LMFDB - Embedded newform 546.2.by.b.397.9

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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.9
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.157898 + 0.589284i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-0.740861 - 2.53991i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.157898 + 0.589284i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-0.740861 - 2.53991i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +0.610072 q^{10} +(2.49118 - 2.49118i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.11704 - 3.42815i) q^{13} +(-2.64511 + 0.0582404i) q^{14} +(-0.589284 + 0.157898i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.330893 + 0.573124i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-1.30246 + 1.30246i) q^{19} +(0.157898 - 0.589284i) q^{20} +(2.53991 - 0.740861i) q^{21} +(-1.76153 - 3.05106i) q^{22} +(5.75342 - 3.32174i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.00780 - 2.31391i) q^{25} +(-3.02223 - 1.96625i) q^{26} -1.00000i q^{27} +(-0.628349 + 2.57005i) q^{28} +(2.81107 - 4.86891i) q^{29} +0.610072i q^{30} +(-2.17918 - 0.583910i) q^{31} +(0.965926 - 0.258819i) q^{32} +(2.49118 + 2.49118i) q^{33} +(0.467954 + 0.467954i) q^{34} +(1.37975 - 0.837624i) q^{35} +(0.866025 + 0.500000i) q^{36} +(2.18111 + 0.584428i) q^{37} +(0.920982 + 1.59519i) q^{38} +(3.42815 + 1.11704i) q^{39} +(-0.528338 - 0.305036i) q^{40} +(-1.83508 - 6.84860i) q^{41} +(-0.0582404 - 2.64511i) q^{42} +(-6.91494 + 3.99234i) q^{43} +(-3.40302 + 0.911835i) q^{44} +(-0.157898 - 0.589284i) q^{45} +(-1.71946 - 6.41710i) q^{46} +(-4.42021 + 1.18439i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.90225 + 3.76343i) q^{49} +(-1.19777 - 4.47012i) q^{50} +(-0.573124 - 0.330893i) q^{51} +(-2.68146 + 2.41034i) q^{52} +(5.24890 + 9.09137i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(1.86137 + 1.07466i) q^{55} +(2.31985 + 1.27212i) q^{56} +(-1.30246 - 1.30246i) q^{57} +(-3.97545 - 3.97545i) q^{58} +(9.32547 - 2.49875i) q^{59} +(0.589284 + 0.157898i) q^{60} +13.1445i q^{61} +(-1.12803 + 1.95380i) q^{62} +(0.740861 + 2.53991i) q^{63} -1.00000i q^{64} +(2.19653 + 0.116958i) q^{65} +(3.05106 - 1.76153i) q^{66} +(-10.1212 - 10.1212i) q^{67} +(0.573124 - 0.330893i) q^{68} +(3.32174 + 5.75342i) q^{69} +(-0.451978 - 1.54953i) q^{70} +(3.44163 - 12.8443i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-1.08908 + 4.06451i) q^{73} +(1.12903 - 1.95553i) q^{74} +(2.31391 + 4.00780i) q^{75} +(1.77920 - 0.476735i) q^{76} +(-8.17298 - 4.48175i) q^{77} +(1.96625 - 3.02223i) q^{78} +(-3.20797 + 5.55637i) q^{79} +(-0.431386 + 0.431386i) q^{80} +1.00000 q^{81} -7.09019 q^{82} +(-5.17053 + 5.17053i) q^{83} +(-2.57005 - 0.628349i) q^{84} +(-0.389981 - 0.104495i) q^{85} +(2.06659 + 7.71261i) q^{86} +(4.86891 + 2.81107i) q^{87} +3.52306i q^{88} +(-3.90841 + 14.5864i) q^{89} -0.610072 q^{90} +(-9.53475 - 0.297406i) q^{91} -6.64347 q^{92} +(0.583910 - 2.17918i) q^{93} +4.57613i q^{94} +(-0.973179 - 0.561865i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-3.44843 - 0.924004i) q^{97} +(2.10758 + 6.67518i) q^{98} +(-2.49118 + 2.49118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.157898	+	0.589284i	0.0706142	+	0.263536i	0.992203	−	0.124632i	$-0.0397749\pi$
$5$	0.157898	+	0.589284i	0.0706142	+	0.263536i	−0.921589	+	0.388167i	$0.873108\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−0.740861	−	2.53991i	−0.280019	−	0.959994i
$7$	−0.740861	−	2.53991i	−0.280019	−	0.959994i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	0.610072			0.192922
$11$	2.49118	−	2.49118i	0.751119	−	0.751119i	−0.223569	−	0.974688i	$-0.571771\pi$
$11$	2.49118	−	2.49118i	0.751119	−	0.751119i	0.974688	+	0.223569i	$0.0717708\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.11704	−	3.42815i	0.309812	−	0.950798i
$13$	1.11704	−	3.42815i	0.309812	−	0.950798i
$14$	−2.64511	+	0.0582404i	−0.706935	+	0.0155654i
$15$	−0.589284	+	0.157898i	−0.152153	+	0.0407691i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.330893	+	0.573124i	−0.0802535	+	0.139003i	−0.903359	−	0.428886i	$-0.858906\pi$
$17$	−0.330893	+	0.573124i	−0.0802535	+	0.139003i	0.823105	+	0.567889i	$0.192240\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	−1.30246	+	1.30246i	−0.298806	+	0.298806i	−0.840546	−	0.541740i	$-0.817766\pi$
$19$	−1.30246	+	1.30246i	−0.298806	+	0.298806i	0.541740	+	0.840546i	$0.317766\pi$
$20$	0.157898	−	0.589284i	0.0353071	−	0.131768i
$21$	2.53991	−	0.740861i	0.554253	−	0.161669i
$22$	−1.76153	−	3.05106i	−0.375560	−	0.650488i
$23$	5.75342	−	3.32174i	1.19967	−	0.692630i	0.239189	−	0.970973i	$-0.423119\pi$
$23$	5.75342	−	3.32174i	1.19967	−	0.692630i	0.960482	+	0.278343i	$0.0897853\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	4.00780	−	2.31391i	0.801561	−	0.462781i
$26$	−3.02223	−	1.96625i	−0.592707	−	0.385614i
$27$		−	1.00000i		−	0.192450i
$28$	−0.628349	+	2.57005i	−0.118747	+	0.485695i
$29$	2.81107	−	4.86891i	0.522002	−	0.904134i	−0.477671	−	0.878539i	$-0.658519\pi$
$29$	2.81107	−	4.86891i	0.522002	−	0.904134i	0.999672	−	0.0255946i	$-0.00814789\pi$
$30$			0.610072i			0.111383i
$31$	−2.17918	−	0.583910i	−0.391393	−	0.104873i	0.0577552	−	0.998331i	$-0.481606\pi$
$31$	−2.17918	−	0.583910i	−0.391393	−	0.104873i	−0.449148	+	0.893457i	$0.648272\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	2.49118	+	2.49118i	0.433659	+	0.433659i
$34$	0.467954	+	0.467954i	0.0802535	+	0.0802535i
$35$	1.37975	−	0.837624i	0.233220	−	0.141584i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	2.18111	+	0.584428i	0.358573	+	0.0960793i	0.433608	−	0.901102i	$-0.357240\pi$
$37$	2.18111	+	0.584428i	0.358573	+	0.0960793i	−0.0750352	+	0.997181i	$0.523907\pi$
$38$	0.920982	+	1.59519i	0.149403	+	0.258774i
$39$	3.42815	+	1.11704i	0.548943	+	0.178870i
$40$	−0.528338	−	0.305036i	−0.0835375	−	0.0482304i
$41$	−1.83508	−	6.84860i	−0.286591	−	1.06957i	−0.947669	−	0.319254i	$-0.896568\pi$
$41$	−1.83508	−	6.84860i	−0.286591	−	1.06957i	0.661078	−	0.750317i	$-0.270099\pi$
$42$	−0.0582404	−	2.64511i	−0.00898669	−	0.408149i
$43$	−6.91494	+	3.99234i	−1.05452	+	0.608826i	−0.923911	−	0.382608i	$-0.875026\pi$
$43$	−6.91494	+	3.99234i	−1.05452	+	0.608826i	−0.130607	+	0.991434i	$0.541693\pi$
$44$	−3.40302	+	0.911835i	−0.513024	+	0.137464i
$45$	−0.157898	−	0.589284i	−0.0235381	−	0.0878453i
$46$	−1.71946	−	6.41710i	−0.253520	−	0.946150i
$47$	−4.42021	+	1.18439i	−0.644753	+	0.172761i	−0.566356	−	0.824161i	$-0.691647\pi$
$47$	−4.42021	+	1.18439i	−0.644753	+	0.172761i	−0.0783978	+	0.996922i	$0.524980\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−5.90225	+	3.76343i	−0.843179	+	0.537634i
$50$	−1.19777	−	4.47012i	−0.169390	−	0.632171i
$51$	−0.573124	−	0.330893i	−0.0802535	−	0.0463344i
$52$	−2.68146	+	2.41034i	−0.371852	+	0.334254i
$53$	5.24890	+	9.09137i	0.720992	+	1.24880i	0.960602	+	0.277926i	$0.0896471\pi$
$53$	5.24890	+	9.09137i	0.720992	+	1.24880i	−0.239610	+	0.970869i	$0.577020\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	1.86137	+	1.07466i	0.250987	+	0.144907i
$56$	2.31985	+	1.27212i	0.310003	+	0.169994i
$57$	−1.30246	−	1.30246i	−0.172516	−	0.172516i
$58$	−3.97545	−	3.97545i	−0.522002	−	0.522002i
$59$	9.32547	−	2.49875i	1.21407	−	0.325310i	0.405714	−	0.914000i	$-0.367023\pi$
$59$	9.32547	−	2.49875i	1.21407	−	0.325310i	0.808358	+	0.588691i	$0.200356\pi$
$60$	0.589284	+	0.157898i	0.0760763	+	0.0203846i
$61$			13.1445i			1.68298i	0.540274	+	0.841489i	$0.318321\pi$
$61$			13.1445i			1.68298i	−0.540274	+	0.841489i	$0.681679\pi$
$62$	−1.12803	+	1.95380i	−0.143260	+	0.248133i
$63$	0.740861	+	2.53991i	0.0933397	+	0.319998i
$64$		−	1.00000i		−	0.125000i
$65$	2.19653	+	0.116958i	0.272446	+	0.0145068i
$66$	3.05106	−	1.76153i	0.375560	−	0.216829i
$67$	−10.1212	−	10.1212i	−1.23650	−	1.23650i	−0.961421	−	0.275082i	$-0.911295\pi$
$67$	−10.1212	−	10.1212i	−1.23650	−	1.23650i	−0.275082	−	0.961421i	$-0.588705\pi$
$68$	0.573124	−	0.330893i	0.0695015	−	0.0401267i
$69$	3.32174	+	5.75342i	0.399890	+	0.692630i
$70$	−0.451978	−	1.54953i	−0.0540217	−	0.185204i
$71$	3.44163	−	12.8443i	0.408446	−	1.52434i	−0.389164	−	0.921168i	$-0.627236\pi$
$71$	3.44163	−	12.8443i	0.408446	−	1.52434i	0.797610	−	0.603173i	$-0.206097\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−1.08908	+	4.06451i	−0.127467	+	0.475715i	−0.999916	−	0.0129916i	$-0.995865\pi$
$73$	−1.08908	+	4.06451i	−0.127467	+	0.475715i	0.872448	+	0.488707i	$0.162531\pi$
$74$	1.12903	−	1.95553i	0.131247	−	0.227326i
$75$	2.31391	+	4.00780i	0.267187	+	0.462781i
$76$	1.77920	−	0.476735i	0.204088	−	0.0546853i
$77$	−8.17298	−	4.48175i	−0.931398	−	0.510742i
$78$	1.96625	−	3.02223i	0.222634	−	0.342200i
$79$	−3.20797	+	5.55637i	−0.360925	+	0.625141i	−0.988113	−	0.153727i	$-0.950872\pi$
$79$	−3.20797	+	5.55637i	−0.360925	+	0.625141i	0.627188	+	0.778868i	$0.284206\pi$
$80$	−0.431386	+	0.431386i	−0.0482304	+	0.0482304i
$81$	1.00000			0.111111
$82$	−7.09019			−0.782980
$83$	−5.17053	+	5.17053i	−0.567540	+	0.567540i	−0.931438	−	0.363899i	$-0.881445\pi$
$83$	−5.17053	+	5.17053i	−0.567540	+	0.567540i	0.363899	+	0.931438i	$0.381445\pi$
$84$	−2.57005	−	0.628349i	−0.280416	−	0.0685585i
$85$	−0.389981	−	0.104495i	−0.0422993	−	0.0113341i
$86$	2.06659	+	7.71261i	0.222846	+	0.831672i
$87$	4.86891	+	2.81107i	0.522002	+	0.301378i
$88$			3.52306i			0.375560i
$89$	−3.90841	+	14.5864i	−0.414290	+	1.54615i	0.371963	+	0.928247i	$0.378685\pi$
$89$	−3.90841	+	14.5864i	−0.414290	+	1.54615i	−0.786253	+	0.617904i	$0.787982\pi$
$90$	−0.610072			−0.0643072
$91$	−9.53475	−	0.297406i	−0.999514	−	0.0311767i
$92$	−6.64347			−0.692630
$93$	0.583910	−	2.17918i	0.0605487	−	0.225971i
$94$			4.57613i			0.471992i
$95$	−0.973179	−	0.561865i	−0.0998460	−	0.0576461i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	−3.44843	−	0.924004i	−0.350135	−	0.0938184i	0.0794650	−	0.996838i	$-0.474679\pi$
$97$	−3.44843	−	0.924004i	−0.350135	−	0.0938184i	−0.429600	+	0.903019i	$0.641345\pi$
$98$	2.10758	+	6.67518i	0.212898	+	0.674295i
$99$	−2.49118	+	2.49118i	−0.250373	+	0.250373i
$100$	−4.62781			−0.462781
$101$	11.1279			1.10727			0.553633	−	0.832761i	$-0.313241\pi$
$101$	11.1279			1.10727			0.553633	+	0.832761i	$0.313241\pi$
$102$	−0.467954	+	0.467954i	−0.0463344	+	0.0463344i
$103$	−1.71734	+	2.97452i	−0.169214	+	0.293088i	−0.938144	−	0.346246i	$-0.887456\pi$
$103$	−1.71734	+	2.97452i	−0.169214	+	0.293088i	0.768929	+	0.639334i	$0.220790\pi$
$104$	1.63420	+	3.21394i	0.160246	+	0.315153i
$105$	0.837624	+	1.37975i	0.0817438	+	0.134649i
$106$	10.1401	−	2.71703i	0.984894	−	0.263902i
$107$	−5.53421	−	9.58554i	−0.535012	−	0.926669i	−0.999163	−	0.0409122i	$-0.986974\pi$
$107$	−5.53421	−	9.58554i	−0.535012	−	0.926669i	0.464150	−	0.885756i	$-0.346360\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−2.28163	+	8.51517i	−0.218541	+	0.815605i	0.766349	+	0.642424i	$0.222071\pi$
$109$	−2.28163	+	8.51517i	−0.218541	+	0.815605i	−0.984890	+	0.173181i	$0.944595\pi$
$110$	1.51980	−	1.51980i	0.144907	−	0.144907i
$111$	−0.584428	+	2.18111i	−0.0554714	+	0.207022i
$112$	1.82919	−	1.91156i	0.172843	−	0.180625i
$113$	3.05025	+	5.28319i	0.286943	+	0.497000i	0.973079	−	0.230474i	$-0.0740276\pi$
$113$	3.05025	+	5.28319i	0.286943	+	0.497000i	−0.686135	+	0.727474i	$0.740694\pi$
$114$	−1.59519	+	0.920982i	−0.149403	+	0.0862578i
$115$	2.86590	+	2.86590i	0.267247	+	0.267247i
$116$	−4.86891	+	2.81107i	−0.452067	+	0.261001i
$117$	−1.11704	+	3.42815i	−0.103271	+	0.316933i
$118$		−	9.65443i		−	0.888763i
$119$	1.70083	+	0.415833i	0.155915	+	0.0381194i
$120$	0.305036	−	0.528338i	0.0278458	−	0.0482304i
$121$		−	1.41196i		−	0.128360i
$122$	12.6966	+	3.40204i	1.14950	+	0.308007i
$123$	6.84860	−	1.83508i	0.617517	−	0.165463i
$124$	1.59527	+	1.59527i	0.143260	+	0.143260i
$125$	4.15330	+	4.15330i	0.371483	+	0.371483i
$126$	2.64511	−	0.0582404i	0.235645	−	0.00518847i
$127$	3.92526	+	2.26625i	0.348311	+	0.201097i	0.663941	−	0.747785i	$-0.268883\pi$
$127$	3.92526	+	2.26625i	0.348311	+	0.201097i	−0.315630	+	0.948882i	$0.602216\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−3.99234	−	6.91494i	−0.351506	−	0.608826i
$130$	0.681477	−	2.09142i	0.0597695	−	0.183429i
$131$	7.91260	+	4.56834i	0.691327	+	0.399138i	0.804109	−	0.594482i	$-0.202643\pi$
$131$	7.91260	+	4.56834i	0.691327	+	0.399138i	−0.112782	+	0.993620i	$0.535976\pi$
$132$	−0.911835	−	3.40302i	−0.0793651	−	0.296194i
$133$	4.27308	+	2.34319i	0.370523	+	0.203181i
$134$	−12.3959	+	7.15678i	−1.07084	+	0.618251i
$135$	0.589284	−	0.157898i	0.0507175	−	0.0135897i
$136$	−0.171283	−	0.639237i	−0.0146874	−	0.0548141i
$137$	3.14526	+	11.7383i	0.268718	+	1.00287i	0.959935	+	0.280222i	$0.0904079\pi$
$137$	3.14526	+	11.7383i	0.268718	+	1.00287i	−0.691218	+	0.722647i	$0.742925\pi$
$138$	6.41710	−	1.71946i	0.546260	−	0.146370i
$139$	17.3447	−	10.0140i	1.47116	−	0.849373i	0.471682	−	0.881769i	$-0.343647\pi$
$139$	17.3447	−	10.0140i	1.47116	−	0.849373i	0.999475	+	0.0323955i	$0.0103136\pi$
$140$	−1.61371	+	0.0355308i	−0.136383	+	0.00300290i
$141$	−1.18439	−	4.42021i	−0.0997437	−	0.372249i
$142$	−11.5159	−	6.64872i	−0.966394	−	0.557948i
$143$	−5.75738	−	11.3229i	−0.481456	−	0.946868i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.31303	+	0.887724i	0.275132	+	0.0737215i
$146$	3.64414	+	2.10395i	0.301591	+	0.174124i
$147$	−3.76343	−	5.90225i	−0.310403	−	0.486809i
$148$	−1.59669	−	1.59669i	−0.131247	−	0.131247i
$149$	12.0621	+	12.0621i	0.988163	+	0.988163i	0.999931	−	0.0117673i	$-0.00374573\pi$
$149$	12.0621	+	12.0621i	0.988163	+	0.988163i	−0.0117673	+	0.999931i	$0.503746\pi$
$150$	4.47012	−	1.19777i	0.364984	−	0.0977972i
$151$	−4.20616	−	1.12704i	−0.342293	−	0.0917170i	0.0835776	−	0.996501i	$-0.473365\pi$
$151$	−4.20616	−	1.12704i	−0.342293	−	0.0917170i	−0.425870	+	0.904784i	$0.640032\pi$
$152$		−	1.84196i		−	0.149403i
$153$	0.330893	−	0.573124i	0.0267512	−	0.0463344i
$154$	−6.44436	+	6.73453i	−0.519301	+	0.542684i
$155$		−	1.37636i		−	0.110552i
$156$	−2.41034	−	2.68146i	−0.192982	−	0.214689i
$157$	−11.3079	+	6.52860i	−0.902466	+	0.521039i	−0.877999	−	0.478662i	$-0.841122\pi$
$157$	−11.3079	+	6.52860i	−0.902466	+	0.521039i	−0.0244663	+	0.999701i	$0.507789\pi$
$158$	4.53676	+	4.53676i	0.360925	+	0.360925i
$159$	−9.09137	+	5.24890i	−0.720992	+	0.416265i
$160$	0.305036	+	0.528338i	0.0241152	+	0.0417688i
$161$	−12.6994	−	12.1522i	−1.00085	−	0.957727i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	12.8802	−	12.8802i	1.00886	−	1.00886i	0.00889471	−	0.999960i	$-0.497169\pi$
$163$	12.8802	−	12.8802i	1.00886	−	1.00886i	0.999960	−	0.00889471i	$-0.00283131\pi$
$164$	−1.83508	+	6.84860i	−0.143295	+	0.534786i
$165$	−1.07466	+	1.86137i	−0.0836622	+	0.144907i
$166$	3.65612	+	6.33258i	0.283770	+	0.491504i
$167$	12.1764	−	3.26266i	0.942239	−	0.252472i	0.245173	−	0.969479i	$-0.421155\pi$
$167$	12.1764	−	3.26266i	0.942239	−	0.252472i	0.697066	+	0.717007i	$0.254489\pi$
$168$	−1.27212	+	2.31985i	−0.0981460	+	0.178981i
$169$	−10.5044	−	7.65879i	−0.808033	−	0.589138i
$170$	−0.201869	+	0.349647i	−0.0154826	+	0.0268167i
$171$	1.30246	−	1.30246i	0.0996020	−	0.0996020i
$172$	7.98468			0.608826
$173$	−0.357161			−0.0271544			−0.0135772	−	0.999908i	$-0.504322\pi$
$173$	−0.357161			−0.0271544			−0.0135772	+	0.999908i	$0.504322\pi$
$174$	3.97545	−	3.97545i	0.301378	−	0.301378i
$175$	−8.84633	−	8.46516i	−0.668720	−	0.639906i
$176$	3.40302	+	0.911835i	0.256512	+	0.0687322i
$177$	2.49875	+	9.32547i	0.187818	+	0.700945i
$178$	13.0778	+	7.55046i	0.980221	+	0.565931i
$179$			2.94047i			0.219781i	0.993944	+	0.109890i	$0.0350500\pi$
$179$			2.94047i			0.219781i	−0.993944	+	0.109890i	$0.964950\pi$
$180$	−0.157898	+	0.589284i	−0.0117690	+	0.0439226i
$181$	−3.08018			−0.228948			−0.114474	−	0.993426i	$-0.536518\pi$
$181$	−3.08018			−0.228948			−0.114474	+	0.993426i	$0.536518\pi$
$182$	−2.75505	+	9.13289i	−0.204218	+	0.676975i
$183$	−13.1445			−0.971668
$184$	−1.71946	+	6.41710i	−0.126760	+	0.473075i
$185$			1.37758i			0.101281i
$186$	−1.95380	−	1.12803i	−0.143260	−	0.0827110i
$187$	0.603441	+	2.25207i	0.0441280	+	0.164688i
$188$	4.42021	+	1.18439i	0.322377	+	0.0863806i
$189$	−2.53991	+	0.740861i	−0.184751	+	0.0538897i
$190$	−0.794597	+	0.794597i	−0.0576461	+	0.0576461i
$191$	1.29474			0.0936839			0.0468419	−	0.998902i	$-0.485084\pi$
$191$	1.29474			0.0936839			0.0468419	+	0.998902i	$0.485084\pi$
$192$	1.00000			0.0721688
$193$	6.12391	−	6.12391i	0.440809	−	0.440809i	−0.451475	−	0.892284i	$-0.649102\pi$
$193$	6.12391	−	6.12391i	0.440809	−	0.440809i	0.892284	+	0.451475i	$0.149102\pi$
$194$	−1.78504	+	3.09178i	−0.128158	+	0.221977i
$195$	−0.116958	+	2.19653i	−0.00837552	+	0.157297i
$196$	6.99322	−	0.308105i	0.499515	−	0.0220075i
$197$	−2.64884	+	0.709754i	−0.188722	+	0.0505679i	−0.351942	−	0.936022i	$-0.614479\pi$
$197$	−2.64884	+	0.709754i	−0.188722	+	0.0505679i	0.163220	+	0.986590i	$0.447812\pi$
$198$	1.76153	+	3.05106i	0.125187	+	0.216829i
$199$	−10.5628	+	18.2954i	−0.748780	+	1.29693i	0.199627	+	0.979872i	$0.436027\pi$
$199$	−10.5628	+	18.2954i	−0.748780	+	1.29693i	−0.948408	+	0.317054i	$0.897306\pi$
$200$	−1.19777	+	4.47012i	−0.0846948	+	0.316085i
$201$	10.1212	−	10.1212i	0.713895	−	0.713895i
$202$	2.88011	−	10.7487i	0.202644	−	0.756277i
$203$	−14.4492	−	3.53266i	−1.01413	−	0.247944i
$204$	0.330893	+	0.573124i	0.0231672	+	0.0401267i
$205$	3.74601	−	2.16276i	0.261633	−	0.151054i
$206$	2.42868	+	2.42868i	0.169214	+	0.169214i
$207$	−5.75342	+	3.32174i	−0.399890	+	0.230877i
$208$	3.52739	−	0.746686i	0.244580	−	0.0517734i
$209$			6.48935i			0.448878i
$210$	1.54953	−	0.451978i	0.106927	−	0.0311895i
$211$	1.43098	−	2.47853i	0.0985129	−	0.170629i	−0.812556	−	0.582883i	$-0.801925\pi$
$211$	1.43098	−	2.47853i	0.0985129	−	0.170629i	0.911069	+	0.412253i	$0.135258\pi$
$212$		−	10.4978i		−	0.720992i
$213$	12.8443	+	3.44163i	0.880079	+	0.235816i
$214$	−10.6913	+	2.86472i	−0.730841	+	0.195828i
$215$	−3.44448	−	3.44448i	−0.234912	−	0.234912i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	0.131394	+	5.96752i	0.00891958	+	0.405101i
$218$	7.63449	+	4.40778i	0.517073	+	0.298532i
$219$	−4.06451	−	1.08908i	−0.274654	−	0.0735934i
$220$	−1.07466	−	1.86137i	−0.0724536	−	0.125493i
$221$	1.59513	+	1.77456i	0.107300	+	0.119370i
$222$	1.95553	+	1.12903i	0.131247	+	0.0757754i
$223$	1.55649	+	5.80890i	0.104230	+	0.388993i	0.998257	−	0.0590214i	$-0.0187980\pi$
$223$	1.55649	+	5.80890i	0.104230	+	0.388993i	−0.894026	+	0.448014i	$0.852131\pi$
$224$	−1.37299	−	2.26161i	−0.0917369	−	0.151110i
$225$	−4.00780	+	2.31391i	−0.267187	+	0.154260i
$226$	5.89263	−	1.57892i	0.391972	−	0.105029i
$227$	−0.859219	−	3.20665i	−0.0570283	−	0.212833i	0.931532	−	0.363660i	$-0.118473\pi$
$227$	−0.859219	−	3.20665i	−0.0570283	−	0.212833i	−0.988560	+	0.150827i	$0.951806\pi$
$228$	0.476735	+	1.77920i	0.0315726	+	0.117830i
$229$	18.6978	−	5.01006i	1.23559	−	0.331074i	0.418833	−	0.908063i	$-0.362439\pi$
$229$	18.6978	−	5.01006i	1.23559	−	0.331074i	0.816752	+	0.576989i	$0.195772\pi$
$230$	3.51000	−	2.02650i	0.231442	−	0.133623i
$231$	4.48175	−	8.17298i	0.294877	−	0.537743i
$232$	1.45511	+	5.43056i	0.0955330	+	0.356534i
$233$	−16.0321	−	9.25613i	−1.05030	−	0.606389i	−0.127564	−	0.991830i	$-0.540716\pi$
$233$	−16.0321	−	9.25613i	−1.05030	−	0.606389i	−0.922732	+	0.385441i	$0.874049\pi$
$234$	3.02223	+	1.96625i	0.197569	+	0.128538i
$235$	−1.39589	−	2.41774i	−0.0910575	−	0.157716i
$236$	−9.32547	−	2.49875i	−0.607036	−	0.162655i
$237$	−5.55637	−	3.20797i	−0.360925	−	0.208380i
$238$	0.841871	−	1.53525i	0.0545704	−	0.0995154i
$239$	−18.2410	−	18.2410i	−1.17991	−	1.17991i	−0.979767	−	0.200144i	$-0.935859\pi$
$239$	−18.2410	−	18.2410i	−1.17991	−	1.17991i	−0.200144	−	0.979767i	$-0.564141\pi$
$240$	−0.431386	−	0.431386i	−0.0278458	−	0.0278458i
$241$	5.86111	−	1.57048i	0.377547	−	0.101163i	−0.0650547	−	0.997882i	$-0.520722\pi$
$241$	5.86111	−	1.57048i	0.377547	−	0.101163i	0.442602	+	0.896718i	$0.354056\pi$
$242$	−1.36385	−	0.365442i	−0.0876714	−	0.0234915i
$243$			1.00000i			0.0641500i
$244$	6.57224	−	11.3835i	0.420745	−	0.728751i
$245$	−3.14969	−	2.88386i	−0.201226	−	0.184243i
$246$		−	7.09019i		−	0.452054i
$247$	3.01013	+	5.91996i	0.191530	+	0.376678i
$248$	1.95380	−	1.12803i	0.124067	−	0.0716298i
$249$	−5.17053	−	5.17053i	−0.327669	−	0.327669i
$250$	5.08674	−	2.93683i	0.321713	−	0.185741i
$251$	1.57998	+	2.73660i	0.0997272	+	0.172733i	0.911572	−	0.411141i	$-0.134870\pi$
$251$	1.57998	+	2.73660i	0.0997272	+	0.172733i	−0.811845	+	0.583874i	$0.801536\pi$
$252$	0.628349	−	2.57005i	0.0395823	−	0.161898i
$253$	6.05775	−	22.6078i	0.380848	−	1.42134i
$254$	3.20496	−	3.20496i	0.201097	−	0.201097i
$255$	0.104495	−	0.389981i	0.00654373	−	0.0244215i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.79960	+	3.11699i	0.112256	+	0.194433i	0.916679	−	0.399623i	$-0.130859\pi$
$257$	1.79960	+	3.11699i	0.112256	+	0.194433i	−0.804424	+	0.594056i	$0.797526\pi$
$258$	−7.71261	+	2.06659i	−0.480166	+	0.128660i
$259$	−0.131510	−	5.97280i	−0.00817164	−	0.371132i
$260$	−1.84377	−	1.19956i	−0.114346	−	0.0743933i
$261$	−2.81107	+	4.86891i	−0.174001	+	0.301378i
$262$	6.46061	−	6.46061i	0.399138	−	0.399138i
$263$	14.0187			0.864432			0.432216	−	0.901770i	$-0.357732\pi$
$263$	14.0187			0.864432			0.432216	+	0.901770i	$0.357732\pi$
$264$	−3.52306			−0.216829
$265$	−4.52861	+	4.52861i	−0.278190	+	0.278190i
$266$	3.36931	−	3.52102i	0.206585	−	0.215888i
$267$	−14.5864	−	3.90841i	−0.892671	−	0.239191i
$268$	3.70462	+	13.8258i	0.226296	+	0.844547i
$269$	−8.85205	−	5.11073i	−0.539719	−	0.311607i	0.205246	−	0.978710i	$-0.434200\pi$
$269$	−8.85205	−	5.11073i	−0.539719	−	0.311607i	−0.744965	+	0.667104i	$0.767534\pi$
$270$		−	0.610072i		−	0.0371278i
$271$	−3.12364	+	11.6576i	−0.189748	+	0.708149i	0.803816	+	0.594878i	$0.202799\pi$
$271$	−3.12364	+	11.6576i	−0.189748	+	0.708149i	−0.993564	+	0.113271i	$0.963867\pi$
$272$	−0.661787			−0.0401267
$273$	0.297406	−	9.53475i	0.0179998	−	0.577070i
$274$	12.1524			0.734151
$275$	4.21980	−	15.7485i	0.254464	−	0.949671i
$276$		−	6.64347i		−	0.399890i
$277$	−19.7235	−	11.3874i	−1.18507	−	0.684200i	−0.227887	−	0.973687i	$-0.573182\pi$
$277$	−19.7235	−	11.3874i	−1.18507	−	0.684200i	−0.957182	+	0.289487i	$0.906515\pi$
$278$	−5.18361	−	19.3455i	−0.310892	−	1.16027i
$279$	2.17918	+	0.583910i	0.130464	+	0.0349578i
$280$	−0.383338	+	1.56792i	−0.0229088	+	0.0937010i
$281$	−11.4925	+	11.4925i	−0.685584	+	0.685584i	−0.961253	−	0.275669i	$-0.911101\pi$
$281$	−11.4925	+	11.4925i	−0.685584	+	0.685584i	0.275669	+	0.961253i	$0.411101\pi$
$282$	−4.57613			−0.272505
$283$	−31.0086			−1.84327			−0.921635	−	0.388058i	$-0.873146\pi$
$283$	−31.0086			−1.84327			−0.921635	+	0.388058i	$0.873146\pi$
$284$	−9.40270	+	9.40270i	−0.557948	+	0.557948i
$285$	0.561865	−	0.973179i	0.0332820	−	0.0576461i
$286$	−12.4272	+	2.63062i	−0.734836	+	0.155552i
$287$	−16.0353	+	9.73478i	−0.946531	+	0.574626i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	8.28102	+	14.3431i	0.487119	+	0.843714i
$290$	1.71495	−	2.97038i	0.100705	−	0.174427i
$291$	0.924004	−	3.44843i	0.0541661	−	0.202151i
$292$	2.97543	−	2.97543i	0.174124	−	0.174124i
$293$	5.39854	−	20.1476i	0.315386	−	1.17704i	−0.608244	−	0.793750i	$-0.708126\pi$
$293$	5.39854	−	20.1476i	0.315386	−	1.17704i	0.923630	−	0.383286i	$-0.125208\pi$
$294$	−6.67518	+	2.10758i	−0.389305	+	0.122917i
$295$	2.94495	+	5.10080i	0.171462	+	0.296980i
$296$	−1.95553	+	1.12903i	−0.113663	+	0.0656234i
$297$	−2.49118	−	2.49118i	−0.144553	−	0.144553i
$298$	14.7730	−	8.52917i	0.855775	−	0.494082i
$299$	−4.96059	−	23.4341i	−0.286878	−	1.35523i
$300$		−	4.62781i		−	0.267187i
$301$	15.2632	+	14.6055i	0.879755	+	0.841848i
$302$	−2.17727	+	3.77114i	−0.125288	+	0.217005i
$303$			11.1279i			0.639281i
$304$	−1.77920	−	0.476735i	−0.102044	−	0.0273426i
$305$	−7.74584	+	2.07549i	−0.443525	+	0.118842i
$306$	−0.467954	−	0.467954i	−0.0267512	−	0.0267512i
$307$	−15.6514	−	15.6514i	−0.893271	−	0.893271i	0.101559	−	0.994830i	$-0.467617\pi$
$307$	−15.6514	−	15.6514i	−0.893271	−	0.893271i	−0.994830	+	0.101559i	$0.967617\pi$
$308$	4.83714	+	7.96780i	0.275621	+	0.454007i
$309$	−2.97452	−	1.71734i	−0.169214	−	0.0976960i
$310$	−1.32946	−	0.356227i	−0.0755081	−	0.0202323i
$311$	3.13129	+	5.42356i	0.177559	+	0.307542i	0.941044	−	0.338284i	$-0.109846\pi$
$311$	3.13129	+	5.42356i	0.177559	+	0.307542i	−0.763485	+	0.645826i	$0.776513\pi$
$312$	−3.21394	+	1.63420i	−0.181953	+	0.0925183i
$313$	2.02929	+	1.17161i	0.114702	+	0.0662235i	0.556254	−	0.831013i	$-0.312238\pi$
$313$	2.02929	+	1.17161i	0.114702	+	0.0662235i	−0.441551	+	0.897236i	$0.645572\pi$
$314$	3.37945	+	12.6123i	0.190713	+	0.711752i
$315$	−1.37975	+	0.837624i	−0.0777399	+	0.0471948i
$316$	5.55637	−	3.20797i	0.312570	−	0.180463i
$317$	25.4884	−	6.82959i	1.43157	−	0.383588i	0.541996	−	0.840381i	$-0.317669\pi$
$317$	25.4884	−	6.82959i	1.43157	−	0.383588i	0.889573	+	0.456793i	$0.151002\pi$
$318$	2.71703	+	10.1401i	0.152364	+	0.568629i
$319$	−5.12646	−	19.1322i	−0.287027	−	1.07120i
$320$	0.589284	−	0.157898i	0.0329420	−	0.00882678i
$321$	9.58554	−	5.53421i	0.535012	−	0.308890i
$322$	−15.0250	+	9.12144i	−0.837308	+	0.508318i
$323$	−0.315497	−	1.17745i	−0.0175547	−	0.0655151i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−3.45552	−	16.3241i	−0.191678	−	0.905497i
$326$	−9.10768	−	15.7750i	−0.504428	−	0.873694i
$327$	−8.51517	−	2.28163i	−0.470890	−	0.126175i
$328$	6.14028	+	3.54509i	0.339040	+	0.195745i
$329$	6.28300	+	10.3494i	0.346393	+	0.570583i
$330$	1.51980	+	1.51980i	0.0836622	+	0.0836622i
$331$	−7.90709	−	7.90709i	−0.434613	−	0.434613i	0.455581	−	0.890194i	$-0.349431\pi$
$331$	−7.90709	−	7.90709i	−0.434613	−	0.434613i	−0.890194	+	0.455581i	$0.849431\pi$
$332$	7.06308	−	1.89255i	0.387637	−	0.103867i
$333$	−2.18111	−	0.584428i	−0.119524	−	0.0320264i
$334$		−	12.6059i		−	0.689767i
$335$	4.36615	−	7.56239i	0.238548	−	0.413178i
$336$	1.91156	+	1.82919i	0.104284	+	0.0997907i
$337$		−	20.8601i		−	1.13632i	−0.822918	−	0.568160i	$-0.807656\pi$
$337$		−	20.8601i		−	1.13632i	0.822918	−	0.568160i	$-0.192344\pi$
$338$	−10.1166	+	8.16425i	−0.550269	+	0.444077i
$339$	−5.28319	+	3.05025i	−0.286943	+	0.165667i
$340$	0.285486	+	0.285486i	0.0154826	+	0.0154826i
$341$	−6.88336	+	3.97411i	−0.372755	+	0.215210i
$342$	−0.920982	−	1.59519i	−0.0498010	−	0.0862578i
$343$	13.9315	+	12.2030i	0.752231	+	0.658899i
$344$	2.06659	−	7.71261i	0.111423	−	0.415836i
$345$	−2.86590	+	2.86590i	−0.154295	+	0.154295i
$346$	−0.0924401	+	0.344991i	−0.00496961	+	0.0185468i
$347$	−5.94859	+	10.3033i	−0.319337	+	0.553108i	−0.980350	−	0.197266i	$-0.936794\pi$
$347$	−5.94859	+	10.3033i	−0.319337	+	0.553108i	0.661013	+	0.750375i	$0.270127\pi$
$348$	−2.81107	−	4.86891i	−0.150689	−	0.261001i
$349$	32.7335	−	8.77090i	1.75218	−	0.469496i	0.767092	−	0.641537i	$-0.221703\pi$
$349$	32.7335	−	8.77090i	1.75218	−	0.469496i	0.985090	+	0.172041i	$0.0550363\pi$
$350$	−10.4663	+	6.35395i	−0.559448	+	0.339633i
$351$	−3.42815	−	1.11704i	−0.182981	−	0.0596234i
$352$	1.76153	−	3.05106i	0.0938899	−	0.162622i
$353$	5.56685	−	5.56685i	0.296294	−	0.296294i	−0.543267	−	0.839560i	$-0.682813\pi$
$353$	5.56685	−	5.56685i	0.296294	−	0.296294i	0.839560	+	0.543267i	$0.182813\pi$
$354$	9.65443			0.513127
$355$	8.11239			0.430561
$356$	10.6780	−	10.6780i	0.565931	−	0.565931i
$357$	−0.415833	+	1.70083i	−0.0220082	+	0.0900174i
$358$	2.84027	+	0.761049i	0.150113	+	0.0402227i
$359$	7.14533	+	26.6667i	0.377116	+	1.40742i	0.850228	+	0.526414i	$0.176464\pi$
$359$	7.14533	+	26.6667i	0.377116	+	1.40742i	−0.473112	+	0.881002i	$0.656869\pi$
$360$	0.528338	+	0.305036i	0.0278458	+	0.0160768i
$361$			15.6072i			0.821430i
$362$	−0.797209	+	2.97522i	−0.0419004	+	0.156374i
$363$	1.41196			0.0741086
$364$	8.10864	+	5.02494i	0.425008	+	0.263378i
$365$	−2.56712			−0.134369
$366$	−3.40204	+	12.6966i	−0.177828	+	0.663662i
$367$		−	3.43459i		−	0.179284i	−0.995974	−	0.0896421i	$-0.971428\pi$
$367$		−	3.43459i		−	0.179284i	0.995974	−	0.0896421i	$-0.0285723\pi$
$368$	5.75342	+	3.32174i	0.299918	+	0.173157i
$369$	1.83508	+	6.84860i	0.0955302	+	0.356524i
$370$	1.33064	+	0.356543i	0.0691765	+	0.0185358i
$371$	19.2025	−	20.0672i	0.996945	−	1.04184i
$372$	−1.59527	+	1.59527i	−0.0827110	+	0.0827110i
$373$	11.8519			0.613666			0.306833	−	0.951763i	$-0.400731\pi$
$373$	11.8519			0.613666			0.306833	+	0.951763i	$0.400731\pi$
$374$	2.33152			0.120560
$375$	−4.15330	+	4.15330i	−0.214476	+	0.214476i
$376$	2.28807	−	3.96305i	0.117998	−	0.204379i
$377$	−13.5513	−	15.0755i	−0.697926	−	0.776430i
$378$	0.0582404	+	2.64511i	0.00299556	+	0.136050i
$379$	19.1079	−	5.11994i	0.981506	−	0.262994i	0.267828	−	0.963467i	$-0.413694\pi$
$379$	19.1079	−	5.11994i	0.981506	−	0.262994i	0.713679	+	0.700473i	$0.247028\pi$
$380$	0.561865	+	0.973179i	0.0288231	+	0.0499230i
$381$	−2.26625	+	3.92526i	−0.116104	+	0.201097i
$382$	0.335102	−	1.25062i	0.0171453	−	0.0639873i
$383$	−12.2027	+	12.2027i	−0.623530	+	0.623530i	−0.946432	−	0.322903i	$-0.895341\pi$
$383$	−12.2027	+	12.2027i	−0.623530	+	0.623530i	0.322903	+	0.946432i	$0.395341\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	1.35052	−	5.52387i	0.0688290	−	0.281522i
$386$	−4.33026	−	7.50023i	−0.220404	−	0.381752i
$387$	6.91494	−	3.99234i	0.351506	−	0.202942i
$388$	2.52443	+	2.52443i	0.128158	+	0.128158i
$389$	−2.98149	+	1.72136i	−0.151167	+	0.0872765i	−0.573676	−	0.819083i	$-0.694483\pi$
$389$	−2.98149	+	1.72136i	−0.151167	+	0.0872765i	0.422508	+	0.906359i	$0.361150\pi$
$390$	2.09142	+	0.681477i	0.105903	+	0.0345079i
$391$			4.39656i			0.222344i
$392$	1.51237	−	6.83467i	0.0763863	−	0.345203i
$393$	−4.56834	+	7.91260i	−0.230442	+	0.399138i
$394$			2.74228i			0.138154i
$395$	−3.78082	−	1.01307i	−0.190233	−	0.0509729i
$396$	3.40302	−	0.911835i	0.171008	−	0.0458214i
$397$	23.8022	+	23.8022i	1.19460	+	1.19460i	0.975762	+	0.218834i	$0.0702255\pi$
$397$	23.8022	+	23.8022i	1.19460	+	1.19460i	0.218834	+	0.975762i	$0.429775\pi$
$398$	14.9381	+	14.9381i	0.748780	+	0.748780i
$399$	−2.34319	+	4.27308i	−0.117306	+	0.213922i
$400$	4.00780	+	2.31391i	0.200390	+	0.115695i
$401$	20.5896	+	5.51698i	1.02820	+	0.275505i	0.733214	−	0.679998i	$-0.238019\pi$
$401$	20.5896	+	5.51698i	1.02820	+	0.275505i	0.294983	+	0.955502i	$0.404686\pi$
$402$	−7.15678	−	12.3959i	−0.356948	−	0.618251i
$403$	−4.43598	+	6.81831i	−0.220972	+	0.339644i
$404$	−9.63704	−	5.56394i	−0.479460	−	0.276817i
$405$	0.157898	+	0.589284i	0.00784602	+	0.0292818i
$406$	−7.15201	+	13.0425i	−0.354948	+	0.647289i
$407$	6.88946	−	3.97763i	0.341498	−	0.197164i
$408$	0.639237	−	0.171283i	0.0316470	−	0.00847978i
$409$	1.94858	+	7.27222i	0.0963513	+	0.359588i	0.997221	−	0.0745019i	$-0.0237367\pi$
$409$	1.94858	+	7.27222i	0.0963513	+	0.359588i	−0.900870	+	0.434090i	$0.857070\pi$
$410$	−1.11953	−	4.17814i	−0.0552895	−	0.206343i
$411$	−11.7383	+	3.14526i	−0.579006	+	0.155144i
$412$	2.97452	−	1.71734i	0.146544	−	0.0846072i
$413$	−13.2555	−	21.8346i	−0.652259	−	1.07441i
$414$	1.71946	+	6.41710i	0.0845067	+	0.315383i
$415$	−3.86333	−	2.23049i	−0.189643	−	0.109491i
$416$	0.191712	−	3.60045i	0.00939943	−	0.176527i
$417$	10.0140	+	17.3447i	0.490386	+	0.849373i
$418$	6.26823	+	1.67957i	0.306589	+	0.0821503i
$419$	−6.59649	−	3.80849i	−0.322260	−	0.186057i	0.330140	−	0.943932i	$-0.392904\pi$
$419$	−6.59649	−	3.80849i	−0.322260	−	0.186057i	−0.652399	+	0.757875i	$0.726237\pi$
$420$	−0.0355308	−	1.61371i	−0.00173373	−	0.0787408i
$421$	13.3231	+	13.3231i	0.649327	+	0.649327i	0.952830	−	0.303503i	$-0.0981562\pi$
$421$	13.3231	+	13.3231i	0.649327	+	0.649327i	−0.303503	+	0.952830i	$0.598156\pi$
$422$	−2.02372	−	2.02372i	−0.0985129	−	0.0985129i
$423$	4.42021	−	1.18439i	0.214918	−	0.0575870i
$424$	−10.1401	−	2.71703i	−0.492447	−	0.131951i
$425$			3.06263i			0.148559i
$426$	6.64872	−	11.5159i	0.322131	−	0.557948i
$427$	33.3858	−	9.73823i	1.61565	−	0.471266i
$428$			11.0684i			0.535012i
$429$	11.3229	−	5.75738i	0.546675	−	0.277969i
$430$	−4.21861	+	2.43561i	−0.203439	+	0.117456i
$431$	−1.09023	−	1.09023i	−0.0525147	−	0.0525147i	0.680362	−	0.732876i	$-0.261823\pi$
$431$	−1.09023	−	1.09023i	−0.0525147	−	0.0525147i	−0.732876	+	0.680362i	$0.761823\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	17.7509	+	30.7454i	0.853053	+	1.47753i	0.878440	+	0.477853i	$0.158585\pi$
$433$	17.7509	+	30.7454i	0.853053	+	1.47753i	−0.0253870	+	0.999678i	$0.508082\pi$
$434$	5.79819	+	1.41759i	0.278322	+	0.0680465i
$435$	−0.887724	+	3.31303i	−0.0425631	+	0.158848i
$436$	6.23354	−	6.23354i	0.298532	−	0.298532i
$437$	−3.16718	+	11.8201i	−0.151507	+	0.565431i
$438$	−2.10395	+	3.64414i	−0.100530	+	0.174124i
$439$	14.2836	+	24.7398i	0.681717	+	1.18077i	0.974457	+	0.224576i	$0.0720998\pi$
$439$	14.2836	+	24.7398i	0.681717	+	1.18077i	−0.292740	+	0.956192i	$0.594567\pi$
$440$	−2.07608	+	0.556285i	−0.0989734	+	0.0265198i
$441$	5.90225	−	3.76343i	0.281060	−	0.179211i
$442$	2.12694	−	1.08149i	0.101168	−	0.0514413i
$443$	−5.73331	+	9.93038i	−0.272398	+	0.471807i	−0.969475	−	0.245189i	$-0.921150\pi$
$443$	−5.73331	+	9.93038i	−0.272398	+	0.471807i	0.697078	+	0.716996i	$0.254483\pi$
$444$	1.59669	−	1.59669i	0.0757754	−	0.0757754i
$445$	−9.21264			−0.436721
$446$	6.01382			0.284763
$447$	−12.0621	+	12.0621i	−0.570516	+	0.570516i
$448$	−2.53991	+	0.740861i	−0.119999	+	0.0350024i
$449$	−0.958153	−	0.256736i	−0.0452180	−	0.0121161i	0.236139	−	0.971719i	$-0.424118\pi$
$449$	−0.958153	−	0.256736i	−0.0452180	−	0.0121161i	−0.281357	+	0.959603i	$0.590785\pi$
$450$	1.19777	+	4.47012i	0.0564632	+	0.210724i
$451$	−21.6326	−	12.4896i	−1.01864	−	0.588112i
$452$		−	6.10050i		−	0.286943i
$453$	1.12704	−	4.20616i	0.0529529	−	0.197623i
$454$	−3.31977			−0.155804
$455$	−1.33026	−	5.66564i	−0.0623637	−	0.265609i
$456$	1.84196			0.0862578
$457$	6.73587	−	25.1386i	0.315091	−	1.17593i	−0.608815	−	0.793313i	$-0.708355\pi$
$457$	6.73587	−	25.1386i	0.315091	−	1.17593i	0.923905	−	0.382622i	$-0.124979\pi$
$458$		−	19.3574i		−	0.904511i
$459$	0.573124	+	0.330893i	0.0267512	+	0.0154448i
$460$	−1.04899	−	3.91489i	−0.0489095	−	0.182533i
$461$	−19.4765	−	5.21871i	−0.907111	−	0.243060i	−0.225044	−	0.974349i	$-0.572252\pi$
$461$	−19.4765	−	5.21871i	−0.907111	−	0.243060i	−0.682068	+	0.731289i	$0.738919\pi$
$462$	−6.73453	−	6.44436i	−0.313319	−	0.299819i
$463$	−14.5403	+	14.5403i	−0.675743	+	0.675743i	−0.959034	−	0.283291i	$-0.908574\pi$
$463$	−14.5403	+	14.5403i	−0.675743	+	0.675743i	0.283291	+	0.959034i	$0.408574\pi$
$464$	5.62213			0.261001
$465$	1.37636			0.0638270
$466$	−13.0901	+	13.0901i	−0.606389	+	0.606389i
$467$	14.1818	−	24.5637i	0.656257	−	1.13667i	−0.325320	−	0.945604i	$-0.605472\pi$
$467$	14.1818	−	24.5637i	0.656257	−	1.13667i	0.981577	−	0.191067i	$-0.0611948\pi$
$468$	2.68146	−	2.41034i	0.123951	−	0.111418i
$469$	−18.2085	+	33.2053i	−0.840792	+	1.53328i
$470$	−2.69664	+	0.722563i	−0.124387	+	0.0333294i
$471$	−6.52860	−	11.3079i	−0.300822	−	0.521039i
$472$	−4.82722	+	8.36098i	−0.222191	+	0.384845i
$473$	−7.28071	+	27.1720i	−0.334768	+	1.24937i
$474$	−4.53676	+	4.53676i	−0.208380	+	0.208380i
$475$	−2.20624	+	8.23380i	−0.101229	+	0.377793i
$476$	−1.26504	−	1.21054i	−0.0579832	−	0.0554848i
$477$	−5.24890	−	9.09137i	−0.240331	−	0.416265i
$478$	−22.3405	+	12.8983i	−1.02183	+	0.589955i
$479$	2.13384	+	2.13384i	0.0974978	+	0.0974978i	0.754173	−	0.656675i	$-0.228038\pi$
$479$	2.13384	+	2.13384i	0.0974978	+	0.0974978i	−0.656675	+	0.754173i	$0.728038\pi$
$480$	−0.528338	+	0.305036i	−0.0241152	+	0.0139229i
$481$	4.43991	−	6.82435i	0.202442	−	0.311164i
$482$		−	6.06787i		−	0.276384i
$483$	12.1522	−	12.6994i	0.552944	−	0.577842i
$484$	−0.705979	+	1.22279i	−0.0320900	+	0.0555814i
$485$		−	2.17800i		−	0.0988981i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	12.8463	−	3.44215i	0.582121	−	0.155979i	0.0442713	−	0.999020i	$-0.485903\pi$
$487$	12.8463	−	3.44215i	0.582121	−	0.155979i	0.537850	+	0.843041i	$0.319237\pi$
$488$	−9.29455	−	9.29455i	−0.420745	−	0.420745i
$489$	12.8802	+	12.8802i	0.582463	+	0.582463i
$490$	−3.60080	+	2.29597i	−0.162667	+	0.103721i
$491$	38.1948	+	22.0518i	1.72371	+	0.995182i	0.910877	+	0.412678i	$0.135407\pi$
$491$	38.1948	+	22.0518i	1.72371	+	0.995182i	0.812828	+	0.582503i	$0.197927\pi$
$492$	−6.84860	−	1.83508i	−0.308759	−	0.0827316i
$493$	1.86033	+	3.22218i	0.0837849	+	0.145120i
$494$	6.49732	−	1.37537i	0.292328	−	0.0618808i
$495$	−1.86137	−	1.07466i	−0.0836622	−	0.0483024i
$496$	−0.583910	−	2.17918i	−0.0262183	−	0.0978482i
$497$	−35.1732	+	0.774448i	−1.57773	+	0.0347387i
$498$	−6.33258	+	3.65612i	−0.283770	+	0.163835i
$499$	−14.3468	+	3.84420i	−0.642249	+	0.172090i	−0.565222	−	0.824939i	$-0.691209\pi$
$499$	−14.3468	+	3.84420i	−0.642249	+	0.172090i	−0.0770271	+	0.997029i	$0.524543\pi$
$500$	−1.52021	−	5.67352i	−0.0679860	−	0.253727i
$501$	3.26266	+	12.1764i	0.145765	+	0.544002i
$502$	3.05228	−	0.817856i	0.136230	−	0.0365027i
$503$	−13.0702	+	7.54607i	−0.582770	+	0.336462i	−0.762233	−	0.647302i	$-0.775897\pi$
$503$	−13.0702	+	7.54607i	−0.582770	+	0.336462i	0.179463	+	0.983765i	$0.442564\pi$
$504$	−2.31985	−	1.27212i	−0.103334	−	0.0566646i
$505$	1.75707	+	6.55749i	0.0781888	+	0.291804i
$506$	−20.2696	−	11.7027i	−0.901095	−	0.520248i
$507$	7.65879	−	10.5044i	0.340139	−	0.466518i
$508$	−2.26625	−	3.92526i	−0.100549	−	0.174155i
$509$	11.8202	+	3.16721i	0.523921	+	0.140384i	0.511080	−	0.859533i	$-0.329246\pi$
$509$	11.8202	+	3.16721i	0.523921	+	0.140384i	0.0128411	+	0.999918i	$0.495912\pi$
$510$	−0.349647	−	0.201869i	−0.0154826	−	0.00893890i
$511$	11.1303	−	0.245069i	0.492377	−	0.0108412i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.30246	+	1.30246i	0.0575052	+	0.0575052i
$514$	3.47655	−	0.931539i	0.153344	−	0.0410884i
$515$	−2.02400	−	0.542329i	−0.0891881	−	0.0238979i
$516$			7.98468i			0.351506i
$517$	−8.06100	+	13.9621i	−0.354522	+	0.614051i
$518$	−5.80332	−	1.41885i	−0.254983	−	0.0623405i
$519$		−	0.357161i		−	0.0156776i
$520$	−1.63589	+	1.47048i	−0.0717383	+	0.0644849i
$521$	−22.6198	+	13.0595i	−0.990991	+	0.572149i	−0.905570	−	0.424196i	$-0.860557\pi$
$521$	−22.6198	+	13.0595i	−0.990991	+	0.572149i	−0.0854203	+	0.996345i	$0.527223\pi$
$522$	3.97545	+	3.97545i	0.174001	+	0.174001i
$523$	−28.2997	+	16.3388i	−1.23746	+	0.714447i	−0.968574	−	0.248726i	$-0.919988\pi$
$523$	−28.2997	+	16.3388i	−1.23746	+	0.714447i	−0.268884	+	0.963173i	$0.586655\pi$
$524$	−4.56834	−	7.91260i	−0.199569	−	0.345664i
$525$	8.46516	−	8.84633i	0.369450	−	0.386085i
$526$	3.62832	−	13.5411i	0.158202	−	0.590418i
$527$	1.05573	−	1.05573i	0.0459883	−	0.0459883i
$528$	−0.911835	+	3.40302i	−0.0396825	+	0.148097i
$529$	10.5679	−	18.3041i	0.459472	−	0.795830i
$530$	3.20221	+	5.54639i	0.139095	+	0.240920i
$531$	−9.32547	+	2.49875i	−0.404691	+	0.108437i
$532$	−2.52900	−	4.16581i	−0.109646	−	0.180611i
$533$	−25.5279	−	1.35927i	−1.10574	−	0.0588766i
$534$	−7.55046	+	13.0778i	−0.326740	+	0.565931i
$535$	4.77476	−	4.77476i	0.206431	−	0.206431i
$536$	14.3136			0.618251
$537$	−2.94047			−0.126891
$538$	−7.22767	+	7.22767i	−0.311607	+	0.311607i
$539$	−5.32818	+	24.0790i	−0.229501	+	1.03715i
$540$	−0.589284	−	0.157898i	−0.0253588	−	0.00679486i
$541$	−9.92791	−	37.0514i	−0.426834	−	1.59297i	−0.759885	−	0.650057i	$-0.774745\pi$
$541$	−9.92791	−	37.0514i	−0.426834	−	1.59297i	0.333051	−	0.942909i	$-0.391922\pi$
$542$	10.4519	+	6.03442i	0.448948	+	0.259200i
$543$		−	3.08018i		−	0.132183i
$544$	−0.171283	+	0.639237i	−0.00734370	+	0.0274071i
$545$	−5.37812			−0.230373
$546$	−9.13289	−	2.75505i	−0.390852	−	0.117905i
$547$	38.1476			1.63107			0.815536	−	0.578706i	$-0.196442\pi$
$547$	38.1476			1.63107			0.815536	+	0.578706i	$0.196442\pi$
$548$	3.14526	−	11.7383i	0.134359	−	0.501434i
$549$		−	13.1445i		−	0.560993i
$550$	−14.1197	−	8.15203i	−0.602068	−	0.347604i
$551$	2.68027	+	10.0029i	0.114183	+	0.426138i
$552$	−6.41710	−	1.71946i	−0.273130	−	0.0731850i
$553$	16.4893	+	4.03145i	0.701198	+	0.171435i
$554$	−16.1042	+	16.1042i	−0.684200	+	0.684200i
$555$	−1.37758			−0.0584748
$556$	−20.0279			−0.849373
$557$	−13.1430	+	13.1430i	−0.556886	+	0.556886i	−0.928419	−	0.371534i	$-0.878832\pi$
$557$	−13.1430	+	13.1430i	−0.556886	+	0.556886i	0.371534	+	0.928419i	$0.378832\pi$
$558$	1.12803	−	1.95380i	0.0477532	−	0.0827110i
$559$	5.96205	+	28.1651i	0.252168	+	1.19126i
$560$	1.41528	+	0.776083i	0.0598064	+	0.0327955i
$561$	−2.25207	+	0.603441i	−0.0950825	+	0.0254773i
$562$	8.12641	+	14.0754i	0.342792	+	0.593733i
$563$	8.03870	−	13.9234i	0.338791	−	0.586803i	−0.645415	−	0.763832i	$-0.723315\pi$
$563$	8.03870	−	13.9234i	0.338791	−	0.586803i	0.984206	+	0.177030i	$0.0566488\pi$
$564$	−1.18439	+	4.42021i	−0.0498718	+	0.186124i
$565$	−2.63167	+	2.63167i	−0.110715	+	0.110715i
$566$	−8.02562	+	29.9520i	−0.337342	+	1.25898i
$567$	−0.740861	−	2.53991i	−0.0311132	−	0.106666i
$568$	6.64872	+	11.5159i	0.278974	+	0.483197i
$569$	−0.581542	+	0.335754i	−0.0243795	+	0.0140755i	−0.512140	−	0.858902i	$-0.671147\pi$
$569$	−0.581542	+	0.335754i	−0.0243795	+	0.0140755i	0.487761	+	0.872977i	$0.337814\pi$
$570$	−0.794597	−	0.794597i	−0.0332820	−	0.0332820i
$571$	−22.2930	+	12.8709i	−0.932933	+	0.538629i	−0.887738	−	0.460349i	$-0.847724\pi$
$571$	−22.2930	+	12.8709i	−0.932933	+	0.538629i	−0.0451952	+	0.998978i	$0.514391\pi$
$572$	−0.675411	+	12.6846i	−0.0282404	+	0.530370i
$573$			1.29474i			0.0540884i
$574$	5.25284	+	18.0084i	0.219249	+	0.751657i
$575$	15.3724	−	26.6257i	0.641072	−	1.11037i
$576$			1.00000i			0.0416667i
$577$	−14.5981	−	3.91154i	−0.607726	−	0.162840i	−0.0581840	−	0.998306i	$-0.518531\pi$
$577$	−14.5981	−	3.91154i	−0.607726	−	0.162840i	−0.549542	+	0.835466i	$0.685198\pi$
$578$	15.9977	−	4.28657i	0.665417	−	0.178298i
$579$	6.12391	+	6.12391i	0.254501	+	0.254501i
$580$	−2.42531	−	2.42531i	−0.100705	−	0.100705i
$581$	16.9633	+	9.30202i	0.703757	+	0.385913i
$582$	−3.09178	−	1.78504i	−0.128158	−	0.0739923i
$583$	35.7242	+	9.57227i	1.47955	+	0.396443i
$584$	−2.10395	−	3.64414i	−0.0870619	−	0.150796i
$585$	−2.19653	−	0.116958i	−0.0908155	−	0.00483561i
$586$	−18.0639	−	10.4292i	−0.746211	−	0.430825i
$587$	−1.31954	−	4.92459i	−0.0544632	−	0.203259i	0.933333	−	0.359012i	$-0.116886\pi$
$587$	−1.31954	−	4.92459i	−0.0544632	−	0.203259i	−0.987796	+	0.155753i	$0.950220\pi$
$588$	0.308105	+	6.99322i	0.0127060	+	0.288395i
$589$	3.59883	−	2.07779i	0.148287	−	0.0856137i
$590$	5.68920	−	1.52442i	0.234221	−	0.0627593i
$591$	−0.709754	−	2.64884i	−0.0291954	−	0.108959i
$592$	0.584428	+	2.18111i	0.0240198	+	0.0896432i
$593$	−6.84690	+	1.83462i	−0.281169	+	0.0753389i	−0.396647	−	0.917971i	$-0.629826\pi$
$593$	−6.84690	+	1.83462i	−0.281169	+	0.0753389i	0.115479	+	0.993310i	$0.463160\pi$
$594$	−3.05106	+	1.76153i	−0.125187	+	0.0722765i
$595$	0.0235139	+	1.06793i	0.000963974	+	0.0437809i
$596$	−4.41502	−	16.4771i	−0.180846	−	0.674928i
$597$	−18.2954	−	10.5628i	−0.748780	−	0.432309i
$598$	−23.9195	−	1.27363i	−0.978141	−	0.0520826i
$599$	12.6914	+	21.9821i	0.518555	+	0.898164i	0.999768	+	0.0215601i	$0.00686331\pi$
$599$	12.6914	+	21.9821i	0.518555	+	0.898164i	−0.481212	+	0.876604i	$0.659803\pi$
$600$	−4.47012	−	1.19777i	−0.182492	−	0.0488986i
$601$	−19.7808	−	11.4204i	−0.806875	−	0.465849i	0.0389947	−	0.999239i	$-0.487584\pi$
$601$	−19.7808	−	11.4204i	−0.806875	−	0.465849i	−0.845869	+	0.533390i	$0.820918\pi$
$602$	18.0583	−	10.9629i	0.735999	−	0.446815i
$603$	10.1212	+	10.1212i	0.412168	+	0.412168i
$604$	3.07912	+	3.07912i	0.125288	+	0.125288i
$605$	0.832045	−	0.222946i	0.0338274	−	0.00906403i
$606$	10.7487	+	2.88011i	0.436637	+	0.116996i
$607$		−	3.99792i		−	0.162270i	−0.996703	−	0.0811352i	$-0.974145\pi$
$607$		−	3.99792i		−	0.162270i	0.996703	−	0.0811352i	$-0.0258546\pi$
$608$	−0.920982	+	1.59519i	−0.0373507	+	0.0646934i
$609$	3.53266	−	14.4492i	0.143151	−	0.585510i
$610$			8.01908i			0.324683i
$611$	−0.877298	+	16.4761i	−0.0354917	+	0.666554i
$612$	−0.573124	+	0.330893i	−0.0231672	+	0.0133756i
$613$	−27.4660	−	27.4660i	−1.10934	−	1.10934i	−0.993237	−	0.116105i	$-0.962959\pi$
$613$	−27.4660	−	27.4660i	−1.10934	−	1.10934i	−0.116105	−	0.993237i	$-0.537041\pi$
$614$	−19.1689	+	11.0672i	−0.773595	+	0.446635i
$615$	2.16276	+	3.74601i	0.0872110	+	0.151054i
$616$	8.94825	−	2.61010i	0.360535	−	0.105164i
$617$	−2.49513	+	9.31195i	−0.100450	+	0.374885i	−0.997789	−	0.0664565i	$-0.978831\pi$
$617$	−2.49513	+	9.31195i	−0.100450	+	0.374885i	0.897339	+	0.441342i	$0.145497\pi$
$618$	−2.42868	+	2.42868i	−0.0976960	+	0.0976960i
$619$	1.45987	−	5.44832i	0.0586772	−	0.218986i	−0.930361	−	0.366644i	$-0.880507\pi$
$619$	1.45987	−	5.44832i	0.0586772	−	0.218986i	0.989039	+	0.147658i	$0.0471734\pi$
$620$	−0.688178	+	1.19196i	−0.0276379	+	0.0478702i
$621$	−3.32174	−	5.75342i	−0.133297	−	0.230877i
$622$	6.04920	−	1.62088i	0.242551	−	0.0649913i
$623$	39.9436	−	0.879484i	1.60031	−	0.0352358i
$624$	0.746686	+	3.52739i	0.0298914	+	0.141208i
$625$	9.77785	−	16.9357i	0.391114	−	0.677430i
$626$	1.65691	−	1.65691i	0.0662235	−	0.0662235i
$627$	−6.48935			−0.259160
$628$	13.0572			0.521039
$629$	−1.05667	+	1.05667i	−0.0421320	+	0.0421320i
$630$	0.451978	+	1.54953i	0.0180072	+	0.0617346i
$631$	1.52391	+	0.408330i	0.0606659	+	0.0162554i	0.289024	−	0.957322i	$-0.406669\pi$
$631$	1.52391	+	0.408330i	0.0606659	+	0.0162554i	−0.228358	+	0.973577i	$0.573336\pi$
$632$	−1.66057	−	6.19733i	−0.0660539	−	0.246517i
$633$	2.47853	+	1.43098i	0.0985129	+	0.0568765i
$634$		−	26.3875i		−	1.04798i
$635$	−0.715674	+	2.67093i	−0.0284007	+	0.105993i
$636$	10.4978			0.416265
$637$	6.30854	+	24.4377i	0.249954	+	0.968258i
$638$	−19.8071			−0.784171
$639$	−3.44163	+	12.8443i	−0.136149	+	0.508114i
$640$		−	0.610072i		−	0.0241152i
$641$	35.6282	+	20.5700i	1.40723	+	0.812465i	0.995120	−	0.0986694i	$-0.0314586\pi$
$641$	35.6282	+	20.5700i	1.40723	+	0.812465i	0.412110	+	0.911134i	$0.364792\pi$
$642$	−2.86472	−	10.6913i	−0.113061	−	0.421951i
$643$	−46.0170	−	12.3302i	−1.81473	−	0.486256i	−0.818619	−	0.574337i	$-0.805260\pi$
$643$	−46.0170	−	12.3302i	−1.81473	−	0.486256i	−0.996113	+	0.0880805i	$0.971927\pi$
$644$	4.92189	+	16.8738i	0.193950	+	0.664921i
$645$	3.44448	−	3.44448i	0.135626	−	0.135626i
$646$	−1.21899			−0.0479604
$647$	−38.2541			−1.50392			−0.751962	−	0.659207i	$-0.770892\pi$
$647$	−38.2541			−1.50392			−0.751962	+	0.659207i	$0.770892\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	17.0066	−	29.4563i	0.667567	−	1.15626i
$650$	−16.6622	−	0.887205i	−0.653546	−	0.0347990i
$651$	−5.96752	+	0.131394i	−0.233885	+	0.00514972i
$652$	−17.5947	+	4.71448i	−0.689061	+	0.184633i
$653$	0.0669528	+	0.115966i	0.00262007	+	0.00453809i	0.867332	−	0.497729i	$-0.165833\pi$
$653$	0.0669528	+	0.115966i	0.00262007	+	0.00453809i	−0.864712	+	0.502267i	$0.832499\pi$
$654$	−4.40778	+	7.63449i	−0.172358	+	0.298532i
$655$	−1.44267	+	5.38410i	−0.0563696	+	0.210374i
$656$	5.01352	−	5.01352i	0.195745	−	0.195745i
$657$	1.08908	−	4.06451i	0.0424892	−	0.158572i
$658$	11.6230	−	3.39028i	0.453110	−	0.132167i
$659$	4.72225	+	8.17917i	0.183953	+	0.318615i	0.943223	−	0.332160i	$-0.107777\pi$
$659$	4.72225	+	8.17917i	0.183953	+	0.318615i	−0.759271	+	0.650775i	$0.774444\pi$
$660$	1.86137	−	1.07466i	0.0724536	−	0.0418311i
$661$	10.7095	+	10.7095i	0.416551	+	0.416551i	0.884013	−	0.467462i	$-0.154832\pi$
$661$	10.7095	+	10.7095i	0.416551	+	0.416551i	−0.467462	+	0.884013i	$0.654832\pi$
$662$	−9.68417	+	5.59116i	−0.376386	+	0.217306i
$663$	−1.77456	+	1.59513i	−0.0689181	+	0.0619498i
$664$		−	7.31224i		−	0.283770i
$665$	−0.706095	+	2.88805i	−0.0273812	+	0.111994i
$666$	−1.12903	+	1.95553i	−0.0437489	+	0.0757754i
$667$		−	37.3505i		−	1.44622i
$668$	−12.1764	−	3.26266i	−0.471119	−	0.126236i
$669$	−5.80890	+	1.55649i	−0.224585	+	0.0601774i
$670$	−6.17467	−	6.17467i	−0.238548	−	0.238548i
$671$	32.7453	+	32.7453i	1.26412	+	1.26412i
$672$	2.26161	−	1.37299i	0.0872436	−	0.0529643i
$673$	−15.0362	−	8.68115i	−0.579602	−	0.334634i	0.181373	−	0.983414i	$-0.441946\pi$
$673$	−15.0362	−	8.68115i	−0.579602	−	0.334634i	−0.760975	+	0.648781i	$0.775279\pi$
$674$	−20.1493	−	5.39898i	−0.776121	−	0.207961i
$675$	−2.31391	−	4.00780i	−0.0890623	−	0.154260i
$676$	5.26770	+	11.8849i	0.202604	+	0.457112i
$677$	0.855137	+	0.493714i	0.0328656	+	0.0189750i	0.516343	−	0.856382i	$-0.327293\pi$
$677$	0.855137	+	0.493714i	0.0328656	+	0.0189750i	−0.483477	+	0.875357i	$0.660626\pi$
$678$	1.57892	+	5.89263i	0.0606382	+	0.226305i
$679$	0.207923	+	9.44325i	0.00797935	+	0.362399i
$680$	0.349647	−	0.201869i	0.0134084	−	0.00774131i
$681$	3.20665	−	0.859219i	0.122879	−	0.0329253i
$682$	2.05715	+	7.67739i	0.0787724	+	0.293983i
$683$	4.96478	+	18.5288i	0.189972	+	0.708985i	0.993511	+	0.113733i	$0.0362810\pi$
$683$	4.96478	+	18.5288i	0.189972	+	0.708985i	−0.803539	+	0.595252i	$0.797052\pi$
$684$	−1.77920	+	0.476735i	−0.0680294	+	0.0182284i
$685$	−6.42055	+	3.70690i	−0.245316	+	0.141634i
$686$	15.3929	−	10.2984i	0.587704	−	0.393197i
$687$	5.01006	+	18.6978i	0.191146	+	0.713366i
$688$	−6.91494	−	3.99234i	−0.263629	−	0.152207i
$689$	37.0298	−	7.83857i	1.41072	−	0.298626i
$690$	2.02650	+	3.51000i	0.0771475	+	0.133623i
$691$	−22.3655	−	5.99281i	−0.850822	−	0.227977i	−0.193045	−	0.981190i	$-0.561836\pi$
$691$	−22.3655	−	5.99281i	−0.850822	−	0.227977i	−0.657777	+	0.753213i	$0.728503\pi$
$692$	0.309310	+	0.178580i	0.0117582	+	0.00678861i
$693$	8.17298	+	4.48175i	0.310466	+	0.170247i
$694$	8.41258	+	8.41258i	0.319337	+	0.319337i
$695$	8.63976	+	8.63976i	0.327725	+	0.327725i
$696$	−5.43056	+	1.45511i	−0.205845	+	0.0551560i
$697$	4.53231	+	1.21443i	0.171674	+	0.0459998i
$698$		−	33.8882i		−	1.28269i
$699$	9.25613	−	16.0321i	0.350099	−	0.606389i
$700$	3.42856	+	11.7542i	0.129588	+	0.444267i
$701$			17.2532i			0.651646i	0.945431	+	0.325823i	$0.105641\pi$
$701$			17.2532i			0.651646i	−0.945431	+	0.325823i	$0.894359\pi$
$702$	−1.96625	+	3.02223i	−0.0742114	+	0.114067i
$703$	−3.60202	+	2.07963i	−0.135853	+	0.0784346i
$704$	−2.49118	−	2.49118i	−0.0938899	−	0.0938899i
$705$	2.41774	−	1.39589i	0.0910575	−	0.0525721i
$706$	−3.93636	−	6.81797i	−0.148147	−	0.256598i
$707$	−8.24422	−	28.2638i	−0.310056	−	1.06297i
$708$	2.49875	−	9.32547i	0.0939088	−	0.350472i
$709$	0.580403	−	0.580403i	0.0217975	−	0.0217975i	−0.696124	−	0.717922i	$-0.745094\pi$
$709$	0.580403	−	0.580403i	0.0217975	−	0.0217975i	0.717922	+	0.696124i	$0.245094\pi$
$710$	2.09964	−	7.83596i	0.0787981	−	0.294079i
$711$	3.20797	−	5.55637i	0.120308	−	0.208380i
$712$	−7.55046	−	13.0778i	−0.282965	−	0.490110i
$713$	−14.4773	+	3.87919i	−0.542181	+	0.145277i
$714$	1.53525	+	0.841871i	0.0574552	+	0.0315062i
$715$	5.76332	−	5.18060i	0.215536	−	0.193743i
$716$	1.47023	−	2.54652i	0.0549452	−	0.0951679i
$717$	18.2410	−	18.2410i	0.681222	−	0.681222i
$718$	27.6074			1.03030
$719$	12.2018			0.455049			0.227524	−	0.973772i	$-0.426937\pi$
$719$	12.2018			0.455049			0.227524	+	0.973772i	$0.426937\pi$
$720$	0.431386	−	0.431386i	0.0160768	−	0.0160768i
$721$	8.82731	+	2.15818i	0.328746	+	0.0803747i
$722$	15.0754	+	4.03943i	0.561047	+	0.150332i
$723$	1.57048	+	5.86111i	0.0584067	+	0.217977i
$724$	2.66751	+	1.54009i	0.0991373	+	0.0572369i
$725$		−	26.0182i		−	0.966290i
$726$	0.365442	−	1.36385i	0.0135628	−	0.0506171i
$727$	26.9918			1.00107			0.500535	−	0.865716i	$-0.333137\pi$
$727$	26.9918			1.00107			0.500535	+	0.865716i	$0.333137\pi$
$728$	6.95239	−	6.53179i	0.257673	−	0.242084i
$729$	−1.00000			−0.0370370
$730$	−0.664419	+	2.47964i	−0.0245912	+	0.0917758i
$731$		−	5.28416i		−	0.195442i
$732$	11.3835	+	6.57224i	0.420745	+	0.242917i
$733$	−6.41419	−	23.9381i	−0.236914	−	0.884173i	−0.977277	−	0.211967i	$-0.932013\pi$
$733$	−6.41419	−	23.9381i	−0.236914	−	0.884173i	0.740363	−	0.672207i	$-0.234653\pi$
$734$	−3.31756	−	0.888938i	−0.122453	−	0.0328113i
$735$	2.88386	−	3.14969i	0.106373	−	0.116178i
$736$	4.69764	−	4.69764i	0.173157	−	0.173157i
$737$	−50.4275			−1.85752
$738$	7.09019			0.260993
$739$	32.6725	−	32.6725i	1.20188	−	1.20188i	0.228282	−	0.973595i	$-0.426689\pi$
$739$	32.6725	−	32.6725i	1.20188	−	1.20188i	0.973595	−	0.228282i	$-0.0733108\pi$
$740$	0.688788	−	1.19302i	0.0253203	−	0.0438561i
$741$	−5.91996	+	3.01013i	−0.217475	+	0.110580i
$742$	−14.4134	−	23.7420i	−0.529133	−	0.871595i
$743$	21.9692	−	5.88663i	0.805972	−	0.215959i	0.167767	−	0.985827i	$-0.446344\pi$
$743$	21.9692	−	5.88663i	0.805972	−	0.215959i	0.638204	+	0.769867i	$0.279678\pi$
$744$	1.12803	+	1.95380i	0.0413555	+	0.0716298i
$745$	−5.20341	+	9.01257i	−0.190638	+	0.330195i
$746$	3.06749	−	11.4480i	0.112309	−	0.419142i
$747$	5.17053	−	5.17053i	0.189180	−	0.189180i
$748$	0.603441	−	2.25207i	0.0220640	−	0.0823439i
$749$	−20.2463	+	21.1579i	−0.739783	+	0.773094i
$750$	2.93683	+	5.08674i	0.107238	+	0.185741i
$751$	−27.6318	+	15.9532i	−1.00830	+	0.582141i	−0.910693	−	0.413085i	$-0.864451\pi$
$751$	−27.6318	+	15.9532i	−1.00830	+	0.582141i	−0.0976045	+	0.995225i	$0.531118\pi$
$752$	−3.23582	−	3.23582i	−0.117998	−	0.117998i
$753$	−2.73660	+	1.57998i	−0.0997272	+	0.0575775i
$754$	−18.0692	+	9.18768i	−0.658041	+	0.334595i
$755$		−	2.65658i		−	0.0966829i
$756$	2.57005	+	0.628349i	0.0934720	+	0.0228528i
$757$	−23.5249	+	40.7463i	−0.855028	+	1.48095i	0.0215919	+	0.999767i	$0.493127\pi$
$757$	−23.5249	+	40.7463i	−0.855028	+	1.48095i	−0.876619	+	0.481184i	$0.840207\pi$
$758$		−	19.7819i		−	0.718513i
$759$	22.6078	+	6.05775i	0.820613	+	0.219883i
$760$	1.08544	−	0.290843i	0.0393730	−	0.0105500i
$761$	−23.1632	−	23.1632i	−0.839666	−	0.839666i	0.149148	−	0.988815i	$-0.452347\pi$
$761$	−23.1632	−	23.1632i	−0.839666	−	0.839666i	−0.988815	+	0.149148i	$0.952347\pi$
$762$	3.20496	+	3.20496i	0.116104	+	0.116104i
$763$	23.3181	−	0.513422i	0.844172	−	0.0185871i
$764$	−1.12127	−	0.647368i	−0.0405663	−	0.0234210i
$765$	0.389981	+	0.104495i	0.0140998	+	0.00377802i
$766$	8.62862	+	14.9452i	0.311765	+	0.539992i
$767$	1.85087	−	34.7603i	0.0668309	−	1.25512i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−7.72927	−	28.8460i	−0.278725	−	1.04021i	−0.953304	−	0.302012i	$-0.902342\pi$
$769$	−7.72927	−	28.8460i	−0.278725	−	1.04021i	0.674580	−	0.738202i	$-0.264325\pi$
$770$	−4.98611	−	2.73419i	−0.179687	−	0.0985333i
$771$	−3.11699	+	1.79960i	−0.112256	+	0.0648109i
$772$	−8.36542	+	2.24151i	−0.301078	+	0.0806736i
$773$	7.27081	+	27.1350i	0.261513	+	0.975979i	0.964350	+	0.264629i	$0.0852494\pi$
$773$	7.27081	+	27.1350i	0.261513	+	0.975979i	−0.702838	+	0.711350i	$0.748084\pi$
$774$	−2.06659	−	7.71261i	−0.0742820	−	0.277224i
$775$	−10.0848	+	2.70223i	−0.362258	+	0.0970669i
$776$	3.09178	−	1.78504i	0.110988	−	0.0640792i
$777$	5.97280	−	0.131510i	0.214273	−	0.00471790i
$778$	0.891042	+	3.32542i	0.0319454	+	0.119222i
$779$	11.3102	+	6.52993i	0.405229	+	0.233959i
$780$	1.19956	−	1.84377i	0.0429510	−	0.0660177i
$781$	−23.4238	−	40.5713i	−0.838170	−	1.45175i
$782$	4.24675	+	1.13791i	0.151864	+	0.0406917i
$783$	−4.86891	−	2.81107i	−0.174001	−	0.100459i
$784$	−6.21036	−	3.22978i	−0.221798	−	0.115349i
$785$	−5.63269	−	5.63269i	−0.201039	−	0.201039i
$786$	6.46061	+	6.46061i	0.230442	+	0.230442i
$787$	27.0027	−	7.23535i	0.962542	−	0.257912i	0.256866	−	0.966447i	$-0.417310\pi$
$787$	27.0027	−	7.23535i	0.962542	−	0.257912i	0.705676	+	0.708535i	$0.250643\pi$
$788$	2.64884	+	0.709754i	0.0943609	+	0.0252839i
$789$			14.0187i			0.499080i
$790$	−1.95709	+	3.38979i	−0.0696303	+	0.120603i
$791$	11.1590	−	11.6615i	0.396768	−	0.414633i
$792$		−	3.52306i		−	0.125187i
$793$	45.0613	+	14.6830i	1.60017	+	0.521408i
$794$	29.1516	−	16.8307i	1.03455	−	0.597298i
$795$	−4.52861	−	4.52861i	−0.160613	−	0.160613i
$796$	18.2954	−	10.5628i	0.648463	−	0.374390i
$797$	7.24475	+	12.5483i	0.256622	+	0.444483i	0.965335	−	0.261015i	$-0.0840571\pi$
$797$	7.24475	+	12.5483i	0.256622	+	0.444483i	−0.708713	+	0.705497i	$0.750724\pi$
$798$	3.52102	+	3.36931i	0.124643	+	0.119272i
$799$	0.783814	−	2.92523i	0.0277294	−	0.103487i
$800$	3.27236	−	3.27236i	0.115695	−	0.115695i
$801$	3.90841	−	14.5864i	0.138097	−	0.515384i
$802$	10.6580	−	18.4602i	0.376346	−	0.651851i
$803$	7.41233	+	12.8385i	0.261575	+	0.453062i
$804$	−13.8258	+	3.70462i	−0.487600	+	0.130652i
$805$	5.15589	−	9.40235i	0.181721	−	0.331389i
$806$	5.43787	+	6.04953i	0.191541	+	0.213086i
$807$	5.11073	−	8.85205i	0.179906	−	0.311607i
$808$	−7.86861	+	7.86861i	−0.276817	+	0.276817i
$809$	23.8796			0.839561			0.419780	−	0.907626i	$-0.362107\pi$
$809$	23.8796			0.839561			0.419780	+	0.907626i	$0.362107\pi$
$810$	0.610072			0.0214357
$811$	−21.0744	+	21.0744i	−0.740023	+	0.740023i	−0.972582	−	0.232559i	$-0.925290\pi$
$811$	−21.0744	+	21.0744i	−0.740023	+	0.740023i	0.232559	+	0.972582i	$0.425290\pi$
$812$	10.7470	+	10.2840i	0.377147	+	0.360896i
$813$	−11.6576	−	3.12364i	−0.408850	−	0.109551i
$814$	−2.05897	−	7.68420i	−0.0721670	−	0.269331i
$815$	9.62386	+	5.55634i	0.337109	+	0.194630i
$816$		−	0.661787i		−	0.0231672i
$817$	3.80658	−	14.2063i	0.133175	−	0.497017i
$818$	7.52875			0.263237
$819$	9.53475	+	0.297406i	0.333171	+	0.0103922i
$820$	−4.32552			−0.151054
$821$	−9.71318	+	36.2501i	−0.338992	+	1.26514i	0.560483	+	0.828166i	$0.310615\pi$
$821$	−9.71318	+	36.2501i	−0.338992	+	1.26514i	−0.899476	+	0.436971i	$0.856051\pi$
$822$			12.1524i			0.423862i
$823$	−5.68947	−	3.28482i	−0.198322	−	0.114502i	0.397550	−	0.917580i	$-0.369860\pi$
$823$	−5.68947	−	3.28482i	−0.198322	−	0.114502i	−0.595873	+	0.803079i	$0.703194\pi$
$824$	−0.888960	−	3.31764i	−0.0309684	−	0.115576i
$825$	15.7485	+	4.21980i	0.548293	+	0.146915i
$826$	−24.5214	+	7.15259i	−0.853207	+	0.248870i
$827$	11.7624	−	11.7624i	0.409019	−	0.409019i	−0.472377	−	0.881396i	$-0.656604\pi$
$827$	11.7624	−	11.7624i	0.409019	−	0.409019i	0.881396	+	0.472377i	$0.156604\pi$
$828$	6.64347			0.230877
$829$	−43.7211			−1.51850			−0.759248	−	0.650802i	$-0.774433\pi$
$829$	−43.7211			−1.51850			−0.759248	+	0.650802i	$0.774433\pi$
$830$	−3.15440	+	3.15440i	−0.109491	+	0.109491i
$831$	11.3874	−	19.7235i	0.395023	−	0.684200i
$832$	−3.42815	−	1.11704i	−0.118850	−	0.0387265i
$833$	−0.203900	−	4.62802i	−0.00706471	−	0.160351i
$834$	19.3455	−	5.18361i	0.669879	−	0.179494i
$835$	3.84527	+	6.66019i	0.133071	+	0.230486i
$836$	3.24467	−	5.61994i	0.112219	−	0.194370i
$837$	−0.583910	+	2.17918i	−0.0201829	+	0.0753236i
$838$	−5.38601	+	5.38601i	−0.186057	+	0.186057i
$839$	−13.9925	+	52.2207i	−0.483075	+	1.80286i	0.105502	+	0.994419i	$0.466355\pi$
$839$	−13.9925	+	52.2207i	−0.483075	+	1.80286i	−0.588577	+	0.808441i	$0.700312\pi$
$840$	−1.56792	−	0.383338i	−0.0540983	−	0.0132264i
$841$	−1.30418	−	2.25890i	−0.0449717	−	0.0778932i
$842$	16.3174	−	9.42084i	0.562334	−	0.324664i
$843$	−11.4925	−	11.4925i	−0.395822	−	0.395822i
$844$	−2.47853	+	1.43098i	−0.0853147	+	0.0492565i
$845$	2.85457	−	7.39940i	0.0982003	−	0.254547i
$846$		−	4.57613i		−	0.157331i
$847$	−3.58624	+	1.04606i	−0.123225	+	0.0359432i
$848$	−5.24890	+	9.09137i	−0.180248	+	0.312199i
$849$		−	31.0086i		−	1.06421i
$850$	2.95827	+	0.792666i	0.101468	+	0.0271882i
$851$	14.4902	−	3.88263i	0.496717	−	0.133095i
$852$	−9.40270	−	9.40270i	−0.322131	−	0.322131i
$853$	−36.5229	−	36.5229i	−1.25052	−	1.25052i	−0.955487	−	0.295034i	$-0.904669\pi$
$853$	−36.5229	−	36.5229i	−1.25052	−	1.25052i	−0.295034	−	0.955487i	$-0.595331\pi$
$854$	−0.765540	−	34.7686i	−0.0261963	−	1.18976i
$855$	0.973179	+	0.561865i	0.0332820	+	0.0192154i
$856$	10.6913	+	2.86472i	0.365420	+	0.0979141i
$857$	−9.54044	−	16.5245i	−0.325895	−	0.564467i	0.655798	−	0.754936i	$-0.272332\pi$
$857$	−9.54044	−	16.5245i	−0.325895	−	0.564467i	−0.981693	+	0.190469i	$0.938999\pi$
$858$	−2.63062	−	12.4272i	−0.0898079	−	0.424258i
$859$	−29.7637	−	17.1841i	−1.01552	−	0.586312i	−0.102719	−	0.994710i	$-0.532754\pi$
$859$	−29.7637	−	17.1841i	−1.01552	−	0.586312i	−0.912804	+	0.408398i	$0.866088\pi$
$860$	1.26077	+	4.70525i	0.0429918	+	0.160448i
$861$	−9.73478	−	16.0353i	−0.331760	−	0.546480i
$862$	−1.33526	+	0.770911i	−0.0454791	+	0.0262573i
$863$	−35.4725	+	9.50484i	−1.20750	+	0.323548i	−0.805780	−	0.592214i	$-0.798254\pi$
$863$	−35.4725	+	9.50484i	−1.20750	+	0.323548i	−0.401719	+	0.915763i	$0.631587\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−0.0563951	−	0.210469i	−0.00191749	−	0.00715617i
$866$	34.2921	−	9.18853i	1.16529	−	0.312239i
$867$	−14.3431	+	8.28102i	−0.487119	+	0.281238i
$868$	2.86997	−	5.23372i	0.0974131	−	0.177644i
$869$	5.85029	+	21.8336i	0.198457	+	0.740653i
$870$	2.97038	+	1.71495i	0.100705	+	0.0581423i
$871$	−46.0029	+	23.3912i	−1.55875	+	0.792580i
$872$	−4.40778	−	7.63449i	−0.149266	−	0.258537i
$873$	3.44843	+	0.924004i	0.116712	+	0.0312728i
$874$	10.5976	+	6.11852i	0.358469	+	0.206962i
$875$	7.47198	−	13.6260i	0.252599	−	0.460644i
$876$	2.97543	+	2.97543i	0.100530	+	0.100530i
$877$	−11.5991	−	11.5991i	−0.391673	−	0.391673i	0.483610	−	0.875283i	$-0.339325\pi$
$877$	−11.5991	−	11.5991i	−0.391673	−	0.391673i	−0.875283	+	0.483610i	$0.839325\pi$
$878$	27.5937	−	7.39371i	0.931243	−	0.249526i
$879$	20.1476	+	5.39854i	0.679562	+	0.182088i
$880$			2.14932i			0.0724536i
$881$	29.0728	−	50.3556i	0.979489	−	1.69652i	0.315240	−	0.949012i	$-0.397915\pi$
$881$	29.0728	−	50.3556i	0.979489	−	1.69652i	0.664248	−	0.747512i	$-0.268752\pi$
$882$	−2.10758	−	6.67518i	−0.0709660	−	0.224765i
$883$			44.4751i			1.49671i	0.663300	+	0.748354i	$0.269155\pi$
$883$			44.4751i			1.49671i	−0.663300	+	0.748354i	$0.730845\pi$
$884$	−0.494147	−	2.33438i	−0.0166200	−	0.0785137i
$885$	−5.10080	+	2.94495i	−0.171462	+	0.0989934i
$886$	8.10812	+	8.10812i	0.272398	+	0.272398i
$887$	29.4888	−	17.0254i	0.990137	−	0.571656i	0.0848218	−	0.996396i	$-0.472968\pi$
$887$	29.4888	−	17.0254i	0.990137	−	0.571656i	0.905315	+	0.424740i	$0.139635\pi$
$888$	−1.12903	−	1.95553i	−0.0378877	−	0.0656234i
$889$	2.84799	−	11.6488i	0.0955186	−	0.390687i
$890$	−2.38441	+	8.89873i	−0.0799255	+	0.298286i
$891$	2.49118	−	2.49118i	0.0834577	−	0.0834577i
$892$	1.55649	−	5.80890i	0.0521152	−	0.194496i
$893$	4.21454	−	7.29979i	0.141034	−	0.244278i
$894$	8.52917	+	14.7730i	0.285258	+	0.494082i
$895$	−1.73277	+	0.464295i	−0.0579202	+	0.0155197i
$896$	0.0582404	+	2.64511i	0.00194568	+	0.0883669i
$897$	23.4341	−	4.96059i	0.782442	−	0.165629i
$898$	−0.495976	+	0.859056i	−0.0165509	+	0.0286671i
$899$	−8.96883	+	8.96883i	−0.299127	+	0.299127i
$900$	4.62781			0.154260
$901$	−6.94731			−0.231449
$902$	−17.6629	+	17.6629i	−0.588112	+	0.588112i
$903$	−14.6055	+	15.2632i	−0.486041	+	0.507927i
$904$	−5.89263	−	1.57892i	−0.195986	−	0.0525143i
$905$	−0.486354	−	1.81510i	−0.0161670	−	0.0603360i
$906$	−3.77114	−	2.17727i	−0.125288	−	0.0723350i
$907$		−	43.7604i		−	1.45304i	−0.687145	−	0.726520i	$-0.741136\pi$
$907$		−	43.7604i		−	1.45304i	0.687145	−	0.726520i	$-0.258864\pi$
$908$	−0.859219	+	3.20665i	−0.0285142	+	0.106416i
$909$	−11.1279			−0.369089
$910$	−5.81688	−	0.181439i	−0.192828	−	0.00601465i
$911$	55.9543			1.85385			0.926925	−	0.375247i	$-0.122442\pi$
$911$	55.9543			1.85385			0.926925	+	0.375247i	$0.122442\pi$
$912$	0.476735	−	1.77920i	0.0157863	−	0.0589152i
$913$			25.7615i			0.852580i
$914$	−22.5387	−	13.0127i	−0.745512	−	0.430422i
$915$	−2.07549	−	7.74584i	−0.0686136	−	0.256069i
$916$	−18.6978	−	5.01006i	−0.617793	−	0.165537i
$917$	5.74103	−	23.4818i	0.189585	−	0.775437i
$918$	0.467954	−	0.467954i	0.0154448	−	0.0154448i
$919$	−12.0759			−0.398346			−0.199173	−	0.979964i	$-0.563826\pi$
$919$	−12.0759			−0.398346			−0.199173	+	0.979964i	$0.563826\pi$
$920$	−4.05300			−0.133623
$921$	15.6514	−	15.6514i	0.515730	−	0.515730i
$922$	−10.0818	+	17.4622i	−0.332026	+	0.575086i
$923$	−40.1878	−	26.1461i	−1.32280	−	0.860610i
$924$	−7.96780	+	4.83714i	−0.262121	+	0.159130i
$925$	10.0938	−	2.70462i	0.331882	−	0.0889274i
$926$	10.2815	+	17.8081i	0.337871	+	0.585211i
$927$	1.71734	−	2.97452i	0.0564048	−	0.0976960i
$928$	1.45511	−	5.43056i	0.0477665	−	0.178267i
$929$	−28.5736	+	28.5736i	−0.937469	+	0.937469i	−0.998157	−	0.0606874i	$-0.980671\pi$
$929$	−28.5736	+	28.5736i	−0.937469	+	0.937469i	0.0606874	+	0.998157i	$0.480671\pi$
$930$	0.356227	−	1.32946i	0.0116811	−	0.0435946i
$931$	2.78573	−	12.5892i	0.0912987	−	0.412595i
$932$	9.25613	+	16.0321i	0.303195	+	0.525148i
$933$	−5.42356	+	3.13129i	−0.177559	+	0.102514i
$934$	−20.0562	−	20.0562i	−0.656257	−	0.656257i
$935$	−1.23183	+	0.711196i	−0.0402851	+	0.0232586i
$936$	−1.63420	−	3.21394i	−0.0534154	−	0.105051i
$937$		−	34.9997i		−	1.14339i	−0.820466	−	0.571696i	$-0.806286\pi$
$937$		−	34.9997i		−	1.14339i	0.820466	−	0.571696i	$-0.193714\pi$
$938$	27.3612	+	26.1823i	0.893374	+	0.854881i
$939$	−1.17161	+	2.02929i	−0.0382342	+	0.0662235i
$940$			2.79177i			0.0910575i
$941$	43.9533	+	11.7772i	1.43284	+	0.383927i	0.890019	−	0.455924i	$-0.150691\pi$
$941$	43.9533	+	11.7772i	1.43284	+	0.383927i	0.542817	+	0.839851i	$0.317358\pi$
$942$	−12.6123	+	3.37945i	−0.410930	+	0.110108i
$943$	−33.3072	−	33.3072i	−1.08463	−	1.08463i
$944$	6.82671	+	6.82671i	0.222191	+	0.222191i
$945$	−0.837624	−	1.37975i	−0.0272479	−	0.0448831i
$946$	24.3617	+	14.0653i	0.792069	+	0.457301i
$947$	−53.9110	−	14.4454i	−1.75187	−	0.469413i	−0.766849	−	0.641828i	$-0.778176\pi$
$947$	−53.9110	−	14.4454i	−1.75187	−	0.469413i	−0.985024	+	0.172415i	$0.944843\pi$
$948$	3.20797	+	5.55637i	0.104190	+	0.180463i
$949$	12.7172	+	8.27378i	0.412818	+	0.268578i
$950$	7.38223	+	4.26213i	0.239511	+	0.138282i
$951$	6.82959	+	25.4884i	0.221464	+	0.826517i
$952$	−1.49671	+	0.908629i	−0.0485085	+	0.0294488i
$953$	−42.5001	+	24.5375i	−1.37671	+	0.794846i	−0.991762	−	0.128091i	$-0.959115\pi$
$953$	−42.5001	+	24.5375i	−1.37671	+	0.794846i	−0.384951	+	0.922937i	$0.625782\pi$
$954$	−10.1401	+	2.71703i	−0.328298	+	0.0879672i
$955$	0.204437	+	0.762968i	0.00661541	+	0.0246891i
$956$	6.67666	+	24.9176i	0.215939	+	0.805894i
$957$	19.1322	−	5.12646i	0.618456	−	0.165715i
$958$	2.61341	−	1.50885i	0.0844355	−	0.0487489i
$959$	27.4839	−	16.6851i	0.887502	−	0.538790i
$960$	0.157898	+	0.589284i	0.00509614	+	0.0190191i
$961$	−22.4389	−	12.9551i	−0.723836	−	0.417907i
$962$	−5.44269	−	6.05489i	−0.175479	−	0.195218i
$963$	5.53421	+	9.58554i	0.178337	+	0.308890i
$964$	−5.86111	−	1.57048i	−0.188774	−	0.0505817i
$965$	4.57568	+	2.64177i	0.147296	+	0.0850416i
$966$	−9.12144	−	15.0250i	−0.293478	−	0.483420i
$967$	−17.4774	−	17.4774i	−0.562035	−	0.562035i	0.367850	−	0.929885i	$-0.380094\pi$
$967$	−17.4774	−	17.4774i	−0.562035	−	0.562035i	−0.929885	+	0.367850i	$0.880094\pi$
$968$	0.998405	+	0.998405i	0.0320900	+	0.0320900i
$969$	1.17745	−	0.315497i	0.0378252	−	0.0101352i
$970$	−2.10379	−	0.563709i	−0.0675486	−	0.0180996i
$971$		−	24.2060i		−	0.776806i	−0.921490	−	0.388403i	$-0.873027\pi$
$971$		−	24.2060i		−	0.776806i	0.921490	−	0.388403i	$-0.126973\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−38.2845	−	36.6349i	−1.22735	−	1.17446i
$974$		−	13.2995i		−	0.426142i
$975$	16.3241	−	3.45552i	0.522789	−	0.110665i
$976$	−11.3835	+	6.57224i	−0.364376	+	0.210372i
$977$	−14.1333	−	14.1333i	−0.452165	−	0.452165i	0.443908	−	0.896072i	$-0.353592\pi$
$977$	−14.1333	−	14.1333i	−0.452165	−	0.452165i	−0.896072	+	0.443908i	$0.853592\pi$
$978$	15.7750	−	9.10768i	0.504428	−	0.291231i
$979$	26.6007	+	46.0738i	0.850163	+	1.47253i
$980$	1.28578	+	4.07234i	0.0410727	+	0.130086i
$981$	2.28163	−	8.51517i	0.0728469	−	0.271868i
$982$	31.1859	−	31.1859i	0.995182	−	0.995182i
$983$	−7.62325	+	28.4504i	−0.243144	+	0.907426i	0.731163	+	0.682203i	$0.238978\pi$
$983$	−7.62325	+	28.4504i	−0.243144	+	0.907426i	−0.974307	+	0.225223i	$0.927689\pi$
$984$	−3.54509	+	6.14028i	−0.113013	+	0.195745i
$985$	−0.836493	−	1.44885i	−0.0266529	−	0.0461642i
$986$	3.59387	−	0.962976i	0.114452	−	0.0306674i
$987$	−10.3494	+	6.28300i	−0.329426	+	0.199990i
$988$	0.353126	−	6.63190i	0.0112344	−	0.210989i
$989$	−26.5230	+	45.9392i	−0.843383	+	1.46078i
$990$	−1.51980	+	1.51980i	−0.0483024	+	0.0483024i
$991$	7.20356			0.228829			0.114414	−	0.993433i	$-0.463501\pi$
$991$	7.20356			0.228829			0.114414	+	0.993433i	$0.463501\pi$
$992$	−2.25606			−0.0716298
$993$	7.90709	−	7.90709i	0.250924	−	0.250924i
$994$	−8.35543	+	34.1751i	−0.265018	+	1.08397i
$995$	−12.4490	−	3.33571i	−0.394661	−	0.105749i
$996$	1.89255	+	7.06308i	0.0599676	+	0.223802i
$997$	−4.40492	−	2.54318i	−0.139505	−	0.0805434i	0.428623	−	0.903483i	$-0.358999\pi$
$997$	−4.40492	−	2.54318i	−0.139505	−	0.0805434i	−0.568128	+	0.822940i	$0.692332\pi$
$998$			14.8529i			0.470159i
$999$	0.584428	−	2.18111i	0.0184905	−	0.0690074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.9	✓	40
7.3	odd	6		546.2.cg.b.241.9	yes	40
13.2	odd	12		546.2.cg.b.145.9	yes	40
91.80	even	12	inner	546.2.by.b.535.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.9	✓	40	1.1	even	1	trivial
546.2.by.b.535.9	yes	40	91.80	even	12	inner
546.2.cg.b.145.9	yes	40	13.2	odd	12
546.2.cg.b.241.9	yes	40	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.157898 + 0.589284i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-0.740861 - 2.53991i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.157898 + 0.589284i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-0.740861 - 2.53991i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +0.610072 q^{10} +(2.49118 - 2.49118i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.11704 - 3.42815i) q^{13} +(-2.64511 + 0.0582404i) q^{14} +(-0.589284 + 0.157898i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.330893 + 0.573124i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-1.30246 + 1.30246i) q^{19} +(0.157898 - 0.589284i) q^{20} +(2.53991 - 0.740861i) q^{21} +(-1.76153 - 3.05106i) q^{22} +(5.75342 - 3.32174i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.00780 - 2.31391i) q^{25} +(-3.02223 - 1.96625i) q^{26} -1.00000i q^{27} +(-0.628349 + 2.57005i) q^{28} +(2.81107 - 4.86891i) q^{29} +0.610072i q^{30} +(-2.17918 - 0.583910i) q^{31} +(0.965926 - 0.258819i) q^{32} +(2.49118 + 2.49118i) q^{33} +(0.467954 + 0.467954i) q^{34} +(1.37975 - 0.837624i) q^{35} +(0.866025 + 0.500000i) q^{36} +(2.18111 + 0.584428i) q^{37} +(0.920982 + 1.59519i) q^{38} +(3.42815 + 1.11704i) q^{39} +(-0.528338 - 0.305036i) q^{40} +(-1.83508 - 6.84860i) q^{41} +(-0.0582404 - 2.64511i) q^{42} +(-6.91494 + 3.99234i) q^{43} +(-3.40302 + 0.911835i) q^{44} +(-0.157898 - 0.589284i) q^{45} +(-1.71946 - 6.41710i) q^{46} +(-4.42021 + 1.18439i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.90225 + 3.76343i) q^{49} +(-1.19777 - 4.47012i) q^{50} +(-0.573124 - 0.330893i) q^{51} +(-2.68146 + 2.41034i) q^{52} +(5.24890 + 9.09137i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(1.86137 + 1.07466i) q^{55} +(2.31985 + 1.27212i) q^{56} +(-1.30246 - 1.30246i) q^{57} +(-3.97545 - 3.97545i) q^{58} +(9.32547 - 2.49875i) q^{59} +(0.589284 + 0.157898i) q^{60} +13.1445i q^{61} +(-1.12803 + 1.95380i) q^{62} +(0.740861 + 2.53991i) q^{63} -1.00000i q^{64} +(2.19653 + 0.116958i) q^{65} +(3.05106 - 1.76153i) q^{66} +(-10.1212 - 10.1212i) q^{67} +(0.573124 - 0.330893i) q^{68} +(3.32174 + 5.75342i) q^{69} +(-0.451978 - 1.54953i) q^{70} +(3.44163 - 12.8443i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-1.08908 + 4.06451i) q^{73} +(1.12903 - 1.95553i) q^{74} +(2.31391 + 4.00780i) q^{75} +(1.77920 - 0.476735i) q^{76} +(-8.17298 - 4.48175i) q^{77} +(1.96625 - 3.02223i) q^{78} +(-3.20797 + 5.55637i) q^{79} +(-0.431386 + 0.431386i) q^{80} +1.00000 q^{81} -7.09019 q^{82} +(-5.17053 + 5.17053i) q^{83} +(-2.57005 - 0.628349i) q^{84} +(-0.389981 - 0.104495i) q^{85} +(2.06659 + 7.71261i) q^{86} +(4.86891 + 2.81107i) q^{87} +3.52306i q^{88} +(-3.90841 + 14.5864i) q^{89} -0.610072 q^{90} +(-9.53475 - 0.297406i) q^{91} -6.64347 q^{92} +(0.583910 - 2.17918i) q^{93} +4.57613i q^{94} +(-0.973179 - 0.561865i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-3.44843 - 0.924004i) q^{97} +(2.10758 + 6.67518i) q^{98} +(-2.49118 + 2.49118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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