LMFDB - Embedded newform 644.2.bc.a.493.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.13
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.948121 + 1.83910i) q^{3} +(4.15893 - 0.397129i) q^{5} +(-2.51495 + 0.821585i) q^{7} +(-0.743179 + 1.04365i) q^{9} +O(q^{10})$	\(q+(0.948121 + 1.83910i) q^{3} +(4.15893 - 0.397129i) q^{5} +(-2.51495 + 0.821585i) q^{7} +(-0.743179 + 1.04365i) q^{9} +(-1.71849 + 0.594775i) q^{11} +(1.51404 + 5.15635i) q^{13} +(4.67353 + 7.27215i) q^{15} +(-1.20544 - 0.482587i) q^{17} +(-1.20904 + 0.484027i) q^{19} +(-3.89546 - 3.84629i) q^{21} +(4.64552 - 1.19129i) q^{23} +(12.2293 - 2.35701i) q^{25} +(3.52015 + 0.506122i) q^{27} +(-0.925829 - 6.43928i) q^{29} +(-8.98607 + 0.428059i) q^{31} +(-2.72319 - 2.59655i) q^{33} +(-10.1332 + 4.41568i) q^{35} +(8.64906 + 6.15897i) q^{37} +(-8.04755 + 7.67332i) q^{39} +(-7.98549 - 3.64685i) q^{41} +(2.43868 - 3.79466i) q^{43} +(-2.67636 + 4.63560i) q^{45} +(0.169102 - 0.0976313i) q^{47} +(5.65000 - 4.13250i) q^{49} +(-0.255382 - 2.67448i) q^{51} +(-4.57014 - 4.79303i) q^{53} +(-6.91087 + 3.15609i) q^{55} +(-2.03649 - 1.76463i) q^{57} +(5.99232 + 1.45372i) q^{59} +(1.23460 + 0.636481i) q^{61} +(1.01161 - 3.23531i) q^{63} +(8.34453 + 20.8436i) q^{65} +(-0.261404 - 1.35629i) q^{67} +(6.59541 + 7.41408i) q^{69} +(-5.41317 - 6.24713i) q^{71} +(-6.43795 + 8.18651i) q^{73} +(15.9297 + 20.2562i) q^{75} +(3.83327 - 2.90772i) q^{77} +(1.25107 - 1.31208i) q^{79} +(3.66386 + 10.5860i) q^{81} +(-4.32512 - 9.47070i) q^{83} +(-5.20501 - 1.52833i) q^{85} +(10.9647 - 7.80791i) q^{87} +(-0.149750 + 3.14365i) q^{89} +(-8.04413 - 11.7241i) q^{91} +(-9.30713 - 16.1204i) q^{93} +(-4.83610 + 2.49318i) q^{95} +(1.75689 - 3.84705i) q^{97} +(0.656409 - 2.23552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

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			0
$2$		0			0
$3$	0.948121	+	1.83910i	0.547398	+	1.06180i	0.986561	+	0.163396i	$0.0522449\pi$
$3$	0.948121	+	1.83910i	0.547398	+	1.06180i	−0.439163	+	0.898408i	$0.644725\pi$
$4$		0			0
$5$	4.15893	−	0.397129i	1.85993	−	0.177602i	0.896052	−	0.443949i	$-0.146423\pi$
$5$	4.15893	−	0.397129i	1.85993	−	0.177602i	0.963877	+	0.266347i	$0.0858168\pi$
$6$		0			0
$7$	−2.51495	+	0.821585i	−0.950564	+	0.310530i
$7$	−2.51495	+	0.821585i	−0.950564	+	0.310530i
$8$		0			0
$9$	−0.743179	+	1.04365i	−0.247726	+	0.347883i
$10$		0			0
$11$	−1.71849	+	0.594775i	−0.518144	+	0.179331i	−0.573609	−	0.819129i	$-0.694457\pi$
$11$	−1.71849	+	0.594775i	−0.518144	+	0.179331i	0.0554649	+	0.998461i	$0.482336\pi$
$12$		0			0
$13$	1.51404	+	5.15635i	0.419920	+	1.43011i	0.849741	+	0.527201i	$0.176758\pi$
$13$	1.51404	+	5.15635i	0.419920	+	1.43011i	−0.429821	+	0.902914i	$0.641423\pi$
$14$		0			0
$15$	4.67353	+	7.27215i	1.20670	+	1.87766i
$16$		0			0
$17$	−1.20544	−	0.482587i	−0.292363	−	0.117045i	0.220844	−	0.975309i	$-0.429119\pi$
$17$	−1.20544	−	0.482587i	−0.292363	−	0.117045i	−0.513208	+	0.858264i	$0.671543\pi$
$18$		0			0
$19$	−1.20904	+	0.484027i	−0.277373	+	0.111043i	−0.506179	−	0.862429i	$-0.668942\pi$
$19$	−1.20904	+	0.484027i	−0.277373	+	0.111043i	0.228805	+	0.973472i	$0.426518\pi$
$20$		0			0
$21$	−3.89546	−	3.84629i	−0.850059	−	0.839329i
$22$		0			0
$23$	4.64552	−	1.19129i	0.968657	−	0.248400i
$23$	4.64552	−	1.19129i	0.968657	−	0.248400i
$24$		0			0
$25$	12.2293	−	2.35701i	2.44587	−	0.471402i
$26$		0			0
$27$	3.52015	+	0.506122i	0.677454	+	0.0974032i
$28$		0			0
$29$	−0.925829	−	6.43928i	−0.171922	−	1.19574i	−0.874818	−	0.484452i	$-0.839019\pi$
$29$	−0.925829	−	6.43928i	−0.171922	−	1.19574i	0.702896	−	0.711293i	$-0.251890\pi$
$30$		0			0
$31$	−8.98607	+	0.428059i	−1.61395	+	0.0768817i	−0.835015	−	0.550227i	$-0.814541\pi$
$31$	−8.98607	+	0.428059i	−1.61395	+	0.0768817i	−0.778931	+	0.627109i	$0.784238\pi$
$32$		0			0
$33$	−2.72319	−	2.59655i	−0.474046	−	0.452002i
$34$		0			0
$35$	−10.1332	+	4.41568i	−1.71283	+	0.746385i
$36$		0			0
$37$	8.64906	+	6.15897i	1.42190	+	1.01253i	0.994079	+	0.108662i	$0.0346568\pi$
$37$	8.64906	+	6.15897i	1.42190	+	1.01253i	0.427817	+	0.903865i	$0.359283\pi$
$38$		0			0
$39$	−8.04755	+	7.67332i	−1.28864	+	1.22871i
$40$		0			0
$41$	−7.98549	−	3.64685i	−1.24712	−	0.569542i	−0.321113	−	0.947041i	$-0.604057\pi$
$41$	−7.98549	−	3.64685i	−1.24712	−	0.569542i	−0.926010	+	0.377499i	$0.876784\pi$
$42$		0			0
$43$	2.43868	−	3.79466i	0.371895	−	0.578681i	−0.603982	−	0.796998i	$-0.706420\pi$
$43$	2.43868	−	3.79466i	0.371895	−	0.578681i	0.975878	+	0.218317i	$0.0700567\pi$
$44$		0			0
$45$	−2.67636	+	4.63560i	−0.398969	+	0.691034i
$46$		0			0
$47$	0.169102	−	0.0976313i	0.0246661	−	0.0142410i	−0.487616	−	0.873058i	$-0.662133\pi$
$47$	0.169102	−	0.0976313i	0.0246661	−	0.0142410i	0.512282	+	0.858817i	$0.328800\pi$
$48$		0			0
$49$	5.65000	−	4.13250i	0.807142	−	0.590357i
$50$		0			0
$51$	−0.255382	−	2.67448i	−0.0357606	−	0.374502i
$52$		0			0
$53$	−4.57014	−	4.79303i	−0.627758	−	0.658373i	0.330658	−	0.943751i	$-0.392729\pi$
$53$	−4.57014	−	4.79303i	−0.627758	−	0.658373i	−0.958415	+	0.285378i	$0.907881\pi$
$54$		0			0
$55$	−6.91087	+	3.15609i	−0.931862	+	0.425567i
$56$		0			0
$57$	−2.03649	−	1.76463i	−0.269740	−	0.233731i
$58$		0			0
$59$	5.99232	+	1.45372i	0.780134	+	0.189258i	0.606001	−	0.795464i	$-0.292773\pi$
$59$	5.99232	+	1.45372i	0.780134	+	0.189258i	0.174133	+	0.984722i	$0.444288\pi$
$60$		0			0
$61$	1.23460	+	0.636481i	0.158074	+	0.0814930i	0.535449	−	0.844568i	$-0.320143\pi$
$61$	1.23460	+	0.636481i	0.158074	+	0.0814930i	−0.377374	+	0.926061i	$0.623173\pi$
$62$		0			0
$63$	1.01161	−	3.23531i	0.127452	−	0.407611i
$64$		0			0
$65$	8.34453	+	20.8436i	1.03501	+	2.58533i
$66$		0			0
$67$	−0.261404	−	1.35629i	−0.0319356	−	0.165698i	0.962460	−	0.271425i	$-0.0874950\pi$
$67$	−0.261404	−	1.35629i	−0.0319356	−	0.165698i	−0.994395	+	0.105728i	$0.966283\pi$
$68$		0			0
$69$	6.59541	+	7.41408i	0.793994	+	0.892551i
$70$		0			0
$71$	−5.41317	−	6.24713i	−0.642425	−	0.741398i	0.337376	−	0.941370i	$-0.390461\pi$
$71$	−5.41317	−	6.24713i	−0.642425	−	0.741398i	−0.979802	+	0.199971i	$0.935915\pi$
$72$		0			0
$73$	−6.43795	+	8.18651i	−0.753505	+	0.958159i	−0.999939	−	0.0110004i	$-0.996498\pi$
$73$	−6.43795	+	8.18651i	−0.753505	+	0.958159i	0.246435	+	0.969159i	$0.420741\pi$
$74$		0			0
$75$	15.9297	+	20.2562i	1.83940	+	2.33899i
$76$		0			0
$77$	3.83327	−	2.90772i	0.436841	−	0.331365i
$78$		0			0
$79$	1.25107	−	1.31208i	0.140756	−	0.147621i	−0.649582	−	0.760291i	$-0.725056\pi$
$79$	1.25107	−	1.31208i	0.140756	−	0.147621i	0.790338	+	0.612671i	$0.209905\pi$
$80$		0			0
$81$	3.66386	+	10.5860i	0.407095	+	1.17623i
$82$		0			0
$83$	−4.32512	−	9.47070i	−0.474744	−	1.03954i	−0.983875	−	0.178855i	$-0.942761\pi$
$83$	−4.32512	−	9.47070i	−0.474744	−	1.03954i	0.509131	−	0.860689i	$-0.329967\pi$
$84$		0			0
$85$	−5.20501	−	1.52833i	−0.564562	−	0.165770i
$86$		0			0
$87$	10.9647	−	7.80791i	1.17554	−	0.837096i
$88$		0			0
$89$	−0.149750	+	3.14365i	−0.0158735	+	0.333226i	0.976937	+	0.213528i	$0.0684955\pi$
$89$	−0.149750	+	3.14365i	−0.0158735	+	0.333226i	−0.992810	+	0.119698i	$0.961807\pi$
$90$		0			0
$91$	−8.04413	−	11.7241i	−0.843254	−	1.22902i
$92$		0			0
$93$	−9.30713	−	16.1204i	−0.965104	−	1.67161i
$94$		0			0
$95$	−4.83610	+	2.49318i	−0.496173	+	0.255795i
$96$		0			0
$97$	1.75689	−	3.84705i	0.178385	−	0.390609i	−0.799225	−	0.601031i	$-0.794757\pi$
$97$	1.75689	−	3.84705i	0.178385	−	0.390609i	0.977611	+	0.210422i	$0.0674839\pi$
$98$		0			0
$99$	0.656409	−	2.23552i	0.0659716	−	0.224679i
$100$		0			0
$101$	0.175930	−	1.84242i	0.0175057	−	0.183328i	−0.982490	−	0.186316i	$-0.940345\pi$
$101$	0.175930	−	1.84242i	0.0175057	−	0.183328i	0.999996	+	0.00298839i	$0.000951237\pi$
$102$		0			0
$103$	−5.71422	−	1.10132i	−0.563038	−	0.108517i	−0.100213	−	0.994966i	$-0.531952\pi$
$103$	−5.71422	−	1.10132i	−0.563038	−	0.108517i	−0.462826	+	0.886449i	$0.653164\pi$
$104$		0			0
$105$	−17.7284	−	14.4494i	−1.73011	−	1.41012i
$106$		0			0
$107$	4.20543	−	8.15739i	0.406554	−	0.788605i	−0.593312	−	0.804973i	$-0.702180\pi$
$107$	4.20543	−	8.15739i	0.406554	−	0.788605i	0.999866	+	0.0163676i	$0.00521020\pi$
$108$		0			0
$109$	7.47584	−	18.6737i	0.716056	−	1.78862i	0.108877	−	0.994055i	$-0.465274\pi$
$109$	7.47584	−	18.6737i	0.716056	−	1.78862i	0.607178	−	0.794565i	$-0.292301\pi$
$110$		0			0
$111$	−3.12659	+	21.7459i	−0.296763	+	2.06403i
$112$		0			0
$113$	0.107232	−	0.0929171i	0.0100875	−	0.00874091i	−0.649802	−	0.760103i	$-0.725148\pi$
$113$	0.107232	−	0.0929171i	0.0100875	−	0.00874091i	0.659890	+	0.751362i	$0.270603\pi$
$114$		0			0
$115$	18.8473	−	6.79934i	1.75752	−	0.634042i
$116$		0			0
$117$	−6.50662	−	2.25196i	−0.601538	−	0.208194i
$118$		0			0
$119$	3.42812	+	0.223310i	0.314256	+	0.0204708i
$120$		0			0
$121$	−6.04713	+	4.75552i	−0.549739	+	0.432320i
$122$		0			0
$123$	−0.864293	−	18.1438i	−0.0779307	−	1.63597i
$124$		0			0
$125$	29.8818	−	8.77408i	2.67271	−	0.784778i
$126$		0			0
$127$	−9.70248	+	11.1973i	−0.860956	+	0.993596i	0.139039	+	0.990287i	$0.455599\pi$
$127$	−9.70248	+	11.1973i	−0.860956	+	0.993596i	−0.999995	+	0.00330919i	$0.998947\pi$
$128$		0			0
$129$	9.29092	+	0.887176i	0.818020	+	0.0781114i
$130$		0			0
$131$	1.02989	−	0.249849i	0.0899821	−	0.0218294i	−0.190515	−	0.981684i	$-0.561016\pi$
$131$	1.02989	−	0.249849i	0.0899821	−	0.0218294i	0.280497	+	0.959855i	$0.409501\pi$
$132$		0			0
$133$	2.64302	−	2.21064i	0.229179	−	0.191687i
$134$		0			0
$135$	14.8411	+	0.706967i	1.27732	+	0.0608460i
$136$		0			0
$137$	−10.0723	−	5.81522i	−0.860531	−	0.496828i	0.00365900	−	0.999993i	$-0.498835\pi$
$137$	−10.0723	−	5.81522i	−0.860531	−	0.496828i	−0.864190	+	0.503165i	$0.832169\pi$
$138$		0			0
$139$			15.4043i			1.30658i	0.757110	+	0.653288i	$0.226611\pi$
$139$			15.4043i			1.30658i	−0.757110	+	0.653288i	$0.773389\pi$
$140$		0			0
$141$	0.339883	+	0.218430i	0.0286233	+	0.0183951i
$142$		0			0
$143$	−5.66874	−	7.96063i	−0.474044	−	0.665701i
$144$		0			0
$145$	−6.40769	−	26.4128i	−0.532129	−	2.19347i
$146$		0			0
$147$	12.9570	+	6.47279i	1.06867	+	0.533867i
$148$		0			0
$149$	0.0542924	−	0.281696i	0.00444781	−	0.0230774i	−0.979637	−	0.200777i	$-0.935653\pi$
$149$	0.0542924	−	0.281696i	0.00444781	−	0.0230774i	0.984085	+	0.177699i	$0.0568655\pi$
$150$		0			0
$151$	4.14373	−	17.0807i	0.337212	−	1.39001i	−0.510650	−	0.859788i	$-0.670595\pi$
$151$	4.14373	−	17.0807i	0.337212	−	1.39001i	0.847862	−	0.530217i	$-0.177890\pi$
$152$		0			0
$153$	1.39951	−	0.899412i	0.113144	−	0.0727131i
$154$		0			0
$155$	−37.2024	+	5.34890i	−2.98817	+	0.429634i
$156$		0			0
$157$	−15.0376	−	11.8257i	−1.20013	−	0.943794i	−0.200775	−	0.979637i	$-0.564346\pi$
$157$	−15.0376	−	11.8257i	−1.20013	−	0.943794i	−0.999357	+	0.0358430i	$0.988588\pi$
$158$		0			0
$159$	4.48180	−	12.9493i	0.355430	−	1.02695i
$160$		0			0
$161$	−10.7045	+	6.81272i	−0.843635	+	0.536917i
$162$		0			0
$163$	3.60139	−	10.4055i	0.282083	−	0.815024i	−0.711579	−	0.702607i	$-0.752019\pi$
$163$	3.60139	−	10.4055i	0.282083	−	0.815024i	0.993661	−	0.112417i	$-0.0358594\pi$
$164$		0			0
$165$	−12.3567	−	9.71742i	−0.961968	−	0.756500i
$166$		0			0
$167$	10.3930	−	1.49428i	0.804231	−	0.115631i	0.272074	−	0.962276i	$-0.412291\pi$
$167$	10.3930	−	1.49428i	0.804231	−	0.115631i	0.532157	+	0.846645i	$0.321381\pi$
$168$		0			0
$169$	−13.3594	+	8.58554i	−1.02764	+	0.660426i
$170$		0			0
$171$	0.393380	−	1.62153i	0.0300825	−	0.124002i
$172$		0			0
$173$	2.24660	−	11.6565i	0.170806	−	0.886225i	−0.790859	−	0.611998i	$-0.790366\pi$
$173$	2.24660	−	11.6565i	0.170806	−	0.886225i	0.961665	−	0.274227i	$-0.0884219\pi$
$174$		0			0
$175$	−28.8197	+	15.9752i	−2.17857	+	1.20761i
$176$		0			0
$177$	3.00791	+	12.3988i	0.226088	+	0.931949i
$178$		0			0
$179$	13.9182	+	19.5453i	1.04029	+	1.46089i	0.880684	+	0.473705i	$0.157084\pi$
$179$	13.9182	+	19.5453i	1.04029	+	1.46089i	0.159608	+	0.987181i	$0.448977\pi$
$180$		0			0
$181$	−1.61780	−	1.03970i	−0.120250	−	0.0772800i	0.479133	−	0.877742i	$-0.340951\pi$
$181$	−1.61780	−	1.03970i	−0.120250	−	0.0772800i	−0.599383	+	0.800462i	$0.704587\pi$
$182$		0			0
$183$			2.87401i			0.212453i
$184$		0			0
$185$	38.4167	+	22.1799i	2.82445	+	1.63070i
$186$		0			0
$187$	2.35858	+	0.112353i	0.172476	+	0.00821605i
$188$		0			0
$189$	−9.26885	+	1.61923i	−0.674210	+	0.117782i
$190$		0			0
$191$	20.6849	−	5.01810i	1.49671	−	0.363097i	0.597945	−	0.801537i	$-0.295984\pi$
$191$	20.6849	−	5.01810i	1.49671	−	0.363097i	0.898761	+	0.438440i	$0.144469\pi$
$192$		0			0
$193$	−15.2554	−	1.45671i	−1.09811	−	0.104857i	−0.469764	−	0.882792i	$-0.655661\pi$
$193$	−15.2554	−	1.45671i	−1.09811	−	0.104857i	−0.628344	+	0.777936i	$0.716267\pi$
$194$		0			0
$195$	−30.4219	+	35.1087i	−2.17855	+	2.51419i
$196$		0			0
$197$	7.60742	−	2.23374i	0.542006	−	0.159147i	0.000741621	−	1.00000i	$-0.499764\pi$
$197$	7.60742	−	2.23374i	0.542006	−	0.159147i	0.541265	+	0.840852i	$0.317946\pi$
$198$		0			0
$199$	−0.161584	−	3.39206i	−0.0114544	−	0.240457i	−0.997333	−	0.0729923i	$-0.976745\pi$
$199$	−0.161584	−	3.39206i	−0.0114544	−	0.240457i	0.985878	−	0.167464i	$-0.0535579\pi$
$200$		0			0
$201$	2.24652	−	1.76668i	0.158457	−	0.124612i
$202$		0			0
$203$	7.61884	+	15.4339i	0.534738	+	1.08324i
$204$		0			0
$205$	−34.6593	−	11.9957i	−2.42071	−	0.837817i
$206$		0			0
$207$	−2.20917	+	5.73363i	−0.153548	+	0.398515i
$208$		0			0
$209$	1.78984	−	1.55090i	0.123806	−	0.107278i
$210$		0			0
$211$	−1.95813	+	13.6191i	−0.134803	+	0.937577i	0.804369	+	0.594130i	$0.202504\pi$
$211$	−1.95813	+	13.6191i	−0.134803	+	0.937577i	−0.939172	+	0.343447i	$0.888405\pi$
$212$		0			0
$213$	6.35675	−	15.8784i	0.435557	−	1.08797i
$214$		0			0
$215$	8.63533	−	16.7502i	0.588924	−	1.14235i
$216$		0			0
$217$	22.2479	−	8.45937i	1.51028	−	0.574260i
$218$		0			0
$219$	−21.1598	−	4.07821i	−1.42984	−	0.275580i
$220$		0			0
$221$	0.663296	−	6.94635i	0.0446181	−	0.467262i
$222$		0			0
$223$	−2.88790	+	9.83528i	−0.193388	+	0.658619i	0.804517	+	0.593929i	$0.202424\pi$
$223$	−2.88790	+	9.83528i	−0.193388	+	0.658619i	−0.997905	+	0.0646899i	$0.979394\pi$
$224$		0			0
$225$	−6.62869	+	14.5148i	−0.441912	+	0.967653i
$226$		0			0
$227$	−1.12204	+	0.578452i	−0.0744725	+	0.0383932i	−0.495060	−	0.868859i	$-0.664854\pi$
$227$	−1.12204	+	0.578452i	−0.0744725	+	0.0383932i	0.420588	+	0.907252i	$0.361824\pi$
$228$		0			0
$229$	4.26317	+	7.38402i	0.281718	+	0.487950i	0.971808	−	0.235774i	$-0.0757624\pi$
$229$	4.26317	+	7.38402i	0.281718	+	0.487950i	−0.690090	+	0.723724i	$0.742429\pi$
$230$		0			0
$231$	8.98198	+	4.29289i	0.590971	+	0.282451i
$232$		0			0
$233$	−0.367581	+	7.71647i	−0.0240810	+	0.505523i	0.954317	+	0.298795i	$0.0965846\pi$
$233$	−0.367581	+	7.71647i	−0.0240810	+	0.505523i	−0.978398	+	0.206728i	$0.933718\pi$
$234$		0			0
$235$	0.664512	−	0.473197i	0.0433480	−	0.0308680i
$236$		0			0
$237$	3.59921	+	1.05682i	0.233794	+	0.0686480i
$238$		0			0
$239$	−9.32070	−	20.4095i	−0.602906	−	1.32018i	−0.927322	−	0.374265i	$-0.877895\pi$
$239$	−9.32070	−	20.4095i	−0.602906	−	1.32018i	0.324416	−	0.945915i	$-0.394832\pi$
$240$		0			0
$241$	1.44813	+	4.18409i	0.0932820	+	0.269521i	0.981984	−	0.188965i	$-0.0605132\pi$
$241$	1.44813	+	4.18409i	0.0932820	+	0.269521i	−0.888702	+	0.458486i	$0.848392\pi$
$242$		0			0
$243$	−8.63247	+	9.05347i	−0.553773	+	0.580781i
$244$		0			0
$245$	21.8568	−	19.4305i	1.39638	−	1.24137i
$246$		0			0
$247$	−4.32636	−	5.50141i	−0.275279	−	0.350046i
$248$		0			0
$249$	13.3168	−	16.9337i	0.843918	−	1.07313i
$250$		0			0
$251$	11.6913	+	13.4925i	0.737948	+	0.851637i	0.993342	−	0.115200i	$-0.0367508\pi$
$251$	11.6913	+	13.4925i	0.737948	+	0.851637i	−0.255395	+	0.966837i	$0.582205\pi$
$252$		0			0
$253$	−7.27473	+	4.81025i	−0.457358	+	0.302418i
$254$		0			0
$255$	−2.12423	−	11.0216i	−0.133025	−	0.690197i
$256$		0			0
$257$	9.25053	+	23.1067i	0.577032	+	1.44136i	0.873743	+	0.486389i	$0.161686\pi$
$257$	9.25053	+	23.1067i	0.577032	+	1.44136i	−0.296711	+	0.954967i	$0.595890\pi$
$258$		0			0
$259$	−26.8121	−	8.38358i	−1.66602	−	0.520931i
$260$		0			0
$261$	7.40840	+	3.81930i	0.458569	+	0.236409i
$262$		0			0
$263$	22.0759	+	5.35556i	1.36126	+	0.330238i	0.848909	−	0.528539i	$-0.177260\pi$
$263$	22.0759	+	5.35556i	1.36126	+	0.330238i	0.512350	+	0.858777i	$0.328775\pi$
$264$		0			0
$265$	−20.9104	−	18.1189i	−1.28451	−	1.11304i
$266$		0			0
$267$	−5.92346	+	2.70515i	−0.362510	+	0.165553i
$268$		0			0
$269$	7.48845	+	7.85366i	0.456579	+	0.478846i	0.911274	−	0.411801i	$-0.135100\pi$
$269$	7.48845	+	7.85366i	0.456579	+	0.478846i	−0.454695	+	0.890647i	$0.650252\pi$
$270$		0			0
$271$	−0.649934	−	6.80642i	−0.0394807	−	0.413460i	−0.993510	−	0.113746i	$-0.963715\pi$
$271$	−0.649934	−	6.80642i	−0.0394807	−	0.413460i	0.954029	−	0.299714i	$-0.0968912\pi$
$272$		0			0
$273$	13.9349	−	25.9098i	0.843380	−	1.56813i
$274$		0			0
$275$	−19.6141	+	11.3242i	−1.18277	+	0.682875i
$276$		0			0
$277$	−5.08816	+	8.81295i	−0.305718	+	0.529519i	−0.977421	−	0.211302i	$-0.932230\pi$
$277$	−5.08816	+	8.81295i	−0.305718	+	0.529519i	0.671703	+	0.740821i	$0.265563\pi$
$278$		0			0
$279$	6.23151	−	9.69643i	0.373071	−	0.580510i
$280$		0			0
$281$	−23.0243	−	10.5148i	−1.37351	−	0.627263i	−0.414351	−	0.910117i	$-0.635991\pi$
$281$	−23.0243	−	10.5148i	−1.37351	−	0.627263i	−0.959163	+	0.282855i	$0.908719\pi$
$282$		0			0
$283$	−4.76406	+	4.54252i	−0.283194	+	0.270025i	−0.818340	−	0.574735i	$-0.805105\pi$
$283$	−4.76406	+	4.54252i	−0.283194	+	0.270025i	0.535146	+	0.844760i	$0.320257\pi$
$284$		0			0
$285$	−9.17041	−	6.53022i	−0.543208	−	0.386817i
$286$		0			0
$287$	23.0793	+	2.61091i	1.36233	+	0.154117i
$288$		0			0
$289$	−11.0833	−	10.5679i	−0.651957	−	0.621640i
$290$		0			0
$291$	8.74086	−	0.416378i	0.512398	−	0.0244085i
$292$		0			0
$293$	1.84076	+	12.8028i	0.107538	+	0.747947i	0.970225	+	0.242207i	$0.0778713\pi$
$293$	1.84076	+	12.8028i	0.107538	+	0.747947i	−0.862686	+	0.505740i	$0.831220\pi$
$294$		0			0
$295$	25.4990	+	3.66620i	1.48461	+	0.213454i
$296$		0			0
$297$	−6.35038	+	1.22393i	−0.368486	+	0.0710199i
$298$		0			0
$299$	13.1762	+	22.1503i	0.761999	+	1.28098i
$300$		0			0
$301$	−3.01554	+	11.5470i	−0.173813	+	0.665557i
$302$		0			0
$303$	3.55519	−	1.42328i	0.204241	−	0.0817656i
$304$		0			0
$305$	5.38738	+	2.15678i	0.308481	+	0.123497i
$306$		0			0
$307$	−6.21582	−	9.67201i	−0.354756	−	0.552011i	0.617310	−	0.786720i	$-0.288223\pi$
$307$	−6.21582	−	9.67201i	−0.354756	−	0.552011i	−0.972066	+	0.234709i	$0.924586\pi$
$308$		0			0
$309$	−3.39232	−	11.5532i	−0.192983	−	0.657238i
$310$		0			0
$311$	−9.00369	+	3.11621i	−0.510553	+	0.176704i	−0.570185	−	0.821516i	$-0.693128\pi$
$311$	−9.00369	+	3.11621i	−0.510553	+	0.176704i	0.0596322	+	0.998220i	$0.481007\pi$
$312$		0			0
$313$	17.0511	−	23.9450i	0.963787	−	1.35345i	0.0284863	−	0.999594i	$-0.490931\pi$
$313$	17.0511	−	23.9450i	0.963787	−	1.35345i	0.935300	−	0.353855i	$-0.115129\pi$
$314$		0			0
$315$	2.92240	−	13.8572i	0.164658	−	0.780763i
$316$		0			0
$317$	−18.6272	+	1.77868i	−1.04621	+	0.0999009i	−0.603979	−	0.797001i	$-0.706419\pi$
$317$	−18.6272	+	1.77868i	−1.04621	+	0.0999009i	−0.442231	+	0.896901i	$0.645813\pi$
$318$		0			0
$319$	5.42095	+	10.5152i	0.303515	+	0.588737i
$320$		0			0
$321$	18.9895			1.05989
$322$		0			0
$323$	1.69102			0.0940908
$324$		0			0
$325$	30.6693	+	59.4901i	1.70123	+	3.29992i
$326$		0			0
$327$	41.4309	−	3.95617i	2.29113	−	0.218777i
$328$		0			0
$329$	−0.345072	+	0.384470i	−0.0190245	+	0.0211965i
$330$		0			0
$331$	−12.4637	+	17.5028i	−0.685066	+	0.962041i	0.314850	+	0.949141i	$0.398046\pi$
$331$	−12.4637	+	17.5028i	−0.685066	+	0.962041i	−0.999917	+	0.0128998i	$0.995894\pi$
$332$		0			0
$333$	−12.8556	+	4.44936i	−0.704482	+	0.243824i
$334$		0			0
$335$	−1.62579	−	5.53692i	−0.0888262	−	0.302514i
$336$		0			0
$337$	6.20757	+	9.65916i	0.338148	+	0.526168i	0.968132	−	0.250440i	$-0.0805752\pi$
$337$	6.20757	+	9.65916i	0.338148	+	0.526168i	−0.629985	+	0.776608i	$0.716939\pi$
$338$		0			0
$339$	0.272553	+	0.109114i	0.0148030	+	0.00592624i
$340$		0			0
$341$	15.1879	−	6.08031i	0.822470	−	0.329267i
$342$		0			0
$343$	−10.8143	+	15.0350i	−0.583917	+	0.811814i
$344$		0			0
$345$	30.3742	+	28.2154i	1.63529	+	1.51907i
$346$		0			0
$347$	−5.43338	+	1.04720i	−0.291679	+	0.0562166i	−0.332992	−	0.942930i	$-0.608058\pi$
$347$	−5.43338	+	1.04720i	−0.291679	+	0.0562166i	0.0413125	+	0.999146i	$0.486846\pi$
$348$		0			0
$349$	−1.40126	−	0.201470i	−0.0750076	−	0.0107845i	0.104709	−	0.994503i	$-0.466609\pi$
$349$	−1.40126	−	0.201470i	−0.0750076	−	0.0107845i	−0.179716	+	0.983718i	$0.557518\pi$
$350$		0			0
$351$	2.71992	+	18.9174i	0.145178	+	1.00974i
$352$		0			0
$353$	6.66112	−	0.317308i	0.354536	−	0.0168886i	0.130441	−	0.991456i	$-0.458361\pi$
$353$	6.66112	−	0.317308i	0.354536	−	0.0168886i	0.224095	+	0.974567i	$0.428058\pi$
$354$		0			0
$355$	−24.9939	−	23.8317i	−1.32654	−	1.26485i
$356$		0			0
$357$	2.83959	+	6.51638i	0.150287	+	0.344884i
$358$		0			0
$359$	15.6209	+	11.1236i	0.824440	+	0.587081i	0.912520	−	0.409032i	$-0.134134\pi$
$359$	15.6209	+	11.1236i	0.824440	+	0.587081i	−0.0880796	+	0.996113i	$0.528073\pi$
$360$		0			0
$361$	−12.5234	+	11.9411i	−0.659129	+	0.628478i
$362$		0			0
$363$	−14.4793	−	6.61247i	−0.759965	−	0.347064i
$364$		0			0
$365$	−23.5238	+	36.6038i	−1.23129	+	1.91593i
$366$		0			0
$367$	−1.98985	+	3.44653i	−0.103870	+	0.179907i	−0.913276	−	0.407342i	$-0.866456\pi$
$367$	−1.98985	+	3.44653i	−0.103870	+	0.179907i	0.809406	+	0.587249i	$0.199789\pi$
$368$		0			0
$369$	9.74067	−	5.62378i	0.507079	−	0.292762i
$370$		0			0
$371$	15.4316	+	8.29949i	0.801168	+	0.430888i
$372$		0			0
$373$	0.144360	+	1.51181i	0.00747470	+	0.0782786i	0.998440	−	0.0558433i	$-0.0177847\pi$
$373$	0.144360	+	1.51181i	0.00747470	+	0.0782786i	−0.990965	+	0.134122i	$0.957179\pi$
$374$		0			0
$375$	44.4680	+	46.6366i	2.29632	+	2.40831i
$376$		0			0
$377$	31.8015	−	14.5232i	1.63786	−	0.747985i
$378$		0			0
$379$	18.5051	+	16.0347i	0.950542	+	0.823649i	0.984430	−	0.175776i	$-0.0562436\pi$
$379$	18.5051	+	16.0347i	0.950542	+	0.823649i	−0.0338883	+	0.999426i	$0.510789\pi$
$380$		0			0
$381$	−29.7920	−	7.22746i	−1.52629	−	0.370274i
$382$		0			0
$383$	−14.1691	−	7.30469i	−0.724008	−	0.373252i	0.0564958	−	0.998403i	$-0.482007\pi$
$383$	−14.1691	−	7.30469i	−0.724008	−	0.373252i	−0.780504	+	0.625151i	$0.785038\pi$
$384$		0			0
$385$	14.7875	−	13.6153i	0.753643	−	0.693900i
$386$		0			0
$387$	2.14792	+	5.36524i	0.109185	+	0.272730i
$388$		0			0
$389$	3.19668	+	16.5860i	0.162078	+	0.840941i	0.968388	+	0.249448i	$0.0802492\pi$
$389$	3.19668	+	16.5860i	0.162078	+	0.840941i	−0.806310	+	0.591493i	$0.798539\pi$
$390$		0			0
$391$	−6.17481	−	0.805839i	−0.312274	−	0.0407530i
$392$		0			0
$393$	1.43596	+	1.65719i	0.0724346	+	0.0835939i
$394$		0			0
$395$	4.68203	−	5.95368i	0.235578	−	0.299562i
$396$		0			0
$397$	−3.09513	−	3.93578i	−0.155340	−	0.197531i	0.702153	−	0.712026i	$-0.252222\pi$
$397$	−3.09513	−	3.93578i	−0.155340	−	0.197531i	−0.857494	+	0.514494i	$0.827980\pi$
$398$		0			0
$399$	6.57148	+	2.76481i	0.328985	+	0.138414i
$400$		0			0
$401$	−21.3500	+	22.3912i	−1.06617	+	1.11816i	−0.0734987	+	0.997295i	$0.523416\pi$
$401$	−21.3500	+	22.3912i	−1.06617	+	1.11816i	−0.992669	+	0.120869i	$0.961432\pi$
$402$		0			0
$403$	−15.8125	−	45.6873i	−0.787677	−	2.27584i
$404$		0			0
$405$	19.4417	+	42.5715i	0.966068	+	2.11539i
$406$		0			0
$407$	−18.5265	−	5.43988i	−0.918325	−	0.269645i
$408$		0			0
$409$	−32.2358	+	22.9550i	−1.59396	+	1.13505i	−0.677064	+	0.735924i	$0.736748\pi$
$409$	−32.2358	+	22.9550i	−1.59396	+	1.13505i	−0.916895	+	0.399129i	$0.869313\pi$
$410$		0			0
$411$	1.14504	−	24.0374i	0.0564808	−	1.18568i
$412$		0			0
$413$	−16.2648	+	1.26716i	−0.800337	+	0.0623528i
$414$		0			0
$415$	−21.7490	−	37.6703i	−1.06761	−	1.84916i
$416$		0			0
$417$	−28.3300	+	14.6051i	−1.38733	+	0.715217i
$418$		0			0
$419$	−6.67614	+	14.6187i	−0.326151	+	0.714171i	−0.999688	−	0.0249826i	$-0.992047\pi$
$419$	−6.67614	+	14.6187i	−0.326151	+	0.714171i	0.673537	+	0.739154i	$0.264774\pi$
$420$		0			0
$421$	1.17094	−	3.98787i	0.0570683	−	0.194357i	−0.926025	−	0.377462i	$-0.876797\pi$
$421$	1.17094	−	3.98787i	0.0570683	−	0.194357i	0.983093	+	0.183105i	$0.0586150\pi$
$422$		0			0
$423$	−0.0237805	+	0.249041i	−0.00115625	+	0.0121088i
$424$		0			0
$425$	−15.8792	−	3.06047i	−0.770256	−	0.148455i
$426$		0			0
$427$	−3.62789	−	0.586391i	−0.175566	−	0.0283775i
$428$		0			0
$429$	9.26573	−	17.9730i	0.447354	−	0.867745i
$430$		0			0
$431$	3.16376	−	7.90270i	0.152393	−	0.380660i	−0.832452	−	0.554098i	$-0.813063\pi$
$431$	3.16376	−	7.90270i	0.152393	−	0.380660i	0.984845	+	0.173438i	$0.0554876\pi$
$432$		0			0
$433$	−2.01717	+	14.0298i	−0.0969392	+	0.674227i	0.882176	+	0.470920i	$0.156078\pi$
$433$	−2.01717	+	14.0298i	−0.0969392	+	0.674227i	−0.979115	+	0.203307i	$0.934831\pi$
$434$		0			0
$435$	42.5006	−	36.8269i	2.03775	−	1.76572i
$436$		0			0
$437$	−5.04001	+	3.68887i	−0.241096	+	0.176463i
$438$		0			0
$439$	9.42585	+	3.26232i	0.449871	+	0.155702i	0.542603	−	0.839989i	$-0.317439\pi$
$439$	9.42585	+	3.26232i	0.449871	+	0.155702i	−0.0927319	+	0.995691i	$0.529560\pi$
$440$		0			0
$441$	0.113919	+	8.96779i	0.00542470	+	0.427038i
$442$		0			0
$443$	−15.4159	+	12.1232i	−0.732432	+	0.575991i	−0.913189	−	0.407537i	$-0.866388\pi$
$443$	−15.4159	+	12.1232i	−0.732432	+	0.575991i	0.180757	+	0.983528i	$0.442145\pi$
$444$		0			0
$445$	0.625634	+	13.1337i	0.0296579	+	0.622596i
$446$		0			0
$447$	0.569542	−	0.167233i	0.0269384	−	0.00790983i
$448$		0			0
$449$	−3.67867	+	4.24541i	−0.173607	+	0.200353i	−0.835884	−	0.548906i	$-0.815045\pi$
$449$	−3.67867	+	4.24541i	−0.173607	+	0.200353i	0.662277	+	0.749259i	$0.269590\pi$
$450$		0			0
$451$	15.8920	+	1.51751i	0.748327	+	0.0714565i
$452$		0			0
$453$	35.3418	−	8.57383i	1.66050	−	0.402833i
$454$		0			0
$455$	−38.1109	−	45.5650i	−1.78667	−	2.13612i
$456$		0			0
$457$	38.4758	+	1.83283i	1.79982	+	0.0857360i	0.920559	−	0.390603i	$-0.127734\pi$
$457$	38.4758	+	1.83283i	1.79982	+	0.0857360i	0.879262	+	0.476339i	$0.158037\pi$
$458$		0			0
$459$	−3.99910	−	2.30888i	−0.186662	−	0.107769i
$460$		0			0
$461$			34.1811i			1.59197i	0.605316	+	0.795985i	$0.293047\pi$
$461$			34.1811i			1.59197i	−0.605316	+	0.795985i	$0.706953\pi$
$462$		0			0
$463$	−16.6535	−	10.7025i	−0.773952	−	0.497388i	0.0930697	−	0.995660i	$-0.470332\pi$
$463$	−16.6535	−	10.7025i	−0.773952	−	0.497388i	−0.867021	+	0.498271i	$0.833968\pi$
$464$		0			0
$465$	−45.1096	−	63.3475i	−2.09191	−	2.93767i
$466$		0			0
$467$	−7.63490	−	31.4715i	−0.353301	−	1.45633i	−0.820231	−	0.572032i	$-0.806155\pi$
$467$	−7.63490	−	31.4715i	−0.353301	−	1.45633i	0.466931	−	0.884294i	$-0.345360\pi$
$468$		0			0
$469$	1.77173	+	3.19625i	0.0818110	+	0.147589i
$470$		0			0
$471$	7.49117	−	38.8679i	0.345175	−	1.79094i
$472$		0			0
$473$	−1.93388	+	7.97156i	−0.0889198	+	0.366533i
$474$		0			0
$475$	−13.6449	+	8.76905i	−0.626071	+	0.402352i
$476$		0			0
$477$	8.39867	−	1.20755i	0.384549	−	0.0552898i
$478$		0			0
$479$	−1.69514	−	1.33307i	−0.0774528	−	0.0609095i	0.578682	−	0.815553i	$-0.303567\pi$
$479$	−1.69514	−	1.33307i	−0.0774528	−	0.0609095i	−0.656135	+	0.754644i	$0.727810\pi$
$480$		0			0
$481$	−18.6628	+	53.9225i	−0.850949	+	2.45866i
$482$		0			0
$483$	−22.6784	−	13.2274i	−1.03191	−	0.601867i
$484$		0			0
$485$	5.77900	−	16.6973i	0.262411	−	0.758187i
$486$		0			0
$487$	24.7812	+	19.4882i	1.12294	+	0.883093i	0.994089	−	0.108571i	$-0.0346273\pi$
$487$	24.7812	+	19.4882i	1.12294	+	0.883093i	0.128855	+	0.991663i	$0.458870\pi$
$488$		0			0
$489$	22.5513	−	3.24239i	1.01981	−	0.146626i
$490$		0			0
$491$	−21.6266	+	13.8985i	−0.975993	+	0.627232i	−0.928380	−	0.371634i	$-0.878798\pi$
$491$	−21.6266	+	13.8985i	−0.975993	+	0.627232i	−0.0476130	+	0.998866i	$0.515161\pi$
$492$		0			0
$493$	−1.99148	+	8.20899i	−0.0896917	+	0.369714i
$494$		0			0
$495$	1.84217	−	9.55806i	0.0827992	−	0.429603i
$496$		0			0
$497$	18.7464	+	11.2639i	0.840893	+	0.505254i
$498$		0			0
$499$	−9.65784	−	39.8102i	−0.432344	−	1.78215i	−0.603994	−	0.796989i	$-0.706425\pi$
$499$	−9.65784	−	39.8102i	−0.432344	−	1.78215i	0.171649	−	0.985158i	$-0.445090\pi$
$500$		0			0
$501$	12.6019	+	17.6969i	0.563012	+	0.790640i
$502$		0			0
$503$	−10.4023	−	6.68513i	−0.463814	−	0.298075i	0.287785	−	0.957695i	$-0.407081\pi$
$503$	−10.4023	−	6.68513i	−0.463814	−	0.298075i	−0.751600	+	0.659620i	$0.770717\pi$
$504$		0			0
$505$		−	7.73236i		−	0.344085i
$506$		0			0
$507$	−28.4559	−	16.4290i	−1.26377	−	0.729639i
$508$		0			0
$509$	−40.8057	−	1.94382i	−1.80868	−	0.0861582i	−0.884137	−	0.467228i	$-0.845253\pi$
$509$	−40.8057	−	1.94382i	−1.80868	−	0.0861582i	−0.924546	+	0.381070i	$0.875556\pi$
$510$		0			0
$511$	9.46523	−	25.8780i	0.418717	−	1.14478i
$512$		0			0
$513$	−4.50099	+	1.09193i	−0.198724	+	0.0482098i
$514$		0			0
$515$	−24.2024	−	2.31105i	−1.06648	−	0.101837i
$516$		0			0
$517$	−0.232532	+	0.268356i	−0.0102267	+	0.0118023i
$518$		0			0
$519$	23.5674	−	6.92002i	1.03450	−	0.303755i
$520$		0			0
$521$	−0.629969	−	13.2247i	−0.0275994	−	0.579383i	−0.969736	−	0.244155i	$-0.921490\pi$
$521$	−0.629969	−	13.2247i	−0.0275994	−	0.579383i	0.942137	−	0.335229i	$-0.108814\pi$
$522$		0			0
$523$	14.5185	−	11.4175i	0.634851	−	0.499252i	−0.248089	−	0.968737i	$-0.579803\pi$
$523$	14.5185	−	11.4175i	0.634851	−	0.499252i	0.882941	+	0.469485i	$0.155560\pi$
$524$		0			0
$525$	−56.7046	−	37.8559i	−2.47479	−	1.65217i
$526$		0			0
$527$	11.0388	+	3.82056i	0.480857	+	0.166426i
$528$		0			0
$529$	20.1617	−	11.0683i	0.876595	−	0.481230i
$530$		0			0
$531$	−5.97054	+	5.17350i	−0.259099	+	0.224511i
$532$		0			0
$533$	6.71408	−	46.6975i	0.290819	−	2.02269i
$534$		0			0
$535$	14.2505	−	35.5961i	0.616104	−	1.53895i
$536$		0			0
$537$	−22.7497	+	44.1282i	−0.981720	+	1.90427i
$538$		0			0
$539$	−7.25155	+	10.4621i	−0.312347	+	0.450636i
$540$		0			0
$541$	−6.46473	−	1.24597i	−0.277941	−	0.0535686i	0.0483760	−	0.998829i	$-0.484595\pi$
$541$	−6.46473	−	1.24597i	−0.277941	−	0.0535686i	−0.326317	+	0.945261i	$0.605808\pi$
$542$		0			0
$543$	0.378235	−	3.96105i	0.0162316	−	0.169985i
$544$		0			0
$545$	23.6756	−	80.6317i	1.01415	−	3.45388i
$546$		0			0
$547$	−5.39994	+	11.8242i	−0.230885	+	0.505567i	−0.989245	−	0.146269i	$-0.953274\pi$
$547$	−5.39994	+	11.8242i	−0.230885	+	0.505567i	0.758360	+	0.651836i	$0.226001\pi$
$548$		0			0
$549$	−1.58179	+	0.815470i	−0.0675092	+	0.0348034i
$550$		0			0
$551$	4.23616	+	7.33724i	0.180466	+	0.312577i
$552$		0			0
$553$	−2.06839	+	4.32768i	−0.0879568	+	0.184032i
$554$		0			0
$555$	−4.36732	+	91.6813i	−0.185382	+	3.89166i
$556$		0			0
$557$	−9.29981	+	6.62236i	−0.394045	+	0.280599i	−0.759857	−	0.650091i	$-0.774731\pi$
$557$	−9.29981	+	6.62236i	−0.394045	+	0.280599i	0.365811	+	0.930689i	$0.380792\pi$
$558$		0			0
$559$	23.2589	+	6.82942i	0.983746	+	0.288854i
$560$		0			0
$561$	2.02959	+	4.44418i	0.0856892	+	0.187633i
$562$		0			0
$563$	2.45103	+	7.08179i	0.103299	+	0.298462i	0.984793	−	0.173733i	$-0.0555830\pi$
$563$	2.45103	+	7.08179i	0.103299	+	0.298462i	−0.881494	+	0.472195i	$0.843462\pi$
$564$		0			0
$565$	0.409070	−	0.429021i	0.0172097	−	0.0180490i
$566$		0			0
$567$	−17.9118	−	23.6132i	−0.752223	−	0.991661i
$568$		0			0
$569$	−7.68033	−	9.76634i	−0.321976	−	0.409426i	0.597940	−	0.801541i	$-0.295986\pi$
$569$	−7.68033	−	9.76634i	−0.321976	−	0.409426i	−0.919916	+	0.392115i	$0.871744\pi$
$570$		0			0
$571$	−9.82240	+	12.4902i	−0.411055	+	0.522699i	−0.946861	−	0.321642i	$-0.895765\pi$
$571$	−9.82240	+	12.4902i	−0.411055	+	0.522699i	0.535807	+	0.844341i	$0.320008\pi$
$572$		0			0
$573$	28.8406	+	33.2838i	1.20483	+	1.39045i
$574$		0			0
$575$	54.0037	−	25.5182i	2.25211	−	1.06418i
$576$		0			0
$577$	7.85801	+	40.7712i	0.327133	+	1.69733i	0.657482	+	0.753470i	$0.271622\pi$
$577$	7.85801	+	40.7712i	0.327133	+	1.69733i	−0.330349	+	0.943859i	$0.607166\pi$
$578$		0			0
$579$	−11.7849	−	29.4373i	−0.489765	−	1.22337i
$580$		0			0
$581$	18.6585	+	20.2649i	0.774084	+	0.840731i
$582$		0			0
$583$	10.7045	+	5.51856i	0.443336	+	0.228556i
$584$		0			0
$585$	−27.9549	−	6.78178i	−1.15579	−	0.280392i
$586$		0			0
$587$	−9.68809	−	8.39478i	−0.399870	−	0.346490i	0.431594	−	0.902068i	$-0.357951\pi$
$587$	−9.68809	−	8.39478i	−0.399870	−	0.346490i	−0.831464	+	0.555579i	$0.812497\pi$
$588$		0			0
$589$	10.6573	−	4.86705i	0.439128	−	0.200543i
$590$		0			0
$591$	11.3208	+	11.8729i	0.465676	+	0.488387i
$592$		0			0
$593$	−0.564957	−	5.91649i	−0.0232000	−	0.242961i	−0.999632	−	0.0271350i	$-0.991362\pi$
$593$	−0.564957	−	5.91649i	−0.0232000	−	0.242961i	0.976432	−	0.215826i	$-0.0692445\pi$
$594$		0			0
$595$	14.3460	−	0.432680i	0.588129	−	0.0177381i
$596$		0			0
$597$	6.08513	−	3.51325i	0.249048	−	0.143788i
$598$		0			0
$599$	12.8661	−	22.2848i	0.525696	−	0.910532i	−0.473856	−	0.880602i	$-0.657138\pi$
$599$	12.8661	−	22.2848i	0.525696	−	0.910532i	0.999552	−	0.0299294i	$-0.00952824\pi$
$600$		0			0
$601$	−20.3413	+	31.6516i	−0.829738	+	1.29110i	0.124552	+	0.992213i	$0.460251\pi$
$601$	−20.3413	+	31.6516i	−0.829738	+	1.29110i	−0.954289	+	0.298884i	$0.903386\pi$
$602$		0			0
$603$	1.60976	+	0.735155i	0.0655547	+	0.0299378i
$604$		0			0
$605$	−23.2610	+	22.1794i	−0.945696	+	0.901719i
$606$		0			0
$607$	19.7466	+	14.0615i	0.801488	+	0.570737i	0.905750	−	0.423813i	$-0.139308\pi$
$607$	19.7466	+	14.0615i	0.801488	+	0.570737i	−0.104261	+	0.994550i	$0.533248\pi$
$608$		0			0
$609$	−21.1608	+	28.6450i	−0.857479	+	1.16075i
$610$		0			0
$611$	0.759449	+	0.724134i	0.0307240	+	0.0292953i
$612$		0			0
$613$	1.86097	−	0.0886491i	0.0751641	−	0.00358051i	−0.00996620	−	0.999950i	$-0.503172\pi$
$613$	1.86097	−	0.0886491i	0.0751641	−	0.00358051i	0.0851303	+	0.996370i	$0.472869\pi$
$614$		0			0
$615$	−10.8000	−	75.1153i	−0.435496	−	3.02894i
$616$		0			0
$617$	−10.6698	−	1.53408i	−0.429548	−	0.0617597i	−0.0758499	−	0.997119i	$-0.524167\pi$
$617$	−10.6698	−	1.53408i	−0.429548	−	0.0617597i	−0.353698	+	0.935360i	$0.615076\pi$
$618$		0			0
$619$	−5.66859	+	1.09253i	−0.227840	+	0.0439125i	−0.301893	−	0.953342i	$-0.597619\pi$
$619$	−5.66859	+	1.09253i	−0.227840	+	0.0439125i	0.0740534	+	0.997254i	$0.476406\pi$
$620$		0			0
$621$	16.9559	−	1.84231i	0.680416	−	0.0739294i
$622$		0			0
$623$	−2.20616	−	8.02916i	−0.0883878	−	0.321682i
$624$		0			0
$625$	62.9804	−	25.2136i	2.51922	−	1.00854i
$626$		0			0
$627$	4.54925	+	1.82124i	0.181680	+	0.0727335i
$628$		0			0
$629$	−7.45372	−	11.5982i	−0.297199	−	0.462451i
$630$		0			0
$631$	−7.89158	−	26.8762i	−0.314159	−	1.06993i	−0.953597	−	0.301084i	$-0.902651\pi$
$631$	−7.89158	−	26.8762i	−0.314159	−	1.06993i	0.639439	−	0.768842i	$-0.279167\pi$
$632$		0			0
$633$	−26.9034	+	9.31136i	−1.06931	+	0.370093i
$634$		0			0
$635$	−35.9052	+	50.4217i	−1.42485	+	2.00093i
$636$		0			0
$637$	29.8629	+	22.8766i	1.18321	+	0.906404i
$638$		0			0
$639$	10.5428	−	1.00671i	0.417065	−	0.0398249i
$640$		0			0
$641$	−7.98141	−	15.4818i	−0.315247	−	0.611493i	0.676971	−	0.736010i	$-0.263292\pi$
$641$	−7.98141	−	15.4818i	−0.315247	−	0.611493i	−0.992218	+	0.124517i	$0.960262\pi$
$642$		0			0
$643$	−24.6880			−0.973600			−0.486800	−	0.873514i	$-0.661836\pi$
$643$	−24.6880			−0.973600			−0.486800	+	0.873514i	$0.661836\pi$
$644$		0			0
$645$	38.9926			1.53533
$646$		0			0
$647$	−1.59514	−	3.09415i	−0.0627116	−	0.121643i	0.855396	−	0.517974i	$-0.173314\pi$
$647$	−1.59514	−	3.09415i	−0.0627116	−	0.121643i	−0.918108	+	0.396331i	$0.870283\pi$
$648$		0			0
$649$	−11.1624	+	1.06588i	−0.438162	+	0.0418394i
$650$		0			0
$651$	36.6513	+	32.8955i	1.43648	+	1.28928i
$652$		0			0
$653$	5.33985	−	7.49877i	0.208965	−	0.293450i	−0.696770	−	0.717294i	$-0.745380\pi$
$653$	5.33985	−	7.49877i	0.208965	−	0.293450i	0.905735	+	0.423845i	$0.139320\pi$
$654$		0			0
$655$	4.18402	−	1.44810i	0.163483	−	0.0565821i
$656$		0			0
$657$	−3.75930	−	12.8030i	−0.146664	−	0.499492i
$658$		0			0
$659$	20.8871	+	32.5010i	0.813646	+	1.26606i	0.960882	+	0.276957i	$0.0893259\pi$
$659$	20.8871	+	32.5010i	0.813646	+	1.26606i	−0.147236	+	0.989101i	$0.547038\pi$
$660$		0			0
$661$	0.195671	+	0.0783349i	0.00761072	+	0.00304687i	0.375465	−	0.926837i	$-0.377483\pi$
$661$	0.195671	+	0.0783349i	0.00761072	+	0.00304687i	−0.367854	+	0.929884i	$0.619907\pi$
$662$		0			0
$663$	13.4039	−	5.36612i	0.520565	−	0.208403i
$664$		0			0
$665$	10.1142	−	10.2435i	0.392212	−	0.397226i
$666$		0			0
$667$	−11.9720	−	28.8109i	−0.463557	−	1.11556i
$668$		0			0
$669$	−20.8261	+	4.01391i	−0.805184	+	0.155187i
$670$		0			0
$671$	−2.50021	−	0.359476i	−0.0965196	−	0.0138774i
$672$		0			0
$673$	−4.48752	−	31.2114i	−0.172981	−	1.20311i	−0.872543	−	0.488538i	$-0.837531\pi$
$673$	−4.48752	−	31.2114i	−0.172981	−	1.20311i	0.699562	−	0.714572i	$-0.253379\pi$
$674$		0			0
$675$	44.2420	−	2.10751i	1.70288	−	0.0811180i
$676$		0			0
$677$	−3.68066	−	3.50950i	−0.141459	−	0.134881i	0.616046	−	0.787710i	$-0.288733\pi$
$677$	−3.68066	−	3.50950i	−0.141459	−	0.134881i	−0.757505	+	0.652829i	$0.773582\pi$
$678$		0			0
$679$	−1.25782	+	11.1186i	−0.0482707	+	0.426693i
$680$		0			0
$681$	−2.12766	−	1.51510i	−0.0815322	−	0.0580588i
$682$		0			0
$683$	12.9345	−	12.3330i	0.494924	−	0.471909i	−0.401024	−	0.916067i	$-0.631346\pi$
$683$	12.9345	−	12.3330i	0.494924	−	0.471909i	0.895948	+	0.444158i	$0.146497\pi$
$684$		0			0
$685$	−44.1992	−	20.1851i	−1.68876	−	0.771233i
$686$		0			0
$687$	−9.53794	+	14.8413i	−0.363895	+	0.566232i
$688$		0			0
$689$	17.7952	−	30.8221i	0.677942	−	1.17423i
$690$		0			0
$691$	−21.2742	+	12.2827i	−0.809308	+	0.467254i	−0.846716	−	0.532046i	$-0.821423\pi$
$691$	−21.2742	+	12.2827i	−0.809308	+	0.467254i	0.0374074	+	0.999300i	$0.488090\pi$
$692$		0			0
$693$	0.185834	+	6.16154i	0.00705924	+	0.234057i
$694$		0			0
$695$	6.11750	+	64.0654i	0.232050	+	2.43014i
$696$		0			0
$697$	7.86614	+	8.24977i	0.297951	+	0.312482i
$698$		0			0
$699$	−14.5399	+	6.64013i	−0.549948	+	0.251153i
$700$		0			0
$701$	6.62790	+	5.74311i	0.250332	+	0.216914i	0.770983	−	0.636855i	$-0.219765\pi$
$701$	6.62790	+	5.74311i	0.250332	+	0.216914i	−0.520651	+	0.853770i	$0.674311\pi$
$702$		0			0
$703$	−13.4382	−	3.26007i	−0.506831	−	0.122956i
$704$		0			0
$705$	1.50029	+	0.773455i	0.0565043	+	0.0291300i
$706$		0			0
$707$	1.07125	+	4.77814i	0.0402885	+	0.179701i
$708$		0			0
$709$	−16.5733	−	41.3981i	−0.622423	−	1.55474i	−0.818720	−	0.574193i	$-0.805316\pi$
$709$	−16.5733	−	41.3981i	−0.622423	−	1.55474i	0.196297	−	0.980545i	$-0.437108\pi$
$710$		0			0
$711$	0.439585	+	2.28078i	0.0164857	+	0.0855360i
$712$		0			0
$713$	−41.2350	+	12.6935i	−1.54426	+	0.475377i
$714$		0			0
$715$	−26.7373	−	30.8564i	−0.999917	−	1.15397i
$716$		0			0
$717$	28.6979	−	36.4924i	1.07174	−	1.36283i
$718$		0			0
$719$	−2.03767	−	2.59111i	−0.0759923	−	0.0966320i	0.746571	−	0.665306i	$-0.231699\pi$
$719$	−2.03767	−	2.59111i	−0.0759923	−	0.0966320i	−0.822563	+	0.568674i	$0.807457\pi$
$720$		0			0
$721$	15.2758	−	1.92493i	0.568902	−	0.0716882i
$722$		0			0
$723$	−6.32195	+	6.63027i	−0.235116	+	0.246582i
$724$		0			0
$725$	−26.4997	−	76.5659i	−0.984175	−	2.84359i
$726$		0			0
$727$	0.377246	+	0.826054i	0.0139913	+	0.0306367i	0.916499	−	0.400038i	$-0.131003\pi$
$727$	0.377246	+	0.826054i	0.0139913	+	0.0306367i	−0.902507	+	0.430674i	$0.858276\pi$
$728$		0			0
$729$	7.41025	+	2.17585i	0.274454	+	0.0805869i
$730$		0			0
$731$	−4.77095	+	3.39738i	−0.176460	+	0.125657i
$732$		0			0
$733$	−0.981980	+	20.6143i	−0.0362703	+	0.761406i	0.905337	+	0.424694i	$0.139618\pi$
$733$	−0.981980	+	20.6143i	−0.0362703	+	0.761406i	−0.941607	+	0.336713i	$0.890685\pi$
$734$		0			0
$735$	56.4576	+	21.7743i	2.08247	+	0.803156i
$736$		0			0
$737$	1.25591	+	2.17530i	0.0462621	+	0.0801283i
$738$		0			0
$739$	8.41791	−	4.33973i	0.309658	−	0.159640i	−0.296392	−	0.955066i	$-0.595784\pi$
$739$	8.41791	−	4.33973i	0.309658	−	0.159640i	0.606050	+	0.795427i	$0.292753\pi$
$740$		0			0
$741$	6.01572	−	13.1726i	0.220993	−	0.483907i
$742$		0			0
$743$	2.06446	−	7.03090i	0.0757376	−	0.257939i	−0.912917	−	0.408145i	$-0.866176\pi$
$743$	2.06446	−	7.03090i	0.0757376	−	0.257939i	0.988655	+	0.150207i	$0.0479939\pi$
$744$		0			0
$745$	0.113928	−	1.19311i	0.00417402	−	0.0437123i
$746$		0			0
$747$	13.0984	+	2.52451i	0.479246	+	0.0923671i
$748$		0			0
$749$	−3.87447	+	23.9706i	−0.141570	+	0.875867i
$750$		0			0
$751$	12.1415	−	23.5512i	0.443049	−	0.859396i	−0.556542	−	0.830819i	$-0.687872\pi$
$751$	12.1415	−	23.5512i	0.443049	−	0.859396i	0.999592	−	0.0285767i	$-0.00909749\pi$
$752$		0			0
$753$	−13.7292	+	34.2939i	−0.500321	+	1.24974i
$754$		0			0
$755$	10.4502	−	72.6829i	0.380322	−	2.64520i
$756$		0			0
$757$	17.2856	−	14.9780i	0.628255	−	0.544386i	−0.281485	−	0.959566i	$-0.590827\pi$
$757$	17.2856	−	14.9780i	0.628255	−	0.544386i	0.909739	+	0.415180i	$0.136281\pi$
$758$		0			0
$759$	−15.7439	−	8.81824i	−0.571466	−	0.320082i
$760$		0			0
$761$	47.8622	+	16.5653i	1.73500	+	0.600490i	0.997218	−	0.0745458i	$-0.0237507\pi$
$761$	47.8622	+	16.5653i	1.73500	+	0.600490i	0.737785	+	0.675036i	$0.235872\pi$
$762$		0			0
$763$	−3.45933	+	53.1057i	−0.125236	+	1.92255i
$764$		0			0
$765$	5.46329	−	4.29638i	0.197526	−	0.155336i
$766$		0			0
$767$	1.57672	+	33.0995i	0.0569322	+	1.19515i
$768$		0			0
$769$	22.0161	−	6.46451i	0.793921	−	0.233116i	0.140470	−	0.990085i	$-0.455139\pi$
$769$	22.0161	−	6.46451i	0.793921	−	0.233116i	0.653451	+	0.756969i	$0.273320\pi$
$770$		0			0
$771$	−33.7249	+	38.9206i	−1.21457	+	1.40169i
$772$		0			0
$773$	30.3964	+	2.90250i	1.09328	+	0.104396i	0.626083	−	0.779756i	$-0.284657\pi$
$773$	30.3964	+	2.90250i	1.09328	+	0.104396i	0.467199	+	0.884152i	$0.345263\pi$
$774$		0			0
$775$	−108.885	+	26.4151i	−3.91125	+	0.948860i
$776$		0			0
$777$	−10.0029	−	57.2587i	−0.358851	−	2.05415i
$778$		0			0
$779$	11.4200	+	0.544000i	0.409163	+	0.0194908i
$780$		0			0
$781$	13.0181	+	7.51602i	0.465825	+	0.268944i
$782$		0			0
$783$		−	23.1358i		−	0.826808i
$784$		0			0
$785$	−67.2367	−	43.2104i	−2.39978	−	1.54225i
$786$		0			0
$787$	14.1675	+	19.8954i	0.505016	+	0.709196i	0.985853	−	0.167614i	$-0.0536063\pi$
$787$	14.1675	+	19.8954i	0.505016	+	0.709196i	−0.480836	+	0.876810i	$0.659667\pi$
$788$		0			0
$789$	11.0812	+	45.6775i	0.394502	+	1.62616i
$790$		0			0
$791$	−0.193345	+	0.321783i	−0.00687454	+	0.0114413i
$792$		0			0
$793$	−1.41268	+	7.32970i	−0.0501659	+	0.260285i
$794$		0			0
$795$	13.4969	−	55.6351i	0.478687	−	1.97317i
$796$		0			0
$797$	−5.02883	+	3.23183i	−0.178130	+	0.114477i	−0.626667	−	0.779287i	$-0.715582\pi$
$797$	−5.02883	+	3.23183i	−0.178130	+	0.114477i	0.448537	+	0.893764i	$0.351945\pi$
$798$		0			0
$799$	−0.250959	+	0.0360825i	−0.00887829	+	0.00127651i
$800$		0			0
$801$	−3.16957	−	2.49258i	−0.111991	−	0.0880709i
$802$		0			0
$803$	6.19441	−	17.8976i	0.218596	−	0.631592i
$804$		0			0
$805$	−41.8138	+	32.5847i	−1.47374	+	1.14846i
$806$		0			0
$807$	−7.34370	+	21.2182i	−0.258510	+	0.746917i
$808$		0			0
$809$	−5.66087	−	4.45176i	−0.199026	−	0.156516i	0.513672	−	0.857986i	$-0.328285\pi$
$809$	−5.66087	−	4.45176i	−0.199026	−	0.156516i	−0.712698	+	0.701471i	$0.752527\pi$
$810$		0			0
$811$	7.99723	−	1.14983i	0.280821	−	0.0403759i	−0.000465345	−	1.00000i	$-0.500148\pi$
$811$	7.99723	−	1.14983i	0.280821	−	0.0403759i	0.281286	+	0.959624i	$0.409239\pi$
$812$		0			0
$813$	11.9015	−	7.64860i	0.417402	−	0.268248i
$814$		0			0
$815$	10.8456	−	44.7061i	0.379904	−	1.56599i
$816$		0			0
$817$	−1.11175	+	5.76829i	−0.0388951	+	0.201807i
$818$		0			0
$819$	18.2140	+	0.317844i	0.636450	+	0.0111064i
$820$		0			0
$821$	5.79542	+	23.8891i	0.202262	+	0.833734i	0.978992	+	0.203900i	$0.0653618\pi$
$821$	5.79542	+	23.8891i	0.202262	+	0.833734i	−0.776730	+	0.629834i	$0.783123\pi$
$822$		0			0
$823$	−6.84662	−	9.61474i	−0.238658	−	0.335149i	0.677824	−	0.735224i	$-0.262923\pi$
$823$	−6.84662	−	9.61474i	−0.238658	−	0.335149i	−0.916482	+	0.400076i	$0.868984\pi$
$824$		0			0
$825$	−39.4228	−	25.3355i	−1.37253	−	0.882070i
$826$		0			0
$827$			22.9028i			0.796410i	0.917297	+	0.398205i	$0.130367\pi$
$827$			22.9028i			0.796410i	−0.917297	+	0.398205i	$0.869633\pi$
$828$		0			0
$829$	−25.6194	−	14.7914i	−0.889799	−	0.513726i	−0.0159224	−	0.999873i	$-0.505068\pi$
$829$	−25.6194	−	14.7914i	−0.889799	−	0.513726i	−0.873877	+	0.486147i	$0.838402\pi$
$830$		0			0
$831$	−21.0321	−	1.00188i	−0.729595	−	0.0347549i
$832$		0			0
$833$	−8.80505	+	2.25488i	−0.305077	+	0.0781270i
$834$		0			0
$835$	42.6301	−	10.3420i	1.47528	−	0.357898i
$836$		0			0
$837$	−31.8490	−	3.04121i	−1.10086	−	0.105120i
$838$		0			0
$839$	−31.1704	+	35.9725i	−1.07612	+	1.24191i	−0.107278	+	0.994229i	$0.534214\pi$
$839$	−31.1704	+	35.9725i	−1.07612	+	1.24191i	−0.968842	+	0.247680i	$0.920332\pi$
$840$		0			0
$841$	−12.7819	+	3.75311i	−0.440756	+	0.129418i
$842$		0			0
$843$	−2.49199	−	52.3133i	−0.0858286	−	1.80176i
$844$		0			0
$845$	−52.1510	+	41.0120i	−1.79405	+	1.41086i
$846$		0			0
$847$	11.3012	−	16.9281i	0.388314	−	0.581658i
$848$		0			0
$849$	−12.8710	−	4.45471i	−0.441733	−	0.152885i
$850$		0			0
$851$	47.5164	+	18.3081i	1.62884	+	0.627593i
$852$		0			0
$853$	16.2820	−	14.1085i	0.557486	−	0.483064i	−0.329948	−	0.943999i	$-0.607031\pi$
$853$	16.2820	−	14.1085i	0.557486	−	0.483064i	0.887434	+	0.460935i	$0.152486\pi$
$854$		0			0
$855$	0.992079	−	6.90006i	0.0339284	−	0.235977i
$856$		0			0
$857$	−8.24053	+	20.5838i	−0.281491	+	0.703131i	0.718480	+	0.695547i	$0.244838\pi$
$857$	−8.24053	+	20.5838i	−0.281491	+	0.703131i	−0.999971	+	0.00758327i	$0.997586\pi$
$858$		0			0
$859$	−7.08005	+	13.7334i	−0.241568	+	0.468577i	−0.978186	−	0.207733i	$-0.933392\pi$
$859$	−7.08005	+	13.7334i	−0.241568	+	0.468577i	0.736618	+	0.676310i	$0.236422\pi$
$860$		0			0
$861$	17.0803	+	44.9206i	0.582095	+	1.53089i
$862$		0			0
$863$	−51.8499	−	9.99326i	−1.76499	−	0.340174i	−0.799512	−	0.600650i	$-0.794909\pi$
$863$	−51.8499	−	9.99326i	−1.76499	−	0.340174i	−0.965480	+	0.260476i	$0.916121\pi$
$864$		0			0
$865$	4.71432	−	49.3706i	0.160292	−	1.67865i
$866$		0			0
$867$	8.92708	−	30.4029i	0.303180	−	1.03254i
$868$		0			0
$869$	−1.36955	+	2.99890i	−0.0464588	+	0.101731i
$870$		0			0
$871$	6.59776	−	3.40138i	0.223556	−	0.115251i
$872$		0			0
$873$	2.70929	+	4.69262i	0.0916955	+	0.158821i
$874$		0			0
$875$	−67.9427	+	46.6168i	−2.29688	+	1.57594i
$876$		0			0
$877$	−0.653523	+	13.7191i	−0.0220679	+	0.463262i	0.960605	+	0.277916i	$0.0896437\pi$
$877$	−0.653523	+	13.7191i	−0.0220679	+	0.463262i	−0.982673	+	0.185346i	$0.940659\pi$
$878$		0			0
$879$	−21.8003	+	15.5239i	−0.735306	+	0.523609i
$880$		0			0
$881$	48.1237	+	14.1304i	1.62133	+	0.476065i	0.961375	−	0.275242i	$-0.0887578\pi$
$881$	48.1237	+	14.1304i	1.62133	+	0.476065i	0.659953	+	0.751307i	$0.270576\pi$
$882$		0			0
$883$	9.41553	+	20.6171i	0.316858	+	0.693822i	0.999311	−	0.0371074i	$-0.0118144\pi$
$883$	9.41553	+	20.6171i	0.316858	+	0.693822i	−0.682454	+	0.730929i	$0.739087\pi$
$884$		0			0
$885$	17.4336	+	50.3711i	0.586024	+	1.69321i
$886$		0			0
$887$	5.33262	−	5.59269i	0.179052	−	0.187784i	−0.628092	−	0.778139i	$-0.716164\pi$
$887$	5.33262	−	5.59269i	0.179052	−	0.187784i	0.807144	+	0.590355i	$0.201012\pi$
$888$		0			0
$889$	15.2018	−	36.1320i	0.509852	−	1.21183i
$890$		0			0
$891$	−12.5926	−	16.0128i	−0.421868	−	0.536449i
$892$		0			0
$893$	−0.157196	+	0.199890i	−0.00526035	+	0.00668908i
$894$		0			0
$895$	65.6466	+	75.7602i	2.19432	+	2.53239i
$896$		0			0
$897$	−28.2439	+	45.2335i	−0.943036	+	1.51030i
$898$		0			0
$899$	11.0760	+	57.4676i	0.369404	+	1.91665i
$900$		0			0
$901$	3.19600	+	7.98322i	0.106474	+	0.265960i
$902$		0			0
$903$	−24.0951	+	5.40208i	−0.801836	+	0.179770i
$904$		0			0
$905$	−7.14121	−	3.68155i	−0.237382	−	0.122379i
$906$		0			0
$907$	−24.1204	−	5.85155i	−0.800905	−	0.194297i	−0.185640	−	0.982618i	$-0.559436\pi$
$907$	−24.1204	−	5.85155i	−0.800905	−	0.194297i	−0.615265	+	0.788320i	$0.710951\pi$
$908$		0			0
$909$	1.79209	+	1.55286i	0.0594399	+	0.0515050i
$910$		0			0
$911$	37.4301	−	17.0937i	1.24011	−	0.566341i	0.316109	−	0.948723i	$-0.397623\pi$
$911$	37.4301	−	17.0937i	1.24011	−	0.566341i	0.924004	+	0.382382i	$0.124896\pi$
$912$		0			0
$913$	13.0656	+	13.7028i	0.432409	+	0.453497i
$914$		0			0
$915$	1.14136	+	11.9528i	0.0377321	+	0.395148i
$916$		0			0
$917$	−2.38486	+	1.47450i	−0.0787550	+	0.0486924i
$918$		0			0
$919$	−11.6147	+	6.70576i	−0.383134	+	0.221203i	−0.679181	−	0.733971i	$-0.737665\pi$
$919$	−11.6147	+	6.70576i	−0.383134	+	0.221203i	0.296047	+	0.955173i	$0.404332\pi$
$920$		0			0
$921$	11.8944	−	20.6017i	0.391935	−	0.678851i
$922$		0			0
$923$	24.0167	−	37.3707i	0.790518	−	1.23007i
$924$		0			0
$925$	120.289	+	54.9341i	3.95507	+	1.80622i
$926$		0			0
$927$	5.39608	−	5.14515i	0.177231	−	0.168989i
$928$		0			0
$929$	22.6351	+	16.1184i	0.742634	+	0.528827i	0.887603	−	0.460609i	$-0.152369\pi$
$929$	22.6351	+	16.1184i	0.742634	+	0.528827i	−0.144969	+	0.989436i	$0.546308\pi$
$930$		0			0
$931$	−4.83084	+	7.73112i	−0.158324	+	0.253377i
$932$		0			0
$933$	−14.2676	−	13.6041i	−0.467101	−	0.445379i
$934$		0			0
$935$	9.85376	−	0.469393i	0.322253	−	0.0153508i
$936$		0			0
$937$	−3.52049	−	24.4855i	−0.115009	−	0.799907i	−0.962924	−	0.269774i	$-0.913051\pi$
$937$	−3.52049	−	24.4855i	−0.115009	−	0.799907i	0.847914	−	0.530133i	$-0.177858\pi$
$938$		0			0
$939$	60.2037	+	8.65598i	1.96467	+	0.282477i
$940$		0			0
$941$	18.0769	−	3.48403i	0.589289	−	0.113576i	0.114114	−	0.993468i	$-0.463597\pi$
$941$	18.0769	−	3.48403i	0.589289	−	0.113576i	0.475175	+	0.879891i	$0.342385\pi$
$942$		0			0
$943$	−41.4412	−	7.42851i	−1.34951	−	0.241906i
$944$		0			0
$945$	−37.9054	+	10.4152i	−1.23306	+	0.338807i
$946$		0			0
$947$	−7.87233	+	3.15161i	−0.255816	+	0.102413i	−0.496026	−	0.868308i	$-0.665208\pi$
$947$	−7.87233	+	3.15161i	−0.255816	+	0.102413i	0.240210	+	0.970721i	$0.422784\pi$
$948$		0			0
$949$	−51.9599	−	20.8016i	−1.68669	−	0.675248i
$950$		0			0
$951$	−20.9320	−	32.5709i	−0.678768	−	1.05618i
$952$		0			0
$953$	12.3179	+	41.9510i	0.399017	+	1.35893i	0.876971	+	0.480543i	$0.159560\pi$
$953$	12.3179	+	41.9510i	0.399017	+	1.35893i	−0.477954	+	0.878385i	$0.658622\pi$
$954$		0			0
$955$	84.0341	−	29.0845i	2.71928	−	0.941152i
$956$		0			0
$957$	−14.1987	+	19.9393i	−0.458980	+	0.644547i
$958$		0			0
$959$	30.1090	+	6.34980i	0.972269	+	0.205046i
$960$		0			0
$961$	49.7066	−	4.74641i	1.60344	−	0.153110i
$962$		0			0
$963$	5.38807	+	10.4514i	0.173628	+	0.336791i
$964$		0			0
$965$	−64.0246			−2.06102
$966$		0			0
$967$	4.21597			0.135576			0.0677882	−	0.997700i	$-0.478406\pi$
$967$	4.21597			0.135576			0.0677882	+	0.997700i	$0.478406\pi$
$968$		0			0
$969$	1.60329	+	3.10995i	0.0515051	+	0.0999060i
$970$		0			0
$971$	15.8908	−	1.51739i	0.509960	−	0.0486952i	0.163095	−	0.986610i	$-0.447852\pi$
$971$	15.8908	−	1.51739i	0.509960	−	0.0486952i	0.346865	+	0.937915i	$0.387246\pi$
$972$		0			0
$973$	−12.6559	−	38.7411i	−0.405731	−	1.24198i
$974$		0			0
$975$	−80.3300	+	112.808i	−2.57262	+	3.61274i
$976$		0			0
$977$	−22.1307	+	7.65951i	−0.708024	+	0.245050i	−0.657263	−	0.753661i	$-0.728286\pi$
$977$	−22.1307	+	7.65951i	−0.708024	+	0.245050i	−0.0507612	+	0.998711i	$0.516165\pi$
$978$		0			0
$979$	−1.61242	−	5.49139i	−0.0515331	−	0.175506i
$980$		0			0
$981$	13.9329	+	21.6801i	0.444845	+	0.692192i
$982$		0			0
$983$	39.1944	+	15.6911i	1.25011	+	0.500468i	0.899856	−	0.436188i	$-0.143672\pi$
$983$	39.1944	+	15.6911i	1.25011	+	0.500468i	0.350252	+	0.936656i	$0.386096\pi$
$984$		0			0
$985$	30.7516	−	12.3111i	0.979828	−	0.392264i
$986$		0			0
$987$	−1.03425	−	0.270098i	−0.0329205	−	0.00859731i
$988$		0			0
$989$	6.80841	−	20.5333i	0.216495	−	0.652922i
$990$		0			0
$991$	−7.54445	+	1.45407i	−0.239657	+	0.0461901i	−0.307665	−	0.951495i	$-0.599548\pi$
$991$	−7.54445	+	1.45407i	−0.239657	+	0.0461901i	0.0680081	+	0.997685i	$0.478336\pi$
$992$		0			0
$993$	−44.0065	−	6.32717i	−1.39650	−	0.200787i
$994$		0			0
$995$	−2.01910	−	14.0432i	−0.0640098	−	0.445198i
$996$		0			0
$997$	45.5141	−	2.16810i	1.44145	−	0.0686646i	0.687779	−	0.725920i	$-0.258586\pi$
$997$	45.5141	−	2.16810i	1.44145	−	0.0686646i	0.753668	+	0.657256i	$0.228283\pi$
$998$		0			0
$999$	27.3288	+	26.0580i	0.864646	+	0.824438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.13	yes	320
7.5	odd	6	inner	644.2.bc.a.33.13	✓	320
23.7	odd	22	inner	644.2.bc.a.605.13	yes	320
161.145	even	66	inner	644.2.bc.a.145.13	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.13	✓	320	7.5	odd	6	inner
644.2.bc.a.145.13	yes	320	161.145	even	66	inner
644.2.bc.a.493.13	yes	320	1.1	even	1	trivial
644.2.bc.a.605.13	yes	320	23.7	odd	22	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.948121 + 1.83910i) q^{3} +(4.15893 - 0.397129i) q^{5} +(-2.51495 + 0.821585i) q^{7} +(-0.743179 + 1.04365i) q^{9} +O(q^{10})\)	\(q+(0.948121 + 1.83910i) q^{3} +(4.15893 - 0.397129i) q^{5} +(-2.51495 + 0.821585i) q^{7} +(-0.743179 + 1.04365i) q^{9} +(-1.71849 + 0.594775i) q^{11} +(1.51404 + 5.15635i) q^{13} +(4.67353 + 7.27215i) q^{15} +(-1.20544 - 0.482587i) q^{17} +(-1.20904 + 0.484027i) q^{19} +(-3.89546 - 3.84629i) q^{21} +(4.64552 - 1.19129i) q^{23} +(12.2293 - 2.35701i) q^{25} +(3.52015 + 0.506122i) q^{27} +(-0.925829 - 6.43928i) q^{29} +(-8.98607 + 0.428059i) q^{31} +(-2.72319 - 2.59655i) q^{33} +(-10.1332 + 4.41568i) q^{35} +(8.64906 + 6.15897i) q^{37} +(-8.04755 + 7.67332i) q^{39} +(-7.98549 - 3.64685i) q^{41} +(2.43868 - 3.79466i) q^{43} +(-2.67636 + 4.63560i) q^{45} +(0.169102 - 0.0976313i) q^{47} +(5.65000 - 4.13250i) q^{49} +(-0.255382 - 2.67448i) q^{51} +(-4.57014 - 4.79303i) q^{53} +(-6.91087 + 3.15609i) q^{55} +(-2.03649 - 1.76463i) q^{57} +(5.99232 + 1.45372i) q^{59} +(1.23460 + 0.636481i) q^{61} +(1.01161 - 3.23531i) q^{63} +(8.34453 + 20.8436i) q^{65} +(-0.261404 - 1.35629i) q^{67} +(6.59541 + 7.41408i) q^{69} +(-5.41317 - 6.24713i) q^{71} +(-6.43795 + 8.18651i) q^{73} +(15.9297 + 20.2562i) q^{75} +(3.83327 - 2.90772i) q^{77} +(1.25107 - 1.31208i) q^{79} +(3.66386 + 10.5860i) q^{81} +(-4.32512 - 9.47070i) q^{83} +(-5.20501 - 1.52833i) q^{85} +(10.9647 - 7.80791i) q^{87} +(-0.149750 + 3.14365i) q^{89} +(-8.04413 - 11.7241i) q^{91} +(-9.30713 - 16.1204i) q^{93} +(-4.83610 + 2.49318i) q^{95} +(1.75689 - 3.84705i) q^{97} +(0.656409 - 2.23552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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