LMFDB - Embedded newform 570.2.i.f.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.f.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.72474 - 2.98735i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.22474 + 5.58542i) q^{17} +1.00000 q^{18} +(3.17423 - 2.98735i) q^{19} +1.00000 q^{20} +(1.72474 + 2.98735i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-1.94949 + 3.37662i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.89898 q^{26} -1.00000 q^{27} +(-1.72474 + 2.98735i) q^{28} +(2.67423 - 4.63191i) q^{29} -1.00000 q^{30} +8.89898 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(3.22474 - 5.58542i) q^{34} +(-1.72474 - 2.98735i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.101021 q^{37} +(-4.17423 - 1.25529i) q^{38} +4.89898 q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.17423 + 8.96204i) q^{41} +(1.72474 - 2.98735i) q^{42} +(-3.89898 - 6.75323i) q^{43} +(1.50000 - 2.59808i) q^{44} +1.00000 q^{45} +3.89898 q^{46} +(5.44949 - 9.43879i) q^{47} +(0.500000 - 0.866025i) q^{48} +4.89898 q^{49} +1.00000 q^{50} +(-3.22474 + 5.58542i) q^{51} +(2.44949 + 4.24264i) q^{52} +(1.27526 - 2.20881i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{55} +3.44949 q^{56} +(4.17423 + 1.25529i) q^{57} -5.34847 q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.77526 + 6.53893i) q^{61} +(-4.44949 - 7.70674i) q^{62} +(-1.72474 + 2.98735i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-1.50000 + 2.59808i) q^{66} +(-3.67423 + 6.36396i) q^{67} -6.44949 q^{68} -3.89898 q^{69} +(-1.72474 + 2.98735i) q^{70} +(-5.67423 - 9.82806i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.77526 - 4.80688i) q^{73} +(0.0505103 + 0.0874863i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} -10.3485 q^{77} +(-2.44949 - 4.24264i) q^{78} +(1.44949 + 2.51059i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.17423 - 8.96204i) q^{82} -7.79796 q^{83} -3.44949 q^{84} +(3.22474 - 5.58542i) q^{85} +(-3.89898 + 6.75323i) q^{86} +5.34847 q^{87} -3.00000 q^{88} +(0.275255 - 0.476756i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(8.44949 - 14.6349i) q^{91} +(-1.94949 - 3.37662i) q^{92} +(4.44949 + 7.70674i) q^{93} -10.8990 q^{94} +(-4.17423 - 1.25529i) q^{95} -1.00000 q^{96} +(6.77526 + 11.7351i) q^{97} +(-2.44949 - 4.24264i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} - 12 q^{11} - 4 q^{12} - 2 q^{14} + 2 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 2 q^{21} + 6 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27} - 2 q^{28} - 4 q^{29} - 4 q^{30} + 16 q^{31} - 2 q^{32} - 6 q^{33} + 8 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 4 q^{43} + 6 q^{44} + 4 q^{45} - 4 q^{46} + 12 q^{47} + 2 q^{48} + 4 q^{50} - 8 q^{51} + 10 q^{53} + 2 q^{54} + 6 q^{55} + 4 q^{56} + 2 q^{57} + 8 q^{58} + 12 q^{59} + 2 q^{60} - 20 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} - 6 q^{66} - 16 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - 2 q^{72} - 16 q^{73} + 10 q^{74} - 4 q^{75} + 4 q^{76} - 12 q^{77} - 4 q^{79} - 2 q^{80} - 2 q^{81} + 6 q^{82} + 8 q^{83} - 4 q^{84} + 8 q^{85} + 4 q^{86} - 8 q^{87} - 12 q^{88} + 6 q^{89} - 2 q^{90} + 24 q^{91} + 2 q^{92} + 8 q^{93} - 24 q^{94} - 2 q^{95} - 4 q^{96} + 32 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 - 12 * q^11 - 4 * q^12 - 2 * q^14 + 2 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 2 * q^21 + 6 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 - 2 * q^28 - 4 * q^29 - 4 * q^30 + 16 * q^31 - 2 * q^32 - 6 * q^33 + 8 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^46 + 12 * q^47 + 2 * q^48 + 4 * q^50 - 8 * q^51 + 10 * q^53 + 2 * q^54 + 6 * q^55 + 4 * q^56 + 2 * q^57 + 8 * q^58 + 12 * q^59 + 2 * q^60 - 20 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 - 6 * q^66 - 16 * q^68 + 4 * q^69 - 2 * q^70 - 8 * q^71 - 2 * q^72 - 16 * q^73 + 10 * q^74 - 4 * q^75 + 4 * q^76 - 12 * q^77 - 4 * q^79 - 2 * q^80 - 2 * q^81 + 6 * q^82 + 8 * q^83 - 4 * q^84 + 8 * q^85 + 4 * q^86 - 8 * q^87 - 12 * q^88 + 6 * q^89 - 2 * q^90 + 24 * q^91 + 2 * q^92 + 8 * q^93 - 24 * q^94 - 2 * q^95 - 4 * q^96 + 32 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	3.44949			1.30378			0.651892	−	0.758312i	$-0.273975\pi$
$7$	3.44949			1.30378			0.651892	+	0.758312i	$0.273975\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000			−0.288675
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710785\pi$
$14$	−1.72474	−	2.98735i	−0.460957	−	0.798402i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.22474	+	5.58542i	0.782116	+	1.35466i	0.930707	+	0.365765i	$0.119193\pi$
$17$	3.22474	+	5.58542i	0.782116	+	1.35466i	−0.148592	+	0.988899i	$0.547474\pi$
$18$	1.00000			0.235702
$19$	3.17423	−	2.98735i	0.728219	−	0.685344i
$19$	3.17423	−	2.98735i	0.728219	−	0.685344i
$20$	1.00000			0.223607
$21$	1.72474	+	2.98735i	0.376370	+	0.651892i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−1.94949	+	3.37662i	−0.406497	+	0.704073i	−0.994494	−	0.104790i	$-0.966583\pi$
$23$	−1.94949	+	3.37662i	−0.406497	+	0.704073i	0.587998	+	0.808863i	$0.299916\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.89898			−0.960769
$27$	−1.00000			−0.192450
$28$	−1.72474	+	2.98735i	−0.325946	+	0.564555i
$29$	2.67423	−	4.63191i	0.496593	−	0.860124i	−0.503399	−	0.864054i	$-0.667918\pi$
$29$	2.67423	−	4.63191i	0.496593	−	0.860124i	0.999992	+	0.00392972i	$0.00125087\pi$
$30$	−1.00000			−0.182574
$31$	8.89898			1.59830			0.799152	−	0.601129i	$-0.205282\pi$
$31$	8.89898			1.59830			0.799152	+	0.601129i	$0.205282\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	3.22474	−	5.58542i	0.553039	−	0.957892i
$35$	−1.72474	−	2.98735i	−0.291535	−	0.504954i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.101021			−0.0166077			−0.00830384	−	0.999966i	$-0.502643\pi$
$37$	−0.101021			−0.0166077			−0.00830384	+	0.999966i	$0.502643\pi$
$38$	−4.17423	−	1.25529i	−0.677150	−	0.203636i
$39$	4.89898			0.784465
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.17423	+	8.96204i	0.808080	+	1.39964i	0.914192	+	0.405281i	$0.132826\pi$
$41$	5.17423	+	8.96204i	0.808080	+	1.39964i	−0.106113	+	0.994354i	$0.533840\pi$
$42$	1.72474	−	2.98735i	0.266134	−	0.460957i
$43$	−3.89898	−	6.75323i	−0.594589	−	1.02986i	−0.993605	−	0.112914i	$-0.963982\pi$
$43$	−3.89898	−	6.75323i	−0.594589	−	1.02986i	0.399016	−	0.916944i	$-0.369352\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	1.00000			0.149071
$46$	3.89898			0.574873
$47$	5.44949	−	9.43879i	0.794890	−	1.37679i	−0.128019	−	0.991772i	$-0.540862\pi$
$47$	5.44949	−	9.43879i	0.794890	−	1.37679i	0.922909	−	0.385018i	$-0.125805\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	4.89898			0.699854
$50$	1.00000			0.141421
$51$	−3.22474	+	5.58542i	−0.451555	+	0.782116i
$52$	2.44949	+	4.24264i	0.339683	+	0.588348i
$53$	1.27526	−	2.20881i	0.175170	−	0.303403i	−0.765050	−	0.643971i	$-0.777286\pi$
$53$	1.27526	−	2.20881i	0.175170	−	0.303403i	0.940220	+	0.340568i	$0.110619\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	3.44949			0.460957
$57$	4.17423	+	1.25529i	0.552891	+	0.166268i
$58$	−5.34847			−0.702288
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−3.77526	+	6.53893i	−0.483372	+	0.837225i	−0.999818	−	0.0190952i	$-0.993921\pi$
$61$	−3.77526	+	6.53893i	−0.483372	+	0.837225i	0.516446	+	0.856320i	$0.327255\pi$
$62$	−4.44949	−	7.70674i	−0.565086	−	0.978757i
$63$	−1.72474	+	2.98735i	−0.217297	+	0.376370i
$64$	1.00000			0.125000
$65$	−4.89898			−0.607644
$66$	−1.50000	+	2.59808i	−0.184637	+	0.319801i
$67$	−3.67423	+	6.36396i	−0.448879	+	0.777482i	−0.998313	−	0.0580554i	$-0.981510\pi$
$67$	−3.67423	+	6.36396i	−0.448879	+	0.777482i	0.549434	+	0.835537i	$0.314843\pi$
$68$	−6.44949			−0.782116
$69$	−3.89898			−0.469382
$70$	−1.72474	+	2.98735i	−0.206146	+	0.357056i
$71$	−5.67423	−	9.82806i	−0.673408	−	1.16638i	−0.976932	−	0.213553i	$-0.931497\pi$
$71$	−5.67423	−	9.82806i	−0.673408	−	1.16638i	0.303524	−	0.952824i	$-0.401837\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−2.77526	−	4.80688i	−0.324819	−	0.562603i	0.656657	−	0.754190i	$-0.271970\pi$
$73$	−2.77526	−	4.80688i	−0.324819	−	0.562603i	−0.981476	+	0.191587i	$0.938637\pi$
$74$	0.0505103	+	0.0874863i	0.00587170	+	0.0101701i
$75$	−1.00000			−0.115470
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	−10.3485			−1.17932
$78$	−2.44949	−	4.24264i	−0.277350	−	0.480384i
$79$	1.44949	+	2.51059i	0.163080	+	0.282463i	0.935972	−	0.352075i	$-0.114524\pi$
$79$	1.44949	+	2.51059i	0.163080	+	0.282463i	−0.772892	+	0.634538i	$0.781190\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.17423	−	8.96204i	0.571399	−	0.989691i
$83$	−7.79796			−0.855937			−0.427969	−	0.903794i	$-0.640771\pi$
$83$	−7.79796			−0.855937			−0.427969	+	0.903794i	$0.640771\pi$
$84$	−3.44949			−0.376370
$85$	3.22474	−	5.58542i	0.349773	−	0.605824i
$86$	−3.89898	+	6.75323i	−0.420438	+	0.728220i
$87$	5.34847			0.573416
$88$	−3.00000			−0.319801
$89$	0.275255	−	0.476756i	0.0291770	−	0.0505360i	−0.851068	−	0.525055i	$-0.824045\pi$
$89$	0.275255	−	0.476756i	0.0291770	−	0.0505360i	0.880245	+	0.474519i	$0.157378\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	8.44949	−	14.6349i	0.885747	−	1.53416i
$92$	−1.94949	−	3.37662i	−0.203248	−	0.352036i
$93$	4.44949	+	7.70674i	0.461391	+	0.799152i
$94$	−10.8990			−1.12414
$95$	−4.17423	−	1.25529i	−0.428267	−	0.128791i
$96$	−1.00000			−0.102062
$97$	6.77526	+	11.7351i	0.687923	+	1.19152i	0.972509	+	0.232867i	$0.0748106\pi$
$97$	6.77526	+	11.7351i	0.687923	+	1.19152i	−0.284586	+	0.958651i	$0.591856\pi$
$98$	−2.44949	−	4.24264i	−0.247436	−	0.428571i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.44949	−	9.43879i	0.542244	−	0.939195i	−0.456530	−	0.889708i	$-0.650908\pi$
$101$	5.44949	−	9.43879i	0.542244	−	0.939195i	0.998775	−	0.0494871i	$-0.0157587\pi$
$102$	6.44949			0.638595
$103$	−13.2474			−1.30531			−0.652655	−	0.757655i	$-0.726345\pi$
$103$	−13.2474			−1.30531			−0.652655	+	0.757655i	$0.726345\pi$
$104$	2.44949	−	4.24264i	0.240192	−	0.416025i
$105$	1.72474	−	2.98735i	0.168318	−	0.291535i
$106$	−2.55051			−0.247727
$107$	−17.3485			−1.67714			−0.838570	−	0.544794i	$-0.816608\pi$
$107$	−17.3485			−1.67714			−0.838570	+	0.544794i	$0.816608\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	6.67423	+	11.5601i	0.639276	+	1.10726i	0.985592	+	0.169140i	$0.0540991\pi$
$109$	6.67423	+	11.5601i	0.639276	+	1.10726i	−0.346316	+	0.938118i	$0.612568\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	−0.0505103	−	0.0874863i	−0.00479422	−	0.00830384i
$112$	−1.72474	−	2.98735i	−0.162973	−	0.282278i
$113$	−14.4495			−1.35929			−0.679647	−	0.733539i	$-0.737867\pi$
$113$	−14.4495			−1.35929			−0.679647	+	0.733539i	$0.737867\pi$
$114$	−1.00000	−	4.24264i	−0.0936586	−	0.397360i
$115$	3.89898			0.363582
$116$	2.67423	+	4.63191i	0.248296	+	0.430062i
$117$	2.44949	+	4.24264i	0.226455	+	0.392232i
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	11.1237	+	19.2669i	1.01971	+	1.76619i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−2.00000			−0.181818
$122$	7.55051			0.683591
$123$	−5.17423	+	8.96204i	−0.466545	+	0.808080i
$124$	−4.44949	+	7.70674i	−0.399576	+	0.692086i
$125$	1.00000			0.0894427
$126$	3.44949			0.307305
$127$	−7.17423	+	12.4261i	−0.636610	+	1.10264i	0.349561	+	0.936914i	$0.386331\pi$
$127$	−7.17423	+	12.4261i	−0.636610	+	1.10264i	−0.986172	+	0.165728i	$0.947003\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.89898	−	6.75323i	0.343286	−	0.594589i
$130$	2.44949	+	4.24264i	0.214834	+	0.372104i
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$	3.00000			0.261116
$133$	10.9495	−	10.3048i	0.949441	−	0.893541i
$134$	7.34847			0.634811
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	3.22474	+	5.58542i	0.276520	+	0.478946i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	1.94949	+	3.37662i	0.165952	+	0.287437i
$139$	−7.34847	+	12.7279i	−0.623289	+	1.07957i	0.365580	+	0.930780i	$0.380871\pi$
$139$	−7.34847	+	12.7279i	−0.623289	+	1.07957i	−0.988869	+	0.148788i	$0.952463\pi$
$140$	3.44949			0.291535
$141$	10.8990			0.917860
$142$	−5.67423	+	9.82806i	−0.476171	+	0.824753i
$143$	−7.34847	+	12.7279i	−0.614510	+	1.06436i
$144$	1.00000			0.0833333
$145$	−5.34847			−0.444166
$146$	−2.77526	+	4.80688i	−0.229682	+	0.397820i
$147$	2.44949	+	4.24264i	0.202031	+	0.349927i
$148$	0.0505103	−	0.0874863i	0.00415192	−	0.00719133i
$149$	−9.22474	−	15.9777i	−0.755721	−	1.30895i	−0.945015	−	0.327026i	$-0.893954\pi$
$149$	−9.22474	−	15.9777i	−0.755721	−	1.30895i	0.189295	−	0.981920i	$-0.439380\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−19.3485			−1.57456			−0.787278	−	0.616598i	$-0.788510\pi$
$151$	−19.3485			−1.57456			−0.787278	+	0.616598i	$0.788510\pi$
$152$	3.17423	−	2.98735i	0.257464	−	0.242306i
$153$	−6.44949			−0.521410
$154$	5.17423	+	8.96204i	0.416952	+	0.722182i
$155$	−4.44949	−	7.70674i	−0.357392	−	0.619020i
$156$	−2.44949	+	4.24264i	−0.196116	+	0.339683i
$157$	−0.601021	−	1.04100i	−0.0479667	−	0.0830807i	0.841045	−	0.540965i	$-0.181941\pi$
$157$	−0.601021	−	1.04100i	−0.0479667	−	0.0830807i	−0.889012	+	0.457884i	$0.848607\pi$
$158$	1.44949	−	2.51059i	0.115315	−	0.199732i
$159$	2.55051			0.202269
$160$	1.00000			0.0790569
$161$	−6.72474	+	11.6476i	−0.529984	+	0.917959i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−12.6969			−0.994501			−0.497250	−	0.867607i	$-0.665657\pi$
$163$	−12.6969			−0.994501			−0.497250	+	0.867607i	$0.665657\pi$
$164$	−10.3485			−0.808080
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	3.89898	+	6.75323i	0.302619	+	0.524152i
$167$	−9.84847	+	17.0580i	−0.762097	+	1.31999i	0.179670	+	0.983727i	$0.442497\pi$
$167$	−9.84847	+	17.0580i	−0.762097	+	1.31999i	−0.941768	+	0.336265i	$0.890836\pi$
$168$	1.72474	+	2.98735i	0.133067	+	0.230479i
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	−6.44949			−0.494653
$171$	1.00000	+	4.24264i	0.0764719	+	0.324443i
$172$	7.79796			0.594589
$173$	4.72474	+	8.18350i	0.359216	+	0.622180i	0.987830	−	0.155537i	$-0.0497109\pi$
$173$	4.72474	+	8.18350i	0.359216	+	0.622180i	−0.628614	+	0.777717i	$0.716378\pi$
$174$	−2.67423	−	4.63191i	−0.202733	−	0.351144i
$175$	−1.72474	+	2.98735i	−0.130378	+	0.225822i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−0.550510			−0.0412625
$179$	−1.20204			−0.0898448			−0.0449224	−	0.998990i	$-0.514304\pi$
$179$	−1.20204			−0.0898448			−0.0449224	+	0.998990i	$0.514304\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	8.57321	−	14.8492i	0.637242	−	1.10374i	−0.348793	−	0.937200i	$-0.613409\pi$
$181$	8.57321	−	14.8492i	0.637242	−	1.10374i	0.986035	−	0.166536i	$-0.0532582\pi$
$182$	−16.8990			−1.25264
$183$	−7.55051			−0.558150
$184$	−1.94949	+	3.37662i	−0.143718	+	0.248927i
$185$	0.0505103	+	0.0874863i	0.00371359	+	0.00643212i
$186$	4.44949	−	7.70674i	0.326252	−	0.565086i
$187$	−9.67423	−	16.7563i	−0.707450	−	1.22534i
$188$	5.44949	+	9.43879i	0.397445	+	0.688395i
$189$	−3.44949			−0.250913
$190$	1.00000	+	4.24264i	0.0725476	+	0.307794i
$191$	15.7980			1.14310			0.571550	−	0.820567i	$-0.306342\pi$
$191$	15.7980			1.14310			0.571550	+	0.820567i	$0.306342\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	3.32577	+	5.76039i	0.239394	+	0.414642i	0.960541	−	0.278140i	$-0.0897180\pi$
$193$	3.32577	+	5.76039i	0.239394	+	0.414642i	−0.721147	+	0.692782i	$0.756385\pi$
$194$	6.77526	−	11.7351i	0.486435	−	0.842530i
$195$	−2.44949	−	4.24264i	−0.175412	−	0.303822i
$196$	−2.44949	+	4.24264i	−0.174964	+	0.303046i
$197$	11.4495			0.815742			0.407871	−	0.913039i	$-0.366271\pi$
$197$	11.4495			0.815742			0.407871	+	0.913039i	$0.366271\pi$
$198$	−3.00000			−0.213201
$199$	−0.775255	+	1.34278i	−0.0549564	+	0.0951872i	−0.892195	−	0.451651i	$-0.850835\pi$
$199$	−0.775255	+	1.34278i	−0.0549564	+	0.0951872i	0.837238	+	0.546838i	$0.184169\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−7.34847			−0.518321
$202$	−10.8990			−0.766850
$203$	9.22474	−	15.9777i	0.647450	−	1.12142i
$204$	−3.22474	−	5.58542i	−0.225777	−	0.391058i
$205$	5.17423	−	8.96204i	0.361384	−	0.625936i
$206$	6.62372	+	11.4726i	0.461497	+	0.799336i
$207$	−1.94949	−	3.37662i	−0.135499	−	0.234691i
$208$	−4.89898			−0.339683
$209$	−9.52270	+	8.96204i	−0.658699	+	0.619917i
$210$	−3.44949			−0.238037
$211$	5.82577	+	10.0905i	0.401062	+	0.694660i	0.993854	−	0.110695i	$-0.0353078\pi$
$211$	5.82577	+	10.0905i	0.401062	+	0.694660i	−0.592792	+	0.805355i	$0.701974\pi$
$212$	1.27526	+	2.20881i	0.0875849	+	0.151701i
$213$	5.67423	−	9.82806i	0.388792	−	0.673408i
$214$	8.67423	+	15.0242i	0.592958	+	1.02703i
$215$	−3.89898	+	6.75323i	−0.265908	+	0.460567i
$216$	−1.00000			−0.0680414
$217$	30.6969			2.08384
$218$	6.67423	−	11.5601i	0.452036	−	0.782950i
$219$	2.77526	−	4.80688i	0.187534	−	0.324819i
$220$	−3.00000			−0.202260
$221$	31.5959			2.12537
$222$	−0.0505103	+	0.0874863i	−0.00339003	+	0.00587170i
$223$	−0.724745	−	1.25529i	−0.0485325	−	0.0840608i	0.840739	−	0.541441i	$-0.182121\pi$
$223$	−0.724745	−	1.25529i	−0.0485325	−	0.0840608i	−0.889271	+	0.457380i	$0.848788\pi$
$224$	−1.72474	+	2.98735i	−0.115239	+	0.199600i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	7.22474	+	12.5136i	0.480583	+	0.832394i
$227$	3.34847			0.222246			0.111123	−	0.993807i	$-0.464555\pi$
$227$	3.34847			0.222246			0.111123	+	0.993807i	$0.464555\pi$
$228$	−3.17423	+	2.98735i	−0.210219	+	0.197842i
$229$	−20.6969			−1.36769			−0.683846	−	0.729626i	$-0.739694\pi$
$229$	−20.6969			−1.36769			−0.683846	+	0.729626i	$0.739694\pi$
$230$	−1.94949	−	3.37662i	−0.128546	−	0.222647i
$231$	−5.17423	−	8.96204i	−0.340440	−	0.589659i
$232$	2.67423	−	4.63191i	0.175572	−	0.304100i
$233$	4.10102	+	7.10318i	0.268667	+	0.465345i	0.968518	−	0.248944i	$-0.0800836\pi$
$233$	4.10102	+	7.10318i	0.268667	+	0.465345i	−0.699851	+	0.714289i	$0.746750\pi$
$234$	2.44949	−	4.24264i	0.160128	−	0.277350i
$235$	−10.8990			−0.710971
$236$	−6.00000			−0.390567
$237$	−1.44949	+	2.51059i	−0.0941545	+	0.163080i
$238$	11.1237	−	19.2669i	0.721044	−	1.24888i
$239$	−10.2020			−0.659915			−0.329958	−	0.943996i	$-0.607034\pi$
$239$	−10.2020			−0.659915			−0.329958	+	0.943996i	$0.607034\pi$
$240$	−1.00000			−0.0645497
$241$	11.3485	−	19.6561i	0.731019	−	1.26616i	−0.225429	−	0.974260i	$-0.572378\pi$
$241$	11.3485	−	19.6561i	0.731019	−	1.26616i	0.956448	−	0.291903i	$-0.0942883\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.77526	−	6.53893i	−0.241686	−	0.418612i
$245$	−2.44949	−	4.24264i	−0.156492	−	0.271052i
$246$	10.3485			0.659794
$247$	−4.89898	−	20.7846i	−0.311715	−	1.32249i
$248$	8.89898			0.565086
$249$	−3.89898	−	6.75323i	−0.247088	−	0.427969i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	10.8990	−	18.8776i	0.687937	−	1.19154i	−0.284566	−	0.958656i	$-0.591850\pi$
$251$	10.8990	−	18.8776i	0.687937	−	1.19154i	0.972504	−	0.232886i	$-0.0748170\pi$
$252$	−1.72474	−	2.98735i	−0.108649	−	0.188185i
$253$	5.84847	−	10.1298i	0.367690	−	0.636858i
$254$	14.3485			0.900303
$255$	6.44949			0.403883
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.89898	−	3.28913i	0.118455	−	0.205170i	−0.800701	−	0.599065i	$-0.795539\pi$
$257$	1.89898	−	3.28913i	0.118455	−	0.205170i	0.919156	+	0.393895i	$0.128873\pi$
$258$	−7.79796			−0.485480
$259$	−0.348469			−0.0216528
$260$	2.44949	−	4.24264i	0.151911	−	0.263117i
$261$	2.67423	+	4.63191i	0.165531	+	0.286708i
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	−9.94949	−	17.2330i	−0.613512	−	1.06263i	−0.990644	−	0.136474i	$-0.956423\pi$
$263$	−9.94949	−	17.2330i	−0.613512	−	1.06263i	0.377132	−	0.926160i	$-0.376910\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$	−2.55051			−0.156677
$266$	−14.3990	−	4.33013i	−0.882858	−	0.265497i
$267$	0.550510			0.0336907
$268$	−3.67423	−	6.36396i	−0.224440	−	0.388741i
$269$	−0.123724	−	0.214297i	−0.00754361	−	0.0130659i	0.862229	−	0.506519i	$-0.169068\pi$
$269$	−0.123724	−	0.214297i	−0.00754361	−	0.0130659i	−0.869773	+	0.493453i	$0.835735\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	2.55051	+	4.41761i	0.154932	+	0.268351i	0.933034	−	0.359787i	$-0.117151\pi$
$271$	2.55051	+	4.41761i	0.154932	+	0.268351i	−0.778102	+	0.628138i	$0.783817\pi$
$272$	3.22474	−	5.58542i	0.195529	−	0.338666i
$273$	16.8990			1.02277
$274$	−12.0000			−0.724947
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$	1.94949	−	3.37662i	0.117345	−	0.203248i
$277$	−3.10102			−0.186322			−0.0931611	−	0.995651i	$-0.529697\pi$
$277$	−3.10102			−0.186322			−0.0931611	+	0.995651i	$0.529697\pi$
$278$	14.6969			0.881464
$279$	−4.44949	+	7.70674i	−0.266384	+	0.461391i
$280$	−1.72474	−	2.98735i	−0.103073	−	0.178528i
$281$	0.174235	−	0.301783i	0.0103940	−	0.0180029i	−0.860782	−	0.508974i	$-0.830025\pi$
$281$	0.174235	−	0.301783i	0.0103940	−	0.0180029i	0.871176	+	0.490972i	$0.163358\pi$
$282$	−5.44949	−	9.43879i	−0.324512	−	0.562072i
$283$	−8.34847	−	14.4600i	−0.496265	−	0.859556i	0.503726	−	0.863864i	$-0.331962\pi$
$283$	−8.34847	−	14.4600i	−0.496265	−	0.859556i	−0.999991	+	0.00430747i	$0.998629\pi$
$284$	11.3485			0.673408
$285$	−1.00000	−	4.24264i	−0.0592349	−	0.251312i
$286$	14.6969			0.869048
$287$	17.8485	+	30.9145i	1.05356	+	1.82482i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−12.2980	+	21.3007i	−0.723409	+	1.25298i
$290$	2.67423	+	4.63191i	0.157036	+	0.271995i
$291$	−6.77526	+	11.7351i	−0.397172	+	0.687923i
$292$	5.55051			0.324819
$293$	−6.55051			−0.382685			−0.191342	−	0.981523i	$-0.561284\pi$
$293$	−6.55051			−0.382685			−0.191342	+	0.981523i	$0.561284\pi$
$294$	2.44949	−	4.24264i	0.142857	−	0.247436i
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	−0.101021			−0.00587170
$297$	3.00000			0.174078
$298$	−9.22474	+	15.9777i	−0.534375	+	0.925565i
$299$	9.55051	+	16.5420i	0.552320	+	0.956647i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−13.4495	−	23.2952i	−0.775216	−	1.34271i
$302$	9.67423	+	16.7563i	0.556690	+	0.964215i
$303$	10.8990			0.626130
$304$	−4.17423	−	1.25529i	−0.239409	−	0.0719961i
$305$	7.55051			0.432341
$306$	3.22474	+	5.58542i	0.184346	+	0.319297i
$307$	−7.12372	−	12.3387i	−0.406572	−	0.704204i	0.587931	−	0.808911i	$-0.299943\pi$
$307$	−7.12372	−	12.3387i	−0.406572	−	0.704204i	−0.994503	+	0.104707i	$0.966609\pi$
$308$	5.17423	−	8.96204i	0.294829	−	0.510659i
$309$	−6.62372	−	11.4726i	−0.376811	−	0.652655i
$310$	−4.44949	+	7.70674i	−0.252714	+	0.437714i
$311$	9.79796			0.555591			0.277796	−	0.960640i	$-0.410396\pi$
$311$	9.79796			0.555591			0.277796	+	0.960640i	$0.410396\pi$
$312$	4.89898			0.277350
$313$	3.79796	−	6.57826i	0.214673	−	0.371825i	−0.738498	−	0.674256i	$-0.764465\pi$
$313$	3.79796	−	6.57826i	0.214673	−	0.371825i	0.953171	+	0.302430i	$0.0977980\pi$
$314$	−0.601021	+	1.04100i	−0.0339175	+	0.0587469i
$315$	3.44949			0.194357
$316$	−2.89898			−0.163080
$317$	−2.27526	+	3.94086i	−0.127791	+	0.221341i	−0.922820	−	0.385230i	$-0.874122\pi$
$317$	−2.27526	+	3.94086i	−0.127791	+	0.221341i	0.795029	+	0.606571i	$0.207455\pi$
$318$	−1.27526	−	2.20881i	−0.0715128	−	0.123864i
$319$	−8.02270	+	13.8957i	−0.449185	+	0.778012i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−8.67423	−	15.0242i	−0.484149	−	0.838570i
$322$	13.4495			0.749511
$323$	26.9217	+	8.09601i	1.49796	+	0.450474i
$324$	1.00000			0.0555556
$325$	2.44949	+	4.24264i	0.135873	+	0.235339i
$326$	6.34847	+	10.9959i	0.351609	+	0.609005i
$327$	−6.67423	+	11.5601i	−0.369086	+	0.639276i
$328$	5.17423	+	8.96204i	0.285699	+	0.494846i
$329$	18.7980	−	32.5590i	1.03637	−	1.79504i
$330$	3.00000			0.165145
$331$	3.65153			0.200706			0.100353	−	0.994952i	$-0.468003\pi$
$331$	3.65153			0.200706			0.100353	+	0.994952i	$0.468003\pi$
$332$	3.89898	−	6.75323i	0.213984	−	0.370632i
$333$	0.0505103	−	0.0874863i	0.00276795	−	0.00479422i
$334$	19.6969			1.07777
$335$	7.34847			0.401490
$336$	1.72474	−	2.98735i	0.0940925	−	0.162973i
$337$	−11.2474	−	19.4812i	−0.612688	−	1.06121i	−0.990785	−	0.135440i	$-0.956755\pi$
$337$	−11.2474	−	19.4812i	−0.612688	−	1.06121i	0.378098	−	0.925766i	$-0.376578\pi$
$338$	−5.50000	+	9.52628i	−0.299161	+	0.518161i
$339$	−7.22474	−	12.5136i	−0.392394	−	0.679647i
$340$	3.22474	+	5.58542i	0.174886	+	0.302912i
$341$	−26.6969			−1.44572
$342$	3.17423	−	2.98735i	0.171643	−	0.161537i
$343$	−7.24745			−0.391325
$344$	−3.89898	−	6.75323i	−0.210219	−	0.364110i
$345$	1.94949	+	3.37662i	0.104957	+	0.181791i
$346$	4.72474	−	8.18350i	0.254004	−	0.439948i
$347$	3.89898	+	6.75323i	0.209308	+	0.362532i	0.951497	−	0.307659i	$-0.0995455\pi$
$347$	3.89898	+	6.75323i	0.209308	+	0.362532i	−0.742189	+	0.670191i	$0.766212\pi$
$348$	−2.67423	+	4.63191i	−0.143354	+	0.248296i
$349$	24.0454			1.28712			0.643561	−	0.765395i	$-0.277456\pi$
$349$	24.0454			1.28712			0.643561	+	0.765395i	$0.277456\pi$
$350$	3.44949			0.184383
$351$	−2.44949	+	4.24264i	−0.130744	+	0.226455i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−20.6515			−1.09917			−0.549585	−	0.835438i	$-0.685214\pi$
$353$	−20.6515			−1.09917			−0.549585	+	0.835438i	$0.685214\pi$
$354$	6.00000			0.318896
$355$	−5.67423	+	9.82806i	−0.301157	+	0.521619i
$356$	0.275255	+	0.476756i	0.0145885	+	0.0252680i
$357$	−11.1237	+	19.2669i	−0.588730	+	1.01971i
$358$	0.601021	+	1.04100i	0.0317649	+	0.0550185i
$359$	−10.7753	−	18.6633i	−0.568696	−	0.985011i	−0.996695	−	0.0812316i	$-0.974115\pi$
$359$	−10.7753	−	18.6633i	−0.568696	−	0.985011i	0.427999	−	0.903779i	$-0.359219\pi$
$360$	1.00000			0.0527046
$361$	1.15153	−	18.9651i	0.0606069	−	0.998162i
$362$	−17.1464			−0.901196
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$	8.44949	+	14.6349i	0.442874	+	0.767080i
$365$	−2.77526	+	4.80688i	−0.145263	+	0.251604i
$366$	3.77526	+	6.53893i	0.197336	+	0.341796i
$367$	−5.55051	+	9.61377i	−0.289734	+	0.501834i	−0.973746	−	0.227636i	$-0.926900\pi$
$367$	−5.55051	+	9.61377i	−0.289734	+	0.501834i	0.684012	+	0.729471i	$0.260234\pi$
$368$	3.89898			0.203248
$369$	−10.3485			−0.538720
$370$	0.0505103	−	0.0874863i	0.00262590	−	0.00454820i
$371$	4.39898	−	7.61926i	0.228384	−	0.395572i
$372$	−8.89898			−0.461391
$373$	5.89898			0.305438			0.152719	−	0.988270i	$-0.451197\pi$
$373$	5.89898			0.305438			0.152719	+	0.988270i	$0.451197\pi$
$374$	−9.67423	+	16.7563i	−0.500243	+	0.866446i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	5.44949	−	9.43879i	0.281036	−	0.486769i
$377$	−13.1010	−	22.6916i	−0.674737	−	1.16868i
$378$	1.72474	+	2.98735i	0.0887113	+	0.153652i
$379$	22.6969			1.16586			0.582932	−	0.812521i	$-0.301906\pi$
$379$	22.6969			1.16586			0.582932	+	0.812521i	$0.301906\pi$
$380$	3.17423	−	2.98735i	0.162835	−	0.153248i
$381$	−14.3485			−0.735094
$382$	−7.89898	−	13.6814i	−0.404147	−	0.700003i
$383$	9.24745	+	16.0171i	0.472523	+	0.818433i	0.999506	−	0.0314428i	$-0.0100102\pi$
$383$	9.24745	+	16.0171i	0.472523	+	0.818433i	−0.526983	+	0.849876i	$0.676677\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	5.17423	+	8.96204i	0.263703	+	0.456748i
$386$	3.32577	−	5.76039i	0.169277	−	0.293196i
$387$	7.79796			0.396393
$388$	−13.5505			−0.687923
$389$	−5.57321	+	9.65309i	−0.282573	+	0.489431i	−0.972018	−	0.234907i	$-0.924521\pi$
$389$	−5.57321	+	9.65309i	−0.282573	+	0.489431i	0.689445	+	0.724338i	$0.257855\pi$
$390$	−2.44949	+	4.24264i	−0.124035	+	0.214834i
$391$	−25.1464			−1.27171
$392$	4.89898			0.247436
$393$	−1.50000	+	2.59808i	−0.0756650	+	0.131056i
$394$	−5.72474	−	9.91555i	−0.288408	−	0.499538i
$395$	1.44949	−	2.51059i	0.0729317	−	0.126321i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	18.7474	+	32.4715i	0.940907	+	1.62970i	0.763745	+	0.645518i	$0.223358\pi$
$397$	18.7474	+	32.4715i	0.940907	+	1.62970i	0.177162	+	0.984182i	$0.443308\pi$
$398$	1.55051			0.0777201
$399$	14.3990	+	4.33013i	0.720851	+	0.216777i
$400$	1.00000			0.0500000
$401$	−7.89898	−	13.6814i	−0.394456	−	0.683218i	0.598575	−	0.801066i	$-0.295734\pi$
$401$	−7.89898	−	13.6814i	−0.394456	−	0.683218i	−0.993032	+	0.117848i	$0.962400\pi$
$402$	3.67423	+	6.36396i	0.183254	+	0.317406i
$403$	21.7980	−	37.7552i	1.08583	−	1.88072i
$404$	5.44949	+	9.43879i	0.271122	+	0.469598i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−18.4495			−0.915633
$407$	0.303062			0.0150222
$408$	−3.22474	+	5.58542i	−0.159649	+	0.276520i
$409$	−19.7474	+	34.2036i	−0.976448	+	1.69126i	−0.301379	+	0.953505i	$0.597447\pi$
$409$	−19.7474	+	34.2036i	−0.976448	+	1.69126i	−0.675070	+	0.737754i	$0.735886\pi$
$410$	−10.3485			−0.511074
$411$	12.0000			0.591916
$412$	6.62372	−	11.4726i	0.326327	−	0.565216i
$413$	10.3485	+	17.9241i	0.509215	+	0.881986i
$414$	−1.94949	+	3.37662i	−0.0958122	+	0.165952i
$415$	3.89898	+	6.75323i	0.191393	+	0.331503i
$416$	2.44949	+	4.24264i	0.120096	+	0.208013i
$417$	−14.6969			−0.719712
$418$	12.5227	+	3.76588i	0.612505	+	0.184195i
$419$	12.1010			0.591174			0.295587	−	0.955316i	$-0.404485\pi$
$419$	12.1010			0.591174			0.295587	+	0.955316i	$0.404485\pi$
$420$	1.72474	+	2.98735i	0.0841589	+	0.145768i
$421$	16.6742	+	28.8806i	0.812652	+	1.40756i	0.911001	+	0.412403i	$0.135311\pi$
$421$	16.6742	+	28.8806i	0.812652	+	1.40756i	−0.0983489	+	0.995152i	$0.531356\pi$
$422$	5.82577	−	10.0905i	0.283594	−	0.491199i
$423$	5.44949	+	9.43879i	0.264963	+	0.458930i
$424$	1.27526	−	2.20881i	0.0619319	−	0.107269i
$425$	−6.44949			−0.312846
$426$	−11.3485			−0.549835
$427$	−13.0227	+	22.5560i	−0.630213	+	1.09156i
$428$	8.67423	−	15.0242i	0.419285	−	0.726223i
$429$	−14.6969			−0.709575
$430$	7.79796			0.376051
$431$	−12.6742	+	21.9524i	−0.610496	+	1.05741i	0.380660	+	0.924715i	$0.375697\pi$
$431$	−12.6742	+	21.9524i	−0.610496	+	1.05741i	−0.991157	+	0.132696i	$0.957637\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	5.67423	−	9.82806i	0.272686	−	0.472307i	−0.696862	−	0.717205i	$-0.745421\pi$
$433$	5.67423	−	9.82806i	0.272686	−	0.472307i	0.969549	+	0.244898i	$0.0787546\pi$
$434$	−15.3485	−	26.5843i	−0.736750	−	1.27609i
$435$	−2.67423	−	4.63191i	−0.128220	−	0.222083i
$436$	−13.3485			−0.639276
$437$	3.89898	+	16.5420i	0.186513	+	0.791310i
$438$	−5.55051			−0.265214
$439$	5.67423	+	9.82806i	0.270816	+	0.469068i	0.969071	−	0.246782i	$-0.0793730\pi$
$439$	5.67423	+	9.82806i	0.270816	+	0.469068i	−0.698255	+	0.715849i	$0.746040\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	−2.44949	+	4.24264i	−0.116642	+	0.202031i
$442$	−15.7980	−	27.3629i	−0.751432	−	1.30152i
$443$	−13.1237	+	22.7310i	−0.623527	+	1.07998i	0.365297	+	0.930891i	$0.380968\pi$
$443$	−13.1237	+	22.7310i	−0.623527	+	1.07998i	−0.988824	+	0.149089i	$0.952366\pi$
$444$	0.101021			0.00479422
$445$	−0.550510			−0.0260967
$446$	−0.724745	+	1.25529i	−0.0343177	+	0.0594399i
$447$	9.22474	−	15.9777i	0.436315	−	0.755721i
$448$	3.44949			0.162973
$449$	33.2474			1.56904			0.784522	−	0.620101i	$-0.212908\pi$
$449$	33.2474			1.56904			0.784522	+	0.620101i	$0.212908\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−15.5227	−	26.8861i	−0.730936	−	1.26602i
$452$	7.22474	−	12.5136i	0.339823	−	0.588591i
$453$	−9.67423	−	16.7563i	−0.454535	−	0.787278i
$454$	−1.67423	−	2.89986i	−0.0785757	−	0.136097i
$455$	−16.8990			−0.792236
$456$	4.17423	+	1.25529i	0.195476	+	0.0587846i
$457$	32.0454			1.49902			0.749510	−	0.661992i	$-0.230289\pi$
$457$	32.0454			1.49902			0.749510	+	0.661992i	$0.230289\pi$
$458$	10.3485	+	17.9241i	0.483552	+	0.837537i
$459$	−3.22474	−	5.58542i	−0.150518	−	0.260705i
$460$	−1.94949	+	3.37662i	−0.0908954	+	0.157435i
$461$	4.10102	+	7.10318i	0.191004	+	0.330828i	0.945583	−	0.325381i	$-0.105492\pi$
$461$	4.10102	+	7.10318i	0.191004	+	0.330828i	−0.754580	+	0.656209i	$0.772159\pi$
$462$	−5.17423	+	8.96204i	−0.240727	+	0.416952i
$463$	−30.3485			−1.41041			−0.705206	−	0.709002i	$-0.749146\pi$
$463$	−30.3485			−1.41041			−0.705206	+	0.709002i	$0.749146\pi$
$464$	−5.34847			−0.248296
$465$	4.44949	−	7.70674i	0.206340	−	0.357392i
$466$	4.10102	−	7.10318i	0.189976	−	0.329048i
$467$	−15.7526			−0.728941			−0.364471	−	0.931215i	$-0.618750\pi$
$467$	−15.7526			−0.728941			−0.364471	+	0.931215i	$0.618750\pi$
$468$	−4.89898			−0.226455
$469$	−12.6742	+	21.9524i	−0.585242	+	1.01367i
$470$	5.44949	+	9.43879i	0.251366	+	0.435379i
$471$	0.601021	−	1.04100i	0.0276936	−	0.0479667i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	11.6969	+	20.2597i	0.537826	+	0.931542i
$474$	2.89898			0.133155
$475$	1.00000	+	4.24264i	0.0458831	+	0.194666i
$476$	−22.2474			−1.01971
$477$	1.27526	+	2.20881i	0.0583899	+	0.101134i
$478$	5.10102	+	8.83523i	0.233315	+	0.404114i
$479$	17.0227	−	29.4842i	0.777787	−	1.34717i	−0.155427	−	0.987847i	$-0.549675\pi$
$479$	17.0227	−	29.4842i	0.777787	−	1.34717i	0.933215	−	0.359320i	$-0.116991\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−0.247449	+	0.428594i	−0.0112827	+	0.0195422i
$482$	−22.6969			−1.03382
$483$	−13.4495			−0.611973
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	6.77526	−	11.7351i	0.307648	−	0.532863i
$486$	−1.00000			−0.0453609
$487$	6.14643			0.278521			0.139261	−	0.990256i	$-0.455527\pi$
$487$	6.14643			0.278521			0.139261	+	0.990256i	$0.455527\pi$
$488$	−3.77526	+	6.53893i	−0.170898	+	0.296004i
$489$	−6.34847	−	10.9959i	−0.287088	−	0.497250i
$490$	−2.44949	+	4.24264i	−0.110657	+	0.191663i
$491$	17.3990	+	30.1359i	0.785205	+	1.36001i	0.928877	+	0.370389i	$0.120776\pi$
$491$	17.3990	+	30.1359i	0.785205	+	1.36001i	−0.143672	+	0.989625i	$0.545891\pi$
$492$	−5.17423	−	8.96204i	−0.233273	−	0.404040i
$493$	34.4949			1.55357
$494$	−15.5505	+	14.6349i	−0.699651	+	0.658457i
$495$	−3.00000			−0.134840
$496$	−4.44949	−	7.70674i	−0.199788	−	0.346043i
$497$	−19.5732	−	33.9018i	−0.877979	−	1.52070i
$498$	−3.89898	+	6.75323i	−0.174717	+	0.302619i
$499$	−7.72474	−	13.3797i	−0.345807	−	0.598955i	0.639693	−	0.768631i	$-0.279062\pi$
$499$	−7.72474	−	13.3797i	−0.345807	−	0.598955i	−0.985500	+	0.169675i	$0.945728\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−19.6969			−0.879994
$502$	−21.7980			−0.972891
$503$	−15.8485	+	27.4504i	−0.706648	+	1.22395i	0.259445	+	0.965758i	$0.416460\pi$
$503$	−15.8485	+	27.4504i	−0.706648	+	1.22395i	−0.966093	+	0.258193i	$0.916873\pi$
$504$	−1.72474	+	2.98735i	−0.0768262	+	0.133067i
$505$	−10.8990			−0.484998
$506$	−11.6969			−0.519992
$507$	5.50000	−	9.52628i	0.244264	−	0.423077i
$508$	−7.17423	−	12.4261i	−0.318305	−	0.551321i
$509$	−3.44949	+	5.97469i	−0.152896	+	0.264824i	−0.932291	−	0.361709i	$-0.882193\pi$
$509$	−3.44949	+	5.97469i	−0.152896	+	0.264824i	0.779395	+	0.626533i	$0.215527\pi$
$510$	−3.22474	−	5.58542i	−0.142794	−	0.247327i
$511$	−9.57321	−	16.5813i	−0.423494	−	0.733513i
$512$	1.00000			0.0441942
$513$	−3.17423	+	2.98735i	−0.140146	+	0.131895i
$514$	−3.79796			−0.167521
$515$	6.62372	+	11.4726i	0.291876	+	0.505544i
$516$	3.89898	+	6.75323i	0.171643	+	0.297294i
$517$	−16.3485	+	28.3164i	−0.719005	+	1.24535i
$518$	0.174235	+	0.301783i	0.00765543	+	0.0132596i
$519$	−4.72474	+	8.18350i	−0.207393	+	0.359216i
$520$	−4.89898			−0.214834
$521$	10.8990			0.477493			0.238746	−	0.971082i	$-0.423264\pi$
$521$	10.8990			0.477493			0.238746	+	0.971082i	$0.423264\pi$
$522$	2.67423	−	4.63191i	0.117048	−	0.202733i
$523$	15.5732	−	26.9736i	0.680969	−	1.17947i	−0.293716	−	0.955893i	$-0.594892\pi$
$523$	15.5732	−	26.9736i	0.680969	−	1.17947i	0.974685	−	0.223580i	$-0.0717745\pi$
$524$	−3.00000			−0.131056
$525$	−3.44949			−0.150548
$526$	−9.94949	+	17.2330i	−0.433818	+	0.751395i
$527$	28.6969	+	49.7046i	1.25006	+	2.16516i
$528$	−1.50000	+	2.59808i	−0.0652791	+	0.113067i
$529$	3.89898	+	6.75323i	0.169521	+	0.293619i
$530$	1.27526	+	2.20881i	0.0553935	+	0.0959444i
$531$	−6.00000			−0.260378
$532$	3.44949	+	14.6349i	0.149554	+	0.634505i
$533$	50.6969			2.19593
$534$	−0.275255	−	0.476756i	−0.0119115	−	0.0206312i
$535$	8.67423	+	15.0242i	0.375020	+	0.649553i
$536$	−3.67423	+	6.36396i	−0.158703	+	0.274881i
$537$	−0.601021	−	1.04100i	−0.0259359	−	0.0449224i
$538$	−0.123724	+	0.214297i	−0.00533414	+	0.00923899i
$539$	−14.6969			−0.633042
$540$	−1.00000			−0.0430331
$541$	−14.4495	+	25.0273i	−0.621232	+	1.07601i	0.368025	+	0.929816i	$0.380034\pi$
$541$	−14.4495	+	25.0273i	−0.621232	+	1.07601i	−0.989257	+	0.146189i	$0.953299\pi$
$542$	2.55051	−	4.41761i	0.109554	−	0.189753i
$543$	17.1464			0.735824
$544$	−6.44949			−0.276520
$545$	6.67423	−	11.5601i	0.285893	−	0.495181i
$546$	−8.44949	−	14.6349i	−0.361605	−	0.626318i
$547$	16.3485	−	28.3164i	0.699010	−	1.21072i	−0.269800	−	0.962916i	$-0.586958\pi$
$547$	16.3485	−	28.3164i	0.699010	−	1.21072i	0.968810	−	0.247805i	$-0.0797091\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−3.77526	−	6.53893i	−0.161124	−	0.279075i
$550$	−3.00000			−0.127920
$551$	−5.34847	−	22.6916i	−0.227852	−	0.966696i
$552$	−3.89898			−0.165952
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	1.55051	+	2.68556i	0.0658749	+	0.114099i
$555$	−0.0505103	+	0.0874863i	−0.00214404	+	0.00371359i
$556$	−7.34847	−	12.7279i	−0.311645	−	0.539784i
$557$	1.82577	−	3.16232i	0.0773602	−	0.133992i	−0.824750	−	0.565497i	$-0.808684\pi$
$557$	1.82577	−	3.16232i	0.0773602	−	0.133992i	0.902110	+	0.431506i	$0.142018\pi$
$558$	8.89898			0.376724
$559$	−38.2020			−1.61577
$560$	−1.72474	+	2.98735i	−0.0728838	+	0.126238i
$561$	9.67423	−	16.7563i	0.408447	−	0.707450i
$562$	−0.348469			−0.0146993
$563$	−29.3939			−1.23880			−0.619402	−	0.785074i	$-0.712625\pi$
$563$	−29.3939			−1.23880			−0.619402	+	0.785074i	$0.712625\pi$
$564$	−5.44949	+	9.43879i	−0.229465	+	0.397445i
$565$	7.22474	+	12.5136i	0.303947	+	0.526452i
$566$	−8.34847	+	14.4600i	−0.350912	+	0.607798i
$567$	−1.72474	−	2.98735i	−0.0724325	−	0.125457i
$568$	−5.67423	−	9.82806i	−0.238086	−	0.412376i
$569$	−2.55051			−0.106923			−0.0534615	−	0.998570i	$-0.517025\pi$
$569$	−2.55051			−0.106923			−0.0534615	+	0.998570i	$0.517025\pi$
$570$	−3.17423	+	2.98735i	−0.132954	+	0.125126i
$571$	−27.7980			−1.16331			−0.581654	−	0.813436i	$-0.697594\pi$
$571$	−27.7980			−1.16331			−0.581654	+	0.813436i	$0.697594\pi$
$572$	−7.34847	−	12.7279i	−0.307255	−	0.532181i
$573$	7.89898	+	13.6814i	0.329985	+	0.571550i
$574$	17.8485	−	30.9145i	0.744981	−	1.29034i
$575$	−1.94949	−	3.37662i	−0.0812993	−	0.140815i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−23.1464			−0.963598			−0.481799	−	0.876282i	$-0.660017\pi$
$577$	−23.1464			−0.963598			−0.481799	+	0.876282i	$0.660017\pi$
$578$	24.5959			1.02306
$579$	−3.32577	+	5.76039i	−0.138214	+	0.239394i
$580$	2.67423	−	4.63191i	0.111042	−	0.192330i
$581$	−26.8990			−1.11596
$582$	13.5505			0.561687
$583$	−3.82577	+	6.62642i	−0.158447	+	0.274438i
$584$	−2.77526	−	4.80688i	−0.114841	−	0.198910i
$585$	2.44949	−	4.24264i	0.101274	−	0.175412i
$586$	3.27526	+	5.67291i	0.135300	+	0.234346i
$587$	−8.24745	−	14.2850i	−0.340409	−	0.589605i	0.644100	−	0.764941i	$-0.277232\pi$
$587$	−8.24745	−	14.2850i	−0.340409	−	0.589605i	−0.984509	+	0.175336i	$0.943899\pi$
$588$	−4.89898			−0.202031
$589$	28.2474	−	26.5843i	1.16392	−	1.09539i
$590$	−6.00000			−0.247016
$591$	5.72474	+	9.91555i	0.235485	+	0.407871i
$592$	0.0505103	+	0.0874863i	0.00207596	+	0.00359567i
$593$	0.426786	−	0.739215i	0.0175260	−	0.0303559i	−0.857129	−	0.515101i	$-0.827754\pi$
$593$	0.426786	−	0.739215i	0.0175260	−	0.0303559i	0.874655	+	0.484745i	$0.161088\pi$
$594$	−1.50000	−	2.59808i	−0.0615457	−	0.106600i
$595$	11.1237	−	19.2669i	0.456028	−	0.789864i
$596$	18.4495			0.755721
$597$	−1.55051			−0.0634582
$598$	9.55051	−	16.5420i	0.390549	−	0.676451i
$599$	−5.32577	+	9.22450i	−0.217605	+	0.376903i	−0.954075	−	0.299567i	$-0.903158\pi$
$599$	−5.32577	+	9.22450i	−0.217605	+	0.376903i	0.736470	+	0.676470i	$0.236491\pi$
$600$	−1.00000			−0.0408248
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	−13.4495	+	23.2952i	−0.548160	+	0.949441i
$603$	−3.67423	−	6.36396i	−0.149626	−	0.259161i
$604$	9.67423	−	16.7563i	0.393639	−	0.681803i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	−5.44949	−	9.43879i	−0.221370	−	0.383425i
$607$	24.5505			0.996474			0.498237	−	0.867041i	$-0.333981\pi$
$607$	24.5505			0.996474			0.498237	+	0.867041i	$0.333981\pi$
$608$	1.00000	+	4.24264i	0.0405554	+	0.172062i
$609$	18.4495			0.747611
$610$	−3.77526	−	6.53893i	−0.152856	−	0.264754i
$611$	−26.6969	−	46.2405i	−1.08004	−	1.87069i
$612$	3.22474	−	5.58542i	0.130353	−	0.225777i
$613$	18.7474	+	32.4715i	0.757202	+	1.31151i	0.944272	+	0.329166i	$0.106768\pi$
$613$	18.7474	+	32.4715i	0.757202	+	1.31151i	−0.187070	+	0.982347i	$0.559899\pi$
$614$	−7.12372	+	12.3387i	−0.287490	+	0.497947i
$615$	10.3485			0.417291
$616$	−10.3485			−0.416952
$617$	11.7980	−	20.4347i	0.474968	−	0.822669i	−0.524621	−	0.851336i	$-0.675793\pi$
$617$	11.7980	−	20.4347i	0.474968	−	0.822669i	0.999589	+	0.0286672i	$0.00912632\pi$
$618$	−6.62372	+	11.4726i	−0.266445	+	0.461497i
$619$	−21.0454			−0.845886			−0.422943	−	0.906156i	$-0.639003\pi$
$619$	−21.0454			−0.845886			−0.422943	+	0.906156i	$0.639003\pi$
$620$	8.89898			0.357392
$621$	1.94949	−	3.37662i	0.0782303	−	0.135499i
$622$	−4.89898	−	8.48528i	−0.196431	−	0.340229i
$623$	0.949490	−	1.64456i	0.0380405	−	0.0658881i
$624$	−2.44949	−	4.24264i	−0.0980581	−	0.169842i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.59592			−0.303594
$627$	−12.5227	−	3.76588i	−0.500109	−	0.150395i
$628$	1.20204			0.0479667
$629$	−0.325765	−	0.564242i	−0.0129891	−	0.0224978i
$630$	−1.72474	−	2.98735i	−0.0687155	−	0.119019i
$631$	0.876276	−	1.51775i	0.0348840	−	0.0604208i	−0.848056	−	0.529906i	$-0.822227\pi$
$631$	0.876276	−	1.51775i	0.0348840	−	0.0604208i	0.882940	+	0.469485i	$0.155560\pi$
$632$	1.44949	+	2.51059i	0.0576576	+	0.0998659i
$633$	−5.82577	+	10.0905i	−0.231553	+	0.401062i
$634$	4.55051			0.180724
$635$	14.3485			0.569402
$636$	−1.27526	+	2.20881i	−0.0505672	+	0.0875849i
$637$	12.0000	−	20.7846i	0.475457	−	0.823516i
$638$	16.0454			0.635244
$639$	11.3485			0.448939
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	20.3485	+	35.2446i	0.803716	+	1.39208i	0.917154	+	0.398532i	$0.130480\pi$
$641$	20.3485	+	35.2446i	0.803716	+	1.39208i	−0.113438	+	0.993545i	$0.536186\pi$
$642$	−8.67423	+	15.0242i	−0.342345	+	0.592958i
$643$	2.12372	+	3.67840i	0.0837515	+	0.145062i	0.904859	−	0.425712i	$-0.139976\pi$
$643$	2.12372	+	3.67840i	0.0837515	+	0.145062i	−0.821107	+	0.570774i	$0.806643\pi$
$644$	−6.72474	−	11.6476i	−0.264992	−	0.458980i
$645$	−7.79796			−0.307044
$646$	−6.44949	−	27.3629i	−0.253752	−	1.07658i
$647$	9.89898			0.389169			0.194585	−	0.980886i	$-0.437664\pi$
$647$	9.89898			0.389169			0.194585	+	0.980886i	$0.437664\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$	2.44949	−	4.24264i	0.0960769	−	0.166410i
$651$	15.3485	+	26.5843i	0.601554	+	1.04192i
$652$	6.34847	−	10.9959i	0.248625	−	0.430632i
$653$	−25.6515			−1.00382			−0.501911	−	0.864919i	$-0.667370\pi$
$653$	−25.6515			−1.00382			−0.501911	+	0.864919i	$0.667370\pi$
$654$	13.3485			0.521966
$655$	1.50000	−	2.59808i	0.0586098	−	0.101515i
$656$	5.17423	−	8.96204i	0.202020	−	0.349909i
$657$	5.55051			0.216546
$658$	−37.5959			−1.46564
$659$	8.29796	−	14.3725i	0.323243	−	0.559873i	−0.657913	−	0.753094i	$-0.728560\pi$
$659$	8.29796	−	14.3725i	0.323243	−	0.559873i	0.981155	+	0.193222i	$0.0618937\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	−0.916881	−	0.399161i	$-0.869302\pi$
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	0.804124	+	0.594462i	$0.202635\pi$
$662$	−1.82577	−	3.16232i	−0.0709604	−	0.122907i
$663$	15.7980	+	27.3629i	0.613542	+	1.06269i
$664$	−7.79796			−0.302619
$665$	−14.3990	−	4.33013i	−0.558368	−	0.167915i
$666$	−0.101021			−0.00391447
$667$	10.4268	+	18.0597i	0.403727	+	0.699275i
$668$	−9.84847	−	17.0580i	−0.381049	−	0.659996i
$669$	0.724745	−	1.25529i	0.0280203	−	0.0485325i
$670$	−3.67423	−	6.36396i	−0.141948	−	0.245861i
$671$	11.3258	−	19.6168i	0.437226	−	0.757298i
$672$	−3.44949			−0.133067
$673$	8.49490			0.327454			0.163727	−	0.986506i	$-0.447648\pi$
$673$	8.49490			0.327454			0.163727	+	0.986506i	$0.447648\pi$
$674$	−11.2474	+	19.4812i	−0.433236	+	0.750386i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	11.0000			0.423077
$677$	−23.9444			−0.920258			−0.460129	−	0.887852i	$-0.652197\pi$
$677$	−23.9444			−0.920258			−0.460129	+	0.887852i	$0.652197\pi$
$678$	−7.22474	+	12.5136i	−0.277465	+	0.480583i
$679$	23.3712	+	40.4801i	0.896903	+	1.55348i
$680$	3.22474	−	5.58542i	0.123663	−	0.214191i
$681$	1.67423	+	2.89986i	0.0641568	+	0.111123i
$682$	13.3485	+	23.1202i	0.511139	+	0.885319i
$683$	−42.2474			−1.61655			−0.808277	−	0.588803i	$-0.799600\pi$
$683$	−42.2474			−1.61655			−0.808277	+	0.588803i	$0.799600\pi$
$684$	−4.17423	−	1.25529i	−0.159606	−	0.0479974i
$685$	−12.0000			−0.458496
$686$	3.62372	+	6.27647i	0.138354	+	0.239637i
$687$	−10.3485	−	17.9241i	−0.394819	−	0.683846i
$688$	−3.89898	+	6.75323i	−0.148647	+	0.257465i
$689$	−6.24745	−	10.8209i	−0.238009	−	0.412243i
$690$	1.94949	−	3.37662i	0.0742158	−	0.128546i
$691$	−26.5505			−1.01003			−0.505015	−	0.863111i	$-0.668513\pi$
$691$	−26.5505			−1.01003			−0.505015	+	0.863111i	$0.668513\pi$
$692$	−9.44949			−0.359216
$693$	5.17423	−	8.96204i	0.196553	−	0.340440i
$694$	3.89898	−	6.75323i	0.148003	−	0.256349i
$695$	14.6969			0.557487
$696$	5.34847			0.202733
$697$	−33.3712	+	57.8006i	−1.26402	+	2.18935i
$698$	−12.0227	−	20.8239i	−0.455066	−	0.788198i
$699$	−4.10102	+	7.10318i	−0.155115	+	0.268667i
$700$	−1.72474	−	2.98735i	−0.0651892	−	0.112911i
$701$	−11.8990	−	20.6096i	−0.449418	−	0.778415i	0.548930	−	0.835868i	$-0.315035\pi$
$701$	−11.8990	−	20.6096i	−0.449418	−	0.778415i	−0.998348	+	0.0574531i	$0.981702\pi$
$702$	4.89898			0.184900
$703$	−0.320663	+	0.301783i	−0.0120940	+	0.0113820i
$704$	−3.00000			−0.113067
$705$	−5.44949	−	9.43879i	−0.205240	−	0.355486i
$706$	10.3258	+	17.8848i	0.388615	+	0.673101i
$707$	18.7980	−	32.5590i	0.706970	−	1.22451i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	4.47219	−	7.74607i	0.167957	−	0.290910i	−0.769745	−	0.638352i	$-0.779616\pi$
$709$	4.47219	−	7.74607i	0.167957	−	0.290910i	0.937701	+	0.347442i	$0.112950\pi$
$710$	11.3485			0.425900
$711$	−2.89898			−0.108720
$712$	0.275255	−	0.476756i	0.0103156	−	0.0178672i
$713$	−17.3485	+	30.0484i	−0.649705	+	1.12532i
$714$	22.2474			0.832590
$715$	14.6969			0.549634
$716$	0.601021	−	1.04100i	0.0224612	−	0.0389039i
$717$	−5.10102	−	8.83523i	−0.190501	−	0.329958i
$718$	−10.7753	+	18.6633i	−0.402129	+	0.696508i
$719$	2.65153	+	4.59259i	0.0988854	+	0.171275i	0.911224	−	0.411912i	$-0.135139\pi$
$719$	2.65153	+	4.59259i	0.0988854	+	0.171275i	−0.812338	+	0.583187i	$0.801806\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	−45.6969			−1.70184
$722$	−17.0000	+	8.48528i	−0.632674	+	0.315789i
$723$	22.6969			0.844108
$724$	8.57321	+	14.8492i	0.318621	+	0.551868i
$725$	2.67423	+	4.63191i	0.0993186	+	0.172025i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−13.8990	−	24.0737i	−0.515485	−	0.892846i	−0.999838	−	0.0179734i	$-0.994279\pi$
$727$	−13.8990	−	24.0737i	−0.515485	−	0.892846i	0.484354	−	0.874872i	$-0.339055\pi$
$728$	8.44949	−	14.6349i	0.313159	−	0.542407i
$729$	1.00000			0.0370370
$730$	5.55051			0.205434
$731$	25.1464	−	43.5549i	0.930074	−	1.61094i
$732$	3.77526	−	6.53893i	0.139537	−	0.241686i
$733$	36.5959			1.35170			0.675851	−	0.737039i	$-0.263776\pi$
$733$	36.5959			1.35170			0.675851	+	0.737039i	$0.263776\pi$
$734$	11.1010			0.409746
$735$	2.44949	−	4.24264i	0.0903508	−	0.156492i
$736$	−1.94949	−	3.37662i	−0.0718591	−	0.124464i
$737$	11.0227	−	19.0919i	0.406027	−	0.703259i
$738$	5.17423	+	8.96204i	0.190466	+	0.329897i
$739$	7.97219	+	13.8082i	0.293262	+	0.507944i	0.974579	−	0.224044i	$-0.0719259\pi$
$739$	7.97219	+	13.8082i	0.293262	+	0.507944i	−0.681317	+	0.731988i	$0.738593\pi$
$740$	−0.101021			−0.00371359
$741$	15.5505	−	14.6349i	0.571262	−	0.537628i
$742$	−8.79796			−0.322983
$743$	−4.84847	−	8.39780i	−0.177873	−	0.308085i	0.763279	−	0.646069i	$-0.223588\pi$
$743$	−4.84847	−	8.39780i	−0.177873	−	0.308085i	−0.941152	+	0.337984i	$0.890255\pi$
$744$	4.44949	+	7.70674i	0.163126	+	0.282543i
$745$	−9.22474	+	15.9777i	−0.337969	+	0.585379i
$746$	−2.94949	−	5.10867i	−0.107988	−	0.187042i
$747$	3.89898	−	6.75323i	0.142656	−	0.247088i
$748$	19.3485			0.707450
$749$	−59.8434			−2.18663
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−26.4949	+	45.8905i	−0.966813	+	1.67457i	−0.262148	+	0.965028i	$0.584431\pi$
$751$	−26.4949	+	45.8905i	−0.966813	+	1.67457i	−0.704664	+	0.709541i	$0.748902\pi$
$752$	−10.8990			−0.397445
$753$	21.7980			0.794362
$754$	−13.1010	+	22.6916i	−0.477111	+	0.826381i
$755$	9.67423	+	16.7563i	0.352081	+	0.609823i
$756$	1.72474	−	2.98735i	0.0627284	−	0.108649i
$757$	−27.1969	−	47.1065i	−0.988490	−	1.71211i	−0.625265	−	0.780412i	$-0.715009\pi$
$757$	−27.1969	−	47.1065i	−0.988490	−	1.71211i	−0.363224	−	0.931702i	$-0.618324\pi$
$758$	−11.3485	−	19.6561i	−0.412195	−	0.713943i
$759$	11.6969			0.424572
$760$	−4.17423	−	1.25529i	−0.151415	−	0.0455343i
$761$	16.5505			0.599956			0.299978	−	0.953946i	$-0.403021\pi$
$761$	16.5505			0.599956			0.299978	+	0.953946i	$0.403021\pi$
$762$	7.17423	+	12.4261i	0.259895	+	0.450152i
$763$	23.0227	+	39.8765i	0.833478	+	1.44363i
$764$	−7.89898	+	13.6814i	−0.285775	+	0.494977i
$765$	3.22474	+	5.58542i	0.116591	+	0.201941i
$766$	9.24745	−	16.0171i	0.334124	−	0.578720i
$767$	29.3939			1.06135
$768$	−1.00000			−0.0360844
$769$	7.10102	−	12.2993i	0.256069	−	0.443525i	−0.709116	−	0.705092i	$-0.750906\pi$
$769$	7.10102	−	12.2993i	0.256069	−	0.443525i	0.965185	+	0.261567i	$0.0842391\pi$
$770$	5.17423	−	8.96204i	0.186466	−	0.322969i
$771$	3.79796			0.136780
$772$	−6.65153			−0.239394
$773$	0.477296	−	0.826701i	0.0171671	−	0.0297344i	−0.857314	−	0.514794i	$-0.827869\pi$
$773$	0.477296	−	0.826701i	0.0171671	−	0.0297344i	0.874481	+	0.485059i	$0.161202\pi$
$774$	−3.89898	−	6.75323i	−0.140146	−	0.242740i
$775$	−4.44949	+	7.70674i	−0.159830	+	0.276834i
$776$	6.77526	+	11.7351i	0.243217	+	0.421265i
$777$	−0.174235	−	0.301783i	−0.00625063	−	0.0108264i
$778$	11.1464			0.399619
$779$	43.1969	+	12.9904i	1.54769	+	0.465429i
$780$	4.89898			0.175412
$781$	17.0227	+	29.4842i	0.609120	+	1.05503i
$782$	12.5732	+	21.7774i	0.449617	+	0.778760i
$783$	−2.67423	+	4.63191i	−0.0955693	+	0.165531i
$784$	−2.44949	−	4.24264i	−0.0874818	−	0.151523i
$785$	−0.601021	+	1.04100i	−0.0214513	+	0.0371548i
$786$	3.00000			0.107006
$787$	−24.0454			−0.857126			−0.428563	−	0.903512i	$-0.640980\pi$
$787$	−24.0454			−0.857126			−0.428563	+	0.903512i	$0.640980\pi$
$788$	−5.72474	+	9.91555i	−0.203936	+	0.353227i
$789$	9.94949	−	17.2330i	0.354211	−	0.613512i
$790$	−2.89898			−0.103141
$791$	−49.8434			−1.77223
$792$	1.50000	−	2.59808i	0.0533002	−	0.0923186i
$793$	18.4949	+	32.0341i	0.656773	+	1.13756i
$794$	18.7474	−	32.4715i	0.665322	−	1.15237i
$795$	−1.27526	−	2.20881i	−0.0452286	−	0.0783383i
$796$	−0.775255	−	1.34278i	−0.0274782	−	0.0475936i
$797$	1.65153			0.0585002			0.0292501	−	0.999572i	$-0.490688\pi$
$797$	1.65153			0.0585002			0.0292501	+	0.999572i	$0.490688\pi$
$798$	−3.44949	−	14.6349i	−0.122111	−	0.518071i
$799$	70.2929			2.48678
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	0.275255	+	0.476756i	0.00972566	+	0.0168453i
$802$	−7.89898	+	13.6814i	−0.278923	+	0.483108i
$803$	8.32577	+	14.4206i	0.293810	+	0.508894i
$804$	3.67423	−	6.36396i	0.129580	−	0.224440i
$805$	13.4495			0.474032
$806$	−43.5959			−1.53560
$807$	0.123724	−	0.214297i	0.00435530	−	0.00754361i
$808$	5.44949	−	9.43879i	0.191712	−	0.332056i
$809$	−28.4949			−1.00183			−0.500914	−	0.865497i	$-0.667003\pi$
$809$	−28.4949			−1.00183			−0.500914	+	0.865497i	$0.667003\pi$
$810$	1.00000			0.0351364
$811$	21.4217	−	37.1034i	0.752217	−	1.30288i	−0.194529	−	0.980897i	$-0.562318\pi$
$811$	21.4217	−	37.1034i	0.752217	−	1.30288i	0.946746	−	0.321981i	$-0.104349\pi$
$812$	9.22474	+	15.9777i	0.323725	+	0.560708i
$813$	−2.55051	+	4.41761i	−0.0894503	+	0.154932i
$814$	−0.151531	−	0.262459i	−0.00531115	−	0.00919918i
$815$	6.34847	+	10.9959i	0.222377	+	0.385169i
$816$	6.44949			0.225777
$817$	−32.5505	−	9.78874i	−1.13880	−	0.342465i
$818$	39.4949			1.38091
$819$	8.44949	+	14.6349i	0.295249	+	0.511386i
$820$	5.17423	+	8.96204i	0.180692	+	0.312968i
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$	−6.00000	−	10.3923i	−0.209274	−	0.362473i
$823$	18.0732	−	31.3037i	0.629993	−	1.09118i	−0.357560	−	0.933890i	$-0.616391\pi$
$823$	18.0732	−	31.3037i	0.629993	−	1.09118i	0.987553	−	0.157289i	$-0.0502754\pi$
$824$	−13.2474			−0.461497
$825$	3.00000			0.104447
$826$	10.3485	−	17.9241i	0.360069	−	0.623658i
$827$	−6.57321	+	11.3851i	−0.228573	+	0.395900i	−0.957385	−	0.288813i	$-0.906739\pi$
$827$	−6.57321	+	11.3851i	−0.228573	+	0.395900i	0.728812	+	0.684713i	$0.240073\pi$
$828$	3.89898			0.135499
$829$	32.8990			1.14263			0.571314	−	0.820731i	$-0.306434\pi$
$829$	32.8990			1.14263			0.571314	+	0.820731i	$0.306434\pi$
$830$	3.89898	−	6.75323i	0.135336	−	0.234408i
$831$	−1.55051	−	2.68556i	−0.0537866	−	0.0931611i
$832$	2.44949	−	4.24264i	0.0849208	−	0.147087i
$833$	15.7980	+	27.3629i	0.547367	+	0.948067i
$834$	7.34847	+	12.7279i	0.254457	+	0.440732i
$835$	19.6969			0.681641
$836$	−3.00000	−	12.7279i	−0.103757	−	0.440204i
$837$	−8.89898			−0.307594
$838$	−6.05051	−	10.4798i	−0.209011	−	0.362018i
$839$	−2.75255	−	4.76756i	−0.0950286	−	0.164594i	0.814592	−	0.580034i	$-0.196961\pi$
$839$	−2.75255	−	4.76756i	−0.0950286	−	0.164594i	−0.909621	+	0.415440i	$0.863628\pi$
$840$	1.72474	−	2.98735i	0.0595094	−	0.103073i
$841$	0.196938	+	0.341107i	0.00679098	+	0.0117623i
$842$	16.6742	−	28.8806i	0.574632	−	0.995292i
$843$	0.348469			0.0120019
$844$	−11.6515			−0.401062
$845$	−5.50000	+	9.52628i	−0.189206	+	0.327714i
$846$	5.44949	−	9.43879i	0.187357	−	0.324512i
$847$	−6.89898			−0.237052
$848$	−2.55051			−0.0875849
$849$	8.34847	−	14.4600i	0.286519	−	0.496265i
$850$	3.22474	+	5.58542i	0.110608	+	0.191578i
$851$	0.196938	−	0.341107i	0.00675096	−	0.0116930i
$852$	5.67423	+	9.82806i	0.194396	+	0.336704i
$853$	−21.6969	−	37.5802i	−0.742889	−	1.28672i	−0.951175	−	0.308653i	$-0.900122\pi$
$853$	−21.6969	−	37.5802i	−0.742889	−	1.28672i	0.208286	−	0.978068i	$-0.433212\pi$
$854$	26.0454			0.891256
$855$	3.17423	−	2.98735i	0.108557	−	0.102165i
$856$	−17.3485			−0.592958
$857$	2.20204	+	3.81405i	0.0752203	+	0.130285i	0.901182	−	0.433441i	$-0.142701\pi$
$857$	2.20204	+	3.81405i	0.0752203	+	0.130285i	−0.825962	+	0.563726i	$0.809367\pi$
$858$	7.34847	+	12.7279i	0.250873	+	0.434524i
$859$	5.52270	−	9.56560i	0.188432	−	0.326374i	−0.756295	−	0.654230i	$-0.772993\pi$
$859$	5.52270	−	9.56560i	0.188432	−	0.326374i	0.944728	+	0.327856i	$0.106326\pi$
$860$	−3.89898	−	6.75323i	−0.132954	−	0.230283i
$861$	−17.8485	+	30.9145i	−0.608274	+	1.05356i
$862$	25.3485			0.863372
$863$	29.0000			0.987171			0.493586	−	0.869697i	$-0.335686\pi$
$863$	29.0000			0.987171			0.493586	+	0.869697i	$0.335686\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	4.72474	−	8.18350i	0.160646	−	0.278247i
$866$	−11.3485			−0.385637
$867$	−24.5959			−0.835321
$868$	−15.3485	+	26.5843i	−0.520961	+	0.902331i
$869$	−4.34847	−	7.53177i	−0.147512	−	0.255498i
$870$	−2.67423	+	4.63191i	−0.0906650	+	0.157036i
$871$	18.0000	+	31.1769i	0.609907	+	1.05639i
$872$	6.67423	+	11.5601i	0.226018	+	0.391475i
$873$	−13.5505			−0.458615
$874$	12.3763	−	11.6476i	0.418634	−	0.393986i
$875$	3.44949			0.116614
$876$	2.77526	+	4.80688i	0.0937672	+	0.162410i
$877$	7.74745	+	13.4190i	0.261613	+	0.453127i	0.966671	−	0.256023i	$-0.0824123\pi$
$877$	7.74745	+	13.4190i	0.261613	+	0.453127i	−0.705058	+	0.709150i	$0.749079\pi$
$878$	5.67423	−	9.82806i	0.191496	−	0.331681i
$879$	−3.27526	−	5.67291i	−0.110472	−	0.191342i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	−7.04541			−0.237366			−0.118683	−	0.992932i	$-0.537867\pi$
$881$	−7.04541			−0.237366			−0.118683	+	0.992932i	$0.537867\pi$
$882$	4.89898			0.164957
$883$	3.47219	−	6.01402i	0.116849	−	0.202388i	−0.801669	−	0.597769i	$-0.796054\pi$
$883$	3.47219	−	6.01402i	0.116849	−	0.202388i	0.918517	+	0.395381i	$0.129387\pi$
$884$	−15.7980	+	27.3629i	−0.531343	+	0.920313i
$885$	6.00000			0.201688
$886$	26.2474			0.881800
$887$	12.1010	−	20.9596i	0.406313	−	0.703754i	−0.588161	−	0.808744i	$-0.700148\pi$
$887$	12.1010	−	20.9596i	0.406313	−	0.703754i	0.994473	+	0.104990i	$0.0334811\pi$
$888$	−0.0505103	−	0.0874863i	−0.00169501	−	0.00293585i
$889$	−24.7474	+	42.8638i	−0.830003	+	1.43761i
$890$	0.275255	+	0.476756i	0.00922657	+	0.0159809i
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	1.44949			0.0485325
$893$	−10.8990	−	46.2405i	−0.364720	−	1.54738i
$894$	−18.4495			−0.617043
$895$	0.601021	+	1.04100i	0.0200899	+	0.0347967i
$896$	−1.72474	−	2.98735i	−0.0576197	−	0.0998002i
$897$	−9.55051	+	16.5420i	−0.318882	+	0.552320i
$898$	−16.6237	−	28.7931i	−0.554741	−	0.960839i
$899$	23.7980	−	41.2193i	0.793706	−	1.37474i
$900$	1.00000			0.0333333
$901$	16.4495			0.548012
$902$	−15.5227	+	26.8861i	−0.516850	+	0.895210i
$903$	13.4495	−	23.2952i	0.447571	−	0.775216i
$904$	−14.4495			−0.480583
$905$	−17.1464			−0.569967
$906$	−9.67423	+	16.7563i	−0.321405	+	0.556690i
$907$	−0.797959	−	1.38211i	−0.0264958	−	0.0458921i	0.852473	−	0.522770i	$-0.175102\pi$
$907$	−0.797959	−	1.38211i	−0.0264958	−	0.0458921i	−0.878969	+	0.476878i	$0.841768\pi$
$908$	−1.67423	+	2.89986i	−0.0555614	+	0.0962352i
$909$	5.44949	+	9.43879i	0.180748	+	0.313065i
$910$	8.44949	+	14.6349i	0.280098	+	0.485144i
$911$	34.0908			1.12948			0.564740	−	0.825269i	$-0.308977\pi$
$911$	34.0908			1.12948			0.564740	+	0.825269i	$0.308977\pi$
$912$	−1.00000	−	4.24264i	−0.0331133	−	0.140488i
$913$	23.3939			0.774224
$914$	−16.0227	−	27.7521i	−0.529984	−	0.917959i
$915$	3.77526	+	6.53893i	0.124806	+	0.216170i
$916$	10.3485	−	17.9241i	0.341923	−	0.592228i
$917$	5.17423	+	8.96204i	0.170868	+	0.295953i
$918$	−3.22474	+	5.58542i	−0.106432	+	0.184346i
$919$	−20.4495			−0.674566			−0.337283	−	0.941403i	$-0.609508\pi$
$919$	−20.4495			−0.674566			−0.337283	+	0.941403i	$0.609508\pi$
$920$	3.89898			0.128546
$921$	7.12372	−	12.3387i	0.234735	−	0.406572i
$922$	4.10102	−	7.10318i	0.135060	−	0.233931i
$923$	−55.5959			−1.82996
$924$	10.3485			0.340440
$925$	0.0505103	−	0.0874863i	0.00166077	−	0.00287653i
$926$	15.1742	+	26.2825i	0.498656	+	0.863698i
$927$	6.62372	−	11.4726i	0.217552	−	0.376811i
$928$	2.67423	+	4.63191i	0.0877861	+	0.152050i
$929$	−19.7247	−	34.1643i	−0.647148	−	1.12089i	−0.983801	−	0.179264i	$-0.942628\pi$
$929$	−19.7247	−	34.1643i	−0.647148	−	1.12089i	0.336653	−	0.941629i	$-0.390705\pi$
$930$	−8.89898			−0.291809
$931$	15.5505	−	14.6349i	0.509647	−	0.479641i
$932$	−8.20204			−0.268667
$933$	4.89898	+	8.48528i	0.160385	+	0.277796i
$934$	7.87628	+	13.6421i	0.257720	+	0.446383i
$935$	−9.67423	+	16.7563i	−0.316381	+	0.547988i
$936$	2.44949	+	4.24264i	0.0800641	+	0.138675i
$937$	−9.02270	+	15.6278i	−0.294759	+	0.510537i	−0.974929	−	0.222517i	$-0.928573\pi$
$937$	−9.02270	+	15.6278i	−0.294759	+	0.510537i	0.680170	+	0.733055i	$0.261906\pi$
$938$	25.3485			0.827657
$939$	7.59592			0.247883
$940$	5.44949	−	9.43879i	0.177743	−	0.307859i
$941$	10.2247	−	17.7098i	0.333317	−	0.577322i	−0.649843	−	0.760069i	$-0.725165\pi$
$941$	10.2247	−	17.7098i	0.333317	−	0.577322i	0.983160	+	0.182746i	$0.0584987\pi$
$942$	−1.20204			−0.0391646
$943$	−40.3485			−1.31393
$944$	3.00000	−	5.19615i	0.0976417	−	0.169120i
$945$	1.72474	+	2.98735i	0.0561060	+	0.0971784i
$946$	11.6969	−	20.2597i	0.380300	−	0.658699i
$947$	9.77526	+	16.9312i	0.317653	+	0.550191i	0.979998	−	0.199008i	$-0.0637719\pi$
$947$	9.77526	+	16.9312i	0.317653	+	0.550191i	−0.662345	+	0.749199i	$0.730439\pi$
$948$	−1.44949	−	2.51059i	−0.0470772	−	0.0815402i
$949$	−27.1918			−0.882684
$950$	3.17423	−	2.98735i	0.102986	−	0.0969223i
$951$	−4.55051			−0.147560
$952$	11.1237	+	19.2669i	0.360522	+	0.624442i
$953$	−8.69694	−	15.0635i	−0.281721	−	0.487956i	0.690087	−	0.723726i	$-0.257572\pi$
$953$	−8.69694	−	15.0635i	−0.281721	−	0.487956i	−0.971809	+	0.235770i	$0.924239\pi$
$954$	1.27526	−	2.20881i	0.0412879	−	0.0715128i
$955$	−7.89898	−	13.6814i	−0.255605	−	0.442721i
$956$	5.10102	−	8.83523i	0.164979	−	0.285752i
$957$	−16.0454			−0.518674
$958$	−34.0454			−1.09996
$959$	20.6969	−	35.8481i	0.668339	−	1.15760i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	48.1918			1.55458
$962$	0.494897			0.0159561
$963$	8.67423	−	15.0242i	0.279523	−	0.484149i
$964$	11.3485	+	19.6561i	0.365510	+	0.633081i
$965$	3.32577	−	5.76039i	0.107060	−	0.185434i
$966$	6.72474	+	11.6476i	0.216365	+	0.374755i
$967$	−1.55051	−	2.68556i	−0.0498610	−	0.0863619i	0.840018	−	0.542559i	$-0.182545\pi$
$967$	−1.55051	−	2.68556i	−0.0498610	−	0.0863619i	−0.889879	+	0.456197i	$0.849211\pi$
$968$	−2.00000			−0.0642824
$969$	6.44949	+	27.3629i	0.207187	+	0.879022i
$970$	−13.5505			−0.435081
$971$	−16.3485	−	28.3164i	−0.524647	−	0.908716i	−0.999588	−	0.0286981i	$-0.990864\pi$
$971$	−16.3485	−	28.3164i	−0.524647	−	0.908716i	0.474941	−	0.880018i	$-0.342469\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−25.3485	+	43.9048i	−0.812635	+	1.40752i
$974$	−3.07321	−	5.32296i	−0.0984721	−	0.170559i
$975$	−2.44949	+	4.24264i	−0.0784465	+	0.135873i
$976$	7.55051			0.241686
$977$	44.9444			1.43790			0.718949	−	0.695063i	$-0.244623\pi$
$977$	44.9444			1.43790			0.718949	+	0.695063i	$0.244623\pi$
$978$	−6.34847	+	10.9959i	−0.203002	+	0.351609i
$979$	−0.825765	+	1.43027i	−0.0263916	+	0.0457116i
$980$	4.89898			0.156492
$981$	−13.3485			−0.426184
$982$	17.3990	−	30.1359i	0.555224	−	0.961676i
$983$	−27.0959	−	46.9315i	−0.864226	−	1.49688i	−0.867814	−	0.496889i	$-0.834476\pi$
$983$	−27.0959	−	46.9315i	−0.864226	−	1.49688i	0.00358852	−	0.999994i	$-0.498858\pi$
$984$	−5.17423	+	8.96204i	−0.164949	+	0.285699i
$985$	−5.72474	−	9.91555i	−0.182406	−	0.315936i
$986$	−17.2474	−	29.8735i	−0.549271	−	0.951365i
$987$	37.5959			1.19669
$988$	20.4495	+	6.14966i	0.650585	+	0.195647i
$989$	30.4041			0.966794
$990$	1.50000	+	2.59808i	0.0476731	+	0.0825723i
$991$	−3.32577	−	5.76039i	−0.105646	−	0.182985i	0.808356	−	0.588694i	$-0.200358\pi$
$991$	−3.32577	−	5.76039i	−0.105646	−	0.182985i	−0.914002	+	0.405709i	$0.867025\pi$
$992$	−4.44949	+	7.70674i	−0.141271	+	0.244689i
$993$	1.82577	+	3.16232i	0.0579389	+	0.100353i
$994$	−19.5732	+	33.9018i	−0.620825	+	1.07530i
$995$	1.55051			0.0491545
$996$	7.79796			0.247088
$997$	7.29796	−	12.6404i	0.231129	−	0.400327i	−0.727012	−	0.686625i	$-0.759091\pi$
$997$	7.29796	−	12.6404i	0.231129	−	0.400327i	0.958141	+	0.286298i	$0.0924248\pi$
$998$	−7.72474	+	13.3797i	−0.244523	+	0.423525i
$999$	0.101021			0.00319615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.f.121.2	✓	4
3.2	odd	2		1710.2.l.n.1261.2		4
19.11	even	3	inner	570.2.i.f.391.2	yes	4
57.11	odd	6		1710.2.l.n.1531.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.f.121.2	✓	4	1.1	even	1	trivial
570.2.i.f.391.2	yes	4	19.11	even	3	inner
1710.2.l.n.1261.2		4	3.2	odd	2
1710.2.l.n.1531.2		4	57.11	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.72474 - 2.98735i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.22474 + 5.58542i) q^{17} +1.00000 q^{18} +(3.17423 - 2.98735i) q^{19} +1.00000 q^{20} +(1.72474 + 2.98735i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-1.94949 + 3.37662i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.89898 q^{26} -1.00000 q^{27} +(-1.72474 + 2.98735i) q^{28} +(2.67423 - 4.63191i) q^{29} -1.00000 q^{30} +8.89898 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(3.22474 - 5.58542i) q^{34} +(-1.72474 - 2.98735i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.101021 q^{37} +(-4.17423 - 1.25529i) q^{38} +4.89898 q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.17423 + 8.96204i) q^{41} +(1.72474 - 2.98735i) q^{42} +(-3.89898 - 6.75323i) q^{43} +(1.50000 - 2.59808i) q^{44} +1.00000 q^{45} +3.89898 q^{46} +(5.44949 - 9.43879i) q^{47} +(0.500000 - 0.866025i) q^{48} +4.89898 q^{49} +1.00000 q^{50} +(-3.22474 + 5.58542i) q^{51} +(2.44949 + 4.24264i) q^{52} +(1.27526 - 2.20881i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{55} +3.44949 q^{56} +(4.17423 + 1.25529i) q^{57} -5.34847 q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.77526 + 6.53893i) q^{61} +(-4.44949 - 7.70674i) q^{62} +(-1.72474 + 2.98735i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-1.50000 + 2.59808i) q^{66} +(-3.67423 + 6.36396i) q^{67} -6.44949 q^{68} -3.89898 q^{69} +(-1.72474 + 2.98735i) q^{70} +(-5.67423 - 9.82806i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.77526 - 4.80688i) q^{73} +(0.0505103 + 0.0874863i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} -10.3485 q^{77} +(-2.44949 - 4.24264i) q^{78} +(1.44949 + 2.51059i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.17423 - 8.96204i) q^{82} -7.79796 q^{83} -3.44949 q^{84} +(3.22474 - 5.58542i) q^{85} +(-3.89898 + 6.75323i) q^{86} +5.34847 q^{87} -3.00000 q^{88} +(0.275255 - 0.476756i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(8.44949 - 14.6349i) q^{91} +(-1.94949 - 3.37662i) q^{92} +(4.44949 + 7.70674i) q^{93} -10.8990 q^{94} +(-4.17423 - 1.25529i) q^{95} -1.00000 q^{96} +(6.77526 + 11.7351i) q^{97} +(-2.44949 - 4.24264i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} - 12 q^{11} - 4 q^{12} - 2 q^{14} + 2 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 2 q^{21} + 6 q^{22} + 2 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27} - 2 q^{28} - 4 q^{29} - 4 q^{30} + 16 q^{31} - 2 q^{32} - 6 q^{33} + 8 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 4 q^{43} + 6 q^{44} + 4 q^{45} - 4 q^{46} + 12 q^{47} + 2 q^{48} + 4 q^{50} - 8 q^{51} + 10 q^{53} + 2 q^{54} + 6 q^{55} + 4 q^{56} + 2 q^{57} + 8 q^{58} + 12 q^{59} + 2 q^{60} - 20 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} - 6 q^{66} - 16 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - 2 q^{72} - 16 q^{73} + 10 q^{74} - 4 q^{75} + 4 q^{76} - 12 q^{77} - 4 q^{79} - 2 q^{80} - 2 q^{81} + 6 q^{82} + 8 q^{83} - 4 q^{84} + 8 q^{85} + 4 q^{86} - 8 q^{87} - 12 q^{88} + 6 q^{89} - 2 q^{90} + 24 q^{91} + 2 q^{92} + 8 q^{93} - 24 q^{94} - 2 q^{95} - 4 q^{96} + 32 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 - 12 * q^11 - 4 * q^12 - 2 * q^14 + 2 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 2 * q^21 + 6 * q^22 + 2 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 - 2 * q^28 - 4 * q^29 - 4 * q^30 + 16 * q^31 - 2 * q^32 - 6 * q^33 + 8 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^46 + 12 * q^47 + 2 * q^48 + 4 * q^50 - 8 * q^51 + 10 * q^53 + 2 * q^54 + 6 * q^55 + 4 * q^56 + 2 * q^57 + 8 * q^58 + 12 * q^59 + 2 * q^60 - 20 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 - 6 * q^66 - 16 * q^68 + 4 * q^69 - 2 * q^70 - 8 * q^71 - 2 * q^72 - 16 * q^73 + 10 * q^74 - 4 * q^75 + 4 * q^76 - 12 * q^77 - 4 * q^79 - 2 * q^80 - 2 * q^81 + 6 * q^82 + 8 * q^83 - 4 * q^84 + 8 * q^85 + 4 * q^86 - 8 * q^87 - 12 * q^88 + 6 * q^89 - 2 * q^90 + 24 * q^91 + 2 * q^92 + 8 * q^93 - 24 * q^94 - 2 * q^95 - 4 * q^96 + 32 * q^97 + 6 * q^99

Introduction

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