LMFDB - Embedded newform 414.2.p.a.113.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.24
Character	$\chi$	$=$	414.113
Dual form			414.2.p.a.11.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998867 + 0.0475819i) q^{2} +(1.69982 - 0.332604i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-2.06892 + 1.97271i) q^{5} +(1.71372 - 0.251347i) q^{6} +(-0.688211 + 3.57078i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.77875 - 1.13073i) q^{9} +O(q^{10})$	\(q+(0.998867 + 0.0475819i) q^{2} +(1.69982 - 0.332604i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-2.06892 + 1.97271i) q^{5} +(1.71372 - 0.251347i) q^{6} +(-0.688211 + 3.57078i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.77875 - 1.13073i) q^{9} +(-2.16044 + 1.87203i) q^{10} +(1.50401 + 0.775374i) q^{11} +(1.72374 - 0.169520i) q^{12} +(0.111032 - 0.0213996i) q^{13} +(-0.857336 + 3.53399i) q^{14} +(-2.86065 + 4.04137i) q^{15} +(0.981929 + 0.189251i) q^{16} +(3.31677 - 7.26271i) q^{17} +(2.82940 - 0.997233i) q^{18} +(-4.65114 + 2.12411i) q^{19} +(-2.24707 + 1.76711i) q^{20} +(0.0178232 + 6.29857i) q^{21} +(1.46542 + 0.846059i) q^{22} +(3.54339 - 3.23177i) q^{23} +(1.72985 - 0.0873096i) q^{24} +(0.150930 - 3.16840i) q^{25} +(0.111924 - 0.0160923i) q^{26} +(4.34728 - 2.84626i) q^{27} +(-1.02452 + 3.48919i) q^{28} +(0.0790546 + 0.827898i) q^{29} +(-3.04970 + 3.90068i) q^{30} +(-6.65577 - 5.23415i) q^{31} +(0.971812 + 0.235759i) q^{32} +(2.81444 + 0.817751i) q^{33} +(3.65858 - 7.09666i) q^{34} +(-5.62025 - 8.74529i) q^{35} +(2.87365 - 0.861475i) q^{36} +(0.317274 + 1.08054i) q^{37} +(-4.74694 + 1.90039i) q^{38} +(0.181616 - 0.0733050i) q^{39} +(-2.32860 + 1.65819i) q^{40} +(-5.50478 - 5.77324i) q^{41} +(-0.281895 + 6.29228i) q^{42} +(-1.57450 - 2.00214i) q^{43} +(1.42350 + 0.914828i) q^{44} +(-3.51840 + 7.82105i) q^{45} +(3.69315 - 3.05951i) q^{46} +(10.7817 - 6.22484i) q^{47} +(1.73204 - 0.00490119i) q^{48} +(-5.77826 - 2.31326i) q^{49} +(0.301517 - 3.15763i) q^{50} +(3.22229 - 13.4484i) q^{51} +(0.112563 - 0.0107485i) q^{52} +(-4.64869 + 5.36487i) q^{53} +(4.47778 - 2.63618i) q^{54} +(-4.64127 + 1.36280i) q^{55} +(-1.18938 + 3.43649i) q^{56} +(-7.19960 + 5.15758i) q^{57} +(0.0395721 + 0.830722i) q^{58} +(0.894373 + 4.64045i) q^{59} +(-3.23185 + 3.75115i) q^{60} +(0.648453 + 1.61976i) q^{61} +(-6.39918 - 5.54492i) q^{62} +(2.12523 + 10.7005i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.187500 + 0.263307i) q^{65} +(2.77234 + 0.950741i) q^{66} +(2.86614 + 5.55954i) q^{67} +(3.99211 - 6.91454i) q^{68} +(4.94822 - 6.67197i) q^{69} +(-5.19777 - 9.00280i) q^{70} +(-8.12268 + 12.6391i) q^{71} +(2.91139 - 0.723765i) q^{72} +(-0.598017 - 1.30947i) q^{73} +(0.265501 + 1.09441i) q^{74} +(-0.797271 - 5.43590i) q^{75} +(-4.83199 + 1.67237i) q^{76} +(-3.80377 + 4.83688i) q^{77} +(0.184898 - 0.0645804i) q^{78} +(7.64161 + 2.64479i) q^{79} +(-2.40487 + 1.54551i) q^{80} +(6.44289 - 6.28404i) q^{81} +(-5.22384 - 6.02863i) q^{82} +(-1.75095 - 1.66953i) q^{83} +(-0.580975 + 6.27174i) q^{84} +(7.46509 + 21.5689i) q^{85} +(-1.47745 - 2.07479i) q^{86} +(0.409741 + 1.38098i) q^{87} +(1.37836 + 0.981525i) q^{88} +(-0.773218 - 5.37785i) q^{89} +(-3.88655 + 7.64478i) q^{90} +0.411197i q^{91} +(3.83455 - 2.88032i) q^{92} +(-13.0545 - 6.68336i) q^{93} +(11.0657 - 5.70478i) q^{94} +(5.43259 - 13.5699i) q^{95} +(1.73032 + 0.0775183i) q^{96} +(3.96875 - 0.962808i) q^{97} +(-5.66164 - 2.58558i) q^{98} +(5.05602 + 0.453932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$3$	1.69982	−	0.332604i	0.981389	−	0.192029i
$3$	1.69982	−	0.332604i	0.981389	−	0.192029i
$4$	0.995472	+	0.0950560i	0.497736	+	0.0475280i
$5$	−2.06892	+	1.97271i	−0.925248	+	0.882222i	−0.993312	−	0.115459i	$-0.963166\pi$
$5$	−2.06892	+	1.97271i	−0.925248	+	0.882222i	0.0680645	+	0.997681i	$0.478318\pi$
$6$	1.71372	−	0.251347i	0.699622	−	0.102612i
$7$	−0.688211	+	3.57078i	−0.260119	+	1.34963i	0.583250	+	0.812293i	$0.301781\pi$
$7$	−0.688211	+	3.57078i	−0.260119	+	1.34963i	−0.843369	+	0.537335i	$0.819431\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	2.77875	−	1.13073i	0.926250	−	0.376910i
$10$	−2.16044	+	1.87203i	−0.683191	+	0.591988i
$11$	1.50401	+	0.775374i	0.453478	+	0.233784i	0.669805	−	0.742537i	$-0.266378\pi$
$11$	1.50401	+	0.775374i	0.453478	+	0.233784i	−0.216328	+	0.976321i	$0.569408\pi$
$12$	1.72374	−	0.169520i	0.497599	−	0.0489363i
$13$	0.111032	−	0.0213996i	0.0307947	−	0.00593519i	−0.173831	−	0.984776i	$-0.555615\pi$
$13$	0.111032	−	0.0213996i	0.0307947	−	0.00593519i	0.204625	+	0.978840i	$0.434402\pi$
$14$	−0.857336	+	3.53399i	−0.229133	+	0.944498i
$15$	−2.86065	+	4.04137i	−0.738616	+	1.04348i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	3.31677	−	7.26271i	0.804434	−	1.76146i	0.174751	−	0.984613i	$-0.444088\pi$
$17$	3.31677	−	7.26271i	0.804434	−	1.76146i	0.629683	−	0.776852i	$-0.283185\pi$
$18$	2.82940	−	0.997233i	0.666897	−	0.235050i
$19$	−4.65114	+	2.12411i	−1.06705	+	0.487303i	−0.869980	−	0.493087i	$-0.835868\pi$
$19$	−4.65114	+	2.12411i	−1.06705	+	0.487303i	−0.197065	+	0.980390i	$0.563141\pi$
$20$	−2.24707	+	1.76711i	−0.502459	+	0.395138i
$21$	0.0178232	+	6.29857i	0.00388933	+	1.37446i
$22$	1.46542	+	0.846059i	0.312428	+	0.180380i
$23$	3.54339	−	3.23177i	0.738849	−	0.673871i
$23$	3.54339	−	3.23177i	0.738849	−	0.673871i
$24$	1.72985	−	0.0873096i	0.353104	−	0.0178220i
$25$	0.150930	−	3.16840i	0.0301859	−	0.633681i
$26$	0.111924	−	0.0160923i	0.0219501	−	0.00315595i
$27$	4.34728	−	2.84626i	0.836634	−	0.547763i
$28$	−1.02452	+	3.48919i	−0.193616	+	0.659395i
$29$	0.0790546	+	0.827898i	0.0146801	+	0.153737i	0.999840	−	0.0179039i	$-0.00569928\pi$
$29$	0.0790546	+	0.827898i	0.0146801	+	0.153737i	−0.985160	+	0.171641i	$0.945093\pi$
$30$	−3.04970	+	3.90068i	−0.556797	+	0.712163i
$31$	−6.65577	−	5.23415i	−1.19541	−	0.940081i	−0.196230	−	0.980558i	$-0.562870\pi$
$31$	−6.65577	−	5.23415i	−1.19541	−	0.940081i	−0.999180	+	0.0404765i	$0.987112\pi$
$32$	0.971812	+	0.235759i	0.171794	+	0.0416767i
$33$	2.81444	+	0.817751i	0.489931	+	0.142352i
$34$	3.65858	−	7.09666i	0.627442	−	1.21707i
$35$	−5.62025	−	8.74529i	−0.949996	−	1.47822i
$36$	2.87365	−	0.861475i	0.478942	−	0.143579i
$37$	0.317274	+	1.08054i	0.0521596	+	0.177639i	0.981453	−	0.191703i	$-0.0614011\pi$
$37$	0.317274	+	1.08054i	0.0521596	+	0.177639i	−0.929293	+	0.369342i	$0.879583\pi$
$38$	−4.74694	+	1.90039i	−0.770056	+	0.308284i
$39$	0.181616	−	0.0733050i	0.0290818	−	0.0117382i
$40$	−2.32860	+	1.65819i	−0.368185	+	0.262183i
$41$	−5.50478	−	5.77324i	−0.859702	−	0.901629i	0.136327	−	0.990664i	$-0.456470\pi$
$41$	−5.50478	−	5.77324i	−0.859702	−	0.901629i	−0.996029	+	0.0890346i	$0.971622\pi$
$42$	−0.281895	+	6.29228i	−0.0434974	+	0.970920i
$43$	−1.57450	−	2.00214i	−0.240109	−	0.305323i	0.651032	−	0.759050i	$-0.274336\pi$
$43$	−1.57450	−	2.00214i	−0.240109	−	0.305323i	−0.891141	+	0.453727i	$0.850094\pi$
$44$	1.42350	+	0.914828i	0.214601	+	0.137916i
$45$	−3.51840	+	7.82105i	−0.524492	+	1.16589i
$46$	3.69315	−	3.05951i	0.544526	−	0.451100i
$47$	10.7817	−	6.22484i	1.57268	−	0.907987i	0.576840	−	0.816857i	$-0.304285\pi$
$47$	10.7817	−	6.22484i	1.57268	−	0.907987i	0.995839	−	0.0911301i	$-0.0290479\pi$
$48$	1.73204	−	0.00490119i	0.249999	−	0.000707426i
$49$	−5.77826	−	2.31326i	−0.825465	−	0.330466i
$50$	0.301517	−	3.15763i	0.0426410	−	0.446557i
$51$	3.22229	−	13.4484i	0.451210	−	1.88316i
$52$	0.112563	−	0.0107485i	0.0156097	−	0.00149055i
$53$	−4.64869	+	5.36487i	−0.638546	+	0.736922i	−0.979117	−	0.203297i	$-0.934834\pi$
$53$	−4.64869	+	5.36487i	−0.638546	+	0.736922i	0.340571	+	0.940219i	$0.389380\pi$
$54$	4.47778	−	2.63618i	0.609349	−	0.358739i
$55$	−4.64127	+	1.36280i	−0.625828	+	0.183760i
$56$	−1.18938	+	3.43649i	−0.158938	+	0.459220i
$57$	−7.19960	+	5.15758i	−0.953610	+	0.683138i
$58$	0.0395721	+	0.830722i	0.00519608	+	0.109079i
$59$	0.894373	+	4.64045i	0.116437	+	0.604135i	0.992531	+	0.121993i	$0.0389287\pi$
$59$	0.894373	+	4.64045i	0.116437	+	0.604135i	−0.876093	+	0.482141i	$0.839859\pi$
$60$	−3.23185	+	3.75115i	−0.417230	+	0.484271i
$61$	0.648453	+	1.61976i	0.0830259	+	0.207389i	0.964072	−	0.265642i	$-0.0855840\pi$
$61$	0.648453	+	1.61976i	0.0830259	+	0.207389i	−0.881046	+	0.473031i	$0.843160\pi$
$62$	−6.39918	−	5.54492i	−0.812696	−	0.704205i
$63$	2.12523	+	10.7005i	0.267753	+	1.34813i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−0.187500	+	0.263307i	−0.0232565	+	0.0326593i
$66$	2.77234	+	0.950741i	0.341252	+	0.117028i
$67$	2.86614	+	5.55954i	0.350155	+	0.679206i	0.996478	−	0.0838583i	$-0.0267243\pi$
$67$	2.86614	+	5.55954i	0.350155	+	0.679206i	−0.646323	+	0.763064i	$0.723694\pi$
$68$	3.99211	−	6.91454i	0.484115	−	0.838511i
$69$	4.94822	−	6.67197i	0.595695	−	0.803211i
$70$	−5.19777	−	9.00280i	−0.621252	−	1.07604i
$71$	−8.12268	+	12.6391i	−0.963984	+	1.49999i	−0.100920	+	0.994894i	$0.532179\pi$
$71$	−8.12268	+	12.6391i	−0.963984	+	1.49999i	−0.863064	+	0.505095i	$0.831458\pi$
$72$	2.91139	−	0.723765i	0.343110	−	0.0852965i
$73$	−0.598017	−	1.30947i	−0.0699926	−	0.153262i	0.871402	−	0.490569i	$-0.163211\pi$
$73$	−0.598017	−	1.30947i	−0.0699926	−	0.153262i	−0.941395	+	0.337307i	$0.890484\pi$
$74$	0.265501	+	1.09441i	0.0308639	+	0.127223i
$75$	−0.797271	−	5.43590i	−0.0920609	−	0.627684i
$76$	−4.83199	+	1.67237i	−0.554267	+	0.191834i
$77$	−3.80377	+	4.83688i	−0.433480	+	0.551214i
$78$	0.184898	−	0.0645804i	0.0209356	−	0.00731229i
$79$	7.64161	+	2.64479i	0.859748	+	0.297562i	0.721143	−	0.692786i	$-0.243617\pi$
$79$	7.64161	+	2.64479i	0.859748	+	0.297562i	0.138605	+	0.990348i	$0.455738\pi$
$80$	−2.40487	+	1.54551i	−0.268872	+	0.172794i
$81$	6.44289	−	6.28404i	0.715877	−	0.698226i
$82$	−5.22384	−	6.02863i	−0.576877	−	0.665751i
$83$	−1.75095	−	1.66953i	−0.192192	−	0.183255i	0.587873	−	0.808953i	$-0.299965\pi$
$83$	−1.75095	−	1.66953i	−0.192192	−	0.183255i	−0.780065	+	0.625699i	$0.784814\pi$
$84$	−0.580975	+	6.27174i	−0.0633895	+	0.684303i
$85$	7.46509	+	21.5689i	0.809702	+	2.33948i
$86$	−1.47745	−	2.07479i	−0.159317	−	0.223730i
$87$	0.409741	+	1.38098i	0.0439288	+	0.148057i
$88$	1.37836	+	0.981525i	0.146934	+	0.104631i
$89$	−0.773218	−	5.37785i	−0.0819610	−	0.570051i	−0.988877	−	0.148739i	$-0.952479\pi$
$89$	−0.773218	−	5.37785i	−0.0819610	−	0.570051i	0.906916	−	0.421312i	$-0.138430\pi$
$90$	−3.88655	+	7.64478i	−0.409679	+	0.805831i
$91$			0.411197i			0.0431052i
$92$	3.83455	−	2.88032i	0.399779	−	0.300294i
$93$	−13.0545	−	6.68336i	−1.35369	−	0.693032i
$94$	11.0657	−	5.70478i	1.14134	−	0.588403i
$95$	5.43259	−	13.5699i	0.557372	−	1.39225i
$96$	1.73032	+	0.0775183i	0.176600	+	0.00791168i
$97$	3.96875	−	0.962808i	0.402965	−	0.0977583i	−0.0291537	−	0.999575i	$-0.509281\pi$
$97$	3.96875	−	0.962808i	0.402965	−	0.0977583i	0.432119	+	0.901817i	$0.357766\pi$
$98$	−5.66164	−	2.58558i	−0.571912	−	0.261184i
$99$	5.05602	+	0.453932i	0.508149	+	0.0456218i
$100$	0.451422	−	3.13971i	0.0451422	−	0.313971i
$101$	7.61139	−	7.98259i	0.757361	−	0.794298i	−0.226351	−	0.974046i	$-0.572680\pi$
$101$	7.61139	−	7.98259i	0.757361	−	0.794298i	0.983713	+	0.179748i	$0.0575283\pi$
$102$	3.85854	−	13.2799i	0.382052	−	1.31490i
$103$	−18.0065	+	0.857754i	−1.77423	+	0.0845170i	−0.908984	−	0.416831i	$-0.863141\pi$
$103$	−18.0065	+	0.857754i	−1.77423	+	0.0845170i	−0.865246	+	0.501348i	$0.832838\pi$
$104$	0.112947	−	0.00538033i	0.0110754	−	0.000527585i
$105$	−12.4621	−	12.9961i	−1.21618	−	1.26829i
$106$	−4.89869	+	5.13760i	−0.475803	+	0.499008i
$107$	1.62576	−	11.3074i	0.157169	−	1.09313i	−0.746650	−	0.665217i	$-0.768339\pi$
$107$	1.62576	−	11.3074i	0.157169	−	1.09313i	0.903819	−	0.427915i	$-0.140752\pi$
$108$	4.59815	−	2.42014i	0.442457	−	0.232878i
$109$	6.37231	+	2.91014i	0.610357	+	0.278740i	0.696516	−	0.717541i	$-0.254732\pi$
$109$	6.37231	+	2.91014i	0.610357	+	0.278740i	−0.0861599	+	0.996281i	$0.527460\pi$
$110$	−4.70086	+	1.14042i	−0.448209	+	0.108734i
$111$	0.898699	+	1.73119i	0.0853007	+	0.164317i
$112$	−1.35155	+	3.37601i	−0.127709	+	0.319003i
$113$	−10.0161	+	5.16367i	−0.942237	+	0.485757i	−0.859682	−	0.510829i	$-0.829338\pi$
$113$	−10.0161	+	5.16367i	−0.942237	+	0.485757i	−0.0825552	+	0.996586i	$0.526308\pi$
$114$	−7.43685	+	4.80917i	−0.696525	+	0.450420i
$115$	−0.955641	+	13.6764i	−0.0891140	+	1.27533i
$116$			0.831664i			0.0772180i
$117$	0.284332	−	0.185011i	0.0262865	−	0.0171043i
$118$	0.672558	+	4.67775i	0.0619140	+	0.430621i
$119$	23.6509	+	16.8417i	2.16807	+	1.54388i
$120$	−3.40668	+	3.59312i	−0.310986	+	0.328006i
$121$	−4.71977	−	6.62799i	−0.429070	−	0.602544i
$122$	0.570648	+	1.64878i	0.0516640	+	0.149273i
$123$	−11.2773	−	7.98254i	−1.01684	−	0.719762i
$124$	−6.12809	−	5.84312i	−0.550319	−	0.524728i
$125$	−3.42208	−	3.94929i	−0.306080	−	0.353235i
$126$	1.61367	+	10.7895i	0.143757	+	0.961204i
$127$	−12.2748	+	7.88851i	−1.08921	+	0.699992i	−0.956667	−	0.291185i	$-0.905950\pi$
$127$	−12.2748	+	7.88851i	−1.08921	+	0.699992i	−0.132543	+	0.991177i	$0.542314\pi$
$128$	0.945001	+	0.327068i	0.0835271	+	0.0289090i
$129$	−3.34228	−	2.87958i	−0.294271	−	0.253533i
$130$	−0.199817	+	0.254087i	−0.0175251	+	0.0222849i
$131$	12.4728	−	4.31689i	1.08976	−	0.377169i	0.277653	−	0.960681i	$-0.410443\pi$
$131$	12.4728	−	4.31689i	1.08976	−	0.377169i	0.812104	+	0.583513i	$0.198322\pi$
$132$	2.72396	+	1.08158i	0.237091	+	0.0941393i
$133$	−4.38374	−	18.0700i	−0.380119	−	1.56687i
$134$	2.59836	+	5.68962i	0.224464	+	0.491508i
$135$	−3.37932	+	14.4646i	−0.290845	+	1.24491i
$136$	4.31660	−	6.71676i	0.370145	−	0.575957i
$137$	−3.25283	−	5.63406i	−0.277908	−	0.481350i	0.692957	−	0.720979i	$-0.256308\pi$
$137$	−3.25283	−	5.63406i	−0.277908	−	0.481350i	−0.970865	+	0.239629i	$0.922974\pi$
$138$	5.26008	−	6.42897i	0.447767	−	0.547270i
$139$	2.60696	−	4.51539i	0.221120	−	0.382991i	−0.734029	−	0.679119i	$-0.762362\pi$
$139$	2.60696	−	4.51539i	0.221120	−	0.382991i	0.955148	+	0.296128i	$0.0956955\pi$
$140$	−4.76351	−	9.23993i	−0.402590	−	0.780916i
$141$	16.2566	−	14.1671i	1.36905	−	1.19309i
$142$	−8.71487	+	12.2383i	−0.731336	+	1.02702i
$143$	0.183586	+	0.0539057i	0.0153522	+	0.00450783i
$144$	2.94253	−	0.584416i	0.245210	−	0.0487013i
$145$	−1.79676	−	1.55690i	−0.149213	−	0.129293i
$146$	−0.535032	−	1.33645i	−0.0442796	−	0.110605i
$147$	−10.5914	−	2.01025i	−0.873562	−	0.165803i
$148$	0.213126	+	1.10580i	0.0175189	+	0.0908965i
$149$	−0.868122	−	18.2241i	−0.0711193	−	1.49298i	−0.699254	−	0.714873i	$-0.746484\pi$
$149$	−0.868122	−	18.2241i	−0.0711193	−	1.49298i	0.628135	−	0.778105i	$-0.283819\pi$
$150$	−0.537717	−	5.46768i	−0.0439044	−	0.446434i
$151$	−1.24341	+	3.59259i	−0.101187	+	0.292361i	−0.984220	−	0.176951i	$-0.943377\pi$
$151$	−1.24341	+	3.59259i	−0.101187	+	0.292361i	0.883033	+	0.469312i	$0.155498\pi$
$152$	−4.90609	+	1.44056i	−0.397937	+	0.116845i
$153$	1.00429	−	23.9316i	0.0811922	−	1.93476i
$154$	−4.02961	+	4.65042i	−0.324715	+	0.374741i
$155$	24.0957	−	2.30086i	1.93541	−	0.184809i
$156$	0.187762	−	0.0557094i	0.0150330	−	0.00446032i
$157$	−0.887826	+	9.29773i	−0.0708562	+	0.742040i	0.888319	+	0.459227i	$0.151874\pi$
$157$	−0.887826	+	9.29773i	−0.0708562	+	0.742040i	−0.959175	+	0.282813i	$0.908733\pi$
$158$	7.50711	+	3.00539i	0.597233	+	0.239096i
$159$	−6.11753	+	10.6655i	−0.485152	+	0.845826i
$160$	−2.47568	+	1.42934i	−0.195720	+	0.112999i
$161$	9.10135	+	14.8768i	0.717287	+	1.17246i
$162$	6.73460	−	5.97036i	0.529120	−	0.469075i
$163$	15.9541	+	10.2531i	1.24962	+	0.803085i	0.986829	−	0.161767i	$-0.0517193\pi$
$163$	15.9541	+	10.2531i	1.24962	+	0.803085i	0.262795	+	0.964852i	$0.415356\pi$
$164$	−4.93107	−	6.27037i	−0.385052	−	0.489633i
$165$	−7.43603	+	3.86021i	−0.578894	+	0.300517i
$166$	−1.66953	−	1.75095i	−0.129581	−	0.135900i
$167$	7.49642	−	5.33818i	0.580091	−	0.413081i	−0.251995	−	0.967729i	$-0.581086\pi$
$167$	7.49642	−	5.33818i	0.580091	−	0.413081i	0.832085	+	0.554648i	$0.187147\pi$
$168$	−0.878738	+	6.23700i	−0.0677961	+	0.481195i
$169$	−12.0569	+	4.82686i	−0.927455	+	0.371297i
$170$	6.43034	+	21.8997i	0.493184	+	1.67963i
$171$	−10.5226	+	11.1616i	−0.804681	+	0.853545i
$172$	−1.37705	−	2.14274i	−0.104999	−	0.163382i
$173$	−5.22016	+	10.1257i	−0.396882	+	0.769843i	−0.999605	−	0.0281072i	$-0.991052\pi$
$173$	−5.22016	+	10.1257i	−0.396882	+	0.769843i	0.602723	+	0.797950i	$0.294082\pi$
$174$	0.343567	+	1.39891i	0.0260457	+	0.106051i
$175$	11.2098	+	2.71947i	0.847381	+	0.205572i
$176$	1.33009	+	1.04600i	0.100260	+	0.0788451i
$177$	3.06370	+	7.59043i	0.230282	+	0.570532i
$178$	−0.516454	−	5.40855i	−0.0387099	−	0.405388i
$179$	−5.51282	+	18.7750i	−0.412048	+	1.40331i	0.448430	+	0.893818i	$0.351983\pi$
$179$	−5.51282	+	18.7750i	−0.412048	+	1.40331i	−0.860478	+	0.509488i	$0.829835\pi$
$180$	−4.24590	+	7.45119i	−0.316471	+	0.555379i
$181$	0.895152	−	0.128703i	0.0665361	−	0.00956645i	−0.108966	−	0.994045i	$-0.534754\pi$
$181$	0.895152	−	0.128703i	0.0665361	−	0.00956645i	0.175502	+	0.984479i	$0.443845\pi$
$182$	−0.0195656	+	0.410732i	−0.00145030	+	0.0304455i
$183$	1.64099	+	2.53761i	0.121305	+	0.187586i
$184$	3.96726	−	2.69460i	0.292470	−	0.198649i
$185$	−2.78800	−	1.60965i	−0.204978	−	0.118344i
$186$	−12.7217	−	7.29695i	−0.932799	−	0.535038i
$187$	10.6198	−	8.35148i	0.776595	−	0.610721i
$188$	11.3246	−	5.17179i	0.825934	−	0.377191i
$189$	7.17152	+	17.4820i	0.521651	+	1.27163i
$190$	6.07212	−	13.2961i	0.440518	−	0.964599i
$191$	−8.75049	−	1.68652i	−0.633163	−	0.122032i	−0.137436	−	0.990511i	$-0.543886\pi$
$191$	−8.75049	−	1.68652i	−0.633163	−	0.122032i	−0.495727	+	0.868478i	$0.665098\pi$
$192$	1.72467	+	0.159762i	0.124467	+	0.0115298i
$193$	−2.14839	+	8.85579i	−0.154645	+	0.637454i	0.840736	+	0.541445i	$0.182123\pi$
$193$	−2.14839	+	8.85579i	−0.154645	+	0.637454i	−0.995381	+	0.0960082i	$0.969392\pi$
$194$	4.01006	−	0.772877i	0.287906	−	0.0554893i
$195$	−0.231139	+	0.509937i	−0.0165522	+	0.0365174i
$196$	−5.53220	−	2.85205i	−0.395157	−	0.203718i
$197$	−4.04140	+	3.50189i	−0.287938	+	0.249500i	−0.786838	−	0.617160i	$-0.788283\pi$
$197$	−4.04140	+	3.50189i	−0.287938	+	0.249500i	0.498900	+	0.866660i	$0.333738\pi$
$198$	5.02869	+	0.693992i	0.357374	+	0.0493199i
$199$	21.9419	+	3.15477i	1.55542	+	0.223636i	0.865746	−	0.500484i	$-0.166845\pi$
$199$	21.9419	+	3.15477i	1.55542	+	0.223636i	0.689674	+	0.724120i	$0.257754\pi$
$200$	0.600304	−	3.11467i	0.0424479	−	0.220241i
$201$	6.72104	+	8.49690i	0.474066	+	0.599325i
$202$	7.98259	−	7.61139i	0.561653	−	0.535535i
$203$	−3.01065	−	0.287482i	−0.211306	−	0.0201773i
$204$	4.48605	−	13.0812i	0.314086	−	0.915870i
$205$	22.7779	+	1.08504i	1.59087	+	0.0757827i
$206$	−18.0269			−1.25599
$207$	6.19193	−	12.9869i	0.430369	−	0.902653i
$208$	0.113075			0.00784035
$209$	−8.64236	−	0.411687i	−0.597805	−	0.0284770i
$210$	−11.8296	−	13.5743i	−0.816322	−	0.936716i
$211$	−2.36170	−	0.225515i	−0.162586	−	0.0155251i	0.0134456	−	0.999910i	$-0.495720\pi$
$211$	−2.36170	−	0.225515i	−0.162586	−	0.0155251i	−0.176032	+	0.984385i	$0.556326\pi$
$212$	−5.13760	+	4.89869i	−0.352852	+	0.336444i
$213$	−9.60323	+	24.1858i	−0.658002	+	1.65719i
$214$	2.16195	−	11.2173i	0.147788	−	0.766797i
$215$	7.20714	+	1.03623i	0.491523	+	0.0706703i
$216$	4.70809	−	2.19861i	0.320345	−	0.149596i
$217$	23.2706	−	20.1641i	1.57971	−	1.36883i
$218$	6.22662	+	3.21005i	0.421720	+	0.217412i
$219$	−1.45206	−	2.02696i	−0.0981208	−	0.136969i
$220$	−4.74979	+	0.915448i	−0.320231	+	0.0617195i
$221$	0.212847	−	0.877369i	0.0143177	−	0.0590182i
$222$	0.815308	+	1.77199i	0.0547199	+	0.118928i
$223$	9.27438	+	1.78749i	0.621058	+	0.119699i	0.490068	−	0.871684i	$-0.336972\pi$
$223$	9.27438	+	1.78749i	0.621058	+	0.119699i	0.130991	+	0.991384i	$0.458184\pi$
$224$	−1.51065	+	3.30787i	−0.100935	+	0.221017i
$225$	−3.16322	−	8.97486i	−0.210881	−	0.598324i
$226$	−10.2505	+	4.68123i	−0.681851	+	0.311391i
$227$	−16.6419	+	13.0873i	−1.10456	+	0.868637i	−0.992154	−	0.125025i	$-0.960099\pi$
$227$	−16.6419	+	13.0873i	−1.10456	+	0.868637i	−0.112408	+	0.993662i	$0.535856\pi$
$228$	−7.65726	+	4.44986i	−0.507114	+	0.294699i
$229$	−18.6400	−	10.7618i	−1.23176	−	0.711160i	−0.264367	−	0.964422i	$-0.585163\pi$
$229$	−18.6400	−	10.7618i	−1.23176	−	0.711160i	−0.967398	+	0.253262i	$0.918496\pi$
$230$	−1.60531	+	13.6154i	−0.105851	+	0.897772i
$231$	−4.85694	+	9.48696i	−0.319563	+	0.624196i
$232$	−0.0395721	+	0.830722i	−0.00259804	+	0.0545395i
$233$	−11.2221	+	1.61349i	−0.735182	+	0.105703i	−0.499728	−	0.866182i	$-0.666567\pi$
$233$	−11.2221	+	1.61349i	−0.735182	+	0.105703i	−0.235454	+	0.971886i	$0.575658\pi$
$234$	0.292813	−	0.171273i	0.0191418	−	0.0111964i
$235$	−10.0267	+	34.1479i	−0.654072	+	2.22757i
$236$	0.449220	+	4.70445i	0.0292418	+	0.306234i
$237$	13.8690	+	1.95402i	0.900888	+	0.126927i
$238$	22.8227	+	17.9480i	1.47938	+	1.16340i
$239$	6.36306	+	1.54366i	0.411592	+	0.0998511i	0.436208	−	0.899846i	$-0.356321\pi$
$239$	6.36306	+	1.54366i	0.411592	+	0.0998511i	−0.0246161	+	0.999697i	$0.507836\pi$
$240$	−3.57379	+	3.42696i	−0.230687	+	0.221209i
$241$	6.60970	−	12.8210i	0.425768	−	0.825875i	−0.574206	−	0.818711i	$-0.694689\pi$
$241$	6.60970	−	12.8210i	0.425768	−	0.825875i	0.999974	−	0.00716414i	$-0.00228044\pi$
$242$	−4.39905	−	6.84506i	−0.282782	−	0.440017i
$243$	8.86164	−	12.8246i	0.568474	−	0.822701i
$244$	0.491549	+	1.67406i	0.0314682	+	0.107171i
$245$	16.5181	−	6.61286i	1.05530	−	0.422480i
$246$	−10.8847	−	8.51010i	−0.693984	−	0.542584i
$247$	−0.470970	+	0.335376i	−0.0299671	+	0.0213395i
$248$	−5.84312	−	6.12809i	−0.371039	−	0.389134i
$249$	−3.53159	−	2.25552i	−0.223805	−	0.142938i
$250$	−3.23029	−	4.10765i	−0.204301	−	0.259790i
$251$	8.07237	+	5.18780i	0.509524	+	0.327451i	0.770016	−	0.638025i	$-0.220248\pi$
$251$	8.07237	+	5.18780i	0.509524	+	0.327451i	−0.260492	+	0.965476i	$0.583885\pi$
$252$	1.09846	+	10.8540i	0.0691963	+	0.683741i
$253$	7.83515	−	2.11318i	0.492592	−	0.132855i
$254$	−12.6362	+	7.29552i	−0.792867	+	0.457762i
$255$	19.8632	+	34.1803i	1.24388	+	2.14046i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−0.325117	+	3.40478i	−0.0202802	+	0.212384i	0.979652	+	0.200706i	$0.0643235\pi$
$257$	−0.325117	+	3.40478i	−0.0202802	+	0.212384i	−0.999932	+	0.0116784i	$0.996283\pi$
$258$	−3.20148	−	3.03535i	−0.199315	−	0.188973i
$259$	−4.07671	+	0.389279i	−0.253315	+	0.0241886i
$260$	−0.211680	+	0.244292i	−0.0131279	+	0.0151503i
$261$	1.15580	+	2.21113i	0.0715424	+	0.136866i
$262$	12.6641	−	3.71852i	0.782392	−	0.229731i
$263$	−10.0497	+	29.0366i	−0.619689	+	1.79047i	−0.00722459	+	0.999974i	$0.502300\pi$
$263$	−10.0497	+	29.0366i	−0.619689	+	1.79047i	−0.612464	+	0.790499i	$0.709822\pi$
$264$	2.66942	+	1.20996i	0.164291	+	0.0744681i
$265$	−0.965578	−	20.2700i	−0.0593150	−	1.24517i
$266$	−3.51897	−	18.2582i	−0.215762	−	1.11948i
$267$	−3.10302	−	8.88418i	−0.189902	−	0.543703i
$268$	2.32470	+	5.80681i	0.142003	+	0.354707i
$269$	−10.3185	−	8.94101i	−0.629128	−	0.545143i	0.280875	−	0.959744i	$-0.409375\pi$
$269$	−10.3185	−	8.94101i	−0.629128	−	0.545143i	−0.910003	+	0.414602i	$0.863921\pi$
$270$	−4.06374	+	14.2874i	−0.247311	+	0.869504i
$271$	4.38865	+	1.28862i	0.266591	+	0.0782783i	0.412296	−	0.911050i	$-0.364727\pi$
$271$	4.38865	+	1.28862i	0.266591	+	0.0782783i	−0.145705	+	0.989328i	$0.546545\pi$
$272$	4.63130	−	6.50376i	0.280814	−	0.394348i
$273$	0.136766	+	0.698960i	0.00827745	+	0.0423030i
$274$	−2.98106	−	5.78246i	−0.180093	−	0.349331i
$275$	2.68370	−	4.64830i	0.161833	−	0.280303i
$276$	5.56002	−	6.17140i	0.334674	−	0.371475i
$277$	1.82309	+	3.15769i	0.109539	+	0.189727i	0.915584	−	0.402128i	$-0.131729\pi$
$277$	1.82309	+	3.15769i	0.109539	+	0.189727i	−0.806045	+	0.591855i	$0.798396\pi$
$278$	2.81886	−	4.38623i	0.169064	−	0.263069i
$279$	−24.4131	−	7.01851i	−1.46158	−	0.420187i
$280$	−4.31846	−	9.45612i	−0.258078	−	0.565111i
$281$	3.86312	+	15.9240i	0.230454	+	0.949946i	0.963059	+	0.269291i	$0.0867894\pi$
$281$	3.86312	+	15.9240i	0.230454	+	0.949946i	−0.732605	+	0.680655i	$0.761695\pi$
$282$	16.9123	−	13.3776i	1.00711	−	0.796623i
$283$	24.4331	−	8.45639i	1.45240	−	0.502680i	0.516911	−	0.856039i	$-0.327082\pi$
$283$	24.4331	−	8.45639i	1.45240	−	0.502680i	0.935488	+	0.353359i	$0.114961\pi$
$284$	−9.28732	+	11.8098i	−0.551101	+	0.700782i
$285$	4.72098	−	24.8733i	0.279647	−	1.47337i
$286$	0.180813	+	0.0625801i	0.0106917	+	0.00370044i
$287$	24.4034	−	15.6831i	1.44049	−	0.925746i
$288$	2.96700	−	0.443743i	0.174832	−	0.0261478i
$289$	−30.6133	−	35.3297i	−1.80078	−	2.07822i
$290$	−1.72064	−	1.64063i	−0.101040	−	0.0963411i
$291$	6.42591	−	2.95662i	0.376693	−	0.173320i
$292$	−0.470836	−	1.36039i	−0.0275536	−	0.0796108i
$293$	6.74513	+	9.47221i	0.394055	+	0.553373i	0.963173	−	0.268883i	$-0.0866546\pi$
$293$	6.74513	+	9.47221i	0.394055	+	0.553373i	−0.569118	+	0.822256i	$0.692715\pi$
$294$	−10.4837	−	2.51193i	−0.611423	−	0.146499i
$295$	−11.0046	−	7.83636i	−0.640714	−	0.456251i
$296$	0.160268	+	1.11469i	0.00931541	+	0.0647901i
$297$	8.74528	−	0.910052i	0.507453	−	0.0528066i
$298$		−	18.2448i		−	1.05689i
$299$	0.324271	−	0.434657i	0.0187530	−	0.0251369i
$300$	−0.276946	−	5.48707i	−0.0159895	−	0.316796i
$301$	8.23278	−	4.24429i	0.474529	−	0.244637i
$302$	−1.41294	+	3.52936i	−0.0813056	+	0.203092i
$303$	10.2829	−	16.1005i	0.590738	−	0.924950i
$304$	−4.96908	+	1.20549i	−0.284996	+	0.0691394i
$305$	−4.53691	−	2.07194i	−0.259782	−	0.118639i
$306$	2.14187	−	23.8567i	0.122442	−	1.36380i
$307$	−2.25269	+	15.6678i	−0.128568	+	0.894209i	0.818804	+	0.574074i	$0.194638\pi$
$307$	−2.25269	+	15.6678i	−0.128568	+	0.894209i	−0.947372	+	0.320136i	$0.896271\pi$
$308$	−4.24632	+	4.45341i	−0.241956	+	0.253757i
$309$	−30.3224	+	7.44705i	−1.72498	+	0.423648i
$310$	24.1779	−	1.15173i	1.37321	−	0.0654141i
$311$	1.44823	−	0.0689877i	0.0821216	−	0.00391193i	−0.00648089	−	0.999979i	$-0.502063\pi$
$311$	1.44823	−	0.0689877i	0.0821216	−	0.00391193i	0.0886025	+	0.996067i	$0.471760\pi$
$312$	0.190200	−	0.0467122i	0.0107679	−	0.00264456i
$313$	−15.7334	+	16.5007i	−0.889302	+	0.932673i	−0.998114	−	0.0613894i	$-0.980447\pi$
$313$	−15.7334	+	16.5007i	−0.889302	+	0.932673i	0.108812	+	0.994062i	$0.465295\pi$
$314$	−1.32922	+	9.24496i	−0.0750124	+	0.521723i
$315$	−25.5058	−	17.9460i	−1.43709	−	1.01114i
$316$	7.35560	+	3.35919i	0.413785	+	0.188969i
$317$	−8.02722	+	1.94738i	−0.450854	+	0.109376i	−0.454755	−	0.890616i	$-0.650273\pi$
$317$	−8.02722	+	1.94738i	−0.450854	+	0.109376i	0.00390143	+	0.999992i	$0.498758\pi$
$318$	−6.61809	+	10.3623i	−0.371124	+	0.581089i
$319$	−0.523031	+	1.30647i	−0.0292841	+	0.0731481i
$320$	−2.54089	+	1.30992i	−0.142040	+	0.0732267i
$321$	−0.997400	−	19.7613i	−0.0556695	−	1.10297i
$322$	8.38317	+	15.2930i	0.467176	+	0.852247i
$323$			40.8250i			2.27157i
$324$	7.01105	−	5.64315i	0.389503	−	0.313508i
$325$	−0.0510446	−	0.355023i	−0.00283145	−	0.0196931i
$326$	15.4482	+	11.0006i	0.855597	+	0.609268i
$327$	11.7997	+	2.82724i	0.652524	+	0.156347i
$328$	−4.62713	−	6.49789i	−0.255490	−	0.358786i
$329$	14.8074	+	42.7833i	0.816360	+	2.35872i
$330$	−7.61128	+	3.50202i	−0.418987	+	0.192780i
$331$	26.1151	+	24.9007i	1.43541	+	1.36866i	0.806578	+	0.591127i	$0.201317\pi$
$331$	26.1151	+	24.9007i	1.43541	+	1.36866i	0.628836	+	0.777538i	$0.283532\pi$
$332$	−1.58432	−	1.82841i	−0.0869511	−	0.100347i
$333$	2.10342	+	2.64379i	0.115267	+	0.144879i
$334$	7.74193	−	4.97544i	0.423620	−	0.272244i
$335$	−16.8972	−	5.84816i	−0.923190	−	0.319519i
$336$	−1.17451	+	6.18812i	−0.0640748	+	0.337590i
$337$	10.4828	−	13.3300i	0.571037	−	0.726132i	−0.411663	−	0.911336i	$-0.635052\pi$
$337$	10.4828	−	13.3300i	0.571037	−	0.726132i	0.982700	+	0.185204i	$0.0592945\pi$
$338$	−12.2729	+	4.24770i	−0.667559	+	0.231045i
$339$	−15.3081	+	12.1087i	−0.831422	+	0.657654i
$340$	5.38102	+	22.1809i	0.291827	+	1.20293i
$341$	−5.95195	−	13.0329i	−0.322316	−	0.705774i
$342$	−11.0417	+	10.6482i	−0.597069	+	0.575790i
$343$	−1.52545	+	2.37364i	−0.0823665	+	0.128165i
$344$	−1.27354	−	2.20583i	−0.0686646	−	0.118931i
$345$	2.92440	+	23.5651i	0.157444	+	1.26870i
$346$	−5.69605	+	9.86585i	−0.306222	+	0.530391i
$347$	−11.7873	−	22.8641i	−0.632773	−	1.22741i	−0.959345	−	0.282237i	$-0.908924\pi$
$347$	−11.7873	−	22.8641i	−0.632773	−	1.22741i	0.326571	−	0.945173i	$-0.394107\pi$
$348$	0.276615	+	1.41368i	0.0148281	+	0.0757809i
$349$	−7.53608	+	10.5829i	−0.403397	+	0.566492i	−0.965443	−	0.260614i	$-0.916075\pi$
$349$	−7.53608	+	10.5829i	−0.403397	+	0.566492i	0.562046	+	0.827106i	$0.310014\pi$
$350$	11.0677	+	3.24977i	0.591594	+	0.173708i
$351$	0.421777	−	0.409055i	0.0225128	−	0.0218338i
$352$	1.27882	+	1.10810i	0.0681612	+	0.0590620i
$353$	4.95909	+	12.3872i	0.263946	+	0.659304i	0.999842	−	0.0177902i	$-0.00566311\pi$
$353$	4.95909	+	12.3872i	0.263946	+	0.659304i	−0.735896	+	0.677094i	$0.763239\pi$
$354$	2.69906	+	7.72761i	0.143454	+	0.410718i
$355$	−8.12818	−	42.1730i	−0.431399	−	2.23831i
$356$	−0.258520	−	5.42700i	−0.0137015	−	0.287630i
$357$	45.8038	+	20.7614i	2.42419	+	1.09881i
$358$	−6.39993	+	18.4914i	−0.338247	+	0.977300i
$359$	3.75350	−	1.10213i	0.198102	−	0.0581681i	−0.181176	−	0.983451i	$-0.557990\pi$
$359$	3.75350	−	1.10213i	0.198102	−	0.0581681i	0.379278	+	0.925283i	$0.376172\pi$
$360$	−4.59564	+	7.24072i	−0.242211	+	0.381620i
$361$	4.67895	−	5.39980i	0.246261	−	0.284200i
$362$	0.900262	−	0.0859646i	0.0473167	−	0.00451820i
$363$	−10.2272	−	9.69655i	−0.536791	−	0.508937i
$364$	−0.0390868	+	0.409335i	−0.00204870	+	0.0214550i
$365$	3.82046	+	1.52948i	0.199972	+	0.0800567i
$366$	1.51839	+	2.61282i	0.0793673	+	0.136574i
$367$	2.15058	−	1.24164i	0.112259	−	0.0648128i	−0.442819	−	0.896611i	$-0.646022\pi$
$367$	2.15058	−	1.24164i	0.112259	−	0.0648128i	0.555078	+	0.831798i	$0.312688\pi$
$368$	4.09098	−	2.50278i	0.213257	−	0.130466i
$369$	−21.8244	−	9.81797i	−1.13613	−	0.511103i
$370$	−2.70825	−	1.74049i	−0.140795	−	0.0904836i
$371$	−15.9575	−	20.2916i	−0.828472	−	1.05349i
$372$	−12.3601	−	7.89400i	−0.640840	−	0.409285i
$373$	−26.1263	−	27.4004i	−1.35277	−	1.41874i	−0.819857	−	0.572568i	$-0.805947\pi$
$373$	−26.1263	−	27.4004i	−1.35277	−	1.41874i	−0.532910	−	0.846172i	$-0.678901\pi$
$374$	11.0051	−	7.83672i	0.569062	−	0.405227i
$375$	−7.13046	−	5.57487i	−0.368215	−	0.287885i
$376$	11.5579	−	4.62708i	0.596053	−	0.238624i
$377$	0.0264943	+	0.0902312i	0.00136452	+	0.00464714i
$378$	6.33157	+	17.8034i	0.325661	+	0.915709i
$379$	0.198062	+	0.308190i	0.0101737	+	0.0158306i	0.846303	−	0.532702i	$-0.178823\pi$
$379$	0.198062	+	0.308190i	0.0101737	+	0.0158306i	−0.836129	+	0.548532i	$0.815187\pi$
$380$	6.69789	−	12.9921i	0.343595	−	0.666481i
$381$	−18.2411	+	17.4917i	−0.934519	+	0.896125i
$382$	−8.66033	−	2.10097i	−0.443101	−	0.107495i
$383$	−27.4241	−	21.5665i	−1.40131	−	1.10200i	−0.980867	−	0.194678i	$-0.937634\pi$
$383$	−27.4241	−	21.5665i	−1.40131	−	1.10200i	−0.420438	−	0.907321i	$-0.638124\pi$
$384$	1.71511	+	0.241644i	0.0875239	+	0.0123314i
$385$	−1.67208	−	17.5108i	−0.0852172	−	0.892435i
$386$	−2.56733	+	8.74353i	−0.130674	+	0.445034i
$387$	−6.63902	−	3.78310i	−0.337480	−	0.192306i
$388$	4.04230	−	0.581195i	0.205217	−	0.0295057i
$389$	−0.266443	+	5.59332i	−0.0135092	+	0.283593i	0.981997	+	0.188896i	$0.0604910\pi$
$389$	−0.266443	+	5.59332i	−0.0135092	+	0.283593i	−0.995506	+	0.0946963i	$0.969812\pi$
$390$	−0.255141	+	0.498362i	−0.0129196	+	0.0252355i
$391$	−11.7188	−	36.4537i	−0.592646	−	1.84354i
$392$	−5.39023	−	3.11205i	−0.272248	−	0.157182i
$393$	19.7657	−	11.4864i	0.997048	−	0.579414i
$394$	−4.20345	+	3.30563i	−0.211767	+	0.166535i
$395$	−21.0272	+	9.60282i	−1.05800	+	0.483170i
$396$	4.98998	+	0.932481i	0.250756	+	0.0468589i
$397$	−1.09195	+	2.39103i	−0.0548032	+	0.120002i	−0.935053	−	0.354509i	$-0.884648\pi$
$397$	−1.09195	+	2.39103i	−0.0548032	+	0.120002i	0.880249	+	0.474511i	$0.157375\pi$
$398$	21.7669	+	4.19523i	1.09108	+	0.210288i
$399$	−13.4617	−	29.2577i	−0.673929	−	1.46472i
$400$	0.747826	−	3.08258i	0.0373913	−	0.154129i
$401$	33.3929	−	6.43595i	1.66756	−	0.321396i	0.733819	−	0.679345i	$-0.237736\pi$
$401$	33.3929	−	6.43595i	1.66756	−	0.321396i	0.933741	+	0.357949i	$0.116524\pi$
$402$	6.30913	+	8.80708i	0.314671	+	0.439257i
$403$	−0.851010	−	0.438726i	−0.0423918	−	0.0218545i
$404$	8.33571	−	7.22294i	0.414717	−	0.359355i
$405$	−0.933235	+	25.7111i	−0.0463728	+	1.27759i
$406$	−2.99356	−	0.430409i	−0.148568	−	0.0213608i
$407$	−0.360635	+	1.87115i	−0.0178760	+	0.0927495i
$408$	5.10340	−	12.8530i	0.252656	−	0.636317i
$409$	−19.7709	+	18.8515i	−0.977606	+	0.932145i	−0.997709	−	0.0676525i	$-0.978449\pi$
$409$	−19.7709	+	18.8515i	−0.977606	+	0.932145i	0.0201030	+	0.999798i	$0.493601\pi$
$410$	22.7004	+	2.16763i	1.12109	+	0.107052i
$411$	−7.40312	−	8.49497i	−0.365169	−	0.419026i
$412$	−18.0065	−	0.857754i	−0.887115	−	0.0422585i
$413$	−17.1855			−0.845645
$414$	6.80286	−	12.6776i	0.334342	−	0.623069i
$415$	6.91607			0.339496
$416$	0.112947	+	0.00538033i	0.00553769	+	0.000263793i
$417$	2.92952	−	8.54242i	0.143459	−	0.418324i
$418$	−8.61299	−	0.822440i	−0.421275	−	0.0402269i
$419$	4.71138	−	4.49229i	0.230166	−	0.219463i	−0.566216	−	0.824257i	$-0.691593\pi$
$419$	4.71138	−	4.49229i	0.230166	−	0.219463i	0.796382	+	0.604794i	$0.206745\pi$
$420$	−11.1703	−	14.1218i	−0.545056	−	0.689074i
$421$	4.10068	−	21.2763i	0.199855	−	1.03695i	−0.733961	−	0.679191i	$-0.762331\pi$
$421$	4.10068	−	21.2763i	0.199855	−	1.03695i	0.933816	−	0.357754i	$-0.116457\pi$
$422$	−2.34829	−	0.337633i	−0.114313	−	0.0164357i
$423$	22.9211	−	29.4885i	1.11446	−	1.43378i
$424$	−5.36487	+	4.64869i	−0.260541	+	0.225760i
$425$	−22.5106	−	11.6050i	−1.09192	−	0.562926i
$426$	−10.7432	+	23.7015i	−0.520508	+	1.14834i
$427$	−6.23007	+	1.20075i	−0.301494	+	0.0581083i
$428$	2.69324	−	11.1017i	0.130183	−	0.536621i
$429$	0.329992	+	0.0305684i	0.0159322	+	0.00147585i
$430$	7.14967	+	1.37799i	0.344788	+	0.0664524i
$431$	8.24129	−	18.0459i	0.396969	−	0.869241i	−0.600600	−	0.799550i	$-0.705071\pi$
$431$	8.24129	−	18.0459i	0.396969	−	0.869241i	0.997569	−	0.0696908i	$-0.0222013\pi$
$432$	4.80737	−	1.97210i	0.231295	−	0.0948825i
$433$	−32.7149	+	14.9404i	−1.57218	+	0.717989i	−0.995116	−	0.0987135i	$-0.968527\pi$
$433$	−32.7149	+	14.9404i	−1.57218	+	0.717989i	−0.577060	+	0.816702i	$0.695800\pi$
$434$	24.2037	−	19.0340i	1.16181	−	0.913660i
$435$	−3.57199	−	2.04883i	−0.171264	−	0.0982341i
$436$	6.06683	+	3.50269i	0.290548	+	0.167748i
$437$	−9.61620	+	22.5580i	−0.460005	+	1.07909i
$438$	−1.35396	−	2.09376i	−0.0646949	−	0.100044i
$439$	−0.0326060	+	0.684484i	−0.00155620	+	0.0326686i	−0.999512	−	0.0312412i	$-0.990054\pi$
$439$	−0.0326060	+	0.684484i	−0.00155620	+	0.0326686i	0.997956	+	0.0639099i	$0.0203570\pi$
$440$	−4.78797	+	0.688407i	−0.228258	+	0.0328185i
$441$	−18.6720	+	0.105674i	−0.889143	+	0.00503208i
$442$	0.254353	−	0.866247i	0.0120983	−	0.0412032i
$443$	0.439267	+	4.60021i	0.0208702	+	0.218562i	0.999890	+	0.0147997i	$0.00471106\pi$
$443$	0.439267	+	4.60021i	0.0208702	+	0.218562i	−0.979020	+	0.203763i	$0.934683\pi$
$444$	0.730070	+	1.80878i	0.0346476	+	0.0858407i
$445$	12.2087	+	9.60099i	0.578746	+	0.455131i
$446$	9.17882	+	2.22676i	0.434630	+	0.105440i
$447$	−7.53706	−	30.6889i	−0.356491	−	1.45154i
$448$	−1.66634	+	3.23225i	−0.0787271	+	0.152709i
$449$	−5.83670	−	9.08208i	−0.275451	−	0.428610i	0.675774	−	0.737109i	$-0.263810\pi$
$449$	−5.83670	−	9.08208i	−0.275451	−	0.428610i	−0.951225	+	0.308499i	$0.900173\pi$
$450$	−2.73259	−	9.11520i	−0.128816	−	0.429695i
$451$	−3.80285	−	12.9513i	−0.179069	−	0.609853i
$452$	−10.4616	+	4.18819i	−0.492073	+	0.196996i
$453$	−0.918654	+	6.52030i	−0.0431621	+	0.306351i
$454$	−17.2458	+	12.2807i	−0.809384	+	0.576360i
$455$	−0.811173	−	0.850733i	−0.0380284	−	0.0398830i
$456$	−7.86032	+	4.08047i	−0.368093	+	0.191086i
$457$	−1.32115	−	1.67998i	−0.0618007	−	0.0785859i	0.754170	−	0.656679i	$-0.228039\pi$
$457$	−1.32115	−	1.67998i	−0.0618007	−	0.0785859i	−0.815971	+	0.578093i	$0.803797\pi$
$458$	−18.1068	−	11.6365i	−0.846075	−	0.543740i
$459$	−6.25264	−	41.0134i	−0.291848	−	1.91434i
$460$	−2.25133	+	13.5236i	−0.104969	+	0.630540i
$461$	−4.86324	+	2.80779i	−0.226504	+	0.130772i	−0.608958	−	0.793202i	$-0.708412\pi$
$461$	−4.86324	+	2.80779i	−0.226504	+	0.130772i	0.382454	+	0.923974i	$0.375079\pi$
$462$	−5.30284	+	9.24511i	−0.246711	+	0.430122i
$463$	12.7063	+	5.08685i	0.590514	+	0.236406i	0.647622	−	0.761962i	$-0.275764\pi$
$463$	12.7063	+	5.08685i	0.590514	+	0.236406i	−0.0571082	+	0.998368i	$0.518188\pi$
$464$	−0.0790546	+	0.827898i	−0.00367002	+	0.0384342i
$465$	40.1929	−	11.9254i	1.86390	−	0.553025i
$466$	−11.2861	+	1.07769i	−0.522820	+	0.0499233i
$467$	9.46630	−	10.9247i	0.438048	−	0.505534i	−0.493202	−	0.869915i	$-0.664174\pi$
$467$	9.46630	−	10.9247i	0.438048	−	0.505534i	0.931250	+	0.364380i	$0.118719\pi$
$468$	0.300631	−	0.157146i	0.0138967	−	0.00726408i
$469$	−21.8244	+	6.40822i	−1.00776	+	0.295904i
$470$	−11.6402	+	33.6322i	−0.536923	+	1.55134i
$471$	1.58332	+	16.0997i	0.0729557	+	0.741836i
$472$	0.224865	+	4.72050i	0.0103502	+	0.217278i
$473$	−0.815664	−	4.23207i	−0.0375043	−	0.194591i
$474$	13.7603	+	2.61172i	0.632032	+	0.119960i
$475$	6.02803	+	15.0573i	0.276585	+	0.690876i
$476$	21.9429	+	19.0136i	1.00575	+	0.871488i
$477$	−6.85131	+	20.1640i	−0.313700	+	0.923248i
$478$	6.28240	+	1.84468i	0.287350	+	0.0843736i
$479$	−0.367535	+	0.516130i	−0.0167931	+	0.0235826i	−0.822887	−	0.568205i	$-0.807638\pi$
$479$	−0.367535	+	0.516130i	−0.0167931	+	0.0235826i	0.806094	+	0.591787i	$0.201578\pi$
$480$	−3.73280	+	3.25303i	−0.170378	+	0.148480i
$481$	0.0583506	+	0.113184i	0.00266056	+	0.00516076i
$482$	7.21226	−	12.4920i	0.328509	−	0.568995i
$483$	20.4187	+	22.2607i	0.929083	+	1.01290i
$484$	−4.06837	−	7.04662i	−0.184926	−	0.320301i
$485$	−6.31167	+	9.82115i	−0.286598	+	0.445955i
$486$	9.46182	−	12.3885i	0.429197	−	0.561952i
$487$	−13.1778	−	28.8552i	−0.597141	−	1.30756i	−0.931030	−	0.364944i	$-0.881088\pi$
$487$	−13.1778	−	28.8552i	−0.597141	−	1.30756i	0.333889	−	0.942612i	$-0.391639\pi$
$488$	0.411337	+	1.69556i	0.0186204	+	0.0767542i
$489$	30.5293	+	12.1220i	1.38058	+	0.548175i
$490$	16.8141	−	5.81941i	0.759582	−	0.262894i
$491$	14.3042	−	18.1893i	0.645539	−	0.820870i	−0.347620	−	0.937635i	$-0.613010\pi$
$491$	14.3042	−	18.1893i	0.645539	−	0.820870i	0.993160	+	0.116765i	$0.0372525\pi$
$492$	−10.4675	−	9.01837i	−0.471910	−	0.406580i
$493$	6.27498	+	2.17179i	0.282611	+	0.0978126i
$494$	−0.486394	+	0.312586i	−0.0218839	+	0.0140639i
$495$	−11.3560	+	9.03490i	−0.510412	+	0.406089i
$496$	−5.54492	−	6.39918i	−0.248974	−	0.287331i
$497$	−39.5414	−	37.7027i	−1.77368	−	1.69120i
$498$	−3.42027	−	2.42100i	−0.153266	−	0.108488i
$499$	11.0636	+	31.9661i	0.495273	+	1.43100i	0.864960	+	0.501841i	$0.167344\pi$
$499$	11.0636	+	31.9661i	0.495273	+	1.43100i	−0.369687	+	0.929156i	$0.620535\pi$
$500$	−3.03118	−	4.25670i	−0.135559	−	0.190365i
$501$	10.9670	−	11.5673i	0.489971	−	0.516787i
$502$	7.81638	+	5.56602i	0.348862	+	0.248424i
$503$	0.142202	+	0.989036i	0.00634047	+	0.0440990i	0.992746	−	0.120230i	$-0.0383632\pi$
$503$	0.142202	+	0.989036i	0.00634047	+	0.0440990i	−0.986406	+	0.164329i	$0.947454\pi$
$504$	0.580757	+	10.8940i	0.0258690	+	0.485258i
$505$			31.5304i			1.40308i
$506$	7.92682	−	1.73798i	0.352390	−	0.0772625i
$507$	−18.8891	+	12.2150i	−0.838894	+	0.542485i
$508$	−12.9690	+	6.68600i	−0.575408	+	0.296643i
$509$	−3.30305	+	8.25061i	−0.146405	+	0.365702i	−0.983385	−	0.181531i	$-0.941895\pi$
$509$	−3.30305	+	8.25061i	−0.146405	+	0.365702i	0.836980	+	0.547233i	$0.184319\pi$
$510$	18.2143	+	35.0867i	0.806544	+	1.55367i
$511$	5.08741	−	1.23419i	0.225054	−	0.0545974i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	−14.1740	+	22.4724i	−0.625800	+	0.992182i
$514$	−0.486754	+	3.38545i	−0.0214698	+	0.149326i
$515$	35.5618	−	37.2961i	1.56704	−	1.64346i
$516$	−3.05342	−	3.18425i	−0.134419	−	0.140179i
$517$	21.0425	−	1.00238i	0.925448	−	0.0440845i
$518$	−4.09062	+	0.194860i	−0.179731	+	0.00856166i
$519$	−5.50547	+	18.9481i	−0.241663	+	0.831729i
$520$	−0.223064	+	0.233943i	−0.00978202	+	0.0102591i
$521$	−1.99278	+	13.8601i	−0.0873051	+	0.607220i	0.898455	+	0.439065i	$0.144690\pi$
$521$	−1.99278	+	13.8601i	−0.0873051	+	0.607220i	−0.985761	+	0.168155i	$0.946219\pi$
$522$	1.04928	+	2.26362i	0.0459259	+	0.0990760i
$523$	9.17637	+	4.19071i	0.401254	+	0.183247i	0.605812	−	0.795608i	$-0.292848\pi$
$523$	9.17637	+	4.19071i	0.401254	+	0.183247i	−0.204558	+	0.978855i	$0.565576\pi$
$524$	12.8267	−	3.11173i	0.560337	−	0.135936i
$525$	19.9591	+	0.894170i	0.871086	+	0.0390248i
$526$	−11.4199	+	28.5255i	−0.497931	+	1.24377i
$527$	−60.0897	+	30.9784i	−2.61755	+	1.34944i
$528$	2.60882	+	1.33561i	0.113534	+	0.0581249i
$529$	2.11128	−	22.9029i	0.0917948	−	0.995778i
$530$		−	20.2930i		−	0.881470i
$531$	7.73234	+	11.8833i	0.335555	+	0.515693i
$532$	−2.64623	−	18.4049i	−0.114729	−	0.797954i
$533$	−0.734750	−	0.523213i	−0.0318256	−	0.0226629i
$534$	−2.67678	−	9.02177i	−0.115836	−	0.390410i
$535$	18.9427	+	26.6013i	0.818965	+	1.15008i
$536$	2.04576	+	5.91085i	0.0883635	+	0.255310i
$537$	−3.12616	+	33.7476i	−0.134904	+	1.45631i
$538$	−9.88135	−	9.42185i	−0.426015	−	0.406205i
$539$	−6.89694	−	7.95949i	−0.297072	−	0.342840i
$540$	−4.73896	+	14.0779i	−0.203932	+	0.605815i
$541$	31.9779	−	20.5509i	1.37484	−	0.883553i	0.375767	−	0.926714i	$-0.377379\pi$
$541$	31.9779	−	20.5509i	1.37484	−	0.883553i	0.999068	+	0.0431609i	$0.0137428\pi$
$542$	4.32236	+	1.49598i	0.185661	+	0.0642580i
$543$	1.47879	−	0.516503i	0.0634608	−	0.0221653i
$544$	4.93552	−	6.27602i	0.211609	−	0.269082i
$545$	−18.9246	+	6.54988i	−0.810642	+	0.280566i
$546$	0.103353	+	0.704676i	0.00442311	+	0.0301573i
$547$	−1.13615	−	4.68329i	−0.0485784	−	0.200243i	0.942351	−	0.334626i	$-0.108610\pi$
$547$	−1.13615	−	4.68329i	−0.0485784	−	0.200243i	−0.990929	+	0.134383i	$0.957095\pi$
$548$	−2.70255	−	5.91775i	−0.115447	−	0.252794i
$549$	3.63340	+	3.76767i	0.155070	+	0.160800i
$550$	2.90183	−	4.51534i	0.123735	−	0.192535i
$551$	−2.12624	−	3.68275i	−0.0905807	−	0.156890i
$552$	5.84737	−	5.89985i	0.248881	−	0.251114i
$553$	−14.7030	+	25.4663i	−0.625235	+	1.08294i
$554$	1.67078	+	3.24086i	0.0709846	+	0.137691i
$555$	−5.27446	−	1.80881i	−0.223888	−	0.0767798i
$556$	3.02437	−	4.24714i	0.128262	−	0.180119i
$557$	−16.0343	−	4.70809i	−0.679395	−	0.199488i	−0.0762125	−	0.997092i	$-0.524283\pi$
$557$	−16.0343	−	4.70809i	−0.679395	−	0.199488i	−0.603182	+	0.797603i	$0.706101\pi$
$558$	−24.0515	−	8.17218i	−1.01818	−	0.345956i
$559$	−0.217664	−	0.188607i	−0.00920622	−	0.00797723i
$560$	−3.86363	−	9.65089i	−0.163268	−	0.407824i
$561$	15.2739	−	17.7282i	0.644866	−	0.748484i
$562$	3.10105	+	16.0898i	0.130810	+	0.678706i
$563$	0.597469	+	12.5424i	0.0251803	+	0.528600i	0.975856	+	0.218414i	$0.0700882\pi$
$563$	0.597469	+	12.5424i	0.0251803	+	0.528600i	−0.950676	+	0.310186i	$0.899609\pi$
$564$	17.5296	−	12.5577i	0.738131	−	0.528775i
$565$	10.5361	−	30.4421i	0.443257	−	1.28071i
$566$	24.8078	−	7.28424i	1.04275	−	0.306179i
$567$	18.0048	+	27.3309i	0.756132	+	1.14779i
$568$	−9.83874	+	11.3545i	−0.412824	+	0.476425i
$569$	8.23203	−	0.786063i	0.345104	−	0.0329535i	0.0789351	−	0.996880i	$-0.474848\pi$
$569$	8.23203	−	0.786063i	0.345104	−	0.0329535i	0.266169	+	0.963926i	$0.414242\pi$
$570$	5.89915	−	24.6205i	0.247088	−	1.03124i
$571$	−0.0767473	+	0.803734i	−0.00321177	+	0.0336352i	−0.996936	−	0.0782249i	$-0.975075\pi$
$571$	−0.0767473	+	0.803734i	−0.00321177	+	0.0336352i	0.993724	+	0.111860i	$0.0356808\pi$
$572$	0.177631	+	0.0711126i	0.00742712	+	0.00297337i
$573$	−15.4352	+	0.0436772i	−0.644813	+	0.00182464i
$574$	25.1220	−	14.5042i	1.04857	−	0.605394i
$575$	−9.70476	−	11.7147i	−0.404716	−	0.488535i
$576$	2.98475	−	0.302065i	0.124365	−	0.0125860i
$577$	9.78674	+	6.28955i	0.407427	+	0.261838i	0.728264	−	0.685297i	$-0.240328\pi$
$577$	9.78674	+	6.28955i	0.407427	+	0.261838i	−0.320836	+	0.947135i	$0.603964\pi$
$578$	−28.8976	−	36.7463i	−1.20198	−	1.52844i
$579$	−0.706398	+	15.7678i	−0.0293569	+	0.655286i
$580$	−1.64063	−	1.72064i	−0.0681234	−	0.0714458i
$581$	7.16654	−	5.10327i	0.297318	−	0.211719i
$582$	6.55931	−	2.64751i	0.271892	−	0.109743i
$583$	−11.1515	+	4.46438i	−0.461847	+	0.184896i
$584$	−0.405572	−	1.38125i	−0.0167827	−	0.0571566i
$585$	−0.223286	+	0.943677i	−0.00923176	+	0.0390163i
$586$	6.28679	+	9.78243i	0.259705	+	0.404108i
$587$	−12.8826	+	24.9888i	−0.531723	+	1.03140i	0.458074	+	0.888914i	$0.348540\pi$
$587$	−12.8826	+	24.9888i	−0.531723	+	1.03140i	−0.989797	+	0.142485i	$0.954491\pi$
$588$	−10.3523	−	3.00792i	−0.426923	−	0.124045i
$589$	42.0748	+	10.2072i	1.73366	+	0.420582i
$590$	−10.6193	−	8.35111i	−0.437190	−	0.343810i
$591$	−5.70489	+	7.29676i	−0.234668	+	0.300149i
$592$	0.107048	+	1.12105i	0.00439964	+	0.0460751i
$593$	8.57528	−	29.2047i	0.352144	−	1.19929i	−0.572961	−	0.819583i	$-0.694205\pi$
$593$	8.57528	−	29.2047i	0.352144	−	1.19929i	0.925105	−	0.379711i	$-0.123977\pi$
$594$	8.77868	−	0.492904i	0.360194	−	0.0202241i
$595$	−82.1555	+	11.8122i	−3.36805	+	0.484252i
$596$	0.868122	−	18.2241i	0.0355597	−	0.746489i
$597$	38.3465	−	1.93544i	1.56942	−	0.0792122i
$598$	0.344585	−	0.418735i	0.0140911	−	0.0171233i
$599$	15.6839	+	9.05509i	0.640826	+	0.369981i	0.784933	−	0.619581i	$-0.212698\pi$
$599$	15.6839	+	9.05509i	0.640826	+	0.369981i	−0.144107	+	0.989562i	$0.546031\pi$
$600$	−0.0155466	−	5.49404i	−0.000634686	−	0.224293i
$601$	−3.61401	+	2.84209i	−0.147419	+	0.115931i	−0.689145	−	0.724624i	$-0.742013\pi$
$601$	−3.61401	+	2.84209i	−0.147419	+	0.115931i	0.541726	+	0.840555i	$0.317771\pi$
$602$	8.42541	−	3.84775i	0.343394	−	0.156823i
$603$	14.2506	+	12.2077i	0.580331	+	0.497137i
$604$	−1.57927	+	3.45813i	−0.0642597	+	0.140709i
$605$	22.8399	+	4.40203i	0.928574	+	0.178968i
$606$	11.0374	−	15.5930i	0.448362	−	0.633422i
$607$	5.81473	−	23.9686i	0.236013	−	0.972857i	−0.723305	−	0.690528i	$-0.757378\pi$
$607$	5.81473	−	23.9686i	0.236013	−	0.972857i	0.959318	−	0.282328i	$-0.0911068\pi$
$608$	−5.02081	+	0.967682i	−0.203621	+	0.0392447i
$609$	−5.21316	+	0.512687i	−0.211248	+	0.0207751i
$610$	−4.43318	−	2.28546i	−0.179494	−	0.0925357i
$611$	1.06391	−	0.921881i	0.0430411	−	0.0372953i
$612$	3.27459	−	23.7278i	0.132367	−	0.959139i
$613$	15.1349	+	2.17608i	0.611295	+	0.0878909i	0.441007	−	0.897504i	$-0.354621\pi$
$613$	15.1349	+	2.17608i	0.611295	+	0.0878909i	0.170287	+	0.985394i	$0.445530\pi$
$614$	−2.99564	+	15.5429i	−0.120894	+	0.627260i
$615$	39.0791	−	5.73163i	1.57582	−	0.231122i
$616$	−4.45341	+	4.24632i	−0.179433	+	0.171089i
$617$	−21.3245	−	2.03624i	−0.858492	−	0.0819761i	−0.343481	−	0.939160i	$-0.611606\pi$
$617$	−21.3245	−	2.03624i	−0.858492	−	0.0819761i	−0.515011	+	0.857183i	$0.672212\pi$
$618$	−30.6424	+	5.99582i	−1.23262	+	0.241187i
$619$	−24.7306	−	1.17806i	−0.994006	−	0.0473504i	−0.455729	−	0.890118i	$-0.650622\pi$
$619$	−24.7306	−	1.17806i	−0.994006	−	0.0473504i	−0.538277	+	0.842768i	$0.680925\pi$
$620$	24.2053			0.972108
$621$	6.20565	−	24.1348i	0.249024	−	0.968497i
$622$	1.44987			0.0581346
$623$	19.7353	+	0.940106i	0.790676	+	0.0376646i
$624$	0.192207	−	0.0376093i	0.00769444	−	0.00150558i
$625$	30.6590	+	2.92758i	1.22636	+	0.117103i
$626$	−16.5007	+	15.7334i	−0.659499	+	0.628831i
$627$	−14.8274	+	2.17469i	−0.592148	+	0.0868489i
$628$	−1.76761	+	9.17124i	−0.0705354	+	0.365972i
$629$	8.89995	+	1.27962i	0.354864	+	0.0510218i
$630$	−24.6231	−	19.1392i	−0.981006	−	0.762526i
$631$	−18.7345	+	16.2335i	−0.745808	+	0.646246i	−0.942495	−	0.334220i	$-0.891527\pi$
$631$	−18.7345	+	16.2335i	−0.745808	+	0.646246i	0.196687	+	0.980466i	$0.436982\pi$
$632$	7.18743	+	3.70538i	0.285901	+	0.147392i
$633$	−4.08946	+	0.402177i	−0.162541	+	0.0159851i
$634$	−8.11079	+	1.56323i	−0.322121	+	0.0620837i
$635$	9.83374	−	40.5352i	0.390240	−	1.60859i
$636$	−7.10365	+	10.0357i	−0.281678	+	0.397940i
$637$	−0.691073	−	0.133193i	−0.0273813	−	0.00527731i
$638$	−0.584602	+	1.28010i	−0.0231446	+	0.0506797i
$639$	−8.27942	+	44.3055i	−0.327529	+	1.75270i
$640$	−2.60034	+	1.18753i	−0.102787	+	0.0469414i
$641$	18.7510	−	14.7460i	0.740620	−	0.582430i	−0.174955	−	0.984576i	$-0.555978\pi$
$641$	18.7510	−	14.7460i	0.740620	−	0.582430i	0.915575	+	0.402146i	$0.131736\pi$
$642$	−0.0559899	−	19.7864i	−0.00220974	−	0.780906i
$643$	−6.63875	−	3.83288i	−0.261807	−	0.151154i	0.363352	−	0.931652i	$-0.381632\pi$
$643$	−6.63875	−	3.83288i	−0.261807	−	0.151154i	−0.625158	+	0.780498i	$0.714966\pi$
$644$	7.64600	+	15.6746i	0.301295	+	0.617666i
$645$	12.5955	−	0.635723i	0.495946	−	0.0250316i
$646$	−1.94253	+	40.7788i	−0.0764280	+	1.60442i
$647$	37.6662	−	5.41558i	1.48081	−	0.212908i	0.645954	−	0.763376i	$-0.276460\pi$
$647$	37.6662	−	5.41558i	1.48081	−	0.212908i	0.834856	+	0.550468i	$0.185551\pi$
$648$	7.27163	−	5.30316i	0.285656	−	0.208328i
$649$	−2.25293	+	7.67277i	−0.0884352	+	0.301183i
$650$	−0.0340941	−	0.357050i	−0.00133728	−	0.0140046i
$651$	32.8490	−	42.0151i	1.28746	−	1.64670i
$652$	14.9073	+	11.7232i	0.583814	+	0.459116i
$653$	32.9107	+	7.98404i	1.28789	+	0.312440i	0.820519	−	0.571619i	$-0.193685\pi$
$653$	32.9107	+	7.98404i	1.28789	+	0.312440i	0.467375	+	0.884059i	$0.345200\pi$
$654$	11.6518	+	3.38549i	0.455621	+	0.132383i
$655$	−17.2893	+	33.5366i	−0.675549	+	1.31038i
$656$	−4.31271	−	6.71070i	−0.168383	−	0.262009i
$657$	−3.14240	−	2.96250i	−0.122597	−	0.115578i
$658$	12.7549	+	43.4394i	0.497240	+	1.69344i
$659$	−2.57610	+	1.03131i	−0.100350	+	0.0401743i	−0.421294	−	0.906924i	$-0.638424\pi$
$659$	−2.57610	+	1.03131i	−0.100350	+	0.0401743i	0.320944	+	0.947098i	$0.396000\pi$
$660$	−7.76929	+	3.13589i	−0.302419	+	0.122064i
$661$	17.5642	−	12.5074i	0.683170	−	0.486483i	−0.185007	−	0.982737i	$-0.559231\pi$
$661$	17.5642	−	12.5074i	0.683170	−	0.486483i	0.868177	+	0.496254i	$0.165292\pi$
$662$	24.9007	+	26.1151i	0.967792	+	1.01499i
$663$	0.0699849	−	1.56216i	0.00271799	−	0.0606692i
$664$	−1.49553	−	1.90172i	−0.0580378	−	0.0738011i
$665$	44.7165	+	28.7376i	1.73403	+	1.11439i
$666$	1.97524	+	2.74088i	0.0765391	+	0.106207i
$667$	2.95570	+	2.67808i	0.114445	+	0.103696i
$668$	7.96990	−	4.60143i	0.308365	−	0.178035i
$669$	16.3593	−	0.0462921i	0.632486	−	0.00178975i
$670$	−16.5998	−	6.64554i	−0.641304	−	0.256740i
$671$	−0.280634	+	2.93893i	−0.0108338	+	0.113456i
$672$	−1.46762	+	6.12523i	−0.0566148	+	0.236286i
$673$	11.1507	−	1.06476i	0.429827	−	0.0410435i	0.122099	−	0.992518i	$-0.461037\pi$
$673$	11.1507	−	1.06476i	0.429827	−	0.0410435i	0.307728	+	0.951474i	$0.400431\pi$
$674$	11.1052	−	12.8161i	0.427758	−	0.493659i
$675$	−8.36196	−	14.2035i	−0.321852	−	0.546693i
$676$	−12.4611	+	3.65892i	−0.479275	+	0.140728i
$677$	5.53804	−	16.0011i	0.212844	−	0.614973i	−0.787154	−	0.616756i	$-0.788446\pi$
$677$	5.53804	−	16.0011i	0.212844	−	0.614973i	0.999998	+	0.00178326i	$0.000567630\pi$
$678$	−15.8669	+	11.3666i	−0.609365	+	0.436531i
$679$	0.706637	+	14.8341i	0.0271182	+	0.569282i
$680$	4.31952	+	22.4118i	0.165646	+	0.859453i
$681$	−23.9353	+	27.7812i	−0.917202	+	1.06458i
$682$	−5.32507	−	13.3014i	−0.203908	−	0.509337i
$683$	19.0515	+	16.5082i	0.728984	+	0.631668i	0.938157	−	0.346211i	$-0.112532\pi$
$683$	19.0515	+	16.5082i	0.728984	+	0.631668i	−0.209173	+	0.977879i	$0.567077\pi$
$684$	−11.5359	+	10.1108i	−0.441086	+	0.386595i
$685$	17.8442	+	5.23953i	0.681792	+	0.200192i
$686$	−1.63666	+	2.29837i	−0.0624881	+	0.0877522i
$687$	−35.2640	−	12.0933i	−1.34540	−	0.461390i
$688$	−1.16714	−	2.26393i	−0.0444967	−	0.0863116i
$689$	−0.401346	+	0.695151i	−0.0152901	+	0.0264831i
$690$	1.79981	+	23.6776i	0.0685176	+	0.901391i
$691$	−9.62073	−	16.6636i	−0.365990	−	0.633913i	0.622945	−	0.782266i	$-0.285936\pi$
$691$	−9.62073	−	16.6636i	−0.365990	−	0.633913i	−0.988934	+	0.148353i	$0.952603\pi$
$692$	−6.15904	+	9.58365i	−0.234131	+	0.364316i
$693$	−5.10050	+	17.7415i	−0.193752	+	0.673945i
$694$	−10.6860	−	23.3991i	−0.405635	−	0.888216i
$695$	3.51396	+	14.4847i	0.133292	+	0.549438i
$696$	0.209036	+	1.42524i	0.00792349	+	0.0540234i
$697$	−60.1874	+	20.8311i	−2.27976	+	0.789033i
$698$	−8.03110	+	10.2124i	−0.303982	+	0.386544i
$699$	−18.5388	+	6.47514i	−0.701202	+	0.244912i
$700$	10.9005	+	3.77271i	0.412002	+	0.142595i
$701$	−5.73189	+	3.68366i	−0.216490	+	0.139130i	−0.644392	−	0.764695i	$-0.722889\pi$
$701$	−5.73189	+	3.68366i	−0.216490	+	0.139130i	0.427901	+	0.903825i	$0.359253\pi$
$702$	0.440763	−	0.388523i	0.0166355	−	0.0146639i
$703$	−3.77086	−	4.35181i	−0.142221	−	0.164132i
$704$	1.22464	+	1.16770i	0.0461555	+	0.0440092i
$705$	−5.68587	+	61.3801i	−0.214142	+	2.31171i
$706$	4.36406	+	12.6091i	0.164244	+	0.474551i
$707$	23.2658	+	32.6723i	0.875002	+	1.22877i
$708$	2.32831	+	7.84729i	0.0875033	+	0.294919i
$709$	−16.4525	−	11.7158i	−0.617887	−	0.439995i	0.227775	−	0.973714i	$-0.426855\pi$
$709$	−16.4525	−	11.7158i	−0.617887	−	0.439995i	−0.845662	+	0.533718i	$0.820794\pi$
$710$	−6.11230	−	42.5120i	−0.229391	−	1.59545i
$711$	24.2246	−	1.29141i	0.908495	−	0.0484316i
$712$		−	5.43315i		−	0.203616i
$713$	−40.4996	+	2.96327i	−1.51672	+	0.110975i
$714$	44.7640	+	22.9174i	1.67525	+	0.857661i
$715$	−0.486165	+	0.250635i	−0.0181815	+	0.00937323i
$716$	−7.27253	+	18.1659i	−0.271787	+	0.678892i
$717$	11.3295	+	0.507561i	0.423106	+	0.0189552i
$718$	3.80169	−	0.922281i	0.141878	−	0.0344192i
$719$	7.91772	+	3.61590i	0.295281	+	0.134850i	0.557547	−	0.830145i	$-0.311743\pi$
$719$	7.91772	+	3.61590i	0.295281	+	0.134850i	−0.262266	+	0.964996i	$0.584470\pi$
$720$	−4.93496	+	7.01385i	−0.183915	+	0.261391i
$721$	9.32941	−	64.8874i	0.347445	−	2.41653i
$722$	4.93059	−	5.17105i	0.183497	−	0.192447i
$723$	6.97094	−	23.9918i	0.259252	−	0.892264i
$724$	0.903333	−	0.0430310i	0.0335721	−	0.00159924i
$725$	2.63505	−	0.125523i	0.0978631	−	0.00466180i
$726$	−9.75427	−	10.1722i	−0.362015	−	0.377526i
$727$	9.38463	−	9.84231i	0.348057	−	0.365031i	−0.526314	−	0.850290i	$-0.676426\pi$
$727$	9.38463	−	9.84231i	0.348057	−	0.365031i	0.874370	+	0.485259i	$0.161275\pi$
$728$	−0.0585195	+	0.407012i	−0.00216888	+	0.0150849i
$729$	10.7976	−	24.7469i	0.399912	−	0.916554i
$730$	3.74336	+	1.70953i	0.138548	+	0.0632727i
$731$	−19.7632	+	4.79450i	−0.730968	+	0.177331i
$732$	1.39234	+	2.68211i	0.0514625	+	0.0991335i
$733$	−15.9707	+	39.8930i	−0.589893	+	1.47348i	0.269926	+	0.962881i	$0.413001\pi$
$733$	−15.9707	+	39.8930i	−0.589893	+	1.47348i	−0.859819	+	0.510600i	$0.829423\pi$
$734$	2.20722	−	1.13790i	0.0814699	−	0.0420007i
$735$	25.8783	−	16.7346i	0.954536	−	0.617267i
$736$	4.20543	−	2.30529i	0.155014	−	0.0849740i
$737$			10.5840i			0.389865i
$738$	−21.3325	−	10.8453i	−0.785260	−	0.399221i
$739$	2.36841	+	16.4726i	0.0871233	+	0.605956i	0.985873	+	0.167494i	$0.0535674\pi$
$739$	2.36841	+	16.4726i	0.0871233	+	0.605956i	−0.898750	+	0.438462i	$0.855523\pi$
$740$	−2.62237	−	1.86738i	−0.0964001	−	0.0686462i
$741$	−0.689014	+	0.726724i	−0.0253116	+	0.0266969i
$742$	−14.9739	−	21.0279i	−0.549709	−	0.771959i
$743$	−11.1492	−	32.2134i	−0.409023	−	1.18179i	−0.941985	−	0.335655i	$-0.891042\pi$
$743$	−11.1492	−	32.2134i	−0.409023	−	1.18179i	0.532962	−	0.846139i	$-0.321079\pi$
$744$	−11.9705	−	8.47318i	−0.438858	−	0.310642i
$745$	37.7469	+	35.9916i	1.38294	+	1.31863i
$746$	−24.7929	−	28.6125i	−0.907733	−	1.04758i
$747$	−6.75324	−	2.65935i	−0.247088	−	0.0973004i
$748$	11.3655	−	7.30419i	0.415566	−	0.267068i
$749$	39.2575	+	13.5872i	1.43444	+	0.496464i
$750$	−6.85712	−	5.90784i	−0.250387	−	0.215724i
$751$	3.78269	−	4.81008i	0.138032	−	0.175522i	−0.712122	−	0.702055i	$-0.752266\pi$
$751$	3.78269	−	4.81008i	0.138032	−	0.175522i	0.850155	+	0.526533i	$0.176508\pi$
$752$	11.7650	−	4.07189i	0.429024	−	0.148487i
$753$	15.4470	+	6.13340i	0.562921	+	0.223513i
$754$	0.0221709	+	0.0913897i	0.000807416	+	0.00332821i
$755$	−4.51462	−	9.88565i	−0.164304	−	0.359776i
$756$	5.47728	+	18.0845i	0.199207	+	0.657728i
$757$	0.535646	−	0.833481i	0.0194684	−	0.0302934i	−0.831383	−	0.555700i	$-0.812450\pi$
$757$	0.535646	−	0.833481i	0.0194684	−	0.0302934i	0.850851	+	0.525406i	$0.176087\pi$
$758$	0.183173	+	0.317265i	0.00665314	+	0.0115236i
$759$	12.6155	−	6.19802i	0.457912	−	0.224974i
$760$	7.30850	−	12.6587i	0.265107	−	0.459179i
$761$	−16.1968	−	31.4173i	−0.587132	−	1.13888i	−0.976038	−	0.217600i	$-0.930177\pi$
$761$	−16.1968	−	31.4173i	−0.587132	−	1.13888i	0.388906	−	0.921277i	$-0.372853\pi$
$762$	−19.0527	+	16.6039i	−0.690207	+	0.601496i
$763$	−14.7769	+	20.7513i	−0.534961	+	0.751248i
$764$	−8.55056	−	2.51067i	−0.309348	−	0.0908328i
$765$	45.1323	+	51.4937i	1.63176	+	1.86176i
$766$	−26.3669	−	22.8470i	−0.952673	−	0.825496i
$767$	0.198608	+	0.496098i	0.00717130	+	0.0179130i
$768$	1.70167	+	0.322979i	0.0614038	+	0.0116545i
$769$	1.27505	+	6.61559i	0.0459795	+	0.238564i	0.997646	−	0.0685676i	$-0.0218429\pi$
$769$	1.27505	+	6.61559i	0.0459795	+	0.238564i	−0.951667	+	0.307132i	$0.900631\pi$
$770$	−0.836989	−	17.5706i	−0.0301630	−	0.633199i
$771$	0.579804	+	5.89563i	0.0208811	+	0.212326i
$772$	−2.98046	+	8.61147i	−0.107269	+	0.309934i
$773$	−16.6991	+	4.90329i	−0.600624	+	0.176359i	−0.567889	−	0.823105i	$-0.692240\pi$
$773$	−16.6991	+	4.90329i	−0.600624	+	0.176359i	−0.0327349	+	0.999464i	$0.510422\pi$
$774$	−6.45149	−	4.09472i	−0.231894	−	0.147181i
$775$	−17.5885	+	20.2982i	−0.631796	+	0.729131i
$776$	4.06537	−	0.388196i	0.145938	−	0.0139354i
$777$	−6.80018	+	2.01763i	−0.243955	+	0.0723822i
$778$	−0.532282	+	5.57431i	−0.0190832	+	0.199849i
$779$	37.8665	+	15.1595i	1.35671	+	0.543144i
$780$	−0.278565	+	0.485657i	−0.00997422	+	0.0173893i
$781$	−22.0167	+	12.7113i	−0.787819	+	0.454847i
$782$	−9.97100	−	36.9700i	−0.356562	−	1.32204i
$783$	2.70008	+	3.37409i	0.0964931	+	0.120580i
$784$	−5.23605	−	3.36500i	−0.187002	−	0.120179i
$785$	−16.5049	−	20.9877i	−0.589084	−	0.749082i
$786$	20.2899	−	10.5329i	0.723716	−	0.375697i
$787$	2.45476	+	2.57447i	0.0875026	+	0.0917701i	0.766029	−	0.642806i	$-0.222230\pi$
$787$	2.45476	+	2.57447i	0.0875026	+	0.0917701i	−0.678527	+	0.734576i	$0.737381\pi$
$788$	−4.35598	+	3.10188i	−0.155175	+	0.110500i
$789$	−7.42489	+	52.6994i	−0.264333	+	1.87615i
$790$	−21.4603	+	8.59142i	−0.763525	+	0.305669i
$791$	−11.5451	−	39.3191i	−0.410497	−	1.39802i
$792$	4.93995	+	1.16886i	0.175534	+	0.0415336i
$793$	0.106661	+	0.165968i	0.00378765	+	0.00589369i
$794$	−1.20448	+	2.33636i	−0.0427453	+	0.0829144i
$795$	−8.38318	−	34.1341i	−0.297321	−	1.21061i
$796$	21.5427	+	5.22619i	0.763559	+	0.185238i
$797$	−10.0868	−	7.93235i	−0.357293	−	0.280978i	0.423336	−	0.905973i	$-0.360859\pi$
$797$	−10.0868	−	7.93235i	−0.357293	−	0.280978i	−0.780629	+	0.624994i	$0.785101\pi$
$798$	−12.0543	−	29.8651i	−0.426719	−	1.05721i
$799$	−9.44868	−	98.9510i	−0.334270	−	3.50064i
$800$	0.893654	−	3.04351i	0.0315955	−	0.107604i
$801$	−8.22948	−	14.0694i	−0.290775	−	0.497118i
$802$	33.6613	−	4.83976i	1.18862	−	0.170898i
$803$	0.115905	−	2.43316i	0.00409022	−	0.0858642i
$804$	5.88292	+	9.09730i	0.207475	+	0.320837i
$805$	−48.1776	−	12.8246i	−1.69804	−	0.452008i
$806$	−0.829171	−	0.478722i	−0.0292063	−	0.0168623i
$807$	−20.5133	−	11.7661i	−0.722103	−	0.414186i
$808$	8.66995	−	6.81813i	0.305008	−	0.239861i
$809$	13.1861	−	6.02188i	0.463598	−	0.211718i	−0.169902	−	0.985461i	$-0.554345\pi$
$809$	13.1861	−	6.02188i	0.463598	−	0.211718i	0.633500	+	0.773743i	$0.281618\pi$
$810$	−2.15556	+	25.6376i	−0.0757387	+	0.900813i
$811$	−3.08577	+	6.75690i	−0.108356	+	0.237267i	−0.956041	−	0.293234i	$-0.905269\pi$
$811$	−3.08577	+	6.75690i	−0.108356	+	0.237267i	0.847685	+	0.530500i	$0.177996\pi$
$812$	−2.96969	−	0.572360i	−0.104216	−	0.0200859i
$813$	7.88850	+	0.730741i	0.276662	+	0.0256282i
$814$	−0.449259	+	1.85187i	−0.0157465	+	0.0649080i
$815$	−53.2342	+	10.2600i	−1.86471	+	0.359394i
$816$	5.70919	−	12.5956i	0.199862	−	0.440934i
$817$	11.5760	+	5.96783i	0.404992	+	0.208788i
$818$	−20.6455	+	17.8894i	−0.721851	+	0.625488i
$819$	0.464954	+	1.14261i	0.0162468	+	0.0399262i
$820$	22.5716	+	3.24530i	0.788234	+	0.113331i
$821$	−3.14805	+	16.3336i	−0.109868	+	0.570047i	0.884718	+	0.466127i	$0.154351\pi$
$821$	−3.14805	+	16.3336i	−0.109868	+	0.570047i	−0.994586	+	0.103921i	$0.966861\pi$
$822$	−6.99053	−	8.83760i	−0.243823	−	0.308247i
$823$	−30.3222	+	28.9122i	−1.05697	+	1.00781i	−0.0570105	+	0.998374i	$0.518157\pi$
$823$	−30.3222	+	28.9122i	−1.05697	+	1.00781i	−0.999955	+	0.00944136i	$0.996995\pi$
$824$	−17.9453	−	1.71356i	−0.625153	−	0.0596948i
$825$	3.01575	−	8.79386i	0.104995	−	0.306163i
$826$	−17.1661	−	0.817720i	−0.597284	−	0.0284521i
$827$	45.4852			1.58168			0.790838	−	0.612026i	$-0.209645\pi$
$827$	45.4852			1.58168			0.790838	+	0.612026i	$0.209645\pi$
$828$	7.39838	−	12.3395i	0.257112	−	0.428828i
$829$	−26.1848			−0.909437			−0.454718	−	0.890635i	$-0.650260\pi$
$829$	−26.1848			−0.909437			−0.454718	+	0.890635i	$0.650260\pi$
$830$	6.90823	+	0.329080i	0.239788	+	0.0114225i
$831$	4.14919	+	4.76113i	0.143934	+	0.165162i
$832$	0.112563	+	0.0107485i	0.00390243	+	0.000372636i
$833$	−35.9657	+	34.2932i	−1.24614	+	1.18819i
$834$	3.33267	−	8.39335i	0.115401	−	0.290638i
$835$	−4.97881	+	25.8325i	−0.172299	+	0.893971i
$836$	−8.56410	−	1.23133i	−0.296195	−	0.0425865i
$837$	−43.8322	−	3.81027i	−1.51506	−	0.131702i
$838$	4.91979	−	4.26302i	0.169951	−	0.147264i
$839$	−26.3268	−	13.5724i	−0.908900	−	0.468571i	−0.0606458	−	0.998159i	$-0.519316\pi$
$839$	−26.3268	−	13.5724i	−0.908900	−	0.468571i	−0.848255	+	0.529589i	$0.822346\pi$
$840$	−10.4857	−	14.6373i	−0.361792	−	0.505036i
$841$	27.7968	−	5.35739i	0.958509	−	0.184738i
$842$	5.10840	−	21.0571i	0.176047	−	0.725676i
$843$	11.8630	+	25.7830i	0.408583	+	0.888012i
$844$	−2.32957	−	0.448987i	−0.0801870	−	0.0154548i
$845$	15.4228	−	33.7711i	0.530559	−	1.16176i
$846$	24.2983	−	28.3645i	0.835393	−	0.975192i
$847$	26.9153	−	12.2918i	0.924820	−	0.422351i
$848$	−5.57999	+	4.38815i	−0.191618	+	0.150690i
$849$	38.7192	−	22.5009i	1.32884	−	0.772228i
$850$	−21.9329	−	12.6630i	−0.752292	−	0.434336i
$851$	4.61628	+	2.80341i	0.158244	+	0.0960996i
$852$	−11.8588	+	23.1635i	−0.406274	+	0.793568i
$853$	0.906922	−	19.0386i	0.0310524	−	0.651871i	−0.928668	−	0.370913i	$-0.879045\pi$
$853$	0.906922	−	19.0386i	0.0310524	−	0.651871i	0.959720	−	0.280958i	$-0.0906521\pi$
$854$	−6.28015	+	0.902949i	−0.214902	+	0.0308983i
$855$	−0.248170	−	43.8503i	−0.00848722	−	1.49965i
$856$	3.21843	−	10.9610i	0.110004	−	0.374639i
$857$	−4.75947	−	49.8435i	−0.162581	−	1.70262i	−0.597270	−	0.802040i	$-0.703748\pi$
$857$	−4.75947	−	49.8435i	−0.162581	−	1.70262i	0.434690	−	0.900580i	$-0.356858\pi$
$858$	0.328164	+	0.0462354i	0.0112033	+	0.00157845i
$859$	−3.41229	−	2.68345i	−0.116426	−	0.0915583i	0.558249	−	0.829674i	$-0.311474\pi$
$859$	−3.41229	−	2.68345i	−0.116426	−	0.0915583i	−0.674674	+	0.738115i	$0.735716\pi$
$860$	7.07601	+	1.71662i	0.241290	+	0.0585363i
$861$	36.2651	−	34.7751i	1.23591	−	1.18513i
$862$	9.09061	−	17.6333i	0.309628	−	0.600594i
$863$	−11.5772	−	18.0145i	−0.394092	−	0.613219i	0.586343	−	0.810063i	$-0.300567\pi$
$863$	−11.5772	−	18.0145i	−0.394092	−	0.613219i	−0.980435	+	0.196844i	$0.936931\pi$
$864$	4.89576	−	1.74112i	0.166557	−	0.0592340i
$865$	−9.17498	−	31.2471i	−0.311959	−	1.06243i
$866$	−33.3887	+	13.3668i	−1.13459	+	0.454223i
$867$	−63.7878	−	49.8718i	−2.16635	−	1.69374i
$868$	25.0819	−	17.8608i	0.851336	−	0.606233i
$869$	9.44239	+	9.90290i	0.320311	+	0.335933i
$870$	−3.47046	−	2.21648i	−0.117659	−	0.0751456i
$871$	0.437205	+	0.555951i	0.0148141	+	0.0188377i
$872$	5.89329	+	3.78739i	0.199572	+	0.128257i
$873$	9.93948	−	7.16299i	0.336400	−	0.242430i
$874$	−10.6787	+	22.0749i	−0.361211	+	0.746694i
$875$	16.4572	−	9.50155i	0.556354	−	0.321211i
$876$	−1.25281	−	2.15581i	−0.0423284	−	0.0728381i
$877$	−33.2589	−	13.3148i	−1.12307	−	0.449611i	−0.265571	−	0.964091i	$-0.585560\pi$
$877$	−33.2589	−	13.3148i	−1.12307	−	0.449611i	−0.857502	+	0.514481i	$0.827985\pi$
$878$	−0.0651381	+	0.682157i	−0.00219831	+	0.0230217i
$879$	14.6160	+	13.8576i	0.492985	+	0.467404i
$880$	−4.81531	+	0.459806i	−0.162324	+	0.0155001i
$881$	−19.0282	+	21.9597i	−0.641076	+	0.739841i	−0.979565	−	0.201130i	$-0.935539\pi$
$881$	−19.0282	+	21.9597i	−0.641076	+	0.739841i	0.338489	+	0.940970i	$0.390084\pi$
$882$	−18.6559	−	0.782896i	−0.628176	−	0.0263615i
$883$	−43.7139	+	12.8356i	−1.47109	+	0.431951i	−0.916453	−	0.400141i	$-0.868961\pi$
$883$	−43.7139	+	12.8356i	−1.47109	+	0.431951i	−0.554637	+	0.832092i	$0.687143\pi$
$884$	0.295283	−	0.853163i	0.00993143	−	0.0286950i
$885$	−21.3123	−	9.66019i	−0.716404	−	0.324724i
$886$	0.219882	+	4.61590i	0.00738709	+	0.155074i
$887$	5.82348	+	30.2151i	0.195533	+	1.01452i	0.938522	+	0.345220i	$0.112196\pi$
$887$	5.82348	+	30.2151i	0.195533	+	1.01452i	−0.742988	+	0.669304i	$0.766592\pi$
$888$	0.643178	+	1.84146i	0.0215836	+	0.0617955i
$889$	−19.7205	−	49.2594i	−0.661405	−	1.65211i
$890$	11.7380	+	10.1710i	0.393458	+	0.340934i
$891$	14.5627	−	4.45564i	0.487868	−	0.149269i
$892$	9.06247	+	2.66098i	0.303434	+	0.0890962i
$893$	−36.9252	+	51.8542i	−1.23566	+	1.73524i
$894$	−6.06829	−	31.0128i	−0.202954	−	1.03722i
$895$	−25.6319	−	49.7190i	−0.856781	−	1.66192i
$896$	−1.81825	+	3.14930i	−0.0607434	+	0.105211i
$897$	0.406632	−	0.846690i	0.0135770	−	0.0282702i
$898$	−5.39795	−	9.34952i	−0.180132	−	0.311997i
$899$	3.80717	−	5.92408i	0.126976	−	0.197579i
$900$	−2.29578	−	9.23490i	−0.0765260	−	0.307830i
$901$	23.5449	+	51.5561i	0.784393	+	1.71758i
$902$	−3.18229	−	13.1176i	−0.105959	−	0.436768i
$903$	12.5825	−	9.95277i	0.418721	−	0.331208i
$904$	−10.6490	+	3.68567i	−0.354182	+	0.122583i
$905$	−1.59810	+	2.03215i	−0.0531227	+	0.0675510i
$906$	−1.22786	+	6.46921i	−0.0407930	+	0.214925i
$907$	53.1348	+	18.3901i	1.76431	+	0.610634i	0.999437	−	0.0335452i	$-0.0106798\pi$
$907$	53.1348	+	18.3901i	1.76431	+	0.610634i	0.764874	+	0.644179i	$0.222801\pi$
$908$	−17.8106	+	11.4462i	−0.591065	+	0.379854i
$909$	12.1240	−	30.7881i	0.402127	−	1.02118i
$910$	−0.769774	−	0.888367i	−0.0255178	−	0.0294491i
$911$	−24.9160	−	23.7573i	−0.825504	−	0.787116i	0.154100	−	0.988055i	$-0.450752\pi$
$911$	−24.9160	−	23.7573i	−0.825504	−	0.787116i	−0.979604	+	0.200939i	$0.935601\pi$
$912$	−8.04557	+	3.70184i	−0.266416	+	0.122580i
$913$	−1.33895	−	3.86864i	−0.0443127	−	0.128033i
$914$	−1.23971	−	1.74094i	−0.0410061	−	0.0575850i
$915$	−8.40104	−	2.01292i	−0.277730	−	0.0665449i
$916$	−17.5326	−	12.4849i	−0.579294	−	0.412513i
$917$	6.83072	+	47.5087i	0.225570	+	1.56888i
$918$	−4.29406	−	41.2644i	−0.141725	−	1.36193i
$919$		−	23.0169i		−	0.759258i	−0.925139	−	0.379629i	$-0.876052\pi$
$919$		−	23.0169i		−	0.759258i	0.925139	−	0.379629i	$-0.123948\pi$
$920$	−2.89226	+	13.4011i	−0.0953551	+	0.441823i
$921$	1.38202	+	27.3817i	0.0455390	+	0.902256i
$922$	−4.99133	+	2.57321i	−0.164381	+	0.0847442i
$923$	−0.631403	+	1.57717i	−0.0207829	+	0.0519131i
$924$	−5.73674	+	8.98232i	−0.188725	+	0.295497i
$925$	3.47146	−	0.842168i	0.114141	−	0.0276903i
$926$	12.4499	+	5.68568i	0.409129	+	0.186843i
$927$	−49.0656	+	22.7440i	−1.61152	+	0.747010i
$928$	−0.118358	+	0.823198i	−0.00388529	+	0.0270228i
$929$	14.3414	−	15.0408i	0.470525	−	0.493473i	−0.445114	−	0.895474i	$-0.646837\pi$
$929$	14.3414	−	15.0408i	0.470525	−	0.493473i	0.915639	+	0.402001i	$0.131685\pi$
$930$	40.7149	−	9.99939i	1.33509	−	0.327893i
$931$	31.7891	−	1.51430i	1.04185	−	0.0496292i
$932$	−11.3246	+	0.539458i	−0.370950	+	0.0176705i
$933$	2.43878	−	0.598954i	0.0798421	−	0.0196089i
$934$	9.97539	−	10.4619i	0.326405	−	0.342323i
$935$	−5.49639	+	38.2282i	−0.179751	+	1.25020i
$936$	0.307768	−	0.142663i	0.0100597	−	0.00466310i
$937$	43.1500	+	19.7059i	1.40965	+	0.643765i	0.967429	−	0.253142i	$-0.0814638\pi$
$937$	43.1500	+	19.7059i	1.40965	+	0.643765i	0.442220	+	0.896907i	$0.354191\pi$
$938$	−22.1046	+	5.36252i	−0.721741	+	0.175092i
$939$	−21.2556	+	33.2811i	−0.693651	+	1.08609i
$940$	−13.2273	+	33.0402i	−0.431427	+	1.07765i
$941$	−1.73181	+	0.892808i	−0.0564553	+	0.0291047i	−0.486223	−	0.873835i	$-0.661626\pi$
$941$	−1.73181	+	0.892808i	−0.0564553	+	0.0291047i	0.429768	+	0.902939i	$0.358595\pi$
$942$	0.815474	+	16.1568i	0.0265696	+	0.526418i
$943$	−38.1634	−	2.66668i	−1.24277	−	0.0868392i
$944$			4.72585i			0.153813i
$945$	−49.3241	−	22.0215i	−1.60451	−	0.716359i
$946$	−0.613371	−	4.26609i	−0.0199424	−	0.138702i
$947$	−18.0014	−	12.8187i	−0.584966	−	0.416553i	0.248892	−	0.968531i	$-0.419934\pi$
$947$	−18.0014	−	12.8187i	−0.584966	−	0.416553i	−0.833858	+	0.551979i	$0.813873\pi$
$948$	13.6204	+	3.26350i	0.442372	+	0.105994i
$949$	−0.0944211	−	0.132596i	−0.00306504	−	0.00430425i
$950$	5.30475	+	15.3271i	0.172109	+	0.497275i
$951$	−12.9971	+	5.98008i	−0.421460	+	0.193917i
$952$	21.0133	+	20.0362i	0.681046	+	0.649376i
$953$	−5.99179	−	6.91489i	−0.194093	−	0.223995i	0.650358	−	0.759628i	$-0.274619\pi$
$953$	−5.99179	−	6.91489i	−0.194093	−	0.223995i	−0.844451	+	0.535632i	$0.820073\pi$
$954$	−7.80299	+	19.8152i	−0.252631	+	0.641541i
$955$	21.4311	−	13.7729i	0.693493	−	0.445681i
$956$	6.18751	+	2.14152i	0.200118	+	0.0692616i
$957$	−0.454519	+	2.39472i	−0.0146925	+	0.0774102i
$958$	−0.391677	+	0.498058i	−0.0126545	+	0.0160915i
$959$	22.3566	−	7.73770i	0.721933	−	0.249863i
$960$	−3.88336	+	3.07173i	−0.125335	+	0.0991397i
$961$	9.59434	+	39.5484i	0.309495	+	1.27576i
$962$	0.0528990	+	0.115833i	0.00170553	+	0.00373459i
$963$	−8.26809	−	33.2588i	−0.266435	−	1.07175i
$964$	7.79848	−	12.1347i	0.251172	−	0.390832i
$965$	−13.0250	−	22.5600i	−0.419291	−	0.726233i
$966$	19.3364	+	23.2071i	0.622138	+	0.746675i
$967$	8.77794	−	15.2038i	0.282280	−	0.488922i	−0.689666	−	0.724127i	$-0.742243\pi$
$967$	8.77794	−	15.2038i	0.282280	−	0.488922i	0.971946	+	0.235205i	$0.0755761\pi$
$968$	−3.72847	−	7.23222i	−0.119837	−	0.232452i
$969$	13.5786	+	69.3951i	0.436207	+	2.22929i
$970$	−6.77183	+	9.50970i	−0.217430	+	0.305338i
$971$	−36.1686	−	10.6201i	−1.16071	−	0.340814i	−0.355999	−	0.934486i	$-0.615859\pi$
$971$	−36.1686	−	10.6201i	−1.16071	−	0.340814i	−0.804707	+	0.593672i	$0.797678\pi$
$972$	10.0406	−	11.9242i	0.322051	−	0.382469i
$973$	14.3293	+	12.4164i	0.459377	+	0.398053i
$974$	−11.7898	−	29.4496i	−0.377771	−	0.943626i
$975$	−0.204849	−	0.586496i	−0.00656041	−	0.0187829i
$976$	0.330194	+	1.71321i	0.0105692	+	0.0548384i
$977$	−0.438067	−	9.19615i	−0.0140150	−	0.294211i	−0.994983	−	0.100042i	$-0.968102\pi$
$977$	−0.438067	−	9.19615i	−0.0140150	−	0.294211i	0.980968	−	0.194169i	$-0.0622009\pi$
$978$	29.9179	+	13.5609i	0.956671	+	0.433629i
$979$	3.00691	−	8.68790i	0.0961013	−	0.277666i
$980$	17.0719	−	5.01277i	0.545343	−	0.160127i
$981$	20.9976	+	0.881167i	0.670403	+	0.0281335i
$982$	15.1535	−	17.4880i	0.483567	−	0.558066i
$983$	−34.8835	+	3.33098i	−1.11261	+	0.106242i	−0.635134	−	0.772402i	$-0.719055\pi$
$983$	−34.8835	+	3.33098i	−1.11261	+	0.106242i	−0.477478	+	0.878644i	$0.658449\pi$
$984$	−10.0265	−	9.50622i	−0.319633	−	0.303047i
$985$	1.45311	−	15.2176i	0.0462998	−	0.484874i
$986$	6.16454	+	2.46791i	0.196319	+	0.0785942i
$987$	39.3998	+	67.7986i	1.25411	+	2.15805i
$988$	−0.500716	+	0.289089i	−0.0159299	+	0.00919714i
$989$	−12.0495	−	2.00594i	−0.383153	−	0.0637852i
$990$	−11.7730	+	8.48433i	−0.374170	+	0.269650i
$991$	50.6440	+	32.5469i	1.60876	+	1.03389i	0.962689	+	0.270609i	$0.0872249\pi$
$991$	50.6440	+	32.5469i	1.60876	+	1.03389i	0.646070	+	0.763278i	$0.276411\pi$
$992$	−5.23415	−	6.65577i	−0.166184	−	0.211321i
$993$	52.6729	+	33.6406i	1.67152	+	1.06755i
$994$	−37.7027	−	39.5414i	−1.19586	−	1.25418i
$995$	−51.6194	+	36.7580i	−1.63645	+	1.16531i
$996$	−3.30120	−	2.58100i	−0.104602	−	0.0817822i
$997$	41.5015	−	16.6147i	1.31437	−	0.526193i	0.394669	−	0.918823i	$-0.370859\pi$
$997$	41.5015	−	16.6147i	1.31437	−	0.526193i	0.919696	+	0.392631i	$0.128435\pi$
$998$	9.53002	+	32.4563i	0.301668	+	1.02739i
$999$	4.45477	+	3.79435i	0.140943	+	0.120048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.113.24	yes	480
9.2	odd	6	inner	414.2.p.a.389.13	yes	480
23.11	odd	22	inner	414.2.p.a.149.13	yes	480
207.11	even	66	inner	414.2.p.a.11.24	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.11.24	✓	480	207.11	even	66	inner
414.2.p.a.113.24	yes	480	1.1	even	1	trivial
414.2.p.a.149.13	yes	480	23.11	odd	22	inner
414.2.p.a.389.13	yes	480	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998867 + 0.0475819i) q^{2} +(1.69982 - 0.332604i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-2.06892 + 1.97271i) q^{5} +(1.71372 - 0.251347i) q^{6} +(-0.688211 + 3.57078i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.77875 - 1.13073i) q^{9} +O(q^{10})\)	\(q+(0.998867 + 0.0475819i) q^{2} +(1.69982 - 0.332604i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-2.06892 + 1.97271i) q^{5} +(1.71372 - 0.251347i) q^{6} +(-0.688211 + 3.57078i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.77875 - 1.13073i) q^{9} +(-2.16044 + 1.87203i) q^{10} +(1.50401 + 0.775374i) q^{11} +(1.72374 - 0.169520i) q^{12} +(0.111032 - 0.0213996i) q^{13} +(-0.857336 + 3.53399i) q^{14} +(-2.86065 + 4.04137i) q^{15} +(0.981929 + 0.189251i) q^{16} +(3.31677 - 7.26271i) q^{17} +(2.82940 - 0.997233i) q^{18} +(-4.65114 + 2.12411i) q^{19} +(-2.24707 + 1.76711i) q^{20} +(0.0178232 + 6.29857i) q^{21} +(1.46542 + 0.846059i) q^{22} +(3.54339 - 3.23177i) q^{23} +(1.72985 - 0.0873096i) q^{24} +(0.150930 - 3.16840i) q^{25} +(0.111924 - 0.0160923i) q^{26} +(4.34728 - 2.84626i) q^{27} +(-1.02452 + 3.48919i) q^{28} +(0.0790546 + 0.827898i) q^{29} +(-3.04970 + 3.90068i) q^{30} +(-6.65577 - 5.23415i) q^{31} +(0.971812 + 0.235759i) q^{32} +(2.81444 + 0.817751i) q^{33} +(3.65858 - 7.09666i) q^{34} +(-5.62025 - 8.74529i) q^{35} +(2.87365 - 0.861475i) q^{36} +(0.317274 + 1.08054i) q^{37} +(-4.74694 + 1.90039i) q^{38} +(0.181616 - 0.0733050i) q^{39} +(-2.32860 + 1.65819i) q^{40} +(-5.50478 - 5.77324i) q^{41} +(-0.281895 + 6.29228i) q^{42} +(-1.57450 - 2.00214i) q^{43} +(1.42350 + 0.914828i) q^{44} +(-3.51840 + 7.82105i) q^{45} +(3.69315 - 3.05951i) q^{46} +(10.7817 - 6.22484i) q^{47} +(1.73204 - 0.00490119i) q^{48} +(-5.77826 - 2.31326i) q^{49} +(0.301517 - 3.15763i) q^{50} +(3.22229 - 13.4484i) q^{51} +(0.112563 - 0.0107485i) q^{52} +(-4.64869 + 5.36487i) q^{53} +(4.47778 - 2.63618i) q^{54} +(-4.64127 + 1.36280i) q^{55} +(-1.18938 + 3.43649i) q^{56} +(-7.19960 + 5.15758i) q^{57} +(0.0395721 + 0.830722i) q^{58} +(0.894373 + 4.64045i) q^{59} +(-3.23185 + 3.75115i) q^{60} +(0.648453 + 1.61976i) q^{61} +(-6.39918 - 5.54492i) q^{62} +(2.12523 + 10.7005i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.187500 + 0.263307i) q^{65} +(2.77234 + 0.950741i) q^{66} +(2.86614 + 5.55954i) q^{67} +(3.99211 - 6.91454i) q^{68} +(4.94822 - 6.67197i) q^{69} +(-5.19777 - 9.00280i) q^{70} +(-8.12268 + 12.6391i) q^{71} +(2.91139 - 0.723765i) q^{72} +(-0.598017 - 1.30947i) q^{73} +(0.265501 + 1.09441i) q^{74} +(-0.797271 - 5.43590i) q^{75} +(-4.83199 + 1.67237i) q^{76} +(-3.80377 + 4.83688i) q^{77} +(0.184898 - 0.0645804i) q^{78} +(7.64161 + 2.64479i) q^{79} +(-2.40487 + 1.54551i) q^{80} +(6.44289 - 6.28404i) q^{81} +(-5.22384 - 6.02863i) q^{82} +(-1.75095 - 1.66953i) q^{83} +(-0.580975 + 6.27174i) q^{84} +(7.46509 + 21.5689i) q^{85} +(-1.47745 - 2.07479i) q^{86} +(0.409741 + 1.38098i) q^{87} +(1.37836 + 0.981525i) q^{88} +(-0.773218 - 5.37785i) q^{89} +(-3.88655 + 7.64478i) q^{90} +0.411197i q^{91} +(3.83455 - 2.88032i) q^{92} +(-13.0545 - 6.68336i) q^{93} +(11.0657 - 5.70478i) q^{94} +(5.43259 - 13.5699i) q^{95} +(1.73032 + 0.0775183i) q^{96} +(3.96875 - 0.962808i) q^{97} +(-5.66164 - 2.58558i) q^{98} +(5.05602 + 0.453932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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