LMFDB - Embedded newform 648.2.d.e.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(325,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("648.325");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.d (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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			325.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	648.325
Dual form			648.2.d.e.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +3.73205i q^{5} -0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.36603 - 5.09808i) q^{10} +4.73205i q^{11} -2.46410i q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} +3.73205 q^{17} +3.26795i q^{19} +(-3.73205 + 6.46410i) q^{20} +(1.73205 - 6.46410i) q^{22} -8.73205 q^{23} -8.92820 q^{25} +(-0.901924 + 3.36603i) q^{26} +(-1.26795 - 0.732051i) q^{28} -5.19615i q^{29} +2.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} +(-5.09808 - 1.36603i) q^{34} -2.73205i q^{35} -5.00000i q^{37} +(1.19615 - 4.46410i) q^{38} +(7.46410 - 7.46410i) q^{40} -4.53590 q^{41} +9.66025i q^{43} +(-4.73205 + 8.19615i) q^{44} +(11.9282 + 3.19615i) q^{46} -3.46410 q^{47} -6.46410 q^{49} +(12.1962 + 3.26795i) q^{50} +(2.46410 - 4.26795i) q^{52} -0.928203i q^{53} -17.6603 q^{55} +(1.46410 + 1.46410i) q^{56} +(-1.90192 + 7.09808i) q^{58} +8.39230i q^{59} +9.00000i q^{61} +(-2.73205 - 0.732051i) q^{62} +8.00000i q^{64} +9.19615 q^{65} +4.73205i q^{67} +(6.46410 + 3.73205i) q^{68} +(-1.00000 + 3.73205i) q^{70} -5.66025 q^{71} +9.00000 q^{73} +(-1.83013 + 6.83013i) q^{74} +(-3.26795 + 5.66025i) q^{76} -3.46410i q^{77} +5.26795 q^{79} +(-12.9282 + 7.46410i) q^{80} +(6.19615 + 1.66025i) q^{82} -14.0000i q^{83} +13.9282i q^{85} +(3.53590 - 13.1962i) q^{86} +(9.46410 - 9.46410i) q^{88} +11.7321 q^{89} +1.80385i q^{91} +(-15.1244 - 8.73205i) q^{92} +(4.73205 + 1.26795i) q^{94} -12.1962 q^{95} -8.00000 q^{97} +(8.83013 + 2.36603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{7} - 8 q^{8} + 2 q^{10} + 4 q^{14} + 8 q^{16} + 8 q^{17} - 8 q^{20} - 28 q^{23} - 8 q^{25} - 14 q^{26} - 12 q^{28} + 8 q^{31} + 8 q^{32} - 10 q^{34} - 16 q^{38} + 16 q^{40} - 32 q^{41}+ \cdots + 18 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^7 - 8 * q^8 + 2 * q^10 + 4 * q^14 + 8 * q^16 + 8 * q^17 - 8 * q^20 - 28 * q^23 - 8 * q^25 - 14 * q^26 - 12 * q^28 + 8 * q^31 + 8 * q^32 - 10 * q^34 - 16 * q^38 + 16 * q^40 - 32 * q^41 - 12 * q^44 + 20 * q^46 - 12 * q^49 + 28 * q^50 - 4 * q^52 - 36 * q^55 - 8 * q^56 - 18 * q^58 - 4 * q^62 + 16 * q^65 + 12 * q^68 - 4 * q^70 + 12 * q^71 + 36 * q^73 + 10 * q^74 - 20 * q^76 + 28 * q^79 - 24 * q^80 + 4 * q^82 + 28 * q^86 + 24 * q^88 + 40 * q^89 - 12 * q^92 + 12 * q^94 - 28 * q^95 - 32 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$			3.73205i			1.66902i	0.550990	+	0.834512i	$0.314250\pi$
$5$			3.73205i			1.66902i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	−0.732051			−0.276689			−0.138345	−	0.990384i	$-0.544178\pi$
$7$	−0.732051			−0.276689			−0.138345	+	0.990384i	$0.544178\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	1.36603	−	5.09808i	0.431975	−	1.61215i
$11$			4.73205i			1.42677i	0.700774	+	0.713384i	$0.252838\pi$
$11$			4.73205i			1.42677i	−0.700774	+	0.713384i	$0.747162\pi$
$12$		0			0
$13$		−	2.46410i		−	0.683419i	−0.939806	−	0.341709i	$-0.888994\pi$
$13$		−	2.46410i		−	0.683419i	0.939806	−	0.341709i	$-0.111006\pi$
$14$	1.00000	+	0.267949i	0.267261	+	0.0716124i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	3.73205			0.905155			0.452578	−	0.891725i	$-0.350505\pi$
$17$	3.73205			0.905155			0.452578	+	0.891725i	$0.350505\pi$
$18$		0			0
$19$			3.26795i			0.749719i	0.927082	+	0.374859i	$0.122309\pi$
$19$			3.26795i			0.749719i	−0.927082	+	0.374859i	$0.877691\pi$
$20$	−3.73205	+	6.46410i	−0.834512	+	1.44542i
$21$		0			0
$22$	1.73205	−	6.46410i	0.369274	−	1.37815i
$23$	−8.73205			−1.82076			−0.910379	−	0.413775i	$-0.864210\pi$
$23$	−8.73205			−1.82076			−0.910379	+	0.413775i	$0.864210\pi$
$24$		0			0
$25$	−8.92820			−1.78564
$26$	−0.901924	+	3.36603i	−0.176882	+	0.660132i
$27$		0			0
$28$	−1.26795	−	0.732051i	−0.239620	−	0.138345i
$29$		−	5.19615i		−	0.964901i	−0.875923	−	0.482451i	$-0.839747\pi$
$29$		−	5.19615i		−	0.964901i	0.875923	−	0.482451i	$-0.160253\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$	−5.09808	−	1.36603i	−0.874313	−	0.234271i
$35$		−	2.73205i		−	0.461801i
$36$		0			0
$37$		−	5.00000i		−	0.821995i	−0.911636	−	0.410997i	$-0.865181\pi$
$37$		−	5.00000i		−	0.821995i	0.911636	−	0.410997i	$-0.134819\pi$
$38$	1.19615	−	4.46410i	0.194042	−	0.724173i
$39$		0			0
$40$	7.46410	−	7.46410i	1.18018	−	1.18018i
$41$	−4.53590			−0.708388			−0.354194	−	0.935172i	$-0.615245\pi$
$41$	−4.53590			−0.708388			−0.354194	+	0.935172i	$0.615245\pi$
$42$		0			0
$43$			9.66025i			1.47317i	0.676342	+	0.736587i	$0.263564\pi$
$43$			9.66025i			1.47317i	−0.676342	+	0.736587i	$0.736436\pi$
$44$	−4.73205	+	8.19615i	−0.713384	+	1.23562i
$45$		0			0
$46$	11.9282	+	3.19615i	1.75872	+	0.471247i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$		0			0
$49$	−6.46410			−0.923443
$50$	12.1962	+	3.26795i	1.72480	+	0.462158i
$51$		0			0
$52$	2.46410	−	4.26795i	0.341709	−	0.591858i
$53$		−	0.928203i		−	0.127499i	−0.997966	−	0.0637493i	$-0.979694\pi$
$53$		−	0.928203i		−	0.127499i	0.997966	−	0.0637493i	$-0.0203058\pi$
$54$		0			0
$55$	−17.6603			−2.38131
$56$	1.46410	+	1.46410i	0.195649	+	0.195649i
$57$		0			0
$58$	−1.90192	+	7.09808i	−0.249735	+	0.932023i
$59$			8.39230i			1.09259i	0.837594	+	0.546293i	$0.183961\pi$
$59$			8.39230i			1.09259i	−0.837594	+	0.546293i	$0.816039\pi$
$60$		0			0
$61$			9.00000i			1.15233i	0.817333	+	0.576166i	$0.195452\pi$
$61$			9.00000i			1.15233i	−0.817333	+	0.576166i	$0.804548\pi$
$62$	−2.73205	−	0.732051i	−0.346971	−	0.0929705i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	9.19615			1.14064
$66$		0			0
$67$			4.73205i			0.578112i	0.957312	+	0.289056i	$0.0933414\pi$
$67$			4.73205i			0.578112i	−0.957312	+	0.289056i	$0.906659\pi$
$68$	6.46410	+	3.73205i	0.783887	+	0.452578i
$69$		0			0
$70$	−1.00000	+	3.73205i	−0.119523	+	0.446065i
$71$	−5.66025			−0.671749			−0.335874	−	0.941907i	$-0.609032\pi$
$71$	−5.66025			−0.671749			−0.335874	+	0.941907i	$0.609032\pi$
$72$		0			0
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	−1.83013	+	6.83013i	−0.212748	+	0.793986i
$75$		0			0
$76$	−3.26795	+	5.66025i	−0.374859	+	0.649276i
$77$		−	3.46410i		−	0.394771i
$78$		0			0
$79$	5.26795			0.592691			0.296345	−	0.955081i	$-0.404232\pi$
$79$	5.26795			0.592691			0.296345	+	0.955081i	$0.404232\pi$
$80$	−12.9282	+	7.46410i	−1.44542	+	0.834512i
$81$		0			0
$82$	6.19615	+	1.66025i	0.684251	+	0.183344i
$83$		−	14.0000i		−	1.53670i	−0.640030	−	0.768350i	$-0.721078\pi$
$83$		−	14.0000i		−	1.53670i	0.640030	−	0.768350i	$-0.278922\pi$
$84$		0			0
$85$			13.9282i			1.51073i
$86$	3.53590	−	13.1962i	0.381286	−	1.42298i
$87$		0			0
$88$	9.46410	−	9.46410i	1.00888	−	1.00888i
$89$	11.7321			1.24359			0.621797	−	0.783178i	$-0.286403\pi$
$89$	11.7321			1.24359			0.621797	+	0.783178i	$0.286403\pi$
$90$		0			0
$91$			1.80385i			0.189095i
$92$	−15.1244	−	8.73205i	−1.57682	−	0.910379i
$93$		0			0
$94$	4.73205	+	1.26795i	0.488074	+	0.130779i
$95$	−12.1962			−1.25130
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	8.83013	+	2.36603i	0.891978	+	0.239005i
$99$		0			0
$100$	−15.4641	−	8.92820i	−1.54641	−	0.892820i
$101$			8.00000i			0.796030i	0.917379	+	0.398015i	$0.130301\pi$
$101$			8.00000i			0.796030i	−0.917379	+	0.398015i	$0.869699\pi$
$102$		0			0
$103$	−3.46410			−0.341328			−0.170664	−	0.985329i	$-0.554591\pi$
$103$	−3.46410			−0.341328			−0.170664	+	0.985329i	$0.554591\pi$
$104$	−4.92820	+	4.92820i	−0.483250	+	0.483250i
$105$		0			0
$106$	−0.339746	+	1.26795i	−0.0329990	+	0.123154i
$107$			10.3923i			1.00466i	0.864675	+	0.502331i	$0.167524\pi$
$107$			10.3923i			1.00466i	−0.864675	+	0.502331i	$0.832476\pi$
$108$		0			0
$109$			12.8564i			1.23142i	0.787973	+	0.615710i	$0.211131\pi$
$109$			12.8564i			1.23142i	−0.787973	+	0.615710i	$0.788869\pi$
$110$	24.1244	+	6.46410i	2.30017	+	0.616328i
$111$		0			0
$112$	−1.46410	−	2.53590i	−0.138345	−	0.239620i
$113$	7.73205			0.727370			0.363685	−	0.931522i	$-0.381518\pi$
$113$	7.73205			0.727370			0.363685	+	0.931522i	$0.381518\pi$
$114$		0			0
$115$		−	32.5885i		−	3.03889i
$116$	5.19615	−	9.00000i	0.482451	−	0.835629i
$117$		0			0
$118$	3.07180	−	11.4641i	0.282782	−	1.05536i
$119$	−2.73205			−0.250447
$120$		0			0
$121$	−11.3923			−1.03566
$122$	3.29423	−	12.2942i	0.298245	−	1.11307i
$123$		0			0
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		−	14.6603i		−	1.31125i
$126$		0			0
$127$	−13.6603			−1.21215			−0.606076	−	0.795407i	$-0.707257\pi$
$127$	−13.6603			−1.21215			−0.606076	+	0.795407i	$0.707257\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	−12.5622	−	3.36603i	−1.10178	−	0.295220i
$131$			0.196152i			0.0171379i	0.999963	+	0.00856896i	$0.00272762\pi$
$131$			0.196152i			0.0171379i	−0.999963	+	0.00856896i	$0.997272\pi$
$132$		0			0
$133$		−	2.39230i		−	0.207439i
$134$	1.73205	−	6.46410i	0.149626	−	0.558413i
$135$		0			0
$136$	−7.46410	−	7.46410i	−0.640041	−	0.640041i
$137$	17.1962			1.46917			0.734583	−	0.678519i	$-0.237378\pi$
$137$	17.1962			1.46917			0.734583	+	0.678519i	$0.237378\pi$
$138$		0			0
$139$		−	19.4641i		−	1.65092i	−0.564458	−	0.825462i	$-0.690915\pi$
$139$		−	19.4641i		−	1.65092i	0.564458	−	0.825462i	$-0.309085\pi$
$140$	2.73205	−	4.73205i	0.230900	−	0.399931i
$141$		0			0
$142$	7.73205	+	2.07180i	0.648859	+	0.173861i
$143$	11.6603			0.975079
$144$		0			0
$145$	19.3923			1.61044
$146$	−12.2942	−	3.29423i	−1.01748	−	0.272632i
$147$		0			0
$148$	5.00000	−	8.66025i	0.410997	−	0.711868i
$149$		−	5.19615i		−	0.425685i	−0.977086	−	0.212843i	$-0.931728\pi$
$149$		−	5.19615i		−	0.425685i	0.977086	−	0.212843i	$-0.0682722\pi$
$150$		0			0
$151$	13.8564			1.12762			0.563809	−	0.825905i	$-0.309335\pi$
$151$	13.8564			1.12762			0.563809	+	0.825905i	$0.309335\pi$
$152$	6.53590	−	6.53590i	0.530131	−	0.530131i
$153$		0			0
$154$	−1.26795	+	4.73205i	−0.102174	+	0.381320i
$155$			7.46410i			0.599531i
$156$		0			0
$157$		−	2.46410i		−	0.196657i	−0.995154	−	0.0983284i	$-0.968650\pi$
$157$		−	2.46410i		−	0.196657i	0.995154	−	0.0983284i	$-0.0313495\pi$
$158$	−7.19615	−	1.92820i	−0.572495	−	0.153400i
$159$		0			0
$160$	20.3923	−	5.46410i	1.61215	−	0.431975i
$161$	6.39230			0.503784
$162$		0			0
$163$			6.53590i			0.511931i	0.966686	+	0.255966i	$0.0823934\pi$
$163$			6.53590i			0.511931i	−0.966686	+	0.255966i	$0.917607\pi$
$164$	−7.85641	−	4.53590i	−0.613482	−	0.354194i
$165$		0			0
$166$	−5.12436	+	19.1244i	−0.397727	+	1.48434i
$167$	14.7321			1.14000			0.570000	−	0.821645i	$-0.306943\pi$
$167$	14.7321			1.14000			0.570000	+	0.821645i	$0.306943\pi$
$168$		0			0
$169$	6.92820			0.532939
$170$	5.09808	−	19.0263i	0.391005	−	1.45925i
$171$		0			0
$172$	−9.66025	+	16.7321i	−0.736587	+	1.27581i
$173$			1.73205i			0.131685i	0.997830	+	0.0658427i	$0.0209736\pi$
$173$			1.73205i			0.131685i	−0.997830	+	0.0658427i	$0.979026\pi$
$174$		0			0
$175$	6.53590			0.494067
$176$	−16.3923	+	9.46410i	−1.23562	+	0.713384i
$177$		0			0
$178$	−16.0263	−	4.29423i	−1.20122	−	0.321866i
$179$		−	14.0000i		−	1.04641i	−0.852207	−	0.523205i	$-0.824736\pi$
$179$		−	14.0000i		−	1.04641i	0.852207	−	0.523205i	$-0.175264\pi$
$180$		0			0
$181$		−	6.53590i		−	0.485810i	−0.970050	−	0.242905i	$-0.921900\pi$
$181$		−	6.53590i		−	0.485810i	0.970050	−	0.242905i	$-0.0781002\pi$
$182$	0.660254	−	2.46410i	0.0489413	−	0.182651i
$183$		0			0
$184$	17.4641	+	17.4641i	1.28747	+	1.28747i
$185$	18.6603			1.37193
$186$		0			0
$187$			17.6603i			1.29145i
$188$	−6.00000	−	3.46410i	−0.437595	−	0.252646i
$189$		0			0
$190$	16.6603	+	4.46410i	1.20866	+	0.323860i
$191$	−16.5885			−1.20030			−0.600149	−	0.799888i	$-0.704892\pi$
$191$	−16.5885			−1.20030			−0.600149	+	0.799888i	$0.704892\pi$
$192$		0			0
$193$	10.8564			0.781461			0.390731	−	0.920505i	$-0.372222\pi$
$193$	10.8564			0.781461			0.390731	+	0.920505i	$0.372222\pi$
$194$	10.9282	+	2.92820i	0.784599	+	0.210233i
$195$		0			0
$196$	−11.1962	−	6.46410i	−0.799725	−	0.461722i
$197$			4.12436i			0.293848i	0.989148	+	0.146924i	$0.0469373\pi$
$197$			4.12436i			0.293848i	−0.989148	+	0.146924i	$0.953063\pi$
$198$		0			0
$199$	2.39230			0.169586			0.0847930	−	0.996399i	$-0.472977\pi$
$199$	2.39230			0.169586			0.0847930	+	0.996399i	$0.472977\pi$
$200$	17.8564	+	17.8564i	1.26264	+	1.26264i
$201$		0			0
$202$	2.92820	−	10.9282i	0.206028	−	0.768906i
$203$			3.80385i			0.266978i
$204$		0			0
$205$		−	16.9282i		−	1.18232i
$206$	4.73205	+	1.26795i	0.329698	+	0.0883422i
$207$		0			0
$208$	8.53590	−	4.92820i	0.591858	−	0.341709i
$209$	−15.4641			−1.06967
$210$		0			0
$211$			26.0526i			1.79353i	0.442505	+	0.896766i	$0.354090\pi$
$211$			26.0526i			1.79353i	−0.442505	+	0.896766i	$0.645910\pi$
$212$	0.928203	−	1.60770i	0.0637493	−	0.110417i
$213$		0			0
$214$	3.80385	−	14.1962i	0.260026	−	0.970429i
$215$	−36.0526			−2.45876
$216$		0			0
$217$	−1.46410			−0.0993897
$218$	4.70577	−	17.5622i	0.318715	−	1.18946i
$219$		0			0
$220$	−30.5885	−	17.6603i	−2.06227	−	1.19065i
$221$		−	9.19615i		−	0.618600i
$222$		0			0
$223$	23.1244			1.54852			0.774261	−	0.632867i	$-0.218122\pi$
$223$	23.1244			1.54852			0.774261	+	0.632867i	$0.218122\pi$
$224$	1.07180	+	4.00000i	0.0716124	+	0.267261i
$225$		0			0
$226$	−10.5622	−	2.83013i	−0.702586	−	0.188257i
$227$			6.73205i			0.446822i	0.974724	+	0.223411i	$0.0717192\pi$
$227$			6.73205i			0.446822i	−0.974724	+	0.223411i	$0.928281\pi$
$228$		0			0
$229$		−	11.3923i		−	0.752825i	−0.926452	−	0.376412i	$-0.877158\pi$
$229$		−	11.3923i		−	0.752825i	0.926452	−	0.376412i	$-0.122842\pi$
$230$	−11.9282	+	44.5167i	−0.786522	+	2.93534i
$231$		0			0
$232$	−10.3923	+	10.3923i	−0.682288	+	0.682288i
$233$	−3.73205			−0.244495			−0.122247	−	0.992500i	$-0.539010\pi$
$233$	−3.73205			−0.244495			−0.122247	+	0.992500i	$0.539010\pi$
$234$		0			0
$235$		−	12.9282i		−	0.843343i
$236$	−8.39230	+	14.5359i	−0.546293	+	0.946206i
$237$		0			0
$238$	3.73205	+	1.00000i	0.241913	+	0.0648204i
$239$	−7.85641			−0.508189			−0.254094	−	0.967179i	$-0.581777\pi$
$239$	−7.85641			−0.508189			−0.254094	+	0.967179i	$0.581777\pi$
$240$		0			0
$241$	−4.46410			−0.287558			−0.143779	−	0.989610i	$-0.545925\pi$
$241$	−4.46410			−0.287558			−0.143779	+	0.989610i	$0.545925\pi$
$242$	15.5622	+	4.16987i	1.00037	+	0.268050i
$243$		0			0
$244$	−9.00000	+	15.5885i	−0.576166	+	0.997949i
$245$		−	24.1244i		−	1.54125i
$246$		0			0
$247$	8.05256			0.512372
$248$	−4.00000	−	4.00000i	−0.254000	−	0.254000i
$249$		0			0
$250$	−5.36603	+	20.0263i	−0.339377	+	1.26657i
$251$			7.26795i			0.458749i	0.973338	+	0.229374i	$0.0736680\pi$
$251$			7.26795i			0.458749i	−0.973338	+	0.229374i	$0.926332\pi$
$252$		0			0
$253$		−	41.3205i		−	2.59780i
$254$	18.6603	+	5.00000i	1.17085	+	0.313728i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	3.33975			0.208328			0.104164	−	0.994560i	$-0.466783\pi$
$257$	3.33975			0.208328			0.104164	+	0.994560i	$0.466783\pi$
$258$		0			0
$259$			3.66025i			0.227437i
$260$	15.9282	+	9.19615i	0.987825	+	0.570321i
$261$		0			0
$262$	0.0717968	−	0.267949i	0.00443562	−	0.0165540i
$263$	16.2487			1.00194			0.500969	−	0.865465i	$-0.332977\pi$
$263$	16.2487			1.00194			0.500969	+	0.865465i	$0.332977\pi$
$264$		0			0
$265$	3.46410			0.212798
$266$	−0.875644	+	3.26795i	−0.0536892	+	0.200371i
$267$		0			0
$268$	−4.73205	+	8.19615i	−0.289056	+	0.500660i
$269$			25.7321i			1.56891i	0.620185	+	0.784455i	$0.287057\pi$
$269$			25.7321i			1.56891i	−0.620185	+	0.784455i	$0.712943\pi$
$270$		0			0
$271$	10.7321			0.651926			0.325963	−	0.945383i	$-0.394312\pi$
$271$	10.7321			0.651926			0.325963	+	0.945383i	$0.394312\pi$
$272$	7.46410	+	12.9282i	0.452578	+	0.783887i
$273$		0			0
$274$	−23.4904	−	6.29423i	−1.41911	−	0.380248i
$275$		−	42.2487i		−	2.54769i
$276$		0			0
$277$			9.85641i			0.592214i	0.955155	+	0.296107i	$0.0956885\pi$
$277$			9.85641i			0.592214i	−0.955155	+	0.296107i	$0.904311\pi$
$278$	−7.12436	+	26.5885i	−0.427290	+	1.59467i
$279$		0			0
$280$	−5.46410	+	5.46410i	−0.326543	+	0.326543i
$281$	−13.7321			−0.819185			−0.409593	−	0.912268i	$-0.634329\pi$
$281$	−13.7321			−0.819185			−0.409593	+	0.912268i	$0.634329\pi$
$282$		0			0
$283$		−	6.39230i		−	0.379983i	−0.981786	−	0.189992i	$-0.939154\pi$
$283$		−	6.39230i		−	0.379983i	0.981786	−	0.189992i	$-0.0608461\pi$
$284$	−9.80385	−	5.66025i	−0.581751	−	0.335874i
$285$		0			0
$286$	−15.9282	−	4.26795i	−0.941854	−	0.252369i
$287$	3.32051			0.196003
$288$		0			0
$289$	−3.07180			−0.180694
$290$	−26.4904	−	7.09808i	−1.55557	−	0.416813i
$291$		0			0
$292$	15.5885	+	9.00000i	0.912245	+	0.526685i
$293$			3.33975i			0.195110i	0.995230	+	0.0975550i	$0.0311022\pi$
$293$			3.33975i			0.195110i	−0.995230	+	0.0975550i	$0.968898\pi$
$294$		0			0
$295$	−31.3205			−1.82355
$296$	−10.0000	+	10.0000i	−0.581238	+	0.581238i
$297$		0			0
$298$	−1.90192	+	7.09808i	−0.110175	+	0.411181i
$299$			21.5167i			1.24434i
$300$		0			0
$301$		−	7.07180i		−	0.407612i
$302$	−18.9282	−	5.07180i	−1.08920	−	0.291849i
$303$		0			0
$304$	−11.3205	+	6.53590i	−0.649276	+	0.374859i
$305$	−33.5885			−1.92327
$306$		0			0
$307$			14.7846i			0.843802i	0.906642	+	0.421901i	$0.138637\pi$
$307$			14.7846i			0.843802i	−0.906642	+	0.421901i	$0.861363\pi$
$308$	3.46410	−	6.00000i	0.197386	−	0.341882i
$309$		0			0
$310$	2.73205	−	10.1962i	0.155170	−	0.579103i
$311$	19.3205			1.09557			0.547783	−	0.836621i	$-0.315472\pi$
$311$	19.3205			1.09557			0.547783	+	0.836621i	$0.315472\pi$
$312$		0			0
$313$	2.46410			0.139279			0.0696396	−	0.997572i	$-0.477815\pi$
$313$	2.46410			0.139279			0.0696396	+	0.997572i	$0.477815\pi$
$314$	−0.901924	+	3.36603i	−0.0508985	+	0.189956i
$315$		0			0
$316$	9.12436	+	5.26795i	0.513285	+	0.296345i
$317$			1.19615i			0.0671826i	0.999436	+	0.0335913i	$0.0106945\pi$
$317$			1.19615i			0.0671826i	−0.999436	+	0.0335913i	$0.989306\pi$
$318$		0			0
$319$	24.5885			1.37669
$320$	−29.8564			−1.66902
$321$		0			0
$322$	−8.73205	−	2.33975i	−0.486618	−	0.130389i
$323$			12.1962i			0.678612i
$324$		0			0
$325$			22.0000i			1.22034i
$326$	2.39230	−	8.92820i	0.132498	−	0.494487i
$327$		0			0
$328$	9.07180	+	9.07180i	0.500906	+	0.500906i
$329$	2.53590			0.139809
$330$		0			0
$331$			13.1244i			0.721380i	0.932686	+	0.360690i	$0.117459\pi$
$331$			13.1244i			0.721380i	−0.932686	+	0.360690i	$0.882541\pi$
$332$	14.0000	−	24.2487i	0.768350	−	1.33082i
$333$		0			0
$334$	−20.1244	−	5.39230i	−1.10116	−	0.295054i
$335$	−17.6603			−0.964883
$336$		0			0
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$	−9.46410	−	2.53590i	−0.514779	−	0.137935i
$339$		0			0
$340$	−13.9282	+	24.1244i	−0.755363	+	1.30833i
$341$			9.46410i			0.512510i
$342$		0			0
$343$	9.85641			0.532196
$344$	19.3205	−	19.3205i	1.04169	−	1.04169i
$345$		0			0
$346$	0.633975	−	2.36603i	0.0340827	−	0.127198i
$347$			6.73205i			0.361395i	0.983539	+	0.180698i	$0.0578356\pi$
$347$			6.73205i			0.361395i	−0.983539	+	0.180698i	$0.942164\pi$
$348$		0			0
$349$			11.8564i			0.634659i	0.948315	+	0.317329i	$0.102786\pi$
$349$			11.8564i			0.634659i	−0.948315	+	0.317329i	$0.897214\pi$
$350$	−8.92820	−	2.39230i	−0.477233	−	0.127874i
$351$		0			0
$352$	25.8564	−	6.92820i	1.37815	−	0.369274i
$353$	6.92820			0.368751			0.184376	−	0.982856i	$-0.440974\pi$
$353$	6.92820			0.368751			0.184376	+	0.982856i	$0.440974\pi$
$354$		0			0
$355$		−	21.1244i		−	1.12116i
$356$	20.3205	+	11.7321i	1.07698	+	0.621797i
$357$		0			0
$358$	−5.12436	+	19.1244i	−0.270831	+	1.01075i
$359$	−1.12436			−0.0593412			−0.0296706	−	0.999560i	$-0.509446\pi$
$359$	−1.12436			−0.0593412			−0.0296706	+	0.999560i	$0.509446\pi$
$360$		0			0
$361$	8.32051			0.437921
$362$	−2.39230	+	8.92820i	−0.125737	+	0.469256i
$363$		0			0
$364$	−1.80385	+	3.12436i	−0.0945473	+	0.163761i
$365$			33.5885i			1.75810i
$366$		0			0
$367$	2.53590			0.132373			0.0661864	−	0.997807i	$-0.478917\pi$
$367$	2.53590			0.132373			0.0661864	+	0.997807i	$0.478917\pi$
$368$	−17.4641	−	30.2487i	−0.910379	−	1.57682i
$369$		0			0
$370$	−25.4904	−	6.83013i	−1.32518	−	0.355081i
$371$			0.679492i			0.0352775i
$372$		0			0
$373$		−	22.9282i		−	1.18718i	−0.804769	−	0.593589i	$-0.797711\pi$
$373$		−	22.9282i		−	1.18718i	0.804769	−	0.593589i	$-0.202289\pi$
$374$	6.46410	−	24.1244i	0.334251	−	1.24744i
$375$		0			0
$376$	6.92820	+	6.92820i	0.357295	+	0.357295i
$377$	−12.8038			−0.659432
$378$		0			0
$379$		−	10.0000i		−	0.513665i	−0.966456	−	0.256833i	$-0.917321\pi$
$379$		−	10.0000i		−	0.513665i	0.966456	−	0.256833i	$-0.0826790\pi$
$380$	−21.1244	−	12.1962i	−1.08366	−	0.625649i
$381$		0			0
$382$	22.6603	+	6.07180i	1.15940	+	0.310660i
$383$	20.1962			1.03198			0.515988	−	0.856596i	$-0.327425\pi$
$383$	20.1962			1.03198			0.515988	+	0.856596i	$0.327425\pi$
$384$		0			0
$385$	12.9282			0.658882
$386$	−14.8301	−	3.97372i	−0.754834	−	0.202257i
$387$		0			0
$388$	−13.8564	−	8.00000i	−0.703452	−	0.406138i
$389$			16.9282i			0.858294i	0.903235	+	0.429147i	$0.141186\pi$
$389$			16.9282i			0.858294i	−0.903235	+	0.429147i	$0.858814\pi$
$390$		0			0
$391$	−32.5885			−1.64807
$392$	12.9282	+	12.9282i	0.652973	+	0.652973i
$393$		0			0
$394$	1.50962	−	5.63397i	0.0760535	−	0.283836i
$395$			19.6603i			0.989215i
$396$		0			0
$397$			32.4641i			1.62933i	0.579934	+	0.814663i	$0.303078\pi$
$397$			32.4641i			1.62933i	−0.579934	+	0.814663i	$0.696922\pi$
$398$	−3.26795	−	0.875644i	−0.163807	−	0.0438921i
$399$		0			0
$400$	−17.8564	−	30.9282i	−0.892820	−	1.54641i
$401$	9.58846			0.478825			0.239412	−	0.970918i	$-0.423045\pi$
$401$	9.58846			0.478825			0.239412	+	0.970918i	$0.423045\pi$
$402$		0			0
$403$		−	4.92820i		−	0.245491i
$404$	−8.00000	+	13.8564i	−0.398015	+	0.689382i
$405$		0			0
$406$	1.39230	−	5.19615i	0.0690989	−	0.257881i
$407$	23.6603			1.17280
$408$		0			0
$409$	28.7128			1.41976			0.709879	−	0.704324i	$-0.248750\pi$
$409$	28.7128			1.41976			0.709879	+	0.704324i	$0.248750\pi$
$410$	−6.19615	+	23.1244i	−0.306006	+	1.14203i
$411$		0			0
$412$	−6.00000	−	3.46410i	−0.295599	−	0.170664i
$413$		−	6.14359i		−	0.302306i
$414$		0			0
$415$	52.2487			2.56479
$416$	−13.4641	+	3.60770i	−0.660132	+	0.176882i
$417$		0			0
$418$	21.1244	+	5.66025i	1.03323	+	0.276852i
$419$			21.4641i			1.04859i	0.851537	+	0.524295i	$0.175671\pi$
$419$			21.4641i			1.04859i	−0.851537	+	0.524295i	$0.824329\pi$
$420$		0			0
$421$		−	13.0000i		−	0.633581i	−0.948495	−	0.316791i	$-0.897395\pi$
$421$		−	13.0000i		−	0.633581i	0.948495	−	0.316791i	$-0.102605\pi$
$422$	9.53590	−	35.5885i	0.464200	−	1.73242i
$423$		0			0
$424$	−1.85641	+	1.85641i	−0.0901551	+	0.0901551i
$425$	−33.3205			−1.61628
$426$		0			0
$427$		−	6.58846i		−	0.318838i
$428$	−10.3923	+	18.0000i	−0.502331	+	0.870063i
$429$		0			0
$430$	49.2487	+	13.1962i	2.37498	+	0.636375i
$431$	21.7128			1.04587			0.522935	−	0.852373i	$-0.324837\pi$
$431$	21.7128			1.04587			0.522935	+	0.852373i	$0.324837\pi$
$432$		0			0
$433$	−21.7846			−1.04690			−0.523451	−	0.852056i	$-0.675356\pi$
$433$	−21.7846			−1.04690			−0.523451	+	0.852056i	$0.675356\pi$
$434$	2.00000	+	0.535898i	0.0960031	+	0.0257239i
$435$		0			0
$436$	−12.8564	+	22.2679i	−0.615710	+	1.06644i
$437$		−	28.5359i		−	1.36506i
$438$		0			0
$439$	−30.0000			−1.43182			−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000			−1.43182			−0.715911	+	0.698192i	$0.753988\pi$
$440$	35.3205	+	35.3205i	1.68384	+	1.68384i
$441$		0			0
$442$	−3.36603	+	12.5622i	−0.160106	+	0.597522i
$443$		−	29.3205i		−	1.39306i	−0.717528	−	0.696530i	$-0.754726\pi$
$443$		−	29.3205i		−	1.39306i	0.717528	−	0.696530i	$-0.245274\pi$
$444$		0			0
$445$			43.7846i			2.07559i
$446$	−31.5885	−	8.46410i	−1.49576	−	0.400787i
$447$		0			0
$448$		−	5.85641i		−	0.276689i
$449$	24.9282			1.17643			0.588217	−	0.808703i	$-0.299830\pi$
$449$	24.9282			1.17643			0.588217	+	0.808703i	$0.299830\pi$
$450$		0			0
$451$		−	21.4641i		−	1.01071i
$452$	13.3923	+	7.73205i	0.629921	+	0.363685i
$453$		0			0
$454$	2.46410	−	9.19615i	0.115646	−	0.431597i
$455$	−6.73205			−0.315603
$456$		0			0
$457$	−6.32051			−0.295661			−0.147830	−	0.989013i	$-0.547229\pi$
$457$	−6.32051			−0.295661			−0.147830	+	0.989013i	$0.547229\pi$
$458$	−4.16987	+	15.5622i	−0.194845	+	0.727173i
$459$		0			0
$460$	32.5885	−	56.4449i	1.51944	−	2.63176i
$461$			41.3205i			1.92449i	0.272188	+	0.962244i	$0.412253\pi$
$461$			41.3205i			1.92449i	−0.272188	+	0.962244i	$0.587747\pi$
$462$		0			0
$463$	13.4641			0.625730			0.312865	−	0.949798i	$-0.398711\pi$
$463$	13.4641			0.625730			0.312865	+	0.949798i	$0.398711\pi$
$464$	18.0000	−	10.3923i	0.835629	−	0.482451i
$465$		0			0
$466$	5.09808	+	1.36603i	0.236164	+	0.0632799i
$467$		−	24.7846i		−	1.14689i	−0.819242	−	0.573447i	$-0.805606\pi$
$467$		−	24.7846i		−	1.14689i	0.819242	−	0.573447i	$-0.194394\pi$
$468$		0			0
$469$		−	3.46410i		−	0.159957i
$470$	−4.73205	+	17.6603i	−0.218273	+	0.814607i
$471$		0			0
$472$	16.7846	−	16.7846i	0.772574	−	0.772574i
$473$	−45.7128			−2.10188
$474$		0			0
$475$		−	29.1769i		−	1.33873i
$476$	−4.73205	−	2.73205i	−0.216893	−	0.125223i
$477$		0			0
$478$	10.7321	+	2.87564i	0.490873	+	0.131529i
$479$	−1.66025			−0.0758589			−0.0379295	−	0.999280i	$-0.512076\pi$
$479$	−1.66025			−0.0758589			−0.0379295	+	0.999280i	$0.512076\pi$
$480$		0			0
$481$	−12.3205			−0.561767
$482$	6.09808	+	1.63397i	0.277760	+	0.0744255i
$483$		0			0
$484$	−19.7321	−	11.3923i	−0.896911	−	0.517832i
$485$		−	29.8564i		−	1.35571i
$486$		0			0
$487$	−25.7128			−1.16516			−0.582579	−	0.812774i	$-0.697956\pi$
$487$	−25.7128			−1.16516			−0.582579	+	0.812774i	$0.697956\pi$
$488$	18.0000	−	18.0000i	0.814822	−	0.814822i
$489$		0			0
$490$	−8.83013	+	32.9545i	−0.398904	+	1.48873i
$491$			13.8038i			0.622959i	0.950253	+	0.311479i	$0.100825\pi$
$491$			13.8038i			0.622959i	−0.950253	+	0.311479i	$0.899175\pi$
$492$		0			0
$493$		−	19.3923i		−	0.873385i
$494$	−11.0000	−	2.94744i	−0.494913	−	0.132612i
$495$		0			0
$496$	4.00000	+	6.92820i	0.179605	+	0.311086i
$497$	4.14359			0.185866
$498$		0			0
$499$			8.19615i			0.366910i	0.983028	+	0.183455i	$0.0587282\pi$
$499$			8.19615i			0.366910i	−0.983028	+	0.183455i	$0.941272\pi$
$500$	14.6603	−	25.3923i	0.655626	−	1.13558i
$501$		0			0
$502$	2.66025	−	9.92820i	0.118733	−	0.443117i
$503$	0.679492			0.0302970			0.0151485	−	0.999885i	$-0.495178\pi$
$503$	0.679492			0.0302970			0.0151485	+	0.999885i	$0.495178\pi$
$504$		0			0
$505$	−29.8564			−1.32859
$506$	−15.1244	+	56.4449i	−0.672360	+	2.50928i
$507$		0			0
$508$	−23.6603	−	13.6603i	−1.04975	−	0.606076i
$509$		−	29.3205i		−	1.29961i	−0.760102	−	0.649804i	$-0.774851\pi$
$509$		−	29.3205i		−	1.29961i	0.760102	−	0.649804i	$-0.225149\pi$
$510$		0			0
$511$	−6.58846			−0.291456
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	−4.56218	−	1.22243i	−0.201229	−	0.0539192i
$515$		−	12.9282i		−	0.569685i
$516$		0			0
$517$		−	16.3923i		−	0.720933i
$518$	1.33975	−	5.00000i	0.0588651	−	0.219687i
$519$		0			0
$520$	−18.3923	−	18.3923i	−0.806556	−	0.806556i
$521$	−26.7846			−1.17346			−0.586728	−	0.809784i	$-0.699584\pi$
$521$	−26.7846			−1.17346			−0.586728	+	0.809784i	$0.699584\pi$
$522$		0			0
$523$		−	13.2679i		−	0.580167i	−0.957001	−	0.290083i	$-0.906317\pi$
$523$		−	13.2679i		−	0.580167i	0.957001	−	0.290083i	$-0.0936831\pi$
$524$	−0.196152	+	0.339746i	−0.00856896	+	0.0148419i
$525$		0			0
$526$	−22.1962	−	5.94744i	−0.967798	−	0.259321i
$527$	7.46410			0.325141
$528$		0			0
$529$	53.2487			2.31516
$530$	−4.73205	−	1.26795i	−0.205547	−	0.0550762i
$531$		0			0
$532$	2.39230	−	4.14359i	0.103720	−	0.179648i
$533$			11.1769i			0.484126i
$534$		0			0
$535$	−38.7846			−1.67680
$536$	9.46410	−	9.46410i	0.408787	−	0.408787i
$537$		0			0
$538$	9.41858	−	35.1506i	0.406064	−	1.51545i
$539$		−	30.5885i		−	1.31754i
$540$		0			0
$541$		−	24.1769i		−	1.03945i	−0.854335	−	0.519723i	$-0.826035\pi$
$541$		−	24.1769i		−	1.03945i	0.854335	−	0.519723i	$-0.173965\pi$
$542$	−14.6603	−	3.92820i	−0.629712	−	0.168731i
$543$		0			0
$544$	−5.46410	−	20.3923i	−0.234271	−	0.874313i
$545$	−47.9808			−2.05527
$546$		0			0
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	29.7846	+	17.1962i	1.27234	+	0.734583i
$549$		0			0
$550$	−15.4641	+	57.7128i	−0.659392	+	2.46088i
$551$	16.9808			0.723405
$552$		0			0
$553$	−3.85641			−0.163991
$554$	3.60770	−	13.4641i	0.153276	−	0.572035i
$555$		0			0
$556$	19.4641	−	33.7128i	0.825462	−	1.42974i
$557$			13.0526i			0.553055i	0.961006	+	0.276527i	$0.0891836\pi$
$557$			13.0526i			0.553055i	−0.961006	+	0.276527i	$0.910816\pi$
$558$		0			0
$559$	23.8038			1.00680
$560$	9.46410	−	5.46410i	0.399931	−	0.230900i
$561$		0			0
$562$	18.7583	+	5.02628i	0.791272	+	0.212021i
$563$			24.2487i			1.02196i	0.859592	+	0.510981i	$0.170718\pi$
$563$			24.2487i			1.02196i	−0.859592	+	0.510981i	$0.829282\pi$
$564$		0			0
$565$			28.8564i			1.21400i
$566$	−2.33975	+	8.73205i	−0.0983469	+	0.367035i
$567$		0			0
$568$	11.3205	+	11.3205i	0.474998	+	0.474998i
$569$	33.5885			1.40810			0.704051	−	0.710150i	$-0.251373\pi$
$569$	33.5885			1.40810			0.704051	+	0.710150i	$0.251373\pi$
$570$		0			0
$571$			26.2487i			1.09847i	0.835667	+	0.549237i	$0.185082\pi$
$571$			26.2487i			1.09847i	−0.835667	+	0.549237i	$0.814918\pi$
$572$	20.1962	+	11.6603i	0.844444	+	0.487540i
$573$		0			0
$574$	−4.53590	−	1.21539i	−0.189325	−	0.0507294i
$575$	77.9615			3.25122
$576$		0			0
$577$	−45.2487			−1.88373			−0.941864	−	0.335994i	$-0.890928\pi$
$577$	−45.2487			−1.88373			−0.941864	+	0.335994i	$0.890928\pi$
$578$	4.19615	+	1.12436i	0.174537	+	0.0467670i
$579$		0			0
$580$	33.5885	+	19.3923i	1.39468	+	0.805222i
$581$			10.2487i			0.425188i
$582$		0			0
$583$	4.39230			0.181911
$584$	−18.0000	−	18.0000i	−0.744845	−	0.744845i
$585$		0			0
$586$	1.22243	−	4.56218i	0.0504982	−	0.188462i
$587$		−	42.3013i		−	1.74596i	−0.487756	−	0.872980i	$-0.662184\pi$
$587$		−	42.3013i		−	1.74596i	0.487756	−	0.872980i	$-0.337816\pi$
$588$		0			0
$589$			6.53590i			0.269307i
$590$	42.7846	+	11.4641i	1.76141	+	0.471970i
$591$		0			0
$592$	17.3205	−	10.0000i	0.711868	−	0.410997i
$593$	14.4115			0.591811			0.295906	−	0.955217i	$-0.404379\pi$
$593$	14.4115			0.591811			0.295906	+	0.955217i	$0.404379\pi$
$594$		0			0
$595$		−	10.1962i		−	0.418001i
$596$	5.19615	−	9.00000i	0.212843	−	0.368654i
$597$		0			0
$598$	7.87564	−	29.3923i	0.322059	−	1.20194i
$599$	8.24871			0.337033			0.168517	−	0.985699i	$-0.446102\pi$
$599$	8.24871			0.337033			0.168517	+	0.985699i	$0.446102\pi$
$600$		0			0
$601$	17.2487			0.703590			0.351795	−	0.936077i	$-0.385571\pi$
$601$	17.2487			0.703590			0.351795	+	0.936077i	$0.385571\pi$
$602$	−2.58846	+	9.66025i	−0.105498	+	0.393723i
$603$		0			0
$604$	24.0000	+	13.8564i	0.976546	+	0.563809i
$605$		−	42.5167i		−	1.72855i
$606$		0			0
$607$	−25.9090			−1.05161			−0.525806	−	0.850604i	$-0.676236\pi$
$607$	−25.9090			−1.05161			−0.525806	+	0.850604i	$0.676236\pi$
$608$	17.8564	−	4.78461i	0.724173	−	0.194042i
$609$		0			0
$610$	45.8827	+	12.2942i	1.85774	+	0.497779i
$611$			8.53590i			0.345325i
$612$		0			0
$613$			24.3923i			0.985196i	0.870257	+	0.492598i	$0.163953\pi$
$613$			24.3923i			0.985196i	−0.870257	+	0.492598i	$0.836047\pi$
$614$	5.41154	−	20.1962i	0.218392	−	0.815050i
$615$		0			0
$616$	−6.92820	+	6.92820i	−0.279145	+	0.279145i
$617$	26.1244			1.05173			0.525863	−	0.850569i	$-0.323742\pi$
$617$	26.1244			1.05173			0.525863	+	0.850569i	$0.323742\pi$
$618$		0			0
$619$		−	6.24871i		−	0.251157i	−0.992084	−	0.125578i	$-0.959921\pi$
$619$		−	6.24871i		−	0.251157i	0.992084	−	0.125578i	$-0.0400787\pi$
$620$	−7.46410	+	12.9282i	−0.299766	+	0.519209i
$621$		0			0
$622$	−26.3923	−	7.07180i	−1.05824	−	0.283553i
$623$	−8.58846			−0.344089
$624$		0			0
$625$	10.0718			0.402872
$626$	−3.36603	−	0.901924i	−0.134533	−	0.0360481i
$627$		0			0
$628$	2.46410	−	4.26795i	0.0983284	−	0.170310i
$629$		−	18.6603i		−	0.744033i
$630$		0			0
$631$	0.784610			0.0312348			0.0156174	−	0.999878i	$-0.495029\pi$
$631$	0.784610			0.0312348			0.0156174	+	0.999878i	$0.495029\pi$
$632$	−10.5359	−	10.5359i	−0.419096	−	0.419096i
$633$		0			0
$634$	0.437822	−	1.63397i	0.0173881	−	0.0648934i
$635$		−	50.9808i		−	2.02311i
$636$		0			0
$637$			15.9282i			0.631098i
$638$	−33.5885	−	9.00000i	−1.32978	−	0.356313i
$639$		0			0
$640$	40.7846	+	10.9282i	1.61215	+	0.431975i
$641$	−23.0526			−0.910521			−0.455261	−	0.890358i	$-0.650454\pi$
$641$	−23.0526			−0.910521			−0.455261	+	0.890358i	$0.650454\pi$
$642$		0			0
$643$		−	6.39230i		−	0.252088i	−0.992025	−	0.126044i	$-0.959772\pi$
$643$		−	6.39230i		−	0.252088i	0.992025	−	0.126044i	$-0.0402280\pi$
$644$	11.0718	+	6.39230i	0.436290	+	0.251892i
$645$		0			0
$646$	4.46410	−	16.6603i	0.175638	−	0.655489i
$647$	−49.7654			−1.95648			−0.978239	−	0.207480i	$-0.933474\pi$
$647$	−49.7654			−1.95648			−0.978239	+	0.207480i	$0.933474\pi$
$648$		0			0
$649$	−39.7128			−1.55886
$650$	8.05256	−	30.0526i	0.315847	−	1.17876i
$651$		0			0
$652$	−6.53590	+	11.3205i	−0.255966	+	0.443345i
$653$			35.5692i			1.39193i	0.718075	+	0.695966i	$0.245023\pi$
$653$			35.5692i			1.39193i	−0.718075	+	0.695966i	$0.754977\pi$
$654$		0			0
$655$	−0.732051			−0.0286036
$656$	−9.07180	−	15.7128i	−0.354194	−	0.613482i
$657$		0			0
$658$	−3.46410	−	0.928203i	−0.135045	−	0.0361851i
$659$			10.0526i			0.391592i	0.980645	+	0.195796i	$0.0627291\pi$
$659$			10.0526i			0.391592i	−0.980645	+	0.195796i	$0.937271\pi$
$660$		0			0
$661$			32.1769i			1.25154i	0.780009	+	0.625768i	$0.215215\pi$
$661$			32.1769i			1.25154i	−0.780009	+	0.625768i	$0.784785\pi$
$662$	4.80385	−	17.9282i	0.186707	−	0.696799i
$663$		0			0
$664$	−28.0000	+	28.0000i	−1.08661	+	1.08661i
$665$	8.92820			0.346221
$666$		0			0
$667$			45.3731i			1.75685i
$668$	25.5167	+	14.7321i	0.987269	+	0.570000i
$669$		0			0
$670$	24.1244	+	6.46410i	0.932005	+	0.249730i
$671$	−42.5885			−1.64411
$672$		0			0
$673$	−37.2487			−1.43583			−0.717916	−	0.696130i	$-0.754904\pi$
$673$	−37.2487			−1.43583			−0.717916	+	0.696130i	$0.754904\pi$
$674$	−5.46410	−	1.46410i	−0.210469	−	0.0563951i
$675$		0			0
$676$	12.0000	+	6.92820i	0.461538	+	0.266469i
$677$		−	29.3205i		−	1.12688i	−0.826157	−	0.563439i	$-0.809478\pi$
$677$		−	29.3205i		−	1.12688i	0.826157	−	0.563439i	$-0.190522\pi$
$678$		0			0
$679$	5.85641			0.224748
$680$	27.8564	−	27.8564i	1.06824	−	1.06824i
$681$		0			0
$682$	3.46410	−	12.9282i	0.132647	−	0.495046i
$683$		−	34.1051i		−	1.30500i	−0.757790	−	0.652498i	$-0.773721\pi$
$683$		−	34.1051i		−	1.30500i	0.757790	−	0.652498i	$-0.226279\pi$
$684$		0			0
$685$			64.1769i			2.45207i
$686$	−13.4641	−	3.60770i	−0.514062	−	0.137742i
$687$		0			0
$688$	−33.4641	+	19.3205i	−1.27581	+	0.736587i
$689$	−2.28719			−0.0871349
$690$		0			0
$691$			12.7321i			0.484350i	0.970233	+	0.242175i	$0.0778608\pi$
$691$			12.7321i			0.484350i	−0.970233	+	0.242175i	$0.922139\pi$
$692$	−1.73205	+	3.00000i	−0.0658427	+	0.114043i
$693$		0			0
$694$	2.46410	−	9.19615i	0.0935360	−	0.349081i
$695$	72.6410			2.75543
$696$		0			0
$697$	−16.9282			−0.641201
$698$	4.33975	−	16.1962i	0.164262	−	0.613033i
$699$		0			0
$700$	11.3205	+	6.53590i	0.427875	+	0.247034i
$701$		−	10.1244i		−	0.382392i	−0.981552	−	0.191196i	$-0.938763\pi$
$701$		−	10.1244i		−	0.382392i	0.981552	−	0.191196i	$-0.0612365\pi$
$702$		0			0
$703$	16.3397			0.616265
$704$	−37.8564			−1.42677
$705$		0			0
$706$	−9.46410	−	2.53590i	−0.356186	−	0.0954398i
$707$		−	5.85641i		−	0.220253i
$708$		0			0
$709$		−	47.3923i		−	1.77986i	−0.456102	−	0.889928i	$-0.650755\pi$
$709$		−	47.3923i		−	1.77986i	0.456102	−	0.889928i	$-0.349245\pi$
$710$	−7.73205	+	28.8564i	−0.290179	+	1.08296i
$711$		0			0
$712$	−23.4641	−	23.4641i	−0.879354	−	0.879354i
$713$	−17.4641			−0.654036
$714$		0			0
$715$			43.5167i			1.62743i
$716$	14.0000	−	24.2487i	0.523205	−	0.906217i
$717$		0			0
$718$	1.53590	+	0.411543i	0.0573192	+	0.0153586i
$719$	48.0526			1.79206			0.896029	−	0.443995i	$-0.146439\pi$
$719$	48.0526			1.79206			0.896029	+	0.443995i	$0.146439\pi$
$720$		0			0
$721$	2.53590			0.0944418
$722$	−11.3660	−	3.04552i	−0.423000	−	0.113342i
$723$		0			0
$724$	6.53590	−	11.3205i	0.242905	−	0.420723i
$725$			46.3923i			1.72297i
$726$		0			0
$727$	−49.5167			−1.83647			−0.918236	−	0.396034i	$-0.870386\pi$
$727$	−49.5167			−1.83647			−0.918236	+	0.396034i	$0.870386\pi$
$728$	3.60770	−	3.60770i	0.133710	−	0.133710i
$729$		0			0
$730$	12.2942	−	45.8827i	0.455030	−	1.69819i
$731$			36.0526i			1.33345i
$732$		0			0
$733$		−	29.4641i		−	1.08828i	−0.838994	−	0.544141i	$-0.816856\pi$
$733$		−	29.4641i		−	1.08828i	0.838994	−	0.544141i	$-0.183144\pi$
$734$	−3.46410	−	0.928203i	−0.127862	−	0.0342606i
$735$		0			0
$736$	12.7846	+	47.7128i	0.471247	+	1.75872i
$737$	−22.3923			−0.824831
$738$		0			0
$739$		−	9.60770i		−	0.353425i	−0.984263	−	0.176712i	$-0.943454\pi$
$739$		−	9.60770i		−	0.353425i	0.984263	−	0.176712i	$-0.0565462\pi$
$740$	32.3205	+	18.6603i	1.18813	+	0.685965i
$741$		0			0
$742$	0.248711	−	0.928203i	0.00913048	−	0.0340754i
$743$	30.7846			1.12938			0.564689	−	0.825304i	$-0.308996\pi$
$743$	30.7846			1.12938			0.564689	+	0.825304i	$0.308996\pi$
$744$		0			0
$745$	19.3923			0.710479
$746$	−8.39230	+	31.3205i	−0.307264	+	1.14673i
$747$		0			0
$748$	−17.6603	+	30.5885i	−0.645723	+	1.11842i
$749$		−	7.60770i		−	0.277979i
$750$		0			0
$751$	−17.5167			−0.639192			−0.319596	−	0.947554i	$-0.603547\pi$
$751$	−17.5167			−0.639192			−0.319596	+	0.947554i	$0.603547\pi$
$752$	−6.92820	−	12.0000i	−0.252646	−	0.437595i
$753$		0			0
$754$	17.4904	+	4.68653i	0.636962	+	0.170673i
$755$			51.7128i			1.88202i
$756$		0			0
$757$		−	18.2487i		−	0.663261i	−0.943409	−	0.331630i	$-0.892401\pi$
$757$		−	18.2487i		−	0.663261i	0.943409	−	0.331630i	$-0.107599\pi$
$758$	−3.66025	+	13.6603i	−0.132946	+	0.496163i
$759$		0			0
$760$	24.3923	+	24.3923i	0.884802	+	0.884802i
$761$	−35.9808			−1.30430			−0.652151	−	0.758089i	$-0.726133\pi$
$761$	−35.9808			−1.30430			−0.652151	+	0.758089i	$0.726133\pi$
$762$		0			0
$763$		−	9.41154i		−	0.340721i
$764$	−28.7321	−	16.5885i	−1.03949	−	0.600149i
$765$		0			0
$766$	−27.5885	−	7.39230i	−0.996811	−	0.267095i
$767$	20.6795			0.746693
$768$		0			0
$769$	−39.3923			−1.42052			−0.710261	−	0.703938i	$-0.751423\pi$
$769$	−39.3923			−1.42052			−0.710261	+	0.703938i	$0.751423\pi$
$770$	−17.6603	−	4.73205i	−0.636431	−	0.170531i
$771$		0			0
$772$	18.8038	+	10.8564i	0.676765	+	0.390731i
$773$			40.6603i			1.46245i	0.682138	+	0.731224i	$0.261051\pi$
$773$			40.6603i			1.46245i	−0.682138	+	0.731224i	$0.738949\pi$
$774$		0			0
$775$	−17.8564			−0.641421
$776$	16.0000	+	16.0000i	0.574367	+	0.574367i
$777$		0			0
$778$	6.19615	−	23.1244i	0.222143	−	0.829048i
$779$		−	14.8231i		−	0.531092i
$780$		0			0
$781$		−	26.7846i		−	0.958429i
$782$	44.5167	+	11.9282i	1.59191	+	0.426552i
$783$		0			0
$784$	−12.9282	−	22.3923i	−0.461722	−	0.799725i
$785$	9.19615			0.328225
$786$		0			0
$787$		−	14.4449i		−	0.514904i	−0.966291	−	0.257452i	$-0.917117\pi$
$787$		−	14.4449i		−	0.514904i	0.966291	−	0.257452i	$-0.0828829\pi$
$788$	−4.12436	+	7.14359i	−0.146924	+	0.254480i
$789$		0			0
$790$	7.19615	−	26.8564i	0.256028	−	0.955508i
$791$	−5.66025			−0.201255
$792$		0			0
$793$	22.1769			0.787525
$794$	11.8827	−	44.3468i	0.421701	−	1.57381i
$795$		0			0
$796$	4.14359	+	2.39230i	0.146866	+	0.0847930i
$797$		−	12.2679i		−	0.434553i	−0.976110	−	0.217277i	$-0.930283\pi$
$797$		−	12.2679i		−	0.434553i	0.976110	−	0.217277i	$-0.0697173\pi$
$798$		0			0
$799$	−12.9282			−0.457367
$800$	13.0718	+	48.7846i	0.462158	+	1.72480i
$801$		0			0
$802$	−13.0981	−	3.50962i	−0.462509	−	0.123929i
$803$			42.5885i			1.50291i
$804$		0			0
$805$			23.8564i			0.840828i
$806$	−1.80385	+	6.73205i	−0.0635378	+	0.237126i
$807$		0			0
$808$	16.0000	−	16.0000i	0.562878	−	0.562878i
$809$	49.0526			1.72460			0.862298	−	0.506401i	$-0.169024\pi$
$809$	49.0526			1.72460			0.862298	+	0.506401i	$0.169024\pi$
$810$		0			0
$811$			48.7846i			1.71306i	0.516098	+	0.856530i	$0.327384\pi$
$811$			48.7846i			1.71306i	−0.516098	+	0.856530i	$0.672616\pi$
$812$	−3.80385	+	6.58846i	−0.133489	+	0.231210i
$813$		0			0
$814$	−32.3205	−	8.66025i	−1.13283	−	0.303542i
$815$	−24.3923			−0.854425
$816$		0			0
$817$	−31.5692			−1.10447
$818$	−39.2224	−	10.5096i	−1.37138	−	0.367460i
$819$		0			0
$820$	16.9282	−	29.3205i	0.591158	−	1.02392i
$821$		−	1.58846i		−	0.0554375i	−0.999616	−	0.0277188i	$-0.991176\pi$
$821$		−	1.58846i		−	0.0554375i	0.999616	−	0.0277188i	$-0.00882429\pi$
$822$		0			0
$823$	−17.6077			−0.613766			−0.306883	−	0.951747i	$-0.599286\pi$
$823$	−17.6077			−0.613766			−0.306883	+	0.951747i	$0.599286\pi$
$824$	6.92820	+	6.92820i	0.241355	+	0.241355i
$825$		0			0
$826$	−2.24871	+	8.39230i	−0.0782427	+	0.292006i
$827$		−	12.3397i		−	0.429095i	−0.976714	−	0.214548i	$-0.931172\pi$
$827$		−	12.3397i		−	0.429095i	0.976714	−	0.214548i	$-0.0688277\pi$
$828$		0			0
$829$		−	53.1769i		−	1.84691i	−0.383706	−	0.923455i	$-0.625352\pi$
$829$		−	53.1769i		−	1.84691i	0.383706	−	0.923455i	$-0.374648\pi$
$830$	−71.3731	−	19.1244i	−2.47740	−	0.663816i
$831$		0			0
$832$	19.7128			0.683419
$833$	−24.1244			−0.835859
$834$		0			0
$835$			54.9808i			1.90269i
$836$	−26.7846	−	15.4641i	−0.926365	−	0.534837i
$837$		0			0
$838$	7.85641	−	29.3205i	0.271395	−	1.01286i
$839$	−41.8038			−1.44323			−0.721615	−	0.692295i	$-0.756600\pi$
$839$	−41.8038			−1.44323			−0.721615	+	0.692295i	$0.756600\pi$
$840$		0			0
$841$	2.00000			0.0689655
$842$	−4.75833	+	17.7583i	−0.163983	+	0.611992i
$843$		0			0
$844$	−26.0526	+	45.1244i	−0.896766	+	1.55324i
$845$			25.8564i			0.889487i
$846$		0			0
$847$	8.33975			0.286557
$848$	3.21539	−	1.85641i	0.110417	−	0.0637493i
$849$		0			0
$850$	45.5167	+	12.1962i	1.56121	+	0.418325i
$851$			43.6603i			1.49665i
$852$		0			0
$853$			5.07180i			0.173655i	0.996223	+	0.0868275i	$0.0276729\pi$
$853$			5.07180i			0.173655i	−0.996223	+	0.0868275i	$0.972327\pi$
$854$	−2.41154	+	9.00000i	−0.0825213	+	0.307974i
$855$		0			0
$856$	20.7846	−	20.7846i	0.710403	−	0.710403i
$857$	−0.124356			−0.00424791			−0.00212395	−	0.999998i	$-0.500676\pi$
$857$	−0.124356			−0.00424791			−0.00212395	+	0.999998i	$0.500676\pi$
$858$		0			0
$859$		−	2.00000i		−	0.0682391i	−0.999418	−	0.0341196i	$-0.989137\pi$
$859$		−	2.00000i		−	0.0682391i	0.999418	−	0.0341196i	$-0.0108627\pi$
$860$	−62.4449	−	36.0526i	−2.12935	−	1.22938i
$861$		0			0
$862$	−29.6603	−	7.94744i	−1.01023	−	0.270691i
$863$	25.5167			0.868597			0.434299	−	0.900769i	$-0.356996\pi$
$863$	25.5167			0.868597			0.434299	+	0.900769i	$0.356996\pi$
$864$		0			0
$865$	−6.46410			−0.219786
$866$	29.7583	+	7.97372i	1.01123	+	0.270958i
$867$		0			0
$868$	−2.53590	−	1.46410i	−0.0860740	−	0.0496948i
$869$			24.9282i			0.845631i
$870$		0			0
$871$	11.6603			0.395093
$872$	25.7128	−	25.7128i	0.870746	−	0.870746i
$873$		0			0
$874$	−10.4449	+	38.9808i	−0.353303	+	1.31854i
$875$			10.7321i			0.362810i
$876$		0			0
$877$		−	57.1051i		−	1.92830i	−0.265353	−	0.964151i	$-0.585488\pi$
$877$		−	57.1051i		−	1.92830i	0.265353	−	0.964151i	$-0.414512\pi$
$878$	40.9808	+	10.9808i	1.38303	+	0.370583i
$879$		0			0
$880$	−35.3205	−	61.1769i	−1.19065	−	2.06227i
$881$	−27.8564			−0.938506			−0.469253	−	0.883064i	$-0.655477\pi$
$881$	−27.8564			−0.938506			−0.469253	+	0.883064i	$0.655477\pi$
$882$		0			0
$883$		−	1.32051i		−	0.0444386i	−0.999753	−	0.0222193i	$-0.992927\pi$
$883$		−	1.32051i		−	0.0444386i	0.999753	−	0.0222193i	$-0.00707321\pi$
$884$	9.19615	−	15.9282i	0.309300	−	0.535723i
$885$		0			0
$886$	−10.7321	+	40.0526i	−0.360550	+	1.34559i
$887$	−2.19615			−0.0737396			−0.0368698	−	0.999320i	$-0.511739\pi$
$887$	−2.19615			−0.0737396			−0.0368698	+	0.999320i	$0.511739\pi$
$888$		0			0
$889$	10.0000			0.335389
$890$	16.0263	−	59.8109i	0.537202	−	2.00487i
$891$		0			0
$892$	40.0526	+	23.1244i	1.34106	+	0.774261i
$893$		−	11.3205i		−	0.378826i
$894$		0			0
$895$	52.2487			1.74648
$896$	−2.14359	+	8.00000i	−0.0716124	+	0.267261i
$897$		0			0
$898$	−34.0526	−	9.12436i	−1.13635	−	0.304484i
$899$		−	10.3923i		−	0.346603i
$900$		0			0
$901$		−	3.46410i		−	0.115406i
$902$	−7.85641	+	29.3205i	−0.261590	+	0.976266i
$903$		0			0
$904$	−15.4641	−	15.4641i	−0.514328	−	0.514328i
$905$	24.3923			0.810828
$906$		0			0
$907$		−	32.3923i		−	1.07557i	−0.843082	−	0.537784i	$-0.819261\pi$
$907$		−	32.3923i		−	1.07557i	0.843082	−	0.537784i	$-0.180739\pi$
$908$	−6.73205	+	11.6603i	−0.223411	+	0.386959i
$909$		0			0
$910$	9.19615	+	2.46410i	0.304849	+	0.0816842i
$911$	−16.7321			−0.554358			−0.277179	−	0.960818i	$-0.589399\pi$
$911$	−16.7321			−0.554358			−0.277179	+	0.960818i	$0.589399\pi$
$912$		0			0
$913$	66.2487			2.19251
$914$	8.63397	+	2.31347i	0.285586	+	0.0765227i
$915$		0			0
$916$	11.3923	−	19.7321i	0.376412	−	0.651965i
$917$		−	0.143594i		−	0.00474188i
$918$		0			0
$919$	16.9808			0.560144			0.280072	−	0.959979i	$-0.409642\pi$
$919$	16.9808			0.560144			0.280072	+	0.959979i	$0.409642\pi$
$920$	−65.1769	+	65.1769i	−2.14882	+	2.14882i
$921$		0			0
$922$	15.1244	−	56.4449i	0.498094	−	1.85891i
$923$			13.9474i			0.459086i
$924$		0			0
$925$			44.6410i			1.46779i
$926$	−18.3923	−	4.92820i	−0.604409	−	0.161951i
$927$		0			0
$928$	−28.3923	+	7.60770i	−0.932023	+	0.249735i
$929$	0.516660			0.0169511			0.00847554	−	0.999964i	$-0.497302\pi$
$929$	0.516660			0.0169511			0.00847554	+	0.999964i	$0.497302\pi$
$930$		0			0
$931$		−	21.1244i		−	0.692323i
$932$	−6.46410	−	3.73205i	−0.211739	−	0.122247i
$933$		0			0
$934$	−9.07180	+	33.8564i	−0.296838	+	1.10782i
$935$	−65.9090			−2.15545
$936$		0			0
$937$	−7.24871			−0.236805			−0.118403	−	0.992966i	$-0.537777\pi$
$937$	−7.24871			−0.236805			−0.118403	+	0.992966i	$0.537777\pi$
$938$	−1.26795	+	4.73205i	−0.0414000	+	0.154507i
$939$		0			0
$940$	12.9282	−	22.3923i	0.421671	−	0.730356i
$941$		−	18.3731i		−	0.598945i	−0.954105	−	0.299472i	$-0.903189\pi$
$941$		−	18.3731i		−	0.598945i	0.954105	−	0.299472i	$-0.0968107\pi$
$942$		0			0
$943$	39.6077			1.28980
$944$	−29.0718	+	16.7846i	−0.946206	+	0.546293i
$945$		0			0
$946$	62.4449	+	16.7321i	2.03026	+	0.544006i
$947$		−	20.1962i		−	0.656287i	−0.944628	−	0.328143i	$-0.893577\pi$
$947$		−	20.1962i		−	0.656287i	0.944628	−	0.328143i	$-0.106423\pi$
$948$		0			0
$949$		−	22.1769i		−	0.719893i
$950$	−10.6795	+	39.8564i	−0.346488	+	1.29311i
$951$		0			0
$952$	5.46410	+	5.46410i	0.177093	+	0.177093i
$953$	−26.6603			−0.863610			−0.431805	−	0.901967i	$-0.642123\pi$
$953$	−26.6603			−0.863610			−0.431805	+	0.901967i	$0.642123\pi$
$954$		0			0
$955$		−	61.9090i		−	2.00333i
$956$	−13.6077	−	7.85641i	−0.440104	−	0.254094i
$957$		0			0
$958$	2.26795	+	0.607695i	0.0732741	+	0.0196337i
$959$	−12.5885			−0.406502
$960$		0			0
$961$	−27.0000			−0.870968
$962$	16.8301	+	4.50962i	0.542625	+	0.145396i
$963$		0			0
$964$	−7.73205	−	4.46410i	−0.249033	−	0.143779i
$965$			40.5167i			1.30428i
$966$		0			0
$967$	10.1962			0.327886			0.163943	−	0.986470i	$-0.447579\pi$
$967$	10.1962			0.327886			0.163943	+	0.986470i	$0.447579\pi$
$968$	22.7846	+	22.7846i	0.732325	+	0.732325i
$969$		0			0
$970$	−10.9282	+	40.7846i	−0.350883	+	1.30951i
$971$		−	51.1244i		−	1.64066i	−0.571891	−	0.820329i	$-0.693790\pi$
$971$		−	51.1244i		−	1.64066i	0.571891	−	0.820329i	$-0.306210\pi$
$972$		0			0
$973$			14.2487i			0.456793i
$974$	35.1244	+	9.41154i	1.12546	+	0.301565i
$975$		0			0
$976$	−31.1769	+	18.0000i	−0.997949	+	0.576166i
$977$	22.7846			0.728944			0.364472	−	0.931214i	$-0.381249\pi$
$977$	22.7846			0.728944			0.364472	+	0.931214i	$0.381249\pi$
$978$		0			0
$979$			55.5167i			1.77432i
$980$	24.1244	−	41.7846i	0.770624	−	1.33476i
$981$		0			0
$982$	5.05256	−	18.8564i	0.161234	−	0.601732i
$983$	1.46410			0.0466976			0.0233488	−	0.999727i	$-0.492567\pi$
$983$	1.46410			0.0466976			0.0233488	+	0.999727i	$0.492567\pi$
$984$		0			0
$985$	−15.3923			−0.490440
$986$	−7.09808	+	26.4904i	−0.226049	+	0.843626i
$987$		0			0
$988$	13.9474	+	8.05256i	0.443727	+	0.256186i
$989$		−	84.3538i		−	2.68230i
$990$		0			0
$991$	2.58846			0.0822251			0.0411125	−	0.999155i	$-0.486910\pi$
$991$	2.58846			0.0822251			0.0411125	+	0.999155i	$0.486910\pi$
$992$	−2.92820	−	10.9282i	−0.0929705	−	0.346971i
$993$		0			0
$994$	−5.66025	−	1.51666i	−0.179532	−	0.0481055i
$995$			8.92820i			0.283043i
$996$		0			0
$997$			27.9282i			0.884495i	0.896893	+	0.442248i	$0.145819\pi$
$997$			27.9282i			0.884495i	−0.896893	+	0.442248i	$0.854181\pi$
$998$	3.00000	−	11.1962i	0.0949633	−	0.354408i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.d.e.325.1	✓	4
3.2	odd	2		648.2.d.i.325.4	yes	4
4.3	odd	2		2592.2.d.h.1297.4		4
8.3	odd	2		2592.2.d.h.1297.1		4
8.5	even	2	inner	648.2.d.e.325.2	yes	4
9.2	odd	6		648.2.n.l.109.1		4
9.4	even	3		648.2.n.m.541.1		4
9.5	odd	6		648.2.n.a.541.2		4
9.7	even	3		648.2.n.b.109.2		4
12.11	even	2		2592.2.d.g.1297.1		4
24.5	odd	2		648.2.d.i.325.3	yes	4
24.11	even	2		2592.2.d.g.1297.4		4
36.7	odd	6		2592.2.r.b.433.1		4
36.11	even	6		2592.2.r.k.433.2		4
36.23	even	6		2592.2.r.a.2161.1		4
36.31	odd	6		2592.2.r.j.2161.2		4
72.5	odd	6		648.2.n.l.541.1		4
72.11	even	6		2592.2.r.a.433.1		4
72.13	even	6		648.2.n.b.541.2		4
72.29	odd	6		648.2.n.a.109.1		4
72.43	odd	6		2592.2.r.j.433.2		4
72.59	even	6		2592.2.r.k.2161.2		4
72.61	even	6		648.2.n.m.109.2		4
72.67	odd	6		2592.2.r.b.2161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.d.e.325.1	✓	4	1.1	even	1	trivial
648.2.d.e.325.2	yes	4	8.5	even	2	inner
648.2.d.i.325.3	yes	4	24.5	odd	2
648.2.d.i.325.4	yes	4	3.2	odd	2
648.2.n.a.109.1		4	72.29	odd	6
648.2.n.a.541.2		4	9.5	odd	6
648.2.n.b.109.2		4	9.7	even	3
648.2.n.b.541.2		4	72.13	even	6
648.2.n.l.109.1		4	9.2	odd	6
648.2.n.l.541.1		4	72.5	odd	6
648.2.n.m.109.2		4	72.61	even	6
648.2.n.m.541.1		4	9.4	even	3
2592.2.d.g.1297.1		4	12.11	even	2
2592.2.d.g.1297.4		4	24.11	even	2
2592.2.d.h.1297.1		4	8.3	odd	2
2592.2.d.h.1297.4		4	4.3	odd	2
2592.2.r.a.433.1		4	72.11	even	6
2592.2.r.a.2161.1		4	36.23	even	6
2592.2.r.b.433.1		4	36.7	odd	6
2592.2.r.b.2161.1		4	72.67	odd	6
2592.2.r.j.433.2		4	72.43	odd	6
2592.2.r.j.2161.2		4	36.31	odd	6
2592.2.r.k.433.2		4	36.11	even	6
2592.2.r.k.2161.2		4	72.59	even	6

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +3.73205i q^{5} -0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.36603 - 5.09808i) q^{10} +4.73205i q^{11} -2.46410i q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} +3.73205 q^{17} +3.26795i q^{19} +(-3.73205 + 6.46410i) q^{20} +(1.73205 - 6.46410i) q^{22} -8.73205 q^{23} -8.92820 q^{25} +(-0.901924 + 3.36603i) q^{26} +(-1.26795 - 0.732051i) q^{28} -5.19615i q^{29} +2.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} +(-5.09808 - 1.36603i) q^{34} -2.73205i q^{35} -5.00000i q^{37} +(1.19615 - 4.46410i) q^{38} +(7.46410 - 7.46410i) q^{40} -4.53590 q^{41} +9.66025i q^{43} +(-4.73205 + 8.19615i) q^{44} +(11.9282 + 3.19615i) q^{46} -3.46410 q^{47} -6.46410 q^{49} +(12.1962 + 3.26795i) q^{50} +(2.46410 - 4.26795i) q^{52} -0.928203i q^{53} -17.6603 q^{55} +(1.46410 + 1.46410i) q^{56} +(-1.90192 + 7.09808i) q^{58} +8.39230i q^{59} +9.00000i q^{61} +(-2.73205 - 0.732051i) q^{62} +8.00000i q^{64} +9.19615 q^{65} +4.73205i q^{67} +(6.46410 + 3.73205i) q^{68} +(-1.00000 + 3.73205i) q^{70} -5.66025 q^{71} +9.00000 q^{73} +(-1.83013 + 6.83013i) q^{74} +(-3.26795 + 5.66025i) q^{76} -3.46410i q^{77} +5.26795 q^{79} +(-12.9282 + 7.46410i) q^{80} +(6.19615 + 1.66025i) q^{82} -14.0000i q^{83} +13.9282i q^{85} +(3.53590 - 13.1962i) q^{86} +(9.46410 - 9.46410i) q^{88} +11.7321 q^{89} +1.80385i q^{91} +(-15.1244 - 8.73205i) q^{92} +(4.73205 + 1.26795i) q^{94} -12.1962 q^{95} -8.00000 q^{97} +(8.83013 + 2.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{7} - 8 q^{8} + 2 q^{10} + 4 q^{14} + 8 q^{16} + 8 q^{17} - 8 q^{20} - 28 q^{23} - 8 q^{25} - 14 q^{26} - 12 q^{28} + 8 q^{31} + 8 q^{32} - 10 q^{34} - 16 q^{38} + 16 q^{40} - 32 q^{41}+ \cdots + 18 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^7 - 8 * q^8 + 2 * q^10 + 4 * q^14 + 8 * q^16 + 8 * q^17 - 8 * q^20 - 28 * q^23 - 8 * q^25 - 14 * q^26 - 12 * q^28 + 8 * q^31 + 8 * q^32 - 10 * q^34 - 16 * q^38 + 16 * q^40 - 32 * q^41 - 12 * q^44 + 20 * q^46 - 12 * q^49 + 28 * q^50 - 4 * q^52 - 36 * q^55 - 8 * q^56 - 18 * q^58 - 4 * q^62 + 16 * q^65 + 12 * q^68 - 4 * q^70 + 12 * q^71 + 36 * q^73 + 10 * q^74 - 20 * q^76 + 28 * q^79 - 24 * q^80 + 4 * q^82 + 28 * q^86 + 24 * q^88 + 40 * q^89 - 12 * q^92 + 12 * q^94 - 28 * q^95 - 32 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more