LMFDB - Embedded newform 180.2.h.b.179.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(179,180)]

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, 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("180.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.h (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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 $ x^8 - 8x^6 + 13x^4 + 12*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.7
Root			$2.15988 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	180.179
Dual form			180.2.h.b.179.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +(1.73205 - 1.41421i) q^{5} +3.16228 q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})$	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +(1.73205 - 1.41421i) q^{5} +3.16228 q^{7} +(-2.59808 + 1.11803i) q^{8} +(3.08114 + 0.711747i) q^{10} -5.47723 q^{11} +2.44949i q^{13} +(2.73861 + 3.53553i) q^{14} +(-3.50000 - 1.93649i) q^{16} +(1.87259 + 4.06121i) q^{20} +(-4.74342 - 6.12372i) q^{22} -4.47214i q^{23} +(1.00000 - 4.89898i) q^{25} +(-2.73861 + 2.12132i) q^{26} +(-1.58114 + 6.12372i) q^{28} -2.82843i q^{29} -7.74597i q^{31} +(-0.866025 - 5.59017i) q^{32} +(5.47723 - 4.47214i) q^{35} +7.34847i q^{37} +(-2.91886 + 5.61073i) q^{40} +1.41421i q^{41} -6.32456 q^{43} +(2.73861 - 10.6066i) q^{44} +(5.00000 - 3.87298i) q^{46} +8.94427i q^{47} +3.00000 q^{49} +(6.34325 - 3.12461i) q^{50} +(-4.74342 - 1.22474i) q^{52} +(-9.48683 + 7.74597i) q^{55} +(-8.21584 + 3.53553i) q^{56} +(3.16228 - 2.44949i) q^{58} +5.47723 q^{59} -10.0000 q^{61} +(8.66025 - 6.70820i) q^{62} +(5.50000 - 5.80948i) q^{64} +(3.46410 + 4.24264i) q^{65} +12.6491 q^{67} +(9.74342 + 2.25074i) q^{70} -14.6969i q^{73} +(-8.21584 + 6.36396i) q^{74} -17.3205 q^{77} +7.74597i q^{79} +(-8.80079 + 1.59565i) q^{80} +(-1.58114 + 1.22474i) q^{82} +8.94427i q^{83} +(-5.47723 - 7.07107i) q^{86} +(14.2302 - 6.12372i) q^{88} +9.89949i q^{89} +7.74597i q^{91} +(8.66025 + 2.23607i) q^{92} +(-10.0000 + 7.74597i) q^{94} +4.89898i q^{97} +(2.59808 + 3.35410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4}+O(q^{10}) $ 8 * q - 4 * q^4	$ 8 q - 4 q^{4} + 12 q^{10} - 28 q^{16} + 8 q^{25} - 36 q^{40} + 40 q^{46} + 24 q^{49} - 80 q^{61} + 44 q^{64} + 40 q^{70} - 80 q^{94}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^10 - 28 * q^16 + 8 * q^25 - 36 * q^40 + 40 * q^46 + 24 * q^49 - 80 * q^61 + 44 * q^64 + 40 * q^70 - 80 * q^94

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 $

$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	1.93649i	−0.250000	+	0.968246i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$6$		0			0
$7$	3.16228			1.19523			0.597614	−	0.801784i	$-0.296115\pi$
$7$	3.16228			1.19523			0.597614	+	0.801784i	$0.296115\pi$
$8$	−2.59808	+	1.11803i	−0.918559	+	0.395285i
$9$		0			0
$10$	3.08114	+	0.711747i	0.974342	+	0.225074i
$11$	−5.47723			−1.65145			−0.825723	−	0.564076i	$-0.809232\pi$
$11$	−5.47723			−1.65145			−0.825723	+	0.564076i	$0.809232\pi$
$12$		0			0
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	2.73861	+	3.53553i	0.731925	+	0.944911i
$15$		0			0
$16$	−3.50000	−	1.93649i	−0.875000	−	0.484123i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	1.87259	+	4.06121i	0.418723	+	0.908114i
$21$		0			0
$22$	−4.74342	−	6.12372i	−1.01130	−	1.30558i
$23$		−	4.47214i		−	0.932505i	−0.884652	−	0.466252i	$-0.845604\pi$
$23$		−	4.47214i		−	0.932505i	0.884652	−	0.466252i	$-0.154396\pi$
$24$		0			0
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$	−2.73861	+	2.12132i	−0.537086	+	0.416025i
$27$		0			0
$28$	−1.58114	+	6.12372i	−0.298807	+	1.15728i
$29$		−	2.82843i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$		0			0
$31$		−	7.74597i		−	1.39122i	−0.718421	−	0.695608i	$-0.755135\pi$
$31$		−	7.74597i		−	1.39122i	0.718421	−	0.695608i	$-0.244865\pi$
$32$	−0.866025	−	5.59017i	−0.153093	−	0.988212i
$33$		0			0
$34$		0			0
$35$	5.47723	−	4.47214i	0.925820	−	0.755929i
$36$		0			0
$37$			7.34847i			1.20808i	0.796954	+	0.604040i	$0.206443\pi$
$37$			7.34847i			1.20808i	−0.796954	+	0.604040i	$0.793557\pi$
$38$		0			0
$39$		0			0
$40$	−2.91886	+	5.61073i	−0.461512	+	0.887134i
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		0			0
$43$	−6.32456			−0.964486			−0.482243	−	0.876038i	$-0.660178\pi$
$43$	−6.32456			−0.964486			−0.482243	+	0.876038i	$0.660178\pi$
$44$	2.73861	−	10.6066i	0.412861	−	1.59901i
$45$		0			0
$46$	5.00000	−	3.87298i	0.737210	−	0.571040i
$47$			8.94427i			1.30466i	0.757937	+	0.652328i	$0.226208\pi$
$47$			8.94427i			1.30466i	−0.757937	+	0.652328i	$0.773792\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	6.34325	−	3.12461i	0.897071	−	0.441886i
$51$		0			0
$52$	−4.74342	−	1.22474i	−0.657794	−	0.169842i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	−9.48683	+	7.74597i	−1.27920	+	1.04447i
$56$	−8.21584	+	3.53553i	−1.09789	+	0.472456i
$57$		0			0
$58$	3.16228	−	2.44949i	0.415227	−	0.321634i
$59$	5.47723			0.713074			0.356537	−	0.934281i	$-0.383957\pi$
$59$	5.47723			0.713074			0.356537	+	0.934281i	$0.383957\pi$
$60$		0			0
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	8.66025	−	6.70820i	1.09985	−	0.851943i
$63$		0			0
$64$	5.50000	−	5.80948i	0.687500	−	0.726184i
$65$	3.46410	+	4.24264i	0.429669	+	0.526235i
$66$		0			0
$67$	12.6491			1.54533			0.772667	−	0.634811i	$-0.218922\pi$
$67$	12.6491			1.54533			0.772667	+	0.634811i	$0.218922\pi$
$68$		0			0
$69$		0			0
$70$	9.74342	+	2.25074i	1.16456	+	0.269015i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$		−	14.6969i		−	1.72015i	−0.510171	−	0.860073i	$-0.670418\pi$
$73$		−	14.6969i		−	1.72015i	0.510171	−	0.860073i	$-0.329582\pi$
$74$	−8.21584	+	6.36396i	−0.955072	+	0.739795i
$75$		0			0
$76$		0			0
$77$	−17.3205			−1.97386
$78$		0			0
$79$			7.74597i			0.871489i	0.900070	+	0.435745i	$0.143515\pi$
$79$			7.74597i			0.871489i	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−8.80079	+	1.59565i	−0.983958	+	0.178399i
$81$		0			0
$82$	−1.58114	+	1.22474i	−0.174608	+	0.135250i
$83$			8.94427i			0.981761i	0.871227	+	0.490881i	$0.163325\pi$
$83$			8.94427i			0.981761i	−0.871227	+	0.490881i	$0.836675\pi$
$84$		0			0
$85$		0			0
$86$	−5.47723	−	7.07107i	−0.590624	−	0.762493i
$87$		0			0
$88$	14.2302	−	6.12372i	1.51695	−	0.652791i
$89$			9.89949i			1.04934i	0.851304	+	0.524672i	$0.175812\pi$
$89$			9.89949i			1.04934i	−0.851304	+	0.524672i	$0.824188\pi$
$90$		0			0
$91$			7.74597i			0.811998i
$92$	8.66025	+	2.23607i	0.902894	+	0.233126i
$93$		0			0
$94$	−10.0000	+	7.74597i	−1.03142	+	0.798935i
$95$		0			0
$96$		0			0
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$	2.59808	+	3.35410i	0.262445	+	0.338815i
$99$		0			0
$100$	8.98683	+	4.38598i	0.898683	+	0.438598i
$101$			5.65685i			0.562878i	0.959579	+	0.281439i	$0.0908117\pi$
$101$			5.65685i			0.562878i	−0.959579	+	0.281439i	$0.909188\pi$
$102$		0			0
$103$	3.16228			0.311588			0.155794	−	0.987790i	$-0.450206\pi$
$103$	3.16228			0.311588			0.155794	+	0.987790i	$0.450206\pi$
$104$	−2.73861	−	6.36396i	−0.268543	−	0.624038i
$105$		0			0
$106$		0			0
$107$			8.94427i			0.864675i	0.901712	+	0.432338i	$0.142311\pi$
$107$			8.94427i			0.864675i	−0.901712	+	0.432338i	$0.857689\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−16.8761	−	3.89840i	−1.60907	−	0.371698i
$111$		0			0
$112$	−11.0680	−	6.12372i	−1.04583	−	0.578638i
$113$	13.8564			1.30350			0.651751	−	0.758433i	$-0.274035\pi$
$113$	13.8564			1.30350			0.651751	+	0.758433i	$0.274035\pi$
$114$		0			0
$115$	−6.32456	−	7.74597i	−0.589768	−	0.722315i
$116$	5.47723	+	1.41421i	0.508548	+	0.131306i
$117$		0			0
$118$	4.74342	+	6.12372i	0.436667	+	0.563735i
$119$		0			0
$120$		0			0
$121$	19.0000			1.72727
$122$	−8.66025	−	11.1803i	−0.784063	−	1.01222i
$123$		0			0
$124$	15.0000	+	3.87298i	1.34704	+	0.347804i
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$		0			0
$127$	3.16228			0.280607			0.140303	−	0.990109i	$-0.455192\pi$
$127$	3.16228			0.280607			0.140303	+	0.990109i	$0.455192\pi$
$128$	11.2583	+	1.11803i	0.995105	+	0.0988212i
$129$		0			0
$130$	−1.74342	+	7.54722i	−0.152908	+	0.661935i
$131$	5.47723			0.478547			0.239274	−	0.970952i	$-0.423091\pi$
$131$	5.47723			0.478547			0.239274	+	0.970952i	$0.423091\pi$
$132$		0			0
$133$		0			0
$134$	10.9545	+	14.1421i	0.946320	+	1.22169i
$135$		0			0
$136$		0			0
$137$	6.92820			0.591916			0.295958	−	0.955201i	$-0.404361\pi$
$137$	6.92820			0.591916			0.295958	+	0.955201i	$0.404361\pi$
$138$		0			0
$139$		−	7.74597i		−	0.657004i	−0.944503	−	0.328502i	$-0.893456\pi$
$139$		−	7.74597i		−	0.657004i	0.944503	−	0.328502i	$-0.106544\pi$
$140$	5.92164	+	12.8427i	0.500470	+	1.08540i
$141$		0			0
$142$		0			0
$143$		−	13.4164i		−	1.12194i
$144$		0			0
$145$	−4.00000	−	4.89898i	−0.332182	−	0.406838i
$146$	16.4317	−	12.7279i	1.35990	−	1.05337i
$147$		0			0
$148$	−14.2302	−	3.67423i	−1.16972	−	0.302020i
$149$		−	11.3137i		−	0.926855i	−0.886135	−	0.463428i	$-0.846619\pi$
$149$		−	11.3137i		−	0.926855i	0.886135	−	0.463428i	$-0.153381\pi$
$150$		0			0
$151$			7.74597i			0.630358i	0.949032	+	0.315179i	$0.102065\pi$
$151$			7.74597i			0.630358i	−0.949032	+	0.315179i	$0.897935\pi$
$152$		0			0
$153$		0			0
$154$	−15.0000	−	19.3649i	−1.20873	−	1.56047i
$155$	−10.9545	−	13.4164i	−0.879883	−	1.07763i
$156$		0			0
$157$			17.1464i			1.36843i	0.729279	+	0.684217i	$0.239856\pi$
$157$			17.1464i			1.36843i	−0.729279	+	0.684217i	$0.760144\pi$
$158$	−8.66025	+	6.70820i	−0.688973	+	0.533676i
$159$		0			0
$160$	−9.40569	−	8.45771i	−0.743585	−	0.668641i
$161$		−	14.1421i		−	1.11456i
$162$		0			0
$163$	−6.32456			−0.495377			−0.247689	−	0.968840i	$-0.579671\pi$
$163$	−6.32456			−0.495377			−0.247689	+	0.968840i	$0.579671\pi$
$164$	−2.73861	−	0.707107i	−0.213850	−	0.0552158i
$165$		0			0
$166$	−10.0000	+	7.74597i	−0.776151	+	0.601204i
$167$		−	4.47214i		−	0.346064i	−0.984916	−	0.173032i	$-0.944644\pi$
$167$		−	4.47214i		−	0.346064i	0.984916	−	0.173032i	$-0.0553564\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$		0			0
$171$		0			0
$172$	3.16228	−	12.2474i	0.241121	−	0.933859i
$173$	−13.8564			−1.05348			−0.526742	−	0.850026i	$-0.676586\pi$
$173$	−13.8564			−1.05348			−0.526742	+	0.850026i	$0.676586\pi$
$174$		0			0
$175$	3.16228	−	15.4919i	0.239046	−	1.17108i
$176$	19.1703	+	10.6066i	1.44501	+	0.799503i
$177$		0			0
$178$	−11.0680	+	8.57321i	−0.829580	+	0.642590i
$179$	−16.4317			−1.22816			−0.614081	−	0.789243i	$-0.710473\pi$
$179$	−16.4317			−1.22816			−0.614081	+	0.789243i	$0.710473\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−8.66025	+	6.70820i	−0.641941	+	0.497245i
$183$		0			0
$184$	5.00000	+	11.6190i	0.368605	+	0.856560i
$185$	10.3923	+	12.7279i	0.764057	+	0.935775i
$186$		0			0
$187$		0			0
$188$	−17.3205	−	4.47214i	−1.26323	−	0.326164i
$189$		0			0
$190$		0			0
$191$	10.9545			0.792636			0.396318	−	0.918113i	$-0.370288\pi$
$191$	10.9545			0.792636			0.396318	+	0.918113i	$0.370288\pi$
$192$		0			0
$193$			9.79796i			0.705273i	0.935760	+	0.352636i	$0.114715\pi$
$193$			9.79796i			0.705273i	−0.935760	+	0.352636i	$0.885285\pi$
$194$	−5.47723	+	4.24264i	−0.393242	+	0.304604i
$195$		0			0
$196$	−1.50000	+	5.80948i	−0.107143	+	0.414963i
$197$	10.3923			0.740421			0.370211	−	0.928948i	$-0.379286\pi$
$197$	10.3923			0.740421			0.370211	+	0.928948i	$0.379286\pi$
$198$		0			0
$199$		−	23.2379i		−	1.64729i	−0.567105	−	0.823646i	$-0.691937\pi$
$199$		−	23.2379i		−	1.64729i	0.567105	−	0.823646i	$-0.308063\pi$
$200$	2.87915	+	13.8460i	0.203587	+	0.979057i
$201$		0			0
$202$	−6.32456	+	4.89898i	−0.444994	+	0.344691i
$203$		−	8.94427i		−	0.627765i
$204$		0			0
$205$	2.00000	+	2.44949i	0.139686	+	0.171080i
$206$	2.73861	+	3.53553i	0.190808	+	0.246332i
$207$		0			0
$208$	4.74342	−	8.57321i	0.328897	−	0.594445i
$209$		0			0
$210$		0			0
$211$		−	7.74597i		−	0.533254i	−0.963800	−	0.266627i	$-0.914091\pi$
$211$		−	7.74597i		−	0.533254i	0.963800	−	0.266627i	$-0.0859092\pi$
$212$		0			0
$213$		0			0
$214$	−10.0000	+	7.74597i	−0.683586	+	0.529503i
$215$	−10.9545	+	8.94427i	−0.747087	+	0.609994i
$216$		0			0
$217$		−	24.4949i		−	1.66282i
$218$	−8.66025	−	11.1803i	−0.586546	−	0.757228i
$219$		0			0
$220$	−10.2566	−	22.2442i	−0.691499	−	1.49970i
$221$		0			0
$222$		0			0
$223$	3.16228			0.211762			0.105881	−	0.994379i	$-0.466234\pi$
$223$	3.16228			0.211762			0.105881	+	0.994379i	$0.466234\pi$
$224$	−2.73861	−	17.6777i	−0.182981	−	1.18114i
$225$		0			0
$226$	12.0000	+	15.4919i	0.798228	+	1.03051i
$227$		−	17.8885i		−	1.18730i	−0.804722	−	0.593652i	$-0.797686\pi$
$227$		−	17.8885i		−	1.18730i	0.804722	−	0.593652i	$-0.202314\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	3.18303	−	13.7793i	0.209883	−	0.908578i
$231$		0			0
$232$	3.16228	+	7.34847i	0.207614	+	0.482451i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	12.6491	+	15.4919i	0.825137	+	1.01058i
$236$	−2.73861	+	10.6066i	−0.178269	+	0.690431i
$237$		0			0
$238$		0			0
$239$	−10.9545			−0.708585			−0.354292	−	0.935135i	$-0.615278\pi$
$239$	−10.9545			−0.708585			−0.354292	+	0.935135i	$0.615278\pi$
$240$		0			0
$241$	8.00000			0.515325			0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000			0.515325			0.257663	+	0.966235i	$0.417048\pi$
$242$	16.4545	+	21.2426i	1.05773	+	1.36553i
$243$		0			0
$244$	5.00000	−	19.3649i	0.320092	−	1.23971i
$245$	5.19615	−	4.24264i	0.331970	−	0.271052i
$246$		0			0
$247$		0			0
$248$	8.66025	+	20.1246i	0.549927	+	1.27791i
$249$		0			0
$250$	6.56797	−	14.3827i	0.415395	−	0.909641i
$251$	16.4317			1.03716			0.518579	−	0.855030i	$-0.326461\pi$
$251$	16.4317			1.03716			0.518579	+	0.855030i	$0.326461\pi$
$252$		0			0
$253$			24.4949i			1.53998i
$254$	2.73861	+	3.53553i	0.171836	+	0.221839i
$255$		0			0
$256$	8.50000	+	13.5554i	0.531250	+	0.847215i
$257$	−6.92820			−0.432169			−0.216085	−	0.976375i	$-0.569329\pi$
$257$	−6.92820			−0.432169			−0.216085	+	0.976375i	$0.569329\pi$
$258$		0			0
$259$			23.2379i			1.44393i
$260$	−9.94789	+	4.58688i	−0.616942	+	0.284466i
$261$		0			0
$262$	4.74342	+	6.12372i	0.293049	+	0.378325i
$263$			22.3607i			1.37882i	0.724372	+	0.689409i	$0.242130\pi$
$263$			22.3607i			1.37882i	−0.724372	+	0.689409i	$0.757870\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−6.32456	+	24.4949i	−0.386334	+	1.49626i
$269$		−	2.82843i		−	0.172452i	−0.996276	−	0.0862261i	$-0.972519\pi$
$269$		−	2.82843i		−	0.172452i	0.996276	−	0.0862261i	$-0.0274808\pi$
$270$		0			0
$271$			23.2379i			1.41160i	0.708410	+	0.705801i	$0.249413\pi$
$271$			23.2379i			1.41160i	−0.708410	+	0.705801i	$0.750587\pi$
$272$		0			0
$273$		0			0
$274$	6.00000	+	7.74597i	0.362473	+	0.467951i
$275$	−5.47723	+	26.8328i	−0.330289	+	1.61808i
$276$		0			0
$277$		−	17.1464i		−	1.03023i	−0.857121	−	0.515115i	$-0.827749\pi$
$277$		−	17.1464i		−	1.03023i	0.857121	−	0.515115i	$-0.172251\pi$
$278$	8.66025	−	6.70820i	0.519408	−	0.402331i
$279$		0			0
$280$	−9.23025	+	17.7427i	−0.551613	+	1.06033i
$281$		−	15.5563i		−	0.928014i	−0.885832	−	0.464007i	$-0.846411\pi$
$281$		−	15.5563i		−	0.928014i	0.885832	−	0.464007i	$-0.153589\pi$
$282$		0			0
$283$	12.6491			0.751912			0.375956	−	0.926638i	$-0.377314\pi$
$283$	12.6491			0.751912			0.375956	+	0.926638i	$0.377314\pi$
$284$		0			0
$285$		0			0
$286$	15.0000	−	11.6190i	0.886969	−	0.687043i
$287$			4.47214i			0.263982i
$288$		0			0
$289$	−17.0000			−1.00000
$290$	2.01312	−	8.71478i	0.118215	−	0.511749i
$291$		0			0
$292$	28.4605	+	7.34847i	1.66552	+	0.430037i
$293$	3.46410			0.202375			0.101187	−	0.994867i	$-0.467736\pi$
$293$	3.46410			0.202375			0.101187	+	0.994867i	$0.467736\pi$
$294$		0			0
$295$	9.48683	−	7.74597i	0.552345	−	0.450988i
$296$	−8.21584	−	19.0919i	−0.477536	−	1.10969i
$297$		0			0
$298$	12.6491	−	9.79796i	0.732743	−	0.567581i
$299$	10.9545			0.633512
$300$		0			0
$301$	−20.0000			−1.15278
$302$	−8.66025	+	6.70820i	−0.498342	+	0.386014i
$303$		0			0
$304$		0			0
$305$	−17.3205	+	14.1421i	−0.991769	+	0.809776i
$306$		0			0
$307$	−25.2982			−1.44385			−0.721923	−	0.691974i	$-0.756741\pi$
$307$	−25.2982			−1.44385			−0.721923	+	0.691974i	$0.756741\pi$
$308$	8.66025	−	33.5410i	0.493464	−	1.91118i
$309$		0			0
$310$	5.51317	−	23.8664i	0.313127	−	1.35552i
$311$	−10.9545			−0.621170			−0.310585	−	0.950546i	$-0.600525\pi$
$311$	−10.9545			−0.621170			−0.310585	+	0.950546i	$0.600525\pi$
$312$		0			0
$313$		−	9.79796i		−	0.553813i	−0.960897	−	0.276907i	$-0.910691\pi$
$313$		−	9.79796i		−	0.553813i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$	−19.1703	+	14.8492i	−1.08184	+	0.837991i
$315$		0			0
$316$	−15.0000	−	3.87298i	−0.843816	−	0.217872i
$317$	17.3205			0.972817			0.486408	−	0.873732i	$-0.338307\pi$
$317$	17.3205			0.972817			0.486408	+	0.873732i	$0.338307\pi$
$318$		0			0
$319$			15.4919i			0.867382i
$320$	1.31044	−	17.8405i	0.0732559	−	0.997313i
$321$		0			0
$322$	15.8114	−	12.2474i	0.881134	−	0.682524i
$323$		0			0
$324$		0			0
$325$	12.0000	+	2.44949i	0.665640	+	0.135873i
$326$	−5.47723	−	7.07107i	−0.303355	−	0.391630i
$327$		0			0
$328$	−1.58114	−	3.67423i	−0.0873038	−	0.202876i
$329$			28.2843i			1.55936i
$330$		0			0
$331$		−	15.4919i		−	0.851514i	−0.904838	−	0.425757i	$-0.860008\pi$
$331$		−	15.4919i		−	0.851514i	0.904838	−	0.425757i	$-0.139992\pi$
$332$	−17.3205	−	4.47214i	−0.950586	−	0.245440i
$333$		0			0
$334$	5.00000	−	3.87298i	0.273588	−	0.211920i
$335$	21.9089	−	17.8885i	1.19701	−	0.977356i
$336$		0			0
$337$		−	4.89898i		−	0.266864i	−0.991058	−	0.133432i	$-0.957400\pi$
$337$		−	4.89898i		−	0.266864i	0.991058	−	0.133432i	$-0.0425998\pi$
$338$	6.06218	+	7.82624i	0.329739	+	0.425691i
$339$		0			0
$340$		0			0
$341$			42.4264i			2.29752i
$342$		0			0
$343$	−12.6491			−0.682988
$344$	16.4317	−	7.07107i	0.885937	−	0.381246i
$345$		0			0
$346$	−12.0000	−	15.4919i	−0.645124	−	0.832851i
$347$			8.94427i			0.480154i	0.970754	+	0.240077i	$0.0771726\pi$
$347$			8.94427i			0.480154i	−0.970754	+	0.240077i	$0.922827\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	20.0591	−	9.88087i	1.07221	−	0.528155i
$351$		0			0
$352$	4.74342	+	30.6186i	0.252825	+	1.63198i
$353$	−34.6410			−1.84376			−0.921878	−	0.387481i	$-0.873345\pi$
$353$	−34.6410			−1.84376			−0.921878	+	0.387481i	$0.873345\pi$
$354$		0			0
$355$		0			0
$356$	−19.1703	−	4.94975i	−1.01602	−	0.262336i
$357$		0			0
$358$	−14.2302	−	18.3712i	−0.752092	−	0.970947i
$359$	32.8634			1.73446			0.867231	−	0.497906i	$-0.165898\pi$
$359$	32.8634			1.73446			0.867231	+	0.497906i	$0.165898\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	−8.66025	−	11.1803i	−0.455173	−	0.587626i
$363$		0			0
$364$	−15.0000	−	3.87298i	−0.786214	−	0.202999i
$365$	−20.7846	−	25.4558i	−1.08792	−	1.33242i
$366$		0			0
$367$	−34.7851			−1.81577			−0.907883	−	0.419225i	$-0.862302\pi$
$367$	−34.7851			−1.81577			−0.907883	+	0.419225i	$0.862302\pi$
$368$	−8.66025	+	15.6525i	−0.451447	+	0.815942i
$369$		0			0
$370$	−5.23025	+	22.6417i	−0.271908	+	1.17708i
$371$		0			0
$372$		0			0
$373$		−	26.9444i		−	1.39513i	−0.716523	−	0.697564i	$-0.754267\pi$
$373$		−	26.9444i		−	1.39513i	0.716523	−	0.697564i	$-0.245733\pi$
$374$		0			0
$375$		0			0
$376$	−10.0000	−	23.2379i	−0.515711	−	1.19840i
$377$	6.92820			0.356821
$378$		0			0
$379$		−	23.2379i		−	1.19365i	−0.802371	−	0.596825i	$-0.796429\pi$
$379$		−	23.2379i		−	1.19365i	0.802371	−	0.596825i	$-0.203571\pi$
$380$		0			0
$381$		0			0
$382$	9.48683	+	12.2474i	0.485389	+	0.626634i
$383$			8.94427i			0.457031i	0.973540	+	0.228515i	$0.0733872\pi$
$383$			8.94427i			0.457031i	−0.973540	+	0.228515i	$0.926613\pi$
$384$		0			0
$385$	−30.0000	+	24.4949i	−1.52894	+	1.24838i
$386$	−10.9545	+	8.48528i	−0.557567	+	0.431889i
$387$		0			0
$388$	−9.48683	−	2.44949i	−0.481621	−	0.124354i
$389$		−	2.82843i		−	0.143407i	−0.997426	−	0.0717035i	$-0.977156\pi$
$389$		−	2.82843i		−	0.143407i	0.997426	−	0.0717035i	$-0.0228435\pi$
$390$		0			0
$391$		0			0
$392$	−7.79423	+	3.35410i	−0.393668	+	0.169408i
$393$		0			0
$394$	9.00000	+	11.6190i	0.453413	+	0.585354i
$395$	10.9545	+	13.4164i	0.551178	+	0.675053i
$396$		0			0
$397$		−	7.34847i		−	0.368809i	−0.982850	−	0.184405i	$-0.940964\pi$
$397$		−	7.34847i		−	0.368809i	0.982850	−	0.184405i	$-0.0590357\pi$
$398$	25.9808	−	20.1246i	1.30230	−	1.00876i
$399$		0			0
$400$	−12.9868	+	15.2099i	−0.649342	+	0.760497i
$401$		−	15.5563i		−	0.776847i	−0.921481	−	0.388424i	$-0.873020\pi$
$401$		−	15.5563i		−	0.776847i	0.921481	−	0.388424i	$-0.126980\pi$
$402$		0			0
$403$	18.9737			0.945146
$404$	−10.9545	−	2.82843i	−0.545004	−	0.140720i
$405$		0			0
$406$	10.0000	−	7.74597i	0.496292	−	0.384426i
$407$		−	40.2492i		−	1.99508i
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$	−1.00656	+	4.35739i	−0.0497106	+	0.215196i
$411$		0			0
$412$	−1.58114	+	6.12372i	−0.0778971	+	0.301694i
$413$	17.3205			0.852286
$414$		0			0
$415$	12.6491	+	15.4919i	0.620920	+	0.760469i
$416$	13.6931	−	2.12132i	0.671358	−	0.104006i
$417$		0			0
$418$		0			0
$419$	5.47723			0.267580			0.133790	−	0.991010i	$-0.457285\pi$
$419$	5.47723			0.267580			0.133790	+	0.991010i	$0.457285\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	8.66025	−	6.70820i	0.421575	−	0.326550i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−31.6228			−1.53033
$428$	−17.3205	−	4.47214i	−0.837218	−	0.216169i
$429$		0			0
$430$	−19.4868	−	4.50148i	−0.939739	−	0.217081i
$431$	−32.8634			−1.58297			−0.791486	−	0.611187i	$-0.790692\pi$
$431$	−32.8634			−1.58297			−0.791486	+	0.611187i	$0.790692\pi$
$432$		0			0
$433$			14.6969i			0.706290i	0.935569	+	0.353145i	$0.114888\pi$
$433$			14.6969i			0.706290i	−0.935569	+	0.353145i	$0.885112\pi$
$434$	27.3861	−	21.2132i	1.31458	−	1.01827i
$435$		0			0
$436$	5.00000	−	19.3649i	0.239457	−	0.927411i
$437$		0			0
$438$		0			0
$439$			7.74597i			0.369695i	0.982767	+	0.184847i	$0.0591791\pi$
$439$			7.74597i			0.369695i	−0.982767	+	0.184847i	$0.940821\pi$
$440$	15.9873	−	30.7312i	0.762163	−	1.46505i
$441$		0			0
$442$		0			0
$443$			8.94427i			0.424955i	0.977166	+	0.212478i	$0.0681533\pi$
$443$			8.94427i			0.424955i	−0.977166	+	0.212478i	$0.931847\pi$
$444$		0			0
$445$	14.0000	+	17.1464i	0.663664	+	0.812819i
$446$	2.73861	+	3.53553i	0.129677	+	0.167412i
$447$		0			0
$448$	17.3925	−	18.3712i	0.821720	−	0.867956i
$449$		−	32.5269i		−	1.53504i	−0.641025	−	0.767520i	$-0.721491\pi$
$449$		−	32.5269i		−	1.53504i	0.641025	−	0.767520i	$-0.278509\pi$
$450$		0			0
$451$		−	7.74597i		−	0.364743i
$452$	−6.92820	+	26.8328i	−0.325875	+	1.26211i
$453$		0			0
$454$	20.0000	−	15.4919i	0.938647	−	0.727072i
$455$	10.9545	+	13.4164i	0.513553	+	0.628971i
$456$		0			0
$457$			4.89898i			0.229165i	0.993414	+	0.114582i	$0.0365530\pi$
$457$			4.89898i			0.229165i	−0.993414	+	0.114582i	$0.963447\pi$
$458$	12.1244	+	15.6525i	0.566534	+	0.731392i
$459$		0			0
$460$	18.1623	−	8.37447i	0.846821	−	0.390461i
$461$			22.6274i			1.05386i	0.849907	+	0.526932i	$0.176658\pi$
$461$			22.6274i			1.05386i	−0.849907	+	0.526932i	$0.823342\pi$
$462$		0			0
$463$	3.16228			0.146964			0.0734818	−	0.997297i	$-0.476589\pi$
$463$	3.16228			0.146964			0.0734818	+	0.997297i	$0.476589\pi$
$464$	−5.47723	+	9.89949i	−0.254274	+	0.459573i
$465$		0			0
$466$		0			0
$467$		−	17.8885i		−	0.827783i	−0.910326	−	0.413892i	$-0.864169\pi$
$467$		−	17.8885i		−	0.827783i	0.910326	−	0.413892i	$-0.135831\pi$
$468$		0			0
$469$	40.0000			1.84703
$470$	−6.36606	+	27.5585i	−0.293644	+	1.27118i
$471$		0			0
$472$	−14.2302	+	6.12372i	−0.655000	+	0.281867i
$473$	34.6410			1.59280
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−9.48683	−	12.2474i	−0.433918	−	0.560185i
$479$	−21.9089			−1.00104			−0.500522	−	0.865724i	$-0.666858\pi$
$479$	−21.9089			−1.00104			−0.500522	+	0.865724i	$0.666858\pi$
$480$		0			0
$481$	−18.0000			−0.820729
$482$	6.92820	+	8.94427i	0.315571	+	0.407400i
$483$		0			0
$484$	−9.50000	+	36.7933i	−0.431818	+	1.67242i
$485$	6.92820	+	8.48528i	0.314594	+	0.385297i
$486$		0			0
$487$	22.1359			1.00308			0.501538	−	0.865136i	$-0.332768\pi$
$487$	22.1359			1.00308			0.501538	+	0.865136i	$0.332768\pi$
$488$	25.9808	−	11.1803i	1.17609	−	0.506110i
$489$		0			0
$490$	9.24342	+	2.13524i	0.417575	+	0.0964603i
$491$	−27.3861			−1.23592			−0.617959	−	0.786210i	$-0.712040\pi$
$491$	−27.3861			−1.23592			−0.617959	+	0.786210i	$0.712040\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−15.0000	+	27.1109i	−0.673520	+	1.21731i
$497$		0			0
$498$		0			0
$499$			15.4919i			0.693514i	0.937955	+	0.346757i	$0.112717\pi$
$499$			15.4919i			0.693514i	−0.937955	+	0.346757i	$0.887283\pi$
$500$	21.7684	−	5.11256i	0.973511	−	0.228641i
$501$		0			0
$502$	14.2302	+	18.3712i	0.635127	+	0.819946i
$503$			8.94427i			0.398805i	0.979918	+	0.199403i	$0.0639002\pi$
$503$			8.94427i			0.398805i	−0.979918	+	0.199403i	$0.936100\pi$
$504$		0			0
$505$	8.00000	+	9.79796i	0.355995	+	0.436003i
$506$	−27.3861	+	21.2132i	−1.21746	+	0.943042i
$507$		0			0
$508$	−1.58114	+	6.12372i	−0.0701517	+	0.271696i
$509$		−	11.3137i		−	0.501471i	−0.968056	−	0.250736i	$-0.919328\pi$
$509$		−	11.3137i		−	0.501471i	0.968056	−	0.250736i	$-0.0806725\pi$
$510$		0			0
$511$		−	46.4758i		−	2.05597i
$512$	−7.79423	+	21.2426i	−0.344459	+	0.938801i
$513$		0			0
$514$	−6.00000	−	7.74597i	−0.264649	−	0.341660i
$515$	5.47723	−	4.47214i	0.241355	−	0.197066i
$516$		0			0
$517$		−	48.9898i		−	2.15457i
$518$	−25.9808	+	20.1246i	−1.14153	+	0.884225i
$519$		0			0
$520$	−13.7434	−	7.14972i	−0.602689	−	0.313536i
$521$		−	41.0122i		−	1.79678i	−0.439202	−	0.898388i	$-0.644739\pi$
$521$		−	41.0122i		−	1.79678i	0.439202	−	0.898388i	$-0.355261\pi$
$522$		0			0
$523$	31.6228			1.38277			0.691384	−	0.722488i	$-0.257001\pi$
$523$	31.6228			1.38277			0.691384	+	0.722488i	$0.257001\pi$
$524$	−2.73861	+	10.6066i	−0.119637	+	0.463352i
$525$		0			0
$526$	−25.0000	+	19.3649i	−1.09005	+	0.844350i
$527$		0			0
$528$		0			0
$529$	3.00000			0.130435
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.46410			−0.150047
$534$		0			0
$535$	12.6491	+	15.4919i	0.546869	+	0.669775i
$536$	−32.8634	+	14.1421i	−1.41948	+	0.610847i
$537$		0			0
$538$	3.16228	−	2.44949i	0.136335	−	0.105605i
$539$	−16.4317			−0.707762
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	−25.9808	+	20.1246i	−1.11597	+	0.864426i
$543$		0			0
$544$		0			0
$545$	−17.3205	+	14.1421i	−0.741929	+	0.605783i
$546$		0			0
$547$	31.6228			1.35209			0.676046	−	0.736859i	$-0.263692\pi$
$547$	31.6228			1.35209			0.676046	+	0.736859i	$0.263692\pi$
$548$	−3.46410	+	13.4164i	−0.147979	+	0.573121i
$549$		0			0
$550$	−34.7434	+	17.1142i	−1.48146	+	0.729751i
$551$		0			0
$552$		0			0
$553$			24.4949i			1.04163i
$554$	19.1703	−	14.8492i	0.814468	−	0.630884i
$555$		0			0
$556$	15.0000	+	3.87298i	0.636142	+	0.164251i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		−	15.4919i		−	0.655239i
$560$	−27.8305	+	5.04587i	−1.17606	+	0.213227i
$561$		0			0
$562$	17.3925	−	13.4722i	0.733659	−	0.568290i
$563$		−	44.7214i		−	1.88478i	−0.334515	−	0.942390i	$-0.608573\pi$
$563$		−	44.7214i		−	1.88478i	0.334515	−	0.942390i	$-0.391427\pi$
$564$		0			0
$565$	24.0000	−	19.5959i	1.00969	−	0.824406i
$566$	10.9545	+	14.1421i	0.460450	+	0.594438i
$567$		0			0
$568$		0			0
$569$			18.3848i			0.770730i	0.922764	+	0.385365i	$0.125924\pi$
$569$			18.3848i			0.770730i	−0.922764	+	0.385365i	$0.874076\pi$
$570$		0			0
$571$			15.4919i			0.648317i	0.946003	+	0.324159i	$0.105081\pi$
$571$			15.4919i			0.648317i	−0.946003	+	0.324159i	$0.894919\pi$
$572$	25.9808	+	6.70820i	1.08631	+	0.280484i
$573$		0			0
$574$	−5.00000	+	3.87298i	−0.208696	+	0.161655i
$575$	−21.9089	−	4.47214i	−0.913664	−	0.186501i
$576$		0			0
$577$			44.0908i			1.83552i	0.397130	+	0.917762i	$0.370006\pi$
$577$			44.0908i			1.83552i	−0.397130	+	0.917762i	$0.629994\pi$
$578$	−14.7224	−	19.0066i	−0.612372	−	0.790569i
$579$		0			0
$580$	11.4868	−	5.29648i	0.476965	−	0.219924i
$581$			28.2843i			1.17343i
$582$		0			0
$583$		0			0
$584$	16.4317	+	38.1838i	0.679948	+	1.58006i
$585$		0			0
$586$	3.00000	+	3.87298i	0.123929	+	0.159991i
$587$			8.94427i			0.369170i	0.982817	+	0.184585i	$0.0590940\pi$
$587$			8.94427i			0.369170i	−0.982817	+	0.184585i	$0.940906\pi$
$588$		0			0
$589$		0			0
$590$	16.8761	+	3.89840i	0.694778	+	0.160494i
$591$		0			0
$592$	14.2302	−	25.7196i	0.584860	−	1.05707i
$593$	−20.7846			−0.853522			−0.426761	−	0.904365i	$-0.640345\pi$
$593$	−20.7846			−0.853522			−0.426761	+	0.904365i	$0.640345\pi$
$594$		0			0
$595$		0			0
$596$	21.9089	+	5.65685i	0.897424	+	0.231714i
$597$		0			0
$598$	9.48683	+	12.2474i	0.387945	+	0.500835i
$599$	−10.9545			−0.447587			−0.223793	−	0.974637i	$-0.571844\pi$
$599$	−10.9545			−0.447587			−0.223793	+	0.974637i	$0.571844\pi$
$600$		0			0
$601$	20.0000			0.815817			0.407909	−	0.913023i	$-0.366258\pi$
$601$	20.0000			0.815817			0.407909	+	0.913023i	$0.366258\pi$
$602$	−17.3205	−	22.3607i	−0.705931	−	0.911353i
$603$		0			0
$604$	−15.0000	−	3.87298i	−0.610341	−	0.157589i
$605$	32.9090	−	26.8701i	1.33794	−	1.09242i
$606$		0			0
$607$	−15.8114			−0.641764			−0.320882	−	0.947119i	$-0.603979\pi$
$607$	−15.8114			−0.641764			−0.320882	+	0.947119i	$0.603979\pi$
$608$		0			0
$609$		0			0
$610$	−30.8114	−	7.11747i	−1.24752	−	0.288178i
$611$	−21.9089			−0.886339
$612$		0			0
$613$		−	22.0454i		−	0.890406i	−0.895430	−	0.445203i	$-0.853132\pi$
$613$		−	22.0454i		−	0.890406i	0.895430	−	0.445203i	$-0.146868\pi$
$614$	−21.9089	−	28.2843i	−0.884171	−	1.14146i
$615$		0			0
$616$	45.0000	−	19.3649i	1.81310	−	0.780235i
$617$	34.6410			1.39459			0.697297	−	0.716782i	$-0.254386\pi$
$617$	34.6410			1.39459			0.697297	+	0.716782i	$0.254386\pi$
$618$		0			0
$619$			7.74597i			0.311337i	0.987809	+	0.155668i	$0.0497531\pi$
$619$			7.74597i			0.311337i	−0.987809	+	0.155668i	$0.950247\pi$
$620$	31.4580	−	14.5050i	1.26338	−	0.582535i
$621$		0			0
$622$	−9.48683	−	12.2474i	−0.380387	−	0.491078i
$623$			31.3050i			1.25421i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	10.9545	−	8.48528i	0.437828	−	0.339140i
$627$		0			0
$628$	−33.2039	−	8.57321i	−1.32498	−	0.342108i
$629$		0			0
$630$		0			0
$631$		−	23.2379i		−	0.925086i	−0.886597	−	0.462543i	$-0.846937\pi$
$631$		−	23.2379i		−	0.925086i	0.886597	−	0.462543i	$-0.153063\pi$
$632$	−8.66025	−	20.1246i	−0.344486	−	0.800514i
$633$		0			0
$634$	15.0000	+	19.3649i	0.595726	+	0.769079i
$635$	5.47723	−	4.47214i	0.217357	−	0.177471i
$636$		0			0
$637$			7.34847i			0.291157i
$638$	−17.3205	+	13.4164i	−0.685725	+	0.531161i
$639$		0			0
$640$	21.0811	−	13.9852i	0.833305	−	0.552813i
$641$		−	41.0122i		−	1.61988i	−0.586510	−	0.809942i	$-0.699498\pi$
$641$		−	41.0122i		−	1.61988i	0.586510	−	0.809942i	$-0.300502\pi$
$642$		0			0
$643$	−44.2719			−1.74591			−0.872956	−	0.487798i	$-0.837800\pi$
$643$	−44.2719			−1.74591			−0.872956	+	0.487798i	$0.837800\pi$
$644$	27.3861	+	7.07107i	1.07916	+	0.278639i
$645$		0			0
$646$		0			0
$647$			8.94427i			0.351636i	0.984423	+	0.175818i	$0.0562570\pi$
$647$			8.94427i			0.351636i	−0.984423	+	0.175818i	$0.943743\pi$
$648$		0			0
$649$	−30.0000			−1.17760
$650$	7.65369	+	15.5377i	0.300203	+	0.609440i
$651$		0			0
$652$	3.16228	−	12.2474i	0.123844	−	0.479647i
$653$	−17.3205			−0.677804			−0.338902	−	0.940822i	$-0.610055\pi$
$653$	−17.3205			−0.677804			−0.338902	+	0.940822i	$0.610055\pi$
$654$		0			0
$655$	9.48683	−	7.74597i	0.370681	−	0.302660i
$656$	2.73861	−	4.94975i	0.106925	−	0.193255i
$657$		0			0
$658$	−31.6228	+	24.4949i	−1.23278	+	0.954911i
$659$	27.3861			1.06681			0.533406	−	0.845859i	$-0.320912\pi$
$659$	27.3861			1.06681			0.533406	+	0.845859i	$0.320912\pi$
$660$		0			0
$661$	−10.0000			−0.388955			−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000			−0.388955			−0.194477	+	0.980907i	$0.562301\pi$
$662$	17.3205	−	13.4164i	0.673181	−	0.521443i
$663$		0			0
$664$	−10.0000	−	23.2379i	−0.388075	−	0.901805i
$665$		0			0
$666$		0			0
$667$	−12.6491			−0.489776
$668$	8.66025	+	2.23607i	0.335075	+	0.0865161i
$669$		0			0
$670$	38.9737	+	9.00296i	1.50568	+	0.347815i
$671$	54.7723			2.11446
$672$		0			0
$673$			34.2929i			1.32189i	0.750433	+	0.660946i	$0.229845\pi$
$673$			34.2929i			1.32189i	−0.750433	+	0.660946i	$0.770155\pi$
$674$	5.47723	−	4.24264i	0.210975	−	0.163420i
$675$		0			0
$676$	−3.50000	+	13.5554i	−0.134615	+	0.521363i
$677$	17.3205			0.665681			0.332841	−	0.942983i	$-0.391993\pi$
$677$	17.3205			0.665681			0.332841	+	0.942983i	$0.391993\pi$
$678$		0			0
$679$			15.4919i			0.594526i
$680$		0			0
$681$		0			0
$682$	−47.4342	+	36.7423i	−1.81635	+	1.40694i
$683$		−	17.8885i		−	0.684486i	−0.939611	−	0.342243i	$-0.888813\pi$
$683$		−	17.8885i		−	0.684486i	0.939611	−	0.342243i	$-0.111187\pi$
$684$		0			0
$685$	12.0000	−	9.79796i	0.458496	−	0.374361i
$686$	−10.9545	−	14.1421i	−0.418243	−	0.539949i
$687$		0			0
$688$	22.1359	+	12.2474i	0.843925	+	0.466930i
$689$		0			0
$690$		0			0
$691$			30.9839i			1.17868i	0.807884	+	0.589341i	$0.200613\pi$
$691$			30.9839i			1.17868i	−0.807884	+	0.589341i	$0.799387\pi$
$692$	6.92820	−	26.8328i	0.263371	−	1.02003i
$693$		0			0
$694$	−10.0000	+	7.74597i	−0.379595	+	0.294033i
$695$	−10.9545	−	13.4164i	−0.415526	−	0.508913i
$696$		0			0
$697$		0			0
$698$	−8.66025	−	11.1803i	−0.327795	−	0.423182i
$699$		0			0
$700$	28.4189	+	13.8697i	1.07413	+	0.524225i
$701$			22.6274i			0.854626i	0.904104	+	0.427313i	$0.140540\pi$
$701$			22.6274i			0.854626i	−0.904104	+	0.427313i	$0.859460\pi$
$702$		0			0
$703$		0			0
$704$	−30.1247	+	31.8198i	−1.13537	+	1.19925i
$705$		0			0
$706$	−30.0000	−	38.7298i	−1.12906	−	1.45762i
$707$			17.8885i			0.672768i
$708$		0			0
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$		0			0
$711$		0			0
$712$	−11.0680	−	25.7196i	−0.414790	−	0.963884i
$713$	−34.6410			−1.29732
$714$		0			0
$715$	−18.9737	−	23.2379i	−0.709575	−	0.869048i
$716$	8.21584	−	31.8198i	0.307040	−	1.18916i
$717$		0			0
$718$	28.4605	+	36.7423i	1.06214	+	1.37121i
$719$	32.8634			1.22560			0.612798	−	0.790239i	$-0.290044\pi$
$719$	32.8634			1.22560			0.612798	+	0.790239i	$0.290044\pi$
$720$		0			0
$721$	10.0000			0.372419
$722$	16.4545	+	21.2426i	0.612372	+	0.790569i
$723$		0			0
$724$	5.00000	−	19.3649i	0.185824	−	0.719691i
$725$	−13.8564	−	2.82843i	−0.514614	−	0.105045i
$726$		0			0
$727$	3.16228			0.117282			0.0586412	−	0.998279i	$-0.481323\pi$
$727$	3.16228			0.117282			0.0586412	+	0.998279i	$0.481323\pi$
$728$	−8.66025	−	20.1246i	−0.320970	−	0.745868i
$729$		0			0
$730$	10.4605	−	45.2833i	0.387160	−	1.67601i
$731$		0			0
$732$		0			0
$733$			2.44949i			0.0904740i	0.998976	+	0.0452370i	$0.0144043\pi$
$733$			2.44949i			0.0904740i	−0.998976	+	0.0452370i	$0.985596\pi$
$734$	−30.1247	−	38.8909i	−1.11192	−	1.43549i
$735$		0			0
$736$	−25.0000	+	3.87298i	−0.921512	+	0.142760i
$737$	−69.2820			−2.55204
$738$		0			0
$739$		−	46.4758i		−	1.70964i	−0.518925	−	0.854820i	$-0.673667\pi$
$739$		−	46.4758i		−	1.70964i	0.518925	−	0.854820i	$-0.326333\pi$
$740$	−29.8437	+	13.7607i	−1.09708	+	0.505852i
$741$		0			0
$742$		0			0
$743$		−	44.7214i		−	1.64067i	−0.571885	−	0.820334i	$-0.693788\pi$
$743$		−	44.7214i		−	1.64067i	0.571885	−	0.820334i	$-0.306212\pi$
$744$		0			0
$745$	−16.0000	−	19.5959i	−0.586195	−	0.717939i
$746$	30.1247	−	23.3345i	1.10295	−	0.854338i
$747$		0			0
$748$		0			0
$749$			28.2843i			1.03348i
$750$		0			0
$751$			38.7298i			1.41327i	0.707577	+	0.706636i	$0.249788\pi$
$751$			38.7298i			1.41327i	−0.707577	+	0.706636i	$0.750212\pi$
$752$	17.3205	−	31.3050i	0.631614	−	1.14157i
$753$		0			0
$754$	6.00000	+	7.74597i	0.218507	+	0.282091i
$755$	10.9545	+	13.4164i	0.398673	+	0.488273i
$756$		0			0
$757$		−	7.34847i		−	0.267085i	−0.991043	−	0.133542i	$-0.957365\pi$
$757$		−	7.34847i		−	0.267085i	0.991043	−	0.133542i	$-0.0426352\pi$
$758$	25.9808	−	20.1246i	0.943664	−	0.730959i
$759$		0			0
$760$		0			0
$761$			1.41421i			0.0512652i	0.999671	+	0.0256326i	$0.00816000\pi$
$761$			1.41421i			0.0512652i	−0.999671	+	0.0256326i	$0.991840\pi$
$762$		0			0
$763$	−31.6228			−1.14482
$764$	−5.47723	+	21.2132i	−0.198159	+	0.767467i
$765$		0			0
$766$	−10.0000	+	7.74597i	−0.361315	+	0.279873i
$767$			13.4164i			0.484438i
$768$		0			0
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$	−53.3669	−	12.3278i	−1.92321	−	0.444264i
$771$		0			0
$772$	−18.9737	−	4.89898i	−0.682877	−	0.176318i
$773$	51.9615			1.86893			0.934463	−	0.356060i	$-0.115880\pi$
$773$	51.9615			1.86893			0.934463	+	0.356060i	$0.115880\pi$
$774$		0			0
$775$	−37.9473	−	7.74597i	−1.36311	−	0.278243i
$776$	−5.47723	−	12.7279i	−0.196621	−	0.456906i
$777$		0			0
$778$	3.16228	−	2.44949i	0.113373	−	0.0878185i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−10.5000	−	5.80948i	−0.375000	−	0.207481i
$785$	24.2487	+	29.6985i	0.865474	+	1.05998i
$786$		0			0
$787$	31.6228			1.12723			0.563615	−	0.826038i	$-0.309410\pi$
$787$	31.6228			1.12723			0.563615	+	0.826038i	$0.309410\pi$
$788$	−5.19615	+	20.1246i	−0.185105	+	0.716910i
$789$		0			0
$790$	−5.51317	+	23.8664i	−0.196150	+	0.849128i
$791$	43.8178			1.55798
$792$		0			0
$793$		−	24.4949i		−	0.869839i
$794$	8.21584	−	6.36396i	0.291569	−	0.225849i
$795$		0			0
$796$	45.0000	+	11.6190i	1.59498	+	0.411823i
$797$	−27.7128			−0.981638			−0.490819	−	0.871262i	$-0.663302\pi$
$797$	−27.7128			−0.981638			−0.490819	+	0.871262i	$0.663302\pi$
$798$		0			0
$799$		0			0
$800$	−28.2522	−	1.34753i	−0.998864	−	0.0476424i
$801$		0			0
$802$	17.3925	−	13.4722i	0.614151	−	0.475720i
$803$			80.4984i			2.84073i
$804$		0			0
$805$	−20.0000	−	24.4949i	−0.704907	−	0.863332i
$806$	16.4317	+	21.2132i	0.578781	+	0.747203i
$807$		0			0
$808$	−6.32456	−	14.6969i	−0.222497	−	0.517036i
$809$			18.3848i			0.646374i	0.946335	+	0.323187i	$0.104754\pi$
$809$			18.3848i			0.646374i	−0.946335	+	0.323187i	$0.895246\pi$
$810$		0			0
$811$			23.2379i			0.815993i	0.912983	+	0.407997i	$0.133772\pi$
$811$			23.2379i			0.815993i	−0.912983	+	0.407997i	$0.866228\pi$
$812$	17.3205	+	4.47214i	0.607831	+	0.156941i
$813$		0			0
$814$	45.0000	−	34.8569i	1.57725	−	1.22173i
$815$	−10.9545	+	8.94427i	−0.383718	+	0.313304i
$816$		0			0
$817$		0			0
$818$	−8.66025	−	11.1803i	−0.302799	−	0.390911i
$819$		0			0
$820$	−5.74342	+	2.64824i	−0.200569	+	0.0924805i
$821$			48.0833i			1.67812i	0.544041	+	0.839059i	$0.316894\pi$
$821$			48.0833i			1.67812i	−0.544041	+	0.839059i	$0.683106\pi$
$822$		0			0
$823$	−15.8114			−0.551150			−0.275575	−	0.961280i	$-0.588868\pi$
$823$	−15.8114			−0.551150			−0.275575	+	0.961280i	$0.588868\pi$
$824$	−8.21584	+	3.53553i	−0.286212	+	0.123166i
$825$		0			0
$826$	15.0000	+	19.3649i	0.521917	+	0.673792i
$827$			8.94427i			0.311023i	0.987834	+	0.155511i	$0.0497025\pi$
$827$			8.94427i			0.311023i	−0.987834	+	0.155511i	$0.950297\pi$
$828$		0			0
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	−6.36606	+	27.5585i	−0.220969	+	0.956571i
$831$		0			0
$832$	14.2302	+	13.4722i	0.493345	+	0.467064i
$833$		0			0
$834$		0			0
$835$	−6.32456	−	7.74597i	−0.218870	−	0.268060i
$836$		0			0
$837$		0			0
$838$	4.74342	+	6.12372i	0.163859	+	0.211541i
$839$	−54.7723			−1.89095			−0.945474	−	0.325697i	$-0.894401\pi$
$839$	−54.7723			−1.89095			−0.945474	+	0.325697i	$0.894401\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	1.73205	+	2.23607i	0.0596904	+	0.0770600i
$843$		0			0
$844$	15.0000	+	3.87298i	0.516321	+	0.133314i
$845$	12.1244	−	9.89949i	0.417091	−	0.340553i
$846$		0			0
$847$	60.0833			2.06449
$848$		0			0
$849$		0			0
$850$		0			0
$851$	32.8634			1.12654
$852$		0			0
$853$		−	2.44949i		−	0.0838689i	−0.999120	−	0.0419345i	$-0.986648\pi$
$853$		−	2.44949i		−	0.0838689i	0.999120	−	0.0419345i	$-0.0133521\pi$
$854$	−27.3861	−	35.3553i	−0.937134	−	1.20983i
$855$		0			0
$856$	−10.0000	−	23.2379i	−0.341793	−	0.794255i
$857$	−34.6410			−1.18331			−0.591657	−	0.806190i	$-0.701526\pi$
$857$	−34.6410			−1.18331			−0.591657	+	0.806190i	$0.701526\pi$
$858$		0			0
$859$			38.7298i			1.32144i	0.750630	+	0.660722i	$0.229750\pi$
$859$			38.7298i			1.32144i	−0.750630	+	0.660722i	$0.770250\pi$
$860$	−11.8433	−	25.6853i	−0.403853	−	0.875863i
$861$		0			0
$862$	−28.4605	−	36.7423i	−0.969368	−	1.25145i
$863$		−	31.3050i		−	1.06563i	−0.846231	−	0.532816i	$-0.821134\pi$
$863$		−	31.3050i		−	1.06563i	0.846231	−	0.532816i	$-0.178866\pi$
$864$		0			0
$865$	−24.0000	+	19.5959i	−0.816024	+	0.666281i
$866$	−16.4317	+	12.7279i	−0.558371	+	0.432512i
$867$		0			0
$868$	47.4342	+	12.2474i	1.61002	+	0.415705i
$869$		−	42.4264i		−	1.43922i
$870$		0			0
$871$			30.9839i			1.04985i
$872$	25.9808	−	11.1803i	0.879820	−	0.378614i
$873$		0			0
$874$		0			0
$875$	−16.4317	−	31.3050i	−0.555492	−	1.05830i
$876$		0			0
$877$			31.8434i			1.07527i	0.843176	+	0.537637i	$0.180683\pi$
$877$			31.8434i			1.07527i	−0.843176	+	0.537637i	$0.819317\pi$
$878$	−8.66025	+	6.70820i	−0.292269	+	0.226391i
$879$		0			0
$880$	48.2039	−	8.73971i	1.62495	−	0.294616i
$881$		−	15.5563i		−	0.524107i	−0.965053	−	0.262053i	$-0.915600\pi$
$881$		−	15.5563i		−	0.524107i	0.965053	−	0.262053i	$-0.0843996\pi$
$882$		0			0
$883$	31.6228			1.06419			0.532096	−	0.846684i	$-0.321405\pi$
$883$	31.6228			1.06419			0.532096	+	0.846684i	$0.321405\pi$
$884$		0			0
$885$		0			0
$886$	−10.0000	+	7.74597i	−0.335957	+	0.260231i
$887$			49.1935i			1.65176i	0.563849	+	0.825878i	$0.309320\pi$
$887$			49.1935i			1.65176i	−0.563849	+	0.825878i	$0.690680\pi$
$888$		0			0
$889$	10.0000			0.335389
$890$	−7.04593	+	30.5017i	−0.236180	+	1.02242i
$891$		0			0
$892$	−1.58114	+	6.12372i	−0.0529404	+	0.205037i
$893$		0			0
$894$		0			0
$895$	−28.4605	+	23.2379i	−0.951330	+	0.776757i
$896$	35.6020	+	3.53553i	1.18938	+	0.118114i
$897$		0			0
$898$	36.3662	−	28.1691i	1.21356	−	0.940016i
$899$	−21.9089			−0.730703
$900$		0			0
$901$		0			0
$902$	8.66025	−	6.70820i	0.288355	−	0.223359i
$903$		0			0
$904$	−36.0000	+	15.4919i	−1.19734	+	0.515254i
$905$	−17.3205	+	14.1421i	−0.575753	+	0.470100i
$906$		0			0
$907$	31.6228			1.05002			0.525009	−	0.851097i	$-0.324062\pi$
$907$	31.6228			1.05002			0.525009	+	0.851097i	$0.324062\pi$
$908$	34.6410	+	8.94427i	1.14960	+	0.296826i
$909$		0			0
$910$	−5.51317	+	23.8664i	−0.182760	+	0.791163i
$911$	−21.9089			−0.725874			−0.362937	−	0.931814i	$-0.618226\pi$
$911$	−21.9089			−0.725874			−0.362937	+	0.931814i	$0.618226\pi$
$912$		0			0
$913$		−	48.9898i		−	1.62133i
$914$	−5.47723	+	4.24264i	−0.181171	+	0.140334i
$915$		0			0
$916$	−7.00000	+	27.1109i	−0.231287	+	0.895769i
$917$	17.3205			0.571974
$918$		0			0
$919$			23.2379i			0.766548i	0.923635	+	0.383274i	$0.125203\pi$
$919$			23.2379i			0.766548i	−0.923635	+	0.383274i	$0.874797\pi$
$920$	25.0919	+	13.0535i	0.827256	+	0.430363i
$921$		0			0
$922$	−25.2982	+	19.5959i	−0.833153	+	0.645357i
$923$		0			0
$924$		0			0
$925$	36.0000	+	7.34847i	1.18367	+	0.241616i
$926$	2.73861	+	3.53553i	0.0899964	+	0.116185i
$927$		0			0
$928$	−15.8114	+	2.44949i	−0.519034	+	0.0804084i
$929$		−	32.5269i		−	1.06717i	−0.845745	−	0.533587i	$-0.820844\pi$
$929$		−	32.5269i		−	1.06717i	0.845745	−	0.533587i	$-0.179156\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	20.0000	−	15.4919i	0.654420	−	0.506912i
$935$		0			0
$936$		0			0
$937$			29.3939i			0.960256i	0.877198	+	0.480128i	$0.159410\pi$
$937$			29.3939i			0.960256i	−0.877198	+	0.480128i	$0.840590\pi$
$938$	34.6410	+	44.7214i	1.13107	+	1.46020i
$939$		0			0
$940$	−36.3246	+	16.7489i	−1.18478	+	0.546290i
$941$		−	36.7696i		−	1.19865i	−0.800505	−	0.599327i	$-0.795435\pi$
$941$		−	36.7696i		−	1.19865i	0.800505	−	0.599327i	$-0.204565\pi$
$942$		0			0
$943$	6.32456			0.205956
$944$	−19.1703	−	10.6066i	−0.623940	−	0.345215i
$945$		0			0
$946$	30.0000	+	38.7298i	0.975384	+	1.25922i
$947$			8.94427i			0.290650i	0.989384	+	0.145325i	$0.0464227\pi$
$947$			8.94427i			0.290650i	−0.989384	+	0.145325i	$0.953577\pi$
$948$		0			0
$949$	36.0000			1.16861
$950$		0			0
$951$		0			0
$952$		0			0
$953$	20.7846			0.673280			0.336640	−	0.941634i	$-0.390710\pi$
$953$	20.7846			0.673280			0.336640	+	0.941634i	$0.390710\pi$
$954$		0			0
$955$	18.9737	−	15.4919i	0.613973	−	0.501307i
$956$	5.47723	−	21.2132i	0.177146	−	0.686084i
$957$		0			0
$958$	−18.9737	−	24.4949i	−0.613011	−	0.791394i
$959$	21.9089			0.707475
$960$		0			0
$961$	−29.0000			−0.935484
$962$	−15.5885	−	20.1246i	−0.502592	−	0.648844i
$963$		0			0
$964$	−4.00000	+	15.4919i	−0.128831	+	0.498962i
$965$	13.8564	+	16.9706i	0.446054	+	0.546302i
$966$		0			0
$967$	−15.8114			−0.508460			−0.254230	−	0.967144i	$-0.581822\pi$
$967$	−15.8114			−0.508460			−0.254230	+	0.967144i	$0.581822\pi$
$968$	−49.3634	+	21.2426i	−1.58660	+	0.682764i
$969$		0			0
$970$	−3.48683	+	15.0944i	−0.111955	+	0.484653i
$971$	49.2950			1.58195			0.790976	−	0.611847i	$-0.209573\pi$
$971$	49.2950			1.58195			0.790976	+	0.611847i	$0.209573\pi$
$972$		0			0
$973$		−	24.4949i		−	0.785270i
$974$	19.1703	+	24.7487i	0.614256	+	0.793001i
$975$		0			0
$976$	35.0000	+	19.3649i	1.12032	+	0.619856i
$977$	34.6410			1.10826			0.554132	−	0.832429i	$-0.313050\pi$
$977$	34.6410			1.10826			0.554132	+	0.832429i	$0.313050\pi$
$978$		0			0
$979$		−	54.2218i		−	1.73294i
$980$	5.61776	+	12.1836i	0.179453	+	0.389192i
$981$		0			0
$982$	−23.7171	−	30.6186i	−0.756843	−	0.977079i
$983$			8.94427i			0.285278i	0.989775	+	0.142639i	$0.0455588\pi$
$983$			8.94427i			0.285278i	−0.989775	+	0.142639i	$0.954441\pi$
$984$		0			0
$985$	18.0000	−	14.6969i	0.573528	−	0.468283i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			28.2843i			0.899388i
$990$		0			0
$991$		−	23.2379i		−	0.738176i	−0.929394	−	0.369088i	$-0.879670\pi$
$991$		−	23.2379i		−	0.738176i	0.929394	−	0.369088i	$-0.120330\pi$
$992$	−43.3013	+	6.70820i	−1.37482	+	0.212986i
$993$		0			0
$994$		0			0
$995$	−32.8634	−	40.2492i	−1.04184	−	1.27599i
$996$		0			0
$997$			56.3383i			1.78425i	0.451788	+	0.892125i	$0.350786\pi$
$997$			56.3383i			1.78425i	−0.451788	+	0.892125i	$0.649214\pi$
$998$	−17.3205	+	13.4164i	−0.548271	+	0.424689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.h.b.179.7	yes	8
3.2	odd	2	inner	180.2.h.b.179.2	yes	8
4.3	odd	2	inner	180.2.h.b.179.5	yes	8
5.2	odd	4		900.2.e.f.251.4		8
5.3	odd	4		900.2.e.f.251.5		8
5.4	even	2	inner	180.2.h.b.179.1	✓	8
8.3	odd	2		2880.2.o.c.2879.3		8
8.5	even	2		2880.2.o.c.2879.4		8
12.11	even	2	inner	180.2.h.b.179.4	yes	8
15.2	even	4		900.2.e.f.251.6		8
15.8	even	4		900.2.e.f.251.3		8
15.14	odd	2	inner	180.2.h.b.179.8	yes	8
20.3	even	4		900.2.e.f.251.2		8
20.7	even	4		900.2.e.f.251.7		8
20.19	odd	2	inner	180.2.h.b.179.3	yes	8
24.5	odd	2		2880.2.o.c.2879.6		8
24.11	even	2		2880.2.o.c.2879.5		8
40.19	odd	2		2880.2.o.c.2879.8		8
40.29	even	2		2880.2.o.c.2879.7		8
60.23	odd	4		900.2.e.f.251.8		8
60.47	odd	4		900.2.e.f.251.1		8
60.59	even	2	inner	180.2.h.b.179.6	yes	8
120.29	odd	2		2880.2.o.c.2879.1		8
120.59	even	2		2880.2.o.c.2879.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.h.b.179.1	✓	8	5.4	even	2	inner
180.2.h.b.179.2	yes	8	3.2	odd	2	inner
180.2.h.b.179.3	yes	8	20.19	odd	2	inner
180.2.h.b.179.4	yes	8	12.11	even	2	inner
180.2.h.b.179.5	yes	8	4.3	odd	2	inner
180.2.h.b.179.6	yes	8	60.59	even	2	inner
180.2.h.b.179.7	yes	8	1.1	even	1	trivial
180.2.h.b.179.8	yes	8	15.14	odd	2	inner
900.2.e.f.251.1		8	60.47	odd	4
900.2.e.f.251.2		8	20.3	even	4
900.2.e.f.251.3		8	15.8	even	4
900.2.e.f.251.4		8	5.2	odd	4
900.2.e.f.251.5		8	5.3	odd	4
900.2.e.f.251.6		8	15.2	even	4
900.2.e.f.251.7		8	20.7	even	4
900.2.e.f.251.8		8	60.23	odd	4
2880.2.o.c.2879.1		8	120.29	odd	2
2880.2.o.c.2879.2		8	120.59	even	2
2880.2.o.c.2879.3		8	8.3	odd	2
2880.2.o.c.2879.4		8	8.5	even	2
2880.2.o.c.2879.5		8	24.11	even	2
2880.2.o.c.2879.6		8	24.5	odd	2
2880.2.o.c.2879.7		8	40.29	even	2
2880.2.o.c.2879.8		8	40.19	odd	2

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +(1.73205 - 1.41421i) q^{5} +3.16228 q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})\)	\(q+(0.866025 + 1.11803i) q^{2} +(-0.500000 + 1.93649i) q^{4} +(1.73205 - 1.41421i) q^{5} +3.16228 q^{7} +(-2.59808 + 1.11803i) q^{8} +(3.08114 + 0.711747i) q^{10} -5.47723 q^{11} +2.44949i q^{13} +(2.73861 + 3.53553i) q^{14} +(-3.50000 - 1.93649i) q^{16} +(1.87259 + 4.06121i) q^{20} +(-4.74342 - 6.12372i) q^{22} -4.47214i q^{23} +(1.00000 - 4.89898i) q^{25} +(-2.73861 + 2.12132i) q^{26} +(-1.58114 + 6.12372i) q^{28} -2.82843i q^{29} -7.74597i q^{31} +(-0.866025 - 5.59017i) q^{32} +(5.47723 - 4.47214i) q^{35} +7.34847i q^{37} +(-2.91886 + 5.61073i) q^{40} +1.41421i q^{41} -6.32456 q^{43} +(2.73861 - 10.6066i) q^{44} +(5.00000 - 3.87298i) q^{46} +8.94427i q^{47} +3.00000 q^{49} +(6.34325 - 3.12461i) q^{50} +(-4.74342 - 1.22474i) q^{52} +(-9.48683 + 7.74597i) q^{55} +(-8.21584 + 3.53553i) q^{56} +(3.16228 - 2.44949i) q^{58} +5.47723 q^{59} -10.0000 q^{61} +(8.66025 - 6.70820i) q^{62} +(5.50000 - 5.80948i) q^{64} +(3.46410 + 4.24264i) q^{65} +12.6491 q^{67} +(9.74342 + 2.25074i) q^{70} -14.6969i q^{73} +(-8.21584 + 6.36396i) q^{74} -17.3205 q^{77} +7.74597i q^{79} +(-8.80079 + 1.59565i) q^{80} +(-1.58114 + 1.22474i) q^{82} +8.94427i q^{83} +(-5.47723 - 7.07107i) q^{86} +(14.2302 - 6.12372i) q^{88} +9.89949i q^{89} +7.74597i q^{91} +(8.66025 + 2.23607i) q^{92} +(-10.0000 + 7.74597i) q^{94} +4.89898i q^{97} +(2.59808 + 3.35410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4}+O(q^{10}) \) 8 * q - 4 * q^4	\( 8 q - 4 q^{4} + 12 q^{10} - 28 q^{16} + 8 q^{25} - 36 q^{40} + 40 q^{46} + 24 q^{49} - 80 q^{61} + 44 q^{64} + 40 q^{70} - 80 q^{94}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^10 - 28 * q^16 + 8 * q^25 - 36 * q^40 + 40 * q^46 + 24 * q^49 - 80 * q^61 + 44 * q^64 + 40 * q^70 - 80 * q^94

Introduction

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