LMFDB - Embedded newform 360.2.m.c.179.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 $ x^16 - 17x^12 - 104x^10 + 713x^8 + 238x^6 + 1004x^4 - 152x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.2
Root			$-0.877859 - 2.23141i$ of defining polynomial
Character	$\chi$	$=$	360.179
Dual form			360.2.m.c.179.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} +(1.64901 - 1.51022i) q^{5} +0.936426 q^{7} +(-2.14700 - 1.84130i) q^{8} +O(q^{10})$	\(q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} +(1.64901 - 1.51022i) q^{5} +0.936426 q^{7} +(-2.14700 - 1.84130i) q^{8} +(-2.76724 + 1.53048i) q^{10} -2.20837i q^{11} +3.33513 q^{13} +(-1.28751 - 0.310029i) q^{14} +(2.34233 + 3.24245i) q^{16} -1.54417 q^{17} -3.12311 q^{19} +(4.31143 - 1.18811i) q^{20} +(-0.731140 + 3.03632i) q^{22} +3.39228i q^{23} +(0.438447 - 4.98074i) q^{25} +(-4.58552 - 1.10418i) q^{26} +(1.66757 + 0.852526i) q^{28} +8.44804 q^{29} -8.30571i q^{31} +(-2.14700 - 5.23358i) q^{32} +(2.12311 + 0.511240i) q^{34} +(1.54417 - 1.41421i) q^{35} +7.60669 q^{37} +(4.29400 + 1.03399i) q^{38} +(-6.32120 + 0.206134i) q^{40} -5.83095i q^{41} -7.77769i q^{43} +(2.01051 - 3.93261i) q^{44} +(1.12311 - 4.66410i) q^{46} +10.7575i q^{47} -6.12311 q^{49} +(-2.25183 + 6.70293i) q^{50} +(5.93912 + 3.03632i) q^{52} -5.08842i q^{53} +(-3.33513 - 3.64162i) q^{55} +(-2.01051 - 1.72424i) q^{56} +(-11.6153 - 2.79695i) q^{58} +10.6937i q^{59} +(-2.74983 + 11.4196i) q^{62} +(1.21922 + 7.90655i) q^{64} +(5.49966 - 5.03680i) q^{65} +12.1453i q^{67} +(-2.74983 - 1.40582i) q^{68} +(-2.59132 + 1.43318i) q^{70} -11.7460 q^{71} +5.59390i q^{73} +(-10.4585 - 2.51840i) q^{74} +(-5.56155 - 2.84329i) q^{76} -2.06798i q^{77} -1.02248i q^{79} +(8.75935 + 1.80938i) q^{80} +(-1.93049 + 8.01706i) q^{82} +14.0877 q^{83} +(-2.54635 + 2.33205i) q^{85} +(-2.57501 + 10.6937i) q^{86} +(-4.06627 + 4.74137i) q^{88} +13.0761i q^{89} +3.12311 q^{91} +(-3.08835 + 6.04090i) q^{92} +(3.56155 - 14.7906i) q^{94} +(-5.15002 + 4.71659i) q^{95} +2.18379i q^{97} +(8.41874 + 2.02722i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4}+O(q^{10}) $ 16 * q + 12 * q^4	$ 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) $ 16 * q + 12 * q^4 - 8 * q^10 - 12 * q^16 + 16 * q^19 + 40 * q^25 - 32 * q^34 - 28 * q^40 - 48 * q^46 - 32 * q^49 + 36 * q^64 + 32 * q^70 - 56 * q^76 - 16 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.37491	−	0.331077i	−0.972211	−	0.234107i
$2$	−1.37491	−	0.331077i	−0.972211	−	0.234107i
$3$		0			0
$3$		0			0
$4$	1.78078	+	0.910404i	0.890388	+	0.455202i
$5$	1.64901	−	1.51022i	0.737458	−	0.675393i
$5$	1.64901	−	1.51022i	0.737458	−	0.675393i
$6$		0			0
$7$	0.936426			0.353936			0.176968	−	0.984217i	$-0.443371\pi$
$7$	0.936426			0.353936			0.176968	+	0.984217i	$0.443371\pi$
$8$	−2.14700	−	1.84130i	−0.759079	−	0.650998i
$9$		0			0
$10$	−2.76724	+	1.53048i	−0.875079	+	0.483980i
$11$		−	2.20837i		−	0.665848i	−0.942954	−	0.332924i	$-0.891965\pi$
$11$		−	2.20837i		−	0.665848i	0.942954	−	0.332924i	$-0.108035\pi$
$12$		0			0
$13$	3.33513			0.924999			0.462500	−	0.886619i	$-0.346953\pi$
$13$	3.33513			0.924999			0.462500	+	0.886619i	$0.346953\pi$
$14$	−1.28751	−	0.310029i	−0.344100	−	0.0828587i
$15$		0			0
$16$	2.34233	+	3.24245i	0.585582	+	0.810613i
$17$	−1.54417			−0.374517			−0.187259	−	0.982311i	$-0.559960\pi$
$17$	−1.54417			−0.374517			−0.187259	+	0.982311i	$0.559960\pi$
$18$		0			0
$19$	−3.12311			−0.716490			−0.358245	−	0.933628i	$-0.616625\pi$
$19$	−3.12311			−0.716490			−0.358245	+	0.933628i	$0.616625\pi$
$20$	4.31143	−	1.18811i	0.964064	−	0.265669i
$21$		0			0
$22$	−0.731140	+	3.03632i	−0.155879	+	0.647345i
$23$			3.39228i			0.707340i	0.935370	+	0.353670i	$0.115066\pi$
$23$			3.39228i			0.707340i	−0.935370	+	0.353670i	$0.884934\pi$
$24$		0			0
$25$	0.438447	−	4.98074i	0.0876894	−	0.996148i
$26$	−4.58552	−	1.10418i	−0.899294	−	0.216548i
$27$		0			0
$28$	1.66757	+	0.852526i	0.315140	+	0.161112i
$29$	8.44804			1.56876			0.784380	−	0.620280i	$-0.212981\pi$
$29$	8.44804			1.56876			0.784380	+	0.620280i	$0.212981\pi$
$30$		0			0
$31$		−	8.30571i		−	1.49175i	−0.666086	−	0.745875i	$-0.732032\pi$
$31$		−	8.30571i		−	1.49175i	0.666086	−	0.745875i	$-0.267968\pi$
$32$	−2.14700	−	5.23358i	−0.379540	−	0.925175i
$33$		0			0
$34$	2.12311	+	0.511240i	0.364110	+	0.0876769i
$35$	1.54417	−	1.41421i	0.261013	−	0.239046i
$36$		0			0
$37$	7.60669			1.25053			0.625266	−	0.780412i	$-0.284990\pi$
$37$	7.60669			1.25053			0.625266	+	0.780412i	$0.284990\pi$
$38$	4.29400	+	1.03399i	0.696579	+	0.167735i
$39$		0			0
$40$	−6.32120	+	0.206134i	−0.999469	+	0.0325927i
$41$		−	5.83095i		−	0.910642i	−0.890327	−	0.455321i	$-0.849525\pi$
$41$		−	5.83095i		−	0.910642i	0.890327	−	0.455321i	$-0.150475\pi$
$42$		0			0
$43$		−	7.77769i		−	1.18609i	−0.805171	−	0.593043i	$-0.797926\pi$
$43$		−	7.77769i		−	1.18609i	0.805171	−	0.593043i	$-0.202074\pi$
$44$	2.01051	−	3.93261i	0.303095	−	0.592864i
$45$		0			0
$46$	1.12311	−	4.66410i	0.165593	−	0.687683i
$47$			10.7575i			1.56914i	0.620040	+	0.784570i	$0.287116\pi$
$47$			10.7575i			1.56914i	−0.620040	+	0.784570i	$0.712884\pi$
$48$		0			0
$49$	−6.12311			−0.874729
$50$	−2.25183	+	6.70293i	−0.318457	+	0.947937i
$51$		0			0
$52$	5.93912	+	3.03632i	0.823608	+	0.421061i
$53$		−	5.08842i		−	0.698949i	−0.936946	−	0.349474i	$-0.886360\pi$
$53$		−	5.08842i		−	0.698949i	0.936946	−	0.349474i	$-0.113640\pi$
$54$		0			0
$55$	−3.33513	−	3.64162i	−0.449709	−	0.491035i
$56$	−2.01051	−	1.72424i	−0.268665	−	0.230412i
$57$		0			0
$58$	−11.6153	−	2.79695i	−1.52517	−	0.367257i
$59$			10.6937i			1.39219i	0.717947	+	0.696097i	$0.245082\pi$
$59$			10.6937i			1.39219i	−0.717947	+	0.696097i	$0.754918\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−2.74983	+	11.4196i	−0.349228	+	1.45030i
$63$		0			0
$64$	1.21922	+	7.90655i	0.152403	+	0.988318i
$65$	5.49966	−	5.03680i	0.682148	−	0.624738i
$66$		0			0
$67$			12.1453i			1.48378i	0.670521	+	0.741890i	$0.266071\pi$
$67$			12.1453i			1.48378i	−0.670521	+	0.741890i	$0.733929\pi$
$68$	−2.74983	−	1.40582i	−0.333466	−	0.170481i
$69$		0			0
$70$	−2.59132	+	1.43318i	−0.309722	+	0.171298i
$71$	−11.7460			−1.39400			−0.697000	−	0.717071i	$-0.745482\pi$
$71$	−11.7460			−1.39400			−0.697000	+	0.717071i	$0.745482\pi$
$72$		0			0
$73$			5.59390i			0.654716i	0.944900	+	0.327358i	$0.106158\pi$
$73$			5.59390i			0.654716i	−0.944900	+	0.327358i	$0.893842\pi$
$74$	−10.4585	−	2.51840i	−1.21578	−	0.292758i
$75$		0			0
$76$	−5.56155	−	2.84329i	−0.637954	−	0.326147i
$77$		−	2.06798i		−	0.235668i
$78$		0			0
$79$		−	1.02248i		−	0.115038i	−0.998344	−	0.0575190i	$-0.981681\pi$
$79$		−	1.02248i		−	0.115038i	0.998344	−	0.0575190i	$-0.0183190\pi$
$80$	8.75935	+	1.80938i	0.979325	+	0.202295i
$81$		0			0
$82$	−1.93049	+	8.01706i	−0.213187	+	0.885336i
$83$	14.0877			1.54632			0.773161	−	0.634210i	$-0.218675\pi$
$83$	14.0877			1.54632			0.773161	+	0.634210i	$0.218675\pi$
$84$		0			0
$85$	−2.54635	+	2.33205i	−0.276191	+	0.252946i
$86$	−2.57501	+	10.6937i	−0.277671	+	1.15313i
$87$		0			0
$88$	−4.06627	+	4.74137i	−0.433466	+	0.505432i
$89$			13.0761i			1.38607i	0.720906	+	0.693033i	$0.243726\pi$
$89$			13.0761i			1.38607i	−0.720906	+	0.693033i	$0.756274\pi$
$90$		0			0
$91$	3.12311			0.327390
$92$	−3.08835	+	6.04090i	−0.321982	+	0.629807i
$93$		0			0
$94$	3.56155	−	14.7906i	0.367346	−	1.52554i
$95$	−5.15002	+	4.71659i	−0.528381	+	0.483912i
$96$		0			0
$97$			2.18379i			0.221730i	0.993835	+	0.110865i	$0.0353622\pi$
$97$			2.18379i			0.221730i	−0.993835	+	0.110865i	$0.964638\pi$
$98$	8.41874	+	2.02722i	0.850421	+	0.204780i
$99$		0			0
$100$	5.31526	−	8.47042i	0.531526	−	0.847042i
$101$	3.29801			0.328165			0.164082	−	0.986447i	$-0.447534\pi$
$101$	3.29801			0.328165			0.164082	+	0.986447i	$0.447534\pi$
$102$		0			0
$103$	−18.0227			−1.77583			−0.887913	−	0.460012i	$-0.847845\pi$
$103$	−18.0227			−1.77583			−0.887913	+	0.460012i	$0.847845\pi$
$104$	−7.16053	−	6.14098i	−0.702148	−	0.602173i
$105$		0			0
$106$	−1.68466	+	6.99614i	−0.163628	+	0.679526i
$107$	−10.9993			−1.06334			−0.531672	−	0.846950i	$-0.678436\pi$
$107$	−10.9993			−1.06334			−0.531672	+	0.846950i	$0.678436\pi$
$108$		0			0
$109$			11.9473i			1.14435i	0.820133	+	0.572173i	$0.193900\pi$
$109$			11.9473i			1.14435i	−0.820133	+	0.572173i	$0.806100\pi$
$110$	3.37987	+	6.11109i	0.322257	+	0.582670i
$111$		0			0
$112$	2.19342	+	3.03632i	0.207259	+	0.286905i
$113$	−12.5435			−1.17999			−0.589996	−	0.807406i	$-0.700871\pi$
$113$	−12.5435			−1.17999			−0.589996	+	0.807406i	$0.700871\pi$
$114$		0			0
$115$	5.12311	+	5.59390i	0.477732	+	0.521634i
$116$	15.0441	+	7.69113i	1.39681	+	0.714103i
$117$		0			0
$118$	3.54042	−	14.7028i	0.325922	−	1.35351i
$119$	−1.44600			−0.132555
$120$		0			0
$121$	6.12311			0.556646
$122$		0			0
$123$		0			0
$124$	7.56155	−	14.7906i	0.679047	−	1.32824i
$125$	−6.79903	−	8.87543i	−0.608124	−	0.793842i
$126$		0			0
$127$	4.68213			0.415472			0.207736	−	0.978185i	$-0.433391\pi$
$127$	4.68213			0.415472			0.207736	+	0.978185i	$0.433391\pi$
$128$	0.941346	−	11.2745i	0.0832041	−	0.996533i
$129$		0			0
$130$	−9.22912	+	5.10435i	−0.809447	+	0.447681i
$131$		−	0.620058i		−	0.0541747i	−0.999633	−	0.0270874i	$-0.991377\pi$
$131$		−	0.620058i		−	0.0541747i	0.999633	−	0.0270874i	$-0.00862323\pi$
$132$		0			0
$133$	−2.92456			−0.253591
$134$	4.02102	−	16.6987i	0.347363	−	1.44255i
$135$		0			0
$136$	3.31534	+	2.84329i	0.284288	+	0.243810i
$137$	−1.54417			−0.131928			−0.0659638	−	0.997822i	$-0.521012\pi$
$137$	−1.54417			−0.131928			−0.0659638	+	0.997822i	$0.521012\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	4.03733	−	1.11258i	0.341217	−	0.0940299i
$141$		0			0
$142$	16.1498	+	3.88884i	1.35526	+	0.326345i
$143$		−	7.36520i		−	0.615909i
$144$		0			0
$145$	13.9309	−	12.7584i	1.15690	−	1.05953i
$146$	1.85201	−	7.69113i	0.153273	−	0.636522i
$147$		0			0
$148$	13.5458	+	6.92516i	1.11346	+	0.569245i
$149$	1.85201			0.151722			0.0758612	−	0.997118i	$-0.475829\pi$
$149$	1.85201			0.151722			0.0758612	+	0.997118i	$0.475829\pi$
$150$		0			0
$151$			17.6339i			1.43503i	0.696545	+	0.717513i	$0.254720\pi$
$151$			17.6339i			1.43503i	−0.696545	+	0.717513i	$0.745280\pi$
$152$	6.70531	+	5.75058i	0.543872	+	0.466433i
$153$		0			0
$154$	−0.684658	+	2.84329i	−0.0551713	+	0.229119i
$155$	−12.5435	−	13.6962i	−1.00752	−	1.10010i
$156$		0			0
$157$	−2.80928			−0.224205			−0.112102	−	0.993697i	$-0.535758\pi$
$157$	−2.80928			−0.224205			−0.112102	+	0.993697i	$0.535758\pi$
$158$	−0.338519	+	1.40582i	−0.0269311	+	0.111841i
$159$		0			0
$160$	−11.4443	−	5.38776i	−0.904751	−	0.425940i
$161$			3.17662i			0.250353i
$162$		0			0
$163$		−	15.5554i		−	1.21839i	−0.793020	−	0.609195i	$-0.791492\pi$
$163$		−	15.5554i		−	1.21839i	0.793020	−	0.609195i	$-0.208508\pi$
$164$	5.30852	−	10.3836i	0.414526	−	0.810825i
$165$		0			0
$166$	−19.3693	−	4.66410i	−1.50335	−	0.362004i
$167$		−	9.43318i		−	0.729961i	−0.931015	−	0.364981i	$-0.881076\pi$
$167$		−	9.43318i		−	0.729961i	0.931015	−	0.364981i	$-0.118924\pi$
$168$		0			0
$169$	−1.87689			−0.144376
$170$	4.27310	−	2.36333i	0.327732	−	0.181259i
$171$		0			0
$172$	7.08084	−	13.8503i	0.539909	−	1.05608i
$173$			1.69614i			0.128955i	0.997919	+	0.0644776i	$0.0205381\pi$
$173$			1.69614i			0.128955i	−0.997919	+	0.0644776i	$0.979462\pi$
$174$		0			0
$175$	0.410574	−	4.66410i	0.0310364	−	0.352572i
$176$	7.16053	−	5.17273i	0.539745	−	0.389909i
$177$		0			0
$178$	4.32920	−	17.9785i	0.324487	−	1.34755i
$179$			8.21342i			0.613900i	0.951726	+	0.306950i	$0.0993084\pi$
$179$			8.21342i			0.613900i	−0.951726	+	0.306950i	$0.900692\pi$
$180$		0			0
$181$			4.66410i			0.346680i	0.984862	+	0.173340i	$0.0554559\pi$
$181$			4.66410i			0.346680i	−0.984862	+	0.173340i	$0.944544\pi$
$182$	−4.29400	−	1.03399i	−0.318293	−	0.0766443i
$183$		0			0
$184$	6.24621	−	7.28323i	0.460477	−	0.536927i
$185$	12.5435	−	11.4878i	0.922215	−	0.844600i
$186$		0			0
$187$			3.41011i			0.249372i
$188$	−9.79366	+	19.1567i	−0.714276	+	1.39714i
$189$		0			0
$190$	8.64239	−	4.77985i	0.626985	−	0.346767i
$191$	13.1921			0.954544			0.477272	−	0.878756i	$-0.341626\pi$
$191$	13.1921			0.954544			0.477272	+	0.878756i	$0.341626\pi$
$192$		0			0
$193$			23.3331i			1.67955i	0.542934	+	0.839775i	$0.317313\pi$
$193$			23.3331i			1.67955i	−0.542934	+	0.839775i	$0.682687\pi$
$194$	0.723002	−	3.00252i	0.0519085	−	0.215569i
$195$		0			0
$196$	−10.9039	−	5.57450i	−0.778849	−	0.398179i
$197$		−	4.92539i		−	0.350920i	−0.984487	−	0.175460i	$-0.943859\pi$
$197$		−	4.92539i		−	0.350920i	0.984487	−	0.175460i	$-0.0561412\pi$
$198$		0			0
$199$			17.6339i			1.25003i	0.780611	+	0.625017i	$0.214908\pi$
$199$			17.6339i			1.25003i	−0.780611	+	0.625017i	$0.785092\pi$
$200$	−10.1124	+	9.88634i	−0.715054	+	0.699070i
$201$		0			0
$202$	−4.53448	−	1.09190i	−0.319045	−	0.0768255i
$203$	7.91096			0.555241
$204$		0			0
$205$	−8.80604	−	9.61528i	−0.615041	−	0.671560i
$206$	24.7796	+	5.96688i	1.72648	+	0.415732i
$207$		0			0
$208$	7.81198	+	10.8140i	0.541663	+	0.749816i
$209$			6.89697i			0.477073i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	4.63252	−	9.06134i	0.318163	−	0.622336i
$213$		0			0
$214$	15.1231	+	3.64162i	1.03379	+	0.248936i
$215$	−11.7460	−	12.8255i	−0.801074	−	0.874689i
$216$		0			0
$217$		−	7.77769i		−	0.527984i
$218$	3.95548	−	16.4265i	0.267899	−	1.11255i
$219$		0			0
$220$	−2.62378	−	9.52122i	−0.176895	−	0.641921i
$221$	−5.15002			−0.346428
$222$		0			0
$223$	21.9989			1.47316			0.736578	−	0.676352i	$-0.236440\pi$
$223$	21.9989			1.47316			0.736578	+	0.676352i	$0.236440\pi$
$224$	−2.01051	−	4.90086i	−0.134333	−	0.327453i
$225$		0			0
$226$	17.2462	+	4.15286i	1.14720	+	0.276244i
$227$	−3.08835			−0.204981			−0.102490	−	0.994734i	$-0.532681\pi$
$227$	−3.08835			−0.204981			−0.102490	+	0.994734i	$0.532681\pi$
$228$		0			0
$229$			2.61914i			0.173077i	0.996248	+	0.0865387i	$0.0275806\pi$
$229$			2.61914i			0.173077i	−0.996248	+	0.0865387i	$0.972419\pi$
$230$	−5.19182	−	9.38727i	−0.342338	−	0.618978i
$231$		0			0
$232$	−18.1379	−	15.5554i	−1.19081	−	1.02126i
$233$	−20.4544			−1.34002			−0.670008	−	0.742354i	$-0.733709\pi$
$233$	−20.4544			−1.34002			−0.670008	+	0.742354i	$0.733709\pi$
$234$		0			0
$235$	16.2462	+	17.7392i	1.05979	+	1.15718i
$236$	−9.73554	+	19.0430i	−0.633730	+	1.23959i
$237$		0			0
$238$	1.98813	+	0.478739i	0.128871	+	0.0310320i
$239$	23.4921			1.51958			0.759789	−	0.650170i	$-0.225302\pi$
$239$	23.4921			1.51958			0.759789	+	0.650170i	$0.225302\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$	−8.41874	−	2.02722i	−0.541177	−	0.130314i
$243$		0			0
$244$		0			0
$245$	−10.0970	+	9.24726i	−0.645076	+	0.590786i
$246$		0			0
$247$	−10.4160			−0.662752
$248$	−15.2933	+	17.8324i	−0.971126	+	1.13236i
$249$		0			0
$250$	6.40963	+	14.4539i	0.405381	+	0.914148i
$251$		−	3.44849i		−	0.217666i	−0.994060	−	0.108833i	$-0.965289\pi$
$251$		−	3.44849i		−	0.217666i	0.994060	−	0.108833i	$-0.0347114\pi$
$252$		0			0
$253$	7.49141			0.470981
$254$	−6.43753	−	1.55014i	−0.403926	−	0.0972647i
$255$		0			0
$256$	−5.02699	+	15.1898i	−0.314187	+	0.949361i
$257$	15.6318			0.975087			0.487543	−	0.873099i	$-0.337893\pi$
$257$	15.6318			0.975087			0.487543	+	0.873099i	$0.337893\pi$
$258$		0			0
$259$	7.12311			0.442608
$260$	14.3792	−	3.96250i	0.891759	−	0.245744i
$261$		0			0
$262$	−0.205287	+	0.852526i	−0.0126827	+	0.0526693i
$263$		−	14.7304i		−	0.908316i	−0.890921	−	0.454158i	$-0.849940\pi$
$263$		−	14.7304i		−	0.908316i	0.890921	−	0.454158i	$-0.150060\pi$
$264$		0			0
$265$	−7.68466	−	8.39084i	−0.472065	−	0.515445i
$266$	4.02102	+	0.968253i	0.246544	+	0.0593674i
$267$		0			0
$268$	−11.0571	+	21.6280i	−0.675420	+	1.32114i
$269$	−15.0441			−0.917253			−0.458626	−	0.888629i	$-0.651658\pi$
$269$	−15.0441			−0.917253			−0.458626	+	0.888629i	$0.651658\pi$
$270$		0			0
$271$		−	10.3507i		−	0.628758i	−0.949297	−	0.314379i	$-0.898204\pi$
$271$		−	10.3507i		−	0.628758i	0.949297	−	0.314379i	$-0.101796\pi$
$272$	−3.61696	−	5.00691i	−0.219311	−	0.303588i
$273$		0			0
$274$	2.12311	+	0.511240i	0.128262	+	0.0308851i
$275$	−10.9993	−	0.968253i	−0.663283	−	0.0583879i
$276$		0			0
$277$	−23.3459			−1.40272			−0.701360	−	0.712807i	$-0.747424\pi$
$277$	−23.3459			−1.40272			−0.701360	+	0.712807i	$0.747424\pi$
$278$	16.4990	+	3.97292i	0.989542	+	0.238280i
$279$		0			0
$280$	−5.91933	+	0.193030i	−0.353748	+	0.0115357i
$281$		−	3.00252i		−	0.179116i	−0.995982	−	0.0895578i	$-0.971455\pi$
$281$		−	3.00252i		−	0.179116i	0.995982	−	0.0895578i	$-0.0285454\pi$
$282$		0			0
$283$		−	23.3331i		−	1.38701i	−0.720453	−	0.693503i	$-0.756066\pi$
$283$		−	23.3331i		−	1.38701i	0.720453	−	0.693503i	$-0.243934\pi$
$284$	−20.9171	−	10.6937i	−1.24120	−	0.634551i
$285$		0			0
$286$	−2.43845	+	10.1265i	−0.144188	+	0.598794i
$287$		−	5.46026i		−	0.322309i
$288$		0			0
$289$	−14.6155			−0.859737
$290$	−23.3778	+	12.9296i	−1.37279	+	0.759249i
$291$		0			0
$292$	−5.09271	+	9.96148i	−0.298028	+	0.582951i
$293$			29.8326i			1.74284i	0.490536	+	0.871421i	$0.336801\pi$
$293$			29.8326i			1.74284i	−0.490536	+	0.871421i	$0.663199\pi$
$294$		0			0
$295$	16.1498	+	17.6339i	0.940278	+	1.02669i
$296$	−16.3316	−	14.0062i	−0.949253	−	0.814094i
$297$		0			0
$298$	−2.54635	−	0.613157i	−0.147506	−	0.0355192i
$299$			11.3137i			0.654289i
$300$		0			0
$301$		−	7.28323i		−	0.419799i
$302$	5.83817	−	24.2451i	0.335949	−	1.39515i
$303$		0			0
$304$	−7.31534	−	10.1265i	−0.419564	−	0.580796i
$305$		0			0
$306$		0			0
$307$		−	4.36758i		−	0.249271i	−0.992203	−	0.124636i	$-0.960224\pi$
$307$		−	4.36758i		−	0.249271i	0.992203	−	0.124636i	$-0.0397762\pi$
$308$	1.88269	−	3.68260i	0.107276	−	0.209836i
$309$		0			0
$310$	12.7117	+	22.9839i	0.721978	+	1.30540i
$311$	10.3000			0.584062			0.292031	−	0.956409i	$-0.405669\pi$
$311$	10.3000			0.584062			0.292031	+	0.956409i	$0.405669\pi$
$312$		0			0
$313$			32.0682i			1.81260i	0.422631	+	0.906302i	$0.361107\pi$
$313$			32.0682i			1.81260i	−0.422631	+	0.906302i	$0.638893\pi$
$314$	3.86252	+	0.930087i	0.217974	+	0.0524878i
$315$		0			0
$316$	0.930870	−	1.82081i	0.0523655	−	0.102428i
$317$			24.5354i			1.37805i	0.724739	+	0.689023i	$0.241960\pi$
$317$			24.5354i			1.37805i	−0.724739	+	0.689023i	$0.758040\pi$
$318$		0			0
$319$		−	18.6564i		−	1.04456i
$320$	13.9512	+	11.1967i	0.779894	+	0.625912i
$321$		0			0
$322$	1.05171	−	4.36758i	0.0586093	−	0.243396i
$323$	4.82262			0.268338
$324$		0			0
$325$	1.46228	−	16.6114i	0.0811127	−	0.921436i
$326$	−5.15002	+	21.3873i	−0.285233	+	1.18453i
$327$		0			0
$328$	−10.7365	+	12.5191i	−0.592826	+	0.691249i
$329$			10.0736i			0.555375i
$330$		0			0
$331$	−1.36932			−0.0752645			−0.0376322	−	0.999292i	$-0.511982\pi$
$331$	−1.36932			−0.0752645			−0.0376322	+	0.999292i	$0.511982\pi$
$332$	25.0870	+	12.8255i	1.37683	+	0.703889i
$333$		0			0
$334$	−3.12311	+	12.9698i	−0.170889	+	0.709676i
$335$	18.3421	+	20.0276i	1.00213	+	1.09423i
$336$		0			0
$337$		−	29.8844i		−	1.62791i	−0.580929	−	0.813954i	$-0.697310\pi$
$337$		−	29.8844i		−	1.62791i	0.580929	−	0.813954i	$-0.302690\pi$
$338$	2.58057	+	0.621396i	0.140364	+	0.0337995i
$339$		0			0
$340$	−6.65759	+	1.83465i	−0.361059	+	0.0994977i
$341$	−18.3421			−0.993279
$342$		0			0
$343$	−12.2888			−0.663534
$344$	−14.3211	+	16.6987i	−0.772140	+	0.900334i
$345$		0			0
$346$	0.561553	−	2.33205i	0.0301893	−	0.125372i
$347$	14.0877			0.756265			0.378133	−	0.925751i	$-0.376566\pi$
$347$	14.0877			0.756265			0.378133	+	0.925751i	$0.376566\pi$
$348$		0			0
$349$		−	33.2228i		−	1.77838i	−0.457540	−	0.889189i	$-0.651269\pi$
$349$		−	33.2228i		−	1.77838i	0.457540	−	0.889189i	$-0.348731\pi$
$350$	−2.10868	+	6.27680i	−0.112714	+	0.335509i
$351$		0			0
$352$	−11.5577	+	4.74137i	−0.616027	+	0.252716i
$353$	7.72087			0.410940			0.205470	−	0.978663i	$-0.434128\pi$
$353$	7.72087			0.410940			0.205470	+	0.978663i	$0.434128\pi$
$354$		0			0
$355$	−19.3693	+	17.7392i	−1.02802	+	0.941497i
$356$	−11.9045	+	23.2856i	−0.630940	+	1.23414i
$357$		0			0
$358$	2.71927	−	11.2927i	0.143718	−	0.596840i
$359$	−1.44600			−0.0763172			−0.0381586	−	0.999272i	$-0.512149\pi$
$359$	−1.44600			−0.0763172			−0.0381586	+	0.999272i	$0.512149\pi$
$360$		0			0
$361$	−9.24621			−0.486643
$362$	1.54417	−	6.41273i	0.0811600	−	0.337046i
$363$		0			0
$364$	5.56155	+	2.84329i	0.291505	+	0.149029i
$365$	8.44804	+	9.22437i	0.442190	+	0.482826i
$366$		0			0
$367$	32.4149			1.69204			0.846022	−	0.533148i	$-0.178991\pi$
$367$	32.4149			1.69204			0.846022	+	0.533148i	$0.178991\pi$
$368$	−10.9993	+	7.94584i	−0.573379	+	0.414206i
$369$		0			0
$370$	−21.0496	+	11.6419i	−1.09431	+	0.605233i
$371$		−	4.76493i		−	0.247383i
$372$		0			0
$373$	9.47954			0.490832			0.245416	−	0.969418i	$-0.421075\pi$
$373$	9.47954			0.490832			0.245416	+	0.969418i	$0.421075\pi$
$374$	1.12901	−	4.68860i	0.0583795	−	0.242442i
$375$		0			0
$376$	19.8078	−	23.0963i	1.02151	−	1.19110i
$377$	28.1753			1.45110
$378$		0			0
$379$	−16.4924			−0.847159			−0.423579	−	0.905859i	$-0.639227\pi$
$379$	−16.4924			−0.847159			−0.423579	+	0.905859i	$0.639227\pi$
$380$	−13.4650	+	3.71059i	−0.690742	+	0.190349i
$381$		0			0
$382$	−18.1379	−	4.36758i	−0.928018	−	0.223465i
$383$			10.0138i			0.511682i	0.966719	+	0.255841i	$0.0823524\pi$
$383$			10.0138i			0.511682i	−0.966719	+	0.255841i	$0.917648\pi$
$384$		0			0
$385$	−3.12311	−	3.41011i	−0.159168	−	0.173795i
$386$	7.72503	−	32.0810i	0.393194	−	1.63288i
$387$		0			0
$388$	−1.98813	+	3.88884i	−0.100932	+	0.197426i
$389$	9.89404			0.501648			0.250824	−	0.968033i	$-0.419298\pi$
$389$	9.89404			0.501648			0.250824	+	0.968033i	$0.419298\pi$
$390$		0			0
$391$		−	5.23827i		−	0.264911i
$392$	13.1463	+	11.2745i	0.663989	+	0.569447i
$393$		0			0
$394$	−1.63068	+	6.77199i	−0.0821526	+	0.341168i
$395$	−1.54417	−	1.68608i	−0.0776958	−	0.0848357i
$396$		0			0
$397$	−10.3007			−0.516977			−0.258488	−	0.966014i	$-0.583224\pi$
$397$	−10.3007			−0.516977			−0.258488	+	0.966014i	$0.583224\pi$
$398$	5.83817	−	24.2451i	0.292641	−	1.21530i
$399$		0			0
$400$	17.1768	−	10.2449i	0.858840	−	0.512244i
$401$		−	0.522293i		−	0.0260821i	−0.999915	−	0.0130410i	$-0.995849\pi$
$401$		−	0.522293i		−	0.0260821i	0.999915	−	0.0130410i	$-0.00415121\pi$
$402$		0			0
$403$		−	27.7006i		−	1.37987i
$404$	5.87302	+	3.00252i	0.292194	+	0.149381i
$405$		0			0
$406$	−10.8769	−	2.61914i	−0.539811	−	0.129986i
$407$		−	16.7984i		−	0.832665i
$408$		0			0
$409$	3.12311			0.154428			0.0772138	−	0.997015i	$-0.475398\pi$
$409$	3.12311			0.154428			0.0772138	+	0.997015i	$0.475398\pi$
$410$	8.92416	+	16.1357i	0.440733	+	0.796883i
$411$		0			0
$412$	−32.0943	−	16.4079i	−1.58117	−	0.808359i
$413$			10.0138i			0.492748i
$414$		0			0
$415$	23.2306	−	21.2755i	1.14035	−	1.04437i
$416$	−7.16053	−	17.4547i	−0.351074	−	0.855787i
$417$		0			0
$418$	2.28343	−	9.48274i	0.111686	−	0.463816i
$419$		−	32.4291i		−	1.58427i	−0.610348	−	0.792134i	$-0.708970\pi$
$419$		−	32.4291i		−	1.58427i	0.610348	−	0.792134i	$-0.291030\pi$
$420$		0			0
$421$		−	30.6037i		−	1.49153i	−0.666207	−	0.745767i	$-0.732083\pi$
$421$		−	30.6037i		−	1.49153i	0.666207	−	0.745767i	$-0.267917\pi$
$422$	−5.49966	−	1.32431i	−0.267719	−	0.0644663i
$423$		0			0
$424$	−9.36932	+	10.9248i	−0.455014	+	0.530558i
$425$	−0.677039	+	7.69113i	−0.0328412	+	0.373074i
$426$		0			0
$427$		0			0
$428$	−19.5873	−	10.0138i	−0.946789	−	0.484036i
$429$		0			0
$430$	11.9036	+	21.5227i	0.574042	+	1.03792i
$431$	1.44600			0.0696516			0.0348258	−	0.999393i	$-0.488912\pi$
$431$	1.44600			0.0696516			0.0348258	+	0.999393i	$0.488912\pi$
$432$		0			0
$433$			15.5554i			0.747544i	0.927521	+	0.373772i	$0.121936\pi$
$433$			15.5554i			0.747544i	−0.927521	+	0.373772i	$0.878064\pi$
$434$	−2.57501	+	10.6937i	−0.123604	+	0.513312i
$435$		0			0
$436$	−10.8769	+	21.2755i	−0.520909	+	1.01891i
$437$		−	10.5945i		−	0.506802i
$438$		0			0
$439$			26.9621i			1.28683i	0.765517	+	0.643415i	$0.222483\pi$
$439$			26.9621i			1.28683i	−0.765517	+	0.643415i	$0.777517\pi$
$440$	0.455221	+	13.9595i	0.0217018	+	0.665495i
$441$		0			0
$442$	7.08084	+	1.70505i	0.336801	+	0.0811011i
$443$	25.0870			1.19192			0.595959	−	0.803015i	$-0.296772\pi$
$443$	25.0870			1.19192			0.595959	+	0.803015i	$0.296772\pi$
$444$		0			0
$445$	19.7479	+	21.5626i	0.936139	+	1.02217i
$446$	−30.2466	−	7.28333i	−1.43222	−	0.344876i
$447$		0			0
$448$	1.14171	+	7.40390i	0.0539409	+	0.349801i
$449$		−	9.89949i		−	0.467186i	−0.972334	−	0.233593i	$-0.924952\pi$
$449$		−	9.89949i		−	0.467186i	0.972334	−	0.233593i	$-0.0750483\pi$
$450$		0			0
$451$	−12.8769			−0.606349
$452$	−22.3371	−	11.4196i	−1.05065	−	0.537135i
$453$		0			0
$454$	4.24621	+	1.02248i	0.199285	+	0.0479874i
$455$	5.15002	−	4.71659i	0.241437	−	0.221117i
$456$		0			0
$457$		−	13.3716i		−	0.625496i	−0.949836	−	0.312748i	$-0.898750\pi$
$457$		−	13.3716i		−	0.625496i	0.949836	−	0.312748i	$-0.101250\pi$
$458$	0.867135	−	3.60109i	0.0405186	−	0.168268i
$459$		0			0
$460$	4.03040	+	14.6256i	0.187918	+	0.681921i
$461$	1.85201			0.0862567			0.0431283	−	0.999070i	$-0.486268\pi$
$461$	1.85201			0.0862567			0.0431283	+	0.999070i	$0.486268\pi$
$462$		0			0
$463$	13.2252			0.614629			0.307315	−	0.951608i	$-0.400570\pi$
$463$	13.2252			0.614629			0.307315	+	0.951608i	$0.400570\pi$
$464$	19.7881	+	27.3924i	0.918639	+	1.27166i
$465$		0			0
$466$	28.1231	+	6.77199i	1.30278	+	0.313706i
$467$	−18.9103			−0.875063			−0.437532	−	0.899203i	$-0.644147\pi$
$467$	−18.9103			−0.875063			−0.437532	+	0.899203i	$0.644147\pi$
$468$		0			0
$469$			11.3732i			0.525163i
$470$	−16.4641	−	29.7686i	−0.759433	−	1.37312i
$471$		0			0
$472$	19.6902	−	22.9593i	0.906316	−	1.05679i
$473$	−17.1760			−0.789754
$474$		0			0
$475$	−1.36932	+	15.5554i	−0.0628286	+	0.713730i
$476$	−2.57501	−	1.31645i	−0.118025	−	0.0603393i
$477$		0			0
$478$	−32.2996	−	7.77769i	−1.47735	−	0.355743i
$479$	14.6381			0.668830			0.334415	−	0.942426i	$-0.391461\pi$
$479$	14.6381			0.668830			0.334415	+	0.942426i	$0.391461\pi$
$480$		0			0
$481$	25.3693			1.15674
$482$	5.49966	+	1.32431i	0.250502	+	0.0603205i
$483$		0			0
$484$	10.9039	+	5.57450i	0.495631	+	0.253386i
$485$	3.29801	+	3.60109i	0.149755	+	0.163517i
$486$		0			0
$487$	−29.4903			−1.33633			−0.668167	−	0.744011i	$-0.732921\pi$
$487$	−29.4903			−1.33633			−0.668167	+	0.744011i	$0.732921\pi$
$488$		0			0
$489$		0			0
$490$	16.9441	−	9.37129i	0.765457	−	0.423352i
$491$		−	16.3505i		−	0.737888i	−0.929452	−	0.368944i	$-0.879719\pi$
$491$		−	16.3505i		−	0.737888i	0.929452	−	0.368944i	$-0.120281\pi$
$492$		0			0
$493$	−13.0452			−0.587528
$494$	14.3211	+	3.44849i	0.644335	+	0.155155i
$495$		0			0
$496$	26.9309	−	19.4547i	1.20923	−	0.873542i
$497$	−10.9993			−0.493387
$498$		0			0
$499$	16.8769			0.755514			0.377757	−	0.925905i	$-0.376696\pi$
$499$	16.8769			0.755514			0.377757	+	0.925905i	$0.376696\pi$
$500$	−4.02733	−	21.9950i	−0.180108	−	0.983647i
$501$		0			0
$502$	−1.14171	+	4.74137i	−0.0509572	+	0.211618i
$503$		−	16.0547i		−	0.715844i	−0.933751	−	0.357922i	$-0.883485\pi$
$503$		−	16.0547i		−	0.715844i	0.933751	−	0.357922i	$-0.116515\pi$
$504$		0			0
$505$	5.43845	−	4.98074i	0.242008	−	0.221640i
$506$	−10.3000	−	2.48023i	−0.457893	−	0.110260i
$507$		0			0
$508$	8.33783	+	4.26263i	0.369931	+	0.189124i
$509$	3.29801			0.146182			0.0730909	−	0.997325i	$-0.476714\pi$
$509$	3.29801			0.146182			0.0730909	+	0.997325i	$0.476714\pi$
$510$		0			0
$511$			5.23827i			0.231728i
$512$	11.9407	−	19.2203i	0.527707	−	0.849426i
$513$		0			0
$514$	−21.4924	−	5.17534i	−0.947990	−	0.228274i
$515$	−29.7195	+	27.2183i	−1.30960	+	1.19938i
$516$		0			0
$517$	23.7565			1.04481
$518$	−9.79366	−	2.35829i	−0.430309	−	0.103618i
$519$		0			0
$520$	−21.0820	+	0.687485i	−0.924508	+	0.0301482i
$521$		−	2.65433i		−	0.116288i	−0.998308	−	0.0581441i	$-0.981482\pi$
$521$		−	2.65433i		−	0.116288i	0.998308	−	0.0581441i	$-0.0185183\pi$
$522$		0			0
$523$			4.36758i			0.190981i	0.995430	+	0.0954905i	$0.0304420\pi$
$523$			4.36758i			0.190981i	−0.995430	+	0.0954905i	$0.969558\pi$
$524$	0.564503	−	1.10418i	0.0246604	−	0.0482365i
$525$		0			0
$526$	−4.87689	+	20.2530i	−0.212643	+	0.883074i
$527$			12.8255i			0.558686i
$528$		0			0
$529$	11.4924			0.499671
$530$	7.78773	+	14.0809i	0.338277	+	0.611635i
$531$		0			0
$532$	−5.20798	−	2.66253i	−0.225795	−	0.115435i
$533$		−	19.4470i		−	0.842343i
$534$		0			0
$535$	−18.1379	+	16.6114i	−0.784172	+	0.718174i
$536$	22.3631	−	26.0759i	0.965939	−	1.12631i
$537$		0			0
$538$	20.6843	+	4.98074i	0.891763	+	0.214735i
$539$			13.5221i			0.582437i
$540$		0			0
$541$			9.90237i			0.425736i	0.977081	+	0.212868i	$0.0682804\pi$
$541$			9.90237i			0.425736i	−0.977081	+	0.212868i	$0.931720\pi$
$542$	−3.42687	+	14.2313i	−0.147197	+	0.611286i
$543$		0			0
$544$	3.31534	+	8.08156i	0.142144	+	0.346494i
$545$	18.0431	+	19.7012i	0.772883	+	0.843908i
$546$		0			0
$547$		−	16.5129i		−	0.706039i	−0.935616	−	0.353019i	$-0.885155\pi$
$547$		−	16.5129i		−	0.706039i	0.935616	−	0.353019i	$-0.114845\pi$
$548$	−2.74983	−	1.40582i	−0.117467	−	0.0600537i
$549$		0			0
$550$	14.8025	+	4.97288i	0.631182	+	0.212044i
$551$	−26.3841			−1.12400
$552$		0			0
$553$		−	0.957477i		−	0.0407161i
$554$	32.0986	+	7.72929i	1.36374	+	0.328386i
$555$		0			0
$556$	−21.3693	−	10.9248i	−0.906261	−	0.463317i
$557$		−	32.6443i		−	1.38318i	−0.722289	−	0.691591i	$-0.756910\pi$
$557$		−	32.6443i		−	1.38318i	0.722289	−	0.691591i	$-0.243090\pi$
$558$		0			0
$559$		−	25.9396i		−	1.09713i
$560$	8.20248	+	1.69435i	0.346618	+	0.0715995i
$561$		0			0
$562$	−0.994066	+	4.12821i	−0.0419321	+	0.174138i
$563$	−14.0877			−0.593724			−0.296862	−	0.954920i	$-0.595940\pi$
$563$	−14.0877			−0.593724			−0.296862	+	0.954920i	$0.595940\pi$
$564$		0			0
$565$	−20.6843	+	18.9435i	−0.870195	+	0.796958i
$566$	−7.72503	+	32.0810i	−0.324707	+	1.34846i
$567$		0			0
$568$	25.2188	+	21.6280i	1.05816	+	0.907491i
$569$		−	30.0467i		−	1.25962i	−0.776748	−	0.629811i	$-0.783132\pi$
$569$		−	30.0467i		−	1.25962i	0.776748	−	0.629811i	$-0.216868\pi$
$570$		0			0
$571$	33.8617			1.41707			0.708535	−	0.705676i	$-0.249356\pi$
$571$	33.8617			1.41707			0.708535	+	0.705676i	$0.249356\pi$
$572$	6.70531	−	13.1158i	0.280363	−	0.548398i
$573$		0			0
$574$	−1.80776	+	7.50738i	−0.0754546	+	0.313352i
$575$	16.8961	+	1.48734i	0.704615	+	0.0620262i
$576$		0			0
$577$			7.77769i			0.323789i	0.986808	+	0.161895i	$0.0517605\pi$
$577$			7.77769i			0.323789i	−0.986808	+	0.161895i	$0.948240\pi$
$578$	20.0951	+	4.83886i	0.835846	+	0.201270i
$579$		0			0
$580$	36.4231	−	10.0372i	1.51239	−	0.416771i
$581$	13.1921			0.547299
$582$		0			0
$583$	−11.2371			−0.465394
$584$	10.3000	−	12.0101i	0.426219	−	0.496981i
$585$		0			0
$586$	9.87689	−	41.0173i	0.408011	−	1.69441i
$587$	10.9993			0.453990			0.226995	−	0.973896i	$-0.427110\pi$
$587$	10.9993			0.453990			0.226995	+	0.973896i	$0.427110\pi$
$588$		0			0
$589$			25.9396i			1.06882i
$590$	−16.3664	−	29.5919i	−0.673795	−	1.21828i
$591$		0			0
$592$	17.8174	+	24.6643i	0.732290	+	1.01370i
$593$	−43.8071			−1.79894			−0.899472	−	0.436978i	$-0.856049\pi$
$593$	−43.8071			−1.79894			−0.899472	+	0.436978i	$0.856049\pi$
$594$		0			0
$595$	−2.38447	+	2.18379i	−0.0977538	+	0.0895267i
$596$	3.29801	+	1.68608i	0.135092	+	0.0690644i
$597$		0			0
$598$	3.74571	−	15.5554i	0.153173	−	0.636107i
$599$	−45.5382			−1.86064			−0.930320	−	0.366749i	$-0.880471\pi$
$599$	−45.5382			−1.86064			−0.930320	+	0.366749i	$0.880471\pi$
$600$		0			0
$601$	−23.3693			−0.953254			−0.476627	−	0.879106i	$-0.658141\pi$
$601$	−23.3693			−0.953254			−0.476627	+	0.879106i	$0.658141\pi$
$602$	−2.41131	+	10.0138i	−0.0982776	+	0.408133i
$603$		0			0
$604$	−16.0540	+	31.4020i	−0.653227	+	1.27773i
$605$	10.0970	−	9.24726i	0.410503	−	0.375955i
$606$		0			0
$607$	−9.71010			−0.394121			−0.197060	−	0.980391i	$-0.563140\pi$
$607$	−9.71010			−0.394121			−0.197060	+	0.980391i	$0.563140\pi$
$608$	6.70531	+	16.3450i	0.271936	+	0.662879i
$609$		0			0
$610$		0			0
$611$			35.8776i			1.45145i
$612$		0			0
$613$	23.8718			0.964172			0.482086	−	0.876124i	$-0.339879\pi$
$613$	23.8718			0.964172			0.482086	+	0.876124i	$0.339879\pi$
$614$	−1.44600	+	6.00505i	−0.0583560	+	0.242344i
$615$		0			0
$616$	−3.80776	+	4.43994i	−0.153419	+	0.178890i
$617$	−15.6318			−0.629314			−0.314657	−	0.949205i	$-0.601889\pi$
$617$	−15.6318			−0.629314			−0.314657	+	0.949205i	$0.601889\pi$
$618$		0			0
$619$	18.7386			0.753169			0.376585	−	0.926382i	$-0.377098\pi$
$619$	18.7386			0.753169			0.376585	+	0.926382i	$0.377098\pi$
$620$	−9.86809	−	35.8095i	−0.396312	−	1.43814i
$621$		0			0
$622$	−14.1617	−	3.41011i	−0.567831	−	0.136733i
$623$			12.2448i			0.490578i
$624$		0			0
$625$	−24.6155	−	4.36758i	−0.984621	−	0.174703i
$626$	10.6170	−	44.0911i	0.424342	−	1.76223i
$627$		0			0
$628$	−5.00270	−	2.55758i	−0.199629	−	0.102059i
$629$	−11.7460			−0.468346
$630$		0			0
$631$			17.6339i			0.701995i	0.936376	+	0.350997i	$0.114157\pi$
$631$			17.6339i			0.701995i	−0.936376	+	0.350997i	$0.885843\pi$
$632$	−1.88269	+	2.19526i	−0.0748895	+	0.0873229i
$633$		0			0
$634$	8.12311	−	33.7341i	0.322610	−	1.33975i
$635$	7.72087	−	7.07107i	0.306393	−	0.280607i
$636$		0			0
$637$	−20.4214			−0.809124
$638$	−6.17669	+	25.6509i	−0.244538	+	1.01553i
$639$		0			0
$640$	−15.4747	−	20.0133i	−0.611691	−	0.791097i
$641$		−	7.07107i		−	0.279290i	−0.990202	−	0.139645i	$-0.955404\pi$
$641$		−	7.07107i		−	0.279290i	0.990202	−	0.139645i	$-0.0445962\pi$
$642$		0			0
$643$			8.73516i			0.344481i	0.985055	+	0.172241i	$0.0551007\pi$
$643$			8.73516i			0.344481i	−0.985055	+	0.172241i	$0.944899\pi$
$644$	−2.89201	+	5.65685i	−0.113961	+	0.222911i
$645$		0			0
$646$	−6.63068	−	1.59666i	−0.260881	−	0.0628196i
$647$		−	1.32431i		−	0.0520639i	−0.999661	−	0.0260319i	$-0.991713\pi$
$647$		−	1.32431i		−	0.0520639i	0.999661	−	0.0260319i	$-0.00828716\pi$
$648$		0			0
$649$	23.6155			0.926991
$650$	−7.51016	+	22.3551i	−0.294573	+	0.876841i
$651$		0			0
$652$	14.1617	−	27.7006i	0.554614	−	1.08484i
$653$		−	15.8459i		−	0.620098i	−0.950721	−	0.310049i	$-0.899654\pi$
$653$		−	15.8459i		−	0.620098i	0.950721	−	0.310049i	$-0.100346\pi$
$654$		0			0
$655$	−0.936426	−	1.02248i	−0.0365892	−	0.0399516i
$656$	18.9066	−	13.6580i	0.738178	−	0.533256i
$657$		0			0
$658$	3.33513	−	13.8503i	0.130017	−	0.539942i
$659$		−	33.3211i		−	1.29800i	−0.760786	−	0.649002i	$-0.775187\pi$
$659$		−	33.3211i		−	1.29800i	0.760786	−	0.649002i	$-0.224813\pi$
$660$		0			0
$661$			44.5960i			1.73458i	0.497800	+	0.867292i	$0.334141\pi$
$661$			44.5960i			1.73458i	−0.497800	+	0.867292i	$0.665859\pi$
$662$	1.88269	+	0.453349i	0.0731729	+	0.0176199i
$663$		0			0
$664$	−30.2462	−	25.9396i	−1.17378	−	1.00665i
$665$	−4.82262	+	4.41674i	−0.187013	+	0.171274i
$666$		0			0
$667$			28.6581i			1.10965i
$668$	8.58800	−	16.7984i	0.332280	−	0.649949i
$669$		0			0
$670$	−18.5881	−	33.6089i	−0.718121	−	1.29843i
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$	−9.89404	+	41.0885i	−0.381104	+	1.58267i
$675$		0			0
$676$	−3.34233	−	1.70873i	−0.128551	−	0.0657205i
$677$		−	5.25145i		−	0.201830i	−0.994895	−	0.100915i	$-0.967823\pi$
$677$		−	5.25145i		−	0.201830i	0.994895	−	0.100915i	$-0.0321770\pi$
$678$		0			0
$679$			2.04496i			0.0784783i
$680$	9.76102	−	0.318307i	0.374318	−	0.0122065i
$681$		0			0
$682$	25.2188	+	6.07263i	0.965677	+	0.232533i
$683$	20.2644			0.775394			0.387697	−	0.921787i	$-0.373271\pi$
$683$	20.2644			0.775394			0.387697	+	0.921787i	$0.373271\pi$
$684$		0			0
$685$	−2.54635	+	2.33205i	−0.0972911	+	0.0891030i
$686$	16.8961	+	4.06854i	0.645095	+	0.155338i
$687$		0			0
$688$	25.2188	−	18.2179i	0.961457	−	0.694551i
$689$		−	16.9706i		−	0.646527i
$690$		0			0
$691$	−23.1231			−0.879644			−0.439822	−	0.898085i	$-0.644959\pi$
$691$	−23.1231			−0.879644			−0.439822	+	0.898085i	$0.644959\pi$
$692$	−1.54417	+	3.02045i	−0.0587007	+	0.114820i
$693$		0			0
$694$	−19.3693	−	4.66410i	−0.735249	−	0.177047i
$695$	−19.7881	+	18.1227i	−0.750605	+	0.687433i
$696$		0			0
$697$			9.00400i			0.341051i
$698$	−10.9993	+	45.6786i	−0.416330	+	1.72896i
$699$		0			0
$700$	4.97735	−	7.93192i	0.188126	−	0.299799i
$701$	20.1941			0.762720			0.381360	−	0.924427i	$-0.375456\pi$
$701$	20.1941			0.762720			0.381360	+	0.924427i	$0.375456\pi$
$702$		0			0
$703$	−23.7565			−0.895993
$704$	17.4606	−	2.69250i	0.658070	−	0.101477i
$705$		0			0
$706$	−10.6155	−	2.55620i	−0.399521	−	0.0962038i
$707$	3.08835			0.116149
$708$		0			0
$709$		−	30.6037i		−	1.14935i	−0.818383	−	0.574673i	$-0.805129\pi$
$709$		−	30.6037i		−	1.14935i	0.818383	−	0.574673i	$-0.194871\pi$
$710$	32.5042	−	17.9771i	1.21986	−	0.674668i
$711$		0			0
$712$	24.0771	−	28.0744i	0.902326	−	1.05213i
$713$	28.1753			1.05517
$714$		0			0
$715$	−11.1231	−	12.1453i	−0.415981	−	0.454207i
$716$	−7.47753	+	14.6263i	−0.279448	+	0.546609i
$717$		0			0
$718$	1.98813	+	0.478739i	0.0741964	+	0.0178664i
$719$	−32.3461			−1.20631			−0.603154	−	0.797625i	$-0.706089\pi$
$719$	−32.3461			−1.20631			−0.603154	+	0.797625i	$0.706089\pi$
$720$		0			0
$721$	−16.8769			−0.628528
$722$	12.7127	+	3.06121i	0.473119	+	0.113926i
$723$		0			0
$724$	−4.24621	+	8.30571i	−0.157809	+	0.308679i
$725$	3.70402	−	42.0775i	0.137564	−	1.56272i
$726$		0			0
$727$	−9.47954			−0.351577			−0.175788	−	0.984428i	$-0.556247\pi$
$727$	−9.47954			−0.351577			−0.175788	+	0.984428i	$0.556247\pi$
$728$	−6.70531	−	5.75058i	−0.248515	−	0.213131i
$729$		0			0
$730$	−8.56135	−	15.4797i	−0.316870	−	0.572928i
$731$			12.0101i			0.444210i
$732$		0			0
$733$	19.6002			0.723951			0.361975	−	0.932188i	$-0.382102\pi$
$733$	19.6002			0.723951			0.361975	+	0.932188i	$0.382102\pi$
$734$	−44.5677	−	10.7318i	−1.64502	−	0.396119i
$735$		0			0
$736$	17.7538	−	7.28323i	0.654413	−	0.268463i
$737$	26.8212			0.987973
$738$		0			0
$739$	35.6155			1.31014			0.655069	−	0.755569i	$-0.272639\pi$
$739$	35.6155			1.31014			0.655069	+	0.755569i	$0.272639\pi$
$740$	32.7957	−	9.03758i	1.20559	−	0.332228i
$741$		0			0
$742$	−1.57756	+	6.55137i	−0.0579140	+	0.240508i
$743$			10.0138i			0.367371i	0.982985	+	0.183686i	$0.0588028\pi$
$743$			10.0138i			0.367371i	−0.982985	+	0.183686i	$0.941197\pi$
$744$		0			0
$745$	3.05398	−	2.79695i	0.111889	−	0.102472i
$746$	−13.0336	−	3.13846i	−0.477192	−	0.114907i
$747$		0			0
$748$	−3.10457	+	6.07263i	−0.113514	+	0.222038i
$749$	−10.3000			−0.376355
$750$		0			0
$751$		−	41.5286i		−	1.51540i	−0.652604	−	0.757699i	$-0.726323\pi$
$751$		−	41.5286i		−	1.51540i	0.652604	−	0.757699i	$-0.273677\pi$
$752$	−34.8806	+	25.1976i	−1.27197	+	0.918861i
$753$		0			0
$754$	−38.7386	−	9.32819i	−1.41078	−	0.339713i
$755$	26.6311	+	29.0784i	0.969207	+	1.05827i
$756$		0			0
$757$	3.33513			0.121217			0.0606087	−	0.998162i	$-0.480696\pi$
$757$	3.33513			0.121217			0.0606087	+	0.998162i	$0.480696\pi$
$758$	22.6757	+	5.46026i	0.823617	+	0.198325i
$759$		0			0
$760$	19.7418	−	0.643779i	0.716109	−	0.0233523i
$761$			49.3019i			1.78719i	0.448870	+	0.893597i	$0.351827\pi$
$761$			49.3019i			1.78719i	−0.448870	+	0.893597i	$0.648173\pi$
$762$		0			0
$763$			11.1878i			0.405025i
$764$	23.4921	+	12.0101i	0.849914	+	0.434510i
$765$		0			0
$766$	3.31534	−	13.7681i	0.119788	−	0.497463i
$767$			35.6647i			1.28778i
$768$		0			0
$769$	25.6155			0.923720			0.461860	−	0.886953i	$-0.347182\pi$
$769$	25.6155			0.923720			0.461860	+	0.886953i	$0.347182\pi$
$770$	3.16499	+	5.72259i	0.114058	+	0.206228i
$771$		0			0
$772$	−21.2425	+	41.5510i	−0.764535	+	1.49545i
$773$			2.27678i			0.0818901i	0.999161	+	0.0409450i	$0.0130369\pi$
$773$			2.27678i			0.0818901i	−0.999161	+	0.0409450i	$0.986963\pi$
$774$		0			0
$775$	−41.3686	−	3.64162i	−1.48600	−	0.130811i
$776$	4.02102	−	4.68860i	0.144346	−	0.168311i
$777$		0			0
$778$	−13.6035	−	3.27569i	−0.487707	−	0.117439i
$779$			18.2107i			0.652465i
$780$		0			0
$781$			25.9396i			0.928192i
$782$	−1.73427	+	7.20217i	−0.0620174	+	0.257549i
$783$		0			0
$784$	−14.3423	−	19.8539i	−0.512226	−	0.709067i
$785$	−4.63252	+	4.24264i	−0.165342	+	0.151426i
$786$		0			0
$787$			19.9230i			0.710177i	0.934833	+	0.355088i	$0.115549\pi$
$787$			19.9230i			0.710177i	−0.934833	+	0.355088i	$0.884451\pi$
$788$	4.48410	−	8.77102i	0.159739	−	0.312455i
$789$		0			0
$790$	1.56489	+	2.82945i	0.0556761	+	0.100667i
$791$	−11.7460			−0.417641
$792$		0			0
$793$		0			0
$794$	14.1626	+	3.41032i	0.502611	+	0.121028i
$795$		0			0
$796$	−16.0540	+	31.4020i	−0.569018	+	1.11302i
$797$			15.6829i			0.555516i	0.960651	+	0.277758i	$0.0895913\pi$
$797$			15.6829i			0.555516i	−0.960651	+	0.277758i	$0.910409\pi$
$798$		0			0
$799$		−	16.6114i		−	0.587670i
$800$	−27.0085	+	8.39900i	−0.954893	+	0.296950i
$801$		0			0
$802$	−0.172919	+	0.718108i	−0.00610598	+	0.0253573i
$803$	12.3534			0.435942
$804$		0			0
$805$	4.79741	+	5.23827i	0.169087	+	0.184625i
$806$	−9.17104	+	38.0860i	−0.323036	+	1.34152i
$807$		0			0
$808$	−7.08084	−	6.07263i	−0.249103	−	0.213635i
$809$		−	20.6695i		−	0.726700i	−0.931653	−	0.363350i	$-0.881633\pi$
$809$		−	20.6695i		−	0.726700i	0.931653	−	0.363350i	$-0.118367\pi$
$810$		0			0
$811$	−49.4773			−1.73738			−0.868691	−	0.495354i	$-0.835038\pi$
$811$	−49.4773			−1.73738			−0.868691	+	0.495354i	$0.835038\pi$
$812$	14.0877	+	7.20217i	0.494380	+	0.252747i
$813$		0			0
$814$	−5.56155	+	23.0963i	−0.194932	+	0.809526i
$815$	−23.4921	−	25.6509i	−0.822892	−	0.898513i
$816$		0			0
$817$			24.2905i			0.849818i
$818$	−4.29400	−	1.03399i	−0.150136	−	0.0361525i
$819$		0			0
$820$	−6.92781	−	25.1397i	−0.241929	−	0.877917i
$821$	12.1521			0.424110			0.212055	−	0.977258i	$-0.431984\pi$
$821$	12.1521			0.424110			0.212055	+	0.977258i	$0.431984\pi$
$822$		0			0
$823$	−28.6692			−0.999345			−0.499673	−	0.866214i	$-0.666546\pi$
$823$	−28.6692			−0.999345			−0.499673	+	0.866214i	$0.666546\pi$
$824$	38.6947	+	33.1851i	1.34799	+	1.15606i
$825$		0			0
$826$	3.31534	−	13.7681i	0.115355	−	0.479055i
$827$	−39.1746			−1.36224			−0.681118	−	0.732174i	$-0.738506\pi$
$827$	−39.1746			−1.36224			−0.681118	+	0.732174i	$0.738506\pi$
$828$		0			0
$829$			4.66410i			0.161991i	0.996714	+	0.0809954i	$0.0258099\pi$
$829$			4.66410i			0.161991i	−0.996714	+	0.0809954i	$0.974190\pi$
$830$	−38.9840	+	21.5609i	−1.35315	+	0.748389i
$831$		0			0
$832$	4.06627	+	26.3694i	0.140973	+	0.914194i
$833$	9.45514			0.327601
$834$		0			0
$835$	−14.2462	−	15.5554i	−0.493010	−	0.538316i
$836$	−6.27903	+	12.2820i	−0.217165	+	0.424781i
$837$		0			0
$838$	−10.7365	+	44.5873i	−0.370887	+	1.54024i
$839$	−24.9381			−0.860959			−0.430479	−	0.902600i	$-0.641656\pi$
$839$	−24.9381			−0.860959			−0.430479	+	0.902600i	$0.641656\pi$
$840$		0			0
$841$	42.3693			1.46101
$842$	−10.1322	+	42.0775i	−0.349178	+	1.45009i
$843$		0			0
$844$	7.12311	+	3.64162i	0.245187	+	0.125350i
$845$	−3.09501	+	2.83453i	−0.106472	+	0.0975108i
$846$		0			0
$847$	5.73384			0.197017
$848$	16.4990	−	11.9188i	0.566577	−	0.409292i
$849$		0			0
$850$	3.47722	−	10.3505i	0.119268	−	0.355019i
$851$			25.8040i			0.884551i
$852$		0			0
$853$	−45.5249			−1.55874			−0.779371	−	0.626563i	$-0.784461\pi$
$853$	−45.5249			−1.55874			−0.779371	+	0.626563i	$0.784461\pi$
$854$		0			0
$855$		0			0
$856$	23.6155	+	20.2530i	0.807162	+	0.692235i
$857$	−40.7188			−1.39093			−0.695464	−	0.718561i	$-0.744801\pi$
$857$	−40.7188			−1.39093			−0.695464	+	0.718561i	$0.744801\pi$
$858$		0			0
$859$	−33.7538			−1.15166			−0.575832	−	0.817568i	$-0.695322\pi$
$859$	−33.7538			−1.15166			−0.575832	+	0.817568i	$0.695322\pi$
$860$	−9.24074	−	33.5329i	−0.315107	−	1.14346i
$861$		0			0
$862$	−1.98813	−	0.478739i	−0.0677160	−	0.0163059i
$863$			45.6786i			1.55492i	0.628935	+	0.777458i	$0.283491\pi$
$863$			45.6786i			1.55492i	−0.628935	+	0.777458i	$0.716509\pi$
$864$		0			0
$865$	2.56155	+	2.79695i	0.0870954	+	0.0950991i
$866$	5.15002	−	21.3873i	0.175005	−	0.726770i
$867$		0			0
$868$	7.08084	−	13.8503i	0.240339	−	0.470111i
$869$	−2.25801			−0.0765978
$870$		0			0
$871$			40.5061i			1.37250i
$872$	21.9986	−	25.6509i	0.744967	−	0.868650i
$873$		0			0
$874$	−3.50758	+	14.5665i	−0.118646	+	0.492718i
$875$	−6.36679	−	8.31118i	−0.215237	−	0.280969i
$876$		0			0
$877$	46.5766			1.57278			0.786389	−	0.617731i	$-0.211948\pi$
$877$	46.5766			1.57278			0.786389	+	0.617731i	$0.211948\pi$
$878$	8.92652	−	37.0706i	0.301256	−	1.25107i
$879$		0			0
$880$	3.99579	−	19.3439i	0.134698	−	0.652082i
$881$			5.83095i			0.196450i	0.995164	+	0.0982249i	$0.0313164\pi$
$881$			5.83095i			0.196450i	−0.995164	+	0.0982249i	$0.968684\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−9.17104	−	4.68860i	−0.308455	−	0.157695i
$885$		0			0
$886$	−34.4924	−	8.30571i	−1.15880	−	0.279036i
$887$			16.2177i			0.544538i	0.962221	+	0.272269i	$0.0877741\pi$
$887$			16.2177i			0.544538i	−0.962221	+	0.272269i	$0.912226\pi$
$888$		0			0
$889$	4.38447			0.147050
$890$	−20.0127	−	36.1848i	−0.670828	−	1.21292i
$891$		0			0
$892$	39.1752	+	20.0279i	1.31168	+	0.670584i
$893$		−	33.5968i		−	1.12427i
$894$		0			0
$895$	12.4041	+	13.5440i	0.414623	+	0.452725i
$896$	0.881502	−	10.5577i	0.0294489	−	0.352709i
$897$		0			0
$898$	−3.27749	+	13.6110i	−0.109371	+	0.454203i
$899$		−	70.1670i		−	2.34020i
$900$		0			0
$901$			7.85741i			0.261768i
$902$	17.7046	+	4.26324i	0.589499	+	0.141950i
$903$		0			0
$904$	26.9309	+	23.0963i	0.895707	+	0.768172i
$905$	7.04383	+	7.69113i	0.234145	+	0.255662i
$906$		0			0
$907$			16.5129i			0.548300i	0.961687	+	0.274150i	$0.0883965\pi$
$907$			16.5129i			0.548300i	−0.961687	+	0.274150i	$0.911603\pi$
$908$	−5.49966	−	2.81164i	−0.182512	−	0.0933077i
$909$		0			0
$910$	−8.64239	+	4.77985i	−0.286492	+	0.158451i
$911$	36.6842			1.21540			0.607700	−	0.794167i	$-0.292092\pi$
$911$	36.6842			1.21540			0.607700	+	0.794167i	$0.292092\pi$
$912$		0			0
$913$		−	31.1107i		−	1.02962i
$914$	−4.42702	+	18.3848i	−0.146433	+	0.608114i
$915$		0			0
$916$	−2.38447	+	4.66410i	−0.0787852	+	0.154106i
$917$		−	0.580639i		−	0.0191744i
$918$		0			0
$919$		−	30.1554i		−	0.994735i	−0.867540	−	0.497368i	$-0.834300\pi$
$919$		−	30.1554i		−	0.994735i	0.867540	−	0.497368i	$-0.165700\pi$
$920$	−0.699266	−	21.4433i	−0.0230541	−	0.706964i
$921$		0			0
$922$	−2.54635	−	0.613157i	−0.0838597	−	0.0201933i
$923$	−39.1746			−1.28945
$924$		0			0
$925$	3.33513	−	37.8869i	0.109658	−	1.24571i
$926$	−18.1836	−	4.37857i	−0.597549	−	0.143889i
$927$		0			0
$928$	−18.1379	−	44.2135i	−0.595407	−	1.45138i
$929$			3.00252i			0.0985096i	0.998786	+	0.0492548i	$0.0156846\pi$
$929$			3.00252i			0.0985096i	−0.998786	+	0.0492548i	$0.984315\pi$
$930$		0			0
$931$	19.1231			0.626734
$932$	−36.4248	−	18.6218i	−1.19313	−	0.609978i
$933$		0			0
$934$	26.0000	+	6.26075i	0.850746	+	0.204858i
$935$	5.15002	+	5.62329i	0.168424	+	0.183901i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	3.76539	−	15.6371i	0.122944	−	0.510570i
$939$		0			0
$940$	12.7811	+	46.3801i	0.416872	+	1.51275i
$941$	−3.29801			−0.107512			−0.0537561	−	0.998554i	$-0.517119\pi$
$941$	−3.29801			−0.107512			−0.0537561	+	0.998554i	$0.517119\pi$
$942$		0			0
$943$	19.7802			0.644133
$944$	−34.6736	+	25.0481i	−1.12853	+	0.815245i
$945$		0			0
$946$	23.6155	+	5.68658i	0.767807	+	0.184887i
$947$	32.9979			1.07229			0.536144	−	0.844126i	$-0.319880\pi$
$947$	32.9979			1.07229			0.536144	+	0.844126i	$0.319880\pi$
$948$		0			0
$949$			18.6564i			0.605612i
$950$	7.03272	−	20.9340i	0.228171	−	0.679187i
$951$		0			0
$952$	3.10457	+	2.66253i	0.100620	+	0.0862931i
$953$	12.5435			0.406323			0.203162	−	0.979145i	$-0.434878\pi$
$953$	12.5435			0.406323			0.203162	+	0.979145i	$0.434878\pi$
$954$		0			0
$955$	21.7538	−	19.9230i	0.703936	−	0.644692i
$956$	41.8342	+	21.3873i	1.35301	+	0.691715i
$957$		0			0
$958$	−20.1261	−	4.84632i	−0.650244	−	0.156578i
$959$	−1.44600			−0.0466939
$960$		0			0
$961$	−37.9848			−1.22532
$962$	−34.8806	−	8.39919i	−1.12460	−	0.270801i
$963$		0			0
$964$	−7.12311	−	3.64162i	−0.229420	−	0.117289i
$965$	35.2381	+	38.4764i	1.13436	+	1.23860i
$966$		0			0
$967$	15.0981			0.485522			0.242761	−	0.970086i	$-0.421947\pi$
$967$	15.0981			0.485522			0.242761	+	0.970086i	$0.421947\pi$
$968$	−13.1463	−	11.2745i	−0.422538	−	0.362375i
$969$		0			0
$970$	−3.34225	−	6.04308i	−0.107313	−	0.194032i
$971$		−	19.8753i		−	0.637829i	−0.947783	−	0.318915i	$-0.896682\pi$
$971$		−	19.8753i		−	0.637829i	0.947783	−	0.318915i	$-0.103318\pi$
$972$		0			0
$973$	−11.2371			−0.360245
$974$	40.5467	+	9.76356i	1.29920	+	0.312845i
$975$		0			0
$976$		0			0
$977$	−37.6305			−1.20390			−0.601952	−	0.798532i	$-0.705610\pi$
$977$	−37.6305			−1.20390			−0.601952	+	0.798532i	$0.705610\pi$
$978$		0			0
$979$	28.8769			0.922910
$980$	−26.3993	+	7.27492i	−0.843295	+	0.232389i
$981$		0			0
$982$	−5.41327	+	22.4805i	−0.172744	+	0.717383i
$983$		−	53.0438i		−	1.69183i	−0.533315	−	0.845917i	$-0.679054\pi$
$983$		−	53.0438i		−	1.69183i	0.533315	−	0.845917i	$-0.320946\pi$
$984$		0			0
$985$	−7.43845	−	8.12201i	−0.237009	−	0.258789i
$986$	17.9361	+	4.31897i	0.571201	+	0.137544i
$987$		0			0
$988$	−18.5485	−	9.48274i	−0.590107	−	0.301686i
$989$	26.3841			0.838966
$990$		0			0
$991$		−	17.6339i		−	0.560159i	−0.959977	−	0.280080i	$-0.909639\pi$
$991$		−	17.6339i		−	0.560159i	0.959977	−	0.280080i	$-0.0903609\pi$
$992$	−43.4686	+	17.8324i	−1.38013	+	0.566178i
$993$		0			0
$994$	15.1231	+	3.64162i	0.479676	+	0.115505i
$995$	26.6311	+	29.0784i	0.844264	+	0.921848i
$996$		0			0
$997$	25.5141			0.808039			0.404019	−	0.914750i	$-0.367613\pi$
$997$	25.5141			0.808039			0.404019	+	0.914750i	$0.367613\pi$
$998$	−23.2043	−	5.58755i	−0.734519	−	0.176871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.m.c.179.2	yes	16
3.2	odd	2	inner	360.2.m.c.179.15	yes	16
4.3	odd	2		1440.2.m.c.719.9		16
5.2	odd	4		1800.2.b.g.251.10		16
5.3	odd	4		1800.2.b.g.251.7		16
5.4	even	2	inner	360.2.m.c.179.16	yes	16
8.3	odd	2	inner	360.2.m.c.179.3	yes	16
8.5	even	2		1440.2.m.c.719.8		16
12.11	even	2		1440.2.m.c.719.7		16
15.2	even	4		1800.2.b.g.251.8		16
15.8	even	4		1800.2.b.g.251.9		16
15.14	odd	2	inner	360.2.m.c.179.1	✓	16
20.3	even	4		7200.2.b.i.4751.12		16
20.7	even	4		7200.2.b.i.4751.7		16
20.19	odd	2		1440.2.m.c.719.12		16
24.5	odd	2		1440.2.m.c.719.10		16
24.11	even	2	inner	360.2.m.c.179.14	yes	16
40.3	even	4		1800.2.b.g.251.12		16
40.13	odd	4		7200.2.b.i.4751.8		16
40.19	odd	2	inner	360.2.m.c.179.13	yes	16
40.27	even	4		1800.2.b.g.251.5		16
40.29	even	2		1440.2.m.c.719.5		16
40.37	odd	4		7200.2.b.i.4751.11		16
60.23	odd	4		7200.2.b.i.4751.9		16
60.47	odd	4		7200.2.b.i.4751.6		16
60.59	even	2		1440.2.m.c.719.6		16
120.29	odd	2		1440.2.m.c.719.11		16
120.53	even	4		7200.2.b.i.4751.5		16
120.59	even	2	inner	360.2.m.c.179.4	yes	16
120.77	even	4		7200.2.b.i.4751.10		16
120.83	odd	4		1800.2.b.g.251.6		16
120.107	odd	4		1800.2.b.g.251.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.m.c.179.1	✓	16	15.14	odd	2	inner
360.2.m.c.179.2	yes	16	1.1	even	1	trivial
360.2.m.c.179.3	yes	16	8.3	odd	2	inner
360.2.m.c.179.4	yes	16	120.59	even	2	inner
360.2.m.c.179.13	yes	16	40.19	odd	2	inner
360.2.m.c.179.14	yes	16	24.11	even	2	inner
360.2.m.c.179.15	yes	16	3.2	odd	2	inner
360.2.m.c.179.16	yes	16	5.4	even	2	inner
1440.2.m.c.719.5		16	40.29	even	2
1440.2.m.c.719.6		16	60.59	even	2
1440.2.m.c.719.7		16	12.11	even	2
1440.2.m.c.719.8		16	8.5	even	2
1440.2.m.c.719.9		16	4.3	odd	2
1440.2.m.c.719.10		16	24.5	odd	2
1440.2.m.c.719.11		16	120.29	odd	2
1440.2.m.c.719.12		16	20.19	odd	2
1800.2.b.g.251.5		16	40.27	even	4
1800.2.b.g.251.6		16	120.83	odd	4
1800.2.b.g.251.7		16	5.3	odd	4
1800.2.b.g.251.8		16	15.2	even	4
1800.2.b.g.251.9		16	15.8	even	4
1800.2.b.g.251.10		16	5.2	odd	4
1800.2.b.g.251.11		16	120.107	odd	4
1800.2.b.g.251.12		16	40.3	even	4
7200.2.b.i.4751.5		16	120.53	even	4
7200.2.b.i.4751.6		16	60.47	odd	4
7200.2.b.i.4751.7		16	20.7	even	4
7200.2.b.i.4751.8		16	40.13	odd	4
7200.2.b.i.4751.9		16	60.23	odd	4
7200.2.b.i.4751.10		16	120.77	even	4
7200.2.b.i.4751.11		16	40.37	odd	4
7200.2.b.i.4751.12		16	20.3	even	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} +(1.64901 - 1.51022i) q^{5} +0.936426 q^{7} +(-2.14700 - 1.84130i) q^{8} +O(q^{10})\)	\(q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} +(1.64901 - 1.51022i) q^{5} +0.936426 q^{7} +(-2.14700 - 1.84130i) q^{8} +(-2.76724 + 1.53048i) q^{10} -2.20837i q^{11} +3.33513 q^{13} +(-1.28751 - 0.310029i) q^{14} +(2.34233 + 3.24245i) q^{16} -1.54417 q^{17} -3.12311 q^{19} +(4.31143 - 1.18811i) q^{20} +(-0.731140 + 3.03632i) q^{22} +3.39228i q^{23} +(0.438447 - 4.98074i) q^{25} +(-4.58552 - 1.10418i) q^{26} +(1.66757 + 0.852526i) q^{28} +8.44804 q^{29} -8.30571i q^{31} +(-2.14700 - 5.23358i) q^{32} +(2.12311 + 0.511240i) q^{34} +(1.54417 - 1.41421i) q^{35} +7.60669 q^{37} +(4.29400 + 1.03399i) q^{38} +(-6.32120 + 0.206134i) q^{40} -5.83095i q^{41} -7.77769i q^{43} +(2.01051 - 3.93261i) q^{44} +(1.12311 - 4.66410i) q^{46} +10.7575i q^{47} -6.12311 q^{49} +(-2.25183 + 6.70293i) q^{50} +(5.93912 + 3.03632i) q^{52} -5.08842i q^{53} +(-3.33513 - 3.64162i) q^{55} +(-2.01051 - 1.72424i) q^{56} +(-11.6153 - 2.79695i) q^{58} +10.6937i q^{59} +(-2.74983 + 11.4196i) q^{62} +(1.21922 + 7.90655i) q^{64} +(5.49966 - 5.03680i) q^{65} +12.1453i q^{67} +(-2.74983 - 1.40582i) q^{68} +(-2.59132 + 1.43318i) q^{70} -11.7460 q^{71} +5.59390i q^{73} +(-10.4585 - 2.51840i) q^{74} +(-5.56155 - 2.84329i) q^{76} -2.06798i q^{77} -1.02248i q^{79} +(8.75935 + 1.80938i) q^{80} +(-1.93049 + 8.01706i) q^{82} +14.0877 q^{83} +(-2.54635 + 2.33205i) q^{85} +(-2.57501 + 10.6937i) q^{86} +(-4.06627 + 4.74137i) q^{88} +13.0761i q^{89} +3.12311 q^{91} +(-3.08835 + 6.04090i) q^{92} +(3.56155 - 14.7906i) q^{94} +(-5.15002 + 4.71659i) q^{95} +2.18379i q^{97} +(8.41874 + 2.02722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4}+O(q^{10}) \) 16 * q + 12 * q^4	\( 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) \) 16 * q + 12 * q^4 - 8 * q^10 - 12 * q^16 + 16 * q^19 + 40 * q^25 - 32 * q^34 - 28 * q^40 - 48 * q^46 - 32 * q^49 + 36 * q^64 + 32 * q^70 - 56 * q^76 - 16 * q^91 + 24 * q^94

Introduction

L-functions

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