LMFDB - Embedded newform 1650.2.d.i.1451.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1451,1650)] 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("1650.1451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,0] 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:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 5x^{8} - 46x^{6} - 45x^{4} + 243x^{2} + 729 $ x^12 + 3x^10 - 5x^8 - 46x^6 - 45x^4 + 243*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1451.10
Root			$-0.839210 - 1.51517i$ of defining polynomial
Character	$\chi$	$=$	1650.1451
Dual form			1650.2.d.i.1451.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(0.839210 + 1.51517i) q^{3} +1.00000 q^{4} +(-0.839210 - 1.51517i) q^{6} +3.51327i q^{7} -1.00000 q^{8} +(-1.59145 + 2.54308i) q^{9} +(-0.486823 - 3.28070i) q^{11} +(0.839210 + 1.51517i) q^{12} -2.03804i q^{13} -3.51327i q^{14} +1.00000 q^{16} -6.34310 q^{17} +(1.59145 - 2.54308i) q^{18} -2.47606i q^{19} +(-5.32319 + 2.94838i) q^{21} +(0.486823 + 3.28070i) q^{22} +4.18641i q^{23} +(-0.839210 - 1.51517i) q^{24} +2.03804i q^{26} +(-5.18876 - 0.277134i) q^{27} +3.51327i q^{28} -9.67274 q^{29} -1.18291 q^{31} -1.00000 q^{32} +(4.56226 - 3.49082i) q^{33} +6.34310 q^{34} +(-1.59145 + 2.54308i) q^{36} +3.08797 q^{37} +2.47606i q^{38} +(3.08797 - 1.71034i) q^{39} -6.58477 q^{41} +(5.32319 - 2.94838i) q^{42} +7.02655i q^{43} +(-0.486823 - 3.28070i) q^{44} -4.18641i q^{46} -0.765721i q^{47} +(0.839210 + 1.51517i) q^{48} -5.34310 q^{49} +(-5.32319 - 9.61085i) q^{51} -2.03804i q^{52} -10.0832i q^{53} +(5.18876 + 0.277134i) q^{54} -3.51327i q^{56} +(3.75165 - 2.07794i) q^{57} +9.67274 q^{58} +0.465146i q^{59} -9.85671i q^{61} +1.18291 q^{62} +(-8.93455 - 5.59121i) q^{63} +1.00000 q^{64} +(-4.56226 + 3.49082i) q^{66} -0.973646 q^{67} -6.34310 q^{68} +(-6.34310 + 3.51327i) q^{69} +7.12421i q^{71} +(1.59145 - 2.54308i) q^{72} +9.70719i q^{73} -3.08797 q^{74} -2.47606i q^{76} +(11.5260 - 1.71034i) q^{77} +(-3.08797 + 1.71034i) q^{78} +0.992165i q^{79} +(-3.93455 - 8.09440i) q^{81} +6.58477 q^{82} +12.6862 q^{83} +(-5.32319 + 2.94838i) q^{84} -7.02655i q^{86} +(-8.11746 - 14.6558i) q^{87} +(0.486823 + 3.28070i) q^{88} +5.08617i q^{89} +7.16019 q^{91} +4.18641i q^{92} +(-0.992707 - 1.79230i) q^{93} +0.765721i q^{94} +(-0.839210 - 1.51517i) q^{96} -14.7080 q^{97} +5.34310 q^{98} +(9.11786 + 3.98305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} - 6 q^{9} + 12 q^{16} - 4 q^{17} + 6 q^{18} + 12 q^{31} - 12 q^{32} - 18 q^{33} + 4 q^{34} - 6 q^{36} + 8 q^{49} - 14 q^{57} - 12 q^{62} - 22 q^{63} + 12 q^{64} + 18 q^{66}+ \cdots + 28 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 - 6 * q^9 + 12 * q^16 - 4 * q^17 + 6 * q^18 + 12 * q^31 - 12 * q^32 - 18 * q^33 + 4 * q^34 - 6 * q^36 + 8 * q^49 - 14 * q^57 - 12 * q^62 - 22 * q^63 + 12 * q^64 + 18 * q^66 - 4 * q^68 - 4 * q^69 + 6 * q^72 + 40 * q^77 + 38 * q^81 + 8 * q^83 + 14 * q^87 + 40 * q^91 - 8 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.839210	+	1.51517i	0.484518	+	0.874781i
$3$	0.839210	+	1.51517i	0.484518	+	0.874781i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−0.839210	−	1.51517i	−0.342606	−	0.618564i
$7$			3.51327i			1.32789i	0.747780	+	0.663947i	$0.231120\pi$
$7$			3.51327i			1.32789i	−0.747780	+	0.663947i	$0.768880\pi$
$8$	−1.00000			−0.353553
$9$	−1.59145	+	2.54308i	−0.530484	+	0.847695i
$10$		0			0
$11$	−0.486823	−	3.28070i	−0.146783	−	0.989169i
$11$	−0.486823	−	3.28070i	−0.146783	−	0.989169i
$12$	0.839210	+	1.51517i	0.242259	+	0.437391i
$13$		−	2.03804i		−	0.565251i	−0.959230	−	0.282625i	$-0.908795\pi$
$13$		−	2.03804i		−	0.565251i	0.959230	−	0.282625i	$-0.0912053\pi$
$14$		−	3.51327i		−	0.938962i
$15$		0			0
$16$	1.00000			0.250000
$17$	−6.34310			−1.53843			−0.769214	−	0.638991i	$-0.779352\pi$
$17$	−6.34310			−1.53843			−0.769214	+	0.638991i	$0.779352\pi$
$18$	1.59145	−	2.54308i	0.375109	−	0.599411i
$19$		−	2.47606i		−	0.568048i	−0.958817	−	0.284024i	$-0.908330\pi$
$19$		−	2.47606i		−	0.568048i	0.958817	−	0.284024i	$-0.0916695\pi$
$20$		0			0
$21$	−5.32319	+	2.94838i	−1.16162	+	0.643388i
$22$	0.486823	+	3.28070i	0.103791	+	0.699448i
$23$			4.18641i			0.872926i	0.899722	+	0.436463i	$0.143769\pi$
$23$			4.18641i			0.872926i	−0.899722	+	0.436463i	$0.856231\pi$
$24$	−0.839210	−	1.51517i	−0.171303	−	0.309282i
$25$		0			0
$26$			2.03804i			0.399692i
$27$	−5.18876	−	0.277134i	−0.998577	−	0.0533344i
$28$			3.51327i			0.663947i
$29$	−9.67274			−1.79618			−0.898091	−	0.439809i	$-0.855046\pi$
$29$	−9.67274			−1.79618			−0.898091	+	0.439809i	$0.855046\pi$
$30$		0			0
$31$	−1.18291			−0.212456			−0.106228	−	0.994342i	$-0.533877\pi$
$31$	−1.18291			−0.212456			−0.106228	+	0.994342i	$0.533877\pi$
$32$	−1.00000			−0.176777
$33$	4.56226	−	3.49082i	0.794187	−	0.607673i
$34$	6.34310			1.08783
$35$		0			0
$36$	−1.59145	+	2.54308i	−0.265242	+	0.423847i
$37$	3.08797			0.507659			0.253829	−	0.967249i	$-0.418310\pi$
$37$	3.08797			0.507659			0.253829	+	0.967249i	$0.418310\pi$
$38$			2.47606i			0.401671i
$39$	3.08797	−	1.71034i	0.494471	−	0.273874i
$40$		0			0
$41$	−6.58477			−1.02837			−0.514184	−	0.857680i	$-0.671905\pi$
$41$	−6.58477			−1.02837			−0.514184	+	0.857680i	$0.671905\pi$
$42$	5.32319	−	2.94838i	0.821387	−	0.454944i
$43$			7.02655i			1.07154i	0.844364	+	0.535769i	$0.179978\pi$
$43$			7.02655i			1.07154i	−0.844364	+	0.535769i	$0.820022\pi$
$44$	−0.486823	−	3.28070i	−0.0733913	−	0.494584i
$45$		0			0
$46$		−	4.18641i		−	0.617252i
$47$		−	0.765721i		−	0.111692i	−0.998439	−	0.0558459i	$-0.982214\pi$
$47$		−	0.765721i		−	0.111692i	0.998439	−	0.0558459i	$-0.0177856\pi$
$48$	0.839210	+	1.51517i	0.121130	+	0.218695i
$49$	−5.34310			−0.763300
$50$		0			0
$51$	−5.32319	−	9.61085i	−0.745396	−	1.34579i
$52$		−	2.03804i		−	0.282625i
$53$		−	10.0832i		−	1.38503i	−0.721404	−	0.692514i	$-0.756503\pi$
$53$		−	10.0832i		−	1.38503i	0.721404	−	0.692514i	$-0.243497\pi$
$54$	5.18876	+	0.277134i	0.706100	+	0.0377131i
$55$		0			0
$56$		−	3.51327i		−	0.469481i
$57$	3.75165	−	2.07794i	0.496918	−	0.275230i
$58$	9.67274			1.27009
$59$			0.465146i			0.0605569i	0.999542	+	0.0302785i	$0.00963940\pi$
$59$			0.465146i			0.0605569i	−0.999542	+	0.0302785i	$0.990361\pi$
$60$		0			0
$61$		−	9.85671i		−	1.26202i	−0.775774	−	0.631011i	$-0.782640\pi$
$61$		−	9.85671i		−	1.26202i	0.775774	−	0.631011i	$-0.217360\pi$
$62$	1.18291			0.150229
$63$	−8.93455	−	5.59121i	−1.12565	−	0.704427i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.56226	+	3.49082i	−0.561575	+	0.429690i
$67$	−0.973646			−0.118950			−0.0594749	−	0.998230i	$-0.518943\pi$
$67$	−0.973646			−0.118950			−0.0594749	+	0.998230i	$0.518943\pi$
$68$	−6.34310			−0.769214
$69$	−6.34310	+	3.51327i	−0.763620	+	0.422949i
$70$		0			0
$71$			7.12421i			0.845488i	0.906249	+	0.422744i	$0.138933\pi$
$71$			7.12421i			0.845488i	−0.906249	+	0.422744i	$0.861067\pi$
$72$	1.59145	−	2.54308i	0.187555	−	0.299705i
$73$			9.70719i			1.13614i	0.822980	+	0.568070i	$0.192310\pi$
$73$			9.70719i			1.13614i	−0.822980	+	0.568070i	$0.807690\pi$
$74$	−3.08797			−0.358969
$75$		0			0
$76$		−	2.47606i		−	0.284024i
$77$	11.5260	−	1.71034i	1.31351	−	0.194912i
$78$	−3.08797	+	1.71034i	−0.349643	+	0.193658i
$79$			0.992165i			0.111627i	0.998441	+	0.0558136i	$0.0177753\pi$
$79$			0.992165i			0.111627i	−0.998441	+	0.0558136i	$0.982225\pi$
$80$		0			0
$81$	−3.93455	−	8.09440i	−0.437173	−	0.899378i
$82$	6.58477			0.727166
$83$	12.6862			1.39249			0.696246	−	0.717804i	$-0.254852\pi$
$83$	12.6862			1.39249			0.696246	+	0.717804i	$0.254852\pi$
$84$	−5.32319	+	2.94838i	−0.580808	+	0.321694i
$85$		0			0
$86$		−	7.02655i		−	0.757692i
$87$	−8.11746	−	14.6558i	−0.870283	−	1.57127i
$88$	0.486823	+	3.28070i	0.0518955	+	0.349724i
$89$			5.08617i			0.539133i	0.962982	+	0.269566i	$0.0868804\pi$
$89$			5.08617i			0.539133i	−0.962982	+	0.269566i	$0.913120\pi$
$90$		0			0
$91$	7.16019			0.750592
$92$			4.18641i			0.436463i
$93$	−0.992707	−	1.79230i	−0.102939	−	0.185853i
$94$			0.765721i			0.0789781i
$95$		0			0
$96$	−0.839210	−	1.51517i	−0.0856515	−	0.154641i
$97$	−14.7080			−1.49337			−0.746686	−	0.665177i	$-0.768356\pi$
$97$	−14.7080			−1.49337			−0.746686	+	0.665177i	$0.768356\pi$
$98$	5.34310			0.539735
$99$	9.11786	+	3.98305i	0.916379	+	0.400312i
$100$		0			0
$101$	7.14958			0.711410			0.355705	−	0.934598i	$-0.384241\pi$
$101$	7.14958			0.711410			0.355705	+	0.934598i	$0.384241\pi$
$102$	5.32319	+	9.61085i	0.527075	+	0.951616i
$103$	−16.6553			−1.64109			−0.820547	−	0.571579i	$-0.806331\pi$
$103$	−16.6553			−1.64109			−0.820547	+	0.571579i	$0.806331\pi$
$104$			2.03804i			0.199846i
$105$		0			0
$106$			10.0832i			0.979363i
$107$	7.16019			0.692202			0.346101	−	0.938197i	$-0.387505\pi$
$107$	7.16019			0.692202			0.346101	+	0.938197i	$0.387505\pi$
$108$	−5.18876	−	0.277134i	−0.499288	−	0.0266672i
$109$			7.38065i			0.706938i	0.935446	+	0.353469i	$0.114998\pi$
$109$			7.38065i			0.706938i	−0.935446	+	0.353469i	$0.885002\pi$
$110$		0			0
$111$	2.59145	+	4.67878i	0.245970	+	0.444090i
$112$			3.51327i			0.331973i
$113$			14.9877i			1.40993i	0.709243	+	0.704964i	$0.249037\pi$
$113$			14.9877i			1.40993i	−0.709243	+	0.704964i	$0.750963\pi$
$114$	−3.75165	+	2.07794i	−0.351374	+	0.194617i
$115$		0			0
$116$	−9.67274			−0.898091
$117$	5.18291	+	3.24344i	0.479160	+	0.299857i
$118$		−	0.465146i		−	0.0428202i
$119$		−	22.2851i		−	2.04287i
$120$		0			0
$121$	−10.5260	+	3.19424i	−0.956910	+	0.290386i
$122$			9.85671i			0.892385i
$123$	−5.52601	−	9.97702i	−0.498263	−	0.899598i
$124$	−1.18291			−0.106228
$125$		0			0
$126$	8.93455	+	5.59121i	0.795953	+	0.498105i
$127$		−	2.30787i		−	0.204790i	−0.994744	−	0.102395i	$-0.967349\pi$
$127$		−	2.30787i		−	0.204790i	0.994744	−	0.102395i	$-0.0326506\pi$
$128$	−1.00000			−0.0883883
$129$	−10.6464	+	5.89675i	−0.937362	+	0.519180i
$130$		0			0
$131$	−13.1585			−1.14966			−0.574831	−	0.818272i	$-0.694932\pi$
$131$	−13.1585			−1.14966			−0.574831	+	0.818272i	$0.694932\pi$
$132$	4.56226	−	3.49082i	0.397094	−	0.303836i
$133$	8.69909			0.754307
$134$	0.973646			0.0841102
$135$		0			0
$136$	6.34310			0.543916
$137$		−	11.5671i		−	0.988240i	−0.869394	−	0.494120i	$-0.835490\pi$
$137$		−	11.5671i		−	0.988240i	0.869394	−	0.494120i	$-0.164510\pi$
$138$	6.34310	−	3.51327i	0.539961	−	0.299070i
$139$		−	16.7456i		−	1.42035i	−0.704027	−	0.710173i	$-0.748617\pi$
$139$		−	16.7456i		−	1.42035i	0.704027	−	0.710173i	$-0.251383\pi$
$140$		0			0
$141$	1.16019	−	0.642601i	0.0977059	−	0.0541167i
$142$		−	7.12421i		−	0.597850i
$143$	−6.68620	+	0.992165i	−0.559128	+	0.0829690i
$144$	−1.59145	+	2.54308i	−0.132621	+	0.211924i
$145$		0			0
$146$		−	9.70719i		−	0.803373i
$147$	−4.48398	−	8.09568i	−0.369833	−	0.667721i
$148$	3.08797			0.253829
$149$	17.7960			1.45790			0.728951	−	0.684566i	$-0.240008\pi$
$149$	17.7960			1.45790			0.728951	+	0.684566i	$0.240008\pi$
$150$		0			0
$151$		−	10.8013i		−	0.879000i	−0.898243	−	0.439500i	$-0.855156\pi$
$151$		−	10.8013i		−	0.879000i	0.898243	−	0.439500i	$-0.144844\pi$
$152$			2.47606i			0.200835i
$153$	10.0947	−	16.1310i	0.816112	−	1.30412i
$154$	−11.5260	+	1.71034i	−0.928792	+	0.137823i
$155$		0			0
$156$	3.08797	−	1.71034i	0.247235	−	0.136937i
$157$	−5.03526			−0.401857			−0.200929	−	0.979606i	$-0.564396\pi$
$157$	−5.03526			−0.401857			−0.200929	+	0.979606i	$0.564396\pi$
$158$		−	0.992165i		−	0.0789324i
$159$	15.2777	−	8.46189i	1.21160	−	0.671071i
$160$		0			0
$161$	−14.7080			−1.15915
$162$	3.93455	+	8.09440i	0.309128	+	0.635956i
$163$	−18.2048			−1.42591			−0.712955	−	0.701210i	$-0.752644\pi$
$163$	−18.2048			−1.42591			−0.712955	+	0.701210i	$0.752644\pi$
$164$	−6.58477			−0.514184
$165$		0			0
$166$	−12.6862			−0.984640
$167$	9.13748			0.707080			0.353540	−	0.935419i	$-0.384978\pi$
$167$	9.13748			0.707080			0.353540	+	0.935419i	$0.384978\pi$
$168$	5.32319	−	2.94838i	0.410693	−	0.227472i
$169$	8.84639			0.680492
$170$		0			0
$171$	6.29684	+	3.94054i	0.481531	+	0.301341i
$172$			7.02655i			0.535769i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	8.11746	+	14.6558i	0.615383	+	1.11105i
$175$		0			0
$176$	−0.486823	−	3.28070i	−0.0366957	−	0.247292i
$177$	−0.704774	+	0.390356i	−0.0529740	+	0.0293409i
$178$		−	5.08617i		−	0.381224i
$179$		−	3.41562i		−	0.255295i	−0.991820	−	0.127648i	$-0.959257\pi$
$179$		−	3.41562i		−	0.255295i	0.991820	−	0.127648i	$-0.0407426\pi$
$180$		0			0
$181$	8.36581			0.621826			0.310913	−	0.950438i	$-0.399365\pi$
$181$	8.36581			0.621826			0.310913	+	0.950438i	$0.399365\pi$
$182$	−7.16019			−0.530749
$183$	14.9346	−	8.27185i	1.10399	−	0.611473i
$184$		−	4.18641i		−	0.308626i
$185$		0			0
$186$	0.992707	+	1.79230i	0.0727888	+	0.131418i
$187$	3.08797	+	20.8098i	0.225815	+	1.52176i
$188$		−	0.765721i		−	0.0558459i
$189$	0.973646	−	18.2295i	0.0708223	−	1.32600i
$190$		0			0
$191$			5.18383i			0.375089i	0.982256	+	0.187544i	$0.0600528\pi$
$191$			5.18383i			0.375089i	−0.982256	+	0.187544i	$0.939947\pi$
$192$	0.839210	+	1.51517i	0.0605648	+	0.109348i
$193$			15.5283i			1.11775i	0.829251	+	0.558877i	$0.188768\pi$
$193$			15.5283i			1.11775i	−0.829251	+	0.558877i	$0.811232\pi$
$194$	14.7080			1.05597
$195$		0			0
$196$	−5.34310			−0.381650
$197$	−27.4178			−1.95344			−0.976720	−	0.214520i	$-0.931181\pi$
$197$	−27.4178			−1.95344			−0.976720	+	0.214520i	$0.931181\pi$
$198$	−9.11786	−	3.98305i	−0.647978	−	0.283063i
$199$	−3.50329			−0.248342			−0.124171	−	0.992261i	$-0.539627\pi$
$199$	−3.50329			−0.248342			−0.124171	+	0.992261i	$0.539627\pi$
$200$		0			0
$201$	−0.817094	−	1.47524i	−0.0576333	−	0.104055i
$202$	−7.14958			−0.503043
$203$		−	33.9830i		−	2.38514i
$204$	−5.32319	−	9.61085i	−0.372698	−	0.672894i
$205$		0			0
$206$	16.6553			1.16043
$207$	−10.6464	−	6.66247i	−0.739975	−	0.463074i
$208$		−	2.03804i		−	0.141313i
$209$	−8.12323	+	1.20541i	−0.561895	+	0.0833796i
$210$		0			0
$211$		−	0.944623i		−	0.0650305i	−0.999471	−	0.0325152i	$-0.989648\pi$
$211$		−	0.944623i		−	0.0650305i	0.999471	−	0.0325152i	$-0.0103517\pi$
$212$		−	10.0832i		−	0.692514i
$213$	−10.7944	+	5.97871i	−0.739617	+	0.409654i
$214$	−7.16019			−0.489461
$215$		0			0
$216$	5.18876	+	0.277134i	0.353050	+	0.0188565i
$217$		−	4.15588i		−	0.282119i
$218$		−	7.38065i		−	0.499881i
$219$	−14.7080	+	8.14637i	−0.993875	+	0.550481i
$220$		0			0
$221$			12.9275i			0.869597i
$222$	−2.59145	−	4.67878i	−0.173927	−	0.314019i
$223$	−16.6553			−1.11532			−0.557660	−	0.830069i	$-0.688301\pi$
$223$	−16.6553			−1.11532			−0.557660	+	0.830069i	$0.688301\pi$
$224$		−	3.51327i		−	0.234741i
$225$		0			0
$226$		−	14.9877i		−	0.996970i
$227$	3.20562			0.212764			0.106382	−	0.994325i	$-0.466073\pi$
$227$	3.20562			0.212764			0.106382	+	0.994325i	$0.466073\pi$
$228$	3.75165	−	2.07794i	0.248459	−	0.137615i
$229$	−13.0520			−0.862501			−0.431251	−	0.902232i	$-0.641928\pi$
$229$	−13.0520			−0.862501			−0.431251	+	0.902232i	$0.641928\pi$
$230$		0			0
$231$	12.2642	+	16.0285i	0.806925	+	1.05460i
$232$	9.67274			0.635046
$233$	−23.8691			−1.56372			−0.781859	−	0.623456i	$-0.785728\pi$
$233$	−23.8691			−1.56372			−0.781859	+	0.623456i	$0.785728\pi$
$234$	−5.18291	−	3.24344i	−0.338817	−	0.212031i
$235$		0			0
$236$			0.465146i			0.0302785i
$237$	−1.50329	+	0.832635i	−0.0976494	+	0.0540854i
$238$			22.2851i			1.44453i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$			21.6027i			1.39155i	0.718260	+	0.695775i	$0.244939\pi$
$241$			21.6027i			1.39155i	−0.718260	+	0.695775i	$0.755061\pi$
$242$	10.5260	−	3.19424i	0.676637	−	0.205334i
$243$	8.96244	−	12.7544i	0.574941	−	0.818195i
$244$		−	9.85671i		−	0.631011i
$245$		0			0
$246$	5.52601	+	9.97702i	0.352325	+	0.636112i
$247$	−5.04632			−0.321089
$248$	1.18291			0.0751146
$249$	10.6464	+	19.2217i	0.674687	+	1.21813i
$250$		0			0
$251$		−	11.5678i		−	0.730152i	−0.930978	−	0.365076i	$-0.881043\pi$
$251$		−	11.5678i		−	0.730152i	0.930978	−	0.365076i	$-0.118957\pi$
$252$	−8.93455	−	5.59121i	−0.562824	−	0.352213i
$253$	13.7344	−	2.03804i	0.863471	−	0.128130i
$254$			2.30787i			0.144809i
$255$		0			0
$256$	1.00000			0.0625000
$257$			8.14637i			0.508157i	0.967184	+	0.254078i	$0.0817721\pi$
$257$			8.14637i			0.508157i	−0.967184	+	0.254078i	$0.918228\pi$
$258$	10.6464	−	5.89675i	0.662815	−	0.367116i
$259$			10.8489i			0.674117i
$260$		0			0
$261$	15.3937	−	24.5986i	0.952847	−	1.52261i
$262$	13.1585			0.812934
$263$	−3.54872			−0.218823			−0.109412	−	0.993997i	$-0.534897\pi$
$263$	−3.54872			−0.218823			−0.109412	+	0.993997i	$0.534897\pi$
$264$	−4.56226	+	3.49082i	−0.280788	+	0.214845i
$265$		0			0
$266$	−8.69909			−0.533376
$267$	−7.70639	+	4.26836i	−0.471623	+	0.261220i
$268$	−0.973646			−0.0594749
$269$			26.5333i			1.61776i	0.587971	+	0.808882i	$0.299927\pi$
$269$			26.5333i			1.61776i	−0.587971	+	0.808882i	$0.700073\pi$
$270$		0			0
$271$			24.1263i			1.46557i	0.680462	+	0.732784i	$0.261779\pi$
$271$			24.1263i			1.46557i	−0.680462	+	0.732784i	$0.738221\pi$
$272$	−6.34310			−0.384607
$273$	6.00891	+	10.8489i	0.363676	+	0.656604i
$274$			11.5671i			0.698791i
$275$		0			0
$276$	−6.34310	+	3.51327i	−0.381810	+	0.211474i
$277$		−	6.11412i		−	0.367362i	−0.982986	−	0.183681i	$-0.941199\pi$
$277$		−	6.11412i		−	0.367362i	0.982986	−	0.183681i	$-0.0588013\pi$
$278$			16.7456i			1.00434i
$279$	1.88254	−	3.00823i	0.112705	−	0.180098i
$280$		0			0
$281$	23.2401			1.38639			0.693193	−	0.720752i	$-0.256203\pi$
$281$	23.2401			1.38639			0.693193	+	0.720752i	$0.256203\pi$
$282$	−1.16019	+	0.642601i	−0.0690885	+	0.0382663i
$283$			12.3878i			0.736380i	0.929751	+	0.368190i	$0.120022\pi$
$283$			12.3878i			0.736380i	−0.929751	+	0.368190i	$0.879978\pi$
$284$			7.12421i			0.422744i
$285$		0			0
$286$	6.68620	−	0.992165i	0.395363	−	0.0586679i
$287$		−	23.1341i		−	1.36556i
$288$	1.59145	−	2.54308i	0.0937773	−	0.149853i
$289$	23.2349			1.36676
$290$		0			0
$291$	−12.3431	−	22.2851i	−0.723565	−	1.30637i
$292$			9.70719i			0.568070i
$293$	−7.63419			−0.445994			−0.222997	−	0.974819i	$-0.571584\pi$
$293$	−7.63419			−0.445994			−0.222997	+	0.974819i	$0.571584\pi$
$294$	4.48398	+	8.09568i	0.261511	+	0.472150i
$295$		0			0
$296$	−3.08797			−0.179484
$297$	1.61681	+	17.1577i	0.0938171	+	0.995589i
$298$	−17.7960			−1.03089
$299$	8.53206			0.493422
$300$		0			0
$301$	−24.6862			−1.42289
$302$			10.8013i			0.621547i
$303$	6.00000	+	10.8328i	0.344691	+	0.622328i
$304$		−	2.47606i		−	0.142012i
$305$		0			0
$306$	−10.0947	+	16.1310i	−0.577078	+	0.922150i
$307$		−	19.4144i		−	1.10804i	−0.832504	−	0.554019i	$-0.813094\pi$
$307$		−	19.4144i		−	1.10804i	0.832504	−	0.554019i	$-0.186906\pi$
$308$	11.5260	−	1.71034i	0.656755	−	0.0974559i
$309$	−13.9773	−	25.2355i	−0.795140	−	1.43560i
$310$		0			0
$311$			5.99860i			0.340149i	0.985431	+	0.170075i	$0.0544009\pi$
$311$			5.99860i			0.340149i	−0.985431	+	0.170075i	$0.945599\pi$
$312$	−3.08797	+	1.71034i	−0.174822	+	0.0968291i
$313$	10.0705			0.569219			0.284610	−	0.958643i	$-0.408136\pi$
$313$	10.0705			0.569219			0.284610	+	0.958643i	$0.408136\pi$
$314$	5.03526			0.284156
$315$		0			0
$316$			0.992165i			0.0558136i
$317$			13.5038i			0.758451i	0.925304	+	0.379226i	$0.123810\pi$
$317$			13.5038i			0.758451i	−0.925304	+	0.379226i	$0.876190\pi$
$318$	−15.2777	+	8.46189i	−0.856728	+	0.474519i
$319$	4.70891	+	31.7334i	0.263649	+	1.77673i
$320$		0			0
$321$	6.00891	+	10.8489i	0.335384	+	0.605525i
$322$	14.7080			0.819645
$323$			15.7059i			0.873901i
$324$	−3.93455	−	8.09440i	−0.218586	−	0.449689i
$325$		0			0
$326$	18.2048			1.00827
$327$	−11.1829	+	6.19392i	−0.618416	+	0.342524i
$328$	6.58477			0.363583
$329$	2.69019			0.148315
$330$		0			0
$331$	33.2642			1.82837			0.914183	−	0.405301i	$-0.132833\pi$
$331$	33.2642			1.82837			0.914183	+	0.405301i	$0.132833\pi$
$332$	12.6862			0.696246
$333$	−4.91436	+	7.85296i	−0.269305	+	0.430340i
$334$	−9.13748			−0.499981
$335$		0			0
$336$	−5.32319	+	2.94838i	−0.290404	+	0.160847i
$337$			11.4523i			0.623844i	0.950108	+	0.311922i	$0.100973\pi$
$337$			11.4523i			0.623844i	−0.950108	+	0.311922i	$0.899027\pi$
$338$	−8.84639			−0.481180
$339$	−22.7089	+	12.5779i	−1.23338	+	0.683136i
$340$		0			0
$341$	0.575866	+	3.88076i	0.0311849	+	0.210155i
$342$	−6.29684	−	3.94054i	−0.340494	−	0.213080i
$343$			5.82114i			0.314312i
$344$		−	7.02655i		−	0.378846i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	−1.63419			−0.0877278			−0.0438639	−	0.999038i	$-0.513967\pi$
$347$	−1.63419			−0.0877278			−0.0438639	+	0.999038i	$0.513967\pi$
$348$	−8.11746	−	14.6558i	−0.435142	−	0.785633i
$349$		−	14.2220i		−	0.761287i	−0.924722	−	0.380644i	$-0.875702\pi$
$349$		−	14.2220i		−	0.761287i	0.924722	−	0.380644i	$-0.124298\pi$
$350$		0			0
$351$	−0.564809	+	10.5749i	−0.0301473	+	0.564446i
$352$	0.486823	+	3.28070i	0.0259478	+	0.174862i
$353$			13.0985i			0.697163i	0.937279	+	0.348581i	$0.113337\pi$
$353$			13.0985i			0.697163i	−0.937279	+	0.348581i	$0.886663\pi$
$354$	0.704774	−	0.390356i	0.0374583	−	0.0207472i
$355$		0			0
$356$			5.08617i			0.269566i
$357$	33.7655	−	18.7018i	1.78706	−	0.989806i
$358$			3.41562i			0.180521i
$359$	19.3455			1.02102			0.510508	−	0.859873i	$-0.329457\pi$
$359$	19.3455			1.02102			0.510508	+	0.859873i	$0.329457\pi$
$360$		0			0
$361$	12.8691			0.677321
$362$	−8.36581			−0.439697
$363$	−13.6733	−	13.2680i	−0.717664	−	0.696390i
$364$	7.16019			0.375296
$365$		0			0
$366$	−14.9346	+	8.27185i	−0.780642	+	0.432377i
$367$	−22.8312			−1.19178			−0.595890	−	0.803066i	$-0.703201\pi$
$367$	−22.8312			−1.19178			−0.595890	+	0.803066i	$0.703201\pi$
$368$			4.18641i			0.218232i
$369$	10.4794	−	16.7456i	0.545534	−	0.871743i
$370$		0			0
$371$	35.4249			1.83917
$372$	−0.992707	−	1.79230i	−0.0514695	−	0.0929264i
$373$			14.9655i			0.774886i	0.921894	+	0.387443i	$0.126642\pi$
$373$			14.9655i			0.774886i	−0.921894	+	0.387443i	$0.873358\pi$
$374$	−3.08797	−	20.8098i	−0.159675	−	1.07605i
$375$		0			0
$376$			0.765721i			0.0394890i
$377$			19.7134i			1.01529i
$378$	−0.973646	+	18.2295i	−0.0500790	+	0.937626i
$379$	11.8464			0.608508			0.304254	−	0.952591i	$-0.401593\pi$
$379$	11.8464			0.608508			0.304254	+	0.952591i	$0.401593\pi$
$380$		0			0
$381$	3.49680	−	1.93679i	0.179147	−	0.0992246i
$382$		−	5.18383i		−	0.265228i
$383$			4.18641i			0.213915i	0.994264	+	0.106958i	$0.0341109\pi$
$383$			4.18641i			0.213915i	−0.994264	+	0.106958i	$0.965889\pi$
$384$	−0.839210	−	1.51517i	−0.0428258	−	0.0773205i
$385$		0			0
$386$		−	15.5283i		−	0.790371i
$387$	−17.8691	−	11.1824i	−0.908338	−	0.568435i
$388$	−14.7080			−0.746686
$389$			8.40413i			0.426106i	0.977041	+	0.213053i	$0.0683407\pi$
$389$			8.40413i			0.426106i	−0.977041	+	0.213053i	$0.931659\pi$
$390$		0			0
$391$		−	26.5548i		−	1.34293i
$392$	5.34310			0.269867
$393$	−11.0427	−	19.9373i	−0.557032	−	1.00570i
$394$	27.4178			1.38129
$395$		0			0
$396$	9.11786	+	3.98305i	0.458190	+	0.200156i
$397$	−9.83977			−0.493844			−0.246922	−	0.969035i	$-0.579419\pi$
$397$	−9.83977			−0.493844			−0.246922	+	0.969035i	$0.579419\pi$
$398$	3.50329			0.175604
$399$	7.30037	+	13.1806i	0.365475	+	0.659854i
$400$		0			0
$401$			24.3052i			1.21375i	0.794799	+	0.606873i	$0.207576\pi$
$401$			24.3052i			1.21375i	−0.794799	+	0.606873i	$0.792424\pi$
$402$	0.817094	+	1.47524i	0.0407529	+	0.0735780i
$403$			2.41081i			0.120091i
$404$	7.14958			0.355705
$405$		0			0
$406$			33.9830i			1.68655i
$407$	−1.50329	−	10.1307i	−0.0745155	−	0.502160i
$408$	5.32319	+	9.61085i	0.263537	+	0.475808i
$409$		−	3.42069i		−	0.169142i	−0.996417	−	0.0845710i	$-0.973048\pi$
$409$		−	3.42069i		−	0.169142i	0.996417	−	0.0845710i	$-0.0269520\pi$
$410$		0			0
$411$	17.5260	−	9.70719i	0.864494	−	0.478820i
$412$	−16.6553			−0.820547
$413$	−1.63419			−0.0804131
$414$	10.6464	+	6.66247i	0.523241	+	0.327443i
$415$		0			0
$416$			2.03804i			0.0999231i
$417$	25.3724	−	14.0531i	1.24249	−	0.688183i
$418$	8.12323	−	1.20541i	0.397320	−	0.0589583i
$419$			18.9492i			0.925731i	0.886429	+	0.462865i	$0.153179\pi$
$419$			18.9492i			0.925731i	−0.886429	+	0.462865i	$0.846821\pi$
$420$		0			0
$421$	−18.6408			−0.908496			−0.454248	−	0.890875i	$-0.650092\pi$
$421$	−18.6408			−0.908496			−0.454248	+	0.890875i	$0.650092\pi$
$422$			0.944623i			0.0459835i
$423$	1.94729	+	1.21861i	0.0946806	+	0.0592508i
$424$			10.0832i			0.489681i
$425$		0			0
$426$	10.7944	−	5.97871i	0.522988	−	0.289669i
$427$	34.6293			1.67583
$428$	7.16019			0.346101
$429$	−7.11442	−	9.29807i	−0.343487	−	0.448915i
$430$		0			0
$431$	15.1168			0.728152			0.364076	−	0.931369i	$-0.381385\pi$
$431$	15.1168			0.728152			0.364076	+	0.931369i	$0.381385\pi$
$432$	−5.18876	−	0.277134i	−0.249644	−	0.0133336i
$433$	24.3918			1.17219			0.586097	−	0.810241i	$-0.300664\pi$
$433$	24.3918			1.17219			0.586097	+	0.810241i	$0.300664\pi$
$434$			4.15588i			0.199488i
$435$		0			0
$436$			7.38065i			0.353469i
$437$	10.3658			0.495864
$438$	14.7080	−	8.14637i	0.702775	−	0.389249i
$439$		−	5.94429i		−	0.283706i	−0.989888	−	0.141853i	$-0.954694\pi$
$439$		−	5.94429i		−	0.283706i	0.989888	−	0.141853i	$-0.0453060\pi$
$440$		0			0
$441$	8.50329	−	13.5880i	0.404919	−	0.647045i
$442$		−	12.9275i		−	0.614898i
$443$		−	13.5514i		−	0.643846i	−0.946766	−	0.321923i	$-0.895671\pi$
$443$		−	13.5514i		−	0.643846i	0.946766	−	0.321923i	$-0.104329\pi$
$444$	2.59145	+	4.67878i	0.122985	+	0.222045i
$445$		0			0
$446$	16.6553			0.788651
$447$	14.9346	+	26.9638i	0.706380	+	1.27535i
$448$			3.51327i			0.165987i
$449$		−	25.3510i		−	1.19639i	−0.801351	−	0.598195i	$-0.795885\pi$
$449$		−	25.3510i		−	1.19639i	0.801351	−	0.598195i	$-0.204115\pi$
$450$		0			0
$451$	3.20562	+	21.6027i	0.150947	+	1.01723i
$452$			14.9877i			0.704964i
$453$	16.3658	−	9.06459i	0.768933	−	0.425892i
$454$	−3.20562			−0.150447
$455$		0			0
$456$	−3.75165	+	2.07794i	−0.175687	+	0.0973083i
$457$			17.9391i			0.839158i	0.907719	+	0.419579i	$0.137822\pi$
$457$			17.9391i			0.839158i	−0.907719	+	0.419579i	$0.862178\pi$
$458$	13.0520			0.609881
$459$	32.9128	+	1.75789i	1.53624	+	0.0820511i
$460$		0			0
$461$	3.83086			0.178421			0.0892105	−	0.996013i	$-0.471566\pi$
$461$	3.83086			0.178421			0.0892105	+	0.996013i	$0.471566\pi$
$462$	−12.2642	−	16.0285i	−0.570582	−	0.745712i
$463$	−0.408837			−0.0190003			−0.00950014	−	0.999955i	$-0.503024\pi$
$463$	−0.408837			−0.0190003			−0.00950014	+	0.999955i	$0.503024\pi$
$464$	−9.67274			−0.449046
$465$		0			0
$466$	23.8691			1.10572
$467$			0.813263i			0.0376333i	0.999823	+	0.0188167i	$0.00598988\pi$
$467$			0.813263i			0.0376333i	−0.999823	+	0.0188167i	$0.994010\pi$
$468$	5.18291	+	3.24344i	0.239580	+	0.149928i
$469$		−	3.42069i		−	0.157953i
$470$		0			0
$471$	−4.22564	−	7.62925i	−0.194707	−	0.351537i
$472$		−	0.465146i		−	0.0214101i
$473$	23.0520	−	3.42069i	1.05993	−	0.157283i
$474$	1.50329	−	0.832635i	0.0690486	−	0.0382442i
$475$		0			0
$476$		−	22.2851i		−	1.02143i
$477$	25.6423	+	16.0469i	1.17408	+	0.734736i
$478$		0			0
$479$	−38.6910			−1.76784			−0.883918	−	0.467643i	$-0.845103\pi$
$479$	−38.6910			−1.76784			−0.883918	+	0.467643i	$0.845103\pi$
$480$		0			0
$481$		−	6.29340i		−	0.286954i
$482$		−	21.6027i		−	0.983975i
$483$	−12.3431	−	22.2851i	−0.561631	−	1.01401i
$484$	−10.5260	+	3.19424i	−0.478455	+	0.145193i
$485$		0			0
$486$	−8.96244	+	12.7544i	−0.406544	+	0.578551i
$487$	−14.7080			−0.666483			−0.333242	−	0.942841i	$-0.608142\pi$
$487$	−14.7080			−0.666483			−0.333242	+	0.942841i	$0.608142\pi$
$488$			9.85671i			0.446192i
$489$	−15.2777	−	27.5833i	−0.690879	−	1.24736i
$490$		0			0
$491$	3.83086			0.172884			0.0864422	−	0.996257i	$-0.472450\pi$
$491$	3.83086			0.172884			0.0864422	+	0.996257i	$0.472450\pi$
$492$	−5.52601	−	9.97702i	−0.249132	−	0.449799i
$493$	61.3552			2.76330
$494$	5.04632			0.227045
$495$		0			0
$496$	−1.18291			−0.0531141
$497$	−25.0293			−1.12272
$498$	−10.6464	−	19.2217i	−0.477076	−	0.861345i
$499$	−38.2122			−1.71061			−0.855307	−	0.518122i	$-0.826631\pi$
$499$	−38.2122			−1.71061			−0.855307	+	0.518122i	$0.826631\pi$
$500$		0			0
$501$	7.66827	+	13.8448i	0.342593	+	0.618540i
$502$			11.5678i			0.516295i
$503$	26.3204			1.17357			0.586784	−	0.809743i	$-0.300394\pi$
$503$	26.3204			1.17357			0.586784	+	0.809743i	$0.300394\pi$
$504$	8.93455	+	5.59121i	0.397977	+	0.249052i
$505$		0			0
$506$	−13.7344	+	2.03804i	−0.610566	+	0.0906019i
$507$	7.42398	+	13.4038i	0.329711	+	0.595281i
$508$		−	2.30787i		−	0.102395i
$509$			30.7690i			1.36381i	0.731440	+	0.681905i	$0.238848\pi$
$509$			30.7690i			1.36381i	−0.731440	+	0.681905i	$0.761152\pi$
$510$		0			0
$511$	−34.1040			−1.50867
$512$	−1.00000			−0.0441942
$513$	−0.686200	+	12.8477i	−0.0302965	+	0.567240i
$514$		−	8.14637i		−	0.359321i
$515$		0			0
$516$	−10.6464	+	5.89675i	−0.468681	+	0.259590i
$517$	−2.51210	+	0.372771i	−0.110482	+	0.0163944i
$518$		−	10.8489i		−	0.476672i
$519$	5.03526	+	9.09099i	0.221023	+	0.399050i
$520$		0			0
$521$		−	10.3677i		−	0.454215i	−0.973870	−	0.227108i	$-0.927073\pi$
$521$		−	10.3677i		−	0.454215i	0.973870	−	0.227108i	$-0.0729269\pi$
$522$	−15.3937	+	24.5986i	−0.673765	+	1.07665i
$523$		−	34.5931i		−	1.51265i	−0.654196	−	0.756325i	$-0.726993\pi$
$523$		−	34.5931i		−	1.51265i	0.654196	−	0.756325i	$-0.273007\pi$
$524$	−13.1585			−0.574831
$525$		0			0
$526$	3.54872			0.154732
$527$	7.50329			0.326849
$528$	4.56226	−	3.49082i	0.198547	−	0.151918i
$529$	5.47399			0.238000
$530$		0			0
$531$	−1.18291	−	0.740259i	−0.0513338	−	0.0321245i
$532$	8.69909			0.377154
$533$			13.4200i			0.581286i
$534$	7.70639	−	4.26836i	0.333488	−	0.184710i
$535$		0			0
$536$	0.973646			0.0420551
$537$	5.17522	−	2.86642i	0.223327	−	0.123695i
$538$		−	26.5333i		−	1.14393i
$539$	2.60114	+	17.5291i	0.112039	+	0.755033i
$540$		0			0
$541$		−	36.5066i		−	1.56954i	−0.619786	−	0.784771i	$-0.712781\pi$
$541$		−	36.5066i		−	1.56954i	0.619786	−	0.784771i	$-0.287219\pi$
$542$		−	24.1263i		−	1.03631i
$543$	7.02067	+	12.6756i	0.301286	+	0.543962i
$544$	6.34310			0.271958
$545$		0			0
$546$	−6.00891	−	10.8489i	−0.257157	−	0.464289i
$547$			2.95047i			0.126153i	0.998009	+	0.0630765i	$0.0200912\pi$
$547$			2.95047i			0.126153i	−0.998009	+	0.0630765i	$0.979909\pi$
$548$		−	11.5671i		−	0.494120i
$549$	25.0665	+	15.6865i	1.06981	+	0.669483i
$550$		0			0
$551$			23.9503i			1.02032i
$552$	6.34310	−	3.51327i	0.269980	−	0.149535i
$553$	−3.48575			−0.148229
$554$			6.11412i			0.259764i
$555$		0			0
$556$		−	16.7456i		−	0.710173i
$557$	5.05201			0.214061			0.107030	−	0.994256i	$-0.465866\pi$
$557$	5.05201			0.214061			0.107030	+	0.994256i	$0.465866\pi$
$558$	−1.88254	+	3.00823i	−0.0796943	+	0.127349i
$559$	14.3204			0.605688
$560$		0			0
$561$	−28.9389	+	22.1426i	−1.22180	+	0.934861i
$562$	−23.2401			−0.980323
$563$	7.84639			0.330686			0.165343	−	0.986236i	$-0.447127\pi$
$563$	7.84639			0.330686			0.165343	+	0.986236i	$0.447127\pi$
$564$	1.16019	−	0.642601i	0.0488530	−	0.0270584i
$565$		0			0
$566$		−	12.3878i		−	0.520699i
$567$	28.4378	−	13.8232i	1.19428	−	0.580518i
$568$		−	7.12421i		−	0.298925i
$569$	8.12323			0.340543			0.170272	−	0.985397i	$-0.445535\pi$
$569$	8.12323			0.340543			0.170272	+	0.985397i	$0.445535\pi$
$570$		0			0
$571$			27.0465i			1.13186i	0.824453	+	0.565931i	$0.191483\pi$
$571$			27.0465i			1.13186i	−0.824453	+	0.565931i	$0.808517\pi$
$572$	−6.68620	+	0.992165i	−0.279564	+	0.0414845i
$573$	−7.85436	+	4.35032i	−0.328120	+	0.181737i
$574$			23.1341i			0.965599i
$575$		0			0
$576$	−1.59145	+	2.54308i	−0.0663106	+	0.105962i
$577$	33.7194			1.40376			0.701879	−	0.712296i	$-0.252345\pi$
$577$	33.7194			1.40376			0.701879	+	0.712296i	$0.252345\pi$
$578$	−23.2349			−0.966445
$579$	−23.5280	+	13.0315i	−0.977790	+	0.541572i
$580$		0			0
$581$			44.5701i			1.84908i
$582$	12.3431	+	22.2851i	0.511638	+	0.923745i
$583$	−33.0798	+	4.90871i	−1.37003	+	0.203298i
$584$		−	9.70719i		−	0.401686i
$585$		0			0
$586$	7.63419			0.315365
$587$			24.3052i			1.00318i	0.865105	+	0.501591i	$0.167252\pi$
$587$			24.3052i			1.00318i	−0.865105	+	0.501591i	$0.832748\pi$
$588$	−4.48398	−	8.09568i	−0.184916	−	0.333860i
$589$			2.92895i			0.120685i
$590$		0			0
$591$	−23.0093	−	41.5425i	−0.946477	−	1.70883i
$592$	3.08797			0.126915
$593$	−2.79438			−0.114751			−0.0573757	−	0.998353i	$-0.518273\pi$
$593$	−2.79438			−0.114751			−0.0573757	+	0.998353i	$0.518273\pi$
$594$	−1.61681	−	17.1577i	−0.0663387	−	0.703988i
$595$		0			0
$596$	17.7960			0.728951
$597$	−2.94000	−	5.30807i	−0.120326	−	0.217245i
$598$	−8.53206			−0.348902
$599$			7.66387i			0.313137i	0.987667	+	0.156569i	$0.0500432\pi$
$599$			7.66387i			0.313137i	−0.987667	+	0.156569i	$0.949957\pi$
$600$		0			0
$601$			34.9276i			1.42473i	0.701811	+	0.712364i	$0.252375\pi$
$601$			34.9276i			1.42473i	−0.701811	+	0.712364i	$0.747625\pi$
$602$	24.6862			1.00613
$603$	1.54951	−	2.47606i	0.0631010	−	0.100833i
$604$		−	10.8013i		−	0.439500i
$605$		0			0
$606$	−6.00000	−	10.8328i	−0.243733	−	0.440052i
$607$			3.51327i			0.142599i	0.997455	+	0.0712997i	$0.0227147\pi$
$607$			3.51327i			0.142599i	−0.997455	+	0.0712997i	$0.977285\pi$
$608$			2.47606i			0.100418i
$609$	51.4899	−	28.5189i	2.08647	−	1.15564i
$610$		0			0
$611$	−1.56057			−0.0631339
$612$	10.0947	−	16.1310i	0.408056	−	0.652059i
$613$			17.2167i			0.695378i	0.937610	+	0.347689i	$0.113033\pi$
$613$			17.2167i			0.695378i	−0.937610	+	0.347689i	$0.886967\pi$
$614$			19.4144i			0.783501i
$615$		0			0
$616$	−11.5260	+	1.71034i	−0.464396	+	0.0689117i
$617$		−	24.8920i		−	1.00211i	−0.865414	−	0.501057i	$-0.832945\pi$
$617$		−	24.8920i		−	1.00211i	0.865414	−	0.501057i	$-0.167055\pi$
$618$	13.9773	+	25.2355i	0.562249	+	1.01512i
$619$	−30.0586			−1.20816			−0.604079	−	0.796925i	$-0.706459\pi$
$619$	−30.0586			−1.20816			−0.604079	+	0.796925i	$0.706459\pi$
$620$		0			0
$621$	1.16019	−	21.7222i	0.0465570	−	0.871684i
$622$		−	5.99860i		−	0.240522i
$623$	−17.8691			−0.715911
$624$	3.08797	−	1.71034i	0.123618	−	0.0684685i
$625$		0			0
$626$	−10.0705			−0.402499
$627$	−8.64348	−	11.2964i	−0.345187	−	0.451137i
$628$	−5.03526			−0.200929
$629$	−19.5873			−0.780996
$630$		0			0
$631$	−21.1829			−0.843278			−0.421639	−	0.906764i	$-0.638545\pi$
$631$	−21.1829			−0.843278			−0.421639	+	0.906764i	$0.638545\pi$
$632$		−	0.992165i		−	0.0394662i
$633$	1.43126	−	0.792737i	0.0568875	−	0.0315085i
$634$		−	13.5038i		−	0.536306i
$635$		0			0
$636$	15.2777	−	8.46189i	0.605798	−	0.335536i
$637$			10.8895i			0.431456i
$638$	−4.70891	−	31.7334i	−0.186428	−	1.25634i
$639$	−18.1175	−	11.3378i	−0.716716	−	0.448518i
$640$		0			0
$641$			31.9177i			1.26067i	0.776321	+	0.630337i	$0.217083\pi$
$641$			31.9177i			1.26067i	−0.776321	+	0.630337i	$0.782917\pi$
$642$	−6.00891	−	10.8489i	−0.237153	−	0.428171i
$643$	−7.72545			−0.304662			−0.152331	−	0.988330i	$-0.548678\pi$
$643$	−7.72545			−0.304662			−0.152331	+	0.988330i	$0.548678\pi$
$644$	−14.7080			−0.579576
$645$		0			0
$646$		−	15.7059i		−	0.617941i
$647$			18.9477i			0.744911i	0.928050	+	0.372456i	$0.121484\pi$
$647$			18.9477i			0.744911i	−0.928050	+	0.372456i	$0.878516\pi$
$648$	3.93455	+	8.09440i	0.154564	+	0.317978i
$649$	1.52601	−	0.226444i	0.0599010	−	0.00888870i
$650$		0			0
$651$	6.29684	−	3.48765i	0.246793	−	0.136692i
$652$	−18.2048			−0.712955
$653$			33.6702i			1.31762i	0.752311	+	0.658808i	$0.228939\pi$
$653$			33.6702i			1.31762i	−0.752311	+	0.658808i	$0.771061\pi$
$654$	11.1829	−	6.19392i	0.437286	−	0.242201i
$655$		0			0
$656$	−6.58477			−0.257092
$657$	−24.6862	−	15.4485i	−0.963100	−	0.602705i
$658$	−2.69019			−0.104874
$659$	−17.7960			−0.693232			−0.346616	−	0.938007i	$-0.612669\pi$
$659$	−17.7960			−0.693232			−0.346616	+	0.938007i	$0.612669\pi$
$660$		0			0
$661$	−30.4698			−1.18514			−0.592570	−	0.805519i	$-0.701887\pi$
$661$	−30.4698			−1.18514			−0.592570	+	0.805519i	$0.701887\pi$
$662$	−33.2642			−1.29285
$663$	−19.5873	+	10.8489i	−0.760707	+	0.421336i
$664$	−12.6862			−0.492320
$665$		0			0
$666$	4.91436	−	7.85296i	0.190427	−	0.304296i
$667$		−	40.4940i		−	1.56794i
$668$	9.13748			0.353540
$669$	−13.9773	−	25.2355i	−0.540393	−	0.975662i
$670$		0			0
$671$	−32.3369	+	4.79848i	−1.24835	+	0.185243i
$672$	5.32319	−	2.94838i	0.205347	−	0.113736i
$673$			15.5283i			0.598573i	0.954163	+	0.299287i	$0.0967487\pi$
$673$			15.5283i			0.598573i	−0.954163	+	0.299287i	$0.903251\pi$
$674$		−	11.4523i		−	0.441124i
$675$		0			0
$676$	8.84639			0.340246
$677$	18.4244			0.708108			0.354054	−	0.935225i	$-0.384803\pi$
$677$	18.4244			0.708108			0.354054	+	0.935225i	$0.384803\pi$
$678$	22.7089	−	12.5779i	0.872131	−	0.483050i
$679$		−	51.6732i		−	1.98304i
$680$		0			0
$681$	2.69019	+	4.85704i	0.103088	+	0.186122i
$682$	−0.575866	−	3.88076i	−0.0220511	−	0.148602i
$683$		−	5.67031i		−	0.216968i	−0.994098	−	0.108484i	$-0.965400\pi$
$683$		−	5.67031i		−	0.216968i	0.994098	−	0.108484i	$-0.0345997\pi$
$684$	6.29684	+	3.94054i	0.240766	+	0.150670i
$685$		0			0
$686$		−	5.82114i		−	0.222252i
$687$	−10.9534	−	19.7760i	−0.417898	−	0.754500i
$688$			7.02655i			0.267885i
$689$	−20.5499			−0.782888
$690$		0			0
$691$	8.94799			0.340397			0.170199	−	0.985410i	$-0.445559\pi$
$691$	8.94799			0.340397			0.170199	+	0.985410i	$0.445559\pi$
$692$	6.00000			0.228086
$693$	−13.9936	+	32.0335i	−0.531571	+	1.21685i
$694$	1.63419			0.0620329
$695$		0			0
$696$	8.11746	+	14.6558i	0.307692	+	0.555527i
$697$	41.7679			1.58207
$698$			14.2220i			0.538312i
$699$	−20.0312	−	36.1656i	−0.757649	−	1.36791i
$700$		0			0
$701$	2.34507			0.0885722			0.0442861	−	0.999019i	$-0.485899\pi$
$701$	2.34507			0.0885722			0.0442861	+	0.999019i	$0.485899\pi$
$702$	0.564809	−	10.5749i	0.0213173	−	0.399124i
$703$		−	7.64601i		−	0.288375i
$704$	−0.486823	−	3.28070i	−0.0183478	−	0.123646i
$705$		0			0
$706$		−	13.0985i		−	0.492969i
$707$			25.1184i			0.944676i
$708$	−0.704774	+	0.390356i	−0.0264870	+	0.0146705i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$	−2.52316	−	1.57898i	−0.0946258	−	0.0592165i
$712$		−	5.08617i		−	0.190612i
$713$		−	4.95213i		−	0.185459i
$714$	−33.7655	+	18.7018i	−1.26364	+	0.699899i
$715$		0			0
$716$		−	3.41562i		−	0.127648i
$717$		0			0
$718$	−19.3455			−0.721967
$719$		−	22.1076i		−	0.824474i	−0.911077	−	0.412237i	$-0.864748\pi$
$719$		−	22.1076i		−	0.824474i	0.911077	−	0.412237i	$-0.135252\pi$
$720$		0			0
$721$		−	58.5146i		−	2.17920i
$722$	−12.8691			−0.478939
$723$	−32.7316	+	18.1292i	−1.21730	+	0.674231i
$724$	8.36581			0.310913
$725$		0			0
$726$	13.6733	+	13.2680i	0.507465	+	0.492422i
$727$	20.8839			0.774542			0.387271	−	0.921966i	$-0.373418\pi$
$727$	20.8839			0.774542			0.387271	+	0.921966i	$0.373418\pi$
$728$	−7.16019			−0.265374
$729$	26.8464	+	2.87596i	0.994311	+	0.106517i
$730$		0			0
$731$		−	44.5701i		−	1.64849i
$732$	14.9346	−	8.27185i	0.551997	−	0.305736i
$733$		−	20.1672i		−	0.744893i	−0.928054	−	0.372447i	$-0.878519\pi$
$733$		−	20.1672i		−	0.744893i	0.928054	−	0.372447i	$-0.121481\pi$
$734$	22.8312			0.842716
$735$		0			0
$736$		−	4.18641i		−	0.154313i
$737$	0.473993	+	3.19424i	0.0174598	+	0.117661i
$738$	−10.4794	+	16.7456i	−0.385750	+	0.616415i
$739$			31.5069i			1.15900i	0.814972	+	0.579501i	$0.196752\pi$
$739$			31.5069i			1.15900i	−0.814972	+	0.579501i	$0.803248\pi$
$740$		0			0
$741$	−4.23492	−	7.64601i	−0.155574	−	0.280883i
$742$	−35.4249			−1.30049
$743$	−53.6073			−1.96666			−0.983331	−	0.181825i	$-0.941800\pi$
$743$	−53.6073			−1.96666			−0.983331	+	0.181825i	$0.941800\pi$
$744$	0.992707	+	1.79230i	0.0363944	+	0.0657089i
$745$		0			0
$746$		−	14.9655i		−	0.547927i
$747$	−20.1895	+	32.2621i	−0.738695	+	1.18041i
$748$	3.08797	+	20.8098i	0.112907	+	0.760882i
$749$			25.1557i			0.919170i
$750$		0			0
$751$	28.8757			1.05369			0.526845	−	0.849962i	$-0.323375\pi$
$751$	28.8757			1.05369			0.526845	+	0.849962i	$0.323375\pi$
$752$		−	0.765721i		−	0.0279230i
$753$	17.5271	−	9.70779i	0.638723	−	0.353772i
$754$		−	19.7134i		−	0.717921i
$755$		0			0
$756$	0.973646	−	18.2295i	0.0354112	−	0.663002i
$757$	−37.3085			−1.35600			−0.678000	−	0.735062i	$-0.737153\pi$
$757$	−37.3085			−1.35600			−0.678000	+	0.735062i	$0.737153\pi$
$758$	−11.8464			−0.430280
$759$	14.6140	+	19.0995i	0.530454	+	0.693267i
$760$		0			0
$761$	−33.3106			−1.20751			−0.603754	−	0.797171i	$-0.706329\pi$
$761$	−33.3106			−1.20751			−0.603754	+	0.797171i	$0.706329\pi$
$762$	−3.49680	+	1.93679i	−0.126676	+	0.0701624i
$763$	−25.9303			−0.938738
$764$			5.18383i			0.187544i
$765$		0			0
$766$		−	4.18641i		−	0.151261i
$767$	0.947987			0.0342298
$768$	0.839210	+	1.51517i	0.0302824	+	0.0546738i
$769$			27.0077i			0.973922i	0.873424	+	0.486961i	$0.161895\pi$
$769$			27.0077i			0.973922i	−0.873424	+	0.486961i	$0.838105\pi$
$770$		0			0
$771$	−12.3431	+	6.83652i	−0.444526	+	0.246211i
$772$			15.5283i			0.558877i
$773$		−	3.69467i		−	0.132888i	−0.997790	−	0.0664441i	$-0.978835\pi$
$773$		−	3.69467i		−	0.132888i	0.997790	−	0.0664441i	$-0.0211654\pi$
$774$	17.8691	+	11.1824i	0.642292	+	0.401944i
$775$		0			0
$776$	14.7080			0.527986
$777$	−16.4378	+	9.10449i	−0.589704	+	0.326622i
$778$		−	8.40413i		−	0.301303i
$779$			16.3043i			0.584163i
$780$		0			0
$781$	23.3724	−	3.46823i	0.836330	−	0.124103i
$782$			26.5548i			0.949598i
$783$	50.1895	+	2.68064i	1.79363	+	0.0957983i
$784$	−5.34310			−0.190825
$785$		0			0
$786$	11.0427	+	19.9373i	0.393881	+	0.711139i
$787$			38.0832i			1.35752i	0.734360	+	0.678760i	$0.237482\pi$
$787$			38.0832i			1.35752i	−0.734360	+	0.678760i	$0.762518\pi$
$788$	−27.4178			−0.976720
$789$	−2.97812	−	5.37690i	−0.106024	−	0.191423i
$790$		0			0
$791$	−52.6561			−1.87223
$792$	−9.11786	−	3.98305i	−0.323989	−	0.141532i
$793$	−20.0884			−0.713359
$794$	9.83977			0.349200
$795$		0			0
$796$	−3.50329			−0.124171
$797$		−	15.4319i		−	0.546627i	−0.961925	−	0.273314i	$-0.911880\pi$
$797$		−	15.4319i		−	0.546627i	0.961925	−	0.273314i	$-0.0881197\pi$
$798$	−7.30037	−	13.1806i	−0.258430	−	0.466587i
$799$			4.85704i			0.171830i
$800$		0			0
$801$	−12.9346	−	8.09440i	−0.457020	−	0.286002i
$802$		−	24.3052i		−	0.858248i
$803$	31.8464	−	4.72568i	1.12383	−	0.166766i
$804$	−0.817094	−	1.47524i	−0.0288167	−	0.0520275i
$805$		0			0
$806$		−	2.41081i		−	0.0849172i
$807$	−40.2024	+	22.2670i	−1.41519	+	0.783836i
$808$	−7.14958			−0.251521
$809$	32.9239			1.15754			0.578771	−	0.815490i	$-0.303533\pi$
$809$	32.9239			1.15754			0.578771	+	0.815490i	$0.303533\pi$
$810$		0			0
$811$		−	46.7600i		−	1.64196i	−0.570954	−	0.820982i	$-0.693426\pi$
$811$		−	46.7600i		−	1.64196i	0.570954	−	0.820982i	$-0.306574\pi$
$812$		−	33.9830i		−	1.19257i
$813$	−36.5553	+	20.2470i	−1.28205	+	0.710094i
$814$	1.50329	+	10.1307i	0.0526904	+	0.355081i
$815$		0			0
$816$	−5.32319	−	9.61085i	−0.186349	−	0.336447i
$817$	17.3982			0.608686
$818$			3.42069i			0.119602i
$819$	−11.3951	+	18.2090i	−0.398177	+	0.636273i
$820$		0			0
$821$	−36.5656			−1.27615			−0.638074	−	0.769975i	$-0.720269\pi$
$821$	−36.5656			−1.27615			−0.638074	+	0.769975i	$0.720269\pi$
$822$	−17.5260	+	9.70719i	−0.611290	+	0.338577i
$823$	−24.7785			−0.863725			−0.431862	−	0.901939i	$-0.642143\pi$
$823$	−24.7785			−0.863725			−0.431862	+	0.901939i	$0.642143\pi$
$824$	16.6553			0.580215
$825$		0			0
$826$	1.63419			0.0568606
$827$	−5.58876			−0.194340			−0.0971701	−	0.995268i	$-0.530979\pi$
$827$	−5.58876			−0.194340			−0.0971701	+	0.995268i	$0.530979\pi$
$828$	−10.6464	−	6.66247i	−0.369987	−	0.231537i
$829$	−29.0974			−1.01060			−0.505298	−	0.862945i	$-0.668617\pi$
$829$	−29.0974			−1.01060			−0.505298	+	0.862945i	$0.668617\pi$
$830$		0			0
$831$	9.26390	−	5.13103i	0.321361	−	0.177993i
$832$		−	2.03804i		−	0.0706563i
$833$	33.8918			1.17428
$834$	−25.3724	+	14.0531i	−0.878574	+	0.486619i
$835$		0			0
$836$	−8.12323	+	1.20541i	−0.280948	+	0.0416898i
$837$	6.13781	+	0.327823i	0.212154	+	0.0113312i
$838$		−	18.9492i		−	0.654590i
$839$		−	33.6449i		−	1.16155i	−0.814063	−	0.580776i	$-0.802749\pi$
$839$		−	33.6449i		−	1.16155i	0.814063	−	0.580776i	$-0.197251\pi$
$840$		0			0
$841$	64.5619			2.22627
$842$	18.6408			0.642404
$843$	19.5033	+	35.2125i	0.671729	+	1.21278i
$844$		−	0.944623i		−	0.0325152i
$845$		0			0
$846$	−1.94729	−	1.21861i	−0.0669493	−	0.0418966i
$847$	−11.2223	−	36.9808i	−0.385601	−	1.27067i
$848$		−	10.0832i		−	0.346257i
$849$	−18.7696	+	10.3960i	−0.644171	+	0.356789i
$850$		0			0
$851$			12.9275i			0.443149i
$852$	−10.7944	+	5.97871i	−0.369808	+	0.204827i
$853$		−	41.4065i		−	1.41773i	−0.705344	−	0.708865i	$-0.749207\pi$
$853$		−	41.4065i		−	1.41773i	0.705344	−	0.708865i	$-0.250793\pi$
$854$	−34.6293			−1.18499
$855$		0			0
$856$	−7.16019			−0.244730
$857$	30.9665			1.05780			0.528899	−	0.848685i	$-0.322605\pi$
$857$	30.9665			1.05780			0.528899	+	0.848685i	$0.322605\pi$
$858$	7.11442	+	9.29807i	0.242882	+	0.317431i
$859$	34.2576			1.16886			0.584428	−	0.811446i	$-0.301319\pi$
$859$	34.2576			1.16886			0.584428	+	0.811446i	$0.301319\pi$
$860$		0			0
$861$	35.0520	−	19.4144i	1.19457	−	0.661640i
$862$	−15.1168			−0.514882
$863$		−	57.3911i		−	1.95362i	−0.214118	−	0.976808i	$-0.568688\pi$
$863$		−	57.3911i		−	1.95362i	0.214118	−	0.976808i	$-0.431312\pi$
$864$	5.18876	+	0.277134i	0.176525	+	0.00942827i
$865$		0			0
$866$	−24.3918			−0.828867
$867$	19.4990	+	35.2047i	0.662220	+	1.19562i
$868$		−	4.15588i		−	0.141060i
$869$	3.25500	−	0.483009i	0.110418	−	0.0163849i
$870$		0			0
$871$			1.98433i			0.0672364i
$872$		−	7.38065i		−	0.249940i
$873$	23.4071	−	37.4037i	0.792210	−	1.26592i
$874$	−10.3658			−0.350629
$875$		0			0
$876$	−14.7080	+	8.14637i	−0.496937	+	0.275240i
$877$			6.65378i			0.224682i	0.993670	+	0.112341i	$0.0358349\pi$
$877$			6.65378i			0.224682i	−0.993670	+	0.112341i	$0.964165\pi$
$878$			5.94429i			0.200610i
$879$	−6.40669	−	11.5671i	−0.216092	−	0.390147i
$880$		0			0
$881$		−	47.1299i		−	1.58785i	−0.608017	−	0.793924i	$-0.708035\pi$
$881$		−	47.1299i		−	1.58785i	0.608017	−	0.793924i	$-0.291965\pi$
$882$	−8.50329	+	13.5880i	−0.286321	+	0.457530i
$883$	27.8665			0.937782			0.468891	−	0.883256i	$-0.344654\pi$
$883$	27.8665			0.937782			0.468891	+	0.883256i	$0.344654\pi$
$884$			12.9275i			0.434799i
$885$		0			0
$886$			13.5514i			0.455268i
$887$	−43.7836			−1.47011			−0.735055	−	0.678007i	$-0.762844\pi$
$887$	−43.7836			−1.47011			−0.735055	+	0.678007i	$0.762844\pi$
$888$	−2.59145	−	4.67878i	−0.0869635	−	0.157010i
$889$	8.10818			0.271940
$890$		0			0
$891$	−24.6399	+	16.8486i	−0.825467	+	0.564451i
$892$	−16.6553			−0.557660
$893$	−1.89597			−0.0634463
$894$	−14.9346	−	26.9638i	−0.499486	−	0.901806i
$895$		0			0
$896$		−	3.51327i		−	0.117370i
$897$	7.16019	+	12.9275i	0.239072	+	0.431636i
$898$			25.3510i			0.845975i
$899$	11.4419			0.381610
$900$		0			0
$901$			63.9585i			2.13077i
$902$	−3.20562	−	21.6027i	−0.106735	−	0.719290i
$903$	−20.7169	−	37.4037i	−0.689415	−	1.24472i
$904$		−	14.9877i		−	0.498485i
$905$		0			0
$906$	−16.3658	+	9.06459i	−0.543718	+	0.301151i
$907$	41.0360			1.36258			0.681290	−	0.732014i	$-0.261419\pi$
$907$	41.0360			1.36258			0.681290	+	0.732014i	$0.261419\pi$
$908$	3.20562			0.106382
$909$	−11.3782	+	18.1820i	−0.377392	+	0.603058i
$910$		0			0
$911$		−	11.3599i		−	0.376370i	−0.982134	−	0.188185i	$-0.939740\pi$
$911$		−	11.3599i		−	0.376370i	0.982134	−	0.188185i	$-0.0602604\pi$
$912$	3.75165	−	2.07794i	0.124229	−	0.0688074i
$913$	−6.17594	−	41.6196i	−0.204394	−	1.37741i
$914$		−	17.9391i		−	0.593374i
$915$		0			0
$916$	−13.0520			−0.431251
$917$		−	46.2294i		−	1.52663i
$918$	−32.9128	−	1.75789i	−1.08628	−	0.0580189i
$919$		−	20.6105i		−	0.679878i	−0.940447	−	0.339939i	$-0.889594\pi$
$919$		−	20.6105i		−	0.679878i	0.940447	−	0.339939i	$-0.110406\pi$
$920$		0			0
$921$	29.4160	−	16.2927i	0.969290	−	0.536864i
$922$	−3.83086			−0.126163
$923$	14.5194			0.477912
$924$	12.2642	+	16.0285i	0.403462	+	0.527298i
$925$		0			0
$926$	0.408837			0.0134352
$927$	26.5061	−	42.3558i	0.870575	−	1.39115i
$928$	9.67274			0.317523
$929$		−	37.8081i		−	1.24044i	−0.784426	−	0.620222i	$-0.787043\pi$
$929$		−	37.8081i		−	1.24044i	0.784426	−	0.620222i	$-0.212957\pi$
$930$		0			0
$931$			13.2299i			0.433591i
$932$	−23.8691			−0.781859
$933$	−9.08887	+	5.03408i	−0.297556	+	0.164809i
$934$		−	0.813263i		−	0.0266108i
$935$		0			0
$936$	−5.18291	−	3.24344i	−0.169409	−	0.106015i
$937$		−	10.2468i		−	0.334750i	−0.985893	−	0.167375i	$-0.946471\pi$
$937$		−	10.2468i		−	0.334750i	0.985893	−	0.167375i	$-0.0535291\pi$
$938$			3.42069i			0.111689i
$939$	8.45128	+	15.2585i	0.275797	+	0.497942i
$940$		0			0
$941$	0.731838			0.0238572			0.0119286	−	0.999929i	$-0.496203\pi$
$941$	0.731838			0.0238572			0.0119286	+	0.999929i	$0.496203\pi$
$942$	4.22564	+	7.62925i	0.137679	+	0.248574i
$943$		−	27.5665i		−	0.897690i
$944$			0.465146i			0.0151392i
$945$		0			0
$946$	−23.0520	+	3.42069i	−0.749486	+	0.111216i
$947$		−	27.7259i		−	0.900970i	−0.892784	−	0.450485i	$-0.851251\pi$
$947$		−	27.7259i		−	0.900970i	0.892784	−	0.450485i	$-0.148749\pi$
$948$	−1.50329	+	0.832635i	−0.0488247	+	0.0270427i
$949$	19.7836			0.642204
$950$		0			0
$951$	−20.4606	+	11.3326i	−0.663479	+	0.367483i
$952$			22.2851i			0.722263i
$953$	−10.4967			−0.340022			−0.170011	−	0.985442i	$-0.554380\pi$
$953$	−10.4967			−0.340022			−0.170011	+	0.985442i	$0.554380\pi$
$954$	−25.6423	−	16.0469i	−0.830201	−	0.519537i
$955$		0			0
$956$		0			0
$957$	−44.1295	+	33.7657i	−1.42651	+	1.09149i
$958$	38.6910			1.25005
$959$	40.6383			1.31228
$960$		0			0
$961$	−29.6007			−0.954862
$962$			6.29340i			0.202907i
$963$	−11.3951	+	18.2090i	−0.367202	+	0.586776i
$964$			21.6027i			0.695775i
$965$		0			0
$966$	12.3431	+	22.2851i	0.397133	+	0.717010i
$967$			51.6198i			1.65998i	0.557778	+	0.829990i	$0.311654\pi$
$967$			51.6198i			1.65998i	−0.557778	+	0.829990i	$0.688346\pi$
$968$	10.5260	−	3.19424i	0.338319	−	0.102667i
$969$	−23.7971	+	13.1806i	−0.764472	+	0.423421i
$970$		0			0
$971$		−	5.43579i		−	0.174443i	−0.996189	−	0.0872215i	$-0.972201\pi$
$971$		−	5.43579i		−	0.174443i	0.996189	−	0.0872215i	$-0.0277988\pi$
$972$	8.96244	−	12.7544i	0.287470	−	0.409098i
$973$	58.8320			1.88607
$974$	14.7080			0.471275
$975$		0			0
$976$		−	9.85671i		−	0.315506i
$977$			29.7490i			0.951756i	0.879511	+	0.475878i	$0.157870\pi$
$977$			29.7490i			0.951756i	−0.879511	+	0.475878i	$0.842130\pi$
$978$	15.2777	+	27.5833i	0.488525	+	0.882016i
$979$	16.6862	−	2.47606i	0.533293	−	0.0791354i
$980$		0			0
$981$	−18.7696	−	11.7460i	−0.599268	−	0.375020i
$982$	−3.83086			−0.122248
$983$		−	17.9642i		−	0.572970i	−0.958085	−	0.286485i	$-0.907513\pi$
$983$		−	17.9642i		−	0.572970i	0.958085	−	0.286485i	$-0.0924869\pi$
$984$	5.52601	+	9.97702i	0.176163	+	0.318056i
$985$		0			0
$986$	−61.3552			−1.95395
$987$	2.25763	+	4.07608i	0.0718612	+	0.129743i
$988$	−5.04632			−0.160545
$989$	−29.4160			−0.935374
$990$		0			0
$991$	−11.6928			−0.371434			−0.185717	−	0.982603i	$-0.559461\pi$
$991$	−11.6928			−0.371434			−0.185717	+	0.982603i	$0.559461\pi$
$992$	1.18291			0.0375573
$993$	27.9157	+	50.4008i	0.885877	+	1.59942i
$994$	25.0293			0.793881
$995$		0			0
$996$	10.6464	+	19.2217i	0.337344	+	0.609063i
$997$		−	11.4754i		−	0.363430i	−0.983351	−	0.181715i	$-0.941835\pi$
$997$		−	11.4754i		−	0.363430i	0.983351	−	0.181715i	$-0.0581648\pi$
$998$	38.2122			1.20959
$999$	−16.0227	−	0.855779i	−0.506936	−	0.0270757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.d.i.1451.10		12
3.2	odd	2		1650.2.d.j.1451.9		12
5.2	odd	4		330.2.f.a.329.9	yes	24
5.3	odd	4		330.2.f.a.329.16	yes	24
5.4	even	2		1650.2.d.j.1451.3		12
11.10	odd	2		1650.2.d.j.1451.10		12
15.2	even	4		330.2.f.a.329.15	yes	24
15.8	even	4		330.2.f.a.329.10	yes	24
15.14	odd	2	inner	1650.2.d.i.1451.4		12
33.32	even	2	inner	1650.2.d.i.1451.9		12
55.32	even	4		330.2.f.a.329.21	yes	24
55.43	even	4		330.2.f.a.329.4	yes	24
55.54	odd	2	inner	1650.2.d.i.1451.3		12
165.32	odd	4		330.2.f.a.329.3	✓	24
165.98	odd	4		330.2.f.a.329.22	yes	24
165.164	even	2		1650.2.d.j.1451.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.f.a.329.3	✓	24	165.32	odd	4
330.2.f.a.329.4	yes	24	55.43	even	4
330.2.f.a.329.9	yes	24	5.2	odd	4
330.2.f.a.329.10	yes	24	15.8	even	4
330.2.f.a.329.15	yes	24	15.2	even	4
330.2.f.a.329.16	yes	24	5.3	odd	4
330.2.f.a.329.21	yes	24	55.32	even	4
330.2.f.a.329.22	yes	24	165.98	odd	4
1650.2.d.i.1451.3		12	55.54	odd	2	inner
1650.2.d.i.1451.4		12	15.14	odd	2	inner
1650.2.d.i.1451.9		12	33.32	even	2	inner
1650.2.d.i.1451.10		12	1.1	even	1	trivial
1650.2.d.j.1451.3		12	5.4	even	2
1650.2.d.j.1451.4		12	165.164	even	2
1650.2.d.j.1451.9		12	3.2	odd	2
1650.2.d.j.1451.10		12	11.10	odd	2

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:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.839210 + 1.51517i) q^{3} +1.00000 q^{4} +(-0.839210 - 1.51517i) q^{6} +3.51327i q^{7} -1.00000 q^{8} +(-1.59145 + 2.54308i) q^{9} +(-0.486823 - 3.28070i) q^{11} +(0.839210 + 1.51517i) q^{12} -2.03804i q^{13} -3.51327i q^{14} +1.00000 q^{16} -6.34310 q^{17} +(1.59145 - 2.54308i) q^{18} -2.47606i q^{19} +(-5.32319 + 2.94838i) q^{21} +(0.486823 + 3.28070i) q^{22} +4.18641i q^{23} +(-0.839210 - 1.51517i) q^{24} +2.03804i q^{26} +(-5.18876 - 0.277134i) q^{27} +3.51327i q^{28} -9.67274 q^{29} -1.18291 q^{31} -1.00000 q^{32} +(4.56226 - 3.49082i) q^{33} +6.34310 q^{34} +(-1.59145 + 2.54308i) q^{36} +3.08797 q^{37} +2.47606i q^{38} +(3.08797 - 1.71034i) q^{39} -6.58477 q^{41} +(5.32319 - 2.94838i) q^{42} +7.02655i q^{43} +(-0.486823 - 3.28070i) q^{44} -4.18641i q^{46} -0.765721i q^{47} +(0.839210 + 1.51517i) q^{48} -5.34310 q^{49} +(-5.32319 - 9.61085i) q^{51} -2.03804i q^{52} -10.0832i q^{53} +(5.18876 + 0.277134i) q^{54} -3.51327i q^{56} +(3.75165 - 2.07794i) q^{57} +9.67274 q^{58} +0.465146i q^{59} -9.85671i q^{61} +1.18291 q^{62} +(-8.93455 - 5.59121i) q^{63} +1.00000 q^{64} +(-4.56226 + 3.49082i) q^{66} -0.973646 q^{67} -6.34310 q^{68} +(-6.34310 + 3.51327i) q^{69} +7.12421i q^{71} +(1.59145 - 2.54308i) q^{72} +9.70719i q^{73} -3.08797 q^{74} -2.47606i q^{76} +(11.5260 - 1.71034i) q^{77} +(-3.08797 + 1.71034i) q^{78} +0.992165i q^{79} +(-3.93455 - 8.09440i) q^{81} +6.58477 q^{82} +12.6862 q^{83} +(-5.32319 + 2.94838i) q^{84} -7.02655i q^{86} +(-8.11746 - 14.6558i) q^{87} +(0.486823 + 3.28070i) q^{88} +5.08617i q^{89} +7.16019 q^{91} +4.18641i q^{92} +(-0.992707 - 1.79230i) q^{93} +0.765721i q^{94} +(-0.839210 - 1.51517i) q^{96} -14.7080 q^{97} +5.34310 q^{98} +(9.11786 + 3.98305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} - 6 q^{9} + 12 q^{16} - 4 q^{17} + 6 q^{18} + 12 q^{31} - 12 q^{32} - 18 q^{33} + 4 q^{34} - 6 q^{36} + 8 q^{49} - 14 q^{57} - 12 q^{62} - 22 q^{63} + 12 q^{64} + 18 q^{66}+ \cdots + 28 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 - 6 * q^9 + 12 * q^16 - 4 * q^17 + 6 * q^18 + 12 * q^31 - 12 * q^32 - 18 * q^33 + 4 * q^34 - 6 * q^36 + 8 * q^49 - 14 * q^57 - 12 * q^62 - 22 * q^63 + 12 * q^64 + 18 * q^66 - 4 * q^68 - 4 * q^69 + 6 * q^72 + 40 * q^77 + 38 * q^81 + 8 * q^83 + 14 * q^87 + 40 * q^91 - 8 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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