LMFDB - Embedded newform 546.2.bg.b.467.11

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			467.11
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.658943 - 1.60181i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00187 + 0.578432i) q^{5} +(-1.05774 - 1.37157i) q^{6} +(0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(-2.13159 - 2.11100i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.658943 - 1.60181i) 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} +(-2.13159 - 2.11100i) q^{9} +(1.00187 - 0.578432i) q^{10} +(1.85690 + 3.21624i) q^{11} +(-1.71668 + 0.230243i) 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} +(-2.89398 + 0.790508i) q^{18} +(0.122255 - 0.211752i) q^{19} -1.15686i q^{20} +(-4.01609 - 2.20705i) q^{21} +3.71379 q^{22} +(-2.36531 - 1.36561i) q^{23} +(-0.658943 + 1.60181i) q^{24} +(-1.83083 - 3.17109i) q^{25} +(-2.92584 - 2.10701i) q^{26} +(-4.78602 + 2.02337i) q^{27} +(-2.42502 + 1.05795i) q^{28} +3.51946i q^{29} +(-0.266360 - 1.98597i) q^{30} +(2.24622 + 3.89056i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.37539 - 0.855076i) 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} +(-5.50785 - 2.94340i) q^{39} +(-1.00187 - 0.578432i) q^{40} +0.471512i q^{41} +(-3.91940 + 2.37451i) q^{42} -1.24061 q^{43} +(1.85690 - 3.21624i) q^{44} +(-0.914511 - 3.34794i) 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} +(-0.0439526 + 0.00589498i) q^{51} +(-3.28764 + 1.48035i) q^{52} +(6.44560 - 3.72137i) q^{53} +(-0.640722 + 5.15650i) 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} +(-1.85308 - 0.762308i) q^{60} +(10.2453 + 5.91511i) q^{61} +4.49243 q^{62} +(-6.18164 + 4.97869i) q^{63} +1.00000 q^{64} +(2.43752 - 3.38480i) q^{65} +(2.44718 - 5.94879i) 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} +(2.13159 + 2.11100i) q^{72} +(0.784266 + 1.35839i) q^{73} +(8.29815 - 4.79094i) q^{74} +(-6.28590 + 0.843074i) 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} +(0.0873358 + 8.99958i) q^{81} +(0.408341 + 0.235756i) q^{82} -3.64267i q^{83} +(0.0966863 + 4.58156i) q^{84} -0.0296195i q^{85} +(-0.620304 + 1.07440i) q^{86} +(5.63751 + 2.31913i) q^{87} +(-1.85690 - 3.21624i) q^{88} +(8.11911 + 4.68757i) q^{89} +(-3.35666 - 0.881980i) q^{90} +(-9.32434 - 2.01414i) q^{91} +2.73122i q^{92} +(7.71207 - 1.03435i) q^{93} +(0.203606 - 0.117552i) q^{94} +(0.244969 - 0.141433i) q^{95} +(1.71668 - 0.230243i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	0.658943	−	1.60181i	0.380441	−	0.924805i
$3$	0.658943	−	1.60181i	0.380441	−	0.924805i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00187	+	0.578432i	0.448052	+	0.258683i	0.707007	−	0.707206i	$-0.250045\pi$
$5$	1.00187	+	0.578432i	0.448052	+	0.258683i	−0.258955	+	0.965889i	$0.583378\pi$
$6$	−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
$9$	−2.13159	−	2.11100i	−0.710529	−	0.703668i
$10$	1.00187	−	0.578432i	0.316820	−	0.182916i
$11$	1.85690	+	3.21624i	0.559875	+	0.969732i	0.997506	+	0.0705774i	$0.0224842\pi$
$11$	1.85690	+	3.21624i	0.559875	+	0.969732i	−0.437631	+	0.899155i	$0.644182\pi$
$12$	−1.71668	+	0.230243i	−0.495563	+	0.0664655i
$13$	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	$-0.167655\pi$
$17$	−0.0128016	−	0.0221731i	−0.00310485	−	0.00537776i	−0.867574	+	0.497309i	$0.834322\pi$
$18$	−2.89398	+	0.790508i	−0.682117	+	0.186325i
$19$	0.122255	−	0.211752i	0.0280473	−	0.0485793i	−0.851661	−	0.524093i	$-0.824404\pi$
$19$	0.122255	−	0.211752i	0.0280473	−	0.0485793i	0.879708	+	0.475514i	$0.157738\pi$
$20$		−	1.15686i		−	0.258683i
$21$	−4.01609	−	2.20705i	−0.876382	−	0.481617i
$22$	3.71379			0.791783
$23$	−2.36531	−	1.36561i	−0.493201	−	0.284750i	0.232700	−	0.972548i	$-0.425244\pi$
$23$	−2.36531	−	1.36561i	−0.493201	−	0.284750i	−0.725902	+	0.687799i	$0.758577\pi$
$24$	−0.658943	+	1.60181i	−0.134506	+	0.326968i
$25$	−1.83083	−	3.17109i	−0.366166	−	0.634219i
$26$	−2.92584	−	2.10701i	−0.573804	−	0.413218i
$27$	−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	$0.894038\pi$
$30$	−0.266360	−	1.98597i	−0.0486305	−	0.362586i
$31$	2.24622	+	3.89056i	0.403432	+	0.698765i	0.994138	−	0.108122i	$-0.0344838\pi$
$31$	2.24622	+	3.89056i	0.403432	+	0.698765i	−0.590705	+	0.806887i	$0.701150\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	6.37539	−	0.855076i	1.10981	−	0.148850i
$34$	−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	$-0.0446437\pi$
$37$	8.29815	+	4.79094i	1.36421	+	0.787625i	0.374026	+	0.927418i	$0.377977\pi$
$38$	−0.122255	−	0.211752i	−0.0198324	−	0.0343508i
$39$	−5.50785	−	2.94340i	−0.881962	−	0.471321i
$40$	−1.00187	−	0.578432i	−0.158410	−	0.0914582i
$41$			0.471512i			0.0736377i	0.999322	+	0.0368189i	$0.0117225\pi$
$41$			0.471512i			0.0736377i	−0.999322	+	0.0368189i	$0.988278\pi$
$42$	−3.91940	+	2.37451i	−0.604777	+	0.366395i
$43$	−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
$45$	−0.914511	−	3.34794i	−0.136327	−	0.499081i
$46$	−2.36531	+	1.36561i	−0.348746	+	0.201349i
$47$	0.203606	+	0.117552i	0.0296990	+	0.0171467i	0.514776	−	0.857325i	$-0.327875\pi$
$47$	0.203606	+	0.117552i	0.0296990	+	0.0171467i	−0.485077	+	0.874471i	$0.661208\pi$
$48$	1.05774	+	1.37157i	0.152671	+	0.197969i
$49$	−6.82442	−	1.55800i	−0.974916	−	0.222571i
$50$	−3.66166			−0.517837
$51$	−0.0439526	+	0.00589498i	−0.00615460	+	0.000825463i
$52$	−3.28764	+	1.48035i	−0.455914	+	0.205287i
$53$	6.44560	−	3.72137i	0.885372	−	0.511170i	0.0129459	−	0.999916i	$-0.495879\pi$
$53$	6.44560	−	3.72137i	0.885372	−	0.511170i	0.872426	+	0.488747i	$0.162546\pi$
$54$	−0.640722	+	5.15650i	−0.0871912	+	0.701711i
$55$			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	−0.306221	−	0.951960i	$-0.599065\pi$
$59$	2.80431	−	1.61907i	0.365090	−	0.210785i	0.671311	+	0.741176i	$0.265731\pi$
$60$	−1.85308	−	0.762308i	−0.239231	−	0.0984135i
$61$	10.2453	+	5.91511i	1.31177	+	0.757353i	0.982390	−	0.186844i	$-0.0598258\pi$
$61$	10.2453	+	5.91511i	1.31177	+	0.757353i	0.329384	+	0.944196i	$0.393159\pi$
$62$	4.49243			0.570539
$63$	−6.18164	+	4.97869i	−0.778813	+	0.627256i
$64$	1.00000			0.125000
$65$	2.43752	−	3.38480i	0.302337	−	0.419833i
$66$	2.44718	−	5.94879i	0.301227	−	0.732245i
$67$	−6.24108	+	3.60329i	−0.762469	+	0.440212i	−0.830182	−	0.557493i	$-0.811763\pi$
$67$	−6.24108	+	3.60329i	−0.762469	+	0.440212i	0.0677122	+	0.997705i	$0.478430\pi$
$68$	−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	$0.836425\pi$
$72$	2.13159	+	2.11100i	0.251210	+	0.248784i
$73$	0.784266	+	1.35839i	0.0917914	+	0.158987i	0.908265	−	0.418395i	$-0.137407\pi$
$73$	0.784266	+	1.35839i	0.0917914	+	0.158987i	−0.816474	+	0.577383i	$0.804074\pi$
$74$	8.29815	−	4.79094i	0.964640	−	0.556935i
$75$	−6.28590	+	0.843074i	−0.725834	+	0.0973498i
$76$	−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	−0.645285	−	0.763942i	$-0.723261\pi$
$79$	3.01266	−	5.21808i	0.338951	−	0.587080i	0.984236	+	0.176862i	$0.0565946\pi$
$80$	−1.00187	+	0.578432i	−0.112013	+	0.0646707i
$81$	0.0873358	+	8.99958i	0.00970398	+	0.999953i
$82$	0.408341	+	0.235756i	0.0450937	+	0.0260349i
$83$		−	3.64267i		−	0.399835i	−0.979813	−	0.199917i	$-0.935933\pi$
$83$		−	3.64267i		−	0.399835i	0.979813	−	0.199917i	$-0.0640673\pi$
$84$	0.0966863	+	4.58156i	0.0105493	+	0.499889i
$85$		−	0.0296195i		−	0.00321269i
$86$	−0.620304	+	1.07440i	−0.0668891	+	0.115855i
$87$	5.63751	+	2.31913i	0.604405	+	0.248636i
$88$	−1.85690	−	3.21624i	−0.197946	−	0.342852i
$89$	8.11911	+	4.68757i	0.860623	+	0.496881i	0.864221	−	0.503112i	$-0.167812\pi$
$89$	8.11911	+	4.68757i	0.860623	+	0.496881i	−0.00359755	+	0.999994i	$0.501145\pi$
$90$	−3.35666	−	0.881980i	−0.353823	−	0.0929688i
$91$	−9.32434	−	2.01414i	−0.977456	−	0.211140i
$92$			2.73122i			0.284750i
$93$	7.71207	−	1.03435i	0.799704	−	0.107257i
$94$	0.203606	−	0.117552i	0.0210004	−	0.0121246i
$95$	0.244969	−	0.141433i	0.0251333	−	0.0145107i
$96$	1.71668	−	0.230243i	0.175208	−	0.0234991i
$97$	12.7955			1.29918			0.649591	−	0.760284i	$-0.274940\pi$
$97$	12.7955			1.29918			0.649591	+	0.760284i	$0.274940\pi$
$98$	−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	0.999999	+	0.00114938i	$0.000365859\pi$
$101$	5.03494	+	8.72077i	0.500995	+	0.867749i	−0.499004	+	0.866600i	$0.666301\pi$
$102$	−0.0168711	+	0.0410116i	−0.00167049	+	0.00406075i
$103$	8.82256	+	5.09371i	0.869313	+	0.501898i	0.867120	−	0.498099i	$-0.165969\pi$
$103$	8.82256	+	5.09371i	0.869313	+	0.501898i	0.00219314	+	0.999998i	$0.499302\pi$
$104$	−0.361803	+	3.58735i	−0.0354777	+	0.351769i
$105$	−2.74699	−	4.53422i	−0.268079	−	0.442494i
$106$		−	7.44274i		−	0.722903i
$107$	15.7423	+	9.08881i	1.52186	+	0.878648i	0.999667	+	0.0258233i	$0.00822071\pi$
$107$	15.7423	+	9.08881i	1.52186	+	0.878648i	0.522197	+	0.852825i	$0.325113\pi$
$108$	4.14530	+	3.13313i	0.398881	+	0.301486i
$109$	−2.40616	+	1.38920i	−0.230469	+	0.133061i	−0.610788	−	0.791794i	$-0.709147\pi$
$109$	−2.40616	+	1.38920i	−0.230469	+	0.133061i	0.380320	+	0.924855i	$0.375814\pi$
$110$	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	$-0.340191\pi$
$114$	−0.419746	+	0.0562970i	−0.0393128	+	0.00527269i
$115$	−1.57983	−	2.73634i	−0.147320	−	0.255165i
$116$	3.04794	−	1.75973i	0.282995	−	0.163387i
$117$	−8.34413	+	6.88299i	−0.771415	+	0.636333i
$118$		−	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
$123$	0.755272	+	0.310699i	0.0681006	+	0.0280148i
$124$	2.24622	−	3.89056i	0.201716	−	0.349383i
$125$		−	10.0204i		−	0.896249i
$126$	1.22085	+	7.84280i	0.108762	+	0.698692i
$127$	−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
$129$	−0.817490	+	1.98722i	−0.0719760	+	0.174965i
$130$	−1.71256	−	3.80335i	−0.150201	−	0.333576i
$131$	7.07051	−	12.2465i	0.617753	−	1.06998i	−0.372141	−	0.928176i	$-0.621376\pi$
$131$	7.07051	−	12.2465i	0.617753	−	1.06998i	0.989895	−	0.141804i	$-0.0452904\pi$
$132$	−3.92821	−	5.09371i	−0.341907	−	0.443351i
$133$	−0.520496	−	0.384164i	−0.0451327	−	0.0333113i
$134$			7.20658i			0.622554i
$135$	−5.96537	−	0.741228i	−0.513417	−	0.0637948i
$136$	0.0128016	+	0.0221731i	0.00109773	+	0.00190133i
$137$	6.70701	+	11.6169i	0.573019	+	0.992498i	0.996254	+	0.0864777i	$0.0275611\pi$
$137$	6.70701	+	11.6169i	0.573019	+	0.992498i	−0.423235	+	0.906020i	$0.639106\pi$
$138$	0.628846	+	4.68864i	0.0535310	+	0.399123i
$139$			15.0565i			1.27708i	0.769589	+	0.638539i	$0.220461\pi$
$139$			15.0565i			1.27708i	−0.769589	+	0.638539i	$0.779539\pi$
$140$	−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
$143$	12.2096	−	5.49769i	1.02102	−	0.459740i
$144$	2.89398	−	0.790508i	0.241165	−	0.0658757i
$145$	−2.03577	+	3.52606i	−0.169062	+	0.292823i
$146$	1.56853			0.129813
$147$	−6.99252	+	9.90478i	−0.576733	+	0.816933i
$148$		−	9.58187i		−	0.787625i
$149$	−4.72601	+	8.18569i	−0.387170	+	0.670598i	−0.992068	−	0.125705i	$-0.959881\pi$
$149$	−4.72601	+	8.18569i	−0.387170	+	0.670598i	0.604898	+	0.796303i	$0.293214\pi$
$150$	−2.41283	+	5.86529i	−0.197007	+	0.478899i
$151$	−12.9798	+	7.49388i	−1.05628	+	0.609843i	−0.924401	−	0.381423i	$-0.875434\pi$
$151$	−12.9798	+	7.49388i	−1.05628	+	0.609843i	−0.131878	+	0.991266i	$0.542101\pi$
$152$	−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
$156$	0.204865	+	6.24164i	0.0164023	+	0.499731i
$157$	1.50376	−	0.868197i	0.120013	−	0.0692896i	−0.438792	−	0.898589i	$-0.644593\pi$
$157$	1.50376	−	0.868197i	0.120013	−	0.0692896i	0.558805	+	0.829299i	$0.311260\pi$
$158$	−3.01266	−	5.21808i	−0.239674	−	0.415128i
$159$	−1.71364	−	12.7768i	−0.135901	−	1.01327i
$160$			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	$-0.499346\pi$
$163$	−11.0173	−	6.36085i	−0.862943	−	0.498221i	−0.864997	+	0.501777i	$0.832680\pi$
$164$	0.408341	−	0.235756i	0.0318861	−	0.0184094i
$165$	6.88194	+	2.83105i	0.535758	+	0.220397i
$166$	−3.15464	−	1.82133i	−0.244848	−	0.141363i
$167$		−	6.85544i		−	0.530490i	−0.964181	−	0.265245i	$-0.914547\pi$
$167$		−	6.85544i		−	0.530490i	0.964181	−	0.265245i	$-0.0854528\pi$
$168$	4.01609	+	2.20705i	0.309848	+	0.170277i
$169$	−12.7382	−	2.59583i	−0.979861	−	0.199679i
$170$	−0.0256513	−	0.0148098i	−0.00196736	−	0.00113586i
$171$	−0.707608	+	0.193288i	−0.0541121	+	0.0147811i
$172$	0.620304	+	1.07440i	0.0472977	+	0.0819221i
$173$	−7.79711	+	13.5050i	−0.592803	+	1.02677i	0.401049	+	0.916056i	$0.368646\pi$
$173$	−7.79711	+	13.5050i	−0.592803	+	1.02677i	−0.993853	+	0.110709i	$0.964688\pi$
$174$	4.82718	−	3.72266i	0.365947	−	0.282214i
$175$	−8.87962	+	3.87387i	−0.671236	+	0.292837i
$176$	−3.71379			−0.279937
$177$	−0.745560	−	5.55884i	−0.0560397	−	0.417828i
$178$	8.11911	−	4.68757i	0.608553	−	0.351348i
$179$	−3.42830	+	1.97933i	−0.256243	+	0.147942i	−0.622620	−	0.782525i	$-0.713932\pi$
$179$	−3.42830	+	1.97933i	−0.256243	+	0.147942i	0.366377	+	0.930467i	$0.380598\pi$
$180$	−2.44214	+	2.46596i	−0.182027	+	0.183802i
$181$			0.429161i			0.0318992i	0.999873	+	0.0159496i	$0.00507714\pi$
$181$			0.429161i			0.0318992i	−0.999873	+	0.0159496i	$0.994923\pi$
$182$	−6.40647	+	7.06804i	−0.474879	+	0.523918i
$183$	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
$186$	2.96026	−	7.19602i	0.217057	−	0.527638i
$187$	0.0475426	−	0.0823462i	0.00347666	−	0.00602175i
$188$		−	0.235104i		−	0.0171467i
$189$	3.90156	+	13.1825i	0.283797	+	0.958884i
$190$		−	0.282866i		−	0.0205212i
$191$	1.57425	+	0.908893i	0.113909	+	0.0657652i	0.555872	−	0.831268i	$-0.312385\pi$
$191$	1.57425	+	0.908893i	0.113909	+	0.0657652i	−0.441963	+	0.897033i	$0.645718\pi$
$192$	0.658943	−	1.60181i	0.0475551	−	0.115601i
$193$	17.1426	−	9.89729i	1.23395	−	0.712422i	0.266100	−	0.963945i	$-0.414265\pi$
$193$	17.1426	−	9.89729i	1.23395	−	0.712422i	0.967851	+	0.251523i	$0.0809315\pi$
$194$	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	$0.855920\pi$
$198$	−7.91627	−	7.83982i	−0.562585	−	0.557152i
$199$	−5.33963	+	3.08284i	−0.378517	+	0.218537i	−0.677173	−	0.735824i	$-0.736795\pi$
$199$	−5.33963	+	3.08284i	−0.378517	+	0.218537i	0.298656	+	0.954361i	$0.403462\pi$
$200$	1.83083	+	3.17109i	0.129459	+	0.224230i
$201$	1.65927	+	12.3714i	0.117036	+	0.872610i
$202$	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
$207$	2.15906	+	7.90410i	0.150065	+	0.549373i
$208$	2.92584	+	2.10701i	0.202870	+	0.146095i
$209$	0.908061			0.0628119
$210$	−5.30024	+	0.111853i	−0.365751	+	0.00771859i
$211$	−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
$213$	−9.67044	+	23.5076i	−0.662607	+	1.61072i
$214$	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
$219$	2.69267	−	0.361144i	0.181954	−	0.0244039i
$220$	3.72075	−	2.14818i	0.250853	−	0.144830i
$221$	−0.0841743	+	0.0379017i	−0.00566218	+	0.00254954i
$222$	−2.20616	−	16.4490i	−0.148068	−	1.10398i
$223$	−2.03477			−0.136258			−0.0681291	−	0.997677i	$-0.521703\pi$
$223$	−2.03477			−0.136258			−0.0681291	+	0.997677i	$0.521703\pi$
$224$	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	0.116902	−	0.993143i	$-0.462704\pi$
$227$	15.6005	−	9.00694i	1.03544	−	0.597812i	0.918538	+	0.395332i	$0.129370\pi$
$228$	−0.161119	+	0.391659i	−0.0106703	+	0.0259383i
$229$	−9.36691	+	16.2240i	−0.618983	+	1.07211i	0.370688	+	0.928757i	$0.379122\pi$
$229$	−9.36691	+	16.2240i	−0.618983	+	1.07211i	−0.989672	+	0.143353i	$0.954212\pi$
$230$	−3.15966			−0.208342
$231$	−0.359073	−	17.0149i	−0.0236252	−	1.11950i
$232$		−	3.51946i		−	0.231064i
$233$	−17.0834	−	9.86309i	−1.11917	−	0.646152i	−0.177980	−	0.984034i	$-0.556956\pi$
$233$	−17.0834	−	9.86309i	−1.11917	−	0.646152i	−0.941189	+	0.337882i	$0.890290\pi$
$234$	1.78878	+	10.6677i	0.116936	+	0.697371i
$235$	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	$0.725830\pi$
$240$	0.266360	+	1.98597i	0.0171935	+	0.128194i
$241$	11.1359	+	19.2880i	0.717327	+	1.24245i	0.962055	+	0.272855i	$0.0879678\pi$
$241$	11.1359	+	19.2880i	0.717327	+	1.24245i	−0.244729	+	0.969592i	$0.578699\pi$
$242$	1.39612	+	2.41815i	0.0897460	+	0.155445i
$243$	14.4732	+	5.79031i	0.928453	+	0.371449i
$244$		−	11.8302i		−	0.757353i
$245$	−5.93601	−	5.50838i	−0.379238	−	0.351918i
$246$	0.646709	−	0.498735i	0.0412327	−	0.0317982i
$247$	−0.715398	−	0.515185i	−0.0455197	−	0.0327805i
$248$	−2.24622	−	3.89056i	−0.142635	−	0.247051i
$249$	−5.83486	−	2.40031i	−0.369769	−	0.152113i
$250$	−8.67790	−	5.01019i	−0.548838	−	0.316872i
$251$	−20.5563			−1.29750			−0.648752	−	0.761000i	$-0.724709\pi$
$251$	−20.5563			−1.29750			−0.648752	+	0.761000i	$0.724709\pi$
$252$	7.40249	+	2.86411i	0.466313	+	0.180422i
$253$		−	10.1432i		−	0.637697i
$254$	−4.41521	+	7.64737i	−0.277035	+	0.479839i
$255$	−0.0474448	−	0.0195176i	−0.00297111	−	0.00122224i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.10857	+	8.84830i	−0.318664	+	0.551942i	−0.980210	−	0.197963i	$-0.936567\pi$
$257$	−5.10857	+	8.84830i	−0.318664	+	0.551942i	0.661546	+	0.749905i	$0.269901\pi$
$258$	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
$261$	7.42960	−	7.50205i	0.459881	−	0.464365i
$262$	−7.07051	−	12.2465i	−0.436818	−	0.756590i
$263$	−24.3841	+	14.0782i	−1.50359	+	0.868097i	−0.503598	+	0.863938i	$0.667991\pi$
$263$	−24.3841	+	14.0782i	−1.50359	+	0.868097i	−0.999991	+	0.00415905i	$0.998676\pi$
$264$	−6.37539	+	0.855076i	−0.392378	+	0.0526263i
$265$	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	−0.833573	−	0.552409i	$-0.813709\pi$
$269$	−14.6822	−	25.4302i	−0.895187	−	1.55051i	−0.0616140	−	0.998100i	$-0.519625\pi$
$270$	−3.62461	+	4.79555i	−0.220587	+	0.291848i
$271$	−14.2082	+	24.6093i	−0.863085	+	1.49491i	0.00585211	+	0.999983i	$0.498137\pi$
$271$	−14.2082	+	24.6093i	−0.863085	+	1.49491i	−0.868937	+	0.494923i	$0.835196\pi$
$272$	0.0256033			0.00155243
$273$	−9.37048	+	13.6086i	−0.567127	+	0.823630i
$274$	13.4140			0.810371
$275$	6.79933	−	11.7768i	0.410015	−	0.710166i
$276$	4.37490	+	1.79972i	0.263338	+	0.108331i
$277$	−13.8268	−	23.9486i	−0.830769	−	1.43893i	−0.897429	−	0.441159i	$-0.854567\pi$
$277$	−13.8268	−	23.9486i	−0.830769	−	1.43893i	0.0666595	−	0.997776i	$-0.478766\pi$
$278$	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	$0.620196\pi$
$282$	−0.0541311	−	0.403598i	−0.00322346	−	0.0240339i
$283$	11.8406	−	6.83616i	0.703849	−	0.406367i	−0.104930	−	0.994480i	$-0.533462\pi$
$283$	11.8406	−	6.83616i	0.703849	−	0.406367i	0.808779	+	0.588112i	$0.200129\pi$
$284$	7.33784	+	12.7095i	0.435421	+	0.754171i
$285$	−0.0651280	−	0.485590i	−0.00385785	−	0.0287639i
$286$	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
$291$	8.43148	−	20.4959i	0.494262	−	1.20149i
$292$	0.784266	−	1.35839i	0.0458957	−	0.0794937i
$293$			4.20649i			0.245746i	0.992422	+	0.122873i	$0.0392107\pi$
$293$			4.20649i			0.245746i	−0.992422	+	0.122873i	$0.960789\pi$
$294$	5.08153	+	11.0081i	0.296361	+	0.642005i
$295$	3.74609			0.218106
$296$	−8.29815	−	4.79094i	−0.482320	−	0.278468i
$297$	−15.3948	−	11.6358i	−0.893295	−	0.675177i
$298$	4.72601	+	8.18569i	0.273771	+	0.474184i
$299$	−5.75471	+	7.99112i	−0.332803	+	0.462138i
$300$	3.87307	+	5.02221i	0.223612	+	0.289958i
$301$	−0.367590	+	3.26169i	−0.0211875	+	0.188001i
$302$			14.9878i			0.862448i
$303$	17.2867	−	2.31852i	0.993098	−	0.133196i
$304$	0.122255	+	0.211752i	0.00701182	+	0.0121448i
$305$	6.84299	+	11.8524i	0.391828	+	0.678666i
$306$	0.0545756	+	0.0540486i	0.00311988	+	0.00308975i
$307$	−21.1492			−1.20705			−0.603524	−	0.797345i	$-0.706237\pi$
$307$	−21.1492			−1.20705			−0.603524	+	0.797345i	$0.706237\pi$
$308$	−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	−0.841208	−	0.540711i	$-0.818155\pi$
$311$	−15.6755	−	27.1507i	−0.888874	−	1.53957i	−0.0476652	−	0.998863i	$-0.515178\pi$
$312$	5.50785	+	2.94340i	0.311821	+	0.166637i
$313$	28.3855	+	16.3884i	1.60444	+	0.926325i	0.990584	+	0.136908i	$0.0437165\pi$
$313$	28.3855	+	16.3884i	1.60444	+	0.926325i	0.613858	+	0.789417i	$0.289617\pi$
$314$		−	1.73639i		−	0.0979903i
$315$	−9.07306	+	1.41236i	−0.511209	+	0.0795775i
$316$	−6.02532			−0.338951
$317$	−11.1137	+	19.2495i	−0.624209	+	1.08116i	0.364484	+	0.931210i	$0.381245\pi$
$317$	−11.1137	+	19.2495i	−0.624209	+	1.08116i	−0.988693	+	0.149952i	$0.952088\pi$
$318$	−11.9219	−	4.90434i	−0.668544	−	0.275022i
$319$	−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
$324$	7.75019	−	4.57542i	0.430566	−	0.254190i
$325$	−12.0382	+	5.42053i	−0.667761	+	0.300677i
$326$	−11.0173	+	6.36085i	−0.610193	+	0.352295i
$327$	0.639708	+	4.76962i	0.0353759	+	0.263760i
$328$		−	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	$-0.503345\pi$
$331$	−16.0419	−	9.26179i	−0.881742	−	0.509074i	−0.871233	+	0.490871i	$0.836679\pi$
$332$	−3.15464	+	1.82133i	−0.173133	+	0.0999586i
$333$	−7.57455	−	27.7297i	−0.415083	−	1.51958i
$334$	−5.93699	−	3.42772i	−0.324857	−	0.187557i
$335$	−8.33704			−0.455501
$336$	3.91940	−	2.37451i	0.213821	−	0.129540i
$337$	−17.9572			−0.978191			−0.489095	−	0.872230i	$-0.662673\pi$
$337$	−17.9572			−0.978191			−0.489095	+	0.872230i	$0.662673\pi$
$338$	−8.61715	+	9.73369i	−0.468711	+	0.529443i
$339$	−29.8524	−	12.2805i	−1.62136	−	0.666985i
$340$	−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
$345$	−5.42412	+	0.727490i	−0.292025	+	0.0391668i
$346$	7.79711	+	13.5050i	0.419175	+	0.726033i
$347$	−0.436830	+	0.252204i	−0.0234503	+	0.0135390i	−0.511679	−	0.859177i	$-0.670976\pi$
$347$	−0.436830	+	0.252204i	−0.0234503	+	0.0135390i	0.488229	+	0.872716i	$0.337643\pi$
$348$	−0.810333	−	6.04179i	−0.0434384	−	0.323874i
$349$	22.5405			1.20656			0.603282	−	0.797528i	$-0.293859\pi$
$349$	22.5405			1.20656			0.603282	+	0.797528i	$0.293859\pi$
$350$	−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	−0.0833068	−	0.996524i	$-0.526548\pi$
$353$	13.8668	−	8.00600i	0.738055	−	0.426116i	0.821362	+	0.570408i	$0.193215\pi$
$354$	−5.18688	−	2.13375i	−0.275679	−	0.113407i
$355$	−14.7032	−	8.48889i	−0.780364	−	0.450543i
$356$		−	9.37514i		−	0.496881i
$357$	0.00247548	+	0.117303i	0.000131017	+	0.00620832i
$358$			3.95866i			0.209222i
$359$	7.67875	−	13.3000i	0.405269	−	0.701947i	−0.589084	−	0.808072i	$-0.700511\pi$
$359$	7.67875	−	13.3000i	0.405269	−	0.701947i	0.994353	+	0.106125i	$0.0338445\pi$
$360$	0.914511	+	3.34794i	0.0481990	+	0.176452i
$361$	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
$364$	2.91787	+	9.08218i	0.152938	+	0.476036i
$365$			1.81458i			0.0949795i
$366$	−2.72383	−	20.3087i	−0.142377	−	1.06155i
$367$	−27.0095	+	15.5939i	−1.40988	+	0.813996i	−0.995376	−	0.0960509i	$-0.969379\pi$
$367$	−27.0095	+	15.5939i	−1.40988	+	0.813996i	−0.414506	+	0.910047i	$0.636045\pi$
$368$	2.36531	−	1.36561i	0.123300	−	0.0711875i
$369$	0.995362	−	1.00507i	0.0518165	−	0.0523218i
$370$	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	−0.800064	−	0.599914i	$-0.795201\pi$
$373$	2.30810	−	3.99775i	0.119509	−	0.206996i	0.919573	+	0.392919i	$0.128535\pi$
$374$	−0.0475426	−	0.0823462i	−0.00245837	−	0.00425802i
$375$	−16.0507	−	6.60286i	−0.828856	−	0.340970i
$376$	−0.203606	−	0.117552i	−0.0105002	−	0.00606228i
$377$	12.6256	+	1.27335i	0.650249	+	0.0655809i
$378$	13.3671	+	3.21239i	0.687532	+	0.165227i
$379$		−	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
$381$	−5.81875	+	14.1447i	−0.298103	+	0.724653i
$382$	1.57425	−	0.908893i	0.0805456	−	0.0465030i
$383$	−1.24813	−	0.720607i	−0.0637763	−	0.0368213i	0.467773	−	0.883849i	$-0.345057\pi$
$383$	−1.24813	−	0.720607i	−0.0637763	−	0.0368213i	−0.531549	+	0.847027i	$0.678390\pi$
$384$	−1.05774	−	1.37157i	−0.0539774	−	0.0699924i
$385$	11.2956	+	1.27300i	0.575676	+	0.0648781i
$386$		−	19.7946i		−	1.00752i
$387$	2.64447	+	2.61893i	0.134426	+	0.133128i
$388$	−6.39773	−	11.0812i	−0.324795	−	0.562562i
$389$	7.08963	−	4.09320i	0.359459	−	0.207533i	−0.309385	−	0.950937i	$-0.600123\pi$
$389$	7.08963	−	4.09320i	0.359459	−	0.207533i	0.668843	+	0.743403i	$0.266790\pi$
$390$	−7.22073	+	0.237001i	−0.365636	+	0.0120010i
$391$			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
$396$	−10.7476	+	2.93578i	−0.540088	+	0.147529i
$397$	6.43999	−	11.1544i	0.323214	−	0.559823i	−0.657935	−	0.753074i	$-0.728570\pi$
$397$	6.43999	−	11.1544i	0.323214	−	0.559823i	0.981149	+	0.193252i	$0.0619034\pi$
$398$			6.16568i			0.309058i
$399$	−0.958335	+	0.580593i	−0.0479768	+	0.0290660i
$400$	3.66166			0.183083
$401$	−4.27201	+	7.39934i	−0.213334	+	0.369505i	−0.952756	−	0.303737i	$-0.901766\pi$
$401$	−4.27201	+	7.39934i	−0.213334	+	0.369505i	0.739422	+	0.673242i	$0.235099\pi$
$402$	11.5436	+	4.74873i	0.575741	+	0.236845i
$403$	14.7695	−	6.65035i	0.735721	−	0.331278i
$404$	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
$408$	0.0439526	−	0.00589498i	0.00217598	−	0.000291845i
$409$	−10.1026	−	17.4982i	−0.499542	−	0.865232i	0.500458	−	0.865761i	$-0.333165\pi$
$409$	−10.1026	−	17.4982i	−0.499542	−	0.865232i	−1.00000		0.000529035i	$0.999832\pi$
$410$	0.272738	+	0.472395i	0.0134695	+	0.0233299i
$411$	23.0276	−	3.08849i	1.13587	−	0.152344i
$412$		−	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
$416$	3.28764	−	1.48035i	0.161190	−	0.0725799i
$417$	24.1177	+	9.92140i	1.18105	+	0.485853i
$418$	0.454031	−	0.786404i	0.0222074	−	0.0384643i
$419$	−2.16600			−0.105816			−0.0529081	−	0.998599i	$-0.516849\pi$
$419$	−2.16600			−0.105816			−0.0529081	+	0.998599i	$0.516849\pi$
$420$	−2.55325	+	4.64607i	−0.124586	+	0.226705i
$421$			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
$423$	−0.185852	−	0.680385i	−0.00903641	−	0.0330815i
$424$	−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
$429$	−0.760825	−	23.1801i	−0.0367330	−	1.11915i
$430$	−1.24293	+	0.717608i	−0.0599396	+	0.0346061i
$431$	17.2738	+	29.9190i	0.832048	+	1.44115i	0.896412	+	0.443222i	$0.146165\pi$
$431$	17.2738	+	29.9190i	0.832048	+	1.44115i	−0.0643642	+	0.997926i	$0.520502\pi$
$432$	0.640722	−	5.15650i	0.0308267	−	0.248092i
$433$			0.715483i			0.0343839i	0.999852	+	0.0171920i	$0.00547264\pi$
$433$			0.715483i			0.0343839i	−0.999852	+	0.0171920i	$0.994527\pi$
$434$	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
$438$	1.03357	−	2.51249i	0.0493861	−	0.120051i
$439$	15.5035	+	8.95097i	0.739944	+	0.427207i	0.822049	−	0.569417i	$-0.192831\pi$
$439$	15.5035	+	8.95097i	0.739944	+	0.427207i	−0.0821052	+	0.996624i	$0.526164\pi$
$440$		−	4.29635i		−	0.204821i
$441$	11.2579	+	17.7274i	0.536091	+	0.844160i
$442$	−0.00926333	+	0.0918479i	−0.000440612	+	0.00436876i
$443$	14.3289	+	8.27278i	0.680785	+	0.393052i	0.800151	−	0.599799i	$-0.204753\pi$
$443$	14.3289	+	8.27278i	0.680785	+	0.393052i	−0.119366	+	0.992850i	$0.538086\pi$
$444$	−15.3483	−	6.31391i	−0.728400	−	0.299645i
$445$	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	$0.283009\pi$
$450$	7.80516	+	7.72978i	0.367939	+	0.364385i
$451$	−1.51649	+	0.875548i	−0.0714089	+	0.0412279i
$452$	−16.1398	+	9.31833i	−0.759153	+	0.438297i
$453$	3.45083	+	25.7292i	0.162134	+	1.20886i
$454$		−	18.0139i		−	0.845433i
$455$	−8.17677	−	7.41142i	−0.383333	−	0.347453i
$456$	0.258628	+	0.335362i	0.0121114	+	0.0157048i
$457$	32.4759	+	18.7500i	1.51916	+	0.877087i	0.999745	+	0.0225635i	$0.00718280\pi$
$457$	32.4759	+	18.7500i	1.51916	+	0.877087i	0.519413	+	0.854523i	$0.326151\pi$
$458$	9.36691	+	16.2240i	0.437687	+	0.758096i
$459$	0.106133	+	0.0802184i	0.00495387	+	0.00374427i
$460$	−1.57983	+	2.73634i	−0.0736599	+	0.127583i
$461$		−	8.31097i		−	0.387080i	−0.981092	−	0.193540i	$-0.938003\pi$
$461$		−	8.31097i		−	0.387080i	0.981092	−	0.193540i	$-0.0619970\pi$
$462$	−14.9149	−	8.19650i	−0.693904	−	0.381336i
$463$		−	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
$465$	8.32482	+	3.42462i	0.386054	+	0.158813i
$466$	−17.0834	+	9.86309i	−0.791372	+	0.456899i
$467$	10.3800	−	17.9787i	0.480328	−	0.831953i	−0.519417	−	0.854521i	$-0.673851\pi$
$467$	10.3800	−	17.9787i	0.480328	−	0.831953i	0.999745	+	0.0225677i	$0.00718413\pi$
$468$	10.1329	+	3.78473i	0.468394	+	0.174949i
$469$	7.62422	+	17.4761i	0.352054	+	0.806972i
$470$	0.271983			0.0125457
$471$	−0.399793	−	2.98083i	−0.0184215	−	0.137349i
$472$	−2.80431	+	1.61907i	−0.129079	+	0.0745237i
$473$	−2.30368	−	3.99009i	−0.105923	−	0.183465i
$474$	−10.3435	+	1.38729i	−0.475095	+	0.0637204i
$475$	−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	−0.804690	−	0.593695i	$-0.797669\pi$
$479$	−15.1644	+	8.75519i	−0.692881	+	0.400035i	0.111809	+	0.993730i	$0.464335\pi$
$480$	1.85308	+	0.762308i	0.0845810	+	0.0347944i
$481$	20.1891	−	28.0350i	0.920542	−	1.27829i
$482$	22.2718			1.01445
$483$	6.48532	+	10.7048i	0.295092	+	0.487084i
$484$	2.79224			0.126920
$485$	12.8194	+	7.40130i	0.582101	+	0.336076i
$486$	12.2511	−	9.63897i	0.555723	−	0.437232i
$487$	0.122893	−	0.0709520i	0.00556879	−	0.00321514i	−0.497213	−	0.867628i	$-0.665643\pi$
$487$	0.122893	−	0.0709520i	0.00556879	−	0.00321514i	0.502782	+	0.864413i	$0.332310\pi$
$488$	−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	$-0.0725875\pi$
$492$	−0.108562	−	0.809434i	−0.00489437	−	0.0364921i
$493$	0.0780373	−	0.0450549i	0.00351463	−	0.00202917i
$494$	−0.803863	+	0.361960i	−0.0361675	+	0.0162854i
$495$	9.06961	−	9.15806i	0.407649	−	0.411624i
$496$	−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	$-0.408523\pi$
$499$	−9.05469	−	5.22772i	−0.405343	−	0.234025i	−0.688787	+	0.724964i	$0.741856\pi$
$500$	−8.67790	+	5.01019i	−0.388087	+	0.224062i
$501$	−10.9811	−	4.51734i	−0.490600	−	0.201820i
$502$	−10.2782	+	17.8023i	−0.458737	+	0.794556i
$503$	13.6155			0.607083			0.303542	−	0.952818i	$-0.401831\pi$
$503$	13.6155			0.607083			0.303542	+	0.952818i	$0.401831\pi$
$504$	6.18164	−	4.97869i	0.275352	−	0.221768i
$505$			11.6495i			0.518395i
$506$	−8.78427	−	5.07160i	−0.390508	−	0.225460i
$507$	−12.5518	+	18.6937i	−0.557444	+	0.830215i
$508$	4.41521	+	7.64737i	0.195893	+	0.339297i
$509$	−8.06558	−	4.65666i	−0.357500	−	0.206403i	0.310483	−	0.950579i	$-0.399509\pi$
$509$	−8.06558	−	4.65666i	−0.357500	−	0.206403i	−0.667984	+	0.744176i	$0.732842\pi$
$510$	−0.0406251	+	0.0313296i	−0.00179891	+	0.00138730i
$511$	3.80373	−	1.65943i	0.168267	−	0.0734090i
$512$	−1.00000			−0.0441942
$513$	−0.156663	+	1.26082i	−0.00691685	+	0.0556665i
$514$	5.10857	+	8.84830i	0.225329	+	0.390282i
$515$	5.89273	+	10.2065i	0.259665	+	0.449753i
$516$	2.12973	−	0.285642i	0.0937560	−	0.0125747i
$517$			0.873127i			0.0384001i
$518$	−10.1372	−	23.2363i	−0.445401	−	1.02094i
$519$	16.4946	+	21.3885i	0.724032	+	0.938851i
$520$	−2.43752	+	3.38480i	−0.106892	+	0.148433i
$521$	−6.86110	−	11.8838i	−0.300590	−	0.520637i	0.675680	−	0.737195i	$-0.263850\pi$
$521$	−6.86110	−	11.8838i	−0.300590	−	0.520637i	−0.976270	+	0.216558i	$0.930517\pi$
$522$	−2.78216	−	10.1852i	−0.121772	−	0.445796i
$523$	−23.6617	−	13.6611i	−1.03465	−	0.597358i	−0.116340	−	0.993209i	$-0.537116\pi$
$523$	−23.6617	−	13.6611i	−1.03465	−	0.597358i	−0.918315	+	0.395851i	$0.870450\pi$
$524$	−14.1410			−0.617753
$525$	0.354033	+	16.7761i	0.0154513	+	0.732170i
$526$			28.1563i			1.22768i
$527$	0.0575105	−	0.0996111i	0.00250520	−	0.00433913i
$528$	−2.44718	+	5.94879i	−0.106500	+	0.258888i
$529$	−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
$534$	−2.15856	−	16.0941i	−0.0934102	−	0.696460i
$535$	10.5145	+	18.2117i	0.454582	+	0.787360i
$536$	6.24108	−	3.60329i	0.269574	−	0.155638i
$537$	0.911455	+	6.79574i	0.0393322	+	0.293258i
$538$	−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	$-0.286553\pi$
$541$	5.89940	+	3.40602i	0.253635	+	0.146436i	−0.367793	+	0.929908i	$0.619886\pi$
$542$	14.2082	+	24.6093i	0.610293	+	1.05706i
$543$	0.687433	+	0.282792i	0.0295006	+	0.0121358i
$544$	0.0128016	−	0.0221731i	0.000548866	−	0.000950663i
$545$	−3.21423			−0.137682
$546$	7.10016	+	14.9194i	0.303859	+	0.638490i
$547$	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
$549$	−9.35189	−	34.2364i	−0.399129	−	1.46117i
$550$	−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
$555$	19.0293	−	2.55223i	0.807748	−	0.108336i
$556$	13.0393	−	7.52827i	0.552991	−	0.319270i
$557$	10.8866	+	18.8561i	0.461279	+	0.798958i	0.999025	−	0.0441487i	$-0.0140575\pi$
$557$	10.8866	+	18.8561i	0.461279	+	0.798958i	−0.537746	+	0.843107i	$0.680724\pi$
$558$	−9.57601	−	9.48354i	−0.405385	−	0.401470i
$559$	−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	$-0.236977\pi$
$563$	−5.19862	−	9.00428i	−0.219096	−	0.379485i	−0.954532	+	0.298109i	$0.903644\pi$
$564$	−0.376592	−	0.154920i	−0.0158574	−	0.00652331i
$565$	10.7800	−	18.6716i	0.453520	−	0.785520i
$566$		−	13.6723i		−	0.574690i
$567$	23.6867	+	2.43694i	0.994749	+	0.102342i
$568$	14.6757			0.615778
$569$	14.6618	+	8.46500i	0.614655	+	0.354871i	0.774785	−	0.632225i	$-0.217858\pi$
$569$	14.6618	+	8.46500i	0.614655	+	0.354871i	−0.160130	+	0.987096i	$0.551191\pi$
$570$	−0.453097	−	0.186392i	−0.0189781	−	0.00780712i
$571$	8.19990	+	14.2026i	0.343155	+	0.594362i	0.985017	−	0.172458i	$-0.0551710\pi$
$571$	8.19990	+	14.2026i	0.343155	+	0.594362i	−0.641862	+	0.766820i	$0.721838\pi$
$572$	−10.8659	−	7.82498i	−0.454328	−	0.327179i
$573$	2.49321	−	1.92274i	0.104156	−	0.0803236i
$574$	0.740818	−	1.00372i	0.0309211	−	0.0418944i
$575$			10.0008i			0.417063i
$576$	−2.13159	−	2.11100i	−0.0888162	−	0.0879584i
$577$	11.8397	+	20.5070i	0.492894	+	0.853718i	0.999966	−	0.00818553i	$-0.00260556\pi$
$577$	11.8397	+	20.5070i	0.492894	+	0.853718i	−0.507072	+	0.861904i	$0.669272\pi$
$578$	−8.49967	−	14.7219i	−0.353540	−	0.612349i
$579$	−4.55757	−	33.9809i	−0.189406	−	1.41220i
$580$	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
$585$	−12.3411	+	2.06938i	−0.510242	+	0.0855583i
$586$	3.64292	+	2.10324i	0.150488	+	0.0868842i
$587$			43.3060i			1.78743i	0.448633	+	0.893716i	$0.351911\pi$
$587$			43.3060i			1.78743i	−0.448633	+	0.893716i	$0.648089\pi$
$588$	12.0741	+	1.10331i	0.497925	+	0.0454996i
$589$	1.09845			0.0452607
$590$	1.87304	−	3.24421i	0.0771120	−	0.133562i
$591$	−16.6346	+	40.4368i	−0.684258	+	1.66335i
$592$	−8.29815	+	4.79094i	−0.341052	+	0.196906i
$593$	−18.9754	−	10.9554i	−0.779226	−	0.449886i	0.0569301	−	0.998378i	$-0.481869\pi$
$593$	−18.9754	−	10.9554i	−0.779226	−	0.449886i	−0.836156	+	0.548492i	$0.815202\pi$
$594$	−17.7743	+	7.51436i	−0.729287	+	0.308318i
$595$	−0.0778729	−	0.00877620i	−0.00319248	−	0.000359789i
$596$	9.45202			0.387170
$597$	1.41961	+	10.5845i	0.0581006	+	0.433194i
$598$	4.04316	+	8.97928i	0.165337	+	0.367190i
$599$	39.3065	−	22.6936i	1.60602	−	0.927237i	0.615773	−	0.787923i	$-0.288844\pi$
$599$	39.3065	−	22.6936i	1.60602	−	0.927237i	0.990248	−	0.139314i	$-0.0444896\pi$
$600$	6.28590	−	0.843074i	0.256621	−	0.0344183i
$601$		−	8.20455i		−	0.334671i	−0.985900	−	0.167335i	$-0.946484\pi$
$601$		−	8.20455i		−	0.334671i	0.985900	−	0.167335i	$-0.0535163\pi$
$602$	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
$606$	6.63547	−	16.1300i	0.269548	−	0.655237i
$607$	−24.0464	−	13.8832i	−0.976012	−	0.563501i	−0.0749481	−	0.997187i	$-0.523879\pi$
$607$	−24.0464	−	13.8832i	−0.976012	−	0.563501i	−0.901064	+	0.433687i	$0.857212\pi$
$608$	0.244511			0.00991621
$609$	7.76761	−	14.1345i	0.314760	−	0.572758i
$610$	13.6860			0.554129
$611$	0.495366	−	0.687876i	0.0200403	−	0.0278285i
$612$	0.0740952	−	0.0202396i	0.00299512	−	0.000818137i
$613$	15.8517	−	9.15200i	0.640245	−	0.369646i	−0.144464	−	0.989510i	$-0.546146\pi$
$613$	15.8517	−	9.15200i	0.640245	−	0.369646i	0.784709	+	0.619864i	$0.212812\pi$
$614$	−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	$0.352759\pi$
$618$	−2.34559	−	17.4885i	−0.0943533	−	0.703492i
$619$	−19.7675	−	34.2384i	−0.794525	−	1.37616i	−0.923140	−	0.384463i	$-0.874387\pi$
$619$	−19.7675	−	34.2384i	−0.794525	−	1.37616i	0.128616	−	0.991695i	$-0.458947\pi$
$620$	4.50085	−	2.59857i	0.180759	−	0.104361i
$621$	14.0836	+	1.74996i	0.565154	+	0.0702233i
$622$	−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
$627$	0.598361	−	1.45454i	0.0238962	−	0.0580888i
$628$	−1.50376	−	0.868197i	−0.0600066	−	0.0346448i
$629$		−	0.245327i		−	0.00978184i
$630$	−3.31339	+	8.56368i	−0.132009	+	0.341185i
$631$			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
$633$	−2.62377	+	6.37806i	−0.104286	+	0.253505i
$634$	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
$637$	−8.05818	+	23.9179i	−0.319277	+	0.947662i
$638$			13.0706i			0.517468i
$639$	31.2825	+	30.9804i	1.23752	+	1.22557i
$640$	1.00187	−	0.578432i	0.0396026	−	0.0228645i
$641$	−13.7967	+	7.96553i	−0.544937	+	0.314620i	−0.747077	−	0.664737i	$-0.768544\pi$
$641$	−13.7967	+	7.96553i	−0.544937	+	0.314620i	0.202140	+	0.979357i	$0.435210\pi$
$642$	−4.18528	−	31.2051i	−0.165180	−	1.23157i
$643$	−20.5219			−0.809303			−0.404652	−	0.914471i	$-0.632607\pi$
$643$	−20.5219			−0.809303			−0.404652	+	0.914471i	$0.632607\pi$
$644$	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	0.975898	+	0.218226i	$0.0700269\pi$
$647$	17.2187	+	29.8237i	0.676938	+	1.17249i	−0.298960	+	0.954266i	$0.596640\pi$
$648$	−0.0873358	−	8.99958i	−0.00343088	−	0.353537i
$649$	10.4146	+	6.01288i	0.408809	+	0.236026i
$650$	−1.32480	+	13.1357i	−0.0519629	+	0.515224i
$651$	−0.434357	−	20.5823i	−0.0170238	−	0.806685i
$652$			12.7217i			0.498221i
$653$	15.3842	+	8.88210i	0.602032	+	0.347583i	0.769841	−	0.638236i	$-0.220336\pi$
$653$	15.3842	+	8.88210i	0.602032	+	0.347583i	−0.167808	+	0.985820i	$0.553669\pi$
$654$	4.45046	+	1.83081i	0.174027	+	0.0715902i
$655$	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	$-0.0592821\pi$
$660$	−0.989207	−	7.37546i	−0.0385048	−	0.287089i
$661$	−17.2613	−	29.8975i	−0.671387	−	1.16288i	−0.977511	−	0.210885i	$-0.932366\pi$
$661$	−17.2613	−	29.8975i	−0.671387	−	1.16288i	0.306124	−	0.951992i	$-0.400968\pi$
$662$	−16.0419	+	9.26179i	−0.623486	+	0.359970i
$663$	0.00524521	+	0.159806i	0.000203707	+	0.00620636i
$664$			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
$669$	−1.34080	+	3.25931i	−0.0518382	+	0.126012i
$670$	−4.16852	+	7.22009i	−0.161044	+	0.278936i
$671$			43.9350i			1.69609i
$672$	−0.0966863	−	4.58156i	−0.00372975	−	0.176737i
$673$	−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
$675$	15.1787	+	11.4725i	0.584228	+	0.441576i
$676$	4.12105	+	12.3295i	0.158502	+	0.474212i
$677$	−23.5469	+	40.7844i	−0.904979	+	1.56747i	−0.0840345	+	0.996463i	$0.526781\pi$
$677$	−23.5469	+	40.7844i	−0.904979	+	1.56747i	−0.820945	+	0.571007i	$0.806553\pi$
$678$	−25.5614	+	19.7127i	−0.981680	+	0.757061i
$679$	3.79127	−	33.6406i	0.145495	−	1.29101i
$680$			0.0296195i			0.00113586i
$681$	−4.14758	−	30.9241i	−0.158935	−	1.18501i
$682$	8.34198	+	14.4487i	0.319431	+	0.553270i
$683$	7.64632	+	13.2438i	0.292578	+	0.506760i	0.974419	−	0.224741i	$-0.0721535\pi$
$683$	7.64632	+	13.2438i	0.292578	+	0.506760i	−0.681840	+	0.731501i	$0.738820\pi$
$684$	0.521196	+	0.516163i	0.0199284	+	0.0197360i
$685$			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
$689$	−11.0178	−	24.4691i	−0.419746	−	0.932197i
$690$	−2.08203	+	5.06117i	−0.0792617	+	0.192675i
$691$	6.72191	−	11.6427i	0.255713	−	0.442909i	−0.709376	−	0.704831i	$-0.751023\pi$
$691$	6.72191	−	11.6427i	0.255713	−	0.442909i	0.965089	+	0.261922i	$0.0843563\pi$
$692$	15.5942			0.592803
$693$	−27.4913	−	10.6367i	−1.04431	−	0.404055i
$694$			0.504408i			0.0191471i
$695$	−8.70919	+	15.0848i	−0.330358	+	0.572197i
$696$	−5.63751	−	2.31913i	−0.213689	−	0.0879062i
$697$	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	$-0.314700\pi$
$702$	18.2664	+	4.16413i	0.689419	+	0.157165i
$703$	2.02898	−	1.17143i	0.0765246	−	0.0441815i
$704$	1.85690	+	3.21624i	0.0699844	+	0.121216i
$705$	0.466908	−	0.0626224i	0.0175848	−	0.00235850i
$706$		−	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	$-0.602248\pi$
$709$	−34.4905	−	19.9131i	−1.29532	−	0.747852i	−0.979592	+	0.200998i	$0.935581\pi$
$710$	−14.7032	+	8.48889i	−0.551801	+	0.318582i
$711$	−17.4371	+	4.76307i	−0.653944	+	0.178629i
$712$	−8.11911	−	4.68757i	−0.304276	−	0.175674i
$713$		−	12.2698i		−	0.459509i
$714$	0.102825	+	0.0565076i	0.00384813	+	0.00211474i
$715$	15.4125	+	1.55443i	0.576396	+	0.0581325i
$716$	3.42830	+	1.97933i	0.128121	+	0.0739710i
$717$	−13.2722	+	32.2631i	−0.495659	+	1.20489i
$718$	−7.67875	−	13.3000i	−0.286569	−	0.496351i
$719$	13.8793	−	24.0396i	0.517609	−	0.896525i	−0.482182	−	0.876071i	$-0.660155\pi$
$719$	13.8793	−	24.0396i	0.517609	−	0.896525i	0.999791	−	0.0204540i	$-0.00651117\pi$
$720$	3.35666	+	0.881980i	0.125095	+	0.0328694i
$721$	16.0060	−	21.6862i	0.596095	−	0.807637i
$722$	18.9402			0.704882
$723$	38.2336	−	5.12794i	1.42192	−	0.190710i
$724$	0.371664	−	0.214580i	0.0138128	−	0.00797481i
$725$	11.1605	−	6.44355i	0.414492	−	0.239307i
$726$	4.79338	−	0.642895i	0.177899	−	0.0238601i
$727$			34.8578i			1.29281i	0.762996	+	0.646403i	$0.223727\pi$
$727$			34.8578i			1.29281i	−0.762996	+	0.646403i	$0.776273\pi$
$728$	9.32434	+	2.01414i	0.345583	+	0.0746491i
$729$	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
$732$	−18.9498	−	7.79545i	−0.700404	−	0.288128i
$733$	17.9806	−	31.1434i	0.664130	−	1.15031i	−0.315390	−	0.948962i	$-0.602135\pi$
$733$	17.9806	−	31.1434i	0.664130	−	1.15031i	0.979520	−	0.201345i	$-0.0645312\pi$
$734$			31.1878i			1.15116i
$735$	−12.7349	+	5.87865i	−0.469733	+	0.216837i
$736$		−	2.73122i		−	0.100674i
$737$	−23.1781	−	13.3819i	−0.853775	−	0.492927i
$738$	−0.372734	−	1.36454i	−0.0137205	−	0.0502295i
$739$	−23.0900	+	13.3310i	−0.849378	+	0.490389i	−0.860441	−	0.509550i	$-0.829812\pi$
$739$	−23.0900	+	13.3310i	−0.849378	+	0.490389i	0.0110630	+	0.999939i	$0.496478\pi$
$740$	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	$0.648869\pi$
$744$	−7.71207	+	1.03435i	−0.282738	+	0.0379212i
$745$	−9.46974	+	5.46736i	−0.346944	+	0.200308i
$746$	−2.30810	−	3.99775i	−0.0845057	−	0.146368i
$747$	−7.68968	+	7.76466i	−0.281351	+	0.284094i
$748$	−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	−0.879638	−	0.475644i	$-0.842215\pi$
$751$	−0.764556	+	1.32425i	−0.0278990	+	0.0483226i	0.851739	+	0.523967i	$0.175548\pi$
$752$	−0.203606	+	0.117552i	−0.00742475	+	0.00428668i
$753$	−13.5455	+	32.9273i	−0.493624	+	1.19994i
$754$	7.41553	−	10.2974i	0.270058	−	0.375008i
$755$	−17.3388			−0.631024
$756$	9.46558	−	9.97009i	0.344260	−	0.362609i
$757$	−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
$759$	−16.2475	−	6.68379i	−0.589746	−	0.242606i
$760$	−0.244969	+	0.141433i	−0.00888596	+	0.00513031i
$761$	−19.1290	−	11.0442i	−0.693427	−	0.400350i	0.111468	−	0.993768i	$-0.464445\pi$
$761$	−19.1290	−	11.0442i	−0.693427	−	0.400350i	−0.804895	+	0.593418i	$0.797778\pi$
$762$	9.34026	+	12.1115i	0.338362	+	0.438754i
$763$	2.93941	+	6.73768i	0.106414	+	0.243920i
$764$		−	1.81779i		−	0.0657652i
$765$	−0.0625269	+	0.0631366i	−0.00226066	+	0.00228271i
$766$	−1.24813	+	0.720607i	−0.0450967	+	0.0260366i
$767$	−4.79356	−	10.6458i	−0.173086	−	0.384399i
$768$	−1.71668	+	0.230243i	−0.0619453	+	0.00830819i
$769$	−33.5491			−1.20981			−0.604906	−	0.796297i	$-0.706789\pi$
$769$	−33.5491			−1.20981			−0.604906	+	0.796297i	$0.706789\pi$
$770$	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	0.416654	−	0.909065i	$-0.363203\pi$
$773$	39.2647	−	22.6695i	1.41225	−	0.815365i	0.995601	+	0.0936997i	$0.0298694\pi$
$774$	3.59029	−	0.980711i	0.129050	−	0.0352509i
$775$	8.22489	−	14.2459i	0.295447	−	0.511729i
$776$	−12.7955			−0.459330
$777$	−22.7523	−	37.5552i	−0.816233	−	1.34729i
$778$		−	8.18640i		−	0.293497i
$779$	0.0998437	+	0.0576448i	0.00357727	+	0.00206534i
$780$	−3.40512	+	6.37184i	−0.121923	+	0.228148i
$781$	−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
$786$	−24.2756	+	3.25588i	−0.865882	+	0.116133i
$787$	−16.3431	−	28.3071i	−0.582568	−	1.00904i	−0.995174	−	0.0981280i	$-0.968715\pi$
$787$	−16.3431	−	28.3071i	−0.582568	−	1.00904i	0.412606	−	0.910910i	$-0.364619\pi$
$788$	12.6222	+	21.8623i	0.449648	+	0.778813i
$789$	6.48281	+	48.3354i	0.230794	+	1.72079i
$790$		−	6.97048i		−	0.247999i
$791$	−48.9978	−	5.52200i	−1.74216	−	0.196340i
$792$	−2.83135	+	10.7756i	−0.100608	+	0.382894i
$793$	24.9264	−	34.6133i	0.885161	−	1.22915i
$794$	−6.43999	−	11.1544i	−0.228547	−	0.395854i
$795$	5.67366	−	13.7920i	0.201224	−	0.489151i
$796$	5.33963	+	3.08284i	0.189258	+	0.109268i
$797$	26.9293			0.953884			0.476942	−	0.878935i	$-0.341745\pi$
$797$	26.9293			0.953884			0.476942	+	0.878935i	$0.341745\pi$
$798$	0.0236408	+	1.12024i	0.000836876	+	0.0396560i
$799$		−	0.00601943i		−	0.000212952i
$800$	1.83083	−	3.17109i	0.0647297	−	0.112115i
$801$	−7.41112	−	27.1314i	−0.261859	−	0.958641i
$802$	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
$807$	−50.4091	+	6.76094i	−1.77448	+	0.237996i
$808$	−5.03494	−	8.72077i	−0.177129	−	0.306796i
$809$	4.33969	−	2.50552i	0.152575	−	0.0880894i	−0.421769	−	0.906703i	$-0.638591\pi$
$809$	4.33969	−	2.50552i	0.152575	−	0.0880894i	0.574344	+	0.818614i	$0.305257\pi$
$810$	5.29315	+	8.96593i	0.185982	+	0.315031i
$811$	40.9851			1.43918			0.719590	−	0.694399i	$-0.244330\pi$
$811$	40.9851			1.43918			0.719590	+	0.694399i	$0.244330\pi$
$812$	−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
$816$	0.0168711	−	0.0410116i	0.000590606	−	0.00143569i
$817$	−0.151671	+	0.262702i	−0.00530629	+	0.00919077i
$818$	−20.2052			−0.706459
$819$	15.6238	+	23.9770i	0.545939	+	0.837825i
$820$	0.545475			0.0190488
$821$	−1.96031	+	3.39536i	−0.0684154	+	0.118499i	−0.898204	−	0.439579i	$-0.855128\pi$
$821$	−1.96031	+	3.39536i	−0.0684154	+	0.118499i	0.829789	+	0.558078i	$0.188461\pi$
$822$	8.83908	−	21.4867i	0.308298	−	0.749435i
$823$	0.415511	+	0.719686i	0.0144838	+	0.0250867i	0.873176	−	0.487404i	$-0.162056\pi$
$823$	0.415511	+	0.719686i	0.0144838	+	0.0250867i	−0.858693	+	0.512491i	$0.828723\pi$
$824$	−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	$0.218851\pi$
$828$	5.76562	−	5.82185i	0.200369	−	0.202323i
$829$	36.1389	−	20.8648i	1.25515	−	0.724664i	0.283026	−	0.959112i	$-0.408662\pi$
$829$	36.1389	−	20.8648i	1.25515	−	0.724664i	0.972129	+	0.234448i	$0.0753284\pi$
$830$	−2.10704	−	3.64949i	−0.0731363	−	0.126676i
$831$	−47.4722	+	6.36704i	−1.64679	+	0.220870i
$832$	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
$837$	−18.6225	−	14.0754i	−0.643687	−	0.486516i
$838$	−1.08300	+	1.87581i	−0.0374117	+	0.0647989i
$839$		−	44.3088i		−	1.52971i	−0.644203	−	0.764855i	$-0.722811\pi$
$839$		−	44.3088i		−	1.52971i	0.644203	−	0.764855i	$-0.277189\pi$
$840$	2.74699	+	4.53422i	0.0947801	+	0.156445i
$841$	16.6134			0.572875
$842$	12.3556	+	7.13353i	0.425803	+	0.245838i
$843$	−8.14518	+	19.7999i	−0.280535	+	0.681946i
$844$	1.99089	+	3.44833i	0.0685294	+	0.118696i
$845$	−11.2606	−	9.96888i	−0.387375	−	0.342940i
$846$	−0.682157	−	0.179240i	−0.0234530	−	0.00616241i
$847$	5.94391	+	4.38704i	0.204235	+	0.150741i
$848$			7.44274i			0.255585i
$849$	−3.14796	−	23.4710i	−0.108038	−	0.805522i
$850$	0.0468753	+	0.0811904i	0.00160781	+	0.00278481i
$851$	−13.0851	−	22.6641i	−0.448552	−	0.776915i
$852$	25.1934	−	3.37898i	0.863113	−	0.115762i
$853$	−39.9111			−1.36653			−0.683264	−	0.730171i	$-0.739440\pi$
$853$	−39.9111			−1.36653			−0.683264	+	0.730171i	$0.739440\pi$
$854$	−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	0.990536	+	0.137250i	$0.0438265\pi$
$857$	17.9784	+	31.1395i	0.614131	+	1.06371i	−0.376406	+	0.926455i	$0.622840\pi$
$858$	−20.4550	−	10.9312i	−0.698322	−	0.373184i
$859$	14.9743	+	8.64539i	0.510915	+	0.294977i	0.733210	−	0.680003i	$-0.238021\pi$
$859$	14.9743	+	8.64539i	0.510915	+	0.294977i	−0.222295	+	0.974980i	$0.571355\pi$
$860$			1.43522i			0.0489405i
$861$	1.04065	−	1.89363i	0.0354652	−	0.0645348i
$862$	34.5475			1.17669
$863$	−24.7603	+	42.8861i	−0.842851	+	1.45986i	0.0446227	+	0.999004i	$0.485791\pi$
$863$	−24.7603	+	42.8861i	−0.842851	+	1.45986i	−0.887474	+	0.460858i	$0.847542\pi$
$864$	−4.14530	−	3.13313i	−0.141026	−	0.106591i
$865$	−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
$870$	6.98953	−	0.937446i	0.236967	−	0.0317824i
$871$	10.6682	+	23.6926i	0.361479	+	0.802795i
$872$	2.40616	−	1.38920i	0.0814830	−	0.0470442i
$873$	−27.2746	−	27.0112i	−0.923107	−	0.914192i
$874$			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	$-0.616230\pi$
$877$	−39.8181	−	22.9890i	−1.34456	−	0.776283i	−0.987473	+	0.157788i	$0.949564\pi$
$878$	15.5035	−	8.95097i	0.523219	−	0.302081i
$879$	6.73799	+	2.77183i	0.227267	+	0.0934917i
$880$	−3.72075	−	2.14818i	−0.125426	−	0.0724150i
$881$	3.09185			0.104167			0.0520835	−	0.998643i	$-0.483414\pi$
$881$	3.09185			0.104167			0.0520835	+	0.998643i	$0.483414\pi$
$882$	20.9813	−	0.885947i	0.706477	−	0.0298314i
$883$	−23.5637			−0.792981			−0.396490	−	0.918039i	$-0.629772\pi$
$883$	−23.5637			−0.792981			−0.396490	+	0.918039i	$0.629772\pi$
$884$	0.0749110	+	0.0539463i	0.00251953	+	0.00181441i
$885$	2.46846	−	6.00052i	0.0829763	−	0.201705i
$886$	14.3289	−	8.27278i	0.481388	−	0.277929i
$887$	0.0628493	−	0.108858i	0.00211027	−	0.00365510i	−0.864968	−	0.501826i	$-0.832662\pi$
$887$	0.0628493	−	0.108858i	0.00211027	−	0.00365510i	0.867079	+	0.498171i	$0.165995\pi$
$888$	−13.1422	+	10.1351i	−0.441022	+	0.340112i
$889$	−2.61644	+	23.2161i	−0.0877524	+	0.778644i
$890$	10.8458			0.363551
$891$	−28.7826	+	16.9922i	−0.964253	+	0.569259i
$892$	1.01738	+	1.76216i	0.0340645	+	0.0590015i
$893$	0.0497838	−	0.0287427i	0.00166595	−	0.000961838i
$894$	16.2261	−	2.17627i	0.542682	−	0.0727852i
$895$	−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
$900$	10.5968	−	2.89458i	0.353226	−	0.0964858i
$901$	−0.165029	−	0.0952793i	−0.00549790	−	0.00317421i
$902$			1.75110i			0.0583051i
$903$	4.98239	+	2.73808i	0.165804	+	0.0911175i
$904$			18.6367i			0.619846i
$905$	−0.248240	+	0.429965i	−0.00825179	+	0.0142925i
$906$	24.0075	+	9.87608i	0.797597	+	0.328111i
$907$	−7.59458	−	13.1542i	−0.252174	−	0.436778i	0.711950	−	0.702230i	$-0.247812\pi$
$907$	−7.59458	−	13.1542i	−0.252174	−	0.436778i	−0.964124	+	0.265452i	$0.914479\pi$
$908$	−15.6005	−	9.00694i	−0.517720	−	0.298906i
$909$	7.67715	−	29.2179i	0.254635	−	0.969095i
$910$	−10.5069	+	3.37558i	−0.348299	+	0.111899i
$911$			46.3110i			1.53435i	0.641437	+	0.767176i	$0.278339\pi$
$911$			46.3110i			1.53435i	−0.641437	+	0.767176i	$0.721661\pi$
$912$	0.419746	−	0.0562970i	0.0138992	−	0.00186418i
$913$	11.7157	−	6.76405i	0.387732	−	0.223857i
$914$	32.4759	−	18.7500i	1.07421	−	0.620194i
$915$	23.4944	−	3.15110i	0.776702	−	0.104172i
$916$	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	−0.846615	−	0.532206i	$-0.821363\pi$
$919$	1.13972	−	1.97406i	0.0375960	−	0.0651181i	0.884211	+	0.467087i	$0.154697\pi$
$920$	1.57983	+	2.73634i	0.0520854	+	0.0902146i
$921$	−13.9361	+	33.8770i	−0.459211	+	1.11628i
$922$	−7.19751	−	4.15548i	−0.237037	−	0.136854i
$923$	−5.30970	+	52.6468i	−0.174771	+	1.73289i
$924$	−14.5558	+	8.81843i	−0.478852	+	0.290105i
$925$		−	35.0856i		−	1.15361i
$926$	−24.9521	−	14.4061i	−0.819976	−	0.473414i
$927$	−8.05324	−	29.4821i	−0.264503	−	0.968321i
$928$	−3.04794	+	1.75973i	−0.100054	+	0.0577660i
$929$	14.3151	+	8.26482i	0.469663	+	0.271160i	0.716099	−	0.697999i	$-0.245926\pi$
$929$	14.3151	+	8.26482i	0.469663	+	0.271160i	−0.246436	+	0.969159i	$0.579259\pi$
$930$	7.12822	−	5.49720i	0.233743	−	0.180260i
$931$	−1.16423	+	1.25461i	−0.0381561	+	0.0411183i
$932$			19.7262i			0.646152i
$933$	−53.8195	+	7.21834i	−1.76197	+	0.236318i
$934$	−10.3800	−	17.9787i	−0.339644	−	0.588280i
$935$	0.0952634	−	0.0550003i	0.00311545	−	0.00179870i
$936$	8.34413	−	6.88299i	0.272736	−	0.224978i
$937$		−	22.3954i		−	0.731626i	−0.930688	−	0.365813i	$-0.880791\pi$
$937$		−	22.3954i		−	0.731626i	0.930688	−	0.365813i	$-0.119209\pi$
$938$	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	−0.280700	−	0.959796i	$-0.590567\pi$
$941$	12.5819	−	7.26415i	0.410158	−	0.236805i	0.690857	+	0.722991i	$0.257233\pi$
$942$	−2.78137	−	1.14418i	−0.0906220	−	0.0372795i
$943$	0.643902	−	1.11527i	0.0209683	−	0.0363182i
$944$			3.23814i			0.105392i
$945$	−3.71630	+	15.4640i	−0.120891	+	0.503043i
$946$	−4.60736			−0.149798
$947$	−1.30451	+	2.25948i	−0.0423910	+	0.0734233i	−0.886442	−	0.462839i	$-0.846831\pi$
$947$	−1.30451	+	2.25948i	−0.0423910	+	0.0734233i	0.844051	+	0.536262i	$0.180164\pi$
$948$	−3.97034	+	9.65142i	−0.128951	+	0.313464i
$949$	5.15677	−	2.32197i	0.167396	−	0.0753744i
$950$	−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	$-0.131000\pi$
$954$	−15.7116	+	15.8649i	−0.508683	+	0.513644i
$955$	1.05147	+	1.82119i	0.0340247	+	0.0589324i
$956$	10.0708	+	17.4432i	0.325714	+	0.564153i
$957$	3.00941	+	22.4379i	0.0972803	+	0.725316i
$958$			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
$962$	−14.1845	−	31.5017i	−0.457326	−	1.01566i
$963$	−14.3696	−	52.6056i	−0.463052	−	1.69519i
$964$	11.1359	−	19.2880i	0.358663	−	0.621223i
$965$	22.8996			0.737166
$966$	12.5133	−	0.264072i	0.402607	−	0.00849638i
$967$			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
$969$	−0.00412516	+	0.0100278i	−0.000132519	+	0.000322138i
$970$	12.8194	−	7.40130i	0.411607	−	0.237642i
$971$	13.4579	−	23.3098i	0.431885	−	0.748047i	−0.565151	−	0.824988i	$-0.691182\pi$
$971$	13.4579	−	23.3098i	0.431885	−	0.748047i	0.997036	+	0.0769409i	$0.0245153\pi$
$972$	−2.22202	−	15.4293i	−0.0712713	−	0.494894i
$973$	39.5853	+	4.46122i	1.26905	+	0.143020i
$974$		−	0.141904i		−	0.00454690i
$975$	0.750147	+	22.8548i	0.0240239	+	0.731939i
$976$	−10.2453	+	5.91511i	−0.327943	+	0.189338i
$977$	−24.1168	−	41.7715i	−0.771564	−	1.33639i	−0.936705	−	0.350119i	$-0.886141\pi$
$977$	−24.1168	−	41.7715i	−0.771564	−	1.33639i	0.165141	−	0.986270i	$-0.447192\pi$
$978$	2.92909	+	21.8391i	0.0936620	+	0.698337i
$979$			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	−0.297984	−	0.954571i	$-0.596314\pi$
$983$	11.9049	−	6.87329i	0.379707	−	0.219224i	0.677691	+	0.735347i	$0.262981\pi$
$984$	−0.755272	−	0.310699i	−0.0240772	−	0.00990473i
$985$	−25.2918	−	14.6022i	−0.805862	−	0.465265i
$986$		−	0.0901098i		−	0.00286968i
$987$	−0.558257	−	0.921467i	−0.0177695	−	0.0293306i
$988$	−0.0884646	+	0.877146i	−0.00281443	+	0.0279057i
$989$	2.93442	+	1.69419i	0.0933092	+	0.0538721i
$990$	−3.39630	−	12.4335i	−0.107942	−	0.395164i
$991$	13.4020	+	23.2129i	0.425729	+	0.737384i	0.996488	−	0.0837336i	$-0.0266845\pi$
$991$	13.4020	+	23.2129i	0.425729	+	0.737384i	−0.570760	+	0.821117i	$0.693351\pi$
$992$	−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
$996$	0.838700	+	6.25329i	0.0265752	+	0.198143i
$997$	10.4342	−	6.02421i	0.330455	−	0.190789i	−0.325588	−	0.945512i	$-0.605562\pi$
$997$	10.4342	−	6.02421i	0.330455	−	0.190789i	0.656043	+	0.754723i	$0.272229\pi$
$998$	−9.05469	+	5.22772i	−0.286621	+	0.165481i
$999$	−49.4089	−	6.13931i	−1.56323	−	0.194239i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.11	✓	36	21.17	even	6
546.2.bg.a.311.17	yes	36	91.38	odd	6
546.2.bg.a.467.11	yes	36	13.12	even	2
546.2.bg.a.467.17	yes	36	3.2	odd	2
546.2.bg.b.311.11	yes	36	273.38	even	6	inner
546.2.bg.b.311.17	yes	36	7.3	odd	6	inner
546.2.bg.b.467.11	yes	36	1.1	even	1	trivial
546.2.bg.b.467.17	yes	36	39.38	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.658943 - 1.60181i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00187 + 0.578432i) q^{5} +(-1.05774 - 1.37157i) q^{6} +(0.296298 - 2.62911i) q^{7} -1.00000 q^{8} +(-2.13159 - 2.11100i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.658943 - 1.60181i) 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} +(-2.13159 - 2.11100i) q^{9} +(1.00187 - 0.578432i) q^{10} +(1.85690 + 3.21624i) q^{11} +(-1.71668 + 0.230243i) 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} +(-2.89398 + 0.790508i) q^{18} +(0.122255 - 0.211752i) q^{19} -1.15686i q^{20} +(-4.01609 - 2.20705i) q^{21} +3.71379 q^{22} +(-2.36531 - 1.36561i) q^{23} +(-0.658943 + 1.60181i) q^{24} +(-1.83083 - 3.17109i) q^{25} +(-2.92584 - 2.10701i) q^{26} +(-4.78602 + 2.02337i) q^{27} +(-2.42502 + 1.05795i) q^{28} +3.51946i q^{29} +(-0.266360 - 1.98597i) q^{30} +(2.24622 + 3.89056i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.37539 - 0.855076i) 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} +(-5.50785 - 2.94340i) q^{39} +(-1.00187 - 0.578432i) q^{40} +0.471512i q^{41} +(-3.91940 + 2.37451i) q^{42} -1.24061 q^{43} +(1.85690 - 3.21624i) q^{44} +(-0.914511 - 3.34794i) 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} +(-0.0439526 + 0.00589498i) q^{51} +(-3.28764 + 1.48035i) q^{52} +(6.44560 - 3.72137i) q^{53} +(-0.640722 + 5.15650i) 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} +(-1.85308 - 0.762308i) q^{60} +(10.2453 + 5.91511i) q^{61} +4.49243 q^{62} +(-6.18164 + 4.97869i) q^{63} +1.00000 q^{64} +(2.43752 - 3.38480i) q^{65} +(2.44718 - 5.94879i) 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} +(2.13159 + 2.11100i) q^{72} +(0.784266 + 1.35839i) q^{73} +(8.29815 - 4.79094i) q^{74} +(-6.28590 + 0.843074i) 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} +(0.0873358 + 8.99958i) q^{81} +(0.408341 + 0.235756i) q^{82} -3.64267i q^{83} +(0.0966863 + 4.58156i) q^{84} -0.0296195i q^{85} +(-0.620304 + 1.07440i) q^{86} +(5.63751 + 2.31913i) q^{87} +(-1.85690 - 3.21624i) q^{88} +(8.11911 + 4.68757i) q^{89} +(-3.35666 - 0.881980i) q^{90} +(-9.32434 - 2.01414i) q^{91} +2.73122i q^{92} +(7.71207 - 1.03435i) q^{93} +(0.203606 - 0.117552i) q^{94} +(0.244969 - 0.141433i) q^{95} +(1.71668 - 0.230243i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more