LMFDB - Embedded newform 945.2.cs.b.104.2

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			104.2
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58909 - 0.942353i) q^{2} +(0.600558 - 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(-1.90382 - 1.17280i) q^{5} +(-3.08585 + 3.64031i) q^{6} +(2.64462 - 0.0773642i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +O(q^{10})$	\(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} +(2.64462 - 0.0773642i) 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} +(-6.92007 - 2.29186i) 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} +(1.46256 - 4.34292i) 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} +(-5.12562 - 2.95432i) 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} +(-7.87926 + 9.86596i) 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} +(6.98803 - 0.409198i) 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} +(-13.7476 - 22.2805i) 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} +(-6.17716 - 4.98425i) 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} +(10.4867 + 12.4792i) 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} +(10.9963 - 2.27234i) 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} +(21.8735 - 13.3454i) 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} +(6.07720 - 2.41541i) 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} +(-18.4783 - 5.52574i) 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
$7$	2.64462	−	0.0773642i	0.999572	−	0.0292409i
$7$	2.64462	−	0.0773642i	0.999572	−	0.0292409i
$8$	−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	0.000796869	−	1.00000i	$-0.499746\pi$
$13$	2.32268	−	0.845385i	0.644195	−	0.234468i	0.643398	+	0.765532i	$0.277524\pi$
$14$	−6.92007	−	2.29186i	−1.84947	−	0.612526i
$15$	−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	0.835891	−	0.548895i	$-0.184952\pi$
$17$	3.20975	+	1.85315i	0.778479	+	0.449455i	−0.0574119	+	0.998351i	$0.518285\pi$
$18$	4.06082	+	7.19949i	0.957145	+	1.69694i
$19$	3.30309	−	1.90704i	0.757782	−	0.437505i	−0.0707171	−	0.997496i	$-0.522529\pi$
$19$	3.30309	−	1.90704i	0.757782	−	0.437505i	0.828499	+	0.559991i	$0.189195\pi$
$20$	−3.93945	−	11.8660i	−0.880889	−	2.65331i
$21$	1.46256	−	4.34292i	0.319157	−	0.947702i
$22$	−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	−0.659264	−	0.751912i	$-0.729132\pi$
$31$	1.08964	−	1.29858i	0.195705	−	0.233232i	0.854968	+	0.518680i	$0.173576\pi$
$32$	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
$35$	−5.12562	−	2.95432i	−0.866388	−	0.499371i
$36$	−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	0.360356	−	0.932815i	$-0.382655\pi$
$41$	7.91430	−	2.88057i	1.23601	−	0.449870i	0.875651	+	0.482945i	$0.160433\pi$
$42$	−7.87926	+	9.86596i	−1.21580	+	1.52235i
$43$	−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	0.984506	−	0.175350i	$-0.0561057\pi$
$47$	4.39353	+	5.23601i	0.640862	+	0.763750i	−0.343644	+	0.939100i	$0.611661\pi$
$48$	27.4058	+	4.97433i	3.95568	+	0.717982i
$49$	6.98803	−	0.409198i	0.998290	−	0.0584568i
$50$	−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
$56$	−13.7476	−	22.2805i	−1.83711	−	2.97736i
$57$	−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	$0.190397\pi$
$59$	−1.09656	+	6.21888i	−0.142759	+	0.809629i	−0.969139	+	0.246515i	$0.920714\pi$
$60$	−21.6433	−	0.726155i	−2.79414	−	0.0937463i
$61$	−1.08931	−	1.29819i	−0.139472	−	0.166216i	0.691787	−	0.722102i	$-0.256824\pi$
$61$	−1.08931	−	1.29819i	−0.139472	−	0.166216i	−0.831259	+	0.555886i	$0.812379\pi$
$62$	−4.04489	+	2.33532i	−0.513701	+	0.296586i
$63$	−6.17716	−	4.98425i	−0.778248	−	0.627956i
$64$	−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
$70$	10.4867	+	12.4792i	1.25340	+	1.49154i
$71$	−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	$-0.914861\pi$
$73$	−6.07570	−	10.5234i	−0.711106	−	1.23167i	0.253336	−	0.967378i	$-0.418472\pi$
$74$	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
$77$	10.9963	−	2.27234i	1.25314	−	0.258957i
$78$	−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	$0.247280\pi$
$83$	−2.58535	+	7.10319i	−0.283779	+	0.779676i	−0.996903	+	0.0786386i	$0.974943\pi$
$84$	21.8735	−	13.3454i	2.38659	−	1.45610i
$85$	−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	0.648058	−	0.761591i	$-0.275581\pi$
$89$	−3.16536	−	5.48257i	−0.335528	−	0.581151i	−0.983586	+	0.180440i	$0.942248\pi$
$90$	0.712473	−	18.4691i	0.0751012	−	1.94681i
$91$	6.07720	−	2.41541i	0.637063	−	0.253204i
$92$	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	$-0.930939\pi$
$97$	−1.30516	−	7.40190i	−0.132518	−	0.751549i	0.844037	−	0.536285i	$-0.180173\pi$
$98$	−18.4783	−	5.52574i	−1.86659	−	0.558184i
$99$	−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	−0.429081	−	0.903266i	$-0.641163\pi$
$101$	3.87878	−	3.25468i	0.385953	−	0.323853i	0.815034	+	0.579413i	$0.196718\pi$
$102$	−16.6508	+	5.96594i	−1.64868	+	0.590716i
$103$	0.747483	−	4.23919i	0.0736517	−	0.417700i	−0.925582	−	0.378548i	$-0.876423\pi$
$103$	0.747483	−	4.23919i	0.0736517	−	0.417700i	0.999233	−	0.0391514i	$-0.0124655\pi$
$104$	−18.7364	−	15.7217i	−1.83726	−	1.54164i
$105$	−7.87783	+	6.55285i	−0.768797	+	0.639493i
$106$	−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
$112$	8.61026	+	41.6666i	0.813593	+	3.93713i
$113$	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
$119$	8.63194	+	4.65256i	0.791289	+	0.426499i
$120$	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
$126$	11.2963	+	18.7257i	1.00636	+	1.66822i
$127$	−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	0.345188	−	0.938534i	$-0.387815\pi$
$131$	−5.94190	−	4.98585i	−0.519146	−	0.435616i	−0.864334	+	0.502918i	$0.832260\pi$
$132$	31.6180	−	26.2614i	2.75199	−	2.28576i
$133$	8.58789	−	5.29894i	0.744664	−	0.459477i
$134$		−	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	$0.459027\pi$
$139$	−10.2640	+	12.2322i	−0.870584	+	1.03752i	−0.998951	+	0.0457953i	$0.985418\pi$
$140$	−11.3364	−	31.0762i	−0.958097	−	2.62642i
$141$	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
$147$	3.53193	−	11.5985i	0.291309	−	0.956629i
$148$	−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
$154$	−30.6117	−	4.47907i	−2.46676	−	0.360934i
$155$	−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	$0.375253\pi$
$157$	−3.67197	+	20.8248i	−0.293055	+	1.66200i	−0.675003	+	0.737815i	$0.735858\pi$
$158$	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	0.240252	−	0.970711i	$-0.422770\pi$
$167$	1.73182	+	0.305366i	0.134012	+	0.0236299i	−0.106240	+	0.994341i	$0.533881\pi$
$168$	−44.4533	+	8.95370i	−3.42964	+	0.690793i
$169$	−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	−0.177758	−	0.984074i	$-0.556884\pi$
$173$	−0.108154	+	0.0190704i	−0.00822277	+	0.00144990i	0.169535	+	0.985524i	$0.445773\pi$
$174$	−12.7626	−	22.3640i	−0.967534	−	1.69541i
$175$	6.29345	+	11.6358i	0.475740	+	0.879586i
$176$	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	−0.936198	−	0.351472i	$-0.885681\pi$
$181$	−14.7978	+	8.54353i	−1.09991	+	0.635036i	−0.163715	+	0.986508i	$0.552348\pi$
$182$	−18.0106	+	0.526872i	−1.33503	+	0.0390543i
$183$	−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
$189$	−11.8072	+	7.04209i	−0.858844	+	0.512236i
$190$	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
$196$	31.4024	+	23.3630i	2.24303	+	1.66878i
$197$	−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	0.569526	−	0.821973i	$-0.307127\pi$
$199$	2.00937	+	1.16011i	0.142440	+	0.0822378i	−0.427086	+	0.904211i	$0.640460\pi$
$200$	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
$203$	−4.48820	+	13.5517i	−0.315010	+	0.951144i
$204$	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
$210$	26.5715	−	9.54225i	1.83361	−	0.658478i
$211$	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	−0.691117	−	0.722743i	$-0.742881\pi$
$223$	−1.48384	+	1.24509i	−0.0993655	+	0.0833775i	0.591752	+	0.806120i	$0.298437\pi$
$224$	9.39123	−	64.1833i	0.627478	−	4.28843i
$225$	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	0.499982	−	0.866036i	$-0.333340\pi$
$227$	19.0744	−	3.36333i	1.26601	−	0.223232i	0.766031	+	0.642803i	$0.222229\pi$
$228$	18.6293	−	31.8962i	1.23376	−	2.11238i
$229$	−1.40951	−	3.87261i	−0.0931433	−	0.255909i	0.884369	−	0.466789i	$-0.154589\pi$
$229$	−1.40951	−	3.87261i	−0.0931433	−	0.255909i	−0.977512	+	0.210880i	$0.932367\pi$
$230$	−1.26530	+	44.3542i	−0.0834312	+	2.92463i
$231$	2.91225	−	19.2292i	0.191612	−	1.26519i
$232$	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
$238$	−17.9645	−	20.1802i	−1.16447	−	1.30809i
$239$	−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	−0.838561	−	0.544808i	$-0.816603\pi$
$241$	2.39087	−	6.56887i	0.154010	−	0.423138i	0.992571	+	0.121670i	$0.0388249\pi$
$242$	−19.3189			−1.24187
$243$	15.2789	+	3.09126i	0.980140	+	0.198305i
$244$		−	9.47560i		−	0.606613i
$245$	−13.7839	−	7.41652i	−0.880620	−	0.473824i
$246$	−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	0.753933	−	0.656952i	$-0.228154\pi$
$251$	−3.04139	−	5.26783i	−0.191971	−	0.332503i	−0.945903	+	0.324449i	$0.894821\pi$
$252$	−8.54461	−	43.5503i	−0.538260	−	2.74341i
$253$	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	0.796695	−	0.604381i	$-0.206579\pi$
$257$	−3.23987	−	8.90146i	−0.202097	−	0.555258i	−0.998793	+	0.0491233i	$0.984357\pi$
$258$	2.36017	−	4.04095i	0.146938	−	0.251579i
$259$	−0.302540	−	0.163067i	−0.0187989	−	0.0101325i
$260$	−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
$266$	−27.2283	+	5.62663i	−1.66948	+	0.344991i
$267$	−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	$-0.526552\pi$
$269$	−2.73308			−0.166639			−0.0833193	+	0.996523i	$0.526552\pi$
$270$	−29.5770	−	12.2492i	−1.80000	−	0.745464i
$271$		−	15.4996i		−	0.941533i	−0.882258	−	0.470766i	$-0.843977\pi$
$271$		−	15.4996i		−	0.941533i	0.882258	−	0.470766i	$-0.156023\pi$
$272$	−20.3851	+	56.0075i	−1.23603	+	3.39595i
$273$	−0.274381	−	11.3236i	−0.0166063	−	0.685337i
$274$	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
$280$	0.0424832	+	58.5414i	0.00253886	+	3.49852i
$281$	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	0.694042	−	0.719934i	$-0.255828\pi$
$283$	28.4045	−	10.3384i	1.68847	−	0.614554i	0.994432	+	0.105380i	$0.0336058\pi$
$284$	−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
$287$	20.7075	−	8.23030i	1.22232	−	0.485819i
$288$	−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	−0.849739	−	0.527204i	$-0.823240\pi$
$293$	−3.13226	+	3.73288i	−0.182989	+	0.218077i	0.666750	+	0.745281i	$0.267685\pi$
$294$	−20.0744	+	26.7013i	−1.17076	+	1.55725i
$295$	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
$301$	−2.54077	+	0.525041i	−0.146448	+	0.0302629i
$302$	−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	−0.947319	−	0.320292i	$-0.896219\pi$
$307$	−3.43908	+	5.95665i	−0.196278	+	0.339964i	0.751040	+	0.660256i	$0.229552\pi$
$308$	55.2672	+	29.7887i	3.14914	+	1.69737i
$309$	−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	−0.990791	−	0.135400i	$-0.956768\pi$
$311$	−29.3229	+	10.6727i	−1.66275	+	0.605191i	−0.671957	+	0.740590i	$0.734546\pi$
$312$	−36.7938	+	20.9974i	−2.08304	+	1.18874i
$313$	−5.63004	−	31.9296i	−0.318229	−	1.80477i	−0.553514	−	0.832840i	$-0.686714\pi$
$313$	−5.63004	−	31.9296i	−0.318229	−	1.80477i	0.235285	−	0.971926i	$-0.424398\pi$
$314$	29.1314	−	50.4570i	1.64398	−	2.84745i
$315$	5.91468	+	16.7337i	0.333255	+	0.942837i
$316$	−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
$322$	−27.5693	−	44.6809i	−1.53637	−	2.48997i
$323$	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
$329$	12.0243	+	13.5073i	0.662921	+	0.744684i
$330$	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
$336$	72.8627	+	11.0350i	3.97498	+	0.602008i
$337$	−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
$343$	18.4490	−	1.62280i	0.996154	−	0.0876227i
$344$	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	$0.310475\pi$
$349$	−7.49060	+	20.5802i	−0.400963	+	1.10164i	−0.961810	+	0.273717i	$0.911747\pi$
$350$	−5.32927	−	36.0569i	−0.284861	−	1.92732i
$351$	−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	$-0.700214\pi$
$353$	7.17955	−	19.7257i	0.382129	−	1.04989i	0.970458	−	0.241269i	$-0.0775637\pi$
$354$	−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
$357$	12.7425	−	11.2293i	0.674406	−	0.594319i
$358$	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
$364$	34.7116	+	11.4962i	1.81938	+	0.602562i
$365$	−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	0.977571	−	0.210606i	$-0.0675437\pi$
$367$	−0.250514	−	1.42073i	−0.0130767	−	0.0741617i	−0.990648	+	0.136444i	$0.956433\pi$
$368$	−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
$371$	15.6452	−	0.457675i	0.812257	−	0.0237613i
$372$	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
$378$	37.2060	−	7.10611i	1.91367	−	0.365499i
$379$	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	−0.181531	−	0.983385i	$-0.558105\pi$
$383$	−13.4733	−	2.37570i	−0.688452	−	0.121393i	−0.506921	+	0.861992i	$0.669216\pi$
$384$	−28.3177	−	79.0344i	−1.44508	−	4.03320i
$385$	−23.6000	−	8.57029i	−1.20277	−	0.436783i
$386$	−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
$392$	−38.0810	−	57.8600i	−1.92338	−	2.92237i
$393$	−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	$-0.935302\pi$
$397$	−13.2405	−	22.9332i	−0.664522	−	1.15099i	0.314893	−	0.949127i	$-0.398031\pi$
$398$	−4.10920	−	4.89716i	−0.205976	−	0.245472i
$399$	−3.45115	−	17.1342i	−0.172773	−	0.857784i
$400$	−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	$0.565381\pi$
$409$	−22.9064	+	27.2988i	−1.13265	+	1.34984i	−0.928690	+	0.370858i	$0.879064\pi$
$410$	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
$413$	−2.41886	+	16.5314i	−0.119024	+	0.813457i
$414$	−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	−0.617769	−	0.786360i	$-0.711963\pi$
$419$	−11.9858	+	4.36247i	−0.585545	+	0.213121i	0.0322240	+	0.999481i	$0.489741\pi$
$420$	−57.2946	−	0.245985i	−2.79569	−	0.0120029i
$421$	−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
$427$	−2.98124	−	3.34894i	−0.144272	−	0.162067i
$428$	−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	$-0.531563\pi$
$433$	−4.11988			−0.197989			−0.0989944	+	0.995088i	$0.531563\pi$
$434$	−10.5165	+	6.48896i	−0.504809	+	0.311480i
$435$	−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	0.357541	−	0.933897i	$-0.383615\pi$
$439$	−13.0796	−	15.5876i	−0.624254	−	0.743957i	−0.981796	+	0.189940i	$0.939171\pi$
$440$	13.6628	+	92.9063i	0.651349	+	4.42914i
$441$	−16.7218	−	12.7036i	−0.796278	−	0.604931i
$442$	−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
$448$	−44.4242	+	82.4206i	−2.09884	+	3.89401i
$449$	−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
$455$	−14.4027	−	2.52881i	−0.675209	−	0.118552i
$456$	−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	0.157544	−	0.987512i	$-0.449642\pi$
$461$	−7.65502	−	2.78620i	−0.356530	−	0.129766i	−0.514074	+	0.857746i	$0.671864\pi$
$462$	−25.6608	+	47.0419i	−1.19385	+	2.18859i
$463$	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	$0.688051\pi$
$467$	−33.5985	+	19.3981i	−1.55475	+	0.897637i	−0.997744	+	0.0671294i	$0.978616\pi$
$468$	−20.3694	−	36.1132i	−0.941575	−	1.66933i
$469$	8.41658	+	21.1762i	0.388642	+	0.977824i
$470$	−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
$476$	20.2513	+	50.9523i	0.928216	+	2.33540i
$477$	−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	−0.315415	−	0.948954i	$-0.602144\pi$
$479$	12.3514	−	10.3641i	0.564351	−	0.473547i	0.879766	+	0.475407i	$0.157699\pi$
$480$	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
$483$	28.1746	−	17.1898i	1.28199	−	0.782164i
$484$	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
$490$	28.6988	+	32.1913i	1.29648	+	1.45426i
$491$	−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
$497$	−20.7587	−	11.1888i	−0.931155	−	0.501887i
$498$	−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	−0.174035	−	0.984740i	$-0.555681\pi$
$503$	−24.9813	−	14.4230i	−1.11386	−	0.643088i	−0.939827	+	0.341651i	$0.889014\pi$
$504$	−12.1505	+	77.5961i	−0.541228	+	3.45640i
$505$	−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	0.997952	−	0.0639702i	$-0.0203763\pi$
$509$	25.0032	+	20.9801i	1.10825	+	0.929929i	0.110294	+	0.993899i	$0.464821\pi$
$510$	38.6971	+	8.17000i	1.71354	+	0.361774i
$511$	−16.8820	−	27.3604i	−0.746818	−	1.21035i
$512$	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
$518$	0.629637	+	0.707294i	0.0276646	+	0.0310767i
$519$	−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	0.501154	−	0.865358i	$-0.332909\pi$
$521$	−11.3864	−	19.7217i	−0.498845	−	0.864025i	−0.999999	+	0.00133298i	$0.999576\pi$
$522$	−43.9973	+	7.30333i	−1.92571	+	0.319658i
$523$	1.89615	−	3.28423i	0.0829128	−	0.143609i	−0.821587	−	0.570083i	$-0.806911\pi$
$523$	1.89615	−	3.28423i	0.0829128	−	0.143609i	0.904500	+	0.426474i	$0.140244\pi$
$524$	−7.53121	−	42.7116i	−0.329002	−	1.86587i
$525$	22.6832	−	3.23636i	0.989974	−	0.141246i
$526$	−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
$532$	55.8293	+	8.16888i	2.42051	+	0.354166i
$533$	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
$546$	−9.96045	+	29.5765i	−0.426268	+	1.26576i
$547$	−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
$553$	−6.79812	−	2.25147i	−0.289086	−	0.0957424i
$554$	−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
$560$	32.4742	−	89.4240i	1.37229	−	3.77885i
$561$	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	−0.905507	−	0.424330i	$-0.860510\pi$
$563$	−7.83923	+	9.34243i	−0.330384	+	0.393736i	0.575124	+	0.818067i	$0.304954\pi$
$564$	62.0892	+	22.9522i	2.61443	+	0.966461i
$565$	−24.0063	+	27.0066i	−1.00995	+	1.13618i
$566$	−83.2844			−3.50071
$567$	4.34971	+	23.4111i	0.182671	+	0.983174i
$568$			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
$574$	−61.3694	+	1.79527i	−2.56151	+	0.0749330i
$575$	−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	−0.720161	−	0.693807i	$-0.755932\pi$
$577$	5.78358	−	10.0175i	0.240774	−	0.417032i	0.960935	+	0.276775i	$0.0892656\pi$
$578$	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
$581$	−6.28773	+	18.9852i	−0.260859	+	0.787641i
$582$	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	0.687715	−	0.725980i	$-0.258614\pi$
$587$	−3.55320	−	4.23454i	−0.146656	−	0.174778i	−0.834372	+	0.551202i	$0.814169\pi$
$588$	56.8145	−	36.9856i	2.34299	−	1.52526i
$589$	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	$0.305553\pi$
$593$			39.8951i			1.63829i	−0.573584	+	0.819147i	$0.694447\pi$
$594$	57.4025	−	19.9193i	2.35525	−	0.817297i
$595$	−10.9772	−	18.9812i	−0.450020	−	0.778153i
$596$	−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	$-0.943034\pi$
$601$	−24.2324	−	28.8790i	−0.988459	−	1.17800i	−0.00443041	−	0.999990i	$-0.501410\pi$
$602$	7.07306	+	1.03492i	0.288277	+	0.0421803i
$603$	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	−0.533468	−	0.845820i	$-0.679112\pi$
$607$	−9.81667	+	3.57297i	−0.398446	+	0.145023i	0.135022	+	0.990843i	$0.456889\pi$
$608$	−31.9827	−	87.8717i	−1.29707	−	3.56367i
$609$	19.3207	+	15.4301i	0.782915	+	0.625260i
$610$	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
$616$	−73.8788	−	82.9909i	−2.97666	−	3.34380i
$617$	−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	−0.966573	−	0.256392i	$-0.917466\pi$
$619$	−1.52586	+	4.19228i	−0.0613296	+	0.168502i	0.905243	+	0.424894i	$0.139688\pi$
$620$	−19.7015	−	7.81391i	−0.791230	−	0.313814i
$621$	−36.7531	−	7.05272i	−1.47485	−	0.283016i
$622$	85.9771			3.44737
$623$	−8.79533	−	14.2544i	−0.352378	−	0.571091i
$624$	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
$630$	0.455375	−	48.8988i	0.0181426	−	1.94818i
$631$	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
$637$	15.8850	−	6.85801i	0.629387	−	0.271724i
$638$	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	$-0.877740\pi$
$643$	1.83202	−	10.3899i	0.0722477	−	0.409737i	0.999387	−	0.0350193i	$-0.0111493\pi$
$644$	21.5617	+	104.341i	0.849651	+	4.11162i
$645$	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	$0.0993847\pi$
$647$			15.6269i			0.614356i	−0.951652	+	0.307178i	$0.900615\pi$
$648$	69.3577	−	55.8642i	2.72463	−	2.19455i
$649$			26.8002i			1.05200i
$650$	−15.3169	−	30.4120i	−0.600778	−	1.19286i
$651$	−4.04596	−	6.63145i	−0.158574	−	0.259907i
$652$	−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
$658$	−18.4033	−	46.3029i	−0.717437	−	1.80507i
$659$	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	0.954226	−	0.299085i	$-0.0966816\pi$
$661$	0.796959	+	2.18963i	0.0309981	+	0.0851666i	−0.923228	+	0.384252i	$0.874459\pi$
$662$	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
$665$	−22.5644	+	0.0163749i	−0.875011	+	0.000634991i
$666$	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
$672$	−98.6323	−	53.8028i	−3.80483	−	2.07549i
$673$	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	$-0.648311\pi$
$677$	12.2072	−	33.5391i	0.469162	−	1.28901i	0.918419	−	0.395609i	$-0.129466\pi$
$678$	49.2729	+	59.3234i	1.89232	+	2.27830i
$679$	−4.02428	−	19.4742i	−0.154438	−	0.747353i
$680$	−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
$686$	−49.2955	−	13.1839i	−1.88211	−	0.503364i
$687$	−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	−0.249845	−	0.968286i	$-0.580380\pi$
$691$	−4.03371	+	0.711252i	−0.153450	+	0.0270573i	0.0963956	+	0.995343i	$0.469269\pi$
$692$	−0.531794	−	0.307031i	−0.0202158	−	0.0116716i
$693$	−29.4909	−	16.2795i	−1.12027	−	0.618408i
$694$	−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
$700$	−14.8637	+	72.4589i	−0.561796	+	2.73869i
$701$			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
$707$	10.0061	−	8.90748i	0.376318	−	0.335000i
$708$	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
$714$	−43.5736	+	17.0658i	−1.63070	+	0.638673i
$715$	−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	−0.535491	−	0.844541i	$-0.679873\pi$
$719$	12.4324	−	21.5335i	0.463649	−	0.803063i	0.999139	+	0.0414778i	$0.0132066\pi$
$720$	−95.4334	+	50.2968i	−3.55659	+	1.87445i
$721$	1.64885	−	11.2689i	0.0614063	−	0.419675i
$722$	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	−0.233976	−	0.972242i	$-0.575174\pi$
$727$	−27.9918	−	10.1882i	−1.03816	−	0.377858i	−0.804181	+	0.594384i	$0.797396\pi$
$728$	−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	0.861613	−	0.507566i	$-0.169455\pi$
$733$	13.8450	+	11.6173i	0.511375	+	0.429095i	−0.350237	+	0.936661i	$0.613899\pi$
$734$	−0.690229	+	3.91448i	−0.0254768	+	0.144486i
$735$	−20.3269	+	17.9393i	−0.749769	+	0.661700i
$736$	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
$742$	−40.9381	−	13.5583i	−1.50289	−	0.497742i
$743$	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
$749$	−54.7073	+	1.60038i	−1.99896	+	0.0584765i
$750$	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
$756$	−75.8834	−	12.2729i	−2.75985	−	0.446360i
$757$			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	$-0.588996\pi$
$761$	8.60956	−	48.8273i	0.312096	−	1.76999i	0.588058	−	0.808818i	$-0.299893\pi$
$762$	1.85233	−	10.2053i	0.0671029	−	0.369699i
$763$	−13.9433	+	0.407889i	−0.504782	+	0.0147666i
$764$	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	0.863473	−	0.504395i	$-0.168285\pi$
$769$	−3.38885	−	9.31078i	−0.122205	−	0.335755i	−0.985678	+	0.168640i	$0.946062\pi$
$770$	53.0263	+	44.4288i	1.91093	+	1.60110i
$771$	−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	−0.336270	−	0.941766i	$-0.609165\pi$
$773$	−36.6997	−	21.1886i	−1.32000	−	0.762101i	−0.983728	+	0.179664i	$0.942499\pi$
$774$	−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
$777$	−0.446611	+	0.393575i	−0.0160221	+	0.0141194i
$778$	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	−0.110955	−	0.993825i	$-0.535391\pi$
$787$	−31.1099	−	26.1043i	−1.10895	−	0.930519i	−0.997994	+	0.0633068i	$0.979835\pi$
$788$	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
$791$	6.18983	−	42.3037i	0.220085	−	1.50415i
$792$	−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	$-0.876834\pi$
$797$	−12.9643	−	35.6190i	−0.459218	−	1.26169i	0.466851	−	0.884336i	$-0.345388\pi$
$798$	−7.21114	+	47.6143i	−0.255272	+	1.68553i
$799$	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
$805$	−14.6021	−	40.0285i	−0.514656	−	1.41082i
$806$	−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	$0.0166980\pi$
$811$			2.98644i			0.104868i	−0.998624	+	0.0524341i	$0.983302\pi$
$812$	−67.9305	+	41.9148i	−2.38389	+	1.47092i
$813$	−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
$819$	−18.5611	−	6.35473i	−0.648579	−	0.222052i
$820$	−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
$826$	21.8411	−	40.5219i	0.759947	−	1.40994i
$827$	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	0.212447	−	0.977173i	$-0.431857\pi$
$829$	33.5410	−	19.3649i	1.16493	−	0.672571i	0.952480	+	0.304602i	$0.0985233\pi$
$830$	−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
$833$	23.1881	+	11.6365i	0.803422	+	0.403179i
$834$	−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	0.920288	−	0.391241i	$-0.127954\pi$
$839$	39.7924	+	14.4832i	1.37378	+	0.500017i	0.453496	+	0.891258i	$0.350176\pi$
$840$	95.1320	+	35.0885i	3.28237	+	1.21067i
$841$	−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
$847$	17.2394	−	6.85188i	0.592352	−	0.235433i
$848$	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	$0.0552519\pi$
$853$	3.46008	+	19.6231i	0.118471	+	0.671882i	−0.866502	+	0.499174i	$0.833637\pi$
$854$	4.56283	+	11.4801i	0.156137	+	0.392841i
$855$	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	0.612334	−	0.790599i	$-0.290231\pi$
$857$	−7.97979	−	9.50994i	−0.272584	−	0.324853i	−0.884919	+	0.465746i	$0.845786\pi$
$858$	−8.94039	+	49.2565i	−0.305220	+	1.68159i
$859$	−37.0788	−	6.53800i	−1.26511	−	0.223074i	−0.499465	−	0.866334i	$-0.666470\pi$
$859$	−37.0788	−	6.53800i	−1.26511	−	0.223074i	−0.765647	+	0.643260i	$0.777581\pi$
$860$	5.82494	+	10.7883i	0.198629	+	0.367878i
$861$	−0.934926	−	38.5842i	−0.0318622	−	1.31494i
$862$	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
$868$	24.5587	−	5.07497i	0.833578	−	0.172256i
$869$	−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
$875$	1.66488	−	29.5335i	0.0562833	−	0.998415i
$876$	−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	$-0.489303\pi$
$881$	26.1892	−	45.3610i	0.882336	−	1.52825i	0.848736	−	0.528816i	$-0.177364\pi$
$882$	31.3231	+	48.6486i	1.05471	+	1.63808i
$883$	−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	$0.523940\pi$
$887$	−31.0964	+	37.0593i	−1.04412	+	1.24433i	−0.968976	+	0.247155i	$0.920504\pi$
$888$	2.08829	+	0.771967i	0.0700784	+	0.0259055i
$889$	−4.89371	+	3.01954i	−0.164130	+	0.101272i
$890$	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
$896$	95.7869	−	85.2699i	3.20002	−	2.84867i
$897$	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
$903$	−0.672897	+	4.44306i	−0.0223926	+	0.147856i
$904$	−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
$910$	34.9069	+	20.1197i	1.15715	+	0.666963i
$911$	−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
$924$	81.5859	−	71.8974i	2.68398	−	2.36525i
$925$	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	$0.179483\pi$
$929$	7.12506	+	40.4082i	0.233766	+	1.32575i	−0.611432	+	0.791297i	$0.709406\pi$
$930$	6.75342	−	16.7814i	0.221453	−	0.550282i
$931$	22.3018	−	14.6781i	0.730911	−	0.481055i
$932$	−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	0.877225	−	0.480079i	$-0.159392\pi$
$937$	0.699518	+	1.21160i	0.0228522	+	0.0395812i	−0.854373	+	0.519660i	$0.826059\pi$
$938$	−1.83590	−	62.7584i	−0.0599442	−	2.04914i
$939$	−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	0.899738	−	0.436430i	$-0.143757\pi$
$941$	19.2084	+	16.1178i	0.626177	+	0.525425i	−0.273561	+	0.961855i	$0.588202\pi$
$942$	−64.4775	−	77.6292i	−2.10079	−	2.52930i
$943$	57.0003	+	20.7464i	1.85618	+	0.675596i
$944$	−101.550			−3.30517
$945$	30.7377	+	0.440542i	0.999897	+	0.0143308i
$946$	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
$952$	−2.83733	−	96.9915i	−0.0919585	−	3.14351i
$953$	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
$959$	−31.9515	−	10.5820i	−1.03177	−	0.341712i
$960$	−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
$966$	−89.1457	+	17.9556i	−2.86821	+	0.577711i
$967$	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	$-0.561593\pi$
$971$	−11.9841			−0.384590			−0.192295	+	0.981337i	$0.561593\pi$
$972$	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
$980$	−32.3846	−	81.3077i	−1.03449	−	2.59728i
$981$	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	0.510524	−	0.859864i	$-0.329451\pi$
$983$	40.2680	−	7.10034i	1.28435	−	0.226466i	0.773826	+	0.633398i	$0.218340\pi$
$984$	−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
$987$	29.1653	−	11.4228i	0.928343	−	0.363590i
$988$	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
$994$	43.2024	+	48.5309i	1.37030	+	1.53931i
$995$	−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	0.621372	−	0.783515i	$-0.286575\pi$
$997$	18.7474	+	6.82351i	0.593737	+	0.216103i	−0.0276353	+	0.999618i	$0.508798\pi$
$998$	−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.104.2	yes	816
5.4	even	2	inner	945.2.cs.b.104.135	yes	816
7.6	odd	2	inner	945.2.cs.b.104.1	✓	816
27.20	odd	18	inner	945.2.cs.b.209.136	yes	816
35.34	odd	2	inner	945.2.cs.b.104.136	yes	816
135.74	odd	18	inner	945.2.cs.b.209.1	yes	816
189.20	even	18	inner	945.2.cs.b.209.135	yes	816
945.209	even	18	inner	945.2.cs.b.209.2	yes	816

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

\(f(q)\)	\(=\)	\(q+(-2.58909 - 0.942353i) q^{2} +(0.600558 - 1.62460i) q^{3} +(4.28329 + 3.59410i) q^{4} +(-1.90382 - 1.17280i) q^{5} +(-3.08585 + 3.64031i) q^{6} +(2.64462 - 0.0773642i) q^{7} +(-4.94766 - 8.56959i) q^{8} +(-2.27866 - 1.95133i) q^{9} +O(q^{10})\)	\(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} +(2.64462 - 0.0773642i) 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} +(-6.92007 - 2.29186i) 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} +(1.46256 - 4.34292i) 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} +(-5.12562 - 2.95432i) 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} +(-7.87926 + 9.86596i) 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} +(6.98803 - 0.409198i) 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} +(-13.7476 - 22.2805i) 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} +(-6.17716 - 4.98425i) 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} +(10.4867 + 12.4792i) 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} +(10.9963 - 2.27234i) 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} +(21.8735 - 13.3454i) 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} +(6.07720 - 2.41541i) 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} +(-18.4783 - 5.52574i) 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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