LMFDB - Embedded newform 675.2.u.b.274.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			274.4
Character	$\chi$	$=$	675.274
Dual form			675.2.u.b.574.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.574906 - 1.57954i) q^{2} +(-0.940501 - 1.45446i) q^{3} +(-0.632343 - 0.530599i) q^{4} +(-2.83808 + 0.649381i) q^{6} +(-2.51261 - 2.99441i) q^{7} +(1.70978 - 0.987144i) q^{8} +(-1.23092 + 2.73584i) q^{9} +O(q^{10})$	\(q+(0.574906 - 1.57954i) q^{2} +(-0.940501 - 1.45446i) q^{3} +(-0.632343 - 0.530599i) q^{4} +(-2.83808 + 0.649381i) q^{6} +(-2.51261 - 2.99441i) q^{7} +(1.70978 - 0.987144i) q^{8} +(-1.23092 + 2.73584i) q^{9} +(-0.324801 - 1.84204i) q^{11} +(-0.177016 + 1.41875i) q^{12} +(-0.250563 - 0.688417i) q^{13} +(-6.17430 + 2.24726i) q^{14} +(-0.862951 - 4.89404i) q^{16} +(-1.63648 - 0.944822i) q^{17} +(3.61372 + 3.51713i) q^{18} +(1.37143 + 2.37538i) q^{19} +(-1.99214 + 6.47073i) q^{21} +(-3.09631 - 0.545962i) q^{22} +(-3.74597 + 4.46428i) q^{23} +(-3.04382 - 1.55840i) q^{24} -1.23143 q^{26} +(5.13686 - 0.782746i) q^{27} +3.22668i q^{28} +(-4.99910 - 1.81953i) q^{29} +(1.02696 + 0.861722i) q^{31} +(-4.33786 - 0.764882i) q^{32} +(-2.37370 + 2.20485i) q^{33} +(-2.43321 + 2.04170i) q^{34} +(2.23000 - 1.07687i) q^{36} +(-2.94112 - 1.69806i) q^{37} +(4.54046 - 0.800605i) q^{38} +(-0.765621 + 1.01189i) q^{39} +(-1.68800 + 0.614382i) q^{41} +(9.07549 + 6.86673i) q^{42} +(4.95373 - 0.873477i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(1.09832 + 1.30892i) q^{47} +(-6.30658 + 5.85798i) q^{48} +(-1.43775 + 8.15389i) q^{49} +(0.164904 + 3.26880i) q^{51} +(-0.206831 + 0.568265i) q^{52} -2.84494i q^{53} +(1.71683 - 8.56388i) q^{54} +(-7.25193 - 2.63949i) q^{56} +(2.16507 - 4.22874i) q^{57} +(-5.74803 + 6.85023i) q^{58} +(1.95529 - 11.0890i) q^{59} +(4.00710 - 3.36235i) q^{61} +(1.95153 - 1.12672i) q^{62} +(11.2850 - 3.18824i) q^{63} +(1.26751 - 2.19540i) q^{64} +(2.11800 + 5.01694i) q^{66} +(0.646086 + 1.77511i) q^{67} +(0.533495 + 1.46577i) q^{68} +(10.0162 + 1.24972i) q^{69} +(6.09193 - 10.5515i) q^{71} +(0.596074 + 5.89280i) q^{72} +(-8.56298 + 4.94384i) q^{73} +(-4.37302 + 3.66940i) q^{74} +(0.393163 - 2.22974i) q^{76} +(-4.69972 + 5.60091i) q^{77} +(1.15816 + 1.79107i) q^{78} +(11.6079 + 4.22493i) q^{79} +(-5.96969 - 6.73519i) q^{81} +3.01948i q^{82} +(3.99588 - 10.9786i) q^{83} +(4.69308 - 3.03470i) q^{84} +(1.46824 - 8.32679i) q^{86} +(2.05523 + 8.98227i) q^{87} +(-2.37370 - 2.82886i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(4.73748 - 0.835346i) q^{92} +(0.287484 - 2.30412i) q^{93} +(2.69893 - 0.982329i) q^{94} +(2.96727 + 7.02862i) q^{96} +(0.338162 - 0.0596270i) q^{97} +(12.0528 + 6.95870i) q^{98} +(5.43934 + 1.37879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.574906	−	1.57954i	0.406520	−	1.11690i	−0.552487	−	0.833521i	$-0.686321\pi$
$2$	0.574906	−	1.57954i	0.406520	−	1.11690i	0.959007	−	0.283383i	$-0.0914566\pi$
$3$	−0.940501	−	1.45446i	−0.542999	−	0.839734i
$3$	−0.940501	−	1.45446i	−0.542999	−	0.839734i
$4$	−0.632343	−	0.530599i	−0.316172	−	0.265300i
$5$		0			0
$5$		0			0
$6$	−2.83808	+	0.649381i	−1.15864	+	0.265109i
$7$	−2.51261	−	2.99441i	−0.949676	−	1.13178i	−0.991164	−	0.132641i	$-0.957654\pi$
$7$	−2.51261	−	2.99441i	−0.949676	−	1.13178i	0.0414879	−	0.999139i	$-0.486790\pi$
$8$	1.70978	−	0.987144i	0.604500	−	0.349008i
$9$	−1.23092	+	2.73584i	−0.410305	+	0.911948i
$10$		0			0
$11$	−0.324801	−	1.84204i	−0.0979313	−	0.555396i	−0.993810	−	0.111096i	$-0.964564\pi$
$11$	−0.324801	−	1.84204i	−0.0979313	−	0.555396i	0.895878	−	0.444299i	$-0.146547\pi$
$12$	−0.177016	+	1.41875i	−0.0511002	+	0.409557i
$13$	−0.250563	−	0.688417i	−0.0694937	−	0.190932i	0.900084	−	0.435717i	$-0.143505\pi$
$13$	−0.250563	−	0.688417i	−0.0694937	−	0.190932i	−0.969578	+	0.244784i	$0.921283\pi$
$14$	−6.17430	+	2.24726i	−1.65015	+	0.600606i
$15$		0			0
$16$	−0.862951	−	4.89404i	−0.215738	−	1.22351i
$17$	−1.63648	−	0.944822i	−0.396905	−	0.229153i	0.288243	−	0.957557i	$-0.406929\pi$
$17$	−1.63648	−	0.944822i	−0.396905	−	0.229153i	−0.685147	+	0.728404i	$0.740262\pi$
$18$	3.61372	+	3.51713i	0.851761	+	0.828997i
$19$	1.37143	+	2.37538i	0.314627	+	0.544950i	0.979358	−	0.202133i	$-0.0647872\pi$
$19$	1.37143	+	2.37538i	0.314627	+	0.544950i	−0.664731	+	0.747083i	$0.731454\pi$
$20$		0			0
$21$	−1.99214	+	6.47073i	−0.434721	+	1.41203i
$22$	−3.09631	−	0.545962i	−0.660135	−	0.116400i
$23$	−3.74597	+	4.46428i	−0.781089	+	0.930866i	−0.998982	−	0.0451066i	$-0.985637\pi$
$23$	−3.74597	+	4.46428i	−0.781089	+	0.930866i	0.217893	+	0.975973i	$0.430082\pi$
$24$	−3.04382	−	1.55840i	−0.621317	−	0.318108i
$25$		0			0
$26$	−1.23143			−0.241504
$27$	5.13686	−	0.782746i	0.988589	−	0.150640i
$28$			3.22668i			0.609786i
$29$	−4.99910	−	1.81953i	−0.928310	−	0.337877i	−0.166771	−	0.985996i	$-0.553334\pi$
$29$	−4.99910	−	1.81953i	−0.928310	−	0.337877i	−0.761540	+	0.648118i	$0.775556\pi$
$30$		0			0
$31$	1.02696	+	0.861722i	0.184447	+	0.154770i	0.730336	−	0.683088i	$-0.239363\pi$
$31$	1.02696	+	0.861722i	0.184447	+	0.154770i	−0.545889	+	0.837858i	$0.683808\pi$
$32$	−4.33786	−	0.764882i	−0.766833	−	0.135213i
$33$	−2.37370	+	2.20485i	−0.413208	+	0.383815i
$34$	−2.43321	+	2.04170i	−0.417291	+	0.350149i
$35$		0			0
$36$	2.23000	−	1.07687i	0.371666	−	0.179478i
$37$	−2.94112	−	1.69806i	−0.483517	−	0.279159i	0.238364	−	0.971176i	$-0.423389\pi$
$37$	−2.94112	−	1.69806i	−0.483517	−	0.279159i	−0.721881	+	0.692017i	$0.756722\pi$
$38$	4.54046	−	0.800605i	0.736559	−	0.129875i
$39$	−0.765621	+	1.01189i	−0.122597	+	0.162032i
$40$		0			0
$41$	−1.68800	+	0.614382i	−0.263621	+	0.0959503i	−0.470449	−	0.882427i	$-0.655908\pi$
$41$	−1.68800	+	0.614382i	−0.263621	+	0.0959503i	0.206828	+	0.978377i	$0.433686\pi$
$42$	9.07549	+	6.86673i	1.40038	+	1.05956i
$43$	4.95373	−	0.873477i	0.755437	−	0.133204i	0.217351	−	0.976094i	$-0.430258\pi$
$43$	4.95373	−	0.873477i	0.755437	−	0.133204i	0.538087	+	0.842890i	$0.319147\pi$
$44$	−0.771999	+	1.33714i	−0.116383	+	0.201582i
$45$		0			0
$46$	4.89793	+	8.48346i	0.722160	+	1.25082i
$47$	1.09832	+	1.30892i	0.160206	+	0.190926i	0.840176	−	0.542314i	$-0.182452\pi$
$47$	1.09832	+	1.30892i	0.160206	+	0.190926i	−0.679970	+	0.733240i	$0.738007\pi$
$48$	−6.30658	+	5.85798i	−0.910277	+	0.845526i
$49$	−1.43775	+	8.15389i	−0.205393	+	1.16484i
$50$		0			0
$51$	0.164904	+	3.26880i	0.0230912	+	0.457724i
$52$	−0.206831	+	0.568265i	−0.0286824	+	0.0788041i
$53$		−	2.84494i		−	0.390783i	−0.980725	−	0.195391i	$-0.937402\pi$
$53$		−	2.84494i		−	0.390783i	0.980725	−	0.195391i	$-0.0625977\pi$
$54$	1.71683	−	8.56388i	0.233631	−	1.16540i
$55$		0			0
$56$	−7.25193	−	2.63949i	−0.969080	−	0.352716i
$57$	2.16507	−	4.22874i	0.286771	−	0.560110i
$58$	−5.74803	+	6.85023i	−0.754753	+	0.899480i
$59$	1.95529	−	11.0890i	0.254557	−	1.44366i	−0.542652	−	0.839958i	$-0.682580\pi$
$59$	1.95529	−	11.0890i	0.254557	−	1.44366i	0.797208	−	0.603704i	$-0.206309\pi$
$60$		0			0
$61$	4.00710	−	3.36235i	0.513056	−	0.430505i	−0.349147	−	0.937068i	$-0.613529\pi$
$61$	4.00710	−	3.36235i	0.513056	−	0.430505i	0.862203	+	0.506563i	$0.169084\pi$
$62$	1.95153	−	1.12672i	0.247844	−	0.143093i
$63$	11.2850	−	3.18824i	1.42178	−	0.401680i
$64$	1.26751	−	2.19540i	0.158439	−	0.274425i
$65$		0			0
$66$	2.11800	+	5.01694i	0.260708	+	0.617542i
$67$	0.646086	+	1.77511i	0.0789319	+	0.216864i	0.972882	−	0.231304i	$-0.0742991\pi$
$67$	0.646086	+	1.77511i	0.0789319	+	0.216864i	−0.893950	+	0.448167i	$0.852077\pi$
$68$	0.533495	+	1.46577i	0.0646958	+	0.177750i
$69$	10.0162	+	1.24972i	1.20581	+	0.150448i
$70$		0			0
$71$	6.09193	−	10.5515i	0.722980	−	1.25224i	−0.236821	−	0.971553i	$-0.576105\pi$
$71$	6.09193	−	10.5515i	0.722980	−	1.25224i	0.959800	−	0.280684i	$-0.0905613\pi$
$72$	0.596074	+	5.89280i	0.0702480	+	0.694473i
$73$	−8.56298	+	4.94384i	−1.00222	+	0.578633i	−0.908905	−	0.417004i	$-0.863080\pi$
$73$	−8.56298	+	4.94384i	−1.00222	+	0.578633i	−0.0933164	+	0.995637i	$0.529747\pi$
$74$	−4.37302	+	3.66940i	−0.508353	+	0.426559i
$75$		0			0
$76$	0.393163	−	2.22974i	0.0450989	−	0.255768i
$77$	−4.69972	+	5.60091i	−0.535583	+	0.638283i
$78$	1.15816	+	1.79107i	0.131136	+	0.202799i
$79$	11.6079	+	4.22493i	1.30599	+	0.475342i	0.898943	−	0.438065i	$-0.144336\pi$
$79$	11.6079	+	4.22493i	1.30599	+	0.475342i	0.407048	+	0.913407i	$0.366558\pi$
$80$		0			0
$81$	−5.96969	−	6.73519i	−0.663299	−	0.748354i
$82$			3.01948i			0.333445i
$83$	3.99588	−	10.9786i	0.438605	−	1.20506i	−0.501796	−	0.864986i	$-0.667327\pi$
$83$	3.99588	−	10.9786i	0.438605	−	1.20506i	0.940400	−	0.340070i	$-0.110451\pi$
$84$	4.69308	−	3.03470i	0.512057	−	0.331113i
$85$		0			0
$86$	1.46824	−	8.32679i	0.158324	−	0.897901i
$87$	2.05523	+	8.98227i	0.220344	+	0.963000i
$88$	−2.37370	−	2.82886i	−0.253037	−	0.301558i
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	0.673331	−	0.739341i	$-0.264863\pi$
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	−0.976954	+	0.213452i	$0.931529\pi$
$90$		0			0
$91$	−1.43183	+	2.48001i	−0.150097	+	0.259976i
$92$	4.73748	−	0.835346i	0.493917	−	0.0870908i
$93$	0.287484	−	2.30412i	0.0298107	−	0.238926i
$94$	2.69893	−	0.982329i	0.278373	−	0.101319i
$95$		0			0
$96$	2.96727	+	7.02862i	0.302846	+	0.717356i
$97$	0.338162	−	0.0596270i	0.0343351	−	0.00605421i	−0.156454	−	0.987685i	$-0.550006\pi$
$97$	0.338162	−	0.0596270i	0.0343351	−	0.00605421i	0.190789	+	0.981631i	$0.438895\pi$
$98$	12.0528	+	6.95870i	1.21752	+	0.702935i
$99$	5.43934	+	1.37879i	0.546674	+	0.138574i
$100$		0			0
$101$	−13.3309	+	11.1860i	−1.32647	+	1.11304i	−0.341586	+	0.939850i	$0.610964\pi$
$101$	−13.3309	+	11.1860i	−1.32647	+	1.11304i	−0.984888	+	0.173194i	$0.944591\pi$
$102$	5.25801	+	1.61878i	0.520621	+	0.160283i
$103$	15.5728	+	2.74590i	1.53443	+	0.270561i	0.876086	−	0.482155i	$-0.160146\pi$
$103$	15.5728	+	2.74590i	1.53443	+	0.270561i	0.658345	+	0.752717i	$0.271257\pi$
$104$	−1.10798	−	0.929702i	−0.108646	−	0.0911648i
$105$		0			0
$106$	−4.49370	−	1.63557i	−0.436467	−	0.158861i
$107$		−	16.5298i		−	1.59800i	−0.601332	−	0.798999i	$-0.705363\pi$
$107$		−	16.5298i		−	1.59800i	0.601332	−	0.798999i	$-0.294637\pi$
$108$	−3.66358	−	2.23065i	−0.352528	−	0.214644i
$109$	4.71844			0.451945			0.225972	−	0.974134i	$-0.427444\pi$
$109$	4.71844			0.451945			0.225972	+	0.974134i	$0.427444\pi$
$110$		0			0
$111$	0.296369	+	5.87477i	0.0281301	+	0.557608i
$112$	−12.4865	+	14.8808i	−1.17986	+	1.40611i
$113$	−19.6418	−	3.46338i	−1.84775	−	0.325807i	−0.863739	−	0.503939i	$-0.831884\pi$
$113$	−19.6418	−	3.46338i	−1.84775	−	0.325807i	−0.984007	+	0.178132i	$0.942995\pi$
$114$	−5.43475	−	5.85095i	−0.509011	−	0.547992i
$115$		0			0
$116$	2.19571	+	3.80308i	0.203867	+	0.353108i
$117$	2.19182	+	0.161881i	0.202634	+	0.0149659i
$118$	−16.3914	−	9.46357i	−1.50895	−	0.871193i
$119$	1.28265	+	7.27425i	0.117580	+	0.666830i
$120$		0			0
$121$	7.04901	−	2.56563i	0.640819	−	0.233239i
$122$	−3.00727	−	8.26241i	−0.272266	−	0.748043i
$123$	2.48116	+	1.87730i	0.223719	+	0.169271i
$124$	−0.192163	−	1.08981i	−0.0172567	−	0.0978676i
$125$		0			0
$126$	1.45188	−	19.6581i	0.129344	−	1.75128i
$127$	0.926176	−	0.534728i	0.0821849	−	0.0474495i	−0.458344	−	0.888775i	$-0.651557\pi$
$127$	0.926176	−	0.534728i	0.0821849	−	0.0474495i	0.540529	+	0.841325i	$0.318224\pi$
$128$	−8.40170	−	10.0128i	−0.742612	−	0.885011i
$129$	−5.92943	−	6.38351i	−0.522057	−	0.562037i
$130$		0			0
$131$	5.85281	+	4.91109i	0.511362	+	0.429084i	0.861608	−	0.507574i	$-0.169458\pi$
$131$	5.85281	+	4.91109i	0.511362	+	0.429084i	−0.350246	+	0.936658i	$0.613902\pi$
$132$	2.67089	−	0.134740i	0.232471	−	0.0117276i
$133$	3.66701	−	10.0750i	0.317970	−	0.873615i
$134$	3.17529			0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	5.35279	−	14.7067i	0.457319	−	1.25647i	−0.470154	−	0.882585i	$-0.655801\pi$
$137$	5.35279	−	14.7067i	0.457319	−	1.25647i	0.927473	−	0.373890i	$-0.121976\pi$
$138$	7.73235	−	15.1025i	0.658222	−	1.28561i
$139$	−6.63160	−	5.56457i	−0.562485	−	0.471981i	0.316658	−	0.948540i	$-0.397439\pi$
$139$	−6.63160	−	5.56457i	−0.562485	−	0.471981i	−0.879142	+	0.476559i	$0.841884\pi$
$140$		0			0
$141$	0.870810	−	2.82850i	0.0733354	−	0.238203i
$142$	−13.1643	−	15.6886i	−1.10472	−	1.31656i
$143$	−1.18671	+	0.685146i	−0.0992375	+	0.0572948i
$144$	14.4516	+	3.66325i	1.20430	+	0.305271i
$145$		0			0
$146$	2.88609	+	16.3678i	0.238854	+	1.35461i
$147$	13.2117	−	5.57759i	1.08968	−	0.460032i
$148$	0.958811	+	2.63431i	0.0788137	+	0.216539i
$149$	−2.31524	+	0.842677i	−0.189672	+	0.0690348i	−0.435110	−	0.900377i	$-0.643290\pi$
$149$	−2.31524	+	0.842677i	−0.189672	+	0.0690348i	0.245438	+	0.969412i	$0.421068\pi$
$150$		0			0
$151$	−1.82563	−	10.3537i	−0.148568	−	0.842571i	−0.964433	−	0.264328i	$-0.914850\pi$
$151$	−1.82563	−	10.3537i	−0.148568	−	0.842571i	0.815865	−	0.578243i	$-0.196261\pi$
$152$	4.68969	+	2.70760i	0.380384	+	0.219615i
$153$	4.59925	−	3.31416i	0.371828	−	0.267934i
$154$	6.14497	+	10.6434i	0.495176	+	0.857669i
$155$		0			0
$156$	1.02104	−	0.233625i	0.0817489	−	0.0187050i
$157$	0.354480	+	0.0625044i	0.0282906	+	0.00498840i	0.187776	−	0.982212i	$-0.439872\pi$
$157$	0.354480	+	0.0625044i	0.0282906	+	0.00498840i	−0.159485	+	0.987200i	$0.550983\pi$
$158$	13.3469	−	15.9062i	1.06182	−	1.26543i
$159$	−4.13786	+	2.67567i	−0.328154	+	0.212195i
$160$		0			0
$161$	22.7800			1.79532
$162$	−14.0705	+	5.55728i	−1.10548	+	0.436621i
$163$		−	14.6186i		−	1.14502i	−0.819899	−	0.572508i	$-0.805971\pi$
$163$		−	14.6186i		−	1.14502i	0.819899	−	0.572508i	$-0.194029\pi$
$164$	1.39339	+	0.507151i	0.108805	+	0.0396019i
$165$		0			0
$166$	−15.0439	−	12.6233i	−1.16763	−	0.979758i
$167$	2.14279	+	0.377832i	0.165814	+	0.0292375i	0.255939	−	0.966693i	$-0.417615\pi$
$167$	2.14279	+	0.377832i	0.165814	+	0.0292375i	−0.0901247	+	0.995930i	$0.528727\pi$
$168$	2.98142	+	13.0301i	0.230021	+	1.00529i
$169$	9.54744	−	8.01125i	0.734419	−	0.616250i
$170$		0			0
$171$	−8.18679	+	0.828119i	−0.626060	+	0.0633278i
$172$	−3.59593	−	2.07611i	−0.274187	−	0.158302i
$173$	−17.3001	+	3.05048i	−1.31531	+	0.231924i	−0.786906	−	0.617072i	$-0.788319\pi$
$173$	−17.3001	+	3.05048i	−1.31531	+	0.231924i	−0.528399	+	0.848996i	$0.677207\pi$
$174$	15.3694	+	1.91763i	1.16515	+	0.145375i
$175$		0			0
$176$	−8.73473	+	3.17918i	−0.658405	+	0.239640i
$177$	−17.9674	+	7.58531i	−1.35052	+	0.570147i
$178$	−9.48320	+	1.67214i	−0.710796	+	0.125333i
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	−0.846646	−	0.532157i	$-0.821382\pi$
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	0.884184	+	0.467138i	$0.154715\pi$
$180$		0			0
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	0.927859	+	0.372932i	$0.121647\pi$
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	−0.140961	+	0.990015i	$0.545019\pi$
$182$	3.09411	+	3.68741i	0.229350	+	0.273329i
$183$	−8.65909	−	2.66587i	−0.640099	−	0.197067i
$184$	−1.99792	+	11.3308i	−0.147289	+	0.835315i
$185$		0			0
$186$	−3.47418	−	1.77875i	−0.254739	−	0.130424i
$187$	−1.20887	+	3.32134i	−0.0884012	+	0.242880i
$188$		−	1.41045i		−	0.102868i
$189$	−15.2508	−	13.4151i	−1.10933	−	0.975806i
$190$		0			0
$191$	9.23566	+	3.36150i	0.668269	+	0.243230i	0.653802	−	0.756665i	$-0.273173\pi$
$191$	9.23566	+	3.36150i	0.668269	+	0.243230i	0.0144664	+	0.999895i	$0.495395\pi$
$192$	−4.38522	+	0.221225i	−0.316476	+	0.0159655i
$193$	−7.17099	+	8.54606i	−0.516179	+	0.615159i	−0.959673	−	0.281119i	$-0.909294\pi$
$193$	−7.17099	+	8.54606i	−0.516179	+	0.615159i	0.443494	+	0.896278i	$0.353739\pi$
$194$	0.100228	−	0.568420i	0.00719594	−	0.0408102i
$195$		0			0
$196$	5.23560	−	4.39319i	0.373971	−	0.313799i
$197$	7.87212	−	4.54497i	0.560865	−	0.323816i	−0.192628	−	0.981272i	$-0.561701\pi$
$197$	7.87212	−	4.54497i	0.560865	−	0.323816i	0.753493	+	0.657456i	$0.228368\pi$
$198$	5.30496	−	7.79898i	0.377007	−	0.554249i
$199$	−7.34694	+	12.7253i	−0.520811	+	0.902071i	0.478896	+	0.877872i	$0.341037\pi$
$199$	−7.34694	+	12.7253i	−0.520811	+	0.902071i	−0.999707	+	0.0241994i	$0.992296\pi$
$200$		0			0
$201$	1.97418	−	2.60920i	0.139248	−	0.184038i
$202$	10.0047	+	27.4876i	0.703925	+	1.93402i
$203$	7.11238	+	19.5411i	0.499191	+	1.37152i
$204$	1.63015	−	2.15450i	0.114133	−	0.150845i
$205$		0			0
$206$	13.2901	−	23.0192i	0.925968	−	1.60382i
$207$	−7.60259	−	15.7435i	−0.528417	−	1.09425i
$208$	−3.15292	+	1.82034i	−0.218615	+	0.126218i
$209$	3.93011	−	3.29775i	0.271851	−	0.228110i
$210$		0			0
$211$	1.36458	−	7.73891i	0.0939415	−	0.532769i	−0.901125	−	0.433559i	$-0.857257\pi$
$211$	1.36458	−	7.73891i	0.0939415	−	0.532769i	0.995067	−	0.0992096i	$-0.0316314\pi$
$212$	−1.50952	+	1.79898i	−0.103675	+	0.123555i
$213$	−21.0763	+	1.06325i	−1.44412	+	0.0728528i
$214$	−26.1095	−	9.50309i	−1.78481	−	0.649618i
$215$		0			0
$216$	8.01024	−	6.40915i	0.545028	−	0.436087i
$217$		−	5.24030i		−	0.355735i
$218$	2.71266	−	7.45297i	0.183724	−	0.504779i
$219$	15.2441	+	7.80484i	1.03010	+	0.527402i
$220$		0			0
$221$	−0.240390	+	1.36332i	−0.0161704	+	0.0917067i
$222$	9.44982	+	2.90931i	0.634231	+	0.195260i
$223$	5.61853	+	6.69591i	0.376245	+	0.448391i	0.920625	−	0.390447i	$-0.127680\pi$
$223$	5.61853	+	6.69591i	0.376245	+	0.448391i	−0.544380	+	0.838838i	$0.683235\pi$
$224$	8.60897	+	14.9112i	0.575211	+	0.996295i
$225$		0			0
$226$	−16.7627	+	29.0339i	−1.11504	+	1.93131i
$227$	−4.00661	+	0.706473i	−0.265928	+	0.0468903i	−0.305022	−	0.952345i	$-0.598664\pi$
$227$	−4.00661	+	0.706473i	−0.265928	+	0.0468903i	0.0390942	+	0.999236i	$0.487553\pi$
$228$	−3.61284	+	1.52523i	−0.239266	+	0.101011i
$229$	15.1816	−	5.52563i	1.00323	−	0.365144i	0.212398	−	0.977183i	$-0.431873\pi$
$229$	15.1816	−	5.52563i	1.00323	−	0.365144i	0.790827	+	0.612039i	$0.209651\pi$
$230$		0			0
$231$	12.5664	+	1.56790i	0.826808	+	0.103160i
$232$	−10.3435	+	1.82384i	−0.679086	+	0.119741i
$233$	14.9070	+	8.60658i	0.976592	+	0.563836i	0.901240	−	0.433321i	$-0.142658\pi$
$233$	14.9070	+	8.60658i	0.976592	+	0.563836i	0.0753527	+	0.997157i	$0.475992\pi$
$234$	1.51579	−	3.36901i	0.0990903	−	0.220239i
$235$		0			0
$236$	−7.12022	+	5.97457i	−0.463487	+	0.388911i
$237$	−4.77225	−	20.8568i	−0.309991	−	1.35479i
$238$	12.2274	+	2.15602i	0.792583	+	0.139754i
$239$	1.17621	+	0.986962i	0.0760830	+	0.0638412i	0.680036	−	0.733179i	$-0.261964\pi$
$239$	1.17621	+	0.986962i	0.0760830	+	0.0638412i	−0.603953	+	0.797020i	$0.706409\pi$
$240$		0			0
$241$	5.18868	+	1.88852i	0.334232	+	0.121650i	0.503684	−	0.863888i	$-0.331978\pi$
$241$	5.18868	+	1.88852i	0.334232	+	0.121650i	−0.169452	+	0.985538i	$0.554200\pi$
$242$		−	12.6092i		−	0.810549i
$243$	−4.18157	+	15.0171i	−0.268248	+	0.963350i
$244$	−4.31792			−0.276427
$245$		0			0
$246$	4.39171	−	2.83982i	0.280005	−	0.181060i
$247$	1.29162	−	1.53930i	0.0821841	−	0.0979432i
$248$	2.60652	+	0.459600i	0.165514	+	0.0291847i
$249$	−19.7261	+	4.51352i	−1.25009	+	0.286033i
$250$		0			0
$251$	10.7204	+	18.5683i	0.676668	+	1.17202i	0.975978	+	0.217868i	$0.0699102\pi$
$251$	10.7204	+	18.5683i	0.676668	+	1.17202i	−0.299310	+	0.954156i	$0.596756\pi$
$252$	−8.82770	−	3.97177i	−0.556093	−	0.250198i
$253$	9.44007	+	5.45023i	0.593492	+	0.342653i
$254$	−0.312161	−	1.77035i	−0.0195867	−	0.111082i
$255$		0			0
$256$	−15.8814	+	5.78037i	−0.992590	+	0.361273i
$257$	5.05727	+	13.8947i	0.315464	+	0.866730i	0.991529	+	0.129888i	$0.0414617\pi$
$257$	5.05727	+	13.8947i	0.315464	+	0.866730i	−0.676065	+	0.736842i	$0.736316\pi$
$258$	−13.4919	+	5.69586i	−0.839967	+	0.354609i
$259$	2.30520	+	13.0735i	0.143238	+	0.812346i
$260$		0			0
$261$	11.1314	−	11.4371i	0.689017	−	0.707938i
$262$	11.1221	−	6.42133i	0.687124	−	0.396711i
$263$	−1.80158	−	2.14704i	−0.111090	−	0.132392i	0.707634	−	0.706579i	$-0.249763\pi$
$263$	−1.80158	−	2.14704i	−0.111090	−	0.132392i	−0.818724	+	0.574187i	$0.805318\pi$
$264$	−1.88201	+	6.11300i	−0.115830	+	0.376229i
$265$		0			0
$266$	−13.8057	−	11.5844i	−0.846483	−	0.710284i
$267$	−4.52197	+	8.83215i	−0.276740	+	0.540519i
$268$	0.533322	−	1.46529i	0.0325778	−	0.0895068i
$269$	0.356528			0.0217379			0.0108689	−	0.999941i	$-0.496540\pi$
$269$	0.356528			0.0217379			0.0108689	+	0.999941i	$0.496540\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	−3.21179	+	8.82433i	−0.194744	+	0.535054i
$273$	4.95372	−	0.249904i	0.299813	−	0.0151249i
$274$	−20.1524	−	16.9099i	−1.21745	−	1.02156i
$275$		0			0
$276$	−5.67059	−	6.10484i	−0.341329	−	0.367468i
$277$	16.0632	+	19.1434i	0.965146	+	1.15022i	0.988611	+	0.150492i	$0.0480858\pi$
$277$	16.0632	+	19.1434i	0.965146	+	1.15022i	−0.0234648	+	0.999725i	$0.507470\pi$
$278$	−12.6020	+	7.27577i	−0.755818	+	0.436372i
$279$	−3.62164	+	1.74890i	−0.216822	+	0.104704i
$280$		0			0
$281$	1.27160	+	7.21162i	0.0758575	+	0.430209i	0.998958	+	0.0456492i	$0.0145356\pi$
$281$	1.27160	+	7.21162i	0.0758575	+	0.430209i	−0.923100	+	0.384560i	$0.874353\pi$
$282$	−3.96710	−	3.00160i	−0.236237	−	0.178743i
$283$	−4.92102	−	13.5204i	−0.292524	−	0.803703i	−0.995696	−	0.0926830i	$-0.970456\pi$
$283$	−4.92102	−	13.5204i	−0.292524	−	0.803703i	0.703172	−	0.711020i	$-0.251767\pi$
$284$	−9.45083	+	3.43982i	−0.560804	+	0.204116i
$285$		0			0
$286$	0.399971	+	2.26835i	0.0236508	+	0.134130i
$287$	6.08099	+	3.51086i	0.358950	+	0.207240i
$288$	7.43214	−	10.9262i	0.437943	−	0.643833i
$289$	−6.71462	−	11.6301i	−0.394978	−	0.684122i
$290$		0			0
$291$	−0.404767	−	0.435764i	−0.0237278	−	0.0255449i
$292$	8.03794	+	1.41731i	0.470385	+	0.0829416i
$293$	−9.26611	+	11.0429i	−0.541332	+	0.645134i	−0.965486	−	0.260456i	$-0.916127\pi$
$293$	−9.26611	+	11.0429i	−0.541332	+	0.645134i	0.424154	+	0.905590i	$0.360572\pi$
$294$	−1.21453	−	24.0750i	−0.0708330	−	1.40409i
$295$		0			0
$296$	−6.70491			−0.389715
$297$	−3.11031	−	9.20806i	−0.180478	−	0.534306i
$298$			4.14147i			0.239909i
$299$	4.01189	+	1.46021i	0.232013	+	0.0844460i
$300$		0			0
$301$	−15.0623	−	12.6388i	−0.868178	−	0.728488i
$302$	−17.4036	−	3.06873i	−1.00147	−	0.176586i
$303$	28.8073	+	8.86888i	1.65493	+	0.509504i
$304$	10.4417	−	8.76166i	0.598875	−	0.502516i
$305$		0			0
$306$	−2.59071	−	9.17004i	−0.148101	−	0.524216i
$307$	26.3554	+	15.2163i	1.50418	+	0.868440i	0.999988	+	0.00484869i	$0.00154339\pi$
$307$	26.3554	+	15.2163i	1.50418	+	0.868440i	0.504193	+	0.863591i	$0.331790\pi$
$308$	5.94367	−	1.04803i	0.338672	−	0.0597171i
$309$	−10.6524	−	25.2325i	−0.605994	−	1.43543i
$310$		0			0
$311$	13.1516	−	4.78678i	0.745757	−	0.271433i	0.0589378	−	0.998262i	$-0.481229\pi$
$311$	13.1516	−	4.78678i	0.745757	−	0.271433i	0.686819	+	0.726828i	$0.259006\pi$
$312$	−0.310163	+	2.48589i	−0.0175595	+	0.140736i
$313$	21.7520	−	3.83547i	1.22950	−	0.216793i	0.479087	−	0.877767i	$-0.340968\pi$
$313$	21.7520	−	3.83547i	1.22950	−	0.216793i	0.750409	+	0.660974i	$0.229857\pi$
$314$	0.302521	−	0.523982i	0.0170722	−	0.0295700i
$315$		0			0
$316$	−5.09844	−	8.83075i	−0.286810	−	0.496769i
$317$	11.1773	+	13.3205i	0.627777	+	0.748156i	0.982387	−	0.186859i	$-0.0598307\pi$
$317$	11.1773	+	13.3205i	0.627777	+	0.748156i	−0.354610	+	0.935014i	$0.615386\pi$
$318$	1.84745	+	8.07418i	0.103600	+	0.452777i
$319$	−1.72792	+	9.79953i	−0.0967450	+	0.548668i
$320$		0			0
$321$	−24.0420	+	15.5463i	−1.34189	+	0.867711i
$322$	13.0964	−	35.9820i	0.729832	−	2.00520i
$323$		−	5.18302i		−	0.288391i
$324$	0.201212	+	7.42647i	0.0111784	+	0.412581i
$325$		0			0
$326$	−23.0906	−	8.40430i	−1.27887	−	0.465471i
$327$	−4.43770	−	6.86279i	−0.245405	−	0.379513i
$328$	−2.27963	+	2.71676i	−0.125872	+	0.150008i
$329$	1.15981	−	6.57762i	0.0639425	−	0.362636i
$330$		0			0
$331$	0.661975	−	0.555463i	0.0363855	−	0.0305310i	−0.624414	−	0.781094i	$-0.714662\pi$
$331$	0.661975	−	0.555463i	0.0363855	−	0.0305310i	0.660799	+	0.750563i	$0.270218\pi$
$332$	−8.35199	+	4.82203i	−0.458375	+	0.264643i
$333$	8.26589	−	5.95628i	0.452968	−	0.326402i
$334$	1.82870	−	3.16741i	0.100062	−	0.173313i
$335$		0			0
$336$	33.3871	+	4.16569i	1.82142	+	0.227257i
$337$	−0.143145	−	0.393289i	−0.00779762	−	0.0214238i	0.935733	−	0.352710i	$-0.114740\pi$
$337$	−0.143145	−	0.393289i	−0.00779762	−	0.0214238i	−0.943530	+	0.331286i	$0.892517\pi$
$338$	−7.16522	−	19.6863i	−0.389737	−	1.07079i
$339$	13.4358	+	31.8256i	0.729732	+	1.72853i
$340$		0			0
$341$	1.25377	−	2.17159i	0.0678953	−	0.117598i
$342$	−3.39859	+	13.4075i	−0.183775	+	0.724992i
$343$	4.33199	−	2.50108i	0.233906	−	0.135046i
$344$	7.60757	−	6.38351i	0.410173	−	0.344176i
$345$		0			0
$346$	−5.12759	+	29.0800i	−0.275661	+	1.56335i
$347$	−15.0475	+	17.9329i	−0.807792	+	0.962689i	−0.999825	−	0.0186996i	$-0.994047\pi$
$347$	−15.0475	+	17.9329i	−0.807792	+	0.962689i	0.192033	+	0.981388i	$0.438492\pi$
$348$	3.46637	−	6.77038i	0.185817	−	0.362931i
$349$	19.8993	+	7.24276i	1.06519	+	0.387696i	0.814374	−	0.580340i	$-0.197080\pi$
$349$	19.8993	+	7.24276i	1.06519	+	0.387696i	0.250811	+	0.968036i	$0.419303\pi$
$350$		0			0
$351$	−1.82596	−	3.34017i	−0.0974627	−	0.178285i
$352$			8.23894i			0.439137i
$353$	−8.05268	+	22.1246i	−0.428601	+	1.17757i	0.518061	+	0.855344i	$0.326654\pi$
$353$	−8.05268	+	22.1246i	−0.428601	+	1.17757i	−0.946662	+	0.322228i	$0.895568\pi$
$354$	1.65172	+	32.7411i	0.0877878	+	1.74017i
$355$		0			0
$356$	−0.821160	+	4.65703i	−0.0435214	+	0.246822i
$357$	9.37379	−	8.70700i	0.496114	−	0.460823i
$358$	−1.08530	−	1.29341i	−0.0573599	−	0.0683589i
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	0.694347	−	0.719640i	$-0.255693\pi$
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	−0.970400	+	0.241502i	$0.922360\pi$
$360$		0			0
$361$	5.73837	−	9.93915i	0.302019	−	0.523113i
$362$	35.0497	−	6.18020i	1.84217	−	0.324824i
$363$	−10.3612	−	7.83953i	−0.543822	−	0.411469i
$364$	2.22130	−	0.808488i	0.116428	−	0.0423763i
$365$		0			0
$366$	−9.18901	+	12.1448i	−0.480317	+	0.634817i
$367$	−20.9353	+	3.69146i	−1.09281	+	0.192693i	−0.690875	−	0.722974i	$-0.742775\pi$
$367$	−20.9353	+	3.69146i	−1.09281	+	0.192693i	−0.401939	+	0.915666i	$0.631664\pi$
$368$	25.0809	+	14.4805i	1.30743	+	0.754848i
$369$	0.396932	−	5.37436i	0.0206635	−	0.279778i
$370$		0			0
$371$	−8.51892	+	7.14822i	−0.442280	+	0.371117i
$372$	−1.40435	+	1.30446i	−0.0728124	+	0.0676330i
$373$	−2.27499	−	0.401142i	−0.117795	−	0.0207704i	0.114440	−	0.993430i	$-0.463493\pi$
$373$	−2.27499	−	0.401142i	−0.117795	−	0.0207704i	−0.232235	+	0.972660i	$0.574604\pi$
$374$	4.55120	+	3.81891i	0.235337	+	0.197471i
$375$		0			0
$376$	3.16998	+	1.15378i	0.163479	+	0.0595016i
$377$			3.89737i			0.200725i
$378$	−29.9575	+	16.3768i	−1.54085	+	0.842331i
$379$	−12.5539			−0.644850			−0.322425	−	0.946595i	$-0.604498\pi$
$379$	−12.5539			−0.644850			−0.322425	+	0.946595i	$0.604498\pi$
$380$		0			0
$381$	−1.64881	−	0.844175i	−0.0844712	−	0.0432484i
$382$	10.6193	−	12.6555i	0.543329	−	0.647514i
$383$	19.3559	+	3.41297i	0.989042	+	0.174395i	0.644689	−	0.764445i	$-0.276987\pi$
$383$	19.3559	+	3.41297i	0.989042	+	0.174395i	0.344353	+	0.938840i	$0.388098\pi$
$384$	−6.66136	+	21.6369i	−0.339936	+	1.10416i
$385$		0			0
$386$	9.37620	+	16.2401i	0.477236	+	0.826597i
$387$	−3.70793	+	14.6278i	−0.188485	+	0.743574i
$388$	−0.245472	−	0.141724i	−0.0124620	−	0.00719492i
$389$	3.27198	+	18.5563i	0.165896	+	0.940843i	0.948136	+	0.317866i	$0.102966\pi$
$389$	3.27198	+	18.5563i	0.165896	+	0.940843i	−0.782240	+	0.622978i	$0.785923\pi$
$390$		0			0
$391$	10.3482	−	3.76642i	0.523329	−	0.190476i
$392$	5.59082	+	15.3607i	0.282379	+	0.775831i
$393$	1.63842	−	13.1316i	0.0826472	−	0.662400i
$394$	−2.65324	−	15.0473i	−0.133668	−	0.758070i
$395$		0			0
$396$	−2.70794	−	3.75798i	−0.136079	−	0.188845i
$397$	17.4225	−	10.0589i	0.874410	−	0.504841i	0.00559897	−	0.999984i	$-0.498218\pi$
$397$	17.4225	−	10.0589i	0.874410	−	0.504841i	0.868811	+	0.495143i	$0.164884\pi$
$398$	15.8763	+	18.9206i	0.795807	+	0.948405i
$399$	−18.1026	+	4.14205i	−0.906261	+	0.207362i
$400$		0			0
$401$	−23.5985	−	19.8015i	−1.17845	−	0.988840i	−0.999988	−	0.00489430i	$-0.998442\pi$
$401$	−23.5985	−	19.8015i	−1.17845	−	0.988840i	−0.178466	−	0.983946i	$-0.557113\pi$
$402$	−2.98636	−	4.61834i	−0.148946	−	0.230342i
$403$	0.335905	−	0.922892i	0.0167326	−	0.0459725i
$404$	14.3650			0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	−2.17261	+	5.96919i	−0.107692	+	0.295882i
$408$	3.50873	+	5.42616i	0.173708	+	0.268635i
$409$	−30.4059	−	25.5136i	−1.50347	−	1.26156i	−0.875388	−	0.483421i	$-0.839394\pi$
$409$	−30.4059	−	25.5136i	−1.50347	−	1.26156i	−0.628086	−	0.778144i	$-0.716161\pi$
$410$		0			0
$411$	−26.4246	+	6.04621i	−1.30343	+	0.298237i
$412$	−8.39037	−	9.99925i	−0.413364	−	0.492628i
$413$	−38.1178	+	22.0073i	−1.87565	+	1.08291i
$414$	−29.2384	+	2.95755i	−1.43699	+	0.145355i
$415$		0			0
$416$	0.560351	+	3.17791i	0.0274735	+	0.155810i
$417$	−1.85643	+	14.8789i	−0.0909097	+	0.728622i
$418$	−2.94949	−	8.10366i	−0.144264	−	0.396363i
$419$	14.5099	−	5.28118i	0.708856	−	0.258002i	0.0376687	−	0.999290i	$-0.488007\pi$
$419$	14.5099	−	5.28118i	0.708856	−	0.258002i	0.671187	+	0.741288i	$0.265785\pi$
$420$		0			0
$421$	−3.14193	−	17.8188i	−0.153128	−	0.868433i	−0.960477	−	0.278359i	$-0.910210\pi$
$421$	−3.14193	−	17.8188i	−0.153128	−	0.868433i	0.807349	−	0.590074i	$-0.200902\pi$
$422$	−11.4394	−	6.60456i	−0.556863	−	0.321505i
$423$	−4.93294	+	1.39365i	−0.239848	+	0.0677616i
$424$	−2.80837	−	4.86424i	−0.136386	−	0.236228i
$425$		0			0
$426$	−10.4374	+	33.9021i	−0.505695	+	1.64256i
$427$	−20.1365	−	3.55061i	−0.974475	−	0.171826i
$428$	−8.77071	+	10.4525i	−0.423948	+	0.505242i
$429$	2.11262	+	1.08164i	0.101998	+	0.0522221i
$430$		0			0
$431$	−28.9683			−1.39535			−0.697677	−	0.716412i	$-0.745783\pi$
$431$	−28.9683			−1.39535			−0.697677	+	0.716412i	$0.745783\pi$
$432$	−8.26365	−	24.4645i	−0.397585	−	1.17705i
$433$			37.5902i			1.80647i	0.429146	+	0.903235i	$0.358815\pi$
$433$			37.5902i			1.80647i	−0.429146	+	0.903235i	$0.641185\pi$
$434$	−8.27727	−	3.01268i	−0.397322	−	0.144613i
$435$		0			0
$436$	−2.98367	−	2.50360i	−0.142892	−	0.119901i
$437$	−15.7417	−	2.77569i	−0.753028	−	0.132779i
$438$	21.0920	−	19.5917i	1.00781	−	0.936126i
$439$	−7.86232	+	6.59727i	−0.375248	+	0.314871i	−0.810834	−	0.585277i	$-0.800986\pi$
$439$	−7.86232	+	6.59727i	−0.375248	+	0.314871i	0.435585	+	0.900147i	$0.356541\pi$
$440$		0			0
$441$	−20.5380	−	13.9702i	−0.978001	−	0.665248i
$442$	2.01521	+	1.16348i	0.0958540	+	0.0553413i
$443$	21.5757	−	3.80437i	1.02509	−	0.180751i	0.364269	−	0.931294i	$-0.381319\pi$
$443$	21.5757	−	3.80437i	1.02509	−	0.180751i	0.660822	+	0.750543i	$0.270208\pi$
$444$	2.92974	−	3.87212i	0.139039	−	0.183763i
$445$		0			0
$446$	13.8066	−	5.02519i	0.653761	−	0.237949i
$447$	3.40312	+	2.57488i	0.160962	+	0.121788i
$448$	−9.75869	+	1.72072i	−0.461055	+	0.0812964i
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	−0.724069	−	0.689728i	$-0.757730\pi$
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	0.959356	+	0.282198i	$0.0910635\pi$
$450$		0			0
$451$	1.67998	+	2.90981i	0.0791072	+	0.137018i
$452$	10.5827	+	12.6120i	0.497768	+	0.593217i
$453$	−13.3420	+	12.3930i	−0.626863	+	0.582272i
$454$	−1.18752	+	6.73475i	−0.0557330	+	0.316078i
$455$		0			0
$456$	−0.472568	−	9.36747i	−0.0221300	−	0.438672i
$457$	−2.60554	+	7.15867i	−0.121882	+	0.334869i	−0.985597	−	0.169113i	$-0.945910\pi$
$457$	−2.60554	+	7.15867i	−0.121882	+	0.334869i	0.863715	+	0.503981i	$0.168132\pi$
$458$		−	27.1566i		−	1.26894i
$459$	−9.14592	−	3.57247i	−0.426895	−	0.166748i
$460$		0			0
$461$	21.4255	+	7.79824i	0.997885	+	0.363200i	0.788768	−	0.614690i	$-0.210719\pi$
$461$	21.4255	+	7.79824i	0.997885	+	0.363200i	0.209116	+	0.977891i	$0.432941\pi$
$462$	9.70106	−	18.9477i	0.451334	−	0.881529i
$463$	−5.65379	+	6.73792i	−0.262754	+	0.313138i	−0.881250	−	0.472650i	$-0.843298\pi$
$463$	−5.65379	+	6.73792i	−0.262754	+	0.313138i	0.618497	+	0.785787i	$0.287742\pi$
$464$	−4.59084	+	26.0360i	−0.213125	+	1.20869i
$465$		0			0
$466$	22.1646	−	18.5983i	1.02675	−	0.861549i
$467$	−9.52416	+	5.49878i	−0.440726	+	0.254453i	−0.703905	−	0.710294i	$-0.748562\pi$
$467$	−9.52416	+	5.49878i	−0.440726	+	0.254453i	0.263180	+	0.964747i	$0.415229\pi$
$468$	−1.30009	−	1.26534i	−0.0600968	−	0.0584906i
$469$	3.69203	−	6.39479i	0.170482	−	0.295284i
$470$		0			0
$471$	−0.242479	−	0.574363i	−0.0111728	−	0.0264653i
$472$	−7.60331	−	20.8899i	−0.349971	−	0.961536i
$473$	−3.21796	−	8.84127i	−0.147962	−	0.406522i
$474$	−35.6878	−	4.45274i	−1.63919	−	0.204521i
$475$		0			0
$476$	3.04864	−	5.28040i	0.139734	−	0.242027i
$477$	7.78332	+	3.50188i	0.356374	+	0.160340i
$478$	2.23516	−	1.29047i	0.102234	−	0.0590247i
$479$	−19.6816	+	16.5148i	−0.899276	+	0.754582i	−0.970049	−	0.242911i	$-0.921898\pi$
$479$	−19.6816	+	16.5148i	−0.899276	+	0.754582i	0.0707730	+	0.997492i	$0.477453\pi$
$480$		0			0
$481$	−0.432034	+	2.45019i	−0.0196991	+	0.111719i
$482$	5.96600	−	7.11000i	0.271744	−	0.323852i
$483$	−21.4246	−	33.1327i	−0.974855	−	1.50759i
$484$	−5.81871	−	2.11784i	−0.264487	−	0.0962654i
$485$		0			0
$486$	21.3162	+	15.2384i	0.966921	+	0.691228i
$487$		−	30.3800i		−	1.37665i	−0.725402	−	0.688325i	$-0.758346\pi$
$487$		−	30.3800i		−	1.37665i	0.725402	−	0.688325i	$-0.241654\pi$
$488$	3.53214	−	9.70448i	0.159893	−	0.439301i
$489$	−21.2621	+	13.7488i	−0.961508	+	0.621742i
$490$		0			0
$491$	1.51218	−	8.57597i	0.0682435	−	0.387028i	−0.931486	−	0.363777i	$-0.881487\pi$
$491$	1.51218	−	8.57597i	0.0682435	−	0.387028i	0.999730	−	0.0232514i	$-0.00740183\pi$
$492$	−0.572850	−	2.50360i	−0.0258261	−	0.112871i
$493$	6.46180	+	7.70088i	0.291025	+	0.346830i
$494$	−1.68882	−	2.92512i	−0.0759837	−	0.131608i
$495$		0			0
$496$	3.33108	−	5.76961i	0.149570	−	0.259063i
$497$	−46.9023	+	8.27013i	−2.10385	+	0.370966i
$498$	−4.21133	+	33.7530i	−0.188714	+	1.51251i
$499$	10.9338	−	3.97957i	0.489463	−	0.178150i	−0.0854858	−	0.996339i	$-0.527244\pi$
$499$	10.9338	−	3.97957i	0.489463	−	0.178150i	0.574949	+	0.818189i	$0.305022\pi$
$500$		0			0
$501$	−1.46576	−	3.47196i	−0.0654851	−	0.155116i
$502$	35.4927	−	6.25832i	1.58412	−	0.279323i
$503$	−32.7350	−	18.8996i	−1.45958	−	0.842689i	−0.460590	−	0.887613i	$-0.652362\pi$
$503$	−32.7350	−	18.8996i	−1.45958	−	0.842689i	−0.998990	+	0.0449234i	$0.985696\pi$
$504$	16.1477	−	16.5912i	0.719277	−	0.739029i
$505$		0			0
$506$	14.0360	−	11.7776i	0.623977	−	0.523579i
$507$	−20.6314	−	6.35179i	−0.916274	−	0.282093i
$508$	−0.869388	−	0.153297i	−0.0385729	−	0.00680143i
$509$	−18.0585	−	15.1528i	−0.800427	−	0.671638i	0.147875	−	0.989006i	$-0.452757\pi$
$509$	−18.0585	−	15.1528i	−0.800427	−	0.671638i	−0.948302	+	0.317368i	$0.897201\pi$
$510$		0			0
$511$	36.3193	+	13.2191i	1.60667	+	0.584780i
$512$			2.26711i			0.100193i
$513$	8.90415	+	11.1285i	0.393128	+	0.491336i
$514$	24.8548			1.09630
$515$		0			0
$516$	0.362352	+	7.18272i	0.0159517	+	0.316202i
$517$	2.05435	−	2.44828i	0.0903503	−	0.107675i
$518$	21.9753	+	3.87485i	0.965541	+	0.170251i
$519$	20.7076	+	22.2934i	0.908963	+	0.978572i
$520$		0			0
$521$	−3.93474	−	6.81517i	−0.172384	−	0.298578i	0.766869	−	0.641804i	$-0.221814\pi$
$521$	−3.93474	−	6.81517i	−0.172384	−	0.298578i	−0.939253	+	0.343226i	$0.888480\pi$
$522$	−11.6658	−	24.1578i	−0.510600	−	1.05736i
$523$	28.8330	+	16.6467i	1.26078	+	0.727911i	0.973225	−	0.229854i	$-0.0738247\pi$
$523$	28.8330	+	16.6467i	1.26078	+	0.727911i	0.287554	+	0.957765i	$0.407158\pi$
$524$	−1.09517	−	6.21099i	−0.0478425	−	0.271328i
$525$		0			0
$526$	−4.42707	+	1.61132i	−0.193029	+	0.0702570i
$527$	−0.866425	−	2.38048i	−0.0377421	−	0.103695i
$528$	12.8390	+	9.71430i	0.558746	+	0.422761i
$529$	−1.90355	−	10.7955i	−0.0827628	−	0.469371i
$530$		0			0
$531$	27.9309	+	18.9990i	1.21210	+	0.824485i
$532$	−7.66461	+	4.42516i	−0.332303	+	0.191855i
$533$	0.845902	+	1.00811i	0.0366401	+	0.0436659i
$534$	11.3510	+	12.2203i	0.491207	+	0.528824i
$535$		0			0
$536$	2.85695	+	2.39727i	0.123402	+	0.103546i
$537$	−1.73759	+	0.0876573i	−0.0749823	+	0.00378269i
$538$	0.204970	−	0.563150i	0.00883687	−	0.0242791i
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	−6.98318	+	19.1861i	−0.299953	+	0.824115i
$543$	16.7131	−	32.6434i	0.717228	−	1.40086i
$544$	6.37614	+	5.35022i	0.273375	+	0.229389i
$545$		0			0
$546$	2.45319	−	7.96827i	0.104987	−	0.341011i
$547$	−13.4286	−	16.0036i	−0.574164	−	0.684262i	0.398316	−	0.917248i	$-0.369595\pi$
$547$	−13.4286	−	16.0036i	−0.574164	−	0.684262i	−0.972480	+	0.232986i	$0.925150\pi$
$548$	−11.1881	+	6.45948i	−0.477934	+	0.275935i
$549$	4.26648	+	15.1016i	0.182089	+	0.644519i
$550$		0			0
$551$	−2.53384	−	14.3701i	−0.107945	−	0.612188i
$552$	18.3592	−	7.75070i	0.781420	−	0.329892i
$553$	−16.5149	−	45.3744i	−0.702286	−	1.92952i
$554$	39.4727	−	14.3669i	1.67703	−	0.610390i
$555$		0			0
$556$	1.24089	+	7.03744i	0.0526255	+	0.298454i
$557$	−7.42911	−	4.28920i	−0.314782	−	0.181739i	0.334283	−	0.942473i	$-0.391506\pi$
$557$	−7.42911	−	4.28920i	−0.314782	−	0.181739i	−0.649064	+	0.760734i	$0.724839\pi$
$558$	0.680352	+	6.72597i	0.0288016	+	0.284733i
$559$	−1.84254	−	3.19137i	−0.0779311	−	0.134981i
$560$		0			0
$561$	5.96770	−	1.36547i	0.251957	−	0.0576502i
$562$	12.1221	+	2.13745i	0.511340	+	0.0901630i
$563$	−10.1013	+	12.0383i	−0.425720	+	0.507354i	−0.935682	−	0.352843i	$-0.885215\pi$
$563$	−10.1013	+	12.0383i	−0.425720	+	0.507354i	0.509962	+	0.860197i	$0.329659\pi$
$564$	−2.05145	+	1.32653i	−0.0863817	+	0.0558572i
$565$		0			0
$566$	−24.1851			−1.01658
$567$	−5.16841	+	34.7986i	−0.217053	+	1.46140i
$568$		−	24.0545i		−	1.00930i
$569$	11.9085	+	4.33435i	0.499231	+	0.181705i	0.579348	−	0.815080i	$-0.303307\pi$
$569$	11.9085	+	4.33435i	0.499231	+	0.181705i	−0.0801169	+	0.996785i	$0.525529\pi$
$570$		0			0
$571$	−20.1644	−	16.9199i	−0.843852	−	0.708076i	0.114575	−	0.993415i	$-0.463449\pi$
$571$	−20.1644	−	16.9199i	−0.843852	−	0.708076i	−0.958427	+	0.285339i	$0.907894\pi$
$572$	1.11394	+	0.196419i	0.0465764	+	0.00821267i
$573$	−3.79697	−	16.5944i	−0.158621	−	0.693241i
$574$	9.04155	−	7.58676i	0.377387	−	0.316665i
$575$		0			0
$576$	4.44607	+	6.17008i	0.185253	+	0.257087i
$577$	19.1525	+	11.0577i	0.797329	+	0.460338i	0.842536	−	0.538640i	$-0.181062\pi$
$577$	19.1525	+	11.0577i	0.797329	+	0.460338i	−0.0452074	+	0.998978i	$0.514395\pi$
$578$	−22.2304	+	3.91983i	−0.924665	+	0.163043i
$579$	19.1742	+	2.39236i	0.796854	+	0.0994230i
$580$		0			0
$581$	−42.9144	+	15.6196i	−1.78039	+	0.648009i
$582$	−0.921009	+	0.388822i	−0.0381771	+	0.0161172i
$583$	−5.24050	+	0.924041i	−0.217039	+	0.0382699i
$584$	−9.76057	+	16.9058i	−0.403895	+	0.699567i
$585$		0			0
$586$	12.1156	+	20.9848i	0.500491	+	0.866876i
$587$	9.19388	+	10.9568i	0.379472	+	0.452237i	0.921647	−	0.388028i	$-0.126844\pi$
$587$	9.19388	+	10.9568i	0.379472	+	0.452237i	−0.542176	+	0.840265i	$0.682399\pi$
$588$	−11.3138	−	3.48318i	−0.466574	−	0.143644i
$589$	−0.638517	+	3.62121i	−0.0263097	+	0.149209i
$590$		0			0
$591$	−14.0142	−	7.17514i	−0.576468	−	0.295146i
$592$	−5.77231	+	15.8593i	−0.237241	+	0.651813i
$593$		−	47.7300i		−	1.96004i	−0.198908	−	0.980018i	$-0.563740\pi$
$593$		−	47.7300i		−	1.96004i	0.198908	−	0.980018i	$-0.436260\pi$
$594$	−16.3326	−	0.380910i	−0.670136	−	0.0156289i
$595$		0			0
$596$	1.91115	+	0.695601i	0.0782837	+	0.0284929i
$597$	25.4182	−	1.28229i	1.04030	−	0.0524808i
$598$	4.61291	−	5.49746i	0.188636	−	0.224808i
$599$	0.0867493	−	0.491980i	0.00354448	−	0.0201018i	−0.982984	−	0.183690i	$-0.941196\pi$
$599$	0.0867493	−	0.491980i	0.00354448	−	0.0201018i	0.986529	+	0.163588i	$0.0523069\pi$
$600$		0			0
$601$	−12.9669	+	10.8805i	−0.528931	+	0.443826i	−0.867732	−	0.497032i	$-0.834423\pi$
$601$	−12.9669	+	10.8805i	−0.528931	+	0.443826i	0.338801	+	0.940858i	$0.389979\pi$
$602$	−28.6229	+	16.5254i	−1.16658	+	0.673527i
$603$	−5.65169	−	0.417415i	−0.230155	−	0.0169985i
$604$	−4.33923	+	7.51577i	−0.176561	+	0.305812i
$605$		0			0
$606$	30.5702	−	40.4035i	1.24183	−	1.64128i
$607$	−0.237578	−	0.652741i	−0.00964301	−	0.0264939i	0.934778	−	0.355233i	$-0.115599\pi$
$607$	−0.237578	−	0.652741i	−0.00964301	−	0.0264939i	−0.944421	+	0.328739i	$0.893376\pi$
$608$	−4.13218	−	11.3531i	−0.167582	−	0.460427i
$609$	21.7326	−	28.7231i	0.880649	−	1.16392i
$610$		0			0
$611$	0.625887	−	1.08407i	0.0253207	−	0.0438567i
$612$	−4.66680	−	0.344674i	−0.188644	−	0.0139326i
$613$	28.2873	−	16.3317i	1.14251	−	0.659630i	0.195461	−	0.980711i	$-0.437380\pi$
$613$	28.2873	−	16.3317i	1.14251	−	0.659630i	0.947052	+	0.321081i	$0.104046\pi$
$614$	39.1866	−	32.8815i	1.58144	−	1.32699i
$615$		0			0
$616$	−2.50660	+	14.2157i	−0.100994	+	0.572765i
$617$	−14.7098	+	17.5305i	−0.592195	+	0.705751i	−0.976026	−	0.217652i	$-0.930160\pi$
$617$	−14.7098	+	17.5305i	−0.592195	+	0.705751i	0.383831	+	0.923403i	$0.374605\pi$
$618$	−45.9799	+	2.31958i	−1.84958	+	0.0933074i
$619$	7.97398	+	2.90229i	0.320501	+	0.116653i	0.497261	−	0.867601i	$-0.334339\pi$
$619$	7.97398	+	2.90229i	0.320501	+	0.116653i	−0.176759	+	0.984254i	$0.556561\pi$
$620$		0			0
$621$	−15.7481	+	25.8645i	−0.631951	+	1.03791i
$622$		−	23.5254i		−	0.943282i
$623$	−7.65892	+	21.0427i	−0.306848	+	0.843058i
$624$	5.61293	+	2.87377i	0.224697	+	0.115043i
$625$		0			0
$626$	6.44708	−	36.5632i	0.257677	−	1.46136i
$627$	−8.49272	−	2.61465i	−0.339167	−	0.104419i
$628$	−0.190988	−	0.227611i	−0.00762127	−	0.00908267i
$629$	3.20872	+	5.55767i	0.127940	+	0.221599i
$630$		0			0
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	−0.881432	−	0.472311i	$-0.843420\pi$
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	0.849749	+	0.527187i	$0.176753\pi$
$632$	24.0176	−	4.23496i	0.955370	−	0.168458i
$633$	−12.5393	+	5.29373i	−0.498394	+	0.210407i
$634$	27.4662	−	9.99688i	1.09082	−	0.397027i
$635$		0			0
$636$	4.03626	+	0.503601i	0.160048	+	0.0199691i
$637$	5.97352	−	1.05329i	0.236680	−	0.0417330i
$638$	14.4854	+	8.36313i	0.573481	+	0.331099i
$639$	21.3687	+	29.6546i	0.845333	+	1.17312i
$640$		0			0
$641$	16.6038	−	13.9322i	0.655809	−	0.550289i	−0.253019	−	0.967461i	$-0.581423\pi$
$641$	16.6038	−	13.9322i	0.655809	−	0.550289i	0.908827	+	0.417173i	$0.136979\pi$
$642$	10.7342	+	46.9130i	0.423644	+	1.85151i
$643$	6.79720	+	1.19853i	0.268056	+	0.0472654i	0.306060	−	0.952012i	$-0.400989\pi$
$643$	6.79720	+	1.19853i	0.268056	+	0.0472654i	−0.0380047	+	0.999278i	$0.512100\pi$
$644$	−14.4048	−	12.0871i	−0.567629	−	0.476297i
$645$		0			0
$646$	−8.18679	−	2.97975i	−0.322105	−	0.117237i
$647$		−	6.18972i		−	0.243343i	−0.992570	−	0.121671i	$-0.961175\pi$
$647$		−	6.18972i		−	0.243343i	0.992570	−	0.121671i	$-0.0388254\pi$
$648$	−16.8555	−	5.62277i	−0.662146	−	0.220883i
$649$	−21.0614			−0.826733
$650$		0			0
$651$	−7.62182	+	4.92851i	−0.298723	+	0.193164i
$652$	−7.75660	+	9.24396i	−0.303772	+	0.362021i
$653$	26.8010	+	4.72574i	1.04881	+	0.184933i	0.671384	−	0.741109i	$-0.265700\pi$
$653$	26.8010	+	4.72574i	1.04881	+	0.184933i	0.377421	+	0.926042i	$0.376811\pi$
$654$	−13.3913	+	3.06407i	−0.523642	+	0.119815i
$655$		0			0
$656$	4.46347	+	7.73096i	0.174269	+	0.301843i
$657$	−2.98527	−	29.5124i	−0.116467	−	1.15139i
$658$	−9.72283	−	5.61348i	−0.379035	−	0.218836i
$659$	−0.917209	−	5.20175i	−0.0357294	−	0.202631i	0.961718	−	0.274043i	$-0.0883609\pi$
$659$	−0.917209	−	5.20175i	−0.0357294	−	0.202631i	−0.997447	+	0.0714110i	$0.977250\pi$
$660$		0			0
$661$	−10.9616	+	3.98968i	−0.426355	+	0.155181i	−0.546280	−	0.837602i	$-0.683957\pi$
$661$	−10.9616	+	3.98968i	−0.426355	+	0.155181i	0.119925	+	0.992783i	$0.461734\pi$
$662$	−0.496803	−	1.36496i	−0.0193088	−	0.0530505i
$663$	2.20898	−	0.932564i	0.0857897	−	0.0362178i
$664$	−4.00536	−	22.7155i	−0.155438	−	0.881533i
$665$		0			0
$666$	−4.65609	−	16.4806i	−0.180420	−	0.638611i
$667$	26.8494	−	15.5015i	1.03961	−	0.600220i
$668$	−1.15450	−	1.37588i	−0.0446690	−	0.0532345i
$669$	4.45470	−	14.4694i	0.172229	−	0.559421i
$670$		0			0
$671$	−7.49510	−	6.28913i	−0.289345	−	0.242789i
$672$	13.5910	−	26.5454i	0.524283	−	1.02401i
$673$	−16.7940	+	46.1412i	−0.647362	+	1.77861i	−0.0201071	+	0.999798i	$0.506401\pi$
$673$	−16.7940	+	46.1412i	−0.647362	+	1.77861i	−0.627255	+	0.778814i	$0.715822\pi$
$674$	−0.703510			−0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	−7.73617	+	21.2550i	−0.297325	+	0.816894i	0.697619	+	0.716469i	$0.254243\pi$
$677$	−7.73617	+	21.2550i	−0.297325	+	0.816894i	−0.994945	+	0.100426i	$0.967980\pi$
$678$	57.9941	−	2.92567i	2.22725	−	0.112360i
$679$	−1.02822	−	0.862775i	−0.0394593	−	0.0331103i
$680$		0			0
$681$	4.79576	+	5.16302i	0.183774	+	0.197847i
$682$	−2.70931	−	3.22884i	−0.103745	−	0.123639i
$683$	14.8425	−	8.56931i	0.567932	−	0.327896i	−0.188391	−	0.982094i	$-0.560327\pi$
$683$	14.8425	−	8.56931i	0.567932	−	0.327896i	0.756323	+	0.654198i	$0.226994\pi$
$684$	5.61626	+	3.82025i	0.214743	+	0.146071i
$685$		0			0
$686$	−1.46007	−	8.28045i	−0.0557456	−	0.316149i
$687$	−22.3151	−	16.8841i	−0.851374	−	0.644169i
$688$	−8.54966	−	23.4900i	−0.325953	−	0.895548i
$689$	−1.95851	+	0.712838i	−0.0746132	+	0.0271570i
$690$		0			0
$691$	3.17011	+	17.9786i	0.120597	+	0.683937i	0.983826	+	0.179126i	$0.0573268\pi$
$691$	3.17011	+	17.9786i	0.120597	+	0.683937i	−0.863230	+	0.504811i	$0.831562\pi$
$692$	12.5582	+	7.25049i	0.477392	+	0.275622i
$693$	−9.53826	−	19.7520i	−0.362328	−	0.750315i
$694$	19.6749	+	34.0779i	0.746848	+	1.29358i
$695$		0			0
$696$	12.3808	+	13.3289i	0.469293	+	0.505232i
$697$	3.34286	+	0.589436i	0.126620	+	0.0223265i
$698$	22.8805	−	27.2679i	0.866038	−	1.03210i
$699$	−1.50214	−	29.7762i	−0.0568163	−	1.12624i
$700$		0			0
$701$	−2.92075			−0.110315			−0.0551575	−	0.998478i	$-0.517566\pi$
$701$	−2.92075			−0.110315			−0.0551575	+	0.998478i	$0.517566\pi$
$702$	−6.32570	+	0.963899i	−0.238748	+	0.0363800i
$703$		−	9.31505i		−	0.351324i
$704$	−4.45570	−	1.62174i	−0.167931	−	0.0611218i
$705$		0			0
$706$	30.3171	+	25.4391i	1.14100	+	0.957412i
$707$	66.9906	+	11.8123i	2.51944	+	0.444246i
$708$	15.3864	+	4.73699i	0.578255	+	0.178027i
$709$	−23.0023	+	19.3012i	−0.863868	+	0.724872i	−0.962798	−	0.270223i	$-0.912903\pi$
$709$	−23.0023	+	19.3012i	−0.863868	+	0.724872i	0.0989295	+	0.995094i	$0.468458\pi$
$710$		0			0
$711$	−25.8471	+	26.5569i	−0.969342	+	0.995961i
$712$	−9.79490	−	5.65509i	−0.367079	−	0.211933i
$713$	−7.69393	+	1.35665i	−0.288140	+	0.0508068i
$714$	−8.36402	−	19.8120i	−0.313016	−	0.741445i
$715$		0			0
$716$	−0.779152	+	0.283588i	−0.0291183	+	0.0105982i
$717$	0.329266	−	2.63900i	0.0122967	−	0.0985552i
$718$	−17.3168	+	3.05341i	−0.646256	+	0.113952i
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	−0.202349	−	0.979314i	$-0.564857\pi$
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	0.949285	−	0.314418i	$-0.101809\pi$
$720$		0			0
$721$	−30.9059	−	53.5306i	−1.15100	−	1.99358i
$722$	−12.4003	−	14.7781i	−0.461490	−	0.549983i
$723$	−2.13317	−	9.32289i	−0.0793335	−	0.346722i
$724$	3.03499	−	17.2123i	0.112794	−	0.639689i
$725$		0			0
$726$	−18.3396	+	11.8590i	−0.680645	+	0.440127i
$727$	−0.526294	+	1.44598i	−0.0195192	+	0.0536285i	−0.949070	−	0.315067i	$-0.897973\pi$
$727$	−0.526294	+	1.44598i	−0.0195192	+	0.0536285i	0.929550	+	0.368695i	$0.120195\pi$
$728$			5.65371i			0.209540i
$729$	25.7746	−	8.04171i	0.954615	−	0.297841i
$730$		0			0
$731$	−8.93196	−	3.25097i	−0.330361	−	0.120241i
$732$	4.06101	+	6.28025i	0.150099	+	0.232125i
$733$	−0.971827	+	1.15818i	−0.0358952	+	0.0427783i	−0.783693	−	0.621148i	$-0.786667\pi$
$733$	−0.971827	+	1.15818i	−0.0358952	+	0.0427783i	0.747798	+	0.663926i	$0.231111\pi$
$734$	−6.20502	+	35.1904i	−0.229031	+	1.29890i
$735$		0			0
$736$	19.6642	−	16.5002i	0.724830	−	0.608205i
$737$	3.05997	−	1.76667i	0.112715	−	0.0650762i
$738$	−8.26082	−	3.71672i	−0.304085	−	0.136814i
$739$	10.6779	−	18.4946i	0.392792	−	0.680336i	−0.600024	−	0.799982i	$-0.704843\pi$
$739$	10.6779	−	18.4946i	0.392792	−	0.680336i	0.992817	+	0.119646i	$0.0381758\pi$
$740$		0			0
$741$	−3.45362	−	0.430906i	−0.126872	−	0.0158297i
$742$	6.39333	+	17.5655i	0.234707	+	0.644851i
$743$	−6.95284	−	19.1028i	−0.255075	−	0.700812i	−0.999454	−	0.0330547i	$-0.989476\pi$
$743$	−6.95284	−	19.1028i	−0.255075	−	0.700812i	0.744379	−	0.667758i	$-0.232746\pi$
$744$	−1.78297	−	4.22334i	−0.0653667	−	0.154835i
$745$		0			0
$746$	−1.94153	+	3.36282i	−0.0710843	+	0.123122i
$747$	25.1171	+	24.4458i	0.918987	+	0.894425i
$748$	2.52672	−	1.45880i	0.0923860	−	0.0533391i
$749$	−49.4970	+	41.5329i	−1.80858	+	1.51758i
$750$		0			0
$751$	0.740289	−	4.19839i	0.0270135	−	0.153201i	−0.968317	−	0.249723i	$-0.919661\pi$
$751$	0.740289	−	4.19839i	0.0270135	−	0.153201i	0.995331	+	0.0965214i	$0.0307716\pi$
$752$	5.45813	−	6.50474i	0.199037	−	0.237204i
$753$	16.9244	−	33.0560i	0.616758	−	1.20463i
$754$	6.15606	+	2.24062i	0.224191	+	0.0815987i
$755$		0			0
$756$	2.52567	+	16.5750i	0.0918578	+	0.602827i
$757$			54.3419i			1.97509i	0.157332	+	0.987546i	$0.449711\pi$
$757$			54.3419i			1.97509i	−0.157332	+	0.987546i	$0.550289\pi$
$758$	−7.21730	+	19.8294i	−0.262144	+	0.720235i
$759$	−0.951252	−	18.8562i	−0.0345282	−	0.684435i
$760$		0			0
$761$	3.15364	−	17.8852i	0.114319	−	0.648338i	−0.872765	−	0.488140i	$-0.837676\pi$
$761$	3.15364	−	17.8852i	0.114319	−	0.648338i	0.987085	−	0.160198i	$-0.0512133\pi$
$762$	−2.28132	+	2.11904i	−0.0826435	+	0.0767649i
$763$	−11.8556	−	14.1289i	−0.429201	−	0.511502i
$764$	−4.05650	−	7.02606i	−0.146759	−	0.254194i
$765$		0			0
$766$	16.5188	−	28.6113i	0.596847	−	1.03377i
$767$	−8.12376	+	1.43244i	−0.293332	+	0.0517224i
$768$	23.3438	+	17.6625i	0.842348	+	0.637340i
$769$	23.3558	−	8.50082i	0.842232	−	0.306547i	0.115363	−	0.993323i	$-0.463197\pi$
$769$	23.3558	−	8.50082i	0.842232	−	0.306547i	0.726869	+	0.686776i	$0.240975\pi$
$770$		0			0
$771$	15.4530	−	20.4236i	0.556526	−	0.735539i
$772$	9.06906	−	1.59912i	0.326403	−	0.0575536i
$773$	33.3274	+	19.2416i	1.19870	+	0.692071i	0.960266	−	0.279087i	$-0.0900316\pi$
$773$	33.3274	+	19.2416i	1.19870	+	0.692071i	0.238437	+	0.971158i	$0.423365\pi$
$774$	20.9735	+	14.2664i	0.753878	+	0.512797i
$775$		0			0
$776$	0.519323	−	0.435764i	0.0186426	−	0.0156430i
$777$	16.8468	−	15.6484i	0.604376	−	0.561385i
$778$	31.1916	+	5.49991i	1.11827	+	0.197181i
$779$	−3.77436	−	3.16707i	−0.135231	−	0.113472i
$780$		0			0
$781$	−21.4150	−	7.79443i	−0.766290	−	0.278907i
$782$		−	18.5107i		−	0.661940i
$783$	−27.1039	−	5.43361i	−0.968615	−	0.194181i
$784$	41.1462			1.46951
$785$		0			0
$786$	−19.7999	−	10.1374i	−0.706239	−	0.361588i
$787$	0.689376	−	0.821566i	0.0245736	−	0.0292857i	−0.753618	−	0.657313i	$-0.771693\pi$
$787$	0.689376	−	0.821566i	0.0245736	−	0.0292857i	0.778191	+	0.628027i	$0.216137\pi$
$788$	−7.38944	−	1.30296i	−0.263238	−	0.0464159i
$789$	−1.42840	+	4.63962i	−0.0508523	+	0.165175i
$790$		0			0
$791$	38.9814	+	67.5177i	1.38602	+	2.40065i
$792$	10.6612	−	3.01198i	0.378828	−	0.107026i
$793$	−3.31873	−	1.91607i	−0.117852	−	0.0680417i
$794$	−5.87212	−	33.3025i	−0.208394	−	1.18186i
$795$		0			0
$796$	11.3978	−	4.14846i	0.403985	−	0.147038i
$797$	−8.63505	−	23.7246i	−0.305869	−	0.840369i	−0.993451	−	0.114262i	$-0.963550\pi$
$797$	−8.63505	−	23.7246i	−0.305869	−	0.840369i	0.687581	−	0.726107i	$-0.258672\pi$
$798$	−3.86473	+	30.9750i	−0.136810	+	1.09650i
$799$	−0.560674	−	3.17974i	−0.0198352	−	0.112491i
$800$		0			0
$801$	17.0989	−	1.72961i	0.604161	−	0.0611127i
$802$	−44.8442	+	25.8908i	−1.58350	+	0.914237i
$803$	11.8880	+	14.1676i	0.419519	+	0.499963i
$804$	−2.63280	+	0.602410i	−0.0928515	+	0.0212454i
$805$		0			0
$806$	−1.26463	−	1.06115i	−0.0445448	−	0.0373775i
$807$	−0.335315	−	0.518556i	−0.0118036	−	0.0182540i
$808$	−11.7508	+	32.2851i	−0.413392	+	1.13579i
$809$	11.7337			0.412536			0.206268	−	0.978495i	$-0.433868\pi$
$809$	11.7337			0.412536			0.206268	+	0.978495i	$0.433868\pi$
$810$		0			0
$811$	−38.4085			−1.34871			−0.674353	−	0.738409i	$-0.735577\pi$
$811$	−38.4085			−1.34871			−0.674353	+	0.738409i	$0.735577\pi$
$812$	5.87103	−	16.1305i	0.206033	−	0.566070i
$813$	11.4239	+	17.6668i	0.400655	+	0.619603i
$814$	8.17953	+	6.86344i	0.286693	+	0.240564i
$815$		0			0
$816$	15.8553	−	3.62786i	0.555048	−	0.127001i
$817$	8.86853	+	10.5691i	0.310271	+	0.369766i
$818$	−57.7802	+	33.3594i	−2.02024	+	1.16639i
$819$	−5.02246	−	6.96996i	−0.175499	−	0.243550i
$820$		0			0
$821$	4.64197	+	26.3259i	0.162006	+	0.918781i	0.952098	+	0.305793i	$0.0989216\pi$
$821$	4.64197	+	26.3259i	0.162006	+	0.918781i	−0.790092	+	0.612988i	$0.789967\pi$
$822$	−5.64141	+	45.2147i	−0.196767	+	1.57704i
$823$	1.49267	+	4.10107i	0.0520311	+	0.142954i	0.962986	−	0.269552i	$-0.0868757\pi$
$823$	1.49267	+	4.10107i	0.0520311	+	0.142954i	−0.910955	+	0.412506i	$0.864653\pi$
$824$	29.3367	−	10.6777i	1.02199	−	0.371974i
$825$		0			0
$826$	12.8473	+	72.8608i	0.447015	+	2.53515i
$827$	33.9009	+	19.5727i	1.17885	+	0.680610i	0.955748	−	0.294185i	$-0.0950482\pi$
$827$	33.9009	+	19.5727i	1.17885	+	0.680610i	0.223102	+	0.974795i	$0.428382\pi$
$828$	−3.54606	+	13.9893i	−0.123234	+	0.486160i
$829$	−16.4433	−	28.4807i	−0.571101	−	0.989176i	−0.996453	−	0.0841481i	$-0.973183\pi$
$829$	−16.4433	−	28.4807i	−0.571101	−	0.989176i	0.425352	−	0.905028i	$-0.360150\pi$
$830$		0			0
$831$	12.7359	−	41.3678i	0.441803	−	1.43503i
$832$	−1.82894	−	0.322492i	−0.0634072	−	0.0111804i
$833$	10.0568	−	11.9853i	0.348448	−	0.415264i
$834$	22.4345	+	11.4863i	0.776844	+	0.397737i
$835$		0			0
$836$	−4.23496			−0.146469
$837$	5.94986	+	3.62269i	0.205657	+	0.125219i
$838$		−	25.9552i		−	0.896607i
$839$	29.7322	+	10.8216i	1.02647	+	0.373604i	0.799735	−	0.600353i	$-0.204973\pi$
$839$	29.7322	+	10.8216i	1.02647	+	0.373604i	0.226734	+	0.973957i	$0.427195\pi$
$840$		0			0
$841$	−0.534920	−	0.448851i	−0.0184455	−	0.0154776i
$842$	−29.9518	−	5.28131i	−1.03221	−	0.182006i
$843$	9.29308	−	8.63203i	0.320071	−	0.297303i
$844$	−4.96914	+	4.16961i	−0.171045	+	0.143524i
$845$		0			0
$846$	−0.634651	+	8.59300i	−0.0218197	+	0.295434i
$847$	−25.3939	−	14.6612i	−0.872545	−	0.503764i
$848$	−13.9233	+	2.45505i	−0.478127	+	0.0843066i
$849$	−15.0366	+	19.8734i	−0.516056	+	0.682052i
$850$		0			0
$851$	18.5980	−	6.76910i	0.637530	−	0.232042i
$852$	13.8916	+	10.5107i	0.475919	+	0.360091i
$853$	−5.57169	+	0.982440i	−0.190771	+	0.0336381i	−0.268217	−	0.963358i	$-0.586435\pi$
$853$	−5.57169	+	0.982440i	−0.190771	+	0.0336381i	0.0774461	+	0.996997i	$0.475323\pi$
$854$	−17.1849	+	29.7652i	−0.588057	+	1.01854i
$855$		0			0
$856$	−16.3173	−	28.2624i	−0.557715	−	0.965990i
$857$	−26.4895	−	31.5690i	−0.904864	−	1.07838i	−0.996584	−	0.0825904i	$-0.973681\pi$
$857$	−26.4895	−	31.5690i	−0.904864	−	1.07838i	0.0917193	−	0.995785i	$-0.470764\pi$
$858$	2.92305	−	2.71513i	0.0997913	−	0.0926929i
$859$	−6.22605	+	35.3097i	−0.212430	+	1.20475i	0.672880	+	0.739751i	$0.265057\pi$
$859$	−6.22605	+	35.3097i	−0.212430	+	1.20475i	−0.885311	+	0.465000i	$0.846054\pi$
$860$		0			0
$861$	−0.612766	−	12.1465i	−0.0208830	−	0.413953i
$862$	−16.6541	+	45.7566i	−0.567239	+	1.55848i
$863$		−	20.9694i		−	0.713806i	−0.934142	−	0.356903i	$-0.883833\pi$
$863$		−	20.9694i		−	0.713806i	0.934142	−	0.356903i	$-0.116167\pi$
$864$	−22.8817	−	0.533646i	−0.778451	−	0.0181550i
$865$		0			0
$866$	59.3753	+	21.6108i	2.01765	+	0.734366i
$867$	−10.6004	+	20.7043i	−0.360008	+	0.703153i
$868$	−2.78050	+	3.31367i	−0.0943764	+	0.112473i
$869$	4.01223	−	22.7545i	0.136106	−	0.771893i
$870$		0			0
$871$	1.06013	−	0.889553i	0.0359210	−	0.0301413i
$872$	8.06751	−	4.65778i	0.273201	−	0.157732i
$873$	−0.253118	+	0.998554i	−0.00856675	+	0.0337959i
$874$	−13.4343	+	23.2689i	−0.454422	+	0.787082i
$875$		0			0
$876$	−5.49828	−	13.0239i	−0.185770	−	0.440035i
$877$	−7.01498	−	19.2735i	−0.236879	−	0.650819i	−0.999990	−	0.00455171i	$-0.998551\pi$
$877$	−7.01498	−	19.2735i	−0.236879	−	0.650819i	0.763111	−	0.646268i	$-0.223671\pi$
$878$	5.90057	+	16.2117i	0.199134	+	0.547117i
$879$	24.7763	+	3.09132i	0.835684	+	0.104268i
$880$		0			0
$881$	19.1438	−	33.1581i	0.644972	−	1.11712i	−0.339336	−	0.940665i	$-0.610202\pi$
$881$	19.1438	−	33.1581i	0.644972	−	1.11712i	0.984308	−	0.176459i	$-0.0564644\pi$
$882$	−33.8740	+	24.4091i	−1.14060	+	0.821897i
$883$	15.1091	−	8.72326i	0.508463	−	0.293561i	−0.223739	−	0.974649i	$-0.571826\pi$
$883$	15.1091	−	8.72326i	0.508463	−	0.293561i	0.732201	+	0.681088i	$0.238493\pi$
$884$	0.875384	−	0.734534i	0.0294423	−	0.0247051i
$885$		0			0
$886$	6.39481	−	36.2668i	0.214838	−	1.21841i
$887$	34.8499	−	41.5325i	1.17015	−	1.39453i	0.267823	−	0.963468i	$-0.413696\pi$
$887$	34.8499	−	41.5325i	1.17015	−	1.39453i	0.902324	−	0.431058i	$-0.141860\pi$
$888$	6.30597	+	9.75203i	0.211615	+	0.327257i
$889$	−3.92831	−	1.42979i	−0.131751	−	0.0479536i
$890$		0			0
$891$	−10.4675	+	13.1840i	−0.350675	+	0.441681i
$892$		−	7.21530i		−	0.241586i
$893$	−1.60293	+	4.40402i	−0.0536400	+	0.147375i
$894$	6.02361	−	3.89506i	0.201460	−	0.130270i
$895$		0			0
$896$	−8.87211	+	50.3162i	−0.296396	+	1.68095i
$897$	−1.64937	−	7.20846i	−0.0550708	−	0.240683i
$898$	−10.7737	−	12.8396i	−0.359523	−	0.428462i
$899$	−3.56595	−	6.17641i	−0.118931	−	0.205995i
$900$		0			0
$901$	−2.68796	+	4.65569i	−0.0895491	+	0.155104i
$902$	5.56200	−	0.980730i	0.185194	−	0.0326547i
$903$	−4.21650	+	33.7944i	−0.140316	+	1.12461i
$904$	−37.0021	+	13.4677i	−1.23067	+	0.447928i
$905$		0			0
$906$	11.9048	+	28.1991i	0.395510	+	0.936851i
$907$	−28.2474	+	4.98078i	−0.937939	+	0.165384i	−0.621665	−	0.783284i	$-0.713543\pi$
$907$	−28.2474	+	4.98078i	−0.937939	+	0.165384i	−0.316275	+	0.948668i	$0.602432\pi$
$908$	2.90841	+	1.67917i	0.0965188	+	0.0557252i
$909$	−14.1938	−	50.2402i	−0.470779	−	1.66636i
$910$		0			0
$911$	−21.7416	+	18.2433i	−0.720330	+	0.604429i	−0.927477	−	0.373881i	$-0.878027\pi$
$911$	−21.7416	+	18.2433i	−0.720330	+	0.604429i	0.207146	+	0.978310i	$0.433582\pi$
$912$	−22.5640	−	6.94676i	−0.747168	−	0.230030i
$913$	−21.5208	−	3.79471i	−0.712236	−	0.125586i
$914$	9.80947	+	8.23112i	0.324468	+	0.272261i
$915$		0			0
$916$	−12.5319	−	4.56122i	−0.414064	−	0.150707i
$917$		−	29.8653i		−	0.986240i
$918$	−10.9009	+	12.3925i	−0.359783	+	0.409014i
$919$	−37.7786			−1.24620			−0.623101	−	0.782141i	$-0.714127\pi$
$919$	−37.7786			−1.24620			−0.623101	+	0.782141i	$0.714127\pi$
$920$		0			0
$921$	−2.65576	−	52.6438i	−0.0875104	−	1.73467i
$922$	24.6353	−	29.3592i	0.811320	−	0.966893i
$923$	−8.79027	−	1.54996i	−0.289335	−	0.0510176i
$924$	−7.11435	−	7.65917i	−0.234045	−	0.251968i
$925$		0			0
$926$	7.39243	+	12.8041i	0.242930	+	0.420768i
$927$	−26.6811	+	39.2247i	−0.876323	+	1.28831i
$928$	20.2937	+	11.7166i	0.666173	+	0.384615i
$929$	6.00421	+	34.0516i	0.196992	+	1.11720i	0.909554	+	0.415586i	$0.136424\pi$
$929$	6.00421	+	34.0516i	0.196992	+	1.11720i	−0.712562	+	0.701609i	$0.752465\pi$
$930$		0			0
$931$	−21.3404	+	7.76726i	−0.699403	+	0.254562i
$932$	−4.85972	−	13.3520i	−0.159185	−	0.437358i
$933$	−19.3312	−	14.6265i	−0.632877	−	0.478849i
$934$	3.21005	+	18.2051i	0.105036	+	0.595688i
$935$		0			0
$936$	3.90735	−	1.88687i	0.127716	−	0.0616741i
$937$	−16.8328	+	9.71839i	−0.549902	+	0.317486i	−0.749082	−	0.662477i	$-0.769505\pi$
$937$	−16.8328	+	9.71839i	−0.549902	+	0.317486i	0.199180	+	0.979963i	$0.436172\pi$
$938$	−7.97826	−	9.50812i	−0.260499	−	0.310451i
$939$	−26.0363	−	28.0302i	−0.849663	−	0.914731i
$940$		0			0
$941$	7.61330	+	6.38832i	0.248187	+	0.208253i	0.758391	−	0.651800i	$-0.225986\pi$
$941$	7.61330	+	6.38832i	0.248187	+	0.208253i	−0.510204	+	0.860053i	$0.670430\pi$
$942$	−1.04663	+	0.0528003i	−0.0341011	+	0.00172033i
$943$	3.58043	−	9.83716i	0.116595	−	0.320342i
$944$	−55.9572			−1.82125
$945$		0			0
$946$	−15.8152			−0.514195
$947$	5.78380	−	15.8909i	0.187948	−	0.516384i	−0.809552	−	0.587048i	$-0.800290\pi$
$947$	5.78380	−	15.8909i	0.187948	−	0.516384i	0.997500	+	0.0706647i	$0.0225120\pi$
$948$	−8.04890	+	15.7208i	−0.261416	+	0.510588i
$949$	5.54899	+	4.65616i	0.180128	+	0.151145i
$950$		0			0
$951$	8.86198	−	28.7849i	0.287369	−	0.933413i
$952$	9.37379	+	11.1712i	0.303806	+	0.362062i
$953$	−15.0319	+	8.67866i	−0.486930	+	0.281129i	−0.723300	−	0.690534i	$-0.757376\pi$
$953$	−15.0319	+	8.67866i	−0.486930	+	0.281129i	0.236370	+	0.971663i	$0.424042\pi$
$954$	10.0060	−	10.2808i	0.323958	−	0.332854i
$955$		0			0
$956$	−0.220091	−	1.24820i	−0.00711825	−	0.0403696i
$957$	15.8782	−	6.70327i	0.513268	−	0.216686i
$958$	14.7708	+	40.5824i	0.477222	+	1.31116i
$959$	−57.4872	+	20.9236i	−1.85636	+	0.675659i
$960$		0			0
$961$	−5.07101	−	28.7591i	−0.163581	−	0.927714i
$962$	3.62179	+	2.09104i	0.116771	+	0.0674179i
$963$	45.2230	+	20.3468i	1.45729	+	0.655667i
$964$	−2.27898	−	3.94730i	−0.0734009	−	0.127134i
$965$		0			0
$966$	−64.6515	+	14.7929i	−2.08013	+	0.475955i
$967$	−16.5284	−	2.91440i	−0.531517	−	0.0937207i	−0.0985525	−	0.995132i	$-0.531421\pi$
$967$	−16.5284	−	2.91440i	−0.531517	−	0.0937207i	−0.432964	+	0.901411i	$0.642532\pi$
$968$	9.51963	−	11.3451i	0.305973	−	0.364644i
$969$	−7.53850	+	4.87464i	−0.242172	+	0.156596i
$970$		0			0
$971$	−33.4811			−1.07446			−0.537230	−	0.843436i	$-0.680529\pi$
$971$	−33.4811			−1.07446			−0.537230	+	0.843436i	$0.680529\pi$
$972$	10.6123	−	7.27725i	0.340389	−	0.233418i
$973$			33.8393i			1.08484i
$974$	−47.9865	−	17.4657i	−1.53759	−	0.559636i
$975$		0			0
$976$	−19.9134	−	16.7093i	−0.637413	−	0.534853i
$977$	22.3894	+	3.94786i	0.716302	+	0.126303i	0.519909	−	0.854222i	$-0.325966\pi$
$977$	22.3894	+	3.94786i	0.716302	+	0.126303i	0.196393	+	0.980525i	$0.437077\pi$
$978$	9.49303	+	41.4887i	0.303554	+	1.32666i
$979$	−8.20843	+	6.88769i	−0.262342	+	0.220131i
$980$		0			0
$981$	−5.80800	+	12.9089i	−0.185435	+	0.412150i
$982$	−12.6767	−	7.31892i	−0.404531	−	0.233556i
$983$	46.4431	−	8.18917i	1.48131	−	0.261194i	0.626206	−	0.779658i	$-0.284607\pi$
$983$	46.4431	−	8.18917i	1.48131	−	0.261194i	0.855100	+	0.518464i	$0.173496\pi$
$984$	6.09542	+	0.760522i	0.194315	+	0.0242445i
$985$		0			0
$986$	15.8788	−	5.77940i	0.505683	−	0.184054i
$987$	−10.6577	+	4.49936i	−0.339238	+	0.143216i
$988$	−1.63350	+	0.288030i	−0.0519686	+	0.00916346i
$989$	−14.6571	+	25.3869i	−0.466069	+	0.807255i
$990$		0			0
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	0.898688	−	0.438588i	$-0.144521\pi$
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	−0.829172	+	0.558993i	$0.811188\pi$
$992$	−3.79569	−	4.52353i	−0.120513	−	0.143622i
$993$	−1.43049	−	0.440404i	−0.0453952	−	0.0139758i
$994$	−13.9014	+	78.8386i	−0.440925	+	2.50061i
$995$		0			0
$996$	14.8685	+	7.61253i	0.471127	+	0.241212i
$997$	−0.733462	+	2.01517i	−0.0232290	+	0.0638211i	−0.950765	−	0.309912i	$-0.899700\pi$
$997$	−0.733462	+	2.01517i	−0.0232290	+	0.0638211i	0.927536	+	0.373733i	$0.121923\pi$
$998$		−	19.5582i		−	0.619104i
$999$	−16.4373	−	6.42052i	−0.520052	−	0.203136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.b.274.4		24
5.2	odd	4		675.2.l.c.301.2		12
5.3	odd	4		27.2.e.a.4.1	✓	12
5.4	even	2	inner	675.2.u.b.274.1		24
15.8	even	4		81.2.e.a.64.2		12
20.3	even	4		432.2.u.c.193.1		12
27.7	even	9	inner	675.2.u.b.574.1		24
45.13	odd	12		243.2.e.d.109.2		12
45.23	even	12		243.2.e.a.109.1		12
45.38	even	12		243.2.e.b.28.1		12
45.43	odd	12		243.2.e.c.28.2		12
135.7	odd	36		675.2.l.c.601.2		12
135.13	odd	36		729.2.a.a.1.6		6
135.23	even	36		729.2.c.b.244.6		12
135.34	even	18	inner	675.2.u.b.574.4		24
135.38	even	36		243.2.e.b.217.1		12
135.43	odd	36		243.2.e.c.217.2		12
135.58	odd	36		729.2.c.e.244.1		12
135.68	even	36		729.2.a.d.1.1		6
135.83	even	36		243.2.e.a.136.1		12
135.88	odd	36		27.2.e.a.7.1	yes	12
135.103	odd	36		729.2.c.e.487.1		12
135.113	even	36		729.2.c.b.487.6		12
135.128	even	36		81.2.e.a.19.2		12
135.133	odd	36		243.2.e.d.136.2		12
540.223	even	36		432.2.u.c.385.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	5.3	odd	4
27.2.e.a.7.1	yes	12	135.88	odd	36
81.2.e.a.19.2		12	135.128	even	36
81.2.e.a.64.2		12	15.8	even	4
243.2.e.a.109.1		12	45.23	even	12
243.2.e.a.136.1		12	135.83	even	36
243.2.e.b.28.1		12	45.38	even	12
243.2.e.b.217.1		12	135.38	even	36
243.2.e.c.28.2		12	45.43	odd	12
243.2.e.c.217.2		12	135.43	odd	36
243.2.e.d.109.2		12	45.13	odd	12
243.2.e.d.136.2		12	135.133	odd	36
432.2.u.c.193.1		12	20.3	even	4
432.2.u.c.385.1		12	540.223	even	36
675.2.l.c.301.2		12	5.2	odd	4
675.2.l.c.601.2		12	135.7	odd	36
675.2.u.b.274.1		24	5.4	even	2	inner
675.2.u.b.274.4		24	1.1	even	1	trivial
675.2.u.b.574.1		24	27.7	even	9	inner
675.2.u.b.574.4		24	135.34	even	18	inner
729.2.a.a.1.6		6	135.13	odd	36
729.2.a.d.1.1		6	135.68	even	36
729.2.c.b.244.6		12	135.23	even	36
729.2.c.b.487.6		12	135.113	even	36
729.2.c.e.244.1		12	135.58	odd	36
729.2.c.e.487.1		12	135.103	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.574906 - 1.57954i) q^{2} +(-0.940501 - 1.45446i) q^{3} +(-0.632343 - 0.530599i) q^{4} +(-2.83808 + 0.649381i) q^{6} +(-2.51261 - 2.99441i) q^{7} +(1.70978 - 0.987144i) q^{8} +(-1.23092 + 2.73584i) q^{9} +O(q^{10})\)	\(q+(0.574906 - 1.57954i) q^{2} +(-0.940501 - 1.45446i) q^{3} +(-0.632343 - 0.530599i) q^{4} +(-2.83808 + 0.649381i) q^{6} +(-2.51261 - 2.99441i) q^{7} +(1.70978 - 0.987144i) q^{8} +(-1.23092 + 2.73584i) q^{9} +(-0.324801 - 1.84204i) q^{11} +(-0.177016 + 1.41875i) q^{12} +(-0.250563 - 0.688417i) q^{13} +(-6.17430 + 2.24726i) q^{14} +(-0.862951 - 4.89404i) q^{16} +(-1.63648 - 0.944822i) q^{17} +(3.61372 + 3.51713i) q^{18} +(1.37143 + 2.37538i) q^{19} +(-1.99214 + 6.47073i) q^{21} +(-3.09631 - 0.545962i) q^{22} +(-3.74597 + 4.46428i) q^{23} +(-3.04382 - 1.55840i) q^{24} -1.23143 q^{26} +(5.13686 - 0.782746i) q^{27} +3.22668i q^{28} +(-4.99910 - 1.81953i) q^{29} +(1.02696 + 0.861722i) q^{31} +(-4.33786 - 0.764882i) q^{32} +(-2.37370 + 2.20485i) q^{33} +(-2.43321 + 2.04170i) q^{34} +(2.23000 - 1.07687i) q^{36} +(-2.94112 - 1.69806i) q^{37} +(4.54046 - 0.800605i) q^{38} +(-0.765621 + 1.01189i) q^{39} +(-1.68800 + 0.614382i) q^{41} +(9.07549 + 6.86673i) q^{42} +(4.95373 - 0.873477i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(1.09832 + 1.30892i) q^{47} +(-6.30658 + 5.85798i) q^{48} +(-1.43775 + 8.15389i) q^{49} +(0.164904 + 3.26880i) q^{51} +(-0.206831 + 0.568265i) q^{52} -2.84494i q^{53} +(1.71683 - 8.56388i) q^{54} +(-7.25193 - 2.63949i) q^{56} +(2.16507 - 4.22874i) q^{57} +(-5.74803 + 6.85023i) q^{58} +(1.95529 - 11.0890i) q^{59} +(4.00710 - 3.36235i) q^{61} +(1.95153 - 1.12672i) q^{62} +(11.2850 - 3.18824i) q^{63} +(1.26751 - 2.19540i) q^{64} +(2.11800 + 5.01694i) q^{66} +(0.646086 + 1.77511i) q^{67} +(0.533495 + 1.46577i) q^{68} +(10.0162 + 1.24972i) q^{69} +(6.09193 - 10.5515i) q^{71} +(0.596074 + 5.89280i) q^{72} +(-8.56298 + 4.94384i) q^{73} +(-4.37302 + 3.66940i) q^{74} +(0.393163 - 2.22974i) q^{76} +(-4.69972 + 5.60091i) q^{77} +(1.15816 + 1.79107i) q^{78} +(11.6079 + 4.22493i) q^{79} +(-5.96969 - 6.73519i) q^{81} +3.01948i q^{82} +(3.99588 - 10.9786i) q^{83} +(4.69308 - 3.03470i) q^{84} +(1.46824 - 8.32679i) q^{86} +(2.05523 + 8.98227i) q^{87} +(-2.37370 - 2.82886i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(4.73748 - 0.835346i) q^{92} +(0.287484 - 2.30412i) q^{93} +(2.69893 - 0.982329i) q^{94} +(2.96727 + 7.02862i) q^{96} +(0.338162 - 0.0596270i) q^{97} +(12.0528 + 6.95870i) q^{98} +(5.43934 + 1.37879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

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