i	−0.829398	+	0.478853i	−0.853647	−	0.520853i	$-0.825614\pi$
$613$	−20.5349	+	11.8558i	−0.829398	+	0.478853i	0.0242485	+	0.999706i	$0.492281\pi$
$614$	−27.5496	−	15.9058i	−1.11181	−	0.641904i
$615$	24.3396			0.981469
$616$	−3.65128	+	5.24746i	−0.147114	+	0.211426i
$617$			11.0717i			0.445728i	0.974850	+	0.222864i	$0.0715406\pi$
$617$			11.0717i			0.445728i	−0.974850	+	0.222864i	$0.928459\pi$
$618$	16.7892	+	9.69324i	0.675360	+	0.389919i
$619$	0.115090	+	0.199341i	0.00462584	+	0.00801219i	0.868329	−	0.495989i	$-0.165194\pi$
$619$	0.115090	+	0.199341i	0.00462584	+	0.00801219i	−0.863703	+	0.504001i	$0.831861\pi$
$620$	−0.586851	+	0.338818i	−0.0235685	+	0.0136073i
$621$	4.67383	−	1.07484i	0.187554	−	0.0431320i
$622$			4.24520i			0.170217i
$623$	−0.248241	+	2.93725i	−0.00994556	+	0.117679i
$624$	20.6311			0.825905
$625$	11.7330	−	20.3221i	0.469318	−	0.812883i
$626$	−15.0245	−	26.0232i	−0.600501	−	1.04010i
$627$	0.606896	+	1.05117i	0.0242371	+	0.0419799i
$628$	−1.22426	+	2.12049i	−0.0488534	+	0.0846166i
$629$		−	28.3313i		−	1.12964i
$630$	7.02833	−	3.30266i	0.280015	−	0.131581i
$631$			11.4264i			0.454878i	0.973792	+	0.227439i	$0.0730352\pi$
$631$			11.4264i			0.454878i	−0.973792	+	0.227439i	$0.926965\pi$
$632$	−7.33443	−	4.23453i	−0.291748	−	0.168441i
$633$	−4.54692	+	2.62516i	−0.180724	+	0.104341i
$634$	7.88685	+	13.6604i	0.313227	+	0.542525i
$635$	16.7199	−	28.9596i	0.663507	−	1.14923i
$636$	0.356379			0.0141314
$637$	−30.6359	−	25.3999i	−1.21384	−	1.00638i
$638$			4.61813i			0.182834i
$639$	−6.45447	+	11.1795i	−0.255335	+	0.442253i
$640$	−10.4727	−	18.1392i	−0.413969	−	0.717015i
$641$	16.2324	−	9.37180i	0.641143	−	0.370164i	−0.143912	−	0.989591i	$-0.545968\pi$
$641$	16.2324	−	9.37180i	0.641143	−	0.370164i	0.785055	+	0.619427i	$0.212635\pi$
$642$	8.97566	−	15.5463i	0.354241	−	0.613563i
$643$	10.8738			0.428822			0.214411	−	0.976744i	$-0.431217\pi$
$643$	10.8738			0.428822			0.214411	+	0.976744i	$0.431217\pi$
$644$	−0.808169	+	2.01244i	−0.0318463	+	0.0793014i
$645$	−25.4143			−1.00069
$646$	6.84635	−	11.8582i	0.269366	−	0.466556i
$647$	21.5922	−	12.4663i	0.848878	−	0.490100i	−0.0113938	−	0.999935i	$-0.503627\pi$
$647$	21.5922	−	12.4663i	0.848878	−	0.490100i	0.860272	+	0.509835i	$0.170294\pi$
$648$	1.46801	+	2.54267i	0.0576690	+	0.0998856i
$649$	−1.84267	+	3.19160i	−0.0723312	+	0.125281i
$650$			2.22974i			0.0874577i
$651$	0.407047	−	4.81629i	0.0159534	−	0.188765i
$652$	1.97716			0.0774315
$653$	−12.5455	+	21.7294i	−0.490942	+	0.850336i	−0.999946	−	0.0104284i	$-0.996680\pi$
$653$	−12.5455	+	21.7294i	−0.490942	+	0.850336i	0.509004	+	0.860764i	$0.330014\pi$
$654$	−3.86636	−	6.69673i	−0.151187	−	0.261863i
$655$	−21.1912	+	12.2347i	−0.828008	+	0.478050i
$656$	35.2466	+	20.3496i	1.37615	+	0.794519i
$657$			7.21590i			0.281519i
$658$	−9.98831	+	14.3548i	−0.389385	+	0.559608i
$659$			29.1937i			1.13722i	0.822606	+	0.568612i	$0.192519\pi$
$659$			29.1937i			1.13722i	−0.822606	+	0.568612i	$0.807481\pi$
$660$	−0.152630	+	0.264363i	−0.00594111	+	0.0102903i
$661$	−23.6269	−	40.9230i	−0.918980	−	1.59172i	−0.800968	−	0.598707i	$-0.795681\pi$
$661$	−23.6269	−	40.9230i	−0.918980	−	1.59172i	−0.118012	−	0.993012i	$-0.537652\pi$
$662$	1.60933	+	2.78745i	0.0625485	+	0.108337i
$663$	−19.5128	+	33.7971i	−0.757814	+	1.31257i
$664$	42.8117			1.66141
$665$	6.95155	+	4.83701i	0.269570	+	0.187571i
$666$		−	5.58181i		−	0.216291i
$667$	4.45978	+	19.3928i	0.172683	+	0.750893i
$668$	−0.149964	+	0.0865820i	−0.00580230	+	0.00334996i
$669$	5.17008	+	8.95485i	0.199887	+	0.346214i
$670$	33.8029	+	19.5161i	1.30592	+	0.753973i
$671$			0.333701i			0.0128824i
$672$	−2.54173	−	0.214814i	−0.0980494	−	0.00828662i
$673$	7.57755			0.292093			0.146047	−	0.989278i	$-0.453345\pi$
$673$	7.57755			0.292093			0.146047	+	0.989278i	$0.453345\pi$
$674$	−7.24167	−	4.18098i	−0.278939	−	0.161045i
$675$	−0.251147	+	0.145000i	−0.00966666	+	0.00558105i
$676$	−1.65109	−	2.85977i	−0.0635033	−	0.109991i
$677$	1.26519	−	2.19137i	0.0486251	−	0.0842211i	−0.840688	−	0.541519i	$-0.817849\pi$
$677$	1.26519	−	2.19137i	0.0486251	−	0.0842211i	0.889314	+	0.457298i	$0.151183\pi$
$678$	−14.3660			−0.551721
$679$	7.47468	−	3.51240i	0.286852	−	0.134794i
$680$	43.7401			1.67735
$681$	19.0764	+	11.0138i	0.731011	+	0.422049i
$682$	−1.01666	−	1.76091i	−0.0389300	−	0.0674288i
$683$	7.77348	+	13.4641i	0.297444	+	0.515188i	0.975550	−	0.219775i	$-0.0705325\pi$
$683$	7.77348	+	13.4641i	0.297444	+	0.515188i	−0.678106	+	0.734964i	$0.737199\pi$
$684$	−0.126041	+	0.218309i	−0.00481928	+	0.00834725i
$685$		−	18.0626i		−	0.690137i
$686$	−17.8674	−	17.5537i	−0.682181	−	0.670203i
$687$			0.0289688i			0.00110523i
$688$	−36.8028	−	21.2481i	−1.40309	−	0.810077i
$689$	5.92713	+	10.2661i	0.225806	+	0.391107i
$690$	4.12701	−	13.4578i	0.157113	−	0.512330i
$691$	−16.6859	−	9.63360i	−0.634761	−	0.366479i	0.147833	−	0.989012i	$-0.452770\pi$
$691$	−16.6859	−	9.63360i	−0.634761	−	0.366479i	−0.782594	+	0.622533i	$0.786104\pi$
$692$			1.81565i			0.0690206i
$693$	−0.926014	−	1.97063i	−0.0351764	−	0.0748582i
$694$	−18.0764			−0.686170
$695$	−31.7681	−	18.3413i	−1.20503	−	0.695725i
$696$	−10.5501	+	6.09113i	−0.399902	+	0.230884i
$697$	−66.6720	+	38.4931i	−2.52538	+	1.45803i
$698$	13.6155	+	7.86090i	0.515353	+	0.297539i
$699$		−	0.706651i		−	0.0267280i
$700$	0.0110436	−	0.130671i	0.000417409	−	0.00493890i
$701$		−	47.7759i		−	1.80447i	−0.431245	−	0.902235i	$-0.641925\pi$
$701$		−	47.7759i		−	1.80447i	0.431245	−	0.902235i	$-0.358075\pi$
$702$	−3.84439	+	6.65867i	−0.145097	+	0.251315i
$703$	5.27171	−	3.04362i	0.198826	−	0.114792i
$704$	−6.10208	+	3.52304i	−0.229981	+	0.132779i
$705$	−5.30337	+	9.18571i	−0.199736	+	0.345954i
$706$		−	29.2901i		−	1.10235i
$707$	1.29727	−	1.86439i	0.0487890	−	0.0701176i
$708$	−0.765375			−0.0287646
$709$	−1.58540	−	0.915330i	−0.0595409	−	0.0343760i	0.469934	−	0.882702i	$-0.344278\pi$
$709$	−1.58540	−	0.915330i	−0.0595409	−	0.0343760i	−0.529475	+	0.848326i	$0.677611\pi$
$710$	18.9447	+	32.8132i	0.710983	+	1.23146i
$711$	2.49808	−	1.44227i	0.0936854	−	0.0540893i
$712$	−1.63556	+	2.83288i	−0.0612953	+	0.106167i
$713$	−5.96978	−	6.41276i	−0.223570	−	0.240160i
$714$	−14.0291	+	20.1620i	−0.525026	+	0.754546i
$715$	−10.1539			−0.379734
$716$	0.791497	−	1.37091i	0.0295796	−	0.0512334i
$717$	2.47093	−	1.42659i	0.0922786	−	0.0532771i
$718$	−21.4504	+	12.3844i	−0.800522	+	0.462182i
$719$	−30.0686	−	17.3601i	−1.12137	−	0.647422i	−0.179618	−	0.983736i	$-0.557486\pi$
$719$	−30.0686	−	17.3601i	−1.12137	−	0.647422i	−0.941750	+	0.336314i	$0.890820\pi$
$720$	7.87576			0.293512
$721$	3.19387	−	37.7907i	0.118946	−	1.40740i
$722$	−22.7543			−0.846827
$723$	−5.18870	−	2.99570i	−0.192970	−	0.111411i
$724$	2.10718	+	3.64974i	0.0783127	+	0.135642i
$725$	−0.601639	−	1.04207i	−0.0223443	−	0.0387015i
$726$	12.0904	+	6.98042i	0.448718	+	0.259068i
$727$	−21.5987			−0.801051			−0.400526	−	0.916286i	$-0.631172\pi$
$727$	−21.5987			−0.801051			−0.400526	+	0.916286i	$0.631172\pi$
$728$	−18.7817	−	39.9691i	−0.696098	−	1.48135i
$729$	−1.00000			−0.0370370
$730$	18.3421	+	10.5898i	0.678871	+	0.391946i
$731$	69.6158	−	40.1927i	2.57483	−	1.48658i
$732$	−0.0600184	+	0.0346516i	−0.00221834	+	0.00128076i
$733$	−16.4820	+	28.5477i	−0.608778	+	1.05443i	0.382664	+	0.923888i	$0.375007\pi$
$733$	−16.4820	+	28.5477i	−0.608778	+	1.05443i	−0.991442	+	0.130547i	$0.958327\pi$
$734$	−6.92622			−0.255651
$735$	−11.6950	−	9.69620i	−0.431378	−	0.357650i
$736$	−3.38425	+	3.15048i	−0.124745	+	0.116128i
$737$	5.47201	−	9.47780i	0.201564	−	0.349119i
$738$	−13.1356	+	7.58387i	−0.483530	+	0.279166i
$739$	8.48704	+	14.7000i	0.312201	+	0.540748i	0.978839	−	0.204634i	$-0.0656004\pi$
$739$	8.48704	+	14.7000i	0.312201	+	0.540748i	−0.666638	+	0.745382i	$0.732267\pi$
$740$	1.32580	+	0.765449i	0.0487372	+	0.0281385i
$741$	−8.38500			−0.308031
$742$	3.17313	+	6.75268i	0.116489	+	0.247899i
$743$			7.62276i			0.279652i	0.990176	+	0.139826i	$0.0446543\pi$
$743$			7.62276i			0.279652i	−0.990176	+	0.139826i	$0.955346\pi$
$744$	2.68187	−	4.64514i	0.0983223	−	0.170299i
$745$	7.53139	−	4.34825i	0.275929	−	0.159308i
$746$	−37.5733	+	21.6930i	−1.37566	+	0.794236i
$747$	−7.29075	+	12.6280i	−0.266755	+	0.462033i
$748$		−	0.965536i		−	0.0353035i
$749$	−34.9931	−	2.95743i	−1.27862	−	0.108062i
$750$			15.5268i			0.566960i
$751$	−33.2981	−	19.2247i	−1.21506	−	0.701518i	−0.251206	−	0.967934i	$-0.580827\pi$
$751$	−33.2981	−	19.2247i	−1.21506	−	0.701518i	−0.963858	+	0.266416i	$0.914160\pi$
$752$	−15.3598	+	8.86796i	−0.560113	+	0.323381i
$753$	17.3949	−	10.0430i	0.633906	−	0.365986i
$754$	−27.6284	−	15.9513i	−1.00617	−	0.580911i
$755$	3.57194			0.129996
$756$	0.258274	−	0.371181i	0.00939335	−	0.0134997i
$757$		−	11.7485i		−	0.427006i	−0.976942	−	0.213503i	$-0.931513\pi$
$757$		−	11.7485i		−	0.427006i	0.976942	−	0.213503i	$-0.0684873\pi$
$758$	6.93246	+	4.00246i	0.251798	+	0.145376i
$759$	−3.77336	−	1.15715i	−0.136964	−	0.0420019i
$760$	4.69897	+	8.13886i	0.170450	+	0.295228i
$761$	−19.3913	−	11.1955i	−0.702932	−	0.405838i	0.105506	−	0.994419i	$-0.466354\pi$
$761$	−19.3913	−	11.1955i	−0.702932	−	0.405838i	−0.808439	+	0.588580i	$0.799687\pi$
$762$			20.8386i			0.754904i
$763$	−8.64010	+	12.4172i	−0.312793	+	0.449533i
$764$		−	3.25667i		−	0.117822i
$765$	−7.44886	+	12.9018i	−0.269314	+	0.466465i
$766$	13.8726	+	24.0281i	0.501238	+	0.868169i
$767$	−12.7294	−	22.0479i	−0.459631	−	0.796104i
$768$	−3.52570	−	2.03556i	−0.127223	−	0.0734521i
$769$	45.1447			1.62796			0.813979	−	0.580894i	$-0.197297\pi$
$769$	45.1447			1.62796			0.813979	+	0.580894i	$0.197297\pi$
$770$	−6.36814	−	0.538201i	−0.229492	−	0.0193954i
$771$	6.05294			0.217991
$772$	−1.87414	+	3.24610i	−0.0674517	+	0.116830i
$773$	10.4108	+	18.0320i	0.374451	+	0.648568i	0.990245	−	0.139340i	$-0.0444980\pi$

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.676219 + 1.17124i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.0854570 + 0.148016i) q^{4} +(-1.08513 + 1.87949i) q^{5} -1.35244i q^{6} +(-2.39455 + 1.12522i) q^{7} -2.93602 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.46757 - 2.54190i) q^{10} +(-0.712709 + 0.411483i) q^{11} +(-0.148016 - 0.0854570i) q^{12} -5.68513i q^{13} +(0.301337 - 3.56550i) q^{14} -2.17025i q^{15} +(1.81448 - 3.14277i) q^{16} +(3.43225 + 5.94483i) q^{17} +(0.676219 + 1.17124i) q^{18} +(-0.737450 + 1.27730i) q^{19} -0.370927 q^{20} +(1.51114 - 2.17174i) q^{21} -1.11301i q^{22} +(-1.07484 - 4.67383i) q^{23} +(2.54267 - 1.46801i) q^{24} +(0.145000 + 0.251147i) q^{25} +(6.65867 + 3.84439i) q^{26} +1.00000i q^{27} +(-0.371181 - 0.258274i) q^{28} -4.14924 q^{29} +(2.54190 + 1.46757i) q^{30} +(1.58212 - 0.913437i) q^{31} +(-0.482054 - 0.834943i) q^{32} +(0.411483 - 0.712709i) q^{33} -9.28381 q^{34} +(0.483555 - 5.72155i) q^{35} +0.170914 q^{36} +(-3.57428 - 2.06361i) q^{37} +(-0.997355 - 1.72747i) q^{38} +(2.84256 + 4.92346i) q^{39} +(3.18596 - 5.51824i) q^{40} +11.2151i q^{41} +(1.52178 + 3.23848i) q^{42} -11.7103i q^{43} +(-0.121812 - 0.0703281i) q^{44} +(1.08513 + 1.87949i) q^{45} +(6.20103 + 1.90163i) q^{46} +(-4.23255 - 2.44366i) q^{47} +3.62896i q^{48} +(4.46777 - 5.38878i) q^{49} -0.392206 q^{50} +(-5.94483 - 3.43225i) q^{51} +(0.841489 - 0.485834i) q^{52} +(-1.80578 + 1.04257i) q^{53} +(-1.17124 - 0.676219i) q^{54} -1.78604i q^{55} +(7.03047 - 3.30366i) q^{56} -1.47490i q^{57} +(2.80579 - 4.85977i) q^{58} +(3.87817 - 2.23906i) q^{59} +(0.321232 - 0.185463i) q^{60} +(0.202743 - 0.351161i) q^{61} +2.47073i q^{62} +(-0.222811 + 2.63635i) q^{63} +8.56182 q^{64} +(10.6852 + 6.16908i) q^{65} +(0.556504 + 0.963894i) q^{66} +(-11.5166 + 6.64914i) q^{67} +(-0.586620 + 1.01606i) q^{68} +(3.26776 + 3.51024i) q^{69} +(6.37435 + 4.43538i) q^{70} -12.9089 q^{71} +(-1.46801 + 2.54267i) q^{72} +(-6.24915 + 3.60795i) q^{73} +(4.83399 - 2.79090i) q^{74} +(-0.251147 - 0.145000i) q^{75} -0.252081 q^{76} +(1.24361 - 1.78727i) q^{77} -7.68878 q^{78} +(2.49808 + 1.44227i) q^{79} +(3.93788 + 6.82061i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.1356 - 7.58387i) q^{82} -14.5815 q^{83} +(0.450590 + 0.0380815i) q^{84} -14.8977 q^{85} +(13.7156 + 7.91872i) q^{86} +(3.59334 - 2.07462i) q^{87} +(2.09253 - 1.20812i) q^{88} +(0.557067 - 0.964869i) q^{89} -2.93513 q^{90} +(6.39700 + 13.6133i) q^{91} +(0.599949 - 0.558506i) q^{92} +(-0.913437 + 1.58212i) q^{93} +(5.72426 - 3.30490i) q^{94} +(-1.60045 - 2.77207i) q^{95} +(0.834943 + 0.482054i) q^{96} -3.12154 q^{97} +(3.29039 + 8.87685i) q^{98} +0.822965i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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