LMFDB - Embedded newform 360.2.bi.a.169.1

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			169.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.169
Dual form			360.2.bi.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 1.50000i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 1.50000i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(-1.73205 + 1.00000i) q^{13} +(3.86603 + 0.232051i) q^{15} +6.00000i q^{17} -2.00000 q^{19} +1.73205i q^{21} +(0.866025 - 0.500000i) q^{23} +(-1.96410 - 4.59808i) q^{25} +5.19615 q^{27} +(-3.50000 + 6.06218i) q^{29} +(3.00000 + 5.19615i) q^{31} +3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-10.3923 - 6.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(7.79423 + 4.50000i) q^{47} +(-3.00000 - 5.19615i) q^{49} +(9.00000 - 5.19615i) q^{51} +8.00000i q^{53} +(-2.00000 - 4.00000i) q^{55} +(1.73205 + 3.00000i) q^{57} +(-6.00000 - 10.3923i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.59808 - 1.50000i) q^{63} +(0.267949 - 4.46410i) q^{65} +(-4.33013 + 2.50000i) q^{67} +(-1.50000 - 0.866025i) q^{69} -10.0000 q^{71} -4.00000i q^{73} +(-5.19615 + 6.92820i) q^{75} +(1.73205 - 1.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.33013 - 2.50000i) q^{83} +(-11.1962 - 7.39230i) q^{85} +12.1244 q^{87} +15.0000 q^{89} +2.00000 q^{91} +(5.19615 - 9.00000i) q^{93} +(2.46410 - 3.73205i) q^{95} +(13.8564 + 8.00000i) q^{97} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		0			0
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	0.240192	+	0.970725i	$0.422790\pi$
$14$		0			0
$15$	3.86603	+	0.232051i	0.998203	+	0.0599153i
$16$		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	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$		0			0
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$		0			0
$27$	5.19615			1.00000
$28$		0			0
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$		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	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$		0			0
$43$	−10.3923	−	6.00000i	−1.58481	−	0.914991i	−0.994142	−	0.108078i	$-0.965531\pi$
$43$	−10.3923	−	6.00000i	−1.58481	−	0.914991i	−0.590669	−	0.806914i	$-0.701136\pi$
$44$		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	$-0.105415\pi$
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.191243	+	0.981543i	$0.438748\pi$
$48$		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	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	2.59808	−	1.50000i	0.327327	−	0.188982i
$64$		0			0
$65$	0.267949	−	4.46410i	0.0332350	−	0.553704i
$66$		0			0
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	−0.740613	−	0.671932i	$-0.765465\pi$
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	0.211604	+	0.977356i	$0.432131\pi$
$68$		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	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		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	$-0.421816\pi$
$83$	−4.33013	−	2.50000i	−0.475293	−	0.274411i	−0.718453	+	0.695576i	$0.755149\pi$
$84$		0			0
$85$	−11.1962	−	7.39230i	−1.21439	−	0.801808i
$86$		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
$95$	2.46410	−	3.73205i	0.252811	−	0.382900i
$96$		0			0
$97$	13.8564	+	8.00000i	1.40690	+	0.812277i	0.995088	−	0.0989899i	$-0.0315611\pi$
$97$	13.8564	+	8.00000i	1.40690	+	0.812277i	0.411816	+	0.911267i	$0.364894\pi$
$98$		0			0
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$		0			0
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$		0			0
$105$	−3.23205	−	2.13397i	−0.315416	−	0.208255i
$106$		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	$-0.606419\pi$
$113$	3.46410	−	2.00000i	0.325875	−	0.188144i	0.654008	+	0.756487i	$0.273086\pi$
$114$		0			0
$115$	−0.133975	+	2.23205i	−0.0124932	+	0.208140i
$116$		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	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$	1.73205	+	1.00000i	0.150188	+	0.0867110i
$134$		0			0
$135$	−6.40192	+	9.69615i	−0.550990	+	0.834512i
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		0			0
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$		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	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.0615699	+	0.998103i	$0.519611\pi$
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.833597	+	0.552372i	$0.813723\pi$
$152$		0			0
$153$	−15.5885	−	9.00000i	−1.26025	−	0.727607i
$154$		0			0
$155$	−13.3923	−	0.803848i	−1.07570	−	0.0645666i
$156$		0			0
$157$	3.46410	−	2.00000i	0.276465	−	0.159617i	−0.355357	−	0.934731i	$-0.615641\pi$
$157$	3.46410	−	2.00000i	0.276465	−	0.159617i	0.631822	+	0.775113i	$0.282307\pi$
$158$		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
$165$	−4.26795	+	6.46410i	−0.332259	+	0.503230i
$166$		0			0
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	−0.396098	−	0.918208i	$-0.629636\pi$
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	0.597143	+	0.802135i	$0.296303\pi$
$168$		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	$-0.484113\pi$
$173$	−10.3923	−	6.00000i	−0.790112	−	0.456172i	−0.840002	+	0.542583i	$0.817446\pi$
$174$		0			0
$175$	−0.598076	+	4.96410i	−0.0452103	+	0.375251i
$176$		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
$185$	−3.73205	−	2.46410i	−0.274386	−	0.181164i
$186$		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	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	1.73205	−	1.00000i	0.124676	−	0.0719816i	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	1.73205	−	1.00000i	0.124676	−	0.0719816i	0.561041	+	0.827788i	$0.310401\pi$
$194$		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
$205$	11.1603	+	0.669873i	0.779466	+	0.0467860i
$206$		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	0.833858	+	0.551979i	$0.186127\pi$
$211$	13.0000	+	22.5167i	0.894957	+	1.55011i	0.0610990	+	0.998132i	$0.480539\pi$
$212$		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	$-0.235899\pi$
$223$	7.79423	+	4.50000i	0.521940	+	0.301342i	−0.215788	+	0.976440i	$0.569232\pi$
$224$		0			0
$225$	14.8923	+	1.79423i	0.992820	+	0.119615i
$226$		0			0
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	0.252136	−	0.967692i	$-0.418867\pi$
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	−0.711977	+	0.702202i	$0.752200\pi$
$228$		0			0
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	0.975533	−	0.219853i	$-0.0705577\pi$
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	−0.678165	+	0.734910i	$0.737224\pi$
$230$		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	0.794063	−	0.607835i	$-0.207962\pi$
$239$	−2.00000	−	3.46410i	−0.129369	−	0.224074i	−0.923432	+	0.383761i	$0.874629\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$		0			0
$245$	13.3923	+	0.803848i	0.855603	+	0.0513559i
$246$		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
$255$	−1.39230	+	23.1962i	−0.0871895	+	1.45260i
$256$		0			0
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	−0.139533	−	0.990217i	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$		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	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	−14.9282	−	9.85641i	−0.917032	−	0.605474i
$266$		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
$275$	9.92820	+	1.19615i	0.598693	+	0.0721307i
$276$		0			0
$277$	25.9808	+	15.0000i	1.56103	+	0.901263i	0.997153	+	0.0754058i	$0.0240252\pi$
$277$	25.9808	+	15.0000i	1.56103	+	0.901263i	0.563880	+	0.825857i	$0.309308\pi$
$278$		0			0
$279$	−18.0000			−1.07763
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	28.5788	−	16.5000i	1.69884	−	0.980823i	0.751968	−	0.659200i	$-0.229105\pi$
$283$	28.5788	−	16.5000i	1.69884	−	0.980823i	0.946868	−	0.321624i	$-0.104229\pi$
$284$		0			0
$285$	−7.73205	−	0.464102i	−0.458007	−	0.0274910i
$286$		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	$-0.800770\pi$
$293$	−12.1244	+	7.00000i	−0.708312	+	0.408944i	0.102123	+	0.994772i	$0.467436\pi$
$294$		0			0
$295$	26.7846	+	1.60770i	1.55946	+	0.0936036i
$296$		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	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$		0			0
$313$	−12.1244	−	7.00000i	−0.685309	−	0.395663i	0.116543	−	0.993186i	$-0.462819\pi$
$313$	−12.1244	−	7.00000i	−0.685309	−	0.395663i	−0.801852	+	0.597522i	$0.796152\pi$
$314$		0			0
$315$	−0.401924	+	6.69615i	−0.0226458	+	0.377285i
$316$		0			0
$317$	−25.9808	−	15.0000i	−1.45922	−	0.842484i	−0.460252	−	0.887788i	$-0.652241\pi$
$317$	−25.9808	−	15.0000i	−1.45922	−	0.842484i	−0.998973	+	0.0453045i	$0.985574\pi$
$318$		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	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$		0			0
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$		0			0
$335$	0.669873	−	11.1603i	0.0365991	−	0.609750i
$336$		0			0
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	−0.676688	−	0.736270i	$-0.736585\pi$
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	0.299285	+	0.954164i	$0.403252\pi$
$338$		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	$-0.700908\pi$
$347$	−3.46410	+	2.00000i	−0.185963	+	0.107366i	0.404128	+	0.914702i	$0.367575\pi$
$348$		0			0
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$		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	$-0.112808\pi$
$353$	20.7846	+	12.0000i	1.10625	+	0.638696i	0.168397	+	0.985719i	$0.446141\pi$
$354$		0			0
$355$	12.3205	−	18.6603i	0.653905	−	0.990383i
$356$		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
$365$	7.46410	+	4.92820i	0.390689	+	0.257954i
$366$		0			0
$367$	−27.7128	−	16.0000i	−1.44660	−	0.835193i	−0.448320	−	0.893873i	$-0.647978\pi$
$367$	−27.7128	−	16.0000i	−1.44660	−	0.835193i	−0.998277	+	0.0586798i	$0.981311\pi$
$368$		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	$-0.633645\pi$
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	0.586994	+	0.809591i	$0.300311\pi$
$374$		0			0
$375$	−6.52628	−	18.2321i	−0.337016	−	0.941499i
$376$		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	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$	−0.267949	+	4.46410i	−0.0136560	+	0.227512i
$386$		0			0
$387$	31.1769	−	18.0000i	1.58481	−	0.914991i
$388$		0			0
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		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	−0.998322	−	0.0579116i	$-0.981556\pi$
$401$	−11.0000	−	19.0526i	−0.549314	−	0.951439i	0.449008	−	0.893528i	$-0.351777\pi$
$402$		0			0
$403$	−10.3923	−	6.00000i	−0.517678	−	0.298881i
$404$		0			0
$405$	20.0885	+	1.20577i	0.998203	+	0.0599153i
$406$		0			0
$407$	−3.46410	−	2.00000i	−0.171709	−	0.0991363i
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		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	0.929954	−	0.367677i	$-0.119847\pi$
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	−0.783394	+	0.621525i	$0.786513\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$		0			0
$423$	−23.3827	+	13.5000i	−1.13691	+	0.656392i
$424$		0			0
$425$	27.5885	−	11.7846i	1.33824	−	0.571638i
$426$		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
$435$	−14.9378	+	22.6244i	−0.716214	+	1.08475i
$436$		0			0
$437$	−1.73205	+	1.00000i	−0.0828552	+	0.0478365i
$438$		0			0
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$		0			0
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	0.673596	−	0.739100i	$-0.264749\pi$
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	−0.303281	+	0.952901i	$0.598082\pi$
$444$		0			0
$445$	−18.4808	+	27.9904i	−0.876072	+	1.32687i
$446$		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
$455$	−2.46410	+	3.73205i	−0.115519	+	0.174961i
$456$		0			0
$457$	−5.19615	−	3.00000i	−0.243066	−	0.140334i	0.373519	−	0.927622i	$-0.378151\pi$
$457$	−5.19615	−	3.00000i	−0.243066	−	0.140334i	−0.616585	+	0.787288i	$0.711484\pi$
$458$		0			0
$459$			31.1769i			1.45521i
$460$		0			0
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	0.359044	+	0.933321i	$0.383103\pi$
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	−0.987801	+	0.155719i	$0.950230\pi$
$462$		0			0
$463$	3.46410	−	2.00000i	0.160990	−	0.0929479i	−0.417340	−	0.908750i	$-0.637038\pi$
$463$	3.46410	−	2.00000i	0.160990	−	0.0929479i	0.578331	+	0.815802i	$0.303704\pi$
$464$		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
$475$	3.92820	+	9.19615i	0.180238	+	0.421948i
$476$		0			0
$477$	−20.7846	−	12.0000i	−0.951662	−	0.549442i
$478$		0			0
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		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	0.824123	+	0.566410i	$0.191668\pi$
$491$	20.0000	+	34.6410i	0.902587	+	1.56333i	0.0784639	+	0.996917i	$0.474998\pi$
$492$		0			0
$493$	−36.3731	−	21.0000i	−1.63816	−	0.945792i
$494$		0			0
$495$	13.3923	+	0.803848i	0.601939	+	0.0361303i
$496$		0			0
$497$	8.66025	+	5.00000i	0.388465	+	0.224281i
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$		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	0.876894	−	0.480684i	$-0.159612\pi$
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	−0.854732	+	0.519070i	$0.826278\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$		0			0
$513$	−10.3923			−0.458831
$514$		0			0
$515$	−1.07180	+	17.8564i	−0.0472290	+	0.786847i
$516$		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
$525$	7.96410	−	3.40192i	0.347582	−	0.148472i
$526$		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
$535$	−24.2583	−	16.0167i	−1.04878	−	0.692461i
$536$		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
$545$	−11.0885	+	16.7942i	−0.474977	+	0.719386i
$546$		0			0
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	0.239616	−	0.970868i	$-0.422978\pi$
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	−0.720988	+	0.692948i	$0.756312\pi$
$548$		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
$555$	−0.464102	+	7.73205i	−0.0197000	+	0.328207i
$556$		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	$-0.812583\pi$
$563$	−18.1865	+	10.5000i	−0.766471	+	0.442522i	0.0651433	+	0.997876i	$0.479250\pi$
$564$		0			0
$565$	−0.535898	+	8.92820i	−0.0225454	+	0.375612i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	0.408883	−	0.912587i	$-0.365918\pi$
$572$		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
$585$	11.1962	+	7.39230i	0.462904	+	0.305634i
$586$		0			0
$587$	30.3109	+	17.5000i	1.25106	+	0.722302i	0.971321	−	0.237773i	$-0.0764173\pi$
$587$	30.3109	+	17.5000i	1.25106	+	0.722302i	0.279743	+	0.960075i	$0.409751\pi$
$588$		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	0.996358	+	0.0852695i	$0.0271751\pi$
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	−0.424333	+	0.905506i	$0.639492\pi$
$600$		0			0
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	−0.798330	−	0.602220i	$-0.794283\pi$
$601$	3.00000	−	5.19615i	0.122373	−	0.211955i	0.920703	+	0.390264i	$0.127616\pi$
$602$		0			0
$603$		−	15.0000i		−	0.610847i
$604$		0			0
$605$	−15.6244	−	0.937822i	−0.635220	−	0.0381279i
$606$		0			0
$607$	−42.4352	+	24.5000i	−1.72239	+	0.994424i	−0.808470	+	0.588537i	$0.799704\pi$
$607$	−42.4352	+	24.5000i	−1.72239	+	0.994424i	−0.913923	+	0.405887i	$0.866962\pi$
$608$		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	$-0.771045\pi$
$617$	−13.8564	+	8.00000i	−0.557838	+	0.322068i	0.194439	+	0.980915i	$0.437711\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		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
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		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
$635$	−5.59808	−	3.69615i	−0.222153	−	0.146677i
$636$		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	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$		0			0
$643$	12.9904	−	7.50000i	0.512291	−	0.295771i	−0.221484	−	0.975164i	$-0.571090\pi$
$643$	12.9904	−	7.50000i	0.512291	−	0.295771i	0.733775	+	0.679393i	$0.237757\pi$
$644$		0			0
$645$	−38.7846	−	25.6077i	−1.52714	−	1.00830i
$646$		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	$-0.866356\pi$
$653$	−25.9808	+	15.0000i	−1.01671	+	0.586995i	−0.103558	+	0.994623i	$0.533023\pi$
$654$		0			0
$655$	26.7846	+	1.60770i	1.04656	+	0.0628178i
$656$		0			0
$657$	10.3923	+	6.00000i	0.405442	+	0.234082i
$658$		0			0
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$		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	$-0.345606\pi$
$673$	−1.73205	−	1.00000i	−0.0667657	−	0.0385472i	−0.533011	+	0.846108i	$0.678940\pi$
$674$		0			0
$675$	−10.2058	−	23.8923i	−0.392820	−	0.919615i
$676$		0			0
$677$	15.5885	+	9.00000i	0.599113	+	0.345898i	0.768693	−	0.639618i	$-0.220908\pi$
$677$	15.5885	+	9.00000i	0.599113	+	0.345898i	−0.169580	+	0.985517i	$0.554241\pi$
$678$		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	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$		0			0
$695$	17.8564	+	1.07180i	0.677332	+	0.0406556i
$696$		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
$705$	29.0885	+	19.2058i	1.09553	+	0.723331i
$706$		0			0
$707$	15.5885	−	9.00000i	0.586264	−	0.338480i
$708$		0			0
$709$	18.5000	−	32.0429i	0.694782	−	1.20340i	−0.275472	−	0.961309i	$-0.588834\pi$
$709$	18.5000	−	32.0429i	0.694782	−	1.20340i	0.970254	−	0.242089i	$-0.0778325\pi$
$710$		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
$715$	7.46410	+	4.92820i	0.279142	+	0.184304i
$716$		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
$725$	34.7487	+	4.18653i	1.29053	+	0.155484i
$726$		0			0
$727$	18.1865	+	10.5000i	0.674501	+	0.389423i	0.797780	−	0.602949i	$-0.206008\pi$
$727$	18.1865	+	10.5000i	0.674501	+	0.389423i	−0.123279	+	0.992372i	$0.539341\pi$
$728$		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	$-0.435164\pi$
$733$	31.1769	−	18.0000i	1.15155	−	0.664845i	0.949263	+	0.314482i	$0.101831\pi$
$734$		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	$-0.755394\pi$
$743$	−12.9904	+	7.50000i	−0.476571	+	0.275148i	0.242415	+	0.970173i	$0.422060\pi$
$744$		0			0
$745$	−33.4808	−	2.00962i	−1.22664	−	0.0736267i
$746$		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	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$		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	0.795589	−	0.605836i	$-0.207161\pi$
$761$	−3.50000	−	6.06218i	−0.126875	−	0.219754i	−0.922464	+	0.386082i	$0.873828\pi$
$762$		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	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$		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
$785$	−0.535898	+	8.92820i	−0.0191270	+	0.318661i
$786$		0			0
$787$	17.3205	−	10.0000i	0.617409	−	0.356462i	−0.158450	−	0.987367i	$-0.550650\pi$
$787$	17.3205	−	10.0000i	0.617409	−	0.356462i	0.775860	+	0.630905i	$0.217316\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.00000			−0.142224
$792$		0			0
$793$			14.0000i			0.497155i
$794$		0			0
$795$	−1.85641	+	30.9282i	−0.0658400	+	1.09691i
$796$		0			0
$797$	25.9808	−	15.0000i	0.920286	−	0.531327i	0.0365596	−	0.999331i	$-0.488360\pi$
$797$	25.9808	−	15.0000i	0.920286	−	0.531327i	0.883726	+	0.468004i	$0.155027\pi$
$798$		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
$805$	1.23205	−	1.86603i	0.0434241	−	0.0657688i
$806$		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
$815$	−37.3205	−	24.6410i	−1.30728	−	0.863137i
$816$		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	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	−14.7224	+	8.50000i	−0.513192	+	0.296291i	−0.734145	−	0.678993i	$-0.762417\pi$
$823$	−14.7224	+	8.50000i	−0.513192	+	0.296291i	0.220953	+	0.975284i	$0.429083\pi$
$824$		0			0
$825$	−6.80385	−	15.9282i	−0.236880	−	0.554549i
$826$		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
$835$	−0.401924	+	6.69615i	−0.0139091	+	0.231730i
$836$		0			0
$837$	15.5885	+	27.0000i	0.538816	+	0.933257i
$838$		0			0
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	−0.233973	−	0.972243i	$-0.575173\pi$
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	0.958974	−	0.283495i	$-0.0914938\pi$
$840$		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	$-0.388097\pi$
$853$	−8.66025	−	5.00000i	−0.296521	−	0.171197i	−0.640879	+	0.767642i	$0.721430\pi$
$854$		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	$-0.558157\pi$
$857$	−32.9090	−	19.0000i	−1.12415	−	0.649028i	−0.942457	+	0.334328i	$0.891491\pi$
$858$		0			0
$859$	5.00000	+	8.66025i	0.170598	+	0.295484i	0.938629	−	0.344928i	$-0.112097\pi$
$859$	5.00000	+	8.66025i	0.170598	+	0.295484i	−0.768031	+	0.640412i	$0.778763\pi$
$860$		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
$875$	−8.52628	−	7.23205i	−0.288241	−	0.244488i
$876$		0			0
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	−0.528958	−	0.848648i	$-0.677417\pi$
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	0.470471	+	0.882415i	$0.344084\pi$
$878$		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	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		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
$895$	−12.3205	+	18.6603i	−0.411829	+	0.623744i
$896$		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
$905$	−23.4090	+	35.4545i	−0.778140	+	1.17855i
$906$		0			0
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	0.514309	−	0.857605i	$-0.328048\pi$
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	−0.485553	+	0.874207i	$0.661382\pi$
$908$		0			0
$909$	−27.0000	−	46.7654i	−0.895533	−	1.55111i
$910$		0			0
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	−0.948136	−	0.317865i	$-0.897034\pi$
$911$	−6.00000	+	10.3923i	−0.198789	+	0.344312i	0.749347	+	0.662177i	$0.230367\pi$
$912$		0			0
$913$	8.66025	−	5.00000i	0.286613	−	0.165476i
$914$		0			0
$915$	14.9378	−	22.6244i	0.493829	−	0.747938i
$916$		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
$925$	9.19615	−	3.92820i	0.302368	−	0.129159i
$926$		0			0
$927$			24.0000i			0.788263i
$928$		0			0
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		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	0.994608	−	0.103710i	$-0.0330714\pi$
$941$	12.5000	+	21.6506i	0.407488	+	0.705791i	−0.587119	+	0.809500i	$0.699738\pi$
$942$		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	$-0.348855\pi$
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	−0.541619	+	0.840624i	$0.682188\pi$
$948$		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
$965$	−0.267949	+	4.46410i	−0.00862559	+	0.143705i
$966$		0			0
$967$	0.866025	−	0.500000i	0.0278495	−	0.0160789i	−0.486011	−	0.873953i	$-0.661548\pi$
$967$	0.866025	−	0.500000i	0.0278495	−	0.0160789i	0.513860	+	0.857874i	$0.328215\pi$
$968$		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
$975$	2.07180	−	17.1962i	0.0663506	−	0.550718i
$976$		0			0
$977$	−1.73205	+	1.00000i	−0.0554132	+	0.0319928i	−0.527451	−	0.849586i	$-0.676852\pi$
$977$	−1.73205	+	1.00000i	−0.0554132	+	0.0319928i	0.472037	+	0.881579i	$0.343519\pi$
$978$		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	$-0.399807\pi$
$983$	−11.2583	−	6.50000i	−0.359085	−	0.207318i	−0.668679	+	0.743551i	$0.733140\pi$
$984$		0			0
$985$	44.7846	+	29.5692i	1.42696	+	0.942154i
$986$		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
$995$	12.3205	−	18.6603i	0.390586	−	0.591570i
$996$		0			0
$997$	41.5692	+	24.0000i	1.31651	+	0.760088i	0.983165	−	0.182717i	$-0.0584893\pi$
$997$	41.5692	+	24.0000i	1.31651	+	0.760088i	0.333345	+	0.942805i	$0.391823\pi$
$998$		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.169.1	yes	4
3.2	odd	2		1080.2.bi.a.289.2		4
4.3	odd	2		720.2.by.b.529.2		4
5.4	even	2	inner	360.2.bi.a.169.2	yes	4
9.2	odd	6		3240.2.f.e.649.2		2
9.4	even	3	inner	360.2.bi.a.49.2	yes	4
9.5	odd	6		1080.2.bi.a.1009.1		4
9.7	even	3		3240.2.f.b.649.1		2
12.11	even	2		2160.2.by.a.289.2		4
15.14	odd	2		1080.2.bi.a.289.1		4
20.19	odd	2		720.2.by.b.529.1		4
36.23	even	6		2160.2.by.a.1009.1		4
36.31	odd	6		720.2.by.b.49.1		4
45.4	even	6	inner	360.2.bi.a.49.1	✓	4
45.14	odd	6		1080.2.bi.a.1009.2		4
45.29	odd	6		3240.2.f.e.649.1		2
45.34	even	6		3240.2.f.b.649.2		2
60.59	even	2		2160.2.by.a.289.1		4
180.59	even	6		2160.2.by.a.1009.2		4
180.139	odd	6		720.2.by.b.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.a.49.1	✓	4	45.4	even	6	inner
360.2.bi.a.49.2	yes	4	9.4	even	3	inner
360.2.bi.a.169.1	yes	4	1.1	even	1	trivial
360.2.bi.a.169.2	yes	4	5.4	even	2	inner
720.2.by.b.49.1		4	36.31	odd	6
720.2.by.b.49.2		4	180.139	odd	6
720.2.by.b.529.1		4	20.19	odd	2
720.2.by.b.529.2		4	4.3	odd	2
1080.2.bi.a.289.1		4	15.14	odd	2
1080.2.bi.a.289.2		4	3.2	odd	2
1080.2.bi.a.1009.1		4	9.5	odd	6
1080.2.bi.a.1009.2		4	45.14	odd	6
2160.2.by.a.289.1		4	60.59	even	2
2160.2.by.a.289.2		4	12.11	even	2
2160.2.by.a.1009.1		4	36.23	even	6
2160.2.by.a.1009.2		4	180.59	even	6
3240.2.f.b.649.1		2	9.7	even	3
3240.2.f.b.649.2		2	45.34	even	6
3240.2.f.e.649.1		2	45.29	odd	6
3240.2.f.e.649.2		2	9.2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 1.50000i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(-1.73205 + 1.00000i) q^{13} +(3.86603 + 0.232051i) q^{15} +6.00000i q^{17} -2.00000 q^{19} +1.73205i q^{21} +(0.866025 - 0.500000i) q^{23} +(-1.96410 - 4.59808i) q^{25} +5.19615 q^{27} +(-3.50000 + 6.06218i) q^{29} +(3.00000 + 5.19615i) q^{31} +3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-10.3923 - 6.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(7.79423 + 4.50000i) q^{47} +(-3.00000 - 5.19615i) q^{49} +(9.00000 - 5.19615i) q^{51} +8.00000i q^{53} +(-2.00000 - 4.00000i) q^{55} +(1.73205 + 3.00000i) q^{57} +(-6.00000 - 10.3923i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.59808 - 1.50000i) q^{63} +(0.267949 - 4.46410i) q^{65} +(-4.33013 + 2.50000i) q^{67} +(-1.50000 - 0.866025i) q^{69} -10.0000 q^{71} -4.00000i q^{73} +(-5.19615 + 6.92820i) q^{75} +(1.73205 - 1.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.33013 - 2.50000i) q^{83} +(-11.1962 - 7.39230i) q^{85} +12.1244 q^{87} +15.0000 q^{89} +2.00000 q^{91} +(5.19615 - 9.00000i) q^{93} +(2.46410 - 3.73205i) q^{95} +(13.8564 + 8.00000i) q^{97} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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