LMFDB - Embedded newform 405.3.l.d.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	405.28
Dual form			405.3.l.d.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.86603 + 0.500000i) q^{2} +(-0.232051 - 0.133975i) q^{4} -5.00000 q^{5} +(11.5622 + 3.09808i) q^{7} +(-5.83013 - 5.83013i) q^{8} +(-9.33013 - 2.50000i) q^{10} +(3.09808 + 5.36603i) q^{11} +(16.0622 - 4.30385i) q^{13} +(20.0263 + 11.5622i) q^{14} +(-7.42820 - 12.8660i) q^{16} +(22.2942 - 22.2942i) q^{17} +30.5885i q^{19} +(1.16025 + 0.669873i) q^{20} +(3.09808 + 11.5622i) q^{22} +(9.36603 - 2.50962i) q^{23} +25.0000 q^{25} +32.1244 q^{26} +(-2.26795 - 2.26795i) q^{28} +(0.990381 - 0.571797i) q^{29} +(2.58846 - 4.48334i) q^{31} +(1.10770 + 4.13397i) q^{32} +(52.7487 - 30.4545i) q^{34} +(-57.8109 - 15.4904i) q^{35} +(16.8827 - 16.8827i) q^{37} +(-15.2942 + 57.0788i) q^{38} +(29.1506 + 29.1506i) q^{40} +(-2.60770 + 4.51666i) q^{41} +(-0.346788 + 1.29423i) q^{43} -1.66025i q^{44} +18.7321 q^{46} +(-17.1244 - 4.58846i) q^{47} +(81.6506 + 47.1410i) q^{49} +(46.6506 + 12.5000i) q^{50} +(-4.30385 - 1.15321i) q^{52} +(-3.98076 - 3.98076i) q^{53} +(-15.4904 - 26.8301i) q^{55} +(-49.3468 - 85.4711i) q^{56} +(2.13397 - 0.571797i) q^{58} +(-33.8038 - 19.5167i) q^{59} +(16.0885 + 27.8660i) q^{61} +(7.07180 - 7.07180i) q^{62} +67.6936i q^{64} +(-80.3109 + 21.5192i) q^{65} +(-12.3468 - 46.0788i) q^{67} +(-8.16025 + 2.18653i) q^{68} +(-100.131 - 57.8109i) q^{70} -103.373 q^{71} +(-73.2750 - 73.2750i) q^{73} +(39.9449 - 23.0622i) q^{74} +(4.09808 - 7.09808i) q^{76} +(19.1962 + 71.6410i) q^{77} +(-83.8634 + 48.4186i) q^{79} +(37.1410 + 64.3301i) q^{80} +(-7.12436 + 7.12436i) q^{82} +(-12.2102 + 45.5692i) q^{83} +(-111.471 + 111.471i) q^{85} +(-1.29423 + 2.24167i) q^{86} +(13.2224 - 49.3468i) q^{88} -18.0577i q^{89} +199.047 q^{91} +(-2.50962 - 0.672450i) q^{92} +(-29.6603 - 17.1244i) q^{94} -152.942i q^{95} +(134.720 + 36.0981i) q^{97} +(128.792 + 128.792i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{4} - 20 q^{5} + 22 q^{7} - 6 q^{8} - 20 q^{10} + 2 q^{11} + 40 q^{13} + 42 q^{14} - 2 q^{16} + 58 q^{17} - 30 q^{20} + 2 q^{22} + 34 q^{23} + 100 q^{25} + 80 q^{26} - 16 q^{28} - 48 q^{29}+ \cdots + 290 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^4 - 20 * q^5 + 22 * q^7 - 6 * q^8 - 20 * q^10 + 2 * q^11 + 40 * q^13 + 42 * q^14 - 2 * q^16 + 58 * q^17 - 30 * q^20 + 2 * q^22 + 34 * q^23 + 100 * q^25 + 80 * q^26 - 16 * q^28 - 48 * q^29 - 52 * q^31 + 46 * q^32 + 114 * q^34 - 110 * q^35 - 26 * q^37 - 30 * q^38 + 30 * q^40 - 52 * q^41 + 106 * q^43 + 68 * q^46 - 20 * q^47 + 240 * q^49 + 100 * q^50 - 38 * q^52 + 88 * q^53 - 10 * q^55 - 90 * q^56 + 12 * q^58 - 156 * q^59 + 2 * q^61 + 56 * q^62 - 200 * q^65 + 58 * q^67 + 2 * q^68 - 210 * q^70 - 268 * q^71 - 158 * q^73 + 42 * q^74 + 6 * q^76 + 56 * q^77 - 138 * q^79 + 10 * q^80 + 20 * q^82 + 256 * q^83 - 290 * q^85 + 26 * q^86 - 6 * q^88 + 332 * q^91 - 62 * q^92 - 84 * q^94 + 286 * q^97 + 290 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.86603	+	0.500000i	0.933013	+	0.250000i	0.693139	−	0.720804i	$-0.256227\pi$
$2$	1.86603	+	0.500000i	0.933013	+	0.250000i	0.239874	+	0.970804i	$0.422894\pi$
$3$		0			0
$3$		0			0
$4$	−0.232051	−	0.133975i	−0.0580127	−	0.0334936i
$5$	−5.00000			−1.00000
$5$	−5.00000			−1.00000
$6$		0			0
$7$	11.5622	+	3.09808i	1.65174	+	0.442582i	0.960099	−	0.279660i	$-0.0902216\pi$
$7$	11.5622	+	3.09808i	1.65174	+	0.442582i	0.691640	+	0.722242i	$0.256888\pi$
$8$	−5.83013	−	5.83013i	−0.728766	−	0.728766i
$9$		0			0
$10$	−9.33013	−	2.50000i	−0.933013	−	0.250000i
$11$	3.09808	+	5.36603i	0.281643	+	0.487820i	0.971790	−	0.235849i	$-0.0757872\pi$
$11$	3.09808	+	5.36603i	0.281643	+	0.487820i	−0.690146	+	0.723670i	$0.742454\pi$
$12$		0			0
$13$	16.0622	−	4.30385i	1.23555	−	0.331065i	0.418813	−	0.908072i	$-0.362446\pi$
$13$	16.0622	−	4.30385i	1.23555	−	0.331065i	0.816739	+	0.577007i	$0.195780\pi$
$14$	20.0263	+	11.5622i	1.43045	+	0.825870i
$15$		0			0
$16$	−7.42820	−	12.8660i	−0.464263	−	0.804127i
$17$	22.2942	−	22.2942i	1.31143	−	1.31143i	0.391060	−	0.920365i	$-0.372108\pi$
$17$	22.2942	−	22.2942i	1.31143	−	1.31143i	0.920365	−	0.391060i	$-0.127892\pi$
$18$		0			0
$19$			30.5885i			1.60992i	0.593330	+	0.804959i	$0.297813\pi$
$19$			30.5885i			1.60992i	−0.593330	+	0.804959i	$0.702187\pi$
$20$	1.16025	+	0.669873i	0.0580127	+	0.0334936i
$21$		0			0
$22$	3.09808	+	11.5622i	0.140822	+	0.525554i
$23$	9.36603	−	2.50962i	0.407218	−	0.109114i	−0.0493944	−	0.998779i	$-0.515729\pi$
$23$	9.36603	−	2.50962i	0.407218	−	0.109114i	0.456613	+	0.889665i	$0.349062\pi$
$24$		0			0
$25$	25.0000			1.00000
$26$	32.1244			1.23555
$27$		0			0
$28$	−2.26795	−	2.26795i	−0.0809982	−	0.0809982i
$29$	0.990381	−	0.571797i	0.0341511	−	0.0197171i	−0.482827	−	0.875716i	$-0.660390\pi$
$29$	0.990381	−	0.571797i	0.0341511	−	0.0197171i	0.516978	+	0.855998i	$0.327057\pi$
$30$		0			0
$31$	2.58846	−	4.48334i	0.0834986	−	0.144624i	−0.821252	−	0.570566i	$-0.806724\pi$
$31$	2.58846	−	4.48334i	0.0834986	−	0.144624i	0.904750	+	0.425942i	$0.140057\pi$
$32$	1.10770	+	4.13397i	0.0346155	+	0.129187i
$33$		0			0
$34$	52.7487	−	30.4545i	1.55143	−	0.895720i
$35$	−57.8109	−	15.4904i	−1.65174	−	0.442582i
$36$		0			0
$37$	16.8827	−	16.8827i	0.456289	−	0.456289i	−0.441146	−	0.897435i	$-0.645428\pi$
$37$	16.8827	−	16.8827i	0.456289	−	0.456289i	0.897435	+	0.441146i	$0.145428\pi$
$38$	−15.2942	+	57.0788i	−0.402480	+	1.50207i
$39$		0			0
$40$	29.1506	+	29.1506i	0.728766	+	0.728766i
$41$	−2.60770	+	4.51666i	−0.0636023	+	0.110162i	−0.896073	−	0.443906i	$-0.853592\pi$
$41$	−2.60770	+	4.51666i	−0.0636023	+	0.110162i	0.832471	+	0.554069i	$0.186926\pi$
$42$		0			0
$43$	−0.346788	+	1.29423i	−0.00806483	+	0.0300983i	−0.969841	−	0.243738i	$-0.921626\pi$
$43$	−0.346788	+	1.29423i	−0.00806483	+	0.0300983i	0.961776	+	0.273837i	$0.0882928\pi$
$44$		−	1.66025i		−	0.0377330i
$45$		0			0
$46$	18.7321			0.407218
$47$	−17.1244	−	4.58846i	−0.364348	−	0.0976268i	0.0720003	−	0.997405i	$-0.477062\pi$
$47$	−17.1244	−	4.58846i	−0.364348	−	0.0976268i	−0.436348	+	0.899778i	$0.643728\pi$
$48$		0			0
$49$	81.6506	+	47.1410i	1.66634	+	0.962062i
$50$	46.6506	+	12.5000i	0.933013	+	0.250000i
$51$		0			0
$52$	−4.30385	−	1.15321i	−0.0827663	−	0.0221772i
$53$	−3.98076	−	3.98076i	−0.0751087	−	0.0751087i	0.668554	−	0.743663i	$-0.266913\pi$
$53$	−3.98076	−	3.98076i	−0.0751087	−	0.0751087i	−0.743663	+	0.668554i	$0.766913\pi$
$54$		0			0
$55$	−15.4904	−	26.8301i	−0.281643	−	0.487820i
$56$	−49.3468	−	85.4711i	−0.881193	−	1.52627i
$57$		0			0
$58$	2.13397	−	0.571797i	0.0367927	−	0.00985856i
$59$	−33.8038	−	19.5167i	−0.572947	−	0.330791i	0.185379	−	0.982667i	$-0.440649\pi$
$59$	−33.8038	−	19.5167i	−0.572947	−	0.330791i	−0.758325	+	0.651876i	$0.773982\pi$
$60$		0			0
$61$	16.0885	+	27.8660i	0.263745	+	0.456820i	0.967234	−	0.253886i	$-0.0817089\pi$
$61$	16.0885	+	27.8660i	0.263745	+	0.456820i	−0.703489	+	0.710706i	$0.748376\pi$
$62$	7.07180	−	7.07180i	0.114061	−	0.114061i
$63$		0			0
$64$			67.6936i			1.05771i
$65$	−80.3109	+	21.5192i	−1.23555	+	0.331065i
$66$		0			0
$67$	−12.3468	−	46.0788i	−0.184280	−	0.687744i	−0.994783	−	0.102009i	$-0.967473\pi$
$67$	−12.3468	−	46.0788i	−0.184280	−	0.687744i	0.810503	−	0.585734i	$-0.199194\pi$
$68$	−8.16025	+	2.18653i	−0.120004	+	0.0321549i
$69$		0			0
$70$	−100.131	−	57.8109i	−1.43045	−	0.825870i
$71$	−103.373			−1.45596			−0.727979	−	0.685599i	$-0.759540\pi$
$71$	−103.373			−1.45596			−0.727979	+	0.685599i	$0.759540\pi$
$72$		0			0
$73$	−73.2750	−	73.2750i	−1.00377	−	1.00377i	−0.999993	−	0.00377412i	$-0.998799\pi$
$73$	−73.2750	−	73.2750i	−1.00377	−	1.00377i	−0.00377412	−	0.999993i	$-0.501201\pi$
$74$	39.9449	−	23.0622i	0.539795	−	0.311651i
$75$		0			0
$76$	4.09808	−	7.09808i	0.0539221	−	0.0933957i
$77$	19.1962	+	71.6410i	0.249301	+	0.930403i
$78$		0			0
$79$	−83.8634	+	48.4186i	−1.06156	+	0.612893i	−0.925864	−	0.377857i	$-0.876661\pi$
$79$	−83.8634	+	48.4186i	−1.06156	+	0.612893i	−0.135699	+	0.990750i	$0.543328\pi$
$80$	37.1410	+	64.3301i	0.464263	+	0.804127i
$81$		0			0
$82$	−7.12436	+	7.12436i	−0.0868824	+	0.0868824i
$83$	−12.2102	+	45.5692i	−0.147111	+	0.549027i	0.852541	+	0.522660i	$0.175060\pi$
$83$	−12.2102	+	45.5692i	−0.147111	+	0.549027i	−0.999652	+	0.0263665i	$0.991606\pi$
$84$		0			0
$85$	−111.471	+	111.471i	−1.31143	+	1.31143i
$86$	−1.29423	+	2.24167i	−0.0150492	+	0.0260659i
$87$		0			0
$88$	13.2224	−	49.3468i	0.150255	−	0.560759i
$89$		−	18.0577i		−	0.202896i	−0.994841	−	0.101448i	$-0.967653\pi$
$89$		−	18.0577i		−	0.202896i	0.994841	−	0.101448i	$-0.0323475\pi$
$90$		0			0
$91$	199.047			2.18733
$92$	−2.50962	−	0.672450i	−0.0272785	−	0.00730924i
$93$		0			0
$94$	−29.6603	−	17.1244i	−0.315535	−	0.182174i
$95$		−	152.942i		−	1.60992i
$96$		0			0
$97$	134.720	+	36.0981i	1.38886	+	0.372145i	0.874333	−	0.485326i	$-0.161299\pi$
$97$	134.720	+	36.0981i	1.38886	+	0.372145i	0.514531	+	0.857472i	$0.327966\pi$
$98$	128.792	+	128.792i	1.31420	+	1.31420i
$99$		0			0
$100$	−5.80127	−	3.34936i	−0.0580127	−	0.0334936i
$101$	43.5692	+	75.4641i	0.431378	+	0.747169i	0.996992	−	0.0775009i	$-0.0246941\pi$
$101$	43.5692	+	75.4641i	0.431378	+	0.747169i	−0.565614	+	0.824670i	$0.691361\pi$
$102$		0			0
$103$	1.24871	−	0.334591i	0.0121234	−	0.00324846i	−0.252752	−	0.967531i	$-0.581336\pi$
$103$	1.24871	−	0.334591i	0.0121234	−	0.00324846i	0.264876	+	0.964283i	$0.414669\pi$
$104$	−118.737	−	68.5526i	−1.14170	−	0.659159i
$105$		0			0
$106$	−5.43782	−	9.41858i	−0.0513002	−	0.0888546i
$107$	4.00000	−	4.00000i	0.0373832	−	0.0373832i	−0.688168	−	0.725551i	$-0.741585\pi$
$107$	4.00000	−	4.00000i	0.0373832	−	0.0373832i	0.725551	+	0.688168i	$0.241585\pi$
$108$		0			0
$109$			14.8423i			0.136168i	0.997680	+	0.0680841i	$0.0216886\pi$
$109$			14.8423i			0.136168i	−0.997680	+	0.0680841i	$0.978311\pi$
$110$	−15.4904	−	57.8109i	−0.140822	−	0.525554i
$111$		0			0
$112$	−46.0263	−	171.772i	−0.410949	−	1.53368i
$113$	46.1410	−	12.3634i	0.408328	−	0.109411i	−0.0488078	−	0.998808i	$-0.515542\pi$
$113$	46.1410	−	12.3634i	0.408328	−	0.109411i	0.457135	+	0.889397i	$0.348876\pi$
$114$		0			0
$115$	−46.8301	+	12.5481i	−0.407218	+	0.109114i
$116$	−0.306425			−0.00264159
$117$		0			0
$118$	−53.3205	−	53.3205i	−0.451869	−	0.451869i
$119$	326.839	−	188.701i	2.74655	−	1.58572i
$120$		0			0
$121$	41.3038	−	71.5404i	0.341354	−	0.591243i
$122$	16.0885	+	60.0429i	0.131873	+	0.492155i
$123$		0			0
$124$	−1.20131	+	0.693575i	−0.00968796	+	0.00559335i
$125$	−125.000			−1.00000
$126$		0			0
$127$	−2.64617	+	2.64617i	−0.0208360	+	0.0208360i	−0.717448	−	0.696612i	$-0.754690\pi$
$127$	−2.64617	+	2.64617i	−0.0208360	+	0.0208360i	0.696612	+	0.717448i	$0.254690\pi$
$128$	−29.4160	+	109.782i	−0.229813	+	0.857672i
$129$		0			0
$130$	−160.622			−1.23555
$131$	−71.0404	+	123.046i	−0.542293	+	0.939279i	0.456479	+	0.889734i	$0.349110\pi$
$131$	−71.0404	+	123.046i	−0.542293	+	0.939279i	−0.998772	+	0.0495446i	$0.984223\pi$
$132$		0			0
$133$	−94.7654	+	353.669i	−0.712522	+	2.65917i
$134$		−	92.1577i		−	0.687744i
$135$		0			0
$136$	−259.956			−1.91144
$137$	153.789	+	41.2077i	1.12255	+	0.300786i	0.771914	−	0.635727i	$-0.219300\pi$
$137$	153.789	+	41.2077i	1.12255	+	0.300786i	0.350634	+	0.936513i	$0.385966\pi$
$138$		0			0
$139$	−160.923	−	92.9090i	−1.15772	−	0.668410i	−0.206963	−	0.978349i	$-0.566358\pi$
$139$	−160.923	−	92.9090i	−1.15772	−	0.668410i	−0.950756	+	0.309939i	$0.899691\pi$
$140$	11.3397	+	11.3397i	0.0809982	+	0.0809982i
$141$		0			0
$142$	−192.897	−	51.6865i	−1.35843	−	0.363990i
$143$	72.8564	+	72.8564i	0.509485	+	0.509485i
$144$		0			0
$145$	−4.95191	+	2.85898i	−0.0341511	+	0.0197171i
$146$	−100.095	−	173.370i	−0.685586	−	1.18747i
$147$		0			0
$148$	−6.17949	+	1.65579i	−0.0417533	+	0.0111878i
$149$	−19.9308	−	11.5070i	−0.133764	−	0.0772285i	0.431625	−	0.902053i	$-0.357940\pi$
$149$	−19.9308	−	11.5070i	−0.133764	−	0.0772285i	−0.565389	+	0.824825i	$0.691274\pi$
$150$		0			0
$151$	−29.8231	−	51.6551i	−0.197504	−	0.342087i	0.750215	−	0.661194i	$-0.229950\pi$
$151$	−29.8231	−	51.6551i	−0.197504	−	0.342087i	−0.947718	+	0.319108i	$0.896617\pi$
$152$	178.335	−	178.335i	1.17325	−	1.17325i
$153$		0			0
$154$			143.282i			0.930403i
$155$	−12.9423	+	22.4167i	−0.0834986	+	0.144624i
$156$		0			0
$157$	−58.2006	−	217.208i	−0.370705	−	1.38349i	−0.859520	−	0.511101i	$-0.829238\pi$
$157$	−58.2006	−	217.208i	−0.370705	−	1.38349i	0.488816	−	0.872387i	$-0.337429\pi$
$158$	−180.701	+	48.4186i	−1.14367	+	0.306447i
$159$		0			0
$160$	−5.53848	−	20.6699i	−0.0346155	−	0.129187i
$161$	116.067			0.720911
$162$		0			0
$163$	6.35383	+	6.35383i	0.0389805	+	0.0389805i	0.726328	−	0.687348i	$-0.241225\pi$
$163$	6.35383	+	6.35383i	0.0389805	+	0.0389805i	−0.687348	+	0.726328i	$0.741225\pi$
$164$	1.21024	−	0.698730i	0.00737948	−	0.00426055i
$165$		0			0
$166$	−45.5692	+	78.9282i	−0.274513	+	0.475471i
$167$	−47.4430	−	177.060i	−0.284090	−	1.06024i	−0.949502	−	0.313761i	$-0.898411\pi$
$167$	−47.4430	−	177.060i	−0.284090	−	1.06024i	0.665412	−	0.746476i	$-0.268256\pi$
$168$		0			0
$169$	93.1122	−	53.7583i	0.550960	−	0.318097i
$170$	−263.744	+	152.272i	−1.55143	+	0.895720i
$171$		0			0
$172$	0.253866	−	0.253866i	0.00147597	−	0.00147597i
$173$	−52.4948	+	195.913i	−0.303438	+	1.13245i	0.630843	+	0.775911i	$0.282709\pi$
$173$	−52.4948	+	195.913i	−0.303438	+	1.13245i	−0.934281	+	0.356537i	$0.883957\pi$
$174$		0			0
$175$	289.054	+	77.4519i	1.65174	+	0.442582i
$176$	46.0263	−	79.7199i	0.261513	−	0.452954i
$177$		0			0
$178$	9.02886	−	33.6962i	0.0507239	−	0.189304i
$179$			52.7077i			0.294456i	0.989103	+	0.147228i	$0.0470351\pi$
$179$			52.7077i			0.294456i	−0.989103	+	0.147228i	$0.952965\pi$
$180$		0			0
$181$	239.962			1.32575			0.662877	−	0.748728i	$-0.269335\pi$
$181$	239.962			1.32575			0.662877	+	0.748728i	$0.269335\pi$
$182$	371.428	+	99.5237i	2.04081	+	0.546834i
$183$		0			0
$184$	−69.2365	−	39.9737i	−0.376285	−	0.217248i
$185$	−84.4134	+	84.4134i	−0.456289	+	0.456289i
$186$		0			0
$187$	188.701	+	50.5622i	1.00909	+	0.270386i
$188$	3.35898	+	3.35898i	0.0178669	+	0.0178669i
$189$		0			0
$190$	76.4711	−	285.394i	0.402480	−	1.50207i
$191$	−76.8827	−	133.165i	−0.402527	−	0.697197i	0.591503	−	0.806303i	$-0.298535\pi$
$191$	−76.8827	−	133.165i	−0.402527	−	0.697197i	−0.994030	+	0.109105i	$0.965201\pi$
$192$		0			0
$193$	−120.703	+	32.3423i	−0.625405	+	0.167577i	−0.557584	−	0.830121i	$-0.688271\pi$
$193$	−120.703	+	32.3423i	−0.625405	+	0.167577i	−0.0678214	+	0.997697i	$0.521605\pi$
$194$	233.342	+	134.720i	1.20279	+	0.694432i
$195$		0			0
$196$	−12.6314	−	21.8782i	−0.0644459	−	0.111624i
$197$	−55.0019	+	55.0019i	−0.279197	+	0.279197i	−0.832789	−	0.553591i	$-0.813257\pi$
$197$	−55.0019	+	55.0019i	−0.279197	+	0.279197i	0.553591	+	0.832789i	$0.313257\pi$
$198$		0			0
$199$			241.923i			1.21569i	0.794054	+	0.607847i	$0.207967\pi$
$199$			241.923i			1.21569i	−0.794054	+	0.607847i	$0.792033\pi$
$200$	−145.753	−	145.753i	−0.728766	−	0.728766i
$201$		0			0
$202$	43.5692	+	162.603i	0.215689	+	0.804963i
$203$	13.2224	−	3.54294i	0.0651351	−	0.0174529i
$204$		0			0
$205$	13.0385	−	22.5833i	0.0636023	−	0.110162i
$206$	2.49742			0.0121234
$207$		0			0
$208$	−174.687	−	174.687i	−0.839839	−	0.839839i
$209$	−164.138	+	94.7654i	−0.785351	+	0.453423i
$210$		0			0
$211$	−109.510	+	189.676i	−0.519003	+	0.898939i	0.480753	+	0.876856i	$0.340363\pi$
$211$	−109.510	+	189.676i	−0.519003	+	0.898939i	−0.999756	+	0.0220835i	$0.992970\pi$
$212$	0.390418	+	1.45706i	0.00184159	+	0.00687292i
$213$		0			0
$214$	9.46410	−	5.46410i	0.0442248	−	0.0255332i
$215$	1.73394	−	6.47114i	0.00806483	−	0.0300983i
$216$		0			0
$217$	43.8179	−	43.8179i	0.201926	−	0.201926i
$218$	−7.42116	+	27.6962i	−0.0340420	+	0.127047i
$219$		0			0
$220$			8.30127i			0.0377330i
$221$	262.143	−	454.045i	1.18617	−	2.05450i
$222$		0			0
$223$	−15.8775	+	59.2558i	−0.0711997	+	0.265721i	−0.992345	−	0.123499i	$-0.960589\pi$
$223$	−15.8775	+	59.2558i	−0.0711997	+	0.265721i	0.921145	+	0.389219i	$0.127255\pi$
$224$			51.2295i			0.228703i
$225$		0			0
$226$	92.2820			0.408328
$227$	−169.184	−	45.3327i	−0.745304	−	0.199704i	−0.133870	−	0.990999i	$-0.542740\pi$
$227$	−169.184	−	45.3327i	−0.745304	−	0.199704i	−0.611434	+	0.791295i	$0.709407\pi$
$228$		0			0
$229$	−121.952	−	70.4090i	−0.532541	−	0.307463i	0.209510	−	0.977807i	$-0.432813\pi$
$229$	−121.952	−	70.4090i	−0.532541	−	0.307463i	−0.742051	+	0.670344i	$0.766147\pi$
$230$	−93.6603			−0.407218
$231$		0			0
$232$	−9.10770	−	2.44040i	−0.0392573	−	0.0105190i
$233$	125.960	+	125.960i	0.540599	+	0.540599i	0.923705	−	0.383105i	$-0.125145\pi$
$233$	125.960	+	125.960i	0.540599	+	0.540599i	−0.383105	+	0.923705i	$0.625145\pi$
$234$		0			0
$235$	85.6218	+	22.9423i	0.364348	+	0.0976268i
$236$	5.22947	+	9.05771i	0.0221588	+	0.0383801i
$237$		0			0
$238$	704.240	−	188.701i	2.95899	−	0.792860i
$239$	177.000	+	102.191i	0.740586	+	0.427577i	0.822282	−	0.569080i	$-0.192700\pi$
$239$	177.000	+	102.191i	0.740586	+	0.427577i	−0.0816965	+	0.996657i	$0.526034\pi$
$240$		0			0
$241$	−167.521	−	290.155i	−0.695108	−	1.20396i	−0.970144	−	0.242529i	$-0.922023\pi$
$241$	−167.521	−	290.155i	−0.695108	−	1.20396i	0.275036	−	0.961434i	$-0.411310\pi$
$242$	112.844	−	112.844i	0.466298	−	0.466298i
$243$		0			0
$244$		−	8.62178i		−	0.0353352i
$245$	−408.253	−	235.705i	−1.66634	−	0.962062i
$246$		0			0
$247$	131.648	+	491.317i	0.532988	+	1.98914i
$248$	−41.2295	+	11.0474i	−0.166248	+	0.0445460i
$249$		0			0
$250$	−233.253	−	62.5000i	−0.933013	−	0.250000i
$251$	−353.965			−1.41022			−0.705110	−	0.709098i	$-0.749102\pi$
$251$	−353.965			−1.41022			−0.705110	+	0.709098i	$0.749102\pi$
$252$		0			0
$253$	42.4833	+	42.4833i	0.167918	+	0.167918i
$254$	−6.26091	+	3.61474i	−0.0246492	+	0.0142312i
$255$		0			0
$256$	25.6051	−	44.3494i	0.100020	−	0.173240i
$257$	37.5474	+	140.129i	0.146099	+	0.545248i	0.999704	+	0.0243278i	$0.00774455\pi$
$257$	37.5474	+	140.129i	0.146099	+	0.545248i	−0.853605	+	0.520921i	$0.825589\pi$
$258$		0			0
$259$	247.504	−	142.897i	0.955616	−	0.551725i
$260$	21.5192	+	5.76606i	0.0827663	+	0.0221772i
$261$		0			0
$262$	−194.086	+	194.086i	−0.740786	+	0.740786i
$263$	−103.703	+	387.023i	−0.394306	+	1.47157i	0.428653	+	0.903469i	$0.358988\pi$
$263$	−103.703	+	387.023i	−0.394306	+	1.47157i	−0.822959	+	0.568101i	$0.807678\pi$
$264$		0			0
$265$	19.9038	+	19.9038i	0.0751087	+	0.0751087i
$266$	−353.669	+	612.573i	−1.32958	+	2.30291i
$267$		0			0
$268$	−3.30831	+	12.3468i	−0.0123444	+	0.0460701i
$269$		−	359.396i		−	1.33604i	−0.744141	−	0.668022i	$-0.767141\pi$
$269$		−	359.396i		−	1.33604i	0.744141	−	0.668022i	$-0.232859\pi$
$270$		0			0
$271$	−154.588			−0.570437			−0.285219	−	0.958463i	$-0.592066\pi$
$271$	−154.588			−0.570437			−0.285219	+	0.958463i	$0.592066\pi$
$272$	−452.444	−	121.232i	−1.66340	−	0.445706i
$273$		0			0
$274$	266.370	+	153.789i	0.972155	+	0.561274i
$275$	77.4519	+	134.151i	0.281643	+	0.487820i
$276$		0			0
$277$	117.308	+	31.4327i	0.423496	+	0.113475i	0.464271	−	0.885693i	$-0.346316\pi$
$277$	117.308	+	31.4327i	0.423496	+	0.113475i	−0.0407757	+	0.999168i	$0.512983\pi$
$278$	−253.832	−	253.832i	−0.913065	−	0.913065i
$279$		0			0
$280$	246.734	+	427.356i	0.881193	+	1.52627i
$281$	134.502	+	232.964i	0.478654	+	0.829054i	0.999700	−	0.0244748i	$-0.00779136\pi$
$281$	134.502	+	232.964i	0.478654	+	0.829054i	−0.521046	+	0.853529i	$0.674458\pi$
$282$		0			0
$283$	126.072	−	33.7808i	0.445483	−	0.119367i	−0.0291019	−	0.999576i	$-0.509265\pi$
$283$	126.072	−	33.7808i	0.445483	−	0.119367i	0.474585	+	0.880210i	$0.342598\pi$
$284$	23.9878	+	13.8494i	0.0844641	+	0.0487654i
$285$		0			0
$286$	99.5237	+	172.380i	0.347985	+	0.602728i
$287$	−44.1436	+	44.1436i	−0.153810	+	0.153810i
$288$		0			0
$289$		−	705.065i		−	2.43967i
$290$	−10.6699	+	2.85898i	−0.0367927	+	0.00985856i
$291$		0			0
$292$	7.18653	+	26.8205i	0.0246114	+	0.0918511i
$293$	164.533	−	44.0866i	0.561547	−	0.150466i	0.0331301	−	0.999451i	$-0.489452\pi$
$293$	164.533	−	44.0866i	0.561547	−	0.150466i	0.528417	+	0.848985i	$0.322786\pi$
$294$		0			0
$295$	169.019	+	97.5833i	0.572947	+	0.330791i
$296$	−196.856			−0.665055
$297$		0			0
$298$	−31.4378	−	31.4378i	−0.105496	−	0.105496i
$299$	139.638	−	80.6199i	0.467016	−	0.269632i
$300$		0			0
$301$	−8.01924	+	13.8897i	−0.0266420	+	0.0461453i
$302$	−29.8231	−	111.301i	−0.0987519	−	0.368547i
$303$		0			0
$304$	393.552	−	227.217i	1.29458	−	0.747425i
$305$	−80.4423	−	139.330i	−0.263745	−	0.456820i
$306$		0			0
$307$	−334.669	+	334.669i	−1.09013	+	1.09013i	−0.0946136	+	0.995514i	$0.530162\pi$
$307$	−334.669	+	334.669i	−1.09013	+	1.09013i	−0.995514	+	0.0946136i	$0.969838\pi$
$308$	5.14359	−	19.1962i	0.0167000	−	0.0623252i
$309$		0			0
$310$	−35.3590	+	35.3590i	−0.114061	+	0.114061i
$311$	227.904	−	394.741i	0.732810	−	1.26926i	−0.222868	−	0.974849i	$-0.571542\pi$
$311$	227.904	−	394.741i	0.732810	−	1.26926i	0.955678	−	0.294415i	$-0.0951248\pi$
$312$		0			0
$313$	99.3494	−	370.777i	0.317410	−	1.18459i	−0.604315	−	0.796746i	$-0.706553\pi$
$313$	99.3494	−	370.777i	0.317410	−	1.18459i	0.921725	−	0.387845i	$-0.126780\pi$
$314$		−	434.415i		−	1.38349i
$315$		0			0
$316$	25.9474			0.0821122
$317$	433.751	+	116.223i	1.36830	+	0.366634i	0.866857	−	0.498557i	$-0.166137\pi$
$317$	433.751	+	116.223i	1.36830	+	0.366634i	0.501442	+	0.865192i	$0.332803\pi$
$318$		0			0
$319$	6.13655	+	3.54294i	0.0192368	+	0.0111064i
$320$		−	338.468i		−	1.05771i
$321$		0			0
$322$	216.583	+	58.0333i	0.672619	+	0.180228i
$323$	681.946	+	681.946i	2.11129	+	2.11129i
$324$		0			0
$325$	401.554	−	107.596i	1.23555	−	0.331065i
$326$	8.67949	+	15.0333i	0.0266242	+	0.0461145i
$327$		0			0
$328$	41.5359	−	11.1295i	0.126634	−	0.0339314i
$329$	−183.779	−	106.105i	−0.558600	−	0.322508i
$330$		0			0
$331$	123.256	+	213.485i	0.372374	+	0.644970i	0.989930	−	0.141556i	$-0.0452106\pi$
$331$	123.256	+	213.485i	0.372374	+	0.644970i	−0.617556	+	0.786527i	$0.711877\pi$
$332$	8.93851	−	8.93851i	0.0269232	−	0.0269232i
$333$		0			0
$334$		−	354.119i		−	1.06024i
$335$	61.7339	+	230.394i	0.184280	+	0.687744i
$336$		0			0
$337$	−88.1929	−	329.140i	−0.261700	−	0.976678i	−0.964239	−	0.265033i	$-0.914617\pi$
$337$	−88.1929	−	329.140i	−0.261700	−	0.976678i	0.702539	−	0.711645i	$-0.252049\pi$
$338$	200.629	−	53.7583i	0.593576	−	0.159048i
$339$		0			0
$340$	40.8013	−	10.9327i	0.120004	−	0.0321549i
$341$	32.0770			0.0940673
$342$		0			0
$343$	383.272	+	383.272i	1.11741	+	1.11741i
$344$	9.56733	−	5.52370i	0.0278120	−	0.0160573i
$345$		0			0
$346$	−195.913	+	339.332i	−0.566224	+	0.980728i
$347$	144.515	+	539.336i	0.416469	+	1.55428i	0.781875	+	0.623435i	$0.214264\pi$
$347$	144.515	+	539.336i	0.416469	+	1.55428i	−0.365406	+	0.930848i	$0.619070\pi$
$348$		0			0
$349$	−240.258	+	138.713i	−0.688417	+	0.397458i	−0.803019	−	0.595954i	$-0.796774\pi$
$349$	−240.258	+	138.713i	−0.688417	+	0.397458i	0.114602	+	0.993412i	$0.463441\pi$
$350$	500.657	+	289.054i	1.43045	+	0.825870i
$351$		0			0
$352$	−18.7513	+	18.7513i	−0.0532707	+	0.0532707i
$353$	144.930	−	540.886i	0.410567	−	1.53226i	−0.382986	−	0.923754i	$-0.625104\pi$
$353$	144.930	−	540.886i	0.410567	−	1.53226i	0.793552	−	0.608502i	$-0.208229\pi$
$354$		0			0
$355$	516.865			1.45596
$356$	−2.41927	+	4.19031i	−0.00679572	+	0.0117705i
$357$		0			0
$358$	−26.3538	+	98.3538i	−0.0736140	+	0.274731i
$359$		−	494.196i		−	1.37659i	−0.725430	−	0.688295i	$-0.758359\pi$
$359$		−	494.196i		−	1.37659i	0.725430	−	0.688295i	$-0.241641\pi$
$360$		0			0
$361$	−574.654			−1.59184
$362$	447.774	+	119.981i	1.23695	+	0.331439i
$363$		0			0
$364$	−46.1891	−	26.6673i	−0.126893	−	0.0732618i
$365$	366.375	+	366.375i	1.00377	+	1.00377i
$366$		0			0
$367$	−191.713	−	51.3693i	−0.522378	−	0.139971i	−0.0120118	−	0.999928i	$-0.503824\pi$
$367$	−191.713	−	51.3693i	−0.522378	−	0.139971i	−0.510366	+	0.859957i	$0.670490\pi$
$368$	−101.862	−	101.862i	−0.276798	−	0.276798i
$369$		0			0
$370$	−199.724	+	115.311i	−0.539795	+	0.311651i
$371$	−33.6936	−	58.3590i	−0.0908183	−	0.157302i
$372$		0			0
$373$	−309.165	+	82.8404i	−0.828860	+	0.222092i	−0.648216	−	0.761456i	$-0.724485\pi$
$373$	−309.165	+	82.8404i	−0.828860	+	0.222092i	−0.180644	+	0.983549i	$0.557818\pi$
$374$	326.839	+	188.701i	0.873901	+	0.504547i
$375$		0			0
$376$	73.0859	+	126.588i	0.194377	+	0.336671i
$377$	13.4468	−	13.4468i	0.0356678	−	0.0356678i
$378$		0			0
$379$			442.161i			1.16665i	0.812238	+	0.583326i	$0.198249\pi$
$379$			442.161i			1.16665i	−0.812238	+	0.583326i	$0.801751\pi$
$380$	−20.4904	+	35.4904i	−0.0539221	+	0.0933957i
$381$		0			0
$382$	−76.8827	−	286.930i	−0.201264	−	0.751126i
$383$	−599.245	+	160.567i	−1.56461	+	0.419236i	−0.934119	−	0.356961i	$-0.883813\pi$
$383$	−599.245	+	160.567i	−1.56461	+	0.419236i	−0.630490	+	0.776197i	$0.717146\pi$
$384$		0			0
$385$	−95.9808	−	358.205i	−0.249301	−	0.930403i
$386$	−241.406			−0.625405
$387$		0			0
$388$	−26.4256	−	26.4256i	−0.0681073	−	0.0681073i
$389$	−467.669	+	270.009i	−1.20223	+	0.694110i	−0.961052	−	0.276369i	$-0.910869\pi$
$389$	−467.669	+	270.009i	−1.20223	+	0.694110i	−0.241183	+	0.970480i	$0.577535\pi$
$390$		0			0
$391$	152.858	−	264.758i	0.390942	−	0.677131i
$392$	−201.195	−	750.872i	−0.513254	−	1.91549i
$393$		0			0
$394$	−130.136	+	75.1340i	−0.330294	+	0.190695i
$395$	419.317	−	242.093i	1.06156	−	0.612893i
$396$		0			0
$397$	−298.002	+	298.002i	−0.750634	+	0.750634i	−0.974598	−	0.223963i	$-0.928100\pi$
$397$	−298.002	+	298.002i	−0.750634	+	0.750634i	0.223963	+	0.974598i	$0.428100\pi$
$398$	−120.962	+	451.435i	−0.303923	+	1.13426i
$399$		0			0
$400$	−185.705	−	321.651i	−0.464263	−	0.804127i
$401$	−66.0307	+	114.369i	−0.164665	+	0.285208i	−0.936536	−	0.350571i	$-0.885988\pi$
$401$	−66.0307	+	114.369i	−0.164665	+	0.285208i	0.771871	+	0.635779i	$0.219321\pi$
$402$		0			0
$403$	22.2807	−	83.1525i	0.0552870	−	0.206334i
$404$		−	23.3487i		−	0.0577937i
$405$		0			0
$406$	26.4449			0.0651351
$407$	142.897	+	38.2891i	0.351098	+	0.0940763i
$408$		0			0
$409$	−598.579	−	345.590i	−1.46352	−	0.844962i	−0.464346	−	0.885654i	$-0.653711\pi$
$409$	−598.579	−	345.590i	−1.46352	−	0.844962i	−0.999172	+	0.0406913i	$0.987044\pi$
$410$	35.6218	−	35.6218i	0.0868824	−	0.0868824i
$411$		0			0
$412$	−0.334591	−	0.0896534i	−0.000812115	−	0.000217605i
$413$	−330.382	−	330.382i	−0.799956	−	0.799956i
$414$		0			0
$415$	61.0512	−	227.846i	0.147111	−	0.549027i
$416$	35.5840	+	61.6333i	0.0855384	+	0.148157i
$417$		0			0
$418$	−353.669	+	94.7654i	−0.846099	+	0.226711i
$419$	−339.531	−	196.028i	−0.810336	−	0.467848i	0.0367366	−	0.999325i	$-0.488304\pi$
$419$	−339.531	−	196.028i	−0.810336	−	0.467848i	−0.847073	+	0.531477i	$0.821637\pi$
$420$		0			0
$421$	−146.658	−	254.019i	−0.348356	−	0.603369i	0.637602	−	0.770366i	$-0.279926\pi$
$421$	−146.658	−	254.019i	−0.348356	−	0.603369i	−0.985957	+	0.166997i	$0.946593\pi$
$422$	−299.186	+	299.186i	−0.708971	+	0.708971i
$423$		0			0
$424$			46.4167i			0.109473i
$425$	557.356	−	557.356i	1.31143	−	1.31143i
$426$		0			0
$427$	99.6865	+	372.035i	0.233458	+	0.871277i
$428$	−1.46410	+	0.392305i	−0.00342080	+	0.000916600i
$429$		0			0
$430$	6.47114	−	11.2083i	0.0150492	−	0.0260659i
$431$	630.792			1.46355			0.731777	−	0.681544i	$-0.238691\pi$
$431$	630.792			1.46355			0.731777	+	0.681544i	$0.238691\pi$
$432$		0			0
$433$	−155.925	−	155.925i	−0.360104	−	0.360104i	0.503747	−	0.863851i	$-0.331954\pi$
$433$	−155.925	−	155.925i	−0.360104	−	0.360104i	−0.863851	+	0.503747i	$0.831954\pi$
$434$	103.674	−	59.8564i	0.238881	−	0.137918i
$435$		0			0
$436$	1.98849	−	3.44417i	0.00456077	−	0.00789948i
$437$	76.7654	+	286.492i	0.175664	+	0.655589i
$438$		0			0
$439$	−505.981	+	292.128i	−1.15258	+	0.665440i	−0.949514	−	0.313726i	$-0.898423\pi$
$439$	−505.981	+	292.128i	−1.15258	+	0.665440i	−0.203062	+	0.979166i	$0.565089\pi$
$440$	−66.1122	+	246.734i	−0.150255	+	0.560759i
$441$		0			0
$442$	716.188	−	716.188i	1.62033	−	1.62033i
$443$	148.713	−	555.004i	0.335695	−	1.25283i	−0.567419	−	0.823429i	$-0.692058\pi$
$443$	148.713	−	555.004i	0.335695	−	1.25283i	0.903114	−	0.429401i	$-0.141275\pi$
$444$		0			0
$445$			90.2886i			0.202896i
$446$	−59.2558	+	102.634i	−0.132860	+	0.230121i
$447$		0			0
$448$	−209.720	+	782.685i	−0.468125	+	1.74707i
$449$			804.631i			1.79205i	0.444003	+	0.896025i	$0.353558\pi$
$449$			804.631i			1.79205i	−0.444003	+	0.896025i	$0.646442\pi$
$450$		0			0
$451$	−32.3154			−0.0716527
$452$	−12.3634	−	3.31278i	−0.0273528	−	0.00732915i
$453$		0			0
$454$	−293.035	−	169.184i	−0.645452	−	0.372652i
$455$	−995.237			−2.18733
$456$		0			0
$457$	29.4545	+	7.89230i	0.0644518	+	0.0172698i	0.290901	−	0.956753i	$-0.406045\pi$
$457$	29.4545	+	7.89230i	0.0644518	+	0.0172698i	−0.226449	+	0.974023i	$0.572712\pi$
$458$	−192.361	−	192.361i	−0.420002	−	0.420002i
$459$		0			0
$460$	12.5481	+	3.36225i	0.0272785	+	0.00730924i
$461$	31.4693	+	54.5064i	0.0682630	+	0.118235i	0.898137	−	0.439716i	$-0.144921\pi$
$461$	31.4693	+	54.5064i	0.0682630	+	0.118235i	−0.829874	+	0.557951i	$0.811588\pi$
$462$		0			0
$463$	105.445	−	28.2539i	0.227743	−	0.0610235i	−0.143143	−	0.989702i	$-0.545721\pi$
$463$	105.445	−	28.2539i	0.227743	−	0.0610235i	0.370886	+	0.928679i	$0.379054\pi$
$464$	−14.7135	−	8.49485i	−0.0317101	−	0.0183079i
$465$		0			0
$466$	172.064	+	298.024i	0.369236	+	0.639536i
$467$	−634.512	+	634.512i	−1.35870	+	1.35870i	−0.483171	+	0.875526i	$0.660515\pi$
$467$	−634.512	+	634.512i	−1.35870	+	1.35870i	−0.875526	+	0.483171i	$0.839485\pi$
$468$		0			0
$469$		−	571.023i		−	1.21753i
$470$	148.301	+	85.6218i	0.315535	+	0.182174i
$471$		0			0
$472$	83.2961	+	310.865i	0.176475	+	0.658613i
$473$	−8.01924	+	2.14875i	−0.0169540	+	0.00454281i
$474$		0			0
$475$			764.711i			1.60992i
$476$	−101.124			−0.212446
$477$		0			0
$478$	279.191	+	279.191i	0.584082	+	0.584082i
$479$	105.037	−	60.6429i	0.219283	−	0.126603i	−0.386335	−	0.922358i	$-0.626259\pi$
$479$	105.037	−	60.6429i	0.219283	−	0.126603i	0.605618	+	0.795755i	$0.292926\pi$
$480$		0			0
$481$	198.512	−	343.833i	0.412707	−	0.714830i
$482$	−167.521	−	625.197i	−0.347554	−	1.29709i
$483$		0			0
$484$	−19.1692	+	11.0673i	−0.0396057	+	0.0228664i
$485$	−673.599	−	180.490i	−1.38886	−	0.372145i
$486$		0			0
$487$	−20.3154	+	20.3154i	−0.0417153	+	0.0417153i	−0.727657	−	0.685941i	$-0.759391\pi$
$487$	−20.3154	+	20.3154i	−0.0417153	+	0.0417153i	0.685941	+	0.727657i	$0.259391\pi$
$488$	68.6647	−	256.260i	0.140706	−	0.525123i
$489$		0			0
$490$	−643.958	−	643.958i	−1.31420	−	1.31420i
$491$	281.940	−	488.335i	0.574217	−	0.994572i	−0.421910	−	0.906638i	$-0.638640\pi$
$491$	281.940	−	488.335i	0.574217	−	0.994572i	0.996126	−	0.0879346i	$-0.0280266\pi$
$492$		0			0
$493$	9.33201	−	34.8275i	0.0189290	−	0.0706441i
$494$			982.634i			1.98914i
$495$		0			0
$496$	−76.9103			−0.155061
$497$	−1195.22	−	320.258i	−2.40486	−	0.644382i
$498$		0			0
$499$	180.767	+	104.366i	0.362259	+	0.209150i	0.670071	−	0.742297i	$-0.266264\pi$
$499$	180.767	+	104.366i	0.362259	+	0.209150i	−0.307812	+	0.951447i	$0.599597\pi$
$500$	29.0064	+	16.7468i	0.0580127	+	0.0334936i
$501$		0			0
$502$	−660.508	−	176.983i	−1.31575	−	0.352555i
$503$	−76.7424	−	76.7424i	−0.152569	−	0.152569i	0.626695	−	0.779264i	$-0.284407\pi$
$503$	−76.7424	−	76.7424i	−0.152569	−	0.152569i	−0.779264	+	0.626695i	$0.784407\pi$
$504$		0			0
$505$	−217.846	−	377.321i	−0.431378	−	0.747169i
$506$	58.0333	+	100.517i	0.114690	+	0.198650i
$507$		0			0
$508$	0.968566	−	0.259526i	0.00190663	−	0.000510879i
$509$	122.427	+	70.6833i	0.240525	+	0.138867i	0.615418	−	0.788201i	$-0.288987\pi$
$509$	122.427	+	70.6833i	0.240525	+	0.138867i	−0.374893	+	0.927068i	$0.622321\pi$
$510$		0			0
$511$	−620.207	−	1074.23i	−1.21371	−	2.10221i
$512$	391.419	−	391.419i	0.764489	−	0.764489i
$513$		0			0
$514$			280.258i			0.545248i
$515$	−6.24356	+	1.67296i	−0.0121234	+	0.00324846i
$516$		0			0
$517$	−28.4308	−	106.105i	−0.0549918	−	0.205232i
$518$	533.298	−	142.897i	1.02953	−	0.275862i
$519$		0			0
$520$	593.683	+	342.763i	1.14170	+	0.659159i
$521$	406.038			0.779344			0.389672	−	0.920954i	$-0.372588\pi$
$521$	406.038			0.779344			0.389672	+	0.920954i	$0.372588\pi$
$522$		0			0
$523$	−354.492	−	354.492i	−0.677805	−	0.677805i	0.281698	−	0.959503i	$-0.409102\pi$
$523$	−354.492	−	354.492i	−0.677805	−	0.677805i	−0.959503	+	0.281698i	$0.909102\pi$
$524$	32.9699	−	19.0352i	0.0629197	−	0.0363267i
$525$		0			0
$526$	−387.023	+	670.344i	−0.735785	+	1.27442i
$527$	−42.2449	−	157.660i	−0.0801612	−	0.299166i
$528$		0			0
$529$	−376.703	+	217.490i	−0.712104	+	0.411134i
$530$	27.1891	+	47.0929i	0.0513002	+	0.0888546i
$531$		0			0
$532$	69.3731	−	69.3731i	0.130401	−	0.130401i
$533$	−22.4462	+	83.7705i	−0.0421130	+	0.157168i
$534$		0			0
$535$	−20.0000	+	20.0000i	−0.0373832	+	0.0373832i
$536$	−196.662	+	340.629i	−0.366907	+	0.635502i
$537$		0			0
$538$	179.698	−	670.642i	0.334011	−	1.24655i
$539$			584.186i			1.08383i
$540$		0			0
$541$	490.727			0.907074			0.453537	−	0.891238i	$-0.350162\pi$
$541$	490.727			0.907074			0.453537	+	0.891238i	$0.350162\pi$
$542$	−288.466	−	77.2942i	−0.532225	−	0.142609i
$543$		0			0
$544$	116.859	+	67.4686i	0.214814	+	0.124023i
$545$		−	74.2116i		−	0.136168i
$546$		0			0
$547$	−764.797	−	204.927i	−1.39817	−	0.374638i	−0.520481	−	0.853873i	$-0.674247\pi$
$547$	−764.797	−	204.927i	−1.39817	−	0.374638i	−0.877686	+	0.479236i	$0.840914\pi$
$548$	−30.1661	−	30.1661i	−0.0550476	−	0.0550476i
$549$		0			0
$550$	77.4519	+	289.054i	0.140822	+	0.525554i
$551$	17.4904	+	30.2942i	0.0317430	+	0.0549805i
$552$		0			0
$553$	−1119.65	+	300.009i	−2.02468	+	0.542512i
$554$	203.184	+	117.308i	0.366758	+	0.211748i
$555$		0			0
$556$	24.8949	+	43.1192i	0.0447750	+	0.0775525i
$557$	486.517	−	486.517i	0.873460	−	0.873460i	−0.119388	−	0.992848i	$-0.538093\pi$
$557$	486.517	−	486.517i	0.873460	−	0.873460i	0.992848	+	0.119388i	$0.0380932\pi$
$558$		0			0
$559$			22.2807i			0.0398581i
$560$	230.131	+	858.862i	0.410949	+	1.53368i
$561$		0			0
$562$	134.502	+	501.968i	0.239327	+	0.893181i
$563$	−150.890	+	40.4308i	−0.268010	+	0.0718131i	−0.390321	−	0.920679i	$-0.627636\pi$
$563$	−150.890	+	40.4308i	−0.268010	+	0.0718131i	0.122311	+	0.992492i	$0.460969\pi$
$564$		0			0
$565$	−230.705	+	61.8172i	−0.408328	+	0.109411i
$566$	252.144			0.445483
$567$		0			0
$568$	602.678	+	602.678i	1.06105	+	1.06105i
$569$	−396.056	+	228.663i	−0.696056	+	0.401868i	−0.805877	−	0.592083i	$-0.798306\pi$
$569$	−396.056	+	228.663i	−0.696056	+	0.401868i	0.109821	+	0.993951i	$0.464972\pi$
$570$		0			0
$571$	158.962	−	275.329i	0.278391	−	0.482188i	−0.692594	−	0.721328i	$-0.743532\pi$
$571$	158.962	−	275.329i	0.278391	−	0.482188i	0.970985	+	0.239140i	$0.0768654\pi$
$572$	−7.14548	−	26.6673i	−0.0124921	−	0.0466211i
$573$		0			0
$574$	−104.445	+	60.3013i	−0.181960	+	0.105054i
$575$	234.151	−	62.7405i	0.407218	−	0.109114i
$576$		0			0
$577$	178.252	−	178.252i	0.308929	−	0.308929i	−0.535565	−	0.844494i	$-0.679901\pi$
$577$	178.252	−	178.252i	0.308929	−	0.308929i	0.844494	+	0.535565i	$0.179901\pi$
$578$	352.533	−	1315.67i	0.609918	−	2.27625i
$579$		0			0
$580$	1.53212			0.00264159
$581$	−282.354	+	489.051i	−0.485979	+	0.841740i
$582$		0			0
$583$	9.02817	−	33.6936i	0.0154857	−	0.0577934i
$584$			854.405i			1.46302i
$585$		0			0
$586$	329.067			0.561547
$587$	101.720	+	27.2558i	0.173288	+	0.0464323i	0.344420	−	0.938816i	$-0.388076\pi$
$587$	101.720	+	27.2558i	0.173288	+	0.0464323i	−0.171132	+	0.985248i	$0.554742\pi$
$588$		0			0
$589$	137.138	+	79.1769i	0.232833	+	0.134426i
$590$	266.603	+	266.603i	0.451869	+	0.451869i
$591$		0			0
$592$	−342.621	−	91.8050i	−0.578752	−	0.155076i
$593$	−615.083	−	615.083i	−1.03724	−	1.03724i	−0.999279	−	0.0379595i	$-0.987914\pi$
$593$	−615.083	−	615.083i	−1.03724	−	1.03724i	−0.0379595	−	0.999279i	$-0.512086\pi$
$594$		0			0
$595$	−1634.20	+	943.503i	−2.74655	+	1.58572i
$596$	3.08330	+	5.34044i	0.00517333	+	0.00896046i
$597$		0			0
$598$	300.878	−	80.6199i	0.503140	−	0.134816i
$599$	−677.727	−	391.286i	−1.13143	−	0.653232i	−0.187136	−	0.982334i	$-0.559921\pi$
$599$	−677.727	−	391.286i	−1.13143	−	0.653232i	−0.944294	+	0.329102i	$0.893254\pi$
$600$		0			0
$601$	319.167	+	552.814i	0.531060	+	0.919824i	0.999343	+	0.0362448i	$0.0115396\pi$
$601$	319.167	+	552.814i	0.531060	+	0.919824i	−0.468283	+	0.883579i	$0.655127\pi$
$602$	−21.9090	+	21.9090i	−0.0363936	+	0.0363936i
$603$		0			0
$604$			15.9821i			0.0264605i
$605$	−206.519	+	357.702i	−0.341354	+	0.591243i
$606$		0			0
$607$	−267.993	−	1000.16i	−0.441504	−	1.64772i	−0.725005	−	0.688744i	$-0.758163\pi$
$607$	−267.993	−	1000.16i	−0.441504	−	1.64772i	0.283501	−	0.958972i	$-0.408504\pi$
$608$	−126.452	+	33.8827i	−0.207980	+	0.0557281i
$609$		0			0
$610$	−80.4423	−	300.215i	−0.131873	−	0.492155i
$611$	−294.802			−0.482492
$612$		0			0
$613$	−186.535	−	186.535i	−0.304298	−	0.304298i	0.538395	−	0.842693i	$-0.319031\pi$
$613$	−186.535	−	186.535i	−0.304298	−	0.304298i	−0.842693	+	0.538395i	$0.819031\pi$
$614$	−791.836	+	457.167i	−1.28963	+	0.744571i
$615$		0			0
$616$	305.760	−	529.592i	0.496364	−	0.859728i
$617$	66.9801	+	249.973i	0.108558	+	0.405143i	0.998724	−	0.0504921i	$-0.0160790\pi$
$617$	66.9801	+	249.973i	0.108558	+	0.405143i	−0.890167	+	0.455635i	$0.849412\pi$
$618$		0			0
$619$	366.373	−	211.526i	0.591879	−	0.341721i	−0.173961	−	0.984753i	$-0.555657\pi$
$619$	366.373	−	211.526i	0.591879	−	0.341721i	0.765840	+	0.643031i	$0.222323\pi$
$620$	6.00654	−	3.46788i	0.00968796	−	0.00559335i
$621$		0			0
$622$	622.645	−	622.645i	1.00104	−	1.00104i
$623$	55.9442	−	208.786i	0.0897980	−	0.335131i
$624$		0			0
$625$	625.000			1.00000
$626$	370.777	−	642.204i	0.592295	−	1.02589i
$627$		0			0
$628$	−15.5948	+	58.2006i	−0.0248325	+	0.0926761i
$629$		−	752.773i		−	1.19678i
$630$		0			0
$631$	−145.562			−0.230684			−0.115342	−	0.993326i	$-0.536796\pi$
$631$	−145.562			−0.230684			−0.115342	+	0.993326i	$0.536796\pi$
$632$	771.221	+	206.648i	1.22029	+	0.326975i
$633$		0			0
$634$	751.278	+	433.751i	1.18498	+	0.684149i
$635$	13.2309	−	13.2309i	0.0208360	−	0.0208360i
$636$		0			0
$637$	1514.37	+	405.775i	2.37735	+	0.637010i
$638$	9.67949	+	9.67949i	0.0151716	+	0.0151716i
$639$		0			0
$640$	147.080	−	548.910i	0.229813	−	0.857672i
$641$	−20.7365	−	35.9167i	−0.0323503	−	0.0560323i	0.849397	−	0.527754i	$-0.176966\pi$
$641$	−20.7365	−	35.9167i	−0.0323503	−	0.0560323i	−0.881747	+	0.471722i	$0.843633\pi$
$642$		0			0
$643$	−290.324	+	77.7922i	−0.451515	+	0.120983i	−0.477408	−	0.878682i	$-0.658424\pi$
$643$	−290.324	+	77.7922i	−0.451515	+	0.120983i	0.0258931	+	0.999665i	$0.491757\pi$
$644$	−26.9334	−	15.5500i	−0.0418220	−	0.0241459i
$645$		0			0
$646$	931.556	+	1613.50i	1.44204	+	2.49768i
$647$	−816.177	+	816.177i	−1.26148	+	1.26148i	−0.311103	+	0.950376i	$0.600698\pi$
$647$	−816.177	+	816.177i	−1.26148	+	1.26148i	−0.950376	+	0.311103i	$0.899302\pi$
$648$		0			0
$649$		−	241.856i		−	0.372660i
$650$	803.109			1.23555
$651$		0			0
$652$	−0.623159	−	2.32566i	−0.000955766	−	0.00356697i
$653$	392.762	−	105.240i	0.601473	−	0.161164i	0.0547818	−	0.998498i	$-0.482554\pi$
$653$	392.762	−	105.240i	0.601473	−	0.161164i	0.546692	+	0.837334i	$0.315887\pi$
$654$		0			0
$655$	355.202	−	615.228i	0.542293	−	0.939279i
$656$	77.4820			0.118113
$657$		0			0
$658$	−289.885	−	289.885i	−0.440554	−	0.440554i
$659$	723.006	−	417.428i	1.09713	−	0.633426i	0.161661	−	0.986846i	$-0.448315\pi$
$659$	723.006	−	417.428i	1.09713	−	0.633426i	0.935464	+	0.353421i	$0.114982\pi$
$660$		0			0
$661$	−205.165	+	355.357i	−0.310386	+	0.537605i	−0.978446	−	0.206503i	$-0.933792\pi$
$661$	−205.165	+	355.357i	−0.310386	+	0.537605i	0.668060	+	0.744108i	$0.267125\pi$
$662$	123.256	+	459.997i	0.186187	+	0.694859i
$663$		0			0
$664$	336.862	−	194.487i	0.507322	−	0.292902i
$665$	473.827	−	1768.35i	0.712522	−	2.65917i
$666$		0			0
$667$	7.84094	−	7.84094i	0.0117555	−	0.0117555i
$668$	−12.7123	+	47.4430i	−0.0190304	+	0.0710224i
$669$		0			0
$670$			460.788i			0.687744i
$671$	−99.6865	+	172.662i	−0.148564	+	0.257321i
$672$		0			0
$673$	330.470	−	1233.33i	0.491041	−	1.83259i	−0.0601214	−	0.998191i	$-0.519149\pi$
$673$	330.470	−	1233.33i	0.491041	−	1.83259i	0.551162	−	0.834398i	$-0.314185\pi$
$674$		−	658.281i		−	0.976678i
$675$		0			0
$676$	−28.8090			−0.0426169
$677$	−905.876	−	242.729i	−1.33807	−	0.358536i	−0.482355	−	0.875976i	$-0.660218\pi$
$677$	−905.876	−	242.729i	−1.33807	−	0.358536i	−0.855719	+	0.517440i	$0.826885\pi$
$678$		0			0
$679$	1445.82	+	834.745i	2.12934	+	1.22937i
$680$	1299.78			1.91144
$681$		0			0
$682$	59.8564	+	16.0385i	0.0877660	+	0.0235168i
$683$	−75.3346	−	75.3346i	−0.110300	−	0.110300i	0.649803	−	0.760103i	$-0.274851\pi$
$683$	−75.3346	−	75.3346i	−0.110300	−	0.110300i	−0.760103	+	0.649803i	$0.774851\pi$
$684$		0			0
$685$	−768.945	−	206.038i	−1.12255	−	0.300786i
$686$	523.559	+	906.831i	0.763205	+	1.32191i
$687$		0			0
$688$	19.2276	−	5.15202i	0.0279471	−	0.00748840i
$689$	−81.0723	−	46.8071i	−0.117667	−	0.0679349i
$690$		0			0
$691$	38.5096	+	66.7006i	0.0557303	+	0.0965277i	0.892545	−	0.450959i	$-0.148918\pi$
$691$	38.5096	+	66.7006i	0.0557303	+	0.0965277i	−0.836814	+	0.547487i	$0.815585\pi$
$692$	38.4289	−	38.4289i	0.0555331	−	0.0555331i
$693$		0			0
$694$			1078.67i			1.55428i
$695$	804.615	+	464.545i	1.15772	+	0.668410i
$696$		0			0
$697$	42.5589	+	158.832i	0.0610601	+	0.227880i
$698$	−517.683	+	138.713i	−0.741667	+	0.198729i
$699$		0			0
$700$	−56.6987	−	56.6987i	−0.0809982	−	0.0809982i
$701$	1086.18			1.54947			0.774734	−	0.632287i	$-0.217884\pi$
$701$	1086.18			1.54947			0.774734	+	0.632287i	$0.217884\pi$
$702$		0			0
$703$	516.415	+	516.415i	0.734588	+	0.734588i
$704$	−363.245	+	209.720i	−0.515974	+	0.297898i
$705$		0			0
$706$	540.886	−	936.843i	0.766128	−	1.32697i
$707$	269.962	+	1007.51i	0.381841	+	1.42505i
$708$		0			0
$709$	−220.233	+	127.151i	−0.310624	+	0.179339i	−0.647206	−	0.762315i	$-0.724063\pi$
$709$	−220.233	+	127.151i	−0.310624	+	0.179339i	0.336582	+	0.941654i	$0.390729\pi$
$710$	964.484	+	258.433i	1.35843	+	0.363990i
$711$		0			0
$712$	−105.279	+	105.279i	−0.147863	+	0.147863i
$713$	12.9921	−	48.4871i	0.0182217	−	0.0680044i
$714$		0			0
$715$	−364.282	−	364.282i	−0.509485	−	0.509485i
$716$	7.06149	−	12.2309i	0.00986241	−	0.0170822i
$717$		0			0
$718$	247.098	−	922.183i	0.344148	−	1.28438i
$719$		−	357.573i		−	0.497320i	−0.968591	−	0.248660i	$-0.920010\pi$
$719$		−	357.573i		−	0.497320i	0.968591	−	0.248660i	$-0.0799902\pi$
$720$		0			0
$721$	15.4744			0.0214624
$722$	−1072.32	−	287.327i	−1.48521	−	0.397960i
$723$		0			0
$724$	−55.6833	−	32.1487i	−0.0769106	−	0.0444043i
$725$	24.7595	−	14.2949i	0.0341511	−	0.0197171i
$726$		0			0
$727$	−207.380	−	55.5673i	−0.285255	−	0.0764337i	0.113355	−	0.993555i	$-0.463840\pi$
$727$	−207.380	−	55.5673i	−0.285255	−	0.0764337i	−0.398609	+	0.917121i	$0.630507\pi$
$728$	−1160.47	−	1160.47i	−1.59405	−	1.59405i
$729$		0			0
$730$	500.477	+	866.852i	0.685586	+	1.18747i
$731$	21.1225	+	36.5852i	0.0288953	+	0.0500481i
$732$		0			0
$733$	596.762	−	159.902i	0.814137	−	0.218147i	0.172355	−	0.985035i	$-0.444862\pi$
$733$	596.762	−	159.902i	0.814137	−	0.218147i	0.641781	+	0.766888i	$0.278196\pi$
$734$	−332.056	−	191.713i	−0.452393	−	0.261189i
$735$		0			0
$736$	20.7494	+	35.9390i	0.0281921	+	0.0488302i
$737$	209.009	−	209.009i	0.283594	−	0.283594i
$738$		0			0
$739$			934.877i			1.26506i	0.774537	+	0.632528i	$0.217983\pi$
$739$			934.877i			1.26506i	−0.774537	+	0.632528i	$0.782017\pi$
$740$	30.8975	−	8.27895i	0.0417533	−	0.0111878i
$741$		0			0
$742$	−33.6936	−	125.746i	−0.0454091	−	0.169469i
$743$	884.352	−	236.962i	1.19025	−	0.318925i	0.391263	−	0.920279i	$-0.372038\pi$
$743$	884.352	−	236.962i	1.19025	−	0.318925i	0.798983	+	0.601354i	$0.205372\pi$
$744$		0			0
$745$	99.6539	+	57.5352i	0.133764	+	0.0772285i
$746$	−618.329			−0.828860
$747$		0			0
$748$	−37.0141	−	37.0141i	−0.0494841	−	0.0494841i
$749$	58.6410	−	33.8564i	0.0782924	−	0.0452021i
$750$		0			0
$751$	541.202	−	937.389i	0.720642	−	1.24819i	−0.240101	−	0.970748i	$-0.577181\pi$
$751$	541.202	−	937.389i	0.720642	−	1.24819i	0.960743	−	0.277440i	$-0.0894860\pi$
$752$	68.1680	+	254.406i	0.0906489	+	0.338306i
$753$		0			0
$754$	31.8154	−	18.3686i	0.0421954	−	0.0243615i
$755$	149.115	+	258.275i	0.197504	+	0.342087i
$756$		0			0
$757$	−184.412	+	184.412i	−0.243608	+	0.243608i	−0.818341	−	0.574733i	$-0.805106\pi$
$757$	−184.412	+	184.412i	−0.243608	+	0.243608i	0.574733	+	0.818341i	$0.305106\pi$
$758$	−221.081	+	825.084i	−0.291663	+	1.08850i
$759$		0			0
$760$	−891.673	+	891.673i	−1.17325	+	1.17325i
$761$	−618.719	+	1071.65i	−0.813034	+	1.40822i	0.0976964	+	0.995216i	$0.468853\pi$
$761$	−618.719	+	1071.65i	−0.813034	+	1.40822i	−0.910731	+	0.413001i	$0.864481\pi$
$762$		0			0
$763$	−45.9826	+	171.610i	−0.0602656	+	0.224914i
$764$			41.2013i			0.0539284i
$765$		0			0
$766$	−1198.49			−1.56461
$767$	−626.960	−	167.993i	−0.817419	−	0.219027i
$768$		0			0
$769$	766.154	+	442.339i	0.996299	+	0.575213i	0.907151	−	0.420805i	$-0.138252\pi$
$769$	766.154	+	442.339i	0.996299	+	0.575213i	0.0891476	+	0.996018i	$0.471586\pi$
$770$		−	716.410i		−	0.930403i
$771$		0			0
$772$	32.3423	+	8.66610i	0.0418942	+	0.0112255i
$773$	936.359	+	936.359i	1.21133	+	1.21133i	0.970589	+	0.240743i	$0.0773911\pi$
$773$	936.359	+	936.359i	1.21133	+	1.21133i	0.240743	+	0.970589i	$0.422609\pi$
$774$		0			0
$775$	64.7114	−	112.083i	0.0834986	−	0.144624i
$776$	−574.977	−	995.890i	−0.740950	−	1.28336i
$777$		0			0
$778$	−1007.69	+	270.009i	−1.29523	+	0.347055i
$779$	−138.158	−	79.7654i	−0.177353	−	0.102395i
$780$		0			0
$781$	−320.258	−	554.703i	−0.410061	−	0.710246i
$782$	417.617	−	417.617i	0.534037	−	0.534037i
$783$		0			0
$784$		−	1400.69i		−	1.78660i
$785$	291.003	+	1086.04i	0.370705	+	1.38349i
$786$		0			0
$787$	272.811	+	1018.14i	0.346647	+	1.29370i	0.890677	+	0.454637i	$0.150231\pi$
$787$	272.811	+	1018.14i	0.346647	+	1.29370i	−0.544030	+	0.839066i	$0.683102\pi$
$788$	20.1321	−	5.39438i	0.0255483	−	0.00684566i
$789$		0			0
$790$	903.503	−	242.093i	1.14367	−	0.306447i
$791$	571.794			0.722874
$792$		0			0
$793$	378.347	+	378.347i	0.477108	+	0.477108i
$794$	−705.080	+	407.078i	−0.888010	+	0.512693i
$795$		0			0
$796$	32.4115	−	56.1384i	0.0407180	−	0.0705257i
$797$	81.4282	+	303.894i	0.102168	+	0.381298i	0.998009	−	0.0630788i	$-0.0200919\pi$
$797$	81.4282	+	303.894i	0.102168	+	0.381298i	−0.895840	+	0.444376i	$0.853425\pi$
$798$		0			0
$799$	−484.070	+	279.478i	−0.605845	+	0.349785i
$800$	27.6924	+	103.349i	0.0346155	+	0.129187i
$801$		0			0
$802$	−180.399	+	180.399i	−0.224937	+	0.224937i
$803$	166.184	−	620.207i	0.206954	−	0.772362i
$804$		0			0
$805$	−580.333			−0.720911
$806$	83.1525	−	144.024i	0.103167	−	0.178690i
$807$		0			0
$808$	185.951	−	693.979i	0.230138	−	0.858885i
$809$			907.404i			1.12164i	0.827939	+	0.560818i	$0.189513\pi$
$809$			907.404i			1.12164i	−0.827939	+	0.560818i	$0.810487\pi$
$810$		0			0
$811$	1386.99			1.71022			0.855112	−	0.518443i	$-0.173488\pi$
$811$	1386.99			1.71022			0.855112	+	0.518443i	$0.173488\pi$
$812$	−3.54294	−	0.949328i	−0.00436323	−	0.00116912i
$813$		0			0
$814$	247.504	+	142.897i	0.304060	+	0.175549i
$815$	−31.7691	−	31.7691i	−0.0389805	−	0.0389805i
$816$		0			0
$817$	−39.5885	−	10.6077i	−0.0484559	−	0.0129837i
$818$	−944.168	−	944.168i	−1.15424	−	1.15424i
$819$		0			0
$820$	−6.05118	+	3.49365i	−0.00737948	+	0.00426055i
$821$	445.231	+	771.162i	0.542303	+	0.939296i	0.998771	+	0.0495565i	$0.0157808\pi$
$821$	445.231	+	771.162i	0.542303	+	0.939296i	−0.456468	+	0.889740i	$0.650886\pi$
$822$		0			0
$823$	61.7372	−	16.5424i	0.0750148	−	0.0201002i	−0.221116	−	0.975247i	$-0.570970\pi$
$823$	61.7372	−	16.5424i	0.0750148	−	0.0201002i	0.296131	+	0.955147i	$0.404303\pi$
$824$	−9.23085	−	5.32944i	−0.0112025	−	0.00646776i
$825$		0			0
$826$	−451.310	−	781.692i	−0.546380	−	0.946359i
$827$	−323.315	+	323.315i	−0.390950	+	0.390950i	−0.875026	−	0.484076i	$-0.839156\pi$
$827$	−323.315	+	323.315i	−0.390950	+	0.390950i	0.484076	+	0.875026i	$0.339156\pi$
$828$		0			0
$829$		−	611.569i		−	0.737719i	−0.929485	−	0.368860i	$-0.879748\pi$
$829$		−	611.569i		−	0.737719i	0.929485	−	0.368860i	$-0.120252\pi$
$830$	227.846	−	394.641i	0.274513	−	0.475471i
$831$		0			0
$832$	291.343	+	1087.31i	0.350172	+	1.30686i
$833$	2871.31	−	769.365i	3.44695	−	0.923608i
$834$		0			0
$835$	237.215	+	885.298i	0.284090	+	1.06024i
$836$	50.7846			0.0607471
$837$		0			0
$838$	−535.559	−	535.559i	−0.639092	−	0.639092i
$839$	734.017	−	423.785i	0.874872	−	0.505107i	0.00590760	−	0.999983i	$-0.498120\pi$
$839$	734.017	−	423.785i	0.874872	−	0.505107i	0.868964	+	0.494875i	$0.164786\pi$
$840$		0			0
$841$	−419.846	+	727.195i	−0.499222	+	0.864679i
$842$	−146.658	−	547.334i	−0.174178	−	0.650040i
$843$		0			0
$844$	50.8236	−	29.3430i	0.0602175	−	0.0347666i
$845$	−465.561	+	268.792i	−0.550960	+	0.318097i
$846$		0			0
$847$	699.200	−	699.200i	0.825502	−	0.825502i
$848$	−21.6467	+	80.7865i	−0.0255267	+	0.0952671i
$849$		0			0
$850$	1318.72	−	761.362i	1.55143	−	0.895720i
$851$	115.755	−	200.493i	0.136022	−	0.235597i
$852$		0			0
$853$	−110.501	+	412.394i	−0.129544	+	0.483463i	−0.999961	−	0.00885150i	$-0.997182\pi$
$853$	−110.501	+	412.394i	−0.129544	+	0.483463i	0.870417	+	0.492315i	$0.163849\pi$
$854$			744.070i			0.871277i
$855$		0			0
$856$	−46.6410			−0.0544872
$857$	−266.705	−	71.4634i	−0.311208	−	0.0833879i	0.0998348	−	0.995004i	$-0.468169\pi$
$857$	−266.705	−	71.4634i	−0.311208	−	0.0833879i	−0.411043	+	0.911616i	$0.634835\pi$
$858$		0			0
$859$	871.419	+	503.114i	1.01446	+	0.585697i	0.912494	−	0.409091i	$-0.134154\pi$
$859$	871.419	+	503.114i	1.01446	+	0.585697i	0.101964	+	0.994788i	$0.467487\pi$
$860$	−1.26933	+	1.26933i	−0.00147597	+	0.00147597i
$861$		0			0
$862$	1177.07	+	315.396i	1.36552	+	0.365889i
$863$	−369.550	−	369.550i	−0.428216	−	0.428216i	0.459805	−	0.888020i	$-0.347919\pi$
$863$	−369.550	−	369.550i	−0.428216	−	0.428216i	−0.888020	+	0.459805i	$0.847919\pi$
$864$		0			0
$865$	262.474	−	979.567i	0.303438	−	1.13245i
$866$	−212.997	−	368.922i	−0.245955	−	0.426007i
$867$		0			0
$868$	−16.0385	+	4.29750i	−0.0184775	+	0.00495103i
$869$	−519.631	−	300.009i	−0.597964	−	0.345235i
$870$		0			0
$871$	−396.633	−	686.988i	−0.455376	−	0.788735i
$872$	86.5326	−	86.5326i	0.0992347	−	0.0992347i
$873$		0			0
$874$			572.985i			0.655589i
$875$	−1445.27	−	387.260i	−1.65174	−	0.442582i
$876$		0			0
$877$	−414.860	−	1548.28i	−0.473044	−	1.76543i	−0.628735	−	0.777620i	$-0.716427\pi$
$877$	−414.860	−	1548.28i	−0.473044	−	1.76543i	0.155690	−	0.987806i	$-0.450240\pi$
$878$	−1090.24	+	292.128i	−1.24173	+	0.332720i
$879$		0			0
$880$	−230.131	+	398.599i	−0.261513	+	0.452954i
$881$	−1314.95			−1.49257			−0.746285	−	0.665627i	$-0.768164\pi$
$881$	−1314.95			−1.49257			−0.746285	+	0.665627i	$0.768164\pi$
$882$		0			0
$883$	1060.20	+	1060.20i	1.20068	+	1.20068i	0.973960	+	0.226719i	$0.0728000\pi$
$883$	1060.20	+	1060.20i	1.20068	+	1.20068i	0.226719	+	0.973960i	$0.427200\pi$
$884$	−121.661	+	70.2410i	−0.137626	+	0.0794581i
$885$		0			0
$886$	555.004	−	961.295i	0.626415	−	1.08498i
$887$	−302.989	−	1130.77i	−0.341589	−	1.27483i	−0.896547	−	0.442948i	$-0.853933\pi$
$887$	−302.989	−	1130.77i	−0.341589	−	1.27483i	0.554958	−	0.831878i	$-0.312734\pi$
$888$		0			0
$889$	−38.7935	+	22.3975i	−0.0436373	+	0.0251940i
$890$	−45.1443	+	168.481i	−0.0507239	+	0.189304i
$891$		0			0
$892$	11.6232	−	11.6232i	0.0130304	−	0.0130304i
$893$	140.354	−	523.808i	0.157171	−	0.586571i
$894$		0			0
$895$		−	263.538i		−	0.294456i
$896$	−680.226	+	1178.19i	−0.759181	+	1.31494i
$897$		0			0
$898$	−402.315	+	1501.46i	−0.448013	+	1.67201i
$899$		−	5.92029i		−	0.00658541i
$900$		0			0
$901$	−177.496			−0.196999
$902$	−60.3013	−	16.1577i	−0.0668528	−	0.0179132i
$903$		0			0
$904$	−341.088	−	196.928i	−0.377310	−	0.217840i
$905$	−1199.81			−1.32575
$906$		0			0
$907$	276.976	+	74.2154i	0.305376	+	0.0818251i	0.408253	−	0.912869i	$-0.366138\pi$
$907$	276.976	+	74.2154i	0.305376	+	0.0818251i	−0.102877	+	0.994694i	$0.532805\pi$
$908$	33.1858	+	33.1858i	0.0365483	+	0.0365483i
$909$		0			0
$910$	−1857.14	−	497.619i	−2.04081	−	0.546834i
$911$	−329.871	−	571.353i	−0.362098	−	0.627172i	0.626208	−	0.779656i	$-0.284606\pi$
$911$	−329.871	−	571.353i	−0.362098	−	0.627172i	−0.988306	+	0.152484i	$0.951273\pi$
$912$		0			0
$913$	−282.354	+	75.6565i	−0.309259	+	0.0828658i
$914$	51.0167	+	29.4545i	0.0558169	+	0.0322259i
$915$		0			0
$916$	18.8660	+	32.6769i	0.0205961	+	0.0356735i
$917$	−1202.59	+	1202.59i	−1.31143	+	1.31143i
$918$		0			0
$919$			43.0502i			0.0468446i	0.999726	+	0.0234223i	$0.00745623\pi$
$919$			43.0502i			0.0468446i	−0.999726	+	0.0234223i	$0.992544\pi$
$920$	346.183	+	199.869i	0.376285	+	0.217248i
$921$		0			0
$922$	31.4693	+	117.445i	0.0341315	+	0.127381i
$923$	−1660.40	+	444.902i	−1.79891	+	0.482017i
$924$		0			0
$925$	422.067	−	422.067i	0.456289	−	0.456289i
$926$	210.890			0.227743
$927$		0			0
$928$	3.46083	+	3.46083i	0.00372935	+	0.00372935i
$929$	−1100.57	+	635.413i	−1.18468	+	0.683975i	−0.957092	−	0.289783i	$-0.906417\pi$
$929$	−1100.57	+	635.413i	−1.18468	+	0.683975i	−0.227587	+	0.973758i	$0.573084\pi$
$930$		0			0
$931$	−1441.97	+	2497.57i	−1.54884	+	2.68267i
$932$	−12.3536	−	46.1044i	−0.0132550	−	0.0494683i
$933$		0			0
$934$	−1501.27	+	866.759i	−1.60736	+	0.928007i
$935$	−943.503	−	252.811i	−1.00909	−	0.270386i
$936$		0			0
$937$	516.286	−	516.286i	0.550999	−	0.550999i	−0.375730	−	0.926729i	$-0.622608\pi$
$937$	516.286	−	516.286i	0.550999	−	0.550999i	0.926729	+	0.375730i	$0.122608\pi$
$938$	285.512	−	1065.54i	0.304383	−	1.13597i
$939$		0			0
$940$	−16.7949	−	16.7949i	−0.0178669	−	0.0178669i
$941$	532.798	−	922.833i	0.566204	−	0.980694i	−0.430733	−	0.902480i	$-0.641745\pi$
$941$	532.798	−	922.833i	0.566204	−	0.980694i	0.996937	−	0.0782145i	$-0.0249219\pi$
$942$		0			0
$943$	−13.0886	+	48.8475i	−0.0138798	+	0.0518001i
$944$			579.895i			0.614295i
$945$		0			0
$946$	−16.0385			−0.0169540
$947$	824.331	+	220.879i	0.870466	+	0.233241i	0.666289	−	0.745693i	$-0.267882\pi$
$947$	824.331	+	220.879i	0.870466	+	0.233241i	0.204177	+	0.978934i	$0.434548\pi$
$948$		0			0
$949$	−1492.32	−	861.592i	−1.57252	−	0.907894i
$950$	−382.356	+	1426.97i	−0.402480	+	1.50207i
$951$		0			0
$952$	−3005.66	−	805.365i	−3.15721	−	0.845971i
$953$	681.160	+	681.160i	0.714753	+	0.714753i	0.967526	−	0.252773i	$-0.0813425\pi$
$953$	681.160	+	681.160i	0.714753	+	0.714753i	−0.252773	+	0.967526i	$0.581342\pi$
$954$		0			0
$955$	384.413	+	665.824i	0.402527	+	0.697197i
$956$	−27.3820	−	47.4270i	−0.0286423	−	0.0496098i
$957$		0			0
$958$	226.322	−	60.6429i	0.236245	−	0.0633016i
$959$	1650.47	+	952.901i	1.72103	+	0.993640i
$960$		0			0
$961$	467.100	+	809.041i	0.486056	+	0.841874i
$962$	542.345	−	542.345i	0.563769	−	0.563769i
$963$		0			0
$964$			89.7743i			0.0931269i
$965$	603.516	−	161.712i	0.625405	−	0.167577i
$966$		0			0
$967$	−67.3970	−	251.529i	−0.0696970	−	0.260113i	0.922282	−	0.386519i	$-0.126322\pi$
$967$	−67.3970	−	251.529i	−0.0696970	−	0.260113i	−0.991979	+	0.126406i	$0.959656\pi$
$968$	−657.896	+	176.283i	−0.679645	+	0.182110i
$969$		0			0
$970$	−1166.71	−	673.599i	−1.20279	−	0.694432i
$971$	1449.90			1.49321			0.746603	−	0.665270i	$-0.231683\pi$
$971$	1449.90			1.49321			0.746603	+	0.665270i	$0.231683\pi$
$972$		0			0
$973$	−1572.78	−	1572.78i	−1.61643	−	1.61643i
$974$	−48.0666	+	27.7513i	−0.0493497	+	0.0284921i
$975$		0			0
$976$	239.017	−	413.989i	0.244894	−	0.424169i
$977$	−33.6889	−	125.729i	−0.0344820	−	0.128689i	0.946539	−	0.322588i	$-0.104553\pi$
$977$	−33.6889	−	125.729i	−0.0344820	−	0.128689i	−0.981021	+	0.193900i	$0.937886\pi$
$978$		0			0
$979$	96.8982	−	55.9442i	0.0989767	−	0.0571442i
$980$	63.1570	+	109.391i	0.0644459	+	0.111624i
$981$		0			0
$982$	770.275	−	770.275i	0.784395	−	0.784395i
$983$	−201.179	+	750.811i	−0.204659	+	0.763796i	0.784895	+	0.619629i	$0.212717\pi$
$983$	−201.179	+	750.811i	−0.204659	+	0.763796i	−0.989553	+	0.144167i	$0.953950\pi$
$984$		0			0
$985$	275.009	−	275.009i	0.279197	−	0.279197i
$986$	34.8275	−	60.3231i	0.0353221	−	0.0611796i
$987$		0			0
$988$	35.2750	−	131.648i	0.0357034	−	0.133247i
$989$			12.9921i			0.0131366i
$990$		0			0
$991$	58.7424			0.0592758			0.0296379	−	0.999561i	$-0.490565\pi$
$991$	58.7424			0.0592758			0.0296379	+	0.999561i	$0.490565\pi$
$992$	21.4012	+	5.73444i	0.0215738	+	0.00578069i
$993$		0			0
$994$	−2070.18	−	1195.22i	−2.08267	−	1.20243i
$995$		−	1209.62i		−	1.21569i
$996$		0			0
$997$	−1485.46	−	398.027i	−1.48993	−	0.399225i	−0.580214	−	0.814464i	$-0.697031\pi$
$997$	−1485.46	−	398.027i	−1.48993	−	0.399225i	−0.909712	+	0.415239i	$0.863698\pi$
$998$	285.133	+	285.133i	0.285705	+	0.285705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.d.28.1		4
3.2	odd	2		405.3.l.a.28.1		4
5.2	odd	4		405.3.l.b.352.1		4
9.2	odd	6		405.3.l.c.298.1		4
9.4	even	3		405.3.g.a.163.1	yes	4
9.5	odd	6		405.3.g.b.163.2	yes	4
9.7	even	3		405.3.l.b.298.1		4
15.2	even	4		405.3.l.c.352.1		4
45.2	even	12		405.3.l.a.217.1		4
45.7	odd	12	inner	405.3.l.d.217.1		4
45.22	odd	12		405.3.g.a.82.1	✓	4
45.32	even	12		405.3.g.b.82.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.a.82.1	✓	4	45.22	odd	12
405.3.g.a.163.1	yes	4	9.4	even	3
405.3.g.b.82.2	yes	4	45.32	even	12
405.3.g.b.163.2	yes	4	9.5	odd	6
405.3.l.a.28.1		4	3.2	odd	2
405.3.l.a.217.1		4	45.2	even	12
405.3.l.b.298.1		4	9.7	even	3
405.3.l.b.352.1		4	5.2	odd	4
405.3.l.c.298.1		4	9.2	odd	6
405.3.l.c.352.1		4	15.2	even	4
405.3.l.d.28.1		4	1.1	even	1	trivial
405.3.l.d.217.1		4	45.7	odd	12	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{2} +(-0.232051 - 0.133975i) q^{4} -5.00000 q^{5} +(11.5622 + 3.09808i) q^{7} +(-5.83013 - 5.83013i) q^{8} +(-9.33013 - 2.50000i) q^{10} +(3.09808 + 5.36603i) q^{11} +(16.0622 - 4.30385i) q^{13} +(20.0263 + 11.5622i) q^{14} +(-7.42820 - 12.8660i) q^{16} +(22.2942 - 22.2942i) q^{17} +30.5885i q^{19} +(1.16025 + 0.669873i) q^{20} +(3.09808 + 11.5622i) q^{22} +(9.36603 - 2.50962i) q^{23} +25.0000 q^{25} +32.1244 q^{26} +(-2.26795 - 2.26795i) q^{28} +(0.990381 - 0.571797i) q^{29} +(2.58846 - 4.48334i) q^{31} +(1.10770 + 4.13397i) q^{32} +(52.7487 - 30.4545i) q^{34} +(-57.8109 - 15.4904i) q^{35} +(16.8827 - 16.8827i) q^{37} +(-15.2942 + 57.0788i) q^{38} +(29.1506 + 29.1506i) q^{40} +(-2.60770 + 4.51666i) q^{41} +(-0.346788 + 1.29423i) q^{43} -1.66025i q^{44} +18.7321 q^{46} +(-17.1244 - 4.58846i) q^{47} +(81.6506 + 47.1410i) q^{49} +(46.6506 + 12.5000i) q^{50} +(-4.30385 - 1.15321i) q^{52} +(-3.98076 - 3.98076i) q^{53} +(-15.4904 - 26.8301i) q^{55} +(-49.3468 - 85.4711i) q^{56} +(2.13397 - 0.571797i) q^{58} +(-33.8038 - 19.5167i) q^{59} +(16.0885 + 27.8660i) q^{61} +(7.07180 - 7.07180i) q^{62} +67.6936i q^{64} +(-80.3109 + 21.5192i) q^{65} +(-12.3468 - 46.0788i) q^{67} +(-8.16025 + 2.18653i) q^{68} +(-100.131 - 57.8109i) q^{70} -103.373 q^{71} +(-73.2750 - 73.2750i) q^{73} +(39.9449 - 23.0622i) q^{74} +(4.09808 - 7.09808i) q^{76} +(19.1962 + 71.6410i) q^{77} +(-83.8634 + 48.4186i) q^{79} +(37.1410 + 64.3301i) q^{80} +(-7.12436 + 7.12436i) q^{82} +(-12.2102 + 45.5692i) q^{83} +(-111.471 + 111.471i) q^{85} +(-1.29423 + 2.24167i) q^{86} +(13.2224 - 49.3468i) q^{88} -18.0577i q^{89} +199.047 q^{91} +(-2.50962 - 0.672450i) q^{92} +(-29.6603 - 17.1244i) q^{94} -152.942i q^{95} +(134.720 + 36.0981i) q^{97} +(128.792 + 128.792i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{4} - 20 q^{5} + 22 q^{7} - 6 q^{8} - 20 q^{10} + 2 q^{11} + 40 q^{13} + 42 q^{14} - 2 q^{16} + 58 q^{17} - 30 q^{20} + 2 q^{22} + 34 q^{23} + 100 q^{25} + 80 q^{26} - 16 q^{28} - 48 q^{29}+ \cdots + 290 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^4 - 20 * q^5 + 22 * q^7 - 6 * q^8 - 20 * q^10 + 2 * q^11 + 40 * q^13 + 42 * q^14 - 2 * q^16 + 58 * q^17 - 30 * q^20 + 2 * q^22 + 34 * q^23 + 100 * q^25 + 80 * q^26 - 16 * q^28 - 48 * q^29 - 52 * q^31 + 46 * q^32 + 114 * q^34 - 110 * q^35 - 26 * q^37 - 30 * q^38 + 30 * q^40 - 52 * q^41 + 106 * q^43 + 68 * q^46 - 20 * q^47 + 240 * q^49 + 100 * q^50 - 38 * q^52 + 88 * q^53 - 10 * q^55 - 90 * q^56 + 12 * q^58 - 156 * q^59 + 2 * q^61 + 56 * q^62 - 200 * q^65 + 58 * q^67 + 2 * q^68 - 210 * q^70 - 268 * q^71 - 158 * q^73 + 42 * q^74 + 6 * q^76 + 56 * q^77 - 138 * q^79 + 10 * q^80 + 20 * q^82 + 256 * q^83 - 290 * q^85 + 26 * q^86 - 6 * q^88 + 332 * q^91 - 62 * q^92 - 84 * q^94 + 286 * q^97 + 290 * q^98

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