LMFDB - Embedded newform 819.2.fy.a.50.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.2
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.721163 - 2.69142i) q^{2} +(-1.27046 + 1.17726i) q^{3} +(-4.99160 + 2.88190i) q^{4} +(-0.822532 - 3.06973i) q^{5} +(4.08470 + 2.57033i) q^{6} +(0.707107 - 0.707107i) q^{7} +(7.41566 + 7.41566i) q^{8} +(0.228118 - 2.99131i) q^{9} +O(q^{10})$	\(q+(-0.721163 - 2.69142i) q^{2} +(-1.27046 + 1.17726i) q^{3} +(-4.99160 + 2.88190i) q^{4} +(-0.822532 - 3.06973i) q^{5} +(4.08470 + 2.57033i) q^{6} +(0.707107 - 0.707107i) q^{7} +(7.41566 + 7.41566i) q^{8} +(0.228118 - 2.99131i) q^{9} +(-7.66875 + 4.42756i) q^{10} +(5.16975 - 1.38523i) q^{11} +(2.94886 - 9.53775i) q^{12} +(-1.12170 - 3.42663i) q^{13} +(-2.41306 - 1.39318i) q^{14} +(4.65886 + 2.93163i) q^{15} +(8.84693 - 15.3233i) q^{16} +(1.70463 - 2.95250i) q^{17} +(-8.21539 + 1.54327i) q^{18} +(-0.235278 + 0.0630426i) q^{19} +(12.9524 + 12.9524i) q^{20} +(-0.0658997 + 1.73080i) q^{21} +(-7.45646 - 12.9150i) q^{22} +3.74751 q^{23} +(-18.1514 - 0.691111i) q^{24} +(-4.41657 + 2.54991i) q^{25} +(-8.41356 + 5.49012i) q^{26} +(3.23174 + 4.06889i) q^{27} +(-1.49178 + 5.56741i) q^{28} +(-5.88646 - 3.39855i) q^{29} +(4.53043 - 14.6531i) q^{30} +(0.734581 - 0.196830i) q^{31} +(-27.3616 - 7.33152i) q^{32} +(-4.93716 + 7.84601i) q^{33} +(-9.17573 - 2.45863i) q^{34} +(-2.75225 - 1.58901i) q^{35} +(7.48200 + 15.5889i) q^{36} +(3.79267 + 1.01624i) q^{37} +(0.339348 + 0.587768i) q^{38} +(5.45910 + 3.03285i) q^{39} +(16.6645 - 28.8637i) q^{40} +(2.18045 - 2.18045i) q^{41} +(4.70582 - 1.07082i) q^{42} -3.05810i q^{43} +(-21.8132 + 21.8132i) q^{44} +(-9.37017 + 1.76019i) q^{45} +(-2.70257 - 10.0861i) q^{46} +(-1.36262 + 5.08536i) q^{47} +(6.79990 + 29.8827i) q^{48} -1.00000i q^{49} +(10.0479 + 10.0479i) q^{50} +(1.31021 + 5.75782i) q^{51} +(15.4743 + 13.8717i) q^{52} +1.93867i q^{53} +(8.62047 - 11.6323i) q^{54} +(-8.50457 - 14.7303i) q^{55} +10.4873 q^{56} +(0.224693 - 0.357076i) q^{57} +(-4.90182 + 18.2938i) q^{58} +(-1.35198 + 5.04566i) q^{59} +(-31.7039 - 1.20712i) q^{60} -10.1569 q^{61} +(-1.05951 - 1.83512i) q^{62} +(-1.95387 - 2.27648i) q^{63} +43.5410i q^{64} +(-9.59620 + 6.26183i) q^{65} +(24.6774 + 7.62971i) q^{66} +(-6.84443 - 6.84443i) q^{67} +19.6503i q^{68} +(-4.76104 + 4.41179i) q^{69} +(-2.29187 + 8.55338i) q^{70} +(0.383730 + 1.43210i) q^{71} +(23.8742 - 20.4909i) q^{72} +(-0.0490419 + 0.0490419i) q^{73} -10.9405i q^{74} +(2.60916 - 8.43900i) q^{75} +(0.992732 - 0.992732i) q^{76} +(2.67606 - 4.63507i) q^{77} +(4.22576 - 16.8799i) q^{78} +(6.04884 + 10.4769i) q^{79} +(-54.3154 - 14.5538i) q^{80} +(-8.89592 - 1.36475i) q^{81} +(-7.44097 - 4.29604i) q^{82} +(2.80056 + 0.750407i) q^{83} +(-4.65904 - 8.82937i) q^{84} +(-10.4655 - 2.80422i) q^{85} +(-8.23063 + 2.20539i) q^{86} +(11.4795 - 2.61218i) q^{87} +(48.6094 + 28.0647i) q^{88} +(3.01993 - 11.2705i) q^{89} +(11.4948 + 23.9497i) q^{90} +(-3.21615 - 1.62983i) q^{91} +(-18.7061 + 10.8000i) q^{92} +(-0.701532 + 1.11486i) q^{93} +14.6695 q^{94} +(0.387048 + 0.670387i) q^{95} +(43.3928 - 22.8973i) q^{96} +(-6.85018 - 6.85018i) q^{97} +(-2.69142 + 0.721163i) q^{98} +(-2.96434 - 15.7803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.721163	−	2.69142i	−0.509939	−	1.90312i	−0.420941	−	0.907088i	$-0.638300\pi$
$2$	−0.721163	−	2.69142i	−0.509939	−	1.90312i	−0.0889984	−	0.996032i	$-0.528367\pi$
$3$	−1.27046	+	1.17726i	−0.733498	+	0.679691i
$3$	−1.27046	+	1.17726i	−0.733498	+	0.679691i
$4$	−4.99160	+	2.88190i	−2.49580	+	1.44095i
$5$	−0.822532	−	3.06973i	−0.367848	−	1.37283i	−0.863519	−	0.504316i	$-0.831745\pi$
$5$	−0.822532	−	3.06973i	−0.367848	−	1.37283i	0.495671	−	0.868510i	$-0.334922\pi$
$6$	4.08470	+	2.57033i	1.66757	+	1.04933i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	7.41566	+	7.41566i	2.62183	+	2.62183i
$9$	0.228118	−	2.99131i	0.0760393	−	0.997105i
$10$	−7.66875	+	4.42756i	−2.42507	+	1.40012i
$11$	5.16975	−	1.38523i	1.55874	−	0.417662i	0.626474	−	0.779443i	$-0.284498\pi$
$11$	5.16975	−	1.38523i	1.55874	−	0.417662i	0.932263	+	0.361780i	$0.117831\pi$
$12$	2.94886	−	9.53775i	0.851264	−	2.75331i
$13$	−1.12170	−	3.42663i	−0.311104	−	0.950376i
$13$	−1.12170	−	3.42663i	−0.311104	−	0.950376i
$14$	−2.41306	−	1.39318i	−0.644917	−	0.372343i
$15$	4.65886	+	2.93163i	1.20291	+	0.756943i
$16$	8.84693	−	15.3233i	2.21173	−	3.83083i
$17$	1.70463	−	2.95250i	0.413433	−	0.716087i	−0.581829	−	0.813311i	$-0.697663\pi$
$17$	1.70463	−	2.95250i	0.413433	−	0.716087i	0.995263	+	0.0972237i	$0.0309962\pi$
$18$	−8.21539	+	1.54327i	−1.93639	+	0.363751i
$19$	−0.235278	+	0.0630426i	−0.0539765	+	0.0144630i	−0.285706	−	0.958317i	$-0.592228\pi$
$19$	−0.235278	+	0.0630426i	−0.0539765	+	0.0144630i	0.231730	+	0.972780i	$0.425561\pi$
$20$	12.9524	+	12.9524i	2.89625	+	2.89625i
$21$	−0.0658997	+	1.73080i	−0.0143805	+	0.377691i
$22$	−7.45646	−	12.9150i	−1.58972	−	2.75348i
$23$	3.74751			0.781409			0.390705	−	0.920516i	$-0.372231\pi$
$23$	3.74751			0.781409			0.390705	+	0.920516i	$0.372231\pi$
$24$	−18.1514	−	0.691111i	−3.70514	−	0.141073i
$25$	−4.41657	+	2.54991i	−0.883315	+	0.509982i
$26$	−8.41356	+	5.49012i	−1.65004	+	1.07670i
$27$	3.23174	+	4.06889i	0.621949	+	0.783058i
$28$	−1.49178	+	5.56741i	−0.281920	+	1.05214i
$29$	−5.88646	−	3.39855i	−1.09309	−	0.631095i	−0.158691	−	0.987328i	$-0.550727\pi$
$29$	−5.88646	−	3.39855i	−1.09309	−	0.631095i	−0.934397	+	0.356234i	$0.884061\pi$
$30$	4.53043	−	14.6531i	0.827140	−	2.67528i
$31$	0.734581	−	0.196830i	0.131935	−	0.0353518i	−0.192247	−	0.981346i	$-0.561578\pi$
$31$	0.734581	−	0.196830i	0.131935	−	0.0353518i	0.324182	+	0.945995i	$0.394911\pi$
$32$	−27.3616	−	7.33152i	−4.83689	−	1.29604i
$33$	−4.93716	+	7.84601i	−0.859449	+	1.36581i
$34$	−9.17573	−	2.45863i	−1.57363	−	0.421652i
$35$	−2.75225	−	1.58901i	−0.465215	−	0.268592i
$36$	7.48200	+	15.5889i	1.24700	+	2.59814i
$37$	3.79267	+	1.01624i	0.623510	+	0.167069i	0.556723	−	0.830698i	$-0.312058\pi$
$37$	3.79267	+	1.01624i	0.623510	+	0.167069i	0.0667873	+	0.997767i	$0.478725\pi$
$38$	0.339348	+	0.587768i	0.0550495	+	0.0953485i
$39$	5.45910	+	3.03285i	0.874156	+	0.485645i
$40$	16.6645	−	28.8637i	2.63488	−	4.56375i
$41$	2.18045	−	2.18045i	0.340529	−	0.340529i	−0.516037	−	0.856566i	$-0.672593\pi$
$41$	2.18045	−	2.18045i	0.340529	−	0.340529i	0.856566	+	0.516037i	$0.172593\pi$
$42$	4.70582	−	1.07082i	0.726124	−	0.165232i
$43$		−	3.05810i		−	0.466356i	−0.972434	−	0.233178i	$-0.925088\pi$
$43$		−	3.05810i		−	0.466356i	0.972434	−	0.233178i	$-0.0749125\pi$
$44$	−21.8132	+	21.8132i	−3.28847	+	3.28847i
$45$	−9.37017	+	1.76019i	−1.39682	+	0.262394i
$46$	−2.70257	−	10.0861i	−0.398471	−	1.48712i
$47$	−1.36262	+	5.08536i	−0.198758	+	0.741775i	0.792504	+	0.609867i	$0.208777\pi$
$47$	−1.36262	+	5.08536i	−0.198758	+	0.741775i	−0.991262	+	0.131908i	$0.957890\pi$
$48$	6.79990	+	29.8827i	0.981482	+	4.31320i
$49$		−	1.00000i		−	0.142857i
$50$	10.0479	+	10.0479i	1.42099	+	1.42099i
$51$	1.31021	+	5.75782i	0.183466	+	0.806256i
$52$	15.4743	+	13.8717i	2.14590	+	1.92366i
$53$			1.93867i			0.266296i	0.991096	+	0.133148i	$0.0425086\pi$
$53$			1.93867i			0.266296i	−0.991096	+	0.133148i	$0.957491\pi$
$54$	8.62047	−	11.6323i	1.17310	−	1.58296i
$55$	−8.50457	−	14.7303i	−1.14676	−	1.98624i
$56$	10.4873			1.40143
$57$	0.224693	−	0.357076i	0.0297613	−	0.0472959i
$58$	−4.90182	+	18.2938i	−0.643640	+	2.40210i
$59$	−1.35198	+	5.04566i	−0.176013	+	0.656889i	0.820364	+	0.571842i	$0.193771\pi$
$59$	−1.35198	+	5.04566i	−0.176013	+	0.656889i	−0.996377	+	0.0850473i	$0.972896\pi$
$60$	−31.7039	−	1.20712i	−4.09295	−	0.155838i
$61$	−10.1569			−1.30046			−0.650231	−	0.759736i	$-0.725328\pi$
$61$	−10.1569			−1.30046			−0.650231	+	0.759736i	$0.725328\pi$
$62$	−1.05951	−	1.83512i	−0.134557	−	0.233060i
$63$	−1.95387	−	2.27648i	−0.246165	−	0.286810i
$64$			43.5410i			5.44262i
$65$	−9.59620	+	6.26183i	−1.19026	+	0.776685i
$66$	24.6774	+	7.62971i	3.03758	+	0.939153i
$67$	−6.84443	−	6.84443i	−0.836180	−	0.836180i	0.152174	−	0.988354i	$-0.451373\pi$
$67$	−6.84443	−	6.84443i	−0.836180	−	0.836180i	−0.988354	+	0.152174i	$0.951373\pi$
$68$			19.6503i			2.38295i
$69$	−4.76104	+	4.41179i	−0.573162	+	0.531117i
$70$	−2.29187	+	8.55338i	−0.273931	+	1.02232i
$71$	0.383730	+	1.43210i	0.0455403	+	0.169959i	0.984951	−	0.172836i	$-0.0552931\pi$
$71$	0.383730	+	1.43210i	0.0455403	+	0.169959i	−0.939410	+	0.342795i	$0.888626\pi$
$72$	23.8742	−	20.4909i	2.81360	−	2.41488i
$73$	−0.0490419	+	0.0490419i	−0.00573992	+	0.00573992i	−0.709971	−	0.704231i	$-0.751292\pi$
$73$	−0.0490419	+	0.0490419i	−0.00573992	+	0.00573992i	0.704231	+	0.709971i	$0.251292\pi$
$74$		−	10.9405i		−	1.27181i
$75$	2.60916	−	8.43900i	0.301279	−	0.974452i
$76$	0.992732	−	0.992732i	0.113874	−	0.113874i
$77$	2.67606	−	4.63507i	0.304965	−	0.528215i
$78$	4.22576	−	16.8799i	0.478473	−	1.91127i
$79$	6.04884	+	10.4769i	0.680548	+	1.17874i	0.974814	+	0.223020i	$0.0715916\pi$
$79$	6.04884	+	10.4769i	0.680548	+	1.17874i	−0.294266	+	0.955724i	$0.595075\pi$
$80$	−54.3154	−	14.5538i	−6.07265	−	1.62716i
$81$	−8.89592	−	1.36475i	−0.988436	−	0.151638i
$82$	−7.44097	−	4.29604i	−0.821717	−	0.474419i
$83$	2.80056	+	0.750407i	0.307401	+	0.0823679i	0.409222	−	0.912435i	$-0.365800\pi$
$83$	2.80056	+	0.750407i	0.307401	+	0.0823679i	−0.101821	+	0.994803i	$0.532467\pi$
$84$	−4.65904	−	8.82937i	−0.508343	−	0.963363i
$85$	−10.4655	−	2.80422i	−1.13514	−	0.304161i
$86$	−8.23063	+	2.20539i	−0.887531	+	0.237813i
$87$	11.4795	−	2.61218i	1.23073	−	0.280056i
$88$	48.6094	+	28.0647i	5.18178	+	2.99170i
$89$	3.01993	−	11.2705i	0.320112	−	1.19467i	−0.599023	−	0.800731i	$-0.704444\pi$
$89$	3.01993	−	11.2705i	0.320112	−	1.19467i	0.919135	−	0.393942i	$-0.128889\pi$
$90$	11.4948	+	23.9497i	1.21166	+	2.52452i
$91$	−3.21615	−	1.62983i	−0.337145	−	0.170853i
$92$	−18.7061	+	10.8000i	−1.95024	+	1.12597i
$93$	−0.701532	+	1.11486i	−0.0727455	+	0.115605i
$94$	14.6695			1.51304
$95$	0.387048	+	0.670387i	0.0397103	+	0.0687802i
$96$	43.3928	−	22.8973i	4.42876	−	2.33695i
$97$	−6.85018	−	6.85018i	−0.695530	−	0.695530i	0.267913	−	0.963443i	$-0.413666\pi$
$97$	−6.85018	−	6.85018i	−0.695530	−	0.695530i	−0.963443	+	0.267913i	$0.913666\pi$
$98$	−2.69142	+	0.721163i	−0.271874	+	0.0728485i
$99$	−2.96434	−	15.7803i	−0.297928	−	1.58598i
$100$	14.6972	−	25.4563i	1.46972	−	2.54563i
$101$	−5.12871	+	8.88318i	−0.510326	+	0.883910i	0.489603	+	0.871946i	$0.337142\pi$
$101$	−5.12871	+	8.88318i	−0.510326	+	0.883910i	−0.999928	+	0.0119643i	$0.996192\pi$
$102$	14.5518	−	7.67864i	1.44084	−	0.760299i
$103$	−14.0858	−	8.13245i	−1.38792	−	0.801314i	−0.394836	−	0.918752i	$-0.629199\pi$
$103$	−14.0858	−	8.13245i	−1.38792	−	0.801314i	−0.993080	+	0.117438i	$0.962532\pi$
$104$	17.0926	−	33.7288i	1.67606	−	3.30739i
$105$	5.36729	−	1.22134i	0.523794	−	0.119191i
$106$	5.21776	−	1.39810i	0.506794	−	0.135795i
$107$	13.7263	−	7.92490i	1.32697	−	0.766129i	0.342144	−	0.939648i	$-0.388847\pi$
$107$	13.7263	−	7.92490i	1.32697	−	0.766129i	0.984831	+	0.173518i	$0.0555136\pi$
$108$	−27.8577	−	10.9967i	−2.68061	−	1.05816i
$109$	1.91036	+	1.91036i	0.182980	+	0.182980i	0.792653	−	0.609673i	$-0.208699\pi$
$109$	1.91036	+	1.91036i	0.182980	+	0.182980i	−0.609673	+	0.792653i	$0.708699\pi$
$110$	−33.5123	+	33.5123i	−3.19528	+	3.19528i
$111$	−6.01480	+	3.17386i	−0.570899	+	0.301250i
$112$	−4.57951	−	17.0909i	−0.432723	−	1.61494i
$113$	4.47564	−	2.58401i	0.421033	−	0.243083i	−0.274486	−	0.961591i	$-0.588508\pi$
$113$	4.47564	−	2.58401i	0.421033	−	0.243083i	0.695519	+	0.718508i	$0.255174\pi$
$114$	−1.12308	−	0.347233i	−0.105186	−	0.0325213i
$115$	−3.08245	−	11.5038i	−0.287440	−	1.07274i
$116$	39.1772			3.63751
$117$	−10.5060	+	2.57368i	−0.971281	+	0.237937i
$118$	14.5550			1.33989
$119$	−0.882381	−	3.29309i	−0.0808877	−	0.301877i
$120$	12.8086	+	56.2885i	1.16926	+	5.13841i
$121$	15.2811	−	8.82257i	1.38919	−	0.802052i
$122$	7.32481	+	27.3366i	0.663157	+	2.47494i
$123$	−0.203210	+	5.33713i	−0.0183228	+	0.481232i
$124$	−3.09949	+	3.09949i	−0.278342	+	0.278342i
$125$	0.224313	+	0.224313i	0.0200632	+	0.0200632i
$126$	−4.71790	+	6.90041i	−0.420304	+	0.614737i
$127$	8.19859	−	4.73346i	0.727507	−	0.420026i	−0.0900025	−	0.995942i	$-0.528688\pi$
$127$	8.19859	−	4.73346i	0.727507	−	0.420026i	0.817509	+	0.575915i	$0.195354\pi$
$128$	62.4638	−	16.7371i	5.52108	−	1.47937i
$129$	3.60018	+	3.88518i	0.316978	+	0.342071i
$130$	23.7736	+	21.3116i	2.08509	+	1.86915i
$131$	−13.7979	−	7.96620i	−1.20552	−	0.696010i	−0.243746	−	0.969839i	$-0.578376\pi$
$131$	−13.7979	−	7.96620i	−1.20552	−	0.696010i	−0.961778	+	0.273829i	$0.911710\pi$
$132$	2.03291	−	53.3926i	0.176942	−	4.64723i
$133$	−0.121789	+	0.210945i	−0.0105604	+	0.0182912i
$134$	−13.4853	+	23.3572i	−1.16495	+	2.01775i
$135$	9.83219	−	13.2674i	0.846220	−	1.14187i
$136$	34.5357	−	9.25381i	2.96141	−	0.793508i
$137$	9.76185	+	9.76185i	0.834012	+	0.834012i	0.988063	−	0.154051i	$-0.0492321\pi$
$137$	9.76185	+	9.76185i	0.834012	+	0.834012i	−0.154051	+	0.988063i	$0.549232\pi$
$138$	15.3075	+	9.63234i	1.30306	+	0.819959i
$139$	−3.83575	−	6.64371i	−0.325344	−	0.563512i	0.656238	−	0.754554i	$-0.272147\pi$
$139$	−3.83575	−	6.64371i	−0.325344	−	0.563512i	−0.981582	+	0.191042i	$0.938813\pi$
$140$	18.3175			1.54811
$141$	−4.25564	−	8.06488i	−0.358390	−	0.679185i
$142$	3.57765	−	2.06555i	0.300229	−	0.173337i
$143$	−10.5456	−	16.1610i	−0.881865	−	1.35145i
$144$	−43.8187	−	29.9595i	−3.65156	−	2.49662i
$145$	−5.59083	+	20.8653i	−0.464293	+	1.73277i
$146$	0.167360	+	0.0966251i	0.0138508	+	0.00799675i
$147$	1.17726	+	1.27046i	0.0970988	+	0.104785i
$148$	−21.8602	+	5.85742i	−1.79690	+	0.481477i
$149$	−2.61214	−	0.699922i	−0.213995	−	0.0573398i	0.150229	−	0.988651i	$-0.451999\pi$
$149$	−2.61214	−	0.699922i	−0.213995	−	0.0573398i	−0.364224	+	0.931311i	$0.618666\pi$
$150$	−24.5945	−	0.936431i	−2.00813	−	0.0764592i
$151$	−7.77372	−	2.08296i	−0.632616	−	0.169509i	−0.0717596	−	0.997422i	$-0.522861\pi$
$151$	−7.77372	−	2.08296i	−0.632616	−	0.169509i	−0.560857	+	0.827913i	$0.689528\pi$
$152$	−2.21224	−	1.27724i	−0.179437	−	0.103598i
$153$	−8.44301	−	5.77260i	−0.682577	−	0.466687i
$154$	−14.4048	−	3.85975i	−1.16077	−	0.311027i
$155$	−1.20843	−	2.09307i	−0.0970637	−	0.168119i
$156$	−35.9901	+	0.593829i	−2.88151	+	0.0475443i
$157$	−1.73962	+	3.01310i	−0.138836	+	0.240472i	−0.927056	−	0.374922i	$-0.877670\pi$
$157$	−1.73962	+	3.01310i	−0.138836	+	0.240472i	0.788220	+	0.615394i	$0.211003\pi$
$158$	23.8355	−	23.8355i	1.89625	−	1.89625i
$159$	−2.28231	−	2.46299i	−0.180999	−	0.195328i
$160$			90.0232i			7.11696i
$161$	2.64989	−	2.64989i	0.208840	−	0.208840i
$162$	2.74231	+	24.9269i	0.215456	+	1.95844i
$163$	5.08909	+	18.9928i	0.398608	+	1.48763i	0.815546	+	0.578692i	$0.196437\pi$
$163$	5.08909	+	18.9928i	0.398608	+	1.48763i	−0.416938	+	0.908935i	$0.636897\pi$
$164$	−4.60010	+	17.1678i	−0.359207	+	1.34058i
$165$	28.1461	+	8.70217i	2.19117	+	0.677463i
$166$		−	8.07864i		−	0.627024i
$167$	−2.01446	−	2.01446i	−0.155884	−	0.155884i	0.624856	−	0.780740i	$-0.285158\pi$
$167$	−2.01446	−	2.01446i	−0.155884	−	0.155884i	−0.780740	+	0.624856i	$0.785158\pi$
$168$	−13.3237	+	12.3463i	−1.02794	+	0.952538i
$169$	−10.4836	+	7.68730i	−0.806429	+	0.591331i
$170$			30.1894i			2.31542i
$171$	0.134909	+	0.718172i	0.0103168	+	0.0549200i
$172$	8.81315	+	15.2648i	0.671996	+	1.16393i
$173$	5.77608			0.439147			0.219574	−	0.975596i	$-0.429533\pi$
$173$	5.77608			0.439147			0.219574	+	0.975596i	$0.429533\pi$
$174$	−15.3090	−	29.0122i	−1.16058	−	2.19941i
$175$	−1.31993	+	4.92605i	−0.0997774	+	0.372374i
$176$	24.5100	−	91.4727i	1.84751	−	6.89502i
$177$	−4.22242	−	8.00192i	−0.317377	−	0.601461i
$178$	−32.5116			−2.43684
$179$	−2.10944	−	3.65366i	−0.157667	−	0.273087i	0.776360	−	0.630290i	$-0.217064\pi$
$179$	−2.10944	−	3.65366i	−0.157667	−	0.273087i	−0.934027	+	0.357203i	$0.883731\pi$
$180$	41.6995	−	35.7901i	3.10809	−	2.66764i
$181$			6.30682i			0.468782i	0.972142	+	0.234391i	$0.0753097\pi$
$181$			6.30682i			0.468782i	−0.972142	+	0.234391i	$0.924690\pi$
$182$	−2.06718	+	9.83139i	−0.153230	+	0.728751i
$183$	12.9039	−	11.9574i	0.953887	−	0.883913i
$184$	27.7902	+	27.7902i	2.04872	+	2.04872i
$185$		−	12.4784i		−	0.917427i
$186$	3.50647	+	1.08412i	0.257107	+	0.0794917i
$187$	4.72260	−	17.6250i	0.345351	−	1.28887i
$188$	−7.85386	−	29.3110i	−0.572802	−	2.13773i
$189$	5.16232	+	0.591953i	0.375504	+	0.0430582i
$190$	1.52517	−	1.52517i	0.110647	−	0.110647i
$191$			17.0279i			1.23210i	0.787708	+	0.616049i	$0.211268\pi$
$191$			17.0279i			1.23210i	−0.787708	+	0.616049i	$0.788732\pi$
$192$	−51.2591	−	55.3169i	−3.69931	−	3.99216i
$193$	−9.40808	+	9.40808i	−0.677209	+	0.677209i	−0.959368	−	0.282159i	$-0.908949\pi$
$193$	−9.40808	+	9.40808i	−0.677209	+	0.677209i	0.282159	+	0.959368i	$0.408949\pi$
$194$	−13.4966	+	23.3768i	−0.968999	+	1.67836i
$195$	4.81975	−	19.2526i	0.345149	−	1.37871i
$196$	2.88190	+	4.99160i	0.205850	+	0.356543i
$197$	6.70357	+	1.79622i	0.477609	+	0.127975i	0.489589	−	0.871953i	$-0.337147\pi$
$197$	6.70357	+	1.79622i	0.477609	+	0.127975i	−0.0119799	+	0.999928i	$0.503813\pi$
$198$	−40.3337	+	19.3585i	−2.86639	+	1.37575i
$199$	0.616592	+	0.355990i	0.0437091	+	0.0252354i	0.521695	−	0.853132i	$-0.325300\pi$
$199$	0.616592	+	0.355990i	0.0437091	+	0.0252354i	−0.477986	+	0.878367i	$0.658633\pi$
$200$	−51.6610	−	13.8425i	−3.65299	−	0.978815i
$201$	16.7532	+	0.637875i	1.18168	+	0.0449922i
$202$	27.6070	+	7.39727i	1.94242	+	0.520470i
$203$	−6.56549	+	1.75922i	−0.460807	+	0.123473i
$204$	−23.1335	−	24.9648i	−1.61967	−	1.74789i
$205$	−8.48690	−	4.89991i	−0.592750	−	0.342225i
$206$	−11.7296	+	43.7756i	−0.817243	+	3.04999i
$207$	0.854874	−	11.2100i	0.0594179	−	0.779147i
$208$	−62.4309	−	13.1270i	−4.32881	−	0.910191i
$209$	−1.12900	+	0.651828i	−0.0780946	+	0.0450879i
$210$	−7.15783	−	13.5648i	−0.493937	−	0.936062i
$211$	−18.9140			−1.30210			−0.651048	−	0.759037i	$-0.725670\pi$
$211$	−18.9140			−1.30210			−0.651048	+	0.759037i	$0.725670\pi$
$212$	−5.58705	−	9.67705i	−0.383720	−	0.664623i
$213$	−2.17346	−	1.36767i	−0.148923	−	0.0937112i
$214$	−31.2281	−	31.2281i	−2.13471	−	2.13471i
$215$	−9.38755	+	2.51539i	−0.640226	+	0.171548i
$216$	−6.20800	+	54.1390i	−0.422401	+	3.68369i
$217$	0.380247	−	0.658607i	0.0258129	−	0.0447092i
$218$	3.76390	−	6.51927i	0.254924	−	0.441541i
$219$	0.00457053	−	0.120041i	0.000308848	−	0.00811160i
$220$	84.9028	+	49.0187i	5.72415	+	3.30484i
$221$	−12.0292	−	2.52931i	−0.809173	−	0.170140i
$222$	12.8798	+	13.8995i	0.864438	+	0.932870i
$223$	7.24363	−	1.94093i	0.485070	−	0.129974i	−0.00799265	−	0.999968i	$-0.502544\pi$
$223$	7.24363	−	1.94093i	0.485070	−	0.129974i	0.493062	+	0.869994i	$0.335877\pi$
$224$	−24.5317	+	14.1634i	−1.63910	+	0.946332i
$225$	6.62008	+	13.7930i	0.441339	+	0.919536i
$226$	−10.1823	−	10.1823i	−0.677318	−	0.677318i
$227$	10.0238	−	10.0238i	0.665302	−	0.665302i	−0.291323	−	0.956625i	$-0.594095\pi$
$227$	10.0238	−	10.0238i	0.665302	−	0.665302i	0.956625	+	0.291323i	$0.0940953\pi$
$228$	−0.0925190	+	2.42993i	−0.00612722	+	0.160926i
$229$	4.04436	+	15.0938i	0.267259	+	0.997425i	0.960853	+	0.277059i	$0.0893596\pi$
$229$	4.04436	+	15.0938i	0.267259	+	0.997425i	−0.693594	+	0.720366i	$0.743974\pi$
$230$	−28.7387	+	16.5923i	−1.89497	+	1.09406i
$231$	2.05687	+	9.03907i	0.135332	+	0.594727i
$232$	−18.4495	−	68.8544i	−1.21127	−	4.52051i
$233$	11.6920			0.765969			0.382985	−	0.923755i	$-0.374896\pi$
$233$	11.6920			0.765969			0.382985	+	0.923755i	$0.374896\pi$
$234$	14.5034	+	26.4200i	0.948117	+	1.72713i
$235$	16.7315			1.09144
$236$	−7.79255	−	29.0822i	−0.507252	−	1.89309i
$237$	−20.0188	−	6.18939i	−1.30036	−	0.402044i
$238$	−8.22674	+	4.74971i	−0.533260	+	0.307878i
$239$	2.64369	+	9.86637i	0.171006	+	0.638202i	0.997198	+	0.0748134i	$0.0238361\pi$
$239$	2.64369	+	9.86637i	0.171006	+	0.638202i	−0.826192	+	0.563389i	$0.809497\pi$
$240$	86.1389	−	45.4534i	5.56024	−	2.93401i
$241$	12.0243	−	12.0243i	0.774553	−	0.774553i	−0.204345	−	0.978899i	$-0.565507\pi$
$241$	12.0243	−	12.0243i	0.774553	−	0.774553i	0.978899	+	0.204345i	$0.0655066\pi$
$242$	−34.7654	−	34.7654i	−2.23481	−	2.23481i
$243$	12.9085	−	8.73897i	0.828083	−	0.560605i
$244$	50.6994	−	29.2713i	3.24570	−	1.87390i
$245$	−3.06973	+	0.822532i	−0.196118	+	0.0525497i
$246$	14.5110	−	3.30202i	0.925187	−	0.210529i
$247$	0.479935	+	0.735496i	0.0305375	+	0.0467985i
$248$	6.90703	+	3.98777i	0.438597	+	0.253224i
$249$	−4.44141	+	2.34362i	−0.281463	+	0.148521i
$250$	0.441954	−	0.765487i	0.0279516	−	0.0484137i
$251$	−6.60210	+	11.4352i	−0.416721	+	0.721782i	−0.995607	−	0.0936263i	$-0.970154\pi$
$251$	−6.60210	+	11.4352i	−0.416721	+	0.721782i	0.578886	+	0.815408i	$0.303487\pi$
$252$	16.3136	+	5.73242i	1.02766	+	0.361108i
$253$	19.3737	−	5.19116i	1.21801	−	0.326365i
$254$	−18.6522	−	18.6522i	−1.17034	−	1.17034i
$255$	16.5973	−	8.75798i	1.03936	−	0.548446i
$256$	−46.5522	−	80.6308i	−2.90952	−	5.03943i
$257$	19.7340			1.23097			0.615485	−	0.788148i	$-0.288960\pi$
$257$	19.7340			1.23097			0.615485	+	0.788148i	$0.288960\pi$
$258$	7.86033	−	12.4914i	0.489363	−	0.777683i
$259$	3.40041	−	1.96323i	0.211291	−	0.121989i
$260$	29.8544	−	58.9119i	1.85149	−	3.65356i
$261$	−11.5089	+	16.8330i	−0.712385	+	1.04194i
$262$	−11.4899	+	42.8807i	−0.709846	+	2.64918i
$263$	14.8635	+	8.58146i	0.916525	+	0.529156i	0.882525	−	0.470266i	$-0.155842\pi$
$263$	14.8635	+	8.58146i	0.916525	+	0.529156i	0.0339999	+	0.999422i	$0.489175\pi$
$264$	−94.7956	+	21.5710i	−5.83427	+	1.32760i
$265$	5.95119	−	1.59462i	0.365579	−	0.0979565i
$266$	0.655570	+	0.175659i	0.0401956	+	0.0107704i
$267$	9.43165	+	17.8740i	0.577208	+	1.09387i
$268$	53.8896	+	14.4397i	3.29183	+	0.882044i
$269$	2.52578	+	1.45826i	0.153999	+	0.0889115i	0.575019	−	0.818140i	$-0.304995\pi$
$269$	2.52578	+	1.45826i	0.153999	+	0.0889115i	−0.421020	+	0.907051i	$0.638328\pi$
$270$	−42.7987	−	16.8946i	−2.60464	−	1.02817i
$271$	−16.9630	−	4.54522i	−1.03043	−	0.276103i	−0.296287	−	0.955099i	$-0.595749\pi$
$271$	−16.9630	−	4.54522i	−1.03043	−	0.276103i	−0.734142	+	0.678996i	$0.762415\pi$
$272$	−30.1614	−	52.2411i	−1.82881	−	3.16758i
$273$	6.00472	−	1.71562i	0.363422	−	0.103834i
$274$	19.2333	−	33.3131i	1.16193	−	2.01252i
$275$	−19.3004	+	19.3004i	−1.16386	+	1.16386i
$276$	11.0509	−	35.7428i	0.665185	−	2.15146i
$277$		−	14.6459i		−	0.879987i	−0.898001	−	0.439993i	$-0.854981\pi$
$277$		−	14.6459i		−	0.879987i	0.898001	−	0.439993i	$-0.145019\pi$
$278$	−15.1148	+	15.1148i	−0.906526	+	0.906526i
$279$	−0.421210	−	2.24226i	−0.0252172	−	0.134241i
$280$	−8.62616	−	32.1933i	−0.515512	−	1.92392i
$281$	−3.27129	+	12.2086i	−0.195149	+	0.728306i	0.797079	+	0.603875i	$0.206377\pi$
$281$	−3.27129	+	12.2086i	−0.195149	+	0.728306i	−0.992228	+	0.124431i	$0.960289\pi$
$282$	−18.6369	+	17.2698i	−1.10981	+	1.02840i
$283$			0.301759i			0.0179377i	0.999960	+	0.00896887i	$0.00285492\pi$
$283$			0.301759i			0.0179377i	−0.999960	+	0.00896887i	$0.997145\pi$
$284$	−6.04260	−	6.04260i	−0.358562	−	0.358562i
$285$	−1.28095	−	0.396041i	−0.0758767	−	0.0234594i
$286$	−35.8909	+	40.0373i	−2.12227	+	2.36745i
$287$		−	3.08362i		−	0.182021i
$288$	−28.1725	+	80.1747i	−1.66008	+	4.72434i
$289$	2.68848	+	4.65659i	0.158146	+	0.273917i
$290$	60.1891			3.53442
$291$	16.7673	+	0.638411i	0.982916	+	0.0374243i
$292$	0.103464	−	0.386132i	0.00605476	−	0.0225967i
$293$	−0.234374	+	0.874697i	−0.0136923	+	0.0511003i	−0.972434	−	0.233178i	$-0.925087\pi$
$293$	−0.234374	+	0.874697i	−0.0136923	+	0.0511003i	0.958742	+	0.284279i	$0.0917541\pi$
$294$	2.57033	−	4.08470i	0.149905	−	0.238225i
$295$	16.6009			0.966540
$296$	20.5890	+	35.6612i	1.19671	+	2.07277i
$297$	22.3436	+	16.5584i	1.29651	+	0.960817i
$298$			7.53513i			0.436498i
$299$	−4.20358	−	12.8413i	−0.243099	−	0.742633i
$300$	11.2965	+	49.6435i	0.652205	+	2.86617i
$301$	−2.16240	−	2.16240i	−0.124639	−	0.124639i
$302$			22.4245i			1.29038i
$303$	−3.94202	−	17.3235i	−0.226463	−	0.995210i
$304$	−1.11547	+	4.16298i	−0.0639764	+	0.238763i
$305$	8.35441	+	31.1791i	0.478372	+	1.78531i
$306$	−9.44769	+	26.8866i	−0.540088	+	1.53701i
$307$	−9.90942	+	9.90942i	−0.565560	+	0.565560i	−0.930882	−	0.365321i	$-0.880959\pi$
$307$	−9.90942	+	9.90942i	−0.565560	+	0.565560i	0.365321	+	0.930882i	$0.380959\pi$
$308$			30.8486i			1.75776i
$309$	27.4694	−	6.25074i	1.56268	−	0.355592i
$310$	−4.76184	+	4.76184i	−0.270454	+	0.270454i
$311$	2.27468	−	3.93986i	0.128985	−	0.223409i	−0.794298	−	0.607528i	$-0.792161\pi$
$311$	2.27468	−	3.93986i	0.128985	−	0.223409i	0.923284	+	0.384119i	$0.125495\pi$
$312$	17.9923	+	62.9734i	1.01861	+	3.56517i
$313$	11.2602	+	19.5033i	0.636466	+	1.10239i	0.986202	+	0.165544i	$0.0529379\pi$
$313$	11.2602	+	19.5033i	0.636466	+	1.10239i	−0.349736	+	0.936848i	$0.613729\pi$
$314$	9.36407	+	2.50909i	0.528445	+	0.141596i
$315$	−5.38107	+	7.87035i	−0.303189	+	0.443444i
$316$	−60.3868	−	34.8644i	−3.39703	−	1.96127i
$317$	−10.6811	−	2.86199i	−0.599910	−	0.160745i	−0.0539318	−	0.998545i	$-0.517175\pi$
$317$	−10.6811	−	2.86199i	−0.599910	−	0.160745i	−0.545979	+	0.837799i	$0.683842\pi$
$318$	−4.98302	+	7.91888i	−0.279434	+	0.444069i
$319$	−35.1393	−	9.41554i	−1.96742	−	0.527169i
$320$	133.659	−	35.8139i	7.47178	−	2.00206i
$321$	−8.10903	+	26.2277i	−0.452602	+	1.46389i
$322$	−9.04296	−	5.22095i	−0.503944	−	0.290952i
$323$	−0.214928	+	0.802124i	−0.0119589	+	0.0446314i
$324$	48.3380	−	18.8249i	2.68544	−	1.04583i
$325$	13.6917	+	12.2737i	0.759477	+	0.680824i
$326$	47.4474	−	27.3937i	2.62787	−	1.51720i
$327$	−4.67603	−	0.178039i	−0.258585	−	0.00984556i
$328$	32.3390			1.78562
$329$	2.63237	+	4.55941i	0.145127	+	0.251368i
$330$	3.12322	−	82.0287i	0.171928	−	4.51553i
$331$	−20.2976	−	20.2976i	−1.11565	−	1.11565i	−0.992372	−	0.123283i	$-0.960658\pi$
$331$	−20.2976	−	20.2976i	−1.11565	−	1.11565i	−0.123283	−	0.992372i	$-0.539342\pi$
$332$	−16.1419	+	4.32520i	−0.885900	+	0.237376i
$333$	3.90507	−	11.1132i	0.213997	−	0.609001i
$334$	−3.96900	+	6.87451i	−0.217174	+	0.376156i
$335$	−15.3808	+	26.6403i	−0.840343	+	1.45552i
$336$	25.9385	+	16.3220i	1.41506	+	0.890440i
$337$	3.30407	+	1.90761i	0.179984	+	0.103914i	0.587285	−	0.809380i	$-0.300197\pi$
$337$	3.30407	+	1.90761i	0.179984	+	0.103914i	−0.407301	+	0.913294i	$0.633530\pi$
$338$	28.2501	+	22.6719i	1.53660	+	1.23319i
$339$	−2.64405	+	8.55187i	−0.143605	+	0.464474i
$340$	60.3212	−	16.1630i	3.27137	−	0.876562i
$341$	3.52494	−	2.03513i	0.190886	−	0.110208i
$342$	1.83561	−	0.881016i	0.0992584	−	0.0476399i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	22.6778	−	22.6778i	1.22271	−	1.22271i
$345$	17.4591	+	10.9863i	0.939968	+	0.591482i
$346$	−4.16550	−	15.5458i	−0.223938	−	0.835750i
$347$	24.5984	−	14.2019i	1.32051	−	0.762396i	0.336699	−	0.941612i	$-0.390689\pi$
$347$	24.5984	−	14.2019i	1.32051	−	0.762396i	0.983810	+	0.179216i	$0.0573561\pi$
$348$	−49.7729	+	46.1217i	−2.66811	+	2.47238i
$349$	7.72971	+	28.8477i	0.413762	+	1.54418i	0.787303	+	0.616567i	$0.211477\pi$
$349$	7.72971	+	28.8477i	0.413762	+	1.54418i	−0.373541	+	0.927614i	$0.621856\pi$
$350$	14.2099			0.759553
$351$	10.3175	−	15.6381i	0.550709	−	0.834697i
$352$	−151.608			−8.08075
$353$	−6.84465	−	25.5446i	−0.364304	−	1.35960i	−0.868362	−	0.495931i	$-0.834827\pi$
$353$	−6.84465	−	25.5446i	−0.364304	−	1.35960i	0.504058	−	0.863670i	$-0.331840\pi$
$354$	−18.4915	+	17.1350i	−0.982810	+	0.910714i
$355$	4.08053	−	2.35590i	0.216572	−	0.125038i
$356$	17.4063	+	64.9611i	0.922531	+	3.44293i
$357$	4.99785	+	3.14493i	0.264514	+	0.166448i
$358$	−8.31227	+	8.31227i	−0.439317	+	0.439317i
$359$	18.6440	+	18.6440i	0.983992	+	0.983992i	0.999874	−	0.0158822i	$-0.00505567\pi$
$359$	18.6440	+	18.6440i	0.983992	+	0.983992i	−0.0158822	+	0.999874i	$0.505056\pi$
$360$	−82.5389	−	56.4330i	−4.35018	−	2.97428i
$361$	−16.4031	+	9.47033i	−0.863321	+	0.498439i
$362$	16.9743	−	4.54825i	0.892149	−	0.239051i
$363$	−9.02756	+	29.1986i	−0.473824	+	1.53253i
$364$	20.7508	−	1.13318i	1.08764	−	0.0593946i
$365$	0.190884	+	0.110207i	0.00999134	+	0.00576850i
$366$	−41.4881	−	26.1067i	−2.16862	−	1.36462i
$367$	17.6055	−	30.4936i	0.918998	−	1.59175i	0.118059	−	0.993007i	$-0.462333\pi$
$367$	17.6055	−	30.4936i	0.918998	−	1.59175i	0.800939	−	0.598745i	$-0.204334\pi$
$368$	33.1539	−	57.4243i	1.72827	−	2.99345i
$369$	−6.02502	−	7.01982i	−0.313650	−	0.365437i
$370$	−33.5845	+	8.99894i	−1.74597	+	0.467832i
$371$	1.37084	+	1.37084i	0.0711707	+	0.0711707i
$372$	0.288861	−	7.58667i	0.0149767	−	0.393351i
$373$	−16.1578	−	27.9861i	−0.836617	−	1.44906i	−0.892707	−	0.450638i	$-0.851196\pi$
$373$	−16.1578	−	27.9861i	−0.836617	−	1.44906i	0.0560893	−	0.998426i	$-0.482137\pi$
$374$	−50.8420			−2.62898
$375$	−0.549055	−	0.0209052i	−0.0283531	−	0.00107954i
$376$	−47.8160	+	27.6066i	−2.46592	+	1.42370i
$377$	−5.04272	+	23.9829i	−0.259714	+	1.23518i
$378$	−2.12969	−	14.3209i	−0.109539	−	0.736586i
$379$	−0.0550195	+	0.205336i	−0.00282616	+	0.0105474i	−0.967325	−	0.253541i	$-0.918405\pi$
$379$	−0.0550195	+	0.205336i	−0.00282616	+	0.0105474i	0.964498	+	0.264089i	$0.0850712\pi$
$380$	−3.86398	−	2.23087i	−0.198218	−	0.114441i
$381$	−4.84344	+	15.6655i	−0.248137	+	0.802569i
$382$	45.8293	−	12.2799i	2.34483	−	0.628295i
$383$	11.3560	+	3.04284i	0.580267	+	0.155482i	0.537001	−	0.843582i	$-0.319557\pi$
$383$	11.3560	+	3.04284i	0.580267	+	0.155482i	0.0432657	+	0.999064i	$0.486224\pi$
$384$	−59.6536	+	94.8000i	−3.04419	+	4.83774i
$385$	−16.4296	−	4.40229i	−0.837328	−	0.224361i
$386$	32.1059	+	18.5363i	1.63414	+	0.943474i
$387$	−9.14774	−	0.697608i	−0.465006	−	0.0354614i
$388$	53.9349	+	14.4518i	2.73813	+	0.733680i
$389$	0.793328	+	1.37408i	0.0402233	+	0.0696688i	0.885436	−	0.464761i	$-0.153860\pi$
$389$	0.793328	+	1.37408i	0.0402233	+	0.0696688i	−0.845213	+	0.534430i	$0.820526\pi$
$390$	−55.2926	+	0.912317i	−2.79985	+	0.0461970i
$391$	6.38811	−	11.0645i	0.323061	−	0.559557i
$392$	7.41566	−	7.41566i	0.374547	−	0.374547i
$393$	26.9079	−	6.12296i	1.35732	−	0.308863i
$394$		−	19.3375i		−	0.974207i
$395$	27.1859	−	27.1859i	1.36787	−	1.36787i
$396$	60.2742	+	70.2262i	3.02889	+	3.52900i
$397$	1.33645	+	4.98771i	0.0670746	+	0.250326i	0.991320	−	0.131474i	$-0.0419710\pi$
$397$	1.33645	+	4.98771i	0.0670746	+	0.250326i	−0.924245	+	0.381800i	$0.875304\pi$
$398$	0.513453	−	1.91623i	0.0257371	−	0.0960521i
$399$	−0.0936092	−	0.411373i	−0.00468632	−	0.0205944i
$400$			90.2354i			4.51177i
$401$	−17.9161	−	17.9161i	−0.894690	−	0.894690i	0.100270	−	0.994960i	$-0.468029\pi$
$401$	−17.9161	−	17.9161i	−0.894690	−	0.894690i	−0.994960	+	0.100270i	$0.968029\pi$
$402$	−10.3650	−	45.5499i	−0.516960	−	2.27182i
$403$	−1.49844	−	2.29635i	−0.0746428	−	0.114389i
$404$		−	59.1218i		−	2.94142i
$405$	3.12778	+	28.4307i	0.155421	+	1.41273i
$406$	9.46958	+	16.4018i	0.469967	+	0.814008i
$407$	21.0148			1.04167
$408$	−32.9819	+	52.4140i	−1.63285	+	2.59488i
$409$	2.25625	−	8.42044i	0.111564	−	0.416364i	−0.887443	−	0.460918i	$-0.847520\pi$
$409$	2.25625	−	8.42044i	0.111564	−	0.416364i	0.999007	+	0.0445544i	$0.0141868\pi$
$410$	−7.06727	+	26.3754i	−0.349028	+	1.30259i
$411$	−23.8942	−	0.909768i	−1.17862	−	0.0448756i
$412$	93.7477			4.61862
$413$	2.61183	+	4.52381i	0.128520	+	0.222602i
$414$	−30.7872	+	5.78340i	−1.51311	+	0.284239i
$415$		−	9.21420i		−	0.452307i
$416$	5.56911	+	101.982i	0.273048	+	5.00007i
$417$	12.6945	+	3.92487i	0.621654	+	0.192202i
$418$	2.56854	+	2.56854i	0.125631	+	0.125631i
$419$		−	13.9580i		−	0.681891i	−0.940083	−	0.340946i	$-0.889253\pi$
$419$		−	13.9580i		−	0.681891i	0.940083	−	0.340946i	$-0.110747\pi$
$420$	−23.2716	+	21.5645i	−1.13554	+	1.05224i
$421$	5.03613	−	18.7951i	0.245446	−	0.916017i	−0.727713	−	0.685882i	$-0.759417\pi$
$421$	5.03613	−	18.7951i	0.245446	−	0.916017i	0.973159	−	0.230135i	$-0.0739167\pi$
$422$	13.6401	+	50.9056i	0.663990	+	2.47804i
$423$	14.9011	+	5.23608i	0.724514	+	0.254587i
$424$	−14.3765	+	14.3765i	−0.698184	+	0.698184i
$425$			17.3866i			0.843374i
$426$	−2.11355	+	6.83602i	−0.102402	+	0.331206i
$427$	−7.18204	+	7.18204i	−0.347563	+	0.347563i
$428$	−45.6776	+	79.1159i	−2.20791	+	3.82421i
$429$	32.4234	+	8.11695i	1.56542	+	0.391890i
$430$	13.5399	+	23.4518i	0.652953	+	1.13095i
$431$	−26.5813	−	7.12244i	−1.28038	−	0.343076i	−0.446378	−	0.894844i	$-0.647286\pi$
$431$	−26.5813	−	7.12244i	−1.28038	−	0.343076i	−0.833997	+	0.551769i	$0.813953\pi$
$432$	90.9399	−	13.5239i	4.37535	−	0.650667i
$433$	4.79646	+	2.76924i	0.230503	+	0.133081i	0.610804	−	0.791782i	$-0.290846\pi$
$433$	4.79646	+	2.76924i	0.230503	+	0.133081i	−0.380301	+	0.924863i	$0.624180\pi$
$434$	−2.04681	−	0.548440i	−0.0982499	−	0.0263260i
$435$	−17.4609	−	33.0903i	−0.837188	−	1.58656i
$436$	−15.0413	−	4.03029i	−0.720345	−	0.193016i
$437$	−0.881707	+	0.236253i	−0.0421778	+	0.0113015i
$438$	−0.326376	+	0.0742678i	−0.0155948	+	0.00354865i
$439$	−16.8471	−	9.72671i	−0.804071	−	0.464230i	0.0408219	−	0.999166i	$-0.487002\pi$
$439$	−16.8471	−	9.72671i	−0.804071	−	0.464230i	−0.844893	+	0.534936i	$0.820336\pi$
$440$	46.1682	−	172.302i	2.20098	−	8.21418i
$441$	−2.99131	−	0.228118i	−0.142444	−	0.0108628i
$442$	1.86761	+	34.1997i	0.0888330	+	1.62671i
$443$	−0.0576708	+	0.0332962i	−0.00274002	+	0.00158195i	−0.501369	−	0.865233i	$-0.667170\pi$
$443$	−0.0576708	+	0.0332962i	−0.00274002	+	0.00158195i	0.498629	+	0.866815i	$0.333837\pi$
$444$	20.8767	−	33.1767i	0.990765	−	1.57450i
$445$	−37.0815			−1.75783
$446$	−10.4477	−	18.0959i	−0.494712	−	0.856867i
$447$	4.14260	−	2.18595i	0.195938	−	0.103392i
$448$	30.7881	+	30.7881i	1.45460	+	1.45460i
$449$	27.5984	−	7.39496i	1.30245	−	0.348990i	0.460072	−	0.887882i	$-0.347824\pi$
$449$	27.5984	−	7.39496i	1.30245	−	0.348990i	0.842375	+	0.538892i	$0.181157\pi$
$450$	32.3487	−	27.7644i	1.52493	−	1.30883i
$451$	8.25196	−	14.2928i	0.388569	−	0.673022i
$452$	−14.8937	+	25.7967i	−0.700543	+	1.21338i
$453$	12.3284	−	6.50538i	0.579237	−	0.305649i
$454$	−34.2070	−	19.7494i	−1.60541	−	0.926886i
$455$	−2.35775	+	11.2133i	−0.110533	+	0.525689i
$456$	4.31420	−	0.981709i	0.202031	−	0.0459728i
$457$	−16.5261	+	4.42814i	−0.773056	+	0.207140i	−0.623721	−	0.781647i	$-0.714380\pi$
$457$	−16.5261	+	4.42814i	−0.773056	+	0.207140i	−0.149335	+	0.988787i	$0.547713\pi$
$458$	37.7070	−	21.7702i	1.76193	−	1.01725i
$459$	17.5223	−	2.60578i	0.817872	−	0.121627i
$460$	48.5393	+	48.5393i	2.26316	+	2.26316i
$461$	8.28158	−	8.28158i	0.385712	−	0.385712i	−0.487443	−	0.873155i	$-0.662070\pi$
$461$	8.28158	−	8.28158i	0.385712	−	0.385712i	0.873155	+	0.487443i	$0.162070\pi$
$462$	22.8446	−	12.0545i	1.06283	−	0.560827i
$463$	10.1589	+	37.9136i	0.472125	+	1.76199i	0.632113	+	0.774876i	$0.282188\pi$
$463$	10.1589	+	37.9136i	0.472125	+	1.76199i	−0.159988	+	0.987119i	$0.551146\pi$
$464$	−104.154	+	60.1334i	−4.83523	+	2.79162i
$465$	3.99935	+	1.23651i	0.185465	+	0.0573418i
$466$	−8.43185	−	31.4681i	−0.390598	−	1.45773i
$467$	16.5544			0.766046			0.383023	−	0.923739i	$-0.374883\pi$
$467$	16.5544			0.766046			0.383023	+	0.923739i	$0.374883\pi$
$468$	45.0247	−	43.1241i	2.08127	−	1.99341i
$469$	−9.67948			−0.446957
$470$	−12.0661	−	45.0314i	−0.556569	−	2.07714i
$471$	−1.33710	−	5.87600i	−0.0616103	−	0.270752i
$472$	−47.4427	+	27.3911i	−2.18373	+	1.26078i
$473$	−4.23617	−	15.8096i	−0.194779	−	0.726926i
$474$	−2.22138	+	58.3426i	−0.102031	+	2.67976i
$475$	0.878370	−	0.878370i	0.0403024	−	0.0403024i
$476$	13.8949	+	13.8949i	0.636870	+	0.636870i
$477$	5.79916	+	0.442245i	0.265525	+	0.0202490i
$478$	24.6480	−	14.2305i	1.12737	−	0.650889i
$479$	−39.7777	+	10.6584i	−1.81749	+	0.486994i	−0.996473	−	0.0839130i	$-0.973258\pi$
$479$	−39.7777	+	10.6584i	−1.81749	+	0.486994i	−0.821015	+	0.570907i	$0.806592\pi$
$480$	−105.981	−	114.371i	−4.83733	−	5.22028i
$481$	−0.771950	−	14.1360i	−0.0351979	−	0.644545i
$482$	−41.0339	−	23.6909i	−1.86904	−	1.07909i
$483$	−0.246960	+	6.48617i	−0.0112371	+	0.295131i
$484$	−50.8516	+	88.0775i	−2.31144	+	4.00352i
$485$	−15.3937	+	26.6627i	−0.698993	+	1.21069i
$486$	−32.8294	−	28.4401i	−1.48917	−	1.29007i
$487$	2.54869	−	0.682920i	0.115492	−	0.0309460i	−0.200610	−	0.979671i	$-0.564292\pi$
$487$	2.54869	−	0.682920i	0.115492	−	0.0309460i	0.316102	+	0.948725i	$0.397626\pi$
$488$	−75.3204	−	75.3204i	−3.40959	−	3.40959i
$489$	−28.8249	−	18.1383i	−1.30351	−	0.820241i
$490$	4.42756	+	7.66875i	0.200017	+	0.346439i
$491$	37.8540			1.70833			0.854163	−	0.520005i	$-0.174070\pi$
$491$	37.8540			1.70833			0.854163	+	0.520005i	$0.174070\pi$
$492$	−14.3667	−	27.2264i	−0.647703	−	1.22746i
$493$	−20.0684	+	11.5865i	−0.903837	+	0.521831i
$494$	1.63342	−	1.82212i	0.0734909	−	0.0819810i
$495$	−46.0031	+	22.0796i	−2.06769	+	0.992403i
$496$	3.48269	−	12.9976i	0.156377	−	0.583608i
$497$	1.28398	+	0.741309i	0.0575946	+	0.0332523i
$498$	9.51065	+	10.2636i	0.426183	+	0.459921i
$499$	42.5361	−	11.3975i	1.90418	−	0.510223i	0.908440	−	0.418016i	$-0.137274\pi$
$499$	42.5361	−	11.3975i	1.90418	−	0.510223i	0.995740	−	0.0922073i	$-0.0293923\pi$
$500$	−1.76613	−	0.473234i	−0.0789838	−	0.0211637i
$501$	4.93083	+	0.187740i	0.220293	+	0.00838761i
$502$	35.5380	+	9.52239i	1.58614	+	0.425005i
$503$	32.6753	+	18.8651i	1.45692	+	0.841153i	0.998858	−	0.0477675i	$-0.0152107\pi$
$503$	32.6753	+	18.8651i	1.45692	+	0.841153i	0.458061	+	0.888921i	$0.348544\pi$
$504$	2.39235	−	31.3709i	0.106564	−	1.39737i
$505$	31.4875	+	8.43706i	1.40118	+	0.375444i
$506$	−27.9432	−	48.3990i	−1.24222	−	2.15160i
$507$	4.26897	−	22.1083i	0.189592	−	0.981863i
$508$	−27.2827	+	47.2551i	−1.21048	+	2.09660i
$509$	−18.7468	+	18.7468i	−0.830935	+	0.830935i	−0.987645	−	0.156709i	$-0.949911\pi$
$509$	−18.7468	+	18.7468i	−0.830935	+	0.830935i	0.156709	+	0.987645i	$0.449911\pi$
$510$	−35.5407	−	38.3543i	−1.57377	−	1.69835i
$511$			0.0693558i			0.00306812i
$512$	−91.9861	+	91.9861i	−4.06525	+	4.06525i
$513$	−1.01687	−	0.753583i	−0.0448960	−	0.0332715i
$514$	−14.2314	−	53.1123i	−0.627720	−	2.34268i
$515$	−13.3784	+	49.9289i	−0.589523	+	2.20013i
$516$	−29.1674	−	9.01792i	−1.28402	−	0.396992i
$517$			28.1775i			1.23925i
$518$	−7.73612	−	7.73612i	−0.339906	−	0.339906i
$519$	−7.33826	+	6.79995i	−0.322114	+	0.298485i
$520$	−117.598	−	24.7265i	−5.15700	−	1.08433i
$521$		−	16.6706i		−	0.730353i	−0.930938	−	0.365176i	$-0.881009\pi$
$521$		−	16.6706i		−	0.730353i	0.930938	−	0.365176i	$-0.118991\pi$
$522$	53.6044	+	18.8360i	2.34620	+	0.824430i
$523$	−20.5374	−	35.5718i	−0.898036	−	1.55544i	−0.830001	−	0.557762i	$-0.811660\pi$
$523$	−20.5374	−	35.5718i	−0.898036	−	1.55544i	−0.0680352	−	0.997683i	$-0.521673\pi$
$524$	91.8313			4.01167
$525$	−4.12232	−	7.81223i	−0.179913	−	0.340954i
$526$	12.3773	−	46.1926i	0.539675	−	2.01409i
$527$	0.671045	−	2.50437i	0.0292312	−	0.109092i
$528$	76.5482	+	145.067i	3.33133	+	6.31322i
$529$	−8.95618			−0.389399
$530$	−8.58356	−	14.8672i	−0.372846	−	0.645788i
$531$	14.7847	+	5.19520i	0.641603	+	0.225453i
$532$		−	1.40394i		−	0.0608683i
$533$	−9.91741	−	5.02579i	−0.429571	−	0.217691i
$534$	41.3045	−	38.2746i	1.78742	−	1.65630i
$535$	−35.6177	−	35.6177i	−1.53989	−	1.53989i
$536$		−	101.512i		−	4.38464i
$537$	6.98126	+	2.15845i	0.301264	+	0.0931441i
$538$	2.10328	−	7.84956i	0.0906789	−	0.338418i
$539$	−1.38523	−	5.16975i	−0.0596661	−	0.222677i
$540$	−10.8431	+	94.5609i	−0.466612	+	4.06925i
$541$	19.1104	−	19.1104i	0.821622	−	0.821622i	−0.164719	−	0.986341i	$-0.552672\pi$
$541$	19.1104	−	19.1104i	0.821622	−	0.821622i	0.986341	+	0.164719i	$0.0526717\pi$
$542$			48.9324i			2.10182i
$543$	−7.42477	−	8.01254i	−0.318627	−	0.343851i
$544$	−68.2877	+	68.2877i	−2.92781	+	2.92781i
$545$	4.29297	−	7.43564i	0.183891	−	0.318508i
$546$	−8.94784	−	14.9240i	−0.382932	−	0.638687i
$547$	−4.77819	−	8.27607i	−0.204301	−	0.353859i	0.745609	−	0.666384i	$-0.232159\pi$
$547$	−4.77819	−	8.27607i	−0.204301	−	0.353859i	−0.949910	+	0.312524i	$0.898825\pi$
$548$	−76.8600	−	20.5946i	−3.28330	−	0.879757i
$549$	−2.31698	+	30.3826i	−0.0988863	+	1.29670i
$550$	65.8640	+	38.0266i	2.80845	+	1.62146i
$551$	1.59921	+	0.428507i	0.0681286	+	0.0182550i
$552$	−68.0226	−	2.58995i	−2.89523	−	0.110235i
$553$	11.6855	+	3.13111i	0.496917	+	0.133148i
$554$	−39.4182	+	10.5621i	−1.67472	+	0.448740i
$555$	14.6903	+	15.8532i	0.623567	+	0.672931i
$556$	38.2931	+	22.1085i	1.62399	+	0.937610i
$557$	4.22781	−	15.7784i	0.179138	−	0.668553i	−0.816671	−	0.577103i	$-0.804183\pi$
$557$	4.22781	−	15.7784i	0.179138	−	0.668553i	0.995810	−	0.0914500i	$-0.0291502\pi$
$558$	−5.73111	+	2.75069i	−0.242617	+	0.116446i
$559$	−10.4790	+	3.43027i	−0.443214	+	0.145085i
$560$	−48.6978	+	28.1157i	−2.05786	+	1.18811i
$561$	14.7493	+	27.9515i	0.622718	+	1.18011i
$562$	35.2177			1.48557
$563$	−14.7165	−	25.4897i	−0.620225	−	1.07426i	−0.989444	−	0.144918i	$-0.953708\pi$
$563$	−14.7165	−	25.4897i	−0.620225	−	1.07426i	0.369219	−	0.929343i	$-0.379625\pi$
$564$	44.4847	+	27.9923i	1.87314	+	1.17869i
$565$	−11.6136	−	11.6136i	−0.488587	−	0.488587i
$566$	0.812161	−	0.217618i	0.0341377	−	0.00914716i
$567$	−7.25539	+	5.32535i	−0.304698	+	0.223644i
$568$	−7.77435	+	13.4656i	−0.326204	+	0.565003i
$569$	13.3708	−	23.1590i	0.560535	−	0.970875i	−0.436915	−	0.899503i	$-0.643929\pi$
$569$	13.3708	−	23.1590i	0.560535	−	0.970875i	0.997450	−	0.0713718i	$-0.0227377\pi$
$570$	−0.142140	+	3.73317i	−0.00595358	+	0.156365i
$571$	−2.59295	−	1.49704i	−0.108512	−	0.0626493i	0.444762	−	0.895649i	$-0.353288\pi$
$571$	−2.59295	−	1.49704i	−0.108512	−	0.0626493i	−0.553274	+	0.833000i	$0.686622\pi$
$572$	99.2137	+	50.2779i	4.14833	+	2.10223i
$573$	−20.0463	−	21.6332i	−0.837446	−	0.903741i
$574$	−8.29932	+	2.22380i	−0.346407	+	0.0928195i
$575$	−16.5511	+	9.55581i	−0.690230	+	0.398505i
$576$	130.245	+	9.93249i	5.42687	+	0.413854i
$577$	28.9311	+	28.9311i	1.20442	+	1.20442i	0.972810	+	0.231607i	$0.0743982\pi$
$577$	28.9311	+	28.9311i	1.20442	+	1.20442i	0.231607	+	0.972810i	$0.425602\pi$
$578$	10.5940	−	10.5940i	0.440652	−	0.440652i
$579$	0.876798	−	23.0283i	0.0364385	−	0.957024i
$580$	−32.2245	−	120.263i	−1.33805	−	4.99367i
$581$	2.51091	−	1.44968i	0.104170	−	0.0601427i
$582$	−10.3737	−	45.5882i	−0.430005	−	1.88969i
$583$	2.68550	+	10.0224i	0.111222	+	0.415086i
$584$	−0.727356			−0.0300982
$585$	16.5420	+	30.1337i	0.683929	+	1.24587i
$586$	2.52320			0.104232
$587$	0.185515	+	0.692352i	0.00765703	+	0.0285764i	0.969649	−	0.244503i	$-0.0786246\pi$
$587$	0.185515	+	0.692352i	0.00765703	+	0.0285764i	−0.961992	+	0.273079i	$0.911958\pi$
$588$	−9.53775	−	2.94886i	−0.393330	−	0.121609i
$589$	−0.160422	+	0.0926198i	−0.00661008	+	0.00381633i
$590$	−11.9719	−	44.6799i	−0.492877	−	1.83944i
$591$	−10.6312	+	5.60983i	−0.437309	+	0.230757i
$592$	49.1256	−	49.1256i	2.01905	−	2.01905i
$593$	−24.3117	−	24.3117i	−0.998360	−	0.998360i	0.00163836	−	0.999999i	$-0.499478\pi$
$593$	−24.3117	−	24.3117i	−0.998360	−	0.998360i	−0.999999	+	0.00163836i	$0.999478\pi$
$594$	28.4522	−	72.0773i	1.16741	−	2.95737i
$595$	−9.38312	+	5.41734i	−0.384670	+	0.222089i
$596$	15.0559	−	4.03421i	0.616713	−	0.165248i
$597$	−1.20245	+	0.273620i	−0.0492128	+	0.0111985i
$598$	−31.5299	+	20.5743i	−1.28935	+	0.841345i
$599$	0.370409	+	0.213856i	0.0151345	+	0.00873792i	0.507548	−	0.861623i	$-0.330552\pi$
$599$	0.370409	+	0.213856i	0.0151345	+	0.00873792i	−0.492414	+	0.870361i	$0.663885\pi$
$600$	81.9294	−	43.2321i	3.34475	−	1.76494i
$601$	6.11891	−	10.5983i	0.249596	−	0.432313i	−0.713818	−	0.700331i	$-0.753036\pi$
$601$	6.11891	−	10.5983i	0.249596	−	0.432313i	0.963414	+	0.268019i	$0.0863689\pi$
$602$	−4.26049	+	7.37938i	−0.173644	+	0.300761i
$603$	−22.0352	+	18.9125i	−0.897341	+	0.770176i
$604$	44.8062	−	12.0058i	1.82314	−	0.488508i
$605$	−39.6522	−	39.6522i	−1.61209	−	1.61209i
$606$	−43.7820	+	23.1027i	−1.77852	+	0.938483i
$607$	14.7174	+	25.4914i	0.597363	+	1.03466i	0.993209	+	0.116346i	$0.0371180\pi$
$607$	14.7174	+	25.4914i	0.597363	+	1.03466i	−0.395846	+	0.918317i	$0.629549\pi$
$608$	6.89978			0.279823
$609$	6.27011	−	9.96430i	0.254078	−	0.403774i
$610$	77.8911	−	44.9704i	3.15372	−	1.82080i
$611$	18.9541	−	1.03506i	0.766800	−	0.0418741i
$612$	58.7802	+	4.48259i	2.37605	+	0.181198i
$613$	4.09959	−	15.2999i	0.165581	−	0.617957i	−0.832384	−	0.554199i	$-0.813025\pi$
$613$	4.09959	−	15.2999i	0.165581	−	0.617957i	0.997965	−	0.0637580i	$-0.0203086\pi$
$614$	33.8167	+	19.5241i	1.36473	+	0.787928i
$615$	16.5507	−	3.76616i	0.667389	−	0.151866i
$616$	54.2168	−	14.5273i	2.18446	−	0.585323i
$617$	32.6329	+	8.74396i	1.31375	+	0.352019i	0.846633	−	0.532177i	$-0.178626\pi$
$617$	32.6329	+	8.74396i	1.31375	+	0.352019i	0.467118	+	0.884195i	$0.345292\pi$
$618$	−36.6333	−	69.4239i	−1.47361	−	2.79264i
$619$	2.74257	+	0.734870i	0.110233	+	0.0295369i	0.313514	−	0.949584i	$-0.398494\pi$
$619$	2.74257	+	0.734870i	0.110233	+	0.0295369i	−0.203281	+	0.979120i	$0.565160\pi$
$620$	12.0640	+	6.96517i	0.484503	+	0.279728i
$621$	12.1110	+	15.2482i	0.485997	+	0.611889i
$622$	−12.2442	−	3.28083i	−0.490949	−	0.131549i
$623$	−5.83405	−	10.1049i	−0.233736	−	0.404843i
$624$	94.7696	−	56.8202i	3.79382	−	2.27463i
$625$	−12.2455	+	21.2098i	−0.489819	+	0.848391i
$626$	44.3711	−	44.3711i	1.77342	−	1.77342i
$627$	0.666974	−	2.15725i	0.0266364	−	0.0861521i
$628$		−	20.0536i		−	0.800227i
$629$	9.46554	−	9.46554i	0.377416	−	0.377416i
$630$	25.0630	+	8.80689i	0.998535	+	0.350875i
$631$	0.943771	+	3.52220i	0.0375709	+	0.140217i	0.982164	−	0.188028i	$-0.0602096\pi$
$631$	0.943771	+	3.52220i	0.0375709	+	0.140217i	−0.944593	+	0.328245i	$0.893543\pi$
$632$	−32.8370	+	122.549i	−1.30618	+	4.87475i
$633$	24.0295	−	22.2667i	0.955085	−	0.885023i
$634$			30.8113i			1.22367i
$635$	−21.2740	−	21.2740i	−0.844235	−	0.844235i
$636$	18.4905	+	5.71686i	0.733196	+	0.226688i
$637$	−3.42663	+	1.12170i	−0.135768	+	0.0444434i
$638$			101.365i			4.01306i
$639$	4.37139	−	0.821169i	0.172930	−	0.0324849i
$640$	−102.757	−	177.980i	−4.06183	−	7.03529i
$641$	24.0328			0.949237			0.474619	−	0.880191i	$-0.342586\pi$
$641$	24.0328			0.949237			0.474619	+	0.880191i	$0.342586\pi$
$642$	76.4376	+	2.91035i	3.01675	+	0.114862i
$643$	−7.27858	+	27.1640i	−0.287039	+	1.07124i	0.660297	+	0.751004i	$0.270430\pi$
$643$	−7.27858	+	27.1640i	−0.287039	+	1.07124i	−0.947336	+	0.320240i	$0.896236\pi$
$644$	−5.59047	+	20.8639i	−0.220295	+	0.822153i
$645$	8.96521	−	14.2473i	0.353005	−	0.560986i
$646$	2.31385			0.0910371
$647$	9.58101	+	16.5948i	0.376668	+	0.652409i	0.990575	−	0.136970i	$-0.0437363\pi$
$647$	9.58101	+	16.5948i	0.376668	+	0.652409i	−0.613907	+	0.789379i	$0.710403\pi$
$648$	−55.8486	−	76.0896i	−2.19394	−	2.98908i
$649$			27.9576i			1.09743i
$650$	23.1598	−	45.7014i	0.908402	−	1.79255i
$651$	0.292265	+	1.28438i	0.0114548	+	0.0503389i
$652$	−80.1380	−	80.1380i	−3.13845	−	3.13845i
$653$			15.9484i			0.624108i	0.950064	+	0.312054i	$0.101017\pi$
$653$			15.9484i			0.624108i	−0.950064	+	0.312054i	$0.898983\pi$
$654$	2.89300	+	12.7135i	0.113125	+	0.497139i
$655$	−13.1049	+	48.9082i	−0.512051	+	1.91100i
$656$	−14.1215	−	52.7021i	−0.551351	−	2.05767i
$657$	0.135513	+	0.157887i	0.00528685	+	0.00615977i
$658$	10.3729	−	10.3729i	0.404378	−	0.404378i
$659$		−	41.4005i		−	1.61274i	−0.591415	−	0.806368i	$-0.701430\pi$
$659$		−	41.4005i		−	1.61274i	0.591415	−	0.806368i	$-0.298570\pi$
$660$	−165.573	+	37.6766i	−6.44492	+	1.46656i
$661$	−1.35593	+	1.35593i	−0.0527395	+	0.0527395i	−0.732985	−	0.680245i	$-0.761873\pi$
$661$	−1.35593	+	1.35593i	−0.0527395	+	0.0527395i	0.680245	+	0.732985i	$0.261873\pi$
$662$	−39.9913	+	69.2670i	−1.55431	+	2.69214i
$663$	18.2602	−	10.9481i	0.709169	−	0.425190i
$664$	15.2032	+	26.3327i	0.589999	+	1.02191i
$665$	0.747719	+	0.200351i	0.0289953	+	0.00776927i
$666$	−32.7265	−	2.49573i	−1.26813	−	0.0967076i
$667$	−22.0596	−	12.7361i	−0.854149	−	0.493143i
$668$	15.8609	+	4.24991i	0.613675	+	0.164434i
$669$	−6.91774	+	10.9935i	−0.267455	+	0.425033i
$670$	82.7923	+	22.1841i	3.19855	+	0.857048i
$671$	−52.5088	+	14.0697i	−2.02708	+	0.543154i
$672$	14.4925	−	46.8742i	0.559060	−	1.80821i
$673$	−1.97135	−	1.13816i	−0.0759899	−	0.0438728i	0.461524	−	0.887128i	$-0.347303\pi$
$673$	−1.97135	−	1.13816i	−0.0759899	−	0.0438728i	−0.537514	+	0.843255i	$0.680636\pi$
$674$	2.75139	−	10.2683i	0.105980	−	0.395522i
$675$	−24.6485	−	9.72989i	−0.948722	−	0.374504i
$676$	30.1758	−	68.5846i	1.16061	−	2.63787i
$677$	−30.9503	+	17.8691i	−1.18952	+	0.686767i	−0.958196	−	0.286111i	$-0.907637\pi$
$677$	−30.9503	+	17.8691i	−1.18952	+	0.686767i	−0.231319	+	0.972878i	$0.574304\pi$
$678$	24.9234	+	0.948955i	0.957179	+	0.0364444i
$679$	−9.68762			−0.371777
$680$	−56.8134	−	98.4038i	−2.17870	−	3.77361i
$681$	−0.934180	+	24.5354i	−0.0357978	+	0.940198i
$682$	−8.01943	−	8.01943i	−0.307080	−	0.307080i
$683$	−39.4213	+	10.5629i	−1.50841	+	0.404178i	−0.915908	−	0.401389i	$-0.868528\pi$
$683$	−39.4213	+	10.5629i	−1.50841	+	0.404178i	−0.592505	+	0.805567i	$0.701861\pi$
$684$	−2.74311	−	3.19604i	−0.104886	−	0.122203i
$685$	21.9368	−	37.9957i	0.838164	−	1.45174i
$686$	−1.39318	+	2.41306i	−0.0531919	+	0.0921310i
$687$	−22.9075	−	14.4147i	−0.873975	−	0.549956i
$688$	−46.8603	−	27.0548i	−1.78653	−	1.03145i
$689$	6.64309	−	2.17460i	0.253082	−	0.0828458i
$690$	16.9778	−	54.9127i	0.646335	−	2.09049i
$691$	36.3427	−	9.73800i	1.38254	−	0.370451i	0.510498	−	0.859879i	$-0.329461\pi$
$691$	36.3427	−	9.73800i	1.38254	−	0.370451i	0.872044	+	0.489428i	$0.162794\pi$
$692$	−28.8319	+	16.6461i	−1.09602	+	0.632790i
$693$	−13.2545	−	9.06227i	−0.503496	−	0.344247i
$694$	−55.9626	−	55.9626i	−2.12431	−	2.12431i
$695$	−17.2394	+	17.2394i	−0.653928	+	0.653928i
$696$	104.499	+	65.7567i	3.96102	+	2.49250i
$697$	−2.72093	−	10.1546i	−0.103063	−	0.384635i
$698$	72.0667	−	41.6078i	2.72777	−	1.57488i
$699$	−14.8542	+	13.7645i	−0.561837	+	0.520623i
$700$	−7.60782	−	28.3928i	−0.287549	−	1.07315i
$701$	−48.7148			−1.83993			−0.919967	−	0.391997i	$-0.871784\pi$
$701$	−48.7148			−1.83993			−0.919967	+	0.391997i	$0.871784\pi$
$702$	−49.5291	−	16.4912i	−1.86936	−	0.622420i
$703$	−0.956398			−0.0360712
$704$	60.3143	+	225.096i	2.27318	+	8.48362i
$705$	−21.2566	+	19.6973i	−0.800570	+	0.741843i
$706$	−63.8150	+	36.8436i	−2.40171	+	1.38663i
$707$	2.65482	+	9.90791i	0.0998446	+	0.372625i
$708$	44.1374	+	27.7738i	1.65879	+	1.04380i
$709$	−4.60804	+	4.60804i	−0.173058	+	0.173058i	−0.788322	−	0.615263i	$-0.789050\pi$
$709$	−4.60804	+	4.60804i	−0.173058	+	0.173058i	0.615263	+	0.788322i	$0.289050\pi$
$710$	−9.28343	−	9.28343i	−0.348401	−	0.348401i
$711$	32.7196	−	15.7040i	1.22708	−	0.588947i
$712$	105.973	−	61.1836i	3.97151	−	2.29295i
$713$	2.75285	−	0.737623i	0.103095	−	0.0276242i
$714$	4.86007	−	15.7193i	0.181883	−	0.588280i
$715$	−40.9359	+	45.6650i	−1.53091	+	1.70778i
$716$	21.0590	+	12.1584i	0.787011	+	0.454381i
$717$	−14.9740	−	9.42249i	−0.559213	−	0.351889i
$718$	36.7334	−	63.6241i	1.37088	−	2.37443i
$719$	12.1532	−	21.0500i	0.453239	−	0.785033i	−0.545346	−	0.838211i	$-0.683602\pi$
$719$	12.1532	−	21.0500i	0.453239	−	0.785033i	0.998585	+	0.0531782i	$0.0169351\pi$
$720$	−55.9252	+	159.154i	−2.08421	+	5.93134i
$721$	−15.7107	+	4.20966i	−0.585096	+	0.156776i
$722$	37.3179	+	37.3179i	1.38883	+	1.38883i
$723$	−1.12062	+	29.4321i	−0.0416763	+	1.09459i
$724$	−18.1757	−	31.4812i	−0.675493	−	1.16999i
$725$	34.6640			1.28739
$726$	85.0959	+	3.24001i	3.15820	+	0.120248i
$727$	−36.4439	+	21.0409i	−1.35163	+	0.780364i	−0.988478	−	0.151366i	$-0.951633\pi$
$727$	−36.4439	+	21.0409i	−1.35163	+	0.780364i	−0.363152	+	0.931730i	$0.618299\pi$
$728$	−11.7636	−	35.9362i	−0.435989	−	1.33188i
$729$	−6.11170	+	26.2992i	−0.226359	+	0.974044i
$730$	0.158955	−	0.593227i	0.00588317	−	0.0219563i
$731$	−9.02905	−	5.21292i	−0.333952	−	0.192807i
$732$	−29.9514	+	96.8743i	−1.10704	+	3.58058i
$733$	−47.6995	+	12.7810i	−1.76182	+	0.472079i	−0.987084	−	0.160204i	$-0.948785\pi$
$733$	−47.6995	+	12.7810i	−1.76182	+	0.472079i	−0.774738	+	0.632283i	$0.782118\pi$
$734$	−94.7674	−	25.3928i	−3.49793	−	0.937267i
$735$	2.93163	−	4.65886i	0.108135	−	0.171845i
$736$	−102.538	−	27.4749i	−3.77959	−	1.01274i
$737$	−44.8650	−	25.9028i	−1.65263	−	0.954144i
$738$	−14.5482	+	21.2783i	−0.535528	+	0.783264i
$739$	−11.2484	−	3.01401i	−0.413781	−	0.110872i	0.0459221	−	0.998945i	$-0.485377\pi$
$739$	−11.2484	−	3.01401i	−0.413781	−	0.110872i	−0.459703	+	0.888073i	$0.652044\pi$
$740$	35.9614	+	62.2870i	1.32197	+	2.28972i
$741$	−1.47561	−	0.369407i	−0.0542078	−	0.0135705i
$742$	2.70091	−	4.67812i	0.0991536	−	0.171739i
$743$	−25.9250	+	25.9250i	−0.951095	+	0.951095i	−0.998859	−	0.0477641i	$-0.984790\pi$
$743$	−25.9250	+	25.9250i	−0.951095	+	0.951095i	0.0477641	+	0.998859i	$0.484790\pi$
$744$	−13.4697	+	3.06507i	−0.493824	+	0.112371i
$745$			8.59429i			0.314871i
$746$	−63.6698	+	63.6698i	−2.33112	+	2.33112i
$747$	2.88356	−	8.20617i	0.105504	−	0.300248i
$748$	27.2202	+	101.587i	0.995268	+	3.71439i
$749$	4.10223	−	15.3097i	0.149892	−	0.559405i
$750$	0.339694	+	1.49281i	0.0124039	+	0.0545098i
$751$			6.39205i			0.233249i	0.993176	+	0.116625i	$0.0372075\pi$
$751$			6.39205i			0.233249i	−0.993176	+	0.116625i	$0.962793\pi$
$752$	65.8696	+	65.8696i	2.40202	+	2.40202i
$753$	−5.07449	−	22.3003i	−0.184925	−	0.812667i
$754$	68.1845	−	3.72348i	2.48313	−	0.135601i
$755$			25.5765i			0.930826i
$756$	−27.4742	+	11.9225i	−0.999228	+	0.433618i
$757$	2.52969	+	4.38156i	0.0919433	+	0.159250i	0.908329	−	0.418257i	$-0.137359\pi$
$757$	2.52969	+	4.38156i	0.0919433	+	0.159250i	−0.816386	+	0.577507i	$0.804025\pi$
$758$	0.592322			0.0215141
$759$	−18.5021	+	29.4030i	−0.671582	+	1.06726i
$760$	−2.10114	+	7.84157i	−0.0762164	+	0.284444i
$761$	−2.55524	+	9.53628i	−0.0926273	+	0.345690i	−0.996649	−	0.0817967i	$-0.973934\pi$
$761$	−2.55524	+	9.53628i	−0.0926273	+	0.345690i	0.904022	+	0.427486i	$0.140601\pi$
$762$	45.6554	+	1.73832i	1.65392	+	0.0629726i
$763$	2.70166			0.0978067
$764$	−49.0728	−	84.9966i	−1.77539	−	3.07507i
$765$	−10.7757	+	30.6659i	−0.389596	+	1.10873i
$766$		−	32.7582i		−	1.18360i
$767$	18.8061	−	1.02698i	0.679050	−	0.0370821i
$768$	154.066	+	47.6339i	5.55938	+	1.71884i
$769$	9.87623	+	9.87623i	0.356146	+	0.356146i	0.862390	−	0.506244i	$-0.168967\pi$
$769$	9.87623	+	9.87623i	0.356146	+	0.356146i	−0.506244	+	0.862390i	$0.668967\pi$
$770$			47.3936i			1.70795i
$771$	−25.0711	+	23.2320i	−0.902915	+	0.836680i
$772$	19.8482	−	74.0746i	0.714354	−	2.66600i
$773$	−1.97616	−	7.37514i	−0.0710776	−	0.265265i	0.921238	−	0.389000i	$-0.127179\pi$
$773$	−1.97616	−	7.37514i	−0.0710776	−	0.265265i	−0.992315	+	0.123735i	$0.960513\pi$
$774$	4.71946	+	25.1235i	0.169637	+	0.903045i
$775$	−2.74243	+	2.74243i	−0.0985110	+	0.0985110i
$776$		−	101.597i		−	3.64713i
$777$	−2.00884	+	6.49736i	−0.0720668	+	0.233092i
$778$	3.12612	−	3.12612i	0.112077	−	0.112077i
$779$	−0.375551	+	0.650474i	−0.0134555	+	0.0233056i
$780$	31.4259	+	109.991i	1.12523	+	3.93832i
$781$	3.96757	+	6.87204i	0.141971	+	0.245901i
$782$	−34.3861	−	9.21374i	−1.22965	−	0.329483i
$783$	−5.19519	−	34.9346i	−0.185661	−	1.24846i
$784$	−15.3233	−	8.84693i	−0.547262	−	0.315962i
$785$	10.6803	+	2.86178i	0.381197	+	0.102141i
$786$	−35.8844	−	68.0047i	−1.27995	−	2.42565i
$787$	31.8934	+	8.54580i	1.13688	+	0.304625i	0.777694	−	0.628643i	$-0.216389\pi$
$787$	31.8934	+	8.54580i	1.13688	+	0.304625i	0.359182	+	0.933268i	$0.383056\pi$
$788$	−38.6381	+	10.3530i	−1.37642	+	0.368812i
$789$	−28.9861	+	6.59587i	−1.03193	+	0.234819i
$790$	−92.7742	−	53.5632i	−3.30076	−	1.90569i
$791$	1.33758	−	4.99193i	0.0475590	−	0.177493i
$792$	95.0390	−	139.004i	3.37706	−	4.93930i
$793$	11.3930	+	34.8041i	0.404579	+	1.23593i
$794$	12.4602	−	7.19390i	0.442196	−	0.255302i
$795$	−5.68345	+	9.03199i	−0.201571	+	0.320332i
$796$	−4.10371			−0.145452
$797$	−2.51964	−	4.36415i	−0.0892504	−	0.154586i	0.817944	−	0.575298i	$-0.195114\pi$
$797$	−2.51964	−	4.36415i	−0.0892504	−	0.154586i	−0.907194	+	0.420712i	$0.861780\pi$
$798$	−1.03967	+	0.548609i	−0.0368039	+	0.0194205i
$799$	12.6918	+	12.6918i	0.449003	+	0.449003i
$800$	139.539	−	37.3894i	4.93345	−	1.32192i
$801$	−33.0248	−	11.6046i	−1.16687	−	0.410027i
$802$	−35.2994	+	61.1403i	−1.24646	+	2.15894i
$803$	−0.185600	+	0.321469i	−0.00654968	+	0.0113444i
$804$	−85.4637	+	45.0971i	−3.01407	+	1.59045i
$805$	−10.3141	−	5.95483i	−0.363523	−	0.209880i
$806$	−5.09982	+	5.68898i	−0.179633	+	0.200386i
$807$	−4.92563	+	1.12084i	−0.173391	+	0.0394555i
$808$	−103.907	+	27.8419i	−3.65545	+	0.979475i
$809$	−8.69782	+	5.02169i	−0.305799	+	0.176553i	−0.645045	−	0.764145i	$-0.723161\pi$
$809$	−8.69782	+	5.02169i	−0.305799	+	0.176553i	0.339246	+	0.940698i	$0.389828\pi$
$810$	74.2631	−	28.9213i	2.60934	−	1.01619i
$811$	10.5237	+	10.5237i	0.369537	+	0.369537i	0.867308	−	0.497771i	$-0.165848\pi$
$811$	10.5237	+	10.5237i	0.369537	+	0.369537i	−0.497771	+	0.867308i	$0.665848\pi$
$812$	27.7024	−	27.7024i	0.972165	−	0.972165i
$813$	26.9017	−	14.1954i	0.943482	−	0.497853i
$814$	−15.1551	−	56.5597i	−0.531187	−	1.98242i
$815$	54.1167	−	31.2443i	1.89563	−	1.09444i
$816$	99.8202	+	30.8622i	3.49441	+	1.08039i
$817$	0.192791	+	0.719504i	0.00674489	+	0.0251723i
$818$	−24.2900			−0.849281
$819$	−5.60900	+	9.24874i	−0.195994	+	0.323177i
$820$	56.4843			1.97252
$821$	−4.63684	−	17.3049i	−0.161827	−	0.603946i	−0.998424	−	0.0561267i	$-0.982125\pi$
$821$	−4.63684	−	17.3049i	−0.161827	−	0.603946i	0.836597	−	0.547819i	$-0.184542\pi$
$822$	14.7831	+	64.9655i	0.515619	+	2.26593i
$823$	15.4695	−	8.93130i	0.539232	−	0.311326i	−0.205536	−	0.978650i	$-0.565894\pi$
$823$	15.4695	−	8.93130i	0.539232	−	0.311326i	0.744768	+	0.667324i	$0.232560\pi$
$824$	−44.1481	−	164.763i	−1.53797	−	5.73979i
$825$	1.79872	−	47.2418i	0.0626234	−	1.64475i
$826$	10.2919	−	10.2919i	0.358102	−	0.358102i
$827$	6.93363	+	6.93363i	0.241106	+	0.241106i	0.817308	−	0.576202i	$-0.195466\pi$
$827$	6.93363	+	6.93363i	0.241106	+	0.241106i	−0.576202	+	0.817308i	$0.695466\pi$
$828$	28.0389	+	58.4194i	0.974418	+	2.03021i
$829$	−11.6387	+	6.71961i	−0.404229	+	0.233382i	−0.688307	−	0.725419i	$-0.741646\pi$
$829$	−11.6387	+	6.71961i	−0.404229	+	0.233382i	0.284078	+	0.958801i	$0.408312\pi$
$830$	−24.7993	+	6.64494i	−0.860795	+	0.230649i
$831$	17.2420	+	18.6070i	0.598119	+	0.645469i
$832$	149.199	−	48.8399i	5.17254	−	1.69322i
$833$	−2.95250	−	1.70463i	−0.102298	−	0.0590619i
$834$	1.40864	−	36.9968i	0.0487773	−	1.28109i
$835$	−4.52690	+	7.84081i	−0.156660	+	0.271343i
$836$	3.75701	−	6.50734i	0.129939	−	0.225061i
$837$	3.17486	+	2.35282i	0.109739	+	0.0813255i
$838$	−37.5667	+	10.0660i	−1.29772	+	0.347723i
$839$	−1.39204	−	1.39204i	−0.0480586	−	0.0480586i	0.682669	−	0.730728i	$-0.260819\pi$
$839$	−1.39204	−	1.39204i	−0.0480586	−	0.0480586i	−0.730728	+	0.682669i	$0.760819\pi$
$840$	48.8590	+	30.7449i	1.68580	+	1.06080i
$841$	8.60026	+	14.8961i	0.296561	+	0.513658i
$842$	−54.2173			−1.86845
$843$	−10.2167	−	19.3617i	−0.351882	−	0.666852i
$844$	94.4113	−	54.5084i	3.24977	−	1.87626i
$845$	32.2210	+	25.8587i	1.10844	+	0.889567i
$846$	3.34637	−	43.8811i	0.115051	−	1.50866i
$847$	4.56690	−	17.0439i	0.156920	−	0.585635i
$848$	29.7068	+	17.1512i	1.02014	+	0.588976i
$849$	−0.355249	−	0.383372i	−0.0121921	−	0.0131573i
$850$	46.7946	−	12.5386i	1.60504	−	0.430069i
$851$	14.2130	+	3.80837i	0.487217	+	0.130549i
$852$	14.7906	+	0.563148i	0.506716	+	0.0192931i
$853$	28.0427	+	7.51402i	0.960164	+	0.257275i	0.704670	−	0.709535i	$-0.251095\pi$
$853$	28.0427	+	7.51402i	0.960164	+	0.257275i	0.255494	+	0.966811i	$0.417762\pi$
$854$	24.5093	+	14.1504i	0.838691	+	0.484218i
$855$	2.09363	−	1.00485i	0.0716006	−	0.0343653i
$856$	160.558	+	43.0214i	5.48776	+	1.47044i
$857$	1.12108	+	1.94177i	0.0382954	+	0.0663295i	0.884538	−	0.466468i	$-0.154474\pi$
$857$	1.12108	+	1.94177i	0.0382954	+	0.0663295i	−0.846242	+	0.532798i	$0.821141\pi$
$858$	−1.53644	−	93.1185i	−0.0524531	−	3.17901i
$859$	4.74807	−	8.22390i	0.162002	−	0.280596i	−0.773585	−	0.633693i	$-0.781538\pi$
$859$	4.74807	−	8.22390i	0.162002	−	0.280596i	0.935587	+	0.353097i	$0.114872\pi$
$860$	39.6098	−	39.6098i	1.35068	−	1.35068i
$861$	3.63023	+	3.91761i	0.123718	+	0.133512i
$862$			76.6778i			2.61166i
$863$	29.7217	−	29.7217i	1.01174	−	1.01174i	0.0118083	−	0.999930i	$-0.496241\pi$
$863$	29.7217	−	29.7217i	1.01174	−	1.01174i	0.999930	−	0.0118083i	$-0.00375878\pi$
$864$	−58.5945	−	135.025i	−1.99342	−	4.59364i
$865$	−4.75101	−	17.7310i	−0.161539	−	0.602873i
$866$	3.99415	−	14.9064i	0.135727	−	0.506539i
$867$	−8.89762	−	2.75095i	−0.302179	−	0.0934272i
$868$			4.38334i			0.148780i
$869$	45.7839	+	45.7839i	1.55311	+	1.55311i
$870$	−76.4676	+	70.8582i	−2.59249	+	2.40232i
$871$	−15.7759	+	31.1307i	−0.534547	+	1.05482i
$872$			28.3332i			0.959483i
$873$	−22.0537	+	18.9284i	−0.746404	+	0.640629i
$874$	1.27171	+	2.20266i	0.0430162	+	0.0745062i
$875$	0.317227			0.0107242
$876$	0.323132	+	0.612368i	0.0109176	+	0.0206900i
$877$	−11.8171	+	44.1019i	−0.399034	+	1.48921i	0.415766	+	0.909472i	$0.363514\pi$
$877$	−11.8171	+	44.1019i	−0.399034	+	1.48921i	−0.814799	+	0.579743i	$0.803153\pi$
$878$	−14.0291	+	52.3573i	−0.473459	+	1.76697i
$879$	−0.731983	−	1.38718i	−0.0246892	−	0.0467885i
$880$	−300.957			−10.1453
$881$	−11.7979	−	20.4345i	−0.397480	−	0.688456i	0.595934	−	0.803034i	$-0.296782\pi$
$881$	−11.7979	−	20.4345i	−0.397480	−	0.688456i	−0.993414	+	0.114577i	$0.963449\pi$
$882$	1.54327	+	8.21539i	0.0519644	+	0.276626i
$883$		−	38.1135i		−	1.28262i	−0.767281	−	0.641311i	$-0.778391\pi$
$883$		−	38.1135i		−	1.28262i	0.767281	−	0.641311i	$-0.221609\pi$
$884$	67.3343	−	22.0417i	2.26470	−	0.741344i
$885$	−21.0907	+	19.5435i	−0.708955	+	0.656949i
$886$	0.131204	+	0.131204i	0.00440789	+	0.00440789i
$887$			31.9646i			1.07327i	0.843815	+	0.536634i	$0.180304\pi$
$887$			31.9646i			1.07327i	−0.843815	+	0.536634i	$0.819696\pi$
$888$	−68.1399	−	21.0674i	−2.28663	−	0.706975i
$889$	2.45022	−	9.14433i	0.0821776	−	0.306691i
$890$	26.7418	+	99.8018i	0.896388	+	3.34536i
$891$	−47.8802	+	5.26751i	−1.60405	+	0.176468i
$892$	−30.5638	+	30.5638i	−1.02335	+	1.02335i
$893$		−	1.28238i		−	0.0429131i
$894$	−8.87081	−	9.57305i	−0.296684	−	0.320171i
$895$	−9.48067	+	9.48067i	−0.316904	+	0.316904i
$896$	32.3337	−	56.0035i	1.08019	−	1.87095i
$897$	20.4580	+	11.3656i	0.683074	+	0.379487i
$898$	−39.8058	−	68.9457i	−1.32834	−	2.30075i
$899$	−4.99302	−	1.33788i	−0.166526	−	0.0446206i
$900$	−72.7950	−	49.7709i	−2.42650	−	1.65903i
$901$	5.72392	+	3.30471i	0.190691	+	0.110096i
$902$	−44.4189	−	11.9020i	−1.47899	−	0.396294i
$903$	5.29295	+	0.201528i	0.176138	+	0.00670643i
$904$	52.3520	+	14.0277i	1.74120	+	0.466553i
$905$	19.3603	−	5.18757i	0.643557	−	0.172441i
$906$	−26.3994	−	28.4893i	−0.877063	−	0.946494i
$907$	−0.323542	−	0.186797i	−0.0107430	−	0.00620249i	0.494619	−	0.869110i	$-0.335308\pi$
$907$	−0.323542	−	0.186797i	−0.0107430	−	0.00620249i	−0.505362	+	0.862908i	$0.668641\pi$
$908$	−21.1472	+	78.9223i	−0.701794	+	2.61913i
$909$	25.4024	+	17.3680i	0.842546	+	0.576060i
$910$	31.8801	−	1.74093i	1.05681	−	0.0577114i
$911$	38.8949	−	22.4560i	1.28864	−	0.743999i	0.310232	−	0.950661i	$-0.399593\pi$
$911$	38.8949	−	22.4560i	1.28864	−	0.743999i	0.978413	+	0.206661i	$0.0662599\pi$
$912$	−3.48375	−	6.60207i	−0.115359	−	0.218616i
$913$	15.5177			0.513560
$914$	23.8360	+	41.2851i	0.788424	+	1.36559i
$915$	−47.3198	−	29.7764i	−1.56434	−	0.984376i
$916$	−63.6867	−	63.6867i	−2.10427	−	2.10427i
$917$	−15.3895	+	4.12361i	−0.508207	+	0.136174i
$918$	−19.6497	−	45.2807i	−0.648537	−	1.49449i
$919$	−12.0634	+	20.8945i	−0.397936	+	0.689245i	−0.993471	−	0.114084i	$-0.963607\pi$
$919$	−12.0634	+	20.8945i	−0.397936	+	0.689245i	0.595535	+	0.803329i	$0.296940\pi$
$920$	62.4502	−	108.167i	2.05892	−	3.56616i
$921$	0.923521	−	24.2554i	0.0304310	−	0.799244i
$922$	−28.2616	−	16.3168i	−0.930745	−	0.537366i
$923$	4.47684	−	2.92129i	0.147357	−	0.0961553i
$924$	−36.3168	−	39.1917i	−1.19473	−	1.28931i
$925$	−19.3419	+	5.18265i	−0.635958	+	0.170404i
$926$	94.7151	−	54.6838i	3.11253	−	1.79702i
$927$	−27.5399	+	40.2799i	−0.904530	+	1.32297i
$928$	136.146	+	136.146i	4.46922	+	4.46922i
$929$	18.0690	−	18.0690i	0.592825	−	0.592825i	−0.345569	−	0.938393i	$-0.612314\pi$
$929$	18.0690	−	18.0690i	0.592825	−	0.592825i	0.938393	+	0.345569i	$0.112314\pi$
$930$	0.443786	−	11.6556i	0.0145523	−	0.382203i
$931$	0.0630426	+	0.235278i	0.00206614	+	0.00771093i
$932$	−58.3619	+	33.6953i	−1.91171	+	1.10372i
$933$	1.74836	+	7.68331i	0.0572387	+	0.251540i
$934$	−11.9384	−	44.5548i	−0.390637	−	1.45788i
$935$	−57.9885			−1.89643
$936$	−96.9945	−	58.8234i	−3.17036	−	1.92270i
$937$	41.5755			1.35821			0.679106	−	0.734040i	$-0.262368\pi$
$937$	41.5755			1.35821			0.679106	+	0.734040i	$0.262368\pi$
$938$	6.98049	+	26.0515i	0.227921	+	0.850613i
$939$	−37.2661	−	11.5219i	−1.21613	−	0.376002i
$940$	−83.5169	+	48.2185i	−2.72402	+	1.57271i
$941$	−8.61636	−	32.1567i	−0.280885	−	1.04828i	−0.951794	−	0.306738i	$-0.900762\pi$
$941$	−8.61636	−	32.1567i	−0.280885	−	1.04828i	0.670909	−	0.741540i	$-0.265904\pi$
$942$	−14.8505	+	7.83625i	−0.483855	+	0.255319i
$943$	8.17126	−	8.17126i	0.266093	−	0.266093i
$944$	65.3554	+	65.3554i	2.12714	+	2.12714i
$945$	−2.42904	−	16.3339i	−0.0790168	−	0.531340i
$946$	−39.4953	+	22.8026i	−1.28410	+	0.741377i
$947$	36.0412	−	9.65720i	1.17118	−	0.313817i	0.379758	−	0.925086i	$-0.376007\pi$
$947$	36.0412	−	9.65720i	1.17118	−	0.313817i	0.791423	+	0.611269i	$0.209341\pi$
$948$	117.763	−	26.7974i	3.82477	−	0.870338i
$949$	0.223059	+	0.113038i	0.00724080	+	0.00366938i
$950$	−2.99751	−	1.73061i	−0.0972521	−	0.0561485i
$951$	16.9392	−	8.93840i	0.549291	−	0.289847i
$952$	17.8770	−	30.9638i	0.579396	−	1.00354i
$953$	23.6155	−	40.9033i	0.764982	−	1.32499i	−0.175274	−	0.984520i	$-0.556081\pi$
$953$	23.6155	−	40.9033i	0.764982	−	1.32499i	0.940256	−	0.340468i	$-0.110586\pi$
$954$	−2.99188	−	15.9269i	−0.0968656	−	0.515652i
$955$	52.2712	−	14.0060i	1.69146	−	0.453224i
$956$	−41.6302	−	41.6302i	−1.34642	−	1.34642i
$957$	55.7274	−	29.4060i	1.80141	−	0.950562i
$958$	57.3724	+	99.3719i	1.85362	+	3.21056i
$959$	13.8053			0.445798
$960$	−127.646	+	202.852i	−4.11976	+	6.54701i
$961$	−26.3459	+	15.2108i	−0.849868	+	0.490672i
$962$	−37.4891	+	12.2720i	−1.20870	+	0.395665i
$963$	−20.5746	−	42.8676i	−0.663009	−	1.38139i
$964$	−25.3677	+	94.6734i	−0.817037	+	3.04923i
$965$	36.6188	+	21.1419i	1.17880	+	0.680580i
$966$	17.6351	−	4.01292i	0.567400	−	0.129114i
$967$	11.6707	−	3.12716i	0.375305	−	0.100563i	−0.0662353	−	0.997804i	$-0.521099\pi$
$967$	11.6707	−	3.12716i	0.375305	−	0.100563i	0.441541	+	0.897241i	$0.354432\pi$
$968$	178.745	+	47.8945i	5.74508	+	1.53939i
$969$	−0.671251	−	1.27209i	−0.0215637	−	0.0408654i
$970$	82.8619	+	22.2028i	2.66054	+	0.712888i
$971$	13.9506	+	8.05440i	0.447697	+	0.258478i	0.706857	−	0.707356i	$-0.250112\pi$
$971$	13.9506	+	8.05440i	0.447697	+	0.258478i	−0.259160	+	0.965834i	$0.583446\pi$
$972$	−39.2495	+	80.8226i	−1.25893	+	2.59239i
$973$	−7.41010	−	1.98553i	−0.237557	−	0.0636532i
$974$	−3.67604	−	6.36709i	−0.117788	−	0.204015i
$975$	−31.8440	+	0.525420i	−1.01982	+	0.0168269i
$976$	−89.8577	+	155.638i	−2.87627	+	4.98185i
$977$	31.4415	−	31.4415i	1.00590	−	1.00590i	0.00591920	−	0.999982i	$-0.498116\pi$
$977$	31.4415	−	31.4415i	1.00590	−	1.00590i	0.999982	−	0.00591920i	$-0.00188415\pi$
$978$	−28.0302	+	90.6604i	−0.896308	+	2.89900i
$979$		−	62.4491i		−	1.99588i
$980$	12.9524	−	12.9524i	0.413750	−	0.413750i
$981$	6.15028	−	5.27871i	0.196363	−	0.168536i
$982$	−27.2989	−	101.881i	−0.871143	−	3.25115i
$983$	4.14560	−	15.4716i	0.132224	−	0.493467i	−0.867770	−	0.496966i	$-0.834447\pi$
$983$	4.14560	−	15.4716i	0.132224	−	0.493467i	0.999994	+	0.00349953i	$0.00111394\pi$
$984$	−41.0852	+	38.0714i	−1.30975	+	1.21367i
$985$		−	22.0556i		−	0.702750i
$986$	45.6568	+	45.6568i	1.45401	+	1.45401i
$987$	−8.71192	−	2.69354i	−0.277304	−	0.0857362i
$988$	−4.51527	−	2.28818i	−0.143650	−	0.0727966i
$989$		−	11.4603i		−	0.364415i
$990$	92.6011	+	107.891i	2.94306	+	3.42899i
$991$	7.63479	+	13.2238i	0.242527	+	0.420069i	0.961433	−	0.275038i	$-0.0886903\pi$
$991$	7.63479	+	13.2238i	0.242527	+	0.420069i	−0.718906	+	0.695107i	$0.755357\pi$
$992$	−21.5424			−0.683971
$993$	49.6826	+	1.89166i	1.57663	+	0.0600299i
$994$	1.06921	−	3.99034i	0.0339133	−	0.126566i
$995$	0.585626	−	2.18559i	0.0185656	−	0.0692877i
$996$	15.4157	−	24.4982i	0.488464	−	0.776254i
$997$	37.7239			1.19473			0.597364	−	0.801970i	$-0.296215\pi$
$997$	37.7239			1.19473			0.597364	+	0.801970i	$0.296215\pi$
$998$	−61.3510	−	106.263i	−1.94203	−	3.36370i
$999$	8.12194	+	18.7162i	0.256967	+	0.592153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.2	yes	336
9.2	odd	6		819.2.ew.a.596.83	✓	336
13.6	odd	12		819.2.ew.a.617.83	yes	336
117.110	even	12	inner	819.2.fy.a.344.2	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.83	✓	336	9.2	odd	6
819.2.ew.a.617.83	yes	336	13.6	odd	12
819.2.fy.a.50.2	yes	336	1.1	even	1	trivial
819.2.fy.a.344.2	yes	336	117.110	even	12	inner

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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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.721163 - 2.69142i) q^{2} +(-1.27046 + 1.17726i) q^{3} +(-4.99160 + 2.88190i) q^{4} +(-0.822532 - 3.06973i) q^{5} +(4.08470 + 2.57033i) q^{6} +(0.707107 - 0.707107i) q^{7} +(7.41566 + 7.41566i) q^{8} +(0.228118 - 2.99131i) q^{9} +O(q^{10})\)	\(q+(-0.721163 - 2.69142i) q^{2} +(-1.27046 + 1.17726i) q^{3} +(-4.99160 + 2.88190i) q^{4} +(-0.822532 - 3.06973i) q^{5} +(4.08470 + 2.57033i) q^{6} +(0.707107 - 0.707107i) q^{7} +(7.41566 + 7.41566i) q^{8} +(0.228118 - 2.99131i) q^{9} +(-7.66875 + 4.42756i) q^{10} +(5.16975 - 1.38523i) q^{11} +(2.94886 - 9.53775i) q^{12} +(-1.12170 - 3.42663i) q^{13} +(-2.41306 - 1.39318i) q^{14} +(4.65886 + 2.93163i) q^{15} +(8.84693 - 15.3233i) q^{16} +(1.70463 - 2.95250i) q^{17} +(-8.21539 + 1.54327i) q^{18} +(-0.235278 + 0.0630426i) q^{19} +(12.9524 + 12.9524i) q^{20} +(-0.0658997 + 1.73080i) q^{21} +(-7.45646 - 12.9150i) q^{22} +3.74751 q^{23} +(-18.1514 - 0.691111i) q^{24} +(-4.41657 + 2.54991i) q^{25} +(-8.41356 + 5.49012i) q^{26} +(3.23174 + 4.06889i) q^{27} +(-1.49178 + 5.56741i) q^{28} +(-5.88646 - 3.39855i) q^{29} +(4.53043 - 14.6531i) q^{30} +(0.734581 - 0.196830i) q^{31} +(-27.3616 - 7.33152i) q^{32} +(-4.93716 + 7.84601i) q^{33} +(-9.17573 - 2.45863i) q^{34} +(-2.75225 - 1.58901i) q^{35} +(7.48200 + 15.5889i) q^{36} +(3.79267 + 1.01624i) q^{37} +(0.339348 + 0.587768i) q^{38} +(5.45910 + 3.03285i) q^{39} +(16.6645 - 28.8637i) q^{40} +(2.18045 - 2.18045i) q^{41} +(4.70582 - 1.07082i) q^{42} -3.05810i q^{43} +(-21.8132 + 21.8132i) q^{44} +(-9.37017 + 1.76019i) q^{45} +(-2.70257 - 10.0861i) q^{46} +(-1.36262 + 5.08536i) q^{47} +(6.79990 + 29.8827i) q^{48} -1.00000i q^{49} +(10.0479 + 10.0479i) q^{50} +(1.31021 + 5.75782i) q^{51} +(15.4743 + 13.8717i) q^{52} +1.93867i q^{53} +(8.62047 - 11.6323i) q^{54} +(-8.50457 - 14.7303i) q^{55} +10.4873 q^{56} +(0.224693 - 0.357076i) q^{57} +(-4.90182 + 18.2938i) q^{58} +(-1.35198 + 5.04566i) q^{59} +(-31.7039 - 1.20712i) q^{60} -10.1569 q^{61} +(-1.05951 - 1.83512i) q^{62} +(-1.95387 - 2.27648i) q^{63} +43.5410i q^{64} +(-9.59620 + 6.26183i) q^{65} +(24.6774 + 7.62971i) q^{66} +(-6.84443 - 6.84443i) q^{67} +19.6503i q^{68} +(-4.76104 + 4.41179i) q^{69} +(-2.29187 + 8.55338i) q^{70} +(0.383730 + 1.43210i) q^{71} +(23.8742 - 20.4909i) q^{72} +(-0.0490419 + 0.0490419i) q^{73} -10.9405i q^{74} +(2.60916 - 8.43900i) q^{75} +(0.992732 - 0.992732i) q^{76} +(2.67606 - 4.63507i) q^{77} +(4.22576 - 16.8799i) q^{78} +(6.04884 + 10.4769i) q^{79} +(-54.3154 - 14.5538i) q^{80} +(-8.89592 - 1.36475i) q^{81} +(-7.44097 - 4.29604i) q^{82} +(2.80056 + 0.750407i) q^{83} +(-4.65904 - 8.82937i) q^{84} +(-10.4655 - 2.80422i) q^{85} +(-8.23063 + 2.20539i) q^{86} +(11.4795 - 2.61218i) q^{87} +(48.6094 + 28.0647i) q^{88} +(3.01993 - 11.2705i) q^{89} +(11.4948 + 23.9497i) q^{90} +(-3.21615 - 1.62983i) q^{91} +(-18.7061 + 10.8000i) q^{92} +(-0.701532 + 1.11486i) q^{93} +14.6695 q^{94} +(0.387048 + 0.670387i) q^{95} +(43.3928 - 22.8973i) q^{96} +(-6.85018 - 6.85018i) q^{97} +(-2.69142 + 0.721163i) q^{98} +(-2.96434 - 15.7803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

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