LMFDB - Embedded newform 273.2.p.f.265.2

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			265.2
Root			$-0.528642 - 0.528642i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.f.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43819 + 1.43819i) q^{2} -1.00000i q^{3} -2.13679i q^{4} +(0.471358 + 0.471358i) q^{5} +(1.43819 + 1.43819i) q^{6} +(2.56584 - 0.645342i) q^{7} +(0.196726 + 0.196726i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(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} +(2.56584 - 0.645342i) 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} +(-0.645342 - 2.56584i) 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} +(-1.37896 - 5.48265i) 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} +(-2.56584 + 0.645342i) 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} +(-3.47878 + 0.874958i) 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} +(-5.48265 + 1.37896i) 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} +(1.91346 - 9.34552i) 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} +(-4.10658 + 13.6323i) q^{98} +(3.28349 + 3.28349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 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} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 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} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * 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 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * 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 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.0171009	+	0.999854i	$0.505444\pi$
$2$	−1.43819	+	1.43819i	−1.01695	+	1.01695i	−0.999854	+	0.0171009i	$0.994556\pi$
$3$		−	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	$-0.202376\pi$
$5$	0.471358	+	0.471358i	0.210798	+	0.210798i	−0.593809	+	0.804606i	$0.702376\pi$
$6$	1.43819	+	1.43819i	0.587139	+	0.587139i
$7$	2.56584	−	0.645342i	0.969796	−	0.243916i
$7$	2.56584	−	0.645342i	0.969796	−	0.243916i
$8$	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	0.00994007	−	0.999951i	$-0.496836\pi$
$11$	−3.28349	−	3.28349i	−0.990011	−	0.990011i	−0.999951	+	0.00994007i	$0.996836\pi$
$12$	−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	$-0.286195\pi$
$17$	5.13168			1.24462			0.622308	+	0.782773i	$0.286195\pi$
$18$	1.43819	−	1.43819i	0.338985	−	0.338985i
$19$	1.77011	+	1.77011i	0.406090	+	0.406090i	0.880373	−	0.474282i	$-0.157292\pi$
$19$	1.77011	+	1.77011i	0.406090	+	0.406090i	−0.474282	+	0.880373i	$0.657292\pi$
$20$	1.00719	−	1.00719i	0.225215	−	0.225215i
$21$	−0.645342	−	2.56584i	−0.140825	−	0.559912i
$22$	9.44458			2.01359
$23$			2.90689i			0.606129i	0.952970	+	0.303065i	$0.0980098\pi$
$23$			2.90689i			0.606129i	−0.952970	+	0.303065i	$0.901990\pi$
$24$	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
$28$	−1.37896	−	5.48265i	−0.260599	−	1.03612i
$29$	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	$-0.211799\pi$
$31$	0.942715	+	0.942715i	0.169317	+	0.169317i	−0.617362	+	0.786679i	$0.711799\pi$
$32$	−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	0.331961	−	0.943293i	$-0.392290\pi$
$37$	−3.71859	−	3.71859i	−0.611332	−	0.611332i	−0.943293	+	0.331961i	$0.892290\pi$
$38$	−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	$-0.276215\pi$
$41$	−0.744932	−	0.744932i	−0.116339	−	0.116339i	−0.762880	+	0.646541i	$0.776215\pi$
$42$	4.61829	+	2.76204i	0.712618	+	0.426192i
$43$			8.69594i			1.32612i	0.748567	+	0.663059i	$0.230742\pi$
$43$			8.69594i			1.32612i	−0.748567	+	0.663059i	$0.769258\pi$
$44$	−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	$-0.640958\pi$
$47$	3.25672	−	3.25672i	0.475042	−	0.475042i	0.903542	+	0.428500i	$0.140958\pi$
$48$		−	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	$-0.565410\pi$
$59$	5.95220	−	5.95220i	0.774911	−	0.774911i	0.978960	+	0.204050i	$0.0654105\pi$
$60$	−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
$63$	−2.56584	+	0.645342i	−0.323265	+	0.0813055i
$64$		−	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	−0.996844	−	0.0793877i	$-0.974704\pi$
$67$	−7.50970	+	7.50970i	−0.917456	+	0.917456i	0.0793877	+	0.996844i	$0.474704\pi$
$68$		−	10.9653i		−	1.32974i
$69$	2.90689			0.349949
$70$	−3.47878	+	0.874958i	−0.415794	+	0.104578i
$71$	−8.19616	+	8.19616i	−0.972705	+	0.972705i	−0.999637	−	0.0269326i	$-0.991426\pi$
$71$	−8.19616	+	8.19616i	−0.972705	+	0.972705i	0.0269326	+	0.999637i	$0.491426\pi$
$72$	−0.196726	−	0.196726i	−0.0231844	−	0.0231844i
$73$	−10.2969	+	10.2969i	−1.20516	+	1.20516i	−0.232584	+	0.972576i	$0.574718\pi$
$73$	−10.2969	+	10.2969i	−1.20516	+	1.20516i	−0.972576	+	0.232584i	$0.925282\pi$
$74$	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	−0.994343	−	0.106219i	$-0.966126\pi$
$83$	−10.0266	−	10.0266i	−1.10056	−	1.10056i	−0.106219	−	0.994343i	$-0.533874\pi$
$84$	−5.48265	+	1.37896i	−0.598207	+	0.150457i
$85$	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	$-0.754070\pi$
$89$	−0.170577	+	0.170577i	−0.0180812	+	0.0180812i	0.698008	+	0.716090i	$0.254070\pi$
$90$	1.35580			0.142914
$91$	1.91346	−	9.34552i	0.200585	−	0.979676i
$92$	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	0.985797	+	0.167940i	$0.0537114\pi$
$97$	11.3630	+	11.3630i	1.15374	+	1.15374i	0.167940	+	0.985797i	$0.446289\pi$
$98$	−4.10658	+	13.6323i	−0.414827	+	1.37707i
$99$	3.28349	+	3.28349i	0.330004	+	0.330004i
$100$	−9.73444			−0.973444
$101$	3.37759			0.336083			0.168041	−	0.985780i	$-0.446256\pi$
$101$	3.37759			0.336083			0.168041	+	0.985780i	$0.446256\pi$
$102$	7.38034	+	7.38034i	0.730762	+	0.730762i
$103$	−10.1407			−0.999196			−0.499598	−	0.866257i	$-0.666519\pi$
$103$	−10.1407			−0.999196			−0.499598	+	0.866257i	$0.666519\pi$
$104$	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	−0.955179	−	0.296030i	$-0.904337\pi$
$109$	−6.88172	+	6.88172i	−0.659149	+	0.659149i	0.296030	+	0.955179i	$0.404337\pi$
$110$	4.45178	+	4.45178i	0.424460	+	0.424460i
$111$	−3.71859	+	3.71859i	−0.352953	+	0.352953i
$112$	9.51340	−	2.39275i	0.898932	−	0.226093i
$113$	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
$119$	13.1671	−	3.31169i	1.20702	−	0.303582i
$120$	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	$0.0788941\pi$
$127$			5.52931i			0.490646i	−0.969441	+	0.245323i	$0.921106\pi$
$128$	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	0.986466	−	0.163966i	$-0.0524289\pi$
$137$	9.62711	+	9.62711i	0.822499	+	0.822499i	−0.163966	+	0.986466i	$0.552429\pi$
$138$	−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	−0.120365	−	0.992730i	$-0.538406\pi$
$149$	10.6486	−	10.6486i	0.872365	−	0.872365i	0.992730	+	0.120365i	$0.0384064\pi$
$150$	6.55189	−	6.55189i	0.534959	−	0.534959i
$151$	3.92400	+	3.92400i	0.319331	+	0.319331i	0.848510	−	0.529179i	$-0.177500\pi$
$151$	3.92400	+	3.92400i	0.319331	+	0.319331i	−0.529179	+	0.848510i	$0.677500\pi$
$152$			0.696452i			0.0564898i
$153$	−5.13168			−0.414872
$154$	24.2333	−	6.09499i	1.95277	−	0.491148i
$155$			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
$161$	1.87594	+	7.45863i	0.147845	+	0.587822i
$162$	−1.43819	+	1.43819i	−0.112995	+	0.112995i
$163$	−3.93488	−	3.93488i	−0.308204	−	0.308204i	0.536009	−	0.844212i	$-0.319931\pi$
$163$	−3.93488	−	3.93488i	−0.308204	−	0.308204i	−0.844212	+	0.536009i	$0.819931\pi$
$164$	−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	$-0.847046\pi$
$167$	−5.48595	+	5.48595i	−0.424515	+	0.424515i	0.462240	+	0.886755i	$0.347046\pi$
$168$	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	$-0.422658\pi$
$173$	6.32899			0.481184			0.240592	+	0.970626i	$0.422658\pi$
$174$	10.5924	+	10.5924i	0.803007	+	0.803007i
$175$	−2.93995	−	11.6891i	−0.222239	−	0.883609i
$176$	−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	$0.165882\pi$
$179$			13.3219i			0.995725i	−0.867256	+	0.497862i	$0.834118\pi$
$180$	−1.00719	+	1.00719i	−0.0750716	+	0.0750716i
$181$	7.49642			0.557205			0.278602	−	0.960407i	$-0.410129\pi$
$181$	7.49642			0.557205			0.278602	+	0.960407i	$0.410129\pi$
$182$	10.6887	+	16.1926i	0.792300	+	1.20027i
$183$	−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
$189$	0.645342	+	2.56584i	0.0469417	+	0.186637i
$190$	−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	0.825271	−	0.564737i	$-0.191022\pi$
$193$	3.61945	+	3.61945i	0.260534	+	0.260534i	−0.564737	+	0.825271i	$0.691022\pi$
$194$	−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	−0.930687	−	0.365816i	$-0.880790\pi$
$197$	−7.92835	+	7.92835i	−0.564871	+	0.564871i	0.365816	+	0.930687i	$0.380790\pi$
$198$	−9.44458			−0.671197
$199$	−19.2250			−1.36283			−0.681414	−	0.731899i	$-0.738635\pi$
$199$	−19.2250			−1.36283			−0.681414	+	0.731899i	$0.738635\pi$
$200$	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
$203$	18.8976	−	4.75300i	1.32635	−	0.333595i
$204$	−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
$210$	0.874958	+	3.47878i	0.0603779	+	0.240058i
$211$	−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	$-0.182769\pi$
$223$	4.42747	+	4.42747i	0.296485	+	0.296485i	−0.543150	+	0.839636i	$0.682769\pi$
$224$	−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	$-0.450353\pi$
$227$	−12.5432	−	12.5432i	−0.832524	−	0.832524i	−0.987861	+	0.155338i	$0.950353\pi$
$228$	−3.78234	−	3.78234i	−0.250492	−	0.250492i
$229$	1.68832	−	1.68832i	0.111567	−	0.111567i	−0.649119	−	0.760687i	$-0.724862\pi$
$229$	1.68832	−	1.68832i	0.111567	−	0.111567i	0.760687	+	0.649119i	$0.224862\pi$
$230$		−	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	$-0.995976\pi$
$233$		−	0.385937i		−	0.0252836i	0.999920	−	0.0126418i	$-0.00402411\pi$
$234$	−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	−0.889156	−	0.457605i	$-0.848707\pi$
$239$	−6.67161	+	6.67161i	−0.431551	+	0.431551i	0.457605	+	0.889156i	$0.348707\pi$
$240$	1.74766	−	1.74766i	0.112811	−	0.112811i
$241$	14.1379	−	14.1379i	0.910701	−	0.910701i	−0.0856260	−	0.996327i	$-0.527289\pi$
$241$	14.1379	−	14.1379i	0.910701	−	0.910701i	0.996327	+	0.0856260i	$0.0272890\pi$
$242$	−15.1911	−	15.1911i	−0.976522	−	0.976522i
$243$		−	1.00000i		−	0.0641500i
$244$	−27.8834			−1.78505
$245$	4.46788	+	1.34590i	0.285443	+	0.0859867i
$246$		−	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	$-0.136743\pi$
$251$	28.8068			1.81827			0.909136	+	0.416499i	$0.136743\pi$
$252$	1.37896	+	5.48265i	0.0868663	+	0.345375i
$253$	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	$-0.533307\pi$
$257$	−3.34882			−0.208894			−0.104447	+	0.994530i	$0.533307\pi$
$258$	−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
$266$	−13.0640	+	3.28576i	−0.801004	+	0.201463i
$267$	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	$-0.722980\pi$
$271$	1.97384	−	1.97384i	0.119902	−	0.119902i	0.764512	+	0.644610i	$0.222980\pi$
$272$	19.0268			1.15367
$273$	−9.34552	−	1.91346i	−0.565616	−	0.115808i
$274$	−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	$-0.926851\pi$
$277$		−	7.58222i		−	0.455572i	0.973711	−	0.227786i	$-0.0731486\pi$
$278$	−8.63065	−	8.63065i	−0.517632	−	0.517632i
$279$	−0.942715	−	0.942715i	−0.0564389	−	0.0564389i
$280$	0.119683	+	0.475852i	0.00715243	+	0.0284376i
$281$	−2.85077	−	2.85077i	−0.170062	−	0.170062i	0.616944	−	0.787007i	$-0.288370\pi$
$281$	−2.85077	−	2.85077i	−0.170062	−	0.170062i	−0.787007	+	0.616944i	$0.788370\pi$
$282$	9.36757			0.557831
$283$	26.6280			1.58287			0.791435	−	0.611253i	$-0.209334\pi$
$283$	26.6280			1.58287			0.791435	+	0.611253i	$0.209334\pi$
$284$	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	−0.285412	+	0.958405i	$0.592130\pi$
$293$	−21.2907	+	21.2907i	−1.24382	+	1.24382i	−0.958405	+	0.285412i	$0.907870\pi$
$294$	13.6323	+	4.10658i	0.795050	+	0.239500i
$295$	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
$301$	5.61186	+	22.3124i	0.323462	+	1.28606i
$302$	−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	$-0.883603\pi$
$307$	−10.0977	+	10.0977i	−0.576305	+	0.576305i	0.357578	+	0.933883i	$0.383603\pi$
$308$	−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	$-0.487072\pi$
$311$	1.43215			0.0812095			0.0406048	+	0.999175i	$0.487072\pi$
$312$	−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	−0.0813239	−	0.996688i	$-0.525915\pi$
$317$	16.2976	−	16.2976i	0.915364	−	0.915364i	0.996688	+	0.0813239i	$0.0259148\pi$
$318$	−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	−0.424759	−	0.905306i	$-0.639641\pi$
$331$	8.74278	−	8.74278i	0.480547	−	0.480547i	0.905306	+	0.424759i	$0.139641\pi$
$332$	−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
$336$	−2.39275	−	9.51340i	−0.130535	−	0.518999i
$337$			27.7843i			1.51351i	0.653700	+	0.756754i	$0.273216\pi$
$337$			27.7843i			1.51351i	−0.653700	+	0.756754i	$0.726784\pi$
$338$	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
$343$	13.6865	−	12.4771i	0.739003	−	0.673702i
$344$	−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	$-0.968191\pi$
$349$	−16.7246	+	16.7246i	−0.895247	+	0.895247i	0.0997639	+	0.995011i	$0.468191\pi$
$350$	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	$-0.312909\pi$
$353$	−5.21713	−	5.21713i	−0.277680	−	0.277680i	−0.832182	+	0.554502i	$0.812909\pi$
$354$	17.1208			0.909960
$355$	−7.72664			−0.410088
$356$	0.364488	+	0.364488i	0.0193178	+	0.0193178i
$357$	−3.31169	−	13.1671i	−0.175273	−	0.696875i
$358$	−19.1594	−	19.1594i	−1.01261	−	1.01261i
$359$	18.8715	+	18.8715i	0.996001	+	0.996001i	0.999992	−	0.00399120i	$-0.00127044\pi$
$359$	18.8715	+	18.8715i	0.996001	+	0.996001i	−0.00399120	+	0.999992i	$0.501270\pi$
$360$		−	0.185457i		−	0.00977443i
$361$		−	12.7334i		−	0.670181i
$362$	−10.7813	+	10.7813i	−0.566652	+	0.566652i
$363$	10.5627			0.554396
$364$	−19.9694	−	4.08866i	−1.04668	−	0.214304i
$365$	−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
$371$	−14.8390	+	3.73219i	−0.770400	+	0.193766i
$372$	−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	−0.820253	−	0.572001i	$-0.806167\pi$
$379$	−4.83296	+	4.83296i	−0.248252	+	0.248252i	0.572001	+	0.820253i	$0.306167\pi$
$380$	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	$-0.0306027\pi$
$383$	17.6014	+	17.6014i	0.899389	+	0.899389i	−0.0959933	+	0.995382i	$0.530603\pi$
$384$	1.57013	−	1.57013i	0.0801252	−	0.0801252i
$385$	−1.99759	−	7.94230i	−0.101807	−	0.404777i
$386$	−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	$0.125398\pi$
$389$			15.1409i			0.767675i	−0.923401	+	0.383838i	$0.874602\pi$
$390$	4.40525	+	2.11906i	0.223069	+	0.107303i
$391$			14.9173i			0.754398i
$392$	1.86472	+	0.561727i	0.0941825	+	0.0283715i
$393$	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	$-0.589045\pi$
$397$	13.6489	−	13.6489i	0.685019	−	0.685019i	0.961127	+	0.276107i	$0.0890445\pi$
$398$	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	0.262330	−	0.964978i	$-0.415509\pi$
$401$	−14.0705	−	14.0705i	−0.702648	−	0.702648i	−0.964978	+	0.262330i	$0.915509\pi$
$402$	−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	−0.998892	−	0.0470710i	$-0.985011\pi$
$409$	−21.1533	−	21.1533i	−1.04596	−	1.04596i	−0.0470710	−	0.998892i	$-0.514989\pi$
$410$	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	−0.621673	−	0.783277i	$-0.713547\pi$
$421$	3.31582	−	3.31582i	0.161603	−	0.161603i	0.783277	+	0.621673i	$0.213547\pi$
$422$	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
$427$	−8.42121	−	33.4822i	−0.407531	−	1.62032i
$428$			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	−0.963781	−	0.266696i	$-0.914068\pi$
$431$	−14.4718	+	14.4718i	−0.697084	+	0.697084i	0.266696	+	0.963781i	$0.414068\pi$
$432$			3.70771i			0.178388i
$433$	19.2969			0.927348			0.463674	−	0.886006i	$-0.346531\pi$
$433$	19.2969			0.927348			0.463674	+	0.886006i	$0.346531\pi$
$434$	−6.95756	+	1.74992i	−0.333973	+	0.0839987i
$435$	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	$-0.834417\pi$
$439$	−36.3616			−1.73545			−0.867723	+	0.497048i	$0.834417\pi$
$440$	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
$448$	−5.84313	−	23.2319i	−0.276062	−	1.09761i
$449$	25.3087	+	25.3087i	1.19439	+	1.19439i	0.975821	+	0.218570i	$0.0701391\pi$
$449$	25.3087	+	25.3087i	1.19439	+	1.19439i	0.218570	+	0.975821i	$0.429861\pi$
$450$	−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
$455$	5.30701	−	3.50316i	0.248796	−	0.164230i
$456$	0.696452			0.0326144
$457$	−5.83035	+	5.83035i	−0.272732	+	0.272732i	−0.830199	−	0.557467i	$-0.811773\pi$
$457$	−5.83035	+	5.83035i	−0.272732	+	0.272732i	0.557467	+	0.830199i	$0.311773\pi$
$458$			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	$-0.219293\pi$
$461$	2.92466	+	2.92466i	0.136215	+	0.136215i	−0.635712	+	0.771927i	$0.719293\pi$
$462$	−6.09499	−	24.2333i	−0.283565	−	1.12743i
$463$	6.45288	+	6.45288i	0.299891	+	0.299891i	0.840971	−	0.541080i	$-0.181985\pi$
$463$	6.45288	+	6.45288i	0.299891	+	0.299891i	−0.541080	+	0.840971i	$0.681985\pi$
$464$	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	$-0.429098\pi$
$467$	9.54769			0.441814			0.220907	+	0.975295i	$0.429098\pi$
$468$	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
$476$	−7.07638	−	28.1352i	−0.324345	−	1.28958i
$477$	5.78328			0.264798
$478$		−	19.1901i		−	0.877735i
$479$	−25.2423	+	25.2423i	−1.15335	+	1.15335i	−0.167475	+	0.985876i	$0.553561\pi$
$479$	−25.2423	+	25.2423i	−1.15335	+	1.15335i	−0.985876	+	0.167475i	$0.946439\pi$
$480$			5.39785i			0.246377i
$481$	−17.8944	+	6.27037i	−0.815913	+	0.285904i
$482$			40.6660i			1.85228i
$483$	7.45863	−	1.87594i	0.339379	−	0.0853583i
$484$	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	−0.930267	−	0.366883i	$-0.880425\pi$
$487$	−12.4328	+	12.4328i	−0.563385	+	0.563385i	0.366883	+	0.930267i	$0.380425\pi$
$488$	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	$-0.900233\pi$
$491$		−	13.6638i		−	0.616639i	0.951283	−	0.308320i	$-0.0997666\pi$
$492$	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	0.222767	−	0.974872i	$-0.428491\pi$
$499$	26.7532	−	26.7532i	1.19764	−	1.19764i	0.974872	−	0.222767i	$-0.0715090\pi$
$500$	−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	$-0.209840\pi$
$509$	4.01477	+	4.01477i	0.177951	+	0.177951i	−0.612511	+	0.790462i	$0.709840\pi$
$510$			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
$518$	27.4444	−	6.90264i	1.20584	−	0.303284i
$519$		−	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
$525$	−11.6891	+	2.93995i	−0.510152	+	0.128310i
$526$	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
$539$	−31.1234	−	9.37561i	−1.34058	−	0.403836i
$540$	1.00719	+	1.00719i	0.0433426	+	0.0433426i
$541$	18.3681	+	18.3681i	0.789708	+	0.789708i	0.981446	−	0.191739i	$-0.0614126\pi$
$541$	18.3681	+	18.3681i	0.789708	+	0.789708i	−0.191739	+	0.981446i	$0.561413\pi$
$542$			5.67752i			0.243870i
$543$		−	7.49642i		−	0.321702i
$544$	−29.3833	+	29.3833i	−1.25980	+	1.25980i
$545$	−6.48750			−0.277894
$546$	16.1926	−	10.6887i	0.692978	−	0.457435i
$547$	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
$553$	6.33941	−	1.59444i	0.269579	−	0.0678026i
$554$	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	0.605697	−	0.795695i	$-0.292894\pi$
$557$	−4.48411	−	4.48411i	−0.189998	−	0.189998i	−0.795695	+	0.605697i	$0.792894\pi$
$558$	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	$-0.483512\pi$
$563$	2.45705			0.103552			0.0517762	+	0.998659i	$0.483512\pi$
$564$	−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
$567$	2.56584	−	0.645342i	0.107755	−	0.0271018i
$568$	−3.22479			−0.135309
$569$			6.90398i			0.289430i	0.989473	+	0.144715i	$0.0462265\pi$
$569$			6.90398i			0.289430i	−0.989473	+	0.144715i	$0.953774\pi$
$570$	−2.39992	+	2.39992i	−0.100522	+	0.100522i
$571$		−	8.21317i		−	0.343711i	−0.985122	−	0.171855i	$-0.945024\pi$
$571$		−	8.21317i		−	0.343711i	0.985122	−	0.171855i	$-0.0549762\pi$
$572$	11.8308	+	33.7626i	0.494669	+	1.41168i
$573$		−	14.2378i		−	0.594791i
$574$	5.49785	−	1.38278i	0.229476	−	0.0577162i
$575$	13.2428			0.552262
$576$			9.05432i			0.377263i
$577$	−8.20907	−	8.20907i	−0.341748	−	0.341748i	0.515276	−	0.857024i	$-0.327689\pi$
$577$	−8.20907	−	8.20907i	−0.341748	−	0.341748i	−0.857024	+	0.515276i	$0.827689\pi$
$578$	−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	$-0.301933\pi$
$587$	−5.56542	−	5.56542i	−0.229709	−	0.229709i	−0.812571	+	0.582862i	$0.801933\pi$
$588$	−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	$-0.644264\pi$
$593$	11.2305	−	11.2305i	0.461181	−	0.461181i	0.899043	+	0.437861i	$0.144264\pi$
$594$			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
$609$	−4.75300	−	18.8976i	−0.192601	−	0.765770i
$610$			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	0.0705898	−	0.997505i	$-0.477512\pi$
$613$	26.4448	−	26.4448i	1.06810	−	1.06810i	0.997505	−	0.0705898i	$-0.0224881\pi$
$614$		−	29.0448i		−	1.17215i
$615$	−0.702259			−0.0283178
$616$	−0.833716	−	3.31480i	−0.0335914	−	0.133557i
$617$	4.98927	−	4.98927i	0.200860	−	0.200860i	−0.599508	−	0.800369i	$-0.704637\pi$
$617$	4.98927	−	4.98927i	0.200860	−	0.200860i	0.800369	+	0.599508i	$0.204637\pi$
$618$	−14.5843	−	14.5843i	−0.586667	−	0.586667i
$619$	28.0127	−	28.0127i	1.12592	−	1.12592i	0.135090	−	0.990833i	$-0.456868\pi$
$619$	28.0127	−	28.0127i	1.12592	−	1.12592i	0.990833	−	0.135090i	$-0.0431324\pi$
$620$	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
$630$	3.47878	−	0.874958i	0.138598	−	0.0348592i
$631$	−2.30759	−	2.30759i	−0.0918639	−	0.0918639i	0.659681	−	0.751545i	$-0.270691\pi$
$631$	−2.30759	−	2.30759i	−0.0918639	−	0.0918639i	−0.751545	+	0.659681i	$0.770691\pi$
$632$	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
$637$	−1.12142	−	25.2139i	−0.0444323	−	0.999012i
$638$	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	$-0.822142\pi$
$641$		−	26.8438i		−	1.06027i	0.847914	−	0.530133i	$-0.177858\pi$
$642$	−9.14653	−	9.14653i	−0.360985	−	0.360985i
$643$	−8.19484	−	8.19484i	−0.323173	−	0.323173i	0.526810	−	0.849983i	$-0.323388\pi$
$643$	−8.19484	−	8.19484i	−0.323173	−	0.323173i	−0.849983	+	0.526810i	$0.823388\pi$
$644$	15.9375	−	4.00849i	0.628025	−	0.157957i
$645$	4.09890	+	4.09890i	0.161394	+	0.161394i
$646$	−26.1280			−1.02799
$647$	23.6489			0.929735			0.464867	−	0.885380i	$-0.346102\pi$
$647$	23.6489			0.929735			0.464867	+	0.885380i	$0.346102\pi$
$648$	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
$658$	6.04529	+	24.0357i	0.235670	+	0.937009i
$659$	−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	$-0.573855\pi$
$661$	19.1091	−	19.1091i	0.743257	−	0.743257i	0.973203	+	0.229946i	$0.0738549\pi$
$662$			25.1476i			0.977388i
$663$	−16.6737	−	8.02059i	−0.647555	−	0.311494i
$664$		−	3.94499i		−	0.153095i
$665$	1.07689	+	4.28164i	0.0417599	+	0.166035i
$666$	−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	$0.199820\pi$
$673$			30.4732i			1.17465i	−0.809350	+	0.587327i	$0.800180\pi$
$674$	−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	0.942740	−	0.333530i	$-0.108240\pi$
$683$	15.9213	+	15.9213i	0.609210	+	0.609210i	−0.333530	+	0.942740i	$0.608240\pi$
$684$	−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	$-0.421293\pi$
$691$	−19.0536	−	19.0536i	−0.724832	−	0.724832i	−0.969585	+	0.244753i	$0.921293\pi$
$692$		−	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
$700$	−24.9770	+	6.28205i	−0.944042	+	0.237439i
$701$		−	33.9216i		−	1.28120i	−0.767874	−	0.640601i	$-0.778685\pi$
$701$		−	33.9216i		−	1.28120i	0.767874	−	0.640601i	$-0.221315\pi$
$702$	−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
$707$	8.66635	−	2.17970i	0.325932	−	0.0819761i
$708$	−12.7186	+	12.7186i	−0.477994	+	0.477994i
$709$	21.1726	+	21.1726i	0.795153	+	0.795153i	0.982327	−	0.187174i	$-0.0599329\pi$
$709$	21.1726	+	21.1726i	0.795153	+	0.795153i	−0.187174	+	0.982327i	$0.559933\pi$
$710$	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	$-0.398580\pi$
$719$	16.7994			0.626513			0.313257	+	0.949669i	$0.398580\pi$
$720$	−1.74766	−	1.74766i	−0.0651314	−	0.0651314i
$721$	−26.0195	+	6.54424i	−0.969016	+	0.243720i
$722$	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	$-0.244138\pi$
$727$	38.8270			1.44001			0.720007	+	0.693966i	$0.244138\pi$
$728$	2.21493	−	1.46208i	0.0820909	−	0.0541882i
$729$	−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	$-0.0530176\pi$
$733$	22.2107	+	22.2107i	0.820370	+	0.820370i	−0.165791	+	0.986161i	$0.553018\pi$
$734$	8.93841	+	8.93841i	0.329923	+	0.329923i
$735$	1.34590	−	4.46788i	0.0496444	−	0.164800i
$736$	−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	0.303946	−	0.952689i	$-0.401696\pi$
$739$	−17.6358	−	17.6358i	−0.648744	−	0.648744i	−0.952689	+	0.303946i	$0.901696\pi$
$740$	−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	0.352664	−	0.935750i	$-0.385276\pi$
$743$	35.1196	−	35.1196i	1.28841	−	1.28841i	0.935750	−	0.352664i	$-0.114724\pi$
$744$	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
$749$	−16.3181	+	4.10421i	−0.596250	+	0.149965i
$750$	12.9556			0.473071
$751$			29.8500i			1.08924i	0.838683	+	0.544620i	$0.183326\pi$
$751$			29.8500i			1.08924i	−0.838683	+	0.544620i	$0.816674\pi$
$752$	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
$756$	5.48265	−	1.37896i	0.199402	−	0.0501523i
$757$	−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	$-0.607537\pi$
$761$	16.8835	−	16.8835i	0.612027	−	0.612027i	0.943474	+	0.331447i	$0.107537\pi$
$762$	−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	$-0.205634\pi$
$769$	5.44838	+	5.44838i	0.196473	+	0.196473i	−0.602013	+	0.798486i	$0.705634\pi$
$770$	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	$-0.378329\pi$
$773$	−15.4259	−	15.4259i	−0.554832	−	0.554832i	−0.927832	+	0.372999i	$0.878329\pi$
$774$	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	0.239518	−	0.970892i	$-0.423011\pi$
$787$	33.9563	−	33.9563i	1.21041	−	1.21041i	0.970892	−	0.239518i	$-0.0769893\pi$
$788$	16.9412	+	16.9412i	0.603505	+	0.603505i
$789$			0.409582i			0.0145815i
$790$	−3.34978			−0.119180
$791$	26.0033	−	6.54016i	0.924570	−	0.232541i
$792$			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	$-0.682198\pi$
$797$	−30.5826			−1.08329			−0.541645	+	0.840607i	$0.682198\pi$
$798$	3.28576	+	13.0640i	0.116315	+	0.462460i
$799$	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	$-0.0577170\pi$
$811$	22.8757	+	22.8757i	0.803274	+	0.803274i	−0.180331	+	0.983606i	$0.557717\pi$
$812$	−10.1561	−	40.3802i	−0.356411	−	1.41707i
$813$	−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
$819$	−1.91346	+	9.34552i	−0.0668618	+	0.326559i
$820$	−1.50058			−0.0524024
$821$	−22.2230	+	22.2230i	−0.775586	+	0.775586i	−0.979077	−	0.203491i	$-0.934771\pi$
$821$	−22.2230	+	22.2230i	−0.775586	+	0.775586i	0.203491	+	0.979077i	$0.434771\pi$
$822$			27.6912i			0.965843i
$823$		−	5.96596i		−	0.207960i	−0.994579	−	0.103980i	$-0.966842\pi$
$823$		−	5.96596i		−	0.207960i	0.994579	−	0.103980i	$-0.0331578\pi$
$824$	−1.99495	−	1.99495i	−0.0694972	−	0.0694972i
$825$	14.9584	+	14.9584i	0.520786	+	0.520786i
$826$	11.0488	+	43.9292i	0.384436	+	1.52849i
$827$	−11.6765	−	11.6765i	−0.406033	−	0.406033i	0.474320	−	0.880353i	$-0.342694\pi$
$827$	−11.6765	−	11.6765i	−0.406033	−	0.406033i	−0.880353	+	0.474320i	$0.842694\pi$
$828$	−6.21141			−0.215862
$829$	−7.66944			−0.266371			−0.133185	−	0.991091i	$-0.542521\pi$
$829$	−7.66944			−0.266371			−0.133185	+	0.991091i	$0.542521\pi$
$830$	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	$-0.668592\pi$
$839$	10.3626	−	10.3626i	0.357758	−	0.357758i	0.862986	+	0.505228i	$0.168592\pi$
$840$	0.475852	−	0.119683i	0.0164185	−	0.00412946i
$841$	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
$847$	6.81653	+	27.1021i	0.234219	+	0.931239i
$848$	−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	0.131912	−	0.991261i	$-0.457888\pi$
$853$	32.8036	−	32.8036i	1.12317	−	1.12317i	0.991261	−	0.131912i	$-0.0421117\pi$
$854$	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	$-0.803729\pi$
$857$	−47.7672			−1.63169			−0.815847	+	0.578267i	$0.803729\pi$
$858$	−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	−0.772017	−	0.635602i	$-0.780752\pi$
$863$	−4.00743	+	4.00743i	−0.136414	+	0.136414i	0.635602	+	0.772017i	$0.280752\pi$
$864$	−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	−0.0652746	+	0.997867i	$0.520792\pi$
$877$	−31.4841	+	31.4841i	−1.06314	+	1.06314i	−0.997867	+	0.0652746i	$0.979208\pi$
$878$	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	$-0.674349\pi$
$881$	−30.9136			−1.04151			−0.520753	+	0.853707i	$0.674349\pi$
$882$	4.10658	−	13.6323i	0.138276	−	0.459022i
$883$		−	9.79360i		−	0.329581i	−0.986329	−	0.164790i	$-0.947305\pi$
$883$		−	9.79360i		−	0.329581i	0.986329	−	0.164790i	$-0.0526948\pi$
$884$	−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
$889$	3.56829	+	14.1873i	0.119677	+	0.475827i
$890$	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
$903$	22.3124	−	5.61186i	0.742510	−	0.186751i
$904$	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	$0.128648\pi$
$907$			23.6864i			0.786494i	−0.919433	+	0.393247i	$0.871352\pi$
$908$	−26.8022	+	26.8022i	−0.889463	+	0.889463i
$909$	−3.37759			−0.112028
$910$	−2.59428	+	12.6707i	−0.0859996	+	0.420029i
$911$	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
$917$	3.78614	+	15.0535i	0.125029	+	0.497109i
$918$	−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	$-0.0657869\pi$
$929$	23.5762	+	23.5762i	0.773511	+	0.773511i	−0.205207	+	0.978719i	$0.565787\pi$
$930$	−1.27814	+	1.27814i	−0.0419118	+	0.0419118i
$931$	16.7784	+	5.05432i	0.549890	+	0.165649i
$932$	−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	$-0.0193324\pi$
$938$	−13.9399	−	55.4241i	−0.455154	−	1.80966i
$939$	23.5529			0.768620
$940$		−	6.56028i		−	0.213973i
$941$	−36.6909	−	36.6909i	−1.19609	−	1.19609i	−0.975328	−	0.220762i	$-0.929146\pi$
$941$	−36.6909	−	36.6909i	−1.19609	−	1.19609i	−0.220762	−	0.975328i	$-0.570854\pi$
$942$	−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	0.335813	−	0.941929i	$-0.390989\pi$
$947$	−18.6522	−	18.6522i	−0.606116	−	0.606116i	−0.941929	+	0.335813i	$0.890989\pi$
$948$	−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	$0.153553\pi$
$953$			28.6423i			0.927816i	−0.885883	+	0.463908i	$0.846447\pi$
$954$	−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	−0.517733	−	0.855542i	$-0.673224\pi$
$967$	10.5047	−	10.5047i	0.337809	−	0.337809i	0.855542	+	0.517733i	$0.173224\pi$
$968$	−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
$973$	3.87273	+	15.3977i	0.124154	+	0.493628i
$974$		−	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	−0.893925	−	0.448218i	$-0.852059\pi$
$977$	−13.9315	+	13.9315i	−0.445707	+	0.445707i	0.448218	+	0.893925i	$0.352059\pi$
$978$		−	11.3182i		−	0.361917i
$979$	1.12018			0.0358011
$980$	2.87591	−	9.54692i	0.0918676	−	0.304965i
$981$	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	$-0.759190\pi$
$983$	−1.27995	+	1.27995i	−0.0408242	+	0.0408242i	0.686400	+	0.727224i	$0.259190\pi$
$984$	−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
$994$	−15.2141	−	60.4904i	−0.482563	−	1.91864i
$995$	−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.f.265.2	yes	12
3.2	odd	2		819.2.y.f.811.5		12
7.6	odd	2		273.2.p.e.265.2	yes	12
13.8	odd	4		273.2.p.e.34.2	✓	12
21.20	even	2		819.2.y.g.811.5		12
39.8	even	4		819.2.y.g.307.5		12
91.34	even	4	inner	273.2.p.f.34.2	yes	12
273.125	odd	4		819.2.y.f.307.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.2	✓	12	13.8	odd	4
273.2.p.e.265.2	yes	12	7.6	odd	2
273.2.p.f.34.2	yes	12	91.34	even	4	inner
273.2.p.f.265.2	yes	12	1.1	even	1	trivial
819.2.y.f.307.5		12	273.125	odd	4
819.2.y.f.811.5		12	3.2	odd	2
819.2.y.g.307.5		12	39.8	even	4
819.2.y.g.811.5		12	21.20	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.43819 + 1.43819i) q^{2} -1.00000i q^{3} -2.13679i q^{4} +(0.471358 + 0.471358i) q^{5} +(1.43819 + 1.43819i) q^{6} +(2.56584 - 0.645342i) q^{7} +(0.196726 + 0.196726i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(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} +(2.56584 - 0.645342i) 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} +(-0.645342 - 2.56584i) 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} +(-1.37896 - 5.48265i) 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} +(-2.56584 + 0.645342i) 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} +(-3.47878 + 0.874958i) 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} +(-5.48265 + 1.37896i) 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} +(1.91346 - 9.34552i) 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} +(-4.10658 + 13.6323i) q^{98} +(3.28349 + 3.28349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * 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 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * 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 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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