LMFDB - Embedded newform 336.2.bq.a.277.1

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			277.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	336.277
Dual form			336.2.bq.a.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.473232 + 1.76612i) q^{5} +(1.00000 + 1.00000i) q^{6} +(2.09077 - 1.62132i) q^{7} +2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.473232 + 1.76612i) q^{5} +(1.00000 + 1.00000i) q^{6} +(2.09077 - 1.62132i) q^{7} +2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.669251 - 2.49768i) q^{10} +(0.400100 - 0.107206i) q^{11} +(-1.93185 - 0.517638i) 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} +(2.73205 + 0.732051i) q^{19} +(2.58579 + 2.58579i) q^{20} +(-2.10721 - 1.59990i) q^{21} +(-0.414214 + 0.414214i) q^{22} +(7.13834 - 4.12132i) q^{23} +(2.73205 - 0.732051i) q^{24} +(1.43488 + 0.828427i) q^{25} +(-0.214413 + 0.800199i) 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} +(1.87404 + 4.45982i) q^{35} +2.00000i q^{36} +(0.732051 - 2.73205i) q^{37} +(-3.86370 + 1.03528i) q^{38} +(-0.507306 - 0.292893i) q^{39} +(-4.99536 - 1.33850i) q^{40} -0.585786i q^{41} +(3.71209 + 0.469450i) q^{42} +(4.58579 + 4.58579i) q^{43} +(0.214413 - 0.800199i) q^{44} +(-0.473232 - 1.76612i) 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} +(-1.13165 - 0.303225i) q^{51} +(-0.303225 - 1.13165i) q^{52} +(-8.36188 + 2.24056i) q^{53} +(-1.36603 - 0.366025i) q^{54} +0.757359i q^{55} +(4.58579 + 5.91359i) q^{56} -2.82843i q^{57} +(-0.972476 + 3.62933i) q^{58} +(-2.00050 + 0.536032i) q^{59} +(1.82843 - 3.16693i) q^{60} +(-5.22973 - 1.40130i) 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} +(3.44584 + 12.8601i) q^{67} +(-1.17157 - 2.02922i) q^{68} +(-5.82843 - 5.82843i) q^{69} +(-5.44879 - 4.13700i) q^{70} -15.8995i q^{71} +(-1.41421 - 2.44949i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(1.03528 + 3.86370i) q^{74} +(0.428825 - 1.60040i) q^{75} +(4.00000 - 4.00000i) q^{76} +(0.662700 - 0.872833i) q^{77} +0.828427 q^{78} +(-5.62132 - 9.73641i) q^{79} +(7.06450 - 1.89293i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.414214 + 0.717439i) q^{82} +(-8.77817 + 8.77817i) q^{83} +(-4.87832 + 2.04989i) q^{84} +(1.51472 + 1.51472i) q^{85} +(-8.85906 - 2.37378i) q^{86} +(-2.30090 - 1.32843i) q^{87} +(0.303225 + 1.13165i) q^{88} +(-13.4722 + 7.77817i) q^{89} +(1.82843 + 1.82843i) q^{90} +(0.194453 - 1.53760i) q^{91} -16.4853i q^{92} +(-2.33195 - 0.624844i) q^{93} +(-7.64564 - 4.41421i) q^{94} +(-2.58579 + 4.47871i) q^{95} +(1.46410 - 5.46410i) 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−0.473232	+	1.76612i	−0.211636	+	0.789835i	0.775688	+	0.631116i	$0.217403\pi$
$5$	−0.473232	+	1.76612i	−0.211636	+	0.789835i	−0.987324	+	0.158719i	$0.949264\pi$
$6$	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
$10$	−0.669251	−	2.49768i	−0.211636	−	0.789835i
$11$	0.400100	−	0.107206i	0.120635	−	0.0323239i	−0.197997	−	0.980203i	$-0.563444\pi$
$11$	0.400100	−	0.107206i	0.120635	−	0.0323239i	0.318631	+	0.947879i	$0.396777\pi$
$12$	−1.93185	−	0.517638i	−0.557678	−	0.149429i
$13$	0.414214	−	0.414214i	0.114882	−	0.114882i	−0.647329	−	0.762211i	$-0.724114\pi$
$13$	0.414214	−	0.414214i	0.114882	−	0.114882i	0.762211	+	0.647329i	$0.224114\pi$
$14$	−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
$19$	2.73205	+	0.732051i	0.626775	+	0.167944i	0.558206	−	0.829702i	$-0.311490\pi$
$19$	2.73205	+	0.732051i	0.626775	+	0.167944i	0.0685694	+	0.997646i	$0.478157\pi$
$20$	2.58579	+	2.58579i	0.578199	+	0.578199i
$21$	−2.10721	−	1.59990i	−0.459830	−	0.349127i
$22$	−0.414214	+	0.414214i	−0.0883106	+	0.0883106i
$23$	7.13834	−	4.12132i	1.48845	−	0.859355i	0.488533	−	0.872545i	$-0.337532\pi$
$23$	7.13834	−	4.12132i	1.48845	−	0.859355i	0.999913	+	0.0131907i	$0.00419886\pi$
$24$	2.73205	−	0.732051i	0.557678	−	0.149429i
$25$	1.43488	+	0.828427i	0.286976	+	0.165685i
$26$	−0.214413	+	0.800199i	−0.0420498	+	0.156932i
$27$	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	−0.510824	−	0.859686i	$-0.670659\pi$
$29$	1.87868	−	1.87868i	0.348862	−	0.348862i	0.859686	+	0.510824i	$0.170659\pi$
$30$	−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
$35$	1.87404	+	4.45982i	0.316770	+	0.753847i
$36$			2.00000i			0.333333i
$37$	0.732051	−	2.73205i	0.120348	−	0.449146i	−0.879283	−	0.476300i	$-0.841978\pi$
$37$	0.732051	−	2.73205i	0.120348	−	0.449146i	0.999631	+	0.0271536i	$0.00864431\pi$
$38$	−3.86370	+	1.03528i	−0.626775	+	0.167944i
$39$	−0.507306	−	0.292893i	−0.0812340	−	0.0469005i
$40$	−4.99536	−	1.33850i	−0.789835	−	0.211636i
$41$		−	0.585786i		−	0.0914845i	−0.998953	−	0.0457422i	$-0.985435\pi$
$41$		−	0.585786i		−	0.0914845i	0.998953	−	0.0457422i	$-0.0145653\pi$
$42$	3.71209	+	0.469450i	0.572788	+	0.0724377i
$43$	4.58579	+	4.58579i	0.699326	+	0.699326i	0.964265	−	0.264939i	$-0.0853519\pi$
$43$	4.58579	+	4.58579i	0.699326	+	0.699326i	−0.264939	+	0.964265i	$0.585352\pi$
$44$	0.214413	−	0.800199i	0.0323239	−	0.120635i
$45$	−0.473232	−	1.76612i	−0.0705452	−	0.263278i
$46$	−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
$51$	−1.13165	−	0.303225i	−0.158463	−	0.0424600i
$52$	−0.303225	−	1.13165i	−0.0420498	−	0.156932i
$53$	−8.36188	+	2.24056i	−1.14859	+	0.307764i	−0.782401	−	0.622775i	$-0.786005\pi$
$53$	−8.36188	+	2.24056i	−1.14859	+	0.307764i	−0.366192	+	0.930540i	$0.619338\pi$
$54$	−1.36603	−	0.366025i	−0.185893	−	0.0498097i
$55$			0.757359i			0.102122i
$56$	4.58579	+	5.91359i	0.612801	+	0.790237i
$57$		−	2.82843i		−	0.374634i
$58$	−0.972476	+	3.62933i	−0.127692	+	0.476554i
$59$	−2.00050	+	0.536032i	−0.260443	+	0.0697854i	−0.386678	−	0.922215i	$-0.626377\pi$
$59$	−2.00050	+	0.536032i	−0.260443	+	0.0697854i	0.126235	+	0.992000i	$0.459711\pi$
$60$	1.82843	−	3.16693i	0.236049	−	0.408849i
$61$	−5.22973	−	1.40130i	−0.669598	−	0.179418i	−0.0920243	−	0.995757i	$-0.529334\pi$
$61$	−5.22973	−	1.40130i	−0.669598	−	0.179418i	−0.577574	+	0.816338i	$0.696000\pi$
$62$			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
$67$	3.44584	+	12.8601i	0.420977	+	1.57111i	0.772555	+	0.634947i	$0.218978\pi$
$67$	3.44584	+	12.8601i	0.420977	+	1.57111i	−0.351579	+	0.936158i	$0.614355\pi$
$68$	−1.17157	−	2.02922i	−0.142074	−	0.246080i
$69$	−5.82843	−	5.82843i	−0.701660	−	0.701660i
$70$	−5.44879	−	4.13700i	−0.651254	−	0.494466i
$71$		−	15.8995i		−	1.88692i	−0.331482	−	0.943461i	$-0.607549\pi$
$71$		−	15.8995i		−	1.88692i	0.331482	−	0.943461i	$-0.392451\pi$
$72$	−1.41421	−	2.44949i	−0.166667	−	0.288675i
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$	1.03528	+	3.86370i	0.120348	+	0.449146i
$75$	0.428825	−	1.60040i	0.0495165	−	0.184798i
$76$	4.00000	−	4.00000i	0.458831	−	0.458831i
$77$	0.662700	−	0.872833i	0.0755217	−	0.0994686i
$78$	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	$-0.384616\pi$
$80$	7.06450	−	1.89293i	0.789835	−	0.211636i
$81$	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	−0.999358	−	0.0358281i	$-0.988593\pi$
$83$	−8.77817	+	8.77817i	−0.963530	+	0.963530i	0.0358281	+	0.999358i	$0.488593\pi$
$84$	−4.87832	+	2.04989i	−0.532268	+	0.223661i
$85$	1.51472	+	1.51472i	0.164294	+	0.164294i
$86$	−8.85906	−	2.37378i	−0.955297	−	0.255971i
$87$	−2.30090	−	1.32843i	−0.246683	−	0.142422i
$88$	0.303225	+	1.13165i	0.0323239	+	0.120635i
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.996967	−	0.0778275i	$-0.975202\pi$
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.431083	+	0.902312i	$0.641868\pi$
$90$	1.82843	+	1.82843i	0.192733	+	0.192733i
$91$	0.194453	−	1.53760i	0.0203842	−	0.161184i
$92$		−	16.4853i		−	1.71871i
$93$	−2.33195	−	0.624844i	−0.241812	−	0.0647934i
$94$	−7.64564	−	4.41421i	−0.788588	−	0.455291i
$95$	−2.58579	+	4.47871i	−0.265296	+	0.459506i
$96$	1.46410	−	5.46410i	0.149429	−	0.557678i
$97$	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
$101$	−7.39595	+	1.98174i	−0.735925	+	0.197190i	−0.607266	−	0.794498i	$-0.707734\pi$
$101$	−7.39595	+	1.98174i	−0.735925	+	0.197190i	−0.128659	+	0.991689i	$0.541067\pi$
$102$	1.60040	−	0.428825i	0.158463	−	0.0424600i
$103$	−15.2913	+	8.82843i	−1.50670	+	0.869891i	−0.506725	+	0.862108i	$0.669144\pi$
$103$	−15.2913	+	8.82843i	−1.50670	+	0.869891i	−0.999970	+	0.00778320i	$0.997523\pi$
$104$	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
$107$	4.15950	−	15.5235i	0.402114	−	1.50071i	−0.407203	−	0.913338i	$-0.633496\pi$
$107$	4.15950	−	15.5235i	0.402114	−	1.50071i	0.809317	−	0.587372i	$-0.199837\pi$
$108$	1.93185	−	0.517638i	0.185893	−	0.0498097i
$109$	0.392038	+	1.46311i	0.0375504	+	0.140140i	0.982156	−	0.188067i	$-0.0602222\pi$
$109$	0.392038	+	1.46311i	0.0375504	+	0.140140i	−0.944606	+	0.328207i	$0.893556\pi$
$110$	−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
$115$	3.90068	+	14.5575i	0.363740	+	1.35750i
$116$	−1.37529	−	5.13265i	−0.127692	−	0.476554i
$117$	−0.151613	+	0.565826i	−0.0140166	+	0.0523107i
$118$	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
$122$	7.39595	−	1.98174i	0.669598	−	0.179418i
$123$	−0.565826	+	0.151613i	−0.0510188	+	0.0136705i
$124$	−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
$131$	5.53275	+	1.48250i	0.483398	+	0.129526i	0.492285	−	0.870434i	$-0.336162\pi$
$131$	5.53275	+	1.48250i	0.483398	+	0.129526i	−0.00888618	+	0.999961i	$0.502829\pi$
$132$	−0.828427			−0.0721053
$133$	6.89898	−	2.89898i	0.598217	−	0.251373i
$134$	−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	0.892823	−	0.450408i	$-0.148721\pi$
$137$	11.1097	+	6.41421i	0.949169	+	0.548003i	0.0563466	+	0.998411i	$0.482055\pi$
$138$	11.2597	+	3.01702i	0.958486	+	0.256825i
$139$	12.8995	+	12.8995i	1.09412	+	1.09412i	0.995084	+	0.0990371i	$0.0315763\pi$
$139$	12.8995	+	12.8995i	1.09412	+	1.09412i	0.0990371	+	0.995084i	$0.468424\pi$
$140$	9.59867	+	1.21390i	0.811236	+	0.102593i
$141$	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
$147$	−6.99964	+	0.0714323i	−0.577320	+	0.00589164i
$148$	−4.00000	−	4.00000i	−0.328798	−	0.328798i
$149$	−3.83788	+	14.3232i	−0.314411	+	1.17340i	0.610125	+	0.792305i	$0.291119\pi$
$149$	−3.83788	+	14.3232i	−0.314411	+	1.17340i	−0.924536	+	0.381094i	$0.875547\pi$
$150$	0.606451	+	2.26330i	0.0495165	+	0.184798i
$151$	8.30153	+	4.79289i	0.675569	+	0.390040i	0.798184	−	0.602414i	$-0.205794\pi$
$151$	8.30153	+	4.79289i	0.675569	+	0.390040i	−0.122614	+	0.992454i	$0.539128\pi$
$152$	−2.07055	+	7.72741i	−0.167944	+	0.626775i
$153$			1.17157i			0.0947161i
$154$	−0.194453	+	1.53760i	−0.0156694	+	0.123903i
$155$	3.12132	+	3.12132i	0.250710	+	0.250710i
$156$	−1.01461	+	0.585786i	−0.0812340	+	0.0469005i
$157$	5.42758	+	20.2560i	0.433168	+	1.61661i	0.745412	+	0.666604i	$0.232253\pi$
$157$	5.42758	+	20.2560i	0.433168	+	1.61661i	−0.312244	+	0.950002i	$0.601081\pi$
$158$	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
$163$	−7.49303	−	2.00775i	−0.586900	−	0.157259i	−0.0468638	−	0.998901i	$-0.514923\pi$
$163$	−7.49303	−	2.00775i	−0.586900	−	0.157259i	−0.540036	+	0.841642i	$0.681589\pi$
$164$	−1.01461	−	0.585786i	−0.0792279	−	0.0457422i
$165$	0.731553	−	0.196019i	0.0569513	−	0.0152601i
$166$	4.54392	−	16.9581i	0.352676	−	1.31621i
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$	4.52520	−	5.96008i	0.349127	−	0.459830i
$169$			12.6569i			0.973604i
$170$	−2.92621	−	0.784076i	−0.224430	−	0.0601359i
$171$	−2.73205	+	0.732051i	−0.208925	+	0.0559813i
$172$	12.5286	−	3.35703i	0.955297	−	0.255971i
$173$	−16.3923	−	4.39230i	−1.24628	−	0.333941i	−0.425384	−	0.905013i	$-0.639861\pi$
$173$	−16.3923	−	4.39230i	−1.24628	−	0.333941i	−0.820900	+	0.571072i	$0.806528\pi$
$174$	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
$179$	−4.82113	−	17.9927i	−0.360348	−	1.34484i	−0.873619	−	0.486611i	$-0.838233\pi$
$179$	−4.82113	−	17.9927i	−0.360348	−	1.34484i	0.513271	−	0.858227i	$-0.328434\pi$
$180$	−3.53225	−	0.946464i	−0.263278	−	0.0705452i
$181$	−15.7279	−	15.7279i	−1.16905	−	1.16905i	−0.982433	−	0.186614i	$-0.940249\pi$
$181$	−15.7279	−	15.7279i	−1.16905	−	1.16905i	−0.186614	−	0.982433i	$-0.559751\pi$
$182$	0.849091	+	2.02066i	0.0629388	+	0.149782i
$183$			5.41421i			0.400230i
$184$	11.6569	+	20.1903i	0.859355	+	1.48845i
$185$	4.47871	+	2.58579i	0.329282	+	0.190111i
$186$	3.29788	−	0.883663i	0.241812	−	0.0647934i
$187$	0.125600	−	0.468746i	0.00918479	−	0.0342781i
$188$	12.4853			0.910583
$189$	2.62484	+	0.331951i	0.190929	+	0.0241459i
$190$		−	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	$-0.412925\pi$
$192$	2.07055	+	7.72741i	0.149429	+	0.557678i
$193$	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	0.811005	−	0.585040i	$-0.198921\pi$
$197$	3.17157	+	3.17157i	0.225965	+	0.225965i	−0.585040	+	0.811005i	$0.698921\pi$
$198$	0.151613	−	0.565826i	0.0107746	−	0.0402115i
$199$	−16.3059	−	9.41421i	−1.15589	−	0.667356i	−0.205578	−	0.978641i	$-0.565907\pi$
$199$	−16.3059	−	9.41421i	−1.15589	−	0.667356i	−0.950317	+	0.311285i	$0.899241\pi$
$200$	−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
$203$	0.881946	−	6.97383i	0.0619005	−	0.489467i
$204$	−1.65685	+	1.65685i	−0.116003	+	0.116003i
$205$	1.03457	+	0.277213i	0.0722576	+	0.0193614i
$206$	12.4853	−	21.6251i	0.869891	−	1.50670i
$207$	−4.12132	+	7.13834i	−0.286452	+	0.496149i
$208$	−2.26330	−	0.606451i	−0.156932	−	0.0420498i
$209$	1.17157			0.0810394
$210$	−2.58579	+	6.33386i	−0.178436	+	0.437078i
$211$	−8.41421	+	8.41421i	−0.579258	+	0.579258i	−0.934699	−	0.355441i	$-0.884331\pi$
$211$	−8.41421	+	8.41421i	−0.579258	+	0.579258i	0.355441	+	0.934699i	$0.384331\pi$
$212$	−4.48112	+	16.7238i	−0.307764	+	1.14859i
$213$	−15.3577	+	4.11509i	−1.05229	+	0.281961i
$214$	5.88242	+	21.9535i	0.402114	+	1.50071i
$215$	−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
$219$	−1.03528	+	3.86370i	−0.0699575	+	0.261085i
$220$	1.31178	+	0.757359i	0.0884405	+	0.0510612i
$221$	−0.177625	−	0.662907i	−0.0119484	−	0.0445919i
$222$	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
$227$	−2.78421	−	10.3908i	−0.184794	−	0.689662i	−0.994674	−	0.103067i	$-0.967134\pi$
$227$	−2.78421	−	10.3908i	−0.184794	−	0.689662i	0.809880	−	0.586596i	$-0.199532\pi$
$228$	−4.89898	−	2.82843i	−0.324443	−	0.187317i
$229$	6.31124	−	23.5539i	0.417059	−	1.55648i	−0.363617	−	0.931548i	$-0.618458\pi$
$229$	6.31124	−	23.5539i	0.417059	−	1.55648i	0.780676	−	0.624936i	$-0.214875\pi$
$230$	−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	−0.346069	−	0.938209i	$-0.612484\pi$
$233$	4.47871	−	2.58579i	0.293410	−	0.169401i	0.639479	+	0.768809i	$0.279150\pi$
$234$	−0.214413	−	0.800199i	−0.0140166	−	0.0523107i
$235$	−11.0253	+	2.95422i	−0.719210	+	0.192712i
$236$	−1.07206	+	4.00100i	−0.0697854	+	0.260443i
$237$	−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
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−7.65685	+	7.65685i	−0.490180	+	0.490180i
$245$	11.1490	+	6.28605i	0.712282	+	0.401601i
$246$	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
$250$	4.45510	−	16.6267i	0.281766	−	1.05156i
$251$	−4.05025	−	4.05025i	−0.255650	−	0.255650i	0.567632	−	0.823282i	$-0.307859\pi$
$251$	−4.05025	−	4.05025i	−0.255650	−	0.255650i	−0.823282	+	0.567632i	$0.807859\pi$
$252$	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
$259$	−2.89898	−	6.89898i	−0.180134	−	0.428682i
$260$	2.14214			0.132850
$261$	−0.687644	+	2.56632i	−0.0425641	+	0.158851i
$262$	−7.82449	+	2.09656i	−0.483398	+	0.129526i
$263$	−1.31178	−	0.757359i	−0.0808881	−	0.0467008i	0.459010	−	0.888431i	$-0.348204\pi$
$263$	−1.31178	−	0.757359i	−0.0808881	−	0.0467008i	−0.539899	+	0.841730i	$0.681537\pi$
$264$	1.01461	−	0.585786i	0.0624450	−	0.0360527i
$265$		−	15.8284i		−	0.972333i
$266$	−6.39960	+	8.42883i	−0.392385	+	0.516804i
$267$	11.0000	+	11.0000i	0.673189	+	0.673189i
$268$	25.7201	+	6.89168i	1.57111	+	0.420977i
$269$	−0.222032	−	0.828633i	−0.0135375	−	0.0505227i	0.958827	−	0.283992i	$-0.0916589\pi$
$269$	−0.222032	−	0.828633i	−0.0135375	−	0.0505227i	−0.972364	+	0.233469i	$0.924992\pi$
$270$	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
$275$	0.662907	+	0.177625i	0.0399748	+	0.0107112i
$276$	−15.9236	+	4.26670i	−0.958486	+	0.256825i
$277$	9.99071	−	2.67700i	0.600284	−	0.160846i	0.0541348	−	0.998534i	$-0.482760\pi$
$277$	9.99071	−	2.67700i	0.600284	−	0.160846i	0.546149	+	0.837688i	$0.316093\pi$
$278$	−24.9199	−	6.67727i	−1.49460	−	0.400476i
$279$			2.41421i			0.144535i
$280$	−12.6143	+	5.30057i	−0.753847	+	0.316770i
$281$			4.82843i			0.288040i	0.989575	+	0.144020i	$0.0460029\pi$
$281$			4.82843i			0.288040i	−0.989575	+	0.144020i	$0.953997\pi$
$282$	−2.28497	+	8.52761i	−0.136068	+	0.507812i
$283$	−22.6566	+	6.07082i	−1.34680	+	0.360873i	−0.858951	−	0.512058i	$-0.828883\pi$
$283$	−22.6566	+	6.07082i	−1.34680	+	0.360873i	−0.487844	+	0.872931i	$0.662217\pi$
$284$	−27.5387	−	15.8995i	−1.63412	−	0.943461i
$285$	4.99536	+	1.33850i	0.295899	+	0.0792860i
$286$			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
$291$	−2.15175	−	8.03043i	−0.126138	−	0.470752i
$292$	−6.92820	+	4.00000i	−0.405442	+	0.234082i
$293$	−10.9497	−	10.9497i	−0.639691	−	0.639691i	0.310788	−	0.950479i	$-0.399407\pi$
$293$	−10.9497	−	10.9497i	−0.639691	−	0.639691i	−0.950479	+	0.310788i	$0.899407\pi$
$294$	8.52226	−	5.03698i	0.497028	−	0.293762i
$295$		−	3.78680i		−	0.220476i
$296$	7.72741	+	2.07055i	0.449146	+	0.120348i
$297$	0.358719	+	0.207107i	0.0208150	+	0.0120176i
$298$	−5.42758	−	20.2560i	−0.314411	−	1.17340i
$299$	1.24969	−	4.66390i	0.0722714	−	0.269720i
$300$	−2.34315	−	2.34315i	−0.135282	−	0.135282i
$301$	17.0229	+	2.15280i	0.981181	+	0.124085i
$302$	−13.5563			−0.780080
$303$	3.82843	+	6.63103i	0.219937	+	0.380943i
$304$	−2.92820	−	10.9282i	−0.167944	−	0.626775i
$305$	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	−0.503597	−	0.863939i	$-0.667990\pi$
$307$	6.31371	−	6.31371i	0.360342	−	0.360342i	0.863939	+	0.503597i	$0.167990\pi$
$308$	−0.849091	−	2.02066i	−0.0483815	−	0.115138i
$309$	12.4853	+	12.4853i	0.710263	+	0.710263i
$310$	−6.02993	−	1.61571i	−0.342477	−	0.0917664i
$311$	10.0081	+	5.77817i	0.567507	+	0.327650i	0.756153	−	0.654395i	$-0.227077\pi$
$311$	10.0081	+	5.77817i	0.567507	+	0.327650i	−0.188646	+	0.982045i	$0.560410\pi$
$312$	0.828427	−	1.43488i	0.0469005	−	0.0812340i
$313$	8.51167	−	4.91421i	0.481108	−	0.277768i	−0.239770	−	0.970830i	$-0.577072\pi$
$313$	8.51167	−	4.91421i	0.481108	−	0.277768i	0.720878	+	0.693062i	$0.243739\pi$
$314$	−20.9706	−	20.9706i	−1.18344	−	1.18344i
$315$	−3.85287	−	2.92530i	−0.217085	−	0.164822i
$316$	−22.4853			−1.26490
$317$	10.9566	+	2.93582i	0.615386	+	0.164892i	0.553029	−	0.833162i	$-0.313472\pi$
$317$	10.9566	+	2.93582i	0.615386	+	0.164892i	0.0623567	+	0.998054i	$0.480138\pi$
$318$	−10.6024	−	6.12132i	−0.594555	−	0.343267i
$319$	0.550253	−	0.953065i	0.0308082	−	0.0533614i
$320$	3.78585	−	14.1290i	0.211636	−	0.789835i
$321$	−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
$325$	0.937492	−	0.251200i	0.0520027	−	0.0139341i
$326$	10.5967	−	2.83939i	0.586900	−	0.157259i
$327$	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
$331$	2.07055	−	7.72741i	0.113808	−	0.424737i	−0.885387	−	0.464854i	$-0.846107\pi$
$331$	2.07055	−	7.72741i	0.113808	−	0.424737i	0.999195	+	0.0401178i	$0.0127733\pi$
$332$	6.42607	+	23.9824i	0.352676	+	1.31621i
$333$	0.732051	+	2.73205i	0.0401161	+	0.149715i
$334$	4.24264	+	7.34847i	0.232147	+	0.402090i
$335$	−24.3431			−1.33001
$336$	−1.32780	+	10.4994i	−0.0724377	+	0.572788i
$337$	−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
$339$	−1.00926	−	3.76662i	−0.0548157	−	0.204575i
$340$	4.13829	−	1.10885i	0.224430	−	0.0601359i
$341$	0.258819	−	0.965926i	0.0140158	−	0.0523078i
$342$	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
$346$	23.1822	−	6.21166i	1.24628	−	0.333941i
$347$	−23.6510	+	6.33726i	−1.26965	+	0.340202i	−0.829897	−	0.557917i	$-0.811601\pi$
$347$	−23.6510	+	6.33726i	−1.26965	+	0.340202i	−0.439753	+	0.898119i	$0.644934\pi$
$348$	−4.60181	+	2.65685i	−0.246683	+	0.142422i
$349$	−3.41421	+	3.41421i	−0.182759	+	0.182759i	−0.792557	−	0.609798i	$-0.791251\pi$
$349$	−3.41421	+	3.41421i	−0.182759	+	0.182759i	0.609798	+	0.792557i	$0.291251\pi$
$350$	−4.89898	+	3.79899i	−0.261861	+	0.203065i
$351$	0.585786			0.0312670
$352$	2.26330	+	0.606451i	0.120635	+	0.0323239i
$353$	−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
$355$	28.0805	+	7.52415i	1.49036	+	0.399340i
$356$			31.1127i			1.64897i
$357$	−2.85765	+	1.20080i	−0.151243	+	0.0635529i
$358$	18.6274	+	18.6274i	0.984490	+	0.984490i
$359$	3.16693	−	1.82843i	0.167144	−	0.0965007i	−0.414094	−	0.910234i	$-0.635902\pi$
$359$	3.16693	−	1.82843i	0.167144	−	0.0965007i	0.581239	+	0.813733i	$0.302568\pi$
$360$	4.99536	−	1.33850i	0.263278	−	0.0705452i
$361$	−9.52628	−	5.50000i	−0.501383	−	0.289474i
$362$	30.3840	+	8.14137i	1.59695	+	0.427901i
$363$	7.65685	+	7.65685i	0.401881	+	0.401881i
$364$	−2.46875	−	1.87440i	−0.129397	−	0.0982453i
$365$	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
$371$	−13.8501	+	18.2418i	−0.719062	+	0.947066i
$372$	−3.41421	+	3.41421i	−0.177019	+	0.177019i
$373$	5.15037	−	19.2214i	0.266676	−	0.995248i	−0.694541	−	0.719454i	$-0.744392\pi$
$373$	5.15037	−	19.2214i	0.266676	−	0.995248i	0.961217	−	0.275795i	$-0.0889410\pi$
$374$	0.177625	+	0.662907i	0.00918479	+	0.0342781i
$375$	10.5409	+	6.08579i	0.544329	+	0.314269i
$376$	−15.2913	+	8.82843i	−0.788588	+	0.455291i
$377$		−	1.55635i		−	0.0801561i
$378$	−3.44949	+	1.44949i	−0.177423	+	0.0745537i
$379$	−4.65685	−	4.65685i	−0.239207	−	0.239207i	0.577315	−	0.816522i	$-0.304100\pi$
$379$	−4.65685	−	4.65685i	−0.239207	−	0.239207i	−0.816522	+	0.577315i	$0.804100\pi$
$380$	5.17157	+	8.95743i	0.265296	+	0.459506i
$381$	−2.90981	−	10.8596i	−0.149074	−	0.556352i
$382$	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
$387$	−6.26430	−	1.67851i	−0.318432	−	0.0853237i
$388$	8.31371	−	14.3998i	0.422065	−	0.731037i
$389$	−3.66954	+	0.983251i	−0.186053	+	0.0498528i	−0.350643	−	0.936509i	$-0.614037\pi$
$389$	−3.66954	+	0.983251i	−0.186053	+	0.0498528i	0.164589	+	0.986362i	$0.447370\pi$
$390$	−0.392038	+	1.46311i	−0.0198516	+	0.0740872i
$391$		−	9.65685i		−	0.488368i
$392$	19.1757	+	4.92893i	0.968517	+	0.248949i
$393$		−	5.72792i		−	0.288935i
$394$	−6.12701	−	1.64173i	−0.308674	−	0.0827090i
$395$	19.8559	−	5.32037i	0.999059	−	0.267697i
$396$	0.214413	+	0.800199i	0.0107746	+	0.0402115i
$397$	31.8471	+	8.53341i	1.59836	+	0.428280i	0.944547	−	0.328376i	$-0.106501\pi$
$397$	31.8471	+	8.53341i	1.59836	+	0.428280i	0.653814	+	0.756655i	$0.273168\pi$
$398$	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
$403$	−0.366025	−	1.36603i	−0.0182330	−	0.0680466i
$404$	−3.96348	+	14.7919i	−0.197190	+	0.735925i
$405$	1.29289	+	1.29289i	0.0642444	+	0.0642444i
$406$	3.85108	+	9.16479i	0.191126	+	0.454841i
$407$		−	1.17157i		−	0.0580727i
$408$	0.857651	−	3.20080i	0.0424600	−	0.158463i
$409$	−18.4837	−	10.6716i	−0.913960	−	0.527675i	−0.0322572	−	0.999480i	$-0.510270\pi$
$409$	−18.4837	−	10.6716i	−0.913960	−	0.527675i	−0.881703	+	0.471804i	$0.843603\pi$
$410$	−1.46311	+	0.392038i	−0.0722576	+	0.0193614i
$411$	3.32024	−	12.3913i	0.163775	−	0.611218i
$412$			35.3137i			1.73978i
$413$	−3.31350	+	4.36417i	−0.163047	+	0.214747i
$414$		−	11.6569i		−	0.572903i
$415$	−11.3492	−	19.6575i	−0.557112	−	0.964947i
$416$	3.20080	−	0.857651i	0.156932	−	0.0420498i
$417$	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	0.309446	−	0.950917i	$-0.399856\pi$
$419$	25.7990	−	25.7990i	1.26036	−	1.26036i	0.950917	−	0.309446i	$-0.100144\pi$
$420$	−1.31178	−	9.58579i	−0.0640085	−	0.467738i
$421$	15.4853	+	15.4853i	0.754706	+	0.754706i	0.975354	−	0.220647i	$-0.0708170\pi$
$421$	15.4853	+	15.4853i	0.754706	+	0.754706i	−0.220647	+	0.975354i	$0.570817\pi$
$422$	4.35552	−	16.2550i	0.212023	−	0.791282i
$423$	−5.40629	−	3.12132i	−0.262863	−	0.151764i
$424$	−6.33726	−	23.6510i	−0.307764	−	1.14859i
$425$	1.68106	−	0.970563i	0.0815436	−	0.0470792i
$426$	15.8995	−	15.8995i	0.770333	−	0.770333i
$427$	−13.2061	+	5.54927i	−0.639089	+	0.268548i
$428$	−22.7279	−	22.7279i	−1.09860	−	1.09860i
$429$	−0.234373	−	0.0628000i	−0.0113156	−	0.00303201i
$430$	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	$0.279278\pi$
$432$	1.03528	−	3.86370i	0.0498097	−	0.185893i
$433$	−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
$436$	2.92621	+	0.784076i	0.140140	+	0.0375504i
$437$	22.5193	−	6.03403i	1.07724	−	0.288647i
$438$	−1.46410	−	5.46410i	−0.0699575	−	0.261085i
$439$	−22.9985	+	13.2782i	−1.09766	+	0.633733i	−0.935605	−	0.353049i	$-0.885145\pi$
$439$	−22.9985	+	13.2782i	−1.09766	+	0.633733i	−0.162053	+	0.986782i	$0.551811\pi$
$440$	−2.14214			−0.102122
$441$	1.88064	+	6.74264i	0.0895542	+	0.321078i
$442$	0.686292	+	0.686292i	0.0326436	+	0.0326436i
$443$	2.48098	−	9.25916i	0.117875	−	0.439916i	−0.881611	−	0.471977i	$-0.843540\pi$
$443$	2.48098	−	9.25916i	0.117875	−	0.439916i	0.999486	+	0.0320612i	$0.0102072\pi$
$444$	−2.82843	+	4.89898i	−0.134231	+	0.232495i
$445$	−7.36176	−	27.4745i	−0.348981	−	1.30241i
$446$	−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
$451$	−0.0628000	−	0.234373i	−0.00295714	−	0.0110362i
$452$	3.89949	−	6.75412i	0.183417	−	0.317687i
$453$	2.48098	−	9.25916i	0.116567	−	0.435033i
$454$	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	−0.869386	−	0.494133i	$-0.835486\pi$
$457$	−18.7299	+	10.8137i	−0.876147	+	0.505844i	−0.00676121	+	0.999977i	$0.502152\pi$
$458$	8.92545	+	33.3102i	0.417059	+	1.55648i
$459$	1.13165	−	0.303225i	0.0528210	−	0.0141533i
$460$	29.1151	+	7.80136i	1.35750	+	0.363740i
$461$	8.00000	−	8.00000i	0.372597	−	0.372597i	−0.495825	−	0.868422i	$-0.665134\pi$
$461$	8.00000	−	8.00000i	0.372597	−	0.372597i	0.868422	+	0.495825i	$0.165134\pi$
$462$	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	$0.528136\pi$
$464$	−10.2653	−	2.75058i	−0.476554	−	0.127692i
$465$	2.20711	−	3.82282i	0.102352	−	0.177279i
$466$	−3.65685	+	6.33386i	−0.169401	+	0.293410i
$467$	9.79655	+	2.62498i	0.453330	+	0.121469i	0.478257	−	0.878220i	$-0.341269\pi$
$467$	9.79655	+	2.62498i	0.453330	+	0.121469i	−0.0249270	+	0.999689i	$0.507935\pi$
$468$	0.828427	+	0.828427i	0.0382941	+	0.0382941i
$469$	28.0547	+	21.3006i	1.29545	+	0.983571i
$470$	11.4142	−	11.4142i	0.526498	−	0.526498i
$471$	18.1610	−	10.4853i	0.836817	−	0.483136i
$472$	−1.51613	−	5.65826i	−0.0697854	−	0.260443i
$473$	2.32640	+	1.34315i	0.106968	+	0.0617579i
$474$	4.11509	−	15.3577i	0.189012	−	0.705404i
$475$	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
$483$	−21.6356	−	2.73615i	−0.984456	−	0.124499i
$484$			21.6569i			0.984402i
$485$	−3.93431	+	14.6830i	−0.178648	+	0.666723i
$486$	1.36603	−	0.366025i	0.0619642	−	0.0166032i
$487$	−0.481813	−	0.278175i	−0.0218330	−	0.0126053i	0.489044	−	0.872259i	$-0.337346\pi$
$487$	−0.481813	−	0.278175i	−0.0218330	−	0.0126053i	−0.510877	+	0.859654i	$0.670679\pi$
$488$	3.96348	−	14.7919i	0.179418	−	0.669598i
$489$			7.75736i			0.350800i
$490$	−18.0996	+	0.184709i	−0.817655	+	0.00834429i
$491$	15.9497	+	15.9497i	0.719802	+	0.719802i	0.968565	−	0.248762i	$-0.0800239\pi$
$491$	15.9497	+	15.9497i	0.719802	+	0.719802i	−0.248762	+	0.968565i	$0.580024\pi$
$492$	−0.303225	+	1.13165i	−0.0136705	+	0.0510188i
$493$	−0.805626	−	3.00664i	−0.0362836	−	0.135412i
$494$	−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
$499$	−3.96078	−	1.06129i	−0.177309	−	0.0475098i	0.169072	−	0.985604i	$-0.445923\pi$
$499$	−3.96078	−	1.06129i	−0.177309	−	0.0475098i	−0.346381	+	0.938094i	$0.612590\pi$
$500$	6.30047	+	23.5137i	0.281766	+	1.05156i
$501$	−5.79555	+	1.55291i	−0.258926	+	0.0693791i
$502$	7.82449	+	2.09656i	0.349224	+	0.0935743i
$503$			40.4853i			1.80515i	0.430533	+	0.902575i	$0.358326\pi$
$503$			40.4853i			1.80515i	−0.430533	+	0.902575i	$0.641674\pi$
$504$	−6.92820	−	2.82843i	−0.308607	−	0.125988i
$505$		−	14.0000i		−	0.622992i
$506$	−1.24969	+	4.66390i	−0.0555554	+	0.207336i
$507$	12.2256	−	3.27583i	0.542957	−	0.145485i
$508$	11.2426	−	19.4728i	0.498812	−	0.863967i
$509$	2.42903	+	0.650857i	0.107665	+	0.0288487i	0.312249	−	0.950000i	$-0.398918\pi$
$509$	2.42903	+	0.650857i	0.107665	+	0.0288487i	−0.204584	+	0.978849i	$0.565584\pi$
$510$			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
$515$	−8.35578	−	31.1842i	−0.368200	−	1.37414i
$516$	−6.48528	−	11.2328i	−0.285499	−	0.494498i
$517$	1.82843	+	1.82843i	0.0804141	+	0.0804141i
$518$	8.42883	+	6.39960i	0.370341	+	0.281182i
$519$			16.9706i			0.744925i
$520$	−2.62357	+	1.51472i	−0.115051	+	0.0664248i
$521$	0.297173	+	0.171573i	0.0130194	+	0.00751674i	0.506496	−	0.862243i	$-0.330941\pi$
$521$	0.297173	+	0.171573i	0.0130194	+	0.00751674i	−0.493476	+	0.869759i	$0.664274\pi$
$522$	−0.972476	−	3.62933i	−0.0425641	−	0.158851i
$523$	−0.920451	+	3.43517i	−0.0402485	+	0.150209i	−0.983126	−	0.182931i	$-0.941442\pi$
$523$	−0.920451	+	3.43517i	−0.0402485	+	0.150209i	0.942877	+	0.333140i	$0.108108\pi$
$524$	8.10051	−	8.10051i	0.353872	−	0.353872i
$525$	−1.69818	−	4.04133i	−0.0741148	−	0.176378i
$526$	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
$532$	1.87780	−	14.8484i	0.0814129	−	0.643758i
$533$	−0.242641	−	0.242641i	−0.0105099	−	0.0105099i
$534$	−21.2504	−	5.69402i	−0.919593	−	0.246404i
$535$	25.4480	+	14.6924i	1.10021	+	0.635207i
$536$	−36.3737	+	9.74631i	−1.57111	+	0.420977i
$537$	−16.1318	+	9.31371i	−0.696139	+	0.401916i
$538$	0.857864	+	0.857864i	0.0369852	+	0.0369852i
$539$	−0.0295882	−	2.89934i	−0.00127446	−	0.124884i
$540$			3.65685i			0.157366i
$541$	−15.1234	−	4.05229i	−0.650204	−	0.174222i	−0.0813829	−	0.996683i	$-0.525934\pi$
$541$	−15.1234	−	4.05229i	−0.650204	−	0.174222i	−0.568821	+	0.822461i	$0.692600\pi$
$542$	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	−0.870191	−	0.492715i	$-0.836005\pi$
$547$	−8.82843	+	8.82843i	−0.377476	+	0.377476i	0.492715	+	0.870191i	$0.336005\pi$
$548$	22.2195	−	12.8284i	0.949169	−	0.548003i
$549$	5.22973	−	1.40130i	0.223199	−	0.0598061i
$550$	−0.937492	+	0.251200i	−0.0399748	+	0.0107112i
$551$	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
$555$	1.33850	−	4.99536i	0.0568162	−	0.212041i
$556$	35.2421	−	9.44309i	1.49460	−	0.400476i
$557$	6.20404	+	23.1538i	0.262874	+	0.981057i	0.963539	+	0.267568i	$0.0862198\pi$
$557$	6.20404	+	23.1538i	0.262874	+	0.981057i	−0.700666	+	0.713490i	$0.747113\pi$
$558$	−1.70711	−	2.95680i	−0.0722676	−	0.125171i
$559$	3.79899			0.160680
$560$	11.7012	−	15.4115i	0.494466	−	0.651254i
$561$	−0.485281			−0.0204886
$562$	−3.41421	−	5.91359i	−0.144020	−	0.249450i
$563$	−1.53452	−	5.72691i	−0.0646723	−	0.241360i	0.926021	−	0.377471i	$-0.123206\pi$
$563$	−1.53452	−	5.72691i	−0.0646723	−	0.241360i	−0.990694	+	0.136111i	$0.956540\pi$
$564$	−3.23143	−	12.0599i	−0.136068	−	0.507812i
$565$	−1.84536	+	6.88700i	−0.0776351	+	0.289738i
$566$	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	−0.478582	−	0.878043i	$-0.658849\pi$
$569$	1.01461	−	0.585786i	0.0425347	−	0.0245574i	0.521117	+	0.853486i	$0.325516\pi$
$570$	−7.06450	+	1.89293i	−0.295899	+	0.0792860i
$571$	−40.6091	+	10.8812i	−1.69944	+	0.455363i	−0.972798	−	0.231656i	$-0.925586\pi$
$571$	−40.6091	+	10.8812i	−1.69944	+	0.455363i	−0.726640	+	0.687019i	$0.758919\pi$
$572$	−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
$579$	−6.76148	−	1.81173i	−0.280998	−	0.0752931i
$580$	9.71573			0.403424
$581$	−4.12091	+	32.5854i	−0.170964	+	1.35187i
$582$	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
$586$	21.1533	+	5.66801i	0.873834	+	0.234143i
$587$	7.12132	+	7.12132i	0.293928	+	0.293928i	0.838630	−	0.544702i	$-0.183357\pi$
$587$	7.12132	+	7.12132i	0.293928	+	0.293928i	−0.544702	+	0.838630i	$0.683357\pi$
$588$	−6.87591	+	12.1952i	−0.283558	+	0.502920i
$589$	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
$592$	−10.9282	+	2.92820i	−0.449146	+	0.120348i
$593$	−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
$595$	5.62277	+	0.711085i	0.230511	+	0.0291516i
$596$	20.9706	+	20.9706i	0.858988	+	0.858988i
$597$	−4.87316	+	18.1869i	−0.199445	+	0.744339i
$598$	1.76733	+	6.59575i	0.0722714	+	0.269720i
$599$	35.7787	+	20.6569i	1.46188	+	0.844016i	0.999098	−	0.0424567i	$-0.0135184\pi$
$599$	35.7787	+	20.6569i	1.46188	+	0.844016i	0.462781	+	0.886473i	$0.346852\pi$
$600$	4.52661	+	1.21290i	0.184798	+	0.0495165i
$601$			14.6569i			0.597866i	0.954274	+	0.298933i	$0.0966306\pi$
$601$			14.6569i			0.597866i	−0.954274	+	0.298933i	$0.903369\pi$
$602$	−22.3709	+	9.40035i	−0.911770	+	0.383130i
$603$	−9.41421	−	9.41421i	−0.383376	−	0.383376i
$604$	16.6031	−	9.58579i	0.675569	−	0.390040i
$605$	−5.12436	−	19.1244i	−0.208335	−	0.777516i
$606$	−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
$611$	3.53225	+	0.946464i	0.142900	+	0.0382898i
$612$	2.02922	+	1.17157i	0.0820265	+	0.0473580i
$613$	−19.8843	+	5.32799i	−0.803121	+	0.215196i	−0.636954	−	0.770902i	$-0.719806\pi$
$613$	−19.8843	+	5.32799i	−0.803121	+	0.215196i	−0.166167	+	0.986098i	$0.553139\pi$
$614$	−3.26822	+	12.1971i	−0.131894	+	0.492237i
$615$		−	1.07107i		−	0.0431896i
$616$	2.46875	+	1.87440i	0.0994686	+	0.0755217i
$617$		−	23.7574i		−	0.956435i	−0.878241	−	0.478218i	$-0.841283\pi$
$617$		−	23.7574i		−	0.956435i	0.878241	−	0.478218i	$-0.158717\pi$
$618$	−24.1197	−	6.46286i	−0.970237	−	0.259974i
$619$	27.8863	−	7.47212i	1.12085	−	0.300330i	0.349620	−	0.936891i	$-0.386311\pi$
$619$	27.8863	−	7.47212i	1.12085	−	0.300330i	0.771226	+	0.636562i	$0.219644\pi$
$620$	8.52761	−	2.28497i	0.342477	−	0.0917664i
$621$	7.96178	+	2.13335i	0.319495	+	0.0856085i
$622$	−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
$627$	−0.303225	−	1.13165i	−0.0121097	−	0.0451938i
$628$	40.5120	+	10.8552i	1.61661	+	0.433168i
$629$	−2.34315	−	2.34315i	−0.0934273	−	0.0934273i
$630$	6.78729	+	0.858355i	0.270412	+	0.0341977i
$631$			17.2426i			0.686419i	0.939259	+	0.343209i	$0.111514\pi$
$631$			17.2426i			0.686419i	−0.939259	+	0.343209i	$0.888486\pi$
$632$	27.5387	−	15.8995i	1.09543	−	0.632448i
$633$	10.3053	+	5.94975i	0.409598	+	0.236481i
$634$	−15.4950	+	4.15188i	−0.615386	+	0.164892i
$635$	−5.32037	+	19.8559i	−0.211133	+	0.787958i
$636$	17.3137			0.686533
$637$	−2.08638	−	3.53003i	−0.0826655	−	0.139865i
$638$			1.55635i			0.0616165i
$639$	7.94975	+	13.7694i	0.314487	+	0.544708i
$640$	5.35401	+	19.9814i	0.211636	+	0.789835i
$641$	−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	0.259610	−	0.965714i	$-0.416406\pi$
$643$	31.0711	−	31.0711i	1.22532	−	1.22532i	0.965714	−	0.259610i	$-0.0835939\pi$
$644$	−26.7279	−	34.4669i	−1.05323	−	1.35819i
$645$	8.38478	+	8.38478i	0.330150	+	0.330150i
$646$	−1.21290	+	4.52661i	−0.0477210	+	0.178097i
$647$	7.43551	+	4.29289i	0.292320	+	0.168771i	0.638988	−	0.769217i	$-0.279353\pi$
$647$	7.43551	+	4.29289i	0.292320	+	0.168771i	−0.346668	+	0.937988i	$0.612687\pi$
$648$	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
$651$	−5.88865	+	2.47443i	−0.230794	+	0.0969807i
$652$	−10.9706	+	10.9706i	−0.429640	+	0.429640i
$653$	−0.497180	−	0.133219i	−0.0194562	−	0.00521326i	0.249078	−	0.968483i	$-0.419872\pi$
$653$	−0.497180	−	0.133219i	−0.0194562	−	0.00521326i	−0.268534	+	0.963270i	$0.586539\pi$
$654$	−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	−0.969417	−	0.245418i	$-0.921075\pi$
$659$	−18.5858	+	18.5858i	−0.723999	+	0.723999i	0.245418	+	0.969417i	$0.421075\pi$
$660$	0.392038	−	1.46311i	0.0152601	−	0.0569513i
$661$	11.2597	−	3.01702i	0.437950	−	0.117348i	−0.0331057	−	0.999452i	$-0.510540\pi$
$661$	11.2597	−	3.01702i	0.437950	−	0.117348i	0.471056	+	0.882104i	$0.343873\pi$
$662$	2.92820	+	10.9282i	0.113808	+	0.424737i
$663$	−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
$667$	5.66801	−	21.1533i	0.219466	−	0.819059i
$668$	−10.3923	−	6.00000i	−0.402090	−	0.232147i
$669$	−5.32037	−	19.8559i	−0.205698	−	0.767674i
$670$	29.8141	−	17.2132i	1.15182	−	0.665004i
$671$	−2.24264			−0.0865762
$672$	−5.79796	−	13.7980i	−0.223661	−	0.532268i
$673$	−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
$675$	0.428825	+	1.60040i	0.0165055	+	0.0615994i
$676$	21.9223	+	12.6569i	0.843166	+	0.486802i
$677$	11.0404	−	41.2034i	0.424317	−	1.58357i	−0.341092	−	0.940030i	$-0.610797\pi$
$677$	11.0404	−	41.2034i	0.424317	−	1.58357i	0.765409	−	0.643544i	$-0.222537\pi$
$678$	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
$682$	0.366025	+	1.36603i	0.0140158	+	0.0523078i
$683$	−15.8549	+	4.24831i	−0.606671	+	0.162557i	−0.549061	−	0.835782i	$-0.685015\pi$
$683$	−15.8549	+	4.24831i	−0.606671	+	0.162557i	−0.0576100	+	0.998339i	$0.518348\pi$
$684$	−1.46410	+	5.46410i	−0.0559813	+	0.208925i
$685$	−16.5858	+	16.5858i	−0.633710	+	0.633710i
$686$	21.0208	+	15.6245i	0.802578	+	0.596547i
$687$	−24.3848			−0.930337
$688$	6.71406	−	25.0572i	0.255971	−	0.955297i
$689$	−2.53553	+	4.39167i	−0.0965961	+	0.167309i
$690$	−10.6569	+	18.4582i	−0.405700	+	0.702692i
$691$	39.3402	+	10.5412i	1.49657	+	0.401005i	0.911950	−	0.410302i	$-0.134577\pi$
$691$	39.3402	+	10.5412i	1.49657	+	0.401005i	0.584620	+	0.811307i	$0.301243\pi$
$692$	−24.0000	+	24.0000i	−0.912343	+	0.912343i
$693$	−0.137499	+	1.08725i	−0.00522314	+	0.0413011i
$694$	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
$698$	1.76733	−	6.59575i	0.0668943	−	0.249653i
$699$	−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	−0.940241	−	0.340511i	$-0.889400\pi$
$701$	−15.8787	+	15.8787i	−0.599729	+	0.599729i	0.340511	+	0.940241i	$0.389400\pi$
$702$	−0.717439	+	0.414214i	−0.0270780	+	0.0156335i
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$	−3.20080	+	0.857651i	−0.120635	+	0.0323239i
$705$	5.70711	+	9.88500i	0.214942	+	0.372291i
$706$		−	27.3137i		−	1.02796i
$707$	−12.2502	+	16.1346i	−0.460716	+	0.606803i
$708$	4.14214			0.155671
$709$	1.52690	−	5.69847i	0.0573440	−	0.214011i	−0.931309	−	0.364231i	$-0.881332\pi$
$709$	1.52690	−	5.69847i	0.0573440	−	0.214011i	0.988652	+	0.150221i	$0.0479984\pi$
$710$	−39.7118	+	10.6407i	−1.49036	+	0.399340i
$711$	9.73641	+	5.62132i	0.365144	+	0.210816i
$712$	−22.0000	−	38.1051i	−0.824485	−	1.42805i
$713$		−	19.8995i		−	0.745242i
$714$	2.65080	−	3.49133i	0.0992038	−	0.130660i
$715$	0.313708	+	0.313708i	0.0117320	+	0.0117320i
$716$	−35.9854	−	9.64226i	−1.34484	−	0.360348i
$717$	−2.86540	−	10.6938i	−0.107010	−	0.399368i
$718$	−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
$723$	22.3536	+	5.98963i	0.831339	+	0.222757i
$724$	−42.9695	+	11.5136i	−1.59695	+	0.427901i
$725$	4.25203	−	1.13933i	0.157916	−	0.0423135i
$726$	−14.7919	−	3.96348i	−0.548979	−	0.147099i
$727$			16.5563i			0.614041i	0.951703	+	0.307021i	$0.0993320\pi$
$727$			16.5563i			0.614041i	−0.951703	+	0.307021i	$0.900668\pi$
$728$	4.34898	+	0.549995i	0.161184	+	0.0203842i
$729$			1.00000i			0.0370370i
$730$	−2.67700	+	9.99071i	−0.0990803	+	0.369773i
$731$	7.33908	−	1.96650i	0.271446	−	0.0727337i
$732$	9.37769	+	5.41421i	0.346610	+	0.200115i
$733$	−40.5689	−	10.8704i	−1.49845	−	0.401507i	−0.585867	−	0.810407i	$-0.699246\pi$
$733$	−40.5689	−	10.8704i	−1.49845	−	0.401507i	−0.912579	+	0.408900i	$0.865912\pi$
$734$		−	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
$739$	−10.0235	−	37.4083i	−0.368721	−	1.37609i	−0.862305	−	0.506389i	$-0.830980\pi$
$739$	−10.0235	−	37.4083i	−0.368721	−	1.37609i	0.493584	−	0.869698i	$-0.335686\pi$
$740$	8.95743	−	5.17157i	0.329282	−	0.190111i
$741$	−1.17157	−	1.17157i	−0.0430388	−	0.0430388i
$742$	4.06396	−	32.1350i	0.149193	−	1.17971i
$743$		−	17.3137i		−	0.635178i	−0.948228	−	0.317589i	$-0.897127\pi$
$743$		−	17.3137i		−	0.635178i	0.948228	−	0.317589i	$-0.102873\pi$
$744$	1.76733	−	6.59575i	0.0647934	−	0.241812i
$745$	−23.4803	−	13.5563i	−0.860251	−	0.496666i
$746$	7.28372	+	27.1832i	0.266676	+	0.995248i
$747$	3.21303	−	11.9912i	0.117559	−	0.438735i
$748$	−0.686292	−	0.686292i	−0.0250933	−	0.0250933i
$749$	−16.4719	−	39.1999i	−0.601872	−	1.43233i
$750$	−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
$756$	3.19980	−	4.21441i	0.116376	−	0.153277i
$757$	−10.3137	−	10.3137i	−0.374858	−	0.374858i	0.494385	−	0.869243i	$-0.335393\pi$
$757$	−10.3137	−	10.3137i	−0.374858	−	0.374858i	−0.869243	+	0.494385i	$0.835393\pi$
$758$	8.99635	+	2.41057i	0.326762	+	0.0875557i
$759$	−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	−0.823513	−	0.567297i	$-0.807989\pi$
$761$	−20.5235	+	11.8492i	−0.743976	+	0.429535i	0.0795372	+	0.996832i	$0.474656\pi$
$762$	11.2426	+	11.2426i	0.407278	+	0.407278i
$763$	3.19182	+	2.42340i	0.115552	+	0.0877329i
$764$	−38.6274			−1.39749
$765$	−2.06914	−	0.554425i	−0.0748101	−	0.0200453i
$766$	−35.6046	−	20.5563i	−1.28645	−	0.742731i
$767$	−0.606602	+	1.05066i	−0.0219031	+	0.0379373i
$768$	15.4548	+	4.14110i	0.557678	+	0.149429i
$769$	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
$773$	−2.06914	+	0.554425i	−0.0744219	+	0.0199413i	−0.295838	−	0.955238i	$-0.595599\pi$
$773$	−2.06914	+	0.554425i	−0.0744219	+	0.0199413i	0.221416	+	0.975179i	$0.428932\pi$
$774$	8.85906	−	2.37378i	0.318432	−	0.0853237i
$775$	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
$779$	0.428825	−	1.60040i	0.0153643	−	0.0573402i
$780$	−0.554425	−	2.06914i	−0.0198516	−	0.0740872i
$781$	−1.70453	−	6.36138i	−0.0609928	−	0.227628i
$782$	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
$787$	12.2933	+	45.8790i	0.438207	+	1.63541i	0.733273	+	0.679934i	$0.237992\pi$
$787$	12.2933	+	45.8790i	0.438207	+	1.63541i	−0.295066	+	0.955477i	$0.595342\pi$
$788$	8.66490	−	2.32175i	0.308674	−	0.0827090i
$789$	−0.392038	+	1.46311i	−0.0139569	+	0.0520879i
$790$	−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
$794$	−45.0386	+	12.0681i	−1.59836	+	0.428280i
$795$	−15.2891	+	4.09670i	−0.542248	+	0.145295i
$796$	−32.6118	+	18.8284i	−1.15589	+	0.667356i
$797$	30.2635	−	30.2635i	1.07199	−	1.07199i	0.0747871	−	0.997200i	$-0.476172\pi$
$797$	30.2635	−	30.2635i	1.07199	−	1.07199i	0.997200	−	0.0747871i	$-0.0238277\pi$
$798$	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
$803$	−1.60040	−	0.428825i	−0.0564768	−	0.0151329i
$804$		−	26.6274i		−	0.939077i
$805$	31.7578	+	24.1122i	1.11932	+	0.849844i
$806$	1.41421	+	1.41421i	0.0498135	+	0.0498135i
$807$	−0.742932	+	0.428932i	−0.0261525	+	0.0150991i
$808$	−5.60521	−	20.9189i	−0.197190	−	0.735925i
$809$	−5.49333	−	3.17157i	−0.193135	−	0.111507i	0.400314	−	0.916378i	$-0.368901\pi$
$809$	−5.49333	−	3.17157i	−0.193135	−	0.111507i	−0.593449	+	0.804871i	$0.702234\pi$
$810$	−2.49768	−	0.669251i	−0.0877595	−	0.0235151i
$811$	−15.5563	−	15.5563i	−0.546257	−	0.546257i	0.379099	−	0.925356i	$-0.376234\pi$
$811$	−15.5563	−	15.5563i	−0.546257	−	0.546257i	−0.925356	+	0.379099i	$0.876234\pi$
$812$	−11.1971	−	8.50140i	−0.392940	−	0.298341i
$813$	−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
$816$	1.21290	+	4.52661i	0.0424600	+	0.158463i
$817$	9.17157	+	15.8856i	0.320873	+	0.555768i
$818$	30.1838			1.05535
$819$	0.600398	+	1.42883i	0.0209796	+	0.0499272i
$820$	1.51472	−	1.51472i	0.0528963	−	0.0528963i
$821$	−1.29410	+	4.82963i	−0.0451642	+	0.168555i	−0.984824	−	0.173554i	$-0.944475\pi$
$821$	−1.29410	+	4.82963i	−0.0451642	+	0.168555i	0.939660	+	0.342110i	$0.111141\pi$
$822$	4.69553	+	17.5240i	0.163775	+	0.611218i
$823$	25.6836	+	14.8284i	0.895274	+	0.516886i	0.875664	−	0.482921i	$-0.160424\pi$
$823$	25.6836	+	14.8284i	0.895274	+	0.516886i	0.0196098	+	0.999808i	$0.493758\pi$
$824$	−24.9706	−	43.2503i	−0.869891	−	1.50670i
$825$		−	0.686292i		−	0.0238936i
$826$	0.972263	−	7.68799i	0.0338293	−	0.267499i
$827$	−20.0503	−	20.0503i	−0.697216	−	0.697216i	0.266593	−	0.963809i	$-0.414102\pi$
$827$	−20.0503	−	20.0503i	−0.697216	−	0.697216i	−0.963809	+	0.266593i	$0.914102\pi$
$828$	8.24264	+	14.2767i	0.286452	+	0.496149i
$829$	3.58668	+	13.3857i	0.124571	+	0.464904i	0.999824	−	0.0187610i	$-0.00597216\pi$
$829$	3.58668	+	13.3857i	0.124571	+	0.464904i	−0.875253	+	0.483664i	$0.839305\pi$
$830$	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
$835$	10.5967	+	2.83939i	0.366716	+	0.0982612i
$836$	1.17157	−	2.02922i	0.0405197	−	0.0701822i
$837$	2.33195	−	0.624844i	0.0806040	−	0.0215978i
$838$	−13.3545	+	49.8398i	−0.461325	+	1.72169i
$839$			19.7990i			0.683537i	0.939784	+	0.341769i	$0.111026\pi$
$839$			19.7990i			0.683537i	−0.939784	+	0.341769i	$0.888974\pi$
$840$	8.38478	+	10.8126i	0.289302	+	0.373069i
$841$			21.9411i			0.756591i
$842$	−29.9153	−	8.01577i	−1.03095	−	0.276242i
$843$	4.66390	−	1.24969i	0.160633	−	0.0430416i
$844$	6.15963	+	22.9881i	0.212023	+	0.791282i
$845$	−22.3536	−	5.98963i	−0.768987	−	0.206049i
$846$	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
$851$	−6.03403	−	22.5193i	−0.206844	−	0.771952i
$852$	−8.23018	+	30.7155i	−0.281961	+	1.05229i
$853$	−9.07107	−	9.07107i	−0.310587	−	0.310587i	0.534550	−	0.845137i	$-0.320481\pi$
$853$	−9.07107	−	9.07107i	−0.310587	−	0.310587i	−0.845137	+	0.534550i	$0.820481\pi$
$854$	12.2502	−	16.1346i	0.419193	−	0.552114i
$855$		−	5.17157i		−	0.176864i
$856$	43.9070	+	11.7648i	1.50071	+	0.402114i
$857$	−14.0665	−	8.12132i	−0.480504	−	0.277419i	0.240123	−	0.970743i	$-0.422812\pi$
$857$	−14.0665	−	8.12132i	−0.480504	−	0.277419i	−0.720626	+	0.693324i	$0.756146\pi$
$858$	0.331453	−	0.0888127i	0.0113156	−	0.00303201i
$859$	1.92971	−	7.20179i	0.0658410	−	0.245722i	−0.925160	−	0.379578i	$-0.876069\pi$
$859$	1.92971	−	7.20179i	0.0658410	−	0.245722i	0.991001	+	0.133856i	$0.0427359\pi$
$860$			23.7157i			0.808700i
$861$	−0.937200	+	1.23437i	−0.0319397	+	0.0420673i
$862$		−	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	$0.835418\pi$
$864$	1.46410	+	5.46410i	0.0498097	+	0.185893i
$865$	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
$870$	−1.77810	+	6.63597i	−0.0602833	+	0.224980i
$871$	6.75412	+	3.89949i	0.228855	+	0.132129i
$872$	−4.13829	+	1.10885i	−0.140140	+	0.0375504i
$873$	−7.19988	+	4.15685i	−0.243679	+	0.140688i
$874$	−23.3137	+	23.3137i	−0.788598	+	0.788598i
$875$	−4.04037	+	31.9485i	−0.136589	+	1.08006i
$876$	5.65685	+	5.65685i	0.191127	+	0.191127i
$877$	−11.8657	−	3.17940i	−0.400676	−	0.107361i	0.0528530	−	0.998602i	$-0.483169\pi$
$877$	−11.8657	−	3.17940i	−0.400676	−	0.107361i	−0.453529	+	0.891241i	$0.649835\pi$
$878$	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	−0.950408	−	0.311007i	$-0.899334\pi$
$883$	−19.0000	+	19.0000i	−0.639401	+	0.639401i	0.311007	+	0.950408i	$0.399334\pi$
$884$	−1.32581	−	0.355251i	−0.0445919	−	0.0119484i
$885$	−3.65776	+	0.980095i	−0.122954	+	0.0329455i
$886$	3.50864	+	13.0944i	0.117875	+	0.439916i
$887$	−5.10911	+	2.94975i	−0.171547	+	0.0990428i	−0.583315	−	0.812246i	$-0.698245\pi$
$887$	−5.10911	+	2.94975i	−0.171547	+	0.0990428i	0.411768	+	0.911289i	$0.364911\pi$
$888$		−	8.00000i		−	0.268462i
$889$	23.5058	−	18.2279i	0.788359	−	0.611345i
$890$	28.4437	+	28.4437i	0.953433	+	0.953433i
$891$	0.107206	−	0.400100i	0.00359155	−	0.0134038i
$892$	20.5563	−	35.6046i	0.688277	−	1.19213i
$893$	4.56993	+	17.0552i	0.152927	+	0.570731i
$894$	−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
$899$	−1.66012	−	6.19565i	−0.0553681	−	0.206637i
$900$	−1.65685	+	2.86976i	−0.0552285	+	0.0956585i
$901$	−2.62498	+	9.79655i	−0.0874507	+	0.326370i
$902$	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
$906$	3.50864	+	13.0944i	0.116567	+	0.435033i
$907$	19.0841	−	5.11358i	0.633679	−	0.169794i	0.0723402	−	0.997380i	$-0.476953\pi$
$907$	19.0841	−	5.11358i	0.633679	−	0.169794i	0.561338	+	0.827586i	$0.310287\pi$
$908$	−20.7816	−	5.56842i	−0.689662	−	0.184794i
$909$	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
$915$	−9.56218	−	2.56218i	−0.316116	−	0.0847030i
$916$	−34.4853	−	34.4853i	−1.13943	−	1.13943i
$917$	13.9713	−	5.87080i	0.461373	−	0.193871i
$918$	−1.17157	+	1.17157i	−0.0386677	+	0.0386677i
$919$	−8.11689	+	4.68629i	−0.267752	+	0.154586i	−0.627865	−	0.778322i	$-0.716071\pi$
$919$	−8.11689	+	4.68629i	−0.267752	+	0.154586i	0.360114	+	0.932908i	$0.382738\pi$
$920$	−41.1749	+	11.0328i	−1.35750	+	0.363740i
$921$	−7.73268	−	4.46447i	−0.254801	−	0.147109i
$922$	−4.14110	+	15.4548i	−0.136380	+	0.508977i
$923$	−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
$928$	14.5173	−	3.88990i	0.476554	−	0.127692i
$929$	−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
$931$	9.72401	−	17.2466i	0.318691	−	0.565233i
$932$		−	10.3431i		−	0.338801i
$933$	2.99100	−	11.1626i	0.0979211	−	0.365446i
$934$	−13.8544	+	3.71228i	−0.453330	+	0.121469i
$935$	0.768426	+	0.443651i	0.0251302	+	0.0145089i
$936$	−1.60040	−	0.428825i	−0.0523107	−	0.0140166i
$937$			27.0000i			0.882052i	0.897494	+	0.441026i	$0.145385\pi$
$937$			27.0000i			0.882052i	−0.897494	+	0.441026i	$0.854615\pi$
$938$	−49.4217	−	6.25012i	−1.61368	−	0.204074i
$939$	−6.94975	−	6.94975i	−0.226796	−	0.226796i
$940$	−5.90843	+	22.0506i	−0.192712	+	0.719210i
$941$	−9.18427	−	34.2761i	−0.299399	−	1.11737i	−0.937661	−	0.347552i	$-0.887013\pi$
$941$	−9.18427	−	34.2761i	−0.299399	−	1.11737i	0.638262	−	0.769819i	$-0.279654\pi$
$942$	−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
$947$	−5.26994	−	1.41208i	−0.171250	−	0.0458863i	0.172175	−	0.985066i	$-0.444921\pi$
$947$	−5.26994	−	1.41208i	−0.171250	−	0.0458863i	−0.343425	+	0.939180i	$0.611587\pi$
$948$	5.81962	+	21.7191i	0.189012	+	0.705404i
$949$	−2.26330	+	0.606451i	−0.0734700	+	0.0196862i
$950$	−6.40159	−	1.71530i	−0.207695	−	0.0556517i
$951$		−	11.3431i		−	0.367827i
$952$	8.68629	−	1.18869i	0.281524	−	0.0385257i
$953$		−	55.2548i		−	1.78988i	−0.446187	−	0.894940i	$-0.647218\pi$
$953$		−	55.2548i		−	1.78988i	0.446187	−	0.894940i	$-0.352782\pi$
$954$	−3.16863	+	11.8255i	−0.102588	+	0.382864i
$955$	34.1104	−	9.13986i	1.10379	−	0.295759i
$956$	11.0711	−	19.1757i	0.358064	−	0.620185i
$957$	−1.06301	−	0.284832i	−0.0343621	−	0.00920730i
$958$			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
$963$	4.15950	+	15.5235i	0.134038	+	0.500236i
$964$	23.1421	+	40.0834i	0.745358	+	1.29100i
$965$	9.05025	+	9.05025i	0.291338	+	0.291338i
$966$	28.4329	−	11.9476i	0.914814	−	0.384408i
$967$		−	35.1838i		−	1.13143i	−0.824600	−	0.565717i	$-0.808600\pi$
$967$		−	35.1838i		−	1.13143i	0.824600	−	0.565717i	$-0.191400\pi$
$968$	−15.3137	−	26.5241i	−0.492201	−	0.852518i
$969$	−2.86976	−	1.65685i	−0.0921898	−	0.0532258i
$970$	−5.56396	−	20.7650i	−0.178648	−	0.666723i
$971$	−3.73067	+	13.9231i	−0.119723	+	0.446812i	−0.999597	−	0.0283952i	$-0.990960\pi$
$971$	−3.73067	+	13.9231i	−0.119723	+	0.446812i	0.879874	+	0.475207i	$0.157627\pi$
$972$	−1.41421	+	1.41421i	−0.0453609	+	0.0453609i
$973$	47.8841	+	6.05567i	1.53509	+	0.194136i
$974$	0.786797			0.0252106
$975$	−0.485281	−	0.840532i	−0.0155414	−	0.0269186i
$976$	5.60521	+	20.9189i	0.179418	+	0.669598i
$977$	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
$980$	22.0367	−	13.0245i	0.703938	−	0.416054i
$981$	−1.07107	−	1.07107i	−0.0341966	−	0.0341966i
$982$	−30.8125	−	8.25620i	−0.983268	−	0.263466i
$983$	−26.4881	−	15.2929i	−0.844838	−	0.487768i	0.0140677	−	0.999901i	$-0.495522\pi$
$983$	−26.4881	−	15.2929i	−0.844838	−	0.487768i	−0.858906	+	0.512134i	$0.828855\pi$
$984$	−0.428825	−	1.60040i	−0.0136705	−	0.0510188i
$985$	−7.10228	+	4.10051i	−0.226298	+	0.130653i
$986$	3.11270	+	3.11270i	0.0991285	+	0.0991285i
$987$	2.07225	−	16.3860i	0.0659605	−	0.521571i
$988$		−	3.31371i		−	0.105423i
$989$	51.6344	+	13.8354i	1.64188	+	0.439940i
$990$	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
$997$	28.7836	−	7.71255i	0.911586	−	0.244259i	0.227601	−	0.973755i	$-0.426912\pi$
$997$	28.7836	−	7.71255i	0.911586	−	0.244259i	0.683985	+	0.729496i	$0.260245\pi$
$998$	5.60139	−	1.50089i	0.177309	−	0.0475098i
$999$	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.277.1	yes	8
7.2	even	3	inner	336.2.bq.a.37.2	✓	8
16.13	even	4	inner	336.2.bq.a.109.2	yes	8
112.93	even	12	inner	336.2.bq.a.205.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.a.37.2	✓	8	7.2	even	3	inner
336.2.bq.a.109.2	yes	8	16.13	even	4	inner
336.2.bq.a.205.1	yes	8	112.93	even	12	inner
336.2.bq.a.277.1	yes	8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.473232 + 1.76612i) q^{5} +(1.00000 + 1.00000i) q^{6} +(2.09077 - 1.62132i) q^{7} +2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.473232 + 1.76612i) q^{5} +(1.00000 + 1.00000i) q^{6} +(2.09077 - 1.62132i) q^{7} +2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.669251 - 2.49768i) q^{10} +(0.400100 - 0.107206i) q^{11} +(-1.93185 - 0.517638i) 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} +(2.73205 + 0.732051i) q^{19} +(2.58579 + 2.58579i) q^{20} +(-2.10721 - 1.59990i) q^{21} +(-0.414214 + 0.414214i) q^{22} +(7.13834 - 4.12132i) q^{23} +(2.73205 - 0.732051i) q^{24} +(1.43488 + 0.828427i) q^{25} +(-0.214413 + 0.800199i) 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} +(1.87404 + 4.45982i) q^{35} +2.00000i q^{36} +(0.732051 - 2.73205i) q^{37} +(-3.86370 + 1.03528i) q^{38} +(-0.507306 - 0.292893i) q^{39} +(-4.99536 - 1.33850i) q^{40} -0.585786i q^{41} +(3.71209 + 0.469450i) q^{42} +(4.58579 + 4.58579i) q^{43} +(0.214413 - 0.800199i) q^{44} +(-0.473232 - 1.76612i) 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} +(-1.13165 - 0.303225i) q^{51} +(-0.303225 - 1.13165i) q^{52} +(-8.36188 + 2.24056i) q^{53} +(-1.36603 - 0.366025i) q^{54} +0.757359i q^{55} +(4.58579 + 5.91359i) q^{56} -2.82843i q^{57} +(-0.972476 + 3.62933i) q^{58} +(-2.00050 + 0.536032i) q^{59} +(1.82843 - 3.16693i) q^{60} +(-5.22973 - 1.40130i) 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} +(3.44584 + 12.8601i) q^{67} +(-1.17157 - 2.02922i) q^{68} +(-5.82843 - 5.82843i) q^{69} +(-5.44879 - 4.13700i) q^{70} -15.8995i q^{71} +(-1.41421 - 2.44949i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(1.03528 + 3.86370i) q^{74} +(0.428825 - 1.60040i) q^{75} +(4.00000 - 4.00000i) q^{76} +(0.662700 - 0.872833i) q^{77} +0.828427 q^{78} +(-5.62132 - 9.73641i) q^{79} +(7.06450 - 1.89293i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.414214 + 0.717439i) q^{82} +(-8.77817 + 8.77817i) q^{83} +(-4.87832 + 2.04989i) q^{84} +(1.51472 + 1.51472i) q^{85} +(-8.85906 - 2.37378i) q^{86} +(-2.30090 - 1.32843i) q^{87} +(0.303225 + 1.13165i) q^{88} +(-13.4722 + 7.77817i) q^{89} +(1.82843 + 1.82843i) q^{90} +(0.194453 - 1.53760i) q^{91} -16.4853i q^{92} +(-2.33195 - 0.624844i) q^{93} +(-7.64564 - 4.41421i) q^{94} +(-2.58579 + 4.47871i) q^{95} +(1.46410 - 5.46410i) 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

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