LMFDB - Embedded newform 360.2.bi.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.a.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(1.73205 + 1.00000i) q^{13} +(2.13397 - 3.23205i) q^{15} +6.00000i q^{17} -2.00000 q^{19} -1.73205i q^{21} +(-0.866025 - 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} -5.19615 q^{27} +(-3.50000 - 6.06218i) q^{29} +(3.00000 - 5.19615i) q^{31} -3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(3.00000 - 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(10.3923 - 6.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(-7.79423 + 4.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(9.00000 + 5.19615i) q^{51} +8.00000i q^{53} +(-2.00000 - 4.00000i) q^{55} +(-1.73205 + 3.00000i) q^{57} +(-6.00000 + 10.3923i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.59808 - 1.50000i) q^{63} +(3.73205 + 2.46410i) q^{65} +(4.33013 + 2.50000i) q^{67} +(-1.50000 + 0.866025i) q^{69} -10.0000 q^{71} -4.00000i q^{73} +(5.19615 - 6.92820i) q^{75} +(-1.73205 - 1.00000i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(4.33013 - 2.50000i) q^{83} +(-0.803848 + 13.3923i) q^{85} -12.1244 q^{87} +15.0000 q^{89} +2.00000 q^{91} +(-5.19615 - 9.00000i) q^{93} +(-4.46410 - 0.267949i) q^{95} +(-13.8564 + 8.00000i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^5 - 6 * q^9	$ 4 q + 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{15} - 8 q^{19} + 6 q^{25} - 14 q^{29} + 12 q^{31} + 8 q^{35} + 12 q^{39} - 10 q^{41} - 12 q^{45} - 12 q^{49} + 36 q^{51} - 8 q^{55} - 24 q^{59} + 14 q^{61} + 8 q^{65} - 6 q^{69} - 40 q^{71} + 8 q^{79} - 18 q^{81} - 24 q^{85} + 60 q^{89} + 8 q^{91} - 4 q^{95} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^15 - 8 * q^19 + 6 * q^25 - 14 * q^29 + 12 * q^31 + 8 * q^35 + 12 * q^39 - 10 * q^41 - 12 * q^45 - 12 * q^49 + 36 * q^51 - 8 * q^55 - 24 * q^59 + 14 * q^61 + 8 * q^65 - 6 * q^69 - 40 * q^71 + 8 * q^79 - 18 * q^81 - 24 * q^85 + 60 * q^89 + 8 * q^91 - 4 * q^95 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	0.654654	+	0.755929i	$0.272814\pi$
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	0.720577	−	0.693375i	$-0.243877\pi$
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	−0.240192	+	0.970725i	$0.577210\pi$
$14$		0			0
$15$	2.13397	−	3.23205i	0.550990	−	0.834512i
$16$		0			0
$17$			6.00000i			1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$			6.00000i			1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$		−	1.73205i		−	0.377964i
$22$		0			0
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$		0			0
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$		0			0
$33$	−3.46410			−0.603023
$34$		0			0
$35$	2.00000	−	1.00000i	0.338062	−	0.169031i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$	3.00000	−	1.73205i	0.480384	−	0.277350i
$40$		0			0
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$		0			0
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.590669	−	0.806914i	$-0.298864\pi$
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.994142	−	0.108078i	$-0.0344695\pi$
$44$		0			0
$45$	−3.00000	−	6.00000i	−0.447214	−	0.894427i
$46$		0			0
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.945662	−	0.325150i	$-0.894585\pi$
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.191243	+	0.981543i	$0.561252\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$		0			0
$53$			8.00000i			1.09888i	0.835532	+	0.549442i	$0.185160\pi$
$53$			8.00000i			1.09888i	−0.835532	+	0.549442i	$0.814840\pi$
$54$		0			0
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$		0			0
$57$	−1.73205	+	3.00000i	−0.229416	+	0.397360i
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	−2.59808	−	1.50000i	−0.327327	−	0.188982i
$64$		0			0
$65$	3.73205	+	2.46410i	0.462904	+	0.305634i
$66$		0			0
$67$	4.33013	+	2.50000i	0.529009	+	0.305424i	0.740613	−	0.671932i	$-0.234535\pi$
$67$	4.33013	+	2.50000i	0.529009	+	0.305424i	−0.211604	+	0.977356i	$0.567869\pi$
$68$		0			0
$69$	−1.50000	+	0.866025i	−0.180579	+	0.104257i
$70$		0			0
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$	5.19615	−	6.92820i	0.600000	−	0.800000i
$76$		0			0
$77$	−1.73205	−	1.00000i	−0.197386	−	0.113961i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	4.33013	−	2.50000i	0.475293	−	0.274411i	−0.243160	−	0.969986i	$-0.578184\pi$
$83$	4.33013	−	2.50000i	0.475293	−	0.274411i	0.718453	+	0.695576i	$0.244851\pi$
$84$		0			0
$85$	−0.803848	+	13.3923i	−0.0871895	+	1.45260i
$86$		0			0
$87$	−12.1244			−1.29987
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$		0			0
$93$	−5.19615	−	9.00000i	−0.538816	−	0.933257i
$94$		0			0
$95$	−4.46410	−	0.267949i	−0.458007	−	0.0274910i
$96$		0			0
$97$	−13.8564	+	8.00000i	−1.40690	+	0.812277i	−0.995088	−	0.0989899i	$-0.968439\pi$
$97$	−13.8564	+	8.00000i	−1.40690	+	0.812277i	−0.411816	+	0.911267i	$0.635106\pi$
$98$		0			0
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	0.118199	−	0.992990i	$-0.462288\pi$
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	−0.800855	+	0.598858i	$0.795621\pi$
$104$		0			0
$105$	0.232051	−	3.86603i	0.0226458	−	0.377285i
$106$		0			0
$107$			13.0000i			1.25676i	0.777908	+	0.628379i	$0.216281\pi$
$107$			13.0000i			1.25676i	−0.777908	+	0.628379i	$0.783719\pi$
$108$		0			0
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$		0			0
$111$	3.00000	+	1.73205i	0.284747	+	0.164399i
$112$		0			0
$113$	−3.46410	−	2.00000i	−0.325875	−	0.188144i	0.328133	−	0.944632i	$-0.393581\pi$
$113$	−3.46410	−	2.00000i	−0.325875	−	0.188144i	−0.654008	+	0.756487i	$0.726914\pi$
$114$		0			0
$115$	−1.86603	−	1.23205i	−0.174008	−	0.114889i
$116$		0			0
$117$		−	6.00000i		−	0.554700i
$118$		0			0
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	4.33013	+	7.50000i	0.390434	+	0.676252i
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$			3.00000i			0.266207i	0.991102	+	0.133103i	$0.0424943\pi$
$127$			3.00000i			0.266207i	−0.991102	+	0.133103i	$0.957506\pi$
$128$		0			0
$129$		−	20.7846i		−	1.82998i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$	−1.73205	+	1.00000i	−0.150188	+	0.0867110i
$134$		0			0
$135$	−11.5981	−	0.696152i	−0.998203	−	0.0599153i
$136$		0			0
$137$	3.46410	−	2.00000i	0.295958	−	0.170872i	−0.344668	−	0.938725i	$-0.612008\pi$
$137$	3.46410	−	2.00000i	0.295958	−	0.170872i	0.640626	+	0.767853i	$0.278675\pi$
$138$		0			0
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$		0			0
$141$			15.5885i			1.31278i
$142$		0			0
$143$		−	4.00000i		−	0.334497i
$144$		0			0
$145$	−7.00000	−	14.0000i	−0.581318	−	1.16264i
$146$		0			0
$147$	5.19615	+	9.00000i	0.428571	+	0.742307i
$148$		0			0
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.833597	−	0.552372i	$-0.813723\pi$
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.0615699	−	0.998103i	$-0.519611\pi$
$152$		0			0
$153$	15.5885	−	9.00000i	1.26025	−	0.727607i
$154$		0			0
$155$	7.39230	−	11.1962i	0.593764	−	0.899297i
$156$		0			0
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	0.355357	−	0.934731i	$-0.384359\pi$
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	−0.631822	+	0.775113i	$0.717693\pi$
$158$		0			0
$159$	12.0000	+	6.92820i	0.951662	+	0.549442i
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$			20.0000i			1.56652i	0.621694	+	0.783260i	$0.286445\pi$
$163$			20.0000i			1.56652i	−0.621694	+	0.783260i	$0.713555\pi$
$164$		0			0
$165$	−7.73205	−	0.464102i	−0.601939	−	0.0361303i
$166$		0			0
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$		0			0
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$		0			0
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$		0			0
$175$	4.59808	−	1.96410i	0.347582	−	0.148472i
$176$		0			0
$177$	10.3923	+	18.0000i	0.781133	+	1.35296i
$178$		0			0
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	19.0000			1.41226			0.706129	−	0.708083i	$-0.250440\pi$
$181$	19.0000			1.41226			0.706129	+	0.708083i	$0.250440\pi$
$182$		0			0
$183$	12.1244			0.896258
$184$		0			0
$185$	−0.267949	+	4.46410i	−0.0197000	+	0.328207i
$186$		0			0
$187$	10.3923	−	6.00000i	0.759961	−	0.438763i
$188$		0			0
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$		0			0
$195$	6.92820	−	3.46410i	0.496139	−	0.248069i
$196$		0			0
$197$		−	24.0000i		−	1.70993i	−0.518686	−	0.854965i	$-0.673579\pi$
$197$		−	24.0000i		−	1.70993i	0.518686	−	0.854965i	$-0.326421\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$	7.50000	−	4.33013i	0.529009	−	0.305424i
$202$		0			0
$203$	−6.06218	−	3.50000i	−0.425481	−	0.245652i
$204$		0			0
$205$	−6.16025	+	9.33013i	−0.430251	+	0.651644i
$206$		0			0
$207$			3.00000i			0.208514i
$208$		0			0
$209$	2.00000	+	3.46410i	0.138343	+	0.239617i
$210$		0			0
$211$	13.0000	−	22.5167i	0.894957	−	1.55011i	0.0610990	−	0.998132i	$-0.480539\pi$
$211$	13.0000	−	22.5167i	0.894957	−	1.55011i	0.833858	−	0.551979i	$-0.186127\pi$
$212$		0			0
$213$	−8.66025	+	15.0000i	−0.593391	+	1.02778i
$214$		0			0
$215$	24.0000	−	12.0000i	1.63679	−	0.818393i
$216$		0			0
$217$		−	6.00000i		−	0.407307i
$218$		0			0
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	−7.79423	+	4.50000i	−0.521940	+	0.301342i	−0.737728	−	0.675098i	$-0.764101\pi$
$223$	−7.79423	+	4.50000i	−0.521940	+	0.301342i	0.215788	+	0.976440i	$0.430768\pi$
$224$		0			0
$225$	−5.89230	−	13.7942i	−0.392820	−	0.919615i
$226$		0			0
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	−0.252136	−	0.967692i	$-0.581133\pi$
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	0.711977	+	0.702202i	$0.247800\pi$
$228$		0			0
$229$	4.50000	−	7.79423i	0.297368	−	0.515057i	−0.678165	−	0.734910i	$-0.737224\pi$
$229$	4.50000	−	7.79423i	0.297368	−	0.515057i	0.975533	+	0.219853i	$0.0705577\pi$
$230$		0			0
$231$	−3.00000	+	1.73205i	−0.197386	+	0.113961i
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$	−18.0000	+	9.00000i	−1.17419	+	0.587095i
$236$		0			0
$237$	6.92820			0.450035
$238$		0			0
$239$	−2.00000	+	3.46410i	−0.129369	+	0.224074i	−0.923432	−	0.383761i	$-0.874629\pi$
$239$	−2.00000	+	3.46410i	−0.129369	+	0.224074i	0.794063	+	0.607835i	$0.207962\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	−7.39230	+	11.1962i	−0.472277	+	0.715296i
$246$		0			0
$247$	−3.46410	−	2.00000i	−0.220416	−	0.127257i
$248$		0			0
$249$		−	8.66025i		−	0.548821i
$250$		0			0
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$		0			0
$253$			2.00000i			0.125739i
$254$		0			0
$255$	19.3923	+	12.8038i	1.21439	+	0.801808i
$256$		0			0
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$	−10.5000	+	18.1865i	−0.649934	+	1.12572i
$262$		0			0
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$	−1.07180	+	17.8564i	−0.0658400	+	1.09691i
$266$		0			0
$267$	12.9904	−	22.5000i	0.794998	−	1.37698i
$268$		0			0
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		0			0
$271$	14.0000			0.850439			0.425220	−	0.905090i	$-0.360197\pi$
$271$	14.0000			0.850439			0.425220	+	0.905090i	$0.360197\pi$
$272$		0			0
$273$	1.73205	−	3.00000i	0.104828	−	0.181568i
$274$		0			0
$275$	−3.92820	−	9.19615i	−0.236880	−	0.554549i
$276$		0			0
$277$	−25.9808	+	15.0000i	−1.56103	+	0.901263i	−0.563880	+	0.825857i	$0.690692\pi$
$277$	−25.9808	+	15.0000i	−1.56103	+	0.901263i	−0.997153	+	0.0754058i	$0.975975\pi$
$278$		0			0
$279$	−18.0000			−1.07763
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−28.5788	−	16.5000i	−1.69884	−	0.980823i	−0.946868	−	0.321624i	$-0.895771\pi$
$283$	−28.5788	−	16.5000i	−1.69884	−	0.980823i	−0.751968	−	0.659200i	$-0.770895\pi$
$284$		0			0
$285$	−4.26795	+	6.46410i	−0.252811	+	0.382900i
$286$		0			0
$287$			5.00000i			0.295141i
$288$		0			0
$289$	−19.0000			−1.11765
$290$		0			0
$291$			27.7128i			1.62455i
$292$		0			0
$293$	12.1244	+	7.00000i	0.708312	+	0.408944i	0.810436	−	0.585827i	$-0.199230\pi$
$293$	12.1244	+	7.00000i	0.708312	+	0.408944i	−0.102123	+	0.994772i	$0.532564\pi$
$294$		0			0
$295$	−14.7846	+	22.3923i	−0.860793	+	1.30373i
$296$		0			0
$297$	5.19615	+	9.00000i	0.301511	+	0.522233i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	6.00000	−	10.3923i	0.345834	−	0.599002i
$302$		0			0
$303$	−31.1769			−1.79107
$304$		0			0
$305$	7.00000	+	14.0000i	0.400819	+	0.801638i
$306$		0			0
$307$		−	7.00000i		−	0.399511i	−0.979846	−	0.199756i	$-0.935985\pi$
$307$		−	7.00000i		−	0.399511i	0.979846	−	0.199756i	$-0.0640148\pi$
$308$		0			0
$309$	−12.0000	+	6.92820i	−0.682656	+	0.394132i
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	12.1244	−	7.00000i	0.685309	−	0.395663i	−0.116543	−	0.993186i	$-0.537181\pi$
$313$	12.1244	−	7.00000i	0.685309	−	0.395663i	0.801852	+	0.597522i	$0.203848\pi$
$314$		0			0
$315$	−5.59808	−	3.69615i	−0.315416	−	0.208255i
$316$		0			0
$317$	25.9808	−	15.0000i	1.45922	−	0.842484i	0.460252	−	0.887788i	$-0.347759\pi$
$317$	25.9808	−	15.0000i	1.45922	−	0.842484i	0.998973	+	0.0453045i	$0.0144258\pi$
$318$		0			0
$319$	−7.00000	+	12.1244i	−0.391925	+	0.678834i
$320$		0			0
$321$	19.5000	+	11.2583i	1.08838	+	0.628379i
$322$		0			0
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	8.00000	+	6.00000i	0.443760	+	0.332820i
$326$		0			0
$327$	7.79423	−	13.5000i	0.431022	−	0.746552i
$328$		0			0
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$		0			0
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$		0			0
$335$	9.33013	+	6.16025i	0.509759	+	0.336571i
$336$		0			0
$337$	6.92820	+	4.00000i	0.377403	+	0.217894i	0.676688	−	0.736270i	$-0.263415\pi$
$337$	6.92820	+	4.00000i	0.377403	+	0.217894i	−0.299285	+	0.954164i	$0.596748\pi$
$338$		0			0
$339$	−6.00000	+	3.46410i	−0.325875	+	0.188144i
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$			13.0000i			0.701934i
$344$		0			0
$345$	−3.46410	+	1.73205i	−0.186501	+	0.0932505i
$346$		0			0
$347$	3.46410	+	2.00000i	0.185963	+	0.107366i	0.590091	−	0.807337i	$-0.299092\pi$
$347$	3.46410	+	2.00000i	0.185963	+	0.107366i	−0.404128	+	0.914702i	$0.632425\pi$
$348$		0			0
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$		0			0
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.937856	−	0.347024i	$-0.887192\pi$
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.168397	+	0.985719i	$0.553859\pi$
$354$		0			0
$355$	−22.3205	−	1.33975i	−1.18465	−	0.0711063i
$356$		0			0
$357$	10.3923			0.550019
$358$		0			0
$359$	14.0000			0.738892			0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000			0.738892			0.369446	+	0.929252i	$0.379548\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	−6.06218	−	10.5000i	−0.318182	−	0.551107i
$364$		0			0
$365$	0.535898	−	8.92820i	0.0280502	−	0.467324i
$366$		0			0
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.448320	−	0.893873i	$-0.352022\pi$
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.998277	+	0.0586798i	$0.0186891\pi$
$368$		0			0
$369$	15.0000			0.780869
$370$		0			0
$371$	4.00000	+	6.92820i	0.207670	+	0.359694i
$372$		0			0
$373$	−3.46410	−	2.00000i	−0.179364	−	0.103556i	0.407630	−	0.913147i	$-0.366355\pi$
$373$	−3.46410	−	2.00000i	−0.179364	−	0.103556i	−0.586994	+	0.809591i	$0.699689\pi$
$374$		0			0
$375$	12.5263	−	14.7679i	0.646854	−	0.762614i
$376$		0			0
$377$		−	14.0000i		−	0.721037i
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	4.50000	+	2.59808i	0.230542	+	0.133103i
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$	−3.73205	−	2.46410i	−0.190203	−	0.125582i
$386$		0			0
$387$	−31.1769	−	18.0000i	−1.58481	−	0.914991i
$388$		0			0
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	−0.825491	+	0.564416i	$0.809102\pi$
$390$		0			0
$391$	3.00000	−	5.19615i	0.151717	−	0.262781i
$392$		0			0
$393$	10.3923	+	18.0000i	0.524222	+	0.907980i
$394$		0			0
$395$	4.00000	+	8.00000i	0.201262	+	0.402524i
$396$		0			0
$397$		−	12.0000i		−	0.602263i	−0.953583	−	0.301131i	$-0.902636\pi$
$397$		−	12.0000i		−	0.602263i	0.953583	−	0.301131i	$-0.0973643\pi$
$398$		0			0
$399$			3.46410i			0.173422i
$400$		0			0
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	0.449008	+	0.893528i	$0.351777\pi$
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	−0.998322	+	0.0579116i	$0.981556\pi$
$402$		0			0
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$		0			0
$405$	−11.0885	+	16.7942i	−0.550990	+	0.834512i
$406$		0			0
$407$	3.46410	−	2.00000i	0.171709	−	0.0991363i
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$		0			0
$411$		−	6.92820i		−	0.341743i
$412$		0			0
$413$			12.0000i			0.590481i
$414$		0			0
$415$	10.0000	−	5.00000i	0.490881	−	0.245440i
$416$		0			0
$417$	6.92820	+	12.0000i	0.339276	+	0.587643i
$418$		0			0
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$		0			0
$423$	23.3827	+	13.5000i	1.13691	+	0.656392i
$424$		0			0
$425$	−3.58846	+	29.7846i	−0.174066	+	1.44477i
$426$		0			0
$427$	6.06218	+	3.50000i	0.293369	+	0.169377i
$428$		0			0
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$		0			0
$431$	−32.0000			−1.54139			−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000			−1.54139			−0.770693	+	0.637207i	$0.780090\pi$
$432$		0			0
$433$			30.0000i			1.44171i	0.693087	+	0.720854i	$0.256250\pi$
$433$			30.0000i			1.44171i	−0.693087	+	0.720854i	$0.743750\pi$
$434$		0			0
$435$	−27.0622	−	1.62436i	−1.29753	−	0.0778819i
$436$		0			0
$437$	1.73205	+	1.00000i	0.0828552	+	0.0478365i
$438$		0			0
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	0.996284	+	0.0861252i	$0.0274485\pi$
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	−0.423556	+	0.905870i	$0.639218\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$		0			0
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$		0			0
$445$	33.4808	+	2.00962i	1.58714	+	0.0952651i
$446$		0			0
$447$	−12.9904	−	22.5000i	−0.614424	−	1.06421i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	10.0000			0.470882
$452$		0			0
$453$	−38.1051			−1.79033
$454$		0			0
$455$	4.46410	+	0.267949i	0.209280	+	0.0125617i
$456$		0			0
$457$	5.19615	−	3.00000i	0.243066	−	0.140334i	−0.373519	−	0.927622i	$-0.621849\pi$
$457$	5.19615	−	3.00000i	0.243066	−	0.140334i	0.616585	+	0.787288i	$0.288516\pi$
$458$		0			0
$459$		−	31.1769i		−	1.45521i
$460$		0			0
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	−0.987801	−	0.155719i	$-0.950230\pi$
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	0.359044	−	0.933321i	$-0.383103\pi$
$462$		0			0
$463$	−3.46410	−	2.00000i	−0.160990	−	0.0929479i	0.417340	−	0.908750i	$-0.362962\pi$
$463$	−3.46410	−	2.00000i	−0.160990	−	0.0929479i	−0.578331	+	0.815802i	$0.696296\pi$
$464$		0			0
$465$	−10.3923	−	20.7846i	−0.481932	−	0.963863i
$466$		0			0
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		0			0
$469$	5.00000			0.230879
$470$		0			0
$471$	−6.00000	+	3.46410i	−0.276465	+	0.159617i
$472$		0			0
$473$	−20.7846	−	12.0000i	−0.955677	−	0.551761i
$474$		0			0
$475$	−9.92820	−	1.19615i	−0.455537	−	0.0548832i
$476$		0			0
$477$	20.7846	−	12.0000i	0.951662	−	0.549442i
$478$		0			0
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$	−0.866025	+	1.50000i	−0.0394055	+	0.0682524i
$484$		0			0
$485$	−32.0000	+	16.0000i	−1.45305	+	0.726523i
$486$		0			0
$487$		−	20.0000i		−	0.906287i	−0.891438	−	0.453143i	$-0.850303\pi$
$487$		−	20.0000i		−	0.906287i	0.891438	−	0.453143i	$-0.149697\pi$
$488$		0			0
$489$	30.0000	+	17.3205i	1.35665	+	0.783260i
$490$		0			0
$491$	20.0000	−	34.6410i	0.902587	−	1.56333i	0.0784639	−	0.996917i	$-0.474998\pi$
$491$	20.0000	−	34.6410i	0.902587	−	1.56333i	0.824123	−	0.566410i	$-0.191668\pi$
$492$		0			0
$493$	36.3731	−	21.0000i	1.63816	−	0.945792i
$494$		0			0
$495$	−7.39230	+	11.1962i	−0.332259	+	0.503230i
$496$		0			0
$497$	−8.66025	+	5.00000i	−0.388465	+	0.224281i
$498$		0			0
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$	−4.50000	+	2.59808i	−0.201045	+	0.116073i
$502$		0			0
$503$			11.0000i			0.490466i	0.969464	+	0.245233i	$0.0788644\pi$
$503$			11.0000i			0.490466i	−0.969464	+	0.245233i	$0.921136\pi$
$504$		0			0
$505$	−18.0000	−	36.0000i	−0.800989	−	1.60198i
$506$		0			0
$507$	−15.5885			−0.692308
$508$		0			0
$509$	0.500000	−	0.866025i	0.0221621	−	0.0383859i	−0.854732	−	0.519070i	$-0.826278\pi$
$509$	0.500000	−	0.866025i	0.0221621	−	0.0383859i	0.876894	+	0.480684i	$0.159612\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		0			0
$513$	10.3923			0.458831
$514$		0			0
$515$	−14.9282	−	9.85641i	−0.657815	−	0.434325i
$516$		0			0
$517$	15.5885	+	9.00000i	0.685580	+	0.395820i
$518$		0			0
$519$		−	20.7846i		−	0.912343i
$520$		0			0
$521$	−5.00000			−0.219054			−0.109527	−	0.993984i	$-0.534934\pi$
$521$	−5.00000			−0.219054			−0.109527	+	0.993984i	$0.534934\pi$
$522$		0			0
$523$			19.0000i			0.830812i	0.909636	+	0.415406i	$0.136360\pi$
$523$			19.0000i			0.830812i	−0.909636	+	0.415406i	$0.863640\pi$
$524$		0			0
$525$	1.03590	−	8.59808i	0.0452103	−	0.375251i
$526$		0			0
$527$	31.1769	+	18.0000i	1.35809	+	0.784092i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	36.0000			1.56227
$532$		0			0
$533$	−8.66025	+	5.00000i	−0.375117	+	0.216574i
$534$		0			0
$535$	−1.74167	+	29.0167i	−0.0752989	+	1.25450i
$536$		0			0
$537$	8.66025	−	15.0000i	0.373718	−	0.647298i
$538$		0			0
$539$	12.0000			0.516877
$540$		0			0
$541$	31.0000			1.33279			0.666397	−	0.745597i	$-0.267836\pi$
$541$	31.0000			1.33279			0.666397	+	0.745597i	$0.267836\pi$
$542$		0			0
$543$	16.4545	−	28.5000i	0.706129	−	1.22305i
$544$		0			0
$545$	20.0885	+	1.20577i	0.860495	+	0.0516496i
$546$		0			0
$547$	11.2583	−	6.50000i	0.481371	−	0.277920i	−0.239616	−	0.970868i	$-0.577022\pi$
$547$	11.2583	−	6.50000i	0.481371	−	0.277920i	0.720988	+	0.692948i	$0.243688\pi$
$548$		0			0
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$		0			0
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$		0			0
$553$	3.46410	+	2.00000i	0.147309	+	0.0850487i
$554$		0			0
$555$	6.46410	+	4.26795i	0.274386	+	0.181164i
$556$		0			0
$557$		−	24.0000i		−	1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$		−	24.0000i		−	1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$		0			0
$561$		−	20.7846i		−	0.877527i
$562$		0			0
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	0.831614	−	0.555354i	$-0.187417\pi$
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	−0.0651433	+	0.997876i	$0.520750\pi$
$564$		0			0
$565$	−7.46410	−	4.92820i	−0.314017	−	0.207331i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	0.408883	+	0.912587i	$0.365918\pi$
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	−0.994765	+	0.102190i	$0.967415\pi$
$572$		0			0
$573$	−31.1769			−1.30243
$574$		0			0
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$		0			0
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$		0			0
$579$	−3.00000	+	1.73205i	−0.124676	+	0.0719816i
$580$		0			0
$581$	2.50000	−	4.33013i	0.103717	−	0.179644i
$582$		0			0
$583$	13.8564	−	8.00000i	0.573874	−	0.331326i
$584$		0			0
$585$	0.803848	−	13.3923i	0.0332350	−	0.553704i
$586$		0			0
$587$	−30.3109	+	17.5000i	−1.25106	+	0.722302i	−0.971321	−	0.237773i	$-0.923583\pi$
$587$	−30.3109	+	17.5000i	−1.25106	+	0.722302i	−0.279743	+	0.960075i	$0.590249\pi$
$588$		0			0
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$		0			0
$591$	−36.0000	−	20.7846i	−1.48084	−	0.854965i
$592$		0			0
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$		0			0
$595$	6.00000	+	12.0000i	0.245976	+	0.491952i
$596$		0			0
$597$	−8.66025	+	15.0000i	−0.354441	+	0.613909i
$598$		0			0
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	−0.424333	−	0.905506i	$-0.639492\pi$
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	0.996358	−	0.0852695i	$-0.0271751\pi$
$600$		0			0
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	0.920703	−	0.390264i	$-0.127616\pi$
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	−0.798330	+	0.602220i	$0.794283\pi$
$602$		0			0
$603$		−	15.0000i		−	0.610847i
$604$		0			0
$605$	8.62436	−	13.0622i	0.350630	−	0.531053i
$606$		0			0
$607$	42.4352	+	24.5000i	1.72239	+	0.994424i	0.913923	+	0.405887i	$0.133038\pi$
$607$	42.4352	+	24.5000i	1.72239	+	0.994424i	0.808470	+	0.588537i	$0.200296\pi$
$608$		0			0
$609$	−10.5000	+	6.06218i	−0.425481	+	0.245652i
$610$		0			0
$611$	−18.0000			−0.728202
$612$		0			0
$613$		−	14.0000i		−	0.565455i	−0.959200	−	0.282727i	$-0.908761\pi$
$613$		−	14.0000i		−	0.565455i	0.959200	−	0.282727i	$-0.0912392\pi$
$614$		0			0
$615$	8.66025	+	17.3205i	0.349215	+	0.698430i
$616$		0			0
$617$	13.8564	+	8.00000i	0.557838	+	0.322068i	0.752277	−	0.658847i	$-0.228955\pi$
$617$	13.8564	+	8.00000i	0.557838	+	0.322068i	−0.194439	+	0.980915i	$0.562289\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	4.50000	+	2.59808i	0.180579	+	0.104257i
$622$		0			0
$623$	12.9904	−	7.50000i	0.520449	−	0.300481i
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		0			0
$627$	6.92820			0.276686
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$	−22.5167	−	39.0000i	−0.894957	−	1.55011i
$634$		0			0
$635$	−0.401924	+	6.69615i	−0.0159499	+	0.265729i
$636$		0			0
$637$	−10.3923	+	6.00000i	−0.411758	+	0.237729i
$638$		0			0
$639$	15.0000	+	25.9808i	0.593391	+	1.02778i
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$		0			0
$643$	−12.9904	−	7.50000i	−0.512291	−	0.295771i	0.221484	−	0.975164i	$-0.428910\pi$
$643$	−12.9904	−	7.50000i	−0.512291	−	0.295771i	−0.733775	+	0.679393i	$0.762243\pi$
$644$		0			0
$645$	2.78461	−	46.3923i	0.109644	−	1.82670i
$646$		0			0
$647$			31.0000i			1.21874i	0.792888	+	0.609368i	$0.208577\pi$
$647$			31.0000i			1.21874i	−0.792888	+	0.609368i	$0.791423\pi$
$648$		0			0
$649$	24.0000			0.942082
$650$		0			0
$651$	−9.00000	−	5.19615i	−0.352738	−	0.203653i
$652$		0			0
$653$	25.9808	+	15.0000i	1.01671	+	0.586995i	0.913148	−	0.407628i	$-0.133644\pi$
$653$	25.9808	+	15.0000i	1.01671	+	0.586995i	0.103558	+	0.994623i	$0.466977\pi$
$654$		0			0
$655$	−14.7846	+	22.3923i	−0.577683	+	0.874940i
$656$		0			0
$657$	−10.3923	+	6.00000i	−0.405442	+	0.234082i
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$	10.3923	+	18.0000i	0.403604	+	0.699062i
$664$		0			0
$665$	−4.00000	+	2.00000i	−0.155113	+	0.0775567i
$666$		0			0
$667$			7.00000i			0.271041i
$668$		0			0
$669$			15.5885i			0.602685i
$670$		0			0
$671$	7.00000	−	12.1244i	0.270232	−	0.468056i
$672$		0			0
$673$	1.73205	−	1.00000i	0.0667657	−	0.0385472i	−0.466246	−	0.884655i	$-0.654394\pi$
$673$	1.73205	−	1.00000i	0.0667657	−	0.0385472i	0.533011	+	0.846108i	$0.321060\pi$
$674$		0			0
$675$	−25.7942	−	3.10770i	−0.992820	−	0.119615i
$676$		0			0
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	−0.768693	−	0.639618i	$-0.779092\pi$
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	0.169580	+	0.985517i	$0.445759\pi$
$678$		0			0
$679$	−8.00000	+	13.8564i	−0.307012	+	0.531760i
$680$		0			0
$681$		−	13.8564i		−	0.530979i
$682$		0			0
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	8.00000	−	4.00000i	0.305664	−	0.152832i
$686$		0			0
$687$	−7.79423	−	13.5000i	−0.297368	−	0.515057i
$688$		0			0
$689$	−8.00000	+	13.8564i	−0.304776	+	0.527887i
$690$		0			0
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	0.957290	−	0.289130i	$-0.0933661\pi$
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	−0.729039	+	0.684472i	$0.760033\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$		0			0
$695$	−9.85641	+	14.9282i	−0.373875	+	0.566259i
$696$		0			0
$697$	−25.9808	−	15.0000i	−0.984092	−	0.568166i
$698$		0			0
$699$	−9.00000	−	5.19615i	−0.340411	−	0.196537i
$700$		0			0
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$		0			0
$703$		−	4.00000i		−	0.150863i
$704$		0			0
$705$	−2.08846	+	34.7942i	−0.0786559	+	1.31043i
$706$		0			0
$707$	−15.5885	−	9.00000i	−0.586264	−	0.338480i
$708$		0			0
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	0.970254	+	0.242089i	$0.0778325\pi$
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	−0.275472	+	0.961309i	$0.588834\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$		0			0
$713$	−5.19615	+	3.00000i	−0.194597	+	0.112351i
$714$		0			0
$715$	0.535898	−	8.92820i	0.0200415	−	0.333896i
$716$		0			0
$717$	3.46410	+	6.00000i	0.129369	+	0.224074i
$718$		0			0
$719$	−28.0000			−1.04422			−0.522112	−	0.852877i	$-0.674856\pi$
$719$	−28.0000			−1.04422			−0.522112	+	0.852877i	$0.674856\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		0			0
$723$	−29.4449			−1.09507
$724$		0			0
$725$	−13.7487	−	32.1865i	−0.510614	−	1.19538i
$726$		0			0
$727$	−18.1865	+	10.5000i	−0.674501	+	0.389423i	−0.797780	−	0.602949i	$-0.793992\pi$
$727$	−18.1865	+	10.5000i	−0.674501	+	0.389423i	0.123279	+	0.992372i	$0.460659\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	36.0000	+	62.3538i	1.33151	+	2.30624i
$732$		0			0
$733$	−31.1769	−	18.0000i	−1.15155	−	0.664845i	−0.202282	−	0.979327i	$-0.564836\pi$
$733$	−31.1769	−	18.0000i	−1.15155	−	0.664845i	−0.949263	+	0.314482i	$0.898169\pi$
$734$		0			0
$735$	10.3923	+	20.7846i	0.383326	+	0.766652i
$736$		0			0
$737$		−	10.0000i		−	0.368355i
$738$		0			0
$739$	−24.0000			−0.882854			−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000			−0.882854			−0.441427	+	0.897297i	$0.645528\pi$
$740$		0			0
$741$	−6.00000	+	3.46410i	−0.220416	+	0.127257i
$742$		0			0
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	0.718986	−	0.695024i	$-0.244606\pi$
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	−0.242415	+	0.970173i	$0.577940\pi$
$744$		0			0
$745$	18.4808	−	27.9904i	0.677083	−	1.02549i
$746$		0			0
$747$	−12.9904	−	7.50000i	−0.475293	−	0.274411i
$748$		0			0
$749$	6.50000	+	11.2583i	0.237505	+	0.411370i
$750$		0			0
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	−0.965013	−	0.262201i	$-0.915552\pi$
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	0.709580	+	0.704625i	$0.248885\pi$
$752$		0			0
$753$	−1.73205	+	3.00000i	−0.0631194	+	0.109326i
$754$		0			0
$755$	−22.0000	−	44.0000i	−0.800662	−	1.60132i
$756$		0			0
$757$			38.0000i			1.38113i	0.723269	+	0.690567i	$0.242639\pi$
$757$			38.0000i			1.38113i	−0.723269	+	0.690567i	$0.757361\pi$
$758$		0			0
$759$	3.00000	+	1.73205i	0.108893	+	0.0628695i
$760$		0			0
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$762$		0			0
$763$	7.79423	−	4.50000i	0.282170	−	0.162911i
$764$		0			0
$765$	36.0000	−	18.0000i	1.30158	−	0.650791i
$766$		0			0
$767$	−20.7846	+	12.0000i	−0.750489	+	0.433295i
$768$		0			0
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$	−18.0000	+	10.3923i	−0.648254	+	0.374270i
$772$		0			0
$773$			4.00000i			0.143870i	0.997409	+	0.0719350i	$0.0229174\pi$
$773$			4.00000i			0.143870i	−0.997409	+	0.0719350i	$0.977083\pi$
$774$		0			0
$775$	18.0000	−	24.0000i	0.646579	−	0.862105i
$776$		0			0
$777$	3.46410			0.124274
$778$		0			0
$779$	5.00000	−	8.66025i	0.179144	−	0.310286i
$780$		0			0
$781$	10.0000	+	17.3205i	0.357828	+	0.619777i
$782$		0			0
$783$	18.1865	+	31.5000i	0.649934	+	1.12572i
$784$		0			0
$785$	−7.46410	−	4.92820i	−0.266405	−	0.175895i
$786$		0			0
$787$	−17.3205	−	10.0000i	−0.617409	−	0.356462i	0.158450	−	0.987367i	$-0.449350\pi$
$787$	−17.3205	−	10.0000i	−0.617409	−	0.356462i	−0.775860	+	0.630905i	$0.782684\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.00000			−0.142224
$792$		0			0
$793$			14.0000i			0.497155i
$794$		0			0
$795$	25.8564	+	17.0718i	0.917032	+	0.605474i
$796$		0			0
$797$	−25.9808	−	15.0000i	−0.920286	−	0.531327i	−0.0365596	−	0.999331i	$-0.511640\pi$
$797$	−25.9808	−	15.0000i	−0.920286	−	0.531327i	−0.883726	+	0.468004i	$0.844973\pi$
$798$		0			0
$799$	−27.0000	−	46.7654i	−0.955191	−	1.65444i
$800$		0			0
$801$	−22.5000	−	38.9711i	−0.794998	−	1.37698i
$802$		0			0
$803$	−6.92820	+	4.00000i	−0.244491	+	0.141157i
$804$		0			0
$805$	−2.23205	−	0.133975i	−0.0786695	−	0.00472198i
$806$		0			0
$807$	−2.59808	+	4.50000i	−0.0914566	+	0.158408i
$808$		0			0
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$		0			0
$813$	12.1244	−	21.0000i	0.425220	−	0.736502i
$814$		0			0
$815$	−2.67949	+	44.6410i	−0.0938585	+	1.56371i
$816$		0			0
$817$	−20.7846	+	12.0000i	−0.727161	+	0.419827i
$818$		0			0
$819$	−3.00000	−	5.19615i	−0.104828	−	0.181568i
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	14.7224	+	8.50000i	0.513192	+	0.296291i	0.734145	−	0.678993i	$-0.237583\pi$
$823$	14.7224	+	8.50000i	0.513192	+	0.296291i	−0.220953	+	0.975284i	$0.570917\pi$
$824$		0			0
$825$	−17.1962	−	2.07180i	−0.598693	−	0.0721307i
$826$		0			0
$827$			3.00000i			0.104320i	0.998639	+	0.0521601i	$0.0166106\pi$
$827$			3.00000i			0.104320i	−0.998639	+	0.0521601i	$0.983389\pi$
$828$		0			0
$829$	−31.0000			−1.07667			−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000			−1.07667			−0.538337	+	0.842729i	$0.680947\pi$
$830$		0			0
$831$			51.9615i			1.80253i
$832$		0			0
$833$	−31.1769	−	18.0000i	−1.08022	−	0.623663i
$834$		0			0
$835$	−5.59808	−	3.69615i	−0.193729	−	0.127911i
$836$		0			0
$837$	−15.5885	+	27.0000i	−0.538816	+	0.933257i
$838$		0			0
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	0.958974	+	0.283495i	$0.0914938\pi$
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	−0.233973	+	0.972243i	$0.575173\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$		0			0
$843$	5.19615			0.178965
$844$		0			0
$845$	−9.00000	−	18.0000i	−0.309609	−	0.619219i
$846$		0			0
$847$		−	7.00000i		−	0.240523i
$848$		0			0
$849$	−49.5000	+	28.5788i	−1.69884	+	0.980823i
$850$		0			0
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	8.66025	−	5.00000i	0.296521	−	0.171197i	−0.344358	−	0.938839i	$-0.611903\pi$
$853$	8.66025	−	5.00000i	0.296521	−	0.171197i	0.640879	+	0.767642i	$0.278570\pi$
$854$		0			0
$855$	6.00000	+	12.0000i	0.205196	+	0.410391i
$856$		0			0
$857$	32.9090	−	19.0000i	1.12415	−	0.649028i	0.181692	−	0.983355i	$-0.441843\pi$
$857$	32.9090	−	19.0000i	1.12415	−	0.649028i	0.942457	+	0.334328i	$0.108509\pi$
$858$		0			0
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	−0.768031	−	0.640412i	$-0.778763\pi$
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	0.938629	+	0.344928i	$0.112097\pi$
$860$		0			0
$861$	7.50000	+	4.33013i	0.255599	+	0.147570i
$862$		0			0
$863$		−	45.0000i		−	1.53182i	−0.642949	−	0.765909i	$-0.722289\pi$
$863$		−	45.0000i		−	1.53182i	0.642949	−	0.765909i	$-0.277711\pi$
$864$		0			0
$865$	24.0000	−	12.0000i	0.816024	−	0.408012i
$866$		0			0
$867$	−16.4545	+	28.5000i	−0.558824	+	0.967911i
$868$		0			0
$869$	4.00000	−	6.92820i	0.135691	−	0.235023i
$870$		0			0
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$		0			0
$873$	41.5692	+	24.0000i	1.40690	+	0.812277i
$874$		0			0
$875$	10.5263	−	3.76795i	0.355853	−	0.127380i
$876$		0			0
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	0.528958	−	0.848648i	$-0.322583\pi$
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	−0.470471	+	0.882415i	$0.655916\pi$
$878$		0			0
$879$	21.0000	−	12.1244i	0.708312	−	0.408944i
$880$		0			0
$881$	49.0000			1.65085			0.825426	−	0.564510i	$-0.190935\pi$
$881$	49.0000			1.65085			0.825426	+	0.564510i	$0.190935\pi$
$882$		0			0
$883$			35.0000i			1.17784i	0.808190	+	0.588922i	$0.200447\pi$
$883$			35.0000i			1.17784i	−0.808190	+	0.588922i	$0.799553\pi$
$884$		0			0
$885$	20.7846	+	41.5692i	0.698667	+	1.39733i
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	1.50000	+	2.59808i	0.0503084	+	0.0871367i
$890$		0			0
$891$	18.0000			0.603023
$892$		0			0
$893$	15.5885	−	9.00000i	0.521648	−	0.301174i
$894$		0			0
$895$	22.3205	+	1.33975i	0.746092	+	0.0447828i
$896$		0			0
$897$	−3.46410			−0.115663
$898$		0			0
$899$	−42.0000			−1.40078
$900$		0			0
$901$	−48.0000			−1.59911
$902$		0			0
$903$	−10.3923	−	18.0000i	−0.345834	−	0.599002i
$904$		0			0
$905$	42.4090	+	2.54552i	1.40972	+	0.0846159i
$906$		0			0
$907$	−0.866025	+	0.500000i	−0.0287559	+	0.0166022i	−0.514309	−	0.857605i	$-0.671952\pi$
$907$	−0.866025	+	0.500000i	−0.0287559	+	0.0166022i	0.485553	+	0.874207i	$0.338618\pi$
$908$		0			0
$909$	−27.0000	+	46.7654i	−0.895533	+	1.55111i
$910$		0			0
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	0.749347	−	0.662177i	$-0.230367\pi$
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	−0.948136	+	0.317865i	$0.897034\pi$
$912$		0			0
$913$	−8.66025	−	5.00000i	−0.286613	−	0.165476i
$914$		0			0
$915$	27.0622	+	1.62436i	0.894648	+	0.0536995i
$916$		0			0
$917$			12.0000i			0.396275i
$918$		0			0
$919$	36.0000			1.18753			0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000			1.18753			0.593765	+	0.804638i	$0.297641\pi$
$920$		0			0
$921$	−10.5000	−	6.06218i	−0.345987	−	0.199756i
$922$		0			0
$923$	−17.3205	−	10.0000i	−0.570111	−	0.329154i
$924$		0			0
$925$	−1.19615	+	9.92820i	−0.0393292	+	0.326437i
$926$		0			0
$927$			24.0000i			0.788263i
$928$		0			0
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	6.00000	−	10.3923i	0.196642	−	0.340594i
$932$		0			0
$933$	−5.19615	−	9.00000i	−0.170114	−	0.294647i
$934$		0			0
$935$	24.0000	−	12.0000i	0.784884	−	0.392442i
$936$		0			0
$937$			28.0000i			0.914720i	0.889282	+	0.457360i	$0.151205\pi$
$937$			28.0000i			0.914720i	−0.889282	+	0.457360i	$0.848795\pi$
$938$		0			0
$939$		−	24.2487i		−	0.791327i
$940$		0			0
$941$	12.5000	−	21.6506i	0.407488	−	0.705791i	−0.587119	−	0.809500i	$-0.699738\pi$
$941$	12.5000	−	21.6506i	0.407488	−	0.705791i	0.994608	+	0.103710i	$0.0330714\pi$
$942$		0			0
$943$	4.33013	−	2.50000i	0.141008	−	0.0814112i
$944$		0			0
$945$	−10.3923	+	5.19615i	−0.338062	+	0.169031i
$946$		0			0
$947$	2.59808	−	1.50000i	0.0844261	−	0.0487435i	−0.457193	−	0.889368i	$-0.651145\pi$
$947$	2.59808	−	1.50000i	0.0844261	−	0.0487435i	0.541619	+	0.840624i	$0.317812\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$		−	51.9615i		−	1.68497i
$952$		0			0
$953$		−	42.0000i		−	1.36051i	−0.732974	−	0.680257i	$-0.761868\pi$
$953$		−	42.0000i		−	1.36051i	0.732974	−	0.680257i	$-0.238132\pi$
$954$		0			0
$955$	−18.0000	−	36.0000i	−0.582466	−	1.16493i
$956$		0			0
$957$	12.1244	+	21.0000i	0.391925	+	0.678834i
$958$		0			0
$959$	2.00000	−	3.46410i	0.0645834	−	0.111862i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	33.7750	−	19.5000i	1.08838	−	0.628379i
$964$		0			0
$965$	−3.73205	−	2.46410i	−0.120139	−	0.0793222i
$966$		0			0
$967$	−0.866025	−	0.500000i	−0.0278495	−	0.0160789i	0.486011	−	0.873953i	$-0.338452\pi$
$967$	−0.866025	−	0.500000i	−0.0278495	−	0.0160789i	−0.513860	+	0.857874i	$0.671785\pi$
$968$		0			0
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$		0			0
$971$	42.0000			1.34784			0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000			1.34784			0.673922	+	0.738802i	$0.264608\pi$
$972$		0			0
$973$			8.00000i			0.256468i
$974$		0			0
$975$	15.9282	−	6.80385i	0.510111	−	0.217898i
$976$		0			0
$977$	1.73205	+	1.00000i	0.0554132	+	0.0319928i	0.527451	−	0.849586i	$-0.323148\pi$
$977$	1.73205	+	1.00000i	0.0554132	+	0.0319928i	−0.472037	+	0.881579i	$0.656481\pi$
$978$		0			0
$979$	−15.0000	−	25.9808i	−0.479402	−	0.830349i
$980$		0			0
$981$	−13.5000	−	23.3827i	−0.431022	−	0.746552i
$982$		0			0
$983$	11.2583	−	6.50000i	0.359085	−	0.207318i	−0.309594	−	0.950869i	$-0.600193\pi$
$983$	11.2583	−	6.50000i	0.359085	−	0.207318i	0.668679	+	0.743551i	$0.266860\pi$
$984$		0			0
$985$	3.21539	−	53.5692i	0.102451	−	1.70686i
$986$		0			0
$987$	7.79423	+	13.5000i	0.248093	+	0.429710i
$988$		0			0
$989$	−12.0000			−0.381578
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$		0			0
$993$	55.4256			1.75888
$994$		0			0
$995$	−22.3205	−	1.33975i	−0.707608	−	0.0424728i
$996$		0			0
$997$	−41.5692	+	24.0000i	−1.31651	+	0.760088i	−0.983165	−	0.182717i	$-0.941511\pi$
$997$	−41.5692	+	24.0000i	−1.31651	+	0.760088i	−0.333345	+	0.942805i	$0.608177\pi$
$998$		0			0
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.a.49.2	yes	4
3.2	odd	2		1080.2.bi.a.1009.1		4
4.3	odd	2		720.2.by.b.49.1		4
5.4	even	2	inner	360.2.bi.a.49.1	✓	4
9.2	odd	6		1080.2.bi.a.289.2		4
9.4	even	3		3240.2.f.b.649.1		2
9.5	odd	6		3240.2.f.e.649.2		2
9.7	even	3	inner	360.2.bi.a.169.1	yes	4
12.11	even	2		2160.2.by.a.1009.1		4
15.14	odd	2		1080.2.bi.a.1009.2		4
20.19	odd	2		720.2.by.b.49.2		4
36.7	odd	6		720.2.by.b.529.2		4
36.11	even	6		2160.2.by.a.289.2		4
45.4	even	6		3240.2.f.b.649.2		2
45.14	odd	6		3240.2.f.e.649.1		2
45.29	odd	6		1080.2.bi.a.289.1		4
45.34	even	6	inner	360.2.bi.a.169.2	yes	4
60.59	even	2		2160.2.by.a.1009.2		4
180.79	odd	6		720.2.by.b.529.1		4
180.119	even	6		2160.2.by.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.a.49.1	✓	4	5.4	even	2	inner
360.2.bi.a.49.2	yes	4	1.1	even	1	trivial
360.2.bi.a.169.1	yes	4	9.7	even	3	inner
360.2.bi.a.169.2	yes	4	45.34	even	6	inner
720.2.by.b.49.1		4	4.3	odd	2
720.2.by.b.49.2		4	20.19	odd	2
720.2.by.b.529.1		4	180.79	odd	6
720.2.by.b.529.2		4	36.7	odd	6
1080.2.bi.a.289.1		4	45.29	odd	6
1080.2.bi.a.289.2		4	9.2	odd	6
1080.2.bi.a.1009.1		4	3.2	odd	2
1080.2.bi.a.1009.2		4	15.14	odd	2
2160.2.by.a.289.1		4	180.119	even	6
2160.2.by.a.289.2		4	36.11	even	6
2160.2.by.a.1009.1		4	12.11	even	2
2160.2.by.a.1009.2		4	60.59	even	2
3240.2.f.b.649.1		2	9.4	even	3
3240.2.f.b.649.2		2	45.4	even	6
3240.2.f.e.649.1		2	45.14	odd	6
3240.2.f.e.649.2		2	9.5	odd	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(1.73205 + 1.00000i) q^{13} +(2.13397 - 3.23205i) q^{15} +6.00000i q^{17} -2.00000 q^{19} -1.73205i q^{21} +(-0.866025 - 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} -5.19615 q^{27} +(-3.50000 - 6.06218i) q^{29} +(3.00000 - 5.19615i) q^{31} -3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(3.00000 - 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(10.3923 - 6.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(-7.79423 + 4.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(9.00000 + 5.19615i) q^{51} +8.00000i q^{53} +(-2.00000 - 4.00000i) q^{55} +(-1.73205 + 3.00000i) q^{57} +(-6.00000 + 10.3923i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.59808 - 1.50000i) q^{63} +(3.73205 + 2.46410i) q^{65} +(4.33013 + 2.50000i) q^{67} +(-1.50000 + 0.866025i) q^{69} -10.0000 q^{71} -4.00000i q^{73} +(5.19615 - 6.92820i) q^{75} +(-1.73205 - 1.00000i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(4.33013 - 2.50000i) q^{83} +(-0.803848 + 13.3923i) q^{85} -12.1244 q^{87} +15.0000 q^{89} +2.00000 q^{91} +(-5.19615 - 9.00000i) q^{93} +(-4.46410 - 0.267949i) q^{95} +(-13.8564 + 8.00000i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^5 - 6 * q^9	\( 4 q + 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{15} - 8 q^{19} + 6 q^{25} - 14 q^{29} + 12 q^{31} + 8 q^{35} + 12 q^{39} - 10 q^{41} - 12 q^{45} - 12 q^{49} + 36 q^{51} - 8 q^{55} - 24 q^{59} + 14 q^{61} + 8 q^{65} - 6 q^{69} - 40 q^{71} + 8 q^{79} - 18 q^{81} - 24 q^{85} + 60 q^{89} + 8 q^{91} - 4 q^{95} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^15 - 8 * q^19 + 6 * q^25 - 14 * q^29 + 12 * q^31 + 8 * q^35 + 12 * q^39 - 10 * q^41 - 12 * q^45 - 12 * q^49 + 36 * q^51 - 8 * q^55 - 24 * q^59 + 14 * q^61 + 8 * q^65 - 6 * q^69 - 40 * q^71 + 8 * q^79 - 18 * q^81 - 24 * q^85 + 60 * q^89 + 8 * q^91 - 4 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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