LMFDB - Embedded newform 546.2.by.a.115.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.6
Character	$\chi$	$=$	546.115
Dual form			546.2.by.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(0.128673 + 0.0344778i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-2.64307 - 0.119073i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(0.128673 + 0.0344778i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-2.64307 - 0.119073i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.133212 q^{10} +(3.06926 - 3.06926i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.49669 - 3.28023i) q^{13} +(-2.58383 + 0.569061i) q^{14} +(0.0344778 - 0.128673i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.67068 - 2.89371i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(2.85706 - 2.85706i) q^{19} +(0.128673 - 0.0344778i) q^{20} +(-0.119073 + 2.64307i) q^{21} +(2.17030 - 3.75906i) q^{22} +(1.26710 + 0.731561i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.31476 - 2.49113i) q^{25} +(0.596701 - 3.55583i) q^{26} +1.00000i q^{27} +(-2.34850 + 1.21841i) q^{28} +(2.15096 + 3.72557i) q^{29} -0.133212i q^{30} +(0.690485 + 2.57692i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-3.06926 - 3.06926i) q^{33} +(-2.36270 - 2.36270i) q^{34} +(-0.335986 - 0.106449i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.86419 + 6.95726i) q^{37} +(2.02025 - 3.49917i) q^{38} +(-3.28023 - 1.49669i) q^{39} +(0.115365 - 0.0666060i) q^{40} +(-11.0520 - 2.96138i) q^{41} +(0.569061 + 2.58383i) q^{42} +(9.78926 + 5.65183i) q^{43} +(1.12343 - 4.19269i) q^{44} +(-0.128673 - 0.0344778i) q^{45} +(1.41327 + 0.378684i) q^{46} +(-3.04405 + 11.3605i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(6.97164 + 0.629439i) q^{49} +(-4.81249 - 1.28950i) q^{50} +(-2.89371 + 1.67068i) q^{51} +(-0.343949 - 3.58911i) q^{52} +(-3.41047 + 5.90712i) q^{53} +(0.258819 + 0.965926i) q^{54} +(0.500752 - 0.289109i) q^{55} +(-1.95313 + 1.78474i) q^{56} +(-2.85706 - 2.85706i) q^{57} +(3.04192 + 3.04192i) q^{58} +(0.728411 - 2.71847i) q^{59} +(-0.0344778 - 0.128673i) q^{60} -5.98123i q^{61} +(1.33391 + 2.31041i) q^{62} +(2.64307 + 0.119073i) q^{63} -1.00000i q^{64} +(0.305678 - 0.370475i) q^{65} +(-3.75906 - 2.17030i) q^{66} +(6.01310 + 6.01310i) q^{67} +(-2.89371 - 1.67068i) q^{68} +(0.731561 - 1.26710i) q^{69} +(-0.352089 - 0.0158620i) q^{70} +(12.0922 - 3.24009i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(7.88613 - 2.11308i) q^{73} +(3.60134 + 6.23771i) q^{74} +(-2.49113 + 4.31476i) q^{75} +(1.04576 - 3.90282i) q^{76} +(-8.47775 + 7.74681i) q^{77} +(-3.55583 - 0.596701i) q^{78} +(-6.41891 - 11.1179i) q^{79} +(0.0941951 - 0.0941951i) q^{80} +1.00000 q^{81} -11.4419 q^{82} +(8.93817 - 8.93817i) q^{83} +(1.21841 + 2.34850i) q^{84} +(-0.115203 - 0.429943i) q^{85} +(10.9185 + 2.92560i) q^{86} +(3.72557 - 2.15096i) q^{87} -4.34059i q^{88} +(-10.6284 + 2.84786i) q^{89} -0.133212 q^{90} +(-4.34643 + 8.49167i) q^{91} +1.46312 q^{92} +(2.57692 - 0.690485i) q^{93} +11.7613i q^{94} +(0.466132 - 0.269121i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.45202 + 5.41903i) q^{97} +(6.89700 - 1.19640i) q^{98} +(-3.06926 + 3.06926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.128673	+	0.0344778i	0.0575443	+	0.0154189i	0.287476	−	0.957788i	$-0.407184\pi$
$5$	0.128673	+	0.0344778i	0.0575443	+	0.0154189i	−0.229932	+	0.973207i	$0.573850\pi$
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	−2.64307	−	0.119073i	−0.998987	−	0.0450055i
$7$	−2.64307	−	0.119073i	−0.998987	−	0.0450055i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	0.133212			0.0421253
$11$	3.06926	−	3.06926i	0.925418	−	0.925418i	−0.0719878	−	0.997406i	$-0.522934\pi$
$11$	3.06926	−	3.06926i	0.925418	−	0.925418i	0.997406	+	0.0719878i	$0.0229343\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.49669	−	3.28023i	0.415106	−	0.909773i
$13$	1.49669	−	3.28023i	0.415106	−	0.909773i
$14$	−2.58383	+	0.569061i	−0.690557	+	0.152088i
$15$	0.0344778	−	0.128673i	0.00890213	−	0.0332232i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.67068	−	2.89371i	−0.405200	−	0.701828i	0.589144	−	0.808028i	$-0.299465\pi$
$17$	−1.67068	−	2.89371i	−0.405200	−	0.701828i	−0.994345	+	0.106200i	$0.966132\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	2.85706	−	2.85706i	0.655456	−	0.655456i	−0.298846	−	0.954301i	$-0.596602\pi$
$19$	2.85706	−	2.85706i	0.655456	−	0.655456i	0.954301	+	0.298846i	$0.0966016\pi$
$20$	0.128673	−	0.0344778i	0.0287721	−	0.00770947i
$21$	−0.119073	+	2.64307i	−0.0259840	+	0.576765i
$22$	2.17030	−	3.75906i	0.462709	−	0.801435i
$23$	1.26710	+	0.731561i	0.264209	+	0.152541i	0.626253	−	0.779620i	$-0.284588\pi$
$23$	1.26710	+	0.731561i	0.264209	+	0.152541i	−0.362044	+	0.932161i	$0.617921\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−4.31476	−	2.49113i	−0.862952	−	0.498225i
$26$	0.596701	−	3.55583i	0.117023	−	0.697356i
$27$			1.00000i			0.192450i
$28$	−2.34850	+	1.21841i	−0.443825	+	0.230259i
$29$	2.15096	+	3.72557i	0.399423	+	0.691821i	0.993655	−	0.112473i	$-0.0358771\pi$
$29$	2.15096	+	3.72557i	0.399423	+	0.691821i	−0.594232	+	0.804294i	$0.702544\pi$
$30$		−	0.133212i		−	0.0243211i
$31$	0.690485	+	2.57692i	0.124015	+	0.462829i	0.999803	−	0.0198670i	$-0.00632426\pi$
$31$	0.690485	+	2.57692i	0.124015	+	0.462829i	−0.875788	+	0.482696i	$0.839658\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−3.06926	−	3.06926i	−0.534290	−	0.534290i
$34$	−2.36270	−	2.36270i	−0.405200	−	0.405200i
$35$	−0.335986	−	0.106449i	−0.0567920	−	0.0179931i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	1.86419	+	6.95726i	0.306471	+	1.14377i	0.931671	+	0.363302i	$0.118351\pi$
$37$	1.86419	+	6.95726i	0.306471	+	1.14377i	−0.625200	+	0.780465i	$0.714983\pi$
$38$	2.02025	−	3.49917i	0.327728	−	0.567641i
$39$	−3.28023	−	1.49669i	−0.525258	−	0.239662i
$40$	0.115365	−	0.0666060i	0.0182408	−	0.0105313i
$41$	−11.0520	−	2.96138i	−1.72604	−	0.462490i	−0.746773	−	0.665079i	$-0.768398\pi$
$41$	−11.0520	−	2.96138i	−1.72604	−	0.462490i	−0.979264	+	0.202589i	$0.935064\pi$
$42$	0.569061	+	2.58383i	0.0878080	+	0.398693i
$43$	9.78926	+	5.65183i	1.49285	+	0.861896i	0.999966	−	0.00819993i	$-0.00261015\pi$
$43$	9.78926	+	5.65183i	1.49285	+	0.861896i	0.492882	+	0.870096i	$0.335943\pi$
$44$	1.12343	−	4.19269i	0.169363	−	0.632072i
$45$	−0.128673	−	0.0344778i	−0.0191814	−	0.00513965i
$46$	1.41327	+	0.378684i	0.208375	+	0.0558339i
$47$	−3.04405	+	11.3605i	−0.444020	+	1.65711i	0.274491	+	0.961590i	$0.411491\pi$
$47$	−3.04405	+	11.3605i	−0.444020	+	1.65711i	−0.718511	+	0.695515i	$0.755176\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	6.97164	+	0.629439i	0.995949	+	0.0899199i
$50$	−4.81249	−	1.28950i	−0.680589	−	0.182363i
$51$	−2.89371	+	1.67068i	−0.405200	+	0.233943i
$52$	−0.343949	−	3.58911i	−0.0476971	−	0.497720i
$53$	−3.41047	+	5.90712i	−0.468465	+	0.811405i	−0.999350	−	0.0360388i	$-0.988526\pi$
$53$	−3.41047	+	5.90712i	−0.468465	+	0.811405i	0.530886	+	0.847443i	$0.321859\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	0.500752	−	0.289109i	0.0675214	−	0.0389835i
$56$	−1.95313	+	1.78474i	−0.260998	+	0.238495i
$57$	−2.85706	−	2.85706i	−0.378427	−	0.378427i
$58$	3.04192	+	3.04192i	0.399423	+	0.399423i
$59$	0.728411	−	2.71847i	0.0948310	−	0.353914i	−0.902163	−	0.431396i	$-0.858021\pi$
$59$	0.728411	−	2.71847i	0.0948310	−	0.353914i	0.996994	+	0.0774817i	$0.0246879\pi$
$60$	−0.0344778	−	0.128673i	−0.00445106	−	0.0166116i
$61$		−	5.98123i		−	0.765819i	−0.923786	−	0.382909i	$-0.874922\pi$
$61$		−	5.98123i		−	0.765819i	0.923786	−	0.382909i	$-0.125078\pi$
$62$	1.33391	+	2.31041i	0.169407	+	0.293422i
$63$	2.64307	+	0.119073i	0.332996	+	0.0150018i
$64$		−	1.00000i		−	0.125000i
$65$	0.305678	−	0.370475i	0.0379147	−	0.0459517i
$66$	−3.75906	−	2.17030i	−0.462709	−	0.267145i
$67$	6.01310	+	6.01310i	0.734617	+	0.734617i	0.971531	−	0.236914i	$-0.0761360\pi$
$67$	6.01310	+	6.01310i	0.734617	+	0.734617i	−0.236914	+	0.971531i	$0.576136\pi$
$68$	−2.89371	−	1.67068i	−0.350914	−	0.202600i
$69$	0.731561	−	1.26710i	0.0880696	−	0.152541i
$70$	−0.352089	−	0.0158620i	−0.0420826	−	0.00189587i
$71$	12.0922	−	3.24009i	1.43508	−	0.384528i	0.544270	−	0.838910i	$-0.316807\pi$
$71$	12.0922	−	3.24009i	1.43508	−	0.384528i	0.890807	+	0.454382i	$0.150140\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	7.88613	−	2.11308i	0.923002	−	0.247318i	0.234134	−	0.972204i	$-0.424775\pi$
$73$	7.88613	−	2.11308i	0.923002	−	0.247318i	0.688868	+	0.724887i	$0.258108\pi$
$74$	3.60134	+	6.23771i	0.418648	+	0.725119i
$75$	−2.49113	+	4.31476i	−0.287651	+	0.498225i
$76$	1.04576	−	3.90282i	0.119957	−	0.447684i
$77$	−8.47775	+	7.74681i	−0.966129	+	0.882831i
$78$	−3.55583	−	0.596701i	−0.402619	−	0.0675630i
$79$	−6.41891	−	11.1179i	−0.722184	−	1.25086i	−0.960123	−	0.279579i	$-0.909805\pi$
$79$	−6.41891	−	11.1179i	−0.722184	−	1.25086i	0.237939	−	0.971280i	$-0.423528\pi$
$80$	0.0941951	−	0.0941951i	0.0105313	−	0.0105313i
$81$	1.00000			0.111111
$82$	−11.4419			−1.26355
$83$	8.93817	−	8.93817i	0.981092	−	0.981092i	−0.0187330	−	0.999825i	$-0.505963\pi$
$83$	8.93817	−	8.93817i	0.981092	−	0.981092i	0.999825	+	0.0187330i	$0.00596324\pi$
$84$	1.21841	+	2.34850i	0.132940	+	0.256243i
$85$	−0.115203	−	0.429943i	−0.0124955	−	0.0466339i
$86$	10.9185	+	2.92560i	1.17737	+	0.315476i
$87$	3.72557	−	2.15096i	0.399423	−	0.230607i
$88$		−	4.34059i		−	0.462709i
$89$	−10.6284	+	2.84786i	−1.12661	+	0.301873i	−0.773554	−	0.633731i	$-0.781523\pi$
$89$	−10.6284	+	2.84786i	−1.12661	+	0.301873i	−0.353052	+	0.935604i	$0.614856\pi$
$90$	−0.133212			−0.0140418
$91$	−4.34643	+	8.49167i	−0.455630	+	0.890169i
$92$	1.46312			0.152541
$93$	2.57692	−	0.690485i	0.267214	−	0.0715999i
$94$			11.7613i			1.21309i
$95$	0.466132	−	0.269121i	0.0478241	−	0.0276113i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	1.45202	+	5.41903i	0.147431	+	0.550219i	0.999635	+	0.0270100i	$0.00859858\pi$
$97$	1.45202	+	5.41903i	0.147431	+	0.550219i	−0.852204	+	0.523209i	$0.824735\pi$
$98$	6.89700	−	1.19640i	0.696702	−	0.120855i
$99$	−3.06926	+	3.06926i	−0.308473	+	0.308473i
$100$	−4.98225			−0.498225
$101$	−0.0389367			−0.00387434			−0.00193717	−	0.999998i	$-0.500617\pi$
$101$	−0.0389367			−0.00387434			−0.00193717	+	0.999998i	$0.500617\pi$
$102$	−2.36270	+	2.36270i	−0.233943	+	0.233943i
$103$	5.92112	+	10.2557i	0.583426	+	1.01052i	0.995070	+	0.0991782i	$0.0316214\pi$
$103$	5.92112	+	10.2557i	0.583426	+	1.01052i	−0.411644	+	0.911345i	$0.635045\pi$
$104$	−1.26116	−	3.37779i	−0.123667	−	0.331220i
$105$	−0.106449	+	0.335986i	−0.0103883	+	0.0327889i
$106$	−1.76539	+	6.58853i	−0.171470	+	0.639935i
$107$	−7.04864	+	12.2086i	−0.681417	+	1.18025i	0.293131	+	0.956072i	$0.405303\pi$
$107$	−7.04864	+	12.2086i	−0.681417	+	1.18025i	−0.974548	+	0.224177i	$0.928031\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	14.7455	−	3.95106i	1.41237	−	0.378443i	0.529597	−	0.848249i	$-0.322343\pi$
$109$	14.7455	−	3.95106i	1.41237	−	0.378443i	0.882769	+	0.469807i	$0.155676\pi$
$110$	0.408863	−	0.408863i	0.0389835	−	0.0389835i
$111$	6.95726	−	1.86419i	0.660354	−	0.176941i
$112$	−1.42466	+	2.22943i	−0.134617	+	0.210661i
$113$	−6.28689	+	10.8892i	−0.591421	+	1.02437i	0.402621	+	0.915367i	$0.368099\pi$
$113$	−6.28689	+	10.8892i	−0.591421	+	1.02437i	−0.994041	+	0.109004i	$0.965234\pi$
$114$	−3.49917	−	2.02025i	−0.327728	−	0.189214i
$115$	0.137819	+	0.137819i	0.0128517	+	0.0128517i
$116$	3.72557	+	2.15096i	0.345911	+	0.199712i
$117$	−1.49669	+	3.28023i	−0.138369	+	0.303258i
$118$		−	2.81436i		−	0.259083i
$119$	4.07117	+	7.84721i	0.373204	+	0.719353i
$120$	−0.0666060	−	0.115365i	−0.00608027	−	0.0105313i
$121$		−	7.84076i		−	0.712796i
$122$	−1.54806	−	5.77743i	−0.140155	−	0.523064i
$123$	−2.96138	+	11.0520i	−0.267019	+	0.996528i
$124$	1.88644	+	1.88644i	0.169407	+	0.169407i
$125$	−0.940279	−	0.940279i	−0.0841011	−	0.0841011i
$126$	2.58383	−	0.569061i	0.230186	−	0.0506960i
$127$	12.4077	−	7.16360i	1.10101	−	0.635666i	0.164521	−	0.986374i	$-0.447392\pi$
$127$	12.4077	−	7.16360i	1.10101	−	0.635666i	0.936485	+	0.350707i	$0.114059\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	5.65183	−	9.78926i	0.497616	−	0.861896i
$130$	0.199376	−	0.436966i	0.0174865	−	0.0383245i
$131$	−11.6207	+	6.70920i	−1.01530	+	0.586186i	−0.912740	−	0.408541i	$-0.866038\pi$
$131$	−11.6207	+	6.70920i	−1.01530	+	0.586186i	−0.102564	+	0.994726i	$0.532704\pi$
$132$	−4.19269	−	1.12343i	−0.364927	−	0.0977819i
$133$	−7.89162	+	7.21122i	−0.684290	+	0.625292i
$134$	7.36451	+	4.25190i	0.636197	+	0.367308i
$135$	−0.0344778	+	0.128673i	−0.00296738	+	0.0110744i
$136$	−3.22751	−	0.864810i	−0.276757	−	0.0741568i
$137$	−8.98430	−	2.40733i	−0.767580	−	0.205672i	−0.146278	−	0.989244i	$-0.546729\pi$
$137$	−8.98430	−	2.40733i	−0.767580	−	0.205672i	−0.621302	+	0.783571i	$0.713396\pi$
$138$	0.378684	−	1.41327i	0.0322357	−	0.120305i
$139$	−10.2322	−	5.90757i	−0.867885	−	0.501073i	−0.00123995	−	0.999999i	$-0.500395\pi$
$139$	−10.2322	−	5.90757i	−0.867885	−	0.501073i	−0.866645	+	0.498926i	$0.833728\pi$
$140$	−0.344197	+	0.0758057i	−0.0290899	+	0.00640675i
$141$	11.3605	+	3.04405i	0.956730	+	0.256355i
$142$	10.8415	−	6.25937i	0.909802	−	0.525275i
$143$	−5.47418	−	14.6616i	−0.457774	−	1.22607i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.148321	+	0.553540i	0.0123174	+	0.0459690i
$146$	7.07051	−	4.08216i	0.585160	−	0.337842i
$147$	0.629439	−	6.97164i	0.0519153	−	0.575011i
$148$	5.09307	+	5.09307i	0.418648	+	0.418648i
$149$	2.83102	+	2.83102i	0.231927	+	0.231927i	0.813496	−	0.581570i	$-0.197561\pi$
$149$	2.83102	+	2.83102i	0.231927	+	0.231927i	−0.581570	+	0.813496i	$0.697561\pi$
$150$	−1.28950	+	4.81249i	−0.105287	+	0.392938i
$151$	5.34068	+	19.9317i	0.434618	+	1.62202i	0.741978	+	0.670425i	$0.233888\pi$
$151$	5.34068	+	19.9317i	0.434618	+	1.62202i	−0.307359	+	0.951594i	$0.599445\pi$
$152$		−	4.04050i		−	0.327728i
$153$	1.67068	+	2.89371i	0.135067	+	0.233943i
$154$	−6.18385	+	9.67705i	−0.498309	+	0.779799i
$155$			0.355386i			0.0285453i
$156$	−3.58911	+	0.343949i	−0.287359	+	0.0275379i
$157$	−3.75270	−	2.16663i	−0.299498	−	0.172916i	0.342719	−	0.939438i	$-0.388652\pi$
$157$	−3.75270	−	2.16663i	−0.299498	−	0.172916i	−0.642218	+	0.766522i	$0.721985\pi$
$158$	−9.07771	−	9.07771i	−0.722184	−	0.722184i
$159$	5.90712	+	3.41047i	0.468465	+	0.270468i
$160$	0.0666060	−	0.115365i	0.00526566	−	0.00912040i
$161$	−3.26193	−	2.08444i	−0.257076	−	0.164277i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	4.91219	−	4.91219i	0.384753	−	0.384753i	−0.488058	−	0.872811i	$-0.662295\pi$
$163$	4.91219	−	4.91219i	0.384753	−	0.384753i	0.872811	+	0.488058i	$0.162295\pi$
$164$	−11.0520	+	2.96138i	−0.863018	+	0.231245i
$165$	−0.289109	−	0.500752i	−0.0225071	−	0.0389835i
$166$	6.32024	−	10.9470i	0.490546	−	0.849650i
$167$	2.16192	−	8.06840i	0.167295	−	0.624352i	−0.830442	−	0.557105i	$-0.811912\pi$
$167$	2.16192	−	8.06840i	0.167295	−	0.624352i	0.997736	−	0.0672465i	$-0.0214214\pi$
$168$	1.78474	+	1.95313i	0.137695	+	0.150687i
$169$	−8.51986	−	9.81896i	−0.655374	−	0.755304i
$170$	−0.222555	−	0.385477i	−0.0170692	−	0.0295647i
$171$	−2.85706	+	2.85706i	−0.218485	+	0.218485i
$172$	11.3037			0.861896
$173$	−7.84651			−0.596559			−0.298280	−	0.954479i	$-0.596413\pi$
$173$	−7.84651			−0.596559			−0.298280	+	0.954479i	$0.596413\pi$
$174$	3.04192	−	3.04192i	0.230607	−	0.230607i
$175$	11.1076	+	7.09800i	0.839655	+	0.536558i
$176$	−1.12343	−	4.19269i	−0.0846816	−	0.316036i
$177$	−2.71847	−	0.728411i	−0.204332	−	0.0547507i
$178$	−9.52914	+	5.50165i	−0.714239	+	0.412366i
$179$		−	4.93191i		−	0.368628i	−0.982867	−	0.184314i	$-0.940994\pi$
$179$		−	4.93191i		−	0.368628i	0.982867	−	0.184314i	$-0.0590063\pi$
$180$	−0.128673	+	0.0344778i	−0.00959071	+	0.00256982i
$181$	0.641409			0.0476755			0.0238378	−	0.999716i	$-0.492411\pi$
$181$	0.641409			0.0476755			0.0238378	+	0.999716i	$0.492411\pi$
$182$	−2.00053	+	9.32727i	−0.148289	+	0.691383i
$183$	−5.98123			−0.442146
$184$	1.41327	−	0.378684i	0.104187	−	0.0279169i
$185$			0.959484i			0.0705427i
$186$	2.31041	−	1.33391i	0.169407	−	0.0978073i
$187$	−14.0093	−	3.75379i	−1.02446	−	0.274504i
$188$	3.04405	+	11.3605i	0.222010	+	0.828553i
$189$	0.119073	−	2.64307i	0.00866132	−	0.192255i
$190$	0.380595	−	0.380595i	0.0276113	−	0.0276113i
$191$	−18.5952			−1.34550			−0.672750	−	0.739870i	$-0.734887\pi$
$191$	−18.5952			−1.34550			−0.672750	+	0.739870i	$0.734887\pi$
$192$	−1.00000			−0.0721688
$193$	−4.16169	+	4.16169i	−0.299565	+	0.299565i	−0.840843	−	0.541279i	$-0.817940\pi$
$193$	−4.16169	+	4.16169i	−0.299565	+	0.299565i	0.541279	+	0.840843i	$0.317940\pi$
$194$	2.80509	+	4.85857i	0.201394	+	0.348825i
$195$	−0.370475	−	0.305678i	−0.0265302	−	0.0218901i
$196$	6.35234	−	2.94071i	0.453739	−	0.210051i
$197$	2.22331	−	8.29752i	0.158405	−	0.591174i	−0.840385	−	0.541990i	$-0.817671\pi$
$197$	2.22331	−	8.29752i	0.158405	−	0.591174i	0.998790	−	0.0491843i	$-0.0156622\pi$
$198$	−2.17030	+	3.75906i	−0.154236	+	0.267145i
$199$	−7.04062	−	12.1947i	−0.499096	−	0.864460i	0.500903	−	0.865503i	$-0.333001\pi$
$199$	−7.04062	−	12.1947i	−0.499096	−	0.864460i	−0.999999	+	0.00104327i	$0.999668\pi$
$200$	−4.81249	+	1.28950i	−0.340294	+	0.0911816i
$201$	6.01310	−	6.01310i	0.424131	−	0.424131i
$202$	−0.0376099	+	0.0100775i	−0.00264622	+	0.000709054i
$203$	−5.24152	−	10.1031i	−0.367883	−	0.709096i
$204$	−1.67068	+	2.89371i	−0.116971	+	0.202600i
$205$	−1.31999	−	0.762099i	−0.0921924	−	0.0532273i
$206$	8.37373	+	8.37373i	0.583426	+	0.583426i
$207$	−1.26710	−	0.731561i	−0.0880696	−	0.0508470i
$208$	−2.09242	−	2.93628i	−0.145083	−	0.203595i
$209$		−	17.5382i		−	1.21314i
$210$	−0.0158620	+	0.352089i	−0.00109458	+	0.0242964i
$211$	5.74753	+	9.95501i	0.395676	+	0.685331i	0.993187	−	0.116530i	$-0.0371770\pi$
$211$	5.74753	+	9.95501i	0.395676	+	0.685331i	−0.597511	+	0.801861i	$0.703844\pi$
$212$			6.82095i			0.468465i
$213$	−3.24009	−	12.0922i	−0.222007	−	0.828542i
$214$	−3.64864	+	13.6169i	−0.249416	+	0.930833i
$215$	1.06475	+	1.06475i	0.0726153	+	0.0726153i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−1.51816	−	6.89321i	−0.103059	−	0.467941i
$218$	13.2205	−	7.63285i	0.895405	−	0.516962i
$219$	−2.11308	−	7.88613i	−0.142789	−	0.532895i
$220$	0.289109	−	0.500752i	0.0194918	−	0.0337607i
$221$	−11.9925	+	1.14926i	−0.806705	+	0.0773076i
$222$	6.23771	−	3.60134i	0.418648	−	0.241706i
$223$	23.9774	+	6.42474i	1.60565	+	0.430232i	0.946742	−	0.321993i	$-0.104353\pi$
$223$	23.9774	+	6.42474i	1.60565	+	0.430232i	0.658906	+	0.752225i	$0.271019\pi$
$224$	−0.799093	+	2.52219i	−0.0533917	+	0.168521i
$225$	4.31476	+	2.49113i	0.287651	+	0.166075i
$226$	−3.25433	+	12.1453i	−0.216475	+	0.807896i
$227$	23.7036	+	6.35137i	1.57327	+	0.421555i	0.936833	−	0.349777i	$-0.113743\pi$
$227$	23.7036	+	6.35137i	1.57327	+	0.421555i	0.636433	+	0.771332i	$0.280409\pi$
$228$	−3.90282	−	1.04576i	−0.258471	−	0.0692570i
$229$	2.92237	−	10.9064i	0.193116	−	0.720718i	−0.799631	−	0.600492i	$-0.794971\pi$
$229$	2.92237	−	10.9064i	0.193116	−	0.720718i	0.992747	−	0.120226i	$-0.0383620\pi$
$230$	0.168793	+	0.0974526i	0.0111299	+	0.00642584i
$231$	7.74681	+	8.47775i	0.509703	+	0.557795i
$232$	4.15533	+	1.11342i	0.272811	+	0.0730995i
$233$	−1.29629	+	0.748411i	−0.0849225	+	0.0490300i	−0.541860	−	0.840469i	$-0.682280\pi$
$233$	−1.29629	+	0.748411i	−0.0849225	+	0.0490300i	0.456937	+	0.889499i	$0.348946\pi$
$234$	−0.596701	+	3.55583i	−0.0390075	+	0.232452i
$235$	−0.783373	+	1.35684i	−0.0511016	+	0.0885106i
$236$	−0.728411	−	2.71847i	−0.0474155	−	0.176957i
$237$	−11.1179	+	6.41891i	−0.722184	+	0.416953i
$238$	5.96346	+	6.52613i	0.386554	+	0.423026i
$239$	6.71829	+	6.71829i	0.434570	+	0.434570i	0.890180	−	0.455610i	$-0.150579\pi$
$239$	6.71829	+	6.71829i	0.434570	+	0.434570i	−0.455610	+	0.890180i	$0.650579\pi$
$240$	−0.0941951	−	0.0941951i	−0.00608027	−	0.00608027i
$241$	0.822951	−	3.07130i	0.0530109	−	0.197840i	−0.934342	−	0.356378i	$-0.884012\pi$
$241$	0.822951	−	3.07130i	0.0530109	−	0.197840i	0.987353	+	0.158539i	$0.0506782\pi$
$242$	−2.02934	−	7.57359i	−0.130451	−	0.486849i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.99062	−	5.17990i	−0.191455	−	0.331609i
$245$	0.875360	+	0.321359i	0.0559247	+	0.0205308i
$246$			11.4419i			0.729509i
$247$	−5.09571	−	13.6480i	−0.324232	−	0.868399i
$248$	2.31041	+	1.33391i	0.146711	+	0.0847036i
$249$	−8.93817	−	8.93817i	−0.566433	−	0.566433i
$250$	−1.15160	−	0.664878i	−0.0728337	−	0.0420506i
$251$	6.52293	−	11.2981i	0.411724	−	0.713127i	−0.583354	−	0.812218i	$-0.698260\pi$
$251$	6.52293	−	11.2981i	0.411724	−	0.713127i	0.995078	+	0.0990910i	$0.0315935\pi$
$252$	2.34850	−	1.21841i	0.147942	−	0.0767529i
$253$	6.13442	−	1.64371i	0.385667	−	0.103339i
$254$	10.1309	−	10.1309i	0.635666	−	0.635666i
$255$	−0.429943	+	0.115203i	−0.0269241	+	0.00721429i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.05642	+	7.02593i	−0.253033	+	0.438266i	−0.964359	−	0.264596i	$-0.914761\pi$
$257$	−4.05642	+	7.02593i	−0.253033	+	0.438266i	0.711327	+	0.702862i	$0.248095\pi$
$258$	2.92560	−	10.9185i	0.182140	−	0.679756i
$259$	−4.09877	−	18.6105i	−0.254685	−	1.15640i
$260$	0.0794876	−	0.473679i	0.00492961	−	0.0293764i
$261$	−2.15096	−	3.72557i	−0.133141	−	0.230607i
$262$	−9.48825	+	9.48825i	−0.586186	+	0.586186i
$263$	−12.8397			−0.791728			−0.395864	−	0.918309i	$-0.629555\pi$
$263$	−12.8397			−0.791728			−0.395864	+	0.918309i	$0.629555\pi$
$264$	−4.34059			−0.267145
$265$	−0.642500	+	0.642500i	−0.0394685	+	0.0394685i
$266$	−5.75632	+	9.00801i	−0.352943	+	0.552316i
$267$	2.84786	+	10.6284i	0.174286	+	0.650446i
$268$	8.21404	+	2.20095i	0.501752	+	0.134444i
$269$	8.86858	−	5.12028i	0.540727	−	0.312189i	−0.204647	−	0.978836i	$-0.565605\pi$
$269$	8.86858	−	5.12028i	0.540727	−	0.312189i	0.745373	+	0.666647i	$0.232271\pi$
$270$			0.133212i			0.00810702i
$271$	−23.6152	+	6.32766i	−1.43452	+	0.384378i	−0.890610	−	0.454767i	$-0.849723\pi$
$271$	−23.6152	+	6.32766i	−1.43452	+	0.384378i	−0.543908	+	0.839145i	$0.683056\pi$
$272$	−3.34137			−0.202600
$273$	8.49167	+	4.34643i	0.513939	+	0.263058i
$274$	−9.30123			−0.561908
$275$	−20.8891	+	5.59721i	−1.25966	+	0.337524i
$276$		−	1.46312i		−	0.0880696i
$277$	−3.65576	+	2.11065i	−0.219653	+	0.126817i	−0.605790	−	0.795625i	$-0.707143\pi$
$277$	−3.65576	+	2.11065i	−0.219653	+	0.126817i	0.386136	+	0.922442i	$0.373809\pi$
$278$	−11.4125	−	3.05798i	−0.684479	−	0.183406i
$279$	−0.690485	−	2.57692i	−0.0413382	−	0.154276i
$280$	−0.312849	+	0.162307i	−0.0186963	+	0.00969972i
$281$	−1.40963	+	1.40963i	−0.0840912	+	0.0840912i	−0.747901	−	0.663810i	$-0.768938\pi$
$281$	−1.40963	+	1.40963i	−0.0840912	+	0.0840912i	0.663810	+	0.747901i	$0.268938\pi$
$282$	11.7613			0.700375
$283$	5.50504			0.327241			0.163620	−	0.986523i	$-0.447683\pi$
$283$	5.50504			0.327241			0.163620	+	0.986523i	$0.447683\pi$
$284$	8.85209	−	8.85209i	0.525275	−	0.525275i
$285$	−0.269121	−	0.466132i	−0.0159414	−	0.0276113i
$286$	−9.08236	−	12.7452i	−0.537051	−	0.753641i
$287$	28.8587	+	9.14314i	1.70347	+	0.539703i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	2.91763	−	5.05348i	0.171625	−	0.297263i
$290$	0.286534	+	0.496291i	0.0168258	+	0.0291432i
$291$	5.41903	−	1.45202i	0.317669	−	0.0851192i
$292$	5.77305	−	5.77305i	0.337842	−	0.337842i
$293$	4.70508	−	1.26072i	0.274874	−	0.0736522i	−0.118749	−	0.992924i	$-0.537888\pi$
$293$	4.70508	−	1.26072i	0.274874	−	0.0736522i	0.393623	+	0.919272i	$0.371222\pi$
$294$	−1.19640	−	6.89700i	−0.0697756	−	0.402241i
$295$	0.187453	−	0.324679i	0.0109140	−	0.0189035i
$296$	6.23771	+	3.60134i	0.362560	+	0.209324i
$297$	3.06926	+	3.06926i	0.178097	+	0.178097i
$298$	3.46728	+	2.00184i	0.200854	+	0.115963i
$299$	4.29614	−	3.06147i	0.248452	−	0.177049i
$300$			4.98225i			0.287651i
$301$	−25.2007	−	16.1038i	−1.45255	−	0.928209i
$302$	10.3174	+	17.8703i	0.593700	+	1.02832i
$303$			0.0389367i			0.00223685i
$304$	−1.04576	−	3.90282i	−0.0599783	−	0.223842i
$305$	0.206220	−	0.769623i	0.0118081	−	0.0440685i
$306$	2.36270	+	2.36270i	0.135067	+	0.135067i
$307$	9.12772	+	9.12772i	0.520947	+	0.520947i	0.917857	−	0.396911i	$-0.129918\pi$
$307$	9.12772	+	9.12772i	0.520947	+	0.520947i	−0.396911	+	0.917857i	$0.629918\pi$
$308$	−3.46854	+	10.9478i	−0.197638	+	0.623809i
$309$	10.2557	−	5.92112i	0.583426	−	0.336841i
$310$	0.0919808	+	0.343277i	0.00522416	+	0.0194968i
$311$	−2.52062	+	4.36584i	−0.142931	+	0.247564i	−0.928599	−	0.371084i	$-0.878986\pi$
$311$	−2.52062	+	4.36584i	−0.142931	+	0.247564i	0.785668	+	0.618648i	$0.212319\pi$
$312$	−3.37779	+	1.26116i	−0.191230	+	0.0713991i
$313$	−14.9827	+	8.65025i	−0.846871	+	0.488941i	−0.859594	−	0.510978i	$-0.829283\pi$
$313$	−14.9827	+	8.65025i	−0.846871	+	0.488941i	0.0127230	+	0.999919i	$0.495950\pi$
$314$	−4.18560	−	1.12153i	−0.236207	−	0.0632915i
$315$	0.335986	+	0.106449i	0.0189307	+	0.00599771i
$316$	−11.1179	−	6.41891i	−0.625430	−	0.361092i
$317$	1.67095	−	6.23606i	0.0938497	−	0.350252i	−0.902993	−	0.429656i	$-0.858635\pi$
$317$	1.67095	−	6.23606i	0.0938497	−	0.350252i	0.996843	+	0.0794037i	$0.0253016\pi$
$318$	6.58853	+	1.76539i	0.369466	+	0.0989982i
$319$	18.0366	+	4.83290i	1.00986	+	0.270590i
$320$	0.0344778	−	0.128673i	0.00192737	−	0.00719303i
$321$	12.2086	+	7.04864i	0.681417	+	0.393416i
$322$	−3.69027	−	1.16917i	−0.205651	−	0.0651553i
$323$	−13.0408	−	3.49426i	−0.725608	−	0.194426i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−14.6293	+	10.4250i	−0.811489	+	0.578274i
$326$	3.47344	−	6.01618i	0.192376	−	0.333206i
$327$	−3.95106	−	14.7455i	−0.218494	−	0.815430i
$328$	−9.90898	+	5.72095i	−0.547132	+	0.315887i
$329$	9.39837	−	29.6642i	0.518149	−	1.63544i
$330$	−0.408863	−	0.408863i	−0.0225071	−	0.0225071i
$331$	−16.4491	−	16.4491i	−0.904123	−	0.904123i	0.0916672	−	0.995790i	$-0.470780\pi$
$331$	−16.4491	−	16.4491i	−0.904123	−	0.904123i	−0.995790	+	0.0916672i	$0.970780\pi$
$332$	3.27160	−	12.2098i	0.179552	−	0.670098i
$333$	−1.86419	−	6.95726i	−0.102157	−	0.381256i
$334$		−	8.35303i		−	0.457057i
$335$	0.566404	+	0.981040i	0.0309460	+	0.0536000i
$336$	2.22943	+	1.42466i	0.121625	+	0.0777213i
$337$		−	16.6393i		−	0.906401i	−0.891409	−	0.453200i	$-0.850282\pi$
$337$		−	16.6393i		−	0.906401i	0.891409	−	0.453200i	$-0.149718\pi$
$338$	−10.7709	−	7.27928i	−0.585859	−	0.395941i
$339$	10.8892	+	6.28689i	0.591421	+	0.341457i
$340$	−0.314740	−	0.314740i	−0.0170692	−	0.0170692i
$341$	10.0285	+	5.78998i	0.543076	+	0.313545i
$342$	−2.02025	+	3.49917i	−0.109243	+	0.189214i
$343$	−18.3516	−	2.49379i	−0.990893	−	0.134652i
$344$	10.9185	−	2.92560i	0.588686	−	0.157738i
$345$	0.137819	−	0.137819i	0.00741992	−	0.00741992i
$346$	−7.57915	+	2.03083i	−0.407457	+	0.109178i
$347$	−13.5651	−	23.4954i	−0.728212	−	1.26130i	−0.957638	−	0.287974i	$-0.907018\pi$
$347$	−13.5651	−	23.4954i	−0.728212	−	1.26130i	0.229427	−	0.973326i	$-0.426315\pi$
$348$	2.15096	−	3.72557i	0.115304	−	0.199712i
$349$	0.102175	−	0.381321i	0.00546929	−	0.0204117i	−0.963137	−	0.269010i	$-0.913303\pi$
$349$	0.102175	−	0.381321i	0.00546929	−	0.0204117i	0.968607	+	0.248599i	$0.0799701\pi$
$350$	12.5662	+	3.98129i	0.671692	+	0.212809i
$351$	3.28023	+	1.49669i	0.175086	+	0.0798872i
$352$	−2.17030	−	3.75906i	−0.115677	−	0.200359i
$353$	−2.63165	+	2.63165i	−0.140069	+	0.140069i	−0.773664	−	0.633596i	$-0.781578\pi$
$353$	−2.63165	+	2.63165i	−0.140069	+	0.140069i	0.633596	+	0.773664i	$0.281578\pi$
$354$	−2.81436			−0.149582
$355$	1.66765			0.0885094
$356$	−7.78051	+	7.78051i	−0.412366	+	0.412366i
$357$	7.84721	−	4.07117i	0.415319	−	0.215469i
$358$	−1.27647	−	4.76386i	−0.0674636	−	0.251778i
$359$	35.4104	+	9.48820i	1.86889	+	0.500768i	0.999983	+	0.00579429i	$0.00184439\pi$
$359$	35.4104	+	9.48820i	1.86889	+	0.500768i	0.868908	+	0.494974i	$0.164822\pi$
$360$	−0.115365	+	0.0666060i	−0.00608027	+	0.00351044i
$361$			2.67437i			0.140756i
$362$	0.619553	−	0.166009i	0.0325630	−	0.00872523i
$363$	−7.84076			−0.411533
$364$	0.481714	+	9.52722i	0.0252486	+	0.499362i
$365$	1.08759			0.0569268
$366$	−5.77743	+	1.54806i	−0.301991	+	0.0809183i
$367$			30.8631i			1.61104i	0.592567	+	0.805521i	$0.298114\pi$
$367$			30.8631i			1.61104i	−0.592567	+	0.805521i	$0.701886\pi$
$368$	1.26710	−	0.731561i	0.0660522	−	0.0381352i
$369$	11.0520	+	2.96138i	0.575346	+	0.154163i
$370$	0.248333	+	0.926791i	0.0129102	+	0.0481816i
$371$	9.71751	−	15.2068i	0.504508	−	0.789499i
$372$	1.88644	−	1.88644i	0.0978073	−	0.0978073i
$373$	−18.4286			−0.954196			−0.477098	−	0.878850i	$-0.658311\pi$
$373$	−18.4286			−0.954196			−0.477098	+	0.878850i	$0.658311\pi$
$374$	−14.5035			−0.749959
$375$	−0.940279	+	0.940279i	−0.0485558	+	0.0485558i
$376$	5.88065	+	10.1856i	0.303271	+	0.525281i
$377$	15.4401	−	1.47964i	0.795203	−	0.0762053i
$378$	−0.569061	−	2.58383i	−0.0292693	−	0.132898i
$379$	1.60912	−	6.00531i	0.0826548	−	0.308472i	−0.912205	−	0.409734i	$-0.865621\pi$
$379$	1.60912	−	6.00531i	0.0826548	−	0.308472i	0.994860	+	0.101262i	$0.0322881\pi$
$380$	0.269121	−	0.466132i	0.0138056	−	0.0239121i
$381$	−7.16360	−	12.4077i	−0.367002	−	0.635666i
$382$	−17.9616	+	4.81279i	−0.918994	+	0.246244i
$383$	7.00640	−	7.00640i	0.358010	−	0.358010i	−0.505069	−	0.863079i	$-0.668533\pi$
$383$	7.00640	−	7.00640i	0.358010	−	0.358010i	0.863079	+	0.505069i	$0.168533\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−1.35795	+	0.704510i	−0.0692075	+	0.0359052i
$386$	−2.94276	+	5.09700i	−0.149782	+	0.259431i
$387$	−9.78926	−	5.65183i	−0.497616	−	0.287299i
$388$	3.96700	+	3.96700i	0.201394	+	0.201394i
$389$	−21.1408	−	12.2056i	−1.07188	−	0.618851i	−0.143186	−	0.989696i	$-0.545735\pi$
$389$	−21.1408	−	12.2056i	−1.07188	−	0.618851i	−0.928695	+	0.370845i	$0.879068\pi$
$390$	−0.436966	−	0.199376i	−0.0221266	−	0.0100958i
$391$		−	4.88883i		−	0.247239i
$392$	5.37478	−	4.48462i	0.271467	−	0.226507i
$393$	6.70920	+	11.6207i	0.338435	+	0.586186i
$394$		−	8.59023i		−	0.432769i
$395$	−0.442620	−	1.65188i	−0.0222706	−	0.0831151i
$396$	−1.12343	+	4.19269i	−0.0564544	+	0.210691i
$397$	−7.37229	−	7.37229i	−0.370005	−	0.370005i	0.497474	−	0.867479i	$-0.334261\pi$
$397$	−7.37229	−	7.37229i	−0.370005	−	0.370005i	−0.867479	+	0.497474i	$0.834261\pi$
$398$	−9.95694	−	9.95694i	−0.499096	−	0.499096i
$399$	7.21122	+	7.89162i	0.361013	+	0.395075i
$400$	−4.31476	+	2.49113i	−0.215738	+	0.124556i
$401$	−0.236980	−	0.884423i	−0.0118342	−	0.0441660i	0.959756	−	0.280834i	$-0.0906112\pi$
$401$	−0.236980	−	0.884423i	−0.0118342	−	0.0441660i	−0.971590	+	0.236668i	$0.923944\pi$
$402$	4.25190	−	7.36451i	0.212066	−	0.367308i
$403$	9.48635	+	1.59189i	0.472549	+	0.0792979i
$404$	−0.0337201	+	0.0194683i	−0.00167764	+	0.000968585i
$405$	0.128673	+	0.0344778i	0.00639381	+	0.00171322i
$406$	−7.67779	−	8.40221i	−0.381042	−	0.416995i
$407$	27.0754	+	15.6320i	1.34208	+	0.774848i
$408$	−0.864810	+	3.22751i	−0.0428145	+	0.159786i
$409$	−3.25426	−	0.871977i	−0.160913	−	0.0431165i	0.177463	−	0.984127i	$-0.443211\pi$
$409$	−3.25426	−	0.871977i	−0.160913	−	0.0431165i	−0.338376	+	0.941011i	$0.609878\pi$
$410$	−1.47226	−	0.394491i	−0.0727098	−	0.0194825i
$411$	−2.40733	+	8.98430i	−0.118745	+	0.443163i
$412$	10.2557	+	5.92112i	0.505261	+	0.291713i
$413$	−2.24894	+	7.09836i	−0.110663	+	0.349287i
$414$	−1.41327	−	0.378684i	−0.0694583	−	0.0186113i
$415$	1.45827	−	0.841932i	0.0715836	−	0.0413288i
$416$	−2.78109	−	2.29467i	−0.136354	−	0.112506i
$417$	−5.90757	+	10.2322i	−0.289295	+	0.501073i
$418$	−4.53921	−	16.9406i	−0.222020	−	0.828590i
$419$	−12.9360	+	7.46860i	−0.631965	+	0.364865i	−0.781513	−	0.623889i	$-0.785552\pi$
$419$	−12.9360	+	7.46860i	−0.631965	+	0.364865i	0.149548	+	0.988755i	$0.452218\pi$
$420$	0.0758057	+	0.344197i	0.00369894	+	0.0167951i
$421$	−19.8845	−	19.8845i	−0.969109	−	0.969109i	0.0304275	−	0.999537i	$-0.490313\pi$
$421$	−19.8845	−	19.8845i	−0.969109	−	0.969109i	−0.999537	+	0.0304275i	$0.990313\pi$
$422$	8.12823	+	8.12823i	0.395676	+	0.395676i
$423$	3.04405	−	11.3605i	0.148007	−	0.552368i
$424$	1.76539	+	6.58853i	0.0857350	+	0.319967i
$425$			16.6475i			0.807525i
$426$	−6.25937	−	10.8415i	−0.303267	−	0.525275i
$427$	−0.712206	+	15.8088i	−0.0344661	+	0.765043i
$428$			14.0973i			0.681417i
$429$	−14.6616	+	5.47418i	−0.707870	+	0.264296i
$430$	1.30405	+	0.752892i	0.0628867	+	0.0363077i
$431$	22.2926	+	22.2926i	1.07380	+	1.07380i	0.997050	+	0.0767484i	$0.0244538\pi$
$431$	22.2926	+	22.2926i	1.07380	+	1.07380i	0.0767484	+	0.997050i	$0.475546\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	12.7366	−	22.0605i	0.612083	−	1.06016i	−0.378806	−	0.925476i	$-0.623665\pi$
$433$	12.7366	−	22.0605i	0.612083	−	1.06016i	0.990889	−	0.134682i	$-0.0430014\pi$
$434$	−3.25052	−	6.26540i	−0.156030	−	0.300749i
$435$	0.553540	−	0.148321i	0.0265402	−	0.00711143i
$436$	10.7945	−	10.7945i	0.516962	−	0.516962i
$437$	5.71030	−	1.53007i	0.273161	−	0.0731932i
$438$	−4.08216	−	7.07051i	−0.195053	−	0.337842i
$439$	−13.4202	+	23.2444i	−0.640509	+	1.10939i	0.344810	+	0.938673i	$0.387943\pi$
$439$	−13.4202	+	23.2444i	−0.640509	+	1.10939i	−0.985319	+	0.170722i	$0.945390\pi$
$440$	0.149654	−	0.558517i	0.00713448	−	0.0266262i
$441$	−6.97164	−	0.629439i	−0.331983	−	0.0299733i
$442$	−11.2864	+	4.21400i	−0.536842	+	0.200439i
$443$	6.95881	+	12.0530i	0.330623	+	0.572656i	0.982634	−	0.185553i	$-0.0594078\pi$
$443$	6.95881	+	12.0530i	0.330623	+	0.572656i	−0.652011	+	0.758209i	$0.726074\pi$
$444$	5.09307	−	5.09307i	0.241706	−	0.241706i
$445$	−1.46577			−0.0694842
$446$	24.8233			1.17542
$447$	2.83102	−	2.83102i	0.133903	−	0.133903i
$448$	−0.119073	+	2.64307i	−0.00562569	+	0.124873i
$449$	−3.68798	−	13.7637i	−0.174047	−	0.649550i	−0.996712	−	0.0810249i	$-0.974181\pi$
$449$	−3.68798	−	13.7637i	−0.174047	−	0.649550i	0.822666	−	0.568526i	$-0.192486\pi$
$450$	4.81249	+	1.28950i	0.226863	+	0.0607877i
$451$	−43.0108	+	24.8323i	−2.02530	+	1.16931i
$452$			12.5738i			0.591421i
$453$	19.9317	−	5.34068i	0.936473	−	0.250927i
$454$	24.5398			1.15171
$455$	−0.852042	+	0.942792i	−0.0399444	+	0.0441988i
$456$	−4.04050			−0.189214
$457$	0.256034	−	0.0686042i	0.0119768	−	0.00320917i	−0.252826	−	0.967512i	$-0.581360\pi$
$457$	0.256034	−	0.0686042i	0.0119768	−	0.00320917i	0.264802	+	0.964303i	$0.414693\pi$
$458$		−	11.2912i		−	0.527602i
$459$	2.89371	−	1.67068i	0.135067	−	0.0779809i
$460$	0.188264	+	0.0504452i	0.00877785	+	0.00235202i
$461$	9.81634	+	36.6351i	0.457192	+	1.70626i	0.681562	+	0.731761i	$0.261301\pi$
$461$	9.81634	+	36.6351i	0.457192	+	1.70626i	−0.224369	+	0.974504i	$0.572032\pi$
$462$	9.67705	+	6.18385i	0.450217	+	0.287699i
$463$	5.29794	−	5.29794i	0.246216	−	0.246216i	−0.573200	−	0.819416i	$-0.694298\pi$
$463$	5.29794	−	5.29794i	0.246216	−	0.246216i	0.819416	+	0.573200i	$0.194298\pi$
$464$	4.30192			0.199712
$465$	0.355386			0.0164807
$466$	−1.05841	+	1.05841i	−0.0490300	+	0.0490300i
$467$	−0.323895	−	0.561003i	−0.0149881	−	0.0259601i	0.858434	−	0.512924i	$-0.171438\pi$
$467$	−0.323895	−	0.561003i	−0.0149881	−	0.0259601i	−0.873422	+	0.486964i	$0.838104\pi$
$468$	0.343949	+	3.58911i	0.0158990	+	0.165907i
$469$	−15.1770	−	16.6090i	−0.700810	−	0.766934i
$470$	−0.405504	+	1.51336i	−0.0187045	+	0.0698061i
$471$	−2.16663	+	3.75270i	−0.0998328	+	0.172916i
$472$	−1.40718	−	2.43731i	−0.0647708	−	0.112186i
$473$	47.3928	−	12.6989i	2.17912	−	0.583894i
$474$	−9.07771	+	9.07771i	−0.416953	+	0.416953i
$475$	−19.4449	+	5.21023i	−0.892191	+	0.239062i
$476$	7.44935	+	4.76030i	0.341440	+	0.218188i
$477$	3.41047	−	5.90712i	0.156155	−	0.270468i
$478$	8.22819	+	4.75055i	0.376349	+	0.217285i
$479$	−17.8903	−	17.8903i	−0.817428	−	0.817428i	0.168307	−	0.985735i	$-0.446170\pi$
$479$	−17.8903	−	17.8903i	−0.817428	−	0.817428i	−0.985735	+	0.168307i	$0.946170\pi$
$480$	−0.115365	−	0.0666060i	−0.00526566	−	0.00304013i
$481$	25.6116	+	4.29785i	1.16779	+	0.195965i
$482$		−	3.17964i		−	0.144829i
$483$	−2.08444	+	3.26193i	−0.0948455	+	0.148423i
$484$	−3.92038	−	6.79029i	−0.178199	−	0.308650i
$485$			0.747344i			0.0339352i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	0.399393	−	1.49055i	0.0180982	−	0.0675434i	−0.956286	−	0.292433i	$-0.905535\pi$
$487$	0.399393	−	1.49055i	0.0180982	−	0.0675434i	0.974384	+	0.224889i	$0.0722020\pi$
$488$	−4.22937	−	4.22937i	−0.191455	−	0.191455i
$489$	−4.91219	−	4.91219i	−0.222137	−	0.222137i
$490$	0.928706	+	0.0838488i	0.0419547	+	0.00378790i
$491$	−11.2592	+	6.50052i	−0.508122	+	0.293364i	−0.732061	−	0.681239i	$-0.761442\pi$
$491$	−11.2592	+	6.50052i	−0.508122	+	0.293364i	0.223939	+	0.974603i	$0.428108\pi$
$492$	2.96138	+	11.0520i	0.133509	+	0.498264i
$493$	7.18715	−	12.4485i	0.323693	−	0.560653i
$494$	−8.45443	−	11.8641i	−0.380383	−	0.533789i
$495$	−0.500752	+	0.289109i	−0.0225071	+	0.0129945i
$496$	2.57692	+	0.690485i	0.115707	+	0.0310037i
$497$	−32.3463	+	7.12392i	−1.45093	+	0.319552i
$498$	−10.9470	−	6.32024i	−0.490546	−	0.283217i
$499$	−0.667766	+	2.49214i	−0.0298933	+	0.111563i	−0.979260	−	0.202605i	$-0.935059\pi$
$499$	−0.667766	+	2.49214i	−0.0298933	+	0.111563i	0.949367	+	0.314169i	$0.101726\pi$
$500$	−1.28445	−	0.344166i	−0.0574421	−	0.0153916i
$501$	−8.06840	−	2.16192i	−0.360470	−	0.0965876i
$502$	3.37652	−	12.6013i	0.150701	−	0.562425i
$503$	3.22228	+	1.86038i	0.143674	+	0.0829504i	0.570114	−	0.821566i	$-0.306899\pi$
$503$	3.22228	+	1.86038i	0.143674	+	0.0829504i	−0.426440	+	0.904516i	$0.640232\pi$
$504$	1.95313	−	1.78474i	0.0869994	−	0.0794984i
$505$	−0.00501009	−	0.00134245i	−0.000222946	−	5.97382e-5i
$506$	5.49997	−	3.17541i	0.244503	−	0.141164i
$507$	−9.81896	+	8.51986i	−0.436075	+	0.378380i
$508$	7.16360	−	12.4077i	0.317833	−	0.550503i
$509$	9.78589	+	36.5214i	0.433752	+	1.61878i	0.744036	+	0.668140i	$0.232909\pi$
$509$	9.78589	+	36.5214i	0.433752	+	1.61878i	−0.310284	+	0.950644i	$0.600424\pi$
$510$	−0.385477	+	0.222555i	−0.0170692	+	0.00985491i
$511$	−21.0952	+	4.64600i	−0.933197	+	0.205527i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.85706	+	2.85706i	0.126142	+	0.126142i
$514$	−2.09976	+	7.83641i	−0.0926164	+	0.345649i
$515$	0.408295	+	1.52378i	0.0179916	+	0.0671456i
$516$		−	11.3037i		−	0.497616i
$517$	25.5255	+	44.2115i	1.12261	+	1.94442i
$518$	−8.77586	−	16.9155i	−0.385589	−	0.743226i
$519$			7.84651i			0.344424i
$520$	−0.0458181	−	0.478112i	−0.00200926	−	0.0209666i
$521$	30.7500	+	17.7535i	1.34718	+	0.777796i	0.987850	−	0.155413i	$-0.0496709\pi$
$521$	30.7500	+	17.7535i	1.34718	+	0.777796i	0.359333	+	0.933209i	$0.383004\pi$
$522$	−3.04192	−	3.04192i	−0.133141	−	0.133141i
$523$	20.6888	+	11.9447i	0.904660	+	0.522305i	0.878709	−	0.477358i	$-0.158405\pi$
$523$	20.6888	+	11.9447i	0.904660	+	0.522305i	0.0259506	+	0.999663i	$0.491739\pi$
$524$	−6.70920	+	11.6207i	−0.293093	+	0.507652i
$525$	7.09800	−	11.1076i	0.309782	−	0.484775i
$526$	−12.4022	+	3.32315i	−0.540761	+	0.144896i
$527$	6.30329	−	6.30329i	0.274576	−	0.274576i
$528$	−4.19269	+	1.12343i	−0.182463	+	0.0488909i
$529$	−10.4296	−	18.0647i	−0.453463	−	0.785420i
$530$	−0.454316	+	0.786898i	−0.0197342	+	0.0341807i
$531$	−0.728411	+	2.71847i	−0.0316103	+	0.117971i
$532$	−3.22873	+	10.1909i	−0.139983	+	0.441832i
$533$	−26.2554	+	31.8210i	−1.13725	+	1.37832i
$534$	5.50165	+	9.52914i	0.238080	+	0.412366i
$535$	−1.32789	+	1.32789i	−0.0574098	+	0.0574098i
$536$	8.50380			0.367308
$537$	−4.93191			−0.212827
$538$	7.24116	−	7.24116i	0.312189	−	0.312189i
$539$	23.3297	−	19.4659i	1.00488	−	0.838455i
$540$	0.0344778	+	0.128673i	0.00148369	+	0.00553720i
$541$	38.2807	+	10.2573i	1.64582	+	0.440995i	0.958437	−	0.285305i	$-0.0920948\pi$
$541$	38.2807	+	10.2573i	1.64582	+	0.440995i	0.687378	+	0.726300i	$0.258761\pi$
$542$	−21.1728	+	12.2241i	−0.909448	+	0.525070i
$543$		−	0.641409i		−	0.0275255i
$544$	−3.22751	+	0.864810i	−0.138379	+	0.0370784i
$545$	2.03357			0.0871088
$546$	9.32727	+	2.00053i	0.399170	+	0.0856146i
$547$	−29.0577			−1.24242			−0.621209	−	0.783645i	$-0.713358\pi$
$547$	−29.0577			−1.24242			−0.621209	+	0.783645i	$0.713358\pi$
$548$	−8.98430	+	2.40733i	−0.383790	+	0.102836i
$549$			5.98123i			0.255273i
$550$	−18.7286	+	10.8130i	−0.798591	+	0.461067i
$551$	16.7896	+	4.49877i	0.715262	+	0.191654i
$552$	−0.378684	−	1.41327i	−0.0161178	−	0.0601526i
$553$	15.6418	+	30.1497i	0.665157	+	1.28209i
$554$	−2.98492	+	2.98492i	−0.126817	+	0.126817i
$555$	0.959484			0.0407278
$556$	−11.8151			−0.501073
$557$	−14.3580	+	14.3580i	−0.608368	+	0.608368i	−0.942519	−	0.334152i	$-0.891550\pi$
$557$	−14.3580	+	14.3580i	−0.608368	+	0.608368i	0.334152	+	0.942519i	$0.391550\pi$
$558$	−1.33391	−	2.31041i	−0.0564691	−	0.0978073i
$559$	33.1908	−	23.6520i	1.40382	−	1.00037i
$560$	−0.260180	+	0.237748i	−0.0109946	+	0.0100467i
$561$	−3.75379	+	14.0093i	−0.158485	+	0.591474i
$562$	−0.996756	+	1.72643i	−0.0420456	+	0.0728251i
$563$	−5.90805	−	10.2330i	−0.248995	−	0.431271i	0.714252	−	0.699888i	$-0.246767\pi$
$563$	−5.90805	−	10.2330i	−0.248995	−	0.431271i	−0.963247	+	0.268617i	$0.913434\pi$
$564$	11.3605	−	3.04405i	0.478365	−	0.128178i
$565$	−1.18439	+	1.18439i	−0.0498276	+	0.0498276i
$566$	5.31746	−	1.42481i	0.223509	−	0.0598892i
$567$	−2.64307	−	0.119073i	−0.110999	−	0.00500061i
$568$	6.25937	−	10.8415i	0.262637	−	0.454901i
$569$	−23.4257	−	13.5248i	−0.982055	−	0.566990i	−0.0791651	−	0.996862i	$-0.525225\pi$
$569$	−23.4257	−	13.5248i	−0.982055	−	0.566990i	−0.902890	+	0.429872i	$0.858559\pi$
$570$	−0.380595	−	0.380595i	−0.0159414	−	0.0159414i
$571$	0.632370	+	0.365099i	0.0264639	+	0.0152789i	0.513174	−	0.858285i	$-0.328470\pi$
$571$	0.632370	+	0.365099i	0.0264639	+	0.0152789i	−0.486710	+	0.873564i	$0.661803\pi$
$572$	−12.0716	−	9.96025i	−0.504738	−	0.416459i
$573$			18.5952i			0.776825i
$574$	30.2417	+	1.36243i	1.26227	+	0.0568666i
$575$	−3.64482	−	6.31302i	−0.152000	−	0.263271i
$576$			1.00000i			0.0416667i
$577$	12.1027	+	45.1679i	0.503842	+	1.88036i	0.473442	+	0.880825i	$0.343011\pi$
$577$	12.1027	+	45.1679i	0.503842	+	1.88036i	0.0303997	+	0.999538i	$0.490322\pi$
$578$	1.51028	−	5.63642i	0.0628192	−	0.234444i
$579$	4.16169	+	4.16169i	0.172954	+	0.172954i
$580$	0.405220	+	0.405220i	0.0168258	+	0.0168258i
$581$	−24.6885	+	22.5599i	−1.02425	+	0.935943i
$582$	4.85857	−	2.80509i	0.201394	−	0.116275i
$583$	7.66285	+	28.5981i	0.317363	+	1.18441i
$584$	4.08216	−	7.07051i	0.168921	−	0.292580i
$585$	−0.305678	+	0.370475i	−0.0126382	+	0.0153172i
$586$	4.21846	−	2.43553i	0.174263	−	0.100611i
$587$	−24.4744	−	6.55790i	−1.01017	−	0.270674i	−0.284468	−	0.958685i	$-0.591817\pi$
$587$	−24.4744	−	6.55790i	−1.01017	−	0.270674i	−0.725700	+	0.688012i	$0.758484\pi$
$588$	−2.94071	−	6.35234i	−0.121273	−	0.261966i
$589$	9.33519	+	5.38968i	0.384650	+	0.222078i
$590$	0.0970330	−	0.362132i	0.00399479	−	0.0149087i
$591$	−8.29752	−	2.22331i	−0.341314	−	0.0914549i
$592$	6.95726	+	1.86419i	0.285942	+	0.0766179i
$593$	3.24493	−	12.1103i	0.133253	−	0.497309i	−0.866745	−	0.498751i	$-0.833792\pi$
$593$	3.24493	−	12.1103i	0.133253	−	0.497309i	0.999999	+	0.00144199i	$0.000459000\pi$
$594$	3.75906	+	2.17030i	0.154236	+	0.0890484i
$595$	0.253295	+	1.15009i	0.0103841	+	0.0471490i
$596$	3.86725	+	1.03623i	0.158409	+	0.0424455i
$597$	−12.1947	+	7.04062i	−0.499096	+	0.288153i
$598$	3.35739	−	4.06907i	0.137294	−	0.166397i
$599$	−9.43306	+	16.3385i	−0.385424	+	0.667574i	−0.991828	−	0.127582i	$-0.959278\pi$
$599$	−9.43306	+	16.3385i	−0.385424	+	0.667574i	0.606404	+	0.795157i	$0.292612\pi$
$600$	1.28950	+	4.81249i	0.0526437	+	0.196469i
$601$	−37.2197	+	21.4888i	−1.51822	+	0.876546i	−0.518451	+	0.855107i	$0.673491\pi$
$601$	−37.2197	+	21.4888i	−1.51822	+	0.876546i	−0.999770	+	0.0214384i	$0.993175\pi$
$602$	−28.5100	−	9.03268i	−1.16198	−	0.368145i
$603$	−6.01310	−	6.01310i	−0.244872	−	0.244872i
$604$	14.5910	+	14.5910i	0.593700	+	0.593700i
$605$	0.270332	−	1.00889i	0.0109906	−	0.0410173i
$606$	0.0100775	+	0.0376099i	0.000409372	+	0.00152780i
$607$			3.29877i			0.133893i	0.997757	+	0.0669466i	$0.0213257\pi$
$607$			3.29877i			0.133893i	−0.997757	+	0.0669466i	$0.978674\pi$
$608$	−2.02025	−	3.49917i	−0.0819319	−	0.141910i
$609$	−10.1031	+	5.24152i	−0.409397	+	0.212397i
$610$		−	0.796772i		−	0.0322604i
$611$	32.7092	+	26.9883i	1.32327	+	1.09183i
$612$	2.89371	+	1.67068i	0.116971	+	0.0675334i
$613$	17.9846	+	17.9846i	0.726391	+	0.726391i	0.969899	−	0.243508i	$-0.0782982\pi$
$613$	17.9846	+	17.9846i	0.726391	+	0.726391i	−0.243508	+	0.969899i	$0.578298\pi$
$614$	11.1791	+	6.45427i	0.451153	+	0.260473i
$615$	−0.762099	+	1.31999i	−0.0307308	+	0.0532273i
$616$	−0.516849	+	11.4725i	−0.0208245	+	0.462240i
$617$	−28.5840	+	7.65907i	−1.15075	+	0.308343i	−0.783266	−	0.621687i	$-0.786448\pi$
$617$	−28.5840	+	7.65907i	−1.15075	+	0.308343i	−0.367485	+	0.930030i	$0.619781\pi$
$618$	8.37373	−	8.37373i	0.336841	−	0.336841i
$619$	−22.0606	+	5.91111i	−0.886689	+	0.237588i	−0.673291	−	0.739378i	$-0.735120\pi$
$619$	−22.0606	+	5.91111i	−0.886689	+	0.237588i	−0.213398	+	0.976965i	$0.568453\pi$
$620$	0.177693	+	0.307774i	0.00713633	+	0.0123605i
$621$	−0.731561	+	1.26710i	−0.0293565	+	0.0508470i
$622$	−1.30477	+	4.86946i	−0.0523164	+	0.195248i
$623$	28.4307	−	6.26155i	1.13905	−	0.250864i
$624$	−2.93628	+	2.09242i	−0.117545	+	0.0837639i
$625$	12.3671	+	21.4204i	0.494683	+	0.856816i
$626$	−12.2333	+	12.2333i	−0.488941	+	0.488941i
$627$	−17.5382			−0.700407
$628$	−4.33325			−0.172916
$629$	17.0178	−	17.0178i	0.678545	−	0.678545i
$630$	0.352089	+	0.0158620i	0.0140275	+	0.000631957i
$631$	−8.61757	−	32.1612i	−0.343060	−	1.28032i	−0.894862	−	0.446342i	$-0.852726\pi$
$631$	−8.61757	−	32.1612i	−0.343060	−	1.28032i	0.551802	−	0.833975i	$-0.313940\pi$
$632$	−12.4004	−	3.32267i	−0.493261	−	0.132169i
$633$	9.95501	−	5.74753i	0.395676	−	0.228444i
$634$		−	6.45604i		−	0.256402i
$635$	1.84352	−	0.493970i	0.0731579	−	0.0196026i
$636$	6.82095			0.270468
$637$	12.4991	−	21.9265i	0.495231	−	0.868761i
$638$	18.6729			0.739267
$639$	−12.0922	+	3.24009i	−0.478359	+	0.128176i
$640$		−	0.133212i		−	0.00526566i
$641$	4.09770	−	2.36581i	0.161849	−	0.0934437i	−0.416888	−	0.908958i	$-0.636879\pi$
$641$	4.09770	−	2.36581i	0.161849	−	0.0934437i	0.578737	+	0.815514i	$0.303546\pi$
$642$	13.6169	+	3.64864i	0.537417	+	0.144000i
$643$	−7.51513	−	28.0468i	−0.296368	−	1.10606i	−0.940125	−	0.340830i	$-0.889292\pi$
$643$	−7.51513	−	28.0468i	−0.296368	−	1.10606i	0.643757	−	0.765230i	$-0.277375\pi$
$644$	−3.86713	−	0.174219i	−0.152386	−	0.00686519i
$645$	1.06475	−	1.06475i	0.0419245	−	0.0419245i
$646$	−13.5008			−0.531182
$647$	47.9112			1.88358			0.941791	−	0.336198i	$-0.109141\pi$
$647$	47.9112			1.88358			0.941791	+	0.336198i	$0.109141\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−6.10800	−	10.5794i	−0.239760	−	0.415277i
$650$	−11.4327	+	13.8561i	−0.448425	+	0.543481i
$651$	−6.89321	+	1.51816i	−0.270166	+	0.0595012i
$652$	1.79799	−	6.71018i	0.0704146	−	0.262791i
$653$	−0.827054	+	1.43250i	−0.0323651	+	0.0560580i	−0.881754	−	0.471709i	$-0.843637\pi$
$653$	−0.827054	+	1.43250i	−0.0323651	+	0.0560580i	0.849389	+	0.527767i	$0.176971\pi$
$654$	−7.63285	−	13.2205i	−0.298468	−	0.516962i
$655$	−1.72658	+	0.462637i	−0.0674633	+	0.0180767i
$656$	−8.09065	+	8.09065i	−0.315887	+	0.315887i
$657$	−7.88613	+	2.11308i	−0.307667	+	0.0824392i
$658$	1.40046	−	31.0859i	0.0545955	−	1.21186i
$659$	13.3063	−	23.0472i	0.518341	−	0.897793i	−0.481432	−	0.876483i	$-0.659883\pi$
$659$	13.3063	−	23.0472i	0.518341	−	0.897793i	0.999773	−	0.0213095i	$-0.00678353\pi$
$660$	−0.500752	−	0.289109i	−0.0194918	−	0.0112536i
$661$	27.9019	+	27.9019i	1.08526	+	1.08526i	0.996009	+	0.0892491i	$0.0284467\pi$
$661$	27.9019	+	27.9019i	1.08526	+	1.08526i	0.0892491	+	0.996009i	$0.471553\pi$
$662$	−20.1459	−	11.6312i	−0.782993	−	0.452061i
$663$	1.14926	+	11.9925i	0.0446336	+	0.465751i
$664$		−	12.6405i		−	0.490546i
$665$	−1.26406	+	0.655803i	−0.0490183	+	0.0254309i
$666$	−3.60134	−	6.23771i	−0.139549	−	0.241706i
$667$			6.29423i			0.243714i
$668$	−2.16192	−	8.06840i	−0.0836473	−	0.312176i
$669$	6.42474	−	23.9774i	0.248395	−	0.927022i
$670$	0.801016	+	0.801016i	0.0309460	+	0.0309460i
$671$	−18.3580	−	18.3580i	−0.708702	−	0.708702i
$672$	2.52219	+	0.799093i	0.0972957	+	0.0308257i
$673$	−2.01759	+	1.16486i	−0.0777725	+	0.0449020i	−0.538382	−	0.842701i	$-0.680964\pi$
$673$	−2.01759	+	1.16486i	−0.0777725	+	0.0449020i	0.460609	+	0.887603i	$0.347631\pi$
$674$	−4.30657	−	16.0723i	−0.165883	−	0.619083i
$675$	2.49113	−	4.31476i	0.0958835	−	0.166075i
$676$	−12.2879	−	4.24354i	−0.472611	−	0.163213i
$677$	−22.7294	+	13.1229i	−0.873564	+	0.504352i	−0.868531	−	0.495635i	$-0.834935\pi$
$677$	−22.7294	+	13.1229i	−0.873564	+	0.504352i	−0.00503283	+	0.999987i	$0.501602\pi$
$678$	12.1453	+	3.25433i	0.466439	+	0.124982i
$679$	−3.19254	−	14.4958i	−0.122518	−	0.556297i
$680$	−0.385477	−	0.222555i	−0.0147824	−	0.00853460i
$681$	6.35137	−	23.7036i	0.243385	−	0.908325i
$682$	11.1854	+	2.99711i	0.428310	+	0.114765i
$683$	−23.2888	−	6.24023i	−0.891123	−	0.238776i	−0.215923	−	0.976410i	$-0.569276\pi$
$683$	−23.2888	−	6.24023i	−0.891123	−	0.238776i	−0.675200	+	0.737635i	$0.735943\pi$
$684$	−1.04576	+	3.90282i	−0.0399856	+	0.149228i
$685$	−1.07304	−	0.619517i	−0.0409986	−	0.0236705i
$686$	−18.3717	+	2.34093i	−0.701435	+	0.0893770i
$687$	−10.9064	−	2.92237i	−0.416107	−	0.111495i
$688$	9.78926	−	5.65183i	0.373212	−	0.215474i
$689$	14.2723	+	20.0282i	0.543732	+	0.763016i
$690$	0.0974526	−	0.168793i	0.00370996	−	0.00642584i
$691$	−5.60363	−	20.9130i	−0.213172	−	0.795570i	−0.986802	−	0.161932i	$-0.948228\pi$
$691$	−5.60363	−	20.9130i	−0.213172	−	0.795570i	0.773630	−	0.633638i	$-0.218439\pi$
$692$	−6.79528	+	3.92325i	−0.258318	+	0.149140i
$693$	8.47775	−	7.74681i	0.322043	−	0.294277i
$694$	−19.1839	−	19.1839i	−0.728212	−	0.728212i
$695$	−1.11293	−	1.11293i	−0.0422158	−	0.0422158i
$696$	1.11342	−	4.15533i	0.0422040	−	0.157508i
$697$	9.89507	+	36.9289i	0.374802	+	1.39878i
$698$		−	0.394773i		−	0.0149424i
$699$	0.748411	+	1.29629i	0.0283075	+	0.0490300i
$700$	13.1684	+	0.593254i	0.497721	+	0.0224229i
$701$			6.76434i			0.255486i	0.991807	+	0.127743i	$0.0407732\pi$
$701$			6.76434i			0.255486i	−0.991807	+	0.127743i	$0.959227\pi$
$702$	3.55583	+	0.596701i	0.134206	+	0.0225210i
$703$	25.2035	+	14.5512i	0.950567	+	0.548810i
$704$	−3.06926	−	3.06926i	−0.115677	−	0.115677i
$705$	1.35684	+	0.783373i	0.0511016	+	0.0295035i
$706$	−1.86086	+	3.22310i	−0.0700343	+	0.121303i
$707$	0.102912	+	0.00463632i	0.00387042	+	0.000174367i
$708$	−2.71847	+	0.728411i	−0.102166	+	0.0273753i
$709$	4.13938	−	4.13938i	0.155457	−	0.155457i	−0.625093	−	0.780550i	$-0.714939\pi$
$709$	4.13938	−	4.13938i	0.155457	−	0.155457i	0.780550	+	0.625093i	$0.214939\pi$
$710$	1.61082	−	0.431618i	0.0604531	−	0.0161984i
$711$	6.41891	+	11.1179i	0.240728	+	0.416953i
$712$	−5.50165	+	9.52914i	−0.206183	+	0.357120i
$713$	−1.01026	+	3.77035i	−0.0378346	+	0.141201i
$714$	6.52613	−	5.96346i	0.244234	−	0.223177i
$715$	−0.198878	−	2.07529i	−0.00743761	−	0.0776115i
$716$	−2.46595	−	4.27116i	−0.0921570	−	0.159621i
$717$	6.71829	−	6.71829i	0.250899	−	0.250899i
$718$	36.6596			1.36812
$719$	−10.1180			−0.377340			−0.188670	−	0.982041i	$-0.560418\pi$
$719$	−10.1180			−0.377340			−0.188670	+	0.982041i	$0.560418\pi$
$720$	−0.0941951	+	0.0941951i	−0.00351044	+	0.00351044i
$721$	−14.4288	−	27.8116i	−0.537355	−	1.03576i
$722$	0.692177	+	2.58324i	0.0257602	+	0.0961382i
$723$	−3.07130	−	0.822951i	−0.114223	−	0.0306059i
$724$	0.555476	−	0.320704i	0.0206441	−	0.0119189i
$725$		−	21.4333i		−	0.796011i
$726$	−7.57359	+	2.02934i	−0.281082	+	0.0753158i
$727$	−23.7007			−0.879009			−0.439505	−	0.898240i	$-0.644846\pi$
$727$	−23.7007			−0.879009			−0.439505	+	0.898240i	$0.644846\pi$
$728$	2.93113	+	9.07791i	0.108635	+	0.336450i
$729$	−1.00000			−0.0370370
$730$	1.05053	−	0.281488i	0.0388817	−	0.0104183i
$731$		−	37.7697i		−	1.39696i
$732$	−5.17990	+	2.99062i	−0.191455	+	0.110536i
$733$	4.98805	+	1.33654i	0.184238	+	0.0493664i	0.349758	−	0.936840i	$-0.386264\pi$
$733$	4.98805	+	1.33654i	0.184238	+	0.0493664i	−0.165520	+	0.986206i	$0.552930\pi$
$734$	7.98796	+	29.8115i	0.294841	+	1.10036i
$735$	0.321359	−	0.875360i	0.0118535	−	0.0322881i
$736$	1.03458	−	1.03458i	0.0381352	−	0.0381352i
$737$	36.9115			1.35965
$738$	11.4419			0.421182
$739$	37.2119	−	37.2119i	1.36886	−	1.36886i	0.506799	−	0.862064i	$-0.330829\pi$
$739$	37.2119	−	37.2119i	1.36886	−	1.36886i	0.862064	−	0.506799i	$-0.169171\pi$
$740$	0.479742	+	0.830938i	0.0176357	+	0.0305459i
$741$	−13.6480	+	5.09571i	−0.501371	+	0.187196i
$742$	5.45057	−	17.2037i	0.200097	−	0.631569i
$743$	9.88631	−	36.8962i	0.362693	−	1.35359i	−0.507828	−	0.861459i	$-0.669551\pi$
$743$	9.88631	−	36.8962i	0.362693	−	1.35359i	0.870521	−	0.492131i	$-0.163782\pi$
$744$	1.33391	−	2.31041i	0.0489036	−	0.0847036i
$745$	0.266669	+	0.461884i	0.00976998	+	0.0169221i
$746$	−17.8006	+	4.76967i	−0.651728	+	0.174630i
$747$	−8.93817	+	8.93817i	−0.327031	+	0.327031i
$748$	−14.0093	+	3.75379i	−0.512232	+	0.137252i
$749$	20.0838	−	31.4289i	0.733845	−	1.14839i
$750$	−0.664878	+	1.15160i	−0.0242779	+	0.0420506i
$751$	−39.9574	−	23.0694i	−1.45807	−	0.841815i	−0.459150	−	0.888359i	$-0.651846\pi$
$751$	−39.9574	−	23.0694i	−1.45807	−	0.841815i	−0.998916	+	0.0465436i	$0.985179\pi$
$752$	8.31649	+	8.31649i	0.303271	+	0.303271i
$753$	−11.2981	−	6.52293i	−0.411724	−	0.237709i
$754$	14.5310	−	5.42540i	0.529187	−	0.197582i
$755$			2.74880i			0.100039i
$756$	−1.21841	−	2.34850i	−0.0443133	−	0.0854142i
$757$	−2.10566	−	3.64711i	−0.0765316	−	0.132557i	0.825220	−	0.564812i	$-0.191051\pi$
$757$	−2.10566	−	3.64711i	−0.0765316	−	0.132557i	−0.901751	+	0.432255i	$0.857718\pi$
$758$		−	6.21716i		−	0.225817i
$759$	−1.64371	−	6.13442i	−0.0596630	−	0.222665i
$760$	0.139307	−	0.519903i	0.00505321	−	0.0188588i
$761$	−1.57017	−	1.57017i	−0.0569187	−	0.0569187i	0.678074	−	0.734993i	$-0.262815\pi$
$761$	−1.57017	−	1.57017i	−0.0569187	−	0.0569187i	−0.734993	+	0.678074i	$0.762815\pi$
$762$	−10.1309	−	10.1309i	−0.367002	−	0.367002i
$763$	−39.4440	+	8.68712i	−1.42797	+	0.314495i
$764$	−16.1039	+	9.29759i	−0.582619	+	0.336375i
$765$	0.115203	+	0.429943i	0.00416517	+	0.0155446i
$766$	4.95427	−	8.58105i	0.179005	−	0.310046i
$767$	−7.82700	−	6.45804i	−0.282617	−	0.233186i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	33.9231	+	9.08967i	1.22330	+	0.327782i	0.811967	−	0.583704i	$-0.198397\pi$
$769$	33.9231	+	9.08967i	1.22330	+	0.327782i	0.411332	+	0.911486i	$0.365064\pi$
$770$	−1.12934	+	1.03197i	−0.0406985	+	0.0371895i
$771$	7.02593	+	4.05642i	0.253033	+	0.146089i
$772$	−1.52328	+	5.68497i	−0.0548241	+	0.204606i
$773$	−21.3337	−	5.71635i	−0.767320	−	0.205603i	−0.146133	−	0.989265i	$-0.546683\pi$
$773$	−21.3337	−	5.71635i	−0.767320	−	0.205603i	−0.621187	+	0.783662i	$0.713349\pi$
$774$	−10.9185	−	2.92560i	−0.392457	−	0.105159i
$775$	3.44017	−	12.8389i	0.123575	−	0.461186i
$776$	4.85857	+	2.80509i	0.174412	+	0.100697i
$777$	−18.6105	+	4.09877i	−0.667648	+	0.147043i
$778$	−23.5795	−	6.31811i	−0.845366	−	0.226515i
$779$	−40.0372	+	23.1155i	−1.43448	+	0.828199i
$780$	−0.473679	−	0.0794876i	−0.0169604	−	0.00284611i
$781$	27.1694	−	47.0588i	0.972197	−	1.68389i
$782$	−1.26532	−	4.72224i	−0.0452478	−	0.168867i
$783$	−3.72557	+	2.15096i	−0.133141	+	0.0768690i
$784$	4.03093	−	5.72290i	0.143962	−	0.204389i
$785$	−0.408171	−	0.408171i	−0.0145682	−	0.0145682i
$786$	9.48825	+	9.48825i	0.338435	+	0.338435i
$787$	−1.56210	+	5.82982i	−0.0556827	+	0.207811i	−0.988162	−	0.153412i	$-0.950974\pi$
$787$	−1.56210	+	5.82982i	−0.0556827	+	0.207811i	0.932480	+	0.361223i	$0.117641\pi$
$788$	−2.22331	−	8.29752i	−0.0792023	−	0.295587i
$789$			12.8397i			0.457105i
$790$	−0.855076	−	1.48103i	−0.0304222	−	0.0526928i
$791$	17.9133	−	28.0323i	0.636924	−	0.996715i
$792$			4.34059i			0.154236i
$793$	−19.6198	−	8.95203i	−0.696721	−	0.317896i
$794$	−9.02917	−	5.21300i	−0.320433	−	0.185002i
$795$	0.642500	+	0.642500i	0.0227871	+	0.0227871i
$796$	−12.1947	−	7.04062i	−0.432230	−	0.249548i
$797$	−23.5531	+	40.7952i	−0.834295	+	1.44504i	0.0603090	+	0.998180i	$0.480791\pi$
$797$	−23.5531	+	40.7952i	−0.834295	+	1.44504i	−0.894604	+	0.446861i	$0.852542\pi$
$798$	9.00801	+	5.75632i	0.318880	+	0.203772i
$799$	37.9598	−	10.1713i	1.34292	−	0.359834i
$800$	−3.52299	+	3.52299i	−0.124556	+	0.124556i
$801$	10.6284	−	2.84786i	0.375535	−	0.100624i
$802$	−0.457811	−	0.792952i	−0.0161659	−	0.0280001i
$803$	17.7190	−	30.6902i	0.625290	−	1.08303i
$804$	2.20095	−	8.21404i	0.0776214	−	0.289687i
$805$	−0.347854	−	0.380675i	−0.0122603	−	0.0134170i
$806$	9.57512	−	0.917596i	0.337269	−	0.0323209i
$807$	−5.12028	−	8.86858i	−0.180242	−	0.312189i
$808$	−0.0275324	+	0.0275324i	−0.000968585	+	0.000968585i
$809$	−1.62721			−0.0572098			−0.0286049	−	0.999591i	$-0.509106\pi$
$809$	−1.62721			−0.0572098			−0.0286049	+	0.999591i	$0.509106\pi$
$810$	0.133212			0.00468059
$811$	−30.9201	+	30.9201i	−1.08575	+	1.08575i	−0.0897926	+	0.995960i	$0.528620\pi$
$811$	−30.9201	+	30.9201i	−1.08575	+	1.08575i	−0.995960	+	0.0897926i	$0.971380\pi$
$812$	−9.59083	−	6.12875i	−0.336572	−	0.215077i
$813$	6.32766	+	23.6152i	0.221921	+	0.828220i
$814$	30.1987	+	8.09171i	1.05846	+	0.283614i
$815$	0.801427	−	0.462704i	0.0280728	−	0.0162078i
$816$			3.34137i			0.116971i
$817$	44.1162	−	11.8209i	1.54343	−	0.413561i
$818$	−3.36906			−0.117796
$819$	4.34643	−	8.49167i	0.151877	−	0.296723i
$820$	−1.52420			−0.0532273
$821$	−17.8113	+	4.77251i	−0.621617	+	0.166562i	−0.555863	−	0.831274i	$-0.687612\pi$
$821$	−17.8113	+	4.77251i	−0.621617	+	0.166562i	−0.0657544	+	0.997836i	$0.520945\pi$
$822$			9.30123i			0.324418i
$823$	9.17724	−	5.29848i	0.319898	−	0.184693i	−0.331449	−	0.943473i	$-0.607537\pi$
$823$	9.17724	−	5.29848i	0.319898	−	0.184693i	0.651347	+	0.758780i	$0.274204\pi$
$824$	11.4387	+	3.06500i	0.398487	+	0.106774i
$825$	5.59721	+	20.8891i	0.194870	+	0.727264i
$826$	−0.335116	+	7.43856i	−0.0116602	+	0.258821i
$827$	−4.38155	+	4.38155i	−0.152361	+	0.152361i	−0.779172	−	0.626810i	$-0.784360\pi$
$827$	−4.38155	+	4.38155i	−0.152361	+	0.152361i	0.626810	+	0.779172i	$0.284360\pi$
$828$	−1.46312			−0.0508470
$829$	−4.45173			−0.154615			−0.0773075	−	0.997007i	$-0.524632\pi$
$829$	−4.45173			−0.154615			−0.0773075	+	0.997007i	$0.524632\pi$
$830$	1.19067	−	1.19067i	0.0413288	−	0.0413288i
$831$	2.11065	+	3.65576i	0.0732178	+	0.126817i
$832$	−3.28023	−	1.49669i	−0.113722	−	0.0518882i
$833$	−9.82600	−	21.2255i	−0.340451	−	0.735420i
$834$	−3.05798	+	11.4125i	−0.105889	+	0.395184i
$835$	0.556361	−	0.963646i	0.0192537	−	0.0333484i
$836$	−8.76908	−	15.1885i	−0.303285	−	0.525305i
$837$	−2.57692	+	0.690485i	−0.0890715	+	0.0238666i
$838$	−10.5622	+	10.5622i	−0.364865	+	0.364865i
$839$	−4.10963	+	1.10117i	−0.141880	+	0.0380167i	−0.329060	−	0.944309i	$-0.606732\pi$
$839$	−4.10963	+	1.10117i	−0.141880	+	0.0380167i	0.187180	+	0.982326i	$0.440065\pi$
$840$	0.162307	+	0.312849i	0.00560014	+	0.0107943i
$841$	5.24675	−	9.08763i	0.180922	−	0.313367i
$842$	−24.3534	−	14.0604i	−0.839273	−	0.484555i
$843$	1.40963	+	1.40963i	0.0485501	+	0.0485501i
$844$	9.95501	+	5.74753i	0.342666	+	0.197838i
$845$	−0.757739	−	1.55718i	−0.0260670	−	0.0535686i
$846$		−	11.7613i		−	0.404362i
$847$	−0.933626	+	20.7237i	−0.0320798	+	0.712074i
$848$	3.41047	+	5.90712i	0.117116	+	0.202851i
$849$		−	5.50504i		−	0.188932i
$850$	4.30870	+	16.0803i	0.147787	+	0.551550i
$851$	−2.72754	+	10.1793i	−0.0934989	+	0.348943i
$852$	−8.85209	−	8.85209i	−0.303267	−	0.303267i
$853$	11.5036	+	11.5036i	0.393875	+	0.393875i	0.876066	−	0.482191i	$-0.160159\pi$
$853$	11.5036	+	11.5036i	0.393875	+	0.393875i	−0.482191	+	0.876066i	$0.660159\pi$
$854$	3.40369	+	15.4545i	0.116472	+	0.528842i
$855$	−0.466132	+	0.269121i	−0.0159414	+	0.00920376i
$856$	3.64864	+	13.6169i	0.124708	+	0.465417i
$857$	3.43120	−	5.94301i	0.117207	−	0.203009i	−0.801453	−	0.598058i	$-0.795939\pi$
$857$	3.43120	−	5.94301i	0.117207	−	0.203009i	0.918660	+	0.395049i	$0.129272\pi$
$858$	−12.7452	+	9.08236i	−0.435115	+	0.310067i
$859$	28.2527	−	16.3117i	0.963971	−	0.556549i	0.0665781	−	0.997781i	$-0.478792\pi$
$859$	28.2527	−	16.3117i	0.963971	−	0.556549i	0.897393	+	0.441232i	$0.145459\pi$
$860$	1.45447	+	0.389725i	0.0495972	+	0.0132895i
$861$	9.14314	−	28.8587i	0.311597	−	0.983501i
$862$	27.3028	+	15.7633i	0.929937	+	0.536899i
$863$	6.72624	−	25.1027i	0.228964	−	0.854505i	−0.751814	−	0.659376i	$-0.770821\pi$
$863$	6.72624	−	25.1027i	0.228964	−	0.854505i	0.980778	−	0.195129i	$-0.0625126\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	−1.00963	−	0.270530i	−0.0343285	−	0.00919831i
$866$	6.59296	−	24.6053i	0.224038	−	0.836121i
$867$	−5.05348	−	2.91763i	−0.171625	−	0.0990878i
$868$	−4.76137	−	5.21062i	−0.161611	−	0.176860i
$869$	−53.8250	−	14.4224i	−1.82589	−	0.489245i
$870$	0.496291	−	0.286534i	0.0168258	−	0.00971440i
$871$	28.7241	−	10.7246i	0.973278	−	0.363391i
$872$	7.63285	−	13.2205i	0.258481	−	0.447702i
$873$	−1.45202	−	5.41903i	−0.0491436	−	0.183406i
$874$	5.11972	−	2.95587i	0.173177	−	0.0999838i
$875$	2.37326	+	2.59719i	0.0802309	+	0.0878009i
$876$	−5.77305	−	5.77305i	−0.195053	−	0.195053i
$877$	−28.5746	−	28.5746i	−0.964896	−	0.964896i	0.0345085	−	0.999404i	$-0.489013\pi$
$877$	−28.5746	−	28.5746i	−0.964896	−	0.964896i	−0.999404	+	0.0345085i	$0.989013\pi$
$878$	−6.94679	+	25.9258i	−0.234443	+	0.874952i
$879$	−1.26072	−	4.70508i	−0.0425231	−	0.158698i
$880$		−	0.578219i		−	0.0194918i
$881$	3.94323	+	6.82987i	0.132851	+	0.230104i	0.924774	−	0.380516i	$-0.124254\pi$
$881$	3.94323	+	6.82987i	0.132851	+	0.230104i	−0.791924	+	0.610620i	$0.790920\pi$
$882$	−6.89700	+	1.19640i	−0.232234	+	0.0402850i
$883$		−	17.8741i		−	0.601513i	−0.953701	−	0.300756i	$-0.902761\pi$
$883$		−	17.8741i		−	0.601513i	0.953701	−	0.300756i	$-0.0972391\pi$
$884$	−9.81121	+	6.99156i	−0.329987	+	0.235151i
$885$	−0.324679	−	0.187453i	−0.0109140	−	0.00630118i
$886$	9.84124	+	9.84124i	0.330623	+	0.330623i
$887$	−42.7064	−	24.6566i	−1.43394	−	0.827887i	−0.436523	−	0.899693i	$-0.643790\pi$
$887$	−42.7064	−	24.6566i	−1.43394	−	0.827887i	−0.997419	+	0.0718063i	$0.977124\pi$
$888$	3.60134	−	6.23771i	0.120853	−	0.209324i
$889$	−33.6475	+	17.4565i	−1.12850	+	0.585471i
$890$	−1.41583	+	0.379370i	−0.0474586	+	0.0127165i
$891$	3.06926	−	3.06926i	0.102824	−	0.102824i
$892$	23.9774	−	6.42474i	0.802824	−	0.215116i
$893$	23.7608	+	41.1548i	0.795123	+	1.37719i
$894$	2.00184	−	3.46728i	0.0669514	−	0.115963i
$895$	0.170041	−	0.634603i	0.00568385	−	0.0212124i
$896$	0.569061	+	2.58383i	0.0190110	+	0.0863197i
$897$	−3.06147	−	4.29614i	−0.102219	−	0.143444i
$898$	−7.12463	−	12.3402i	−0.237752	−	0.411799i
$899$	−8.11531	+	8.11531i	−0.270661	+	0.270661i
$900$	4.98225			0.166075
$901$	22.7913			0.759289
$902$	−35.1182	+	35.1182i	−1.16931	+	1.16931i
$903$	−16.1038	+	25.2007i	−0.535902	+	0.838628i
$904$	3.25433	+	12.1453i	0.108237	+	0.403948i
$905$	0.0825319	+	0.0221143i	0.00274345	+	0.000735106i
$906$	17.8703	−	10.3174i	0.593700	−	0.342773i
$907$			46.0369i			1.52863i	0.644843	+	0.764315i	$0.276923\pi$
$907$			46.0369i			1.52863i	−0.644843	+	0.764315i	$0.723077\pi$
$908$	23.7036	−	6.35137i	0.786633	−	0.210778i
$909$	0.0389367			0.00129145
$910$	−0.578997	+	1.13119i	−0.0191936	+	0.0374987i
$911$	3.09215			0.102448			0.0512238	−	0.998687i	$-0.483688\pi$
$911$	3.09215			0.102448			0.0512238	+	0.998687i	$0.483688\pi$
$912$	−3.90282	+	1.04576i	−0.129235	+	0.0346285i
$913$		−	54.8672i		−	1.81584i
$914$	0.229554	−	0.132533i	0.00759297	−	0.00438380i
$915$	−0.769623	−	0.206220i	−0.0254429	−	0.00681741i
$916$	−2.92237	−	10.9064i	−0.0965579	−	0.360359i
$917$	31.5132	−	16.3492i	1.04066	−	0.539898i
$918$	2.36270	−	2.36270i	0.0779809	−	0.0779809i
$919$	37.9525			1.25194			0.625969	−	0.779848i	$-0.284703\pi$
$919$	37.9525			1.25194			0.625969	+	0.779848i	$0.284703\pi$
$920$	0.194905			0.00642584
$921$	9.12772	−	9.12772i	0.300769	−	0.300769i
$922$	18.9637	+	32.8461i	0.624536	+	1.08173i
$923$	7.46994	−	44.5145i	0.245876	−	1.46521i
$924$	10.9478	+	3.46854i	0.360156	+	0.114107i
$925$	9.28788	−	34.6629i	0.305384	−	1.13971i
$926$	3.74621	−	6.48862i	0.123108	−	0.213229i
$927$	−5.92112	−	10.2557i	−0.194475	−	0.336841i
$928$	4.15533	−	1.11342i	0.136406	−	0.0365498i
$929$	39.3985	−	39.3985i	1.29262	−	1.29262i	0.359466	−	0.933158i	$-0.382959\pi$
$929$	39.3985	−	39.3985i	1.29262	−	1.29262i	0.933158	−	0.359466i	$-0.117041\pi$
$930$	0.343277	−	0.0919808i	0.0112565	−	0.00301617i
$931$	21.7168	−	18.1201i	0.711739	−	0.593862i
$932$	−0.748411	+	1.29629i	−0.0245150	+	0.0424613i
$933$	4.36584	+	2.52062i	0.142931	+	0.0825213i
$934$	−0.458057	−	0.458057i	−0.0149881	−	0.0149881i
$935$	−1.67320	−	0.966021i	−0.0547194	−	0.0315923i
$936$	1.26116	+	3.37779i	0.0412223	+	0.110407i
$937$		−	2.71210i		−	0.0886004i	−0.999018	−	0.0443002i	$-0.985894\pi$
$937$		−	2.71210i		−	0.0886004i	0.999018	−	0.0443002i	$-0.0141058\pi$
$938$	−18.9586	−	12.1150i	−0.619021	−	0.395568i
$939$	8.65025	+	14.9827i	0.282290	+	0.488941i
$940$			1.56675i			0.0511016i
$941$	−5.14266	−	19.1927i	−0.167646	−	0.625663i	−0.997688	−	0.0679619i	$-0.978350\pi$
$941$	−5.14266	−	19.1927i	−0.167646	−	0.625663i	0.830042	−	0.557701i	$-0.188316\pi$
$942$	−1.12153	+	4.18560i	−0.0365413	+	0.136374i
$943$	−11.8376	−	11.8376i	−0.385485	−	0.385485i
$944$	−1.99005	−	1.99005i	−0.0647708	−	0.0647708i
$945$	0.106449	−	0.335986i	0.00346278	−	0.0109296i
$946$	42.4912	−	24.5323i	1.38151	−	0.797614i
$947$	−5.05213	−	18.8548i	−0.164172	−	0.612699i	−0.998144	−	0.0608925i	$-0.980605\pi$
$947$	−5.05213	−	18.8548i	−0.164172	−	0.612699i	0.833972	−	0.551807i	$-0.186061\pi$
$948$	−6.41891	+	11.1179i	−0.208477	+	0.361092i
$949$	4.87166	−	29.0310i	0.158141	−	0.942385i
$950$	−17.4338	+	10.0654i	−0.565627	+	0.326565i
$951$	−6.23606	−	1.67095i	−0.202218	−	0.0541842i
$952$	8.42757	+	2.67006i	0.273139	+	0.0865373i
$953$	−37.8786	−	21.8692i	−1.22701	−	0.708413i	−0.260605	−	0.965445i	$-0.583922\pi$
$953$	−37.8786	−	21.8692i	−1.22701	−	0.708413i	−0.966403	+	0.257032i	$0.917255\pi$
$954$	1.76539	−	6.58853i	0.0571567	−	0.213312i
$955$	−2.39270	−	0.641121i	−0.0774258	−	0.0207462i
$956$	9.17736	+	2.45907i	0.296817	+	0.0795319i
$957$	4.83290	−	18.0366i	0.156225	−	0.583041i
$958$	−21.9110	−	12.6503i	−0.707913	−	0.408714i
$959$	23.4595	+	7.43255i	0.757546	+	0.240009i
$960$	−0.128673	−	0.0344778i	−0.00415290	−	0.00111277i
$961$	20.6830	−	11.9413i	0.667194	−	0.385205i
$962$	25.8512	−	2.47736i	0.833477	−	0.0798732i
$963$	7.04864	−	12.2086i	0.227139	−	0.393416i
$964$	−0.822951	−	3.07130i	−0.0265055	−	0.0989198i
$965$	−0.678982	+	0.392010i	−0.0218572	+	0.0126193i
$966$	−1.16917	+	3.69027i	−0.0376174	+	0.118733i
$967$	16.3348	+	16.3348i	0.525292	+	0.525292i	0.919165	−	0.393873i	$-0.128865\pi$
$967$	16.3348	+	16.3348i	0.525292	+	0.525292i	−0.393873	+	0.919165i	$0.628865\pi$
$968$	−5.54425	−	5.54425i	−0.178199	−	0.178199i
$969$	−3.49426	+	13.0408i	−0.112252	+	0.418930i
$970$	0.193427	+	0.721879i	0.00621057	+	0.0231781i
$971$			14.1362i			0.453653i	0.973935	+	0.226827i	$0.0728351\pi$
$971$			14.1362i			0.453653i	−0.973935	+	0.226827i	$0.927165\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	26.3410	+	16.8325i	0.844454	+	0.539625i
$974$		−	1.54313i		−	0.0494452i
$975$	10.4250	+	14.6293i	0.333867	+	0.468513i
$976$	−5.17990	−	2.99062i	−0.165805	−	0.0957273i
$977$	−7.67867	−	7.67867i	−0.245662	−	0.245662i	0.573525	−	0.819188i	$-0.305575\pi$
$977$	−7.67867	−	7.67867i	−0.245662	−	0.245662i	−0.819188	+	0.573525i	$0.805575\pi$
$978$	−6.01618	−	3.47344i	−0.192376	−	0.111069i
$979$	−23.8804	+	41.3621i	−0.763222	+	1.32194i
$980$	0.918763	−	0.159375i	0.0293488	−	0.00509105i
$981$	−14.7455	+	3.95106i	−0.470789	+	0.126148i
$982$	−9.19312	+	9.19312i	−0.293364	+	0.293364i
$983$	−27.8717	+	7.46820i	−0.888969	+	0.238199i	−0.674273	−	0.738482i	$-0.735543\pi$
$983$	−27.8717	+	7.46820i	−0.888969	+	0.238199i	−0.214696	+	0.976681i	$0.568876\pi$
$984$	5.72095	+	9.90898i	0.182377	+	0.315887i
$985$	0.572160	−	0.991011i	0.0182305	−	0.0315762i
$986$	3.72034	−	13.8845i	0.118480	−	0.442173i
$987$	−29.6642	−	9.39837i	−0.944223	−	0.299153i
$988$	−11.2370	−	9.27163i	−0.357497	−	0.294970i
$989$	8.26932	+	14.3229i	0.262949	+	0.455441i
$990$	−0.408863	+	0.408863i	−0.0129945	+	0.0129945i
$991$	43.9553			1.39629			0.698143	−	0.715958i	$-0.254010\pi$
$991$	43.9553			1.39629			0.698143	+	0.715958i	$0.254010\pi$
$992$	2.66783			0.0847036
$993$	−16.4491	+	16.4491i	−0.521995	+	0.521995i
$994$	−29.4003	+	15.2530i	−0.932521	+	0.483796i
$995$	−0.485490	−	1.81187i	−0.0153911	−	0.0574402i
$996$	−12.2098	−	3.27160i	−0.386881	−	0.103665i
$997$	−12.9411	+	7.47155i	−0.409849	+	0.236626i	−0.690725	−	0.723118i	$-0.742708\pi$
$997$	−12.9411	+	7.47155i	−0.409849	+	0.236626i	0.280876	+	0.959744i	$0.409375\pi$
$998$			2.58005i			0.0816700i
$999$	−6.95726	+	1.86419i	−0.220118	+	0.0589805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.115.6	yes	32
7.5	odd	6		546.2.cg.a.271.2	yes	32
13.6	odd	12		546.2.cg.a.409.2	yes	32
91.19	even	12	inner	546.2.by.a.19.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.6	✓	32	91.19	even	12	inner
546.2.by.a.115.6	yes	32	1.1	even	1	trivial
546.2.cg.a.271.2	yes	32	7.5	odd	6
546.2.cg.a.409.2	yes	32	13.6	odd	12

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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(0.128673 + 0.0344778i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-2.64307 - 0.119073i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(0.128673 + 0.0344778i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-2.64307 - 0.119073i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.133212 q^{10} +(3.06926 - 3.06926i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.49669 - 3.28023i) q^{13} +(-2.58383 + 0.569061i) q^{14} +(0.0344778 - 0.128673i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.67068 - 2.89371i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(2.85706 - 2.85706i) q^{19} +(0.128673 - 0.0344778i) q^{20} +(-0.119073 + 2.64307i) q^{21} +(2.17030 - 3.75906i) q^{22} +(1.26710 + 0.731561i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.31476 - 2.49113i) q^{25} +(0.596701 - 3.55583i) q^{26} +1.00000i q^{27} +(-2.34850 + 1.21841i) q^{28} +(2.15096 + 3.72557i) q^{29} -0.133212i q^{30} +(0.690485 + 2.57692i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-3.06926 - 3.06926i) q^{33} +(-2.36270 - 2.36270i) q^{34} +(-0.335986 - 0.106449i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.86419 + 6.95726i) q^{37} +(2.02025 - 3.49917i) q^{38} +(-3.28023 - 1.49669i) q^{39} +(0.115365 - 0.0666060i) q^{40} +(-11.0520 - 2.96138i) q^{41} +(0.569061 + 2.58383i) q^{42} +(9.78926 + 5.65183i) q^{43} +(1.12343 - 4.19269i) q^{44} +(-0.128673 - 0.0344778i) q^{45} +(1.41327 + 0.378684i) q^{46} +(-3.04405 + 11.3605i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(6.97164 + 0.629439i) q^{49} +(-4.81249 - 1.28950i) q^{50} +(-2.89371 + 1.67068i) q^{51} +(-0.343949 - 3.58911i) q^{52} +(-3.41047 + 5.90712i) q^{53} +(0.258819 + 0.965926i) q^{54} +(0.500752 - 0.289109i) q^{55} +(-1.95313 + 1.78474i) q^{56} +(-2.85706 - 2.85706i) q^{57} +(3.04192 + 3.04192i) q^{58} +(0.728411 - 2.71847i) q^{59} +(-0.0344778 - 0.128673i) q^{60} -5.98123i q^{61} +(1.33391 + 2.31041i) q^{62} +(2.64307 + 0.119073i) q^{63} -1.00000i q^{64} +(0.305678 - 0.370475i) q^{65} +(-3.75906 - 2.17030i) q^{66} +(6.01310 + 6.01310i) q^{67} +(-2.89371 - 1.67068i) q^{68} +(0.731561 - 1.26710i) q^{69} +(-0.352089 - 0.0158620i) q^{70} +(12.0922 - 3.24009i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(7.88613 - 2.11308i) q^{73} +(3.60134 + 6.23771i) q^{74} +(-2.49113 + 4.31476i) q^{75} +(1.04576 - 3.90282i) q^{76} +(-8.47775 + 7.74681i) q^{77} +(-3.55583 - 0.596701i) q^{78} +(-6.41891 - 11.1179i) q^{79} +(0.0941951 - 0.0941951i) q^{80} +1.00000 q^{81} -11.4419 q^{82} +(8.93817 - 8.93817i) q^{83} +(1.21841 + 2.34850i) q^{84} +(-0.115203 - 0.429943i) q^{85} +(10.9185 + 2.92560i) q^{86} +(3.72557 - 2.15096i) q^{87} -4.34059i q^{88} +(-10.6284 + 2.84786i) q^{89} -0.133212 q^{90} +(-4.34643 + 8.49167i) q^{91} +1.46312 q^{92} +(2.57692 - 0.690485i) q^{93} +11.7613i q^{94} +(0.466132 - 0.269121i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.45202 + 5.41903i) q^{97} +(6.89700 - 1.19640i) q^{98} +(-3.06926 + 3.06926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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