LMFDB - Embedded newform 273.2.t.c.205.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.2
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.c.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.976547i q^{2} +(-0.500000 + 0.866025i) q^{3} +1.04636 q^{4} +(0.233786 + 0.134976i) q^{5} +(0.845714 + 0.488273i) q^{6} +(1.06153 + 2.42346i) q^{7} -2.97491i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.976547i q^{2} +(-0.500000 + 0.866025i) q^{3} +1.04636 q^{4} +(0.233786 + 0.134976i) q^{5} +(0.845714 + 0.488273i) q^{6} +(1.06153 + 2.42346i) q^{7} -2.97491i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.131811 - 0.228303i) q^{10} +(0.741794 + 0.428275i) q^{11} +(-0.523178 + 0.906171i) q^{12} +(1.45289 + 3.29986i) q^{13} +(2.36662 - 1.03663i) q^{14} +(-0.233786 + 0.134976i) q^{15} -0.812427 q^{16} +2.17296 q^{17} +(-0.845714 + 0.488273i) q^{18} +(1.73063 - 0.999181i) q^{19} +(0.244623 + 0.141233i) q^{20} +(-2.62954 - 0.292422i) q^{21} +(0.418231 - 0.724397i) q^{22} +1.92330 q^{23} +(2.57635 + 1.48745i) q^{24} +(-2.46356 - 4.26702i) q^{25} +(3.22247 - 1.41882i) q^{26} +1.00000 q^{27} +(1.11073 + 2.53580i) q^{28} +(-2.97054 - 5.14513i) q^{29} +(0.131811 + 0.228303i) q^{30} +(-0.0946014 + 0.0546182i) q^{31} -5.15645i q^{32} +(-0.741794 + 0.428275i) q^{33} -2.12200i q^{34} +(-0.0789401 + 0.709852i) q^{35} +(-0.523178 - 0.906171i) q^{36} +3.49754i q^{37} +(-0.975748 - 1.69004i) q^{38} +(-3.58421 - 0.391690i) q^{39} +(0.401542 - 0.695492i) q^{40} +(-7.03015 + 4.05886i) q^{41} +(-0.285564 + 2.56787i) q^{42} +(-1.78890 + 3.09847i) q^{43} +(0.776181 + 0.448128i) q^{44} -0.269953i q^{45} -1.87820i q^{46} +(-0.592480 - 0.342068i) q^{47} +(0.406214 - 0.703583i) q^{48} +(-4.74633 + 5.14513i) q^{49} +(-4.16694 + 2.40578i) q^{50} +(-1.08648 + 1.88184i) q^{51} +(1.52024 + 3.45283i) q^{52} +(-4.21705 - 7.30414i) q^{53} -0.976547i q^{54} +(0.115614 + 0.200249i) q^{55} +(7.20958 - 3.15794i) q^{56} +1.99836i q^{57} +(-5.02446 + 2.90088i) q^{58} +5.00939i q^{59} +(-0.244623 + 0.141233i) q^{60} +(-5.48018 - 9.49195i) q^{61} +(0.0533372 + 0.0923828i) q^{62} +(1.56802 - 2.13104i) q^{63} -6.66037 q^{64} +(-0.105738 + 0.967568i) q^{65} +(0.418231 + 0.724397i) q^{66} +(4.83448 + 2.79119i) q^{67} +2.27369 q^{68} +(-0.961652 + 1.66563i) q^{69} +(0.693204 + 0.0770887i) q^{70} +(-12.5152 - 7.22567i) q^{71} +(-2.57635 + 1.48745i) q^{72} +(-3.56030 + 2.05554i) q^{73} +3.41551 q^{74} +4.92713 q^{75} +(1.81086 - 1.04550i) q^{76} +(-0.250474 + 2.25233i) q^{77} +(-0.382503 + 3.50015i) q^{78} +(-0.782735 + 1.35574i) q^{79} +(-0.189934 - 0.109658i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.96367 + 6.86527i) q^{82} +7.98255i q^{83} +(-2.75144 - 0.305978i) q^{84} +(0.508008 + 0.293299i) q^{85} +(3.02580 + 1.74695i) q^{86} +5.94109 q^{87} +(1.27408 - 2.20677i) q^{88} +2.71383i q^{89} -0.263621 q^{90} +(-6.45481 + 7.02392i) q^{91} +2.01246 q^{92} -0.109236i q^{93} +(-0.334046 + 0.578585i) q^{94} +0.539463 q^{95} +(4.46561 + 2.57822i) q^{96} +(-8.93689 - 5.15972i) q^{97} +(5.02446 + 4.63501i) q^{98} -0.856550i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.976547i		−	0.690523i	−0.938507	−	0.345261i	$-0.887790\pi$
$2$		−	0.976547i		−	0.690523i	0.938507	−	0.345261i	$-0.112210\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.04636			0.523178
$5$	0.233786	+	0.134976i	0.104552	+	0.0603632i	0.551364	−	0.834265i	$-0.314107\pi$
$5$	0.233786	+	0.134976i	0.104552	+	0.0603632i	−0.446812	+	0.894628i	$0.647441\pi$
$6$	0.845714	+	0.488273i	0.345261	+	0.199337i
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$8$		−	2.97491i		−	1.05179i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.131811	−	0.228303i	0.0416822	−	0.0721957i
$11$	0.741794	+	0.428275i	0.223659	+	0.129130i	0.607643	−	0.794210i	$-0.292115\pi$
$11$	0.741794	+	0.428275i	0.223659	+	0.129130i	−0.383984	+	0.923340i	$0.625448\pi$
$12$	−0.523178	+	0.906171i	−0.151028	+	0.261589i
$13$	1.45289	+	3.29986i	0.402960	+	0.915218i
$13$	1.45289	+	3.29986i	0.402960	+	0.915218i
$14$	2.36662	−	1.03663i	0.632507	−	0.277051i
$15$	−0.233786	+	0.134976i	−0.0603632	+	0.0348507i
$16$	−0.812427			−0.203107
$17$	2.17296			0.527021			0.263510	−	0.964657i	$-0.415120\pi$
$17$	2.17296			0.527021			0.263510	+	0.964657i	$0.415120\pi$
$18$	−0.845714	+	0.488273i	−0.199337	+	0.115087i
$19$	1.73063	−	0.999181i	0.397034	−	0.229228i	−0.288169	−	0.957580i	$-0.593047\pi$
$19$	1.73063	−	0.999181i	0.397034	−	0.229228i	0.685204	+	0.728352i	$0.259713\pi$
$20$	0.244623	+	0.141233i	0.0546994	+	0.0315807i
$21$	−2.62954	−	0.292422i	−0.573813	−	0.0638117i
$22$	0.418231	−	0.724397i	0.0891671	−	0.154442i
$23$	1.92330			0.401037			0.200518	−	0.979690i	$-0.435737\pi$
$23$	1.92330			0.401037			0.200518	+	0.979690i	$0.435737\pi$
$24$	2.57635	+	1.48745i	0.525895	+	0.303625i
$25$	−2.46356	−	4.26702i	−0.492713	−	0.853403i
$26$	3.22247	−	1.41882i	0.631979	−	0.278253i
$27$	1.00000			0.192450
$28$	1.11073	+	2.53580i	0.209909	+	0.479222i
$29$	−2.97054	−	5.14513i	−0.551616	−	0.955427i	−0.998158	−	0.0606646i	$-0.980678\pi$
$29$	−2.97054	−	5.14513i	−0.551616	−	0.955427i	0.446542	−	0.894763i	$-0.352655\pi$
$30$	0.131811	+	0.228303i	0.0240652	+	0.0416822i
$31$	−0.0946014	+	0.0546182i	−0.0169909	+	0.00980971i	−0.508471	−	0.861079i	$-0.669789\pi$
$31$	−0.0946014	+	0.0546182i	−0.0169909	+	0.00980971i	0.491480	+	0.870889i	$0.336456\pi$
$32$		−	5.15645i		−	0.911540i
$33$	−0.741794	+	0.428275i	−0.129130	+	0.0745531i
$34$		−	2.12200i		−	0.363920i
$35$	−0.0789401	+	0.709852i	−0.0133433	+	0.119987i
$36$	−0.523178	−	0.906171i	−0.0871963	−	0.151028i
$37$			3.49754i			0.574992i	0.957782	+	0.287496i	$0.0928228\pi$
$37$			3.49754i			0.574992i	−0.957782	+	0.287496i	$0.907177\pi$
$38$	−0.975748	−	1.69004i	−0.158287	−	0.274161i
$39$	−3.58421	−	0.391690i	−0.573933	−	0.0627205i
$40$	0.401542	−	0.695492i	0.0634894	−	0.109967i
$41$	−7.03015	+	4.05886i	−1.09793	+	0.633888i	−0.935675	−	0.352862i	$-0.885208\pi$
$41$	−7.03015	+	4.05886i	−1.09793	+	0.633888i	−0.162250	+	0.986750i	$0.551875\pi$
$42$	−0.285564	+	2.56787i	−0.0440635	+	0.396231i
$43$	−1.78890	+	3.09847i	−0.272805	+	0.472512i	−0.969579	−	0.244779i	$-0.921285\pi$
$43$	−1.78890	+	3.09847i	−0.272805	+	0.472512i	0.696774	+	0.717291i	$0.254618\pi$
$44$	0.776181	+	0.448128i	0.117014	+	0.0675578i
$45$		−	0.269953i		−	0.0402422i
$46$		−	1.87820i		−	0.276925i
$47$	−0.592480	−	0.342068i	−0.0864221	−	0.0498958i	0.456166	−	0.889895i	$-0.349222\pi$
$47$	−0.592480	−	0.342068i	−0.0864221	−	0.0498958i	−0.542588	+	0.839999i	$0.682556\pi$
$48$	0.406214	−	0.703583i	0.0586319	−	0.101553i
$49$	−4.74633	+	5.14513i	−0.678046	+	0.735019i
$50$	−4.16694	+	2.40578i	−0.589295	+	0.340229i
$51$	−1.08648	+	1.88184i	−0.152138	+	0.263510i
$52$	1.52024	+	3.45283i	0.210820	+	0.478822i
$53$	−4.21705	−	7.30414i	−0.579256	−	1.00330i	−0.995565	−	0.0940780i	$-0.970010\pi$
$53$	−4.21705	−	7.30414i	−0.579256	−	1.00330i	0.416308	−	0.909223i	$-0.363324\pi$
$54$		−	0.976547i		−	0.132891i
$55$	0.115614	+	0.200249i	0.0155894	+	0.0270016i
$56$	7.20958	−	3.15794i	0.963420	−	0.421998i
$57$			1.99836i			0.264690i
$58$	−5.02446	+	2.90088i	−0.659744	+	0.380904i
$59$			5.00939i			0.652167i	0.945341	+	0.326084i	$0.105729\pi$
$59$			5.00939i			0.652167i	−0.945341	+	0.326084i	$0.894271\pi$
$60$	−0.244623	+	0.141233i	−0.0315807	+	0.0182331i
$61$	−5.48018	−	9.49195i	−0.701665	−	1.21532i	−0.967882	−	0.251406i	$-0.919107\pi$
$61$	−5.48018	−	9.49195i	−0.701665	−	1.21532i	0.266216	−	0.963913i	$-0.414226\pi$
$62$	0.0533372	+	0.0923828i	0.00677383	+	0.0117326i
$63$	1.56802	−	2.13104i	0.197551	−	0.268486i
$64$	−6.66037			−0.832546
$65$	−0.105738	+	0.967568i	−0.0131151	+	0.120012i
$66$	0.418231	+	0.724397i	0.0514806	+	0.0891671i
$67$	4.83448	+	2.79119i	0.590626	+	0.340998i	0.765345	−	0.643620i	$-0.222568\pi$
$67$	4.83448	+	2.79119i	0.590626	+	0.340998i	−0.174719	+	0.984618i	$0.555902\pi$
$68$	2.27369			0.275726
$69$	−0.961652	+	1.66563i	−0.115769	+	0.200518i
$70$	0.693204	+	0.0770887i	0.0828537	+	0.00921386i
$71$	−12.5152	−	7.22567i	−1.48529	−	0.857530i	−0.485425	−	0.874278i	$-0.661335\pi$
$71$	−12.5152	−	7.22567i	−1.48529	−	0.857530i	−0.999860	+	0.0167483i	$0.994669\pi$
$72$	−2.57635	+	1.48745i	−0.303625	+	0.175298i
$73$	−3.56030	+	2.05554i	−0.416701	+	0.240583i	−0.693665	−	0.720298i	$-0.744005\pi$
$73$	−3.56030	+	2.05554i	−0.416701	+	0.240583i	0.276964	+	0.960880i	$0.410672\pi$
$74$	3.41551			0.397045
$75$	4.92713			0.568935
$76$	1.81086	−	1.04550i	0.207720	−	0.119927i
$77$	−0.250474	+	2.25233i	−0.0285442	+	0.256677i
$78$	−0.382503	+	3.50015i	−0.0433100	+	0.396314i
$79$	−0.782735	+	1.35574i	−0.0880645	+	0.152532i	−0.906693	−	0.421791i	$-0.861401\pi$
$79$	−0.782735	+	1.35574i	−0.0880645	+	0.152532i	0.818628	+	0.574323i	$0.194735\pi$
$80$	−0.189934	−	0.109658i	−0.0212353	−	0.0122602i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.96367	+	6.86527i	0.437714	+	0.758143i
$83$			7.98255i			0.876198i	0.898927	+	0.438099i	$0.144348\pi$
$83$			7.98255i			0.876198i	−0.898927	+	0.438099i	$0.855652\pi$
$84$	−2.75144	−	0.305978i	−0.300206	−	0.0333849i
$85$	0.508008	+	0.293299i	0.0551012	+	0.0318127i
$86$	3.02580	+	1.74695i	0.326280	+	0.188378i
$87$	5.94109			0.636951
$88$	1.27408	−	2.20677i	0.135817	−	0.235242i
$89$			2.71383i			0.287665i	0.989602	+	0.143833i	$0.0459427\pi$
$89$			2.71383i			0.287665i	−0.989602	+	0.143833i	$0.954057\pi$
$90$	−0.263621			−0.0277881
$91$	−6.45481	+	7.02392i	−0.676648	+	0.736307i
$92$	2.01246			0.209814
$93$		−	0.109236i		−	0.0113273i
$94$	−0.334046	+	0.578585i	−0.0344542	+	0.0596764i
$95$	0.539463			0.0553478
$96$	4.46561	+	2.57822i	0.455770	+	0.263139i
$97$	−8.93689	−	5.15972i	−0.907404	−	0.523890i	−0.0278089	−	0.999613i	$-0.508853\pi$
$97$	−8.93689	−	5.15972i	−0.907404	−	0.523890i	−0.879595	+	0.475723i	$0.842186\pi$
$98$	5.02446	+	4.63501i	0.507548	+	0.468207i
$99$		−	0.856550i		−	0.0860865i
$100$	−2.57776	−	4.46482i	−0.257776	−	0.446482i
$101$	−5.65484	+	9.79447i	−0.562678	+	0.974586i	0.434584	+	0.900631i	$0.356895\pi$
$101$	−5.65484	+	9.79447i	−0.562678	+	0.974586i	−0.997262	+	0.0739548i	$0.976438\pi$
$102$	1.83771	+	1.06100i	0.181960	+	0.105055i
$103$	7.93581	−	13.7452i	0.781938	−	1.35436i	−0.148873	−	0.988856i	$-0.547564\pi$
$103$	7.93581	−	13.7452i	0.781938	−	1.35436i	0.930811	−	0.365501i	$-0.119102\pi$
$104$	9.81680	−	4.32223i	0.962616	−	0.423829i
$105$	−0.575280	−	0.423290i	−0.0561415	−	0.0413089i
$106$	−7.13284	+	4.11815i	−0.692803	+	0.399990i
$107$	11.0959			1.07268			0.536341	−	0.844001i	$-0.319806\pi$
$107$	11.0959			1.07268			0.536341	+	0.844001i	$0.319806\pi$
$108$	1.04636			0.100686
$109$	6.15552	−	3.55389i	0.589592	−	0.340401i	−0.175344	−	0.984507i	$-0.556104\pi$
$109$	6.15552	−	3.55389i	0.589592	−	0.340401i	0.764936	+	0.644106i	$0.222770\pi$
$110$	0.195553	−	0.112902i	0.0186452	−	0.0107648i
$111$	−3.02896	−	1.74877i	−0.287496	−	0.165986i
$112$	−0.862412	−	1.96889i	−0.0814903	−	0.186042i
$113$	7.53381	−	13.0489i	0.708721	−	1.22754i	−0.256610	−	0.966515i	$-0.582606\pi$
$113$	7.53381	−	13.0489i	0.708721	−	1.22754i	0.965332	−	0.261026i	$-0.0840609\pi$
$114$	1.95150			0.182774
$115$	0.449641	+	0.259601i	0.0419293	+	0.0242079i
$116$	−3.10825	−	5.38364i	−0.288593	−	0.499859i
$117$	2.13132	−	2.90817i	0.197041	−	0.268861i
$118$	4.89191			0.450336
$119$	2.30666	+	5.26609i	0.211451	+	0.482742i
$120$	0.401542	+	0.695492i	0.0366556	+	0.0634894i
$121$	−5.13316	−	8.89090i	−0.466651	−	0.808263i
$122$	−9.26934	+	5.35165i	−0.839206	+	0.484516i
$123$		−	8.11772i		−	0.731950i
$124$	−0.0989868	+	0.0571501i	−0.00888928	+	0.00513223i
$125$		−	2.67985i		−	0.239693i
$126$	−2.08106	−	1.53124i	−0.185396	−	0.136414i
$127$	0.799919	+	1.38550i	0.0709813	+	0.122943i	0.899332	−	0.437267i	$-0.144054\pi$
$127$	0.799919	+	1.38550i	0.0709813	+	0.122943i	−0.828350	+	0.560210i	$0.810720\pi$
$128$		−	3.80873i		−	0.336648i
$129$	−1.78890	−	3.09847i	−0.157504	−	0.272805i
$130$	0.944875	+	0.103258i	0.0828710	+	0.00905630i
$131$	6.29272	−	10.8993i	0.549797	−	0.952277i	−0.448491	−	0.893788i	$-0.648038\pi$
$131$	6.29272	−	10.8993i	0.549797	−	0.952277i	0.998288	−	0.0584895i	$-0.0186284\pi$
$132$	−0.776181	+	0.448128i	−0.0675578	+	0.0390045i
$133$	4.25859	+	3.13346i	0.369266	+	0.271706i
$134$	2.72573	−	4.72110i	0.235467	−	0.407841i
$135$	0.233786	+	0.134976i	0.0201211	+	0.0116169i
$136$		−	6.46437i		−	0.554315i
$137$			17.7573i			1.51711i	0.651611	+	0.758553i	$0.274093\pi$
$137$			17.7573i			1.51711i	−0.651611	+	0.758553i	$0.725907\pi$
$138$	1.62657	+	0.939098i	0.138463	+	0.0799414i
$139$	11.4869	−	19.8959i	0.974308	−	1.68755i	0.292107	−	0.956386i	$-0.405644\pi$
$139$	11.4869	−	19.8959i	0.974308	−	1.68755i	0.682201	−	0.731165i	$-0.261023\pi$
$140$	−0.0825995	+	0.742758i	−0.00698093	+	0.0627745i
$141$	0.592480	−	0.342068i	0.0498958	−	0.0288074i
$142$	−7.05621	+	12.2217i	−0.592144	+	1.02562i
$143$	−0.335502	+	3.07006i	−0.0280561	+	0.256731i
$144$	0.406214	+	0.703583i	0.0338511	+	0.0586319i
$145$		−	1.60381i		−	0.133189i
$146$	2.00733	+	3.47680i	0.166128	+	0.287742i
$147$	−2.08265	−	6.68300i	−0.171774	−	0.551205i
$148$			3.65967i			0.300823i
$149$	−11.1178	+	6.41884i	−0.910803	+	0.525852i	−0.880689	−	0.473694i	$-0.842920\pi$
$149$	−11.1178	+	6.41884i	−0.910803	+	0.525852i	−0.0301133	+	0.999546i	$0.509587\pi$
$150$		−	4.81157i		−	0.392863i
$151$	7.32362	−	4.22830i	0.595988	−	0.344094i	−0.171474	−	0.985189i	$-0.554853\pi$
$151$	7.32362	−	4.22830i	0.595988	−	0.344094i	0.767462	+	0.641095i	$0.221520\pi$
$152$	−2.97247	−	5.14848i	−0.241100	−	0.417597i
$153$	−1.08648	−	1.88184i	−0.0878368	−	0.152138i
$154$	2.19951	+	0.244600i	0.177242	+	0.0197104i
$155$	−0.0294886			−0.00236858
$156$	−3.75036	−	0.409847i	−0.300269	−	0.0328140i
$157$	8.35754	+	14.4757i	0.667004	+	1.15529i	0.978738	+	0.205116i	$0.0657571\pi$
$157$	8.35754	+	14.4757i	0.667004	+	1.15529i	−0.311733	+	0.950170i	$0.600910\pi$
$158$	1.32394	+	0.764377i	0.105327	+	0.0608106i
$159$	8.43410			0.668868
$160$	0.695998	−	1.20550i	0.0550235	−	0.0953035i
$161$	2.04164	+	4.66105i	0.160904	+	0.367342i
$162$	0.845714	+	0.488273i	0.0664456	+	0.0383624i
$163$	18.7003	−	10.7966i	1.46472	−	0.845656i	0.465496	−	0.885050i	$-0.345876\pi$
$163$	18.7003	−	10.7966i	1.46472	−	0.845656i	0.999224	+	0.0393940i	$0.0125427\pi$
$164$	−7.35604	+	4.24701i	−0.574410	+	0.331636i
$165$	−0.231228			−0.0180011
$166$	7.79533			0.605035
$167$	−10.3948	+	6.00144i	−0.804373	+	0.464405i	−0.844998	−	0.534769i	$-0.820398\pi$
$167$	−10.3948	+	6.00144i	−0.804373	+	0.464405i	0.0406249	+	0.999174i	$0.487065\pi$
$168$	−0.869929	+	7.82265i	−0.0671165	+	0.603530i
$169$	−8.77820	+	9.58870i	−0.675246	+	0.737592i
$170$	0.286420	−	0.496094i	0.0219674	−	0.0380487i
$171$	−1.73063	−	0.999181i	−0.132345	−	0.0764093i
$172$	−1.87183	+	3.24210i	−0.142725	+	0.247208i
$173$	−3.54154	−	6.13414i	−0.269259	−	0.466370i	0.699412	−	0.714719i	$-0.253445\pi$
$173$	−3.54154	−	6.13414i	−0.269259	−	0.466370i	−0.968671	+	0.248349i	$0.920112\pi$
$174$		−	5.80175i		−	0.439830i
$175$	7.72581	−	10.4999i	0.584016	−	0.793718i
$176$	−0.602654	−	0.347942i	−0.0454267	−	0.0262271i
$177$	−4.33826	−	2.50470i	−0.326084	−	0.188264i
$178$	2.65018			0.198640
$179$	−6.80438	+	11.7855i	−0.508583	+	0.880892i	0.491368	+	0.870952i	$0.336497\pi$
$179$	−6.80438	+	11.7855i	−0.508583	+	0.880892i	−0.999951	+	0.00993940i	$0.996836\pi$
$180$		−	0.282467i		−	0.0210538i
$181$	−10.9994			−0.817576			−0.408788	−	0.912629i	$-0.634048\pi$
$181$	−10.9994			−0.817576			−0.408788	+	0.912629i	$0.634048\pi$
$182$	6.85919	+	6.30342i	0.508437	+	0.467241i
$183$	10.9604			0.810213
$184$		−	5.72166i		−	0.421806i
$185$	−0.472085	+	0.817675i	−0.0347084	+	0.0601167i
$186$	−0.106674			−0.00782175
$187$	1.61189	+	0.930626i	0.117873	+	0.0680541i
$188$	−0.619945	−	0.357925i	−0.0452141	−	0.0261044i
$189$	1.06153	+	2.42346i	0.0772146	+	0.176281i
$190$		−	0.526811i		−	0.0382189i
$191$	6.32207	+	10.9501i	0.457449	+	0.792325i	0.998825	−	0.0484554i	$-0.0154299\pi$
$191$	6.32207	+	10.9501i	0.457449	+	0.792325i	−0.541376	+	0.840780i	$0.682097\pi$
$192$	3.33018	−	5.76805i	0.240335	−	0.416273i
$193$	14.7814	+	8.53405i	1.06399	+	0.614295i	0.926533	−	0.376213i	$-0.122774\pi$
$193$	14.7814	+	8.53405i	1.06399	+	0.614295i	0.137456	+	0.990508i	$0.456107\pi$
$194$	−5.03871	+	8.72729i	−0.361758	+	0.626583i
$195$	−0.785069	−	0.575355i	−0.0562200	−	0.0412020i
$196$	−4.96635	+	5.38364i	−0.354739	+	0.384546i
$197$	7.05210	−	4.07153i	0.502442	−	0.290085i	−0.227280	−	0.973830i	$-0.572983\pi$
$197$	7.05210	−	4.07153i	0.502442	−	0.290085i	0.729721	+	0.683745i	$0.239650\pi$
$198$	−0.836461			−0.0594447
$199$	9.84965			0.698223			0.349112	−	0.937081i	$-0.386483\pi$
$199$	9.84965			0.698223			0.349112	+	0.937081i	$0.386483\pi$
$200$	−12.6940	+	7.32888i	−0.897600	+	0.518230i
$201$	−4.83448	+	2.79119i	−0.340998	+	0.196875i
$202$	9.56476	+	5.52222i	0.672974	+	0.388542i
$203$	9.31572	−	12.6607i	0.653835	−	0.888606i
$204$	−1.13685	+	1.96908i	−0.0795952	+	0.137863i
$205$	−2.19140			−0.153054
$206$	−13.4229	−	7.74969i	−0.935215	−	0.539947i
$207$	−0.961652	−	1.66563i	−0.0668394	−	0.115769i
$208$	−1.18037	−	2.68090i	−0.0818439	−	0.185887i
$209$	1.71170			0.118401
$210$	−0.413363	+	0.561788i	−0.0285247	+	0.0387670i
$211$	2.89735	+	5.01836i	0.199462	+	0.345478i	0.948354	−	0.317214i	$-0.102747\pi$
$211$	2.89735	+	5.01836i	0.199462	+	0.345478i	−0.748892	+	0.662692i	$0.769414\pi$
$212$	−4.41254	−	7.64274i	−0.303054	−	0.524905i
$213$	12.5152	−	7.22567i	0.857530	−	0.495095i
$214$		−	10.8357i		−	0.740712i
$215$	−0.836439	+	0.482919i	−0.0570447	+	0.0329348i
$216$		−	2.97491i		−	0.202417i
$217$	−0.232787	−	0.171284i	−0.0158026	−	0.0116275i
$218$	−3.47054	−	6.01116i	−0.235055	−	0.407127i
$219$		−	4.11108i		−	0.277801i
$220$	0.120973	+	0.209532i	0.00815602	+	0.0141266i
$221$	3.15708	+	7.17048i	0.212368	+	0.482339i
$222$	−1.70776	+	2.95792i	−0.114617	+	0.198523i
$223$	−19.1896	+	11.0791i	−1.28503	+	0.741911i	−0.977763	−	0.209713i	$-0.932747\pi$
$223$	−19.1896	+	11.0791i	−1.28503	+	0.741911i	−0.307265	+	0.951624i	$0.599414\pi$
$224$	12.4964	−	5.47370i	0.834954	−	0.365727i
$225$	−2.46356	+	4.26702i	−0.164238	+	0.284468i
$226$	−12.7429	−	7.35712i	−0.847645	−	0.489388i
$227$			27.1745i			1.80363i	0.432120	+	0.901816i	$0.357766\pi$
$227$			27.1745i			1.80363i	−0.432120	+	0.901816i	$0.642234\pi$
$228$			2.09100i			0.138480i
$229$	1.14109	+	0.658811i	0.0754056	+	0.0435354i	0.537229	−	0.843437i	$-0.319471\pi$
$229$	1.14109	+	0.658811i	0.0754056	+	0.0435354i	−0.461823	+	0.886972i	$0.652805\pi$
$230$	0.253512	−	0.439096i	0.0167161	−	0.0289531i
$231$	−1.82534	−	1.34308i	−0.120099	−	0.0883684i
$232$	−15.3063	+	8.83710i	−1.00491	+	0.580184i
$233$	−9.48801	+	16.4337i	−0.621580	+	1.07661i	0.367611	+	0.929980i	$0.380176\pi$
$233$	−9.48801	+	16.4337i	−0.621580	+	1.07661i	−0.989192	+	0.146629i	$0.953158\pi$
$234$	−2.83997	−	2.08133i	−0.185655	−	0.136061i
$235$	−0.0923423	−	0.159942i	−0.00602375	−	0.0104334i
$236$			5.24161i			0.341200i
$237$	−0.782735	−	1.35574i	−0.0508441	−	0.0880645i
$238$	5.14259	−	2.25256i	0.333344	−	0.146012i
$239$			11.7016i			0.756912i	0.925619	+	0.378456i	$0.123545\pi$
$239$			11.7016i			0.756912i	−0.925619	+	0.378456i	$0.876455\pi$
$240$	0.189934	−	0.109658i	0.0122602	−	0.00707842i
$241$		−	21.4556i		−	1.38208i	−0.722817	−	0.691039i	$-0.757153\pi$
$241$		−	21.4556i		−	1.38208i	0.722817	−	0.691039i	$-0.242847\pi$
$242$	−8.68238	+	5.01277i	−0.558124	+	0.322233i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−5.73422	−	9.93196i	−0.367096	−	0.635829i
$245$	−1.80409	+	0.562218i	−0.115259	+	0.0359188i
$246$	−7.92734			−0.505428
$247$	5.81159	+	4.25915i	0.369782	+	0.271003i
$248$	0.162484	+	0.281431i	0.0103178	+	0.0178709i
$249$	−6.91309	−	3.99127i	−0.438099	−	0.252937i
$250$	−2.61700			−0.165514
$251$	−6.14063	+	10.6359i	−0.387593	+	0.671331i	−0.992125	−	0.125250i	$-0.960027\pi$
$251$	−6.14063	+	10.6359i	−0.387593	+	0.671331i	0.604532	+	0.796581i	$0.293360\pi$
$252$	1.64070	−	2.22983i	0.103355	−	0.140466i
$253$	1.42670	+	0.823703i	0.0896956	+	0.0517858i
$254$	1.35301	−	0.781158i	0.0848951	−	0.0490142i
$255$	−0.508008	+	0.293299i	−0.0318127	+	0.0183671i
$256$	−17.0401			−1.06501
$257$	−0.990284			−0.0617722			−0.0308861	−	0.999523i	$-0.509833\pi$
$257$	−0.990284			−0.0617722			−0.0308861	+	0.999523i	$0.509833\pi$
$258$	−3.02580	+	1.74695i	−0.188378	+	0.108760i
$259$	−8.47615	+	3.71273i	−0.526682	+	0.230698i
$260$	−0.110639	+	1.01242i	−0.00686155	+	0.0627876i
$261$	−2.97054	+	5.14513i	−0.183872	+	0.318476i
$262$	−10.6437	−	6.14514i	−0.657569	−	0.379648i
$263$	−0.187525	+	0.324803i	−0.0115633	+	0.0200282i	−0.871749	−	0.489952i	$-0.837014\pi$
$263$	−0.187525	+	0.324803i	−0.0115633	+	0.0200282i	0.860186	+	0.509981i	$0.170347\pi$
$264$	1.27408	+	2.20677i	0.0784142	+	0.135817i
$265$		−	2.27681i		−	0.139863i
$266$	3.05998	−	4.15871i	0.187619	−	0.254987i
$267$	−2.35025	−	1.35692i	−0.143833	−	0.0830419i
$268$	5.05859	+	2.92058i	0.309002	+	0.178403i
$269$	17.0590			1.04010			0.520051	−	0.854135i	$-0.325913\pi$
$269$	17.0590			1.04010			0.520051	+	0.854135i	$0.325913\pi$
$270$	0.131811	−	0.228303i	0.00802175	−	0.0138941i
$271$			13.3623i			0.811701i	0.913939	+	0.405850i	$0.133025\pi$
$271$			13.3623i			0.811701i	−0.913939	+	0.405850i	$0.866975\pi$
$272$	−1.76537			−0.107042
$273$	−2.85549	−	9.10199i	−0.172822	−	0.550877i
$274$	17.3408			1.04760
$275$		−	4.22033i		−	0.254495i
$276$	−1.00623	+	1.74284i	−0.0605680	+	0.104907i
$277$	−4.70390			−0.282630			−0.141315	−	0.989965i	$-0.545133\pi$
$277$	−4.70390			−0.282630			−0.141315	+	0.989965i	$0.545133\pi$
$278$	−19.4293	−	11.2175i	−1.16529	−	0.672782i
$279$	0.0946014	+	0.0546182i	0.00566364	+	0.00326990i
$280$	2.11174	+	0.234840i	0.126201	+	0.0140344i
$281$		−	31.2950i		−	1.86691i	−0.358700	−	0.933453i	$-0.616780\pi$
$281$		−	31.2950i		−	1.86691i	0.358700	−	0.933453i	$-0.383220\pi$
$282$	−0.334046	−	0.578585i	−0.0198921	−	0.0344542i
$283$	7.76972	−	13.4575i	0.461862	−	0.799968i	−0.537192	−	0.843460i	$-0.680515\pi$
$283$	7.76972	−	13.4575i	0.461862	−	0.799968i	0.999054	+	0.0434919i	$0.0138483\pi$
$284$	−13.0954	−	7.56063i	−0.777069	−	0.448641i
$285$	−0.269732	+	0.467189i	−0.0159775	+	0.0276739i
$286$	2.99805	+	0.327633i	0.177279	+	0.0193733i
$287$	−17.2992	−	12.7287i	−1.02114	−	0.751352i
$288$	−4.46561	+	2.57822i	−0.263139	+	0.151923i
$289$	−12.2782			−0.722249
$290$	−1.56620			−0.0919703
$291$	8.93689	−	5.15972i	0.523890	−	0.302468i
$292$	−3.72534	+	2.15082i	−0.218009	+	0.125867i
$293$	−5.22137	−	3.01456i	−0.305036	−	0.176113i	0.339667	−	0.940546i	$-0.389686\pi$
$293$	−5.22137	−	3.01456i	−0.305036	−	0.176113i	−0.644703	+	0.764433i	$0.723019\pi$
$294$	−6.52627	+	2.03381i	−0.380620	+	0.118614i
$295$	−0.676149	+	1.17112i	−0.0393669	+	0.0681855i
$296$	10.4049			0.604770
$297$	0.741794	+	0.428275i	0.0430432	+	0.0248510i
$298$	6.26830	+	10.8570i	0.363113	+	0.628930i
$299$	2.79436	+	6.34664i	0.161602	+	0.367036i
$300$	5.15553			0.297655
$301$	−9.40798	−	1.04623i	−0.542267	−	0.0603036i
$302$	−4.12913	−	7.15186i	−0.237605	−	0.411543i
$303$	−5.65484	−	9.79447i	−0.324862	−	0.562678i
$304$	−1.40601	+	0.811762i	−0.0806404	+	0.0465577i
$305$		−	2.95878i		−	0.169419i
$306$	−1.83771	+	1.06100i	−0.105055	+	0.0606534i
$307$		−	13.7607i		−	0.785363i	−0.919675	−	0.392681i	$-0.871547\pi$
$307$		−	13.7607i		−	0.785363i	0.919675	−	0.392681i	$-0.128453\pi$
$308$	−0.262085	+	2.35674i	−0.0149337	+	0.134288i
$309$	7.93581	+	13.7452i	0.451452	+	0.781938i
$310$			0.0287970i			0.00163556i
$311$	−14.0828	−	24.3920i	−0.798560	−	1.38315i	−0.920554	−	0.390615i	$-0.872262\pi$
$311$	−14.0828	−	24.3920i	−0.798560	−	1.38315i	0.121995	−	0.992531i	$-0.461071\pi$
$312$	−1.16524	+	10.6627i	−0.0659688	+	0.603657i
$313$	−6.10426	+	10.5729i	−0.345033	+	0.597615i	−0.985360	−	0.170488i	$-0.945466\pi$
$313$	−6.10426	+	10.5729i	−0.345033	+	0.597615i	0.640327	+	0.768103i	$0.278799\pi$
$314$	14.1362	−	8.16153i	0.797751	−	0.460582i
$315$	0.654220	−	0.286562i	0.0368611	−	0.0161459i
$316$	−0.819019	+	1.41858i	−0.0460734	+	0.0798015i
$317$	11.1776	+	6.45338i	0.627795	+	0.362458i	0.779898	−	0.625907i	$-0.215271\pi$
$317$	11.1776	+	6.45338i	0.627795	+	0.362458i	−0.152103	+	0.988365i	$0.548604\pi$
$318$		−	8.23630i		−	0.461868i
$319$		−	5.08884i		−	0.284920i
$320$	−1.55710	−	0.898992i	−0.0870445	−	0.0502552i
$321$	−5.54796	+	9.60935i	−0.309657	+	0.536341i
$322$	4.55174	−	1.99375i	0.253658	−	0.111108i
$323$	3.76060	−	2.17118i	0.209245	−	0.120808i
$324$	−0.523178	+	0.906171i	−0.0290654	+	0.0503428i
$325$	10.5013	−	14.3289i	0.582506	−	0.794827i
$326$	−10.5434	−	18.2617i	−0.583945	−	1.01142i
$327$			7.10779i			0.393062i
$328$	12.0747	+	20.9141i	0.666716	+	1.15479i
$329$	0.200057	−	1.79897i	0.0110295	−	0.0991802i
$330$			0.225805i			0.0124302i
$331$	−13.4228	+	7.74964i	−0.737782	+	0.425958i	−0.821262	−	0.570551i	$-0.806730\pi$
$331$	−13.4228	+	7.74964i	−0.737782	+	0.425958i	0.0834805	+	0.996509i	$0.473396\pi$
$332$			8.35259i			0.458408i
$333$	3.02896	−	1.74877i	0.165986	−	0.0958320i
$334$	5.86068	+	10.1510i	0.320682	+	0.555438i
$335$	0.753489	+	1.30508i	0.0411675	+	0.0713042i
$336$	2.13631	+	0.237572i	0.116545	+	0.0129606i
$337$	34.6418			1.88706			0.943528	−	0.331292i	$-0.107484\pi$
$337$	34.6418			1.88706			0.943528	+	0.331292i	$0.107484\pi$
$338$	9.36382	+	8.57233i	0.509324	+	0.466273i
$339$	7.53381	+	13.0489i	0.409180	+	0.708721i
$340$	0.531557	+	0.306895i	0.0288277	+	0.0166437i
$341$	−0.0935664			−0.00506690
$342$	−0.975748	+	1.69004i	−0.0527624	+	0.0913871i
$343$	−17.5074	−	6.04084i	−0.945309	−	0.326175i
$344$	9.21766	+	5.32182i	0.496983	+	0.286933i
$345$	−0.449641	+	0.259601i	−0.0242079	+	0.0139764i
$346$	−5.99027	+	3.45848i	−0.322039	+	0.185929i
$347$	30.8011			1.65349			0.826746	−	0.562575i	$-0.190189\pi$
$347$	30.8011			1.65349			0.826746	+	0.562575i	$0.190189\pi$
$348$	6.21649			0.333239
$349$	−10.6230	+	6.13321i	−0.568638	+	0.328303i	−0.756605	−	0.653872i	$-0.773144\pi$
$349$	−10.6230	+	6.13321i	−0.568638	+	0.328303i	0.187967	+	0.982175i	$0.439810\pi$
$350$	−10.2536	−	7.54462i	−0.548080	−	0.403277i
$351$	1.45289	+	3.29986i	0.0775497	+	0.176134i
$352$	2.20838	−	3.82502i	0.117707	−	0.203874i
$353$	−3.36012	−	1.93996i	−0.178841	−	0.103254i	0.407907	−	0.913023i	$-0.366259\pi$
$353$	−3.36012	−	1.93996i	−0.178841	−	0.103254i	−0.586748	+	0.809770i	$0.699592\pi$
$354$	−2.44595	+	4.23651i	−0.130001	+	0.225168i
$355$	−1.95059	−	3.37852i	−0.103527	−	0.179313i
$356$			2.83963i			0.150500i
$357$	−5.71390	−	0.635422i	−0.302412	−	0.0336301i
$358$	11.5091	+	6.64479i	0.608276	+	0.351188i
$359$	32.2363	+	18.6117i	1.70137	+	0.982286i	0.944379	+	0.328859i	$0.106664\pi$
$359$	32.2363	+	18.6117i	1.70137	+	0.982286i	0.756990	+	0.653427i	$0.226669\pi$
$360$	−0.803085			−0.0423263
$361$	−7.50327	+	12.9961i	−0.394909	+	0.684003i
$362$			10.7414i			0.564555i
$363$	10.2663			0.538842
$364$	−6.75403	+	7.34952i	−0.354007	+	0.385220i
$365$	−1.10980			−0.0580894
$366$		−	10.7033i		−	0.559471i
$367$	−8.57322	+	14.8492i	−0.447518	+	0.775124i	−0.998224	−	0.0595753i	$-0.981025\pi$
$367$	−8.57322	+	14.8492i	−0.447518	+	0.775124i	0.550706	+	0.834700i	$0.314359\pi$
$368$	−1.56254			−0.0814533
$369$	7.03015	+	4.05886i	0.365975	+	0.211296i
$370$	0.798498	+	0.461013i	0.0415120	+	0.0239669i
$371$	13.2248	−	17.9734i	0.686597	−	0.933132i
$372$		−	0.114300i		−	0.00592618i
$373$	−5.67303	−	9.82597i	−0.293738	−	0.508770i	0.680952	−	0.732328i	$-0.261566\pi$
$373$	−5.67303	−	9.82597i	−0.293738	−	0.508770i	−0.974691	+	0.223558i	$0.928233\pi$
$374$	0.908800	−	1.57409i	0.0469929	−	0.0813941i
$375$	2.32082	+	1.33993i	0.119847	+	0.0691935i
$376$	−1.01762	+	1.76257i	−0.0524799	+	0.0908978i
$377$	12.6624	−	17.2777i	0.652144	−	0.889848i
$378$	2.36662	−	1.03663i	0.121726	−	0.0533185i
$379$	18.3332	−	10.5847i	0.941713	−	0.543698i	0.0512161	−	0.998688i	$-0.483690\pi$
$379$	18.3332	−	10.5847i	0.941713	−	0.543698i	0.890497	+	0.454989i	$0.150357\pi$
$380$	0.564471			0.0289567
$381$	−1.59984			−0.0819622
$382$	10.6933	−	6.17380i	0.547119	−	0.315879i
$383$	−18.5097	+	10.6866i	−0.945803	+	0.546060i	−0.891775	−	0.452480i	$-0.850540\pi$
$383$	−18.5097	+	10.6866i	−0.945803	+	0.546060i	−0.0540285	+	0.998539i	$0.517206\pi$
$384$	3.29846	+	1.90437i	0.168324	+	0.0971818i
$385$	−0.362569	+	0.492756i	−0.0184782	+	0.0251132i
$386$	8.33390	−	14.4347i	0.424184	−	0.734709i
$387$	3.57780			0.181870
$388$	−9.35117	−	5.39890i	−0.474734	−	0.274088i
$389$	1.28830	+	2.23141i	0.0653195	+	0.113137i	0.896836	−	0.442364i	$-0.145860\pi$
$389$	1.28830	+	2.23141i	0.0653195	+	0.113137i	−0.831516	+	0.555501i	$0.812527\pi$
$390$	−0.561861	+	0.766657i	−0.0284510	+	0.0388212i
$391$	4.17927			0.211355
$392$	15.3063	+	14.1199i	0.773085	+	0.713162i
$393$	6.29272	+	10.8993i	0.317426	+	0.549797i
$394$	−3.97604	−	6.88671i	−0.200310	−	0.346948i
$395$	−0.365985	+	0.211301i	−0.0184147	+	0.0106317i
$396$		−	0.896256i		−	0.0450386i
$397$	−10.1386	+	5.85352i	−0.508842	+	0.293780i	−0.732357	−	0.680921i	$-0.761580\pi$
$397$	−10.1386	+	5.85352i	−0.508842	+	0.293780i	0.223516	+	0.974700i	$0.428247\pi$
$398$		−	9.61865i		−	0.482139i
$399$	−4.84295	+	2.12131i	−0.242451	+	0.106199i
$400$	2.00147	+	3.46664i	0.100073	+	0.173332i
$401$		−	37.5533i		−	1.87532i	−0.347549	−	0.937662i	$-0.612986\pi$
$401$		−	37.5533i		−	1.87532i	0.347549	−	0.937662i	$-0.387014\pi$
$402$	2.72573	+	4.72110i	0.135947	+	0.235467i
$403$	−0.317678	−	0.232818i	−0.0158247	−	0.0115975i
$404$	−5.91697	+	10.2485i	−0.294380	+	0.509882i
$405$	−0.233786	+	0.134976i	−0.0116169	+	0.00670703i
$406$	−12.3638	−	9.09724i	−0.613603	−	0.451488i
$407$	−1.49791	+	2.59445i	−0.0742486	+	0.128602i
$408$	5.59831	+	3.23218i	0.277158	+	0.160017i
$409$			8.89957i			0.440055i	0.975494	+	0.220028i	$0.0706148\pi$
$409$			8.89957i			0.440055i	−0.975494	+	0.220028i	$0.929385\pi$
$410$			2.14001i			0.105687i
$411$	−15.3783	−	8.87864i	−0.758553	−	0.437951i
$412$	8.30368	−	14.3824i	0.409093	−	0.708570i
$413$	−12.1401	+	5.31760i	−0.597373	+	0.261662i
$414$	−1.62657	+	0.939098i	−0.0799414	+	0.0461542i
$415$	−1.07746	+	1.86621i	−0.0528902	+	0.0916085i
$416$	17.0156	−	7.49177i	0.834257	−	0.367314i
$417$	11.4869	+	19.8959i	0.562517	+	0.974308i
$418$		−	1.67155i		−	0.0817583i
$419$	16.0435	+	27.7881i	0.783775	+	1.35754i	0.929728	+	0.368247i	$0.120042\pi$
$419$	16.0435	+	27.7881i	0.783775	+	1.35754i	−0.145953	+	0.989292i	$0.546625\pi$
$420$	−0.601947	−	0.442912i	−0.0293720	−	0.0216119i
$421$			10.0906i			0.491785i	0.969297	+	0.245892i	$0.0790810\pi$
$421$			10.0906i			0.491785i	−0.969297	+	0.245892i	$0.920919\pi$
$422$	4.90067	−	2.82940i	0.238561	−	0.137733i
$423$			0.684137i			0.0332639i
$424$	−21.7292	+	12.5453i	−1.05526	+	0.609256i
$425$	−5.35323	−	9.27207i	−0.259670	−	0.449761i
$426$	−7.05621	−	12.2217i	−0.341875	−	0.592144i
$427$	17.1860	−	23.3570i	0.831690	−	1.13032i
$428$	11.6103			0.561204
$429$	−2.49100	−	1.82558i	−0.120266	−	0.0881399i
$430$	0.471593	+	0.816822i	0.0227422	+	0.0393907i
$431$	0.967588	+	0.558637i	0.0466071	+	0.0269086i	0.523122	−	0.852258i	$-0.324767\pi$
$431$	0.967588	+	0.558637i	0.0466071	+	0.0269086i	−0.476515	+	0.879166i	$0.658100\pi$
$432$	−0.812427			−0.0390879
$433$	−14.9651	+	25.9203i	−0.719176	+	1.24565i	0.242151	+	0.970239i	$0.422147\pi$
$433$	−14.9651	+	25.9203i	−0.719176	+	1.24565i	−0.961327	+	0.275410i	$0.911186\pi$
$434$	−0.167267	+	0.227327i	−0.00802908	+	0.0109121i
$435$	1.38894	+	0.801906i	0.0665947	+	0.0384485i
$436$	6.44087	−	3.71864i	0.308462	−	0.178090i
$437$	3.32853	−	1.92173i	0.159225	−	0.0919288i
$438$	−4.01466			−0.191828
$439$	−19.1161			−0.912360			−0.456180	−	0.889887i	$-0.650783\pi$
$439$	−19.1161			−0.912360			−0.456180	+	0.889887i	$0.650783\pi$
$440$	0.595723	−	0.343941i	0.0284000	−	0.0163967i
$441$	6.82898	+	1.53787i	0.325189	+	0.0732320i
$442$	7.00231	−	3.08304i	0.333066	−	0.146645i
$443$	6.70719	−	11.6172i	0.318668	−	0.551950i	−0.661542	−	0.749908i	$-0.730098\pi$
$443$	6.70719	−	11.6172i	0.318668	−	0.551950i	0.980210	+	0.197958i	$0.0634311\pi$
$444$	−3.16937	−	1.82984i	−0.150412	−	0.0868402i
$445$	−0.366303	+	0.634455i	−0.0173644	+	0.0300761i
$446$	10.8193	+	18.7395i	0.512307	+	0.887341i
$447$		−	12.8377i		−	0.607202i
$448$	−7.07015	−	16.1411i	−0.334033	−	0.762597i
$449$	−13.9832	−	8.07323i	−0.659910	−	0.380999i	0.132333	−	0.991205i	$-0.457753\pi$
$449$	−13.9832	−	8.07323i	−0.659910	−	0.380999i	−0.792243	+	0.610206i	$0.791087\pi$
$450$	4.16694	+	2.40578i	0.196432	+	0.113410i
$451$	−6.95323			−0.327415
$452$	7.88305	−	13.6538i	0.370787	−	0.642223i
$453$			8.45659i			0.397325i
$454$	26.5371			1.24545
$455$	−2.45711	+	0.770847i	−0.115191	+	0.0361379i
$456$	5.94495			0.278398
$457$		−	7.65880i		−	0.358264i	−0.983825	−	0.179132i	$-0.942671\pi$
$457$		−	7.65880i		−	0.358264i	0.983825	−	0.179132i	$-0.0573289\pi$
$458$	0.643360	−	1.11433i	0.0300622	−	0.0520693i
$459$	2.17296			0.101425
$460$	0.470485	+	0.271635i	0.0219365	+	0.0126650i
$461$	26.3366	+	15.2054i	1.22662	+	0.708187i	0.966320	−	0.257342i	$-0.0828468\pi$
$461$	26.3366	+	15.2054i	1.22662	+	0.708187i	0.260295	+	0.965529i	$0.416180\pi$
$462$	−1.31158	+	1.78253i	−0.0610204	+	0.0829309i
$463$			0.0512983i			0.00238403i	0.999999	+	0.00119202i	$0.000379431\pi$
$463$			0.0512983i			0.00238403i	−0.999999	+	0.00119202i	$0.999621\pi$
$464$	2.41335	+	4.18005i	0.112037	+	0.194054i
$465$	0.0147443	−	0.0255379i	0.000683751	−	0.00118429i
$466$	16.0483	+	9.26549i	0.743423	+	0.429216i
$467$	11.2666	−	19.5143i	0.521356	−	0.903015i	−0.478335	−	0.878177i	$-0.658760\pi$
$467$	11.2666	−	19.5143i	0.521356	−	0.903015i	0.999691	−	0.0248380i	$-0.00790699\pi$
$468$	2.23012	−	3.04299i	0.103087	−	0.140662i
$469$	−1.63241	+	14.6791i	−0.0753777	+	0.677818i
$470$	−0.156190	+	0.0901766i	−0.00720453	+	0.00415954i
$471$	−16.7151			−0.770190
$472$	14.9025			0.685943
$473$	−2.65399	+	1.53228i	−0.122031	+	0.0704544i
$474$	−1.32394	+	0.764377i	−0.0608106	+	0.0351090i
$475$	−8.52705	−	4.92309i	−0.391248	−	0.225887i
$476$	2.41358	+	5.51021i	0.110626	+	0.252560i
$477$	−4.21705	+	7.30414i	−0.193085	+	0.334434i
$478$	11.4271			0.522665
$479$	−25.7792	−	14.8836i	−1.17788	−	0.680049i	−0.222357	−	0.974965i	$-0.571375\pi$
$479$	−25.7792	−	14.8836i	−1.17788	−	0.680049i	−0.955523	+	0.294916i	$0.904708\pi$
$480$	0.695998	+	1.20550i	0.0317678	+	0.0550235i
$481$	−11.5414	+	5.08155i	−0.526243	+	0.231699i
$482$	−20.9524			−0.954357
$483$	−5.05741	−	0.562417i	−0.230120	−	0.0255908i
$484$	−5.37111	−	9.30304i	−0.244142	−	0.422866i
$485$	−1.39288	−	2.41254i	−0.0632474	−	0.109548i
$486$	−0.845714	+	0.488273i	−0.0383624	+	0.0221485i
$487$			7.87082i			0.356661i	0.983971	+	0.178330i	$0.0570696\pi$
$487$			7.87082i			0.356661i	−0.983971	+	0.178330i	$0.942930\pi$
$488$	−28.2377	+	16.3030i	−1.27826	+	0.738004i
$489$			21.5932i			0.976480i
$490$	0.549032	+	1.76178i	0.0248027	+	0.0795893i
$491$	11.3549	+	19.6673i	0.512441	+	0.887574i	0.999896	+	0.0144261i	$0.00459212\pi$
$491$	11.3549	+	19.6673i	0.512441	+	0.887574i	−0.487455	+	0.873148i	$0.662075\pi$
$492$		−	8.49403i		−	0.382940i
$493$	−6.45488	−	11.1802i	−0.290713	−	0.503530i
$494$	4.15926	−	5.67529i	0.187134	−	0.255343i
$495$	0.115614	−	0.200249i	0.00519646	−	0.00900053i
$496$	0.0768568	−	0.0443733i	0.00345097	−	0.00199242i
$497$	4.22589	−	38.0004i	0.189557	−	1.70455i
$498$	−3.89767	+	6.75096i	−0.174659	+	0.302518i
$499$	20.7627	+	11.9874i	0.929467	+	0.536628i	0.886643	−	0.462455i	$-0.153031\pi$
$499$	20.7627	+	11.9874i	0.929467	+	0.536628i	0.0428241	+	0.999083i	$0.486365\pi$
$500$		−	2.80408i		−	0.125402i
$501$		−	12.0029i		−	0.536249i
$502$	10.3864	+	5.99662i	0.463570	+	0.267642i
$503$	−8.75880	+	15.1707i	−0.390535	+	0.676427i	−0.992520	−	0.122080i	$-0.961043\pi$
$503$	−8.75880	+	15.1707i	−0.390535	+	0.676427i	0.601985	+	0.798508i	$0.294377\pi$
$504$	−6.33965	−	4.66471i	−0.282390	−	0.207782i
$505$	−2.64404	+	1.52654i	−0.117658	+	0.0679301i
$506$	0.804385	−	1.39324i	0.0357593	−	0.0619369i
$507$	−3.91496	−	12.3965i	−0.173869	−	0.550548i
$508$	0.837000	+	1.44973i	0.0371359	+	0.0643212i
$509$		−	14.5540i		−	0.645095i	−0.946553	−	0.322548i	$-0.895461\pi$
$509$		−	14.5540i		−	0.645095i	0.946553	−	0.322548i	$-0.104539\pi$
$510$	0.286420	+	0.496094i	0.0126829	+	0.0219674i
$511$	−8.76086	−	6.44623i	−0.387558	−	0.285165i
$512$			9.02303i			0.398765i
$513$	1.73063	−	0.999181i	0.0764093	−	0.0441149i
$514$			0.967059i			0.0426551i
$515$	3.71056	−	2.14229i	0.163507	−	0.0944007i
$516$	−1.87183	−	3.24210i	−0.0824026	−	0.142725i
$517$	−0.292999	−	0.507489i	−0.0128861	−	0.0223193i
$518$	3.62565	+	8.27736i	0.159302	+	0.363686i
$519$	7.08309			0.310913
$520$	2.87843	+	0.314560i	0.126227	+	0.0137944i
$521$	−14.8659	−	25.7484i	−0.651286	−	1.12806i	−0.982811	−	0.184614i	$-0.940897\pi$
$521$	−14.8659	−	25.7484i	−0.651286	−	1.12806i	0.331526	−	0.943446i	$-0.392437\pi$
$522$	5.02446	+	2.90088i	0.219915	+	0.126968i
$523$	−8.39584			−0.367125			−0.183562	−	0.983008i	$-0.558763\pi$
$523$	−8.39584			−0.367125			−0.183562	+	0.983008i	$0.558763\pi$
$524$	6.58442	−	11.4046i	0.287642	−	0.498210i
$525$	5.23027	+	11.9407i	0.228268	+	0.521135i
$526$	0.317186	+	0.183127i	0.0138300	+	0.00798473i
$527$	−0.205565	+	0.118683i	−0.00895457	+	0.00516992i
$528$	0.602654	−	0.347942i	0.0262271	−	0.0151422i
$529$	−19.3009			−0.839170
$530$	−2.22341			−0.0965787
$531$	4.33826	−	2.50470i	0.188264	−	0.108695i
$532$	4.45600	+	3.27872i	0.193192	+	0.142151i
$533$	−23.6077	−	17.3015i	−1.02257	−	0.749409i
$534$	−1.32509	+	2.29513i	−0.0573423	+	0.0993198i
$535$	2.59407	+	1.49769i	0.112151	+	0.0647506i
$536$	8.30354	−	14.3821i	0.358658	−	0.621214i
$537$	−6.80438	−	11.7855i	−0.293631	−	0.508583i
$538$		−	16.6589i		−	0.718215i
$539$	−5.72433	+	1.78390i	−0.246564	+	0.0768379i
$540$	0.244623	+	0.141233i	0.0105269	+	0.00607771i
$541$	38.2304	+	22.0723i	1.64365	+	0.948964i	0.979519	+	0.201350i	$0.0645328\pi$
$541$	38.2304	+	22.0723i	1.64365	+	0.948964i	0.664134	+	0.747614i	$0.268801\pi$
$542$	13.0489			0.560498
$543$	5.49968	−	9.52572i	0.236014	−	0.408788i
$544$		−	11.2048i		−	0.480400i
$545$	1.91877			0.0821909
$546$	−8.88852	+	2.78852i	−0.380393	+	0.119338i
$547$	3.55444			0.151977			0.0759885	−	0.997109i	$-0.475789\pi$
$547$	3.55444			0.151977			0.0759885	+	0.997109i	$0.475789\pi$
$548$			18.5804i			0.793717i
$549$	−5.48018	+	9.49195i	−0.233888	+	0.405107i
$550$	−4.12135			−0.175735
$551$	−10.2818	−	5.93622i	−0.438021	−	0.252892i
$552$	4.95510	+	2.86083i	0.210903	+	0.121765i
$553$	−4.11647	−	0.457778i	−0.175050	−	0.0194667i
$554$			4.59358i			0.195163i
$555$	−0.472085	−	0.817675i	−0.0200389	−	0.0347084i
$556$	12.0194	−	20.8182i	0.509736	−	0.882889i
$557$	21.1719	+	12.2236i	0.897083	+	0.517931i	0.876253	−	0.481852i	$-0.160036\pi$
$557$	21.1719	+	12.2236i	0.897083	+	0.517931i	0.0208303	+	0.999783i	$0.493369\pi$
$558$	0.0533372	−	0.0923828i	0.00225794	−	0.00391087i
$559$	−12.8236	−	1.40139i	−0.542381	−	0.0592724i
$560$	0.0641331	−	0.576703i	0.00271012	−	0.0243701i
$561$	−1.61189	+	0.930626i	−0.0680541	+	0.0392910i
$562$	−30.5611			−1.28914
$563$	−13.6017			−0.573245			−0.286622	−	0.958044i	$-0.592532\pi$
$563$	−13.6017			−0.573245			−0.286622	+	0.958044i	$0.592532\pi$
$564$	0.619945	−	0.357925i	0.0261044	−	0.0150714i
$565$	3.52260	−	2.03377i	0.148197	−	0.0855614i
$566$	−13.1419	−	7.58749i	−0.552396	−	0.318926i
$567$	−2.62954	−	0.292422i	−0.110430	−	0.0122806i
$568$	−21.4957	+	37.2317i	−0.901941	+	1.56221i
$569$	0.836836			0.0350820			0.0175410	−	0.999846i	$-0.494416\pi$
$569$	0.836836			0.0350820			0.0175410	+	0.999846i	$0.494416\pi$
$570$	0.456232	+	0.263406i	0.0191095	+	0.0110328i
$571$	−14.1413	−	24.4935i	−0.591796	−	1.02502i	−0.993990	−	0.109467i	$-0.965086\pi$
$571$	−14.1413	−	24.4935i	−0.591796	−	1.02502i	0.402194	−	0.915554i	$-0.368248\pi$
$572$	−0.351054	+	3.21237i	−0.0146783	+	0.134316i
$573$	−12.6441			−0.528217
$574$	−12.4302	+	16.8935i	−0.518826	+	0.705119i
$575$	−4.73818	−	8.20677i	−0.197596	−	0.342246i
$576$	3.33018	+	5.76805i	0.138758	+	0.240335i
$577$	23.7679	−	13.7224i	0.989472	−	0.571272i	0.0843557	−	0.996436i	$-0.473117\pi$
$577$	23.7679	−	13.7224i	0.989472	−	0.571272i	0.905116	+	0.425164i	$0.139783\pi$
$578$			11.9903i			0.498729i
$579$	−14.7814	+	8.53405i	−0.614295	+	0.354663i
$580$		−	1.67816i		−	0.0696818i
$581$	−19.3454	+	8.47368i	−0.802582	+	0.351548i
$582$	−5.03871	−	8.72729i	−0.208861	−	0.361758i
$583$		−	7.22423i		−	0.299197i
$584$	6.11504	+	10.5916i	0.253042	+	0.438282i
$585$	0.890807	−	0.392212i	0.0368303	−	0.0162160i
$586$	−2.94386	+	5.09892i	−0.121610	+	0.210634i
$587$	−4.70300	+	2.71528i	−0.194113	+	0.112071i	−0.593907	−	0.804534i	$-0.702415\pi$
$587$	−4.70300	+	2.71528i	−0.194113	+	0.112071i	0.399793	+	0.916605i	$0.369082\pi$
$588$	−2.17920	−	6.99280i	−0.0898686	−	0.288378i
$589$	−0.109147	+	0.189048i	−0.00449732	+	0.00778959i
$590$	1.14366	+	0.660292i	0.0470837	+	0.0271838i
$591$			8.14307i			0.334961i
$592$		−	2.84150i		−	0.116785i
$593$	−21.9497	−	12.6726i	−0.901364	−	0.520403i	−0.0237218	−	0.999719i	$-0.507552\pi$
$593$	−21.9497	−	12.6726i	−0.901364	−	0.520403i	−0.877643	+	0.479316i	$0.840885\pi$
$594$	0.418231	−	0.724397i	0.0171602	−	0.0297224i
$595$	−0.171534	+	1.54248i	−0.00703221	+	0.0632356i
$596$	−11.6331	+	6.71640i	−0.476512	+	0.275114i
$597$	−4.92483	+	8.53005i	−0.201560	+	0.349112i
$598$	6.19779	−	2.72882i	0.253447	−	0.111590i
$599$	−10.4813	−	18.1541i	−0.428253	−	0.741756i	0.568465	−	0.822707i	$-0.307537\pi$
$599$	−10.4813	−	18.1541i	−0.428253	−	0.741756i	−0.996718	+	0.0809515i	$0.974204\pi$
$600$		−	14.6578i		−	0.598400i
$601$	15.7239	+	27.2345i	0.641390	+	1.11092i	0.985123	+	0.171852i	$0.0549752\pi$
$601$	15.7239	+	27.2345i	0.641390	+	1.11092i	−0.343733	+	0.939067i	$0.611691\pi$
$602$	−1.02169	+	9.18733i	−0.0416410	+	0.374448i
$603$		−	5.58238i		−	0.227332i
$604$	7.66312	−	4.42430i	0.311808	−	0.180022i
$605$		−	2.77142i		−	0.112674i
$606$	−9.56476	+	5.52222i	−0.388542	+	0.224325i
$607$	9.97909	+	17.2843i	0.405039	+	0.701548i	0.994326	−	0.106376i	$-0.0339247\pi$
$607$	9.97909	+	17.2843i	0.405039	+	0.701548i	−0.589287	+	0.807924i	$0.700591\pi$
$608$	−5.15223	−	8.92392i	−0.208950	−	0.361913i
$609$	6.30662	+	14.3980i	0.255557	+	0.583436i
$610$	−2.88939			−0.116988
$611$	0.267969	−	2.45209i	0.0108409	−	0.0992010i
$612$	−1.13685	−	1.96908i	−0.0459543	−	0.0795952i
$613$	4.21477	+	2.43340i	0.170233	+	0.0982841i	0.582696	−	0.812690i	$-0.301998\pi$
$613$	4.21477	+	2.43340i	0.170233	+	0.0982841i	−0.412463	+	0.910974i	$0.635331\pi$
$614$	−13.4379			−0.542311
$615$	1.09570	−	1.89781i	0.0441829	−	0.0765270i
$616$	6.70049	+	0.745138i	0.269970	+	0.0300225i
$617$	21.6231	+	12.4841i	0.870512	+	0.502590i	0.867518	−	0.497405i	$-0.165714\pi$
$617$	21.6231	+	12.4841i	0.870512	+	0.502590i	0.00299347	+	0.999996i	$0.499047\pi$
$618$	13.4229	−	7.74969i	0.539947	−	0.311738i
$619$	−17.1875	+	9.92322i	−0.690825	+	0.398848i	−0.803921	−	0.594736i	$-0.797257\pi$
$619$	−17.1875	+	9.92322i	−0.690825	+	0.398848i	0.113096	+	0.993584i	$0.463923\pi$
$620$	−0.0308556			−0.00123919
$621$	1.92330			0.0771795
$622$	−23.8200	+	13.7525i	−0.955094	+	0.551424i
$623$	−6.57686	+	2.88080i	−0.263496	+	0.115417i
$624$	2.91191	+	0.318219i	0.116570	+	0.0127390i
$625$	−11.9561	+	20.7086i	−0.478244	+	0.828343i
$626$	10.3249	+	5.96109i	0.412667	+	0.238253i
$627$	−0.855849	+	1.48237i	−0.0341793	+	0.0592003i
$628$	8.74496	+	15.1467i	0.348962	+	0.604420i
$629$			7.60002i			0.303033i
$630$	−0.279841	−	0.638876i	−0.0111491	−	0.0254534i
$631$	−34.8669	−	20.1304i	−1.38803	−	0.801380i	−0.394937	−	0.918708i	$-0.629234\pi$
$631$	−34.8669	−	20.1304i	−1.38803	−	0.801380i	−0.993093	+	0.117329i	$0.962567\pi$
$632$	4.03319	+	2.32856i	0.160432	+	0.0926253i
$633$	−5.79471			−0.230319
$634$	6.30202	−	10.9154i	0.250285	−	0.433507i
$635$			0.431880i			0.0171387i
$636$	8.82507			0.349937
$637$	−23.8741	−	8.18690i	−0.945928	−	0.324377i
$638$	−4.96949			−0.196744
$639$			14.4513i			0.571687i
$640$	0.514089	−	0.890428i	0.0203211	−	0.0351972i
$641$	17.8340			0.704400			0.352200	−	0.935925i	$-0.385434\pi$
$641$	17.8340			0.704400			0.352200	+	0.935925i	$0.385434\pi$
$642$	9.38398	+	5.41784i	0.370356	+	0.213825i
$643$	30.6543	+	17.6983i	1.20889	+	0.697953i	0.962517	−	0.271222i	$-0.0874279\pi$
$643$	30.6543	+	17.6983i	1.20889	+	0.697953i	0.246373	+	0.969175i	$0.420761\pi$
$644$	2.13628	+	4.87712i	0.0841812	+	0.192185i
$645$		−	0.965837i		−	0.0380298i
$646$	−2.12026	−	3.67240i	−0.0834207	−	0.144489i
$647$	−18.5936	+	32.2050i	−0.730988	+	1.26611i	0.225473	+	0.974249i	$0.427607\pi$
$647$	−18.5936	+	32.2050i	−0.730988	+	1.26611i	−0.956461	+	0.291860i	$0.905726\pi$
$648$	2.57635	+	1.48745i	0.101208	+	0.0584327i
$649$	−2.14540	+	3.71594i	−0.0842142	+	0.145863i
$650$	−13.9929	−	10.2550i	−0.548846	−	0.402234i
$651$	0.264730	−	0.115957i	0.0103756	−	0.00454472i
$652$	19.5672	−	11.2971i	0.766309	−	0.442429i
$653$	−48.8766			−1.91269			−0.956344	−	0.292243i	$-0.905598\pi$
$653$	−48.8766			−1.91269			−0.956344	+	0.292243i	$0.905598\pi$
$654$	6.94109			0.271418
$655$	2.94230	−	1.69874i	0.114965	−	0.0663751i
$656$	5.71149	−	3.29753i	0.222996	−	0.128747i
$657$	3.56030	+	2.05554i	0.138900	+	0.0801942i
$658$	−1.75678	−	0.195365i	−0.0684862	−	0.00761611i
$659$	−4.54386	+	7.87020i	−0.177004	+	0.306579i	−0.940853	−	0.338815i	$-0.889974\pi$
$659$	−4.54386	+	7.87020i	−0.177004	+	0.306579i	0.763849	+	0.645395i	$0.223307\pi$
$660$	−0.241947			−0.00941776
$661$	−0.714628	−	0.412591i	−0.0277958	−	0.0160479i	0.486038	−	0.873938i	$-0.338442\pi$
$661$	−0.714628	−	0.412591i	−0.0277958	−	0.0160479i	−0.513834	+	0.857890i	$0.671775\pi$
$662$	7.56788	+	13.1080i	0.294134	+	0.509455i
$663$	−7.78836	−	0.851127i	−0.302475	−	0.0330550i
$664$	23.7474			0.921576
$665$	0.572654	+	1.30737i	0.0222066	+	0.0506976i
$666$	−1.70776	−	2.95792i	−0.0661742	−	0.114617i
$667$	−5.71326	−	9.89566i	−0.221218	−	0.383161i
$668$	−10.8767	+	6.27964i	−0.420830	+	0.242966i
$669$		−	22.1582i		−	0.856685i
$670$	1.27447	−	0.735817i	0.0492372	−	0.0284271i
$671$		−	9.38809i		−	0.362423i
$672$	−1.50786	+	13.5591i	−0.0581669	+	0.523053i
$673$	−4.51142	−	7.81401i	−0.173903	−	0.301208i	0.765878	−	0.642985i	$-0.222304\pi$
$673$	−4.51142	−	7.81401i	−0.173903	−	0.301208i	−0.939781	+	0.341777i	$0.888971\pi$
$674$		−	33.8293i		−	1.30306i
$675$	−2.46356	−	4.26702i	−0.0948226	−	0.164238i
$676$	−9.18513	+	10.0332i	−0.353274	+	0.385892i
$677$	17.0440	−	29.5211i	0.655055	−	1.13459i	−0.326825	−	0.945085i	$-0.605979\pi$
$677$	17.0440	−	29.5211i	0.655055	−	1.13459i	0.981880	−	0.189503i	$-0.0606878\pi$
$678$	12.7429	−	7.35712i	0.489388	−	0.282548i
$679$	3.01763	−	27.1354i	0.115806	−	1.04136i
$680$	0.872537	−	1.51128i	0.0334603	−	0.0579549i
$681$	−23.5338	−	13.5872i	−0.901816	−	0.520664i
$682$			0.0913720i			0.00349881i
$683$			45.1344i			1.72702i	0.504333	+	0.863509i	$0.331738\pi$
$683$			45.1344i			1.72702i	−0.504333	+	0.863509i	$0.668262\pi$
$684$	−1.81086	−	1.04550i	−0.0692399	−	0.0399757i
$685$	−2.39681	+	4.15140i	−0.0915775	+	0.158617i
$686$	−5.89917	+	17.0968i	−0.225231	+	0.652758i
$687$	−1.14109	+	0.658811i	−0.0435354	+	0.0251352i
$688$	1.45335	−	2.51728i	0.0554085	−	0.0959704i
$689$	17.9758	−	24.5278i	0.684822	−	0.934436i
$690$	0.253512	+	0.439096i	0.00965104	+	0.0167161i
$691$			1.12706i			0.0428753i	0.999770	+	0.0214376i	$0.00682433\pi$
$691$			1.12706i			0.0428753i	−0.999770	+	0.0214376i	$0.993176\pi$
$692$	−3.70572	−	6.41849i	−0.140870	−	0.243994i
$693$	2.07582	−	0.909250i	0.0788537	−	0.0345395i
$694$		−	30.0788i		−	1.14177i
$695$	5.37096	−	3.10092i	0.203732	−	0.117625i
$696$		−	17.6742i		−	0.669939i
$697$	−15.2763	+	8.81975i	−0.578630	+	0.334072i
$698$	5.98937	+	10.3739i	0.226701	+	0.392658i
$699$	−9.48801	−	16.4337i	−0.358870	−	0.621580i
$700$	8.08395	−	10.9866i	0.305545	−	0.415256i
$701$	27.0972			1.02345			0.511723	−	0.859151i	$-0.329007\pi$
$701$	27.0972			1.02345			0.511723	+	0.859151i	$0.329007\pi$
$702$	3.22247	−	1.41882i	0.121624	−	0.0535499i
$703$	3.49468	+	6.05296i	0.131804	+	0.228292i
$704$	−4.94062	−	2.85247i	−0.186207	−	0.107506i
$705$	0.184685			0.00695562
$706$	−1.89447	+	3.28131i	−0.0712992	+	0.123494i
$707$	−29.7393	−	3.30720i	−1.11846	−	0.124380i
$708$	−4.53936	−	2.62080i	−0.170600	−	0.0984958i
$709$	1.88215	−	1.08666i	0.0706856	−	0.0408103i	−0.464241	−	0.885709i	$-0.653673\pi$
$709$	1.88215	−	1.08666i	0.0706856	−	0.0408103i	0.534926	+	0.844899i	$0.320339\pi$
$710$	−3.29928	+	1.90484i	−0.123820	+	0.0714875i
$711$	1.56547			0.0587097
$712$	8.07340			0.302563
$713$	−0.181947	+	0.105047i	−0.00681398	+	0.00393405i
$714$	−0.620520	+	5.57989i	−0.0232224	+	0.208822i
$715$	−0.492821	+	0.672451i	−0.0184304	+	0.0251482i
$716$	−7.11980	+	12.3319i	−0.266079	+	0.460863i
$717$	−10.1339	−	5.85079i	−0.378456	−	0.218502i
$718$	18.1752	−	31.4803i	0.678291	−	1.17483i
$719$	18.7379	+	32.4550i	0.698805	+	1.21037i	0.968881	+	0.247527i	$0.0796178\pi$
$719$	18.7379	+	32.4550i	0.698805	+	1.21037i	−0.270076	+	0.962839i	$0.587049\pi$
$720$			0.219317i			0.00817346i
$721$	41.7351	+	4.64121i	1.55430	+	0.172848i
$722$	12.6913	+	7.32730i	0.472320	+	0.272694i
$723$	18.5811	+	10.7278i	0.691039	+	0.398972i
$724$	−11.5092			−0.427738
$725$	−14.6362	+	25.3507i	−0.543576	+	0.941502i
$726$		−	10.0255i		−	0.372083i
$727$	−17.7356			−0.657775			−0.328888	−	0.944369i	$-0.606674\pi$
$727$	−17.7356			−0.657775			−0.328888	+	0.944369i	$0.606674\pi$
$728$	20.8955	+	19.2025i	0.774440	+	0.711691i
$729$	1.00000			0.0370370
$730$			1.08377i			0.0401121i
$731$	−3.88722	+	6.73285i	−0.143774	+	0.249024i
$732$	11.4684			0.423886
$733$	26.7507	+	15.4445i	0.988058	+	0.570456i	0.904693	−	0.426063i	$-0.140100\pi$
$733$	26.7507	+	15.4445i	0.988058	+	0.570456i	0.0833651	+	0.996519i	$0.473433\pi$
$734$	14.5010	+	8.37215i	0.535241	+	0.309022i
$735$	0.415153	−	1.84350i	0.0153131	−	0.0679986i
$736$		−	9.91741i		−	0.365561i
$737$	2.39079	+	4.14097i	0.0880660	+	0.152535i
$738$	3.96367	−	6.86527i	0.145905	−	0.252714i
$739$	37.1382	+	21.4417i	1.36615	+	0.788748i	0.990434	−	0.137987i	$-0.0440632\pi$
$739$	37.1382	+	21.4417i	1.36615	+	0.788748i	0.375717	+	0.926735i	$0.377397\pi$
$740$	−0.493969	+	0.855579i	−0.0181587	+	0.0314517i
$741$	−6.59433	+	2.90341i	−0.242249	+	0.106659i
$742$	−17.5519	−	12.9146i	−0.644349	−	0.474111i
$743$	−7.88851	+	4.55444i	−0.289401	+	0.167086i	−0.637672	−	0.770308i	$-0.720102\pi$
$743$	−7.88851	+	4.55444i	−0.289401	+	0.167086i	0.348270	+	0.937394i	$0.386769\pi$
$744$	−0.324968			−0.0119139
$745$	−3.46557			−0.126969
$746$	−9.59552	+	5.53998i	−0.351317	+	0.202833i
$747$	6.91309	−	3.99127i	0.252937	−	0.146033i
$748$	1.68661	+	0.973766i	0.0616686	+	0.0356044i
$749$	11.7786	+	26.8905i	0.430381	+	0.982558i
$750$	1.30850	−	2.26639i	0.0477797	−	0.0827569i
$751$	−24.3205			−0.887469			−0.443734	−	0.896158i	$-0.646347\pi$
$751$	−24.3205			−0.887469			−0.443734	+	0.896158i	$0.646347\pi$
$752$	0.481347	+	0.277906i	0.0175529	+	0.0101342i
$753$	−6.14063	−	10.6359i	−0.223777	−	0.387593i
$754$	−16.8725	−	12.3654i	−0.614460	−	0.450321i
$755$	2.28288			0.0830825
$756$	1.11073	+	2.53580i	0.0403970	+	0.0922263i
$757$	−8.95806	−	15.5158i	−0.325586	−	0.563932i	0.656045	−	0.754722i	$-0.272228\pi$
$757$	−8.95806	−	15.5158i	−0.325586	−	0.563932i	−0.981631	+	0.190790i	$0.938895\pi$
$758$	−10.3364	−	17.9032i	−0.375436	−	0.650274i
$759$	−1.42670	+	0.823703i	−0.0517858	+	0.0298985i
$760$		−	1.60485i		−	0.0582142i
$761$	43.6045	−	25.1751i	1.58066	−	0.912596i	0.585901	−	0.810383i	$-0.300741\pi$
$761$	43.6045	−	25.1751i	1.58066	−	0.912596i	0.994763	−	0.102213i	$-0.0325924\pi$
$762$			1.56232i			0.0565968i
$763$	15.1470	+	11.1451i	0.548357	+	0.403481i
$764$	6.61514	+	11.4578i	0.239327	+	0.414527i
$765$		−	0.586597i		−	0.0212085i
$766$	10.4360	+	18.0756i	0.377067	+	0.653099i
$767$	−16.5303	+	7.27811i	−0.596875	+	0.262797i
$768$	8.52007	−	14.7572i	0.307442	−	0.532504i
$769$	8.74545	−	5.04919i	0.315369	−	0.182078i	−0.333958	−	0.942588i	$-0.608384\pi$
$769$	8.74545	−	5.04919i	0.315369	−	0.182078i	0.649326	+	0.760510i	$0.275051\pi$
$770$	0.481199	+	0.354066i	0.0173412	+	0.0127596i
$771$	0.495142	−	0.857611i	0.0178321	−	0.0308861i
$772$	15.4666	+	8.92966i	0.556656	+	0.321385i
$773$			20.0887i			0.722540i	0.932461	+	0.361270i	$0.117657\pi$
$773$			20.0887i			0.722540i	−0.932461	+	0.361270i	$0.882343\pi$
$774$		−	3.49389i		−	0.125585i
$775$	0.466113	+	0.269111i	0.0167433	+	0.00966674i
$776$	−15.3497	+	26.5864i	−0.551022	+	0.954398i
$777$	1.02276	−	9.19693i	0.0366912	−	0.329938i
$778$	2.17907	−	1.25809i	0.0781235	−	0.0451046i
$779$	−8.11108	+	14.0488i	−0.290609	+	0.503350i
$780$	−0.821462	−	0.602026i	−0.0294131	−	0.0215560i
$781$	−6.18915	−	10.7199i	−0.221465	−	0.383589i
$782$		−	4.08125i		−	0.145945i
$783$	−2.97054	−	5.14513i	−0.106159	−	0.183872i
$784$	3.85604	−	4.18005i	0.137716	−	0.149287i
$785$			4.51228i			0.161050i
$786$	10.6437	−	6.14514i	0.379648	−	0.219190i
$787$			27.4272i			0.977673i	0.872375	+	0.488837i	$0.162579\pi$
$787$			27.4272i			0.977673i	−0.872375	+	0.488837i	$0.837421\pi$
$788$	7.37901	−	4.26027i	0.262866	−	0.151766i
$789$	−0.187525	−	0.324803i	−0.00667608	−	0.0115633i
$790$	0.206346	+	0.357401i	0.00734145	+	0.0127158i
$791$	39.6209	+	4.40610i	1.40876	+	0.156663i
$792$	−2.54816			−0.0905449
$793$	23.3600	−	31.8746i	0.829539	−	1.13190i
$794$	5.71624	+	9.90082i	0.202862	+	0.351367i
$795$	1.97177	+	1.13840i	0.0699316	+	0.0403750i
$796$	10.3062			0.365295
$797$	5.27175	−	9.13093i	0.186735	−	0.323434i	−0.757425	−	0.652922i	$-0.773543\pi$
$797$	5.27175	−	9.13093i	0.186735	−	0.323434i	0.944160	+	0.329488i	$0.106876\pi$
$798$	2.07156	+	4.72937i	0.0733325	+	0.167418i
$799$	−1.28744	−	0.743302i	−0.0455463	−	0.0262961i
$800$	−22.0026	+	12.7032i	−0.777911	+	0.449127i
$801$	2.35025	−	1.35692i	0.0830419	−	0.0479442i
$802$	−36.6726			−1.29495
$803$	−3.52134			−0.124265
$804$	−5.05859	+	2.92058i	−0.178403	+	0.103001i
$805$	−0.151826	+	1.36526i	−0.00535116	+	0.0481191i
$806$	−0.227357	+	0.310228i	−0.00800832	+	0.0109273i
$807$	−8.52948	+	14.7735i	−0.300252	+	0.520051i
$808$	29.1377	+	16.8226i	1.02506	+	0.591818i
$809$	22.5557	−	39.0675i	0.793015	−	1.37354i	−0.131078	−	0.991372i	$-0.541844\pi$
$809$	22.5557	−	39.0675i	0.793015	−	1.37354i	0.924092	−	0.382170i	$-0.124823\pi$
$810$	0.131811	+	0.228303i	0.00463136	+	0.00802175i
$811$		−	47.4243i		−	1.66529i	−0.553806	−	0.832646i	$-0.686825\pi$
$811$		−	47.4243i		−	1.66529i	0.553806	−	0.832646i	$-0.313175\pi$
$812$	9.74756	−	13.2476i	0.342072	−	0.464899i
$813$	−11.5721	−	6.68114i	−0.405850	−	0.234318i
$814$	2.53361	+	1.46278i	0.0888028	+	0.0512703i
$815$	5.82915			0.204186
$816$	0.882687	−	1.52886i	0.0309002	−	0.0535208i
$817$			7.14975i			0.250138i
$818$	8.69085			0.303868
$819$	9.31030	+	2.07807i	0.325328	+	0.0726135i
$820$	−2.29298			−0.0800745
$821$		−	2.29657i		−	0.0801508i	−0.999197	−	0.0400754i	$-0.987240\pi$
$821$		−	2.29657i		−	0.0801508i	0.999197	−	0.0400754i	$-0.0127598\pi$
$822$	−8.67041	+	15.0176i	−0.302415	+	0.523799i
$823$	−13.9893			−0.487636			−0.243818	−	0.969821i	$-0.578400\pi$
$823$	−13.9893			−0.487636			−0.243818	+	0.969821i	$0.578400\pi$
$824$	−40.8908	−	23.6083i	−1.42450	−	0.822435i
$825$	3.65491	+	2.11016i	0.127248	+	0.0734665i
$826$	5.19288	+	11.8553i	0.180684	+	0.412500i
$827$			24.9362i			0.867115i	0.901126	+	0.433558i	$0.142742\pi$
$827$			24.9362i			0.867115i	−0.901126	+	0.433558i	$0.857258\pi$
$828$	−1.00623	−	1.74284i	−0.0349689	−	0.0605680i
$829$	20.3143	−	35.1854i	0.705546	−	1.22204i	−0.260949	−	0.965353i	$-0.584035\pi$
$829$	20.3143	−	35.1854i	0.705546	−	1.22204i	0.966494	−	0.256688i	$-0.0826314\pi$
$830$	1.82244	+	1.05219i	0.0632578	+	0.0365219i
$831$	2.35195	−	4.07370i	0.0815883	−	0.141315i
$832$	−9.67680	−	21.9783i	−0.335483	−	0.761961i
$833$	−10.3136	+	11.1802i	−0.357345	+	0.387370i
$834$	19.4293	−	11.2175i	0.672782	−	0.388431i
$835$	−3.24021			−0.112132
$836$	1.79104			0.0619446
$837$	−0.0946014	+	0.0546182i	−0.00326990	+	0.00188788i
$838$	27.1364	−	15.6672i	0.937412	−	0.541215i
$839$	−13.2505	−	7.65020i	−0.457459	−	0.264114i	0.253516	−	0.967331i	$-0.418413\pi$
$839$	−13.2505	−	7.65020i	−0.457459	−	0.264114i	−0.710975	+	0.703217i	$0.751746\pi$
$840$	−1.25925	+	1.71140i	−0.0434482	+	0.0590491i
$841$	−3.14826	+	5.45295i	−0.108561	+	0.188033i
$842$	9.85393			0.339589
$843$	27.1023	+	15.6475i	0.933453	+	0.538929i
$844$	3.03166	+	5.25099i	0.104354	+	0.180747i
$845$	−3.34647	+	1.05685i	−0.115122	+	0.0363568i
$846$	0.668092			0.0229695
$847$	16.0978	−	21.8779i	0.553125	−	0.751735i
$848$	3.42605	+	5.93409i	0.117651	+	0.203777i
$849$	7.76972	+	13.4575i	0.266656	+	0.461862i
$850$	−9.05461	+	5.22768i	−0.310571	+	0.179308i
$851$			6.72683i			0.230593i
$852$	13.0954	−	7.56063i	0.448641	−	0.259023i
$853$		−	10.9869i		−	0.376183i	−0.982151	−	0.188092i	$-0.939770\pi$
$853$		−	10.9869i		−	0.376183i	0.982151	−	0.188092i	$-0.0602302\pi$
$854$	−22.8092	−	16.7830i	−0.780513	−	0.574301i
$855$	−0.269732	−	0.467189i	−0.00922463	−	0.0159775i
$856$		−	33.0094i		−	1.12824i
$857$	−7.19211	−	12.4571i	−0.245678	−	0.425526i	0.716644	−	0.697439i	$-0.245677\pi$
$857$	−7.19211	−	12.4571i	−0.245678	−	0.425526i	−0.962322	+	0.271913i	$0.912344\pi$
$858$	−1.78277	+	2.43257i	−0.0608626	+	0.0830467i
$859$	12.9855	−	22.4915i	0.443058	−	0.767399i	−0.554857	−	0.831946i	$-0.687227\pi$
$859$	12.9855	−	22.4915i	0.443058	−	0.767399i	0.997915	+	0.0645470i	$0.0205602\pi$
$860$	−0.875213	+	0.505305i	−0.0298445	+	0.0172307i
$861$	19.6730	−	8.61717i	0.670453	−	0.293672i
$862$	0.545536	−	0.944895i	0.0185810	−	0.0321833i
$863$	−35.9901	−	20.7789i	−1.22512	−	0.707322i	−0.259113	−	0.965847i	$-0.583430\pi$
$863$	−35.9901	−	20.7789i	−1.22512	−	0.707322i	−0.966004	+	0.258525i	$0.916763\pi$
$864$		−	5.15645i		−	0.175426i
$865$		−	1.91210i		−	0.0650133i
$866$	25.3124	+	14.6141i	0.860149	+	0.496607i
$867$	6.13912	−	10.6333i	0.208495	−	0.361124i
$868$	−0.243578	−	0.179224i	−0.00826757	−	0.00608327i
$869$	−1.16126	+	0.670451i	−0.0393929	+	0.0227435i
$870$	0.783099	−	1.35637i	0.0265495	−	0.0459852i
$871$	−2.18656	+	20.0084i	−0.0740887	+	0.677960i
$872$	−10.5725	−	18.3121i	−0.358030	−	0.620127i
$873$			10.3194i			0.349260i
$874$	−1.87666	−	3.25047i	−0.0634789	−	0.109949i
$875$	6.49452	−	2.84473i	0.219555	−	0.0961696i
$876$		−	4.30165i		−	0.145339i
$877$	−25.9308	+	14.9712i	−0.875621	+	0.505540i	−0.869212	−	0.494440i	$-0.835373\pi$
$877$	−25.9308	+	14.9712i	−0.875621	+	0.505540i	−0.00640883	+	0.999979i	$0.502040\pi$
$878$			18.6677i			0.630006i
$879$	5.22137	−	3.01456i	0.176113	−	0.101679i
$880$	−0.0939279	−	0.162688i	−0.00316631	−	0.00548421i
$881$	10.5608	+	18.2919i	0.355803	+	0.616269i	0.987255	−	0.159146i	$-0.0508741\pi$
$881$	10.5608	+	18.2919i	0.355803	+	0.616269i	−0.631452	+	0.775415i	$0.717541\pi$
$882$	1.50180	−	6.66882i	0.0505684	−	0.224551i
$883$	20.7966			0.699862			0.349931	−	0.936775i	$-0.386205\pi$
$883$	20.7966			0.699862			0.349931	+	0.936775i	$0.386205\pi$
$884$	3.30343	+	7.50288i	0.111106	+	0.252349i
$885$	−0.676149	−	1.17112i	−0.0227285	−	0.0393669i
$886$	−11.3447	−	6.54989i	−0.381134	−	0.220048i
$887$	30.1149			1.01116			0.505580	−	0.862780i	$-0.331279\pi$
$887$	30.1149			1.01116			0.505580	+	0.862780i	$0.331279\pi$
$888$	−5.20243	+	9.01088i	−0.174582	+	0.302385i
$889$	−2.50857	+	3.40932i	−0.0841348	+	0.114345i
$890$	0.619575	+	0.357712i	0.0207682	+	0.0119905i
$891$	−0.741794	+	0.428275i	−0.0248510	+	0.0143477i
$892$	−20.0791	+	11.5927i	−0.672298	+	0.388152i
$893$	−1.36715			−0.0457501
$894$	−12.5366			−0.419287
$895$	−3.18153	+	1.83686i	−0.106347	+	0.0613995i
$896$	9.23031	−	4.04307i	0.308363	−	0.135069i
$897$	−6.89353	−	0.753338i	−0.230168	−	0.0251532i
$898$	−7.88389	+	13.6553i	−0.263089	+	0.455683i
$899$	0.562036	+	0.324491i	0.0187449	+	0.0108224i
$900$	−2.57776	+	4.46482i	−0.0859255	+	0.148827i
$901$	−9.16349	−	15.8716i	−0.305280	−	0.528761i
$902$			6.79016i			0.226088i
$903$	5.61005	−	7.62443i	0.186691	−	0.253725i
$904$	−38.8194	−	22.4124i	−1.29111	−	0.745425i
$905$	−2.57149	−	1.48465i	−0.0854794	−	0.0493515i
$906$	8.25826			0.274362
$907$	−11.6388	+	20.1590i	−0.386460	+	0.669369i	−0.991971	−	0.126469i	$-0.959636\pi$
$907$	−11.6388	+	20.1590i	−0.386460	+	0.669369i	0.605510	+	0.795837i	$0.292969\pi$
$908$			28.4342i			0.943620i
$909$	11.3097			0.375118
$910$	0.752769	+	2.39948i	0.0249540	+	0.0795420i
$911$	−44.5525			−1.47609			−0.738044	−	0.674752i	$-0.764251\pi$
$911$	−44.5525			−1.47609			−0.738044	+	0.674752i	$0.764251\pi$
$912$		−	1.62352i		−	0.0537603i
$913$	−3.41873	+	5.92141i	−0.113143	+	0.195970i
$914$	−7.47918			−0.247389
$915$	2.56238	+	1.47939i	0.0847096	+	0.0489071i
$916$	1.19399	+	0.689351i	0.0394506	+	0.0227768i
$917$	33.0939	+	3.68026i	1.09286	+	0.121533i
$918$		−	2.12200i		−	0.0700365i
$919$	24.9437	+	43.2037i	0.822815	+	1.42516i	0.903578	+	0.428424i	$0.140931\pi$
$919$	24.9437	+	43.2037i	0.822815	+	1.42516i	−0.0807626	+	0.996733i	$0.525736\pi$
$920$	0.772288	−	1.33764i	0.0254616	−	0.0441008i
$921$	11.9171	+	6.88034i	0.392681	+	0.226715i
$922$	14.8488	−	25.7189i	0.489019	−	0.847006i
$923$	5.66044	−	51.7967i	0.186316	−	1.70491i
$924$	−1.90996	−	1.40534i	−0.0628330	−	0.0462324i
$925$	14.9241	−	8.61641i	0.490700	−	0.283306i
$926$	0.0500952			0.00164623
$927$	−15.8716			−0.521292
$928$	−26.5306	+	15.3175i	−0.870910	+	0.502820i
$929$	33.8457	−	19.5408i	1.11044	−	0.641113i	0.171497	−	0.985185i	$-0.445140\pi$
$929$	33.8457	−	19.5408i	1.11044	−	0.641113i	0.938943	+	0.344071i	$0.111806\pi$
$930$	−0.0249390	−	0.0143985i	−0.000817781	−	0.000472146i
$931$	−3.07323	+	13.6468i	−0.100721	+	0.447255i
$932$	−9.92784	+	17.1955i	−0.325197	+	0.563258i
$933$	28.1655			0.922097
$934$	−19.0567	−	11.0024i	−0.623553	−	0.360008i
$935$	0.251225	+	0.435134i	0.00821593	+	0.0142304i
$936$	−8.65156	−	6.34048i	−0.282785	−	0.207245i
$937$	−38.4496			−1.25610			−0.628048	−	0.778175i	$-0.716146\pi$
$937$	−38.4496			−1.25610			−0.628048	+	0.778175i	$0.716146\pi$
$938$	14.3348	+	1.59413i	0.468049	+	0.0520500i
$939$	−6.10426	−	10.5729i	−0.199205	−	0.345033i
$940$	−0.0966229	−	0.167356i	−0.00315149	−	0.00545854i
$941$	51.4932	−	29.7296i	1.67863	−	0.969158i	0.716095	−	0.698003i	$-0.245928\pi$
$941$	51.4932	−	29.7296i	1.67863	−	0.969158i	0.962536	−	0.271155i	$-0.0874056\pi$
$942$			16.3231i			0.531834i
$943$	−13.5211	+	7.80642i	−0.440308	+	0.254212i
$944$		−	4.06977i		−	0.132460i
$945$	−0.0789401	+	0.709852i	−0.00256792	+	0.0230915i
$946$	1.49635	+	2.59175i	0.0486504	+	0.0842650i
$947$		−	34.9364i		−	1.13528i	−0.823277	−	0.567639i	$-0.807857\pi$
$947$		−	34.9364i		−	1.13528i	0.823277	−	0.567639i	$-0.192143\pi$
$948$	−0.819019	−	1.41858i	−0.0266005	−	0.0460734i
$949$	−11.9557	−	8.76202i	−0.388099	−	0.284427i
$950$	−4.80763	+	8.32706i	−0.155980	+	0.270166i
$951$	−11.1776	+	6.45338i	−0.362458	+	0.209265i
$952$	15.6661	−	6.86210i	0.507743	−	0.222402i
$953$	−11.3153	+	19.5987i	−0.366540	+	0.634865i	−0.989022	−	0.147769i	$-0.952791\pi$
$953$	−11.3153	+	19.5987i	−0.366540	+	0.634865i	0.622482	+	0.782634i	$0.286124\pi$
$954$	7.13284	+	4.11815i	0.230934	+	0.133330i
$955$			3.41332i			0.110452i
$956$			12.2440i			0.396000i
$957$	4.40706	+	2.54442i	0.142460	+	0.0822494i
$958$	−14.5345	+	25.1746i	−0.469590	+	0.813353i
$959$	−43.0341	+	18.8498i	−1.38964	+	0.608692i
$960$	1.55710	−	0.898992i	0.0502552	−	0.0290148i
$961$	−15.4940	+	26.8365i	−0.499808	+	0.865692i
$962$	4.96237	+	11.2707i	0.159993	+	0.363383i
$963$	−5.54796	−	9.60935i	−0.178780	−	0.309657i
$964$		−	22.4502i		−	0.723073i
$965$	2.30379	+	3.99028i	0.0741616	+	0.128452i
$966$	−0.549226	+	4.93880i	−0.0176711	+	0.158903i
$967$			0.0768624i			0.00247173i	0.999999	+	0.00123586i	$0.000393388\pi$
$967$			0.0768624i			0.00247173i	−0.999999	+	0.00123586i	$0.999607\pi$
$968$	−26.4496	+	15.2707i	−0.850123	+	0.490819i
$969$			4.34237i			0.139497i
$970$	−2.35596	+	1.36021i	−0.0756452	+	0.0436738i
$971$	1.39708	+	2.41982i	0.0448345	+	0.0776557i	0.887572	−	0.460669i	$-0.152391\pi$
$971$	1.39708	+	2.41982i	0.0448345	+	0.0776557i	−0.842737	+	0.538325i	$0.819057\pi$
$972$	−0.523178	−	0.906171i	−0.0167809	−	0.0290654i
$973$	60.4107	+	6.71806i	1.93668	+	0.215371i
$974$	7.68622			0.246283
$975$	7.15859	+	16.2588i	0.229258	+	0.520700i
$976$	4.45225	+	7.71152i	0.142513	+	0.246840i
$977$	−2.83594	−	1.63733i	−0.0907298	−	0.0523829i	0.453949	−	0.891028i	$-0.350015\pi$
$977$	−2.83594	−	1.63733i	−0.0907298	−	0.0523829i	−0.544678	+	0.838645i	$0.683348\pi$
$978$	21.0868			0.674282
$979$	−1.16227	+	2.01310i	−0.0371462	+	0.0643390i
$980$	−1.88773	+	0.588280i	−0.0603012	+	0.0187919i
$981$	−6.15552	−	3.55389i	−0.196531	−	0.113467i
$982$	19.2061	−	11.0886i	0.612891	−	0.353853i
$983$	4.04611	−	2.33602i	0.129051	−	0.0745076i	−0.434085	−	0.900872i	$-0.642928\pi$
$983$	4.04611	−	2.33602i	0.129051	−	0.0745076i	0.563136	+	0.826364i	$0.309595\pi$
$984$	−24.1495			−0.769858
$985$	2.19824			0.0700419
$986$	−10.9180	+	6.30350i	−0.347699	+	0.200744i
$987$	1.45792	+	1.07274i	0.0464062	+	0.0341456i
$988$	6.08099	+	4.45659i	0.193462	+	0.141783i
$989$	−3.44060	+	5.95929i	−0.109405	+	0.189495i
$990$	−0.195553	−	0.112902i	−0.00621508	−	0.00358828i
$991$	3.31788	−	5.74673i	0.105396	−	0.182551i	−0.808504	−	0.588491i	$-0.799722\pi$
$991$	3.31788	−	5.74673i	0.105396	−	0.182551i	0.913900	+	0.405940i	$0.133056\pi$
$992$	0.281636	+	0.487807i	0.00894194	+	0.0154879i
$993$		−	15.4993i		−	0.491854i
$994$	−37.1092	−	4.12678i	−1.17703	−	0.130894i
$995$	2.30271	+	1.32947i	0.0730008	+	0.0421470i
$996$	−7.23355	−	4.17629i	−0.229204	−	0.132331i
$997$	−13.4800			−0.426915			−0.213457	−	0.976952i	$-0.568472\pi$
$997$	−13.4800			−0.426915			−0.213457	+	0.976952i	$0.568472\pi$
$998$	11.7062	−	20.2758i	0.370554	−	0.641818i
$999$			3.49754i			0.110657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.205.2	yes	12
3.2	odd	2		819.2.bm.e.478.5		12
7.4	even	3		273.2.bl.c.88.5	yes	12
13.4	even	6		273.2.bl.c.121.5	yes	12
21.11	odd	6		819.2.do.f.361.2		12
39.17	odd	6		819.2.do.f.667.2		12
91.4	even	6	inner	273.2.t.c.4.5	✓	12
273.95	odd	6		819.2.bm.e.550.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.5	✓	12	91.4	even	6	inner
273.2.t.c.205.2	yes	12	1.1	even	1	trivial
273.2.bl.c.88.5	yes	12	7.4	even	3
273.2.bl.c.121.5	yes	12	13.4	even	6
819.2.bm.e.478.5		12	3.2	odd	2
819.2.bm.e.550.2		12	273.95	odd	6
819.2.do.f.361.2		12	21.11	odd	6
819.2.do.f.667.2		12	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.976547i q^{2} +(-0.500000 + 0.866025i) q^{3} +1.04636 q^{4} +(0.233786 + 0.134976i) q^{5} +(0.845714 + 0.488273i) q^{6} +(1.06153 + 2.42346i) q^{7} -2.97491i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.976547i q^{2} +(-0.500000 + 0.866025i) q^{3} +1.04636 q^{4} +(0.233786 + 0.134976i) q^{5} +(0.845714 + 0.488273i) q^{6} +(1.06153 + 2.42346i) q^{7} -2.97491i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.131811 - 0.228303i) q^{10} +(0.741794 + 0.428275i) q^{11} +(-0.523178 + 0.906171i) q^{12} +(1.45289 + 3.29986i) q^{13} +(2.36662 - 1.03663i) q^{14} +(-0.233786 + 0.134976i) q^{15} -0.812427 q^{16} +2.17296 q^{17} +(-0.845714 + 0.488273i) q^{18} +(1.73063 - 0.999181i) q^{19} +(0.244623 + 0.141233i) q^{20} +(-2.62954 - 0.292422i) q^{21} +(0.418231 - 0.724397i) q^{22} +1.92330 q^{23} +(2.57635 + 1.48745i) q^{24} +(-2.46356 - 4.26702i) q^{25} +(3.22247 - 1.41882i) q^{26} +1.00000 q^{27} +(1.11073 + 2.53580i) q^{28} +(-2.97054 - 5.14513i) q^{29} +(0.131811 + 0.228303i) q^{30} +(-0.0946014 + 0.0546182i) q^{31} -5.15645i q^{32} +(-0.741794 + 0.428275i) q^{33} -2.12200i q^{34} +(-0.0789401 + 0.709852i) q^{35} +(-0.523178 - 0.906171i) q^{36} +3.49754i q^{37} +(-0.975748 - 1.69004i) q^{38} +(-3.58421 - 0.391690i) q^{39} +(0.401542 - 0.695492i) q^{40} +(-7.03015 + 4.05886i) q^{41} +(-0.285564 + 2.56787i) q^{42} +(-1.78890 + 3.09847i) q^{43} +(0.776181 + 0.448128i) q^{44} -0.269953i q^{45} -1.87820i q^{46} +(-0.592480 - 0.342068i) q^{47} +(0.406214 - 0.703583i) q^{48} +(-4.74633 + 5.14513i) q^{49} +(-4.16694 + 2.40578i) q^{50} +(-1.08648 + 1.88184i) q^{51} +(1.52024 + 3.45283i) q^{52} +(-4.21705 - 7.30414i) q^{53} -0.976547i q^{54} +(0.115614 + 0.200249i) q^{55} +(7.20958 - 3.15794i) q^{56} +1.99836i q^{57} +(-5.02446 + 2.90088i) q^{58} +5.00939i q^{59} +(-0.244623 + 0.141233i) q^{60} +(-5.48018 - 9.49195i) q^{61} +(0.0533372 + 0.0923828i) q^{62} +(1.56802 - 2.13104i) q^{63} -6.66037 q^{64} +(-0.105738 + 0.967568i) q^{65} +(0.418231 + 0.724397i) q^{66} +(4.83448 + 2.79119i) q^{67} +2.27369 q^{68} +(-0.961652 + 1.66563i) q^{69} +(0.693204 + 0.0770887i) q^{70} +(-12.5152 - 7.22567i) q^{71} +(-2.57635 + 1.48745i) q^{72} +(-3.56030 + 2.05554i) q^{73} +3.41551 q^{74} +4.92713 q^{75} +(1.81086 - 1.04550i) q^{76} +(-0.250474 + 2.25233i) q^{77} +(-0.382503 + 3.50015i) q^{78} +(-0.782735 + 1.35574i) q^{79} +(-0.189934 - 0.109658i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.96367 + 6.86527i) q^{82} +7.98255i q^{83} +(-2.75144 - 0.305978i) q^{84} +(0.508008 + 0.293299i) q^{85} +(3.02580 + 1.74695i) q^{86} +5.94109 q^{87} +(1.27408 - 2.20677i) q^{88} +2.71383i q^{89} -0.263621 q^{90} +(-6.45481 + 7.02392i) q^{91} +2.01246 q^{92} -0.109236i q^{93} +(-0.334046 + 0.578585i) q^{94} +0.539463 q^{95} +(4.46561 + 2.57822i) q^{96} +(-8.93689 - 5.15972i) q^{97} +(5.02446 + 4.63501i) q^{98} -0.856550i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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