LMFDB - Embedded newform 180.3.f.g.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(19,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("180.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.f (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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$2.34521 - 4.06202i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.3.f.g.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.69042 + 1.73205i) q^{5} +9.38083 q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.69042 + 1.73205i) q^{5} +9.38083 q^{7} -8.00000 q^{8} +(7.69042 - 6.39199i) q^{10} -16.2481i q^{11} +16.2481i q^{13} +(9.38083 - 16.2481i) q^{14} +(-8.00000 + 13.8564i) q^{16} -10.3923i q^{17} -20.7846i q^{19} +(-3.38083 - 19.7122i) q^{20} +(-28.1425 - 16.2481i) q^{22} -28.0000 q^{23} +(19.0000 + 16.2481i) q^{25} +(28.1425 + 16.2481i) q^{26} +(-18.7617 - 32.4962i) q^{28} +9.38083 q^{29} +34.6410i q^{31} +(16.0000 + 27.7128i) q^{32} +(-18.0000 - 10.3923i) q^{34} +(44.0000 + 16.2481i) q^{35} +48.7442i q^{37} +(-36.0000 - 20.7846i) q^{38} +(-37.5233 - 13.8564i) q^{40} -18.7617 q^{41} +37.5233 q^{43} +(-56.2850 + 32.4962i) q^{44} +(-28.0000 + 48.4974i) q^{46} -4.00000 q^{47} +39.0000 q^{49} +(47.1425 - 16.6609i) q^{50} +(56.2850 - 32.4962i) q^{52} +31.1769i q^{53} +(28.1425 - 76.2102i) q^{55} -75.0467 q^{56} +(9.38083 - 16.2481i) q^{58} +16.2481i q^{59} -58.0000 q^{61} +(60.0000 + 34.6410i) q^{62} +64.0000 q^{64} +(-28.1425 + 76.2102i) q^{65} -18.7617 q^{67} +(-36.0000 + 20.7846i) q^{68} +(72.1425 - 59.9622i) q^{70} +97.4885i q^{71} +(84.4275 + 48.7442i) q^{74} +(-72.0000 + 41.5692i) q^{76} -152.420i q^{77} +6.92820i q^{79} +(-61.5233 + 51.1359i) q^{80} +(-18.7617 + 32.4962i) q^{82} +32.0000 q^{83} +(18.0000 - 48.7442i) q^{85} +(37.5233 - 64.9923i) q^{86} +129.985i q^{88} -75.0467 q^{89} +152.420i q^{91} +(56.0000 + 96.9948i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(36.0000 - 97.4885i) q^{95} -162.481i q^{97} +(39.0000 - 67.5500i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 12 q^{10} - 32 q^{16} + 24 q^{20} - 112 q^{23} + 76 q^{25} + 64 q^{32} - 72 q^{34} + 176 q^{35} - 144 q^{38} - 112 q^{46} - 16 q^{47} + 156 q^{49} + 76 q^{50} - 232 q^{61} + 240 q^{62} + 256 q^{64} - 144 q^{68} + 176 q^{70} - 288 q^{76} - 96 q^{80} + 128 q^{83} + 72 q^{85} + 224 q^{92} - 16 q^{94} + 144 q^{95} + 156 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 12 * q^10 - 32 * q^16 + 24 * q^20 - 112 * q^23 + 76 * q^25 + 64 * q^32 - 72 * q^34 + 176 * q^35 - 144 * q^38 - 112 * q^46 - 16 * q^47 + 156 * q^49 + 76 * q^50 - 232 * q^61 + 240 * q^62 + 256 * q^64 - 144 * q^68 + 176 * q^70 - 288 * q^76 - 96 * q^80 + 128 * q^83 + 72 * q^85 + 224 * q^92 - 16 * q^94 + 144 * q^95 + 156 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	4.69042	+	1.73205i	0.938083	+	0.346410i
$5$	4.69042	+	1.73205i	0.938083	+	0.346410i
$6$		0			0
$7$	9.38083			1.34012			0.670059	−	0.742307i	$-0.266269\pi$
$7$	9.38083			1.34012			0.670059	+	0.742307i	$0.266269\pi$
$8$	−8.00000			−1.00000
$9$		0			0
$10$	7.69042	−	6.39199i	0.769042	−	0.639199i
$11$		−	16.2481i		−	1.47710i	−0.674200	−	0.738549i	$-0.735511\pi$
$11$		−	16.2481i		−	1.47710i	0.674200	−	0.738549i	$-0.264489\pi$
$12$		0			0
$13$			16.2481i			1.24985i	0.780684	+	0.624926i	$0.214871\pi$
$13$			16.2481i			1.24985i	−0.780684	+	0.624926i	$0.785129\pi$
$14$	9.38083	−	16.2481i	0.670059	−	1.16058i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$		−	10.3923i		−	0.611312i	−0.952142	−	0.305656i	$-0.901124\pi$
$17$		−	10.3923i		−	0.611312i	0.952142	−	0.305656i	$-0.0988758\pi$
$18$		0			0
$19$		−	20.7846i		−	1.09393i	−0.837157	−	0.546963i	$-0.815784\pi$
$19$		−	20.7846i		−	1.09393i	0.837157	−	0.546963i	$-0.184216\pi$
$20$	−3.38083	−	19.7122i	−0.169042	−	0.985609i
$21$		0			0
$22$	−28.1425	−	16.2481i	−1.27920	−	0.738549i
$23$	−28.0000			−1.21739			−0.608696	−	0.793404i	$-0.708307\pi$
$23$	−28.0000			−1.21739			−0.608696	+	0.793404i	$0.708307\pi$
$24$		0			0
$25$	19.0000	+	16.2481i	0.760000	+	0.649923i
$26$	28.1425	+	16.2481i	1.08240	+	0.624926i
$27$		0			0
$28$	−18.7617	−	32.4962i	−0.670059	−	1.16058i
$29$	9.38083			0.323477			0.161738	−	0.986834i	$-0.448290\pi$
$29$	9.38083			0.323477			0.161738	+	0.986834i	$0.448290\pi$
$30$		0			0
$31$			34.6410i			1.11745i	0.829352	+	0.558726i	$0.188710\pi$
$31$			34.6410i			1.11745i	−0.829352	+	0.558726i	$0.811290\pi$
$32$	16.0000	+	27.7128i	0.500000	+	0.866025i
$33$		0			0
$34$	−18.0000	−	10.3923i	−0.529412	−	0.305656i
$35$	44.0000	+	16.2481i	1.25714	+	0.464231i
$36$		0			0
$37$			48.7442i			1.31741i	0.752401	+	0.658706i	$0.228896\pi$
$37$			48.7442i			1.31741i	−0.752401	+	0.658706i	$0.771104\pi$
$38$	−36.0000	−	20.7846i	−0.947368	−	0.546963i
$39$		0			0
$40$	−37.5233	−	13.8564i	−0.938083	−	0.346410i
$41$	−18.7617			−0.457602			−0.228801	−	0.973473i	$-0.573480\pi$
$41$	−18.7617			−0.457602			−0.228801	+	0.973473i	$0.573480\pi$
$42$		0			0
$43$	37.5233			0.872635			0.436318	−	0.899793i	$-0.356282\pi$
$43$	37.5233			0.872635			0.436318	+	0.899793i	$0.356282\pi$
$44$	−56.2850	+	32.4962i	−1.27920	+	0.738549i
$45$		0			0
$46$	−28.0000	+	48.4974i	−0.608696	+	1.05429i
$47$	−4.00000			−0.0851064			−0.0425532	−	0.999094i	$-0.513549\pi$
$47$	−4.00000			−0.0851064			−0.0425532	+	0.999094i	$0.513549\pi$
$48$		0			0
$49$	39.0000			0.795918
$50$	47.1425	−	16.6609i	0.942850	−	0.333218i
$51$		0			0
$52$	56.2850	−	32.4962i	1.08240	−	0.624926i
$53$			31.1769i			0.588244i	0.955768	+	0.294122i	$0.0950271\pi$
$53$			31.1769i			0.588244i	−0.955768	+	0.294122i	$0.904973\pi$
$54$		0			0
$55$	28.1425	−	76.2102i	0.511682	−	1.38564i
$56$	−75.0467			−1.34012
$57$		0			0
$58$	9.38083	−	16.2481i	0.161738	−	0.280139i
$59$			16.2481i			0.275391i	0.990475	+	0.137696i	$0.0439696\pi$
$59$			16.2481i			0.275391i	−0.990475	+	0.137696i	$0.956030\pi$
$60$		0			0
$61$	−58.0000			−0.950820			−0.475410	−	0.879764i	$-0.657700\pi$
$61$	−58.0000			−0.950820			−0.475410	+	0.879764i	$0.657700\pi$
$62$	60.0000	+	34.6410i	0.967742	+	0.558726i
$63$		0			0
$64$	64.0000			1.00000
$65$	−28.1425	+	76.2102i	−0.432961	+	1.17247i
$66$		0			0
$67$	−18.7617			−0.280025			−0.140012	−	0.990150i	$-0.544714\pi$
$67$	−18.7617			−0.280025			−0.140012	+	0.990150i	$0.544714\pi$
$68$	−36.0000	+	20.7846i	−0.529412	+	0.305656i
$69$		0			0
$70$	72.1425	−	59.9622i	1.03061	−	0.856602i
$71$			97.4885i			1.37308i	0.727093	+	0.686538i	$0.240871\pi$
$71$			97.4885i			1.37308i	−0.727093	+	0.686538i	$0.759129\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	84.4275	+	48.7442i	1.14091	+	0.658706i
$75$		0			0
$76$	−72.0000	+	41.5692i	−0.947368	+	0.546963i
$77$		−	152.420i		−	1.97949i
$78$		0			0
$79$			6.92820i			0.0876988i	0.999038	+	0.0438494i	$0.0139622\pi$
$79$			6.92820i			0.0876988i	−0.999038	+	0.0438494i	$0.986038\pi$
$80$	−61.5233	+	51.1359i	−0.769042	+	0.639199i
$81$		0			0
$82$	−18.7617	+	32.4962i	−0.228801	+	0.396295i
$83$	32.0000			0.385542			0.192771	−	0.981244i	$-0.438253\pi$
$83$	32.0000			0.385542			0.192771	+	0.981244i	$0.438253\pi$
$84$		0			0
$85$	18.0000	−	48.7442i	0.211765	−	0.573462i
$86$	37.5233	−	64.9923i	0.436318	−	0.755725i
$87$		0			0
$88$			129.985i			1.47710i
$89$	−75.0467			−0.843221			−0.421610	−	0.906777i	$-0.638535\pi$
$89$	−75.0467			−0.843221			−0.421610	+	0.906777i	$0.638535\pi$
$90$		0			0
$91$			152.420i			1.67495i
$92$	56.0000	+	96.9948i	0.608696	+	1.05429i
$93$		0			0
$94$	−4.00000	+	6.92820i	−0.0425532	+	0.0737043i
$95$	36.0000	−	97.4885i	0.378947	−	1.02619i
$96$		0			0
$97$		−	162.481i		−	1.67506i	−0.546392	−	0.837530i	$-0.683999\pi$
$97$		−	162.481i		−	1.67506i	0.546392	−	0.837530i	$-0.316001\pi$
$98$	39.0000	−	67.5500i	0.397959	−	0.689286i
$99$		0			0
$100$	18.2850	−	98.3141i	0.182850	−	0.983141i
$101$	121.951			1.20743			0.603717	−	0.797199i	$-0.293686\pi$
$101$	121.951			1.20743			0.603717	+	0.797199i	$0.293686\pi$
$102$		0			0
$103$	−159.474			−1.54829			−0.774146	−	0.633007i	$-0.781821\pi$
$103$	−159.474			−1.54829			−0.774146	+	0.633007i	$0.781821\pi$
$104$		−	129.985i		−	1.24985i
$105$		0			0
$106$	54.0000	+	31.1769i	0.509434	+	0.294122i
$107$	−184.000			−1.71963			−0.859813	−	0.510609i	$-0.829420\pi$
$107$	−184.000			−1.71963			−0.859813	+	0.510609i	$0.829420\pi$
$108$		0			0
$109$	−22.0000			−0.201835			−0.100917	−	0.994895i	$-0.532178\pi$
$109$	−22.0000			−0.201835			−0.100917	+	0.994895i	$0.532178\pi$
$110$	−103.858	−	124.954i	−0.944159	−	1.13595i
$111$		0			0
$112$	−75.0467	+	129.985i	−0.670059	+	1.16058i
$113$			86.6025i			0.766394i	0.923667	+	0.383197i	$0.125177\pi$
$113$			86.6025i			0.766394i	−0.923667	+	0.383197i	$0.874823\pi$
$114$		0			0
$115$	−131.332	−	48.4974i	−1.14201	−	0.421717i
$116$	−18.7617	−	32.4962i	−0.161738	−	0.280139i
$117$		0			0
$118$	28.1425	+	16.2481i	0.238496	+	0.137696i
$119$		−	97.4885i		−	0.819231i
$120$		0			0
$121$	−143.000			−1.18182
$122$	−58.0000	+	100.459i	−0.475410	+	0.823434i
$123$		0			0
$124$	120.000	−	69.2820i	0.967742	−	0.558726i
$125$	60.9754	+	109.119i	0.487803	+	0.872954i
$126$		0			0
$127$	9.38083			0.0738648			0.0369324	−	0.999318i	$-0.488241\pi$
$127$	9.38083			0.0738648			0.0369324	+	0.999318i	$0.488241\pi$
$128$	64.0000	−	110.851i	0.500000	−	0.866025i
$129$		0			0
$130$	103.858	+	124.954i	0.798904	+	0.961188i
$131$		−	178.729i		−	1.36434i	−0.731193	−	0.682171i	$-0.761036\pi$
$131$		−	178.729i		−	1.36434i	0.731193	−	0.682171i	$-0.238964\pi$
$132$		0			0
$133$		−	194.977i		−	1.46599i
$134$	−18.7617	+	32.4962i	−0.140012	+	0.242509i
$135$		0			0
$136$			83.1384i			0.611312i
$137$		−	211.310i		−	1.54241i	−0.636587	−	0.771205i	$-0.719654\pi$
$137$		−	211.310i		−	1.54241i	0.636587	−	0.771205i	$-0.280346\pi$
$138$		0			0
$139$		−	90.0666i		−	0.647961i	−0.946064	−	0.323981i	$-0.894979\pi$
$139$		−	90.0666i		−	0.647961i	0.946064	−	0.323981i	$-0.105021\pi$
$140$	−31.7150	−	184.917i	−0.226536	−	1.32083i
$141$		0			0
$142$	168.855	+	97.4885i	1.18912	+	0.686538i
$143$	264.000			1.84615
$144$		0			0
$145$	44.0000	+	16.2481i	0.303448	+	0.112056i
$146$		0			0
$147$		0			0
$148$	168.855	−	97.4885i	1.14091	−	0.658706i
$149$	234.521			1.57397			0.786983	−	0.616975i	$-0.211642\pi$
$149$	234.521			1.57397			0.786983	+	0.616975i	$0.211642\pi$
$150$		0			0
$151$			48.4974i			0.321175i	0.987022	+	0.160587i	$0.0513389\pi$
$151$			48.4974i			0.321175i	−0.987022	+	0.160587i	$0.948661\pi$
$152$			166.277i			1.09393i
$153$		0			0
$154$	−264.000	−	152.420i	−1.71429	−	0.989743i
$155$	−60.0000	+	162.481i	−0.387097	+	1.04826i
$156$		0			0
$157$			16.2481i			0.103491i	0.998660	+	0.0517455i	$0.0164785\pi$
$157$			16.2481i			0.103491i	−0.998660	+	0.0517455i	$0.983522\pi$
$158$	12.0000	+	6.92820i	0.0759494	+	0.0438494i
$159$		0			0
$160$	27.0467	+	157.697i	0.169042	+	0.985609i
$161$	−262.663			−1.63145
$162$		0			0
$163$	206.378			1.26612			0.633062	−	0.774101i	$-0.281798\pi$
$163$	206.378			1.26612			0.633062	+	0.774101i	$0.281798\pi$
$164$	37.5233	+	64.9923i	0.228801	+	0.396295i
$165$		0			0
$166$	32.0000	−	55.4256i	0.192771	−	0.333889i
$167$	−244.000			−1.46108			−0.730539	−	0.682871i	$-0.760731\pi$
$167$	−244.000			−1.46108			−0.730539	+	0.682871i	$0.760731\pi$
$168$		0			0
$169$	−95.0000			−0.562130
$170$	−66.4275	−	79.9211i	−0.390750	−	0.470124i
$171$		0			0
$172$	−75.0467	−	129.985i	−0.436318	−	0.755725i
$173$			38.1051i			0.220261i	0.993917	+	0.110130i	$0.0351268\pi$
$173$			38.1051i			0.220261i	−0.993917	+	0.110130i	$0.964873\pi$
$174$		0			0
$175$	178.236	+	152.420i	1.01849	+	0.870974i
$176$	225.140	+	129.985i	1.27920	+	0.738549i
$177$		0			0
$178$	−75.0467	+	129.985i	−0.421610	+	0.730251i
$179$			146.233i			0.816942i	0.912771	+	0.408471i	$0.133938\pi$
$179$			146.233i			0.816942i	−0.912771	+	0.408471i	$0.866062\pi$
$180$		0			0
$181$	230.000			1.27072			0.635359	−	0.772217i	$-0.280852\pi$
$181$	230.000			1.27072			0.635359	+	0.772217i	$0.280852\pi$
$182$	264.000	+	152.420i	1.45055	+	0.837475i
$183$		0			0
$184$	224.000			1.21739
$185$	−84.4275	+	228.631i	−0.456365	+	1.23584i
$186$		0			0
$187$	−168.855			−0.902968
$188$	8.00000	+	13.8564i	0.0425532	+	0.0737043i
$189$		0			0
$190$	−132.855	−	159.842i	−0.699237	−	0.841275i
$191$			32.4962i			0.170137i	0.996375	+	0.0850685i	$0.0271109\pi$
$191$			32.4962i			0.170137i	−0.996375	+	0.0850685i	$0.972889\pi$
$192$		0			0
$193$			162.481i			0.841869i	0.907091	+	0.420935i	$0.138298\pi$
$193$			162.481i			0.841869i	−0.907091	+	0.420935i	$0.861702\pi$
$194$	−281.425	−	162.481i	−1.45064	−	0.837530i
$195$		0			0
$196$	−78.0000	−	135.100i	−0.397959	−	0.689286i
$197$		−	342.946i		−	1.74084i	−0.492307	−	0.870421i	$-0.663846\pi$
$197$		−	342.946i		−	1.74084i	0.492307	−	0.870421i	$-0.336154\pi$
$198$		0			0
$199$		−	20.7846i		−	0.104445i	−0.998635	−	0.0522226i	$-0.983369\pi$
$199$		−	20.7846i		−	0.104445i	0.998635	−	0.0522226i	$-0.0166305\pi$
$200$	−152.000	−	129.985i	−0.760000	−	0.649923i
$201$		0			0
$202$	121.951	−	211.225i	0.603717	−	1.04567i
$203$	88.0000			0.433498
$204$		0			0
$205$	−88.0000	−	32.4962i	−0.429268	−	0.158518i
$206$	−159.474	+	276.217i	−0.774146	+	1.34086i
$207$		0			0
$208$	−225.140	−	129.985i	−1.08240	−	0.624926i
$209$	−337.710			−1.61584
$210$		0			0
$211$		−	297.913i		−	1.41191i	−0.708257	−	0.705954i	$-0.750518\pi$
$211$		−	297.913i		−	1.41191i	0.708257	−	0.705954i	$-0.249482\pi$
$212$	108.000	−	62.3538i	0.509434	−	0.294122i
$213$		0			0
$214$	−184.000	+	318.697i	−0.859813	+	1.48924i
$215$	176.000	+	64.9923i	0.818605	+	0.302290i
$216$		0			0
$217$			324.962i			1.49752i
$218$	−22.0000	+	38.1051i	−0.100917	+	0.174794i
$219$		0			0
$220$	−320.285	+	54.9320i	−1.45584	+	0.249691i
$221$	168.855			0.764050
$222$		0			0
$223$	−159.474			−0.715131			−0.357565	−	0.933888i	$-0.616393\pi$
$223$	−159.474			−0.715131			−0.357565	+	0.933888i	$0.616393\pi$
$224$	150.093	+	259.969i	0.670059	+	1.16058i
$225$		0			0
$226$	150.000	+	86.6025i	0.663717	+	0.383197i
$227$	128.000			0.563877			0.281938	−	0.959433i	$-0.409023\pi$
$227$	128.000			0.563877			0.281938	+	0.959433i	$0.409023\pi$
$228$		0			0
$229$	134.000			0.585153			0.292576	−	0.956242i	$-0.405487\pi$
$229$	134.000			0.585153			0.292576	+	0.956242i	$0.405487\pi$
$230$	−215.332	+	178.976i	−0.936225	+	0.778155i
$231$		0			0
$232$	−75.0467			−0.323477
$233$			301.377i			1.29346i	0.762718	+	0.646731i	$0.223865\pi$
$233$			301.377i			1.29346i	−0.762718	+	0.646731i	$0.776135\pi$
$234$		0			0
$235$	−18.7617	−	6.92820i	−0.0798369	−	0.0294817i
$236$	56.2850	−	32.4962i	0.238496	−	0.137696i
$237$		0			0
$238$	−168.855	−	97.4885i	−0.709475	−	0.409615i
$239$			162.481i			0.679836i	0.940455	+	0.339918i	$0.110399\pi$
$239$			162.481i			0.679836i	−0.940455	+	0.339918i	$0.889601\pi$
$240$		0			0
$241$	50.0000			0.207469			0.103734	−	0.994605i	$-0.466921\pi$
$241$	50.0000			0.207469			0.103734	+	0.994605i	$0.466921\pi$
$242$	−143.000	+	247.683i	−0.590909	+	1.02348i
$243$		0			0
$244$	116.000	+	200.918i	0.475410	+	0.823434i
$245$	182.926	+	67.5500i	0.746638	+	0.275714i
$246$		0			0
$247$	337.710			1.36725
$248$		−	277.128i		−	1.11745i
$249$		0			0
$250$	249.975	+	3.50670i	0.999902	+	0.0140268i
$251$			146.233i			0.582600i	0.956632	+	0.291300i	$0.0940878\pi$
$251$			146.233i			0.582600i	−0.956632	+	0.291300i	$0.905912\pi$
$252$		0			0
$253$			454.946i			1.79821i
$254$	9.38083	−	16.2481i	0.0369324	−	0.0639688i
$255$		0			0
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$			24.2487i			0.0943530i	0.998887	+	0.0471765i	$0.0150223\pi$
$257$			24.2487i			0.0943530i	−0.998887	+	0.0471765i	$0.984978\pi$
$258$		0			0
$259$			457.261i			1.76549i
$260$	320.285	−	54.9320i	1.23187	−	0.211277i
$261$		0			0
$262$	−309.567	−	178.729i	−1.18156	−	0.682171i
$263$	−340.000			−1.29278			−0.646388	−	0.763009i	$-0.723721\pi$
$263$	−340.000			−1.29278			−0.646388	+	0.763009i	$0.723721\pi$
$264$		0			0
$265$	−54.0000	+	146.233i	−0.203774	+	0.551821i
$266$	−337.710	−	194.977i	−1.26959	−	0.732996i
$267$		0			0
$268$	37.5233	+	64.9923i	0.140012	+	0.242509i
$269$	178.236			0.662587			0.331293	−	0.943528i	$-0.392515\pi$
$269$	178.236			0.662587			0.331293	+	0.943528i	$0.392515\pi$
$270$		0			0
$271$		−	394.908i		−	1.45722i	−0.684927	−	0.728612i	$-0.740166\pi$
$271$		−	394.908i		−	1.45722i	0.684927	−	0.728612i	$-0.259834\pi$
$272$	144.000	+	83.1384i	0.529412	+	0.305656i
$273$		0			0
$274$	−366.000	−	211.310i	−1.33577	−	0.771205i
$275$	264.000	−	308.713i	0.960000	−	1.12259i
$276$		0			0
$277$		−	113.737i		−	0.410601i	−0.978699	−	0.205301i	$-0.934183\pi$
$277$		−	113.737i		−	0.410601i	0.978699	−	0.205301i	$-0.0658172\pi$
$278$	−156.000	−	90.0666i	−0.561151	−	0.323981i
$279$		0			0
$280$	−352.000	−	129.985i	−1.25714	−	0.464231i
$281$	−75.0467			−0.267070			−0.133535	−	0.991044i	$-0.542633\pi$
$281$	−75.0467			−0.267070			−0.133535	+	0.991044i	$0.542633\pi$
$282$		0			0
$283$	318.948			1.12703			0.563513	−	0.826107i	$-0.309450\pi$
$283$	318.948			1.12703			0.563513	+	0.826107i	$0.309450\pi$
$284$	337.710	−	194.977i	1.18912	−	0.686538i
$285$		0			0
$286$	264.000	−	457.261i	0.923077	−	1.59882i
$287$	−176.000			−0.613240
$288$		0			0
$289$	181.000			0.626298
$290$	72.1425	−	59.9622i	0.248767	−	0.206766i
$291$		0			0
$292$		0			0
$293$		−	349.874i		−	1.19411i	−0.802200	−	0.597055i	$-0.796337\pi$
$293$		−	349.874i		−	1.19411i	0.802200	−	0.597055i	$-0.203663\pi$
$294$		0			0
$295$	−28.1425	+	76.2102i	−0.0953983	+	0.258340i
$296$		−	389.954i		−	1.31741i
$297$		0			0
$298$	234.521	−	406.202i	0.786983	−	1.36309i
$299$		−	454.946i		−	1.52156i
$300$		0			0
$301$	352.000			1.16944
$302$	84.0000	+	48.4974i	0.278146	+	0.160587i
$303$		0			0
$304$	288.000	+	166.277i	0.947368	+	0.546963i
$305$	−272.044	−	100.459i	−0.891948	−	0.329374i
$306$		0			0
$307$	262.663			0.855581			0.427790	−	0.903878i	$-0.359292\pi$
$307$	262.663			0.855581			0.427790	+	0.903878i	$0.359292\pi$
$308$	−528.000	+	304.841i	−1.71429	+	0.989743i
$309$		0			0
$310$	221.425	+	266.404i	0.714274	+	0.859367i
$311$		−	32.4962i		−	0.104489i	−0.998634	−	0.0522446i	$-0.983362\pi$
$311$		−	32.4962i		−	0.104489i	0.998634	−	0.0522446i	$-0.0166376\pi$
$312$		0			0
$313$		−	357.458i		−	1.14204i	−0.820937	−	0.571019i	$-0.806548\pi$
$313$		−	357.458i		−	1.14204i	0.820937	−	0.571019i	$-0.193452\pi$
$314$	28.1425	+	16.2481i	0.0896258	+	0.0517455i
$315$		0			0
$316$	24.0000	−	13.8564i	0.0759494	−	0.0438494i
$317$		−	45.0333i		−	0.142061i	−0.997474	−	0.0710305i	$-0.977371\pi$
$317$		−	45.0333i		−	0.142061i	0.997474	−	0.0710305i	$-0.0226288\pi$
$318$		0			0
$319$		−	152.420i		−	0.477807i
$320$	300.187	+	110.851i	0.938083	+	0.346410i
$321$		0			0
$322$	−262.663	+	454.946i	−0.815724	+	1.41288i
$323$	−216.000			−0.668731
$324$		0			0
$325$	−264.000	+	308.713i	−0.812308	+	0.949888i
$326$	206.378	−	357.458i	0.633062	−	1.09650i
$327$		0			0
$328$	150.093			0.457602
$329$	−37.5233			−0.114053
$330$		0			0
$331$		−	325.626i		−	0.983763i	−0.870662	−	0.491881i	$-0.836309\pi$
$331$		−	325.626i		−	0.983763i	0.870662	−	0.491881i	$-0.163691\pi$
$332$	−64.0000	−	110.851i	−0.192771	−	0.333889i
$333$		0			0
$334$	−244.000	+	422.620i	−0.730539	+	1.26533i
$335$	−88.0000	−	32.4962i	−0.262687	−	0.0970034i
$336$		0			0
$337$			64.9923i			0.192856i	0.995340	+	0.0964278i	$0.0307417\pi$
$337$			64.9923i			0.192856i	−0.995340	+	0.0964278i	$0.969258\pi$
$338$	−95.0000	+	164.545i	−0.281065	+	0.486819i
$339$		0			0
$340$	−204.855	+	35.1346i	−0.602515	+	0.103337i
$341$	562.850			1.65059
$342$		0			0
$343$	−93.8083			−0.273494
$344$	−300.187			−0.872635
$345$		0			0
$346$	66.0000	+	38.1051i	0.190751	+	0.110130i
$347$	104.000			0.299712			0.149856	−	0.988708i	$-0.452119\pi$
$347$	104.000			0.299712			0.149856	+	0.988708i	$0.452119\pi$
$348$		0			0
$349$	−598.000			−1.71347			−0.856734	−	0.515759i	$-0.827510\pi$
$349$	−598.000			−1.71347			−0.856734	+	0.515759i	$0.827510\pi$
$350$	442.236	−	156.293i	1.26353	−	0.446551i
$351$		0			0
$352$	450.280	−	259.969i	1.27920	−	0.738549i
$353$			79.6743i			0.225706i	0.993612	+	0.112853i	$0.0359990\pi$
$353$			79.6743i			0.225706i	−0.993612	+	0.112853i	$0.964001\pi$
$354$		0			0
$355$	−168.855	+	457.261i	−0.475648	+	1.28806i
$356$	150.093	+	259.969i	0.421610	+	0.730251i
$357$		0			0
$358$	253.282	+	146.233i	0.707493	+	0.408471i
$359$		−	194.977i		−	0.543111i	−0.962423	−	0.271556i	$-0.912462\pi$
$359$		−	194.977i		−	0.543111i	0.962423	−	0.271556i	$-0.0875381\pi$
$360$		0			0
$361$	−71.0000			−0.196676
$362$	230.000	−	398.372i	0.635359	−	1.10047i
$363$		0			0
$364$	528.000	−	304.841i	1.45055	−	0.837475i
$365$		0			0
$366$		0			0
$367$	−553.469			−1.50809			−0.754045	−	0.656823i	$-0.771900\pi$
$367$	−553.469			−1.50809			−0.754045	+	0.656823i	$0.771900\pi$
$368$	224.000	−	387.979i	0.608696	−	1.05429i
$369$		0			0
$370$	311.573	+	374.863i	0.842088	+	1.01314i
$371$			292.465i			0.788316i
$372$		0			0
$373$		−	276.217i		−	0.740529i	−0.928926	−	0.370264i	$-0.879267\pi$
$373$		−	276.217i		−	0.740529i	0.928926	−	0.370264i	$-0.120733\pi$
$374$	−168.855	+	292.465i	−0.451484	+	0.781993i
$375$		0			0
$376$	32.0000			0.0851064
$377$			152.420i			0.404298i
$378$		0			0
$379$		−	103.923i		−	0.274203i	−0.990557	−	0.137102i	$-0.956221\pi$
$379$		−	103.923i		−	0.274203i	0.990557	−	0.137102i	$-0.0437787\pi$
$380$	−409.710	+	70.2693i	−1.07818	+	0.184919i
$381$		0			0
$382$	56.2850	+	32.4962i	0.147343	+	0.0850685i
$383$	−220.000			−0.574413			−0.287206	−	0.957869i	$-0.592727\pi$
$383$	−220.000			−0.574413			−0.287206	+	0.957869i	$0.592727\pi$
$384$		0			0
$385$	264.000	−	714.915i	0.685714	−	1.85692i
$386$	281.425	+	162.481i	0.729080	+	0.420935i
$387$		0			0
$388$	−562.850	+	324.962i	−1.45064	+	0.837530i
$389$	347.091			0.892264			0.446132	−	0.894967i	$-0.352801\pi$
$389$	347.091			0.892264			0.446132	+	0.894967i	$0.352801\pi$
$390$		0			0
$391$			290.985i			0.744206i
$392$	−312.000			−0.795918
$393$		0			0
$394$	−594.000	−	342.946i	−1.50761	−	0.870421i
$395$	−12.0000	+	32.4962i	−0.0303797	+	0.0822687i
$396$		0			0
$397$		−	341.210i		−	0.859470i	−0.902955	−	0.429735i	$-0.858607\pi$
$397$		−	341.210i		−	0.859470i	0.902955	−	0.429735i	$-0.141393\pi$
$398$	−36.0000	−	20.7846i	−0.0904523	−	0.0522226i
$399$		0			0
$400$	−377.140	+	133.287i	−0.942850	+	0.333218i
$401$	−581.612			−1.45040			−0.725201	−	0.688537i	$-0.758253\pi$
$401$	−581.612			−1.45040			−0.725201	+	0.688537i	$0.758253\pi$
$402$		0			0
$403$	−562.850			−1.39665
$404$	−243.902	−	422.450i	−0.603717	−	1.04567i
$405$		0			0
$406$	88.0000	−	152.420i	0.216749	−	0.375420i
$407$	792.000			1.94595
$408$		0			0
$409$	122.000			0.298289			0.149144	−	0.988815i	$-0.452348\pi$
$409$	122.000			0.298289			0.149144	+	0.988815i	$0.452348\pi$
$410$	−144.285	+	119.924i	−0.351915	+	0.292498i
$411$		0			0
$412$	318.948	+	552.435i	0.774146	+	1.34086i
$413$			152.420i			0.369057i
$414$		0			0
$415$	150.093	+	55.4256i	0.361671	+	0.133556i
$416$	−450.280	+	259.969i	−1.08240	+	0.624926i
$417$		0			0
$418$	−337.710	+	584.931i	−0.807919	+	1.39936i
$419$			503.690i			1.20213i	0.799202	+	0.601063i	$0.205256\pi$
$419$			503.690i			1.20213i	−0.799202	+	0.601063i	$0.794744\pi$
$420$		0			0
$421$	74.0000			0.175772			0.0878860	−	0.996131i	$-0.471989\pi$
$421$	74.0000			0.175772			0.0878860	+	0.996131i	$0.471989\pi$
$422$	−516.000	−	297.913i	−1.22275	−	0.705954i
$423$		0			0
$424$		−	249.415i		−	0.588244i
$425$	168.855	−	197.454i	0.397306	−	0.464597i
$426$		0			0
$427$	−544.088			−1.27421
$428$	368.000	+	637.395i	0.859813	+	1.48924i
$429$		0			0
$430$	288.570	−	239.849i	0.671093	−	0.557788i
$431$		−	779.908i		−	1.80953i	−0.425911	−	0.904765i	$-0.640046\pi$
$431$		−	779.908i		−	1.80953i	0.425911	−	0.904765i	$-0.359954\pi$
$432$		0			0
$433$		−	97.4885i		−	0.225147i	−0.993643	−	0.112573i	$-0.964091\pi$
$433$		−	97.4885i		−	0.225147i	0.993643	−	0.112573i	$-0.0359093\pi$
$434$	562.850	+	324.962i	1.29689	+	0.748759i
$435$		0			0
$436$	44.0000	+	76.2102i	0.100917	+	0.174794i
$437$			581.969i			1.33174i
$438$		0			0
$439$			339.482i			0.773307i	0.922225	+	0.386654i	$0.126369\pi$
$439$			339.482i			0.773307i	−0.922225	+	0.386654i	$0.873631\pi$
$440$	−225.140	+	609.682i	−0.511682	+	1.38564i
$441$		0			0
$442$	168.855	−	292.465i	0.382025	−	0.661686i
$443$	176.000			0.397291			0.198646	−	0.980071i	$-0.436346\pi$
$443$	176.000			0.397291			0.198646	+	0.980071i	$0.436346\pi$
$444$		0			0
$445$	−352.000	−	129.985i	−0.791011	−	0.292100i
$446$	−159.474	+	276.217i	−0.357565	+	0.619321i
$447$		0			0
$448$	600.373			1.34012
$449$	−469.042			−1.04464			−0.522318	−	0.852751i	$-0.674933\pi$
$449$	−469.042			−1.04464			−0.522318	+	0.852751i	$0.674933\pi$
$450$		0			0
$451$			304.841i			0.675922i
$452$	300.000	−	173.205i	0.663717	−	0.383197i
$453$		0			0
$454$	128.000	−	221.703i	0.281938	−	0.488332i
$455$	−264.000	+	714.915i	−0.580220	+	1.57124i
$456$		0			0
$457$		−	357.458i		−	0.782183i	−0.920352	−	0.391092i	$-0.872098\pi$
$457$		−	357.458i		−	0.782183i	0.920352	−	0.391092i	$-0.127902\pi$
$458$	134.000	−	232.095i	0.292576	−	0.506757i
$459$		0			0
$460$	94.6633	+	551.941i	0.205790	+	1.19987i
$461$	−497.184			−1.07849			−0.539245	−	0.842149i	$-0.681290\pi$
$461$	−497.184			−1.07849			−0.539245	+	0.842149i	$0.681290\pi$
$462$		0			0
$463$	347.091			0.749656			0.374828	−	0.927094i	$-0.377702\pi$
$463$	347.091			0.749656			0.374828	+	0.927094i	$0.377702\pi$
$464$	−75.0467	+	129.985i	−0.161738	+	0.280139i
$465$		0			0
$466$	522.000	+	301.377i	1.12017	+	0.646731i
$467$	−520.000			−1.11349			−0.556745	−	0.830683i	$-0.687950\pi$
$467$	−520.000			−1.11349			−0.556745	+	0.830683i	$0.687950\pi$
$468$		0			0
$469$	−176.000			−0.375267
$470$	−30.7617	+	25.5680i	−0.0654503	+	0.0543999i
$471$		0			0
$472$		−	129.985i		−	0.275391i
$473$		−	609.682i		−	1.28897i
$474$		0			0
$475$	337.710	−	394.908i	0.710968	−	0.831384i
$476$	−337.710	+	194.977i	−0.709475	+	0.409615i
$477$		0			0
$478$	281.425	+	162.481i	0.588755	+	0.339918i
$479$			812.404i			1.69604i	0.529963	+	0.848021i	$0.322206\pi$
$479$			812.404i			1.69604i	−0.529963	+	0.848021i	$0.677794\pi$
$480$		0			0
$481$	−792.000			−1.64657
$482$	50.0000	−	86.6025i	0.103734	−	0.179673i
$483$		0			0
$484$	286.000	+	495.367i	0.590909	+	1.02348i
$485$	281.425	−	762.102i	0.580258	−	1.57135i
$486$		0			0
$487$	290.806			0.597137			0.298569	−	0.954388i	$-0.403491\pi$
$487$	290.806			0.597137			0.298569	+	0.954388i	$0.403491\pi$
$488$	464.000			0.950820
$489$		0			0
$490$	299.926	−	249.288i	0.612094	−	0.508750i
$491$			406.202i			0.827295i	0.910437	+	0.413648i	$0.135745\pi$
$491$			406.202i			0.827295i	−0.910437	+	0.413648i	$0.864255\pi$
$492$		0			0
$493$		−	97.4885i		−	0.197745i
$494$	337.710	−	584.931i	0.683623	−	1.18407i
$495$		0			0
$496$	−480.000	−	277.128i	−0.967742	−	0.558726i
$497$			914.523i			1.84009i
$498$		0			0
$499$		−	838.313i		−	1.67999i	−0.542598	−	0.839993i	$-0.682559\pi$
$499$		−	838.313i		−	1.67999i	0.542598	−	0.839993i	$-0.317441\pi$
$500$	256.049	−	429.463i	0.512098	−	0.858927i
$501$		0			0
$502$	253.282	+	146.233i	0.504547	+	0.291300i
$503$	932.000			1.85288			0.926441	−	0.376439i	$-0.122852\pi$
$503$	932.000			1.85288			0.926441	+	0.376439i	$0.122852\pi$
$504$		0			0
$505$	572.000	+	211.225i	1.13267	+	0.418267i
$506$	787.990	+	454.946i	1.55729	+	0.899103i
$507$		0			0
$508$	−18.7617	−	32.4962i	−0.0369324	−	0.0639688i
$509$	−440.899			−0.866206			−0.433103	−	0.901344i	$-0.642581\pi$
$509$	−440.899			−0.866206			−0.433103	+	0.901344i	$0.642581\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−1.00000
$513$		0			0
$514$	42.0000	+	24.2487i	0.0817121	+	0.0471765i
$515$	−748.000	−	276.217i	−1.45243	−	0.536344i
$516$		0			0
$517$			64.9923i			0.125710i
$518$	792.000	+	457.261i	1.52896	+	0.882744i
$519$		0			0
$520$	225.140	−	609.682i	0.432961	−	1.17247i
$521$	431.518			0.828250			0.414125	−	0.910220i	$-0.364088\pi$
$521$	431.518			0.828250			0.414125	+	0.910220i	$0.364088\pi$
$522$		0			0
$523$	−243.902			−0.466351			−0.233176	−	0.972435i	$-0.574912\pi$
$523$	−243.902			−0.466351			−0.233176	+	0.972435i	$0.574912\pi$
$524$	−619.135	+	357.458i	−1.18156	+	0.682171i
$525$		0			0
$526$	−340.000	+	588.897i	−0.646388	+	1.11958i
$527$	360.000			0.683112
$528$		0			0
$529$	255.000			0.482042
$530$	199.282	+	239.763i	0.376005	+	0.452384i
$531$		0			0
$532$	−675.420	+	389.954i	−1.26959	+	0.732996i
$533$		−	304.841i		−	0.571934i
$534$		0			0
$535$	−863.036	−	318.697i	−1.61315	−	0.595696i
$536$	150.093			0.280025
$537$		0			0
$538$	178.236	−	308.713i	0.331293	−	0.573817i
$539$		−	633.675i		−	1.17565i
$540$		0			0
$541$	374.000			0.691312			0.345656	−	0.938361i	$-0.387656\pi$
$541$	374.000			0.691312			0.345656	+	0.938361i	$0.387656\pi$
$542$	−684.000	−	394.908i	−1.26199	−	0.728612i
$543$		0			0
$544$	288.000	−	166.277i	0.529412	−	0.305656i
$545$	−103.189	−	38.1051i	−0.189338	−	0.0699176i
$546$		0			0
$547$	938.083			1.71496			0.857480	−	0.514517i	$-0.172029\pi$
$547$	938.083			1.71496			0.857480	+	0.514517i	$0.172029\pi$
$548$	−732.000	+	422.620i	−1.33577	+	0.771205i
$549$		0			0
$550$	−270.707	−	765.975i	−0.492195	−	1.39268i
$551$		−	194.977i		−	0.353860i
$552$		0			0
$553$			64.9923i			0.117527i
$554$	−196.997	−	113.737i	−0.355591	−	0.205301i
$555$		0			0
$556$	−312.000	+	180.133i	−0.561151	+	0.323981i
$557$			426.084i			0.764963i	0.923963	+	0.382482i	$0.124930\pi$
$557$			426.084i			0.764963i	−0.923963	+	0.382482i	$0.875070\pi$
$558$		0			0
$559$			609.682i			1.09067i
$560$	−577.140	+	479.697i	−1.03061	+	0.856602i
$561$		0			0
$562$	−75.0467	+	129.985i	−0.133535	+	0.231289i
$563$	−136.000			−0.241563			−0.120782	−	0.992679i	$-0.538540\pi$
$563$	−136.000			−0.241563			−0.120782	+	0.992679i	$0.538540\pi$
$564$		0			0
$565$	−150.000	+	406.202i	−0.265487	+	0.718941i
$566$	318.948	−	552.435i	0.563513	−	0.976033i
$567$		0			0
$568$		−	779.908i		−	1.37308i
$569$	881.798			1.54973			0.774867	−	0.632125i	$-0.217817\pi$
$569$	881.798			1.54973			0.774867	+	0.632125i	$0.217817\pi$
$570$		0			0
$571$			949.164i			1.66228i	0.556061	+	0.831142i	$0.312312\pi$
$571$			949.164i			1.66228i	−0.556061	+	0.831142i	$0.687688\pi$
$572$	−528.000	−	914.523i	−0.923077	−	1.59882i
$573$		0			0
$574$	−176.000	+	304.841i	−0.306620	+	0.531082i
$575$	−532.000	−	454.946i	−0.925217	−	0.791211i
$576$		0			0
$577$			389.954i			0.675830i	0.941177	+	0.337915i	$0.109722\pi$
$577$			389.954i			0.675830i	−0.941177	+	0.337915i	$0.890278\pi$
$578$	181.000	−	313.501i	0.313149	−	0.542390i
$579$		0			0
$580$	−31.7150	−	184.917i	−0.0546811	−	0.318822i
$581$	300.187			0.516672
$582$		0			0
$583$	506.565			0.868893
$584$		0			0
$585$		0			0
$586$	−606.000	−	349.874i	−1.03413	−	0.597055i
$587$	680.000			1.15843			0.579216	−	0.815174i	$-0.303359\pi$
$587$	680.000			1.15843			0.579216	+	0.815174i	$0.303359\pi$
$588$		0			0
$589$	720.000			1.22241
$590$	103.858	+	124.954i	0.176030	+	0.211787i
$591$		0			0
$592$	−675.420	−	389.954i	−1.14091	−	0.658706i
$593$			114.315i			0.192775i	0.995344	+	0.0963873i	$0.0307287\pi$
$593$			114.315i			0.192775i	−0.995344	+	0.0963873i	$0.969271\pi$
$594$		0			0
$595$	168.855	−	457.261i	0.283790	−	0.768507i
$596$	−469.042	−	812.404i	−0.786983	−	1.36309i
$597$		0			0
$598$	−787.990	−	454.946i	−1.31771	−	0.760780i
$599$		−	1104.87i		−	1.84452i	−0.386567	−	0.922261i	$-0.626339\pi$
$599$		−	1104.87i		−	1.84452i	0.386567	−	0.922261i	$-0.373661\pi$
$600$		0			0
$601$	−682.000			−1.13478			−0.567388	−	0.823451i	$-0.692046\pi$
$601$	−682.000			−1.13478			−0.567388	+	0.823451i	$0.692046\pi$
$602$	352.000	−	609.682i	0.584718	−	1.01276i
$603$		0			0
$604$	168.000	−	96.9948i	0.278146	−	0.160587i
$605$	−670.729	−	247.683i	−1.10864	−	0.409394i
$606$		0			0
$607$	−272.044			−0.448178			−0.224089	−	0.974569i	$-0.571941\pi$
$607$	−272.044			−0.448178			−0.224089	+	0.974569i	$0.571941\pi$
$608$	576.000	−	332.554i	0.947368	−	0.546963i
$609$		0			0
$610$	−446.044	+	370.735i	−0.731220	+	0.607763i
$611$		−	64.9923i		−	0.106370i
$612$		0			0
$613$			341.210i			0.556623i	0.960491	+	0.278311i	$0.0897747\pi$
$613$			341.210i			0.556623i	−0.960491	+	0.278311i	$0.910225\pi$
$614$	262.663	−	454.946i	0.427790	−	0.740955i
$615$		0			0
$616$			1219.36i			1.97949i
$617$			336.018i			0.544599i	0.962212	+	0.272300i	$0.0877842\pi$
$617$			336.018i			0.544599i	−0.962212	+	0.272300i	$0.912216\pi$
$618$		0			0
$619$			381.051i			0.615592i	0.951452	+	0.307796i	$0.0995914\pi$
$619$			381.051i			0.615592i	−0.951452	+	0.307796i	$0.900409\pi$
$620$	682.850	−	117.115i	1.10137	−	0.188896i
$621$		0			0
$622$	−56.2850	−	32.4962i	−0.0904903	−	0.0522446i
$623$	−704.000			−1.13002
$624$		0			0
$625$	97.0000	+	617.427i	0.155200	+	0.987883i
$626$	−619.135	−	357.458i	−0.989033	−	0.571019i
$627$		0			0
$628$	56.2850	−	32.4962i	0.0896258	−	0.0517455i
$629$	506.565			0.805350
$630$		0			0
$631$		−	145.492i		−	0.230574i	−0.993332	−	0.115287i	$-0.963221\pi$
$631$		−	145.492i		−	0.230574i	0.993332	−	0.115287i	$-0.0367788\pi$
$632$		−	55.4256i		−	0.0876988i
$633$		0			0
$634$	−78.0000	−	45.0333i	−0.123028	−	0.0710305i
$635$	44.0000	+	16.2481i	0.0692913	+	0.0255875i
$636$		0			0
$637$			633.675i			0.994780i
$638$	−264.000	−	152.420i	−0.413793	−	0.238904i
$639$		0			0
$640$	492.187	−	409.087i	0.769042	−	0.639199i
$641$	431.518			0.673195			0.336598	−	0.941649i	$-0.390724\pi$
$641$	431.518			0.673195			0.336598	+	0.941649i	$0.390724\pi$
$642$		0			0
$643$	−356.472			−0.554388			−0.277194	−	0.960814i	$-0.589405\pi$
$643$	−356.472			−0.554388			−0.277194	+	0.960814i	$0.589405\pi$
$644$	525.327	+	909.892i	0.815724	+	1.41288i
$645$		0			0
$646$	−216.000	+	374.123i	−0.334365	+	0.579138i
$647$	−364.000			−0.562597			−0.281298	−	0.959620i	$-0.590765\pi$
$647$	−364.000			−0.562597			−0.281298	+	0.959620i	$0.590765\pi$
$648$		0			0
$649$	264.000			0.406780
$650$	270.707	+	765.975i	0.416473	+	1.17842i
$651$		0			0
$652$	−412.757	−	714.915i	−0.633062	−	1.09650i
$653$		−	162.813i		−	0.249330i	−0.992199	−	0.124665i	$-0.960214\pi$
$653$		−	162.813i		−	0.249330i	0.992199	−	0.124665i	$-0.0397857\pi$
$654$		0			0
$655$	309.567	−	838.313i	0.472622	−	1.27987i
$656$	150.093	−	259.969i	0.228801	−	0.396295i
$657$		0			0
$658$	−37.5233	+	64.9923i	−0.0570263	+	0.0987725i
$659$			178.729i			0.271212i	0.990763	+	0.135606i	$0.0432982\pi$
$659$			178.729i			0.271212i	−0.990763	+	0.135606i	$0.956702\pi$
$660$		0			0
$661$	662.000			1.00151			0.500756	−	0.865588i	$-0.333055\pi$
$661$	662.000			1.00151			0.500756	+	0.865588i	$0.333055\pi$
$662$	−564.000	−	325.626i	−0.851964	−	0.491881i
$663$		0			0
$664$	−256.000			−0.385542
$665$	337.710	−	914.523i	0.507834	−	1.37522i
$666$		0			0
$667$	−262.663			−0.393798
$668$	488.000	+	845.241i	0.730539	+	1.26533i
$669$		0			0
$670$	−144.285	+	119.924i	−0.215351	+	0.178992i
$671$			942.388i			1.40445i
$672$		0			0
$673$			1202.36i			1.78656i	0.449497	+	0.893282i	$0.351603\pi$
$673$			1202.36i			1.78656i	−0.449497	+	0.893282i	$0.648397\pi$
$674$	112.570	+	64.9923i	0.167018	+	0.0964278i
$675$		0			0
$676$	190.000	+	329.090i	0.281065	+	0.486819i
$677$			495.367i			0.731708i	0.930672	+	0.365854i	$0.119223\pi$
$677$			495.367i			0.731708i	−0.930672	+	0.365854i	$0.880777\pi$
$678$		0			0
$679$		−	1524.20i		−	2.24478i
$680$	−144.000	+	389.954i	−0.211765	+	0.573462i
$681$		0			0
$682$	562.850	−	974.885i	0.825293	−	1.42945i
$683$	−88.0000			−0.128843			−0.0644217	−	0.997923i	$-0.520520\pi$
$683$	−88.0000			−0.128843			−0.0644217	+	0.997923i	$0.520520\pi$
$684$		0			0
$685$	366.000	−	991.133i	0.534307	−	1.44691i
$686$	−93.8083	+	162.481i	−0.136747	+	0.236852i
$687$		0			0
$688$	−300.187	+	519.938i	−0.436318	+	0.755725i
$689$	−506.565			−0.735218
$690$		0			0
$691$			339.482i			0.491291i	0.969360	+	0.245645i	$0.0789999\pi$
$691$			339.482i			0.491291i	−0.969360	+	0.245645i	$0.921000\pi$
$692$	132.000	−	76.2102i	0.190751	−	0.110130i
$693$		0			0
$694$	104.000	−	180.133i	0.149856	−	0.259558i
$695$	156.000	−	422.450i	0.224460	−	0.607842i
$696$		0			0
$697$			194.977i			0.279737i
$698$	−598.000	+	1035.77i	−0.856734	+	1.48391i
$699$		0			0
$700$	171.528	−	922.268i	0.245041	−	1.31753i
$701$	−834.894			−1.19100			−0.595502	−	0.803354i	$-0.703047\pi$
$701$	−834.894			−1.19100			−0.595502	+	0.803354i	$0.703047\pi$
$702$		0			0
$703$	1013.13			1.44115
$704$		−	1039.88i		−	1.47710i
$705$		0			0
$706$	138.000	+	79.6743i	0.195467	+	0.112853i
$707$	1144.00			1.61810
$708$		0			0
$709$	−490.000			−0.691114			−0.345557	−	0.938398i	$-0.612310\pi$
$709$	−490.000			−0.691114			−0.345557	+	0.938398i	$0.612310\pi$
$710$	623.145	+	749.727i	0.877669	+	1.05595i
$711$		0			0
$712$	600.373			0.843221
$713$		−	969.948i		−	1.36038i
$714$		0			0
$715$	1238.27	+	457.261i	1.73185	+	0.639526i
$716$	506.565	−	292.465i	0.707493	−	0.408471i
$717$		0			0
$718$	−337.710	−	194.977i	−0.470348	−	0.271556i
$719$			584.931i			0.813534i	0.913532	+	0.406767i	$0.133344\pi$
$719$			584.931i			0.813534i	−0.913532	+	0.406767i	$0.866656\pi$
$720$		0			0
$721$	−1496.00			−2.07490
$722$	−71.0000	+	122.976i	−0.0983380	+	0.170326i
$723$		0			0
$724$	−460.000	−	796.743i	−0.635359	−	1.10047i
$725$	178.236	+	152.420i	0.245842	+	0.210235i
$726$		0			0
$727$	178.236			0.245166			0.122583	−	0.992458i	$-0.460882\pi$
$727$	178.236			0.245166			0.122583	+	0.992458i	$0.460882\pi$
$728$		−	1219.36i		−	1.67495i
$729$		0			0
$730$		0			0
$731$		−	389.954i		−	0.533453i
$732$		0			0
$733$		−	81.2404i		−	0.110833i	−0.998463	−	0.0554164i	$-0.982351\pi$
$733$		−	81.2404i		−	0.110833i	0.998463	−	0.0554164i	$-0.0176486\pi$
$734$	−553.469	+	958.637i	−0.754045	+	1.30604i
$735$		0			0
$736$	−448.000	−	775.959i	−0.608696	−	1.05429i
$737$			304.841i			0.413624i
$738$		0			0
$739$		−	311.769i		−	0.421880i	−0.977499	−	0.210940i	$-0.932348\pi$
$739$		−	311.769i		−	0.421880i	0.977499	−	0.210940i	$-0.0676524\pi$
$740$	960.855	−	164.796i	1.29845	−	0.222697i
$741$		0			0
$742$	506.565	+	292.465i	0.682702	+	0.394158i
$743$	−676.000			−0.909825			−0.454913	−	0.890536i	$-0.650329\pi$
$743$	−676.000			−0.909825			−0.454913	+	0.890536i	$0.650329\pi$
$744$		0			0
$745$	1100.00	+	406.202i	1.47651	+	0.545237i
$746$	−478.422	−	276.217i	−0.641317	−	0.370264i
$747$		0			0
$748$	337.710	+	584.931i	0.451484	+	0.781993i
$749$	−1726.07			−2.30450
$750$		0			0
$751$			1281.72i			1.70668i	0.521354	+	0.853341i	$0.325427\pi$
$751$			1281.72i			1.70668i	−0.521354	+	0.853341i	$0.674573\pi$
$752$	32.0000	−	55.4256i	0.0425532	−	0.0737043i
$753$		0			0
$754$	264.000	+	152.420i	0.350133	+	0.202149i
$755$	−84.0000	+	227.473i	−0.111258	+	0.301289i
$756$		0			0
$757$			341.210i			0.450739i	0.974273	+	0.225370i	$0.0723590\pi$
$757$			341.210i			0.450739i	−0.974273	+	0.225370i	$0.927641\pi$
$758$	−180.000	−	103.923i	−0.237467	−	0.137102i
$759$		0			0
$760$	−288.000	+	779.908i	−0.378947	+	1.02619i
$761$	994.368			1.30666			0.653330	−	0.757073i	$-0.273371\pi$
$761$	994.368			1.30666			0.653330	+	0.757073i	$0.273371\pi$
$762$		0			0
$763$	−206.378			−0.270483
$764$	112.570	−	64.9923i	0.147343	−	0.0850685i
$765$		0			0
$766$	−220.000	+	381.051i	−0.287206	+	0.497456i
$767$	−264.000			−0.344198
$768$		0			0
$769$	314.000			0.408322			0.204161	−	0.978937i	$-0.434553\pi$
$769$	314.000			0.408322			0.204161	+	0.978937i	$0.434553\pi$
$770$	−974.270	−	1172.18i	−1.26529	−	1.52231i
$771$		0			0
$772$	562.850	−	324.962i	0.729080	−	0.420935i
$773$			904.131i			1.16964i	0.811164	+	0.584819i	$0.198835\pi$
$773$			904.131i			1.16964i	−0.811164	+	0.584819i	$0.801165\pi$
$774$		0			0
$775$	−562.850	+	658.179i	−0.726258	+	0.849264i
$776$			1299.85i			1.67506i
$777$		0			0
$778$	347.091	−	601.179i	0.446132	−	0.772723i
$779$			389.954i			0.500583i
$780$		0			0
$781$	1584.00			2.02817
$782$	504.000	+	290.985i	0.644501	+	0.372103i
$783$		0			0
$784$	−312.000	+	540.400i	−0.397959	+	0.689286i
$785$	−28.1425	+	76.2102i	−0.0358503	+	0.0970831i
$786$		0			0
$787$	431.518			0.548308			0.274154	−	0.961686i	$-0.411602\pi$
$787$	431.518			0.548308			0.274154	+	0.961686i	$0.411602\pi$
$788$	−1188.00	+	685.892i	−1.50761	+	0.870421i
$789$		0			0
$790$	44.2850	+	53.2808i	0.0560569	+	0.0674440i
$791$			812.404i			1.02706i
$792$		0			0
$793$		−	942.388i		−	1.18838i
$794$	−590.992	−	341.210i	−0.744323	−	0.429735i
$795$		0			0
$796$	−72.0000	+	41.5692i	−0.0904523	+	0.0522226i
$797$			1292.11i			1.62122i	0.585589	+	0.810608i	$0.300863\pi$
$797$			1292.11i			1.62122i	−0.585589	+	0.810608i	$0.699137\pi$
$798$		0			0
$799$			41.5692i			0.0520266i
$800$	−146.280	+	786.513i	−0.182850	+	0.983141i
$801$		0			0
$802$	−581.612	+	1007.38i	−0.725201	+	1.25609i
$803$		0			0
$804$		0			0
$805$	−1232.00	−	454.946i	−1.53043	−	0.565150i
$806$	−562.850	+	974.885i	−0.698325	+	1.20953i
$807$		0			0
$808$	−975.606			−1.20743
$809$	1219.51			1.50743			0.753713	−	0.657203i	$-0.228261\pi$
$809$	1219.51			1.50743			0.753713	+	0.657203i	$0.228261\pi$
$810$		0			0
$811$		−	1018.45i		−	1.25579i	−0.778298	−	0.627895i	$-0.783917\pi$
$811$		−	1018.45i		−	1.25579i	0.778298	−	0.627895i	$-0.216083\pi$
$812$	−176.000	−	304.841i	−0.216749	−	0.375420i
$813$		0			0
$814$	792.000	−	1371.78i	0.972973	−	1.68524i
$815$	968.000	+	357.458i	1.18773	+	0.438598i
$816$		0			0
$817$		−	779.908i		−	0.954599i
$818$	122.000	−	211.310i	0.149144	−	0.258325i
$819$		0			0
$820$	63.4300	+	369.833i	0.0773537	+	0.451016i
$821$	−497.184			−0.605584			−0.302792	−	0.953057i	$-0.597919\pi$
$821$	−497.184			−0.605584			−0.302792	+	0.953057i	$0.597919\pi$
$822$		0			0
$823$	−440.899			−0.535722			−0.267861	−	0.963458i	$-0.586317\pi$
$823$	−440.899			−0.535722			−0.267861	+	0.963458i	$0.586317\pi$
$824$	1275.79			1.54829
$825$		0			0
$826$	264.000	+	152.420i	0.319613	+	0.184528i
$827$	752.000			0.909311			0.454655	−	0.890667i	$-0.349762\pi$
$827$	752.000			0.909311			0.454655	+	0.890667i	$0.349762\pi$
$828$		0			0
$829$	−1030.00			−1.24246			−0.621230	−	0.783628i	$-0.713367\pi$
$829$	−1030.00			−1.24246			−0.621230	+	0.783628i	$0.713367\pi$
$830$	246.093	−	204.544i	0.296498	−	0.246438i
$831$		0			0
$832$			1039.88i			1.24985i
$833$		−	405.300i		−	0.486554i
$834$		0			0
$835$	−1144.46	−	422.620i	−1.37061	−	0.506132i
$836$	675.420	+	1169.86i	0.807919	+	1.39936i
$837$		0			0
$838$	872.417	+	503.690i	1.04107	+	0.601063i
$839$			519.938i			0.619712i	0.950783	+	0.309856i	$0.100281\pi$
$839$			519.938i			0.619712i	−0.950783	+	0.309856i	$0.899719\pi$
$840$		0			0
$841$	−753.000			−0.895363
$842$	74.0000	−	128.172i	0.0878860	−	0.152223i
$843$		0			0
$844$	−1032.00	+	595.825i	−1.22275	+	0.705954i
$845$	−445.589	−	164.545i	−0.527325	−	0.194728i
$846$		0			0
$847$	−1341.46			−1.58378
$848$	−432.000	−	249.415i	−0.509434	−	0.294122i
$849$		0			0
$850$	−173.145	−	489.919i	−0.203700	−	0.576375i
$851$		−	1364.84i		−	1.60381i
$852$		0			0
$853$		−	698.667i		−	0.819071i	−0.912294	−	0.409535i	$-0.865691\pi$
$853$		−	698.667i		−	0.819071i	0.912294	−	0.409535i	$-0.134309\pi$
$854$	−544.088	+	942.388i	−0.637106	+	1.10350i
$855$		0			0
$856$	1472.00			1.71963
$857$		−	897.202i		−	1.04691i	−0.852053	−	0.523455i	$-0.824643\pi$
$857$		−	897.202i		−	1.04691i	0.852053	−	0.523455i	$-0.175357\pi$
$858$		0			0
$859$			533.472i			0.621038i	0.950567	+	0.310519i	$0.100503\pi$
$859$			533.472i			0.621038i	−0.950567	+	0.310519i	$0.899497\pi$
$860$	−126.860	−	739.666i	−0.147512	−	0.860077i
$861$		0			0
$862$	−1350.84	−	779.908i	−1.56710	−	0.904765i
$863$	−220.000			−0.254925			−0.127462	−	0.991843i	$-0.540683\pi$
$863$	−220.000			−0.254925			−0.127462	+	0.991843i	$0.540683\pi$
$864$		0			0
$865$	−66.0000	+	178.729i	−0.0763006	+	0.206623i
$866$	−168.855	−	97.4885i	−0.194983	−	0.112573i
$867$		0			0
$868$	1125.70	−	649.923i	1.29689	−	0.748759i
$869$	112.570			0.129540
$870$		0			0
$871$		−	304.841i		−	0.349990i
$872$	176.000			0.201835
$873$		0			0
$874$	1008.00	+	581.969i	1.15332	+	0.665869i
$875$	572.000	+	1023.63i	0.653714	+	1.16986i
$876$		0			0
$877$		−	763.660i		−	0.870764i	−0.900246	−	0.435382i	$-0.856613\pi$
$877$		−	763.660i		−	0.870764i	0.900246	−	0.435382i	$-0.143387\pi$
$878$	588.000	+	339.482i	0.669704	+	0.386654i
$879$		0			0
$880$	830.860	+	999.636i	0.944159	+	1.13595i
$881$	−1088.18			−1.23516			−0.617580	−	0.786508i	$-0.711887\pi$
$881$	−1088.18			−1.23516			−0.617580	+	0.786508i	$0.711887\pi$
$882$		0			0
$883$	−1257.03			−1.42359			−0.711796	−	0.702386i	$-0.752118\pi$
$883$	−1257.03			−1.42359			−0.711796	+	0.702386i	$0.752118\pi$
$884$	−337.710	−	584.931i	−0.382025	−	0.661686i
$885$		0			0
$886$	176.000	−	304.841i	0.198646	−	0.344064i
$887$	140.000			0.157835			0.0789177	−	0.996881i	$-0.474854\pi$
$887$	140.000			0.157835			0.0789177	+	0.996881i	$0.474854\pi$
$888$		0			0
$889$	88.0000			0.0989876
$890$	−577.140	+	479.697i	−0.648472	+	0.538986i
$891$		0			0
$892$	318.948	+	552.435i	0.357565	+	0.619321i
$893$			83.1384i			0.0931002i
$894$		0			0
$895$	−253.282	+	685.892i	−0.282997	+	0.766360i
$896$	600.373	−	1039.88i	0.670059	−	1.16058i
$897$		0			0
$898$	−469.042	+	812.404i	−0.522318	+	0.904681i
$899$			324.962i			0.361470i
$900$		0			0
$901$	324.000			0.359600
$902$	528.000	+	304.841i	0.585366	+	0.337961i
$903$		0			0
$904$		−	692.820i		−	0.766394i
$905$	1078.80	+	398.372i	1.19204	+	0.440190i
$906$		0			0
$907$	−75.0467			−0.0827416			−0.0413708	−	0.999144i	$-0.513172\pi$
$907$	−75.0467			−0.0827416			−0.0413708	+	0.999144i	$0.513172\pi$
$908$	−256.000	−	443.405i	−0.281938	−	0.488332i
$909$		0			0
$910$	974.270	+	1172.18i	1.07063	+	1.28811i
$911$		−	649.923i		−	0.713417i	−0.934216	−	0.356709i	$-0.883899\pi$
$911$		−	649.923i		−	0.713417i	0.934216	−	0.356709i	$-0.116101\pi$
$912$		0			0
$913$		−	519.938i		−	0.569484i
$914$	−619.135	−	357.458i	−0.677390	−	0.391092i
$915$		0			0
$916$	−268.000	−	464.190i	−0.292576	−	0.506757i
$917$		−	1676.63i		−	1.82838i
$918$		0			0
$919$			1101.58i			1.19868i	0.800496	+	0.599339i	$0.204570\pi$
$919$			1101.58i			1.19868i	−0.800496	+	0.599339i	$0.795430\pi$
$920$	1050.65	+	387.979i	1.14201	+	0.421717i
$921$		0			0
$922$	−497.184	+	861.148i	−0.539245	+	0.934000i
$923$	−1584.00			−1.71614
$924$		0			0
$925$	−792.000	+	926.140i	−0.856216	+	1.00123i
$926$	347.091	−	601.179i	0.374828	−	0.649221i
$927$		0			0
$928$	150.093	+	259.969i	0.161738	+	0.280139i
$929$	1219.51			1.31271			0.656355	−	0.754452i	$-0.272097\pi$
$929$	1219.51			1.31271			0.656355	+	0.754452i	$0.272097\pi$
$930$		0			0
$931$		−	810.600i		−	0.870676i
$932$	1044.00	−	602.754i	1.12017	−	0.646731i
$933$		0			0
$934$	−520.000	+	900.666i	−0.556745	+	0.964311i
$935$	−792.000	−	292.465i	−0.847059	−	0.312797i
$936$		0			0
$937$		−	1754.79i		−	1.87278i	−0.350965	−	0.936389i	$-0.614146\pi$
$937$		−	1754.79i		−	1.87278i	0.350965	−	0.936389i	$-0.385854\pi$
$938$	−176.000	+	304.841i	−0.187633	+	0.324990i
$939$		0			0
$940$	13.5233	+	78.8487i	0.0143865	+	0.0838816i
$941$	−1285.17			−1.36575			−0.682877	−	0.730534i	$-0.739271\pi$
$941$	−1285.17			−1.36575			−0.682877	+	0.730534i	$0.739271\pi$
$942$		0			0
$943$	525.327			0.557080
$944$	−225.140	−	129.985i	−0.238496	−	0.137696i
$945$		0			0
$946$	−1056.00	−	609.682i	−1.11628	−	0.644484i
$947$	−1480.00			−1.56283			−0.781415	−	0.624012i	$-0.785502\pi$
$947$	−1480.00			−1.56283			−0.781415	+	0.624012i	$0.785502\pi$
$948$		0			0
$949$		0			0
$950$	−346.290	−	979.838i	−0.364516	−	1.03141i
$951$		0			0
$952$			779.908i			0.819231i
$953$			1486.10i			1.55939i	0.626159	+	0.779695i	$0.284626\pi$
$953$			1486.10i			1.55939i	−0.626159	+	0.779695i	$0.715374\pi$
$954$		0			0
$955$	−56.2850	+	152.420i	−0.0589372	+	0.159603i
$956$	562.850	−	324.962i	0.588755	−	0.339918i
$957$		0			0
$958$	1407.12	+	812.404i	1.46881	+	0.848021i
$959$		−	1982.27i		−	2.06701i
$960$		0			0
$961$	−239.000			−0.248699
$962$	−792.000	+	1371.78i	−0.823285	+	1.42597i
$963$		0			0
$964$	−100.000	−	173.205i	−0.103734	−	0.179673i
$965$	−281.425	+	762.102i	−0.291632	+	0.789743i
$966$		0			0
$967$	1247.65			1.29023			0.645114	−	0.764086i	$-0.276810\pi$
$967$	1247.65			1.29023			0.645114	+	0.764086i	$0.276810\pi$
$968$	1144.00			1.18182
$969$		0			0
$970$	−1038.58	−	1249.54i	−1.07070	−	1.28819i
$971$		−	438.698i		−	0.451800i	−0.974150	−	0.225900i	$-0.927468\pi$
$971$		−	438.698i		−	0.451800i	0.974150	−	0.225900i	$-0.0725323\pi$
$972$		0			0
$973$		−	844.900i		−	0.868345i
$974$	290.806	−	503.690i	0.298569	−	0.517136i
$975$		0			0
$976$	464.000	−	803.672i	0.475410	−	0.823434i
$977$		−	869.490i		−	0.889959i	−0.895541	−	0.444979i	$-0.853211\pi$
$977$		−	869.490i		−	0.889959i	0.895541	−	0.444979i	$-0.146789\pi$
$978$		0			0
$979$			1219.36i			1.24552i
$980$	−131.852	−	768.775i	−0.134543	−	0.784464i
$981$		0			0
$982$	703.562	+	406.202i	0.716459	+	0.413648i
$983$	860.000			0.874873			0.437436	−	0.899249i	$-0.355887\pi$
$983$	860.000			0.874873			0.437436	+	0.899249i	$0.355887\pi$
$984$		0			0
$985$	594.000	−	1608.56i	0.603046	−	1.63306i
$986$	−168.855	−	97.4885i	−0.171253	−	0.0988727i
$987$		0			0
$988$	−675.420	−	1169.86i	−0.683623	−	1.18407i
$989$	−1050.65			−1.06234
$990$		0			0
$991$		−	436.477i		−	0.440441i	−0.975450	−	0.220220i	$-0.929322\pi$
$991$		−	436.477i		−	0.440441i	0.975450	−	0.220220i	$-0.0706777\pi$
$992$	−960.000	+	554.256i	−0.967742	+	0.558726i
$993$		0			0
$994$	1584.00	+	914.523i	1.59356	+	0.920043i
$995$	36.0000	−	97.4885i	0.0361809	−	0.0979784i
$996$		0			0
$997$			1056.12i			1.05930i	0.848215	+	0.529651i	$0.177677\pi$
$997$			1056.12i			1.05930i	−0.848215	+	0.529651i	$0.822323\pi$
$998$	−1452.00	−	838.313i	−1.45491	−	0.839993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.f.g.19.2	yes	4
3.2	odd	2		180.3.f.d.19.3	yes	4
4.3	odd	2		180.3.f.d.19.2	yes	4
5.2	odd	4		900.3.c.s.451.8		8
5.3	odd	4		900.3.c.s.451.1		8
5.4	even	2		180.3.f.d.19.4	yes	4
12.11	even	2	inner	180.3.f.g.19.3	yes	4
15.2	even	4		900.3.c.s.451.2		8
15.8	even	4		900.3.c.s.451.7		8
15.14	odd	2	inner	180.3.f.g.19.1	yes	4
20.3	even	4		900.3.c.s.451.4		8
20.7	even	4		900.3.c.s.451.5		8
20.19	odd	2	inner	180.3.f.g.19.4	yes	4
60.23	odd	4		900.3.c.s.451.6		8
60.47	odd	4		900.3.c.s.451.3		8
60.59	even	2		180.3.f.d.19.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.f.d.19.1	✓	4	60.59	even	2
180.3.f.d.19.2	yes	4	4.3	odd	2
180.3.f.d.19.3	yes	4	3.2	odd	2
180.3.f.d.19.4	yes	4	5.4	even	2
180.3.f.g.19.1	yes	4	15.14	odd	2	inner
180.3.f.g.19.2	yes	4	1.1	even	1	trivial
180.3.f.g.19.3	yes	4	12.11	even	2	inner
180.3.f.g.19.4	yes	4	20.19	odd	2	inner
900.3.c.s.451.1		8	5.3	odd	4
900.3.c.s.451.2		8	15.2	even	4
900.3.c.s.451.3		8	60.47	odd	4
900.3.c.s.451.4		8	20.3	even	4
900.3.c.s.451.5		8	20.7	even	4
900.3.c.s.451.6		8	60.23	odd	4
900.3.c.s.451.7		8	15.8	even	4
900.3.c.s.451.8		8	5.2	odd	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.69042 + 1.73205i) q^{5} +9.38083 q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(4.69042 + 1.73205i) q^{5} +9.38083 q^{7} -8.00000 q^{8} +(7.69042 - 6.39199i) q^{10} -16.2481i q^{11} +16.2481i q^{13} +(9.38083 - 16.2481i) q^{14} +(-8.00000 + 13.8564i) q^{16} -10.3923i q^{17} -20.7846i q^{19} +(-3.38083 - 19.7122i) q^{20} +(-28.1425 - 16.2481i) q^{22} -28.0000 q^{23} +(19.0000 + 16.2481i) q^{25} +(28.1425 + 16.2481i) q^{26} +(-18.7617 - 32.4962i) q^{28} +9.38083 q^{29} +34.6410i q^{31} +(16.0000 + 27.7128i) q^{32} +(-18.0000 - 10.3923i) q^{34} +(44.0000 + 16.2481i) q^{35} +48.7442i q^{37} +(-36.0000 - 20.7846i) q^{38} +(-37.5233 - 13.8564i) q^{40} -18.7617 q^{41} +37.5233 q^{43} +(-56.2850 + 32.4962i) q^{44} +(-28.0000 + 48.4974i) q^{46} -4.00000 q^{47} +39.0000 q^{49} +(47.1425 - 16.6609i) q^{50} +(56.2850 - 32.4962i) q^{52} +31.1769i q^{53} +(28.1425 - 76.2102i) q^{55} -75.0467 q^{56} +(9.38083 - 16.2481i) q^{58} +16.2481i q^{59} -58.0000 q^{61} +(60.0000 + 34.6410i) q^{62} +64.0000 q^{64} +(-28.1425 + 76.2102i) q^{65} -18.7617 q^{67} +(-36.0000 + 20.7846i) q^{68} +(72.1425 - 59.9622i) q^{70} +97.4885i q^{71} +(84.4275 + 48.7442i) q^{74} +(-72.0000 + 41.5692i) q^{76} -152.420i q^{77} +6.92820i q^{79} +(-61.5233 + 51.1359i) q^{80} +(-18.7617 + 32.4962i) q^{82} +32.0000 q^{83} +(18.0000 - 48.7442i) q^{85} +(37.5233 - 64.9923i) q^{86} +129.985i q^{88} -75.0467 q^{89} +152.420i q^{91} +(56.0000 + 96.9948i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(36.0000 - 97.4885i) q^{95} -162.481i q^{97} +(39.0000 - 67.5500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 12 q^{10} - 32 q^{16} + 24 q^{20} - 112 q^{23} + 76 q^{25} + 64 q^{32} - 72 q^{34} + 176 q^{35} - 144 q^{38} - 112 q^{46} - 16 q^{47} + 156 q^{49} + 76 q^{50} - 232 q^{61} + 240 q^{62} + 256 q^{64} - 144 q^{68} + 176 q^{70} - 288 q^{76} - 96 q^{80} + 128 q^{83} + 72 q^{85} + 224 q^{92} - 16 q^{94} + 144 q^{95} + 156 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 12 * q^10 - 32 * q^16 + 24 * q^20 - 112 * q^23 + 76 * q^25 + 64 * q^32 - 72 * q^34 + 176 * q^35 - 144 * q^38 - 112 * q^46 - 16 * q^47 + 156 * q^49 + 76 * q^50 - 232 * q^61 + 240 * q^62 + 256 * q^64 - 144 * q^68 + 176 * q^70 - 288 * q^76 - 96 * q^80 + 128 * q^83 + 72 * q^85 + 224 * q^92 - 16 * q^94 + 144 * q^95 + 156 * q^98

Introduction

L-functions

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