LMFDB - Embedded newform 546.2.bi.e.257.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			257.11
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.805192 + 1.53351i) q^{3} +1.00000 q^{4} +(2.64914 + 1.52948i) q^{5} +(-0.805192 - 1.53351i) q^{6} +(0.969634 + 2.46167i) q^{7} -1.00000 q^{8} +(-1.70333 + 2.46955i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.805192 + 1.53351i) q^{3} +1.00000 q^{4} +(2.64914 + 1.52948i) q^{5} +(-0.805192 - 1.53351i) q^{6} +(0.969634 + 2.46167i) q^{7} -1.00000 q^{8} +(-1.70333 + 2.46955i) q^{9} +(-2.64914 - 1.52948i) q^{10} +(-1.13290 + 1.96224i) q^{11} +(0.805192 + 1.53351i) q^{12} +(3.11743 - 1.81152i) q^{13} +(-0.969634 - 2.46167i) q^{14} +(-0.212417 + 5.29402i) q^{15} +1.00000 q^{16} -3.59543 q^{17} +(1.70333 - 2.46955i) q^{18} +(-0.413821 - 0.716759i) q^{19} +(2.64914 + 1.52948i) q^{20} +(-2.99426 + 3.46906i) q^{21} +(1.13290 - 1.96224i) q^{22} -4.62091i q^{23} +(-0.805192 - 1.53351i) q^{24} +(2.17863 + 3.77350i) q^{25} +(-3.11743 + 1.81152i) q^{26} +(-5.15859 - 0.623627i) q^{27} +(0.969634 + 2.46167i) q^{28} +(7.61619 - 4.39721i) q^{29} +(0.212417 - 5.29402i) q^{30} +(-4.78177 - 8.28226i) q^{31} -1.00000 q^{32} +(-3.92133 - 0.157339i) q^{33} +3.59543 q^{34} +(-1.19638 + 8.00434i) q^{35} +(-1.70333 + 2.46955i) q^{36} -1.34601i q^{37} +(0.413821 + 0.716759i) q^{38} +(5.28812 + 3.32201i) q^{39} +(-2.64914 - 1.52948i) q^{40} +(7.03626 - 4.06239i) q^{41} +(2.99426 - 3.46906i) q^{42} +(-4.70036 + 8.14127i) q^{43} +(-1.13290 + 1.96224i) q^{44} +(-8.28949 + 3.93696i) q^{45} +4.62091i q^{46} +(2.73905 + 1.58139i) q^{47} +(0.805192 + 1.53351i) q^{48} +(-5.11962 + 4.77383i) q^{49} +(-2.17863 - 3.77350i) q^{50} +(-2.89501 - 5.51364i) q^{51} +(3.11743 - 1.81152i) q^{52} +(1.44524 - 0.834408i) q^{53} +(5.15859 + 0.623627i) q^{54} +(-6.00243 + 3.46551i) q^{55} +(-0.969634 - 2.46167i) q^{56} +(0.765955 - 1.21173i) q^{57} +(-7.61619 + 4.39721i) q^{58} +10.7942i q^{59} +(-0.212417 + 5.29402i) q^{60} +(-9.14560 + 5.28021i) q^{61} +(4.78177 + 8.28226i) q^{62} +(-7.73081 - 1.79848i) q^{63} +1.00000 q^{64} +(11.0292 - 0.0309078i) q^{65} +(3.92133 + 0.157339i) q^{66} +(3.51789 + 2.03106i) q^{67} -3.59543 q^{68} +(7.08623 - 3.72072i) q^{69} +(1.19638 - 8.00434i) q^{70} +(3.81286 - 6.60406i) q^{71} +(1.70333 - 2.46955i) q^{72} +(5.74190 + 9.94525i) q^{73} +1.34601i q^{74} +(-4.03250 + 6.37935i) q^{75} +(-0.413821 - 0.716759i) q^{76} +(-5.92889 - 0.886170i) q^{77} +(-5.28812 - 3.32201i) q^{78} +(2.91514 - 5.04917i) q^{79} +(2.64914 + 1.52948i) q^{80} +(-3.19732 - 8.41292i) q^{81} +(-7.03626 + 4.06239i) q^{82} +3.79233i q^{83} +(-2.99426 + 3.46906i) q^{84} +(-9.52479 - 5.49914i) q^{85} +(4.70036 - 8.14127i) q^{86} +(12.8757 + 8.13894i) q^{87} +(1.13290 - 1.96224i) q^{88} -8.34716i q^{89} +(8.28949 - 3.93696i) q^{90} +(7.48213 + 5.91758i) q^{91} -4.62091i q^{92} +(8.85073 - 14.0017i) q^{93} +(-2.73905 - 1.58139i) q^{94} -2.53173i q^{95} +(-0.805192 - 1.53351i) q^{96} +(7.99888 - 13.8545i) q^{97} +(5.11962 - 4.77383i) q^{98} +(-2.91614 - 6.14011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.805192	+	1.53351i	0.464878	+	0.885375i
$3$	0.805192	+	1.53351i	0.464878	+	0.885375i
$4$	1.00000			0.500000
$5$	2.64914	+	1.52948i	1.18473	+	0.684005i	0.957104	−	0.289743i	$-0.0935700\pi$
$5$	2.64914	+	1.52948i	1.18473	+	0.684005i	0.227627	+	0.973748i	$0.426903\pi$
$6$	−0.805192	−	1.53351i	−0.328718	−	0.626055i
$7$	0.969634	+	2.46167i	0.366487	+	0.930423i
$7$	0.969634	+	2.46167i	0.366487	+	0.930423i
$8$	−1.00000			−0.353553
$9$	−1.70333	+	2.46955i	−0.567778	+	0.823182i
$10$	−2.64914	−	1.52948i	−0.837732	−	0.483665i
$11$	−1.13290	+	1.96224i	−0.341583	+	0.591639i	−0.984727	−	0.174106i	$-0.944296\pi$
$11$	−1.13290	+	1.96224i	−0.341583	+	0.591639i	0.643144	+	0.765745i	$0.277630\pi$
$12$	0.805192	+	1.53351i	0.232439	+	0.442687i
$13$	3.11743	−	1.81152i	0.864621	−	0.502425i
$13$	3.11743	−	1.81152i	0.864621	−	0.502425i
$14$	−0.969634	−	2.46167i	−0.259146	−	0.657908i
$15$	−0.212417	+	5.29402i	−0.0548458	+	1.36691i
$16$	1.00000			0.250000
$17$	−3.59543			−0.872019			−0.436010	−	0.899942i	$-0.643609\pi$
$17$	−3.59543			−0.872019			−0.436010	+	0.899942i	$0.643609\pi$
$18$	1.70333	−	2.46955i	0.401479	−	0.582078i
$19$	−0.413821	−	0.716759i	−0.0949370	−	0.164436i	0.814645	−	0.579959i	$-0.196932\pi$
$19$	−0.413821	−	0.716759i	−0.0949370	−	0.164436i	−0.909582	+	0.415524i	$0.863598\pi$
$20$	2.64914	+	1.52948i	0.592366	+	0.342003i
$21$	−2.99426	+	3.46906i	−0.653402	+	0.757012i
$22$	1.13290	−	1.96224i	0.241536	−	0.418352i
$23$		−	4.62091i		−	0.963526i	−0.876302	−	0.481763i	$-0.839997\pi$
$23$		−	4.62091i		−	0.963526i	0.876302	−	0.481763i	$-0.160003\pi$
$24$	−0.805192	−	1.53351i	−0.164359	−	0.313027i
$25$	2.17863	+	3.77350i	0.435726	+	0.754699i
$26$	−3.11743	+	1.81152i	−0.611379	+	0.355268i
$27$	−5.15859	−	0.623627i	−0.992772	−	0.120017i
$28$	0.969634	+	2.46167i	0.183244	+	0.465212i
$29$	7.61619	−	4.39721i	1.41429	−	0.816542i	0.418503	−	0.908216i	$-0.362555\pi$
$29$	7.61619	−	4.39721i	1.41429	−	0.816542i	0.995789	+	0.0916739i	$0.0292218\pi$
$30$	0.212417	−	5.29402i	0.0387818	−	0.966551i
$31$	−4.78177	−	8.28226i	−0.858831	−	1.48754i	−0.873045	−	0.487639i	$-0.837858\pi$
$31$	−4.78177	−	8.28226i	−0.858831	−	1.48754i	0.0142145	−	0.999899i	$-0.495475\pi$
$32$	−1.00000			−0.176777
$33$	−3.92133	−	0.157339i	−0.682616	−	0.0273892i
$34$	3.59543			0.616611
$35$	−1.19638	+	8.00434i	−0.202225	+	1.35298i
$36$	−1.70333	+	2.46955i	−0.283889	+	0.411591i
$37$		−	1.34601i		−	0.221282i	−0.993860	−	0.110641i	$-0.964710\pi$
$37$		−	1.34601i		−	0.221282i	0.993860	−	0.110641i	$-0.0352904\pi$
$38$	0.413821	+	0.716759i	0.0671306	+	0.116274i
$39$	5.28812	+	3.32201i	0.846777	+	0.531947i
$40$	−2.64914	−	1.52948i	−0.418866	−	0.241832i
$41$	7.03626	−	4.06239i	1.09888	−	0.634438i	0.162953	−	0.986634i	$-0.447898\pi$
$41$	7.03626	−	4.06239i	1.09888	−	0.634438i	0.935926	+	0.352196i	$0.114565\pi$
$42$	2.99426	−	3.46906i	0.462025	−	0.535288i
$43$	−4.70036	+	8.14127i	−0.716799	+	1.24153i	0.245463	+	0.969406i	$0.421060\pi$
$43$	−4.70036	+	8.14127i	−0.716799	+	1.24153i	−0.962262	+	0.272126i	$0.912273\pi$
$44$	−1.13290	+	1.96224i	−0.170791	+	0.295819i
$45$	−8.28949	+	3.93696i	−1.23572	+	0.586887i
$46$			4.62091i			0.681316i
$47$	2.73905	+	1.58139i	0.399531	+	0.230669i	0.686282	−	0.727336i	$-0.259242\pi$
$47$	2.73905	+	1.58139i	0.399531	+	0.230669i	−0.286751	+	0.958005i	$0.592575\pi$
$48$	0.805192	+	1.53351i	0.116219	+	0.221344i
$49$	−5.11962	+	4.77383i	−0.731374	+	0.681976i
$50$	−2.17863	−	3.77350i	−0.308105	−	0.533653i
$51$	−2.89501	−	5.51364i	−0.405382	−	0.772064i
$52$	3.11743	−	1.81152i	0.432310	−	0.251212i
$53$	1.44524	−	0.834408i	0.198519	−	0.114615i	−0.397446	−	0.917626i	$-0.630103\pi$
$53$	1.44524	−	0.834408i	0.198519	−	0.114615i	0.595964	+	0.803011i	$0.296770\pi$
$54$	5.15859	+	0.623627i	0.701996	+	0.0848649i
$55$	−6.00243	+	3.46551i	−0.809368	+	0.467289i
$56$	−0.969634	−	2.46167i	−0.129573	−	0.328954i
$57$	0.765955	−	1.21173i	0.101453	−	0.160497i
$58$	−7.61619	+	4.39721i	−1.00006	+	0.577382i
$59$			10.7942i			1.40529i	0.711543	+	0.702643i	$0.247997\pi$
$59$			10.7942i			1.40529i	−0.711543	+	0.702643i	$0.752003\pi$
$60$	−0.212417	+	5.29402i	−0.0274229	+	0.683455i
$61$	−9.14560	+	5.28021i	−1.17097	+	0.676062i	−0.953909	−	0.300095i	$-0.902982\pi$
$61$	−9.14560	+	5.28021i	−1.17097	+	0.676062i	−0.217065	+	0.976157i	$0.569648\pi$
$62$	4.78177	+	8.28226i	0.607285	+	1.05185i
$63$	−7.73081	−	1.79848i	−0.973991	−	0.226588i
$64$	1.00000			0.125000
$65$	11.0292	−	0.0309078i	1.36800	−	0.00383365i
$66$	3.92133	+	0.157339i	0.482683	+	0.0193671i
$67$	3.51789	+	2.03106i	0.429779	+	0.248133i	0.699252	−	0.714875i	$-0.253516\pi$
$67$	3.51789	+	2.03106i	0.429779	+	0.248133i	−0.269474	+	0.963008i	$0.586850\pi$
$68$	−3.59543			−0.436010
$69$	7.08623	−	3.72072i	0.853082	−	0.447922i
$70$	1.19638	−	8.00434i	0.142995	−	0.956702i
$71$	3.81286	−	6.60406i	0.452503	−	0.783758i	−0.546038	−	0.837760i	$-0.683865\pi$
$71$	3.81286	−	6.60406i	0.452503	−	0.783758i	0.998541	+	0.0540027i	$0.0171980\pi$
$72$	1.70333	−	2.46955i	0.200740	−	0.291039i
$73$	5.74190	+	9.94525i	0.672038	+	1.16400i	0.977325	+	0.211744i	$0.0679142\pi$
$73$	5.74190	+	9.94525i	0.672038	+	1.16400i	−0.305287	+	0.952260i	$0.598752\pi$
$74$			1.34601i			0.156470i
$75$	−4.03250	+	6.37935i	−0.465633	+	0.736623i
$76$	−0.413821	−	0.716759i	−0.0474685	−	0.0822179i
$77$	−5.92889	−	0.886170i	−0.675660	−	0.100988i
$78$	−5.28812	−	3.32201i	−0.598762	−	0.376144i
$79$	2.91514	−	5.04917i	0.327979	−	0.568077i	−0.654132	−	0.756381i	$-0.726966\pi$
$79$	2.91514	−	5.04917i	0.327979	−	0.568077i	0.982111	+	0.188304i	$0.0602991\pi$
$80$	2.64914	+	1.52948i	0.296183	+	0.171001i
$81$	−3.19732	−	8.41292i	−0.355257	−	0.934769i
$82$	−7.03626	+	4.06239i	−0.777025	+	0.448615i
$83$			3.79233i			0.416262i	0.978101	+	0.208131i	$0.0667381\pi$
$83$			3.79233i			0.416262i	−0.978101	+	0.208131i	$0.933262\pi$
$84$	−2.99426	+	3.46906i	−0.326701	+	0.378506i
$85$	−9.52479	−	5.49914i	−1.03311	−	0.596465i
$86$	4.70036	−	8.14127i	0.506853	−	0.877896i
$87$	12.8757	+	8.13894i	1.38042	+	0.872586i
$88$	1.13290	−	1.96224i	0.120768	−	0.209176i
$89$		−	8.34716i		−	0.884798i	−0.896818	−	0.442399i	$-0.854128\pi$
$89$		−	8.34716i		−	0.884798i	0.896818	−	0.442399i	$-0.145872\pi$
$90$	8.28949	−	3.93696i	0.873789	−	0.414992i
$91$	7.48213	+	5.91758i	0.784340	+	0.620331i
$92$		−	4.62091i		−	0.481763i
$93$	8.85073	−	14.0017i	0.917778	−	1.45191i
$94$	−2.73905	−	1.58139i	−0.282511	−	0.163108i
$95$		−	2.53173i		−	0.259750i
$96$	−0.805192	−	1.53351i	−0.0821795	−	0.156514i
$97$	7.99888	−	13.8545i	0.812164	−	1.40671i	−0.0991832	−	0.995069i	$-0.531623\pi$
$97$	7.99888	−	13.8545i	0.812164	−	1.40671i	0.911347	−	0.411639i	$-0.135044\pi$
$98$	5.11962	−	4.77383i	0.517160	−	0.482230i
$99$	−2.91614	−	6.14011i	−0.293083	−	0.617104i
$100$	2.17863	+	3.77350i	0.217863	+	0.377350i
$101$	−3.56996	+	6.18335i	−0.355224	+	0.615266i	−0.987156	−	0.159758i	$-0.948929\pi$
$101$	−3.56996	+	6.18335i	−0.355224	+	0.615266i	0.631932	+	0.775024i	$0.282262\pi$
$102$	2.89501	+	5.51364i	0.286648	+	0.545932i
$103$	1.53644	+	0.887062i	0.151390	+	0.0874048i	0.573781	−	0.819009i	$-0.305476\pi$
$103$	1.53644	+	0.887062i	0.151390	+	0.0874048i	−0.422392	+	0.906413i	$0.638809\pi$
$104$	−3.11743	+	1.81152i	−0.305690	+	0.177634i
$105$	−13.2381	+	4.61036i	−1.29191	+	0.449925i
$106$	−1.44524	+	0.834408i	−0.140374	+	0.0810449i
$107$			6.29055i			0.608130i	0.952651	+	0.304065i	$0.0983440\pi$
$107$			6.29055i			0.608130i	−0.952651	+	0.304065i	$0.901656\pi$
$108$	−5.15859	−	0.623627i	−0.496386	−	0.0600086i
$109$	9.02357	−	5.20976i	0.864302	−	0.499005i	−0.00114874	−	0.999999i	$-0.500366\pi$
$109$	9.02357	−	5.20976i	0.864302	−	0.499005i	0.865450	+	0.500995i	$0.167032\pi$
$110$	6.00243	−	3.46551i	0.572309	−	0.330423i
$111$	2.06412	−	1.08379i	0.195918	−	0.102869i
$112$	0.969634	+	2.46167i	0.0916218	+	0.232606i
$113$	−7.25521	−	4.18880i	−0.682513	−	0.394049i	0.118288	−	0.992979i	$-0.462259\pi$
$113$	−7.25521	−	4.18880i	−0.682513	−	0.394049i	−0.800801	+	0.598930i	$0.795593\pi$
$114$	−0.765955	+	1.21173i	−0.0717382	+	0.113489i
$115$	7.06760	−	12.2414i	0.659057	−	1.14152i
$116$	7.61619	−	4.39721i	0.707146	−	0.408271i
$117$	−0.836399	+	10.7843i	−0.0773251	+	0.997006i
$118$		−	10.7942i		−	0.993687i
$119$	−3.48625	−	8.85075i	−0.319584	−	0.811347i
$120$	0.212417	−	5.29402i	0.0193909	−	0.483276i
$121$	2.93307	+	5.08022i	0.266642	+	0.461838i
$122$	9.14560	−	5.28021i	0.828004	−	0.478048i
$123$	11.8953	+	7.51920i	1.07256	+	0.677984i
$124$	−4.78177	−	8.28226i	−0.429415	−	0.743769i
$125$		−	1.96613i		−	0.175856i
$126$	7.73081	+	1.79848i	0.688715	+	0.160222i
$127$	−0.0429290	−	0.0743552i	−0.00380933	−	0.00659795i	0.864114	−	0.503295i	$-0.167879\pi$
$127$	−0.0429290	−	0.0743552i	−0.00380933	−	0.00659795i	−0.867924	+	0.496697i	$0.834546\pi$
$128$	−1.00000			−0.0883883
$129$	−16.2694	−	0.652793i	−1.43244	−	0.0574753i
$130$	−11.0292	+	0.0309078i	−0.967325	+	0.00271080i
$131$	−1.03041	+	1.78473i	−0.0900276	+	0.155932i	−0.907523	−	0.420003i	$-0.862029\pi$
$131$	−1.03041	+	1.78473i	−0.0900276	+	0.155932i	0.817495	+	0.575936i	$0.195362\pi$
$132$	−3.92133	−	0.157339i	−0.341308	−	0.0136946i
$133$	1.36317	−	1.71368i	0.118202	−	0.148595i
$134$	−3.51789	−	2.03106i	−0.303900	−	0.175456i
$135$	−12.7120	−	9.54205i	−1.09408	−	0.821249i
$136$	3.59543			0.308305
$137$	8.97465			0.766756			0.383378	−	0.923592i	$-0.374761\pi$
$137$	8.97465			0.766756			0.383378	+	0.923592i	$0.374761\pi$
$138$	−7.08623	+	3.72072i	−0.603220	+	0.316729i
$139$	−18.0789	−	10.4379i	−1.53343	−	0.885328i	−0.999200	−	0.0399902i	$-0.987267\pi$
$139$	−18.0789	−	10.4379i	−1.53343	−	0.885328i	−0.534233	−	0.845338i	$-0.679399\pi$
$140$	−1.19638	+	8.00434i	−0.101113	+	0.676490i
$141$	−0.219626	+	5.47369i	−0.0184958	+	0.460968i
$142$	−3.81286	+	6.60406i	−0.319968	+	0.554200i
$143$	0.0228937	+	8.16944i	0.00191447	+	0.683163i
$144$	−1.70333	+	2.46955i	−0.141944	+	0.205796i
$145$	26.9018			2.23407
$146$	−5.74190	−	9.94525i	−0.475203	−	0.823075i
$147$	−11.4430	−	4.00716i	−0.943804	−	0.330505i
$148$		−	1.34601i		−	0.110641i
$149$	−0.851501	−	1.47484i	−0.0697576	−	0.120824i	0.829037	−	0.559194i	$-0.188889\pi$
$149$	−0.851501	−	1.47484i	−0.0697576	−	0.120824i	−0.898795	+	0.438370i	$0.855556\pi$
$150$	4.03250	−	6.37935i	0.329252	−	0.520871i
$151$	−19.2492	+	11.1135i	−1.56648	+	0.904406i	−0.569902	+	0.821712i	$0.693019\pi$
$151$	−19.2492	+	11.1135i	−1.56648	+	0.904406i	−0.996575	+	0.0826936i	$0.973648\pi$
$152$	0.413821	+	0.716759i	0.0335653	+	0.0581368i
$153$	6.12421	−	8.87907i	0.495113	−	0.717830i
$154$	5.92889	+	0.886170i	0.477764	+	0.0714096i
$155$		−	29.2545i		−	2.34978i
$156$	5.28812	+	3.32201i	0.423389	+	0.265974i
$157$	10.2785	−	5.93431i	0.820316	−	0.473610i	−0.0302095	−	0.999544i	$-0.509617\pi$
$157$	10.2785	−	5.93431i	0.820316	−	0.473610i	0.850525	+	0.525934i	$0.176284\pi$
$158$	−2.91514	+	5.04917i	−0.231916	+	0.401691i
$159$	2.44327	+	1.54443i	0.193764	+	0.122482i
$160$	−2.64914	−	1.52948i	−0.209433	−	0.120916i
$161$	11.3751	−	4.48059i	0.896487	−	0.353120i
$162$	3.19732	+	8.41292i	0.251205	+	0.660981i
$163$	8.32458	−	4.80620i	0.652031	−	0.376451i	−0.137203	−	0.990543i	$-0.543811\pi$
$163$	8.32458	−	4.80620i	0.652031	−	0.376451i	0.789234	+	0.614092i	$0.210478\pi$
$164$	7.03626	−	4.06239i	0.549440	−	0.317219i
$165$	−10.1475	−	6.41442i	−0.789983	−	0.499362i
$166$		−	3.79233i		−	0.294342i
$167$	21.5888	−	12.4643i	1.67059	−	0.964517i	0.703285	−	0.710908i	$-0.251716\pi$
$167$	21.5888	−	12.4643i	1.67059	−	0.964517i	0.967307	−	0.253608i	$-0.0816174\pi$
$168$	2.99426	−	3.46906i	0.231012	−	0.267644i
$169$	6.43680	−	11.2946i	0.495138	−	0.868814i
$170$	9.52479	+	5.49914i	0.730518	+	0.421765i
$171$	2.47494	+	0.198929i	0.189264	+	0.0152125i
$172$	−4.70036	+	8.14127i	−0.358399	+	0.620766i
$173$	2.01276	+	3.48621i	0.153028	+	0.265051i	0.932339	−	0.361585i	$-0.117764\pi$
$173$	2.01276	+	3.48621i	0.153028	+	0.265051i	−0.779312	+	0.626637i	$0.784431\pi$
$174$	−12.8757	−	8.13894i	−0.976103	−	0.617012i
$175$	−7.17662	+	9.02197i	−0.542502	+	0.681997i
$176$	−1.13290	+	1.96224i	−0.0853957	+	0.147910i
$177$	−16.5531	+	8.69141i	−1.24421	+	0.653286i
$178$			8.34716i			0.625646i
$179$	−10.9445	−	6.31879i	−0.818028	−	0.472289i	0.0317081	−	0.999497i	$-0.489905\pi$
$179$	−10.9445	−	6.31879i	−0.818028	−	0.472289i	−0.849736	+	0.527209i	$0.823239\pi$
$180$	−8.28949	+	3.93696i	−0.617862	+	0.293443i
$181$		−	1.79097i		−	0.133122i	−0.997782	−	0.0665610i	$-0.978797\pi$
$181$		−	1.79097i		−	0.133122i	0.997782	−	0.0665610i	$-0.0212027\pi$
$182$	−7.48213	−	5.91758i	−0.554612	−	0.438640i
$183$	−15.4612	−	9.77332i	−1.14293	−	0.722465i
$184$			4.62091i			0.340658i
$185$	2.05870	−	3.56576i	0.151358	−	0.262160i
$186$	−8.85073	+	14.0017i	−0.648967	+	1.02666i
$187$	4.07327	−	7.05510i	0.297867	−	0.515920i
$188$	2.73905	+	1.58139i	0.199765	+	0.115335i
$189$	−3.46679	−	13.3034i	−0.252172	−	0.967683i
$190$			2.53173i			0.183671i
$191$	−8.45391	+	4.88087i	−0.611703	+	0.353167i	−0.773632	−	0.633635i	$-0.781562\pi$
$191$	−8.45391	+	4.88087i	−0.611703	+	0.353167i	0.161928	+	0.986803i	$0.448229\pi$
$192$	0.805192	+	1.53351i	0.0581097	+	0.110672i
$193$	−9.03423	−	5.21591i	−0.650298	−	0.375450i	0.138272	−	0.990394i	$-0.455845\pi$
$193$	−9.03423	−	5.21591i	−0.650298	−	0.375450i	−0.788570	+	0.614945i	$0.789178\pi$
$194$	−7.99888	+	13.8545i	−0.574286	+	0.994693i
$195$	8.92802	+	16.8886i	0.639349	+	1.20941i
$196$	−5.11962	+	4.77383i	−0.365687	+	0.340988i
$197$	3.77403	+	6.53681i	0.268888	+	0.465728i	0.968575	−	0.248721i	$-0.0800104\pi$
$197$	3.77403	+	6.53681i	0.268888	+	0.465728i	−0.699687	+	0.714450i	$0.746677\pi$
$198$	2.91614	+	6.14011i	0.207241	+	0.436358i
$199$			12.2381i			0.867534i	0.901025	+	0.433767i	$0.142816\pi$
$199$			12.2381i			0.867534i	−0.901025	+	0.433767i	$0.857184\pi$
$200$	−2.17863	−	3.77350i	−0.154052	−	0.266826i
$201$	−0.282076	+	7.03013i	−0.0198961	+	0.495867i
$202$	3.56996	−	6.18335i	0.251181	−	0.435059i
$203$	18.2094	+	14.4849i	1.27805	+	1.01664i
$204$	−2.89501	−	5.51364i	−0.202691	−	0.386032i
$205$	24.8534			1.73584
$206$	−1.53644	−	0.887062i	−0.107049	−	0.0618045i
$207$	11.4115	+	7.87095i	0.793157	+	0.547069i
$208$	3.11743	−	1.81152i	0.216155	−	0.125606i
$209$	1.87527			0.129715
$210$	13.2381	−	4.61036i	0.913515	−	0.318145i
$211$	−3.36247	−	5.82397i	−0.231482	−	0.400939i	0.726762	−	0.686889i	$-0.241024\pi$
$211$	−3.36247	−	5.82397i	−0.231482	−	0.400939i	−0.958244	+	0.285950i	$0.907691\pi$
$212$	1.44524	−	0.834408i	0.0992593	−	0.0573074i
$213$	13.1975	+	0.529535i	0.904278	+	0.0362831i
$214$		−	6.29055i		−	0.430013i
$215$	−24.9038	+	14.3782i	−1.69843	+	0.980588i
$216$	5.15859	+	0.623627i	0.350998	+	0.0424325i
$217$	15.7516	−	19.8019i	1.06929	−	1.34424i
$218$	−9.02357	+	5.20976i	−0.611154	+	0.352850i
$219$	−10.6279	+	16.8131i	−0.718164	+	1.13612i
$220$	−6.00243	+	3.46551i	−0.404684	+	0.233644i
$221$	−11.2085	+	6.51318i	−0.753966	+	0.438124i
$222$	−2.06412	+	1.08379i	−0.138535	+	0.0727395i
$223$	6.23733	+	10.8034i	0.417683	+	0.723448i	0.995706	−	0.0925727i	$-0.0295091\pi$
$223$	6.23733	+	10.8034i	0.417683	+	0.723448i	−0.578023	+	0.816020i	$0.696176\pi$
$224$	−0.969634	−	2.46167i	−0.0647864	−	0.164477i
$225$	−13.0298	−	1.04729i	−0.868650	−	0.0698196i
$226$	7.25521	+	4.18880i	0.482609	+	0.278635i
$227$			21.4471i			1.42350i	0.702434	+	0.711748i	$0.252096\pi$
$227$			21.4471i			1.42350i	−0.702434	+	0.711748i	$0.747904\pi$
$228$	0.765955	−	1.21173i	0.0507266	−	0.0802487i
$229$	11.7463	−	20.3453i	0.776220	−	1.34445i	−0.157886	−	0.987457i	$-0.550468\pi$
$229$	11.7463	−	20.3453i	0.776220	−	1.34445i	0.934106	−	0.356995i	$-0.116199\pi$
$230$	−7.06760	+	12.2414i	−0.466024	+	0.807176i
$231$	−3.41494	−	9.80558i	−0.224687	−	0.645160i
$232$	−7.61619	+	4.39721i	−0.500028	+	0.288691i
$233$	−11.1727	−	6.45055i	−0.731947	−	0.422590i	0.0871872	−	0.996192i	$-0.472212\pi$
$233$	−11.1727	−	6.45055i	−0.731947	−	0.422590i	−0.819134	+	0.573602i	$0.805545\pi$
$234$	0.836399	−	10.7843i	0.0546771	−	0.704990i
$235$	4.83741	+	8.37864i	0.315558	+	0.546562i
$236$			10.7942i			0.702643i
$237$	10.0902	+	0.404859i	0.655431	+	0.0262984i
$238$	3.48625	+	8.85075i	0.225980	+	0.573709i
$239$	23.0402			1.49035			0.745175	−	0.666869i	$-0.232366\pi$
$239$	23.0402			1.49035			0.745175	+	0.666869i	$0.232366\pi$
$240$	−0.212417	+	5.29402i	−0.0137114	+	0.341728i
$241$	−27.7786			−1.78938			−0.894688	−	0.446692i	$-0.852602\pi$
$241$	−27.7786			−1.78938			−0.894688	+	0.446692i	$0.852602\pi$
$242$	−2.93307	−	5.08022i	−0.188545	−	0.326569i
$243$	10.3269	−	11.6771i	0.662470	−	0.749089i
$244$	−9.14560	+	5.28021i	−0.585487	+	0.338031i
$245$	−20.8641	+	4.81619i	−1.33296	+	0.307695i
$246$	−11.8953	−	7.51920i	−0.758414	−	0.479407i
$247$	−2.58848	−	1.48480i	−0.164701	−	0.0944758i
$248$	4.78177	+	8.28226i	0.303642	+	0.525924i
$249$	−5.81559	+	3.05355i	−0.368548	+	0.193511i
$250$			1.96613i			0.124349i
$251$	−6.68358	+	11.5763i	−0.421864	+	0.730690i	−0.996122	−	0.0879848i	$-0.971957\pi$
$251$	−6.68358	+	11.5763i	−0.421864	+	0.730690i	0.574258	+	0.818674i	$0.305291\pi$
$252$	−7.73081	−	1.79848i	−0.486995	−	0.113294i
$253$	9.06735	+	5.23504i	0.570059	+	0.329124i
$254$	0.0429290	+	0.0743552i	0.00269360	+	0.00466546i
$255$	0.763729	−	19.0343i	0.0478265	−	1.19197i
$256$	1.00000			0.0625000
$257$	2.71126			0.169124			0.0845618	−	0.996418i	$-0.473051\pi$
$257$	2.71126			0.169124			0.0845618	+	0.996418i	$0.473051\pi$
$258$	16.2694	+	0.652793i	1.01289	+	0.0406411i
$259$	3.31343	−	1.30514i	0.205886	−	0.0810972i
$260$	11.0292	−	0.0309078i	0.684002	−	0.00191682i
$261$	−2.11380	+	26.2985i	−0.130841	+	1.62783i
$262$	1.03041	−	1.78473i	0.0636591	−	0.110261i
$263$	−12.7361	−	7.35317i	−0.785340	−	0.453416i	0.0529797	−	0.998596i	$-0.483128\pi$
$263$	−12.7361	−	7.35317i	−0.785340	−	0.453416i	−0.838319	+	0.545180i	$0.816461\pi$
$264$	3.92133	+	0.157339i	0.241341	+	0.00968355i
$265$	5.10485			0.313588
$266$	−1.36317	+	1.71368i	−0.0835811	+	0.105073i
$267$	12.8005	−	6.72107i	0.783378	−	0.411323i
$268$	3.51789	+	2.03106i	0.214889	+	0.124066i
$269$	−7.51872			−0.458424			−0.229212	−	0.973376i	$-0.573615\pi$
$269$	−7.51872			−0.458424			−0.229212	+	0.973376i	$0.573615\pi$
$270$	12.7120	+	9.54205i	0.773628	+	0.580711i
$271$	−0.0247852			−0.00150559			−0.000752797	−	1.00000i	$-0.500240\pi$
$271$	−0.0247852			−0.00150559			−0.000752797		1.00000i	$0.500240\pi$
$272$	−3.59543			−0.218005
$273$	−3.05014	+	16.2387i	−0.184603	+	0.982813i
$274$	−8.97465			−0.542178
$275$	−9.87269			−0.595346
$276$	7.08623	−	3.72072i	0.426541	−	0.223961i
$277$	6.18124			0.371395			0.185697	−	0.982607i	$-0.440546\pi$
$277$	6.18124			0.371395			0.185697	+	0.982607i	$0.440546\pi$
$278$	18.0789	+	10.4379i	1.08430	+	0.626021i
$279$	28.5984	+	2.29866i	1.71214	+	0.137617i
$280$	1.19638	−	8.00434i	0.0714974	−	0.478351i
$281$	−29.5748			−1.76428			−0.882142	−	0.470984i	$-0.843899\pi$
$281$	−29.5748			−1.76428			−0.882142	+	0.470984i	$0.843899\pi$
$282$	0.219626	−	5.47369i	0.0130785	−	0.325953i
$283$	18.3623	+	10.6015i	1.09152	+	0.630192i	0.933982	−	0.357320i	$-0.116310\pi$
$283$	18.3623	+	10.6015i	1.09152	+	0.630192i	0.157543	+	0.987512i	$0.449643\pi$
$284$	3.81286	−	6.60406i	0.226251	−	0.391879i
$285$	3.88244	−	2.03852i	0.229976	−	0.120752i
$286$	−0.0228937	−	8.16944i	−0.00135374	−	0.483069i
$287$	16.8228	+	13.3819i	0.993021	+	0.789909i
$288$	1.70333	−	2.46955i	0.100370	−	0.145519i
$289$	−4.07291			−0.239583
$290$	−26.9018			−1.57973
$291$	27.6867	+	1.11090i	1.62302	+	0.0651219i
$292$	5.74190	+	9.94525i	0.336019	+	0.582002i
$293$	−10.1781	−	5.87631i	−0.594609	−	0.343298i	0.172309	−	0.985043i	$-0.444877\pi$
$293$	−10.1781	−	5.87631i	−0.594609	−	0.343298i	−0.766918	+	0.641745i	$0.778211\pi$
$294$	11.4430	+	4.00716i	0.667370	+	0.233702i
$295$	−16.5095	+	28.5954i	−0.961223	+	1.66489i
$296$			1.34601i			0.0782351i
$297$	7.06789	−	9.41591i	0.410121	−	0.546367i
$298$	0.851501	+	1.47484i	0.0493261	+	0.0854353i
$299$	−8.37086	−	14.4054i	−0.484100	−	0.833085i
$300$	−4.03250	+	6.37935i	−0.232816	+	0.368312i
$301$	−24.5987	−	3.67668i	−1.41785	−	0.211920i
$302$	19.2492	−	11.1135i	1.10767	−	0.639512i
$303$	−12.3568	−	0.495801i	−0.709877	−	0.0284830i
$304$	−0.413821	−	0.716759i	−0.0237342	−	0.0411089i
$305$	−32.3040			−1.84972
$306$	−6.12421	+	8.87907i	−0.350098	+	0.507583i
$307$	−12.2431			−0.698749			−0.349375	−	0.936983i	$-0.613606\pi$
$307$	−12.2431			−0.698749			−0.349375	+	0.936983i	$0.613606\pi$
$308$	−5.92889	−	0.886170i	−0.337830	−	0.0504942i
$309$	−0.123196	+	3.07040i	−0.00700840	+	0.174669i
$310$			29.2545i			1.66154i
$311$	4.81504	+	8.33990i	0.273036	+	0.472912i	0.969638	−	0.244546i	$-0.0786388\pi$
$311$	4.81504	+	8.33990i	0.273036	+	0.472912i	−0.696602	+	0.717458i	$0.745306\pi$
$312$	−5.28812	−	3.32201i	−0.299381	−	0.188072i
$313$	12.0523	+	6.95841i	0.681237	+	0.393312i	0.800321	−	0.599572i	$-0.204662\pi$
$313$	12.0523	+	6.95841i	0.681237	+	0.393312i	−0.119084	+	0.992884i	$0.537996\pi$
$314$	−10.2785	+	5.93431i	−0.580051	+	0.334893i
$315$	−17.7293	−	16.5886i	−0.998930	−	0.934660i
$316$	2.91514	−	5.04917i	0.163990	−	0.284038i
$317$	11.8204	−	20.4735i	0.663900	−	1.14991i	−0.315682	−	0.948865i	$-0.602233\pi$
$317$	11.8204	−	20.4735i	0.663900	−	1.14991i	0.979582	−	0.201044i	$-0.0644334\pi$
$318$	−2.44327	−	1.54443i	−0.137012	−	0.0866075i
$319$			19.9264i			1.11567i
$320$	2.64914	+	1.52948i	0.148091	+	0.0855006i
$321$	−9.64664	+	5.06510i	−0.538423	+	0.282706i
$322$	−11.3751	+	4.48059i	−0.633912	+	0.249694i
$323$	1.48786	+	2.57705i	0.0827869	+	0.143391i
$324$	−3.19732	−	8.41292i	−0.177629	−	0.467384i
$325$	13.6275	+	7.81700i	0.755917	+	0.433609i
$326$	−8.32458	+	4.80620i	−0.461056	+	0.266191i
$327$	15.2550	+	9.64292i	0.843601	+	0.533255i
$328$	−7.03626	+	4.06239i	−0.388512	+	0.224308i
$329$	−1.23698	+	8.27599i	−0.0681970	+	0.456270i
$330$	10.1475	+	6.41442i	0.558602	+	0.353102i
$331$	13.0461	−	7.53219i	0.717081	−	0.414007i	−0.0965965	−	0.995324i	$-0.530796\pi$
$331$	13.0461	−	7.53219i	0.717081	−	0.414007i	0.813677	+	0.581317i	$0.197462\pi$
$332$			3.79233i			0.208131i
$333$	3.32403	+	2.29270i	0.182156	+	0.125639i
$334$	−21.5888	+	12.4643i	−1.18129	+	0.682016i
$335$	6.21292	+	10.7611i	0.339448	+	0.587942i
$336$	−2.99426	+	3.46906i	−0.163350	+	0.189253i
$337$	−9.93070			−0.540960			−0.270480	−	0.962726i	$-0.587182\pi$
$337$	−9.93070			−0.540960			−0.270480	+	0.962726i	$0.587182\pi$
$338$	−6.43680	+	11.2946i	−0.350116	+	0.614344i
$339$	0.581746	−	14.4988i	0.0315961	−	0.787464i
$340$	−9.52479	−	5.49914i	−0.516554	−	0.298233i
$341$	21.6691			1.17345
$342$	−2.47494	−	0.198929i	−0.133830	−	0.0107568i
$343$	−16.7158	−	7.97393i	−0.902566	−	0.430552i
$344$	4.70036	−	8.14127i	0.253427	−	0.438948i
$345$	24.4632	+	0.981558i	1.31705	+	0.0528453i
$346$	−2.01276	−	3.48621i	−0.108207	−	0.187420i
$347$		−	3.36902i		−	0.180859i	−0.995903	−	0.0904293i	$-0.971176\pi$
$347$		−	3.36902i		−	0.180859i	0.995903	−	0.0904293i	$-0.0288239\pi$
$348$	12.8757	+	8.13894i	0.690209	+	0.436293i
$349$	15.4110	+	26.6927i	0.824935	+	1.42883i	0.901969	+	0.431800i	$0.142121\pi$
$349$	15.4110	+	26.6927i	0.824935	+	1.42883i	−0.0770347	+	0.997028i	$0.524545\pi$
$350$	7.17662	−	9.02197i	0.383607	−	0.482245i
$351$	−17.2113	+	7.40077i	−0.918671	+	0.395024i
$352$	1.13290	−	1.96224i	0.0603839	−	0.104588i
$353$	−17.0077	−	9.81940i	−0.905228	−	0.522634i	−0.0263354	−	0.999653i	$-0.508384\pi$
$353$	−17.0077	−	9.81940i	−0.905228	−	0.522634i	−0.878893	+	0.477019i	$0.841717\pi$
$354$	16.5531	−	8.69141i	0.879786	−	0.461943i
$355$	20.2016	−	11.6634i	1.07219	−	0.619028i
$356$		−	8.34716i		−	0.442399i
$357$	10.7656	−	12.4728i	0.569779	−	0.660128i
$358$	10.9445	+	6.31879i	0.578433	+	0.333958i
$359$	5.20022	−	9.00705i	0.274457	−	0.475374i	−0.695541	−	0.718487i	$-0.744835\pi$
$359$	5.20022	−	9.00705i	0.274457	−	0.475374i	0.969998	+	0.243113i	$0.0781685\pi$
$360$	8.28949	−	3.93696i	0.436895	−	0.207496i
$361$	9.15750	−	15.8613i	0.481974	−	0.834803i
$362$			1.79097i			0.0941315i
$363$	−5.42891	+	8.58845i	−0.284944	+	0.450777i
$364$	7.48213	+	5.91758i	0.392170	+	0.310165i
$365$			35.1285i			1.83871i
$366$	15.4612	+	9.77332i	0.808172	+	0.510860i
$367$	−19.6101	−	11.3219i	−1.02364	−	0.590998i	−0.108482	−	0.994098i	$-0.534599\pi$
$367$	−19.6101	−	11.3219i	−1.02364	−	0.590998i	−0.915156	+	0.403101i	$0.867932\pi$
$368$		−	4.62091i		−	0.240882i
$369$	−1.95284	+	24.2960i	−0.101661	+	1.26480i
$370$	−2.05870	+	3.56576i	−0.107026	+	0.185375i
$371$	3.45539	+	2.74862i	0.179395	+	0.142701i
$372$	8.85073	−	14.0017i	0.458889	−	0.725955i
$373$	−8.39025	−	14.5323i	−0.434431	−	0.752456i	0.562818	−	0.826581i	$-0.309717\pi$
$373$	−8.39025	−	14.5323i	−0.434431	−	0.752456i	−0.997249	+	0.0741246i	$0.976384\pi$
$374$	−4.07327	+	7.05510i	−0.210624	+	0.364811i
$375$	3.01508	−	1.58311i	0.155698	−	0.0817513i
$376$	−2.73905	−	1.58139i	−0.141255	−	0.0815539i
$377$	15.7774	−	27.5049i	0.812575	−	1.41657i
$378$	3.46679	+	13.3034i	0.178312	+	0.684255i
$379$	−3.91399	+	2.25974i	−0.201048	+	0.116075i	−0.597144	−	0.802134i	$-0.703698\pi$
$379$	−3.91399	+	2.25974i	−0.201048	+	0.116075i	0.396096	+	0.918209i	$0.370365\pi$
$380$		−	2.53173i		−	0.129875i
$381$	0.0794587	−	0.125702i	0.00407079	−	0.00643993i
$382$	8.45391	−	4.88087i	0.432540	−	0.249727i
$383$	−2.99527	+	1.72932i	−0.153051	+	0.0883641i	−0.574570	−	0.818456i	$-0.694831\pi$
$383$	−2.99527	+	1.72932i	−0.153051	+	0.0883641i	0.421519	+	0.906820i	$0.361497\pi$
$384$	−0.805192	−	1.53351i	−0.0410898	−	0.0782568i
$385$	−14.3511	−	11.4157i	−0.731399	−	0.581799i
$386$	9.03423	+	5.21591i	0.459830	+	0.265483i
$387$	−12.0990	−	25.4751i	−0.615024	−	1.29497i
$388$	7.99888	−	13.8545i	0.406082	−	0.703354i
$389$	−3.12443	+	1.80389i	−0.158415	+	0.0914609i	−0.577112	−	0.816665i	$-0.695820\pi$
$389$	−3.12443	+	1.80389i	−0.158415	+	0.0914609i	0.418697	+	0.908126i	$0.362487\pi$
$390$	−8.92802	−	16.8886i	−0.452088	−	0.855185i
$391$			16.6141i			0.840213i
$392$	5.11962	−	4.77383i	0.258580	−	0.241115i
$393$	−3.56659	−	0.143105i	−0.179910	−	0.00721871i
$394$	−3.77403	−	6.53681i	−0.190133	−	0.329320i
$395$	15.4452	−	8.91731i	0.777134	−	0.448679i
$396$	−2.91614	−	6.14011i	−0.146542	−	0.308552i
$397$	15.1719	+	26.2786i	0.761458	+	1.31888i	0.942099	+	0.335335i	$0.108850\pi$
$397$	15.1719	+	26.2786i	0.761458	+	1.31888i	−0.180641	+	0.983549i	$0.557817\pi$
$398$		−	12.2381i		−	0.613439i
$399$	3.72557	+	0.710593i	0.186512	+	0.0355741i
$400$	2.17863	+	3.77350i	0.108931	+	0.188675i
$401$	−33.2182			−1.65884			−0.829419	−	0.558627i	$-0.811328\pi$
$401$	−33.2182			−1.65884			−0.829419	+	0.558627i	$0.811328\pi$
$402$	0.282076	−	7.03013i	0.0140687	−	0.350631i
$403$	−29.9103	−	17.1572i	−1.48994	−	0.854659i
$404$	−3.56996	+	6.18335i	−0.177612	+	0.307633i
$405$	4.39727	−	27.1772i	0.218502	−	1.35045i
$406$	−18.2094	−	14.4849i	−0.903717	−	0.718871i
$407$	2.64120	+	1.52490i	0.130919	+	0.0755863i
$408$	2.89501	+	5.51364i	0.143324	+	0.272966i
$409$	15.4590			0.764400			0.382200	−	0.924080i	$-0.375166\pi$
$409$	15.4590			0.764400			0.382200	+	0.924080i	$0.375166\pi$
$410$	−24.8534			−1.22742
$411$	7.22631	+	13.7628i	0.356448	+	0.678866i
$412$	1.53644	+	0.887062i	0.0756948	+	0.0437024i
$413$	−26.5718	+	10.4664i	−1.30751	+	0.515019i
$414$	−11.4115	−	7.87095i	−0.560847	−	0.386836i
$415$	−5.80030	+	10.0464i	−0.284725	+	0.493159i
$416$	−3.11743	+	1.81152i	−0.152845	+	0.0888170i
$417$	1.44963	−	36.1287i	0.0709885	−	1.76923i
$418$	−1.87527			−0.0917226
$419$	−6.78747	−	11.7562i	−0.331590	−	0.574330i	0.651234	−	0.758877i	$-0.274252\pi$
$419$	−6.78747	−	11.7562i	−0.331590	−	0.574330i	−0.982824	+	0.184547i	$0.940918\pi$
$420$	−13.2381	+	4.61036i	−0.645953	+	0.224963i
$421$		−	22.2151i		−	1.08270i	−0.840797	−	0.541350i	$-0.817913\pi$
$421$		−	22.2151i		−	1.08270i	0.840797	−	0.541350i	$-0.182087\pi$
$422$	3.36247	+	5.82397i	0.163683	+	0.283507i
$423$	−8.57082	+	4.07057i	−0.416727	+	0.197918i
$424$	−1.44524	+	0.834408i	−0.0701869	+	0.0405224i
$425$	−7.83310	−	13.5673i	−0.379961	−	0.658112i
$426$	−13.1975	−	0.529535i	−0.639421	−	0.0256561i
$427$	−21.8660	−	17.3936i	−1.05817	−	0.841733i
$428$			6.29055i			0.304065i
$429$	−12.5095	+	6.61307i	−0.603965	+	0.319282i
$430$	24.9038	−	14.3782i	1.20097	−	0.693380i
$431$	−4.40288	+	7.62602i	−0.212079	+	0.367332i	−0.952365	−	0.304960i	$-0.901357\pi$
$431$	−4.40288	+	7.62602i	−0.212079	+	0.367332i	0.740286	+	0.672292i	$0.234690\pi$
$432$	−5.15859	−	0.623627i	−0.248193	−	0.0300043i
$433$	−3.16975	−	1.83006i	−0.152328	−	0.0879468i	0.421898	−	0.906643i	$-0.361364\pi$
$433$	−3.16975	−	1.83006i	−0.152328	−	0.0879468i	−0.574227	+	0.818696i	$0.694697\pi$
$434$	−15.7516	+	19.8019i	−0.756102	+	0.950521i
$435$	21.6611	+	41.2543i	1.03857	+	1.97799i
$436$	9.02357	−	5.20976i	0.432151	−	0.249502i
$437$	−3.31208	+	1.91223i	−0.158438	+	0.0914743i
$438$	10.6279	−	16.8131i	0.507819	−	0.803362i
$439$		−	17.7844i		−	0.848805i	−0.905474	−	0.424402i	$-0.860484\pi$
$439$		−	17.7844i		−	0.848805i	0.905474	−	0.424402i	$-0.139516\pi$
$440$	6.00243	−	3.46551i	0.286155	−	0.165212i
$441$	−3.06879	−	20.7746i	−0.146133	−	0.989265i
$442$	11.2085	−	6.51318i	0.533134	−	0.309801i
$443$	−20.0861	−	11.5967i	−0.954319	−	0.550976i	−0.0598990	−	0.998204i	$-0.519078\pi$
$443$	−20.0861	−	11.5967i	−0.954319	−	0.550976i	−0.894420	+	0.447228i	$0.852411\pi$
$444$	2.06412	−	1.08379i	0.0979589	−	0.0514346i
$445$	12.7668	−	22.1128i	0.605206	−	1.04825i
$446$	−6.23733	−	10.8034i	−0.295346	−	0.511555i
$447$	1.57607	−	2.49332i	0.0745456	−	0.117930i
$448$	0.969634	+	2.46167i	0.0458109	+	0.116303i
$449$	4.03168	−	6.98308i	0.190267	−	0.329552i	−0.755072	−	0.655642i	$-0.772398\pi$
$449$	4.03168	−	6.98308i	0.190267	−	0.329552i	0.945339	+	0.326090i	$0.105731\pi$
$450$	13.0298	+	1.04729i	0.614228	+	0.0493699i
$451$			18.4091i			0.866853i
$452$	−7.25521	−	4.18880i	−0.341256	−	0.197024i
$453$	−32.5420	−	20.5704i	−1.52896	−	0.966482i
$454$		−	21.4471i		−	1.00656i
$455$	10.7704	+	27.1203i	0.504923	+	1.27142i
$456$	−0.765955	+	1.21173i	−0.0358691	+	0.0567444i
$457$		−	15.3575i		−	0.718393i	−0.933262	−	0.359197i	$-0.883051\pi$
$457$		−	15.3575i		−	0.718393i	0.933262	−	0.359197i	$-0.116949\pi$
$458$	−11.7463	+	20.3453i	−0.548870	+	0.950671i
$459$	18.5473	+	2.24221i	0.865716	+	0.104657i
$460$	7.06760	−	12.2414i	0.329528	−	0.570760i
$461$	−1.90360	−	1.09904i	−0.0886596	−	0.0511876i	0.455015	−	0.890484i	$-0.349634\pi$
$461$	−1.90360	−	1.09904i	−0.0886596	−	0.0511876i	−0.543674	+	0.839296i	$0.682967\pi$
$462$	3.41494	+	9.80558i	0.158877	+	0.456197i
$463$			9.47072i			0.440142i	0.975484	+	0.220071i	$0.0706289\pi$
$463$			9.47072i			0.440142i	−0.975484	+	0.220071i	$0.929371\pi$
$464$	7.61619	−	4.39721i	0.353573	−	0.204135i
$465$	44.8622	−	23.5555i	2.08043	−	1.09236i
$466$	11.1727	+	6.45055i	0.517564	+	0.298816i
$467$	7.74149	−	13.4087i	0.358234	−	0.620479i	−0.629432	−	0.777055i	$-0.716712\pi$
$467$	7.74149	−	13.4087i	0.358234	−	0.620479i	0.987666	+	0.156577i	$0.0500458\pi$
$468$	−0.836399	+	10.7843i	−0.0386626	+	0.498503i
$469$	−1.58872	+	10.6293i	−0.0733601	+	0.490814i
$470$	−4.83741	−	8.37864i	−0.223133	−	0.386478i
$471$	17.3765	+	10.9840i	0.800669	+	0.506117i
$472$		−	10.7942i		−	0.496844i
$473$	−10.6501	−	18.4465i	−0.489692	−	0.848172i
$474$	−10.0902	−	0.404859i	−0.463460	−	0.0185958i
$475$	1.80312	−	3.12310i	0.0827330	−	0.143298i
$476$	−3.48625	−	8.85075i	−0.159792	−	0.405673i
$477$	−0.401111	+	4.99035i	−0.0183656	+	0.228493i
$478$	−23.0402			−1.05384
$479$	−35.7766	−	20.6556i	−1.63467	−	0.943779i	−0.982625	−	0.185601i	$-0.940577\pi$
$479$	−35.7766	−	20.6556i	−1.63467	−	0.943779i	−0.652048	−	0.758178i	$-0.726090\pi$
$480$	0.212417	−	5.29402i	0.00969545	−	0.241638i
$481$	−2.43832	−	4.19609i	−0.111178	−	0.191325i
$482$	27.7786			1.26528
$483$	16.0302	+	13.8362i	0.729400	+	0.629569i
$484$	2.93307	+	5.08022i	0.133321	+	0.230919i
$485$	42.3803	−	24.4683i	1.92439	−	1.11105i
$486$	−10.3269	+	11.6771i	−0.468437	+	0.529686i
$487$		−	2.53448i		−	0.114848i	−0.998350	−	0.0574240i	$-0.981711\pi$
$487$		−	2.53448i		−	0.114848i	0.998350	−	0.0574240i	$-0.0182887\pi$
$488$	9.14560	−	5.28021i	0.414002	−	0.239024i
$489$	14.0733	+	8.89595i	0.636415	+	0.402289i
$490$	20.8641	−	4.81619i	0.942543	−	0.217573i
$491$	22.3657	−	12.9129i	1.00935	−	0.582749i	0.0983491	−	0.995152i	$-0.468644\pi$
$491$	22.3657	−	12.9129i	1.00935	−	0.582749i	0.911001	+	0.412403i	$0.135310\pi$
$492$	11.8953	+	7.51920i	0.536280	+	0.338992i
$493$	−27.3835	+	15.8099i	−1.23329	+	0.712040i
$494$	2.58848	+	1.48480i	0.116461	+	0.0668045i
$495$	1.66591	−	20.7262i	0.0748772	−	0.931573i
$496$	−4.78177	−	8.28226i	−0.214708	−	0.371885i
$497$	19.9541	+	2.98246i	0.895063	+	0.133782i
$498$	5.81559	−	3.05355i	0.260603	−	0.136833i
$499$	−24.8498	−	14.3470i	−1.11243	−	0.642261i	−0.172972	−	0.984927i	$-0.555337\pi$
$499$	−24.8498	−	14.3470i	−1.11243	−	0.642261i	−0.939458	+	0.342665i	$0.888670\pi$
$500$		−	1.96613i		−	0.0879278i
$501$	36.4973	+	23.0706i	1.63058	+	1.03072i
$502$	6.68358	−	11.5763i	0.298303	−	0.516676i
$503$	−14.9785	+	25.9435i	−0.667858	+	1.15676i	0.310644	+	0.950526i	$0.399455\pi$
$503$	−14.9785	+	25.9435i	−0.667858	+	1.15676i	−0.978502	+	0.206238i	$0.933878\pi$
$504$	7.73081	+	1.79848i	0.344358	+	0.0801108i
$505$	−18.9146	+	10.9204i	−0.841690	+	0.485950i
$506$	−9.06735	−	5.23504i	−0.403093	−	0.232726i
$507$	22.5033	+	0.776618i	0.999405	+	0.0344908i
$508$	−0.0429290	−	0.0743552i	−0.00190467	−	0.00329898i
$509$			12.9462i			0.573832i	0.957956	+	0.286916i	$0.0926301\pi$
$509$			12.9462i			0.573832i	−0.957956	+	0.286916i	$0.907370\pi$
$510$	−0.763729	+	19.0343i	−0.0338185	+	0.842851i
$511$	−18.9144	+	23.7779i	−0.836723	+	1.05187i
$512$	−1.00000			−0.0441942
$513$	1.68774	+	3.95554i	0.0745157	+	0.174641i
$514$	−2.71126			−0.119588
$515$	2.71349	+	4.69990i	0.119571	+	0.207102i
$516$	−16.2694	−	0.652793i	−0.716222	−	0.0287376i
$517$	−6.20614	+	3.58312i	−0.272946	+	0.157585i
$518$	−3.31343	+	1.30514i	−0.145584	+	0.0573444i
$519$	−3.72549	+	5.89367i	−0.163531	+	0.258703i
$520$	−11.0292	+	0.0309078i	−0.483663	+	0.00135540i
$521$	19.0122	+	32.9301i	0.832940	+	1.44269i	0.895696	+	0.444666i	$0.146678\pi$
$521$	19.0122	+	32.9301i	0.832940	+	1.44269i	−0.0627562	+	0.998029i	$0.519989\pi$
$522$	2.11380	−	26.2985i	0.0925183	−	1.15105i
$523$			33.5733i			1.46806i	0.679119	+	0.734028i	$0.262362\pi$
$523$			33.5733i			1.46806i	−0.679119	+	0.734028i	$0.737638\pi$
$524$	−1.03041	+	1.78473i	−0.0450138	+	0.0779662i
$525$	−19.6139	−	3.74104i	−0.856020	−	0.163272i
$526$	12.7361	+	7.35317i	0.555319	+	0.320614i
$527$	17.1925	+	29.7783i	0.748917	+	1.29716i
$528$	−3.92133	−	0.157339i	−0.170654	−	0.00684731i
$529$	1.64720			0.0716173
$530$	−5.10485			−0.221740
$531$	−26.6568	−	18.3861i	−1.15681	−	0.797890i
$532$	1.36317	−	1.71368i	0.0591008	−	0.0742976i
$533$	14.5760	−	25.4105i	0.631356	−	1.10065i
$534$	−12.8005	+	6.72107i	−0.553932	+	0.290849i
$535$	−9.62128	+	16.6645i	−0.415964	+	0.720471i
$536$	−3.51789	−	2.03106i	−0.151950	−	0.0877282i
$537$	0.877563	−	21.8713i	0.0378696	−	0.943818i
$538$	7.51872			0.324155
$539$	−3.56740	−	15.4542i	−0.153659	−	0.665661i
$540$	−12.7120	−	9.54205i	−0.547038	−	0.410624i
$541$	1.91892	+	1.10789i	0.0825009	+	0.0476319i	0.540683	−	0.841226i	$-0.318166\pi$
$541$	1.91892	+	1.10789i	0.0825009	+	0.0476319i	−0.458182	+	0.888858i	$0.651499\pi$
$542$	0.0247852			0.00106462
$543$	2.74648	−	1.44208i	0.117863	−	0.0618854i
$544$	3.59543			0.154153
$545$	31.8730			1.36529
$546$	3.05014	−	16.2387i	0.130534	−	0.694954i
$547$	35.2174			1.50579			0.752895	−	0.658141i	$-0.228657\pi$
$547$	35.2174			1.50579			0.752895	+	0.658141i	$0.228657\pi$
$548$	8.97465			0.383378
$549$	2.53827	−	31.5794i	0.108331	−	1.34778i
$550$	9.87269			0.420973
$551$	−6.30348	−	3.63931i	−0.268537	−	0.155040i
$552$	−7.08623	+	3.72072i	−0.301610	+	0.158364i
$553$	15.2560	+	2.28026i	0.648752	+	0.0969665i
$554$	−6.18124			−0.262616
$555$	7.12580	+	0.285915i	0.302473	+	0.0121364i
$556$	−18.0789	−	10.4379i	−0.766716	−	0.442664i
$557$	−4.07382	+	7.05607i	−0.172613	+	0.298975i	−0.939333	−	0.343007i	$-0.888554\pi$
$557$	−4.07382	+	7.05607i	−0.172613	+	0.298975i	0.766719	+	0.641982i	$0.221888\pi$
$558$	−28.5984	−	2.29866i	−1.21067	−	0.0973099i
$559$	0.0949852	+	33.8947i	0.00401745	+	1.43359i
$560$	−1.19638	+	8.00434i	−0.0505563	+	0.338245i
$561$	14.0989	+	0.565701i	0.595255	+	0.0238839i
$562$	29.5748			1.24754
$563$	21.8949			0.922761			0.461380	−	0.887202i	$-0.347354\pi$
$563$	21.8949			0.922761			0.461380	+	0.887202i	$0.347354\pi$
$564$	−0.219626	+	5.47369i	−0.00924790	+	0.230484i
$565$	−12.8134	−	22.1934i	−0.539063	−	0.933684i
$566$	−18.3623	−	10.6015i	−0.771824	−	0.445613i
$567$	17.6096	−	16.0282i	0.739533	−	0.673120i
$568$	−3.81286	+	6.60406i	−0.159984	+	0.277100i
$569$			39.3854i			1.65112i	0.564314	+	0.825560i	$0.309141\pi$
$569$			39.3854i			1.65112i	−0.564314	+	0.825560i	$0.690859\pi$
$570$	−3.88244	+	2.03852i	−0.162617	+	0.0853844i
$571$	−10.0406	−	17.3909i	−0.420187	−	0.727786i	0.575770	−	0.817612i	$-0.304702\pi$
$571$	−10.0406	−	17.3909i	−0.420187	−	0.727786i	−0.995958	+	0.0898257i	$0.971369\pi$
$572$	0.0228937	+	8.16944i	0.000957235	+	0.341581i
$573$	−14.2919	−	9.03416i	−0.597053	−	0.377407i
$574$	−16.8228	−	13.3819i	−0.702172	−	0.558550i
$575$	17.4370	−	10.0672i	0.727172	−	0.419833i
$576$	−1.70333	+	2.46955i	−0.0709722	+	0.102898i
$577$	10.1331	+	17.5510i	0.421847	+	0.730660i	0.996120	−	0.0880038i	$-0.0280488\pi$
$577$	10.1331	+	17.5510i	0.421847	+	0.730660i	−0.574274	+	0.818663i	$0.694715\pi$
$578$	4.07291			0.169411
$579$	0.724394	−	18.0539i	0.0301048	−	0.750296i
$580$	26.9018			1.11704
$581$	−9.33546	+	3.67717i	−0.387300	+	0.152555i
$582$	−27.6867	−	1.11090i	−1.14765	−	0.0460482i
$583$			3.78121i			0.156602i
$584$	−5.74190	−	9.94525i	−0.237601	−	0.411538i
$585$	−18.7101	+	27.2898i	−0.773567	+	1.12829i
$586$	10.1781	+	5.87631i	0.420452	+	0.242748i
$587$	5.90203	−	3.40754i	0.243603	−	0.140644i	−0.373229	−	0.927739i	$-0.621749\pi$
$587$	5.90203	−	3.40754i	0.243603	−	0.140644i	0.616831	+	0.787095i	$0.288416\pi$
$588$	−11.4430	−	4.00716i	−0.471902	−	0.165252i
$589$	−3.95759	+	6.85474i	−0.163070	+	0.282445i
$590$	16.5095	−	28.5954i	0.679687	−	1.17725i
$591$	−6.98547	+	11.0509i	−0.287344	+	0.454574i
$592$		−	1.34601i		−	0.0553206i
$593$	30.3893	+	17.5453i	1.24794	+	0.720498i	0.970698	−	0.240302i	$-0.0772464\pi$
$593$	30.3893	+	17.5453i	1.24794	+	0.720498i	0.277242	+	0.960800i	$0.410580\pi$
$594$	−7.06789	+	9.41591i	−0.289999	+	0.386339i
$595$	4.30150	−	28.7790i	0.176344	−	1.17982i
$596$	−0.851501	−	1.47484i	−0.0348788	−	0.0604119i
$597$	−18.7673	+	9.85399i	−0.768093	+	0.403297i
$598$	8.37086	+	14.4054i	0.342310	+	0.589080i
$599$	3.02800	−	1.74821i	0.123721	−	0.0714301i	−0.436863	−	0.899528i	$-0.643910\pi$
$599$	3.02800	−	1.74821i	0.123721	−	0.0714301i	0.560583	+	0.828098i	$0.310577\pi$
$600$	4.03250	−	6.37935i	0.164626	−	0.260436i
$601$	−30.2974	+	17.4922i	−1.23586	+	0.713521i	−0.968244	−	0.250006i	$-0.919567\pi$
$601$	−30.2974	+	17.4922i	−1.23586	+	0.713521i	−0.267611	+	0.963527i	$0.586234\pi$
$602$	24.5987	+	3.67668i	1.00257	+	0.149850i
$603$	−11.0079	+	5.22803i	−0.448277	+	0.212902i
$604$	−19.2492	+	11.1135i	−0.783239	+	0.452203i
$605$			17.9443i			0.729539i
$606$	12.3568	+	0.495801i	0.501959	+	0.0201405i
$607$	−15.1664	+	8.75631i	−0.615584	+	0.355408i	−0.775148	−	0.631780i	$-0.782325\pi$
$607$	−15.1664	+	8.75631i	−0.615584	+	0.355408i	0.159564	+	0.987188i	$0.448991\pi$
$608$	0.413821	+	0.716759i	0.0167826	+	0.0290684i
$609$	−7.55068	+	39.5875i	−0.305969	+	1.60416i
$610$	32.3040			1.30795
$611$	11.4035	−	0.0319568i	0.461337	−	0.00129283i
$612$	6.12421	−	8.87907i	0.247556	−	0.358915i
$613$	11.5436	+	6.66471i	0.466242	+	0.269185i	0.714665	−	0.699467i	$-0.246579\pi$
$613$	11.5436	+	6.66471i	0.466242	+	0.269185i	−0.248423	+	0.968652i	$0.579912\pi$
$614$	12.2431			0.494090
$615$	20.0117	+	38.1130i	0.806951	+	1.53687i
$616$	5.92889	+	0.886170i	0.238882	+	0.0357048i
$617$	−16.4579	+	28.5059i	−0.662569	+	1.14760i	0.317369	+	0.948302i	$0.397201\pi$
$617$	−16.4579	+	28.5059i	−0.662569	+	1.14760i	−0.979938	+	0.199301i	$0.936133\pi$
$618$	0.123196	−	3.07040i	0.00495569	−	0.123510i
$619$	3.67239	+	6.36076i	0.147606	+	0.255661i	0.930342	−	0.366693i	$-0.119510\pi$
$619$	3.67239	+	6.36076i	0.147606	+	0.255661i	−0.782736	+	0.622353i	$0.786177\pi$
$620$		−	29.2545i		−	1.17489i
$621$	−2.88172	+	23.8374i	−0.115640	+	0.956562i
$622$	−4.81504	−	8.33990i	−0.193066	−	0.334399i
$623$	20.5479	−	8.09369i	0.823236	−	0.324267i
$624$	5.28812	+	3.32201i	0.211694	+	0.132987i
$625$	13.9003	−	24.0760i	0.556012	−	0.963041i
$626$	−12.0523	−	6.95841i	−0.481707	−	0.278114i
$627$	1.50995	+	2.87576i	0.0603018	+	0.114847i
$628$	10.2785	−	5.93431i	0.410158	−	0.236805i
$629$			4.83947i			0.192962i
$630$	17.7293	+	16.5886i	0.706351	+	0.660904i
$631$	−23.3905	−	13.5045i	−0.931159	−	0.537605i	−0.0439813	−	0.999032i	$-0.514004\pi$
$631$	−23.3905	−	13.5045i	−0.931159	−	0.537605i	−0.887178	+	0.461427i	$0.847338\pi$
$632$	−2.91514	+	5.04917i	−0.115958	+	0.200845i
$633$	6.22371	−	9.84581i	0.247370	−	0.391336i
$634$	−11.8204	+	20.4735i	−0.469448	+	0.813108i
$635$		−	0.262636i		−	0.0104224i
$636$	2.44327	+	1.54443i	0.0968819	+	0.0612408i
$637$	−7.31219	+	24.1564i	−0.289719	+	0.957112i
$638$		−	19.9264i		−	0.788895i
$639$	9.81447	+	20.6649i	0.388254	+	0.817492i
$640$	−2.64914	−	1.52948i	−0.104716	−	0.0604581i
$641$		−	20.7741i		−	0.820526i	−0.911967	−	0.410263i	$-0.865437\pi$
$641$		−	20.7741i		−	0.820526i	0.911967	−	0.410263i	$-0.134563\pi$
$642$	9.64664	−	5.06510i	0.380723	−	0.199903i
$643$	0.127258	−	0.220417i	0.00501857	−	0.00869242i	−0.863505	−	0.504340i	$-0.831736\pi$
$643$	0.127258	−	0.220417i	0.00501857	−	0.00869242i	0.868524	+	0.495647i	$0.165069\pi$
$644$	11.3751	−	4.48059i	0.448243	−	0.176560i
$645$	−42.1016	−	26.6132i	−1.65775	−	1.04789i
$646$	−1.48786	−	2.57705i	−0.0585392	−	0.101393i
$647$	−12.2158	+	21.1583i	−0.480251	+	0.831819i	−0.999743	−	0.0226559i	$-0.992788\pi$
$647$	−12.2158	+	21.1583i	−0.480251	+	0.831819i	0.519492	+	0.854475i	$0.326121\pi$
$648$	3.19732	+	8.41292i	0.125602	+	0.330491i
$649$	−21.1809	−	12.2288i	−0.831422	−	0.480022i
$650$	−13.6275	−	7.81700i	−0.534514	−	0.306608i
$651$	43.0495	+	8.21102i	1.68724	+	0.321815i
$652$	8.32458	−	4.80620i	0.326016	−	0.188225i
$653$			0.782789i			0.0306329i	0.999883	+	0.0153164i	$0.00487557\pi$
$653$			0.782789i			0.0306329i	−0.999883	+	0.0153164i	$0.995124\pi$
$654$	−15.2550	−	9.64292i	−0.596516	−	0.377068i
$655$	−5.45942	+	3.15200i	−0.213317	+	0.123159i
$656$	7.03626	−	4.06239i	0.274720	−	0.158610i
$657$	−34.3406	−	2.76020i	−1.33976	−	0.107686i
$658$	1.23698	−	8.27599i	0.0482226	−	0.322632i
$659$	−37.5123	−	21.6577i	−1.46127	−	0.843666i	−0.462202	−	0.886775i	$-0.652940\pi$
$659$	−37.5123	−	21.6577i	−1.46127	−	0.843666i	−0.999070	+	0.0431091i	$0.986274\pi$
$660$	−10.1475	−	6.41442i	−0.394991	−	0.249681i
$661$	6.51294	−	11.2807i	0.253324	−	0.438770i	−0.711115	−	0.703076i	$-0.751809\pi$
$661$	6.51294	−	11.2807i	0.253324	−	0.438770i	0.964439	+	0.264306i	$0.0851428\pi$
$662$	−13.0461	+	7.53219i	−0.507053	+	0.292747i
$663$	−19.0131	−	11.9440i	−0.738406	−	0.463868i
$664$		−	3.79233i		−	0.147171i
$665$	6.23227	−	2.45485i	0.241677	−	0.0951949i
$666$	−3.32403	−	2.29270i	−0.128804	−	0.0888403i
$667$	−20.3191	−	35.1937i	−0.786759	−	1.36271i
$668$	21.5888	−	12.4643i	0.835296	−	0.482258i
$669$	−11.5449	+	18.2638i	−0.446351	+	0.706120i
$670$	−6.21292	−	10.7611i	−0.240026	−	0.415738i
$671$		−	23.9279i		−	0.923725i
$672$	2.99426	−	3.46906i	0.115506	−	0.133822i
$673$	−16.1195	−	27.9199i	−0.621363	−	1.07623i	−0.989232	−	0.146355i	$-0.953246\pi$
$673$	−16.1195	−	27.9199i	−0.621363	−	1.07623i	0.367869	−	0.929877i	$-0.380087\pi$
$674$	9.93070			0.382516
$675$	−8.88541	−	20.8246i	−0.341999	−	0.801539i
$676$	6.43680	−	11.2946i	0.247569	−	0.434407i
$677$	12.3401	−	21.3737i	0.474268	−	0.821457i	−0.525298	−	0.850919i	$-0.676046\pi$
$677$	12.3401	−	21.3737i	0.474268	−	0.821457i	0.999566	+	0.0294618i	$0.00937935\pi$
$678$	−0.581746	+	14.4988i	−0.0223418	+	0.556821i
$679$	41.8611	+	6.25683i	1.60648	+	0.240115i
$680$	9.52479	+	5.49914i	0.365259	+	0.210882i
$681$	−32.8895	+	17.2691i	−1.26033	+	0.661752i
$682$	−21.6691			−0.829752
$683$	16.2437			0.621546			0.310773	−	0.950484i	$-0.399412\pi$
$683$	16.2437			0.621546			0.310773	+	0.950484i	$0.399412\pi$
$684$	2.47494	+	0.198929i	0.0946318	+	0.00760624i
$685$	23.7751	+	13.7266i	0.908400	+	0.524465i
$686$	16.7158	+	7.97393i	0.638210	+	0.304446i
$687$	40.6578	+	1.63135i	1.55119	+	0.0622398i
$688$	−4.70036	+	8.14127i	−0.179200	+	0.310383i
$689$	2.99389	−	5.21929i	0.114058	−	0.198839i
$690$	−24.4632	−	0.981558i	−0.931298	−	0.0373673i
$691$	−16.1544			−0.614541			−0.307271	−	0.951622i	$-0.599416\pi$
$691$	−16.1544			−0.614541			−0.307271	+	0.951622i	$0.599416\pi$
$692$	2.01276	+	3.48621i	0.0765138	+	0.132526i
$693$	12.2873	−	13.1322i	0.466757	−	0.498852i
$694$			3.36902i			0.127886i
$695$	−31.9290	−	55.3027i	−1.21114	−	2.09775i
$696$	−12.8757	−	8.13894i	−0.488051	−	0.308506i
$697$	−25.2984	+	14.6060i	−0.958243	+	0.553242i
$698$	−15.4110	−	26.6927i	−0.583317	−	1.01033i
$699$	0.895862	−	22.3274i	0.0338846	−	0.844500i
$700$	−7.17662	+	9.02197i	−0.271251	+	0.340998i
$701$			36.9386i			1.39515i	0.716510	+	0.697577i	$0.245738\pi$
$701$			36.9386i			1.39515i	−0.716510	+	0.697577i	$0.754262\pi$
$702$	17.2113	−	7.40077i	0.649598	−	0.279324i
$703$	−0.964763	+	0.557006i	−0.0363867	+	0.0210079i
$704$	−1.13290	+	1.96224i	−0.0426979	+	0.0739549i
$705$	−8.95372	+	14.1646i	−0.337217	+	0.533471i
$706$	17.0077	+	9.81940i	0.640093	+	0.369558i
$707$	−18.6829	−	2.79247i	−0.702643	−	0.105021i
$708$	−16.5531	+	8.69141i	−0.622103	+	0.326643i
$709$	−2.33135	+	1.34600i	−0.0875556	+	0.0505502i	−0.543139	−	0.839643i	$-0.682764\pi$
$709$	−2.33135	+	1.34600i	−0.0875556	+	0.0505502i	0.455583	+	0.890193i	$0.349431\pi$
$710$	−20.2016	+	11.6634i	−0.758152	+	0.437719i
$711$	7.50371	+	15.7995i	0.281411	+	0.592528i
$712$			8.34716i			0.312823i
$713$	−38.2716	+	22.0961i	−1.43328	+	0.827506i
$714$	−10.7656	+	12.4728i	−0.402894	+	0.466781i
$715$	−12.4344	+	21.6770i	−0.465019	+	0.810674i
$716$	−10.9445	−	6.31879i	−0.409014	−	0.236144i
$717$	18.5518	+	35.3325i	0.692830	+	1.31952i
$718$	−5.20022	+	9.00705i	−0.194071	+	0.336140i
$719$	−9.62506	−	16.6711i	−0.358954	−	0.621727i	0.628832	−	0.777541i	$-0.283533\pi$
$719$	−9.62506	−	16.6711i	−0.358954	−	0.621727i	−0.987786	+	0.155814i	$0.950200\pi$
$720$	−8.28949	+	3.93696i	−0.308931	+	0.146722i
$721$	−0.693871	+	4.64232i	−0.0258411	+	0.172889i
$722$	−9.15750	+	15.8613i	−0.340807	+	0.590295i
$723$	−22.3671	−	42.5988i	−0.831841	−	1.58427i
$724$		−	1.79097i		−	0.0665610i
$725$	33.1857	+	19.1598i	1.23249	+	0.711577i
$726$	5.42891	−	8.58845i	0.201486	−	0.318747i
$727$		−	29.4029i		−	1.09049i	−0.838276	−	0.545246i	$-0.816436\pi$
$727$		−	29.4029i		−	1.09049i	0.838276	−	0.545246i	$-0.183564\pi$
$728$	−7.48213	−	5.91758i	−0.277306	−	0.219320i
$729$	26.2222	+	6.43408i	0.971192	+	0.238299i
$730$		−	35.1285i		−	1.30016i
$731$	16.8998	−	29.2713i	0.625062	−	1.08264i
$732$	−15.4612	−	9.77332i	−0.571464	−	0.361232i
$733$	−13.5812	+	23.5234i	−0.501635	+	0.868857i	0.498363	+	0.866968i	$0.333935\pi$
$733$	−13.5812	+	23.5234i	−0.501635	+	0.868857i	−0.999998	+	0.00188874i	$0.999399\pi$
$734$	19.6101	+	11.3219i	0.723821	+	0.417898i
$735$	−24.1853	−	28.1174i	−0.892088	−	1.03713i
$736$			4.62091i			0.170329i
$737$	−7.97085	+	4.60197i	−0.293610	+	0.169516i
$738$	1.95284	−	24.2960i	0.0718851	−	0.894347i
$739$	15.9336	+	9.19930i	0.586129	+	0.338402i	0.763565	−	0.645731i	$-0.223447\pi$
$739$	15.9336	+	9.19930i	0.586129	+	0.338402i	−0.177437	+	0.984132i	$0.556780\pi$
$740$	2.05870	−	3.56576i	0.0756791	−	0.131080i
$741$	0.192745	−	5.16502i	0.00708066	−	0.189742i
$742$	−3.45539	−	2.74862i	−0.126851	−	0.100905i
$743$	16.4058	+	28.4156i	0.601869	+	1.04247i	0.992538	+	0.121937i	$0.0389105\pi$
$743$	16.4058	+	28.4156i	0.601869	+	1.04247i	−0.390669	+	0.920531i	$0.627756\pi$
$744$	−8.85073	+	14.0017i	−0.324484	+	0.513328i
$745$		−	5.20942i		−	0.190858i
$746$	8.39025	+	14.5323i	0.307189	+	0.532067i
$747$	−9.36533	−	6.45960i	−0.342660	−	0.236344i
$748$	4.07327	−	7.05510i	0.148933	−	0.257960i
$749$	−15.4852	+	6.09953i	−0.565818	+	0.222872i
$750$	−3.01508	+	1.58311i	−0.110095	+	0.0578069i
$751$	11.4802			0.418917			0.209459	−	0.977818i	$-0.432830\pi$
$751$	11.4802			0.418917			0.209459	+	0.977818i	$0.432830\pi$
$752$	2.73905	+	1.58139i	0.0998827	+	0.0576673i
$753$	−23.1340	−	0.928225i	−0.843049	−	0.0338264i
$754$	−15.7774	+	27.5049i	−0.574577	+	1.00167i
$755$	−67.9918			−2.47447
$756$	−3.46679	−	13.3034i	−0.126086	−	0.483841i
$757$	−6.81712	−	11.8076i	−0.247772	−	0.429154i	0.715135	−	0.698986i	$-0.246365\pi$
$757$	−6.81712	−	11.8076i	−0.247772	−	0.429154i	−0.962907	+	0.269832i	$0.913032\pi$
$758$	3.91399	−	2.25974i	0.142163	−	0.0820776i
$759$	−0.727050	+	18.1201i	−0.0263902	+	0.657719i
$760$			2.53173i			0.0918353i
$761$	29.4337	−	16.9936i	1.06697	−	0.616016i	0.139619	−	0.990205i	$-0.455412\pi$
$761$	29.4337	−	16.9936i	1.06697	−	0.616016i	0.927352	+	0.374189i	$0.122079\pi$
$762$	−0.0794587	+	0.125702i	−0.00287848	+	0.00455372i
$763$	21.5743	+	17.1615i	0.781041	+	0.621287i
$764$	−8.45391	+	4.88087i	−0.305852	+	0.176584i
$765$	29.8043	−	14.1550i	1.07758	−	0.511777i
$766$	2.99527	−	1.72932i	0.108223	−	0.0624828i
$767$	19.5539	+	33.6502i	0.706051	+	1.21504i
$768$	0.805192	+	1.53351i	0.0290549	+	0.0553359i
$769$	19.7746	+	34.2506i	0.713090	+	1.23511i	0.963692	+	0.267018i	$0.0860382\pi$
$769$	19.7746	+	34.2506i	0.713090	+	1.23511i	−0.250602	+	0.968090i	$0.580628\pi$
$770$	14.3511	+	11.4157i	0.517177	+	0.411394i
$771$	2.18308	+	4.15775i	0.0786218	+	0.149738i
$772$	−9.03423	−	5.21591i	−0.325149	−	0.187725i
$773$			8.09302i			0.291086i	0.989352	+	0.145543i	$0.0464929\pi$
$773$			8.09302i			0.291086i	−0.989352	+	0.145543i	$0.953507\pi$
$774$	12.0990	+	25.4751i	0.434888	+	0.915682i
$775$	20.8354	−	36.0880i	0.748429	−	1.29632i
$776$	−7.99888	+	13.8545i	−0.287143	+	0.497347i
$777$	4.66939	+	4.03030i	0.167513	+	0.144586i
$778$	3.12443	−	1.80389i	0.112016	−	0.0646726i
$779$	−5.82350	−	3.36220i	−0.208649	−	0.120463i
$780$	8.92802	+	16.8886i	0.319675	+	0.604707i
$781$	8.63918	+	14.9635i	0.309134	+	0.535436i
$782$		−	16.6141i		−	0.594120i
$783$	−42.0311	+	17.9338i	−1.50207	+	0.640900i
$784$	−5.11962	+	4.77383i	−0.182844	+	0.170494i
$785$	36.3057			1.29581
$786$	3.56659	+	0.143105i	0.127216	+	0.00510440i
$787$	−7.98791			−0.284738			−0.142369	−	0.989814i	$-0.545472\pi$
$787$	−7.98791			−0.284738			−0.142369	+	0.989814i	$0.545472\pi$
$788$	3.77403	+	6.53681i	0.134444	+	0.232864i
$789$	1.02122	−	25.4517i	0.0363564	−	0.906103i
$790$	−15.4452	+	8.91731i	−0.549517	+	0.317264i
$791$	3.27653	−	21.9215i	0.116500	−	0.779439i
$792$	2.91614	+	6.14011i	0.103621	+	0.218179i
$793$	−18.9456	+	33.0282i	−0.672778	+	1.17286i
$794$	−15.1719	−	26.2786i	−0.538432	−	0.932592i
$795$	4.11038	+	7.82836i	0.145780	+	0.277643i
$796$			12.2381i			0.433767i
$797$	−12.1440	+	21.0340i	−0.430162	+	0.745063i	−0.996887	−	0.0788442i	$-0.974877\pi$
$797$	−12.1440	+	21.0340i	−0.430162	+	0.745063i	0.566725	+	0.823907i	$0.308210\pi$
$798$	−3.72557	−	0.710593i	−0.131884	−	0.0251547i
$799$	−9.84804	−	5.68577i	−0.348398	−	0.201148i
$800$	−2.17863	−	3.77350i	−0.0770262	−	0.133413i
$801$	20.6137	+	14.2180i	0.728349	+	0.502368i
$802$	33.2182			1.17298
$803$	−26.0200			−0.918227
$804$	−0.282076	+	7.03013i	−0.00994805	+	0.247933i
$805$	36.9873	+	5.52836i	1.30363	+	0.194849i
$806$	29.9103	+	17.1572i	1.05355	+	0.604335i
$807$	−6.05401	−	11.5301i	−0.213111	−	0.405877i
$808$	3.56996	−	6.18335i	0.125591	−	0.217529i
$809$	−17.1927	−	9.92621i	−0.604463	−	0.348987i	0.166332	−	0.986070i	$-0.446808\pi$
$809$	−17.1927	−	9.92621i	−0.604463	−	0.348987i	−0.770795	+	0.637083i	$0.780141\pi$
$810$	−4.39727	+	27.1772i	−0.154504	+	0.954911i
$811$	−44.1058			−1.54876			−0.774382	−	0.632719i	$-0.781939\pi$
$811$	−44.1058			−1.54876			−0.774382	+	0.632719i	$0.781939\pi$
$812$	18.2094	+	14.4849i	0.639025	+	0.508319i
$813$	−0.0199568	−	0.0380085i	−0.000699917	−	0.00133301i
$814$	−2.64120	−	1.52490i	−0.0925739	−	0.0534476i
$815$	29.4040			1.02998
$816$	−2.89501	−	5.51364i	−0.101346	−	0.193016i
$817$	7.78043			0.272203
$818$	−15.4590			−0.540513
$819$	−27.3583	+	8.39786i	−0.955976	+	0.293445i
$820$	24.8534			0.867918
$821$	−48.6744			−1.69875			−0.849375	−	0.527790i	$-0.823021\pi$
$821$	−48.6744			−1.69875			−0.849375	+	0.527790i	$0.823021\pi$
$822$	−7.22631	−	13.7628i	−0.252047	−	0.480031i
$823$	1.25808			0.0438537			0.0219269	−	0.999760i	$-0.493020\pi$
$823$	1.25808			0.0438537			0.0219269	+	0.999760i	$0.493020\pi$
$824$	−1.53644	−	0.887062i	−0.0535243	−	0.0309023i
$825$	−7.94941	−	15.1399i	−0.276763	−	0.527104i
$826$	26.5718	−	10.4664i	0.924550	−	0.364174i
$827$	45.8818			1.59547			0.797734	−	0.603010i	$-0.206032\pi$
$827$	45.8818			1.59547			0.797734	+	0.603010i	$0.206032\pi$
$828$	11.4115	+	7.87095i	0.396579	+	0.273534i
$829$	9.08503	+	5.24525i	0.315536	+	0.182175i	0.649401	−	0.760446i	$-0.275020\pi$
$829$	9.08503	+	5.24525i	0.315536	+	0.182175i	−0.333865	+	0.942621i	$0.608353\pi$
$830$	5.80030	−	10.0464i	0.201331	−	0.348716i
$831$	4.97708	+	9.47902i	0.172653	+	0.328824i
$832$	3.11743	−	1.81152i	0.108078	−	0.0628031i
$833$	18.4072	−	17.1640i	0.637772	−	0.594696i
$834$	−1.44963	+	36.1287i	−0.0501964	+	1.25104i
$835$	76.2557			2.63894
$836$	1.87527			0.0648577
$837$	19.5021	+	45.7069i	0.674093	+	1.57986i
$838$	6.78747	+	11.7562i	0.234469	+	0.406113i
$839$	25.7265	+	14.8532i	0.888179	+	0.512790i	0.873346	−	0.487100i	$-0.161945\pi$
$839$	25.7265	+	14.8532i	0.888179	+	0.512790i	0.0148325	+	0.999890i	$0.495278\pi$
$840$	13.2381	−	4.61036i	0.456757	−	0.159073i
$841$	24.1709	−	41.8653i	0.833481	−	1.44363i
$842$			22.2151i			0.765584i
$843$	−23.8134	−	45.3534i	−0.820176	−	1.56205i
$844$	−3.36247	−	5.82397i	−0.115741	−	0.200469i
$845$	34.3268	−	20.0760i	1.18088	−	0.690634i
$846$	8.57082	−	4.07057i	0.294671	−	0.139949i
$847$	−9.66181	+	12.1462i	−0.331984	+	0.417348i
$848$	1.44524	−	0.834408i	0.0496296	−	0.0286537i
$849$	−1.47235	+	36.6950i	−0.0505308	+	1.25937i
$850$	7.83310	+	13.5673i	0.268673	+	0.465356i
$851$	−6.21978			−0.213211
$852$	13.1975	+	0.529535i	0.452139	+	0.0181416i
$853$	32.2400			1.10388			0.551939	−	0.833885i	$-0.313888\pi$
$853$	32.2400			1.10388			0.551939	+	0.833885i	$0.313888\pi$
$854$	21.8660	+	17.3936i	0.748240	+	0.595195i
$855$	6.25221	+	4.31237i	0.213821	+	0.147480i
$856$		−	6.29055i		−	0.215006i
$857$	12.4374	+	21.5422i	0.424853	+	0.735867i	0.996407	−	0.0846975i	$-0.0269924\pi$
$857$	12.4374	+	21.5422i	0.424853	+	0.735867i	−0.571554	+	0.820565i	$0.693659\pi$
$858$	12.5095	−	6.61307i	0.427068	−	0.225767i
$859$	−36.6844	−	21.1798i	−1.25166	−	0.722644i	−0.280218	−	0.959937i	$-0.590407\pi$
$859$	−36.6844	−	21.1798i	−1.25166	−	0.722644i	−0.971438	+	0.237293i	$0.923740\pi$
$860$	−24.9038	+	14.3782i	−0.849214	+	0.490294i
$861$	−6.97573	+	36.5731i	−0.237732	+	1.24641i
$862$	4.40288	−	7.62602i	0.149963	−	0.259743i
$863$	−21.7601	+	37.6895i	−0.740721	+	1.28297i	0.211446	+	0.977390i	$0.432183\pi$
$863$	−21.7601	+	37.6895i	−0.740721	+	1.28297i	−0.952167	+	0.305577i	$0.901151\pi$
$864$	5.15859	+	0.623627i	0.175499	+	0.0212162i
$865$			12.3139i			0.418686i
$866$	3.16975	+	1.83006i	0.107712	+	0.0621878i
$867$	−3.27947	−	6.24586i	−0.111377	−	0.212121i
$868$	15.7516	−	19.8019i	0.534645	−	0.672120i
$869$	6.60514	+	11.4404i	0.224064	+	0.388090i
$870$	−21.6611	−	41.2543i	−0.734381	−	1.39865i
$871$	14.6461	−	0.0410437i	0.496264	−	0.00139071i
$872$	−9.02357	+	5.20976i	−0.305577	+	0.176425i
$873$	20.5895	+	43.3524i	0.696849	+	1.46726i
$874$	3.31208	−	1.91223i	0.112033	−	0.0646821i
$875$	4.83995	−	1.90642i	0.163620	−	0.0644488i
$876$	−10.6279	+	16.8131i	−0.359082	+	0.568062i
$877$	1.76857	−	1.02108i	0.0597203	−	0.0344795i	−0.469843	−	0.882750i	$-0.655689\pi$
$877$	1.76857	−	1.02108i	0.0597203	−	0.0344795i	0.529563	+	0.848271i	$0.322356\pi$
$878$			17.7844i			0.600196i
$879$	0.816111	−	20.3398i	0.0275267	−	0.686044i
$880$	−6.00243	+	3.46551i	−0.202342	+	0.116822i
$881$	−9.47062	−	16.4036i	−0.319073	−	0.552651i	0.661222	−	0.750191i	$-0.270038\pi$
$881$	−9.47062	−	16.4036i	−0.319073	−	0.552651i	−0.980295	+	0.197539i	$0.936705\pi$
$882$	3.06879	+	20.7746i	0.103332	+	0.699516i
$883$	10.7657			0.362296			0.181148	−	0.983456i	$-0.442019\pi$
$883$	10.7657			0.362296			0.181148	+	0.983456i	$0.442019\pi$
$884$	−11.2085	+	6.51318i	−0.376983	+	0.219062i
$885$	−57.1448	−	2.29287i	−1.92090	−	0.0770740i
$886$	20.0861	+	11.5967i	0.674805	+	0.389599i
$887$	−18.6812			−0.627254			−0.313627	−	0.949546i	$-0.601544\pi$
$887$	−18.6812			−0.627254			−0.313627	+	0.949546i	$0.601544\pi$
$888$	−2.06412	+	1.08379i	−0.0692674	+	0.0363698i
$889$	0.141412	−	0.177774i	0.00474282	−	0.00596236i
$890$	−12.7668	+	22.1128i	−0.427945	+	0.741223i
$891$	20.1304	+	3.25710i	0.674395	+	0.109117i
$892$	6.23733	+	10.8034i	0.208841	+	0.361724i
$893$		−	2.61765i		−	0.0875962i
$894$	−1.57607	+	2.49332i	−0.0527117	+	0.0833891i
$895$	−19.3289	−	33.4787i	−0.646096	−	1.11907i
$896$	−0.969634	−	2.46167i	−0.0323932	−	0.0822386i
$897$	15.3507	−	24.4359i	0.512545	−	0.815892i
$898$	−4.03168	+	6.98308i	−0.134539	+	0.233028i
$899$	−72.8377	−	42.0529i	−2.42927	−	1.40254i
$900$	−13.0298	−	1.04729i	−0.434325	−	0.0349098i
$901$	−5.19624	+	3.00005i	−0.173112	+	0.0999462i
$902$		−	18.4091i		−	0.612957i
$903$	−14.1684	−	40.6829i	−0.471496	−	1.35384i
$904$	7.25521	+	4.18880i	0.241305	+	0.139317i
$905$	2.73926	−	4.74454i	0.0910561	−	0.157714i
$906$	32.5420	+	20.5704i	1.08114	+	0.683406i
$907$	15.5213	−	26.8836i	0.515375	−	0.892656i	−0.484466	−	0.874810i	$-0.660986\pi$
$907$	15.5213	−	26.8836i	0.515375	−	0.892656i	0.999841	−	0.0178455i	$-0.00568070\pi$
$908$			21.4471i			0.711748i
$909$	−9.18924	−	19.3485i	−0.304788	−	0.641748i
$910$	−10.7704	−	27.1203i	−0.357035	−	0.899028i
$911$		−	11.8527i		−	0.392697i	−0.980534	−	0.196349i	$-0.937092\pi$
$911$		−	11.8527i		−	0.392697i	0.980534	−	0.196349i	$-0.0629084\pi$
$912$	0.765955	−	1.21173i	0.0253633	−	0.0401243i
$913$	−7.44148	−	4.29634i	−0.246277	−	0.142188i
$914$			15.3575i			0.507981i
$915$	−26.0109	−	49.5386i	−0.859893	−	1.63770i
$916$	11.7463	−	20.3453i	0.388110	−	0.672226i
$917$	−5.39253	−	0.806002i	−0.178077	−	0.0266165i
$918$	−18.5473	−	2.24221i	−0.612154	−	0.0740038i
$919$	4.54584	+	7.87363i	0.149953	+	0.259727i	0.931210	−	0.364483i	$-0.118754\pi$
$919$	4.54584	+	7.87363i	0.149953	+	0.259727i	−0.781257	+	0.624210i	$0.785421\pi$
$920$	−7.06760	+	12.2414i	−0.233012	+	0.403588i
$921$	−9.85803	−	18.7749i	−0.324833	−	0.618655i
$922$	1.90360	+	1.09904i	0.0626918	+	0.0361951i
$923$	−0.0770504	−	27.4948i	−0.00253614	−	0.905002i
$924$	−3.41494	−	9.80558i	−0.112343	−	0.322580i
$925$	5.07916	−	2.93245i	0.167002	−	0.0964184i
$926$		−	9.47072i		−	0.311227i
$927$	−4.80770	+	2.28334i	−0.157906	+	0.0749947i
$928$	−7.61619	+	4.39721i	−0.250014	+	0.144346i
$929$	−2.76571	+	1.59678i	−0.0907399	+	0.0523887i	−0.544683	−	0.838642i	$-0.683350\pi$
$929$	−2.76571	+	1.59678i	−0.0907399	+	0.0523887i	0.453943	+	0.891030i	$0.350017\pi$
$930$	−44.8622	+	23.5555i	−1.47109	+	0.772415i
$931$	5.54029	+	1.69402i	0.181576	+	0.0555192i
$932$	−11.1727	−	6.45055i	−0.365973	−	0.211295i
$933$	−8.91232	+	14.0992i	−0.291776	+	0.461586i
$934$	−7.74149	+	13.4087i	−0.253309	+	0.438745i
$935$	21.5813	−	12.4600i	0.705784	−	0.407485i
$936$	0.836399	−	10.7843i	0.0273386	−	0.352495i
$937$			50.2345i			1.64109i	0.571581	+	0.820545i	$0.306330\pi$
$937$			50.2345i			1.64109i	−0.571581	+	0.820545i	$0.693670\pi$
$938$	1.58872	−	10.6293i	0.0518734	−	0.347058i
$939$	−0.966394	+	24.0852i	−0.0315371	+	0.785992i
$940$	4.83741	+	8.37864i	0.157779	+	0.273281i
$941$	−23.4013	+	13.5107i	−0.762861	+	0.440438i	−0.830322	−	0.557284i	$-0.811843\pi$
$941$	−23.4013	+	13.5107i	−0.762861	+	0.440438i	0.0674613	+	0.997722i	$0.478510\pi$
$942$	−17.3765	−	10.9840i	−0.566158	−	0.357878i
$943$	−18.7719	−	32.5139i	−0.611298	−	1.05880i
$944$			10.7942i			0.351322i
$945$	11.1634	−	40.5450i	0.363144	−	1.31893i
$946$	10.6501	+	18.4465i	0.346265	+	0.599748i
$947$	28.3520			0.921317			0.460658	−	0.887578i	$-0.347613\pi$
$947$	28.3520			0.921317			0.460658	+	0.887578i	$0.347613\pi$
$948$	10.0902	+	0.404859i	0.327715	+	0.0131492i
$949$	35.9160	+	20.6021i	1.16588	+	0.668773i
$950$	−1.80312	+	3.12310i	−0.0585011	+	0.101327i
$951$	40.9142	+	1.64164i	1.32673	+	0.0532337i
$952$	3.48625	+	8.85075i	0.112990	+	0.286854i
$953$	−16.5831	−	9.57426i	−0.537180	−	0.310141i	0.206755	−	0.978393i	$-0.433710\pi$
$953$	−16.5831	−	9.57426i	−0.537180	−	0.310141i	−0.743935	+	0.668252i	$0.767043\pi$
$954$	0.401111	−	4.99035i	0.0129864	−	0.161569i
$955$	−29.8608			−0.966273
$956$	23.0402			0.745175
$957$	−30.5575	+	16.0446i	−0.987783	+	0.518648i
$958$	35.7766	+	20.6556i	1.15589	+	0.667353i
$959$	8.70212	+	22.0926i	0.281006	+	0.713407i
$960$	−0.212417	+	5.29402i	−0.00685572	+	0.170864i
$961$	−30.2306	+	52.3609i	−0.975180	+	1.68906i
$962$	2.43832	+	4.19609i	0.0786146	+	0.135287i
$963$	−15.5348	−	10.7149i	−0.500602	−	0.345283i
$964$	−27.7786			−0.894688
$965$	−15.9553	−	27.6354i	−0.513619	−	0.889614i
$966$	−16.0302	−	13.8362i	−0.515764	−	0.445173i
$967$		−	40.5538i		−	1.30412i	−0.758167	−	0.652061i	$-0.773905\pi$
$967$		−	40.5538i		−	1.30412i	0.758167	−	0.652061i	$-0.226095\pi$
$968$	−2.93307	−	5.08022i	−0.0942723	−	0.163284i
$969$	−2.75393	+	4.35668i	−0.0884691	+	0.139957i
$970$	−42.3803	+	24.4683i	−1.36075	+	0.785630i
$971$	12.1157	+	20.9850i	0.388812	+	0.673442i	0.992290	−	0.123938i	$-0.0395522\pi$
$971$	12.1157	+	20.9850i	0.388812	+	0.673442i	−0.603478	+	0.797380i	$0.706219\pi$
$972$	10.3269	−	11.6771i	0.331235	−	0.374544i
$973$	8.16462	−	54.6252i	0.261746	−	1.75120i
$974$			2.53448i			0.0812099i
$975$	−1.01474	+	27.1921i	−0.0324976	+	0.870845i
$976$	−9.14560	+	5.28021i	−0.292744	+	0.169016i
$977$	6.91109	−	11.9704i	0.221105	−	0.382966i	−0.734039	−	0.679108i	$-0.762367\pi$
$977$	6.91109	−	11.9704i	0.221105	−	0.382966i	0.955144	+	0.296142i	$0.0957002\pi$
$978$	−14.0733	−	8.89595i	−0.450013	−	0.284461i
$979$	16.3792	+	9.45652i	0.523481	+	0.302232i
$980$	−20.8641	+	4.81619i	−0.666479	+	0.153848i
$981$	−2.50440	+	31.1581i	−0.0799593	+	0.994801i
$982$	−22.3657	+	12.9129i	−0.713719	+	0.412066i
$983$	−6.38037	+	3.68371i	−0.203502	+	0.117492i	−0.598288	−	0.801281i	$-0.704152\pi$
$983$	−6.38037	+	3.68371i	−0.203502	+	0.117492i	0.394786	+	0.918773i	$0.370819\pi$
$984$	−11.8953	−	7.51920i	−0.379207	−	0.239703i
$985$			23.0892i			0.735684i
$986$	27.3835	−	15.8099i	0.872067	−	0.503488i
$987$	−13.6874	+	4.76683i	−0.435673	+	0.151730i
$988$	−2.58848	−	1.48480i	−0.0823506	−	0.0472379i
$989$	37.6201	+	21.7200i	1.19625	+	0.690654i
$990$	−1.66591	+	20.7262i	−0.0529462	+	0.658722i
$991$	30.4130	−	52.6768i	0.966100	−	1.67333i	0.259471	−	0.965751i	$-0.416452\pi$
$991$	30.4130	−	52.6768i	0.966100	−	1.67333i	0.706629	−	0.707584i	$-0.250215\pi$
$992$	4.78177	+	8.28226i	0.151821	+	0.262962i
$993$	22.0554	+	13.9416i	0.699906	+	0.442423i
$994$	−19.9541	−	2.98246i	−0.632905	−	0.0945980i
$995$	−18.7179	+	32.4204i	−0.593397	+	1.02779i
$996$	−5.81559	+	3.05355i	−0.184274	+	0.0967555i
$997$		−	41.1210i		−	1.30231i	−0.758943	−	0.651157i	$-0.774284\pi$
$997$		−	41.1210i		−	1.30231i	0.758943	−	0.651157i	$-0.225716\pi$
$998$	24.8498	+	14.3470i	0.786606	+	0.454147i
$999$	−0.839407	+	6.94351i	−0.0265577	+	0.219683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.257.11	yes	34
3.2	odd	2		546.2.bi.f.257.17	yes	34
7.3	odd	6		546.2.bn.f.101.6	yes	34
13.4	even	6		546.2.bn.e.173.12	yes	34
21.17	even	6		546.2.bn.e.101.12	yes	34
39.17	odd	6		546.2.bn.f.173.6	yes	34
91.17	odd	6		546.2.bi.f.17.17	yes	34
273.17	even	6	inner	546.2.bi.e.17.11	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.11	✓	34	273.17	even	6	inner
546.2.bi.e.257.11	yes	34	1.1	even	1	trivial
546.2.bi.f.17.17	yes	34	91.17	odd	6
546.2.bi.f.257.17	yes	34	3.2	odd	2
546.2.bn.e.101.12	yes	34	21.17	even	6
546.2.bn.e.173.12	yes	34	13.4	even	6
546.2.bn.f.101.6	yes	34	7.3	odd	6
546.2.bn.f.173.6	yes	34	39.17	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.805192 + 1.53351i) q^{3} +1.00000 q^{4} +(2.64914 + 1.52948i) q^{5} +(-0.805192 - 1.53351i) q^{6} +(0.969634 + 2.46167i) q^{7} -1.00000 q^{8} +(-1.70333 + 2.46955i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.805192 + 1.53351i) q^{3} +1.00000 q^{4} +(2.64914 + 1.52948i) q^{5} +(-0.805192 - 1.53351i) q^{6} +(0.969634 + 2.46167i) q^{7} -1.00000 q^{8} +(-1.70333 + 2.46955i) q^{9} +(-2.64914 - 1.52948i) q^{10} +(-1.13290 + 1.96224i) q^{11} +(0.805192 + 1.53351i) q^{12} +(3.11743 - 1.81152i) q^{13} +(-0.969634 - 2.46167i) q^{14} +(-0.212417 + 5.29402i) q^{15} +1.00000 q^{16} -3.59543 q^{17} +(1.70333 - 2.46955i) q^{18} +(-0.413821 - 0.716759i) q^{19} +(2.64914 + 1.52948i) q^{20} +(-2.99426 + 3.46906i) q^{21} +(1.13290 - 1.96224i) q^{22} -4.62091i q^{23} +(-0.805192 - 1.53351i) q^{24} +(2.17863 + 3.77350i) q^{25} +(-3.11743 + 1.81152i) q^{26} +(-5.15859 - 0.623627i) q^{27} +(0.969634 + 2.46167i) q^{28} +(7.61619 - 4.39721i) q^{29} +(0.212417 - 5.29402i) q^{30} +(-4.78177 - 8.28226i) q^{31} -1.00000 q^{32} +(-3.92133 - 0.157339i) q^{33} +3.59543 q^{34} +(-1.19638 + 8.00434i) q^{35} +(-1.70333 + 2.46955i) q^{36} -1.34601i q^{37} +(0.413821 + 0.716759i) q^{38} +(5.28812 + 3.32201i) q^{39} +(-2.64914 - 1.52948i) q^{40} +(7.03626 - 4.06239i) q^{41} +(2.99426 - 3.46906i) q^{42} +(-4.70036 + 8.14127i) q^{43} +(-1.13290 + 1.96224i) q^{44} +(-8.28949 + 3.93696i) q^{45} +4.62091i q^{46} +(2.73905 + 1.58139i) q^{47} +(0.805192 + 1.53351i) q^{48} +(-5.11962 + 4.77383i) q^{49} +(-2.17863 - 3.77350i) q^{50} +(-2.89501 - 5.51364i) q^{51} +(3.11743 - 1.81152i) q^{52} +(1.44524 - 0.834408i) q^{53} +(5.15859 + 0.623627i) q^{54} +(-6.00243 + 3.46551i) q^{55} +(-0.969634 - 2.46167i) q^{56} +(0.765955 - 1.21173i) q^{57} +(-7.61619 + 4.39721i) q^{58} +10.7942i q^{59} +(-0.212417 + 5.29402i) q^{60} +(-9.14560 + 5.28021i) q^{61} +(4.78177 + 8.28226i) q^{62} +(-7.73081 - 1.79848i) q^{63} +1.00000 q^{64} +(11.0292 - 0.0309078i) q^{65} +(3.92133 + 0.157339i) q^{66} +(3.51789 + 2.03106i) q^{67} -3.59543 q^{68} +(7.08623 - 3.72072i) q^{69} +(1.19638 - 8.00434i) q^{70} +(3.81286 - 6.60406i) q^{71} +(1.70333 - 2.46955i) q^{72} +(5.74190 + 9.94525i) q^{73} +1.34601i q^{74} +(-4.03250 + 6.37935i) q^{75} +(-0.413821 - 0.716759i) q^{76} +(-5.92889 - 0.886170i) q^{77} +(-5.28812 - 3.32201i) q^{78} +(2.91514 - 5.04917i) q^{79} +(2.64914 + 1.52948i) q^{80} +(-3.19732 - 8.41292i) q^{81} +(-7.03626 + 4.06239i) q^{82} +3.79233i q^{83} +(-2.99426 + 3.46906i) q^{84} +(-9.52479 - 5.49914i) q^{85} +(4.70036 - 8.14127i) q^{86} +(12.8757 + 8.13894i) q^{87} +(1.13290 - 1.96224i) q^{88} -8.34716i q^{89} +(8.28949 - 3.93696i) q^{90} +(7.48213 + 5.91758i) q^{91} -4.62091i q^{92} +(8.85073 - 14.0017i) q^{93} +(-2.73905 - 1.58139i) q^{94} -2.53173i q^{95} +(-0.805192 - 1.53351i) q^{96} +(7.99888 - 13.8545i) q^{97} +(5.11962 - 4.77383i) q^{98} +(-2.91614 - 6.14011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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