LMFDB - Embedded newform 126.2.l.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(5,126)]

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([5, 5]))

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

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

chi := DirichletCharacter("126.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.l (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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.7
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	126.5
Dual form			126.2.l.a.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.734581 + 1.56856i) q^{3} -1.00000 q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 - 0.734581i) q^{6} +(-2.16249 + 1.52435i) q^{7} -1.00000i q^{8} +(-1.92078 - 2.30447i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.734581 + 1.56856i) q^{3} -1.00000 q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 - 0.734581i) q^{6} +(-2.16249 + 1.52435i) q^{7} -1.00000i q^{8} +(-1.92078 - 2.30447i) q^{9} +(-0.837727 + 0.483662i) q^{10} +(4.82689 + 2.78681i) q^{11} +(0.734581 - 1.56856i) q^{12} +(-3.76893 - 2.17600i) q^{13} +(-1.52435 - 2.16249i) q^{14} +(-1.66932 + 0.143276i) q^{15} +1.00000 q^{16} +(1.97267 + 3.41677i) q^{17} +(2.30447 - 1.92078i) q^{18} +(3.86796 + 2.23317i) q^{19} +(-0.483662 - 0.837727i) q^{20} +(-0.802507 - 4.51176i) q^{21} +(-2.78681 + 4.82689i) q^{22} +(2.29786 - 1.32667i) q^{23} +(1.56856 + 0.734581i) q^{24} +(2.03214 - 3.51977i) 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} +(-0.143276 - 1.66932i) q^{30} +6.16655i q^{31} +1.00000i q^{32} +(-7.91702 + 5.52415i) 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} +(-2.23317 + 3.86796i) q^{38} +(6.18177 - 4.31337i) q^{39} +(0.837727 - 0.483662i) q^{40} +(0.0818856 - 0.141830i) q^{41} +(4.51176 - 0.802507i) q^{42} +(-4.35045 - 7.53520i) q^{43} +(-4.82689 - 2.78681i) q^{44} +(1.00151 - 2.72368i) q^{45} +(1.32667 + 2.29786i) q^{46} -9.49001 q^{47} +(-0.734581 + 1.56856i) q^{48} +(2.35274 - 6.59277i) q^{49} +(3.51977 + 2.03214i) q^{50} +(-6.80851 + 0.584367i) q^{51} +(3.76893 + 2.17600i) q^{52} +(-1.74520 + 1.00759i) q^{53} +(1.32004 + 5.02568i) q^{54} +5.39149i q^{55} +(1.52435 + 2.16249i) q^{56} +(-6.34420 + 4.42670i) q^{57} +(2.66249 + 4.61157i) q^{58} +1.67386 q^{59} +(1.66932 - 0.143276i) q^{60} -5.17221i q^{61} -6.16655 q^{62} +(7.66649 + 2.05547i) q^{63} -1.00000 q^{64} -4.20979i q^{65} +(-5.52415 - 7.91702i) q^{66} -5.44252 q^{67} +(-1.97267 - 3.41677i) q^{68} +(0.393002 + 4.57889i) q^{69} +(1.07431 - 2.32290i) q^{70} +3.64006i q^{71} +(-2.30447 + 1.92078i) q^{72} +(-2.15468 + 1.24401i) q^{73} +(0.421942 + 0.243608i) q^{74} +(4.02821 + 5.77310i) q^{75} +(-3.86796 - 2.23317i) q^{76} +(-14.6862 + 1.33140i) q^{77} +(4.31337 + 6.18177i) q^{78} +4.60242 q^{79} +(0.483662 + 0.837727i) q^{80} +(-1.62120 + 8.85278i) q^{81} +(0.141830 + 0.0818856i) q^{82} +(-4.20979 - 7.29158i) q^{83} +(0.802507 + 4.51176i) q^{84} +(-1.90821 + 3.30512i) q^{85} +(7.53520 - 4.35045i) q^{86} +(0.788713 + 9.18936i) q^{87} +(2.78681 - 4.82689i) 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} +(-9.67262 - 4.52983i) q^{93} -9.49001i q^{94} +4.32040i q^{95} +(-1.56856 - 0.734581i) 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 - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^7	$ 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.734581	+	1.56856i	−0.424111	+	0.905610i
$3$	−0.734581	+	1.56856i	−0.424111	+	0.905610i
$4$	−1.00000			−0.500000
$5$	0.483662	+	0.837727i	0.216300	+	0.374643i	0.953674	−	0.300842i	$-0.0972677\pi$
$5$	0.483662	+	0.837727i	0.216300	+	0.374643i	−0.737374	+	0.675485i	$0.763934\pi$
$6$	−1.56856	−	0.734581i	−0.640363	−	0.299892i
$7$	−2.16249	+	1.52435i	−0.817345	+	0.576149i
$7$	−2.16249	+	1.52435i	−0.817345	+	0.576149i
$8$		−	1.00000i		−	0.353553i
$9$	−1.92078	−	2.30447i	−0.640260	−	0.768158i
$10$	−0.837727	+	0.483662i	−0.264913	+	0.152947i
$11$	4.82689	+	2.78681i	1.45536	+	0.840254i	0.998778	−	0.0494264i	$-0.0157393\pi$
$11$	4.82689	+	2.78681i	1.45536	+	0.840254i	0.456584	+	0.889680i	$0.349073\pi$
$12$	0.734581	−	1.56856i	0.212055	−	0.452805i
$13$	−3.76893	−	2.17600i	−1.04531	−	0.603512i	−0.123980	−	0.992285i	$-0.539566\pi$
$13$	−3.76893	−	2.17600i	−1.04531	−	0.603512i	−0.921334	+	0.388772i	$0.872899\pi$
$14$	−1.52435	−	2.16249i	−0.407399	−	0.577950i
$15$	−1.66932	+	0.143276i	−0.431016	+	0.0369937i
$16$	1.00000			0.250000
$17$	1.97267	+	3.41677i	0.478443	+	0.828688i	0.999695	−	0.0247150i	$-0.00786784\pi$
$17$	1.97267	+	3.41677i	0.478443	+	0.828688i	−0.521251	+	0.853403i	$0.674535\pi$
$18$	2.30447	−	1.92078i	0.543170	−	0.452732i
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.873082	−	0.487574i	$-0.162118\pi$
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.0142896	+	0.999898i	$0.495451\pi$
$20$	−0.483662	−	0.837727i	−0.108150	−	0.187322i
$21$	−0.802507	−	4.51176i	−0.175121	−	0.984547i
$22$	−2.78681	+	4.82689i	−0.594149	+	1.02910i
$23$	2.29786	−	1.32667i	0.479137	−	0.276630i	−0.240920	−	0.970545i	$-0.577449\pi$
$23$	2.29786	−	1.32667i	0.479137	−	0.276630i	0.720057	+	0.693915i	$0.244116\pi$
$24$	1.56856	+	0.734581i	0.320182	+	0.149946i
$25$	2.03214	−	3.51977i	0.406428	−	0.703955i
$26$	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	$0.168717\pi$
$30$	−0.143276	−	1.66932i	−0.0261585	−	0.304774i
$31$			6.16655i			1.10754i	0.832668	+	0.553772i	$0.186812\pi$
$31$			6.16655i			1.10754i	−0.832668	+	0.553772i	$0.813188\pi$
$32$			1.00000i			0.176777i
$33$	−7.91702	+	5.52415i	−1.37818	+	0.961631i
$34$	−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	−0.845306	−	0.534282i	$-0.820582\pi$
$37$	0.243608	−	0.421942i	0.0400490	−	0.0693669i	0.885355	+	0.464915i	$0.153915\pi$
$38$	−2.23317	+	3.86796i	−0.362268	+	0.627466i
$39$	6.18177	−	4.31337i	0.989876	−	0.690691i
$40$	0.837727	−	0.483662i	0.132456	−	0.0764737i
$41$	0.0818856	−	0.141830i	0.0127884	−	0.0221501i	−0.859560	−	0.511034i	$-0.829263\pi$
$41$	0.0818856	−	0.141830i	0.0127884	−	0.0221501i	0.872349	+	0.488884i	$0.162596\pi$
$42$	4.51176	−	0.802507i	0.696180	−	0.123829i
$43$	−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
$45$	1.00151	−	2.72368i	0.149297	−	0.406022i
$46$	1.32667	+	2.29786i	0.195607	+	0.338801i
$47$	−9.49001			−1.38426			−0.692130	−	0.721773i	$-0.743328\pi$
$47$	−9.49001			−1.38426			−0.692130	+	0.721773i	$0.743328\pi$
$48$	−0.734581	+	1.56856i	−0.106028	+	0.226403i
$49$	2.35274	−	6.59277i	0.336106	−	0.941824i
$50$	3.51977	+	2.03214i	0.497771	+	0.287388i
$51$	−6.80851	+	0.584367i	−0.953382	+	0.0818278i
$52$	3.76893	+	2.17600i	0.522657	+	0.301756i
$53$	−1.74520	+	1.00759i	−0.239722	+	0.138403i	−0.615049	−	0.788489i	$-0.710864\pi$
$53$	−1.74520	+	1.00759i	−0.239722	+	0.138403i	0.375327	+	0.926892i	$0.377530\pi$
$54$	1.32004	+	5.02568i	0.179635	+	0.683909i
$55$			5.39149i			0.726988i
$56$	1.52435	+	2.16249i	0.203699	+	0.288975i
$57$	−6.34420	+	4.42670i	−0.840310	+	0.586331i
$58$	2.66249	+	4.61157i	0.349602	+	0.605529i
$59$	1.67386			0.217918			0.108959	−	0.994046i	$-0.465248\pi$
$59$	1.67386			0.217918			0.108959	+	0.994046i	$0.465248\pi$
$60$	1.66932	−	0.143276i	0.215508	−	0.0184968i
$61$		−	5.17221i		−	0.662234i	−0.943590	−	0.331117i	$-0.892574\pi$
$61$		−	5.17221i		−	0.662234i	0.943590	−	0.331117i	$-0.107426\pi$
$62$	−6.16655			−0.783152
$63$	7.66649	+	2.05547i	0.965887	+	0.258965i
$64$	−1.00000			−0.125000
$65$		−	4.20979i		−	0.522160i
$66$	−5.52415	−	7.91702i	−0.679975	−	0.974518i
$67$	−5.44252			−0.664909			−0.332455	−	0.943119i	$-0.607877\pi$
$67$	−5.44252			−0.664909			−0.332455	+	0.943119i	$0.607877\pi$
$68$	−1.97267	−	3.41677i	−0.239222	−	0.414344i
$69$	0.393002	+	4.57889i	0.0473118	+	0.551234i
$70$	1.07431	−	2.32290i	0.128405	−	0.277640i
$71$			3.64006i			0.431996i	0.976394	+	0.215998i	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$	−2.30447	+	1.92078i	−0.271585	+	0.226366i
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	−0.620765	−	0.783997i	$-0.713178\pi$
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	0.368579	+	0.929597i	$0.379845\pi$
$74$	0.421942	+	0.243608i	0.0490498	+	0.0283189i
$75$	4.02821	+	5.77310i	0.465138	+	0.666620i
$76$	−3.86796	−	2.23317i	−0.443686	−	0.256162i
$77$	−14.6862	+	1.33140i	−1.67364	+	0.151728i
$78$	4.31337	+	6.18177i	0.488393	+	0.699948i
$79$	4.60242			0.517812			0.258906	−	0.965902i	$-0.416638\pi$
$79$	4.60242			0.517812			0.258906	+	0.965902i	$0.416638\pi$
$80$	0.483662	+	0.837727i	0.0540751	+	0.0936608i
$81$	−1.62120	+	8.85278i	−0.180133	+	0.983642i
$82$	0.141830	+	0.0818856i	0.0156625	+	0.00904275i
$83$	−4.20979	−	7.29158i	−0.462085	−	0.800355i	0.536980	−	0.843595i	$-0.319565\pi$
$83$	−4.20979	−	7.29158i	−0.462085	−	0.800355i	−0.999065	+	0.0432405i	$0.986232\pi$
$84$	0.802507	+	4.51176i	0.0875607	+	0.492273i
$85$	−1.90821	+	3.30512i	−0.206975	+	0.358491i
$86$	7.53520	−	4.35045i	0.812541	−	0.469121i
$87$	0.788713	+	9.18936i	0.0845589	+	0.985202i
$88$	2.78681	−	4.82689i	0.297075	−	0.514548i
$89$	−2.05811	+	3.56475i	−0.218159	+	0.377863i	−0.954245	−	0.299025i	$-0.903338\pi$
$89$	−2.05811	+	3.56475i	−0.218159	+	0.377863i	0.736086	+	0.676888i	$0.236672\pi$
$90$	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
$93$	−9.67262	−	4.52983i	−1.00300	−	0.469721i
$94$		−	9.49001i		−	0.978820i
$95$			4.32040i			0.443263i
$96$	−1.56856	−	0.734581i	−0.160091	−	0.0749729i
$97$	10.2669	−	5.92762i	1.04245	−	0.601859i	0.121924	−	0.992539i	$-0.461094\pi$
$97$	10.2669	−	5.92762i	1.04245	−	0.601859i	0.920526	+	0.390681i	$0.127760\pi$
$98$	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
$101$	2.65813	−	4.60402i	0.264494	−	0.458117i	−0.702937	−	0.711252i	$-0.748128\pi$
$101$	2.65813	−	4.60402i	0.264494	−	0.458117i	0.967431	+	0.253135i	$0.0814618\pi$
$102$	−0.584367	−	6.80851i	−0.0578610	−	0.674143i
$103$	7.74616	−	4.47225i	0.763252	−	0.440664i	−0.0672102	−	0.997739i	$-0.521410\pi$
$103$	7.74616	−	4.47225i	0.763252	−	0.440664i	0.830462	+	0.557075i	$0.188076\pi$
$104$	−2.17600	+	3.76893i	−0.213374	+	0.369574i
$105$	3.39148	−	2.85445i	0.330975	−	0.278566i
$106$	−1.00759	−	1.74520i	−0.0978659	−	0.169509i
$107$	16.5898	+	9.57813i	1.60380	+	0.925953i	0.990718	+	0.135931i	$0.0434026\pi$
$107$	16.5898	+	9.57813i	1.60380	+	0.925953i	0.613079	+	0.790022i	$0.289931\pi$
$108$	−5.02568	+	1.32004i	−0.483597	+	0.127021i
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.796955	−	0.604038i	$-0.793557\pi$
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.124635	−	0.992203i	$-0.539776\pi$
$110$	−5.39149			−0.514058
$111$	0.482893	+	0.692066i	0.0458342	+	0.0656880i
$112$	−2.16249	+	1.52435i	−0.204336	+	0.144037i
$113$	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	$0.536672\pi$
$114$	−4.42670	−	6.34420i	−0.414598	−	0.594189i
$115$	2.22278	+	1.28332i	0.207275	+	0.119670i
$116$	−4.61157	+	2.66249i	−0.428174	+	0.247206i
$117$	2.22477	+	12.8650i	0.205680	+	1.18937i
$118$			1.67386i			0.154091i
$119$	−9.47423	−	4.38170i	−0.868501	−	0.401670i
$120$	0.143276	+	1.66932i	0.0130792	+	0.152387i
$121$	10.0326	+	17.3769i	0.912053	+	1.57972i
$122$	5.17221			0.468270
$123$	0.162318	+	0.232628i	0.0146357	+	0.0209754i
$124$		−	6.16655i		−	0.553772i
$125$	8.76810			0.784243
$126$	−2.05547	+	7.66649i	−0.183116	+	0.682985i
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	15.0152	−	1.28874i	1.32201	−	0.113467i
$130$	4.20979			0.369223
$131$	−9.37335	−	16.2351i	−0.818954	−	1.41847i	−0.906454	−	0.422305i	$-0.861221\pi$
$131$	−9.37335	−	16.2351i	−0.818954	−	1.41847i	0.0875000	−	0.996165i	$-0.472112\pi$
$132$	7.91702	−	5.52415i	0.689089	−	0.480815i
$133$	−11.7686	+	1.06690i	−1.02046	+	0.0925121i
$134$		−	5.44252i		−	0.470162i
$135$	3.53657	+	3.57170i	0.304379	+	0.307403i
$136$	3.41677	−	1.97267i	0.292986	−	0.169155i
$137$	14.6656	+	8.46717i	1.25296	+	0.723399i	0.971697	−	0.236230i	$-0.0759120\pi$
$137$	14.6656	+	8.46717i	1.25296	+	0.723399i	0.281267	+	0.959630i	$0.409245\pi$
$138$	−4.57889	+	0.393002i	−0.389781	+	0.0334545i
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.0166466	−	0.999861i	$-0.505299\pi$
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.874229	+	0.485514i	$0.838632\pi$
$140$	2.32290	+	1.07431i	0.196321	+	0.0907958i
$141$	6.97118	−	14.8857i	0.587079	−	1.25360i
$142$	−3.64006			−0.305467
$143$	−12.1282	−	21.0066i	−1.01421	−	1.75666i
$144$	−1.92078	−	2.30447i	−0.160065	−	0.192039i
$145$	4.46088	+	2.57549i	0.370456	+	0.213883i
$146$	−1.24401	−	2.15468i	−0.102955	−	0.178323i
$147$	8.61290	+	8.53335i	0.710380	+	0.703819i
$148$	−0.243608	+	0.421942i	−0.0200245	+	0.0346834i
$149$	−7.56951	+	4.37026i	−0.620118	+	0.358025i	−0.776915	−	0.629606i	$-0.783217\pi$
$149$	−7.56951	+	4.37026i	−0.620118	+	0.358025i	0.156797	+	0.987631i	$0.449883\pi$
$150$	−5.77310	+	4.02821i	−0.471372	+	0.328902i
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.0702195	+	0.997532i	$0.522370\pi$
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.828778	+	0.559578i	$0.810963\pi$
$152$	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
$156$	−6.18177	+	4.31337i	−0.494938	+	0.345346i
$157$		−	1.42457i		−	0.113693i	−0.998383	−	0.0568467i	$-0.981895\pi$
$157$		−	1.42457i		−	0.113693i	0.998383	−	0.0568467i	$-0.0181046\pi$
$158$			4.60242i			0.366149i
$159$	−0.298480	−	3.47761i	−0.0236710	−	0.275793i
$160$	−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	−0.974162	−	0.225851i	$-0.927484\pi$
$163$	−3.72148	+	6.44579i	−0.291489	+	0.504873i	0.682673	+	0.730724i	$0.260817\pi$
$164$	−0.0818856	+	0.141830i	−0.00639419	+	0.0110751i
$165$	−8.45689	−	3.96049i	−0.658368	−	0.308323i
$166$	7.29158	−	4.20979i	0.565936	−	0.326743i
$167$	−3.24855	+	5.62665i	−0.251380	+	0.435404i	−0.963906	−	0.266242i	$-0.914218\pi$
$167$	−3.24855	+	5.62665i	−0.251380	+	0.435404i	0.712526	+	0.701646i	$0.247551\pi$
$168$	−4.51176	+	0.802507i	−0.348090	+	0.0619147i
$169$	2.96991	+	5.14404i	0.228455	+	0.395695i
$170$	−3.30512	−	1.90821i	−0.253491	−	0.146353i
$171$	−2.28323	−	13.2030i	−0.174603	−	1.00966i
$172$	4.35045	+	7.53520i	0.331718	+	0.574553i
$173$	11.8188			0.898564			0.449282	−	0.893390i	$-0.351680\pi$
$173$	11.8188			0.898564			0.449282	+	0.893390i	$0.351680\pi$
$174$	−9.18936	+	0.788713i	−0.696643	+	0.0597922i
$175$	0.970861	+	10.7092i	0.0733902	+	0.809537i
$176$	4.82689	+	2.78681i	0.363841	+	0.210063i
$177$	−1.22959	+	2.62556i	−0.0924215	+	0.197349i
$178$	−3.56475	−	2.05811i	−0.267189	−	0.154262i
$179$	−2.10764	+	1.21685i	−0.157533	+	0.0909515i	−0.576694	−	0.816960i	$-0.695657\pi$
$179$	−2.10764	+	1.21685i	−0.157533	+	0.0909515i	0.419161	+	0.907912i	$0.362324\pi$
$180$	−1.00151	+	2.72368i	−0.0746483	+	0.203011i
$181$			11.5342i			0.857327i	0.903464	+	0.428663i	$0.141015\pi$
$181$			11.5342i			0.857327i	−0.903464	+	0.428663i	$0.858985\pi$
$182$	1.03959	+	11.4673i	0.0770593	+	0.850010i
$183$	8.11294	+	3.79941i	0.599726	+	0.280861i
$184$	−1.32667	−	2.29786i	−0.0978035	−	0.169401i
$185$	0.471297			0.0346504
$186$	4.52983	−	9.67262i	0.332143	−	0.709231i
$187$			21.9898i			1.60806i
$188$	9.49001			0.692130
$189$	−8.85579	+	10.5155i	−0.644164	+	0.764887i
$190$	−4.32040			−0.313435
$191$		−	22.0689i		−	1.59685i	−0.602094	−	0.798425i	$-0.705667\pi$
$191$		−	22.0689i		−	1.59685i	0.602094	−	0.798425i	$-0.294333\pi$
$192$	0.734581	−	1.56856i	0.0530138	−	0.113201i
$193$	−19.9396			−1.43528			−0.717641	−	0.696413i	$-0.754778\pi$
$193$	−19.9396			−1.43528			−0.717641	+	0.696413i	$0.754778\pi$
$194$	5.92762	+	10.2669i	0.425578	+	0.737123i
$195$	6.60331	+	3.09243i	0.472873	+	0.221453i
$196$	−2.35274	+	6.59277i	−0.168053	+	0.470912i
$197$		−	4.62560i		−	0.329560i	−0.986330	−	0.164780i	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$	16.4763	−	2.84928i	1.17092	−	0.202489i
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.977440	−	0.211212i	$-0.932259\pi$
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.305805	+	0.952094i	$0.598925\pi$
$200$	−3.51977	−	2.03214i	−0.248886	−	0.143694i
$201$	3.99797	−	8.53693i	0.281995	−	0.602149i
$202$	4.60402	+	2.65813i	0.323938	+	0.187025i
$203$	−5.91393	+	12.7872i	−0.415076	+	0.897489i
$204$	6.80851	−	0.584367i	0.476691	−	0.0409139i
$205$	0.158420			0.0110645
$206$	4.47225	+	7.74616i	0.311596	+	0.539701i
$207$	−7.47097	−	2.74712i	−0.519268	−	0.190938i
$208$	−3.76893	−	2.17600i	−0.261329	−	0.150878i
$209$	12.4468	+	21.5585i	0.860965	+	1.49123i
$210$	2.85445	+	3.39148i	0.196976	+	0.234035i
$211$	−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	$0.240588\pi$
$212$	1.74520	−	1.00759i	0.119861	−	0.0692017i
$213$	−5.70967	−	2.67392i	−0.391220	−	0.183214i
$214$	−9.57813	+	16.5898i	−0.654747	+	1.13406i
$215$	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
$219$	−0.368514	−	4.29358i	−0.0249018	−	0.290133i
$220$		−	5.39149i		−	0.363494i
$221$		−	17.1701i		−	1.15499i
$222$	−0.692066	+	0.482893i	−0.0464484	+	0.0324097i
$223$	7.08622	−	4.09123i	0.474528	−	0.273969i	−0.243605	−	0.969875i	$-0.578330\pi$
$223$	7.08622	−	4.09123i	0.474528	−	0.273969i	0.718133	+	0.695905i	$0.244997\pi$
$224$	−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
$227$	−5.34688	+	9.26106i	−0.354885	+	0.614678i	−0.987098	−	0.160116i	$-0.948813\pi$
$227$	−5.34688	+	9.26106i	−0.354885	+	0.614678i	0.632214	+	0.774794i	$0.282147\pi$
$228$	6.34420	−	4.42670i	0.420155	−	0.293165i
$229$	25.2942	−	14.6036i	1.67149	−	0.965034i	0.704682	−	0.709524i	$-0.251090\pi$
$229$	25.2942	−	14.6036i	1.67149	−	0.965034i	0.966806	−	0.255510i	$-0.0822435\pi$
$230$	−1.28332	+	2.22278i	−0.0846197	+	0.146566i
$231$	8.69979	−	24.0142i	0.572404	−	1.58002i
$232$	−2.66249	−	4.61157i	−0.174801	−	0.302764i
$233$	5.57664	+	3.21967i	0.365338	+	0.210928i	0.671420	−	0.741077i	$-0.265685\pi$
$233$	5.57664	+	3.21967i	0.365338	+	0.210928i	−0.306082	+	0.952005i	$0.599018\pi$
$234$	−12.8650	+	2.22477i	−0.841013	+	0.145438i
$235$	−4.58996	−	7.95004i	−0.299416	−	0.518603i
$236$	−1.67386			−0.108959
$237$	−3.38085	+	7.21918i	−0.219610	+	0.468936i
$238$	4.38170	−	9.47423i	0.284023	−	0.614123i
$239$	−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	$0.714570\pi$
$240$	−1.66932	+	0.143276i	−0.107754	+	0.00924841i
$241$	9.08846	+	5.24722i	0.585439	+	0.338003i	0.763292	−	0.646054i	$-0.223582\pi$
$241$	9.08846	+	5.24722i	0.585439	+	0.338003i	−0.177853	+	0.984057i	$0.556915\pi$
$242$	−17.3769	+	10.0326i	−1.11703	+	0.644919i
$243$	−12.6952	−	9.04604i	−0.814400	−	0.580304i
$244$			5.17221i			0.331117i
$245$	6.66087	−	1.21772i	0.425548	−	0.0777971i
$246$	−0.232628	+	0.162318i	−0.0148318	+	0.0103490i
$247$	−9.71873	−	16.8333i	−0.618388	−	1.07108i
$248$	6.16655			0.391576
$249$	14.5297	−	1.24707i	0.920785	−	0.0790300i
$250$			8.76810i			0.554543i
$251$	7.85271			0.495659			0.247829	−	0.968804i	$-0.420283\pi$
$251$	7.85271			0.495659			0.247829	+	0.968804i	$0.420283\pi$
$252$	−7.66649	−	2.05547i	−0.482943	−	0.129483i
$253$	14.7887			0.929758
$254$			3.31883i			0.208242i
$255$	−3.78256	−	5.42104i	−0.236873	−	0.339478i
$256$	1.00000			0.0625000
$257$	−1.71568	−	2.97164i	−0.107021	−	0.185366i	0.807541	−	0.589811i	$-0.200798\pi$
$257$	−1.71568	−	2.97164i	−0.107021	−	0.185366i	−0.914562	+	0.404445i	$0.867465\pi$
$258$	1.28874	+	15.0152i	0.0802334	+	0.934805i
$259$	0.116385	+	1.28379i	0.00723178	+	0.0797708i
$260$			4.20979i			0.261080i
$261$	−14.9935	−	5.51318i	−0.928072	−	0.341257i
$262$	16.2351	−	9.37335i	1.00301	−	0.579088i
$263$	−3.17080	−	1.83066i	−0.195520	−	0.112883i	0.399044	−	0.916932i	$-0.369342\pi$
$263$	−3.17080	−	1.83066i	−0.195520	−	0.112883i	−0.594564	+	0.804048i	$0.702675\pi$
$264$	5.52415	+	7.91702i	0.339988	+	0.487259i
$265$	−1.68817	−	0.974668i	−0.103704	−	0.0598734i
$266$	−1.06690	−	11.7686i	−0.0654160	−	0.721577i
$267$	−4.07969	−	5.84687i	−0.249673	−	0.357823i
$268$	5.44252			0.332455
$269$	−6.34303	−	10.9865i	−0.386741	−	0.669856i	0.605268	−	0.796022i	$-0.293066\pi$
$269$	−6.34303	−	10.9865i	−0.386741	−	0.669856i	−0.992009	+	0.126166i	$0.959733\pi$
$270$	−3.57170	+	3.53657i	−0.217367	+	0.215229i
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.124223	−	0.992254i	$-0.539644\pi$
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.921429	+	0.388547i	$0.872977\pi$
$272$	1.97267	+	3.41677i	0.119611	+	0.207172i
$273$	−6.79297	+	18.7508i	−0.411129	+	1.13485i
$274$	−8.46717	+	14.6656i	−0.511520	+	0.885979i
$275$	19.6179	−	11.3264i	1.18300	−	0.683006i
$276$	−0.393002	−	4.57889i	−0.0236559	−	0.275617i
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	−0.731812	−	0.681506i	$-0.761325\pi$
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	0.956108	+	0.293015i	$0.0946585\pi$
$278$	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	$0.564414\pi$
$282$	14.8857	+	6.97118i	0.886429	+	0.415128i
$283$		−	16.1802i		−	0.961815i	−0.876771	−	0.480908i	$-0.840307\pi$
$283$		−	16.1802i		−	0.961815i	0.876771	−	0.480908i	$-0.159693\pi$
$284$		−	3.64006i		−	0.215998i
$285$	−6.77681	−	3.17368i	−0.401424	−	0.187993i
$286$	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
$290$	−2.57549	+	4.46088i	−0.151238	+	0.261952i
$291$	1.75595	+	20.4587i	0.102935	+	1.19931i
$292$	2.15468	−	1.24401i	0.126093	−	0.0727999i
$293$	−4.43406	+	7.68002i	−0.259041	+	0.448672i	−0.965985	−	0.258597i	$-0.916740\pi$
$293$	−4.43406	+	7.68002i	−0.259041	+	0.448672i	0.706944	+	0.707269i	$0.250073\pi$
$294$	−8.53335	+	8.61290i	−0.497675	+	0.502314i
$295$	0.809584	+	1.40224i	0.0471358	+	0.0816416i
$296$	−0.421942	−	0.243608i	−0.0245249	−	0.0141595i
$297$	27.9371	+	7.63390i	1.62108	+	0.442964i
$298$	−4.37026	−	7.56951i	−0.253162	−	0.438490i
$299$	−11.5473			−0.667799
$300$	−4.02821	−	5.77310i	−0.232569	−	0.333310i
$301$	20.8940	+	9.66321i	1.20431	+	0.556978i
$302$	−19.1341	−	11.0471i	−1.10104	−	0.635687i
$303$	5.26908	+	7.55147i	0.302701	+	0.433821i
$304$	3.86796	+	2.23317i	0.221843	+	0.128081i
$305$	4.33290	−	2.50160i	0.248101	−	0.143241i
$306$	11.1088	+	4.08478i	0.635050	+	0.233512i
$307$		−	27.1427i		−	1.54912i	−0.632501	−	0.774559i	$-0.717972\pi$
$307$		−	27.1427i		−	1.54912i	0.632501	−	0.774559i	$-0.282028\pi$
$308$	14.6862	−	1.33140i	0.836822	−	0.0758638i
$309$	1.32482	+	15.4356i	0.0753664	+	0.878099i
$310$	−2.98252	−	5.16588i	−0.169396	−	0.293402i
$311$	16.8955			0.958055			0.479028	−	0.877800i	$-0.340989\pi$
$311$	16.8955			0.958055			0.479028	+	0.877800i	$0.340989\pi$
$312$	−4.31337	−	6.18177i	−0.244196	−	0.349974i
$313$			4.27739i			0.241772i	0.992666	+	0.120886i	$0.0385736\pi$
$313$			4.27739i			0.241772i	−0.992666	+	0.120886i	$0.961426\pi$
$314$	1.42457			0.0803934
$315$	1.98606	+	7.41658i	0.111902	+	0.417877i
$316$	−4.60242			−0.258906
$317$			6.62940i			0.372344i	0.982517	+	0.186172i	$0.0596082\pi$
$317$			6.62940i			0.372344i	−0.982517	+	0.186172i	$0.940392\pi$
$318$	3.47761	−	0.298480i	0.195015	−	0.0167379i
$319$	29.6794			1.66173
$320$	−0.483662	−	0.837727i	−0.0270375	−	0.0468304i
$321$	−27.2105	+	18.9862i	−1.51874	+	1.05971i
$322$	−6.37165	−	2.94680i	−0.355078	−	0.164219i
$323$			17.6212i			0.980472i
$324$	1.62120	−	8.85278i	0.0900667	−	0.491821i
$325$	−15.3180	+	8.84386i	−0.849691	+	0.490569i
$326$	−6.44579	−	3.72148i	−0.356999	−	0.206114i
$327$	33.2084	−	2.85024i	1.83643	−	0.157619i
$328$	−0.141830	−	0.0818856i	−0.00783125	−	0.00452137i
$329$	20.5221	−	14.4661i	1.13142	−	0.797539i
$330$	3.96049	−	8.45689i	0.218018	−	0.465537i
$331$	−0.757792			−0.0416520			−0.0208260	−	0.999783i	$-0.506630\pi$
$331$	−0.757792			−0.0416520			−0.0208260	+	0.999783i	$0.506630\pi$
$332$	4.20979	+	7.29158i	0.231042	+	0.400177i
$333$	−1.44027	+	0.249069i	−0.0789265	+	0.0136489i
$334$	−5.62665	−	3.24855i	−0.307877	−	0.177753i
$335$	−2.63234	−	4.55935i	−0.143820	−	0.249104i
$336$	−0.802507	−	4.51176i	−0.0437803	−	0.246137i
$337$	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	$0.149130\pi$
$338$	−5.14404	+	2.96991i	−0.279799	+	0.161542i
$339$	−11.9931	+	8.36823i	−0.651374	+	0.454500i
$340$	1.90821	−	3.30512i	0.103487	−	0.179245i
$341$	−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
$345$	−3.64578	+	2.54386i	−0.196282	+	0.136957i
$346$			11.8188i			0.635381i
$347$			20.9661i			1.12552i	0.826620	+	0.562761i	$0.190261\pi$
$347$			20.9661i			1.12552i	−0.826620	+	0.562761i	$0.809739\pi$
$348$	−0.788713	−	9.18936i	−0.0422795	−	0.492601i
$349$	−5.36406	+	3.09694i	−0.287132	+	0.165776i	−0.636648	−	0.771155i	$-0.719679\pi$
$349$	−5.36406	+	3.09694i	−0.287132	+	0.165776i	0.349516	+	0.936930i	$0.386346\pi$
$350$	−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
$353$	9.41889	−	16.3140i	0.501317	−	0.868306i	−0.498682	−	0.866785i	$-0.666182\pi$
$353$	9.41889	−	16.3140i	0.501317	−	0.868306i	0.999999	−	0.00152110i	$-0.000484180\pi$
$354$	−2.62556	−	1.22959i	−0.139547	−	0.0653518i
$355$	−3.04938	+	1.76056i	−0.161844	+	0.0934409i
$356$	2.05811	−	3.56475i	0.109080	−	0.188931i
$357$	13.8326	−	11.6422i	0.732097	−	0.616171i
$358$	−1.21685	−	2.10764i	−0.0643124	−	0.111392i
$359$	−24.0735	−	13.8988i	−1.27055	−	0.733553i	−0.295459	−	0.955355i	$-0.595473\pi$
$359$	−24.0735	−	13.8988i	−1.27055	−	0.733553i	−0.975092	+	0.221803i	$0.928806\pi$
$360$	−2.72368	−	1.00151i	−0.143550	−	0.0527843i
$361$	0.474089	+	0.821146i	0.0249520	+	0.0432182i
$362$	−11.5342			−0.606222
$363$	−34.6266	+	2.97196i	−1.81742	+	0.155988i
$364$	−11.4673	+	1.03959i	−0.601048	+	0.0544892i
$365$	−2.08428	−	1.20336i	−0.109096	−	0.0629866i
$366$	−3.79941	+	8.11294i	−0.198598	+	0.424070i
$367$	−18.8390	−	10.8767i	−0.983388	−	0.567759i	−0.0800968	−	0.996787i	$-0.525523\pi$
$367$	−18.8390	−	10.8767i	−0.983388	−	0.567759i	−0.903291	+	0.429028i	$0.858856\pi$
$368$	2.29786	−	1.32667i	0.119784	−	0.0691575i
$369$	−0.484128	+	0.0837212i	−0.0252027	+	0.00435835i
$370$			0.471297i			0.0245016i
$371$	2.23806	−	4.83920i	0.116194	−	0.251239i
$372$	9.67262	+	4.52983i	0.501502	+	0.234861i
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	0.673264	−	0.739402i	$-0.264892\pi$
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	−0.976973	+	0.213362i	$0.931558\pi$
$374$	−21.9898			−1.13707
$375$	−6.44088	+	13.7533i	−0.332606	+	0.710218i
$376$			9.49001i			0.489410i
$377$	−23.1743			−1.19354
$378$	−10.5155	−	8.85579i	−0.540857	−	0.455493i
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$		−	4.32040i		−	0.221632i
$381$	−2.43795	+	5.20579i	−0.124900	+	0.266701i
$382$	22.0689			1.12914
$383$	5.92412	+	10.2609i	0.302708	+	0.524306i	0.976748	−	0.214389i	$-0.0687759\pi$
$383$	5.92412	+	10.2609i	0.302708	+	0.524306i	−0.674040	+	0.738695i	$0.735443\pi$
$384$	1.56856	+	0.734581i	0.0800454	+	0.0374864i
$385$	−8.21849	−	11.6591i	−0.418853	−	0.594200i
$386$		−	19.9396i		−	1.01490i
$387$	−9.00841	+	24.4990i	−0.457923	+	1.24535i
$388$	−10.2669	+	5.92762i	−0.521225	+	0.300929i
$389$	−5.50224	−	3.17672i	−0.278975	−	0.161066i	0.353984	−	0.935251i	$-0.384827\pi$
$389$	−5.50224	−	3.17672i	−0.278975	−	0.161066i	−0.632959	+	0.774185i	$0.718160\pi$
$390$	−3.09243	+	6.60331i	−0.156591	+	0.334372i
$391$	9.06586	+	5.23418i	0.458480	+	0.264704i
$392$	−6.59277	−	2.35274i	−0.332985	−	0.118831i
$393$	32.3513	−	2.77668i	1.63191	−	0.140065i
$394$	4.62560			0.233034
$395$	2.22601	+	3.85557i	0.112003	+	0.193995i
$396$	2.84928	+	16.4763i	0.143182	+	0.827965i
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	0.301924	−	0.953332i	$-0.402371\pi$
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	−0.674648	+	0.738140i	$0.735704\pi$
$398$	−10.4514	−	18.1024i	−0.523883	−	0.907391i
$399$	6.97146	−	19.2435i	0.349009	−	0.963378i
$400$	2.03214	−	3.51977i	0.101607	−	0.175989i
$401$	−20.0216	+	11.5595i	−0.999833	+	0.577254i	−0.908199	−	0.418539i	$-0.862542\pi$
$401$	−20.0216	+	11.5595i	−0.999833	+	0.577254i	−0.0916343	+	0.995793i	$0.529209\pi$
$402$	8.53693	+	3.99797i	0.425784	+	0.199401i
$403$	13.4184	−	23.2413i	0.668417	−	1.15773i
$404$	−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
$408$	0.584367	+	6.80851i	0.0289305	+	0.337071i
$409$			1.55989i			0.0771318i	0.999256	+	0.0385659i	$0.0122790\pi$
$409$			1.55989i			0.0771318i	−0.999256	+	0.0385659i	$0.987721\pi$
$410$			0.158420i			0.00782380i
$411$	−24.0543	+	16.7840i	−1.18651	+	0.827896i
$412$	−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
$416$	2.17600	−	3.76893i	0.106687	−	0.184787i
$417$	17.2274	−	12.0205i	0.843628	−	0.588646i
$418$	−21.5585	+	12.4468i	−1.05446	+	0.608794i
$419$	3.40822	−	5.90321i	0.166502	−	0.288391i	−0.770685	−	0.637216i	$-0.780086\pi$
$419$	3.40822	−	5.90321i	0.166502	−	0.288391i	0.937188	+	0.348825i	$0.113419\pi$
$420$	−3.39148	+	2.85445i	−0.165487	+	0.139283i
$421$	−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
$423$	18.2282	+	21.8695i	0.886287	+	1.06333i
$424$	1.00759	+	1.74520i	0.0489330	+	0.0847544i
$425$	16.0350			0.777812
$426$	2.67392	−	5.70967i	0.129552	−	0.276634i
$427$	7.88424	+	11.1849i	0.381545	+	0.541274i
$428$	−16.5898	−	9.57813i	−0.801899	−	0.462976i
$429$	41.8593	−	3.59274i	2.02098	−	0.173459i
$430$	7.28898	+	4.20829i	0.351506	+	0.202942i
$431$	12.2628	−	7.07990i	0.590676	−	0.341027i	−0.174689	−	0.984624i	$-0.555892\pi$
$431$	12.2628	−	7.07990i	0.590676	−	0.341027i	0.765365	+	0.643597i	$0.222559\pi$
$432$	5.02568	−	1.32004i	0.241798	−	0.0635106i
$433$			23.4830i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$433$			23.4830i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$434$	13.3351	−	9.39995i	0.640105	−	0.451212i
$435$	−7.31670	+	5.10527i	−0.350809	+	0.244779i
$436$	9.62168	+	16.6652i	0.460795	+	0.798121i
$437$	11.8507			0.566897
$438$	4.29358	−	0.368514i	0.205155	−	0.0176083i
$439$			4.23080i			0.201925i	0.994890	+	0.100963i	$0.0321922\pi$
$439$			4.23080i			0.201925i	−0.994890	+	0.100963i	$0.967808\pi$
$440$	5.39149			0.257029
$441$	−19.7120	+	7.24144i	−0.938665	+	0.344830i
$442$	17.1701			0.816699
$443$			29.8098i			1.41631i	0.706058	+	0.708154i	$0.250472\pi$
$443$			29.8098i			1.41631i	−0.706058	+	0.708154i	$0.749528\pi$
$444$	−0.482893	−	0.692066i	−0.0229171	−	0.0328440i
$445$	−3.98172			−0.188751
$446$	4.09123	+	7.08622i	0.193725	+	0.335542i
$447$	−1.29461	−	15.0836i	−0.0612328	−	0.713428i
$448$	2.16249	−	1.52435i	0.102168	−	0.0720186i
$449$			8.41716i			0.397230i	0.980078	+	0.198615i	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$	−2.07770	−	12.0145i	−0.0979435	−	0.566370i
$451$	0.790505	−	0.456399i	0.0372234	−	0.0214910i
$452$	−7.31199	−	4.22158i	−0.343927	−	0.198566i
$453$	−21.8980	−	31.3836i	−1.02886	−	1.47453i
$454$	−9.26106	−	5.34688i	−0.434643	−	0.250941i
$455$	6.41717	+	9.10363i	0.300841	+	0.426785i
$456$	4.42670	+	6.34420i	0.207299	+	0.297094i
$457$	−3.88219			−0.181601			−0.0908006	−	0.995869i	$-0.528943\pi$
$457$	−3.88219			−0.181601			−0.0908006	+	0.995869i	$0.528943\pi$
$458$	14.6036	+	25.2942i	0.682382	+	1.18192i
$459$	14.4243	+	14.5676i	0.673269	+	0.679957i
$460$	−2.22278	−	1.28332i	−0.103638	−	0.0598352i
$461$	−17.0423	−	29.5181i	−0.793739	−	1.37480i	−0.923637	−	0.383269i	$-0.874798\pi$
$461$	−17.0423	−	29.5181i	−0.793739	−	1.37480i	0.129898	−	0.991527i	$-0.458535\pi$
$462$	24.0142	+	8.69979i	1.11724	+	0.404751i
$463$	−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	$0.258308\pi$
$464$	4.61157	−	2.66249i	0.214087	−	0.123603i
$465$	−0.883517	−	10.2939i	−0.0409721	−	0.477369i
$466$	−3.21967	+	5.57664i	−0.149148	+	0.258333i
$467$	15.4057	−	26.6835i	0.712893	−	1.23477i	−0.250874	−	0.968020i	$-0.580718\pi$
$467$	15.4057	−	26.6835i	0.712893	−	1.23477i	0.963767	−	0.266747i	$-0.0859488\pi$
$468$	−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
$471$	2.23453	+	1.04647i	0.102962	+	0.0482186i
$472$		−	1.67386i		−	0.0770457i
$473$		−	48.4954i		−	2.22982i
$474$	−7.21918	−	3.38085i	−0.331588	−	0.155287i
$475$	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
$479$	−20.8747	+	36.1560i	−0.953788	+	1.65201i	−0.216670	+	0.976245i	$0.569519\pi$
$479$	−20.8747	+	36.1560i	−0.953788	+	1.65201i	−0.737118	+	0.675764i	$0.763814\pi$
$480$	−0.143276	−	1.66932i	−0.00653962	−	0.0761936i
$481$	−1.83629	+	1.06018i	−0.0837276	+	0.0483401i
$482$	−5.24722	+	9.08846i	−0.239004	+	0.413968i
$483$	−7.82967	−	9.30274i	−0.356262	−	0.423289i
$484$	−10.0326	−	17.3769i	−0.456026	−	0.789861i
$485$	9.93146	+	5.73393i	0.450964	+	0.260364i
$486$	9.04604	−	12.6952i	0.410337	−	0.575868i
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	0.999725	−	0.0234338i	$-0.00745988\pi$
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	−0.520157	+	0.854071i	$0.674127\pi$
$488$	−5.17221			−0.234135
$489$	−7.37690	−	10.5723i	−0.333595	−	0.478097i
$490$	1.21772	+	6.66087i	0.0550109	+	0.300908i
$491$	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	$0.347628\pi$
$492$	−0.162318	−	0.232628i	−0.00731785	−	0.0104877i
$493$	18.1942	+	10.5044i	0.819427	+	0.473097i
$494$	16.8333	−	9.71873i	0.757368	−	0.437266i
$495$	12.4245	−	10.3559i	0.558442	−	0.465462i
$496$			6.16655i			0.276886i
$497$	−5.54872	−	7.87161i	−0.248894	−	0.353090i
$498$	1.24707	+	14.5297i	0.0558827	+	0.651093i
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	−0.990605	−	0.136758i	$-0.956332\pi$
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	0.376867	−	0.926267i	$-0.377001\pi$
$500$	−8.76810			−0.392121
$501$	−6.43944	−	9.22879i	−0.287693	−	0.412312i
$502$			7.85271i			0.350484i
$503$	−11.2791			−0.502909			−0.251454	−	0.967869i	$-0.580909\pi$
$503$	−11.2791			−0.502909			−0.251454	+	0.967869i	$0.580909\pi$
$504$	2.05547	−	7.66649i	0.0915580	−	0.341493i
$505$	5.14255			0.228840
$506$			14.7887i			0.657438i
$507$	−10.2504	+	0.879780i	−0.455236	+	0.0390724i
$508$	−3.31883			−0.147249
$509$	9.31667	+	16.1370i	0.412954	+	0.715258i	0.995211	−	0.0977470i	$-0.0311636\pi$
$509$	9.31667	+	16.1370i	0.412954	+	0.715258i	−0.582257	+	0.813005i	$0.697830\pi$
$510$	5.42104	−	3.78256i	0.240047	−	0.167494i
$511$	2.76319	−	5.97463i	0.122236	−	0.264302i
$512$			1.00000i			0.0441942i
$513$	22.3870	+	6.11732i	0.988412	+	0.270086i
$514$	2.97164	−	1.71568i	0.131074	−	0.0756753i
$515$	7.49305	+	4.32611i	0.330183	+	0.190631i
$516$	−15.0152	+	1.28874i	−0.661007	+	0.0567336i
$517$	−45.8072	−	26.4468i	−2.01460	−	1.16313i
$518$	−1.28379	+	0.116385i	−0.0564065	+	0.00511364i
$519$	−8.68184	+	18.5385i	−0.381091	+	0.813749i
$520$	−4.20979			−0.184611
$521$	−7.64255	−	13.2373i	−0.334826	−	0.579936i	0.648625	−	0.761108i	$-0.275344\pi$
$521$	−7.64255	−	13.2373i	−0.334826	−	0.579936i	−0.983451	+	0.181172i	$0.942011\pi$
$522$	5.51318	−	14.9935i	0.241305	−	0.656246i
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.389368	−	0.921082i	$-0.627306\pi$
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.992365	+	0.123339i	$0.960640\pi$
$524$	9.37335	+	16.2351i	0.409477	+	0.709235i
$525$	−17.5112	−	6.34390i	−0.764251	−	0.276870i
$526$	1.83066	−	3.17080i	0.0798207	−	0.138253i
$527$	−21.0697	+	12.1646i	−0.917809	+	0.529897i
$528$	−7.91702	+	5.52415i	−0.344544	+	0.240408i
$529$	−7.97989	+	13.8216i	−0.346952	+	0.600938i
$530$	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
$534$	5.84687	−	4.07969i	0.253019	−	0.176545i
$535$			18.5303i			0.801135i
$536$			5.44252i			0.235081i
$537$	−0.360468	−	4.19984i	−0.0155554	−	0.181237i
$538$	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	−0.803769	−	0.594942i	$-0.797175\pi$
$541$	2.63647	−	4.56649i	0.113351	−	0.196329i	0.917119	+	0.398613i	$0.130508\pi$
$542$	9.93828	−	17.2136i	0.426886	−	0.739388i
$543$	−18.0920	−	8.47277i	−0.776404	−	0.363601i
$544$	−3.41677	+	1.97267i	−0.146493	+	0.0845776i
$545$	9.30729	−	16.1207i	0.398680	−	0.690535i
$546$	−18.7508	−	6.79297i	−0.802459	−	0.290712i
$547$	−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
$549$	−11.9192	+	9.93469i	−0.508700	+	0.424002i
$550$	11.3264	+	19.6179i	0.482958	+	0.836508i
$551$	23.7832			1.01320
$552$	4.57889	−	0.393002i	0.194890	−	0.0167273i
$553$	−9.95268	+	7.01567i	−0.423231	+	0.298337i
$554$	6.46579	+	3.73302i	0.274705	+	0.158601i
$555$	−0.346206	+	0.739259i	−0.0146956	+	0.0313798i
$556$	10.5033	+	6.06406i	0.445438	+	0.257174i
$557$	23.8694	−	13.7810i	1.01138	−	0.583920i	0.0997845	−	0.995009i	$-0.468185\pi$
$557$	23.8694	−	13.7810i	1.01138	−	0.583920i	0.911595	+	0.411089i	$0.134851\pi$
$558$	11.8446	+	14.2106i	0.501421	+	0.601585i
$559$			37.8662i			1.60157i
$560$	−2.32290	−	1.07431i	−0.0981605	−	0.0453979i
$561$	−34.4924	−	16.1533i	−1.45627	−	0.681993i
$562$	−11.1282	−	19.2746i	−0.469416	−	0.813052i
$563$	−18.8515			−0.794497			−0.397249	−	0.917711i	$-0.630035\pi$
$563$	−18.8515			−0.794497			−0.397249	+	0.917711i	$0.630035\pi$
$564$	−6.97118	+	14.8857i	−0.293540	+	0.626800i
$565$			8.16727i			0.343600i
$566$	16.1802			0.680106
$567$	−9.98886	−	21.6153i	−0.419493	−	0.907759i
$568$	3.64006			0.152734
$569$		−	4.46988i		−	0.187387i	−0.995601	−	0.0936936i	$-0.970133\pi$
$569$		−	4.46988i		−	0.187387i	0.995601	−	0.0936936i	$-0.0298674\pi$
$570$	3.17368	−	6.77681i	0.132931	−	0.283850i
$571$	18.6249			0.779428			0.389714	−	0.920936i	$-0.372574\pi$
$571$	18.6249			0.779428			0.389714	+	0.920936i	$0.372574\pi$
$572$	12.1282	+	21.0066i	0.507104	+	0.878329i
$573$	34.6165	+	16.2114i	1.44612	+	0.677241i
$574$	−0.431528	+	0.0391210i	−0.0180116	+	0.00163288i
$575$		−	10.7839i		−	0.449721i
$576$	1.92078	+	2.30447i	0.0800325	+	0.0960197i
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.344495	−	0.938788i	$-0.388050\pi$
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.985262	+	0.171053i	$0.0547170\pi$
$578$	1.24210	+	0.717124i	0.0516644	+	0.0298284i
$579$	14.6472	−	31.2765i	0.608719	−	1.29981i
$580$	−4.46088	−	2.57549i	−0.185228	−	0.106941i
$581$	20.2185	+	9.35079i	0.838806	+	0.387936i
$582$	−20.4587	+	1.75595i	−0.848039	+	0.0727863i
$583$	−11.2319			−0.465176
$584$	1.24401	+	2.15468i	0.0514773	+	0.0891614i
$585$	−9.70134	+	8.08608i	−0.401101	+	0.334318i
$586$	−7.68002	−	4.43406i	−0.317259	−	0.183170i
$587$	13.2295	+	22.9141i	0.546039	+	0.945766i	0.998541	+	0.0540032i	$0.0171981\pi$
$587$	13.2295	+	22.9141i	0.546039	+	0.945766i	−0.452502	+	0.891763i	$0.649469\pi$
$588$	−8.61290	−	8.53335i	−0.355190	−	0.351909i
$589$	−13.7709	+	23.8520i	−0.567422	+	0.982803i
$590$	−1.40224	+	0.809584i	−0.0577293	+	0.0333300i
$591$	7.25554	+	3.39788i	0.298453	+	0.139770i
$592$	0.243608	−	0.421942i	0.0100122	−	0.0173417i
$593$	−17.3351	+	30.0254i	−0.711869	+	1.23299i	0.252285	+	0.967653i	$0.418818\pi$
$593$	−17.3351	+	30.0254i	−0.711869	+	1.23299i	−0.964155	+	0.265341i	$0.914516\pi$
$594$	−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
$597$	−3.09604	−	36.0722i	−0.126712	−	1.47634i
$598$		−	11.5473i		−	0.472205i
$599$			24.4887i			1.00058i	0.865857	+	0.500291i	$0.166774\pi$
$599$			24.4887i			1.00058i	−0.865857	+	0.500291i	$0.833226\pi$
$600$	5.77310	−	4.02821i	0.235686	−	0.164451i
$601$	−19.3812	+	11.1898i	−0.790577	+	0.456440i	−0.840166	−	0.542330i	$-0.817542\pi$
$601$	−19.3812	+	11.1898i	−0.790577	+	0.456440i	0.0495885	+	0.998770i	$0.484209\pi$
$602$	−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
$605$	−9.70476	+	16.8091i	−0.394554	+	0.683388i
$606$	−7.55147	+	5.26908i	−0.306758	+	0.214042i
$607$	−28.2180	+	16.2917i	−1.14533	+	0.661259i	−0.947746	−	0.319026i	$-0.896644\pi$
$607$	−28.2180	+	16.2917i	−1.14533	+	0.661259i	−0.197589	+	0.980285i	$0.563311\pi$
$608$	−2.23317	+	3.86796i	−0.0905670	+	0.156867i
$609$	−15.7133	−	18.6696i	−0.636737	−	0.756532i
$610$	2.50160	+	4.33290i	0.101287	+	0.175434i
$611$	35.7672	+	20.6502i	1.44699	+	0.835418i
$612$	−4.08478	+	11.1088i	−0.165118	+	0.449048i
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	0.959869	−	0.280449i	$-0.0904832\pi$
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	−0.722810	+	0.691047i	$0.757150\pi$
$614$	27.1427			1.09539
$615$	−0.116372	+	0.248491i	−0.00469258	+	0.0100201i
$616$	1.33140	+	14.6862i	0.0536438	+	0.591723i
$617$	−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	$-0.681080\pi$
$618$	−15.4356	+	1.32482i	−0.620910	+	0.0532921i
$619$	−4.28374	−	2.47322i	−0.172178	−	0.0994070i	0.411434	−	0.911439i	$-0.365028\pi$
$619$	−4.28374	−	2.47322i	−0.172178	−	0.0994070i	−0.583612	+	0.812032i	$0.698361\pi$
$620$	5.16588	−	2.98252i	0.207467	−	0.119781i
$621$	9.79706	−	9.70071i	0.393143	−	0.389276i
$622$			16.8955i			0.677447i
$623$	−0.983266	−	10.8460i	−0.0393937	−	0.434536i
$624$	6.18177	−	4.31337i	0.247469	−	0.172673i
$625$	−5.91991	−	10.2536i	−0.236797	−	0.410144i
$626$	−4.27739			−0.170959
$627$	−42.9591	+	3.68714i	−1.71562	+	0.147250i
$628$			1.42457i			0.0568467i
$629$	1.92224			0.0766447
$630$	−7.41658	+	1.98606i	−0.295484	+	0.0791267i
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$		−	4.60242i		−	0.183074i
$633$	−6.62686	−	9.49739i	−0.263394	−	0.377487i
$634$	−6.62940			−0.263287
$635$	1.60519	+	2.78027i	0.0637001	+	0.110332i
$636$	0.298480	+	3.47761i	0.0118355	+	0.137896i
$637$	−23.2132	+	19.7282i	−0.919739	+	0.781658i
$638$			29.6794i			1.17502i
$639$	8.38843	−	6.99177i	0.331841	−	0.276590i
$640$	0.837727	−	0.483662i	0.0331141	−	0.0191184i
$641$	−12.1954	−	7.04105i	−0.481691	−	0.278105i	0.239430	−	0.970914i	$-0.423040\pi$
$641$	−12.1954	−	7.04105i	−0.481691	−	0.278105i	−0.721121	+	0.692809i	$0.756373\pi$
$642$	−18.9862	−	27.2105i	−0.749327	−	1.07391i
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	0.637549	−	0.770410i	$-0.279948\pi$
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	−0.348420	+	0.937339i	$0.613282\pi$
$644$	2.94680	−	6.37165i	0.116120	−	0.251078i
$645$	8.34189	+	11.9553i	0.328461	+	0.470740i
$646$	−17.6212			−0.693299
$647$	−12.1662	−	21.0725i	−0.478304	−	0.828446i	0.521387	−	0.853320i	$-0.325415\pi$
$647$	−12.1662	−	21.0725i	−0.478304	−	0.828446i	−0.999691	+	0.0248742i	$0.992081\pi$
$648$	8.85278	+	1.62120i	0.347770	+	0.0636868i
$649$	8.07955	+	4.66473i	0.317150	+	0.183107i
$650$	−8.84386	−	15.3180i	−0.346885	−	0.600822i
$651$	27.8220	−	4.94869i	1.09043	−	0.193955i
$652$	3.72148	−	6.44579i	0.145744	−	0.252437i
$653$	−36.0653	+	20.8223i	−1.41134	+	0.814840i	−0.995515	−	0.0946029i	$-0.969842\pi$
$653$	−36.0653	+	20.8223i	−1.41134	+	0.814840i	−0.415829	+	0.909443i	$0.636509\pi$
$654$	2.85024	+	33.2084i	0.111453	+	1.29855i
$655$	9.06707	−	15.7046i	0.354280	−	0.613631i
$656$	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	$0.398933\pi$
$660$	8.45689	+	3.96049i	0.329184	+	0.154162i
$661$			19.5131i			0.758972i	0.925198	+	0.379486i	$0.123899\pi$
$661$			19.5131i			0.758972i	−0.925198	+	0.379486i	$0.876101\pi$
$662$		−	0.757792i		−	0.0294524i
$663$	26.9324	+	12.6128i	1.04597	+	0.489842i
$664$	−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
$668$	3.24855	−	5.62665i	0.125690	−	0.217702i
$669$	1.21195	+	14.1205i	0.0468567	+	0.545931i
$670$	4.55935	−	2.63234i	0.176143	−	0.101696i
$671$	14.4140	−	24.9657i	0.556445	−	0.963790i
$672$	4.51176	−	0.802507i	0.174045	−	0.0309574i
$673$	−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
$675$	5.56665	−	20.3718i	0.214260	−	0.784110i
$676$	−2.96991	−	5.14404i	−0.114227	−	0.197848i
$677$	24.7531			0.951339			0.475669	−	0.879624i	$-0.342206\pi$
$677$	24.7531			0.951339			0.475669	+	0.879624i	$0.342206\pi$
$678$	−8.36823	−	11.9931i	−0.321380	−	0.460591i
$679$	−13.1664	+	28.4688i	−0.505281	+	1.09253i
$680$	3.30512	+	1.90821i	0.126746	+	0.0731767i
$681$	−10.5988	−	15.1899i	−0.406149	−	0.582079i
$682$	−29.7652	−	17.1850i	−1.13977	−	0.658046i
$683$	−18.3119	+	10.5724i	−0.700687	+	0.404542i	−0.807603	−	0.589726i	$-0.799236\pi$
$683$	−18.3119	+	10.5724i	−0.700687	+	0.404542i	0.106916	+	0.994268i	$0.465902\pi$
$684$	2.28323	+	13.2030i	0.0873014	+	0.504831i
$685$			16.3810i			0.625886i
$686$	−17.8432	+	4.96188i	−0.681257	+	0.189445i
$687$	4.32605	+	50.4031i	0.165049	+	1.92300i
$688$	−4.35045	−	7.53520i	−0.165859	−	0.287277i
$689$	8.77006			0.334113
$690$	−2.54386	−	3.64578i	−0.0968432	−	0.138793i
$691$			6.44470i			0.245168i	0.992458	+	0.122584i	$0.0391181\pi$
$691$			6.44470i			0.245168i	−0.992458	+	0.122584i	$0.960882\pi$
$692$	−11.8188			−0.449282
$693$	31.2771	+	31.2866i	1.18812	+	1.18848i
$694$	−20.9661			−0.795864
$695$		−	11.7318i		−	0.445014i
$696$	9.18936	−	0.788713i	0.348322	−	0.0298961i
$697$	0.646134			0.0244741
$698$	−3.09694	−	5.36406i	−0.117221	−	0.203033i
$699$	−9.14675	+	6.38220i	−0.345962	+	0.241397i
$700$	−0.970861	−	10.7092i	−0.0366951	−	0.404768i
$701$		−	24.5717i		−	0.928061i	−0.885819	−	0.464031i	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$	5.96071	−	21.8139i	0.224972	−	0.823312i
$703$	1.88454	−	1.08804i	0.0710767	−	0.0410361i
$704$	−4.82689	−	2.78681i	−0.181920	−	0.105032i
$705$	15.8418	−	1.35969i	0.596638	−	0.0512088i
$706$	16.3140	+	9.41889i	0.613985	+	0.354484i
$707$	1.26993	+	14.0081i	0.0477606	+	0.526827i
$708$	1.22959	−	2.62556i	0.0462107	−	0.0986745i
$709$	44.2740			1.66275			0.831373	−	0.555715i	$-0.187555\pi$
$709$	44.2740			1.66275			0.831373	+	0.555715i	$0.187555\pi$
$710$	−1.76056	−	3.04938i	−0.0660727	−	0.114441i
$711$	−8.84023	−	10.6061i	−0.331535	−	0.397762i
$712$	3.56475	+	2.05811i	0.133595	+	0.0771309i
$713$	8.18098	+	14.1699i	0.306380	+	0.530666i
$714$	11.6422	+	13.8326i	0.435699	+	0.517671i
$715$	11.7319	−	20.3202i	0.438747	−	0.759931i
$716$	2.10764	−	1.21685i	0.0787663	−	0.0454757i
$717$	6.58458	−	4.59442i	0.245906	−	0.171582i
$718$	13.8988	−	24.0735i	0.518700	−	0.898415i
$719$	2.22433	−	3.85266i	0.0829537	−	0.143680i	−0.821564	−	0.570117i	$-0.806898\pi$
$719$	2.22433	−	3.85266i	0.0829537	−	0.143680i	0.904517	+	0.426437i	$0.140231\pi$
$720$	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
$723$	−14.9068	+	10.4013i	−0.554390	+	0.386829i
$724$		−	11.5342i		−	0.428663i
$725$		−	21.6422i		−	0.803773i
$726$	−2.97196	−	34.6266i	−0.110300	−	1.28511i
$727$	30.4270	−	17.5670i	1.12848	−	0.651525i	0.184924	−	0.982753i	$-0.440796\pi$
$727$	30.4270	−	17.5670i	1.12848	−	0.651525i	0.943551	+	0.331227i	$0.107463\pi$
$728$	−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
$731$	17.1640	−	29.7289i	0.634834	−	1.09956i
$732$	−8.11294	−	3.79941i	−0.299863	−	0.140430i
$733$	−5.03789	+	2.90863i	−0.186079	+	0.107433i	−0.590145	−	0.807297i	$-0.700930\pi$
$733$	−5.03789	+	2.90863i	−0.186079	+	0.107433i	0.404067	+	0.914729i	$0.367596\pi$
$734$	10.8767	−	18.8390i	0.401467	−	0.695360i
$735$	−2.98289	+	11.3425i	−0.110025	+	0.418375i
$736$	1.32667	+	2.29786i	0.0489018	+	0.0847003i
$737$	−26.2704	−	15.1672i	−0.967684	−	0.558693i
$738$	−0.0837212	−	0.484128i	−0.00308182	−	0.0178210i
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	0.746537	−	0.665344i	$-0.231715\pi$
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	−0.949473	+	0.313847i	$0.898382\pi$
$740$	−0.471297			−0.0173252
$741$	33.5433	−	2.87899i	1.23225	−	0.105762i
$742$	4.83920	+	2.23806i	0.177652	+	0.0821618i
$743$	−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	$0.670329\pi$
$744$	−4.52983	+	9.67262i	−0.166072	+	0.354615i
$745$	−7.32216	−	4.22745i	−0.268263	−	0.154882i
$746$	10.1595	−	5.86560i	0.371966	−	0.214755i
$747$	−8.71716	+	23.7069i	−0.318944	+	0.867390i
$748$		−	21.9898i		−	0.804028i
$749$	−50.4757	+	4.57598i	−1.84434	+	0.167202i
$750$	−13.7533	−	6.44088i	−0.502200	−	0.235188i
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	0.822356	−	0.568973i	$-0.192659\pi$
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	−0.903923	+	0.427695i	$0.859326\pi$
$752$	−9.49001			−0.346065
$753$	−5.76845	+	12.3175i	−0.210214	+	0.448874i
$754$		−	23.1743i		−	0.843957i
$755$	−21.3722			−0.777813
$756$	8.85579	−	10.5155i	0.322082	−	0.382444i
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$			34.8881i			1.26719i
$759$	−10.8635	+	23.1970i	−0.394320	+	0.841998i
$760$	4.32040			0.156717
$761$	−10.4970	−	18.1813i	−0.380516	−	0.659073i	0.610620	−	0.791924i	$-0.290920\pi$
$761$	−10.4970	−	18.1813i	−0.380516	−	0.659073i	−0.991136	+	0.132851i	$0.957587\pi$
$762$	−5.20579	−	2.43795i	−0.188586	−	0.0883176i
$763$	46.2104	+	21.3717i	1.67293	+	0.773707i
$764$			22.0689i			0.798425i
$765$	11.2818	−	1.95099i	0.407895	−	0.0705382i
$766$	−10.2609	+	5.92412i	−0.370740	+	0.214047i
$767$	−6.30868	−	3.64232i	−0.227793	−	0.131516i
$768$	−0.734581	+	1.56856i	−0.0265069	+	0.0566006i
$769$	34.1729	+	19.7298i	1.23231	+	0.711473i	0.967511	−	0.252831i	$-0.0813616\pi$
$769$	34.1729	+	19.7298i	1.23231	+	0.711473i	0.264797	+	0.964304i	$0.414695\pi$
$770$	11.6591	−	8.21849i	0.420163	−	0.296174i
$771$	5.92151	−	0.508238i	0.213258	−	0.0183037i
$772$	19.9396			0.717641
$773$	17.3164	+	29.9929i	0.622829	+	1.07877i	0.988956	+	0.148206i	$0.0473499\pi$
$773$	17.3164	+	29.9929i	0.622829	+	1.07877i	−0.366128	+	0.930565i	$0.619317\pi$
$774$	−24.4990	−	9.00841i	−0.880597	−	0.323800i
$775$	21.7048	+	12.5313i	0.779661	+	0.450137i
$776$	−5.92762	−	10.2669i	−0.212789	−	0.368562i
$777$	−2.09920	−	0.760492i	−0.0753084	−	0.0272825i
$778$	3.17672	−	5.50224i	0.113891	−	0.197265i
$779$	0.633461	−	0.365729i	0.0226961	−	0.0131036i
$780$	−6.60331	−	3.09243i	−0.236437	−	0.110727i
$781$	−10.1442	+	17.5702i	−0.362986	+	0.628711i
$782$	−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
$786$	2.77668	+	32.3513i	0.0990409	+	1.15393i
$787$		−	35.3099i		−	1.25866i	−0.777137	−	0.629332i	$-0.783329\pi$
$787$		−	35.3099i		−	1.25866i	0.777137	−	0.629332i	$-0.216671\pi$
$788$			4.62560i			0.164780i
$789$	5.20072	−	3.62883i	0.185151	−	0.129190i
$790$	−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
$794$	4.28768	−	7.42647i	0.152164	−	0.263556i
$795$	2.76893	−	1.93203i	0.0982038	−	0.0685222i
$796$	18.1024	−	10.4514i	0.641622	−	0.370441i
$797$	9.60992	−	16.6449i	0.340401	−	0.589591i	−0.644106	−	0.764936i	$-0.722771\pi$
$797$	9.60992	−	16.6449i	0.340401	−	0.589591i	0.984507	+	0.175344i	$0.0561039\pi$
$798$	19.2435	+	6.97146i	0.681211	+	0.246787i
$799$	−18.7207	−	32.4252i	−0.662290	−	1.14712i
$800$	3.51977	+	2.03214i	0.124443	+	0.0718471i
$801$	12.1680	−	2.10424i	0.429937	−	0.0743498i
$802$	−11.5595	−	20.0216i	−0.408180	−	0.706989i
$803$	−13.8672			−0.489363
$804$	−3.99797	+	8.53693i	−0.140998	+	0.301074i
$805$	−6.76296	+	0.613110i	−0.238363	+	0.0216093i
$806$	23.2413	+	13.4184i	0.818640	+	0.472642i
$807$	21.8924	−	1.87900i	0.770649	−	0.0661441i
$808$	−4.60402	−	2.65813i	−0.161969	−	0.0935127i
$809$	−34.0157	+	19.6390i	−1.19593	+	0.690469i	−0.959645	−	0.281215i	$-0.909263\pi$
$809$	−34.0157	+	19.6390i	−1.19593	+	0.690469i	−0.236283	+	0.971684i	$0.575929\pi$
$810$	−2.92363	−	8.20033i	−0.102726	−	0.288130i
$811$		−	9.68436i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$811$		−	9.68436i		−	0.340064i	0.985439	−	0.170032i	$-0.0543871\pi$
$812$	5.91393	−	12.7872i	0.207538	−	0.448744i
$813$	28.2336	−	19.7002i	0.990196	−	0.690915i
$814$	1.35778	+	2.35174i	0.0475901	+	0.0824285i
$815$	−7.19975			−0.252196
$816$	−6.80851	+	0.584367i	−0.238345	+	0.0204570i
$817$		−	38.8611i		−	1.35958i
$818$	−1.55989			−0.0545404
$819$	−24.4218	−	24.4292i	−0.853366	−	0.853625i
$820$	−0.158420			−0.00553226
$821$		−	12.6924i		−	0.442968i	−0.975164	−	0.221484i	$-0.928910\pi$
$821$		−	12.6924i		−	0.442968i	0.975164	−	0.221484i	$-0.0710900\pi$
$822$	−16.7840	−	24.0543i	−0.585411	−	0.838992i
$823$	17.4767			0.609201			0.304600	−	0.952480i	$-0.401477\pi$
$823$	17.4767			0.609201			0.304600	+	0.952480i	$0.401477\pi$
$824$	−4.47225	−	7.74616i	−0.155798	−	0.269850i
$825$	3.35523	+	39.0920i	0.116814	+	1.36101i
$826$	−2.55154	−	3.61971i	−0.0887796	−	0.125946i
$827$		−	46.9482i		−	1.63255i	−0.577665	−	0.816274i	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$	7.47097	+	2.74712i	0.259634	+	0.0954690i
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	−0.534295	−	0.845298i	$-0.679423\pi$
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	0.464902	+	0.885362i	$0.346089\pi$
$830$	7.05332	+	4.07224i	0.244824	+	0.141349i
$831$	7.39979	+	10.6051i	0.256696	+	0.367888i
$832$	3.76893	+	2.17600i	0.130664	+	0.0754391i
$833$	27.1672	−	4.96661i	0.941286	−	0.172083i
$834$	12.0205	+	17.2274i	0.416236	+	0.596535i
$835$	−6.28480			−0.217495
$836$	−12.4468	−	21.5585i	−0.430482	−	0.745617i
$837$	8.14011	+	30.9911i	0.281363	+	1.07121i
$838$	5.90321	+	3.40822i	0.203923	+	0.117735i
$839$	8.51664	+	14.7513i	0.294027	+	0.509270i	0.974758	−	0.223264i	$-0.0716711\pi$
$839$	8.51664	+	14.7513i	0.294027	+	0.509270i	−0.680731	+	0.732533i	$0.738338\pi$
$840$	−2.85445	−	3.39148i	−0.0984879	−	0.117017i
$841$	−0.322276	+	0.558199i	−0.0111130	+	0.0192482i
$842$	11.7039	−	6.75727i	0.403344	−	0.232871i
$843$	−3.29653	−	38.4081i	−0.113538	−	1.32284i
$844$	3.34310	−	5.79042i	0.115074	−	0.199314i
$845$	−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
$849$	25.3797	+	11.8857i	0.871030	+	0.407916i
$850$			16.0350i			0.549996i
$851$		−	1.29275i		−	0.0443150i
$852$	5.70967	+	2.67392i	0.195610	+	0.0916071i
$853$	2.87158	−	1.65791i	0.0983209	−	0.0567656i	−0.450033	−	0.893012i	$-0.648588\pi$
$853$	2.87158	−	1.65791i	0.0983209	−	0.0567656i	0.548354	+	0.836246i	$0.315255\pi$
$854$	−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
$857$	−4.74512	+	8.21879i	−0.162090	+	0.280748i	−0.935618	−	0.353014i	$-0.885157\pi$
$857$	−4.74512	+	8.21879i	−0.162090	+	0.280748i	0.773528	+	0.633762i	$0.218490\pi$
$858$	3.59274	+	41.8593i	0.122654	+	1.42905i
$859$	−25.5104	+	14.7284i	−0.870404	+	0.502528i	−0.867482	−	0.497468i	$-0.834263\pi$
$859$	−25.5104	+	14.7284i	−0.870404	+	0.502528i	−0.00292142	+	0.999996i	$0.500930\pi$
$860$	−4.20829	+	7.28898i	−0.143502	+	0.248552i
$861$	−0.705617	−	0.255629i	−0.0240474	−	0.00871180i
$862$	7.07990	+	12.2628i	0.241143	+	0.417671i
$863$	13.4610	+	7.77172i	0.458218	+	0.264553i	0.711295	−	0.702894i	$-0.248109\pi$
$863$	13.4610	+	7.77172i	0.458218	+	0.264553i	−0.253076	+	0.967446i	$0.581442\pi$
$864$	1.32004	+	5.02568i	0.0449088	+	0.170977i
$865$	5.71629	+	9.90090i	0.194360	+	0.336641i
$866$	−23.4830			−0.797985
$867$	1.42152	+	2.03727i	0.0482773	+	0.0691895i
$868$	9.39995	+	13.3351i	0.319055	+	0.452623i
$869$	22.2154	+	12.8260i	0.753604	+	0.435094i
$870$	−5.10527	−	7.31670i	−0.173085	−	0.248059i
$871$	20.5125	+	11.8429i	0.695039	+	0.401281i
$872$	−16.6652	+	9.62168i	−0.564356	+	0.325831i
$873$	−33.3806	−	12.2742i	−1.12976	−	0.415420i
$874$			11.8507i			0.400857i
$875$	−18.9609	+	13.3656i	−0.640997	+	0.451840i
$876$	0.368514	+	4.29358i	0.0124509	+	0.145067i
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	0.938988	+	0.343950i	$0.111765\pi$
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	−0.171624	+	0.985163i	$0.554901\pi$
$878$	−4.23080			−0.142783
$879$	−8.78942	−	12.5967i	−0.296460	−	0.424877i
$880$			5.39149i			0.181747i
$881$	15.6912			0.528651			0.264326	−	0.964433i	$-0.414851\pi$
$881$	15.6912			0.528651			0.264326	+	0.964433i	$0.414851\pi$
$882$	−7.24144	−	19.7120i	−0.243832	−	0.663736i
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$			17.1701i			0.577493i
$885$	−2.79421	+	0.239824i	−0.0939262	+	0.00806159i
$886$	−29.8098			−1.00148
$887$	0.0302741	+	0.0524362i	0.00101650	+	0.00176064i	0.866533	−	0.499119i	$-0.166343\pi$
$887$	0.0302741	+	0.0524362i	0.00101650	+	0.00176064i	−0.865517	+	0.500880i	$0.833010\pi$
$888$	0.692066	−	0.482893i	0.0232242	−	0.0162048i
$889$	−7.17694	+	5.05904i	−0.240707	+	0.169675i
$890$		−	3.98172i		−	0.133467i
$891$	−32.4963	+	38.2134i	−1.08867	+	1.28020i
$892$	−7.08622	+	4.09123i	−0.237264	+	0.136985i
$893$	−36.7070	−	21.1928i	−1.22835	−	0.709190i
$894$	15.0836	−	1.29461i	0.504470	−	0.0432981i
$895$	−2.03877	−	1.17709i	−0.0681487	−	0.0393456i
$896$	1.52435	+	2.16249i	0.0509248	+	0.0722438i
$897$	8.48245	−	18.1127i	0.283221	−	0.604766i
$898$	−8.41716			−0.280884
$899$	16.4184	+	28.4375i	0.547583	+	0.948442i
$900$	12.0145	−	2.07770i	0.400484	−	0.0692565i
$901$	−6.88542	−	3.97530i	−0.229386	−	0.132436i
$902$	0.456399	+	0.790505i	0.0151964	+	0.0263210i
$903$	−30.5057	+	25.6752i	−1.01517	+	0.854418i
$904$	4.22158	−	7.31199i	0.140408	−	0.243193i
$905$	−9.66247	+	5.57863i	−0.321192	+	0.185440i
$906$	31.3836	−	21.8980i	1.04265	−	0.727514i
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	−0.993735	−	0.111760i	$-0.964351\pi$
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	0.593654	+	0.804720i	$0.297685\pi$
$908$	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	$0.194742\pi$
$912$	−6.34420	+	4.42670i	−0.210077	+	0.146583i
$913$		−	46.9275i		−	1.55307i
$914$		−	3.88219i		−	0.128411i
$915$	0.741053	+	8.63406i	0.0244985	+	0.285433i
$916$	−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	−0.612932	−	0.790136i	$-0.710010\pi$
$919$	11.4534	−	19.8378i	0.377812	−	0.654389i	0.990744	+	0.135747i	$0.0433433\pi$
$920$	1.28332	−	2.22278i	0.0423098	−	0.0732828i
$921$	42.5751	+	19.9386i	1.40290	+	0.656998i
$922$	29.5181	−	17.0423i	0.972128	−	0.561258i
$923$	7.92076	−	13.7192i	0.260715	−	0.451572i
$924$	−8.69979	+	24.0142i	−0.286202	+	0.790009i
$925$	−0.990094	−	1.71489i	−0.0325541	−	0.0563853i
$926$	−10.5822	−	6.10962i	−0.347752	−	0.200775i
$927$	−25.1849	−	9.26062i	−0.827179	−	0.304159i
$928$	2.66249	+	4.61157i	0.0874006	+	0.151382i
$929$	28.7973			0.944809			0.472404	−	0.881382i	$-0.343386\pi$
$929$	28.7973			0.944809			0.472404	+	0.881382i	$0.343386\pi$
$930$	10.2939	−	0.883517i	0.337551	−	0.0289717i
$931$	23.8231	−	20.2465i	0.780770	−	0.663553i
$932$	−5.57664	−	3.21967i	−0.182669	−	0.105464i
$933$	−12.4111	+	26.5016i	−0.406321	+	0.867625i
$934$	26.6835	+	15.4057i	0.873112	+	0.504091i
$935$	−18.4215	+	10.6356i	−0.602447	+	0.347823i
$936$	12.8650	−	2.22477i	0.420506	−	0.0727190i
$937$		−	53.6825i		−	1.75373i	−0.480736	−	0.876865i	$-0.659631\pi$
$937$		−	53.6825i		−	1.75373i	0.480736	−	0.876865i	$-0.340369\pi$
$938$	8.29628	+	11.7694i	0.270883	+	0.384284i
$939$	−6.70936	−	3.14209i	−0.218952	−	0.102538i
$940$	4.58996	+	7.95004i	0.149708	+	0.259302i
$941$	−45.9021			−1.49637			−0.748184	−	0.663492i	$-0.769074\pi$
$941$	−45.9021			−1.49637			−0.748184	+	0.663492i	$0.769074\pi$
$942$	−1.04647	+	2.23453i	−0.0340957	+	0.0728051i
$943$		−	0.434541i		−	0.0141506i
$944$	1.67386			0.0544796
$945$	−13.0923	−	2.33281i	−0.425893	−	0.0758864i
$946$	48.4954			1.57672
$947$			28.9183i			0.939718i	0.882741	+	0.469859i	$0.155695\pi$
$947$			28.9183i			0.939718i	−0.882741	+	0.469859i	$0.844305\pi$
$948$	3.38085	−	7.21918i	0.109805	−	0.234468i
$949$	10.8278			0.351485
$950$	9.07623	+	15.7205i	0.294472	+	0.510040i
$951$	−10.3986	−	4.86984i	−0.337199	−	0.157915i
$952$	−4.38170	+	9.47423i	−0.142012	+	0.307061i
$953$		−	12.8715i		−	0.416949i	−0.978028	−	0.208475i	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$	−2.08640	+	5.67412i	−0.0675498	+	0.183706i
$955$	18.4877	−	10.6739i	0.598249	−	0.345399i
$956$	4.01452	+	2.31778i	0.129839	+	0.0749624i
$957$	−21.8019	+	46.5540i	−0.704756	+	1.50488i
$958$	−36.1560	−	20.8747i	−1.16815	−	0.674430i
$959$	−44.6211	+	4.04521i	−1.44089	+	0.130627i
$960$	1.66932	−	0.143276i	0.0538770	−	0.00462421i
$961$	−7.02628			−0.226654
$962$	−1.06018	−	1.83629i	−0.0341816	−	0.0592043i
$963$	−9.79284	−	56.6283i	−0.315570	−	1.82482i
$964$	−9.08846	−	5.24722i	−0.292719	−	0.169002i
$965$	−9.64402	−	16.7039i	−0.310452	−	0.537719i
$966$	9.30274	−	7.82967i	0.299311	−	0.251916i
$967$	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	$0.134704\pi$
$968$	17.3769	−	10.0326i	0.558516	−	0.322459i
$969$	−27.6400	−	12.9442i	−0.887926	−	0.415829i
$970$	−5.73393	+	9.93146i	−0.184105	+	0.318880i
$971$	−19.6863	+	34.0977i	−0.631764	+	1.09425i	0.355426	+	0.934704i	$0.384336\pi$
$971$	−19.6863	+	34.0977i	−0.631764	+	1.09425i	−0.987191	+	0.159544i	$0.948998\pi$
$972$	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
$975$	−2.61983	−	30.5238i	−0.0839017	−	0.977544i
$976$		−	5.17221i		−	0.165559i
$977$			26.8438i			0.858809i	0.903112	+	0.429405i	$0.141277\pi$
$977$			26.8438i			0.858809i	−0.903112	+	0.429405i	$0.858723\pi$
$978$	10.5723	−	7.37690i	0.338066	−	0.235887i
$979$	−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
$983$	5.98457	−	10.3656i	0.190878	−	0.330611i	−0.754663	−	0.656112i	$-0.772200\pi$
$983$	5.98457	−	10.3656i	0.190878	−	0.330611i	0.945541	+	0.325502i	$0.105533\pi$
$984$	0.232628	−	0.162318i	0.00741592	−	0.00517450i
$985$	3.87499	−	2.23723i	0.123467	−	0.0712839i
$986$	−10.5044	+	18.1942i	−0.334530	+	0.579423i
$987$	7.61580	+	42.8166i	0.242414	+	1.36287i
$988$	9.71873	+	16.8333i	0.309194	+	0.535540i
$989$	−19.9935	−	11.5432i	−0.635755	−	0.367053i
$990$	10.3559	+	12.4245i	0.329131	+	0.394878i
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	0.767334	−	0.641248i	$-0.221583\pi$
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	−0.939004	+	0.343906i	$0.888250\pi$
$992$	−6.16655			−0.195788
$993$	0.556660	−	1.18864i	0.0176651	−	0.0377205i
$994$	7.87161	−	5.54872i	0.249672	−	0.175995i
$995$	−17.5109	−	10.1099i	−0.555132	−	0.320506i
$996$	−14.5297	+	1.24707i	−0.460392	+	0.0395150i
$997$	−11.6653	−	6.73498i	−0.369445	−	0.213299i	0.303771	−	0.952745i	$-0.401754\pi$
$997$	−11.6653	−	6.73498i	−0.369445	−	0.213299i	−0.673216	+	0.739446i	$0.735088\pi$
$998$	23.7462	−	13.7099i	0.751672	−	0.433978i
$999$	0.667317	−	2.44212i	0.0211130	−	0.0772653i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	1.1	even	1	trivial
126.2.l.a.101.3	yes	16	63.38	even	6	inner
126.2.t.a.47.1	yes	16	9.2	odd	6
126.2.t.a.59.1	yes	16	7.3	odd	6
378.2.l.a.143.6		16	63.52	odd	6
378.2.l.a.341.2		16	3.2	odd	2
378.2.t.a.17.6		16	21.17	even	6
378.2.t.a.89.6		16	9.7	even	3
882.2.l.b.227.2		16	63.11	odd	6
882.2.l.b.509.6		16	7.6	odd	2
882.2.m.a.293.7		16	7.5	odd	6
882.2.m.a.587.7		16	63.2	odd	6
882.2.m.b.293.6		16	7.2	even	3
882.2.m.b.587.6		16	63.47	even	6
882.2.t.a.803.4		16	63.20	even	6
882.2.t.a.815.4		16	7.4	even	3
1008.2.ca.c.257.5		16	4.3	odd	2
1008.2.ca.c.353.5		16	252.227	odd	6
1008.2.df.c.689.7		16	28.3	even	6
1008.2.df.c.929.7		16	36.11	even	6
1134.2.k.a.647.3		16	63.59	even	6
1134.2.k.a.971.3		16	9.4	even	3
1134.2.k.b.647.6		16	63.31	odd	6
1134.2.k.b.971.6		16	9.5	odd	6
2646.2.l.a.521.7		16	63.25	even	3
2646.2.l.a.1097.3		16	21.20	even	2
2646.2.m.a.881.3		16	21.5	even	6
2646.2.m.a.1763.3		16	63.16	even	3
2646.2.m.b.881.2		16	21.2	odd	6
2646.2.m.b.1763.2		16	63.61	odd	6
2646.2.t.b.1979.7		16	63.34	odd	6
2646.2.t.b.2285.7		16	21.11	odd	6
3024.2.ca.c.2033.4		16	252.115	even	6
3024.2.ca.c.2609.4		16	12.11	even	2
3024.2.df.c.17.4		16	84.59	odd	6
3024.2.df.c.1601.4		16	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.734581 + 1.56856i) q^{3} -1.00000 q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 - 0.734581i) q^{6} +(-2.16249 + 1.52435i) q^{7} -1.00000i q^{8} +(-1.92078 - 2.30447i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.734581 + 1.56856i) q^{3} -1.00000 q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 - 0.734581i) q^{6} +(-2.16249 + 1.52435i) q^{7} -1.00000i q^{8} +(-1.92078 - 2.30447i) q^{9} +(-0.837727 + 0.483662i) q^{10} +(4.82689 + 2.78681i) q^{11} +(0.734581 - 1.56856i) q^{12} +(-3.76893 - 2.17600i) q^{13} +(-1.52435 - 2.16249i) q^{14} +(-1.66932 + 0.143276i) q^{15} +1.00000 q^{16} +(1.97267 + 3.41677i) q^{17} +(2.30447 - 1.92078i) q^{18} +(3.86796 + 2.23317i) q^{19} +(-0.483662 - 0.837727i) q^{20} +(-0.802507 - 4.51176i) q^{21} +(-2.78681 + 4.82689i) q^{22} +(2.29786 - 1.32667i) q^{23} +(1.56856 + 0.734581i) q^{24} +(2.03214 - 3.51977i) 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} +(-0.143276 - 1.66932i) q^{30} +6.16655i q^{31} +1.00000i q^{32} +(-7.91702 + 5.52415i) 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} +(-2.23317 + 3.86796i) q^{38} +(6.18177 - 4.31337i) q^{39} +(0.837727 - 0.483662i) q^{40} +(0.0818856 - 0.141830i) q^{41} +(4.51176 - 0.802507i) q^{42} +(-4.35045 - 7.53520i) q^{43} +(-4.82689 - 2.78681i) q^{44} +(1.00151 - 2.72368i) q^{45} +(1.32667 + 2.29786i) q^{46} -9.49001 q^{47} +(-0.734581 + 1.56856i) q^{48} +(2.35274 - 6.59277i) q^{49} +(3.51977 + 2.03214i) q^{50} +(-6.80851 + 0.584367i) q^{51} +(3.76893 + 2.17600i) q^{52} +(-1.74520 + 1.00759i) q^{53} +(1.32004 + 5.02568i) q^{54} +5.39149i q^{55} +(1.52435 + 2.16249i) q^{56} +(-6.34420 + 4.42670i) q^{57} +(2.66249 + 4.61157i) q^{58} +1.67386 q^{59} +(1.66932 - 0.143276i) q^{60} -5.17221i q^{61} -6.16655 q^{62} +(7.66649 + 2.05547i) q^{63} -1.00000 q^{64} -4.20979i q^{65} +(-5.52415 - 7.91702i) q^{66} -5.44252 q^{67} +(-1.97267 - 3.41677i) q^{68} +(0.393002 + 4.57889i) q^{69} +(1.07431 - 2.32290i) q^{70} +3.64006i q^{71} +(-2.30447 + 1.92078i) q^{72} +(-2.15468 + 1.24401i) q^{73} +(0.421942 + 0.243608i) q^{74} +(4.02821 + 5.77310i) q^{75} +(-3.86796 - 2.23317i) q^{76} +(-14.6862 + 1.33140i) q^{77} +(4.31337 + 6.18177i) q^{78} +4.60242 q^{79} +(0.483662 + 0.837727i) q^{80} +(-1.62120 + 8.85278i) q^{81} +(0.141830 + 0.0818856i) q^{82} +(-4.20979 - 7.29158i) q^{83} +(0.802507 + 4.51176i) q^{84} +(-1.90821 + 3.30512i) q^{85} +(7.53520 - 4.35045i) q^{86} +(0.788713 + 9.18936i) q^{87} +(2.78681 - 4.82689i) 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} +(-9.67262 - 4.52983i) q^{93} -9.49001i q^{94} +4.32040i q^{95} +(-1.56856 - 0.734581i) q^{96} +(10.2669 - 5.92762i) q^{97} +(6.59277 + 2.35274i) q^{98} +(-2.84928 - 16.4763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^7	\( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

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