LMFDB - Embedded newform 945.2.cs.b.104.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.1
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58909 - 0.942353i) q^{2} +(-0.600558 + 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(1.90382 + 1.17280i) q^{5} +(3.08585 - 3.64031i) q^{6} +(-0.535422 + 2.59101i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +O(q^{10})$	\(q+(-2.58909 - 0.942353i) q^{2} +(-0.600558 + 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(1.90382 + 1.17280i) q^{5} +(3.08585 - 3.64031i) q^{6} +(-0.535422 + 2.59101i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +(-3.82398 - 4.83056i) q^{10} +(4.17954 - 0.736966i) q^{11} +(-8.41135 + 4.80017i) q^{12} +(-2.32268 + 0.845385i) q^{13} +(3.82790 - 6.20380i) q^{14} +(-3.04869 + 2.38862i) q^{15} +(2.79248 + 15.8369i) q^{16} +(-3.20975 - 1.85315i) q^{17} +(4.06082 + 7.19949i) q^{18} +(-3.30309 + 1.90704i) q^{19} +(3.93945 + 11.8660i) q^{20} +(-3.88780 - 2.42590i) q^{21} +(-11.5157 - 2.03053i) q^{22} +(5.51719 + 4.62947i) q^{23} +(16.8935 - 2.89144i) q^{24} +(2.24908 + 4.46560i) q^{25} +6.81028 q^{26} +(4.53861 - 2.53003i) q^{27} +(-11.6057 + 9.17366i) q^{28} +(-1.84543 + 5.07027i) q^{29} +(10.1443 - 3.31142i) q^{30} +(-1.08964 + 1.29858i) q^{31} +(4.25739 - 24.1448i) q^{32} +(-1.31278 + 7.23268i) q^{33} +(6.56402 + 7.82270i) q^{34} +(-4.05808 + 4.30488i) q^{35} +(-2.74686 - 16.5479i) q^{36} +(-0.112498 - 0.0649508i) q^{37} +(10.3491 - 1.82483i) q^{38} +(0.0214872 - 4.28113i) q^{39} +(0.630951 - 22.1176i) q^{40} +(-7.91430 + 2.88057i) q^{41} +(7.77983 + 9.94456i) q^{42} +(-0.965713 + 0.170281i) q^{43} +(20.5509 + 11.8651i) q^{44} +(-2.04964 - 6.38741i) q^{45} +(-9.92193 - 17.1853i) q^{46} +(-4.39353 - 5.23601i) q^{47} +(-27.4058 - 4.97433i) q^{48} +(-6.42665 - 2.77457i) q^{49} +(-1.61491 - 13.6813i) q^{50} +(4.93827 - 4.10164i) q^{51} +(-12.9871 - 4.72691i) q^{52} +5.91585 q^{53} +(-14.1351 + 2.27351i) q^{54} +(8.82141 + 3.49871i) q^{55} +(24.8530 - 8.23107i) q^{56} +(-1.11449 - 6.51150i) q^{57} +(9.55598 - 11.3884i) q^{58} +(1.09656 - 6.21888i) q^{59} +(-21.6433 - 0.726155i) q^{60} +(1.08931 + 1.29819i) q^{61} +(4.04489 - 2.33532i) q^{62} +(6.27597 - 4.85924i) q^{63} +(-17.6945 + 30.6478i) q^{64} +(-5.41343 - 1.11457i) q^{65} +(10.2146 - 17.4890i) q^{66} +(2.94577 + 8.09344i) q^{67} +(-7.08787 - 19.4738i) q^{68} +(-10.8344 + 6.18297i) q^{69} +(14.5635 - 7.32158i) q^{70} +(-7.71904 - 4.45659i) q^{71} +(-5.44810 + 29.1817i) q^{72} +(6.07570 + 10.5234i) q^{73} +(0.230061 + 0.274177i) q^{74} +(-8.60553 + 0.972011i) q^{75} +(-21.0022 - 3.70325i) q^{76} +(-0.328335 + 11.2238i) q^{77} +(-4.08997 + 11.0640i) q^{78} +(-2.54347 - 0.925746i) q^{79} +(-13.2572 + 33.4257i) q^{80} +(1.38459 + 8.89286i) q^{81} +23.2054 q^{82} +(2.58535 - 7.10319i) q^{83} +(-7.93365 - 24.3640i) q^{84} +(-3.93742 - 7.29247i) q^{85} +(2.66079 + 0.469168i) q^{86} +(-7.12889 - 6.04308i) q^{87} +(-26.9944 - 32.1707i) q^{88} +(3.16536 + 5.48257i) q^{89} +(-0.712473 + 18.4691i) q^{90} +(-0.946787 - 6.47071i) q^{91} +(6.99290 + 39.6587i) q^{92} +(-1.45528 - 2.55010i) q^{93} +(6.44109 + 17.6968i) q^{94} +(-8.52508 - 0.243196i) q^{95} +(36.6689 + 21.4169i) q^{96} +(1.30516 + 7.40190i) q^{97} +(14.0246 + 13.2398i) q^{98} +(-10.9618 - 6.47638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−2.58909	−	0.942353i	−1.83077	−	0.666344i	−0.992675	−	0.120812i	$-0.961450\pi$
$2$	−2.58909	−	0.942353i	−1.83077	−	0.666344i	−0.838090	−	0.545532i	$-0.816328\pi$
$3$	−0.600558	+	1.62460i	−0.346732	+	0.937964i
$3$	−0.600558	+	1.62460i	−0.346732	+	0.937964i
$4$	4.28329	+	3.59410i	2.14164	+	1.79705i
$5$	1.90382	+	1.17280i	0.851415	+	0.524492i
$5$	1.90382	+	1.17280i	0.851415	+	0.524492i
$6$	3.08585	−	3.64031i	1.25979	−	1.48615i
$7$	−0.535422	+	2.59101i	−0.202371	+	0.979309i
$7$	−0.535422	+	2.59101i	−0.202371	+	0.979309i
$8$	−4.94766	−	8.56959i	−1.74926	−	3.02981i
$9$	−2.27866	−	1.95133i	−0.759554	−	0.650445i
$10$	−3.82398	−	4.83056i	−1.20925	−	1.52756i
$11$	4.17954	−	0.736966i	1.26018	−	0.222203i	0.496635	−	0.867960i	$-0.334569\pi$
$11$	4.17954	−	0.736966i	1.26018	−	0.222203i	0.763544	+	0.645756i	$0.223458\pi$
$12$	−8.41135	+	4.80017i	−2.42815	+	1.38569i
$13$	−2.32268	+	0.845385i	−0.644195	+	0.234468i	−0.643398	−	0.765532i	$-0.722476\pi$
$13$	−2.32268	+	0.845385i	−0.644195	+	0.234468i	−0.000796869		1.00000i	$0.500254\pi$
$14$	3.82790	−	6.20380i	1.02305	−	1.65804i
$15$	−3.04869	+	2.38862i	−0.787168	+	0.616739i
$16$	2.79248	+	15.8369i	0.698120	+	3.95923i
$17$	−3.20975	−	1.85315i	−0.778479	−	0.449455i	0.0574119	−	0.998351i	$-0.481715\pi$
$17$	−3.20975	−	1.85315i	−0.778479	−	0.449455i	−0.835891	+	0.548895i	$0.815048\pi$
$18$	4.06082	+	7.19949i	0.957145	+	1.69694i
$19$	−3.30309	+	1.90704i	−0.757782	+	0.437505i	−0.828499	−	0.559991i	$-0.810805\pi$
$19$	−3.30309	+	1.90704i	−0.757782	+	0.437505i	0.0707171	+	0.997496i	$0.477471\pi$
$20$	3.93945	+	11.8660i	0.880889	+	2.65331i
$21$	−3.88780	−	2.42590i	−0.848388	−	0.529374i
$22$	−11.5157	−	2.03053i	−2.45515	−	0.432910i
$23$	5.51719	+	4.62947i	1.15041	+	0.965312i	0.999729	−	0.0232696i	$-0.00740762\pi$
$23$	5.51719	+	4.62947i	1.15041	+	0.965312i	0.150685	+	0.988582i	$0.451852\pi$
$24$	16.8935	−	2.89144i	3.44838	−	0.590212i
$25$	2.24908	+	4.46560i	0.449817	+	0.893121i
$26$	6.81028			1.33561
$27$	4.53861	−	2.53003i	0.873455	−	0.486904i
$28$	−11.6057	+	9.17366i	−2.19327	+	1.73366i
$29$	−1.84543	+	5.07027i	−0.342688	+	0.941526i	0.641924	+	0.766768i	$0.278137\pi$
$29$	−1.84543	+	5.07027i	−0.342688	+	0.941526i	−0.984611	+	0.174758i	$0.944086\pi$
$30$	10.1443	−	3.31142i	1.85208	−	0.604580i
$31$	−1.08964	+	1.29858i	−0.195705	+	0.233232i	−0.854968	−	0.518680i	$-0.826424\pi$
$31$	−1.08964	+	1.29858i	−0.195705	+	0.233232i	0.659264	+	0.751912i	$0.270868\pi$
$32$	4.25739	−	24.1448i	0.752607	−	4.26825i
$33$	−1.31278	+	7.23268i	−0.228525	+	1.25905i
$34$	6.56402	+	7.82270i	1.12572	+	1.34158i
$35$	−4.05808	+	4.30488i	−0.685941	+	0.727657i
$36$	−2.74686	−	16.5479i	−0.457810	−	2.75798i
$37$	−0.112498	−	0.0649508i	−0.0184946	−	0.0106778i	0.490724	−	0.871315i	$-0.336732\pi$
$37$	−0.112498	−	0.0649508i	−0.0184946	−	0.0106778i	−0.509219	+	0.860637i	$0.670066\pi$
$38$	10.3491	−	1.82483i	1.67885	−	0.296026i
$39$	0.0214872	−	4.28113i	0.00344071	−	0.685529i
$40$	0.630951	−	22.1176i	0.0997622	−	3.49710i
$41$	−7.91430	+	2.88057i	−1.23601	+	0.449870i	−0.875651	−	0.482945i	$-0.839567\pi$
$41$	−7.91430	+	2.88057i	−1.23601	+	0.449870i	−0.360356	+	0.932815i	$0.617345\pi$
$42$	7.77983	+	9.94456i	1.20045	+	1.53448i
$43$	−0.965713	+	0.170281i	−0.147270	+	0.0259676i	−0.246797	−	0.969067i	$-0.579378\pi$
$43$	−0.965713	+	0.170281i	−0.147270	+	0.0259676i	0.0995272	+	0.995035i	$0.468267\pi$
$44$	20.5509	+	11.8651i	3.09816	+	1.78873i
$45$	−2.04964	−	6.38741i	−0.305543	−	0.952178i
$46$	−9.92193	−	17.1853i	−1.46291	−	2.53383i
$47$	−4.39353	−	5.23601i	−0.640862	−	0.763750i	0.343644	−	0.939100i	$-0.388339\pi$
$47$	−4.39353	−	5.23601i	−0.640862	−	0.763750i	−0.984506	+	0.175350i	$0.943894\pi$
$48$	−27.4058	−	4.97433i	−3.95568	−	0.717982i
$49$	−6.42665	−	2.77457i	−0.918092	−	0.396367i
$50$	−1.61491	−	13.6813i	−0.228383	−	1.93483i
$51$	4.93827	−	4.10164i	0.691497	−	0.574345i
$52$	−12.9871	−	4.72691i	−1.80099	−	0.655505i
$53$	5.91585			0.812605			0.406302	−	0.913739i	$-0.366818\pi$
$53$	5.91585			0.812605			0.406302	+	0.913739i	$0.366818\pi$
$54$	−14.1351	+	2.27351i	−1.92354	+	0.309385i
$55$	8.82141	+	3.49871i	1.18948	+	0.471766i
$56$	24.8530	−	8.23107i	3.32112	−	1.09992i
$57$	−1.11449	−	6.51150i	−0.147617	−	0.862469i
$58$	9.55598	−	11.3884i	1.25476	−	1.49537i
$59$	1.09656	−	6.21888i	0.142759	−	0.809629i	−0.826379	−	0.563114i	$-0.809603\pi$
$59$	1.09656	−	6.21888i	0.142759	−	0.809629i	0.969139	−	0.246515i	$-0.0792855\pi$
$60$	−21.6433	−	0.726155i	−2.79414	−	0.0937463i
$61$	1.08931	+	1.29819i	0.139472	+	0.166216i	0.831259	−	0.555886i	$-0.187621\pi$
$61$	1.08931	+	1.29819i	0.139472	+	0.166216i	−0.691787	+	0.722102i	$0.743176\pi$
$62$	4.04489	−	2.33532i	0.513701	−	0.296586i
$63$	6.27597	−	4.85924i	0.790698	−	0.612207i
$64$	−17.6945	+	30.6478i	−2.21181	+	3.83097i
$65$	−5.41343	−	1.11457i	−0.671454	−	0.138245i
$66$	10.2146	−	17.4890i	1.25734	−	2.15274i
$67$	2.94577	+	8.09344i	0.359883	+	0.988770i	0.979069	+	0.203526i	$0.0652403\pi$
$67$	2.94577	+	8.09344i	0.359883	+	0.988770i	−0.619186	+	0.785244i	$0.712537\pi$
$68$	−7.08787	−	19.4738i	−0.859530	−	2.36154i
$69$	−10.8344	+	6.18297i	−1.30431	+	0.744343i
$70$	14.5635	−	7.32158i	1.74067	−	0.875097i
$71$	−7.71904	−	4.45659i	−0.916082	−	0.528900i	−0.0336988	−	0.999432i	$-0.510729\pi$
$71$	−7.71904	−	4.45659i	−0.916082	−	0.528900i	−0.882383	+	0.470532i	$0.844062\pi$
$72$	−5.44810	+	29.1817i	−0.642065	+	3.43910i
$73$	6.07570	+	10.5234i	0.711106	+	1.23167i	0.964442	+	0.264294i	$0.0851389\pi$
$73$	6.07570	+	10.5234i	0.711106	+	1.23167i	−0.253336	+	0.967378i	$0.581528\pi$
$74$	0.230061	+	0.274177i	0.0267441	+	0.0318724i
$75$	−8.60553	+	0.972011i	−0.993681	+	0.112238i
$76$	−21.0022	−	3.70325i	−2.40912	−	0.424792i
$77$	−0.328335	+	11.2238i	−0.0374172	+	1.27907i
$78$	−4.08997	+	11.0640i	−0.463097	+	1.25275i
$79$	−2.54347	−	0.925746i	−0.286162	−	0.104155i	0.194951	−	0.980813i	$-0.437545\pi$
$79$	−2.54347	−	0.925746i	−0.286162	−	0.104155i	−0.481113	+	0.876658i	$0.659767\pi$
$80$	−13.2572	+	33.4257i	−1.48220	+	3.73711i
$81$	1.38459	+	8.89286i	0.153843	+	0.988095i
$82$	23.2054			2.56261
$83$	2.58535	−	7.10319i	0.283779	−	0.779676i	−0.713124	−	0.701038i	$-0.752720\pi$
$83$	2.58535	−	7.10319i	0.283779	−	0.779676i	0.996903	−	0.0786386i	$-0.0250573\pi$
$84$	−7.93365	−	24.3640i	−0.865632	−	2.65833i
$85$	−3.93742	−	7.29247i	−0.427074	−	0.790979i
$86$	2.66079	+	0.469168i	0.286920	+	0.0505917i
$87$	−7.12889	−	6.04308i	−0.764297	−	0.647886i
$88$	−26.9944	−	32.1707i	−2.87761	−	3.42941i
$89$	3.16536	+	5.48257i	0.335528	+	0.581151i	0.983586	−	0.180440i	$-0.0577521\pi$
$89$	3.16536	+	5.48257i	0.335528	+	0.581151i	−0.648058	+	0.761591i	$0.724419\pi$
$90$	−0.712473	+	18.4691i	−0.0751012	+	1.94681i
$91$	−0.946787	−	6.47071i	−0.0992503	−	0.678315i
$92$	6.99290	+	39.6587i	0.729061	+	4.13471i
$93$	−1.45528	−	2.55010i	−0.150906	−	0.264433i
$94$	6.44109	+	17.6968i	0.664348	+	1.82528i
$95$	−8.52508	−	0.243196i	−0.874655	−	0.0249514i
$96$	36.6689	+	21.4169i	3.74251	+	2.18586i
$97$	1.30516	+	7.40190i	0.132518	+	0.751549i	0.976556	+	0.215265i	$0.0690615\pi$
$97$	1.30516	+	7.40190i	0.132518	+	0.751549i	−0.844037	+	0.536285i	$0.819827\pi$
$98$	14.0246	+	13.2398i	1.41669	+	1.33742i
$99$	−10.9618	−	6.47638i	−1.10170	−	0.650901i
$100$	−6.41638	+	27.2109i	−0.641638	+	2.72109i
$101$	−3.87878	+	3.25468i	−0.385953	+	0.323853i	−0.815034	−	0.579413i	$-0.803282\pi$
$101$	−3.87878	+	3.25468i	−0.385953	+	0.323853i	0.429081	+	0.903266i	$0.358837\pi$
$102$	−16.6508	+	5.96594i	−1.64868	+	0.590716i
$103$	−0.747483	+	4.23919i	−0.0736517	+	0.417700i	0.925582	+	0.378548i	$0.123577\pi$
$103$	−0.747483	+	4.23919i	−0.0736517	+	0.417700i	−0.999233	+	0.0391514i	$0.987535\pi$
$104$	18.7364	+	15.7217i	1.83726	+	1.54164i
$105$	−4.55660	−	9.17809i	−0.444678	−	0.895690i
$106$	−15.3167	−	5.57482i	−1.48769	−	0.541474i
$107$	−20.6863			−1.99982			−0.999908	−	0.0135502i	$-0.995687\pi$
$107$	−20.6863			−1.99982			−0.999908	+	0.0135502i	$0.995687\pi$
$108$	28.5333	+	5.47539i	2.74562	+	0.526870i
$109$	−5.27233			−0.504997			−0.252499	−	0.967597i	$-0.581252\pi$
$109$	−5.27233			−0.504997			−0.252499	+	0.967597i	$0.581252\pi$
$110$	−19.5424	−	17.3714i	−1.86330	−	1.65630i
$111$	0.173081	−	0.143758i	0.0164281	−	0.0136449i
$112$	−42.5288	−	1.24411i	−4.01859	−	0.117558i
$113$	2.80608	−	15.9141i	0.263974	−	1.49707i	−0.507968	−	0.861376i	$-0.669603\pi$
$113$	2.80608	−	15.9141i	0.263974	−	1.49707i	0.771942	−	0.635693i	$-0.219286\pi$
$114$	−3.25062	+	17.9091i	−0.304449	+	1.67734i
$115$	5.07431	+	15.2843i	0.473182	+	1.42526i
$116$	−26.1276	+	15.0848i	−2.42589	+	1.40059i
$117$	6.94222	+	2.60597i	0.641809	+	0.240922i
$118$	−8.69946	+	15.0679i	−0.800850	+	1.38711i
$119$	6.52010	−	7.32427i	0.597697	−	0.671415i
$120$	35.5534	+	14.3079i	3.24556	+	1.30613i
$121$	6.58881	−	2.39813i	0.598983	−	0.218012i
$122$	−1.59697	−	4.38765i	−0.144583	−	0.397239i
$123$	0.0732156	−	14.5875i	0.00660163	−	1.31531i
$124$	−9.33445	+	1.64592i	−0.838258	+	0.147808i
$125$	−0.955403	+	11.1394i	−0.0854538	+	0.996342i
$126$	−20.8282	+	6.66685i	−1.85552	+	0.593930i
$127$	−1.88223	+	1.08671i	−0.167021	+	0.0964295i	−0.581180	−	0.813775i	$-0.697409\pi$
$127$	−1.88223	+	1.08671i	−0.167021	+	0.0964295i	0.414159	+	0.910204i	$0.364076\pi$
$128$	37.1310	−	31.1566i	3.28194	−	2.75388i
$129$	0.303327	−	1.67116i	0.0267065	−	0.147138i
$130$	12.9656	+	7.98709i	1.13716	+	0.700514i
$131$	5.94190	+	4.98585i	0.519146	+	0.435616i	0.864334	−	0.502918i	$-0.167740\pi$
$131$	5.94190	+	4.98585i	0.519146	+	0.435616i	−0.345188	+	0.938534i	$0.612185\pi$
$132$	−31.6180	+	26.2614i	−2.75199	+	2.28576i
$133$	−3.17261	−	9.57941i	−0.275100	−	0.830641i
$134$		−	23.7306i		−	2.05001i
$135$	11.6079	+	0.506152i	0.999051	+	0.0435626i
$136$			36.6750i			3.14486i
$137$	−11.9544	−	4.35106i	−1.02134	−	0.371736i	−0.223560	−	0.974690i	$-0.571768\pi$
$137$	−11.9544	−	4.35106i	−1.02134	−	0.371736i	−0.797776	+	0.602954i	$0.793990\pi$
$138$	33.8779	−	5.79843i	2.88388	−	0.493595i
$139$	10.2640	−	12.2322i	0.870584	−	1.03752i	−0.128366	−	0.991727i	$-0.540973\pi$
$139$	10.2640	−	12.2322i	0.870584	−	1.03752i	0.998951	−	0.0457953i	$-0.0145822\pi$
$140$	−32.8541	+	3.85385i	−2.77668	+	0.325710i
$141$	11.1450	−	3.99321i	0.938578	−	0.336289i
$142$	15.7856	+	18.8126i	1.32470	+	1.57872i
$143$	−9.08470	+	5.24505i	−0.759701	+	0.438613i
$144$	24.5400	−	41.5361i	2.04500	−	3.46134i
$145$	−9.45978	+	7.48859i	−0.785592	+	0.621893i
$146$	−5.81377	−	32.9715i	−0.481151	−	2.72874i
$147$	8.36714	−	8.77445i	0.690110	−	0.723705i
$148$	−0.248422	−	0.682533i	−0.0204201	−	0.0561038i
$149$	4.26992	+	11.7315i	0.349806	+	0.961083i	0.982431	+	0.186625i	$0.0597550\pi$
$149$	4.26992	+	11.7315i	0.349806	+	0.961083i	−0.632626	+	0.774458i	$0.718023\pi$
$150$	23.1965	+	5.59282i	1.89399	+	0.456652i
$151$	−0.0971539	−	0.550987i	−0.00790627	−	0.0448387i	0.980599	−	0.196023i	$-0.0628026\pi$
$151$	−0.0971539	−	0.550987i	−0.00790627	−	0.0448387i	−0.988506	+	0.151184i	$0.951691\pi$
$152$	32.6851	+	18.8708i	2.65111	+	1.53062i
$153$	3.69782	+	10.4860i	0.298951	+	0.847743i
$154$	11.4269	−	28.7501i	0.920804	−	2.31675i
$155$	−3.59745	+	1.19434i	−0.288954	+	0.0959315i
$156$	15.4789	−	18.2601i	1.23930	−	1.46198i
$157$	3.67197	−	20.8248i	0.293055	−	1.66200i	−0.381948	−	0.924184i	$-0.624747\pi$
$157$	3.67197	−	20.8248i	0.293055	−	1.66200i	0.675003	−	0.737815i	$-0.264142\pi$
$158$	5.71289	+	4.79369i	0.454493	+	0.381365i
$159$	−3.55281	+	9.61090i	−0.281756	+	0.762194i
$160$	36.4224	−	40.9744i	2.87944	−	3.23931i
$161$	−14.9490	+	11.8164i	−1.17815	+	0.931260i
$162$	4.79537	−	24.3292i	0.376760	−	1.91148i
$163$			0.324585i			0.0254235i	0.999919	+	0.0127117i	$0.00404638\pi$
$163$			0.324585i			0.0254235i	−0.999919	+	0.0127117i	$0.995954\pi$
$164$	−44.2523	−	16.1065i	−3.45552	−	1.25771i
$165$	−10.9818	+	12.2301i	−0.854930	+	0.952113i
$166$	−13.3874	+	15.9545i	−1.03907	+	1.23831i
$167$	−1.73182	−	0.305366i	−0.134012	−	0.0236299i	0.106240	−	0.994341i	$-0.466119\pi$
$167$	−1.73182	−	0.305366i	−0.134012	−	0.0236299i	−0.240252	+	0.970711i	$0.577230\pi$
$168$	−1.55344	+	45.3194i	−0.119850	+	3.49647i
$169$	−5.27843	+	4.42912i	−0.406033	+	0.340702i
$170$	3.32228	+	22.5913i	0.254807	+	1.73267i
$171$	11.2479	+	2.09994i	0.860149	+	0.160586i
$172$	−4.74843	−	2.74151i	−0.362065	−	0.209038i
$173$	0.108154	−	0.0190704i	0.00822277	−	0.00144990i	−0.169535	−	0.985524i	$-0.554227\pi$
$173$	0.108154	−	0.0190704i	0.00822277	−	0.00144990i	0.177758	+	0.984074i	$0.443116\pi$
$174$	12.7626	+	22.3640i	0.967534	+	1.69541i
$175$	−12.7746	+	3.43641i	−0.965671	+	0.259768i
$176$	23.3426	+	64.1331i	1.75951	+	4.83422i
$177$	9.44465	+	5.51626i	0.709904	+	0.414628i
$178$	−3.02890	−	17.1778i	−0.227026	−	1.28753i
$179$	−12.3335	−	7.12078i	−0.921853	−	0.532232i	−0.0376270	−	0.999292i	$-0.511980\pi$
$179$	−12.3335	−	7.12078i	−0.921853	−	0.532232i	−0.884226	+	0.467060i	$0.845313\pi$
$180$	14.1778	−	34.7257i	1.05675	−	2.58830i
$181$	14.7978	−	8.54353i	1.09991	−	0.635036i	0.163715	−	0.986508i	$-0.447652\pi$
$181$	14.7978	−	8.54353i	1.09991	−	0.635036i	0.936198	+	0.351472i	$0.114319\pi$
$182$	−3.64637	+	17.6455i	−0.270287	+	1.30797i
$183$	−2.76323	+	0.990057i	−0.204264	+	0.0731871i
$184$	12.3755	−	70.1851i	0.912336	−	5.17412i
$185$	−0.138002	−	0.255593i	−0.0101461	−	0.0187915i
$186$	1.36477	+	7.97383i	0.100070	+	0.584669i
$187$	−14.7810	−	5.37984i	−1.08089	−	0.393413i
$188$		−	38.2181i		−	2.78734i
$189$	4.12525	+	13.1142i	0.300068	+	0.953918i
$190$	21.8431	+	8.66329i	1.58466	+	0.628501i
$191$	2.11519	−	5.81144i	0.153050	−	0.420501i	−0.839345	−	0.543600i	$-0.817061\pi$
$191$	2.11519	−	5.81144i	0.153050	−	0.420501i	0.992394	+	0.123099i	$0.0392832\pi$
$192$	−39.1638	−	47.1522i	−2.82641	−	3.40292i
$193$	0.269008	−	0.320591i	0.0193636	−	0.0230767i	−0.756276	−	0.654253i	$-0.772983\pi$
$193$	0.269008	−	0.320591i	0.0193636	−	0.0230767i	0.775639	+	0.631176i	$0.217428\pi$
$194$	3.59604	−	20.3941i	0.258180	−	1.46421i
$195$	5.06181	−	8.12531i	0.362484	−	0.581865i
$196$	−17.5551	−	34.9823i	−1.25393	−	2.49874i
$197$	−0.580991	−	1.00631i	−0.0413939	−	0.0716963i	0.844586	−	0.535420i	$-0.179847\pi$
$197$	−0.580991	−	1.00631i	−0.0413939	−	0.0716963i	−0.885980	+	0.463723i	$0.846513\pi$
$198$	22.2781	+	27.0979i	1.58324	+	1.92576i
$199$	−2.00937	−	1.16011i	−0.142440	−	0.0822378i	0.427086	−	0.904211i	$-0.359540\pi$
$199$	−2.00937	−	1.16011i	−0.142440	−	0.0822378i	−0.569526	+	0.821973i	$0.692873\pi$
$200$	27.1407	−	41.3680i	1.91914	−	2.92516i
$201$	−14.9177	−	0.0748728i	−1.05221	−	0.00528112i
$202$	13.1096	−	4.77150i	0.922387	−	0.335721i
$203$	−12.1490	−	7.49626i	−0.852695	−	0.526134i
$204$	35.8938	+	0.180153i	2.51307	+	0.0126132i
$205$	−18.4458	−	3.79779i	−1.28831	−	0.265249i
$206$	5.93011	−	10.2713i	0.413171	−	0.715633i
$207$	−3.53816	−	21.3149i	−0.245919	−	1.48149i
$208$	−19.8743	−	34.4234i	−1.37804	−	2.38683i
$209$	−12.4000	+	10.4048i	−0.857725	+	0.719717i
$210$	3.14846	+	28.0569i	0.217264	+	1.93611i
$211$	0.643794	−	3.65114i	0.0443206	−	0.251355i	−0.954595	−	0.297906i	$-0.903712\pi$
$211$	0.643794	−	3.65114i	0.0443206	−	0.251355i	0.998916	+	0.0465510i	$0.0148230\pi$
$212$	25.3393	+	21.2622i	1.74031	+	1.46029i
$213$	11.8759	−	9.86393i	0.813724	−	0.675865i
$214$	53.5587	+	19.4938i	3.66119	+	1.33257i
$215$	−2.03825	−	0.808402i	−0.139008	−	0.0551326i
$216$	−44.1368	−	26.3763i	−3.00313	−	1.79468i
$217$	−2.78121	−	3.51854i	−0.188801	−	0.238854i
$218$	13.6505	+	4.96839i	0.924532	+	0.336502i
$219$	−20.7452	+	3.55067i	−1.40183	+	0.239932i
$220$	25.2099	+	46.6910i	1.69965	+	3.14791i
$221$	9.02184	+	1.59079i	0.606875	+	0.107008i
$222$	−0.583593	+	0.209099i	−0.0391682	+	0.0140338i
$223$	1.48384	−	1.24509i	0.0993655	−	0.0833775i	−0.591752	−	0.806120i	$-0.701563\pi$
$223$	1.48384	−	1.24509i	0.0993655	−	0.0833775i	0.691117	+	0.722743i	$0.257119\pi$
$224$	60.2800	+	23.9586i	4.02763	+	1.60080i
$225$	3.58899	−	14.5643i	0.239266	−	0.970954i
$226$	−22.2619	+	38.5587i	−1.48084	+	2.56488i
$227$	−19.0744	+	3.36333i	−1.26601	+	0.223232i	−0.766031	−	0.642803i	$-0.777771\pi$
$227$	−19.0744	+	3.36333i	−1.26601	+	0.223232i	−0.499982	+	0.866036i	$0.666660\pi$
$228$	18.6293	−	31.8962i	1.23376	−	2.11238i
$229$	1.40951	+	3.87261i	0.0931433	+	0.255909i	0.977512	−	0.210880i	$-0.0676329\pi$
$229$	1.40951	+	3.87261i	0.0931433	+	0.255909i	−0.884369	+	0.466789i	$0.845411\pi$
$230$	1.26530	−	44.3542i	0.0834312	−	2.92463i
$231$	−18.0370	−	7.27396i	−1.18675	−	0.478591i
$232$	52.5807	−	9.27140i	3.45209	−	0.608697i
$233$	−8.89160	+	15.4007i	−0.582508	+	1.00893i	0.412673	+	0.910879i	$0.364595\pi$
$233$	−8.89160	+	15.4007i	−0.582508	+	1.00893i	−0.995181	+	0.0980545i	$0.968738\pi$
$234$	−15.5183	−	13.2891i	−1.01446	−	0.868737i
$235$	−2.22372	−	15.1212i	−0.145059	−	0.986396i
$236$	27.0481	−	22.6961i	1.76068	−	1.47739i
$237$	3.03147	−	3.57616i	0.196915	−	0.232296i
$238$	−23.7832	+	12.8190i	−1.54164	+	0.830932i
$239$	−5.59862	+	6.67217i	−0.362144	+	0.431587i	−0.916094	−	0.400963i	$-0.868675\pi$
$239$	−5.59862	+	6.67217i	−0.362144	+	0.431587i	0.553950	+	0.832550i	$0.313120\pi$
$240$	−46.3418	−	41.6117i	−2.99135	−	2.68602i
$241$	−2.39087	+	6.56887i	−0.154010	+	0.423138i	−0.992571	−	0.121670i	$-0.961175\pi$
$241$	−2.39087	+	6.56887i	−0.154010	+	0.423138i	0.838561	+	0.544808i	$0.183397\pi$
$242$	−19.3189			−1.24187
$243$	−15.2789	−	3.09126i	−0.980140	−	0.198305i
$244$			9.47560i			0.606613i
$245$	−8.98118	−	12.8195i	−0.573787	−	0.819005i
$246$	−13.9362	+	37.6995i	−0.888538	+	2.40363i
$247$	6.05983	−	7.22183i	0.385578	−	0.459514i
$248$	16.5194	+	2.91282i	1.04899	+	0.184964i
$249$	9.98720	+	8.46604i	0.632913	+	0.536513i
$250$	12.9709	−	27.9407i	0.820353	−	1.76713i
$251$	3.04139	+	5.26783i	0.191971	+	0.332503i	0.945903	−	0.324449i	$-0.105179\pi$
$251$	3.04139	+	5.26783i	0.191971	+	0.332503i	−0.753933	+	0.656952i	$0.771846\pi$
$252$	44.3464	+	1.74296i	2.79356	+	0.109796i
$253$	26.4711	+	15.2831i	1.66422	+	0.960840i
$254$	5.89733	−	1.03986i	0.370031	−	0.0652465i
$255$	14.2120	−	2.01720i	0.889990	−	0.126322i
$256$	−58.9865	+	21.4693i	−3.68666	+	1.34183i
$257$	3.23987	+	8.90146i	0.202097	+	0.555258i	0.998793	−	0.0491233i	$-0.0156427\pi$
$257$	3.23987	+	8.90146i	0.202097	+	0.555258i	−0.796695	+	0.604381i	$0.793421\pi$
$258$	−2.36017	+	4.04095i	−0.146938	+	0.251579i
$259$	0.228522	−	0.256707i	0.0141997	−	0.0159510i
$260$	−19.1814	−	24.2305i	−1.18958	−	1.50271i
$261$	14.0989	−	7.95239i	0.872700	−	0.492240i
$262$	−10.6857	−	18.5082i	−0.660165	−	1.14344i
$263$	6.47287	−	5.43138i	0.399134	−	0.334913i	−0.421025	−	0.907049i	$-0.638329\pi$
$263$	6.47287	−	5.43138i	0.399134	−	0.334913i	0.820159	+	0.572136i	$0.193885\pi$
$264$	68.4763	−	24.5348i	4.21442	−	1.51001i
$265$	11.2627	+	6.93811i	0.691864	+	0.426205i
$266$	−0.813003	+	27.7917i	−0.0498484	+	1.70402i
$267$	−10.8080	+	1.84985i	−0.661437	+	0.113209i
$268$	−16.4711	+	45.2539i	−1.00613	+	2.76432i
$269$	2.73308			0.166639			0.0833193	−	0.996523i	$-0.473448\pi$
$269$	2.73308			0.166639			0.0833193	+	0.996523i	$0.473448\pi$
$270$	−29.5770	−	12.2492i	−1.80000	−	0.745464i
$271$			15.4996i			0.941533i	0.882258	+	0.470766i	$0.156023\pi$
$271$			15.4996i			0.941533i	−0.882258	+	0.470766i	$0.843977\pi$
$272$	20.3851	−	56.0075i	1.23603	−	3.39595i
$273$	11.0809	+	2.34788i	0.670648	+	0.142100i
$274$	26.8509	+	22.5306i	1.62212	+	1.36112i
$275$	12.6911	+	17.0067i	0.765304	+	1.02554i
$276$	−68.6293	−	12.4567i	−4.13100	−	0.749803i
$277$	15.4469	+	18.4089i	0.928115	+	1.10608i	0.994122	+	0.108265i	$0.0345296\pi$
$277$	15.4469	+	18.4089i	0.928115	+	1.10608i	−0.0660068	+	0.997819i	$0.521026\pi$
$278$	−38.1016	+	21.9980i	−2.28518	+	1.31935i
$279$	5.01687	−	0.832775i	0.300352	−	0.0498569i
$280$	56.9690	+	13.4771i	3.40455	+	0.805408i
$281$	25.4902	−	4.49461i	1.52062	−	0.268126i	0.649943	−	0.759983i	$-0.274793\pi$
$281$	25.4902	−	4.49461i	1.52062	−	0.268126i	0.870676	+	0.491857i	$0.163682\pi$
$282$	−32.6184	−	0.163714i	−1.94240	−	0.00974900i
$283$	−28.4045	+	10.3384i	−1.68847	+	0.614554i	−0.994432	−	0.105380i	$-0.966394\pi$
$283$	−28.4045	+	10.3384i	−1.68847	+	0.614554i	−0.694042	+	0.719934i	$0.744172\pi$
$284$	−17.0454	−	46.8319i	−1.01146	−	2.77896i
$285$	5.51490	−	13.7038i	0.326674	−	0.811744i
$286$	28.4638	−	5.01894i	1.68310	−	0.296776i
$287$	−3.22609	−	22.0484i	−0.190430	−	1.30147i
$288$	−56.8158	+	46.7103i	−3.34790	+	2.75243i
$289$	−1.63166	−	2.82612i	−0.0959802	−	0.166243i
$290$	31.5492	−	10.4742i	1.85263	−	0.615066i
$291$	−12.8090	−	2.32491i	−0.750875	−	0.136289i
$292$	−11.7983	+	66.9115i	−0.690443	+	3.91570i
$293$	3.13226	−	3.73288i	0.182989	−	0.218077i	−0.666750	−	0.745281i	$-0.732315\pi$
$293$	3.13226	−	3.73288i	0.182989	−	0.218077i	0.849739	+	0.527204i	$0.176760\pi$
$294$	−29.9319	+	14.8331i	−1.74567	+	0.865083i
$295$	9.38114	−	10.5536i	0.546191	−	0.614454i
$296$			1.28542i			0.0747133i
$297$	17.1047	−	13.9191i	0.992518	−	0.807671i
$298$		−	34.3977i		−	1.99261i
$299$	−16.7283	−	6.08862i	−0.967425	−	0.352114i
$300$	−40.3535	−	26.7658i	−2.32981	−	1.54532i
$301$	0.0758642	−	2.59334i	0.00437274	−	0.149478i
$302$	−0.267684	+	1.51811i	−0.0154035	+	0.0873574i
$303$	−2.95813	−	8.25610i	−0.169940	−	0.474300i
$304$	−39.4255	−	46.9855i	−2.26121	−	2.69480i
$305$	0.551338	+	3.74906i	0.0315695	+	0.214671i
$306$	0.307514	−	30.6339i	0.0175794	−	1.75122i
$307$	3.43908	−	5.95665i	0.196278	−	0.339964i	−0.751040	−	0.660256i	$-0.770448\pi$
$307$	3.43908	−	5.95665i	0.196278	−	0.339964i	0.947319	+	0.320292i	$0.103781\pi$
$308$	−41.7459	+	46.8947i	−2.37869	+	2.67207i
$309$	−6.43809	−	3.76024i	−0.366250	−	0.213913i
$310$	10.4396	+	0.297812i	0.592930	+	0.0169146i
$311$	29.3229	−	10.6727i	1.66275	−	0.605191i	0.671957	−	0.740590i	$-0.265454\pi$
$311$	29.3229	−	10.6727i	1.66275	−	0.605191i	0.990791	+	0.135400i	$0.0432318\pi$
$312$	−36.7938	+	20.9974i	−2.08304	+	1.18874i
$313$	5.63004	+	31.9296i	0.318229	+	1.80477i	0.553514	+	0.832840i	$0.313286\pi$
$313$	5.63004	+	31.9296i	0.318229	+	1.80477i	−0.235285	+	0.971926i	$0.575602\pi$
$314$	−29.1314	+	50.4570i	−1.64398	+	2.84745i
$315$	17.6472	−	1.89068i	0.994310	−	0.106528i
$316$	−7.56717	−	13.1067i	−0.425686	−	0.737310i
$317$	−15.1331	+	12.6982i	−0.849961	+	0.713202i	−0.959781	−	0.280749i	$-0.909417\pi$
$317$	−15.1331	+	12.6982i	−0.849961	+	0.713202i	0.109820	+	0.993952i	$0.464973\pi$
$318$	18.2554	−	21.5355i	1.02371	−	1.20765i
$319$	−3.97643	+	22.5514i	−0.222637	+	1.26264i
$320$	−69.6308	+	37.5958i	−3.89248	+	2.10167i
$321$	12.4233	−	33.6069i	0.693401	−	1.87576i
$322$	49.8396	−	16.5064i	2.77745	−	0.919866i
$323$	14.1361			0.786556
$324$	−26.0312	+	43.0670i	−1.44618	+	2.39261i
$325$	−8.99905	−	8.47082i	−0.499177	−	0.469876i
$326$	0.305874	−	0.840381i	0.0169408	−	0.0465444i
$327$	3.16634	−	8.56543i	0.175099	−	0.473670i
$328$	63.8426	+	53.5703i	3.52512	+	2.95792i
$329$	15.9189	−	8.58020i	0.877639	−	0.473042i
$330$	39.9579	−	21.3162i	2.19961	−	1.17342i
$331$	−6.62998	+	5.56321i	−0.364417	+	0.305782i	−0.806548	−	0.591168i	$-0.798667\pi$
$331$	−6.62998	+	5.56321i	−0.364417	+	0.305782i	0.442132	+	0.896950i	$0.354222\pi$
$332$	36.6034	−	21.1330i	2.00887	−	1.15982i
$333$	0.129604	+	0.367522i	0.00710227	+	0.0201401i
$334$	4.19608	+	2.42261i	0.229599	+	0.132559i
$335$	−3.88375	+	18.8633i	−0.212192	+	1.03061i
$336$	27.5622	−	68.3452i	1.50364	−	3.72854i
$337$	−6.78989	−	18.6551i	−0.369869	−	1.01621i	−0.975411	−	0.220394i	$-0.929266\pi$
$337$	−6.78989	−	18.6551i	−0.369869	−	1.01621i	0.605542	−	0.795813i	$-0.292956\pi$
$338$	17.8401	−	6.49328i	0.970375	−	0.353188i
$339$	24.1688	+	14.1161i	1.31267	+	0.766680i
$340$	9.34476	−	45.3872i	0.506791	−	2.46147i
$341$	−3.59717	+	6.23048i	−0.194798	+	0.337400i
$342$	−27.1430	−	16.0364i	−1.46772	−	0.867151i
$343$	10.6299	−	15.1659i	0.573960	−	0.818883i
$344$	6.23726	+	7.43327i	0.336290	+	0.400775i
$345$	−27.8783	−	0.935343i	−1.50091	−	0.0503572i
$346$	−0.297991	−	0.0525438i	−0.0160201	−	0.00282477i
$347$	18.3894	+	15.4305i	0.987194	+	0.828355i	0.985159	−	0.171643i	$-0.0549077\pi$
$347$	18.3894	+	15.4305i	0.987194	+	0.828355i	0.00203533	+	0.999998i	$0.499352\pi$
$348$	−8.81562	−	51.5062i	−0.472567	−	2.76102i
$349$	7.49060	−	20.5802i	0.400963	−	1.10164i	−0.560848	−	0.827919i	$-0.689525\pi$
$349$	7.49060	−	20.5802i	0.400963	−	1.10164i	0.961810	−	0.273717i	$-0.0882530\pi$
$350$	36.3130	+	3.14103i	1.94101	+	0.167895i
$351$	−8.40287	+	9.71331i	−0.448512	+	0.518458i
$352$		−	104.052i		−	5.54598i
$353$	−7.17955	+	19.7257i	−0.382129	+	1.04989i	0.588329	+	0.808622i	$0.299786\pi$
$353$	−7.17955	+	19.7257i	−0.382129	+	1.04989i	−0.970458	+	0.241269i	$0.922436\pi$
$354$	−19.2548	−	23.1823i	−1.02338	−	1.23213i
$355$	−9.46900	−	17.5374i	−0.502562	−	0.930791i
$356$	−6.14677	+	34.8600i	−0.325778	+	1.84758i
$357$	7.98333	+	14.9912i	0.422523	+	0.793419i
$358$	25.2224	+	30.0589i	1.33305	+	1.58866i
$359$	27.0838	−	15.6368i	1.42943	−	0.825280i	0.432351	−	0.901705i	$-0.357684\pi$
$359$	27.0838	−	15.6368i	1.42943	−	0.825280i	0.997075	+	0.0764253i	$0.0243507\pi$
$360$	−44.5965	+	49.1673i	−2.35044	+	2.59134i
$361$	−2.22638	+	3.85621i	−0.117178	+	0.202958i
$362$	−46.3640	+	8.17522i	−2.43684	+	0.429680i
$363$	−0.0609534	+	12.1444i	−0.00319922	+	0.637416i
$364$	19.2011	−	31.1188i	1.00641	−	1.63107i
$365$	−0.774805	+	27.1603i	−0.0405551	+	1.42163i
$366$	8.08725	+	0.0405903i	0.422727	+	0.00212169i
$367$	0.250514	+	1.42073i	0.0130767	+	0.0741617i	0.990648	−	0.136444i	$-0.0435674\pi$
$367$	0.250514	+	1.42073i	0.0130767	+	0.0741617i	−0.977571	+	0.210606i	$0.932456\pi$
$368$	−57.9101	+	100.303i	−3.01877	+	5.22866i
$369$	23.6550	+	8.87961i	1.23143	+	0.462254i
$370$	0.116442	+	0.791800i	0.00605354	+	0.0411637i
$371$	−3.16748	+	15.3280i	−0.164447	+	0.795791i
$372$	2.93192	−	16.1532i	0.152013	−	0.837506i
$373$	30.7168	+	5.41620i	1.59046	+	0.280440i	0.897658	−	0.440693i	$-0.145267\pi$
$373$	30.7168	+	5.41620i	1.59046	+	0.280440i	0.692797	+	0.721133i	$0.256378\pi$
$374$	33.1997	+	27.8578i	1.71671	+	1.44049i
$375$	−17.5234	−	8.24203i	−0.904904	−	0.425616i
$376$	−23.1328	+	63.5567i	−1.19298	+	3.27769i
$377$		−	13.3367i		−	0.686875i
$378$	1.67755	−	37.8413i	0.0862838	−	1.94635i
$379$	5.98338			0.307346			0.153673	−	0.988122i	$-0.450890\pi$
$379$	5.98338			0.307346			0.153673	+	0.988122i	$0.450890\pi$
$380$	−35.6413	−	31.6817i	−1.82836	−	1.62524i
$381$	−0.635077	−	3.71050i	−0.0325360	−	0.190095i
$382$	−10.9529	+	13.0531i	−0.560397	+	0.667855i
$383$	13.4733	+	2.37570i	0.688452	+	0.121393i	0.506921	−	0.861992i	$-0.330784\pi$
$383$	13.4733	+	2.37570i	0.688452	+	0.121393i	0.181531	+	0.983385i	$0.441895\pi$
$384$	28.3177	+	79.0344i	1.44508	+	4.03320i
$385$	−13.7884	+	20.9831i	−0.702720	+	1.06940i
$386$	−0.998596	+	0.576540i	−0.0508272	+	0.0293451i
$387$	2.53281	+	1.49642i	0.128750	+	0.0760671i
$388$	−21.0129	+	36.3953i	−1.06677	+	1.84769i
$389$	−16.3502	+	2.88298i	−0.828989	+	0.146173i	−0.572013	−	0.820245i	$-0.693837\pi$
$389$	−16.3502	+	2.88298i	−0.828989	+	0.146173i	−0.256976	+	0.966418i	$0.582726\pi$
$390$	−20.7624	+	16.2672i	−1.05135	+	0.823720i
$391$	−9.12970	−	25.0837i	−0.461709	−	1.26853i
$392$	8.01993	+	68.8013i	0.405067	+	3.47499i
$393$	−11.6685	+	6.65893i	−0.588597	+	0.335899i
$394$	0.555944	+	3.15292i	0.0280081	+	0.158842i
$395$	−3.75660	−	4.74543i	−0.189015	−	0.238769i
$396$	−23.6758	−	67.1381i	−1.18975	−	3.37382i
$397$	13.2405	+	22.9332i	0.664522	+	1.15099i	0.979415	+	0.201858i	$0.0646980\pi$
$397$	13.2405	+	22.9332i	0.664522	+	1.15099i	−0.314893	+	0.949127i	$0.601969\pi$
$398$	4.10920	+	4.89716i	0.205976	+	0.245472i
$399$	17.4681	+	0.598762i	0.874497	+	0.0299756i
$400$	−64.4410	+	48.0887i	−3.22205	+	2.40443i
$401$	−18.6595	+	22.2376i	−0.931813	+	1.11049i	0.0618499	+	0.998085i	$0.480300\pi$
$401$	−18.6595	+	22.2376i	−0.931813	+	1.11049i	−0.993662	+	0.112405i	$0.964144\pi$
$402$	38.5528	+	14.2516i	1.92284	+	0.710805i
$403$	1.43307	−	3.93734i	0.0713865	−	0.196133i
$404$	−28.3116			−1.40855
$405$	−7.79352	+	18.5543i	−0.387263	+	0.921969i
$406$	24.3909	+	30.8572i	1.21050	+	1.53142i
$407$	−0.518057	−	0.188557i	−0.0256791	−	0.00934643i
$408$	−59.5823	−	22.0255i	−2.94976	−	1.09042i
$409$	22.9064	−	27.2988i	1.13265	−	1.34984i	0.203959	−	0.978979i	$-0.434619\pi$
$409$	22.9064	−	27.2988i	1.13265	−	1.34984i	0.928690	−	0.370858i	$-0.120936\pi$
$410$	44.1789	+	27.2153i	2.18184	+	1.34407i
$411$	14.2481	−	16.8081i	0.702805	−	0.829084i
$412$	−18.4378	+	15.4711i	−0.908363	+	0.762207i
$413$	15.5260	+	6.17091i	0.763987	+	0.303651i
$414$	−10.9255	+	58.5204i	−0.536960	+	2.87612i
$415$	13.2527	−	10.4911i	0.650548	−	0.514989i
$416$	10.5232	+	59.6798i	0.515940	+	2.92604i
$417$	13.7083	+	24.0211i	0.671299	+	1.17632i
$418$	41.9097	−	15.2539i	2.04987	−	0.746092i
$419$	11.9858	−	4.36247i	0.585545	−	0.213121i	−0.0322240	−	0.999481i	$-0.510259\pi$
$419$	11.9858	−	4.36247i	0.585545	−	0.213121i	0.617769	+	0.786360i	$0.288037\pi$
$420$	13.4698	−	55.6893i	0.657259	−	2.71736i
$421$	−1.37299	−	7.78664i	−0.0669156	−	0.379497i	−0.999813	−	0.0193543i	$-0.993839\pi$
$421$	−1.37299	−	7.78664i	−0.0669156	−	0.379497i	0.932897	−	0.360143i	$-0.117272\pi$
$422$	−5.10751	+	8.84646i	−0.248629	+	0.430639i
$423$	−0.205830	+	20.5043i	−0.0100078	+	0.996954i
$424$	−29.2696	−	50.6964i	−1.42146	−	2.46204i
$425$	1.05644	−	18.5014i	0.0512449	−	0.897448i
$426$	−40.0431	+	14.3473i	−1.94010	+	0.695130i
$427$	−3.94686	+	2.12733i	−0.191002	+	0.102949i
$428$	−88.6052	−	74.3486i	−4.28289	−	3.59377i
$429$	−3.06524	−	17.9090i	−0.147991	−	0.864653i
$430$	4.51542	+	4.01378i	0.217753	+	0.193562i
$431$			8.27361i			0.398526i	0.979946	+	0.199263i	$0.0638548\pi$
$431$			8.27361i			0.398526i	−0.979946	+	0.199263i	$0.936145\pi$
$432$	52.7419	+	64.8126i	2.53754	+	3.11830i
$433$	4.11988			0.197989			0.0989944	−	0.995088i	$-0.468437\pi$
$433$	4.11988			0.197989			0.0989944	+	0.995088i	$0.468437\pi$
$434$	3.88510	+	11.7307i	0.186491	+	0.563093i
$435$	−6.48482	−	19.8657i	−0.310923	−	0.952488i
$436$	−22.5829	−	18.9493i	−1.08152	−	0.907506i
$437$	−27.0524	−	4.77007i	−1.29409	−	0.228183i
$438$	57.0571	+	10.3563i	2.72630	+	0.494841i
$439$	13.0796	+	15.5876i	0.624254	+	0.743957i	0.981796	−	0.189940i	$-0.0608294\pi$
$439$	13.0796	+	15.5876i	0.624254	+	0.743957i	−0.357541	+	0.933897i	$0.616385\pi$
$440$	−13.6628	−	92.9063i	−0.651349	−	4.42914i
$441$	9.23004	+	18.8628i	0.439526	+	0.898230i
$442$	−21.8593	−	12.6205i	−1.03974	−	0.600295i
$443$	−1.30387	−	7.39462i	−0.0619488	−	0.351329i	−0.999988	−	0.00480128i	$-0.998472\pi$
$443$	−1.30387	−	7.39462i	−0.0619488	−	0.351329i	0.938040	−	0.346528i	$-0.112639\pi$
$444$	1.25803	+	0.00631414i	0.0597037	+	0.000299656i
$445$	−0.403664	+	14.1502i	−0.0191355	+	0.670783i
$446$	−5.01512	+	1.82536i	−0.237473	+	0.0864331i
$447$	−21.6234	−	0.108529i	−1.02275	−	0.00513323i
$448$	−69.9346	−	62.2561i	−3.30410	−	2.94132i
$449$	−2.60326	−	1.50299i	−0.122855	−	0.0709306i	0.437313	−	0.899309i	$-0.355930\pi$
$449$	−2.60326	−	1.50299i	−0.122855	−	0.0709306i	−0.560168	+	0.828379i	$0.689264\pi$
$450$	−23.0169	+	34.3263i	−1.08503	+	1.61816i
$451$	−30.9553	+	17.8720i	−1.45763	+	0.841561i
$452$	69.2160	−	58.0791i	3.25565	−	2.73181i
$453$	0.953481	+	0.173063i	0.0447984	+	0.00813121i
$454$	52.5549	+	9.26684i	2.46652	+	0.434915i
$455$	5.78633	−	13.4295i	0.271268	−	0.629584i
$456$	−50.2868	+	41.7673i	−2.35490	+	1.95593i
$457$	−8.32570	+	22.8747i	−0.389460	+	1.07003i	0.577786	+	0.816189i	$0.303917\pi$
$457$	−8.32570	+	22.8747i	−0.389460	+	1.07003i	−0.967245	+	0.253843i	$0.918305\pi$
$458$		−	11.3548i		−	0.530575i
$459$	−19.2563	−	0.289965i	−0.898808	−	0.0135344i
$460$	−33.1985	+	83.7045i	−1.54789	+	3.90274i
$461$	7.65502	+	2.78620i	0.356530	+	0.129766i	0.514074	−	0.857746i	$-0.328136\pi$
$461$	7.65502	+	2.78620i	0.356530	+	0.129766i	−0.157544	+	0.987512i	$0.550358\pi$
$462$	39.8449	+	35.8302i	1.85375	+	1.66697i
$463$	16.2168	−	19.3264i	0.753657	−	0.898173i	−0.243773	−	0.969832i	$-0.578385\pi$
$463$	16.2168	−	19.3264i	0.753657	−	0.898173i	0.997429	+	0.0716594i	$0.0228295\pi$
$464$	−85.4509	−	15.0673i	−3.96696	−	0.699482i
$465$	0.220151	−	6.56169i	0.0102093	−	0.304291i
$466$	37.5341	−	31.4948i	1.73873	−	1.45897i
$467$	33.5985	−	19.3981i	1.55475	−	0.897637i	0.557008	−	0.830507i	$-0.311949\pi$
$467$	33.5985	−	19.3981i	1.55475	−	0.897637i	0.997744	−	0.0671294i	$-0.0213840\pi$
$468$	20.3694	+	36.1132i	0.941575	+	1.66933i
$469$	−22.5474	+	3.29911i	−1.04114	+	0.152339i
$470$	−8.49205	+	41.2456i	−0.391709	+	1.90252i
$471$	31.6268	+	18.4720i	1.45728	+	0.851144i
$472$	−58.7186	+	21.3718i	−2.70274	+	0.983718i
$473$	−3.91074	+	1.42339i	−0.179816	+	0.0654477i
$474$	−11.2188	+	6.40229i	−0.515294	+	0.294067i
$475$	−15.9450	−	10.4612i	−0.731608	−	0.479993i
$476$	54.2517	−	7.93804i	2.48662	−	0.363839i
$477$	−13.4802	−	11.5438i	−0.617217	−	0.528555i
$478$	20.7829	−	11.9990i	0.950587	−	0.548821i
$479$	−12.3514	+	10.3641i	−0.564351	+	0.473547i	−0.879766	−	0.475407i	$-0.842301\pi$
$479$	−12.3514	+	10.3641i	−0.564351	+	0.473547i	0.315415	+	0.948954i	$0.397856\pi$
$480$	44.6934	+	83.7794i	2.03997	+	3.82399i
$481$	0.316205	+	0.0557555i	0.0144177	+	0.00254223i
$482$	12.3804	−	14.7544i	0.563911	−	0.672043i
$483$	−10.2191	−	31.3826i	−0.464987	−	1.42796i
$484$	36.8409	+	13.4090i	1.67459	+	0.609499i
$485$	−6.19616	+	15.6226i	−0.281353	+	0.709386i
$486$	36.6454	+	22.4017i	1.66227	+	1.01616i
$487$			15.4928i			0.702046i	0.936367	+	0.351023i	$0.114166\pi$
$487$			15.4928i			0.702046i	−0.936367	+	0.351023i	$0.885834\pi$
$488$	5.73542	−	15.7579i	0.259630	−	0.713328i
$489$	−0.527322	−	0.194932i	−0.0238463	−	0.00881513i
$490$	11.1727	+	41.6542i	0.504730	+	1.88174i
$491$	−8.60025	−	1.51646i	−0.388124	−	0.0684367i	−0.0238187	−	0.999716i	$-0.507582\pi$
$491$	−8.60025	−	1.51646i	−0.388124	−	0.0684367i	−0.364305	+	0.931280i	$0.618694\pi$
$492$	52.7427	−	62.2195i	2.37783	−	2.80507i
$493$	15.3194	−	12.8545i	0.689949	−	0.578936i
$494$	−22.4950	+	12.9875i	−1.01210	+	0.584335i
$495$	−13.2739	−	25.1859i	−0.596616	−	1.13202i
$496$	−23.6083	−	13.6303i	−1.06004	−	0.612016i
$497$	15.6800	−	17.6139i	0.703345	−	0.790093i
$498$	−17.8798	−	31.3308i	−0.801213	−	1.40397i
$499$	20.5635	−	7.48451i	0.920549	−	0.335053i	0.162092	−	0.986776i	$-0.448176\pi$
$499$	20.5635	−	7.48451i	0.920549	−	0.335053i	0.758457	+	0.651723i	$0.225954\pi$
$500$	−44.1286	+	44.2796i	−1.97349	+	1.98024i
$501$	1.53616	−	2.63012i	0.0686303	−	0.117505i
$502$	−2.91027	−	16.5050i	−0.129892	−	0.736653i
$503$	24.9813	+	14.4230i	1.11386	+	0.643088i	0.939827	−	0.341651i	$-0.110986\pi$
$503$	24.9813	+	14.4230i	1.11386	+	0.643088i	0.174035	+	0.984740i	$0.444319\pi$
$504$	−72.6930	−	29.7406i	−3.23801	−	1.32475i
$505$	−11.2016	+	1.64731i	−0.498465	+	0.0733043i
$506$	−54.1340	−	64.5144i	−2.40655	−	2.86802i
$507$	−4.02556	−	11.2353i	−0.178782	−	0.498976i
$508$	−11.9679	−	2.11026i	−0.530988	−	0.0936275i
$509$	−25.0032	−	20.9801i	−1.10825	−	0.929929i	−0.110294	−	0.993899i	$-0.535179\pi$
$509$	−25.0032	−	20.9801i	−1.10825	−	0.929929i	−0.997952	+	0.0639702i	$0.979624\pi$
$510$	−38.6971	−	8.17000i	−1.71354	−	0.361774i
$511$	−30.5193	+	10.1077i	−1.35009	+	0.447139i
$512$	76.0111			3.35925
$513$	−10.1666	+	17.0122i	−0.448865	+	0.751108i
$514$		−	26.0998i		−	1.15121i
$515$	−6.39479	+	7.19402i	−0.281788	+	0.317006i
$516$	7.30557	−	6.06788i	0.321610	−	0.267123i
$517$	−22.2217	−	18.6462i	−0.977309	−	0.820059i
$518$	−0.833574	+	0.449291i	−0.0366251	+	0.0197407i
$519$	−0.0339707	+	0.187159i	−0.00149115	+	0.00821539i
$520$	17.2324	+	51.9054i	0.755690	+	2.27620i
$521$	11.3864	+	19.7217i	0.498845	+	0.864025i	0.999999	−	0.00133298i	$-0.000424301\pi$
$521$	11.3864	+	19.7217i	0.498845	+	0.864025i	−0.501154	+	0.865358i	$0.667091\pi$
$522$	−43.9973	+	7.30333i	−1.92571	+	0.319658i
$523$	−1.89615	+	3.28423i	−0.0829128	+	0.143609i	−0.904500	−	0.426474i	$-0.859756\pi$
$523$	−1.89615	+	3.28423i	−0.0829128	+	0.143609i	0.821587	+	0.570083i	$0.193089\pi$
$524$	7.53121	+	42.7116i	0.329002	+	1.86587i
$525$	2.08911	−	22.8174i	0.0911761	−	0.995835i
$526$	−21.8771	+	7.96263i	−0.953889	+	0.347187i
$527$	5.90392	−	2.14885i	0.257179	−	0.0936055i
$528$	−118.209	−	0.593299i	−5.14440	−	0.0258200i
$529$	5.01348	+	28.4328i	0.217977	+	1.23621i
$530$	−22.6221	−	28.5769i	−0.982642	−	1.24130i
$531$	−14.6338	+	12.0310i	−0.635052	+	0.522099i
$532$	20.8402	−	52.4341i	0.903537	−	2.27330i
$533$	15.9472	−	13.3813i	0.690749	−	0.579607i
$534$	29.7261	+	5.39548i	1.28637	+	0.233485i
$535$	−39.3830	−	24.2608i	−1.70267	−	1.04889i
$536$	54.7828	−	65.2876i	2.36626	−	2.81999i
$537$	18.9754	−	15.7607i	0.818850	−	0.680123i
$538$	−7.07619	−	2.57552i	−0.305076	−	0.111039i
$539$	−28.9052	−	6.86019i	−1.24503	−	0.295490i
$540$	47.9009	+	43.8881i	2.06133	+	1.88864i
$541$	−6.34193			−0.272661			−0.136331	−	0.990663i	$-0.543531\pi$
$541$	−6.34193			−0.272661			−0.136331	+	0.990663i	$0.543531\pi$
$542$	14.6061	−	40.1299i	0.627385	−	1.72373i
$543$	4.99288	+	29.1715i	0.214265	+	1.25187i
$544$	−58.4092	+	69.6094i	−2.50427	+	2.98448i
$545$	−10.0376	−	6.18338i	−0.429963	−	0.264867i
$546$	−26.4770	−	16.5210i	−1.13311	−	0.707035i
$547$	−12.9288	−	15.4080i	−0.552797	−	0.658798i	0.415209	−	0.909726i	$-0.363709\pi$
$547$	−12.9288	−	15.4080i	−0.552797	−	0.658798i	−0.968006	+	0.250929i	$0.919264\pi$
$548$	−35.5661	−	61.6023i	−1.51931	−	2.63152i
$549$	0.0510324	−	5.08374i	0.00217801	−	0.216969i
$550$	−16.8322	−	55.9914i	−0.717728	−	2.38748i
$551$	−3.57360	−	20.2669i	−0.152241	−	0.863399i
$552$	106.591	+	62.2555i	4.53680	+	2.64977i
$553$	3.76044	−	6.09448i	0.159910	−	0.259164i
$554$	−22.6458	−	62.2188i	−0.962128	−	2.64343i
$555$	0.498114	−	0.0707005i	0.0211438	−	0.00300107i
$556$	87.9276	−	15.5040i	3.72896	−	0.657517i
$557$	5.05366	−	8.75319i	0.214130	−	0.370885i	−0.738873	−	0.673845i	$-0.764642\pi$
$557$	5.05366	−	8.75319i	0.214130	−	0.370885i	0.953003	+	0.302960i	$0.0979749\pi$
$558$	−13.7739	−	2.57153i	−0.583096	−	0.108862i
$559$	2.09909	−	1.21191i	0.0887819	−	0.0512582i
$560$	−79.5082	−	52.2463i	−3.35983	−	2.20781i
$561$	17.6169	−	20.7823i	0.743788	−	0.877430i
$562$	−70.2320	−	12.3838i	−2.96256	−	0.522379i
$563$	7.83923	−	9.34243i	0.330384	−	0.393736i	−0.575124	−	0.818067i	$-0.695046\pi$
$563$	7.83923	−	9.34243i	0.330384	−	0.393736i	0.905507	+	0.424330i	$0.139490\pi$
$564$	62.0892	+	22.9522i	2.61443	+	0.966461i
$565$	24.0063	−	27.0066i	1.00995	−	1.13618i
$566$	83.2844			3.50071
$567$	−23.7828	−	1.17395i	−0.998784	−	0.0493011i
$568$			88.1987i			3.70074i
$569$	1.00470	−	2.76039i	0.0421192	−	0.115722i	−0.916850	−	0.399232i	$-0.869277\pi$
$569$	1.00470	−	2.76039i	0.0421192	−	0.115722i	0.958969	+	0.283510i	$0.0914990\pi$
$570$	−27.1924	+	30.2835i	−1.13896	+	1.26843i
$571$	16.2781	+	13.6589i	0.681216	+	0.571608i	0.916361	−	0.400352i	$-0.131112\pi$
$571$	16.2781	+	13.6589i	0.681216	+	0.571608i	−0.235146	+	0.971960i	$0.575557\pi$
$572$	−57.7636	−	10.1853i	−2.41522	−	0.425868i
$573$	8.17098	+	6.92645i	0.341348	+	0.289357i
$574$	−12.4247	+	60.1253i	−0.518596	+	2.50958i
$575$	−8.26478	+	35.0497i	−0.344665	+	1.46167i
$576$	100.124	−	35.3080i	4.17182	−	1.47117i
$577$	−5.78358	+	10.0175i	−0.240774	+	0.417032i	−0.960935	−	0.276775i	$-0.910734\pi$
$577$	−5.78358	+	10.0175i	−0.240774	+	0.417032i	0.720161	+	0.693807i	$0.244068\pi$
$578$	1.56132	+	8.85470i	0.0649425	+	0.368307i
$579$	0.359278	+	0.629564i	0.0149311	+	0.0261638i
$580$	−67.4337	−	1.92369i	−2.80003	−	0.0798769i
$581$	17.0202	+	10.5019i	0.706115	+	0.435691i
$582$	30.9727	+	18.0900i	1.28386	+	0.749854i
$583$	24.7255	−	4.35978i	1.02403	−	0.180564i
$584$	60.1209	−	104.132i	2.48782	−	4.30903i
$585$	10.1605	+	13.1031i	0.420084	+	0.541748i
$586$	−11.6274	+	6.71308i	−0.480323	+	0.277315i
$587$	3.55320	+	4.23454i	0.146656	+	0.174778i	0.834372	−	0.551202i	$-0.185831\pi$
$587$	3.55320	+	4.23454i	0.146656	+	0.174778i	−0.687715	+	0.725980i	$0.741386\pi$
$588$	67.3751	−	7.51113i	2.77850	−	0.309754i
$589$	1.12273	−	6.36731i	0.0462612	−	0.262360i
$590$	−34.2339	+	18.4839i	−1.40939	+	0.760970i
$591$	1.98376	−	0.339534i	0.0816011	−	0.0139666i
$592$	0.714473	−	1.96300i	0.0293647	−	0.0806788i
$593$		−	39.8951i		−	1.63829i	−0.573584	−	0.819147i	$-0.694447\pi$
$593$		−	39.8951i		−	1.63829i	0.573584	−	0.819147i	$-0.305553\pi$
$594$	−57.4025	+	19.9193i	−2.35525	+	0.817297i
$595$	21.0030	−	6.29735i	0.861040	−	0.258166i
$596$	−23.8750	+	65.5959i	−0.977957	+	2.68691i
$597$	3.09145	−	2.56771i	0.126525	−	0.105089i
$598$	37.5736	+	31.5280i	1.53650	+	1.28928i
$599$	25.5890	+	4.51203i	1.04554	+	0.184356i	0.669931	−	0.742423i	$-0.266323\pi$
$599$	25.5890	+	4.51203i	1.04554	+	0.184356i	0.375606	+	0.926779i	$0.377435\pi$
$600$	50.9070	+	68.9367i	2.07827	+	2.81433i
$601$	24.2324	+	28.8790i	0.988459	+	1.17800i	0.984029	+	0.178010i	$0.0569658\pi$
$601$	24.2324	+	28.8790i	0.988459	+	1.17800i	0.00443041	+	0.999990i	$0.498590\pi$
$602$	−2.64026	+	6.64291i	−0.107609	+	0.270745i
$603$	9.08059	−	24.1904i	0.369790	−	0.985108i
$604$	1.56417	−	2.70922i	0.0636450	−	0.110236i
$605$	15.3565	+	3.16174i	0.624329	+	0.128543i
$606$	−0.121277	+	24.1634i	−0.00492656	+	0.981571i
$607$	9.81667	−	3.57297i	0.398446	−	0.145023i	−0.135022	−	0.990843i	$-0.543111\pi$
$607$	9.81667	−	3.57297i	0.398446	−	0.145023i	0.533468	+	0.845820i	$0.320888\pi$
$608$	31.9827	+	87.8717i	1.29707	+	3.56367i
$609$	19.4746	−	15.2354i	0.789152	−	0.617370i
$610$	2.10548	−	10.2262i	0.0852482	−	0.414048i
$611$	14.6312	+	8.44732i	0.591915	+	0.341742i
$612$	−21.8490	+	58.2049i	−0.883192	+	2.35279i
$613$	−40.9366	+	23.6348i	−1.65342	+	0.954600i	−0.677762	+	0.735281i	$0.737050\pi$
$613$	−40.9366	+	23.6348i	−1.65342	+	0.954600i	−0.975653	+	0.219319i	$0.929616\pi$
$614$	−14.5174	+	12.1815i	−0.585873	+	0.491606i
$615$	17.2477	−	27.6862i	0.695492	−	1.11642i
$616$	97.8079	−	52.7178i	3.94079	−	2.12406i
$617$	−15.3338	−	12.8666i	−0.617316	−	0.517990i	0.279642	−	0.960104i	$-0.409784\pi$
$617$	−15.3338	−	12.8666i	−0.617316	−	0.517990i	−0.896959	+	0.442114i	$0.854229\pi$
$618$	13.1253	+	15.8026i	0.527978	+	0.635672i
$619$	1.52586	−	4.19228i	0.0613296	−	0.168502i	−0.905243	−	0.424894i	$-0.860312\pi$
$619$	1.52586	−	4.19228i	0.0613296	−	0.168502i	0.966573	+	0.256392i	$0.0825337\pi$
$620$	−19.7015	−	7.81391i	−0.791230	−	0.313814i
$621$	36.7531	+	7.05272i	1.47485	+	0.283016i
$622$	−85.9771			−3.44737
$623$	−15.9002	+	5.26599i	−0.637027	+	0.210977i
$624$	67.8600	−	11.6147i	2.71657	−	0.464959i
$625$	−14.8833	+	20.0870i	−0.595330	+	0.803481i
$626$	15.5122	−	87.9741i	0.619993	−	3.51615i
$627$	−9.45678	−	26.3937i	−0.377668	−	1.05406i
$628$	90.5745	−	76.0011i	3.61432	−	3.03277i
$629$	0.240727	+	0.416952i	0.00959842	+	0.0166250i
$630$	−47.4721	−	11.7348i	−1.89133	−	0.467525i
$631$	4.80524	−	8.32292i	0.191294	−	0.331330i	−0.754386	−	0.656432i	$-0.772065\pi$
$631$	4.80524	−	8.32292i	0.191294	−	0.331330i	0.945679	+	0.325101i	$0.105398\pi$
$632$	4.65093	+	26.3767i	0.185004	+	1.04921i
$633$	5.54501	+	3.23863i	0.220394	+	0.128724i
$634$	51.1473	−	18.6161i	2.03132	−	0.739339i
$635$	−4.85792	−	0.138582i	−0.192781	−	0.00549948i
$636$	−49.7603	+	28.3971i	−1.97312	+	1.12602i
$637$	17.2726	+	1.01143i	0.684365	+	0.0400744i
$638$	31.5467	−	54.6406i	1.24895	−	2.16324i
$639$	8.89278	+	25.2175i	0.351793	+	0.997588i
$640$	107.231	−	15.7694i	4.23869	−	0.623342i
$641$	20.6747	+	24.6392i	0.816603	+	0.973190i	0.999951	−	0.00985806i	$-0.00313797\pi$
$641$	20.6747	+	24.6392i	0.816603	+	0.973190i	−0.183348	+	0.983048i	$0.558694\pi$
$642$	−63.8347	+	75.3044i	−2.51935	+	2.97203i
$643$	−1.83202	+	10.3899i	−0.0722477	+	0.409737i	0.927139	+	0.374718i	$0.122260\pi$
$643$	−1.83202	+	10.3899i	−0.0722477	+	0.409737i	−0.999387	+	0.0350193i	$0.988851\pi$
$644$	−106.500	−	3.11550i	−4.19670	−	0.122768i
$645$	2.53742	−	2.82586i	0.0999108	−	0.111268i
$646$	−36.5998	−	13.3212i	−1.44000	−	0.524117i
$647$		−	15.6269i		−	0.614356i	−0.951652	−	0.307178i	$-0.900615\pi$
$647$		−	15.6269i		−	0.614356i	0.951652	−	0.307178i	$-0.0993847\pi$
$648$	69.3577	−	55.8642i	2.72463	−	2.19455i
$649$		−	26.8002i		−	1.05200i
$650$	15.3169	+	30.4120i	0.600778	+	1.19286i
$651$	7.38651	−	2.40527i	0.289500	−	0.0942700i
$652$	−1.16659	+	1.39029i	−0.0456873	+	0.0544480i
$653$	−2.88263	+	16.3482i	−0.112806	+	0.639755i	0.875007	+	0.484110i	$0.160857\pi$
$653$	−2.88263	+	16.3482i	−0.112806	+	0.639755i	−0.987813	+	0.155645i	$0.950254\pi$
$654$	−16.2696	+	19.1929i	−0.636192	+	0.750502i
$655$	5.46493	+	16.4608i	0.213532	+	0.643178i
$656$	−67.7200	−	117.294i	−2.64402	−	4.57958i
$657$	6.69024	−	35.8350i	0.261011	−	1.39806i
$658$	−49.3012	+	7.21369i	−1.92196	+	0.281219i
$659$	23.5838	−	4.15847i	0.918696	−	0.161991i	0.305746	−	0.952113i	$-0.401094\pi$
$659$	23.5838	−	4.15847i	0.918696	−	0.161991i	0.612949	+	0.790122i	$0.289983\pi$
$660$	−90.9944	+	12.9154i	−3.54195	+	0.502731i
$661$	−0.796959	−	2.18963i	−0.0309981	−	0.0851666i	0.923228	−	0.384252i	$-0.125541\pi$
$661$	−0.796959	−	2.18963i	−0.0309981	−	0.0851666i	−0.954226	+	0.299085i	$0.903318\pi$
$662$	22.4081	−	8.15590i	0.870917	−	0.316988i
$663$	−8.00254	+	13.7015i	−0.310793	+	0.532124i
$664$	−73.6628	+	12.9887i	−2.85867	+	0.504061i
$665$	5.19464	−	21.9583i	0.201440	−	0.851508i
$666$	0.0107780	−	1.07368i	0.000417639	−	0.0416043i
$667$	−33.6543	+	19.4303i	−1.30310	+	0.752345i
$668$	−6.32035	−	7.53230i	−0.244542	−	0.291434i
$669$	1.13165	+	3.15840i	0.0437519	+	0.122111i
$670$	27.8312	−	45.1789i	1.07521	−	1.74541i
$671$	5.50953	+	4.62305i	0.212693	+	0.178471i
$672$	−75.1248	+	83.5424i	−2.89800	+	3.22272i
$673$	0.130488	−	0.358514i	0.00502996	−	0.0138197i	−0.937152	−	0.348921i	$-0.886548\pi$
$673$	0.130488	−	0.358514i	0.00502996	−	0.0138197i	0.942182	+	0.335101i	$0.108770\pi$
$674$			54.6982i			2.10690i
$675$	21.5058	+	14.5774i	0.827759	+	0.561084i
$676$	−38.5277			−1.48184
$677$	−12.2072	+	33.5391i	−0.469162	+	1.28901i	0.449257	+	0.893402i	$0.351689\pi$
$677$	−12.2072	+	33.5391i	−0.469162	+	1.28901i	−0.918419	+	0.395609i	$0.870534\pi$
$678$	−49.2729	−	59.3234i	−1.89232	−	2.27830i
$679$	−19.8772	−	0.581476i	−0.762817	−	0.0223150i
$680$	−43.0124	+	69.8227i	−1.64945	+	2.67758i
$681$	5.99121	−	33.0082i	0.229584	−	1.26488i
$682$	15.1847	−	12.7415i	0.581453	−	0.487897i
$683$	10.5925	+	18.3468i	0.405312	+	0.702021i	0.994358	−	0.106079i	$-0.0338296\pi$
$683$	10.5925	+	18.3468i	0.405312	+	0.702021i	−0.589046	+	0.808100i	$0.700496\pi$
$684$	40.6306	+	49.4208i	1.55355	+	1.88965i
$685$	−17.6562	−	22.3038i	−0.674609	−	0.852184i
$686$	−41.8134	+	29.2489i	−1.59644	+	1.11673i
$687$	−7.13794	−	0.0358257i	−0.272329	−	0.00136684i
$688$	−5.39347	−	14.8184i	−0.205624	−	0.564947i
$689$	−13.7406	+	5.00118i	−0.523476	+	0.190530i
$690$	71.2980	+	28.6928i	2.71427	+	1.09232i
$691$	4.03371	−	0.711252i	0.153450	−	0.0270573i	−0.0963956	−	0.995343i	$-0.530731\pi$
$691$	4.03371	−	0.711252i	0.153450	−	0.0270573i	0.249845	+	0.968286i	$0.419620\pi$
$692$	0.531794	+	0.307031i	0.0202158	+	0.0116716i
$693$	22.6496	−	24.9346i	0.860386	−	0.947186i
$694$	−33.0708	−	57.2804i	−1.25535	−	2.17433i
$695$	33.8868	−	11.2503i	1.28540	−	0.426748i
$696$	−16.5154	+	90.9908i	−0.626016	+	3.44900i
$697$	30.7411	+	5.42048i	1.16440	+	0.205315i
$698$	−38.7877	+	46.2254i	−1.46814	+	1.74966i
$699$	−19.6801	−	23.6943i	−0.744369	−	0.896202i
$700$	−67.0682	−	31.1942i	−2.53494	−	1.17903i
$701$			33.1780i			1.25311i	0.779376	+	0.626557i	$0.215536\pi$
$701$			33.1780i			1.25311i	−0.779376	+	0.626557i	$0.784464\pi$
$702$	30.9092	−	17.2302i	1.16659	−	0.650312i
$703$	0.495456			0.0186865
$704$	−51.3685	+	141.134i	−1.93602	+	5.31918i
$705$	25.9013	+	5.46847i	0.975500	+	0.205954i
$706$	37.1771	−	44.3059i	1.39918	−	1.66747i
$707$	−6.35612	−	11.7926i	−0.239047	−	0.443506i
$708$	20.6281	+	57.5728i	0.775253	+	2.16372i
$709$	−17.4420	+	14.6356i	−0.655050	+	0.549652i	−0.908598	−	0.417671i	$-0.862847\pi$
$709$	−17.4420	+	14.6356i	−0.655050	+	0.549652i	0.253549	+	0.967323i	$0.418402\pi$
$710$	7.98966	+	54.3292i	0.299847	+	2.03894i
$711$	3.98926	+	7.07262i	0.149609	+	0.265244i
$712$	31.3222	−	54.2517i	1.17385	−	2.03317i
$713$	−12.0235	+	2.12006i	−0.450283	+	0.0793970i
$714$	−6.54257	−	46.3368i	−0.244850	−	1.73411i
$715$	−23.4471	−	0.668877i	−0.876870	−	0.0250146i
$716$	−27.2353	−	74.8284i	−1.01783	−	2.79647i
$717$	−7.47733	−	13.1025i	−0.279246	−	0.489323i
$718$	−84.8578	+	14.9627i	−3.16687	+	0.558404i
$719$	−12.4324	+	21.5335i	−0.463649	+	0.803063i	−0.999139	−	0.0414778i	$-0.986793\pi$
$719$	−12.4324	+	21.5335i	−0.463649	+	0.803063i	0.535491	+	0.844541i	$0.320127\pi$
$720$	95.4334	−	50.2968i	3.55659	−	1.87445i
$721$	−10.5836	−	4.20649i	−0.394152	−	0.156658i
$722$	9.39822	−	7.88605i	0.349766	−	0.293488i
$723$	−9.23594	−	7.82920i	−0.343488	−	0.291171i
$724$	94.0896	+	16.5905i	3.49681	+	0.616583i
$725$	−26.7924	+	3.16251i	−0.995043	+	0.117453i
$726$	11.6021	−	31.3856i	0.430595	−	1.16483i
$727$	27.9918	+	10.1882i	1.03816	+	0.377858i	0.804181	−	0.594384i	$-0.202604\pi$
$727$	27.9918	+	10.1882i	1.03816	+	0.377858i	0.233976	+	0.972242i	$0.424826\pi$
$728$	−50.7670	+	40.1284i	−1.88155	+	1.48726i
$729$	14.1979	−	22.9656i	0.525849	−	0.850578i
$730$	27.6006	−	69.5904i	1.02154	−	2.57566i
$731$	3.41526	+	1.24305i	0.126318	+	0.0459759i
$732$	−15.3941	−	5.69065i	−0.568982	−	0.210332i
$733$	−13.8450	−	11.6173i	−0.511375	−	0.429095i	0.350237	−	0.936661i	$-0.386101\pi$
$733$	−13.8450	−	11.6173i	−0.511375	−	0.429095i	−0.861613	+	0.507566i	$0.830545\pi$
$734$	0.690229	−	3.91448i	0.0254768	−	0.144486i
$735$	26.2202	−	6.89203i	0.967147	−	0.254216i
$736$	135.267	−	113.502i	4.98600	−	4.18375i
$737$	18.2765	+	31.6559i	0.673225	+	1.16606i
$738$	−52.8772	−	45.2815i	−1.94644	−	1.66683i
$739$	−1.83692	+	3.18165i	−0.0675724	+	0.117039i	−0.897832	−	0.440338i	$-0.854859\pi$
$739$	−1.83692	+	3.18165i	−0.0675724	+	0.117039i	0.830260	+	0.557377i	$0.188192\pi$
$740$	0.327523	−	1.59077i	0.0120400	−	0.0584779i
$741$	8.09331	+	14.1819i	0.297315	+	0.520987i
$742$	22.6453	−	36.7008i	0.831335	−	1.34733i
$743$	12.4259	−	4.52266i	0.455863	−	0.165920i	−0.103875	−	0.994590i	$-0.533124\pi$
$743$	12.4259	−	4.52266i	0.455863	−	0.165920i	0.559738	+	0.828670i	$0.310902\pi$
$744$	−14.6530	+	25.0882i	−0.537207	+	0.919777i
$745$	−5.62954	+	27.3425i	−0.206250	+	1.00175i
$746$	−74.4247	−	42.9691i	−2.72488	−	1.57321i
$747$	−19.7518	+	11.1409i	−0.722682	+	0.407623i
$748$	−43.9755	−	76.1678i	−1.60790	−	2.78497i
$749$	11.0759	−	53.5983i	0.404704	−	1.95844i
$750$	37.6028	+	37.8526i	1.37306	+	1.38218i
$751$	−4.13512	+	23.4514i	−0.150893	+	0.855755i	0.811553	+	0.584279i	$0.198623\pi$
$751$	−4.13512	+	23.4514i	−0.150893	+	0.855755i	−0.962445	+	0.271475i	$0.912488\pi$
$752$	70.6534	−	84.2015i	2.57647	−	3.07051i
$753$	−10.3847	+	1.77740i	−0.378438	+	0.0647721i
$754$	−12.5679	+	34.5300i	−0.457695	+	1.25751i
$755$	0.461233	−	1.16292i	0.0167860	−	0.0423231i
$756$	−29.4642	+	70.9984i	−1.07160	+	2.58219i
$757$			19.8307i			0.720759i	0.932806	+	0.360379i	$0.117353\pi$
$757$			19.8307i			0.720759i	−0.932806	+	0.360379i	$0.882647\pi$
$758$	−15.4915	−	5.63846i	−0.562678	−	0.204798i
$759$	−40.7263	+	33.8266i	−1.47827	+	1.22783i
$760$	40.0951	+	74.2597i	1.45440	+	2.69368i
$761$	−8.60956	+	48.8273i	−0.312096	+	1.76999i	0.275962	+	0.961169i	$0.411004\pi$
$761$	−8.60956	+	48.8273i	−0.312096	+	1.76999i	−0.588058	+	0.808818i	$0.700107\pi$
$762$	−1.85233	+	10.2053i	−0.0671029	+	0.369699i
$763$	2.82292	−	13.6606i	0.102197	−	0.494549i
$764$	29.9469	−	17.2898i	1.08344	−	0.625525i
$765$	−5.25798	+	24.3003i	−0.190103	+	0.878579i
$766$	−32.6448	−	18.8475i	−1.17951	−	0.680988i
$767$	2.71040	+	15.3715i	0.0978670	+	0.555031i
$768$	0.545687	−	108.723i	0.0196908	−	3.92321i
$769$	3.38885	+	9.31078i	0.122205	+	0.335755i	0.985678	−	0.168640i	$-0.0539376\pi$
$769$	3.38885	+	9.31078i	0.122205	+	0.335755i	−0.863473	+	0.504395i	$0.831715\pi$
$770$	55.4728	−	41.3336i	1.99910	−	1.48956i
$771$	−16.4070	−	0.0823478i	−0.590885	−	0.00296568i
$772$	2.30447	−	0.406341i	0.0829399	−	0.0146245i
$773$	36.6997	+	21.1886i	1.32000	+	0.762101i	0.983728	−	0.179664i	$-0.0575012\pi$
$773$	36.6997	+	21.1886i	1.32000	+	0.762101i	0.336270	+	0.941766i	$0.390835\pi$
$774$	−5.14753	−	6.26116i	−0.185024	−	0.225053i
$775$	−8.24962	−	1.94528i	−0.296335	−	0.0698764i
$776$	56.9738	−	47.8067i	2.04524	−	1.71616i
$777$	0.279807	+	0.525425i	0.0100380	+	0.0188495i
$778$	45.0490	+	7.94336i	1.61509	+	0.284783i
$779$	20.6483	−	24.6077i	0.739803	−	0.881663i
$780$	50.8844	−	16.6103i	1.82195	−	0.594746i
$781$	−35.5464	−	12.9378i	−1.27195	−	0.462952i
$782$			73.5473i			2.63005i
$783$	4.45226	+	27.6810i	0.159111	+	0.989237i
$784$	25.9944	−	109.526i	0.928370	−	3.91165i
$785$	31.4141	−	35.3402i	1.12122	−	1.26135i
$786$	36.4858	−	6.24478i	1.30141	−	0.222744i
$787$	31.1099	+	26.1043i	1.10895	+	0.930519i	0.997994	−	0.0633068i	$-0.0201647\pi$
$787$	31.1099	+	26.1043i	1.10895	+	0.930519i	0.110955	+	0.993825i	$0.464609\pi$
$788$	1.12822	−	6.39843i	0.0401910	−	0.227935i
$789$	4.93650	+	13.7777i	0.175744	+	0.490499i
$790$	5.25430	+	15.8264i	0.186940	+	0.563078i
$791$	39.7310	+	15.7913i	1.41267	+	0.561475i
$792$	−1.26464	+	125.981i	−0.0449372	+	4.47655i
$793$	−3.62758	−	2.09439i	−0.128819	−	0.0743739i
$794$	−12.6697	−	71.8535i	−0.449631	−	2.54998i
$795$	−18.0356	+	14.1307i	−0.639656	+	0.501165i
$796$	−4.43714	−	12.1909i	−0.157270	−	0.432096i
$797$	12.9643	+	35.6190i	0.459218	+	1.26169i	0.926069	+	0.377355i	$0.123166\pi$
$797$	12.9643	+	35.6190i	0.459218	+	1.26169i	−0.466851	+	0.884336i	$0.654612\pi$
$798$	−44.6622	−	18.0113i	−1.58103	−	0.637594i
$799$	4.39903	+	24.9482i	0.155627	+	0.882602i
$800$	117.397	−	35.2920i	4.15060	−	1.24776i
$801$	3.48553	−	18.6696i	0.123155	−	0.659658i
$802$	69.2669	−	39.9913i	2.44590	−	1.41214i
$803$	33.1490	+	39.5054i	1.16980	+	1.39412i
$804$	−63.6277	−	53.9365i	−2.24398	−	1.90219i
$805$	−42.3185	+	4.96405i	−1.49153	+	0.174960i
$806$	−7.42073	+	8.84368i	−0.261384	+	0.311505i
$807$	−1.64137	+	4.44016i	−0.0577790	+	0.156301i
$808$	47.0822	+	17.1365i	1.65634	+	0.602860i
$809$		−	44.6611i		−	1.57020i	−0.619369	−	0.785100i	$-0.712612\pi$
$809$		−	44.6611i		−	1.57020i	0.619369	−	0.785100i	$-0.287388\pi$
$810$	37.6628	−	40.6945i	1.32334	−	1.42986i
$811$		−	2.98644i		−	0.104868i	−0.998624	−	0.0524341i	$-0.983302\pi$
$811$		−	2.98644i		−	0.104868i	0.998624	−	0.0524341i	$-0.0166980\pi$
$812$	−25.0955	−	75.7735i	−0.880678	−	2.65913i
$813$	−25.1807	−	9.30839i	−0.883124	−	0.326460i
$814$	1.16361	+	0.976384i	0.0407845	+	0.0342223i
$815$	−0.380673	+	0.617953i	−0.0133344	+	0.0216459i
$816$	78.7475	+	66.7534i	2.75671	+	2.33684i
$817$	2.86511	−	2.40411i	0.100237	−	0.0841092i
$818$	−85.0319	+	49.0932i	−2.97307	+	1.71650i
$819$	−10.4691	+	16.5921i	−0.365821	+	0.579773i
$820$	−65.3588	−	82.5630i	−2.28243	−	2.88323i
$821$	25.6546	−	4.52359i	0.895351	−	0.157875i	0.293006	−	0.956111i	$-0.405344\pi$
$821$	25.6546	−	4.52359i	0.895351	−	0.157875i	0.602345	+	0.798236i	$0.294233\pi$
$822$	−52.7287	+	30.0911i	−1.83913	+	1.04955i
$823$	4.99962	+	13.7363i	0.174276	+	0.478819i	0.995821	−	0.0913244i	$-0.0291100\pi$
$823$	4.99962	+	13.7363i	0.174276	+	0.478819i	−0.821546	+	0.570143i	$0.806888\pi$
$824$	40.0264	−	14.5684i	1.39439	−	0.507515i
$825$	−35.2508	+	10.4045i	−1.22728	+	0.362240i
$826$	−34.3832	−	30.6081i	−1.19634	−	1.06499i
$827$	7.63477	−	13.2238i	0.265487	−	0.459837i	−0.702204	−	0.711976i	$-0.747801\pi$
$827$	7.63477	−	13.2238i	0.265487	−	0.459837i	0.967691	+	0.252139i	$0.0811339\pi$
$828$	61.4530	−	104.014i	2.13564	−	3.61475i
$829$	−33.5410	+	19.3649i	−1.16493	+	0.672571i	−0.952480	−	0.304602i	$-0.901477\pi$
$829$	−33.5410	+	19.3649i	−1.16493	+	0.672571i	−0.212447	+	0.977173i	$0.568143\pi$
$830$	−44.1987	+	14.6738i	−1.53416	+	0.509335i
$831$	−39.1839	+	14.0395i	−1.35928	+	0.487024i
$832$	15.1894	−	86.1435i	0.526598	−	2.98649i
$833$	15.4862	+	20.8152i	0.536567	+	0.721204i
$834$	−12.8557	−	75.1110i	−0.445157	−	2.60088i
$835$	−2.93894	−	2.61244i	−0.101706	−	0.0904072i
$836$	−90.5087			−3.13031
$837$	−1.65999	+	8.65055i	−0.0573778	+	0.299007i
$838$	−35.1433			−1.21401
$839$	−39.7924	−	14.4832i	−1.37378	−	0.500017i	−0.453496	−	0.891258i	$-0.649824\pi$
$839$	−39.7924	−	14.4832i	−1.37378	−	0.500017i	−0.920288	+	0.391241i	$0.872046\pi$
$840$	−56.1080	+	84.4582i	−1.93591	+	2.91409i
$841$	−0.0867865	−	0.0728225i	−0.00299264	−	0.00251112i
$842$	−3.78295	+	21.4542i	−0.130369	+	0.739359i
$843$	−8.00639	+	44.1107i	−0.275755	+	1.51925i
$844$	15.8801	−	13.3250i	0.546617	−	0.458666i
$845$	−15.2437	+	2.24173i	−0.524398	+	0.0771180i
$846$	19.8552	−	52.8936i	0.682637	−	1.81852i
$847$	2.68578	+	18.3557i	0.0922845	+	0.630708i
$848$	16.5199	+	93.6890i	0.567296	+	3.21729i
$849$	0.262772	−	52.3549i	0.00901830	−	1.79681i
$850$	−20.1700	+	46.9062i	−0.691827	+	1.60887i
$851$	−0.319986	−	0.879153i	−0.0109690	−	0.0301370i
$852$	86.3199	+	0.433244i	2.95727	+	0.0148427i
$853$	−3.46008	−	19.6231i	−0.118471	−	0.671882i	−0.984973	−	0.172709i	$-0.944748\pi$
$853$	−3.46008	−	19.6231i	−0.118471	−	0.671882i	0.866502	−	0.499174i	$-0.166363\pi$
$854$	12.2235	−	1.78853i	0.418279	−	0.0612021i
$855$	18.9512	+	17.1894i	0.648118	+	0.587867i
$856$	102.349	+	177.273i	3.49820	+	6.05906i
$857$	7.97979	+	9.50994i	0.272584	+	0.324853i	0.884919	−	0.465746i	$-0.154214\pi$
$857$	7.97979	+	9.50994i	0.272584	+	0.324853i	−0.612334	+	0.790599i	$0.709769\pi$
$858$	−8.94039	+	49.2565i	−0.305220	+	1.68159i
$859$	37.0788	+	6.53800i	1.26511	+	0.223074i	0.765647	−	0.643260i	$-0.222419\pi$
$859$	37.0788	+	6.53800i	1.26511	+	0.223074i	0.499465	+	0.866334i	$0.333530\pi$
$860$	−5.82494	−	10.7883i	−0.198629	−	0.367878i
$861$	37.7572	+	8.00020i	1.28676	+	0.272646i
$862$	7.79666	−	21.4212i	0.265555	−	0.729607i
$863$	−20.9351			−0.712640			−0.356320	−	0.934364i	$-0.615969\pi$
$863$	−20.9351			−0.712640			−0.356320	+	0.934364i	$0.615969\pi$
$864$	−41.7645	−	120.355i	−1.42086	−	4.09457i
$865$	0.228271	+	0.0905359i	0.00776145	+	0.00307831i
$866$	−10.6668	−	3.88238i	−0.362471	−	0.131929i
$867$	5.57123	−	0.953553i	0.189209	−	0.0323843i
$868$	0.733293	−	25.0669i	0.0248896	−	0.850826i
$869$	−11.3128	−	1.99475i	−0.383759	−	0.0676671i
$870$	−1.93070	+	57.5452i	−0.0654568	+	1.95096i
$871$	−13.6841	−	16.3081i	−0.463669	−	0.552580i
$872$	26.0857	+	45.1817i	0.883372	+	1.53005i
$873$	11.4696	−	19.4132i	0.388186	−	0.657038i
$874$	65.5461	+	37.8431i	2.21713	+	1.28006i
$875$	−28.3508	−	8.43976i	−0.958433	−	0.285316i
$876$	−101.619	−	59.3517i	−3.43338	−	2.00531i
$877$	−14.0880	−	38.7065i	−0.475718	−	1.30703i	−0.913095	−	0.407747i	$-0.866315\pi$
$877$	−14.0880	−	38.7065i	−0.475718	−	1.30703i	0.437376	−	0.899278i	$-0.355908\pi$
$878$	−19.1752	−	52.6834i	−0.647131	−	1.77798i
$879$	4.18334	+	7.33048i	0.141101	+	0.247251i
$880$	−30.7752	+	149.474i	−1.03743	+	5.03878i
$881$	−26.1892	+	45.3610i	−0.882336	+	1.52825i	−0.0336000	+	0.999435i	$0.510697\pi$
$881$	−26.1892	+	45.3610i	−0.882336	+	1.52825i	−0.848736	+	0.528816i	$0.822636\pi$
$882$	−6.12199	−	57.5356i	−0.206138	−	1.93732i
$883$	−6.24454	+	3.60529i	−0.210145	+	0.121328i	−0.601379	−	0.798964i	$-0.705382\pi$
$883$	−6.24454	+	3.60529i	−0.210145	+	0.121328i	0.391234	+	0.920291i	$0.372048\pi$
$884$	32.9256	+	39.2393i	1.10741	+	1.31976i
$885$	11.5115	+	21.5787i	0.386954	+	0.725359i
$886$	−3.59250	+	20.3741i	−0.120692	+	0.684481i
$887$	31.0964	−	37.0593i	1.04412	−	1.24433i	0.0751395	−	0.997173i	$-0.476060\pi$
$887$	31.0964	−	37.0593i	1.04412	−	1.24433i	0.968976	−	0.247155i	$-0.0794958\pi$
$888$	−2.08829	−	0.771967i	−0.0700784	−	0.0259055i
$889$	−1.80788	−	5.45872i	−0.0606342	−	0.183080i
$890$	14.3796	−	36.2557i	0.482005	−	1.21529i
$891$	12.3407	+	36.1476i	0.413428	+	1.21099i
$892$	10.8307			0.362639
$893$	24.4975	+	8.91637i	0.819778	+	0.298375i
$894$	55.8826	+	20.6578i	1.86899	+	0.690901i
$895$	−15.1296	−	28.0215i	−0.505728	−	0.936655i
$896$	60.8462	+	112.889i	2.03273	+	3.77134i
$897$	19.9379	−	23.5203i	0.665708	−	0.785321i
$898$	5.32374	+	6.34458i	0.177655	+	0.211721i
$899$	−4.57330	−	7.92119i	−0.152528	−	0.264186i
$900$	67.7183	−	49.4839i	2.25728	−	1.64946i
$901$	−18.9884	−	10.9630i	−0.632596	−	0.365229i
$902$	96.9878	−	17.1016i	3.22934	−	0.569420i
$903$	4.16759	+	1.68070i	0.138689	+	0.0559302i
$904$	−150.261	+	54.6904i	−4.99759	+	1.81897i
$905$	38.1923	+	1.08952i	1.26955	+	0.0362167i
$906$	−2.30556	−	1.34659i	−0.0765972	−	0.0447375i
$907$	−32.1642	+	5.67142i	−1.06799	+	0.188316i	−0.679901	−	0.733304i	$-0.737977\pi$
$907$	−32.1642	+	5.67142i	−1.06799	+	0.188316i	−0.388094	+	0.921620i	$0.626866\pi$
$908$	−93.7893	−	54.1493i	−3.11251	−	1.79701i
$909$	15.1894	+	0.152477i	0.503801	+	0.00505733i
$910$	−27.6367	+	29.3174i	−0.916147	+	0.971863i
$911$	−35.9786	−	42.8777i	−1.19203	−	1.42060i	−0.882888	−	0.469583i	$-0.844404\pi$
$911$	−35.9786	−	42.8777i	−1.19203	−	1.42060i	−0.309138	−	0.951017i	$-0.600040\pi$
$912$	100.010	−	35.8333i	3.31166	−	1.18656i
$913$	5.57076	−	31.5934i	0.184365	−	1.04559i
$914$	43.1120	−	51.3789i	1.42602	−	1.69946i
$915$	−6.42184	−	1.35582i	−0.212300	−	0.0448222i
$916$	−7.88120	+	21.6534i	−0.260402	+	0.715449i
$917$	−16.0998	+	12.7260i	−0.531662	+	0.420249i
$918$	49.5832	+	18.8970i	1.63649	+	0.623694i
$919$	18.2315			0.601403			0.300701	−	0.953718i	$-0.402779\pi$
$919$	18.2315			0.601403			0.300701	+	0.953718i	$0.402779\pi$
$920$	105.874	−	119.106i	3.49056	−	3.92681i
$921$	7.61183	+	9.16444i	0.250818	+	0.301979i
$922$	−17.1940	−	14.4275i	−0.566254	−	0.475143i
$923$	21.6964	+	3.82566i	0.714145	+	0.125923i
$924$	−51.1144	−	95.9834i	−1.68154	−	3.15762i
$925$	0.0370271	−	0.648452i	0.00121744	−	0.0213210i
$926$	−60.1990	+	34.7559i	−1.97826	+	1.14215i
$927$	9.97533	−	8.20108i	0.327633	−	0.269359i
$928$	114.564	+	66.1437i	3.76076	+	2.17127i
$929$	−7.12506	−	40.4082i	−0.233766	−	1.32575i	−0.845198	−	0.534454i	$-0.820517\pi$
$929$	−7.12506	−	40.4082i	−0.233766	−	1.32575i	0.611432	−	0.791297i	$-0.290594\pi$
$930$	−6.75342	+	16.7814i	−0.221453	+	0.550282i
$931$	26.5190	−	3.09123i	0.869126	−	0.101311i
$932$	−93.4370	+	34.0083i	−3.06063	+	1.11398i
$933$	−0.271267	+	54.0475i	−0.00888090	+	1.76944i
$934$	−105.269	+	18.5618i	−3.44452	+	0.607362i
$935$	−21.8309	−	27.5774i	−0.713947	−	0.901877i
$936$	−12.0156	−	72.3855i	−0.392743	−	2.36599i
$937$	−0.699518	−	1.21160i	−0.0228522	−	0.0395812i	0.854373	−	0.519660i	$-0.173941\pi$
$937$	−0.699518	−	1.21160i	−0.0228522	−	0.0395812i	−0.877225	+	0.480079i	$0.840608\pi$
$938$	61.4862	+	12.7059i	2.00760	+	0.414862i
$939$	−55.2540	−	10.0290i	−1.80315	−	0.327283i
$940$	44.8222	−	72.7605i	1.46194	−	2.37319i
$941$	−19.2084	−	16.1178i	−0.626177	−	0.525425i	0.273561	−	0.961855i	$-0.411798\pi$
$941$	−19.2084	−	16.1178i	−0.626177	−	0.525425i	−0.899738	+	0.436430i	$0.856243\pi$
$942$	−64.4775	−	77.6292i	−2.10079	−	2.52930i
$943$	−57.0003	−	20.7464i	−1.85618	−	0.675596i
$944$	101.550			3.30517
$945$	−7.52658	+	29.8052i	−0.244840	+	0.969564i
$946$	11.4666			0.372812
$947$	−22.7121	−	8.26651i	−0.738043	−	0.268626i	−0.0544776	−	0.998515i	$-0.517349\pi$
$947$	−22.7121	−	8.26651i	−0.738043	−	0.268626i	−0.683565	+	0.729889i	$0.739572\pi$
$948$	25.8377	−	4.42229i	0.839170	−	0.143629i
$949$	−23.0082	−	19.3062i	−0.746878	−	0.626705i
$950$	31.4250	+	42.1109i	1.01956	+	1.36626i
$951$	−11.5412	−	32.2113i	−0.374249	−	1.04452i
$952$	−95.0253	−	19.6366i	−3.07979	−	0.636427i
$953$	2.88411	+	4.99543i	0.0934256	+	0.161818i	0.908950	−	0.416904i	$-0.136885\pi$
$953$	2.88411	+	4.99543i	0.0934256	+	0.161818i	−0.815525	+	0.578722i	$0.803552\pi$
$954$	24.0232	+	42.5911i	0.777780	+	1.37894i
$955$	10.8426	−	8.58326i	0.350858	−	0.277748i
$956$	−47.9609	+	8.45681i	−1.55117	+	0.273513i
$957$	−34.2490	−	20.0035i	−1.10711	−	0.646623i
$958$	41.7456	−	15.1942i	1.34874	−	0.490901i
$959$	17.6743	−	28.6444i	0.570733	−	0.924975i
$960$	−19.2609	−	135.701i	−0.621642	−	4.37973i
$961$	4.88410	+	27.6991i	0.157551	+	0.893519i
$962$	−0.766143	−	0.442333i	−0.0247015	−	0.0142614i
$963$	47.1370	+	40.3658i	1.51897	+	1.30077i
$964$	−33.8500	+	19.5433i	−1.09023	+	0.629447i
$965$	0.888132	−	0.294856i	0.0285900	−	0.00949176i
$966$	−3.11523	+	90.8826i	−0.100231	+	2.92410i
$967$	55.7011	+	9.82161i	1.79123	+	0.315842i	0.967827	−	0.251618i	$-0.0809627\pi$
$967$	55.7011	+	9.82161i	1.79123	+	0.315842i	0.823401	+	0.567460i	$0.192074\pi$
$968$	−53.1502	−	44.5983i	−1.70831	−	1.43344i
$969$	−8.48957	+	22.9656i	−0.272724	+	0.737761i
$970$	30.7644	−	34.6094i	0.987787	−	1.11124i
$971$	11.9841			0.384590			0.192295	−	0.981337i	$-0.438407\pi$
$971$	11.9841			0.384590			0.192295	+	0.981337i	$0.438407\pi$
$972$	−54.3335	−	68.1546i	−1.74275	−	2.18606i
$973$	26.1981	+	33.1436i	0.839874	+	1.06254i
$974$	14.5997	−	40.1123i	0.467804	−	1.28528i
$975$	19.1662	−	9.53266i	0.613808	−	0.305289i
$976$	−17.5175	+	20.8765i	−0.560720	+	0.668240i
$977$	5.51174	−	31.2586i	0.176336	−	1.00005i	−0.760254	−	0.649626i	$-0.774926\pi$
$977$	5.51174	−	31.2586i	0.176336	−	1.00005i	0.936590	−	0.350426i	$-0.113963\pi$
$978$	1.18159	+	1.00162i	0.0377831	+	0.0320283i
$979$	17.2702	+	20.5818i	0.551959	+	0.657799i
$980$	7.60545	−	87.1887i	0.242947	−	2.78514i
$981$	12.0138	+	10.2881i	0.383573	+	0.328473i
$982$	20.8378	+	12.0307i	0.664962	+	0.383916i
$983$	−40.2680	+	7.10034i	−1.28435	+	0.226466i	−0.773826	−	0.633398i	$-0.781660\pi$
$983$	−40.2680	+	7.10034i	−1.28435	+	0.226466i	−0.510524	+	0.859864i	$0.670549\pi$
$984$	−125.372	+	71.5467i	−3.99670	+	2.28083i
$985$	0.0740910	−	2.59721i	0.00236074	−	0.0827541i
$986$	−51.7767	+	18.8452i	−1.64891	+	0.600152i
$987$	4.37917	+	31.0148i	0.139391	+	0.987213i
$988$	51.9120	−	9.15349i	1.65154	−	0.291211i
$989$	−6.11634	−	3.53127i	−0.194488	−	0.112288i
$990$	10.6333	+	77.7173i	0.337947	+	2.47002i
$991$	5.98709	+	10.3699i	0.190186	+	0.329412i	0.945312	−	0.326168i	$-0.105758\pi$
$991$	5.98709	+	10.3699i	0.190186	+	0.329412i	−0.755126	+	0.655580i	$0.772424\pi$
$992$	26.7150	+	31.8377i	0.848201	+	1.01085i
$993$	−5.05632	−	14.1121i	−0.160457	−	0.447834i
$994$	−57.1956	+	30.8280i	−1.81413	+	0.977806i
$995$	−2.46490	−	4.56522i	−0.0781426	−	0.144727i
$996$	12.3502	+	72.1575i	0.391332	+	2.28640i
$997$	−18.7474	−	6.82351i	−0.593737	−	0.216103i	0.0276353	−	0.999618i	$-0.491202\pi$
$997$	−18.7474	−	6.82351i	−0.593737	−	0.216103i	−0.621372	+	0.783515i	$0.713425\pi$
$998$	−60.2939			−1.90857
$999$	−0.674912	−	0.0101629i	−0.0213533	−	0.000321541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.1	✓	816
5.4	even	2	inner	945.2.cs.b.104.136	yes	816
7.6	odd	2	inner	945.2.cs.b.104.2	yes	816
27.20	odd	18	inner	945.2.cs.b.209.135	yes	816
35.34	odd	2	inner	945.2.cs.b.104.135	yes	816
135.74	odd	18	inner	945.2.cs.b.209.2	yes	816
189.20	even	18	inner	945.2.cs.b.209.136	yes	816
945.209	even	18	inner	945.2.cs.b.209.1	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.1	✓	816	1.1	even	1	trivial
945.2.cs.b.104.2	yes	816	7.6	odd	2	inner
945.2.cs.b.104.135	yes	816	35.34	odd	2	inner
945.2.cs.b.104.136	yes	816	5.4	even	2	inner
945.2.cs.b.209.1	yes	816	945.209	even	18	inner
945.2.cs.b.209.2	yes	816	135.74	odd	18	inner
945.2.cs.b.209.135	yes	816	27.20	odd	18	inner
945.2.cs.b.209.136	yes	816	189.20	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.58909 - 0.942353i) q^{2} +(-0.600558 + 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(1.90382 + 1.17280i) q^{5} +(3.08585 - 3.64031i) q^{6} +(-0.535422 + 2.59101i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +O(q^{10})\)	\(q+(-2.58909 - 0.942353i) q^{2} +(-0.600558 + 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(1.90382 + 1.17280i) q^{5} +(3.08585 - 3.64031i) q^{6} +(-0.535422 + 2.59101i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +(-3.82398 - 4.83056i) q^{10} +(4.17954 - 0.736966i) q^{11} +(-8.41135 + 4.80017i) q^{12} +(-2.32268 + 0.845385i) q^{13} +(3.82790 - 6.20380i) q^{14} +(-3.04869 + 2.38862i) q^{15} +(2.79248 + 15.8369i) q^{16} +(-3.20975 - 1.85315i) q^{17} +(4.06082 + 7.19949i) q^{18} +(-3.30309 + 1.90704i) q^{19} +(3.93945 + 11.8660i) q^{20} +(-3.88780 - 2.42590i) q^{21} +(-11.5157 - 2.03053i) q^{22} +(5.51719 + 4.62947i) q^{23} +(16.8935 - 2.89144i) q^{24} +(2.24908 + 4.46560i) q^{25} +6.81028 q^{26} +(4.53861 - 2.53003i) q^{27} +(-11.6057 + 9.17366i) q^{28} +(-1.84543 + 5.07027i) q^{29} +(10.1443 - 3.31142i) q^{30} +(-1.08964 + 1.29858i) q^{31} +(4.25739 - 24.1448i) q^{32} +(-1.31278 + 7.23268i) q^{33} +(6.56402 + 7.82270i) q^{34} +(-4.05808 + 4.30488i) q^{35} +(-2.74686 - 16.5479i) q^{36} +(-0.112498 - 0.0649508i) q^{37} +(10.3491 - 1.82483i) q^{38} +(0.0214872 - 4.28113i) q^{39} +(0.630951 - 22.1176i) q^{40} +(-7.91430 + 2.88057i) q^{41} +(7.77983 + 9.94456i) q^{42} +(-0.965713 + 0.170281i) q^{43} +(20.5509 + 11.8651i) q^{44} +(-2.04964 - 6.38741i) q^{45} +(-9.92193 - 17.1853i) q^{46} +(-4.39353 - 5.23601i) q^{47} +(-27.4058 - 4.97433i) q^{48} +(-6.42665 - 2.77457i) q^{49} +(-1.61491 - 13.6813i) q^{50} +(4.93827 - 4.10164i) q^{51} +(-12.9871 - 4.72691i) q^{52} +5.91585 q^{53} +(-14.1351 + 2.27351i) q^{54} +(8.82141 + 3.49871i) q^{55} +(24.8530 - 8.23107i) q^{56} +(-1.11449 - 6.51150i) q^{57} +(9.55598 - 11.3884i) q^{58} +(1.09656 - 6.21888i) q^{59} +(-21.6433 - 0.726155i) q^{60} +(1.08931 + 1.29819i) q^{61} +(4.04489 - 2.33532i) q^{62} +(6.27597 - 4.85924i) q^{63} +(-17.6945 + 30.6478i) q^{64} +(-5.41343 - 1.11457i) q^{65} +(10.2146 - 17.4890i) q^{66} +(2.94577 + 8.09344i) q^{67} +(-7.08787 - 19.4738i) q^{68} +(-10.8344 + 6.18297i) q^{69} +(14.5635 - 7.32158i) q^{70} +(-7.71904 - 4.45659i) q^{71} +(-5.44810 + 29.1817i) q^{72} +(6.07570 + 10.5234i) q^{73} +(0.230061 + 0.274177i) q^{74} +(-8.60553 + 0.972011i) q^{75} +(-21.0022 - 3.70325i) q^{76} +(-0.328335 + 11.2238i) q^{77} +(-4.08997 + 11.0640i) q^{78} +(-2.54347 - 0.925746i) q^{79} +(-13.2572 + 33.4257i) q^{80} +(1.38459 + 8.89286i) q^{81} +23.2054 q^{82} +(2.58535 - 7.10319i) q^{83} +(-7.93365 - 24.3640i) q^{84} +(-3.93742 - 7.29247i) q^{85} +(2.66079 + 0.469168i) q^{86} +(-7.12889 - 6.04308i) q^{87} +(-26.9944 - 32.1707i) q^{88} +(3.16536 + 5.48257i) q^{89} +(-0.712473 + 18.4691i) q^{90} +(-0.946787 - 6.47071i) q^{91} +(6.99290 + 39.6587i) q^{92} +(-1.45528 - 2.55010i) q^{93} +(6.44109 + 17.6968i) q^{94} +(-8.52508 - 0.243196i) q^{95} +(36.6689 + 21.4169i) q^{96} +(1.30516 + 7.40190i) q^{97} +(14.0246 + 13.2398i) q^{98} +(-10.9618 - 6.47638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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