LMFDB - Embedded newform 2394.2.o.j.1261.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2394,2,Mod(505,2394)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2394.505"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2394, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.o (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,3,0,2,-2,0,-3,6,0,-2,1,0,-1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$19.1161862439$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2394.1261
Dual form			2394.2.o.j.505.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-3.50000 + 2.59808i) q^{19} -3.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 2.59808i) q^{35} +5.00000 q^{37} +(-4.00000 - 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(5.00000 + 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +1.00000 q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +(4.50000 + 7.79423i) q^{55} -1.00000 q^{56} +(3.00000 + 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +1.00000 q^{64} -6.00000 q^{65} +(-4.00000 + 6.92820i) q^{67} -3.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-7.00000 - 12.1244i) q^{73} +(2.50000 + 4.33013i) q^{74} +(-0.500000 - 4.33013i) q^{76} +3.00000 q^{77} +(2.00000 + 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-4.50000 + 7.79423i) q^{85} +(-5.00000 + 8.66025i) q^{86} -3.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(-12.0000 - 5.19615i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 3 q^{5} + 2 q^{7} - 2 q^{8} - 3 q^{10} + 6 q^{11} - 2 q^{13} + q^{14} - q^{16} + 3 q^{17} - 7 q^{19} - 6 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - q^{28} - 8 q^{31} + q^{32}+ \cdots + q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 3 * q^5 + 2 * q^7 - 2 * q^8 - 3 * q^10 + 6 * q^11 - 2 * q^13 + q^14 - q^16 + 3 * q^17 - 7 * q^19 - 6 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - q^28 - 8 * q^31 + q^32 - 3 * q^34 + 3 * q^35 + 10 * q^37 - 8 * q^38 - 3 * q^40 - 3 * q^41 + 10 * q^43 - 3 * q^44 + 2 * q^49 - 8 * q^50 - 2 * q^52 + 12 * q^53 + 9 * q^55 - 2 * q^56 + 6 * q^59 - 8 * q^61 - 4 * q^62 + 2 * q^64 - 12 * q^65 - 8 * q^67 - 6 * q^68 - 3 * q^70 - 14 * q^73 + 5 * q^74 - q^76 + 6 * q^77 + 4 * q^79 + 3 * q^80 + 3 * q^82 - 9 * q^85 - 10 * q^86 - 6 * q^88 - 3 * q^89 - 2 * q^91 - 24 * q^95 - 8 * q^97 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	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
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	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
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$	−3.00000			−0.670820
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	−4.00000	−	1.73205i	−0.648886	−	0.280976i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−4.00000			−0.565685
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	4.50000	+	7.79423i	0.606780	+	1.05097i
$56$	−1.00000			−0.133631
$57$		0			0
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000			−0.744208
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$		0			0
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	3.00000			0.341882
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$		0			0
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−12.0000	−	5.19615i	−1.23117	−	0.533114i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	12.0000			1.16554
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−8.00000			−0.724286
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	3.00000			0.268328
$126$		0			0
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−3.50000	+	2.59808i	−0.303488	+	0.225282i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	−3.00000			−0.253546
$141$		0			0
$142$		0			0
$143$	−3.00000	+	5.19615i	−0.250873	+	0.434524i
$144$		0			0
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$		0			0
$148$	−2.50000	+	4.33013i	−0.205499	+	0.355934i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	3.50000	−	2.59808i	0.283887	−	0.210732i
$153$		0			0
$154$	1.50000	+	2.59808i	0.120873	+	0.209359i
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		0			0
$160$	3.00000			0.237171
$161$		0			0
$162$		0			0
$163$	−22.0000			−1.72317			−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000			−1.72317			−0.861586	+	0.507611i	$0.830529\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$		0			0
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−9.00000			−0.690268
$171$		0			0
$172$	−10.0000			−0.762493
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−3.00000			−0.224860
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$		0			0
$181$	8.00000	−	13.8564i	0.594635	−	1.02994i	−0.398963	−	0.916967i	$-0.630630\pi$
$181$	8.00000	−	13.8564i	0.594635	−	1.02994i	0.993598	−	0.112972i	$-0.0360369\pi$
$182$	−2.00000			−0.148250
$183$		0			0
$184$		0			0
$185$	7.50000	+	12.9904i	0.551411	+	0.955072i
$186$		0			0
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	−1.50000	−	12.9904i	−0.108821	−	0.942421i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$		0			0
$202$	−3.00000			−0.211079
$203$		0			0
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	−0.500000	−	0.866025i	−0.0348367	−	0.0603388i
$207$		0			0
$208$	2.00000			0.138675
$209$	−10.5000	+	7.79423i	−0.726300	+	0.539138i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−15.0000	+	25.9808i	−1.02299	+	1.77187i
$216$		0			0
$217$	−4.00000			−0.271538
$218$	5.50000	−	9.52628i	0.372507	−	0.645201i
$219$		0			0
$220$	−9.00000			−0.606780
$221$	−6.00000			−0.403604
$222$		0			0
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	−28.0000			−1.85029			−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000			−1.85029			−0.925146	+	0.379611i	$0.876058\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000			−0.390567
$237$		0			0
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$		0			0
$247$	−1.00000	−	8.66025i	−0.0636285	−	0.551039i
$248$	4.00000			0.254000
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	3.00000	−	5.19615i	0.189358	−	0.327978i	−0.755678	−	0.654943i	$-0.772693\pi$
$251$	3.00000	−	5.19615i	0.189358	−	0.327978i	0.945036	+	0.326965i	$0.106026\pi$
$252$		0			0
$253$		0			0
$254$	−2.00000			−0.125491
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$	5.00000			0.310685
$260$	3.00000	−	5.19615i	0.186052	−	0.322252i
$261$		0			0
$262$		0			0
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	−0.983728	−	0.179664i	$-0.942499\pi$
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	0.336270	−	0.941766i	$-0.390834\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$	−4.00000	−	1.73205i	−0.245256	−	0.106199i
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	6.00000			0.362473
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	−19.0000			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$277$	−19.0000			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$278$	−5.00000			−0.299880
$279$		0			0
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	12.0000	−	20.7846i	0.715860	−	1.23991i	−0.246767	−	0.969075i	$-0.579368\pi$
$281$	12.0000	−	20.7846i	0.715860	−	1.23991i	0.962627	−	0.270831i	$-0.0872985\pi$
$282$		0			0
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$		0			0
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−1.50000	−	2.59808i	−0.0885422	−	0.153360i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$	14.0000			0.819288
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$		0			0
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	−5.00000			−0.290619
$297$		0			0
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$		0			0
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$		0			0
$304$	4.00000	+	1.73205i	0.229416	+	0.0993399i
$305$	−24.0000			−1.37424
$306$		0			0
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	−1.50000	+	2.59808i	−0.0854704	+	0.148039i
$309$		0			0
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	−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
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	−0.956647	−	0.291250i	$-0.905929\pi$
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	0.730554	+	0.682855i	$0.239262\pi$
$314$	7.00000	−	12.1244i	0.395033	−	0.684217i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$		0			0
$319$		0			0
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$	−12.0000	−	5.19615i	−0.667698	−	0.289122i
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	−11.0000	−	19.0526i	−0.609234	−	1.05522i
$327$		0			0
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$		0			0
$330$		0			0
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$		0			0
$333$		0			0
$334$	6.00000			0.328305
$335$	−24.0000			−1.31126
$336$		0			0
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	0.609936	−	0.792451i	$-0.291195\pi$
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	1.00000			0.0539949
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	33.0000			1.75641			0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000			1.75641			0.878206	+	0.478282i	$0.158740\pi$
$354$		0			0
$355$		0			0
$356$	−1.50000	−	2.59808i	−0.0794998	−	0.137698i
$357$		0			0
$358$	1.50000	+	2.59808i	0.0792775	+	0.137313i
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	16.0000			0.840941
$363$		0			0
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	21.0000	−	36.3731i	1.09919	−	1.90385i
$366$		0			0
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	−0.852680	−	0.522433i	$-0.825025\pi$
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	0.878780	+	0.477227i	$0.158358\pi$
$368$		0			0
$369$		0			0
$370$	−7.50000	+	12.9904i	−0.389906	+	0.675338i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	10.5000	−	7.79423i	0.538639	−	0.399835i
$381$		0			0
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	4.50000	+	7.79423i	0.229341	+	0.397231i
$386$	−0.500000	+	0.866025i	−0.0254493	+	0.0440795i
$387$		0			0
$388$	8.00000			0.406138
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000			−0.0505076
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	4.00000			0.200000
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$		0			0
$407$	15.0000			0.743522
$408$		0			0
$409$	20.0000	−	34.6410i	0.988936	−	1.71289i	0.366002	−	0.930614i	$-0.380726\pi$
$409$	20.0000	−	34.6410i	0.988936	−	1.71289i	0.622935	−	0.782274i	$-0.285940\pi$
$410$	9.00000			0.444478
$411$		0			0
$412$	0.500000	−	0.866025i	0.0246332	−	0.0426660i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$		0			0
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−12.0000	−	5.19615i	−0.586939	−	0.254152i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	0.999109	−	0.0422075i	$-0.0134391\pi$
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	−0.536107	+	0.844150i	$0.680106\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	−12.0000			−0.582086
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	−30.0000			−1.44673
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	0.128204	+	0.991748i	$0.459079\pi$
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	−0.922981	+	0.384846i	$0.874254\pi$
$432$		0			0
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	−0.607238	−	0.794520i	$-0.707723\pi$
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	0.991693	+	0.128624i	$0.0410559\pi$
$434$	−2.00000	−	3.46410i	−0.0960031	−	0.166282i
$435$		0			0
$436$	11.0000			0.526804
$437$		0			0
$438$		0			0
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	−0.998353	−	0.0573756i	$-0.981727\pi$
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	0.449488	−	0.893287i	$-0.351607\pi$
$440$	−4.50000	−	7.79423i	−0.214529	−	0.371575i
$441$		0			0
$442$	−3.00000	−	5.19615i	−0.142695	−	0.247156i
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−9.00000			−0.426641
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$		0			0
$448$	1.00000			0.0472456
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	−6.00000			−0.281284
$456$		0			0
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	−14.0000	−	24.2487i	−0.654177	−	1.13307i
$459$		0			0
$460$		0			0
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−4.00000	+	6.92820i	−0.184703	+	0.319915i
$470$		0			0
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$		0			0
$475$	−2.00000	−	17.3205i	−0.0917663	−	0.794719i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	−0.287954	−	0.957644i	$-0.592975\pi$
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	0.973321	−	0.229447i	$-0.0736918\pi$
$480$		0			0
$481$	−5.00000	+	8.66025i	−0.227980	+	0.394874i
$482$	28.0000			1.27537
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	12.0000	−	20.7846i	0.544892	−	0.943781i
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$		0			0
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$		0			0
$493$		0			0
$494$	7.00000	−	5.19615i	0.314945	−	0.233786i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$		0			0
$498$		0			0
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	6.00000			0.267793
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.164124	+	0.986440i	$0.552480\pi$
$503$	−21.0000	+	36.3731i	−0.936344	+	1.62179i	−0.772220	+	0.635355i	$0.780854\pi$
$504$		0			0
$505$	−9.00000			−0.400495
$506$		0			0
$507$		0			0
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−15.0000			−0.661622
$515$	−1.50000	−	2.59808i	−0.0660979	−	0.114485i
$516$		0			0
$517$		0			0
$518$	2.50000	+	4.33013i	0.109844	+	0.190255i
$519$		0			0
$520$	6.00000			0.263117
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$		0			0
$526$	10.5000	−	18.1865i	0.457822	−	0.792971i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	18.0000	+	31.1769i	0.781870	+	1.35424i
$531$		0			0
$532$	−0.500000	−	4.33013i	−0.0216777	−	0.187735i
$533$	6.00000			0.259889
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$		0			0
$538$	−7.50000	+	12.9904i	−0.323348	+	0.560055i
$539$	3.00000			0.129219
$540$		0			0
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	−0.312507	−	0.949915i	$-0.601169\pi$
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	0.978905	−	0.204318i	$-0.0654977\pi$
$542$	−12.5000	+	21.6506i	−0.536921	+	0.929974i
$543$		0			0
$544$	3.00000			0.128624
$545$	16.5000	−	28.5788i	0.706782	−	1.22418i
$546$		0			0
$547$	5.00000	−	8.66025i	0.213785	−	0.370286i	−0.739111	−	0.673583i	$-0.764754\pi$
$547$	5.00000	−	8.66025i	0.213785	−	0.370286i	0.952896	+	0.303298i	$0.0980876\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$		0			0
$550$	−12.0000			−0.511682
$551$		0			0
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$	−9.50000	−	16.4545i	−0.403616	−	0.699084i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	1.50000	−	2.59808i	0.0633866	−	0.109789i
$561$		0			0
$562$	24.0000			1.01238
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−18.0000	−	31.1769i	−0.757266	−	1.31162i
$566$	−15.5000	+	26.8468i	−0.651514	+	1.12845i
$567$		0			0
$568$		0			0
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$		0			0
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$		0			0
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	8.00000			0.332756
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$		0			0
$586$	13.5000	+	23.3827i	0.557680	+	0.965930i
$587$	21.0000	+	36.3731i	0.866763	+	1.50128i	0.865286	+	0.501278i	$0.167137\pi$
$587$	21.0000	+	36.3731i	0.866763	+	1.50128i	0.00147660	+	0.999999i	$0.499530\pi$
$588$		0			0
$589$	14.0000	−	10.3923i	0.576860	−	0.428207i
$590$	−18.0000			−0.741048
$591$		0			0
$592$	−2.50000	−	4.33013i	−0.102749	−	0.177967i
$593$	7.50000	−	12.9904i	0.307988	−	0.533451i	−0.669934	−	0.742421i	$-0.733678\pi$
$593$	7.50000	−	12.9904i	0.307988	−	0.533451i	0.977922	+	0.208970i	$0.0670110\pi$
$594$		0			0
$595$	−4.50000	+	7.79423i	−0.184482	+	0.319532i
$596$	−18.0000			−0.737309
$597$		0			0
$598$		0			0
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	−0.895042	−	0.445983i	$-0.852854\pi$
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	0.833753	+	0.552137i	$0.186188\pi$
$600$		0			0
$601$	44.0000			1.79480			0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000			1.79480			0.897399	+	0.441221i	$0.145454\pi$
$602$	−5.00000	+	8.66025i	−0.203785	+	0.352966i
$603$		0			0
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	−40.0000			−1.62355			−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000			−1.62355			−0.811775	+	0.583970i	$0.801498\pi$
$608$	0.500000	+	4.33013i	0.0202777	+	0.175610i
$609$		0			0
$610$	−12.0000	−	20.7846i	−0.485866	−	0.841544i
$611$		0			0
$612$		0			0
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	0.928010	−	0.372554i	$-0.121518\pi$
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	−0.786647	+	0.617403i	$0.788185\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$		0			0
$616$	−3.00000			−0.120873
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$		0			0
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	12.0000			0.481932
$621$		0			0
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$	−1.50000	+	2.59808i	−0.0600962	+	0.104090i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−8.00000			−0.319744
$627$		0			0
$628$	14.0000			0.558661
$629$	7.50000	+	12.9904i	0.299045	+	0.517960i
$630$		0			0
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	−0.559625	−	0.828746i	$-0.689055\pi$
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	0.997528	+	0.0702759i	$0.0223880\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$		0			0
$634$	24.0000			0.953162
$635$	−6.00000			−0.238103
$636$		0			0
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$		0			0
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$		0			0
$645$		0			0
$646$	−1.50000	−	12.9904i	−0.0590167	−	0.511100i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	9.00000	+	15.5885i	0.353281	+	0.611900i
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	11.0000	−	19.0526i	0.430793	−	0.746156i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$		0			0
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	−0.940263	−	0.340448i	$-0.889421\pi$
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	0.764968	+	0.644068i	$0.222755\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	16.0000	+	27.7128i	0.621858	+	1.07709i
$663$		0			0
$664$		0			0
$665$	−12.0000	−	5.19615i	−0.465340	−	0.201498i
$666$		0			0
$667$		0			0
$668$	3.00000	+	5.19615i	0.116073	+	0.201045i
$669$		0			0
$670$	−12.0000	−	20.7846i	−0.463600	−	0.802980i
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	5.00000			0.192736			0.0963679	−	0.995346i	$-0.469277\pi$
$673$	5.00000			0.192736			0.0963679	+	0.995346i	$0.469277\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	3.00000			0.115299			0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000			0.115299			0.0576497	+	0.998337i	$0.481639\pi$
$678$		0			0
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	−19.0000			−0.722794			−0.361397	−	0.932412i	$-0.617700\pi$
$691$	−19.0000			−0.722794			−0.361397	+	0.932412i	$0.617700\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$	−15.0000			−0.568982
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$	10.0000	+	17.3205i	0.378506	+	0.655591i
$699$		0			0
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	0.996904	+	0.0786236i	$0.0250525\pi$
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	−0.430362	+	0.902656i	$0.641614\pi$
$702$		0			0
$703$	−17.5000	+	12.9904i	−0.660025	+	0.489942i
$704$	3.00000			0.113067
$705$		0			0
$706$	16.5000	+	28.5788i	0.620986	+	1.07558i
$707$	−1.50000	+	2.59808i	−0.0564133	+	0.0977107i
$708$		0			0
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	−0.717769	−	0.696281i	$-0.754837\pi$
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	0.961882	+	0.273466i	$0.0881700\pi$
$710$		0			0
$711$		0			0
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$		0			0
$714$		0			0
$715$	−18.0000			−0.673162
$716$	−1.50000	+	2.59808i	−0.0560576	+	0.0970947i
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$	−1.00000			−0.0372419
$722$	18.5000	−	4.33013i	0.688499	−	0.161151i
$723$		0			0
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$		0			0
$726$		0			0
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	1.00000	−	1.73205i	0.0370625	−	0.0641941i
$729$		0			0
$730$	42.0000			1.55449
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$		0			0
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	1.00000			0.0369107
$735$		0			0
$736$		0			0
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$		0			0
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$	−15.0000			−0.551411
$741$		0			0
$742$	12.0000			0.440534
$743$	16.5000	+	28.5788i	0.605326	+	1.04846i	0.992000	+	0.126239i	$0.0402907\pi$
$743$	16.5000	+	28.5788i	0.605326	+	1.04846i	−0.386674	+	0.922217i	$0.626376\pi$
$744$		0			0
$745$	−27.0000	+	46.7654i	−0.989203	+	1.71335i
$746$	11.5000	+	19.9186i	0.421045	+	0.729271i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	12.0000			0.438470
$750$		0			0
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	−0.760263	−	0.649616i	$-0.774930\pi$
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	0.942715	+	0.333599i	$0.108263\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	12.0000	+	20.7846i	0.436725	+	0.756429i
$756$		0			0
$757$	−5.50000	−	9.52628i	−0.199901	−	0.346239i	0.748595	−	0.663027i	$-0.230729\pi$
$757$	−5.50000	−	9.52628i	−0.199901	−	0.346239i	−0.948496	+	0.316789i	$0.897395\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$		0			0
$760$	12.0000	+	5.19615i	0.435286	+	0.188484i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		0			0
$763$	−5.50000	−	9.52628i	−0.199113	−	0.344874i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	6.00000	−	10.3923i	0.216789	−	0.375489i
$767$	−12.0000			−0.433295
$768$		0			0
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	−0.988061	−	0.154062i	$-0.950765\pi$
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	0.627452	+	0.778655i	$0.284098\pi$
$770$	−4.50000	+	7.79423i	−0.162169	+	0.280885i
$771$		0			0
$772$	−1.00000			−0.0359908
$773$	−19.5000	+	33.7750i	−0.701366	+	1.21480i	0.266621	+	0.963802i	$0.414093\pi$
$773$	−19.5000	+	33.7750i	−0.701366	+	1.21480i	−0.967987	+	0.251000i	$0.919240\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$		0			0
$778$		0			0
$779$	12.0000	+	5.19615i	0.429945	+	0.186171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	21.0000	−	36.3731i	0.749522	−	1.29821i
$786$		0			0
$787$	23.0000			0.819861			0.409931	−	0.912117i	$-0.365553\pi$
$787$	23.0000			0.819861			0.409931	+	0.912117i	$0.365553\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		0			0
$790$	−12.0000			−0.426941
$791$	−12.0000			−0.426671
$792$		0			0
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$		0			0
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	15.0000			0.531327			0.265664	−	0.964066i	$-0.414409\pi$
$797$	15.0000			0.531327			0.265664	+	0.964066i	$0.414409\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$		0			0
$802$	18.0000	−	31.1769i	0.635602	−	1.10090i
$803$	−21.0000	−	36.3731i	−0.741074	−	1.28358i
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	12.0000			0.421898			0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000			0.421898			0.210949	+	0.977497i	$0.432345\pi$
$810$		0			0
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	−0.798009	−	0.602645i	$-0.794113\pi$
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	0.920911	+	0.389774i	$0.127447\pi$
$812$		0			0
$813$		0			0
$814$	7.50000	+	12.9904i	0.262875	+	0.455313i
$815$	−33.0000	−	57.1577i	−1.15594	−	2.00215i
$816$		0			0
$817$	−40.0000	−	17.3205i	−1.39942	−	0.605968i
$818$	40.0000			1.39857
$819$		0			0
$820$	4.50000	+	7.79423i	0.157147	+	0.272186i
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	1.00000			0.0348367
$825$		0			0
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	10.5000	−	18.1865i	0.365121	−	0.632408i	−0.623675	−	0.781684i	$-0.714361\pi$
$827$	10.5000	−	18.1865i	0.365121	−	0.632408i	0.988796	+	0.149276i	$0.0476944\pi$
$828$		0			0
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	1.50000	+	2.59808i	0.0519719	+	0.0900180i
$834$		0			0
$835$	18.0000			0.622916
$836$	−1.50000	−	12.9904i	−0.0518786	−	0.449282i
$837$		0			0
$838$	3.00000	+	5.19615i	0.103633	+	0.179498i
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	0.958974	+	0.283495i	$0.0914938\pi$
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	−0.233973	+	0.972243i	$0.575173\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−9.50000	+	16.4545i	−0.327392	+	0.567059i
$843$		0			0
$844$	20.0000			0.688428
$845$	−13.5000	+	23.3827i	−0.464414	+	0.804389i
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	−12.0000			−0.412082
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$		0			0
$852$		0			0
$853$	−10.0000	−	17.3205i	−0.342393	−	0.593043i	0.642483	−	0.766300i	$-0.277904\pi$
$853$	−10.0000	−	17.3205i	−0.342393	−	0.593043i	−0.984877	+	0.173257i	$0.944571\pi$
$854$	−8.00000			−0.273754
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−19.5000	−	33.7750i	−0.666107	−	1.15373i	−0.978984	−	0.203938i	$-0.934626\pi$
$857$	−19.5000	−	33.7750i	−0.666107	−	1.15373i	0.312877	−	0.949794i	$-0.398707\pi$
$858$		0			0
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$	−15.0000	−	25.9808i	−0.511496	−	0.885937i
$861$		0			0
$862$	−33.0000			−1.12398
$863$	−15.0000			−0.510606			−0.255303	−	0.966861i	$-0.582175\pi$
$863$	−15.0000			−0.510606			−0.255303	+	0.966861i	$0.582175\pi$
$864$		0			0
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$	16.0000			0.543702
$867$		0			0
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	5.50000	+	9.52628i	0.186254	+	0.322601i
$873$		0			0
$874$		0			0
$875$	3.00000			0.101419
$876$		0			0
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$	11.5000	−	19.9186i	0.388106	−	0.672220i
$879$		0			0
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	−39.0000			−1.31394			−0.656972	−	0.753915i	$-0.728163\pi$
$881$	−39.0000			−1.31394			−0.656972	+	0.753915i	$0.728163\pi$
$882$		0			0
$883$	23.0000	−	39.8372i	0.774012	−	1.34063i	−0.161337	−	0.986899i	$-0.551581\pi$
$883$	23.0000	−	39.8372i	0.774012	−	1.34063i	0.935348	−	0.353728i	$-0.115086\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$		0			0
$886$	36.0000			1.20944
$887$	−9.00000	+	15.5885i	−0.302190	+	0.523409i	−0.976632	−	0.214919i	$-0.931051\pi$
$887$	−9.00000	+	15.5885i	−0.302190	+	0.523409i	0.674441	+	0.738328i	$0.264385\pi$
$888$		0			0
$889$	−1.00000	+	1.73205i	−0.0335389	+	0.0580911i
$890$	−4.50000	−	7.79423i	−0.150840	−	0.261263i
$891$		0			0
$892$	−1.00000			−0.0334825
$893$		0			0
$894$		0			0
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$		0			0
$900$		0			0
$901$	36.0000			1.19933
$902$	4.50000	−	7.79423i	0.149834	−	0.259519i
$903$		0			0
$904$	12.0000			0.399114
$905$	48.0000			1.59557
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$		0			0
$910$	−3.00000	−	5.19615i	−0.0994490	−	0.172251i
$911$	15.0000			0.496972			0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000			0.496972			0.248486	+	0.968635i	$0.420067\pi$
$912$		0			0
$913$		0			0
$914$	14.5000	+	25.1147i	0.479617	+	0.830722i
$915$		0			0
$916$	14.0000	−	24.2487i	0.462573	−	0.801200i
$917$		0			0
$918$		0			0
$919$	−46.0000			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$920$		0			0
$921$		0			0
$922$	7.50000	−	12.9904i	0.246999	−	0.427815i
$923$		0			0
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$		0			0
$928$		0			0
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	−3.50000	+	2.59808i	−0.114708	+	0.0851485i
$932$	−24.0000			−0.786146
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	−13.5000	+	23.3827i	−0.441497	+	0.764696i
$936$		0			0
$937$	−7.00000	+	12.1244i	−0.228680	+	0.396085i	−0.957417	−	0.288708i	$-0.906774\pi$
$937$	−7.00000	+	12.1244i	−0.228680	+	0.396085i	0.728737	+	0.684794i	$0.240108\pi$
$938$	−8.00000			−0.261209
$939$		0			0
$940$		0			0
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	0.461133	+	0.887331i	$0.347443\pi$
$941$	−16.5000	+	28.5788i	−0.537885	+	0.931644i	−0.999018	+	0.0443125i	$0.985890\pi$
$942$		0			0
$943$		0			0
$944$	3.00000	−	5.19615i	0.0976417	−	0.169120i
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	0.558898	−	0.829237i	$-0.311224\pi$
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	−0.997589	+	0.0694014i	$0.977891\pi$
$948$		0			0
$949$	28.0000			0.908918
$950$	14.0000	−	10.3923i	0.454220	−	0.337171i
$951$		0			0
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	−0.995112	−	0.0987513i	$-0.968515\pi$
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	0.412035	−	0.911168i	$-0.364818\pi$
$954$		0			0
$955$	18.0000	+	31.1769i	0.582466	+	1.00886i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$	30.0000			0.969256
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−10.0000			−0.322413
$963$		0			0
$964$	14.0000	+	24.2487i	0.450910	+	0.780998i
$965$	−1.50000	+	2.59808i	−0.0482867	+	0.0836350i
$966$		0			0
$967$	5.00000	+	8.66025i	0.160789	+	0.278495i	0.935152	−	0.354247i	$-0.115263\pi$
$967$	5.00000	+	8.66025i	0.160789	+	0.278495i	−0.774363	+	0.632742i	$0.781929\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	24.0000			0.770594
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	−2.50000	+	4.33013i	−0.0801463	+	0.138817i
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$		0			0
$976$	8.00000			0.256074
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$	−3.00000			−0.0958315
$981$		0			0
$982$	16.5000	−	28.5788i	0.526536	−	0.911987i
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$		0			0
$987$		0			0
$988$	8.00000	+	3.46410i	0.254514	+	0.110208i
$989$		0			0
$990$		0			0
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$	−24.0000			−0.760851
$996$		0			0
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$	10.0000	−	17.3205i	0.316544	−	0.548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.o.j.1261.1		2
3.2	odd	2		798.2.k.a.463.1	✓	2
19.11	even	3	inner	2394.2.o.j.505.1		2
57.11	odd	6		798.2.k.a.505.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.a.463.1	✓	2	3.2	odd	2
798.2.k.a.505.1	yes	2	57.11	odd	6
2394.2.o.j.505.1		2	19.11	even	3	inner
2394.2.o.j.1261.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-3.50000 + 2.59808i) q^{19} -3.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 2.59808i) q^{35} +5.00000 q^{37} +(-4.00000 - 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(5.00000 + 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +1.00000 q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +(4.50000 + 7.79423i) q^{55} -1.00000 q^{56} +(3.00000 + 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +1.00000 q^{64} -6.00000 q^{65} +(-4.00000 + 6.92820i) q^{67} -3.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-7.00000 - 12.1244i) q^{73} +(2.50000 + 4.33013i) q^{74} +(-0.500000 - 4.33013i) q^{76} +3.00000 q^{77} +(2.00000 + 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-4.50000 + 7.79423i) q^{85} +(-5.00000 + 8.66025i) q^{86} -3.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(-12.0000 - 5.19615i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 3 q^{5} + 2 q^{7} - 2 q^{8} - 3 q^{10} + 6 q^{11} - 2 q^{13} + q^{14} - q^{16} + 3 q^{17} - 7 q^{19} - 6 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - q^{28} - 8 q^{31} + q^{32}+ \cdots + q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 3 * q^5 + 2 * q^7 - 2 * q^8 - 3 * q^10 + 6 * q^11 - 2 * q^13 + q^14 - q^16 + 3 * q^17 - 7 * q^19 - 6 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - q^28 - 8 * q^31 + q^32 - 3 * q^34 + 3 * q^35 + 10 * q^37 - 8 * q^38 - 3 * q^40 - 3 * q^41 + 10 * q^43 - 3 * q^44 + 2 * q^49 - 8 * q^50 - 2 * q^52 + 12 * q^53 + 9 * q^55 - 2 * q^56 + 6 * q^59 - 8 * q^61 - 4 * q^62 + 2 * q^64 - 12 * q^65 - 8 * q^67 - 6 * q^68 - 3 * q^70 - 14 * q^73 + 5 * q^74 - q^76 + 6 * q^77 + 4 * q^79 + 3 * q^80 + 3 * q^82 - 9 * q^85 - 10 * q^86 - 6 * q^88 - 3 * q^89 - 2 * q^91 - 24 * q^95 - 8 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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