LMFDB - Embedded newform 546.2.bn.f.101.2

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			101.2
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26448 - 0.730045i) q^{5} +(-0.565041 + 1.63729i) q^{6} +(-2.63261 + 0.263392i) q^{7} -1.00000 q^{8} +(2.78311 - 1.11994i) q^{9} +O(q^{10})$	\(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} +(-0.565041 + 1.63729i) 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} +(1.13542 + 1.30799i) q^{12} +(-0.214878 + 3.59914i) q^{13} +(-1.08820 + 2.41160i) q^{14} +(-1.90978 + 1.65781i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.79359 - 6.57069i) q^{17} +(0.421657 - 2.97022i) q^{18} -3.45362 q^{19} +(-1.26448 - 0.730045i) q^{20} +(4.38990 - 1.31482i) 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} +(-2.36146 - 1.85028i) q^{36} +(-4.81918 - 2.78236i) q^{37} +(-1.72681 + 2.99093i) q^{38} +(-0.819830 - 6.19095i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(-2.60543 + 1.50425i) q^{41} +(1.05628 - 4.45918i) q^{42} +(5.61139 - 9.71922i) q^{43} +(1.75974 + 3.04796i) q^{44} +(2.70157 - 3.44794i) q^{45} +(3.12372 - 1.80348i) q^{46} +(-11.0787 + 6.39629i) q^{47} +(0.565041 - 1.63729i) q^{48} +(6.86125 - 1.38682i) q^{49} +(1.43407 + 2.48388i) q^{50} +(8.61461 + 9.92393i) q^{51} +(3.22439 - 1.61348i) q^{52} +(-4.21555 - 2.43385i) q^{53} +(0.261103 + 5.18959i) 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} +(2.39060 + 0.825011i) q^{60} -0.999644i q^{61} +(5.34484 + 9.25753i) q^{62} +(-7.03186 + 3.68142i) q^{63} +1.00000 q^{64} +(2.35583 + 4.70790i) q^{65} +(1.98865 - 5.76241i) q^{66} -5.52864i q^{67} +(-3.79359 + 6.57069i) q^{68} +(-5.90566 - 2.03808i) 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} +(1.62061 - 4.69598i) q^{75} +(1.72681 + 2.99093i) q^{76} +(9.26540 - 0.927001i) q^{77} +(-5.77144 - 2.38548i) 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} +(-3.33362 - 3.14436i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(-5.61139 - 9.71922i) q^{86} +(0.257925 - 0.223895i) 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} +(6.04010 - 17.5021i) q^{93} +12.7926i q^{94} +(-4.36702 + 2.52130i) q^{95} +(-1.13542 - 1.30799i) 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} + 3 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 + 3 * 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} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 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} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 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 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * 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 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * 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	−0.189856	−	0.981812i	$-0.560802\pi$
$5$	1.26448	−	0.730045i	0.565491	−	0.326486i	0.755346	+	0.655326i	$0.227469\pi$
$6$	−0.565041	+	1.63729i	−0.230677	+	0.668422i
$7$	−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	$-0.678026\pi$
$11$	−3.51948			−1.06116			−0.530581	+	0.847634i	$0.678026\pi$
$12$	1.13542	+	1.30799i	0.327767	+	0.377583i
$13$	−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
$15$	−1.90978	+	1.65781i	−0.493103	+	0.428045i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.79359	−	6.57069i	−0.920080	−	1.59363i	−0.799288	−	0.600948i	$-0.794790\pi$
$17$	−3.79359	−	6.57069i	−0.920080	−	1.59363i	−0.120793	−	0.992678i	$-0.538544\pi$
$18$	0.421657	−	2.97022i	0.0993855	−	0.700088i
$19$	−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
$21$	4.38990	−	1.31482i	0.957955	−	0.286918i
$22$	−1.75974	+	3.04796i	−0.375177	+	0.649826i
$23$	3.12372	+	1.80348i	0.651341	+	0.376052i	0.788970	−	0.614432i	$-0.210615\pi$
$23$	3.12372	+	1.80348i	0.651341	+	0.376052i	−0.137629	+	0.990484i	$0.543948\pi$
$24$	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	−0.515772	−	0.856726i	$-0.672495\pi$
$29$	−0.170773	+	0.0985961i	−0.0317118	+	0.0183088i	0.484060	+	0.875035i	$0.339162\pi$
$30$	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
$36$	−2.36146	−	1.85028i	−0.393576	−	0.308379i
$37$	−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
$39$	−0.819830	−	6.19095i	−0.131278	−	0.991346i
$40$	−1.26448	+	0.730045i	−0.199931	+	0.115430i
$41$	−2.60543	+	1.50425i	−0.406900	+	0.234924i	−0.689457	−	0.724327i	$-0.742151\pi$
$41$	−2.60543	+	1.50425i	−0.406900	+	0.234924i	0.282557	+	0.959250i	$0.408817\pi$
$42$	1.05628	−	4.45918i	0.162988	−	0.688066i
$43$	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
$45$	2.70157	−	3.44794i	0.402726	−	0.513989i
$46$	3.12372	−	1.80348i	0.460568	−	0.265909i
$47$	−11.0787	+	6.39629i	−1.61599	+	0.932994i	−0.628051	+	0.778172i	$0.716147\pi$
$47$	−11.0787	+	6.39629i	−1.61599	+	0.932994i	−0.987942	+	0.154822i	$0.950520\pi$
$48$	0.565041	−	1.63729i	0.0815567	−	0.236323i
$49$	6.86125	−	1.38682i	0.980178	−	0.198116i
$50$	1.43407	+	2.48388i	0.202808	+	0.351273i
$51$	8.61461	+	9.92393i	1.20629	+	1.38963i
$52$	3.22439	−	1.61348i	0.447142	−	0.223750i
$53$	−4.21555	−	2.43385i	−0.579051	−	0.334315i	0.181705	−	0.983353i	$-0.441838\pi$
$53$	−4.21555	−	2.43385i	−0.579051	−	0.334315i	−0.760756	+	0.649038i	$0.775172\pi$
$54$	0.261103	+	5.18959i	0.0355316	+	0.706213i
$55$	−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	−0.424439	−	0.905456i	$-0.639529\pi$
$59$	1.13289	−	0.654074i	0.147490	−	0.0851532i	0.571929	+	0.820303i	$0.306195\pi$
$60$	2.39060	+	0.825011i	0.308625	+	0.106508i
$61$		−	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
$63$	−7.03186	+	3.68142i	−0.885932	+	0.463816i
$64$	1.00000			0.125000
$65$	2.35583	+	4.70790i	0.292205	+	0.583943i
$66$	1.98865	−	5.76241i	0.244786	−	0.709304i
$67$		−	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
$69$	−5.90566	−	2.03808i	−0.710958	−	0.245356i
$70$	0.384576	+	3.84385i	0.0459656	+	0.459427i
$71$	5.33718	−	9.24427i	0.633407	−	1.09709i	−0.353443	−	0.935456i	$-0.614989\pi$
$71$	5.33718	−	9.24427i	0.633407	−	1.09709i	0.986850	−	0.161637i	$-0.0516773\pi$
$72$	−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
$75$	1.62061	−	4.69598i	0.187132	−	0.542245i
$76$	1.72681	+	2.99093i	0.198079	+	0.343083i
$77$	9.26540	−	0.927001i	1.05589	−	0.105642i
$78$	−5.77144	−	2.38548i	−0.653486	−	0.270103i
$79$	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	$-0.934379\pi$
$83$		−	3.72979i		−	0.409398i	0.978825	−	0.204699i	$-0.0656215\pi$
$84$	−3.33362	−	3.14436i	−0.363728	−	0.343077i
$85$	−9.59380	−	5.53898i	−1.04059	−	0.600787i
$86$	−5.61139	−	9.71922i	−0.605092	−	1.04805i
$87$	0.257925	−	0.223895i	0.0276524	−	0.0240041i
$88$	3.51948			0.375177
$89$	12.5228	+	7.23003i	1.32741	+	0.766382i	0.984899	−	0.173131i	$-0.0553885\pi$
$89$	12.5228	+	7.23003i	1.32741	+	0.766382i	0.342513	+	0.939513i	$0.388722\pi$
$90$	−1.63522	−	4.06360i	−0.172367	−	0.428341i
$91$	−0.382294	−	9.53173i	−0.0400753	−	0.999197i
$92$		−	3.60696i		−	0.376052i
$93$	6.04010	−	17.5021i	0.626330	−	1.81489i
$94$			12.7926i			1.31945i
$95$	−4.36702	+	2.52130i	−0.448047	+	0.258680i
$96$	−1.13542	−	1.30799i	−0.115883	−	0.133496i
$97$	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	$-0.696158\pi$
$101$	−11.6172			−1.15596			−0.577979	+	0.816052i	$0.696158\pi$
$102$	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
$105$	4.59104	−	4.86739i	0.448040	−	0.475008i
$106$	−4.21555	+	2.43385i	−0.409451	+	0.236397i
$107$	0.303807	+	0.175403i	0.0293701	+	0.0169568i	0.514613	−	0.857422i	$-0.327936\pi$
$107$	0.303807	+	0.175403i	0.0293701	+	0.0169568i	−0.485243	+	0.874379i	$0.661269\pi$
$108$	4.62487	+	2.36867i	0.445028	+	0.227926i
$109$	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
$111$	9.11107	+	3.14429i	0.864784	+	0.298443i
$112$	1.08820	−	2.41160i	0.102825	−	0.227875i
$113$	−5.03517	−	2.90706i	−0.473669	−	0.273473i	0.244105	−	0.969749i	$-0.421506\pi$
$113$	−5.03517	−	2.90706i	−0.473669	−	0.273473i	−0.717774	+	0.696276i	$0.754839\pi$
$114$	1.95144	−	5.65459i	0.182769	−	0.529601i
$115$	5.26649			0.491103
$116$	0.170773	+	0.0985961i	0.0158559	+	0.00915442i
$117$	3.43281	+	10.2575i	0.317363	+	0.948304i
$118$		−	1.30815i		−	0.120425i
$119$	11.7177	+	16.2988i	1.07416	+	1.49411i
$120$	1.90978	−	1.65781i	0.174338	−	0.151337i
$121$	1.38671			0.126065
$122$	−0.865717	−	0.499822i	−0.0783783	−	0.0452518i
$123$	3.93507	−	3.41589i	0.354813	−	0.308001i
$124$	10.6897			0.959961
$125$			11.4882i			1.02754i
$126$	−0.327726	+	7.93049i	−0.0291962	+	0.706504i
$127$	−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
$129$	−6.34134	+	18.3750i	−0.558324	+	1.61783i
$130$	5.25507	+	0.313742i	0.460901	+	0.0275170i
$131$	−6.32520	−	10.9556i	−0.552635	−	0.957192i	−0.998083	−	0.0618843i	$-0.980289\pi$
$131$	−6.32520	−	10.9556i	−0.552635	−	0.957192i	0.445448	−	0.895308i	$-0.353044\pi$
$132$	−3.99607	−	4.60343i	−0.347813	−	0.400677i
$133$	9.09204	−	0.909656i	0.788380	−	0.0788772i
$134$	−4.78794	−	2.76432i	−0.413615	−	0.238801i
$135$	−3.45848	+	6.75272i	−0.297658	+	0.581182i
$136$	3.79359	+	6.57069i	0.325298	+	0.563432i
$137$	−0.625790	−	1.08390i	−0.0534648	−	0.0926038i	0.838054	−	0.545587i	$-0.183693\pi$
$137$	−0.625790	−	1.08390i	−0.0534648	−	0.0926038i	−0.891519	+	0.452983i	$0.850360\pi$
$138$	−4.71786	+	4.09541i	−0.401611	+	0.348624i
$139$	−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
$141$	16.7325	−	14.5249i	1.40913	−	1.22322i
$142$	−5.33718	−	9.24427i	−0.447886	−	0.775762i
$143$	0.756260	−	12.6671i	0.0632416	−	1.05928i
$144$	−0.421657	+	2.97022i	−0.0351381	+	0.247518i
$145$	−0.143959	+	0.249345i	−0.0119552	+	0.0207069i
$146$	−2.94410	−	5.09933i	−0.243655	−	0.422024i
$147$	−11.2106	+	4.61768i	−0.924633	+	0.380859i
$148$			5.56471i			0.457417i
$149$	3.24622			0.265941			0.132970	−	0.991120i	$-0.457549\pi$
$149$	3.24622			0.265941			0.132970	+	0.991120i	$0.457549\pi$
$150$	−3.25653	−	3.75148i	−0.265895	−	0.306307i
$151$	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
$153$	−17.9168	−	14.0384i	−1.44849	−	1.13494i
$154$	3.82989	−	8.48757i	0.308622	−	0.683948i
$155$			15.6079i			1.25366i
$156$	−4.95161	+	3.80547i	−0.396446	+	0.304681i
$157$	−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
$159$	7.96985	+	2.75045i	0.632051	+	0.218125i
$160$	1.26448	+	0.730045i	0.0999656	+	0.0577151i
$161$	−8.69856	−	3.92510i	−0.685542	−	0.309341i
$162$	−2.15296	−	8.73869i	−0.169153	−	0.686577i
$163$			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
$165$	6.72142	−	5.83463i	0.523262	−	0.454225i
$166$	−3.23009	−	1.86490i	−0.250704	−	0.144744i
$167$	−11.6602	+	6.73204i	−0.902297	+	0.520941i	−0.877945	−	0.478762i	$-0.841086\pi$
$167$	−11.6602	+	6.73204i	−0.902297	+	0.520941i	−0.0243520	+	0.999703i	$0.507752\pi$
$168$	−4.38990	+	1.31482i	−0.338688	+	0.101441i
$169$	−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	$-0.626335\pi$
$173$	−10.1687			−0.773111			−0.386556	+	0.922266i	$0.626335\pi$
$174$	−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
$177$	−1.71104	+	1.48529i	−0.128610	+	0.111641i
$178$	12.5228	−	7.23003i	0.938622	−	0.541914i
$179$			8.54026i			0.638329i	0.947699	+	0.319164i	$0.103402\pi$
$179$			8.54026i			0.638329i	−0.947699	+	0.319164i	$0.896598\pi$
$180$	−4.33679	−	0.615658i	−0.323245	−	0.0458884i
$181$			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
$186$	−12.1372	−	13.9819i	−0.889945	−	1.02521i
$187$	13.3514	+	23.1254i	0.976354	+	1.69110i
$188$	11.0787	+	6.39629i	0.807997	+	0.466497i
$189$	10.7451	−	8.57574i	0.781589	−	0.623794i
$190$			5.04260i			0.365829i
$191$			20.7254i			1.49964i	0.661642	+	0.749819i	$0.269860\pi$
$191$			20.7254i			1.49964i	−0.661642	+	0.749819i	$0.730140\pi$
$192$	−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
$195$	−5.55633	−	7.22979i	−0.397897	−	0.517736i
$196$	−4.63164	−	5.24861i	−0.330832	−	0.374901i
$197$	3.21420	+	5.56716i	0.229002	+	0.396644i	0.957513	−	0.288391i	$-0.0931203\pi$
$197$	3.21420	+	5.56716i	0.229002	+	0.396644i	−0.728510	+	0.685035i	$0.759787\pi$
$198$	−1.48401	+	10.4536i	−0.105464	+	0.742906i
$199$	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
$204$	4.28707	−	12.4224i	0.300155	−	0.869744i
$205$	−2.19633	+	3.80416i	−0.153399	+	0.265694i
$206$		−	18.7349i		−	1.30532i
$207$	10.7135	+	1.52090i	0.744638	+	0.105710i
$208$	−3.00951	−	1.98566i	−0.208672	−	0.137681i
$209$	12.1549			0.840775
$210$	−1.91976	−	6.40966i	−0.132476	−	0.442308i
$211$	−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
$213$	−6.03145	+	17.4771i	−0.413268	+	1.19751i
$214$	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
$219$	−3.32708	+	9.64071i	−0.224823	+	0.651459i
$220$	4.45029	+	2.56938i	0.300039	+	0.173227i
$221$	24.4640	−	12.2418i	1.64563	−	0.823470i
$222$	7.27857	−	6.31827i	0.488506	−	0.424055i
$223$	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
$225$	−1.20937	+	8.51899i	−0.0806247	+	0.567933i
$226$	−5.03517	+	2.90706i	−0.334935	+	0.193375i
$227$	−22.0466	+	12.7286i	−1.46328	+	0.844826i	−0.999161	−	0.0409469i	$-0.986963\pi$
$227$	−22.0466	+	12.7286i	−1.46328	+	0.844826i	−0.464120	+	0.885773i	$0.653629\pi$
$228$	−3.92130	−	4.51729i	−0.259695	−	0.299165i
$229$	−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
$231$	−15.4502	+	4.62748i	−1.01655	+	0.304466i
$232$	0.170773	−	0.0985961i	0.0112118	−	0.00647315i
$233$	6.18721	−	3.57219i	0.405338	−	0.234022i	−0.283447	−	0.958988i	$-0.591478\pi$
$233$	6.18721	−	3.57219i	0.405338	−	0.234022i	0.688785	+	0.724966i	$0.258145\pi$
$234$	10.5996	+	2.15584i	0.692920	+	0.140932i
$235$	−9.33916	+	16.1759i	−0.609219	+	1.05520i
$236$	−1.13289	−	0.654074i	−0.0737448	−	0.0425766i
$237$	−0.396590	−	0.456866i	−0.0257613	−	0.0296767i
$238$	19.9741	−	1.99840i	1.29473	−	0.129537i
$239$	7.32463			0.473791			0.236896	−	0.971535i	$-0.423870\pi$
$239$	7.32463			0.473791			0.236896	+	0.971535i	$0.423870\pi$
$240$	−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	−0.590614	−	0.806954i	$-0.701114\pi$
$251$	6.39321	−	11.0734i	0.403536	−	0.698944i	0.994150	+	0.108010i	$0.0344478\pi$
$252$	6.70414	+	4.24906i	0.422321	+	0.267666i
$253$	−10.9939	−	6.34731i	−0.691178	−	0.399052i
$254$	−15.7588			−0.988795
$255$	18.1379	+	6.25951i	1.13584	+	0.391986i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.6730	−	18.4862i	0.665764	−	1.15314i	−0.313314	−	0.949650i	$-0.601439\pi$
$257$	10.6730	−	18.4862i	0.665764	−	1.15314i	0.979078	−	0.203487i	$-0.0652275\pi$
$258$	12.7425	+	14.6793i	0.793316	+	0.913891i
$259$	13.4199	+	6.05552i	0.833870	+	0.376272i
$260$	2.89925	−	4.39416i	0.179804	−	0.272514i
$261$	−0.364860	+	0.465661i	−0.0225843	+	0.0288237i
$262$	−12.6504			−0.781544
$263$			15.9137i			0.981283i	0.871362	+	0.490641i	$0.163237\pi$
$263$			15.9137i			0.981283i	−0.871362	+	0.490641i	$0.836763\pi$
$264$	−5.98472	+	1.15899i	−0.368334	+	0.0713307i
$265$	−7.10729			−0.436597
$266$	3.75823	−	8.32876i	0.230432	−	0.510669i
$267$	−23.6754	−	8.17053i	−1.44891	−	0.500028i
$268$	−4.78794	+	2.76432i	−0.292470	+	0.168858i
$269$	7.74959	+	13.4227i	0.472501	+	0.818396i	0.999505	−	0.0314670i	$-0.0100179\pi$
$269$	7.74959	+	13.4227i	0.472501	+	0.818396i	−0.527004	+	0.849863i	$0.676685\pi$
$270$	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
$273$	3.78894	+	16.0824i	0.229317	+	0.973352i
$274$	−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
$279$	−4.50738	+	31.7507i	−0.269850	+	1.90086i
$280$	3.13658	−	2.25498i	0.187447	−	0.134761i
$281$	7.30448			0.435749			0.217874	−	0.975977i	$-0.430088\pi$
$281$	7.30448			0.435749			0.217874	+	0.975977i	$0.430088\pi$
$282$	−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
$285$	6.59566	−	5.72546i	0.390693	−	0.339147i
$286$	−10.5919	−	6.98849i	−0.626312	−	0.413238i
$287$	6.46287	−	4.64634i	0.381491	−	0.274265i
$288$	2.36146	+	1.85028i	0.139150	+	0.109029i
$289$	−20.2826	+	35.1306i	−1.19310	+	2.06650i
$290$	0.143959	+	0.249345i	0.00845358	+	0.0146420i
$291$	−1.95218	+	5.65675i	−0.114439	+	0.331604i
$292$	−5.88820			−0.344581
$293$	−13.1158	−	7.57239i	−0.766231	−	0.442384i	0.0652973	−	0.997866i	$-0.479200\pi$
$293$	−13.1158	−	7.57239i	−0.766231	−	0.442384i	−0.831529	+	0.555482i	$0.812534\pi$
$294$	−1.60627	+	12.0175i	−0.0936793	+	0.700874i
$295$	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
$309$	−24.5050	+	21.2719i	−1.39404	+	1.21012i
$310$	13.5168	+	7.80394i	0.767704	+	0.443234i
$311$	5.96970	−	10.3398i	0.338511	−	0.586318i	−0.645642	−	0.763640i	$-0.723410\pi$
$311$	5.96970	−	10.3398i	0.338511	−	0.586318i	0.984153	+	0.177322i	$0.0567435\pi$
$312$	0.819830	+	6.19095i	0.0464137	+	0.350494i
$313$	−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
$315$	−6.20402	+	9.78865i	−0.349557	+	0.551528i
$316$	0.174645	−	0.302494i	0.00982454	−	0.0170166i
$317$	−11.5121	−	19.9395i	−0.646582	−	1.11991i	−0.983934	−	0.178534i	$-0.942864\pi$
$317$	−11.5121	−	19.9395i	−0.646582	−	1.11991i	0.337352	−	0.941379i	$-0.390469\pi$
$318$	6.36689	−	5.52687i	0.357037	−	0.309932i
$319$	0.601033	−	0.347007i	0.0336514	−	0.0194286i
$320$	1.26448	−	0.730045i	0.0706863	−	0.0408108i
$321$	−0.574372	−	0.198220i	−0.0320583	−	0.0110635i
$322$	−7.74851	+	5.57062i	−0.431808	+	0.310439i
$323$	13.1016	+	22.6927i	0.728994	+	1.26265i
$324$	−8.64441	−	2.50483i	−0.480245	−	0.139157i
$325$	−8.63168	−	5.69515i	−0.478800	−	0.315910i
$326$	0.787553	+	0.454694i	0.0436185	+	0.0251832i
$327$	−15.3618	−	5.30145i	−0.849508	−	0.293171i
$328$	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
$333$	−16.5284	−	2.34640i	−0.905752	−	0.128582i
$334$			13.4641i			0.736722i
$335$	−4.03616	−	6.99083i	−0.220519	−	0.381950i
$336$	−1.05628	+	4.45918i	−0.0576249	+	0.243268i
$337$	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
$339$	9.51941	+	3.28521i	0.517023	+	0.178428i
$340$			11.0780i			0.600787i
$341$	18.8110	−	32.5816i	1.01867	−	1.76439i
$342$	−1.45625	+	10.2580i	−0.0787447	+	0.554690i
$343$	−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	−0.999581	−	0.0289382i	$-0.990787\pi$
$347$	−27.4634	+	15.8560i	−1.47431	+	0.851194i	−0.474729	+	0.880132i	$0.657454\pi$
$348$	−0.322861	−	0.111422i	−0.0173072	−	0.00597283i
$349$	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
$351$	−9.21520	−	16.3120i	−0.491871	−	0.870668i
$352$	−1.75974	−	3.04796i	−0.0937944	−	0.162457i
$353$			0.567754i			0.0302185i	0.999886	+	0.0151092i	$0.00480960\pi$
$353$			0.567754i			0.0302185i	−0.999886	+	0.0151092i	$0.995190\pi$
$354$	0.430782	+	2.22445i	0.0228958	+	0.118228i
$355$		−	15.5855i		−	0.827194i
$356$		−	14.4601i		−	0.766382i
$357$	−25.2928	−	23.8568i	−1.33864	−	1.26264i
$358$	7.39608	+	4.27013i	0.390895	+	0.225683i
$359$	3.12906	+	5.41969i	0.165145	+	0.286040i	0.936707	−	0.350115i	$-0.113857\pi$
$359$	3.12906	+	5.41969i	0.165145	+	0.286040i	−0.771562	+	0.636155i	$0.780524\pi$
$360$	−2.70157	+	3.44794i	−0.142385	+	0.181722i
$361$	−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
$366$	1.63671	+	0.564840i	0.0855522	+	0.0295247i
$367$		−	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
$369$	−5.56654	+	7.10442i	−0.289782	+	0.369841i
$370$	−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
$378$	−2.05428	−	13.5934i	−0.105661	−	0.699168i
$379$	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
$381$	17.8928	+	20.6123i	0.916676	+	1.05600i
$382$	17.9487	+	10.3627i	0.918338	+	0.530202i
$383$		−	1.34855i		−	0.0689079i	−0.999406	−	0.0344540i	$-0.989031\pi$
$383$		−	1.34855i		−	0.0689079i	0.999406	−	0.0344540i	$-0.0109692\pi$
$384$	−0.565041	+	1.63729i	−0.0288346	+	0.0835528i
$385$	11.0391	−	7.93633i	0.562606	−	0.404473i
$386$	8.21554	+	4.74324i	0.418160	+	0.241425i
$387$	4.73217	−	33.3341i	0.240550	−	1.69447i
$388$	−3.45494			−0.175398
$389$	−3.70239	−	2.13758i	−0.187719	−	0.108379i	0.403196	−	0.915114i	$-0.367899\pi$
$389$	−3.70239	−	2.13758i	−0.187719	−	0.108379i	−0.590914	+	0.806734i	$0.701233\pi$
$390$	−9.03935	+	1.19703i	−0.457725	+	0.0606137i
$391$		−	27.3667i		−	1.38399i
$392$	−6.86125	+	1.38682i	−0.346545	+	0.0700447i
$393$	14.3635	+	16.5465i	0.724541	+	0.834663i
$394$	6.42840			0.323858
$395$	0.441668	+	0.254997i	0.0222228	+	0.0128303i
$396$	8.31109	+	6.51200i	0.417648	+	0.327240i
$397$	−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
$399$	−15.1611	+	4.54090i	−0.759003	+	0.227329i
$400$	−1.43407	−	2.48388i	−0.0717034	−	0.124194i
$401$	−10.9880	+	19.0318i	−0.548717	+	0.950405i	0.449646	+	0.893207i	$0.351550\pi$
$401$	−10.9880	+	19.0318i	−0.548717	+	0.950405i	−0.998363	+	0.0571984i	$0.981783\pi$
$402$	9.05200	+	3.12391i	0.451473	+	0.155806i
$403$	−32.1707	−	21.2261i	−1.60254	−	1.05735i
$404$	5.80861	+	10.0608i	0.288989	+	0.500544i
$405$	3.65728	−	12.6216i	0.181732	−	0.627173i
$406$	−0.0519388	−	0.519130i	−0.00257768	−	0.0257640i
$407$	16.9610	+	9.79244i	0.840726	+	0.485393i
$408$	−8.61461	−	9.92393i	−0.426487	−	0.491308i
$409$	−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
$411$	1.42106	+	1.63705i	0.0700959	+	0.0807497i
$412$	−16.2249	−	9.36744i	−0.799343	−	0.461501i
$413$	−2.81017	+	2.02031i	−0.138280	+	0.0994131i
$414$	6.67388	−	8.51769i	0.328003	−	0.418622i
$415$	−2.72292	−	4.71623i	−0.133663	−	0.231511i
$416$	−3.22439	+	1.61348i	−0.158089	+	0.0791074i
$417$	16.4182	+	5.66603i	0.804002	+	0.277467i
$418$	6.07747	−	10.5265i	0.297259	−	0.514868i
$419$	−12.4744	−	21.6063i	−0.609413	−	1.05553i	−0.991337	−	0.131341i	$-0.958072\pi$
$419$	−12.4744	−	21.6063i	−0.609413	−	1.05553i	0.381924	−	0.924194i	$-0.375262\pi$
$420$	−6.51080	−	1.54227i	−0.317695	−	0.0752549i
$421$			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
$423$	−23.6698	+	30.2091i	−1.15086	+	1.46882i
$424$	4.21555	+	2.43385i	0.204725	+	0.118198i
$425$	21.7611			1.05557
$426$	12.1199	+	13.9619i	0.587209	+	0.676457i
$427$	0.263298	+	2.63167i	0.0127419	+	0.127355i
$428$		−	0.350806i		−	0.0169568i
$429$	2.88537	+	21.7889i	0.139307	+	1.05198i
$430$	−14.1909	−	8.19314i	−0.684348	−	0.395108i
$431$	−22.7370			−1.09520			−0.547602	−	0.836739i	$-0.684459\pi$
$431$	−22.7370			−1.09520			−0.547602	+	0.836739i	$0.684459\pi$
$432$	−0.261103	−	5.18959i	−0.0125623	−	0.249684i
$433$	−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
$435$	0.162686	−	0.471407i	0.00780018	−	0.0226022i
$436$		−	9.38242i		−	0.449337i
$437$	−10.7882	−	6.22855i	−0.516068	−	0.297952i
$438$	6.68556	+	7.70169i	0.319449	+	0.368001i
$439$	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
$441$	17.5425	−	11.5439i	0.835356	−	0.549709i
$442$	1.63032	−	27.3073i	0.0775465	−	1.29888i
$443$	−1.94173	+	1.12106i	−0.0922543	+	0.0532630i	−0.545417	−	0.838165i	$-0.683629\pi$
$443$	−1.94173	+	1.12106i	−0.0922543	+	0.0532630i	0.453163	+	0.891428i	$0.350296\pi$
$444$	−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	−0.943564	−	0.331190i	$-0.892550\pi$
$449$	−3.91929	+	6.78842i	−0.184963	+	0.320365i	0.758601	+	0.651555i	$0.225883\pi$
$450$	6.77298	+	5.30684i	0.319281	+	0.250167i
$451$	9.16975	−	5.29416i	0.431787	−	0.249292i
$452$			5.81411i			0.273473i
$453$	−15.2045	−	5.24719i	−0.714372	−	0.246535i
$454$			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
$459$	35.0897	+	17.9715i	1.63785	+	0.838840i
$460$	−2.63325	−	4.56092i	−0.122776	−	0.212654i
$461$	−20.3030	−	11.7219i	−0.945606	−	0.545946i	−0.0538925	−	0.998547i	$-0.517163\pi$
$461$	−20.3030	−	11.7219i	−0.945606	−	0.545946i	−0.891713	+	0.452601i	$0.850496\pi$
$462$	−3.71756	+	15.6940i	−0.172957	+	0.730150i
$463$			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	0.933337	−	0.359001i	$-0.116882\pi$
$467$	3.36611	+	5.83027i	0.155765	+	0.269792i	−0.777572	+	0.628793i	$0.783549\pi$
$468$	7.16683	−	8.10164i	0.331287	−	0.374498i
$469$	1.45620	+	14.5547i	0.0672410	+	0.672075i
$470$	9.33916	+	16.1759i	0.430783	+	0.746138i
$471$	30.6852	+	10.5897i	1.41390	+	0.487946i
$472$	−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
$477$	−14.4581	−	2.05250i	−0.661993	−	0.0939776i
$478$	3.66232	−	6.34332i	0.167510	−	0.290137i
$479$		−	12.9489i		−	0.591650i	−0.955242	−	0.295825i	$-0.904405\pi$
$479$		−	12.9489i		−	0.591650i	0.955242	−	0.295825i	$-0.0955946\pi$
$480$	−2.39060	−	0.825011i	−0.109115	−	0.0376564i
$481$	11.0496	−	16.7471i	0.503820	−	0.763600i
$482$	17.4268			0.793769
$483$	16.0841	+	3.80997i	0.731852	+	0.173360i
$484$	−0.693357	−	1.20093i	−0.0315162	−	0.0545877i
$485$		−	5.04452i		−	0.229060i
$486$	6.53873	+	14.1508i	0.296603	+	0.641893i
$487$	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	−0.128140	−	0.991756i	$-0.540901\pi$
$491$	14.7725	−	8.52893i	0.666676	−	0.384905i	0.794816	+	0.606851i	$0.207567\pi$
$492$	−4.92578	−	1.69992i	−0.222071	−	0.0766384i
$493$	1.29569	+	0.748066i	0.0583549	+	0.0336912i
$494$	−10.3937	−	6.85773i	−0.467635	−	0.308544i
$495$	−9.50811	+	12.1349i	−0.427358	+	0.545425i
$496$	−5.34484	−	9.25753i	−0.239990	−	0.415675i
$497$	−11.6158	+	25.7423i	−0.521042	+	1.15470i
$498$	6.10676	+	2.10748i	0.273650	+	0.0944386i
$499$	−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
$501$	17.6108	−	15.2874i	0.786794	−	0.682988i
$502$	−6.39321	−	11.0734i	−0.285343	−	0.494228i
$503$	4.33129	−	7.50201i	0.193122	−	0.334498i	−0.753161	−	0.657836i	$-0.771472\pi$
$503$	4.33129	−	7.50201i	0.193122	−	0.334498i	0.946283	+	0.323338i	$0.104805\pi$
$504$	7.03186	−	3.68142i	0.313224	−	0.163984i
$505$	−14.6897	+	8.48110i	−0.653683	+	0.377404i
$506$	−10.9939	+	6.34731i	−0.488737	+	0.282172i
$507$	22.4583	−	1.62038i	0.997407	−	0.0719637i
$508$	−7.87940	+	13.6475i	−0.349592	+	0.605511i
$509$	−5.00911	−	2.89201i	−0.222025	−	0.128186i	0.384863	−	0.922974i	$-0.374249\pi$
$509$	−5.00911	−	2.89201i	−0.222025	−	0.128186i	−0.606887	+	0.794788i	$0.707582\pi$
$510$	14.4898	−	12.5781i	0.641621	−	0.556968i
$511$	−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	−0.721109	−	0.692822i	$-0.756367\pi$
$521$	5.46547	−	9.46647i	0.239447	−	0.414734i	0.960556	+	0.278088i	$0.0897007\pi$
$522$	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
$525$	−3.02956	+	12.7895i	−0.132221	+	0.558181i
$526$	13.7817	+	7.95686i	0.600910	+	0.346936i
$527$	81.1044			3.53296
$528$	−1.98865	+	5.76241i	−0.0865448	+	0.250777i
$529$	−4.99491	−	8.65143i	−0.217170	−	0.376149i
$530$	−3.55364	+	6.15509i	−0.154360	+	0.267360i
$531$	2.42043	−	3.08913i	0.105038	−	0.134057i
$532$	−5.33380	−	7.41911i	−0.231250	−	0.321659i
$533$	−4.85414	−	9.70054i	−0.210256	−	0.420177i
$534$	−18.9136	+	16.4182i	−0.818470	+	0.710485i
$535$	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
$540$	7.57727	−	0.381234i	0.326074	−	0.0164057i
$541$	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
$546$	15.8222	+	4.75989i	0.677130	+	0.203705i
$547$	−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
$552$	5.90566	+	2.03808i	0.251361	+	0.0867466i
$553$	−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	$-0.663863\pi$
$557$	−23.2398			−0.984703			−0.492351	+	0.870396i	$0.663863\pi$
$558$	25.2432	+	19.7788i	1.06863	+	0.837305i
$559$	33.7751	+	22.2847i	1.42853	+	0.942541i
$560$	−0.384576	−	3.84385i	−0.0162513	−	0.162432i
$561$	−30.3189	−	34.9270i	−1.28007	−	1.47462i
$562$	3.65224	−	6.32587i	0.154060	−	0.266841i
$563$	−5.93878	−	10.2863i	−0.250290	−	0.433515i	0.713316	−	0.700843i	$-0.247193\pi$
$563$	−5.93878	−	10.2863i	−0.250290	−	0.433515i	−0.963606	+	0.267328i	$0.913859\pi$
$564$	−20.9452	−	7.22833i	−0.881951	−	0.304368i
$565$	−8.48913			−0.357141
$566$	12.9252	+	7.46234i	0.543285	+	0.313666i
$567$	−15.4475	+	18.1211i	−0.648734	+	0.761015i
$568$	−5.33718	+	9.24427i	−0.223943	+	0.387881i
$569$	−1.67254	−	0.965640i	−0.0701164	−	0.0404817i	0.464532	−	0.885556i	$-0.346223\pi$
$569$	−1.67254	−	0.965640i	−0.0701164	−	0.0404817i	−0.534648	+	0.845075i	$0.679556\pi$
$570$	−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
$582$	3.92279	+	4.51901i	0.162605	+	0.187319i
$583$	14.8365	+	8.56588i	0.614467	+	0.354763i
$584$	−2.94410	+	5.09933i	−0.121828	+	0.211012i
$585$	11.8291	+	10.4642i	0.489074	+	0.432642i
$586$	−13.1158	+	7.57239i	−0.541807	+	0.312813i
$587$	−3.62595	+	2.09345i	−0.149659	+	0.0864058i	−0.572960	−	0.819584i	$-0.694205\pi$
$587$	−3.62595	+	2.09345i	−0.149659	+	0.0864058i	0.423300	+	0.905989i	$0.360871\pi$
$588$	9.60431	+	7.39981i	0.396075	+	0.305163i
$589$	18.4591	−	31.9720i	0.760592	−	1.31738i
$590$	−0.955007	−	1.65412i	−0.0393170	−	0.0680991i
$591$	−7.29892	−	8.40827i	−0.300237	−	0.345870i
$592$	4.81918	−	2.78236i	0.198067	−	0.114354i
$593$	25.7814	−	14.8849i	1.05872	−	0.611250i	0.133639	−	0.991030i	$-0.457334\pi$
$593$	25.7814	−	14.8849i	1.05872	−	0.611250i	0.925077	+	0.379780i	$0.124000\pi$
$594$	−0.918945	−	18.2646i	−0.0377048	−	0.749407i
$595$	26.7156	+	12.0550i	1.09523	+	0.494209i
$596$	−1.62311	−	2.81131i	−0.0664852	−	0.115156i
$597$	−1.65478	+	1.43645i	−0.0677256	+	0.0587902i
$598$	5.81977	+	11.6303i	0.237988	+	0.475596i
$599$	14.8413	+	8.56865i	0.606401	+	0.350106i	0.771556	−	0.636162i	$-0.219479\pi$
$599$	14.8413	+	8.56865i	0.606401	+	0.350106i	−0.165155	+	0.986268i	$0.552812\pi$
$600$	−1.62061	+	4.69598i	−0.0661613	+	0.191713i
$601$	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
$606$	6.56421	−	19.0208i	0.266653	−	0.772667i
$607$			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
$609$	−0.620042	+	0.657364i	−0.0251254	+	0.0266377i
$610$	−1.45957			−0.0590963
$611$	−20.6406	−	41.2482i	−0.835028	−	1.66872i
$612$	−3.19919	+	22.5356i	−0.129320	+	0.910947i
$613$		−	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
$615$	2.48204	−	7.19209i	0.100085	−	0.290013i
$616$	−9.26540	+	0.927001i	−0.373314	+	0.0373500i
$617$	2.03229	−	3.52003i	0.0818170	−	0.141711i	−0.822213	−	0.569179i	$-0.807261\pi$
$617$	2.03229	−	3.52003i	0.0818170	−	0.141711i	0.904030	+	0.427468i	$0.140594\pi$
$618$	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
$621$	−18.7187	+	0.941788i	−0.751154	+	0.0377927i
$622$	−5.96970	−	10.3398i	−0.239363	−	0.414589i
$623$	−34.8719	−	15.7354i	−1.39711	−	0.630427i
$624$	5.77144	+	2.38548i	0.231042	+	0.0954957i
$625$	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
$630$	5.37521	+	10.2672i	0.214154	+	0.409053i
$631$	−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
$633$	14.1831	+	16.3388i	0.563728	+	0.649408i
$634$	−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
$639$	4.50092	−	31.7052i	0.178054	−	1.25424i
$640$		−	1.46009i		−	0.0577151i
$641$	−19.9139	+	11.4973i	−0.786552	+	0.454116i	−0.838747	−	0.544521i	$-0.816711\pi$
$641$	−19.9139	+	11.4973i	−0.786552	+	0.454116i	0.0521953	+	0.998637i	$0.483378\pi$
$642$	−0.458849	+	0.398311i	−0.0181093	+	0.0157201i
$643$	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	$-0.185288\pi$
$647$	42.4942			1.67062			0.835309	+	0.549780i	$0.185288\pi$
$648$	−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
$651$	−11.2913	+	47.6671i	−0.442541	+	1.86822i
$652$	0.787553	−	0.454694i	0.0308430	−	0.0178072i
$653$	18.7413	+	10.8203i	0.733404	+	0.423431i	0.819666	−	0.572841i	$-0.194159\pi$
$653$	18.7413	+	10.8203i	0.733404	+	0.423431i	−0.0862619	+	0.996272i	$0.527492\pi$
$654$	−12.2721	+	10.6530i	−0.479876	+	0.416564i
$655$	−15.9961	−	9.23536i	−0.625020	−	0.360855i
$656$		−	3.00849i		−	0.117462i
$657$	2.48280	−	17.4893i	0.0968633	−	0.682321i
$658$	−3.36946	−	33.6778i	−0.131355	−	1.31290i
$659$	4.44211	+	2.56466i	0.173040	+	0.0999048i	0.584019	−	0.811740i	$-0.301480\pi$
$659$	4.44211	+	2.56466i	0.173040	+	0.0999048i	−0.410978	+	0.911645i	$0.634813\pi$
$660$	−8.41365	−	2.90361i	−0.327501	−	0.113023i
$661$	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
$663$	−37.5687	+	28.8728i	−1.45905	+	1.12133i
$664$			3.72979i			0.144744i
$665$	10.8326	−	7.78784i	0.420069	−	0.301999i
$666$	−10.2963	+	13.1408i	−0.398972	+	0.509197i
$667$	−0.711265			−0.0275403
$668$	11.6602	+	6.73204i	0.451148	+	0.260471i
$669$	−8.59637	−	9.90291i	−0.332355	−	0.382869i
$670$	−8.07231			−0.311861
$671$			3.51822i			0.135819i
$672$	3.33362	+	3.14436i	0.128597	+	0.121296i
$673$	−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
$675$	−0.748878	−	14.8844i	−0.0288243	−	0.572902i
$676$	5.11430	+	11.9517i	0.196704	+	0.459682i
$677$	18.1468	+	31.4312i	0.697439	+	1.20800i	0.969352	+	0.245678i	$0.0790105\pi$
$677$	18.1468	+	31.4312i	0.697439	+	1.20800i	−0.271913	+	0.962322i	$0.587656\pi$
$678$	7.60478	−	6.60144i	0.292060	−	0.253527i
$679$	−3.75966	+	8.33193i	−0.144283	+	0.319750i
$680$	9.59380	+	5.53898i	0.367905	+	0.212410i
$681$	33.2976	−	28.9045i	1.27597	−	1.10762i
$682$	−18.8110	−	32.5816i	−0.720311	−	1.24762i
$683$	−18.2874	−	31.6746i	−0.699747	−	1.21200i	−0.968554	−	0.248803i	$-0.919963\pi$
$683$	−18.2874	−	31.6746i	−0.699747	−	1.21200i	0.268808	−	0.963194i	$-0.413370\pi$
$684$	8.15558	+	6.39016i	0.311837	+	0.244334i
$685$	−1.58259	−	0.913710i	−0.0604677	−	0.0349110i
$686$	−4.12197	+	18.0557i	−0.157377	+	0.689371i
$687$	12.5215	+	14.4246i	0.477726	+	0.550334i
$688$	5.61139	+	9.71922i	0.213932	+	0.370542i
$689$	9.66561	−	14.6494i	0.368230	−	0.558098i
$690$	−2.97579	+	8.62279i	−0.113286	+	0.328264i
$691$	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
$693$	24.7485	−	12.9567i	0.940117	−	0.492184i
$694$			31.7120i			1.20377i
$695$	−14.6413			−0.555375
$696$	−0.257925	+	0.223895i	−0.00977661	+	0.00848673i
$697$	19.7679	+	11.4130i	0.748761	+	0.432297i
$698$	7.75670			0.293595
$699$	−9.34475	+	8.11185i	−0.353451	+	0.306818i
$700$	−7.55068	+	0.755444i	−0.285389	+	0.0285531i
$701$		−	42.7684i		−	1.61534i	−0.589635	−	0.807670i	$-0.700728\pi$
$701$		−	42.7684i		−	1.61534i	0.589635	−	0.807670i	$-0.299272\pi$
$702$	−18.7342	−	0.175385i	−0.707076	−	0.00661948i
$703$	16.6436	+	9.60922i	0.627727	+	0.362418i
$704$	−3.51948			−0.132645
$705$	10.5540	−	30.5819i	0.397487	−	1.15178i
$706$	0.491689	+	0.283877i	0.0185050	+	0.0106838i
$707$	30.5836	−	3.05988i	1.15021	−	0.115079i
$708$	2.14182	+	0.739157i	0.0804946	+	0.0277792i
$709$			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
$711$	0.824833	+	0.646283i	0.0309337	+	0.0242375i
$712$	−12.5228	−	7.23003i	−0.469311	−	0.270957i
$713$	−33.3916	+	19.2786i	−1.25052	+	0.721990i
$714$	−33.3070	+	9.97579i	−1.24648	+	0.373334i
$715$	−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	$-0.615764\pi$
$719$	−19.0766			−0.711439			−0.355719	+	0.934593i	$0.615764\pi$
$720$	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
$723$	−19.7867	−	22.7940i	−0.735875	−	0.847719i
$724$	22.0628	−	12.7380i	0.819957	−	0.473402i
$725$		−	0.565574i		−	0.0210049i
$726$	−0.783550	+	2.27046i	−0.0290803	+	0.0842645i
$727$			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
$732$	1.30752	−	1.13501i	0.0483274	−	0.0419513i
$733$	−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
$735$	−10.8044	+	14.0232i	−0.398526	+	0.517252i
$736$			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
$741$	2.83138	+	21.3812i	0.104013	+	0.785459i
$742$	10.4568	−	7.51772i	0.383883	−	0.275984i
$743$	19.9808	+	34.6077i	0.733023	+	1.26963i	0.955585	+	0.294715i	$0.0952248\pi$
$743$	19.9808	+	34.6077i	0.733023	+	1.26963i	−0.222562	+	0.974919i	$0.571442\pi$
$744$	−6.04010	+	17.5021i	−0.221441	+	0.641659i
$745$	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
$750$	−18.8095	−	6.49130i	−0.686827	−	0.237029i
$751$	−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
$753$	−7.22485	+	20.9351i	−0.263288	+	0.762918i
$754$	−0.709723	−	0.0423724i	−0.0258466	−	0.00154311i
$755$	13.5590			0.493462
$756$	−12.7993	−	5.01763i	−0.465508	−	0.182490i
$757$	−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
$759$	20.7848	+	7.17298i	0.754441	+	0.260363i
$760$	4.36702	−	2.52130i	0.158409	−	0.0914572i
$761$			41.8084i			1.51555i	0.652515	+	0.757776i	$0.273714\pi$
$761$			41.8084i			1.51555i	−0.652515	+	0.757776i	$0.726286\pi$
$762$	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
$765$	−32.9040	−	4.67110i	−1.18965	−	0.168884i
$766$	−1.16788	−	0.674277i	−0.0421973	−	0.0243626i
$767$	2.11067	+	4.21798i	0.0762119	+	0.152302i
$768$	1.13542	+	1.30799i	0.0409708	+	0.0471979i
$769$	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
$771$	−12.0614	+	34.9497i	−0.434380	+	1.25868i
$772$	8.21554	−	4.74324i	0.295684	−	0.170713i
$773$	−20.0435	+	11.5721i	−0.720916	+	0.416221i	−0.815090	−	0.579335i	$-0.803312\pi$
$773$	−20.0435	+	11.5721i	−0.720916	+	0.416221i	0.0941738	+	0.995556i	$0.469979\pi$
$774$	−26.5021	−	20.7653i	−0.952600	−	0.746392i
$775$	−15.3297	−	26.5518i	−0.550660	−	0.953770i
$776$	−1.72747	+	2.99206i	−0.0620125	+	0.107409i
$777$	−24.8141	−	5.87791i	−0.890199	−	0.210869i
$778$	−3.70239	+	2.13758i	−0.132737	+	0.0766358i
$779$	8.99817	−	5.19510i	0.322393	−	0.186134i
$780$	−3.48302	+	8.42682i	−0.124712	+	0.301729i
$781$	−18.7841	+	32.5350i	−0.672147	+	1.16419i
$782$	−23.7002	−	13.6833i	−0.847519	−	0.489315i
$783$	0.467084	−	0.911987i	0.0166922	−	0.0325918i
$784$	−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	−0.953710	−	0.300727i	$-0.902771\pi$
$797$	−6.10975	+	10.5824i	−0.216418	+	0.374848i	0.737292	+	0.675574i	$0.236104\pi$
$798$	−3.64800	+	15.4003i	−0.129138	+	0.545166i
$799$	84.0560	+	48.5298i	2.97369	+	1.71686i
$800$	−2.86814			−0.101404
$801$	42.9496	+	6.09719i	1.51755	+	0.215434i
$802$	10.9880	+	19.0318i	0.388001	+	0.672038i
$803$	−10.3617	+	17.9470i	−0.365656	+	0.633335i
$804$	7.23138	−	6.27731i	0.255031	−	0.221384i
$805$	−13.8646	+	1.38715i	−0.488663	+	0.0488907i
$806$	−34.4676	+	17.2476i	−1.21407	+	0.607520i
$807$	−17.5980	−	20.2727i	−0.619480	−	0.713634i
$808$	11.6172			0.408693
$809$			29.4579i			1.03568i	0.855476	+	0.517842i	$0.173264\pi$
$809$			29.4579i			1.03568i	−0.855476	+	0.517842i	$0.826736\pi$
$810$	−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
$813$	−8.47368	+	24.5538i	−0.297185	+	0.861139i
$814$	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
$819$	−11.7390	−	26.0997i	−0.410193	−	0.911999i
$820$	4.39267			0.153399
$821$	−11.8239	+	20.4797i	−0.412658	+	0.714745i	−0.995179	−	0.0980703i	$-0.968733\pi$
$821$	−11.8239	+	20.4797i	−0.412658	+	0.714745i	0.582521	+	0.812816i	$0.302066\pi$
$822$	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
$825$	−5.70371	+	16.5274i	−0.198578	+	0.575410i
$826$	0.344555	+	3.44384i	0.0119886	+	0.119827i
$827$	−38.3054			−1.33201			−0.666004	−	0.745948i	$-0.731997\pi$
$827$	−38.3054			−1.33201			−0.666004	+	0.745948i	$0.731997\pi$
$828$	−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
$831$	−0.816764	−	0.940902i	−0.0283332	−	0.0326395i
$832$	−0.214878	+	3.59914i	−0.00744957	+	0.124778i
$833$	−35.1411	−	39.8221i	−1.21757	−	1.37975i
$834$	13.1160	−	11.3856i	0.454170	−	0.394249i
$835$	−9.82939	+	17.0250i	−0.340160	+	0.589175i
$836$	−6.07747	−	10.5265i	−0.210194	−	0.364066i
$837$	−2.79110	−	55.4750i	−0.0964746	−	1.91750i
$838$	−24.9488			−0.861840
$839$	28.0544	+	16.1972i	0.968547	+	0.559191i	0.898793	−	0.438373i	$-0.144445\pi$
$839$	28.0544	+	16.1972i	0.968547	+	0.559191i	0.0697541	+	0.997564i	$0.477779\pi$
$840$	−4.59104	+	4.86739i	−0.158406	+	0.167941i
$841$	−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
$855$	−9.33021	+	11.9079i	−0.319086	+	0.407241i
$856$	−0.303807	−	0.175403i	−0.0103839	−	0.00599514i
$857$	1.02659	−	1.77810i	0.0350675	−	0.0607387i	−0.847959	−	0.530062i	$-0.822169\pi$
$857$	1.02659	−	1.77810i	0.0350675	−	0.0607387i	0.883027	+	0.469323i	$0.155502\pi$
$858$	20.3124	+	8.39565i	0.693455	+	0.286623i
$859$	−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
$861$	−9.45977	+	10.0292i	−0.322388	+	0.341793i
$862$	−11.3685	+	19.6908i	−0.387213	+	0.670672i
$863$	−10.0096	−	17.3372i	−0.340732	−	0.590165i	0.643837	−	0.765163i	$-0.277342\pi$
$863$	−10.0096	−	17.3372i	−0.340732	−	0.590165i	−0.984569	+	0.174998i	$0.944008\pi$
$864$	−4.62487	−	2.36867i	−0.157341	−	0.0805839i
$865$	−12.8581	+	7.42361i	−0.437187	+	0.252410i
$866$	−11.9025	+	6.87194i	−0.404465	+	0.233518i
$867$	22.9210	−	66.4172i	0.778439	−	2.25565i
$868$	−28.1417	+	2.81557i	−0.955192	+	0.0955667i
$869$	−0.614659	−	1.06462i	−0.0208509	−	0.0361148i
$870$	−0.326907	−	0.376593i	−0.0110832	−	0.0127677i
$871$	19.8984	+	1.18799i	0.674230	+	0.0402534i
$872$	−8.12542	−	4.69121i	−0.275161	−	0.158864i
$873$	1.45680	−	10.2619i	0.0493052	−	0.347314i
$874$	−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
$879$	24.7964	+	8.55742i	0.836363	+	0.288635i
$880$		−	5.13875i		−	0.173227i
$881$	−13.7225	−	23.7681i	−0.462323	−	0.800768i	0.536753	−	0.843740i	$-0.319651\pi$
$881$	−13.7225	−	23.7681i	−0.462323	−	0.800768i	−0.999076	+	0.0429719i	$0.986317\pi$
$882$	−1.22605	−	20.9642i	−0.0412833	−	0.705901i
$883$	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
$885$	−1.07924	+	3.12725i	−0.0362781	+	0.105121i
$886$			2.24211i			0.0753253i
$887$	25.3915	−	43.9794i	0.852563	−	1.47668i	−0.0263247	−	0.999653i	$-0.508380\pi$
$887$	25.3915	−	43.9794i	0.852563	−	1.47668i	0.878888	−	0.477029i	$-0.158286\pi$
$888$	−9.11107	−	3.14429i	−0.305747	−	0.105516i
$889$	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
$894$	−1.83425	+	5.31501i	−0.0613464	+	0.177761i
$895$	6.23477	+	10.7989i	0.208405	+	0.360969i
$896$	−1.08820	+	2.41160i	−0.0363542	+	0.0805659i
$897$	8.60435	−	20.8174i	0.287291	−	0.695071i
$898$	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
$903$	11.8544	−	50.0444i	0.394491	−	1.66537i
$904$	5.03517	+	2.90706i	0.167467	+	0.0966873i
$905$	18.5986	+	32.2137i	0.618237	+	1.07082i
$906$	−12.1465	+	10.5439i	−0.403540	+	0.350299i
$907$	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	$0.258710\pi$
$911$			43.8367i			1.45238i	−0.687496	+	0.726188i	$0.741290\pi$
$912$	−1.95144	+	5.65459i	−0.0646186	+	0.187242i
$913$			13.1269i			0.434437i
$914$	−5.66636	+	3.27147i	−0.187426	+	0.108211i
$915$	1.65722	+	1.90910i	0.0547860	+	0.0631129i
$916$	−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
$924$	11.7326	+	11.0665i	0.385974	+	0.364061i
$925$	13.8221	−	7.98018i	0.454467	−	0.262387i
$926$	32.3336	+	18.6678i	1.06255	+	0.613462i
$927$	34.6647	−	44.2416i	1.13854	−	1.45309i
$928$	−0.170773	−	0.0985961i	−0.00560591	−	0.00323657i
$929$			7.60883i			0.249638i	0.992180	+	0.124819i	$0.0398350\pi$
$929$			7.60883i			0.249638i	−0.992180	+	0.124819i	$0.960165\pi$
$930$	−25.5547	−	8.81910i	−0.837971	−	0.289190i
$931$	−23.6962	+	4.78954i	−0.776611	+	0.156971i
$932$	−6.18721	−	3.57219i	−0.202669	−	0.117011i
$933$	−6.74625	+	19.5483i	−0.220862	+	0.639983i
$934$	6.73221			0.220285
$935$	33.7652	+	19.4943i	1.10424	+	0.637532i
$936$	−3.43281	−	10.2575i	−0.112205	−	0.335276i
$937$		−	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
$939$	12.0117	−	10.4269i	0.391987	−	0.340270i
$940$	18.6783			0.609219
$941$	−17.8743	−	10.3197i	−0.582684	−	0.336413i	0.179515	−	0.983755i	$-0.442547\pi$
$941$	−17.8743	−	10.3197i	−0.582684	−	0.336413i	−0.762199	+	0.647342i	$0.775880\pi$
$942$	24.5135	−	21.2793i	0.798693	−	0.693318i
$943$	−10.8515			−0.353374
$944$			1.30815i			0.0425766i
$945$	7.32620	−	18.6882i	0.238321	−	0.607928i
$946$	19.7492	+	34.2066i	0.642101	+	1.11215i
$947$	−30.3820	+	52.6232i	−0.987282	+	1.71002i	−0.355962	+	0.934500i	$0.615847\pi$
$947$	−30.3820	+	52.6232i	−0.987282	+	1.71002i	−0.631320	+	0.775522i	$0.717487\pi$
$948$	−0.197363	+	0.571890i	−0.00641006	+	0.0185741i
$949$	17.7206	+	11.6920i	0.575235	+	0.379538i
$950$	−4.95273	−	8.57838i	−0.160688	−	0.278319i
$951$	26.1420	+	30.1153i	0.847712	+	0.976554i
$952$	−11.7177	−	16.2988i	−0.379773	−	0.528249i
$953$	3.76601	+	2.17431i	0.121993	+	0.0704328i	0.559755	−	0.828658i	$-0.310895\pi$
$953$	3.76601	+	2.17431i	0.121993	+	0.0704328i	−0.437762	+	0.899091i	$0.644229\pi$
$954$	−9.00659	+	11.4949i	−0.291599	+	0.372160i
$955$	15.1305	+	26.2068i	0.489611	+	0.848032i
$956$	−3.66232	−	6.34332i	−0.118448	−	0.205158i
$957$	−0.907760	+	0.787994i	−0.0293437	+	0.0254722i
$958$	−11.2141	−	6.47445i	−0.362310	−	0.209180i
$959$	1.93295	+	2.68865i	0.0624182	+	0.0868212i
$960$	−1.90978	+	1.65781i	−0.0616378	+	0.0535056i
$961$	−41.6345	−	72.1131i	−1.34305	−	2.32623i
$962$	−8.97856	−	17.9428i	−0.289480	−	0.578499i
$963$	1.04197	+	0.147920i	0.0335770	+	0.00476665i
$964$	8.71341	−	15.0921i	0.280640	−	0.486083i
$965$	6.92556	+	11.9954i	0.222942	+	0.386146i
$966$	11.3416	−	12.0242i	0.364909	−	0.386874i
$967$		−	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
$969$	−29.7516	−	34.2735i	−0.955760	−	1.10102i
$970$	−4.36868	−	2.52226i	−0.140270	−	0.0809849i
$971$	1.24035			0.0398046			0.0199023	−	0.999802i	$-0.493664\pi$
$971$	1.24035			0.0398046			0.0199023	+	0.999802i	$0.493664\pi$
$972$	15.5243	+	1.41269i	0.497943	+	0.0453122i
$973$	24.1827	+	10.9121i	0.775261	+	0.349825i
$974$		−	8.67630i		−	0.278007i
$975$	16.5533	+	6.84189i	0.530129	+	0.219116i
$976$	0.865717	+	0.499822i	0.0277109	+	0.0159989i
$977$	0.572082			0.0183025			0.00915126	−	0.999958i	$-0.497087\pi$
$977$	0.572082			0.0183025			0.00915126	+	0.999958i	$0.497087\pi$
$978$	−1.48893	−	0.513842i	−0.0476109	−	0.0164308i
$979$	−44.0736	−	25.4459i	−1.40860	−	0.813255i
$980$	−9.68832	−	3.25543i	−0.309482	−	0.103991i
$981$	27.8679	+	3.95617i	0.889752	+	0.126311i
$982$		−	17.0579i		−	0.544338i
$983$	6.05482	+	3.49575i	0.193119	+	0.111497i	0.593442	−	0.804877i	$-0.297769\pi$
$983$	6.05482	+	3.49575i	0.193119	+	0.111497i	−0.400323	+	0.916374i	$0.631102\pi$
$984$	−3.93507	+	3.41589i	−0.125445	+	0.108895i
$985$	8.12856	+	4.69303i	0.258997	+	0.149532i
$986$	1.29569	−	0.748066i	0.0412631	−	0.0238233i
$987$	−40.2244	+	42.6456i	−1.28036	+	1.35742i
$988$	−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
$996$	4.87851	−	4.23487i	0.154582	−	0.134187i
$997$	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
$999$	28.8786	−	1.45296i	0.913678	−	0.0459697i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.70046 + 0.329307i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26448 - 0.730045i) q^{5} +(-0.565041 + 1.63729i) q^{6} +(-2.63261 + 0.263392i) q^{7} -1.00000 q^{8} +(2.78311 - 1.11994i) q^{9} +O(q^{10})\)	\(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} +(-0.565041 + 1.63729i) 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} +(1.13542 + 1.30799i) q^{12} +(-0.214878 + 3.59914i) q^{13} +(-1.08820 + 2.41160i) q^{14} +(-1.90978 + 1.65781i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.79359 - 6.57069i) q^{17} +(0.421657 - 2.97022i) q^{18} -3.45362 q^{19} +(-1.26448 - 0.730045i) q^{20} +(4.38990 - 1.31482i) 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} +(-2.36146 - 1.85028i) q^{36} +(-4.81918 - 2.78236i) q^{37} +(-1.72681 + 2.99093i) q^{38} +(-0.819830 - 6.19095i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(-2.60543 + 1.50425i) q^{41} +(1.05628 - 4.45918i) q^{42} +(5.61139 - 9.71922i) q^{43} +(1.75974 + 3.04796i) q^{44} +(2.70157 - 3.44794i) q^{45} +(3.12372 - 1.80348i) q^{46} +(-11.0787 + 6.39629i) q^{47} +(0.565041 - 1.63729i) q^{48} +(6.86125 - 1.38682i) q^{49} +(1.43407 + 2.48388i) q^{50} +(8.61461 + 9.92393i) q^{51} +(3.22439 - 1.61348i) q^{52} +(-4.21555 - 2.43385i) q^{53} +(0.261103 + 5.18959i) 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} +(2.39060 + 0.825011i) q^{60} -0.999644i q^{61} +(5.34484 + 9.25753i) q^{62} +(-7.03186 + 3.68142i) q^{63} +1.00000 q^{64} +(2.35583 + 4.70790i) q^{65} +(1.98865 - 5.76241i) q^{66} -5.52864i q^{67} +(-3.79359 + 6.57069i) q^{68} +(-5.90566 - 2.03808i) 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} +(1.62061 - 4.69598i) q^{75} +(1.72681 + 2.99093i) q^{76} +(9.26540 - 0.927001i) q^{77} +(-5.77144 - 2.38548i) 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} +(-3.33362 - 3.14436i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(-5.61139 - 9.71922i) q^{86} +(0.257925 - 0.223895i) 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} +(6.04010 - 17.5021i) q^{93} +12.7926i q^{94} +(-4.36702 + 2.52130i) q^{95} +(-1.13542 - 1.30799i) q^{96} +(1.72747 - 2.99206i) q^{97} +(2.22961 - 6.63542i) q^{98} +(-9.79510 + 3.94162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * 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 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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