LMFDB - Embedded newform 546.2.bg.b.311.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.17
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.71668 - 0.230243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00187 - 0.578432i) q^{5} +(1.05774 + 1.37157i) q^{6} +(-0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(2.89398 - 0.790508i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.71668 - 0.230243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00187 - 0.578432i) q^{5} +(1.05774 + 1.37157i) q^{6} +(-0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(2.89398 - 0.790508i) q^{9} +(1.00187 + 0.578432i) q^{10} +(1.85690 - 3.21624i) q^{11} +(-0.658943 + 1.60181i) q^{12} +(-0.361803 + 3.58735i) q^{13} +(2.12873 - 1.57116i) q^{14} +(1.58672 - 1.22366i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.0128016 - 0.0221731i) q^{17} +(2.13159 + 2.11100i) q^{18} +(-0.122255 - 0.211752i) q^{19} +1.15686i q^{20} +(-1.11398 - 4.44511i) q^{21} +3.71379 q^{22} +(2.36531 - 1.36561i) q^{23} +(-1.71668 + 0.230243i) q^{24} +(-1.83083 + 3.17109i) q^{25} +(-3.28764 + 1.48035i) q^{26} +(4.78602 - 2.02337i) q^{27} +(2.42502 + 1.05795i) q^{28} +3.51946i q^{29} +(1.85308 + 0.762308i) q^{30} +(-2.24622 + 3.89056i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.44718 - 5.94879i) q^{33} +0.0256033 q^{34} +(-1.81761 - 2.46265i) q^{35} +(-0.762388 + 2.90151i) q^{36} +(-8.29815 + 4.79094i) q^{37} +(0.122255 - 0.211752i) q^{38} +(0.204865 + 6.24164i) q^{39} +(-1.00187 + 0.578432i) q^{40} -0.471512i q^{41} +(3.29259 - 3.18729i) q^{42} -1.24061 q^{43} +(1.85690 + 3.21624i) q^{44} +(2.44214 - 2.46596i) q^{45} +(2.36531 + 1.36561i) q^{46} +(0.203606 - 0.117552i) q^{47} +(-1.05774 - 1.37157i) q^{48} +(-6.82442 + 1.55800i) q^{49} -3.66166 q^{50} +(0.0168711 - 0.0410116i) q^{51} +(-2.92584 - 2.10701i) q^{52} +(-6.44560 - 3.72137i) q^{53} +(4.14530 + 3.13313i) q^{54} -4.29635i q^{55} +(0.296298 + 2.62911i) q^{56} +(-0.258628 - 0.335362i) q^{57} +(-3.04794 + 1.75973i) q^{58} +(2.80431 + 1.61907i) q^{59} +(0.266360 + 1.98597i) q^{60} +(10.2453 - 5.91511i) q^{61} -4.49243 q^{62} +(-2.93581 - 7.37435i) q^{63} +1.00000 q^{64} +(1.71256 + 3.80335i) q^{65} +(6.37539 - 0.855076i) q^{66} +(6.24108 + 3.60329i) q^{67} +(0.0128016 + 0.0221731i) q^{68} +(3.74606 - 2.88892i) q^{69} +(1.22391 - 2.80542i) q^{70} -14.6757 q^{71} +(-2.89398 + 0.790508i) q^{72} +(-0.784266 + 1.35839i) q^{73} +(-8.29815 - 4.79094i) q^{74} +(-2.41283 + 5.86529i) q^{75} +0.244511 q^{76} +(-9.00603 - 3.92901i) q^{77} +(-5.30298 + 3.29824i) q^{78} +(3.01266 + 5.21808i) q^{79} +(-1.00187 - 0.578432i) q^{80} +(7.75019 - 4.57542i) q^{81} +(0.408341 - 0.235756i) q^{82} +3.64267i q^{83} +(4.40657 + 1.25782i) q^{84} -0.0296195i q^{85} +(-0.620304 - 1.07440i) q^{86} +(0.810333 + 6.04179i) q^{87} +(-1.85690 + 3.21624i) q^{88} +(8.11911 - 4.68757i) q^{89} +(3.35666 + 0.881980i) q^{90} +(9.53874 - 0.111706i) q^{91} +2.73122i q^{92} +(-2.96026 + 7.19602i) q^{93} +(0.203606 + 0.117552i) q^{94} +(-0.244969 - 0.141433i) q^{95} +(0.658943 - 1.60181i) q^{96} -12.7955 q^{97} +(-4.76147 - 5.13112i) q^{98} +(2.83135 - 10.7756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.71668	−	0.230243i	0.991125	−	0.132931i
$3$	1.71668	−	0.230243i	0.991125	−	0.132931i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00187	−	0.578432i	0.448052	−	0.258683i	−0.258955	−	0.965889i	$-0.583378\pi$
$5$	1.00187	−	0.578432i	0.448052	−	0.258683i	0.707007	+	0.707206i	$0.250045\pi$
$6$	1.05774	+	1.37157i	0.431819	+	0.559940i
$7$	−0.296298	−	2.62911i	−0.111990	−	0.993709i
$7$	−0.296298	−	2.62911i	−0.111990	−	0.993709i
$8$	−1.00000			−0.353553
$9$	2.89398	−	0.790508i	0.964659	−	0.263503i
$10$	1.00187	+	0.578432i	0.316820	+	0.182916i
$11$	1.85690	−	3.21624i	0.559875	−	0.969732i	−0.437631	−	0.899155i	$-0.644182\pi$
$11$	1.85690	−	3.21624i	0.559875	−	0.969732i	0.997506	−	0.0705774i	$-0.0224842\pi$
$12$	−0.658943	+	1.60181i	−0.190220	+	0.462403i
$13$	−0.361803	+	3.58735i	−0.100346	+	0.994953i
$13$	−0.361803	+	3.58735i	−0.100346	+	0.994953i
$14$	2.12873	−	1.57116i	0.568926	−	0.419909i
$15$	1.58672	−	1.22366i	0.409688	−	0.315947i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.0128016	−	0.0221731i	0.00310485	−	0.00537776i	−0.864469	−	0.502686i	$-0.832345\pi$
$17$	0.0128016	−	0.0221731i	0.00310485	−	0.00537776i	0.867574	+	0.497309i	$0.165678\pi$
$18$	2.13159	+	2.11100i	0.502420	+	0.497568i
$19$	−0.122255	−	0.211752i	−0.0280473	−	0.0485793i	0.851661	−	0.524093i	$-0.175596\pi$
$19$	−0.122255	−	0.211752i	−0.0280473	−	0.0485793i	−0.879708	+	0.475514i	$0.842262\pi$
$20$			1.15686i			0.258683i
$21$	−1.11398	−	4.44511i	−0.243091	−	0.970003i
$22$	3.71379			0.791783
$23$	2.36531	−	1.36561i	0.493201	−	0.284750i	−0.232700	−	0.972548i	$-0.574756\pi$
$23$	2.36531	−	1.36561i	0.493201	−	0.284750i	0.725902	+	0.687799i	$0.241423\pi$
$24$	−1.71668	+	0.230243i	−0.350416	+	0.0469982i
$25$	−1.83083	+	3.17109i	−0.366166	+	0.634219i
$26$	−3.28764	+	1.48035i	−0.644759	+	0.290320i
$27$	4.78602	−	2.02337i	0.921070	−	0.389397i
$28$	2.42502	+	1.05795i	0.458286	+	0.199934i
$29$			3.51946i			0.653548i	0.945103	+	0.326774i	$0.105962\pi$
$29$			3.51946i			0.653548i	−0.945103	+	0.326774i	$0.894038\pi$
$30$	1.85308	+	0.762308i	0.338324	+	0.139178i
$31$	−2.24622	+	3.89056i	−0.403432	+	0.698765i	−0.994138	−	0.108122i	$-0.965516\pi$
$31$	−2.24622	+	3.89056i	−0.403432	+	0.698765i	0.590705	+	0.806887i	$0.298850\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.44718	−	5.94879i	0.425999	−	1.03555i
$34$	0.0256033			0.00439092
$35$	−1.81761	−	2.46265i	−0.307233	−	0.416263i
$36$	−0.762388	+	2.90151i	−0.127065	+	0.483585i
$37$	−8.29815	+	4.79094i	−1.36421	+	0.787625i	−0.990181	−	0.139793i	$-0.955356\pi$
$37$	−8.29815	+	4.79094i	−1.36421	+	0.787625i	−0.374026	+	0.927418i	$0.622023\pi$
$38$	0.122255	−	0.211752i	0.0198324	−	0.0343508i
$39$	0.204865	+	6.24164i	0.0328046	+	0.999462i
$40$	−1.00187	+	0.578432i	−0.158410	+	0.0914582i
$41$		−	0.471512i		−	0.0736377i	−0.999322	−	0.0368189i	$-0.988278\pi$
$41$		−	0.471512i		−	0.0736377i	0.999322	−	0.0368189i	$-0.0117225\pi$
$42$	3.29259	−	3.18729i	0.508058	−	0.491810i
$43$	−1.24061			−0.189191			−0.0945955	−	0.995516i	$-0.530156\pi$
$43$	−1.24061			−0.189191			−0.0945955	+	0.995516i	$0.530156\pi$
$44$	1.85690	+	3.21624i	0.279937	+	0.484866i
$45$	2.44214	−	2.46596i	0.364053	−	0.367603i
$46$	2.36531	+	1.36561i	0.348746	+	0.201349i
$47$	0.203606	−	0.117552i	0.0296990	−	0.0171467i	−0.485077	−	0.874471i	$-0.661208\pi$
$47$	0.203606	−	0.117552i	0.0296990	−	0.0171467i	0.514776	+	0.857325i	$0.327875\pi$
$48$	−1.05774	−	1.37157i	−0.152671	−	0.197969i
$49$	−6.82442	+	1.55800i	−0.974916	+	0.222571i
$50$	−3.66166			−0.517837
$51$	0.0168711	−	0.0410116i	0.00236243	−	0.00574277i
$52$	−2.92584	−	2.10701i	−0.405741	−	0.292189i
$53$	−6.44560	−	3.72137i	−0.885372	−	0.511170i	−0.0129459	−	0.999916i	$-0.504121\pi$
$53$	−6.44560	−	3.72137i	−0.885372	−	0.511170i	−0.872426	+	0.488747i	$0.837454\pi$
$54$	4.14530	+	3.13313i	0.564104	+	0.426365i
$55$		−	4.29635i		−	0.579320i
$56$	0.296298	+	2.62911i	0.0395945	+	0.351329i
$57$	−0.258628	−	0.335362i	−0.0342561	−	0.0444198i
$58$	−3.04794	+	1.75973i	−0.400215	+	0.231064i
$59$	2.80431	+	1.61907i	0.365090	+	0.210785i	0.671311	−	0.741176i	$-0.265731\pi$
$59$	2.80431	+	1.61907i	0.365090	+	0.210785i	−0.306221	+	0.951960i	$0.599065\pi$
$60$	0.266360	+	1.98597i	0.0343870	+	0.256387i
$61$	10.2453	−	5.91511i	1.31177	−	0.757353i	0.329384	−	0.944196i	$-0.393159\pi$
$61$	10.2453	−	5.91511i	1.31177	−	0.757353i	0.982390	+	0.186844i	$0.0598258\pi$
$62$	−4.49243			−0.570539
$63$	−2.93581	−	7.37435i	−0.369877	−	0.929081i
$64$	1.00000			0.125000
$65$	1.71256	+	3.80335i	0.212417	+	0.471748i
$66$	6.37539	−	0.855076i	0.784756	−	0.105253i
$67$	6.24108	+	3.60329i	0.762469	+	0.440212i	0.830182	−	0.557493i	$-0.188237\pi$
$67$	6.24108	+	3.60329i	0.762469	+	0.440212i	−0.0677122	+	0.997705i	$0.521570\pi$
$68$	0.0128016	+	0.0221731i	0.00155243	+	0.00268888i
$69$	3.74606	−	2.88892i	0.450972	−	0.347785i
$70$	1.22391	−	2.80542i	0.146285	−	0.335312i
$71$	−14.6757			−1.74168			−0.870841	−	0.491564i	$-0.836425\pi$
$71$	−14.6757			−1.74168			−0.870841	+	0.491564i	$0.836425\pi$
$72$	−2.89398	+	0.790508i	−0.341058	+	0.0931623i
$73$	−0.784266	+	1.35839i	−0.0917914	+	0.158987i	−0.908265	−	0.418395i	$-0.862593\pi$
$73$	−0.784266	+	1.35839i	−0.0917914	+	0.158987i	0.816474	+	0.577383i	$0.195926\pi$
$74$	−8.29815	−	4.79094i	−0.964640	−	0.556935i
$75$	−2.41283	+	5.86529i	−0.278609	+	0.677265i
$76$	0.244511			0.0280473
$77$	−9.00603	−	3.92901i	−1.02633	−	0.447753i
$78$	−5.30298	+	3.29824i	−0.600445	+	0.373452i
$79$	3.01266	+	5.21808i	0.338951	+	0.587080i	0.984236	−	0.176862i	$-0.0565946\pi$
$79$	3.01266	+	5.21808i	0.338951	+	0.587080i	−0.645285	+	0.763942i	$0.723261\pi$
$80$	−1.00187	−	0.578432i	−0.112013	−	0.0646707i
$81$	7.75019	−	4.57542i	0.861133	−	0.508380i
$82$	0.408341	−	0.235756i	0.0450937	−	0.0260349i
$83$			3.64267i			0.399835i	0.979813	+	0.199917i	$0.0640673\pi$
$83$			3.64267i			0.399835i	−0.979813	+	0.199917i	$0.935933\pi$
$84$	4.40657	+	1.25782i	0.480797	+	0.137239i
$85$		−	0.0296195i		−	0.00321269i
$86$	−0.620304	−	1.07440i	−0.0668891	−	0.115855i
$87$	0.810333	+	6.04179i	0.0868768	+	0.647748i
$88$	−1.85690	+	3.21624i	−0.197946	+	0.342852i
$89$	8.11911	−	4.68757i	0.860623	−	0.496881i	−0.00359755	−	0.999994i	$-0.501145\pi$
$89$	8.11911	−	4.68757i	0.860623	−	0.496881i	0.864221	+	0.503112i	$0.167812\pi$
$90$	3.35666	+	0.881980i	0.353823	+	0.0929688i
$91$	9.53874	−	0.111706i	0.999931	−	0.0117100i
$92$			2.73122i			0.284750i
$93$	−2.96026	+	7.19602i	−0.306964	+	0.746193i
$94$	0.203606	+	0.117552i	0.0210004	+	0.0121246i
$95$	−0.244969	−	0.141433i	−0.0251333	−	0.0145107i
$96$	0.658943	−	1.60181i	0.0672531	−	0.163484i
$97$	−12.7955			−1.29918			−0.649591	−	0.760284i	$-0.725060\pi$
$97$	−12.7955			−1.29918			−0.649591	+	0.760284i	$0.725060\pi$
$98$	−4.76147	−	5.13112i	−0.480981	−	0.518321i
$99$	2.83135	−	10.7756i	0.284561	−	1.08299i
$100$	−1.83083	−	3.17109i	−0.183083	−	0.317109i
$101$	−5.03494	+	8.72077i	−0.500995	+	0.867749i	0.499004	+	0.866600i	$0.333699\pi$
$101$	−5.03494	+	8.72077i	−0.500995	+	0.867749i	−0.999999	+	0.00114938i	$0.999634\pi$
$102$	0.0439526	−	0.00589498i	0.00435196	−	0.000583690i
$103$	8.82256	−	5.09371i	0.869313	−	0.501898i	0.00219314	−	0.999998i	$-0.499302\pi$
$103$	8.82256	−	5.09371i	0.869313	−	0.501898i	0.867120	+	0.498099i	$0.165969\pi$
$104$	0.361803	−	3.58735i	0.0354777	−	0.351769i
$105$	−3.68727	−	3.80908i	−0.359841	−	0.371728i
$106$		−	7.44274i		−	0.722903i
$107$	−15.7423	+	9.08881i	−1.52186	+	0.878648i	−0.522197	+	0.852825i	$0.674887\pi$
$107$	−15.7423	+	9.08881i	−1.52186	+	0.878648i	−0.999667	+	0.0258233i	$0.991779\pi$
$108$	−0.640722	+	5.15650i	−0.0616535	+	0.496184i
$109$	2.40616	+	1.38920i	0.230469	+	0.133061i	0.610788	−	0.791794i	$-0.290853\pi$
$109$	2.40616	+	1.38920i	0.230469	+	0.133061i	−0.380320	+	0.924855i	$0.624186\pi$
$110$	3.72075	−	2.14818i	0.354760	−	0.204821i
$111$	−13.1422	+	10.1351i	−1.24740	+	0.961981i
$112$	−2.12873	+	1.57116i	−0.201146	+	0.148460i
$113$		−	18.6367i		−	1.75319i	−0.481229	−	0.876595i	$-0.659809\pi$
$113$		−	18.6367i		−	1.75319i	0.481229	−	0.876595i	$-0.340191\pi$
$114$	0.161119	−	0.391659i	0.0150901	−	0.0366823i
$115$	1.57983	−	2.73634i	0.147320	−	0.255165i
$116$	−3.04794	−	1.75973i	−0.282995	−	0.163387i
$117$	1.78878	+	10.6677i	0.165373	+	0.986231i
$118$			3.23814i			0.298095i
$119$	−0.0620885	−	0.0270870i	−0.00569164	−	0.00248306i
$120$	−1.58672	+	1.22366i	−0.144847	+	0.111704i
$121$	−1.39612	−	2.41815i	−0.126920	−	0.219832i
$122$	10.2453	+	5.91511i	0.927564	+	0.535529i
$123$	−0.108562	−	0.809434i	−0.00978874	−	0.0729842i
$124$	−2.24622	−	3.89056i	−0.201716	−	0.349383i
$125$			10.0204i			0.896249i
$126$	4.91847	−	6.22966i	0.438172	−	0.554982i
$127$	−8.83042			−0.783573			−0.391787	−	0.920056i	$-0.628143\pi$
$127$	−8.83042			−0.783573			−0.391787	+	0.920056i	$0.628143\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.12973	+	0.285642i	−0.187512	+	0.0251494i
$130$	−2.43752	+	3.38480i	−0.213785	+	0.296866i
$131$	−7.07051	−	12.2465i	−0.617753	−	1.06998i	−0.989895	−	0.141804i	$-0.954710\pi$
$131$	−7.07051	−	12.2465i	−0.617753	−	1.06998i	0.372141	−	0.928176i	$-0.378624\pi$
$132$	3.92821	+	5.09371i	0.341907	+	0.443351i
$133$	−0.520496	+	0.384164i	−0.0451327	+	0.0333113i
$134$			7.20658i			0.622554i
$135$	3.62461	−	4.79555i	0.311957	−	0.412735i
$136$	−0.0128016	+	0.0221731i	−0.00109773	+	0.00190133i
$137$	6.70701	−	11.6169i	0.573019	−	0.992498i	−0.423235	−	0.906020i	$-0.639106\pi$
$137$	6.70701	−	11.6169i	0.573019	−	0.992498i	0.996254	−	0.0864777i	$-0.0275611\pi$
$138$	4.37490	+	1.79972i	0.372416	+	0.153202i
$139$		−	15.0565i		−	1.27708i	−0.769589	−	0.638539i	$-0.779539\pi$
$139$		−	15.0565i		−	1.27708i	0.769589	−	0.638539i	$-0.220461\pi$
$140$	3.04152	−	0.342777i	0.257056	−	0.0289699i
$141$	0.322461	−	0.248678i	0.0271561	−	0.0209425i
$142$	−7.33784	−	12.7095i	−0.615778	−	1.06656i
$143$	10.8659	+	7.82498i	0.908656	+	0.654358i
$144$	−2.13159	−	2.11100i	−0.177632	−	0.175917i
$145$	2.03577	+	3.52606i	0.169062	+	0.292823i
$146$	−1.56853			−0.129813
$147$	−11.3566	+	4.24586i	−0.936678	+	0.350193i
$148$		−	9.58187i		−	0.787625i
$149$	−4.72601	−	8.18569i	−0.387170	−	0.670598i	0.604898	−	0.796303i	$-0.293214\pi$
$149$	−4.72601	−	8.18569i	−0.387170	−	0.670598i	−0.992068	+	0.125705i	$0.959881\pi$
$150$	−6.28590	+	0.843074i	−0.513242	+	0.0688367i
$151$	12.9798	+	7.49388i	1.05628	+	0.609843i	0.924401	−	0.381423i	$-0.124566\pi$
$151$	12.9798	+	7.49388i	1.05628	+	0.609843i	0.131878	+	0.991266i	$0.457899\pi$
$152$	0.122255	+	0.211752i	0.00991621	+	0.0171754i
$153$	0.0195196	−	0.0742882i	0.00157807	−	0.00600584i
$154$	−1.10039	−	9.76396i	−0.0886718	−	0.786802i
$155$			5.19714i			0.417444i
$156$	−5.50785	−	2.94340i	−0.440981	−	0.235661i
$157$	1.50376	+	0.868197i	0.120013	+	0.0692896i	0.558805	−	0.829299i	$-0.311260\pi$
$157$	1.50376	+	0.868197i	0.120013	+	0.0692896i	−0.438792	+	0.898589i	$0.644593\pi$
$158$	−3.01266	+	5.21808i	−0.239674	+	0.415128i
$159$	−11.9219	−	4.90434i	−0.945465	−	0.388940i
$160$		−	1.15686i		−	0.0914582i
$161$	−4.29118	−	5.81403i	−0.338192	−	0.458210i
$162$	7.83753	+	4.42415i	0.615774	+	0.347594i
$163$	11.0173	−	6.36085i	0.862943	−	0.498221i	−0.00205345	−	0.999998i	$-0.500654\pi$
$163$	11.0173	−	6.36085i	0.862943	−	0.498221i	0.864997	+	0.501777i	$0.167320\pi$
$164$	0.408341	+	0.235756i	0.0318861	+	0.0184094i
$165$	−0.989207	−	7.37546i	−0.0770097	−	0.574179i
$166$	−3.15464	+	1.82133i	−0.244848	+	0.141363i
$167$			6.85544i			0.530490i	0.964181	+	0.265245i	$0.0854528\pi$
$167$			6.85544i			0.530490i	−0.964181	+	0.265245i	$0.914547\pi$
$168$	1.11398	+	4.44511i	0.0859457	+	0.342948i
$169$	−12.7382	−	2.59583i	−0.979861	−	0.199679i
$170$	0.0256513	−	0.0148098i	0.00196736	−	0.00113586i
$171$	−0.521196	−	0.516163i	−0.0398568	−	0.0394719i
$172$	0.620304	−	1.07440i	0.0472977	−	0.0819221i
$173$	7.79711	+	13.5050i	0.592803	+	1.02677i	0.993853	+	0.110709i	$0.0353122\pi$
$173$	7.79711	+	13.5050i	0.592803	+	1.02677i	−0.401049	+	0.916056i	$0.631354\pi$
$174$	−4.82718	+	3.72266i	−0.365947	+	0.282214i
$175$	8.87962	+	3.87387i	0.671236	+	0.292837i
$176$	−3.71379			−0.279937
$177$	5.18688	+	2.13375i	0.389870	+	0.160382i
$178$	8.11911	+	4.68757i	0.608553	+	0.351348i
$179$	3.42830	+	1.97933i	0.256243	+	0.147942i	0.622620	−	0.782525i	$-0.286068\pi$
$179$	3.42830	+	1.97933i	0.256243	+	0.147942i	−0.366377	+	0.930467i	$0.619402\pi$
$180$	0.914511	+	3.34794i	0.0681636	+	0.249541i
$181$		−	0.429161i		−	0.0318992i	−0.999873	−	0.0159496i	$-0.994923\pi$
$181$		−	0.429161i		−	0.0318992i	0.999873	−	0.0159496i	$-0.00507714\pi$
$182$	4.86611	+	8.20494i	0.360700	+	0.608190i
$183$	16.2259	−	12.5133i	1.19946	−	0.925007i
$184$	−2.36531	+	1.36561i	−0.174373	+	0.100674i
$185$	−5.54247	+	9.59983i	−0.407490	+	0.705794i
$186$	−7.71207	+	1.03435i	−0.565476	+	0.0758424i
$187$	−0.0475426	−	0.0823462i	−0.00347666	−	0.00602175i
$188$			0.235104i			0.0171467i
$189$	−6.73774	−	11.9834i	−0.490098	−	0.871667i
$190$		−	0.282866i		−	0.0205212i
$191$	−1.57425	+	0.908893i	−0.113909	+	0.0657652i	−0.555872	−	0.831268i	$-0.687615\pi$
$191$	−1.57425	+	0.908893i	−0.113909	+	0.0657652i	0.441963	+	0.897033i	$0.354282\pi$
$192$	1.71668	−	0.230243i	0.123891	−	0.0166164i
$193$	−17.1426	−	9.89729i	−1.23395	−	0.712422i	−0.266100	−	0.963945i	$-0.585735\pi$
$193$	−17.1426	−	9.89729i	−1.23395	−	0.712422i	−0.967851	+	0.251523i	$0.919069\pi$
$194$	−6.39773	−	11.0812i	−0.459330	−	0.795583i
$195$	3.81561	+	6.13483i	0.273242	+	0.439325i
$196$	2.06294	−	6.68912i	0.147353	−	0.477794i
$197$	−25.2444			−1.79859			−0.899296	−	0.437341i	$-0.855920\pi$
$197$	−25.2444			−1.79859			−0.899296	+	0.437341i	$0.855920\pi$
$198$	10.7476	−	2.93578i	0.763800	−	0.208637i
$199$	−5.33963	−	3.08284i	−0.378517	−	0.218537i	0.298656	−	0.954361i	$-0.403462\pi$
$199$	−5.33963	−	3.08284i	−0.378517	−	0.218537i	−0.677173	+	0.735824i	$0.736795\pi$
$200$	1.83083	−	3.17109i	0.129459	−	0.224230i
$201$	11.5436	+	4.74873i	0.814221	+	0.334949i
$202$	−10.0699			−0.708514
$203$	9.25305	−	1.04281i	0.649437	−	0.0731909i
$204$	0.0270815	+	0.0351166i	0.00189608	+	0.00245865i
$205$	−0.272738	−	0.472395i	−0.0190488	−	0.0329935i
$206$	8.82256	+	5.09371i	0.614697	+	0.354896i
$207$	5.76562	−	5.82185i	0.400738	−	0.404646i
$208$	3.28764	−	1.48035i	0.227957	−	0.102644i
$209$	−0.908061			−0.0628119
$210$	1.45513	−	5.09781i	0.100413	−	0.351782i
$211$	−3.98179			−0.274117			−0.137059	−	0.990563i	$-0.543765\pi$
$211$	−3.98179			−0.274117			−0.137059	+	0.990563i	$0.543765\pi$
$212$	6.44560	−	3.72137i	0.442686	−	0.255585i
$213$	−25.1934	+	3.37898i	−1.72623	+	0.231524i
$214$	−15.7423	−	9.08881i	−1.07612	−	0.621298i
$215$	−1.24293	+	0.717608i	−0.0847673	+	0.0489405i
$216$	−4.78602	+	2.02337i	−0.325647	+	0.137673i
$217$	10.8943	+	4.75278i	0.739550	+	0.322640i
$218$			2.77840i			0.188177i
$219$	−1.03357	+	2.51249i	−0.0698425	+	0.169778i
$220$	3.72075	+	2.14818i	0.250853	+	0.144830i
$221$	0.0749110	+	0.0539463i	0.00503906	+	0.00362882i
$222$	−15.3483	−	6.31391i	−1.03011	−	0.423762i
$223$	2.03477			0.136258			0.0681291	−	0.997677i	$-0.478297\pi$
$223$	2.03477			0.136258			0.0681291	+	0.997677i	$0.478297\pi$
$224$	−2.42502	−	1.05795i	−0.162029	−	0.0706874i
$225$	−2.79161	+	10.6244i	−0.186107	+	0.708290i
$226$	16.1398	−	9.31833i	1.07361	−	0.619846i
$227$	15.6005	+	9.00694i	1.03544	+	0.597812i	0.918538	−	0.395332i	$-0.129370\pi$
$227$	15.6005	+	9.00694i	1.03544	+	0.597812i	0.116902	+	0.993143i	$0.462704\pi$
$228$	0.419746	−	0.0562970i	0.0277984	−	0.00372836i
$229$	9.36691	+	16.2240i	0.618983	+	1.07211i	0.989672	+	0.143353i	$0.0457884\pi$
$229$	9.36691	+	16.2240i	0.618983	+	1.07211i	−0.370688	+	0.928757i	$0.620878\pi$
$230$	3.15966			0.208342
$231$	−16.3651	−	4.67128i	−1.07674	−	0.307348i
$232$		−	3.51946i		−	0.231064i
$233$	17.0834	−	9.86309i	1.11917	−	0.646152i	0.177980	−	0.984034i	$-0.443044\pi$
$233$	17.0834	−	9.86309i	1.11917	−	0.646152i	0.941189	+	0.337882i	$0.109710\pi$
$234$	−8.34413	+	6.88299i	−0.545473	+	0.449955i
$235$	0.135992	−	0.235545i	0.00887112	−	0.0153652i
$236$	−2.80431	+	1.61907i	−0.182545	+	0.105392i
$237$	6.37320	+	8.26413i	0.413984	+	0.536813i
$238$	−0.00758619	−	0.0673137i	−0.000491740	−	0.00436330i
$239$	−20.1417			−1.30286			−0.651428	−	0.758711i	$-0.725830\pi$
$239$	−20.1417			−1.30286			−0.651428	+	0.758711i	$0.725830\pi$
$240$	−1.85308	−	0.762308i	−0.119616	−	0.0492068i
$241$	−11.1359	+	19.2880i	−0.717327	+	1.24245i	0.244729	+	0.969592i	$0.421301\pi$
$241$	−11.1359	+	19.2880i	−0.717327	+	1.24245i	−0.962055	+	0.272855i	$0.912032\pi$
$242$	1.39612	−	2.41815i	0.0897460	−	0.155445i
$243$	12.2511	−	9.63897i	0.785911	−	0.618340i
$244$			11.8302i			0.757353i
$245$	−5.93601	+	5.50838i	−0.379238	+	0.351918i
$246$	0.646709	−	0.498735i	0.0412327	−	0.0317982i
$247$	0.803863	−	0.361960i	0.0511486	−	0.0230310i
$248$	2.24622	−	3.89056i	0.142635	−	0.247051i
$249$	0.838700	+	6.25329i	0.0531504	+	0.396286i
$250$	−8.67790	+	5.01019i	−0.548838	+	0.316872i
$251$	20.5563			1.29750			0.648752	−	0.761000i	$-0.275291\pi$
$251$	20.5563			1.29750			0.648752	+	0.761000i	$0.275291\pi$
$252$	7.85428	+	1.14469i	0.494773	+	0.0721086i
$253$		−	10.1432i		−	0.637697i
$254$	−4.41521	−	7.64737i	−0.277035	−	0.479839i
$255$	−0.00681970	−	0.0508472i	−0.000427066	−	0.00318418i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.10857	+	8.84830i	0.318664	+	0.551942i	0.980210	−	0.197963i	$-0.0634326\pi$
$257$	5.10857	+	8.84830i	0.318664	+	0.551942i	−0.661546	+	0.749905i	$0.730099\pi$
$258$	−1.31224	−	1.70158i	−0.0816963	−	0.105936i
$259$	15.0546	+	20.3972i	0.935448	+	1.26742i
$260$	−4.15008	−	0.418557i	−0.257377	−	0.0259578i
$261$	2.78216	+	10.1852i	0.172212	+	0.630451i
$262$	7.07051	−	12.2465i	0.436818	−	0.756590i
$263$	24.3841	+	14.0782i	1.50359	+	0.868097i	0.999991	+	0.00415905i	$0.00132387\pi$
$263$	24.3841	+	14.0782i	1.50359	+	0.868097i	0.503598	+	0.863938i	$0.332009\pi$
$264$	−2.44718	+	5.94879i	−0.150613	+	0.366122i
$265$	−8.61025			−0.528923
$266$	−0.592944	−	0.258681i	−0.0363557	−	0.0158607i
$267$	12.8586	−	9.91642i	0.786935	−	0.606875i
$268$	−6.24108	+	3.60329i	−0.381235	+	0.220106i
$269$	14.6822	−	25.4302i	0.895187	−	1.55051i	0.0616140	−	0.998100i	$-0.480375\pi$
$269$	14.6822	−	25.4302i	0.895187	−	1.55051i	0.833573	−	0.552409i	$-0.186291\pi$
$270$	5.96537	+	0.741228i	0.363041	+	0.0451097i
$271$	14.2082	+	24.6093i	0.863085	+	1.49491i	0.868937	+	0.494923i	$0.164804\pi$
$271$	14.2082	+	24.6093i	0.863085	+	1.49491i	−0.00585211	+	0.999983i	$0.501863\pi$
$272$	−0.0256033			−0.00155243
$273$	16.3492	−	2.38800i	0.989501	−	0.144528i
$274$	13.4140			0.810371
$275$	6.79933	+	11.7768i	0.410015	+	0.710166i
$276$	0.628846	+	4.68864i	0.0378521	+	0.282223i
$277$	−13.8268	+	23.9486i	−0.830769	+	1.43893i	0.0666595	+	0.997776i	$0.478766\pi$
$277$	−13.8268	+	23.9486i	−0.830769	+	1.43893i	−0.897429	+	0.441159i	$0.854567\pi$
$278$	13.0393	−	7.52827i	0.782048	−	0.451516i
$279$	−3.42498	+	13.0348i	−0.205048	+	0.780375i
$280$	1.81761	+	2.46265i	0.108623	+	0.147171i
$281$	−12.3610			−0.737394			−0.368697	−	0.929550i	$-0.620196\pi$
$281$	−12.3610			−0.737394			−0.368697	+	0.929550i	$0.620196\pi$
$282$	0.376592	+	0.154920i	0.0224257	+	0.00922536i
$283$	11.8406	+	6.83616i	0.703849	+	0.406367i	0.808779	−	0.588112i	$-0.200129\pi$
$283$	11.8406	+	6.83616i	0.703849	+	0.406367i	−0.104930	+	0.994480i	$0.533462\pi$
$284$	7.33784	−	12.7095i	0.435421	−	0.754171i
$285$	−0.453097	−	0.186392i	−0.0268391	−	0.0110409i
$286$	−1.34366	+	13.3227i	−0.0794523	+	0.787786i
$287$	−1.23965	+	0.139708i	−0.0731745	+	0.00824669i
$288$	0.762388	−	2.90151i	0.0449241	−	0.170973i
$289$	8.49967	+	14.7219i	0.499981	+	0.865992i
$290$	−2.03577	+	3.52606i	−0.119545	+	0.207057i
$291$	−21.9657	+	2.94607i	−1.28765	+	0.172702i
$292$	−0.784266	−	1.35839i	−0.0458957	−	0.0794937i
$293$		−	4.20649i		−	0.245746i	−0.992422	−	0.122873i	$-0.960789\pi$
$293$		−	4.20649i		−	0.245746i	0.992422	−	0.122873i	$-0.0392107\pi$
$294$	−9.35533	−	7.71219i	−0.545614	−	0.449784i
$295$	3.74609			0.218106
$296$	8.29815	−	4.79094i	0.482320	−	0.278468i
$297$	2.37951	−	19.1502i	0.138073	−	1.11120i
$298$	4.72601	−	8.18569i	0.273771	−	0.474184i
$299$	4.04316	+	8.97928i	0.233822	+	0.519285i
$300$	−3.87307	−	5.02221i	−0.223612	−	0.289958i
$301$	0.367590	+	3.26169i	0.0211875	+	0.188001i
$302$			14.9878i			0.862448i
$303$	−6.63547	+	16.1300i	−0.381198	+	0.926646i
$304$	−0.122255	+	0.211752i	−0.00701182	+	0.0121448i
$305$	6.84299	−	11.8524i	0.391828	−	0.678666i
$306$	0.0740952	−	0.0202396i	0.00423574	−	0.00115702i
$307$	21.1492			1.20705			0.603524	−	0.797345i	$-0.293763\pi$
$307$	21.1492			1.20705			0.603524	+	0.797345i	$0.293763\pi$
$308$	7.90564	−	5.83494i	0.450466	−	0.332477i
$309$	13.9727	−	10.7756i	0.794880	−	0.613003i
$310$	−4.50085	+	2.59857i	−0.255631	+	0.147589i
$311$	15.6755	−	27.1507i	0.888874	−	1.53957i	0.0476652	−	0.998863i	$-0.484822\pi$
$311$	15.6755	−	27.1507i	0.888874	−	1.53957i	0.841208	−	0.540711i	$-0.181845\pi$
$312$	−0.204865	−	6.24164i	−0.0115982	−	0.353363i
$313$	28.3855	−	16.3884i	1.60444	−	0.926325i	0.613858	−	0.789417i	$-0.289617\pi$
$313$	28.3855	−	16.3884i	1.60444	−	0.926325i	0.990584	−	0.136908i	$-0.0437165\pi$
$314$			1.73639i			0.0979903i
$315$	−7.20687	−	5.69000i	−0.406061	−	0.320595i
$316$	−6.02532			−0.338951
$317$	−11.1137	−	19.2495i	−0.624209	−	1.08116i	−0.988693	−	0.149952i	$-0.952088\pi$
$317$	−11.1137	−	19.2495i	−0.624209	−	1.08116i	0.364484	−	0.931210i	$-0.381245\pi$
$318$	−1.71364	−	12.7768i	−0.0960963	−	0.716487i
$319$	11.3194	+	6.53528i	0.633766	+	0.365905i
$320$	1.00187	−	0.578432i	0.0560065	−	0.0323354i
$321$	−24.9318	+	19.2271i	−1.39156	+	1.07315i
$322$	2.88951	−	6.62328i	0.161026	−	0.369101i
$323$	−0.00626027			−0.000348331
$324$	0.0873358	+	8.99958i	0.00485199	+	0.499976i
$325$	−10.7134	−	7.71515i	−0.594274	−	0.427960i
$326$	11.0173	+	6.36085i	0.610193	+	0.352295i
$327$	4.45046	+	1.83081i	0.246111	+	0.101244i
$328$			0.471512i			0.0260349i
$329$	−0.369385	−	0.500472i	−0.0203648	−	0.0275919i
$330$	5.89273	−	4.54441i	0.324384	−	0.250161i
$331$	16.0419	−	9.26179i	0.881742	−	0.509074i	0.0105099	−	0.999945i	$-0.496655\pi$
$331$	16.0419	−	9.26179i	0.881742	−	0.509074i	0.871233	+	0.490871i	$0.163321\pi$
$332$	−3.15464	−	1.82133i	−0.173133	−	0.0999586i
$333$	−20.2274	+	20.4246i	−1.10845	+	1.11926i
$334$	−5.93699	+	3.42772i	−0.324857	+	0.187557i
$335$	8.33704			0.455501
$336$	−3.29259	+	3.18729i	−0.179626	+	0.173881i
$337$	−17.9572			−0.978191			−0.489095	−	0.872230i	$-0.662673\pi$
$337$	−17.9572			−0.978191			−0.489095	+	0.872230i	$0.662673\pi$
$338$	−4.12105	−	12.3295i	−0.224155	−	0.670637i
$339$	−4.29097	−	31.9932i	−0.233053	−	1.73763i
$340$	0.0256513	+	0.0148098i	0.00139113	+	0.000803172i
$341$	8.34198	+	14.4487i	0.451743	+	0.782442i
$342$	0.186412	−	0.709450i	0.0100800	−	0.0383627i
$343$	6.11820	+	17.4805i	0.330352	+	0.943858i
$344$	1.24061			0.0668891
$345$	2.08203	−	5.06117i	0.112093	−	0.272484i
$346$	−7.79711	+	13.5050i	−0.419175	+	0.726033i
$347$	0.436830	+	0.252204i	0.0234503	+	0.0135390i	0.511679	−	0.859177i	$-0.329024\pi$
$347$	0.436830	+	0.252204i	0.0234503	+	0.0135390i	−0.488229	+	0.872716i	$0.662357\pi$
$348$	−5.63751	−	2.31913i	−0.302202	−	0.124318i
$349$	−22.5405			−1.20656			−0.603282	−	0.797528i	$-0.706141\pi$
$349$	−22.5405			−1.20656			−0.603282	+	0.797528i	$0.706141\pi$
$350$	1.08494	+	9.62691i	0.0579927	+	0.514580i
$351$	5.52694	+	17.9012i	0.295006	+	0.955495i
$352$	−1.85690	−	3.21624i	−0.0989728	−	0.171426i
$353$	13.8668	+	8.00600i	0.738055	+	0.426116i	0.821362	−	0.570408i	$-0.193215\pi$
$353$	13.8668	+	8.00600i	0.738055	+	0.426116i	−0.0833068	+	0.996524i	$0.526548\pi$
$354$	0.745560	+	5.55884i	0.0396260	+	0.295449i
$355$	−14.7032	+	8.48889i	−0.780364	+	0.450543i
$356$			9.37514i			0.496881i
$357$	−0.112823	−	0.0322043i	−0.00597121	−	0.00170443i
$358$			3.95866i			0.209222i
$359$	7.67875	+	13.3000i	0.405269	+	0.701947i	0.994353	−	0.106125i	$-0.0338445\pi$
$359$	7.67875	+	13.3000i	0.405269	+	0.701947i	−0.589084	+	0.808072i	$0.700511\pi$
$360$	−2.44214	+	2.46596i	−0.128712	+	0.129967i
$361$	9.47011	−	16.4027i	0.498427	−	0.863300i
$362$	0.371664	−	0.214580i	0.0195342	−	0.0112781i
$363$	−2.95345	−	3.82974i	−0.155016	−	0.201009i
$364$	−4.67263	+	8.31664i	−0.244912	+	0.435911i
$365$			1.81458i			0.0949795i
$366$	18.9498	+	7.79545i	0.990520	+	0.407474i
$367$	−27.0095	−	15.5939i	−1.40988	−	0.813996i	−0.414506	−	0.910047i	$-0.636045\pi$
$367$	−27.0095	−	15.5939i	−1.40988	−	0.813996i	−0.995376	+	0.0960509i	$0.969379\pi$
$368$	−2.36531	−	1.36561i	−0.123300	−	0.0711875i
$369$	−0.372734	−	1.36454i	−0.0194037	−	0.0710353i
$370$	−11.0849			−0.576278
$371$	−7.87407	+	18.0488i	−0.408801	+	0.937048i
$372$	−4.75181	−	6.16167i	−0.246370	−	0.319468i
$373$	2.30810	+	3.99775i	0.119509	+	0.206996i	0.919573	−	0.392919i	$-0.128535\pi$
$373$	2.30810	+	3.99775i	0.119509	+	0.206996i	−0.800064	+	0.599914i	$0.795201\pi$
$374$	0.0475426	−	0.0823462i	0.00245837	−	0.00425802i
$375$	2.30712	+	17.2018i	0.119139	+	0.888296i
$376$	−0.203606	+	0.117552i	−0.0105002	+	0.00606228i
$377$	−12.6256	−	1.27335i	−0.650249	−	0.0655809i
$378$	7.00909	−	11.8268i	0.360509	−	0.608304i
$379$		−	3.52362i		−	0.180996i	−0.995897	−	0.0904982i	$-0.971154\pi$
$379$		−	3.52362i		−	0.180996i	0.995897	−	0.0904982i	$-0.0288459\pi$
$380$	0.244969	−	0.141433i	0.0125666	−	0.00725535i
$381$	−15.1590	+	2.03315i	−0.776619	+	0.104161i
$382$	−1.57425	−	0.908893i	−0.0805456	−	0.0465030i
$383$	−1.24813	+	0.720607i	−0.0637763	+	0.0368213i	−0.531549	−	0.847027i	$-0.678390\pi$
$383$	−1.24813	+	0.720607i	−0.0637763	+	0.0368213i	0.467773	+	0.883849i	$0.345057\pi$
$384$	1.05774	+	1.37157i	0.0539774	+	0.0699924i
$385$	−11.2956	+	1.27300i	−0.575676	+	0.0648781i
$386$		−	19.7946i		−	1.00752i
$387$	−3.59029	+	0.980711i	−0.182505	+	0.0498523i
$388$	6.39773	−	11.0812i	0.324795	−	0.562562i
$389$	−7.08963	−	4.09320i	−0.359459	−	0.207533i	0.309385	−	0.950937i	$-0.399877\pi$
$389$	−7.08963	−	4.09320i	−0.359459	−	0.207533i	−0.668843	+	0.743403i	$0.733210\pi$
$390$	−3.40512	+	6.37184i	−0.172425	+	0.322650i
$391$		−	0.0699283i		−	0.00353643i
$392$	6.82442	−	1.55800i	0.344685	−	0.0786908i
$393$	−14.9575	−	19.3953i	−0.754505	−	0.978366i
$394$	−12.6222	−	21.8623i	−0.635898	−	1.10141i
$395$	6.03661	+	3.48524i	0.303735	+	0.175362i
$396$	7.91627	+	7.83982i	0.397808	+	0.393966i
$397$	−6.43999	−	11.1544i	−0.323214	−	0.559823i	0.657935	−	0.753074i	$-0.271430\pi$
$397$	−6.43999	−	11.1544i	−0.323214	−	0.559823i	−0.981149	+	0.193252i	$0.938097\pi$
$398$		−	6.16568i		−	0.309058i
$399$	−0.805073	+	0.779327i	−0.0403041	+	0.0390152i
$400$	3.66166			0.183083
$401$	−4.27201	−	7.39934i	−0.213334	−	0.369505i	0.739422	−	0.673242i	$-0.235099\pi$
$401$	−4.27201	−	7.39934i	−0.213334	−	0.369505i	−0.952756	+	0.303737i	$0.901766\pi$
$402$	1.65927	+	12.3714i	0.0827567	+	0.617029i
$403$	−13.1441	−	9.46558i	−0.654755	−	0.471514i
$404$	−5.03494	−	8.72077i	−0.250498	−	0.433874i
$405$	5.11815	−	9.06696i	0.254323	−	0.450541i
$406$	5.52962	+	7.49197i	0.274431	+	0.371820i
$407$			35.5851i			1.76389i
$408$	−0.0168711	+	0.0410116i	−0.000835244	+	0.00203037i
$409$	10.1026	−	17.4982i	0.499542	−	0.865232i	−0.500458	−	0.865761i	$-0.666835\pi$
$409$	10.1026	−	17.4982i	0.499542	−	0.865232i	1.00000		0.000529035i	$0.000168397\pi$
$410$	0.272738	−	0.472395i	0.0134695	−	0.0233299i
$411$	8.83908	−	21.4867i	0.436000	−	1.05986i
$412$			10.1874i			0.501898i
$413$	3.42579	−	7.85256i	0.168572	−	0.386399i
$414$	7.92468	+	2.08225i	0.389477	+	0.102337i
$415$	2.10704	+	3.64949i	0.103430	+	0.179147i
$416$	2.92584	+	2.10701i	0.143451	+	0.103305i
$417$	−3.46667	−	25.8472i	−0.169763	−	1.26575i
$418$	−0.454031	−	0.786404i	−0.0222074	−	0.0384643i
$419$	2.16600			0.105816			0.0529081	−	0.998599i	$-0.483151\pi$
$419$	2.16600			0.105816			0.0529081	+	0.998599i	$0.483151\pi$
$420$	5.14240	−	1.28873i	0.250923	−	0.0628835i
$421$			14.2671i			0.695334i	0.937618	+	0.347667i	$0.113026\pi$
$421$			14.2671i			0.695334i	−0.937618	+	0.347667i	$0.886974\pi$
$422$	−1.99089	−	3.44833i	−0.0969152	−	0.167862i
$423$	0.496305	−	0.501145i	0.0241312	−	0.0243665i
$424$	6.44560	+	3.72137i	0.313026	+	0.180726i
$425$	0.0468753	+	0.0811904i	0.00227379	+	0.00393831i
$426$	−15.5230	−	20.1287i	−0.752092	−	0.975237i
$427$	−18.5871	−	25.1833i	−0.899494	−	1.21871i
$428$		−	18.1776i		−	0.878648i
$429$	20.4550	+	10.9312i	0.987576	+	0.527762i
$430$	−1.24293	−	0.717608i	−0.0599396	−	0.0346061i
$431$	17.2738	−	29.9190i	0.832048	−	1.44115i	−0.0643642	−	0.997926i	$-0.520502\pi$
$431$	17.2738	−	29.9190i	0.832048	−	1.44115i	0.896412	−	0.443222i	$-0.146165\pi$
$432$	−4.14530	−	3.13313i	−0.199441	−	0.150743i
$433$		−	0.715483i		−	0.0343839i	−0.999852	−	0.0171920i	$-0.994527\pi$
$433$		−	0.715483i		−	0.0343839i	0.999852	−	0.0171920i	$-0.00547264\pi$
$434$	1.33110	+	11.8111i	0.0638947	+	0.566950i
$435$	4.30662	+	5.58439i	0.206487	+	0.267751i
$436$	−2.40616	+	1.38920i	−0.115234	+	0.0665306i
$437$	−0.578343	−	0.333907i	−0.0276659	−	0.0159729i
$438$	−2.69267	+	0.361144i	−0.128661	+	0.0172561i
$439$	15.5035	−	8.95097i	0.739944	−	0.427207i	−0.0821052	−	0.996624i	$-0.526164\pi$
$439$	15.5035	−	8.95097i	0.739944	−	0.427207i	0.822049	+	0.569417i	$0.192831\pi$
$440$			4.29635i			0.204821i
$441$	−18.5181	+	9.90356i	−0.881813	+	0.471598i
$442$	−0.00926333	+	0.0918479i	−0.000440612	+	0.00436876i
$443$	−14.3289	+	8.27278i	−0.680785	+	0.393052i	−0.800151	−	0.599799i	$-0.795247\pi$
$443$	−14.3289	+	8.27278i	−0.680785	+	0.393052i	0.119366	+	0.992850i	$0.461914\pi$
$444$	−2.20616	−	16.4490i	−0.104700	−	0.780635i
$445$	5.42288	−	9.39271i	0.257069	−	0.445257i
$446$	1.01738	+	1.76216i	0.0481745	+	0.0834407i
$447$	−9.99775	−	12.9641i	−0.472877	−	0.613180i
$448$	−0.296298	−	2.62911i	−0.0139988	−	0.124214i
$449$	26.7037			1.26023			0.630113	−	0.776503i	$-0.283009\pi$
$449$	26.7037			1.26023			0.630113	+	0.776503i	$0.283009\pi$
$450$	−10.5968	+	2.89458i	−0.499536	+	0.136452i
$451$	−1.51649	−	0.875548i	−0.0714089	−	0.0412279i
$452$	16.1398	+	9.31833i	0.759153	+	0.438297i
$453$	24.0075	+	9.87608i	1.12797	+	0.464019i
$454$			18.0139i			0.845433i
$455$	9.49200	−	5.62943i	0.444992	−	0.263912i
$456$	0.258628	+	0.335362i	0.0121114	+	0.0157048i
$457$	−32.4759	+	18.7500i	−1.51916	+	0.877087i	−0.519413	+	0.854523i	$0.673849\pi$
$457$	−32.4759	+	18.7500i	−1.51916	+	0.877087i	−0.999745	+	0.0225635i	$0.992817\pi$
$458$	−9.36691	+	16.2240i	−0.437687	+	0.758096i
$459$	0.0164046	−	0.132023i	0.000765700	−	0.00616232i
$460$	1.57983	+	2.73634i	0.0736599	+	0.127583i
$461$			8.31097i			0.387080i	0.981092	+	0.193540i	$0.0619970\pi$
$461$			8.31097i			0.387080i	−0.981092	+	0.193540i	$0.938003\pi$
$462$	−4.13710	−	16.5082i	−0.192475	−	0.768032i
$463$		−	28.8122i		−	1.33902i	−0.742805	−	0.669508i	$-0.766505\pi$
$463$		−	28.8122i		−	1.33902i	0.742805	−	0.669508i	$-0.233495\pi$
$464$	3.04794	−	1.75973i	0.141497	−	0.0816935i
$465$	1.19661	+	8.92182i	0.0554913	+	0.413739i
$466$	17.0834	+	9.86309i	0.791372	+	0.456899i
$467$	−10.3800	−	17.9787i	−0.480328	−	0.831953i	0.519417	−	0.854521i	$-0.326149\pi$
$467$	−10.3800	−	17.9787i	−0.480328	−	0.831953i	−0.999745	+	0.0225677i	$0.992816\pi$
$468$	−10.1329	−	3.78473i	−0.468394	−	0.174949i
$469$	7.62422	−	17.4761i	0.352054	−	0.806972i
$470$	0.271983			0.0125457
$471$	2.78137	+	1.14418i	0.128159	+	0.0527212i
$472$	−2.80431	−	1.61907i	−0.129079	−	0.0745237i
$473$	−2.30368	+	3.99009i	−0.105923	+	0.183465i
$474$	−3.97034	+	9.65142i	−0.182364	+	0.443304i
$475$	0.895316			0.0410799
$476$	0.0545023	−	0.0402267i	0.00249811	−	0.00184379i
$477$	−21.5952	−	5.67426i	−0.988776	−	0.259806i
$478$	−10.0708	−	17.4432i	−0.460629	−	0.797833i
$479$	−15.1644	−	8.75519i	−0.692881	−	0.400035i	0.111809	−	0.993730i	$-0.464335\pi$
$479$	−15.1644	−	8.75519i	−0.692881	−	0.400035i	−0.804690	+	0.593695i	$0.797669\pi$
$480$	−0.266360	−	1.98597i	−0.0121576	−	0.0906465i
$481$	−14.1845	−	31.5017i	−0.646757	−	1.43636i
$482$	−22.2718			−1.01445
$483$	−8.70522	−	8.99280i	−0.396101	−	0.409187i
$484$	2.79224			0.126920
$485$	−12.8194	+	7.40130i	−0.582101	+	0.336076i
$486$	14.4732	+	5.79031i	0.656516	+	0.262654i
$487$	−0.122893	−	0.0709520i	−0.00556879	−	0.00321514i	0.497213	−	0.867628i	$-0.334357\pi$
$487$	−0.122893	−	0.0709520i	−0.00556879	−	0.00321514i	−0.502782	+	0.864413i	$0.667690\pi$
$488$	−10.2453	+	5.91511i	−0.463782	+	0.267765i
$489$	17.4487	−	13.4562i	0.789056	−	0.608511i
$490$	−7.73840	−	2.38654i	−0.349585	−	0.107813i
$491$		−	10.0187i		−	0.452138i	−0.974111	−	0.226069i	$-0.927413\pi$
$491$		−	10.0187i		−	0.452138i	0.974111	−	0.226069i	$-0.0725875\pi$
$492$	0.755272	+	0.310699i	0.0340503	+	0.0140074i
$493$	0.0780373	+	0.0450549i	0.00351463	+	0.00202917i
$494$	0.715398	+	0.515185i	0.0321873	+	0.0231793i
$495$	−3.39630	−	12.4335i	−0.152652	−	0.558846i
$496$	4.49243			0.201716
$497$	4.34837	+	38.5839i	0.195051	+	1.73073i
$498$	−4.99616	+	3.85298i	−0.223883	+	0.172656i
$499$	9.05469	−	5.22772i	0.405343	−	0.234025i	−0.283444	−	0.958989i	$-0.591477\pi$
$499$	9.05469	−	5.22772i	0.405343	−	0.234025i	0.688787	+	0.724964i	$0.258144\pi$
$500$	−8.67790	−	5.01019i	−0.388087	−	0.224062i
$501$	1.57842	+	11.7686i	0.0705186	+	0.525782i
$502$	10.2782	+	17.8023i	0.458737	+	0.794556i
$503$	−13.6155			−0.607083			−0.303542	−	0.952818i	$-0.598169\pi$
$503$	−13.6155			−0.607083			−0.303542	+	0.952818i	$0.598169\pi$
$504$	2.93581	+	7.37435i	0.130771	+	0.328480i
$505$			11.6495i			0.518395i
$506$	8.78427	−	5.07160i	0.390508	−	0.225460i
$507$	−22.4651	−	1.52332i	−0.997709	−	0.0676530i
$508$	4.41521	−	7.64737i	0.195893	−	0.339297i
$509$	−8.06558	+	4.65666i	−0.357500	+	0.206403i	−0.667984	−	0.744176i	$-0.732842\pi$
$509$	−8.06558	+	4.65666i	−0.357500	+	0.206403i	0.310483	+	0.950579i	$0.399509\pi$
$510$	0.0406251	−	0.0313296i	0.00179891	−	0.00138730i
$511$	3.80373	+	1.65943i	0.168267	+	0.0734090i
$512$	−1.00000			−0.0441942
$513$	−1.01357	−	0.766084i	−0.0447502	−	0.0338234i
$514$	−5.10857	+	8.84830i	−0.225329	+	0.390282i
$515$	5.89273	−	10.2065i	0.259665	−	0.449753i
$516$	0.817490	−	1.98722i	0.0359880	−	0.0874824i
$517$		−	0.873127i		−	0.0384001i
$518$	−10.1372	+	23.2363i	−0.445401	+	1.02094i
$519$	16.4946	+	21.3885i	0.724032	+	0.938851i
$520$	−1.71256	−	3.80335i	−0.0751007	−	0.166788i
$521$	6.86110	−	11.8838i	0.300590	−	0.520637i	−0.675680	−	0.737195i	$-0.736150\pi$
$521$	6.86110	−	11.8838i	0.300590	−	0.520637i	0.976270	+	0.216558i	$0.0694830\pi$
$522$	−7.42960	+	7.50205i	−0.325185	+	0.328356i
$523$	−23.6617	+	13.6611i	−1.03465	+	0.597358i	−0.918315	−	0.395851i	$-0.870450\pi$
$523$	−23.6617	+	13.6611i	−1.03465	+	0.597358i	−0.116340	+	0.993209i	$0.537116\pi$
$524$	14.1410			0.617753
$525$	16.1354	+	4.60571i	0.704206	+	0.201010i
$526$			28.1563i			1.22768i
$527$	0.0575105	+	0.0996111i	0.00250520	+	0.00433913i
$528$	−6.37539	+	0.855076i	−0.277453	+	0.0372124i
$529$	−7.77021	+	13.4584i	−0.337835	+	0.585147i
$530$	−4.30512	−	7.45669i	−0.187003	−	0.323898i
$531$	9.39549	+	2.46872i	0.407729	+	0.107133i
$532$	−0.0724480	−	0.642845i	−0.00314102	−	0.0278709i
$533$	1.69148	+	0.170594i	0.0732661	+	0.00738925i
$534$	15.0172	+	6.17768i	0.649857	+	0.267334i
$535$	−10.5145	+	18.2117i	−0.454582	+	0.787360i
$536$	−6.24108	−	3.60329i	−0.269574	−	0.155638i
$537$	6.34101	+	2.60853i	0.273635	+	0.112566i
$538$	29.3643			1.26599
$539$	−7.66133	+	24.8420i	−0.329997	+	1.07002i
$540$	2.34076	+	5.53678i	0.100730	+	0.238265i
$541$	−5.89940	+	3.40602i	−0.253635	+	0.146436i	−0.621428	−	0.783472i	$-0.713447\pi$
$541$	−5.89940	+	3.40602i	−0.253635	+	0.146436i	0.367793	+	0.929908i	$0.380114\pi$
$542$	−14.2082	+	24.6093i	−0.610293	+	1.05706i
$543$	−0.0988114	−	0.736731i	−0.00424040	−	0.0316162i
$544$	−0.0128016	−	0.0221731i	−0.000548866	−	0.000950663i
$545$	3.21423			0.137682
$546$	10.2427	+	12.9649i	0.438346	+	0.554845i
$547$	14.2644			0.609901			0.304951	−	0.952368i	$-0.401360\pi$
$547$	14.2644			0.609901			0.304951	+	0.952368i	$0.401360\pi$
$548$	6.70701	+	11.6169i	0.286509	+	0.496249i
$549$	24.9736	−	25.2172i	1.06585	−	1.07624i
$550$	−6.79933	+	11.7768i	−0.289924	+	0.502164i
$551$	0.745255	−	0.430273i	0.0317489	−	0.0183302i
$552$	−3.74606	+	2.88892i	−0.159443	+	0.122960i
$553$	12.8263	−	9.46672i	0.545428	−	0.402566i
$554$	−27.6535			−1.17489
$555$	−7.30434	+	17.7559i	−0.310052	+	0.753698i
$556$	13.0393	+	7.52827i	0.552991	+	0.319270i
$557$	10.8866	−	18.8561i	0.461279	−	0.798958i	−0.537746	−	0.843107i	$-0.680724\pi$
$557$	10.8866	−	18.8561i	0.461279	−	0.798958i	0.999025	+	0.0441487i	$0.0140575\pi$
$558$	−13.0010	+	3.55130i	−0.550376	+	0.150339i
$559$	0.448855	−	4.45050i	0.0189846	−	0.188236i
$560$	−1.22391	+	2.80542i	−0.0517195	+	0.118551i
$561$	−0.100575	−	0.130416i	−0.00424628	−	0.00550615i
$562$	−6.18049	−	10.7049i	−0.260708	−	0.451560i
$563$	5.19862	−	9.00428i	0.219096	−	0.379485i	−0.735436	−	0.677594i	$-0.763023\pi$
$563$	5.19862	−	9.00428i	0.219096	−	0.379485i	0.954532	+	0.298109i	$0.0963560\pi$
$564$	0.0541311	+	0.403598i	0.00227933	+	0.0169945i
$565$	−10.7800	−	18.6716i	−0.453520	−	0.785520i
$566$			13.6723i			0.574690i
$567$	−14.3256	−	19.0204i	−0.601621	−	0.798782i
$568$	14.6757			0.615778
$569$	−14.6618	+	8.46500i	−0.614655	+	0.354871i	−0.774785	−	0.632225i	$-0.782142\pi$
$569$	−14.6618	+	8.46500i	−0.614655	+	0.354871i	0.160130	+	0.987096i	$0.448809\pi$
$570$	−0.0651280	−	0.485590i	−0.00272791	−	0.0203391i
$571$	8.19990	−	14.2026i	0.343155	−	0.594362i	−0.641862	−	0.766820i	$-0.721838\pi$
$571$	8.19990	−	14.2026i	0.343155	−	0.594362i	0.985017	+	0.172458i	$0.0551710\pi$
$572$	−12.2096	+	5.49769i	−0.510509	+	0.229870i
$573$	−2.49321	+	1.92274i	−0.104156	+	0.0803236i
$574$	−0.740818	−	1.00372i	−0.0309211	−	0.0418944i
$575$			10.0008i			0.417063i
$576$	2.89398	−	0.790508i	0.120582	−	0.0329378i
$577$	−11.8397	+	20.5070i	−0.492894	+	0.853718i	−0.999966	−	0.00818553i	$-0.997394\pi$
$577$	−11.8397	+	20.5070i	−0.492894	+	0.853718i	0.507072	+	0.861904i	$0.330728\pi$
$578$	−8.49967	+	14.7219i	−0.353540	+	0.612349i
$579$	−31.7071	−	13.0435i	−1.31770	−	0.542069i
$580$	−4.07154			−0.169062
$581$	9.57696	−	1.07931i	0.397319	−	0.0447775i
$582$	−13.5342	−	17.5498i	−0.561011	−	0.727463i
$583$	−23.9376	+	13.8204i	−0.991395	+	0.572382i
$584$	0.784266	−	1.35839i	0.0324532	−	0.0562106i
$585$	7.96269	+	9.65302i	0.329217	+	0.399103i
$586$	3.64292	−	2.10324i	0.150488	−	0.0868842i
$587$		−	43.3060i		−	1.78743i	−0.448633	−	0.893716i	$-0.648089\pi$
$587$		−	43.3060i		−	1.78743i	0.448633	−	0.893716i	$-0.351911\pi$
$588$	2.00128	−	11.9580i	0.0825316	−	0.493141i
$589$	1.09845			0.0452607
$590$	1.87304	+	3.24421i	0.0771120	+	0.133562i
$591$	−43.3366	+	5.81236i	−1.78263	+	0.239089i
$592$	8.29815	+	4.79094i	0.341052	+	0.196906i
$593$	−18.9754	+	10.9554i	−0.779226	+	0.449886i	−0.836156	−	0.548492i	$-0.815202\pi$
$593$	−18.9754	+	10.9554i	−0.779226	+	0.449886i	0.0569301	+	0.998378i	$0.481869\pi$
$594$	17.7743	−	7.51436i	0.729287	−	0.308318i
$595$	−0.0778729	+	0.00877620i	−0.00319248	+	0.000359789i
$596$	9.45202			0.387170
$597$	−9.87624	−	4.06283i	−0.404208	−	0.166281i
$598$	−5.75471	+	7.99112i	−0.235328	+	0.326781i
$599$	−39.3065	−	22.6936i	−1.60602	−	0.927237i	−0.990248	−	0.139314i	$-0.955510\pi$
$599$	−39.3065	−	22.6936i	−1.60602	−	0.927237i	−0.615773	−	0.787923i	$-0.711156\pi$
$600$	2.41283	−	5.86529i	0.0985033	−	0.239449i
$601$			8.20455i			0.334671i	0.985900	+	0.167335i	$0.0535163\pi$
$601$			8.20455i			0.334671i	−0.985900	+	0.167335i	$0.946484\pi$
$602$	−2.64091	+	1.94919i	−0.107636	+	0.0794430i
$603$	20.9100	+	5.49421i	0.851520	+	0.223741i
$604$	−12.9798	+	7.49388i	−0.528140	+	0.304922i
$605$	−2.79747	−	1.61512i	−0.113733	−	0.0656640i
$606$	−17.2867	+	2.31852i	−0.702226	+	0.0941835i
$607$	−24.0464	+	13.8832i	−0.976012	+	0.563501i	−0.901064	−	0.433687i	$-0.857212\pi$
$607$	−24.0464	+	13.8832i	−0.976012	+	0.563501i	−0.0749481	+	0.997187i	$0.523879\pi$
$608$	−0.244511			−0.00991621
$609$	15.6444	−	3.92062i	0.633944	−	0.158872i
$610$	13.6860			0.554129
$611$	0.348035	+	0.772937i	0.0140800	+	0.0312697i
$612$	0.0545756	+	0.0540486i	0.00220609	+	0.00218478i
$613$	−15.8517	−	9.15200i	−0.640245	−	0.369646i	0.144464	−	0.989510i	$-0.453854\pi$
$613$	−15.8517	−	9.15200i	−0.640245	−	0.369646i	−0.784709	+	0.619864i	$0.787188\pi$
$614$	10.5746	+	18.3157i	0.426756	+	0.739163i
$615$	−0.576969	−	0.748155i	−0.0232656	−	0.0301685i
$616$	9.00603	+	3.92901i	0.362863	+	0.158304i
$617$	22.1693			0.892502			0.446251	−	0.894908i	$-0.352759\pi$
$617$	22.1693			0.892502			0.446251	+	0.894908i	$0.352759\pi$
$618$	16.3183	+	6.71293i	0.656419	+	0.270034i
$619$	19.7675	−	34.2384i	0.794525	−	1.37616i	−0.128616	−	0.991695i	$-0.541053\pi$
$619$	19.7675	−	34.2384i	0.794525	−	1.37616i	0.923140	−	0.384463i	$-0.125613\pi$
$620$	−4.50085	−	2.59857i	−0.180759	−	0.104361i
$621$	8.55728	−	11.3217i	0.343392	−	0.454326i
$622$	31.3509			1.25706
$623$	−14.7298	−	19.9571i	−0.590137	−	0.799564i
$624$	5.30298	−	3.29824i	0.212289	−	0.132035i
$625$	−3.35805	−	5.81632i	−0.134322	−	0.232653i
$626$	28.3855	+	16.3884i	1.13451	+	0.655011i
$627$	−1.55885	+	0.209075i	−0.0622545	+	0.00834965i
$628$	−1.50376	+	0.868197i	−0.0600066	+	0.0346448i
$629$			0.245327i			0.00978184i
$630$	1.32425	−	9.08634i	0.0527594	−	0.362008i
$631$			38.3301i			1.52590i	0.646460	+	0.762948i	$0.276249\pi$
$631$			38.3301i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$632$	−3.01266	−	5.21808i	−0.119837	−	0.207564i
$633$	−6.83545	+	0.916780i	−0.271685	+	0.0364387i
$634$	11.1137	−	19.2495i	0.441382	−	0.764497i
$635$	−8.84697	+	5.10780i	−0.351081	+	0.202697i
$636$	10.2082	−	7.87246i	0.404782	−	0.312163i
$637$	−3.12000	−	25.0453i	−0.123619	−	0.992330i
$638$			13.0706i			0.517468i
$639$	−42.4711	+	11.6012i	−1.68013	+	0.458938i
$640$	1.00187	+	0.578432i	0.0396026	+	0.0228645i
$641$	13.7967	+	7.96553i	0.544937	+	0.314620i	0.747077	−	0.664737i	$-0.231456\pi$
$641$	13.7967	+	7.96553i	0.544937	+	0.314620i	−0.202140	+	0.979357i	$0.564790\pi$
$642$	−29.1171	−	11.9780i	−1.14916	−	0.472734i
$643$	20.5219			0.809303			0.404652	−	0.914471i	$-0.367393\pi$
$643$	20.5219			0.809303			0.404652	+	0.914471i	$0.367393\pi$
$644$	7.18068	−	0.809256i	0.282959	−	0.0318892i
$645$	−1.96849	+	1.51808i	−0.0775094	+	0.0597743i
$646$	−0.00313014	−	0.00542155i	−0.000123154	−	0.000213308i
$647$	−17.2187	+	29.8237i	−0.676938	+	1.17249i	0.298960	+	0.954266i	$0.403360\pi$
$647$	−17.2187	+	29.8237i	−0.676938	+	1.17249i	−0.975898	+	0.218226i	$0.929973\pi$
$648$	−7.75019	+	4.57542i	−0.304456	+	0.179740i
$649$	10.4146	−	6.01288i	0.408809	−	0.236026i
$650$	1.32480	−	13.1357i	0.0519629	−	0.515224i
$651$	19.7962	+	5.65067i	0.775875	+	0.221467i
$652$			12.7217i			0.498221i
$653$	−15.3842	+	8.88210i	−0.602032	+	0.347583i	−0.769841	−	0.638236i	$-0.779664\pi$
$653$	−15.3842	+	8.88210i	−0.602032	+	0.347583i	0.167808	+	0.985820i	$0.446331\pi$
$654$	0.639708	+	4.76962i	0.0250145	+	0.186507i
$655$	−14.1675	−	8.17963i	−0.553571	−	0.319604i
$656$	−0.408341	+	0.235756i	−0.0159430	+	0.00920472i
$657$	−1.19583	+	4.55112i	−0.0466538	+	0.177556i
$658$	0.248729	−	0.570132i	0.00969646	−	0.0222261i
$659$		−	9.50676i		−	0.370331i	−0.982707	−	0.185165i	$-0.940718\pi$
$659$		−	9.50676i		−	0.370331i	0.982707	−	0.185165i	$-0.0592821\pi$
$660$	6.88194	+	2.83105i	0.267879	+	0.110199i
$661$	17.2613	−	29.8975i	0.671387	−	1.16288i	−0.306124	−	0.951992i	$-0.599032\pi$
$661$	17.2613	−	29.8975i	0.671387	−	1.16288i	0.977511	−	0.210885i	$-0.0676345\pi$
$662$	16.0419	+	9.26179i	0.623486	+	0.359970i
$663$	0.141019	+	0.0753607i	0.00547672	+	0.00292677i
$664$		−	3.64267i		−	0.141363i
$665$	−0.299258	+	0.685956i	−0.0116047	+	0.0266002i
$666$	−27.8019	−	7.30510i	−1.07730	−	0.283067i
$667$	4.80622	+	8.32462i	0.186098	+	0.322331i
$668$	−5.93699	−	3.42772i	−0.229709	−	0.132622i
$669$	3.49304	−	0.468492i	0.135049	−	0.0181129i
$670$	4.16852	+	7.22009i	0.161044	+	0.278936i
$671$		−	43.9350i		−	1.69609i
$672$	−4.40657	−	1.25782i	−0.169987	−	0.0485214i
$673$	−30.8952			−1.19092			−0.595460	−	0.803385i	$-0.703030\pi$
$673$	−30.8952			−1.19092			−0.595460	+	0.803385i	$0.703030\pi$
$674$	−8.97860	−	15.5514i	−0.345843	−	0.599017i
$675$	−2.34611	+	18.8814i	−0.0903017	+	0.726744i
$676$	8.61715	−	9.73369i	0.331429	−	0.374373i
$677$	23.5469	+	40.7844i	0.904979	+	1.56747i	0.820945	+	0.571007i	$0.193447\pi$
$677$	23.5469	+	40.7844i	0.904979	+	1.56747i	0.0840345	+	0.996463i	$0.473219\pi$
$678$	25.5614	−	19.7127i	0.981680	−	0.757061i
$679$	3.79127	+	33.6406i	0.145495	+	1.29101i
$680$			0.0296195i			0.00113586i
$681$	28.8548	+	11.8701i	1.10572	+	0.454864i
$682$	−8.34198	+	14.4487i	−0.319431	+	0.553270i
$683$	7.64632	−	13.2438i	0.292578	−	0.506760i	−0.681840	−	0.731501i	$-0.738820\pi$
$683$	7.64632	−	13.2438i	0.292578	−	0.506760i	0.974419	+	0.224741i	$0.0721535\pi$
$684$	0.707608	−	0.193288i	0.0270561	−	0.00739054i
$685$		−	15.5182i		−	0.592920i
$686$	−12.0794	+	14.0388i	−0.461195	+	0.536003i
$687$	19.8155	+	25.6947i	0.756007	+	0.980313i
$688$	0.620304	+	1.07440i	0.0236489	+	0.0409610i
$689$	15.6819	−	21.7762i	0.597433	−	0.829609i
$690$	5.42412	−	0.727490i	0.206493	−	0.0276951i
$691$	−6.72191	−	11.6427i	−0.255713	−	0.442909i	0.709376	−	0.704831i	$-0.248977\pi$
$691$	−6.72191	−	11.6427i	−0.255713	−	0.442909i	−0.965089	+	0.261922i	$0.915644\pi$
$692$	−15.5942			−0.592803
$693$	−29.1691	−	4.25113i	−1.10804	−	0.161487i
$694$			0.504408i			0.0191471i
$695$	−8.70919	−	15.0848i	−0.330358	−	0.572197i
$696$	−0.810333	−	6.04179i	−0.0307156	−	0.229013i
$697$	−0.0104549	−	0.00603612i	−0.000396006	−	0.000228634i
$698$	−11.2702	−	19.5206i	−0.426585	−	0.738866i
$699$	27.0558	−	20.8651i	1.02334	−	0.789190i
$700$	−7.79468	+	5.75304i	−0.294611	+	0.217445i
$701$		−	44.2310i		−	1.67058i	−0.549809	−	0.835290i	$-0.685300\pi$
$701$		−	44.2310i		−	1.67058i	0.549809	−	0.835290i	$-0.314700\pi$
$702$	−12.7394	+	13.7371i	−0.480819	+	0.518472i
$703$	2.02898	+	1.17143i	0.0765246	+	0.0441815i
$704$	1.85690	−	3.21624i	0.0699844	−	0.121216i
$705$	0.179222	−	0.435666i	0.00674988	−	0.0164081i
$706$			16.0120i			0.602619i
$707$	24.4197	+	10.6534i	0.918397	+	0.400664i
$708$	−4.44132	+	3.42509i	−0.166915	+	0.128723i
$709$	34.4905	−	19.9131i	1.29532	−	0.747852i	0.315726	−	0.948850i	$-0.397752\pi$
$709$	34.4905	−	19.9131i	1.29532	−	0.747852i	0.979592	+	0.200998i	$0.0644185\pi$
$710$	−14.7032	−	8.48889i	−0.551801	−	0.318582i
$711$	12.8435	+	12.7195i	0.481669	+	0.477017i
$712$	−8.11911	+	4.68757i	−0.304276	+	0.175674i
$713$			12.2698i			0.459509i
$714$	−0.0285216	−	0.113809i	−0.00106739	−	0.00425921i
$715$	15.4125	+	1.55443i	0.576396	+	0.0581325i
$716$	−3.42830	+	1.97933i	−0.128121	+	0.0739710i
$717$	−34.5768	+	4.63748i	−1.29129	+	0.173190i
$718$	−7.67875	+	13.3000i	−0.286569	+	0.496351i
$719$	−13.8793	−	24.0396i	−0.517609	−	0.896525i	−0.999791	−	0.0204540i	$-0.993489\pi$
$719$	−13.8793	−	24.0396i	−0.517609	−	0.896525i	0.482182	−	0.876071i	$-0.339845\pi$
$720$	−3.35666	−	0.881980i	−0.125095	−	0.0328694i
$721$	−16.0060	−	21.6862i	−0.596095	−	0.807637i
$722$	18.9402			0.704882
$723$	−14.6759	+	35.6752i	−0.545801	+	1.32677i
$724$	0.371664	+	0.214580i	0.0138128	+	0.00797481i
$725$	−11.1605	−	6.44355i	−0.414492	−	0.239307i
$726$	1.83993	−	4.47264i	0.0682861	−	0.165995i
$727$		−	34.8578i		−	1.29281i	−0.762996	−	0.646403i	$-0.776273\pi$
$727$		−	34.8578i		−	1.29281i	0.762996	−	0.646403i	$-0.223727\pi$
$728$	−9.53874	+	0.111706i	−0.353529	+	0.00414012i
$729$	18.8120	−	19.3678i	0.696739	−	0.717324i
$730$	−1.57147	+	0.907290i	−0.0581628	+	0.0335803i
$731$	−0.0158818	+	0.0275081i	−0.000587410	+	0.00101742i
$732$	2.72383	+	20.3087i	0.100676	+	0.750631i
$733$	−17.9806	−	31.1434i	−0.664130	−	1.15031i	−0.979520	−	0.201345i	$-0.935469\pi$
$733$	−17.9806	−	31.1434i	−0.664130	−	1.15031i	0.315390	−	0.948962i	$-0.397865\pi$
$734$		−	31.1878i		−	1.15116i
$735$	−8.92196	+	10.8229i	−0.329091	+	0.399207i
$736$		−	2.73122i		−	0.100674i
$737$	23.1781	−	13.3819i	0.853775	−	0.492927i
$738$	0.995362	−	1.00507i	0.0366398	−	0.0369971i
$739$	23.0900	+	13.3310i	0.849378	+	0.490389i	0.860441	−	0.509550i	$-0.170188\pi$
$739$	23.0900	+	13.3310i	0.849378	+	0.490389i	−0.0110630	+	0.999939i	$0.503522\pi$
$740$	−5.54247	−	9.59983i	−0.203745	−	0.352897i
$741$	1.29664	−	0.806454i	0.0476331	−	0.0296258i
$742$	−19.5678	+	2.20527i	−0.718355	+	0.0809579i
$743$	−24.5770			−0.901644			−0.450822	−	0.892614i	$-0.648869\pi$
$743$	−24.5770			−0.901644			−0.450822	+	0.892614i	$0.648869\pi$
$744$	2.96026	−	7.19602i	0.108528	−	0.263819i
$745$	−9.46974	−	5.46736i	−0.346944	−	0.200308i
$746$	−2.30810	+	3.99775i	−0.0845057	+	0.146368i
$747$	2.87956	+	10.5418i	0.105357	+	0.385704i
$748$	0.0950852			0.00347666
$749$	28.5599	+	38.6951i	1.04355	+	1.41389i
$750$	−13.7436	+	10.5989i	−0.501846	+	0.387018i
$751$	−0.764556	−	1.32425i	−0.0278990	−	0.0483226i	0.851739	−	0.523967i	$-0.175548\pi$
$751$	−0.764556	−	1.32425i	−0.0278990	−	0.0483226i	−0.879638	+	0.475644i	$0.842215\pi$
$752$	−0.203606	−	0.117552i	−0.00742475	−	0.00428668i
$753$	35.2886	−	4.73296i	1.28599	−	0.172479i
$754$	−5.21002	−	11.5707i	−0.189738	−	0.421381i
$755$	17.3388			0.631024
$756$	13.7468	+	0.156667i	0.499968	+	0.00569793i
$757$	−20.0619			−0.729164			−0.364582	−	0.931171i	$-0.618788\pi$
$757$	−20.0619			−0.729164			−0.364582	+	0.931171i	$0.618788\pi$
$758$	3.05155	−	1.76181i	0.110837	−	0.0639919i
$759$	−2.33540	−	17.4126i	−0.0847698	−	0.632038i
$760$	0.244969	+	0.141433i	0.00888596	+	0.00513031i
$761$	−19.1290	+	11.0442i	−0.693427	+	0.400350i	−0.804895	−	0.593418i	$-0.797778\pi$
$761$	−19.1290	+	11.0442i	−0.693427	+	0.400350i	0.111468	+	0.993768i	$0.464445\pi$
$762$	−9.34026	−	12.1115i	−0.338362	−	0.438754i
$763$	2.93941	−	6.73768i	0.106414	−	0.243920i
$764$		−	1.81779i		−	0.0657652i
$765$	−0.0234145	−	0.0857182i	−0.000846552	−	0.00309915i
$766$	−1.24813	−	0.720607i	−0.0450967	−	0.0260366i
$767$	−6.82278	+	9.47426i	−0.246356	+	0.342096i
$768$	−0.658943	+	1.60181i	−0.0237776	+	0.0578003i
$769$	33.5491			1.20981			0.604906	−	0.796297i	$-0.293211\pi$
$769$	33.5491			1.20981			0.604906	+	0.796297i	$0.293211\pi$
$770$	−6.75024	−	9.14576i	−0.243262	−	0.329590i
$771$	10.8070	+	14.0135i	0.389206	+	0.504683i
$772$	17.1426	−	9.89729i	0.616976	−	0.356211i
$773$	39.2647	+	22.6695i	1.41225	+	0.815365i	0.995601	−	0.0936997i	$-0.0298694\pi$
$773$	39.2647	+	22.6695i	1.41225	+	0.815365i	0.416654	+	0.909065i	$0.363203\pi$
$774$	−2.64447	−	2.61893i	−0.0950533	−	0.0941354i
$775$	−8.22489	−	14.2459i	−0.295447	−	0.511729i
$776$	12.7955			0.459330
$777$	30.5403	+	31.5492i	1.09563	+	1.13182i
$778$		−	8.18640i		−	0.293497i
$779$	−0.0998437	+	0.0576448i	−0.00357727	+	0.00206534i
$780$	−7.22073	+	0.237001i	−0.258544	+	0.00848600i
$781$	−27.2512	+	47.2005i	−0.975125	+	1.68897i
$782$	0.0605597	−	0.0349641i	0.00216561	−	0.00125032i
$783$	7.12117	+	16.8442i	0.254490	+	0.601963i
$784$	4.76147	+	5.13112i	0.170053	+	0.183254i
$785$	2.00877			0.0716962
$786$	9.31813	−	22.6512i	0.332367	−	0.807943i
$787$	16.3431	−	28.3071i	0.582568	−	1.00904i	−0.412606	−	0.910910i	$-0.635381\pi$
$787$	16.3431	−	28.3071i	0.582568	−	1.00904i	0.995174	−	0.0981280i	$-0.0312855\pi$
$788$	12.6222	−	21.8623i	0.449648	−	0.778813i
$789$	45.1011	+	18.5534i	1.60564	+	0.660520i
$790$			6.97048i			0.247999i
$791$	−48.9978	+	5.52200i	−1.74216	+	0.196340i
$792$	−2.83135	+	10.7756i	−0.100608	+	0.382894i
$793$	17.5128	+	38.8935i	0.621899	+	1.38115i
$794$	6.43999	−	11.1544i	0.228547	−	0.395854i
$795$	−14.7810	+	1.98245i	−0.524229	+	0.0703103i
$796$	5.33963	−	3.08284i	0.189258	−	0.109268i
$797$	−26.9293			−0.953884			−0.476942	−	0.878935i	$-0.658255\pi$
$797$	−26.9293			−0.953884			−0.476942	+	0.878935i	$0.658255\pi$
$798$	−1.07745	−	0.307550i	−0.0381415	−	0.0108872i
$799$		−	0.00601943i		−	0.000212952i
$800$	1.83083	+	3.17109i	0.0647297	+	0.112115i
$801$	19.7909	−	19.9839i	0.699278	−	0.706097i
$802$	4.27201	−	7.39934i	0.150850	−	0.261280i
$803$	2.91260	+	5.04477i	0.102783	+	0.178026i
$804$	−9.88430	+	7.62266i	−0.348592	+	0.268831i
$805$	−7.66224	−	3.34277i	−0.270059	−	0.117817i
$806$	1.62537	−	16.1159i	0.0572514	−	0.567660i
$807$	19.3494	−	47.0360i	0.681132	−	1.65575i
$808$	5.03494	−	8.72077i	0.177129	−	0.306796i
$809$	−4.33969	−	2.50552i	−0.152575	−	0.0880894i	0.421769	−	0.906703i	$-0.361409\pi$
$809$	−4.33969	−	2.50552i	−0.152575	−	0.0880894i	−0.574344	+	0.818614i	$0.694743\pi$
$810$	10.4113	−	0.101036i	0.365816	−	0.00355003i
$811$	−40.9851			−1.43918			−0.719590	−	0.694399i	$-0.755670\pi$
$811$	−40.9851			−1.43918			−0.719590	+	0.694399i	$0.755670\pi$
$812$	−3.72343	+	8.53478i	−0.130667	+	0.299512i
$813$	30.0570	+	38.9749i	1.05414	+	1.36691i
$814$	−30.8176	+	17.7925i	−1.08016	+	0.623628i
$815$	7.35865	−	12.7456i	0.257762	−	0.446457i
$816$	−0.0439526	+	0.00589498i	−0.00153865	+	0.000206366i
$817$	0.151671	+	0.262702i	0.00530629	+	0.00919077i
$818$	20.2052			0.706459
$819$	27.5166	−	7.86373i	0.961507	−	0.274781i
$820$	0.545475			0.0190488
$821$	−1.96031	−	3.39536i	−0.0684154	−	0.118499i	0.829789	−	0.558078i	$-0.188461\pi$
$821$	−1.96031	−	3.39536i	−0.0684154	−	0.118499i	−0.898204	+	0.439579i	$0.855128\pi$
$822$	23.0276	−	3.08849i	0.803179	−	0.107723i
$823$	0.415511	−	0.719686i	0.0144838	−	0.0250867i	−0.858693	−	0.512491i	$-0.828723\pi$
$823$	0.415511	−	0.719686i	0.0144838	−	0.0250867i	0.873176	+	0.487404i	$0.162056\pi$
$824$	−8.82256	+	5.09371i	−0.307349	+	0.177448i
$825$	14.3838	+	18.6515i	0.500779	+	0.649360i
$826$	8.51341	−	0.959453i	0.296219	−	0.0333836i
$827$	44.4483			1.54562			0.772810	−	0.634637i	$-0.218851\pi$
$827$	44.4483			1.54562			0.772810	+	0.634637i	$0.218851\pi$
$828$	2.15906	+	7.90410i	0.0750324	+	0.274686i
$829$	36.1389	+	20.8648i	1.25515	+	0.724664i	0.972129	−	0.234448i	$-0.0753284\pi$
$829$	36.1389	+	20.8648i	1.25515	+	0.724664i	0.283026	+	0.959112i	$0.408662\pi$
$830$	−2.10704	+	3.64949i	−0.0731363	+	0.126676i
$831$	−18.2221	+	44.2957i	−0.632117	+	1.53660i
$832$	−0.361803	+	3.58735i	−0.0125433	+	0.124369i
$833$	−0.0528181	+	0.171263i	−0.00183004	+	0.00593392i
$834$	20.6510	−	15.9258i	0.715087	−	0.551467i
$835$	3.96541	+	6.86829i	0.137229	+	0.237687i
$836$	0.454031	−	0.786404i	0.0157030	−	0.0271984i
$837$	−2.87840	+	23.1652i	−0.0994920	+	0.800707i
$838$	1.08300	+	1.87581i	0.0374117	+	0.0647989i
$839$			44.3088i			1.52971i	0.644203	+	0.764855i	$0.277189\pi$
$839$			44.3088i			1.52971i	−0.644203	+	0.764855i	$0.722811\pi$
$840$	3.68727	+	3.80908i	0.127223	+	0.131426i
$841$	16.6134			0.572875
$842$	−12.3556	+	7.13353i	−0.425803	+	0.245838i
$843$	−21.2198	+	2.84603i	−0.730850	+	0.0980226i
$844$	1.99089	−	3.44833i	0.0685294	−	0.118696i
$845$	−14.2636	+	4.76749i	−0.490682	+	0.164007i
$846$	0.682157	+	0.179240i	0.0234530	+	0.00616241i
$847$	−5.94391	+	4.38704i	−0.204235	+	0.150741i
$848$			7.44274i			0.255585i
$849$	21.9004	+	9.00928i	0.751621	+	0.309198i
$850$	−0.0468753	+	0.0811904i	−0.00160781	+	0.00278481i
$851$	−13.0851	+	22.6641i	−0.448552	+	0.776915i
$852$	9.67044	−	23.5076i	0.331304	−	0.805359i
$853$	39.9111			1.36653			0.683264	−	0.730171i	$-0.260560\pi$
$853$	39.9111			1.36653			0.683264	+	0.730171i	$0.260560\pi$
$854$	12.5158	−	28.6886i	0.428282	−	0.981703i
$855$	−0.820738	−	0.215653i	−0.0280686	−	0.00737519i
$856$	15.7423	−	9.08881i	0.538060	−	0.310649i
$857$	−17.9784	+	31.1395i	−0.614131	+	1.06371i	0.376406	+	0.926455i	$0.377160\pi$
$857$	−17.9784	+	31.1395i	−0.614131	+	1.06371i	−0.990536	+	0.137250i	$0.956173\pi$
$858$	0.760825	+	23.1801i	0.0259742	+	0.791357i
$859$	14.9743	−	8.64539i	0.510915	−	0.294977i	−0.222295	−	0.974980i	$-0.571355\pi$
$859$	14.9743	−	8.64539i	0.510915	−	0.294977i	0.733210	+	0.680003i	$0.238021\pi$
$860$		−	1.43522i		−	0.0489405i
$861$	−2.09592	+	0.525256i	−0.0714289	+	0.0179007i
$862$	34.5475			1.17669
$863$	−24.7603	−	42.8861i	−0.842851	−	1.45986i	−0.887474	−	0.460858i	$-0.847542\pi$
$863$	−24.7603	−	42.8861i	−0.842851	−	1.45986i	0.0446227	−	0.999004i	$-0.485791\pi$
$864$	0.640722	−	5.15650i	0.0217978	−	0.175428i
$865$	15.6235	+	9.02020i	0.531213	+	0.306696i
$866$	0.619627	−	0.357742i	0.0210558	−	0.0121566i
$867$	17.9808	+	23.3157i	0.610661	+	0.791844i
$868$	−9.56315	+	7.05831i	−0.324595	+	0.239575i
$869$	22.3768			0.759080
$870$	−2.68292	+	6.52184i	−0.0909593	+	0.221111i
$871$	−15.1843	+	21.0853i	−0.514501	+	0.714447i
$872$	−2.40616	−	1.38920i	−0.0814830	−	0.0470442i
$873$	−37.0297	+	10.1149i	−1.25327	+	0.342338i
$874$		−	0.667813i		−	0.0225891i
$875$	26.3446	−	2.96902i	0.890611	−	0.100371i
$876$	−1.65909	−	2.15135i	−0.0560556	−	0.0726873i
$877$	39.8181	−	22.9890i	1.34456	−	0.776283i	0.357088	−	0.934071i	$-0.383770\pi$
$877$	39.8181	−	22.9890i	1.34456	−	0.776283i	0.987473	+	0.157788i	$0.0504363\pi$
$878$	15.5035	+	8.95097i	0.523219	+	0.302081i
$879$	−0.968516	−	7.22119i	−0.0326672	−	0.243565i
$880$	−3.72075	+	2.14818i	−0.125426	+	0.0724150i
$881$	−3.09185			−0.104167			−0.0520835	−	0.998643i	$-0.516586\pi$
$881$	−3.09185			−0.104167			−0.0520835	+	0.998643i	$0.516586\pi$
$882$	−17.8358	−	11.0853i	−0.600562	−	0.373263i
$883$	−23.5637			−0.792981			−0.396490	−	0.918039i	$-0.629772\pi$
$883$	−23.5637			−0.792981			−0.396490	+	0.918039i	$0.629772\pi$
$884$	−0.0841743	+	0.0379017i	−0.00283109	+	0.00127477i
$885$	6.43083	−	0.862512i	0.216170	−	0.0289930i
$886$	−14.3289	−	8.27278i	−0.481388	−	0.277929i
$887$	−0.0628493	−	0.108858i	−0.00211027	−	0.00365510i	0.864968	−	0.501826i	$-0.167338\pi$
$887$	−0.0628493	−	0.108858i	−0.00211027	−	0.00365510i	−0.867079	+	0.498171i	$0.834005\pi$
$888$	13.1422	−	10.1351i	0.441022	−	0.340112i
$889$	2.61644	+	23.2161i	0.0877524	+	0.778644i
$890$	10.8458			0.363551
$891$	−0.324347	−	33.4225i	−0.0108660	−	1.11970i
$892$	−1.01738	+	1.76216i	−0.0340645	+	0.0590015i
$893$	−0.0497838	−	0.0287427i	−0.00166595	−	0.000961838i
$894$	6.22835	−	15.1403i	0.208307	−	0.506369i
$895$	4.57963			0.153080
$896$	2.12873	−	1.57116i	0.0711157	−	0.0524886i
$897$	9.00823	+	14.4836i	0.300776	+	0.483595i
$898$	13.3519	+	23.1261i	0.445557	+	0.771728i
$899$	−13.6927	−	7.90548i	−0.456677	−	0.263662i
$900$	−7.80516	−	7.72978i	−0.260172	−	0.257659i
$901$	−0.165029	+	0.0952793i	−0.00549790	+	0.00317421i
$902$		−	1.75110i		−	0.0583051i
$903$	1.38202	+	5.51464i	0.0459906	+	0.183516i
$904$			18.6367i			0.619846i
$905$	−0.248240	−	0.429965i	−0.00825179	−	0.0142925i
$906$	3.45083	+	25.7292i	0.114646	+	0.854794i
$907$	−7.59458	+	13.1542i	−0.252174	+	0.436778i	−0.964124	−	0.265452i	$-0.914479\pi$
$907$	−7.59458	+	13.1542i	−0.252174	+	0.436778i	0.711950	+	0.702230i	$0.247812\pi$
$908$	−15.6005	+	9.00694i	−0.517720	+	0.298906i
$909$	−7.67715	+	29.2179i	−0.254635	+	0.969095i
$910$	9.62123	+	5.40560i	0.318941	+	0.179194i
$911$			46.3110i			1.53435i	0.641437	+	0.767176i	$0.278339\pi$
$911$			46.3110i			1.53435i	−0.641437	+	0.767176i	$0.721661\pi$
$912$	−0.161119	+	0.391659i	−0.00533517	+	0.0129691i
$913$	11.7157	+	6.76405i	0.387732	+	0.223857i
$914$	−32.4759	−	18.7500i	−1.07421	−	0.620194i
$915$	9.01828	−	21.9223i	0.298135	−	0.724730i
$916$	−18.7338			−0.618983
$917$	−30.1024	+	22.2177i	−0.994067	+	0.733695i
$918$	0.122538	−	0.0518048i	0.00404435	−	0.00170981i
$919$	1.13972	+	1.97406i	0.0375960	+	0.0651181i	0.884211	−	0.467087i	$-0.154697\pi$
$919$	1.13972	+	1.97406i	0.0375960	+	0.0651181i	−0.846615	+	0.532206i	$0.821363\pi$
$920$	−1.57983	+	2.73634i	−0.0520854	+	0.0902146i
$921$	36.3064	−	4.86946i	1.19634	−	0.160454i
$922$	−7.19751	+	4.15548i	−0.237037	+	0.136854i
$923$	5.30970	−	52.6468i	0.174771	−	1.73289i
$924$	12.2280	−	11.8369i	0.402271	−	0.389407i
$925$		−	35.0856i		−	1.15361i
$926$	24.9521	−	14.4061i	0.819976	−	0.473414i
$927$	21.5057	−	21.7154i	0.706339	−	0.713227i
$928$	3.04794	+	1.75973i	0.100054	+	0.0577660i
$929$	14.3151	−	8.26482i	0.469663	−	0.271160i	−0.246436	−	0.969159i	$-0.579259\pi$
$929$	14.3151	−	8.26482i	0.469663	−	0.271160i	0.716099	+	0.697999i	$0.245926\pi$
$930$	−7.12822	+	5.49720i	−0.233743	+	0.180260i
$931$	1.16423	+	1.25461i	0.0381561	+	0.0411183i
$932$			19.7262i			0.646152i
$933$	20.6585	−	50.2182i	0.676328	−	1.64407i
$934$	10.3800	−	17.9787i	0.339644	−	0.588280i
$935$	−0.0952634	−	0.0550003i	−0.00311545	−	0.00179870i
$936$	−1.78878	−	10.6677i	−0.0584682	−	0.348685i
$937$			22.3954i			0.731626i	0.930688	+	0.365813i	$0.119209\pi$
$937$			22.3954i			0.731626i	−0.930688	+	0.365813i	$0.880791\pi$
$938$	18.9469	−	2.13529i	0.618637	−	0.0697198i
$939$	44.9554	−	34.6691i	1.46707	−	1.13138i
$940$	0.135992	+	0.235545i	0.00443556	+	0.00768262i
$941$	12.5819	+	7.26415i	0.410158	+	0.236805i	0.690857	−	0.722991i	$-0.257233\pi$
$941$	12.5819	+	7.26415i	0.410158	+	0.236805i	−0.280700	+	0.959796i	$0.590567\pi$
$942$	0.399793	+	2.98083i	0.0130260	+	0.0971207i
$943$	−0.643902	−	1.11527i	−0.0209683	−	0.0363182i
$944$		−	3.23814i		−	0.105392i
$945$	−13.6820	−	8.10857i	−0.445075	−	0.263772i
$946$	−4.60736			−0.149798
$947$	−1.30451	−	2.25948i	−0.0423910	−	0.0734233i	0.844051	−	0.536262i	$-0.180164\pi$
$947$	−1.30451	−	2.25948i	−0.0423910	−	0.0734233i	−0.886442	+	0.462839i	$0.846831\pi$
$948$	−10.3435	+	1.38729i	−0.335943	+	0.0450571i
$949$	−4.58927	−	3.30491i	−0.148974	−	0.107282i
$950$	0.447658	+	0.775366i	0.0145239	+	0.0251562i
$951$	−23.5108	−	30.4864i	−0.762389	−	0.988590i
$952$	0.0620885	+	0.0270870i	0.00201230	+	0.000877896i
$953$		−	24.6984i		−	0.800061i	−0.916502	−	0.400030i	$-0.869000\pi$
$953$		−	24.6984i		−	0.800061i	0.916502	−	0.400030i	$-0.131000\pi$
$954$	−5.88355	−	21.5391i	−0.190487	−	0.697355i
$955$	−1.05147	+	1.82119i	−0.0340247	+	0.0589324i
$956$	10.0708	−	17.4432i	0.325714	−	0.564153i
$957$	20.9365	+	8.61275i	0.676782	+	0.278411i
$958$		−	17.5104i		−	0.565735i
$959$	−32.5293	−	14.1914i	−1.05043	−	0.458264i
$960$	1.58672	−	1.22366i	0.0512111	−	0.0394934i
$961$	5.40903	+	9.36871i	0.174485	+	0.302216i
$962$	20.1891	−	28.0350i	0.650922	−	0.903885i
$963$	−38.3730	+	38.7472i	−1.23655	+	1.24861i
$964$	−11.1359	−	19.2880i	−0.358663	−	0.621223i
$965$	−22.8996			−0.737166
$966$	3.43539	−	12.0353i	0.110532	−	0.387231i
$967$			24.8951i			0.800571i	0.916390	+	0.400286i	$0.131089\pi$
$967$			24.8951i			0.800571i	−0.916390	+	0.400286i	$0.868911\pi$
$968$	1.39612	+	2.41815i	0.0448730	+	0.0777223i
$969$	−0.0107469	+	0.00144139i	−0.000345239	+	4.63040e-5i
$970$	−12.8194	−	7.40130i	−0.411607	−	0.237642i
$971$	−13.4579	−	23.3098i	−0.431885	−	0.748047i	0.565151	−	0.824988i	$-0.308818\pi$
$971$	−13.4579	−	23.3098i	−0.431885	−	0.748047i	−0.997036	+	0.0769409i	$0.975485\pi$
$972$	2.22202	+	15.4293i	0.0712713	+	0.494894i
$973$	−39.5853	+	4.46122i	−1.26905	+	0.143020i
$974$		−	0.141904i		−	0.00454690i
$975$	−20.1679	−	10.7777i	−0.645889	−	0.345164i
$976$	−10.2453	−	5.91511i	−0.327943	−	0.189338i
$977$	−24.1168	+	41.7715i	−0.771564	+	1.33639i	0.165141	+	0.986270i	$0.447192\pi$
$977$	−24.1168	+	41.7715i	−0.771564	+	1.33639i	−0.936705	+	0.350119i	$0.886141\pi$
$978$	20.3778	+	8.38288i	0.651609	+	0.268055i
$979$		−	34.8173i		−	1.11277i
$980$	−1.80239	−	7.89493i	−0.0575753	−	0.252194i
$981$	8.06155	+	2.11822i	0.257385	+	0.0676294i
$982$	8.67645	−	5.00935i	0.276877	−	0.159855i
$983$	11.9049	+	6.87329i	0.379707	+	0.219224i	0.677691	−	0.735347i	$-0.262981\pi$
$983$	11.9049	+	6.87329i	0.379707	+	0.219224i	−0.297984	+	0.954571i	$0.596314\pi$
$984$	0.108562	+	0.809434i	0.00346084	+	0.0258038i
$985$	−25.2918	+	14.6022i	−0.805862	+	0.465265i
$986$			0.0901098i			0.00286968i
$987$	−0.749346	−	0.774101i	−0.0238519	−	0.0246399i
$988$	−0.0884646	+	0.877146i	−0.00281443	+	0.0279057i
$989$	−2.93442	+	1.69419i	−0.0933092	+	0.0538721i
$990$	9.06961	−	9.15806i	0.288251	−	0.291062i
$991$	13.4020	−	23.2129i	0.425729	−	0.737384i	−0.570760	−	0.821117i	$-0.693351\pi$
$991$	13.4020	−	23.2129i	0.425729	−	0.737384i	0.996488	+	0.0837336i	$0.0266845\pi$
$992$	2.24622	+	3.89056i	0.0713174	+	0.123525i
$993$	25.4063	−	19.5931i	0.806245	−	0.621767i
$994$	−31.2405	+	23.0578i	−0.990888	+	0.731348i
$995$	−7.13286			−0.226127
$996$	−5.83486	−	2.40031i	−0.184885	−	0.0760567i
$997$	10.4342	+	6.02421i	0.330455	+	0.190789i	0.656043	−	0.754723i	$-0.272229\pi$
$997$	10.4342	+	6.02421i	0.330455	+	0.190789i	−0.325588	+	0.945512i	$0.605562\pi$
$998$	9.05469	+	5.22772i	0.286621	+	0.165481i
$999$	−30.0213	+	39.7197i	−0.949831	+	1.25668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.311.17	yes	36
3.2	odd	2		546.2.bg.a.311.11	✓	36
7.5	odd	6	inner	546.2.bg.b.467.11	yes	36
13.12	even	2		546.2.bg.a.311.17	yes	36
21.5	even	6		546.2.bg.a.467.17	yes	36
39.38	odd	2	inner	546.2.bg.b.311.11	yes	36
91.12	odd	6		546.2.bg.a.467.11	yes	36
273.194	even	6	inner	546.2.bg.b.467.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.11	✓	36	3.2	odd	2
546.2.bg.a.311.17	yes	36	13.12	even	2
546.2.bg.a.467.11	yes	36	91.12	odd	6
546.2.bg.a.467.17	yes	36	21.5	even	6
546.2.bg.b.311.11	yes	36	39.38	odd	2	inner
546.2.bg.b.311.17	yes	36	1.1	even	1	trivial
546.2.bg.b.467.11	yes	36	7.5	odd	6	inner
546.2.bg.b.467.17	yes	36	273.194	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.71668 - 0.230243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00187 - 0.578432i) q^{5} +(1.05774 + 1.37157i) q^{6} +(-0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(2.89398 - 0.790508i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.71668 - 0.230243i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00187 - 0.578432i) q^{5} +(1.05774 + 1.37157i) q^{6} +(-0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(2.89398 - 0.790508i) q^{9} +(1.00187 + 0.578432i) q^{10} +(1.85690 - 3.21624i) q^{11} +(-0.658943 + 1.60181i) q^{12} +(-0.361803 + 3.58735i) q^{13} +(2.12873 - 1.57116i) q^{14} +(1.58672 - 1.22366i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.0128016 - 0.0221731i) q^{17} +(2.13159 + 2.11100i) q^{18} +(-0.122255 - 0.211752i) q^{19} +1.15686i q^{20} +(-1.11398 - 4.44511i) q^{21} +3.71379 q^{22} +(2.36531 - 1.36561i) q^{23} +(-1.71668 + 0.230243i) q^{24} +(-1.83083 + 3.17109i) q^{25} +(-3.28764 + 1.48035i) q^{26} +(4.78602 - 2.02337i) q^{27} +(2.42502 + 1.05795i) q^{28} +3.51946i q^{29} +(1.85308 + 0.762308i) q^{30} +(-2.24622 + 3.89056i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.44718 - 5.94879i) q^{33} +0.0256033 q^{34} +(-1.81761 - 2.46265i) q^{35} +(-0.762388 + 2.90151i) q^{36} +(-8.29815 + 4.79094i) q^{37} +(0.122255 - 0.211752i) q^{38} +(0.204865 + 6.24164i) q^{39} +(-1.00187 + 0.578432i) q^{40} -0.471512i q^{41} +(3.29259 - 3.18729i) q^{42} -1.24061 q^{43} +(1.85690 + 3.21624i) q^{44} +(2.44214 - 2.46596i) q^{45} +(2.36531 + 1.36561i) q^{46} +(0.203606 - 0.117552i) q^{47} +(-1.05774 - 1.37157i) q^{48} +(-6.82442 + 1.55800i) q^{49} -3.66166 q^{50} +(0.0168711 - 0.0410116i) q^{51} +(-2.92584 - 2.10701i) q^{52} +(-6.44560 - 3.72137i) q^{53} +(4.14530 + 3.13313i) q^{54} -4.29635i q^{55} +(0.296298 + 2.62911i) q^{56} +(-0.258628 - 0.335362i) q^{57} +(-3.04794 + 1.75973i) q^{58} +(2.80431 + 1.61907i) q^{59} +(0.266360 + 1.98597i) q^{60} +(10.2453 - 5.91511i) q^{61} -4.49243 q^{62} +(-2.93581 - 7.37435i) q^{63} +1.00000 q^{64} +(1.71256 + 3.80335i) q^{65} +(6.37539 - 0.855076i) q^{66} +(6.24108 + 3.60329i) q^{67} +(0.0128016 + 0.0221731i) q^{68} +(3.74606 - 2.88892i) q^{69} +(1.22391 - 2.80542i) q^{70} -14.6757 q^{71} +(-2.89398 + 0.790508i) q^{72} +(-0.784266 + 1.35839i) q^{73} +(-8.29815 - 4.79094i) q^{74} +(-2.41283 + 5.86529i) q^{75} +0.244511 q^{76} +(-9.00603 - 3.92901i) q^{77} +(-5.30298 + 3.29824i) q^{78} +(3.01266 + 5.21808i) q^{79} +(-1.00187 - 0.578432i) q^{80} +(7.75019 - 4.57542i) q^{81} +(0.408341 - 0.235756i) q^{82} +3.64267i q^{83} +(4.40657 + 1.25782i) q^{84} -0.0296195i q^{85} +(-0.620304 - 1.07440i) q^{86} +(0.810333 + 6.04179i) q^{87} +(-1.85690 + 3.21624i) q^{88} +(8.11911 - 4.68757i) q^{89} +(3.35666 + 0.881980i) q^{90} +(9.53874 - 0.111706i) q^{91} +2.73122i q^{92} +(-2.96026 + 7.19602i) q^{93} +(0.203606 + 0.117552i) q^{94} +(-0.244969 - 0.141433i) q^{95} +(0.658943 - 1.60181i) q^{96} -12.7955 q^{97} +(-4.76147 - 5.13112i) q^{98} +(2.83135 - 10.7756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Introduction

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