LMFDB - Embedded newform 198.2.e.c.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.e (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:	$1.58103796002$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	198.133
Dual form			198.2.e.c.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +1.44949 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.724745 - 1.57313i) q^{12} +(2.22474 + 3.85337i) q^{13} +(2.22474 + 3.85337i) q^{14} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.44949 q^{17} +(-1.94949 + 2.28024i) q^{18} -6.00000 q^{19} +(-0.724745 + 1.25529i) q^{20} +(4.44949 - 6.29253i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(1.72474 + 0.158919i) q^{24} +(1.44949 - 2.51059i) q^{25} -4.44949 q^{26} +(5.00000 + 1.41421i) q^{27} -4.44949 q^{28} +(-2.67423 + 4.63191i) q^{29} +(2.50000 + 0.230351i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.41421i) q^{33} +(2.22474 - 3.85337i) q^{34} -6.44949 q^{35} +(-1.00000 - 2.82843i) q^{36} +4.55051 q^{37} +(3.00000 - 5.19615i) q^{38} +(3.22474 + 6.99964i) q^{39} +(-0.724745 - 1.25529i) q^{40} +(-1.67423 - 2.89986i) q^{41} +(3.22474 + 6.99964i) q^{42} +(-0.224745 + 0.389270i) q^{43} +1.00000 q^{44} +(-1.44949 - 4.09978i) q^{45} -6.00000 q^{46} +(1.94949 - 3.37662i) q^{47} +(-1.00000 + 1.41421i) q^{48} +(-6.39898 - 11.0834i) q^{49} +(1.44949 + 2.51059i) q^{50} +(-7.67423 - 0.707107i) q^{51} +(2.22474 - 3.85337i) q^{52} -12.3485 q^{53} +(-3.72474 + 3.62302i) q^{54} +1.44949 q^{55} +(2.22474 - 3.85337i) q^{56} +(-10.3485 - 0.953512i) q^{57} +(-2.67423 - 4.63191i) q^{58} +(0.275255 + 0.476756i) q^{59} +(-1.44949 + 2.04989i) q^{60} +(-6.89898 + 11.9494i) q^{61} +1.00000 q^{62} +(8.67423 - 10.1459i) q^{63} +1.00000 q^{64} +(3.22474 - 5.58542i) q^{65} +(-0.724745 - 1.57313i) q^{66} +(2.17423 + 3.76588i) q^{67} +(2.22474 + 3.85337i) q^{68} +(4.34847 + 9.43879i) q^{69} +(3.22474 - 5.58542i) q^{70} +8.79796 q^{71} +(2.94949 + 0.548188i) q^{72} -13.3485 q^{73} +(-2.27526 + 3.94086i) q^{74} +(2.89898 - 4.09978i) q^{75} +(3.00000 + 5.19615i) q^{76} +(2.22474 + 3.85337i) q^{77} +(-7.67423 - 0.707107i) q^{78} +(-2.67423 + 4.63191i) q^{79} +1.44949 q^{80} +(8.39898 + 3.23375i) q^{81} +3.34847 q^{82} +(4.00000 - 6.92820i) q^{83} +(-7.67423 - 0.707107i) q^{84} +(3.22474 + 5.58542i) q^{85} +(-0.224745 - 0.389270i) q^{86} +(-5.34847 + 7.56388i) q^{87} +(-0.500000 + 0.866025i) q^{88} +1.79796 q^{89} +(4.27526 + 0.794593i) q^{90} +19.7980 q^{91} +(3.00000 - 5.19615i) q^{92} +(-0.724745 - 1.57313i) q^{93} +(1.94949 + 3.37662i) q^{94} +(4.34847 + 7.53177i) q^{95} +(-0.724745 - 1.57313i) q^{96} +(-5.39898 + 9.35131i) q^{97} +12.7980 q^{98} +(-1.94949 + 2.28024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 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 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} - 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 24 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22} + 12 q^{23} + 2 q^{24} - 4 q^{25} - 8 q^{26} + 20 q^{27} - 8 q^{28} + 4 q^{29} + 10 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} + 4 q^{34} - 16 q^{35} - 4 q^{36} + 28 q^{37} + 12 q^{38} + 8 q^{39} + 2 q^{40} + 8 q^{41} + 8 q^{42} + 4 q^{43} + 4 q^{44} + 4 q^{45} - 24 q^{46} - 2 q^{47} - 4 q^{48} - 6 q^{49} - 4 q^{50} - 16 q^{51} + 4 q^{52} - 20 q^{53} - 10 q^{54} - 4 q^{55} + 4 q^{56} - 12 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} - 8 q^{61} + 4 q^{62} + 20 q^{63} + 4 q^{64} + 8 q^{65} + 2 q^{66} - 6 q^{67} + 4 q^{68} - 12 q^{69} + 8 q^{70} - 4 q^{71} + 2 q^{72} - 24 q^{73} - 14 q^{74} - 8 q^{75} + 12 q^{76} + 4 q^{77} - 16 q^{78} + 4 q^{79} - 4 q^{80} + 14 q^{81} - 16 q^{82} + 16 q^{83} - 16 q^{84} + 8 q^{85} + 4 q^{86} + 8 q^{87} - 2 q^{88} - 32 q^{89} + 22 q^{90} + 40 q^{91} + 12 q^{92} + 2 q^{93} - 2 q^{94} - 12 q^{95} + 2 q^{96} - 2 q^{97} + 12 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 - 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 24 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 12 * q^23 + 2 * q^24 - 4 * q^25 - 8 * q^26 + 20 * q^27 - 8 * q^28 + 4 * q^29 + 10 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 + 4 * q^34 - 16 * q^35 - 4 * q^36 + 28 * q^37 + 12 * q^38 + 8 * q^39 + 2 * q^40 + 8 * q^41 + 8 * q^42 + 4 * q^43 + 4 * q^44 + 4 * q^45 - 24 * q^46 - 2 * q^47 - 4 * q^48 - 6 * q^49 - 4 * q^50 - 16 * q^51 + 4 * q^52 - 20 * q^53 - 10 * q^54 - 4 * q^55 + 4 * q^56 - 12 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 - 8 * q^61 + 4 * q^62 + 20 * q^63 + 4 * q^64 + 8 * q^65 + 2 * q^66 - 6 * q^67 + 4 * q^68 - 12 * q^69 + 8 * q^70 - 4 * q^71 + 2 * q^72 - 24 * q^73 - 14 * q^74 - 8 * q^75 + 12 * q^76 + 4 * q^77 - 16 * q^78 + 4 * q^79 - 4 * q^80 + 14 * q^81 - 16 * q^82 + 16 * q^83 - 16 * q^84 + 8 * q^85 + 4 * q^86 + 8 * q^87 - 2 * q^88 - 32 * q^89 + 22 * q^90 + 40 * q^91 + 12 * q^92 + 2 * q^93 - 2 * q^94 - 12 * q^95 + 2 * q^96 - 2 * q^97 + 12 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.724745	−	1.25529i	−0.324116	−	0.561385i	0.657217	−	0.753701i	$-0.271733\pi$
$5$	−0.724745	−	1.25529i	−0.324116	−	0.561385i	−0.981333	+	0.192316i	$0.938400\pi$
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	2.22474	−	3.85337i	0.840875	−	1.45644i	−0.0482818	−	0.998834i	$-0.515375\pi$
$7$	2.22474	−	3.85337i	0.840875	−	1.45644i	0.889156	−	0.457604i	$-0.151292\pi$
$8$	1.00000			0.353553
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$	1.44949			0.458369
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.724745	−	1.57313i	−0.209216	−	0.454124i
$13$	2.22474	+	3.85337i	0.617033	+	1.06873i	0.990024	+	0.140898i	$0.0449989\pi$
$13$	2.22474	+	3.85337i	0.617033	+	1.06873i	−0.372991	+	0.927835i	$0.621668\pi$
$14$	2.22474	+	3.85337i	0.594588	+	1.02986i
$15$	−1.05051	−	2.28024i	−0.271241	−	0.588755i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.44949			−1.07916			−0.539580	−	0.841934i	$-0.681417\pi$
$17$	−4.44949			−1.07916			−0.539580	+	0.841934i	$0.681417\pi$
$18$	−1.94949	+	2.28024i	−0.459499	+	0.537457i
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−0.724745	+	1.25529i	−0.162058	+	0.280692i
$21$	4.44949	−	6.29253i	0.970958	−	1.37314i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	1.72474	+	0.158919i	0.352062	+	0.0324391i
$25$	1.44949	−	2.51059i	0.289898	−	0.502118i
$26$	−4.44949			−0.872617
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	−4.44949			−0.840875
$29$	−2.67423	+	4.63191i	−0.496593	+	0.860124i	−0.999992	−	0.00392972i	$-0.998749\pi$
$29$	−2.67423	+	4.63191i	−0.496593	+	0.860124i	0.503399	+	0.864054i	$0.332082\pi$
$30$	2.50000	+	0.230351i	0.456435	+	0.0420561i
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.00000	+	1.41421i	−0.174078	+	0.246183i
$34$	2.22474	−	3.85337i	0.381541	−	0.660848i
$35$	−6.44949			−1.09016
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	4.55051			0.748099			0.374050	−	0.927409i	$-0.377969\pi$
$37$	4.55051			0.748099			0.374050	+	0.927409i	$0.377969\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	3.22474	+	6.99964i	0.516372	+	1.12084i
$40$	−0.724745	−	1.25529i	−0.114592	−	0.198480i
$41$	−1.67423	−	2.89986i	−0.261472	−	0.452882i	0.705162	−	0.709047i	$-0.250874\pi$
$41$	−1.67423	−	2.89986i	−0.261472	−	0.452882i	−0.966633	+	0.256165i	$0.917541\pi$
$42$	3.22474	+	6.99964i	0.497589	+	1.08007i
$43$	−0.224745	+	0.389270i	−0.0342733	+	0.0593630i	−0.882653	−	0.470025i	$-0.844245\pi$
$43$	−0.224745	+	0.389270i	−0.0342733	+	0.0593630i	0.848380	+	0.529388i	$0.177578\pi$
$44$	1.00000			0.150756
$45$	−1.44949	−	4.09978i	−0.216077	−	0.611159i
$46$	−6.00000			−0.884652
$47$	1.94949	−	3.37662i	0.284362	−	0.492530i	−0.688092	−	0.725623i	$-0.741551\pi$
$47$	1.94949	−	3.37662i	0.284362	−	0.492530i	0.972454	+	0.233093i	$0.0748848\pi$
$48$	−1.00000	+	1.41421i	−0.144338	+	0.204124i
$49$	−6.39898	−	11.0834i	−0.914140	−	1.58334i
$50$	1.44949	+	2.51059i	0.204989	+	0.355051i
$51$	−7.67423	−	0.707107i	−1.07461	−	0.0990148i
$52$	2.22474	−	3.85337i	0.308517	−	0.534366i
$53$	−12.3485			−1.69619			−0.848096	−	0.529842i	$-0.822251\pi$
$53$	−12.3485			−1.69619			−0.848096	+	0.529842i	$0.822251\pi$
$54$	−3.72474	+	3.62302i	−0.506874	+	0.493031i
$55$	1.44949			0.195449
$56$	2.22474	−	3.85337i	0.297294	−	0.514928i
$57$	−10.3485	−	0.953512i	−1.37069	−	0.126296i
$58$	−2.67423	−	4.63191i	−0.351144	−	0.608200i
$59$	0.275255	+	0.476756i	0.0358352	+	0.0620683i	0.883387	−	0.468645i	$-0.155258\pi$
$59$	0.275255	+	0.476756i	0.0358352	+	0.0620683i	−0.847552	+	0.530713i	$0.821924\pi$
$60$	−1.44949	+	2.04989i	−0.187128	+	0.264639i
$61$	−6.89898	+	11.9494i	−0.883324	+	1.52996i	−0.0357010	+	0.999363i	$0.511366\pi$
$61$	−6.89898	+	11.9494i	−0.883324	+	1.52996i	−0.847623	+	0.530599i	$0.821967\pi$
$62$	1.00000			0.127000
$63$	8.67423	−	10.1459i	1.09285	−	1.27826i
$64$	1.00000			0.125000
$65$	3.22474	−	5.58542i	0.399980	−	0.692786i
$66$	−0.724745	−	1.57313i	−0.0892099	−	0.193639i
$67$	2.17423	+	3.76588i	0.265625	+	0.460076i	0.967727	−	0.252000i	$-0.0810884\pi$
$67$	2.17423	+	3.76588i	0.265625	+	0.460076i	−0.702102	+	0.712076i	$0.747755\pi$
$68$	2.22474	+	3.85337i	0.269790	+	0.467290i
$69$	4.34847	+	9.43879i	0.523494	+	1.13630i
$70$	3.22474	−	5.58542i	0.385431	−	0.667586i
$71$	8.79796			1.04413			0.522063	−	0.852907i	$-0.325163\pi$
$71$	8.79796			1.04413			0.522063	+	0.852907i	$0.325163\pi$
$72$	2.94949	+	0.548188i	0.347601	+	0.0646046i
$73$	−13.3485			−1.56232			−0.781160	−	0.624331i	$-0.785372\pi$
$73$	−13.3485			−1.56232			−0.781160	+	0.624331i	$0.785372\pi$
$74$	−2.27526	+	3.94086i	−0.264493	+	0.458115i
$75$	2.89898	−	4.09978i	0.334745	−	0.473401i
$76$	3.00000	+	5.19615i	0.344124	+	0.596040i
$77$	2.22474	+	3.85337i	0.253533	+	0.439132i
$78$	−7.67423	−	0.707107i	−0.868936	−	0.0800641i
$79$	−2.67423	+	4.63191i	−0.300875	+	0.521131i	−0.976334	−	0.216267i	$-0.930612\pi$
$79$	−2.67423	+	4.63191i	−0.300875	+	0.521131i	0.675459	+	0.737397i	$0.263945\pi$
$80$	1.44949			0.162058
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	3.34847			0.369777
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	−0.558560	−	0.829464i	$-0.688646\pi$
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	0.997617	+	0.0689950i	$0.0219793\pi$
$84$	−7.67423	−	0.707107i	−0.837328	−	0.0771517i
$85$	3.22474	+	5.58542i	0.349773	+	0.605824i
$86$	−0.224745	−	0.389270i	−0.0242349	−	0.0419760i
$87$	−5.34847	+	7.56388i	−0.573416	+	0.810933i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	1.79796			0.190583			0.0952916	−	0.995449i	$-0.469622\pi$
$89$	1.79796			0.190583			0.0952916	+	0.995449i	$0.469622\pi$
$90$	4.27526	+	0.794593i	0.450651	+	0.0837575i
$91$	19.7980			2.07539
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	−0.724745	−	1.57313i	−0.0751525	−	0.163126i
$94$	1.94949	+	3.37662i	0.201075	+	0.348271i
$95$	4.34847	+	7.53177i	0.446144	+	0.772743i
$96$	−0.724745	−	1.57313i	−0.0739690	−	0.160557i
$97$	−5.39898	+	9.35131i	−0.548183	+	0.949481i	0.450216	+	0.892920i	$0.351347\pi$
$97$	−5.39898	+	9.35131i	−0.548183	+	0.949481i	−0.998399	+	0.0565616i	$0.981986\pi$
$98$	12.7980			1.29279
$99$	−1.94949	+	2.28024i	−0.195931	+	0.229173i
$100$	−2.89898			−0.289898
$101$	9.34847	−	16.1920i	0.930207	−	1.61117i	0.147243	−	0.989100i	$-0.452960\pi$
$101$	9.34847	−	16.1920i	0.930207	−	1.61117i	0.782965	−	0.622066i	$-0.213707\pi$
$102$	4.44949	−	6.29253i	0.440565	−	0.623053i
$103$	5.50000	+	9.52628i	0.541931	+	0.938652i	0.998793	+	0.0491146i	$0.0156400\pi$
$103$	5.50000	+	9.52628i	0.541931	+	0.938652i	−0.456862	+	0.889538i	$0.651027\pi$
$104$	2.22474	+	3.85337i	0.218154	+	0.377854i
$105$	−11.1237	−	1.02494i	−1.08556	−	0.100024i
$106$	6.17423	−	10.6941i	0.599695	−	1.03870i
$107$	−1.34847			−0.130361			−0.0651807	−	0.997873i	$-0.520762\pi$
$107$	−1.34847			−0.130361			−0.0651807	+	0.997873i	$0.520762\pi$
$108$	−1.27526	−	5.03723i	−0.122711	−	0.484708i
$109$	6.89898			0.660802			0.330401	−	0.943841i	$-0.392816\pi$
$109$	6.89898			0.660802			0.330401	+	0.943841i	$0.392816\pi$
$110$	−0.724745	+	1.25529i	−0.0691017	+	0.119688i
$111$	7.84847	+	0.723161i	0.744944	+	0.0686394i
$112$	2.22474	+	3.85337i	0.210219	+	0.364109i
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	−0.982205	−	0.187813i	$-0.939860\pi$
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	0.328452	−	0.944521i	$-0.393473\pi$
$114$	6.00000	−	8.48528i	0.561951	−	0.794719i
$115$	4.34847	−	7.53177i	0.405497	−	0.702341i
$116$	5.34847			0.496593
$117$	4.44949	+	12.5851i	0.411355	+	1.16349i
$118$	−0.550510			−0.0506786
$119$	−9.89898	+	17.1455i	−0.907438	+	1.57173i
$120$	−1.05051	−	2.28024i	−0.0958980	−	0.208156i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−6.89898	−	11.9494i	−0.624604	−	1.08185i
$123$	−2.42679	−	5.26758i	−0.218816	−	0.474962i
$124$	−0.500000	+	0.866025i	−0.0449013	+	0.0777714i
$125$	−11.4495			−1.02407
$126$	4.44949	+	12.5851i	0.396392	+	1.12117i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.449490	+	0.635674i	−0.0395754	+	0.0559680i
$130$	3.22474	+	5.58542i	0.282829	+	0.489874i
$131$	1.77526	+	3.07483i	0.155105	+	0.268649i	0.933097	−	0.359624i	$-0.117095\pi$
$131$	1.77526	+	3.07483i	0.155105	+	0.268649i	−0.777992	+	0.628274i	$0.783762\pi$
$132$	1.72474	+	0.158919i	0.150120	+	0.0138321i
$133$	−13.3485	+	23.1202i	−1.15746	+	2.00478i
$134$	−4.34847			−0.375651
$135$	−1.84847	−	7.30142i	−0.159091	−	0.628406i
$136$	−4.44949			−0.381541
$137$	0.0505103	−	0.0874863i	0.00431538	−	0.00747446i	−0.863860	−	0.503733i	$-0.831960\pi$
$137$	0.0505103	−	0.0874863i	0.00431538	−	0.00747446i	0.868175	+	0.496258i	$0.165293\pi$
$138$	−10.3485	−	0.953512i	−0.880920	−	0.0811683i
$139$	3.12372	+	5.41045i	0.264951	+	0.458908i	0.967551	−	0.252677i	$-0.0813109\pi$
$139$	3.12372	+	5.41045i	0.264951	+	0.458908i	−0.702600	+	0.711585i	$0.747978\pi$
$140$	3.22474	+	5.58542i	0.272541	+	0.472054i
$141$	3.89898	−	5.51399i	0.328353	−	0.464362i
$142$	−4.39898	+	7.61926i	−0.369154	+	0.639394i
$143$	−4.44949			−0.372085
$144$	−1.94949	+	2.28024i	−0.162457	+	0.190020i
$145$	7.75255			0.643814
$146$	6.67423	−	11.5601i	0.552364	−	0.956722i
$147$	−9.27526	−	20.1329i	−0.765010	−	1.66053i
$148$	−2.27526	−	3.94086i	−0.187025	−	0.323936i
$149$	0.898979	+	1.55708i	0.0736473	+	0.127561i	0.900497	−	0.434862i	$-0.143203\pi$
$149$	0.898979	+	1.55708i	0.0736473	+	0.127561i	−0.826850	+	0.562423i	$0.809869\pi$
$150$	2.10102	+	4.56048i	0.171548	+	0.372361i
$151$	11.1237	−	19.2669i	0.905236	−	1.56791i	0.0846355	−	0.996412i	$-0.473027\pi$
$151$	11.1237	−	19.2669i	0.905236	−	1.56791i	0.820600	−	0.571503i	$-0.193639\pi$
$152$	−6.00000			−0.486664
$153$	−13.1237	−	2.43916i	−1.06099	−	0.197194i
$154$	−4.44949			−0.358550
$155$	−0.724745	+	1.25529i	−0.0582129	+	0.100828i
$156$	4.44949	−	6.29253i	0.356244	−	0.503806i
$157$	−8.72474	−	15.1117i	−0.696310	−	1.20605i	−0.969737	−	0.244152i	$-0.921490\pi$
$157$	−8.72474	−	15.1117i	−0.696310	−	1.20605i	0.273426	−	0.961893i	$-0.411843\pi$
$158$	−2.67423	−	4.63191i	−0.212751	−	0.368495i
$159$	−21.2980	−	1.96240i	−1.68904	−	0.155629i
$160$	−0.724745	+	1.25529i	−0.0572961	+	0.0992398i
$161$	26.6969			2.10401
$162$	−7.00000	+	5.65685i	−0.549972	+	0.444444i
$163$	4.55051			0.356423			0.178212	−	0.983992i	$-0.442969\pi$
$163$	4.55051			0.356423			0.178212	+	0.983992i	$0.442969\pi$
$164$	−1.67423	+	2.89986i	−0.130736	+	0.226441i
$165$	2.50000	+	0.230351i	0.194625	+	0.0179328i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	0.945099	−	0.326783i	$-0.105965\pi$
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	−0.755552	+	0.655089i	$0.772631\pi$
$168$	4.44949	−	6.29253i	0.343286	−	0.485479i
$169$	−3.39898	+	5.88721i	−0.261460	+	0.452862i
$170$	−6.44949			−0.494653
$171$	−17.6969	−	3.28913i	−1.35332	−	0.251526i
$172$	0.449490			0.0342733
$173$	1.22474	−	2.12132i	0.0931156	−	0.161281i	−0.815705	−	0.578468i	$-0.803651\pi$
$173$	1.22474	−	2.12132i	0.0931156	−	0.161281i	0.908821	+	0.417187i	$0.136984\pi$
$174$	−3.87628	−	8.41385i	−0.293860	−	0.637852i
$175$	−6.44949	−	11.1708i	−0.487536	−	0.844436i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	0.398979	+	0.866025i	0.0299891	+	0.0650945i
$178$	−0.898979	+	1.55708i	−0.0673814	+	0.116708i
$179$	7.65153			0.571902			0.285951	−	0.958244i	$-0.407690\pi$
$179$	7.65153			0.571902			0.285951	+	0.958244i	$0.407690\pi$
$180$	−2.82577	+	3.30518i	−0.210620	+	0.246354i
$181$	2.55051			0.189578			0.0947890	−	0.995497i	$-0.469782\pi$
$181$	2.55051			0.189578			0.0947890	+	0.995497i	$0.469782\pi$
$182$	−9.89898	+	17.1455i	−0.733761	+	1.27091i
$183$	−13.7980	+	19.5133i	−1.01997	+	1.44246i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−3.29796	−	5.71223i	−0.242471	−	0.419972i
$186$	1.72474	+	0.158919i	0.126464	+	0.0116525i
$187$	2.22474	−	3.85337i	0.162689	−	0.281786i
$188$	−3.89898			−0.284362
$189$	16.5732	−	16.1206i	1.20552	−	1.17260i
$190$	−8.69694			−0.630942
$191$	4.39898	−	7.61926i	0.318299	−	0.551310i	−0.661834	−	0.749650i	$-0.730222\pi$
$191$	4.39898	−	7.61926i	0.318299	−	0.551310i	0.980133	+	0.198340i	$0.0635551\pi$
$192$	1.72474	+	0.158919i	0.124473	+	0.0114690i
$193$	−6.44949	−	11.1708i	−0.464244	−	0.804095i	0.534923	−	0.844901i	$-0.320341\pi$
$193$	−6.44949	−	11.1708i	−0.464244	−	0.804095i	−0.999167	+	0.0408061i	$0.987007\pi$
$194$	−5.39898	−	9.35131i	−0.387624	−	0.671385i
$195$	6.44949	−	9.12096i	0.461858	−	0.653165i
$196$	−6.39898	+	11.0834i	−0.457070	+	0.791668i
$197$	0.247449			0.0176300			0.00881500	−	0.999961i	$-0.497194\pi$
$197$	0.247449			0.0176300			0.00881500	+	0.999961i	$0.497194\pi$
$198$	−1.00000	−	2.82843i	−0.0710669	−	0.201008i
$199$	5.00000			0.354441			0.177220	−	0.984171i	$-0.443289\pi$
$199$	5.00000			0.354441			0.177220	+	0.984171i	$0.443289\pi$
$200$	1.44949	−	2.51059i	0.102494	−	0.177526i
$201$	3.15153	+	6.84072i	0.222292	+	0.482507i
$202$	9.34847	+	16.1920i	0.657756	+	1.13927i
$203$	11.8990	+	20.6096i	0.835145	+	1.44651i
$204$	3.22474	+	6.99964i	0.225777	+	0.490073i
$205$	−2.42679	+	4.20332i	−0.169494	+	0.293572i
$206$	−11.0000			−0.766406
$207$	6.00000	+	16.9706i	0.417029	+	1.17954i
$208$	−4.44949			−0.308517
$209$	3.00000	−	5.19615i	0.207514	−	0.359425i
$210$	6.44949	−	9.12096i	0.445057	−	0.629406i
$211$	7.89898	+	13.6814i	0.543788	+	0.941869i	0.998682	+	0.0513231i	$0.0163438\pi$
$211$	7.89898	+	13.6814i	0.543788	+	0.941869i	−0.454894	+	0.890546i	$0.650323\pi$
$212$	6.17423	+	10.6941i	0.424048	+	0.734473i
$213$	15.1742	+	1.39816i	1.03972	+	0.0958003i
$214$	0.674235	−	1.16781i	0.0460897	−	0.0798298i
$215$	0.651531			0.0444340
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	−4.44949			−0.302051
$218$	−3.44949	+	5.97469i	−0.233629	+	0.404657i
$219$	−23.0227	−	2.12132i	−1.55573	−	0.143346i
$220$	−0.724745	−	1.25529i	−0.0488623	−	0.0846320i
$221$	−9.89898	−	17.1455i	−0.665877	−	1.15333i
$222$	−4.55051	+	6.43539i	−0.305410	+	0.431915i
$223$	−9.44949	+	16.3670i	−0.632785	+	1.09602i	0.354195	+	0.935171i	$0.384755\pi$
$223$	−9.44949	+	16.3670i	−0.632785	+	1.09602i	−0.986980	+	0.160844i	$0.948579\pi$
$224$	−4.44949			−0.297294
$225$	5.65153	−	6.61037i	0.376769	−	0.440691i
$226$	13.8990			0.924546
$227$	10.2247	−	17.7098i	0.678640	−	1.17544i	−0.296750	−	0.954955i	$-0.595903\pi$
$227$	10.2247	−	17.7098i	0.678640	−	1.17544i	0.975391	−	0.220484i	$-0.0707637\pi$
$228$	4.34847	+	9.43879i	0.287984	+	0.625099i
$229$	−5.55051	−	9.61377i	−0.366788	−	0.635296i	0.622273	−	0.782800i	$-0.286209\pi$
$229$	−5.55051	−	9.61377i	−0.366788	−	0.635296i	−0.989061	+	0.147505i	$0.952876\pi$
$230$	4.34847	+	7.53177i	0.286730	+	0.496630i
$231$	3.22474	+	6.99964i	0.212173	+	0.460542i
$232$	−2.67423	+	4.63191i	−0.175572	+	0.304100i
$233$	−8.44949			−0.553544			−0.276772	−	0.960936i	$-0.589265\pi$
$233$	−8.44949			−0.553544			−0.276772	+	0.960936i	$0.589265\pi$
$234$	−13.1237	−	2.43916i	−0.857925	−	0.159453i
$235$	−5.65153			−0.368665
$236$	0.275255	−	0.476756i	0.0179176	−	0.0310342i
$237$	−5.34847	+	7.56388i	−0.347420	+	0.491327i
$238$	−9.89898	−	17.1455i	−0.641656	−	1.11138i
$239$	−1.87628	−	3.24980i	−0.121366	−	0.210212i	0.798940	−	0.601410i	$-0.205394\pi$
$239$	−1.87628	−	3.24980i	−0.121366	−	0.210212i	−0.920307	+	0.391198i	$0.872061\pi$
$240$	2.50000	+	0.230351i	0.161374	+	0.0148691i
$241$	10.3485	−	17.9241i	0.666604	−	1.15459i	−0.312244	−	0.950002i	$-0.601081\pi$
$241$	10.3485	−	17.9241i	0.666604	−	1.15459i	0.978848	−	0.204589i	$-0.0655859\pi$
$242$	1.00000			0.0642824
$243$	13.9722	+	6.91215i	0.896317	+	0.443415i
$244$	13.7980			0.883324
$245$	−9.27526	+	16.0652i	−0.592574	+	1.02637i
$246$	5.77526	+	0.532134i	0.368217	+	0.0339276i
$247$	−13.3485	−	23.1202i	−0.849343	−	1.47110i
$248$	−0.500000	−	0.866025i	−0.0317500	−	0.0549927i
$249$	8.00000	−	11.3137i	0.506979	−	0.716977i
$250$	5.72474	−	9.91555i	0.362065	−	0.627114i
$251$	−22.6969			−1.43262			−0.716309	−	0.697783i	$-0.754170\pi$
$251$	−22.6969			−1.43262			−0.716309	+	0.697783i	$0.754170\pi$
$252$	−13.1237	−	2.43916i	−0.826717	−	0.153652i
$253$	−6.00000			−0.377217
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$	4.67423	+	10.1459i	0.292712	+	0.635361i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−0.325765	−	0.707107i	−0.0202813	−	0.0440225i
$259$	10.1237	−	17.5348i	0.629058	−	1.08956i
$260$	−6.44949			−0.399980
$261$	−10.4268	+	12.1958i	−0.645402	+	0.754900i
$262$	−3.55051			−0.219351
$263$	1.32577	−	2.29629i	0.0817502	−	0.141595i	−0.822252	−	0.569124i	$-0.807282\pi$
$263$	1.32577	−	2.29629i	0.0817502	−	0.141595i	0.904002	+	0.427529i	$0.140616\pi$
$264$	−1.00000	+	1.41421i	−0.0615457	+	0.0870388i
$265$	8.94949	+	15.5010i	0.549763	+	0.952217i
$266$	−13.3485	−	23.1202i	−0.818447	−	1.41759i
$267$	3.10102	+	0.285729i	0.189779	+	0.0174863i
$268$	2.17423	−	3.76588i	0.132813	−	0.230038i
$269$	20.3485			1.24067			0.620334	−	0.784338i	$-0.286997\pi$
$269$	20.3485			1.24067			0.620334	+	0.784338i	$0.286997\pi$
$270$	7.24745	+	2.04989i	0.441066	+	0.124752i
$271$	−4.20204			−0.255256			−0.127628	−	0.991822i	$-0.540736\pi$
$271$	−4.20204			−0.255256			−0.127628	+	0.991822i	$0.540736\pi$
$272$	2.22474	−	3.85337i	0.134895	−	0.233645i
$273$	34.1464	+	3.14626i	2.06664	+	0.190421i
$274$	0.0505103	+	0.0874863i	0.00305144	+	0.00528524i
$275$	1.44949	+	2.51059i	0.0874075	+	0.151394i
$276$	6.00000	−	8.48528i	0.361158	−	0.510754i
$277$	−2.10102	+	3.63907i	−0.126238	+	0.218651i	−0.922216	−	0.386675i	$-0.873624\pi$
$277$	−2.10102	+	3.63907i	−0.126238	+	0.218651i	0.795978	+	0.605325i	$0.206957\pi$
$278$	−6.24745			−0.374697
$279$	−1.00000	−	2.82843i	−0.0598684	−	0.169334i
$280$	−6.44949			−0.385431
$281$	−0.101021	+	0.174973i	−0.00602638	+	0.0104380i	−0.869023	−	0.494772i	$-0.835252\pi$
$281$	−0.101021	+	0.174973i	−0.00602638	+	0.0104380i	0.862996	+	0.505210i	$0.168585\pi$
$282$	2.82577	+	6.13361i	0.168272	+	0.365251i
$283$	−7.02270	−	12.1637i	−0.417456	−	0.723056i	0.578226	−	0.815876i	$-0.303745\pi$
$283$	−7.02270	−	12.1637i	−0.417456	−	0.723056i	−0.995683	+	0.0928206i	$0.970412\pi$
$284$	−4.39898	−	7.61926i	−0.261031	−	0.452120i
$285$	6.30306	+	13.6814i	0.373361	+	0.810418i
$286$	2.22474	−	3.85337i	0.131552	−	0.227855i
$287$	−14.8990			−0.879459
$288$	−1.00000	−	2.82843i	−0.0589256	−	0.166667i
$289$	2.79796			0.164586
$290$	−3.87628	+	6.71391i	−0.227623	+	0.394254i
$291$	−10.7980	+	15.2706i	−0.632988	+	0.895180i
$292$	6.67423	+	11.5601i	0.390580	+	0.676504i
$293$	15.4722	+	26.7986i	0.903895	+	1.56559i	0.822393	+	0.568919i	$0.192638\pi$
$293$	15.4722	+	26.7986i	0.903895	+	1.56559i	0.0815018	+	0.996673i	$0.474028\pi$
$294$	22.0732	+	2.03383i	1.28734	+	0.118616i
$295$	0.398979	−	0.691053i	0.0232295	−	0.0402346i
$296$	4.55051			0.264493
$297$	−3.72474	+	3.62302i	−0.216132	+	0.210229i
$298$	−1.79796			−0.104153
$299$	−13.3485	+	23.1202i	−0.771962	+	1.33708i
$300$	−5.00000	−	0.460702i	−0.288675	−	0.0265986i
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	11.1237	+	19.2669i	0.640098	+	1.10868i
$303$	18.6969	−	26.4415i	1.07411	−	1.51902i
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	20.0000			1.14520
$306$	8.67423	−	10.1459i	0.495873	−	0.580002i
$307$	−18.4495			−1.05297			−0.526484	−	0.850185i	$-0.676490\pi$
$307$	−18.4495			−1.05297			−0.526484	+	0.850185i	$0.676490\pi$
$308$	2.22474	−	3.85337i	0.126767	−	0.219566i
$309$	7.97219	+	17.3045i	0.453522	+	0.984416i
$310$	−0.724745	−	1.25529i	−0.0411627	−	0.0712960i
$311$	−4.94949	−	8.57277i	−0.280660	−	0.486117i	0.690888	−	0.722962i	$-0.257220\pi$
$311$	−4.94949	−	8.57277i	−0.280660	−	0.486117i	−0.971547	+	0.236845i	$0.923887\pi$
$312$	3.22474	+	6.99964i	0.182565	+	0.396276i
$313$	7.34847	−	12.7279i	0.415360	−	0.719425i	−0.580106	−	0.814541i	$-0.696989\pi$
$313$	7.34847	−	12.7279i	0.415360	−	0.719425i	0.995466	+	0.0951162i	$0.0303223\pi$
$314$	17.4495			0.984732
$315$	−19.0227	−	3.53553i	−1.07181	−	0.199205i
$316$	5.34847			0.300875
$317$	4.79796	−	8.31031i	0.269480	−	0.466753i	−0.699247	−	0.714880i	$-0.746481\pi$
$317$	4.79796	−	8.31031i	0.269480	−	0.466753i	0.968728	+	0.248126i	$0.0798148\pi$
$318$	12.3485	−	17.4634i	0.692468	−	0.979297i
$319$	−2.67423	−	4.63191i	−0.149728	−	0.259337i
$320$	−0.724745	−	1.25529i	−0.0405145	−	0.0701731i
$321$	−2.32577	−	0.214297i	−0.129812	−	0.0119609i
$322$	−13.3485	+	23.1202i	−0.743881	+	1.28844i
$323$	26.6969			1.48546
$324$	−1.39898	−	8.89060i	−0.0777211	−	0.493922i
$325$	12.8990			0.715507
$326$	−2.27526	+	3.94086i	−0.126015	+	0.218264i
$327$	11.8990	+	1.09638i	0.658015	+	0.0606297i
$328$	−1.67423	−	2.89986i	−0.0924441	−	0.160118i
$329$	−8.67423	−	15.0242i	−0.478226	−	0.828312i
$330$	−1.44949	+	2.04989i	−0.0797918	+	0.112843i
$331$	11.2753	−	19.5293i	0.619744	−	1.07343i	−0.369788	−	0.929116i	$-0.620570\pi$
$331$	11.2753	−	19.5293i	0.619744	−	1.07343i	0.989532	−	0.144312i	$-0.0460969\pi$
$332$	−8.00000			−0.439057
$333$	13.4217	+	2.49454i	0.735504	+	0.136700i
$334$	−4.89898			−0.268060
$335$	3.15153	−	5.45861i	0.172187	−	0.298236i
$336$	3.22474	+	6.99964i	0.175924	+	0.381861i
$337$	−17.4722	−	30.2627i	−0.951771	−	1.64852i	−0.741590	−	0.670853i	$-0.765928\pi$
$337$	−17.4722	−	30.2627i	−0.951771	−	1.64852i	−0.210181	−	0.977663i	$-0.567405\pi$
$338$	−3.39898	−	5.88721i	−0.184880	−	0.320222i
$339$	−10.0732	−	21.8649i	−0.547102	−	1.18754i
$340$	3.22474	−	5.58542i	0.174886	−	0.302912i
$341$	1.00000			0.0541530
$342$	11.6969	−	13.6814i	0.632498	−	0.739807i
$343$	−25.7980			−1.39296
$344$	−0.224745	+	0.389270i	−0.0121174	+	0.0209880i
$345$	8.69694	−	12.2993i	0.468227	−	0.662174i
$346$	1.22474	+	2.12132i	0.0658427	+	0.114043i
$347$	−0.123724	−	0.214297i	−0.00664187	−	0.0115041i	0.862685	−	0.505741i	$-0.168781\pi$
$347$	−0.123724	−	0.214297i	−0.00664187	−	0.0115041i	−0.869327	+	0.494237i	$0.835448\pi$
$348$	9.22474	+	0.849971i	0.494498	+	0.0455632i
$349$	−16.0227	+	27.7521i	−0.857676	+	1.48554i	0.0164647	+	0.999864i	$0.494759\pi$
$349$	−16.0227	+	27.7521i	−0.857676	+	1.48554i	−0.874140	+	0.485673i	$0.838574\pi$
$350$	12.8990			0.689479
$351$	5.67423	+	22.4131i	0.302868	+	1.19632i
$352$	1.00000			0.0533002
$353$	−12.7980	+	22.1667i	−0.681167	+	1.17982i	0.293459	+	0.955972i	$0.405194\pi$
$353$	−12.7980	+	22.1667i	−0.681167	+	1.17982i	−0.974625	+	0.223843i	$0.928140\pi$
$354$	−0.949490	−	0.0874863i	−0.0504648	−	0.00464985i
$355$	−6.37628	−	11.0440i	−0.338418	−	0.586156i
$356$	−0.898979	−	1.55708i	−0.0476458	−	0.0825250i
$357$	−19.7980	+	27.9985i	−1.04782	+	1.48184i
$358$	−3.82577	+	6.62642i	−0.202198	+	0.350217i
$359$	30.6969			1.62012			0.810061	−	0.586345i	$-0.199434\pi$
$359$	30.6969			1.62012			0.810061	+	0.586345i	$0.199434\pi$
$360$	−1.44949	−	4.09978i	−0.0763948	−	0.216077i
$361$	17.0000			0.894737
$362$	−1.27526	+	2.20881i	−0.0670259	+	0.116092i
$363$	−0.724745	−	1.57313i	−0.0380392	−	0.0825680i
$364$	−9.89898	−	17.1455i	−0.518848	−	0.898670i
$365$	9.67423	+	16.7563i	0.506373	+	0.877063i
$366$	−10.0000	−	21.7060i	−0.522708	−	1.13459i
$367$	−5.74745	+	9.95487i	−0.300014	+	0.519640i	−0.976139	−	0.217147i	$-0.930325\pi$
$367$	−5.74745	+	9.95487i	−0.300014	+	0.519640i	0.676124	+	0.736787i	$0.263658\pi$
$368$	−6.00000			−0.312772
$369$	−3.34847	−	9.47090i	−0.174314	−	0.493035i
$370$	6.59592			0.342905
$371$	−27.4722	+	47.5832i	−1.42629	+	2.47040i
$372$	−1.00000	+	1.41421i	−0.0518476	+	0.0733236i
$373$	10.5505	+	18.2740i	0.546285	+	0.946193i	0.998525	+	0.0542967i	$0.0172917\pi$
$373$	10.5505	+	18.2740i	0.546285	+	0.946193i	−0.452240	+	0.891896i	$0.649375\pi$
$374$	2.22474	+	3.85337i	0.115039	+	0.199253i
$375$	−19.7474	−	1.81954i	−1.01975	−	0.0939605i
$376$	1.94949	−	3.37662i	0.100537	−	0.174136i
$377$	−23.7980			−1.22566
$378$	5.67423	+	22.4131i	0.291851	+	1.15281i
$379$	6.69694			0.343999			0.171999	−	0.985097i	$-0.444977\pi$
$379$	6.69694			0.343999			0.171999	+	0.985097i	$0.444977\pi$
$380$	4.34847	−	7.53177i	0.223072	−	0.386372i
$381$	3.44949	+	0.317837i	0.176723	+	0.0162833i
$382$	4.39898	+	7.61926i	0.225071	+	0.389835i
$383$	−11.8485	−	20.5222i	−0.605428	−	1.04863i	−0.991984	−	0.126367i	$-0.959668\pi$
$383$	−11.8485	−	20.5222i	−0.605428	−	1.04863i	0.386555	−	0.922266i	$-0.373665\pi$
$384$	−1.00000	+	1.41421i	−0.0510310	+	0.0721688i
$385$	3.22474	−	5.58542i	0.164348	−	0.284659i
$386$	12.8990			0.656541
$387$	−0.876276	+	1.02494i	−0.0445436	+	0.0521008i
$388$	10.7980			0.548183
$389$	−9.07321	+	15.7153i	−0.460030	+	0.796796i	−0.998962	−	0.0455538i	$-0.985495\pi$
$389$	−9.07321	+	15.7153i	−0.460030	+	0.796796i	0.538932	+	0.842349i	$0.318828\pi$
$390$	4.67423	+	10.1459i	0.236689	+	0.513758i
$391$	−13.3485	−	23.1202i	−0.675061	−	1.16924i
$392$	−6.39898	−	11.0834i	−0.323197	−	0.559794i
$393$	2.57321	+	5.58542i	0.129801	+	0.281747i
$394$	−0.123724	+	0.214297i	−0.00623314	+	0.0107961i
$395$	7.75255			0.390073
$396$	2.94949	+	0.548188i	0.148217	+	0.0275475i
$397$	27.2474			1.36751			0.683755	−	0.729712i	$-0.260346\pi$
$397$	27.2474			1.36751			0.683755	+	0.729712i	$0.260346\pi$
$398$	−2.50000	+	4.33013i	−0.125314	+	0.217050i
$399$	−26.6969	+	37.7552i	−1.33652	+	1.89012i
$400$	1.44949	+	2.51059i	0.0724745	+	0.125529i
$401$	−12.9495	−	22.4292i	−0.646667	−	1.12006i	−0.983914	−	0.178643i	$-0.942829\pi$
$401$	−12.9495	−	22.4292i	−0.646667	−	1.12006i	0.337247	−	0.941416i	$-0.390504\pi$
$402$	−7.50000	−	0.691053i	−0.374066	−	0.0344666i
$403$	2.22474	−	3.85337i	0.110822	−	0.191950i
$404$	−18.6969			−0.930207
$405$	−2.02781	−	12.8868i	−0.100763	−	0.640352i
$406$	−23.7980			−1.18107
$407$	−2.27526	+	3.94086i	−0.112780	+	0.195341i
$408$	−7.67423	−	0.707107i	−0.379931	−	0.0350070i
$409$	8.67423	+	15.0242i	0.428913	+	0.742900i	0.996777	−	0.0802230i	$-0.0255632\pi$
$409$	8.67423	+	15.0242i	0.428913	+	0.742900i	−0.567864	+	0.823123i	$0.692230\pi$
$410$	−2.42679	−	4.20332i	−0.119850	−	0.207587i
$411$	0.101021	−	0.142865i	0.00498297	−	0.00704699i
$412$	5.50000	−	9.52628i	0.270966	−	0.469326i
$413$	2.44949			0.120532
$414$	−17.6969	−	3.28913i	−0.869757	−	0.161652i
$415$	−11.5959			−0.569221
$416$	2.22474	−	3.85337i	0.109077	−	0.188927i
$417$	4.52781	+	9.82806i	0.221728	+	0.481282i
$418$	3.00000	+	5.19615i	0.146735	+	0.254152i
$419$	−7.62372	−	13.2047i	−0.372443	−	0.645091i	0.617498	−	0.786573i	$-0.288147\pi$
$419$	−7.62372	−	13.2047i	−0.372443	−	0.645091i	−0.989941	+	0.141482i	$0.954813\pi$
$420$	4.67423	+	10.1459i	0.228079	+	0.495069i
$421$	5.72474	−	9.91555i	0.279007	−	0.483254i	−0.692131	−	0.721772i	$-0.743328\pi$
$421$	5.72474	−	9.91555i	0.279007	−	0.483254i	0.971138	+	0.238517i	$0.0766614\pi$
$422$	−15.7980			−0.769033
$423$	7.60102	−	8.89060i	0.369574	−	0.432276i
$424$	−12.3485			−0.599695
$425$	−6.44949	+	11.1708i	−0.312846	+	0.541866i
$426$	−8.79796	+	12.4422i	−0.426263	+	0.602826i
$427$	30.6969	+	53.1687i	1.48553	+	2.57301i
$428$	0.674235	+	1.16781i	0.0325904	+	0.0564482i
$429$	−7.67423	−	0.707107i	−0.370516	−	0.0341394i
$430$	−0.325765	+	0.564242i	−0.0157098	+	0.0272102i
$431$	−6.44949			−0.310661			−0.155330	−	0.987863i	$-0.549644\pi$
$431$	−6.44949			−0.310661			−0.155330	+	0.987863i	$0.549644\pi$
$432$	−3.72474	+	3.62302i	−0.179207	+	0.174313i
$433$	−36.4949			−1.75383			−0.876916	−	0.480643i	$-0.840403\pi$
$433$	−36.4949			−1.75383			−0.876916	+	0.480643i	$0.840403\pi$
$434$	2.22474	−	3.85337i	0.106791	−	0.184968i
$435$	13.3712	+	1.23202i	0.641099	+	0.0590711i
$436$	−3.44949	−	5.97469i	−0.165201	−	0.286136i
$437$	−18.0000	−	31.1769i	−0.861057	−	1.49139i
$438$	13.3485	−	18.8776i	0.637815	−	0.902006i
$439$	20.3485	−	35.2446i	0.971179	−	1.68213i	0.279173	−	0.960241i	$-0.409940\pi$
$439$	20.3485	−	35.2446i	0.971179	−	1.68213i	0.692006	−	0.721891i	$-0.256727\pi$
$440$	1.44949			0.0691017
$441$	−12.7980	−	36.1981i	−0.609427	−	1.72372i
$442$	19.7980			0.941693
$443$	−19.0732	+	33.0358i	−0.906196	+	1.56958i	−0.0868917	+	0.996218i	$0.527693\pi$
$443$	−19.0732	+	33.0358i	−0.906196	+	1.56958i	−0.819304	+	0.573359i	$0.805640\pi$
$444$	−3.29796	−	7.15855i	−0.156514	−	0.339730i
$445$	−1.30306	−	2.25697i	−0.0617710	−	0.106991i
$446$	−9.44949	−	16.3670i	−0.447446	−	0.775000i
$447$	1.30306	+	2.82843i	0.0616327	+	0.133780i
$448$	2.22474	−	3.85337i	0.105109	−	0.182055i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	2.89898	+	8.19955i	0.136659	+	0.386531i
$451$	3.34847			0.157673
$452$	−6.94949	+	12.0369i	−0.326877	+	0.566167i
$453$	22.2474	−	31.4626i	1.04528	−	1.47824i
$454$	10.2247	+	17.7098i	0.479871	+	0.831161i
$455$	−14.3485	−	24.8523i	−0.672667	−	1.16509i
$456$	−10.3485	−	0.953512i	−0.484611	−	0.0446523i
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	11.1010			0.518717
$459$	−22.2474	−	6.29253i	−1.03842	−	0.293710i
$460$	−8.69694			−0.405497
$461$	6.12372	−	10.6066i	0.285210	−	0.493999i	−0.687450	−	0.726232i	$-0.741270\pi$
$461$	6.12372	−	10.6066i	0.285210	−	0.493999i	0.972660	+	0.232233i	$0.0746032\pi$
$462$	−7.67423	−	0.707107i	−0.357038	−	0.0328976i
$463$	−5.00000	−	8.66025i	−0.232370	−	0.402476i	0.726135	−	0.687552i	$-0.241315\pi$
$463$	−5.00000	−	8.66025i	−0.232370	−	0.402476i	−0.958505	+	0.285076i	$0.907981\pi$
$464$	−2.67423	−	4.63191i	−0.124148	−	0.215031i
$465$	−1.44949	+	2.04989i	−0.0672185	+	0.0950613i
$466$	4.22474	−	7.31747i	0.195708	−	0.338975i
$467$	−40.1464			−1.85776			−0.928878	−	0.370387i	$-0.879225\pi$
$467$	−40.1464			−1.85776			−0.928878	+	0.370387i	$0.879225\pi$
$468$	8.67423	−	10.1459i	0.400967	−	0.468994i
$469$	19.3485			0.893429
$470$	2.82577	−	4.89437i	0.130343	−	0.225760i
$471$	−12.6464	−	27.4504i	−0.582717	−	1.26485i
$472$	0.275255	+	0.476756i	0.0126696	+	0.0219445i
$473$	−0.224745	−	0.389270i	−0.0103338	−	0.0178986i
$474$	−3.87628	−	8.41385i	−0.178043	−	0.386461i
$475$	−8.69694	+	15.0635i	−0.399043	+	0.691163i
$476$	19.7980			0.907438
$477$	−36.4217	−	6.76928i	−1.66763	−	0.309944i
$478$	3.75255			0.171638
$479$	8.89898	−	15.4135i	0.406605	−	0.704260i	−0.587902	−	0.808932i	$-0.700046\pi$
$479$	8.89898	−	15.4135i	0.406605	−	0.704260i	0.994507	+	0.104672i	$0.0333793\pi$
$480$	−1.44949	+	2.04989i	−0.0661599	+	0.0935642i
$481$	10.1237	+	17.5348i	0.461602	+	0.799518i
$482$	10.3485	+	17.9241i	0.471360	+	0.816419i
$483$	46.0454	+	4.24264i	2.09514	+	0.193047i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	15.6515			0.710699
$486$	−12.9722	+	8.64420i	−0.588431	+	0.392109i
$487$	1.00000			0.0453143			0.0226572	−	0.999743i	$-0.492787\pi$
$487$	1.00000			0.0453143			0.0226572	+	0.999743i	$0.492787\pi$
$488$	−6.89898	+	11.9494i	−0.312302	+	0.540923i
$489$	7.84847	+	0.723161i	0.354920	+	0.0327025i
$490$	−9.27526	−	16.0652i	−0.419013	−	0.725752i
$491$	12.2474	+	21.2132i	0.552720	+	0.957338i	0.998077	+	0.0619856i	$0.0197433\pi$
$491$	12.2474	+	21.2132i	0.552720	+	0.957338i	−0.445357	+	0.895353i	$0.646923\pi$
$492$	−3.34847	+	4.73545i	−0.150961	+	0.213491i
$493$	11.8990	−	20.6096i	0.535903	−	0.928211i
$494$	26.6969			1.20115
$495$	4.27526	+	0.794593i	0.192158	+	0.0357143i
$496$	1.00000			0.0449013
$497$	19.5732	−	33.9018i	0.877979	−	1.52070i
$498$	5.79796	+	12.5851i	0.259813	+	0.563950i
$499$	13.2753	+	22.9934i	0.594282	+	1.02933i	0.993648	+	0.112535i	$0.0358970\pi$
$499$	13.2753	+	22.9934i	0.594282	+	1.02933i	−0.399366	+	0.916792i	$0.630770\pi$
$500$	5.72474	+	9.91555i	0.256018	+	0.443437i
$501$	3.55051	+	7.70674i	0.158625	+	0.344312i
$502$	11.3485	−	19.6561i	0.506507	−	0.877296i
$503$	34.4949			1.53805			0.769026	−	0.639218i	$-0.220742\pi$
$503$	34.4949			1.53805			0.769026	+	0.639218i	$0.220742\pi$
$504$	8.67423	−	10.1459i	0.386381	−	0.451934i
$505$	−27.1010			−1.20598
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	−6.79796	+	9.61377i	−0.301908	+	0.426962i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	17.8990	+	31.0019i	0.793358	+	1.37414i	0.923876	+	0.382691i	$0.125003\pi$
$509$	17.8990	+	31.0019i	0.793358	+	1.37414i	−0.130518	+	0.991446i	$0.541664\pi$
$510$	−11.1237	−	1.02494i	−0.492567	−	0.0453853i
$511$	−29.6969	+	51.4366i	−1.31372	+	2.27542i
$512$	1.00000			0.0441942
$513$	−30.0000	−	8.48528i	−1.32453	−	0.374634i
$514$	−6.00000			−0.264649
$515$	7.97219	−	13.8082i	0.351297	−	0.608464i
$516$	0.775255	+	0.0714323i	0.0341287	+	0.00314463i
$517$	1.94949	+	3.37662i	0.0857385	+	0.148503i
$518$	10.1237	+	17.5348i	0.444811	+	0.770435i
$519$	2.44949	−	3.46410i	0.107521	−	0.152057i
$520$	3.22474	−	5.58542i	0.141414	−	0.244937i
$521$	−34.5959			−1.51567			−0.757837	−	0.652444i	$-0.773744\pi$
$521$	−34.5959			−1.51567			−0.757837	+	0.652444i	$0.773744\pi$
$522$	−5.34847	−	15.1278i	−0.234096	−	0.662124i
$523$	0.651531			0.0284895			0.0142447	−	0.999899i	$-0.495466\pi$
$523$	0.651531			0.0284895			0.0142447	+	0.999899i	$0.495466\pi$
$524$	1.77526	−	3.07483i	0.0775524	−	0.134325i
$525$	−9.34847	−	20.2918i	−0.408001	−	0.885607i
$526$	1.32577	+	2.29629i	0.0578061	+	0.100123i
$527$	2.22474	+	3.85337i	0.0969114	+	0.167855i
$528$	−0.724745	−	1.57313i	−0.0315405	−	0.0684618i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−17.8990			−0.777482
$531$	0.550510	+	1.55708i	0.0238901	+	0.0675714i
$532$	26.6969			1.15746
$533$	7.44949	−	12.9029i	0.322673	−	0.558886i
$534$	−1.79796	+	2.54270i	−0.0778053	+	0.110033i
$535$	0.977296	+	1.69273i	0.0422522	+	0.0731830i
$536$	2.17423	+	3.76588i	0.0939126	+	0.162661i
$537$	13.1969	+	1.21597i	0.569490	+	0.0524730i
$538$	−10.1742	+	17.6223i	−0.438642	+	0.759751i
$539$	12.7980			0.551247
$540$	−5.39898	+	5.25153i	−0.232335	+	0.225990i
$541$	−6.24745			−0.268599			−0.134299	−	0.990941i	$-0.542878\pi$
$541$	−6.24745			−0.268599			−0.134299	+	0.990941i	$0.542878\pi$
$542$	2.10102	−	3.63907i	0.0902466	−	0.156312i
$543$	4.39898	+	0.405324i	0.188778	+	0.0173941i
$544$	2.22474	+	3.85337i	0.0953851	+	0.165212i
$545$	−5.00000	−	8.66025i	−0.214176	−	0.370965i
$546$	−19.7980	+	27.9985i	−0.847274	+	1.19823i
$547$	−6.34847	+	10.9959i	−0.271441	+	0.470150i	−0.969231	−	0.246153i	$-0.920833\pi$
$547$	−6.34847	+	10.9959i	−0.271441	+	0.470150i	0.697790	+	0.716302i	$0.254167\pi$
$548$	−0.101021			−0.00431538
$549$	−26.8990	+	31.4626i	−1.14802	+	1.34279i
$550$	−2.89898			−0.123613
$551$	16.0454	−	27.7915i	0.683557	−	1.18396i
$552$	4.34847	+	9.43879i	0.185083	+	0.401742i
$553$	11.8990	+	20.6096i	0.505996	+	0.876411i
$554$	−2.10102	−	3.63907i	−0.0892638	−	0.154609i
$555$	−4.78036	−	10.3763i	−0.202915	−	0.440447i
$556$	3.12372	−	5.41045i	0.132475	−	0.229454i
$557$	12.8990			0.546547			0.273274	−	0.961936i	$-0.411894\pi$
$557$	12.8990			0.546547			0.273274	+	0.961936i	$0.411894\pi$
$558$	2.94949	+	0.548188i	0.124862	+	0.0232067i
$559$	−2.00000			−0.0845910
$560$	3.22474	−	5.58542i	0.136270	−	0.236027i
$561$	4.44949	−	6.29253i	0.187858	−	0.265671i
$562$	−0.101021	−	0.174973i	−0.00426129	−	0.00738078i
$563$	−2.02270	−	3.50343i	−0.0852468	−	0.147652i	0.820250	−	0.572006i	$-0.193835\pi$
$563$	−2.02270	−	3.50343i	−0.0852468	−	0.147652i	−0.905496	+	0.424354i	$0.860501\pi$
$564$	−6.72474	−	0.619620i	−0.283163	−	0.0260907i
$565$	−10.0732	+	17.4473i	−0.423783	+	0.734014i
$566$	14.0454			0.590373
$567$	31.1464	−	25.1701i	1.30803	−	1.05705i
$568$	8.79796			0.369154
$569$	11.9217	−	20.6490i	0.499783	−	0.865649i	−0.500217	−	0.865900i	$-0.666746\pi$
$569$	11.9217	−	20.6490i	0.499783	−	0.865649i	1.00000		0.000250593i	$7.97663e-5\pi$
$570$	−15.0000	−	1.38211i	−0.628281	−	0.0578900i
$571$	17.9217	+	31.0413i	0.749999	+	1.29904i	0.947822	+	0.318799i	$0.103279\pi$
$571$	17.9217	+	31.0413i	0.749999	+	1.29904i	−0.197823	+	0.980238i	$0.563387\pi$
$572$	2.22474	+	3.85337i	0.0930213	+	0.161118i
$573$	8.79796	−	12.4422i	0.367540	−	0.519780i
$574$	7.44949	−	12.9029i	0.310936	−	0.538556i
$575$	17.3939			0.725375
$576$	2.94949	+	0.548188i	0.122895	+	0.0228412i
$577$	15.2020			0.632869			0.316435	−	0.948614i	$-0.397514\pi$
$577$	15.2020			0.632869			0.316435	+	0.948614i	$0.397514\pi$
$578$	−1.39898	+	2.42310i	−0.0581899	+	0.100788i
$579$	−9.34847	−	20.2918i	−0.388509	−	0.843298i
$580$	−3.87628	−	6.71391i	−0.160954	−	0.278780i
$581$	−17.7980	−	30.8270i	−0.738384	−	1.27892i
$582$	−7.82577	−	16.9866i	−0.324388	−	0.704118i
$583$	6.17423	−	10.6941i	0.255711	−	0.442904i
$584$	−13.3485			−0.552364
$585$	12.5732	−	14.7064i	0.519838	−	0.608034i
$586$	−30.9444			−1.27830
$587$	7.72474	−	13.3797i	0.318834	−	0.552237i	−0.661411	−	0.750024i	$-0.730042\pi$
$587$	7.72474	−	13.3797i	0.318834	−	0.552237i	0.980245	+	0.197787i	$0.0633753\pi$
$588$	−12.7980	+	18.0990i	−0.527779	+	0.746392i
$589$	3.00000	+	5.19615i	0.123613	+	0.214104i
$590$	0.398979	+	0.691053i	0.0164257	+	0.0284502i
$591$	0.426786	+	0.0393242i	0.0175556	+	0.00161758i
$592$	−2.27526	+	3.94086i	−0.0935124	+	0.161968i
$593$	−30.4495			−1.25041			−0.625205	−	0.780460i	$-0.714985\pi$
$593$	−30.4495			−1.25041			−0.625205	+	0.780460i	$0.714985\pi$
$594$	−1.27526	−	5.03723i	−0.0523244	−	0.206680i
$595$	28.6969			1.17646
$596$	0.898979	−	1.55708i	0.0368236	−	0.0637804i
$597$	8.62372	+	0.794593i	0.352946	+	0.0325205i
$598$	−13.3485	−	23.1202i	−0.545859	−	0.945456i
$599$	17.6969	+	30.6520i	0.723077	+	1.25241i	0.959761	+	0.280820i	$0.0906063\pi$
$599$	17.6969	+	30.6520i	0.723077	+	1.25241i	−0.236683	+	0.971587i	$0.576060\pi$
$600$	2.89898	−	4.09978i	0.118350	−	0.167373i
$601$	1.65153	−	2.86054i	0.0673673	−	0.116684i	−0.830374	−	0.557206i	$-0.811873\pi$
$601$	1.65153	−	2.86054i	0.0673673	−	0.116684i	0.897742	+	0.440522i	$0.145207\pi$
$602$	−2.00000			−0.0815139
$603$	4.34847	+	12.2993i	0.177083	+	0.500867i
$604$	−22.2474			−0.905236
$605$	−0.724745	+	1.25529i	−0.0294651	+	0.0510350i
$606$	13.5505	+	29.4128i	0.550452	+	1.19481i
$607$	−10.6742	−	18.4883i	−0.433254	−	0.750418i	0.563897	−	0.825845i	$-0.309301\pi$
$607$	−10.6742	−	18.4883i	−0.433254	−	0.750418i	−0.997151	+	0.0754272i	$0.975968\pi$
$608$	3.00000	+	5.19615i	0.121666	+	0.210732i
$609$	17.2474	+	37.4373i	0.698902	+	1.51704i
$610$	−10.0000	+	17.3205i	−0.404888	+	0.701287i
$611$	17.3485			0.701844
$612$	4.44949	+	12.5851i	0.179860	+	0.508721i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	9.22474	−	15.9777i	0.372280	−	0.644809i
$615$	−4.85357	+	6.86399i	−0.195715	+	0.276783i
$616$	2.22474	+	3.85337i	0.0896375	+	0.155257i
$617$	22.2980	+	38.6212i	0.897682	+	1.55483i	0.830450	+	0.557094i	$0.188084\pi$
$617$	22.2980	+	38.6212i	0.897682	+	1.55483i	0.0672323	+	0.997737i	$0.478583\pi$
$618$	−18.9722	−	1.74810i	−0.763174	−	0.0703191i
$619$	20.0732	−	34.7678i	0.806811	−	1.39744i	−0.108251	−	0.994124i	$-0.534525\pi$
$619$	20.0732	−	34.7678i	0.806811	−	1.39744i	0.915062	−	0.403313i	$-0.132142\pi$
$620$	1.44949			0.0582129
$621$	7.65153	+	30.2234i	0.307045	+	1.21282i
$622$	9.89898			0.396913
$623$	4.00000	−	6.92820i	0.160257	−	0.277573i
$624$	−7.67423	−	0.707107i	−0.307215	−	0.0283069i
$625$	1.05051	+	1.81954i	0.0420204	+	0.0727815i
$626$	7.34847	+	12.7279i	0.293704	+	0.508710i
$627$	6.00000	−	8.48528i	0.239617	−	0.338869i
$628$	−8.72474	+	15.1117i	−0.348155	+	0.603023i
$629$	−20.2474			−0.807319
$630$	12.5732	−	14.7064i	0.500929	−	0.585916i
$631$	23.6969			0.943360			0.471680	−	0.881770i	$-0.343648\pi$
$631$	23.6969			0.943360			0.471680	+	0.881770i	$0.343648\pi$
$632$	−2.67423	+	4.63191i	−0.106375	+	0.184247i
$633$	11.4495	+	24.8523i	0.455076	+	0.987789i
$634$	4.79796	+	8.31031i	0.190551	+	0.330045i
$635$	−1.44949	−	2.51059i	−0.0575212	−	0.0996297i
$636$	8.94949	+	19.4258i	0.354870	+	0.770282i
$637$	28.4722	−	49.3153i	1.12811	−	1.95394i
$638$	5.34847			0.211748
$639$	25.9495	+	4.82294i	1.02655	+	0.190792i
$640$	1.44949			0.0572961
$641$	1.10102	−	1.90702i	0.0434877	−	0.0753229i	−0.843462	−	0.537188i	$-0.819486\pi$
$641$	1.10102	−	1.90702i	0.0434877	−	0.0753229i	0.886950	+	0.461866i	$0.152820\pi$
$642$	1.34847	−	1.90702i	0.0532198	−	0.0752642i
$643$	−4.79796	−	8.31031i	−0.189213	−	0.327727i	0.755775	−	0.654831i	$-0.227260\pi$
$643$	−4.79796	−	8.31031i	−0.189213	−	0.327727i	−0.944988	+	0.327105i	$0.893927\pi$
$644$	−13.3485	−	23.1202i	−0.526003	−	0.911065i
$645$	1.12372	+	0.103540i	0.0442466	+	0.00407690i
$646$	−13.3485	+	23.1202i	−0.525188	+	0.909653i
$647$	9.59592			0.377254			0.188627	−	0.982049i	$-0.439596\pi$
$647$	9.59592			0.377254			0.188627	+	0.982049i	$0.439596\pi$
$648$	8.39898	+	3.23375i	0.329943	+	0.127034i
$649$	−0.550510			−0.0216094
$650$	−6.44949	+	11.1708i	−0.252970	+	0.438157i
$651$	−7.67423	−	0.707107i	−0.300777	−	0.0277137i
$652$	−2.27526	−	3.94086i	−0.0891059	−	0.154336i
$653$	13.8712	+	24.0256i	0.542821	+	0.940193i	0.998741	+	0.0501725i	$0.0159771\pi$
$653$	13.8712	+	24.0256i	0.542821	+	0.940193i	−0.455920	+	0.890021i	$0.650690\pi$
$654$	−6.89898	+	9.75663i	−0.269771	+	0.381514i
$655$	2.57321	−	4.45694i	0.100544	−	0.174147i
$656$	3.34847			0.130736
$657$	−39.3712	−	7.31747i	−1.53602	−	0.285482i
$658$	17.3485			0.676314
$659$	−13.4495	+	23.2952i	−0.523918	+	0.907452i	0.475695	+	0.879611i	$0.342197\pi$
$659$	−13.4495	+	23.2952i	−0.523918	+	0.907452i	−0.999612	+	0.0278416i	$0.991137\pi$
$660$	−1.05051	−	2.28024i	−0.0408911	−	0.0887582i
$661$	−13.0732	−	22.6435i	−0.508489	−	0.880729i	−0.999952	−	0.00983026i	$-0.996871\pi$
$661$	−13.0732	−	22.6435i	−0.508489	−	0.880729i	0.491463	−	0.870899i	$-0.336462\pi$
$662$	11.2753	+	19.5293i	0.438225	+	0.759028i
$663$	−14.3485	−	31.1448i	−0.557248	−	1.20956i
$664$	4.00000	−	6.92820i	0.155230	−	0.268866i
$665$	38.6969			1.50060
$666$	−8.87117	+	10.3763i	−0.343751	+	0.402072i
$667$	−32.0908			−1.24256
$668$	2.44949	−	4.24264i	0.0947736	−	0.164153i
$669$	−18.8990	+	26.7272i	−0.730677	+	1.03333i
$670$	3.15153	+	5.45861i	0.121754	+	0.210885i
$671$	−6.89898	−	11.9494i	−0.266332	−	0.461301i
$672$	−7.67423	−	0.707107i	−0.296040	−	0.0272772i
$673$	0.348469	−	0.603566i	0.0134325	−	0.0232658i	−0.859231	−	0.511588i	$-0.829058\pi$
$673$	0.348469	−	0.603566i	0.0134325	−	0.0232658i	0.872664	+	0.488322i	$0.162391\pi$
$674$	34.9444			1.34601
$675$	10.7980	−	10.5031i	0.415614	−	0.404263i
$676$	6.79796			0.261460
$677$	−1.55051	+	2.68556i	−0.0595910	+	0.103215i	−0.894282	−	0.447504i	$-0.852313\pi$
$677$	−1.55051	+	2.68556i	−0.0595910	+	0.103215i	0.834691	+	0.550719i	$0.185646\pi$
$678$	23.9722	+	2.20881i	0.920647	+	0.0848287i
$679$	24.0227	+	41.6085i	0.921907	+	1.59679i
$680$	3.22474	+	5.58542i	0.123663	+	0.214191i
$681$	20.4495	−	28.9199i	0.783626	−	1.10821i
$682$	−0.500000	+	0.866025i	−0.0191460	+	0.0331618i
$683$	−47.0454			−1.80014			−0.900071	−	0.435743i	$-0.856486\pi$
$683$	−47.0454			−1.80014			−0.900071	+	0.435743i	$0.856486\pi$
$684$	6.00000	+	16.9706i	0.229416	+	0.648886i
$685$	−0.146428			−0.00559473
$686$	12.8990	−	22.3417i	0.492485	−	0.853010i
$687$	−8.04541	−	17.4634i	−0.306951	−	0.666269i
$688$	−0.224745	−	0.389270i	−0.00856832	−	0.0148408i
$689$	−27.4722	−	47.5832i	−1.04661	−	1.81278i
$690$	6.30306	+	13.6814i	0.239953	+	0.520843i
$691$	−1.97219	+	3.41594i	−0.0750258	+	0.129948i	−0.901097	−	0.433617i	$-0.857237\pi$
$691$	−1.97219	+	3.41594i	−0.0750258	+	0.129948i	0.826072	+	0.563565i	$0.190571\pi$
$692$	−2.44949			−0.0931156
$693$	4.44949	+	12.5851i	0.169022	+	0.478067i
$694$	0.247449			0.00939302
$695$	4.52781	−	7.84239i	0.171749	−	0.297479i
$696$	−5.34847	+	7.56388i	−0.202733	+	0.286708i
$697$	7.44949	+	12.9029i	0.282170	+	0.488732i
$698$	−16.0227	−	27.7521i	−0.606468	−	1.05043i
$699$	−14.5732	−	1.34278i	−0.551210	−	0.0507887i
$700$	−6.44949	+	11.1708i	−0.243768	+	0.422218i
$701$	15.7980			0.596681			0.298340	−	0.954460i	$-0.403567\pi$
$701$	15.7980			0.596681			0.298340	+	0.954460i	$0.403567\pi$
$702$	−22.2474	−	6.29253i	−0.839676	−	0.237496i
$703$	−27.3031			−1.02975
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−9.74745	−	0.898133i	−0.367110	−	0.0338257i
$706$	−12.7980	−	22.1667i	−0.481658	−	0.834255i
$707$	−41.5959	−	72.0462i	−1.56438	−	2.70958i
$708$	0.550510	−	0.778539i	0.0206894	−	0.0292593i
$709$	−21.6237	+	37.4534i	−0.812096	+	1.40659i	0.0992985	+	0.995058i	$0.468340\pi$
$709$	−21.6237	+	37.4534i	−0.812096	+	1.40659i	−0.911394	+	0.411534i	$0.864993\pi$
$710$	12.7526			0.478595
$711$	−10.4268	+	12.1958i	−0.391035	+	0.457378i
$712$	1.79796			0.0673814
$713$	3.00000	−	5.19615i	0.112351	−	0.194597i
$714$	−14.3485	−	31.1448i	−0.536978	−	1.16557i
$715$	3.22474	+	5.58542i	0.120599	+	0.208883i
$716$	−3.82577	−	6.62642i	−0.142976	−	0.247641i
$717$	−2.71964	−	5.90326i	−0.101567	−	0.220461i
$718$	−15.3485	+	26.5843i	−0.572800	+	0.992118i
$719$	−3.89898			−0.145407			−0.0727037	−	0.997354i	$-0.523163\pi$
$719$	−3.89898			−0.145407			−0.0727037	+	0.997354i	$0.523163\pi$
$720$	4.27526	+	0.794593i	0.159329	+	0.0296127i
$721$	48.9444			1.82278
$722$	−8.50000	+	14.7224i	−0.316337	+	0.547912i
$723$	20.6969	−	29.2699i	0.769727	−	1.08856i
$724$	−1.27526	−	2.20881i	−0.0473945	−	0.0820897i
$725$	7.75255	+	13.4278i	0.287923	+	0.498696i
$726$	1.72474	+	0.158919i	0.0640113	+	0.00589802i
$727$	−15.5000	+	26.8468i	−0.574863	+	0.995692i	0.421193	+	0.906971i	$0.361611\pi$
$727$	−15.5000	+	26.8468i	−0.574863	+	0.995692i	−0.996056	+	0.0887213i	$0.971722\pi$
$728$	19.7980			0.733761
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−19.3485			−0.716119
$731$	1.00000	−	1.73205i	0.0369863	−	0.0640622i
$732$	23.7980	+	2.19275i	0.879598	+	0.0810465i
$733$	−16.0227	−	27.7521i	−0.591812	−	1.02505i	−0.993988	−	0.109486i	$-0.965079\pi$
$733$	−16.0227	−	27.7521i	−0.591812	−	1.02505i	0.402176	−	0.915562i	$-0.368254\pi$
$734$	−5.74745	−	9.95487i	−0.212142	−	0.367441i
$735$	−18.5505	+	26.2344i	−0.684246	+	0.967670i
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−4.34847			−0.160178
$738$	9.87628	+	1.83559i	0.363551	+	0.0675690i
$739$	10.6969			0.393493			0.196747	−	0.980454i	$-0.436962\pi$
$739$	10.6969			0.393493			0.196747	+	0.980454i	$0.436962\pi$
$740$	−3.29796	+	5.71223i	−0.121235	+	0.209986i
$741$	−19.3485	−	41.9978i	−0.710784	−	1.54283i
$742$	−27.4722	−	47.5832i	−1.00854	−	1.74684i
$743$	13.4495	+	23.2952i	0.493414	+	0.854618i	0.999971	−	0.00758832i	$-0.00241546\pi$
$743$	13.4495	+	23.2952i	0.493414	+	0.854618i	−0.506557	+	0.862206i	$0.669082\pi$
$744$	−0.724745	−	1.57313i	−0.0265704	−	0.0576738i
$745$	1.30306	−	2.25697i	0.0477405	−	0.0826889i
$746$	−21.1010			−0.772563
$747$	15.5959	−	18.2419i	0.570625	−	0.667437i
$748$	−4.44949			−0.162689
$749$	−3.00000	+	5.19615i	−0.109618	+	0.189863i
$750$	11.4495	−	16.1920i	0.418076	−	0.591249i
$751$	12.8485	+	22.2542i	0.468847	+	0.812067i	0.999366	−	0.0356059i	$-0.0113361\pi$
$751$	12.8485	+	22.2542i	0.468847	+	0.812067i	−0.530519	+	0.847673i	$0.678003\pi$
$752$	1.94949	+	3.37662i	0.0710906	+	0.123132i
$753$	−39.1464	−	3.60697i	−1.42658	−	0.131445i
$754$	11.8990	−	20.6096i	0.433335	−	0.750559i
$755$	−32.2474			−1.17360
$756$	−22.2474	−	6.29253i	−0.809132	−	0.228857i
$757$	−15.2474			−0.554178			−0.277089	−	0.960844i	$-0.589370\pi$
$757$	−15.2474			−0.554178			−0.277089	+	0.960844i	$0.589370\pi$
$758$	−3.34847	+	5.79972i	−0.121622	+	0.210655i
$759$	−10.3485	−	0.953512i	−0.375626	−	0.0346103i
$760$	4.34847	+	7.53177i	0.157736	+	0.273206i
$761$	5.77526	+	10.0030i	0.209353	+	0.362610i	0.951511	−	0.307615i	$-0.0995309\pi$
$761$	5.77526	+	10.0030i	0.209353	+	0.362610i	−0.742158	+	0.670225i	$0.766198\pi$
$762$	−2.00000	+	2.82843i	−0.0724524	+	0.102463i
$763$	15.3485	−	26.5843i	0.555652	−	0.962417i
$764$	−8.79796			−0.318299
$765$	6.44949	+	18.2419i	0.233182	+	0.659538i
$766$	23.6969			0.856205
$767$	−1.22474	+	2.12132i	−0.0442230	+	0.0765964i
$768$	−0.724745	−	1.57313i	−0.0261520	−	0.0567655i
$769$	0.449490	+	0.778539i	0.0162090	+	0.0280748i	0.874016	−	0.485897i	$-0.161507\pi$
$769$	0.449490	+	0.778539i	0.0162090	+	0.0280748i	−0.857807	+	0.513972i	$0.828174\pi$
$770$	3.22474	+	5.58542i	0.116212	+	0.201285i
$771$	4.34847	+	9.43879i	0.156606	+	0.339930i
$772$	−6.44949	+	11.1708i	−0.232122	+	0.402047i
$773$	−19.3939			−0.697549			−0.348775	−	0.937207i	$-0.613402\pi$
$773$	−19.3939			−0.697549			−0.348775	+	0.937207i	$0.613402\pi$
$774$	−0.449490	−	1.27135i	−0.0161566	−	0.0456977i
$775$	−2.89898			−0.104134
$776$	−5.39898	+	9.35131i	−0.193812	+	0.335692i
$777$	20.2474	−	28.6342i	0.726373	−	1.02725i
$778$	−9.07321	−	15.7153i	−0.325290	−	0.563420i
$779$	10.0454	+	17.3992i	0.359914	+	0.623389i
$780$	−11.1237	−	1.02494i	−0.398293	−	0.0366989i
$781$	−4.39898	+	7.61926i	−0.157408	+	0.272638i
$782$	26.6969			0.954681
$783$	−19.9217	+	19.3776i	−0.711943	+	0.692499i
$784$	12.7980			0.457070
$785$	−12.6464	+	21.9043i	−0.451370	+	0.781796i
$786$	−6.12372	−	0.564242i	−0.218426	−	0.0201259i
$787$	−2.34847	−	4.06767i	−0.0837139	−	0.144997i	0.821129	−	0.570743i	$-0.193345\pi$
$787$	−2.34847	−	4.06767i	−0.0837139	−	0.144997i	−0.904842	+	0.425747i	$0.860012\pi$
$788$	−0.123724	−	0.214297i	−0.00440750	−	0.00763401i
$789$	2.65153	−	3.74983i	0.0943970	−	0.133498i
$790$	−3.87628	+	6.71391i	−0.137912	+	0.238870i
$791$	−61.8434			−2.19890
$792$	−1.94949	+	2.28024i	−0.0692721	+	0.0810248i
$793$	−61.3939			−2.18016
$794$	−13.6237	+	23.5970i	−0.483488	+	0.837426i
$795$	12.9722	+	28.1575i	0.460076	+	0.998642i
$796$	−2.50000	−	4.33013i	−0.0886102	−	0.153477i
$797$	3.17423	+	5.49794i	0.112437	+	0.194747i	0.916752	−	0.399456i	$-0.130801\pi$
$797$	3.17423	+	5.49794i	0.112437	+	0.194747i	−0.804315	+	0.594203i	$0.797468\pi$
$798$	−19.3485	−	41.9978i	−0.684928	−	1.48671i
$799$	−8.67423	+	15.0242i	−0.306872	+	0.531519i
$800$	−2.89898			−0.102494
$801$	5.30306	+	0.985620i	0.187374	+	0.0348252i
$802$	25.8990			0.914525
$803$	6.67423	−	11.5601i	0.235529	−	0.407948i
$804$	4.34847	−	6.14966i	0.153359	−	0.216882i
$805$	−19.3485	−	33.5125i	−0.681944	−	1.18116i
$806$	2.22474	+	3.85337i	0.0783633	+	0.135729i
$807$	35.0959	+	3.23375i	1.23543	+	0.113833i
$808$	9.34847	−	16.1920i	0.328878	−	0.569633i
$809$	−51.3485			−1.80532			−0.902658	−	0.430359i	$-0.858387\pi$
$809$	−51.3485			−1.80532			−0.902658	+	0.430359i	$0.858387\pi$
$810$	12.1742	+	4.68729i	0.427759	+	0.164695i
$811$	−8.44949			−0.296702			−0.148351	−	0.988935i	$-0.547396\pi$
$811$	−8.44949			−0.296702			−0.148351	+	0.988935i	$0.547396\pi$
$812$	11.8990	−	20.6096i	0.417572	−	0.723256i
$813$	−7.24745	−	0.667783i	−0.254179	−	0.0234202i
$814$	−2.27526	−	3.94086i	−0.0797477	−	0.138127i
$815$	−3.29796	−	5.71223i	−0.115522	−	0.200091i
$816$	4.44949	−	6.29253i	0.155763	−	0.220283i
$817$	1.34847	−	2.33562i	0.0471770	−	0.0817129i
$818$	−17.3485			−0.606575
$819$	58.3939	+	10.8530i	2.04045	+	0.379235i
$820$	4.85357			0.169494
$821$	−2.12372	+	3.67840i	−0.0741185	+	0.128377i	−0.900703	−	0.434436i	$-0.856948\pi$
$821$	−2.12372	+	3.67840i	−0.0741185	+	0.128377i	0.826584	+	0.562813i	$0.190281\pi$
$822$	0.0732141	+	0.158919i	0.00255363	+	0.00554292i
$823$	−4.89898	−	8.48528i	−0.170768	−	0.295778i	0.767921	−	0.640545i	$-0.221291\pi$
$823$	−4.89898	−	8.48528i	−0.170768	−	0.295778i	−0.938688	+	0.344767i	$0.887958\pi$
$824$	5.50000	+	9.52628i	0.191602	+	0.331864i
$825$	2.10102	+	4.56048i	0.0731481	+	0.158775i
$826$	−1.22474	+	2.12132i	−0.0426143	+	0.0738102i
$827$	19.5959			0.681417			0.340708	−	0.940169i	$-0.389333\pi$
$827$	19.5959			0.681417			0.340708	+	0.940169i	$0.389333\pi$
$828$	11.6969	−	13.6814i	0.406497	−	0.475463i
$829$	−25.6515			−0.890914			−0.445457	−	0.895303i	$-0.646959\pi$
$829$	−25.6515			−0.890914			−0.445457	+	0.895303i	$0.646959\pi$
$830$	5.79796	−	10.0424i	0.201250	−	0.348575i
$831$	−4.20204	+	5.94258i	−0.145767	+	0.206146i
$832$	2.22474	+	3.85337i	0.0771292	+	0.133592i
$833$	28.4722	+	49.3153i	0.986503	+	1.70867i
$834$	−10.7753	−	0.992836i	−0.373117	−	0.0343791i
$835$	3.55051	−	6.14966i	0.122870	−	0.212818i
$836$	−6.00000			−0.207514
$837$	−1.27526	−	5.03723i	−0.0440793	−	0.174112i
$838$	15.2474			0.526714
$839$	14.1464	−	24.5023i	0.488389	−	0.845914i	−0.511522	−	0.859270i	$-0.670918\pi$
$839$	14.1464	−	24.5023i	0.488389	−	0.845914i	0.999911	+	0.0133558i	$0.00425141\pi$
$840$	−11.1237	−	1.02494i	−0.383805	−	0.0353639i
$841$	0.196938	+	0.341107i	0.00679098	+	0.0117623i
$842$	5.72474	+	9.91555i	0.197288	+	0.341712i
$843$	−0.202041	+	0.285729i	−0.00695866	+	0.00984104i
$844$	7.89898	−	13.6814i	0.271894	−	0.470934i
$845$	9.85357			0.338973
$846$	3.89898	+	11.0280i	0.134050	+	0.379150i
$847$	−4.44949			−0.152886
$848$	6.17423	−	10.6941i	0.212024	−	0.367236i
$849$	−10.1793	−	22.0953i	−0.349354	−	0.758308i
$850$	−6.44949	−	11.1708i	−0.221216	−	0.383157i
$851$	13.6515	+	23.6451i	0.467968	+	0.810545i
$852$	−6.37628	−	13.8404i	−0.218448	−	0.474163i
$853$	7.65153	−	13.2528i	0.261983	−	0.453769i	−0.704785	−	0.709420i	$-0.748957\pi$
$853$	7.65153	−	13.2528i	0.261983	−	0.453769i	0.966769	+	0.255652i	$0.0822901\pi$
$854$	−61.3939			−2.10086
$855$	8.69694	+	24.5987i	0.297429	+	0.841256i
$856$	−1.34847			−0.0460897
$857$	−10.1237	+	17.5348i	−0.345820	+	0.598978i	−0.985502	−	0.169662i	$-0.945732\pi$
$857$	−10.1237	+	17.5348i	−0.345820	+	0.598978i	0.639683	+	0.768639i	$0.279066\pi$
$858$	4.44949	−	6.29253i	0.151903	−	0.214823i
$859$	−6.37628	−	11.0440i	−0.217556	−	0.376818i	0.736504	−	0.676433i	$-0.236475\pi$
$859$	−6.37628	−	11.0440i	−0.217556	−	0.376818i	−0.954060	+	0.299615i	$0.903142\pi$
$860$	−0.325765	−	0.564242i	−0.0111085	−	0.0192405i
$861$	−25.6969	−	2.36773i	−0.875749	−	0.0806919i
$862$	3.22474	−	5.58542i	0.109835	−	0.190240i
$863$	1.10102			0.0374792			0.0187396	−	0.999824i	$-0.494035\pi$
$863$	1.10102			0.0374792			0.0187396	+	0.999824i	$0.494035\pi$
$864$	−1.27526	−	5.03723i	−0.0433851	−	0.171370i
$865$	−3.55051			−0.120721
$866$	18.2474	−	31.6055i	0.620074	−	1.07400i
$867$	4.82577	+	0.444648i	0.163892	+	0.0151010i
$868$	2.22474	+	3.85337i	0.0755128	+	0.130792i
$869$	−2.67423	−	4.63191i	−0.0907172	−	0.157127i
$870$	−7.75255	+	10.9638i	−0.262836	+	0.371706i
$871$	−9.67423	+	16.7563i	−0.327799	+	0.567764i
$872$	6.89898			0.233629
$873$	−21.0505	+	24.6219i	−0.712452	+	0.833326i
$874$	36.0000			1.21772
$875$	−25.4722	+	44.1191i	−0.861117	+	1.49150i
$876$	9.67423	+	20.9989i	0.326862	+	0.709487i
$877$	−2.55051	−	4.41761i	−0.0861246	−	0.149172i	0.819745	−	0.572728i	$-0.194115\pi$
$877$	−2.55051	−	4.41761i	−0.0861246	−	0.149172i	−0.905870	+	0.423556i	$0.860782\pi$
$878$	20.3485	+	35.2446i	0.686728	+	1.18945i
$879$	22.4268	+	48.6796i	0.756437	+	1.64192i
$880$	−0.724745	+	1.25529i	−0.0244311	+	0.0423160i
$881$	−34.3939			−1.15876			−0.579380	−	0.815058i	$-0.696705\pi$
$881$	−34.3939			−1.15876			−0.579380	+	0.815058i	$0.696705\pi$
$882$	37.7474	+	7.01569i	1.27102	+	0.236231i
$883$	7.44949			0.250695			0.125348	−	0.992113i	$-0.459995\pi$
$883$	7.44949			0.250695			0.125348	+	0.992113i	$0.459995\pi$
$884$	−9.89898	+	17.1455i	−0.332939	+	0.576667i
$885$	0.797959	−	1.12848i	0.0268231	−	0.0379336i
$886$	−19.0732	−	33.0358i	−0.640777	−	1.10986i
$887$	−10.4722	−	18.1384i	−0.351622	−	0.609027i	0.634912	−	0.772585i	$-0.281036\pi$
$887$	−10.4722	−	18.1384i	−0.351622	−	0.609027i	−0.986534	+	0.163558i	$0.947703\pi$
$888$	7.84847	+	0.723161i	0.263377	+	0.0242677i
$889$	4.44949	−	7.70674i	0.149231	−	0.258476i
$890$	2.60612			0.0873574
$891$	−7.00000	+	5.65685i	−0.234509	+	0.189512i
$892$	18.8990			0.632785
$893$	−11.6969	+	20.2597i	−0.391423	+	0.677965i
$894$	−3.10102	−	0.285729i	−0.103714	−	0.00955621i
$895$	−5.54541	−	9.60493i	−0.185363	−	0.321057i
$896$	2.22474	+	3.85337i	0.0743235	+	0.128732i
$897$	−26.6969	+	37.7552i	−0.891385	+	1.26061i
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	5.34847			0.178381
$900$	−8.55051	−	1.58919i	−0.285017	−	0.0529729i
$901$	54.9444			1.83046
$902$	−1.67423	+	2.89986i	−0.0557459	+	0.0965548i
$903$	1.44949	+	3.14626i	0.0482360	+	0.104701i
$904$	−6.94949	−	12.0369i	−0.231137	−	0.400340i
$905$	−1.84847	−	3.20164i	−0.0614452	−	0.106426i
$906$	16.1237	+	34.9982i	0.535675	+	1.16274i
$907$	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	$-0.0478985\pi$
$908$	−20.4495			−0.678640
$909$	36.4495	−	42.6335i	1.20895	−	1.41406i
$910$	28.6969			0.951294
$911$	−8.74745	+	15.1510i	−0.289816	+	0.501976i	−0.973766	−	0.227553i	$-0.926927\pi$
$911$	−8.74745	+	15.1510i	−0.289816	+	0.501976i	0.683950	+	0.729529i	$0.260261\pi$
$912$	6.00000	−	8.48528i	0.198680	−	0.280976i
$913$	4.00000	+	6.92820i	0.132381	+	0.229290i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$	34.4949	+	3.17837i	1.14037	+	0.105074i
$916$	−5.55051	+	9.61377i	−0.183394	+	0.317648i
$917$	15.7980			0.521695
$918$	16.5732	−	16.1206i	0.546998	−	0.532059i
$919$	−44.8990			−1.48108			−0.740540	−	0.672012i	$-0.765430\pi$
$919$	−44.8990			−1.48108			−0.740540	+	0.672012i	$0.765430\pi$
$920$	4.34847	−	7.53177i	0.143365	−	0.248315i
$921$	−31.8207	−	2.93197i	−1.04853	−	0.0966116i
$922$	6.12372	+	10.6066i	0.201674	+	0.349310i
$923$	19.5732	+	33.9018i	0.644260	+	1.11589i
$924$	4.44949	−	6.29253i	0.146377	−	0.207009i
$925$	6.59592	−	11.4245i	0.216872	−	0.375634i
$926$	10.0000			0.328620
$927$	11.0000	+	31.1127i	0.361287	+	1.02188i
$928$	5.34847			0.175572
$929$	−11.6010	+	20.0936i	−0.380617	+	0.659248i	−0.991151	−	0.132742i	$-0.957622\pi$
$929$	−11.6010	+	20.0936i	−0.380617	+	0.659248i	0.610533	+	0.791990i	$0.290955\pi$
$930$	−1.05051	−	2.28024i	−0.0344476	−	0.0747720i
$931$	38.3939	+	66.5001i	1.25831	+	2.17945i
$932$	4.22474	+	7.31747i	0.138386	+	0.239692i
$933$	−7.17423	−	15.5724i	−0.234874	−	0.509818i
$934$	20.0732	−	34.7678i	0.656816	−	1.13764i
$935$	−6.44949			−0.210921
$936$	4.44949	+	12.5851i	0.145436	+	0.411355i
$937$	40.7423			1.33099			0.665497	−	0.746400i	$-0.268220\pi$
$937$	40.7423			1.33099			0.665497	+	0.746400i	$0.268220\pi$
$938$	−9.67423	+	16.7563i	−0.315875	+	0.547111i
$939$	14.6969	−	20.7846i	0.479616	−	0.678280i
$940$	2.82577	+	4.89437i	0.0921663	+	0.159637i
$941$	9.67423	+	16.7563i	0.315371	+	0.546239i	0.979516	−	0.201365i	$-0.0645377\pi$
$941$	9.67423	+	16.7563i	0.315371	+	0.546239i	−0.664145	+	0.747604i	$0.731204\pi$
$942$	30.0959	+	2.77305i	0.980578	+	0.0903508i
$943$	10.0454	−	17.3992i	0.327123	−	0.566594i
$944$	−0.550510			−0.0179176
$945$	−32.2474	−	9.12096i	−1.04901	−	0.296705i
$946$	0.449490			0.0146142
$947$	26.0732	−	45.1601i	0.847266	−	1.46751i	−0.0363734	−	0.999338i	$-0.511581\pi$
$947$	26.0732	−	45.1601i	0.847266	−	1.46751i	0.883639	−	0.468169i	$-0.155086\pi$
$948$	9.22474	+	0.849971i	0.299606	+	0.0276058i
$949$	−29.6969	−	51.4366i	−0.964003	−	1.66970i
$950$	−8.69694	−	15.0635i	−0.282166	−	0.488726i
$951$	9.59592	−	13.5707i	0.311169	−	0.440059i
$952$	−9.89898	+	17.1455i	−0.320828	+	0.555690i
$953$	46.8990			1.51921			0.759603	−	0.650386i	$-0.225393\pi$
$953$	46.8990			1.51921			0.759603	+	0.650386i	$0.225393\pi$
$954$	24.0732	−	28.1575i	0.779399	−	0.911631i
$955$	−12.7526			−0.412663
$956$	−1.87628	+	3.24980i	−0.0606831	+	0.105106i
$957$	−3.87628	−	8.41385i	−0.125302	−	0.271981i
$958$	8.89898	+	15.4135i	0.287513	+	0.497987i
$959$	−0.224745	−	0.389270i	−0.00725739	−	0.0125702i
$960$	−1.05051	−	2.28024i	−0.0339051	−	0.0735944i
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	−20.2474			−0.652804
$963$	−3.97730	−	0.739215i	−0.128167	−	0.0238209i
$964$	−20.6969			−0.666604
$965$	−9.34847	+	16.1920i	−0.300938	+	0.521240i
$966$	−26.6969	+	37.7552i	−0.858960	+	1.21475i
$967$	−1.24745	−	2.16064i	−0.0401152	−	0.0694816i	0.845271	−	0.534338i	$-0.179439\pi$
$967$	−1.24745	−	2.16064i	−0.0401152	−	0.0694816i	−0.885386	+	0.464857i	$0.846106\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	46.0454	+	4.24264i	1.47919	+	0.136293i
$970$	−7.82577	+	13.5546i	−0.251270	+	0.435213i
$971$	−47.5959			−1.52743			−0.763713	−	0.645556i	$-0.776626\pi$
$971$	−47.5959			−1.52743			−0.763713	+	0.645556i	$0.776626\pi$
$972$	−1.00000	−	15.5563i	−0.0320750	−	0.498970i
$973$	27.7980			0.891162
$974$	−0.500000	+	0.866025i	−0.0160210	+	0.0277492i
$975$	22.2474	+	2.04989i	0.712489	+	0.0656490i
$976$	−6.89898	−	11.9494i	−0.220831	−	0.382490i
$977$	16.6969	+	28.9199i	0.534182	+	0.925231i	0.999202	+	0.0399309i	$0.0127138\pi$
$977$	16.6969	+	28.9199i	0.534182	+	0.925231i	−0.465020	+	0.885300i	$0.653953\pi$
$978$	−4.55051	+	6.43539i	−0.145509	+	0.205781i
$979$	−0.898979	+	1.55708i	−0.0287315	+	0.0497644i
$980$	18.5505			0.592574
$981$	20.3485	+	3.78194i	0.649677	+	0.120748i
$982$	−24.4949			−0.781664
$983$	17.6464	−	30.5645i	0.562834	−	0.974856i	−0.434414	−	0.900713i	$-0.643044\pi$
$983$	17.6464	−	30.5645i	0.562834	−	0.974856i	0.997248	−	0.0741431i	$-0.0236222\pi$
$984$	−2.42679	−	5.26758i	−0.0773631	−	0.167924i
$985$	−0.179337	−	0.310621i	−0.00571416	−	0.00989721i
$986$	11.8990	+	20.6096i	0.378941	+	0.656345i
$987$	−12.5732	−	27.2914i	−0.400210	−	0.868696i
$988$	−13.3485	+	23.1202i	−0.424671	+	0.735552i
$989$	−2.69694			−0.0857577
$990$	−2.82577	+	3.30518i	−0.0898087	+	0.105046i
$991$	−11.7980			−0.374775			−0.187387	−	0.982286i	$-0.560002\pi$
$991$	−11.7980			−0.374775			−0.187387	+	0.982286i	$0.560002\pi$
$992$	−0.500000	+	0.866025i	−0.0158750	+	0.0274963i
$993$	22.5505	−	31.8912i	0.715619	−	1.01204i
$994$	19.5732	+	33.9018i	0.620825	+	1.07530i
$995$	−3.62372	−	6.27647i	−0.114880	−	0.198978i
$996$	−13.7980	−	1.27135i	−0.437205	−	0.0402842i
$997$	−12.4495	+	21.5631i	−0.394279	+	0.682912i	−0.993009	−	0.118039i	$-0.962339\pi$
$997$	−12.4495	+	21.5631i	−0.394279	+	0.682912i	0.598730	+	0.800951i	$0.295672\pi$
$998$	−26.5505			−0.840442
$999$	22.7526	+	6.43539i	0.719859	+	0.203607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.e.c.133.2	yes	4
3.2	odd	2		594.2.e.c.397.2		4
9.2	odd	6		1782.2.a.m.1.1		2
9.4	even	3	inner	198.2.e.c.67.2	✓	4
9.5	odd	6		594.2.e.c.199.2		4
9.7	even	3		1782.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.e.c.67.2	✓	4	9.4	even	3	inner
198.2.e.c.133.2	yes	4	1.1	even	1	trivial
594.2.e.c.199.2		4	9.5	odd	6
594.2.e.c.397.2		4	3.2	odd	2
1782.2.a.m.1.1		2	9.2	odd	6
1782.2.a.o.1.2		2	9.7	even	3

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +1.44949 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.724745 - 1.57313i) q^{12} +(2.22474 + 3.85337i) q^{13} +(2.22474 + 3.85337i) q^{14} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.44949 q^{17} +(-1.94949 + 2.28024i) q^{18} -6.00000 q^{19} +(-0.724745 + 1.25529i) q^{20} +(4.44949 - 6.29253i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(1.72474 + 0.158919i) q^{24} +(1.44949 - 2.51059i) q^{25} -4.44949 q^{26} +(5.00000 + 1.41421i) q^{27} -4.44949 q^{28} +(-2.67423 + 4.63191i) q^{29} +(2.50000 + 0.230351i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.41421i) q^{33} +(2.22474 - 3.85337i) q^{34} -6.44949 q^{35} +(-1.00000 - 2.82843i) q^{36} +4.55051 q^{37} +(3.00000 - 5.19615i) q^{38} +(3.22474 + 6.99964i) q^{39} +(-0.724745 - 1.25529i) q^{40} +(-1.67423 - 2.89986i) q^{41} +(3.22474 + 6.99964i) q^{42} +(-0.224745 + 0.389270i) q^{43} +1.00000 q^{44} +(-1.44949 - 4.09978i) q^{45} -6.00000 q^{46} +(1.94949 - 3.37662i) q^{47} +(-1.00000 + 1.41421i) q^{48} +(-6.39898 - 11.0834i) q^{49} +(1.44949 + 2.51059i) q^{50} +(-7.67423 - 0.707107i) q^{51} +(2.22474 - 3.85337i) q^{52} -12.3485 q^{53} +(-3.72474 + 3.62302i) q^{54} +1.44949 q^{55} +(2.22474 - 3.85337i) q^{56} +(-10.3485 - 0.953512i) q^{57} +(-2.67423 - 4.63191i) q^{58} +(0.275255 + 0.476756i) q^{59} +(-1.44949 + 2.04989i) q^{60} +(-6.89898 + 11.9494i) q^{61} +1.00000 q^{62} +(8.67423 - 10.1459i) q^{63} +1.00000 q^{64} +(3.22474 - 5.58542i) q^{65} +(-0.724745 - 1.57313i) q^{66} +(2.17423 + 3.76588i) q^{67} +(2.22474 + 3.85337i) q^{68} +(4.34847 + 9.43879i) q^{69} +(3.22474 - 5.58542i) q^{70} +8.79796 q^{71} +(2.94949 + 0.548188i) q^{72} -13.3485 q^{73} +(-2.27526 + 3.94086i) q^{74} +(2.89898 - 4.09978i) q^{75} +(3.00000 + 5.19615i) q^{76} +(2.22474 + 3.85337i) q^{77} +(-7.67423 - 0.707107i) q^{78} +(-2.67423 + 4.63191i) q^{79} +1.44949 q^{80} +(8.39898 + 3.23375i) q^{81} +3.34847 q^{82} +(4.00000 - 6.92820i) q^{83} +(-7.67423 - 0.707107i) q^{84} +(3.22474 + 5.58542i) q^{85} +(-0.224745 - 0.389270i) q^{86} +(-5.34847 + 7.56388i) q^{87} +(-0.500000 + 0.866025i) q^{88} +1.79796 q^{89} +(4.27526 + 0.794593i) q^{90} +19.7980 q^{91} +(3.00000 - 5.19615i) q^{92} +(-0.724745 - 1.57313i) q^{93} +(1.94949 + 3.37662i) q^{94} +(4.34847 + 7.53177i) q^{95} +(-0.724745 - 1.57313i) q^{96} +(-5.39898 + 9.35131i) q^{97} +12.7980 q^{98} +(-1.94949 + 2.28024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} - 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 24 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22} + 12 q^{23} + 2 q^{24} - 4 q^{25} - 8 q^{26} + 20 q^{27} - 8 q^{28} + 4 q^{29} + 10 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} + 4 q^{34} - 16 q^{35} - 4 q^{36} + 28 q^{37} + 12 q^{38} + 8 q^{39} + 2 q^{40} + 8 q^{41} + 8 q^{42} + 4 q^{43} + 4 q^{44} + 4 q^{45} - 24 q^{46} - 2 q^{47} - 4 q^{48} - 6 q^{49} - 4 q^{50} - 16 q^{51} + 4 q^{52} - 20 q^{53} - 10 q^{54} - 4 q^{55} + 4 q^{56} - 12 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} - 8 q^{61} + 4 q^{62} + 20 q^{63} + 4 q^{64} + 8 q^{65} + 2 q^{66} - 6 q^{67} + 4 q^{68} - 12 q^{69} + 8 q^{70} - 4 q^{71} + 2 q^{72} - 24 q^{73} - 14 q^{74} - 8 q^{75} + 12 q^{76} + 4 q^{77} - 16 q^{78} + 4 q^{79} - 4 q^{80} + 14 q^{81} - 16 q^{82} + 16 q^{83} - 16 q^{84} + 8 q^{85} + 4 q^{86} + 8 q^{87} - 2 q^{88} - 32 q^{89} + 22 q^{90} + 40 q^{91} + 12 q^{92} + 2 q^{93} - 2 q^{94} - 12 q^{95} + 2 q^{96} - 2 q^{97} + 12 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 - 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 24 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 12 * q^23 + 2 * q^24 - 4 * q^25 - 8 * q^26 + 20 * q^27 - 8 * q^28 + 4 * q^29 + 10 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 + 4 * q^34 - 16 * q^35 - 4 * q^36 + 28 * q^37 + 12 * q^38 + 8 * q^39 + 2 * q^40 + 8 * q^41 + 8 * q^42 + 4 * q^43 + 4 * q^44 + 4 * q^45 - 24 * q^46 - 2 * q^47 - 4 * q^48 - 6 * q^49 - 4 * q^50 - 16 * q^51 + 4 * q^52 - 20 * q^53 - 10 * q^54 - 4 * q^55 + 4 * q^56 - 12 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 - 8 * q^61 + 4 * q^62 + 20 * q^63 + 4 * q^64 + 8 * q^65 + 2 * q^66 - 6 * q^67 + 4 * q^68 - 12 * q^69 + 8 * q^70 - 4 * q^71 + 2 * q^72 - 24 * q^73 - 14 * q^74 - 8 * q^75 + 12 * q^76 + 4 * q^77 - 16 * q^78 + 4 * q^79 - 4 * q^80 + 14 * q^81 - 16 * q^82 + 16 * q^83 - 16 * q^84 + 8 * q^85 + 4 * q^86 + 8 * q^87 - 2 * q^88 - 32 * q^89 + 22 * q^90 + 40 * q^91 + 12 * q^92 + 2 * q^93 - 2 * q^94 - 12 * q^95 + 2 * q^96 - 2 * q^97 + 12 * q^98 + 2 * q^99

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