LMFDB - Embedded newform 1456.2.s.f.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(113,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1456.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (of order $3$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.f.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{3} +1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.50000 + 2.59808i) q^{17} +(-4.00000 - 6.92820i) q^{19} +2.00000 q^{21} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{25} +4.00000 q^{27} +(4.50000 - 7.79423i) q^{29} +6.00000 q^{31} +(-2.00000 - 3.46410i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-5.00000 + 5.19615i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-1.00000 - 1.73205i) q^{43} +(-0.500000 - 0.866025i) q^{45} +12.0000 q^{47} +(-0.500000 + 0.866025i) q^{49} +6.00000 q^{51} -5.00000 q^{53} +(1.00000 - 1.73205i) q^{55} -16.0000 q^{57} +(-7.00000 - 12.1244i) q^{59} +(5.50000 + 9.52628i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-3.50000 - 0.866025i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-6.00000 - 10.3923i) q^{69} +(6.00000 + 10.3923i) q^{71} +9.00000 q^{73} +(-4.00000 + 6.92820i) q^{75} +2.00000 q^{77} +10.0000 q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{83} +(1.50000 + 2.59808i) q^{85} +(-9.00000 - 15.5885i) q^{87} +(-5.00000 + 8.66025i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(6.00000 - 10.3923i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-5.00000 - 8.66025i) q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{5} + q^{7} - q^{9} + 2 q^{11} - 7 q^{13} + 2 q^{15} + 3 q^{17} - 8 q^{19} + 4 q^{21} + 6 q^{23} - 8 q^{25} + 8 q^{27} + 9 q^{29} + 12 q^{31} - 4 q^{33} + q^{35} - 3 q^{37} - 10 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^5 + q^7 - q^9 + 2 * q^11 - 7 * q^13 + 2 * q^15 + 3 * q^17 - 8 * q^19 + 4 * q^21 + 6 * q^23 - 8 * q^25 + 8 * q^27 + 9 * q^29 + 12 * q^31 - 4 * q^33 + q^35 - 3 * q^37 - 10 * q^39 + 3 * q^41 - 2 * q^43 - q^45 + 24 * q^47 - q^49 + 12 * q^51 - 10 * q^53 + 2 * q^55 - 32 * q^57 - 14 * q^59 + 11 * q^61 + q^63 - 7 * q^65 - 2 * q^67 - 12 * q^69 + 12 * q^71 + 18 * q^73 - 8 * q^75 + 4 * q^77 + 20 * q^79 + 11 * q^81 - 12 * q^83 + 3 * q^85 - 18 * q^87 - 10 * q^89 - 2 * q^91 + 12 * q^93 - 8 * q^95 - 10 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$		0			0
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$		0			0
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$		0			0
$33$	−2.00000	−	3.46410i	−0.348155	−	0.603023i
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$		0			0
$39$	−5.00000	+	5.19615i	−0.800641	+	0.832050i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	6.00000			0.840168
$52$		0			0
$53$	−5.00000			−0.686803			−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000			−0.686803			−0.343401	+	0.939189i	$0.611579\pi$
$54$		0			0
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$		0			0
$57$	−16.0000			−2.11925
$58$		0			0
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	0.966978	+	0.254858i	$0.0820288\pi$
$61$	5.50000	+	9.52628i	0.704203	+	1.21972i	−0.262776	+	0.964857i	$0.584638\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$		0			0
$65$	−3.50000	−	0.866025i	−0.434122	−	0.107417i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$		0			0
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$		0			0
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$		0			0
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$		0			0
$77$	2.00000			0.227921
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$		0			0
$87$	−9.00000	−	15.5885i	−0.964901	−	1.67126i
$88$		0			0
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$		0			0
$93$	6.00000	−	10.3923i	0.622171	−	1.07763i
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$	2.00000			0.195180
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	3.00000	+	5.19615i	0.284747	+	0.493197i
$112$		0			0
$113$	6.50000	+	11.2583i	0.611469	+	1.05909i	0.990993	+	0.133913i	$0.0427543\pi$
$113$	6.50000	+	11.2583i	0.611469	+	1.05909i	−0.379525	+	0.925182i	$0.623912\pi$
$114$		0			0
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$		0			0
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$		0			0
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$		0			0
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$	4.00000			0.344265
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	−0.993724	−	0.111856i	$-0.964321\pi$
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	0.399992	−	0.916519i	$-0.369013\pi$
$140$		0			0
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$		0			0
$143$	−5.00000	+	5.19615i	−0.418121	+	0.434524i
$144$		0			0
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$		0			0
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$		0			0
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$		0			0
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$		0			0
$153$	1.50000	−	2.59808i	0.121268	−	0.210042i
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$		0			0
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$		0			0
$167$	5.00000	−	8.66025i	0.386912	−	0.670151i	−0.605121	−	0.796134i	$-0.706875\pi$
$167$	5.00000	−	8.66025i	0.386912	−	0.670151i	0.992032	+	0.125983i	$0.0402085\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$		0			0
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	−0.825505	+	0.564396i	$0.809109\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$		0			0
$177$	−28.0000			−2.10461
$178$		0			0
$179$	−8.00000	+	13.8564i	−0.597948	+	1.03568i	0.395175	+	0.918606i	$0.370684\pi$
$179$	−8.00000	+	13.8564i	−0.597948	+	1.03568i	−0.993124	+	0.117071i	$0.962650\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$	22.0000			1.62629
$184$		0			0
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$	6.00000			0.438763
$188$		0			0
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$		0			0
$191$	11.0000	+	19.0526i	0.795932	+	1.37859i	0.922246	+	0.386604i	$0.126352\pi$
$191$	11.0000	+	19.0526i	0.795932	+	1.37859i	−0.126314	+	0.991990i	$0.540315\pi$
$192$		0			0
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	0.0719816	+	0.997406i	$0.477068\pi$
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$	−5.00000	+	5.19615i	−0.358057	+	0.372104i
$196$		0			0
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$		0			0
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$	9.00000			0.631676
$204$		0			0
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$		0			0
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−16.0000			−1.10674
$210$		0			0
$211$	3.00000	−	5.19615i	0.206529	−	0.357718i	−0.744090	−	0.668079i	$-0.767117\pi$
$211$	3.00000	−	5.19615i	0.206529	−	0.357718i	0.950619	+	0.310361i	$0.100450\pi$
$212$		0			0
$213$	24.0000			1.64445
$214$		0			0
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	3.00000	+	5.19615i	0.203653	+	0.352738i
$218$		0			0
$219$	9.00000	−	15.5885i	0.608164	−	1.05337i
$220$		0			0
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$		0			0
$225$	2.00000	+	3.46410i	0.133333	+	0.230940i
$226$		0			0
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	2.00000	−	3.46410i	0.131590	−	0.227921i
$232$		0			0
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$		0			0
$237$	10.0000	−	17.3205i	0.649570	−	1.12509i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		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
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$		0			0
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$		0			0
$247$	8.00000	+	27.7128i	0.509028	+	1.76332i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	4.00000	+	6.92820i	0.252478	+	0.437304i	0.964207	−	0.265149i	$-0.0854212\pi$
$251$	4.00000	+	6.92820i	0.252478	+	0.437304i	−0.711730	+	0.702454i	$0.752088\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$		0			0
$255$	6.00000			0.375735
$256$		0			0
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	0.326929	+	0.945049i	$0.393986\pi$
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	−0.981901	+	0.189396i	$0.939347\pi$
$258$		0			0
$259$	−3.00000			−0.186411
$260$		0			0
$261$	−9.00000			−0.557086
$262$		0			0
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	−0.833546	−	0.552450i	$-0.813693\pi$
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	0.895209	+	0.445647i	$0.147026\pi$
$264$		0			0
$265$	−5.00000			−0.307148
$266$		0			0
$267$	10.0000	+	17.3205i	0.611990	+	1.06000i
$268$		0			0
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	9.00000	−	15.5885i	0.546711	−	0.946931i	−0.451786	−	0.892126i	$-0.649213\pi$
$271$	9.00000	−	15.5885i	0.546711	−	0.946931i	0.998497	−	0.0548050i	$-0.0174537\pi$
$272$		0			0
$273$	−7.00000	−	1.73205i	−0.423659	−	0.104828i
$274$		0			0
$275$	−4.00000	+	6.92820i	−0.241209	+	0.417786i
$276$		0			0
$277$	14.5000	+	25.1147i	0.871221	+	1.50900i	0.860735	+	0.509053i	$0.170004\pi$
$277$	14.5000	+	25.1147i	0.871221	+	1.50900i	0.0104855	+	0.999945i	$0.496662\pi$
$278$		0			0
$279$	−3.00000	−	5.19615i	−0.179605	−	0.311086i
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$		0			0
$285$	−16.0000			−0.947758
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−20.0000			−1.17242
$292$		0			0
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	−7.00000	−	12.1244i	−0.407556	−	0.705907i
$296$		0			0
$297$	4.00000	−	6.92820i	0.232104	−	0.402015i
$298$		0			0
$299$	−15.0000	+	15.5885i	−0.867472	+	0.901504i
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$		0			0
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$		0			0
$305$	5.50000	+	9.52628i	0.314929	+	0.545473i
$306$		0			0
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$		0			0
$309$	−16.0000	+	27.7128i	−0.910208	+	1.57653i
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	−21.0000			−1.17948			−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000			−1.17948			−0.589739	+	0.807594i	$0.700769\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	12.0000	+	20.7846i	0.669775	+	1.16008i
$322$		0			0
$323$	12.0000	−	20.7846i	0.667698	−	1.15649i
$324$		0			0
$325$	14.0000	+	3.46410i	0.776580	+	0.192154i
$326$		0			0
$327$	2.00000	−	3.46410i	0.110600	−	0.191565i
$328$		0			0
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$		0			0
$333$	3.00000			0.164399
$334$		0			0
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$		0			0
$339$	26.0000			1.41213
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$		0			0
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	−0.774197	+	0.632945i	$0.781846\pi$
$348$		0			0
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$		0			0
$351$	−14.0000	−	3.46410i	−0.747265	−	0.184900i
$352$		0			0
$353$	13.5000	−	23.3827i	0.718532	−	1.24453i	−0.243049	−	0.970014i	$-0.578147\pi$
$353$	13.5000	−	23.3827i	0.718532	−	1.24453i	0.961581	−	0.274521i	$-0.0885192\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$	3.00000	+	5.19615i	0.158777	+	0.275010i
$358$		0			0
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$	9.00000			0.471082
$366$		0			0
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$		0			0
$369$	−3.00000			−0.156174
$370$		0			0
$371$	−2.50000	−	4.33013i	−0.129794	−	0.224809i
$372$		0			0
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$		0			0
$375$	−9.00000	+	15.5885i	−0.464758	+	0.804984i
$376$		0			0
$377$	−22.5000	+	23.3827i	−1.15881	+	1.20427i
$378$		0			0
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	−0.965392	−	0.260804i	$-0.916012\pi$
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	0.708559	+	0.705652i	$0.249346\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$		0			0
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	0.839345	−	0.543599i	$-0.182939\pi$
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	−0.890443	+	0.455095i	$0.849605\pi$
$384$		0			0
$385$	2.00000			0.101929
$386$		0			0
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$		0			0
$389$	−21.0000			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	−12.0000	+	20.7846i	−0.605320	+	1.04844i
$394$		0			0
$395$	10.0000			0.503155
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$		0			0
$399$	−8.00000	−	13.8564i	−0.400501	−	0.693688i
$400$		0			0
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	−0.571901	−	0.820323i	$-0.693794\pi$
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	0.996371	+	0.0851195i	$0.0271272\pi$
$402$		0			0
$403$	−21.0000	−	5.19615i	−1.04608	−	0.258839i
$404$		0			0
$405$	5.50000	−	9.52628i	0.273297	−	0.473365i
$406$		0			0
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	0.659374	−	0.751815i	$-0.270822\pi$
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	−0.980778	+	0.195127i	$0.937488\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$		0			0
$413$	7.00000	−	12.1244i	0.344447	−	0.596601i
$414$		0			0
$415$	−6.00000			−0.294528
$416$		0			0
$417$	−28.0000			−1.37117
$418$		0			0
$419$	17.0000	−	29.4449i	0.830504	−	1.43848i	−0.0671345	−	0.997744i	$-0.521386\pi$
$419$	17.0000	−	29.4449i	0.830504	−	1.43848i	0.897639	−	0.440732i	$-0.145281\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$		0			0
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$		0			0
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	−5.50000	+	9.52628i	−0.266164	+	0.461009i
$428$		0			0
$429$	4.00000	+	13.8564i	0.193122	+	0.668994i
$430$		0			0
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.00201168	+	0.999998i	$0.500640\pi$
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.865018	+	0.501741i	$0.832693\pi$
$432$		0			0
$433$	13.5000	+	23.3827i	0.648769	+	1.12370i	0.983417	+	0.181357i	$0.0580490\pi$
$433$	13.5000	+	23.3827i	0.648769	+	1.12370i	−0.334649	+	0.942343i	$0.608618\pi$
$434$		0			0
$435$	−9.00000	−	15.5885i	−0.431517	−	0.747409i
$436$		0			0
$437$	−48.0000			−2.29615
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$		0			0
$447$	2.00000			0.0945968
$448$		0			0
$449$	−11.0000	−	19.0526i	−0.519122	−	0.899146i	−0.999753	−	0.0222229i	$-0.992926\pi$
$449$	−11.0000	−	19.0526i	−0.519122	−	0.899146i	0.480631	−	0.876923i	$-0.340408\pi$
$450$		0			0
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$		0			0
$453$	−20.0000	+	34.6410i	−0.939682	+	1.62758i
$454$		0			0
$455$	−1.00000	−	3.46410i	−0.0468807	−	0.162400i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$		0			0
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$		0			0
$461$	−2.50000	−	4.33013i	−0.116437	−	0.201674i	0.801917	−	0.597436i	$-0.203814\pi$
$461$	−2.50000	−	4.33013i	−0.116437	−	0.201674i	−0.918353	+	0.395762i	$0.870481\pi$
$462$		0			0
$463$	22.0000			1.02243			0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000			1.02243			0.511213	+	0.859454i	$0.329196\pi$
$464$		0			0
$465$	6.00000	−	10.3923i	0.278243	−	0.481932i
$466$		0			0
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	−2.00000			−0.0923514
$470$		0			0
$471$	13.0000	−	22.5167i	0.599008	−	1.03751i
$472$		0			0
$473$	−4.00000			−0.183920
$474$		0			0
$475$	16.0000	+	27.7128i	0.734130	+	1.27155i
$476$		0			0
$477$	2.50000	+	4.33013i	0.114467	+	0.198263i
$478$		0			0
$479$	−13.0000	+	22.5167i	−0.593985	+	1.02881i	0.399704	+	0.916644i	$0.369113\pi$
$479$	−13.0000	+	22.5167i	−0.593985	+	1.02881i	−0.993689	+	0.112168i	$0.964220\pi$
$480$		0			0
$481$	7.50000	−	7.79423i	0.341971	−	0.355386i
$482$		0			0
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$		0			0
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$	−2.00000			−0.0898933
$496$		0			0
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	−38.0000			−1.70111			−0.850557	−	0.525883i	$-0.823735\pi$
$499$	−38.0000			−1.70111			−0.850557	+	0.525883i	$0.823735\pi$
$500$		0			0
$501$	−10.0000	−	17.3205i	−0.446767	−	0.773823i
$502$		0			0
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	0.842870	−	0.538117i	$-0.180864\pi$
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	−0.887458	+	0.460889i	$0.847531\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$		0			0
$507$	22.0000	−	13.8564i	0.977054	−	0.615385i
$508$		0			0
$509$	−0.500000	+	0.866025i	−0.0221621	+	0.0383859i	−0.876894	−	0.480684i	$-0.840388\pi$
$509$	−0.500000	+	0.866025i	−0.0221621	+	0.0383859i	0.854732	+	0.519070i	$0.173722\pi$
$510$		0			0
$511$	4.50000	+	7.79423i	0.199068	+	0.344796i
$512$		0			0
$513$	−16.0000	−	27.7128i	−0.706417	−	1.22355i
$514$		0			0
$515$	−16.0000			−0.705044
$516$		0			0
$517$	12.0000	−	20.7846i	0.527759	−	0.914106i
$518$		0			0
$519$	4.00000			0.175581
$520$		0			0
$521$	1.00000			0.0438108			0.0219054	−	0.999760i	$-0.493027\pi$
$521$	1.00000			0.0438108			0.0219054	+	0.999760i	$0.493027\pi$
$522$		0			0
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	−0.560208	−	0.828352i	$-0.689279\pi$
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	0.997478	+	0.0709788i	$0.0226123\pi$
$524$		0			0
$525$	−8.00000			−0.349149
$526$		0			0
$527$	9.00000	+	15.5885i	0.392046	+	0.679044i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−7.00000	+	12.1244i	−0.303774	+	0.526152i
$532$		0			0
$533$	−7.50000	+	7.79423i	−0.324861	+	0.337606i
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$	16.0000	+	27.7128i	0.690451	+	1.19590i
$538$		0			0
$539$	1.00000	+	1.73205i	0.0430730	+	0.0746047i
$540$		0			0
$541$	−21.0000			−0.902861			−0.451430	−	0.892306i	$-0.649086\pi$
$541$	−21.0000			−0.902861			−0.451430	+	0.892306i	$0.649086\pi$
$542$		0			0
$543$	17.0000	−	29.4449i	0.729540	−	1.26360i
$544$		0			0
$545$	2.00000			0.0856706
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	5.50000	−	9.52628i	0.234734	−	0.406572i
$550$		0			0
$551$	−72.0000			−3.06730
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$		0			0
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$		0			0
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$		0			0
$559$	2.00000	+	6.92820i	0.0845910	+	0.293032i
$560$		0			0
$561$	6.00000	−	10.3923i	0.253320	−	0.438763i
$562$		0			0
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	0.987106	+	0.160066i	$0.0511708\pi$
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	−0.354932	+	0.934892i	$0.615496\pi$
$564$		0			0
$565$	6.50000	+	11.2583i	0.273457	+	0.473642i
$566$		0			0
$567$	11.0000			0.461957
$568$		0			0
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$		0			0
$571$	16.0000			0.669579			0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000			0.669579			0.334790	+	0.942293i	$0.391335\pi$
$572$		0			0
$573$	44.0000			1.83813
$574$		0			0
$575$	−12.0000	+	20.7846i	−0.500435	+	0.866778i
$576$		0			0
$577$	−3.00000			−0.124892			−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000			−0.124892			−0.0624458	+	0.998048i	$0.519890\pi$
$578$		0			0
$579$	23.0000	+	39.8372i	0.955847	+	1.65558i
$580$		0			0
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$		0			0
$583$	−5.00000	+	8.66025i	−0.207079	+	0.358671i
$584$		0			0
$585$	1.00000	+	3.46410i	0.0413449	+	0.143223i
$586$		0			0
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$		0			0
$589$	−24.0000	−	41.5692i	−0.988903	−	1.71283i
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$		0			0
$593$	1.00000			0.0410651			0.0205325	−	0.999789i	$-0.493464\pi$
$593$	1.00000			0.0410651			0.0205325	+	0.999789i	$0.493464\pi$
$594$		0			0
$595$	−1.50000	+	2.59808i	−0.0614940	+	0.106511i
$596$		0			0
$597$	−16.0000			−0.654836
$598$		0			0
$599$	8.00000			0.326871			0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000			0.326871			0.163436	+	0.986554i	$0.447742\pi$
$600$		0			0
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$		0			0
$609$	9.00000	−	15.5885i	0.364698	−	0.631676i
$610$		0			0
$611$	−42.0000	−	10.3923i	−1.69914	−	0.420428i
$612$		0			0
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	−0.0716275	−	0.997431i	$-0.522819\pi$
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	0.899615	−	0.436684i	$-0.143847\pi$
$614$		0			0
$615$	−3.00000	−	5.19615i	−0.120972	−	0.209529i
$616$		0			0
$617$	18.5000	+	32.0429i	0.744782	+	1.29000i	0.950297	+	0.311346i	$0.100780\pi$
$617$	18.5000	+	32.0429i	0.744782	+	1.29000i	−0.205515	+	0.978654i	$0.565887\pi$
$618$		0			0
$619$	14.0000			0.562708			0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000			0.562708			0.281354	+	0.959604i	$0.409217\pi$
$620$		0			0
$621$	12.0000	−	20.7846i	0.481543	−	0.834058i
$622$		0			0
$623$	−10.0000			−0.400642
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−16.0000	+	27.7128i	−0.638978	+	1.10674i
$628$		0			0
$629$	−9.00000			−0.358854
$630$		0			0
$631$	−22.0000	−	38.1051i	−0.875806	−	1.51694i	−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−22.0000	−	38.1051i	−0.875806	−	1.51694i	−0.0199047	−	0.999802i	$-0.506336\pi$
$632$		0			0
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$	2.50000	−	2.59808i	0.0990536	−	0.102940i
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	12.5000	+	21.6506i	0.493720	+	0.855149i	0.999974	−	0.00723604i	$-0.00230332\pi$
$641$	12.5000	+	21.6506i	0.493720	+	0.855149i	−0.506254	+	0.862385i	$0.668970\pi$
$642$		0			0
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	0.664052	−	0.747686i	$-0.268835\pi$
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	−0.979541	+	0.201243i	$0.935502\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$		0			0
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	−0.447849	−	0.894109i	$-0.647810\pi$
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	0.998246	−	0.0592060i	$-0.0188569\pi$
$648$		0			0
$649$	−28.0000			−1.09910
$650$		0			0
$651$	12.0000			0.470317
$652$		0			0
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	−0.695934	−	0.718106i	$-0.745009\pi$
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	0.969865	+	0.243643i	$0.0783426\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$		0			0
$657$	−4.50000	−	7.79423i	−0.175562	−	0.304082i
$658$		0			0
$659$	−20.0000	−	34.6410i	−0.779089	−	1.34942i	−0.932467	−	0.361255i	$-0.882348\pi$
$659$	−20.0000	−	34.6410i	−0.779089	−	1.34942i	0.153378	−	0.988168i	$-0.450985\pi$
$660$		0			0
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	−0.789896	−	0.613241i	$-0.789865\pi$
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	0.926030	+	0.377450i	$0.123199\pi$
$662$		0			0
$663$	−21.0000	−	5.19615i	−0.815572	−	0.201802i
$664$		0			0
$665$	4.00000	−	6.92820i	0.155113	−	0.268664i
$666$		0			0
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	22.0000			0.849301
$672$		0			0
$673$	22.5000	−	38.9711i	0.867311	−	1.50223i	0.00257747	−	0.999997i	$-0.499180\pi$
$673$	22.5000	−	38.9711i	0.867311	−	1.50223i	0.864734	−	0.502230i	$-0.167487\pi$
$674$		0			0
$675$	−16.0000			−0.615840
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$	28.0000			1.07296
$682$		0			0
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$		0			0
$687$	22.0000	−	38.1051i	0.839352	−	1.45380i
$688$		0			0
$689$	17.5000	+	4.33013i	0.666697	+	0.164965i
$690$		0			0
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	−0.382791	−	0.923835i	$-0.625037\pi$
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	0.991460	−	0.130410i	$-0.0416295\pi$
$692$		0			0
$693$	−1.00000	−	1.73205i	−0.0379869	−	0.0657952i
$694$		0			0
$695$	−7.00000	−	12.1244i	−0.265525	−	0.459903i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	−10.0000	+	17.3205i	−0.378235	+	0.655122i
$700$		0			0
$701$	10.0000			0.377695			0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000			0.377695			0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	24.0000			0.905177
$704$		0			0
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$		0			0
$707$	−9.00000			−0.338480
$708$		0			0
$709$	10.5000	+	18.1865i	0.394336	+	0.683010i	0.993016	−	0.117978i	$-0.0376414\pi$
$709$	10.5000	+	18.1865i	0.394336	+	0.683010i	−0.598680	+	0.800988i	$0.704308\pi$
$710$		0			0
$711$	−5.00000	−	8.66025i	−0.187515	−	0.324785i
$712$		0			0
$713$	18.0000	−	31.1769i	0.674105	−	1.16758i
$714$		0			0
$715$	−5.00000	+	5.19615i	−0.186989	+	0.194325i
$716$		0			0
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$		0			0
$721$	−8.00000	−	13.8564i	−0.297936	−	0.516040i
$722$		0			0
$723$	−34.0000			−1.26447
$724$		0			0
$725$	−18.0000	+	31.1769i	−0.668503	+	1.15788i
$726$		0			0
$727$	24.0000			0.890111			0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000			0.890111			0.445055	+	0.895503i	$0.353184\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	−27.0000			−0.997268			−0.498634	−	0.866813i	$-0.666165\pi$
$733$	−27.0000			−0.997268			−0.498634	+	0.866813i	$0.666165\pi$
$734$		0			0
$735$	1.00000	+	1.73205i	0.0368856	+	0.0638877i
$736$		0			0
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$		0			0
$739$	20.0000	−	34.6410i	0.735712	−	1.27429i	−0.218698	−	0.975793i	$-0.570181\pi$
$739$	20.0000	−	34.6410i	0.735712	−	1.27429i	0.954410	−	0.298498i	$-0.0964856\pi$
$740$		0			0
$741$	56.0000	+	13.8564i	2.05721	+	0.509028i
$742$		0			0
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	−0.974633	−	0.223810i	$-0.928151\pi$
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	0.681141	+	0.732152i	$0.261484\pi$
$744$		0			0
$745$	0.500000	+	0.866025i	0.0183186	+	0.0317287i
$746$		0			0
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$		0			0
$749$	−12.0000			−0.438470
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$		0			0
$753$	16.0000			0.583072
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$		0			0
$759$	−24.0000			−0.871145
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		0			0
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$		0			0
$765$	1.50000	−	2.59808i	0.0542326	−	0.0939336i
$766$		0			0
$767$	14.0000	+	48.4974i	0.505511	+	1.75114i
$768$		0			0
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$		0			0
$771$	21.0000	+	36.3731i	0.756297	+	1.30994i
$772$		0			0
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$774$		0			0
$775$	−24.0000			−0.862105
$776$		0			0
$777$	−3.00000	+	5.19615i	−0.107624	+	0.186411i
$778$		0			0
$779$	−24.0000			−0.859889
$780$		0			0
$781$	24.0000			0.858788
$782$		0			0
$783$	18.0000	−	31.1769i	0.643268	−	1.11417i
$784$		0			0
$785$	13.0000			0.463990
$786$		0			0
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	0.713871	−	0.700278i	$-0.246941\pi$
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	−0.963394	+	0.268091i	$0.913607\pi$
$788$		0			0
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$		0			0
$791$	−6.50000	+	11.2583i	−0.231113	+	0.400300i
$792$		0			0
$793$	−11.0000	−	38.1051i	−0.390621	−	1.35315i
$794$		0			0
$795$	−5.00000	+	8.66025i	−0.177332	+	0.307148i
$796$		0			0
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$		0			0
$801$	10.0000			0.353333
$802$		0			0
$803$	9.00000	−	15.5885i	0.317603	−	0.550105i
$804$		0			0
$805$	6.00000			0.211472
$806$		0			0
$807$	28.0000			0.985647
$808$		0			0
$809$	−9.50000	+	16.4545i	−0.334002	+	0.578509i	−0.983293	−	0.182032i	$-0.941733\pi$
$809$	−9.50000	+	16.4545i	−0.334002	+	0.578509i	0.649290	+	0.760541i	$0.275066\pi$
$810$		0			0
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$		0			0
$813$	−18.0000	−	31.1769i	−0.631288	−	1.09342i
$814$		0			0
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$		0			0
$819$	−2.50000	+	2.59808i	−0.0873571	+	0.0907841i
$820$		0			0
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$		0			0
$825$	8.00000	+	13.8564i	0.278524	+	0.482418i
$826$		0			0
$827$	−26.0000			−0.904109			−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000			−0.904109			−0.452054	+	0.891990i	$0.649309\pi$
$828$		0			0
$829$	−22.5000	+	38.9711i	−0.781457	+	1.35352i	0.149635	+	0.988741i	$0.452190\pi$
$829$	−22.5000	+	38.9711i	−0.781457	+	1.35352i	−0.931093	+	0.364783i	$0.881143\pi$
$830$		0			0
$831$	58.0000			2.01200
$832$		0			0
$833$	−3.00000			−0.103944
$834$		0			0
$835$	5.00000	−	8.66025i	0.173032	−	0.299700i
$836$		0			0
$837$	24.0000			0.829561
$838$		0			0
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$		0			0
$845$	11.5000	+	6.06218i	0.395612	+	0.208545i
$846$		0			0
$847$	−3.50000	+	6.06218i	−0.120261	+	0.208299i
$848$		0			0
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$	9.00000	+	15.5885i	0.308516	+	0.534365i
$852$		0			0
$853$	−55.0000			−1.88316			−0.941582	−	0.336784i	$-0.890661\pi$
$853$	−55.0000			−1.88316			−0.941582	+	0.336784i	$0.890661\pi$
$854$		0			0
$855$	−4.00000	+	6.92820i	−0.136797	+	0.236940i
$856$		0			0
$857$	17.0000			0.580709			0.290354	−	0.956919i	$-0.406227\pi$
$857$	17.0000			0.580709			0.290354	+	0.956919i	$0.406227\pi$
$858$		0			0
$859$	−18.0000			−0.614152			−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000			−0.614152			−0.307076	+	0.951685i	$0.599351\pi$
$860$		0			0
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$		0			0
$863$	−30.0000			−1.02121			−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000			−1.02121			−0.510606	+	0.859815i	$0.670579\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$	−8.00000	−	13.8564i	−0.271694	−	0.470588i
$868$		0			0
$869$	10.0000	−	17.3205i	0.339227	−	0.587558i
$870$		0			0
$871$	5.00000	−	5.19615i	0.169419	−	0.176065i
$872$		0			0
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$	−4.50000	−	7.79423i	−0.152128	−	0.263493i
$876$		0			0
$877$	26.5000	+	45.8993i	0.894841	+	1.54991i	0.834001	+	0.551763i	$0.186045\pi$
$877$	26.5000	+	45.8993i	0.894841	+	1.54991i	0.0608407	+	0.998147i	$0.480622\pi$
$878$		0			0
$879$	−18.0000			−0.607125
$880$		0			0
$881$	5.50000	−	9.52628i	0.185300	−	0.320949i	−0.758378	−	0.651815i	$-0.774008\pi$
$881$	5.50000	−	9.52628i	0.185300	−	0.320949i	0.943677	+	0.330867i	$0.107341\pi$
$882$		0			0
$883$	−42.0000			−1.41341			−0.706706	−	0.707507i	$-0.749820\pi$
$883$	−42.0000			−1.41341			−0.706706	+	0.707507i	$0.749820\pi$
$884$		0			0
$885$	−28.0000			−0.941210
$886$		0			0
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$		0			0
$889$	−8.00000			−0.268311
$890$		0			0
$891$	−11.0000	−	19.0526i	−0.368514	−	0.638285i
$892$		0			0
$893$	−48.0000	−	83.1384i	−1.60626	−	2.78212i
$894$		0			0
$895$	−8.00000	+	13.8564i	−0.267411	+	0.463169i
$896$		0			0
$897$	12.0000	+	41.5692i	0.400668	+	1.38796i
$898$		0			0
$899$	27.0000	−	46.7654i	0.900500	−	1.55971i
$900$		0			0
$901$	−7.50000	−	12.9904i	−0.249861	−	0.432772i
$902$		0			0
$903$	−2.00000	−	3.46410i	−0.0665558	−	0.115278i
$904$		0			0
$905$	17.0000			0.565099
$906$		0			0
$907$	15.0000	−	25.9808i	0.498067	−	0.862677i	−0.501931	−	0.864908i	$-0.667377\pi$
$907$	15.0000	−	25.9808i	0.498067	−	0.862677i	0.999998	+	0.00223080i	$0.000710087\pi$
$908$		0			0
$909$	9.00000			0.298511
$910$		0			0
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$		0			0
$915$	22.0000			0.727298
$916$		0			0
$917$	−6.00000	−	10.3923i	−0.198137	−	0.343184i
$918$		0			0
$919$	2.00000	+	3.46410i	0.0659739	+	0.114270i	0.897126	−	0.441776i	$-0.145651\pi$
$919$	2.00000	+	3.46410i	0.0659739	+	0.114270i	−0.831152	+	0.556046i	$0.812318\pi$
$920$		0			0
$921$	18.0000	−	31.1769i	0.593120	−	1.02731i
$922$		0			0
$923$	−12.0000	−	41.5692i	−0.394985	−	1.36827i
$924$		0			0
$925$	6.00000	−	10.3923i	0.197279	−	0.341697i
$926$		0			0
$927$	8.00000	+	13.8564i	0.262754	+	0.455104i
$928$		0			0
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.774536	−	0.632529i	$-0.782017\pi$
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.160518	−	0.987033i	$-0.551317\pi$
$930$		0			0
$931$	8.00000			0.262189
$932$		0			0
$933$	−18.0000	+	31.1769i	−0.589294	+	1.02069i
$934$		0			0
$935$	6.00000			0.196221
$936$		0			0
$937$	21.0000			0.686040			0.343020	−	0.939328i	$-0.388550\pi$
$937$	21.0000			0.686040			0.343020	+	0.939328i	$0.388550\pi$
$938$		0			0
$939$	6.00000	−	10.3923i	0.195803	−	0.339140i
$940$		0			0
$941$	−34.0000			−1.10837			−0.554184	−	0.832394i	$-0.686970\pi$
$941$	−34.0000			−1.10837			−0.554184	+	0.832394i	$0.686970\pi$
$942$		0			0
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$		0			0
$945$	2.00000	+	3.46410i	0.0650600	+	0.112687i
$946$		0			0
$947$	−15.0000	+	25.9808i	−0.487435	+	0.844261i	−0.999896	−	0.0144491i	$-0.995401\pi$
$947$	−15.0000	+	25.9808i	−0.487435	+	0.844261i	0.512461	+	0.858710i	$0.328734\pi$
$948$		0			0
$949$	−31.5000	−	7.79423i	−1.02253	−	0.253011i
$950$		0			0
$951$	−21.0000	+	36.3731i	−0.680972	+	1.17948i
$952$		0			0
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$		0			0
$955$	11.0000	+	19.0526i	0.355952	+	0.616526i
$956$		0			0
$957$	−36.0000			−1.16371
$958$		0			0
$959$	1.50000	−	2.59808i	0.0484375	−	0.0838963i
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−11.5000	+	19.9186i	−0.370198	+	0.641202i
$966$		0			0
$967$	6.00000			0.192947			0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000			0.192947			0.0964735	+	0.995336i	$0.469244\pi$
$968$		0			0
$969$	−24.0000	−	41.5692i	−0.770991	−	1.33540i
$970$		0			0
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$		0			0
$973$	7.00000	−	12.1244i	0.224410	−	0.388689i
$974$		0			0
$975$	20.0000	−	20.7846i	0.640513	−	0.665640i
$976$		0			0
$977$	−21.5000	+	37.2391i	−0.687846	+	1.19138i	0.284687	+	0.958620i	$0.408110\pi$
$977$	−21.5000	+	37.2391i	−0.687846	+	1.19138i	−0.972533	+	0.232764i	$0.925223\pi$
$978$		0			0
$979$	10.0000	+	17.3205i	0.319601	+	0.553566i
$980$		0			0
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$		0			0
$983$	44.0000			1.40338			0.701691	−	0.712481i	$-0.252429\pi$
$983$	44.0000			1.40338			0.701691	+	0.712481i	$0.252429\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$	24.0000			0.763928
$988$		0			0
$989$	−12.0000			−0.381578
$990$		0			0
$991$	−27.0000	+	46.7654i	−0.857683	+	1.48555i	0.0164499	+	0.999865i	$0.494764\pi$
$991$	−27.0000	+	46.7654i	−0.857683	+	1.48555i	−0.874133	+	0.485686i	$0.838570\pi$
$992$		0			0
$993$	12.0000			0.380808
$994$		0			0
$995$	−4.00000	−	6.92820i	−0.126809	−	0.219639i
$996$		0			0
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$		0			0
$999$	−6.00000	+	10.3923i	−0.189832	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.f.113.1		2
4.3	odd	2		728.2.s.a.113.1	✓	2
13.3	even	3	inner	1456.2.s.f.1121.1		2
52.3	odd	6		728.2.s.a.393.1	yes	2
52.35	odd	6		9464.2.a.g.1.1		1
52.43	odd	6		9464.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.s.a.113.1	✓	2	4.3	odd	2
728.2.s.a.393.1	yes	2	52.3	odd	6
1456.2.s.f.113.1		2	1.1	even	1	trivial
1456.2.s.f.1121.1		2	13.3	even	3	inner
9464.2.a.f.1.1		1	52.43	odd	6
9464.2.a.g.1.1		1	52.35	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} +1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{15} +(1.50000 + 2.59808i) q^{17} +(-4.00000 - 6.92820i) q^{19} +2.00000 q^{21} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{25} +4.00000 q^{27} +(4.50000 - 7.79423i) q^{29} +6.00000 q^{31} +(-2.00000 - 3.46410i) q^{33} +(0.500000 + 0.866025i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-5.00000 + 5.19615i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-1.00000 - 1.73205i) q^{43} +(-0.500000 - 0.866025i) q^{45} +12.0000 q^{47} +(-0.500000 + 0.866025i) q^{49} +6.00000 q^{51} -5.00000 q^{53} +(1.00000 - 1.73205i) q^{55} -16.0000 q^{57} +(-7.00000 - 12.1244i) q^{59} +(5.50000 + 9.52628i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-3.50000 - 0.866025i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-6.00000 - 10.3923i) q^{69} +(6.00000 + 10.3923i) q^{71} +9.00000 q^{73} +(-4.00000 + 6.92820i) q^{75} +2.00000 q^{77} +10.0000 q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000 q^{83} +(1.50000 + 2.59808i) q^{85} +(-9.00000 - 15.5885i) q^{87} +(-5.00000 + 8.66025i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(6.00000 - 10.3923i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-5.00000 - 8.66025i) q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{5} + q^{7} - q^{9} + 2 q^{11} - 7 q^{13} + 2 q^{15} + 3 q^{17} - 8 q^{19} + 4 q^{21} + 6 q^{23} - 8 q^{25} + 8 q^{27} + 9 q^{29} + 12 q^{31} - 4 q^{33} + q^{35} - 3 q^{37} - 10 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^5 + q^7 - q^9 + 2 * q^11 - 7 * q^13 + 2 * q^15 + 3 * q^17 - 8 * q^19 + 4 * q^21 + 6 * q^23 - 8 * q^25 + 8 * q^27 + 9 * q^29 + 12 * q^31 - 4 * q^33 + q^35 - 3 * q^37 - 10 * q^39 + 3 * q^41 - 2 * q^43 - q^45 + 24 * q^47 - q^49 + 12 * q^51 - 10 * q^53 + 2 * q^55 - 32 * q^57 - 14 * q^59 + 11 * q^61 + q^63 - 7 * q^65 - 2 * q^67 - 12 * q^69 + 12 * q^71 + 18 * q^73 - 8 * q^75 + 4 * q^77 + 20 * q^79 + 11 * q^81 - 12 * q^83 + 3 * q^85 - 18 * q^87 - 10 * q^89 - 2 * q^91 + 12 * q^93 - 8 * q^95 - 10 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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