LMFDB - Embedded newform 546.2.by.a.19.6

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			19.6
Character	$\chi$	$=$	546.19
Dual form			546.2.by.a.115.6

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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	−0.229932	−	0.973207i	$-0.573850\pi$
$5$	0.128673	−	0.0344778i	0.0575443	−	0.0154189i	0.287476	+	0.957788i	$0.407184\pi$
$6$	−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	0.997406	−	0.0719878i	$-0.0229343\pi$
$11$	3.06926	+	3.06926i	0.925418	+	0.925418i	−0.0719878	+	0.997406i	$0.522934\pi$
$12$	−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	−0.994345	−	0.106200i	$-0.966132\pi$
$17$	−1.67068	+	2.89371i	−0.405200	+	0.701828i	0.589144	+	0.808028i	$0.299465\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	2.85706	+	2.85706i	0.655456	+	0.655456i	0.954301	−	0.298846i	$-0.0966016\pi$
$19$	2.85706	+	2.85706i	0.655456	+	0.655456i	−0.298846	+	0.954301i	$0.596602\pi$
$20$	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	−0.362044	−	0.932161i	$-0.617921\pi$
$23$	1.26710	−	0.731561i	0.264209	−	0.152541i	0.626253	+	0.779620i	$0.284588\pi$
$24$	−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	−0.594232	−	0.804294i	$-0.702544\pi$
$29$	2.15096	−	3.72557i	0.399423	−	0.691821i	0.993655	+	0.112473i	$0.0358771\pi$
$30$			0.133212i			0.0243211i
$31$	0.690485	−	2.57692i	0.124015	−	0.462829i	−0.875788	−	0.482696i	$-0.839658\pi$
$31$	0.690485	−	2.57692i	0.124015	−	0.462829i	0.999803	+	0.0198670i	$0.00632426\pi$
$32$	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	−0.625200	−	0.780465i	$-0.714983\pi$
$37$	1.86419	−	6.95726i	0.306471	−	1.14377i	0.931671	−	0.363302i	$-0.118351\pi$
$38$	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	−0.979264	−	0.202589i	$-0.935064\pi$
$41$	−11.0520	+	2.96138i	−1.72604	+	0.462490i	−0.746773	+	0.665079i	$0.768398\pi$
$42$	0.569061	−	2.58383i	0.0878080	−	0.398693i
$43$	9.78926	−	5.65183i	1.49285	−	0.861896i	0.492882	−	0.870096i	$-0.335943\pi$
$43$	9.78926	−	5.65183i	1.49285	−	0.861896i	0.999966	+	0.00819993i	$0.00261015\pi$
$44$	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	−0.718511	−	0.695515i	$-0.755176\pi$
$47$	−3.04405	−	11.3605i	−0.444020	−	1.65711i	0.274491	−	0.961590i	$-0.411491\pi$
$48$	−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	0.530886	−	0.847443i	$-0.321859\pi$
$53$	−3.41047	−	5.90712i	−0.468465	−	0.811405i	−0.999350	+	0.0360388i	$0.988526\pi$
$54$	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	0.996994	−	0.0774817i	$-0.0246879\pi$
$59$	0.728411	+	2.71847i	0.0948310	+	0.353914i	−0.902163	+	0.431396i	$0.858021\pi$
$60$	−0.0344778	+	0.128673i	−0.00445106	+	0.0166116i
$61$			5.98123i			0.765819i	0.923786	+	0.382909i	$0.125078\pi$
$61$			5.98123i			0.765819i	−0.923786	+	0.382909i	$0.874922\pi$
$62$	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	−0.236914	−	0.971531i	$-0.576136\pi$
$67$	6.01310	−	6.01310i	0.734617	−	0.734617i	0.971531	+	0.236914i	$0.0761360\pi$
$68$	−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	0.890807	−	0.454382i	$-0.150140\pi$
$71$	12.0922	+	3.24009i	1.43508	+	0.384528i	0.544270	+	0.838910i	$0.316807\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	7.88613	+	2.11308i	0.923002	+	0.247318i	0.688868	−	0.724887i	$-0.258108\pi$
$73$	7.88613	+	2.11308i	0.923002	+	0.247318i	0.234134	+	0.972204i	$0.424775\pi$
$74$	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	0.237939	+	0.971280i	$0.423528\pi$
$79$	−6.41891	+	11.1179i	−0.722184	+	1.25086i	−0.960123	+	0.279579i	$0.909805\pi$
$80$	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	0.999825	−	0.0187330i	$-0.00596324\pi$
$83$	8.93817	+	8.93817i	0.981092	+	0.981092i	−0.0187330	+	0.999825i	$0.505963\pi$
$84$	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	−0.353052	−	0.935604i	$-0.614856\pi$
$89$	−10.6284	−	2.84786i	−1.12661	−	0.301873i	−0.773554	+	0.633731i	$0.781523\pi$
$90$	−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	−0.852204	−	0.523209i	$-0.824735\pi$
$97$	1.45202	−	5.41903i	0.147431	−	0.550219i	0.999635	−	0.0270100i	$-0.00859858\pi$
$98$	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	−0.411644	−	0.911345i	$-0.635045\pi$
$103$	5.92112	−	10.2557i	0.583426	−	1.01052i	0.995070	−	0.0991782i	$-0.0316214\pi$
$104$	−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	−0.974548	−	0.224177i	$-0.928031\pi$
$107$	−7.04864	−	12.2086i	−0.681417	−	1.18025i	0.293131	−	0.956072i	$-0.405303\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.7455	+	3.95106i	1.41237	+	0.378443i	0.882769	−	0.469807i	$-0.155676\pi$
$109$	14.7455	+	3.95106i	1.41237	+	0.378443i	0.529597	+	0.848249i	$0.322343\pi$
$110$	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	−0.994041	−	0.109004i	$-0.965234\pi$
$113$	−6.28689	−	10.8892i	−0.591421	−	1.02437i	0.402621	−	0.915367i	$-0.368099\pi$
$114$	−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	0.936485	−	0.350707i	$-0.114059\pi$
$127$	12.4077	+	7.16360i	1.10101	+	0.635666i	0.164521	+	0.986374i	$0.447392\pi$
$128$	−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	−0.102564	−	0.994726i	$-0.532704\pi$
$131$	−11.6207	−	6.70920i	−1.01530	−	0.586186i	−0.912740	+	0.408541i	$0.866038\pi$
$132$	−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	−0.621302	−	0.783571i	$-0.713396\pi$
$137$	−8.98430	+	2.40733i	−0.767580	+	0.205672i	−0.146278	+	0.989244i	$0.546729\pi$
$138$	0.378684	+	1.41327i	0.0322357	+	0.120305i
$139$	−10.2322	+	5.90757i	−0.867885	+	0.501073i	−0.866645	−	0.498926i	$-0.833728\pi$
$139$	−10.2322	+	5.90757i	−0.867885	+	0.501073i	−0.00123995	+	0.999999i	$0.500395\pi$
$140$	−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	−0.581570	−	0.813496i	$-0.697561\pi$
$149$	2.83102	−	2.83102i	0.231927	−	0.231927i	0.813496	+	0.581570i	$0.197561\pi$
$150$	−1.28950	−	4.81249i	−0.105287	−	0.392938i
$151$	5.34068	−	19.9317i	0.434618	−	1.62202i	−0.307359	−	0.951594i	$-0.599445\pi$
$151$	5.34068	−	19.9317i	0.434618	−	1.62202i	0.741978	−	0.670425i	$-0.233888\pi$
$152$			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	−0.642218	−	0.766522i	$-0.721985\pi$
$157$	−3.75270	+	2.16663i	−0.299498	+	0.172916i	0.342719	+	0.939438i	$0.388652\pi$
$158$	−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	0.872811	−	0.488058i	$-0.162295\pi$
$163$	4.91219	+	4.91219i	0.384753	+	0.384753i	−0.488058	+	0.872811i	$0.662295\pi$
$164$	−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	0.997736	+	0.0672465i	$0.0214214\pi$
$167$	2.16192	+	8.06840i	0.167295	+	0.624352i	−0.830442	+	0.557105i	$0.811912\pi$
$168$	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	$0.0590063\pi$
$179$			4.93191i			0.368628i	−0.982867	+	0.184314i	$0.940994\pi$
$180$	−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	0.541279	−	0.840843i	$-0.317940\pi$
$193$	−4.16169	−	4.16169i	−0.299565	−	0.299565i	−0.840843	+	0.541279i	$0.817940\pi$
$194$	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	0.998790	+	0.0491843i	$0.0156622\pi$
$197$	2.22331	+	8.29752i	0.158405	+	0.591174i	−0.840385	+	0.541990i	$0.817671\pi$
$198$	−2.17030	−	3.75906i	−0.154236	−	0.267145i
$199$	−7.04062	+	12.1947i	−0.499096	+	0.864460i	−0.999999	−	0.00104327i	$-0.999668\pi$
$199$	−7.04062	+	12.1947i	−0.499096	+	0.864460i	0.500903	+	0.865503i	$0.333001\pi$
$200$	−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	−0.597511	−	0.801861i	$-0.703844\pi$
$211$	5.74753	−	9.95501i	0.395676	−	0.685331i	0.993187	+	0.116530i	$0.0371770\pi$
$212$		−	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	0.658906	−	0.752225i	$-0.271019\pi$
$223$	23.9774	−	6.42474i	1.60565	−	0.430232i	0.946742	+	0.321993i	$0.104353\pi$
$224$	−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	0.636433	−	0.771332i	$-0.280409\pi$
$227$	23.7036	−	6.35137i	1.57327	−	0.421555i	0.936833	+	0.349777i	$0.113743\pi$
$228$	−3.90282	+	1.04576i	−0.258471	+	0.0692570i
$229$	2.92237	+	10.9064i	0.193116	+	0.720718i	0.992747	+	0.120226i	$0.0383620\pi$
$229$	2.92237	+	10.9064i	0.193116	+	0.720718i	−0.799631	+	0.600492i	$0.794971\pi$
$230$	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	0.456937	−	0.889499i	$-0.348946\pi$
$233$	−1.29629	−	0.748411i	−0.0849225	−	0.0490300i	−0.541860	+	0.840469i	$0.682280\pi$
$234$	−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	−0.455610	−	0.890180i	$-0.650579\pi$
$239$	6.71829	−	6.71829i	0.434570	−	0.434570i	0.890180	+	0.455610i	$0.150579\pi$
$240$	−0.0941951	+	0.0941951i	−0.00608027	+	0.00608027i
$241$	0.822951	+	3.07130i	0.0530109	+	0.197840i	0.987353	−	0.158539i	$-0.0506782\pi$
$241$	0.822951	+	3.07130i	0.0530109	+	0.197840i	−0.934342	+	0.356378i	$0.884012\pi$
$242$	−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	0.995078	−	0.0990910i	$-0.0315935\pi$
$251$	6.52293	+	11.2981i	0.411724	+	0.713127i	−0.583354	+	0.812218i	$0.698260\pi$
$252$	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	0.711327	−	0.702862i	$-0.248095\pi$
$257$	−4.05642	−	7.02593i	−0.253033	−	0.438266i	−0.964359	+	0.264596i	$0.914761\pi$
$258$	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	0.745373	−	0.666647i	$-0.232271\pi$
$269$	8.86858	+	5.12028i	0.540727	+	0.312189i	−0.204647	+	0.978836i	$0.565605\pi$
$270$		−	0.133212i		−	0.00810702i
$271$	−23.6152	−	6.32766i	−1.43452	−	0.384378i	−0.543908	−	0.839145i	$-0.683056\pi$
$271$	−23.6152	−	6.32766i	−1.43452	−	0.384378i	−0.890610	+	0.454767i	$0.849723\pi$
$272$	−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	0.386136	−	0.922442i	$-0.373809\pi$
$277$	−3.65576	−	2.11065i	−0.219653	−	0.126817i	−0.605790	+	0.795625i	$0.707143\pi$
$278$	−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	0.663810	−	0.747901i	$-0.268938\pi$
$281$	−1.40963	−	1.40963i	−0.0840912	−	0.0840912i	−0.747901	+	0.663810i	$0.768938\pi$
$282$	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	0.393623	−	0.919272i	$-0.371222\pi$
$293$	4.70508	+	1.26072i	0.274874	+	0.0736522i	−0.118749	+	0.992924i	$0.537888\pi$
$294$	−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	−0.396911	−	0.917857i	$-0.629918\pi$
$307$	9.12772	−	9.12772i	0.520947	−	0.520947i	0.917857	+	0.396911i	$0.129918\pi$
$308$	−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	0.785668	−	0.618648i	$-0.212319\pi$
$311$	−2.52062	−	4.36584i	−0.142931	−	0.247564i	−0.928599	+	0.371084i	$0.878986\pi$
$312$	−3.37779	−	1.26116i	−0.191230	−	0.0713991i
$313$	−14.9827	−	8.65025i	−0.846871	−	0.488941i	0.0127230	−	0.999919i	$-0.495950\pi$
$313$	−14.9827	−	8.65025i	−0.846871	−	0.488941i	−0.859594	+	0.510978i	$0.829283\pi$
$314$	−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	0.996843	−	0.0794037i	$-0.0253016\pi$
$317$	1.67095	+	6.23606i	0.0938497	+	0.350252i	−0.902993	+	0.429656i	$0.858635\pi$
$318$	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	−0.995790	−	0.0916672i	$-0.970780\pi$
$331$	−16.4491	+	16.4491i	−0.904123	+	0.904123i	0.0916672	+	0.995790i	$0.470780\pi$
$332$	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	$0.149718\pi$
$337$			16.6393i			0.906401i	−0.891409	+	0.453200i	$0.850282\pi$
$338$	−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	0.229427	+	0.973326i	$0.426315\pi$
$347$	−13.5651	+	23.4954i	−0.728212	+	1.26130i	−0.957638	+	0.287974i	$0.907018\pi$
$348$	2.15096	+	3.72557i	0.115304	+	0.199712i
$349$	0.102175	+	0.381321i	0.00546929	+	0.0204117i	0.968607	−	0.248599i	$-0.0799701\pi$
$349$	0.102175	+	0.381321i	0.00546929	+	0.0204117i	−0.963137	+	0.269010i	$0.913303\pi$
$350$	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	0.633596	−	0.773664i	$-0.281578\pi$
$353$	−2.63165	−	2.63165i	−0.140069	−	0.140069i	−0.773664	+	0.633596i	$0.781578\pi$
$354$	−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	0.868908	−	0.494974i	$-0.164822\pi$
$359$	35.4104	−	9.48820i	1.86889	−	0.500768i	0.999983	−	0.00579429i	$-0.00184439\pi$
$360$	−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	$-0.701886\pi$
$367$		−	30.8631i		−	1.61104i	0.592567	−	0.805521i	$-0.298114\pi$
$368$	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	0.994860	−	0.101262i	$-0.0322881\pi$
$379$	1.60912	+	6.00531i	0.0826548	+	0.308472i	−0.912205	+	0.409734i	$0.865621\pi$
$380$	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	0.863079	−	0.505069i	$-0.168533\pi$
$383$	7.00640	+	7.00640i	0.358010	+	0.358010i	−0.505069	+	0.863079i	$0.668533\pi$
$384$	−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	−0.928695	−	0.370845i	$-0.879068\pi$
$389$	−21.1408	+	12.2056i	−1.07188	+	0.618851i	−0.143186	+	0.989696i	$0.545735\pi$
$390$	−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	−0.867479	−	0.497474i	$-0.834261\pi$
$397$	−7.37229	+	7.37229i	−0.370005	+	0.370005i	0.497474	+	0.867479i	$0.334261\pi$
$398$	−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	−0.971590	−	0.236668i	$-0.923944\pi$
$401$	−0.236980	+	0.884423i	−0.0118342	+	0.0441660i	0.959756	+	0.280834i	$0.0906112\pi$
$402$	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	−0.338376	−	0.941011i	$-0.609878\pi$
$409$	−3.25426	+	0.871977i	−0.160913	+	0.0431165i	0.177463	+	0.984127i	$0.443211\pi$
$410$	−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	0.149548	−	0.988755i	$-0.452218\pi$
$419$	−12.9360	−	7.46860i	−0.631965	−	0.364865i	−0.781513	+	0.623889i	$0.785552\pi$
$420$	0.0758057	−	0.344197i	0.00369894	−	0.0167951i
$421$	−19.8845	+	19.8845i	−0.969109	+	0.969109i	−0.999537	−	0.0304275i	$-0.990313\pi$
$421$	−19.8845	+	19.8845i	−0.969109	+	0.969109i	0.0304275	+	0.999537i	$0.490313\pi$
$422$	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	0.0767484	−	0.997050i	$-0.475546\pi$
$431$	22.2926	−	22.2926i	1.07380	−	1.07380i	0.997050	−	0.0767484i	$-0.0244538\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	12.7366	+	22.0605i	0.612083	+	1.06016i	0.990889	+	0.134682i	$0.0430014\pi$
$433$	12.7366	+	22.0605i	0.612083	+	1.06016i	−0.378806	+	0.925476i	$0.623665\pi$
$434$	−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	−0.985319	−	0.170722i	$-0.945390\pi$
$439$	−13.4202	−	23.2444i	−0.640509	−	1.10939i	0.344810	−	0.938673i	$-0.387943\pi$
$440$	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	−0.652011	−	0.758209i	$-0.726074\pi$
$443$	6.95881	−	12.0530i	0.330623	−	0.572656i	0.982634	+	0.185553i	$0.0594078\pi$
$444$	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	0.822666	+	0.568526i	$0.192486\pi$
$449$	−3.68798	+	13.7637i	−0.174047	+	0.649550i	−0.996712	+	0.0810249i	$0.974181\pi$
$450$	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	0.264802	−	0.964303i	$-0.414693\pi$
$457$	0.256034	+	0.0686042i	0.0119768	+	0.00320917i	−0.252826	+	0.967512i	$0.581360\pi$
$458$			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	−0.224369	−	0.974504i	$-0.572032\pi$
$461$	9.81634	−	36.6351i	0.457192	−	1.70626i	0.681562	−	0.731761i	$-0.261301\pi$
$462$	9.67705	−	6.18385i	0.450217	−	0.287699i
$463$	5.29794	+	5.29794i	0.246216	+	0.246216i	0.819416	−	0.573200i	$-0.194298\pi$
$463$	5.29794	+	5.29794i	0.246216	+	0.246216i	−0.573200	+	0.819416i	$0.694298\pi$
$464$	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	−0.873422	−	0.486964i	$-0.838104\pi$
$467$	−0.323895	+	0.561003i	−0.0149881	+	0.0259601i	0.858434	+	0.512924i	$0.171438\pi$
$468$	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	−0.985735	−	0.168307i	$-0.946170\pi$
$479$	−17.8903	+	17.8903i	−0.817428	+	0.817428i	0.168307	+	0.985735i	$0.446170\pi$
$480$	−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	0.974384	−	0.224889i	$-0.0722020\pi$
$487$	0.399393	+	1.49055i	0.0180982	+	0.0675434i	−0.956286	+	0.292433i	$0.905535\pi$
$488$	−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	0.223939	−	0.974603i	$-0.428108\pi$
$491$	−11.2592	−	6.50052i	−0.508122	−	0.293364i	−0.732061	+	0.681239i	$0.761442\pi$
$492$	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	0.949367	−	0.314169i	$-0.101726\pi$
$499$	−0.667766	−	2.49214i	−0.0298933	−	0.111563i	−0.979260	+	0.202605i	$0.935059\pi$
$500$	−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	−0.426440	−	0.904516i	$-0.640232\pi$
$503$	3.22228	−	1.86038i	0.143674	−	0.0829504i	0.570114	+	0.821566i	$0.306899\pi$
$504$	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	−0.310284	−	0.950644i	$-0.600424\pi$
$509$	9.78589	−	36.5214i	0.433752	−	1.61878i	0.744036	−	0.668140i	$-0.232909\pi$
$510$	−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	0.359333	−	0.933209i	$-0.383004\pi$
$521$	30.7500	−	17.7535i	1.34718	−	0.777796i	0.987850	+	0.155413i	$0.0496709\pi$
$522$	−3.04192	+	3.04192i	−0.133141	+	0.133141i
$523$	20.6888	−	11.9447i	0.904660	−	0.522305i	0.0259506	−	0.999663i	$-0.491739\pi$
$523$	20.6888	−	11.9447i	0.904660	−	0.522305i	0.878709	+	0.477358i	$0.158405\pi$
$524$	−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	0.687378	−	0.726300i	$-0.258761\pi$
$541$	38.2807	−	10.2573i	1.64582	−	0.440995i	0.958437	+	0.285305i	$0.0920948\pi$
$542$	−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	0.334152	−	0.942519i	$-0.391550\pi$
$557$	−14.3580	−	14.3580i	−0.608368	−	0.608368i	−0.942519	+	0.334152i	$0.891550\pi$
$558$	−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	−0.963247	−	0.268617i	$-0.913434\pi$
$563$	−5.90805	+	10.2330i	−0.248995	+	0.431271i	0.714252	+	0.699888i	$0.246767\pi$
$564$	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	−0.902890	−	0.429872i	$-0.858559\pi$
$569$	−23.4257	+	13.5248i	−0.982055	+	0.566990i	−0.0791651	+	0.996862i	$0.525225\pi$
$570$	−0.380595	+	0.380595i	−0.0159414	+	0.0159414i
$571$	0.632370	−	0.365099i	0.0264639	−	0.0152789i	−0.486710	−	0.873564i	$-0.661803\pi$
$571$	0.632370	−	0.365099i	0.0264639	−	0.0152789i	0.513174	+	0.858285i	$0.328470\pi$
$572$	−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	0.0303997	−	0.999538i	$-0.490322\pi$
$577$	12.1027	−	45.1679i	0.503842	−	1.88036i	0.473442	−	0.880825i	$-0.343011\pi$
$578$	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	−0.725700	−	0.688012i	$-0.758484\pi$
$587$	−24.4744	+	6.55790i	−1.01017	+	0.270674i	−0.284468	+	0.958685i	$0.591817\pi$
$588$	−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	0.999999	−	0.00144199i	$-0.000459000\pi$
$593$	3.24493	+	12.1103i	0.133253	+	0.497309i	−0.866745	+	0.498751i	$0.833792\pi$
$594$	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	0.606404	−	0.795157i	$-0.292612\pi$
$599$	−9.43306	−	16.3385i	−0.385424	−	0.667574i	−0.991828	+	0.127582i	$0.959278\pi$
$600$	1.28950	−	4.81249i	0.0526437	−	0.196469i
$601$	−37.2197	−	21.4888i	−1.51822	−	0.876546i	−0.999770	−	0.0214384i	$-0.993175\pi$
$601$	−37.2197	−	21.4888i	−1.51822	−	0.876546i	−0.518451	−	0.855107i	$-0.673491\pi$
$602$	−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	$-0.978674\pi$
$607$		−	3.29877i		−	0.133893i	0.997757	−	0.0669466i	$-0.0213257\pi$
$608$	−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	−0.243508	−	0.969899i	$-0.578298\pi$
$613$	17.9846	−	17.9846i	0.726391	−	0.726391i	0.969899	+	0.243508i	$0.0782982\pi$
$614$	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	−0.367485	−	0.930030i	$-0.619781\pi$
$617$	−28.5840	−	7.65907i	−1.15075	−	0.308343i	−0.783266	+	0.621687i	$0.786448\pi$
$618$	8.37373	+	8.37373i	0.336841	+	0.336841i
$619$	−22.0606	−	5.91111i	−0.886689	−	0.237588i	−0.213398	−	0.976965i	$-0.568453\pi$
$619$	−22.0606	−	5.91111i	−0.886689	−	0.237588i	−0.673291	+	0.739378i	$0.735120\pi$
$620$	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	0.551802	+	0.833975i	$0.313940\pi$
$631$	−8.61757	+	32.1612i	−0.343060	+	1.28032i	−0.894862	+	0.446342i	$0.852726\pi$
$632$	−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	0.578737	−	0.815514i	$-0.303546\pi$
$641$	4.09770	+	2.36581i	0.161849	+	0.0934437i	−0.416888	+	0.908958i	$0.636879\pi$
$642$	13.6169	−	3.64864i	0.537417	−	0.144000i
$643$	−7.51513	+	28.0468i	−0.296368	+	1.10606i	0.643757	+	0.765230i	$0.277375\pi$
$643$	−7.51513	+	28.0468i	−0.296368	+	1.10606i	−0.940125	+	0.340830i	$0.889292\pi$
$644$	−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	0.849389	−	0.527767i	$-0.176971\pi$
$653$	−0.827054	−	1.43250i	−0.0323651	−	0.0560580i	−0.881754	+	0.471709i	$0.843637\pi$
$654$	−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	0.999773	+	0.0213095i	$0.00678353\pi$
$659$	13.3063	+	23.0472i	0.518341	+	0.897793i	−0.481432	+	0.876483i	$0.659883\pi$
$660$	−0.500752	+	0.289109i	−0.0194918	+	0.0112536i
$661$	27.9019	−	27.9019i	1.08526	−	1.08526i	0.0892491	−	0.996009i	$-0.471553\pi$
$661$	27.9019	−	27.9019i	1.08526	−	1.08526i	0.996009	−	0.0892491i	$-0.0284467\pi$
$662$	−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	0.460609	−	0.887603i	$-0.347631\pi$
$673$	−2.01759	−	1.16486i	−0.0777725	−	0.0449020i	−0.538382	+	0.842701i	$0.680964\pi$
$674$	−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	−0.00503283	−	0.999987i	$-0.501602\pi$
$677$	−22.7294	−	13.1229i	−0.873564	−	0.504352i	−0.868531	+	0.495635i	$0.834935\pi$
$678$	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	−0.675200	−	0.737635i	$-0.735943\pi$
$683$	−23.2888	+	6.24023i	−0.891123	+	0.238776i	−0.215923	+	0.976410i	$0.569276\pi$
$684$	−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	0.773630	+	0.633638i	$0.218439\pi$
$691$	−5.60363	+	20.9130i	−0.213172	+	0.795570i	−0.986802	+	0.161932i	$0.948228\pi$
$692$	−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	$-0.959227\pi$
$701$		−	6.76434i		−	0.255486i	0.991807	−	0.127743i	$-0.0407732\pi$
$702$	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	0.780550	−	0.625093i	$-0.214939\pi$
$709$	4.13938	+	4.13938i	0.155457	+	0.155457i	−0.625093	+	0.780550i	$0.714939\pi$
$710$	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	−0.165520	−	0.986206i	$-0.552930\pi$
$733$	4.98805	−	1.33654i	0.184238	−	0.0493664i	0.349758	+	0.936840i	$0.386264\pi$
$734$	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	0.862064	+	0.506799i	$0.169171\pi$
$739$	37.2119	+	37.2119i	1.36886	+	1.36886i	0.506799	+	0.862064i	$0.330829\pi$
$740$	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	0.870521	+	0.492131i	$0.163782\pi$
$743$	9.88631	+	36.8962i	0.362693	+	1.35359i	−0.507828	+	0.861459i	$0.669551\pi$
$744$	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	−0.998916	−	0.0465436i	$-0.985179\pi$
$751$	−39.9574	+	23.0694i	−1.45807	+	0.841815i	−0.459150	+	0.888359i	$0.651846\pi$
$752$	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	−0.901751	−	0.432255i	$-0.857718\pi$
$757$	−2.10566	+	3.64711i	−0.0765316	+	0.132557i	0.825220	+	0.564812i	$0.191051\pi$
$758$			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	−0.734993	−	0.678074i	$-0.762815\pi$
$761$	−1.57017	+	1.57017i	−0.0569187	+	0.0569187i	0.678074	+	0.734993i	$0.262815\pi$
$762$	−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	0.411332	−	0.911486i	$-0.365064\pi$
$769$	33.9231	−	9.08967i	1.22330	−	0.327782i	0.811967	+	0.583704i	$0.198397\pi$
$770$	−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	−0.621187	−	0.783662i	$-0.713349\pi$
$773$	−21.3337	+	5.71635i	−0.767320	+	0.205603i	−0.146133	+	0.989265i	$0.546683\pi$
$774$	−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	0.932480	−	0.361223i	$-0.117641\pi$
$787$	−1.56210	−	5.82982i	−0.0556827	−	0.207811i	−0.988162	+	0.153412i	$0.950974\pi$
$788$	−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	−0.894604	−	0.446861i	$-0.852542\pi$
$797$	−23.5531	−	40.7952i	−0.834295	−	1.44504i	0.0603090	−	0.998180i	$-0.480791\pi$
$798$	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	−0.995960	−	0.0897926i	$-0.971380\pi$
$811$	−30.9201	−	30.9201i	−1.08575	−	1.08575i	−0.0897926	−	0.995960i	$-0.528620\pi$
$812$	−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	−0.0657544	−	0.997836i	$-0.520945\pi$
$821$	−17.8113	−	4.77251i	−0.621617	−	0.166562i	−0.555863	+	0.831274i	$0.687612\pi$
$822$		−	9.30123i		−	0.324418i
$823$	9.17724	+	5.29848i	0.319898	+	0.184693i	0.651347	−	0.758780i	$-0.274204\pi$
$823$	9.17724	+	5.29848i	0.319898	+	0.184693i	−0.331449	+	0.943473i	$0.607537\pi$
$824$	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	0.626810	−	0.779172i	$-0.284360\pi$
$827$	−4.38155	−	4.38155i	−0.152361	−	0.152361i	−0.779172	+	0.626810i	$0.784360\pi$
$828$	−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	0.187180	−	0.982326i	$-0.440065\pi$
$839$	−4.10963	−	1.10117i	−0.141880	−	0.0380167i	−0.329060	+	0.944309i	$0.606732\pi$
$840$	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	−0.482191	−	0.876066i	$-0.660159\pi$
$853$	11.5036	−	11.5036i	0.393875	−	0.393875i	0.876066	+	0.482191i	$0.160159\pi$
$854$	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	0.918660	−	0.395049i	$-0.129272\pi$
$857$	3.43120	+	5.94301i	0.117207	+	0.203009i	−0.801453	+	0.598058i	$0.795939\pi$
$858$	−12.7452	−	9.08236i	−0.435115	−	0.310067i
$859$	28.2527	+	16.3117i	0.963971	+	0.556549i	0.897393	−	0.441232i	$-0.145459\pi$
$859$	28.2527	+	16.3117i	0.963971	+	0.556549i	0.0665781	+	0.997781i	$0.478792\pi$
$860$	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	0.980778	+	0.195129i	$0.0625126\pi$
$863$	6.72624	+	25.1027i	0.228964	+	0.854505i	−0.751814	+	0.659376i	$0.770821\pi$
$864$	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	−0.999404	−	0.0345085i	$-0.989013\pi$
$877$	−28.5746	+	28.5746i	−0.964896	+	0.964896i	0.0345085	+	0.999404i	$0.489013\pi$
$878$	−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	−0.791924	−	0.610620i	$-0.790920\pi$
$881$	3.94323	−	6.82987i	0.132851	−	0.230104i	0.924774	+	0.380516i	$0.124254\pi$
$882$	−6.89700	−	1.19640i	−0.232234	−	0.0402850i
$883$			17.8741i			0.601513i	0.953701	+	0.300756i	$0.0972391\pi$
$883$			17.8741i			0.601513i	−0.953701	+	0.300756i	$0.902761\pi$
$884$	−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	−0.997419	−	0.0718063i	$-0.977124\pi$
$887$	−42.7064	+	24.6566i	−1.43394	+	0.827887i	−0.436523	+	0.899693i	$0.643790\pi$
$888$	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	$-0.723077\pi$
$907$		−	46.0369i		−	1.52863i	0.644843	−	0.764315i	$-0.276923\pi$
$908$	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	0.933158	+	0.359466i	$0.117041\pi$
$929$	39.3985	+	39.3985i	1.29262	+	1.29262i	0.359466	+	0.933158i	$0.382959\pi$
$930$	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	$0.0141058\pi$
$937$			2.71210i			0.0886004i	−0.999018	+	0.0443002i	$0.985894\pi$
$938$	−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	0.830042	+	0.557701i	$0.188316\pi$
$941$	−5.14266	+	19.1927i	−0.167646	+	0.625663i	−0.997688	+	0.0679619i	$0.978350\pi$
$942$	−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	0.833972	+	0.551807i	$0.186061\pi$
$947$	−5.05213	+	18.8548i	−0.164172	+	0.612699i	−0.998144	+	0.0608925i	$0.980605\pi$
$948$	−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	−0.966403	−	0.257032i	$-0.917255\pi$
$953$	−37.8786	+	21.8692i	−1.22701	+	0.708413i	−0.260605	+	0.965445i	$0.583922\pi$
$954$	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	−0.393873	−	0.919165i	$-0.628865\pi$
$967$	16.3348	−	16.3348i	0.525292	−	0.525292i	0.919165	+	0.393873i	$0.128865\pi$
$968$	−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	$-0.927165\pi$
$971$		−	14.1362i		−	0.453653i	0.973935	−	0.226827i	$-0.0728351\pi$
$972$	−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	−0.819188	−	0.573525i	$-0.805575\pi$
$977$	−7.67867	+	7.67867i	−0.245662	+	0.245662i	0.573525	+	0.819188i	$0.305575\pi$
$978$	−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	−0.214696	−	0.976681i	$-0.568876\pi$
$983$	−27.8717	−	7.46820i	−0.888969	−	0.238199i	−0.674273	+	0.738482i	$0.735543\pi$
$984$	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	0.280876	−	0.959744i	$-0.409375\pi$
$997$	−12.9411	−	7.47155i	−0.409849	−	0.236626i	−0.690725	+	0.723118i	$0.742708\pi$
$998$		−	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.19.6	✓	32
7.3	odd	6		546.2.cg.a.409.2	yes	32
13.11	odd	12		546.2.cg.a.271.2	yes	32
91.24	even	12	inner	546.2.by.a.115.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.6	✓	32	1.1	even	1	trivial
546.2.by.a.115.6	yes	32	91.24	even	12	inner
546.2.cg.a.271.2	yes	32	13.11	odd	12
546.2.cg.a.409.2	yes	32	7.3	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.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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