LMFDB - Embedded newform 693.2.l.b.529.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(529,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("693.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.l (of order $3$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$74$
Relative dimension:	$37$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.8
Character	$\chi$	$=$	693.529
Dual form			693.2.l.b.562.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80662 q^{2} +(0.189816 - 1.72162i) q^{3} +1.26386 q^{4} +(-0.196591 + 0.340506i) q^{5} +(-0.342924 + 3.11030i) q^{6} +(2.59423 + 0.519577i) q^{7} +1.32992 q^{8} +(-2.92794 - 0.653580i) q^{9} +O(q^{10})$	\(q-1.80662 q^{2} +(0.189816 - 1.72162i) q^{3} +1.26386 q^{4} +(-0.196591 + 0.340506i) q^{5} +(-0.342924 + 3.11030i) q^{6} +(2.59423 + 0.519577i) q^{7} +1.32992 q^{8} +(-2.92794 - 0.653580i) q^{9} +(0.355165 - 0.615163i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.239900 - 2.17588i) q^{12} +(3.40582 + 5.89906i) q^{13} +(-4.68678 - 0.938676i) q^{14} +(0.548905 + 0.403088i) q^{15} -4.93038 q^{16} +(-1.97397 + 3.41902i) q^{17} +(5.28966 + 1.18077i) q^{18} +(0.212295 + 0.367706i) q^{19} +(-0.248464 + 0.430352i) q^{20} +(1.38694 - 4.36765i) q^{21} +(0.903308 + 1.56457i) q^{22} +(0.693594 - 1.20134i) q^{23} +(0.252440 - 2.28962i) q^{24} +(2.42270 + 4.19625i) q^{25} +(-6.15301 - 10.6573i) q^{26} +(-1.68098 + 4.91674i) q^{27} +(3.27874 + 0.656672i) q^{28} +(-4.27135 + 7.39820i) q^{29} +(-0.991661 - 0.728226i) q^{30} -6.71654 q^{31} +6.24745 q^{32} +(-1.58587 + 0.696424i) q^{33} +(3.56621 - 6.17686i) q^{34} +(-0.686922 + 0.781207i) q^{35} +(-3.70050 - 0.826033i) q^{36} +(4.78657 + 8.29058i) q^{37} +(-0.383535 - 0.664303i) q^{38} +(10.8024 - 4.74380i) q^{39} +(-0.261451 + 0.452847i) q^{40} +(-2.69420 - 4.66649i) q^{41} +(-2.50567 + 7.89067i) q^{42} +(3.00948 - 5.21258i) q^{43} +(-0.631930 - 1.09453i) q^{44} +(0.798155 - 0.868493i) q^{45} +(-1.25306 + 2.17036i) q^{46} +5.60094 q^{47} +(-0.935863 + 8.48823i) q^{48} +(6.46008 + 2.69581i) q^{49} +(-4.37689 - 7.58100i) q^{50} +(5.51156 + 4.04741i) q^{51} +(4.30448 + 7.45558i) q^{52} +(1.15378 - 1.99841i) q^{53} +(3.03689 - 8.88265i) q^{54} +0.393182 q^{55} +(3.45013 + 0.690998i) q^{56} +(0.673346 - 0.295695i) q^{57} +(7.71669 - 13.3657i) q^{58} -6.95559 q^{59} +(0.693739 + 0.509447i) q^{60} +12.8303 q^{61} +12.1342 q^{62} +(-7.25617 - 3.21683i) q^{63} -1.42598 q^{64} -2.67822 q^{65} +(2.86506 - 1.25817i) q^{66} -4.37024 q^{67} +(-2.49482 + 4.32116i) q^{68} +(-1.93659 - 1.42214i) q^{69} +(1.24100 - 1.41134i) q^{70} +7.99918 q^{71} +(-3.89394 - 0.869212i) q^{72} +(4.58593 - 7.94307i) q^{73} +(-8.64749 - 14.9779i) q^{74} +(7.68420 - 3.37446i) q^{75} +(0.268311 + 0.464728i) q^{76} +(-0.847149 - 2.50646i) q^{77} +(-19.5158 + 8.57021i) q^{78} +2.27947 q^{79} +(0.969269 - 1.67882i) q^{80} +(8.14567 + 3.82729i) q^{81} +(4.86738 + 8.43054i) q^{82} +(-1.01097 + 1.75104i) q^{83} +(1.75290 - 5.52010i) q^{84} +(-0.776132 - 1.34430i) q^{85} +(-5.43698 + 9.41712i) q^{86} +(11.9261 + 8.75794i) q^{87} +(-0.664962 - 1.15175i) q^{88} +(3.79532 + 6.57369i) q^{89} +(-1.44196 + 1.56903i) q^{90} +(5.77048 + 17.0731i) q^{91} +(0.876605 - 1.51832i) q^{92} +(-1.27490 + 11.5633i) q^{93} -10.1187 q^{94} -0.166941 q^{95} +(1.18586 - 10.7557i) q^{96} +(-3.12673 + 5.41566i) q^{97} +(-11.6709 - 4.87028i) q^{98} +(0.897953 + 2.86246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q + 80 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 74 * q + 80 * q^4 - 7 * q^5 - 23 * q^6 - q^7 - 6 * q^8 - 4 * q^9	\( 74 q + 80 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 9 q^{10} - 37 q^{11} - 4 q^{12} - 25 q^{13} + 10 q^{14} + 18 q^{15} + 92 q^{16} - 6 q^{17} - 6 q^{18} - 13 q^{19} - 15 q^{20} + 11 q^{21} + 4 q^{23} - 33 q^{24} - 46 q^{25} - 12 q^{26} - 21 q^{27} - 26 q^{28} - 9 q^{29} - 17 q^{30} + 66 q^{31} + 8 q^{32} - 16 q^{34} - 30 q^{35} - 57 q^{36} + 18 q^{37} - 29 q^{38} - 14 q^{39} - 57 q^{40} - 2 q^{41} - 48 q^{42} - 10 q^{43} - 40 q^{44} + 32 q^{45} - 12 q^{46} - 14 q^{47} + 46 q^{48} + 11 q^{49} - 46 q^{50} + 14 q^{51} - 36 q^{52} + 13 q^{53} + 10 q^{54} + 14 q^{55} + 3 q^{56} - 63 q^{57} + 22 q^{58} + 66 q^{59} + 122 q^{60} + 110 q^{61} + 36 q^{62} + 18 q^{63} + 122 q^{64} - 46 q^{65} + 16 q^{66} - 68 q^{67} - 20 q^{68} - 15 q^{69} + 43 q^{70} - 8 q^{71} + 45 q^{72} - 66 q^{73} - 16 q^{74} + 15 q^{75} - 77 q^{76} + 2 q^{77} + 94 q^{78} - 8 q^{79} - 29 q^{80} - 28 q^{81} - 54 q^{82} + 7 q^{83} + 75 q^{84} + 5 q^{85} - 10 q^{87} + 3 q^{88} - 26 q^{89} + 12 q^{90} - 35 q^{91} - 15 q^{92} - 37 q^{93} + 64 q^{94} + 76 q^{95} - 140 q^{96} - 29 q^{97} + 27 q^{98} + 2 q^{99}+O(q^{100}) \) 74 * q + 80 * q^4 - 7 * q^5 - 23 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 9 * q^10 - 37 * q^11 - 4 * q^12 - 25 * q^13 + 10 * q^14 + 18 * q^15 + 92 * q^16 - 6 * q^17 - 6 * q^18 - 13 * q^19 - 15 * q^20 + 11 * q^21 + 4 * q^23 - 33 * q^24 - 46 * q^25 - 12 * q^26 - 21 * q^27 - 26 * q^28 - 9 * q^29 - 17 * q^30 + 66 * q^31 + 8 * q^32 - 16 * q^34 - 30 * q^35 - 57 * q^36 + 18 * q^37 - 29 * q^38 - 14 * q^39 - 57 * q^40 - 2 * q^41 - 48 * q^42 - 10 * q^43 - 40 * q^44 + 32 * q^45 - 12 * q^46 - 14 * q^47 + 46 * q^48 + 11 * q^49 - 46 * q^50 + 14 * q^51 - 36 * q^52 + 13 * q^53 + 10 * q^54 + 14 * q^55 + 3 * q^56 - 63 * q^57 + 22 * q^58 + 66 * q^59 + 122 * q^60 + 110 * q^61 + 36 * q^62 + 18 * q^63 + 122 * q^64 - 46 * q^65 + 16 * q^66 - 68 * q^67 - 20 * q^68 - 15 * q^69 + 43 * q^70 - 8 * q^71 + 45 * q^72 - 66 * q^73 - 16 * q^74 + 15 * q^75 - 77 * q^76 + 2 * q^77 + 94 * q^78 - 8 * q^79 - 29 * q^80 - 28 * q^81 - 54 * q^82 + 7 * q^83 + 75 * q^84 + 5 * q^85 - 10 * q^87 + 3 * q^88 - 26 * q^89 + 12 * q^90 - 35 * q^91 - 15 * q^92 - 37 * q^93 + 64 * q^94 + 76 * q^95 - 140 * q^96 - 29 * q^97 + 27 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.80662			−1.27747			−0.638735	−	0.769427i	$-0.720542\pi$
$2$	−1.80662			−1.27747			−0.638735	+	0.769427i	$0.720542\pi$
$3$	0.189816	−	1.72162i	0.109590	−	0.993977i
$3$	0.189816	−	1.72162i	0.109590	−	0.993977i
$4$	1.26386			0.631930
$5$	−0.196591	+	0.340506i	−0.0879183	+	0.152279i	−0.906631	−	0.421924i	$-0.861355\pi$
$5$	−0.196591	+	0.340506i	−0.0879183	+	0.152279i	0.818713	+	0.574203i	$0.194688\pi$
$6$	−0.342924	+	3.11030i	−0.139998	+	1.26978i
$7$	2.59423	+	0.519577i	0.980528	+	0.196382i
$7$	2.59423	+	0.519577i	0.980528	+	0.196382i
$8$	1.32992			0.470199
$9$	−2.92794	−	0.653580i	−0.975980	−	0.217860i
$10$	0.355165	−	0.615163i	0.112313	−	0.194532i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	0.239900	−	2.17588i	0.0692532	−	0.628123i
$13$	3.40582	+	5.89906i	0.944606	+	1.63610i	0.756539	+	0.653948i	$0.226889\pi$
$13$	3.40582	+	5.89906i	0.944606	+	1.63610i	0.188066	+	0.982156i	$0.439778\pi$
$14$	−4.68678	−	0.938676i	−1.25259	−	0.250872i
$15$	0.548905	+	0.403088i	0.141727	+	0.104077i
$16$	−4.93038			−1.23259
$17$	−1.97397	+	3.41902i	−0.478759	+	0.829235i	−0.999703	−	0.0243559i	$-0.992247\pi$
$17$	−1.97397	+	3.41902i	−0.478759	+	0.829235i	0.520945	+	0.853591i	$0.325580\pi$
$18$	5.28966	+	1.18077i	1.24679	+	0.278310i
$19$	0.212295	+	0.367706i	0.0487038	+	0.0843575i	0.889350	−	0.457228i	$-0.151158\pi$
$19$	0.212295	+	0.367706i	0.0487038	+	0.0843575i	−0.840646	+	0.541585i	$0.817824\pi$
$20$	−0.248464	+	0.430352i	−0.0555581	+	0.0962295i
$21$	1.38694	−	4.36765i	0.302655	−	0.953100i
$22$	0.903308	+	1.56457i	0.192586	+	0.333568i
$23$	0.693594	−	1.20134i	0.144624	−	0.250497i	−0.784608	−	0.619992i	$-0.787136\pi$
$23$	0.693594	−	1.20134i	0.144624	−	0.250497i	0.929233	+	0.369495i	$0.120469\pi$
$24$	0.252440	−	2.28962i	0.0515292	−	0.467367i
$25$	2.42270	+	4.19625i	0.484541	+	0.839249i
$26$	−6.15301	−	10.6573i	−1.20671	−	2.09007i
$27$	−1.68098	+	4.91674i	−0.323506	+	0.946226i
$28$	3.27874	+	0.656672i	0.619624	+	0.124099i
$29$	−4.27135	+	7.39820i	−0.793170	+	1.37381i	0.130824	+	0.991406i	$0.458238\pi$
$29$	−4.27135	+	7.39820i	−0.793170	+	1.37381i	−0.923994	+	0.382406i	$0.875096\pi$
$30$	−0.991661	−	0.728226i	−0.181052	−	0.132955i
$31$	−6.71654			−1.20633			−0.603163	−	0.797618i	$-0.706093\pi$
$31$	−6.71654			−1.20633			−0.603163	+	0.797618i	$0.706093\pi$
$32$	6.24745			1.10440
$33$	−1.58587	+	0.696424i	−0.276065	+	0.121232i
$34$	3.56621	−	6.17686i	0.611600	−	1.05932i
$35$	−0.686922	+	0.781207i	−0.116111	+	0.132048i
$36$	−3.70050	−	0.826033i	−0.616751	−	0.137672i
$37$	4.78657	+	8.29058i	0.786907	+	1.36296i	0.927853	+	0.372946i	$0.121652\pi$
$37$	4.78657	+	8.29058i	0.786907	+	1.36296i	−0.140946	+	0.990017i	$0.545014\pi$
$38$	−0.383535	−	0.664303i	−0.0622177	−	0.107764i
$39$	10.8024	−	4.74380i	1.72977	−	0.759615i
$40$	−0.261451	+	0.452847i	−0.0413391	+	0.0716014i
$41$	−2.69420	−	4.66649i	−0.420763	−	0.728783i	0.575251	−	0.817977i	$-0.304904\pi$
$41$	−2.69420	−	4.66649i	−0.420763	−	0.728783i	−0.996014	+	0.0891940i	$0.971571\pi$
$42$	−2.50567	+	7.89067i	−0.386633	+	1.21756i
$43$	3.00948	−	5.21258i	0.458942	−	0.794911i	−0.539964	−	0.841688i	$-0.681562\pi$
$43$	3.00948	−	5.21258i	0.458942	−	0.794911i	0.998905	+	0.0467779i	$0.0148953\pi$
$44$	−0.631930	−	1.09453i	−0.0952670	−	0.165007i
$45$	0.798155	−	0.868493i	0.118982	−	0.129467i
$46$	−1.25306	+	2.17036i	−0.184753	+	0.320002i
$47$	5.60094			0.816981			0.408491	−	0.912762i	$-0.366055\pi$
$47$	5.60094			0.816981			0.408491	+	0.912762i	$0.366055\pi$
$48$	−0.935863	+	8.48823i	−0.135080	+	1.22517i
$49$	6.46008	+	2.69581i	0.922869	+	0.385115i
$50$	−4.37689	−	7.58100i	−0.618986	−	1.07212i
$51$	5.51156	+	4.04741i	0.771773	+	0.566751i
$52$	4.30448	+	7.45558i	0.596924	+	1.03390i
$53$	1.15378	−	1.99841i	0.158484	−	0.274503i	−0.775838	−	0.630932i	$-0.782673\pi$
$53$	1.15378	−	1.99841i	0.158484	−	0.274503i	0.934322	+	0.356429i	$0.116006\pi$
$54$	3.03689	−	8.88265i	0.413269	−	1.20878i
$55$	0.393182			0.0530167
$56$	3.45013	+	0.690998i	0.461043	+	0.0923384i
$57$	0.673346	−	0.295695i	0.0891868	−	0.0391657i
$58$	7.71669	−	13.3657i	1.01325	−	1.75500i
$59$	−6.95559			−0.905540			−0.452770	−	0.891627i	$-0.649564\pi$
$59$	−6.95559			−0.905540			−0.452770	+	0.891627i	$0.649564\pi$
$60$	0.693739	+	0.509447i	0.0895613	+	0.0657693i
$61$	12.8303			1.64275			0.821377	−	0.570386i	$-0.193206\pi$
$61$	12.8303			1.64275			0.821377	+	0.570386i	$0.193206\pi$
$62$	12.1342			1.54104
$63$	−7.25617	−	3.21683i	−0.914192	−	0.405282i
$64$	−1.42598			−0.178248
$65$	−2.67822			−0.332192
$66$	2.86506	−	1.25817i	0.352665	−	0.154870i
$67$	−4.37024			−0.533910			−0.266955	−	0.963709i	$-0.586018\pi$
$67$	−4.37024			−0.533910			−0.266955	+	0.963709i	$0.586018\pi$
$68$	−2.49482	+	4.32116i	−0.302542	+	0.524018i
$69$	−1.93659	−	1.42214i	−0.233139	−	0.171205i
$70$	1.24100	−	1.41134i	0.148328	−	0.168688i
$71$	7.99918			0.949328			0.474664	−	0.880167i	$-0.342570\pi$
$71$	7.99918			0.949328			0.474664	+	0.880167i	$0.342570\pi$
$72$	−3.89394	−	0.869212i	−0.458905	−	0.102438i
$73$	4.58593	−	7.94307i	0.536743	−	0.929666i	−0.462334	−	0.886706i	$-0.652988\pi$
$73$	4.58593	−	7.94307i	0.536743	−	0.929666i	0.999077	−	0.0429601i	$-0.0136788\pi$
$74$	−8.64749	−	14.9779i	−1.00525	−	1.74114i
$75$	7.68420	−	3.37446i	0.887295	−	0.389649i
$76$	0.268311	+	0.464728i	0.0307774	+	0.0533080i
$77$	−0.847149	−	2.50646i	−0.0965416	−	0.285638i
$78$	−19.5158	+	8.57021i	−2.20973	+	0.970386i
$79$	2.27947			0.256460			0.128230	−	0.991744i	$-0.459070\pi$
$79$	2.27947			0.256460			0.128230	+	0.991744i	$0.459070\pi$
$80$	0.969269	−	1.67882i	0.108368	−	0.187698i
$81$	8.14567	+	3.82729i	0.905074	+	0.425254i
$82$	4.86738	+	8.43054i	0.537512	+	0.930998i
$83$	−1.01097	+	1.75104i	−0.110968	+	0.192202i	−0.916161	−	0.400811i	$-0.868728\pi$
$83$	−1.01097	+	1.75104i	−0.110968	+	0.192202i	0.805193	+	0.593013i	$0.202062\pi$
$84$	1.75290	−	5.52010i	0.191257	−	0.602292i
$85$	−0.776132	−	1.34430i	−0.0841833	−	0.145810i
$86$	−5.43698	+	9.41712i	−0.586284	+	1.01547i
$87$	11.9261	+	8.75794i	1.27861	+	0.938949i
$88$	−0.664962	−	1.15175i	−0.0708852	−	0.122777i
$89$	3.79532	+	6.57369i	0.402303	+	0.696810i	0.994003	−	0.109348i	$-0.0348764\pi$
$89$	3.79532	+	6.57369i	0.402303	+	0.696810i	−0.591700	+	0.806158i	$0.701543\pi$
$90$	−1.44196	+	1.56903i	−0.151996	+	0.165391i
$91$	5.77048	+	17.0731i	0.604911	+	1.78975i
$92$	0.876605	−	1.51832i	0.0913924	−	0.158296i
$93$	−1.27490	+	11.5633i	−0.132201	+	1.19906i
$94$	−10.1187			−1.04367
$95$	−0.166941			−0.0171278
$96$	1.18586	−	10.7557i	0.121032	−	1.09775i
$97$	−3.12673	+	5.41566i	−0.317472	+	0.549877i	−0.979960	−	0.199195i	$-0.936167\pi$
$97$	−3.12673	+	5.41566i	−0.317472	+	0.549877i	0.662488	+	0.749072i	$0.269500\pi$
$98$	−11.6709	−	4.87028i	−1.17894	−	0.491973i
$99$	0.897953	+	2.86246i	0.0902477	+	0.287688i
$100$	3.06196	+	5.30346i	0.306196	+	0.530346i
$101$	9.14090	+	15.8325i	0.909554	+	1.57539i	0.814685	+	0.579904i	$0.196910\pi$
$101$	9.14090	+	15.8325i	0.909554	+	1.57539i	0.0948688	+	0.995490i	$0.469757\pi$
$102$	−9.95727	−	7.31212i	−0.985917	−	0.724008i
$103$	1.26013	−	2.18260i	0.124164	−	0.215058i	−0.797242	−	0.603660i	$-0.793708\pi$
$103$	1.26013	−	2.18260i	0.124164	−	0.215058i	0.921406	+	0.388602i	$0.127042\pi$
$104$	4.52949	+	7.84530i	0.444153	+	0.769295i
$105$	1.21455	+	1.33090i	0.118528	+	0.129883i
$106$	−2.08444	+	3.61036i	−0.202459	+	0.350670i
$107$	−8.44460	−	14.6265i	−0.816371	−	1.41400i	−0.908340	−	0.418233i	$-0.862649\pi$
$107$	−8.44460	−	14.6265i	−0.816371	−	1.41400i	0.0919690	−	0.995762i	$-0.470684\pi$
$108$	−2.12453	+	6.21406i	−0.204433	+	0.597948i
$109$	0.983798	−	1.70399i	0.0942308	−	0.163212i	−0.815057	−	0.579381i	$-0.803294\pi$
$109$	0.983798	−	1.70399i	0.0942308	−	0.163212i	0.909287	+	0.416169i	$0.136628\pi$
$110$	−0.710329			−0.0677273
$111$	15.1818	−	6.66696i	1.44099	−	0.632800i
$112$	−12.7905	−	2.56171i	−1.20859	−	0.242059i
$113$	0.112157	+	0.194262i	0.0105509	+	0.0182746i	0.871253	−	0.490835i	$-0.163308\pi$
$113$	0.112157	+	0.194262i	0.0105509	+	0.0182746i	−0.860702	+	0.509109i	$0.829975\pi$
$114$	−1.21648	+	0.534207i	−0.113934	+	0.0500330i
$115$	0.272709	+	0.472346i	0.0254302	+	0.0440465i
$116$	−5.39839	+	9.35028i	−0.501228	+	0.868152i
$117$	−6.11654	−	19.4981i	−0.565474	−	1.80260i
$118$	12.5661			1.15680
$119$	−6.89739	+	7.84411i	−0.632283	+	0.719068i
$120$	0.730002	+	0.536077i	0.0666398	+	0.0489369i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−23.1794			−2.09857
$123$	−8.54531	+	3.75261i	−0.770505	+	0.338361i
$124$	−8.48876			−0.762313
$125$	−3.87104			−0.346236
$126$	13.1091	+	5.81157i	1.16785	+	0.517736i
$127$	−4.35898			−0.386797			−0.193399	−	0.981120i	$-0.561951\pi$
$127$	−4.35898			−0.386797			−0.193399	+	0.981120i	$0.561951\pi$
$128$	−9.91870			−0.876697
$129$	−8.40282	−	6.17061i	−0.739827	−	0.543292i
$130$	4.83851			0.424366
$131$	−1.27065	+	2.20083i	−0.111017	+	0.192287i	−0.916181	−	0.400766i	$-0.868744\pi$
$131$	−1.27065	+	2.20083i	−0.111017	+	0.192287i	0.805164	+	0.593053i	$0.202077\pi$
$132$	−2.00432	+	0.880182i	−0.174454	+	0.0766100i
$133$	0.359691	+	1.06422i	0.0311892	+	0.0922794i
$134$	7.89535			0.682054
$135$	−1.34371	−	1.53897i	−0.115648	−	0.132454i
$136$	−2.62523	+	4.54704i	−0.225112	+	0.389905i
$137$	0.0551928	+	0.0955968i	0.00471544	+	0.00816739i	0.868373	−	0.495911i	$-0.165166\pi$
$137$	0.0551928	+	0.0955968i	0.00471544	+	0.00816739i	−0.863658	+	0.504078i	$0.831832\pi$
$138$	3.49868	+	2.56925i	0.297827	+	0.218710i
$139$	−9.29147	−	16.0933i	−0.788093	−	1.36502i	−0.927134	−	0.374730i	$-0.877735\pi$
$139$	−9.29147	−	16.0933i	−0.788093	−	1.36502i	0.139041	−	0.990287i	$-0.455598\pi$
$140$	−0.868173	+	0.987336i	−0.0733740	+	0.0834451i
$141$	1.06315	−	9.64269i	0.0895331	−	0.812061i
$142$	−14.4514			−1.21274
$143$	3.40582	−	5.89906i	0.284809	−	0.493304i
$144$	14.4359	+	3.22240i	1.20299	+	0.268533i
$145$	−1.67942	−	2.90884i	−0.139468	−	0.241566i
$146$	−8.28502	+	14.3501i	−0.685673	+	1.18762i
$147$	5.86737	−	10.6101i	0.483933	−	0.875105i
$148$	6.04955	+	10.4781i	0.497270	+	0.861297i
$149$	6.87797	−	11.9130i	0.563465	−	0.975950i	−0.433726	−	0.901045i	$-0.642801\pi$
$149$	6.87797	−	11.9130i	0.563465	−	0.975950i	0.997191	−	0.0749050i	$-0.0238653\pi$
$150$	−13.8824	+	6.09635i	−1.13349	+	0.497765i
$151$	−4.26922	−	7.39451i	−0.347424	−	0.601756i	0.638367	−	0.769732i	$-0.279610\pi$
$151$	−4.26922	−	7.39451i	−0.347424	−	0.601756i	−0.985791	+	0.167976i	$0.946277\pi$
$152$	0.282336	+	0.489020i	0.0229005	+	0.0396648i
$153$	8.01428	−	8.72054i	0.647916	−	0.705014i
$154$	1.53047	+	4.52821i	0.123329	+	0.364893i
$155$	1.32041	−	2.28702i	0.106058	−	0.183698i
$156$	13.6527	−	5.99549i	1.09309	−	0.480023i
$157$	−21.0813			−1.68247			−0.841235	−	0.540669i	$-0.818171\pi$
$157$	−21.0813			−1.68247			−0.841235	+	0.540669i	$0.818171\pi$
$158$	−4.11812			−0.327620
$159$	−3.22150	−	2.36571i	−0.255481	−	0.187613i
$160$	−1.22819	+	2.12729i	−0.0970973	+	0.168177i
$161$	2.42353	−	2.75618i	0.191001	−	0.217217i
$162$	−14.7161	−	6.91444i	−1.15620	−	0.543249i
$163$	−2.58499	−	4.47734i	−0.202472	−	0.350692i	0.746852	−	0.664990i	$-0.231564\pi$
$163$	−2.58499	−	4.47734i	−0.202472	−	0.350692i	−0.949324	+	0.314298i	$0.898231\pi$
$164$	−3.40509	−	5.89778i	−0.265892	−	0.460539i
$165$	0.0746322	−	0.676910i	0.00581011	−	0.0526974i
$166$	1.82643	−	3.16346i	0.141758	−	0.245532i
$167$	7.84419	+	13.5865i	0.607002	+	1.05136i	0.991732	+	0.128329i	$0.0409613\pi$
$167$	7.84419	+	13.5865i	0.607002	+	1.05136i	−0.384730	+	0.923029i	$0.625705\pi$
$168$	1.84452	−	5.80865i	0.142308	−	0.448147i
$169$	−16.6993	+	28.9240i	−1.28456	+	2.22492i
$170$	1.40217	+	2.42863i	0.107542	+	0.186268i
$171$	−0.381262	−	1.21537i	−0.0291558	−	0.0929418i
$172$	3.80356	−	6.58796i	0.290019	−	0.502327i
$173$	19.4753			1.48068			0.740341	−	0.672231i	$-0.234664\pi$
$173$	19.4753			1.48068			0.740341	+	0.672231i	$0.234664\pi$
$174$	−21.5459	−	15.8222i	−1.63339	−	1.19948i
$175$	4.10478	+	12.1448i	0.310292	+	0.918062i
$176$	2.46519	+	4.26983i	0.185821	+	0.321851i
$177$	−1.32028	+	11.9749i	−0.0992382	+	0.900086i
$178$	−6.85669	−	11.8761i	−0.513930	−	0.890153i
$179$	7.30536	−	12.6533i	0.546029	−	0.945749i	−0.452513	−	0.891758i	$-0.649472\pi$
$179$	7.30536	−	12.6533i	0.546029	−	0.945749i	0.998541	−	0.0539914i	$-0.0171944\pi$
$180$	1.00876	−	1.09765i	0.0751882	−	0.0818142i
$181$	7.93075			0.589488			0.294744	−	0.955576i	$-0.404766\pi$
$181$	7.93075			0.589488			0.294744	+	0.955576i	$0.404766\pi$
$182$	−10.4250	−	30.8446i	−0.772755	−	2.28635i
$183$	2.43539	−	22.0889i	0.180030	−	1.63286i
$184$	0.922427	−	1.59769i	0.0680022	−	0.117783i
$185$	−3.76399			−0.276734
$186$	2.30326	−	20.8905i	0.168883	−	1.53176i
$187$	3.94795			0.288702
$188$	7.07880			0.516275
$189$	−6.91549	+	11.8818i	−0.503028	+	0.864270i
$190$	0.301599			0.0218803
$191$	−18.0721			−1.30765			−0.653825	−	0.756646i	$-0.726837\pi$
$191$	−18.0721			−1.30765			−0.653825	+	0.756646i	$0.726837\pi$
$192$	−0.270674	+	2.45500i	−0.0195342	+	0.177174i
$193$	−24.7759			−1.78341			−0.891703	−	0.452620i	$-0.850489\pi$
$193$	−24.7759			−1.78341			−0.891703	+	0.452620i	$0.850489\pi$
$194$	5.64880	−	9.78401i	0.405560	−	0.702451i
$195$	−0.508368	+	4.61087i	−0.0364050	+	0.330191i
$196$	8.16463	+	3.40712i	0.583188	+	0.243366i
$197$	4.02726			0.286930			0.143465	−	0.989655i	$-0.454176\pi$
$197$	4.02726			0.286930			0.143465	+	0.989655i	$0.454176\pi$
$198$	−1.62226	−	5.17137i	−0.115289	−	0.367513i
$199$	−1.38653	+	2.40153i	−0.0982883	+	0.170240i	−0.910976	−	0.412459i	$-0.864670\pi$
$199$	−1.38653	+	2.40153i	−0.0982883	+	0.170240i	0.812688	+	0.582699i	$0.198003\pi$
$200$	3.22201	+	5.58069i	0.227831	+	0.394614i
$201$	−0.829540	+	7.52389i	−0.0585113	+	0.530694i
$202$	−16.5141	−	28.6033i	−1.16193	−	2.01252i
$203$	−14.9248	+	16.9734i	−1.04752	+	1.19130i
$204$	6.96584	+	5.11536i	0.487706	+	0.358147i
$205$	2.11862			0.147971
$206$	−2.27656	+	3.94312i	−0.158616	+	0.274731i
$207$	−2.81597	+	3.06413i	−0.195724	+	0.212972i
$208$	−16.7920	−	29.0846i	−1.16432	−	2.01665i
$209$	0.212295	−	0.367706i	0.0146848	−	0.0254347i
$210$	−2.19423	−	2.40443i	−0.151416	−	0.165921i
$211$	8.69222	+	15.0554i	0.598397	+	1.03645i	0.993058	+	0.117628i	$0.0375289\pi$
$211$	8.69222	+	15.0554i	0.598397	+	1.03645i	−0.394660	+	0.918827i	$0.629138\pi$
$212$	1.45822	−	2.52571i	0.100151	−	0.173467i
$213$	1.51837	−	13.7715i	0.104037	−	0.943610i
$214$	15.2561	+	26.4244i	1.04289	+	1.80634i
$215$	1.18328	+	2.04949i	0.0806987	+	0.139774i
$216$	−2.23558	+	6.53888i	−0.152112	+	0.444915i
$217$	−17.4243	−	3.48976i	−1.18284	−	0.236900i
$218$	−1.77734	+	3.07845i	−0.120377	+	0.208499i
$219$	−12.8045	−	9.40295i	−0.865245	−	0.635392i
$220$	0.496927			0.0335028
$221$	−26.8920			−1.80895
$222$	−27.4276	+	12.0446i	−1.84082	+	0.808383i
$223$	8.10029	−	14.0301i	0.542435	−	0.939526i	−0.456328	−	0.889812i	$-0.650836\pi$
$223$	8.10029	−	14.0301i	0.542435	−	0.939526i	0.998763	−	0.0497140i	$-0.0158310\pi$
$224$	16.2073	+	3.24603i	1.08290	+	0.216885i
$225$	−4.35095	−	13.8698i	−0.290063	−	0.924653i
$226$	−0.202625	−	0.350956i	−0.0134784	−	0.0233453i
$227$	10.1242	+	17.5356i	0.671968	+	1.16388i	0.977345	+	0.211651i	$0.0678839\pi$
$227$	10.1242	+	17.5356i	0.671968	+	1.16388i	−0.305378	+	0.952231i	$0.598783\pi$
$228$	0.851014	−	0.373716i	0.0563598	−	0.0247500i
$229$	4.71199	−	8.16140i	0.311377	−	0.539320i	−0.667284	−	0.744803i	$-0.732543\pi$
$229$	4.71199	−	8.16140i	0.311377	−	0.539320i	0.978661	+	0.205483i	$0.0658766\pi$
$230$	−0.492680	−	0.853347i	−0.0324864	−	0.0562680i
$231$	−4.47597	+	0.982703i	−0.294497	+	0.0646571i
$232$	−5.68057	+	9.83904i	−0.372948	+	0.645965i
$233$	−11.8949	−	20.6026i	−0.779262	−	1.34972i	−0.932368	−	0.361512i	$-0.882261\pi$
$233$	−11.8949	−	20.6026i	−0.779262	−	1.34972i	0.153105	−	0.988210i	$-0.451073\pi$
$234$	11.0502	+	35.2255i	0.722376	+	2.30276i
$235$	−1.10110	+	1.90715i	−0.0718276	+	0.124409i
$236$	−8.79088			−0.572238
$237$	0.432678	−	3.92437i	0.0281055	−	0.254915i
$238$	12.4609	−	14.1713i	0.807722	−	0.918588i
$239$	1.34472	+	2.32912i	0.0869825	+	0.150658i	0.906234	−	0.422776i	$-0.138944\pi$
$239$	1.34472	+	2.32912i	0.0869825	+	0.150658i	−0.819252	+	0.573434i	$0.805611\pi$
$240$	−2.70631	−	1.98738i	−0.174692	−	0.128285i
$241$	−6.04050	−	10.4625i	−0.389103	−	0.673946i	0.603226	−	0.797570i	$-0.293882\pi$
$241$	−6.04050	−	10.4625i	−0.389103	−	0.673946i	−0.992329	+	0.123624i	$0.960548\pi$
$242$	0.903308	−	1.56457i	0.0580668	−	0.100575i
$243$	8.13530	−	13.2972i	0.521880	−	0.853019i
$244$	16.2157			1.03810
$245$	−2.18793	+	1.66972i	−0.139782	+	0.106675i
$246$	15.4381	−	6.77952i	0.984296	−	0.432246i
$247$	−1.44608	+	2.50468i	−0.0920118	+	0.159369i
$248$	−8.93248			−0.567213
$249$	2.82273	+	2.07287i	0.178883	+	0.131363i
$250$	6.99348			0.442307
$251$	10.0800			0.636243			0.318121	−	0.948050i	$-0.396948\pi$
$251$	10.0800			0.636243			0.318121	+	0.948050i	$0.396948\pi$
$252$	−9.17078	−	4.06562i	−0.577705	−	0.256110i
$253$	−1.38719			−0.0872118
$254$	7.87500			0.494122
$255$	−2.46169	+	1.08103i	−0.154157	+	0.0676969i
$256$	20.7712			1.29820
$257$	−7.39861	+	12.8148i	−0.461513	+	0.799363i	−0.999037	−	0.0438853i	$-0.986026\pi$
$257$	−7.39861	+	12.8148i	−0.461513	+	0.799363i	0.537524	+	0.843248i	$0.319360\pi$
$258$	15.1807	+	11.1479i	0.945107	+	0.694039i
$259$	8.10988	+	23.9947i	0.503923	+	1.49096i
$260$	−3.38489			−0.209922
$261$	17.3416	−	18.8698i	1.07342	−	1.16801i
$262$	2.29557	−	3.97605i	0.141821	−	0.245641i
$263$	13.3717	+	23.1605i	0.824536	+	1.42814i	0.902273	+	0.431165i	$0.141897\pi$
$263$	13.3717	+	23.1605i	0.824536	+	1.42814i	−0.0777369	+	0.996974i	$0.524769\pi$
$264$	−2.10909	+	0.926191i	−0.129806	+	0.0570031i
$265$	0.453648	+	0.785741i	0.0278674	+	0.0482677i
$266$	−0.649823	−	1.92263i	−0.0398432	−	0.117884i
$267$	12.0378	−	5.28631i	0.736701	−	0.323517i
$268$	−5.52337			−0.337393
$269$	−9.47838	+	16.4170i	−0.577907	+	1.00096i	0.417812	+	0.908533i	$0.362797\pi$
$269$	−9.47838	+	16.4170i	−0.577907	+	1.00096i	−0.995719	+	0.0924305i	$0.970536\pi$
$270$	2.42757	+	2.78033i	0.147737	+	0.169206i
$271$	2.34932	+	4.06914i	0.142711	+	0.247182i	0.928517	−	0.371291i	$-0.121085\pi$
$271$	2.34932	+	4.06914i	0.142711	+	0.247182i	−0.785806	+	0.618473i	$0.787751\pi$
$272$	9.73243	−	16.8571i	0.590116	−	1.02211i
$273$	30.4887	−	6.69382i	1.84526	−	0.405129i
$274$	−0.0997122	−	0.172707i	−0.00602384	−	0.0104336i
$275$	2.42270	−	4.19625i	0.146095	−	0.253043i
$276$	−2.44758	−	1.79738i	−0.147327	−	0.108190i
$277$	−4.80416	−	8.32105i	−0.288654	−	0.499964i	0.684835	−	0.728699i	$-0.259874\pi$
$277$	−4.80416	−	8.32105i	−0.288654	−	0.499964i	−0.973489	+	0.228735i	$0.926541\pi$
$278$	16.7861	+	29.0744i	1.00676	+	1.74377i
$279$	19.6656	+	4.38980i	1.17735	+	0.262810i
$280$	−0.913554	+	1.03895i	−0.0545953	+	0.0620889i
$281$	−4.24105	+	7.34572i	−0.253000	+	0.438209i	−0.964350	−	0.264629i	$-0.914751\pi$
$281$	−4.24105	+	7.34572i	−0.253000	+	0.438209i	0.711350	+	0.702838i	$0.248084\pi$
$282$	−1.92070	+	17.4206i	−0.114376	+	1.03738i
$283$	4.79241			0.284879			0.142440	−	0.989803i	$-0.454505\pi$
$283$	4.79241			0.284879			0.142440	+	0.989803i	$0.454505\pi$
$284$	10.1098			0.599909
$285$	−0.0316881	+	0.287409i	−0.00187704	+	0.0170247i
$286$	−6.15301	+	10.6573i	−0.363835	+	0.630181i
$287$	−4.56477	−	13.5058i	−0.269450	−	0.797222i
$288$	−18.2922	−	4.08321i	−1.07788	−	0.240605i
$289$	0.706859	+	1.22432i	0.0415800	+	0.0720186i
$290$	3.03407	+	5.25516i	0.178167	+	0.308594i
$291$	8.73020	+	6.41102i	0.511773	+	0.375820i
$292$	5.79597	−	10.0389i	0.339184	−	0.587483i
$293$	−1.45010	−	2.51165i	−0.0847158	−	0.146732i	0.820554	−	0.571569i	$-0.193665\pi$
$293$	−1.45010	−	2.51165i	−0.0847158	−	0.146732i	−0.905270	+	0.424837i	$0.860332\pi$
$294$	−10.6001	+	19.1683i	−0.618210	+	1.11792i
$295$	1.36741	−	2.36842i	0.0796135	−	0.137895i
$296$	6.36577	+	11.0258i	0.370003	+	0.640864i
$297$	5.09851	−	1.00259i	0.295846	−	0.0581763i
$298$	−12.4258	+	21.5222i	−0.719810	+	1.24675i
$299$	9.44903			0.546452
$300$	9.71175	−	4.26484i	0.560708	−	0.246231i
$301$	10.5156	−	11.9590i	0.606111	−	0.689304i
$302$	7.71284	+	13.3590i	0.443824	+	0.768726i
$303$	28.9926	−	12.7319i	1.66558	−	0.731428i
$304$	−1.04669	−	1.81293i	−0.0600321	−	0.103979i
$305$	−2.52233	+	4.36880i	−0.144428	+	0.250157i
$306$	−14.4787	+	15.7547i	−0.827693	+	0.900634i
$307$	15.6014			0.890421			0.445210	−	0.895426i	$-0.353129\pi$
$307$	15.6014			0.890421			0.445210	+	0.895426i	$0.353129\pi$
$308$	−1.07068	−	3.16781i	−0.0610075	−	0.180503i
$309$	−3.51842	−	2.58375i	−0.200156	−	0.146984i
$310$	−2.38548	+	4.13177i	−0.135486	+	0.234669i
$311$	24.2965			1.37773			0.688865	−	0.724890i	$-0.258109\pi$
$311$	24.2965			1.37773			0.688865	+	0.724890i	$0.258109\pi$
$312$	14.3664	−	6.30888i	0.813336	−	0.357170i
$313$	−17.1323			−0.968374			−0.484187	−	0.874965i	$-0.660885\pi$
$313$	−17.1323			−0.968374			−0.484187	+	0.874965i	$0.660885\pi$
$314$	38.0858			2.14931
$315$	2.52185	−	1.83837i	0.142090	−	0.103580i
$316$	2.88092			0.162065
$317$	7.98335			0.448390			0.224195	−	0.974544i	$-0.428025\pi$
$317$	7.98335			0.448390			0.224195	+	0.974544i	$0.428025\pi$
$318$	5.82001	+	4.27392i	0.326370	+	0.239670i
$319$	8.54271			0.478300
$320$	0.280336	−	0.485556i	0.0156712	−	0.0271434i
$321$	−26.7841	+	11.7620i	−1.49494	+	0.656494i
$322$	−4.37839	+	4.97936i	−0.243998	+	0.277489i
$323$	−1.67626			−0.0932695
$324$	10.2950	+	4.83715i	0.571943	+	0.268731i
$325$	−16.5026	+	28.5833i	−0.915400	+	1.58552i
$326$	4.67009	+	8.08883i	0.258652	+	0.447999i
$327$	−2.74688	−	2.01717i	−0.151903	−	0.111550i
$328$	−3.58308	−	6.20607i	−0.197842	−	0.342673i
$329$	14.5301	+	2.91012i	0.801073	+	0.160440i
$330$	−0.134832	+	1.22292i	−0.00742224	+	0.0673193i
$331$	−35.6510			−1.95956			−0.979778	−	0.200086i	$-0.935878\pi$
$331$	−35.6510			−1.95956			−0.979778	+	0.200086i	$0.935878\pi$
$332$	−1.27772	+	2.21307i	−0.0701239	+	0.121458i
$333$	−8.59623	−	27.4027i	−0.471070	−	1.50166i
$334$	−14.1714	−	24.5456i	−0.775427	−	1.34308i
$335$	0.859151	−	1.48809i	0.0469404	−	0.0813032i
$336$	−6.83813	+	21.5342i	−0.373051	+	1.17479i
$337$	−0.720020	−	1.24711i	−0.0392220	−	0.0679345i	0.845748	−	0.533583i	$-0.179155\pi$
$337$	−0.720020	−	1.24711i	−0.0392220	−	0.0679345i	−0.884970	+	0.465648i	$0.845821\pi$
$338$	30.1692	−	52.2545i	1.64099	−	2.84227i
$339$	0.355734	−	0.156218i	0.0193208	−	0.00848459i
$340$	−0.980921	−	1.69900i	−0.0531979	−	0.0921415i
$341$	3.35827	+	5.81669i	0.181860	+	0.314991i
$342$	0.688793	+	2.19571i	0.0372457	+	0.118730i
$343$	15.3583	+	10.3501i	0.829268	+	0.558850i
$344$	4.00238	−	6.93233i	0.215794	−	0.373766i
$345$	0.864964	−	0.379842i	0.0465681	−	0.0204500i
$346$	−35.1844			−1.89153
$347$	12.6403			0.678569			0.339284	−	0.940684i	$-0.389815\pi$
$347$	12.6403			0.678569			0.339284	+	0.940684i	$0.389815\pi$
$348$	15.0729	+	11.0688i	0.807993	+	0.593350i
$349$	−3.22434	+	5.58472i	−0.172595	+	0.298943i	−0.939326	−	0.343025i	$-0.888548\pi$
$349$	−3.22434	+	5.58472i	−0.172595	+	0.298943i	0.766731	+	0.641968i	$0.221882\pi$
$350$	−7.41576	−	21.9410i	−0.396389	−	1.17280i
$351$	−34.7293	+	6.82931i	−1.85371	+	0.364521i
$352$	−3.12373	−	5.41045i	−0.166495	−	0.288378i
$353$	12.7629	+	22.1059i	0.679299	+	1.17658i	0.975192	+	0.221360i	$0.0710495\pi$
$353$	12.7629	+	22.1059i	0.679299	+	1.17658i	−0.295893	+	0.955221i	$0.595617\pi$
$354$	2.38524	−	21.6340i	0.126774	−	1.14983i
$355$	−1.57257	+	2.72377i	−0.0834633	+	0.144563i
$356$	4.79675	+	8.30822i	0.254227	+	0.440335i
$357$	12.1953	+	13.3636i	0.645445	+	0.707277i
$358$	−13.1980	+	22.8596i	−0.697535	+	1.20817i
$359$	−5.77324	−	9.99954i	−0.304700	−	0.527756i	0.672495	−	0.740102i	$-0.265223\pi$
$359$	−5.77324	−	9.99954i	−0.304700	−	0.527756i	−0.977194	+	0.212346i	$0.931890\pi$
$360$	1.06149	−	1.15503i	0.0559452	−	0.0608754i
$361$	9.40986	−	16.2984i	0.495256	−	0.857808i
$362$	−14.3278			−0.753053
$363$	1.39606	+	1.02519i	0.0732740	+	0.0538087i
$364$	7.29308	+	21.5780i	0.382261	+	1.13100i
$365$	1.80311	+	3.12308i	0.0943790	+	0.163469i
$366$	−4.39982	+	39.9062i	−0.229982	+	2.08593i
$367$	−4.74363	−	8.21620i	−0.247615	−	0.428882i	0.715248	−	0.698870i	$-0.246314\pi$
$367$	−4.74363	−	8.21620i	−0.247615	−	0.428882i	−0.962864	+	0.269988i	$0.912980\pi$
$368$	−3.41968	+	5.92306i	−0.178263	+	0.308761i
$369$	4.83852	+	15.4241i	0.251884	+	0.802945i
$370$	6.80008			0.353519
$371$	4.03151	−	4.58487i	0.209306	−	0.238035i
$372$	−1.61130	+	14.6144i	−0.0835419	+	0.757721i
$373$	18.8703	−	32.6842i	0.977065	−	1.69233i	0.304118	−	0.952634i	$-0.401638\pi$
$373$	18.8703	−	32.6842i	0.977065	−	1.69233i	0.672946	−	0.739691i	$-0.265028\pi$
$374$	−7.13242			−0.368809
$375$	−0.734784	+	6.66446i	−0.0379441	+	0.344151i
$376$	7.44882			0.384144
$377$	−58.1899			−2.99693
$378$	12.4936	−	21.4658i	0.642603	−	1.10408i
$379$	−4.43450			−0.227785			−0.113893	−	0.993493i	$-0.536332\pi$
$379$	−4.43450			−0.227785			−0.113893	+	0.993493i	$0.536332\pi$
$380$	−0.210990			−0.0108236
$381$	−0.827403	+	7.50450i	−0.0423891	+	0.384467i
$382$	32.6493			1.67048
$383$	4.70012	−	8.14085i	0.240165	−	0.415978i	−0.720596	−	0.693355i	$-0.756132\pi$
$383$	4.70012	−	8.14085i	0.240165	−	0.415978i	0.960761	+	0.277377i	$0.0894651\pi$
$384$	−1.88272	+	17.0762i	−0.0960774	+	0.871417i
$385$	1.02001	+	0.204289i	0.0519843	+	0.0104115i
$386$	44.7605			2.27825
$387$	−12.2184	+	13.2952i	−0.621097	+	0.675832i
$388$	−3.95175	+	6.84463i	−0.200620	+	0.347483i
$389$	−14.4292	−	24.9921i	−0.731589	−	1.26715i	−0.956204	−	0.292701i	$-0.905446\pi$
$389$	−14.4292	−	24.9921i	−0.731589	−	1.26715i	0.224615	−	0.974448i	$-0.427888\pi$
$390$	0.918426	−	8.33007i	0.0465063	−	0.421810i
$391$	2.73827	+	4.74283i	0.138480	+	0.239855i
$392$	8.59141	+	3.58522i	0.433932	+	0.181081i
$393$	3.54779	+	2.60532i	0.178963	+	0.131421i
$394$	−7.27570			−0.366545
$395$	−0.448123	+	0.776172i	−0.0225475	+	0.0390534i
$396$	1.13489	+	3.61775i	0.0570302	+	0.181799i
$397$	9.71842	+	16.8328i	0.487754	+	0.844814i	0.999901	−	0.0140837i	$-0.00448313\pi$
$397$	9.71842	+	16.8328i	0.487754	+	0.844814i	−0.512147	+	0.858898i	$0.671150\pi$
$398$	2.50492	−	4.33865i	0.125560	−	0.217477i
$399$	1.90045	−	0.417246i	0.0951416	−	0.0208884i
$400$	−11.9448	−	20.6891i	−0.597242	−	1.03445i
$401$	1.94664	−	3.37168i	0.0972106	−	0.168374i	−0.813318	−	0.581819i	$-0.802341\pi$
$401$	1.94664	−	3.37168i	0.0972106	−	0.168374i	0.910529	+	0.413445i	$0.135675\pi$
$402$	1.49866	−	13.5928i	0.0747464	−	0.677946i
$403$	−22.8753	−	39.6212i	−1.13950	−	1.97367i
$404$	11.5528	+	20.0101i	0.574774	+	0.995538i
$405$	−2.90458	+	2.02124i	−0.144330	+	0.100436i
$406$	26.9634	−	30.6643i	1.33817	−	1.52184i
$407$	4.78657	−	8.29058i	0.237261	−	0.410949i
$408$	7.32995	+	5.38275i	0.362887	+	0.266486i
$409$	37.1103			1.83499			0.917493	−	0.397752i	$-0.130210\pi$
$409$	37.1103			1.83499			0.917493	+	0.397752i	$0.130210\pi$
$410$	−3.82753			−0.189028
$411$	0.175058	−	0.0768753i	0.00863496	−	0.00379198i
$412$	1.59262	−	2.75850i	0.0784629	−	0.135902i
$413$	−18.0444	−	3.61396i	−0.887907	−	0.177831i
$414$	5.08738	−	5.53571i	0.250031	−	0.272065i
$415$	−0.397494	−	0.688480i	−0.0195122	−	0.0337961i
$416$	21.2777	+	36.8541i	1.04323	+	1.80692i
$417$	−29.4702	+	12.9416i	−1.44316	+	0.633754i
$418$	−0.383535	+	0.664303i	−0.0187593	+	0.0324921i
$419$	9.94532	+	17.2258i	0.485861	+	0.841535i	0.999868	−	0.0162504i	$-0.00517291\pi$
$419$	9.94532	+	17.2258i	0.485861	+	0.841535i	−0.514007	+	0.857786i	$0.671840\pi$
$420$	1.53502	+	1.68207i	0.0749014	+	0.0820768i
$421$	2.37809	−	4.11898i	0.115901	−	0.200747i	−0.802238	−	0.597004i	$-0.796358\pi$
$421$	2.37809	−	4.11898i	0.115901	−	0.200747i	0.918140	+	0.396257i	$0.129691\pi$
$422$	−15.7035	−	27.1993i	−0.764435	−	1.32404i
$423$	−16.3992	−	3.66066i	−0.797358	−	0.177988i
$424$	1.53445	−	2.65774i	0.0745192	−	0.129071i
$425$	−19.1294			−0.927913
$426$	−2.74311	+	24.8799i	−0.132904	+	1.20543i
$427$	33.2848	+	6.66634i	1.61077	+	0.322607i
$428$	−10.6728	−	18.4858i	−0.515889	−	0.893545i
$429$	−9.50945	−	6.98326i	−0.459121	−	0.337155i
$430$	−2.13772	−	3.70265i	−0.103090	−	0.178557i
$431$	−15.7220	+	27.2313i	−0.757302	+	1.31169i	0.186920	+	0.982375i	$0.440150\pi$
$431$	−15.7220	+	27.2313i	−0.757302	+	1.31169i	−0.944222	+	0.329310i	$0.893184\pi$
$432$	8.28789	−	24.2414i	0.398751	−	1.16631i
$433$	−31.1541			−1.49717			−0.748586	−	0.663037i	$-0.769267\pi$
$433$	−31.1541			−1.49717			−0.748586	+	0.663037i	$0.769267\pi$
$434$	31.4789	+	6.30465i	1.51104	+	0.302633i
$435$	−5.32670	+	2.33918i	−0.255396	+	0.112155i
$436$	1.24338	−	2.15360i	0.0595472	−	0.103139i
$437$	0.588986			0.0281750
$438$	23.1327	+	16.9875i	1.10532	+	0.811694i
$439$	−1.01072			−0.0482389			−0.0241195	−	0.999709i	$-0.507678\pi$
$439$	−1.01072			−0.0482389			−0.0241195	+	0.999709i	$0.507678\pi$
$440$	0.522903			0.0249284
$441$	−17.1528	−	12.1153i	−0.816800	−	0.576921i
$442$	48.5835			2.31088
$443$	1.50737			0.0716173			0.0358086	−	0.999359i	$-0.488599\pi$
$443$	1.50737			0.0716173			0.0358086	+	0.999359i	$0.488599\pi$
$444$	19.1876	−	8.42610i	0.910605	−	0.399885i
$445$	−2.98451			−0.141479
$446$	−14.6341	+	25.3470i	−0.692945	+	1.20022i
$447$	−19.2041	−	14.1025i	−0.908321	−	0.667026i
$448$	−3.69933	−	0.740908i	−0.174777	−	0.0350046i
$449$	5.70325			0.269153			0.134577	−	0.990903i	$-0.457033\pi$
$449$	5.70325			0.269153			0.134577	+	0.990903i	$0.457033\pi$
$450$	7.86049	+	25.0574i	0.370547	+	1.18122i
$451$	−2.69420	+	4.66649i	−0.126865	+	0.219736i
$452$	0.141751	+	0.245520i	0.00666740	+	0.0115483i
$453$	−13.5409	+	5.94637i	−0.636206	+	0.279385i
$454$	−18.2906	−	31.6802i	−0.858418	−	1.48682i
$455$	−6.94792	−	1.39154i	−0.325724	−	0.0652365i
$456$	0.895498	−	0.393251i	0.0419356	−	0.0184157i
$457$	−2.99816			−0.140248			−0.0701241	−	0.997538i	$-0.522340\pi$
$457$	−2.99816			−0.140248			−0.0701241	+	0.997538i	$0.522340\pi$
$458$	−8.51274	+	14.7445i	−0.397774	+	0.688966i
$459$	−13.4922	−	15.4528i	−0.629762	−	0.721276i
$460$	0.344666	+	0.596978i	0.0160701	+	0.0278343i
$461$	−7.89488	+	13.6743i	−0.367701	+	0.636877i	−0.989206	−	0.146533i	$-0.953188\pi$
$461$	−7.89488	+	13.6743i	−0.367701	+	0.636877i	0.621505	+	0.783411i	$0.286522\pi$
$462$	8.08635	−	1.77537i	0.376211	−	0.0825975i
$463$	1.38928	+	2.40630i	0.0645653	+	0.111830i	0.896501	−	0.443042i	$-0.146101\pi$
$463$	1.38928	+	2.40630i	0.0645653	+	0.111830i	−0.831936	+	0.554872i	$0.812767\pi$
$464$	21.0594	−	36.4759i	0.977658	−	1.69335i
$465$	−3.68674	−	2.70736i	−0.170969	−	0.125551i
$466$	21.4895	+	37.2210i	0.995484	+	1.72423i
$467$	−4.20575	−	7.28456i	−0.194619	−	0.337089i	0.752157	−	0.658984i	$-0.229014\pi$
$467$	−4.20575	−	7.28456i	−0.194619	−	0.337089i	−0.946775	+	0.321895i	$0.895680\pi$
$468$	−7.73044	−	24.6428i	−0.357340	−	1.13911i
$469$	−11.3374	−	2.27068i	−0.523513	−	0.104850i
$470$	1.98926	−	3.44549i	0.0917576	−	0.158929i
$471$	−4.00156	+	36.2939i	−0.184382	+	1.67234i
$472$	−9.25040			−0.425784
$473$	−6.01897			−0.276752
$474$	−0.781683	+	7.08983i	−0.0359039	+	0.325647i
$475$	−1.02866	+	1.78168i	−0.0471980	+	0.0817493i
$476$	−8.71733	+	9.91384i	−0.399558	+	0.454400i
$477$	−4.68434	+	5.09714i	−0.214481	+	0.233382i
$478$	−2.42939	−	4.20782i	−0.111118	−	0.192461i
$479$	−14.7055	−	25.4706i	−0.671910	−	1.16378i	−0.977362	−	0.211575i	$-0.932141\pi$
$479$	−14.7055	−	25.4706i	−0.671910	−	1.16378i	0.305452	−	0.952208i	$-0.401193\pi$
$480$	3.42926	+	2.51827i	0.156524	+	0.114943i
$481$	−32.6044	+	56.4725i	−1.48663	+	2.57492i
$482$	10.9129	+	18.9016i	0.497067	+	0.860946i
$483$	−4.28506	−	4.69556i	−0.194977	−	0.213656i
$484$	−0.631930	+	1.09453i	−0.0287241	+	0.0497515i
$485$	−1.22938	−	2.12934i	−0.0558231	−	0.0966884i
$486$	−14.6974	+	24.0230i	−0.666686	+	1.08971i
$487$	4.25385	−	7.36789i	0.192760	−	0.333871i	−0.753404	−	0.657558i	$-0.771589\pi$
$487$	4.25385	−	7.36789i	0.192760	−	0.333871i	0.946164	+	0.323688i	$0.104923\pi$
$488$	17.0633			0.772421
$489$	−8.19894	+	3.60050i	−0.370769	+	0.162820i
$490$	3.95275	−	3.01655i	0.178567	−	0.136274i
$491$	−1.58893	−	2.75210i	−0.0717072	−	0.124201i	0.827942	−	0.560813i	$-0.189511\pi$
$491$	−1.58893	−	2.75210i	−0.0717072	−	0.124201i	−0.899650	+	0.436613i	$0.856178\pi$
$492$	−10.8001	+	4.74277i	−0.486905	+	0.213820i
$493$	−16.8631	−	29.2077i	−0.759475	−	1.31545i
$494$	2.61251	−	4.52500i	0.117542	−	0.203589i
$495$	−1.15121	−	0.256976i	−0.0517432	−	0.0115502i
$496$	33.1151			1.48691
$497$	20.7517	+	4.15619i	0.930843	+	0.186431i
$498$	−5.09959	−	3.74488i	−0.228518	−	0.167812i
$499$	3.35753	−	5.81542i	0.150304	−	0.260334i	−0.781035	−	0.624487i	$-0.785308\pi$
$499$	3.35753	−	5.81542i	0.150304	−	0.260334i	0.931339	+	0.364153i	$0.118641\pi$
$500$	−4.89245			−0.218797
$501$	24.8798	−	10.9258i	1.11155	−	0.488127i
$502$	−18.2106			−0.812781
$503$	−1.05989			−0.0472582			−0.0236291	−	0.999721i	$-0.507522\pi$
$503$	−1.05989			−0.0472582			−0.0236291	+	0.999721i	$0.507522\pi$
$504$	−9.65015	−	4.27814i	−0.429852	−	0.190563i
$505$	−7.18808			−0.319866
$506$	2.50611			0.111410
$507$	46.6263	+	34.2400i	2.07075	+	1.52065i
$508$	−5.50914			−0.244428
$509$	1.50607	−	2.60859i	0.0667554	−	0.115624i	−0.830716	−	0.556697i	$-0.812069\pi$
$509$	1.50607	−	2.60859i	0.0667554	−	0.115624i	0.897471	+	0.441073i	$0.145402\pi$
$510$	4.44733	−	1.95301i	0.196931	−	0.0864808i
$511$	16.0240	−	18.2234i	0.708860	−	0.806157i
$512$	−17.6882			−0.781717
$513$	−2.16478	+	0.425691i	−0.0955772	+	0.0187947i
$514$	13.3664	−	23.1514i	0.589568	−	1.02116i
$515$	0.495460	+	0.858161i	0.0218326	+	0.0378151i
$516$	−10.6200	−	7.79878i	−0.467519	−	0.343322i
$517$	−2.80047	−	4.85056i	−0.123165	−	0.213327i
$518$	−14.6514	−	43.3492i	−0.643747	−	1.90465i
$519$	3.69672	−	33.5291i	0.162268	−	1.47176i
$520$	−3.56183			−0.156196
$521$	15.5657	−	26.9605i	0.681945	−	1.18116i	−0.292442	−	0.956283i	$-0.594468\pi$
$521$	15.5657	−	26.9605i	0.681945	−	1.18116i	0.974387	−	0.224879i	$-0.0721988\pi$
$522$	−31.3296	+	34.0905i	−1.37126	+	1.49210i
$523$	10.2656	+	17.7805i	0.448882	+	0.777486i	0.998314	−	0.0580528i	$-0.0184892\pi$
$523$	10.2656	+	17.7805i	0.448882	+	0.777486i	−0.549432	+	0.835538i	$0.685156\pi$
$524$	−1.60592	+	2.78153i	−0.0701549	+	0.121512i
$525$	21.6879	−	4.76159i	0.946537	−	0.207813i
$526$	−24.1576	−	41.8421i	−1.05332	−	1.82440i
$527$	13.2583	−	22.9640i	0.577539	−	1.00033i
$528$	7.81895	−	3.43363i	0.340276	−	0.149430i
$529$	10.5379	+	18.2521i	0.458168	+	0.793570i
$530$	−0.819567	−	1.41953i	−0.0355997	−	0.0616605i
$531$	20.3655	+	4.54603i	0.883789	+	0.197281i
$532$	0.454599	+	1.34502i	0.0197094	+	0.0583141i
$533$	18.3519	−	31.7865i	0.794910	−	1.37682i
$534$	−21.7477	+	9.55032i	−0.941114	+	0.413283i
$535$	6.64054			0.287096
$536$	−5.81209			−0.251044
$537$	−20.3974	−	14.9788i	−0.880214	−	0.646385i
$538$	17.1238	−	29.6593i	0.738259	−	1.27870i
$539$	−0.895403	−	6.94250i	−0.0385678	−	0.299034i
$540$	−1.69826	−	1.94504i	−0.0730815	−	0.0837014i
$541$	−7.54625	−	13.0705i	−0.324438	−	0.561944i	0.656960	−	0.753925i	$-0.271842\pi$
$541$	−7.54625	−	13.0705i	−0.324438	−	0.561944i	−0.981399	+	0.191981i	$0.938509\pi$
$542$	−4.24431	−	7.35137i	−0.182309	−	0.315768i
$543$	1.50538	−	13.6537i	0.0646021	−	0.585937i
$544$	−12.3323	+	21.3602i	−0.528743	+	0.915810i
$545$	0.386812	+	0.669978i	0.0165692	+	0.0286987i
$546$	−55.0814	+	12.0932i	−2.35727	+	0.517540i
$547$	1.95960	−	3.39412i	0.0837863	−	0.145122i	−0.821087	−	0.570803i	$-0.806632\pi$
$547$	1.95960	−	3.39412i	0.0837863	−	0.145122i	0.904873	+	0.425681i	$0.139965\pi$
$548$	0.0697560	+	0.120821i	0.00297983	+	0.00516121i
$549$	−37.5664	−	8.38564i	−1.60329	−	0.357890i
$550$	−4.37689	+	7.58100i	−0.186631	+	0.323255i
$551$	−3.62715			−0.154522
$552$	−2.57552	−	1.89133i	−0.109621	−	0.0805005i
$553$	5.91346	+	1.18436i	0.251466	+	0.0503640i
$554$	8.67927	+	15.0329i	0.368747	+	0.638689i
$555$	−0.714464	+	6.48015i	−0.0303273	+	0.275067i
$556$	−11.7431	−	20.3397i	−0.498019	−	0.862594i
$557$	−1.82696	+	3.16440i	−0.0774110	+	0.134080i	−0.902132	−	0.431460i	$-0.857999\pi$
$557$	−1.82696	+	3.16440i	−0.0774110	+	0.134080i	0.824721	+	0.565540i	$0.191332\pi$
$558$	−35.5282	−	7.93067i	−1.50403	−	0.335732i
$559$	40.9991			1.73408
$560$	3.38679	−	3.85165i	0.143118	−	0.162762i
$561$	0.749382	−	6.79686i	0.0316389	−	0.286964i
$562$	7.66195	−	13.2709i	0.323200	−	0.559799i
$563$	14.5433			0.612927			0.306463	−	0.951882i	$-0.400854\pi$
$563$	14.5433			0.612927			0.306463	+	0.951882i	$0.400854\pi$
$564$	1.34367	−	12.1870i	0.0565786	−	0.513165i
$565$	−0.0881964			−0.00371045
$566$	−8.65804			−0.363925
$567$	19.1432	+	14.1612i	0.803938	+	0.594713i
$568$	10.6383			0.446373
$569$	−32.5716			−1.36547			−0.682736	−	0.730665i	$-0.739210\pi$
$569$	−32.5716			−1.36547			−0.682736	+	0.730665i	$0.739210\pi$
$570$	0.0572482	−	0.519238i	0.00239786	−	0.0217485i
$571$	−2.05109			−0.0858354			−0.0429177	−	0.999079i	$-0.513665\pi$
$571$	−2.05109			−0.0858354			−0.0429177	+	0.999079i	$0.513665\pi$
$572$	4.30448	−	7.45558i	0.179979	−	0.311733i
$573$	−3.43036	+	31.1132i	−0.143306	+	1.29977i
$574$	8.24679	+	24.3998i	0.344214	+	1.01843i
$575$	6.72149			0.280306
$576$	4.17519	+	0.931994i	0.173966	+	0.0388331i
$577$	11.1023	−	19.2297i	0.462193	−	0.800542i	−0.536877	−	0.843661i	$-0.680396\pi$
$577$	11.1023	−	19.2297i	0.462193	−	0.800542i	0.999070	+	0.0431184i	$0.0137293\pi$
$578$	−1.27702	−	2.21187i	−0.0531172	−	0.0920016i
$579$	−4.70285	+	42.6546i	−0.195444	+	1.77267i
$580$	−2.12255	−	3.67637i	−0.0881342	−	0.152653i
$581$	−3.53248	+	4.01734i	−0.146552	+	0.166667i
$582$	−15.7721	−	11.5822i	−0.653775	−	0.480099i
$583$	−2.30757			−0.0955697
$584$	6.09894	−	10.5637i	0.252376	−	0.437128i
$585$	7.84167	+	1.75043i	0.324213	+	0.0723714i
$586$	2.61977	+	4.53758i	0.108222	+	0.187446i
$587$	−0.773644	+	1.33999i	−0.0319317	+	0.0553074i	−0.881550	−	0.472091i	$-0.843499\pi$
$587$	−0.773644	+	1.33999i	−0.0319317	+	0.0553074i	0.849618	+	0.527399i	$0.176833\pi$
$588$	7.41553	−	13.4097i	0.305811	−	0.553005i
$589$	−1.42589	−	2.46971i	−0.0587526	−	0.101763i
$590$	−2.47038	+	4.27882i	−0.101704	+	0.176156i
$591$	0.764436	−	6.93340i	0.0314447	−	0.285202i
$592$	−23.5996	−	40.8757i	−0.969937	−	1.67998i
$593$	−23.1378	−	40.0758i	−0.950155	−	1.64572i	−0.745085	−	0.666969i	$-0.767591\pi$
$593$	−23.1378	−	40.0758i	−0.950155	−	1.64572i	−0.205069	−	0.978747i	$-0.565742\pi$
$594$	−9.21105	+	1.81130i	−0.377934	+	0.0743185i
$595$	−1.31500	−	3.89068i	−0.0539097	−	0.159503i
$596$	8.69278	−	15.0563i	0.356070	−	0.616732i
$597$	3.87134	+	2.84292i	0.158443	+	0.116353i
$598$	−17.0708			−0.698076
$599$	−40.0613			−1.63686			−0.818429	−	0.574607i	$-0.805155\pi$
$599$	−40.0613			−1.63686			−0.818429	+	0.574607i	$0.805155\pi$
$600$	10.2194	−	4.48777i	0.417205	−	0.183213i
$601$	1.03086	−	1.78551i	0.0420499	−	0.0728325i	−0.844234	−	0.535974i	$-0.819945\pi$
$601$	1.03086	−	1.78551i	0.0420499	−	0.0728325i	0.886284	+	0.463142i	$0.153278\pi$
$602$	−18.9977	+	21.6053i	−0.774288	+	0.880565i
$603$	12.7958	+	2.85630i	0.521085	+	0.116318i
$604$	−5.39569	−	9.34561i	−0.219548	−	0.380268i
$605$	−0.196591	−	0.340506i	−0.00799257	−	0.0138435i
$606$	−52.3785	+	23.0016i	−2.12773	+	0.934377i
$607$	−10.8606	+	18.8111i	−0.440818	+	0.763519i	−0.997750	−	0.0670388i	$-0.978645\pi$
$607$	−10.8606	+	18.8111i	−0.440818	+	0.763519i	0.556933	+	0.830558i	$0.311978\pi$
$608$	1.32630	+	2.29722i	0.0537887	+	0.0931647i
$609$	26.3887	+	28.9166i	1.06932	+	1.17176i
$610$	4.55688	−	7.89274i	0.184502	−	0.319568i
$611$	19.0758	+	33.0403i	0.771725	+	1.33667i
$612$	10.1289	−	11.0215i	0.409437	−	0.445519i
$613$	4.59695	−	7.96214i	0.185669	−	0.321588i	−0.758133	−	0.652100i	$-0.773888\pi$
$613$	4.59695	−	7.96214i	0.185669	−	0.321588i	0.943802	+	0.330512i	$0.107221\pi$
$614$	−28.1858			−1.13749
$615$	0.402148	−	3.64746i	0.0162162	−	0.147080i
$616$	−1.12664	−	3.33340i	−0.0453938	−	0.134306i
$617$	−13.8624	−	24.0104i	−0.558079	−	0.966621i	−0.997657	−	0.0684165i	$-0.978205\pi$
$617$	−13.8624	−	24.0104i	−0.558079	−	0.966621i	0.439578	−	0.898204i	$-0.355128\pi$
$618$	6.35643	+	4.66784i	0.255693	+	0.187768i
$619$	−7.44910	−	12.9022i	−0.299404	−	0.518584i	0.676595	−	0.736355i	$-0.263455\pi$
$619$	−7.44910	−	12.9022i	−0.299404	−	0.518584i	−0.976000	+	0.217771i	$0.930121\pi$
$620$	1.66881	−	2.89047i	0.0670212	−	0.116084i
$621$	4.74075	+	5.42965i	0.190240	+	0.217884i
$622$	−43.8945			−1.76001
$623$	6.43041	+	19.0256i	0.257629	+	0.762246i
$624$	−53.2600	+	23.3887i	−2.13210	+	0.936298i
$625$	−11.3525	+	19.6631i	−0.454100	+	0.786525i
$626$	30.9514			1.23707
$627$	−0.592752	−	0.435287i	−0.0236722	−	0.0173837i
$628$	−26.6438			−1.06320
$629$	−37.7942			−1.50695
$630$	−4.55601	+	3.32123i	−0.181516	+	0.132321i
$631$	−30.9122			−1.23059			−0.615297	−	0.788295i	$-0.710964\pi$
$631$	−30.9122			−1.23059			−0.615297	+	0.788295i	$0.710964\pi$
$632$	3.03152			0.120587
$633$	27.5695	−	12.1069i	1.09579	−	0.481208i
$634$	−14.4228			−0.572804
$635$	0.856938	−	1.48426i	0.0340065	−	0.0589010i
$636$	−4.07152	−	2.98992i	−0.161446	−	0.118558i
$637$	6.09917	+	47.2898i	0.241658	+	1.87369i
$638$	−15.4334			−0.611014
$639$	−23.4211	−	5.22811i	−0.926525	−	0.206821i
$640$	1.94993	−	3.37738i	0.0770777	−	0.133503i
$641$	−16.5941	−	28.7417i	−0.655426	−	1.13523i	−0.981787	−	0.189986i	$-0.939156\pi$
$641$	−16.5941	−	28.7417i	−0.655426	−	1.13523i	0.326361	−	0.945245i	$-0.394177\pi$
$642$	48.3886	−	21.2495i	1.90975	−	0.838651i
$643$	−8.69286	−	15.0565i	−0.342813	−	0.593769i	0.642141	−	0.766587i	$-0.278046\pi$
$643$	−8.69286	−	15.0565i	−0.342813	−	0.593769i	−0.984954	+	0.172817i	$0.944713\pi$
$644$	3.06300	−	3.48342i	0.120699	−	0.137266i
$645$	3.75305	−	1.64812i	0.147776	−	0.0648948i
$646$	3.02835			0.119149
$647$	−6.60900	+	11.4471i	−0.259827	+	0.450033i	−0.966195	−	0.257811i	$-0.916999\pi$
$647$	−6.60900	+	11.4471i	−0.259827	+	0.450033i	0.706369	+	0.707844i	$0.250332\pi$
$648$	10.8331	+	5.09000i	0.425565	+	0.199954i
$649$	3.47779	+	6.02371i	0.136515	+	0.236451i
$650$	29.8139	−	51.6391i	1.16940	−	2.02545i
$651$	−9.31543	+	29.3355i	−0.365100	+	1.14975i
$652$	−3.26707	−	5.65872i	−0.127948	−	0.221613i
$653$	4.32296	−	7.48759i	0.169171	−	0.293012i	−0.768958	−	0.639299i	$-0.779224\pi$
$653$	4.32296	−	7.48759i	0.169171	−	0.293012i	0.938128	+	0.346287i	$0.112558\pi$
$654$	4.96255	+	3.64425i	0.194051	+	0.142501i
$655$	−0.499596	−	0.865326i	−0.0195208	−	0.0338111i
$656$	13.2834	+	23.0075i	0.518630	+	0.898294i
$657$	−18.6188	+	20.2596i	−0.726387	+	0.790401i
$658$	−26.2504	−	5.25747i	−1.02335	−	0.204957i
$659$	13.5945	−	23.5464i	0.529568	−	0.917239i	−0.469837	−	0.882753i	$-0.655687\pi$
$659$	13.5945	−	23.5464i	0.529568	−	0.917239i	0.999405	−	0.0344861i	$-0.0109794\pi$
$660$	0.0943246	−	0.855519i	0.00367158	−	0.0333010i
$661$	46.2801			1.80009			0.900044	−	0.435799i	$-0.143534\pi$
$661$	46.2801			1.80009			0.900044	+	0.435799i	$0.143534\pi$
$662$	64.4077			2.50327
$663$	−5.10453	+	46.2978i	−0.198243	+	1.79806i
$664$	−1.34451	+	2.32875i	−0.0521770	+	0.0903732i
$665$	−0.433085	−	0.0867389i	−0.0167943	−	0.00336359i
$666$	15.5301	+	49.5062i	0.601778	+	1.91833i
$667$	5.92517	+	10.2627i	0.229424	+	0.397373i
$668$	9.91395	+	17.1715i	0.383582	+	0.664384i
$669$	−22.6169	−	16.6087i	−0.874421	−	0.642131i
$670$	−1.55216	+	2.68841i	−0.0599650	+	0.103862i
$671$	−6.41516	−	11.1114i	−0.247654	−	0.428950i
$672$	8.66483	−	27.2867i	0.334253	−	1.05261i
$673$	9.28754	−	16.0865i	0.358008	−	0.620089i	−0.629620	−	0.776903i	$-0.716789\pi$
$673$	9.28754	−	16.0865i	0.358008	−	0.620089i	0.987628	+	0.156815i	$0.0501226\pi$
$674$	1.30080	+	2.25305i	0.0501049	+	0.0867843i
$675$	−24.7044	+	4.85797i	−0.950871	+	0.186983i
$676$	−21.1055	+	36.5558i	−0.811751	+	1.40599i
$677$	15.6374			0.600994			0.300497	−	0.953783i	$-0.402847\pi$
$677$	15.6374			0.600994			0.300497	+	0.953783i	$0.402847\pi$
$678$	−0.642674	+	0.282226i	−0.0246818	+	0.0108388i
$679$	−10.9253	+	12.4249i	−0.419275	+	0.476824i
$680$	−1.03220	−	1.78782i	−0.0395829	−	0.0685596i
$681$	32.1114	−	14.1015i	1.23051	−	0.540370i
$682$	−6.06710	−	10.5085i	−0.232321	−	0.402392i
$683$	−19.3600	+	33.5325i	−0.740789	+	1.28308i	0.211347	+	0.977411i	$0.432215\pi$
$683$	−19.3600	+	33.5325i	−0.740789	+	1.28308i	−0.952136	+	0.305674i	$0.901118\pi$
$684$	−0.481861	−	1.53606i	−0.0184244	−	0.0587327i
$685$	−0.0434017			−0.00165829
$686$	−27.7465	−	18.6986i	−1.05937	−	0.713915i
$687$	−13.1564	−	9.66140i	−0.501948	−	0.368605i
$688$	−14.8379	+	25.7000i	−0.565689	+	0.979802i
$689$	15.7183			0.598821
$690$	−1.56266	+	0.686229i	−0.0594893	+	0.0261243i
$691$	8.18849			0.311505			0.155752	−	0.987796i	$-0.450220\pi$
$691$	8.18849			0.311505			0.155752	+	0.987796i	$0.450220\pi$
$692$	24.6141			0.935687
$693$	0.842230	+	7.89244i	0.0319937	+	0.299809i
$694$	−22.8362			−0.866851
$695$	7.30649			0.277151
$696$	15.8608	+	11.6474i	0.601203	+	0.441493i
$697$	21.2731			0.805776
$698$	5.82514	−	10.0894i	0.220485	−	0.381891i
$699$	−37.7277	+	16.5678i	−1.42699	+	0.626652i
$700$	5.18787	+	15.3493i	0.196083	+	0.580150i
$701$	24.5731			0.928115			0.464057	−	0.885805i	$-0.346393\pi$
$701$	24.5731			0.928115			0.464057	+	0.885805i	$0.346393\pi$
$702$	62.7424	−	12.3379i	2.36806	−	0.465665i
$703$	−2.03233	+	3.52010i	−0.0766507	+	0.132763i
$704$	0.712991	+	1.23494i	0.0268719	+	0.0465435i
$705$	3.07439	+	2.25768i	0.115788	+	0.0850290i
$706$	−23.0576	−	39.9369i	−0.867784	−	1.50305i
$707$	15.4874	+	45.8226i	0.582464	+	1.72334i
$708$	−1.66865	+	15.1345i	−0.0627116	+	0.568791i
$709$	29.6766			1.11453			0.557264	−	0.830335i	$-0.311851\pi$
$709$	29.6766			1.11453			0.557264	+	0.830335i	$0.311851\pi$
$710$	2.84103	−	4.92080i	0.106622	−	0.184674i
$711$	−6.67414	−	1.48981i	−0.250300	−	0.0558724i
$712$	5.04749	+	8.74250i	0.189163	+	0.327639i
$713$	−4.65855	+	8.06884i	−0.174464	+	0.302181i
$714$	−22.0323	−	24.1429i	−0.824537	−	0.903525i
$715$	1.33911	+	2.31941i	0.0500799	+	0.0867409i
$716$	9.23295	−	15.9919i	0.345052	−	0.597647i
$717$	4.26510	−	1.87299i	0.159283	−	0.0699480i
$718$	10.4300	+	18.0653i	0.389245	+	0.674192i
$719$	6.16271	+	10.6741i	0.229830	+	0.398078i	0.957758	−	0.287576i	$-0.0928495\pi$
$719$	6.16271	+	10.6741i	0.229830	+	0.398078i	−0.727927	+	0.685654i	$0.759516\pi$
$720$	−3.93521	+	4.28200i	−0.146657	+	0.159581i
$721$	4.40309	−	5.00745i	0.163980	−	0.186487i
$722$	−17.0000	+	29.4449i	−0.632675	+	1.09582i
$723$	−19.1589	+	8.41350i	−0.712528	+	0.312901i
$724$	10.0234			0.372515
$725$	−41.3929			−1.53729
$726$	−2.52214	−	1.85213i	−0.0936054	−	0.0687391i
$727$	−2.36454	+	4.09551i	−0.0876960	+	0.151894i	−0.906537	−	0.422127i	$-0.861284\pi$
$727$	−2.36454	+	4.09551i	−0.0876960	+	0.151894i	0.818841	+	0.574021i	$0.194617\pi$
$728$	7.67430	+	22.7059i	0.284428	+	0.841538i
$729$	−21.3486	−	16.5299i	−0.790688	−	0.612219i
$730$	−3.25752	−	5.64220i	−0.120566	−	0.208827i
$731$	11.8813	+	20.5790i	0.439445	+	0.761141i
$732$	3.07800	−	27.9173i	0.113766	−	1.03185i
$733$	20.6099	−	35.6973i	0.761243	−	1.31851i	−0.180967	−	0.983489i	$-0.557923\pi$
$733$	20.6099	−	35.6973i	0.761243	−	1.31851i	0.942210	−	0.335022i	$-0.108744\pi$
$734$	8.56991	+	14.8435i	0.316321	+	0.547884i
$735$	2.45932	+	4.08373i	0.0907135	+	0.150630i
$736$	4.33319	−	7.50531i	0.159724	−	0.276649i
$737$	2.18512	+	3.78474i	0.0804900	+	0.139413i
$738$	−8.74135	−	27.8654i	−0.321774	−	1.02574i
$739$	24.0533	−	41.6615i	0.884815	−	1.53254i	0.0388894	−	0.999244i	$-0.487618\pi$
$739$	24.0533	−	41.6615i	0.884815	−	1.53254i	0.845926	−	0.533301i	$-0.179049\pi$
$740$	−4.75715			−0.174876
$741$	4.03762	+	2.96502i	0.148326	+	0.108923i
$742$	−7.28340	+	8.28309i	−0.267382	+	0.304082i
$743$	−18.3781	−	31.8318i	−0.674228	−	1.16780i	−0.976694	−	0.214636i	$-0.931143\pi$
$743$	−18.3781	−	31.8318i	−0.674228	−	1.16780i	0.302466	−	0.953160i	$-0.402190\pi$
$744$	−1.69552	+	15.3783i	−0.0621609	+	0.563797i
$745$	2.70430	+	4.68398i	0.0990777	+	0.171608i
$746$	−34.0913	+	59.0478i	−1.24817	+	2.16190i
$747$	4.10449	−	4.46620i	0.150176	−	0.163410i
$748$	4.98965			0.182440
$749$	−14.3077	−	42.3321i	−0.522791	−	1.54678i
$750$	1.32747	−	12.0401i	0.0484724	−	0.439643i
$751$	−24.2357	+	41.9774i	−0.884373	+	1.53178i	−0.0379420	+	0.999280i	$0.512080\pi$
$751$	−24.2357	+	41.9774i	−0.884373	+	1.53178i	−0.846431	+	0.532499i	$0.821253\pi$
$752$	−27.6148			−1.00701
$753$	1.91334	−	17.3539i	0.0697259	−	0.632410i
$754$	105.127			3.82849
$755$	3.35716			0.122180
$756$	−8.74020	+	15.0169i	−0.317878	+	0.546158i
$757$	−10.1983			−0.370662			−0.185331	−	0.982676i	$-0.559336\pi$
$757$	−10.1983			−0.370662			−0.185331	+	0.982676i	$0.559336\pi$
$758$	8.01144			0.290989
$759$	−0.263310	+	2.38821i	−0.00955755	+	0.0866865i
$760$	−0.222019			−0.00805348
$761$	−8.84904	+	15.3270i	−0.320777	+	0.555603i	−0.980649	−	0.195776i	$-0.937277\pi$
$761$	−8.84904	+	15.3270i	−0.320777	+	0.555603i	0.659871	+	0.751379i	$0.270611\pi$
$762$	1.49480	−	13.5578i	0.0541508	−	0.491145i
$763$	3.43755	−	3.90938i	0.124448	−	0.141529i
$764$	−22.8406			−0.826343
$765$	1.39386	+	4.44329i	0.0503951	+	0.160648i
$766$	−8.49132	+	14.7074i	−0.306804	+	0.531400i
$767$	−23.6895	−	41.0314i	−0.855378	−	1.48156i
$768$	3.94271	−	35.7601i	0.142270	−	1.29038i
$769$	15.5945	+	27.0104i	0.562350	+	0.974020i	0.997291	+	0.0735603i	$0.0234361\pi$
$769$	15.5945	+	27.0104i	0.562350	+	0.974020i	−0.434940	+	0.900459i	$0.643231\pi$
$770$	−1.84276	−	0.369071i	−0.0664084	−	0.0133004i
$771$	20.6578	+	15.1700i	0.743971	+	0.546335i
$772$	−31.3132			−1.12699
$773$	−7.71728	+	13.3667i	−0.277571	+	0.480768i	−0.970781	−	0.239969i	$-0.922863\pi$
$773$	−7.71728	+	13.3667i	−0.277571	+	0.480768i	0.693209	+	0.720736i	$0.256196\pi$
$774$	22.0740	−	24.0193i	0.793433	−	0.863355i
$775$	−16.2722	−	28.1842i	−0.584514	−	1.01241i
$776$	−4.15831	+	7.20241i	−0.149275	+	0.258552i
$777$	42.8491	−	9.40755i	1.53720	−	0.337494i
$778$	26.0680	+	45.1511i	0.934583	+	1.61874i
$779$	1.14393	−	1.98134i	0.0409855	−	0.0709890i
$780$	−0.642506	+	5.82749i	−0.0230054	+	0.208658i
$781$	−3.99959	−	6.92750i	−0.143117	−	0.247885i
$782$	−4.94700	−	8.56846i	−0.176904	−	0.306408i
$783$	−29.1949	−	33.4374i	−1.04334	−	1.19495i
$784$	−31.8506	−	13.2913i	−1.13752	−	0.474691i
$785$	4.14440	−	7.17831i	0.147920	−	0.256205i
$786$	−6.40950	−	4.70681i	−0.228619	−	0.167887i
$787$	13.9225			0.496285			0.248142	−	0.968724i	$-0.420180\pi$
$787$	13.9225			0.496285			0.248142	+	0.968724i	$0.420180\pi$
$788$	5.08989			0.181320
$789$	42.4117	−	18.6248i	1.50990	−	0.663060i
$790$	0.809586	−	1.40224i	0.0288038	−	0.0498896i
$791$	0.190028	+	0.562235i	0.00675661	+	0.0199908i
$792$	1.19421	+	3.80685i	0.0424344	+	0.135271i
$793$	43.6978	+	75.6868i	1.55175	+	2.68772i
$794$	−17.5574	−	30.4104i	−0.623091	−	1.07922i
$795$	1.43886	−	0.631863i	0.0510310	−	0.0224099i
$796$	−1.75237	+	3.03520i	−0.0621113	+	0.107580i
$797$	−2.65130	−	4.59219i	−0.0939140	−	0.162664i	0.815241	−	0.579122i	$-0.196605\pi$
$797$	−2.65130	−	4.59219i	−0.0939140	−	0.162664i	−0.909155	+	0.416458i	$0.863271\pi$
$798$	−3.43338	+	0.753802i	−0.121541	+	0.0266843i
$799$	−11.0561	+	19.1497i	−0.391137	+	0.677469i
$800$	15.1357	+	26.2158i	0.535129	+	0.926870i
$801$	−6.81604	−	21.7279i	−0.240833	−	0.767718i
$802$	−3.51683	+	6.09133i	−0.124184	+	0.215092i
$803$	−9.17187			−0.323668
$804$	−1.04842	+	9.50913i	−0.0369750	+	0.335361i
$805$	0.462050	+	1.36707i	0.0162851	+	0.0481828i
$806$	41.3269	+	71.5804i	1.45568	+	2.52131i
$807$	26.4647	+	19.4344i	0.931602	+	0.684122i
$808$	12.1567	+	21.0560i	0.427671	+	0.740748i
$809$	9.47989	−	16.4196i	0.333295	−	0.577284i	−0.649861	−	0.760053i	$-0.725173\pi$
$809$	9.47989	−	16.4196i	0.333295	−	0.577284i	0.983156	+	0.182769i	$0.0585061\pi$
$810$	5.24746	−	3.65160i	0.184377	−	0.128304i
$811$	54.8975			1.92771			0.963857	−	0.266421i	$-0.0858413\pi$
$811$	54.8975			1.92771			0.963857	+	0.266421i	$0.0858413\pi$
$812$	−18.8629	+	21.4519i	−0.661957	+	0.752815i
$813$	7.45144	−	3.27224i	0.261333	−	0.114763i
$814$	−8.64749	+	14.9779i	−0.303094	+	0.524975i
$815$	2.03275			0.0712040
$816$	−27.1741	−	19.9553i	−0.951283	−	0.698574i
$817$	2.55559			0.0894089
$818$	−67.0440			−2.34414
$819$	−5.73697	−	53.7605i	−0.200466	−	1.87855i
$820$	2.67764			0.0935072
$821$	2.52985			0.0882924			0.0441462	−	0.999025i	$-0.485943\pi$
$821$	2.52985			0.0882924			0.0441462	+	0.999025i	$0.485943\pi$
$822$	−0.316262	+	0.138884i	−0.0110309	+	0.00484414i
$823$	−17.6917			−0.616692			−0.308346	−	0.951274i	$-0.599776\pi$
$823$	−17.6917			−0.616692			−0.308346	+	0.951274i	$0.599776\pi$
$824$	1.67587	−	2.90270i	0.0583818	−	0.101120i
$825$	−6.76447	−	4.96748i	−0.235509	−	0.172946i
$826$	32.5993	+	6.52904i	1.13427	+	0.227174i
$827$	42.5046			1.47803			0.739015	−	0.673689i	$-0.235291\pi$
$827$	42.5046			1.47803			0.739015	+	0.673689i	$0.235291\pi$
$828$	−3.55899	+	3.87263i	−0.123684	+	0.134583i
$829$	−6.60564	+	11.4413i	−0.229423	+	0.397373i	−0.957637	−	0.287977i	$-0.907017\pi$
$829$	−6.60564	+	11.4413i	−0.229423	+	0.397373i	0.728214	+	0.685350i	$0.240351\pi$
$830$	0.718119	+	1.24382i	0.0249263	+	0.0431736i
$831$	−15.2376	+	6.69147i	−0.528586	+	0.232124i
$832$	−4.85665	−	8.41196i	−0.168374	−	0.291632i
$833$	−21.9690	+	16.7657i	−0.761182	+	0.580897i
$834$	53.2413	−	23.3805i	1.84360	−	0.809601i
$835$	−6.16840			−0.213466
$836$	0.268311	−	0.464728i	0.00927973	−	0.0160730i
$837$	11.2904	−	33.0234i	0.390253	−	1.14146i
$838$	−17.9674	−	31.1204i	−0.620672	−	1.07504i
$839$	−0.215369	+	0.373030i	−0.00743536	+	0.0128784i	−0.869719	−	0.493547i	$-0.835700\pi$
$839$	−0.215369	+	0.373030i	−0.00743536	+	0.0128784i	0.862284	+	0.506425i	$0.169033\pi$
$840$	1.61526	+	1.77000i	0.0557318	+	0.0610708i
$841$	−21.9889	−	38.0859i	−0.758239	−	1.31331i
$842$	−4.29630	+	7.44141i	−0.148060	+	0.256448i
$843$	11.8415	+	8.69581i	0.407843	+	0.299500i
$844$	10.9857	+	19.0279i	0.378145	+	0.654966i
$845$	−6.56586	−	11.3724i	−0.225872	−	0.391223i
$846$	29.6271	+	6.61341i	1.01860	+	0.227374i
$847$	−1.74708	+	1.98688i	−0.0600305	+	0.0682701i
$848$	−5.68859	+	9.85293i	−0.195347	+	0.338351i
$849$	0.909674	−	8.25070i	0.0312199	−	0.283163i
$850$	34.5595			1.18538
$851$	13.2797			0.455224
$852$	1.91901	−	17.4053i	0.0657440	−	0.596295i
$853$	−7.34280	+	12.7181i	−0.251413	+	0.435459i	−0.963915	−	0.266210i	$-0.914228\pi$
$853$	−7.34280	+	12.7181i	−0.251413	+	0.435459i	0.712502	+	0.701670i	$0.247562\pi$
$854$	−60.1329	−	12.0435i	−2.05770	−	0.412120i
$855$	0.488794	+	0.109110i	0.0167164	+	0.00373147i
$856$	−11.2307	−	19.4521i	−0.383857	−	0.664859i
$857$	10.9361	+	18.9419i	0.373571	+	0.647043i	0.990112	−	0.140279i	$-0.0448000\pi$
$857$	10.9361	+	18.9419i	0.373571	+	0.647043i	−0.616541	+	0.787323i	$0.711467\pi$
$858$	17.1799	+	12.6161i	0.586513	+	0.430706i
$859$	−1.50836	+	2.61255i	−0.0514645	+	0.0891392i	−0.890610	−	0.454768i	$-0.849722\pi$
$859$	−1.50836	+	2.61255i	−0.0514645	+	0.0891392i	0.839145	+	0.543907i	$0.183056\pi$
$860$	1.49549	+	2.59027i	0.0509959	+	0.0883275i
$861$	−24.1183	+	5.29519i	−0.821949	+	0.180460i
$862$	28.4036	−	49.1965i	0.967430	−	1.67564i
$863$	−5.49520	−	9.51796i	−0.187059	−	0.323995i	0.757210	−	0.653172i	$-0.226562\pi$
$863$	−5.49520	−	9.51796i	−0.187059	−	0.323995i	−0.944268	+	0.329177i	$0.893229\pi$
$864$	−10.5019	+	30.7171i	−0.357281	+	1.04502i
$865$	−3.82868	+	6.63147i	−0.130179	+	0.225477i
$866$	56.2836			1.91259
$867$	2.24198	−	0.984548i	0.0761416	−	0.0334370i
$868$	−22.0218	−	4.41056i	−0.747469	−	0.149704i
$869$	−1.13973	−	1.97408i	−0.0386628	−	0.0669659i
$870$	9.62329	−	4.22600i	0.326260	−	0.143275i
$871$	−14.8843	−	25.7803i	−0.504334	−	0.873533i
$872$	1.30838	−	2.26617i	0.0443072	−	0.0767423i
$873$	12.6945	−	13.8132i	0.429642	−	0.467504i
$874$	−1.06407			−0.0359927
$875$	−10.0424	−	2.01130i	−0.339494	−	0.0679945i
$876$	−16.1830	−	11.8840i	−0.546774	−	0.401523i
$877$	−16.1048	+	27.8943i	−0.543819	+	0.941923i	0.454861	+	0.890563i	$0.349689\pi$
$877$	−16.1048	+	27.8943i	−0.543819	+	0.941923i	−0.998680	+	0.0513604i	$0.983644\pi$
$878$	1.82598			0.0616238
$879$	−4.59935	+	2.01977i	−0.155132	+	0.0681251i
$880$	−1.93854			−0.0653481
$881$	20.0660			0.676042			0.338021	−	0.941139i	$-0.390243\pi$
$881$	20.0660			0.676042			0.338021	+	0.941139i	$0.390243\pi$
$882$	30.9885	+	21.8878i	1.04344	+	0.736999i
$883$	−34.9928			−1.17760			−0.588800	−	0.808278i	$-0.700400\pi$
$883$	−34.9928			−1.17760			−0.588800	+	0.808278i	$0.700400\pi$
$884$	−33.9877			−1.14313
$885$	−3.81796	−	2.80372i	−0.128339	−	0.0942459i
$886$	−2.72324			−0.0914889
$887$	−19.8485	+	34.3787i	−0.666448	+	1.15432i	0.312442	+	0.949937i	$0.398853\pi$
$887$	−19.8485	+	34.3787i	−0.666448	+	1.15432i	−0.978890	+	0.204386i	$0.934480\pi$
$888$	20.1906	−	8.86655i	0.677552	−	0.297542i
$889$	−11.3082	−	2.26483i	−0.379265	−	0.0759598i
$890$	5.39186			0.180735
$891$	−0.758305	−	8.96800i	−0.0254042	−	0.300439i
$892$	10.2376	−	17.7321i	0.342781	−	0.593714i
$893$	1.18905	+	2.05950i	0.0397901	+	0.0689185i
$894$	34.6944	+	25.4778i	1.16035	+	0.852105i
$895$	2.87234	+	4.97504i	0.0960118	+	0.166297i
$896$	−25.7314	−	5.15353i	−0.859626	−	0.172167i
$897$	1.79357	−	16.2676i	0.0598857	−	0.543160i
$898$	−10.3036			−0.343835
$899$	28.6887	−	49.6903i	0.956822	−	1.65726i
$900$	−5.49899	−	17.5295i	−0.183300	−	0.584315i
$901$	4.55508	+	7.88963i	0.151752	+	0.262842i
$902$	4.86738	−	8.43054i	0.162066	−	0.280706i
$903$	−18.5928	−	20.3739i	−0.618728	−	0.678001i
$904$	0.149160	+	0.258353i	0.00496100	+	0.00859271i
$905$	−1.55912	+	2.70047i	−0.0518268	+	0.0897666i
$906$	24.4632	−	10.7428i	0.812734	−	0.356906i
$907$	8.44679	+	14.6303i	0.280471	+	0.485790i	0.971501	−	0.237036i	$-0.0761760\pi$
$907$	8.44679	+	14.6303i	0.280471	+	0.485790i	−0.691030	+	0.722826i	$0.742843\pi$
$908$	12.7956	+	22.1626i	0.424636	+	0.735491i
$909$	−16.4162	−	52.3309i	−0.544491	−	1.73571i
$910$	12.5522	+	2.51398i	0.416102	+	0.0833376i
$911$	−25.2236	+	43.6885i	−0.835694	+	1.44747i	0.0577694	+	0.998330i	$0.481601\pi$
$911$	−25.2236	+	43.6885i	−0.835694	+	1.44747i	−0.893464	+	0.449135i	$0.851732\pi$
$912$	−3.31985	+	1.45789i	−0.109931	+	0.0482754i
$913$	2.02193			0.0669162
$914$	5.41653			0.179163
$915$	7.04263	+	5.17175i	0.232822	+	0.170973i
$916$	5.95529	−	10.3149i	0.196768	−	0.340812i
$917$	−4.43985	+	5.04926i	−0.146617	+	0.166741i
$918$	24.3752	+	27.9173i	0.804503	+	0.921409i
$919$	−20.4439	−	35.4099i	−0.674382	−	1.16806i	−0.976649	−	0.214841i	$-0.931077\pi$
$919$	−20.4439	−	35.4099i	−0.674382	−	1.16806i	0.302267	−	0.953223i	$-0.402257\pi$
$920$	0.362682	+	0.628184i	0.0119573	+	0.0207106i
$921$	2.96140	−	26.8597i	0.0975813	−	0.885058i
$922$	14.2630	−	24.7043i	0.469727	−	0.813591i
$923$	27.2438	+	47.1877i	0.896741	+	1.55320i
$924$	−5.65699	+	1.24200i	−0.186101	+	0.0408587i
$925$	−23.1929	+	40.1712i	−0.762577	+	1.32082i
$926$	−2.50989	−	4.34726i	−0.0824802	−	0.142860i
$927$	−5.11608	+	5.56694i	−0.168034	+	0.182842i
$928$	−26.6851	+	46.2199i	−0.875980	+	1.51724i
$929$	20.0653			0.658320			0.329160	−	0.944274i	$-0.393235\pi$
$929$	20.0653			0.658320			0.329160	+	0.944274i	$0.393235\pi$
$930$	6.66053	+	4.89115i	0.218407	+	0.160387i
$931$	0.380179	+	2.94771i	0.0124599	+	0.0966074i
$932$	−15.0335	−	26.0388i	−0.492439	−	0.852929i
$933$	4.61186	−	41.8294i	0.150986	−	1.36943i
$934$	7.59816	+	13.1604i	0.248620	+	0.430622i
$935$	−0.776132	+	1.34430i	−0.0253822	+	0.0439633i
$936$	−8.13453	−	25.9309i	−0.265885	−	0.847579i
$937$	−34.0553			−1.11254			−0.556269	−	0.831002i	$-0.687768\pi$
$937$	−34.0553			−1.11254			−0.556269	+	0.831002i	$0.687768\pi$
$938$	20.4824	+	4.10224i	0.668773	+	0.133943i
$939$	−3.25198	+	29.4953i	−0.106124	+	0.962541i
$940$	−1.39163	+	2.41037i	−0.0453900	+	0.0786177i
$941$	−8.96028			−0.292097			−0.146048	−	0.989277i	$-0.546656\pi$
$941$	−8.96028			−0.292097			−0.146048	+	0.989277i	$0.546656\pi$
$942$	7.22928	−	65.5692i	0.235543	−	2.13636i
$943$	−7.47471			−0.243410
$944$	34.2937			1.11616
$945$	−2.68628	−	4.69061i	−0.0873848	−	0.152586i
$946$	10.8740			0.353543
$947$	10.8385			0.352205			0.176102	−	0.984372i	$-0.443651\pi$
$947$	10.8385			0.352205			0.176102	+	0.984372i	$0.443651\pi$
$948$	0.546844	−	4.95985i	0.0177607	−	0.161088i
$949$	62.4755			2.02804
$950$	1.85839	−	3.21882i	0.0602940	−	0.104432i
$951$	1.51536	−	13.7443i	0.0491391	−	0.445689i
$952$	−9.17300	+	10.4321i	−0.297299	+	0.338105i
$953$	9.38023			0.303856			0.151928	−	0.988392i	$-0.451452\pi$
$953$	9.38023			0.303856			0.151928	+	0.988392i	$0.451452\pi$
$954$	8.46279	−	9.20858i	0.273993	−	0.298139i
$955$	3.55281	−	6.15365i	0.114966	−	0.199128i
$956$	1.69953	+	2.94368i	0.0549668	+	0.0952053i
$957$	1.62154	−	14.7073i	0.0524169	−	0.475419i
$958$	26.5671	+	46.0156i	0.858345	+	1.48670i
$959$	0.0935132	+	0.276677i	0.00301970	+	0.00893437i
$960$	−0.782730	−	0.574797i	−0.0252625	−	0.0185515i
$961$	14.1119			0.455221
$962$	58.9036	−	102.024i	1.89913	−	3.28939i
$963$	15.1657	+	48.3447i	0.488708	+	1.55789i
$964$	−7.63434	−	13.2231i	−0.245886	−	0.425886i
$965$	4.87072	−	8.43634i	0.156794	−	0.271575i
$966$	7.74146	+	8.48308i	0.249078	+	0.272939i
$967$	11.1960	+	19.3921i	0.360040	+	0.623607i	0.987967	−	0.154665i	$-0.0494298\pi$
$967$	11.1960	+	19.3921i	0.360040	+	0.623607i	−0.627927	+	0.778272i	$0.716096\pi$
$968$	−0.664962	+	1.15175i	−0.0213727	+	0.0370186i
$969$	−0.318180	+	2.88588i	−0.0102214	+	0.0927077i
$970$	2.22101	+	3.84690i	0.0713123	+	0.123517i
$971$	−8.72650	−	15.1147i	−0.280047	−	0.485055i	0.691349	−	0.722521i	$-0.257017\pi$
$971$	−8.72650	−	15.1147i	−0.280047	−	0.485055i	−0.971396	+	0.237466i	$0.923683\pi$
$972$	10.2819	−	16.8058i	0.329791	−	0.539048i
$973$	−15.7425	−	46.5774i	−0.504682	−	1.49320i
$974$	−7.68507	+	13.3109i	−0.246246	+	0.426510i
$975$	46.0772	+	33.8368i	1.47565	+	1.08364i
$976$	−63.2583			−2.02485
$977$	21.7376			0.695447			0.347723	−	0.937597i	$-0.386955\pi$
$977$	21.7376			0.695447			0.347723	+	0.937597i	$0.386955\pi$
$978$	14.8123	−	6.50472i	0.473646	−	0.207998i
$979$	3.79532	−	6.57369i	0.121299	−	0.210096i
$980$	−2.76524	+	2.11030i	−0.0883323	+	0.0674109i
$981$	−3.99419	+	4.34618i	−0.127525	+	0.138763i
$982$	2.87058	+	4.97199i	0.0916038	+	0.158662i
$983$	−13.3461	−	23.1161i	−0.425674	−	0.737288i	0.570809	−	0.821083i	$-0.306629\pi$
$983$	−13.3461	−	23.1161i	−0.425674	−	0.737288i	−0.996483	+	0.0837943i	$0.973296\pi$
$984$	−11.3646	+	4.99068i	−0.362290	+	0.159097i
$985$	−0.791723	+	1.37131i	−0.0252264	+	0.0436934i
$986$	30.4651	+	52.7671i	0.970206	+	1.68045i
$987$	7.76817	−	24.4630i	0.247263	−	0.778665i
$988$	−1.82764	+	3.16556i	−0.0581450	+	0.100710i
$989$	−4.17472	−	7.23082i	−0.132748	−	0.229927i
$990$	2.07980	+	0.464257i	0.0661004	+	0.0147551i
$991$	−21.0046	+	36.3810i	−0.667233	+	1.15568i	0.311442	+	0.950265i	$0.399188\pi$
$991$	−21.0046	+	36.3810i	−0.667233	+	1.15568i	−0.978675	+	0.205416i	$0.934145\pi$
$992$	−41.9612			−1.33227
$993$	−6.76712	+	61.3774i	−0.214748	+	1.94775i
$994$	−37.4904	−	7.50864i	−1.18912	−	0.238160i
$995$	−0.545158	−	0.944241i	−0.0172827	−	0.0299345i
$996$	3.56754	+	2.61982i	0.113042	+	0.0830121i
$997$	−11.7347	−	20.3250i	−0.371640	−	0.643700i	0.618178	−	0.786038i	$-0.287871\pi$
$997$	−11.7347	−	20.3250i	−0.371640	−	0.643700i	−0.989818	+	0.142338i	$0.954538\pi$
$998$	−6.06577	+	10.5062i	−0.192009	+	0.332569i
$999$	−48.8087	+	9.59796i	−1.54424	+	0.303666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.l.b.529.8	yes	74
7.2	even	3		693.2.k.b.331.30	yes	74
9.4	even	3		693.2.k.b.67.30	✓	74
63.58	even	3	inner	693.2.l.b.562.8	yes	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.b.67.30	✓	74	9.4	even	3
693.2.k.b.331.30	yes	74	7.2	even	3
693.2.l.b.529.8	yes	74	1.1	even	1	trivial
693.2.l.b.562.8	yes	74	63.58	even	3	inner

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.80662 q^{2} +(0.189816 - 1.72162i) q^{3} +1.26386 q^{4} +(-0.196591 + 0.340506i) q^{5} +(-0.342924 + 3.11030i) q^{6} +(2.59423 + 0.519577i) q^{7} +1.32992 q^{8} +(-2.92794 - 0.653580i) q^{9} +O(q^{10})\)	\(q-1.80662 q^{2} +(0.189816 - 1.72162i) q^{3} +1.26386 q^{4} +(-0.196591 + 0.340506i) q^{5} +(-0.342924 + 3.11030i) q^{6} +(2.59423 + 0.519577i) q^{7} +1.32992 q^{8} +(-2.92794 - 0.653580i) q^{9} +(0.355165 - 0.615163i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.239900 - 2.17588i) q^{12} +(3.40582 + 5.89906i) q^{13} +(-4.68678 - 0.938676i) q^{14} +(0.548905 + 0.403088i) q^{15} -4.93038 q^{16} +(-1.97397 + 3.41902i) q^{17} +(5.28966 + 1.18077i) q^{18} +(0.212295 + 0.367706i) q^{19} +(-0.248464 + 0.430352i) q^{20} +(1.38694 - 4.36765i) q^{21} +(0.903308 + 1.56457i) q^{22} +(0.693594 - 1.20134i) q^{23} +(0.252440 - 2.28962i) q^{24} +(2.42270 + 4.19625i) q^{25} +(-6.15301 - 10.6573i) q^{26} +(-1.68098 + 4.91674i) q^{27} +(3.27874 + 0.656672i) q^{28} +(-4.27135 + 7.39820i) q^{29} +(-0.991661 - 0.728226i) q^{30} -6.71654 q^{31} +6.24745 q^{32} +(-1.58587 + 0.696424i) q^{33} +(3.56621 - 6.17686i) q^{34} +(-0.686922 + 0.781207i) q^{35} +(-3.70050 - 0.826033i) q^{36} +(4.78657 + 8.29058i) q^{37} +(-0.383535 - 0.664303i) q^{38} +(10.8024 - 4.74380i) q^{39} +(-0.261451 + 0.452847i) q^{40} +(-2.69420 - 4.66649i) q^{41} +(-2.50567 + 7.89067i) q^{42} +(3.00948 - 5.21258i) q^{43} +(-0.631930 - 1.09453i) q^{44} +(0.798155 - 0.868493i) q^{45} +(-1.25306 + 2.17036i) q^{46} +5.60094 q^{47} +(-0.935863 + 8.48823i) q^{48} +(6.46008 + 2.69581i) q^{49} +(-4.37689 - 7.58100i) q^{50} +(5.51156 + 4.04741i) q^{51} +(4.30448 + 7.45558i) q^{52} +(1.15378 - 1.99841i) q^{53} +(3.03689 - 8.88265i) q^{54} +0.393182 q^{55} +(3.45013 + 0.690998i) q^{56} +(0.673346 - 0.295695i) q^{57} +(7.71669 - 13.3657i) q^{58} -6.95559 q^{59} +(0.693739 + 0.509447i) q^{60} +12.8303 q^{61} +12.1342 q^{62} +(-7.25617 - 3.21683i) q^{63} -1.42598 q^{64} -2.67822 q^{65} +(2.86506 - 1.25817i) q^{66} -4.37024 q^{67} +(-2.49482 + 4.32116i) q^{68} +(-1.93659 - 1.42214i) q^{69} +(1.24100 - 1.41134i) q^{70} +7.99918 q^{71} +(-3.89394 - 0.869212i) q^{72} +(4.58593 - 7.94307i) q^{73} +(-8.64749 - 14.9779i) q^{74} +(7.68420 - 3.37446i) q^{75} +(0.268311 + 0.464728i) q^{76} +(-0.847149 - 2.50646i) q^{77} +(-19.5158 + 8.57021i) q^{78} +2.27947 q^{79} +(0.969269 - 1.67882i) q^{80} +(8.14567 + 3.82729i) q^{81} +(4.86738 + 8.43054i) q^{82} +(-1.01097 + 1.75104i) q^{83} +(1.75290 - 5.52010i) q^{84} +(-0.776132 - 1.34430i) q^{85} +(-5.43698 + 9.41712i) q^{86} +(11.9261 + 8.75794i) q^{87} +(-0.664962 - 1.15175i) q^{88} +(3.79532 + 6.57369i) q^{89} +(-1.44196 + 1.56903i) q^{90} +(5.77048 + 17.0731i) q^{91} +(0.876605 - 1.51832i) q^{92} +(-1.27490 + 11.5633i) q^{93} -10.1187 q^{94} -0.166941 q^{95} +(1.18586 - 10.7557i) q^{96} +(-3.12673 + 5.41566i) q^{97} +(-11.6709 - 4.87028i) q^{98} +(0.897953 + 2.86246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q + 80 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 74 * q + 80 * q^4 - 7 * q^5 - 23 * q^6 - q^7 - 6 * q^8 - 4 * q^9	\( 74 q + 80 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 9 q^{10} - 37 q^{11} - 4 q^{12} - 25 q^{13} + 10 q^{14} + 18 q^{15} + 92 q^{16} - 6 q^{17} - 6 q^{18} - 13 q^{19} - 15 q^{20} + 11 q^{21} + 4 q^{23} - 33 q^{24} - 46 q^{25} - 12 q^{26} - 21 q^{27} - 26 q^{28} - 9 q^{29} - 17 q^{30} + 66 q^{31} + 8 q^{32} - 16 q^{34} - 30 q^{35} - 57 q^{36} + 18 q^{37} - 29 q^{38} - 14 q^{39} - 57 q^{40} - 2 q^{41} - 48 q^{42} - 10 q^{43} - 40 q^{44} + 32 q^{45} - 12 q^{46} - 14 q^{47} + 46 q^{48} + 11 q^{49} - 46 q^{50} + 14 q^{51} - 36 q^{52} + 13 q^{53} + 10 q^{54} + 14 q^{55} + 3 q^{56} - 63 q^{57} + 22 q^{58} + 66 q^{59} + 122 q^{60} + 110 q^{61} + 36 q^{62} + 18 q^{63} + 122 q^{64} - 46 q^{65} + 16 q^{66} - 68 q^{67} - 20 q^{68} - 15 q^{69} + 43 q^{70} - 8 q^{71} + 45 q^{72} - 66 q^{73} - 16 q^{74} + 15 q^{75} - 77 q^{76} + 2 q^{77} + 94 q^{78} - 8 q^{79} - 29 q^{80} - 28 q^{81} - 54 q^{82} + 7 q^{83} + 75 q^{84} + 5 q^{85} - 10 q^{87} + 3 q^{88} - 26 q^{89} + 12 q^{90} - 35 q^{91} - 15 q^{92} - 37 q^{93} + 64 q^{94} + 76 q^{95} - 140 q^{96} - 29 q^{97} + 27 q^{98} + 2 q^{99}+O(q^{100}) \) 74 * q + 80 * q^4 - 7 * q^5 - 23 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 9 * q^10 - 37 * q^11 - 4 * q^12 - 25 * q^13 + 10 * q^14 + 18 * q^15 + 92 * q^16 - 6 * q^17 - 6 * q^18 - 13 * q^19 - 15 * q^20 + 11 * q^21 + 4 * q^23 - 33 * q^24 - 46 * q^25 - 12 * q^26 - 21 * q^27 - 26 * q^28 - 9 * q^29 - 17 * q^30 + 66 * q^31 + 8 * q^32 - 16 * q^34 - 30 * q^35 - 57 * q^36 + 18 * q^37 - 29 * q^38 - 14 * q^39 - 57 * q^40 - 2 * q^41 - 48 * q^42 - 10 * q^43 - 40 * q^44 + 32 * q^45 - 12 * q^46 - 14 * q^47 + 46 * q^48 + 11 * q^49 - 46 * q^50 + 14 * q^51 - 36 * q^52 + 13 * q^53 + 10 * q^54 + 14 * q^55 + 3 * q^56 - 63 * q^57 + 22 * q^58 + 66 * q^59 + 122 * q^60 + 110 * q^61 + 36 * q^62 + 18 * q^63 + 122 * q^64 - 46 * q^65 + 16 * q^66 - 68 * q^67 - 20 * q^68 - 15 * q^69 + 43 * q^70 - 8 * q^71 + 45 * q^72 - 66 * q^73 - 16 * q^74 + 15 * q^75 - 77 * q^76 + 2 * q^77 + 94 * q^78 - 8 * q^79 - 29 * q^80 - 28 * q^81 - 54 * q^82 + 7 * q^83 + 75 * q^84 + 5 * q^85 - 10 * q^87 + 3 * q^88 - 26 * q^89 + 12 * q^90 - 35 * q^91 - 15 * q^92 - 37 * q^93 + 64 * q^94 + 76 * q^95 - 140 * q^96 - 29 * q^97 + 27 * q^98 + 2 * q^99

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