LMFDB - Embedded newform 430.2.p.a.59.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(59,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 8]))

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

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

chi := DirichletCharacter("430.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.p (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			59.10
Character	$\chi$	$=$	430.59
Dual form			430.2.p.a.379.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 + 0.222521i) q^{2} +(2.10581 + 0.480636i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.17028 + 0.538429i) q^{5} -2.15996 q^{6} +1.96131i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.50050 + 0.722602i) q^{9} +O(q^{10})$	\(q+(-0.974928 + 0.222521i) q^{2} +(2.10581 + 0.480636i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.17028 + 0.538429i) q^{5} -2.15996 q^{6} +1.96131i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.50050 + 0.722602i) q^{9} +(-2.23567 - 0.0419976i) q^{10} +(2.97979 + 1.43499i) q^{11} +(2.10581 - 0.480636i) q^{12} +(-4.09313 + 3.26416i) q^{13} +(-0.436432 - 1.91214i) q^{14} +(4.31139 + 2.17694i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-3.75696 - 2.99608i) q^{17} +(-1.62367 - 0.370592i) q^{18} +(3.32775 - 1.60256i) q^{19} +(2.18897 - 0.456540i) q^{20} +(-0.942676 + 4.13014i) q^{21} +(-3.22439 - 0.735946i) q^{22} +(-0.291518 + 0.605344i) q^{23} +(-1.94606 + 0.937172i) q^{24} +(4.42019 + 2.33708i) q^{25} +(3.26416 - 4.09313i) q^{26} +(-2.25373 - 1.79729i) q^{27} +(0.850980 + 1.76708i) q^{28} +(-0.432287 - 1.89397i) q^{29} +(-4.68771 - 1.16298i) q^{30} +(-2.39205 - 10.4803i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(5.58514 + 4.45400i) q^{33} +(4.32946 + 2.08496i) q^{34} +(-1.05603 + 4.25658i) q^{35} +1.66543 q^{36} -10.0260i q^{37} +(-2.88771 + 2.30287i) q^{38} +(-10.1882 + 4.90638i) q^{39} +(-2.03249 + 0.932184i) q^{40} +(2.24820 + 9.85002i) q^{41} -4.23635i q^{42} +(1.36674 + 6.41343i) q^{43} +3.30731 q^{44} +(2.86742 + 2.37616i) q^{45} +(0.149508 - 0.655035i) q^{46} +(-0.948801 - 1.97021i) q^{47} +(1.68872 - 1.34671i) q^{48} +3.15327 q^{49} +(-4.82941 - 1.29490i) q^{50} +(-6.47141 - 8.11489i) q^{51} +(-2.27151 + 4.71685i) q^{52} +(7.89046 + 6.29243i) q^{53} +(2.59715 + 1.25072i) q^{54} +(5.69432 + 4.71873i) q^{55} +(-1.22286 - 1.53341i) q^{56} +(7.77784 - 1.77524i) q^{57} +(0.842897 + 1.75029i) q^{58} +(1.73230 - 2.17223i) q^{59} +(4.82897 + 0.0907131i) q^{60} +(0.462020 - 2.02424i) q^{61} +(4.66416 + 9.68523i) q^{62} +(-1.41725 + 2.94294i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-10.6407 + 4.88027i) q^{65} +(-6.43622 - 3.09952i) q^{66} +(-2.77067 - 5.75336i) q^{67} +(-4.68485 - 1.06929i) q^{68} +(-0.904831 + 1.13462i) q^{69} +(0.0823702 - 4.38485i) q^{70} +(-10.1317 + 4.87919i) q^{71} +(-1.62367 + 0.370592i) q^{72} +(8.52581 - 6.79911i) q^{73} +(2.23100 + 9.77465i) q^{74} +(8.18477 + 7.04593i) q^{75} +(2.30287 - 2.88771i) q^{76} +(-2.81446 + 5.84428i) q^{77} +(8.84099 - 7.05045i) q^{78} -5.38164 q^{79} +(1.77411 - 1.36108i) q^{80} +(-6.99720 - 8.77421i) q^{81} +(-4.38367 - 9.10279i) q^{82} +(4.43242 + 1.01167i) q^{83} +(0.942676 + 4.13014i) q^{84} +(-6.54047 - 8.52517i) q^{85} +(-2.75959 - 5.94850i) q^{86} -4.19611i q^{87} +(-3.22439 + 0.735946i) q^{88} +(-1.53082 + 6.70696i) q^{89} +(-3.32428 - 1.67852i) q^{90} +(-6.40203 - 8.02789i) q^{91} +0.671881i q^{92} -23.2191i q^{93} +(1.36342 + 1.70968i) q^{94} +(8.08500 - 1.68624i) q^{95} +(-1.34671 + 1.68872i) q^{96} +(0.838828 - 1.74184i) q^{97} +(-3.07421 + 0.701668i) q^{98} +(3.43424 + 4.30640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$3$	2.10581	+	0.480636i	1.21579	+	0.277496i	0.781861	−	0.623453i	$-0.214271\pi$
$3$	2.10581	+	0.480636i	1.21579	+	0.277496i	0.433926	+	0.900948i	$0.357128\pi$
$4$	0.900969	−	0.433884i	0.450484	−	0.216942i
$5$	2.17028	+	0.538429i	0.970577	+	0.240793i
$5$	2.17028	+	0.538429i	0.970577	+	0.240793i
$6$	−2.15996			−0.881800
$7$			1.96131i			0.741305i	0.928772	+	0.370653i	$0.120866\pi$
$7$			1.96131i			0.741305i	−0.928772	+	0.370653i	$0.879134\pi$
$8$	−0.781831	+	0.623490i	−0.276419	+	0.220437i
$9$	1.50050	+	0.722602i	0.500166	+	0.240867i
$10$	−2.23567	−	0.0419976i	−0.706982	−	0.0132808i
$11$	2.97979	+	1.43499i	0.898439	+	0.432666i	0.825325	−	0.564658i	$-0.190992\pi$
$11$	2.97979	+	1.43499i	0.898439	+	0.432666i	0.0731144	+	0.997324i	$0.476706\pi$
$12$	2.10581	−	0.480636i	0.607894	−	0.138748i
$13$	−4.09313	+	3.26416i	−1.13523	+	0.905315i	−0.996381	−	0.0849990i	$-0.972911\pi$
$13$	−4.09313	+	3.26416i	−1.13523	+	0.905315i	−0.138848	+	0.990314i	$0.544340\pi$
$14$	−0.436432	−	1.91214i	−0.116641	−	0.511040i
$15$	4.31139	+	2.17694i	1.11320	+	0.562083i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	−3.75696	−	2.99608i	−0.911197	−	0.726655i	0.0510894	−	0.998694i	$-0.483731\pi$
$17$	−3.75696	−	2.99608i	−0.911197	−	0.726655i	−0.962286	+	0.272039i	$0.912302\pi$
$18$	−1.62367	−	0.370592i	−0.382703	−	0.0873495i
$19$	3.32775	−	1.60256i	0.763438	−	0.367652i	−0.0112987	−	0.999936i	$-0.503597\pi$
$19$	3.32775	−	1.60256i	0.763438	−	0.367652i	0.774737	+	0.632284i	$0.217882\pi$
$20$	2.18897	−	0.456540i	0.489468	−	0.102085i
$21$	−0.942676	+	4.13014i	−0.205709	+	0.901269i
$22$	−3.22439	−	0.735946i	−0.687443	−	0.156904i
$23$	−0.291518	+	0.605344i	−0.0607857	+	0.126223i	−0.929149	−	0.369706i	$-0.879458\pi$
$23$	−0.291518	+	0.605344i	−0.0607857	+	0.126223i	0.868363	+	0.495929i	$0.165173\pi$
$24$	−1.94606	+	0.937172i	−0.397237	+	0.191299i
$25$	4.42019	+	2.33708i	0.884038	+	0.467415i
$26$	3.26416	−	4.09313i	0.640154	−	0.802728i
$27$	−2.25373	−	1.79729i	−0.433730	−	0.345888i
$28$	0.850980	+	1.76708i	0.160820	+	0.333946i
$29$	−0.432287	−	1.89397i	−0.0802736	−	0.351702i	0.918801	−	0.394722i	$-0.129159\pi$
$29$	−0.432287	−	1.89397i	−0.0802736	−	0.351702i	−0.999074	+	0.0430203i	$0.986302\pi$
$30$	−4.68771	−	1.16298i	−0.855854	−	0.212331i
$31$	−2.39205	−	10.4803i	−0.429626	−	1.88231i	−0.469193	−	0.883096i	$-0.655455\pi$
$31$	−2.39205	−	10.4803i	−0.429626	−	1.88231i	0.0395676	−	0.999217i	$-0.487402\pi$
$32$	−0.433884	+	0.900969i	−0.0767005	+	0.159270i
$33$	5.58514	+	4.45400i	0.972248	+	0.775342i
$34$	4.32946	+	2.08496i	0.742496	+	0.357567i
$35$	−1.05603	+	4.25658i	−0.178501	+	0.719493i
$36$	1.66543			0.277571
$37$		−	10.0260i		−	1.64827i	−0.566395	−	0.824134i	$-0.691662\pi$
$37$		−	10.0260i		−	1.64827i	0.566395	−	0.824134i	$-0.308338\pi$
$38$	−2.88771	+	2.30287i	−0.468449	+	0.373576i
$39$	−10.1882	+	4.90638i	−1.63142	+	0.785649i
$40$	−2.03249	+	0.932184i	−0.321366	+	0.147391i
$41$	2.24820	+	9.85002i	0.351110	+	1.53831i	0.774622	+	0.632424i	$0.217940\pi$
$41$	2.24820	+	9.85002i	0.351110	+	1.53831i	−0.423512	+	0.905891i	$0.639203\pi$
$42$		−	4.23635i		−	0.653683i
$43$	1.36674	+	6.41343i	0.208426	+	0.978038i
$43$	1.36674	+	6.41343i	0.208426	+	0.978038i
$44$	3.30731			0.498596
$45$	2.86742	+	2.37616i	0.427450	+	0.354216i
$46$	0.149508	−	0.655035i	0.0220437	−	0.0965797i
$47$	−0.948801	−	1.97021i	−0.138397	−	0.287384i	0.820238	−	0.572022i	$-0.193841\pi$
$47$	−0.948801	−	1.97021i	−0.138397	−	0.287384i	−0.958635	+	0.284638i	$0.908127\pi$
$48$	1.68872	−	1.34671i	0.243746	−	0.194381i
$49$	3.15327			0.450467
$50$	−4.82941	−	1.29490i	−0.682982	−	0.183126i
$51$	−6.47141	−	8.11489i	−0.906178	−	1.13631i
$52$	−2.27151	+	4.71685i	−0.315002	+	0.654109i
$53$	7.89046	+	6.29243i	1.08384	+	0.864332i	0.991332	−	0.131380i	$-0.0419409\pi$
$53$	7.89046	+	6.29243i	1.08384	+	0.864332i	0.0925059	+	0.995712i	$0.470512\pi$
$54$	2.59715	+	1.25072i	0.353428	+	0.170202i
$55$	5.69432	+	4.71873i	0.767822	+	0.636273i
$56$	−1.22286	−	1.53341i	−0.163411	−	0.204911i
$57$	7.77784	−	1.77524i	1.03020	−	0.235137i
$58$	0.842897	+	1.75029i	0.110678	+	0.229825i
$59$	1.73230	−	2.17223i	0.225526	−	0.282800i	−0.656176	−	0.754608i	$-0.727827\pi$
$59$	1.73230	−	2.17223i	0.225526	−	0.282800i	0.881701	+	0.471808i	$0.156398\pi$
$60$	4.82897	+	0.0907131i	0.623417	+	0.0117110i
$61$	0.462020	−	2.02424i	0.0591556	−	0.259177i	−0.936699	−	0.350135i	$-0.886136\pi$
$61$	0.462020	−	2.02424i	0.0591556	−	0.259177i	0.995855	+	0.0909577i	$0.0289928\pi$
$62$	4.66416	+	9.68523i	0.592349	+	1.23003i
$63$	−1.41725	+	2.94294i	−0.178556	+	0.370776i
$64$	0.222521	−	0.974928i	0.0278151	−	0.121866i
$65$	−10.6407	+	4.88027i	−1.31982	+	0.605323i
$66$	−6.43622	−	3.09952i	−0.792244	−	0.381525i
$67$	−2.77067	−	5.75336i	−0.338491	−	0.702884i	0.660353	−	0.750956i	$-0.270407\pi$
$67$	−2.77067	−	5.75336i	−0.338491	−	0.702884i	−0.998844	+	0.0480713i	$0.984693\pi$
$68$	−4.68485	−	1.06929i	−0.568122	−	0.129670i
$69$	−0.904831	+	1.13462i	−0.108929	+	0.136592i
$70$	0.0823702	−	4.38485i	0.00984513	−	0.524089i
$71$	−10.1317	+	4.87919i	−1.20242	+	0.579053i	−0.924364	−	0.381512i	$-0.875403\pi$
$71$	−10.1317	+	4.87919i	−1.20242	+	0.579053i	−0.278053	+	0.960566i	$0.589689\pi$
$72$	−1.62367	+	0.370592i	−0.191352	+	0.0436747i
$73$	8.52581	−	6.79911i	0.997871	−	0.795776i	0.0189097	−	0.999821i	$-0.493980\pi$
$73$	8.52581	−	6.79911i	0.997871	−	0.795776i	0.978961	+	0.204046i	$0.0654091\pi$
$74$	2.23100	+	9.77465i	0.259349	+	1.13628i
$75$	8.18477	+	7.04593i	0.945096	+	0.813594i
$76$	2.30287	−	2.88771i	0.264158	−	0.331243i
$77$	−2.81446	+	5.84428i	−0.320737	+	0.666018i
$78$	8.84099	−	7.05045i	1.00104	−	0.798307i
$79$	−5.38164			−0.605482			−0.302741	−	0.953073i	$-0.597902\pi$
$79$	−5.38164			−0.605482			−0.302741	+	0.953073i	$0.597902\pi$
$80$	1.77411	−	1.36108i	0.198351	−	0.152174i
$81$	−6.99720	−	8.77421i	−0.777466	−	0.974912i
$82$	−4.38367	−	9.10279i	−0.484096	−	1.00523i
$83$	4.43242	+	1.01167i	0.486521	+	0.111045i	0.458743	−	0.888569i	$-0.348300\pi$
$83$	4.43242	+	1.01167i	0.486521	+	0.111045i	0.0277779	+	0.999614i	$0.491157\pi$
$84$	0.942676	+	4.13014i	0.102854	+	0.450635i
$85$	−6.54047	−	8.52517i	−0.709413	−	0.924684i
$86$	−2.75959	−	5.94850i	−0.297575	−	0.641443i
$87$		−	4.19611i		−	0.449870i
$88$	−3.22439	+	0.735946i	−0.343721	+	0.0784522i
$89$	−1.53082	+	6.70696i	−0.162267	+	0.710936i	0.826681	+	0.562671i	$0.190226\pi$
$89$	−1.53082	+	6.70696i	−0.162267	+	0.710936i	−0.988948	+	0.148265i	$0.952631\pi$
$90$	−3.32428	−	1.67852i	−0.350409	−	0.176931i
$91$	−6.40203	−	8.02789i	−0.671115	−	0.841551i
$92$			0.671881i			0.0700484i
$93$		−	23.2191i		−	2.40771i
$94$	1.36342	+	1.70968i	0.140627	+	0.176340i
$95$	8.08500	−	1.68624i	0.829503	−	0.173005i
$96$	−1.34671	+	1.68872i	−0.137448	+	0.172355i
$97$	0.838828	−	1.74184i	0.0851700	−	0.176857i	−0.854034	−	0.520218i	$-0.825851\pi$
$97$	0.838828	−	1.74184i	0.0851700	−	0.176857i	0.939204	+	0.343360i	$0.111565\pi$
$98$	−3.07421	+	0.701668i	−0.310542	+	0.0708791i
$99$	3.43424	+	4.30640i	0.345154	+	0.432809i
$100$	4.99647	+	0.187786i	0.499647	+	0.0187786i
$101$	8.03855	−	3.87116i	0.799866	−	0.385195i	0.0111384	−	0.999938i	$-0.496454\pi$
$101$	8.03855	−	3.87116i	0.799866	−	0.385195i	0.788728	+	0.614743i	$0.210740\pi$
$102$	8.11489	+	6.47141i	0.803493	+	0.640765i
$103$	−10.0207	−	7.99122i	−0.987366	−	0.787398i	−0.0102155	−	0.999948i	$-0.503252\pi$
$103$	−10.0207	−	7.99122i	−0.987366	−	0.787398i	−0.977150	+	0.212550i	$0.931823\pi$
$104$	1.16496	−	5.10404i	0.114234	−	0.500493i
$105$	−4.26965	+	8.45597i	−0.416675	+	0.825218i
$106$	−9.09283	−	4.37887i	−0.883173	−	0.425314i
$107$	6.73214	+	1.53657i	0.650821	+	0.148546i	0.535170	−	0.844744i	$-0.320248\pi$
$107$	6.73214	+	1.53657i	0.650821	+	0.148546i	0.115651	+	0.993290i	$0.463105\pi$
$108$	−2.81035	−	0.641444i	−0.270426	−	0.0617230i
$109$	−15.6620	−	7.54241i	−1.50014	−	0.722432i	−0.509701	−	0.860351i	$-0.670244\pi$
$109$	−15.6620	−	7.54241i	−1.50014	−	0.722432i	−0.990443	+	0.137920i	$0.955958\pi$
$110$	−6.60156	−	3.33331i	−0.629434	−	0.317819i
$111$	4.81887	−	21.1129i	0.457387	−	2.00394i
$112$	1.53341	+	1.22286i	0.144894	+	0.115549i
$113$	−9.21382	−	7.34778i	−0.866763	−	0.691221i	0.0855528	−	0.996334i	$-0.472734\pi$
$113$	−9.21382	−	7.34778i	−0.866763	−	0.691221i	−0.952316	+	0.305113i	$0.901306\pi$
$114$	−7.18781	+	3.46147i	−0.673200	+	0.324196i
$115$	−0.958609	+	1.15680i	−0.0893908	+	0.107872i
$116$	−1.21124	−	1.51885i	−0.112461	−	0.141021i
$117$	−8.50041	+	1.94016i	−0.785864	+	0.179368i
$118$	−1.20550	+	2.50324i	−0.110975	+	0.230442i
$119$	5.87623	−	7.36856i	0.538673	−	0.675475i
$120$	−4.72808	+	0.986107i	−0.431613	+	0.0900189i
$121$	−0.0384553	−	0.0482214i	−0.00349593	−	0.00438376i
$122$			2.07630i			0.187979i
$123$			21.8228i			1.96770i
$124$	−6.70239	−	8.40453i	−0.601892	−	0.754749i
$125$	8.33468	+	7.45206i	0.745476	+	0.666532i
$126$	0.726846	−	3.18452i	0.0647526	−	0.283700i
$127$	−9.24649	+	2.11045i	−0.820494	+	0.187272i	−0.612108	−	0.790774i	$-0.709678\pi$
$127$	−9.24649	+	2.11045i	−0.820494	+	0.187272i	−0.208386	+	0.978047i	$0.566821\pi$
$128$			1.00000i			0.0883883i
$129$	−0.204436	+	14.1623i	−0.0179996	+	1.24692i
$130$	9.28798	−	7.12569i	0.814610	−	0.624965i
$131$	−1.10875	−	4.85775i	−0.0968718	−	0.424423i	0.903116	−	0.429397i	$-0.141274\pi$
$131$	−1.10875	−	4.85775i	−0.0968718	−	0.424423i	−0.999988	+	0.00497389i	$0.998417\pi$
$132$	6.96456	+	1.58961i	0.606187	+	0.138358i
$133$	3.14312	+	6.52675i	0.272543	+	0.565941i
$134$	3.98145	+	4.99258i	0.343945	+	0.431293i
$135$	−3.92350	−	5.11408i	−0.337681	−	0.440150i
$136$	4.80533			0.412054
$137$	−1.97908	+	1.57827i	−0.169084	+	0.134840i	−0.704376	−	0.709827i	$-0.748773\pi$
$137$	−1.97908	+	1.57827i	−0.169084	+	0.134840i	0.535292	+	0.844667i	$0.320202\pi$
$138$	0.629668	−	1.30752i	0.0536009	−	0.111303i
$139$	6.18116	−	7.75092i	0.524279	−	0.657425i	−0.447233	−	0.894418i	$-0.647590\pi$
$139$	6.18116	−	7.75092i	0.524279	−	0.657425i	0.971511	+	0.236993i	$0.0761618\pi$
$140$	0.895415	+	4.29324i	0.0756764	+	0.362845i
$141$	−1.05104	−	4.60490i	−0.0885134	−	0.387802i
$142$	8.79200	−	7.01138i	0.737808	−	0.588382i
$143$	−16.8807	+	3.85290i	−1.41163	+	0.322196i
$144$	1.50050	−	0.722602i	0.125042	−	0.0602168i
$145$	0.0815878	−	4.34320i	0.00677550	−	0.360683i
$146$	−6.79911	+	8.52581i	−0.562698	+	0.705601i
$147$	6.64016	+	1.51557i	0.547671	+	0.125002i
$148$	−4.35013	−	9.03314i	−0.357578	−	0.742519i
$149$	−5.54630	−	2.67096i	−0.454371	−	0.218814i	0.192678	−	0.981262i	$-0.438283\pi$
$149$	−5.54630	−	2.67096i	−0.454371	−	0.218814i	−0.647049	+	0.762449i	$0.723997\pi$
$150$	−9.54743	−	5.04799i	−0.779544	−	0.412167i
$151$	−1.71476	+	7.51287i	−0.139545	+	0.611388i	0.855989	+	0.516993i	$0.172949\pi$
$151$	−1.71476	+	7.51287i	−0.139545	+	0.611388i	−0.995535	+	0.0943950i	$0.969908\pi$
$152$	−1.60256	+	3.32775i	−0.129985	+	0.269916i
$153$	−3.47234	−	7.21039i	−0.280722	−	0.582926i
$154$	1.44342	−	6.32403i	0.116314	−	0.509605i
$155$	0.451465	−	24.0330i	0.0362626	−	1.93038i
$156$	−7.05045	+	8.84099i	−0.564488	+	0.707846i
$157$	2.46114	+	5.11061i	0.196420	+	0.407871i	0.975795	−	0.218687i	$-0.0701774\pi$
$157$	2.46114	+	5.11061i	0.196420	+	0.407871i	−0.779375	+	0.626558i	$0.784463\pi$
$158$	5.24671	−	1.19753i	0.417406	−	0.0952702i
$159$	13.5914	+	17.0431i	1.07787	+	1.35160i
$160$	−1.42675	+	1.72173i	−0.112795	+	0.136115i
$161$	−1.18727	−	0.571757i	−0.0935697	−	0.0450608i
$162$	8.77421	+	6.99720i	0.689367	+	0.549752i
$163$	0.526622	−	1.09354i	0.0412482	−	0.0856529i	−0.879326	−	0.476220i	$-0.842007\pi$
$163$	0.526622	−	1.09354i	0.0412482	−	0.0856529i	0.920575	+	0.390567i	$0.127721\pi$
$164$	6.29932	+	7.89910i	0.491895	+	0.616816i
$165$	9.72313	+	12.6736i	0.756945	+	0.986639i
$166$	−4.54641			−0.352870
$167$	−13.9096	+	11.0926i	−1.07636	+	0.858369i	−0.990442	−	0.137933i	$-0.955954\pi$
$167$	−13.9096	+	11.0926i	−1.07636	+	0.858369i	−0.0859192	+	0.996302i	$0.527383\pi$
$168$	−1.83808	−	3.81682i	−0.141811	−	0.294474i
$169$	3.20617	−	14.0472i	0.246629	−	1.08055i
$170$	8.27351	+	6.85603i	0.634549	+	0.525834i
$171$	6.15130			0.470401
$172$	4.01407	+	5.18529i	0.306070	+	0.395375i
$173$			13.2913i			1.01052i	0.862968	+	0.505259i	$0.168603\pi$
$173$			13.2913i			1.01052i	−0.862968	+	0.505259i	$0.831397\pi$
$174$	0.933722	+	4.09090i	0.0707853	+	0.310131i
$175$	−4.58373	+	8.66936i	−0.346498	+	0.655342i
$176$	2.97979	−	1.43499i	0.224610	−	0.108166i
$177$	4.69193	−	3.74169i	0.352667	−	0.281243i
$178$		−	6.87944i		−	0.515636i
$179$	−12.6436			−0.945027			−0.472513	−	0.881323i	$-0.656653\pi$
$179$	−12.6436			−0.945027			−0.472513	+	0.881323i	$0.656653\pi$
$180$	3.61444	+	0.896714i	0.269404	+	0.0668371i
$181$	21.8908	+	10.5420i	1.62713	+	0.783584i	0.999989	+	0.00467722i	$0.00148881\pi$
$181$	21.8908	+	10.5420i	1.62713	+	0.783584i	0.627140	+	0.778907i	$0.284225\pi$
$182$	8.02789	+	6.40203i	0.595066	+	0.474550i
$183$	1.94585	−	4.04059i	0.143841	−	0.298689i
$184$	−0.149508	−	0.655035i	−0.0110218	−	0.0482899i
$185$	5.39830	−	21.7592i	0.396891	−	1.59977i
$186$	5.16674	+	22.6370i	0.378844	+	1.65982i
$187$	−6.89560	−	14.3189i	−0.504256	−	1.04710i
$188$	−1.70968	−	1.36342i	−0.124691	−	0.0994380i
$189$	3.52503	−	4.42025i	0.256409	−	0.321526i
$190$	−7.50707	+	3.44304i	−0.544620	+	0.249785i
$191$	1.31073	−	0.631212i	0.0948408	−	0.0456729i	−0.385862	−	0.922557i	$-0.626096\pi$
$191$	1.31073	−	0.631212i	0.0948408	−	0.0456729i	0.480703	+	0.876884i	$0.340382\pi$
$192$	0.937172	−	1.94606i	0.0676345	−	0.140445i
$193$	16.5351	+	3.77403i	1.19022	+	0.271660i	0.771366	−	0.636392i	$-0.219574\pi$
$193$	16.5351	+	3.77403i	1.19022	+	0.271660i	0.418856	+	0.908053i	$0.362431\pi$
$194$	−0.430200	+	1.88483i	−0.0308865	+	0.135323i
$195$	−24.7529	+	5.16257i	−1.77259	+	0.369699i
$196$	2.84099	−	1.36815i	0.202928	−	0.0977251i
$197$	6.06797	+	1.38497i	0.432325	+	0.0986753i	0.433145	−	0.901324i	$-0.357404\pi$
$197$	6.06797	+	1.38497i	0.432325	+	0.0986753i	−0.000819946		1.00000i	$0.500261\pi$
$198$	−4.30640	−	3.43424i	−0.306042	−	0.244061i
$199$	−9.53457	+	11.9560i	−0.675888	+	0.847536i	−0.994968	−	0.100191i	$-0.968054\pi$
$199$	−9.53457	+	11.9560i	−0.675888	+	0.847536i	0.319081	+	0.947728i	$0.396626\pi$
$200$	−4.91299	+	0.928742i	−0.347401	+	0.0656720i
$201$	−3.06922	−	13.4471i	−0.216486	−	0.948488i
$202$	−6.97560	+	5.56285i	−0.490801	+	0.391401i
$203$	3.71466	−	0.847848i	0.260718	−	0.0595073i
$204$	−9.35145	−	4.50342i	−0.654733	−	0.315303i
$205$	−0.424315	+	22.5878i	−0.0296355	+	1.57760i
$206$	11.5476	+	5.56105i	0.804562	+	0.387457i
$207$	−0.874845	+	0.697666i	−0.0608059	+	0.0484911i
$208$			5.23530i			0.363003i
$209$	12.2156			0.844974
$210$	2.28097	−	9.19404i	0.157402	−	0.634449i
$211$	−8.29880	+	3.99649i	−0.571313	+	0.275130i	−0.697155	−	0.716920i	$-0.745551\pi$
$211$	−8.29880	+	3.99649i	−0.571313	+	0.275130i	0.125842	+	0.992050i	$0.459837\pi$
$212$	9.83924	+	2.24574i	0.675762	+	0.154238i
$213$	−23.6806	+	5.40494i	−1.62257	+	0.370341i
$214$	−6.90527			−0.472035
$215$	−0.486970	+	14.6548i	−0.0332111	+	0.999448i
$216$	2.88262			0.196138
$217$	20.5551	−	4.69156i	1.39537	−	0.318484i
$218$	16.9476	+	3.86819i	1.14784	+	0.261987i
$219$	21.2216	−	10.2198i	1.43402	−	0.690589i
$220$	7.17778	+	1.78075i	0.483926	+	0.120058i
$221$	25.1574			1.69227
$222$			21.6558i			1.45344i
$223$	8.86030	−	7.06585i	0.593330	−	0.473164i	−0.280196	−	0.959943i	$-0.590399\pi$
$223$	8.86030	−	7.06585i	0.593330	−	0.473164i	0.873526	+	0.486778i	$0.161828\pi$
$224$	−1.76708	−	0.850980i	−0.118068	−	0.0568585i
$225$	4.94371	+	6.70082i	0.329581	+	0.446721i
$226$	10.6178	+	5.11328i	0.706289	+	0.340131i
$227$	5.02515	−	1.14696i	0.333531	−	0.0761262i	−0.0524759	−	0.998622i	$-0.516711\pi$
$227$	5.02515	−	1.14696i	0.333531	−	0.0761262i	0.386007	+	0.922496i	$0.373854\pi$
$228$	6.23735	−	4.97412i	0.413078	−	0.329419i
$229$	2.31234	+	10.1310i	0.152804	+	0.669478i	0.992063	+	0.125745i	$0.0401322\pi$
$229$	2.31234	+	10.1310i	0.152804	+	0.669478i	−0.839259	+	0.543732i	$0.817011\pi$
$230$	0.677163	−	1.34111i	0.0446508	−	0.0884300i
$231$	−8.73568	+	10.9542i	−0.574765	+	0.720733i
$232$	1.51885	+	1.21124i	0.0997172	+	0.0795218i
$233$	−0.253065	−	0.0577605i	−0.0165789	−	0.00378402i	0.214223	−	0.976785i	$-0.431278\pi$
$233$	−0.253065	−	0.0577605i	−0.0165789	−	0.00378402i	−0.230802	+	0.973001i	$0.574135\pi$
$234$	7.85556	−	3.78304i	0.513534	−	0.247305i
$235$	−0.998344	−	4.78675i	−0.0651248	−	0.312253i
$236$	0.618249	−	2.70873i	0.0402446	−	0.176323i
$237$	−11.3327	−	2.58661i	−0.736137	−	0.168019i
$238$	−4.08924	+	8.49140i	−0.265066	+	0.550416i
$239$	−23.5421	+	11.3373i	−1.52281	+	0.733349i	−0.993366	−	0.114994i	$-0.963315\pi$
$239$	−23.5421	+	11.3373i	−1.52281	+	0.733349i	−0.529448	+	0.848342i	$0.677601\pi$
$240$	4.39011	−	2.01348i	0.283380	−	0.129970i
$241$	−12.1379	+	15.2204i	−0.781868	+	0.980432i	0.218121	+	0.975922i	$0.430007\pi$
$241$	−12.1379	+	15.2204i	−0.781868	+	0.980432i	−0.999990	+	0.00451039i	$0.998564\pi$
$242$	0.0482214	+	0.0384553i	0.00309979	+	0.00247200i
$243$	−6.76536	−	14.0484i	−0.433998	−	0.901206i
$244$	−0.462020	−	2.02424i	−0.0295778	−	0.129589i
$245$	6.84345	+	1.69781i	0.437212	+	0.108469i
$246$	−4.85603	−	21.2757i	−0.309609	−	1.35649i
$247$	−8.38989	+	17.4218i	−0.533836	+	1.10852i
$248$	8.40453	+	6.70239i	0.533688	+	0.425602i
$249$	8.84757	+	4.26076i	0.560692	+	0.270015i
$250$	−9.78395	−	5.41058i	−0.618791	−	0.342195i
$251$	−17.2890			−1.09127			−0.545635	−	0.838023i	$-0.683712\pi$
$251$	−17.2890			−1.09127			−0.545635	+	0.838023i	$0.683712\pi$
$252$			3.26642i			0.205765i
$253$	−1.73732	+	1.38547i	−0.109225	+	0.0871037i
$254$	8.54505	−	4.11508i	0.536164	−	0.258203i
$255$	−9.67544	−	21.0959i	−0.605900	−	1.32108i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$			8.06238i			0.502918i	0.967868	+	0.251459i	$0.0809103\pi$
$257$			8.06238i			0.502918i	−0.967868	+	0.251459i	$0.919090\pi$
$258$	−2.95210	−	13.8527i	−0.183790	−	0.862434i
$259$	19.6641			1.22187
$260$	−7.46949	+	9.01381i	−0.463238	+	0.559013i
$261$	0.719942	−	3.15427i	0.0445633	−	0.195245i
$262$	2.16190	+	4.48923i	0.133563	+	0.277346i
$263$	12.3499	−	9.84868i	0.761525	−	0.607296i	−0.163790	−	0.986495i	$-0.552372\pi$
$263$	12.3499	−	9.84868i	0.761525	−	0.607296i	0.925315	+	0.379199i	$0.123801\pi$
$264$	−7.14366			−0.439662
$265$	13.7364	+	17.9048i	0.843823	+	1.09988i
$266$	−4.51665	−	5.66370i	−0.276934	−	0.347264i
$267$	−6.44722	+	13.3878i	−0.394563	+	0.819319i
$268$	−4.99258	−	3.98145i	−0.304970	−	0.243206i
$269$	25.5151	+	12.2874i	1.55568	+	0.749178i	0.996790	−	0.0800614i	$-0.0255116\pi$
$269$	25.5151	+	12.2874i	1.55568	+	0.749178i	0.558894	+	0.829239i	$0.311226\pi$
$270$	4.96311	+	4.11280i	0.302046	+	0.250297i
$271$	−12.5910	−	15.7886i	−0.764846	−	0.959087i	0.235071	−	0.971978i	$-0.424468\pi$
$271$	−12.5910	−	15.7886i	−0.764846	−	0.959087i	−0.999917	+	0.0128914i	$0.995896\pi$
$272$	−4.68485	+	1.06929i	−0.284061	+	0.0648351i
$273$	−9.62292	−	19.9822i	−0.582406	−	1.20938i
$274$	1.57827	−	1.97908i	0.0953465	−	0.119561i
$275$	9.81754	+	13.3069i	0.592020	+	0.802437i
$276$	−0.322930	+	1.41485i	−0.0194381	+	0.0851640i
$277$	−2.12240	−	4.40720i	−0.127523	−	0.264803i	0.827426	−	0.561575i	$-0.189804\pi$
$277$	−2.12240	−	4.40720i	−0.127523	−	0.264803i	−0.954949	+	0.296772i	$0.904090\pi$
$278$	−4.30144	+	8.93203i	−0.257983	+	0.535708i
$279$	3.98379	−	17.4541i	0.238503	−	1.04495i
$280$	−1.82830	−	3.98635i	−0.109262	−	0.238230i
$281$	14.3133	+	6.89294i	0.853862	+	0.411198i	0.809010	−	0.587795i	$-0.200004\pi$
$281$	14.3133	+	6.89294i	0.853862	+	0.411198i	0.0448524	+	0.998994i	$0.485718\pi$
$282$	2.04937	+	4.25557i	0.122038	+	0.253415i
$283$	12.7264	+	2.90473i	0.756508	+	0.172668i	0.583344	−	0.812225i	$-0.301744\pi$
$283$	12.7264	+	2.90473i	0.756508	+	0.172668i	0.173164	+	0.984893i	$0.444601\pi$
$284$	−7.01138	+	8.79200i	−0.416049	+	0.521709i
$285$	17.8359	+	0.335051i	1.05651	+	0.0198467i
$286$	15.6001	−	7.51261i	0.922453	−	0.444230i
$287$	−19.3189	+	4.40942i	−1.14036	+	0.260280i
$288$	−1.30208	+	1.03838i	−0.0767260	+	0.0611869i
$289$	1.35543	+	5.93851i	0.0797310	+	0.349324i
$290$	0.886910	+	4.25246i	0.0520811	+	0.249713i
$291$	2.60360	−	3.26481i	0.152626	−	0.191387i
$292$	4.73147	−	9.82500i	0.276888	−	0.574965i
$293$	−17.9457	+	14.3113i	−1.04840	+	0.836072i	−0.986786	−	0.162028i	$-0.948197\pi$
$293$	−17.9457	+	14.3113i	−1.04840	+	0.836072i	−0.0616152	+	0.998100i	$0.519625\pi$
$294$	−6.81093			−0.397221
$295$	4.92915	−	3.78162i	0.286986	−	0.220174i
$296$	6.25112	+	7.83866i	0.363339	+	0.455613i
$297$	−4.13654	−	8.58960i	−0.240026	−	0.498419i
$298$	6.00159	+	1.36982i	0.347663	+	0.0793518i
$299$	−0.782718	−	3.42931i	−0.0452657	−	0.198322i
$300$	10.4313	+	2.79693i	0.602254	+	0.161481i
$301$	−12.5787	+	2.68060i	−0.725025	+	0.154507i
$302$		−	7.70607i		−	0.443435i
$303$	18.7883	−	4.28830i	1.07936	−	0.246356i
$304$	0.821886	−	3.60092i	0.0471384	−	0.206527i
$305$	2.09262	−	4.14439i	0.119823	−	0.237307i
$306$	4.98975	+	6.25695i	0.285245	+	0.357686i
$307$		−	18.7645i		−	1.07094i	−0.844553	−	0.535472i	$-0.820134\pi$
$307$		−	18.7645i		−	1.07094i	0.844553	−	0.535472i	$-0.179866\pi$
$308$			6.48666i			0.369612i
$309$	−17.2607	−	21.6442i	−0.981927	−	1.23130i
$310$	4.90771	+	23.5309i	0.278739	+	1.33647i
$311$	−18.1965	+	22.8176i	−1.03183	+	1.29387i	−0.0768966	+	0.997039i	$0.524501\pi$
$311$	−18.1965	+	22.8176i	−1.03183	+	1.29387i	−0.954930	+	0.296831i	$0.904070\pi$
$312$	4.90638	−	10.1882i	0.277769	−	0.576793i
$313$	−7.57457	+	1.72885i	−0.428140	+	0.0977202i	−0.431161	−	0.902275i	$-0.641896\pi$
$313$	−7.57457	+	1.72885i	−0.428140	+	0.0977202i	0.00302030	+	0.999995i	$0.499039\pi$
$314$	−3.53665	−	4.43482i	−0.199585	−	0.250271i
$315$	−4.66038	+	5.62391i	−0.262582	+	0.316871i
$316$	−4.84869	+	2.33501i	−0.272760	+	0.131354i
$317$	−23.0658	−	18.3944i	−1.29550	−	1.03313i	−0.996894	−	0.0787554i	$-0.974905\pi$
$317$	−23.0658	−	18.3944i	−1.29550	−	1.03313i	−0.298611	−	0.954375i	$-0.596523\pi$
$318$	−17.0431	−	13.5914i	−0.955728	−	0.762168i
$319$	1.42971	−	6.26396i	0.0800483	−	0.350714i
$320$	1.00786	−	1.99605i	0.0563411	−	0.111583i
$321$	13.4381	+	6.47143i	0.750039	+	0.361200i
$322$	1.28473	+	0.293231i	0.0715950	+	0.0163411i
$323$	−17.3036	−	3.94944i	−0.962799	−	0.219753i
$324$	−10.1112	−	4.86932i	−0.561736	−	0.270518i
$325$	−25.7210	+	4.86225i	−1.42674	+	0.269709i
$326$	−0.270083	+	1.18331i	−0.0149585	+	0.0655375i
$327$	−29.3559	−	23.4106i	−1.62339	−	1.29461i
$328$	−7.89910	−	6.29932i	−0.436155	−	0.347822i
$329$	3.86418	−	1.86089i	0.213039	−	0.102594i
$330$	−12.2995	−	10.1923i	−0.677065	−	0.561065i
$331$	2.07533	+	2.60238i	0.114071	+	0.143040i	0.835589	−	0.549356i	$-0.185127\pi$
$331$	2.07533	+	2.60238i	0.114071	+	0.143040i	−0.721518	+	0.692396i	$0.756555\pi$
$332$	4.43242	−	1.01167i	0.243261	−	0.0555226i
$333$	7.24482	−	15.0440i	0.397014	−	0.824408i
$334$	11.0926	−	13.9096i	0.606959	−	0.761102i
$335$	−2.91534	−	13.9782i	−0.159282	−	0.763709i
$336$	2.64132	+	3.31211i	0.144096	+	0.180690i
$337$			5.67368i			0.309065i	0.987988	+	0.154532i	$0.0493871\pi$
$337$			5.67368i			0.309065i	−0.987988	+	0.154532i	$0.950613\pi$
$338$			14.4084i			0.783714i
$339$	−15.8709	−	19.9015i	−0.861989	−	1.08090i
$340$	−9.59169	−	4.84311i	−0.520182	−	0.262654i
$341$	7.91127	−	34.6615i	0.428419	−	1.87703i
$342$	−5.99707	+	1.36879i	−0.324284	+	0.0740158i
$343$			19.9137i			1.07524i
$344$	−5.06727	−	4.16207i	−0.273209	−	0.224404i
$345$	−2.57464	+	1.97525i	−0.138614	+	0.106344i
$346$	−2.95759	−	12.9580i	−0.159001	−	0.696629i
$347$	−0.965228	−	0.220307i	−0.0518162	−	0.0118267i	0.196534	−	0.980497i	$-0.437031\pi$
$347$	−0.965228	−	0.220307i	−0.0518162	−	0.0118267i	−0.248350	+	0.968670i	$0.579888\pi$
$348$	−1.82062	−	3.78056i	−0.0975957	−	0.202659i
$349$	−19.7254	−	24.7349i	−1.05588	−	1.32403i	−0.943869	−	0.330320i	$-0.892843\pi$
$349$	−19.7254	−	24.7349i	−1.05588	−	1.32403i	−0.112008	−	0.993707i	$-0.535728\pi$
$350$	2.53969	−	9.47197i	0.135752	−	0.506298i
$351$	15.0914			0.805520
$352$	−2.58576	+	2.06208i	−0.137822	+	0.109909i
$353$	5.77450	−	11.9909i	0.307346	−	0.638210i	−0.688893	−	0.724863i	$-0.741903\pi$
$353$	5.77450	−	11.9909i	0.307346	−	0.638210i	0.996239	+	0.0866535i	$0.0276173\pi$
$354$	−3.74169	+	4.69193i	−0.198869	+	0.249373i
$355$	−24.6158	+	5.13396i	−1.30647	+	0.272483i
$356$	1.53082	+	6.70696i	0.0811333	+	0.355468i
$357$	15.9158	−	12.6924i	0.842353	−	0.671754i
$358$	12.3266	−	2.81347i	0.651481	−	0.148696i
$359$	−0.150199	+	0.0723318i	−0.00792718	+	0.00381753i	−0.437843	−	0.899051i	$-0.644257\pi$
$359$	−0.150199	+	0.0723318i	−0.00792718	+	0.00381753i	0.429916	+	0.902869i	$0.358543\pi$
$360$	−3.72335	−	0.0699439i	−0.196238	−	0.00368637i
$361$	−3.34058	+	4.18896i	−0.175820	+	0.220472i
$362$	−23.6878	−	5.40658i	−1.24500	−	0.284163i
$363$	−0.0578024	−	0.120028i	−0.00303384	−	0.00629983i
$364$	−9.25119	−	4.45514i	−0.484894	−	0.233513i
$365$	22.1642	−	10.1654i	1.16013	−	0.532081i
$366$	−0.997944	+	4.37228i	−0.0521634	+	0.228543i
$367$	13.4460	−	27.9210i	0.701877	−	1.45746i	−0.178869	−	0.983873i	$-0.557244\pi$
$367$	13.4460	−	27.9210i	0.701877	−	1.45746i	0.880746	−	0.473589i	$-0.157042\pi$
$368$	0.291518	+	0.605344i	0.0151964	+	0.0315557i
$369$	−3.74422	+	16.4045i	−0.194916	+	0.853984i
$370$	−0.421069	+	22.4149i	−0.0218903	+	1.16530i
$371$	−12.3414	+	15.4756i	−0.640734	+	0.803455i
$372$	−10.0744	−	20.9197i	−0.522333	−	1.08464i
$373$	−3.99002	+	0.910696i	−0.206595	+	0.0471541i	−0.324566	−	0.945863i	$-0.605218\pi$
$373$	−3.99002	+	0.910696i	−0.206595	+	0.0471541i	0.117971	+	0.993017i	$0.462361\pi$
$374$	9.90896	+	12.4254i	0.512380	+	0.642505i
$375$	13.9695	+	19.6985i	0.721381	+	1.01723i
$376$	1.97021	+	0.948801i	0.101606	+	0.0489307i
$377$	7.95163	+	6.34121i	0.409530	+	0.326589i
$378$	−2.45306	+	5.09382i	−0.126172	+	0.261998i
$379$	−9.46599	−	11.8700i	−0.486235	−	0.609720i	0.476828	−	0.878997i	$-0.341787\pi$
$379$	−9.46599	−	11.8700i	−0.486235	−	0.609720i	−0.963063	+	0.269277i	$0.913215\pi$
$380$	6.55270	−	5.02720i	0.336146	−	0.257890i
$381$	−20.4857			−1.04951
$382$	−1.13741	+	0.907050i	−0.0581947	+	0.0464087i
$383$	10.8097	+	22.4467i	0.552352	+	1.14697i	0.971057	+	0.238849i	$0.0767700\pi$
$383$	10.8097	+	22.4467i	0.552352	+	1.14697i	−0.418705	+	0.908123i	$0.637516\pi$
$384$	−0.480636	+	2.10581i	−0.0245274	+	0.107461i
$385$	−9.25488	+	11.1683i	−0.471672	+	0.569190i
$386$	−16.9603			−0.863257
$387$	−2.58356	+	10.6109i	−0.131330	+	0.539384i
$388$		−	1.93330i		−	0.0981485i
$389$	6.38927	+	27.9932i	0.323949	+	1.41931i	0.830460	+	0.557079i	$0.188078\pi$
$389$	6.38927	+	27.9932i	0.323949	+	1.41931i	−0.506511	+	0.862234i	$0.669065\pi$
$390$	22.9835	−	10.5412i	1.16382	−	0.533773i
$391$	2.90888	−	1.40084i	0.147108	−	0.0708436i
$392$	−2.46532	+	1.96603i	−0.124518	+	0.0992995i
$393$		−	10.7624i		−	0.542890i
$394$	−6.22402			−0.313562
$395$	−11.6796	−	2.89763i	−0.587667	−	0.145796i
$396$	4.96262	+	2.38987i	0.249381	+	0.120096i
$397$	22.8402	+	18.2145i	1.14632	+	0.914158i	0.997209	−	0.0746631i	$-0.0237881\pi$
$397$	22.8402	+	18.2145i	1.14632	+	0.914158i	0.149109	+	0.988821i	$0.452360\pi$
$398$	6.63506	−	13.7778i	0.332586	−	0.690621i
$399$	3.48180	+	15.2548i	0.174308	+	0.763693i
$400$	4.58314	−	1.99870i	0.229157	−	0.0999350i
$401$	5.37655	+	23.5562i	0.268492	+	1.17634i	0.911768	+	0.410706i	$0.134718\pi$
$401$	5.37655	+	23.5562i	0.268492	+	1.17634i	−0.643276	+	0.765635i	$0.722425\pi$
$402$	5.98454	+	12.4270i	0.298482	+	0.619803i
$403$	44.0003	+	35.0890i	2.19181	+	1.74791i
$404$	5.56285	−	6.97560i	0.276762	−	0.347049i
$405$	−10.4616	−	22.8099i	−0.519839	−	1.13344i
$406$	−3.43287	+	1.65318i	−0.170370	+	0.0820460i
$407$	14.3872	−	29.8754i	0.713149	−	1.48087i
$408$	10.1191	+	2.30962i	0.500970	+	0.114343i
$409$	−0.693204	+	3.03713i	−0.0342767	+	0.150176i	−0.989170	−	0.146772i	$-0.953112\pi$
$409$	−0.693204	+	3.03713i	−0.0342767	+	0.150176i	0.954894	+	0.296948i	$0.0959688\pi$
$410$	−4.61257	−	22.1159i	−0.227799	−	1.09222i
$411$	−4.92613	+	2.37230i	−0.242988	+	0.117017i
$412$	−12.4956	−	2.85203i	−0.615612	−	0.140510i
$413$	4.26041	+	3.39757i	0.209641	+	0.167183i
$414$	0.697666	−	0.874845i	0.0342884	−	0.0429963i
$415$	9.07486	+	4.58215i	0.445467	+	0.224929i
$416$	−1.16496	−	5.10404i	−0.0571171	−	0.250246i
$417$	16.7417	−	13.3511i	0.819844	−	0.653804i
$418$	−11.9094	+	2.71824i	−0.582506	+	0.132953i
$419$	25.7250	+	12.3885i	1.25675	+	0.605218i	0.939313	−	0.343062i	$-0.111464\pi$
$419$	25.7250	+	12.3885i	1.25675	+	0.605218i	0.317436	+	0.948280i	$0.397178\pi$
$420$	−0.177916	+	9.47109i	−0.00868143	+	0.462142i
$421$	20.2688	+	9.76093i	0.987839	+	0.475718i	0.856794	−	0.515658i	$-0.172452\pi$
$421$	20.2688	+	9.76093i	0.987839	+	0.475718i	0.131045	+	0.991376i	$0.458167\pi$
$422$	7.20143	−	5.74295i	0.350560	−	0.279562i
$423$		−	3.64190i		−	0.177075i
$424$	−10.0923			−0.490124
$425$	−9.60442	−	22.0235i	−0.465883	−	1.06830i
$426$	21.8842	−	10.5389i	1.06029	−	0.510609i
$427$	3.97016	+	0.906164i	0.192130	+	0.0438523i
$428$	6.73214	−	1.53657i	0.325410	−	0.0742728i
$429$	−37.3993			−1.80565
$430$	−2.78624	−	14.3957i	−0.134364	−	0.694223i
$431$	21.5858			1.03975			0.519875	−	0.854242i	$-0.325978\pi$
$431$	21.5858			1.03975			0.519875	+	0.854242i	$0.325978\pi$
$432$	−2.81035	+	0.641444i	−0.135213	+	0.0308615i
$433$	−0.688758	−	0.157204i	−0.0330996	−	0.00755476i	0.205939	−	0.978565i	$-0.433975\pi$
$433$	−0.688758	−	0.157204i	−0.0330996	−	0.00755476i	−0.239039	+	0.971010i	$0.576832\pi$
$434$	−18.9957	+	9.14786i	−0.911824	+	0.439111i
$435$	2.25931	−	9.10671i	0.108325	−	0.436633i
$436$	−17.3835			−0.832518
$437$			2.48161i			0.118711i
$438$	−18.4154	+	14.6858i	−0.879923	+	0.701715i
$439$	−5.09498	−	2.45361i	−0.243170	−	0.117104i	0.308330	−	0.951280i	$-0.400230\pi$
$439$	−5.09498	−	2.45361i	−0.243170	−	0.117104i	−0.551500	+	0.834175i	$0.685944\pi$
$440$	−7.39407	−	0.138899i	−0.352499	−	0.00662176i
$441$	4.73147	+	2.27856i	0.225308	+	0.108503i
$442$	−24.5266	+	5.59804i	−1.16661	+	0.266272i
$443$	26.1456	−	20.8505i	1.24222	−	0.990635i	0.242427	−	0.970170i	$-0.422057\pi$
$443$	26.1456	−	20.8505i	1.24222	−	0.990635i	0.999791	−	0.0204654i	$-0.00651478\pi$
$444$	−4.81887	−	21.1129i	−0.228694	−	1.00197i
$445$	−6.93352	+	13.7317i	−0.328680	+	0.650946i
$446$	−7.06585	+	8.86030i	−0.334578	+	0.419547i
$447$	−10.3957	−	8.29028i	−0.491699	−	0.392117i
$448$	1.91214	+	0.436432i	0.0903399	+	0.0206195i
$449$	3.20300	−	1.54248i	0.151159	−	0.0727942i	−0.356775	−	0.934190i	$-0.616124\pi$
$449$	3.20300	−	1.54248i	0.151159	−	0.0727942i	0.507934	+	0.861396i	$0.330409\pi$
$450$	−6.31083	−	5.43273i	−0.297495	−	0.256102i
$451$	−7.43551	+	32.5771i	−0.350125	+	1.53400i
$452$	−11.4894	−	2.62239i	−0.540418	−	0.123347i
$453$	−7.22191	+	14.9965i	−0.339315	+	0.704595i
$454$	−4.64394	+	2.23640i	−0.217951	+	0.104960i
$455$	−9.57171	−	20.8698i	−0.448729	−	0.978389i
$456$	−4.97412	+	6.23735i	−0.232934	+	0.292090i
$457$	22.7412	+	18.1355i	1.06379	+	0.848344i	0.988861	−	0.148845i	$-0.0475556\pi$
$457$	22.7412	+	18.1355i	1.06379	+	0.848344i	0.0749288	+	0.997189i	$0.476127\pi$
$458$	−4.50873	−	9.36248i	−0.210679	−	0.437480i
$459$	3.08235	+	13.5047i	0.143872	+	0.630344i
$460$	−0.361760	+	1.45817i	−0.0168671	+	0.0679874i
$461$	−5.37672	−	23.5570i	−0.250419	−	1.09716i	−0.931154	−	0.364627i	$-0.881197\pi$
$461$	−5.37672	−	23.5570i	−0.250419	−	1.09716i	0.680735	−	0.732530i	$-0.261661\pi$
$462$	6.07912	−	12.6234i	0.282826	−	0.587295i
$463$	−4.16290	−	3.31980i	−0.193466	−	0.154284i	0.521966	−	0.852966i	$-0.325199\pi$
$463$	−4.16290	−	3.31980i	−0.193466	−	0.154284i	−0.715432	+	0.698682i	$0.753770\pi$
$464$	−1.75029	−	0.842897i	−0.0812553	−	0.0391305i
$465$	12.5018	−	50.3919i	0.579759	−	2.33687i
$466$	0.259573			0.0120245
$467$			14.3868i			0.665742i	0.942972	+	0.332871i	$0.108017\pi$
$467$			14.3868i			0.665742i	−0.942972	+	0.332871i	$0.891983\pi$
$468$	−6.81680	+	5.43622i	−0.315107	+	0.251289i
$469$	11.2841	−	5.43414i	0.521052	−	0.250925i
$470$	2.03847	+	4.44458i	0.0940274	+	0.205013i
$471$	2.72634	+	11.9449i	0.125623	+	0.550390i
$472$			2.77839i			0.127886i
$473$	−5.13060	+	21.0719i	−0.235905	+	0.968887i
$474$	11.6241			0.533914
$475$	18.4546	+	0.693591i	0.846755	+	0.0318241i
$476$	2.09720	−	9.18845i	0.0961251	−	0.421152i
$477$	7.29270	+	15.1434i	0.333910	+	0.693371i
$478$	20.4291	−	16.2917i	0.934405	−	0.745163i
$479$	1.41467			0.0646380			0.0323190	−	0.999478i	$-0.489711\pi$
$479$	1.41467			0.0646380			0.0323190	+	0.999478i	$0.489711\pi$
$480$	−3.83200	+	2.93989i	−0.174906	+	0.134187i
$481$	32.7265	+	41.0378i	1.49220	+	1.87116i
$482$	8.44668	−	17.5397i	0.384736	−	0.798912i
$483$	−2.22534	−	1.77465i	−0.101257	−	0.0807495i
$484$	−0.0555695	−	0.0267608i	−0.00252588	−	0.00121640i
$485$	2.75835	−	3.32863i	0.125250	−	0.151145i
$486$	9.72181	+	12.1908i	0.440990	+	0.552984i
$487$	−12.0365	+	2.74726i	−0.545428	+	0.124490i	−0.486352	−	0.873763i	$-0.661673\pi$
$487$	−12.0365	+	2.74726i	−0.545428	+	0.124490i	−0.0590760	+	0.998253i	$0.518815\pi$
$488$	0.900872	+	1.87068i	0.0407806	+	0.0846817i
$489$	1.63456	−	2.04967i	0.0739174	−	0.0926895i
$490$	−7.04967	−	0.132430i	−0.318472	−	0.00598256i
$491$	0.159045	−	0.696822i	0.00717760	−	0.0314471i	−0.971212	−	0.238216i	$-0.923438\pi$
$491$	0.159045	−	0.696822i	0.00717760	−	0.0314471i	0.978390	+	0.206768i	$0.0662947\pi$
$492$	9.46856	+	19.6617i	0.426875	+	0.886416i
$493$	−4.05040	+	8.41074i	−0.182421	+	0.378801i
$494$	4.30283	−	18.8519i	0.193593	−	0.848188i
$495$	5.13455	+	11.1952i	0.230781	+	0.503185i
$496$	−9.68523	−	4.66416i	−0.434880	−	0.209427i
$497$	−9.56960	−	19.8715i	−0.429255	−	0.891358i
$498$	−9.57385	−	2.18517i	−0.429014	−	0.0979197i
$499$	1.72140	−	2.15856i	0.0770603	−	0.0966306i	−0.741807	−	0.670613i	$-0.766031\pi$
$499$	1.72140	−	2.15856i	0.0770603	−	0.0966306i	0.818867	+	0.573983i	$0.194602\pi$
$500$	10.7426	+	3.09779i	0.480424	+	0.138537i
$501$	−34.6225	+	16.6733i	−1.54682	+	0.744909i
$502$	16.8555	−	3.84716i	0.752298	−	0.171707i
$503$	2.41887	−	1.92899i	0.107852	−	0.0860093i	−0.568079	−	0.822974i	$-0.692313\pi$
$503$	2.41887	−	1.92899i	0.107852	−	0.0860093i	0.675931	+	0.736965i	$0.263742\pi$
$504$	−0.726846	−	3.18452i	−0.0323763	−	0.141850i
$505$	19.5302	−	4.07330i	0.869083	−	0.181260i
$506$	1.38547	−	1.73732i	0.0615916	−	0.0772335i
$507$	13.5032	−	28.0396i	0.599696	−	1.24528i
$508$	−7.41511	+	5.91336i	−0.328992	+	0.262363i
$509$	−11.0567			−0.490079			−0.245039	−	0.969513i	$-0.578801\pi$
$509$	−11.0567			−0.490079			−0.245039	+	0.969513i	$0.578801\pi$
$510$	14.1271	+	18.4140i	0.625560	+	0.815386i
$511$	13.3352	+	16.7218i	0.589913	+	0.739727i
$512$	0.433884	+	0.900969i	0.0191751	+	0.0398176i
$513$	−10.3801	−	2.36919i	−0.458292	−	0.104602i
$514$	−1.79405	−	7.86024i	−0.0791321	−	0.346700i
$515$	−17.4449	−	22.7386i	−0.768714	−	1.00198i
$516$	5.96061	+	12.8485i	0.262401	+	0.565625i
$517$		−	7.23231i		−	0.318077i
$518$	−19.1711	+	4.37568i	−0.842330	+	0.192256i
$519$	−6.38827	+	27.9888i	−0.280414	+	1.22857i
$520$	5.27646	−	10.4499i	0.231388	−	0.458260i
$521$	−0.663857	−	0.832450i	−0.0290841	−	0.0364703i	0.767077	−	0.641555i	$-0.221711\pi$
$521$	−0.663857	−	0.832450i	−0.0290841	−	0.0364703i	−0.796161	+	0.605085i	$0.793139\pi$
$522$			3.23539i			0.141609i
$523$			20.1747i			0.882176i	0.897464	+	0.441088i	$0.145407\pi$
$523$			20.1747i			0.882176i	−0.897464	+	0.441088i	$0.854593\pi$
$524$	−3.10664	−	3.89561i	−0.135714	−	0.170180i
$525$	−13.8193	+	16.0529i	−0.603122	+	0.700605i
$526$	−9.84868	+	12.3499i	−0.429423	+	0.538479i
$527$	−22.4128	+	46.5408i	−0.976319	+	2.02735i
$528$	6.96456	−	1.58961i	0.303093	−	0.0691791i
$529$	14.0588	+	17.6292i	0.611252	+	0.766486i
$530$	−17.3762	−	14.3992i	−0.754775	−	0.625461i
$531$	4.16896	−	2.00767i	0.180918	−	0.0871253i
$532$	5.66370	+	4.51665i	0.245553	+	0.195822i
$533$	−41.3542	−	32.9789i	−1.79125	−	1.42847i
$534$	3.30651	−	14.4868i	0.143087	−	0.626904i
$535$	13.7833	+	6.95956i	0.595903	+	0.300888i
$536$	5.75336	+	2.77067i	0.248507	+	0.119675i
$537$	−26.6250	−	6.07697i	−1.14895	−	0.262241i
$538$	−27.6096	−	6.30171i	−1.19033	−	0.271686i
$539$	9.39606	+	4.52490i	0.404717	+	0.194901i
$540$	−5.75386	−	2.90528i	−0.247607	−	0.125024i
$541$	−2.41252	+	10.5699i	−0.103722	+	0.454438i	0.896219	+	0.443612i	$0.146303\pi$
$541$	−2.41252	+	10.5699i	−0.103722	+	0.454438i	−0.999941	+	0.0108257i	$0.996554\pi$
$542$	15.7886	+	12.5910i	0.678177	+	0.540828i
$543$	41.0308	+	32.7210i	1.76080	+	1.40419i
$544$	4.32946	−	2.08496i	0.185624	−	0.0893918i
$545$	−29.9297	−	24.8020i	−1.28205	−	1.06240i
$546$	13.8281	+	17.3399i	0.591789	+	0.742080i
$547$	−21.2762	+	4.85614i	−0.909703	+	0.207634i	−0.651670	−	0.758503i	$-0.725931\pi$
$547$	−21.2762	+	4.85614i	−0.909703	+	0.207634i	−0.258033	+	0.966136i	$0.583074\pi$
$548$	−1.09831	+	2.28066i	−0.0469174	+	0.0974249i
$549$	2.15598	−	2.70351i	0.0920150	−	0.115383i
$550$	−12.5325	−	10.7887i	−0.534386	−	0.460031i
$551$	−4.47375	−	5.60990i	−0.190588	−	0.238990i
$552$		−	1.45124i		−	0.0617687i
$553$		−	10.5551i		−	0.448847i
$554$	3.04988	+	3.82443i	0.129577	+	0.162484i
$555$	21.8260	−	43.2261i	0.926464	−	1.83485i
$556$	2.20603	−	9.66525i	0.0935565	−	0.409898i
$557$	−11.2945	+	2.57790i	−0.478564	+	0.109229i	−0.454997	−	0.890493i	$-0.650360\pi$
$557$	−11.2945	+	2.57790i	−0.478564	+	0.109229i	−0.0235672	+	0.999722i	$0.507502\pi$
$558$			17.9030i			0.757894i
$559$	−26.5287	−	21.7897i	−1.12204	−	0.921606i
$560$	2.66951	+	3.47957i	0.112807	+	0.147039i
$561$	−7.63863	−	33.4670i	−0.322503	−	1.41298i
$562$	−15.4883	−	3.53510i	−0.653334	−	0.149119i
$563$	−12.9204	−	26.8295i	−0.544531	−	1.13073i	−0.973769	−	0.227539i	$-0.926932\pi$
$563$	−12.9204	−	26.8295i	−0.544531	−	1.13073i	0.429238	−	0.903192i	$-0.358782\pi$
$564$	−2.94494	−	3.69284i	−0.124004	−	0.155497i
$565$	−16.0403	−	20.9077i	−0.674819	−	0.879593i
$566$	−13.0537			−0.548689
$567$	17.2089	−	13.7237i	0.722707	−	0.576340i
$568$	4.87919	−	10.1317i	0.204726	−	0.425119i
$569$	5.52880	−	6.93290i	0.231779	−	0.290642i	−0.652317	−	0.757946i	$-0.726203\pi$
$569$	5.52880	−	6.93290i	0.231779	−	0.290642i	0.884097	+	0.467304i	$0.154775\pi$
$570$	−17.4633	+	3.64221i	−0.731456	+	0.152555i
$571$	−1.84540	−	8.08523i	−0.0772277	−	0.338356i	0.921523	−	0.388323i	$-0.126946\pi$
$571$	−1.84540	−	8.08523i	−0.0772277	−	0.338356i	−0.998751	+	0.0499668i	$0.984088\pi$
$572$	−13.5373	+	10.7956i	−0.566021	+	0.451387i
$573$	3.06352	−	0.699228i	0.127980	−	0.0292107i
$574$	17.8534	−	8.59774i	0.745186	−	0.358863i
$575$	−2.70330	+	1.99443i	−0.112735	+	0.0831736i
$576$	1.03838	−	1.30208i	0.0432657	−	0.0542535i
$577$	8.53909	+	1.94899i	0.355487	+	0.0811376i	0.396535	−	0.918020i	$-0.370213\pi$
$577$	8.53909	+	1.94899i	0.355487	+	0.0811376i	−0.0410480	+	0.999157i	$0.513070\pi$
$578$	−2.64289	−	5.48801i	−0.109930	−	0.228271i
$579$	33.0057	+	15.8947i	1.37167	+	0.660562i
$580$	−1.81093	−	3.94848i	−0.0751949	−	0.163952i
$581$	−1.98420	+	8.69334i	−0.0823185	+	0.360661i
$582$	−1.81183	+	3.76231i	−0.0751029	+	0.155953i
$583$	14.4823	+	30.0728i	0.599796	+	1.24549i
$584$	−2.42657	+	10.6315i	−0.100412	+	0.439935i
$585$	−19.4929	−	0.366178i	−0.805931	−	0.0151396i
$586$	14.3113	−	17.9457i	0.591192	−	0.741332i
$587$	9.99293	+	20.7505i	0.412452	+	0.856466i	0.998919	+	0.0464925i	$0.0148044\pi$
$587$	9.99293	+	20.7505i	0.412452	+	0.856466i	−0.586466	+	0.809974i	$0.699481\pi$
$588$	6.64016	−	1.51557i	0.273836	−	0.0625012i
$589$	−24.7554	−	31.0423i	−1.02003	−	1.27908i
$590$	−3.96408	+	4.78364i	−0.163198	+	0.196940i
$591$	12.1123	+	5.83297i	0.498233	+	0.239936i
$592$	−7.83866	−	6.25112i	−0.322167	−	0.256920i
$593$	4.26427	−	8.85485i	0.175113	−	0.363625i	−0.794877	−	0.606770i	$-0.792465\pi$
$593$	4.26427	−	8.85485i	0.175113	−	0.363625i	0.969990	+	0.243145i	$0.0781791\pi$
$594$	5.94419	+	7.45378i	0.243893	+	0.305832i
$595$	16.7205	−	12.8279i	0.685473	−	0.525892i
$596$	−6.15593			−0.252157
$597$	−25.8244	+	20.5943i	−1.05692	+	0.842868i
$598$	1.52619	+	3.16916i	0.0624104	+	0.129597i
$599$	8.20148	−	35.9330i	0.335103	−	1.46818i	−0.474004	−	0.880523i	$-0.657192\pi$
$599$	8.20148	−	35.9330i	0.335103	−	1.46818i	0.809107	−	0.587661i	$-0.199951\pi$
$600$	−10.7922	−	0.405610i	−0.440589	−	0.0165589i
$601$	45.4636			1.85450			0.927250	−	0.374442i	$-0.122166\pi$
$601$	45.4636			1.85450			0.927250	+	0.374442i	$0.122166\pi$
$602$	11.6668	−	5.41242i	0.475505	−	0.220594i
$603$		−	10.6350i		−	0.433090i
$604$	1.71476	+	7.51287i	0.0697727	+	0.305694i
$605$	−0.0574947	−	0.125359i	−0.00233749	−	0.00509657i
$606$	−17.3630	+	8.36156i	−0.705322	+	0.339665i
$607$	19.2271	−	15.3331i	0.780403	−	0.622351i	−0.150085	−	0.988673i	$-0.547955\pi$
$607$	19.2271	−	15.3331i	0.780403	−	0.622351i	0.930488	+	0.366323i	$0.119383\pi$
$608$			3.69352i			0.149792i
$609$	8.22987			0.333491
$610$	−1.11794	+	4.50614i	−0.0452640	+	0.182448i
$611$	10.3146	+	4.96726i	0.417285	+	0.200954i
$612$	−6.25695	−	4.98975i	−0.252922	−	0.201699i
$613$	−18.1778	+	37.7467i	−0.734196	+	1.52457i	0.113176	+	0.993575i	$0.463898\pi$
$613$	−18.1778	+	37.7467i	−0.734196	+	1.52457i	−0.847372	+	0.531000i	$0.821817\pi$
$614$	4.17548	+	18.2940i	0.168509	+	0.738285i
$615$	−11.7500	+	47.3615i	−0.473807	+	1.90980i
$616$	−1.44342	−	6.32403i	−0.0581570	−	0.254802i
$617$	8.58235	+	17.8214i	0.345513	+	0.717464i	0.999228	−	0.0392759i	$-0.0125051\pi$
$617$	8.58235	+	17.8214i	0.345513	+	0.717464i	−0.653716	+	0.756740i	$0.726791\pi$
$618$	21.6442	+	17.2607i	0.870659	+	0.694327i
$619$	1.08089	−	1.35539i	0.0434445	−	0.0544777i	−0.759635	−	0.650350i	$-0.774622\pi$
$619$	1.08089	−	1.35539i	0.0434445	−	0.0544777i	0.803079	+	0.595872i	$0.203194\pi$
$620$	−10.0208	−	21.8489i	−0.402444	−	0.877473i
$621$	1.74498	−	0.840337i	0.0700236	−	0.0337216i
$622$	12.6628	−	26.2946i	0.507733	−	1.05432i
$623$	−13.1544	−	3.00241i	−0.527021	−	0.120289i
$624$	−2.51628	+	11.0245i	−0.100732	+	0.441334i
$625$	14.0761	+	20.6606i	0.563046	+	0.826426i
$626$	6.99996	−	3.37100i	0.279775	−	0.134732i
$627$	25.7238	+	5.87128i	1.02731	+	0.234476i
$628$	4.43482	+	3.53665i	0.176969	+	0.141128i
$629$	−30.0387	+	37.6674i	−1.19772	+	1.50190i
$630$	3.29209	−	6.51993i	0.131160	−	0.259760i
$631$	−11.0384	−	48.3623i	−0.439431	−	1.92527i	−0.374035	−	0.927415i	$-0.622026\pi$
$631$	−11.0384	−	48.3623i	−0.439431	−	1.92527i	−0.0653967	−	0.997859i	$-0.520831\pi$
$632$	4.20754	−	3.35540i	0.167367	−	0.133471i
$633$	−19.3965	+	4.42713i	−0.770942	+	0.175963i
$634$	26.5806	+	12.8006i	1.05565	+	0.508375i
$635$	−21.2038	−	0.398317i	−0.841446	−	0.0158067i
$636$	19.6401	+	9.45819i	0.778782	+	0.375042i
$637$	−12.9067	+	10.2928i	−0.511383	+	0.407814i
$638$			6.42505i			0.254370i
$639$	−18.7284			−0.740883
$640$	−0.538429	+	2.17028i	−0.0212833	+	0.0857877i
$641$	−0.715862	+	0.344741i	−0.0282748	+	0.0136164i	−0.447968	−	0.894050i	$-0.647852\pi$
$641$	−0.715862	+	0.344741i	−0.0282748	+	0.0136164i	0.419693	+	0.907666i	$0.362138\pi$
$642$	−14.5412	−	3.31893i	−0.573894	−	0.130988i
$643$	−34.1858	+	7.80269i	−1.34816	+	0.307708i	−0.834841	−	0.550491i	$-0.814440\pi$
$643$	−34.1858	+	7.80269i	−1.34816	+	0.307708i	−0.513316	+	0.858199i	$0.671583\pi$
$644$	−1.31777			−0.0519273
$645$	−8.06909	+	30.6261i	−0.317720	+	1.20590i
$646$	17.7486			0.698310
$647$	41.9968	−	9.58550i	1.65107	−	0.376845i	0.707158	−	0.707056i	$-0.249977\pi$
$647$	41.9968	−	9.58550i	1.65107	−	0.376845i	0.943907	+	0.330211i	$0.107120\pi$
$648$	10.9413	+	2.49727i	0.429813	+	0.0981021i
$649$	8.27900	−	3.98696i	0.324979	−	0.156502i
$650$	23.9941	−	10.4638i	0.941128	−	0.410424i
$651$	45.5399			1.78485
$652$		−	1.21374i		−	0.0475338i
$653$	33.1189	−	26.4114i	1.29604	−	1.03356i	0.299197	−	0.954191i	$-0.403281\pi$
$653$	33.1189	−	26.4114i	1.29604	−	1.03356i	0.996845	−	0.0793678i	$-0.0252901\pi$
$654$	33.8292	+	16.2913i	1.32283	+	0.637040i
$655$	0.209260	−	11.1396i	0.00817647	−	0.435261i
$656$	9.10279	+	4.38367i	0.355404	+	0.171154i
$657$	17.7060	−	4.04128i	0.690778	−	0.157665i
$658$	−3.35321	+	2.67410i	−0.130722	+	0.104247i
$659$	−9.65003	−	42.2796i	−0.375912	−	1.64698i	−0.709828	−	0.704375i	$-0.751227\pi$
$659$	−9.65003	−	42.2796i	−0.375912	−	1.64698i	0.333916	−	0.942603i	$-0.391630\pi$
$660$	14.2591	+	7.19982i	0.555035	+	0.280253i
$661$	−29.1186	+	36.5136i	−1.13258	+	1.42021i	−0.239170	+	0.970978i	$0.576875\pi$
$661$	−29.1186	+	36.5136i	−1.13258	+	1.42021i	−0.893413	+	0.449236i	$0.851696\pi$
$662$	−2.60238	−	2.07533i	−0.101145	−	0.0806601i
$663$	52.9766	+	12.0916i	2.05744	+	0.469597i
$664$	−4.09617	+	1.97261i	−0.158962	+	0.0765522i
$665$	3.30724	+	15.8572i	0.128249	+	0.614915i
$666$	−3.71557	+	16.2790i	−0.143975	+	0.630797i
$667$	1.27252	+	0.290445i	0.0492723	+	0.0112461i
$668$	−7.71927	+	16.0292i	−0.298668	+	0.620190i
$669$	22.0542	−	10.6207i	0.852663	−	0.410621i
$670$	5.95269	+	12.9790i	0.229972	+	0.501422i
$671$	4.28148	−	5.36881i	0.165285	−	0.207261i
$672$	−3.31211	−	2.64132i	−0.127767	−	0.101891i
$673$	−5.65303	−	11.7386i	−0.217908	−	0.452491i	0.763146	−	0.646227i	$-0.223654\pi$
$673$	−5.65303	−	11.7386i	−0.217908	−	0.452491i	−0.981054	+	0.193736i	$0.937940\pi$
$674$	−1.26251	−	5.53143i	−0.0486302	−	0.213063i
$675$	−5.76150	−	13.2115i	−0.221760	−	0.508510i
$676$	−3.20617	−	14.0472i	−0.123314	−	0.540275i
$677$	−15.2238	+	31.6126i	−0.585100	+	1.21497i	0.372811	+	0.927907i	$0.378394\pi$
$677$	−15.2238	+	31.6126i	−0.585100	+	1.21497i	−0.957911	+	0.287065i	$0.907320\pi$
$678$	19.9015	+	15.8709i	0.764312	+	0.609518i
$679$	3.41629	+	1.64520i	0.131105	+	0.0631370i
$680$	10.4289	+	2.58733i	0.399930	+	0.0992196i
$681$	11.1333			0.426627
$682$			35.5529i			1.36139i
$683$	10.1219	−	8.07191i	0.387302	−	0.308863i	−0.410411	−	0.911901i	$-0.634615\pi$
$683$	10.1219	−	8.07191i	0.387302	−	0.308863i	0.797713	+	0.603038i	$0.206043\pi$
$684$	5.54213	−	2.66895i	0.211908	−	0.102050i
$685$	−5.14494	+	2.35968i	−0.196578	+	0.0901586i
$686$	−4.43121	−	19.4144i	−0.169185	−	0.741246i
$687$			22.4454i			0.856345i
$688$	5.86637	+	2.93014i	0.223653	+	0.111711i
$689$	−52.8361			−2.01290
$690$	2.07056	−	2.49864i	0.0788248	−	0.0951217i
$691$	−10.0950	+	44.2290i	−0.384031	+	1.68255i	0.300671	+	0.953728i	$0.402789\pi$
$691$	−10.0950	+	44.2290i	−0.384031	+	1.68255i	−0.684702	+	0.728823i	$0.740068\pi$
$692$	5.76687	+	11.9750i	0.219224	+	0.455222i
$693$	−8.44618	+	6.73560i	−0.320844	+	0.255864i
$694$	0.990051			0.0375818
$695$	17.5881	−	13.4935i	0.667156	−	0.511839i
$696$	2.61623	+	3.28065i	0.0991680	+	0.124353i
$697$	21.0650	−	43.7419i	0.797894	−	1.65684i
$698$	24.7349	+	19.7254i	0.936229	+	0.746618i
$699$	−0.505144	−	0.243265i	−0.0191063	−	0.00920112i
$700$	−0.368306	+	9.79963i	−0.0139207	+	0.370391i
$701$	−5.32249	−	6.67419i	−0.201028	−	0.252081i	0.671091	−	0.741375i	$-0.265826\pi$
$701$	−5.32249	−	6.67419i	−0.201028	−	0.252081i	−0.872119	+	0.489294i	$0.837254\pi$
$702$	−14.7130	+	3.35816i	−0.555308	+	0.126745i
$703$	−16.0673	−	33.3641i	−0.605990	−	1.25835i
$704$	2.06208	−	2.58576i	0.0777174	−	0.0974546i
$705$	0.198368	−	10.5598i	0.00747097	−	0.397705i
$706$	−2.96150	+	12.9752i	−0.111458	+	0.488327i
$707$	7.59255	+	15.7661i	0.285547	+	0.592945i
$708$	2.60382	−	5.40690i	0.0978577	−	0.203204i
$709$	11.2082	−	49.1063i	0.420933	−	1.84423i	−0.106063	−	0.994359i	$-0.533825\pi$
$709$	11.2082	−	49.1063i	0.420933	−	1.84423i	0.526996	−	0.849868i	$-0.323318\pi$
$710$	22.8562	−	10.4828i	0.857777	−	0.393411i
$711$	−8.07514	−	3.88878i	−0.302842	−	0.145841i
$712$	−2.98488	−	6.19816i	−0.111863	−	0.232286i
$713$	7.04150	+	1.60718i	0.263706	+	0.0601892i
$714$	−12.6924	+	15.9158i	−0.475002	+	0.595634i
$715$	−38.7102	−	0.727179i	−1.44768	−	0.0271950i
$716$	−11.3915	+	5.48585i	−0.425720	+	0.205016i
$717$	−55.0243	+	12.5589i	−2.05492	+	0.469022i
$718$	0.130337	−	0.103941i	0.00486415	−	0.00387903i
$719$	5.45932	+	23.9189i	0.203598	+	0.892023i	0.968724	+	0.248141i	$0.0798198\pi$
$719$	5.45932	+	23.9189i	0.203598	+	0.892023i	−0.765125	+	0.643881i	$0.777323\pi$
$720$	3.64556	−	0.760333i	0.135862	−	0.0283360i
$721$	15.6732	−	19.6536i	0.583702	−	0.731939i
$722$	2.32470	−	4.82728i	0.0865163	−	0.179653i
$723$	−32.8755	+	26.2173i	−1.22265	+	0.975032i
$724$	24.2969			0.902988
$725$	2.51557	−	9.38200i	0.0934259	−	0.348439i
$726$	0.0830618	+	0.104156i	0.00308271	+	0.00386560i
$727$	−5.41152	−	11.2371i	−0.200702	−	0.416762i	0.776189	−	0.630501i	$-0.217150\pi$
$727$	−5.41152	−	11.2371i	−0.200702	−	0.416762i	−0.976891	+	0.213738i	$0.931436\pi$
$728$	10.0106	+	2.28486i	0.371018	+	0.0846824i
$729$	−0.00254171	−	0.0111359i	−9.41373e−5	−	0.000412442i
$730$	−19.3465	+	14.8425i	−0.716045	+	0.549347i
$731$	14.0803	−	28.1898i	0.520780	−	1.04264i
$732$		−	4.48472i		−	0.165760i
$733$	−36.8855	+	8.41887i	−1.36240	+	0.310958i	−0.840390	−	0.541983i	$-0.817674\pi$
$733$	−36.8855	+	8.41887i	−1.36240	+	0.310958i	−0.522007	+	0.852941i	$0.674817\pi$
$734$	−6.89591	+	30.2129i	−0.254533	+	1.11518i
$735$	13.5950	+	6.86447i	0.501457	+	0.253200i
$736$	−0.418911	−	0.525298i	−0.0154413	−	0.0193627i
$737$		−	21.1197i		−	0.777953i
$738$		−	16.8264i		−	0.619387i
$739$	−12.1091	−	15.1844i	−0.445441	−	0.558565i	0.507527	−	0.861636i	$-0.330560\pi$
$739$	−12.1091	−	15.1844i	−0.445441	−	0.558565i	−0.952968	+	0.303070i	$0.901988\pi$
$740$	−4.57728	−	21.9466i	−0.168264	−	0.806774i
$741$	−26.0410	+	32.6544i	−0.956641	+	1.19959i
$742$	8.58833	−	17.8338i	0.315287	−	0.654701i
$743$	12.3405	−	2.81664i	0.452730	−	0.103333i	0.00992521	−	0.999951i	$-0.496841\pi$
$743$	12.3405	−	2.81664i	0.452730	−	0.103333i	0.442805	+	0.896618i	$0.353984\pi$
$744$	14.4769	+	18.1534i	0.530748	+	0.665537i
$745$	−10.5989	−	8.78301i	−0.388313	−	0.321784i
$746$	3.68733	−	1.77573i	0.135003	−	0.0650139i
$747$	5.91980	+	4.72088i	0.216594	+	0.172728i
$748$	−12.4254	−	9.90896i	−0.454319	−	0.362308i
$749$	−3.01368	+	13.2038i	−0.110118	+	0.482457i
$750$	−18.0026	−	16.0961i	−0.657361	−	0.587748i
$751$	35.4477	+	17.0707i	1.29351	+	0.622919i	0.948826	−	0.315801i	$-0.102273\pi$
$751$	35.4477	+	17.0707i	1.29351	+	0.622919i	0.344680	+	0.938720i	$0.387987\pi$
$752$	−2.13194	−	0.486601i	−0.0777437	−	0.0177445i
$753$	−36.4072	−	8.30971i	−1.32675	−	0.302823i
$754$	−9.16332	−	4.41282i	−0.333708	−	0.160705i
$755$	−7.76665	+	15.3817i	−0.282657	+	0.559798i
$756$	1.25807	−	5.51197i	0.0457556	−	0.200468i
$757$	23.5828	+	18.8067i	0.857133	+	0.683541i	0.950038	−	0.312134i	$-0.101044\pi$
$757$	23.5828	+	18.8067i	0.857133	+	0.683541i	−0.0929051	+	0.995675i	$0.529615\pi$
$758$	11.8700	+	9.46599i	0.431137	+	0.343820i
$759$	−4.32437	+	2.08251i	−0.156965	+	0.0755903i
$760$	−5.26975	+	6.35927i	−0.191154	+	0.230675i
$761$	−4.41426	−	5.53531i	−0.160017	−	0.200655i	0.695359	−	0.718662i	$-0.255245\pi$
$761$	−4.41426	−	5.53531i	−0.160017	−	0.200655i	−0.855376	+	0.518008i	$0.826674\pi$
$762$	19.9721	−	4.55849i	0.723511	−	0.165137i
$763$	14.7930	−	30.7180i	0.535542	−	1.11207i
$764$	0.907050	−	1.13741i	0.0328159	−	0.0411499i
$765$	−3.65366	−	17.5181i	−0.132098	−	0.633370i
$766$	−15.5336	−	19.4785i	−0.561251	−	0.703786i
$767$			14.5457i			0.525215i
$768$		−	2.15996i		−	0.0779408i
$769$	4.20671	+	5.27505i	0.151698	+	0.190223i	0.851874	−	0.523747i	$-0.175466\pi$
$769$	4.20671	+	5.27505i	0.151698	+	0.190223i	−0.700176	+	0.713971i	$0.746895\pi$
$770$	6.53766	−	12.9477i	0.235601	−	0.466603i
$771$	−3.87507	+	16.9778i	−0.139557	+	0.611441i
$772$	16.5351	−	3.77403i	0.595111	−	0.135830i
$773$			0.864409i			0.0310906i	0.999879	+	0.0155453i	$0.00494842\pi$
$773$			0.864409i			0.0310906i	−0.999879	+	0.0155453i	$0.995052\pi$
$774$	0.157630	−	10.9198i	0.00566588	−	0.392504i
$775$	13.9199	−	51.9152i	0.500017	−	1.86485i
$776$	0.430200	+	1.88483i	0.0154433	+	0.0676614i
$777$	41.4088	+	9.45130i	1.48553	+	0.339063i
$778$	−12.4582	−	25.8696i	−0.446646	−	0.927471i
$779$	23.2667	+	29.1755i	0.833616	+	1.04532i
$780$	−20.0617	+	15.3912i	−0.718323	+	0.551094i
$781$	−37.1920			−1.33084
$782$	−2.52423	+	2.01301i	−0.0902663	+	0.0719850i
$783$	−2.42975	+	5.04544i	−0.0868323	+	0.180309i
$784$	1.96603	−	2.46532i	0.0702153	−	0.0880472i
$785$	2.58965	+	12.4166i	0.0924286	+	0.443167i
$786$	2.39485	+	10.4925i	0.0854216	+	0.374256i
$787$	−29.7179	+	23.6992i	−1.05933	+	0.844786i	−0.988275	−	0.152687i	$-0.951207\pi$
$787$	−29.7179	+	23.6992i	−1.05933	+	0.844786i	−0.0710531	+	0.997473i	$0.522636\pi$
$788$	6.06797	−	1.38497i	0.216162	−	0.0493377i
$789$	30.7400	−	14.8036i	1.09437	−	0.527023i
$790$	12.0316	+	0.226016i	0.428065	+	0.00804129i
$791$	14.4113	−	18.0712i	0.512406	−	0.642536i
$792$	−5.36999	−	1.22567i	−0.190814	−	0.0435521i
$793$	4.71634	+	9.79358i	0.167482	+	0.347780i
$794$	−26.3207	−	12.6754i	−0.934085	−	0.449832i
$795$	20.3206	+	44.3062i	0.720697	+	1.57138i
$796$	−3.40285	+	14.9088i	−0.120611	+	0.528430i
$797$	−12.9900	+	26.9740i	−0.460129	+	0.955467i	0.533817	+	0.845600i	$0.320757\pi$
$797$	−12.9900	+	26.9740i	−0.460129	+	0.955467i	−0.993946	+	0.109868i	$0.964957\pi$
$798$	−6.78900	−	14.0975i	−0.240328	−	0.499047i
$799$	−2.33828	+	10.2447i	−0.0827224	+	0.362430i
$800$	−4.02348	+	2.96843i	−0.142252	+	0.104950i
$801$	−7.14345	+	8.95761i	−0.252402	+	0.316501i
$802$	−10.4835	−	21.7692i	−0.370185	−	0.768698i
$803$	35.1618	−	8.02544i	1.24083	−	0.283212i
$804$	−8.59976	−	10.7838i	−0.303290	−	0.380314i
$805$	−2.26884	−	1.88013i	−0.0799663	−	0.0662658i
$806$	−50.7051	−	24.4183i	−1.78601	−	0.860098i
$807$	47.8241	+	38.1384i	1.68349	+	1.34254i
$808$	−3.87116	+	8.03855i	−0.136187	+	0.282795i
$809$	−26.3911	−	33.0934i	−0.927862	−	1.16350i	−0.986259	−	0.165209i	$-0.947170\pi$
$809$	−26.3911	−	33.0934i	−0.927862	−	1.16350i	0.0583962	−	0.998293i	$-0.481401\pi$
$810$	15.2750	+	19.9101i	0.536707	+	0.699571i
$811$	−34.0618			−1.19607			−0.598036	−	0.801469i	$-0.704052\pi$
$811$	−34.0618			−1.19607			−0.598036	+	0.801469i	$0.704052\pi$
$812$	2.97893	−	2.37562i	0.104540	−	0.0833678i
$813$	−18.9256	−	39.2993i	−0.663748	−	1.37829i
$814$	−7.37862	+	32.3278i	−0.258620	+	1.13309i
$815$	1.73171	−	2.08974i	0.0606592	−	0.0732004i
$816$	−10.3793			−0.363349
$817$	14.8261	+	19.1520i	0.518698	+	0.670043i
$818$		−	3.11523i		−	0.108922i
$819$	−3.80526	−	16.6719i	−0.132967	−	0.582565i
$820$	9.41816	+	20.5350i	0.328897	+	0.717112i
$821$	25.5539	−	12.3061i	0.891839	−	0.429487i	0.0689043	−	0.997623i	$-0.478050\pi$
$821$	25.5539	−	12.3061i	0.891839	−	0.429487i	0.822934	+	0.568136i	$0.192335\pi$
$822$	4.27474	−	3.40899i	0.149099	−	0.118902i
$823$			3.26904i			0.113952i	0.998376	+	0.0569758i	$0.0181458\pi$
$823$			3.26904i			0.113952i	−0.998376	+	0.0569758i	$0.981854\pi$
$824$	12.8169			0.446498
$825$	14.2780	+	32.7404i	0.497097	+	1.13988i
$826$	−4.90963	−	2.36435i	−0.170828	−	0.0822663i
$827$	−15.5902	−	12.4328i	−0.542124	−	0.432329i	0.313756	−	0.949503i	$-0.398412\pi$
$827$	−15.5902	−	12.4328i	−0.542124	−	0.432329i	−0.855880	+	0.517174i	$0.826984\pi$
$828$	−0.485502	+	1.00816i	−0.0168724	+	0.0350358i
$829$	−9.84075	−	43.1151i	−0.341783	−	1.49745i	−0.795307	−	0.606206i	$-0.792691\pi$
$829$	−9.84075	−	43.1151i	−0.341783	−	1.49745i	0.453524	−	0.891244i	$-0.350167\pi$
$830$	−9.86695	−	2.44792i	−0.342487	−	0.0849684i
$831$	−2.35109	−	10.3008i	−0.0815585	−	0.357331i
$832$	2.27151	+	4.71685i	0.0787506	+	0.163527i
$833$	−11.8467	−	9.44743i	−0.410464	−	0.327334i
$834$	−13.3511	+	16.7417i	−0.462309	+	0.579717i
$835$	−36.1603	+	16.5846i	−1.25138	+	0.573933i
$836$	11.0059	−	5.30017i	0.380647	−	0.183310i
$837$	−13.4450	+	27.9189i	−0.464728	+	0.965017i
$838$	−27.8367	−	6.35355i	−0.961604	−	0.219480i
$839$	1.51293	−	6.62857i	0.0522321	−	0.228844i	−0.942074	−	0.335405i	$-0.891127\pi$
$839$	1.51293	−	6.62857i	0.0522321	−	0.228844i	0.994306	+	0.106561i	$0.0339840\pi$
$840$	−1.93406	−	9.27322i	−0.0667315	−	0.319957i
$841$	22.7278	−	10.9452i	0.783719	−	0.377419i
$842$	−21.9326	−	5.00597i	−0.755847	−	0.172517i
$843$	26.8281	+	21.3947i	0.924009	+	0.736873i
$844$	−5.74295	+	7.20143i	−0.197680	+	0.247883i
$845$	14.5217	−	28.7599i	0.499561	−	0.989371i
$846$	0.810398	+	3.55059i	0.0278621	+	0.122072i
$847$	0.0945770	−	0.0754227i	0.00324971	−	0.00259155i
$848$	9.83924	−	2.24574i	0.337881	−	0.0771191i
$849$	25.4033	+	12.2336i	0.871838	+	0.419855i
$850$	14.2643	+	19.3342i	0.489262	+	0.663157i
$851$	6.06919	+	2.92277i	0.208049	+	0.100191i
$852$	−18.9904	+	15.1443i	−0.650599	+	0.518836i
$853$		−	14.7448i		−	0.504852i	−0.967616	−	0.252426i	$-0.918772\pi$
$853$		−	14.7448i		−	0.504852i	0.967616	−	0.252426i	$-0.0812285\pi$
$854$	−4.07226			−0.139350
$855$	13.3500	+	3.31203i	0.456561	+	0.113269i
$856$	−6.22144	+	2.99609i	−0.212644	+	0.102404i
$857$	−16.2927	−	3.71870i	−0.556547	−	0.127028i	−0.0650096	−	0.997885i	$-0.520708\pi$
$857$	−16.2927	−	3.71870i	−0.556547	−	0.127028i	−0.491538	+	0.870856i	$0.663565\pi$
$858$	36.4616	−	8.32212i	1.24478	−	0.284112i
$859$	55.6849			1.89994			0.949972	−	0.312334i	$-0.101111\pi$
$859$	55.6849			1.89994			0.949972	+	0.312334i	$0.101111\pi$
$860$	5.91973	+	13.4148i	0.201861	+	0.457441i
$861$	−42.8012			−1.45866
$862$	−21.0446	+	4.80329i	−0.716781	+	0.163601i
$863$	−38.3310	−	8.74880i	−1.30480	−	0.297813i	−0.487046	−	0.873376i	$-0.661926\pi$
$863$	−38.3310	−	8.74880i	−1.30480	−	0.297813i	−0.817757	+	0.575564i	$0.804783\pi$
$864$	2.59715	−	1.25072i	0.0883570	−	0.0425505i
$865$	−7.15641	+	28.8457i	−0.243325	+	0.980784i
$866$	0.706470			0.0240068
$867$			13.1568i			0.446829i
$868$	16.4839	−	13.1455i	0.559499	−	0.446186i
$869$	−16.0361	−	7.72260i	−0.543989	−	0.261971i
$870$	−0.176226	+	9.38113i	−0.00597463	+	0.318050i
$871$	30.1206	+	14.5053i	1.02060	+	0.491493i
$872$	16.9476	−	3.86819i	0.573919	−	0.130993i
$873$	2.51732	−	2.00749i	0.0851983	−	0.0679434i
$874$	−0.552210	−	2.41939i	−0.0186788	−	0.0818371i
$875$	−14.6158	+	16.3469i	−0.494104	+	0.552625i
$876$	14.6858	−	18.4154i	0.496187	−	0.622199i
$877$	9.34191	+	7.44993i	0.315454	+	0.251566i	0.768397	−	0.639973i	$-0.221055\pi$
$877$	9.34191	+	7.44993i	0.315454	+	0.251566i	−0.452943	+	0.891539i	$0.649626\pi$
$878$	5.51322	+	1.25836i	0.186062	+	0.0424674i
$879$	−44.6687	+	21.5113i	−1.50664	+	0.725559i
$880$	7.23960	−	1.50992i	0.244047	−	0.0508994i
$881$	4.99462	−	21.8829i	0.168273	−	0.737252i	−0.818415	−	0.574628i	$-0.805147\pi$
$881$	4.99462	−	21.8829i	0.168273	−	0.737252i	0.986688	−	0.162625i	$-0.0519959\pi$
$882$	−5.11987	−	1.16858i	−0.172395	−	0.0393480i
$883$	−13.5141	+	28.0624i	−0.454787	+	0.944375i	0.539929	+	0.841711i	$0.318451\pi$
$883$	−13.5141	+	28.0624i	−0.454787	+	0.944375i	−0.994716	+	0.102664i	$0.967263\pi$
$884$	22.6660	−	10.9154i	0.762341	−	0.367124i
$885$	12.1974	−	5.59423i	0.410012	−	0.188048i
$886$	−20.8505	+	26.1456i	−0.700485	+	0.878380i
$887$	15.3202	+	12.2175i	0.514402	+	0.410222i	0.845987	−	0.533203i	$-0.179012\pi$
$887$	15.3202	+	12.2175i	0.514402	+	0.410222i	−0.331585	+	0.943425i	$0.607583\pi$
$888$	9.39610	+	19.5112i	0.315313	+	0.654753i
$889$	−4.13925	−	18.1352i	−0.138826	−	0.608236i
$890$	3.70409	−	14.9303i	0.124161	−	0.500464i
$891$	−8.25926	−	36.1862i	−0.276696	−	1.21228i
$892$	4.91710	−	10.2105i	0.164637	−	0.341871i
$893$	−6.31475	−	5.03584i	−0.211315	−	0.168518i
$894$	11.9798	+	5.76917i	0.400664	+	0.192950i
$895$	−27.4401	−	6.80768i	−0.917221	−	0.227556i
$896$	−1.96131			−0.0655227
$897$		−	7.59766i		−	0.253679i
$898$	−2.77946	+	2.21654i	−0.0927517	+	0.0739670i
$899$	−18.8153	+	9.06097i	−0.627525	+	0.302200i
$900$	7.36150	+	3.89223i	0.245383	+	0.129741i
$901$	−10.7915	−	47.2808i	−0.359518	−	1.57515i
$902$		−	33.4149i		−	1.11259i
$903$	−27.7767	−	0.400963i	−0.924351	−	0.0133432i
$904$	11.7849			0.391961
$905$	41.8329	+	34.6658i	1.39057	+	1.15233i
$906$	3.70382	−	16.2275i	0.123051	−	0.539122i
$907$	−21.4481	−	44.5375i	−0.712174	−	1.47884i	−0.870868	−	0.491516i	$-0.836443\pi$
$907$	−21.4481	−	44.5375i	−0.712174	−	1.47884i	0.158694	−	0.987328i	$-0.449272\pi$
$908$	4.02986	−	3.21370i	0.133735	−	0.106650i
$909$	14.8591			0.492847
$910$	13.9757	+	18.2166i	0.463289	+	0.603874i
$911$	8.08105	+	10.1333i	0.267737	+	0.335732i	0.897466	−	0.441083i	$-0.145406\pi$
$911$	8.08105	+	10.1333i	0.267737	+	0.335732i	−0.629729	+	0.776815i	$0.716834\pi$
$912$	3.46147	−	7.18781i	0.114621	−	0.238012i
$913$	11.7559	+	9.37504i	0.389064	+	0.310268i
$914$	−26.2066	−	12.6204i	−0.866837	−	0.417447i
$915$	6.39860	−	7.72150i	0.211531	−	0.255265i
$916$	6.47904	+	8.12446i	0.214073	+	0.268440i
$917$	9.52754	−	2.17460i	0.314627	−	0.0718116i
$918$	−6.01014	−	12.4802i	−0.198364	−	0.411908i
$919$	21.1788	−	26.5573i	0.698623	−	0.876045i	−0.298297	−	0.954473i	$-0.596419\pi$
$919$	21.1788	−	26.5573i	0.698623	−	0.876045i	0.996920	+	0.0784278i	$0.0249900\pi$
$920$	0.0282174	−	1.50211i	0.000930299	−	0.0495230i
$921$	9.01888	−	39.5143i	0.297182	−	1.30204i
$922$	10.4838	+	21.7699i	0.345267	+	0.716954i
$923$	25.5440	−	53.0428i	0.840793	−	1.74592i
$924$	−3.11773	+	13.6597i	−0.102566	+	0.449370i
$925$	23.4316	−	44.3169i	0.770426	−	1.45713i
$926$	4.79725	+	2.31023i	0.157647	+	0.0759190i
$927$	−9.26153	−	19.2318i	−0.304188	−	0.631654i
$928$	1.89397	+	0.432287i	0.0621727	+	0.0141905i
$929$	−17.4131	+	21.8353i	−0.571304	+	0.716393i	−0.980602	−	0.196008i	$-0.937202\pi$
$929$	−17.4131	+	21.8353i	−0.571304	+	0.716393i	0.409298	+	0.912401i	$0.365774\pi$
$930$	−0.975147	+	51.9104i	−0.0319763	+	1.70221i
$931$	10.4933	−	5.05330i	0.343903	−	0.165615i
$932$	−0.253065	+	0.0577605i	−0.00828943	+	0.00189201i
$933$	−49.2852	+	39.3036i	−1.61352	+	1.28674i
$934$	−3.20136	−	14.0261i	−0.104752	−	0.458948i
$935$	−7.25567	−	34.7887i	−0.237286	−	1.13771i
$936$	5.43622	−	6.81680i	0.177688	−	0.222814i
$937$	3.15806	−	6.55778i	0.103169	−	0.214233i	−0.842994	−	0.537923i	$-0.819209\pi$
$937$	3.15806	−	6.55778i	0.103169	−	0.214233i	0.946163	+	0.323690i	$0.104923\pi$
$938$	−9.79198	+	7.80885i	−0.319720	+	0.254968i
$939$	−16.7815			−0.547644
$940$	−2.97637	−	3.87955i	−0.0970785	−	0.126537i
$941$	−16.6950	−	20.9349i	−0.544242	−	0.682458i	0.431316	−	0.902201i	$-0.358049\pi$
$941$	−16.6950	−	20.9349i	−0.544242	−	0.682458i	−0.975558	+	0.219743i	$0.929478\pi$
$942$	−5.31596	−	11.0387i	−0.173203	−	0.359661i
$943$	−6.61804	−	1.51052i	−0.215513	−	0.0491895i
$944$	−0.618249	−	2.70873i	−0.0201223	−	0.0881615i
$945$	10.0303	−	7.69519i	0.326285	−	0.250324i
$946$	0.313031	−	21.6852i	0.0101775	−	0.705048i
$947$		−	48.1648i		−	1.56514i	−0.622560	−	0.782572i	$-0.713907\pi$
$947$		−	48.1648i		−	1.56514i	0.622560	−	0.782572i	$-0.286093\pi$
$948$	−11.3327	+	2.58661i	−0.368069	+	0.0840093i
$949$	−12.7039	+	55.6592i	−0.412385	+	1.80677i
$950$	−18.1462	+	3.43033i	−0.588742	+	0.111295i
$951$	−39.7311	−	49.8212i	−1.28837	−	1.61556i
$952$			9.42475i			0.305458i
$953$		−	57.0403i		−	1.84772i	−0.382736	−	0.923858i	$-0.625018\pi$
$953$		−	57.0403i		−	1.84772i	0.382736	−	0.923858i	$-0.374982\pi$
$954$	−10.4796	−	13.1410i	−0.339289	−	0.425455i
$955$	3.18450	−	0.664172i	0.103048	−	0.0214921i
$956$	−16.2917	+	20.4291i	−0.526910	+	0.660724i
$957$	6.02137	−	12.5035i	0.194643	−	0.404181i
$958$	−1.37920	+	0.314794i	−0.0445600	+	0.0101705i
$959$	−3.09547	−	3.88159i	−0.0999578	−	0.125343i
$960$	3.08173	−	3.71888i	0.0994625	−	0.120026i
$961$	−76.1842	+	36.6884i	−2.45755	+	1.18350i
$962$	−41.0378	−	32.7265i	−1.32311	−	1.05515i
$963$	8.99124	+	7.17028i	0.289739	+	0.231059i
$964$	−4.33195	+	18.9795i	−0.139523	+	0.611289i
$965$	33.8536	+	17.0936i	1.08979	+	0.550264i
$966$	2.56445	+	1.23497i	0.0825098	+	0.0397346i
$967$	20.3509	+	4.64496i	0.654441	+	0.149372i	0.536834	−	0.843688i	$-0.319620\pi$
$967$	20.3509	+	4.64496i	0.654441	+	0.149372i	0.117608	+	0.993060i	$0.462477\pi$
$968$	0.0601311	+	0.0137245i	0.00193269	+	0.000441123i
$969$	−34.5398	−	16.6335i	−1.10958	−	0.534345i
$970$	−1.94850	+	3.85896i	−0.0625625	+	0.123904i
$971$	−7.32903	+	32.1106i	−0.235200	+	1.03048i	0.710055	+	0.704146i	$0.248670\pi$
$971$	−7.32903	+	32.1106i	−0.235200	+	1.03048i	−0.945255	+	0.326332i	$0.894187\pi$
$972$	−12.1908	−	9.72181i	−0.391019	−	0.311827i
$973$	15.2020	+	12.1232i	0.487352	+	0.388651i
$974$	11.1234	−	5.35676i	0.356418	−	0.171642i
$975$	−56.5003	−	2.12349i	−1.80946	−	0.0680061i
$976$	−1.29455	−	1.62332i	−0.0414376	−	0.0519610i
$977$	6.07463	−	1.38649i	0.194344	−	0.0443579i	−0.124241	−	0.992252i	$-0.539649\pi$
$977$	6.07463	−	1.38649i	0.194344	−	0.0443579i	0.318585	+	0.947894i	$0.396792\pi$
$978$	−1.13748	+	2.36201i	−0.0363727	+	0.0755287i
$979$	−14.1859	+	17.7886i	−0.453384	+	0.568526i
$980$	6.90239	−	1.43959i	0.220489	−	0.0459860i
$981$	−18.0506	−	22.6347i	−0.576311	−	0.722672i
$982$			0.714742i			0.0228083i
$983$		−	3.29275i		−	0.105022i	−0.998620	−	0.0525111i	$-0.983277\pi$
$983$		−	3.29275i		−	0.105022i	0.998620	−	0.0525111i	$-0.0167225\pi$
$984$	−13.6063	−	17.0617i	−0.433753	−	0.543909i
$985$	12.4235	+	6.27294i	0.395844	+	0.199873i
$986$	2.07728	−	9.10117i	0.0661541	−	0.289840i
$987$	9.03163	−	2.06141i	0.287480	−	0.0656154i
$988$			19.3367i			0.615183i
$989$	−4.28076	−	1.04228i	−0.136120	−	0.0331427i
$990$	−7.49698	−	9.77193i	−0.238270	−	0.310572i
$991$	−4.95370	−	21.7036i	−0.157360	−	0.689437i	−0.990630	−	0.136572i	$-0.956392\pi$
$991$	−4.95370	−	21.7036i	−0.157360	−	0.689437i	0.833271	−	0.552865i	$-0.186466\pi$
$992$	10.4803	+	2.39205i	0.332749	+	0.0759478i
$993$	3.11944	+	6.47759i	0.0989926	+	0.205560i
$994$	13.7515	+	17.2438i	0.436171	+	0.546941i
$995$	−27.1301	+	20.8141i	−0.860081	+	0.659850i
$996$	9.82006			0.311160
$997$	−36.4691	+	29.0831i	−1.15499	+	0.921071i	−0.997787	−	0.0664955i	$-0.978818\pi$
$997$	−36.4691	+	29.0831i	−1.15499	+	0.921071i	−0.157200	+	0.987567i	$0.550247\pi$
$998$	−1.19791	+	2.48749i	−0.0379193	+	0.0787402i
$999$	−18.0196	+	22.5959i	−0.570116	+	0.714903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.p.a.59.10	✓	132
5.4	even	2	inner	430.2.p.a.59.13	yes	132
43.35	even	7	inner	430.2.p.a.379.13	yes	132
215.164	even	14	inner	430.2.p.a.379.10	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.p.a.59.10	✓	132	1.1	even	1	trivial
430.2.p.a.59.13	yes	132	5.4	even	2	inner
430.2.p.a.379.10	yes	132	215.164	even	14	inner
430.2.p.a.379.13	yes	132	43.35	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.974928 + 0.222521i) q^{2} +(2.10581 + 0.480636i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.17028 + 0.538429i) q^{5} -2.15996 q^{6} +1.96131i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.50050 + 0.722602i) q^{9} +O(q^{10})\)	\(q+(-0.974928 + 0.222521i) q^{2} +(2.10581 + 0.480636i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.17028 + 0.538429i) q^{5} -2.15996 q^{6} +1.96131i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.50050 + 0.722602i) q^{9} +(-2.23567 - 0.0419976i) q^{10} +(2.97979 + 1.43499i) q^{11} +(2.10581 - 0.480636i) q^{12} +(-4.09313 + 3.26416i) q^{13} +(-0.436432 - 1.91214i) q^{14} +(4.31139 + 2.17694i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-3.75696 - 2.99608i) q^{17} +(-1.62367 - 0.370592i) q^{18} +(3.32775 - 1.60256i) q^{19} +(2.18897 - 0.456540i) q^{20} +(-0.942676 + 4.13014i) q^{21} +(-3.22439 - 0.735946i) q^{22} +(-0.291518 + 0.605344i) q^{23} +(-1.94606 + 0.937172i) q^{24} +(4.42019 + 2.33708i) q^{25} +(3.26416 - 4.09313i) q^{26} +(-2.25373 - 1.79729i) q^{27} +(0.850980 + 1.76708i) q^{28} +(-0.432287 - 1.89397i) q^{29} +(-4.68771 - 1.16298i) q^{30} +(-2.39205 - 10.4803i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(5.58514 + 4.45400i) q^{33} +(4.32946 + 2.08496i) q^{34} +(-1.05603 + 4.25658i) q^{35} +1.66543 q^{36} -10.0260i q^{37} +(-2.88771 + 2.30287i) q^{38} +(-10.1882 + 4.90638i) q^{39} +(-2.03249 + 0.932184i) q^{40} +(2.24820 + 9.85002i) q^{41} -4.23635i q^{42} +(1.36674 + 6.41343i) q^{43} +3.30731 q^{44} +(2.86742 + 2.37616i) q^{45} +(0.149508 - 0.655035i) q^{46} +(-0.948801 - 1.97021i) q^{47} +(1.68872 - 1.34671i) q^{48} +3.15327 q^{49} +(-4.82941 - 1.29490i) q^{50} +(-6.47141 - 8.11489i) q^{51} +(-2.27151 + 4.71685i) q^{52} +(7.89046 + 6.29243i) q^{53} +(2.59715 + 1.25072i) q^{54} +(5.69432 + 4.71873i) q^{55} +(-1.22286 - 1.53341i) q^{56} +(7.77784 - 1.77524i) q^{57} +(0.842897 + 1.75029i) q^{58} +(1.73230 - 2.17223i) q^{59} +(4.82897 + 0.0907131i) q^{60} +(0.462020 - 2.02424i) q^{61} +(4.66416 + 9.68523i) q^{62} +(-1.41725 + 2.94294i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-10.6407 + 4.88027i) q^{65} +(-6.43622 - 3.09952i) q^{66} +(-2.77067 - 5.75336i) q^{67} +(-4.68485 - 1.06929i) q^{68} +(-0.904831 + 1.13462i) q^{69} +(0.0823702 - 4.38485i) q^{70} +(-10.1317 + 4.87919i) q^{71} +(-1.62367 + 0.370592i) q^{72} +(8.52581 - 6.79911i) q^{73} +(2.23100 + 9.77465i) q^{74} +(8.18477 + 7.04593i) q^{75} +(2.30287 - 2.88771i) q^{76} +(-2.81446 + 5.84428i) q^{77} +(8.84099 - 7.05045i) q^{78} -5.38164 q^{79} +(1.77411 - 1.36108i) q^{80} +(-6.99720 - 8.77421i) q^{81} +(-4.38367 - 9.10279i) q^{82} +(4.43242 + 1.01167i) q^{83} +(0.942676 + 4.13014i) q^{84} +(-6.54047 - 8.52517i) q^{85} +(-2.75959 - 5.94850i) q^{86} -4.19611i q^{87} +(-3.22439 + 0.735946i) q^{88} +(-1.53082 + 6.70696i) q^{89} +(-3.32428 - 1.67852i) q^{90} +(-6.40203 - 8.02789i) q^{91} +0.671881i q^{92} -23.2191i q^{93} +(1.36342 + 1.70968i) q^{94} +(8.08500 - 1.68624i) q^{95} +(-1.34671 + 1.68872i) q^{96} +(0.838828 - 1.74184i) q^{97} +(-3.07421 + 0.701668i) q^{98} +(3.43424 + 4.30640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Introduction

L-functions

Modular forms

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Database

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