LMFDB - Embedded newform 336.2.bq.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.76612 + 0.473232i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.76612 + 0.473232i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +(2.49768 - 0.669251i) q^{10} +(-0.107206 - 0.400100i) q^{11} +(0.517638 - 1.93185i) q^{12} +(0.414214 + 0.414214i) q^{13} +(-1.41421 + 3.46410i) q^{14} +1.82843 q^{15} +(-2.00000 - 3.46410i) q^{16} +(0.585786 - 1.01461i) q^{17} +(0.707107 - 1.22474i) q^{18} +(-0.732051 + 2.73205i) q^{19} +(2.58579 - 2.58579i) q^{20} +(-1.59990 + 2.10721i) q^{21} +(-0.414214 - 0.414214i) q^{22} +(-7.13834 + 4.12132i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(-1.43488 - 0.828427i) q^{25} +(0.800199 + 0.214413i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.717439 + 5.24264i) q^{28} +(1.87868 + 1.87868i) q^{29} +(2.23936 - 1.29289i) q^{30} +(1.20711 - 2.09077i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-0.207107 - 0.358719i) q^{33} -1.65685i q^{34} +(-4.45982 + 1.87404i) q^{35} -2.00000i q^{36} +(-2.73205 - 0.732051i) q^{37} +(1.03528 + 3.86370i) q^{38} +(0.507306 + 0.292893i) q^{39} +(1.33850 - 4.99536i) q^{40} +0.585786i q^{41} +(-0.469450 + 3.71209i) q^{42} +(4.58579 - 4.58579i) q^{43} +(-0.800199 - 0.214413i) q^{44} +(1.76612 - 0.473232i) q^{45} +(-5.82843 + 10.0951i) q^{46} +(3.12132 + 5.40629i) q^{47} +(-2.82843 - 2.82843i) q^{48} +(1.74264 - 6.77962i) q^{49} -2.34315 q^{50} +(0.303225 - 1.13165i) q^{51} +(1.13165 - 0.303225i) q^{52} +(2.24056 + 8.36188i) q^{53} +(0.366025 - 1.36603i) q^{54} -0.757359i q^{55} +(4.58579 + 5.91359i) q^{56} +2.82843i q^{57} +(3.62933 + 0.972476i) q^{58} +(0.536032 + 2.00050i) q^{59} +(1.82843 - 3.16693i) q^{60} +(1.40130 - 5.22973i) q^{61} -3.41421i q^{62} +(-1.00000 + 2.44949i) q^{63} -8.00000 q^{64} +(0.535534 + 0.927572i) q^{65} +(-0.507306 - 0.292893i) q^{66} +(-12.8601 + 3.44584i) q^{67} +(-1.17157 - 2.02922i) q^{68} +(-5.82843 + 5.82843i) q^{69} +(-4.13700 + 5.44879i) q^{70} +15.8995i q^{71} +(-1.41421 - 2.44949i) q^{72} +(3.46410 + 2.00000i) q^{73} +(-3.86370 + 1.03528i) q^{74} +(-1.60040 - 0.428825i) q^{75} +(4.00000 + 4.00000i) q^{76} +(0.872833 + 0.662700i) q^{77} +0.828427 q^{78} +(-5.62132 - 9.73641i) q^{79} +(-1.89293 - 7.06450i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.414214 + 0.717439i) q^{82} +(-8.77817 - 8.77817i) q^{83} +(2.04989 + 4.87832i) q^{84} +(1.51472 - 1.51472i) q^{85} +(2.37378 - 8.85906i) q^{86} +(2.30090 + 1.32843i) q^{87} +(-1.13165 + 0.303225i) q^{88} +(13.4722 - 7.77817i) q^{89} +(1.82843 - 1.82843i) q^{90} +(-1.53760 - 0.194453i) q^{91} +16.4853i q^{92} +(0.624844 - 2.33195i) q^{93} +(7.64564 + 4.41421i) q^{94} +(-2.58579 + 4.47871i) q^{95} +(-5.46410 - 1.46410i) q^{96} +8.31371 q^{97} +(-2.65962 - 9.53553i) q^{98} +(-0.292893 - 0.292893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) $ 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6	$ 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 8 * q^13 - 8 * q^15 - 16 * q^16 + 16 * q^17 + 8 * q^19 + 32 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 8 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^33 - 16 * q^35 - 8 * q^37 + 8 * q^40 - 4 * q^42 + 48 * q^43 - 8 * q^44 + 8 * q^45 - 24 * q^46 + 8 * q^47 - 20 * q^49 - 64 * q^50 + 8 * q^51 - 8 * q^52 - 16 * q^53 - 4 * q^54 + 48 * q^56 - 12 * q^58 - 20 * q^59 - 8 * q^60 - 4 * q^61 - 8 * q^63 - 64 * q^64 - 24 * q^65 - 32 * q^67 - 32 * q^68 - 24 * q^69 - 44 * q^70 - 16 * q^75 + 32 * q^76 - 8 * q^77 - 16 * q^78 - 28 * q^79 + 32 * q^80 + 4 * q^81 - 8 * q^82 - 8 * q^83 + 80 * q^85 + 8 * q^86 + 8 * q^88 - 8 * q^90 - 28 * q^91 - 4 * q^93 - 32 * q^95 - 16 * q^96 - 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	1.76612	+	0.473232i	0.789835	+	0.211636i	0.631116	−	0.775688i	$-0.282597\pi$
$5$	1.76612	+	0.473232i	0.789835	+	0.211636i	0.158719	+	0.987324i	$0.449264\pi$
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$8$		−	2.82843i		−	1.00000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	2.49768	−	0.669251i	0.789835	−	0.211636i
$11$	−0.107206	−	0.400100i	−0.0323239	−	0.120635i	0.947879	−	0.318631i	$-0.103223\pi$
$11$	−0.107206	−	0.400100i	−0.0323239	−	0.120635i	−0.980203	+	0.197997i	$0.936556\pi$
$12$	0.517638	−	1.93185i	0.149429	−	0.557678i
$13$	0.414214	+	0.414214i	0.114882	+	0.114882i	0.762211	−	0.647329i	$-0.224114\pi$
$13$	0.414214	+	0.414214i	0.114882	+	0.114882i	−0.647329	+	0.762211i	$0.724114\pi$
$14$	−1.41421	+	3.46410i	−0.377964	+	0.925820i
$15$	1.82843			0.472098
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	−0.786203	−	0.617968i	$-0.787956\pi$
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	0.928278	+	0.371888i	$0.121290\pi$
$18$	0.707107	−	1.22474i	0.166667	−	0.288675i
$19$	−0.732051	+	2.73205i	−0.167944	+	0.626775i	0.829702	+	0.558206i	$0.188510\pi$
$19$	−0.732051	+	2.73205i	−0.167944	+	0.626775i	−0.997646	+	0.0685694i	$0.978157\pi$
$20$	2.58579	−	2.58579i	0.578199	−	0.578199i
$21$	−1.59990	+	2.10721i	−0.349127	+	0.459830i
$22$	−0.414214	−	0.414214i	−0.0883106	−	0.0883106i
$23$	−7.13834	+	4.12132i	−1.48845	+	0.859355i	−0.999913	−	0.0131907i	$-0.995801\pi$
$23$	−7.13834	+	4.12132i	−1.48845	+	0.859355i	−0.488533	+	0.872545i	$0.662468\pi$
$24$	−0.732051	−	2.73205i	−0.149429	−	0.557678i
$25$	−1.43488	−	0.828427i	−0.286976	−	0.165685i
$26$	0.800199	+	0.214413i	0.156932	+	0.0420498i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.717439	+	5.24264i	0.135583	+	0.990766i
$29$	1.87868	+	1.87868i	0.348862	+	0.348862i	0.859686	−	0.510824i	$-0.170659\pi$
$29$	1.87868	+	1.87868i	0.348862	+	0.348862i	−0.510824	+	0.859686i	$0.670659\pi$
$30$	2.23936	−	1.29289i	0.408849	−	0.236049i
$31$	1.20711	−	2.09077i	0.216803	−	0.375513i	−0.737026	−	0.675864i	$-0.763770\pi$
$31$	1.20711	−	2.09077i	0.216803	−	0.375513i	0.953829	+	0.300351i	$0.0971038\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$	−0.207107	−	0.358719i	−0.0360527	−	0.0624450i
$34$		−	1.65685i		−	0.284148i
$35$	−4.45982	+	1.87404i	−0.753847	+	0.316770i
$36$		−	2.00000i		−	0.333333i
$37$	−2.73205	−	0.732051i	−0.449146	−	0.120348i	0.0271536	−	0.999631i	$-0.491356\pi$
$37$	−2.73205	−	0.732051i	−0.449146	−	0.120348i	−0.476300	+	0.879283i	$0.658022\pi$
$38$	1.03528	+	3.86370i	0.167944	+	0.626775i
$39$	0.507306	+	0.292893i	0.0812340	+	0.0469005i
$40$	1.33850	−	4.99536i	0.211636	−	0.789835i
$41$			0.585786i			0.0914845i	0.998953	+	0.0457422i	$0.0145653\pi$
$41$			0.585786i			0.0914845i	−0.998953	+	0.0457422i	$0.985435\pi$
$42$	−0.469450	+	3.71209i	−0.0724377	+	0.572788i
$43$	4.58579	−	4.58579i	0.699326	−	0.699326i	−0.264939	−	0.964265i	$-0.585352\pi$
$43$	4.58579	−	4.58579i	0.699326	−	0.699326i	0.964265	+	0.264939i	$0.0853519\pi$
$44$	−0.800199	−	0.214413i	−0.120635	−	0.0323239i
$45$	1.76612	−	0.473232i	0.263278	−	0.0705452i
$46$	−5.82843	+	10.0951i	−0.859355	+	1.48845i
$47$	3.12132	+	5.40629i	0.455291	+	0.788588i	0.998705	−	0.0508774i	$-0.0162018\pi$
$47$	3.12132	+	5.40629i	0.455291	+	0.788588i	−0.543414	+	0.839465i	$0.682868\pi$
$48$	−2.82843	−	2.82843i	−0.408248	−	0.408248i
$49$	1.74264	−	6.77962i	0.248949	−	0.968517i
$50$	−2.34315			−0.331371
$51$	0.303225	−	1.13165i	0.0424600	−	0.158463i
$52$	1.13165	−	0.303225i	0.156932	−	0.0420498i
$53$	2.24056	+	8.36188i	0.307764	+	1.14859i	0.930540	+	0.366192i	$0.119338\pi$
$53$	2.24056	+	8.36188i	0.307764	+	1.14859i	−0.622775	+	0.782401i	$0.713995\pi$
$54$	0.366025	−	1.36603i	0.0498097	−	0.185893i
$55$		−	0.757359i		−	0.102122i
$56$	4.58579	+	5.91359i	0.612801	+	0.790237i
$57$			2.82843i			0.374634i
$58$	3.62933	+	0.972476i	0.476554	+	0.127692i
$59$	0.536032	+	2.00050i	0.0697854	+	0.260443i	0.992000	−	0.126235i	$-0.0402893\pi$
$59$	0.536032	+	2.00050i	0.0697854	+	0.260443i	−0.922215	+	0.386678i	$0.873623\pi$
$60$	1.82843	−	3.16693i	0.236049	−	0.408849i
$61$	1.40130	−	5.22973i	0.179418	−	0.669598i	−0.816338	−	0.577574i	$-0.804000\pi$
$61$	1.40130	−	5.22973i	0.179418	−	0.669598i	0.995757	−	0.0920243i	$-0.0293338\pi$
$62$		−	3.41421i		−	0.433606i
$63$	−1.00000	+	2.44949i	−0.125988	+	0.308607i
$64$	−8.00000			−1.00000
$65$	0.535534	+	0.927572i	0.0664248	+	0.115051i
$66$	−0.507306	−	0.292893i	−0.0624450	−	0.0360527i
$67$	−12.8601	+	3.44584i	−1.57111	+	0.420977i	−0.936158	−	0.351579i	$-0.885645\pi$
$67$	−12.8601	+	3.44584i	−1.57111	+	0.420977i	−0.634947	+	0.772555i	$0.718978\pi$
$68$	−1.17157	−	2.02922i	−0.142074	−	0.246080i
$69$	−5.82843	+	5.82843i	−0.701660	+	0.701660i
$70$	−4.13700	+	5.44879i	−0.494466	+	0.651254i
$71$			15.8995i			1.88692i	0.331482	+	0.943461i	$0.392451\pi$
$71$			15.8995i			1.88692i	−0.331482	+	0.943461i	$0.607549\pi$
$72$	−1.41421	−	2.44949i	−0.166667	−	0.288675i
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	0.688830	−	0.724923i	$-0.258125\pi$
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	−0.283387	+	0.959006i	$0.591458\pi$
$74$	−3.86370	+	1.03528i	−0.449146	+	0.120348i
$75$	−1.60040	−	0.428825i	−0.184798	−	0.0495165i
$76$	4.00000	+	4.00000i	0.458831	+	0.458831i
$77$	0.872833	+	0.662700i	0.0994686	+	0.0755217i
$78$	0.828427			0.0938009
$79$	−5.62132	−	9.73641i	−0.632448	−	1.09543i	−0.987050	−	0.160415i	$-0.948717\pi$
$79$	−5.62132	−	9.73641i	−0.632448	−	1.09543i	0.354602	−	0.935017i	$-0.384616\pi$
$80$	−1.89293	−	7.06450i	−0.211636	−	0.789835i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.414214	+	0.717439i	0.0457422	+	0.0792279i
$83$	−8.77817	−	8.77817i	−0.963530	−	0.963530i	0.0358281	−	0.999358i	$-0.488593\pi$
$83$	−8.77817	−	8.77817i	−0.963530	−	0.963530i	−0.999358	+	0.0358281i	$0.988593\pi$
$84$	2.04989	+	4.87832i	0.223661	+	0.532268i
$85$	1.51472	−	1.51472i	0.164294	−	0.164294i
$86$	2.37378	−	8.85906i	0.255971	−	0.955297i
$87$	2.30090	+	1.32843i	0.246683	+	0.142422i
$88$	−1.13165	+	0.303225i	−0.120635	+	0.0323239i
$89$	13.4722	−	7.77817i	1.42805	−	0.824485i	0.431083	−	0.902312i	$-0.358132\pi$
$89$	13.4722	−	7.77817i	1.42805	−	0.824485i	0.996967	+	0.0778275i	$0.0247983\pi$
$90$	1.82843	−	1.82843i	0.192733	−	0.192733i
$91$	−1.53760	−	0.194453i	−0.161184	−	0.0203842i
$92$			16.4853i			1.71871i
$93$	0.624844	−	2.33195i	0.0647934	−	0.241812i
$94$	7.64564	+	4.41421i	0.788588	+	0.455291i
$95$	−2.58579	+	4.47871i	−0.265296	+	0.459506i
$96$	−5.46410	−	1.46410i	−0.557678	−	0.149429i
$97$	8.31371			0.844129			0.422065	−	0.906566i	$-0.361306\pi$
$97$	8.31371			0.844129			0.422065	+	0.906566i	$0.361306\pi$
$98$	−2.65962	−	9.53553i	−0.268662	−	0.963234i
$99$	−0.292893	−	0.292893i	−0.0294369	−	0.0294369i
$100$	−2.86976	+	1.65685i	−0.286976	+	0.165685i
$101$	1.98174	+	7.39595i	0.197190	+	0.735925i	0.991689	+	0.128659i	$0.0410672\pi$
$101$	1.98174	+	7.39595i	0.197190	+	0.735925i	−0.794498	+	0.607266i	$0.792266\pi$
$102$	−0.428825	−	1.60040i	−0.0424600	−	0.158463i
$103$	15.2913	−	8.82843i	1.50670	−	0.869891i	0.506725	−	0.862108i	$-0.330856\pi$
$103$	15.2913	−	8.82843i	1.50670	−	0.869891i	0.999970	−	0.00778320i	$-0.00247749\pi$
$104$	1.17157	−	1.17157i	0.114882	−	0.114882i
$105$	−3.82282	+	2.96447i	−0.373069	+	0.289302i
$106$	8.65685	+	8.65685i	0.840828	+	0.840828i
$107$	−15.5235	−	4.15950i	−1.50071	−	0.402114i	−0.587372	−	0.809317i	$-0.699837\pi$
$107$	−15.5235	−	4.15950i	−1.50071	−	0.402114i	−0.913338	+	0.407203i	$0.866504\pi$
$108$	−0.517638	−	1.93185i	−0.0498097	−	0.185893i
$109$	−1.46311	+	0.392038i	−0.140140	+	0.0375504i	−0.328207	−	0.944606i	$-0.606444\pi$
$109$	−1.46311	+	0.392038i	−0.140140	+	0.0375504i	0.188067	+	0.982156i	$0.439778\pi$
$110$	−0.535534	−	0.927572i	−0.0510612	−	0.0884405i
$111$	−2.82843			−0.268462
$112$	9.79796	+	4.00000i	0.925820	+	0.377964i
$113$	3.89949			0.366834			0.183417	−	0.983035i	$-0.441284\pi$
$113$	3.89949			0.366834			0.183417	+	0.983035i	$0.441284\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	−14.5575	+	3.90068i	−1.35750	+	0.363740i
$116$	5.13265	−	1.37529i	0.476554	−	0.127692i
$117$	0.565826	+	0.151613i	0.0523107	+	0.0140166i
$118$	2.07107	+	2.07107i	0.190657	+	0.190657i
$119$	0.420266	+	3.07107i	0.0385257	+	0.281524i
$120$		−	5.17157i		−	0.472098i
$121$	9.37769	−	5.41421i	0.852518	−	0.492201i
$122$	−1.98174	−	7.39595i	−0.179418	−	0.669598i
$123$	0.151613	+	0.565826i	0.0136705	+	0.0510188i
$124$	−2.41421	−	4.18154i	−0.216803	−	0.375513i
$125$	−8.60660	−	8.60660i	−0.769798	−	0.769798i
$126$	0.507306	+	3.70711i	0.0451944	+	0.330255i
$127$	11.2426			0.997623			0.498812	−	0.866710i	$-0.333770\pi$
$127$	11.2426			0.997623			0.498812	+	0.866710i	$0.333770\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$	3.24264	−	5.61642i	0.285499	−	0.494498i
$130$	1.31178	+	0.757359i	0.115051	+	0.0664248i
$131$	−1.48250	+	5.53275i	−0.129526	+	0.483398i	−0.999961	−	0.00888618i	$-0.997171\pi$
$131$	−1.48250	+	5.53275i	−0.129526	+	0.483398i	0.870434	+	0.492285i	$0.163838\pi$
$132$	−0.828427			−0.0721053
$133$	−2.89898	−	6.89898i	−0.251373	−	0.598217i
$134$	−13.3137	+	13.3137i	−1.15013	+	1.15013i
$135$	1.58346	−	0.914214i	0.136283	−	0.0786830i
$136$	−2.86976	−	1.65685i	−0.246080	−	0.142074i
$137$	−11.1097	−	6.41421i	−0.949169	−	0.548003i	−0.0563466	−	0.998411i	$-0.517945\pi$
$137$	−11.1097	−	6.41421i	−0.949169	−	0.548003i	−0.892823	+	0.450408i	$0.851279\pi$
$138$	−3.01702	+	11.2597i	−0.256825	+	0.958486i
$139$	12.8995	−	12.8995i	1.09412	−	1.09412i	0.0990371	−	0.995084i	$-0.468424\pi$
$139$	12.8995	−	12.8995i	1.09412	−	1.09412i	0.995084	−	0.0990371i	$-0.0315763\pi$
$140$	−1.21390	+	9.59867i	−0.102593	+	0.811236i
$141$	4.41421	+	4.41421i	0.371744	+	0.371744i
$142$	11.2426	+	19.4728i	0.943461	+	1.63412i
$143$	0.121320	−	0.210133i	0.0101453	−	0.0175722i
$144$	−3.46410	−	2.00000i	−0.288675	−	0.166667i
$145$	2.42893	+	4.20703i	0.201712	+	0.349375i
$146$	5.65685			0.468165
$147$	−0.0714323	−	6.99964i	−0.00589164	−	0.577320i
$148$	−4.00000	+	4.00000i	−0.328798	+	0.328798i
$149$	14.3232	+	3.83788i	1.17340	+	0.314411i	0.792305	−	0.610125i	$-0.208881\pi$
$149$	14.3232	+	3.83788i	1.17340	+	0.314411i	0.381094	+	0.924536i	$0.375547\pi$
$150$	−2.26330	+	0.606451i	−0.184798	+	0.0495165i
$151$	−8.30153	−	4.79289i	−0.675569	−	0.390040i	0.122614	−	0.992454i	$-0.460872\pi$
$151$	−8.30153	−	4.79289i	−0.675569	−	0.390040i	−0.798184	+	0.602414i	$0.794206\pi$
$152$	7.72741	+	2.07055i	0.626775	+	0.167944i
$153$		−	1.17157i		−	0.0947161i
$154$	1.53760	+	0.194453i	0.123903	+	0.0156694i
$155$	3.12132	−	3.12132i	0.250710	−	0.250710i
$156$	1.01461	−	0.585786i	0.0812340	−	0.0469005i
$157$	−20.2560	+	5.42758i	−1.61661	+	0.433168i	−0.950002	−	0.312244i	$-0.898919\pi$
$157$	−20.2560	+	5.42758i	−1.61661	+	0.433168i	−0.666604	+	0.745412i	$0.732253\pi$
$158$	−13.7694	−	7.94975i	−1.09543	−	0.632448i
$159$	4.32843	+	7.49706i	0.343267	+	0.594555i
$160$	−7.31371	−	7.31371i	−0.578199	−	0.578199i
$161$	8.24264	−	20.1903i	0.649611	−	1.59122i
$162$		−	1.41421i		−	0.111111i
$163$	2.00775	−	7.49303i	0.157259	−	0.586900i	−0.841642	−	0.540036i	$-0.818411\pi$
$163$	2.00775	−	7.49303i	0.157259	−	0.586900i	0.998901	−	0.0468638i	$-0.0149227\pi$
$164$	1.01461	+	0.585786i	0.0792279	+	0.0457422i
$165$	−0.196019	−	0.731553i	−0.0152601	−	0.0569513i
$166$	−16.9581	−	4.54392i	−1.31621	−	0.352676i
$167$			6.00000i			0.464294i	0.972681	+	0.232147i	$0.0745750\pi$
$167$			6.00000i			0.464294i	−0.972681	+	0.232147i	$0.925425\pi$
$168$	5.96008	+	4.52520i	0.459830	+	0.349127i
$169$		−	12.6569i		−	0.973604i
$170$	0.784076	−	2.92621i	0.0601359	−	0.224430i
$171$	0.732051	+	2.73205i	0.0559813	+	0.208925i
$172$	−3.35703	−	12.5286i	−0.255971	−	0.955297i
$173$	4.39230	−	16.3923i	0.333941	−	1.24628i	−0.571072	−	0.820900i	$-0.693472\pi$
$173$	4.39230	−	16.3923i	0.333941	−	1.24628i	0.905013	−	0.425384i	$-0.139861\pi$
$174$	3.75736			0.284845
$175$	4.34315	−	0.594346i	0.328311	−	0.0449283i
$176$	−1.17157	+	1.17157i	−0.0883106	+	0.0883106i
$177$	1.03553	+	1.79360i	0.0778355	+	0.134815i
$178$	11.0000	−	19.0526i	0.824485	−	1.42805i
$179$	17.9927	−	4.82113i	1.34484	−	0.360348i	0.486611	−	0.873619i	$-0.338233\pi$
$179$	17.9927	−	4.82113i	1.34484	−	0.360348i	0.858227	+	0.513271i	$0.171566\pi$
$180$	0.946464	−	3.53225i	0.0705452	−	0.263278i
$181$	−15.7279	+	15.7279i	−1.16905	+	1.16905i	−0.186614	+	0.982433i	$0.559751\pi$
$181$	−15.7279	+	15.7279i	−1.16905	+	1.16905i	−0.982433	+	0.186614i	$0.940249\pi$
$182$	−2.02066	+	0.849091i	−0.149782	+	0.0629388i
$183$		−	5.41421i		−	0.400230i
$184$	11.6569	+	20.1903i	0.859355	+	1.48845i
$185$	−4.47871	−	2.58579i	−0.329282	−	0.190111i
$186$	−0.883663	−	3.29788i	−0.0647934	−	0.241812i
$187$	−0.468746	−	0.125600i	−0.0342781	−	0.00918479i
$188$	12.4853			0.910583
$189$	−0.331951	+	2.62484i	−0.0241459	+	0.190929i
$190$			7.31371i			0.530592i
$191$	−9.65685	−	16.7262i	−0.698745	−	1.21026i	−0.968902	−	0.247446i	$-0.920409\pi$
$191$	−9.65685	−	16.7262i	−0.698745	−	1.21026i	0.270156	−	0.962817i	$-0.412925\pi$
$192$	−7.72741	+	2.07055i	−0.557678	+	0.149429i
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	10.1822	−	5.87868i	0.731037	−	0.422065i
$195$	0.757359	+	0.757359i	0.0542356	+	0.0542356i
$196$	−10.0000	−	9.79796i	−0.714286	−	0.699854i
$197$	3.17157	−	3.17157i	0.225965	−	0.225965i	−0.585040	−	0.811005i	$-0.698921\pi$
$197$	3.17157	−	3.17157i	0.225965	−	0.225965i	0.811005	+	0.585040i	$0.198921\pi$
$198$	−0.565826	−	0.151613i	−0.0402115	−	0.0107746i
$199$	16.3059	+	9.41421i	1.15589	+	0.667356i	0.950317	−	0.311285i	$-0.100759\pi$
$199$	16.3059	+	9.41421i	1.15589	+	0.667356i	0.205578	+	0.978641i	$0.434093\pi$
$200$	−2.34315	+	4.05845i	−0.165685	+	0.286976i
$201$	−11.5300	+	6.65685i	−0.813264	+	0.469538i
$202$	7.65685	+	7.65685i	0.538734	+	0.538734i
$203$	−6.97383	−	0.881946i	−0.489467	−	0.0619005i
$204$	−1.65685	−	1.65685i	−0.116003	−	0.116003i
$205$	−0.277213	+	1.03457i	−0.0193614	+	0.0722576i
$206$	12.4853	−	21.6251i	0.869891	−	1.50670i
$207$	−4.12132	+	7.13834i	−0.286452	+	0.496149i
$208$	0.606451	−	2.26330i	0.0420498	−	0.156932i
$209$	1.17157			0.0810394
$210$	−2.58579	+	6.33386i	−0.178436	+	0.437078i
$211$	−8.41421	−	8.41421i	−0.579258	−	0.579258i	0.355441	−	0.934699i	$-0.384331\pi$
$211$	−8.41421	−	8.41421i	−0.579258	−	0.579258i	−0.934699	+	0.355441i	$0.884331\pi$
$212$	16.7238	+	4.48112i	1.14859	+	0.307764i
$213$	4.11509	+	15.3577i	0.281961	+	1.05229i
$214$	−21.9535	+	5.88242i	−1.50071	+	0.402114i
$215$	10.2692	−	5.92893i	0.700354	−	0.404350i
$216$	−2.00000	−	2.00000i	−0.136083	−	0.136083i
$217$	0.866025	+	6.32843i	0.0587896	+	0.429602i
$218$	−1.51472	+	1.51472i	−0.102590	+	0.102590i
$219$	3.86370	+	1.03528i	0.261085	+	0.0699575i
$220$	−1.31178	−	0.757359i	−0.0884405	−	0.0510612i
$221$	0.662907	−	0.177625i	0.0445919	−	0.0119484i
$222$	−3.46410	+	2.00000i	−0.232495	+	0.134231i
$223$	20.5563			1.37655			0.688277	−	0.725448i	$-0.258367\pi$
$223$	20.5563			1.37655			0.688277	+	0.725448i	$0.258367\pi$
$224$	14.8284	−	2.02922i	0.990766	−	0.135583i
$225$	−1.65685			−0.110457
$226$	4.77589	−	2.75736i	0.317687	−	0.183417i
$227$	10.3908	−	2.78421i	0.689662	−	0.184794i	0.103067	−	0.994674i	$-0.467134\pi$
$227$	10.3908	−	2.78421i	0.689662	−	0.184794i	0.586596	+	0.809880i	$0.300468\pi$
$228$	4.89898	+	2.82843i	0.324443	+	0.187317i
$229$	−23.5539	−	6.31124i	−1.55648	−	0.417059i	−0.624936	−	0.780676i	$-0.714875\pi$
$229$	−23.5539	−	6.31124i	−1.55648	−	0.417059i	−0.931548	+	0.363617i	$0.881542\pi$
$230$	−15.0711	+	15.0711i	−0.993757	+	0.993757i
$231$	1.01461	+	0.414214i	0.0667566	+	0.0272533i
$232$	5.31371	−	5.31371i	0.348862	−	0.348862i
$233$	−4.47871	+	2.58579i	−0.293410	+	0.169401i	−0.639479	−	0.768809i	$-0.720850\pi$
$233$	−4.47871	+	2.58579i	−0.293410	+	0.169401i	0.346069	+	0.938209i	$0.387516\pi$
$234$	0.800199	−	0.214413i	0.0523107	−	0.0140166i
$235$	2.95422	+	11.0253i	0.192712	+	0.719210i
$236$	4.00100	+	1.07206i	0.260443	+	0.0697854i
$237$	−7.94975	−	7.94975i	−0.516392	−	0.516392i
$238$	2.68629	+	3.46410i	0.174126	+	0.224544i
$239$	11.0711			0.716128			0.358064	−	0.933697i	$-0.383437\pi$
$239$	11.0711			0.716128			0.358064	+	0.933697i	$0.383437\pi$
$240$	−3.65685	−	6.33386i	−0.236049	−	0.408849i
$241$	−11.5711	+	20.0417i	−0.745358	+	1.29100i	0.204669	+	0.978831i	$0.434388\pi$
$241$	−11.5711	+	20.0417i	−0.745358	+	1.29100i	−0.950027	+	0.312167i	$0.898945\pi$
$242$	7.65685	−	13.2621i	0.492201	−	0.852518i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−7.65685	−	7.65685i	−0.490180	−	0.490180i
$245$	6.28605	−	11.1490i	0.401601	−	0.712282i
$246$	0.585786	+	0.585786i	0.0373484	+	0.0373484i
$247$	−1.43488	+	0.828427i	−0.0912991	+	0.0527116i
$248$	−5.91359	−	3.41421i	−0.375513	−	0.216803i
$249$	−10.7510	−	6.20711i	−0.681318	−	0.393359i
$250$	−16.6267	−	4.45510i	−1.05156	−	0.281766i
$251$	−4.05025	+	4.05025i	−0.255650	+	0.255650i	−0.823282	−	0.567632i	$-0.807859\pi$
$251$	−4.05025	+	4.05025i	−0.255650	+	0.255650i	0.567632	+	0.823282i	$0.307859\pi$
$252$	3.24264	+	4.18154i	0.204267	+	0.263412i
$253$	2.41421	+	2.41421i	0.151780	+	0.151780i
$254$	13.7694	−	7.94975i	0.863967	−	0.498812i
$255$	1.07107	−	1.85514i	0.0670729	−	0.116174i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	10.1213	+	17.5306i	0.631351	+	1.09353i	0.987276	+	0.159017i	$0.0508324\pi$
$257$	10.1213	+	17.5306i	0.631351	+	1.09353i	−0.355925	+	0.934514i	$0.615834\pi$
$258$		−	9.17157i		−	0.570997i
$259$	6.89898	−	2.89898i	0.428682	−	0.180134i
$260$	2.14214			0.132850
$261$	2.56632	+	0.687644i	0.158851	+	0.0425641i
$262$	2.09656	+	7.82449i	0.129526	+	0.483398i
$263$	1.31178	+	0.757359i	0.0808881	+	0.0467008i	0.539899	−	0.841730i	$-0.318463\pi$
$263$	1.31178	+	0.757359i	0.0808881	+	0.0467008i	−0.459010	+	0.888431i	$0.651796\pi$
$264$	−1.01461	+	0.585786i	−0.0624450	+	0.0360527i
$265$			15.8284i			0.972333i
$266$	−8.42883	−	6.39960i	−0.516804	−	0.392385i
$267$	11.0000	−	11.0000i	0.673189	−	0.673189i
$268$	−6.89168	+	25.7201i	−0.420977	+	1.57111i
$269$	0.828633	−	0.222032i	0.0505227	−	0.0135375i	−0.233469	−	0.972364i	$-0.575008\pi$
$269$	0.828633	−	0.222032i	0.0505227	−	0.0135375i	0.283992	+	0.958827i	$0.408341\pi$
$270$	1.29289	−	2.23936i	0.0786830	−	0.136283i
$271$	−12.8640	−	22.2810i	−0.781430	−	1.35348i	−0.931109	−	0.364742i	$-0.881157\pi$
$271$	−12.8640	−	22.2810i	−0.781430	−	1.35348i	0.149679	−	0.988735i	$-0.452176\pi$
$272$	−4.68629			−0.284148
$273$	−1.53553	+	0.210133i	−0.0929347	+	0.0127178i
$274$	−18.1421			−1.09601
$275$	−0.177625	+	0.662907i	−0.0107112	+	0.0399748i
$276$	4.26670	+	15.9236i	0.256825	+	0.958486i
$277$	−2.67700	−	9.99071i	−0.160846	−	0.600284i	−0.998534	−	0.0541348i	$-0.982760\pi$
$277$	−2.67700	−	9.99071i	−0.160846	−	0.600284i	0.837688	−	0.546149i	$-0.183907\pi$
$278$	6.67727	−	24.9199i	0.400476	−	1.49460i
$279$		−	2.41421i		−	0.144535i
$280$	5.30057	+	12.6143i	0.316770	+	0.753847i
$281$		−	4.82843i		−	0.288040i	−0.989575	−	0.144020i	$-0.953997\pi$
$281$		−	4.82843i		−	0.288040i	0.989575	−	0.144020i	$-0.0460029\pi$
$282$	8.52761	+	2.28497i	0.507812	+	0.136068i
$283$	6.07082	+	22.6566i	0.360873	+	1.34680i	0.872931	+	0.487844i	$0.162217\pi$
$283$	6.07082	+	22.6566i	0.360873	+	1.34680i	−0.512058	+	0.858951i	$0.671117\pi$
$284$	27.5387	+	15.8995i	1.63412	+	0.943461i
$285$	−1.33850	+	4.99536i	−0.0792860	+	0.295899i
$286$		−	0.343146i		−	0.0202906i
$287$	−0.949747	−	1.22474i	−0.0560618	−	0.0722944i
$288$	−5.65685			−0.333333
$289$	7.81371	+	13.5337i	0.459630	+	0.796102i
$290$	5.94964	+	3.43503i	0.349375	+	0.201712i
$291$	8.03043	−	2.15175i	0.470752	−	0.126138i
$292$	6.92820	−	4.00000i	0.405442	−	0.234082i
$293$	−10.9497	+	10.9497i	−0.639691	+	0.639691i	−0.950479	−	0.310788i	$-0.899407\pi$
$293$	−10.9497	+	10.9497i	−0.639691	+	0.639691i	0.310788	+	0.950479i	$0.399407\pi$
$294$	−5.03698	−	8.52226i	−0.293762	−	0.497028i
$295$			3.78680i			0.220476i
$296$	−2.07055	+	7.72741i	−0.120348	+	0.449146i
$297$	−0.358719	−	0.207107i	−0.0208150	−	0.0120176i
$298$	20.2560	−	5.42758i	1.17340	−	0.314411i
$299$	−4.66390	−	1.24969i	−0.269720	−	0.0722714i
$300$	−2.34315	+	2.34315i	−0.135282	+	0.135282i
$301$	−2.15280	+	17.0229i	−0.124085	+	0.981181i
$302$	−13.5563			−0.780080
$303$	3.82843	+	6.63103i	0.219937	+	0.380943i
$304$	10.9282	−	2.92820i	0.626775	−	0.167944i
$305$	4.94975	−	8.57321i	0.283422	−	0.490901i
$306$	−0.828427	−	1.43488i	−0.0473580	−	0.0820265i
$307$	6.31371	+	6.31371i	0.360342	+	0.360342i	0.863939	−	0.503597i	$-0.167990\pi$
$307$	6.31371	+	6.31371i	0.360342	+	0.360342i	−0.503597	+	0.863939i	$0.667990\pi$
$308$	2.02066	−	0.849091i	0.115138	−	0.0483815i
$309$	12.4853	−	12.4853i	0.710263	−	0.710263i
$310$	1.61571	−	6.02993i	0.0917664	−	0.342477i
$311$	−10.0081	−	5.77817i	−0.567507	−	0.327650i	0.188646	−	0.982045i	$-0.439590\pi$
$311$	−10.0081	−	5.77817i	−0.567507	−	0.327650i	−0.756153	+	0.654395i	$0.772923\pi$
$312$	0.828427	−	1.43488i	0.0469005	−	0.0812340i
$313$	−8.51167	+	4.91421i	−0.481108	+	0.277768i	−0.720878	−	0.693062i	$-0.756261\pi$
$313$	−8.51167	+	4.91421i	−0.481108	+	0.277768i	0.239770	+	0.970830i	$0.422928\pi$
$314$	−20.9706	+	20.9706i	−1.18344	+	1.18344i
$315$	−2.92530	+	3.85287i	−0.164822	+	0.217085i
$316$	−22.4853			−1.26490
$317$	−2.93582	+	10.9566i	−0.164892	+	0.615386i	0.833162	+	0.553029i	$0.186528\pi$
$317$	−2.93582	+	10.9566i	−0.164892	+	0.615386i	−0.998054	+	0.0623567i	$0.980138\pi$
$318$	10.6024	+	6.12132i	0.594555	+	0.343267i
$319$	0.550253	−	0.953065i	0.0308082	−	0.0533614i
$320$	−14.1290	−	3.78585i	−0.789835	−	0.211636i
$321$	−16.0711			−0.897000
$322$	−4.18154	−	30.5563i	−0.233028	−	1.70284i
$323$	2.34315	+	2.34315i	0.130376	+	0.130376i
$324$	−1.00000	−	1.73205i	−0.0555556	−	0.0962250i
$325$	−0.251200	−	0.937492i	−0.0139341	−	0.0520027i
$326$	−2.83939	−	10.5967i	−0.157259	−	0.586900i
$327$	−1.31178	+	0.757359i	−0.0725419	+	0.0418821i
$328$	1.65685			0.0914845
$329$	−15.2913	−	6.24264i	−0.843036	−	0.344168i
$330$	−0.757359	−	0.757359i	−0.0416913	−	0.0416913i
$331$	−7.72741	−	2.07055i	−0.424737	−	0.113808i	0.0401178	−	0.999195i	$-0.487227\pi$
$331$	−7.72741	−	2.07055i	−0.424737	−	0.113808i	−0.464854	+	0.885387i	$0.653893\pi$
$332$	−23.9824	+	6.42607i	−1.31621	+	0.352676i
$333$	−2.73205	+	0.732051i	−0.149715	+	0.0401161i
$334$	4.24264	+	7.34847i	0.232147	+	0.402090i
$335$	−24.3431			−1.33001
$336$	10.4994	+	1.32780i	0.572788	+	0.0724377i
$337$	−18.6569			−1.01630			−0.508152	−	0.861268i	$-0.669671\pi$
$337$	−18.6569			−1.01630			−0.508152	+	0.861268i	$0.669671\pi$
$338$	−8.94975	−	15.5014i	−0.486802	−	0.843166i
$339$	3.76662	−	1.00926i	0.204575	−	0.0548157i
$340$	−1.10885	−	4.13829i	−0.0601359	−	0.224430i
$341$	−0.965926	−	0.258819i	−0.0523078	−	0.0140158i
$342$	2.82843	+	2.82843i	0.152944	+	0.152944i
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$	−12.9706	−	12.9706i	−0.699326	−	0.699326i
$345$	−13.0519	+	7.53553i	−0.702692	+	0.405700i
$346$	−6.21166	−	23.1822i	−0.333941	−	1.24628i
$347$	6.33726	+	23.6510i	0.340202	+	1.26965i	0.898119	+	0.439753i	$0.144934\pi$
$347$	6.33726	+	23.6510i	0.340202	+	1.26965i	−0.557917	+	0.829897i	$0.688399\pi$
$348$	4.60181	−	2.65685i	0.246683	−	0.142422i
$349$	−3.41421	−	3.41421i	−0.182759	−	0.182759i	0.609798	−	0.792557i	$-0.291251\pi$
$349$	−3.41421	−	3.41421i	−0.182759	−	0.182759i	−0.792557	+	0.609798i	$0.791251\pi$
$350$	4.89898	−	3.79899i	0.261861	−	0.203065i
$351$	0.585786			0.0312670
$352$	−0.606451	+	2.26330i	−0.0323239	+	0.120635i
$353$	−9.65685	+	16.7262i	−0.513982	+	0.890244i	0.485886	+	0.874022i	$0.338497\pi$
$353$	−9.65685	+	16.7262i	−0.513982	+	0.890244i	−0.999868	+	0.0162216i	$0.994836\pi$
$354$	2.53653	+	1.46447i	0.134815	+	0.0778355i
$355$	−7.52415	+	28.0805i	−0.399340	+	1.49036i
$356$		−	31.1127i		−	1.64897i
$357$	1.20080	+	2.85765i	0.0635529	+	0.151243i
$358$	18.6274	−	18.6274i	0.984490	−	0.984490i
$359$	−3.16693	+	1.82843i	−0.167144	+	0.0965007i	−0.581239	−	0.813733i	$-0.697432\pi$
$359$	−3.16693	+	1.82843i	−0.167144	+	0.0965007i	0.414094	+	0.910234i	$0.364098\pi$
$360$	−1.33850	−	4.99536i	−0.0705452	−	0.263278i
$361$	9.52628	+	5.50000i	0.501383	+	0.289474i
$362$	−8.14137	+	30.3840i	−0.427901	+	1.59695i
$363$	7.65685	−	7.65685i	0.401881	−	0.401881i
$364$	−1.87440	+	2.46875i	−0.0982453	+	0.129397i
$365$	5.17157	+	5.17157i	0.270692	+	0.270692i
$366$	−3.82843	−	6.63103i	−0.200115	−	0.346610i
$367$	−5.69239	+	9.85951i	−0.297140	+	0.514662i	−0.975480	−	0.220086i	$-0.929366\pi$
$367$	−5.69239	+	9.85951i	−0.297140	+	0.514662i	0.678340	+	0.734748i	$0.262700\pi$
$368$	28.5533	+	16.4853i	1.48845	+	0.859355i
$369$	0.292893	+	0.507306i	0.0152474	+	0.0264093i
$370$	−7.31371			−0.380222
$371$	−18.2418	−	13.8501i	−0.947066	−	0.719062i
$372$	−3.41421	−	3.41421i	−0.177019	−	0.177019i
$373$	−19.2214	−	5.15037i	−0.995248	−	0.266676i	−0.275795	−	0.961217i	$-0.588941\pi$
$373$	−19.2214	−	5.15037i	−0.995248	−	0.266676i	−0.719454	+	0.694541i	$0.755608\pi$
$374$	−0.662907	+	0.177625i	−0.0342781	+	0.00918479i
$375$	−10.5409	−	6.08579i	−0.544329	−	0.314269i
$376$	15.2913	−	8.82843i	0.788588	−	0.455291i
$377$			1.55635i			0.0801561i
$378$	1.44949	+	3.44949i	0.0745537	+	0.177423i
$379$	−4.65685	+	4.65685i	−0.239207	+	0.239207i	−0.816522	−	0.577315i	$-0.804100\pi$
$379$	−4.65685	+	4.65685i	−0.239207	+	0.239207i	0.577315	+	0.816522i	$0.304100\pi$
$380$	5.17157	+	8.95743i	0.265296	+	0.459506i
$381$	10.8596	−	2.90981i	0.556352	−	0.149074i
$382$	−23.6544	−	13.6569i	−1.21026	−	0.698745i
$383$	14.5355	+	25.1763i	0.742731	+	1.28645i	0.951247	+	0.308429i	$0.0998032\pi$
$383$	14.5355	+	25.1763i	0.742731	+	1.28645i	−0.208516	+	0.978019i	$0.566863\pi$
$384$	−8.00000	+	8.00000i	−0.408248	+	0.408248i
$385$	1.22792	+	1.58346i	0.0625807	+	0.0807008i
$386$		−	9.89949i		−	0.503871i
$387$	1.67851	−	6.26430i	0.0853237	−	0.318432i
$388$	8.31371	−	14.3998i	0.422065	−	0.731037i
$389$	0.983251	+	3.66954i	0.0498528	+	0.186053i	0.986362	−	0.164589i	$-0.0526299\pi$
$389$	0.983251	+	3.66954i	0.0498528	+	0.186053i	−0.936509	+	0.350643i	$0.885963\pi$
$390$	1.46311	+	0.392038i	0.0740872	+	0.0198516i
$391$			9.65685i			0.488368i
$392$	−19.1757	−	4.92893i	−0.968517	−	0.248949i
$393$			5.72792i			0.288935i
$394$	1.64173	−	6.12701i	0.0827090	−	0.308674i
$395$	−5.32037	−	19.8559i	−0.267697	−	0.999059i
$396$	−0.800199	+	0.214413i	−0.0402115	+	0.0107746i
$397$	−8.53341	+	31.8471i	−0.428280	+	1.59836i	0.328376	+	0.944547i	$0.393499\pi$
$397$	−8.53341	+	31.8471i	−0.428280	+	1.59836i	−0.756655	+	0.653814i	$0.773168\pi$
$398$	26.6274			1.33471
$399$	−4.58579	−	5.91359i	−0.229576	−	0.296050i
$400$			6.62742i			0.331371i
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$	−9.41421	+	16.3059i	−0.469538	+	0.813264i
$403$	1.36603	−	0.366025i	0.0680466	−	0.0182330i
$404$	14.7919	+	3.96348i	0.735925	+	0.197190i
$405$	1.29289	−	1.29289i	0.0642444	−	0.0642444i
$406$	−9.16479	+	3.85108i	−0.454841	+	0.191126i
$407$			1.17157i			0.0580727i
$408$	−3.20080	−	0.857651i	−0.158463	−	0.0424600i
$409$	18.4837	+	10.6716i	0.913960	+	0.527675i	0.881703	−	0.471804i	$-0.156397\pi$
$409$	18.4837	+	10.6716i	0.913960	+	0.527675i	0.0322572	+	0.999480i	$0.489730\pi$
$410$	0.392038	+	1.46311i	0.0193614	+	0.0722576i
$411$	−12.3913	−	3.32024i	−0.611218	−	0.163775i
$412$		−	35.3137i		−	1.73978i
$413$	−4.36417	−	3.31350i	−0.214747	−	0.163047i
$414$			11.6569i			0.572903i
$415$	−11.3492	−	19.6575i	−0.557112	−	0.964947i
$416$	−0.857651	−	3.20080i	−0.0420498	−	0.156932i
$417$	9.12132	−	15.7986i	0.446673	−	0.773660i
$418$	1.43488	−	0.828427i	0.0701822	−	0.0405197i
$419$	25.7990	+	25.7990i	1.26036	+	1.26036i	0.950917	+	0.309446i	$0.100144\pi$
$419$	25.7990	+	25.7990i	1.26036	+	1.26036i	0.309446	+	0.950917i	$0.399856\pi$
$420$	1.31178	+	9.58579i	0.0640085	+	0.467738i
$421$	15.4853	−	15.4853i	0.754706	−	0.754706i	−0.220647	−	0.975354i	$-0.570817\pi$
$421$	15.4853	−	15.4853i	0.754706	−	0.754706i	0.975354	+	0.220647i	$0.0708170\pi$
$422$	−16.2550	−	4.35552i	−0.791282	−	0.212023i
$423$	5.40629	+	3.12132i	0.262863	+	0.151764i
$424$	23.6510	−	6.33726i	1.14859	−	0.307764i
$425$	−1.68106	+	0.970563i	−0.0815436	+	0.0470792i
$426$	15.8995	+	15.8995i	0.770333	+	0.770333i
$427$	5.54927	+	13.2061i	0.268548	+	0.639089i
$428$	−22.7279	+	22.7279i	−1.09860	+	1.09860i
$429$	0.0628000	−	0.234373i	0.00303201	−	0.0113156i
$430$	8.38478	−	14.5229i	0.404350	−	0.700354i
$431$	−7.19239	+	12.4576i	−0.346445	+	0.600061i	−0.985615	−	0.169005i	$-0.945945\pi$
$431$	−7.19239	+	12.4576i	−0.346445	+	0.600061i	0.639170	+	0.769065i	$0.279278\pi$
$432$	−3.86370	−	1.03528i	−0.185893	−	0.0498097i
$433$	−16.9706			−0.815553			−0.407777	−	0.913082i	$-0.633696\pi$
$433$	−16.9706			−0.815553			−0.407777	+	0.913082i	$0.633696\pi$
$434$	5.53553	+	7.13834i	0.265714	+	0.342651i
$435$	3.43503	+	3.43503i	0.164697	+	0.164697i
$436$	−0.784076	+	2.92621i	−0.0375504	+	0.140140i
$437$	−6.03403	−	22.5193i	−0.288647	−	1.07724i
$438$	5.46410	−	1.46410i	0.261085	−	0.0699575i
$439$	22.9985	−	13.2782i	1.09766	−	0.633733i	0.162053	−	0.986782i	$-0.448189\pi$
$439$	22.9985	−	13.2782i	1.09766	−	0.633733i	0.935605	+	0.353049i	$0.114855\pi$
$440$	−2.14214			−0.102122
$441$	−1.88064	−	6.74264i	−0.0895542	−	0.321078i
$442$	0.686292	−	0.686292i	0.0326436	−	0.0326436i
$443$	−9.25916	−	2.48098i	−0.439916	−	0.117875i	0.0320612	−	0.999486i	$-0.489793\pi$
$443$	−9.25916	−	2.48098i	−0.439916	−	0.117875i	−0.471977	+	0.881611i	$0.656460\pi$
$444$	−2.82843	+	4.89898i	−0.134231	+	0.232495i
$445$	27.4745	−	7.36176i	1.30241	−	0.348981i
$446$	25.1763	−	14.5355i	1.19213	−	0.688277i
$447$	14.8284			0.701361
$448$	16.7262	−	12.9706i	0.790237	−	0.612801i
$449$	−10.2426			−0.483380			−0.241690	−	0.970354i	$-0.577702\pi$
$449$	−10.2426			−0.483380			−0.241690	+	0.970354i	$0.577702\pi$
$450$	−2.02922	+	1.17157i	−0.0956585	+	0.0552285i
$451$	0.234373	−	0.0628000i	0.0110362	−	0.00295714i
$452$	3.89949	−	6.75412i	0.183417	−	0.317687i
$453$	−9.25916	−	2.48098i	−0.435033	−	0.116567i
$454$	10.7574	−	10.7574i	0.504868	−	0.504868i
$455$	−2.62357	−	1.07107i	−0.122995	−	0.0502124i
$456$	8.00000			0.374634
$457$	18.7299	−	10.8137i	0.876147	−	0.505844i	0.00676121	−	0.999977i	$-0.497848\pi$
$457$	18.7299	−	10.8137i	0.876147	−	0.505844i	0.869386	+	0.494133i	$0.164514\pi$
$458$	−33.3102	+	8.92545i	−1.55648	+	0.417059i
$459$	−0.303225	−	1.13165i	−0.0141533	−	0.0528210i
$460$	−7.80136	+	29.1151i	−0.363740	+	1.35750i
$461$	8.00000	+	8.00000i	0.372597	+	0.372597i	0.868422	−	0.495825i	$-0.165134\pi$
$461$	8.00000	+	8.00000i	0.372597	+	0.372597i	−0.495825	+	0.868422i	$0.665134\pi$
$462$	1.53553	−	0.210133i	0.0714395	−	0.00977627i
$463$	−3.79899			−0.176554			−0.0882770	−	0.996096i	$-0.528136\pi$
$463$	−3.79899			−0.176554			−0.0882770	+	0.996096i	$0.528136\pi$
$464$	2.75058	−	10.2653i	0.127692	−	0.476554i
$465$	2.20711	−	3.82282i	0.102352	−	0.177279i
$466$	−3.65685	+	6.33386i	−0.169401	+	0.293410i
$467$	−2.62498	+	9.79655i	−0.121469	+	0.453330i	−0.999689	−	0.0249270i	$-0.992065\pi$
$467$	−2.62498	+	9.79655i	−0.121469	+	0.453330i	0.878220	+	0.478257i	$0.158731\pi$
$468$	0.828427	−	0.828427i	0.0382941	−	0.0382941i
$469$	21.3006	−	28.0547i	0.983571	−	1.29545i
$470$	11.4142	+	11.4142i	0.526498	+	0.526498i
$471$	−18.1610	+	10.4853i	−0.836817	+	0.483136i
$472$	5.65826	−	1.51613i	0.260443	−	0.0697854i
$473$	−2.32640	−	1.34315i	−0.106968	−	0.0617579i
$474$	−15.3577	−	4.11509i	−0.705404	−	0.189012i
$475$	3.31371	−	3.31371i	0.152043	−	0.152043i
$476$	5.73951	+	2.34315i	0.263070	+	0.107398i
$477$	6.12132	+	6.12132i	0.280276	+	0.280276i
$478$	13.5592	−	7.82843i	0.620185	−	0.358064i
$479$	7.58579	−	13.1390i	0.346603	−	0.600335i	−0.639040	−	0.769173i	$-0.720668\pi$
$479$	7.58579	−	13.1390i	0.346603	−	0.600335i	0.985644	+	0.168839i	$0.0540016\pi$
$480$	−8.95743	−	5.17157i	−0.408849	−	0.236049i
$481$	−0.828427	−	1.43488i	−0.0377730	−	0.0654248i
$482$			32.7279i			1.49072i
$483$	2.73615	−	21.6356i	0.124499	−	0.984456i
$484$		−	21.6569i		−	0.984402i
$485$	14.6830	+	3.93431i	0.666723	+	0.178648i
$486$	−0.366025	−	1.36603i	−0.0166032	−	0.0619642i
$487$	0.481813	+	0.278175i	0.0218330	+	0.0126053i	0.510877	−	0.859654i	$-0.329321\pi$
$487$	0.481813	+	0.278175i	0.0218330	+	0.0126053i	−0.489044	+	0.872259i	$0.662654\pi$
$488$	−14.7919	−	3.96348i	−0.669598	−	0.179418i
$489$		−	7.75736i		−	0.350800i
$490$	−0.184709	−	18.0996i	−0.00834429	−	0.817655i
$491$	15.9497	−	15.9497i	0.719802	−	0.719802i	−0.248762	−	0.968565i	$-0.580024\pi$
$491$	15.9497	−	15.9497i	0.719802	−	0.719802i	0.968565	+	0.248762i	$0.0800239\pi$
$492$	1.13165	+	0.303225i	0.0510188	+	0.0136705i
$493$	3.00664	−	0.805626i	0.135412	−	0.0362836i
$494$	−1.17157	+	2.02922i	−0.0527116	+	0.0912991i
$495$	−0.378680	−	0.655892i	−0.0170204	−	0.0294802i
$496$	−9.65685			−0.433606
$497$	−25.7782	−	33.2422i	−1.15631	−	1.49112i
$498$	−17.5563			−0.786719
$499$	1.06129	−	3.96078i	0.0475098	−	0.177309i	−0.938094	−	0.346381i	$-0.887410\pi$
$499$	1.06129	−	3.96078i	0.0475098	−	0.177309i	0.985604	+	0.169072i	$0.0540771\pi$
$500$	−23.5137	+	6.30047i	−1.05156	+	0.281766i
$501$	1.55291	+	5.79555i	0.0693791	+	0.258926i
$502$	−2.09656	+	7.82449i	−0.0935743	+	0.349224i
$503$		−	40.4853i		−	1.80515i	−0.430533	−	0.902575i	$-0.641674\pi$
$503$		−	40.4853i		−	1.80515i	0.430533	−	0.902575i	$-0.358326\pi$
$504$	6.92820	+	2.82843i	0.308607	+	0.125988i
$505$			14.0000i			0.622992i
$506$	4.66390	+	1.24969i	0.207336	+	0.0555554i
$507$	−3.27583	−	12.2256i	−0.145485	−	0.542957i
$508$	11.2426	−	19.4728i	0.498812	−	0.863967i
$509$	−0.650857	+	2.42903i	−0.0288487	+	0.107665i	−0.978849	−	0.204584i	$-0.934416\pi$
$509$	−0.650857	+	2.42903i	−0.0288487	+	0.107665i	0.950000	+	0.312249i	$0.101082\pi$
$510$		−	3.02944i		−	0.134146i
$511$	−10.4853	+	1.43488i	−0.463842	+	0.0634753i
$512$			22.6274i			1.00000i
$513$	1.41421	+	2.44949i	0.0624391	+	0.108148i
$514$	24.7921	+	14.3137i	1.09353	+	0.631351i
$515$	31.1842	−	8.35578i	1.37414	−	0.368200i
$516$	−6.48528	−	11.2328i	−0.285499	−	0.494498i
$517$	1.82843	−	1.82843i	0.0804141	−	0.0804141i
$518$	6.39960	−	8.42883i	0.281182	−	0.370341i
$519$		−	16.9706i		−	0.744925i
$520$	2.62357	−	1.51472i	0.115051	−	0.0664248i
$521$	−0.297173	−	0.171573i	−0.0130194	−	0.00751674i	0.493476	−	0.869759i	$-0.335726\pi$
$521$	−0.297173	−	0.171573i	−0.0130194	−	0.00751674i	−0.506496	+	0.862243i	$0.669059\pi$
$522$	3.62933	−	0.972476i	0.158851	−	0.0425641i
$523$	3.43517	+	0.920451i	0.150209	+	0.0402485i	0.333140	−	0.942877i	$-0.391892\pi$
$523$	3.43517	+	0.920451i	0.150209	+	0.0402485i	−0.182931	+	0.983126i	$0.558558\pi$
$524$	8.10051	+	8.10051i	0.353872	+	0.353872i
$525$	4.04133	−	1.69818i	0.176378	−	0.0741148i
$526$	2.14214			0.0934016
$527$	−1.41421	−	2.44949i	−0.0616041	−	0.106701i
$528$	−0.828427	+	1.43488i	−0.0360527	+	0.0624450i
$529$	22.4706	−	38.9202i	0.976981	−	1.69218i
$530$	11.1924	+	19.3858i	0.486166	+	0.842065i
$531$	1.46447	+	1.46447i	0.0635524	+	0.0635524i
$532$	−14.8484	−	1.87780i	−0.643758	−	0.0814129i
$533$	−0.242641	+	0.242641i	−0.0105099	+	0.0105099i
$534$	5.69402	−	21.2504i	0.246404	−	0.919593i
$535$	−25.4480	−	14.6924i	−1.10021	−	0.635207i
$536$	9.74631	+	36.3737i	0.420977	+	1.57111i
$537$	16.1318	−	9.31371i	0.696139	−	0.401916i
$538$	0.857864	−	0.857864i	0.0369852	−	0.0369852i
$539$	−2.89934	+	0.0295882i	−0.124884	+	0.00127446i
$540$		−	3.65685i		−	0.157366i
$541$	4.05229	−	15.1234i	0.174222	−	0.650204i	−0.822461	−	0.568821i	$-0.807400\pi$
$541$	4.05229	−	15.1234i	0.174222	−	0.650204i	0.996683	−	0.0813829i	$-0.0259337\pi$
$542$	−31.5101	−	18.1924i	−1.35348	−	0.781430i
$543$	−11.1213	+	19.2627i	−0.477262	+	0.826641i
$544$	−5.73951	+	3.31371i	−0.246080	+	0.142074i
$545$	−2.76955			−0.118635
$546$	−1.73205	+	1.34315i	−0.0741249	+	0.0574813i
$547$	−8.82843	−	8.82843i	−0.377476	−	0.377476i	0.492715	−	0.870191i	$-0.336005\pi$
$547$	−8.82843	−	8.82843i	−0.377476	−	0.377476i	−0.870191	+	0.492715i	$0.836005\pi$
$548$	−22.2195	+	12.8284i	−0.949169	+	0.548003i
$549$	−1.40130	−	5.22973i	−0.0598061	−	0.223199i
$550$	0.251200	+	0.937492i	0.0107112	+	0.0399748i
$551$	−6.50794	+	3.75736i	−0.277247	+	0.160069i
$552$	16.4853	+	16.4853i	0.701660	+	0.701660i
$553$	27.5387	+	11.2426i	1.17107	+	0.478086i
$554$	−10.3431	−	10.3431i	−0.439438	−	0.439438i
$555$	−4.99536	−	1.33850i	−0.212041	−	0.0568162i
$556$	−9.44309	−	35.2421i	−0.400476	−	1.49460i
$557$	−23.1538	+	6.20404i	−0.981057	+	0.262874i	−0.713490	−	0.700666i	$-0.752887\pi$
$557$	−23.1538	+	6.20404i	−0.981057	+	0.262874i	−0.267568	+	0.963539i	$0.586220\pi$
$558$	−1.70711	−	2.95680i	−0.0722676	−	0.125171i
$559$	3.79899			0.160680
$560$	15.4115	+	11.7012i	0.651254	+	0.494466i
$561$	−0.485281			−0.0204886
$562$	−3.41421	−	5.91359i	−0.144020	−	0.249450i
$563$	5.72691	−	1.53452i	0.241360	−	0.0646723i	−0.136111	−	0.990694i	$-0.543460\pi$
$563$	5.72691	−	1.53452i	0.241360	−	0.0646723i	0.377471	+	0.926021i	$0.376794\pi$
$564$	12.0599	−	3.23143i	0.507812	−	0.136068i
$565$	6.88700	+	1.84536i	0.289738	+	0.0776351i
$566$	23.4558	+	23.4558i	0.985923	+	0.985923i
$567$	0.358719	+	2.62132i	0.0150648	+	0.110085i
$568$	44.9706			1.88692
$569$	−1.01461	+	0.585786i	−0.0425347	+	0.0245574i	−0.521117	−	0.853486i	$-0.674484\pi$
$569$	−1.01461	+	0.585786i	−0.0425347	+	0.0245574i	0.478582	+	0.878043i	$0.341151\pi$
$570$	1.89293	+	7.06450i	0.0792860	+	0.295899i
$571$	10.8812	+	40.6091i	0.455363	+	1.69944i	0.687019	+	0.726640i	$0.258919\pi$
$571$	10.8812	+	40.6091i	0.455363	+	1.69944i	−0.231656	+	0.972798i	$0.574414\pi$
$572$	−0.242641	−	0.420266i	−0.0101453	−	0.0175722i
$573$	−13.6569	−	13.6569i	−0.570523	−	0.570523i
$574$	−2.02922	−	0.828427i	−0.0846982	−	0.0345779i
$575$	13.6569			0.569530
$576$	−6.92820	+	4.00000i	−0.288675	+	0.166667i
$577$	−18.7426	+	32.4632i	−0.780266	+	1.35146i	0.151520	+	0.988454i	$0.451583\pi$
$577$	−18.7426	+	32.4632i	−0.780266	+	1.35146i	−0.931786	+	0.363007i	$0.881750\pi$
$578$	19.1396	+	11.0503i	0.796102	+	0.459630i
$579$	1.81173	−	6.76148i	0.0752931	−	0.280998i
$580$	9.71573			0.403424
$581$	32.5854	+	4.12091i	1.35187	+	0.170964i
$582$	8.31371	−	8.31371i	0.344614	−	0.344614i
$583$	3.10538	−	1.79289i	0.128612	−	0.0742541i
$584$	5.65685	−	9.79796i	0.234082	−	0.405442i
$585$	0.927572	+	0.535534i	0.0383504	+	0.0221416i
$586$	−5.66801	+	21.1533i	−0.234143	+	0.873834i
$587$	7.12132	−	7.12132i	0.293928	−	0.293928i	−0.544702	−	0.838630i	$-0.683357\pi$
$587$	7.12132	−	7.12132i	0.293928	−	0.293928i	0.838630	+	0.544702i	$0.183357\pi$
$588$	−12.1952	−	6.87591i	−0.502920	−	0.283558i
$589$	4.82843	+	4.82843i	0.198952	+	0.198952i
$590$	2.67767	+	4.63786i	0.110238	+	0.190938i
$591$	2.24264	−	3.88437i	0.0922499	−	0.159782i
$592$	2.92820	+	10.9282i	0.120348	+	0.449146i
$593$	−9.70711	−	16.8132i	−0.398623	−	0.690435i	0.594933	−	0.803775i	$-0.297178\pi$
$593$	−9.70711	−	16.8132i	−0.398623	−	0.690435i	−0.993556	+	0.113340i	$0.963845\pi$
$594$	−0.585786			−0.0240351
$595$	−0.711085	+	5.62277i	−0.0291516	+	0.230511i
$596$	20.9706	−	20.9706i	0.858988	−	0.858988i
$597$	18.1869	+	4.87316i	0.744339	+	0.199445i
$598$	−6.59575	+	1.76733i	−0.269720	+	0.0722714i
$599$	−35.7787	−	20.6569i	−1.46188	−	0.844016i	−0.462781	−	0.886473i	$-0.653148\pi$
$599$	−35.7787	−	20.6569i	−1.46188	−	0.844016i	−0.999098	+	0.0424567i	$0.986482\pi$
$600$	−1.21290	+	4.52661i	−0.0495165	+	0.184798i
$601$		−	14.6569i		−	0.597866i	−0.954274	−	0.298933i	$-0.903369\pi$
$601$		−	14.6569i		−	0.597866i	0.954274	−	0.298933i	$-0.0966306\pi$
$602$	9.40035	+	22.3709i	0.383130	+	0.911770i
$603$	−9.41421	+	9.41421i	−0.383376	+	0.383376i
$604$	−16.6031	+	9.58579i	−0.675569	+	0.390040i
$605$	19.1244	−	5.12436i	0.777516	−	0.208335i
$606$	9.37769	+	5.41421i	0.380943	+	0.219937i
$607$	−15.0355	−	26.0423i	−0.610273	−	1.05702i	−0.991194	−	0.132417i	$-0.957726\pi$
$607$	−15.0355	−	26.0423i	−0.610273	−	1.05702i	0.380921	−	0.924608i	$-0.375607\pi$
$608$	11.3137	−	11.3137i	0.458831	−	0.458831i
$609$	−6.96447	+	0.953065i	−0.282214	+	0.0386202i
$610$		−	14.0000i		−	0.566843i
$611$	−0.946464	+	3.53225i	−0.0382898	+	0.142900i
$612$	−2.02922	−	1.17157i	−0.0820265	−	0.0473580i
$613$	5.32799	+	19.8843i	0.215196	+	0.803121i	0.986098	+	0.166167i	$0.0531392\pi$
$613$	5.32799	+	19.8843i	0.215196	+	0.803121i	−0.770902	+	0.636954i	$0.780194\pi$
$614$	12.1971	+	3.26822i	0.492237	+	0.131894i
$615$			1.07107i			0.0431896i
$616$	1.87440	−	2.46875i	0.0755217	−	0.0994686i
$617$			23.7574i			0.956435i	0.878241	+	0.478218i	$0.158717\pi$
$617$			23.7574i			0.956435i	−0.878241	+	0.478218i	$0.841283\pi$
$618$	6.46286	−	24.1197i	0.259974	−	0.970237i
$619$	−7.47212	−	27.8863i	−0.300330	−	1.12085i	−0.936891	−	0.349620i	$-0.886311\pi$
$619$	−7.47212	−	27.8863i	−0.300330	−	1.12085i	0.636562	−	0.771226i	$-0.280356\pi$
$620$	−2.28497	−	8.52761i	−0.0917664	−	0.342477i
$621$	−2.13335	+	7.96178i	−0.0856085	+	0.319495i
$622$	−16.3431			−0.655300
$623$	−15.5563	+	38.1051i	−0.623252	+	1.52665i
$624$		−	2.34315i		−	0.0938009i
$625$	−6.98528	−	12.0989i	−0.279411	−	0.483954i
$626$	−6.94975	+	12.0373i	−0.277768	+	0.481108i
$627$	1.13165	−	0.303225i	0.0451938	−	0.0121097i
$628$	−10.8552	+	40.5120i	−0.433168	+	1.61661i
$629$	−2.34315	+	2.34315i	−0.0934273	+	0.0934273i
$630$	−0.858355	+	6.78729i	−0.0341977	+	0.270412i
$631$		−	17.2426i		−	0.686419i	−0.939259	−	0.343209i	$-0.888486\pi$
$631$		−	17.2426i		−	0.686419i	0.939259	−	0.343209i	$-0.111514\pi$
$632$	−27.5387	+	15.8995i	−1.09543	+	0.632448i
$633$	−10.3053	−	5.94975i	−0.409598	−	0.236481i
$634$	4.15188	+	15.4950i	0.164892	+	0.615386i
$635$	19.8559	+	5.32037i	0.787958	+	0.211133i
$636$	17.3137			0.686533
$637$	3.53003	−	2.08638i	0.139865	−	0.0826655i
$638$		−	1.55635i		−	0.0616165i
$639$	7.94975	+	13.7694i	0.314487	+	0.544708i
$640$	−19.9814	+	5.35401i	−0.789835	+	0.211636i
$641$	−12.2635	+	21.2409i	−0.484377	+	0.838966i	−0.999839	−	0.0179465i	$-0.994287\pi$
$641$	−12.2635	+	21.2409i	−0.484377	+	0.838966i	0.515462	+	0.856913i	$0.327620\pi$
$642$	−19.6830	+	11.3640i	−0.776824	+	0.448500i
$643$	31.0711	+	31.0711i	1.22532	+	1.22532i	0.965714	+	0.259610i	$0.0835939\pi$
$643$	31.0711	+	31.0711i	1.22532	+	1.22532i	0.259610	+	0.965714i	$0.416406\pi$
$644$	−26.7279	−	34.4669i	−1.05323	−	1.35819i
$645$	8.38478	−	8.38478i	0.330150	−	0.330150i
$646$	4.52661	+	1.21290i	0.178097	+	0.0477210i
$647$	−7.43551	−	4.29289i	−0.292320	−	0.168771i	0.346668	−	0.937988i	$-0.387313\pi$
$647$	−7.43551	−	4.29289i	−0.292320	−	0.168771i	−0.638988	+	0.769217i	$0.720647\pi$
$648$	−2.44949	−	1.41421i	−0.0962250	−	0.0555556i
$649$	0.742932	−	0.428932i	0.0291626	−	0.0168371i
$650$	−0.970563	−	0.970563i	−0.0380686	−	0.0380686i
$651$	2.47443	+	5.88865i	0.0969807	+	0.230794i
$652$	−10.9706	−	10.9706i	−0.429640	−	0.429640i
$653$	0.133219	−	0.497180i	0.00521326	−	0.0194562i	−0.963270	−	0.268534i	$-0.913461\pi$
$653$	0.133219	−	0.497180i	0.00521326	−	0.0194562i	0.968483	+	0.249078i	$0.0801275\pi$
$654$	−1.07107	+	1.85514i	−0.0418821	+	0.0725419i
$655$	−5.23654	+	9.06996i	−0.204609	+	0.354393i
$656$	2.02922	−	1.17157i	0.0792279	−	0.0457422i
$657$	4.00000			0.156055
$658$	−23.1421	+	3.16693i	−0.902174	+	0.123460i
$659$	−18.5858	−	18.5858i	−0.723999	−	0.723999i	0.245418	−	0.969417i	$-0.421075\pi$
$659$	−18.5858	−	18.5858i	−0.723999	−	0.723999i	−0.969417	+	0.245418i	$0.921075\pi$
$660$	−1.46311	−	0.392038i	−0.0569513	−	0.0152601i
$661$	−3.01702	−	11.2597i	−0.117348	−	0.437950i	0.882104	−	0.471056i	$-0.156127\pi$
$661$	−3.01702	−	11.2597i	−0.117348	−	0.437950i	−0.999452	+	0.0331057i	$0.989460\pi$
$662$	−10.9282	+	2.92820i	−0.424737	+	0.113808i
$663$	0.594346	−	0.343146i	0.0230825	−	0.0133267i
$664$	−24.8284	+	24.8284i	−0.963530	+	0.963530i
$665$	−1.85514	−	13.5563i	−0.0719394	−	0.525693i
$666$	−2.82843	+	2.82843i	−0.109599	+	0.109599i
$667$	−21.1533	−	5.66801i	−0.819059	−	0.219466i
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$	19.8559	−	5.32037i	0.767674	−	0.205698i
$670$	−29.8141	+	17.2132i	−1.15182	+	0.665004i
$671$	−2.24264			−0.0865762
$672$	13.7980	−	5.79796i	0.532268	−	0.223661i
$673$	−30.9411			−1.19269			−0.596346	−	0.802727i	$-0.703382\pi$
$673$	−30.9411			−1.19269			−0.596346	+	0.802727i	$0.703382\pi$
$674$	−22.8499	+	13.1924i	−0.880145	+	0.508152i
$675$	−1.60040	+	0.428825i	−0.0615994	+	0.0165055i
$676$	−21.9223	−	12.6569i	−0.843166	−	0.486802i
$677$	−41.2034	−	11.0404i	−1.58357	−	0.424317i	−0.643544	−	0.765409i	$-0.722537\pi$
$677$	−41.2034	−	11.0404i	−1.58357	−	0.424317i	−0.940030	+	0.341092i	$0.889203\pi$
$678$	3.89949	−	3.89949i	0.149759	−	0.149759i
$679$	−17.3821	+	13.4792i	−0.667062	+	0.517284i
$680$	−4.28427	−	4.28427i	−0.164294	−	0.164294i
$681$	9.31615	−	5.37868i	0.356996	−	0.206111i
$682$	−1.36603	+	0.366025i	−0.0523078	+	0.0140158i
$683$	4.24831	+	15.8549i	0.162557	+	0.606671i	0.998339	+	0.0576100i	$0.0183480\pi$
$683$	4.24831	+	15.8549i	0.162557	+	0.606671i	−0.835782	+	0.549061i	$0.814985\pi$
$684$	5.46410	+	1.46410i	0.208925	+	0.0559813i
$685$	−16.5858	−	16.5858i	−0.633710	−	0.633710i
$686$	21.0208	+	15.6245i	0.802578	+	0.596547i
$687$	−24.3848			−0.930337
$688$	−25.0572	−	6.71406i	−0.955297	−	0.255971i
$689$	−2.53553	+	4.39167i	−0.0965961	+	0.167309i
$690$	−10.6569	+	18.4582i	−0.405700	+	0.702692i
$691$	−10.5412	+	39.3402i	−0.401005	+	1.49657i	0.410302	+	0.911950i	$0.365423\pi$
$691$	−10.5412	+	39.3402i	−0.401005	+	1.49657i	−0.811307	+	0.584620i	$0.801243\pi$
$692$	−24.0000	−	24.0000i	−0.912343	−	0.912343i
$693$	1.08725	+	0.137499i	0.0413011	+	0.00522314i
$694$	24.4853	+	24.4853i	0.929449	+	0.929449i
$695$	28.8866	−	16.6777i	1.09573	−	0.632620i
$696$	3.75736	−	6.50794i	0.142422	−	0.246683i
$697$	0.594346	+	0.343146i	0.0225125	+	0.0129976i
$698$	−6.59575	−	1.76733i	−0.249653	−	0.0668943i
$699$	−3.65685	+	3.65685i	−0.138315	+	0.138315i
$700$	3.31371	−	8.11689i	0.125246	−	0.306790i
$701$	−15.8787	−	15.8787i	−0.599729	−	0.599729i	0.340511	−	0.940241i	$-0.389400\pi$
$701$	−15.8787	−	15.8787i	−0.599729	−	0.599729i	−0.940241	+	0.340511i	$0.889400\pi$
$702$	0.717439	−	0.414214i	0.0270780	−	0.0156335i
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$	0.857651	+	3.20080i	0.0323239	+	0.120635i
$705$	5.70711	+	9.88500i	0.214942	+	0.372291i
$706$			27.3137i			1.02796i
$707$	−16.1346	−	12.2502i	−0.606803	−	0.460716i
$708$	4.14214			0.155671
$709$	−5.69847	−	1.52690i	−0.214011	−	0.0573440i	0.150221	−	0.988652i	$-0.452002\pi$
$709$	−5.69847	−	1.52690i	−0.214011	−	0.0573440i	−0.364231	+	0.931309i	$0.618668\pi$
$710$	10.6407	+	39.7118i	0.399340	+	1.49036i
$711$	−9.73641	−	5.62132i	−0.365144	−	0.210816i
$712$	−22.0000	−	38.1051i	−0.824485	−	1.42805i
$713$			19.8995i			0.745242i
$714$	3.49133	+	2.65080i	0.130660	+	0.0992038i
$715$	0.313708	−	0.313708i	0.0117320	−	0.0117320i
$716$	9.64226	−	35.9854i	0.360348	−	1.34484i
$717$	10.6938	−	2.86540i	0.399368	−	0.107010i
$718$	−2.58579	+	4.47871i	−0.0965007	+	0.167144i
$719$	10.4350	+	18.0740i	0.389161	+	0.674046i	0.992337	−	0.123562i	$-0.0394317\pi$
$719$	10.4350	+	18.0740i	0.389161	+	0.674046i	−0.603176	+	0.797608i	$0.706098\pi$
$720$	−5.17157	−	5.17157i	−0.192733	−	0.192733i
$721$	−17.6569	+	43.2503i	−0.657576	+	1.61072i
$722$	15.5563			0.578947
$723$	−5.98963	+	22.3536i	−0.222757	+	0.831339i
$724$	11.5136	+	42.9695i	0.427901	+	1.59695i
$725$	−1.13933	−	4.25203i	−0.0423135	−	0.157916i
$726$	3.96348	−	14.7919i	0.147099	−	0.548979i
$727$		−	16.5563i		−	0.614041i	−0.951703	−	0.307021i	$-0.900668\pi$
$727$		−	16.5563i		−	0.614041i	0.951703	−	0.307021i	$-0.0993320\pi$
$728$	−0.549995	+	4.34898i	−0.0203842	+	0.161184i
$729$		−	1.00000i		−	0.0370370i
$730$	9.99071	+	2.67700i	0.369773	+	0.0990803i
$731$	−1.96650	−	7.33908i	−0.0727337	−	0.271446i
$732$	−9.37769	−	5.41421i	−0.346610	−	0.200115i
$733$	10.8704	−	40.5689i	0.401507	−	1.49845i	−0.408900	−	0.912579i	$-0.634088\pi$
$733$	10.8704	−	40.5689i	0.401507	−	1.49845i	0.810407	−	0.585867i	$-0.199246\pi$
$734$			16.1005i			0.594280i
$735$	3.18629	−	12.3960i	0.117528	−	0.457235i
$736$	46.6274			1.71871
$737$	2.75736	+	4.77589i	0.101569	+	0.175922i
$738$	0.717439	+	0.414214i	0.0264093	+	0.0152474i
$739$	37.4083	−	10.0235i	1.37609	−	0.368721i	0.506389	−	0.862305i	$-0.330980\pi$
$739$	37.4083	−	10.0235i	1.37609	−	0.368721i	0.869698	+	0.493584i	$0.164314\pi$
$740$	−8.95743	+	5.17157i	−0.329282	+	0.190111i
$741$	−1.17157	+	1.17157i	−0.0430388	+	0.0430388i
$742$	−32.1350	−	4.06396i	−1.17971	−	0.149193i
$743$			17.3137i			0.635178i	0.948228	+	0.317589i	$0.102873\pi$
$743$			17.3137i			0.635178i	−0.948228	+	0.317589i	$0.897127\pi$
$744$	−6.59575	−	1.76733i	−0.241812	−	0.0647934i
$745$	23.4803	+	13.5563i	0.860251	+	0.496666i
$746$	−27.1832	+	7.28372i	−0.995248	+	0.266676i
$747$	−11.9912	−	3.21303i	−0.438735	−	0.117559i
$748$	−0.686292	+	0.686292i	−0.0250933	+	0.0250933i
$749$	39.1999	−	16.4719i	1.43233	−	0.601872i
$750$	−17.2132			−0.628537
$751$	−7.96447	−	13.7949i	−0.290627	−	0.503382i	0.683331	−	0.730109i	$-0.260531\pi$
$751$	−7.96447	−	13.7949i	−0.290627	−	0.503382i	−0.973958	+	0.226727i	$0.927197\pi$
$752$	12.4853	−	21.6251i	0.455291	−	0.788588i
$753$	−2.86396	+	4.96053i	−0.104369	+	0.180772i
$754$	1.10051	+	1.90613i	0.0400780	+	0.0694172i
$755$	−12.3934	−	12.3934i	−0.451042	−	0.451042i
$756$	4.21441	+	3.19980i	0.153277	+	0.116376i
$757$	−10.3137	+	10.3137i	−0.374858	+	0.374858i	−0.869243	−	0.494385i	$-0.835393\pi$
$757$	−10.3137	+	10.3137i	−0.374858	+	0.374858i	0.494385	+	0.869243i	$0.335393\pi$
$758$	−2.41057	+	8.99635i	−0.0875557	+	0.326762i
$759$	2.95680	+	1.70711i	0.107325	+	0.0619641i
$760$	12.6677	+	7.31371i	0.459506	+	0.265296i
$761$	20.5235	−	11.8492i	0.743976	−	0.429535i	−0.0795372	−	0.996832i	$-0.525344\pi$
$761$	20.5235	−	11.8492i	0.743976	−	0.429535i	0.823513	+	0.567297i	$0.192011\pi$
$762$	11.2426	−	11.2426i	0.407278	−	0.407278i
$763$	2.42340	−	3.19182i	0.0877329	−	0.115552i
$764$	−38.6274			−1.39749
$765$	0.554425	−	2.06914i	0.0200453	−	0.0748101i
$766$	35.6046	+	20.5563i	1.28645	+	0.742731i
$767$	−0.606602	+	1.05066i	−0.0219031	+	0.0379373i
$768$	−4.14110	+	15.4548i	−0.149429	+	0.557678i
$769$	19.8284			0.715031			0.357516	−	0.933907i	$-0.383624\pi$
$769$	19.8284			0.715031			0.357516	+	0.933907i	$0.383624\pi$
$770$	2.62357	+	1.07107i	0.0945469	+	0.0385986i
$771$	14.3137	+	14.3137i	0.515496	+	0.515496i
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	0.554425	+	2.06914i	0.0199413	+	0.0744219i	0.975179	−	0.221416i	$-0.0710678\pi$
$773$	0.554425	+	2.06914i	0.0199413	+	0.0744219i	−0.955238	+	0.295838i	$0.904401\pi$
$774$	−2.37378	−	8.85906i	−0.0853237	−	0.318432i
$775$	−3.46410	+	2.00000i	−0.124434	+	0.0718421i
$776$		−	23.5147i		−	0.844129i
$777$	5.91359	−	4.58579i	0.212149	−	0.164514i
$778$	3.79899	+	3.79899i	0.136200	+	0.136200i
$779$	−1.60040	−	0.428825i	−0.0573402	−	0.0153643i
$780$	2.06914	−	0.554425i	0.0740872	−	0.0198516i
$781$	6.36138	−	1.70453i	0.227628	−	0.0609928i
$782$	6.82843	+	11.8272i	0.244184	+	0.422939i
$783$	2.65685			0.0949482
$784$	−26.9706	+	7.52255i	−0.963234	+	0.268662i
$785$	−38.3431			−1.36853
$786$	4.05025	+	7.01524i	0.144468	+	0.250225i
$787$	−45.8790	+	12.2933i	−1.63541	+	0.438207i	−0.955477	−	0.295066i	$-0.904658\pi$
$787$	−45.8790	+	12.2933i	−1.63541	+	0.438207i	−0.679934	+	0.733273i	$0.737992\pi$
$788$	−2.32175	−	8.66490i	−0.0827090	−	0.308674i
$789$	1.46311	+	0.392038i	0.0520879	+	0.0139569i
$790$	−20.5563	−	20.5563i	−0.731362	−	0.731362i
$791$	−8.15295	+	6.32233i	−0.289885	+	0.224796i
$792$	−0.828427	+	0.828427i	−0.0294369	+	0.0294369i
$793$	2.74666	−	1.58579i	0.0975369	−	0.0563129i
$794$	12.0681	+	45.0386i	0.428280	+	1.59836i
$795$	4.09670	+	15.2891i	0.145295	+	0.542248i
$796$	32.6118	−	18.8284i	1.15589	−	0.667356i
$797$	30.2635	+	30.2635i	1.07199	+	1.07199i	0.997200	+	0.0747871i	$0.0238277\pi$
$797$	30.2635	+	30.2635i	1.07199	+	1.07199i	0.0747871	+	0.997200i	$0.476172\pi$
$798$	−9.79796	−	4.00000i	−0.346844	−	0.141598i
$799$	7.31371			0.258740
$800$	4.68629	+	8.11689i	0.165685	+	0.286976i
$801$	7.77817	−	13.4722i	0.274828	−	0.476017i
$802$	29.3939	+	16.9706i	1.03793	+	0.599251i
$803$	0.428825	−	1.60040i	0.0151329	−	0.0564768i
$804$			26.6274i			0.939077i
$805$	24.1122	−	31.7578i	0.849844	−	1.11932i
$806$	1.41421	−	1.41421i	0.0498135	−	0.0498135i
$807$	0.742932	−	0.428932i	0.0261525	−	0.0150991i
$808$	20.9189	−	5.60521i	0.735925	−	0.197190i
$809$	5.49333	+	3.17157i	0.193135	+	0.111507i	0.593449	−	0.804871i	$-0.297766\pi$
$809$	5.49333	+	3.17157i	0.193135	+	0.111507i	−0.400314	+	0.916378i	$0.631099\pi$
$810$	0.669251	−	2.49768i	0.0235151	−	0.0877595i
$811$	−15.5563	+	15.5563i	−0.546257	+	0.546257i	−0.925356	−	0.379099i	$-0.876234\pi$
$811$	−15.5563	+	15.5563i	−0.546257	+	0.546257i	0.379099	+	0.925356i	$0.376234\pi$
$812$	−8.50140	+	11.1971i	−0.298341	+	0.392940i
$813$	−18.1924	−	18.1924i	−0.638035	−	0.638035i
$814$	0.828427	+	1.43488i	0.0290364	+	0.0502924i
$815$	7.09188	−	12.2835i	0.248418	−	0.430272i
$816$	−4.52661	+	1.21290i	−0.158463	+	0.0424600i
$817$	9.17157	+	15.8856i	0.320873	+	0.555768i
$818$	30.1838			1.05535
$819$	−1.42883	+	0.600398i	−0.0499272	+	0.0209796i
$820$	1.51472	+	1.51472i	0.0528963	+	0.0528963i
$821$	4.82963	+	1.29410i	0.168555	+	0.0451642i	0.342110	−	0.939660i	$-0.388859\pi$
$821$	4.82963	+	1.29410i	0.168555	+	0.0451642i	−0.173554	+	0.984824i	$0.555525\pi$
$822$	−17.5240	+	4.69553i	−0.611218	+	0.163775i
$823$	−25.6836	−	14.8284i	−0.895274	−	0.516886i	−0.0196098	−	0.999808i	$-0.506242\pi$
$823$	−25.6836	−	14.8284i	−0.895274	−	0.516886i	−0.875664	+	0.482921i	$0.839576\pi$
$824$	−24.9706	−	43.2503i	−0.869891	−	1.50670i
$825$			0.686292i			0.0238936i
$826$	−7.68799	−	0.972263i	−0.267499	−	0.0338293i
$827$	−20.0503	+	20.0503i	−0.697216	+	0.697216i	−0.963809	−	0.266593i	$-0.914102\pi$
$827$	−20.0503	+	20.0503i	−0.697216	+	0.697216i	0.266593	+	0.963809i	$0.414102\pi$
$828$	8.24264	+	14.2767i	0.286452	+	0.496149i
$829$	−13.3857	+	3.58668i	−0.464904	+	0.124571i	−0.483664	−	0.875253i	$-0.660695\pi$
$829$	−13.3857	+	3.58668i	−0.464904	+	0.124571i	0.0187610	+	0.999824i	$0.494028\pi$
$830$	−27.7999	−	16.0503i	−0.964947	−	0.557112i
$831$	−5.17157	−	8.95743i	−0.179400	−	0.310730i
$832$	−3.31371	−	3.31371i	−0.114882	−	0.114882i
$833$	−5.85786	−	5.73951i	−0.202963	−	0.198862i
$834$		−	25.7990i		−	0.893346i
$835$	−2.83939	+	10.5967i	−0.0982612	+	0.366716i
$836$	1.17157	−	2.02922i	0.0405197	−	0.0701822i
$837$	−0.624844	−	2.33195i	−0.0215978	−	0.0806040i
$838$	49.8398	+	13.3545i	1.72169	+	0.461325i
$839$		−	19.7990i		−	0.683537i	−0.939784	−	0.341769i	$-0.888974\pi$
$839$		−	19.7990i		−	0.683537i	0.939784	−	0.341769i	$-0.111026\pi$
$840$	8.38478	+	10.8126i	0.289302	+	0.373069i
$841$		−	21.9411i		−	0.756591i
$842$	8.01577	−	29.9153i	0.276242	−	1.03095i
$843$	−1.24969	−	4.66390i	−0.0430416	−	0.160633i
$844$	−22.9881	+	6.15963i	−0.791282	+	0.212023i
$845$	5.98963	−	22.3536i	0.206049	−	0.768987i
$846$	8.82843			0.303528
$847$	−10.8284	+	26.5241i	−0.372069	+	0.911380i
$848$	24.4853	−	24.4853i	0.840828	−	0.840828i
$849$	11.7279	+	20.3134i	0.402501	+	0.697153i
$850$	−1.37258	+	2.37738i	−0.0470792	+	0.0815436i
$851$	22.5193	−	6.03403i	0.771952	−	0.206844i
$852$	30.7155	+	8.23018i	1.05229	+	0.281961i
$853$	−9.07107	+	9.07107i	−0.310587	+	0.310587i	−0.845137	−	0.534550i	$-0.820481\pi$
$853$	−9.07107	+	9.07107i	−0.310587	+	0.310587i	0.534550	+	0.845137i	$0.320481\pi$
$854$	16.1346	+	12.2502i	0.552114	+	0.419193i
$855$			5.17157i			0.176864i
$856$	−11.7648	+	43.9070i	−0.402114	+	1.50071i
$857$	14.0665	+	8.12132i	0.480504	+	0.277419i	0.720626	−	0.693324i	$-0.243854\pi$
$857$	14.0665	+	8.12132i	0.480504	+	0.277419i	−0.240123	+	0.970743i	$0.577188\pi$
$858$	−0.0888127	−	0.331453i	−0.00303201	−	0.0113156i
$859$	−7.20179	−	1.92971i	−0.245722	−	0.0658410i	0.133856	−	0.991001i	$-0.457264\pi$
$859$	−7.20179	−	1.92971i	−0.245722	−	0.0658410i	−0.379578	+	0.925160i	$0.623931\pi$
$860$		−	23.7157i		−	0.808700i
$861$	−1.23437	−	0.937200i	−0.0420673	−	0.0319397i
$862$			20.3431i			0.692890i
$863$	−0.192388	−	0.333226i	−0.00654897	−	0.0113431i	0.862732	−	0.505661i	$-0.168751\pi$
$863$	−0.192388	−	0.333226i	−0.00654897	−	0.0113431i	−0.869281	+	0.494318i	$0.835418\pi$
$864$	−5.46410	+	1.46410i	−0.185893	+	0.0498097i
$865$	15.5147	−	26.8723i	0.527516	−	0.913685i
$866$	−20.7846	+	12.0000i	−0.706290	+	0.407777i
$867$	11.0503	+	11.0503i	0.375286	+	0.375286i
$868$	11.8272	+	4.82843i	0.401441	+	0.163887i
$869$	−3.29289	+	3.29289i	−0.111704	+	0.111704i
$870$	6.63597	+	1.77810i	0.224980	+	0.0602833i
$871$	−6.75412	−	3.89949i	−0.228855	−	0.132129i
$872$	1.10885	+	4.13829i	0.0375504	+	0.140140i
$873$	7.19988	−	4.15685i	0.243679	−	0.140688i
$874$	−23.3137	−	23.3137i	−0.788598	−	0.788598i
$875$	31.9485	+	4.04037i	1.08006	+	0.136589i
$876$	5.65685	−	5.65685i	0.191127	−	0.191127i
$877$	3.17940	−	11.8657i	0.107361	−	0.400676i	−0.891241	−	0.453529i	$-0.850165\pi$
$877$	3.17940	−	11.8657i	0.107361	−	0.400676i	0.998602	+	0.0528530i	$0.0168315\pi$
$878$	18.7782	−	32.5248i	0.633733	−	1.09766i
$879$	−7.74264	+	13.4106i	−0.261153	+	0.452330i
$880$	−2.62357	+	1.51472i	−0.0884405	+	0.0510612i
$881$	50.4853			1.70089			0.850446	−	0.526062i	$-0.176332\pi$
$881$	50.4853			1.70089			0.850446	+	0.526062i	$0.176332\pi$
$882$	−7.07107	−	6.92820i	−0.238095	−	0.233285i
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	0.311007	−	0.950408i	$-0.399334\pi$
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	−0.950408	+	0.311007i	$0.899334\pi$
$884$	0.355251	−	1.32581i	0.0119484	−	0.0445919i
$885$	0.980095	+	3.65776i	0.0329455	+	0.122954i
$886$	−13.0944	+	3.50864i	−0.439916	+	0.117875i
$887$	5.10911	−	2.94975i	0.171547	−	0.0990428i	−0.411768	−	0.911289i	$-0.635089\pi$
$887$	5.10911	−	2.94975i	0.171547	−	0.0990428i	0.583315	+	0.812246i	$0.301755\pi$
$888$			8.00000i			0.268462i
$889$	−23.5058	+	18.2279i	−0.788359	+	0.611345i
$890$	28.4437	−	28.4437i	0.953433	−	0.953433i
$891$	−0.400100	−	0.107206i	−0.0134038	−	0.00359155i
$892$	20.5563	−	35.6046i	0.688277	−	1.19213i
$893$	−17.0552	+	4.56993i	−0.570731	+	0.152927i
$894$	18.1610	−	10.4853i	0.607396	−	0.350680i
$895$	34.0589			1.13846
$896$	11.3137	−	27.7128i	0.377964	−	0.925820i
$897$	−4.82843			−0.161216
$898$	−12.5446	+	7.24264i	−0.418619	+	0.241690i
$899$	6.19565	−	1.66012i	0.206637	−	0.0553681i
$900$	−1.65685	+	2.86976i	−0.0552285	+	0.0956585i
$901$	9.79655	+	2.62498i	0.326370	+	0.0874507i
$902$	0.242641	−	0.242641i	0.00807905	−	0.00807905i
$903$	2.32640	+	17.0000i	0.0774176	+	0.565725i
$904$		−	11.0294i		−	0.366834i
$905$	−35.2204	+	20.3345i	−1.17077	+	0.675942i
$906$	−13.0944	+	3.50864i	−0.435033	+	0.116567i
$907$	−5.11358	−	19.0841i	−0.169794	−	0.633679i	−0.997380	−	0.0723402i	$-0.976953\pi$
$907$	−5.11358	−	19.0841i	−0.169794	−	0.633679i	0.827586	−	0.561338i	$-0.189713\pi$
$908$	5.56842	−	20.7816i	0.184794	−	0.689662i
$909$	5.41421	+	5.41421i	0.179578	+	0.179578i
$910$	−3.97056	+	0.543359i	−0.131623	+	0.0180122i
$911$	−13.2721			−0.439724			−0.219862	−	0.975531i	$-0.570561\pi$
$911$	−13.2721			−0.439724			−0.219862	+	0.975531i	$0.570561\pi$
$912$	9.79796	−	5.65685i	0.324443	−	0.187317i
$913$	−2.57107	+	4.45322i	−0.0850899	+	0.147380i
$914$	15.2929	−	26.4881i	0.505844	−	0.876147i
$915$	2.56218	−	9.56218i	0.0847030	−	0.316116i
$916$	−34.4853	+	34.4853i	−1.13943	+	1.13943i
$917$	−5.87080	−	13.9713i	−0.193871	−	0.461373i
$918$	−1.17157	−	1.17157i	−0.0386677	−	0.0386677i
$919$	8.11689	−	4.68629i	0.267752	−	0.154586i	−0.360114	−	0.932908i	$-0.617262\pi$
$919$	8.11689	−	4.68629i	0.267752	−	0.154586i	0.627865	+	0.778322i	$0.283929\pi$
$920$	11.0328	+	41.1749i	0.363740	+	1.35750i
$921$	7.73268	+	4.46447i	0.254801	+	0.147109i
$922$	15.4548	+	4.14110i	0.508977	+	0.136380i
$923$	−6.58579	+	6.58579i	−0.216774	+	0.216774i
$924$	1.73205	−	1.34315i	0.0569803	−	0.0441863i
$925$	3.31371	+	3.31371i	0.108954	+	0.108954i
$926$	−4.65279	+	2.68629i	−0.152900	+	0.0882770i
$927$	8.82843	−	15.2913i	0.289964	−	0.502232i
$928$	−3.88990	−	14.5173i	−0.127692	−	0.476554i
$929$	−6.17157	−	10.6895i	−0.202483	−	0.350710i	0.746845	−	0.664998i	$-0.231568\pi$
$929$	−6.17157	−	10.6895i	−0.202483	−	0.350710i	−0.949328	+	0.314288i	$0.898234\pi$
$930$		−	6.24264i		−	0.204704i
$931$	17.2466	+	9.72401i	0.565233	+	0.318691i
$932$			10.3431i			0.338801i
$933$	−11.1626	−	2.99100i	−0.365446	−	0.0979211i
$934$	3.71228	+	13.8544i	0.121469	+	0.453330i
$935$	−0.768426	−	0.443651i	−0.0251302	−	0.0145089i
$936$	0.428825	−	1.60040i	0.0140166	−	0.0523107i
$937$		−	27.0000i		−	0.882052i	−0.897494	−	0.441026i	$-0.854615\pi$
$937$		−	27.0000i		−	0.882052i	0.897494	−	0.441026i	$-0.145385\pi$
$938$	6.25012	−	49.4217i	0.204074	−	1.61368i
$939$	−6.94975	+	6.94975i	−0.226796	+	0.226796i
$940$	22.0506	+	5.90843i	0.719210	+	0.192712i
$941$	34.2761	−	9.18427i	1.11737	−	0.299399i	0.347552	−	0.937661i	$-0.387013\pi$
$941$	34.2761	−	9.18427i	1.11737	−	0.299399i	0.769819	+	0.638262i	$0.220346\pi$
$942$	−14.8284	+	25.6836i	−0.483136	+	0.836817i
$943$	−2.41421	−	4.18154i	−0.0786176	−	0.136170i
$944$	5.85786	−	5.85786i	0.190657	−	0.190657i
$945$	−1.82843	+	4.47871i	−0.0594787	+	0.145693i
$946$	−3.79899			−0.123516
$947$	1.41208	−	5.26994i	0.0458863	−	0.171250i	−0.939180	−	0.343425i	$-0.888413\pi$
$947$	1.41208	−	5.26994i	0.0458863	−	0.171250i	0.985066	+	0.172175i	$0.0550795\pi$
$948$	−21.7191	+	5.81962i	−0.705404	+	0.189012i
$949$	0.606451	+	2.26330i	0.0196862	+	0.0734700i
$950$	1.71530	−	6.40159i	0.0556517	−	0.207695i
$951$			11.3431i			0.367827i
$952$	8.68629	−	1.18869i	0.281524	−	0.0385257i
$953$			55.2548i			1.78988i	0.446187	+	0.894940i	$0.352782\pi$
$953$			55.2548i			1.78988i	−0.446187	+	0.894940i	$0.647218\pi$
$954$	11.8255	+	3.16863i	0.382864	+	0.102588i
$955$	−9.13986	−	34.1104i	−0.295759	−	1.10379i
$956$	11.0711	−	19.1757i	0.358064	−	0.620185i
$957$	0.284832	−	1.06301i	0.00920730	−	0.0343621i
$958$		−	21.4558i		−	0.693207i
$959$	33.6274	−	4.60181i	1.08589	−	0.148600i
$960$	−14.6274			−0.472098
$961$	12.5858	+	21.7992i	0.405993	+	0.703201i
$962$	−2.02922	−	1.17157i	−0.0654248	−	0.0377730i
$963$	−15.5235	+	4.15950i	−0.500236	+	0.134038i
$964$	23.1421	+	40.0834i	0.745358	+	1.29100i
$965$	9.05025	−	9.05025i	0.291338	−	0.291338i
$966$	−11.9476	−	28.4329i	−0.384408	−	0.914814i
$967$			35.1838i			1.13143i	0.824600	+	0.565717i	$0.191400\pi$
$967$			35.1838i			1.13143i	−0.824600	+	0.565717i	$0.808600\pi$
$968$	−15.3137	−	26.5241i	−0.492201	−	0.852518i
$969$	2.86976	+	1.65685i	0.0921898	+	0.0532258i
$970$	20.7650	−	5.56396i	0.666723	−	0.178648i
$971$	13.9231	+	3.73067i	0.446812	+	0.119723i	0.475207	−	0.879874i	$-0.342373\pi$
$971$	13.9231	+	3.73067i	0.446812	+	0.119723i	−0.0283952	+	0.999597i	$0.509040\pi$
$972$	−1.41421	−	1.41421i	−0.0453609	−	0.0453609i
$973$	−6.05567	+	47.8841i	−0.194136	+	1.53509i
$974$	0.786797			0.0252106
$975$	−0.485281	−	0.840532i	−0.0155414	−	0.0269186i
$976$	−20.9189	+	5.60521i	−0.669598	+	0.179418i
$977$	16.6569	−	28.8505i	0.532900	−	0.923010i	−0.466362	−	0.884594i	$-0.654436\pi$
$977$	16.6569	−	28.8505i	0.532900	−	0.923010i	0.999262	−	0.0384158i	$-0.0122311\pi$
$978$	−5.48528	−	9.50079i	−0.175400	−	0.303802i
$979$	−4.55635	−	4.55635i	−0.145622	−	0.145622i
$980$	−13.0245	−	22.0367i	−0.416054	−	0.703938i
$981$	−1.07107	+	1.07107i	−0.0341966	+	0.0341966i
$982$	8.25620	−	30.8125i	0.263466	−	0.983268i
$983$	26.4881	+	15.2929i	0.844838	+	0.487768i	0.858906	−	0.512134i	$-0.171145\pi$
$983$	26.4881	+	15.2929i	0.844838	+	0.487768i	−0.0140677	+	0.999901i	$0.504478\pi$
$984$	1.60040	−	0.428825i	0.0510188	−	0.0136705i
$985$	7.10228	−	4.10051i	0.226298	−	0.130653i
$986$	3.11270	−	3.11270i	0.0991285	−	0.0991285i
$987$	−16.3860	−	2.07225i	−0.521571	−	0.0659605i
$988$			3.31371i			0.105423i
$989$	−13.8354	+	51.6344i	−0.439940	+	1.64188i
$990$	−0.927572	−	0.535534i	−0.0294802	−	0.0170204i
$991$	15.2782	−	26.4626i	0.485327	−	0.840611i	−0.514531	−	0.857472i	$-0.672034\pi$
$991$	15.2782	−	26.4626i	0.485327	−	0.840611i	0.999858	+	0.0168606i	$0.00536715\pi$
$992$	−11.8272	+	6.82843i	−0.375513	+	0.216803i
$993$	−8.00000			−0.253872
$994$	−55.0775	−	22.4853i	−1.74695	−	0.713190i
$995$	24.3431	+	24.3431i	0.771730	+	0.771730i
$996$	−21.5020	+	12.4142i	−0.681318	+	0.393359i
$997$	−7.71255	−	28.7836i	−0.244259	−	0.911586i	−0.973755	−	0.227601i	$-0.926912\pi$
$997$	−7.71255	−	28.7836i	−0.244259	−	0.911586i	0.729496	−	0.683985i	$-0.239755\pi$
$998$	−1.50089	−	5.60139i	−0.0475098	−	0.177309i
$999$	−2.44949	+	1.41421i	−0.0774984	+	0.0447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.a.109.2	yes	8
7.2	even	3	inner	336.2.bq.a.205.1	yes	8
16.5	even	4	inner	336.2.bq.a.277.1	yes	8
112.37	even	12	inner	336.2.bq.a.37.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.a.37.2	✓	8	112.37	even	12	inner
336.2.bq.a.109.2	yes	8	1.1	even	1	trivial
336.2.bq.a.205.1	yes	8	7.2	even	3	inner
336.2.bq.a.277.1	yes	8	16.5	even	4	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.76612 + 0.473232i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.76612 + 0.473232i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(0.866025 - 0.500000i) q^{9} +(2.49768 - 0.669251i) q^{10} +(-0.107206 - 0.400100i) q^{11} +(0.517638 - 1.93185i) q^{12} +(0.414214 + 0.414214i) q^{13} +(-1.41421 + 3.46410i) q^{14} +1.82843 q^{15} +(-2.00000 - 3.46410i) q^{16} +(0.585786 - 1.01461i) q^{17} +(0.707107 - 1.22474i) q^{18} +(-0.732051 + 2.73205i) q^{19} +(2.58579 - 2.58579i) q^{20} +(-1.59990 + 2.10721i) q^{21} +(-0.414214 - 0.414214i) q^{22} +(-7.13834 + 4.12132i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(-1.43488 - 0.828427i) q^{25} +(0.800199 + 0.214413i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.717439 + 5.24264i) q^{28} +(1.87868 + 1.87868i) q^{29} +(2.23936 - 1.29289i) q^{30} +(1.20711 - 2.09077i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-0.207107 - 0.358719i) q^{33} -1.65685i q^{34} +(-4.45982 + 1.87404i) q^{35} -2.00000i q^{36} +(-2.73205 - 0.732051i) q^{37} +(1.03528 + 3.86370i) q^{38} +(0.507306 + 0.292893i) q^{39} +(1.33850 - 4.99536i) q^{40} +0.585786i q^{41} +(-0.469450 + 3.71209i) q^{42} +(4.58579 - 4.58579i) q^{43} +(-0.800199 - 0.214413i) q^{44} +(1.76612 - 0.473232i) q^{45} +(-5.82843 + 10.0951i) q^{46} +(3.12132 + 5.40629i) q^{47} +(-2.82843 - 2.82843i) q^{48} +(1.74264 - 6.77962i) q^{49} -2.34315 q^{50} +(0.303225 - 1.13165i) q^{51} +(1.13165 - 0.303225i) q^{52} +(2.24056 + 8.36188i) q^{53} +(0.366025 - 1.36603i) q^{54} -0.757359i q^{55} +(4.58579 + 5.91359i) q^{56} +2.82843i q^{57} +(3.62933 + 0.972476i) q^{58} +(0.536032 + 2.00050i) q^{59} +(1.82843 - 3.16693i) q^{60} +(1.40130 - 5.22973i) q^{61} -3.41421i q^{62} +(-1.00000 + 2.44949i) q^{63} -8.00000 q^{64} +(0.535534 + 0.927572i) q^{65} +(-0.507306 - 0.292893i) q^{66} +(-12.8601 + 3.44584i) q^{67} +(-1.17157 - 2.02922i) q^{68} +(-5.82843 + 5.82843i) q^{69} +(-4.13700 + 5.44879i) q^{70} +15.8995i q^{71} +(-1.41421 - 2.44949i) q^{72} +(3.46410 + 2.00000i) q^{73} +(-3.86370 + 1.03528i) q^{74} +(-1.60040 - 0.428825i) q^{75} +(4.00000 + 4.00000i) q^{76} +(0.872833 + 0.662700i) q^{77} +0.828427 q^{78} +(-5.62132 - 9.73641i) q^{79} +(-1.89293 - 7.06450i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.414214 + 0.717439i) q^{82} +(-8.77817 - 8.77817i) q^{83} +(2.04989 + 4.87832i) q^{84} +(1.51472 - 1.51472i) q^{85} +(2.37378 - 8.85906i) q^{86} +(2.30090 + 1.32843i) q^{87} +(-1.13165 + 0.303225i) q^{88} +(13.4722 - 7.77817i) q^{89} +(1.82843 - 1.82843i) q^{90} +(-1.53760 - 0.194453i) q^{91} +16.4853i q^{92} +(0.624844 - 2.33195i) q^{93} +(7.64564 + 4.41421i) q^{94} +(-2.58579 + 4.47871i) q^{95} +(-5.46410 - 1.46410i) q^{96} +8.31371 q^{97} +(-2.65962 - 9.53553i) q^{98} +(-0.292893 - 0.292893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6	\( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 8 * q^13 - 8 * q^15 - 16 * q^16 + 16 * q^17 + 8 * q^19 + 32 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 8 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^33 - 16 * q^35 - 8 * q^37 + 8 * q^40 - 4 * q^42 + 48 * q^43 - 8 * q^44 + 8 * q^45 - 24 * q^46 + 8 * q^47 - 20 * q^49 - 64 * q^50 + 8 * q^51 - 8 * q^52 - 16 * q^53 - 4 * q^54 + 48 * q^56 - 12 * q^58 - 20 * q^59 - 8 * q^60 - 4 * q^61 - 8 * q^63 - 64 * q^64 - 24 * q^65 - 32 * q^67 - 32 * q^68 - 24 * q^69 - 44 * q^70 - 16 * q^75 + 32 * q^76 - 8 * q^77 - 16 * q^78 - 28 * q^79 + 32 * q^80 + 4 * q^81 - 8 * q^82 - 8 * q^83 + 80 * q^85 + 8 * q^86 + 8 * q^88 - 8 * q^90 - 28 * q^91 - 4 * q^93 - 32 * q^95 - 16 * q^96 - 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more