LMFDB - Embedded newform 126.2.t.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(47,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("126.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.t (of order $6$, degree $2$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.1
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	126.59
Dual form			126.2.t.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.72571 + 0.148116i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.967324 q^{5} +(1.56856 + 0.734581i) q^{6} +(2.40137 - 1.11060i) q^{7} -1.00000i q^{8} +(2.95612 - 0.511208i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72571 + 0.148116i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.967324 q^{5} +(1.56856 + 0.734581i) q^{6} +(2.40137 - 1.11060i) q^{7} -1.00000i q^{8} +(2.95612 - 0.511208i) q^{9} +(-0.837727 - 0.483662i) q^{10} -5.57361i q^{11} +(-0.991125 - 1.42045i) q^{12} +(3.76893 + 2.17600i) q^{13} +(-2.63495 - 0.238876i) q^{14} +(-1.66932 + 0.143276i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.97267 + 3.41677i) q^{17} +(-2.81568 - 1.03534i) q^{18} +(3.86796 - 2.23317i) q^{19} +(0.483662 + 0.837727i) q^{20} +(-3.97956 + 2.27225i) q^{21} +(-2.78681 + 4.82689i) q^{22} +2.65334i q^{23} +(0.148116 + 1.72571i) q^{24} -4.06428 q^{25} +(-2.17600 - 3.76893i) q^{26} +(-5.02568 + 1.32004i) q^{27} +(2.16249 + 1.52435i) q^{28} +(4.61157 - 2.66249i) q^{29} +(1.51731 + 0.710578i) q^{30} +(-5.34038 + 3.08327i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.825539 + 9.61842i) q^{33} +(3.41677 - 1.97267i) q^{34} +(2.32290 - 1.07431i) q^{35} +(1.92078 + 2.30447i) q^{36} +(0.243608 + 0.421942i) q^{37} -4.46634 q^{38} +(-6.82637 - 3.19689i) q^{39} -0.967324i q^{40} +(-0.0818856 + 0.141830i) q^{41} +(4.58252 + 0.0219535i) q^{42} +(-4.35045 - 7.53520i) q^{43} +(4.82689 - 2.78681i) q^{44} +(2.85953 - 0.494504i) q^{45} +(1.32667 - 2.29786i) q^{46} +(-4.74500 + 8.21859i) q^{47} +(0.734581 - 1.56856i) q^{48} +(4.53314 - 5.33392i) q^{49} +(3.51977 + 2.03214i) q^{50} +(2.89818 - 6.18852i) q^{51} +4.35199i q^{52} +(1.74520 + 1.00759i) q^{53} +(5.01239 + 1.36965i) q^{54} -5.39149i q^{55} +(-1.11060 - 2.40137i) q^{56} +(-6.34420 + 4.42670i) q^{57} -5.32498 q^{58} +(0.836931 + 1.44961i) q^{59} +(-0.958739 - 1.37403i) q^{60} +(-4.47927 - 2.58611i) q^{61} +6.16655 q^{62} +(6.53099 - 4.51067i) q^{63} -1.00000 q^{64} +(3.64578 + 2.10489i) q^{65} +(4.09427 - 8.74256i) q^{66} +(2.72126 + 4.71336i) q^{67} -3.94535 q^{68} +(-0.393002 - 4.57889i) q^{69} +(-2.54885 - 0.231071i) q^{70} +3.64006i q^{71} +(-0.511208 - 2.95612i) q^{72} +(-2.15468 - 1.24401i) q^{73} -0.487217i q^{74} +(7.01376 - 0.601984i) q^{75} +(3.86796 + 2.23317i) q^{76} +(-6.19005 - 13.3843i) q^{77} +(4.31337 + 6.18177i) q^{78} +(-2.30121 + 3.98581i) q^{79} +(-0.483662 + 0.837727i) q^{80} +(8.47733 - 3.02239i) q^{81} +(0.141830 - 0.0818856i) q^{82} +(4.20979 + 7.29158i) q^{83} +(-3.95760 - 2.31027i) q^{84} +(-1.90821 + 3.30512i) q^{85} +8.70089i q^{86} +(-7.56386 + 5.27772i) q^{87} -5.57361 q^{88} +(2.05811 + 3.56475i) q^{89} +(-2.72368 - 1.00151i) q^{90} +(11.4673 + 1.03959i) q^{91} +(-2.29786 + 1.32667i) q^{92} +(8.75925 - 6.11182i) q^{93} +(8.21859 - 4.74500i) q^{94} +(3.74157 - 2.16020i) q^{95} +(-1.42045 + 0.991125i) q^{96} +(-10.2669 + 5.92762i) q^{97} +(-6.59277 + 2.35274i) q^{98} +(-2.84928 - 16.4763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31} + 18 q^{33} - 30 q^{35} - 2 q^{37} - 30 q^{39} + 6 q^{41} + 30 q^{42} - 2 q^{43} + 12 q^{44} + 12 q^{45} + 6 q^{46} - 18 q^{47} + 10 q^{49} - 12 q^{50} + 36 q^{53} + 18 q^{54} + 6 q^{57} - 12 q^{58} + 30 q^{59} - 6 q^{60} - 60 q^{61} - 36 q^{62} + 42 q^{63} - 16 q^{64} + 42 q^{65} + 48 q^{66} + 14 q^{67} + 36 q^{68} + 42 q^{69} + 30 q^{75} - 18 q^{77} - 16 q^{79} + 54 q^{81} - 18 q^{84} - 12 q^{85} - 48 q^{87} + 24 q^{89} - 18 q^{90} - 12 q^{91} + 6 q^{92} + 30 q^{93} - 66 q^{95} - 6 q^{96} - 6 q^{97} + 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.72571	+	0.148116i	−0.996337	+	0.0855146i
$3$	−1.72571	+	0.148116i	−0.996337	+	0.0855146i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.967324			0.432600			0.216300	−	0.976327i	$-0.430601\pi$
$5$	0.967324			0.432600			0.216300	+	0.976327i	$0.430601\pi$
$6$	1.56856	+	0.734581i	0.640363	+	0.299892i
$7$	2.40137	−	1.11060i	0.907632	−	0.419767i
$7$	2.40137	−	1.11060i	0.907632	−	0.419767i
$8$		−	1.00000i		−	0.353553i
$9$	2.95612	−	0.511208i	0.985375	−	0.170403i
$10$	−0.837727	−	0.483662i	−0.264913	−	0.152947i
$11$		−	5.57361i		−	1.68051i	−0.542193	−	0.840254i	$-0.682406\pi$
$11$		−	5.57361i		−	1.68051i	0.542193	−	0.840254i	$-0.317594\pi$
$12$	−0.991125	−	1.42045i	−0.286113	−	0.410048i
$13$	3.76893	+	2.17600i	1.04531	+	0.603512i	0.921334	−	0.388772i	$-0.127101\pi$
$13$	3.76893	+	2.17600i	1.04531	+	0.603512i	0.123980	+	0.992285i	$0.460434\pi$
$14$	−2.63495	−	0.238876i	−0.704219	−	0.0638424i
$15$	−1.66932	+	0.143276i	−0.431016	+	0.0369937i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.97267	+	3.41677i	−0.478443	+	0.828688i	−0.999695	−	0.0247150i	$-0.992132\pi$
$17$	−1.97267	+	3.41677i	−0.478443	+	0.828688i	0.521251	+	0.853403i	$0.325465\pi$
$18$	−2.81568	−	1.03534i	−0.663663	−	0.244033i
$19$	3.86796	−	2.23317i	0.887371	−	0.512324i	0.0142896	−	0.999898i	$-0.495451\pi$
$19$	3.86796	−	2.23317i	0.887371	−	0.512324i	0.873082	+	0.487574i	$0.162118\pi$
$20$	0.483662	+	0.837727i	0.108150	+	0.187322i
$21$	−3.97956	+	2.27225i	−0.868411	+	0.495845i
$22$	−2.78681	+	4.82689i	−0.594149	+	1.02910i
$23$			2.65334i			0.553260i	0.960976	+	0.276630i	$0.0892177\pi$
$23$			2.65334i			0.553260i	−0.960976	+	0.276630i	$0.910782\pi$
$24$	0.148116	+	1.72571i	0.0302340	+	0.352258i
$25$	−4.06428			−0.812857
$26$	−2.17600	−	3.76893i	−0.426748	−	0.739149i
$27$	−5.02568	+	1.32004i	−0.967193	+	0.254042i
$28$	2.16249	+	1.52435i	0.408673	+	0.288074i
$29$	4.61157	−	2.66249i	0.856347	−	0.494412i	−0.00644015	−	0.999979i	$-0.502050\pi$
$29$	4.61157	−	2.66249i	0.856347	−	0.494412i	0.862787	+	0.505567i	$0.168717\pi$
$30$	1.51731	+	0.710578i	0.277021	+	0.129733i
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.895915	−	0.444226i	$-0.853479\pi$
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.0632466	+	0.997998i	$0.520145\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.825539	+	9.61842i	0.143708	+	1.67435i
$34$	3.41677	−	1.97267i	0.585971	−	0.338311i
$35$	2.32290	−	1.07431i	0.392642	−	0.181592i
$36$	1.92078	+	2.30447i	0.320130	+	0.384079i
$37$	0.243608	+	0.421942i	0.0400490	+	0.0693669i	0.885355	−	0.464915i	$-0.153915\pi$
$37$	0.243608	+	0.421942i	0.0400490	+	0.0693669i	−0.845306	+	0.534282i	$0.820582\pi$
$38$	−4.46634			−0.724536
$39$	−6.82637	−	3.19689i	−1.09309	−	0.511912i
$40$		−	0.967324i		−	0.152947i
$41$	−0.0818856	+	0.141830i	−0.0127884	+	0.0221501i	−0.872349	−	0.488884i	$-0.837404\pi$
$41$	−0.0818856	+	0.141830i	−0.0127884	+	0.0221501i	0.859560	+	0.511034i	$0.170737\pi$
$42$	4.58252	+	0.0219535i	0.707099	+	0.00338750i
$43$	−4.35045	−	7.53520i	−0.663437	−	1.14911i	−0.979707	−	0.200437i	$-0.935764\pi$
$43$	−4.35045	−	7.53520i	−0.663437	−	1.14911i	0.316270	−	0.948669i	$-0.397570\pi$
$44$	4.82689	−	2.78681i	0.727681	−	0.420127i
$45$	2.85953	−	0.494504i	0.426273	−	0.0737163i
$46$	1.32667	−	2.29786i	0.195607	−	0.338801i
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	0.279009	+	0.960289i	$0.409994\pi$
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	−0.971139	+	0.238516i	$0.923339\pi$
$48$	0.734581	−	1.56856i	0.106028	−	0.226403i
$49$	4.53314	−	5.33392i	0.647591	−	0.761988i
$50$	3.51977	+	2.03214i	0.497771	+	0.287388i
$51$	2.89818	−	6.18852i	0.405826	−	0.866567i
$52$			4.35199i			0.603512i
$53$	1.74520	+	1.00759i	0.239722	+	0.138403i	0.615049	−	0.788489i	$-0.289136\pi$
$53$	1.74520	+	1.00759i	0.239722	+	0.138403i	−0.375327	+	0.926892i	$0.622470\pi$
$54$	5.01239	+	1.36965i	0.682100	+	0.186386i
$55$		−	5.39149i		−	0.726988i
$56$	−1.11060	−	2.40137i	−0.148410	−	0.320896i
$57$	−6.34420	+	4.42670i	−0.840310	+	0.586331i
$58$	−5.32498			−0.699205
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	0.915349	−	0.402662i	$-0.131915\pi$
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	−0.806390	+	0.591384i	$0.798582\pi$
$60$	−0.958739	−	1.37403i	−0.123773	−	0.177387i
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	0.185039	−	0.982731i	$-0.440759\pi$
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	−0.758551	+	0.651614i	$0.774092\pi$
$62$	6.16655			0.783152
$63$	6.53099	−	4.51067i	0.822828	−	0.568291i
$64$	−1.00000			−0.125000
$65$	3.64578	+	2.10489i	0.452203	+	0.261080i
$66$	4.09427	−	8.74256i	0.503970	−	1.07614i
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	0.982993	−	0.183645i	$-0.0587898\pi$
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	−0.650538	+	0.759474i	$0.725456\pi$
$68$	−3.94535			−0.478443
$69$	−0.393002	−	4.57889i	−0.0473118	−	0.551234i
$70$	−2.54885	−	0.231071i	−0.304645	−	0.0276182i
$71$			3.64006i			0.431996i	0.976394	+	0.215998i	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$	−0.511208	−	2.95612i	−0.0602465	−	0.348382i
$73$	−2.15468	−	1.24401i	−0.252186	−	0.145600i	0.368579	−	0.929597i	$-0.379845\pi$
$73$	−2.15468	−	1.24401i	−0.252186	−	0.145600i	−0.620765	+	0.783997i	$0.713178\pi$
$74$		−	0.487217i		−	0.0566378i
$75$	7.01376	−	0.601984i	0.809879	−	0.0695111i
$76$	3.86796	+	2.23317i	0.443686	+	0.256162i
$77$	−6.19005	−	13.3843i	−0.705422	−	1.52528i
$78$	4.31337	+	6.18177i	0.488393	+	0.699948i
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	−0.965949	−	0.258732i	$-0.916695\pi$
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	0.707043	+	0.707170i	$0.250029\pi$
$80$	−0.483662	+	0.837727i	−0.0540751	+	0.0936608i
$81$	8.47733	−	3.02239i	0.941926	−	0.335821i
$82$	0.141830	−	0.0818856i	0.0156625	−	0.00904275i
$83$	4.20979	+	7.29158i	0.462085	+	0.800355i	0.999065	−	0.0432405i	$-0.0137682\pi$
$83$	4.20979	+	7.29158i	0.462085	+	0.800355i	−0.536980	+	0.843595i	$0.680435\pi$
$84$	−3.95760	−	2.31027i	−0.431810	−	0.252072i
$85$	−1.90821	+	3.30512i	−0.206975	+	0.358491i
$86$			8.70089i			0.938242i
$87$	−7.56386	+	5.27772i	−0.810931	+	0.565831i
$88$	−5.57361			−0.594149
$89$	2.05811	+	3.56475i	0.218159	+	0.377863i	0.954245	−	0.299025i	$-0.0966615\pi$
$89$	2.05811	+	3.56475i	0.218159	+	0.377863i	−0.736086	+	0.676888i	$0.763328\pi$
$90$	−2.72368	−	1.00151i	−0.287101	−	0.105569i
$91$	11.4673	+	1.03959i	1.20210	+	0.108978i
$92$	−2.29786	+	1.32667i	−0.239569	+	0.138315i
$93$	8.75925	−	6.11182i	0.908292	−	0.633766i
$94$	8.21859	−	4.74500i	0.847683	−	0.489410i
$95$	3.74157	−	2.16020i	0.383877	−	0.221632i
$96$	−1.42045	+	0.991125i	−0.144974	+	0.101156i
$97$	−10.2669	+	5.92762i	−1.04245	+	0.601859i	−0.920526	−	0.390681i	$-0.872240\pi$
$97$	−10.2669	+	5.92762i	−1.04245	+	0.601859i	−0.121924	+	0.992539i	$0.538906\pi$
$98$	−6.59277	+	2.35274i	−0.665970	+	0.237663i
$99$	−2.84928	−	16.4763i	−0.286363	−	1.65593i
$100$	−2.03214	−	3.51977i	−0.203214	−	0.351977i
$101$	5.31626			0.528988			0.264494	−	0.964387i	$-0.414795\pi$
$101$	5.31626			0.528988			0.264494	+	0.964387i	$0.414795\pi$
$102$	−5.60416	+	3.91033i	−0.554894	+	0.387180i
$103$		−	8.94450i		−	0.881327i	−0.897672	−	0.440664i	$-0.854743\pi$
$103$		−	8.94450i		−	0.881327i	0.897672	−	0.440664i	$-0.145257\pi$
$104$	2.17600	−	3.76893i	0.213374	−	0.369574i
$105$	−3.84952	+	2.19800i	−0.375675	+	0.214503i
$106$	−1.00759	−	1.74520i	−0.0978659	−	0.169509i
$107$	−16.5898	+	9.57813i	−1.60380	+	0.925953i	−0.613079	+	0.790022i	$0.710069\pi$
$107$	−16.5898	+	9.57813i	−1.60380	+	0.925953i	−0.990718	+	0.135931i	$0.956597\pi$
$108$	−3.65603	−	3.69235i	−0.351802	−	0.355296i
$109$	−9.62168	+	16.6652i	−0.921590	+	1.59624i	−0.124635	+	0.992203i	$0.539776\pi$
$109$	−9.62168	+	16.6652i	−0.921590	+	1.59624i	−0.796955	+	0.604038i	$0.793557\pi$
$110$	−2.69574	+	4.66917i	−0.257029	+	0.445188i
$111$	−0.482893	−	0.692066i	−0.0458342	−	0.0656880i
$112$	−0.238876	+	2.63495i	−0.0225717	+	0.248979i
$113$	7.31199	+	4.22158i	0.687854	+	0.397133i	0.802808	−	0.596238i	$-0.203339\pi$
$113$	7.31199	+	4.22158i	0.687854	+	0.397133i	−0.114953	+	0.993371i	$0.536672\pi$
$114$	7.70759	−	0.661535i	0.721882	−	0.0619584i
$115$			2.56664i			0.239341i
$116$	4.61157	+	2.66249i	0.428174	+	0.247206i
$117$	12.2538	+	4.50580i	1.13287	+	0.416561i
$118$		−	1.67386i		−	0.154091i
$119$	−0.942449	+	10.3958i	−0.0863942	+	0.952979i
$120$	0.143276	+	1.66932i	0.0130792	+	0.152387i
$121$	−20.0652			−1.82411
$122$	2.58611	+	4.47927i	0.234135	+	0.405534i
$123$	0.120303	−	0.256885i	0.0108474	−	0.0231626i
$124$	−5.34038	−	3.08327i	−0.479581	−	0.276886i
$125$	−8.76810			−0.784243
$126$	−7.91134	+	0.640858i	−0.704798	+	0.0570922i
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.62367	+	12.3592i	0.759272	+	1.08816i
$130$	−2.10489	−	3.64578i	−0.184611	−	0.319756i
$131$	−18.7467			−1.63791			−0.818954	−	0.573859i	$-0.805446\pi$
$131$	−18.7467			−1.63791			−0.818954	+	0.573859i	$0.805446\pi$
$132$	−7.91702	+	5.52415i	−0.689089	+	0.480815i
$133$	6.80824	−	9.65842i	0.590350	−	0.837491i
$134$		−	5.44252i		−	0.470162i
$135$	−4.86146	+	1.27691i	−0.418408	+	0.109899i
$136$	3.41677	+	1.97267i	0.292986	+	0.169155i
$137$		−	16.9343i		−	1.44680i	−0.690430	−	0.723399i	$-0.742579\pi$
$137$		−	16.9343i		−	1.44680i	0.690430	−	0.723399i	$-0.257421\pi$
$138$	−1.94910	+	4.16194i	−0.165918	+	0.354288i
$139$	10.5033	+	6.06406i	0.890875	+	0.514347i	0.874229	−	0.485514i	$-0.161368\pi$
$139$	10.5033	+	6.06406i	0.890875	+	0.514347i	0.0166466	+	0.999861i	$0.494701\pi$
$140$	2.09183	+	1.47454i	0.176792	+	0.124621i
$141$	6.97118	−	14.8857i	0.587079	−	1.25360i
$142$	1.82003	−	3.15239i	0.152734	−	0.264543i
$143$	12.1282	−	21.0066i	1.01421	−	1.75666i
$144$	−1.03534	+	2.81568i	−0.0862785	+	0.234640i
$145$	4.46088	−	2.57549i	0.370456	−	0.213883i
$146$	1.24401	+	2.15468i	0.102955	+	0.178323i
$147$	−7.03282	+	9.87620i	−0.580058	+	0.814576i
$148$	−0.243608	+	0.421942i	−0.0200245	+	0.0346834i
$149$		−	8.74051i		−	0.716051i	−0.933712	−	0.358025i	$-0.883450\pi$
$149$		−	8.74051i		−	0.716051i	0.933712	−	0.358025i	$-0.116550\pi$
$150$	−6.37509	−	2.98555i	−0.520524	−	0.243769i
$151$	22.0941			1.79799			0.898997	−	0.437954i	$-0.144297\pi$
$151$	22.0941			1.79799			0.898997	+	0.437954i	$0.144297\pi$
$152$	−2.23317	−	3.86796i	−0.181134	−	0.313733i
$153$	−4.08478	+	11.1088i	−0.330235	+	0.898096i
$154$	−1.33140	+	14.6862i	−0.107288	+	1.18345i
$155$	−5.16588	+	2.98252i	−0.414934	+	0.239562i
$156$	−0.644598	−	7.51026i	−0.0516091	−	0.601302i
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	−0.449961	−	0.893048i	$-0.648562\pi$
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	0.548422	+	0.836202i	$0.315229\pi$
$158$	3.98581	−	2.30121i	0.317094	−	0.183074i
$159$	−3.16094	−	1.48032i	−0.250679	−	0.117397i
$160$	0.837727	−	0.483662i	0.0662282	−	0.0382368i
$161$	2.94680	+	6.37165i	0.232241	+	0.502157i
$162$	−8.85278	−	1.62120i	−0.695540	−	0.127374i
$163$	−3.72148	−	6.44579i	−0.291489	−	0.504873i	0.682673	−	0.730724i	$-0.260817\pi$
$163$	−3.72148	−	6.44579i	−0.291489	−	0.504873i	−0.974162	+	0.225851i	$0.927484\pi$
$164$	−0.163771			−0.0127884
$165$	0.798564	+	9.30413i	0.0621681	+	0.724325i
$166$		−	8.41959i		−	0.653487i
$167$	3.24855	−	5.62665i	0.251380	−	0.435404i	−0.712526	−	0.701646i	$-0.752449\pi$
$167$	3.24855	−	5.62665i	0.251380	−	0.435404i	0.963906	+	0.266242i	$0.0857822\pi$
$168$	2.27225	+	3.97956i	0.175308	+	0.307030i
$169$	2.96991	+	5.14404i	0.228455	+	0.395695i
$170$	3.30512	−	1.90821i	0.253491	−	0.146353i
$171$	10.2926	−	8.57886i	0.787092	−	0.656042i
$172$	4.35045	−	7.53520i	0.331718	−	0.574553i
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	−0.549057	−	0.835785i	$-0.685013\pi$
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	0.998339	+	0.0576053i	$0.0183465\pi$
$174$	9.18936	−	0.788713i	0.696643	−	0.0597922i
$175$	−9.75984	+	4.51379i	−0.737775	+	0.341211i
$176$	4.82689	+	2.78681i	0.363841	+	0.210063i
$177$	−1.65901	−	2.37763i	−0.124699	−	0.178714i
$178$		−	4.11622i		−	0.308523i
$179$	2.10764	+	1.21685i	0.157533	+	0.0909515i	0.576694	−	0.816960i	$-0.304343\pi$
$179$	2.10764	+	1.21685i	0.157533	+	0.0909515i	−0.419161	+	0.907912i	$0.637676\pi$
$180$	1.85802	+	2.22917i	0.138488	+	0.166153i
$181$		−	11.5342i		−	0.857327i	−0.903464	−	0.428663i	$-0.858985\pi$
$181$		−	11.5342i		−	0.857327i	0.903464	−	0.428663i	$-0.141015\pi$
$182$	−9.41114	−	6.63394i	−0.697600	−	0.491740i
$183$	8.11294	+	3.79941i	0.599726	+	0.280861i
$184$	2.65334			0.195607
$185$	0.235648	+	0.408155i	0.0173252	+	0.0300081i
$186$	−10.6416	+	0.913362i	−0.780283	+	0.0669709i
$187$	19.0438	+	10.9949i	1.39262	+	0.804028i
$188$	−9.49001			−0.692130
$189$	−10.6025	+	8.75143i	−0.771216	+	0.636573i
$190$	−4.32040			−0.313435
$191$	19.1122	+	11.0345i	1.38291	+	0.798425i	0.992503	−	0.122216i	$-0.0390002\pi$
$191$	19.1122	+	11.0345i	1.38291	+	0.798425i	0.390409	+	0.920641i	$0.372334\pi$
$192$	1.72571	−	0.148116i	0.124542	−	0.0106893i
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	0.961932	+	0.273289i	$0.0881116\pi$
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	−0.244291	+	0.969702i	$0.578555\pi$
$194$	11.8552			0.851157
$195$	−6.60331	−	3.09243i	−0.472873	−	0.221453i
$196$	6.88588	+	1.25885i	0.491848	+	0.0899180i
$197$		−	4.62560i		−	0.329560i	−0.986330	−	0.164780i	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$	−5.77060	+	15.6935i	−0.410099	+	1.11529i
$199$	−18.1024	−	10.4514i	−1.28324	−	0.740882i	−0.305805	−	0.952094i	$-0.598925\pi$
$199$	−18.1024	−	10.4514i	−1.28324	−	0.740882i	−0.977440	+	0.211212i	$0.932259\pi$
$200$			4.06428i			0.287388i
$201$	−5.39422	−	7.73081i	−0.380479	−	0.545289i
$202$	−4.60402	−	2.65813i	−0.323938	−	0.187025i
$203$	8.11712	−	11.5152i	0.569710	−	0.808211i
$204$	6.80851	−	0.584367i	0.476691	−	0.0409139i
$205$	−0.0792099	+	0.137196i	−0.00553226	+	0.00958215i
$206$	−4.47225	+	7.74616i	−0.311596	+	0.539701i
$207$	1.35641	+	7.84361i	0.0942770	+	0.545169i
$208$	−3.76893	+	2.17600i	−0.261329	+	0.150878i
$209$	−12.4468	−	21.5585i	−0.860965	−	1.49123i
$210$	4.43278	+	0.0212362i	0.305891	+	0.00146544i
$211$	−3.34310	+	5.79042i	−0.230148	+	0.398629i	−0.957852	−	0.287263i	$-0.907254\pi$
$211$	−3.34310	+	5.79042i	−0.230148	+	0.398629i	0.727703	+	0.685892i	$0.240588\pi$
$212$			2.01518i			0.138403i
$213$	−0.539150	−	6.28168i	−0.0369420	−	0.430414i
$214$	19.1563			1.30949
$215$	−4.20829	−	7.28898i	−0.287003	−	0.497104i
$216$	1.32004	+	5.02568i	0.0898176	+	0.341954i
$217$	−9.39995	+	13.3351i	−0.638110	+	0.905246i
$218$	16.6652	−	9.62168i	1.12871	−	0.651663i
$219$	3.90260	+	1.82765i	0.263714	+	0.123501i
$220$	4.66917	−	2.69574i	0.314795	−	0.181747i
$221$	−14.8697	+	8.58505i	−1.00025	+	0.577493i
$222$	0.0721645	+	0.840793i	0.00484336	+	0.0564304i
$223$	−7.08622	+	4.09123i	−0.474528	+	0.273969i	−0.718133	−	0.695905i	$-0.755003\pi$
$223$	−7.08622	+	4.09123i	−0.474528	+	0.273969i	0.243605	+	0.969875i	$0.421670\pi$
$224$	1.52435	−	2.16249i	0.101850	−	0.144488i
$225$	−12.0145	+	2.07770i	−0.800968	+	0.138513i
$226$	−4.22158	−	7.31199i	−0.280815	−	0.486386i
$227$	−10.6938			−0.709769			−0.354885	−	0.934910i	$-0.615480\pi$
$227$	−10.6938			−0.709769			−0.354885	+	0.934910i	$0.615480\pi$
$228$	−7.00573	−	3.28089i	−0.463966	−	0.217282i
$229$		−	29.2072i		−	1.93007i	−0.262125	−	0.965034i	$-0.584423\pi$
$229$		−	29.2072i		−	1.93007i	0.262125	−	0.965034i	$-0.415577\pi$
$230$	1.28332	−	2.22278i	0.0846197	−	0.146566i
$231$	12.6646	+	22.1805i	0.833272	+	1.45937i
$232$	−2.66249	−	4.61157i	−0.174801	−	0.302764i
$233$	−5.57664	+	3.21967i	−0.365338	+	0.210928i	−0.671420	−	0.741077i	$-0.734315\pi$
$233$	−5.57664	+	3.21967i	−0.365338	+	0.210928i	0.306082	+	0.952005i	$0.400982\pi$
$234$	−8.35922	−	10.0290i	−0.546459	−	0.655619i
$235$	−4.58996	+	7.95004i	−0.299416	+	0.518603i
$236$	−0.836931	+	1.44961i	−0.0544796	+	0.0943614i
$237$	3.38085	−	7.21918i	0.219610	−	0.468936i
$238$	6.01407	−	8.53178i	0.389834	−	0.553033i
$239$	−4.01452	−	2.31778i	−0.259678	−	0.149925i	0.364510	−	0.931200i	$-0.381237\pi$
$239$	−4.01452	−	2.31778i	−0.259678	−	0.149925i	−0.624187	+	0.781275i	$0.714570\pi$
$240$	0.710578	−	1.51731i	0.0458676	−	0.0979419i
$241$			10.4944i			0.676007i	0.941145	+	0.338003i	$0.109752\pi$
$241$			10.4944i			0.676007i	−0.941145	+	0.338003i	$0.890248\pi$
$242$	17.3769	+	10.0326i	1.11703	+	0.644919i
$243$	−14.1817	+	6.47138i	−0.909758	+	0.415139i
$244$		−	5.17221i		−	0.331117i
$245$	4.38501	−	5.15963i	0.280148	−	0.329636i
$246$	−0.232628	+	0.162318i	−0.0148318	+	0.0103490i
$247$	19.4375			1.23678
$248$	3.08327	+	5.34038i	0.195788	+	0.339115i
$249$	−8.34486	−	11.9596i	−0.528834	−	0.757908i
$250$	7.59340	+	4.38405i	0.480249	+	0.277272i
$251$	−7.85271			−0.495659			−0.247829	−	0.968804i	$-0.579717\pi$
$251$	−7.85271			−0.495659			−0.247829	+	0.968804i	$0.579717\pi$
$252$	7.17185	+	3.40067i	0.451784	+	0.214222i
$253$	14.7887			0.929758
$254$	−2.87419	−	1.65941i	−0.180343	−	0.104121i
$255$	2.80348	−	5.98631i	0.175560	−	0.374877i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.43136			−0.214042			−0.107021	−	0.994257i	$-0.534131\pi$
$257$	−3.43136			−0.214042			−0.107021	+	0.994257i	$0.534131\pi$
$258$	−1.28874	−	15.0152i	−0.0802334	−	0.934805i
$259$	1.05360	+	0.742687i	0.0654677	+	0.0461483i
$260$			4.20979i			0.261080i
$261$	12.2713	−	10.2281i	0.759574	−	0.633105i
$262$	16.2351	+	9.37335i	1.00301	+	0.579088i
$263$			3.66132i			0.225767i	0.993608	+	0.112883i	$0.0360087\pi$
$263$			3.66132i			0.225767i	−0.993608	+	0.112883i	$0.963991\pi$
$264$	9.61842	−	0.825539i	0.591973	−	0.0508084i
$265$	1.68817	+	0.974668i	0.103704	+	0.0598734i
$266$	−10.7253	+	4.96031i	−0.657612	+	0.304136i
$267$	−4.07969	−	5.84687i	−0.249673	−	0.357823i
$268$	−2.72126	+	4.71336i	−0.166227	+	0.287914i
$269$	6.34303	−	10.9865i	0.386741	−	0.669856i	−0.605268	−	0.796022i	$-0.706934\pi$
$269$	6.34303	−	10.9865i	0.386741	−	0.669856i	0.992009	+	0.126166i	$0.0402673\pi$
$270$	4.84861	+	1.32490i	0.295077	+	0.0806306i
$271$	−17.2136	+	9.93828i	−1.04565	+	0.603708i	−0.921429	−	0.388547i	$-0.872977\pi$
$271$	−17.2136	+	9.93828i	−1.04565	+	0.603708i	−0.124223	+	0.992254i	$0.539644\pi$
$272$	−1.97267	−	3.41677i	−0.119611	−	0.207172i
$273$	−19.9431	−	0.0955416i	−1.20701	−	0.00578244i
$274$	−8.46717	+	14.6656i	−0.511520	+	0.885979i
$275$			22.6527i			1.36601i
$276$	3.76893	−	2.62979i	0.226863	−	0.158295i
$277$	−7.46605			−0.448591			−0.224296	−	0.974521i	$-0.572008\pi$
$277$	−7.46605			−0.448591			−0.224296	+	0.974521i	$0.572008\pi$
$278$	−6.06406	−	10.5033i	−0.363698	−	0.629944i
$279$	−14.2106	+	11.8446i	−0.850769	+	0.709117i
$280$	−1.07431	−	2.32290i	−0.0642023	−	0.138820i
$281$	−19.2746	+	11.1282i	−1.14983	+	0.663854i	−0.948845	−	0.315741i	$-0.897747\pi$
$281$	−19.2746	+	11.1282i	−1.14983	+	0.663854i	−0.200983	+	0.979595i	$0.564414\pi$
$282$	−13.4801	+	9.40579i	−0.802726	+	0.560106i
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	−0.0219073	−	0.999760i	$-0.506974\pi$
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	0.854864	+	0.518852i	$0.173641\pi$
$284$	−3.15239	+	1.82003i	−0.187060	+	0.107999i
$285$	−6.13690	+	4.28205i	−0.363518	+	0.253647i
$286$	−21.0066	+	12.1282i	−1.24215	+	0.717153i
$287$	−0.0391210	+	0.431528i	−0.00230924	+	0.0254723i
$288$	2.30447	−	1.92078i	0.135792	−	0.113183i
$289$	0.717124	+	1.24210i	0.0421838	+	0.0730644i
$290$	−5.15098			−0.302476
$291$	16.8397	−	11.7500i	0.987164	−	0.688799i
$292$		−	2.48801i		−	0.145600i
$293$	4.43406	−	7.68002i	0.259041	−	0.448672i	−0.706944	−	0.707269i	$-0.749927\pi$
$293$	4.43406	−	7.68002i	0.259041	−	0.448672i	0.965985	+	0.258597i	$0.0832603\pi$
$294$	11.0287	−	5.03663i	0.643207	−	0.293742i
$295$	0.809584	+	1.40224i	0.0471358	+	0.0816416i
$296$	0.421942	−	0.243608i	0.0245249	−	0.0141595i
$297$	7.35741	+	28.0112i	0.426920	+	1.62538i
$298$	−4.37026	+	7.56951i	−0.253162	+	0.438490i
$299$	−5.77366	+	10.0003i	−0.333899	+	0.578331i
$300$	4.02821	+	5.77310i	0.232569	+	0.333310i
$301$	−18.8156	−	13.2632i	−1.08451	−	0.764476i
$302$	−19.1341	−	11.0471i	−1.10104	−	0.635687i
$303$	−9.17430	+	0.787421i	−0.527050	+	0.0452362i
$304$			4.46634i			0.256162i
$305$	−4.33290	−	2.50160i	−0.248101	−	0.143241i
$306$	9.09195	−	7.57814i	0.519752	−	0.433214i
$307$			27.1427i			1.54912i	0.632501	+	0.774559i	$0.282028\pi$
$307$			27.1427i			1.54912i	−0.632501	+	0.774559i	$0.717972\pi$
$308$	8.49611	−	12.0529i	0.484111	−	0.686777i
$309$	1.32482	+	15.4356i	0.0753664	+	0.878099i
$310$	5.96505			0.338792
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	0.999711	−	0.0240499i	$-0.00765605\pi$
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	−0.520683	+	0.853750i	$0.674323\pi$
$312$	−3.19689	+	6.82637i	−0.180988	+	0.386467i
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	0.601024	−	0.799231i	$-0.294760\pi$
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	−0.391643	+	0.920117i	$0.628093\pi$
$314$	−1.42457			−0.0803934
$315$	6.31759	−	4.36328i	0.355956	−	0.245843i
$316$	−4.60242			−0.258906
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	0.330029	−	0.943971i	$-0.392942\pi$
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	−0.652488	+	0.757799i	$0.726275\pi$
$318$	1.99730	+	2.86246i	0.112003	+	0.160519i
$319$	−14.8397	−	25.7031i	−0.830864	−	1.43910i
$320$	−0.967324			−0.0540751
$321$	27.2105	−	18.9862i	1.51874	−	1.05971i
$322$	0.633821	−	6.99141i	0.0353214	−	0.389616i
$323$			17.6212i			0.980472i
$324$	6.85613	+	5.83039i	0.380896	+	0.323911i
$325$	−15.3180	−	8.84386i	−0.849691	−	0.490569i
$326$			7.44296i			0.412227i
$327$	14.1358	−	30.1844i	0.781712	−	1.66920i
$328$	0.141830	+	0.0818856i	0.00783125	+	0.00452137i
$329$	−2.26694	+	25.0057i	−0.124980	+	1.37861i
$330$	3.96049	−	8.45689i	0.218018	−	0.465537i
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	−0.855425	−	0.517927i	$-0.826704\pi$
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	0.876251	+	0.481856i	$0.160037\pi$
$332$	−4.20979	+	7.29158i	−0.231042	+	0.400177i
$333$	0.935837	+	1.12278i	0.0512836	+	0.0615279i
$334$	−5.62665	+	3.24855i	−0.307877	+	0.177753i
$335$	2.63234	+	4.55935i	0.143820	+	0.249104i
$336$	0.0219535	−	4.58252i	0.00119766	−	0.249997i
$337$	1.01088	−	1.75089i	0.0550660	−	0.0953772i	−0.837178	−	0.546930i	$-0.815796\pi$
$337$	1.01088	−	1.75089i	0.0550660	−	0.0953772i	0.892244	+	0.451553i	$0.149130\pi$
$338$		−	5.93982i		−	0.323084i
$339$	−13.2436	−	6.20219i	−0.719295	−	0.336857i
$340$	−3.81643			−0.206975
$341$	17.1850	+	29.7652i	0.930618	+	1.61188i
$342$	−13.2030	+	2.28323i	−0.713939	+	0.123463i
$343$	4.96188	−	17.8432i	0.267916	−	0.963442i
$344$	−7.53520	+	4.35045i	−0.406271	+	0.234560i
$345$	−0.380160	−	4.42927i	−0.0204671	−	0.238464i
$346$	−10.2354	+	5.90938i	−0.550256	+	0.317690i
$347$	18.1572	−	10.4831i	0.974730	−	0.562761i	0.0740550	−	0.997254i	$-0.476406\pi$
$347$	18.1572	−	10.4831i	0.974730	−	0.562761i	0.900675	+	0.434494i	$0.143073\pi$
$348$	−8.35257	−	3.91163i	−0.447745	−	0.209686i
$349$	5.36406	−	3.09694i	0.287132	−	0.165776i	−0.349516	−	0.936930i	$-0.613654\pi$
$349$	5.36406	−	3.09694i	0.287132	−	0.165776i	0.636648	+	0.771155i	$0.280321\pi$
$350$	10.7092	+	0.970861i	0.572429	+	0.0518947i
$351$	−21.8139	−	5.96071i	−1.16434	−	0.318159i
$352$	−2.78681	−	4.82689i	−0.148537	−	0.257274i
$353$	18.8378			1.00263			0.501317	−	0.865264i	$-0.332849\pi$
$353$	18.8378			1.00263			0.501317	+	0.865264i	$0.332849\pi$
$354$	0.247925	+	2.88859i	0.0131771	+	0.153527i
$355$			3.52112i			0.186882i
$356$	−2.05811	+	3.56475i	−0.109080	+	0.188931i
$357$	0.0866143	−	18.0796i	0.00458411	−	0.956876i
$358$	−1.21685	−	2.10764i	−0.0643124	−	0.111392i
$359$	24.0735	−	13.8988i	1.27055	−	0.733553i	0.295459	−	0.955355i	$-0.404527\pi$
$359$	24.0735	−	13.8988i	1.27055	−	0.733553i	0.975092	+	0.221803i	$0.0711942\pi$
$360$	−0.494504	−	2.85953i	−0.0260626	−	0.150710i
$361$	0.474089	−	0.821146i	0.0249520	−	0.0432182i
$362$	−5.76708	+	9.98887i	−0.303111	+	0.525003i
$363$	34.6266	−	2.97196i	1.81742	−	0.155988i
$364$	4.83332	+	10.4507i	0.253335	+	0.547767i
$365$	−2.08428	−	1.20336i	−0.109096	−	0.0629866i
$366$	−5.12631	−	7.34686i	−0.267957	−	0.384026i
$367$		−	21.7534i		−	1.13552i	−0.823195	−	0.567759i	$-0.807810\pi$
$367$		−	21.7534i		−	1.13552i	0.823195	−	0.567759i	$-0.192190\pi$
$368$	−2.29786	−	1.32667i	−0.119784	−	0.0691575i
$369$	−0.169559	+	0.461128i	−0.00882690	+	0.0240053i
$370$		−	0.471297i		−	0.0245016i
$371$	5.30990	+	0.481379i	0.275676	+	0.0249920i
$372$	9.67262	+	4.52983i	0.501502	+	0.234861i
$373$	11.7312			0.607419			0.303709	−	0.952765i	$-0.401775\pi$
$373$	11.7312			0.607419			0.303709	+	0.952765i	$0.401775\pi$
$374$	−10.9949	−	19.0438i	−0.568533	−	0.984729i
$375$	15.1312	−	1.29869i	0.781370	−	0.0670642i
$376$	8.21859	+	4.74500i	0.423841	+	0.244705i
$377$	23.1743			1.19354
$378$	13.5577	−	2.27773i	0.697334	−	0.117154i
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$	3.74157	+	2.16020i	0.191939	+	0.110816i
$381$	−5.72732	+	0.491570i	−0.293420	+	0.0251839i
$382$	−11.0345	−	19.1122i	−0.564572	−	0.977867i
$383$	11.8482			0.605416			0.302708	−	0.953083i	$-0.402109\pi$
$383$	11.8482			0.605416			0.302708	+	0.953083i	$0.402109\pi$
$384$	−1.56856	−	0.734581i	−0.0800454	−	0.0374864i
$385$	−5.98779	−	12.9470i	−0.305166	−	0.659838i
$386$		−	19.9396i		−	1.01490i
$387$	−16.7125	−	20.0510i	−0.849545	−	1.01925i
$388$	−10.2669	−	5.92762i	−0.521225	−	0.300929i
$389$			6.35344i			0.322132i	0.986944	+	0.161066i	$0.0514933\pi$
$389$			6.35344i			0.322132i	−0.986944	+	0.161066i	$0.948507\pi$
$390$	4.17242	+	5.97978i	0.211279	+	0.302798i
$391$	−9.06586	−	5.23418i	−0.458480	−	0.264704i
$392$	−5.33392	−	4.53314i	−0.269404	−	0.228958i
$393$	32.3513	−	2.77668i	1.63191	−	0.140065i
$394$	−2.31280	+	4.00588i	−0.116517	+	0.201814i
$395$	−2.22601	+	3.85557i	−0.112003	+	0.193995i
$396$	12.8442	−	10.7057i	0.645448	−	0.537981i
$397$	−7.42647	+	4.28768i	−0.372724	+	0.215192i	−0.674648	−	0.738140i	$-0.735704\pi$
$397$	−7.42647	+	4.28768i	−0.372724	+	0.215192i	0.301924	+	0.953332i	$0.402371\pi$
$398$	10.4514	+	18.1024i	0.523883	+	0.907391i
$399$	−10.3185	+	17.6760i	−0.516569	+	0.884907i
$400$	2.03214	−	3.51977i	0.101607	−	0.175989i
$401$		−	23.1190i		−	1.15451i	−0.816565	−	0.577254i	$-0.804124\pi$
$401$		−	23.1190i		−	1.15451i	0.816565	−	0.577254i	$-0.195876\pi$
$402$	0.806122	+	9.39219i	0.0402057	+	0.468440i
$403$	−26.8367			−1.33683
$404$	2.65813	+	4.60402i	0.132247	+	0.229058i
$405$	8.20033	−	2.92363i	0.407478	−	0.145276i
$406$	−12.7872	+	5.91393i	−0.634620	+	0.293503i
$407$	2.35174	−	1.35778i	0.116572	−	0.0673026i
$408$	−6.18852	−	2.89818i	−0.306378	−	0.143481i
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	−0.533027	−	0.846098i	$-0.678946\pi$
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	0.466229	+	0.884664i	$0.345612\pi$
$410$	0.137196	−	0.0792099i	0.00677561	−	0.00391190i
$411$	2.50824	+	29.2237i	0.123722	+	1.44150i
$412$	7.74616	−	4.47225i	0.381626	−	0.220332i
$413$	3.61971	+	2.55154i	0.178114	+	0.125553i
$414$	2.74712	−	7.47097i	0.135014	−	0.367178i
$415$	4.07224	+	7.05332i	0.199898	+	0.346234i
$416$	4.35199			0.213374
$417$	−19.0237	−	8.90909i	−0.931596	−	0.436280i
$418$			24.8936i			1.21759i
$419$	−3.40822	+	5.90321i	−0.166502	+	0.288391i	−0.937188	−	0.348825i	$-0.886581\pi$
$419$	−3.40822	+	5.90321i	−0.166502	+	0.288391i	0.770685	+	0.637216i	$0.219914\pi$
$420$	−3.82829	−	2.23478i	−0.186801	−	0.109046i
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	0.653050	−	0.757315i	$-0.273489\pi$
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	−0.982379	+	0.186900i	$0.940156\pi$
$422$	5.79042	−	3.34310i	0.281873	−	0.162740i
$423$	−9.82541	+	26.7208i	−0.477728	+	1.29921i
$424$	1.00759	−	1.74520i	0.0489330	−	0.0847544i
$425$	8.01750	−	13.8867i	0.388906	−	0.673605i
$426$	−2.67392	+	5.70967i	−0.129552	+	0.276634i
$427$	−13.6285	−	1.23552i	−0.659529	−	0.0597910i
$428$	−16.5898	−	9.57813i	−0.801899	−	0.462976i
$429$	−17.8182	+	38.0476i	−0.860272	+	1.83695i
$430$			8.41658i			0.405884i
$431$	−12.2628	−	7.07990i	−0.590676	−	0.341027i	0.174689	−	0.984624i	$-0.444108\pi$
$431$	−12.2628	−	7.07990i	−0.590676	−	0.341027i	−0.765365	+	0.643597i	$0.777441\pi$
$432$	1.36965	−	5.01239i	0.0658973	−	0.241159i
$433$		−	23.4830i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$433$		−	23.4830i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$434$	14.8081	−	6.84856i	0.710814	−	0.328742i
$435$	−7.31670	+	5.10527i	−0.350809	+	0.244779i
$436$	−19.2434			−0.921590
$437$	5.92536	+	10.2630i	0.283449	+	0.490947i
$438$	−2.46593	−	3.53409i	−0.117827	−	0.168865i
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	0.584881	−	0.811119i	$-0.301141\pi$
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	−0.410009	+	0.912081i	$0.634474\pi$
$440$	−5.39149			−0.257029
$441$	10.6738	−	18.0851i	0.508275	−	0.861195i
$442$	17.1701			0.816699
$443$	−25.8161	−	14.9049i	−1.22656	−	0.708154i	−0.260250	−	0.965541i	$-0.583805\pi$
$443$	−25.8161	−	14.9049i	−1.22656	−	0.708154i	−0.966308	+	0.257388i	$0.917138\pi$
$444$	0.357900	−	0.764231i	0.0169852	−	0.0362688i
$445$	1.99086	+	3.44827i	0.0943757	+	0.163464i
$446$	8.18246			0.387451
$447$	1.29461	+	15.0836i	0.0612328	+	0.713428i
$448$	−2.40137	+	1.11060i	−0.113454	+	0.0524709i
$449$			8.41716i			0.397230i	0.980078	+	0.198615i	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$	11.4437	+	4.20793i	0.539463	+	0.198364i
$451$	0.790505	+	0.456399i	0.0372234	+	0.0214910i
$452$			8.44316i			0.397133i
$453$	−38.1280	+	3.27249i	−1.79141	+	0.153755i
$454$	9.26106	+	5.34688i	0.434643	+	0.250941i
$455$	11.0926	+	1.00562i	0.520027	+	0.0471441i
$456$	4.42670	+	6.34420i	0.207299	+	0.297094i
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	−0.817048	−	0.576570i	$-0.804391\pi$
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	0.907848	+	0.419299i	$0.137724\pi$
$458$	−14.6036	+	25.2942i	−0.682382	+	1.18192i
$459$	5.40374	−	19.7756i	0.252225	−	0.923047i
$460$	−2.22278	+	1.28332i	−0.103638	+	0.0598352i
$461$	17.0423	+	29.5181i	0.793739	+	1.37480i	0.923637	+	0.383269i	$0.125202\pi$
$461$	17.0423	+	29.5181i	0.793739	+	1.37480i	−0.129898	+	0.991527i	$0.541465\pi$
$462$	0.122361	−	25.5412i	0.00569273	−	1.18828i
$463$	−6.10962	+	10.5822i	−0.283938	+	0.491796i	−0.972351	−	0.233523i	$-0.924974\pi$
$463$	−6.10962	+	10.5822i	−0.283938	+	0.491796i	0.688413	+	0.725319i	$0.258308\pi$
$464$			5.32498i			0.247206i
$465$	8.47304	−	5.91211i	0.392928	−	0.274167i
$466$	6.43935			0.298297
$467$	−15.4057	−	26.6835i	−0.712893	−	1.23477i	−0.963767	−	0.266747i	$-0.914051\pi$
$467$	−15.4057	−	26.6835i	−0.712893	−	1.23477i	0.250874	−	0.968020i	$-0.419282\pi$
$468$	2.22477	+	12.8650i	0.102840	+	0.594686i
$469$	11.7694	+	8.29628i	0.543460	+	0.383087i
$470$	7.95004	−	4.58996i	0.366708	−	0.211719i
$471$	−2.02353	+	1.41193i	−0.0932395	+	0.0650583i
$472$	1.44961	−	0.836931i	0.0667236	−	0.0385229i
$473$	−41.9983	+	24.2477i	−1.93108	+	1.11491i
$474$	−6.53749	+	4.56157i	−0.300277	+	0.209520i
$475$	−15.7205	+	9.07623i	−0.721306	+	0.416446i
$476$	−9.47423	+	4.38170i	−0.434250	+	0.200835i
$477$	5.67412	+	2.08640i	0.259800	+	0.0955299i
$478$	2.31778	+	4.01452i	0.106013	+	0.183620i
$479$	−41.7493			−1.90758			−0.953788	−	0.300481i	$-0.902853\pi$
$479$	−41.7493			−1.90758			−0.953788	+	0.300481i	$0.902853\pi$
$480$	−1.37403	+	0.958739i	−0.0627157	+	0.0437603i
$481$			2.12036i			0.0966803i
$482$	5.24722	−	9.08846i	0.239004	−	0.413968i
$483$	−6.02906	−	10.5591i	−0.274332	−	0.480457i
$484$	−10.0326	−	17.3769i	−0.456026	−	0.789861i
$485$	−9.93146	+	5.73393i	−0.450964	+	0.260364i
$486$	15.5174	+	1.48648i	0.703885	+	0.0674281i
$487$	10.5832	−	18.3306i	0.479568	−	0.830637i	−0.520157	−	0.854071i	$-0.674127\pi$
$487$	10.5832	−	18.3306i	0.479568	−	0.830637i	0.999725	+	0.0234338i	$0.00745988\pi$
$488$	−2.58611	+	4.47927i	−0.117068	+	0.202767i
$489$	7.37690	+	10.5723i	0.333595	+	0.478097i
$490$	−6.37734	+	2.27586i	−0.288099	+	0.102813i
$491$	32.3428	+	18.6731i	1.45961	+	0.842707i	0.998992	−	0.0448915i	$-0.0142942\pi$
$491$	32.3428	+	18.6731i	1.45961	+	0.842707i	0.460619	+	0.887598i	$0.347628\pi$
$492$	0.282621	−	0.0242571i	0.0127415	−	0.00109359i
$493$			21.0089i			0.946193i
$494$	−16.8333	−	9.71873i	−0.757368	−	0.437266i
$495$	−2.75617	−	15.9379i	−0.123881	−	0.716356i
$496$		−	6.16655i		−	0.276886i
$497$	4.04266	+	8.74113i	0.181338	+	0.392093i
$498$	1.24707	+	14.5297i	0.0558827	+	0.651093i
$499$	27.4197			1.22748			0.613738	−	0.789510i	$-0.289665\pi$
$499$	27.4197			1.22748			0.613738	+	0.789510i	$0.289665\pi$
$500$	−4.38405	−	7.59340i	−0.196061	−	0.339587i
$501$	−4.77265	+	10.1911i	−0.213226	+	0.455305i
$502$	6.80065	+	3.92635i	0.303528	+	0.175242i
$503$	11.2791			0.502909			0.251454	−	0.967869i	$-0.419091\pi$
$503$	11.2791			0.502909			0.251454	+	0.967869i	$0.419091\pi$
$504$	−4.51067	−	6.53099i	−0.200921	−	0.290914i
$505$	5.14255			0.228840
$506$	−12.8074	−	7.39435i	−0.569358	−	0.328719i
$507$	−5.88710	−	8.43720i	−0.261455	−	0.374709i
$508$	1.65941	+	2.87419i	0.0736246	+	0.127522i
$509$	18.6333			0.825909			0.412954	−	0.910752i	$-0.364497\pi$
$509$	18.6333			0.825909			0.412954	+	0.910752i	$0.364497\pi$
$510$	−5.42104	+	3.78256i	−0.240047	+	0.167494i
$511$	−6.55578	−	0.594327i	−0.290010	−	0.0262915i
$512$			1.00000i			0.0441942i
$513$	−16.4913	+	16.3291i	−0.728107	+	0.720946i
$514$	2.97164	+	1.71568i	0.131074	+	0.0756753i
$515$		−	8.65223i		−	0.381263i
$516$	−6.39151	+	13.6479i	−0.281371	+	0.600815i
$517$	45.8072	+	26.4468i	2.01460	+	1.16313i
$518$	−0.541103	−	1.16999i	−0.0237747	−	0.0514063i
$519$	−8.68184	+	18.5385i	−0.381091	+	0.813749i
$520$	2.10489	−	3.64578i	0.0923056	−	0.159878i
$521$	7.64255	−	13.2373i	0.334826	−	0.579936i	−0.648625	−	0.761108i	$-0.724656\pi$
$521$	7.64255	−	13.2373i	0.334826	−	0.579936i	0.983451	+	0.181172i	$0.0579891\pi$
$522$	−15.7413	+	2.72217i	−0.688978	+	0.119146i
$523$	−31.5991	+	18.2437i	−1.38173	+	0.797743i	−0.992365	−	0.123339i	$-0.960640\pi$
$523$	−31.5991	+	18.2437i	−1.38173	+	0.797743i	−0.389368	+	0.921082i	$0.627306\pi$
$524$	−9.37335	−	16.2351i	−0.409477	−	0.709235i
$525$	16.1741	−	9.23507i	0.705894	−	0.403051i
$526$	1.83066	−	3.17080i	0.0798207	−	0.138253i
$527$		−	24.3292i		−	1.05979i
$528$	−8.74256	−	4.09427i	−0.380471	−	0.178180i
$529$	15.9598			0.693903
$530$	−0.974668	−	1.68817i	−0.0423369	−	0.0733296i
$531$	3.21512	+	3.85737i	0.139524	+	0.167396i
$532$	11.7686	+	1.06690i	0.510232	+	0.0462561i
$533$	−0.617243	+	0.356365i	−0.0267358	+	0.0154359i
$534$	0.609676	+	7.10338i	0.0263833	+	0.307393i
$535$	−16.0477	+	9.26516i	−0.693803	+	0.400568i
$536$	4.71336	−	2.72126i	0.203586	−	0.117540i
$537$	−3.81740	−	1.78775i	−0.164733	−	0.0771470i
$538$	−10.9865	+	6.34303i	−0.473660	+	0.273467i
$539$	−29.7292	−	25.2659i	−1.28053	−	1.08828i
$540$	−3.53657	−	3.57170i	−0.152190	−	0.153701i
$541$	2.63647	+	4.56649i	0.113351	+	0.196329i	0.917119	−	0.398613i	$-0.130508\pi$
$541$	2.63647	+	4.56649i	0.113351	+	0.196329i	−0.803769	+	0.594942i	$0.797175\pi$
$542$	19.8766			0.853771
$543$	1.70839	+	19.9046i	0.0733140	+	0.854186i
$544$			3.94535i			0.169155i
$545$	−9.30729	+	16.1207i	−0.398680	+	0.690535i
$546$	17.2235	+	10.0543i	0.737096	+	0.430284i
$547$	−9.29831	−	16.1051i	−0.397567	−	0.688606i	0.595858	−	0.803090i	$-0.296812\pi$
$547$	−9.29831	−	16.1051i	−0.397567	−	0.688606i	−0.993425	+	0.114484i	$0.963479\pi$
$548$	14.6656	−	8.46717i	0.626482	−	0.361700i
$549$	−14.5633	−	5.35501i	−0.621547	−	0.228546i
$550$	11.3264	−	19.6179i	0.482958	−	0.836508i
$551$	11.8916	−	20.5968i	0.506599	−	0.877455i
$552$	−4.57889	+	0.393002i	−0.194890	+	0.0167273i
$553$	−1.09941	+	12.1271i	−0.0467516	+	0.515697i
$554$	6.46579	+	3.73302i	0.274705	+	0.158601i
$555$	−0.467114	−	0.669452i	−0.0198279	−	0.0284167i
$556$			12.1281i			0.514347i
$557$	−23.8694	−	13.7810i	−1.01138	−	0.583920i	−0.0997845	−	0.995009i	$-0.531815\pi$
$557$	−23.8694	−	13.7810i	−1.01138	−	0.583920i	−0.911595	+	0.411089i	$0.865149\pi$
$558$	18.2291	−	3.15239i	0.771698	−	0.133451i
$559$		−	37.8662i		−	1.60157i
$560$	−0.231071	+	2.54885i	−0.00976452	+	0.107708i
$561$	−34.4924	−	16.1533i	−1.45627	−	0.681993i
$562$	22.2564			0.938831
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	0.596137	−	0.802883i	$-0.296702\pi$
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	−0.993385	+	0.114828i	$0.963368\pi$
$564$	16.3770	−	1.40562i	0.689595	−	0.0591872i
$565$	7.07306	+	4.08364i	0.297566	+	0.171800i
$566$	−16.1802			−0.680106
$567$	17.0005	−	16.6728i	0.713955	−	0.700191i
$568$	3.64006			0.152734
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	0.578942	−	0.815369i	$-0.303466\pi$
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	−0.416659	+	0.909063i	$0.636799\pi$
$570$	7.45573	−	0.639918i	0.312286	−	0.0268032i
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	0.602697	−	0.797970i	$-0.294093\pi$
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	−0.992411	+	0.122966i	$0.960759\pi$
$572$	24.2563			1.01421
$573$	−34.6165	−	16.2114i	−1.44612	−	0.677241i
$574$	0.249644	−	0.354154i	0.0104199	−	0.0147821i
$575$		−	10.7839i		−	0.449721i
$576$	−2.95612	+	0.511208i	−0.123172	+	0.0213003i
$577$	31.9418	+	18.4416i	1.32976	+	0.767735i	0.985262	−	0.171053i	$-0.0547170\pi$
$577$	31.9418	+	18.4416i	1.32976	+	0.767735i	0.344495	+	0.938788i	$0.388050\pi$
$578$		−	1.43425i		−	0.0596569i
$579$	−19.7626	−	28.3231i	−0.821306	−	1.17707i
$580$	4.46088	+	2.57549i	0.185228	+	0.106941i
$581$	18.2073	+	12.8344i	0.755366	+	0.532459i
$582$	−20.4587	+	1.75595i	−0.848039	+	0.0727863i
$583$	5.61593	−	9.72707i	0.232588	−	0.402854i
$584$	−1.24401	+	2.15468i	−0.0514773	+	0.0891614i
$585$	11.8534	+	4.35857i	0.490078	+	0.180205i
$586$	−7.68002	+	4.43406i	−0.317259	+	0.183170i
$587$	−13.2295	−	22.9141i	−0.546039	−	0.945766i	−0.998541	−	0.0540032i	$-0.982802\pi$
$587$	−13.2295	−	22.9141i	−0.546039	−	0.945766i	0.452502	−	0.891763i	$-0.350531\pi$
$588$	−12.0695	−	1.15250i	−0.497736	−	0.0475284i
$589$	−13.7709	+	23.8520i	−0.567422	+	0.982803i
$590$		−	1.61917i		−	0.0666601i
$591$	0.685123	+	7.98242i	0.0281822	+	0.328353i
$592$	−0.487217			−0.0200245
$593$	17.3351	+	30.0254i	0.711869	+	1.23299i	0.964155	+	0.265341i	$0.0854845\pi$
$593$	17.3351	+	30.0254i	0.711869	+	1.23299i	−0.252285	+	0.967653i	$0.581182\pi$
$594$	7.63390	−	27.9371i	0.313223	−	1.14627i
$595$	−0.911654	+	10.0561i	−0.0373742	+	0.412259i
$596$	7.56951	−	4.37026i	0.310059	−	0.179013i
$597$	32.7874	+	15.3548i	1.34190	+	0.628432i
$598$	10.0003	−	5.77366i	0.408942	−	0.236103i
$599$	21.2079	−	12.2444i	0.866530	−	0.500291i	0.000336253	−	1.00000i	$-0.499893\pi$
$599$	21.2079	−	12.2444i	0.866530	−	0.500291i	0.866193	+	0.499709i	$0.166560\pi$
$600$	−0.601984	−	7.01376i	−0.0245759	−	0.286336i
$601$	19.3812	−	11.1898i	0.790577	−	0.456440i	−0.0495885	−	0.998770i	$-0.515791\pi$
$601$	19.3812	−	11.1898i	0.790577	−	0.456440i	0.840166	+	0.542330i	$0.182458\pi$
$602$	9.66321	+	20.8940i	0.393843	+	0.851578i
$603$	10.4539	+	12.5421i	0.425715	+	0.510755i
$604$	11.0471	+	19.1341i	0.449499	+	0.778555i
$605$	−19.4095			−0.789109
$606$	8.33889	+	3.90523i	0.338744	+	0.158639i
$607$			32.5834i			1.32252i	0.750158	+	0.661259i	$0.229978\pi$
$607$			32.5834i			1.32252i	−0.750158	+	0.661259i	$0.770022\pi$
$608$	2.23317	−	3.86796i	0.0905670	−	0.156867i
$609$	−12.3022	+	21.0742i	−0.498509	+	0.853969i
$610$	2.50160	+	4.33290i	0.101287	+	0.175434i
$611$	−35.7672	+	20.6502i	−1.44699	+	0.835418i
$612$	−11.6629	+	2.01689i	−0.471446	+	0.0815281i
$613$	5.86931	−	10.1659i	0.237059	−	0.410598i	−0.722810	−	0.691047i	$-0.757150\pi$
$613$	5.86931	−	10.1659i	0.237059	−	0.410598i	0.959869	+	0.280449i	$0.0904832\pi$
$614$	13.5714	−	23.5063i	0.547696	−	0.948637i
$615$	0.116372	−	0.248491i	0.00469258	−	0.0100201i
$616$	−13.3843	+	6.19005i	−0.539269	+	0.249404i
$617$	−38.1947	−	22.0517i	−1.53766	−	0.887770i	−0.998975	−	0.0452639i	$-0.985587\pi$
$617$	−38.1947	−	22.0517i	−1.53766	−	0.887770i	−0.538687	−	0.842506i	$-0.681080\pi$
$618$	6.57046	−	14.0300i	0.264303	−	0.564370i
$619$		−	4.94644i		−	0.198814i	−0.995047	−	0.0994070i	$-0.968305\pi$
$619$		−	4.94644i		−	0.198814i	0.995047	−	0.0994070i	$-0.0316946\pi$
$620$	−5.16588	−	2.98252i	−0.207467	−	0.119781i
$621$	−3.50253	−	13.3349i	−0.140552	−	0.535109i
$622$		−	16.8955i		−	0.677447i
$623$	8.90128	+	6.27454i	0.356622	+	0.251384i
$624$	6.18177	−	4.31337i	0.247469	−	0.172673i
$625$	11.8398			0.473593
$626$	−2.13870	−	3.70433i	−0.0854795	−	0.148055i
$627$	24.6727	+	35.3601i	0.985333	+	1.41215i
$628$	1.23372	+	0.712287i	0.0492307	+	0.0284233i
$629$	−1.92224			−0.0766447
$630$	−7.65283	+	0.619917i	−0.304896	+	0.0246981i
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$	3.98581	+	2.30121i	0.158547	+	0.0915371i
$633$	4.91155	−	10.4877i	0.195217	−	0.416850i
$634$	3.31470	+	5.74123i	0.131644	+	0.228013i
$635$	3.21038			0.127400
$636$	−0.298480	−	3.47761i	−0.0118355	−	0.137896i
$637$	28.6917	−	10.2391i	1.13681	−	0.405688i
$638$			29.6794i			1.17502i
$639$	1.86083	+	10.7605i	0.0736133	+	0.425678i
$640$	0.837727	+	0.483662i	0.0331141	+	0.0191184i
$641$			14.0821i			0.556209i	0.960551	+	0.278105i	$0.0897062\pi$
$641$			14.0821i			0.556209i	−0.960551	+	0.278105i	$0.910294\pi$
$642$	−33.0581	+	2.83734i	−1.30470	+	0.111981i
$643$	−7.33157	−	4.23288i	−0.289129	−	0.166929i	0.348420	−	0.937339i	$-0.386718\pi$
$643$	−7.33157	−	4.23288i	−0.289129	−	0.166929i	−0.637549	+	0.770410i	$0.720052\pi$
$644$	−4.04461	+	5.73783i	−0.159380	+	0.226102i
$645$	8.34189	+	11.9553i	0.328461	+	0.470740i
$646$	8.81062	−	15.2604i	0.346649	−	0.600414i
$647$	12.1662	−	21.0725i	0.478304	−	0.828446i	−0.521387	−	0.853320i	$-0.674585\pi$
$647$	12.1662	−	21.0725i	0.478304	−	0.828446i	0.999691	+	0.0248742i	$0.00791854\pi$
$648$	−3.02239	−	8.47733i	−0.118731	−	0.333021i
$649$	8.07955	−	4.66473i	0.317150	−	0.183107i
$650$	8.84386	+	15.3180i	0.346885	+	0.600822i
$651$	14.2464	−	24.4047i	0.558361	−	0.956498i
$652$	3.72148	−	6.44579i	0.145744	−	0.252437i
$653$		−	41.6446i		−	1.62968i	−0.579686	−	0.814840i	$-0.696825\pi$
$653$		−	41.6446i		−	1.62968i	0.579686	−	0.814840i	$-0.303175\pi$
$654$	−27.3342	+	19.0726i	−1.06885	+	0.745797i
$655$	−18.1341			−0.708560
$656$	−0.0818856	−	0.141830i	−0.00319709	−	0.00553753i
$657$	−7.00545	−	2.57594i	−0.273309	−	0.100497i
$658$	14.4661	−	20.5221i	0.563946	−	0.800033i
$659$	−9.09866	+	5.25312i	−0.354434	+	0.204632i	−0.666636	−	0.745383i	$-0.732267\pi$
$659$	−9.09866	+	5.25312i	−0.354434	+	0.204632i	0.312203	+	0.950016i	$0.398933\pi$
$660$	−7.65833	+	5.34364i	−0.298100	+	0.208001i
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	−0.791243	−	0.611502i	$-0.790566\pi$
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	0.133954	+	0.990987i	$0.457232\pi$
$662$	−0.656267	+	0.378896i	−0.0255065	+	0.0147262i
$663$	24.3892	−	17.0177i	0.947199	−	0.660914i
$664$	7.29158	−	4.20979i	0.282968	−	0.163372i
$665$	6.58578	−	9.34282i	0.255386	−	0.362299i
$666$	−0.249069	−	1.44027i	−0.00965124	−	0.0558095i
$667$	7.06450	+	12.2361i	0.273539	+	0.473783i
$668$	6.49710			0.251380
$669$	11.6228	−	8.10984i	0.449362	−	0.313545i
$670$		−	5.26468i		−	0.203392i
$671$	−14.4140	+	24.9657i	−0.556445	+	0.963790i
$672$	−2.31027	+	3.95760i	−0.0891207	+	0.152668i
$673$	−3.10277	−	5.37415i	−0.119603	−	0.207158i	0.800007	−	0.599990i	$-0.204829\pi$
$673$	−3.10277	−	5.37415i	−0.119603	−	0.207158i	−0.919610	+	0.392832i	$0.871495\pi$
$674$	−1.75089	+	1.01088i	−0.0674419	+	0.0389376i
$675$	20.4258	−	5.36503i	0.786189	−	0.206500i
$676$	−2.96991	+	5.14404i	−0.114227	+	0.197848i
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	−0.523942	−	0.851754i	$-0.675539\pi$
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	0.999612	+	0.0278703i	$0.00887255\pi$
$678$	8.36823	+	11.9931i	0.321380	+	0.460591i
$679$	−18.0715	+	25.6369i	−0.693520	+	0.983852i
$680$	3.30512	+	1.90821i	0.126746	+	0.0731767i
$681$	18.4543	−	1.58391i	0.707169	−	0.0606956i
$682$		−	34.3699i		−	1.31609i
$683$	18.3119	+	10.5724i	0.700687	+	0.404542i	0.807603	−	0.589726i	$-0.200764\pi$
$683$	18.3119	+	10.5724i	0.700687	+	0.404542i	−0.106916	+	0.994268i	$0.534098\pi$
$684$	12.5758	+	4.62419i	0.480847	+	0.176810i
$685$		−	16.3810i		−	0.625886i
$686$	−13.2187	+	12.9717i	−0.504693	+	0.495263i
$687$	4.32605	+	50.4031i	0.165049	+	1.92300i
$688$	8.70089			0.331718
$689$	4.38503	+	7.59509i	0.167056	+	0.289350i
$690$	−1.88541	+	4.02594i	−0.0717762	+	0.153265i
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	0.602390	−	0.798202i	$-0.294215\pi$
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	−0.390068	+	0.920786i	$0.627549\pi$
$692$	11.8188			0.449282
$693$	−25.1407	−	36.4012i	−0.955017	−	1.38277i
$694$	−20.9661			−0.795864
$695$	10.1601	+	5.86591i	0.385393	+	0.222507i
$696$	5.27772	+	7.56386i	0.200052	+	0.286707i
$697$	−0.323067	−	0.559568i	−0.0122370	−	0.0211952i
$698$	−6.19389			−0.234442
$699$	9.14675	−	6.38220i	0.345962	−	0.241397i
$700$	−8.78898	−	6.19537i	−0.332192	−	0.234163i
$701$		−	24.5717i		−	0.928061i	−0.885819	−	0.464031i	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$	15.9110	+	16.0691i	0.600523	+	0.606488i
$703$	1.88454	+	1.08804i	0.0710767	+	0.0410361i
$704$			5.57361i			0.210063i
$705$	6.74339	−	14.3993i	0.253971	−	0.542308i
$706$	−16.3140	−	9.41889i	−0.613985	−	0.354484i
$707$	12.7663	−	5.90424i	0.480126	−	0.222052i
$708$	1.22959	−	2.62556i	0.0462107	−	0.0986745i
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	0.0655765	+	0.997848i	$0.479111\pi$
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	−0.896950	+	0.442133i	$0.854222\pi$
$710$	1.76056	−	3.04938i	0.0660727	−	0.114441i
$711$	−4.76508	+	12.9589i	−0.178704	+	0.485998i
$712$	3.56475	−	2.05811i	0.133595	−	0.0771309i
$713$	−8.18098	−	14.1699i	−0.306380	−	0.530666i
$714$	−9.11483	+	15.6141i	−0.341114	+	0.584344i
$715$	11.7319	−	20.3202i	0.438747	−	0.759931i
$716$			2.43370i			0.0909515i
$717$	7.27118	+	3.40520i	0.271547	+	0.127169i
$718$	−27.7977			−1.03740
$719$	−2.22433	−	3.85266i	−0.0829537	−	0.143680i	0.821564	−	0.570117i	$-0.193102\pi$
$719$	−2.22433	−	3.85266i	−0.0829537	−	0.143680i	−0.904517	+	0.426437i	$0.859769\pi$
$720$	−1.00151	+	2.72368i	−0.0373241	+	0.101505i
$721$	−9.93376	−	21.4790i	−0.369952	−	0.799921i
$722$	−0.821146	+	0.474089i	−0.0305599	+	0.0176438i
$723$	−1.55439	−	18.1103i	−0.0578084	−	0.673530i
$724$	9.98887	−	5.76708i	0.371233	−	0.214332i
$725$	−18.7427	+	10.8211i	−0.696088	+	0.401886i
$726$	−31.4735	−	14.7395i	−1.16809	−	0.547034i
$727$	−30.4270	+	17.5670i	−1.12848	+	0.651525i	−0.943551	−	0.331227i	$-0.892537\pi$
$727$	−30.4270	+	17.5670i	−1.12848	+	0.651525i	−0.184924	+	0.982753i	$0.559204\pi$
$728$	1.03959	−	11.4673i	0.0385297	−	0.425005i
$729$	23.5150	−	13.2682i	0.870925	−	0.491416i
$730$	1.20336	+	2.08428i	0.0445382	+	0.0771425i
$731$	34.3280			1.26967
$732$	0.766086	+	8.92572i	0.0283153	+	0.329904i
$733$			5.81725i			0.214865i	0.994212	+	0.107433i	$0.0342630\pi$
$733$			5.81725i			0.214865i	−0.994212	+	0.107433i	$0.965737\pi$
$734$	−10.8767	+	18.8390i	−0.401467	+	0.695360i
$735$	−6.80302	+	9.55349i	−0.250933	+	0.352386i
$736$	1.32667	+	2.29786i	0.0489018	+	0.0847003i
$737$	26.2704	−	15.1672i	0.967684	−	0.558693i
$738$	0.377406	−	0.314569i	0.0138925	−	0.0115794i
$739$	−5.51675	+	9.55529i	−0.202937	+	0.351497i	−0.949473	−	0.313847i	$-0.898382\pi$
$739$	−5.51675	+	9.55529i	−0.202937	+	0.351497i	0.746537	+	0.665344i	$0.231715\pi$
$740$	−0.235648	+	0.408155i	−0.00866261	+	0.0150041i
$741$	−33.5433	+	2.87899i	−1.23225	+	0.105762i
$742$	−4.35782	−	3.07184i	−0.159980	−	0.112771i
$743$	−0.543196	−	0.313615i	−0.0199279	−	0.0115054i	0.490003	−	0.871721i	$-0.336996\pi$
$743$	−0.543196	−	0.313615i	−0.0199279	−	0.0115054i	−0.509931	+	0.860215i	$0.670329\pi$
$744$	−6.11182	−	8.75925i	−0.224070	−	0.321130i
$745$		−	8.45491i		−	0.309764i
$746$	−10.1595	−	5.86560i	−0.371966	−	0.214755i
$747$	16.1722	+	19.4027i	0.591709	+	0.709909i
$748$			21.9898i			0.804028i
$749$	−29.2008	+	41.4253i	−1.06697	+	1.51365i
$750$	−13.7533	−	6.44088i	−0.502200	−	0.235188i
$751$	4.47058			0.163134			0.0815668	−	0.996668i	$-0.474008\pi$
$751$	4.47058			0.163134			0.0815668	+	0.996668i	$0.474008\pi$
$752$	−4.74500	−	8.21859i	−0.173033	−	0.299701i
$753$	13.5515	−	1.16311i	0.493843	−	0.0423861i
$754$	−20.0695	−	11.5871i	−0.730889	−	0.421979i
$755$	21.3722			0.777813
$756$	−12.8802	−	4.80630i	−0.468448	−	0.174803i
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$	−30.2140	−	17.4441i	−1.09742	−	0.633597i
$759$	−25.5210	+	2.19044i	−0.926352	+	0.0795079i
$760$	−2.16020	−	3.74157i	−0.0783586	−	0.135721i
$761$	−20.9940			−0.761032			−0.380516	−	0.924774i	$-0.624254\pi$
$761$	−20.9940			−0.761032			−0.380516	+	0.924774i	$0.624254\pi$
$762$	5.20579	+	2.43795i	0.188586	+	0.0883176i
$763$	−4.59678	+	50.7052i	−0.166415	+	1.83565i
$764$			22.0689i			0.798425i
$765$	−3.95131	+	10.7458i	−0.142860	+	0.388517i
$766$	−10.2609	−	5.92412i	−0.370740	−	0.214047i
$767$			7.28463i			0.263033i
$768$	0.991125	+	1.42045i	0.0357641	+	0.0512560i
$769$	−34.1729	−	19.7298i	−1.23231	−	0.711473i	−0.264797	−	0.964304i	$-0.585305\pi$
$769$	−34.1729	−	19.7298i	−1.23231	−	0.711473i	−0.967511	+	0.252831i	$0.918638\pi$
$770$	−1.28790	+	14.2063i	−0.0464127	+	0.511959i
$771$	5.92151	−	0.508238i	0.213258	−	0.0183037i
$772$	−9.96979	+	17.2682i	−0.358821	+	0.621496i
$773$	−17.3164	+	29.9929i	−0.622829	+	1.07877i	0.366128	+	0.930565i	$0.380683\pi$
$773$	−17.3164	+	29.9929i	−0.622829	+	1.07877i	−0.988956	+	0.148206i	$0.952650\pi$
$774$	4.44797	+	25.7209i	0.159879	+	0.924519i
$775$	21.7048	−	12.5313i	0.779661	−	0.450137i
$776$	5.92762	+	10.2669i	0.212789	+	0.368562i
$777$	−1.92821	−	1.12560i	−0.0691742	−	0.0403808i
$778$	3.17672	−	5.50224i	0.113891	−	0.197265i
$779$			0.731457i			0.0262072i
$780$	−0.623535	−	7.26485i	−0.0223261	−	0.260123i
$781$	20.2883			0.725973
$782$	5.23418	+	9.06586i	0.187174	+	0.324195i
$783$	−19.6617	+	19.4683i	−0.702651	+	0.695741i
$784$	2.35274	+	6.59277i	0.0840264	+	0.235456i
$785$	1.19340	−	0.689012i	0.0425944	−	0.0245919i
$786$	−29.4054	−	13.7710i	−1.04886	−	0.491195i
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.156449	−	0.987686i	$-0.449995\pi$
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.933586	+	0.358355i	$0.116662\pi$
$788$	4.00588	−	2.31280i	0.142704	−	0.0823900i
$789$	−0.542299	−	6.31837i	−0.0193064	−	0.224940i
$790$	3.85557	−	2.22601i	0.137175	−	0.0791980i
$791$	22.2473	+	2.01687i	0.791022	+	0.0717116i
$792$	−16.4763	+	2.84928i	−0.585459	+	0.101245i
$793$	−11.2547	−	19.4937i	−0.399667	−	0.692243i
$794$	8.57535			0.304328
$795$	−3.05766	−	1.43194i	−0.108444	−	0.0507859i
$796$		−	20.9028i		−	0.740882i
$797$	−9.60992	+	16.6449i	−0.340401	+	0.589591i	−0.984507	−	0.175344i	$-0.943896\pi$
$797$	−9.60992	+	16.6449i	−0.340401	+	0.589591i	0.644106	+	0.764936i	$0.277229\pi$
$798$	17.7741	−	10.1486i	0.629195	−	0.359258i
$799$	−18.7207	−	32.4252i	−0.662290	−	1.14712i
$800$	−3.51977	+	2.03214i	−0.124443	+	0.0718471i
$801$	7.90635	+	9.48571i	0.279357	+	0.335161i
$802$	−11.5595	+	20.0216i	−0.408180	+	0.706989i
$803$	−6.93361	+	12.0094i	−0.244682	+	0.423801i
$804$	3.99797	−	8.53693i	0.140998	−	0.301074i
$805$	2.85051	+	6.16345i	0.100467	+	0.217233i
$806$	23.2413	+	13.4184i	0.818640	+	0.472642i
$807$	−9.31894	+	19.8989i	−0.328042	+	0.700474i
$808$		−	5.31626i		−	0.187025i
$809$	34.0157	+	19.6390i	1.19593	+	0.690469i	0.959645	−	0.281215i	$-0.0907374\pi$
$809$	34.0157	+	19.6390i	1.19593	+	0.690469i	0.236283	+	0.971684i	$0.424071\pi$
$810$	−8.56351	−	1.56823i	−0.300891	−	0.0551019i
$811$			9.68436i			0.340064i	0.985439	+	0.170032i	$0.0543871\pi$
$811$			9.68436i			0.340064i	−0.985439	+	0.170032i	$0.945613\pi$
$812$	14.0310	+	1.27201i	0.492393	+	0.0446389i
$813$	28.2336	−	19.7002i	0.990196	−	0.690915i
$814$	−2.71556			−0.0951803
$815$	−3.59987	−	6.23517i	−0.126098	−	0.218408i
$816$	3.91033	+	5.60416i	0.136889	+	0.196185i
$817$	−33.6547	−	19.4306i	−1.17743	−	0.679790i
$818$	1.55989			0.0545404
$819$	34.4301	−	2.78901i	1.20308	−	0.0974558i
$820$	−0.158420			−0.00553226
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	0.679393	−	0.733775i	$-0.262243\pi$
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	−0.295771	+	0.955259i	$0.595577\pi$
$822$	12.4396	−	26.5626i	0.433883	−	0.926477i
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	0.672572	−	0.740032i	$-0.265190\pi$
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	−0.977172	+	0.212448i	$0.931856\pi$
$824$	−8.94450			−0.311596
$825$	−3.35523	−	39.0920i	−0.116814	−	1.36101i
$826$	−1.85899	−	4.01956i	−0.0646826	−	0.139858i
$827$		−	46.9482i		−	1.63255i	−0.577665	−	0.816274i	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$	−6.11456	+	5.09649i	−0.212496	+	0.177115i
$829$	−1.99797	−	1.15353i	−0.0693924	−	0.0400637i	0.464902	−	0.885362i	$-0.346089\pi$
$829$	−1.99797	−	1.15353i	−0.0693924	−	0.0400637i	−0.534295	+	0.845298i	$0.679423\pi$
$830$		−	8.14447i		−	0.282699i
$831$	12.8842	−	1.10584i	0.446948	−	0.0383611i
$832$	−3.76893	−	2.17600i	−0.130664	−	0.0754391i
$833$	9.28237	+	26.0108i	0.321615	+	0.901219i
$834$	12.0205	+	17.2274i	0.416236	+	0.596535i
$835$	3.14240	−	5.44280i	0.108747	−	0.188356i
$836$	12.4468	−	21.5585i	0.430482	−	0.745617i
$837$	22.7690	−	22.5451i	0.787013	−	0.779272i
$838$	5.90321	−	3.40822i	0.203923	−	0.117735i
$839$	−8.51664	−	14.7513i	−0.294027	−	0.509270i	0.680731	−	0.732533i	$-0.261662\pi$
$839$	−8.51664	−	14.7513i	−0.294027	−	0.509270i	−0.974758	+	0.223264i	$0.928329\pi$
$840$	2.19800	+	3.84952i	0.0758383	+	0.132821i
$841$	−0.322276	+	0.558199i	−0.0111130	+	0.0192482i
$842$			13.5145i			0.465742i
$843$	31.6141	−	22.0589i	1.08885	−	0.759749i
$844$	−6.68620			−0.230148
$845$	2.87287	+	4.97595i	0.0988296	+	0.171178i
$846$	21.8695	−	18.2282i	0.751888	−	0.626699i
$847$	−48.1838	+	22.2844i	−1.65562	+	0.765700i
$848$	−1.74520	+	1.00759i	−0.0599304	+	0.0346008i
$849$	−22.9832	+	16.0366i	−0.788781	+	0.550376i
$850$	−13.8867	+	8.01750i	−0.476311	+	0.274998i
$851$	−1.11956	+	0.646377i	−0.0383779	+	0.0221575i
$852$	5.17052	−	3.60776i	0.177139	−	0.123600i
$853$	−2.87158	+	1.65791i	−0.0983209	+	0.0567656i	−0.548354	−	0.836246i	$-0.684745\pi$
$853$	−2.87158	+	1.65791i	−0.0983209	+	0.0567656i	0.450033	+	0.893012i	$0.351412\pi$
$854$	11.1849	+	7.88424i	0.382738	+	0.269793i
$855$	9.95624	−	8.29854i	0.340496	−	0.283804i
$856$	9.57813	+	16.5898i	0.327374	+	0.567028i
$857$	−9.49024			−0.324180			−0.162090	−	0.986776i	$-0.551824\pi$
$857$	−9.49024			−0.324180			−0.162090	+	0.986776i	$0.551824\pi$
$858$	34.4548	−	24.0410i	1.17627	−	0.820747i
$859$			29.4569i			1.00506i	0.864561	+	0.502528i	$0.167597\pi$
$859$			29.4569i			1.00506i	−0.864561	+	0.502528i	$0.832403\pi$
$860$	4.20829	−	7.28898i	0.143502	−	0.248552i
$861$	0.00359536	−	0.750485i	0.000122529	−	0.0255765i
$862$	7.07990	+	12.2628i	0.241143	+	0.417671i
$863$	−13.4610	+	7.77172i	−0.458218	+	0.264553i	−0.711295	−	0.702894i	$-0.751891\pi$
$863$	−13.4610	+	7.77172i	−0.458218	+	0.264553i	0.253076	+	0.967446i	$0.418558\pi$
$864$	−3.69235	+	3.65603i	−0.125616	+	0.124381i
$865$	5.71629	−	9.90090i	0.194360	−	0.336641i
$866$	−11.7415	+	20.3369i	−0.398992	+	0.691075i
$867$	−1.42152	−	2.03727i	−0.0482773	−	0.0691895i
$868$	−16.2485	−	1.47304i	−0.551510	−	0.0499983i
$869$	22.2154	+	12.8260i	0.753604	+	0.435094i
$870$	8.88909	−	0.762941i	0.301368	−	0.0258661i
$871$			23.6858i			0.802562i
$872$	16.6652	+	9.62168i	0.564356	+	0.325831i
$873$	−27.3201	+	22.7713i	−0.924645	+	0.770692i
$874$		−	11.8507i		−	0.400857i
$875$	−21.0554	+	9.73785i	−0.711804	+	0.329199i
$876$	0.368514	+	4.29358i	0.0124509	+	0.145067i
$877$	−45.4497			−1.53473			−0.767364	−	0.641212i	$-0.778432\pi$
$877$	−45.4497			−1.53473			−0.767364	+	0.641212i	$0.778432\pi$
$878$	−2.11540	−	3.66398i	−0.0713913	−	0.123653i
$879$	−6.51436	+	13.9102i	−0.219724	+	0.469180i
$880$	4.66917	+	2.69574i	0.157398	+	0.0908735i
$881$	−15.6912			−0.528651			−0.264326	−	0.964433i	$-0.585149\pi$
$881$	−15.6912			−0.528651			−0.264326	+	0.964433i	$0.585149\pi$
$882$	−18.2863	+	10.3253i	−0.615732	+	0.347670i
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$	−14.8697	−	8.58505i	−0.500124	−	0.288747i
$885$	−1.60480	−	2.29994i	−0.0539447	−	0.0773117i
$886$	14.9049	+	25.8161i	0.500740	+	0.867307i
$887$	0.0605481			0.00203301			0.00101650	−	0.999999i	$-0.499676\pi$
$887$	0.0605481			0.00203301			0.00101650	+	0.999999i	$0.499676\pi$
$888$	−0.692066	+	0.482893i	−0.0232242	+	0.0162048i
$889$	7.96973	−	3.68589i	0.267296	−	0.123621i
$890$		−	3.98172i		−	0.133467i
$891$	−16.8456	−	47.2494i	−0.564350	−	1.58291i
$892$	−7.08622	−	4.09123i	−0.237264	−	0.136985i
$893$			42.3856i			1.41838i
$894$	6.42062	−	13.7100i	0.214737	−	0.458532i
$895$	2.03877	+	1.17709i	0.0681487	+	0.0393456i
$896$	2.63495	+	0.238876i	0.0880274	+	0.00798029i
$897$	8.48245	−	18.1127i	0.283221	−	0.604766i
$898$	4.20858	−	7.28948i	0.140442	−	0.243253i
$899$	−16.4184	+	28.4375i	−0.547583	+	0.948442i
$900$	−7.80660	−	9.36604i	−0.260220	−	0.312201i
$901$	−6.88542	+	3.97530i	−0.229386	+	0.132436i
$902$	−0.456399	−	0.790505i	−0.0151964	−	0.0263210i
$903$	34.4347	+	20.1014i	1.14592	+	0.668934i
$904$	4.22158	−	7.31199i	0.140408	−	0.243193i
$905$		−	11.1573i		−	0.370880i
$906$	34.6560	+	16.2299i	1.15137	+	0.539203i
$907$	24.0980			0.800162			0.400081	−	0.916480i	$-0.368982\pi$
$907$	24.0980			0.800162			0.400081	+	0.916480i	$0.368982\pi$
$908$	−5.34688	−	9.26106i	−0.177442	−	0.307339i
$909$	15.7155	−	2.71772i	0.521251	−	0.0901410i
$910$	−9.10363	−	6.41717i	−0.301782	−	0.212727i
$911$	22.0494	−	12.7302i	0.730528	−	0.421771i	−0.0880873	−	0.996113i	$-0.528075\pi$
$911$	22.0494	−	12.7302i	0.730528	−	0.421771i	0.818615	+	0.574342i	$0.194742\pi$
$912$	−0.661535	−	7.70759i	−0.0219056	−	0.255224i
$913$	40.6404	−	23.4638i	1.34500	−	0.776537i
$914$	−3.36207	+	1.94109i	−0.111208	+	0.0642057i
$915$	7.84785	+	3.67526i	0.259442	+	0.121500i
$916$	25.2942	−	14.6036i	0.835744	−	0.482517i
$917$	−45.0177	+	20.8201i	−1.48662	+	0.687540i
$918$	−14.5676	+	14.4243i	−0.480802	+	0.476073i
$919$	11.4534	+	19.8378i	0.377812	+	0.654389i	0.990744	−	0.135747i	$-0.0433433\pi$
$919$	11.4534	+	19.8378i	0.377812	+	0.654389i	−0.612932	+	0.790136i	$0.710010\pi$
$920$	2.56664			0.0846197
$921$	−4.02027	−	46.8404i	−0.132472	−	1.54344i
$922$		−	34.0846i		−	1.12252i
$923$	−7.92076	+	13.7192i	−0.260715	+	0.451572i
$924$	−12.8766	+	22.0582i	−0.423608	+	0.725660i
$925$	−0.990094	−	1.71489i	−0.0325541	−	0.0563853i
$926$	10.5822	−	6.10962i	0.347752	−	0.200775i
$927$	−4.57250	−	26.4410i	−0.150181	−	0.868437i
$928$	2.66249	−	4.61157i	0.0874006	−	0.151382i
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	−0.527097	−	0.849805i	$-0.676720\pi$
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	0.999501	+	0.0315768i	$0.0100529\pi$
$930$	−10.2939	+	0.883517i	−0.337551	+	0.0289717i
$931$	5.62246	−	30.7547i	0.184269	−	1.00794i
$932$	−5.57664	−	3.21967i	−0.182669	−	0.105464i
$933$	−16.7455	−	23.9992i	−0.548224	−	0.785697i
$934$			30.8115i			1.00818i
$935$	18.4215	+	10.6356i	0.602447	+	0.347823i
$936$	4.50580	−	12.2538i	0.147277	−	0.400529i
$937$			53.6825i			1.75373i	0.480736	+	0.876865i	$0.340369\pi$
$937$			53.6825i			1.75373i	−0.480736	+	0.876865i	$0.659631\pi$
$938$	−6.04446	−	13.0695i	−0.197359	−	0.426734i
$939$	−6.70936	−	3.14209i	−0.218952	−	0.102538i
$940$	−9.17991			−0.299416
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	−0.948693	−	0.316200i	$-0.897593\pi$
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	0.200509	−	0.979692i	$-0.435740\pi$
$942$	2.45840	−	0.211002i	0.0800989	−	0.00687481i
$943$	−0.376324	−	0.217271i	−0.0122548	−	0.00707530i
$944$	−1.67386			−0.0544796
$945$	−10.2560	+	8.46547i	−0.333629	+	0.275382i
$946$	48.4954			1.57672
$947$	−25.0440	−	14.4591i	−0.813820	−	0.469859i	0.0344607	−	0.999406i	$-0.489029\pi$
$947$	−25.0440	−	14.4591i	−0.813820	−	0.469859i	−0.848281	+	0.529547i	$0.822362\pi$
$948$	7.94242	−	0.681690i	0.257958	−	0.0221403i
$949$	−5.41390	−	9.37715i	−0.175743	−	0.304395i
$950$	18.1525			0.588944
$951$	10.3986	+	4.86984i	0.337199	+	0.157915i
$952$	10.3958	+	0.942449i	0.336929	+	0.0305450i
$953$		−	12.8715i		−	0.416949i	−0.978028	−	0.208475i	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$	−3.87073	−	4.64394i	−0.125319	−	0.150353i
$955$	18.4877	+	10.6739i	0.598249	+	0.345399i
$956$		−	4.63557i		−	0.149925i
$957$	29.4160	+	42.1580i	0.950884	+	1.36278i
$958$	36.1560	+	20.8747i	1.16815	+	0.674430i
$959$	−18.8073	−	40.6656i	−0.607319	−	1.31316i
$960$	1.66932	−	0.143276i	0.0538770	−	0.00462421i
$961$	3.51314	−	6.08494i	0.113327	−	0.196288i
$962$	1.06018	−	1.83629i	0.0341816	−	0.0592043i
$963$	−44.1451	+	36.7950i	−1.42256	+	1.18570i
$964$	−9.08846	+	5.24722i	−0.292719	+	0.169002i
$965$	9.64402	+	16.7039i	0.310452	+	0.537719i
$966$	−0.0582503	+	12.1590i	−0.00187417	+	0.391210i
$967$	3.11725	−	5.39923i	0.100244	−	0.173627i	−0.811541	−	0.584295i	$-0.801371\pi$
$967$	3.11725	−	5.39923i	0.100244	−	0.173627i	0.911785	+	0.410668i	$0.134704\pi$
$968$			20.0652i			0.644919i
$969$	−2.60998	−	30.4091i	−0.0838447	−	0.976881i
$970$	11.4679			0.368211
$971$	19.6863	+	34.0977i	0.631764	+	1.09425i	0.987191	+	0.159544i	$0.0510023\pi$
$971$	19.6863	+	34.0977i	0.631764	+	1.09425i	−0.355426	+	0.934704i	$0.615664\pi$
$972$	−12.6952	−	9.04604i	−0.407200	−	0.290152i
$973$	31.9570	+	2.89712i	1.02449	+	0.0928774i
$974$	−18.3306	+	10.5832i	−0.587349	+	0.339106i
$975$	27.7443	+	12.9931i	0.888529	+	0.416111i
$976$	4.47927	−	2.58611i	0.143378	−	0.0827793i
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	−0.0796807	−	0.996820i	$-0.525390\pi$
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	0.823431	+	0.567416i	$0.192057\pi$
$978$	−1.10242	−	12.8444i	−0.0352514	−	0.410717i
$979$	19.8685	−	11.4711i	0.635001	−	0.366618i
$980$	6.66087	+	1.21772i	0.212774	+	0.0388986i
$981$	−19.9235	+	54.1832i	−0.636108	+	1.72994i
$982$	−18.6731	−	32.3428i	−0.595884	−	1.03210i
$983$	11.9691			0.381756			0.190878	−	0.981614i	$-0.438866\pi$
$983$	11.9691			0.381756			0.190878	+	0.981614i	$0.438866\pi$
$984$	−0.256885	−	0.120303i	−0.00818921	−	0.00383513i
$985$		−	4.47445i		−	0.142568i
$986$	10.5044	−	18.1942i	0.334530	−	0.579423i
$987$	0.208339	−	43.4882i	0.00663151	−	1.38424i
$988$	9.71873	+	16.8333i	0.309194	+	0.535540i
$989$	19.9935	−	11.5432i	0.635755	−	0.367053i
$990$	−5.58204	+	15.1807i	−0.177409	+	0.482475i
$991$	−5.40420	+	9.36036i	−0.171670	+	0.297342i	−0.939004	−	0.343906i	$-0.888250\pi$
$991$	−5.40420	+	9.36036i	−0.171670	+	0.297342i	0.767334	+	0.641248i	$0.221583\pi$
$992$	−3.08327	+	5.34038i	−0.0978940	+	0.169557i
$993$	−0.556660	+	1.18864i	−0.0176651	+	0.0377205i
$994$	0.869525	−	9.59137i	0.0275797	−	0.304220i
$995$	−17.5109	−	10.1099i	−0.555132	−	0.320506i
$996$	6.18487	−	13.2067i	0.195975	−	0.418469i
$997$		−	13.4700i		−	0.426598i	−0.976987	−	0.213299i	$-0.931579\pi$
$997$		−	13.4700i		−	0.426598i	0.976987	−	0.213299i	$-0.0684208\pi$
$998$	−23.7462	−	13.7099i	−0.751672	−	0.433978i
$999$	−1.78128	−	1.79897i	−0.0563572	−	0.0569170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.t.a.59.1	yes	16
3.2	odd	2		378.2.t.a.17.6		16
4.3	odd	2		1008.2.df.c.689.7		16
7.2	even	3		882.2.l.b.509.6		16
7.3	odd	6		882.2.m.b.293.6		16
7.4	even	3		882.2.m.a.293.7		16
7.5	odd	6		126.2.l.a.5.7	✓	16
7.6	odd	2		882.2.t.a.815.4		16
9.2	odd	6		126.2.l.a.101.3	yes	16
9.4	even	3		1134.2.k.b.647.6		16
9.5	odd	6		1134.2.k.a.647.3		16
9.7	even	3		378.2.l.a.143.6		16
12.11	even	2		3024.2.df.c.17.4		16
21.2	odd	6		2646.2.l.a.1097.3		16
21.5	even	6		378.2.l.a.341.2		16
21.11	odd	6		2646.2.m.a.881.3		16
21.17	even	6		2646.2.m.b.881.2		16
21.20	even	2		2646.2.t.b.2285.7		16
28.19	even	6		1008.2.ca.c.257.5		16
36.7	odd	6		3024.2.ca.c.2033.4		16
36.11	even	6		1008.2.ca.c.353.5		16
63.2	odd	6		882.2.t.a.803.4		16
63.5	even	6		1134.2.k.b.971.6		16
63.11	odd	6		882.2.m.b.587.6		16
63.16	even	3		2646.2.t.b.1979.7		16
63.20	even	6		882.2.l.b.227.2		16
63.25	even	3		2646.2.m.b.1763.2		16
63.34	odd	6		2646.2.l.a.521.7		16
63.38	even	6		882.2.m.a.587.7		16
63.40	odd	6		1134.2.k.a.971.3		16
63.47	even	6	inner	126.2.t.a.47.1	yes	16
63.52	odd	6		2646.2.m.a.1763.3		16
63.61	odd	6		378.2.t.a.89.6		16
84.47	odd	6		3024.2.ca.c.2609.4		16
252.47	odd	6		1008.2.df.c.929.7		16
252.187	even	6		3024.2.df.c.1601.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	7.5	odd	6
126.2.l.a.101.3	yes	16	9.2	odd	6
126.2.t.a.47.1	yes	16	63.47	even	6	inner
126.2.t.a.59.1	yes	16	1.1	even	1	trivial
378.2.l.a.143.6		16	9.7	even	3
378.2.l.a.341.2		16	21.5	even	6
378.2.t.a.17.6		16	3.2	odd	2
378.2.t.a.89.6		16	63.61	odd	6
882.2.l.b.227.2		16	63.20	even	6
882.2.l.b.509.6		16	7.2	even	3
882.2.m.a.293.7		16	7.4	even	3
882.2.m.a.587.7		16	63.38	even	6
882.2.m.b.293.6		16	7.3	odd	6
882.2.m.b.587.6		16	63.11	odd	6
882.2.t.a.803.4		16	63.2	odd	6
882.2.t.a.815.4		16	7.6	odd	2
1008.2.ca.c.257.5		16	28.19	even	6
1008.2.ca.c.353.5		16	36.11	even	6
1008.2.df.c.689.7		16	4.3	odd	2
1008.2.df.c.929.7		16	252.47	odd	6
1134.2.k.a.647.3		16	9.5	odd	6
1134.2.k.a.971.3		16	63.40	odd	6
1134.2.k.b.647.6		16	9.4	even	3
1134.2.k.b.971.6		16	63.5	even	6
2646.2.l.a.521.7		16	63.34	odd	6
2646.2.l.a.1097.3		16	21.2	odd	6
2646.2.m.a.881.3		16	21.11	odd	6
2646.2.m.a.1763.3		16	63.52	odd	6
2646.2.m.b.881.2		16	21.17	even	6
2646.2.m.b.1763.2		16	63.25	even	3
2646.2.t.b.1979.7		16	63.16	even	3
2646.2.t.b.2285.7		16	21.20	even	2
3024.2.ca.c.2033.4		16	36.7	odd	6
3024.2.ca.c.2609.4		16	84.47	odd	6
3024.2.df.c.17.4		16	12.11	even	2
3024.2.df.c.1601.4		16	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72571 + 0.148116i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.967324 q^{5} +(1.56856 + 0.734581i) q^{6} +(2.40137 - 1.11060i) q^{7} -1.00000i q^{8} +(2.95612 - 0.511208i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72571 + 0.148116i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.967324 q^{5} +(1.56856 + 0.734581i) q^{6} +(2.40137 - 1.11060i) q^{7} -1.00000i q^{8} +(2.95612 - 0.511208i) q^{9} +(-0.837727 - 0.483662i) q^{10} -5.57361i q^{11} +(-0.991125 - 1.42045i) q^{12} +(3.76893 + 2.17600i) q^{13} +(-2.63495 - 0.238876i) q^{14} +(-1.66932 + 0.143276i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.97267 + 3.41677i) q^{17} +(-2.81568 - 1.03534i) q^{18} +(3.86796 - 2.23317i) q^{19} +(0.483662 + 0.837727i) q^{20} +(-3.97956 + 2.27225i) q^{21} +(-2.78681 + 4.82689i) q^{22} +2.65334i q^{23} +(0.148116 + 1.72571i) q^{24} -4.06428 q^{25} +(-2.17600 - 3.76893i) q^{26} +(-5.02568 + 1.32004i) q^{27} +(2.16249 + 1.52435i) q^{28} +(4.61157 - 2.66249i) q^{29} +(1.51731 + 0.710578i) q^{30} +(-5.34038 + 3.08327i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.825539 + 9.61842i) q^{33} +(3.41677 - 1.97267i) q^{34} +(2.32290 - 1.07431i) q^{35} +(1.92078 + 2.30447i) q^{36} +(0.243608 + 0.421942i) q^{37} -4.46634 q^{38} +(-6.82637 - 3.19689i) q^{39} -0.967324i q^{40} +(-0.0818856 + 0.141830i) q^{41} +(4.58252 + 0.0219535i) q^{42} +(-4.35045 - 7.53520i) q^{43} +(4.82689 - 2.78681i) q^{44} +(2.85953 - 0.494504i) q^{45} +(1.32667 - 2.29786i) q^{46} +(-4.74500 + 8.21859i) q^{47} +(0.734581 - 1.56856i) q^{48} +(4.53314 - 5.33392i) q^{49} +(3.51977 + 2.03214i) q^{50} +(2.89818 - 6.18852i) q^{51} +4.35199i q^{52} +(1.74520 + 1.00759i) q^{53} +(5.01239 + 1.36965i) q^{54} -5.39149i q^{55} +(-1.11060 - 2.40137i) q^{56} +(-6.34420 + 4.42670i) q^{57} -5.32498 q^{58} +(0.836931 + 1.44961i) q^{59} +(-0.958739 - 1.37403i) q^{60} +(-4.47927 - 2.58611i) q^{61} +6.16655 q^{62} +(6.53099 - 4.51067i) q^{63} -1.00000 q^{64} +(3.64578 + 2.10489i) q^{65} +(4.09427 - 8.74256i) q^{66} +(2.72126 + 4.71336i) q^{67} -3.94535 q^{68} +(-0.393002 - 4.57889i) q^{69} +(-2.54885 - 0.231071i) q^{70} +3.64006i q^{71} +(-0.511208 - 2.95612i) q^{72} +(-2.15468 - 1.24401i) q^{73} -0.487217i q^{74} +(7.01376 - 0.601984i) q^{75} +(3.86796 + 2.23317i) q^{76} +(-6.19005 - 13.3843i) q^{77} +(4.31337 + 6.18177i) q^{78} +(-2.30121 + 3.98581i) q^{79} +(-0.483662 + 0.837727i) q^{80} +(8.47733 - 3.02239i) q^{81} +(0.141830 - 0.0818856i) q^{82} +(4.20979 + 7.29158i) q^{83} +(-3.95760 - 2.31027i) q^{84} +(-1.90821 + 3.30512i) q^{85} +8.70089i q^{86} +(-7.56386 + 5.27772i) q^{87} -5.57361 q^{88} +(2.05811 + 3.56475i) q^{89} +(-2.72368 - 1.00151i) q^{90} +(11.4673 + 1.03959i) q^{91} +(-2.29786 + 1.32667i) q^{92} +(8.75925 - 6.11182i) q^{93} +(8.21859 - 4.74500i) q^{94} +(3.74157 - 2.16020i) q^{95} +(-1.42045 + 0.991125i) q^{96} +(-10.2669 + 5.92762i) q^{97} +(-6.59277 + 2.35274i) q^{98} +(-2.84928 - 16.4763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31} + 18 q^{33} - 30 q^{35} - 2 q^{37} - 30 q^{39} + 6 q^{41} + 30 q^{42} - 2 q^{43} + 12 q^{44} + 12 q^{45} + 6 q^{46} - 18 q^{47} + 10 q^{49} - 12 q^{50} + 36 q^{53} + 18 q^{54} + 6 q^{57} - 12 q^{58} + 30 q^{59} - 6 q^{60} - 60 q^{61} - 36 q^{62} + 42 q^{63} - 16 q^{64} + 42 q^{65} + 48 q^{66} + 14 q^{67} + 36 q^{68} + 42 q^{69} + 30 q^{75} - 18 q^{77} - 16 q^{79} + 54 q^{81} - 18 q^{84} - 12 q^{85} - 48 q^{87} + 24 q^{89} - 18 q^{90} - 12 q^{91} + 6 q^{92} + 30 q^{93} - 66 q^{95} - 6 q^{96} - 6 q^{97} + 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

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