LMFDB - Embedded newform 114.2.h.f.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.h (of order $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	114.107
Dual form			114.2.h.f.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} -0.449490 q^{7} -1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} -0.449490 q^{7} -1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +(-1.22474 - 0.707107i) q^{10} -3.14626i q^{11} +(-0.724745 + 1.57313i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-2.00000 + 1.41421i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.550510 + 0.317837i) q^{17} +(1.94949 + 2.28024i) q^{18} +(3.17423 + 2.98735i) q^{19} -1.41421i q^{20} +(-0.775255 + 0.0714323i) q^{21} +(2.72474 - 1.57313i) q^{22} +(-6.12372 - 3.53553i) q^{23} +(-1.72474 + 0.158919i) q^{24} +(-1.50000 + 2.59808i) q^{25} -3.46410i q^{26} +(5.00000 - 1.41421i) q^{27} +(0.224745 - 0.389270i) q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 1.02494i) q^{30} +4.24264i q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 - 5.42650i) q^{33} +(-0.550510 - 0.317837i) q^{34} +(0.550510 - 0.317837i) q^{35} +(-1.00000 + 2.82843i) q^{36} -7.70674i q^{37} +(-1.00000 + 4.24264i) q^{38} +(-5.44949 - 2.51059i) q^{39} +(1.22474 - 0.707107i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-0.449490 - 0.635674i) q^{42} +(4.44949 + 7.70674i) q^{43} +(2.72474 + 1.57313i) q^{44} +(-3.22474 + 2.75699i) q^{45} -7.07107i q^{46} +(11.5732 + 6.68180i) q^{47} +(-1.00000 - 1.41421i) q^{48} -6.79796 q^{49} -3.00000 q^{50} +(-0.898979 + 0.635674i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-5.44949 + 9.43879i) q^{53} +(3.72474 + 3.62302i) q^{54} +(2.22474 + 3.85337i) q^{55} +0.449490 q^{56} +(5.94949 + 4.64796i) q^{57} +2.44949 q^{58} +(5.72474 + 9.91555i) q^{59} +(-0.224745 - 2.43916i) q^{60} +(0.775255 - 1.34278i) q^{61} +(-3.67423 + 2.12132i) q^{62} +(-1.32577 + 0.246405i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(4.44949 - 3.14626i) q^{66} +(2.17423 + 1.25529i) q^{67} -0.635674i q^{68} +(-11.1237 - 5.12472i) q^{69} +(0.550510 + 0.317837i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-2.94949 + 0.548188i) q^{72} +(-4.39898 - 7.61926i) q^{73} +(6.67423 - 3.85337i) q^{74} +(-2.17423 + 4.71940i) q^{75} +(-4.17423 + 1.25529i) q^{76} +1.41421i q^{77} +(-0.550510 - 5.97469i) q^{78} +(-7.34847 + 4.24264i) q^{79} +(1.22474 + 0.707107i) q^{80} +(8.39898 - 3.23375i) q^{81} +(1.50000 - 2.59808i) q^{82} -17.0027i q^{83} +(0.325765 - 0.707107i) q^{84} +(0.449490 - 0.778539i) q^{85} +(-4.44949 + 7.70674i) q^{86} +(1.77526 - 3.85337i) q^{87} +3.14626i q^{88} +(3.55051 - 6.14966i) q^{89} +(-4.00000 - 1.41421i) q^{90} +(1.34847 + 0.778539i) q^{91} +(6.12372 - 3.53553i) q^{92} +(0.674235 + 7.31747i) q^{93} +13.3636i q^{94} +(-6.00000 - 1.41421i) q^{95} +(0.724745 - 1.57313i) q^{96} +(2.84847 - 1.64456i) q^{97} +(-3.39898 - 5.88721i) q^{98} +(-1.72474 - 9.27987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{12} - 12 q^{13} + 4 q^{14} - 8 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 8 q^{21} + 6 q^{22} - 2 q^{24} - 6 q^{25} + 20 q^{27} - 4 q^{28} - 4 q^{30} + 2 q^{32} - 2 q^{33} - 12 q^{34} + 12 q^{35} - 4 q^{36} - 4 q^{38} - 12 q^{39} - 6 q^{41} + 8 q^{42} + 8 q^{43} + 6 q^{44} - 8 q^{45} + 12 q^{47} - 4 q^{48} + 12 q^{49} - 12 q^{50} + 16 q^{51} + 12 q^{52} - 12 q^{53} + 10 q^{54} + 4 q^{55} - 8 q^{56} + 14 q^{57} + 18 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{63} + 4 q^{64} + 8 q^{66} - 6 q^{67} - 20 q^{69} + 12 q^{70} + 12 q^{71} - 2 q^{72} + 2 q^{73} + 12 q^{74} + 6 q^{75} - 2 q^{76} - 12 q^{78} + 14 q^{81} + 6 q^{82} + 16 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{89} - 16 q^{90} - 24 q^{91} - 12 q^{93} - 24 q^{95} - 2 q^{96} - 18 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^12 - 12 * q^13 + 4 * q^14 - 8 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 8 * q^21 + 6 * q^22 - 2 * q^24 - 6 * q^25 + 20 * q^27 - 4 * q^28 - 4 * q^30 + 2 * q^32 - 2 * q^33 - 12 * q^34 + 12 * q^35 - 4 * q^36 - 4 * q^38 - 12 * q^39 - 6 * q^41 + 8 * q^42 + 8 * q^43 + 6 * q^44 - 8 * q^45 + 12 * q^47 - 4 * q^48 + 12 * q^49 - 12 * q^50 + 16 * q^51 + 12 * q^52 - 12 * q^53 + 10 * q^54 + 4 * q^55 - 8 * q^56 + 14 * q^57 + 18 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^63 + 4 * q^64 + 8 * q^66 - 6 * q^67 - 20 * q^69 + 12 * q^70 + 12 * q^71 - 2 * q^72 + 2 * q^73 + 12 * q^74 + 6 * q^75 - 2 * q^76 - 12 * q^78 + 14 * q^81 + 6 * q^82 + 16 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^89 - 16 * q^90 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 2 * q^96 - 18 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$	−0.449490			−0.169891			−0.0849456	−	0.996386i	$-0.527072\pi$
$7$	−0.449490			−0.169891			−0.0849456	+	0.996386i	$0.527072\pi$
$8$	−1.00000			−0.353553
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$	−1.22474	−	0.707107i	−0.387298	−	0.223607i
$11$		−	3.14626i		−	0.948634i	−0.880354	−	0.474317i	$-0.842695\pi$
$11$		−	3.14626i		−	0.948634i	0.880354	−	0.474317i	$-0.157305\pi$
$12$	−0.724745	+	1.57313i	−0.209216	+	0.454124i
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$	−0.224745	−	0.389270i	−0.0600656	−	0.104037i
$15$	−2.00000	+	1.41421i	−0.516398	+	0.365148i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.550510	+	0.317837i	−0.133518	+	0.0770869i	−0.565271	−	0.824905i	$-0.691229\pi$
$17$	−0.550510	+	0.317837i	−0.133518	+	0.0770869i	0.431753	+	0.901992i	$0.357895\pi$
$18$	1.94949	+	2.28024i	0.459499	+	0.537457i
$19$	3.17423	+	2.98735i	0.728219	+	0.685344i
$19$	3.17423	+	2.98735i	0.728219	+	0.685344i
$20$		−	1.41421i		−	0.316228i
$21$	−0.775255	+	0.0714323i	−0.169175	+	0.0155878i
$22$	2.72474	−	1.57313i	0.580918	−	0.335393i
$23$	−6.12372	−	3.53553i	−1.27688	−	0.737210i	−0.300610	−	0.953747i	$-0.597190\pi$
$23$	−6.12372	−	3.53553i	−1.27688	−	0.737210i	−0.976274	+	0.216537i	$0.930524\pi$
$24$	−1.72474	+	0.158919i	−0.352062	+	0.0324391i
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		−	3.46410i		−	0.679366i
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	0.224745	−	0.389270i	0.0424728	−	0.0735650i
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	−0.729616	−	0.683857i	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$	−2.22474	−	1.02494i	−0.406181	−	0.187128i
$31$			4.24264i			0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$			4.24264i			0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.500000	−	5.42650i	−0.0870388	−	0.944633i
$34$	−0.550510	−	0.317837i	−0.0944117	−	0.0545086i
$35$	0.550510	−	0.317837i	0.0930532	−	0.0537243i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		−	7.70674i		−	1.26698i	−0.773751	−	0.633490i	$-0.781622\pi$
$37$		−	7.70674i		−	1.26698i	0.773751	−	0.633490i	$-0.218378\pi$
$38$	−1.00000	+	4.24264i	−0.162221	+	0.688247i
$39$	−5.44949	−	2.51059i	−0.872617	−	0.402016i
$40$	1.22474	−	0.707107i	0.193649	−	0.111803i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	−0.449490	−	0.635674i	−0.0693578	−	0.0980867i
$43$	4.44949	+	7.70674i	0.678541	+	1.17527i	0.975420	+	0.220352i	$0.0707207\pi$
$43$	4.44949	+	7.70674i	0.678541	+	1.17527i	−0.296880	+	0.954915i	$0.595946\pi$
$44$	2.72474	+	1.57313i	0.410771	+	0.237159i
$45$	−3.22474	+	2.75699i	−0.480717	+	0.410989i
$46$		−	7.07107i		−	1.04257i
$47$	11.5732	+	6.68180i	1.68813	+	0.974640i	0.955952	+	0.293524i	$0.0948280\pi$
$47$	11.5732	+	6.68180i	1.68813	+	0.974640i	0.732175	+	0.681117i	$0.238505\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$	−6.79796			−0.971137
$50$	−3.00000			−0.424264
$51$	−0.898979	+	0.635674i	−0.125882	+	0.0890122i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	−5.44949	+	9.43879i	−0.748545	+	1.29652i	0.199975	+	0.979801i	$0.435914\pi$
$53$	−5.44949	+	9.43879i	−0.748545	+	1.29652i	−0.948520	+	0.316717i	$0.897419\pi$
$54$	3.72474	+	3.62302i	0.506874	+	0.493031i
$55$	2.22474	+	3.85337i	0.299985	+	0.519588i
$56$	0.449490			0.0600656
$57$	5.94949	+	4.64796i	0.788029	+	0.615638i
$58$	2.44949			0.321634
$59$	5.72474	+	9.91555i	0.745298	+	1.29089i	0.950055	+	0.312082i	$0.101026\pi$
$59$	5.72474	+	9.91555i	0.745298	+	1.29089i	−0.204757	+	0.978813i	$0.565640\pi$
$60$	−0.224745	−	2.43916i	−0.0290144	−	0.314894i
$61$	0.775255	−	1.34278i	0.0992612	−	0.171926i	−0.812118	−	0.583493i	$-0.801685\pi$
$61$	0.775255	−	1.34278i	0.0992612	−	0.171926i	0.911379	+	0.411568i	$0.135019\pi$
$62$	−3.67423	+	2.12132i	−0.466628	+	0.269408i
$63$	−1.32577	+	0.246405i	−0.167031	+	0.0310441i
$64$	1.00000			0.125000
$65$	4.89898			0.607644
$66$	4.44949	−	3.14626i	0.547694	−	0.387278i
$67$	2.17423	+	1.25529i	0.265625	+	0.153359i	0.626898	−	0.779101i	$-0.284324\pi$
$67$	2.17423	+	1.25529i	0.265625	+	0.153359i	−0.361273	+	0.932460i	$0.617658\pi$
$68$		−	0.635674i		−	0.0770869i
$69$	−11.1237	−	5.12472i	−1.33914	−	0.616944i
$70$	0.550510	+	0.317837i	0.0657986	+	0.0379888i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−2.94949	+	0.548188i	−0.347601	+	0.0646046i
$73$	−4.39898	−	7.61926i	−0.514862	−	0.891766i	−0.999851	−	0.0172466i	$-0.994510\pi$
$73$	−4.39898	−	7.61926i	−0.514862	−	0.891766i	0.484990	−	0.874520i	$-0.338823\pi$
$74$	6.67423	−	3.85337i	0.775864	−	0.447945i
$75$	−2.17423	+	4.71940i	−0.251059	+	0.544949i
$76$	−4.17423	+	1.25529i	−0.478818	+	0.143992i
$77$			1.41421i			0.161165i
$78$	−0.550510	−	5.97469i	−0.0623330	−	0.676501i
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	−0.852745	−	0.522328i	$-0.825064\pi$
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	0.0259772	+	0.999663i	$0.491730\pi$
$80$	1.22474	+	0.707107i	0.136931	+	0.0790569i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$		−	17.0027i		−	1.86629i	−0.359506	−	0.933143i	$-0.617055\pi$
$83$		−	17.0027i		−	1.86629i	0.359506	−	0.933143i	$-0.382945\pi$
$84$	0.325765	−	0.707107i	0.0355439	−	0.0771517i
$85$	0.449490	−	0.778539i	0.0487540	−	0.0844444i
$86$	−4.44949	+	7.70674i	−0.479801	+	0.831039i
$87$	1.77526	−	3.85337i	0.190327	−	0.413125i
$88$			3.14626i			0.335393i
$89$	3.55051	−	6.14966i	0.376353	−	0.651863i	−0.614175	−	0.789170i	$-0.710511\pi$
$89$	3.55051	−	6.14966i	0.376353	−	0.651863i	0.990529	+	0.137307i	$0.0438445\pi$
$90$	−4.00000	−	1.41421i	−0.421637	−	0.149071i
$91$	1.34847	+	0.778539i	0.141358	+	0.0816131i
$92$	6.12372	−	3.53553i	0.638442	−	0.368605i
$93$	0.674235	+	7.31747i	0.0699149	+	0.758787i
$94$			13.3636i			1.37835i
$95$	−6.00000	−	1.41421i	−0.615587	−	0.145095i
$96$	0.724745	−	1.57313i	0.0739690	−	0.160557i
$97$	2.84847	−	1.64456i	0.289218	−	0.166980i	−0.348371	−	0.937357i	$-0.613265\pi$
$97$	2.84847	−	1.64456i	0.289218	−	0.166980i	0.637589	+	0.770377i	$0.279932\pi$
$98$	−3.39898	−	5.88721i	−0.343349	−	0.594698i
$99$	−1.72474	−	9.27987i	−0.173343	−	0.932662i
$100$	−1.50000	−	2.59808i	−0.150000	−	0.259808i
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	0.861684	−	0.507445i	$-0.169410\pi$
$101$	8.57321	+	4.94975i	0.853067	+	0.492518i	−0.00861771	+	0.999963i	$0.502743\pi$
$102$	−1.00000	−	0.460702i	−0.0990148	−	0.0456163i
$103$		−	5.02118i		−	0.494752i	−0.968920	−	0.247376i	$-0.920432\pi$
$103$		−	5.02118i		−	0.494752i	0.968920	−	0.247376i	$-0.0795682\pi$
$104$	3.00000	+	1.73205i	0.294174	+	0.169842i
$105$	0.898979	−	0.635674i	0.0877314	−	0.0620355i
$106$	−10.8990			−1.05860
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$	−1.27526	+	5.03723i	−0.122711	+	0.484708i
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$	−2.22474	+	3.85337i	−0.212121	+	0.367405i
$111$	−1.22474	−	13.2922i	−0.116248	−	1.26164i
$112$	0.224745	+	0.389270i	0.0212364	+	0.0367825i
$113$	−18.7980			−1.76836			−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−18.7980			−1.76836			−0.884182	+	0.467143i	$0.845283\pi$
$114$	−1.05051	+	7.47639i	−0.0983893	+	0.700228i
$115$	10.0000			0.932505
$116$	1.22474	+	2.12132i	0.113715	+	0.196960i
$117$	−9.79796	−	3.46410i	−0.905822	−	0.320256i
$118$	−5.72474	+	9.91555i	−0.527005	+	0.912800i
$119$	0.247449	−	0.142865i	0.0226836	−	0.0130964i
$120$	2.00000	−	1.41421i	0.182574	−	0.129099i
$121$	1.10102			0.100093
$122$	1.55051			0.140377
$123$	−3.00000	−	4.24264i	−0.270501	−	0.382546i
$124$	−3.67423	−	2.12132i	−0.329956	−	0.190500i
$125$		−	11.3137i		−	1.01193i
$126$	−0.876276	−	1.02494i	−0.0780648	−	0.0913093i
$127$	−9.00000	−	5.19615i	−0.798621	−	0.461084i	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	−9.00000	−	5.19615i	−0.798621	−	0.461084i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.89898	+	12.5851i	0.783511	+	1.10805i
$130$	2.44949	+	4.24264i	0.214834	+	0.372104i
$131$	1.92679	−	1.11243i	0.168344	−	0.0971935i	−0.413461	−	0.910522i	$-0.635680\pi$
$131$	1.92679	−	1.11243i	0.168344	−	0.0971935i	0.581805	+	0.813328i	$0.302347\pi$
$132$	4.94949	+	2.28024i	0.430798	+	0.198469i
$133$	−1.42679	−	1.34278i	−0.123718	−	0.116434i
$134$			2.51059i			0.216882i
$135$	−5.12372	+	5.26758i	−0.440980	+	0.453362i
$136$	0.550510	−	0.317837i	0.0472059	−	0.0272543i
$137$	3.39898	+	1.96240i	0.290394	+	0.167659i	0.638120	−	0.769937i	$-0.279712\pi$
$137$	3.39898	+	1.96240i	0.290394	+	0.167659i	−0.347725	+	0.937596i	$0.613046\pi$
$138$	−1.12372	−	12.1958i	−0.0956578	−	1.03817i
$139$	7.17423	−	12.4261i	0.608511	−	1.05397i	−0.382975	−	0.923759i	$-0.625101\pi$
$139$	7.17423	−	12.4261i	0.608511	−	1.05397i	0.991486	−	0.130213i	$-0.0415661\pi$
$140$			0.635674i			0.0537243i
$141$	21.0227	+	9.68520i	1.77043	+	0.815641i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−5.44949	+	9.43879i	−0.455709	+	0.789312i
$144$	−1.94949	−	2.28024i	−0.162457	−	0.190020i
$145$			3.46410i			0.287678i
$146$	4.39898	−	7.61926i	0.364062	−	0.630574i
$147$	−11.7247	+	1.08032i	−0.967041	+	0.0891035i
$148$	6.67423	+	3.85337i	0.548619	+	0.316745i
$149$	1.77526	−	1.02494i	0.145435	−	0.0839667i	−0.425517	−	0.904950i	$-0.639908\pi$
$149$	1.77526	−	1.02494i	0.145435	−	0.0839667i	0.570952	+	0.820984i	$0.306574\pi$
$150$	−5.17423	+	0.476756i	−0.422474	+	0.0389270i
$151$		−	9.61377i		−	0.782357i	−0.920315	−	0.391179i	$-0.872067\pi$
$151$		−	9.61377i		−	0.782357i	0.920315	−	0.391179i	$-0.127933\pi$
$152$	−3.17423	−	2.98735i	−0.257464	−	0.242306i
$153$	−1.44949	+	1.23924i	−0.117184	+	0.100187i
$154$	−1.22474	+	0.707107i	−0.0986928	+	0.0569803i
$155$	−3.00000	−	5.19615i	−0.240966	−	0.417365i
$156$	4.89898	−	3.46410i	0.392232	−	0.277350i
$157$	−5.34847	−	9.26382i	−0.426854	−	0.739333i	0.569737	−	0.821827i	$-0.307045\pi$
$157$	−5.34847	−	9.26382i	−0.426854	−	0.739333i	−0.996592	+	0.0824935i	$0.973712\pi$
$158$	−7.34847	−	4.24264i	−0.584613	−	0.337526i
$159$	−7.89898	+	17.1455i	−0.626430	+	1.35973i
$160$			1.41421i			0.111803i
$161$	2.75255	+	1.58919i	0.216931	+	0.125245i
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$	18.3485			1.43716			0.718582	−	0.695443i	$-0.244792\pi$
$163$	18.3485			1.43716			0.718582	+	0.695443i	$0.244792\pi$
$164$	3.00000			0.234261
$165$	4.44949	+	6.29253i	0.346392	+	0.489873i
$166$	14.7247	−	8.50134i	1.14286	−	0.659832i
$167$	−2.44949	+	4.24264i	−0.189547	+	0.328305i	−0.945099	−	0.326783i	$-0.894035\pi$
$167$	−2.44949	+	4.24264i	−0.189547	+	0.328305i	0.755552	+	0.655089i	$0.227369\pi$
$168$	0.775255	−	0.0714323i	0.0598122	−	0.00551112i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.898979			0.0689486
$171$	11.0000	+	7.07107i	0.841191	+	0.540738i
$172$	−8.89898			−0.678541
$173$	0.550510	+	0.953512i	0.0418545	+	0.0724942i	0.886194	−	0.463315i	$-0.153340\pi$
$173$	0.550510	+	0.953512i	0.0418545	+	0.0724942i	−0.844339	+	0.535809i	$0.820007\pi$
$174$	4.22474	−	0.389270i	0.320277	−	0.0295104i
$175$	0.674235	−	1.16781i	0.0509673	−	0.0882780i
$176$	−2.72474	+	1.57313i	−0.205385	+	0.118579i
$177$	11.4495	+	16.1920i	0.860596	+	1.21707i
$178$	7.10102			0.532244
$179$	−7.65153			−0.571902			−0.285951	−	0.958244i	$-0.592310\pi$
$179$	−7.65153			−0.571902			−0.285951	+	0.958244i	$0.592310\pi$
$180$	−0.775255	−	4.17121i	−0.0577841	−	0.310904i
$181$	18.6742	+	10.7816i	1.38804	+	0.801388i	0.993095	−	0.117314i	$-0.0374285\pi$
$181$	18.6742	+	10.7816i	1.38804	+	0.801388i	0.394950	+	0.918703i	$0.370762\pi$
$182$			1.55708i			0.115418i
$183$	1.12372	−	2.43916i	0.0830681	−	0.180308i
$184$	6.12372	+	3.53553i	0.451447	+	0.260643i
$185$	5.44949	+	9.43879i	0.400654	+	0.693954i
$186$	−6.00000	+	4.24264i	−0.439941	+	0.311086i
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	−11.5732	+	6.68180i	−0.844063	+	0.487320i
$189$	−2.24745	+	0.635674i	−0.163478	+	0.0462385i
$190$	−1.77526	−	5.90326i	−0.128791	−	0.428267i
$191$			8.19955i			0.593299i	0.954986	+	0.296649i	$0.0958693\pi$
$191$			8.19955i			0.593299i	−0.954986	+	0.296649i	$0.904131\pi$
$192$	1.72474	−	0.158919i	0.124473	−	0.0114690i
$193$	−22.3485	+	12.9029i	−1.60868	+	0.928771i	−0.619012	+	0.785382i	$0.712467\pi$
$193$	−22.3485	+	12.9029i	−1.60868	+	0.928771i	−0.989666	+	0.143389i	$0.954200\pi$
$194$	2.84847	+	1.64456i	0.204508	+	0.118073i
$195$	8.44949	−	0.778539i	0.605081	−	0.0557523i
$196$	3.39898	−	5.88721i	0.242784	−	0.420515i
$197$		−	20.2918i		−	1.44573i	−0.690989	−	0.722865i	$-0.742825\pi$
$197$		−	20.2918i		−	1.44573i	0.690989	−	0.722865i	$-0.257175\pi$
$198$	7.17423	−	6.13361i	0.509851	−	0.435897i
$199$	1.44949	−	2.51059i	0.102752	−	0.177971i	−0.810066	−	0.586339i	$-0.800569\pi$
$199$	1.44949	−	2.51059i	0.102752	−	0.177971i	0.912817	+	0.408368i	$0.133902\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$	3.94949	+	1.81954i	0.278576	+	0.128340i
$202$			9.89949i			0.696526i
$203$	−0.550510	+	0.953512i	−0.0386382	+	0.0669234i
$204$	−0.101021	−	1.09638i	−0.00707285	−	0.0767617i
$205$	3.67423	+	2.12132i	0.256620	+	0.148159i
$206$	4.34847	−	2.51059i	0.302972	−	0.174921i
$207$	−20.0000	−	7.07107i	−1.39010	−	0.491473i
$208$			3.46410i			0.240192i
$209$	9.39898	−	9.98698i	0.650141	−	0.690814i
$210$	1.00000	+	0.460702i	0.0690066	+	0.0317914i
$211$	−1.34847	+	0.778539i	−0.0928325	+	0.0535968i	−0.545698	−	0.837982i	$-0.683735\pi$
$211$	−1.34847	+	0.778539i	−0.0928325	+	0.0535968i	0.452865	+	0.891579i	$0.350402\pi$
$212$	−5.44949	−	9.43879i	−0.374272	−	0.648259i
$213$	6.00000	+	8.48528i	0.411113	+	0.581402i
$214$	−2.44949	−	4.24264i	−0.167444	−	0.290021i
$215$	−10.8990	−	6.29253i	−0.743304	−	0.429147i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$		−	1.90702i		−	0.129457i
$218$		0			0
$219$	−8.79796	−	12.4422i	−0.594511	−	0.840765i
$220$	−4.44949			−0.299985
$221$	2.20204			0.148125
$222$	10.8990	−	7.70674i	0.731492	−	0.517243i
$223$	−15.6742	+	9.04952i	−1.04962	+	0.606001i	−0.922544	−	0.385892i	$-0.873894\pi$
$223$	−15.6742	+	9.04952i	−1.04962	+	0.606001i	−0.127080	+	0.991892i	$0.540561\pi$
$224$	−0.224745	+	0.389270i	−0.0150164	+	0.0260092i
$225$	−3.00000	+	8.48528i	−0.200000	+	0.565685i
$226$	−9.39898	−	16.2795i	−0.625211	−	1.08290i
$227$	0.550510			0.0365386			0.0182693	−	0.999833i	$-0.494184\pi$
$227$	0.550510			0.0365386			0.0182693	+	0.999833i	$0.494184\pi$
$228$	−7.00000	+	2.82843i	−0.463586	+	0.187317i
$229$	0.898979			0.0594062			0.0297031	−	0.999559i	$-0.490544\pi$
$229$	0.898979			0.0594062			0.0297031	+	0.999559i	$0.490544\pi$
$230$	5.00000	+	8.66025i	0.329690	+	0.571040i
$231$	0.224745	+	2.43916i	0.0147871	+	0.160485i
$232$	−1.22474	+	2.12132i	−0.0804084	+	0.139272i
$233$	−15.3990	+	8.89060i	−1.00882	+	0.582443i	−0.910846	−	0.412746i	$-0.864570\pi$
$233$	−15.3990	+	8.89060i	−1.00882	+	0.582443i	−0.0979745	+	0.995189i	$0.531236\pi$
$234$	−1.89898	−	10.2173i	−0.124140	−	0.667928i
$235$	−18.8990			−1.23283
$236$	−11.4495			−0.745298
$237$	−12.0000	+	8.48528i	−0.779484	+	0.551178i
$238$	0.247449	+	0.142865i	0.0160397	+	0.00926054i
$239$		−	21.0703i		−	1.36293i	−0.731852	−	0.681463i	$-0.761344\pi$
$239$		−	21.0703i		−	1.36293i	0.731852	−	0.681463i	$-0.238656\pi$
$240$	2.22474	+	1.02494i	0.143607	+	0.0661599i
$241$	−5.84847	−	3.37662i	−0.376733	−	0.217507i	0.299663	−	0.954045i	$-0.403126\pi$
$241$	−5.84847	−	3.37662i	−0.376733	−	0.217507i	−0.676396	+	0.736538i	$0.736459\pi$
$242$	0.550510	+	0.953512i	0.0353881	+	0.0612941i
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$	0.775255	+	1.34278i	0.0496306	+	0.0859628i
$245$	8.32577	−	4.80688i	0.531914	−	0.307100i
$246$	2.17423	−	4.71940i	0.138624	−	0.300898i
$247$	−4.34847	−	14.4600i	−0.276686	−	0.920066i
$248$		−	4.24264i		−	0.269408i
$249$	−2.70204	−	29.3253i	−0.171235	−	1.85841i
$250$	9.79796	−	5.65685i	0.619677	−	0.357771i
$251$	−3.27526	−	1.89097i	−0.206732	−	0.119357i	0.393060	−	0.919513i	$-0.371417\pi$
$251$	−3.27526	−	1.89097i	−0.206732	−	0.119357i	−0.599792	+	0.800156i	$0.704750\pi$
$252$	0.449490	−	1.27135i	0.0283152	−	0.0800875i
$253$	−11.1237	+	19.2669i	−0.699343	+	1.21130i
$254$		−	10.3923i		−	0.652071i
$255$	0.651531	−	1.41421i	0.0408004	−	0.0885615i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	−6.44949	+	13.9993i	−0.401528	+	0.871557i
$259$			3.46410i			0.215249i
$260$	−2.44949	+	4.24264i	−0.151911	+	0.263117i
$261$	2.44949	−	6.92820i	0.151620	−	0.428845i
$262$	1.92679	+	1.11243i	0.119037	+	0.0687262i
$263$	7.77526	−	4.48905i	0.479443	−	0.276806i	−0.240741	−	0.970589i	$-0.577391\pi$
$263$	7.77526	−	4.48905i	0.479443	−	0.276806i	0.720184	+	0.693783i	$0.244057\pi$
$264$	0.500000	+	5.42650i	0.0307729	+	0.333978i
$265$		−	15.4135i		−	0.946843i
$266$	0.449490	−	1.90702i	0.0275600	−	0.116927i
$267$	5.14643	−	11.1708i	0.314956	−	0.683645i
$268$	−2.17423	+	1.25529i	−0.132813	+	0.0766793i
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	0.949377	+	0.314138i	$0.101715\pi$
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	−0.202637	+	0.979254i	$0.564951\pi$
$270$	−7.12372	−	1.80348i	−0.433536	−	0.109756i
$271$	10.0227	+	17.3598i	0.608836	+	1.05453i	0.991433	+	0.130619i	$0.0416965\pi$
$271$	10.0227	+	17.3598i	0.608836	+	1.05453i	−0.382597	+	0.923915i	$0.624970\pi$
$272$	0.550510	+	0.317837i	0.0333796	+	0.0192717i
$273$	2.44949	+	1.12848i	0.148250	+	0.0682990i
$274$			3.92480i			0.237106i
$275$	8.17423	+	4.71940i	0.492925	+	0.284590i
$276$	10.0000	−	7.07107i	0.601929	−	0.425628i
$277$	20.2474			1.21655			0.608276	−	0.793726i	$-0.291862\pi$
$277$	20.2474			1.21655			0.608276	+	0.793726i	$0.291862\pi$
$278$	14.3485			0.860564
$279$	2.32577	+	12.5136i	0.139240	+	0.749171i
$280$	−0.550510	+	0.317837i	−0.0328993	+	0.0189944i
$281$	11.2980	−	19.5686i	0.673980	−	1.16737i	−0.302786	−	0.953058i	$-0.597917\pi$
$281$	11.2980	−	19.5686i	0.673980	−	1.16737i	0.976766	−	0.214309i	$-0.0687498\pi$
$282$	2.12372	+	23.0488i	0.126466	+	1.37254i
$283$	4.72474	+	8.18350i	0.280857	+	0.486458i	0.971596	−	0.236646i	$-0.0760480\pi$
$283$	4.72474	+	8.18350i	0.280857	+	0.486458i	−0.690739	+	0.723104i	$0.742715\pi$
$284$	−6.00000			−0.356034
$285$	−10.5732	−	1.48565i	−0.626303	−	0.0880021i
$286$	−10.8990			−0.644470
$287$	0.674235	+	1.16781i	0.0397988	+	0.0689336i
$288$	1.00000	−	2.82843i	0.0589256	−	0.166667i
$289$	−8.29796	+	14.3725i	−0.488115	+	0.845440i
$290$	−3.00000	+	1.73205i	−0.176166	+	0.101710i
$291$	4.65153	−	3.28913i	0.272678	−	0.192812i
$292$	8.79796			0.514862
$293$	−19.3485			−1.13035			−0.565175	−	0.824971i	$-0.691191\pi$
$293$	−19.3485			−1.13035			−0.565175	+	0.824971i	$0.691191\pi$
$294$	−6.79796	−	9.61377i	−0.396465	−	0.560686i
$295$	−14.0227	−	8.09601i	−0.816433	−	0.471368i
$296$			7.70674i			0.447945i
$297$	−4.44949	−	15.7313i	−0.258186	−	0.912824i
$298$	1.77526	+	1.02494i	0.102838	+	0.0593734i
$299$	12.2474	+	21.2132i	0.708288	+	1.22679i
$300$	−3.00000	−	4.24264i	−0.173205	−	0.244949i
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	8.32577	−	4.80688i	0.479094	−	0.276605i
$303$	15.5732	+	7.17461i	0.894658	+	0.412170i
$304$	1.00000	−	4.24264i	0.0573539	−	0.243332i
$305$			2.19275i			0.125557i
$306$	−1.79796	−	0.635674i	−0.102782	−	0.0363391i
$307$	18.5227	−	10.6941i	1.05715	−	0.610344i	0.132505	−	0.991182i	$-0.457698\pi$
$307$	18.5227	−	10.6941i	1.05715	−	0.610344i	0.924642	+	0.380838i	$0.124365\pi$
$308$	−1.22474	−	0.707107i	−0.0697863	−	0.0402911i
$309$	−0.797959	−	8.66025i	−0.0453943	−	0.492665i
$310$	3.00000	−	5.19615i	0.170389	−	0.295122i
$311$			15.5563i			0.882120i	0.897478	+	0.441060i	$0.145397\pi$
$311$			15.5563i			0.882120i	−0.897478	+	0.441060i	$0.854603\pi$
$312$	5.44949	+	2.51059i	0.308517	+	0.142134i
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	5.34847	−	9.26382i	0.301832	−	0.522788i
$315$	1.44949	−	1.23924i	0.0816695	−	0.0698233i
$316$		−	8.48528i		−	0.477334i
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	−18.7980	+	1.73205i	−1.05414	+	0.0971286i
$319$	−6.67423	−	3.85337i	−0.373685	−	0.215747i
$320$	−1.22474	+	0.707107i	−0.0684653	+	0.0395285i
$321$	−8.44949	+	0.778539i	−0.471605	+	0.0434538i
$322$			3.17837i			0.177124i
$323$	−2.69694	−	0.635674i	−0.150062	−	0.0353699i
$324$	−1.39898	+	8.89060i	−0.0777211	+	0.493922i
$325$	9.00000	−	5.19615i	0.499230	−	0.288231i
$326$	9.17423	+	15.8902i	0.508114	+	0.880079i
$327$		0			0
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−5.20204	−	3.00340i	−0.286798	−	0.165583i
$330$	−3.22474	+	6.99964i	−0.177516	+	0.385317i
$331$			23.2952i			1.28042i	0.768200	+	0.640210i	$0.221153\pi$
$331$			23.2952i			1.28042i	−0.768200	+	0.640210i	$0.778847\pi$
$332$	14.7247	+	8.50134i	0.808125	+	0.466571i
$333$	−4.22474	−	22.7310i	−0.231515	−	1.24565i
$334$	−4.89898			−0.268060
$335$	−3.55051			−0.193985
$336$	0.449490	+	0.635674i	0.0245217	+	0.0346789i
$337$	−17.8485	+	10.3048i	−0.972268	+	0.561339i	−0.899927	−	0.436041i	$-0.856380\pi$
$337$	−17.8485	+	10.3048i	−0.972268	+	0.561339i	−0.0723411	+	0.997380i	$0.523047\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	−32.4217	+	2.98735i	−1.76090	+	0.162250i
$340$	0.449490	+	0.778539i	0.0243770	+	0.0422222i
$341$	13.3485			0.722860
$342$	−0.623724	+	13.0618i	−0.0337272	+	0.706302i
$343$	6.20204			0.334879
$344$	−4.44949	−	7.70674i	−0.239900	−	0.415520i
$345$	17.2474	−	1.58919i	0.928571	−	0.0855589i
$346$	−0.550510	+	0.953512i	−0.0295956	+	0.0512611i
$347$	3.27526	−	1.89097i	0.175825	−	0.101513i	−0.409505	−	0.912308i	$-0.634298\pi$
$347$	3.27526	−	1.89097i	0.175825	−	0.101513i	0.585330	+	0.810795i	$0.300965\pi$
$348$	2.44949	+	3.46410i	0.131306	+	0.185695i
$349$	32.4949			1.73941			0.869706	−	0.493570i	$-0.164308\pi$
$349$	32.4949			1.73941			0.869706	+	0.493570i	$0.164308\pi$
$350$	1.34847			0.0720787
$351$	−17.4495	−	4.41761i	−0.931385	−	0.235795i
$352$	−2.72474	−	1.57313i	−0.145229	−	0.0838482i
$353$			24.9951i			1.33036i	0.746684	+	0.665179i	$0.231645\pi$
$353$			24.9951i			1.33036i	−0.746684	+	0.665179i	$0.768355\pi$
$354$	−8.29796	+	18.0116i	−0.441032	+	0.957304i
$355$	−7.34847	−	4.24264i	−0.390016	−	0.225176i
$356$	3.55051	+	6.14966i	0.188177	+	0.325932i
$357$	0.404082	−	0.285729i	0.0213863	−	0.0151224i
$358$	−3.82577	−	6.62642i	−0.202198	−	0.350217i
$359$	20.8207	−	12.0208i	1.09887	−	0.634434i	0.162948	−	0.986635i	$-0.447900\pi$
$359$	20.8207	−	12.0208i	1.09887	−	0.634434i	0.935925	+	0.352200i	$0.114566\pi$
$360$	3.22474	−	2.75699i	0.169959	−	0.145306i
$361$	1.15153	+	18.9651i	0.0606069	+	0.998162i
$362$			21.5631i			1.13333i
$363$	1.89898	−	0.174973i	0.0996706	−	0.00918368i
$364$	−1.34847	+	0.778539i	−0.0706790	+	0.0408065i
$365$	10.7753	+	6.22110i	0.564003	+	0.325627i
$366$	2.67423	−	0.246405i	0.139784	−	0.0128798i
$367$	4.32577	−	7.49245i	0.225803	−	0.391102i	−0.730757	−	0.682638i	$-0.760833\pi$
$367$	4.32577	−	7.49245i	0.225803	−	0.391102i	0.956560	+	0.291535i	$0.0941661\pi$
$368$			7.07107i			0.368605i
$369$	−5.84847	−	6.84072i	−0.304459	−	0.356113i
$370$	−5.44949	+	9.43879i	−0.283305	+	0.490699i
$371$	2.44949	−	4.24264i	0.127171	−	0.220267i
$372$	−6.67423	−	3.07483i	−0.346043	−	0.159423i
$373$		−	25.4558i		−	1.31805i	−0.752119	−	0.659027i	$-0.770968\pi$
$373$		−	25.4558i		−	1.31805i	0.752119	−	0.659027i	$-0.229032\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$	−1.79796	−	19.5133i	−0.0928462	−	1.00766i
$376$	−11.5732	−	6.68180i	−0.596843	−	0.344587i
$377$	−7.34847	+	4.24264i	−0.378465	+	0.218507i
$378$	−1.67423	−	1.62851i	−0.0861133	−	0.0837615i
$379$			1.55708i			0.0799817i	0.999200	+	0.0399909i	$0.0127329\pi$
$379$			1.55708i			0.0799817i	−0.999200	+	0.0399909i	$0.987267\pi$
$380$	4.22474	−	4.48905i	0.216725	−	0.230283i
$381$	−16.3485	−	7.53177i	−0.837557	−	0.385864i
$382$	−7.10102	+	4.09978i	−0.363320	+	0.209763i
$383$	10.2247	+	17.7098i	0.522460	+	0.904927i	0.999659	+	0.0261318i	$0.00831896\pi$
$383$	10.2247	+	17.7098i	0.522460	+	0.904927i	−0.477198	+	0.878796i	$0.658348\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	−22.3485	−	12.9029i	−1.13751	−	0.656740i
$387$	17.3485	+	20.2918i	0.881872	+	1.03149i
$388$			3.28913i			0.166980i
$389$	−13.1010	−	7.56388i	−0.664248	−	0.383504i	0.129646	−	0.991560i	$-0.458616\pi$
$389$	−13.1010	−	7.56388i	−0.664248	−	0.383504i	−0.793894	+	0.608057i	$0.791949\pi$
$390$	4.89898	+	6.92820i	0.248069	+	0.350823i
$391$	4.49490			0.227317
$392$	6.79796			0.343349
$393$	3.14643	−	2.22486i	0.158716	−	0.112229i
$394$	17.5732	−	10.1459i	0.885326	−	0.511143i
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$	8.89898	+	3.14626i	0.447191	+	0.158106i
$397$	2.67423	+	4.63191i	0.134216	+	0.232469i	0.925298	−	0.379242i	$-0.123815\pi$
$397$	2.67423	+	4.63191i	0.134216	+	0.232469i	−0.791082	+	0.611711i	$0.790482\pi$
$398$	2.89898			0.145313
$399$	−2.67423	−	2.08921i	−0.133879	−	0.104591i
$400$	3.00000			0.150000
$401$	−3.39898	−	5.88721i	−0.169737	−	0.293993i	0.768590	−	0.639741i	$-0.220958\pi$
$401$	−3.39898	−	5.88721i	−0.169737	−	0.293993i	−0.938327	+	0.345748i	$0.887625\pi$
$402$	0.398979	+	4.33013i	0.0198993	+	0.215967i
$403$	7.34847	−	12.7279i	0.366053	−	0.634023i
$404$	−8.57321	+	4.94975i	−0.426533	+	0.246259i
$405$	−8.00000	+	9.89949i	−0.397523	+	0.491910i
$406$	−1.10102			−0.0546427
$407$	−24.2474			−1.20190
$408$	0.898979	−	0.635674i	0.0445061	−	0.0314706i
$409$	3.15153	+	1.81954i	0.155833	+	0.0899703i	0.575889	−	0.817528i	$-0.304656\pi$
$409$	3.15153	+	1.81954i	0.155833	+	0.0899703i	−0.420056	+	0.907498i	$0.637989\pi$
$410$			4.24264i			0.209529i
$411$	6.17423	+	2.84448i	0.304553	+	0.140308i
$412$	4.34847	+	2.51059i	0.214234	+	0.123688i
$413$	−2.57321	−	4.45694i	−0.126620	−	0.219312i
$414$	−3.87628	−	20.8560i	−0.190509	−	1.02502i
$415$	12.0227	+	20.8239i	0.590171	+	1.02221i
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$	10.3990	−	22.5720i	0.509240	−	1.10536i
$418$	13.3485	+	3.14626i	0.652895	+	0.153889i
$419$		−	24.5344i		−	1.19859i	−0.800530	−	0.599293i	$-0.795448\pi$
$419$		−	24.5344i		−	1.19859i	0.800530	−	0.599293i	$-0.204552\pi$
$420$	0.101021	+	1.09638i	0.00492930	+	0.0534977i
$421$	−3.97730	+	2.29629i	−0.193842	+	0.111914i	−0.593780	−	0.804628i	$-0.702365\pi$
$421$	−3.97730	+	2.29629i	−0.193842	+	0.111914i	0.399938	+	0.916542i	$0.369032\pi$
$422$	−1.34847	−	0.778539i	−0.0656425	−	0.0378987i
$423$	37.7980	+	13.3636i	1.83780	+	0.649760i
$424$	5.44949	−	9.43879i	0.264651	−	0.458388i
$425$		−	1.90702i		−	0.0925042i
$426$	−4.34847	+	9.43879i	−0.210684	+	0.457311i
$427$	−0.348469	+	0.603566i	−0.0168636	+	0.0292086i
$428$	2.44949	−	4.24264i	0.118401	−	0.205076i
$429$	−7.89898	+	17.1455i	−0.381366	+	0.827794i
$430$		−	12.5851i		−	0.606905i
$431$	1.65153	−	2.86054i	0.0795514	−	0.137787i	−0.823505	−	0.567309i	$-0.807985\pi$
$431$	1.65153	−	2.86054i	0.0795514	−	0.137787i	0.903056	+	0.429522i	$0.141318\pi$
$432$	−3.72474	−	3.62302i	−0.179207	−	0.174313i
$433$	−17.6969	−	10.2173i	−0.850461	−	0.491014i	0.0103456	−	0.999946i	$-0.496707\pi$
$433$	−17.6969	−	10.2173i	−0.850461	−	0.491014i	−0.860806	+	0.508933i	$0.830040\pi$
$434$	1.65153	−	0.953512i	0.0792760	−	0.0457700i
$435$	0.550510	+	5.97469i	0.0263949	+	0.286465i
$436$		0			0
$437$	−8.87628	−	29.5163i	−0.424610	−	1.41196i
$438$	6.37628	−	13.8404i	0.304670	−	0.661318i
$439$	−9.67423	+	5.58542i	−0.461726	+	0.266578i	−0.712770	−	0.701398i	$-0.752560\pi$
$439$	−9.67423	+	5.58542i	−0.461726	+	0.266578i	0.251044	+	0.967976i	$0.419226\pi$
$440$	−2.22474	−	3.85337i	−0.106061	−	0.183702i
$441$	−20.0505	+	3.72656i	−0.954786	+	0.177455i
$442$	1.10102	+	1.90702i	0.0523702	+	0.0907079i
$443$	−16.3207	−	9.42274i	−0.775418	−	0.447688i	0.0593859	−	0.998235i	$-0.481086\pi$
$443$	−16.3207	−	9.42274i	−0.775418	−	0.447688i	−0.834804	+	0.550547i	$0.814419\pi$
$444$	12.1237	+	5.58542i	0.575366	+	0.265072i
$445$			10.0424i			0.476053i
$446$	−15.6742	−	9.04952i	−0.742197	−	0.428507i
$447$	2.89898	−	2.04989i	0.137117	−	0.0969564i
$448$	−0.449490			−0.0212364
$449$	30.7980			1.45345			0.726723	−	0.686931i	$-0.241042\pi$
$449$	30.7980			1.45345			0.726723	+	0.686931i	$0.241042\pi$
$450$	−8.84847	+	1.64456i	−0.417121	+	0.0775255i
$451$	−8.17423	+	4.71940i	−0.384910	+	0.222228i
$452$	9.39898	−	16.2795i	0.442091	−	0.765724i
$453$	−1.52781	−	16.5813i	−0.0717826	−	0.779057i
$454$	0.275255	+	0.476756i	0.0129184	+	0.0223753i
$455$	−2.20204			−0.103233
$456$	−5.94949	−	4.64796i	−0.278610	−	0.217661i
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	0.449490	+	0.778539i	0.0210033	+	0.0363787i
$459$	−2.30306	+	2.36773i	−0.107498	+	0.110516i
$460$	−5.00000	+	8.66025i	−0.233126	+	0.403786i
$461$	−33.2474	+	19.1954i	−1.54849	+	0.894020i	−0.550231	+	0.835013i	$0.685460\pi$
$461$	−33.2474	+	19.1954i	−1.54849	+	0.894020i	−0.998258	+	0.0590072i	$0.981207\pi$
$462$	−2.00000	+	1.41421i	−0.0930484	+	0.0657952i
$463$	−19.7980			−0.920089			−0.460045	−	0.887896i	$-0.652167\pi$
$463$	−19.7980			−0.920089			−0.460045	+	0.887896i	$0.652167\pi$
$464$	−2.44949			−0.113715
$465$	−6.00000	−	8.48528i	−0.278243	−	0.393496i
$466$	−15.3990	−	8.89060i	−0.713344	−	0.411849i
$467$			12.6172i			0.583853i	0.956441	+	0.291926i	$0.0942962\pi$
$467$			12.6172i			0.583853i	−0.956441	+	0.291926i	$0.905704\pi$
$468$	7.89898	−	6.75323i	0.365130	−	0.312168i
$469$	−0.977296	−	0.564242i	−0.0451273	−	0.0260543i
$470$	−9.44949	−	16.3670i	−0.435872	−	0.754953i
$471$	−10.6969	−	15.1278i	−0.492889	−	0.697050i
$472$	−5.72474	−	9.91555i	−0.263503	−	0.456400i
$473$	24.2474	−	13.9993i	1.11490	−	0.643687i
$474$	−13.3485	−	6.14966i	−0.613115	−	0.282463i
$475$	−12.5227	+	3.76588i	−0.574581	+	0.172791i
$476$			0.285729i			0.0130964i
$477$	−10.8990	+	30.8270i	−0.499030	+	1.41147i
$478$	18.2474	−	10.5352i	0.834619	−	0.481867i
$479$	0.853572	+	0.492810i	0.0390007	+	0.0225171i	0.519374	−	0.854547i	$-0.326165\pi$
$479$	0.853572	+	0.492810i	0.0390007	+	0.0225171i	−0.480373	+	0.877064i	$0.659499\pi$
$480$	0.224745	+	2.43916i	0.0102582	+	0.111332i
$481$	−13.3485	+	23.1202i	−0.608638	+	1.05419i
$482$		−	6.75323i		−	0.307601i
$483$	5.00000	+	2.30351i	0.227508	+	0.104813i
$484$	−0.550510	+	0.953512i	−0.0250232	+	0.0433414i
$485$	−2.32577	+	4.02834i	−0.105608	+	0.182918i
$486$	12.9722	+	8.64420i	0.588431	+	0.392109i
$487$			25.0273i			1.13409i	0.823686	+	0.567046i	$0.191914\pi$
$487$			25.0273i			1.13409i	−0.823686	+	0.567046i	$0.808086\pi$
$488$	−0.775255	+	1.34278i	−0.0350942	+	0.0607849i
$489$	31.6464	−	2.91591i	1.43110	−	0.131862i
$490$	8.32577	+	4.80688i	0.376120	+	0.217153i
$491$	−13.8990	+	8.02458i	−0.627252	+	0.362144i	−0.779687	−	0.626169i	$-0.784622\pi$
$491$	−13.8990	+	8.02458i	−0.627252	+	0.362144i	0.152435	+	0.988314i	$0.451289\pi$
$492$	5.17423	−	0.476756i	0.233273	−	0.0214938i
$493$			1.55708i			0.0701273i
$494$	10.3485	−	10.9959i	0.465600	−	0.494728i
$495$	8.67423	+	10.1459i	0.389878	+	0.456024i
$496$	3.67423	−	2.12132i	0.164978	−	0.0952501i
$497$	−1.34847	−	2.33562i	−0.0604871	−	0.104767i
$498$	24.0454	−	17.0027i	1.07750	−	0.761908i
$499$	−3.72474	−	6.45145i	−0.166742	−	0.288806i	0.770530	−	0.637403i	$-0.219992\pi$
$499$	−3.72474	−	6.45145i	−0.166742	−	0.288806i	−0.937273	+	0.348597i	$0.886658\pi$
$500$	9.79796	+	5.65685i	0.438178	+	0.252982i
$501$	−3.55051	+	7.70674i	−0.158625	+	0.344312i
$502$		−	3.78194i		−	0.168796i
$503$	−13.4722	−	7.77817i	−0.600695	−	0.346812i	0.168620	−	0.985681i	$-0.446069\pi$
$503$	−13.4722	−	7.77817i	−0.600695	−	0.346812i	−0.769315	+	0.638870i	$0.779402\pi$
$504$	1.32577	−	0.246405i	0.0590543	−	0.0109757i
$505$	−14.0000			−0.622992
$506$	−22.2474			−0.989020
$507$	−1.00000	−	1.41421i	−0.0444116	−	0.0628074i
$508$	9.00000	−	5.19615i	0.399310	−	0.230542i
$509$	8.69694	−	15.0635i	0.385485	−	0.667680i	−0.606351	−	0.795197i	$-0.707367\pi$
$509$	8.69694	−	15.0635i	0.385485	−	0.667680i	0.991836	+	0.127517i	$0.0407008\pi$
$510$	1.55051	−	0.142865i	0.0686577	−	0.00632615i
$511$	1.97730	+	3.42478i	0.0874704	+	0.151503i
$512$	−1.00000			−0.0441942
$513$	20.0959	+	10.4477i	0.887256	+	0.461276i
$514$	−15.0000			−0.661622
$515$	3.55051	+	6.14966i	0.156454	+	0.270987i
$516$	−15.3485	+	1.41421i	−0.675679	+	0.0622573i
$517$	21.0227	−	36.4124i	0.924577	−	1.60142i
$518$	−3.00000	+	1.73205i	−0.131812	+	0.0761019i
$519$	1.10102	+	1.55708i	0.0483294	+	0.0683481i
$520$	−4.89898			−0.214834
$521$	−25.8990			−1.13465			−0.567327	−	0.823492i	$-0.692023\pi$
$521$	−25.8990			−1.13465			−0.567327	+	0.823492i	$0.692023\pi$
$522$	7.22474	−	1.34278i	0.316218	−	0.0587719i
$523$	−5.69694	−	3.28913i	−0.249110	−	0.143824i	0.370247	−	0.928933i	$-0.379273\pi$
$523$	−5.69694	−	3.28913i	−0.249110	−	0.143824i	−0.619357	+	0.785110i	$0.712606\pi$
$524$			2.22486i			0.0971935i
$525$	0.977296	−	2.12132i	0.0426527	−	0.0925820i
$526$	7.77526	+	4.48905i	0.339017	+	0.195732i
$527$	−1.34847	−	2.33562i	−0.0587402	−	0.101741i
$528$	−4.44949	+	3.14626i	−0.193639	+	0.136924i
$529$	13.5000	+	23.3827i	0.586957	+	1.01664i
$530$	13.3485	−	7.70674i	0.579820	−	0.334759i
$531$	22.3207	+	26.1076i	0.968634	+	1.13297i
$532$	1.87628	−	0.564242i	0.0813469	−	0.0244630i
$533$			10.3923i			0.450141i
$534$	12.2474	−	1.12848i	0.529999	−	0.0488343i
$535$	6.00000	−	3.46410i	0.259403	−	0.149766i
$536$	−2.17423	−	1.25529i	−0.0939126	−	0.0542205i
$537$	−13.1969	+	1.21597i	−0.569490	+	0.0524730i
$538$	−12.2474	+	21.2132i	−0.528025	+	0.914566i
$539$			21.3882i			0.921254i
$540$	−2.00000	−	7.07107i	−0.0860663	−	0.304290i
$541$	−5.34847	+	9.26382i	−0.229949	+	0.398283i	−0.957793	−	0.287460i	$-0.907189\pi$
$541$	−5.34847	+	9.26382i	−0.229949	+	0.398283i	0.727844	+	0.685743i	$0.240522\pi$
$542$	−10.0227	+	17.3598i	−0.430512	+	0.745669i
$543$	33.9217	+	15.6278i	1.45572	+	0.670652i
$544$			0.635674i			0.0272543i
$545$		0			0
$546$	0.247449	+	2.68556i	0.0105898	+	0.114931i
$547$	−32.3939	−	18.7026i	−1.38506	−	0.799666i	−0.392309	−	0.919834i	$-0.628323\pi$
$547$	−32.3939	−	18.7026i	−1.38506	−	0.799666i	−0.992754	+	0.120168i	$0.961657\pi$
$548$	−3.39898	+	1.96240i	−0.145197	+	0.0838296i
$549$	1.55051	−	4.38551i	0.0661742	−	0.187169i
$550$			9.43879i			0.402471i
$551$	10.2247	−	3.07483i	0.435589	−	0.130992i
$552$	11.1237	+	5.12472i	0.473457	+	0.218123i
$553$	3.30306	−	1.90702i	0.140460	−	0.0810949i
$554$	10.1237	+	17.5348i	0.430116	+	0.744982i
$555$	10.8990	+	15.4135i	0.462636	+	0.654266i
$556$	7.17423	+	12.4261i	0.304255	+	0.526986i
$557$	0.247449	+	0.142865i	0.0104847	+	0.00605337i	0.505233	−	0.862983i	$-0.331406\pi$
$557$	0.247449	+	0.142865i	0.0104847	+	0.00605337i	−0.494748	+	0.869036i	$0.664740\pi$
$558$	−9.67423	+	8.27098i	−0.409543	+	0.350139i
$559$		−	30.8270i		−	1.30384i
$560$	−0.550510	−	0.317837i	−0.0232633	−	0.0134311i
$561$	2.00000	+	2.82843i	0.0844401	+	0.119416i
$562$	22.5959			0.953151
$563$	40.8434			1.72134			0.860671	−	0.509161i	$-0.170044\pi$
$563$	40.8434			1.72134			0.860671	+	0.509161i	$0.170044\pi$
$564$	−18.8990	+	13.3636i	−0.795791	+	0.562709i
$565$	23.0227	−	13.2922i	0.968572	−	0.559206i
$566$	−4.72474	+	8.18350i	−0.198596	+	0.343978i
$567$	−3.77526	+	1.45354i	−0.158546	+	0.0610428i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−34.2929			−1.43763			−0.718816	−	0.695201i	$-0.755315\pi$
$569$	−34.2929			−1.43763			−0.718816	+	0.695201i	$0.755315\pi$
$570$	−4.00000	−	9.89949i	−0.167542	−	0.414644i
$571$	33.0454			1.38291			0.691454	−	0.722421i	$-0.256971\pi$
$571$	33.0454			1.38291			0.691454	+	0.722421i	$0.256971\pi$
$572$	−5.44949	−	9.43879i	−0.227855	−	0.394656i
$573$	1.30306	+	14.1421i	0.0544362	+	0.590796i
$574$	−0.674235	+	1.16781i	−0.0281420	+	0.0487434i
$575$	18.3712	−	10.6066i	0.766131	−	0.442326i
$576$	2.94949	−	0.548188i	0.122895	−	0.0228412i
$577$	18.5959			0.774158			0.387079	−	0.922047i	$-0.373484\pi$
$577$	18.5959			0.774158			0.387079	+	0.922047i	$0.373484\pi$
$578$	−16.5959			−0.690299
$579$	−36.4949	+	25.8058i	−1.51668	+	1.07245i
$580$	−3.00000	−	1.73205i	−0.124568	−	0.0719195i
$581$			7.64253i			0.317065i
$582$	5.17423	+	2.38378i	0.214479	+	0.0988108i
$583$	29.6969	+	17.1455i	1.22992	+	0.710096i
$584$	4.39898	+	7.61926i	0.182031	+	0.315287i
$585$	14.4495	−	2.68556i	0.597413	−	0.111034i
$586$	−9.67423	−	16.7563i	−0.399639	−	0.692195i
$587$	−13.8990	+	8.02458i	−0.573672	+	0.331210i	−0.758615	−	0.651540i	$-0.774123\pi$
$587$	−13.8990	+	8.02458i	−0.573672	+	0.331210i	0.184942	+	0.982749i	$0.440790\pi$
$588$	4.92679	−	10.6941i	0.203177	−	0.441017i
$589$	−12.6742	+	13.4671i	−0.522233	+	0.554904i
$590$		−	16.1920i		−	0.666615i
$591$	−3.22474	−	34.9982i	−0.132648	−	1.43963i
$592$	−6.67423	+	3.85337i	−0.274309	+	0.158373i
$593$	15.0959	+	8.71563i	0.619915	+	0.357908i	0.776836	−	0.629703i	$-0.216823\pi$
$593$	15.0959	+	8.71563i	0.619915	+	0.357908i	−0.156921	+	0.987611i	$0.550157\pi$
$594$	11.3990	−	11.7190i	0.467706	−	0.480838i
$595$	−0.202041	+	0.349945i	−0.00828287	+	0.0143464i
$596$			2.04989i			0.0839667i
$597$	2.10102	−	4.56048i	0.0859890	−	0.186648i
$598$	−12.2474	+	21.2132i	−0.500835	+	0.867472i
$599$	−2.57321	+	4.45694i	−0.105139	+	0.182106i	−0.913795	−	0.406176i	$-0.866862\pi$
$599$	−2.57321	+	4.45694i	−0.105139	+	0.182106i	0.808656	+	0.588282i	$0.200195\pi$
$600$	2.17423	−	4.71940i	0.0887628	−	0.192669i
$601$		−	14.0314i		−	0.572352i	−0.958177	−	0.286176i	$-0.907616\pi$
$601$		−	14.0314i		−	0.572352i	0.958177	−	0.286176i	$-0.0923842\pi$
$602$	2.00000	−	3.46410i	0.0815139	−	0.141186i
$603$	7.10102	+	2.51059i	0.289176	+	0.102239i
$604$	8.32577	+	4.80688i	0.338771	+	0.195589i
$605$	−1.34847	+	0.778539i	−0.0548231	+	0.0316521i
$606$	1.57321	+	17.0741i	0.0639075	+	0.693588i
$607$			11.5208i			0.467614i	0.972283	+	0.233807i	$0.0751185\pi$
$607$			11.5208i			0.467614i	−0.972283	+	0.233807i	$0.924882\pi$
$608$	4.17423	−	1.25529i	0.169288	−	0.0509089i
$609$	−0.797959	+	1.73205i	−0.0323349	+	0.0701862i
$610$	−1.89898	+	1.09638i	−0.0768874	+	0.0443910i
$611$	−23.1464	−	40.0908i	−0.936404	−	1.62190i
$612$	−0.348469	−	1.87492i	−0.0140860	−	0.0757890i
$613$	−23.8990	−	41.3942i	−0.965271	−	1.67190i	−0.708886	−	0.705323i	$-0.750802\pi$
$613$	−23.8990	−	41.3942i	−0.965271	−	1.67190i	−0.256385	−	0.966575i	$-0.582531\pi$
$614$	18.5227	+	10.6941i	0.747515	+	0.431578i
$615$	6.67423	+	3.07483i	0.269131	+	0.123989i
$616$		−	1.41421i		−	0.0569803i
$617$	8.05051	+	4.64796i	0.324101	+	0.187120i	0.653219	−	0.757169i	$-0.273418\pi$
$617$	8.05051	+	4.64796i	0.324101	+	0.187120i	−0.329118	+	0.944289i	$0.606751\pi$
$618$	7.10102	−	5.02118i	0.285645	−	0.201981i
$619$	−30.6969			−1.23381			−0.616907	−	0.787036i	$-0.711615\pi$
$619$	−30.6969			−1.23381			−0.616907	+	0.787036i	$0.711615\pi$
$620$	6.00000			0.240966
$621$	−35.6186	−	9.01742i	−1.42933	−	0.361856i
$622$	−13.4722	+	7.77817i	−0.540186	+	0.311876i
$623$	−1.59592	+	2.76421i	−0.0639391	+	0.110746i
$624$	0.550510	+	5.97469i	0.0220380	+	0.239179i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	19.0000			0.759393
$627$	14.6237	−	18.7187i	0.584015	−	0.747552i
$628$	10.6969			0.426854
$629$	2.44949	+	4.24264i	0.0976676	+	0.169165i
$630$	1.79796	+	0.635674i	0.0716324	+	0.0253259i
$631$	17.1237	−	29.6592i	0.681685	−	1.18071i	−0.292782	−	0.956179i	$-0.594581\pi$
$631$	17.1237	−	29.6592i	0.681685	−	1.18071i	0.974466	−	0.224533i	$-0.0720857\pi$
$632$	7.34847	−	4.24264i	0.292306	−	0.168763i
$633$	−2.20204	+	1.55708i	−0.0875233	+	0.0618883i
$634$	−6.00000			−0.238290
$635$	14.6969			0.583230
$636$	−10.8990	−	15.4135i	−0.432173	−	0.611184i
$637$	20.3939	+	11.7744i	0.808035	+	0.466519i
$638$		−	7.70674i		−	0.305113i
$639$	11.6969	+	13.6814i	0.462724	+	0.541229i
$640$	−1.22474	−	0.707107i	−0.0484123	−	0.0279508i
$641$	−13.1969	−	22.8578i	−0.521248	−	0.902828i	−0.999695	−	0.0247111i	$-0.992133\pi$
$641$	−13.1969	−	22.8578i	−0.521248	−	0.902828i	0.478447	−	0.878116i	$-0.341200\pi$
$642$	−4.89898	−	6.92820i	−0.193347	−	0.273434i
$643$	−5.07321	−	8.78706i	−0.200068	−	0.346528i	0.748482	−	0.663155i	$-0.230783\pi$
$643$	−5.07321	−	8.78706i	−0.200068	−	0.346528i	−0.948550	+	0.316627i	$0.897450\pi$
$644$	−2.75255	+	1.58919i	−0.108466	+	0.0626227i
$645$	−19.7980	−	9.12096i	−0.779544	−	0.359137i
$646$	−0.797959	−	2.65345i	−0.0313953	−	0.104399i
$647$			14.7778i			0.580976i	0.956879	+	0.290488i	$0.0938176\pi$
$647$			14.7778i			0.580976i	−0.956879	+	0.290488i	$0.906182\pi$
$648$	−8.39898	+	3.23375i	−0.329943	+	0.127034i
$649$	31.1969	−	18.0116i	1.22459	−	0.707016i
$650$	9.00000	+	5.19615i	0.353009	+	0.203810i
$651$	−0.303062	−	3.28913i	−0.0118779	−	0.128911i
$652$	−9.17423	+	15.8902i	−0.359291	+	0.622310i
$653$			8.19955i			0.320873i	0.987046	+	0.160437i	$0.0512902\pi$
$653$			8.19955i			0.320873i	−0.987046	+	0.160437i	$0.948710\pi$
$654$		0			0
$655$	−1.57321	+	2.72489i	−0.0614706	+	0.106470i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	−17.1515	−	20.0614i	−0.669145	−	0.782672i
$658$		−	6.00680i		−	0.234169i
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$	−7.67423	+	0.707107i	−0.298719	+	0.0275241i
$661$	25.7196	+	14.8492i	1.00038	+	0.577569i	0.908360	−	0.418189i	$-0.137335\pi$
$661$	25.7196	+	14.8492i	1.00038	+	0.577569i	0.0920180	+	0.995757i	$0.470668\pi$
$662$	−20.1742	+	11.6476i	−0.784094	+	0.452697i
$663$	3.79796	−	0.349945i	0.147501	−	0.0135908i
$664$			17.0027i			0.659832i
$665$	2.69694	+	0.635674i	0.104583	+	0.0246504i
$666$	17.5732	−	15.0242i	0.680948	−	0.582177i
$667$	−15.0000	+	8.66025i	−0.580802	+	0.335326i
$668$	−2.44949	−	4.24264i	−0.0947736	−	0.164153i
$669$	−25.5959	+	18.0990i	−0.989595	+	0.699750i
$670$	−1.77526	−	3.07483i	−0.0685841	−	0.118791i
$671$	−4.22474	−	2.43916i	−0.163094	−	0.0941626i
$672$	−0.325765	+	0.707107i	−0.0125667	+	0.0272772i
$673$			3.46410i			0.133531i	0.997769	+	0.0667657i	$0.0212680\pi$
$673$			3.46410i			0.133531i	−0.997769	+	0.0667657i	$0.978732\pi$
$674$	−17.8485	−	10.3048i	−0.687497	−	0.396927i
$675$	−3.82577	+	15.1117i	−0.147254	+	0.581650i
$676$	1.00000			0.0384615
$677$	−32.6969			−1.25665			−0.628323	−	0.777953i	$-0.716258\pi$
$677$	−32.6969			−1.25665			−0.628323	+	0.777953i	$0.716258\pi$
$678$	−18.7980	−	26.5843i	−0.721931	−	1.02096i
$679$	−1.28036	+	0.739215i	−0.0491356	+	0.0283685i
$680$	−0.449490	+	0.778539i	−0.0172371	+	0.0298556i
$681$	0.949490	−	0.0874863i	0.0363845	−	0.00335248i
$682$	6.67423	+	11.5601i	0.255570	+	0.442660i
$683$	17.3939			0.665558			0.332779	−	0.943005i	$-0.392014\pi$
$683$	17.3939			0.665558			0.332779	+	0.943005i	$0.392014\pi$
$684$	−11.6237	+	5.99075i	−0.444444	+	0.229062i
$685$	−5.55051			−0.212074
$686$	3.10102	+	5.37113i	0.118398	+	0.205071i
$687$	1.55051	−	0.142865i	0.0591557	−	0.00545062i
$688$	4.44949	−	7.70674i	0.169635	−	0.293817i
$689$	32.6969	−	18.8776i	1.24565	−	0.719179i
$690$	10.0000	+	14.1421i	0.380693	+	0.538382i
$691$	−40.0000			−1.52167			−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000			−1.52167			−0.760836	+	0.648944i	$0.775211\pi$
$692$	−1.10102			−0.0418545
$693$	0.775255	+	4.17121i	0.0294495	+	0.158451i
$694$	3.27526	+	1.89097i	0.124327	+	0.0717802i
$695$			20.2918i			0.769712i
$696$	−1.77526	+	3.85337i	−0.0672909	+	0.146062i
$697$	1.65153	+	0.953512i	0.0625562	+	0.0361168i
$698$	16.2474	+	28.1414i	0.614975	+	1.06517i
$699$	−25.1464	+	17.7812i	−0.951125	+	0.672547i
$700$	0.674235	+	1.16781i	0.0254837	+	0.0441390i
$701$	−8.57321	+	4.94975i	−0.323806	+	0.186949i	−0.653088	−	0.757282i	$-0.726527\pi$
$701$	−8.57321	+	4.94975i	−0.323806	+	0.186949i	0.329282	+	0.944232i	$0.393193\pi$
$702$	−4.89898	−	17.3205i	−0.184900	−	0.653720i
$703$	23.0227	−	24.4630i	0.868318	−	0.922640i
$704$		−	3.14626i		−	0.118579i
$705$	−32.5959	+	3.00340i	−1.22763	+	0.113115i
$706$	−21.6464	+	12.4976i	−0.814674	+	0.470352i
$707$	−3.85357	−	2.22486i	−0.144928	−	0.0836745i
$708$	−19.7474	+	1.81954i	−0.742155	+	0.0683824i
$709$	8.67423	−	15.0242i	0.325768	−	0.564246i	−0.655900	−	0.754848i	$-0.727711\pi$
$709$	8.67423	−	15.0242i	0.325768	−	0.564246i	0.981667	+	0.190602i	$0.0610439\pi$
$710$		−	8.48528i		−	0.318447i
$711$	−19.3485	+	16.5420i	−0.725624	+	0.620372i
$712$	−3.55051	+	6.14966i	−0.133061	+	0.230468i
$713$	15.0000	−	25.9808i	0.561754	−	0.972987i
$714$	0.449490	+	0.207081i	0.0168217	+	0.00774980i
$715$		−	15.4135i		−	0.576432i
$716$	3.82577	−	6.62642i	0.142976	−	0.247641i
$717$	−3.34847	−	36.3410i	−0.125051	−	1.35718i
$718$	20.8207	+	12.0208i	0.777020	+	0.448613i
$719$	26.1464	−	15.0956i	0.975097	−	0.562973i	0.0743109	−	0.997235i	$-0.476324\pi$
$719$	26.1464	−	15.0956i	0.975097	−	0.562973i	0.900786	+	0.434262i	$0.142991\pi$
$720$	4.00000	+	1.41421i	0.149071	+	0.0527046i
$721$			2.25697i			0.0840539i
$722$	−15.8485	+	10.4798i	−0.589819	+	0.390017i
$723$	−10.6237	−	4.89437i	−0.395101	−	0.182024i
$724$	−18.6742	+	10.7816i	−0.694022	+	0.400694i
$725$	3.67423	+	6.36396i	0.136458	+	0.236352i
$726$	1.10102	+	1.55708i	0.0408627	+	0.0577886i
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	0.782267	−	0.622944i	$-0.214063\pi$
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	−0.930618	+	0.365991i	$0.880730\pi$
$728$	−1.34847	−	0.778539i	−0.0499776	−	0.0288546i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$			12.4422i			0.460506i
$731$	−4.89898	−	2.82843i	−0.181195	−	0.104613i
$732$	1.55051	+	2.19275i	0.0573085	+	0.0810465i
$733$	−20.0454			−0.740394			−0.370197	−	0.928953i	$-0.620710\pi$
$733$	−20.0454			−0.740394			−0.370197	+	0.928953i	$0.620710\pi$
$734$	8.65153			0.319334
$735$	13.5959	−	9.61377i	0.501493	−	0.354609i
$736$	−6.12372	+	3.53553i	−0.225723	+	0.130322i
$737$	3.94949	−	6.84072i	0.145481	−	0.251981i
$738$	3.00000	−	8.48528i	0.110432	−	0.312348i
$739$	−12.1742	−	21.0864i	−0.447836	−	0.775676i	0.550408	−	0.834895i	$-0.314472\pi$
$739$	−12.1742	−	21.0864i	−0.447836	−	0.775676i	−0.998245	+	0.0592200i	$0.981139\pi$
$740$	−10.8990			−0.400654
$741$	−9.79796	−	24.2487i	−0.359937	−	0.890799i
$742$	4.89898			0.179847
$743$	−2.32577	−	4.02834i	−0.0853241	−	0.147786i	0.820205	−	0.572069i	$-0.193859\pi$
$743$	−2.32577	−	4.02834i	−0.0853241	−	0.147786i	−0.905529	+	0.424284i	$0.860526\pi$
$744$	−0.674235	−	7.31747i	−0.0247186	−	0.268272i
$745$	−1.44949	+	2.51059i	−0.0531052	+	0.0919809i
$746$	22.0454	−	12.7279i	0.807140	−	0.466002i
$747$	−9.32066	−	50.1492i	−0.341025	−	1.83486i
$748$	−2.00000			−0.0731272
$749$	2.20204			0.0804608
$750$	16.0000	−	11.3137i	0.584237	−	0.413118i
$751$	17.6969	+	10.2173i	0.645770	+	0.372836i	0.786834	−	0.617165i	$-0.211719\pi$
$751$	17.6969	+	10.2173i	0.645770	+	0.372836i	−0.141063	+	0.990001i	$0.545052\pi$
$752$		−	13.3636i		−	0.487320i
$753$	−5.94949	−	2.74094i	−0.216811	−	0.0998854i
$754$	−7.34847	−	4.24264i	−0.267615	−	0.154508i
$755$	6.79796	+	11.7744i	0.247403	+	0.428515i
$756$	0.573214	−	2.26418i	0.0208476	−	0.0823476i
$757$	19.6969	+	34.1161i	0.715897	+	1.23997i	0.962612	+	0.270883i	$0.0873155\pi$
$757$	19.6969	+	34.1161i	0.715897	+	1.23997i	−0.246715	+	0.969088i	$0.579351\pi$
$758$	−1.34847	+	0.778539i	−0.0489786	+	0.0282778i
$759$	−16.1237	+	34.9982i	−0.585254	+	1.27035i
$760$	6.00000	+	1.41421i	0.217643	+	0.0512989i
$761$			31.5734i			1.14453i	0.820067	+	0.572267i	$0.193936\pi$
$761$			31.5734i			1.14453i	−0.820067	+	0.572267i	$0.806064\pi$
$762$	−1.65153	−	17.9241i	−0.0598286	−	0.649321i
$763$		0			0
$764$	−7.10102	−	4.09978i	−0.256906	−	0.148325i
$765$	0.898979	−	2.54270i	0.0325027	−	0.0919314i
$766$	−10.2247	+	17.7098i	−0.369435	+	0.639880i
$767$		−	39.6622i		−	1.43212i
$768$	−0.724745	+	1.57313i	−0.0261520	+	0.0567655i
$769$	−1.79796	+	3.11416i	−0.0648361	+	0.112299i	−0.896621	−	0.442798i	$-0.853986\pi$
$769$	−1.79796	+	3.11416i	−0.0648361	+	0.112299i	0.831785	+	0.555098i	$0.187319\pi$
$770$	1.00000	−	1.73205i	0.0360375	−	0.0624188i
$771$	−10.8712	+	23.5970i	−0.391516	+	0.849825i
$772$		−	25.8058i		−	0.928771i
$773$	−1.22474	+	2.12132i	−0.0440510	+	0.0762986i	−0.887210	−	0.461365i	$-0.847360\pi$
$773$	−1.22474	+	2.12132i	−0.0440510	+	0.0762986i	0.843159	+	0.537664i	$0.180693\pi$
$774$	−8.89898	+	25.1701i	−0.319867	+	0.904721i
$775$	−11.0227	−	6.36396i	−0.395947	−	0.228600i
$776$	−2.84847	+	1.64456i	−0.102254	+	0.0590364i
$777$	0.550510	+	5.97469i	0.0197494	+	0.214341i
$778$		−	15.1278i		−	0.542356i
$779$	3.00000	−	12.7279i	0.107486	−	0.456025i
$780$	−3.55051	+	7.70674i	−0.127129	+	0.275946i
$781$	16.3485	−	9.43879i	0.584994	−	0.337747i
$782$	2.24745	+	3.89270i	0.0803686	+	0.139203i
$783$	3.12372	−	12.3387i	0.111633	−	0.440947i
$784$	3.39898	+	5.88721i	0.121392	+	0.210257i
$785$	13.1010	+	7.56388i	0.467595	+	0.269966i
$786$	3.50000	+	1.61246i	0.124841	+	0.0575144i
$787$			7.53177i			0.268479i	0.990949	+	0.134239i	$0.0428591\pi$
$787$			7.53177i			0.268479i	−0.990949	+	0.134239i	$0.957141\pi$
$788$	17.5732	+	10.1459i	0.626020	+	0.361433i
$789$	12.6969	−	8.97809i	0.452023	−	0.319629i
$790$	12.0000			0.426941
$791$	8.44949			0.300429
$792$	1.72474	+	9.27987i	0.0612861	+	0.329746i
$793$	−4.65153	+	2.68556i	−0.165181	+	0.0953671i
$794$	−2.67423	+	4.63191i	−0.0949050	+	0.164380i
$795$	−2.44949	−	26.5843i	−0.0868744	−	0.942849i
$796$	1.44949	+	2.51059i	0.0513758	+	0.0889855i
$797$	37.3485			1.32295			0.661475	−	0.749967i	$-0.269931\pi$
$797$	37.3485			1.32295			0.661475	+	0.749967i	$0.269931\pi$
$798$	0.472194	−	3.36056i	0.0167155	−	0.118963i
$799$	−8.49490			−0.300528
$800$	1.50000	+	2.59808i	0.0530330	+	0.0918559i
$801$	7.10102	−	20.0847i	0.250902	−	0.709659i
$802$	3.39898	−	5.88721i	0.120022	−	0.207884i
$803$	−23.9722	+	13.8404i	−0.845960	+	0.488415i
$804$	−3.55051	+	2.51059i	−0.125217	+	0.0885417i
$805$	−4.49490			−0.158424
$806$	14.6969			0.517678
$807$	24.4949	+	34.6410i	0.862261	+	1.21942i
$808$	−8.57321	−	4.94975i	−0.301605	−	0.174132i
$809$			8.02458i			0.282129i	0.990000	+	0.141065i	$0.0450525\pi$
$809$			8.02458i			0.282129i	−0.990000	+	0.141065i	$0.954947\pi$
$810$	−12.5732	−	1.97846i	−0.441778	−	0.0695158i
$811$	3.00000	+	1.73205i	0.105344	+	0.0608205i	0.551746	−	0.834012i	$-0.313962\pi$
$811$	3.00000	+	1.73205i	0.105344	+	0.0608205i	−0.446402	+	0.894832i	$0.647295\pi$
$812$	−0.550510	−	0.953512i	−0.0193191	−	0.0334617i
$813$	20.0454	+	28.3485i	0.703023	+	0.994225i
$814$	−12.1237	−	20.9989i	−0.424936	−	0.736011i
$815$	−22.4722	+	12.9743i	−0.787167	+	0.454471i
$816$	1.00000	+	0.460702i	0.0350070	+	0.0161278i
$817$	−8.89898	+	37.7552i	−0.311336	+	1.32089i
$818$			3.63907i			0.127237i
$819$	4.40408	+	1.55708i	0.153891	+	0.0544087i
$820$	−3.67423	+	2.12132i	−0.128310	+	0.0740797i
$821$	−5.44949	−	3.14626i	−0.190189	−	0.109805i	0.401882	−	0.915691i	$-0.368356\pi$
$821$	−5.44949	−	3.14626i	−0.190189	−	0.109805i	−0.592071	+	0.805886i	$0.701689\pi$
$822$	0.623724	+	6.76928i	0.0217549	+	0.236106i
$823$	24.3485	−	42.1728i	0.848734	−	1.47005i	−0.0336040	−	0.999435i	$-0.510699\pi$
$823$	24.3485	−	42.1728i	0.848734	−	1.47005i	0.882338	−	0.470616i	$-0.155968\pi$
$824$			5.02118i			0.174921i
$825$	14.8485	+	6.84072i	0.516957	+	0.238163i
$826$	2.57321	−	4.45694i	0.0895336	−	0.155077i
$827$	−10.6237	+	18.4008i	−0.369423	+	0.639860i	−0.989475	−	0.144701i	$-0.953778\pi$
$827$	−10.6237	+	18.4008i	−0.369423	+	0.639860i	0.620052	+	0.784560i	$0.287111\pi$
$828$	16.1237	−	13.7850i	0.560338	−	0.479061i
$829$			19.2275i			0.667800i	0.942609	+	0.333900i	$0.108365\pi$
$829$			19.2275i			0.667800i	−0.942609	+	0.333900i	$0.891635\pi$
$830$	−12.0227	+	20.8239i	−0.417314	+	0.722809i
$831$	34.9217	−	3.21770i	1.21142	−	0.111621i
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$	3.74235	−	2.16064i	0.129665	−	0.0748619i
$834$	24.7474	−	2.28024i	0.856934	−	0.0789582i
$835$		−	6.92820i		−	0.239760i
$836$	3.94949	+	13.1332i	0.136596	+	0.454223i
$837$	6.00000	+	21.2132i	0.207390	+	0.733236i
$838$	21.2474	−	12.2672i	0.733981	−	0.423764i
$839$	6.67423	+	11.5601i	0.230420	+	0.399099i	0.957932	−	0.286996i	$-0.0926566\pi$
$839$	6.67423	+	11.5601i	0.230420	+	0.399099i	−0.727512	+	0.686095i	$0.759323\pi$
$840$	−0.898979	+	0.635674i	−0.0310177	+	0.0219329i
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−3.97730	−	2.29629i	−0.137067	−	0.0791355i
$843$	16.3763	−	35.5464i	0.564029	−	1.22428i
$844$		−	1.55708i		−	0.0535968i
$845$	1.22474	+	0.707107i	0.0421325	+	0.0243252i
$846$	7.32577	+	39.4158i	0.251865	+	1.35514i
$847$	−0.494897			−0.0170049
$848$	10.8990			0.374272
$849$	9.44949	+	13.3636i	0.324306	+	0.458637i
$850$	1.65153	−	0.953512i	0.0566470	−	0.0327052i
$851$	−27.2474	+	47.1940i	−0.934031	+	1.61779i
$852$	−10.3485	+	0.953512i	−0.354533	+	0.0326668i
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	−0.696938			−0.0238487
$855$	−18.4722	−	0.882079i	−0.631736	−	0.0301665i
$856$	4.89898			0.167444
$857$	8.29796	+	14.3725i	0.283453	+	0.490955i	0.972233	−	0.234016i	$-0.0751867\pi$
$857$	8.29796	+	14.3725i	0.283453	+	0.490955i	−0.688780	+	0.724970i	$0.741853\pi$
$858$	−18.7980	+	1.73205i	−0.641752	+	0.0591312i
$859$	−9.42168	+	16.3188i	−0.321464	+	0.556791i	−0.980790	−	0.195065i	$-0.937508\pi$
$859$	−9.42168	+	16.3188i	−0.321464	+	0.556791i	0.659327	+	0.751857i	$0.270841\pi$
$860$	10.8990	−	6.29253i	0.371652	−	0.214573i
$861$	1.34847	+	1.90702i	0.0459557	+	0.0649912i
$862$	3.30306			0.112503
$863$	16.6515			0.566825			0.283412	−	0.958998i	$-0.408533\pi$
$863$	16.6515			0.566825			0.283412	+	0.958998i	$0.408533\pi$
$864$	1.27526	−	5.03723i	0.0433851	−	0.171370i
$865$	−1.34847	−	0.778539i	−0.0458493	−	0.0264711i
$866$		−	20.4347i		−	0.694398i
$867$	−12.0278	+	26.1076i	−0.408486	+	0.886660i
$868$	1.65153	+	0.953512i	0.0560566	+	0.0323643i
$869$	13.3485	+	23.1202i	0.452816	+	0.784300i
$870$	−4.89898	+	3.46410i	−0.166091	+	0.117444i
$871$	−4.34847	−	7.53177i	−0.147342	−	0.255204i
$872$		0			0
$873$	7.50000	−	6.41212i	0.253837	−	0.217017i
$874$	21.1237	−	22.4452i	0.714521	−	0.759221i
$875$			5.08540i			0.171918i
$876$	15.1742	−	1.39816i	0.512690	−	0.0472394i
$877$	−36.3712	+	20.9989i	−1.22817	+	0.709083i	−0.966646	−	0.256115i	$-0.917557\pi$
$877$	−36.3712	+	20.9989i	−1.22817	+	0.709083i	−0.261521	+	0.965198i	$0.584224\pi$
$878$	−9.67423	−	5.58542i	−0.326490	−	0.188499i
$879$	−33.3712	+	3.07483i	−1.12558	+	0.103712i
$880$	2.22474	−	3.85337i	0.0749961	−	0.129897i
$881$			10.2815i			0.346394i	0.984887	+	0.173197i	$0.0554098\pi$
$881$			10.2815i			0.346394i	−0.984887	+	0.173197i	$0.944590\pi$
$882$	−13.2526	−	15.5010i	−0.446237	−	0.521945i
$883$	10.4217	−	18.0509i	0.350718	−	0.607461i	−0.635658	−	0.771971i	$-0.719271\pi$
$883$	10.4217	−	18.0509i	0.350718	−	0.607461i	0.986375	+	0.164510i	$0.0526044\pi$
$884$	−1.10102	+	1.90702i	−0.0370313	+	0.0641401i
$885$	−25.4722	−	11.7351i	−0.856238	−	0.394471i
$886$		−	18.8455i		−	0.633126i
$887$	28.0454	−	48.5761i	0.941673	−	1.63102i	0.179393	−	0.983778i	$-0.442587\pi$
$887$	28.0454	−	48.5761i	0.941673	−	1.63102i	0.762280	−	0.647247i	$-0.224080\pi$
$888$	1.22474	+	13.2922i	0.0410997	+	0.446056i
$889$	4.04541	+	2.33562i	0.135679	+	0.0783341i
$890$	−8.69694	+	5.02118i	−0.291522	+	0.168310i
$891$	−10.1742	−	26.4254i	−0.340850	−	0.885285i
$892$		−	18.0990i		−	0.606001i
$893$	16.7753	+	55.7828i	0.561363	+	1.86670i
$894$	3.22474	+	1.48565i	0.107852	+	0.0496874i
$895$	9.37117	−	5.41045i	0.313244	−	0.180851i
$896$	−0.224745	−	0.389270i	−0.00750820	−	0.0130046i
$897$	24.4949	+	34.6410i	0.817861	+	1.15663i
$898$	15.3990	+	26.6718i	0.513871	+	0.890050i
$899$	9.00000	+	5.19615i	0.300167	+	0.173301i
$900$	−5.84847	−	6.84072i	−0.194949	−	0.228024i
$901$		−	6.92820i		−	0.230812i
$902$	−8.17423	−	4.71940i	−0.272172	−	0.157139i
$903$	−4.00000	−	5.65685i	−0.133112	−	0.188248i
$904$	18.7980			0.625211
$905$	−30.4949			−1.01368
$906$	13.5959	−	9.61377i	0.451694	−	0.319396i
$907$	−32.9166	+	19.0044i	−1.09298	+	0.631031i	−0.934368	−	0.356311i	$-0.884034\pi$
$907$	−32.9166	+	19.0044i	−1.09298	+	0.631031i	−0.158610	+	0.987341i	$0.550701\pi$
$908$	−0.275255	+	0.476756i	−0.00913466	+	0.0158217i
$909$	28.0000	+	9.89949i	0.928701	+	0.328346i
$910$	−1.10102	−	1.90702i	−0.0364985	−	0.0632172i
$911$	−28.6515			−0.949268			−0.474634	−	0.880183i	$-0.657419\pi$
$911$	−28.6515			−0.949268			−0.474634	+	0.880183i	$0.657419\pi$
$912$	1.05051	−	7.47639i	0.0347859	−	0.247568i
$913$	−53.4949			−1.77042
$914$	−6.50000	−	11.2583i	−0.215001	−	0.372392i
$915$	0.348469	+	3.78194i	0.0115200	+	0.125027i
$916$	−0.449490	+	0.778539i	−0.0148516	+	0.0257237i
$917$	−0.866070	+	0.500026i	−0.0286002	+	0.0165123i
$918$	−3.20204	−	0.810647i	−0.105683	−	0.0267553i
$919$	−36.6969			−1.21052			−0.605260	−	0.796028i	$-0.706931\pi$
$919$	−36.6969			−1.21052			−0.605260	+	0.796028i	$0.706931\pi$
$920$	−10.0000			−0.329690
$921$	30.2474	−	21.3882i	0.996687	−	0.704764i
$922$	−33.2474	−	19.1954i	−1.09495	−	0.632168i
$923$		−	20.7846i		−	0.684134i
$924$	−2.22474	−	1.02494i	−0.0731887	−	0.0337182i
$925$	20.0227	+	11.5601i	0.658342	+	0.380094i
$926$	−9.89898	−	17.1455i	−0.325301	−	0.563437i
$927$	−2.75255	−	14.8099i	−0.0904056	−	0.486422i
$928$	−1.22474	−	2.12132i	−0.0402042	−	0.0696358i
$929$	−24.0959	+	13.9118i	−0.790561	+	0.456431i	−0.840160	−	0.542338i	$-0.817539\pi$
$929$	−24.0959	+	13.9118i	−0.790561	+	0.456431i	0.0495987	+	0.998769i	$0.484206\pi$
$930$	4.34847	−	9.43879i	0.142592	−	0.309510i
$931$	−21.5783	−	20.3079i	−0.707201	−	0.665563i
$932$		−	17.7812i		−	0.582443i
$933$	2.47219	+	26.8307i	0.0809360	+	0.878399i
$934$	−10.9268	+	6.30858i	−0.357535	+	0.206423i
$935$	−2.44949	−	1.41421i	−0.0801069	−	0.0462497i
$936$	9.79796	+	3.46410i	0.320256	+	0.113228i
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	−0.990430	−	0.138017i	$-0.955927\pi$
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	0.614741	+	0.788729i	$0.289260\pi$
$938$		−	1.12848i		−	0.0368463i
$939$	13.7702	−	29.8895i	0.449372	−	0.975407i
$940$	9.44949	−	16.3670i	0.308208	−	0.533833i
$941$	21.4949	−	37.2303i	0.700714	−	1.21367i	−0.267503	−	0.963557i	$-0.586198\pi$
$941$	21.4949	−	37.2303i	0.700714	−	1.21367i	0.968216	−	0.250114i	$-0.0804683\pi$
$942$	7.75255	−	16.8277i	0.252592	−	0.548276i
$943$			21.2132i			0.690797i
$944$	5.72474	−	9.91555i	0.186325	−	0.322724i
$945$	2.30306	−	2.36773i	0.0749186	−	0.0770221i
$946$	24.2474	+	13.9993i	0.788353	+	0.455156i
$947$	−6.55051	+	3.78194i	−0.212863	+	0.122896i	−0.602641	−	0.798012i	$-0.705885\pi$
$947$	−6.55051	+	3.78194i	−0.212863	+	0.122896i	0.389778	+	0.920909i	$0.372552\pi$
$948$	−1.34847	−	14.6349i	−0.0437962	−	0.475321i
$949$			30.4770i			0.989326i
$950$	−9.52270	−	8.96204i	−0.308957	−	0.290767i
$951$	−4.34847	+	9.43879i	−0.141009	+	0.306074i
$952$	−0.247449	+	0.142865i	−0.00801986	+	0.00463027i
$953$	−12.3990	−	21.4757i	−0.401642	−	0.695665i	0.592282	−	0.805731i	$-0.298227\pi$
$953$	−12.3990	−	21.4757i	−0.401642	−	0.695665i	−0.993924	+	0.110066i	$0.964894\pi$
$954$	−32.1464	+	5.97469i	−1.04078	+	0.193438i
$955$	−5.79796	−	10.0424i	−0.187618	−	0.324963i
$956$	18.2474	+	10.5352i	0.590165	+	0.340732i
$957$	−12.1237	−	5.58542i	−0.391904	−	0.180551i
$958$			0.985620i			0.0318439i
$959$	−1.52781	−	0.882079i	−0.0493354	−	0.0284838i
$960$	−2.00000	+	1.41421i	−0.0645497	+	0.0456435i
$961$	13.0000			0.419355
$962$	−26.6969			−0.860744
$963$	−14.4495	+	2.68556i	−0.465628	+	0.0865410i
$964$	5.84847	−	3.37662i	0.188367	−	0.108753i
$965$	18.2474	−	31.6055i	0.587406	−	1.01742i
$966$	0.505103	+	5.48188i	0.0162514	+	0.176377i
$967$	25.6969	+	44.5084i	0.826358	+	1.43129i	0.900877	+	0.434074i	$0.142924\pi$
$967$	25.6969	+	44.5084i	0.826358	+	1.43129i	−0.0745193	+	0.997220i	$0.523742\pi$
$968$	−1.10102			−0.0353881
$969$	−4.75255	−	0.667783i	−0.152674	−	0.0214523i
$970$	−4.65153			−0.149352
$971$	−4.07321	−	7.05501i	−0.130716	−	0.226406i	0.793237	−	0.608913i	$-0.208394\pi$
$971$	−4.07321	−	7.05501i	−0.130716	−	0.226406i	−0.923953	+	0.382507i	$0.875061\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	−3.22474	+	5.58542i	−0.103381	+	0.179060i
$974$	−21.6742	+	12.5136i	−0.694487	+	0.400962i
$975$	14.6969	−	10.3923i	0.470679	−	0.332820i
$976$	−1.55051			−0.0496306
$977$	40.1010			1.28295			0.641473	−	0.767146i	$-0.278324\pi$
$977$	40.1010			1.28295			0.641473	+	0.767146i	$0.278324\pi$
$978$	18.3485	+	25.9487i	0.586719	+	0.829746i
$979$	−19.3485	−	11.1708i	−0.618380	−	0.357022i
$980$			9.61377i			0.307100i
$981$		0			0
$982$	−13.8990	−	8.02458i	−0.443534	−	0.256075i
$983$	−28.8990	−	50.0545i	−0.921734	−	1.59649i	−0.796731	−	0.604334i	$-0.793439\pi$
$983$	−28.8990	−	50.0545i	−0.921734	−	1.59649i	−0.125003	−	0.992156i	$-0.539894\pi$
$984$	3.00000	+	4.24264i	0.0956365	+	0.135250i
$985$	14.3485	+	24.8523i	0.457180	+	0.791859i
$986$	−1.34847	+	0.778539i	−0.0429440	+	0.0247937i
$987$	−9.44949	−	4.35340i	−0.300781	−	0.138570i
$988$	14.6969	+	3.46410i	0.467572	+	0.110208i
$989$		−	62.9253i		−	2.00091i
$990$	−4.44949	+	12.5851i	−0.141414	+	0.399979i
$991$	15.3031	−	8.83523i	0.486118	−	0.280660i	−0.236845	−	0.971548i	$-0.576113\pi$
$991$	15.3031	−	8.83523i	0.486118	−	0.280660i	0.722962	+	0.690887i	$0.242780\pi$
$992$	3.67423	+	2.12132i	0.116657	+	0.0673520i
$993$	3.70204	+	40.1783i	0.117481	+	1.27502i
$994$	1.34847	−	2.33562i	0.0427708	−	0.0740813i
$995$			4.09978i			0.129972i
$996$	26.7474	+	12.3226i	0.847525	+	0.390456i
$997$	21.7196	−	37.6195i	0.687868	−	1.19142i	−0.284658	−	0.958629i	$-0.591880\pi$
$997$	21.7196	−	37.6195i	0.687868	−	1.19142i	0.972526	−	0.232793i	$-0.0747865\pi$
$998$	3.72474	−	6.45145i	0.117905	−	0.204217i
$999$	−10.8990	−	38.5337i	−0.344828	−	1.21915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.h.f.107.2	yes	4
3.2	odd	2		114.2.h.e.107.1	yes	4
4.3	odd	2		912.2.bn.h.449.1		4
12.11	even	2		912.2.bn.g.449.2		4
19.8	odd	6		114.2.h.e.65.2	✓	4
57.8	even	6	inner	114.2.h.f.65.2	yes	4
76.27	even	6		912.2.bn.g.65.1		4
228.179	odd	6		912.2.bn.h.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.e.65.2	✓	4	19.8	odd	6
114.2.h.e.107.1	yes	4	3.2	odd	2
114.2.h.f.65.2	yes	4	57.8	even	6	inner
114.2.h.f.107.2	yes	4	1.1	even	1	trivial
912.2.bn.g.65.1		4	76.27	even	6
912.2.bn.g.449.2		4	12.11	even	2
912.2.bn.h.65.1		4	228.179	odd	6
912.2.bn.h.449.1		4	4.3	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} -0.449490 q^{7} -1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} -0.449490 q^{7} -1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +(-1.22474 - 0.707107i) q^{10} -3.14626i q^{11} +(-0.724745 + 1.57313i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-2.00000 + 1.41421i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.550510 + 0.317837i) q^{17} +(1.94949 + 2.28024i) q^{18} +(3.17423 + 2.98735i) q^{19} -1.41421i q^{20} +(-0.775255 + 0.0714323i) q^{21} +(2.72474 - 1.57313i) q^{22} +(-6.12372 - 3.53553i) q^{23} +(-1.72474 + 0.158919i) q^{24} +(-1.50000 + 2.59808i) q^{25} -3.46410i q^{26} +(5.00000 - 1.41421i) q^{27} +(0.224745 - 0.389270i) q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 1.02494i) q^{30} +4.24264i q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 - 5.42650i) q^{33} +(-0.550510 - 0.317837i) q^{34} +(0.550510 - 0.317837i) q^{35} +(-1.00000 + 2.82843i) q^{36} -7.70674i q^{37} +(-1.00000 + 4.24264i) q^{38} +(-5.44949 - 2.51059i) q^{39} +(1.22474 - 0.707107i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-0.449490 - 0.635674i) q^{42} +(4.44949 + 7.70674i) q^{43} +(2.72474 + 1.57313i) q^{44} +(-3.22474 + 2.75699i) q^{45} -7.07107i q^{46} +(11.5732 + 6.68180i) q^{47} +(-1.00000 - 1.41421i) q^{48} -6.79796 q^{49} -3.00000 q^{50} +(-0.898979 + 0.635674i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-5.44949 + 9.43879i) q^{53} +(3.72474 + 3.62302i) q^{54} +(2.22474 + 3.85337i) q^{55} +0.449490 q^{56} +(5.94949 + 4.64796i) q^{57} +2.44949 q^{58} +(5.72474 + 9.91555i) q^{59} +(-0.224745 - 2.43916i) q^{60} +(0.775255 - 1.34278i) q^{61} +(-3.67423 + 2.12132i) q^{62} +(-1.32577 + 0.246405i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(4.44949 - 3.14626i) q^{66} +(2.17423 + 1.25529i) q^{67} -0.635674i q^{68} +(-11.1237 - 5.12472i) q^{69} +(0.550510 + 0.317837i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-2.94949 + 0.548188i) q^{72} +(-4.39898 - 7.61926i) q^{73} +(6.67423 - 3.85337i) q^{74} +(-2.17423 + 4.71940i) q^{75} +(-4.17423 + 1.25529i) q^{76} +1.41421i q^{77} +(-0.550510 - 5.97469i) q^{78} +(-7.34847 + 4.24264i) q^{79} +(1.22474 + 0.707107i) q^{80} +(8.39898 - 3.23375i) q^{81} +(1.50000 - 2.59808i) q^{82} -17.0027i q^{83} +(0.325765 - 0.707107i) q^{84} +(0.449490 - 0.778539i) q^{85} +(-4.44949 + 7.70674i) q^{86} +(1.77526 - 3.85337i) q^{87} +3.14626i q^{88} +(3.55051 - 6.14966i) q^{89} +(-4.00000 - 1.41421i) q^{90} +(1.34847 + 0.778539i) q^{91} +(6.12372 - 3.53553i) q^{92} +(0.674235 + 7.31747i) q^{93} +13.3636i q^{94} +(-6.00000 - 1.41421i) q^{95} +(0.724745 - 1.57313i) q^{96} +(2.84847 - 1.64456i) q^{97} +(-3.39898 - 5.88721i) q^{98} +(-1.72474 - 9.27987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{12} - 12 q^{13} + 4 q^{14} - 8 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 8 q^{21} + 6 q^{22} - 2 q^{24} - 6 q^{25} + 20 q^{27} - 4 q^{28} - 4 q^{30} + 2 q^{32} - 2 q^{33} - 12 q^{34} + 12 q^{35} - 4 q^{36} - 4 q^{38} - 12 q^{39} - 6 q^{41} + 8 q^{42} + 8 q^{43} + 6 q^{44} - 8 q^{45} + 12 q^{47} - 4 q^{48} + 12 q^{49} - 12 q^{50} + 16 q^{51} + 12 q^{52} - 12 q^{53} + 10 q^{54} + 4 q^{55} - 8 q^{56} + 14 q^{57} + 18 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{63} + 4 q^{64} + 8 q^{66} - 6 q^{67} - 20 q^{69} + 12 q^{70} + 12 q^{71} - 2 q^{72} + 2 q^{73} + 12 q^{74} + 6 q^{75} - 2 q^{76} - 12 q^{78} + 14 q^{81} + 6 q^{82} + 16 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{89} - 16 q^{90} - 24 q^{91} - 12 q^{93} - 24 q^{95} - 2 q^{96} - 18 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^12 - 12 * q^13 + 4 * q^14 - 8 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 8 * q^21 + 6 * q^22 - 2 * q^24 - 6 * q^25 + 20 * q^27 - 4 * q^28 - 4 * q^30 + 2 * q^32 - 2 * q^33 - 12 * q^34 + 12 * q^35 - 4 * q^36 - 4 * q^38 - 12 * q^39 - 6 * q^41 + 8 * q^42 + 8 * q^43 + 6 * q^44 - 8 * q^45 + 12 * q^47 - 4 * q^48 + 12 * q^49 - 12 * q^50 + 16 * q^51 + 12 * q^52 - 12 * q^53 + 10 * q^54 + 4 * q^55 - 8 * q^56 + 14 * q^57 + 18 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^63 + 4 * q^64 + 8 * q^66 - 6 * q^67 - 20 * q^69 + 12 * q^70 + 12 * q^71 - 2 * q^72 + 2 * q^73 + 12 * q^74 + 6 * q^75 - 2 * q^76 - 12 * q^78 + 14 * q^81 + 6 * q^82 + 16 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^89 - 16 * q^90 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 2 * q^96 - 18 * q^97 + 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more