LMFDB - Embedded newform 570.2.i.f.391.1

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			391.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	570.391
Dual form			570.2.i.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} -1.44949 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} +(0.724745 - 1.25529i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.775255 - 1.34278i) q^{17} +1.00000 q^{18} +(-4.17423 - 1.25529i) q^{19} +1.00000 q^{20} +(-0.724745 + 1.25529i) q^{21} +(1.50000 - 2.59808i) q^{22} +(2.94949 + 5.10867i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.89898 q^{26} -1.00000 q^{27} +(0.724745 + 1.25529i) q^{28} +(-4.67423 - 8.09601i) q^{29} -1.00000 q^{30} -0.898979 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(0.775255 + 1.34278i) q^{34} +(0.724745 - 1.25529i) q^{35} +(-0.500000 + 0.866025i) q^{36} -9.89898 q^{37} +(3.17423 - 2.98735i) q^{38} -4.89898 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.17423 + 3.76588i) q^{41} +(-0.724745 - 1.25529i) q^{42} +(5.89898 - 10.2173i) q^{43} +(1.50000 + 2.59808i) q^{44} +1.00000 q^{45} -5.89898 q^{46} +(0.550510 + 0.953512i) q^{47} +(0.500000 + 0.866025i) q^{48} -4.89898 q^{49} +1.00000 q^{50} +(-0.775255 - 1.34278i) q^{51} +(-2.44949 + 4.24264i) q^{52} +(3.72474 + 6.45145i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} -1.44949 q^{56} +(-3.17423 + 2.98735i) q^{57} +9.34847 q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-6.22474 - 10.7816i) q^{61} +(0.449490 - 0.778539i) q^{62} +(0.724745 + 1.25529i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.67423 + 6.36396i) q^{67} -1.55051 q^{68} +5.89898 q^{69} +(0.724745 + 1.25529i) q^{70} +(1.67423 - 2.89986i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.22474 + 9.04952i) q^{73} +(4.94949 - 8.57277i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} +4.34847 q^{77} +(2.44949 - 4.24264i) q^{78} +(-3.44949 + 5.97469i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.17423 - 3.76588i) q^{82} +11.7980 q^{83} +1.44949 q^{84} +(0.775255 + 1.34278i) q^{85} +(5.89898 + 10.2173i) q^{86} -9.34847 q^{87} -3.00000 q^{88} +(2.72474 + 4.71940i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(3.55051 + 6.14966i) q^{91} +(2.94949 - 5.10867i) q^{92} +(-0.449490 + 0.778539i) q^{93} -1.10102 q^{94} +(3.17423 - 2.98735i) q^{95} -1.00000 q^{96} +(9.22474 - 15.9777i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$7$	−1.44949			−0.547856			−0.273928	−	0.961750i	$-0.588323\pi$
$7$	−1.44949			−0.547856			−0.273928	+	0.961750i	$0.588323\pi$
$8$	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	−0.975172	−	0.221449i	$-0.928921\pi$
$13$	−2.44949	−	4.24264i	−0.679366	−	1.17670i	0.295806	−	0.955248i	$-0.404412\pi$
$14$	0.724745	−	1.25529i	0.193696	−	0.335492i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.775255	−	1.34278i	0.188027	−	0.325672i	−0.756565	−	0.653918i	$-0.773124\pi$
$17$	0.775255	−	1.34278i	0.188027	−	0.325672i	0.944592	+	0.328246i	$0.106457\pi$
$18$	1.00000			0.235702
$19$	−4.17423	−	1.25529i	−0.957635	−	0.287984i
$19$	−4.17423	−	1.25529i	−0.957635	−	0.287984i
$20$	1.00000			0.223607
$21$	−0.724745	+	1.25529i	−0.158152	+	0.273928i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	2.94949	+	5.10867i	0.615011	+	1.06523i	0.990383	+	0.138356i	$0.0441818\pi$
$23$	2.94949	+	5.10867i	0.615011	+	1.06523i	−0.375371	+	0.926874i	$0.622485\pi$
$24$	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
$28$	0.724745	+	1.25529i	0.136964	+	0.237228i
$29$	−4.67423	−	8.09601i	−0.867984	−	1.50339i	−0.864054	−	0.503399i	$-0.832082\pi$
$29$	−4.67423	−	8.09601i	−0.867984	−	1.50339i	−0.00392972	−	0.999992i	$-0.501251\pi$
$30$	−1.00000			−0.182574
$31$	−0.898979			−0.161461			−0.0807307	−	0.996736i	$-0.525725\pi$
$31$	−0.898979			−0.161461			−0.0807307	+	0.996736i	$0.525725\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	0.775255	+	1.34278i	0.132955	+	0.230285i
$35$	0.724745	−	1.25529i	0.122504	−	0.212184i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−9.89898			−1.62738			−0.813691	−	0.581298i	$-0.802545\pi$
$37$	−9.89898			−1.62738			−0.813691	+	0.581298i	$0.802545\pi$
$38$	3.17423	−	2.98735i	0.514929	−	0.484611i
$39$	−4.89898			−0.784465
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.17423	+	3.76588i	−0.339558	+	0.588132i	−0.984350	−	0.176226i	$-0.943611\pi$
$41$	−2.17423	+	3.76588i	−0.339558	+	0.588132i	0.644791	+	0.764359i	$0.276944\pi$
$42$	−0.724745	−	1.25529i	−0.111831	−	0.193696i
$43$	5.89898	−	10.2173i	0.899586	−	1.55813i	0.0715617	−	0.997436i	$-0.477202\pi$
$43$	5.89898	−	10.2173i	0.899586	−	1.55813i	0.828024	−	0.560692i	$-0.189465\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	1.00000			0.149071
$46$	−5.89898			−0.869757
$47$	0.550510	+	0.953512i	0.0803002	+	0.139084i	0.903379	−	0.428843i	$-0.141079\pi$
$47$	0.550510	+	0.953512i	0.0803002	+	0.139084i	−0.823079	+	0.567927i	$0.807745\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−4.89898			−0.699854
$50$	1.00000			0.141421
$51$	−0.775255	−	1.34278i	−0.108557	−	0.188027i
$52$	−2.44949	+	4.24264i	−0.339683	+	0.588348i
$53$	3.72474	+	6.45145i	0.511633	+	0.886174i	0.999909	+	0.0134852i	$0.00429260\pi$
$53$	3.72474	+	6.45145i	0.511633	+	0.886174i	−0.488276	+	0.872689i	$0.662374\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	−1.44949			−0.193696
$57$	−3.17423	+	2.98735i	−0.420438	+	0.395684i
$58$	9.34847			1.22751
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−6.22474	−	10.7816i	−0.796997	−	1.38044i	−0.921563	−	0.388228i	$-0.873087\pi$
$61$	−6.22474	−	10.7816i	−0.796997	−	1.38044i	0.124566	−	0.992211i	$-0.460246\pi$
$62$	0.449490	−	0.778539i	0.0570853	−	0.0988746i
$63$	0.724745	+	1.25529i	0.0913093	+	0.158152i
$64$	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	$-0.0184900\pi$
$67$	3.67423	+	6.36396i	0.448879	+	0.777482i	−0.549434	+	0.835537i	$0.685157\pi$
$68$	−1.55051			−0.188027
$69$	5.89898			0.710154
$70$	0.724745	+	1.25529i	0.0866236	+	0.150036i
$71$	1.67423	−	2.89986i	0.198695	−	0.344150i	−0.749410	−	0.662106i	$-0.769663\pi$
$71$	1.67423	−	2.89986i	0.198695	−	0.344150i	0.948106	+	0.317956i	$0.102996\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−5.22474	+	9.04952i	−0.611510	+	1.05917i	0.379476	+	0.925202i	$0.376104\pi$
$73$	−5.22474	+	9.04952i	−0.611510	+	1.05917i	−0.990986	+	0.133965i	$0.957229\pi$
$74$	4.94949	−	8.57277i	0.575366	−	0.996564i
$75$	−1.00000			−0.115470
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	4.34847			0.495554
$78$	2.44949	−	4.24264i	0.277350	−	0.480384i
$79$	−3.44949	+	5.97469i	−0.388098	+	0.672205i	−0.992194	−	0.124706i	$-0.960201\pi$
$79$	−3.44949	+	5.97469i	−0.388098	+	0.672205i	0.604096	+	0.796912i	$0.293534\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.17423	−	3.76588i	−0.240104	−	0.415872i
$83$	11.7980			1.29499			0.647497	−	0.762068i	$-0.275816\pi$
$83$	11.7980			1.29499			0.647497	+	0.762068i	$0.275816\pi$
$84$	1.44949			0.158152
$85$	0.775255	+	1.34278i	0.0840882	+	0.145645i
$86$	5.89898	+	10.2173i	0.636103	+	1.10176i
$87$	−9.34847			−1.00226
$88$	−3.00000			−0.319801
$89$	2.72474	+	4.71940i	0.288822	+	0.500255i	0.973529	−	0.228564i	$-0.0734030\pi$
$89$	2.72474	+	4.71940i	0.288822	+	0.500255i	−0.684707	+	0.728819i	$0.740070\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	3.55051	+	6.14966i	0.372195	+	0.644660i
$92$	2.94949	−	5.10867i	0.307506	−	0.532615i
$93$	−0.449490	+	0.778539i	−0.0466099	+	0.0807307i
$94$	−1.10102			−0.113562
$95$	3.17423	−	2.98735i	0.325670	−	0.306495i
$96$	−1.00000			−0.102062
$97$	9.22474	−	15.9777i	0.936631	−	1.62229i	0.164931	−	0.986305i	$-0.447260\pi$
$97$	9.22474	−	15.9777i	0.936631	−	1.62229i	0.771699	−	0.635987i	$-0.219407\pi$
$98$	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
$101$	0.550510	+	0.953512i	0.0547778	+	0.0948780i	0.892114	−	0.451810i	$-0.149222\pi$
$101$	0.550510	+	0.953512i	0.0547778	+	0.0948780i	−0.837336	+	0.546688i	$0.815888\pi$
$102$	1.55051			0.153523
$103$	11.2474			1.10824			0.554122	−	0.832435i	$-0.313054\pi$
$103$	11.2474			1.10824			0.554122	+	0.832435i	$0.313054\pi$
$104$	−2.44949	−	4.24264i	−0.240192	−	0.416025i
$105$	−0.724745	−	1.25529i	−0.0707279	−	0.122504i
$106$	−7.44949			−0.723558
$107$	−2.65153			−0.256333			−0.128167	−	0.991753i	$-0.540909\pi$
$107$	−2.65153			−0.256333			−0.128167	+	0.991753i	$0.540909\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−0.674235	+	1.16781i	−0.0645800	+	0.111856i	−0.896508	−	0.443028i	$-0.853904\pi$
$109$	−0.674235	+	1.16781i	−0.0645800	+	0.111856i	0.831928	+	0.554884i	$0.187237\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−4.94949	+	8.57277i	−0.469785	+	0.813691i
$112$	0.724745	−	1.25529i	0.0684820	−	0.118614i
$113$	−9.55051			−0.898436			−0.449218	−	0.893422i	$-0.648297\pi$
$113$	−9.55051			−0.898436			−0.449218	+	0.893422i	$0.648297\pi$
$114$	−1.00000	−	4.24264i	−0.0936586	−	0.397360i
$115$	−5.89898			−0.550083
$116$	−4.67423	+	8.09601i	−0.433992	+	0.751696i
$117$	−2.44949	+	4.24264i	−0.226455	+	0.392232i
$118$	3.00000	+	5.19615i	0.276172	+	0.478345i
$119$	−1.12372	+	1.94635i	−0.103012	+	0.178421i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−2.00000			−0.181818
$122$	12.4495			1.12712
$123$	2.17423	+	3.76588i	0.196044	+	0.339558i
$124$	0.449490	+	0.778539i	0.0403654	+	0.0699149i
$125$	1.00000			0.0894427
$126$	−1.44949			−0.129131
$127$	0.174235	+	0.301783i	0.0154608	+	0.0267789i	0.873652	−	0.486551i	$-0.161745\pi$
$127$	0.174235	+	0.301783i	0.0154608	+	0.0267789i	−0.858191	+	0.513330i	$0.828412\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.89898	−	10.2173i	−0.519376	−	0.899586i
$130$	−2.44949	+	4.24264i	−0.214834	+	0.372104i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$	3.00000			0.261116
$133$	6.05051	+	1.81954i	0.524646	+	0.157774i
$134$	−7.34847			−0.634811
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	0.775255	−	1.34278i	0.0664776	−	0.115143i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	−2.94949	+	5.10867i	−0.251077	+	0.434879i
$139$	7.34847	+	12.7279i	0.623289	+	1.07957i	0.988869	+	0.148788i	$0.0475373\pi$
$139$	7.34847	+	12.7279i	0.623289	+	1.07957i	−0.365580	+	0.930780i	$0.619129\pi$
$140$	−1.44949			−0.122504
$141$	1.10102			0.0927227
$142$	1.67423	+	2.89986i	0.140499	+	0.243351i
$143$	7.34847	+	12.7279i	0.614510	+	1.06436i
$144$	1.00000			0.0833333
$145$	9.34847			0.776348
$146$	−5.22474	−	9.04952i	−0.432403	−	0.748944i
$147$	−2.44949	+	4.24264i	−0.202031	+	0.349927i
$148$	4.94949	+	8.57277i	0.406846	+	0.704677i
$149$	−6.77526	+	11.7351i	−0.555051	+	0.961376i	0.442849	+	0.896596i	$0.353968\pi$
$149$	−6.77526	+	11.7351i	−0.555051	+	0.961376i	−0.997900	+	0.0647795i	$0.979366\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−4.65153			−0.378536			−0.189268	−	0.981925i	$-0.560612\pi$
$151$	−4.65153			−0.378536			−0.189268	+	0.981925i	$0.560612\pi$
$152$	−4.17423	−	1.25529i	−0.338575	−	0.101818i
$153$	−1.55051			−0.125351
$154$	−2.17423	+	3.76588i	−0.175205	+	0.303464i
$155$	0.449490	−	0.778539i	0.0361039	−	0.0625338i
$156$	2.44949	+	4.24264i	0.196116	+	0.339683i
$157$	−10.3990	+	18.0116i	−0.829929	+	1.43748i	0.0681644	+	0.997674i	$0.478286\pi$
$157$	−10.3990	+	18.0116i	−0.829929	+	1.43748i	−0.898093	+	0.439805i	$0.855048\pi$
$158$	−3.44949	−	5.97469i	−0.274427	−	0.475321i
$159$	7.44949			0.590783
$160$	1.00000			0.0790569
$161$	−4.27526	−	7.40496i	−0.336937	−	0.583593i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	16.6969			1.30781			0.653903	−	0.756579i	$-0.273131\pi$
$163$	16.6969			1.30781			0.653903	+	0.756579i	$0.273131\pi$
$164$	4.34847			0.339558
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	−5.89898	+	10.2173i	−0.457850	+	0.793019i
$167$	4.84847	+	8.39780i	0.375186	+	0.649841i	0.990355	−	0.138554i	$-0.0442456\pi$
$167$	4.84847	+	8.39780i	0.375186	+	0.649841i	−0.615169	+	0.788395i	$0.710912\pi$
$168$	−0.724745	+	1.25529i	−0.0559153	+	0.0968481i
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$	−1.55051			−0.118919
$171$	1.00000	+	4.24264i	0.0764719	+	0.324443i
$172$	−11.7980			−0.899586
$173$	2.27526	−	3.94086i	0.172984	−	0.299618i	−0.766477	−	0.642271i	$-0.777992\pi$
$173$	2.27526	−	3.94086i	0.172984	−	0.299618i	0.939462	+	0.342653i	$0.111326\pi$
$174$	4.67423	−	8.09601i	0.354353	−	0.613757i
$175$	0.724745	+	1.25529i	0.0547856	+	0.0948914i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−5.44949			−0.408457
$179$	−20.7980			−1.55451			−0.777256	−	0.629184i	$-0.783389\pi$
$179$	−20.7980			−1.55451			−0.777256	+	0.629184i	$0.783389\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−8.57321	−	14.8492i	−0.637242	−	1.10374i	−0.986035	−	0.166536i	$-0.946742\pi$
$181$	−8.57321	−	14.8492i	−0.637242	−	1.10374i	0.348793	−	0.937200i	$-0.386591\pi$
$182$	−7.10102			−0.526363
$183$	−12.4495			−0.920293
$184$	2.94949	+	5.10867i	0.217439	+	0.376616i
$185$	4.94949	−	8.57277i	0.363894	−	0.630282i
$186$	−0.449490	−	0.778539i	−0.0329582	−	0.0570853i
$187$	−2.32577	+	4.02834i	−0.170077	+	0.294582i
$188$	0.550510	−	0.953512i	0.0401501	−	0.0695420i
$189$	1.44949			0.105435
$190$	1.00000	+	4.24264i	0.0725476	+	0.307794i
$191$	−3.79796			−0.274811			−0.137405	−	0.990515i	$-0.543876\pi$
$191$	−3.79796			−0.274811			−0.137405	+	0.990515i	$0.543876\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	10.6742	−	18.4883i	0.768348	−	1.33082i	−0.170110	−	0.985425i	$-0.554412\pi$
$193$	10.6742	−	18.4883i	0.768348	−	1.33082i	0.938458	−	0.345393i	$-0.112254\pi$
$194$	9.22474	+	15.9777i	0.662298	+	1.14713i
$195$	2.44949	−	4.24264i	0.175412	−	0.303822i
$196$	2.44949	+	4.24264i	0.174964	+	0.303046i
$197$	6.55051			0.466705			0.233352	−	0.972392i	$-0.425030\pi$
$197$	6.55051			0.466705			0.233352	+	0.972392i	$0.425030\pi$
$198$	−3.00000			−0.213201
$199$	−3.22474	−	5.58542i	−0.228596	−	0.395940i	0.728796	−	0.684731i	$-0.240080\pi$
$199$	−3.22474	−	5.58542i	−0.228596	−	0.395940i	−0.957392	+	0.288791i	$0.906747\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	7.34847			0.518321
$202$	−1.10102			−0.0774675
$203$	6.77526	+	11.7351i	0.475530	+	0.823642i
$204$	−0.775255	+	1.34278i	−0.0542787	+	0.0940135i
$205$	−2.17423	−	3.76588i	−0.151855	−	0.263021i
$206$	−5.62372	+	9.74058i	−0.391823	+	0.678658i
$207$	2.94949	−	5.10867i	0.205004	−	0.355077i
$208$	4.89898			0.339683
$209$	12.5227	+	3.76588i	0.866214	+	0.260492i
$210$	1.44949			0.100024
$211$	13.1742	−	22.8184i	0.906952	−	1.57089i	0.0886760	−	0.996061i	$-0.471736\pi$
$211$	13.1742	−	22.8184i	0.906952	−	1.57089i	0.818276	−	0.574826i	$-0.194930\pi$
$212$	3.72474	−	6.45145i	0.255817	−	0.443087i
$213$	−1.67423	−	2.89986i	−0.114717	−	0.198695i
$214$	1.32577	−	2.29629i	0.0906275	−	0.156971i
$215$	5.89898	+	10.2173i	0.402307	+	0.696816i
$216$	−1.00000			−0.0680414
$217$	1.30306			0.0884576
$218$	−0.674235	−	1.16781i	−0.0456649	−	0.0790940i
$219$	5.22474	+	9.04952i	0.353056	+	0.611510i
$220$	−3.00000			−0.202260
$221$	−7.59592			−0.510957
$222$	−4.94949	−	8.57277i	−0.332188	−	0.575366i
$223$	1.72474	−	2.98735i	0.115497	−	0.200047i	−0.802481	−	0.596678i	$-0.796487\pi$
$223$	1.72474	−	2.98735i	0.115497	−	0.200047i	0.917978	+	0.396630i	$0.129820\pi$
$224$	0.724745	+	1.25529i	0.0484241	+	0.0838729i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	4.77526	−	8.27098i	0.317645	−	0.550178i
$227$	−11.3485			−0.753224			−0.376612	−	0.926371i	$-0.622911\pi$
$227$	−11.3485			−0.753224			−0.376612	+	0.926371i	$0.622911\pi$
$228$	4.17423	+	1.25529i	0.276445	+	0.0831339i
$229$	8.69694			0.574710			0.287355	−	0.957824i	$-0.407224\pi$
$229$	8.69694			0.574710			0.287355	+	0.957824i	$0.407224\pi$
$230$	2.94949	−	5.10867i	0.194484	−	0.336855i
$231$	2.17423	−	3.76588i	0.143054	−	0.247777i
$232$	−4.67423	−	8.09601i	−0.306879	−	0.531529i
$233$	13.8990	−	24.0737i	0.910552	−	1.57712i	0.0972668	−	0.995258i	$-0.468990\pi$
$233$	13.8990	−	24.0737i	0.910552	−	1.57712i	0.813286	−	0.581865i	$-0.197677\pi$
$234$	−2.44949	−	4.24264i	−0.160128	−	0.277350i
$235$	−1.10102			−0.0718227
$236$	−6.00000			−0.390567
$237$	3.44949	+	5.97469i	0.224068	+	0.388098i
$238$	−1.12372	−	1.94635i	−0.0728402	−	0.126163i
$239$	−29.7980			−1.92747			−0.963735	−	0.266862i	$-0.914013\pi$
$239$	−29.7980			−1.92747			−0.963735	+	0.266862i	$0.914013\pi$
$240$	−1.00000			−0.0645497
$241$	−3.34847	−	5.79972i	−0.215694	−	0.373593i	0.737793	−	0.675027i	$-0.235868\pi$
$241$	−3.34847	−	5.79972i	−0.215694	−	0.373593i	−0.953487	+	0.301434i	$0.902535\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−6.22474	+	10.7816i	−0.398498	+	0.690220i
$245$	2.44949	−	4.24264i	0.156492	−	0.271052i
$246$	−4.34847			−0.277248
$247$	4.89898	+	20.7846i	0.311715	+	1.32249i
$248$	−0.898979			−0.0570853
$249$	5.89898	−	10.2173i	0.373833	−	0.647497i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	1.10102	+	1.90702i	0.0694958	+	0.120370i	0.898679	−	0.438606i	$-0.144528\pi$
$251$	1.10102	+	1.90702i	0.0694958	+	0.120370i	−0.829184	+	0.558976i	$0.811194\pi$
$252$	0.724745	−	1.25529i	0.0456546	−	0.0790761i
$253$	−8.84847	−	15.3260i	−0.556298	−	0.963537i
$254$	−0.348469			−0.0218649
$255$	1.55051			0.0970967
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.89898	−	13.6814i	−0.492725	−	0.853424i	0.507240	−	0.861805i	$-0.330666\pi$
$257$	−7.89898	−	13.6814i	−0.492725	−	0.853424i	−0.999965	+	0.00838040i	$0.997332\pi$
$258$	11.7980			0.734509
$259$	14.3485			0.891570
$260$	−2.44949	−	4.24264i	−0.151911	−	0.263117i
$261$	−4.67423	+	8.09601i	−0.289328	+	0.501131i
$262$	1.50000	+	2.59808i	0.0926703	+	0.160510i
$263$	−5.05051	+	8.74774i	−0.311428	+	0.539409i	−0.978672	−	0.205431i	$-0.934141\pi$
$263$	−5.05051	+	8.74774i	−0.311428	+	0.539409i	0.667244	+	0.744839i	$0.267474\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−7.44949			−0.457619
$266$	−4.60102	+	4.33013i	−0.282107	+	0.265497i
$267$	5.44949			0.333503
$268$	3.67423	−	6.36396i	0.224440	−	0.388741i
$269$	12.1237	−	20.9989i	0.739197	−	1.28033i	−0.213661	−	0.976908i	$-0.568539\pi$
$269$	12.1237	−	20.9989i	0.739197	−	1.28033i	0.952858	−	0.303418i	$-0.0981279\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	7.44949	−	12.9029i	0.452524	−	0.783795i	−0.546018	−	0.837774i	$-0.683857\pi$
$271$	7.44949	−	12.9029i	0.452524	−	0.783795i	0.998542	+	0.0539785i	$0.0171903\pi$
$272$	0.775255	+	1.34278i	0.0470067	+	0.0814181i
$273$	7.10102			0.429773
$274$	−12.0000			−0.724947
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	−2.94949	−	5.10867i	−0.177538	−	0.307506i
$277$	−12.8990			−0.775025			−0.387512	−	0.921865i	$-0.626666\pi$
$277$	−12.8990			−0.775025			−0.387512	+	0.921865i	$0.626666\pi$
$278$	−14.6969			−0.881464
$279$	0.449490	+	0.778539i	0.0269102	+	0.0466099i
$280$	0.724745	−	1.25529i	0.0433118	−	0.0750182i
$281$	−7.17423	−	12.4261i	−0.427979	−	0.741281i	0.568714	−	0.822535i	$-0.307441\pi$
$281$	−7.17423	−	12.4261i	−0.427979	−	0.741281i	−0.996693	+	0.0812537i	$0.974108\pi$
$282$	−0.550510	+	0.953512i	−0.0327824	+	0.0567808i
$283$	6.34847	−	10.9959i	0.377377	−	0.653637i	−0.613302	−	0.789848i	$-0.710159\pi$
$283$	6.34847	−	10.9959i	0.377377	−	0.653637i	0.990680	+	0.136211i	$0.0434927\pi$
$284$	−3.34847			−0.198695
$285$	−1.00000	−	4.24264i	−0.0592349	−	0.251312i
$286$	−14.6969			−0.869048
$287$	3.15153	−	5.45861i	0.186029	−	0.322212i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	7.29796	+	12.6404i	0.429292	+	0.743555i
$290$	−4.67423	+	8.09601i	−0.274481	+	0.475414i
$291$	−9.22474	−	15.9777i	−0.540764	−	0.936631i
$292$	10.4495			0.611510
$293$	−11.4495			−0.668886			−0.334443	−	0.942416i	$-0.608548\pi$
$293$	−11.4495			−0.668886			−0.334443	+	0.942416i	$0.608548\pi$
$294$	−2.44949	−	4.24264i	−0.142857	−	0.247436i
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	−9.89898			−0.575366
$297$	3.00000			0.174078
$298$	−6.77526	−	11.7351i	−0.392480	−	0.679795i
$299$	14.4495	−	25.0273i	0.835636	−	1.44736i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−8.55051	+	14.8099i	−0.492843	+	0.853629i
$302$	2.32577	−	4.02834i	0.133833	−	0.231805i
$303$	1.10102			0.0632520
$304$	3.17423	−	2.98735i	0.182055	−	0.171336i
$305$	12.4495			0.712856
$306$	0.775255	−	1.34278i	0.0443184	−	0.0767617i
$307$	5.12372	−	8.87455i	0.292426	−	0.506497i	−0.681957	−	0.731393i	$-0.738871\pi$
$307$	5.12372	−	8.87455i	0.292426	−	0.506497i	0.974383	+	0.224895i	$0.0722040\pi$
$308$	−2.17423	−	3.76588i	−0.123889	−	0.214581i
$309$	5.62372	−	9.74058i	0.319923	−	0.554122i
$310$	0.449490	+	0.778539i	0.0255293	+	0.0442180i
$311$	−9.79796			−0.555591			−0.277796	−	0.960640i	$-0.589604\pi$
$311$	−9.79796			−0.555591			−0.277796	+	0.960640i	$0.589604\pi$
$312$	−4.89898			−0.277350
$313$	−15.7980	−	27.3629i	−0.892953	−	1.54664i	−0.836317	−	0.548246i	$-0.815296\pi$
$313$	−15.7980	−	27.3629i	−0.892953	−	1.54664i	−0.0566362	−	0.998395i	$-0.518038\pi$
$314$	−10.3990	−	18.0116i	−0.586848	−	1.01645i
$315$	−1.44949			−0.0816695
$316$	6.89898			0.388098
$317$	−4.72474	−	8.18350i	−0.265368	−	0.459631i	0.702292	−	0.711889i	$-0.252160\pi$
$317$	−4.72474	−	8.18350i	−0.265368	−	0.459631i	−0.967660	+	0.252258i	$0.918827\pi$
$318$	−3.72474	+	6.45145i	−0.208873	+	0.361779i
$319$	14.0227	+	24.2880i	0.785121	+	1.35987i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−1.32577	+	2.29629i	−0.0739970	+	0.128167i
$322$	8.55051			0.476501
$323$	−4.92168	+	4.63191i	−0.273850	+	0.257726i
$324$	1.00000			0.0555556
$325$	−2.44949	+	4.24264i	−0.135873	+	0.235339i
$326$	−8.34847	+	14.4600i	−0.462379	+	0.800864i
$327$	0.674235	+	1.16781i	0.0372853	+	0.0645800i
$328$	−2.17423	+	3.76588i	−0.120052	+	0.207936i
$329$	−0.797959	−	1.38211i	−0.0439929	−	0.0761979i
$330$	3.00000			0.165145
$331$	18.3485			1.00852			0.504262	−	0.863551i	$-0.331765\pi$
$331$	18.3485			1.00852			0.504262	+	0.863551i	$0.331765\pi$
$332$	−5.89898	−	10.2173i	−0.323749	−	0.560749i
$333$	4.94949	+	8.57277i	0.271230	+	0.469785i
$334$	−9.69694			−0.530593
$335$	−7.34847			−0.401490
$336$	−0.724745	−	1.25529i	−0.0395381	−	0.0684820i
$337$	13.2474	−	22.9453i	0.721635	−	1.24991i	−0.238710	−	0.971091i	$-0.576724\pi$
$337$	13.2474	−	22.9453i	0.721635	−	1.24991i	0.960344	−	0.278817i	$-0.0899422\pi$
$338$	−5.50000	−	9.52628i	−0.299161	−	0.518161i
$339$	−4.77526	+	8.27098i	−0.259356	+	0.449218i
$340$	0.775255	−	1.34278i	0.0420441	−	0.0728225i
$341$	2.69694			0.146047
$342$	−4.17423	−	1.25529i	−0.225717	−	0.0678786i
$343$	17.2474			0.931275
$344$	5.89898	−	10.2173i	0.318052	−	0.550882i
$345$	−2.94949	+	5.10867i	−0.158795	+	0.275041i
$346$	2.27526	+	3.94086i	0.122318	+	0.211862i
$347$	−5.89898	+	10.2173i	−0.316674	+	0.548495i	−0.979792	−	0.200020i	$-0.935899\pi$
$347$	−5.89898	+	10.2173i	−0.316674	+	0.548495i	0.663118	+	0.748515i	$0.269233\pi$
$348$	4.67423	+	8.09601i	0.250565	+	0.433992i
$349$	−20.0454			−1.07301			−0.536503	−	0.843898i	$-0.680255\pi$
$349$	−20.0454			−1.07301			−0.536503	+	0.843898i	$0.680255\pi$
$350$	−1.44949			−0.0774785
$351$	2.44949	+	4.24264i	0.130744	+	0.226455i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	−35.3485			−1.88141			−0.940705	−	0.339227i	$-0.889835\pi$
$353$	−35.3485			−1.88141			−0.940705	+	0.339227i	$0.889835\pi$
$354$	6.00000			0.318896
$355$	1.67423	+	2.89986i	0.0888591	+	0.153909i
$356$	2.72474	−	4.71940i	0.144411	−	0.250128i
$357$	1.12372	+	1.94635i	0.0594738	+	0.103012i
$358$	10.3990	−	18.0116i	0.549603	−	0.951941i
$359$	−13.2247	+	22.9059i	−0.697975	+	1.20893i	0.271192	+	0.962525i	$0.412582\pi$
$359$	−13.2247	+	22.9059i	−0.697975	+	1.20893i	−0.969167	+	0.246403i	$0.920751\pi$
$360$	1.00000			0.0527046
$361$	15.8485	+	10.4798i	0.834130	+	0.551568i
$362$	17.1464			0.901196
$363$	−1.00000	+	1.73205i	−0.0524864	+	0.0909091i
$364$	3.55051	−	6.14966i	0.186097	−	0.322330i
$365$	−5.22474	−	9.04952i	−0.273476	−	0.473674i
$366$	6.22474	−	10.7816i	0.325373	−	0.563562i
$367$	−10.4495	−	18.0990i	−0.545459	−	0.944763i	−0.998578	−	0.0533125i	$-0.983022\pi$
$367$	−10.4495	−	18.0990i	−0.545459	−	0.944763i	0.453119	−	0.891450i	$-0.350311\pi$
$368$	−5.89898			−0.307506
$369$	4.34847			0.226372
$370$	4.94949	+	8.57277i	0.257312	+	0.445677i
$371$	−5.39898	−	9.35131i	−0.280301	−	0.485496i
$372$	0.898979			0.0466099
$373$	−3.89898			−0.201882			−0.100941	−	0.994892i	$-0.532185\pi$
$373$	−3.89898			−0.201882			−0.100941	+	0.994892i	$0.532185\pi$
$374$	−2.32577	−	4.02834i	−0.120262	−	0.208301i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	0.550510	+	0.953512i	0.0283904	+	0.0491736i
$377$	−22.8990	+	39.6622i	−1.17936	+	2.04271i
$378$	−0.724745	+	1.25529i	−0.0372769	+	0.0645654i
$379$	−6.69694			−0.343999			−0.171999	−	0.985097i	$-0.555023\pi$
$379$	−6.69694			−0.343999			−0.171999	+	0.985097i	$0.555023\pi$
$380$	−4.17423	−	1.25529i	−0.214134	−	0.0643953i
$381$	0.348469			0.0178526
$382$	1.89898	−	3.28913i	0.0971602	−	0.168286i
$383$	−15.2474	+	26.4094i	−0.779108	+	1.34946i	0.153348	+	0.988172i	$0.450994\pi$
$383$	−15.2474	+	26.4094i	−0.779108	+	1.34946i	−0.932456	+	0.361283i	$0.882339\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−2.17423	+	3.76588i	−0.110809	+	0.191927i
$386$	10.6742	+	18.4883i	0.543304	+	0.941031i
$387$	−11.7980			−0.599724
$388$	−18.4495			−0.936631
$389$	11.5732	+	20.0454i	0.586785	+	1.01634i	0.994650	+	0.103300i	$0.0329401\pi$
$389$	11.5732	+	20.0454i	0.586785	+	1.01634i	−0.407865	+	0.913042i	$0.633727\pi$
$390$	2.44949	+	4.24264i	0.124035	+	0.214834i
$391$	9.14643			0.462555
$392$	−4.89898			−0.247436
$393$	−1.50000	−	2.59808i	−0.0756650	−	0.131056i
$394$	−3.27526	+	5.67291i	−0.165005	+	0.285797i
$395$	−3.44949	−	5.97469i	−0.173563	−	0.300619i
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	−5.74745	+	9.95487i	−0.288456	+	0.499621i	−0.973441	−	0.228936i	$-0.926475\pi$
$397$	−5.74745	+	9.95487i	−0.288456	+	0.499621i	0.684985	+	0.728557i	$0.259809\pi$
$398$	6.44949			0.323284
$399$	4.60102	−	4.33013i	0.230339	−	0.216777i
$400$	1.00000			0.0500000
$401$	1.89898	−	3.28913i	0.0948305	−	0.164251i	−0.814707	−	0.579872i	$-0.803102\pi$
$401$	1.89898	−	3.28913i	0.0948305	−	0.164251i	0.909538	+	0.415621i	$0.136436\pi$
$402$	−3.67423	+	6.36396i	−0.183254	+	0.317406i
$403$	2.20204	+	3.81405i	0.109691	+	0.189991i
$404$	0.550510	−	0.953512i	0.0273889	−	0.0474390i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−13.5505			−0.672501
$407$	29.6969			1.47202
$408$	−0.775255	−	1.34278i	−0.0383808	−	0.0664776i
$409$	4.74745	+	8.22282i	0.234746	+	0.406592i	0.959199	−	0.282732i	$-0.0912408\pi$
$409$	4.74745	+	8.22282i	0.234746	+	0.406592i	−0.724453	+	0.689325i	$0.757907\pi$
$410$	4.34847			0.214756
$411$	12.0000			0.591916
$412$	−5.62372	−	9.74058i	−0.277061	−	0.479884i
$413$	−4.34847	+	7.53177i	−0.213974	+	0.370614i
$414$	2.94949	+	5.10867i	0.144960	+	0.251077i
$415$	−5.89898	+	10.2173i	−0.289570	+	0.501549i
$416$	−2.44949	+	4.24264i	−0.120096	+	0.208013i
$417$	14.6969			0.719712
$418$	−9.52270	+	8.96204i	−0.465771	+	0.438348i
$419$	21.8990			1.06984			0.534918	−	0.844904i	$-0.320343\pi$
$419$	21.8990			1.06984			0.534918	+	0.844904i	$0.320343\pi$
$420$	−0.724745	+	1.25529i	−0.0353639	+	0.0612521i
$421$	9.32577	−	16.1527i	0.454510	−	0.787234i	−0.544150	−	0.838988i	$-0.683148\pi$
$421$	9.32577	−	16.1527i	0.454510	−	0.787234i	0.998660	+	0.0517536i	$0.0164811\pi$
$422$	13.1742	+	22.8184i	0.641312	+	1.11078i
$423$	0.550510	−	0.953512i	0.0267667	−	0.0463613i
$424$	3.72474	+	6.45145i	0.180890	+	0.313310i
$425$	−1.55051			−0.0752108
$426$	3.34847			0.162234
$427$	9.02270	+	15.6278i	0.436639	+	0.756281i
$428$	1.32577	+	2.29629i	0.0640833	+	0.110996i
$429$	14.6969			0.709575
$430$	−11.7980			−0.568948
$431$	−5.32577	−	9.22450i	−0.256533	−	0.444328i	0.708778	−	0.705432i	$-0.249247\pi$
$431$	−5.32577	−	9.22450i	−0.256533	−	0.444328i	−0.965311	+	0.261104i	$0.915914\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−1.67423	−	2.89986i	−0.0804586	−	0.139358i	0.822988	−	0.568058i	$-0.192305\pi$
$433$	−1.67423	−	2.89986i	−0.0804586	−	0.139358i	−0.903447	+	0.428700i	$0.858972\pi$
$434$	−0.651531	+	1.12848i	−0.0312745	+	0.0541690i
$435$	4.67423	−	8.09601i	0.224112	−	0.388174i
$436$	1.34847			0.0645800
$437$	−5.89898	−	25.0273i	−0.282186	−	1.19722i
$438$	−10.4495			−0.499296
$439$	−1.67423	+	2.89986i	−0.0799069	+	0.138403i	−0.903210	−	0.429200i	$-0.858796\pi$
$439$	−1.67423	+	2.89986i	−0.0799069	+	0.138403i	0.823303	+	0.567603i	$0.192129\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	2.44949	+	4.24264i	0.116642	+	0.202031i
$442$	3.79796	−	6.57826i	0.180650	−	0.312896i
$443$	−0.876276	−	1.51775i	−0.0416331	−	0.0721107i	0.844458	−	0.535622i	$-0.179923\pi$
$443$	−0.876276	−	1.51775i	−0.0416331	−	0.0721107i	−0.886091	+	0.463511i	$0.846589\pi$
$444$	9.89898			0.469785
$445$	−5.44949			−0.258331
$446$	1.72474	+	2.98735i	0.0816690	+	0.141455i
$447$	6.77526	+	11.7351i	0.320459	+	0.555051i
$448$	−1.44949			−0.0684820
$449$	8.75255			0.413058			0.206529	−	0.978440i	$-0.433783\pi$
$449$	8.75255			0.413058			0.206529	+	0.978440i	$0.433783\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$	6.52270	−	11.2977i	0.307142	−	0.531986i
$452$	4.77526	+	8.27098i	0.224609	+	0.389034i
$453$	−2.32577	+	4.02834i	−0.109274	+	0.189268i
$454$	5.67423	−	9.82806i	0.266305	−	0.461254i
$455$	−7.10102			−0.332901
$456$	−3.17423	+	2.98735i	−0.148647	+	0.139895i
$457$	−12.0454			−0.563460			−0.281730	−	0.959494i	$-0.590908\pi$
$457$	−12.0454			−0.563460			−0.281730	+	0.959494i	$0.590908\pi$
$458$	−4.34847	+	7.53177i	−0.203191	+	0.351936i
$459$	−0.775255	+	1.34278i	−0.0361858	+	0.0626757i
$460$	2.94949	+	5.10867i	0.137521	+	0.238193i
$461$	13.8990	−	24.0737i	0.647340	−	1.12123i	−0.336416	−	0.941714i	$-0.609215\pi$
$461$	13.8990	−	24.0737i	0.647340	−	1.12123i	0.983756	−	0.179512i	$-0.0574519\pi$
$462$	2.17423	+	3.76588i	0.101155	+	0.175205i
$463$	−15.6515			−0.727388			−0.363694	−	0.931518i	$-0.618485\pi$
$463$	−15.6515			−0.727388			−0.363694	+	0.931518i	$0.618485\pi$
$464$	9.34847			0.433992
$465$	−0.449490	−	0.778539i	−0.0208446	−	0.0361039i
$466$	13.8990	+	24.0737i	0.643858	+	1.11519i
$467$	−40.2474			−1.86243			−0.931215	−	0.364471i	$-0.881250\pi$
$467$	−40.2474			−1.86243			−0.931215	+	0.364471i	$0.881250\pi$
$468$	4.89898			0.226455
$469$	−5.32577	−	9.22450i	−0.245921	−	0.425948i
$470$	0.550510	−	0.953512i	0.0253931	−	0.0439822i
$471$	10.3990	+	18.0116i	0.479160	+	0.829929i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−17.6969	+	30.6520i	−0.813706	+	1.40938i
$474$	−6.89898			−0.316881
$475$	1.00000	+	4.24264i	0.0458831	+	0.194666i
$476$	2.24745			0.103012
$477$	3.72474	−	6.45145i	0.170544	−	0.295391i
$478$	14.8990	−	25.8058i	0.681463	−	1.18033i
$479$	−5.02270	−	8.69958i	−0.229493	−	0.397494i	0.728165	−	0.685402i	$-0.240374\pi$
$479$	−5.02270	−	8.69958i	−0.229493	−	0.397494i	−0.957658	+	0.287908i	$0.907040\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	24.2474	+	41.9978i	1.10559	+	1.91494i
$482$	6.69694			0.305037
$483$	−8.55051			−0.389062
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	9.22474	+	15.9777i	0.418874	+	0.725511i
$486$	−1.00000			−0.0453609
$487$	−28.1464			−1.27544			−0.637718	−	0.770270i	$-0.720122\pi$
$487$	−28.1464			−1.27544			−0.637718	+	0.770270i	$0.720122\pi$
$488$	−6.22474	−	10.7816i	−0.281781	−	0.488059i
$489$	8.34847	−	14.4600i	0.377531	−	0.653903i
$490$	2.44949	+	4.24264i	0.110657	+	0.191663i
$491$	7.60102	−	13.1654i	0.343029	−	0.594144i	−0.641964	−	0.766734i	$-0.721880\pi$
$491$	7.60102	−	13.1654i	0.343029	−	0.594144i	0.984994	+	0.172590i	$0.0552137\pi$
$492$	2.17423	−	3.76588i	0.0980221	−	0.169779i
$493$	−14.4949			−0.652817
$494$	−20.4495	−	6.14966i	−0.920066	−	0.276686i
$495$	−3.00000			−0.134840
$496$	0.449490	−	0.778539i	0.0201827	−	0.0349574i
$497$	−2.42679	+	4.20332i	−0.108856	+	0.188545i
$498$	5.89898	+	10.2173i	0.264340	+	0.457850i
$499$	−5.27526	+	9.13701i	−0.236153	+	0.409029i	−0.959607	−	0.281344i	$-0.909220\pi$
$499$	−5.27526	+	9.13701i	−0.236153	+	0.409029i	0.723454	+	0.690372i	$0.242553\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	9.69694			0.433227
$502$	−2.20204			−0.0982819
$503$	−1.15153	−	1.99451i	−0.0513442	−	0.0889308i	0.839211	−	0.543806i	$-0.183017\pi$
$503$	−1.15153	−	1.99451i	−0.0513442	−	0.0889308i	−0.890555	+	0.454875i	$0.849684\pi$
$504$	0.724745	+	1.25529i	0.0322827	+	0.0559153i
$505$	−1.10102			−0.0489948
$506$	17.6969			0.786725
$507$	5.50000	+	9.52628i	0.244264	+	0.423077i
$508$	0.174235	−	0.301783i	0.00773041	−	0.0133895i
$509$	1.44949	+	2.51059i	0.0642475	+	0.111280i	0.896360	−	0.443327i	$-0.146202\pi$
$509$	1.44949	+	2.51059i	0.0642475	+	0.111280i	−0.832112	+	0.554607i	$0.812869\pi$
$510$	−0.775255	+	1.34278i	−0.0343289	+	0.0594594i
$511$	7.57321	−	13.1172i	0.335019	−	0.580270i
$512$	1.00000			0.0441942
$513$	4.17423	+	1.25529i	0.184297	+	0.0554226i
$514$	15.7980			0.696818
$515$	−5.62372	+	9.74058i	−0.247811	+	0.429221i
$516$	−5.89898	+	10.2173i	−0.259688	+	0.449793i
$517$	−1.65153	−	2.86054i	−0.0726342	−	0.125806i
$518$	−7.17423	+	12.4261i	−0.315218	+	0.545973i
$519$	−2.27526	−	3.94086i	−0.0998726	−	0.172984i
$520$	4.89898			0.214834
$521$	1.10102			0.0482366			0.0241183	−	0.999709i	$-0.492322\pi$
$521$	1.10102			0.0482366			0.0241183	+	0.999709i	$0.492322\pi$
$522$	−4.67423	−	8.09601i	−0.204586	−	0.354353i
$523$	−1.57321	−	2.72489i	−0.0687918	−	0.119151i	0.829578	−	0.558391i	$-0.188581\pi$
$523$	−1.57321	−	2.72489i	−0.0687918	−	0.119151i	−0.898370	+	0.439240i	$0.855248\pi$
$524$	−3.00000			−0.131056
$525$	1.44949			0.0632609
$526$	−5.05051	−	8.74774i	−0.220213	−	0.381420i
$527$	−0.696938	+	1.20713i	−0.0303591	+	0.0525835i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−5.89898	+	10.2173i	−0.256477	+	0.444232i
$530$	3.72474	−	6.45145i	0.161793	−	0.280233i
$531$	−6.00000			−0.260378
$532$	−1.44949	−	6.14966i	−0.0628434	−	0.266622i
$533$	21.3031			0.922738
$534$	−2.72474	+	4.71940i	−0.117911	+	0.204228i
$535$	1.32577	−	2.29629i	0.0573178	−	0.0992774i
$536$	3.67423	+	6.36396i	0.158703	+	0.274881i
$537$	−10.3990	+	18.0116i	−0.448749	+	0.777256i
$538$	12.1237	+	20.9989i	0.522691	+	0.905327i
$539$	14.6969			0.633042
$540$	−1.00000			−0.0430331
$541$	−9.55051	−	16.5420i	−0.410609	−	0.711195i	0.584348	−	0.811503i	$-0.301350\pi$
$541$	−9.55051	−	16.5420i	−0.410609	−	0.711195i	−0.994956	+	0.100308i	$0.968017\pi$
$542$	7.44949	+	12.9029i	0.319983	+	0.554227i
$543$	−17.1464			−0.735824
$544$	−1.55051			−0.0664776
$545$	−0.674235	−	1.16781i	−0.0288810	−	0.0500234i
$546$	−3.55051	+	6.14966i	−0.151948	+	0.263181i
$547$	1.65153	+	2.86054i	0.0706144	+	0.122308i	0.899171	−	0.437598i	$-0.144171\pi$
$547$	1.65153	+	2.86054i	0.0706144	+	0.122308i	−0.828556	+	0.559906i	$0.810837\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−6.22474	+	10.7816i	−0.265666	+	0.460146i
$550$	−3.00000			−0.127920
$551$	9.34847	+	39.6622i	0.398258	+	1.68967i
$552$	5.89898			0.251077
$553$	5.00000	−	8.66025i	0.212622	−	0.368271i
$554$	6.44949	−	11.1708i	0.274013	−	0.474604i
$555$	−4.94949	−	8.57277i	−0.210094	−	0.363894i
$556$	7.34847	−	12.7279i	0.311645	−	0.539784i
$557$	9.17423	+	15.8902i	0.388725	+	0.673291i	0.992278	−	0.124031i	$-0.0395824\pi$
$557$	9.17423	+	15.8902i	0.388725	+	0.673291i	−0.603553	+	0.797323i	$0.706249\pi$
$558$	−0.898979			−0.0380568
$559$	−57.7980			−2.44459
$560$	0.724745	+	1.25529i	0.0306261	+	0.0530459i
$561$	2.32577	+	4.02834i	0.0981939	+	0.170077i
$562$	14.3485			0.605254
$563$	29.3939			1.23880			0.619402	−	0.785074i	$-0.287375\pi$
$563$	29.3939			1.23880			0.619402	+	0.785074i	$0.287375\pi$
$564$	−0.550510	−	0.953512i	−0.0231807	−	0.0401501i
$565$	4.77526	−	8.27098i	0.200896	−	0.347963i
$566$	6.34847	+	10.9959i	0.266846	+	0.462191i
$567$	0.724745	−	1.25529i	0.0304364	−	0.0527174i
$568$	1.67423	−	2.89986i	0.0702493	−	0.121675i
$569$	−7.44949			−0.312299			−0.156149	−	0.987733i	$-0.549908\pi$
$569$	−7.44949			−0.312299			−0.156149	+	0.987733i	$0.549908\pi$
$570$	4.17423	+	1.25529i	0.174839	+	0.0525785i
$571$	−8.20204			−0.343245			−0.171622	−	0.985163i	$-0.554901\pi$
$571$	−8.20204			−0.343245			−0.171622	+	0.985163i	$0.554901\pi$
$572$	7.34847	−	12.7279i	0.307255	−	0.532181i
$573$	−1.89898	+	3.28913i	−0.0793310	+	0.137405i
$574$	3.15153	+	5.45861i	0.131542	+	0.227838i
$575$	2.94949	−	5.10867i	0.123002	−	0.213046i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	11.1464			0.464032			0.232016	−	0.972712i	$-0.425468\pi$
$577$	11.1464			0.464032			0.232016	+	0.972712i	$0.425468\pi$
$578$	−14.5959			−0.607110
$579$	−10.6742	−	18.4883i	−0.443606	−	0.768348i
$580$	−4.67423	−	8.09601i	−0.194087	−	0.336169i
$581$	−17.1010			−0.709470
$582$	18.4495			0.764756
$583$	−11.1742	−	19.3543i	−0.462790	−	0.801575i
$584$	−5.22474	+	9.04952i	−0.216201	+	0.374472i
$585$	−2.44949	−	4.24264i	−0.101274	−	0.175412i
$586$	5.72474	−	9.91555i	0.236487	−	0.409608i
$587$	16.2474	−	28.1414i	0.670604	−	1.16152i	−0.307129	−	0.951668i	$-0.599368\pi$
$587$	16.2474	−	28.1414i	0.670604	−	1.16152i	0.977733	−	0.209852i	$-0.0672983\pi$
$588$	4.89898			0.202031
$589$	3.75255	+	1.12848i	0.154621	+	0.0464984i
$590$	−6.00000			−0.247016
$591$	3.27526	−	5.67291i	0.134726	−	0.233352i
$592$	4.94949	−	8.57277i	0.203423	−	0.352339i
$593$	17.5732	+	30.4377i	0.721645	+	1.24993i	0.960340	+	0.278832i	$0.0899472\pi$
$593$	17.5732	+	30.4377i	0.721645	+	1.24993i	−0.238695	+	0.971095i	$0.576719\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	−1.12372	−	1.94635i	−0.0460682	−	0.0797925i
$596$	13.5505			0.555051
$597$	−6.44949			−0.263960
$598$	14.4495	+	25.0273i	0.590884	+	1.02344i
$599$	−12.6742	−	21.9524i	−0.517855	−	0.896951i	−0.999785	−	0.0207416i	$-0.993397\pi$
$599$	−12.6742	−	21.9524i	−0.517855	−	0.896951i	0.481930	−	0.876210i	$-0.339936\pi$
$600$	−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	$0.373334\pi$
$602$	−8.55051	−	14.8099i	−0.348493	−	0.603607i
$603$	3.67423	−	6.36396i	0.149626	−	0.259161i
$604$	2.32577	+	4.02834i	0.0946341	+	0.163911i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$	−0.550510	+	0.953512i	−0.0223630	+	0.0387338i
$607$	29.4495			1.19532			0.597659	−	0.801750i	$-0.296098\pi$
$607$	29.4495			1.19532			0.597659	+	0.801750i	$0.296098\pi$
$608$	1.00000	+	4.24264i	0.0405554	+	0.172062i
$609$	13.5505			0.549094
$610$	−6.22474	+	10.7816i	−0.252033	+	0.436533i
$611$	2.69694	−	4.67123i	0.109106	−	0.188978i
$612$	0.775255	+	1.34278i	0.0313378	+	0.0542787i
$613$	−5.74745	+	9.95487i	−0.232137	+	0.402074i	−0.958437	−	0.285305i	$-0.907905\pi$
$613$	−5.74745	+	9.95487i	−0.232137	+	0.402074i	0.726300	+	0.687378i	$0.241239\pi$
$614$	5.12372	+	8.87455i	0.206777	+	0.358148i
$615$	−4.34847			−0.175347
$616$	4.34847			0.175205
$617$	−7.79796	−	13.5065i	−0.313934	−	0.543750i	0.665276	−	0.746597i	$-0.268314\pi$
$617$	−7.79796	−	13.5065i	−0.313934	−	0.543750i	−0.979210	+	0.202848i	$0.934980\pi$
$618$	5.62372	+	9.74058i	0.226219	+	0.391823i
$619$	23.0454			0.926273			0.463137	−	0.886287i	$-0.346724\pi$
$619$	23.0454			0.926273			0.463137	+	0.886287i	$0.346724\pi$
$620$	−0.898979			−0.0361039
$621$	−2.94949	−	5.10867i	−0.118359	−	0.205004i
$622$	4.89898	−	8.48528i	0.196431	−	0.340229i
$623$	−3.94949	−	6.84072i	−0.158233	−	0.274068i
$624$	2.44949	−	4.24264i	0.0980581	−	0.169842i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	31.5959			1.26283
$627$	9.52270	−	8.96204i	0.380300	−	0.357909i
$628$	20.7980			0.829929
$629$	−7.67423	+	13.2922i	−0.305992	+	0.529993i
$630$	0.724745	−	1.25529i	0.0288745	−	0.0500121i
$631$	13.1237	+	22.7310i	0.522447	+	0.904905i	0.999659	+	0.0261167i	$0.00831416\pi$
$631$	13.1237	+	22.7310i	0.522447	+	0.904905i	−0.477212	+	0.878788i	$0.658353\pi$
$632$	−3.44949	+	5.97469i	−0.137213	+	0.237660i
$633$	−13.1742	−	22.8184i	−0.523629	−	0.906952i
$634$	9.44949			0.375287
$635$	−0.348469			−0.0138286
$636$	−3.72474	−	6.45145i	−0.147696	−	0.255817i
$637$	12.0000	+	20.7846i	0.475457	+	0.823516i
$638$	−28.0454			−1.11033
$639$	−3.34847			−0.132463
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	5.65153	−	9.78874i	0.223222	−	0.386632i	−0.732563	−	0.680700i	$-0.761676\pi$
$641$	5.65153	−	9.78874i	0.223222	−	0.386632i	0.955785	+	0.294068i	$0.0950092\pi$
$642$	−1.32577	−	2.29629i	−0.0523238	−	0.0906275i
$643$	−10.1237	+	17.5348i	−0.399241	+	0.691505i	−0.993632	−	0.112670i	$-0.964060\pi$
$643$	−10.1237	+	17.5348i	−0.399241	+	0.691505i	0.594392	+	0.804176i	$0.297393\pi$
$644$	−4.27526	+	7.40496i	−0.168469	+	0.291796i
$645$	11.7980			0.464544
$646$	−1.55051	−	6.57826i	−0.0610040	−	0.258818i
$647$	0.101021			0.00397153			0.00198576	−	0.999998i	$-0.499368\pi$
$647$	0.101021			0.00397153			0.00198576	+	0.999998i	$0.499368\pi$
$648$	−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
$651$	0.651531	−	1.12848i	0.0255355	−	0.0442288i
$652$	−8.34847	−	14.4600i	−0.326951	−	0.566296i
$653$	−40.3485			−1.57896			−0.789479	−	0.613778i	$-0.789649\pi$
$653$	−40.3485			−1.57896			−0.789479	+	0.613778i	$0.789649\pi$
$654$	−1.34847			−0.0527293
$655$	1.50000	+	2.59808i	0.0586098	+	0.101515i
$656$	−2.17423	−	3.76588i	−0.0848896	−	0.147033i
$657$	10.4495			0.407673
$658$	1.59592			0.0622154
$659$	−11.2980	−	19.5686i	−0.440106	−	0.762286i	0.557591	−	0.830116i	$-0.311726\pi$
$659$	−11.2980	−	19.5686i	−0.440106	−	0.762286i	−0.997697	+	0.0678299i	$0.978392\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	0.968433	−	0.249274i	$-0.0801919\pi$
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	−0.700094	+	0.714051i	$0.746859\pi$
$662$	−9.17423	+	15.8902i	−0.356567	+	0.617592i
$663$	−3.79796	+	6.57826i	−0.147501	+	0.255478i
$664$	11.7980			0.457850
$665$	−4.60102	+	4.33013i	−0.178420	+	0.167915i
$666$	−9.89898			−0.383578
$667$	27.5732	−	47.7582i	1.06764	−	1.84921i
$668$	4.84847	−	8.39780i	0.187593	−	0.324920i
$669$	−1.72474	−	2.98735i	−0.0666825	−	0.115497i
$670$	3.67423	−	6.36396i	0.141948	−	0.245861i
$671$	18.6742	+	32.3447i	0.720911	+	1.24865i
$672$	1.44949			0.0559153
$673$	−40.4949			−1.56096			−0.780482	−	0.625179i	$-0.785026\pi$
$673$	−40.4949			−1.56096			−0.780482	+	0.625179i	$0.785026\pi$
$674$	13.2474	+	22.9453i	0.510273	+	0.883818i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	11.0000			0.423077
$677$	29.9444			1.15086			0.575428	−	0.817852i	$-0.304835\pi$
$677$	29.9444			1.15086			0.575428	+	0.817852i	$0.304835\pi$
$678$	−4.77526	−	8.27098i	−0.183393	−	0.317645i
$679$	−13.3712	+	23.1596i	−0.513139	+	0.888782i
$680$	0.775255	+	1.34278i	0.0297297	+	0.0514933i
$681$	−5.67423	+	9.82806i	−0.217437	+	0.376612i
$682$	−1.34847	+	2.33562i	−0.0516356	+	0.0894354i
$683$	−17.7526			−0.679282			−0.339641	−	0.940555i	$-0.610306\pi$
$683$	−17.7526			−0.679282			−0.339641	+	0.940555i	$0.610306\pi$
$684$	3.17423	−	2.98735i	0.121370	−	0.114224i
$685$	−12.0000			−0.458496
$686$	−8.62372	+	14.9367i	−0.329255	+	0.570287i
$687$	4.34847	−	7.53177i	0.165904	−	0.287355i
$688$	5.89898	+	10.2173i	0.224896	+	0.389532i
$689$	18.2474	−	31.6055i	0.695172	−	1.20407i
$690$	−2.94949	−	5.10867i	−0.112285	−	0.194484i
$691$	−31.4495			−1.19639			−0.598197	−	0.801349i	$-0.704116\pi$
$691$	−31.4495			−1.19639			−0.598197	+	0.801349i	$0.704116\pi$
$692$	−4.55051			−0.172984
$693$	−2.17423	−	3.76588i	−0.0825923	−	0.143054i
$694$	−5.89898	−	10.2173i	−0.223922	−	0.387845i
$695$	−14.6969			−0.557487
$696$	−9.34847			−0.354353
$697$	3.37117	+	5.83904i	0.127692	+	0.221170i
$698$	10.0227	−	17.3598i	0.379365	−	0.657079i
$699$	−13.8990	−	24.0737i	−0.525708	−	0.910552i
$700$	0.724745	−	1.25529i	0.0273928	−	0.0474457i
$701$	−2.10102	+	3.63907i	−0.0793544	+	0.137446i	−0.902972	−	0.429700i	$-0.858619\pi$
$701$	−2.10102	+	3.63907i	−0.0793544	+	0.137446i	0.823617	+	0.567146i	$0.191953\pi$
$702$	−4.89898			−0.184900
$703$	41.3207	+	12.4261i	1.55844	+	0.468661i
$704$	−3.00000			−0.113067
$705$	−0.550510	+	0.953512i	−0.0207334	+	0.0359113i
$706$	17.6742	−	30.6127i	0.665179	−	1.15212i
$707$	−0.797959	−	1.38211i	−0.0300103	−	0.0519794i
$708$	−3.00000	+	5.19615i	−0.112747	+	0.195283i
$709$	−22.4722	−	38.9230i	−0.843961	−	1.46178i	−0.886521	−	0.462689i	$-0.846885\pi$
$709$	−22.4722	−	38.9230i	−0.843961	−	1.46178i	0.0425596	−	0.999094i	$-0.486449\pi$
$710$	−3.34847			−0.125666
$711$	6.89898			0.258732
$712$	2.72474	+	4.71940i	0.102114	+	0.176867i
$713$	−2.65153	−	4.59259i	−0.0993006	−	0.171994i
$714$	−2.24745			−0.0841087
$715$	−14.6969			−0.549634
$716$	10.3990	+	18.0116i	0.388628	+	0.673124i
$717$	−14.8990	+	25.8058i	−0.556413	+	0.963735i
$718$	−13.2247	−	22.9059i	−0.493543	−	0.854842i
$719$	17.3485	−	30.0484i	0.646989	−	1.12062i	−0.336850	−	0.941558i	$-0.609361\pi$
$719$	17.3485	−	30.0484i	0.646989	−	1.12062i	0.983838	−	0.179059i	$-0.0573053\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	−16.3031			−0.607158
$722$	−17.0000	+	8.48528i	−0.632674	+	0.315789i
$723$	−6.69694			−0.249062
$724$	−8.57321	+	14.8492i	−0.318621	+	0.551868i
$725$	−4.67423	+	8.09601i	−0.173597	+	0.300678i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−4.10102	+	7.10318i	−0.152098	+	0.263442i	−0.931999	−	0.362462i	$-0.881936\pi$
$727$	−4.10102	+	7.10318i	−0.152098	+	0.263442i	0.779900	+	0.625904i	$0.215270\pi$
$728$	3.55051	+	6.14966i	0.131591	+	0.227922i
$729$	1.00000			0.0370370
$730$	10.4495			0.386753
$731$	−9.14643	−	15.8421i	−0.338293	−	0.585940i
$732$	6.22474	+	10.7816i	0.230073	+	0.398498i
$733$	−2.59592			−0.0958824			−0.0479412	−	0.998850i	$-0.515266\pi$
$733$	−2.59592			−0.0958824			−0.0479412	+	0.998850i	$0.515266\pi$
$734$	20.8990			0.771395
$735$	−2.44949	−	4.24264i	−0.0903508	−	0.156492i
$736$	2.94949	−	5.10867i	0.108720	−	0.188308i
$737$	−11.0227	−	19.0919i	−0.406027	−	0.703259i
$738$	−2.17423	+	3.76588i	−0.0800347	+	0.138624i
$739$	−18.9722	+	32.8608i	−0.697903	+	1.20880i	0.271289	+	0.962498i	$0.412550\pi$
$739$	−18.9722	+	32.8608i	−0.697903	+	1.20880i	−0.969192	+	0.246306i	$0.920783\pi$
$740$	−9.89898			−0.363894
$741$	20.4495	+	6.14966i	0.751231	+	0.225914i
$742$	10.7980			0.396406
$743$	9.84847	−	17.0580i	0.361305	−	0.625799i	−0.626871	−	0.779123i	$-0.715665\pi$
$743$	9.84847	−	17.0580i	0.361305	−	0.625799i	0.988176	+	0.153324i	$0.0489979\pi$
$744$	−0.449490	+	0.778539i	−0.0164791	+	0.0285426i
$745$	−6.77526	−	11.7351i	−0.248226	−	0.429940i
$746$	1.94949	−	3.37662i	0.0713759	−	0.123627i
$747$	−5.89898	−	10.2173i	−0.215832	−	0.373833i
$748$	4.65153			0.170077
$749$	3.84337			0.140434
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	0.905050	+	0.425306i	$0.139833\pi$
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	−0.0841993	+	0.996449i	$0.526833\pi$
$752$	−1.10102			−0.0401501
$753$	2.20204			0.0802468
$754$	−22.8990	−	39.6622i	−0.833932	−	1.44441i
$755$	2.32577	−	4.02834i	0.0846433	−	0.146606i
$756$	−0.724745	−	1.25529i	−0.0263587	−	0.0456546i
$757$	2.19694	−	3.80521i	0.0798491	−	0.138303i	−0.823336	−	0.567555i	$-0.807889\pi$
$757$	2.19694	−	3.80521i	0.0798491	−	0.138303i	0.903185	+	0.429252i	$0.141223\pi$
$758$	3.34847	−	5.79972i	0.121622	−	0.210655i
$759$	−17.6969			−0.642358
$760$	3.17423	−	2.98735i	0.115142	−	0.108362i
$761$	21.4495			0.777543			0.388772	−	0.921334i	$-0.372899\pi$
$761$	21.4495			0.777543			0.388772	+	0.921334i	$0.372899\pi$
$762$	−0.174235	+	0.301783i	−0.00631185	+	0.0109325i
$763$	0.977296	−	1.69273i	0.0353805	−	0.0612808i
$764$	1.89898	+	3.28913i	0.0687027	+	0.118997i
$765$	0.775255	−	1.34278i	0.0280294	−	0.0485484i
$766$	−15.2474	−	26.4094i	−0.550913	−	0.954209i
$767$	−29.3939			−1.06135
$768$	−1.00000			−0.0360844
$769$	16.8990	+	29.2699i	0.609393	+	1.05550i	0.991341	+	0.131315i	$0.0419201\pi$
$769$	16.8990	+	29.2699i	0.609393	+	1.05550i	−0.381948	+	0.924184i	$0.624747\pi$
$770$	−2.17423	−	3.76588i	−0.0783540	−	0.135713i
$771$	−15.7980			−0.568950
$772$	−21.3485			−0.768348
$773$	22.5227	+	39.0105i	0.810085	+	1.40311i	0.912804	+	0.408399i	$0.133913\pi$
$773$	22.5227	+	39.0105i	0.810085	+	1.40311i	−0.102718	+	0.994710i	$0.532754\pi$
$774$	5.89898	−	10.2173i	0.212034	−	0.367254i
$775$	0.449490	+	0.778539i	0.0161461	+	0.0279659i
$776$	9.22474	−	15.9777i	0.331149	−	0.573567i
$777$	7.17423	−	12.4261i	0.257374	−	0.445785i
$778$	−23.1464			−0.829840
$779$	13.8031	−	12.9904i	0.494546	−	0.465429i
$780$	−4.89898			−0.175412
$781$	−5.02270	+	8.69958i	−0.179726	+	0.311295i
$782$	−4.57321	+	7.92104i	−0.163538	+	0.283256i
$783$	4.67423	+	8.09601i	0.167044	+	0.289328i
$784$	2.44949	−	4.24264i	0.0874818	−	0.151523i
$785$	−10.3990	−	18.0116i	−0.371155	−	0.642860i
$786$	3.00000			0.107006
$787$	20.0454			0.714542			0.357271	−	0.934001i	$-0.383707\pi$
$787$	20.0454			0.714542			0.357271	+	0.934001i	$0.383707\pi$
$788$	−3.27526	−	5.67291i	−0.116676	−	0.202089i
$789$	5.05051	+	8.74774i	0.179803	+	0.311428i
$790$	6.89898			0.245455
$791$	13.8434			0.492213
$792$	1.50000	+	2.59808i	0.0533002	+	0.0923186i
$793$	−30.4949	+	52.8187i	−1.08291	+	1.87565i
$794$	−5.74745	−	9.95487i	−0.203969	−	0.353285i
$795$	−3.72474	+	6.45145i	−0.132103	+	0.228809i
$796$	−3.22474	+	5.58542i	−0.114298	+	0.197970i
$797$	16.3485			0.579092			0.289546	−	0.957164i	$-0.406496\pi$
$797$	16.3485			0.579092			0.289546	+	0.957164i	$0.406496\pi$
$798$	1.44949	+	6.14966i	0.0513114	+	0.217696i
$799$	1.70714			0.0603944
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	2.72474	−	4.71940i	0.0962741	−	0.166752i
$802$	1.89898	+	3.28913i	0.0670553	+	0.116143i
$803$	15.6742	−	27.1486i	0.553132	−	0.958052i
$804$	−3.67423	−	6.36396i	−0.129580	−	0.224440i
$805$	8.55051			0.301366
$806$	−4.40408			−0.155127
$807$	−12.1237	−	20.9989i	−0.426775	−	0.739197i
$808$	0.550510	+	0.953512i	0.0193669	+	0.0335444i
$809$	20.4949			0.720562			0.360281	−	0.932844i	$-0.382681\pi$
$809$	20.4949			0.720562			0.360281	+	0.932844i	$0.382681\pi$
$810$	1.00000			0.0351364
$811$	−10.4217	−	18.0509i	−0.365955	−	0.633852i	0.622974	−	0.782242i	$-0.285924\pi$
$811$	−10.4217	−	18.0509i	−0.365955	−	0.633852i	−0.988929	+	0.148390i	$0.952591\pi$
$812$	6.77526	−	11.7351i	0.237765	−	0.411821i
$813$	−7.44949	−	12.9029i	−0.261265	−	0.452524i
$814$	−14.8485	+	25.7183i	−0.520439	+	0.901426i
$815$	−8.34847	+	14.4600i	−0.292434	+	0.506511i
$816$	1.55051			0.0542787
$817$	−37.4495	+	35.2446i	−1.31019	+	1.23305i
$818$	−9.49490			−0.331981
$819$	3.55051	−	6.14966i	0.124065	−	0.214887i
$820$	−2.17423	+	3.76588i	−0.0759276	+	0.131510i
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$	−6.00000	+	10.3923i	−0.209274	+	0.362473i
$823$	0.926786	+	1.60524i	0.0323057	+	0.0559552i	0.881726	−	0.471761i	$-0.156382\pi$
$823$	0.926786	+	1.60524i	0.0323057	+	0.0559552i	−0.849421	+	0.527717i	$0.823048\pi$
$824$	11.2474			0.391823
$825$	3.00000			0.104447
$826$	−4.34847	−	7.53177i	−0.151303	−	0.262064i
$827$	10.5732	+	18.3133i	0.367667	+	0.636817i	0.989200	−	0.146570i	$-0.0468234\pi$
$827$	10.5732	+	18.3133i	0.367667	+	0.636817i	−0.621534	+	0.783388i	$0.713490\pi$
$828$	−5.89898			−0.205004
$829$	23.1010			0.802332			0.401166	−	0.916005i	$-0.368605\pi$
$829$	23.1010			0.802332			0.401166	+	0.916005i	$0.368605\pi$
$830$	−5.89898	−	10.2173i	−0.204757	−	0.354649i
$831$	−6.44949	+	11.1708i	−0.223730	+	0.387512i
$832$	−2.44949	−	4.24264i	−0.0849208	−	0.147087i
$833$	−3.79796	+	6.57826i	−0.131591	+	0.227923i
$834$	−7.34847	+	12.7279i	−0.254457	+	0.440732i
$835$	−9.69694			−0.335576
$836$	−3.00000	−	12.7279i	−0.103757	−	0.440204i
$837$	0.898979			0.0310733
$838$	−10.9495	+	18.9651i	−0.378244	+	0.655138i
$839$	−27.2474	+	47.1940i	−0.940686	+	1.62932i	−0.176520	+	0.984297i	$0.556484\pi$
$839$	−27.2474	+	47.1940i	−0.940686	+	1.62932i	−0.764166	+	0.645020i	$0.776849\pi$
$840$	−0.724745	−	1.25529i	−0.0250061	−	0.0433118i
$841$	−29.1969	+	50.5706i	−1.00679	+	1.74381i
$842$	9.32577	+	16.1527i	0.321387	+	0.556659i
$843$	−14.3485			−0.494188
$844$	−26.3485			−0.906952
$845$	−5.50000	−	9.52628i	−0.189206	−	0.327714i
$846$	0.550510	+	0.953512i	0.0189269	+	0.0327824i
$847$	2.89898			0.0996101
$848$	−7.44949			−0.255817
$849$	−6.34847	−	10.9959i	−0.217879	−	0.377377i
$850$	0.775255	−	1.34278i	0.0265910	−	0.0460570i
$851$	−29.1969	−	50.5706i	−1.00086	−	1.73354i
$852$	−1.67423	+	2.89986i	−0.0573583	+	0.0993475i
$853$	7.69694	−	13.3315i	0.263538	−	0.456461i	−0.703641	−	0.710555i	$-0.748444\pi$
$853$	7.69694	−	13.3315i	0.263538	−	0.456461i	0.967180	+	0.254094i	$0.0817772\pi$
$854$	−18.0454			−0.617501
$855$	−4.17423	−	1.25529i	−0.142756	−	0.0429302i
$856$	−2.65153			−0.0906275
$857$	21.7980	−	37.7552i	0.744604	−	1.28969i	−0.205775	−	0.978599i	$-0.565972\pi$
$857$	21.7980	−	37.7552i	0.744604	−	1.28969i	0.950380	−	0.311093i	$-0.100695\pi$
$858$	−7.34847	+	12.7279i	−0.250873	+	0.434524i
$859$	−16.5227	−	28.6182i	−0.563747	−	0.976439i	−0.997165	−	0.0752459i	$-0.976026\pi$
$859$	−16.5227	−	28.6182i	−0.563747	−	0.976439i	0.433418	−	0.901193i	$-0.357308\pi$
$860$	5.89898	−	10.2173i	0.201154	−	0.348408i
$861$	−3.15153	−	5.45861i	−0.107404	−	0.186029i
$862$	10.6515			0.362793
$863$	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
$865$	2.27526	+	3.94086i	0.0773610	+	0.133993i
$866$	3.34847			0.113786
$867$	14.5959			0.495703
$868$	−0.651531	−	1.12848i	−0.0221144	−	0.0383033i
$869$	10.3485	−	17.9241i	0.351048	−	0.608033i
$870$	4.67423	+	8.09601i	0.158471	+	0.274481i
$871$	18.0000	−	31.1769i	0.609907	−	1.05639i
$872$	−0.674235	+	1.16781i	−0.0228325	+	0.0395470i
$873$	−18.4495			−0.624421
$874$	24.6237	+	7.40496i	0.832910	+	0.250476i
$875$	−1.44949			−0.0490017
$876$	5.22474	−	9.04952i	0.176528	−	0.305755i
$877$	−16.7474	+	29.0074i	−0.565521	+	0.979511i	0.431480	+	0.902123i	$0.357992\pi$
$877$	−16.7474	+	29.0074i	−0.565521	+	0.979511i	−0.997001	+	0.0773888i	$0.975342\pi$
$878$	−1.67423	−	2.89986i	−0.0565027	−	0.0978655i
$879$	−5.72474	+	9.91555i	−0.193091	+	0.334443i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	37.0454			1.24809			0.624046	−	0.781388i	$-0.285488\pi$
$881$	37.0454			1.24809			0.624046	+	0.781388i	$0.285488\pi$
$882$	−4.89898			−0.164957
$883$	−23.4722	−	40.6550i	−0.789902	−	1.36815i	−0.926026	−	0.377459i	$-0.876798\pi$
$883$	−23.4722	−	40.6550i	−0.789902	−	1.36815i	0.136124	−	0.990692i	$-0.456535\pi$
$884$	3.79796	+	6.57826i	0.127739	+	0.221251i
$885$	6.00000			0.201688
$886$	1.75255			0.0588781
$887$	21.8990	+	37.9301i	0.735296	+	1.27357i	0.954593	+	0.297912i	$0.0962901\pi$
$887$	21.8990	+	37.9301i	0.735296	+	1.27357i	−0.219298	+	0.975658i	$0.570377\pi$
$888$	−4.94949	+	8.57277i	−0.166094	+	0.287683i
$889$	−0.252551	−	0.437432i	−0.00847030	−	0.0146710i
$890$	2.72474	−	4.71940i	0.0913337	−	0.158195i
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−3.44949			−0.115497
$893$	−1.10102	−	4.67123i	−0.0368442	−	0.156317i
$894$	−13.5505			−0.453197
$895$	10.3990	−	18.0116i	0.347600	−	0.602060i
$896$	0.724745	−	1.25529i	0.0242120	−	0.0419365i
$897$	−14.4495	−	25.0273i	−0.482454	−	0.835636i
$898$	−4.37628	+	7.57993i	−0.146038	+	0.252946i
$899$	4.20204	+	7.27815i	0.140146	+	0.242740i
$900$	1.00000			0.0333333
$901$	11.5505			0.384803
$902$	6.52270	+	11.2977i	0.217182	+	0.376171i
$903$	8.55051	+	14.8099i	0.284543	+	0.492843i
$904$	−9.55051			−0.317645
$905$	17.1464			0.569967
$906$	−2.32577	−	4.02834i	−0.0772684	−	0.133833i
$907$	18.7980	−	32.5590i	0.624176	−	1.08110i	−0.364524	−	0.931194i	$-0.618768\pi$
$907$	18.7980	−	32.5590i	0.624176	−	1.08110i	0.988700	−	0.149910i	$-0.0478985\pi$
$908$	5.67423	+	9.82806i	0.188306	+	0.326156i
$909$	0.550510	−	0.953512i	0.0182593	−	0.0316260i
$910$	3.55051	−	6.14966i	0.117698	−	0.203859i
$911$	−54.0908			−1.79211			−0.896054	−	0.443944i	$-0.853579\pi$
$911$	−54.0908			−1.79211			−0.896054	+	0.443944i	$0.853579\pi$
$912$	−1.00000	−	4.24264i	−0.0331133	−	0.140488i
$913$	−35.3939			−1.17137
$914$	6.02270	−	10.4316i	0.199213	−	0.345048i
$915$	6.22474	−	10.7816i	0.205784	−	0.356428i
$916$	−4.34847	−	7.53177i	−0.143677	−	0.248857i
$917$	−2.17423	+	3.76588i	−0.0717996	+	0.124360i
$918$	−0.775255	−	1.34278i	−0.0255872	−	0.0443184i
$919$	−15.5505			−0.512964			−0.256482	−	0.966549i	$-0.582563\pi$
$919$	−15.5505			−0.512964			−0.256482	+	0.966549i	$0.582563\pi$
$920$	−5.89898			−0.194484
$921$	−5.12372	−	8.87455i	−0.168832	−	0.292426i
$922$	13.8990	+	24.0737i	0.457739	+	0.792826i
$923$	−16.4041			−0.539947
$924$	−4.34847			−0.143054
$925$	4.94949	+	8.57277i	0.162738	+	0.281871i
$926$	7.82577	−	13.5546i	0.257171	−	0.445433i
$927$	−5.62372	−	9.74058i	−0.184707	−	0.319923i
$928$	−4.67423	+	8.09601i	−0.153439	+	0.265765i
$929$	−17.2753	+	29.9216i	−0.566783	+	0.981696i	0.430099	+	0.902782i	$0.358479\pi$
$929$	−17.2753	+	29.9216i	−0.566783	+	0.981696i	−0.996881	+	0.0789146i	$0.974855\pi$
$930$	0.898979			0.0294787
$931$	20.4495	+	6.14966i	0.670205	+	0.201547i
$932$	−27.7980			−0.910552
$933$	−4.89898	+	8.48528i	−0.160385	+	0.277796i
$934$	20.1237	−	34.8553i	0.658468	−	1.14050i
$935$	−2.32577	−	4.02834i	−0.0760607	−	0.131741i
$936$	−2.44949	+	4.24264i	−0.0800641	+	0.138675i
$937$	13.0227	+	22.5560i	0.425433	+	0.736872i	0.996461	−	0.0840590i	$-0.0267884\pi$
$937$	13.0227	+	22.5560i	0.425433	+	0.736872i	−0.571028	+	0.820931i	$0.693455\pi$
$938$	10.6515			0.347785
$939$	−31.5959			−1.03109
$940$	0.550510	+	0.953512i	0.0179557	+	0.0311001i
$941$	7.77526	+	13.4671i	0.253466	+	0.439016i	0.964478	−	0.264164i	$-0.0850960\pi$
$941$	7.77526	+	13.4671i	0.253466	+	0.439016i	−0.711012	+	0.703180i	$0.751763\pi$
$942$	−20.7980			−0.677634
$943$	−25.6515			−0.835329
$944$	3.00000	+	5.19615i	0.0976417	+	0.169120i
$945$	−0.724745	+	1.25529i	−0.0235760	+	0.0408347i
$946$	−17.6969	−	30.6520i	−0.575377	−	0.996582i
$947$	12.2247	−	21.1739i	0.397251	−	0.688059i	−0.596135	−	0.802884i	$-0.703298\pi$
$947$	12.2247	−	21.1739i	0.397251	−	0.688059i	0.993386	+	0.114826i	$0.0366310\pi$
$948$	3.44949	−	5.97469i	0.112034	−	0.194049i
$949$	51.1918			1.66176
$950$	−4.17423	−	1.25529i	−0.135430	−	0.0407271i
$951$	−9.44949			−0.306421
$952$	−1.12372	+	1.94635i	−0.0364201	+	0.0630815i
$953$	20.6969	−	35.8481i	0.670440	−	1.16124i	−0.307340	−	0.951600i	$-0.599439\pi$
$953$	20.6969	−	35.8481i	0.670440	−	1.16124i	0.977780	−	0.209636i	$-0.0672278\pi$
$954$	3.72474	+	6.45145i	0.120593	+	0.208873i
$955$	1.89898	−	3.28913i	0.0614495	−	0.106434i
$956$	14.8990	+	25.8058i	0.481867	+	0.834619i
$957$	28.0454			0.906579
$958$	10.0454			0.324552
$959$	−8.69694	−	15.0635i	−0.280839	−	0.486427i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−30.1918			−0.973930
$962$	−48.4949			−1.56354
$963$	1.32577	+	2.29629i	0.0427222	+	0.0739970i
$964$	−3.34847	+	5.79972i	−0.107847	+	0.186796i
$965$	10.6742	+	18.4883i	0.343616	+	0.595160i
$966$	4.27526	−	7.40496i	0.137554	−	0.238251i
$967$	−6.44949	+	11.1708i	−0.207402	+	0.359230i	−0.950895	−	0.309513i	$-0.899834\pi$
$967$	−6.44949	+	11.1708i	−0.207402	+	0.359230i	0.743494	+	0.668743i	$0.233167\pi$
$968$	−2.00000			−0.0642824
$969$	1.55051	+	6.57826i	0.0498096	+	0.211324i
$970$	−18.4495			−0.592377
$971$	−1.65153	+	2.86054i	−0.0530001	+	0.0917989i	−0.891308	−	0.453398i	$-0.850212\pi$
$971$	−1.65153	+	2.86054i	−0.0530001	+	0.0917989i	0.838308	+	0.545197i	$0.183545\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−10.6515	−	18.4490i	−0.341472	−	0.591448i
$974$	14.0732	−	24.3755i	0.450935	−	0.781042i
$975$	2.44949	+	4.24264i	0.0784465	+	0.135873i
$976$	12.4495			0.398498
$977$	−8.94439			−0.286156			−0.143078	−	0.989711i	$-0.545700\pi$
$977$	−8.94439			−0.286156			−0.143078	+	0.989711i	$0.545700\pi$
$978$	8.34847	+	14.4600i	0.266955	+	0.462379i
$979$	−8.17423	−	14.1582i	−0.261250	−	0.452498i
$980$	−4.89898			−0.156492
$981$	1.34847			0.0430533
$982$	7.60102	+	13.1654i	0.242558	+	0.420123i
$983$	12.0959	−	20.9507i	0.385800	−	0.668225i	−0.606080	−	0.795404i	$-0.707259\pi$
$983$	12.0959	−	20.9507i	0.385800	−	0.668225i	0.991880	+	0.127179i	$0.0405922\pi$
$984$	2.17423	+	3.76588i	0.0693121	+	0.120052i
$985$	−3.27526	+	5.67291i	−0.104358	+	0.180754i
$986$	7.24745	−	12.5529i	0.230806	−	0.399767i
$987$	−1.59592			−0.0507986
$988$	15.5505	−	14.6349i	0.494728	−	0.465600i
$989$	69.5959			2.21302
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	−10.6742	+	18.4883i	−0.339078	+	0.587301i	−0.984260	−	0.176729i	$-0.943448\pi$
$991$	−10.6742	+	18.4883i	−0.339078	+	0.587301i	0.645181	+	0.764029i	$0.276782\pi$
$992$	0.449490	+	0.778539i	0.0142713	+	0.0247186i
$993$	9.17423	−	15.8902i	0.291136	−	0.504262i
$994$	−2.42679	−	4.20332i	−0.0769730	−	0.133321i
$995$	6.44949			0.204463
$996$	−11.7980			−0.373833
$997$	−12.2980	−	21.3007i	−0.389480	−	0.674600i	0.602899	−	0.797817i	$-0.294012\pi$
$997$	−12.2980	−	21.3007i	−0.389480	−	0.674600i	−0.992380	+	0.123218i	$0.960679\pi$
$998$	−5.27526	−	9.13701i	−0.166985	−	0.289227i
$999$	9.89898			0.313190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.f.391.1	yes	4
3.2	odd	2		1710.2.l.n.1531.1		4
19.7	even	3	inner	570.2.i.f.121.1	✓	4
57.26	odd	6		1710.2.l.n.1261.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.f.121.1	✓	4	19.7	even	3	inner
570.2.i.f.391.1	yes	4	1.1	even	1	trivial
1710.2.l.n.1261.1		4	57.26	odd	6
1710.2.l.n.1531.1		4	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} -1.44949 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} +(0.724745 - 1.25529i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.775255 - 1.34278i) q^{17} +1.00000 q^{18} +(-4.17423 - 1.25529i) q^{19} +1.00000 q^{20} +(-0.724745 + 1.25529i) q^{21} +(1.50000 - 2.59808i) q^{22} +(2.94949 + 5.10867i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.89898 q^{26} -1.00000 q^{27} +(0.724745 + 1.25529i) q^{28} +(-4.67423 - 8.09601i) q^{29} -1.00000 q^{30} -0.898979 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(0.775255 + 1.34278i) q^{34} +(0.724745 - 1.25529i) q^{35} +(-0.500000 + 0.866025i) q^{36} -9.89898 q^{37} +(3.17423 - 2.98735i) q^{38} -4.89898 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.17423 + 3.76588i) q^{41} +(-0.724745 - 1.25529i) q^{42} +(5.89898 - 10.2173i) q^{43} +(1.50000 + 2.59808i) q^{44} +1.00000 q^{45} -5.89898 q^{46} +(0.550510 + 0.953512i) q^{47} +(0.500000 + 0.866025i) q^{48} -4.89898 q^{49} +1.00000 q^{50} +(-0.775255 - 1.34278i) q^{51} +(-2.44949 + 4.24264i) q^{52} +(3.72474 + 6.45145i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} -1.44949 q^{56} +(-3.17423 + 2.98735i) q^{57} +9.34847 q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-6.22474 - 10.7816i) q^{61} +(0.449490 - 0.778539i) q^{62} +(0.724745 + 1.25529i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.67423 + 6.36396i) q^{67} -1.55051 q^{68} +5.89898 q^{69} +(0.724745 + 1.25529i) q^{70} +(1.67423 - 2.89986i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.22474 + 9.04952i) q^{73} +(4.94949 - 8.57277i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} +4.34847 q^{77} +(2.44949 - 4.24264i) q^{78} +(-3.44949 + 5.97469i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.17423 - 3.76588i) q^{82} +11.7980 q^{83} +1.44949 q^{84} +(0.775255 + 1.34278i) q^{85} +(5.89898 + 10.2173i) q^{86} -9.34847 q^{87} -3.00000 q^{88} +(2.72474 + 4.71940i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(3.55051 + 6.14966i) q^{91} +(2.94949 - 5.10867i) q^{92} +(-0.449490 + 0.778539i) q^{93} -1.10102 q^{94} +(3.17423 - 2.98735i) q^{95} -1.00000 q^{96} +(9.22474 - 15.9777i) 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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