LMFDB - Embedded newform 273.2.p.e.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 $ x^12 + 60x^8 - 8x^7 + 80x^5 + 320x^4 + 160x^3 + 32x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.2
Root			$-0.528642 + 0.528642i$ of defining polynomial
Character	$\chi$	$=$	273.34
Dual form			273.2.p.e.265.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43819 - 1.43819i) q^{2} -1.00000i q^{3} +2.13679i q^{4} +(-0.471358 + 0.471358i) q^{5} +(-1.43819 + 1.43819i) q^{6} +(-0.645342 - 2.56584i) q^{7} +(0.196726 - 0.196726i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.43819 - 1.43819i) q^{2} -1.00000i q^{3} +2.13679i q^{4} +(-0.471358 + 0.471358i) q^{5} +(-1.43819 + 1.43819i) q^{6} +(-0.645342 - 2.56584i) q^{7} +(0.196726 - 0.196726i) q^{8} -1.00000 q^{9} +1.35580 q^{10} +(-3.28349 + 3.28349i) q^{11} +2.13679 q^{12} +(-1.56296 - 3.24918i) q^{13} +(-2.76204 + 4.61829i) q^{14} +(0.471358 + 0.471358i) q^{15} +3.70771 q^{16} -5.13168 q^{17} +(1.43819 + 1.43819i) q^{18} +(-1.77011 + 1.77011i) q^{19} +(-1.00719 - 1.00719i) q^{20} +(-2.56584 + 0.645342i) q^{21} +9.44458 q^{22} -2.90689i q^{23} +(-0.196726 - 0.196726i) q^{24} +4.55564i q^{25} +(-2.42511 + 6.92077i) q^{26} +1.00000i q^{27} +(5.48265 - 1.37896i) q^{28} +7.36508 q^{29} -1.35580i q^{30} +(-0.942715 + 0.942715i) q^{31} +(-5.72585 - 5.72585i) q^{32} +(3.28349 + 3.28349i) q^{33} +(7.38034 + 7.38034i) q^{34} +(1.51362 + 0.905241i) q^{35} -2.13679i q^{36} +(-3.71859 + 3.71859i) q^{37} +5.09151 q^{38} +(-3.24918 + 1.56296i) q^{39} +0.185457i q^{40} +(0.744932 - 0.744932i) q^{41} +(4.61829 + 2.76204i) q^{42} -8.69594i q^{43} +(-7.01613 - 7.01613i) q^{44} +(0.471358 - 0.471358i) q^{45} +(-4.18067 + 4.18067i) q^{46} +(-3.25672 - 3.25672i) q^{47} -3.70771i q^{48} +(-6.16707 + 3.31169i) q^{49} +(6.55189 - 6.55189i) q^{50} +5.13168i q^{51} +(6.94281 - 3.33970i) q^{52} -5.78328 q^{53} +(1.43819 - 1.43819i) q^{54} -3.09540i q^{55} +(-0.631723 - 0.377812i) q^{56} +(1.77011 + 1.77011i) q^{57} +(-10.5924 - 10.5924i) q^{58} +(-5.95220 - 5.95220i) q^{59} +(-1.00719 + 1.00719i) q^{60} -13.0492i q^{61} +2.71161 q^{62} +(0.645342 + 2.56584i) q^{63} +9.05432i q^{64} +(2.26824 + 0.794814i) q^{65} -9.44458i q^{66} +(-7.50970 - 7.50970i) q^{67} -10.9653i q^{68} -2.90689 q^{69} +(-0.874958 - 3.47878i) q^{70} +(-8.19616 - 8.19616i) q^{71} +(-0.196726 + 0.196726i) q^{72} +(10.2969 + 10.2969i) q^{73} +10.6961 q^{74} +4.55564 q^{75} +(-3.78234 - 3.78234i) q^{76} +(10.5439 + 6.30594i) q^{77} +(6.92077 + 2.42511i) q^{78} +2.47069 q^{79} +(-1.74766 + 1.74766i) q^{80} +1.00000 q^{81} -2.14271 q^{82} +(10.0266 - 10.0266i) q^{83} +(-1.37896 - 5.48265i) q^{84} +(2.41886 - 2.41886i) q^{85} +(-12.5064 + 12.5064i) q^{86} -7.36508i q^{87} +1.29190i q^{88} +(0.170577 + 0.170577i) q^{89} -1.35580 q^{90} +(-7.32823 + 6.10713i) q^{91} +6.21141 q^{92} +(0.942715 + 0.942715i) q^{93} +9.36757i q^{94} -1.66871i q^{95} +(-5.72585 + 5.72585i) q^{96} +(-11.3630 + 11.3630i) q^{97} +(13.6323 + 4.10658i) q^{98} +(3.28349 - 3.28349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 q^{28} - 8 q^{29} - 24 q^{31} + 20 q^{32} + 4 q^{33} - 20 q^{35} - 4 q^{37} - 40 q^{38} - 16 q^{39} + 20 q^{41} + 8 q^{44} + 12 q^{45} + 20 q^{46} - 32 q^{47} + 20 q^{50} + 56 q^{52} - 16 q^{53} + 20 q^{56} - 8 q^{59} - 8 q^{60} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 q^{70} - 12 q^{71} + 32 q^{73} - 64 q^{74} - 4 q^{75} + 12 q^{77} + 16 q^{78} + 24 q^{79} + 4 q^{80} + 12 q^{81} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * q^28 - 8 * q^29 - 24 * q^31 + 20 * q^32 + 4 * q^33 - 20 * q^35 - 4 * q^37 - 40 * q^38 - 16 * q^39 + 20 * q^41 + 8 * q^44 + 12 * q^45 + 20 * q^46 - 32 * q^47 + 20 * q^50 + 56 * q^52 - 16 * q^53 + 20 * q^56 - 8 * q^59 - 8 * q^60 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * q^70 - 12 * q^71 + 32 * q^73 - 64 * q^74 - 4 * q^75 + 12 * q^77 + 16 * q^78 + 24 * q^79 + 4 * q^80 + 12 * q^81 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.43819	−	1.43819i	−1.01695	−	1.01695i	−0.999854	−	0.0171009i	$-0.994556\pi$
$2$	−1.43819	−	1.43819i	−1.01695	−	1.01695i	−0.0171009	−	0.999854i	$-0.505444\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			2.13679i			1.06839i
$5$	−0.471358	+	0.471358i	−0.210798	+	0.210798i	−0.804606	−	0.593809i	$-0.797624\pi$
$5$	−0.471358	+	0.471358i	−0.210798	+	0.210798i	0.593809	+	0.804606i	$0.297624\pi$
$6$	−1.43819	+	1.43819i	−0.587139	+	0.587139i
$7$	−0.645342	−	2.56584i	−0.243916	−	0.969796i
$7$	−0.645342	−	2.56584i	−0.243916	−	0.969796i
$8$	0.196726	−	0.196726i	0.0695532	−	0.0695532i
$9$	−1.00000			−0.333333
$10$	1.35580			0.428743
$11$	−3.28349	+	3.28349i	−0.990011	+	0.990011i	−0.999951	−	0.00994007i	$-0.996836\pi$
$11$	−3.28349	+	3.28349i	−0.990011	+	0.990011i	0.00994007	+	0.999951i	$0.496836\pi$
$12$	2.13679			0.616837
$13$	−1.56296	−	3.24918i	−0.433486	−	0.901160i
$13$	−1.56296	−	3.24918i	−0.433486	−	0.901160i
$14$	−2.76204	+	4.61829i	−0.738187	+	1.23429i
$15$	0.471358	+	0.471358i	0.121704	+	0.121704i
$16$	3.70771			0.926929
$17$	−5.13168			−1.24462			−0.622308	−	0.782773i	$-0.713805\pi$
$17$	−5.13168			−1.24462			−0.622308	+	0.782773i	$0.713805\pi$
$18$	1.43819	+	1.43819i	0.338985	+	0.338985i
$19$	−1.77011	+	1.77011i	−0.406090	+	0.406090i	−0.880373	−	0.474282i	$-0.842708\pi$
$19$	−1.77011	+	1.77011i	−0.406090	+	0.406090i	0.474282	+	0.880373i	$0.342708\pi$
$20$	−1.00719	−	1.00719i	−0.225215	−	0.225215i
$21$	−2.56584	+	0.645342i	−0.559912	+	0.140825i
$22$	9.44458			2.01359
$23$		−	2.90689i		−	0.606129i	−0.952970	−	0.303065i	$-0.901990\pi$
$23$		−	2.90689i		−	0.606129i	0.952970	−	0.303065i	$-0.0980098\pi$
$24$	−0.196726	−	0.196726i	−0.0401565	−	0.0401565i
$25$			4.55564i			0.911129i
$26$	−2.42511	+	6.92077i	−0.475604	+	1.35727i
$27$			1.00000i			0.192450i
$28$	5.48265	−	1.37896i	1.03612	−	0.260599i
$29$	7.36508			1.36766			0.683830	−	0.729641i	$-0.260313\pi$
$29$	7.36508			1.36766			0.683830	+	0.729641i	$0.260313\pi$
$30$		−	1.35580i		−	0.247535i
$31$	−0.942715	+	0.942715i	−0.169317	+	0.169317i	−0.786679	−	0.617362i	$-0.788201\pi$
$31$	−0.942715	+	0.942715i	−0.169317	+	0.169317i	0.617362	+	0.786679i	$0.288201\pi$
$32$	−5.72585	−	5.72585i	−1.01220	−	1.01220i
$33$	3.28349	+	3.28349i	0.571583	+	0.571583i
$34$	7.38034	+	7.38034i	1.26572	+	1.26572i
$35$	1.51362	+	0.905241i	0.255848	+	0.153014i
$36$		−	2.13679i		−	0.356131i
$37$	−3.71859	+	3.71859i	−0.611332	+	0.611332i	−0.943293	−	0.331961i	$-0.892290\pi$
$37$	−3.71859	+	3.71859i	−0.611332	+	0.611332i	0.331961	+	0.943293i	$0.392290\pi$
$38$	5.09151			0.825951
$39$	−3.24918	+	1.56296i	−0.520285	+	0.250273i
$40$			0.185457i			0.0293233i
$41$	0.744932	−	0.744932i	0.116339	−	0.116339i	−0.646541	−	0.762880i	$-0.723785\pi$
$41$	0.744932	−	0.744932i	0.116339	−	0.116339i	0.762880	+	0.646541i	$0.223785\pi$
$42$	4.61829	+	2.76204i	0.712618	+	0.426192i
$43$		−	8.69594i		−	1.32612i	−0.748567	−	0.663059i	$-0.769258\pi$
$43$		−	8.69594i		−	1.32612i	0.748567	−	0.663059i	$-0.230742\pi$
$44$	−7.01613	−	7.01613i	−1.05772	−	1.05772i
$45$	0.471358	−	0.471358i	0.0702659	−	0.0702659i
$46$	−4.18067	+	4.18067i	−0.616406	+	0.616406i
$47$	−3.25672	−	3.25672i	−0.475042	−	0.475042i	0.428500	−	0.903542i	$-0.359042\pi$
$47$	−3.25672	−	3.25672i	−0.475042	−	0.475042i	−0.903542	+	0.428500i	$0.859042\pi$
$48$		−	3.70771i		−	0.535163i
$49$	−6.16707	+	3.31169i	−0.881010	+	0.473099i
$50$	6.55189	−	6.55189i	0.926577	−	0.926577i
$51$			5.13168i			0.718579i
$52$	6.94281	−	3.33970i	0.962794	−	0.463134i
$53$	−5.78328			−0.794394			−0.397197	−	0.917733i	$-0.630017\pi$
$53$	−5.78328			−0.794394			−0.397197	+	0.917733i	$0.630017\pi$
$54$	1.43819	−	1.43819i	0.195713	−	0.195713i
$55$		−	3.09540i		−	0.417384i
$56$	−0.631723	−	0.377812i	−0.0844176	−	0.0504872i
$57$	1.77011	+	1.77011i	0.234456	+	0.234456i
$58$	−10.5924	−	10.5924i	−1.39085	−	1.39085i
$59$	−5.95220	−	5.95220i	−0.774911	−	0.774911i	0.204050	−	0.978960i	$-0.434590\pi$
$59$	−5.95220	−	5.95220i	−0.774911	−	0.774911i	−0.978960	+	0.204050i	$0.934590\pi$
$60$	−1.00719	+	1.00719i	−0.130028	+	0.130028i
$61$		−	13.0492i		−	1.67078i	−0.549657	−	0.835390i	$-0.685242\pi$
$61$		−	13.0492i		−	1.67078i	0.549657	−	0.835390i	$-0.314758\pi$
$62$	2.71161			0.344375
$63$	0.645342	+	2.56584i	0.0813055	+	0.323265i
$64$			9.05432i			1.13179i
$65$	2.26824	+	0.794814i	0.281340	+	0.0985846i
$66$		−	9.44458i		−	1.16255i
$67$	−7.50970	−	7.50970i	−0.917456	−	0.917456i	0.0793877	−	0.996844i	$-0.474704\pi$
$67$	−7.50970	−	7.50970i	−0.917456	−	0.917456i	−0.996844	+	0.0793877i	$0.974704\pi$
$68$		−	10.9653i		−	1.32974i
$69$	−2.90689			−0.349949
$70$	−0.874958	−	3.47878i	−0.104578	−	0.415794i
$71$	−8.19616	−	8.19616i	−0.972705	−	0.972705i	0.0269326	−	0.999637i	$-0.491426\pi$
$71$	−8.19616	−	8.19616i	−0.972705	−	0.972705i	−0.999637	+	0.0269326i	$0.991426\pi$
$72$	−0.196726	+	0.196726i	−0.0231844	+	0.0231844i
$73$	10.2969	+	10.2969i	1.20516	+	1.20516i	0.972576	+	0.232584i	$0.0747179\pi$
$73$	10.2969	+	10.2969i	1.20516	+	1.20516i	0.232584	+	0.972576i	$0.425282\pi$
$74$	10.6961			1.24339
$75$	4.55564			0.526040
$76$	−3.78234	−	3.78234i	−0.433864	−	0.433864i
$77$	10.5439	+	6.30594i	1.20159	+	0.718629i
$78$	6.92077	+	2.42511i	0.783623	+	0.274590i
$79$	2.47069			0.277975			0.138987	−	0.990294i	$-0.455615\pi$
$79$	2.47069			0.277975			0.138987	+	0.990294i	$0.455615\pi$
$80$	−1.74766	+	1.74766i	−0.195394	+	0.195394i
$81$	1.00000			0.111111
$82$	−2.14271			−0.236623
$83$	10.0266	−	10.0266i	1.10056	−	1.10056i	0.106219	−	0.994343i	$-0.466126\pi$
$83$	10.0266	−	10.0266i	1.10056	−	1.10056i	0.994343	−	0.106219i	$-0.0338745\pi$
$84$	−1.37896	−	5.48265i	−0.150457	−	0.598207i
$85$	2.41886	−	2.41886i	0.262362	−	0.262362i
$86$	−12.5064	+	12.5064i	−1.34860	+	1.34860i
$87$		−	7.36508i		−	0.789619i
$88$			1.29190i			0.137717i
$89$	0.170577	+	0.170577i	0.0180812	+	0.0180812i	0.716090	−	0.698008i	$-0.245930\pi$
$89$	0.170577	+	0.170577i	0.0180812	+	0.0180812i	−0.698008	+	0.716090i	$0.745930\pi$
$90$	−1.35580			−0.142914
$91$	−7.32823	+	6.10713i	−0.768207	+	0.640201i
$92$	6.21141			0.647585
$93$	0.942715	+	0.942715i	0.0977550	+	0.0977550i
$94$			9.36757i			0.966192i
$95$		−	1.66871i		−	0.171206i
$96$	−5.72585	+	5.72585i	−0.584393	+	0.584393i
$97$	−11.3630	+	11.3630i	−1.15374	+	1.15374i	−0.167940	+	0.985797i	$0.553711\pi$
$97$	−11.3630	+	11.3630i	−1.15374	+	1.15374i	−0.985797	+	0.167940i	$0.946289\pi$
$98$	13.6323	+	4.10658i	1.37707	+	0.414827i
$99$	3.28349	−	3.28349i	0.330004	−	0.330004i
$100$	−9.73444			−0.973444
$101$	−3.37759			−0.336083			−0.168041	−	0.985780i	$-0.553744\pi$
$101$	−3.37759			−0.336083			−0.168041	+	0.985780i	$0.553744\pi$
$102$	7.38034	−	7.38034i	0.730762	−	0.730762i
$103$	10.1407			0.999196			0.499598	−	0.866257i	$-0.333481\pi$
$103$	10.1407			0.999196			0.499598	+	0.866257i	$0.333481\pi$
$104$	−0.946672	−	0.331724i	−0.0928289	−	0.0325282i
$105$	0.905241	−	1.51362i	0.0883425	−	0.147714i
$106$	8.31746	+	8.31746i	0.807863	+	0.807863i
$107$	−6.35975			−0.614820			−0.307410	−	0.951577i	$-0.599462\pi$
$107$	−6.35975			−0.614820			−0.307410	+	0.951577i	$0.599462\pi$
$108$	−2.13679			−0.205612
$109$	−6.88172	−	6.88172i	−0.659149	−	0.659149i	0.296030	−	0.955179i	$-0.404337\pi$
$109$	−6.88172	−	6.88172i	−0.659149	−	0.659149i	−0.955179	+	0.296030i	$0.904337\pi$
$110$	−4.45178	+	4.45178i	−0.424460	+	0.424460i
$111$	3.71859	+	3.71859i	0.352953	+	0.352953i
$112$	−2.39275	−	9.51340i	−0.226093	−	0.898932i
$113$	10.1344			0.953365			0.476682	−	0.879076i	$-0.341839\pi$
$113$	10.1344			0.953365			0.476682	+	0.879076i	$0.341839\pi$
$114$		−	5.09151i		−	0.476863i
$115$	1.37019	+	1.37019i	0.127771	+	0.127771i
$116$			15.7376i			1.46120i
$117$	1.56296	+	3.24918i	0.144495	+	0.300387i
$118$			17.1208i			1.57610i
$119$	3.31169	+	13.1671i	0.303582	+	1.20702i
$120$	0.185457			0.0169298
$121$		−	10.5627i		−	0.960242i
$122$	−18.7673	+	18.7673i	−1.69911	+	1.69911i
$123$	−0.744932	−	0.744932i	−0.0671683	−	0.0671683i
$124$	−2.01438	−	2.01438i	−0.180897	−	0.180897i
$125$	−4.50413	−	4.50413i	−0.402861	−	0.402861i
$126$	2.76204	−	4.61829i	0.246062	−	0.411430i
$127$		−	5.52931i		−	0.490646i	−0.969441	−	0.245323i	$-0.921106\pi$
$127$		−	5.52931i		−	0.490646i	0.969441	−	0.245323i	$-0.0788941\pi$
$128$	1.57013	−	1.57013i	0.138781	−	0.138781i
$129$	−8.69594			−0.765635
$130$	−2.11906	−	4.40525i	−0.185854	−	0.386366i
$131$			5.86687i			0.512591i	0.966598	+	0.256296i	$0.0825021\pi$
$131$			5.86687i			0.512591i	−0.966598	+	0.256296i	$0.917498\pi$
$132$	−7.01613	+	7.01613i	−0.610675	+	0.610675i
$133$	5.68414	+	3.39949i	0.492877	+	0.294773i
$134$			21.6008i			1.86602i
$135$	−0.471358	−	0.471358i	−0.0405680	−	0.0405680i
$136$	−1.00954	+	1.00954i	−0.0865669	+	0.0865669i
$137$	9.62711	−	9.62711i	0.822499	−	0.822499i	−0.163966	−	0.986466i	$-0.552429\pi$
$137$	9.62711	−	9.62711i	0.822499	−	0.822499i	0.986466	+	0.163966i	$0.0524289\pi$
$138$	4.18067	+	4.18067i	0.355882	+	0.355882i
$139$			6.00105i			0.509002i	0.967072	+	0.254501i	$0.0819112\pi$
$139$			6.00105i			0.509002i	−0.967072	+	0.254501i	$0.918089\pi$
$140$	−1.93431	+	3.23427i	−0.163479	+	0.273346i
$141$	−3.25672	+	3.25672i	−0.274265	+	0.274265i
$142$			23.5753i			1.97839i
$143$	15.8006	+	5.53670i	1.32131	+	0.463002i
$144$	−3.70771			−0.308976
$145$	−3.47159	+	3.47159i	−0.288300	+	0.288300i
$146$		−	29.6178i		−	2.45119i
$147$	3.31169	+	6.16707i	0.273144	+	0.508651i
$148$	−7.94584	−	7.94584i	−0.653144	−	0.653144i
$149$	10.6486	+	10.6486i	0.872365	+	0.872365i	0.992730	−	0.120365i	$-0.0384064\pi$
$149$	10.6486	+	10.6486i	0.872365	+	0.872365i	−0.120365	+	0.992730i	$0.538406\pi$
$150$	−6.55189	−	6.55189i	−0.534959	−	0.534959i
$151$	3.92400	−	3.92400i	0.319331	−	0.319331i	−0.529179	−	0.848510i	$-0.677500\pi$
$151$	3.92400	−	3.92400i	0.319331	−	0.319331i	0.848510	+	0.529179i	$0.177500\pi$
$152$			0.696452i			0.0564898i
$153$	5.13168			0.414872
$154$	−6.09499	−	24.2333i	−0.491148	−	1.95277i
$155$		−	0.888712i		−	0.0713831i
$156$	−3.33970	−	6.94281i	−0.267390	−	0.555869i
$157$			11.1941i			0.893388i	0.894687	+	0.446694i	$0.147399\pi$
$157$			11.1941i			0.893388i	−0.894687	+	0.446694i	$0.852601\pi$
$158$	−3.55333	−	3.55333i	−0.282688	−	0.282688i
$159$			5.78328i			0.458644i
$160$	5.39785			0.426738
$161$	−7.45863	+	1.87594i	−0.587822	+	0.147845i
$162$	−1.43819	−	1.43819i	−0.112995	−	0.112995i
$163$	−3.93488	+	3.93488i	−0.308204	+	0.308204i	−0.844212	−	0.536009i	$-0.819931\pi$
$163$	−3.93488	+	3.93488i	−0.308204	+	0.308204i	0.536009	+	0.844212i	$0.319931\pi$
$164$	1.59176	+	1.59176i	0.124296	+	0.124296i
$165$	−3.09540			−0.240977
$166$	−28.8403			−2.23844
$167$	5.48595	+	5.48595i	0.424515	+	0.424515i	0.886755	−	0.462240i	$-0.152954\pi$
$167$	5.48595	+	5.48595i	0.424515	+	0.424515i	−0.462240	+	0.886755i	$0.652954\pi$
$168$	−0.377812	+	0.631723i	−0.0291488	+	0.0487385i
$169$	−8.11434	+	10.1567i	−0.624180	+	0.781281i
$170$	−6.95756			−0.533620
$171$	1.77011	−	1.77011i	0.135363	−	0.135363i
$172$	18.5814			1.41682
$173$	−6.32899			−0.481184			−0.240592	−	0.970626i	$-0.577342\pi$
$173$	−6.32899			−0.481184			−0.240592	+	0.970626i	$0.577342\pi$
$174$	−10.5924	+	10.5924i	−0.803007	+	0.803007i
$175$	11.6891	−	2.93995i	0.883609	−	0.222239i
$176$	−12.1743	+	12.1743i	−0.917669	+	0.917669i
$177$	−5.95220	+	5.95220i	−0.447395	+	0.447395i
$178$		−	0.490646i		−	0.0367755i
$179$		−	13.3219i		−	0.995725i	−0.867256	−	0.497862i	$-0.834118\pi$
$179$		−	13.3219i		−	0.995725i	0.867256	−	0.497862i	$-0.165882\pi$
$180$	1.00719	+	1.00719i	0.0750716	+	0.0750716i
$181$	−7.49642			−0.557205			−0.278602	−	0.960407i	$-0.589871\pi$
$181$	−7.49642			−0.557205			−0.278602	+	0.960407i	$0.589871\pi$
$182$	19.3226	+	1.75618i	1.43229	+	0.130177i
$183$	−13.0492			−0.964626
$184$	−0.571862	−	0.571862i	−0.0421582	−	0.0421582i
$185$		−	3.50557i		−	0.257735i
$186$		−	2.71161i		−	0.198825i
$187$	16.8498	−	16.8498i	1.23218	−	1.23218i
$188$	6.95892	−	6.95892i	0.507531	−	0.507531i
$189$	2.56584	−	0.645342i	0.186637	−	0.0469417i
$190$	−2.39992	+	2.39992i	−0.174109	+	0.174109i
$191$	14.2378			1.03021			0.515104	−	0.857128i	$-0.327753\pi$
$191$	14.2378			1.03021			0.515104	+	0.857128i	$0.327753\pi$
$192$	9.05432			0.653439
$193$	3.61945	−	3.61945i	0.260534	−	0.260534i	−0.564737	−	0.825271i	$-0.691022\pi$
$193$	3.61945	−	3.61945i	0.260534	−	0.260534i	0.825271	+	0.564737i	$0.191022\pi$
$194$	32.6843			2.34660
$195$	0.794814	−	2.26824i	0.0569178	−	0.162432i
$196$	−7.07638	−	13.1777i	−0.505455	−	0.941265i
$197$	−7.92835	−	7.92835i	−0.564871	−	0.564871i	0.365816	−	0.930687i	$-0.380790\pi$
$197$	−7.92835	−	7.92835i	−0.564871	−	0.564871i	−0.930687	+	0.365816i	$0.880790\pi$
$198$	−9.44458			−0.671197
$199$	19.2250			1.36283			0.681414	−	0.731899i	$-0.261365\pi$
$199$	19.2250			1.36283			0.681414	+	0.731899i	$0.261365\pi$
$200$	0.896214	+	0.896214i	0.0633719	+	0.0633719i
$201$	−7.50970	+	7.50970i	−0.529694	+	0.529694i
$202$	4.85762	+	4.85762i	0.341781	+	0.341781i
$203$	−4.75300	−	18.8976i	−0.333595	−	1.32635i
$204$	−10.9653			−0.767725
$205$			0.702259i			0.0490479i
$206$	−14.5843	−	14.5843i	−1.01614	−	1.01614i
$207$			2.90689i			0.202043i
$208$	−5.79500	−	12.0470i	−0.401811	−	0.835311i
$209$		−	11.6243i		−	0.804068i
$210$	−3.47878	+	0.874958i	−0.240058	+	0.0603779i
$211$	−7.53906			−0.519010			−0.259505	−	0.965742i	$-0.583559\pi$
$211$	−7.53906			−0.519010			−0.259505	+	0.965742i	$0.583559\pi$
$212$		−	12.3576i		−	0.848726i
$213$	−8.19616	+	8.19616i	−0.561591	+	0.561591i
$214$	9.14653	+	9.14653i	0.625244	+	0.625244i
$215$	4.09890	+	4.09890i	0.279542	+	0.279542i
$216$	0.196726	+	0.196726i	0.0133855	+	0.0133855i
$217$	3.02723	+	1.81048i	0.205502	+	0.122904i
$218$			19.7944i			1.34065i
$219$	10.2969	−	10.2969i	0.695799	−	0.695799i
$220$	6.61421			0.445930
$221$	8.02059	+	16.6737i	0.539523	+	1.12160i
$222$		−	10.6961i		−	0.717874i
$223$	−4.42747	+	4.42747i	−0.296485	+	0.296485i	−0.839636	−	0.543150i	$-0.817231\pi$
$223$	−4.42747	+	4.42747i	−0.296485	+	0.296485i	0.543150	+	0.839636i	$0.317231\pi$
$224$	−10.9965	+	18.3868i	−0.734734	+	1.22852i
$225$		−	4.55564i		−	0.303710i
$226$	−14.5752	−	14.5752i	−0.969529	−	0.969529i
$227$	12.5432	−	12.5432i	0.832524	−	0.832524i	−0.155338	−	0.987861i	$-0.549647\pi$
$227$	12.5432	−	12.5432i	0.832524	−	0.832524i	0.987861	+	0.155338i	$0.0496466\pi$
$228$	−3.78234	+	3.78234i	−0.250492	+	0.250492i
$229$	−1.68832	−	1.68832i	−0.111567	−	0.111567i	0.649119	−	0.760687i	$-0.275138\pi$
$229$	−1.68832	−	1.68832i	−0.111567	−	0.111567i	−0.760687	+	0.649119i	$0.775138\pi$
$230$		−	3.94118i		−	0.259874i
$231$	6.30594	−	10.5439i	0.414900	−	0.693737i
$232$	1.44890	−	1.44890i	0.0951251	−	0.0951251i
$233$			0.385937i			0.0252836i	0.999920	+	0.0126418i	$0.00402411\pi$
$233$			0.385937i			0.0252836i	−0.999920	+	0.0126418i	$0.995976\pi$
$234$	2.42511	−	6.92077i	0.158535	−	0.452425i
$235$	3.07016			0.200275
$236$	12.7186	−	12.7186i	0.827909	−	0.827909i
$237$		−	2.47069i		−	0.160489i
$238$	14.1739	−	23.6996i	0.918758	−	1.53622i
$239$	−6.67161	−	6.67161i	−0.431551	−	0.431551i	0.457605	−	0.889156i	$-0.348707\pi$
$239$	−6.67161	−	6.67161i	−0.431551	−	0.431551i	−0.889156	+	0.457605i	$0.848707\pi$
$240$	1.74766	+	1.74766i	0.112811	+	0.112811i
$241$	−14.1379	−	14.1379i	−0.910701	−	0.910701i	0.0856260	−	0.996327i	$-0.472711\pi$
$241$	−14.1379	−	14.1379i	−0.910701	−	0.910701i	−0.996327	+	0.0856260i	$0.972711\pi$
$242$	−15.1911	+	15.1911i	−0.976522	+	0.976522i
$243$		−	1.00000i		−	0.0641500i
$244$	27.8834			1.78505
$245$	1.34590	−	4.46788i	0.0859867	−	0.285443i
$246$			2.14271i			0.136614i
$247$	8.51800	+	2.98480i	0.541987	+	0.189918i
$248$			0.370913i			0.0235530i
$249$	−10.0266	−	10.0266i	−0.635410	−	0.635410i
$250$			12.9556i			0.819383i
$251$	−28.8068			−1.81827			−0.909136	−	0.416499i	$-0.863257\pi$
$251$	−28.8068			−1.81827			−0.909136	+	0.416499i	$0.863257\pi$
$252$	−5.48265	+	1.37896i	−0.345375	+	0.0868663i
$253$	9.54477	+	9.54477i	0.600074	+	0.600074i
$254$	−7.95220	+	7.95220i	−0.498965	+	0.498965i
$255$	−2.41886	−	2.41886i	−0.151475	−	0.151475i
$256$	13.5923			0.849522
$257$	3.34882			0.208894			0.104447	−	0.994530i	$-0.466693\pi$
$257$	3.34882			0.208894			0.104447	+	0.994530i	$0.466693\pi$
$258$	12.5064	+	12.5064i	0.778616	+	0.778616i
$259$	11.9411	+	7.14154i	0.741982	+	0.443754i
$260$	−1.69835	+	4.84674i	−0.105327	+	0.300582i
$261$	−7.36508			−0.455887
$262$	8.43769	−	8.43769i	0.521282	−	0.521282i
$263$	−0.409582			−0.0252559			−0.0126280	−	0.999920i	$-0.504020\pi$
$263$	−0.409582			−0.0252559			−0.0126280	+	0.999920i	$0.504020\pi$
$264$	1.29190			0.0795108
$265$	2.72599	−	2.72599i	0.167456	−	0.167456i
$266$	−3.28576	−	13.0640i	−0.201463	−	0.801004i
$267$	0.170577	−	0.170577i	0.0104392	−	0.0104392i
$268$	16.0466	−	16.0466i	0.980204	−	0.980204i
$269$			28.2084i			1.71990i	0.510382	+	0.859948i	$0.329504\pi$
$269$			28.2084i			1.71990i	−0.510382	+	0.859948i	$0.670496\pi$
$270$			1.35580i			0.0825117i
$271$	−1.97384	−	1.97384i	−0.119902	−	0.119902i	0.644610	−	0.764512i	$-0.277020\pi$
$271$	−1.97384	−	1.97384i	−0.119902	−	0.119902i	−0.764512	+	0.644610i	$0.777020\pi$
$272$	−19.0268			−1.15367
$273$	6.10713	+	7.32823i	0.369620	+	0.443525i
$274$	−27.6912			−1.67289
$275$	−14.9584	−	14.9584i	−0.902027	−	0.902027i
$276$		−	6.21141i		−	0.373883i
$277$			7.58222i			0.455572i	0.973711	+	0.227786i	$0.0731486\pi$
$277$			7.58222i			0.455572i	−0.973711	+	0.227786i	$0.926851\pi$
$278$	8.63065	−	8.63065i	0.517632	−	0.517632i
$279$	0.942715	−	0.942715i	0.0564389	−	0.0564389i
$280$	0.475852	−	0.119683i	0.0284376	−	0.00715243i
$281$	−2.85077	+	2.85077i	−0.170062	+	0.170062i	−0.787007	−	0.616944i	$-0.788370\pi$
$281$	−2.85077	+	2.85077i	−0.170062	+	0.170062i	0.616944	+	0.787007i	$0.288370\pi$
$282$	9.36757			0.557831
$283$	−26.6280			−1.58287			−0.791435	−	0.611253i	$-0.790666\pi$
$283$	−26.6280			−1.58287			−0.791435	+	0.611253i	$0.790666\pi$
$284$	17.5134	−	17.5134i	1.03923	−	1.03923i
$285$	−1.66871			−0.0988457
$286$	−14.7615	−	30.6871i	−0.872864	−	1.81457i
$287$	−2.39211	−	1.43064i	−0.141202	−	0.0844480i
$288$	5.72585	+	5.72585i	0.337399	+	0.337399i
$289$	9.33413			0.549067
$290$	9.98561			0.586375
$291$	11.3630	+	11.3630i	0.666110	+	0.666110i
$292$	−22.0023	+	22.0023i	−1.28759	+	1.28759i
$293$	21.2907	+	21.2907i	1.24382	+	1.24382i	0.958405	+	0.285412i	$0.0921304\pi$
$293$	21.2907	+	21.2907i	1.24382	+	1.24382i	0.285412	+	0.958405i	$0.407870\pi$
$294$	4.10658	−	13.6323i	0.239500	−	0.795050i
$295$	5.61123			0.326699
$296$			1.46309i			0.0850402i
$297$	−3.28349	−	3.28349i	−0.190528	−	0.190528i
$298$		−	30.6294i		−	1.77431i
$299$	−9.44502	+	4.54335i	−0.546220	+	0.262749i
$300$			9.73444i			0.562018i
$301$	−22.3124	+	5.61186i	−1.28606	+	0.323462i
$302$	−11.2869			−0.649490
$303$			3.37759i			0.194037i
$304$	−6.56305	+	6.56305i	−0.376417	+	0.376417i
$305$	6.15085	+	6.15085i	0.352197	+	0.352197i
$306$	−7.38034	−	7.38034i	−0.421906	−	0.421906i
$307$	10.0977	+	10.0977i	0.576305	+	0.576305i	0.933883	−	0.357578i	$-0.116397\pi$
$307$	10.0977	+	10.0977i	0.576305	+	0.576305i	−0.357578	+	0.933883i	$0.616397\pi$
$308$	−13.4745	+	22.5301i	−0.767778	+	1.28377i
$309$		−	10.1407i		−	0.576886i
$310$	−1.27814	+	1.27814i	−0.0725934	+	0.0725934i
$311$	−1.43215			−0.0812095			−0.0406048	−	0.999175i	$-0.512928\pi$
$311$	−1.43215			−0.0812095			−0.0406048	+	0.999175i	$0.512928\pi$
$312$	−0.331724	+	0.946672i	−0.0187802	+	0.0535948i
$313$			23.5529i			1.33129i	0.746269	+	0.665644i	$0.231843\pi$
$313$			23.5529i			1.33129i	−0.746269	+	0.665644i	$0.768157\pi$
$314$	16.0993	−	16.0993i	0.908535	−	0.908535i
$315$	−1.51362	−	0.905241i	−0.0852826	−	0.0510046i
$316$			5.27935i			0.296987i
$317$	16.2976	+	16.2976i	0.915364	+	0.915364i	0.996688	−	0.0813239i	$-0.0259148\pi$
$317$	16.2976	+	16.2976i	0.915364	+	0.915364i	−0.0813239	+	0.996688i	$0.525915\pi$
$318$	8.31746	−	8.31746i	0.466420	−	0.466420i
$319$	−24.1832	+	24.1832i	−1.35400	+	1.35400i
$320$	−4.26782	−	4.26782i	−0.238578	−	0.238578i
$321$			6.35975i			0.354966i
$322$	13.4249	+	8.02897i	0.748140	+	0.447437i
$323$	9.08362	−	9.08362i	0.505426	−	0.505426i
$324$			2.13679i			0.118710i
$325$	14.8021	−	7.12027i	0.821073	−	0.394962i
$326$	11.3182			0.626858
$327$	−6.88172	+	6.88172i	−0.380560	+	0.380560i
$328$		−	0.293095i		−	0.0161835i
$329$	−6.25452	+	10.4579i	−0.344823	+	0.576564i
$330$	4.45178	+	4.45178i	0.245062	+	0.245062i
$331$	8.74278	+	8.74278i	0.480547	+	0.480547i	0.905306	−	0.424759i	$-0.139641\pi$
$331$	8.74278	+	8.74278i	0.480547	+	0.480547i	−0.424759	+	0.905306i	$0.639641\pi$
$332$	21.4247	+	21.4247i	1.17583	+	1.17583i
$333$	3.71859	−	3.71859i	0.203777	−	0.203777i
$334$		−	15.7797i		−	0.863426i
$335$	7.07951			0.386795
$336$	−9.51340	+	2.39275i	−0.518999	+	0.130535i
$337$		−	27.7843i		−	1.51351i	−0.653700	−	0.756754i	$-0.726784\pi$
$337$		−	27.7843i		−	1.51351i	0.653700	−	0.756754i	$-0.273216\pi$
$338$	26.2772	−	2.93724i	1.42929	−	0.159765i
$339$		−	10.1344i		−	0.550425i
$340$	5.16858	+	5.16858i	0.280306	+	0.280306i
$341$		−	6.19080i		−	0.335251i
$342$	−5.09151			−0.275317
$343$	12.4771	+	13.6865i	0.673702	+	0.739003i
$344$	−1.71072	−	1.71072i	−0.0922357	−	0.0922357i
$345$	1.37019	−	1.37019i	0.0737684	−	0.0737684i
$346$	9.10230	+	9.10230i	0.489343	+	0.489343i
$347$	−24.5460			−1.31770			−0.658848	−	0.752276i	$-0.728956\pi$
$347$	−24.5460			−1.31770			−0.658848	+	0.752276i	$0.728956\pi$
$348$	15.7376			0.843624
$349$	16.7246	+	16.7246i	0.895247	+	0.895247i	0.995011	−	0.0997639i	$-0.0318087\pi$
$349$	16.7246	+	16.7246i	0.895247	+	0.895247i	−0.0997639	+	0.995011i	$0.531809\pi$
$350$	−21.0393	−	12.5829i	−1.12460	−	0.672583i
$351$	3.24918	−	1.56296i	0.173428	−	0.0834244i
$352$	37.6016			2.00417
$353$	5.21713	−	5.21713i	0.277680	−	0.277680i	−0.554502	−	0.832182i	$-0.687091\pi$
$353$	5.21713	−	5.21713i	0.277680	−	0.277680i	0.832182	+	0.554502i	$0.187091\pi$
$354$	17.1208			0.909960
$355$	7.72664			0.410088
$356$	−0.364488	+	0.364488i	−0.0193178	+	0.0193178i
$357$	13.1671	−	3.31169i	0.696875	−	0.175273i
$358$	−19.1594	+	19.1594i	−1.01261	+	1.01261i
$359$	18.8715	−	18.8715i	0.996001	−	0.996001i	−0.00399120	−	0.999992i	$-0.501270\pi$
$359$	18.8715	−	18.8715i	0.996001	−	0.996001i	0.999992	+	0.00399120i	$0.00127044\pi$
$360$		−	0.185457i		−	0.00977443i
$361$			12.7334i			0.670181i
$362$	10.7813	+	10.7813i	0.566652	+	0.566652i
$363$	−10.5627			−0.554396
$364$	−13.0496	−	15.6589i	−0.683987	−	0.820748i
$365$	−9.70704			−0.508090
$366$	18.7673	+	18.7673i	0.980981	+	0.980981i
$367$		−	6.21503i		−	0.324422i	−0.986756	−	0.162211i	$-0.948137\pi$
$367$		−	6.21503i		−	0.324422i	0.986756	−	0.162211i	$-0.0518626\pi$
$368$		−	10.7779i		−	0.561839i
$369$	−0.744932	+	0.744932i	−0.0387796	+	0.0387796i
$370$	−5.04168	+	5.04168i	−0.262105	+	0.262105i
$371$	3.73219	+	14.8390i	0.193766	+	0.770400i
$372$	−2.01438	+	2.01438i	−0.104441	+	0.104441i
$373$	−33.1828			−1.71814			−0.859069	−	0.511860i	$-0.828957\pi$
$373$	−33.1828			−1.71814			−0.859069	+	0.511860i	$0.828957\pi$
$374$	−48.4666			−2.50615
$375$	−4.50413	+	4.50413i	−0.232592	+	0.232592i
$376$	−1.28136			−0.0660813
$377$	−11.5113	−	23.9305i	−0.592862	−	1.23248i
$378$	−4.61829	−	2.76204i	−0.237539	−	0.142064i
$379$	−4.83296	−	4.83296i	−0.248252	−	0.248252i	0.572001	−	0.820253i	$-0.306167\pi$
$379$	−4.83296	−	4.83296i	−0.248252	−	0.248252i	−0.820253	+	0.572001i	$0.806167\pi$
$380$	3.56567			0.182915
$381$	−5.52931			−0.283275
$382$	−20.4766	−	20.4766i	−1.04767	−	1.04767i
$383$	−17.6014	+	17.6014i	−0.899389	+	0.899389i	−0.995382	−	0.0959933i	$-0.969397\pi$
$383$	−17.6014	+	17.6014i	−0.899389	+	0.899389i	0.0959933	+	0.995382i	$0.469397\pi$
$384$	−1.57013	−	1.57013i	−0.0801252	−	0.0801252i
$385$	−7.94230	+	1.99759i	−0.404777	+	0.101807i
$386$	−10.4109			−0.529902
$387$			8.69594i			0.442039i
$388$	−24.2803	−	24.2803i	−1.23265	−	1.23265i
$389$		−	15.1409i		−	0.767675i	−0.923401	−	0.383838i	$-0.874602\pi$
$389$		−	15.1409i		−	0.767675i	0.923401	−	0.383838i	$-0.125398\pi$
$390$	−4.40525	+	2.11906i	−0.223069	+	0.107303i
$391$			14.9173i			0.754398i
$392$	−0.561727	+	1.86472i	−0.0283715	+	0.0941825i
$393$	5.86687			0.295945
$394$			22.8050i			1.14890i
$395$	−1.16458	+	1.16458i	−0.0585964	+	0.0585964i
$396$	7.01613	+	7.01613i	0.352574	+	0.352574i
$397$	−13.6489	−	13.6489i	−0.685019	−	0.685019i	0.276107	−	0.961127i	$-0.410955\pi$
$397$	−13.6489	−	13.6489i	−0.685019	−	0.685019i	−0.961127	+	0.276107i	$0.910955\pi$
$398$	−27.6493	−	27.6493i	−1.38593	−	1.38593i
$399$	3.39949	−	5.68414i	0.170187	−	0.284563i
$400$			16.8910i			0.844551i
$401$	−14.0705	+	14.0705i	−0.702648	+	0.702648i	−0.964978	−	0.262330i	$-0.915509\pi$
$401$	−14.0705	+	14.0705i	−0.702648	+	0.702648i	0.262330	+	0.964978i	$0.415509\pi$
$402$	21.6008			1.07735
$403$	4.53647	+	1.58963i	0.225978	+	0.0791851i
$404$		−	7.21719i		−	0.359069i
$405$	−0.471358	+	0.471358i	−0.0234220	+	0.0234220i
$406$	−20.3427	+	34.0141i	−1.00959	+	1.68809i
$407$		−	24.4199i		−	1.21045i
$408$	1.00954	+	1.00954i	0.0499794	+	0.0499794i
$409$	21.1533	−	21.1533i	1.04596	−	1.04596i	0.0470710	−	0.998892i	$-0.485011\pi$
$409$	21.1533	−	21.1533i	1.04596	−	1.04596i	0.998892	−	0.0470710i	$-0.0149887\pi$
$410$	1.00998	−	1.00998i	0.0498795	−	0.0498795i
$411$	−9.62711	−	9.62711i	−0.474870	−	0.474870i
$412$			21.6686i			1.06753i
$413$	−11.4312	+	19.1136i	−0.562492	+	0.940519i
$414$	4.18067	−	4.18067i	0.205469	−	0.205469i
$415$			9.45223i			0.463992i
$416$	−9.65507	+	27.5536i	−0.473379	+	1.35093i
$417$	6.00105			0.293873
$418$	−16.7179	+	16.7179i	−0.817700	+	0.817700i
$419$		−	36.3211i		−	1.77440i	−0.461384	−	0.887201i	$-0.652647\pi$
$419$		−	36.3211i		−	1.77440i	0.461384	−	0.887201i	$-0.347353\pi$
$420$	3.23427	+	1.93431i	0.157816	+	0.0943846i
$421$	3.31582	+	3.31582i	0.161603	+	0.161603i	0.783277	−	0.621673i	$-0.213547\pi$
$421$	3.31582	+	3.31582i	0.161603	+	0.161603i	−0.621673	+	0.783277i	$0.713547\pi$
$422$	10.8426	+	10.8426i	0.527810	+	0.527810i
$423$	3.25672	+	3.25672i	0.158347	+	0.158347i
$424$	−1.13772	+	1.13772i	−0.0552526	+	0.0552526i
$425$		−	23.3781i		−	1.13400i
$426$	23.5753			1.14223
$427$	−33.4822	+	8.42121i	−1.62032	+	0.407531i
$428$		−	13.5894i		−	0.656870i
$429$	5.53670	−	15.8006i	0.267315	−	0.762861i
$430$		−	11.7900i		−	0.568564i
$431$	−14.4718	−	14.4718i	−0.697084	−	0.697084i	0.266696	−	0.963781i	$-0.414068\pi$
$431$	−14.4718	−	14.4718i	−0.697084	−	0.697084i	−0.963781	+	0.266696i	$0.914068\pi$
$432$			3.70771i			0.178388i
$433$	−19.2969			−0.927348			−0.463674	−	0.886006i	$-0.653469\pi$
$433$	−19.2969			−0.927348			−0.463674	+	0.886006i	$0.653469\pi$
$434$	−1.74992	−	6.95756i	−0.0839987	−	0.333973i
$435$	3.47159	+	3.47159i	0.166450	+	0.166450i
$436$	14.7048	−	14.7048i	0.704230	−	0.704230i
$437$	5.14552	+	5.14552i	0.246143	+	0.246143i
$438$	−29.6178			−1.41519
$439$	36.3616			1.73545			0.867723	−	0.497048i	$-0.165583\pi$
$439$	36.3616			1.73545			0.867723	+	0.497048i	$0.165583\pi$
$440$	−0.608946	−	0.608946i	−0.0290304	−	0.0290304i
$441$	6.16707	−	3.31169i	0.293670	−	0.157700i
$442$	12.4449	−	35.5152i	0.591943	−	1.68928i
$443$	−16.9420			−0.804938			−0.402469	−	0.915434i	$-0.631848\pi$
$443$	−16.9420			−0.804938			−0.402469	+	0.915434i	$0.631848\pi$
$444$	−7.94584	+	7.94584i	−0.377093	+	0.377093i
$445$	−0.160806			−0.00762294
$446$	12.7351			0.603024
$447$	10.6486	−	10.6486i	0.503660	−	0.503660i
$448$	23.2319	−	5.84313i	1.09761	−	0.276062i
$449$	25.3087	−	25.3087i	1.19439	−	1.19439i	0.218570	−	0.975821i	$-0.429861\pi$
$449$	25.3087	−	25.3087i	1.19439	−	1.19439i	0.975821	−	0.218570i	$-0.0701391\pi$
$450$	−6.55189	+	6.55189i	−0.308859	+	0.308859i
$451$			4.89196i			0.230353i
$452$			21.6551i			1.01857i
$453$	−3.92400	−	3.92400i	−0.184366	−	0.184366i
$454$	−36.0791			−1.69328
$455$	0.575577	−	6.33286i	0.0269835	−	0.296889i
$456$	0.696452			0.0326144
$457$	−5.83035	−	5.83035i	−0.272732	−	0.272732i	0.557467	−	0.830199i	$-0.311773\pi$
$457$	−5.83035	−	5.83035i	−0.272732	−	0.272732i	−0.830199	+	0.557467i	$0.811773\pi$
$458$			4.85624i			0.226917i
$459$		−	5.13168i		−	0.239526i
$460$	−2.92780	+	2.92780i	−0.136509	+	0.136509i
$461$	−2.92466	+	2.92466i	−0.136215	+	0.136215i	−0.771927	−	0.635712i	$-0.780707\pi$
$461$	−2.92466	+	2.92466i	−0.136215	+	0.136215i	0.635712	+	0.771927i	$0.280707\pi$
$462$	−24.2333	+	6.09499i	−1.12743	+	0.283565i
$463$	6.45288	−	6.45288i	0.299891	−	0.299891i	−0.541080	−	0.840971i	$-0.681985\pi$
$463$	6.45288	−	6.45288i	0.299891	−	0.299891i	0.840971	+	0.541080i	$0.181985\pi$
$464$	27.3076			1.26772
$465$	−0.888712			−0.0412130
$466$	0.555051	−	0.555051i	0.0257123	−	0.0257123i
$467$	−9.54769			−0.441814			−0.220907	−	0.975295i	$-0.570902\pi$
$467$	−9.54769			−0.441814			−0.220907	+	0.975295i	$0.570902\pi$
$468$	−6.94281	+	3.33970i	−0.320931	+	0.154378i
$469$	−14.4224	+	24.1150i	−0.665963	+	1.11353i
$470$	−4.41548	−	4.41548i	−0.203671	−	0.203671i
$471$	11.1941			0.515798
$472$	−2.34191			−0.107795
$473$	28.5531	+	28.5531i	1.31287	+	1.31287i
$474$	−3.55333	+	3.55333i	−0.163210	+	0.163210i
$475$	−8.06398	−	8.06398i	−0.370001	−	0.370001i
$476$	−28.1352	+	7.07638i	−1.28958	+	0.324345i
$477$	5.78328			0.264798
$478$			19.1901i			0.877735i
$479$	25.2423	+	25.2423i	1.15335	+	1.15335i	0.985876	+	0.167475i	$0.0535614\pi$
$479$	25.2423	+	25.2423i	1.15335	+	1.15335i	0.167475	+	0.985876i	$0.446439\pi$
$480$		−	5.39785i		−	0.246377i
$481$	17.8944	+	6.27037i	0.815913	+	0.285904i
$482$			40.6660i			1.85228i
$483$	1.87594	+	7.45863i	0.0853583	+	0.339379i
$484$	22.5702			1.02592
$485$		−	10.7121i		−	0.486410i
$486$	−1.43819	+	1.43819i	−0.0652377	+	0.0652377i
$487$	−12.4328	−	12.4328i	−0.563385	−	0.563385i	0.366883	−	0.930267i	$-0.380425\pi$
$487$	−12.4328	−	12.4328i	−0.563385	−	0.563385i	−0.930267	+	0.366883i	$0.880425\pi$
$488$	−2.56712	−	2.56712i	−0.116208	−	0.116208i
$489$	3.93488	+	3.93488i	0.177941	+	0.177941i
$490$	−8.36134	+	4.49001i	−0.377727	+	0.202838i
$491$			13.6638i			0.616639i	0.951283	+	0.308320i	$0.0997666\pi$
$491$			13.6638i			0.616639i	−0.951283	+	0.308320i	$0.900233\pi$
$492$	1.59176	−	1.59176i	0.0717621	−	0.0717621i
$493$	−37.7952			−1.70221
$494$	−7.95780	−	16.5432i	−0.358038	−	0.744314i
$495$			3.09540i			0.139128i
$496$	−3.49532	+	3.49532i	−0.156945	+	0.156945i
$497$	−15.7407	+	26.3193i	−0.706067	+	1.18058i
$498$			28.8403i			1.29237i
$499$	26.7532	+	26.7532i	1.19764	+	1.19764i	0.974872	+	0.222767i	$0.0715090\pi$
$499$	26.7532	+	26.7532i	1.19764	+	1.19764i	0.222767	+	0.974872i	$0.428491\pi$
$500$	9.62436	−	9.62436i	0.430414	−	0.430414i
$501$	5.48595	−	5.48595i	0.245094	−	0.245094i
$502$	41.4298	+	41.4298i	1.84910	+	1.84910i
$503$			14.2532i			0.635517i	0.948172	+	0.317758i	$0.102930\pi$
$503$			14.2532i			0.635517i	−0.948172	+	0.317758i	$0.897070\pi$
$504$	0.631723	+	0.377812i	0.0281392	+	0.0168291i
$505$	1.59205	−	1.59205i	0.0708454	−	0.0708454i
$506$		−	27.4544i		−	1.22050i
$507$	10.1567	+	8.11434i	0.451073	+	0.360370i
$508$	11.8149			0.524204
$509$	−4.01477	+	4.01477i	−0.177951	+	0.177951i	−0.790462	−	0.612511i	$-0.790160\pi$
$509$	−4.01477	+	4.01477i	−0.177951	+	0.177951i	0.612511	+	0.790462i	$0.290160\pi$
$510$			6.95756i			0.308086i
$511$	19.7752	−	33.0652i	0.874801	−	1.46272i
$512$	−22.6886	−	22.6886i	−1.00271	−	1.00271i
$513$	−1.77011	−	1.77011i	−0.0781521	−	0.0781521i
$514$	−4.81625	−	4.81625i	−0.212436	−	0.212436i
$515$	−4.77991	+	4.77991i	−0.210628	+	0.210628i
$516$		−	18.5814i		−	0.817999i
$517$	21.3868			0.940592
$518$	−6.90264	−	27.4444i	−0.303284	−	1.20584i
$519$			6.32899i			0.277812i
$520$	0.602582	−	0.289861i	0.0264250	−	0.0127112i
$521$		−	10.5379i		−	0.461673i	−0.972993	−	0.230837i	$-0.925854\pi$
$521$		−	10.5379i		−	0.461673i	0.972993	−	0.230837i	$-0.0741463\pi$
$522$	10.5924	+	10.5924i	0.463616	+	0.463616i
$523$		−	22.3250i		−	0.976203i	−0.872787	−	0.488101i	$-0.837690\pi$
$523$		−	22.3250i		−	0.976203i	0.872787	−	0.488101i	$-0.162310\pi$
$524$	−12.5363			−0.547649
$525$	−2.93995	−	11.6891i	−0.128310	−	0.510152i
$526$	0.589057	+	0.589057i	0.0256841	+	0.0256841i
$527$	4.83771	−	4.83771i	0.210734	−	0.210734i
$528$	12.1743	+	12.1743i	0.529817	+	0.529817i
$529$	14.5500			0.632607
$530$	−7.84099			−0.340591
$531$	5.95220	+	5.95220i	0.258304	+	0.258304i
$532$	−7.26398	+	12.1458i	−0.314933	+	0.526587i
$533$	−3.58471	−	1.25612i	−0.155271	−	0.0544087i
$534$	−0.490646			−0.0212323
$535$	2.99772	−	2.99772i	0.129603	−	0.129603i
$536$	−2.95471			−0.127624
$537$	−13.3219			−0.574882
$538$	40.5691	−	40.5691i	1.74906	−	1.74906i
$539$	9.37561	−	31.1234i	0.403836	−	1.34058i
$540$	1.00719	−	1.00719i	0.0433426	−	0.0433426i
$541$	18.3681	−	18.3681i	0.789708	−	0.789708i	−0.191739	−	0.981446i	$-0.561413\pi$
$541$	18.3681	−	18.3681i	0.789708	−	0.789708i	0.981446	+	0.191739i	$0.0614126\pi$
$542$			5.67752i			0.243870i
$543$			7.49642i			0.321702i
$544$	29.3833	+	29.3833i	1.25980	+	1.25980i
$545$	6.48750			0.277894
$546$	1.75618	−	19.3226i	0.0751576	−	0.826932i
$547$	8.63950			0.369398			0.184699	−	0.982795i	$-0.440869\pi$
$547$	8.63950			0.369398			0.184699	+	0.982795i	$0.440869\pi$
$548$	20.5711	+	20.5711i	0.878753	+	0.878753i
$549$			13.0492i			0.556927i
$550$			43.0262i			1.83464i
$551$	−13.0370	+	13.0370i	−0.555394	+	0.555394i
$552$	−0.571862	+	0.571862i	−0.0243401	+	0.0243401i
$553$	−1.59444	−	6.33941i	−0.0678026	−	0.269579i
$554$	10.9047	−	10.9047i	0.463296	−	0.463296i
$555$	−3.50557			−0.148803
$556$	−12.8230			−0.543815
$557$	−4.48411	+	4.48411i	−0.189998	+	0.189998i	−0.795695	−	0.605697i	$-0.792894\pi$
$557$	−4.48411	+	4.48411i	−0.189998	+	0.189998i	0.605697	+	0.795695i	$0.292894\pi$
$558$	−2.71161			−0.114792
$559$	−28.2547	+	13.5914i	−1.19505	+	0.574854i
$560$	5.61205	+	3.35638i	0.237153	+	0.141833i
$561$	−16.8498	−	16.8498i	−0.711401	−	0.711401i
$562$	8.19989			0.345892
$563$	−2.45705			−0.103552			−0.0517762	−	0.998659i	$-0.516488\pi$
$563$	−2.45705			−0.103552			−0.0517762	+	0.998659i	$0.516488\pi$
$564$	−6.95892	−	6.95892i	−0.293023	−	0.293023i
$565$	−4.77693	+	4.77693i	−0.200967	+	0.200967i
$566$	38.2962	+	38.2962i	1.60971	+	1.60971i
$567$	−0.645342	−	2.56584i	−0.0271018	−	0.107755i
$568$	−3.22479			−0.135309
$569$		−	6.90398i		−	0.289430i	−0.989473	−	0.144715i	$-0.953774\pi$
$569$		−	6.90398i		−	0.289430i	0.989473	−	0.144715i	$-0.0462265\pi$
$570$	2.39992	+	2.39992i	0.100522	+	0.100522i
$571$			8.21317i			0.343711i	0.985122	+	0.171855i	$0.0549762\pi$
$571$			8.21317i			0.343711i	−0.985122	+	0.171855i	$0.945024\pi$
$572$	−11.8308	+	33.7626i	−0.494669	+	1.41168i
$573$		−	14.2378i		−	0.594791i
$574$	1.38278	+	5.49785i	0.0577162	+	0.229476i
$575$	13.2428			0.552262
$576$		−	9.05432i		−	0.377263i
$577$	8.20907	−	8.20907i	0.341748	−	0.341748i	−0.515276	−	0.857024i	$-0.672311\pi$
$577$	8.20907	−	8.20907i	0.341748	−	0.341748i	0.857024	+	0.515276i	$0.172311\pi$
$578$	−13.4243	−	13.4243i	−0.558376	−	0.558376i
$579$	−3.61945	−	3.61945i	−0.150419	−	0.150419i
$580$	−7.41804	−	7.41804i	−0.308017	−	0.308017i
$581$	−32.1972	−	19.2561i	−1.33577	−	0.798876i
$582$		−	32.6843i		−	1.35481i
$583$	18.9894	−	18.9894i	0.786459	−	0.786459i
$584$	4.05133			0.167645
$585$	−2.26824	−	0.794814i	−0.0937801	−	0.0328615i
$586$		−	61.2402i		−	2.52981i
$587$	5.56542	−	5.56542i	0.229709	−	0.229709i	−0.582862	−	0.812571i	$-0.698067\pi$
$587$	5.56542	−	5.56542i	0.229709	−	0.229709i	0.812571	+	0.582862i	$0.198067\pi$
$588$	−13.1777	+	7.07638i	−0.543440	+	0.291825i
$589$		−	3.33741i		−	0.137516i
$590$	−8.07002	−	8.07002i	−0.332238	−	0.332238i
$591$	−7.92835	+	7.92835i	−0.326129	+	0.326129i
$592$	−13.7875	+	13.7875i	−0.566662	+	0.566662i
$593$	−11.2305	−	11.2305i	−0.461181	−	0.461181i	0.437861	−	0.899043i	$-0.355736\pi$
$593$	−11.2305	−	11.2305i	−0.461181	−	0.461181i	−0.899043	+	0.437861i	$0.855736\pi$
$594$			9.44458i			0.387516i
$595$	−7.76739	−	4.64541i	−0.318432	−	0.190443i
$596$	−22.7537	+	22.7537i	−0.932029	+	0.932029i
$597$		−	19.2250i		−	0.786829i
$598$	20.1179	+	7.04954i	0.822684	+	0.288277i
$599$	−29.5289			−1.20652			−0.603258	−	0.797546i	$-0.706131\pi$
$599$	−29.5289			−1.20652			−0.603258	+	0.797546i	$0.706131\pi$
$600$	0.896214	−	0.896214i	0.0365878	−	0.0365878i
$601$		−	38.2776i		−	1.56138i	−0.624920	−	0.780688i	$-0.714869\pi$
$601$		−	38.2776i		−	1.56138i	0.624920	−	0.780688i	$-0.285131\pi$
$602$	40.1604	+	24.0185i	1.63682	+	0.978923i
$603$	7.50970	+	7.50970i	0.305819	+	0.305819i
$604$	8.38476	+	8.38476i	0.341171	+	0.341171i
$605$	4.97879	+	4.97879i	0.202417	+	0.202417i
$606$	4.85762	−	4.85762i	0.197327	−	0.197327i
$607$			2.32455i			0.0943506i	0.998887	+	0.0471753i	$0.0150219\pi$
$607$			2.32455i			0.0943506i	−0.998887	+	0.0471753i	$0.984978\pi$
$608$	20.2708			0.822088
$609$	−18.8976	+	4.75300i	−0.765770	+	0.192601i
$610$		−	17.6922i		−	0.716336i
$611$	−5.49156	+	15.6718i	−0.222165	+	0.634013i
$612$			10.9653i			0.443246i
$613$	26.4448	+	26.4448i	1.06810	+	1.06810i	0.997505	+	0.0705898i	$0.0224881\pi$
$613$	26.4448	+	26.4448i	1.06810	+	1.06810i	0.0705898	+	0.997505i	$0.477512\pi$
$614$		−	29.0448i		−	1.17215i
$615$	0.702259			0.0283178
$616$	3.31480	−	0.833716i	0.133557	−	0.0335914i
$617$	4.98927	+	4.98927i	0.200860	+	0.200860i	0.800369	−	0.599508i	$-0.204637\pi$
$617$	4.98927	+	4.98927i	0.200860	+	0.200860i	−0.599508	+	0.800369i	$0.704637\pi$
$618$	−14.5843	+	14.5843i	−0.586667	+	0.586667i
$619$	−28.0127	−	28.0127i	−1.12592	−	1.12592i	−0.990833	−	0.135090i	$-0.956868\pi$
$619$	−28.0127	−	28.0127i	−1.12592	−	1.12592i	−0.135090	−	0.990833i	$-0.543132\pi$
$620$	1.89899			0.0762652
$621$	2.90689			0.116650
$622$	2.05970	+	2.05970i	0.0825864	+	0.0825864i
$623$	0.327594	−	0.547755i	0.0131248	−	0.0219454i
$624$	−12.0470	+	5.79500i	−0.482267	+	0.231985i
$625$	−18.5321			−0.741284
$626$	33.8736	−	33.8736i	1.35386	−	1.35386i
$627$	−11.6243			−0.464229
$628$	−23.9194			−0.954490
$629$	19.0826	−	19.0826i	0.760874	−	0.760874i
$630$	0.874958	+	3.47878i	0.0348592	+	0.138598i
$631$	−2.30759	+	2.30759i	−0.0918639	+	0.0918639i	−0.751545	−	0.659681i	$-0.770691\pi$
$631$	−2.30759	+	2.30759i	−0.0918639	+	0.0918639i	0.659681	+	0.751545i	$0.270691\pi$
$632$	0.486050	−	0.486050i	0.0193340	−	0.0193340i
$633$			7.53906i			0.299651i
$634$		−	46.8781i		−	1.86177i
$635$	2.60628	+	2.60628i	0.103427	+	0.103427i
$636$	−12.3576			−0.490012
$637$	20.3991	+	14.8619i	0.808243	+	0.588849i
$638$	69.5601			2.75391
$639$	8.19616	+	8.19616i	0.324235	+	0.324235i
$640$			1.48018i			0.0585094i
$641$			26.8438i			1.06027i	0.847914	+	0.530133i	$0.177858\pi$
$641$			26.8438i			1.06027i	−0.847914	+	0.530133i	$0.822142\pi$
$642$	9.14653	−	9.14653i	0.360985	−	0.360985i
$643$	8.19484	−	8.19484i	0.323173	−	0.323173i	−0.526810	−	0.849983i	$-0.676612\pi$
$643$	8.19484	−	8.19484i	0.323173	−	0.323173i	0.849983	+	0.526810i	$0.176612\pi$
$644$	−4.00849	−	15.9375i	−0.157957	−	0.628025i
$645$	4.09890	−	4.09890i	0.161394	−	0.161394i
$646$	−26.1280			−1.02799
$647$	−23.6489			−0.929735			−0.464867	−	0.885380i	$-0.653898\pi$
$647$	−23.6489			−0.929735			−0.464867	+	0.885380i	$0.653898\pi$
$648$	0.196726	−	0.196726i	0.00772813	−	0.00772813i
$649$	39.0880			1.53434
$650$	−31.5286	−	11.0479i	−1.23665	−	0.433336i
$651$	1.81048	−	3.02723i	0.0709584	−	0.118647i
$652$	−8.40800	−	8.40800i	−0.329283	−	0.329283i
$653$	−44.5101			−1.74181			−0.870907	−	0.491448i	$-0.836468\pi$
$653$	−44.5101			−1.74181			−0.870907	+	0.491448i	$0.836468\pi$
$654$	19.7944			0.774024
$655$	−2.76540	−	2.76540i	−0.108053	−	0.108053i
$656$	2.76200	−	2.76200i	0.107838	−	0.107838i
$657$	−10.2969	−	10.2969i	−0.401720	−	0.401720i
$658$	24.0357	−	6.04529i	0.937009	−	0.235670i
$659$	−49.6491			−1.93405			−0.967027	−	0.254672i	$-0.918032\pi$
$659$	−49.6491			−1.93405			−0.967027	+	0.254672i	$0.918032\pi$
$660$		−	6.61421i		−	0.257458i
$661$	−19.1091	−	19.1091i	−0.743257	−	0.743257i	0.229946	−	0.973203i	$-0.426145\pi$
$661$	−19.1091	−	19.1091i	−0.743257	−	0.743257i	−0.973203	+	0.229946i	$0.926145\pi$
$662$		−	25.1476i		−	0.977388i
$663$	16.6737	−	8.02059i	0.647555	−	0.311494i
$664$		−	3.94499i		−	0.153095i
$665$	−4.28164	+	1.07689i	−0.166035	+	0.0417599i
$666$	−10.6961			−0.414465
$667$		−	21.4095i		−	0.828979i
$668$	−11.7223	+	11.7223i	−0.453549	+	0.453549i
$669$	4.42747	+	4.42747i	0.171176	+	0.171176i
$670$	−10.1817	−	10.1817i	−0.393353	−	0.393353i
$671$	42.8470	+	42.8470i	1.65409	+	1.65409i
$672$	18.3868	+	10.9965i	0.709285	+	0.424199i
$673$		−	30.4732i		−	1.17465i	−0.809350	−	0.587327i	$-0.800180\pi$
$673$		−	30.4732i		−	1.17465i	0.809350	−	0.587327i	$-0.199820\pi$
$674$	−39.9592	+	39.9592i	−1.53917	+	1.53917i
$675$	−4.55564			−0.175347
$676$	−21.7026	−	17.3386i	−0.834715	−	0.666870i
$677$		−	14.6625i		−	0.563527i	−0.959484	−	0.281764i	$-0.909081\pi$
$677$		−	14.6625i		−	0.563527i	0.959484	−	0.281764i	$-0.0909194\pi$
$678$	−14.5752	+	14.5752i	−0.559758	+	0.559758i
$679$	36.4886	+	21.8226i	1.40031	+	0.837474i
$680$		−	0.951704i		−	0.0364962i
$681$	−12.5432	−	12.5432i	−0.480658	−	0.480658i
$682$	−8.90355	+	8.90355i	−0.340935	+	0.340935i
$683$	15.9213	−	15.9213i	0.609210	−	0.609210i	−0.333530	−	0.942740i	$-0.608240\pi$
$683$	15.9213	−	15.9213i	0.609210	−	0.609210i	0.942740	+	0.333530i	$0.108240\pi$
$684$	3.78234	+	3.78234i	0.144621	+	0.144621i
$685$			9.07562i			0.346762i
$686$	1.73934	−	37.6283i	0.0664085	−	1.43666i
$687$	−1.68832	+	1.68832i	−0.0644133	+	0.0644133i
$688$		−	32.2421i		−	1.22922i
$689$	9.03901	+	18.7909i	0.344359	+	0.715876i
$690$	−3.94118			−0.150038
$691$	19.0536	−	19.0536i	0.724832	−	0.724832i	−0.244753	−	0.969585i	$-0.578707\pi$
$691$	19.0536	−	19.0536i	0.724832	−	0.724832i	0.969585	+	0.244753i	$0.0787070\pi$
$692$		−	13.5237i		−	0.514094i
$693$	−10.5439	−	6.30594i	−0.400529	−	0.239543i
$694$	35.3018	+	35.3018i	1.34004	+	1.34004i
$695$	−2.82864	−	2.82864i	−0.107296	−	0.107296i
$696$	−1.44890	−	1.44890i	−0.0549205	−	0.0549205i
$697$	−3.82275	+	3.82275i	−0.144797	+	0.144797i
$698$		−	48.1063i		−	1.82085i
$699$	0.385937			0.0145975
$700$	6.28205	+	24.9770i	0.237439	+	0.944042i
$701$			33.9216i			1.28120i	0.767874	+	0.640601i	$0.221315\pi$
$701$			33.9216i			1.28120i	−0.767874	+	0.640601i	$0.778685\pi$
$702$	−6.92077	−	2.42511i	−0.261208	−	0.0915299i
$703$		−	13.1646i		−	0.496513i
$704$	−29.7298	−	29.7298i	−1.12048	−	1.12048i
$705$		−	3.07016i		−	0.115629i
$706$	−15.0065			−0.564776
$707$	2.17970	+	8.66635i	0.0819761	+	0.325932i
$708$	−12.7186	−	12.7186i	−0.477994	−	0.477994i
$709$	21.1726	−	21.1726i	0.795153	−	0.795153i	−0.187174	−	0.982327i	$-0.559933\pi$
$709$	21.1726	−	21.1726i	0.795153	−	0.795153i	0.982327	+	0.187174i	$0.0599329\pi$
$710$	−11.1124	−	11.1124i	−0.417040	−	0.417040i
$711$	−2.47069			−0.0926583
$712$	0.0671141			0.00251521
$713$	2.74037	+	2.74037i	0.102628	+	0.102628i
$714$	−23.6996	−	14.1739i	−0.886935	−	0.530445i
$715$	−10.0575	+	4.83797i	−0.376130	+	0.180930i
$716$	28.4660			1.06383
$717$	−6.67161	+	6.67161i	−0.249156	+	0.249156i
$718$	−54.2817			−2.02578
$719$	−16.7994			−0.626513			−0.313257	−	0.949669i	$-0.601420\pi$
$719$	−16.7994			−0.626513			−0.313257	+	0.949669i	$0.601420\pi$
$720$	1.74766	−	1.74766i	0.0651314	−	0.0651314i
$721$	−6.54424	−	26.0195i	−0.243720	−	0.969016i
$722$	18.3131	−	18.3131i	0.681544	−	0.681544i
$723$	−14.1379	+	14.1379i	−0.525794	+	0.525794i
$724$		−	16.0183i		−	0.595314i
$725$			33.5527i			1.24612i
$726$	15.1911	+	15.1911i	0.563795	+	0.563795i
$727$	−38.8270			−1.44001			−0.720007	−	0.693966i	$-0.755862\pi$
$727$	−38.8270			−1.44001			−0.720007	+	0.693966i	$0.755862\pi$
$728$	−0.240223	+	2.64309i	−0.00890326	+	0.0979593i
$729$	−1.00000			−0.0370370
$730$	13.9606	+	13.9606i	0.516704	+	0.516704i
$731$			44.6248i			1.65051i
$732$		−	27.8834i		−	1.03060i
$733$	−22.2107	+	22.2107i	−0.820370	+	0.820370i	−0.986161	−	0.165791i	$-0.946982\pi$
$733$	−22.2107	+	22.2107i	−0.820370	+	0.820370i	0.165791	+	0.986161i	$0.446982\pi$
$734$	−8.93841	+	8.93841i	−0.329923	+	0.329923i
$735$	−4.46788	−	1.34590i	−0.164800	−	0.0496444i
$736$	−16.6445	+	16.6445i	−0.613523	+	0.613523i
$737$	49.3161			1.81658
$738$	2.14271			0.0788742
$739$	−17.6358	+	17.6358i	−0.648744	+	0.648744i	−0.952689	−	0.303946i	$-0.901696\pi$
$739$	−17.6358	+	17.6358i	−0.648744	+	0.648744i	0.303946	+	0.952689i	$0.401696\pi$
$740$	7.49066			0.275362
$741$	2.98480	−	8.51800i	0.109649	−	0.312916i
$742$	15.9737	−	26.7089i	0.586411	−	0.980513i
$743$	35.1196	+	35.1196i	1.28841	+	1.28841i	0.935750	+	0.352664i	$0.114724\pi$
$743$	35.1196	+	35.1196i	1.28841	+	1.28841i	0.352664	+	0.935750i	$0.385276\pi$
$744$	0.370913			0.0135983
$745$	−10.0386			−0.367785
$746$	47.7231	+	47.7231i	1.74727	+	1.74727i
$747$	−10.0266	+	10.0266i	−0.366854	+	0.366854i
$748$	36.0045	+	36.0045i	1.31646	+	1.31646i
$749$	4.10421	+	16.3181i	0.149965	+	0.596250i
$750$	12.9556			0.473071
$751$		−	29.8500i		−	1.08924i	−0.838683	−	0.544620i	$-0.816674\pi$
$751$		−	29.8500i		−	1.08924i	0.838683	−	0.544620i	$-0.183326\pi$
$752$	−12.0750	−	12.0750i	−0.440330	−	0.440330i
$753$			28.8068i			1.04978i
$754$	−17.8611	+	50.9720i	−0.650464	+	1.85629i
$755$			3.69922i			0.134628i
$756$	1.37896	+	5.48265i	0.0501523	+	0.199402i
$757$	−45.3819			−1.64943			−0.824716	−	0.565546i	$-0.808665\pi$
$757$	−45.3819			−1.64943			−0.824716	+	0.565546i	$0.808665\pi$
$758$			13.9014i			0.504923i
$759$	9.54477	−	9.54477i	0.346453	−	0.346453i
$760$	−0.328278	−	0.328278i	−0.0119079	−	0.0119079i
$761$	−16.8835	−	16.8835i	−0.612027	−	0.612027i	0.331447	−	0.943474i	$-0.392463\pi$
$761$	−16.8835	−	16.8835i	−0.612027	−	0.612027i	−0.943474	+	0.331447i	$0.892463\pi$
$762$	7.95220	+	7.95220i	0.288078	+	0.288078i
$763$	−13.2163	+	22.0984i	−0.478463	+	0.800017i
$764$			30.4230i			1.10067i
$765$	−2.41886	+	2.41886i	−0.0874539	+	0.0874539i
$766$	50.6283			1.82928
$767$	−10.0367	+	28.6428i	−0.362406	+	1.03423i
$768$		−	13.5923i		−	0.490472i
$769$	−5.44838	+	5.44838i	−0.196473	+	0.196473i	−0.798486	−	0.602013i	$-0.794366\pi$
$769$	−5.44838	+	5.44838i	−0.196473	+	0.196473i	0.602013	+	0.798486i	$0.294366\pi$
$770$	14.2955	+	8.54963i	0.515173	+	0.308107i
$771$		−	3.34882i		−	0.120605i
$772$	7.73399	+	7.73399i	0.278353	+	0.278353i
$773$	15.4259	−	15.4259i	0.554832	−	0.554832i	−0.372999	−	0.927832i	$-0.621671\pi$
$773$	15.4259	−	15.4259i	0.554832	−	0.554832i	0.927832	+	0.372999i	$0.121671\pi$
$774$	12.5064	−	12.5064i	0.449534	−	0.449534i
$775$	−4.29468	−	4.29468i	−0.154269	−	0.154269i
$776$			4.47079i			0.160492i
$777$	7.14154	−	11.9411i	0.256201	−	0.428383i
$778$	−21.7755	+	21.7755i	−0.780691	+	0.780691i
$779$			2.63722i			0.0944882i
$780$	4.84674	+	1.69835i	0.173541	+	0.0608107i
$781$	53.8240			1.92598
$782$	21.4539	−	21.4539i	0.767188	−	0.767188i
$783$			7.36508i			0.263206i
$784$	−22.8657	+	12.2788i	−0.816633	+	0.438529i
$785$	−5.27643	−	5.27643i	−0.188324	−	0.188324i
$786$	−8.43769	−	8.43769i	−0.300962	−	0.300962i
$787$	−33.9563	−	33.9563i	−1.21041	−	1.21041i	−0.970892	−	0.239518i	$-0.923011\pi$
$787$	−33.9563	−	33.9563i	−1.21041	−	1.21041i	−0.239518	−	0.970892i	$-0.576989\pi$
$788$	16.9412	−	16.9412i	0.603505	−	0.603505i
$789$			0.409582i			0.0145815i
$790$	3.34978			0.119180
$791$	−6.54016	−	26.0033i	−0.232541	−	0.924570i
$792$		−	1.29190i		−	0.0459056i
$793$	−42.3992	+	20.3954i	−1.50564	+	0.724260i
$794$			39.2595i			1.39327i
$795$	−2.72599	−	2.72599i	−0.0966810	−	0.0966810i
$796$			41.0798i			1.45604i
$797$	30.5826			1.08329			0.541645	−	0.840607i	$-0.317802\pi$
$797$	30.5826			1.08329			0.541645	+	0.840607i	$0.317802\pi$
$798$	−13.0640	+	3.28576i	−0.462460	+	0.116315i
$799$	16.7124	+	16.7124i	0.591244	+	0.591244i
$800$	26.0850	−	26.0850i	0.922242	−	0.922242i
$801$	−0.170577	−	0.170577i	−0.00602706	−	0.00602706i
$802$	40.4722			1.42912
$803$	−67.6196			−2.38624
$804$	−16.0466	−	16.0466i	−0.565921	−	0.565921i
$805$	2.63144	−	4.39992i	0.0927461	−	0.155077i
$806$	−4.23813	−	8.81051i	−0.149282	−	0.310337i
$807$	28.2084			0.992982
$808$	−0.664460	+	0.664460i	−0.0233756	+	0.0233756i
$809$	30.5995			1.07582			0.537910	−	0.843002i	$-0.319214\pi$
$809$	30.5995			1.07582			0.537910	+	0.843002i	$0.319214\pi$
$810$	1.35580			0.0476381
$811$	−22.8757	+	22.8757i	−0.803274	+	0.803274i	−0.983606	−	0.180331i	$-0.942283\pi$
$811$	−22.8757	+	22.8757i	−0.803274	+	0.803274i	0.180331	+	0.983606i	$0.442283\pi$
$812$	40.3802	−	10.1561i	1.41707	−	0.356411i
$813$	−1.97384	+	1.97384i	−0.0692256	+	0.0692256i
$814$	−35.1205	+	35.1205i	−1.23097	+	1.23097i
$815$		−	3.70947i		−	0.129937i
$816$			19.0268i			0.666071i
$817$	15.3927	+	15.3927i	0.538524	+	0.538524i
$818$	−60.8449			−2.12739
$819$	7.32823	−	6.10713i	0.256069	−	0.213400i
$820$	−1.50058			−0.0524024
$821$	−22.2230	−	22.2230i	−0.775586	−	0.775586i	0.203491	−	0.979077i	$-0.434771\pi$
$821$	−22.2230	−	22.2230i	−0.775586	−	0.775586i	−0.979077	+	0.203491i	$0.934771\pi$
$822$			27.6912i			0.965843i
$823$			5.96596i			0.207960i	0.994579	+	0.103980i	$0.0331578\pi$
$823$			5.96596i			0.207960i	−0.994579	+	0.103980i	$0.966842\pi$
$824$	1.99495	−	1.99495i	0.0694972	−	0.0694972i
$825$	−14.9584	+	14.9584i	−0.520786	+	0.520786i
$826$	43.9292	−	11.0488i	1.52849	−	0.384436i
$827$	−11.6765	+	11.6765i	−0.406033	+	0.406033i	−0.880353	−	0.474320i	$-0.842694\pi$
$827$	−11.6765	+	11.6765i	−0.406033	+	0.406033i	0.474320	+	0.880353i	$0.342694\pi$
$828$	−6.21141			−0.215862
$829$	7.66944			0.266371			0.133185	−	0.991091i	$-0.457479\pi$
$829$	7.66944			0.266371			0.133185	+	0.991091i	$0.457479\pi$
$830$	13.5941	−	13.5941i	0.471858	−	0.471858i
$831$	7.58222			0.263024
$832$	29.4191	−	14.1515i	1.01992	−	0.490615i
$833$	31.6474	−	16.9945i	1.09652	−	0.588826i
$834$	−8.63065	−	8.63065i	−0.298855	−	0.298855i
$835$	−5.17169			−0.178974
$836$	24.8386			0.859061
$837$	−0.942715	−	0.942715i	−0.0325850	−	0.0325850i
$838$	−52.2367	+	52.2367i	−1.80449	+	1.80449i
$839$	−10.3626	−	10.3626i	−0.357758	−	0.357758i	0.505228	−	0.862986i	$-0.331408\pi$
$839$	−10.3626	−	10.3626i	−0.357758	−	0.357758i	−0.862986	+	0.505228i	$0.831408\pi$
$840$	−0.119683	−	0.475852i	−0.00412946	−	0.0164185i
$841$	25.2444			0.870496
$842$		−	9.53757i		−	0.328686i
$843$	2.85077	+	2.85077i	0.0981856	+	0.0981856i
$844$		−	16.1094i		−	0.554507i
$845$	−0.962660	−	8.61217i	−0.0331165	−	0.296268i
$846$		−	9.36757i		−	0.322064i
$847$	−27.1021	+	6.81653i	−0.931239	+	0.234219i
$848$	−21.4427			−0.736347
$849$			26.6280i			0.913871i
$850$	−33.6222	+	33.6222i	−1.15323	+	1.15323i
$851$	10.8095	+	10.8095i	0.370547	+	0.370547i
$852$	−17.5134	−	17.5134i	−0.600001	−	0.600001i
$853$	−32.8036	−	32.8036i	−1.12317	−	1.12317i	−0.991261	−	0.131912i	$-0.957888\pi$
$853$	−32.8036	−	32.8036i	−1.12317	−	1.12317i	−0.131912	−	0.991261i	$-0.542112\pi$
$854$	60.2651	+	36.0425i	2.06223	+	1.23335i
$855$			1.66871i			0.0570686i
$856$	−1.25113	+	1.25113i	−0.0427627	+	0.0427627i
$857$	47.7672			1.63169			0.815847	−	0.578267i	$-0.196271\pi$
$857$	47.7672			1.63169			0.815847	+	0.578267i	$0.196271\pi$
$858$	−30.6871	+	14.7615i	−1.04764	+	0.503948i
$859$			9.80510i			0.334546i	0.985911	+	0.167273i	$0.0534961\pi$
$859$			9.80510i			0.334546i	−0.985911	+	0.167273i	$0.946504\pi$
$860$	−8.75847	+	8.75847i	−0.298661	+	0.298661i
$861$	−1.43064	+	2.39211i	−0.0487561	+	0.0815230i
$862$			41.6266i			1.41781i
$863$	−4.00743	−	4.00743i	−0.136414	−	0.136414i	0.635602	−	0.772017i	$-0.280752\pi$
$863$	−4.00743	−	4.00743i	−0.136414	−	0.136414i	−0.772017	+	0.635602i	$0.780752\pi$
$864$	5.72585	−	5.72585i	0.194798	−	0.194798i
$865$	2.98322	−	2.98322i	0.101432	−	0.101432i
$866$	27.7526	+	27.7526i	0.943071	+	0.943071i
$867$		−	9.33413i		−	0.317004i
$868$	−3.86862	+	6.46855i	−0.131309	+	0.219557i
$869$	−8.11251	+	8.11251i	−0.275198	+	0.275198i
$870$		−	9.98561i		−	0.338544i
$871$	−12.6630	+	36.1377i	−0.429071	+	1.22448i
$872$	−2.70763			−0.0916918
$873$	11.3630	−	11.3630i	0.384579	−	0.384579i
$874$		−	14.8005i		−	0.500633i
$875$	−8.65016	+	14.4636i	−0.292429	+	0.488958i
$876$	22.0023	+	22.0023i	0.743388	+	0.743388i
$877$	−31.4841	−	31.4841i	−1.06314	−	1.06314i	−0.997867	−	0.0652746i	$-0.979208\pi$
$877$	−31.4841	−	31.4841i	−1.06314	−	1.06314i	−0.0652746	−	0.997867i	$-0.520792\pi$
$878$	−52.2950	−	52.2950i	−1.76487	−	1.76487i
$879$	21.2907	−	21.2907i	0.718118	−	0.718118i
$880$		−	11.4769i		−	0.386885i
$881$	30.9136			1.04151			0.520753	−	0.853707i	$-0.325651\pi$
$881$	30.9136			1.04151			0.520753	+	0.853707i	$0.325651\pi$
$882$	−13.6323	−	4.10658i	−0.459022	−	0.138276i
$883$			9.79360i			0.329581i	0.986329	+	0.164790i	$0.0526948\pi$
$883$			9.79360i			0.329581i	−0.986329	+	0.164790i	$0.947305\pi$
$884$	−35.6283	+	17.1383i	−1.19831	+	0.576423i
$885$		−	5.61123i		−	0.188619i
$886$	24.3658	+	24.3658i	0.818586	+	0.818586i
$887$			1.94407i			0.0652754i	0.999467	+	0.0326377i	$0.0103907\pi$
$887$			1.94407i			0.0652754i	−0.999467	+	0.0326377i	$0.989609\pi$
$888$	1.46309			0.0490980
$889$	−14.1873	+	3.56829i	−0.475827	+	0.119677i
$890$	0.231270	+	0.231270i	0.00775218	+	0.00775218i
$891$	−3.28349	+	3.28349i	−0.110001	+	0.110001i
$892$	−9.46056	−	9.46056i	−0.316763	−	0.316763i
$893$	11.5295			0.385820
$894$	−30.6294			−1.02440
$895$	6.27938	+	6.27938i	0.209896	+	0.209896i
$896$	−5.04197	−	3.01543i	−0.168440	−	0.100738i
$897$	4.54335	+	9.44502i	0.151698	+	0.315360i
$898$	−72.7975			−2.42928
$899$	−6.94317	+	6.94317i	−0.231568	+	0.231568i
$900$	9.73444			0.324481
$901$	29.6779			0.988715
$902$	7.03557	−	7.03557i	0.234259	−	0.234259i
$903$	5.61186	+	22.3124i	0.186751	+	0.742510i
$904$	1.99370	−	1.99370i	0.0663095	−	0.0663095i
$905$	3.53350	−	3.53350i	0.117457	−	0.117457i
$906$			11.2869i			0.374983i
$907$		−	23.6864i		−	0.786494i	−0.919433	−	0.393247i	$-0.871352\pi$
$907$		−	23.6864i		−	0.786494i	0.919433	−	0.393247i	$-0.128648\pi$
$908$	26.8022	+	26.8022i	0.889463	+	0.889463i
$909$	3.37759			0.112028
$910$	−9.93565	+	8.28007i	−0.329364	+	0.274482i
$911$	17.2535			0.571634			0.285817	−	0.958284i	$-0.407735\pi$
$911$	17.2535			0.571634			0.285817	+	0.958284i	$0.407735\pi$
$912$	6.56305	+	6.56305i	0.217324	+	0.217324i
$913$			65.8445i			2.17914i
$914$			16.7703i			0.554712i
$915$	6.15085	−	6.15085i	0.203341	−	0.203341i
$916$	3.60757	−	3.60757i	0.119198	−	0.119198i
$917$	15.0535	−	3.78614i	0.497109	−	0.125029i
$918$	−7.38034	+	7.38034i	−0.243587	+	0.243587i
$919$	−51.2821			−1.69164			−0.845821	−	0.533467i	$-0.820889\pi$
$919$	−51.2821			−1.69164			−0.845821	+	0.533467i	$0.820889\pi$
$920$	0.539103			0.0177737
$921$	10.0977	−	10.0977i	0.332730	−	0.332730i
$922$	8.41243			0.277049
$923$	−13.8205	+	39.4410i	−0.454909	+	1.29822i
$924$	22.5301	+	13.4745i	0.741185	+	0.443277i
$925$	−16.9406	−	16.9406i	−0.557003	−	0.557003i
$926$	−18.5609			−0.609950
$927$	−10.1407			−0.333065
$928$	−42.1714	−	42.1714i	−1.38434	−	1.38434i
$929$	−23.5762	+	23.5762i	−0.773511	+	0.773511i	−0.978719	−	0.205207i	$-0.934213\pi$
$929$	−23.5762	+	23.5762i	−0.773511	+	0.773511i	0.205207	+	0.978719i	$0.434213\pi$
$930$	1.27814	+	1.27814i	0.0419118	+	0.0419118i
$931$	5.05432	−	16.7784i	0.165649	−	0.549890i
$932$	−0.824665			−0.0270128
$933$			1.43215i			0.0468863i
$934$	13.7314	+	13.7314i	0.449305	+	0.449305i
$935$			15.8846i			0.519482i
$936$	0.946672	+	0.331724i	0.0309430	+	0.0108427i
$937$		−	3.71594i		−	0.121394i	−0.998156	−	0.0606972i	$-0.980668\pi$
$937$		−	3.71594i		−	0.121394i	0.998156	−	0.0606972i	$-0.0193324\pi$
$938$	55.4241	−	13.9399i	1.80966	−	0.455154i
$939$	23.5529			0.768620
$940$			6.56028i			0.213973i
$941$	36.6909	−	36.6909i	1.19609	−	1.19609i	0.220762	−	0.975328i	$-0.429146\pi$
$941$	36.6909	−	36.6909i	1.19609	−	1.19609i	0.975328	−	0.220762i	$-0.0708545\pi$
$942$	−16.0993	−	16.0993i	−0.524543	−	0.524543i
$943$	−2.16544	−	2.16544i	−0.0705164	−	0.0705164i
$944$	−22.0691	−	22.0691i	−0.718287	−	0.718287i
$945$	−0.905241	+	1.51362i	−0.0294475	+	0.0492379i
$946$		−	82.1295i		−	2.67026i
$947$	−18.6522	+	18.6522i	−0.606116	+	0.606116i	−0.941929	−	0.335813i	$-0.890989\pi$
$947$	−18.6522	+	18.6522i	−0.606116	+	0.606116i	0.335813	+	0.941929i	$0.390989\pi$
$948$	5.27935			0.171465
$949$	17.3629	−	49.5500i	0.563622	−	1.60846i
$950$			23.1951i			0.752548i
$951$	16.2976	−	16.2976i	0.528486	−	0.528486i
$952$	3.24180	+	1.93881i	0.105067	+	0.0628372i
$953$		−	28.6423i		−	0.927816i	−0.885883	−	0.463908i	$-0.846447\pi$
$953$		−	28.6423i		−	0.927816i	0.885883	−	0.463908i	$-0.153553\pi$
$954$	−8.31746	−	8.31746i	−0.269288	−	0.269288i
$955$	−6.71107	+	6.71107i	−0.217165	+	0.217165i
$956$	14.2558	−	14.2558i	0.461066	−	0.461066i
$957$	24.1832	+	24.1832i	0.781732	+	0.781732i
$958$		−	72.6066i		−	2.34581i
$959$	−30.9144	−	18.4888i	−0.998278	−	0.597036i
$960$	−4.26782	+	4.26782i	−0.137743	+	0.137743i
$961$			29.2226i			0.942664i
$962$	−16.7175	−	34.7535i	−0.538994	−	1.12050i
$963$	6.35975			0.204940
$964$	30.2097	−	30.2097i	0.972987	−	0.972987i
$965$			3.41211i			0.109840i
$966$	8.02897	−	13.4249i	0.258328	−	0.431939i
$967$	10.5047	+	10.5047i	0.337809	+	0.337809i	0.855542	−	0.517733i	$-0.173224\pi$
$967$	10.5047	+	10.5047i	0.337809	+	0.337809i	−0.517733	+	0.855542i	$0.673224\pi$
$968$	−2.07795	−	2.07795i	−0.0667878	−	0.0667878i
$969$	−9.08362	−	9.08362i	−0.291808	−	0.291808i
$970$	−15.4060	+	15.4060i	−0.494657	+	0.494657i
$971$			37.4505i			1.20184i	0.799308	+	0.600922i	$0.205200\pi$
$971$			37.4505i			1.20184i	−0.799308	+	0.600922i	$0.794800\pi$
$972$	2.13679			0.0685375
$973$	15.3977	−	3.87273i	0.493628	−	0.124154i
$974$			35.7615i			1.14587i
$975$	−7.12027	−	14.8021i	−0.228031	−	0.474047i
$976$		−	48.3828i		−	1.54869i
$977$	−13.9315	−	13.9315i	−0.445707	−	0.445707i	0.448218	−	0.893925i	$-0.352059\pi$
$977$	−13.9315	−	13.9315i	−0.445707	−	0.445707i	−0.893925	+	0.448218i	$0.852059\pi$
$978$		−	11.3182i		−	0.361917i
$979$	−1.12018			−0.0358011
$980$	9.54692	+	2.87591i	0.304965	+	0.0918676i
$981$	6.88172	+	6.88172i	0.219716	+	0.219716i
$982$	19.6512	−	19.6512i	0.627094	−	0.627094i
$983$	1.27995	+	1.27995i	0.0408242	+	0.0408242i	0.727224	−	0.686400i	$-0.240810\pi$
$983$	1.27995	+	1.27995i	0.0408242	+	0.0408242i	−0.686400	+	0.727224i	$0.740810\pi$
$984$	−0.293095			−0.00934353
$985$	7.47418			0.238147
$986$	54.3568	+	54.3568i	1.73107	+	1.73107i
$987$	10.4579	+	6.25452i	0.332879	+	0.199084i
$988$	−6.37787	+	18.2011i	−0.202907	+	0.579056i
$989$	−25.2782			−0.803799
$990$	4.45178	−	4.45178i	0.141487	−	0.141487i
$991$	7.83949			0.249029			0.124515	−	0.992218i	$-0.460263\pi$
$991$	7.83949			0.249029			0.124515	+	0.992218i	$0.460263\pi$
$992$	10.7957			0.342764
$993$	8.74278	−	8.74278i	0.277444	−	0.277444i
$994$	60.4904	−	15.2141i	1.91864	−	0.482563i
$995$	−9.06187	+	9.06187i	−0.287281	+	0.287281i
$996$	21.4247	−	21.4247i	0.678868	−	0.678868i
$997$		−	26.8688i		−	0.850944i	−0.904972	−	0.425472i	$-0.860108\pi$
$997$		−	26.8688i		−	0.850944i	0.904972	−	0.425472i	$-0.139892\pi$
$998$		−	76.9525i		−	2.43589i
$999$	−3.71859	−	3.71859i	−0.117651	−	0.117651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.e.34.2	✓	12
3.2	odd	2		819.2.y.g.307.5		12
7.6	odd	2		273.2.p.f.34.2	yes	12
13.5	odd	4		273.2.p.f.265.2	yes	12
21.20	even	2		819.2.y.f.307.5		12
39.5	even	4		819.2.y.f.811.5		12
91.83	even	4	inner	273.2.p.e.265.2	yes	12
273.83	odd	4		819.2.y.g.811.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.2	✓	12	1.1	even	1	trivial
273.2.p.e.265.2	yes	12	91.83	even	4	inner
273.2.p.f.34.2	yes	12	7.6	odd	2
273.2.p.f.265.2	yes	12	13.5	odd	4
819.2.y.f.307.5		12	21.20	even	2
819.2.y.f.811.5		12	39.5	even	4
819.2.y.g.307.5		12	3.2	odd	2
819.2.y.g.811.5		12	273.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43819 - 1.43819i) q^{2} -1.00000i q^{3} +2.13679i q^{4} +(-0.471358 + 0.471358i) q^{5} +(-1.43819 + 1.43819i) q^{6} +(-0.645342 - 2.56584i) q^{7} +(0.196726 - 0.196726i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.43819 - 1.43819i) q^{2} -1.00000i q^{3} +2.13679i q^{4} +(-0.471358 + 0.471358i) q^{5} +(-1.43819 + 1.43819i) q^{6} +(-0.645342 - 2.56584i) q^{7} +(0.196726 - 0.196726i) q^{8} -1.00000 q^{9} +1.35580 q^{10} +(-3.28349 + 3.28349i) q^{11} +2.13679 q^{12} +(-1.56296 - 3.24918i) q^{13} +(-2.76204 + 4.61829i) q^{14} +(0.471358 + 0.471358i) q^{15} +3.70771 q^{16} -5.13168 q^{17} +(1.43819 + 1.43819i) q^{18} +(-1.77011 + 1.77011i) q^{19} +(-1.00719 - 1.00719i) q^{20} +(-2.56584 + 0.645342i) q^{21} +9.44458 q^{22} -2.90689i q^{23} +(-0.196726 - 0.196726i) q^{24} +4.55564i q^{25} +(-2.42511 + 6.92077i) q^{26} +1.00000i q^{27} +(5.48265 - 1.37896i) q^{28} +7.36508 q^{29} -1.35580i q^{30} +(-0.942715 + 0.942715i) q^{31} +(-5.72585 - 5.72585i) q^{32} +(3.28349 + 3.28349i) q^{33} +(7.38034 + 7.38034i) q^{34} +(1.51362 + 0.905241i) q^{35} -2.13679i q^{36} +(-3.71859 + 3.71859i) q^{37} +5.09151 q^{38} +(-3.24918 + 1.56296i) q^{39} +0.185457i q^{40} +(0.744932 - 0.744932i) q^{41} +(4.61829 + 2.76204i) q^{42} -8.69594i q^{43} +(-7.01613 - 7.01613i) q^{44} +(0.471358 - 0.471358i) q^{45} +(-4.18067 + 4.18067i) q^{46} +(-3.25672 - 3.25672i) q^{47} -3.70771i q^{48} +(-6.16707 + 3.31169i) q^{49} +(6.55189 - 6.55189i) q^{50} +5.13168i q^{51} +(6.94281 - 3.33970i) q^{52} -5.78328 q^{53} +(1.43819 - 1.43819i) q^{54} -3.09540i q^{55} +(-0.631723 - 0.377812i) q^{56} +(1.77011 + 1.77011i) q^{57} +(-10.5924 - 10.5924i) q^{58} +(-5.95220 - 5.95220i) q^{59} +(-1.00719 + 1.00719i) q^{60} -13.0492i q^{61} +2.71161 q^{62} +(0.645342 + 2.56584i) q^{63} +9.05432i q^{64} +(2.26824 + 0.794814i) q^{65} -9.44458i q^{66} +(-7.50970 - 7.50970i) q^{67} -10.9653i q^{68} -2.90689 q^{69} +(-0.874958 - 3.47878i) q^{70} +(-8.19616 - 8.19616i) q^{71} +(-0.196726 + 0.196726i) q^{72} +(10.2969 + 10.2969i) q^{73} +10.6961 q^{74} +4.55564 q^{75} +(-3.78234 - 3.78234i) q^{76} +(10.5439 + 6.30594i) q^{77} +(6.92077 + 2.42511i) q^{78} +2.47069 q^{79} +(-1.74766 + 1.74766i) q^{80} +1.00000 q^{81} -2.14271 q^{82} +(10.0266 - 10.0266i) q^{83} +(-1.37896 - 5.48265i) q^{84} +(2.41886 - 2.41886i) q^{85} +(-12.5064 + 12.5064i) q^{86} -7.36508i q^{87} +1.29190i q^{88} +(0.170577 + 0.170577i) q^{89} -1.35580 q^{90} +(-7.32823 + 6.10713i) q^{91} +6.21141 q^{92} +(0.942715 + 0.942715i) q^{93} +9.36757i q^{94} -1.66871i q^{95} +(-5.72585 + 5.72585i) q^{96} +(-11.3630 + 11.3630i) q^{97} +(13.6323 + 4.10658i) q^{98} +(3.28349 - 3.28349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 q^{28} - 8 q^{29} - 24 q^{31} + 20 q^{32} + 4 q^{33} - 20 q^{35} - 4 q^{37} - 40 q^{38} - 16 q^{39} + 20 q^{41} + 8 q^{44} + 12 q^{45} + 20 q^{46} - 32 q^{47} + 20 q^{50} + 56 q^{52} - 16 q^{53} + 20 q^{56} - 8 q^{59} - 8 q^{60} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 q^{70} - 12 q^{71} + 32 q^{73} - 64 q^{74} - 4 q^{75} + 12 q^{77} + 16 q^{78} + 24 q^{79} + 4 q^{80} + 12 q^{81} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * q^28 - 8 * q^29 - 24 * q^31 + 20 * q^32 + 4 * q^33 - 20 * q^35 - 4 * q^37 - 40 * q^38 - 16 * q^39 + 20 * q^41 + 8 * q^44 + 12 * q^45 + 20 * q^46 - 32 * q^47 + 20 * q^50 + 56 * q^52 - 16 * q^53 + 20 * q^56 - 8 * q^59 - 8 * q^60 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * q^70 - 12 * q^71 + 32 * q^73 - 64 * q^74 - 4 * q^75 + 12 * q^77 + 16 * q^78 + 24 * q^79 + 4 * q^80 + 12 * q^81 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more