LMFDB - Embedded newform 507.2.t.b.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38591 + 0.0558504i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-0.0758757 + 0.00612532i) q^{4} +(-1.08360 + 0.410955i) q^{5} +(0.439231 + 1.31566i) q^{6} +(-0.389218 + 0.913528i) q^{7} +(2.85867 - 0.347105i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(-1.38591 + 0.0558504i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-0.0758757 + 0.00612532i) q^{4} +(-1.08360 + 0.410955i) q^{5} +(0.439231 + 1.31566i) q^{6} +(-0.389218 + 0.913528i) q^{7} +(2.85867 - 0.347105i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(1.47882 - 0.630068i) q^{10} +(1.94766 - 3.07997i) q^{11} +(0.0269934 + 0.0711758i) q^{12} +(3.40592 + 1.18311i) q^{13} +(0.488402 - 1.28781i) q^{14} +(0.696206 + 0.926482i) q^{15} +(-3.79221 + 0.616294i) q^{16} +(-4.47322 - 1.90586i) q^{17} +(1.14151 - 0.787928i) q^{18} +(-3.01875 - 1.74288i) q^{19} +(0.0797016 - 0.0378189i) q^{20} +(0.985747 + 0.119691i) q^{21} +(-2.52727 + 4.37736i) q^{22} +(-2.61738 - 4.53344i) q^{23} +(-1.12873 - 2.64923i) q^{24} +(-2.73725 + 2.42499i) q^{25} +(-4.78638 - 1.44946i) q^{26} +(0.748511 + 0.663123i) q^{27} +(0.0239365 - 0.0716986i) q^{28} +(0.0493053 + 1.22350i) q^{29} +(-1.01663 - 1.24514i) q^{30} +(-4.88945 + 5.51904i) q^{31} +(-0.421679 + 0.0860864i) q^{32} +(-3.50024 - 1.01386i) q^{33} +(6.30594 + 2.39153i) q^{34} +(0.0463374 - 1.14985i) q^{35} +(0.0608556 - 0.0457300i) q^{36} +(-2.26111 - 0.461609i) q^{37} +(4.28108 + 2.24688i) q^{38} +(0.188810 - 3.60060i) q^{39} +(-2.95501 + 1.55091i) q^{40} +(-3.65572 + 1.05889i) q^{41} +(-1.37285 - 0.110828i) q^{42} +(0.850111 + 4.16412i) q^{43} +(-0.128914 + 0.245625i) q^{44} +(0.696206 - 0.926482i) q^{45} +(3.88066 + 6.13678i) q^{46} +(-10.5658 - 7.29305i) q^{47} +(1.64702 + 3.47102i) q^{48} +(4.16603 + 4.33729i) q^{49} +(3.65816 - 3.51371i) q^{50} +(-0.586086 + 4.82685i) q^{51} +(-0.265673 - 0.0689066i) q^{52} +(0.163967 + 1.35039i) q^{53} +(-1.07441 - 0.877226i) q^{54} +(-0.844750 + 4.13786i) q^{55} +(-0.795554 + 2.74657i) q^{56} +(-0.834196 + 3.38447i) q^{57} +(-0.136666 - 1.69291i) q^{58} +(1.11874 - 6.88387i) q^{59} +(-0.0585001 - 0.0660330i) q^{60} +(-12.0921 - 9.08662i) q^{61} +(6.46811 - 7.92200i) q^{62} +(-0.159286 - 0.980128i) q^{63} +(8.04024 - 1.98174i) q^{64} +(-4.17685 + 0.117665i) q^{65} +(4.90766 + 1.20963i) q^{66} +(-0.176479 + 2.18608i) q^{67} +(0.351082 + 0.117209i) q^{68} +(-3.62625 + 3.77533i) q^{69} +1.59618i q^{70} +(-8.03953 - 7.72207i) q^{71} +(-2.23060 + 1.82123i) q^{72} +(-3.63959 - 6.93466i) q^{73} +(3.15949 + 0.513467i) q^{74} +(3.09080 + 1.95450i) q^{75} +(0.239726 + 0.113751i) q^{76} +(2.05558 + 2.97802i) q^{77} +(-0.0605786 + 5.00067i) q^{78} +(4.09628 - 5.93448i) q^{79} +(3.85597 - 2.22624i) q^{80} +(0.428693 - 0.903450i) q^{81} +(5.00738 - 1.67171i) q^{82} +(-0.464489 - 1.88451i) q^{83} +(-0.0755274 - 0.00304365i) q^{84} +(5.63040 + 0.226898i) q^{85} +(-1.41075 - 5.72363i) q^{86} +(1.16147 - 0.387757i) q^{87} +(4.49863 - 9.48066i) q^{88} +(0.800318 - 0.462064i) q^{89} +(-0.913138 + 1.32291i) q^{90} +(-2.40644 + 2.65091i) q^{91} +(0.226364 + 0.327946i) q^{92} +(6.66147 + 3.16091i) q^{93} +(15.0506 + 9.51744i) q^{94} +(3.98737 + 0.648010i) q^{95} +(0.200006 + 0.381080i) q^{96} +(-5.97605 + 4.87929i) q^{97} +(-6.01600 - 5.77844i) q^{98} +3.64412i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38591	+	0.0558504i	−0.979989	+	0.0394922i	−0.525087	−	0.851049i	$-0.675967\pi$
$2$	−1.38591	+	0.0558504i	−0.979989	+	0.0394922i	−0.454903	+	0.890541i	$0.650326\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	−0.0758757	+	0.00612532i	−0.0379378	+	0.00306266i
$5$	−1.08360	+	0.410955i	−0.484601	+	0.183785i	−0.584792	−	0.811183i	$-0.698824\pi$
$5$	−1.08360	+	0.410955i	−0.484601	+	0.183785i	0.100191	+	0.994968i	$0.468055\pi$
$6$	0.439231	+	1.31566i	0.179315	+	0.537115i
$7$	−0.389218	+	0.913528i	−0.147111	+	0.345281i	−0.977191	−	0.212363i	$-0.931884\pi$
$7$	−0.389218	+	0.913528i	−0.147111	+	0.345281i	0.830080	+	0.557644i	$0.188294\pi$
$8$	2.85867	−	0.347105i	1.01069	−	0.122720i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	1.47882	−	0.630068i	0.467645	−	0.199245i
$11$	1.94766	−	3.07997i	0.587241	−	0.928647i	−0.412602	−	0.910911i	$-0.635380\pi$
$11$	1.94766	−	3.07997i	0.587241	−	0.928647i	0.999843	−	0.0177356i	$-0.00564571\pi$
$12$	0.0269934	+	0.0711758i	0.00779233	+	0.0205467i
$13$	3.40592	+	1.18311i	0.944631	+	0.328135i
$13$	3.40592	+	1.18311i	0.944631	+	0.328135i
$14$	0.488402	−	1.28781i	0.130531	−	0.344182i
$15$	0.696206	+	0.926482i	0.179760	+	0.239217i
$16$	−3.79221	+	0.616294i	−0.948052	+	0.154073i
$17$	−4.47322	−	1.90586i	−1.08492	−	0.462239i	−0.225880	−	0.974155i	$-0.572526\pi$
$17$	−4.47322	−	1.90586i	−1.08492	−	0.462239i	−0.859035	+	0.511916i	$0.828936\pi$
$18$	1.14151	−	0.787928i	0.269057	−	0.185716i
$19$	−3.01875	−	1.74288i	−0.692550	−	0.399844i	0.112017	−	0.993706i	$-0.464269\pi$
$19$	−3.01875	−	1.74288i	−0.692550	−	0.399844i	−0.804567	+	0.593863i	$0.797602\pi$
$20$	0.0797016	−	0.0378189i	0.0178218	−	0.00845656i
$21$	0.985747	+	0.119691i	0.215108	+	0.0261188i
$22$	−2.52727	+	4.37736i	−0.538815	+	0.933256i
$23$	−2.61738	−	4.53344i	−0.545762	−	0.945288i	−0.998559	−	0.0536739i	$-0.982907\pi$
$23$	−2.61738	−	4.53344i	−0.545762	−	0.945288i	0.452796	−	0.891614i	$-0.350426\pi$
$24$	−1.12873	−	2.64923i	−0.230401	−	0.540772i
$25$	−2.73725	+	2.42499i	−0.547450	+	0.484998i
$26$	−4.78638	−	1.44946i	−0.938687	−	0.284263i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	0.0239365	−	0.0716986i	0.00452358	−	0.0135498i
$29$	0.0493053	+	1.22350i	0.00915576	+	0.227198i	0.997288	+	0.0735941i	$0.0234469\pi$
$29$	0.0493053	+	1.22350i	0.00915576	+	0.227198i	−0.988133	+	0.153604i	$0.950912\pi$
$30$	−1.01663	−	1.24514i	−0.185610	−	0.227331i
$31$	−4.88945	+	5.51904i	−0.878170	+	0.991249i	−0.999999	−	0.00130179i	$-0.999586\pi$
$31$	−4.88945	+	5.51904i	−0.878170	+	0.991249i	0.121829	+	0.992551i	$0.461124\pi$
$32$	−0.421679	+	0.0860864i	−0.0745431	+	0.0152181i
$33$	−3.50024	−	1.01386i	−0.609314	−	0.176490i
$34$	6.30594	+	2.39153i	1.08146	+	0.410144i
$35$	0.0463374	−	1.14985i	0.00783244	−	0.194360i
$36$	0.0608556	−	0.0457300i	0.0101426	−	0.00762167i
$37$	−2.26111	−	0.461609i	−0.371725	−	0.0758881i	0.0105315	−	0.999945i	$-0.496648\pi$
$37$	−2.26111	−	0.461609i	−0.371725	−	0.0758881i	−0.382256	+	0.924056i	$0.624853\pi$
$38$	4.28108	+	2.24688i	0.694482	+	0.364492i
$39$	0.188810	−	3.60060i	0.0302337	−	0.576558i
$40$	−2.95501	+	1.55091i	−0.467228	+	0.245220i
$41$	−3.65572	+	1.05889i	−0.570928	+	0.165371i	−0.551111	−	0.834432i	$-0.685796\pi$
$41$	−3.65572	+	1.05889i	−0.570928	+	0.165371i	−0.0198177	+	0.999804i	$0.506309\pi$
$42$	−1.37285	−	0.110828i	−0.211835	−	0.0171011i
$43$	0.850111	+	4.16412i	0.129641	+	0.635022i	0.991738	+	0.128280i	$0.0409455\pi$
$43$	0.850111	+	4.16412i	0.129641	+	0.635022i	−0.862097	+	0.506743i	$0.830849\pi$
$44$	−0.128914	+	0.245625i	−0.0194345	+	0.0370294i
$45$	0.696206	−	0.926482i	0.103784	−	0.138112i
$46$	3.88066	+	6.13678i	0.572173	+	0.904819i
$47$	−10.5658	−	7.29305i	−1.54118	−	1.06380i	−0.970039	−	0.242950i	$-0.921885\pi$
$47$	−10.5658	−	7.29305i	−1.54118	−	1.06380i	−0.571143	−	0.820851i	$-0.693500\pi$
$48$	1.64702	+	3.47102i	0.237727	+	0.500999i
$49$	4.16603	+	4.33729i	0.595147	+	0.619613i
$50$	3.65816	−	3.51371i	0.517341	−	0.496913i
$51$	−0.586086	+	4.82685i	−0.0820684	+	0.675894i
$52$	−0.265673	−	0.0689066i	−0.0368422	−	0.00955563i
$53$	0.163967	+	1.35039i	0.0225226	+	0.185490i	0.999628	−	0.0272644i	$-0.00867960\pi$
$53$	0.163967	+	1.35039i	0.0225226	+	0.185490i	−0.977106	+	0.212755i	$0.931757\pi$
$54$	−1.07441	−	0.877226i	−0.146208	−	0.119375i
$55$	−0.844750	+	4.13786i	−0.113906	+	0.557949i
$56$	−0.795554	+	2.74657i	−0.106310	+	0.367026i
$57$	−0.834196	+	3.38447i	−0.110492	+	0.448284i
$58$	−0.136666	−	1.69291i	−0.0179451	−	0.222290i
$59$	1.11874	−	6.88387i	0.145647	−	0.896204i	−0.806649	−	0.591030i	$-0.798721\pi$
$59$	1.11874	−	6.88387i	0.145647	−	0.896204i	0.952297	−	0.305174i	$-0.0987145\pi$
$60$	−0.0585001	−	0.0660330i	−0.00755233	−	0.00852482i
$61$	−12.0921	−	9.08662i	−1.54823	−	1.16342i	−0.924127	−	0.382085i	$-0.875206\pi$
$61$	−12.0921	−	9.08662i	−1.54823	−	1.16342i	−0.624107	−	0.781338i	$-0.714537\pi$
$62$	6.46811	−	7.92200i	0.821451	−	1.00609i
$63$	−0.159286	−	0.980128i	−0.0200682	−	0.123485i
$64$	8.04024	−	1.98174i	1.00503	−	0.247718i
$65$	−4.17685	+	0.117665i	−0.518075	+	0.0145946i
$66$	4.90766	+	1.20963i	0.604091	+	0.148895i
$67$	−0.176479	+	2.18608i	−0.0215603	+	0.267072i	0.976992	+	0.213277i	$0.0684138\pi$
$67$	−0.176479	+	2.18608i	−0.0215603	+	0.267072i	−0.998552	+	0.0537949i	$0.982868\pi$
$68$	0.351082	+	0.117209i	0.0425750	+	0.0142136i
$69$	−3.62625	+	3.77533i	−0.436549	+	0.454496i
$70$			1.59618i			0.190780i
$71$	−8.03953	−	7.72207i	−0.954117	−	0.916442i	0.0424613	−	0.999098i	$-0.486480\pi$
$71$	−8.03953	−	7.72207i	−0.954117	−	0.916442i	−0.996578	+	0.0826565i	$0.973660\pi$
$72$	−2.23060	+	1.82123i	−0.262879	+	0.214634i
$73$	−3.63959	−	6.93466i	−0.425982	−	0.811641i	0.573992	−	0.818861i	$-0.305394\pi$
$73$	−3.63959	−	6.93466i	−0.425982	−	0.811641i	−0.999974	+	0.00722004i	$0.997702\pi$
$74$	3.15949	+	0.513467i	0.367283	+	0.0596893i
$75$	3.09080	+	1.95450i	0.356895	+	0.225687i
$76$	0.239726	+	0.113751i	0.0274984	+	0.0130482i
$77$	2.05558	+	2.97802i	0.234255	+	0.339377i
$78$	−0.0605786	+	5.00067i	−0.00685918	+	0.566215i
$79$	4.09628	−	5.93448i	0.460867	−	0.667682i	−0.521798	−	0.853069i	$-0.674739\pi$
$79$	4.09628	−	5.93448i	0.460867	−	0.667682i	0.982666	+	0.185387i	$0.0593540\pi$
$80$	3.85597	−	2.22624i	0.431110	−	0.248902i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	5.00738	−	1.67171i	0.552973	−	0.184609i
$83$	−0.464489	−	1.88451i	−0.0509843	−	0.206851i	0.939925	−	0.341380i	$-0.110894\pi$
$83$	−0.464489	−	1.88451i	−0.0509843	−	0.206851i	−0.990910	+	0.134528i	$0.957048\pi$
$84$	−0.0755274	−	0.00304365i	−0.00824071	−	0.000332089i
$85$	5.63040	+	0.226898i	0.610703	+	0.0246105i
$86$	−1.41075	−	5.72363i	−0.152125	−	0.617195i
$87$	1.16147	−	0.387757i	0.124523	−	0.0415719i
$88$	4.49863	−	9.48066i	0.479556	−	1.01064i
$89$	0.800318	−	0.462064i	0.0848335	−	0.0489787i	−0.456983	−	0.889475i	$-0.651070\pi$
$89$	0.800318	−	0.462064i	0.0848335	−	0.0489787i	0.541817	+	0.840497i	$0.317737\pi$
$90$	−0.913138	+	1.32291i	−0.0962532	+	0.139447i
$91$	−2.40644	+	2.65091i	−0.252264	+	0.277891i
$92$	0.226364	+	0.327946i	0.0236001	+	0.0341907i
$93$	6.66147	+	3.16091i	0.690762	+	0.327771i
$94$	15.0506	+	9.51744i	1.55235	+	0.981649i
$95$	3.98737	+	0.648010i	0.409095	+	0.0664844i
$96$	0.200006	+	0.381080i	0.0204130	+	0.0388938i
$97$	−5.97605	+	4.87929i	−0.606776	+	0.495417i	−0.885305	−	0.465011i	$-0.846051\pi$
$97$	−5.97605	+	4.87929i	−0.606776	+	0.495417i	0.278529	+	0.960428i	$0.410153\pi$
$98$	−6.01600	−	5.77844i	−0.607707	−	0.583711i
$99$			3.64412i			0.366248i
$100$	0.192837	−	0.200764i	0.0192837	−	0.0200764i
$101$	9.09829	+	3.03746i	0.905314	+	0.302238i	0.730940	−	0.682442i	$-0.239082\pi$
$101$	9.09829	+	3.03746i	0.905314	+	0.302238i	0.174373	+	0.984680i	$0.444210\pi$
$102$	0.542683	−	6.72234i	0.0537336	−	0.665610i
$103$	7.30545	+	1.80063i	0.719827	+	0.177422i	0.582180	−	0.813060i	$-0.302200\pi$
$103$	7.30545	+	1.80063i	0.719827	+	0.177422i	0.137647	+	0.990481i	$0.456046\pi$
$104$	10.1470	+	2.19990i	0.994999	+	0.215718i
$105$	−1.11734	+	0.275400i	−0.109042	+	0.0268763i
$106$	−0.302664	−	1.86237i	−0.0293973	−	0.180889i
$107$	−7.78707	+	9.53742i	−0.752804	+	0.922018i	−0.998884	−	0.0472320i	$-0.984960\pi$
$107$	−7.78707	+	9.53742i	−0.752804	+	0.922018i	0.246080	+	0.969250i	$0.420857\pi$
$108$	−0.0608556	−	0.0457300i	−0.00585583	−	0.00440037i
$109$	−11.5268	−	13.0110i	−1.10407	−	1.24623i	−0.966755	−	0.255704i	$-0.917693\pi$
$109$	−11.5268	−	13.0110i	−1.10407	−	1.24623i	−0.137310	−	0.990528i	$-0.543846\pi$
$110$	0.939650	−	5.78190i	0.0895921	−	0.551282i
$111$	0.185697	+	2.30027i	0.0176256	+	0.218332i
$112$	0.912994	−	3.70416i	0.0862698	−	0.350010i
$113$	−4.13881	+	14.2888i	−0.389346	+	1.34418i	0.491541	+	0.870854i	$0.336434\pi$
$113$	−4.13881	+	14.2888i	−0.389346	+	1.34418i	−0.880888	+	0.473325i	$0.843054\pi$
$114$	0.967101	−	4.73717i	0.0905773	−	0.443677i
$115$	4.69924	+	3.83681i	0.438206	+	0.357784i
$116$	−0.0112354	−	0.0925317i	−0.00104318	−	0.00859135i
$117$	−3.51098	+	0.820396i	−0.324590	+	0.0758456i
$118$	−1.16601	+	9.60294i	−0.107340	+	0.884022i
$119$	3.48211	−	3.34462i	0.319205	−	0.306600i
$120$	2.31181	+	2.40685i	0.211038	+	0.219714i
$121$	−0.977251	−	2.05951i	−0.0888410	−	0.187228i
$122$	17.2661	+	11.9179i	1.56320	+	1.07900i
$123$	2.03417	+	3.21679i	0.183415	+	0.290048i
$124$	0.337184	−	0.448710i	0.0302800	−	0.0402954i
$125$	4.66238	−	8.88343i	0.417016	−	0.794558i
$126$	0.275498	+	1.34948i	0.0245433	+	0.120221i
$127$	2.83849	+	0.229146i	0.251875	+	0.0203335i	0.205759	−	0.978603i	$-0.434034\pi$
$127$	2.83849	+	0.229146i	0.251875	+	0.0203335i	0.0461158	+	0.998936i	$0.485316\pi$
$128$	−10.2056	+	2.95610i	−0.902059	+	0.261285i
$129$	3.76320	−	1.97508i	0.331331	−	0.173896i
$130$	5.78219	−	0.396353i	0.507132	−	0.0347625i
$131$	16.1080	+	8.45416i	1.40737	+	0.738643i	0.985764	−	0.168137i	$-0.0537752\pi$
$131$	16.1080	+	8.45416i	1.40737	+	0.738643i	0.421603	+	0.906780i	$0.361468\pi$
$132$	0.271793	+	0.0554870i	0.0236566	+	0.00482953i
$133$	2.76712	−	2.07936i	0.239940	−	0.180303i
$134$	0.122491	−	3.03958i	0.0105816	−	0.262579i
$135$	−1.08360	−	0.410955i	−0.0932614	−	0.0353694i
$136$	−13.4490	−	3.89554i	−1.15324	−	0.334040i
$137$	−7.99613	+	1.63242i	−0.683155	+	0.139467i	−0.529054	−	0.848588i	$-0.677453\pi$
$137$	−7.99613	+	1.63242i	−0.683155	+	0.139467i	−0.154101	+	0.988055i	$0.549248\pi$
$138$	4.81482	−	5.43481i	0.409865	−	0.462642i
$139$	−5.76419	−	7.05986i	−0.488913	−	0.598809i	0.469945	−	0.882695i	$-0.344274\pi$
$139$	−5.76419	−	7.05986i	−0.488913	−	0.598809i	−0.958858	+	0.283886i	$0.908376\pi$
$140$	0.00352732	+	0.0875294i	0.000298113	+	0.00739759i
$141$	−4.06551	+	12.1777i	−0.342378	+	1.02555i
$142$	11.5734	+	10.2531i	0.971217	+	0.860423i
$143$	10.2775	−	8.18584i	0.859447	−	0.684535i
$144$	2.87575	−	2.54769i	0.239646	−	0.212308i
$145$	−0.556230	−	1.30552i	−0.0461924	−	0.108418i
$146$	5.43147	+	9.40758i	0.449511	+	0.778576i
$147$	3.00699	−	5.20826i	0.248012	−	0.429570i
$148$	0.174391	+	0.0211749i	0.0143348	+	0.00174057i
$149$	15.2113	−	7.21786i	1.24616	−	0.591310i	0.312652	−	0.949868i	$-0.398783\pi$
$149$	15.2113	−	7.21786i	1.24616	−	0.591310i	0.933508	+	0.358557i	$0.116731\pi$
$150$	−4.39274	−	2.53615i	−0.358666	−	0.207076i
$151$	14.3672	−	9.91699i	1.16919	−	0.807033i	0.184755	−	0.982785i	$-0.440851\pi$
$151$	14.3672	−	9.91699i	1.16919	−	0.807033i	0.984435	+	0.175751i	$0.0562355\pi$
$152$	−9.23458	−	3.93448i	−0.749023	−	0.319129i
$153$	4.79934	−	0.779968i	0.388003	−	0.0630567i
$154$	−3.01518	−	4.01248i	−0.242970	−	0.323335i
$155$	3.03012	−	7.98978i	0.243385	−	0.641754i
$156$	0.00772878	+	0.274355i	0.000618798	+	0.0219660i
$157$	6.09950	+	16.0831i	0.486793	+	1.28357i	0.923374	+	0.383902i	$0.125420\pi$
$157$	6.09950	+	16.0831i	0.486793	+	1.28357i	−0.436581	+	0.899665i	$0.643811\pi$
$158$	−5.34565	+	8.45347i	−0.425277	+	0.672522i
$159$	1.25145	−	0.533195i	0.0992468	−	0.0422851i
$160$	0.421554	−	0.266575i	0.0333268	−	0.0210746i
$161$	5.16016	−	0.626557i	0.406677	−	0.0493796i
$162$	−0.543673	+	1.27605i	−0.0427150	+	0.100256i
$163$	5.42838	+	16.2600i	0.425183	+	1.27358i	0.915600	+	0.402091i	$0.131716\pi$
$163$	5.42838	+	16.2600i	0.425183	+	1.27358i	−0.490417	+	0.871488i	$0.663155\pi$
$164$	0.270894	−	0.102737i	0.0211533	−	0.00802239i
$165$	4.20951	−	0.339827i	0.327710	−	0.0264555i
$166$	0.748992	+	2.58582i	0.0581331	+	0.200699i
$167$	−2.93704	+	0.118359i	−0.227275	+	0.00915887i	−0.153642	−	0.988127i	$-0.549100\pi$
$167$	−2.93704	+	0.118359i	−0.227275	+	0.00915887i	−0.0736328	+	0.997285i	$0.523459\pi$
$168$	2.85947			0.220613
$169$	10.2005	+	8.05912i	0.784655	+	0.619932i
$170$	−7.81593			−0.599454
$171$	3.48293	−	0.140357i	0.266346	−	0.0107334i
$172$	−0.0900093	−	0.310748i	−0.00686314	−	0.0236943i
$173$	−20.9386	+	1.69034i	−1.59193	+	0.128514i	−0.844399	−	0.535714i	$-0.820042\pi$
$173$	−20.9386	+	1.69034i	−1.59193	+	0.128514i	−0.747530	+	0.664228i	$0.768760\pi$
$174$	−1.58805	+	0.602267i	−0.120390	+	0.0456578i
$175$	−1.14991	−	3.44440i	−0.0869251	−	0.260372i
$176$	−5.48775	+	12.8802i	−0.413655	+	0.970884i
$177$	−6.92333	+	0.840645i	−0.520390	+	0.0631868i
$178$	−1.08337	+	0.685079i	−0.0812017	+	0.0513488i
$179$	−2.10505	+	0.896879i	−0.157339	+	0.0670359i	−0.469200	−	0.883092i	$-0.655458\pi$
$179$	−2.10505	+	0.896879i	−0.157339	+	0.0670359i	0.311861	+	0.950128i	$0.399048\pi$
$180$	−0.0471501	+	0.0745619i	−0.00351436	+	0.00555752i
$181$	−5.65122	−	14.9011i	−0.420052	−	1.10759i	−0.963397	−	0.268077i	$-0.913612\pi$
$181$	−5.65122	−	14.9011i	−0.420052	−	1.10759i	0.543345	−	0.839509i	$-0.317157\pi$
$182$	3.18707	−	3.80834i	0.236241	−	0.282293i
$183$	−5.36363	+	14.1427i	−0.396491	+	1.04546i
$184$	−9.05581	−	12.0511i	−0.667603	−	0.888418i
$185$	2.63984	−	0.429016i	0.194085	−	0.0315419i
$186$	−9.40876	−	4.00870i	−0.689884	−	0.293932i
$187$	−14.5823	+	10.0654i	−1.06636	+	0.736057i
$188$	0.846360	+	0.488646i	0.0617271	+	0.0356382i
$189$	−0.897115	+	0.425686i	−0.0652555	+	0.0309641i
$190$	−5.56234	−	0.675390i	−0.403535	−	0.0489980i
$191$	7.62869	−	13.2133i	0.551993	−	0.956080i	−0.446138	−	0.894964i	$-0.647201\pi$
$191$	7.62869	−	13.2133i	0.551993	−	0.956080i	0.998131	−	0.0611154i	$-0.0194658\pi$
$192$	−4.14044	−	7.17144i	−0.298810	−	0.517554i
$193$	−2.07009	−	4.85867i	−0.149008	−	0.349735i	0.828703	−	0.559688i	$-0.189079\pi$
$193$	−2.07009	−	4.85867i	−0.149008	−	0.349735i	−0.977711	+	0.209953i	$0.932669\pi$
$194$	8.00978	−	7.09605i	0.575069	−	0.509466i
$195$	1.27509	+	3.97921i	0.0913113	+	0.284957i
$196$	−0.342667	−	0.303577i	−0.0244762	−	0.0216841i
$197$	−5.12146	+	15.3406i	−0.364889	+	1.09298i	0.592844	+	0.805317i	$0.298005\pi$
$197$	−5.12146	+	15.3406i	−0.364889	+	1.09298i	−0.957733	+	0.287658i	$0.907123\pi$
$198$	−0.203526	−	5.05044i	−0.0144639	−	0.358919i
$199$	−2.35338	−	2.88236i	−0.166826	−	0.204325i	0.684425	−	0.729083i	$-0.260053\pi$
$199$	−2.35338	−	2.88236i	−0.166826	−	0.204325i	−0.851251	+	0.524758i	$0.824156\pi$
$200$	−6.98316	+	7.88236i	−0.493784	+	0.557367i
$201$	2.14887	−	0.438695i	0.151570	−	0.0309431i
$202$	−12.7791	−	3.70151i	−0.899134	−	0.260437i
$203$	−1.13689	−	0.431166i	−0.0797941	−	0.0302619i
$204$	0.0149037	−	0.369830i	0.00104346	−	0.0258933i
$205$	3.52619	−	2.64976i	0.246279	−	0.185067i
$206$	−10.2253	−	2.08751i	−0.712430	−	0.145444i
$207$	4.63516	+	2.43272i	0.322166	+	0.169086i
$208$	−13.6451	−	2.38754i	−0.946116	−	0.165546i
$209$	−11.2475	+	5.90315i	−0.778007	+	0.408330i
$210$	1.53316	−	0.444086i	0.105798	−	0.0306448i
$211$	−1.11585	−	0.0900806i	−0.0768182	−	0.00620141i	0.0419977	−	0.999118i	$-0.486628\pi$
$211$	−1.11585	−	0.0900806i	−0.0768182	−	0.00620141i	−0.118816	+	0.992916i	$0.537910\pi$
$212$	−0.0207127	−	0.101457i	−0.00142255	−	0.00696811i
$213$	−5.18045	+	9.87053i	−0.354959	+	0.676318i
$214$	10.2595	−	13.6530i	0.701327	−	0.933297i
$215$	−2.63245	−	4.16288i	−0.179531	−	0.283906i
$216$	2.36992	+	1.63584i	0.161252	+	0.111304i
$217$	−3.13874	−	6.61475i	−0.213072	−	0.449039i
$218$	16.7018	+	17.3884i	1.13119	+	1.17769i
$219$	−5.64827	+	5.42524i	−0.381675	+	0.366604i
$220$	0.0387503	−	0.319137i	0.00261254	−	0.0215162i
$221$	−12.9806	−	11.7835i	−0.873168	−	0.792644i
$222$	−0.385831	−	3.17760i	−0.0258953	−	0.213267i
$223$	2.13181	+	1.74057i	0.142756	+	0.116557i	0.701133	−	0.713031i	$-0.252678\pi$
$223$	2.13181	+	1.74057i	0.142756	+	0.116557i	−0.558376	+	0.829588i	$0.688575\pi$
$224$	0.0854827	−	0.418722i	0.00571156	−	0.0279771i
$225$	1.01742	−	3.51254i	0.0678281	−	0.234170i
$226$	4.93800	−	20.0342i	0.328471	−	1.33266i
$227$	−1.21184	−	15.0113i	−0.0804323	−	0.996333i	−0.903556	−	0.428471i	$-0.859053\pi$
$227$	−1.21184	−	15.0113i	−0.0804323	−	0.996333i	0.823123	−	0.567863i	$-0.192230\pi$
$228$	0.0425643	−	0.261908i	0.00281889	−	0.0173453i
$229$	−3.85310	−	4.34925i	−0.254620	−	0.287407i	0.607277	−	0.794490i	$-0.292262\pi$
$229$	−3.85310	−	4.34925i	−0.254620	−	0.287407i	−0.861897	+	0.507084i	$0.830723\pi$
$230$	−6.72703	−	5.05503i	−0.443567	−	0.333319i
$231$	2.28854	−	2.80296i	0.150575	−	0.184421i
$232$	0.565630	+	3.48046i	0.0371354	+	0.228503i
$233$	3.74967	−	0.924211i	0.245649	−	0.0605471i	−0.114569	−	0.993415i	$-0.536549\pi$
$233$	3.74967	−	0.924211i	0.245649	−	0.0605471i	0.360218	+	0.932868i	$0.382702\pi$
$234$	4.82009	−	1.33309i	0.315099	−	0.0871467i
$235$	14.4462	+	3.56067i	0.942368	+	0.232273i
$236$	−0.0427191	+	0.529171i	−0.00278078	+	0.0344461i
$237$	−6.83984	−	2.28347i	−0.444295	−	0.148327i
$238$	−4.63911	+	4.82983i	−0.300709	+	0.313071i
$239$			14.6979i			0.950727i	0.879789	+	0.475363i	$0.157683\pi$
$239$			14.6979i			0.950727i	−0.879789	+	0.475363i	$0.842317\pi$
$240$	−3.21114	−	3.08435i	−0.207279	−	0.199094i
$241$	−12.1620	+	9.93000i	−0.783426	+	0.639647i	−0.937332	−	0.348438i	$-0.886712\pi$
$241$	−12.1620	+	9.93000i	−0.783426	+	0.639647i	0.153906	+	0.988085i	$0.450815\pi$
$242$	1.46941	+	2.79973i	0.0944573	+	0.179973i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	0.973154	+	0.615386i	0.0622998	+	0.0393960i
$245$	−6.29674	−	2.98784i	−0.402284	−	0.190886i
$246$	−2.99885	−	4.34458i	−0.191200	−	0.277000i
$247$	−8.21961	−	9.50760i	−0.523001	−	0.604954i
$248$	−12.0616	+	17.4743i	−0.765913	+	1.10962i
$249$	−1.68087	+	0.970452i	−0.106521	+	0.0614999i
$250$	−5.96552	+	12.5721i	−0.377293	+	0.795127i
$251$	8.93993	−	2.98459i	0.564283	−	0.188386i	−0.0201931	−	0.999796i	$-0.506428\pi$
$251$	8.93993	−	2.98459i	0.564283	−	0.188386i	0.584477	+	0.811411i	$0.301300\pi$
$252$	0.0180896	+	0.0733922i	0.00113953	+	0.00462327i
$253$	−19.0606	−	0.768118i	−1.19833	−	0.0482912i
$254$	−3.94670	−	0.159046i	−0.247638	−	0.00997946i
$255$	−1.34854	−	5.47123i	−0.0844487	−	0.342622i
$256$	−1.73038	+	0.577685i	−0.108149	+	0.0361053i
$257$	−1.28426	+	2.70653i	−0.0801101	+	0.168828i	−0.939553	−	0.342403i	$-0.888759\pi$
$257$	−1.28426	+	2.70653i	−0.0801101	+	0.168828i	0.859443	+	0.511231i	$0.170810\pi$
$258$	−5.10516	+	2.94746i	−0.317833	+	0.183501i
$259$	1.30176	−	1.88592i	0.0808873	−	0.117186i
$260$	0.316201	−	0.0345125i	0.0196099	−	0.00214037i
$261$	−0.695590	−	1.00774i	−0.0430560	−	0.0623773i
$262$	−22.7965	−	10.8171i	−1.40838	−	0.668282i
$263$	0.872668	+	0.551842i	0.0538110	+	0.0340280i	0.561100	−	0.827748i	$-0.310378\pi$
$263$	0.872668	+	0.551842i	0.0538110	+	0.0340280i	−0.507289	+	0.861776i	$0.669352\pi$
$264$	−10.3579	−	1.68333i	−0.637487	−	0.103602i
$265$	−0.732624	−	1.39590i	−0.0450047	−	0.0857493i
$266$	−3.71886	+	3.03636i	−0.228018	+	0.186171i
$267$	−0.666483	−	0.640166i	−0.0407881	−	0.0391775i
$268$		−	0.166951i		−	0.0101982i
$269$	−12.5247	+	13.0396i	−0.763647	+	0.795041i	−0.983580	−	0.180474i	$-0.942237\pi$
$269$	−12.5247	+	13.0396i	−0.763647	+	0.795041i	0.219933	+	0.975515i	$0.429416\pi$
$270$	1.52473	+	0.509029i	0.0927920	+	0.0309785i
$271$	2.25190	−	27.8948i	0.136793	−	1.69449i	−0.456679	−	0.889632i	$-0.650961\pi$
$271$	2.25190	−	27.8948i	0.136793	−	1.69449i	0.593472	−	0.804855i	$-0.297757\pi$
$272$	18.1379	+	4.47060i	1.09977	+	0.271070i
$273$	3.21576	+	1.57390i	0.194627	+	0.0952569i
$274$	10.9908	−	2.70898i	0.663977	−	0.163656i
$275$	2.13769	+	13.1537i	0.128907	+	0.793198i
$276$	0.252019	−	0.308667i	0.0151698	−	0.0185796i
$277$	−10.3436	−	7.77271i	−0.621487	−	0.467017i	0.242759	−	0.970087i	$-0.421948\pi$
$277$	−10.3436	−	7.77271i	−0.621487	−	0.467017i	−0.864246	+	0.503070i	$0.832204\pi$
$278$	8.38297	+	9.46242i	0.502777	+	0.567518i
$279$	1.18277	−	7.27788i	0.0708106	−	0.435715i
$280$	−0.266656	−	3.30312i	−0.0159357	−	0.197399i
$281$	0.243194	−	0.986678i	0.0145077	−	0.0588602i	−0.963242	−	0.268636i	$-0.913427\pi$
$281$	0.243194	−	0.986678i	0.0145077	−	0.0588602i	0.977750	+	0.209776i	$0.0672733\pi$
$282$	4.95432	−	17.1043i	0.295026	−	1.01855i
$283$	0.0590539	−	0.289265i	0.00351039	−	0.0171950i	−0.977998	−	0.208616i	$-0.933104\pi$
$283$	0.0590539	−	0.289265i	0.00351039	−	0.0171950i	0.981508	+	0.191420i	$0.0613094\pi$
$284$	0.657305	+	0.536673i	0.0390039	+	0.0318457i
$285$	−0.486930	−	4.01023i	−0.0288432	−	0.237545i
$286$	−13.7865	+	11.9189i	−0.815215	+	0.704778i
$287$	0.455545	−	3.75175i	0.0268899	−	0.221459i
$288$	0.310389	−	0.298133i	0.0182898	−	0.0175676i
$289$	4.60107	+	4.79022i	0.270651	+	0.281778i
$290$	0.843801	+	1.77827i	0.0495497	+	0.104424i
$291$	6.34929	+	4.38260i	0.372202	+	0.256912i
$292$	0.318633	+	0.503878i	0.0186466	+	0.0294873i
$293$	−5.43085	+	7.22714i	−0.317273	+	0.422214i	−0.929703	−	0.368311i	$-0.879936\pi$
$293$	−5.43085	+	7.22714i	−0.317273	+	0.422214i	0.612429	+	0.790525i	$0.290192\pi$
$294$	−3.87654	+	7.38614i	−0.226085	+	0.430768i
$295$	1.61670	+	7.91911i	0.0941278	+	0.461069i
$296$	−6.62400	−	0.534744i	−0.385012	−	0.0310814i
$297$	3.50024	−	1.01386i	0.203105	−	0.0588300i
$298$	−20.6785	+	10.8529i	−1.19787	+	0.628691i
$299$	−3.55105	−	18.5372i	−0.205362	−	1.07203i
$300$	−0.246488	−	0.129367i	−0.0142310	−	0.00746901i
$301$	−4.13492	−	0.844150i	−0.238333	−	0.0486560i
$302$	−19.3579	+	14.5465i	−1.11392	+	0.837058i
$303$	0.386228	−	9.58414i	0.0221882	−	0.550595i
$304$	12.5219	+	4.74892i	0.718178	+	0.272369i
$305$	16.8372	+	4.87695i	0.964095	+	0.279254i
$306$	−6.60791	+	1.34901i	−0.377749	+	0.0771180i
$307$	20.9318	−	23.6271i	1.19464	−	1.34847i	0.272240	−	0.962229i	$-0.412236\pi$
$307$	20.9318	−	23.6271i	1.19464	−	1.34847i	0.922399	−	0.386239i	$-0.126226\pi$
$308$	−0.174210	−	0.213368i	−0.00992652	−	0.0121578i
$309$	−0.302964	−	7.51799i	−0.0172350	−	0.427683i
$310$	−3.75326	+	11.2424i	−0.213171	+	0.638524i
$311$	21.8928	+	19.3954i	1.24143	+	1.09981i	0.991303	+	0.131597i	$0.0420104\pi$
$311$	21.8928	+	19.3954i	1.24143	+	1.09981i	0.250126	+	0.968213i	$0.419528\pi$
$312$	−0.710044	−	10.3585i	−0.0401983	−	0.586433i
$313$	23.7288	−	21.0219i	1.34123	−	1.18823i	0.376066	−	0.926593i	$-0.377276\pi$
$313$	23.7288	−	21.0219i	1.34123	−	1.18823i	0.965167	−	0.261636i	$-0.0842620\pi$
$314$	−9.35163	−	21.9491i	−0.527743	−	1.23866i
$315$	0.575392	+	0.996607i	0.0324196	+	0.0561525i
$316$	−0.274457	+	0.475374i	−0.0154394	+	0.0267419i
$317$	−20.1962	−	2.45227i	−1.13433	−	0.137733i	−0.468240	−	0.883601i	$-0.655112\pi$
$317$	−20.1962	−	2.45227i	−1.13433	−	0.137733i	−0.666093	+	0.745869i	$0.732035\pi$
$318$	−1.70463	+	0.808857i	−0.0955909	+	0.0453584i
$319$	3.86437	+	2.23110i	0.216363	+	0.124917i
$320$	−7.89800	+	5.45160i	−0.441512	+	0.304753i
$321$	11.3274	+	4.82614i	0.632232	+	0.269369i
$322$	−7.11654	+	1.15655i	−0.396589	+	0.0644521i
$323$	10.1819	+	13.5496i	0.566534	+	0.753920i
$324$	−0.0269934	+	0.0711758i	−0.00149963	+	0.00395421i
$325$	−12.1919	+	5.02086i	−0.676283	+	0.278507i
$326$	−8.43139	−	22.2317i	−0.466971	−	1.23130i
$327$	−9.29039	+	14.6916i	−0.513760	+	0.812446i
$328$	−10.0830	+	4.29594i	−0.556738	+	0.237204i
$329$	10.7748	−	6.81357i	0.594034	−	0.375645i
$330$	−5.81504	+	0.706074i	−0.320108	+	0.0388681i
$331$	−4.68998	+	11.0078i	−0.257785	+	0.605043i	−0.997709	−	0.0676469i	$-0.978451\pi$
$331$	−4.68998	+	11.0078i	−0.257785	+	0.605043i	0.739925	+	0.672690i	$0.234861\pi$
$332$	0.0467866	+	0.140143i	0.00256775	+	0.00769134i
$333$	2.15778	−	0.818340i	0.118246	−	0.0448447i
$334$	4.06387	−	0.328070i	0.222365	−	0.0179512i
$335$	−0.707149	−	2.44136i	−0.0386357	−	0.133386i
$336$	−3.81192	+	0.153615i	−0.207958	+	0.00838040i
$337$	31.3012			1.70509			0.852543	−	0.522658i	$-0.175059\pi$
$337$	31.3012			1.70509			0.852543	+	0.522658i	$0.175059\pi$
$338$	−14.5872	−	10.5995i	−0.793436	−	0.576539i
$339$	14.8762			0.807962
$340$	−0.428600	+	0.0172720i	−0.0232441	+	0.000936706i
$341$	7.47554	+	25.8086i	0.404823	+	1.39761i
$342$	−4.81920	+	0.389046i	−0.260593	+	0.0210372i
$343$	−12.0829	+	4.58246i	−0.652418	+	0.247429i
$344$	3.87557	+	11.6088i	0.208957	+	0.625902i
$345$	2.37791	−	5.58117i	0.128023	−	0.300480i
$346$	28.9246	−	3.51209i	1.55500	−	0.188811i
$347$	−11.8825	+	7.51402i	−0.637885	+	0.403374i	−0.813893	−	0.581015i	$-0.802656\pi$
$347$	−11.8825	+	7.51402i	−0.637885	+	0.403374i	0.176008	+	0.984389i	$0.443681\pi$
$348$	−0.0857525	+	0.0365357i	−0.00459682	+	0.00195852i
$349$	6.39782	−	10.1173i	0.342467	−	0.541569i	−0.629405	−	0.777078i	$-0.716701\pi$
$349$	6.39782	−	10.1173i	0.342467	−	0.541569i	0.971872	+	0.235509i	$0.0756756\pi$
$350$	1.78605	+	4.70942i	0.0954683	+	0.251729i
$351$	1.76482	+	3.14411i	0.0941991	+	0.167820i
$352$	−0.556143	+	1.46643i	−0.0296425	+	0.0781609i
$353$	−18.6919	−	24.8744i	−0.994870	−	1.32393i	−0.945665	−	0.325143i	$-0.894587\pi$
$353$	−18.6919	−	24.8744i	−0.994870	−	1.32393i	−0.0492055	−	0.998789i	$-0.515669\pi$
$354$	9.54820	−	1.55173i	0.507481	−	0.0824737i
$355$	11.8851	+	5.06375i	0.630794	+	0.268756i
$356$	−0.0578944	+	0.0399616i	−0.00306840	+	0.00211796i
$357$	−4.18135	−	2.41410i	−0.221300	−	0.127768i
$358$	2.86733	−	1.36057i	0.151543	−	0.0719081i
$359$	−4.91436	−	0.596712i	−0.259370	−	0.0314932i	−0.0101814	−	0.999948i	$-0.503241\pi$
$359$	−4.91436	−	0.596712i	−0.259370	−	0.0314932i	−0.249189	+	0.968455i	$0.580164\pi$
$360$	1.66864	−	2.89016i	0.0879448	−	0.152325i
$361$	−3.42475	−	5.93184i	−0.180250	−	0.312202i
$362$	8.66434	+	20.3360i	0.455388	+	1.06883i
$363$	−1.70631	+	1.51166i	−0.0895581	+	0.0793415i
$364$	0.166353	−	0.215880i	0.00871926	−	0.0113152i
$365$	6.79370	+	6.01869i	0.355598	+	0.315033i
$366$	6.64366	−	19.9002i	0.347270	−	1.04020i
$367$	0.118430	+	2.93880i	0.00618198	+	0.153404i	0.999332	+	0.0365550i	$0.0116384\pi$
$367$	0.118430	+	2.93880i	0.00618198	+	0.153404i	−0.993150	+	0.116849i	$0.962721\pi$
$368$	12.7196	+	15.5787i	0.663055	+	0.812095i
$369$	2.52384	−	2.84883i	0.131386	−	0.148304i
$370$	−3.63463	+	0.742016i	−0.188956	+	0.0385756i
$371$	−1.29744	−	0.375807i	−0.0673596	−	0.0195109i
$372$	−0.524805	−	0.199032i	−0.0272099	−	0.0103193i
$373$	−0.952436	+	23.6345i	−0.0493153	+	1.22375i	0.765273	+	0.643706i	$0.222604\pi$
$373$	−0.952436	+	23.6345i	−0.0493153	+	1.22375i	−0.814588	+	0.580040i	$0.803037\pi$
$374$	19.6477	−	14.7643i	1.01596	−	0.763442i
$375$	−9.82985	−	2.00678i	−0.507611	−	0.103630i
$376$	−32.7356	−	17.1810i	−1.68821	−	0.886040i
$377$	−1.27960	+	4.22547i	−0.0659027	+	0.217623i
$378$	1.21955	−	0.640069i	0.0627269	−	0.0329216i
$379$	23.7880	−	6.89028i	1.22191	−	0.353930i	0.396272	−	0.918133i	$-0.370304\pi$
$379$	23.7880	−	6.89028i	1.22191	−	0.353930i	0.825636	+	0.564203i	$0.190817\pi$
$380$	−0.306513	−	0.0247443i	−0.0157238	−	0.00126936i
$381$	−0.569617	−	2.79017i	−0.0291824	−	0.142945i
$382$	−9.83475	+	18.7385i	−0.503189	+	0.958747i
$383$	18.0422	−	24.0098i	0.921913	−	1.22684i	−0.0517061	−	0.998662i	$-0.516466\pi$
$383$	18.0422	−	24.0098i	0.921913	−	1.22684i	0.973619	−	0.228181i	$-0.0732777\pi$
$384$	5.67877	+	8.98026i	0.289794	+	0.458272i
$385$	−3.45126	−	2.38223i	−0.175892	−	0.121410i
$386$	3.14032	+	6.61808i	0.159838	+	0.336852i
$387$	−2.94409	−	3.06512i	−0.149656	−	0.155809i
$388$	0.423549	−	0.406825i	0.0215025	−	0.0206534i
$389$	2.73390	−	22.5157i	0.138614	−	1.14159i	−0.742889	−	0.669414i	$-0.766545\pi$
$389$	2.73390	−	22.5157i	0.138614	−	1.14159i	0.881504	−	0.472177i	$-0.156532\pi$
$390$	−1.98941	−	5.44362i	−0.100738	−	0.275649i
$391$	3.06802	+	25.2674i	0.155157	+	1.27783i
$392$	13.4148	+	10.9528i	0.677549	+	0.553202i
$393$	3.63883	−	17.8242i	0.183555	−	0.899110i
$394$	6.24112	−	21.5468i	0.314423	−	1.08551i
$395$	−1.99992	+	8.11399i	−0.100627	+	0.408259i
$396$	−0.0223214	−	0.276500i	−0.00112169	−	0.0138946i
$397$	−4.85419	+	29.8691i	−0.243625	+	1.49908i	0.520414	+	0.853914i	$0.325778\pi$
$397$	−4.85419	+	29.8691i	−0.243625	+	1.49908i	−0.764039	+	0.645170i	$0.776786\pi$
$398$	3.42256	+	3.86327i	0.171557	+	0.193648i
$399$	−2.76712	−	2.07936i	−0.138529	−	0.104098i
$400$	8.88571	−	10.8830i	0.444286	−	0.544151i
$401$	3.42768	+	21.0914i	0.171170	+	1.05325i	0.920410	+	0.390954i	$0.127855\pi$
$401$	3.42768	+	21.0914i	0.171170	+	1.05325i	−0.749240	+	0.662298i	$0.769581\pi$
$402$	−2.95365	+	0.728009i	−0.147315	+	0.0363098i
$403$	−23.1826	+	13.0127i	−1.15481	+	0.648207i
$404$	−0.708944	−	0.174739i	−0.0352713	−	0.00869359i
$405$	−0.0932535	+	1.15515i	−0.00463381	+	0.0574000i
$406$	1.59971	+	0.534063i	0.0793924	+	0.0265051i
$407$	−5.82562	+	6.06511i	−0.288765	+	0.300636i
$408$			14.0018i			0.693192i
$409$	13.7449	+	13.2022i	0.679643	+	0.652806i	0.950827	−	0.309721i	$-0.100236\pi$
$409$	13.7449	+	13.2022i	0.679643	+	0.652806i	−0.271184	+	0.962528i	$0.587415\pi$
$410$	−4.73900	+	3.86927i	−0.234043	+	0.191090i
$411$	3.79263	+	7.22626i	0.187077	+	0.356445i
$412$	−0.565335	−	0.0918759i	−0.0278521	−	0.00452640i
$413$	5.85318	+	3.70132i	0.288016	+	0.182130i
$414$	−6.55980	−	3.11266i	−0.322396	−	0.152979i
$415$	1.27777	+	1.85117i	0.0627231	+	0.0908701i
$416$	−1.53805	−	0.205688i	−0.0754093	−	0.0100847i
$417$	−5.17742	+	7.50079i	−0.253539	+	0.367315i
$418$	15.2584	−	8.80944i	0.746313	−	0.430884i
$419$	13.0018	−	27.4008i	0.635181	−	1.33862i	−0.289245	−	0.957255i	$-0.593404\pi$
$419$	13.0018	−	27.4008i	0.635181	−	1.33862i	0.924426	−	0.381361i	$-0.124544\pi$
$420$	0.0830923	−	0.0277403i	0.00405449	−	0.00135359i
$421$	2.09887	+	8.51546i	0.102293	+	0.415018i	0.999655	−	0.0262773i	$-0.00836528\pi$
$421$	2.09887	+	8.51546i	0.102293	+	0.415018i	−0.897362	+	0.441295i	$0.854519\pi$
$422$	1.55150	+	0.0625234i	0.0755259	+	0.00304359i
$423$	12.8280	+	0.516951i	0.623719	+	0.0251350i
$424$	0.937453	+	3.80340i	0.0455268	+	0.184709i
$425$	16.8660	−	5.63070i	0.818122	−	0.273129i
$426$	6.62839	−	13.9690i	0.321147	−	0.676802i
$427$	13.0073	−	7.50980i	0.629470	−	0.363424i
$428$	0.532429	−	0.771357i	0.0257359	−	0.0372849i
$429$	−10.7220	−	7.59427i	−0.517664	−	0.366655i
$430$	3.88084	+	5.62237i	0.187151	+	0.271135i
$431$	10.3651	+	4.91829i	0.499268	+	0.236906i	0.661637	−	0.749824i	$-0.269862\pi$
$431$	10.3651	+	4.91829i	0.499268	+	0.236906i	−0.162369	+	0.986730i	$0.551913\pi$
$432$	−3.24719	−	2.05340i	−0.156230	−	0.0987941i
$433$	−6.89502	−	1.12055i	−0.331354	−	0.0538502i	−0.00754140	−	0.999972i	$-0.502401\pi$
$433$	−6.89502	−	1.12055i	−0.331354	−	0.0538502i	−0.323812	+	0.946121i	$0.604965\pi$
$434$	4.71946	+	8.99218i	0.226541	+	0.431639i
$435$	−1.09922	+	0.897488i	−0.0527037	+	0.0430312i
$436$	0.954299	+	0.916616i	0.0457026	+	0.0438980i
$437$			18.2471i			0.872879i
$438$	7.52502	−	7.83437i	0.359559	−	0.374341i
$439$	26.0478	+	8.69604i	1.24319	+	0.415039i	0.860792	−	0.508957i	$-0.169969\pi$
$439$	26.0478	+	8.69604i	1.24319	+	0.415039i	0.382402	+	0.923996i	$0.375097\pi$
$440$	−0.978587	+	12.1220i	−0.0466523	+	0.577893i
$441$	−5.83922	−	1.43924i	−0.278058	−	0.0685352i
$442$	18.6481	+	15.6059i	0.886998	+	0.742299i
$443$	23.3824	−	5.76325i	1.11093	−	0.273820i	0.359182	−	0.933268i	$-0.383056\pi$
$443$	23.3824	−	5.76325i	1.11093	−	0.273820i	0.751751	+	0.659447i	$0.229210\pi$
$444$	−0.0281797	−	0.173397i	−0.00133735	−	0.00822905i
$445$	−0.677337	+	0.829587i	−0.0321089	+	0.0393262i
$446$	−3.05171	−	2.29321i	−0.144503	−	0.108587i
$447$	−11.1649	−	12.6026i	−0.528084	−	0.596083i
$448$	−1.31903	+	8.11632i	−0.0623183	+	0.383460i
$449$	−2.54590	−	31.5366i	−0.120149	−	1.48831i	−0.723219	−	0.690619i	$-0.757338\pi$
$449$	−2.54590	−	31.5366i	−0.120149	−	1.48831i	0.603071	−	0.797688i	$-0.293944\pi$
$450$	−1.21388	+	4.92491i	−0.0572229	+	0.232162i
$451$	−3.85873	+	13.3219i	−0.181701	+	0.627304i
$452$	0.226511	−	1.10953i	0.0106542	−	0.0521877i
$453$	−13.5227	−	11.0409i	−0.635350	−	0.518747i
$454$	2.51789	+	20.7367i	0.118170	+	0.973220i
$455$	1.51822	−	3.86147i	0.0711750	−	0.181028i
$456$	−1.20992	+	9.96462i	−0.0566599	+	0.466636i
$457$	−7.34222	+	7.05230i	−0.343455	+	0.329893i	−0.844527	−	0.535513i	$-0.820118\pi$
$457$	−7.34222	+	7.05230i	−0.343455	+	0.329893i	0.501073	+	0.865405i	$0.332939\pi$
$458$	5.58298	+	5.81249i	0.260875	+	0.271600i
$459$	−2.08443	−	4.39285i	−0.0972930	−	0.205041i
$460$	−0.380059	−	0.262336i	−0.0177204	−	0.0122315i
$461$	−7.57015	−	11.9712i	−0.352577	−	0.557556i	0.621602	−	0.783333i	$-0.286482\pi$
$461$	−7.57015	−	11.9712i	−0.352577	−	0.557556i	−0.974179	+	0.225778i	$0.927508\pi$
$462$	−3.01518	+	4.01248i	−0.140279	+	0.186677i
$463$	4.54273	−	8.65546i	0.211119	−	0.402253i	−0.756752	−	0.653702i	$-0.773215\pi$
$463$	4.54273	−	8.65546i	0.211119	−	0.402253i	0.967871	+	0.251449i	$0.0809071\pi$
$464$	−0.941010	−	4.60937i	−0.0436853	−	0.213985i
$465$	−8.51736	−	0.687592i	−0.394983	−	0.0318863i
$466$	−5.14510	+	1.49030i	−0.238342	+	0.0690367i
$467$	−6.47318	+	3.39739i	−0.299543	+	0.157212i	−0.607799	−	0.794091i	$-0.707947\pi$
$467$	−6.47318	+	3.39739i	−0.299543	+	0.157212i	0.308255	+	0.951304i	$0.400255\pi$
$468$	0.261372	−	0.0837539i	0.0120819	−	0.00387153i
$469$	−1.92836	−	1.01208i	−0.0890433	−	0.0467335i
$470$	−20.2201	−	4.12796i	−0.932683	−	0.190409i
$471$	13.7511	−	10.3333i	0.633616	−	0.476132i
$472$	0.808673	−	20.0670i	0.0372222	−	0.923659i
$473$	14.4811	+	5.49196i	0.665842	+	0.252521i
$474$	9.60696	+	2.78269i	0.441262	+	0.127813i
$475$	12.4895	−	2.54976i	0.573060	−	0.116991i
$476$	−0.243721	+	0.275104i	−0.0111709	+	0.0126094i
$477$	−0.860320	−	1.05370i	−0.0393913	−	0.0482456i
$478$	−0.820883	−	20.3700i	−0.0375463	−	0.931702i
$479$	0.691865	−	2.07239i	0.0316121	−	0.0946899i	−0.931548	−	0.363618i	$-0.881541\pi$
$479$	0.691865	−	2.07239i	0.0316121	−	0.0946899i	0.963160	+	0.268928i	$0.0866695\pi$
$480$	−0.373333	−	0.330744i	−0.0170403	−	0.0150964i
$481$	−7.15503	−	4.24734i	−0.326241	−	0.193662i
$482$	16.3009	−	14.4414i	0.742488	−	0.657787i
$483$	−2.03747	−	4.78211i	−0.0927079	−	0.217593i
$484$	0.0867647	+	0.150281i	0.00394385	+	0.00683095i
$485$	4.47047	−	7.74309i	0.202994	−	0.351596i
$486$	1.37693	+	0.167189i	0.0624586	+	0.00758385i
$487$	1.99912	−	0.948595i	0.0905888	−	0.0429849i	−0.382859	−	0.923807i	$-0.625061\pi$
$487$	1.99912	−	0.948595i	0.0905888	−	0.0429849i	0.473448	+	0.880822i	$0.343009\pi$
$488$	−37.7213	−	21.7784i	−1.70756	−	0.985862i
$489$	14.1077	−	9.73786i	0.637973	−	0.440361i
$490$	8.89362	+	3.78922i	0.401773	+	0.171179i
$491$	−22.9340	+	3.72713i	−1.03500	+	0.168203i	−0.654095	−	0.756413i	$-0.726950\pi$
$491$	−22.9340	+	3.72713i	−1.03500	+	0.168203i	−0.380901	+	0.924616i	$0.624386\pi$
$492$	−0.174048	−	0.231616i	−0.00784669	−	0.0104420i
$493$	2.11126	−	5.56695i	0.0950865	−	0.250723i
$494$	11.9227	+	12.7177i	0.536427	+	0.572194i
$495$	−1.49757	−	3.94877i	−0.0673108	−	0.177484i
$496$	15.1404	−	23.9427i	0.679826	−	1.07506i
$497$	10.1835	−	4.33877i	0.456791	−	0.194620i
$498$	2.27534	−	1.43884i	0.101961	−	0.0644760i
$499$	20.5180	−	2.49134i	0.918514	−	0.111528i	0.352395	−	0.935851i	$-0.385367\pi$
$499$	20.5180	−	2.49134i	0.918514	−	0.111528i	0.566119	+	0.824324i	$0.308444\pi$
$500$	−0.299348	+	0.702594i	−0.0133872	+	0.0314210i
$501$	0.930821	+	2.78815i	0.0415860	+	0.124565i
$502$	−12.2233	+	4.63568i	−0.545552	+	0.206901i
$503$	−26.0363	+	2.10187i	−1.16090	+	0.0937176i	−0.645865	−	0.763451i	$-0.723503\pi$
$503$	−26.0363	+	2.10187i	−1.16090	+	0.0937176i	−0.515035	+	0.857169i	$0.672221\pi$
$504$	−0.795554	−	2.74657i	−0.0354368	−	0.122342i
$505$	−11.1072	+	0.447603i	−0.494262	+	0.0199181i
$506$	26.4593			1.17626
$507$	4.90297	−	12.0400i	0.217748	−	0.534714i
$508$	−0.216776			−0.00961786
$509$	−31.8606	+	1.28394i	−1.41220	+	0.0569095i	−0.734588	−	0.678514i	$-0.762624\pi$
$509$	−31.8606	+	1.28394i	−1.41220	+	0.0569095i	−0.677608	+	0.735423i	$0.736983\pi$
$510$	2.17453	+	7.50734i	0.0962897	+	0.332431i
$511$	7.75160	−	0.625774i	0.342911	−	0.0276826i
$512$	22.2352	−	8.43271i	0.982668	−	0.372677i
$513$	−1.10383	−	3.30637i	−0.0487352	−	0.145980i
$514$	1.62872	−	3.82274i	0.0718396	−	0.168614i
$515$	−8.65617	+	1.05105i	−0.381436	+	0.0463147i
$516$	−0.273437	+	0.172911i	−0.0120374	+	0.00761199i
$517$	−43.0410	+	18.3380i	−1.89294	+	0.806506i
$518$	−1.69880	+	2.68643i	−0.0746408	+	0.118035i
$519$	7.44907	+	19.6416i	0.326978	+	0.862170i
$520$	−11.8994	+	1.78617i	−0.521823	+	0.0783288i
$521$	−4.48910	+	11.8368i	−0.196671	+	0.518579i	−0.996681	−	0.0814082i	$-0.974058\pi$
$521$	−4.48910	+	11.8368i	−0.196671	+	0.518579i	0.800010	+	0.599987i	$0.204827\pi$
$522$	1.02031	+	1.35779i	0.0446578	+	0.0594287i
$523$	−30.2677	+	4.91897i	−1.32351	+	0.215092i	−0.780776	−	0.624811i	$-0.785176\pi$
$523$	−30.2677	+	4.91897i	−1.32351	+	0.215092i	−0.542736	+	0.839903i	$0.682612\pi$
$524$	−1.27399	−	0.542798i	−0.0556546	−	0.0237122i
$525$	−2.98849	+	2.06280i	−0.130428	+	0.0900281i
$526$	−1.24026	−	0.716067i	−0.0540781	−	0.0312220i
$527$	32.3901	−	15.3693i	1.41093	−	0.669497i
$528$	13.8985	+	1.68758i	0.604854	+	0.0734426i
$529$	−2.20140	+	3.81293i	−0.0957129	+	0.165780i
$530$	1.09332	+	1.89368i	0.0474906	+	0.0822561i
$531$	2.73365	+	6.41611i	0.118630	+	0.278435i
$532$	−0.197220	+	0.174722i	−0.00855059	+	0.00757516i
$533$	−13.7039	−	0.718608i	−0.593581	−	0.0311264i
$534$	0.959442	+	0.849991i	0.0415191	+	0.0367827i
$535$	4.51861	−	13.5349i	0.195357	−	0.585164i
$536$	0.254306	+	6.31053i	0.0109843	+	0.272574i
$537$	1.44713	+	1.77241i	0.0624483	+	0.0764853i
$538$	16.6299	−	18.7713i	0.716968	−	0.809289i
$539$	21.4727	−	4.38369i	0.924897	−	0.188819i
$540$	0.0847361	+	0.0245441i	0.00364646	+	0.00105621i
$541$	10.5084	+	3.98531i	0.451791	+	0.171342i	0.569996	−	0.821647i	$-0.306945\pi$
$541$	10.5084	+	3.98531i	0.451791	+	0.171342i	−0.118205	+	0.992989i	$0.537714\pi$
$542$	−1.56300	+	38.7855i	−0.0671367	+	1.66598i
$543$	−12.7405	+	9.57383i	−0.546745	+	0.410853i
$544$	2.05033	+	0.418578i	0.0879073	+	0.0179464i
$545$	17.8374	+	9.36178i	0.764069	+	0.401014i
$546$	−4.54468	−	2.00169i	−0.194494	−	0.0856645i
$547$	25.4299	−	13.3467i	1.08731	−	0.570662i	0.176837	−	0.984240i	$-0.443413\pi$
$547$	25.4299	−	13.3467i	1.08731	−	0.570662i	0.910469	+	0.413578i	$0.135721\pi$
$548$	0.596712	−	0.172840i	0.0254903	−	0.00738335i
$549$	15.0766	+	1.21711i	0.643454	+	0.0519450i
$550$	−3.69729	−	18.1105i	−0.157653	−	0.772235i
$551$	1.98357	−	3.77937i	0.0845029	−	0.161007i
$552$	−9.05581	+	12.0511i	−0.385441	+	0.512929i
$553$	3.82697	+	6.05187i	0.162739	+	0.257352i
$554$	14.7695	+	10.1946i	0.627494	+	0.433128i
$555$	−1.14653	−	2.41626i	−0.0486674	−	0.102564i
$556$	0.480606	+	0.500364i	0.0203822	+	0.0212201i
$557$	6.88133	−	6.60960i	0.291571	−	0.280058i	−0.532638	−	0.846343i	$-0.678799\pi$
$557$	6.88133	−	6.60960i	0.291571	−	0.280058i	0.824209	+	0.566285i	$0.191620\pi$
$558$	−1.23275	+	10.1526i	−0.0521863	+	0.429793i
$559$	−2.03119	+	15.1884i	−0.0859101	+	0.642401i
$560$	0.532924	+	4.38903i	0.0225202	+	0.185470i
$561$	13.7251	+	11.2062i	0.579473	+	0.473125i
$562$	−0.281940	+	1.38103i	−0.0118929	+	0.0582554i
$563$	3.05876	−	10.5601i	0.128911	−	0.445053i	−0.869930	−	0.493175i	$-0.835836\pi$
$563$	3.05876	−	10.5601i	0.128911	−	0.445053i	0.998841	+	0.0481215i	$0.0153235\pi$
$564$	0.233881	−	0.948894i	0.00984818	−	0.0399556i
$565$	−1.38725	−	17.1842i	−0.0583622	−	0.722946i
$566$	−0.0656881	+	0.404195i	−0.00276108	+	0.0169896i
$567$	0.658472	+	0.743262i	0.0276532	+	0.0312141i
$568$	−25.6627	−	19.2843i	−1.07678	−	0.809150i
$569$	−12.2611	+	15.0172i	−0.514013	+	0.629552i	−0.964770	−	0.263095i	$-0.915257\pi$
$569$	−12.2611	+	15.0172i	−0.514013	+	0.629552i	0.450757	+	0.892647i	$0.351154\pi$
$570$	0.898816	+	5.53063i	0.0376472	+	0.231653i
$571$	−30.3983	+	7.49252i	−1.27213	+	0.313552i	−0.816878	−	0.576810i	$-0.804297\pi$
$571$	−30.3983	+	7.49252i	−1.27213	+	0.313552i	−0.455252	+	0.890362i	$0.650451\pi$
$572$	−0.729671	+	0.684059i	−0.0305091	+	0.0286020i
$573$	−14.8140	−	3.65133i	−0.618865	−	0.152537i
$574$	−0.421809	+	5.22504i	−0.0176060	+	0.218089i
$575$	18.1580	+	6.06203i	0.757240	+	0.252804i
$576$	−5.73636	+	5.97218i	−0.239015	+	0.248841i
$577$			6.67603i			0.277927i	0.990298	+	0.138963i	$0.0443771\pi$
$577$			6.67603i			0.277927i	−0.990298	+	0.138963i	$0.955623\pi$
$578$	−6.64423	−	6.38187i	−0.276363	−	0.265451i
$579$	−4.09091	+	3.34012i	−0.170012	+	0.138811i
$580$	0.0502011	+	0.0956501i	0.00208449	+	0.00397166i
$581$	1.90234	+	0.309160i	0.0789222	+	0.0128261i
$582$	−9.04434	−	5.71930i	−0.374900	−	0.237072i
$583$	4.47851	+	2.12508i	0.185481	+	0.0880119i
$584$	−12.8114	−	18.5606i	−0.530141	−	0.768042i
$585$	3.46735	−	2.33183i	0.143357	−	0.0964095i
$586$	7.12305	−	10.3195i	0.294250	−	0.426295i
$587$	−8.45795	+	4.88320i	−0.349097	+	0.201551i	−0.664287	−	0.747477i	$-0.731265\pi$
$587$	−8.45795	+	4.88320i	−0.349097	+	0.201551i	0.315191	+	0.949028i	$0.397932\pi$
$588$	−0.196255	+	0.413599i	−0.00809342	+	0.0170565i
$589$	24.3791	−	8.13892i	1.00452	−	0.335359i
$590$	−2.68289	−	10.8849i	−0.110453	−	0.448125i
$591$	16.1598	+	0.651219i	0.664727	+	0.0267876i
$592$	8.85910	+	0.357009i	0.364107	+	0.0146730i
$593$	−3.41870	−	13.8702i	−0.140389	−	0.569581i	−0.998431	−	0.0560010i	$-0.982165\pi$
$593$	−3.41870	−	13.8702i	−0.140389	−	0.569581i	0.858042	−	0.513580i	$-0.171681\pi$
$594$	−4.79441	+	1.60061i	−0.196717	+	0.0656738i
$595$	−2.39873	+	5.05522i	−0.0983384	+	0.207244i
$596$	−1.10996	+	0.640834i	−0.0454656	+	0.0262496i
$597$	−2.11381	+	3.06238i	−0.0865125	+	0.125335i
$598$	5.95675	+	25.4926i	0.243590	+	1.04247i
$599$	−20.4864	−	29.6797i	−0.837052	−	1.21268i	−0.974992	−	0.222238i	$-0.928664\pi$
$599$	−20.4864	−	29.6797i	−0.837052	−	1.21268i	0.137941	−	0.990441i	$-0.455952\pi$
$600$	9.51398	+	4.51444i	0.388407	+	0.184301i
$601$	8.05555	+	5.09402i	0.328593	+	0.207789i	0.688567	−	0.725173i	$-0.258240\pi$
$601$	8.05555	+	5.09402i	0.328593	+	0.207789i	−0.359974	+	0.932962i	$0.617215\pi$
$602$	5.77779	+	0.938982i	0.235485	+	0.0382700i
$603$	−1.01923	−	1.94198i	−0.0415061	−	0.0790834i
$604$	−1.02938	+	0.840462i	−0.0418848	+	0.0341979i
$605$	1.90532	+	1.83008i	0.0774621	+	0.0744034i
$606$			13.3044i			0.540453i
$607$	−19.4479	+	20.2474i	−0.789367	+	0.821818i	−0.987378	−	0.158382i	$-0.949372\pi$
$607$	−19.4479	+	20.2474i	−0.789367	+	0.821818i	0.198011	+	0.980200i	$0.436552\pi$
$608$	1.42298	+	0.475062i	0.0577096	+	0.0192663i
$609$	−0.0978397	+	1.21196i	−0.00396466	+	0.0491112i
$610$	−23.6073	−	5.81867i	−0.955831	−	0.235591i
$611$	−27.3578	−	37.3400i	−1.10678	−	1.51061i
$612$	−0.359375	+	0.0885781i	−0.0145269	+	0.00358056i
$613$	−4.70549	−	28.9540i	−0.190053	−	1.16944i	−0.890243	−	0.455486i	$-0.849466\pi$
$613$	−4.70549	−	28.9540i	−0.190053	−	1.16944i	0.700190	−	0.713956i	$-0.253099\pi$
$614$	−27.6900	+	33.9141i	−1.11748	+	1.36866i
$615$	−3.52619	−	2.64976i	−0.142190	−	0.106848i
$616$	6.90990	+	7.79967i	0.278408	+	0.314258i
$617$	3.49994	−	21.5360i	0.140902	−	0.867006i	−0.816309	−	0.577616i	$-0.803983\pi$
$617$	3.49994	−	21.5360i	0.140902	−	0.867006i	0.957211	−	0.289390i	$-0.0934526\pi$
$618$	0.839765	+	10.4024i	0.0337803	+	0.418444i
$619$	−10.0338	+	40.7085i	−0.403291	+	1.63621i	0.321259	+	0.946991i	$0.395894\pi$
$619$	−10.0338	+	40.7085i	−0.403291	+	1.63621i	−0.724550	+	0.689223i	$0.757952\pi$
$620$	−0.180973	+	0.624790i	−0.00726804	+	0.0250922i
$621$	1.04709	−	5.12898i	0.0420182	−	0.205819i
$622$	−31.4248	−	25.6576i	−1.26002	−	1.02878i
$623$	0.110610	+	0.910956i	0.00443150	+	0.0364967i
$624$	1.50302	+	13.7706i	0.0601691	+	0.551265i
$625$	0.802503	−	6.60921i	0.0321001	−	0.264368i
$626$	−31.7120	+	30.4598i	−1.26747	+	1.21742i
$627$	8.79934	+	9.16109i	0.351412	+	0.365859i
$628$	−0.561317	−	1.18295i	−0.0223990	−	0.0472049i
$629$	9.23469	+	6.37425i	0.368211	+	0.254158i
$630$	−0.853104	−	1.34908i	−0.0339885	−	0.0537485i
$631$	7.22876	−	9.61973i	0.287772	−	0.382955i	−0.632287	−	0.774734i	$-0.717884\pi$
$631$	7.22876	−	9.61973i	0.287772	−	0.382955i	0.920059	+	0.391779i	$0.128140\pi$
$632$	9.65001	−	18.3866i	0.383857	−	0.731378i
$633$	0.223925	+	1.09686i	0.00890020	+	0.0435961i
$634$	28.1272	+	2.27066i	1.11707	+	0.0901795i
$635$	−3.16995	+	0.918188i	−0.125796	+	0.0364372i
$636$	−0.0916889	+	0.0481221i	−0.00363570	+	0.00190816i
$637$	9.05766	+	19.7013i	0.358878	+	0.780594i
$638$	−5.48030	−	2.87628i	−0.216967	−	0.113873i
$639$	10.9221	+	2.22977i	0.432072	+	0.0882082i
$640$	9.84400	−	7.39729i	0.389118	−	0.292403i
$641$	0.486395	−	12.0698i	0.0192114	−	0.476727i	−0.960735	−	0.277467i	$-0.910505\pi$
$641$	0.486395	−	12.0698i	0.0192114	−	0.476727i	0.979947	−	0.199260i	$-0.0638538\pi$
$642$	−15.9683	−	6.05598i	−0.630219	−	0.239010i
$643$	25.5505	+	7.40079i	1.00761	+	0.291859i	0.740681	−	0.671857i	$-0.234503\pi$
$643$	25.5505	+	7.40079i	1.00761	+	0.291859i	0.266932	+	0.963715i	$0.413990\pi$
$644$	−0.387693	+	0.0791480i	−0.0152772	+	0.00311887i
$645$	−3.26613	+	3.68670i	−0.128604	+	0.145164i
$646$	−14.8679	−	18.2099i	−0.584971	−	0.716460i
$647$	1.55132	+	38.4956i	0.0609886	+	1.51342i	0.683005	+	0.730413i	$0.260672\pi$
$647$	1.55132	+	38.4956i	0.0609886	+	1.51342i	−0.622017	+	0.783004i	$0.713686\pi$
$648$	0.911897	−	2.73147i	0.0358227	−	0.107302i
$649$	−19.0232	−	16.8531i	−0.746727	−	0.661542i
$650$	16.6165	−	7.63940i	0.651751	−	0.299642i
$651$	−5.48034	+	4.85516i	−0.214791	+	0.190289i
$652$	−0.511479	−	1.20049i	−0.0200311	−	0.0470146i
$653$	−4.26209	−	7.38216i	−0.166788	−	0.288886i	0.770500	−	0.637439i	$-0.220006\pi$
$653$	−4.26209	−	7.38216i	−0.166788	−	0.288886i	−0.937289	+	0.348553i	$0.886673\pi$
$654$	12.0552	−	20.8801i	0.471394	−	0.816478i
$655$	−20.9290	−	2.54124i	−0.817762	−	0.0992943i
$656$	13.2107	−	6.26855i	0.515790	−	0.244746i
$657$	6.78249	+	3.91587i	0.264610	+	0.152773i
$658$	−14.5524	+	10.0448i	−0.567312	+	0.391587i
$659$	12.3266	+	5.25186i	0.480175	+	0.204583i	0.618471	−	0.785808i	$-0.287752\pi$
$659$	12.3266	+	5.25186i	0.480175	+	0.204583i	−0.138296	+	0.990391i	$0.544163\pi$
$660$	−0.317318	+	0.0515692i	−0.0123516	+	0.00200733i
$661$	−25.9995	−	34.5991i	−1.01126	−	1.34575i	−0.937314	−	0.348487i	$-0.886696\pi$
$661$	−25.9995	−	34.5991i	−1.01126	−	1.34575i	−0.0739506	−	0.997262i	$-0.523561\pi$
$662$	5.88512	−	15.5178i	0.228732	−	0.603116i
$663$	−7.70684	+	15.7464i	−0.299309	+	0.611541i
$664$	−1.98194	−	5.22595i	−0.0769142	−	0.202806i
$665$	−2.14393	+	3.39035i	−0.0831380	+	0.131472i
$666$	−2.94480	+	1.25466i	−0.114109	+	0.0486172i
$667$	5.41761	−	3.42589i	0.209771	−	0.132651i
$668$	0.222125	−	0.0269708i	0.00859427	−	0.00104353i
$669$	1.07874	−	2.53189i	0.0417065	−	0.0978887i
$670$	1.11640	+	3.34402i	0.0431303	+	0.129191i
$671$	−51.5378	+	19.5457i	−1.98960	+	0.754554i
$672$	−0.425973	+	0.0343881i	−0.0164323	+	0.00132655i
$673$	10.4115	+	35.9447i	0.401334	+	1.38557i	0.865984	+	0.500071i	$0.166693\pi$
$673$	10.4115	+	35.9447i	0.401334	+	1.38557i	−0.464650	+	0.885494i	$0.653820\pi$
$674$	−43.3808	+	1.74819i	−1.67097	+	0.0673376i
$675$	−3.65693			−0.140755
$676$	−0.823336	−	0.549009i	−0.0316668	−	0.0211157i
$677$	−45.0037			−1.72963			−0.864817	−	0.502088i	$-0.832565\pi$
$677$	−45.0037			−1.72963			−0.864817	+	0.502088i	$0.832565\pi$
$678$	−20.6171	+	0.830840i	−0.791794	+	0.0319082i
$679$	−2.13139	−	7.35840i	−0.0817951	−	0.282389i
$680$	16.1742	−	1.30572i	0.620253	−	0.0500720i
$681$	−14.0814	+	5.34039i	−0.539602	+	0.204644i
$682$	−11.8019	−	35.3509i	−0.451917	−	1.35366i
$683$	−12.0418	+	28.2632i	−0.460768	+	1.08146i	0.513909	+	0.857845i	$0.328197\pi$
$683$	−12.0418	+	28.2632i	−0.460768	+	1.08146i	−0.974677	+	0.223618i	$0.928213\pi$
$684$	−0.263410	+	0.0319837i	−0.0100717	+	0.00122293i
$685$	7.99375	−	5.05494i	0.305426	−	0.193139i
$686$	16.4900	−	7.02573i	0.629591	−	0.268244i
$687$	−3.10554	+	4.91101i	−0.118484	+	0.187367i
$688$	−5.79012	−	15.2673i	−0.220746	−	0.582060i
$689$	−1.03920	+	4.79330i	−0.0395902	+	0.182610i
$690$	−2.98388	+	7.86783i	−0.113594	+	0.299523i
$691$	−8.87967	−	11.8167i	−0.337798	−	0.449528i	0.598297	−	0.801274i	$-0.295844\pi$
$691$	−8.87967	−	11.8167i	−0.337798	−	0.449528i	−0.936095	+	0.351746i	$0.885588\pi$
$692$	1.57837	−	0.256511i	0.0600007	−	0.00975107i
$693$	−3.32901	−	1.41836i	−0.126458	−	0.0538789i
$694$	16.0484	−	11.0774i	0.609190	−	0.420494i
$695$	9.14736	+	5.28123i	0.346979	+	0.200329i
$696$	3.18568	−	1.51162i	0.120753	−	0.0572979i
$697$	18.3710	+	2.23064i	0.695850	+	0.0844915i
$698$	−8.30177	+	14.3791i	−0.314227	+	0.544256i
$699$	−1.93094	−	3.34449i	−0.0730350	−	0.126500i
$700$	0.108348	+	0.254303i	0.00409518	+	0.00961174i
$701$	−1.72974	+	1.53241i	−0.0653312	+	0.0578784i	−0.695157	−	0.718858i	$-0.744665\pi$
$701$	−1.72974	+	1.53241i	−0.0653312	+	0.0578784i	0.629825	+	0.776737i	$0.283126\pi$
$702$	−2.62149	−	4.25890i	−0.0989417	−	0.160742i
$703$	6.02121	+	5.33433i	0.227094	+	0.201188i
$704$	9.55593	−	28.6235i	0.360153	−	1.07879i
$705$	−0.599100	−	14.8665i	−0.0225634	−	0.559905i
$706$	27.2946	+	33.4299i	1.02725	+	1.25815i
$707$	−6.31602	+	7.12931i	−0.237538	+	0.268125i
$708$	0.520163	−	0.106192i	0.0195489	−	0.00399094i
$709$	13.2668	+	3.84278i	0.498245	+	0.144318i	0.517819	−	0.855490i	$-0.326744\pi$
$709$	13.2668	+	3.84278i	0.498245	+	0.144318i	−0.0195743	+	0.999808i	$0.506231\pi$
$710$	−16.7545	−	6.35414i	−0.628785	−	0.238467i
$711$	−0.290355	+	7.20509i	−0.0108892	+	0.270212i
$712$	2.12746	−	1.59868i	0.0797299	−	0.0599131i
$713$	37.8178	+	7.72056i	1.41629	+	0.289137i
$714$	5.92982	+	3.11221i	0.221918	+	0.116472i
$715$	−7.77267	+	13.0938i	−0.290682	+	0.489679i
$716$	0.154229	−	0.0809454i	0.00576379	−	0.00302507i
$717$	14.1176	−	4.08921i	0.527231	−	0.152714i
$718$	6.84421	+	0.552522i	0.255424	+	0.0206199i
$719$	1.02836	+	5.03724i	0.0383513	+	0.187857i	0.994454	−	0.105176i	$-0.0335405\pi$
$719$	1.02836	+	5.03724i	0.0383513	+	0.187857i	−0.956102	+	0.293033i	$0.905335\pi$
$720$	−2.06917	+	3.94248i	−0.0771136	+	0.146928i
$721$	−4.48834	+	5.97290i	−0.167155	+	0.222442i
$722$	5.07770	+	8.02975i	0.188973	+	0.298836i
$723$	12.9216	+	8.91916i	0.480561	+	0.331707i
$724$	0.520064	+	1.09601i	0.0193280	+	0.0407329i
$725$	−3.10193	−	3.22945i	−0.115203	−	0.119939i
$726$	2.28037	−	2.19033i	0.0846326	−	0.0812907i
$727$	2.84444	−	23.4261i	0.105494	−	0.868825i	−0.839865	−	0.542795i	$-0.817366\pi$
$727$	2.84444	−	23.4261i	0.105494	−	0.868825i	0.945360	−	0.326030i	$-0.105711\pi$
$728$	−5.95908	+	8.41337i	−0.220858	+	0.311820i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−9.75163	−	7.96196i	−0.360924	−	0.294685i
$731$	4.13350	−	20.2472i	0.152883	−	0.748870i
$732$	0.320340	−	1.10594i	0.0118401	−	0.0408768i
$733$	4.18993	−	16.9992i	0.154758	−	0.627880i	−0.841408	−	0.540400i	$-0.818273\pi$
$733$	4.18993	−	16.9992i	0.154758	−	0.627880i	0.996166	−	0.0874791i	$-0.0278811\pi$
$734$	−0.328267	−	4.06631i	−0.0121165	−	0.150090i
$735$	−1.11801	+	6.87940i	−0.0412385	+	0.253751i
$736$	1.49396	+	1.68634i	0.0550683	+	0.0621592i
$737$	6.38935	+	4.80129i	0.235355	+	0.176858i
$738$	−3.33872	+	4.08919i	−0.122900	+	0.150525i
$739$	5.25258	+	32.3204i	0.193219	+	1.18893i	0.884570	+	0.466407i	$0.154452\pi$
$739$	5.25258	+	32.3204i	0.193219	+	1.18893i	−0.691351	+	0.722519i	$0.742984\pi$
$740$	−0.197672	+	0.0487217i	−0.00726656	+	0.00179105i
$741$	−6.84539	+	10.5403i	−0.251472	+	0.387206i
$742$	1.81912	+	0.448374i	0.0667822	+	0.0164603i
$743$	1.42633	−	17.6682i	0.0523269	−	0.648185i	−0.916434	−	0.400187i	$-0.868945\pi$
$743$	1.42633	−	17.6682i	0.0523269	−	0.648185i	0.968760	−	0.247998i	$-0.0797727\pi$
$744$	20.1401	+	6.72375i	0.738372	+	0.246505i
$745$	−13.5168	+	14.0724i	−0.495216	+	0.515575i
$746$		−	32.8085i		−	1.20121i
$747$	1.39978	+	1.34451i	0.0512155	+	0.0491931i
$748$	1.04479	−	0.853043i	0.0382012	−	0.0311903i
$749$	−5.68184	−	10.8258i	−0.207610	−	0.395568i
$750$	13.7354	+	2.23222i	0.501546	+	0.0815092i
$751$	26.9642	+	17.0511i	0.983938	+	0.622205i	0.926560	−	0.376148i	$-0.122752\pi$
$751$	26.9642	+	17.0511i	0.983938	+	0.622205i	0.0573782	+	0.998353i	$0.481726\pi$
$752$	44.5624	+	21.1451i	1.62502	+	0.771083i
$753$	−5.35400	−	7.75660i	−0.195110	−	0.282666i
$754$	1.53742	−	5.92760i	0.0559895	−	0.215870i
$755$	−11.4929	+	16.6503i	−0.418270	+	0.605968i
$756$	0.0654617	−	0.0377943i	0.00238082	−	0.00137457i
$757$	−3.01605	+	6.35619i	−0.109620	+	0.231019i	−0.950846	−	0.309665i	$-0.899783\pi$
$757$	−3.01605	+	6.35619i	−0.109620	+	0.231019i	0.841226	+	0.540684i	$0.181835\pi$
$758$	−32.5833	+	10.8779i	−1.18348	+	0.395103i
$759$	4.56521	+	18.5218i	0.165707	+	0.672299i
$760$	11.6235	+	0.468410i	0.421628	+	0.0169910i
$761$	44.8810	+	1.80864i	1.62694	+	0.0655633i	0.836850	−	0.547433i	$-0.184395\pi$
$761$	44.8810	+	1.80864i	1.62694	+	0.0655633i	0.790086	+	0.612996i	$0.210036\pi$
$762$	0.945273	+	3.83512i	0.0342436	+	0.138932i
$763$	16.3724	−	5.46590i	0.592720	−	0.197879i
$764$	−0.497897	+	1.04929i	−0.0180133	+	0.0379622i
$765$	−4.88003	+	2.81749i	−0.176438	+	0.101866i
$766$	−23.6640	+	34.2832i	−0.855014	+	1.23870i
$767$	11.9547	−	22.1223i	0.431658	−	0.798790i
$768$	1.03630	+	1.50134i	0.0373942	+	0.0541748i
$769$	−18.1007	−	8.58890i	−0.652729	−	0.309724i	0.0733795	−	0.997304i	$-0.476622\pi$
$769$	−18.1007	−	8.58890i	−0.652729	−	0.309724i	−0.726108	+	0.687580i	$0.758673\pi$
$770$	4.91620	+	3.10881i	0.177167	+	0.112034i
$771$	2.95697	+	0.480555i	0.106493	+	0.0173068i
$772$	0.186830	+	0.355975i	0.00672416	+	0.0128118i
$773$	7.92131	−	6.46755i	0.284910	−	0.232622i	−0.479203	−	0.877704i	$-0.659074\pi$
$773$	7.92131	−	6.46755i	0.284910	−	0.232622i	0.764113	+	0.645082i	$0.223177\pi$
$774$	4.25144	+	4.08356i	0.152815	+	0.146781i
$775$		−	26.9639i		−	0.968570i
$776$	−15.3899	+	16.0226i	−0.552465	+	0.575177i
$777$	−2.17364	−	0.725666i	−0.0779787	−	0.0260331i
$778$	−2.53144	+	31.3575i	−0.0907566	+	1.12422i
$779$	12.8813	+	3.17494i	0.461519	+	0.113754i
$780$	−0.121122	−	0.294115i	−0.00433688	−	0.0105310i
$781$	−39.4420	+	9.72159i	−1.41135	+	0.347866i
$782$	−5.66322	−	34.8472i	−0.202516	−	1.24613i
$783$	−0.774424	+	0.948497i	−0.0276757	+	0.0338965i
$784$	−18.4715	−	13.8804i	−0.659696	−	0.495729i
$785$	−13.2188	−	14.9210i	−0.471800	−	0.532552i
$786$	−4.04762	+	24.9060i	−0.144374	+	0.888367i
$787$	0.623019	+	7.71748i	0.0222082	+	0.275098i	0.998325	+	0.0578525i	$0.0184253\pi$
$787$	0.623019	+	7.71748i	0.0222082	+	0.275098i	−0.976117	+	0.217246i	$0.930293\pi$
$788$	0.294628	−	1.19535i	0.0104957	−	0.0425826i
$789$	0.287263	−	0.991746i	0.0102268	−	0.0353071i
$790$	2.31855	−	11.3570i	0.0824902	−	0.404064i
$791$	−11.4423	−	9.34238i	−0.406843	−	0.332177i
$792$	1.26489	+	10.4173i	0.0449460	+	0.370164i
$793$	−30.4342	−	45.2545i	−1.08075	−	1.60703i
$794$	5.05930	−	41.6671i	0.179548	−	1.47871i
$795$	−1.13696	+	1.09206i	−0.0403237	+	0.0387314i
$796$	0.196219	+	0.204286i	0.00695481	+	0.00724072i
$797$	9.09657	+	19.1706i	0.322217	+	0.679058i	0.998332	−	0.0577385i	$-0.0183890\pi$
$797$	9.09657	+	19.1706i	0.322217	+	0.679058i	−0.676115	+	0.736796i	$0.736338\pi$
$798$	3.95113	+	2.72727i	0.139868	+	0.0965441i
$799$	33.3636	+	52.7604i	1.18032	+	1.86653i
$800$	0.945482	−	1.25821i	0.0334278	−	0.0444844i
$801$	−0.429464	+	0.818274i	−0.0151743	+	0.0289123i
$802$	−5.92843	−	29.0394i	−0.209340	−	1.02542i
$803$	−28.4473	−	2.29650i	−1.00388	−	0.0810417i
$804$	−0.160360	+	0.0464488i	−0.00565545	+	0.00163812i
$805$	−5.33406	+	2.79953i	−0.188001	+	0.0986705i
$806$	31.4024	−	19.3292i	1.10610	−	0.680842i
$807$	16.0094	+	8.40238i	0.563558	+	0.295778i
$808$	27.0633	+	5.52501i	0.952083	+	0.194369i
$809$	36.2144	−	27.2134i	1.27323	−	0.956771i	0.273244	−	0.961945i	$-0.411903\pi$
$809$	36.2144	−	27.2134i	1.27323	−	0.956771i	0.999987	+	0.00517382i	$0.00164688\pi$
$810$	0.0647256	−	1.60615i	0.00227423	−	0.0564344i
$811$	−27.8207	−	10.5510i	−0.976918	−	0.370496i	−0.186089	−	0.982533i	$-0.559581\pi$
$811$	−27.8207	−	10.5510i	−0.976918	−	0.370496i	−0.790829	+	0.612037i	$0.790350\pi$
$812$	0.0889033	+	0.0257512i	0.00311990	+	0.000903689i
$813$	−27.4199	+	5.59782i	−0.961659	+	0.196324i
$814$	7.73507	−	8.73109i	0.271114	−	0.306024i
$815$	−12.5643	−	15.3885i	−0.440108	−	0.539035i
$816$	−0.752199	−	18.6656i	−0.0263322	−	0.653428i
$817$	4.69128	−	14.0521i	0.164127	−	0.491621i
$818$	−19.7867	−	17.5294i	−0.691824	−	0.612903i
$819$	0.617080	−	3.52669i	0.0215625	−	0.123232i
$820$	−0.251321	+	0.222651i	−0.00877651	+	0.00777531i
$821$	15.7661	+	37.0044i	0.550241	+	1.29146i	0.930401	+	0.366543i	$0.119459\pi$
$821$	15.7661	+	37.0044i	0.550241	+	1.29146i	−0.380160	+	0.924921i	$0.624131\pi$
$822$	−5.65985	−	9.80315i	−0.197410	−	0.341924i
$823$	−3.94682	+	6.83610i	−0.137578	+	0.238291i	−0.926579	−	0.376100i	$-0.877265\pi$
$823$	−3.94682	+	6.83610i	−0.137578	+	0.238291i	0.789002	+	0.614391i	$0.210598\pi$
$824$	21.5089	+	2.61165i	0.749297	+	0.0909811i
$825$	12.0396	−	5.71288i	0.419166	−	0.198897i
$826$	−8.31872	−	4.80281i	−0.289445	−	0.167111i
$827$	−3.81027	+	2.63004i	−0.132496	+	0.0914554i	−0.632469	−	0.774585i	$-0.717959\pi$
$827$	−3.81027	+	2.63004i	−0.132496	+	0.0914554i	0.499973	+	0.866041i	$0.333343\pi$
$828$	−0.366597	−	0.156192i	−0.0127401	−	0.00542806i
$829$	4.79895	−	0.779905i	0.166674	−	0.0270872i	−0.0765014	−	0.997069i	$-0.524375\pi$
$829$	4.79895	−	0.779905i	0.166674	−	0.0270872i	0.243176	+	0.969982i	$0.421811\pi$
$830$	−1.87426	−	2.49419i	−0.0650567	−	0.0865747i
$831$	−4.58806	+	12.0977i	−0.159158	+	0.419665i
$832$	29.7290	+	2.76281i	1.03067	+	0.0957834i
$833$	−10.3693	−	27.3415i	−0.359274	−	0.947328i
$834$	6.75654	−	10.6846i	0.233960	−	0.369978i
$835$	3.13394	−	1.33525i	0.108454	−	0.0462081i
$836$	0.817254	−	0.516800i	0.0282653	−	0.0178739i
$837$	−7.31960	+	0.888761i	−0.253003	+	0.0307201i
$838$	−16.4891	+	38.7013i	−0.569606	+	1.33691i
$839$	−6.63835	−	19.8843i	−0.229181	−	0.686482i	−0.998846	−	0.0480334i	$-0.984705\pi$
$839$	−6.63835	−	19.8843i	−0.229181	−	0.686482i	0.769664	−	0.638449i	$-0.220424\pi$
$840$	−3.09852	+	1.17511i	−0.106909	+	0.0405453i
$841$	27.4114	−	2.21288i	0.945222	−	0.0763062i
$842$	−3.38445	−	11.6845i	−0.116636	−	0.402674i
$843$	−1.01538	+	0.0409185i	−0.0349716	+	0.00140931i
$844$	0.0852175			0.00293331
$845$	−14.3652	−	4.54090i	−0.494179	−	0.156212i
$846$	−17.8074			−0.612230
$847$	2.26179	−	0.0911468i	0.0777159	−	0.00313184i
$848$	−1.45403	−	5.01990i	−0.0499317	−	0.172384i
$849$	−0.294274	+	0.0237563i	−0.0100995	+	0.000815314i
$850$	−23.0604	+	8.74564i	−0.790964	+	0.299973i
$851$	3.82552	+	11.4588i	0.131137	+	0.392804i
$852$	0.332610	−	0.780665i	0.0113950	−	0.0267451i
$853$	−5.69349	+	0.691315i	−0.194941	+	0.0236702i	−0.217425	−	0.976077i	$-0.569766\pi$
$853$	−5.69349	+	0.691315i	−0.194941	+	0.0236702i	0.0224835	+	0.999747i	$0.492843\pi$
$854$	−17.6076	+	11.1344i	−0.602521	+	0.381011i
$855$	−3.71642	+	1.58342i	−0.127099	+	0.0541518i
$856$	−18.9501	+	29.9673i	−0.647702	+	1.02426i
$857$	5.27367	+	13.9055i	0.180145	+	0.475003i	0.994422	−	0.105473i	$-0.0336356\pi$
$857$	5.27367	+	13.9055i	0.180145	+	0.475003i	−0.814277	+	0.580476i	$0.802866\pi$
$858$	15.2840	+	9.92618i	0.521786	+	0.338874i
$859$	12.1445	−	32.0225i	0.414366	−	1.09259i	−0.551641	−	0.834081i	$-0.685998\pi$
$859$	12.1445	−	32.0225i	0.414366	−	1.09259i	0.966008	−	0.258513i	$-0.0832325\pi$
$860$	0.225238	+	0.299737i	0.00768054	+	0.0102209i
$861$	−3.73036	+	0.606243i	−0.127130	+	0.0206607i
$862$	−14.6398	−	6.23743i	−0.498633	−	0.212448i
$863$	21.4052	−	14.7750i	0.728643	−	0.502946i	−0.145050	−	0.989424i	$-0.546334\pi$
$863$	21.4052	−	14.7750i	0.728643	−	0.502946i	0.873692	+	0.486479i	$0.161719\pi$
$864$	−0.372717	−	0.215188i	−0.0126801	−	0.00732086i
$865$	21.9944	−	10.4365i	0.747831	−	0.354850i
$866$	9.61849	+	1.16790i	0.326850	+	0.0396867i
$867$	3.32100	−	5.75214i	0.112787	−	0.195353i
$868$	0.278671	+	0.482673i	0.00945872	+	0.0163830i
$869$	−10.2999	−	24.1748i	−0.349400	−	0.820073i
$870$	1.47330	−	1.30523i	0.0499497	−	0.0442515i
$871$	−3.18744	+	7.23681i	−0.108002	+	0.245210i
$872$	−37.4674	−	33.1932i	−1.26881	−	1.12406i
$873$	2.44308	−	7.31792i	0.0826858	−	0.247674i
$874$	−1.01911	−	25.2890i	−0.0344719	−	0.855412i
$875$	6.30058	+	7.71681i	0.212998	+	0.260876i
$876$	0.395335	−	0.446241i	0.0133571	−	0.0150771i
$877$	−53.0627	+	10.8328i	−1.79180	+	0.365799i	−0.976883	−	0.213776i	$-0.931424\pi$
$877$	−53.0627	+	10.8328i	−1.79180	+	0.365799i	−0.814919	+	0.579575i	$0.803219\pi$
$878$	−36.5857	−	10.5972i	−1.23471	−	0.357637i
$879$	8.45276	+	3.20571i	0.285104	+	0.108126i
$880$	0.653331	−	16.2122i	0.0220238	−	0.546514i
$881$	−24.8837	+	18.6989i	−0.838354	+	0.629982i	−0.930716	−	0.365743i	$-0.880815\pi$
$881$	−24.8837	+	18.6989i	−0.838354	+	0.629982i	0.0923614	+	0.995726i	$0.470558\pi$
$882$	8.17304	+	1.66854i	0.275201	+	0.0561826i
$883$	−3.54670	−	1.86145i	−0.119356	−	0.0626428i	0.403988	−	0.914764i	$-0.367624\pi$
$883$	−3.54670	−	1.86145i	−0.119356	−	0.0626428i	−0.523344	+	0.852121i	$0.675316\pi$
$884$	1.05709	+	0.814570i	0.0355537	+	0.0273970i
$885$	7.15666	−	3.75610i	0.240568	−	0.126260i
$886$	−32.0842	+	9.29329i	−1.07789	+	0.312214i
$887$	−32.3356	−	2.61040i	−1.08572	−	0.0876485i	−0.475375	−	0.879783i	$-0.657688\pi$
$887$	−32.3356	−	2.61040i	−1.08572	−	0.0876485i	−0.610346	+	0.792135i	$0.708970\pi$
$888$	1.32928	+	6.51124i	0.0446077	+	0.218503i
$889$	−1.31412	+	2.50385i	−0.0440742	+	0.0839764i
$890$	0.892398	−	1.18757i	0.0299133	−	0.0398073i
$891$	−1.94766	−	3.07997i	−0.0652490	−	0.103183i
$892$	−0.172414	−	0.119009i	−0.00577284	−	0.00398470i
$893$	19.1847	+	40.4308i	0.641991	+	1.35297i
$894$	16.1775	+	16.8426i	0.541057	+	0.563300i
$895$	1.91246	−	1.83694i	0.0639264	−	0.0614021i
$896$	1.27174	−	10.4737i	0.0424858	−	0.349902i
$897$	−16.8173	+	8.56821i	−0.561514	+	0.286084i
$898$	5.28974	+	43.5649i	0.176521	+	1.45378i
$899$	−6.99361	−	5.71011i	−0.233250	−	0.190443i
$900$	−0.0556820	+	0.272749i	−0.00185607	+	0.00909162i
$901$	1.84019	−	6.35308i	0.0613057	−	0.211652i
$902$	4.60384	−	18.6785i	0.153291	−	0.621927i
$903$	0.339585	+	4.20652i	0.0113007	+	0.139984i
$904$	−6.87175	+	42.2836i	−0.228551	+	1.40633i
$905$	12.2473	+	13.8244i	0.407115	+	0.459538i
$906$	19.3579	+	14.5465i	0.643123	+	0.483276i
$907$	−13.5473	+	16.5924i	−0.449831	+	0.550943i	−0.948883	−	0.315629i	$-0.897784\pi$
$907$	−13.5473	+	16.5924i	−0.449831	+	0.550943i	0.499051	+	0.866572i	$0.333682\pi$
$908$	0.183898	+	1.13157i	0.00610286	+	0.0375524i
$909$	−9.31320	+	2.29550i	−0.308899	+	0.0761368i
$910$	−1.88845	+	5.43646i	−0.0626016	+	0.180217i
$911$	−23.1746	−	5.71202i	−0.767809	−	0.189248i	−0.164090	−	0.986445i	$-0.552469\pi$
$911$	−23.1746	−	5.71202i	−0.767809	−	0.189248i	−0.603719	+	0.797198i	$0.706315\pi$
$912$	1.07762	−	13.3487i	0.0356836	−	0.442020i
$913$	−6.70889	−	2.23976i	−0.222032	−	0.0741251i
$914$	9.78182	−	10.1840i	0.323554	−	0.336855i
$915$		−	17.5293i		−	0.579500i
$916$	0.318997	+	0.306401i	0.0105400	+	0.0101238i
$917$	−13.9926	+	11.4246i	−0.462078	+	0.377275i
$918$	3.13419	+	5.97170i	0.103444	+	0.197095i
$919$	19.4982	+	3.16876i	0.643186	+	0.104528i	0.473251	−	0.880928i	$-0.343080\pi$
$919$	19.4982	+	3.16876i	0.643186	+	0.104528i	0.169934	+	0.985455i	$0.445644\pi$
$920$	14.7653	+	9.33703i	0.486799	+	0.307833i
$921$	−28.5178	−	13.5319i	−0.939694	−	0.445890i
$922$	11.1602	+	16.1683i	0.367541	+	0.532475i
$923$	−18.2459	−	35.8124i	−0.600572	−	1.17878i
$924$	−0.156476	+	0.226694i	−0.00514768	+	0.00745770i
$925$	7.30863	−	4.21964i	0.240306	−	0.138741i
$926$	−5.81243	+	12.2494i	−0.191008	+	0.402541i
$927$	−7.13687	+	2.38264i	−0.234406	+	0.0782561i
$928$	−0.126118	−	0.511679i	−0.00414001	−	0.0167967i
$929$	−36.4673	−	1.46958i	−1.19645	−	0.0482154i	−0.565974	−	0.824423i	$-0.691500\pi$
$929$	−36.4673	−	1.46958i	−1.19645	−	0.0482154i	−0.630477	+	0.776208i	$0.717141\pi$
$930$	11.8427	+	0.477246i	0.388338	+	0.0156495i
$931$	−5.01684	−	20.3541i	−0.164420	−	0.667079i
$932$	−0.278848	+	0.0930930i	−0.00913396	+	0.00304936i
$933$	12.5386	−	26.4246i	0.410496	−	0.865103i
$934$	8.78153	−	5.07002i	0.287340	−	0.165896i
$935$	11.6649	−	16.8996i	0.381484	−	0.552675i
$936$	−9.75195	+	3.56392i	−0.318752	+	0.116490i
$937$	0.917493	+	1.32922i	0.0299732	+	0.0434237i	0.837684	−	0.546155i	$-0.183909\pi$
$937$	0.917493	+	1.32922i	0.0299732	+	0.0434237i	−0.807711	+	0.589579i	$0.799294\pi$
$938$	2.72906	+	1.29496i	0.0891071	+	0.0422818i
$939$	−26.7937	−	16.9433i	−0.874379	−	0.552924i
$940$	−1.11793	−	0.181681i	−0.0364628	−	0.00592578i
$941$	13.1572	+	25.0689i	0.428911	+	0.817222i	0.999993	−	0.00367082i	$-0.00116846\pi$
$941$	13.1572	+	25.0689i	0.428911	+	0.817222i	−0.571082	+	0.820893i	$0.693476\pi$
$942$	−18.4807	+	15.0890i	−0.602134	+	0.491627i
$943$	14.3689	+	13.8015i	0.467915	+	0.449438i
$944$			26.7945i			0.872088i
$945$	0.797176	−	0.829948i	0.0259321	−	0.0269982i
$946$	−20.3763	−	6.80261i	−0.662491	−	0.221172i
$947$	−0.493589	+	6.11420i	−0.0160395	+	0.198685i	0.983775	+	0.179408i	$0.0574183\pi$
$947$	−0.493589	+	6.11420i	−0.0160395	+	0.198685i	−0.999814	+	0.0192764i	$0.993864\pi$
$948$	0.532964	+	0.131364i	0.0173099	+	0.00426650i
$949$	−4.19170	−	27.9249i	−0.136068	−	0.906481i
$950$	−17.1670	+	4.23129i	−0.556972	+	0.137281i
$951$	3.26350	+	20.0811i	0.105826	+	0.651174i
$952$	8.79327	−	10.7698i	0.284992	−	0.349051i
$953$	33.7128	+	25.3335i	1.09207	+	0.820634i	0.984817	−	0.173598i	$-0.0555393\pi$
$953$	33.7128	+	25.3335i	1.09207	+	0.820634i	0.107249	+	0.994232i	$0.465796\pi$
$954$	1.25118	+	1.41229i	0.0405084	+	0.0457246i
$955$	−2.83638	+	17.4530i	−0.0917832	+	0.564765i
$956$	−0.0900292	−	1.11521i	−0.00291175	−	0.0360685i
$957$	1.06787	−	4.33253i	0.0345194	−	0.140051i
$958$	−0.843122	+	2.91079i	−0.0272400	+	0.0940435i
$959$	1.62097	−	7.94005i	0.0523440	−	0.256398i
$960$	7.43372	+	6.06944i	0.239922	+	0.195890i
$961$	−2.81652	−	23.1961i	−0.0908555	−	0.748263i
$962$	10.1535	+	5.48684i	0.327361	+	0.176903i
$963$	1.48412	−	12.2229i	0.0478252	−	0.393876i
$964$	0.861978	−	0.827941i	0.0277624	−	0.0266662i
$965$	4.23984	+	4.41414i	0.136485	+	0.142096i
$966$	3.09083	+	6.51380i	0.0994460	+	0.209578i
$967$	−17.4910	−	12.0732i	−0.562473	−	0.388247i	0.252630	−	0.967563i	$-0.418704\pi$
$967$	−17.4910	−	12.0732i	−0.562473	−	0.388247i	−0.815103	+	0.579316i	$0.803320\pi$
$968$	−3.50850	−	5.54825i	−0.112768	−	0.178328i
$969$	10.1819	−	13.5496i	0.327089	−	0.435276i
$970$	−5.76324	+	10.9809i	−0.185046	+	0.352577i
$971$	−8.68602	−	42.5469i	−0.278748	−	1.36540i	−0.842163	−	0.539223i	$-0.818718\pi$
$971$	−8.68602	−	42.5469i	−0.278748	−	1.36540i	0.563416	−	0.826174i	$-0.309487\pi$
$972$	0.0758757	+	0.00612532i	0.00243371	+	0.000196470i
$973$	8.69290	−	2.51793i	0.278682	−	0.0807211i
$974$	−2.71763	+	1.42632i	−0.0870785	+	0.0457023i
$975$	8.21461	+	10.3136i	0.263078	+	0.330300i
$976$	51.4558	+	27.0061i	1.64706	+	0.864444i
$977$	24.9147	+	5.08636i	0.797091	+	0.162727i	0.581275	−	0.813707i	$-0.302554\pi$
$977$	24.9147	+	5.08636i	0.797091	+	0.162727i	0.215815	+	0.976434i	$0.430759\pi$
$978$	−19.0082	+	14.2838i	−0.607816	+	0.456744i
$979$	0.135601	−	3.36490i	0.00433382	−	0.107543i
$980$	0.496071	+	0.188135i	0.0158464	+	0.00600975i
$981$	16.6963	+	4.83614i	0.533071	+	0.154406i
$982$	31.5764	−	6.44636i	1.00764	−	0.205712i
$983$	13.0511	−	14.7316i	0.416264	−	0.469865i	−0.502554	−	0.864546i	$-0.667606\pi$
$983$	13.0511	−	14.7316i	0.416264	−	0.469865i	0.918818	+	0.394681i	$0.129145\pi$
$984$	6.93159	+	8.48965i	0.220971	+	0.270640i
$985$	−0.754705	−	18.7278i	−0.0240469	−	0.596717i
$986$	−2.61511	+	7.83322i	−0.0832822	+	0.249461i
$987$	−9.54230	−	8.45374i	−0.303735	−	0.269086i
$988$	0.681905	+	0.671048i	0.0216943	+	0.0213489i
$989$	16.6527	−	14.7530i	0.529526	−	0.469119i
$990$	2.29604	+	5.38901i	0.0729731	+	0.171274i
$991$	−22.6010	−	39.1462i	−0.717946	−	1.24352i	−0.961812	−	0.273710i	$-0.911749\pi$
$991$	−22.6010	−	39.1462i	−0.717946	−	1.24352i	0.243866	−	0.969809i	$-0.421584\pi$
$992$	1.58666	−	2.74818i	0.0503766	−	0.0872548i
$993$	11.8780	+	1.44225i	0.376937	+	0.0457685i
$994$	−13.8711	+	6.58191i	−0.439964	+	0.208765i
$995$	3.73464	+	2.15619i	0.118396	+	0.0683560i
$996$	0.121593	−	0.0839296i	0.00385282	−	0.00265941i
$997$	45.7242	+	19.4813i	1.44810	+	0.616978i	0.965861	−	0.259061i	$-0.0834132\pi$
$997$	45.7242	+	19.4813i	1.44810	+	0.616978i	0.482240	+	0.876039i	$0.339823\pi$
$998$	−28.2971	+	4.59873i	−0.895729	+	0.145570i
$999$	−1.38636	−	1.84491i	−0.0438626	−	0.0583705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.5	yes	360
169.4	even	78	inner	507.2.t.b.4.5	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.5	✓	360	169.4	even	78	inner
507.2.t.b.127.5	yes	360	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38591 + 0.0558504i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-0.0758757 + 0.00612532i) q^{4} +(-1.08360 + 0.410955i) q^{5} +(0.439231 + 1.31566i) q^{6} +(-0.389218 + 0.913528i) q^{7} +(2.85867 - 0.347105i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(-1.38591 + 0.0558504i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-0.0758757 + 0.00612532i) q^{4} +(-1.08360 + 0.410955i) q^{5} +(0.439231 + 1.31566i) q^{6} +(-0.389218 + 0.913528i) q^{7} +(2.85867 - 0.347105i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(1.47882 - 0.630068i) q^{10} +(1.94766 - 3.07997i) q^{11} +(0.0269934 + 0.0711758i) q^{12} +(3.40592 + 1.18311i) q^{13} +(0.488402 - 1.28781i) q^{14} +(0.696206 + 0.926482i) q^{15} +(-3.79221 + 0.616294i) q^{16} +(-4.47322 - 1.90586i) q^{17} +(1.14151 - 0.787928i) q^{18} +(-3.01875 - 1.74288i) q^{19} +(0.0797016 - 0.0378189i) q^{20} +(0.985747 + 0.119691i) q^{21} +(-2.52727 + 4.37736i) q^{22} +(-2.61738 - 4.53344i) q^{23} +(-1.12873 - 2.64923i) q^{24} +(-2.73725 + 2.42499i) q^{25} +(-4.78638 - 1.44946i) q^{26} +(0.748511 + 0.663123i) q^{27} +(0.0239365 - 0.0716986i) q^{28} +(0.0493053 + 1.22350i) q^{29} +(-1.01663 - 1.24514i) q^{30} +(-4.88945 + 5.51904i) q^{31} +(-0.421679 + 0.0860864i) q^{32} +(-3.50024 - 1.01386i) q^{33} +(6.30594 + 2.39153i) q^{34} +(0.0463374 - 1.14985i) q^{35} +(0.0608556 - 0.0457300i) q^{36} +(-2.26111 - 0.461609i) q^{37} +(4.28108 + 2.24688i) q^{38} +(0.188810 - 3.60060i) q^{39} +(-2.95501 + 1.55091i) q^{40} +(-3.65572 + 1.05889i) q^{41} +(-1.37285 - 0.110828i) q^{42} +(0.850111 + 4.16412i) q^{43} +(-0.128914 + 0.245625i) q^{44} +(0.696206 - 0.926482i) q^{45} +(3.88066 + 6.13678i) q^{46} +(-10.5658 - 7.29305i) q^{47} +(1.64702 + 3.47102i) q^{48} +(4.16603 + 4.33729i) q^{49} +(3.65816 - 3.51371i) q^{50} +(-0.586086 + 4.82685i) q^{51} +(-0.265673 - 0.0689066i) q^{52} +(0.163967 + 1.35039i) q^{53} +(-1.07441 - 0.877226i) q^{54} +(-0.844750 + 4.13786i) q^{55} +(-0.795554 + 2.74657i) q^{56} +(-0.834196 + 3.38447i) q^{57} +(-0.136666 - 1.69291i) q^{58} +(1.11874 - 6.88387i) q^{59} +(-0.0585001 - 0.0660330i) q^{60} +(-12.0921 - 9.08662i) q^{61} +(6.46811 - 7.92200i) q^{62} +(-0.159286 - 0.980128i) q^{63} +(8.04024 - 1.98174i) q^{64} +(-4.17685 + 0.117665i) q^{65} +(4.90766 + 1.20963i) q^{66} +(-0.176479 + 2.18608i) q^{67} +(0.351082 + 0.117209i) q^{68} +(-3.62625 + 3.77533i) q^{69} +1.59618i q^{70} +(-8.03953 - 7.72207i) q^{71} +(-2.23060 + 1.82123i) q^{72} +(-3.63959 - 6.93466i) q^{73} +(3.15949 + 0.513467i) q^{74} +(3.09080 + 1.95450i) q^{75} +(0.239726 + 0.113751i) q^{76} +(2.05558 + 2.97802i) q^{77} +(-0.0605786 + 5.00067i) q^{78} +(4.09628 - 5.93448i) q^{79} +(3.85597 - 2.22624i) q^{80} +(0.428693 - 0.903450i) q^{81} +(5.00738 - 1.67171i) q^{82} +(-0.464489 - 1.88451i) q^{83} +(-0.0755274 - 0.00304365i) q^{84} +(5.63040 + 0.226898i) q^{85} +(-1.41075 - 5.72363i) q^{86} +(1.16147 - 0.387757i) q^{87} +(4.49863 - 9.48066i) q^{88} +(0.800318 - 0.462064i) q^{89} +(-0.913138 + 1.32291i) q^{90} +(-2.40644 + 2.65091i) q^{91} +(0.226364 + 0.327946i) q^{92} +(6.66147 + 3.16091i) q^{93} +(15.0506 + 9.51744i) q^{94} +(3.98737 + 0.648010i) q^{95} +(0.200006 + 0.381080i) q^{96} +(-5.97605 + 4.87929i) q^{97} +(-6.01600 - 5.77844i) q^{98} +3.64412i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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