LMFDB - Embedded newform 630.2.i.g.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$1.39898 + 1.02120i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.g.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.184900 + 1.72215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.184900 + 1.72215i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(-2.93162 + 0.636851i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.184900 + 1.72215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.184900 + 1.72215i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(-2.93162 + 0.636851i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.480820 + 0.832805i) q^{11} +(0.184900 + 1.72215i) q^{12} +(-2.94219 + 5.09603i) q^{13} +(-2.25729 + 1.38008i) q^{14} +(1.39898 - 1.02120i) q^{15} +1.00000 q^{16} +(3.89714 + 6.75005i) q^{17} +(-2.93162 + 0.636851i) q^{18} +(0.774437 - 1.34137i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.79408 - 3.63223i) q^{21} +(-0.480820 + 0.832805i) q^{22} +(1.95495 + 3.38607i) q^{23} +(0.184900 + 1.72215i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.94219 + 5.09603i) q^{26} +(-1.63881 - 4.93095i) q^{27} +(-2.25729 + 1.38008i) q^{28} +(-0.543215 - 0.940877i) q^{29} +(1.39898 - 1.02120i) q^{30} +2.55756 q^{31} +1.00000 q^{32} +(-1.52312 - 0.674061i) q^{33} +(3.89714 + 6.75005i) q^{34} +(2.32383 + 1.26483i) q^{35} +(-2.93162 + 0.636851i) q^{36} +(5.84787 - 10.1288i) q^{37} +(0.774437 - 1.34137i) q^{38} +(-9.32015 - 4.12466i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.15042 - 1.99258i) q^{41} +(-2.79408 - 3.63223i) q^{42} +(-2.18820 - 3.79008i) q^{43} +(-0.480820 + 0.832805i) q^{44} +(2.01734 + 2.22044i) q^{45} +(1.95495 + 3.38607i) q^{46} -3.55502 q^{47} +(0.184900 + 1.72215i) q^{48} +(3.19076 - 6.23049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-10.9040 + 7.95955i) q^{51} +(-2.94219 + 5.09603i) q^{52} +(0.274437 + 0.475340i) q^{53} +(-1.63881 - 4.93095i) q^{54} +0.961641 q^{55} +(-2.25729 + 1.38008i) q^{56} +(2.45323 + 1.08568i) q^{57} +(-0.543215 - 0.940877i) q^{58} -6.00868 q^{59} +(1.39898 - 1.02120i) q^{60} +14.6881 q^{61} +2.55756 q^{62} +(5.73863 - 5.48344i) q^{63} +1.00000 q^{64} +5.88439 q^{65} +(-1.52312 - 0.674061i) q^{66} -0.821956 q^{67} +(3.89714 + 6.75005i) q^{68} +(-5.46986 + 3.99280i) q^{69} +(2.32383 + 1.26483i) q^{70} -3.96164 q^{71} +(-2.93162 + 0.636851i) q^{72} +(0.368764 + 0.638718i) q^{73} +(5.84787 - 10.1288i) q^{74} +(-1.58388 - 0.700949i) q^{75} +(0.774437 - 1.34137i) q^{76} +(-0.0639849 - 2.54346i) q^{77} +(-9.32015 - 4.12466i) q^{78} -6.79796 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.18884 - 3.73401i) q^{81} +(1.15042 - 1.99258i) q^{82} +(6.12526 + 10.6093i) q^{83} +(-2.79408 - 3.63223i) q^{84} +(3.89714 - 6.75005i) q^{85} +(-2.18820 - 3.79008i) q^{86} +(1.51989 - 1.10947i) q^{87} +(-0.480820 + 0.832805i) q^{88} +(-2.85680 + 4.94812i) q^{89} +(2.01734 + 2.22044i) q^{90} +(-0.391531 - 15.5637i) q^{91} +(1.95495 + 3.38607i) q^{92} +(0.472891 + 4.40450i) q^{93} -3.55502 q^{94} -1.54887 q^{95} +(0.184900 + 1.72215i) q^{96} +(7.80249 + 13.5143i) q^{97} +(3.19076 - 6.23049i) q^{98} +(0.879212 - 2.74768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.184900	+	1.72215i	0.106752	+	0.994286i
$3$	0.184900	+	1.72215i	0.106752	+	0.994286i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.184900	+	1.72215i	0.0754849	+	0.703066i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$8$	1.00000			0.353553
$9$	−2.93162	+	0.636851i	−0.977208	+	0.212284i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.480820	+	0.832805i	−0.144973	+	0.251100i	−0.929363	−	0.369168i	$-0.879643\pi$
$11$	−0.480820	+	0.832805i	−0.144973	+	0.251100i	0.784390	+	0.620268i	$0.212976\pi$
$12$	0.184900	+	1.72215i	0.0533759	+	0.497143i
$13$	−2.94219	+	5.09603i	−0.816018	+	1.41338i	0.0925769	+	0.995706i	$0.470490\pi$
$13$	−2.94219	+	5.09603i	−0.816018	+	1.41338i	−0.908595	+	0.417679i	$0.862844\pi$
$14$	−2.25729	+	1.38008i	−0.603287	+	0.368842i
$15$	1.39898	−	1.02120i	0.361215	−	0.263674i
$16$	1.00000			0.250000
$17$	3.89714	+	6.75005i	0.945195	+	1.63713i	0.755360	+	0.655311i	$0.227462\pi$
$17$	3.89714	+	6.75005i	0.945195	+	1.63713i	0.189836	+	0.981816i	$0.439204\pi$
$18$	−2.93162	+	0.636851i	−0.690990	+	0.150107i
$19$	0.774437	−	1.34137i	0.177668	−	0.307730i	−0.763413	−	0.645910i	$-0.776478\pi$
$19$	0.774437	−	1.34137i	0.177668	−	0.307730i	0.941081	+	0.338180i	$0.109811\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−2.79408	−	3.63223i	−0.609719	−	0.792618i
$22$	−0.480820	+	0.832805i	−0.102511	+	0.177555i
$23$	1.95495	+	3.38607i	0.407634	+	0.706044i	0.994624	−	0.103551i	$-0.0330204\pi$
$23$	1.95495	+	3.38607i	0.407634	+	0.706044i	−0.586990	+	0.809594i	$0.699687\pi$
$24$	0.184900	+	1.72215i	0.0377425	+	0.351533i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.94219	+	5.09603i	−0.577012	+	0.999414i
$27$	−1.63881	−	4.93095i	−0.315389	−	0.948962i
$28$	−2.25729	+	1.38008i	−0.426589	+	0.260811i
$29$	−0.543215	−	0.940877i	−0.100873	−	0.174716i	0.811172	−	0.584808i	$-0.198830\pi$
$29$	−0.543215	−	0.940877i	−0.100873	−	0.174716i	−0.912044	+	0.410091i	$0.865497\pi$
$30$	1.39898	−	1.02120i	0.255417	−	0.186446i
$31$	2.55756			0.459351			0.229675	−	0.973267i	$-0.426234\pi$
$31$	2.55756			0.459351			0.229675	+	0.973267i	$0.426234\pi$
$32$	1.00000			0.176777
$33$	−1.52312	−	0.674061i	−0.265142	−	0.117339i
$34$	3.89714	+	6.75005i	0.668354	+	1.15762i
$35$	2.32383	+	1.26483i	0.392799	+	0.213796i
$36$	−2.93162	+	0.636851i	−0.488604	+	0.106142i
$37$	5.84787	−	10.1288i	0.961384	−	1.66517i	0.242351	−	0.970189i	$-0.422081\pi$
$37$	5.84787	−	10.1288i	0.961384	−	1.66517i	0.719033	−	0.694976i	$-0.244585\pi$
$38$	0.774437	−	1.34137i	0.125630	−	0.217598i
$39$	−9.32015	−	4.12466i	−1.49242	−	0.660474i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.15042	−	1.99258i	0.179665	−	0.311188i	−0.762101	−	0.647458i	$-0.775832\pi$
$41$	1.15042	−	1.99258i	0.179665	−	0.311188i	0.941766	+	0.336270i	$0.109165\pi$
$42$	−2.79408	−	3.63223i	−0.431136	−	0.560465i
$43$	−2.18820	−	3.79008i	−0.333698	−	0.577982i	0.649536	−	0.760331i	$-0.274963\pi$
$43$	−2.18820	−	3.79008i	−0.333698	−	0.577982i	−0.983234	+	0.182349i	$0.941630\pi$
$44$	−0.480820	+	0.832805i	−0.0724864	+	0.125550i
$45$	2.01734	+	2.22044i	0.300727	+	0.331003i
$46$	1.95495	+	3.38607i	0.288241	+	0.499248i
$47$	−3.55502			−0.518553			−0.259276	−	0.965803i	$-0.583484\pi$
$47$	−3.55502			−0.518553			−0.259276	+	0.965803i	$0.583484\pi$
$48$	0.184900	+	1.72215i	0.0266880	+	0.248571i
$49$	3.19076	−	6.23049i	0.455822	−	0.890071i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−10.9040	+	7.95955i	−1.52687	+	1.11456i
$52$	−2.94219	+	5.09603i	−0.408009	+	0.706692i
$53$	0.274437	+	0.475340i	0.0376969	+	0.0652929i	0.884258	−	0.466998i	$-0.154665\pi$
$53$	0.274437	+	0.475340i	0.0376969	+	0.0652929i	−0.846561	+	0.532291i	$0.821331\pi$
$54$	−1.63881	−	4.93095i	−0.223014	−	0.671018i
$55$	0.961641			0.129668
$56$	−2.25729	+	1.38008i	−0.301644	+	0.184421i
$57$	2.45323	+	1.08568i	0.324938	+	0.143802i
$58$	−0.543215	−	0.940877i	−0.0713277	−	0.123543i
$59$	−6.00868			−0.782264			−0.391132	−	0.920335i	$-0.627916\pi$
$59$	−6.00868			−0.782264			−0.391132	+	0.920335i	$0.627916\pi$
$60$	1.39898	−	1.02120i	0.180607	−	0.131837i
$61$	14.6881			1.88062			0.940312	−	0.340314i	$-0.110534\pi$
$61$	14.6881			1.88062			0.940312	+	0.340314i	$0.110534\pi$
$62$	2.55756			0.324810
$63$	5.73863	−	5.48344i	0.723000	−	0.690848i
$64$	1.00000			0.125000
$65$	5.88439			0.729869
$66$	−1.52312	−	0.674061i	−0.187483	−	0.0829712i
$67$	−0.821956			−0.100418			−0.0502089	−	0.998739i	$-0.515989\pi$
$67$	−0.821956			−0.100418			−0.0502089	+	0.998739i	$0.515989\pi$
$68$	3.89714	+	6.75005i	0.472598	+	0.818563i
$69$	−5.46986	+	3.99280i	−0.658493	+	0.480677i
$70$	2.32383	+	1.26483i	0.277751	+	0.151177i
$71$	−3.96164			−0.470160			−0.235080	−	0.971976i	$-0.575535\pi$
$71$	−3.96164			−0.470160			−0.235080	+	0.971976i	$0.575535\pi$
$72$	−2.93162	+	0.636851i	−0.345495	+	0.0750536i
$73$	0.368764	+	0.638718i	0.0431606	+	0.0747563i	0.886799	−	0.462156i	$-0.152924\pi$
$73$	0.368764	+	0.638718i	0.0431606	+	0.0747563i	−0.843638	+	0.536912i	$0.819591\pi$
$74$	5.84787	−	10.1288i	0.679801	−	1.17745i
$75$	−1.58388	−	0.700949i	−0.182891	−	0.0809386i
$76$	0.774437	−	1.34137i	0.0888341	−	0.153865i
$77$	−0.0639849	−	2.54346i	−0.00729176	−	0.289854i
$78$	−9.32015	−	4.12466i	−1.05530	−	0.467025i
$79$	−6.79796			−0.764830			−0.382415	−	0.923991i	$-0.624908\pi$
$79$	−6.79796			−0.764830			−0.382415	+	0.923991i	$0.624908\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	8.18884	−	3.73401i	0.909871	−	0.414890i
$82$	1.15042	−	1.99258i	0.127042	−	0.220043i
$83$	6.12526	+	10.6093i	0.672334	+	1.16452i	0.977240	+	0.212134i	$0.0680415\pi$
$83$	6.12526	+	10.6093i	0.672334	+	1.16452i	−0.304906	+	0.952382i	$0.598625\pi$
$84$	−2.79408	−	3.63223i	−0.304859	−	0.396309i
$85$	3.89714	−	6.75005i	0.422704	−	0.732145i
$86$	−2.18820	−	3.79008i	−0.235960	−	0.408695i
$87$	1.51989	−	1.10947i	0.162950	−	0.118947i
$88$	−0.480820	+	0.832805i	−0.0512556	+	0.0887774i
$89$	−2.85680	+	4.94812i	−0.302820	+	0.524500i	−0.976774	−	0.214274i	$-0.931261\pi$
$89$	−2.85680	+	4.94812i	−0.302820	+	0.524500i	0.673954	+	0.738774i	$0.264595\pi$
$90$	2.01734	+	2.22044i	0.212646	+	0.234054i
$91$	−0.391531	−	15.5637i	−0.0410436	−	1.63152i
$92$	1.95495	+	3.38607i	0.203817	+	0.353022i
$93$	0.472891	+	4.40450i	0.0490365	+	0.456726i
$94$	−3.55502			−0.366672
$95$	−1.54887			−0.158911
$96$	0.184900	+	1.72215i	0.0188712	+	0.175767i
$97$	7.80249	+	13.5143i	0.792223	+	1.37217i	0.924588	+	0.380970i	$0.124410\pi$
$97$	7.80249	+	13.5143i	0.792223	+	1.37217i	−0.132365	+	0.991201i	$0.542257\pi$
$98$	3.19076	−	6.23049i	0.322315	−	0.629375i
$99$	0.879212	−	2.74768i	0.0883641	−	0.276153i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.80772	−	8.32722i	0.478386	−	0.828590i	−0.521307	−	0.853370i	$-0.674555\pi$
$101$	4.80772	−	8.32722i	0.478386	−	0.828590i	0.999693	+	0.0247799i	$0.00788850\pi$
$102$	−10.9040	+	7.95955i	−1.07966	+	0.788113i
$103$	−1.54448	−	2.67512i	−0.152183	−	0.263588i	0.779847	−	0.625970i	$-0.215297\pi$
$103$	−1.54448	−	2.67512i	−0.152183	−	0.263588i	−0.932030	+	0.362382i	$0.881963\pi$
$104$	−2.94219	+	5.09603i	−0.288506	+	0.499707i
$105$	−1.74856	+	4.23586i	−0.170642	+	0.413378i
$106$	0.274437	+	0.475340i	0.0266557	+	0.0461691i
$107$	−1.73194	+	2.99980i	−0.167433	+	0.290002i	−0.937516	−	0.347941i	$-0.886881\pi$
$107$	−1.73194	+	2.99980i	−0.167433	+	0.290002i	0.770084	+	0.637943i	$0.220214\pi$
$108$	−1.63881	−	4.93095i	−0.157695	−	0.474481i
$109$	−7.17178	−	12.4219i	−0.686932	−	1.18980i	−0.972826	−	0.231539i	$-0.925624\pi$
$109$	−7.17178	−	12.4219i	−0.686932	−	1.18980i	0.285894	−	0.958261i	$-0.407709\pi$
$110$	0.961641			0.0916889
$111$	18.5246	+	8.19811i	1.75828	+	0.778130i
$112$	−2.25729	+	1.38008i	−0.213294	+	0.130405i
$113$	0.362337	−	0.627585i	0.0340858	−	0.0590383i	−0.848479	−	0.529229i	$-0.822481\pi$
$113$	0.362337	−	0.627585i	0.0340858	−	0.0590383i	0.882565	+	0.470190i	$0.155815\pi$
$114$	2.45323	+	1.08568i	0.229766	+	0.101683i
$115$	1.95495	−	3.38607i	0.182300	−	0.315752i
$116$	−0.543215	−	0.940877i	−0.0504363	−	0.0873582i
$117$	5.38000	−	16.8134i	0.497381	−	1.55440i
$118$	−6.00868			−0.553144
$119$	−18.1126	−	9.85847i	−1.66038	−	0.903725i
$120$	1.39898	−	1.02120i	0.127709	−	0.0932228i
$121$	5.03762	+	8.72542i	0.457966	+	0.793220i
$122$	14.6881			1.32980
$123$	3.64424	+	1.61277i	0.328590	+	0.145418i
$124$	2.55756			0.229675
$125$	1.00000			0.0894427
$126$	5.73863	−	5.48344i	0.511238	−	0.488503i
$127$	13.1020			1.16262			0.581309	−	0.813683i	$-0.302541\pi$
$127$	13.1020			1.16262			0.581309	+	0.813683i	$0.302541\pi$
$128$	1.00000			0.0883883
$129$	6.12250	−	4.46921i	0.539056	−	0.393492i
$130$	5.88439			0.516095
$131$	8.75462	+	15.1634i	0.764895	+	1.32484i	0.940302	+	0.340340i	$0.110542\pi$
$131$	8.75462	+	15.1634i	0.764895	+	1.32484i	−0.175408	+	0.984496i	$0.556124\pi$
$132$	−1.52312	−	0.674061i	−0.132571	−	0.0586695i
$133$	0.103058	+	4.09664i	0.00893625	+	0.355224i
$134$	−0.821956			−0.0710061
$135$	−3.45093	+	3.88473i	−0.297008	+	0.334344i
$136$	3.89714	+	6.75005i	0.334177	+	0.578812i
$137$	4.34792	−	7.53082i	0.371468	−	0.643401i	−0.618324	−	0.785924i	$-0.712188\pi$
$137$	4.34792	−	7.53082i	0.371468	−	0.643401i	0.989792	+	0.142522i	$0.0455212\pi$
$138$	−5.46986	+	3.99280i	−0.465625	+	0.339890i
$139$	−6.56877	+	11.3774i	−0.557156	+	0.965022i	0.440576	+	0.897715i	$0.354774\pi$
$139$	−6.56877	+	11.3774i	−0.557156	+	0.965022i	−0.997732	+	0.0673073i	$0.978559\pi$
$140$	2.32383	+	1.26483i	0.196400	+	0.106898i
$141$	−0.657321	−	6.12229i	−0.0553564	−	0.515590i
$142$	−3.96164			−0.332454
$143$	−2.82933	−	4.90055i	−0.236601	−	0.409805i
$144$	−2.93162	+	0.636851i	−0.244302	+	0.0530709i
$145$	−0.543215	+	0.940877i	−0.0451116	+	0.0781355i
$146$	0.368764	+	0.638718i	0.0305191	+	0.0528607i
$147$	11.3198	+	4.34296i	0.933644	+	0.358201i
$148$	5.84787	−	10.1288i	0.480692	−	0.832583i
$149$	8.49218	+	14.7089i	0.695707	+	1.20500i	0.969942	+	0.243336i	$0.0782419\pi$
$149$	8.49218	+	14.7089i	0.695707	+	1.20500i	−0.274235	+	0.961663i	$0.588425\pi$
$150$	−1.58388	−	0.700949i	−0.129323	−	0.0572322i
$151$	7.91384	−	13.7072i	0.644019	−	1.11547i	−0.340508	−	0.940241i	$-0.610599\pi$
$151$	7.91384	−	13.7072i	0.644019	−	1.11547i	0.984527	−	0.175232i	$-0.0560675\pi$
$152$	0.774437	−	1.34137i	0.0628152	−	0.108799i
$153$	−15.7237	−	17.3067i	−1.27119	−	1.39916i
$154$	−0.0639849	−	2.54346i	−0.00515605	−	0.204958i
$155$	−1.27878	−	2.21491i	−0.102714	−	0.177906i
$156$	−9.32015	−	4.12466i	−0.746210	−	0.330237i
$157$	10.6557			0.850418			0.425209	−	0.905095i	$-0.360201\pi$
$157$	10.6557			0.850418			0.425209	+	0.905095i	$0.360201\pi$
$158$	−6.79796			−0.540816
$159$	−0.767864	+	0.560513i	−0.0608956	+	0.0444516i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−9.08593	−	4.94537i	−0.716072	−	0.389749i
$162$	8.18884	−	3.73401i	0.643376	−	0.293372i
$163$	3.88853	−	6.73513i	0.304573	−	0.527536i	−0.672593	−	0.740013i	$-0.734820\pi$
$163$	3.88853	−	6.73513i	0.304573	−	0.527536i	0.977166	+	0.212476i	$0.0681528\pi$
$164$	1.15042	−	1.99258i	0.0898324	−	0.155594i
$165$	0.177807	+	1.65609i	0.0138423	+	0.128927i
$166$	6.12526	+	10.6093i	0.475412	+	0.823438i
$167$	−7.14183	+	12.3700i	−0.552651	+	0.957220i	0.445431	+	0.895316i	$0.353051\pi$
$167$	−7.14183	+	12.3700i	−0.552651	+	0.957220i	−0.998082	+	0.0619037i	$0.980283\pi$
$168$	−2.79408	−	3.63223i	−0.215568	−	0.280233i
$169$	−10.8130	−	18.7287i	−0.831770	−	1.44067i
$170$	3.89714	−	6.75005i	0.298897	−	0.517705i
$171$	−1.41611	+	4.42558i	−0.108293	+	0.338433i
$172$	−2.18820	−	3.79008i	−0.166849	−	0.288991i
$173$	1.96561			0.149442			0.0747211	−	0.997204i	$-0.476193\pi$
$173$	1.96561			0.149442			0.0747211	+	0.997204i	$0.476193\pi$
$174$	1.51989	−	1.10947i	0.115223	−	0.0841085i
$175$	−0.0665372	−	2.64491i	−0.00502974	−	0.199937i
$176$	−0.480820	+	0.832805i	−0.0362432	+	0.0627751i
$177$	−1.11100	−	10.3479i	−0.0835081	−	0.777794i
$178$	−2.85680	+	4.94812i	−0.214126	+	0.370877i
$179$	7.02161	+	12.1618i	0.524819	+	0.909014i	0.999582	+	0.0289001i	$0.00920048\pi$
$179$	7.02161	+	12.1618i	0.524819	+	0.909014i	−0.474763	+	0.880114i	$0.657466\pi$
$180$	2.01734	+	2.22044i	0.150364	+	0.165502i
$181$	−17.5794			−1.30667			−0.653334	−	0.757070i	$-0.726630\pi$
$181$	−17.5794			−1.30667			−0.653334	+	0.757070i	$0.726630\pi$
$182$	−0.391531	−	15.5637i	−0.0290222	−	1.15366i
$183$	2.71583	+	25.2952i	0.200760	+	1.86988i
$184$	1.95495	+	3.38607i	0.144121	+	0.249624i
$185$	−11.6957			−0.859888
$186$	0.472891	+	4.40450i	0.0346740	+	0.322954i
$187$	−7.49530			−0.548111
$188$	−3.55502			−0.259276
$189$	10.5044	+	8.86892i	0.764082	+	0.645119i
$190$	−1.54887			−0.112367
$191$	−19.3643			−1.40115			−0.700577	−	0.713577i	$-0.747074\pi$
$191$	−19.3643			−1.40115			−0.700577	+	0.713577i	$0.747074\pi$
$192$	0.184900	+	1.72215i	0.0133440	+	0.124286i
$193$	−15.9094			−1.14518			−0.572592	−	0.819841i	$-0.694062\pi$
$193$	−15.9094			−1.14518			−0.572592	+	0.819841i	$0.694062\pi$
$194$	7.80249	+	13.5143i	0.560186	+	0.970271i
$195$	1.08802	+	10.1338i	0.0779148	+	0.725698i
$196$	3.19076	−	6.23049i	0.227911	−	0.445035i
$197$	20.8910			1.48842			0.744211	−	0.667945i	$-0.232826\pi$
$197$	20.8910			1.48842			0.744211	+	0.667945i	$0.232826\pi$
$198$	0.879212	−	2.74768i	0.0624829	−	0.195269i
$199$	−6.51900	−	11.2912i	−0.462120	−	0.800415i	0.536947	−	0.843616i	$-0.319578\pi$
$199$	−6.51900	−	11.2912i	−0.462120	−	0.800415i	−0.999066	+	0.0432012i	$0.986244\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−0.151979	−	1.41553i	−0.0107198	−	0.0998440i
$202$	4.80772	−	8.32722i	0.338270	−	0.585901i
$203$	2.52468	+	1.37415i	0.177198	+	0.0964468i
$204$	−10.9040	+	7.95955i	−0.763435	+	0.557280i
$205$	−2.30083			−0.160697
$206$	−1.54448	−	2.67512i	−0.107609	−	0.186385i
$207$	−7.88759	−	8.68167i	−0.548225	−	0.603417i
$208$	−2.94219	+	5.09603i	−0.204004	+	0.353346i
$209$	0.744731	+	1.28991i	0.0515141	+	0.0892250i
$210$	−1.74856	+	4.23586i	−0.120662	+	0.292302i
$211$	8.63625	−	14.9584i	0.594544	−	1.02978i	−0.399067	−	0.916922i	$-0.630666\pi$
$211$	8.63625	−	14.9584i	0.594544	−	1.02978i	0.993611	−	0.112858i	$-0.0360006\pi$
$212$	0.274437	+	0.475340i	0.0188484	+	0.0326465i
$213$	−0.732506	−	6.82255i	−0.0501905	−	0.467474i
$214$	−1.73194	+	2.99980i	−0.118393	+	0.205062i
$215$	−2.18820	+	3.79008i	−0.149234	+	0.258481i
$216$	−1.63881	−	4.93095i	−0.111507	−	0.335509i
$217$	−5.77316	+	3.52963i	−0.391907	+	0.239607i
$218$	−7.17178	−	12.4219i	−0.485734	−	0.841316i
$219$	−1.03179	+	0.753167i	−0.0697216	+	0.0508943i
$220$	0.961641			0.0648338
$221$	−45.8646			−3.08519
$222$	18.5246	+	8.19811i	1.24329	+	0.550221i
$223$	−13.6681	−	23.6739i	−0.915287	−	1.58532i	−0.806481	−	0.591261i	$-0.798630\pi$
$223$	−13.6681	−	23.6739i	−0.915287	−	1.58532i	−0.108806	−	0.994063i	$-0.534703\pi$
$224$	−2.25729	+	1.38008i	−0.150822	+	0.0922105i
$225$	0.914283	−	2.85729i	0.0609522	−	0.190486i
$226$	0.362337	−	0.627585i	0.0241023	−	0.0417464i
$227$	−3.73097	+	6.46223i	−0.247633	+	0.428914i	−0.962869	−	0.269970i	$-0.912986\pi$
$227$	−3.73097	+	6.46223i	−0.247633	+	0.428914i	0.715235	+	0.698884i	$0.246319\pi$
$228$	2.45323	+	1.08568i	0.162469	+	0.0719011i
$229$	4.73672	+	8.20425i	0.313012	+	0.542152i	0.979013	−	0.203799i	$-0.0653288\pi$
$229$	4.73672	+	8.20425i	0.313012	+	0.542152i	−0.666001	+	0.745951i	$0.731995\pi$
$230$	1.95495	−	3.38607i	0.128905	−	0.223271i
$231$	4.36839	−	0.580476i	0.287419	−	0.0381925i
$232$	−0.543215	−	0.940877i	−0.0356638	−	0.0617716i
$233$	7.21133	−	12.4904i	0.472430	−	0.818272i	−0.527072	−	0.849820i	$-0.676710\pi$
$233$	7.21133	−	12.4904i	0.472430	−	0.818272i	0.999502	+	0.0315480i	$0.0100437\pi$
$234$	5.38000	−	16.8134i	0.351701	−	1.09913i
$235$	1.77751	+	3.07874i	0.115952	+	0.200835i
$236$	−6.00868			−0.391132
$237$	−1.25694	−	11.7071i	−0.0816470	−	0.760460i
$238$	−18.1126	−	9.85847i	−1.17407	−	0.639030i
$239$	−4.82726	+	8.36106i	−0.312249	+	0.540832i	−0.978849	−	0.204584i	$-0.934416\pi$
$239$	−4.82726	+	8.36106i	−0.312249	+	0.540832i	0.666600	+	0.745416i	$0.267749\pi$
$240$	1.39898	−	1.02120i	0.0903037	−	0.0659185i
$241$	2.08005	−	3.60276i	0.133988	−	0.232074i	−0.791222	−	0.611529i	$-0.790555\pi$
$241$	2.08005	−	3.60276i	0.133988	−	0.232074i	0.925210	+	0.379454i	$0.123888\pi$
$242$	5.03762	+	8.72542i	0.323831	+	0.560891i
$243$	7.94466	+	13.4120i	0.509650	+	0.860382i
$244$	14.6881			0.940312
$245$	−6.99115	+	0.351971i	−0.446648	+	0.0224866i
$246$	3.64424	+	1.61277i	0.232348	+	0.102826i
$247$	4.55709	+	7.89311i	0.289961	+	0.502227i
$248$	2.55756			0.162405
$249$	−17.1382	+	12.5103i	−1.08609	+	0.792806i
$250$	1.00000			0.0632456
$251$	22.3874			1.41308			0.706539	−	0.707674i	$-0.250255\pi$
$251$	22.3874			1.41308			0.706539	+	0.707674i	$0.250255\pi$
$252$	5.73863	−	5.48344i	0.361500	−	0.345424i
$253$	−3.75991			−0.236384
$254$	13.1020			0.822095
$255$	12.3452	+	5.46339i	0.773086	+	0.342131i
$256$	1.00000			0.0625000
$257$	7.74058	+	13.4071i	0.482844	+	0.836311i	0.999806	−	0.0196976i	$-0.00627036\pi$
$257$	7.74058	+	13.4071i	0.482844	+	0.836311i	−0.516962	+	0.856009i	$0.672937\pi$
$258$	6.12250	−	4.46921i	0.381170	−	0.278241i
$259$	0.778202	+	30.9342i	0.0483551	+	1.92216i
$260$	5.88439			0.364934
$261$	2.19170	+	2.41235i	0.135663	+	0.149321i
$262$	8.75462	+	15.1634i	0.540862	+	0.936801i
$263$	−7.85472	+	13.6048i	−0.484343	+	0.838906i	−0.999838	−	0.0179863i	$-0.994274\pi$
$263$	−7.85472	+	13.6048i	−0.484343	+	0.838906i	0.515496	+	0.856892i	$0.327608\pi$
$264$	−1.52312	−	0.674061i	−0.0937417	−	0.0414856i
$265$	0.274437	−	0.475340i	0.0168586	−	0.0291999i
$266$	0.103058	+	4.09664i	0.00631888	+	0.251181i
$267$	−9.04964	−	4.00494i	−0.553829	−	0.245098i
$268$	−0.821956			−0.0502089
$269$	−4.56038	−	7.89882i	−0.278052	−	0.481599i	0.692849	−	0.721083i	$-0.256355\pi$
$269$	−4.56038	−	7.89882i	−0.278052	−	0.481599i	−0.970900	+	0.239483i	$0.923022\pi$
$270$	−3.45093	+	3.88473i	−0.210017	+	0.236417i
$271$	13.3929	−	23.1972i	0.813561	−	1.40913i	−0.0967955	−	0.995304i	$-0.530859\pi$
$271$	13.3929	−	23.1972i	0.813561	−	1.40913i	0.910357	−	0.413825i	$-0.135807\pi$
$272$	3.89714	+	6.75005i	0.236299	+	0.409282i
$273$	26.7307	−	3.55200i	1.61781	−	0.214977i
$274$	4.34792	−	7.53082i	0.262668	−	0.454954i
$275$	−0.480820	−	0.832805i	−0.0289946	−	0.0502201i
$276$	−5.46986	+	3.99280i	−0.329247	+	0.240338i
$277$	−2.22622	+	3.85593i	−0.133761	+	0.231680i	−0.925123	−	0.379667i	$-0.876039\pi$
$277$	−2.22622	+	3.85593i	−0.133761	+	0.231680i	0.791363	+	0.611347i	$0.209372\pi$
$278$	−6.56877	+	11.3774i	−0.393969	+	0.682374i
$279$	−7.49779	+	1.62878i	−0.448881	+	0.0975126i
$280$	2.32383	+	1.26483i	0.138876	+	0.0755883i
$281$	10.7630	+	18.6420i	0.642065	+	1.11209i	0.984971	+	0.172720i	$0.0552555\pi$
$281$	10.7630	+	18.6420i	0.642065	+	1.11209i	−0.342906	+	0.939370i	$0.611411\pi$
$282$	−0.657321	−	6.12229i	−0.0391429	−	0.364577i
$283$	−5.49623			−0.326717			−0.163358	−	0.986567i	$-0.552233\pi$
$283$	−5.49623			−0.326717			−0.163358	+	0.986567i	$0.552233\pi$
$284$	−3.96164			−0.235080
$285$	−0.286386	−	2.66740i	−0.0169641	−	0.158003i
$286$	−2.82933	−	4.90055i	−0.167302	−	0.289776i
$287$	0.153091	+	6.08550i	0.00903667	+	0.359216i
$288$	−2.93162	+	0.636851i	−0.172748	+	0.0375268i
$289$	−21.8754	+	37.8893i	−1.28679	+	2.22878i
$290$	−0.543215	+	0.940877i	−0.0318987	+	0.0552502i
$291$	−21.8310	+	15.9359i	−1.27976	+	0.934178i
$292$	0.368764	+	0.638718i	0.0215803	+	0.0373781i
$293$	7.28966	−	12.6261i	0.425866	−	0.737622i	−0.570635	−	0.821204i	$-0.693303\pi$
$293$	7.28966	−	12.6261i	0.425866	−	0.737622i	0.996501	+	0.0835819i	$0.0266360\pi$
$294$	11.3198	+	4.34296i	0.660186	+	0.253286i
$295$	3.00434	+	5.20367i	0.174919	+	0.302969i
$296$	5.84787	−	10.1288i	0.339900	−	0.588725i
$297$	4.89450	+	1.00609i	0.284008	+	0.0583794i
$298$	8.49218	+	14.7089i	0.491939	+	0.852063i
$299$	−23.0073			−1.33055
$300$	−1.58388	−	0.700949i	−0.0914453	−	0.0404693i
$301$	10.1700	+	5.53543i	0.586191	+	0.319057i
$302$	7.91384	−	13.7072i	0.455390	−	0.788759i
$303$	15.2297	+	6.73994i	0.874923	+	0.387199i
$304$	0.774437	−	1.34137i	0.0444170	−	0.0769326i
$305$	−7.34407	−	12.7203i	−0.420520	−	0.728362i
$306$	−15.7237	−	17.3067i	−0.898865	−	0.989358i
$307$	3.42914			0.195712			0.0978558	−	0.995201i	$-0.468802\pi$
$307$	3.42914			0.195712			0.0978558	+	0.995201i	$0.468802\pi$
$308$	−0.0639849	−	2.54346i	−0.00364588	−	0.144927i
$309$	4.32140	−	3.15447i	0.245836	−	0.179451i
$310$	−1.27878	−	2.21491i	−0.0726297	−	0.125798i
$311$	−34.6413			−1.96433			−0.982164	−	0.188025i	$-0.939791\pi$
$311$	−34.6413			−1.96433			−0.982164	+	0.188025i	$0.939791\pi$
$312$	−9.32015	−	4.12466i	−0.527650	−	0.233513i
$313$	30.5887			1.72897			0.864487	−	0.502655i	$-0.167644\pi$
$313$	30.5887			1.72897			0.864487	+	0.502655i	$0.167644\pi$
$314$	10.6557			0.601336
$315$	−7.61811	−	2.22809i	−0.429232	−	0.125538i
$316$	−6.79796			−0.382415
$317$	−10.0424			−0.564039			−0.282020	−	0.959409i	$-0.591004\pi$
$317$	−10.0424			−0.564039			−0.282020	+	0.959409i	$0.591004\pi$
$318$	−0.767864	+	0.560513i	−0.0430597	+	0.0314320i
$319$	1.04476			0.0584951
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−5.48635	−	2.42800i	−0.306218	−	0.135518i
$322$	−9.08593	−	4.94537i	−0.506339	−	0.275594i
$323$	12.0724			0.671724
$324$	8.18884	−	3.73401i	0.454936	−	0.207445i
$325$	−2.94219	−	5.09603i	−0.163204	−	0.282677i
$326$	3.88853	−	6.73513i	0.215366	−	0.373024i
$327$	20.0663	−	14.6477i	1.10967	−	0.810020i
$328$	1.15042	−	1.99258i	0.0635211	−	0.110022i
$329$	8.02472	−	4.90621i	0.442417	−	0.270488i
$330$	0.177807	+	1.65609i	0.00978795	+	0.0911649i
$331$	−14.4680			−0.795234			−0.397617	−	0.917551i	$-0.630163\pi$
$331$	−14.4680			−0.795234			−0.397617	+	0.917551i	$0.630163\pi$
$332$	6.12526	+	10.6093i	0.336167	+	0.582258i
$333$	−10.6932	+	33.4181i	−0.585985	+	1.83130i
$334$	−7.14183	+	12.3700i	−0.390783	+	0.676857i
$335$	0.410978	+	0.711834i	0.0224541	+	0.0388917i
$336$	−2.79408	−	3.63223i	−0.152430	−	0.198154i
$337$	0.772692	−	1.33834i	0.0420912	−	0.0729041i	−0.844212	−	0.536009i	$-0.819931\pi$
$337$	0.772692	−	1.33834i	0.0420912	−	0.0729041i	0.886304	+	0.463105i	$0.153265\pi$
$338$	−10.8130	−	18.7287i	−0.588150	−	1.01871i
$339$	1.14779	+	0.507959i	0.0623396	+	0.0275885i
$340$	3.89714	−	6.75005i	0.211352	−	0.366073i
$341$	−1.22973	+	2.12995i	−0.0665934	+	0.115343i
$342$	−1.41611	+	4.42558i	−0.0765745	+	0.239308i
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	−2.18820	−	3.79008i	−0.117980	−	0.204348i
$345$	6.19279	+	2.74064i	0.333409	+	0.147551i
$346$	1.96561			0.105672
$347$	13.1517			0.706021			0.353011	−	0.935619i	$-0.385158\pi$
$347$	13.1517			0.706021			0.353011	+	0.935619i	$0.385158\pi$
$348$	1.51989	−	1.10947i	0.0814748	−	0.0594737i
$349$	0.752263	+	1.30296i	0.0402677	+	0.0697457i	0.885457	−	0.464722i	$-0.153846\pi$
$349$	0.752263	+	1.30296i	0.0402677	+	0.0697457i	−0.845189	+	0.534467i	$0.820512\pi$
$350$	−0.0665372	−	2.64491i	−0.00355656	−	0.141377i
$351$	29.9500	+	6.15639i	1.59861	+	0.328604i
$352$	−0.480820	+	0.832805i	−0.0256278	+	0.0443887i
$353$	18.0095	−	31.1933i	0.958547	−	1.66025i	0.232515	−	0.972593i	$-0.425305\pi$
$353$	18.0095	−	31.1933i	0.958547	−	1.66025i	0.726033	−	0.687660i	$-0.241362\pi$
$354$	−1.11100	−	10.3479i	−0.0590491	−	0.549983i
$355$	1.98082	+	3.43088i	0.105131	+	0.182092i
$356$	−2.85680	+	4.94812i	−0.151410	+	0.262250i
$357$	13.6288	−	33.0155i	0.721312	−	1.74737i
$358$	7.02161	+	12.1618i	0.371103	+	0.642770i
$359$	6.85269	−	11.8692i	0.361671	−	0.626433i	−0.626565	−	0.779369i	$-0.715540\pi$
$359$	6.85269	−	11.8692i	0.361671	−	0.626433i	0.988236	+	0.152936i	$0.0488730\pi$
$360$	2.01734	+	2.22044i	0.106323	+	0.117027i
$361$	8.30049	+	14.3769i	0.436868	+	0.756678i
$362$	−17.5794			−0.923953
$363$	−14.0951	+	10.2889i	−0.739799	+	0.540026i
$364$	−0.391531	−	15.5637i	−0.0205218	−	0.815760i
$365$	0.368764	−	0.638718i	0.0193020	−	0.0334320i
$366$	2.71583	+	25.2952i	0.141959	+	1.32220i
$367$	−16.0160	+	27.7406i	−0.836029	+	1.44805i	0.0571604	+	0.998365i	$0.481795\pi$
$367$	−16.0160	+	27.7406i	−0.836029	+	1.44805i	−0.893190	+	0.449680i	$0.851538\pi$
$368$	1.95495	+	3.38607i	0.101909	+	0.176511i
$369$	−2.10361	+	6.57413i	−0.109510	+	0.342236i
$370$	−11.6957			−0.608032
$371$	−1.27549	−	0.694236i	−0.0662203	−	0.0360429i
$372$	0.472891	+	4.40450i	0.0245183	+	0.228363i
$373$	−3.86024	−	6.68613i	−0.199876	−	0.346195i	0.748612	−	0.663008i	$-0.230720\pi$
$373$	−3.86024	−	6.68613i	−0.199876	−	0.346195i	−0.948488	+	0.316813i	$0.897387\pi$
$374$	−7.49530			−0.387573
$375$	0.184900	+	1.72215i	0.00954817	+	0.0889316i
$376$	−3.55502			−0.183336
$377$	6.39298			0.329255
$378$	10.5044	+	8.86892i	0.540287	+	0.456168i
$379$	−2.47157			−0.126956			−0.0634780	−	0.997983i	$-0.520219\pi$
$379$	−2.47157			−0.126956			−0.0634780	+	0.997983i	$0.520219\pi$
$380$	−1.54887			−0.0794556
$381$	2.42256	+	22.5637i	0.124112	+	1.15597i
$382$	−19.3643			−0.990766
$383$	−12.3131	−	21.3268i	−0.629168	−	1.08975i	−0.987719	−	0.156240i	$-0.950063\pi$
$383$	−12.3131	−	21.3268i	−0.629168	−	1.08975i	0.358552	−	0.933510i	$-0.383271\pi$
$384$	0.184900	+	1.72215i	0.00943562	+	0.0878833i
$385$	−2.17071	+	1.32714i	−0.110629	+	0.0676374i
$386$	−15.9094			−0.809767
$387$	8.82871	+	9.71754i	0.448789	+	0.493970i
$388$	7.80249	+	13.5143i	0.396112	+	0.686085i
$389$	4.14338	−	7.17655i	0.210078	−	0.363866i	−0.741661	−	0.670775i	$-0.765962\pi$
$389$	4.14338	−	7.17655i	0.210078	−	0.363866i	0.951739	+	0.306909i	$0.0992949\pi$
$390$	1.08802	+	10.1338i	0.0550941	+	0.513146i
$391$	−15.2374	+	26.3920i	−0.770588	+	1.33470i
$392$	3.19076	−	6.23049i	0.161158	−	0.314688i
$393$	−24.4951	+	17.8805i	−1.23561	+	0.901952i
$394$	20.8910			1.05247
$395$	3.39898	+	5.88720i	0.171021	+	0.296217i
$396$	0.879212	−	2.74768i	0.0441821	−	0.138076i
$397$	9.42143	−	16.3184i	0.472848	−	0.818997i	−0.526669	−	0.850070i	$-0.676559\pi$
$397$	9.42143	−	16.3184i	0.472848	−	0.818997i	0.999517	+	0.0310737i	$0.00989266\pi$
$398$	−6.51900	−	11.2912i	−0.326768	−	0.565979i
$399$	−7.03599	+	0.934949i	−0.352240	+	0.0468060i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	5.84903	+	10.1308i	0.292087	+	0.505909i	0.974303	−	0.225241i	$-0.0723171\pi$
$401$	5.84903	+	10.1308i	0.292087	+	0.505909i	−0.682216	+	0.731150i	$0.738984\pi$
$402$	−0.151979	−	1.41553i	−0.00758003	−	0.0706004i
$403$	−7.52483	+	13.0334i	−0.374838	+	0.649239i
$404$	4.80772	−	8.32722i	0.239193	−	0.414295i
$405$	−7.32817	−	5.22474i	−0.364140	−	0.259619i
$406$	2.52468	+	1.37415i	0.125298	+	0.0681982i
$407$	5.62355	+	9.74027i	0.278749	+	0.482807i
$408$	−10.9040	+	7.95955i	−0.539830	+	0.394057i
$409$	−18.0739			−0.893695			−0.446848	−	0.894610i	$-0.647453\pi$
$409$	−18.0739			−0.893695			−0.446848	+	0.894610i	$0.647453\pi$
$410$	−2.30083			−0.113630
$411$	13.7732	+	6.09534i	0.679380	+	0.300661i
$412$	−1.54448	−	2.67512i	−0.0760913	−	0.131794i
$413$	13.5634	−	8.29246i	0.667409	−	0.408045i
$414$	−7.88759	−	8.68167i	−0.387654	−	0.426681i
$415$	6.12526	−	10.6093i	0.300677	−	0.520788i
$416$	−2.94219	+	5.09603i	−0.144253	+	0.249853i
$417$	−20.8083	−	9.20875i	−1.01899	−	0.450954i
$418$	0.744731	+	1.28991i	0.0364260	+	0.0630916i
$419$	9.88791	−	17.1264i	0.483056	−	0.836677i	−0.516755	−	0.856133i	$-0.672860\pi$
$419$	9.88791	−	17.1264i	0.483056	−	0.836677i	0.999811	+	0.0194561i	$0.00619346\pi$
$420$	−1.74856	+	4.23586i	−0.0853211	+	0.206689i
$421$	−15.4734	−	26.8008i	−0.754129	−	1.30619i	−0.945806	−	0.324732i	$-0.894726\pi$
$421$	−15.4734	−	26.8008i	−0.754129	−	1.30619i	0.191677	−	0.981458i	$-0.438608\pi$
$422$	8.63625	−	14.9584i	0.420406	−	0.728164i
$423$	10.4220	−	2.26402i	0.506734	−	0.110080i
$424$	0.274437	+	0.475340i	0.0133279	+	0.0230845i
$425$	−7.79428			−0.378078
$426$	−0.732506	−	6.82255i	−0.0354900	−	0.330554i
$427$	−33.1555	+	20.2708i	−1.60450	+	0.980973i
$428$	−1.73194	+	2.99980i	−0.0837163	+	0.145001i
$429$	7.91636	−	5.77866i	0.382205	−	0.278996i
$430$	−2.18820	+	3.79008i	−0.105525	+	0.182774i
$431$	1.01707	+	1.76162i	0.0489907	+	0.0848544i	0.889481	−	0.456972i	$-0.151066\pi$
$431$	1.01707	+	1.76162i	0.0489907	+	0.0848544i	−0.840490	+	0.541827i	$0.817733\pi$
$432$	−1.63881	−	4.93095i	−0.0788473	−	0.237241i
$433$	−17.9368			−0.861989			−0.430994	−	0.902355i	$-0.641837\pi$
$433$	−17.9368			−0.861989			−0.430994	+	0.902355i	$0.641837\pi$
$434$	−5.77316	+	3.52963i	−0.277120	+	0.169428i
$435$	−1.72077	−	0.761532i	−0.0825048	−	0.0365127i
$436$	−7.17178	−	12.4219i	−0.343466	−	0.594900i
$437$	6.05593			0.289695
$438$	−1.03179	+	0.753167i	−0.0493006	+	0.0359877i
$439$	−34.2741			−1.63581			−0.817906	−	0.575352i	$-0.804865\pi$
$439$	−34.2741			−1.63581			−0.817906	+	0.575352i	$0.804865\pi$
$440$	0.961641			0.0458444
$441$	−5.38621	+	20.2975i	−0.256486	+	0.966548i
$442$	−45.8646			−2.18156
$443$	13.9945			0.664901			0.332451	−	0.943121i	$-0.392125\pi$
$443$	13.9945			0.664901			0.332451	+	0.943121i	$0.392125\pi$
$444$	18.5246	+	8.19811i	0.879140	+	0.389065i
$445$	5.71360			0.270850
$446$	−13.6681	−	23.6739i	−0.647206	−	1.12099i
$447$	−23.7608	+	17.3445i	−1.12385	+	0.820367i
$448$	−2.25729	+	1.38008i	−0.106647	+	0.0652027i
$449$	24.3772			1.15043			0.575215	−	0.818002i	$-0.304918\pi$
$449$	24.3772			1.15043			0.575215	+	0.818002i	$0.304918\pi$
$450$	0.914283	−	2.85729i	0.0430997	−	0.134694i
$451$	1.10629	+	1.91614i	0.0520930	+	0.0902277i
$452$	0.362337	−	0.627585i	0.0170429	−	0.0295191i
$453$	25.0691	+	11.0944i	1.17785	+	0.521260i
$454$	−3.73097	+	6.46223i	−0.175103	+	0.303288i
$455$	−13.2828	+	8.12093i	−0.622707	+	0.380715i
$456$	2.45323	+	1.08568i	0.114883	+	0.0508417i
$457$	−34.3746			−1.60798			−0.803989	−	0.594644i	$-0.797293\pi$
$457$	−34.3746			−1.60798			−0.803989	+	0.594644i	$0.797293\pi$
$458$	4.73672	+	8.20425i	0.221333	+	0.383359i
$459$	26.8975	−	30.2787i	1.25547	−	1.41329i
$460$	1.95495	−	3.38607i	0.0911498	−	0.157876i
$461$	−14.6870	−	25.4386i	−0.684042	−	1.18479i	−0.973737	−	0.227676i	$-0.926887\pi$
$461$	−14.6870	−	25.4386i	−0.684042	−	1.18479i	0.289695	−	0.957119i	$-0.406446\pi$
$462$	4.36839	−	0.580476i	0.203236	−	0.0270062i
$463$	10.5391	−	18.2542i	0.489792	−	0.848345i	−0.510139	−	0.860092i	$-0.670406\pi$
$463$	10.5391	−	18.2542i	0.489792	−	0.848345i	0.999931	+	0.0117473i	$0.00373938\pi$
$464$	−0.543215	−	0.940877i	−0.0252181	−	0.0436791i
$465$	3.57797	−	2.61179i	0.165924	−	0.121119i
$466$	7.21133	−	12.4904i	0.334058	−	0.578606i
$467$	−20.8663	+	36.1415i	−0.965578	+	1.67243i	−0.257524	+	0.966272i	$0.582907\pi$
$467$	−20.8663	+	36.1415i	−0.965578	+	1.67243i	−0.708054	+	0.706158i	$0.750427\pi$
$468$	5.38000	−	16.8134i	0.248690	−	0.777199i
$469$	1.85540	−	1.13436i	0.0856742	−	0.0523801i
$470$	1.77751	+	3.07874i	0.0819904	+	0.142012i
$471$	1.97023	+	18.3508i	0.0907836	+	0.845558i
$472$	−6.00868			−0.276572
$473$	4.20853			0.193509
$474$	−1.25694	−	11.7071i	−0.0577331	−	0.537726i
$475$	0.774437	+	1.34137i	0.0355336	+	0.0615460i
$476$	−18.1126	−	9.85847i	−0.830190	−	0.451862i
$477$	−1.10727	−	1.21874i	−0.0506983	−	0.0558023i
$478$	−4.82726	+	8.36106i	−0.220794	+	0.382426i
$479$	9.11638	−	15.7900i	0.416538	−	0.721465i	−0.579051	−	0.815292i	$-0.696577\pi$
$479$	9.11638	−	15.7900i	0.416538	−	0.721465i	0.995589	+	0.0938267i	$0.0299100\pi$
$480$	1.39898	−	1.02120i	0.0638544	−	0.0466114i
$481$	34.4111	+	59.6018i	1.56901	+	2.71761i
$482$	2.08005	−	3.60276i	0.0947438	−	0.164101i
$483$	6.83669	−	16.5618i	0.311080	−	0.753586i
$484$	5.03762	+	8.72542i	0.228983	+	0.396610i
$485$	7.80249	−	13.5143i	0.354293	−	0.613653i
$486$	7.94466	+	13.4120i	0.360377	+	0.608382i
$487$	12.5910	+	21.8083i	0.570554	+	0.988228i	0.996509	+	0.0834838i	$0.0266047\pi$
$487$	12.5910	+	21.8083i	0.570554	+	0.988228i	−0.425956	+	0.904744i	$0.640062\pi$
$488$	14.6881			0.664901
$489$	12.3179	+	5.45132i	0.557036	+	0.246517i
$490$	−6.99115	+	0.351971i	−0.315828	+	0.0159004i
$491$	18.6196	−	32.2501i	0.840290	−	1.45542i	−0.0493598	−	0.998781i	$-0.515718\pi$
$491$	18.6196	−	32.2501i	0.840290	−	1.45542i	0.889650	−	0.456644i	$-0.150949\pi$
$492$	3.64424	+	1.61277i	0.164295	+	0.0727091i
$493$	4.23397	−	7.33346i	0.190689	−	0.330282i
$494$	4.55709	+	7.89311i	0.205033	+	0.355128i
$495$	−2.81917	+	0.612422i	−0.126712	+	0.0275263i
$496$	2.55756			0.114838
$497$	8.94259	−	5.46738i	0.401130	−	0.245246i
$498$	−17.1382	+	12.5103i	−0.767981	+	0.560599i
$499$	−3.69263	−	6.39582i	−0.165305	−	0.286316i	0.771459	−	0.636279i	$-0.219527\pi$
$499$	−3.69263	−	6.39582i	−0.165305	−	0.286316i	−0.936763	+	0.349963i	$0.886194\pi$
$500$	1.00000			0.0447214
$501$	−22.6236	−	10.0121i	−1.01075	−	0.447308i
$502$	22.3874			0.999197
$503$	−18.0307			−0.803947			−0.401974	−	0.915651i	$-0.631676\pi$
$503$	−18.0307			−0.803947			−0.401974	+	0.915651i	$0.631676\pi$
$504$	5.73863	−	5.48344i	0.255619	−	0.244252i
$505$	−9.61545			−0.427882
$506$	−3.75991			−0.167149
$507$	30.2543	−	22.0846i	1.34364	−	0.980811i
$508$	13.1020			0.581309
$509$	−10.9524	−	18.9701i	−0.485457	−	0.840836i	0.514403	−	0.857548i	$-0.328013\pi$
$509$	−10.9524	−	18.9701i	−0.485457	−	0.840836i	−0.999860	+	0.0167122i	$0.994680\pi$
$510$	12.3452	+	5.46339i	0.546654	+	0.241923i
$511$	−1.71389	−	0.932851i	−0.0758181	−	0.0412669i
$512$	1.00000			0.0441942
$513$	−7.88336	−	1.62047i	−0.348059	−	0.0715456i
$514$	7.74058	+	13.4071i	0.341423	+	0.591361i
$515$	−1.54448	+	2.67512i	−0.0680581	+	0.117880i
$516$	6.12250	−	4.46921i	0.269528	−	0.196746i
$517$	1.70933	−	2.96064i	0.0751761	−	0.130209i
$518$	0.778202	+	30.9342i	0.0341922	+	1.35917i
$519$	0.363440	+	3.38508i	0.0159532	+	0.148588i
$520$	5.88439			0.258047
$521$	−12.3028	−	21.3090i	−0.538994	−	0.933565i	−0.998959	−	0.0456279i	$-0.985471\pi$
$521$	−12.3028	−	21.3090i	−0.538994	−	0.933565i	0.459964	−	0.887937i	$-0.347862\pi$
$522$	2.19170	+	2.41235i	0.0959282	+	0.105586i
$523$	−1.34318	+	2.32646i	−0.0587333	+	0.101729i	−0.893897	−	0.448272i	$-0.852039\pi$
$523$	−1.34318	+	2.32646i	−0.0587333	+	0.101729i	0.835164	+	0.550001i	$0.185373\pi$
$524$	8.75462	+	15.1634i	0.382447	+	0.662418i
$525$	4.54265	−	0.603631i	0.198257	−	0.0263446i
$526$	−7.85472	+	13.6048i	−0.342482	+	0.593196i
$527$	9.96715	+	17.2636i	0.434176	+	0.752015i
$528$	−1.52312	−	0.674061i	−0.0662854	−	0.0293347i
$529$	3.85637	−	6.67943i	0.167668	−	0.290410i
$530$	0.274437	−	0.475340i	0.0119208	−	0.0206474i
$531$	17.6152	−	3.82663i	0.764434	−	0.166062i
$532$	0.103058	+	4.09664i	0.00446812	+	0.177612i
$533$	6.76949	+	11.7251i	0.293219	+	0.507871i
$534$	−9.04964	−	4.00494i	−0.391616	−	0.173311i
$535$	3.46387			0.149756
$536$	−0.821956			−0.0355031
$537$	−19.6462	+	14.3410i	−0.847794	+	0.618859i
$538$	−4.56038	−	7.89882i	−0.196612	−	0.340542i
$539$	3.65461	+	5.65303i	0.157415	+	0.243493i
$540$	−3.45093	+	3.88473i	−0.148504	+	0.167172i
$541$	13.7482	−	23.8125i	0.591080	−	1.02378i	−0.403007	−	0.915197i	$-0.632035\pi$
$541$	13.7482	−	23.8125i	0.591080	−	1.02378i	0.994087	−	0.108584i	$-0.0346315\pi$
$542$	13.3929	−	23.1972i	0.575275	−	0.996405i
$543$	−3.25043	−	30.2744i	−0.139489	−	1.29920i
$544$	3.89714	+	6.75005i	0.167089	+	0.289406i
$545$	−7.17178	+	12.4219i	−0.307205	+	0.532095i
$546$	26.7307	−	3.55200i	1.14397	−	0.152011i
$547$	0.0925609	+	0.160320i	0.00395762	+	0.00685480i	0.867997	−	0.496569i	$-0.165407\pi$
$547$	0.0925609	+	0.160320i	0.00395762	+	0.00685480i	−0.864040	+	0.503423i	$0.832074\pi$
$548$	4.34792	−	7.53082i	0.185734	−	0.321701i
$549$	−43.0601	+	9.35415i	−1.83776	+	0.399225i
$550$	−0.480820	−	0.832805i	−0.0205023	−	0.0355109i
$551$	−1.68275			−0.0716874
$552$	−5.46986	+	3.99280i	−0.232813	+	0.169945i
$553$	15.3450	−	9.38173i	0.652535	−	0.398952i
$554$	−2.22622	+	3.85593i	−0.0945831	+	0.163823i
$555$	−2.16254	−	20.1418i	−0.0917945	−	0.854974i
$556$	−6.56877	+	11.3774i	−0.278578	+	0.482511i
$557$	−12.0082	−	20.7988i	−0.508804	−	0.881275i	−0.999948	−	0.0101964i	$-0.996754\pi$
$557$	−12.0082	−	20.7988i	−0.508804	−	0.881275i	0.491144	−	0.871079i	$-0.336579\pi$
$558$	−7.49779	+	1.62878i	−0.317407	+	0.0689518i
$559$	25.7525			1.08921
$560$	2.32383	+	1.26483i	0.0981998	+	0.0534490i
$561$	−1.38588	−	12.9081i	−0.0585118	−	0.544979i
$562$	10.7630	+	18.6420i	0.454009	+	0.786366i
$563$	−14.3498			−0.604771			−0.302385	−	0.953186i	$-0.597783\pi$
$563$	−14.3498			−0.604771			−0.302385	+	0.953186i	$0.597783\pi$
$564$	−0.657321	−	6.12229i	−0.0276782	−	0.257795i
$565$	−0.724673			−0.0304872
$566$	−5.49623			−0.231024
$567$	−13.3314	+	19.7300i	−0.559866	+	0.828583i
$568$	−3.96164			−0.166227
$569$	−9.24379			−0.387520			−0.193760	−	0.981049i	$-0.562068\pi$
$569$	−9.24379			−0.387520			−0.193760	+	0.981049i	$0.562068\pi$
$570$	−0.286386	−	2.66740i	−0.0119954	−	0.111725i
$571$	41.3063			1.72861			0.864307	−	0.502965i	$-0.167757\pi$
$571$	41.3063			1.72861			0.864307	+	0.502965i	$0.167757\pi$
$572$	−2.82933	−	4.90055i	−0.118300	−	0.204902i
$573$	−3.58046	−	33.3484i	−0.149576	−	1.39315i
$574$	0.153091	+	6.08550i	0.00638989	+	0.254004i
$575$	−3.90989			−0.163054
$576$	−2.93162	+	0.636851i	−0.122151	+	0.0265354i
$577$	−0.822047	−	1.42383i	−0.0342223	−	0.0592747i	0.848407	−	0.529344i	$-0.177562\pi$
$577$	−0.822047	−	1.42383i	−0.0342223	−	0.0592747i	−0.882629	+	0.470070i	$0.844229\pi$
$578$	−21.8754	+	37.8893i	−0.909897	+	1.57599i
$579$	−2.94164	−	27.3984i	−0.122250	−	1.13864i
$580$	−0.543215	+	0.940877i	−0.0225558	+	0.0390678i
$581$	−28.4681	−	15.4949i	−1.18106	−	0.642835i
$582$	−21.8310	+	15.9359i	−0.904926	+	0.660563i
$583$	−0.527821			−0.0218601
$584$	0.368764	+	0.638718i	0.0152596	+	0.0264303i
$585$	−17.2508	+	3.74748i	−0.713233	+	0.154939i
$586$	7.28966	−	12.6261i	0.301133	−	0.521578i
$587$	−14.5885	−	25.2681i	−0.602133	−	1.04292i	−0.992498	−	0.122264i	$-0.960984\pi$
$587$	−14.5885	−	25.2681i	−0.602133	−	1.04292i	0.390365	−	0.920660i	$-0.372349\pi$
$588$	11.3198	+	4.34296i	0.466822	+	0.179101i
$589$	1.98067	−	3.43062i	0.0816120	−	0.141356i
$590$	3.00434	+	5.20367i	0.123687	+	0.214232i
$591$	3.86274	+	35.9775i	0.158892	+	1.47992i
$592$	5.84787	−	10.1288i	0.240346	−	0.416291i
$593$	−15.0169	+	26.0101i	−0.616672	+	1.06811i	0.373417	+	0.927664i	$0.378186\pi$
$593$	−15.0169	+	26.0101i	−0.616672	+	1.06811i	−0.990089	+	0.140444i	$0.955147\pi$
$594$	4.89450	+	1.00609i	0.200824	+	0.0412805i
$595$	0.518610	+	20.6152i	0.0212609	+	0.845141i
$596$	8.49218	+	14.7089i	0.347853	+	0.602500i
$597$	18.2399	−	13.3145i	0.746509	−	0.544925i
$598$	−23.0073			−0.940839
$599$	37.8792			1.54770			0.773851	−	0.633368i	$-0.218328\pi$
$599$	37.8792			1.54770			0.773851	+	0.633368i	$0.218328\pi$
$600$	−1.58388	−	0.700949i	−0.0646616	−	0.0286161i
$601$	−6.77702	−	11.7381i	−0.276441	−	0.478809i	0.694057	−	0.719920i	$-0.255822\pi$
$601$	−6.77702	−	11.7381i	−0.276441	−	0.478809i	−0.970498	+	0.241111i	$0.922488\pi$
$602$	10.1700	+	5.53543i	0.414500	+	0.225607i
$603$	2.40966	−	0.523463i	0.0981291	−	0.0213171i
$604$	7.91384	−	13.7072i	0.322009	−	0.557737i
$605$	5.03762	−	8.72542i	0.204809	−	0.354739i
$606$	15.2297	+	6.73994i	0.618664	+	0.273791i
$607$	−11.8784	−	20.5739i	−0.482127	−	0.835069i	0.517662	−	0.855585i	$-0.326802\pi$
$607$	−11.8784	−	20.5739i	−0.482127	−	0.835069i	−0.999790	+	0.0205159i	$0.993469\pi$
$608$	0.774437	−	1.34137i	0.0314076	−	0.0543995i
$609$	−1.89969	+	4.60197i	−0.0769794	+	0.186481i
$610$	−7.34407	−	12.7203i	−0.297353	−	0.515030i
$611$	10.4596	−	18.1165i	0.423148	−	0.732914i
$612$	−15.7237	−	17.3067i	−0.635594	−	0.699582i
$613$	4.72021	+	8.17564i	0.190647	+	0.330211i	0.945465	−	0.325724i	$-0.105608\pi$
$613$	4.72021	+	8.17564i	0.190647	+	0.330211i	−0.754818	+	0.655935i	$0.772275\pi$
$614$	3.42914			0.138389
$615$	−0.425423	−	3.96238i	−0.0171547	−	0.159779i
$616$	−0.0639849	−	2.54346i	−0.00257803	−	0.102479i
$617$	8.40889	−	14.5646i	0.338529	−	0.586350i	−0.645627	−	0.763653i	$-0.723404\pi$
$617$	8.40889	−	14.5646i	0.338529	−	0.586350i	0.984156	+	0.177303i	$0.0567373\pi$
$618$	4.32140	−	3.15447i	0.173832	−	0.126891i
$619$	16.3229	−	28.2721i	0.656073	−	1.13635i	−0.325551	−	0.945525i	$-0.605550\pi$
$619$	16.3229	−	28.2721i	0.656073	−	1.13635i	0.981624	−	0.190827i	$-0.0611171\pi$
$620$	−1.27878	−	2.21491i	−0.0513570	−	0.0889529i
$621$	13.4927	−	15.1889i	0.541445	−	0.609508i
$622$	−34.6413			−1.38899
$623$	−0.380167	−	15.1120i	−0.0152311	−	0.605449i
$624$	−9.32015	−	4.12466i	−0.373105	−	0.165118i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	30.5887			1.22257
$627$	−2.08373	+	1.52104i	−0.0832160	+	0.0607447i
$628$	10.6557			0.425209
$629$	91.1598			3.63478
$630$	−7.61811	−	2.22809i	−0.303513	−	0.0887690i
$631$	0.702170			0.0279530			0.0139765	−	0.999902i	$-0.495551\pi$
$631$	0.702170			0.0279530			0.0139765	+	0.999902i	$0.495551\pi$
$632$	−6.79796			−0.270408
$633$	27.3575	+	12.1071i	1.08736	+	0.481215i
$634$	−10.0424			−0.398836
$635$	−6.55102	−	11.3467i	−0.259969	−	0.450280i
$636$	−0.767864	+	0.560513i	−0.0304478	+	0.0222258i
$637$	22.3630	+	34.5915i	0.886053	+	1.37057i
$638$	1.04476			0.0413623
$639$	11.6140	−	2.52297i	0.459444	−	0.0998073i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−12.7260	+	22.0421i	−0.502647	+	0.870610i	0.497348	+	0.867551i	$0.334307\pi$
$641$	−12.7260	+	22.0421i	−0.502647	+	0.870610i	−0.999995	+	0.00305935i	$0.999026\pi$
$642$	−5.48635	−	2.42800i	−0.216529	−	0.0958254i
$643$	3.50111	−	6.06410i	0.138070	−	0.239145i	−0.788696	−	0.614784i	$-0.789243\pi$
$643$	3.50111	−	6.06410i	0.138070	−	0.239145i	0.926766	+	0.375639i	$0.122577\pi$
$644$	−9.08593	−	4.94537i	−0.358036	−	0.194875i
$645$	−6.93170	−	3.06764i	−0.272935	−	0.120788i
$646$	12.0724			0.474981
$647$	−18.5443	−	32.1197i	−0.729052	−	1.26276i	−0.957284	−	0.289149i	$-0.906628\pi$
$647$	−18.5443	−	32.1197i	−0.729052	−	1.26276i	0.228232	−	0.973607i	$-0.426706\pi$
$648$	8.18884	−	3.73401i	0.321688	−	0.146686i
$649$	2.88910	−	5.00406i	0.113407	−	0.196427i
$650$	−2.94219	−	5.09603i	−0.115402	−	0.199883i
$651$	−7.14602	−	9.28963i	−0.280075	−	0.364089i
$652$	3.88853	−	6.73513i	0.152287	−	0.263768i
$653$	11.8804	+	20.5774i	0.464916	+	0.805258i	0.999198	−	0.0400487i	$-0.0127513\pi$
$653$	11.8804	+	20.5774i	0.464916	+	0.805258i	−0.534282	+	0.845306i	$0.679418\pi$
$654$	20.0663	−	14.6477i	0.784655	−	0.572770i
$655$	8.75462	−	15.1634i	0.342071	−	0.592485i
$656$	1.15042	−	1.99258i	0.0449162	−	0.0777971i
$657$	−1.48785	−	1.63763i	−0.0580464	−	0.0638902i
$658$	8.02472	−	4.90621i	0.312836	−	0.191264i
$659$	−6.82703	−	11.8248i	−0.265943	−	0.460627i	0.701867	−	0.712308i	$-0.252350\pi$
$659$	−6.82703	−	11.8248i	−0.265943	−	0.460627i	−0.967810	+	0.251681i	$0.919017\pi$
$660$	0.177807	+	1.65609i	0.00692113	+	0.0644633i
$661$	−0.987650			−0.0384151			−0.0192076	−	0.999816i	$-0.506114\pi$
$661$	−0.987650			−0.0384151			−0.0192076	+	0.999816i	$0.506114\pi$
$662$	−14.4680			−0.562316
$663$	−8.48034	−	78.9858i	−0.329349	−	3.06756i
$664$	6.12526	+	10.6093i	0.237706	+	0.411719i
$665$	3.49627	−	2.13757i	0.135579	−	0.0828915i
$666$	−10.6932	+	33.4181i	−0.414354	+	1.29492i
$667$	2.12391	−	3.67873i	0.0822383	−	0.142441i
$668$	−7.14183	+	12.3700i	−0.276326	+	0.478610i
$669$	38.2429	−	27.9159i	1.47856	−	1.07929i
$670$	0.410978	+	0.711834i	0.0158775	+	0.0275006i
$671$	−7.06236	+	12.2324i	−0.272639	+	0.472225i
$672$	−2.79408	−	3.63223i	−0.107784	−	0.140116i
$673$	9.55432	+	16.5486i	0.368292	+	0.637901i	0.989299	−	0.145905i	$-0.0466093\pi$
$673$	9.55432	+	16.5486i	0.368292	+	0.637901i	−0.621007	+	0.783805i	$0.713276\pi$
$674$	0.772692	−	1.33834i	0.0297630	−	0.0515510i
$675$	5.08974	+	1.04622i	0.195904	+	0.0402692i
$676$	−10.8130	−	18.7287i	−0.415885	−	0.720334i
$677$	14.9499			0.574571			0.287285	−	0.957845i	$-0.407247\pi$
$677$	14.9499			0.574571			0.287285	+	0.957845i	$0.407247\pi$
$678$	1.14779	+	0.507959i	0.0440808	+	0.0195080i
$679$	−36.2634	−	19.7377i	−1.39166	−	0.757464i
$680$	3.89714	−	6.75005i	0.149449	−	0.258852i
$681$	−11.8188	−	5.23044i	−0.452898	−	0.200431i
$682$	−1.22973	+	2.12995i	−0.0470886	+	0.0815599i
$683$	12.5655	+	21.7641i	0.480805	+	0.832779i	0.999757	−	0.0220243i	$-0.00701113\pi$
$683$	12.5655	+	21.7641i	0.480805	+	0.832779i	−0.518952	+	0.854803i	$0.673678\pi$
$684$	−1.41611	+	4.42558i	−0.0541463	+	0.169216i
$685$	−8.69584			−0.332251
$686$	1.39610	+	18.4676i	0.0533035	+	0.705095i
$687$	−13.2532	+	9.67433i	−0.505639	+	0.369099i
$688$	−2.18820	−	3.79008i	−0.0834245	−	0.144496i
$689$	−3.22979			−0.123045
$690$	6.19279	+	2.74064i	0.235756	+	0.104334i
$691$	−11.9676			−0.455271			−0.227635	−	0.973746i	$-0.573099\pi$
$691$	−11.9676			−0.455271			−0.227635	+	0.973746i	$0.573099\pi$
$692$	1.96561			0.0747211
$693$	1.80738	+	7.41571i	0.0686568	+	0.281700i
$694$	13.1517			0.499233
$695$	13.1375			0.498335
$696$	1.51989	−	1.10947i	0.0576114	−	0.0420543i
$697$	17.9333			0.679273
$698$	0.752263	+	1.30296i	0.0284736	+	0.0493177i
$699$	22.8437	+	10.1095i	0.864029	+	0.382378i
$700$	−0.0665372	−	2.64491i	−0.00251487	−	0.0999684i
$701$	0.886836			0.0334953			0.0167477	−	0.999860i	$-0.494669\pi$
$701$	0.886836			0.0334953			0.0167477	+	0.999860i	$0.494669\pi$
$702$	29.9500	+	6.15639i	1.13039	+	0.232358i
$703$	−9.05762	−	15.6882i	−0.341614	−	0.591694i
$704$	−0.480820	+	0.832805i	−0.0181216	+	0.0313875i
$705$	−4.97340	+	3.63040i	−0.187309	+	0.136729i
$706$	18.0095	−	31.1933i	0.677795	−	1.17398i
$707$	0.639785	+	25.4320i	0.0240616	+	0.956470i
$708$	−1.11100	−	10.3479i	−0.0417540	−	0.388897i
$709$	0.510807			0.0191838			0.00959189	−	0.999954i	$-0.496947\pi$
$709$	0.510807			0.0191838			0.00959189	+	0.999954i	$0.496947\pi$
$710$	1.98082	+	3.43088i	0.0743389	+	0.128759i
$711$	19.9291	−	4.32928i	0.747398	−	0.162361i
$712$	−2.85680	+	4.94812i	−0.107063	+	0.185439i
$713$	4.99988	+	8.66005i	0.187247	+	0.324322i
$714$	13.6288	−	33.0155i	0.510045	−	1.23557i
$715$	−2.82933	+	4.90055i	−0.105811	+	0.183270i
$716$	7.02161	+	12.1618i	0.262410	+	0.454507i
$717$	−15.2916	−	6.76732i	−0.571075	−	0.252730i
$718$	6.85269	−	11.8692i	0.255740	−	0.442955i
$719$	−15.6774	+	27.1540i	−0.584668	+	1.01268i	0.410248	+	0.911974i	$0.365442\pi$
$719$	−15.6774	+	27.1540i	−0.584668	+	1.01268i	−0.994917	+	0.100701i	$0.967891\pi$
$720$	2.01734	+	2.22044i	0.0751819	+	0.0827508i
$721$	7.17824	+	3.90703i	0.267332	+	0.145506i
$722$	8.30049	+	14.3769i	0.308912	+	0.535052i
$723$	6.58910	+	2.91602i	0.245051	+	0.108448i
$724$	−17.5794			−0.653334
$725$	1.08643			0.0403490
$726$	−14.0951	+	10.2889i	−0.523117	+	0.381856i
$727$	−10.9429	−	18.9536i	−0.405848	−	0.702949i	0.588572	−	0.808445i	$-0.299690\pi$
$727$	−10.9429	−	18.9536i	−0.405848	−	0.702949i	−0.994420	+	0.105496i	$0.966357\pi$
$728$	−0.391531	−	15.5637i	−0.0145111	−	0.576829i
$729$	−21.6286	+	16.1618i	−0.801059	+	0.598585i
$730$	0.368764	−	0.638718i	0.0136486	−	0.0236400i
$731$	17.0555	−	29.5410i	0.630820	−	1.09261i
$732$	2.71583	+	25.2952i	0.100380	+	0.934938i
$733$	0.723740	+	1.25355i	0.0267320	+	0.0463011i	0.879082	−	0.476671i	$-0.158157\pi$
$733$	0.723740	+	1.25355i	0.0267320	+	0.0463011i	−0.852350	+	0.522972i	$0.824823\pi$
$734$	−16.0160	+	27.7406i	−0.591162	+	1.02392i
$735$	−1.89881	−	11.9747i	−0.0700386	−	0.441695i
$736$	1.95495	+	3.38607i	0.0720603	+	0.124812i
$737$	0.395213	−	0.684529i	0.0145579	−	0.0252150i
$738$	−2.10361	+	6.57413i	−0.0774350	+	0.241997i
$739$	−9.06843	−	15.7070i	−0.333588	−	0.577791i	0.649625	−	0.760255i	$-0.274926\pi$
$739$	−9.06843	−	15.7070i	−0.333588	−	0.577791i	−0.983212	+	0.182464i	$0.941593\pi$
$740$	−11.6957			−0.429944
$741$	−12.7505	+	9.30744i	−0.468403	+	0.341917i
$742$	−1.27549	−	0.694236i	−0.0468248	−	0.0254862i
$743$	14.8404	−	25.7043i	0.544440	−	0.942998i	−0.454202	−	0.890899i	$-0.650076\pi$
$743$	14.8404	−	25.7043i	0.544440	−	0.942998i	0.998642	−	0.0520988i	$-0.0165911\pi$
$744$	0.472891	+	4.40450i	0.0173370	+	0.161477i
$745$	8.49218	−	14.7089i	0.311129	−	0.538892i
$746$	−3.86024	−	6.68613i	−0.141333	−	0.244797i
$747$	−24.7135	−	27.2015i	−0.904218	−	0.995250i
$748$	−7.49530			−0.274055
$749$	−0.230476	−	9.16165i	−0.00842143	−	0.334759i
$750$	0.184900	+	1.72215i	0.00675158	+	0.0628841i
$751$	−6.22241	−	10.7775i	−0.227059	−	0.393277i	0.729876	−	0.683579i	$-0.239578\pi$
$751$	−6.22241	−	10.7775i	−0.227059	−	0.393277i	−0.956935	+	0.290302i	$0.906244\pi$
$752$	−3.55502			−0.129638
$753$	4.13941	+	38.5545i	0.150849	+	1.40500i
$754$	6.39298			0.232819
$755$	−15.8277			−0.576028
$756$	10.5044	+	8.86892i	0.382041	+	0.322560i
$757$	18.2077			0.661769			0.330885	−	0.943671i	$-0.392653\pi$
$757$	18.2077			0.661769			0.330885	+	0.943671i	$0.392653\pi$
$758$	−2.47157			−0.0897715
$759$	−0.695206	−	6.47515i	−0.0252344	−	0.235033i
$760$	−1.54887			−0.0561836
$761$	−5.52796	−	9.57471i	−0.200388	−	0.347083i	0.748265	−	0.663400i	$-0.230887\pi$
$761$	−5.52796	−	9.57471i	−0.200388	−	0.347083i	−0.948654	+	0.316317i	$0.897554\pi$
$762$	2.42256	+	22.5637i	0.0877602	+	0.817398i
$763$	33.3320	+	18.1422i	1.20670	+	0.656792i
$764$	−19.3643			−0.700577
$765$	−7.12618	+	22.2705i	−0.257648	+	0.805191i
$766$	−12.3131	−	21.3268i	−0.444889	−	0.770570i
$767$	17.6787	−	30.6204i	0.638341	−	1.10564i
$768$	0.184900	+	1.72215i	0.00667199	+	0.0621429i
$769$	−5.83441	+	10.1055i	−0.210394	+	0.364413i	−0.951838	−	0.306602i	$-0.900808\pi$
$769$	−5.83441	+	10.1055i	−0.210394	+	0.364413i	0.741444	+	0.671015i	$0.234141\pi$
$770$	−2.17071	+	1.32714i	−0.0782268	+	0.0478269i
$771$	−21.6578	+	15.8094i	−0.779987	+	0.569363i
$772$	−15.9094			−0.572592
$773$	−16.6025	−	28.7563i	−0.597149	−	1.03429i	−0.993240	−	0.116081i	$-0.962967\pi$
$773$	−16.6025	−	28.7563i	−0.597149	−	1.03429i	0.396091	−	0.918211i	$-0.370367\pi$
$774$	8.82871	+	9.71754i	0.317341	+	0.349290i
$775$	−1.27878	+	2.21491i	−0.0459351	+	0.0795619i
$776$	7.80249	+	13.5143i	0.280093	+	0.485136i
$777$	−53.1296	+	7.05991i	−1.90601	+	0.253273i
$778$	4.14338	−	7.17655i	0.148548	−	0.257292i
$779$	−1.78185	−	3.08625i	−0.0638414	−	0.110577i
$780$	1.08802	+	10.1338i	0.0389574	+	0.362849i
$781$	1.90484	−	3.29928i	0.0681605	−	0.118057i
$782$	−15.2374	+	26.3920i	−0.544888	+	0.943774i
$783$	−3.74919	+	4.22049i	−0.133985	+	0.150828i
$784$	3.19076	−	6.23049i	0.113956	−	0.222518i
$785$	−5.32785	−	9.22811i	−0.190159	−	0.329365i
$786$	−24.4951	+	17.8805i	−0.873710	+	0.637777i
$787$	−16.7755			−0.597980			−0.298990	−	0.954256i	$-0.596650\pi$
$787$	−16.7755			−0.597980			−0.298990	+	0.954256i	$0.596650\pi$
$788$	20.8910			0.744211
$789$	−24.8818	−	11.0115i	−0.885817	−	0.392020i
$790$	3.39898	+	5.88720i	0.120930	+	0.209457i
$791$	0.0482178	+	1.91670i	0.00171443	+	0.0681500i
$792$	0.879212	−	2.74768i	0.0312414	−	0.0976347i
$793$	−43.2154	+	74.8512i	−1.53462	+	2.65804i
$794$	9.42143	−	16.3184i	0.334354	−	0.579118i
$795$	0.869351	+	0.384733i	0.0308327	+	0.0136451i
$796$	−6.51900	−	11.2912i	−0.231060	−	0.400208i
$797$	−4.46594	+	7.73524i	−0.158192	+	0.273996i	−0.934217	−	0.356706i	$-0.883900\pi$
$797$	−4.46594	+	7.73524i	−0.158192	+	0.273996i	0.776025	+	0.630702i	$0.217233\pi$
$798$	−7.03599	+	0.934949i	−0.249071	+	0.0330968i
$799$	−13.8544	−	23.9965i	−0.490134	−	0.848936i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	5.22385	−	16.3254i	0.184576	−	0.576829i
$802$	5.84903	+	10.1308i	0.206537	+	0.357732i
$803$	−0.709237			−0.0250284
$804$	−0.151979	−	1.41553i	−0.00535989	−	0.0499220i
$805$	0.260153	+	10.3413i	0.00916920	+	0.364484i
$806$	−7.52483	+	13.0334i	−0.265051	+	0.459081i
$807$	12.7598	−	9.31417i	0.449165	−	0.327874i
$808$	4.80772	−	8.32722i	0.169135	−	0.292951i
$809$	13.9856	+	24.2237i	0.491706	+	0.851660i	0.999954	−	0.00955059i	$-0.00304009\pi$
$809$	13.9856	+	24.2237i	0.491706	+	0.851660i	−0.508248	+	0.861211i	$0.669707\pi$
$810$	−7.32817	−	5.22474i	−0.257486	−	0.183579i
$811$	52.5752			1.84617			0.923083	−	0.384600i	$-0.125661\pi$
$811$	52.5752			1.84617			0.923083	+	0.384600i	$0.125661\pi$
$812$	2.52468	+	1.37415i	0.0885990	+	0.0482234i
$813$	42.4255	+	18.7755i	1.48793	+	0.658485i
$814$	5.62355	+	9.74027i	0.197105	+	0.341396i
$815$	−7.77706			−0.272419
$816$	−10.9040	+	7.95955i	−0.381718	+	0.278640i
$817$	−6.77851			−0.237150
$818$	−18.0739			−0.631938
$819$	11.0596	+	45.3776i	0.386453	+	1.58562i
$820$	−2.30083			−0.0803485
$821$	15.7961			0.551289			0.275644	−	0.961260i	$-0.411109\pi$
$821$	15.7961			0.551289			0.275644	+	0.961260i	$0.411109\pi$
$822$	13.7732	+	6.09534i	0.480394	+	0.212599i
$823$	−15.5152			−0.540825			−0.270413	−	0.962745i	$-0.587160\pi$
$823$	−15.5152			−0.540825			−0.270413	+	0.962745i	$0.587160\pi$
$824$	−1.54448	−	2.67512i	−0.0538047	−	0.0931924i
$825$	1.34532	−	0.982032i	0.0468379	−	0.0341900i
$826$	13.5634	−	8.29246i	0.471930	−	0.288532i
$827$	−37.0759			−1.28925			−0.644627	−	0.764497i	$-0.722987\pi$
$827$	−37.0759			−1.28925			−0.644627	+	0.764497i	$0.722987\pi$
$828$	−7.88759	−	8.68167i	−0.274113	−	0.301709i
$829$	24.4304	+	42.3146i	0.848501	+	1.46965i	0.882546	+	0.470227i	$0.155828\pi$
$829$	24.4304	+	42.3146i	0.848501	+	1.46965i	−0.0340444	+	0.999420i	$0.510839\pi$
$830$	6.12526	−	10.6093i	0.212611	−	0.368253i
$831$	−7.05213	−	3.12094i	−0.244636	−	0.108264i
$832$	−2.94219	+	5.09603i	−0.102002	+	0.176673i
$833$	54.4910	−	2.74336i	1.88800	−	0.0950517i
$834$	−20.8083	−	9.20875i	−0.720532	−	0.318873i
$835$	14.2837			0.494306
$836$	0.744731	+	1.28991i	0.0257571	+	0.0446125i
$837$	−4.19135	−	12.6112i	−0.144874	−	0.435906i
$838$	9.88791	−	17.1264i	0.341572	−	0.591620i
$839$	23.9417	+	41.4683i	0.826561	+	1.43165i	0.900721	+	0.434399i	$0.143039\pi$
$839$	23.9417	+	41.4683i	0.826561	+	1.43165i	−0.0741600	+	0.997246i	$0.523628\pi$
$840$	−1.74856	+	4.23586i	−0.0603312	+	0.146151i
$841$	13.9098	−	24.0925i	0.479649	−	0.830777i
$842$	−15.4734	−	26.8008i	−0.533250	−	0.923616i
$843$	−30.1143	+	21.9824i	−1.03719	+	0.757114i
$844$	8.63625	−	14.9584i	0.297272	−	0.514890i
$845$	−10.8130	+	18.7287i	−0.371979	+	0.644286i
$846$	10.4220	−	2.26402i	0.358315	−	0.0778385i
$847$	−23.4132	−	12.7435i	−0.804486	−	0.437872i
$848$	0.274437	+	0.475340i	0.00942422	+	0.0163232i
$849$	−1.01625	−	9.46535i	−0.0348776	−	0.324850i
$850$	−7.79428			−0.267342
$851$	45.7291			1.56757
$852$	−0.732506	−	6.82255i	−0.0250952	−	0.233737i
$853$	6.59345	+	11.4202i	0.225756	+	0.391020i	0.956546	−	0.291582i	$-0.0941816\pi$
$853$	6.59345	+	11.4202i	0.225756	+	0.391020i	−0.730790	+	0.682602i	$0.760848\pi$
$854$	−33.1555	+	20.2708i	−1.13456	+	0.693653i
$855$	4.54072	−	0.986402i	0.155289	−	0.0337342i
$856$	−1.73194	+	2.99980i	−0.0591964	+	0.102531i
$857$	−21.2638	+	36.8300i	−0.726359	+	1.25809i	0.232054	+	0.972703i	$0.425456\pi$
$857$	−21.2638	+	36.8300i	−0.726359	+	1.25809i	−0.958412	+	0.285387i	$0.907878\pi$
$858$	7.91636	−	5.77866i	0.270260	−	0.197280i
$859$	18.4709	+	31.9925i	0.630217	+	1.09157i	0.987507	+	0.157575i	$0.0503675\pi$
$859$	18.4709	+	31.9925i	0.630217	+	1.09157i	−0.357290	+	0.933994i	$0.616299\pi$
$860$	−2.18820	+	3.79008i	−0.0746172	+	0.129241i
$861$	−10.4519	+	1.38885i	−0.356198	+	0.0473320i
$862$	1.01707	+	1.76162i	0.0346417	+	0.0600011i
$863$	−22.8978	+	39.6602i	−0.779451	+	1.35005i	0.152807	+	0.988256i	$0.451169\pi$
$863$	−22.8978	+	39.6602i	−0.779451	+	1.35005i	−0.932259	+	0.361793i	$0.882165\pi$
$864$	−1.63881	−	4.93095i	−0.0557535	−	0.167754i
$865$	−0.982803	−	1.70226i	−0.0334163	−	0.0578787i
$866$	−17.9368			−0.609518
$867$	−69.2960	−	30.6671i	−2.35341	−	1.04151i
$868$	−5.77316	+	3.52963i	−0.195954	+	0.119804i
$869$	3.26860	−	5.66138i	0.110880	−	0.192049i
$870$	−1.72077	−	0.761532i	−0.0583397	−	0.0258184i
$871$	2.41835	−	4.18871i	0.0819428	−	0.141929i
$872$	−7.17178	−	12.4219i	−0.242867	−	0.420658i
$873$	−31.4806	−	34.6499i	−1.06546	−	1.17272i
$874$	6.05593			0.204845
$875$	−2.25729	+	1.38008i	−0.0763105	+	0.0466552i
$876$	−1.03179	+	0.753167i	−0.0348608	+	0.0254471i
$877$	0.0372312	+	0.0644862i	0.00125721	+	0.00217755i	0.866653	−	0.498911i	$-0.166266\pi$
$877$	0.0372312	+	0.0644862i	0.00125721	+	0.00217755i	−0.865396	+	0.501088i	$0.832933\pi$
$878$	−34.2741			−1.15669
$879$	23.0919	+	10.2194i	0.778869	+	0.344690i
$880$	0.961641			0.0324169
$881$	−44.0695			−1.48474			−0.742369	−	0.669991i	$-0.766298\pi$
$881$	−44.0695			−1.48474			−0.742369	+	0.669991i	$0.766298\pi$
$882$	−5.38621	+	20.2975i	−0.181363	+	0.683453i
$883$	−0.388820			−0.0130848			−0.00654242	−	0.999979i	$-0.502083\pi$
$883$	−0.388820			−0.0130848			−0.00654242	+	0.999979i	$0.502083\pi$
$884$	−45.8646			−1.54259
$885$	−8.40602	+	6.13609i	−0.282565	+	0.206262i
$886$	13.9945			0.470156
$887$	18.4983	+	32.0400i	0.621111	+	1.07580i	0.989279	+	0.146037i	$0.0466519\pi$
$887$	18.4983	+	32.0400i	0.621111	+	1.07580i	−0.368168	+	0.929759i	$0.620015\pi$
$888$	18.5246	+	8.19811i	0.621646	+	0.275111i
$889$	−29.5752	+	18.0819i	−0.991919	+	0.606446i
$890$	5.71360			0.191520
$891$	−0.827655	+	8.61510i	−0.0277275	+	0.288617i
$892$	−13.6681	−	23.6739i	−0.457643	−	0.792662i
$893$	−2.75314	+	4.76858i	−0.0921303	+	0.159574i
$894$	−23.7608	+	17.3445i	−0.794679	+	0.580087i
$895$	7.02161	−	12.1618i	0.234706	−	0.406523i
$896$	−2.25729	+	1.38008i	−0.0754109	+	0.0461052i
$897$	−4.25404	−	39.6221i	−0.142038	−	1.32294i
$898$	24.3772			0.813477
$899$	−1.38930	−	2.40634i	−0.0463359	−	0.0802561i
$900$	0.914283	−	2.85729i	0.0304761	−	0.0952429i
$901$	−2.13904	+	3.70493i	−0.0712618	+	0.123429i
$902$	1.10629	+	1.91614i	0.0368353	+	0.0638006i
$903$	−7.65243	+	18.5379i	−0.254657	+	0.616902i
$904$	0.362337	−	0.627585i	0.0120511	−	0.0208732i
$905$	8.78971	+	15.2242i	0.292180	+	0.506070i
$906$	25.0691	+	11.0944i	0.832865	+	0.368586i
$907$	10.3447	−	17.9176i	0.343490	−	0.594943i	−0.641588	−	0.767050i	$-0.721724\pi$
$907$	10.3447	−	17.9176i	0.343490	−	0.594943i	0.985078	+	0.172107i	$0.0550574\pi$
$908$	−3.73097	+	6.46223i	−0.123817	+	0.214457i
$909$	−8.79124	+	27.4741i	−0.291587	+	0.911258i
$910$	−13.2828	+	8.12093i	−0.440320	+	0.269206i
$911$	19.5423	+	33.8483i	0.647466	+	1.12144i	0.983726	+	0.179675i	$0.0575046\pi$
$911$	19.5423	+	33.8483i	0.647466	+	1.12144i	−0.336260	+	0.941769i	$0.609162\pi$
$912$	2.45323	+	1.08568i	0.0812345	+	0.0359505i
$913$	−11.7806			−0.389881
$914$	−34.3746			−1.13701
$915$	20.5484	−	14.9996i	0.679309	−	0.495871i
$916$	4.73672	+	8.20425i	0.156506	+	0.271076i
$917$	−40.6885	−	22.1463i	−1.34365	−	0.731335i
$918$	26.8975	−	30.2787i	0.887749	−	0.999345i
$919$	15.7521	−	27.2834i	0.519614	−	0.899997i	−0.480126	−	0.877199i	$-0.659409\pi$
$919$	15.7521	−	27.2834i	0.519614	−	0.899997i	0.999740	−	0.0227981i	$-0.00725750\pi$
$920$	1.95495	−	3.38607i	0.0644527	−	0.111635i
$921$	0.634047	+	5.90551i	0.0208926	+	0.194593i
$922$	−14.6870	−	25.4386i	−0.483690	−	0.837776i
$923$	11.6559	−	20.1886i	0.383659	−	0.664517i
$924$	4.36839	−	0.580476i	0.143710	−	0.0190963i
$925$	5.84787	+	10.1288i	0.192277	+	0.333033i
$926$	10.5391	−	18.2542i	0.346335	−	0.599870i
$927$	6.23150	+	6.85886i	0.204669	+	0.225274i
$928$	−0.543215	−	0.940877i	−0.0178319	−	0.0308858i
$929$	25.0906			0.823197			0.411599	−	0.911365i	$-0.364971\pi$
$929$	25.0906			0.823197			0.411599	+	0.911365i	$0.364971\pi$
$930$	3.57797	−	2.61179i	0.117326	−	0.0856439i
$931$	−5.88633	−	9.10510i	−0.192917	−	0.298408i
$932$	7.21133	−	12.4904i	0.236215	−	0.409136i
$933$	−6.40516	−	59.6576i	−0.209696	−	1.95310i
$934$	−20.8663	+	36.1415i	−0.682767	+	1.18259i
$935$	3.74765	+	6.49112i	0.122561	+	0.212282i
$936$	5.38000	−	16.8134i	0.175851	−	0.549563i
$937$	38.4082			1.25474			0.627370	−	0.778721i	$-0.284131\pi$
$937$	38.4082			1.25474			0.627370	+	0.778721i	$0.284131\pi$
$938$	1.85540	−	1.13436i	0.0605808	−	0.0370383i
$939$	5.65583	+	52.6784i	0.184571	+	1.71909i
$940$	1.77751	+	3.07874i	0.0579760	+	0.100417i
$941$	−1.64141			−0.0535085			−0.0267543	−	0.999642i	$-0.508517\pi$
$941$	−1.64141			−0.0535085			−0.0267543	+	0.999642i	$0.508517\pi$
$942$	1.97023	+	18.3508i	0.0641937	+	0.597900i
$943$	8.99600			0.292950
$944$	−6.00868			−0.195566
$945$	2.42852	−	13.5315i	0.0789997	−	0.440181i
$946$	4.20853			0.136831
$947$	−43.7932			−1.42309			−0.711544	−	0.702641i	$-0.752004\pi$
$947$	−43.7932			−1.42309			−0.711544	+	0.702641i	$0.752004\pi$
$948$	−1.25694	−	11.7071i	−0.0408235	−	0.380230i
$949$	−4.33990			−0.140879
$950$	0.774437	+	1.34137i	0.0251261	+	0.0435196i
$951$	−1.85684	−	17.2946i	−0.0602122	−	0.560816i
$952$	−18.1126	−	9.85847i	−0.587033	−	0.319515i
$953$	−18.7035			−0.605866			−0.302933	−	0.953012i	$-0.597966\pi$
$953$	−18.7035			−0.605866			−0.302933	+	0.953012i	$0.597966\pi$
$954$	−1.10727	−	1.21874i	−0.0358491	−	0.0394582i
$955$	9.68217	+	16.7700i	0.313308	+	0.542665i
$956$	−4.82726	+	8.36106i	−0.156125	+	0.270416i
$957$	0.193175	+	1.79923i	0.00624446	+	0.0581609i
$958$	9.11638	−	15.7900i	0.294537	−	0.510153i
$959$	0.578597	+	22.9998i	0.0186839	+	0.742701i
$960$	1.39898	−	1.02120i	0.0451518	−	0.0329592i
$961$	−24.4589			−0.788997
$962$	34.4111	+	59.6018i	1.10946	+	1.92164i
$963$	3.16696	−	9.89727i	0.102054	−	0.318935i
$964$	2.08005	−	3.60276i	0.0669940	−	0.116037i
$965$	7.95470	+	13.7779i	0.256071	+	0.443528i
$966$	6.83669	−	16.5618i	0.219967	−	0.532866i
$967$	−18.5396	+	32.1115i	−0.596193	+	1.03264i	0.397185	+	0.917739i	$0.369987\pi$
$967$	−18.5396	+	32.1115i	−0.596193	+	1.03264i	−0.993377	+	0.114897i	$0.963346\pi$
$968$	5.03762	+	8.72542i	0.161915	+	0.280446i
$969$	2.23217	+	20.7905i	0.0717078	+	0.667886i
$970$	7.80249	−	13.5143i	0.250523	−	0.433918i
$971$	8.50573	−	14.7324i	0.272962	−	0.472784i	−0.696657	−	0.717404i	$-0.745330\pi$
$971$	8.50573	−	14.7324i	0.272962	−	0.472784i	0.969619	+	0.244620i	$0.0786633\pi$
$972$	7.94466	+	13.4120i	0.254825	+	0.430191i
$973$	−0.874136	−	34.7477i	−0.0280235	−	1.11396i
$974$	12.5910	+	21.8083i	0.403442	+	0.698783i
$975$	8.23213	−	6.00916i	0.263639	−	0.192447i
$976$	14.6881			0.470156
$977$	7.72418			0.247118			0.123559	−	0.992337i	$-0.460569\pi$
$977$	7.72418			0.247118			0.123559	+	0.992337i	$0.460569\pi$
$978$	12.3179	+	5.45132i	0.393884	+	0.174314i
$979$	−2.74721	−	4.75832i	−0.0878014	−	0.152076i
$980$	−6.99115	+	0.351971i	−0.223324	+	0.0112433i
$981$	28.9358	+	31.8489i	0.923850	+	1.01686i
$982$	18.6196	−	32.2501i	0.594175	−	1.02914i
$983$	−30.7645	+	53.2856i	−0.981234	+	1.69955i	−0.323631	+	0.946183i	$0.604904\pi$
$983$	−30.7645	+	53.2856i	−0.981234	+	1.69955i	−0.657603	+	0.753364i	$0.728430\pi$
$984$	3.64424	+	1.61277i	0.116174	+	0.0514131i
$985$	−10.4455	−	18.0921i	−0.332821	−	0.576463i
$986$	4.23397	−	7.33346i	0.134837	−	0.233545i
$987$	9.93301	+	12.9126i	0.316171	+	0.411014i
$988$	4.55709	+	7.89311i	0.144980	+	0.251113i
$989$	8.55565	−	14.8188i	0.272054	−	0.471211i
$990$	−2.81917	+	0.612422i	−0.0895991	+	0.0194640i
$991$	−7.41984	−	12.8515i	−0.235699	−	0.408243i	0.723777	−	0.690034i	$-0.242405\pi$
$991$	−7.41984	−	12.8515i	−0.235699	−	0.408243i	−0.959476	+	0.281792i	$0.909071\pi$
$992$	2.55756			0.0812025
$993$	−2.67513	−	24.9162i	−0.0848927	−	0.790690i
$994$	8.94259	−	5.46738i	0.283642	−	0.173415i
$995$	−6.51900	+	11.2912i	−0.206666	+	0.357956i
$996$	−17.1382	+	12.5103i	−0.543045	+	0.396403i
$997$	−27.8834	+	48.2954i	−0.883075	+	1.52953i	−0.0351706	+	0.999381i	$0.511197\pi$
$997$	−27.8834	+	48.2954i	−0.883075	+	1.52953i	−0.847904	+	0.530149i	$0.822136\pi$
$998$	−3.69263	−	6.39582i	−0.116888	−	0.202456i
$999$	−59.5282	−	12.2364i	−1.88339	−	0.387142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.121.3	✓	12
3.2	odd	2		1890.2.i.g.1171.2		12
7.4	even	3		630.2.l.g.571.6	yes	12
9.2	odd	6		1890.2.l.g.1801.5		12
9.7	even	3		630.2.l.g.331.6	yes	12
21.11	odd	6		1890.2.l.g.361.5		12
63.11	odd	6		1890.2.i.g.991.2		12
63.25	even	3	inner	630.2.i.g.151.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.3	✓	12	1.1	even	1	trivial
630.2.i.g.151.3	yes	12	63.25	even	3	inner
630.2.l.g.331.6	yes	12	9.7	even	3
630.2.l.g.571.6	yes	12	7.4	even	3
1890.2.i.g.991.2		12	63.11	odd	6
1890.2.i.g.1171.2		12	3.2	odd	2
1890.2.l.g.361.5		12	21.11	odd	6
1890.2.l.g.1801.5		12	9.2	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.184900 + 1.72215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.184900 + 1.72215i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(-2.93162 + 0.636851i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.184900 + 1.72215i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.184900 + 1.72215i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(-2.93162 + 0.636851i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.480820 + 0.832805i) q^{11} +(0.184900 + 1.72215i) q^{12} +(-2.94219 + 5.09603i) q^{13} +(-2.25729 + 1.38008i) q^{14} +(1.39898 - 1.02120i) q^{15} +1.00000 q^{16} +(3.89714 + 6.75005i) q^{17} +(-2.93162 + 0.636851i) q^{18} +(0.774437 - 1.34137i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.79408 - 3.63223i) q^{21} +(-0.480820 + 0.832805i) q^{22} +(1.95495 + 3.38607i) q^{23} +(0.184900 + 1.72215i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.94219 + 5.09603i) q^{26} +(-1.63881 - 4.93095i) q^{27} +(-2.25729 + 1.38008i) q^{28} +(-0.543215 - 0.940877i) q^{29} +(1.39898 - 1.02120i) q^{30} +2.55756 q^{31} +1.00000 q^{32} +(-1.52312 - 0.674061i) q^{33} +(3.89714 + 6.75005i) q^{34} +(2.32383 + 1.26483i) q^{35} +(-2.93162 + 0.636851i) q^{36} +(5.84787 - 10.1288i) q^{37} +(0.774437 - 1.34137i) q^{38} +(-9.32015 - 4.12466i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.15042 - 1.99258i) q^{41} +(-2.79408 - 3.63223i) q^{42} +(-2.18820 - 3.79008i) q^{43} +(-0.480820 + 0.832805i) q^{44} +(2.01734 + 2.22044i) q^{45} +(1.95495 + 3.38607i) q^{46} -3.55502 q^{47} +(0.184900 + 1.72215i) q^{48} +(3.19076 - 6.23049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-10.9040 + 7.95955i) q^{51} +(-2.94219 + 5.09603i) q^{52} +(0.274437 + 0.475340i) q^{53} +(-1.63881 - 4.93095i) q^{54} +0.961641 q^{55} +(-2.25729 + 1.38008i) q^{56} +(2.45323 + 1.08568i) q^{57} +(-0.543215 - 0.940877i) q^{58} -6.00868 q^{59} +(1.39898 - 1.02120i) q^{60} +14.6881 q^{61} +2.55756 q^{62} +(5.73863 - 5.48344i) q^{63} +1.00000 q^{64} +5.88439 q^{65} +(-1.52312 - 0.674061i) q^{66} -0.821956 q^{67} +(3.89714 + 6.75005i) q^{68} +(-5.46986 + 3.99280i) q^{69} +(2.32383 + 1.26483i) q^{70} -3.96164 q^{71} +(-2.93162 + 0.636851i) q^{72} +(0.368764 + 0.638718i) q^{73} +(5.84787 - 10.1288i) q^{74} +(-1.58388 - 0.700949i) q^{75} +(0.774437 - 1.34137i) q^{76} +(-0.0639849 - 2.54346i) q^{77} +(-9.32015 - 4.12466i) q^{78} -6.79796 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.18884 - 3.73401i) q^{81} +(1.15042 - 1.99258i) q^{82} +(6.12526 + 10.6093i) q^{83} +(-2.79408 - 3.63223i) q^{84} +(3.89714 - 6.75005i) q^{85} +(-2.18820 - 3.79008i) q^{86} +(1.51989 - 1.10947i) q^{87} +(-0.480820 + 0.832805i) q^{88} +(-2.85680 + 4.94812i) q^{89} +(2.01734 + 2.22044i) q^{90} +(-0.391531 - 15.5637i) q^{91} +(1.95495 + 3.38607i) q^{92} +(0.472891 + 4.40450i) q^{93} -3.55502 q^{94} -1.54887 q^{95} +(0.184900 + 1.72215i) q^{96} +(7.80249 + 13.5143i) q^{97} +(3.19076 - 6.23049i) q^{98} +(0.879212 - 2.74768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more