LMFDB - Embedded newform 546.2.bn.e.101.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.16
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.e.173.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26448 + 0.730045i) q^{5} +(-1.13542 + 1.30799i) q^{6} +(-2.63261 + 0.263392i) q^{7} +1.00000 q^{8} +(2.78311 + 1.11994i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26448 + 0.730045i) q^{5} +(-1.13542 + 1.30799i) q^{6} +(-2.63261 + 0.263392i) q^{7} +1.00000 q^{8} +(2.78311 + 1.11994i) q^{9} -1.46009i q^{10} +3.51948 q^{11} +(-0.565041 - 1.63729i) q^{12} +(-0.214878 + 3.59914i) q^{13} +(1.08820 - 2.41160i) q^{14} +(-2.39060 + 0.825011i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.79359 + 6.57069i) q^{17} +(-2.36146 + 1.85028i) q^{18} -3.45362 q^{19} +(1.26448 + 0.730045i) q^{20} +(-4.56338 - 0.419048i) q^{21} +(-1.75974 + 3.04796i) q^{22} +(-3.12372 - 1.80348i) q^{23} +(1.70046 + 0.329307i) q^{24} +(-1.43407 + 2.48388i) q^{25} +(-3.00951 - 1.98566i) q^{26} +(4.36376 + 2.82092i) q^{27} +(1.54441 + 2.14821i) q^{28} +(0.170773 - 0.0985961i) q^{29} +(0.480817 - 2.48282i) q^{30} +(-5.34484 + 9.25753i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.98472 + 1.15899i) q^{33} -7.58718 q^{34} +(3.13658 - 2.25498i) q^{35} +(-0.421657 - 2.97022i) q^{36} +(-4.81918 - 2.78236i) q^{37} +(1.72681 - 2.99093i) q^{38} +(-1.55061 + 6.04943i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(2.60543 - 1.50425i) q^{41} +(2.64459 - 3.74248i) q^{42} +(5.61139 - 9.71922i) q^{43} +(-1.75974 - 3.04796i) q^{44} +(-4.33679 + 0.615658i) q^{45} +(3.12372 - 1.80348i) q^{46} +(11.0787 - 6.39629i) q^{47} +(-1.13542 + 1.30799i) q^{48} +(6.86125 - 1.38682i) q^{49} +(-1.43407 - 2.48388i) q^{50} +(4.28707 + 12.4224i) q^{51} +(3.22439 - 1.61348i) q^{52} +(4.21555 + 2.43385i) q^{53} +(-4.62487 + 2.36867i) q^{54} +(-4.45029 + 2.56938i) q^{55} +(-2.63261 + 0.263392i) q^{56} +(-5.87274 - 1.13730i) q^{57} +0.197192i q^{58} +(-1.13289 + 0.654074i) q^{59} +(1.90978 + 1.65781i) q^{60} -0.999644i q^{61} +(-5.34484 - 9.25753i) q^{62} +(-7.62183 - 2.21532i) q^{63} +1.00000 q^{64} +(-2.35583 - 4.70790i) q^{65} +(-3.99607 + 4.60343i) q^{66} -5.52864i q^{67} +(3.79359 - 6.57069i) q^{68} +(-4.71786 - 4.09541i) q^{69} +(0.384576 + 3.84385i) q^{70} +(-5.33718 + 9.24427i) q^{71} +(2.78311 + 1.11994i) q^{72} +(2.94410 - 5.09933i) q^{73} +(4.81918 - 2.78236i) q^{74} +(-3.25653 + 3.75148i) q^{75} +(1.72681 + 2.99093i) q^{76} +(-9.26540 + 0.927001i) q^{77} +(-4.46365 - 4.36759i) q^{78} +(0.174645 + 0.302494i) q^{79} -1.46009i q^{80} +(6.49145 + 6.23386i) q^{81} +3.00849i q^{82} +3.72979i q^{83} +(1.91878 + 4.16152i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(5.61139 + 9.71922i) q^{86} +(0.322861 - 0.111422i) q^{87} +3.51948 q^{88} +(-12.5228 - 7.23003i) q^{89} +(1.63522 - 4.06360i) q^{90} +(-0.382294 - 9.53173i) q^{91} +3.60696i q^{92} +(-12.1372 + 13.9819i) q^{93} +12.7926i q^{94} +(4.36702 - 2.52130i) q^{95} +(-0.565041 - 1.63729i) q^{96} +(1.72747 - 2.99206i) q^{97} +(-2.22961 + 6.63542i) q^{98} +(9.79510 + 3.94162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.70046	+	0.329307i	0.981760	+	0.190125i
$3$	1.70046	+	0.329307i	0.981760	+	0.190125i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.26448	+	0.730045i	−0.565491	+	0.326486i	−0.755346	−	0.655326i	$-0.772531\pi$
$5$	−1.26448	+	0.730045i	−0.565491	+	0.326486i	0.189856	+	0.981812i	$0.439198\pi$
$6$	−1.13542	+	1.30799i	−0.463532	+	0.533983i
$7$	−2.63261	+	0.263392i	−0.995032	+	0.0995528i
$7$	−2.63261	+	0.263392i	−0.995032	+	0.0995528i
$8$	1.00000			0.353553
$9$	2.78311	+	1.11994i	0.927705	+	0.373315i
$10$		−	1.46009i		−	0.461721i
$11$	3.51948			1.06116			0.530581	−	0.847634i	$-0.321974\pi$
$11$	3.51948			1.06116			0.530581	+	0.847634i	$0.321974\pi$
$12$	−0.565041	−	1.63729i	−0.163113	−	0.472646i
$13$	−0.214878	+	3.59914i	−0.0595966	+	0.998223i
$13$	−0.214878	+	3.59914i	−0.0595966	+	0.998223i
$14$	1.08820	−	2.41160i	0.290834	−	0.644528i
$15$	−2.39060	+	0.825011i	−0.617249	+	0.213017i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.79359	+	6.57069i	0.920080	+	1.59363i	0.799288	+	0.600948i	$0.205210\pi$
$17$	3.79359	+	6.57069i	0.920080	+	1.59363i	0.120793	+	0.992678i	$0.461456\pi$
$18$	−2.36146	+	1.85028i	−0.556601	+	0.436114i
$19$	−3.45362			−0.792316			−0.396158	−	0.918182i	$-0.629657\pi$
$19$	−3.45362			−0.792316			−0.396158	+	0.918182i	$0.629657\pi$
$20$	1.26448	+	0.730045i	0.282745	+	0.163243i
$21$	−4.56338	−	0.419048i	−0.995810	−	0.0914439i
$22$	−1.75974	+	3.04796i	−0.375177	+	0.649826i
$23$	−3.12372	−	1.80348i	−0.651341	−	0.376052i	0.137629	−	0.990484i	$-0.456052\pi$
$23$	−3.12372	−	1.80348i	−0.651341	−	0.376052i	−0.788970	+	0.614432i	$0.789385\pi$
$24$	1.70046	+	0.329307i	0.347105	+	0.0672194i
$25$	−1.43407	+	2.48388i	−0.286814	+	0.496776i
$26$	−3.00951	−	1.98566i	−0.590213	−	0.389420i
$27$	4.36376	+	2.82092i	0.839807	+	0.542885i
$28$	1.54441	+	2.14821i	0.291866	+	0.405973i
$29$	0.170773	−	0.0985961i	0.0317118	−	0.0183088i	−0.484060	−	0.875035i	$-0.660838\pi$
$29$	0.170773	−	0.0985961i	0.0317118	−	0.0183088i	0.515772	+	0.856726i	$0.327505\pi$
$30$	0.480817	−	2.48282i	0.0877849	−	0.453299i
$31$	−5.34484	+	9.25753i	−0.959961	+	1.66270i	−0.237377	+	0.971418i	$0.576288\pi$
$31$	−5.34484	+	9.25753i	−0.959961	+	1.66270i	−0.722584	+	0.691283i	$0.757046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.98472	+	1.15899i	1.04181	+	0.201754i
$34$	−7.58718			−1.30119
$35$	3.13658	−	2.25498i	0.530179	−	0.381160i
$36$	−0.421657	−	2.97022i	−0.0702762	−	0.495037i
$37$	−4.81918	−	2.78236i	−0.792269	−	0.457417i	0.0484917	−	0.998824i	$-0.484559\pi$
$37$	−4.81918	−	2.78236i	−0.792269	−	0.457417i	−0.840761	+	0.541407i	$0.817892\pi$
$38$	1.72681	−	2.99093i	0.280126	−	0.485192i
$39$	−1.55061	+	6.04943i	−0.248297	+	0.968684i
$40$	−1.26448	+	0.730045i	−0.199931	+	0.115430i
$41$	2.60543	−	1.50425i	0.406900	−	0.234924i	−0.282557	−	0.959250i	$-0.591183\pi$
$41$	2.60543	−	1.50425i	0.406900	−	0.234924i	0.689457	+	0.724327i	$0.257849\pi$
$42$	2.64459	−	3.74248i	0.408070	−	0.577476i
$43$	5.61139	−	9.71922i	0.855730	−	1.48217i	−0.0202369	−	0.999795i	$-0.506442\pi$
$43$	5.61139	−	9.71922i	0.855730	−	1.48217i	0.875967	−	0.482372i	$-0.160225\pi$
$44$	−1.75974	−	3.04796i	−0.265291	−	0.459497i
$45$	−4.33679	+	0.615658i	−0.646490	+	0.0917768i
$46$	3.12372	−	1.80348i	0.460568	−	0.265909i
$47$	11.0787	−	6.39629i	1.61599	−	0.932994i	0.628051	−	0.778172i	$-0.283853\pi$
$47$	11.0787	−	6.39629i	1.61599	−	0.932994i	0.987942	−	0.154822i	$-0.0494803\pi$
$48$	−1.13542	+	1.30799i	−0.163883	+	0.188792i
$49$	6.86125	−	1.38682i	0.980178	−	0.198116i
$50$	−1.43407	−	2.48388i	−0.202808	−	0.351273i
$51$	4.28707	+	12.4224i	0.600309	+	1.73949i
$52$	3.22439	−	1.61348i	0.447142	−	0.223750i
$53$	4.21555	+	2.43385i	0.579051	+	0.334315i	0.760756	−	0.649038i	$-0.224828\pi$
$53$	4.21555	+	2.43385i	0.579051	+	0.334315i	−0.181705	+	0.983353i	$0.558162\pi$
$54$	−4.62487	+	2.36867i	−0.629365	+	0.322335i
$55$	−4.45029	+	2.56938i	−0.600077	+	0.346455i
$56$	−2.63261	+	0.263392i	−0.351797	+	0.0351972i
$57$	−5.87274	−	1.13730i	−0.777864	−	0.150639i
$58$			0.197192i			0.0258926i
$59$	−1.13289	+	0.654074i	−0.147490	+	0.0851532i	−0.571929	−	0.820303i	$-0.693805\pi$
$59$	−1.13289	+	0.654074i	−0.147490	+	0.0851532i	0.424439	+	0.905456i	$0.360471\pi$
$60$	1.90978	+	1.65781i	0.246551	+	0.214023i
$61$		−	0.999644i		−	0.127991i	−0.997950	−	0.0639956i	$-0.979616\pi$
$61$		−	0.999644i		−	0.127991i	0.997950	−	0.0639956i	$-0.0203844\pi$
$62$	−5.34484	−	9.25753i	−0.678795	−	1.17571i
$63$	−7.62183	−	2.21532i	−0.960261	−	0.279105i
$64$	1.00000			0.125000
$65$	−2.35583	−	4.70790i	−0.292205	−	0.583943i
$66$	−3.99607	+	4.60343i	−0.491883	+	0.566643i
$67$		−	5.52864i		−	0.675431i	−0.941248	−	0.337715i	$-0.890346\pi$
$67$		−	5.52864i		−	0.675431i	0.941248	−	0.337715i	$-0.109654\pi$
$68$	3.79359	−	6.57069i	0.460040	−	0.796813i
$69$	−4.71786	−	4.09541i	−0.567964	−	0.493029i
$70$	0.384576	+	3.84385i	0.0459656	+	0.459427i
$71$	−5.33718	+	9.24427i	−0.633407	+	1.09709i	0.353443	+	0.935456i	$0.385011\pi$
$71$	−5.33718	+	9.24427i	−0.633407	+	1.09709i	−0.986850	+	0.161637i	$0.948323\pi$
$72$	2.78311	+	1.11994i	0.327993	+	0.131987i
$73$	2.94410	−	5.09933i	0.344581	−	0.596832i	−0.640697	−	0.767794i	$-0.721354\pi$
$73$	2.94410	−	5.09933i	0.344581	−	0.596832i	0.985278	+	0.170963i	$0.0546877\pi$
$74$	4.81918	−	2.78236i	0.560219	−	0.323442i
$75$	−3.25653	+	3.75148i	−0.376032	+	0.433184i
$76$	1.72681	+	2.99093i	0.198079	+	0.343083i
$77$	−9.26540	+	0.927001i	−1.05589	+	0.105642i
$78$	−4.46365	−	4.36759i	−0.505409	−	0.494532i
$79$	0.174645	+	0.302494i	0.0196491	+	0.0340332i	0.875683	−	0.482887i	$-0.160412\pi$
$79$	0.174645	+	0.302494i	0.0196491	+	0.0340332i	−0.856034	+	0.516920i	$0.827078\pi$
$80$		−	1.46009i		−	0.163243i
$81$	6.49145	+	6.23386i	0.721272	+	0.692652i
$82$			3.00849i			0.332232i
$83$			3.72979i			0.409398i	0.978825	+	0.204699i	$0.0656215\pi$
$83$			3.72979i			0.409398i	−0.978825	+	0.204699i	$0.934379\pi$
$84$	1.91878	+	4.16152i	0.209356	+	0.454059i
$85$	−9.59380	−	5.53898i	−1.04059	−	0.600787i
$86$	5.61139	+	9.71922i	0.605092	+	1.04805i
$87$	0.322861	−	0.111422i	0.0346144	−	0.0119457i
$88$	3.51948			0.375177
$89$	−12.5228	−	7.23003i	−1.32741	−	0.766382i	−0.342513	−	0.939513i	$-0.611278\pi$
$89$	−12.5228	−	7.23003i	−1.32741	−	0.766382i	−0.984899	+	0.173131i	$0.944612\pi$
$90$	1.63522	−	4.06360i	0.172367	−	0.428341i
$91$	−0.382294	−	9.53173i	−0.0400753	−	0.999197i
$92$			3.60696i			0.376052i
$93$	−12.1372	+	13.9819i	−1.25857	+	1.44986i
$94$			12.7926i			1.31945i
$95$	4.36702	−	2.52130i	0.448047	−	0.258680i
$96$	−0.565041	−	1.63729i	−0.0576693	−	0.167106i
$97$	1.72747	−	2.99206i	0.175398	−	0.303798i	−0.764901	−	0.644148i	$-0.777212\pi$
$97$	1.72747	−	2.99206i	0.175398	−	0.303798i	0.940299	+	0.340350i	$0.110545\pi$
$98$	−2.22961	+	6.63542i	−0.225224	+	0.670279i
$99$	9.79510	+	3.94162i	0.984445	+	0.396147i
$100$	2.86814			0.286814
$101$	11.6172			1.15596			0.577979	−	0.816052i	$-0.303842\pi$
$101$	11.6172			1.15596			0.577979	+	0.816052i	$0.303842\pi$
$102$	−12.9017	−	2.49851i	−1.27746	−	0.247389i
$103$	16.2249	−	9.36744i	1.59869	−	0.923001i	0.606944	−	0.794745i	$-0.292395\pi$
$103$	16.2249	−	9.36744i	1.59869	−	0.923001i	0.991741	−	0.128257i	$-0.0409381\pi$
$104$	−0.214878	+	3.59914i	−0.0210706	+	0.352925i
$105$	6.07620	−	2.80159i	0.592977	−	0.273408i
$106$	−4.21555	+	2.43385i	−0.409451	+	0.236397i
$107$	−0.303807	−	0.175403i	−0.0293701	−	0.0169568i	0.485243	−	0.874379i	$-0.338731\pi$
$107$	−0.303807	−	0.175403i	−0.0293701	−	0.0169568i	−0.514613	+	0.857422i	$0.672064\pi$
$108$	0.261103	−	5.18959i	0.0251246	−	0.499368i
$109$	8.12542	+	4.69121i	0.778274	+	0.449337i	0.835818	−	0.549006i	$-0.184994\pi$
$109$	8.12542	+	4.69121i	0.778274	+	0.449337i	−0.0575444	+	0.998343i	$0.518327\pi$
$110$		−	5.13875i		−	0.489961i
$111$	−7.27857	−	6.31827i	−0.690851	−	0.599704i
$112$	1.08820	−	2.41160i	0.102825	−	0.227875i
$113$	5.03517	+	2.90706i	0.473669	+	0.273473i	0.717774	−	0.696276i	$-0.245161\pi$
$113$	5.03517	+	2.90706i	0.473669	+	0.273473i	−0.244105	+	0.969749i	$0.578494\pi$
$114$	3.92130	−	4.51729i	0.367264	−	0.423083i
$115$	5.26649			0.491103
$116$	−0.170773	−	0.0985961i	−0.0158559	−	0.00915442i
$117$	−4.62887	+	9.77617i	−0.427939	+	0.903808i
$118$		−	1.30815i		−	0.120425i
$119$	−11.7177	−	16.2988i	−1.07416	−	1.49411i
$120$	−2.39060	+	0.825011i	−0.218231	+	0.0753129i
$121$	1.38671			0.126065
$122$	0.865717	+	0.499822i	0.0783783	+	0.0452518i
$123$	4.92578	−	1.69992i	0.444143	−	0.153277i
$124$	10.6897			0.959961
$125$		−	11.4882i		−	1.02754i
$126$	5.72944	−	5.49304i	0.510419	−	0.489359i
$127$	−7.87940	−	13.6475i	−0.699183	−	1.21102i	−0.968750	−	0.248039i	$-0.920214\pi$
$127$	−7.87940	−	13.6475i	−0.699183	−	1.21102i	0.269567	−	0.962982i	$-0.413120\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	12.7425	−	14.6793i	1.12192	−	1.29244i
$130$	5.25507	+	0.313742i	0.460901	+	0.0275170i
$131$	6.32520	+	10.9556i	0.552635	+	0.957192i	0.998083	+	0.0618843i	$0.0197110\pi$
$131$	6.32520	+	10.9556i	0.552635	+	0.957192i	−0.445448	+	0.895308i	$0.646956\pi$
$132$	−1.98865	−	5.76241i	−0.173090	−	0.501554i
$133$	9.09204	−	0.909656i	0.788380	−	0.0788772i
$134$	4.78794	+	2.76432i	0.413615	+	0.238801i
$135$	−7.57727	−	0.381234i	−0.652147	−	0.0328114i
$136$	3.79359	+	6.57069i	0.325298	+	0.563432i
$137$	0.625790	+	1.08390i	0.0534648	+	0.0926038i	0.891519	−	0.452983i	$-0.149640\pi$
$137$	0.625790	+	1.08390i	0.0534648	+	0.0926038i	−0.838054	+	0.545587i	$0.816307\pi$
$138$	5.90566	−	2.03808i	0.502723	−	0.173493i
$139$	−8.68419	−	5.01382i	−0.736583	−	0.425267i	0.0842424	−	0.996445i	$-0.473153\pi$
$139$	−8.68419	−	5.01382i	−0.736583	−	0.425267i	−0.820826	+	0.571179i	$0.806486\pi$
$140$	−3.52116	−	1.58887i	−0.297592	−	0.134284i
$141$	20.9452	−	7.22833i	1.76390	−	0.608735i
$142$	−5.33718	−	9.24427i	−0.447886	−	0.775762i
$143$	−0.756260	+	12.6671i	−0.0632416	+	1.05928i
$144$	−2.36146	+	1.85028i	−0.196788	+	0.154190i
$145$	−0.143959	+	0.249345i	−0.0119552	+	0.0207069i
$146$	2.94410	+	5.09933i	0.243655	+	0.422024i
$147$	12.1240	−	0.0987658i	0.999967	−	0.00814606i
$148$			5.56471i			0.457417i
$149$	−3.24622			−0.265941			−0.132970	−	0.991120i	$-0.542451\pi$
$149$	−3.24622			−0.265941			−0.132970	+	0.991120i	$0.542451\pi$
$150$	−1.62061	−	4.69598i	−0.132323	−	0.383425i
$151$	8.04225	+	4.64320i	0.654469	+	0.377858i	0.790166	−	0.612892i	$-0.209994\pi$
$151$	8.04225	+	4.64320i	0.654469	+	0.377858i	−0.135697	+	0.990750i	$0.543327\pi$
$152$	−3.45362			−0.280126
$153$	3.19919	+	22.5356i	0.258639	+	1.82189i
$154$	3.82989	−	8.48757i	0.308622	−	0.683948i
$155$		−	15.6079i		−	1.25366i
$156$	6.01427	−	1.68184i	0.481527	−	0.134655i
$157$	−16.2305	−	9.37071i	−1.29534	−	0.747864i	−0.315743	−	0.948845i	$-0.602254\pi$
$157$	−16.2305	−	9.37071i	−1.29534	−	0.747864i	−0.979595	+	0.200981i	$0.935587\pi$
$158$	−0.349290			−0.0277880
$159$	6.36689	+	5.52687i	0.504927	+	0.438309i
$160$	1.26448	+	0.730045i	0.0999656	+	0.0577151i
$161$	8.69856	+	3.92510i	0.685542	+	0.309341i
$162$	−8.64441	+	2.50483i	−0.679169	+	0.196798i
$163$			0.909388i			0.0712288i	0.999366	+	0.0356144i	$0.0113388\pi$
$163$			0.909388i			0.0712288i	−0.999366	+	0.0356144i	$0.988661\pi$
$164$	−2.60543	−	1.50425i	−0.203450	−	0.117462i
$165$	−8.41365	+	2.90361i	−0.655002	+	0.226046i
$166$	−3.23009	−	1.86490i	−0.250704	−	0.144744i
$167$	11.6602	−	6.73204i	0.902297	−	0.520941i	0.0243520	−	0.999703i	$-0.492248\pi$
$167$	11.6602	−	6.73204i	0.902297	−	0.520941i	0.877945	+	0.478762i	$0.158914\pi$
$168$	−4.56338	−	0.419048i	−0.352072	−	0.0323303i
$169$	−12.9077	−	1.54676i	−0.992896	−	0.118981i
$170$	9.59380	−	5.53898i	0.735811	−	0.424821i
$171$	−9.61183	−	3.86787i	−0.735035	−	0.295783i
$172$	−11.2228			−0.855730
$173$	10.1687			0.773111			0.386556	−	0.922266i	$-0.373665\pi$
$173$	10.1687			0.773111			0.386556	+	0.922266i	$0.373665\pi$
$174$	−0.0649367	+	0.335317i	−0.00492284	+	0.0254203i
$175$	3.12110	−	6.91680i	0.235933	−	0.522861i
$176$	−1.75974	+	3.04796i	−0.132645	+	0.229748i
$177$	−2.14182	+	0.739157i	−0.160989	+	0.0555585i
$178$	12.5228	−	7.23003i	0.938622	−	0.541914i
$179$		−	8.54026i		−	0.638329i	−0.947699	−	0.319164i	$-0.896598\pi$
$179$		−	8.54026i		−	0.638329i	0.947699	−	0.319164i	$-0.103402\pi$
$180$	2.70157	+	3.44794i	0.201363	+	0.256994i
$181$			25.4759i			1.89361i	0.321810	+	0.946804i	$0.395709\pi$
$181$			25.4759i			1.89361i	−0.321810	+	0.946804i	$0.604291\pi$
$182$	8.44587	+	4.43479i	0.626049	+	0.328728i
$183$	0.329189	−	1.69985i	0.0243344	−	0.125657i
$184$	−3.12372	−	1.80348i	−0.230284	−	0.132954i
$185$	8.12499			0.597361
$186$	−6.04010	−	17.5021i	−0.442882	−	1.28332i
$187$	13.3514	+	23.1254i	0.976354	+	1.69110i
$188$	−11.0787	−	6.39629i	−0.807997	−	0.466497i
$189$	−12.2311	−	6.27699i	−0.889681	−	0.456583i
$190$			5.04260i			0.365829i
$191$		−	20.7254i		−	1.49964i	−0.661642	−	0.749819i	$-0.730140\pi$
$191$		−	20.7254i		−	1.49964i	0.661642	−	0.749819i	$-0.269860\pi$
$192$	1.70046	+	0.329307i	0.122720	+	0.0237657i
$193$			9.48648i			0.682852i	0.939909	+	0.341426i	$0.110910\pi$
$193$			9.48648i			0.682852i	−0.939909	+	0.341426i	$0.889090\pi$
$194$	1.72747	+	2.99206i	0.124025	+	0.214818i
$195$	−2.45565	−	8.78137i	−0.175852	−	0.628847i
$196$	−4.63164	−	5.24861i	−0.330832	−	0.374901i
$197$	−3.21420	−	5.56716i	−0.229002	−	0.396644i	0.728510	−	0.685035i	$-0.240213\pi$
$197$	−3.21420	−	5.56716i	−0.229002	−	0.396644i	−0.957513	+	0.288391i	$0.906880\pi$
$198$	−8.31109	+	6.51200i	−0.590644	+	0.462788i
$199$	1.09564	−	0.632567i	0.0776678	−	0.0448415i	−0.460663	−	0.887575i	$-0.652388\pi$
$199$	1.09564	−	0.632567i	0.0776678	−	0.0448415i	0.538331	+	0.842734i	$0.319055\pi$
$200$	−1.43407	+	2.48388i	−0.101404	+	0.175637i
$201$	1.82062	−	9.40122i	0.128416	−	0.663111i
$202$	−5.80861	+	10.0608i	−0.408693	+	0.707876i
$203$	−0.423610	+	0.304545i	−0.0297316	+	0.0213749i
$204$	8.61461	−	9.92393i	0.603143	−	0.694814i
$205$	−2.19633	+	3.80416i	−0.153399	+	0.265694i
$206$			18.7349i			1.30532i
$207$	−6.67388	−	8.51769i	−0.463867	−	0.592020i
$208$	−3.00951	−	1.98566i	−0.208672	−	0.137681i
$209$	−12.1549			−0.840775
$210$	−0.611849	+	6.66294i	−0.0422216	+	0.459787i
$211$	−6.24577	−	10.8180i	−0.429977	−	0.744742i	0.566894	−	0.823791i	$-0.308145\pi$
$211$	−6.24577	−	10.8180i	−0.429977	−	0.744742i	−0.996871	+	0.0790492i	$0.974812\pi$
$212$		−	4.86770i		−	0.334315i
$213$	−12.1199	+	13.9619i	−0.830438	+	0.956655i
$214$	0.303807	−	0.175403i	0.0207678	−	0.0119903i
$215$			16.3863i			1.11754i
$216$	4.36376	+	2.82092i	0.296917	+	0.191939i
$217$	11.6325	−	25.7792i	0.789666	−	1.75001i
$218$	−8.12542	+	4.69121i	−0.550323	+	0.317729i
$219$	6.68556	−	7.70169i	0.451768	−	0.520432i
$220$	4.45029	+	2.56938i	0.300039	+	0.173227i
$221$	−24.4640	+	12.2418i	−1.64563	+	0.823470i
$222$	9.11107	−	3.14429i	0.611495	−	0.211031i
$223$	3.78556	+	6.55677i	0.253500	+	0.439074i	0.964487	−	0.264131i	$-0.0850850\pi$
$223$	3.78556	+	6.55677i	0.253500	+	0.439074i	−0.710987	+	0.703205i	$0.751752\pi$
$224$	1.54441	+	2.14821i	0.103190	+	0.143533i
$225$	−6.77298	+	5.30684i	−0.451532	+	0.353789i
$226$	−5.03517	+	2.90706i	−0.334935	+	0.193375i
$227$	22.0466	−	12.7286i	1.46328	−	0.844826i	0.464120	−	0.885773i	$-0.346371\pi$
$227$	22.0466	−	12.7286i	1.46328	−	0.844826i	0.999161	+	0.0409469i	$0.0130374\pi$
$228$	1.95144	+	5.65459i	0.129237	+	0.374485i
$229$	−5.51406	−	9.55063i	−0.364379	−	0.631124i	0.624297	−	0.781187i	$-0.285386\pi$
$229$	−5.51406	−	9.55063i	−0.364379	−	0.631124i	−0.988676	+	0.150063i	$0.952052\pi$
$230$	−2.63325	+	4.56092i	−0.173631	+	0.300738i
$231$	−16.0607	−	1.47483i	−1.05672	−	0.0970368i
$232$	0.170773	−	0.0985961i	0.0112118	−	0.00647315i
$233$	−6.18721	+	3.57219i	−0.405338	+	0.234022i	−0.688785	−	0.724966i	$-0.741855\pi$
$233$	−6.18721	+	3.57219i	−0.405338	+	0.234022i	0.283447	+	0.958988i	$0.408522\pi$
$234$	−6.15198	−	8.89681i	−0.402167	−	0.581602i
$235$	−9.33916	+	16.1759i	−0.609219	+	1.05520i
$236$	1.13289	+	0.654074i	0.0737448	+	0.0425766i
$237$	0.197363	+	0.571890i	0.0128201	+	0.0371482i
$238$	19.9741	−	1.99840i	1.29473	−	0.129537i
$239$	−7.32463			−0.473791			−0.236896	−	0.971535i	$-0.576130\pi$
$239$	−7.32463			−0.473791			−0.236896	+	0.971535i	$0.576130\pi$
$240$	0.480817	−	2.48282i	0.0310366	−	0.160266i
$241$	8.71341	+	15.0921i	0.561280	+	0.972165i	0.997385	+	0.0722695i	$0.0230242\pi$
$241$	8.71341	+	15.0921i	0.561280	+	0.972165i	−0.436105	+	0.899896i	$0.643643\pi$
$242$	−0.693357	+	1.20093i	−0.0445707	+	0.0771986i
$243$	8.98559	+	12.7381i	0.576426	+	0.817150i
$244$	−0.865717	+	0.499822i	−0.0554219	+	0.0319978i
$245$	−7.66344	+	6.76262i	−0.489600	+	0.432048i
$246$	−0.990716	+	5.11581i	−0.0631657	+	0.326172i
$247$	0.742109	−	12.4301i	0.0472193	−	0.790907i
$248$	−5.34484	+	9.25753i	−0.339397	+	0.587854i
$249$	−1.22824	+	6.34235i	−0.0778368	+	0.401930i
$250$	9.94906	+	5.74410i	0.629234	+	0.363288i
$251$	−6.39321	+	11.0734i	−0.403536	+	0.698944i	−0.994150	−	0.108010i	$-0.965552\pi$
$251$	−6.39321	+	11.0734i	−0.403536	+	0.698944i	0.590614	+	0.806954i	$0.298886\pi$
$252$	1.89239	+	7.70836i	0.119209	+	0.485581i
$253$	−10.9939	−	6.34731i	−0.691178	−	0.399052i
$254$	15.7588			0.988795
$255$	−14.4898	−	12.5781i	−0.907388	−	0.787672i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.6730	+	18.4862i	−0.665764	+	1.15314i	0.313314	+	0.949650i	$0.398561\pi$
$257$	−10.6730	+	18.4862i	−0.665764	+	1.15314i	−0.979078	+	0.203487i	$0.934772\pi$
$258$	6.34134	+	18.3750i	0.394794	+	1.14398i
$259$	13.4199	+	6.05552i	0.833870	+	0.376272i
$260$	−2.89925	+	4.39416i	−0.179804	+	0.272514i
$261$	0.585704	−	0.0831475i	0.0362542	−	0.00514670i
$262$	−12.6504			−0.781544
$263$		−	15.9137i		−	0.981283i	−0.871362	−	0.490641i	$-0.836763\pi$
$263$		−	15.9137i		−	0.981283i	0.871362	−	0.490641i	$-0.163237\pi$
$264$	5.98472	+	1.15899i	0.368334	+	0.0713307i
$265$	−7.10729			−0.436597
$266$	−3.75823	+	8.32876i	−0.230432	+	0.510669i
$267$	−18.9136	−	16.4182i	−1.15749	−	1.00478i
$268$	−4.78794	+	2.76432i	−0.292470	+	0.168858i
$269$	−7.74959	−	13.4227i	−0.472501	−	0.818396i	0.527004	−	0.849863i	$-0.323315\pi$
$269$	−7.74959	−	13.4227i	−0.472501	−	0.818396i	−0.999505	+	0.0314670i	$0.989982\pi$
$270$	4.11879	−	6.37149i	0.250662	−	0.387757i
$271$	7.49829	−	12.9874i	0.455489	−	0.788930i	−0.543227	−	0.839586i	$-0.682798\pi$
$271$	7.49829	−	12.9874i	0.455489	−	0.788930i	0.998716	+	0.0506559i	$0.0161312\pi$
$272$	−7.58718			−0.460040
$273$	2.48879	−	16.3342i	0.150628	−	0.988590i
$274$	−1.25158			−0.0756107
$275$	−5.04717	+	8.74195i	−0.304356	+	0.527159i
$276$	−1.18780	+	6.13349i	−0.0714970	+	0.369193i
$277$	0.359676	+	0.622977i	0.0216108	+	0.0374310i	0.876629	−	0.481168i	$-0.159787\pi$
$277$	0.359676	+	0.622977i	0.0216108	+	0.0374310i	−0.855018	+	0.518599i	$0.826454\pi$
$278$	8.68419	−	5.01382i	0.520843	−	0.300709i
$279$	−25.2432	+	19.7788i	−1.51127	+	1.18413i
$280$	3.13658	−	2.25498i	0.187447	−	0.134761i
$281$	−7.30448			−0.435749			−0.217874	−	0.975977i	$-0.569912\pi$
$281$	−7.30448			−0.435749			−0.217874	+	0.975977i	$0.569912\pi$
$282$	−4.21268	+	21.7532i	−0.250861	+	1.29539i
$283$			14.9247i			0.887180i	0.896230	+	0.443590i	$0.146295\pi$
$283$			14.9247i			0.887180i	−0.896230	+	0.443590i	$0.853705\pi$
$284$	10.6744			0.633407
$285$	8.25622	−	2.84928i	0.489056	−	0.168777i
$286$	−10.5919	−	6.98849i	−0.626312	−	0.413238i
$287$	−6.46287	+	4.64634i	−0.381491	+	0.274265i
$288$	−0.421657	−	2.97022i	−0.0248464	−	0.175022i
$289$	−20.2826	+	35.1306i	−1.19310	+	2.06650i
$290$	−0.143959	−	0.249345i	−0.00845358	−	0.0146420i
$291$	3.92279	−	4.51901i	0.229958	−	0.264909i
$292$	−5.88820			−0.344581
$293$	13.1158	+	7.57239i	0.766231	+	0.442384i	0.831529	−	0.555482i	$-0.187466\pi$
$293$	13.1158	+	7.57239i	0.766231	+	0.442384i	−0.0652973	+	0.997866i	$0.520800\pi$
$294$	−5.97644	+	10.5490i	−0.348553	+	0.615232i
$295$	0.955007	−	1.65412i	0.0556027	−	0.0963066i
$296$	−4.81918	−	2.78236i	−0.280109	−	0.161721i
$297$	15.3582	+	9.92815i	0.891171	+	0.576089i
$298$	1.62311	−	2.81131i	0.0940242	−	0.162855i
$299$	7.16221	−	10.8552i	0.414201	−	0.627772i
$300$	4.87714	+	0.944496i	0.281582	+	0.0545305i
$301$	−12.2126	+	27.0649i	−0.703925	+	1.55999i
$302$	−8.04225	+	4.64320i	−0.462780	+	0.267186i
$303$	19.7546	+	3.82563i	1.13487	+	0.219777i
$304$	1.72681	−	2.99093i	0.0990395	−	0.171541i
$305$	0.729785	+	1.26403i	0.0417874	+	0.0723779i
$306$	−21.1160	−	8.49721i	−1.20712	−	0.485753i
$307$	−0.289284			−0.0165103			−0.00825515	−	0.999966i	$-0.502628\pi$
$307$	−0.289284			−0.0165103			−0.00825515	+	0.999966i	$0.502628\pi$
$308$	5.43551	+	7.56057i	0.309717	+	0.430804i
$309$	30.6745	−	10.5860i	1.74501	−	0.602215i
$310$	13.5168	+	7.80394i	0.767704	+	0.443234i
$311$	−5.96970	+	10.3398i	−0.338511	+	0.586318i	−0.984153	−	0.177322i	$-0.943256\pi$
$311$	−5.96970	+	10.3398i	−0.338511	+	0.586318i	0.645642	+	0.763640i	$0.276590\pi$
$312$	−1.55061	+	6.04943i	−0.0877862	+	0.342482i
$313$	−7.95301	+	4.59167i	−0.449530	+	0.259537i	−0.707632	−	0.706581i	$-0.750236\pi$
$313$	−7.95301	+	4.59167i	−0.449530	+	0.259537i	0.258101	+	0.966118i	$0.416903\pi$
$314$	16.2305	−	9.37071i	0.915942	−	0.528820i
$315$	11.2549	−	2.76306i	0.634142	−	0.155681i
$316$	0.174645	−	0.302494i	0.00982454	−	0.0170166i
$317$	11.5121	+	19.9395i	0.646582	+	1.11991i	0.983934	+	0.178534i	$0.0571356\pi$
$317$	11.5121	+	19.9395i	0.646582	+	1.11991i	−0.337352	+	0.941379i	$0.609531\pi$
$318$	−7.96985	+	2.75045i	−0.446927	+	0.154238i
$319$	0.601033	−	0.347007i	0.0336514	−	0.0194286i
$320$	−1.26448	+	0.730045i	−0.0706863	+	0.0408108i
$321$	−0.458849	−	0.398311i	−0.0256105	−	0.0222315i
$322$	−7.74851	+	5.57062i	−0.431808	+	0.310439i
$323$	−13.1016	−	22.6927i	−0.728994	−	1.26265i
$324$	2.15296	−	8.73869i	0.119609	−	0.485483i
$325$	−8.63168	−	5.69515i	−0.478800	−	0.315910i
$326$	−0.787553	−	0.454694i	−0.0436185	−	0.0251832i
$327$	12.2721	+	10.6530i	0.678648	+	0.589110i
$328$	2.60543	−	1.50425i	0.143861	−	0.0830581i
$329$	−27.4811	+	19.7569i	−1.51508	+	1.08924i
$330$	1.69223	−	8.73824i	0.0931540	−	0.481024i
$331$		−	23.6690i		−	1.30097i	−0.759521	−	0.650483i	$-0.774566\pi$
$331$		−	23.6690i		−	1.30097i	0.759521	−	0.650483i	$-0.225434\pi$
$332$	3.23009	−	1.86490i	0.177274	−	0.102349i
$333$	−10.2963	−	13.1408i	−0.564231	−	0.720113i
$334$			13.4641i			0.736722i
$335$	4.03616	+	6.99083i	0.220519	+	0.381950i
$336$	2.64459	−	3.74248i	0.144274	−	0.204169i
$337$	19.1537			1.04337			0.521684	−	0.853139i	$-0.325304\pi$
$337$	19.1537			1.04337			0.521684	+	0.853139i	$0.325304\pi$
$338$	7.79336	−	10.4050i	0.423903	−	0.565956i
$339$	7.60478	+	6.60144i	0.413035	+	0.358541i
$340$			11.0780i			0.600787i
$341$	−18.8110	+	32.5816i	−1.01867	+	1.76439i
$342$	8.15558	−	6.39016i	0.441004	−	0.345540i
$343$	−17.6977	+	5.45814i	−0.955586	+	0.294712i
$344$	5.61139	−	9.71922i	0.302546	−	0.524025i
$345$	8.95545	+	1.73429i	0.482145	+	0.0933711i
$346$	−5.08435	+	8.80635i	−0.273336	+	0.473432i
$347$	27.4634	−	15.8560i	1.47431	−	0.851194i	0.474729	−	0.880132i	$-0.342546\pi$
$347$	27.4634	−	15.8560i	1.47431	−	0.851194i	0.999581	+	0.0289382i	$0.00921259\pi$
$348$	−0.257925	−	0.223895i	−0.0138262	−	0.0120020i
$349$	3.87835	+	6.71749i	0.207603	+	0.359579i	0.950959	−	0.309317i	$-0.100100\pi$
$349$	3.87835	+	6.71749i	0.207603	+	0.359579i	−0.743356	+	0.668896i	$0.766767\pi$
$350$	4.42957	+	6.16136i	0.236771	+	0.329338i
$351$	−11.0906	+	15.0997i	−0.591970	+	0.805960i
$352$	−1.75974	−	3.04796i	−0.0937944	−	0.162457i
$353$		−	0.567754i		−	0.0302185i	−0.999886	−	0.0151092i	$-0.995190\pi$
$353$		−	0.567754i		−	0.0302185i	0.999886	−	0.0151092i	$-0.00480960\pi$
$354$	0.430782	−	2.22445i	0.0228958	−	0.118228i
$355$		−	15.5855i		−	0.827194i
$356$			14.4601i			0.766382i
$357$	−14.5581	−	31.5742i	−0.770498	−	1.67108i
$358$	7.39608	+	4.27013i	0.390895	+	0.225683i
$359$	−3.12906	−	5.41969i	−0.165145	−	0.286040i	0.771562	−	0.636155i	$-0.219476\pi$
$359$	−3.12906	−	5.41969i	−0.165145	−	0.286040i	−0.936707	+	0.350115i	$0.886143\pi$
$360$	−4.33679	+	0.615658i	−0.228569	+	0.0324480i
$361$	−7.07248			−0.372236
$362$	−22.0628	−	12.7380i	−1.15959	−	0.669492i
$363$	2.35805	+	0.456654i	0.123765	+	0.0239681i
$364$	−8.06357	+	5.09694i	−0.422646	+	0.267152i
$365$			8.59731i			0.450004i
$366$	1.30752	+	1.13501i	0.0683452	+	0.0593281i
$367$		−	21.5855i		−	1.12676i	−0.826199	−	0.563378i	$-0.809501\pi$
$367$		−	21.5855i		−	1.12676i	0.826199	−	0.563378i	$-0.190499\pi$
$368$	3.12372	−	1.80348i	0.162835	−	0.0940130i
$369$	8.93588	−	1.26855i	0.465183	−	0.0660382i
$370$	−4.06249	+	7.03645i	−0.211199	+	0.365807i
$371$	−11.7390	−	5.29703i	−0.609456	−	0.275008i
$372$	18.1773	+	3.52018i	0.942451	+	0.182513i
$373$	−0.756112			−0.0391500			−0.0195750	−	0.999808i	$-0.506231\pi$
$373$	−0.756112			−0.0391500			−0.0195750	+	0.999808i	$0.506231\pi$
$374$	−26.7029			−1.38077
$375$	3.78314	−	19.5352i	0.195360	−	1.00879i
$376$	11.0787	−	6.39629i	0.571340	−	0.329863i
$377$	0.318166	+	0.635824i	0.0163864	+	0.0327466i
$378$	11.5516	−	7.45394i	0.594149	−	0.383389i
$379$	6.26101	−	3.61480i	0.321607	−	0.185680i	−0.330502	−	0.943805i	$-0.607218\pi$
$379$	6.26101	−	3.61480i	0.321607	−	0.185680i	0.652108	+	0.758126i	$0.273885\pi$
$380$	−4.36702	−	2.52130i	−0.224024	−	0.129340i
$381$	−8.90437	−	25.8018i	−0.456184	−	1.32186i
$382$	17.9487	+	10.3627i	0.918338	+	0.530202i
$383$			1.34855i			0.0689079i	0.999406	+	0.0344540i	$0.0109692\pi$
$383$			1.34855i			0.0689079i	−0.999406	+	0.0344540i	$0.989031\pi$
$384$	−1.13542	+	1.30799i	−0.0579415	+	0.0667479i
$385$	11.0391	−	7.93633i	0.562606	−	0.404473i
$386$	−8.21554	−	4.74324i	−0.418160	−	0.241425i
$387$	26.5021	−	20.7653i	1.34718	−	1.05556i
$388$	−3.45494			−0.175398
$389$	3.70239	+	2.13758i	0.187719	+	0.108379i	0.590914	−	0.806734i	$-0.298767\pi$
$389$	3.70239	+	2.13758i	0.187719	+	0.108379i	−0.403196	+	0.915114i	$0.632101\pi$
$390$	8.83272	+	2.26404i	0.447262	+	0.114644i
$391$		−	27.3667i		−	1.38399i
$392$	6.86125	−	1.38682i	0.346545	−	0.0700447i
$393$	7.14799	+	20.7124i	0.360569	+	1.04480i
$394$	6.42840			0.323858
$395$	−0.441668	−	0.254997i	−0.0222228	−	0.0128303i
$396$	−1.48401	−	10.4536i	−0.0745744	−	0.525314i
$397$	−5.72958			−0.287560			−0.143780	−	0.989610i	$-0.545926\pi$
$397$	−5.72958			−0.287560			−0.143780	+	0.989610i	$0.545926\pi$
$398$			1.26513i			0.0634155i
$399$	15.7602	+	1.44724i	0.788996	+	0.0724524i
$400$	−1.43407	−	2.48388i	−0.0717034	−	0.124194i
$401$	10.9880	−	19.0318i	0.548717	−	0.950405i	−0.449646	−	0.893207i	$-0.648450\pi$
$401$	10.9880	−	19.0318i	0.548717	−	0.950405i	0.998363	−	0.0571984i	$-0.0182168\pi$
$402$	7.23138	+	6.27731i	0.360669	+	0.313084i
$403$	−32.1707	−	21.2261i	−1.60254	−	1.05735i
$404$	−5.80861	−	10.0608i	−0.288989	−	0.500544i
$405$	−12.7593	−	3.14352i	−0.634014	−	0.156203i
$406$	−0.0519388	−	0.519130i	−0.00257768	−	0.0257640i
$407$	−16.9610	−	9.79244i	−0.840726	−	0.485393i
$408$	4.28707	+	12.4224i	0.212241	+	0.615002i
$409$	−4.21950	−	7.30838i	−0.208641	−	0.361376i	0.742646	−	0.669684i	$-0.233571\pi$
$409$	−4.21950	−	7.30838i	−0.208641	−	0.361376i	−0.951287	+	0.308308i	$0.900237\pi$
$410$	−2.19633	−	3.80416i	−0.108469	−	0.187874i
$411$	0.707194	+	2.04920i	0.0348833	+	0.101080i
$412$	−16.2249	−	9.36744i	−0.799343	−	0.461501i
$413$	2.81017	−	2.02031i	0.138280	−	0.0994131i
$414$	10.7135	−	1.52090i	0.526539	−	0.0747483i
$415$	−2.72292	−	4.71623i	−0.133663	−	0.231511i
$416$	3.22439	−	1.61348i	0.158089	−	0.0791074i
$417$	−13.1160	−	11.3856i	−0.642294	−	0.557553i
$418$	6.07747	−	10.5265i	0.297259	−	0.514868i
$419$	12.4744	+	21.6063i	0.609413	+	1.05553i	0.991337	+	0.131341i	$0.0419282\pi$
$419$	12.4744	+	21.6063i	0.609413	+	1.05553i	−0.381924	+	0.924194i	$0.624738\pi$
$420$	−5.46435	−	3.86135i	−0.266633	−	0.188414i
$421$			23.2628i			1.13376i	0.823800	+	0.566881i	$0.191850\pi$
$421$			23.2628i			1.13376i	−0.823800	+	0.566881i	$0.808150\pi$
$422$	12.4915			0.608079
$423$	37.9967	−	5.39408i	1.84746	−	0.262269i
$424$	4.21555	+	2.43385i	0.204725	+	0.118198i
$425$	−21.7611			−1.05557
$426$	−6.03145	−	17.4771i	−0.292225	−	0.846766i
$427$	0.263298	+	2.63167i	0.0127419	+	0.127355i
$428$			0.350806i			0.0169568i
$429$	−5.45735	+	21.2908i	−0.263483	+	1.02793i
$430$	−14.1909	−	8.19314i	−0.684348	−	0.395108i
$431$	22.7370			1.09520			0.547602	−	0.836739i	$-0.315541\pi$
$431$	22.7370			1.09520			0.547602	+	0.836739i	$0.315541\pi$
$432$	−4.62487	+	2.36867i	−0.222514	+	0.113963i
$433$	−11.9025	−	6.87194i	−0.572000	−	0.330244i	0.185948	−	0.982560i	$-0.440464\pi$
$433$	−11.9025	−	6.87194i	−0.572000	−	0.330244i	−0.757948	+	0.652315i	$0.773798\pi$
$434$	16.5092	+	22.9637i	0.792468	+	1.10229i
$435$	−0.326907	+	0.376593i	−0.0156740	+	0.0180563i
$436$		−	9.38242i		−	0.449337i
$437$	10.7882	+	6.22855i	0.516068	+	0.297952i
$438$	3.32708	+	9.64071i	0.158974	+	0.460651i
$439$	10.5448	+	6.08806i	0.503277	+	0.290567i	0.730066	−	0.683377i	$-0.239489\pi$
$439$	10.5448	+	6.08806i	0.503277	+	0.290567i	−0.226789	+	0.973944i	$0.572823\pi$
$440$	−4.45029	+	2.56938i	−0.212159	+	0.122490i
$441$	20.6488	+	3.82455i	0.983276	+	0.182121i
$442$	1.63032	−	27.3073i	0.0775465	−	1.29888i
$443$	1.94173	−	1.12106i	0.0922543	−	0.0532630i	−0.453163	−	0.891428i	$-0.649704\pi$
$443$	1.94173	−	1.12106i	0.0922543	−	0.0532630i	0.545417	+	0.838165i	$0.316371\pi$
$444$	−1.83250	+	9.46256i	−0.0869665	+	0.449073i
$445$	21.1130			1.00085
$446$	−7.57111			−0.358503
$447$	−5.52006	−	1.06900i	−0.261090	−	0.0505620i
$448$	−2.63261	+	0.263392i	−0.124379	+	0.0124441i
$449$	3.91929	−	6.78842i	0.184963	−	0.320365i	−0.758601	−	0.651555i	$-0.774117\pi$
$449$	3.91929	−	6.78842i	0.184963	−	0.320365i	0.943564	+	0.331190i	$0.107450\pi$
$450$	−1.20937	−	8.51899i	−0.0570102	−	0.401589i
$451$	9.16975	−	5.29416i	0.431787	−	0.249292i
$452$		−	5.81411i		−	0.273473i
$453$	12.1465	+	10.5439i	0.570691	+	0.495397i
$454$			25.4572i			1.19476i
$455$	7.44200	+	11.7735i	0.348886	+	0.551952i
$456$	−5.87274	−	1.13730i	−0.275016	−	0.0532590i
$457$	−5.66636	−	3.27147i	−0.265061	−	0.153033i	0.361580	−	0.932341i	$-0.382237\pi$
$457$	−5.66636	−	3.27147i	−0.265061	−	0.153033i	−0.626641	+	0.779308i	$0.715571\pi$
$458$	11.0281			0.515310
$459$	−1.98103	+	39.3743i	−0.0924667	+	1.83784i
$460$	−2.63325	−	4.56092i	−0.122776	−	0.212654i
$461$	20.3030	+	11.7219i	0.945606	+	0.545946i	0.891713	−	0.452601i	$-0.149504\pi$
$461$	20.3030	+	11.7219i	0.945606	+	0.545946i	0.0538925	+	0.998547i	$0.482837\pi$
$462$	9.30759	−	13.1716i	0.433028	−	0.612796i
$463$			37.3356i			1.73513i	0.497321	+	0.867567i	$0.334317\pi$
$463$			37.3356i			1.73513i	−0.497321	+	0.867567i	$0.665683\pi$
$464$			0.197192i			0.00915442i
$465$	5.13978	−	26.5406i	0.238352	−	1.23079i
$466$		−	7.14438i		−	0.330957i
$467$	−3.36611	−	5.83027i	−0.155765	−	0.269792i	0.777572	−	0.628793i	$-0.216451\pi$
$467$	−3.36611	−	5.83027i	−0.155765	−	0.269792i	−0.933337	+	0.359001i	$0.883118\pi$
$468$	10.7808	−	0.879368i	0.498345	−	0.0406488i
$469$	1.45620	+	14.5547i	0.0672410	+	0.672075i
$470$	−9.33916	−	16.1759i	−0.430783	−	0.746138i
$471$	−24.5135	−	21.2793i	−1.12952	−	0.980499i
$472$	−1.13289	+	0.654074i	−0.0521454	+	0.0301062i
$473$	19.7492	−	34.2066i	0.908068	−	1.57282i
$474$	−0.593953	−	0.115023i	−0.0272812	−	0.00528320i
$475$	4.95273	−	8.57838i	0.227247	−	0.393603i
$476$	−8.25637	+	18.2972i	−0.378430	+	0.838653i
$477$	9.00659	+	11.4949i	0.412383	+	0.526314i
$478$	3.66232	−	6.34332i	0.167510	−	0.290137i
$479$			12.9489i			0.591650i	0.955242	+	0.295825i	$0.0955946\pi$
$479$			12.9489i			0.591650i	−0.955242	+	0.295825i	$0.904405\pi$
$480$	1.90978	+	1.65781i	0.0871691	+	0.0756684i
$481$	11.0496	−	16.7471i	0.503820	−	0.763600i
$482$	−17.4268			−0.793769
$483$	13.4990	+	9.53896i	0.614225	+	0.434038i
$484$	−0.693357	−	1.20093i	−0.0315162	−	0.0545877i
$485$			5.04452i			0.229060i
$486$	−15.5243	+	1.41269i	−0.704197	+	0.0640811i
$487$	7.51390	−	4.33815i	0.340487	−	0.196580i	−0.320000	−	0.947417i	$-0.603683\pi$
$487$	7.51390	−	4.33815i	0.340487	−	0.196580i	0.660488	+	0.750837i	$0.270350\pi$
$488$		−	0.999644i		−	0.0452518i
$489$	−0.299467	+	1.54638i	−0.0135424	+	0.0699295i
$490$	−2.02488	−	10.0180i	−0.0914746	−	0.452569i
$491$	−14.7725	+	8.52893i	−0.666676	+	0.384905i	−0.794816	−	0.606851i	$-0.792433\pi$
$491$	−14.7725	+	8.52893i	−0.666676	+	0.384905i	0.128140	+	0.991756i	$0.459099\pi$
$492$	−3.93507	−	3.41589i	−0.177406	−	0.154000i
$493$	1.29569	+	0.748066i	0.0583549	+	0.0336912i
$494$	10.3937	+	6.85773i	0.467635	+	0.308544i
$495$	−15.2632	+	2.16679i	−0.686031	+	0.0973901i
$496$	−5.34484	−	9.25753i	−0.239990	−	0.415675i
$497$	11.6158	−	25.7423i	0.521042	−	1.15470i
$498$	−4.87851	−	4.23487i	−0.218611	−	0.189769i
$499$	−20.1546	+	11.6362i	−0.902243	+	0.520910i	−0.877927	−	0.478794i	$-0.841074\pi$
$499$	−20.1546	+	11.6362i	−0.902243	+	0.520910i	−0.0243156	+	0.999704i	$0.507741\pi$
$500$	−9.94906	+	5.74410i	−0.444936	+	0.256884i
$501$	22.0447	−	7.60776i	0.984883	−	0.339890i
$502$	−6.39321	−	11.0734i	−0.285343	−	0.494228i
$503$	−4.33129	+	7.50201i	−0.193122	+	0.334498i	−0.946283	−	0.323338i	$-0.895195\pi$
$503$	−4.33129	+	7.50201i	−0.193122	+	0.334498i	0.753161	+	0.657836i	$0.228528\pi$
$504$	−7.62183	−	2.21532i	−0.339503	−	0.0986784i
$505$	−14.6897	+	8.48110i	−0.653683	+	0.377404i
$506$	10.9939	−	6.34731i	0.488737	−	0.282172i
$507$	−21.4396	−	6.88077i	−0.952165	−	0.305586i
$508$	−7.87940	+	13.6475i	−0.349592	+	0.605511i
$509$	5.00911	+	2.89201i	0.222025	+	0.128186i	0.606887	−	0.794788i	$-0.292418\pi$
$509$	5.00911	+	2.89201i	0.222025	+	0.128186i	−0.384863	+	0.922974i	$0.625751\pi$
$510$	18.1379	−	6.25951i	0.803159	−	0.277176i
$511$	−6.40754	+	14.2000i	−0.283453	+	0.628171i
$512$	1.00000			0.0441942
$513$	−15.0708	−	9.74238i	−0.665392	−	0.430137i
$514$	−10.6730	−	18.4862i	−0.470766	−	0.815391i
$515$	−13.6773	+	23.6898i	−0.602694	+	1.04390i
$516$	−19.0839	−	3.69574i	−0.840121	−	0.162696i
$517$	38.9912	−	22.5116i	1.71483	−	0.990058i
$518$	−11.9542	+	8.59419i	−0.525236	+	0.377607i
$519$	17.2914	+	3.34862i	0.759010	+	0.146988i
$520$	−2.35583	−	4.70790i	−0.103310	−	0.206455i
$521$	−5.46547	+	9.46647i	−0.239447	+	0.414734i	−0.960556	−	0.278088i	$-0.910299\pi$
$521$	−5.46547	+	9.46647i	−0.239447	+	0.414734i	0.721109	+	0.692822i	$0.243633\pi$
$522$	−0.220844	+	0.548808i	−0.00966609	+	0.0240207i
$523$	11.7895	+	6.80668i	0.515519	+	0.297635i	0.735100	−	0.677959i	$-0.237135\pi$
$523$	11.7895	+	6.80668i	0.515519	+	0.297635i	−0.219580	+	0.975594i	$0.570469\pi$
$524$	6.32520	−	10.9556i	0.276318	−	0.478596i
$525$	7.58506	−	10.7339i	0.331039	−	0.468467i
$526$	13.7817	+	7.95686i	0.600910	+	0.346936i
$527$	−81.1044			−3.53296
$528$	−3.99607	+	4.60343i	−0.173907	+	0.200338i
$529$	−4.99491	−	8.65143i	−0.217170	−	0.376149i
$530$	3.55364	−	6.15509i	0.154360	−	0.267360i
$531$	−3.88549	+	0.551590i	−0.168616	+	0.0239370i
$532$	−5.33380	−	7.41911i	−0.231250	−	0.321659i
$533$	4.85414	+	9.70054i	0.210256	+	0.420177i
$534$	23.6754	−	8.17053i	1.02453	−	0.353573i
$535$	0.512208			0.0221447
$536$		−	5.52864i		−	0.238801i
$537$	2.81236	−	14.5223i	0.121362	−	0.626685i
$538$	15.4992			0.668218
$539$	24.1480	−	4.88086i	1.04013	−	0.210234i
$540$	3.45848	+	6.75272i	0.148829	+	0.290591i
$541$	3.38852	−	1.95636i	0.145684	−	0.0841105i	−0.425386	−	0.905012i	$-0.639862\pi$
$541$	3.38852	−	1.95636i	0.145684	−	0.0841105i	0.571070	+	0.820901i	$0.306528\pi$
$542$	7.49829	+	12.9874i	0.322079	+	0.557858i
$543$	−8.38938	+	43.3207i	−0.360023	+	1.85907i
$544$	3.79359	−	6.57069i	0.162649	−	0.281716i
$545$	−13.6992			−0.586809
$546$	12.9014	+	10.3224i	0.552130	+	0.441760i
$547$	−10.8125			−0.462308			−0.231154	−	0.972917i	$-0.574250\pi$
$547$	−10.8125			−0.462308			−0.231154	+	0.972917i	$0.574250\pi$
$548$	0.625790	−	1.08390i	0.0267324	−	0.0463019i
$549$	1.11955	−	2.78212i	0.0477810	−	0.118738i
$550$	−5.04717	−	8.74195i	−0.215212	−	0.372758i
$551$	−0.589787	+	0.340514i	−0.0251258	+	0.0145064i
$552$	−4.71786	−	4.09541i	−0.200805	−	0.174312i
$553$	−0.539446	−	0.750348i	−0.0229396	−	0.0319080i
$554$	−0.719351			−0.0305623
$555$	13.8162	+	2.67561i	0.586465	+	0.113573i
$556$			10.0276i			0.425267i
$557$	23.2398			0.984703			0.492351	−	0.870396i	$-0.336137\pi$
$557$	23.2398			0.984703			0.492351	+	0.870396i	$0.336137\pi$
$558$	−4.50738	−	31.7507i	−0.190812	−	1.34411i
$559$	33.7751	+	22.2847i	1.42853	+	0.942541i
$560$	0.384576	+	3.84385i	0.0162513	+	0.162432i
$561$	15.0882	+	43.7205i	0.637026	+	1.84588i
$562$	3.65224	−	6.32587i	0.154060	−	0.266841i
$563$	5.93878	+	10.2863i	0.250290	+	0.433515i	0.963606	−	0.267328i	$-0.0861408\pi$
$563$	5.93878	+	10.2863i	0.250290	+	0.433515i	−0.713316	+	0.700843i	$0.752807\pi$
$564$	−16.7325	−	14.5249i	−0.704566	−	0.611609i
$565$	−8.48913			−0.357141
$566$	−12.9252	−	7.46234i	−0.543285	−	0.313666i
$567$	−18.7314	−	14.7015i	−0.786645	−	0.617406i
$568$	−5.33718	+	9.24427i	−0.223943	+	0.387881i
$569$	1.67254	+	0.965640i	0.0701164	+	0.0404817i	0.534648	−	0.845075i	$-0.320444\pi$
$569$	1.67254	+	0.965640i	0.0701164	+	0.0404817i	−0.464532	+	0.885556i	$0.653777\pi$
$570$	−1.66056	+	8.57474i	−0.0695533	+	0.359156i
$571$	6.46083	−	11.1905i	0.270377	−	0.468307i	−0.698581	−	0.715531i	$-0.746185\pi$
$571$	6.46083	−	11.1905i	0.270377	−	0.468307i	0.968958	+	0.247224i	$0.0795182\pi$
$572$	11.3482	−	5.67861i	0.474490	−	0.237435i
$573$	6.82502	−	35.2427i	0.285119	−	1.47229i
$574$	−0.792412	−	7.92018i	−0.0330746	−	0.330582i
$575$	8.95926	−	5.17263i	0.373627	−	0.215714i
$576$	2.78311	+	1.11994i	0.115963	+	0.0466643i
$577$	−18.9813	+	32.8766i	−0.790203	+	1.36867i	0.135638	+	0.990758i	$0.456692\pi$
$577$	−18.9813	+	32.8766i	−0.790203	+	1.36867i	−0.925841	+	0.377913i	$0.876642\pi$
$578$	−20.2826	−	35.1306i	−0.843646	−	1.46124i
$579$	−3.12396	+	16.1314i	−0.129827	+	0.670397i
$580$	0.287918			0.0119552
$581$	−0.982396	−	9.81907i	−0.0407567	−	0.407364i
$582$	1.95218	+	5.65675i	0.0809205	+	0.234480i
$583$	14.8365	+	8.56588i	0.614467	+	0.354763i
$584$	2.94410	−	5.09933i	0.121828	−	0.211012i
$585$	−1.28396	−	15.7410i	−0.0530851	−	0.650811i
$586$	−13.1158	+	7.57239i	−0.541807	+	0.312813i
$587$	3.62595	−	2.09345i	0.149659	−	0.0864058i	−0.423300	−	0.905989i	$-0.639129\pi$
$587$	3.62595	−	2.09345i	0.149659	−	0.0864058i	0.572960	+	0.819584i	$0.305795\pi$
$588$	−6.14751	−	10.4503i	−0.253519	−	0.430962i
$589$	18.4591	−	31.9720i	0.760592	−	1.31738i
$590$	0.955007	+	1.65412i	0.0393170	+	0.0680991i
$591$	−3.63231	−	10.5252i	−0.149413	−	0.432948i
$592$	4.81918	−	2.78236i	0.198067	−	0.114354i
$593$	−25.7814	+	14.8849i	−1.05872	+	0.611250i	−0.925077	−	0.379780i	$-0.876000\pi$
$593$	−25.7814	+	14.8849i	−1.05872	+	0.611250i	−0.133639	+	0.991030i	$0.542666\pi$
$594$	−16.2771	+	8.33649i	−0.667858	+	0.342050i
$595$	26.7156	+	12.0550i	1.09523	+	0.494209i
$596$	1.62311	+	2.81131i	0.0664852	+	0.115156i
$597$	2.07140	−	0.714853i	0.0847766	−	0.0292570i
$598$	5.81977	+	11.6303i	0.237988	+	0.475596i
$599$	−14.8413	−	8.56865i	−0.606401	−	0.350106i	0.165155	−	0.986268i	$-0.447188\pi$
$599$	−14.8413	−	8.56865i	−0.606401	−	0.350106i	−0.771556	+	0.636162i	$0.780521\pi$
$600$	−3.25653	+	3.75148i	−0.132947	+	0.153154i
$601$	17.6704	−	10.2020i	0.720790	−	0.416149i	−0.0942531	−	0.995548i	$-0.530046\pi$
$601$	17.6704	−	10.2020i	0.720790	−	0.416149i	0.815044	+	0.579400i	$0.196713\pi$
$602$	−17.3326	−	24.1089i	−0.706423	−	0.982605i
$603$	6.19177	−	15.3868i	0.252148	−	0.626600i
$604$		−	9.28639i		−	0.377858i
$605$	−1.75347	+	1.01236i	−0.0712885	+	0.0411584i
$606$	−13.1904	+	15.1952i	−0.535823	+	0.617262i
$607$			10.6029i			0.430359i	0.976574	+	0.215180i	$0.0690337\pi$
$607$			10.6029i			0.430359i	−0.976574	+	0.215180i	$0.930966\pi$
$608$	1.72681	+	2.99093i	0.0700315	+	0.121298i
$609$	−0.820620	+	0.378369i	−0.0332532	+	0.0153323i
$610$	−1.45957			−0.0590963
$611$	20.6406	+	41.2482i	0.835028	+	1.66872i
$612$	17.9168	−	14.0384i	0.724244	−	0.567468i
$613$		−	22.8515i		−	0.922964i	−0.887150	−	0.461482i	$-0.847318\pi$
$613$		−	22.8515i		−	0.922964i	0.887150	−	0.461482i	$-0.152682\pi$
$614$	0.144642	−	0.250527i	0.00583727	−	0.0101104i
$615$	−4.98751	+	5.74555i	−0.201116	+	0.231683i
$616$	−9.26540	+	0.927001i	−0.373314	+	0.0373500i
$617$	−2.03229	+	3.52003i	−0.0818170	+	0.141711i	−0.904030	−	0.427468i	$-0.859406\pi$
$617$	−2.03229	+	3.52003i	−0.0818170	+	0.141711i	0.822213	+	0.569179i	$0.192739\pi$
$618$	−6.16952	+	31.8579i	−0.248174	+	1.28151i
$619$	−5.71042	+	9.89074i	−0.229521	+	0.397542i	−0.957666	−	0.287881i	$-0.907049\pi$
$619$	−5.71042	+	9.89074i	−0.229521	+	0.397542i	0.728145	+	0.685423i	$0.240383\pi$
$620$	−13.5168	+	7.80394i	−0.542849	+	0.313414i
$621$	−8.54372	−	16.6817i	−0.342848	−	0.669415i
$622$	−5.96970	−	10.3398i	−0.239363	−	0.414589i
$623$	34.8719	+	15.7354i	1.39711	+	0.630427i
$624$	−4.46365	−	4.36759i	−0.178689	−	0.174843i
$625$	1.21656	+	2.10715i	0.0486624	+	0.0842858i
$626$		−	9.18334i		−	0.367040i
$627$	−20.6690	−	4.00270i	−0.825439	−	0.159853i
$628$			18.7414i			0.747864i
$629$		−	42.2205i		−	1.68344i
$630$	−3.23457	+	11.1286i	−0.128869	+	0.443373i
$631$	−2.43600	−	1.40642i	−0.0969755	−	0.0559888i	0.450728	−	0.892661i	$-0.351164\pi$
$631$	−2.43600	−	1.40642i	−0.0969755	−	0.0559888i	−0.547703	+	0.836673i	$0.684498\pi$
$632$	0.174645	+	0.302494i	0.00694700	+	0.0120326i
$633$	−7.05824	−	20.4523i	−0.280540	−	0.812907i
$634$	−23.0241			−0.914405
$635$	19.9266	+	11.5046i	0.790763	+	0.456547i
$636$	1.60297	−	8.27732i	0.0635618	−	0.328217i
$637$	3.51701	+	24.9926i	0.139349	+	0.990243i
$638$			0.694013i			0.0274762i
$639$	−25.2070	+	19.7505i	−0.997175	+	0.781318i
$640$		−	1.46009i		−	0.0577151i
$641$	19.9139	−	11.4973i	0.786552	−	0.454116i	−0.0521953	−	0.998637i	$-0.516622\pi$
$641$	19.9139	−	11.4973i	0.786552	−	0.454116i	0.838747	+	0.544521i	$0.183289\pi$
$642$	0.574372	−	0.198220i	0.0226686	−	0.00782310i
$643$	5.08228	−	8.80277i	0.200426	−	0.347147i	−0.748240	−	0.663428i	$-0.769101\pi$
$643$	5.08228	−	8.80277i	0.200426	−	0.347147i	0.948666	+	0.316281i	$0.102434\pi$
$644$	−0.950045	−	9.49572i	−0.0374370	−	0.374184i
$645$	−5.39611	+	27.8642i	−0.212472	+	1.09715i
$646$	26.2033			1.03095
$647$	−42.4942			−1.67062			−0.835309	−	0.549780i	$-0.814712\pi$
$647$	−42.4942			−1.67062			−0.835309	+	0.549780i	$0.814712\pi$
$648$	6.49145	+	6.23386i	0.255008	+	0.244889i
$649$	−3.98718	+	2.30200i	−0.156510	+	0.0903613i
$650$	9.24798	−	4.62768i	0.362736	−	0.181513i
$651$	28.2698	−	40.0058i	1.10798	−	1.56795i
$652$	0.787553	−	0.454694i	0.0308430	−	0.0178072i
$653$	−18.7413	−	10.8203i	−0.733404	−	0.423431i	0.0862619	−	0.996272i	$-0.472508\pi$
$653$	−18.7413	−	10.8203i	−0.733404	−	0.423431i	−0.819666	+	0.572841i	$0.805841\pi$
$654$	−15.3618	+	5.30145i	−0.600693	+	0.207303i
$655$	−15.9961	−	9.23536i	−0.625020	−	0.360855i
$656$			3.00849i			0.117462i
$657$	13.9047	−	10.8948i	0.542475	−	0.425046i
$658$	−3.36946	−	33.6778i	−0.131355	−	1.31290i
$659$	−4.44211	−	2.56466i	−0.173040	−	0.0999048i	0.410978	−	0.911645i	$-0.365187\pi$
$659$	−4.44211	−	2.56466i	−0.173040	−	0.0999048i	−0.584019	+	0.811740i	$0.698520\pi$
$660$	6.72142	+	5.83463i	0.261631	+	0.227113i
$661$	23.9481			0.931472			0.465736	−	0.884924i	$-0.345790\pi$
$661$	23.9481			0.931472			0.465736	+	0.884924i	$0.345790\pi$
$662$	20.4980	+	11.8345i	0.796676	+	0.459961i
$663$	−45.6313	+	12.7605i	−1.77217	+	0.495575i
$664$			3.72979i			0.144744i
$665$	−10.8326	+	7.78784i	−0.420069	+	0.301999i
$666$	16.5284	−	2.34640i	0.640463	−	0.0909212i
$667$	−0.711265			−0.0275403
$668$	−11.6602	−	6.73204i	−0.451148	−	0.260471i
$669$	4.27799	+	12.3961i	0.165397	+	0.479262i
$670$	−8.07231			−0.311861
$671$		−	3.51822i		−	0.135819i
$672$	1.91878	+	4.16152i	0.0740186	+	0.160534i
$673$	−8.33251	−	14.4323i	−0.321195	−	0.556326i	0.659540	−	0.751669i	$-0.270751\pi$
$673$	−8.33251	−	14.4323i	−0.321195	−	0.556326i	−0.980735	+	0.195344i	$0.937418\pi$
$674$	−9.57684	+	16.5876i	−0.368886	+	0.638930i
$675$	−13.2647	+	6.79367i	−0.510560	+	0.261489i
$676$	5.11430	+	11.9517i	0.196704	+	0.459682i
$677$	−18.1468	−	31.4312i	−0.697439	−	1.20800i	−0.969352	−	0.245678i	$-0.920989\pi$
$677$	−18.1468	−	31.4312i	−0.697439	−	1.20800i	0.271913	−	0.962322i	$-0.412344\pi$
$678$	−9.51941	+	3.28521i	−0.365591	+	0.126168i
$679$	−3.75966	+	8.33193i	−0.144283	+	0.319750i
$680$	−9.59380	−	5.53898i	−0.367905	−	0.212410i
$681$	41.6808	−	14.3843i	1.59721	−	0.551209i
$682$	−18.8110	−	32.5816i	−0.720311	−	1.24762i
$683$	18.2874	+	31.6746i	0.699747	+	1.21200i	0.968554	+	0.248803i	$0.0800371\pi$
$683$	18.2874	+	31.6746i	0.699747	+	1.21200i	−0.268808	+	0.963194i	$0.586630\pi$
$684$	1.45625	+	10.2580i	0.0556809	+	0.392225i
$685$	−1.58259	−	0.913710i	−0.0604677	−	0.0349110i
$686$	4.12197	−	18.0557i	0.157377	−	0.689371i
$687$	−6.23134	−	18.0563i	−0.237741	−	0.688890i
$688$	5.61139	+	9.71922i	0.213932	+	0.370542i
$689$	−9.66561	+	14.6494i	−0.368230	+	0.558098i
$690$	−5.97967	+	6.88850i	−0.227642	+	0.262241i
$691$	8.73134	−	15.1231i	0.332156	−	0.575311i	−0.650778	−	0.759268i	$-0.725557\pi$
$691$	8.73134	−	15.1231i	0.332156	−	0.575311i	0.982934	+	0.183957i	$0.0588907\pi$
$692$	−5.08435	−	8.80635i	−0.193278	−	0.334767i
$693$	−26.8249	−	7.79678i	−1.01899	−	0.296175i
$694$			31.7120i			1.20377i
$695$	14.6413			0.555375
$696$	0.322861	−	0.111422i	0.0122380	−	0.00422343i
$697$	19.7679	+	11.4130i	0.748761	+	0.432297i
$698$	−7.75670			−0.293595
$699$	−11.6974	+	4.03687i	−0.442438	+	0.152688i
$700$	−7.55068	+	0.755444i	−0.285389	+	0.0285531i
$701$			42.7684i			1.61534i	0.589635	+	0.807670i	$0.299272\pi$
$701$			42.7684i			1.61534i	−0.589635	+	0.807670i	$0.700728\pi$
$702$	−7.53141	−	17.1545i	−0.284255	−	0.647456i
$703$	16.6436	+	9.60922i	0.627727	+	0.362418i
$704$	3.51948			0.132645
$705$	−21.2077	+	24.4310i	−0.798727	+	0.920124i
$706$	0.491689	+	0.283877i	0.0185050	+	0.0106838i
$707$	−30.5836	+	3.05988i	−1.15021	+	0.115079i
$708$	1.71104	+	1.48529i	0.0643048	+	0.0558207i
$709$			36.5874i			1.37407i	0.726626	+	0.687033i	$0.241087\pi$
$709$			36.5874i			1.37407i	−0.726626	+	0.687033i	$0.758913\pi$
$710$	13.4975	+	7.79277i	0.506551	+	0.292457i
$711$	0.147281	+	1.03747i	0.00552345	+	0.0389081i
$712$	−12.5228	−	7.23003i	−0.469311	−	0.270957i
$713$	33.3916	−	19.2786i	1.25052	−	0.721990i
$714$	34.6231	+	3.17939i	1.29574	+	0.118986i
$715$	−8.29128	−	16.5693i	−0.310076	−	0.619658i
$716$	−7.39608	+	4.27013i	−0.276404	+	0.159582i
$717$	−12.4552	−	2.41205i	−0.465149	−	0.0900796i
$718$	6.25812			0.233551
$719$	19.0766			0.711439			0.355719	−	0.934593i	$-0.384236\pi$
$719$	19.0766			0.711439			0.355719	+	0.934593i	$0.384236\pi$
$720$	1.63522	−	4.06360i	0.0609410	−	0.151441i
$721$	−40.2464	+	28.9343i	−1.49886	+	1.07757i
$722$	3.53624	−	6.12495i	0.131605	−	0.227947i
$723$	9.84686	+	28.5328i	0.366209	+	1.06115i
$724$	22.0628	−	12.7380i	0.819957	−	0.473402i
$725$			0.565574i			0.0210049i
$726$	−1.57450	+	1.81380i	−0.0584351	+	0.0673165i
$727$			9.70964i			0.360111i	0.983656	+	0.180055i	$0.0576277\pi$
$727$			9.70964i			0.360111i	−0.983656	+	0.180055i	$0.942372\pi$
$728$	−0.382294	−	9.53173i	−0.0141688	−	0.353269i
$729$	11.0849	+	24.6196i	0.410551	+	0.911838i
$730$	−7.44549	−	4.29865i	−0.275570	−	0.159100i
$731$	85.1493			3.14936
$732$	−1.63671	+	0.564840i	−0.0604945	+	0.0208771i
$733$	−16.1353	−	27.9472i	−0.595972	−	1.03225i	−0.993409	−	0.114624i	$-0.963434\pi$
$733$	−16.1353	−	27.9472i	−0.595972	−	1.03225i	0.397437	−	0.917629i	$-0.369900\pi$
$734$	18.6936	+	10.7928i	0.689995	+	0.398369i
$735$	−15.2583	+	8.97592i	−0.562812	+	0.331082i
$736$			3.60696i			0.132954i
$737$		−	19.4579i		−	0.716741i
$738$	−3.36934	+	8.37297i	−0.124027	+	0.308213i
$739$		−	22.4830i		−	0.827050i	−0.910493	−	0.413525i	$-0.864297\pi$
$739$		−	22.4830i		−	0.827050i	0.910493	−	0.413525i	$-0.135703\pi$
$740$	−4.06249	−	7.03645i	−0.149340	−	0.258665i
$741$	5.35523	−	20.8925i	0.196729	−	0.767503i
$742$	10.4568	−	7.51772i	0.383883	−	0.275984i
$743$	−19.9808	−	34.6077i	−0.733023	−	1.26963i	−0.955585	−	0.294715i	$-0.904775\pi$
$743$	−19.9808	−	34.6077i	−0.733023	−	1.26963i	0.222562	−	0.974919i	$-0.428558\pi$
$744$	−12.1372	+	13.9819i	−0.444973	+	0.512603i
$745$	4.10476	−	2.36989i	0.150387	−	0.0868259i
$746$	0.378056	−	0.654812i	0.0138416	−	0.0239744i
$747$	−4.17716	+	10.3804i	−0.152834	+	0.379800i
$748$	13.3514	−	23.1254i	0.488177	−	0.845548i
$749$	0.846003	+	0.381747i	0.0309123	+	0.0139487i
$750$	15.0264	+	13.0439i	0.548686	+	0.476295i
$751$	−15.6040	+	27.0270i	−0.569399	+	0.986228i	0.427227	+	0.904145i	$0.359491\pi$
$751$	−15.6040	+	27.0270i	−0.569399	+	0.986228i	−0.996625	+	0.0820832i	$0.973843\pi$
$752$			12.7926i			0.466497i
$753$	−14.5179	+	16.7245i	−0.529062	+	0.609473i
$754$	−0.709723	−	0.0423724i	−0.0258466	−	0.00154311i
$755$	−13.5590			−0.493462
$756$	0.679514	+	13.7309i	0.0247137	+	0.499389i
$757$	−0.452106	−	0.783071i	−0.0164321	−	0.0284612i	0.857692	−	0.514163i	$-0.171897\pi$
$757$	−0.452106	−	0.783071i	−0.0164321	−	0.0284612i	−0.874125	+	0.485702i	$0.838564\pi$
$758$			7.22959i			0.262591i
$759$	−16.6044	−	14.4137i	−0.602701	−	0.523184i
$760$	4.36702	−	2.52130i	0.158409	−	0.0914572i
$761$		−	41.8084i		−	1.51555i	−0.652515	−	0.757776i	$-0.726286\pi$
$761$		−	41.8084i		−	1.51555i	0.652515	−	0.757776i	$-0.273714\pi$
$762$	26.7972	+	5.18947i	0.970759	+	0.187995i
$763$	−22.6267	−	10.2100i	−0.819140	−	0.369625i
$764$	−17.9487	+	10.3627i	−0.649363	+	0.374910i
$765$	−20.4973	−	26.1601i	−0.741081	−	0.945822i
$766$	−1.16788	−	0.674277i	−0.0421973	−	0.0243626i
$767$	−2.11067	−	4.21798i	−0.0762119	−	0.152302i
$768$	−0.565041	−	1.63729i	−0.0203892	−	0.0590807i
$769$	10.4819	+	18.1551i	0.377986	+	0.654691i	0.990769	−	0.135560i	$-0.0432834\pi$
$769$	10.4819	+	18.1551i	0.377986	+	0.654691i	−0.612783	+	0.790251i	$0.709950\pi$
$770$	1.35351	+	13.5283i	0.0487770	+	0.487527i
$771$	−24.2366	+	27.9203i	−0.872861	+	1.00552i
$772$	8.21554	−	4.74324i	0.295684	−	0.170713i
$773$	20.0435	−	11.5721i	0.720916	−	0.416221i	−0.0941738	−	0.995556i	$-0.530021\pi$
$773$	20.0435	−	11.5721i	0.720916	−	0.416221i	0.815090	+	0.579335i	$0.196688\pi$
$774$	4.73217	+	33.3341i	0.170094	+	1.19817i
$775$	−15.3297	−	26.5518i	−0.550660	−	0.953770i
$776$	1.72747	−	2.99206i	0.0620125	−	0.107409i
$777$	20.8258	+	14.7164i	0.747122	+	0.527948i
$778$	−3.70239	+	2.13758i	−0.132737	+	0.0766358i
$779$	−8.99817	+	5.19510i	−0.322393	+	0.186134i
$780$	−6.37707	+	6.51734i	−0.228336	+	0.233358i
$781$	−18.7841	+	32.5350i	−0.672147	+	1.16419i
$782$	23.7002	+	13.6833i	0.847519	+	0.489315i
$783$	1.02335	+	0.0514874i	0.0365714	+	0.00184001i
$784$	−2.22961	+	6.63542i	−0.0796288	+	0.236979i
$785$	27.3642			0.976669
$786$	−21.5115	−	4.16586i	−0.767288	−	0.148591i
$787$	−16.1516	−	27.9754i	−0.575743	−	0.997217i	−0.995960	−	0.0897931i	$-0.971379\pi$
$787$	−16.1516	−	27.9754i	−0.575743	−	0.997217i	0.420217	−	0.907424i	$-0.361954\pi$
$788$	−3.21420	+	5.56716i	−0.114501	+	0.198322i
$789$	5.24050	−	27.0606i	0.186567	−	0.963384i
$790$	0.441668	−	0.254997i	0.0157139	−	0.00907240i
$791$	−14.0213	−	6.32692i	−0.498541	−	0.224959i
$792$	9.79510	+	3.94162i	0.348054	+	0.140059i
$793$	3.59786	+	0.214802i	0.127764	+	0.00762784i
$794$	2.86479	−	4.96196i	0.101668	−	0.176094i
$795$	−12.0856	−	2.34048i	−0.428634	−	0.0830081i
$796$	−1.09564	−	0.632567i	−0.0388339	−	0.0224208i
$797$	6.10975	−	10.5824i	0.216418	−	0.374848i	−0.737292	−	0.675574i	$-0.763896\pi$
$797$	6.10975	−	10.5824i	0.216418	−	0.374848i	0.953710	+	0.300727i	$0.0972291\pi$
$798$	−9.13343	+	12.9251i	−0.323320	+	0.457544i
$799$	84.0560	+	48.5298i	2.97369	+	1.71686i
$800$	2.86814			0.101404
$801$	−26.7551	−	34.1468i	−0.945345	−	1.20652i
$802$	10.9880	+	19.0318i	0.388001	+	0.672038i
$803$	10.3617	−	17.9470i	0.365656	−	0.633335i
$804$	−9.05200	+	3.12391i	−0.319239	+	0.110172i
$805$	−13.8646	+	1.38715i	−0.488663	+	0.0488907i
$806$	34.4676	−	17.2476i	1.21407	−	0.607520i
$807$	−8.75768	−	25.3767i	−0.308285	−	0.893303i
$808$	11.6172			0.408693
$809$		−	29.4579i		−	1.03568i	−0.855476	−	0.517842i	$-0.826736\pi$
$809$		−	29.4579i		−	1.03568i	0.855476	−	0.517842i	$-0.173264\pi$
$810$	9.10201	−	9.47811i	0.319812	−	0.333027i
$811$	36.5632			1.28391			0.641954	−	0.766743i	$-0.278124\pi$
$811$	36.5632			1.28391			0.641954	+	0.766743i	$0.278124\pi$
$812$	0.475549	+	0.214585i	0.0166885	+	0.00753044i
$813$	17.0274	−	19.6153i	0.597176	−	0.687940i
$814$	16.9610	−	9.79244i	0.594483	−	0.343225i
$815$	−0.663894	−	1.14990i	−0.0232552	−	0.0402792i
$816$	−12.9017	−	2.49851i	−0.451649	−	0.0874653i
$817$	−19.3796	+	33.5665i	−0.678008	+	1.17434i
$818$	8.43899			0.295062
$819$	9.61103	−	26.9560i	0.335837	−	0.941920i
$820$	4.39267			0.153399
$821$	11.8239	−	20.4797i	0.412658	−	0.714745i	−0.582521	−	0.812816i	$-0.697934\pi$
$821$	11.8239	−	20.4797i	0.412658	−	0.714745i	0.995179	+	0.0980703i	$0.0312670\pi$
$822$	−2.12826	−	0.412153i	−0.0742315	−	0.0143755i
$823$	−7.11240	−	12.3190i	−0.247923	−	0.429415i	0.715027	−	0.699097i	$-0.246415\pi$
$823$	−7.11240	−	12.3190i	−0.247923	−	0.429415i	−0.962949	+	0.269683i	$0.913081\pi$
$824$	16.2249	−	9.36744i	0.565221	−	0.326330i
$825$	−11.4613	+	13.2033i	−0.399030	+	0.459678i
$826$	0.344555	+	3.44384i	0.0119886	+	0.119827i
$827$	38.3054			1.33201			0.666004	−	0.745948i	$-0.268003\pi$
$827$	38.3054			1.33201			0.666004	+	0.745948i	$0.268003\pi$
$828$	−4.03960	+	10.0386i	−0.140386	+	0.348865i
$829$		−	21.9217i		−	0.761373i	−0.924704	−	0.380687i	$-0.875688\pi$
$829$		−	21.9217i		−	0.761373i	0.924704	−	0.380687i	$-0.124312\pi$
$830$	5.44583			0.189028
$831$	0.406463	+	1.17779i	0.0141000	+	0.0408570i
$832$	−0.214878	+	3.59914i	−0.00744957	+	0.124778i
$833$	35.1411	+	39.8221i	1.21757	+	1.37975i
$834$	16.4182	−	5.66603i	0.568515	−	0.196198i
$835$	−9.82939	+	17.0250i	−0.340160	+	0.589175i
$836$	6.07747	+	10.5265i	0.210194	+	0.364066i
$837$	−49.4383	+	25.3203i	−1.70884	+	0.875199i
$838$	−24.9488			−0.861840
$839$	−28.0544	−	16.1972i	−0.968547	−	0.559191i	−0.0697541	−	0.997564i	$-0.522221\pi$
$839$	−28.0544	−	16.1972i	−0.968547	−	0.559191i	−0.898793	+	0.438373i	$0.855555\pi$
$840$	6.07620	−	2.80159i	0.209649	−	0.0966642i
$841$	−14.4806	+	25.0811i	−0.499330	+	0.864864i
$842$	−20.1462	−	11.6314i	−0.694284	−	0.400845i
$843$	−12.4210	−	2.40541i	−0.427801	−	0.0828468i
$844$	−6.24577	+	10.8180i	−0.214988	+	0.372371i
$845$	17.4506	−	7.46734i	0.600319	−	0.256884i
$846$	−14.3270	+	35.6032i	−0.492571	+	1.22406i
$847$	−3.65067	+	0.365249i	−0.125439	+	0.0125501i
$848$	−4.21555	+	2.43385i	−0.144763	+	0.0835788i
$849$	−4.91480	+	25.3788i	−0.168675	+	0.870998i
$850$	10.8805	−	18.8456i	0.373199	−	0.646400i
$851$	10.0359	+	17.3826i	0.344025	+	0.595869i
$852$	18.1513	+	3.51514i	0.621853	+	0.120427i
$853$	−14.9608			−0.512249			−0.256125	−	0.966644i	$-0.582446\pi$
$853$	−14.9608			−0.512249			−0.256125	+	0.966644i	$0.582446\pi$
$854$	−2.41074	−	1.08781i	−0.0824939	−	0.0372242i
$855$	14.9776	−	2.12625i	0.512225	−	0.0727162i
$856$	−0.303807	−	0.175403i	−0.0103839	−	0.00599514i
$857$	−1.02659	+	1.77810i	−0.0350675	+	0.0607387i	−0.883027	−	0.469323i	$-0.844498\pi$
$857$	−1.02659	+	1.77810i	−0.0350675	+	0.0607387i	0.847959	+	0.530062i	$0.177831\pi$
$858$	−15.7097	−	15.3716i	−0.536321	−	0.524778i
$859$	−45.8673	+	26.4815i	−1.56497	+	0.903536i	−0.568230	+	0.822870i	$0.692372\pi$
$859$	−45.8673	+	26.4815i	−1.56497	+	0.903536i	−0.996741	+	0.0806667i	$0.974295\pi$
$860$	14.1909	−	8.19314i	0.483907	−	0.279384i
$861$	−12.5199	+	5.77264i	−0.426677	+	0.196731i
$862$	−11.3685	+	19.6908i	−0.387213	+	0.670672i
$863$	10.0096	+	17.3372i	0.340732	+	0.590165i	0.984569	−	0.174998i	$-0.0559918\pi$
$863$	10.0096	+	17.3372i	0.340732	+	0.590165i	−0.643837	+	0.765163i	$0.722658\pi$
$864$	0.261103	−	5.18959i	0.00888290	−	0.176553i
$865$	−12.8581	+	7.42361i	−0.437187	+	0.252410i
$866$	11.9025	−	6.87194i	0.404465	−	0.233518i
$867$	−46.0585	+	53.0588i	−1.56423	+	1.80197i
$868$	−28.1417	+	2.81557i	−0.955192	+	0.0955667i
$869$	0.614659	+	1.06462i	0.0208509	+	0.0361148i
$870$	−0.162686	−	0.471407i	−0.00551556	−	0.0159822i
$871$	19.8984	+	1.18799i	0.674230	+	0.0402534i
$872$	8.12542	+	4.69121i	0.275161	+	0.158864i
$873$	8.15869	−	6.39259i	0.276130	−	0.216356i
$874$	−10.7882	+	6.22855i	−0.364915	+	0.210684i
$875$	3.02590	+	30.2439i	0.102294	+	1.02243i
$876$	−10.0126	−	1.93902i	−0.338296	−	0.0655135i
$877$		−	0.242356i		−	0.00818379i	−0.999992	−	0.00409190i	$-0.998698\pi$
$877$		−	0.242356i		−	0.00818379i	0.999992	−	0.00409190i	$-0.00130249\pi$
$878$	−10.5448	+	6.08806i	−0.355871	+	0.205462i
$879$	19.8092	+	17.1956i	0.668147	+	0.579995i
$880$		−	5.13875i		−	0.173227i
$881$	13.7225	+	23.7681i	0.462323	+	0.800768i	0.999076	−	0.0429719i	$-0.0136826\pi$
$881$	13.7225	+	23.7681i	0.462323	+	0.800768i	−0.536753	+	0.843740i	$0.680349\pi$
$882$	−13.6366	+	15.9701i	−0.459167	+	0.537741i
$883$	13.7372			0.462293			0.231146	−	0.972919i	$-0.425752\pi$
$883$	13.7372			0.462293			0.231146	+	0.972919i	$0.425752\pi$
$884$	22.8337	+	15.0656i	0.767980	+	0.506710i
$885$	2.16866	−	2.49827i	0.0728988	−	0.0839785i
$886$			2.24211i			0.0753253i
$887$	−25.3915	+	43.9794i	−0.852563	+	1.47668i	0.0263247	+	0.999653i	$0.491620\pi$
$887$	−25.3915	+	43.9794i	−0.852563	+	1.47668i	−0.878888	+	0.477029i	$0.841714\pi$
$888$	−7.27857	−	6.31827i	−0.244253	−	0.212027i
$889$	24.3380	+	33.8532i	0.816271	+	1.13540i
$890$	−10.5565	+	18.2844i	−0.353855	+	0.612894i
$891$	22.8465	+	21.9399i	0.765387	+	0.735016i
$892$	3.78556	−	6.55677i	0.126750	−	0.219537i
$893$	−38.2616	+	22.0904i	−1.28038	+	0.739226i
$894$	3.68581	−	4.24601i	0.123272	−	0.142008i
$895$	6.23477	+	10.7989i	0.208405	+	0.360969i
$896$	1.08820	−	2.41160i	0.0363542	−	0.0805659i
$897$	15.7537	−	16.1002i	0.526001	−	0.537571i
$898$	3.91929	+	6.78842i	0.130789	+	0.226532i
$899$			2.10792i			0.0703030i
$900$	7.98235	+	3.21215i	0.266078	+	0.107072i
$901$			36.9321i			1.23039i
$902$			10.5883i			0.352552i
$903$	−29.6797	+	42.0010i	−0.987679	+	1.39771i
$904$	5.03517	+	2.90706i	0.167467	+	0.0966873i
$905$	−18.5986	−	32.2137i	−0.618237	−	1.07082i
$906$	−15.2045	+	5.24719i	−0.505137	+	0.174326i
$907$	17.8742			0.593504			0.296752	−	0.954955i	$-0.404097\pi$
$907$	17.8742			0.593504			0.296752	+	0.954955i	$0.404097\pi$
$908$	−22.0466	−	12.7286i	−0.731640	−	0.422413i
$909$	32.3321	+	13.0106i	1.07239	+	0.431536i
$910$	−13.9172	+	0.558184i	−0.461350	+	0.0185036i
$911$		−	43.8367i		−	1.45238i	−0.687496	−	0.726188i	$-0.741290\pi$
$911$		−	43.8367i		−	1.45238i	0.687496	−	0.726188i	$-0.258710\pi$
$912$	3.92130	−	4.51729i	0.129847	−	0.149583i
$913$			13.1269i			0.434437i
$914$	5.66636	−	3.27147i	0.187426	−	0.108211i
$915$	0.824717	+	2.38975i	0.0272643	+	0.0790025i
$916$	−5.51406	+	9.55063i	−0.182190	+	0.315562i
$917$	−19.5374	−	27.1757i	−0.645181	−	0.897421i
$918$	−33.1087	−	21.4028i	−1.09275	−	0.706397i
$919$	53.7240			1.77219			0.886096	−	0.463502i	$-0.153407\pi$
$919$	53.7240			1.77219			0.886096	+	0.463502i	$0.153407\pi$
$920$	5.26649			0.173631
$921$	−0.491915	−	0.0952630i	−0.0162091	−	0.00313902i
$922$	−20.3030	+	11.7219i	−0.668644	+	0.386042i
$923$	−32.1246	−	21.1957i	−1.05739	−	0.697664i
$924$	6.75311	+	14.6464i	0.222161	+	0.481831i
$925$	13.8221	−	7.98018i	0.454467	−	0.262387i
$926$	−32.3336	−	18.6678i	−1.06255	−	0.613462i
$927$	55.6467	−	7.89970i	1.82768	−	0.259460i
$928$	−0.170773	−	0.0985961i	−0.00560591	−	0.00323657i
$929$		−	7.60883i		−	0.249638i	−0.992180	−	0.124819i	$-0.960165\pi$
$929$		−	7.60883i		−	0.249638i	0.992180	−	0.124819i	$-0.0398350\pi$
$930$	20.4149	+	17.7215i	0.669431	+	0.581110i
$931$	−23.6962	+	4.78954i	−0.776611	+	0.156971i
$932$	6.18721	+	3.57219i	0.202669	+	0.117011i
$933$	−13.5562	+	15.6166i	−0.443810	+	0.511264i
$934$	6.73221			0.220285
$935$	−33.7652	−	19.4943i	−1.10424	−	0.637532i
$936$	−4.62887	+	9.77617i	−0.151299	+	0.319544i
$937$		−	25.7440i		−	0.841020i	−0.907288	−	0.420510i	$-0.861851\pi$
$937$		−	25.7440i		−	0.841020i	0.907288	−	0.420510i	$-0.138149\pi$
$938$	−13.3329	−	6.01626i	−0.435334	−	0.196438i
$939$	−15.0358	+	5.18896i	−0.490675	+	0.169335i
$940$	18.6783			0.609219
$941$	17.8743	+	10.3197i	0.582684	+	0.336413i	0.762199	−	0.647342i	$-0.224120\pi$
$941$	17.8743	+	10.3197i	0.582684	+	0.336413i	−0.179515	+	0.983755i	$0.557453\pi$
$942$	30.6852	−	10.5897i	0.999777	−	0.345030i
$943$	−10.8515			−0.353374
$944$		−	1.30815i		−	0.0425766i
$945$	20.0484	−	0.992152i	0.652174	−	0.0322747i
$946$	19.7492	+	34.2066i	0.642101	+	1.11215i
$947$	30.3820	−	52.6232i	0.987282	−	1.71002i	0.355962	−	0.934500i	$-0.384153\pi$
$947$	30.3820	−	52.6232i	0.987282	−	1.71002i	0.631320	−	0.775522i	$-0.282513\pi$
$948$	0.396590	−	0.456866i	0.0128806	−	0.0148383i
$949$	17.7206	+	11.6920i	0.575235	+	0.379538i
$950$	4.95273	+	8.57838i	0.160688	+	0.278319i
$951$	13.0096	+	37.6973i	0.421865	+	1.22242i
$952$	−11.7177	−	16.2988i	−0.379773	−	0.528249i
$953$	−3.76601	−	2.17431i	−0.121993	−	0.0704328i	0.437762	−	0.899091i	$-0.355771\pi$
$953$	−3.76601	−	2.17431i	−0.121993	−	0.0704328i	−0.559755	+	0.828658i	$0.689105\pi$
$954$	−14.4581	+	2.05250i	−0.468100	+	0.0664522i
$955$	15.1305	+	26.2068i	0.489611	+	0.848032i
$956$	3.66232	+	6.34332i	0.118448	+	0.205158i
$957$	1.13630	−	0.392146i	0.0367315	−	0.0126763i
$958$	−11.2141	−	6.47445i	−0.362310	−	0.209180i
$959$	−1.93295	−	2.68865i	−0.0624182	−	0.0868212i
$960$	−2.39060	+	0.825011i	−0.0771562	+	0.0266271i
$961$	−41.6345	−	72.1131i	−1.34305	−	2.32623i
$962$	8.97856	+	17.9428i	0.289480	+	0.578499i
$963$	−0.649087	−	0.828412i	−0.0209165	−	0.0266952i
$964$	8.71341	−	15.0921i	0.280640	−	0.486083i
$965$	−6.92556	−	11.9954i	−0.222942	−	0.386146i
$966$	−15.0105	+	6.92097i	−0.482954	+	0.222679i
$967$		−	34.3376i		−	1.10422i	−0.833771	−	0.552111i	$-0.813823\pi$
$967$		−	34.3376i		−	1.10422i	0.833771	−	0.552111i	$-0.186177\pi$
$968$	1.38671			0.0445707
$969$	−14.8059	−	42.9024i	−0.475635	−	1.37822i
$970$	−4.36868	−	2.52226i	−0.140270	−	0.0809849i
$971$	−1.24035			−0.0398046			−0.0199023	−	0.999802i	$-0.506336\pi$
$971$	−1.24035			−0.0398046			−0.0199023	+	0.999802i	$0.506336\pi$
$972$	6.53873	−	14.1508i	0.209730	−	0.453887i
$973$	24.1827	+	10.9121i	0.775261	+	0.349825i
$974$			8.67630i			0.278007i
$975$	−12.8024	−	12.5268i	−0.410004	−	0.401180i
$976$	0.865717	+	0.499822i	0.0277109	+	0.0159989i
$977$	−0.572082			−0.0183025			−0.00915126	−	0.999958i	$-0.502913\pi$
$977$	−0.572082			−0.0183025			−0.00915126	+	0.999958i	$0.502913\pi$
$978$	−1.18947	−	1.03253i	−0.0380350	−	0.0330168i
$979$	−44.0736	−	25.4459i	−1.40860	−	0.813255i
$980$	9.68832	+	3.25543i	0.309482	+	0.103991i
$981$	17.3601	+	22.1562i	0.554264	+	0.707393i
$982$		−	17.0579i		−	0.544338i
$983$	−6.05482	−	3.49575i	−0.193119	−	0.111497i	0.400323	−	0.916374i	$-0.368898\pi$
$983$	−6.05482	−	3.49575i	−0.193119	−	0.111497i	−0.593442	+	0.804877i	$0.702231\pi$
$984$	4.92578	−	1.69992i	0.157028	−	0.0541915i
$985$	8.12856	+	4.69303i	0.258997	+	0.149532i
$986$	−1.29569	+	0.748066i	−0.0412631	+	0.0238233i
$987$	−53.2366	+	24.5461i	−1.69454	+	0.781312i
$988$	−11.1358	+	5.57236i	−0.354278	+	0.177280i
$989$	−35.0569	+	20.2401i	−1.11474	+	0.643598i
$990$	5.75512	−	14.3017i	0.182910	−	0.454539i
$991$	−42.7518			−1.35806			−0.679028	−	0.734113i	$-0.737598\pi$
$991$	−42.7518			−1.35806			−0.679028	+	0.734113i	$0.737598\pi$
$992$	10.6897			0.339397
$993$	7.79436	−	40.2482i	0.247347	−	1.27724i
$994$	16.4856	+	22.9308i	0.522891	+	0.727320i
$995$	−0.923605	+	1.59973i	−0.0292803	+	0.0507149i
$996$	6.10676	−	2.10748i	0.193500	−	0.0667782i
$997$	7.73983	−	4.46859i	0.245123	−	0.141522i	−0.372406	−	0.928070i	$-0.621467\pi$
$997$	7.73983	−	4.46859i	0.245123	−	0.141522i	0.617529	+	0.786548i	$0.288134\pi$
$998$		−	23.2725i		−	0.736678i
$999$	−13.1810	−	25.7361i	−0.417028	−	0.814253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.101.16	yes	34
3.2	odd	2		546.2.bn.f.101.2	yes	34
7.5	odd	6		546.2.bi.f.257.13	yes	34
13.4	even	6		546.2.bi.e.17.7	✓	34
21.5	even	6		546.2.bi.e.257.7	yes	34
39.17	odd	6		546.2.bi.f.17.13	yes	34
91.82	odd	6		546.2.bn.f.173.2	yes	34
273.173	even	6	inner	546.2.bn.e.173.16	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.7	✓	34	13.4	even	6
546.2.bi.e.257.7	yes	34	21.5	even	6
546.2.bi.f.17.13	yes	34	39.17	odd	6
546.2.bi.f.257.13	yes	34	7.5	odd	6
546.2.bn.e.101.16	yes	34	1.1	even	1	trivial
546.2.bn.e.173.16	yes	34	273.173	even	6	inner
546.2.bn.f.101.2	yes	34	3.2	odd	2
546.2.bn.f.173.2	yes	34	91.82	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26448 + 0.730045i) q^{5} +(-1.13542 + 1.30799i) q^{6} +(-2.63261 + 0.263392i) q^{7} +1.00000 q^{8} +(2.78311 + 1.11994i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26448 + 0.730045i) q^{5} +(-1.13542 + 1.30799i) q^{6} +(-2.63261 + 0.263392i) q^{7} +1.00000 q^{8} +(2.78311 + 1.11994i) q^{9} -1.46009i q^{10} +3.51948 q^{11} +(-0.565041 - 1.63729i) q^{12} +(-0.214878 + 3.59914i) q^{13} +(1.08820 - 2.41160i) q^{14} +(-2.39060 + 0.825011i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.79359 + 6.57069i) q^{17} +(-2.36146 + 1.85028i) q^{18} -3.45362 q^{19} +(1.26448 + 0.730045i) q^{20} +(-4.56338 - 0.419048i) q^{21} +(-1.75974 + 3.04796i) q^{22} +(-3.12372 - 1.80348i) q^{23} +(1.70046 + 0.329307i) q^{24} +(-1.43407 + 2.48388i) q^{25} +(-3.00951 - 1.98566i) q^{26} +(4.36376 + 2.82092i) q^{27} +(1.54441 + 2.14821i) q^{28} +(0.170773 - 0.0985961i) q^{29} +(0.480817 - 2.48282i) q^{30} +(-5.34484 + 9.25753i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.98472 + 1.15899i) q^{33} -7.58718 q^{34} +(3.13658 - 2.25498i) q^{35} +(-0.421657 - 2.97022i) q^{36} +(-4.81918 - 2.78236i) q^{37} +(1.72681 - 2.99093i) q^{38} +(-1.55061 + 6.04943i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(2.60543 - 1.50425i) q^{41} +(2.64459 - 3.74248i) q^{42} +(5.61139 - 9.71922i) q^{43} +(-1.75974 - 3.04796i) q^{44} +(-4.33679 + 0.615658i) q^{45} +(3.12372 - 1.80348i) q^{46} +(11.0787 - 6.39629i) q^{47} +(-1.13542 + 1.30799i) q^{48} +(6.86125 - 1.38682i) q^{49} +(-1.43407 - 2.48388i) q^{50} +(4.28707 + 12.4224i) q^{51} +(3.22439 - 1.61348i) q^{52} +(4.21555 + 2.43385i) q^{53} +(-4.62487 + 2.36867i) q^{54} +(-4.45029 + 2.56938i) q^{55} +(-2.63261 + 0.263392i) q^{56} +(-5.87274 - 1.13730i) q^{57} +0.197192i q^{58} +(-1.13289 + 0.654074i) q^{59} +(1.90978 + 1.65781i) q^{60} -0.999644i q^{61} +(-5.34484 - 9.25753i) q^{62} +(-7.62183 - 2.21532i) q^{63} +1.00000 q^{64} +(-2.35583 - 4.70790i) q^{65} +(-3.99607 + 4.60343i) q^{66} -5.52864i q^{67} +(3.79359 - 6.57069i) q^{68} +(-4.71786 - 4.09541i) q^{69} +(0.384576 + 3.84385i) q^{70} +(-5.33718 + 9.24427i) q^{71} +(2.78311 + 1.11994i) q^{72} +(2.94410 - 5.09933i) q^{73} +(4.81918 - 2.78236i) q^{74} +(-3.25653 + 3.75148i) q^{75} +(1.72681 + 2.99093i) q^{76} +(-9.26540 + 0.927001i) q^{77} +(-4.46365 - 4.36759i) q^{78} +(0.174645 + 0.302494i) q^{79} -1.46009i q^{80} +(6.49145 + 6.23386i) q^{81} +3.00849i q^{82} +3.72979i q^{83} +(1.91878 + 4.16152i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(5.61139 + 9.71922i) q^{86} +(0.322861 - 0.111422i) q^{87} +3.51948 q^{88} +(-12.5228 - 7.23003i) q^{89} +(1.63522 - 4.06360i) q^{90} +(-0.382294 - 9.53173i) q^{91} +3.60696i q^{92} +(-12.1372 + 13.9819i) q^{93} +12.7926i q^{94} +(4.36702 - 2.52130i) q^{95} +(-0.565041 - 1.63729i) q^{96} +(1.72747 - 2.99206i) q^{97} +(-2.22961 + 6.63542i) q^{98} +(9.79510 + 3.94162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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