LMFDB - Embedded newform 504.2.t.b.457.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(193,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	504.457
Dual form			504.2.t.b.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-3.00000 + 3.46410i) q^{21} +5.00000 q^{23} -4.00000 q^{25} +5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +(4.00000 - 6.92820i) q^{31} +(4.50000 + 2.59808i) q^{33} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} -5.19615i q^{39} +(2.50000 + 4.33013i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +8.66025i q^{51} +(0.500000 + 0.866025i) q^{53} -3.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(-5.00000 - 8.66025i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(1.50000 + 2.59808i) q^{65} +(6.00000 - 10.3923i) q^{67} +(7.50000 + 4.33013i) q^{69} +12.0000 q^{71} +(2.50000 + 4.33013i) q^{73} +(-6.00000 - 3.46410i) q^{75} +(-1.50000 + 7.79423i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.50000 - 12.9904i) q^{83} +(-2.50000 - 4.33013i) q^{85} +(1.50000 - 0.866025i) q^{87} +(2.50000 - 4.33013i) q^{89} +(7.50000 - 2.59808i) q^{91} +(12.0000 - 6.92820i) q^{93} +(3.50000 - 6.06218i) q^{95} +(-3.50000 + 6.06218i) q^{97} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 6 q^{11} - 3 q^{13} - 3 q^{15} + 5 q^{17} - 7 q^{19} - 6 q^{21} + 10 q^{23} - 8 q^{25} + q^{29} + 8 q^{31} + 9 q^{33} + q^{35} - 3 q^{37} + 5 q^{41} + 7 q^{43}+ \cdots + 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 + 5 * q^17 - 7 * q^19 - 6 * q^21 + 10 * q^23 - 8 * q^25 + q^29 + 8 * q^31 + 9 * q^33 + q^35 - 3 * q^37 + 5 * q^41 + 7 * q^43 - 3 * q^45 - 8 * q^47 - 13 * q^49 + q^53 - 6 * q^55 - 21 * q^57 - 10 * q^61 - 15 * q^63 + 3 * q^65 + 12 * q^67 + 15 * q^69 + 24 * q^71 + 5 * q^73 - 12 * q^75 - 3 * q^77 + 8 * q^79 - 9 * q^81 + 15 * q^83 - 5 * q^85 + 3 * q^87 + 5 * q^89 + 15 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		0			0
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	0.579510	−	0.814965i	$-0.303244\pi$
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	−0.995535	+	0.0943882i	$0.969911\pi$
$14$		0			0
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$		0			0
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−3.00000	+	3.46410i	−0.654654	+	0.755929i
$22$		0			0
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		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
$39$		−	5.19615i		−	0.832050i
$40$		0			0
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$		0			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$		0			0
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$		0			0
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$			8.66025i			1.21268i
$52$		0			0
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	−10.5000	+	6.06218i	−1.39076	+	0.802955i
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$		0			0
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$		0			0
$69$	7.50000	+	4.33013i	0.902894	+	0.521286i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$		0			0
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$		0			0
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	−0.0800311	−	0.996792i	$-0.525502\pi$
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	0.903263	−	0.429087i	$-0.141165\pi$
$84$		0			0
$85$	−2.50000	−	4.33013i	−0.271163	−	0.469668i
$86$		0			0
$87$	1.50000	−	0.866025i	0.160817	−	0.0928477i
$88$		0			0
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	−0.702564	−	0.711621i	$-0.747962\pi$
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	0.967563	+	0.252628i	$0.0812949\pi$
$90$		0			0
$91$	7.50000	−	2.59808i	0.786214	−	0.272352i
$92$		0			0
$93$	12.0000	−	6.92820i	1.24434	−	0.718421i
$94$		0			0
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$		0			0
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$		0			0
$99$	4.50000	+	7.79423i	0.452267	+	0.783349i
$100$		0			0
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$		0			0
$103$	−15.0000			−1.47799			−0.738997	−	0.673709i	$-0.764700\pi$
$103$	−15.0000			−1.47799			−0.738997	+	0.673709i	$0.764700\pi$
$104$		0			0
$105$	3.00000	−	3.46410i	0.292770	−	0.338062i
$106$		0			0
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$		0			0
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$		0			0
$111$	−4.50000	+	2.59808i	−0.427121	+	0.246598i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$	−5.00000			−0.466252
$116$		0			0
$117$	4.50000	−	7.79423i	0.416025	−	0.720577i
$118$		0			0
$119$	−12.5000	+	4.33013i	−1.14587	+	0.396942i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$			8.66025i			0.780869i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$		0			0
$129$	10.5000	−	6.06218i	0.924473	−	0.533745i
$130$		0			0
$131$	−7.00000			−0.611593			−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000			−0.611593			−0.305796	+	0.952097i	$0.598923\pi$
$132$		0			0
$133$	−14.0000	−	12.1244i	−1.21395	−	1.05131i
$134$		0			0
$135$		−	5.19615i		−	0.447214i
$136$		0			0
$137$	23.0000			1.96502			0.982511	−	0.186203i	$-0.0596182\pi$
$137$	23.0000			1.96502			0.982511	+	0.186203i	$0.0596182\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	−4.50000	−	7.79423i	−0.376309	−	0.651786i
$144$		0			0
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$		0			0
$147$	−7.50000	−	9.52628i	−0.618590	−	0.785714i
$148$		0			0
$149$	−5.00000			−0.409616			−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000			−0.409616			−0.204808	+	0.978802i	$0.565657\pi$
$150$		0			0
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$		0			0
$153$	−7.50000	+	12.9904i	−0.606339	+	1.05021i
$154$		0			0
$155$	−4.00000	+	6.92820i	−0.321288	+	0.556487i
$156$		0			0
$157$	3.00000	−	5.19615i	0.239426	−	0.414698i	−0.721124	−	0.692806i	$-0.756374\pi$
$157$	3.00000	−	5.19615i	0.239426	−	0.414698i	0.960550	+	0.278108i	$0.0897074\pi$
$158$		0			0
$159$			1.73205i			0.137361i
$160$		0			0
$161$	−2.50000	+	12.9904i	−0.197028	+	1.02379i
$162$		0			0
$163$	2.50000	−	4.33013i	0.195815	−	0.339162i	−0.751352	−	0.659901i	$-0.770598\pi$
$163$	2.50000	−	4.33013i	0.195815	−	0.339162i	0.947167	+	0.320740i	$0.103931\pi$
$164$		0			0
$165$	−4.50000	−	2.59808i	−0.350325	−	0.202260i
$166$		0			0
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	0.911099	+	0.412188i	$0.135235\pi$
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	−0.0985846	+	0.995129i	$0.531432\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$	−21.0000			−1.60591
$172$		0			0
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	0.825505	−	0.564396i	$-0.190891\pi$
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	−0.901533	+	0.432710i	$0.857557\pi$
$174$		0			0
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.50000	−	4.33013i	−0.186859	−	0.323649i	0.757343	−	0.653018i	$-0.226497\pi$
$179$	−2.50000	−	4.33013i	−0.186859	−	0.323649i	−0.944201	+	0.329369i	$0.893164\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	17.3205i		−	1.28037i
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	7.50000	+	12.9904i	0.548454	+	0.949951i
$188$		0			0
$189$	−13.5000	−	2.59808i	−0.981981	−	0.188982i
$190$		0			0
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$		0			0
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	−0.335805	−	0.941932i	$-0.609008\pi$
$193$	9.00000	−	15.5885i	0.647834	−	1.12208i	0.983639	−	0.180150i	$-0.0576584\pi$
$194$		0			0
$195$			5.19615i			0.372104i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	0.976923	+	0.213591i	$0.0685161\pi$
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	−0.303486	+	0.952836i	$0.598151\pi$
$200$		0			0
$201$	18.0000	−	10.3923i	1.26962	−	0.733017i
$202$		0			0
$203$	2.00000	+	1.73205i	0.140372	+	0.121566i
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$		0			0
$207$	7.50000	+	12.9904i	0.521286	+	0.902894i
$208$		0			0
$209$	−10.5000	+	18.1865i	−0.726300	+	1.25799i
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$		0			0
$215$	−3.50000	+	6.06218i	−0.238698	+	0.413437i
$216$		0			0
$217$	16.0000	+	13.8564i	1.08615	+	0.940634i
$218$		0			0
$219$			8.66025i			0.585206i
$220$		0			0
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$		0			0
$223$	−10.5000	+	18.1865i	−0.703132	+	1.21786i	0.264229	+	0.964460i	$0.414882\pi$
$223$	−10.5000	+	18.1865i	−0.703132	+	1.21786i	−0.967361	+	0.253401i	$0.918451\pi$
$224$		0			0
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$		0			0
$227$	11.0000			0.730096			0.365048	−	0.930989i	$-0.381053\pi$
$227$	11.0000			0.730096			0.365048	+	0.930989i	$0.381053\pi$
$228$		0			0
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$		0			0
$231$	−9.00000	+	10.3923i	−0.592157	+	0.683763i
$232$		0			0
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$		0			0
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$		0			0
$237$			13.8564i			0.900070i
$238$		0			0
$239$	12.5000	+	21.6506i	0.808558	+	1.40046i	0.913863	+	0.406023i	$0.133085\pi$
$239$	12.5000	+	21.6506i	0.808558	+	1.40046i	−0.105305	+	0.994440i	$0.533582\pi$
$240$		0			0
$241$	−5.00000			−0.322078			−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000			−0.322078			−0.161039	+	0.986948i	$0.551485\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	21.0000			1.33620
$248$		0			0
$249$	22.5000	−	12.9904i	1.42588	−	0.823232i
$250$		0			0
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$		−	8.66025i		−	0.542326i
$256$		0			0
$257$	−21.0000			−1.30994			−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000			−1.30994			−0.654972	+	0.755653i	$0.727320\pi$
$258$		0			0
$259$	−6.00000	−	5.19615i	−0.372822	−	0.322873i
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	27.0000			1.66489			0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000			1.66489			0.832446	+	0.554107i	$0.186940\pi$
$264$		0			0
$265$	−0.500000	−	0.866025i	−0.0307148	−	0.0531995i
$266$		0			0
$267$	7.50000	−	4.33013i	0.458993	−	0.264999i
$268$		0			0
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$		0			0
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	0.270385	+	0.962752i	$0.412849\pi$
$271$	−11.5000	+	19.9186i	−0.698575	+	1.20997i	−0.968960	+	0.247216i	$0.920484\pi$
$272$		0			0
$273$	13.5000	+	2.59808i	0.817057	+	0.157243i
$274$		0			0
$275$	−12.0000			−0.723627
$276$		0			0
$277$	−5.00000			−0.300421			−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000			−0.300421			−0.150210	+	0.988654i	$0.547995\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$	10.5000	−	6.06218i	0.621966	−	0.359092i
$286$		0			0
$287$	−12.5000	+	4.33013i	−0.737852	+	0.255599i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−10.5000	+	6.06218i	−0.615521	+	0.355371i
$292$		0			0
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			15.5885i			0.904534i
$298$		0			0
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$		0			0
$301$	14.0000	+	12.1244i	0.806947	+	0.698836i
$302$		0			0
$303$	−13.5000	−	7.79423i	−0.775555	−	0.447767i
$304$		0			0
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	−22.5000	−	12.9904i	−1.27998	−	0.738997i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.720257	+	0.693708i	$0.244024\pi$
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.240640	+	0.970614i	$0.422643\pi$
$314$		0			0
$315$	7.50000	−	2.59808i	0.422577	−	0.146385i
$316$		0			0
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		0			0
$319$	1.50000	−	2.59808i	0.0839839	−	0.145464i
$320$		0			0
$321$	13.5000	−	7.79423i	0.753497	−	0.435031i
$322$		0			0
$323$	−35.0000			−1.94745
$324$		0			0
$325$	6.00000	+	10.3923i	0.332820	+	0.576461i
$326$		0			0
$327$		−	12.1244i		−	0.670478i
$328$		0			0
$329$	20.0000	−	6.92820i	1.10264	−	0.381964i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	−9.00000			−0.493197
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$		0			0
$339$		−	25.9808i		−	1.41108i
$340$		0			0
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	−7.50000	−	4.33013i	−0.403786	−	0.233126i
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	−0.974847	−	0.222875i	$-0.928456\pi$
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	0.680439	+	0.732805i	$0.261789\pi$
$350$		0			0
$351$	13.5000	−	7.79423i	0.720577	−	0.416025i
$352$		0			0
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$		0			0
$355$	−12.0000			−0.636894
$356$		0			0
$357$	−22.5000	−	4.33013i	−1.19083	−	0.229175i
$358$		0			0
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	−0.902891	−	0.429870i	$-0.858559\pi$
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	0.823724	+	0.566991i	$0.191893\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$		0			0
$365$	−2.50000	−	4.33013i	−0.130856	−	0.226649i
$366$		0			0
$367$	−13.0000			−0.678594			−0.339297	−	0.940679i	$-0.610189\pi$
$367$	−13.0000			−0.678594			−0.339297	+	0.940679i	$0.610189\pi$
$368$		0			0
$369$	−7.50000	+	12.9904i	−0.390434	+	0.676252i
$370$		0			0
$371$	−2.50000	+	0.866025i	−0.129794	+	0.0449618i
$372$		0			0
$373$	−1.00000			−0.0517780			−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000			−0.0517780			−0.0258890	+	0.999665i	$0.508242\pi$
$374$		0			0
$375$	13.5000	+	7.79423i	0.697137	+	0.402492i
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	36.0000			1.84920			0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000			1.84920			0.924598	+	0.380945i	$0.124401\pi$
$380$		0			0
$381$	−6.00000	−	3.46410i	−0.307389	−	0.177471i
$382$		0			0
$383$	−3.00000			−0.153293			−0.0766464	−	0.997058i	$-0.524421\pi$
$383$	−3.00000			−0.153293			−0.0766464	+	0.997058i	$0.524421\pi$
$384$		0			0
$385$	1.50000	−	7.79423i	0.0764471	−	0.397231i
$386$		0			0
$387$	21.0000			1.06749
$388$		0			0
$389$	−17.0000			−0.861934			−0.430967	−	0.902368i	$-0.641828\pi$
$389$	−17.0000			−0.861934			−0.430967	+	0.902368i	$0.641828\pi$
$390$		0			0
$391$	12.5000	+	21.6506i	0.632152	+	1.09492i
$392$		0			0
$393$	−10.5000	−	6.06218i	−0.529655	−	0.305796i
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	8.50000	−	14.7224i	0.426603	−	0.738898i	−0.569966	−	0.821668i	$-0.693044\pi$
$397$	8.50000	−	14.7224i	0.426603	−	0.738898i	0.996569	+	0.0827707i	$0.0263769\pi$
$398$		0			0
$399$	−10.5000	−	30.3109i	−0.525657	−	1.51744i
$400$		0			0
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		0			0
$403$	−24.0000			−1.19553
$404$		0			0
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$		0			0
$407$	−4.50000	+	7.79423i	−0.223057	+	0.386346i
$408$		0			0
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		0			0
$411$	34.5000	+	19.9186i	1.70176	+	0.982511i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−7.50000	+	12.9904i	−0.368161	+	0.637673i
$416$		0			0
$417$			15.5885i			0.763370i
$418$		0			0
$419$	−11.5000	−	19.9186i	−0.561812	−	0.973087i	−0.997338	−	0.0729107i	$-0.976771\pi$
$419$	−11.5000	−	19.9186i	−0.561812	−	0.973087i	0.435527	−	0.900176i	$-0.356562\pi$
$420$		0			0
$421$	−3.50000	+	6.06218i	−0.170580	+	0.295452i	−0.938623	−	0.344946i	$-0.887897\pi$
$421$	−3.50000	+	6.06218i	−0.170580	+	0.295452i	0.768043	+	0.640398i	$0.221231\pi$
$422$		0			0
$423$	12.0000	−	20.7846i	0.583460	−	1.01058i
$424$		0			0
$425$	−10.0000	−	17.3205i	−0.485071	−	0.840168i
$426$		0			0
$427$	25.0000	−	8.66025i	1.20983	−	0.419099i
$428$		0			0
$429$		−	15.5885i		−	0.752618i
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−1.50000	+	0.866025i	−0.0719195	+	0.0415227i
$436$		0			0
$437$	−17.5000	+	30.3109i	−0.837139	+	1.44997i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$		0			0
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$		0			0
$447$	−7.50000	−	4.33013i	−0.354738	−	0.204808i
$448$		0			0
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	7.50000	+	12.9904i	0.353161	+	0.611693i
$452$		0			0
$453$	−7.50000	−	4.33013i	−0.352381	−	0.203447i
$454$		0			0
$455$	−7.50000	+	2.59808i	−0.351605	+	0.121800i
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$		0			0
$459$	−22.5000	+	12.9904i	−1.05021	+	0.606339i
$460$		0			0
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	0.999920	+	0.0126168i	$0.00401615\pi$
$462$		0			0
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	−0.910546	−	0.413407i	$-0.864339\pi$
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	0.0972525	−	0.995260i	$-0.468995\pi$
$464$		0			0
$465$	−12.0000	+	6.92820i	−0.556487	+	0.321288i
$466$		0			0
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	0.363892	+	0.931441i	$0.381448\pi$
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	−0.988598	+	0.150581i	$0.951886\pi$
$468$		0			0
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$	9.00000	−	5.19615i	0.414698	−	0.239426i
$472$		0			0
$473$	10.5000	−	18.1865i	0.482791	−	0.836218i
$474$		0			0
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$		0			0
$479$	7.00000			0.319838			0.159919	−	0.987130i	$-0.448877\pi$
$479$	7.00000			0.319838			0.159919	+	0.987130i	$0.448877\pi$
$480$		0			0
$481$	9.00000			0.410365
$482$		0			0
$483$	−15.0000	+	17.3205i	−0.682524	+	0.788110i
$484$		0			0
$485$	3.50000	−	6.06218i	0.158927	−	0.275269i
$486$		0			0
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	−0.891303	−	0.453409i	$-0.850208\pi$
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	0.0529875	−	0.998595i	$-0.483126\pi$
$488$		0			0
$489$	7.50000	−	4.33013i	0.339162	−	0.195815i
$490$		0			0
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	0.999552	−	0.0299272i	$-0.00952753\pi$
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	−0.525694	+	0.850674i	$0.676194\pi$
$492$		0			0
$493$	5.00000			0.225189
$494$		0			0
$495$	−4.50000	−	7.79423i	−0.202260	−	0.350325i
$496$		0			0
$497$	−6.00000	+	31.1769i	−0.269137	+	1.39848i
$498$		0			0
$499$	1.00000			0.0447661			0.0223831	−	0.999749i	$-0.492875\pi$
$499$	1.00000			0.0447661			0.0223831	+	0.999749i	$0.492875\pi$
$500$		0			0
$501$			36.3731i			1.62503i
$502$		0			0
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$	6.00000	−	3.46410i	0.266469	−	0.153846i
$508$		0			0
$509$	−21.0000			−0.930809			−0.465404	−	0.885098i	$-0.654091\pi$
$509$	−21.0000			−0.930809			−0.465404	+	0.885098i	$0.654091\pi$
$510$		0			0
$511$	−12.5000	+	4.33013i	−0.552967	+	0.191554i
$512$		0			0
$513$	−31.5000	−	18.1865i	−1.39076	−	0.802955i
$514$		0			0
$515$	15.0000			0.660979
$516$		0			0
$517$	−12.0000	−	20.7846i	−0.527759	−	0.914106i
$518$		0			0
$519$		−	3.46410i		−	0.152057i
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	−0.451918	−	0.892059i	$-0.649260\pi$
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	0.998505	−	0.0546569i	$-0.0174065\pi$
$524$		0			0
$525$	12.0000	−	13.8564i	0.523723	−	0.604743i
$526$		0			0
$527$	40.0000			1.74243
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.50000	−	12.9904i	0.324861	−	0.562676i
$534$		0			0
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$		0			0
$537$		−	8.66025i		−	0.373718i
$538$		0			0
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−15.5000	+	26.8468i	−0.666397	+	1.15423i	0.312507	+	0.949915i	$0.398831\pi$
$541$	−15.5000	+	26.8468i	−0.666397	+	1.15423i	−0.978905	+	0.204318i	$0.934502\pi$
$542$		0			0
$543$	3.00000	+	1.73205i	0.128742	+	0.0743294i
$544$		0			0
$545$	3.50000	+	6.06218i	0.149924	+	0.259675i
$546$		0			0
$547$	17.5000	−	30.3109i	0.748246	−	1.29600i	−0.200417	−	0.979711i	$-0.564230\pi$
$547$	17.5000	−	30.3109i	0.748246	−	1.29600i	0.948663	−	0.316289i	$-0.102437\pi$
$548$		0			0
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$		0			0
$551$	3.50000	+	6.06218i	0.149105	+	0.258257i
$552$		0			0
$553$	−20.0000	+	6.92820i	−0.850487	+	0.294617i
$554$		0			0
$555$	4.50000	−	2.59808i	0.191014	−	0.110282i
$556$		0			0
$557$	−9.50000	−	16.4545i	−0.402528	−	0.697199i	0.591502	−	0.806303i	$-0.298535\pi$
$557$	−9.50000	−	16.4545i	−0.402528	−	0.697199i	−0.994030	+	0.109104i	$0.965202\pi$
$558$		0			0
$559$	−21.0000			−0.888205
$560$		0			0
$561$			25.9808i			1.09691i
$562$		0			0
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$		0			0
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$		0			0
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$		0			0
$573$		−	27.7128i		−	1.15772i
$574$		0			0
$575$	−20.0000			−0.834058
$576$		0			0
$577$	4.50000	+	7.79423i	0.187337	+	0.324478i	0.944362	−	0.328909i	$-0.106681\pi$
$577$	4.50000	+	7.79423i	0.187337	+	0.324478i	−0.757024	+	0.653387i	$0.773348\pi$
$578$		0			0
$579$	27.0000	−	15.5885i	1.12208	−	0.647834i
$580$		0			0
$581$	30.0000	+	25.9808i	1.24461	+	1.07786i
$582$		0			0
$583$	1.50000	+	2.59808i	0.0621237	+	0.107601i
$584$		0			0
$585$	−4.50000	+	7.79423i	−0.186052	+	0.322252i
$586$		0			0
$587$	17.5000	−	30.3109i	0.722302	−	1.25106i	−0.237773	−	0.971321i	$-0.576417\pi$
$587$	17.5000	−	30.3109i	0.722302	−	1.25106i	0.960075	−	0.279743i	$-0.0902494\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$	−9.00000	−	5.19615i	−0.370211	−	0.213741i
$592$		0			0
$593$	16.5000	−	28.5788i	0.677574	−	1.17359i	−0.298136	−	0.954524i	$-0.596365\pi$
$593$	16.5000	−	28.5788i	0.677574	−	1.17359i	0.975709	−	0.219069i	$-0.0703019\pi$
$594$		0			0
$595$	12.5000	−	4.33013i	0.512450	−	0.177518i
$596$		0			0
$597$			32.9090i			1.34687i
$598$		0			0
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$		0			0
$601$	−3.50000	+	6.06218i	−0.142768	+	0.247281i	−0.928538	−	0.371237i	$-0.878934\pi$
$601$	−3.50000	+	6.06218i	−0.142768	+	0.247281i	0.785770	+	0.618519i	$0.212267\pi$
$602$		0			0
$603$	36.0000			1.46603
$604$		0			0
$605$	2.00000			0.0813116
$606$		0			0
$607$	−23.0000			−0.933541			−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000			−0.933541			−0.466771	+	0.884378i	$0.654583\pi$
$608$		0			0
$609$	1.50000	+	4.33013i	0.0607831	+	0.175466i
$610$		0			0
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$		0			0
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.863655	−	0.504084i	$-0.831830\pi$
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.00472215	−	0.999989i	$-0.501503\pi$
$614$		0			0
$615$		−	8.66025i		−	0.349215i
$616$		0			0
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$		0			0
$619$	15.0000			0.602901			0.301450	−	0.953482i	$-0.402529\pi$
$619$	15.0000			0.602901			0.301450	+	0.953482i	$0.402529\pi$
$620$		0			0
$621$			25.9808i			1.04257i
$622$		0			0
$623$	10.0000	+	8.66025i	0.400642	+	0.346966i
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−31.5000	+	18.1865i	−1.25799	+	0.726300i
$628$		0			0
$629$	−15.0000			−0.598089
$630$		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
$633$			22.5167i			0.894957i
$634$		0			0
$635$	4.00000			0.158735
$636$		0			0
$637$	3.00000	+	20.7846i	0.118864	+	0.823516i
$638$		0			0
$639$	18.0000	+	31.1769i	0.712069	+	1.23334i
$640$		0			0
$641$	−17.0000			−0.671460			−0.335730	−	0.941958i	$-0.608983\pi$
$641$	−17.0000			−0.671460			−0.335730	+	0.941958i	$0.608983\pi$
$642$		0			0
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	−0.883099	−	0.469187i	$-0.844547\pi$
$643$	−21.5000	−	37.2391i	−0.847877	−	1.46857i	0.0352216	−	0.999380i	$-0.488786\pi$
$644$		0			0
$645$	−10.5000	+	6.06218i	−0.413437	+	0.238698i
$646$		0			0
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	12.0000	+	34.6410i	0.470317	+	1.35769i
$652$		0			0
$653$	−13.0000			−0.508729			−0.254365	−	0.967108i	$-0.581866\pi$
$653$	−13.0000			−0.508729			−0.254365	+	0.967108i	$0.581866\pi$
$654$		0			0
$655$	7.00000			0.273513
$656$		0			0
$657$	−7.50000	+	12.9904i	−0.292603	+	0.506803i
$658$		0			0
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	0.432225	+	0.901766i	$0.357729\pi$
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	−0.997065	+	0.0765653i	$0.975605\pi$
$660$		0			0
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.0602929	−	0.998181i	$-0.480797\pi$
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.834303	−	0.551306i	$-0.185870\pi$
$662$		0			0
$663$	22.5000	−	12.9904i	0.873828	−	0.504505i
$664$		0			0
$665$	14.0000	+	12.1244i	0.542897	+	0.470162i
$666$		0			0
$667$	2.50000	−	4.33013i	0.0968004	−	0.167663i
$668$		0			0
$669$	−31.5000	+	18.1865i	−1.21786	+	0.703132i
$670$		0			0
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$		0			0
$675$		−	20.7846i		−	0.800000i
$676$		0			0
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		0			0
$679$	−14.0000	−	12.1244i	−0.537271	−	0.465290i
$680$		0			0
$681$	16.5000	+	9.52628i	0.632281	+	0.365048i
$682$		0			0
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	0.949657	+	0.313291i	$0.101432\pi$
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	−0.203510	+	0.979073i	$0.565235\pi$
$684$		0			0
$685$	−23.0000			−0.878785
$686$		0			0
$687$	−1.50000	−	0.866025i	−0.0572286	−	0.0330409i
$688$		0			0
$689$	1.50000	−	2.59808i	0.0571454	−	0.0989788i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$		0			0
$693$	−22.5000	+	7.79423i	−0.854704	+	0.296078i
$694$		0			0
$695$	−4.50000	−	7.79423i	−0.170695	−	0.295652i
$696$		0			0
$697$	−12.5000	+	21.6506i	−0.473471	+	0.820076i
$698$		0			0
$699$	−16.5000	+	9.52628i	−0.624087	+	0.360317i
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	−10.5000	−	18.1865i	−0.396015	−	0.685918i
$704$		0			0
$705$			13.8564i			0.521862i
$706$		0			0
$707$	4.50000	−	23.3827i	0.169240	−	0.879396i
$708$		0			0
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$		0			0
$711$	−12.0000	+	20.7846i	−0.450035	+	0.779484i
$712$		0			0
$713$	20.0000	−	34.6410i	0.749006	−	1.29732i
$714$		0			0
$715$	4.50000	+	7.79423i	0.168290	+	0.291488i
$716$		0			0
$717$			43.3013i			1.61712i
$718$		0			0
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385939\pi$
$720$		0			0
$721$	7.50000	−	38.9711i	0.279315	−	1.45136i
$722$		0			0
$723$	−7.50000	−	4.33013i	−0.278928	−	0.161039i
$724$		0			0
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	−0.793794	−	0.608186i	$-0.791897\pi$
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	0.923602	+	0.383353i	$0.125231\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	35.0000			1.29452
$732$		0			0
$733$	−29.0000			−1.07114			−0.535570	−	0.844491i	$-0.679903\pi$
$733$	−29.0000			−1.07114			−0.535570	+	0.844491i	$0.679903\pi$
$734$		0			0
$735$	7.50000	+	9.52628i	0.276642	+	0.351382i
$736$		0			0
$737$	18.0000	−	31.1769i	0.663039	−	1.14842i
$738$		0			0
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$		0			0
$741$	31.5000	+	18.1865i	1.15718	+	0.668099i
$742$		0			0
$743$	24.5000	+	42.4352i	0.898818	+	1.55680i	0.829007	+	0.559238i	$0.188906\pi$
$743$	24.5000	+	42.4352i	0.898818	+	1.55680i	0.0698106	+	0.997560i	$0.477761\pi$
$744$		0			0
$745$	5.00000			0.183186
$746$		0			0
$747$	45.0000			1.64646
$748$		0			0
$749$	18.0000	+	15.5885i	0.657706	+	0.569590i
$750$		0			0
$751$	−7.00000			−0.255434			−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000			−0.255434			−0.127717	+	0.991811i	$0.540765\pi$
$752$		0			0
$753$	−30.0000	−	17.3205i	−1.09326	−	0.631194i
$754$		0			0
$755$	5.00000			0.181969
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$		0			0
$759$	22.5000	+	12.9904i	0.816698	+	0.471521i
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$		0			0
$763$	17.5000	−	6.06218i	0.633543	−	0.219466i
$764$		0			0
$765$	7.50000	−	12.9904i	0.271163	−	0.469668i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	−0.997585	−	0.0694574i	$-0.977873\pi$
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	0.438641	−	0.898663i	$-0.355460\pi$
$770$		0			0
$771$	−31.5000	−	18.1865i	−1.13444	−	0.654972i
$772$		0			0
$773$	8.50000	+	14.7224i	0.305724	+	0.529529i	0.977422	−	0.211296i	$-0.0677683\pi$
$773$	8.50000	+	14.7224i	0.305724	+	0.529529i	−0.671698	+	0.740825i	$0.734435\pi$
$774$		0			0
$775$	−16.0000	+	27.7128i	−0.574737	+	0.995474i
$776$		0			0
$777$	−4.50000	−	12.9904i	−0.161437	−	0.466027i
$778$		0			0
$779$	−35.0000			−1.25401
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$	4.50000	+	2.59808i	0.160817	+	0.0928477i
$784$		0			0
$785$	−3.00000	+	5.19615i	−0.107075	+	0.185459i
$786$		0			0
$787$	−26.0000	+	45.0333i	−0.926800	+	1.60526i	−0.138159	+	0.990410i	$0.544119\pi$
$787$	−26.0000	+	45.0333i	−0.926800	+	1.60526i	−0.788641	+	0.614855i	$0.789215\pi$
$788$		0			0
$789$	40.5000	+	23.3827i	1.44184	+	0.832446i
$790$		0			0
$791$	37.5000	−	12.9904i	1.33335	−	0.461885i
$792$		0			0
$793$	−15.0000	+	25.9808i	−0.532666	+	0.922604i
$794$		0			0
$795$		−	1.73205i		−	0.0614295i
$796$		0			0
$797$	16.5000	+	28.5788i	0.584460	+	1.01231i	0.994943	+	0.100446i	$0.0320269\pi$
$797$	16.5000	+	28.5788i	0.584460	+	1.01231i	−0.410483	+	0.911868i	$0.634640\pi$
$798$		0			0
$799$	20.0000	−	34.6410i	0.707549	−	1.22551i
$800$		0			0
$801$	15.0000			0.529999
$802$		0			0
$803$	7.50000	+	12.9904i	0.264669	+	0.458421i
$804$		0			0
$805$	2.50000	−	12.9904i	0.0881134	−	0.457851i
$806$		0			0
$807$		−	5.19615i		−	0.182913i
$808$		0			0
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$		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
$813$	−34.5000	+	19.9186i	−1.20997	+	0.698575i
$814$		0			0
$815$	−2.50000	+	4.33013i	−0.0875712	+	0.151678i
$816$		0			0
$817$	24.5000	+	42.4352i	0.857146	+	1.48462i
$818$		0			0
$819$	18.0000	+	15.5885i	0.628971	+	0.544705i
$820$		0			0
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$		0			0
$825$	−18.0000	−	10.3923i	−0.626680	−	0.361814i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	−7.50000	−	4.33013i	−0.260172	−	0.150210i
$832$		0			0
$833$	−5.00000	−	34.6410i	−0.173240	−	1.20024i
$834$		0			0
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$		0			0
$837$	36.0000	+	20.7846i	1.24434	+	0.718421i
$838$		0			0
$839$	1.50000	−	2.59808i	0.0517858	−	0.0896956i	−0.838971	−	0.544177i	$-0.816842\pi$
$839$	1.50000	−	2.59808i	0.0517858	−	0.0896956i	0.890756	+	0.454481i	$0.150175\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$		0			0
$843$	−40.5000	+	23.3827i	−1.39489	+	0.805342i
$844$		0			0
$845$	−2.00000	+	3.46410i	−0.0688021	+	0.119169i
$846$		0			0
$847$	1.00000	−	5.19615i	0.0343604	−	0.178542i
$848$		0			0
$849$	6.00000	−	3.46410i	0.205919	−	0.118888i
$850$		0			0
$851$	−7.50000	+	12.9904i	−0.257097	+	0.445305i
$852$		0			0
$853$	26.5000	−	45.8993i	0.907343	−	1.57156i	0.0896015	−	0.995978i	$-0.471441\pi$
$853$	26.5000	−	45.8993i	0.907343	−	1.57156i	0.817741	−	0.575586i	$-0.195226\pi$
$854$		0			0
$855$	21.0000			0.718185
$856$		0			0
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$		0			0
$859$	−23.0000			−0.784750			−0.392375	−	0.919805i	$-0.628346\pi$
$859$	−23.0000			−0.784750			−0.392375	+	0.919805i	$0.628346\pi$
$860$		0			0
$861$	−22.5000	−	4.33013i	−0.766798	−	0.147570i
$862$		0			0
$863$	−23.5000	+	40.7032i	−0.799949	+	1.38555i	0.119699	+	0.992810i	$0.461807\pi$
$863$	−23.5000	+	40.7032i	−0.799949	+	1.38555i	−0.919648	+	0.392743i	$0.871526\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$		0			0
$869$	12.0000	+	20.7846i	0.407072	+	0.705070i
$870$		0			0
$871$	−36.0000			−1.21981
$872$		0			0
$873$	−21.0000			−0.710742
$874$		0			0
$875$	−4.50000	+	23.3827i	−0.152128	+	0.790479i
$876$		0			0
$877$	−37.0000			−1.24940			−0.624701	−	0.780864i	$-0.714779\pi$
$877$	−37.0000			−1.24940			−0.624701	+	0.780864i	$0.714779\pi$
$878$		0			0
$879$		−	46.7654i		−	1.57736i
$880$		0			0
$881$	22.0000			0.741199			0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000			0.741199			0.370599	+	0.928793i	$0.379152\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.00000			−0.100730			−0.0503651	−	0.998731i	$-0.516038\pi$
$887$	−3.00000			−0.100730			−0.0503651	+	0.998731i	$0.516038\pi$
$888$		0			0
$889$	2.00000	−	10.3923i	0.0670778	−	0.348547i
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$	56.0000			1.87397
$894$		0			0
$895$	2.50000	+	4.33013i	0.0835658	+	0.144740i
$896$		0			0
$897$		−	25.9808i		−	0.867472i
$898$		0			0
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	−2.50000	+	4.33013i	−0.0832871	+	0.144257i
$902$		0			0
$903$	10.5000	+	30.3109i	0.349418	+	1.00868i
$904$		0			0
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	−37.0000			−1.22856			−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000			−1.22856			−0.614282	+	0.789086i	$0.710554\pi$
$908$		0			0
$909$	−13.5000	−	23.3827i	−0.447767	−	0.775555i
$910$		0			0
$911$	−6.50000	+	11.2583i	−0.215355	+	0.373005i	−0.953382	−	0.301765i	$-0.902424\pi$
$911$	−6.50000	+	11.2583i	−0.215355	+	0.373005i	0.738028	+	0.674771i	$0.235757\pi$
$912$		0			0
$913$	22.5000	−	38.9711i	0.744641	−	1.28976i
$914$		0			0
$915$			17.3205i			0.572598i
$916$		0			0
$917$	3.50000	−	18.1865i	0.115580	−	0.600572i
$918$		0			0
$919$	20.5000	−	35.5070i	0.676233	−	1.17127i	−0.299874	−	0.953979i	$-0.596945\pi$
$919$	20.5000	−	35.5070i	0.676233	−	1.17127i	0.976107	−	0.217291i	$-0.0697219\pi$
$920$		0			0
$921$	6.00000	+	3.46410i	0.197707	+	0.114146i
$922$		0			0
$923$	−18.0000	−	31.1769i	−0.592477	−	1.02620i
$924$		0			0
$925$	6.00000	−	10.3923i	0.197279	−	0.341697i
$926$		0			0
$927$	−22.5000	−	38.9711i	−0.738997	−	1.27998i
$928$		0			0
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$		0			0
$931$	38.5000	−	30.3109i	1.26179	−	0.993399i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.50000	−	12.9904i	−0.245276	−	0.424831i
$936$		0			0
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$		0			0
$939$			58.8897i			1.92179i
$940$		0			0
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$		0			0
$943$	12.5000	+	21.6506i	0.407056	+	0.705042i
$944$		0			0
$945$	13.5000	+	2.59808i	0.439155	+	0.0845154i
$946$		0			0
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	−0.885720	−	0.464220i	$-0.846335\pi$
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	0.0408333	−	0.999166i	$-0.486999\pi$
$948$		0			0
$949$	7.50000	−	12.9904i	0.243460	−	0.421686i
$950$		0			0
$951$			51.9615i			1.68497i
$952$		0			0
$953$	46.0000			1.49009			0.745043	−	0.667016i	$-0.232429\pi$
$953$	46.0000			1.49009			0.745043	+	0.667016i	$0.232429\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$		0			0
$957$	4.50000	−	2.59808i	0.145464	−	0.0839839i
$958$		0			0
$959$	−11.5000	+	59.7558i	−0.371354	+	1.92961i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	27.0000			0.870063
$964$		0			0
$965$	−9.00000	+	15.5885i	−0.289720	+	0.501810i
$966$		0			0
$967$	10.5000	+	18.1865i	0.337657	+	0.584839i	0.983992	−	0.178215i	$-0.0570322\pi$
$967$	10.5000	+	18.1865i	0.337657	+	0.584839i	−0.646334	+	0.763054i	$0.723699\pi$
$968$		0			0
$969$	−52.5000	−	30.3109i	−1.68654	−	0.973726i
$970$		0			0
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	−0.916705	−	0.399564i	$-0.869162\pi$
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	0.804385	+	0.594108i	$0.202495\pi$
$972$		0			0
$973$	−22.5000	+	7.79423i	−0.721317	+	0.249871i
$974$		0			0
$975$			20.7846i			0.665640i
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$	7.50000	−	12.9904i	0.239701	−	0.415174i
$980$		0			0
$981$	10.5000	−	18.1865i	0.335239	−	0.580651i
$982$		0			0
$983$	27.0000			0.861166			0.430583	−	0.902551i	$-0.358308\pi$
$983$	27.0000			0.861166			0.430583	+	0.902551i	$0.358308\pi$
$984$		0			0
$985$	6.00000			0.191176
$986$		0			0
$987$	36.0000	+	6.92820i	1.14589	+	0.220527i
$988$		0			0
$989$	17.5000	−	30.3109i	0.556468	−	0.963830i
$990$		0			0
$991$	−10.5000	−	18.1865i	−0.333543	−	0.577714i	0.649660	−	0.760224i	$-0.274911\pi$
$991$	−10.5000	−	18.1865i	−0.333543	−	0.577714i	−0.983204	+	0.182510i	$0.941578\pi$
$992$		0			0
$993$		−	13.8564i		−	0.439720i
$994$		0			0
$995$	−9.50000	−	16.4545i	−0.301170	−	0.521642i
$996$		0			0
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$		0			0
$999$	−13.5000	−	7.79423i	−0.427121	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.b.457.1	yes	2
3.2	odd	2		1512.2.t.b.289.1		2
4.3	odd	2		1008.2.t.a.961.1		2
7.4	even	3		504.2.q.b.25.1	✓	2
9.4	even	3		504.2.q.b.121.1	yes	2
9.5	odd	6		1512.2.q.a.793.1		2
12.11	even	2		3024.2.t.e.289.1		2
21.11	odd	6		1512.2.q.a.1369.1		2
28.11	odd	6		1008.2.q.d.529.1		2
36.23	even	6		3024.2.q.c.2305.1		2
36.31	odd	6		1008.2.q.d.625.1		2
63.4	even	3	inner	504.2.t.b.193.1	yes	2
63.32	odd	6		1512.2.t.b.361.1		2
84.11	even	6		3024.2.q.c.2881.1		2
252.67	odd	6		1008.2.t.a.193.1		2
252.95	even	6		3024.2.t.e.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.b.25.1	✓	2	7.4	even	3
504.2.q.b.121.1	yes	2	9.4	even	3
504.2.t.b.193.1	yes	2	63.4	even	3	inner
504.2.t.b.457.1	yes	2	1.1	even	1	trivial
1008.2.q.d.529.1		2	28.11	odd	6
1008.2.q.d.625.1		2	36.31	odd	6
1008.2.t.a.193.1		2	252.67	odd	6
1008.2.t.a.961.1		2	4.3	odd	2
1512.2.q.a.793.1		2	9.5	odd	6
1512.2.q.a.1369.1		2	21.11	odd	6
1512.2.t.b.289.1		2	3.2	odd	2
1512.2.t.b.361.1		2	63.32	odd	6
3024.2.q.c.2305.1		2	36.23	even	6
3024.2.q.c.2881.1		2	84.11	even	6
3024.2.t.e.289.1		2	12.11	even	2
3024.2.t.e.1873.1		2	252.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-3.00000 + 3.46410i) q^{21} +5.00000 q^{23} -4.00000 q^{25} +5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +(4.00000 - 6.92820i) q^{31} +(4.50000 + 2.59808i) q^{33} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} -5.19615i q^{39} +(2.50000 + 4.33013i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +8.66025i q^{51} +(0.500000 + 0.866025i) q^{53} -3.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(-5.00000 - 8.66025i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(1.50000 + 2.59808i) q^{65} +(6.00000 - 10.3923i) q^{67} +(7.50000 + 4.33013i) q^{69} +12.0000 q^{71} +(2.50000 + 4.33013i) q^{73} +(-6.00000 - 3.46410i) q^{75} +(-1.50000 + 7.79423i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.50000 - 12.9904i) q^{83} +(-2.50000 - 4.33013i) q^{85} +(1.50000 - 0.866025i) q^{87} +(2.50000 - 4.33013i) q^{89} +(7.50000 - 2.59808i) q^{91} +(12.0000 - 6.92820i) q^{93} +(3.50000 - 6.06218i) q^{95} +(-3.50000 + 6.06218i) q^{97} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 6 q^{11} - 3 q^{13} - 3 q^{15} + 5 q^{17} - 7 q^{19} - 6 q^{21} + 10 q^{23} - 8 q^{25} + q^{29} + 8 q^{31} + 9 q^{33} + q^{35} - 3 q^{37} + 5 q^{41} + 7 q^{43}+ \cdots + 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 + 5 * q^17 - 7 * q^19 - 6 * q^21 + 10 * q^23 - 8 * q^25 + q^29 + 8 * q^31 + 9 * q^33 + q^35 - 3 * q^37 + 5 * q^41 + 7 * q^43 - 3 * q^45 - 8 * q^47 - 13 * q^49 + q^53 - 6 * q^55 - 21 * q^57 - 10 * q^61 - 15 * q^63 + 3 * q^65 + 12 * q^67 + 15 * q^69 + 24 * q^71 + 5 * q^73 - 12 * q^75 - 3 * q^77 + 8 * q^79 - 9 * q^81 + 15 * q^83 - 5 * q^85 + 3 * q^87 + 5 * q^89 + 15 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 + 9 * q^99

Introduction

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