LMFDB - Embedded newform 990.2.o.a.329.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.7
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.46936 + 0.917053i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.434042 + 2.19354i) q^{5} +(0.813975 - 1.52887i) q^{6} +(0.730956 + 1.26605i) q^{7} +1.00000i q^{8} +(1.31803 - 2.69496i) q^{9} +(-1.47266 - 1.68264i) q^{10} +(0.272953 - 3.30537i) q^{11} +(0.0595124 + 1.73103i) q^{12} +(0.570213 - 0.987638i) q^{13} +(-1.26605 - 0.730956i) q^{14} +(-2.64935 - 2.82505i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.35616i q^{17} +(0.206035 + 2.99292i) q^{18} +0.954923i q^{19} +(2.11668 + 0.720878i) q^{20} +(-2.23507 - 1.18996i) q^{21} +(1.41630 + 2.99901i) q^{22} +(4.32940 - 7.49874i) q^{23} +(-0.917053 - 1.46936i) q^{24} +(-4.62322 + 1.90417i) q^{25} +1.14043i q^{26} +(0.534769 + 5.16856i) q^{27} +1.46191 q^{28} +(-3.18664 - 5.51942i) q^{29} +(3.70693 + 1.12189i) q^{30} +(-3.59915 + 6.23391i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.63014 + 5.10709i) q^{33} +(3.67808 + 6.37062i) q^{34} +(-2.45987 + 2.15290i) q^{35} +(-1.67489 - 2.48892i) q^{36} +0.0593138i q^{37} +(-0.477461 - 0.826988i) q^{38} +(0.0678695 + 1.97411i) q^{39} +(-2.19354 + 0.434042i) q^{40} +(2.56352 - 4.44015i) q^{41} +(2.53061 - 0.0870019i) q^{42} +(-6.04274 - 10.4663i) q^{43} +(-2.72606 - 1.88907i) q^{44} +(6.48357 + 1.72142i) q^{45} +8.65879i q^{46} +(-0.0693378 - 0.120097i) q^{47} +(1.52887 + 0.813975i) q^{48} +(2.43141 - 4.21132i) q^{49} +(3.05174 - 3.96067i) q^{50} +(6.74599 + 10.8088i) q^{51} +(-0.570213 - 0.987638i) q^{52} -5.83161 q^{53} +(-3.04740 - 4.20872i) q^{54} +(7.36894 - 0.835938i) q^{55} +(-1.26605 + 0.730956i) q^{56} +(-0.875715 - 1.40312i) q^{57} +(5.51942 + 3.18664i) q^{58} +(9.09738 + 5.25237i) q^{59} +(-3.77124 + 0.881881i) q^{60} +(8.08229 - 4.66631i) q^{61} -7.19830i q^{62} +(4.37538 - 0.301206i) q^{63} -1.00000 q^{64} +(2.41392 + 0.822107i) q^{65} +(-4.83131 - 3.10780i) q^{66} +(10.2925 + 5.94237i) q^{67} +(-6.37062 - 3.67808i) q^{68} +(0.515306 + 14.9886i) q^{69} +(1.05386 - 3.09440i) q^{70} +2.67757i q^{71} +(2.69496 + 1.31803i) q^{72} +1.85282 q^{73} +(-0.0296569 - 0.0513673i) q^{74} +(5.04693 - 7.03765i) q^{75} +(0.826988 + 0.477461i) q^{76} +(4.38429 - 2.07051i) q^{77} +(-1.04583 - 1.67569i) q^{78} +(-4.77518 + 2.75695i) q^{79} +(1.68264 - 1.47266i) q^{80} +(-5.52561 - 7.10406i) q^{81} +5.12704i q^{82} +(0.681456 - 0.393439i) q^{83} +(-2.14807 + 1.34065i) q^{84} +(16.1360 - 3.19288i) q^{85} +(10.4663 + 6.04274i) q^{86} +(9.74392 + 5.18769i) q^{87} +(3.30537 + 0.272953i) q^{88} -12.2219i q^{89} +(-6.47565 + 1.75100i) q^{90} +1.66720 q^{91} +(-4.32940 - 7.49874i) q^{92} +(-0.428388 - 12.4605i) q^{93} +(0.120097 + 0.0693378i) q^{94} +(-2.09466 + 0.414476i) q^{95} +(-1.73103 + 0.0595124i) q^{96} +(2.15852 - 1.24622i) q^{97} +4.86281i q^{98} +(-8.54809 - 5.09217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.46936	+	0.917053i	−0.848334	+	0.529461i
$3$	−1.46936	+	0.917053i	−0.848334	+	0.529461i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.434042	+	2.19354i	0.194109	+	0.980980i
$5$	0.434042	+	2.19354i	0.194109	+	0.980980i
$6$	0.813975	−	1.52887i	0.332304	−	0.624159i
$7$	0.730956	+	1.26605i	0.276275	+	0.478523i	0.970456	−	0.241278i	$-0.0775665\pi$
$7$	0.730956	+	1.26605i	0.276275	+	0.478523i	−0.694181	+	0.719801i	$0.744233\pi$
$8$			1.00000i			0.353553i
$9$	1.31803	−	2.69496i	0.439342	−	0.898320i
$10$	−1.47266	−	1.68264i	−0.465696	−	0.532097i
$11$	0.272953	−	3.30537i	0.0822983	−	0.996608i
$11$	0.272953	−	3.30537i	0.0822983	−	0.996608i
$12$	0.0595124	+	1.73103i	0.0171798	+	0.499705i
$13$	0.570213	−	0.987638i	0.158149	−	0.273921i	−0.776052	−	0.630668i	$-0.782781\pi$
$13$	0.570213	−	0.987638i	0.158149	−	0.273921i	0.934201	+	0.356747i	$0.116114\pi$
$14$	−1.26605	−	0.730956i	−0.338367	−	0.195356i
$15$	−2.64935	−	2.82505i	−0.684060	−	0.729426i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	7.35616i		−	1.78413i	−0.451906	−	0.892065i	$-0.649256\pi$
$17$		−	7.35616i		−	1.78413i	0.451906	−	0.892065i	$-0.350744\pi$
$18$	0.206035	+	2.99292i	0.0485630	+	0.705437i
$19$			0.954923i			0.219074i	0.993983	+	0.109537i	$0.0349369\pi$
$19$			0.954923i			0.219074i	−0.993983	+	0.109537i	$0.965063\pi$
$20$	2.11668	+	0.720878i	0.473304	+	0.161193i
$21$	−2.23507	−	1.18996i	−0.487733	−	0.259670i
$22$	1.41630	+	2.99901i	0.301957	+	0.639392i
$23$	4.32940	−	7.49874i	0.902742	−	1.56359i	0.0788216	−	0.996889i	$-0.474884\pi$
$23$	4.32940	−	7.49874i	0.902742	−	1.56359i	0.823920	−	0.566706i	$-0.191782\pi$
$24$	−0.917053	−	1.46936i	−0.187193	−	0.299931i
$25$	−4.62322	+	1.90417i	−0.924643	+	0.380835i
$26$			1.14043i			0.223656i
$27$	0.534769	+	5.16856i	0.102916	+	0.994690i
$28$	1.46191			0.276275
$29$	−3.18664	−	5.51942i	−0.591744	−	1.02493i	−0.993998	−	0.109402i	$-0.965106\pi$
$29$	−3.18664	−	5.51942i	−0.591744	−	1.02493i	0.402254	−	0.915528i	$-0.368227\pi$
$30$	3.70693	+	1.12189i	0.676790	+	0.204828i
$31$	−3.59915	+	6.23391i	−0.646426	+	1.11964i	0.337544	+	0.941310i	$0.390404\pi$
$31$	−3.59915	+	6.23391i	−0.646426	+	1.11964i	−0.983970	+	0.178333i	$0.942930\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.63014	+	5.10709i	0.457848	+	0.889030i
$34$	3.67808	+	6.37062i	0.630786	+	1.09255i
$35$	−2.45987	+	2.15290i	−0.415794	+	0.363906i
$36$	−1.67489	−	2.48892i	−0.279148	−	0.414821i
$37$			0.0593138i			0.00975113i	0.999988	+	0.00487556i	$0.00155195\pi$
$37$			0.0593138i			0.00975113i	−0.999988	+	0.00487556i	$0.998448\pi$
$38$	−0.477461	−	0.826988i	−0.0774545	−	0.134155i
$39$	0.0678695	+	1.97411i	0.0108678	+	0.316110i
$40$	−2.19354	+	0.434042i	−0.346829	+	0.0686280i
$41$	2.56352	−	4.44015i	0.400355	−	0.693435i	−0.593414	−	0.804898i	$-0.702220\pi$
$41$	2.56352	−	4.44015i	0.400355	−	0.693435i	0.993769	+	0.111463i	$0.0355535\pi$
$42$	2.53061	−	0.0870019i	0.390482	−	0.0134247i
$43$	−6.04274	−	10.4663i	−0.921509	−	1.59610i	−0.797081	−	0.603872i	$-0.793624\pi$
$43$	−6.04274	−	10.4663i	−0.921509	−	1.59610i	−0.124428	−	0.992229i	$-0.539709\pi$
$44$	−2.72606	−	1.88907i	−0.410969	−	0.284788i
$45$	6.48357	+	1.72142i	0.966514	+	0.256614i
$46$			8.65879i			1.27667i
$47$	−0.0693378	−	0.120097i	−0.0101140	−	0.0175179i	0.860924	−	0.508733i	$-0.169886\pi$
$47$	−0.0693378	−	0.120097i	−0.0101140	−	0.0175179i	−0.871038	+	0.491215i	$0.836553\pi$
$48$	1.52887	+	0.813975i	0.220673	+	0.117487i
$49$	2.43141	−	4.21132i	0.347344	−	0.601617i
$50$	3.05174	−	3.96067i	0.431581	−	0.560123i
$51$	6.74599	+	10.8088i	0.944628	+	1.51354i
$52$	−0.570213	−	0.987638i	−0.0790743	−	0.136961i
$53$	−5.83161			−0.801033			−0.400516	−	0.916290i	$-0.631169\pi$
$53$	−5.83161			−0.801033			−0.400516	+	0.916290i	$0.631169\pi$
$54$	−3.04740	−	4.20872i	−0.414699	−	0.572734i
$55$	7.36894	−	0.835938i	0.993627	−	0.112718i
$56$	−1.26605	+	0.730956i	−0.169183	+	0.0976781i
$57$	−0.875715	−	1.40312i	−0.115991	−	0.185848i
$58$	5.51942	+	3.18664i	0.724735	+	0.418426i
$59$	9.09738	+	5.25237i	1.18438	+	0.683801i	0.957023	−	0.290011i	$-0.0936591\pi$
$59$	9.09738	+	5.25237i	1.18438	+	0.683801i	0.227354	+	0.973812i	$0.426992\pi$
$60$	−3.77124	+	0.881881i	−0.486866	+	0.113850i
$61$	8.08229	−	4.66631i	1.03483	−	0.597460i	0.116466	−	0.993195i	$-0.462843\pi$
$61$	8.08229	−	4.66631i	1.03483	−	0.597460i	0.918365	+	0.395734i	$0.129510\pi$
$62$		−	7.19830i		−	0.914184i
$63$	4.37538	−	0.301206i	0.551246	−	0.0379483i
$64$	−1.00000			−0.125000
$65$	2.41392	+	0.822107i	0.299410	+	0.101970i
$66$	−4.83131	−	3.10780i	−0.594693	−	0.382544i
$67$	10.2925	+	5.94237i	1.25743	+	0.725976i	0.972574	−	0.232595i	$-0.0747217\pi$
$67$	10.2925	+	5.94237i	1.25743	+	0.725976i	0.284854	+	0.958571i	$0.408055\pi$
$68$	−6.37062	−	3.67808i	−0.772551	−	0.446033i
$69$	0.515306	+	14.9886i	0.0620355	+	1.80442i
$70$	1.05386	−	3.09440i	0.125960	−	0.369851i
$71$			2.67757i			0.317770i	0.987297	+	0.158885i	$0.0507898\pi$
$71$			2.67757i			0.317770i	−0.987297	+	0.158885i	$0.949210\pi$
$72$	2.69496	+	1.31803i	0.317604	+	0.155331i
$73$	1.85282			0.216856			0.108428	−	0.994104i	$-0.465418\pi$
$73$	1.85282			0.216856			0.108428	+	0.994104i	$0.465418\pi$
$74$	−0.0296569	−	0.0513673i	−0.00344754	−	0.00597132i
$75$	5.04693	−	7.03765i	0.582769	−	0.812638i
$76$	0.826988	+	0.477461i	0.0948620	+	0.0547686i
$77$	4.38429	−	2.07051i	0.499637	−	0.235957i
$78$	−1.04583	−	1.67569i	−0.118417	−	0.189735i
$79$	−4.77518	+	2.75695i	−0.537250	+	0.310181i	−0.743964	−	0.668220i	$-0.767056\pi$
$79$	−4.77518	+	2.75695i	−0.537250	+	0.310181i	0.206714	+	0.978401i	$0.433723\pi$
$80$	1.68264	−	1.47266i	0.188125	−	0.164648i
$81$	−5.52561	−	7.10406i	−0.613957	−	0.789339i
$82$			5.12704i			0.566187i
$83$	0.681456	−	0.393439i	0.0747995	−	0.0431855i	−0.462134	−	0.886810i	$-0.652916\pi$
$83$	0.681456	−	0.393439i	0.0747995	−	0.0431855i	0.536933	+	0.843625i	$0.319583\pi$
$84$	−2.14807	+	1.34065i	−0.234374	+	0.146277i
$85$	16.1360	−	3.19288i	1.75020	−	0.346317i
$86$	10.4663	+	6.04274i	1.12861	+	0.651605i
$87$	9.74392	+	5.18769i	1.04466	+	0.556178i
$88$	3.30537	+	0.272953i	0.352354	+	0.0290969i
$89$		−	12.2219i		−	1.29552i	−0.761845	−	0.647759i	$-0.775706\pi$
$89$		−	12.2219i		−	1.29552i	0.761845	−	0.647759i	$-0.224294\pi$
$90$	−6.47565	+	1.75100i	−0.682593	+	0.184571i
$91$	1.66720			0.174770
$92$	−4.32940	−	7.49874i	−0.451371	−	0.781797i
$93$	−0.428388	−	12.4605i	−0.0444218	−	1.29209i
$94$	0.120097	+	0.0693378i	0.0123870	+	0.00715165i
$95$	−2.09466	+	0.414476i	−0.214908	+	0.0425244i
$96$	−1.73103	+	0.0595124i	−0.176672	+	0.00607396i
$97$	2.15852	−	1.24622i	0.219164	−	0.126535i	−0.386399	−	0.922332i	$-0.626281\pi$
$97$	2.15852	−	1.24622i	0.219164	−	0.126535i	0.605563	+	0.795797i	$0.292948\pi$
$98$			4.86281i			0.491218i
$99$	−8.54809	−	5.09217i	−0.859115	−	0.511782i
$100$	−0.662545	+	4.95591i	−0.0662545	+	0.495591i
$101$	0.746276	+	1.29259i	0.0742572	+	0.128617i	0.900763	−	0.434311i	$-0.143008\pi$
$101$	0.746276	+	1.29259i	0.0742572	+	0.128617i	−0.826506	+	0.562928i	$0.809675\pi$
$102$	−11.2466	−	5.98773i	−1.11358	−	0.592873i
$103$	−2.01805	−	1.16512i	−0.198844	−	0.114803i	0.397272	−	0.917701i	$-0.369957\pi$
$103$	−2.01805	−	1.16512i	−0.198844	−	0.114803i	−0.596116	+	0.802898i	$0.703290\pi$
$104$	0.987638	+	0.570213i	0.0968458	+	0.0559140i
$105$	1.64011	−	5.41921i	0.160058	−	0.528861i
$106$	5.05032	−	2.91580i	0.490530	−	0.283208i
$107$			15.7119i			1.51893i	0.650549	+	0.759464i	$0.274539\pi$
$107$			15.7119i			1.51893i	−0.650549	+	0.759464i	$0.725461\pi$
$108$	4.74349	+	2.12116i	0.456442	+	0.204108i
$109$			14.1259i			1.35301i	0.736437	+	0.676506i	$0.236507\pi$
$109$			14.1259i			1.35301i	−0.736437	+	0.676506i	$0.763493\pi$
$110$	−5.96372	+	4.40841i	−0.568618	+	0.420326i
$111$	−0.0543939	−	0.0871532i	−0.00516284	−	0.00827222i
$112$	0.730956	−	1.26605i	0.0690688	−	0.119631i
$113$	2.02683	−	3.51058i	0.190668	−	0.330247i	−0.754804	−	0.655951i	$-0.772268\pi$
$113$	2.02683	−	3.51058i	0.190668	−	0.330247i	0.945472	+	0.325704i	$0.105601\pi$
$114$	1.45995	+	0.777283i	0.136737	+	0.0727992i
$115$	18.3279	+	6.24193i	1.70909	+	0.582063i
$116$	−6.37328			−0.591744
$117$	−1.91009	−	2.83843i	−0.176588	−	0.262413i
$118$	−10.5047			−0.967040
$119$	9.31329	−	5.37703i	0.853747	−	0.492911i
$120$	2.82505	−	2.64935i	0.257891	−	0.241852i
$121$	−10.8510	−	1.80442i	−0.986454	−	0.164038i
$122$	−4.66631	+	8.08229i	−0.422468	+	0.731736i
$123$	0.305123	+	8.87506i	0.0275120	+	0.800237i
$124$	3.59915	+	6.23391i	0.323213	+	0.559821i
$125$	−6.18355	−	9.31471i	−0.553073	−	0.833133i
$126$	−3.63859	+	2.44854i	−0.324151	+	0.218133i
$127$	0.0141620			0.00125668			0.000628338	−	1.00000i	$-0.499800\pi$
$127$	0.0141620			0.00125668			0.000628338		1.00000i	$0.499800\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	18.4771	+	9.83727i	1.62682	+	0.866124i
$130$	−2.50157	+	0.494992i	−0.219402	+	0.0434137i
$131$	0.622860	−	1.07883i	0.0544195	−	0.0942574i	−0.837532	−	0.546388i	$-0.816002\pi$
$131$	0.622860	−	1.07883i	0.0544195	−	0.0942574i	0.891952	+	0.452130i	$0.149336\pi$
$132$	5.73794	+	0.275778i	0.499424	+	0.0240034i
$133$	−1.20898	+	0.698006i	−0.104832	+	0.0605248i
$134$	−11.8847			−1.02669
$135$	−11.1053	+	3.41641i	−0.955794	+	0.294037i
$136$	7.35616			0.630786
$137$	−5.28642	−	9.15634i	−0.451649	−	0.782279i	0.546840	−	0.837237i	$-0.315831\pi$
$137$	−5.28642	−	9.15634i	−0.451649	−	0.782279i	−0.998489	+	0.0549582i	$0.982497\pi$
$138$	−7.94058	−	12.7229i	−0.675947	−	1.08304i
$139$	2.90692	+	1.67831i	0.246562	+	0.142353i	0.618189	−	0.786029i	$-0.287867\pi$
$139$	2.90692	+	1.67831i	0.246562	+	0.142353i	−0.371627	+	0.928382i	$0.621200\pi$
$140$	0.634531	+	3.20676i	0.0536276	+	0.271021i
$141$	0.212017	+	0.112878i	0.0178551	+	0.00950608i
$142$	−1.33879	−	2.31885i	−0.112349	−	0.194593i
$143$	−3.10887	−	2.15435i	−0.259977	−	0.180155i
$144$	−2.99292	+	0.206035i	−0.249410	+	0.0171696i
$145$	10.7239	−	9.38567i	0.890573	−	0.779438i
$146$	−1.60459	+	0.926408i	−0.132797	+	0.0766701i
$147$	0.289398	+	8.41767i	0.0238691	+	0.694278i
$148$	0.0513673	+	0.0296569i	0.00422236	+	0.00243778i
$149$	3.88265	−	6.72495i	0.318079	−	0.550929i	−0.662008	−	0.749497i	$-0.730296\pi$
$149$	3.88265	−	6.72495i	0.318079	−	0.550929i	0.980087	+	0.198568i	$0.0636289\pi$
$150$	−0.851945	+	8.61825i	−0.0695610	+	0.703677i
$151$	−8.89030	+	5.13282i	−0.723482	+	0.417703i	−0.816033	−	0.578005i	$-0.803831\pi$
$151$	−8.89030	+	5.13282i	−0.723482	+	0.417703i	0.0925506	+	0.995708i	$0.470498\pi$
$152$	−0.954923			−0.0774545
$153$	−19.8246	−	9.69561i	−1.60272	−	0.783844i
$154$	−2.76165	+	3.98526i	−0.222540	+	0.321141i
$155$	−15.2365	−	5.18909i	−1.22382	−	0.416798i
$156$	1.74356	+	0.928278i	0.139597	+	0.0743217i
$157$	11.7982	+	6.81172i	0.941602	+	0.543634i	0.890462	−	0.455057i	$-0.150381\pi$
$157$	11.7982	+	6.81172i	0.941602	+	0.543634i	0.0511399	+	0.998691i	$0.483715\pi$
$158$	2.75695	−	4.77518i	0.219331	−	0.379893i
$159$	8.56872	−	5.34789i	0.679543	−	0.424116i
$160$	−0.720878	+	2.11668i	−0.0569904	+	0.167338i
$161$	12.6584			0.997621
$162$	8.33735	+	3.38949i	0.655044	+	0.266303i
$163$		−	23.2225i		−	1.81893i	−0.415782	−	0.909465i	$-0.636492\pi$
$163$		−	23.2225i		−	1.81893i	0.415782	−	0.909465i	$-0.363508\pi$
$164$	−2.56352	−	4.44015i	−0.200177	−	0.346717i
$165$	−10.0610	+	7.98600i	−0.783248	+	0.621709i
$166$	−0.393439	+	0.681456i	−0.0305368	+	0.0528913i
$167$	14.1264	+	8.15590i	1.09314	+	0.631122i	0.934410	−	0.356200i	$-0.115928\pi$
$167$	14.1264	+	8.15590i	1.09314	+	0.631122i	0.158726	+	0.987323i	$0.449261\pi$
$168$	1.18996	−	2.23507i	0.0918073	−	0.172440i
$169$	5.84971	+	10.1320i	0.449978	+	0.779385i
$170$	−12.3778	+	10.8331i	−0.949331	+	0.830863i
$171$	2.57348	+	1.25861i	0.196799	+	0.0962486i
$172$	−12.0855			−0.921509
$173$	−19.9676	+	11.5283i	−1.51811	+	0.876482i	−0.518339	+	0.855175i	$0.673449\pi$
$173$	−19.9676	+	11.5283i	−1.51811	+	0.876482i	−0.999773	+	0.0213067i	$0.993217\pi$
$174$	−11.0323	+	0.379289i	−0.836358	+	0.0287538i
$175$	−5.79015	−	4.46137i	−0.437694	−	0.337248i
$176$	−2.99901	+	1.41630i	−0.226059	+	0.106758i
$177$	−18.1840	+	0.625163i	−1.36679	+	0.0469901i
$178$	6.11095	+	10.5845i	0.458035	+	0.793339i
$179$		−	0.268284i		−	0.0200525i	−0.999950	−	0.0100262i	$-0.996808\pi$
$179$		−	0.268284i		−	0.0200525i	0.999950	−	0.0100262i	$-0.00319150\pi$
$180$	4.73258	−	4.75423i	0.352745	−	0.354360i
$181$	−12.7559			−0.948138			−0.474069	−	0.880488i	$-0.657215\pi$
$181$	−12.7559			−0.948138			−0.474069	+	0.880488i	$0.657215\pi$
$182$	−1.44384	+	0.833601i	−0.107024	+	0.0617906i
$183$	−7.59652	+	14.2684i	−0.561551	+	1.05475i
$184$	7.49874	+	4.32940i	0.552814	+	0.319167i
$185$	−0.130107	+	0.0257447i	−0.00956566	+	0.00189279i
$186$	6.60122	+	10.5769i	0.484025	+	0.775534i
$187$	−24.3149	−	2.00788i	−1.77808	−	0.146831i
$188$	−0.138676			−0.0101140
$189$	−6.15278	+	4.45504i	−0.447549	+	0.324056i
$190$	1.60679	−	1.40628i	0.116569	−	0.102022i
$191$	−5.52490	+	3.18981i	−0.399768	+	0.230806i	−0.686384	−	0.727239i	$-0.740803\pi$
$191$	−5.52490	+	3.18981i	−0.399768	+	0.230806i	0.286616	+	0.958046i	$0.407470\pi$
$192$	1.46936	−	0.917053i	0.106042	−	0.0661826i
$193$	13.2188	−	22.8957i	0.951513	−	1.64807i	0.209359	−	0.977839i	$-0.432862\pi$
$193$	13.2188	−	22.8957i	0.951513	−	1.64807i	0.742154	−	0.670229i	$-0.233804\pi$
$194$	−1.24622	+	2.15852i	−0.0894735	+	0.154973i
$195$	−4.30082	+	1.00572i	−0.307988	+	0.0720211i
$196$	−2.43141	−	4.21132i	−0.173672	−	0.300809i
$197$			10.1674i			0.724399i	0.932101	+	0.362199i	$0.117974\pi$
$197$			10.1674i			0.724399i	−0.932101	+	0.362199i	$0.882026\pi$
$198$	9.94895	+	0.135901i	0.707041	+	0.00965804i
$199$	−21.5699			−1.52905			−0.764524	−	0.644596i	$-0.777026\pi$
$199$	−21.5699			−1.52905			−0.764524	+	0.644596i	$0.777026\pi$
$200$	−1.90417	−	4.62322i	−0.134645	−	0.326911i
$201$	−20.5728	+	0.707290i	−1.45109	+	0.0498884i
$202$	−1.29259	−	0.746276i	−0.0909462	−	0.0525078i
$203$	4.65858	−	8.06890i	0.326969	−	0.566326i
$204$	12.7337	−	0.437783i	0.891539	−	0.0306509i
$205$	10.8523	+	3.69597i	0.757958	+	0.258138i
$206$	2.33024			0.162356
$207$	−14.5025	−	21.5511i	−1.00800	−	1.49790i
$208$	−1.14043			−0.0790743
$209$	3.15638	+	0.260649i	0.218331	+	0.0180295i
$210$	1.28923	+	5.51323i	0.0889655	+	0.380449i
$211$	0.0962850	+	0.0555901i	0.00662853	+	0.00382698i	0.503311	−	0.864106i	$-0.332115\pi$
$211$	0.0962850	+	0.0555901i	0.00662853	+	0.00382698i	−0.496682	+	0.867933i	$0.665448\pi$
$212$	−2.91580	+	5.05032i	−0.200258	+	0.346857i
$213$	−2.45548	−	3.93431i	−0.168247	−	0.269575i
$214$	−7.85596	−	13.6069i	−0.537022	−	0.930150i
$215$	20.3355	−	17.7978i	1.38687	−	1.21380i
$216$	−5.16856	+	0.534769i	−0.351676	+	0.0363864i
$217$	−10.5233			−0.714366
$218$	−7.06293	−	12.2333i	−0.478362	−	0.828547i
$219$	−2.72245	+	1.69913i	−0.183966	+	0.114817i
$220$	2.96052	−	6.79965i	0.199598	−	0.458433i
$221$	−7.26522	−	4.19458i	−0.488712	−	0.282158i
$222$	0.0906831	+	0.0482799i	0.00608625	+	0.00324034i
$223$	9.25457	−	5.34313i	0.619732	−	0.357802i	−0.157033	−	0.987593i	$-0.550193\pi$
$223$	9.25457	−	5.34313i	0.619732	−	0.357802i	0.776765	+	0.629791i	$0.216859\pi$
$224$			1.46191i			0.0976781i
$225$	−0.961849	+	14.9691i	−0.0641232	+	0.997942i
$226$			4.05366i			0.269646i
$227$	−10.0736	+	5.81600i	−0.668609	+	0.386022i	−0.795549	−	0.605889i	$-0.792818\pi$
$227$	−10.0736	+	5.81600i	−0.668609	+	0.386022i	0.126940	+	0.991910i	$0.459484\pi$
$228$	−1.65300	+	0.0568298i	−0.109472	+	0.00376364i
$229$	−6.26887	+	10.8580i	−0.414259	+	0.717517i	−0.995350	−	0.0963211i	$-0.969292\pi$
$229$	−6.26887	+	10.8580i	−0.414259	+	0.717517i	0.581092	+	0.813838i	$0.302626\pi$
$230$	−18.9934	+	3.75828i	−1.25239	+	0.247814i
$231$	−4.54333	+	7.06295i	−0.298929	+	0.464708i
$232$	5.51942	−	3.18664i	0.362368	−	0.209213i
$233$		−	20.8890i		−	1.36848i	−0.729255	−	0.684242i	$-0.760133\pi$
$233$		−	20.8890i		−	1.36848i	0.729255	−	0.684242i	$-0.239867\pi$
$234$	3.07340	+	1.50311i	0.200915	+	0.0982615i
$235$	0.233341	−	0.204222i	0.0152215	−	0.0133220i
$236$	9.09738	−	5.25237i	0.592189	−	0.341900i
$237$	4.48818	−	8.43005i	0.291539	−	0.547590i
$238$	−5.37703	+	9.31329i	−0.348541	+	0.603691i
$239$	−11.2009	+	19.4006i	−0.724529	+	1.25492i	0.234639	+	0.972083i	$0.424609\pi$
$239$	−11.2009	+	19.4006i	−0.724529	+	1.25492i	−0.959168	+	0.282838i	$0.908724\pi$
$240$	−1.12189	+	3.70693i	−0.0724177	+	0.239282i
$241$	21.7023	−	12.5298i	1.39797	−	0.807117i	0.403787	−	0.914853i	$-0.367694\pi$
$241$	21.7023	−	12.5298i	1.39797	−	0.807117i	0.994179	+	0.107736i	$0.0343602\pi$
$242$	10.2994	−	3.86282i	0.662074	−	0.248312i
$243$	14.6339	+	5.37112i	0.938765	+	0.344557i
$244$		−	9.33263i		−	0.597460i
$245$	10.2930	+	3.50549i	0.657597	+	0.223958i
$246$	−4.70177	−	7.53346i	−0.299774	−	0.480316i
$247$	0.943118	+	0.544509i	0.0600092	+	0.0346463i
$248$	−6.23391	−	3.59915i	−0.395853	−	0.228546i
$249$	−0.640499	+	1.20303i	−0.0405900	+	0.0762392i
$250$	10.0125	+	4.97500i	0.633244	+	0.314647i
$251$		−	18.9960i		−	1.19902i	−0.800368	−	0.599510i	$-0.795362\pi$
$251$		−	18.9960i		−	1.19902i	0.800368	−	0.599510i	$-0.204638\pi$
$252$	1.92684	−	3.93979i	0.121379	−	0.248184i
$253$	−23.6044	−	16.3571i	−1.48400	−	1.02836i
$254$	−0.0122647	+	0.00708101i	−0.000769554	+	0.000444302i
$255$	−20.7815	+	19.4891i	−1.30139	+	1.22045i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.35849	−	16.2094i	0.583767	−	1.01111i	−0.411261	−	0.911518i	$-0.634912\pi$
$257$	9.35849	−	16.2094i	0.583767	−	1.01111i	0.995028	−	0.0995962i	$-0.0317551\pi$
$258$	−20.9203	+	0.719236i	−1.30244	+	0.0447777i
$259$	−0.0750944	+	0.0433558i	−0.00466614	+	0.00269400i
$260$	1.91892	−	1.67946i	0.119007	−	0.104156i
$261$	−19.0747	+	1.31312i	−1.18069	+	0.0812801i
$262$			1.24572i			0.0769609i
$263$	−14.5206	+	8.38350i	−0.895382	+	0.516949i	−0.875699	−	0.482857i	$-0.839599\pi$
$263$	−14.5206	+	8.38350i	−0.895382	+	0.516949i	−0.0196827	+	0.999806i	$0.506266\pi$
$264$	−5.10709	+	2.63014i	−0.314320	+	0.161874i
$265$	−2.53116	−	12.7918i	−0.155488	−	0.785797i
$266$	0.698006	−	1.20898i	0.0427975	−	0.0741275i
$267$	11.2081	+	17.9583i	0.685926	+	1.09903i
$268$	10.2925	−	5.94237i	0.628714	−	0.362988i
$269$		−	5.34056i		−	0.325620i	−0.986657	−	0.162810i	$-0.947944\pi$
$269$		−	5.34056i		−	0.325620i	0.986657	−	0.162810i	$-0.0520557\pi$
$270$	7.90929	−	8.51136i	0.481344	−	0.517985i
$271$			1.48944i			0.0904768i	0.998976	+	0.0452384i	$0.0144048\pi$
$271$			1.48944i			0.0904768i	−0.998976	+	0.0452384i	$0.985595\pi$
$272$	−6.37062	+	3.67808i	−0.386276	+	0.223016i
$273$	−2.44972	+	1.52891i	−0.148264	+	0.0925340i
$274$	9.15634	+	5.28642i	0.553155	+	0.319364i
$275$	5.03209	+	15.8012i	0.303446	+	0.952849i
$276$	13.2382	+	7.04804i	0.796845	+	0.424242i
$277$	8.50699	+	14.7345i	0.511136	+	0.885313i	0.999917	+	0.0129065i	$0.00410839\pi$
$277$	8.50699	+	14.7345i	0.511136	+	0.885313i	−0.488781	+	0.872407i	$0.662558\pi$
$278$	−3.35663			−0.201317
$279$	12.0564	+	17.9160i	0.721795	+	1.07260i
$280$	−2.15290	−	2.45987i	−0.128660	−	0.147005i
$281$	−11.7572	−	20.3640i	−0.701373	−	1.21481i	−0.967985	−	0.251010i	$-0.919237\pi$
$281$	−11.7572	−	20.3640i	−0.701373	−	1.21481i	0.266611	−	0.963804i	$-0.414096\pi$
$282$	−0.240051	+	0.00825292i	−0.0142948	+	0.000491454i
$283$	−5.77935	+	10.0101i	−0.343547	+	0.595041i	−0.985089	−	0.172047i	$-0.944962\pi$
$283$	−5.77935	+	10.0101i	−0.343547	+	0.595041i	0.641542	+	0.767088i	$0.278295\pi$
$284$	2.31885	+	1.33879i	0.137598	+	0.0794424i
$285$	2.69771	−	2.52993i	0.159798	−	0.149860i
$286$	3.76953	+	0.311282i	0.222897	+	0.0184065i
$287$	7.49529			0.442433
$288$	2.48892	−	1.67489i	0.146661	−	0.0986938i
$289$	−37.1131			−2.18312
$290$	−4.59435	+	13.4902i	−0.269790	+	0.792171i
$291$	−2.02879	+	3.81062i	−0.118930	+	0.223383i
$292$	0.926408	−	1.60459i	0.0542139	−	0.0939013i
$293$	−12.0012	−	6.92888i	−0.701116	−	0.404789i	0.106647	−	0.994297i	$-0.465988\pi$
$293$	−12.0012	−	6.92888i	−0.701116	−	0.404789i	−0.807763	+	0.589508i	$0.799322\pi$
$294$	−4.45946	−	7.14522i	−0.260081	−	0.416717i
$295$	−7.57264	+	22.2352i	−0.440896	+	1.29458i
$296$	−0.0593138			−0.00344754
$297$	17.2300	−	0.356838i	0.999786	−	0.0207058i
$298$			7.76530i			0.449832i
$299$	−4.93736	−	8.55175i	−0.285535	−	0.494561i
$300$	−3.57132	−	7.88959i	−0.206190	−	0.455506i
$301$	8.83395	−	15.3009i	0.509180	−	0.881926i
$302$	5.13282	−	8.89030i	0.295360	−	0.511579i
$303$	−2.28192	−	1.21490i	−0.131093	−	0.0697942i
$304$	0.826988	−	0.477461i	0.0474310	−	0.0273843i
$305$	13.7438	+	15.7034i	0.786967	+	0.899176i
$306$	22.0164	−	1.51563i	1.25859	−	0.0866428i
$307$	8.41931			0.480515			0.240258	−	0.970709i	$-0.422768\pi$
$307$	8.41931			0.480515			0.240258	+	0.970709i	$0.422768\pi$
$308$	0.399033	−	4.83216i	0.0227370	−	0.275338i
$309$	4.03372	−	0.138678i	0.229470	−	0.00788914i
$310$	15.7897	−	3.12436i	0.896797	−	0.177452i
$311$	10.2267	+	5.90436i	0.579900	+	0.334806i	0.761094	−	0.648642i	$-0.224663\pi$
$311$	10.2267	+	5.90436i	0.579900	+	0.334806i	−0.181193	+	0.983447i	$0.557996\pi$
$312$	−1.97411	+	0.0678695i	−0.111762	+	0.00384235i
$313$	6.84104	−	3.94968i	0.386679	−	0.223249i	−0.294041	−	0.955793i	$-0.595000\pi$
$313$	6.84104	−	3.94968i	0.386679	−	0.223249i	0.680720	+	0.732544i	$0.261667\pi$
$314$	−13.6234			−0.768815
$315$	2.55980	+	9.46682i	0.144229	+	0.533395i
$316$			5.51391i			0.310181i
$317$	10.8028	+	18.7110i	0.606747	+	1.05092i	0.991773	+	0.128011i	$0.0408592\pi$
$317$	10.8028	+	18.7110i	0.606747	+	1.05092i	−0.385026	+	0.922906i	$0.625807\pi$
$318$	−4.74678	+	8.91577i	−0.266186	+	0.499972i
$319$	−19.1135	+	9.02649i	−1.07015	+	0.505387i
$320$	−0.434042	−	2.19354i	−0.0242637	−	0.122622i
$321$	−14.4087	−	23.0864i	−0.804213	−	1.28856i
$322$	−10.9625	+	6.32920i	−0.610916	+	0.352712i
$323$	7.02457			0.390857
$324$	−8.91510	+	1.23329i	−0.495283	+	0.0685163i
$325$	−0.755583	+	5.65185i	−0.0419122	+	0.313508i
$326$	11.6113	+	20.1113i	0.643089	+	1.11386i
$327$	−12.9542	−	20.7559i	−0.716367	−	1.14781i
$328$	4.44015	+	2.56352i	0.245166	+	0.141547i
$329$	0.101366	−	0.175571i	0.00558847	−	0.00967952i
$330$	4.72009	−	11.9466i	0.259832	−	0.657638i
$331$	5.61795	+	9.73058i	0.308791	+	0.534841i	0.978098	−	0.208144i	$-0.0667424\pi$
$331$	5.61795	+	9.73058i	0.308791	+	0.534841i	−0.669307	+	0.742986i	$0.733409\pi$
$332$		−	0.786878i		−	0.0431855i
$333$	0.159848	+	0.0781771i	0.00875963	+	0.00428408i
$334$	−16.3118			−0.892542
$335$	−8.56744	+	25.1562i	−0.468089	+	1.37443i
$336$	0.0870019	+	2.53061i	0.00474634	+	0.138056i
$337$	−8.52470	+	14.7652i	−0.464370	+	0.804313i	−0.999173	−	0.0406641i	$-0.987053\pi$
$337$	−8.52470	+	14.7652i	−0.464370	+	0.804313i	0.534803	+	0.844977i	$0.320386\pi$
$338$	−10.1320	−	5.84971i	−0.551108	−	0.318183i
$339$	0.241243	+	7.01701i	0.0131025	+	0.381111i
$340$	5.30289	−	15.5706i	0.287590	−	0.844436i
$341$	19.6230	+	13.5981i	1.06264	+	0.736378i
$342$	−2.85800	+	0.196748i	−0.154543	+	0.0106389i
$343$	17.3424			0.936401
$344$	10.4663	−	6.04274i	0.564307	−	0.325803i
$345$	−32.6544	+	7.63603i	−1.75806	+	0.411110i
$346$	11.5283	−	19.9676i	0.619766	−	1.07347i
$347$	7.65873	+	4.42177i	0.411142	+	0.237373i	0.691280	−	0.722587i	$-0.257047\pi$
$347$	7.65873	+	4.42177i	0.411142	+	0.237373i	−0.280138	+	0.959960i	$0.590380\pi$
$348$	9.36463	−	5.84464i	0.501997	−	0.313305i
$349$	−7.77437	+	4.48853i	−0.416152	+	0.240266i	−0.693430	−	0.720524i	$-0.743901\pi$
$349$	−7.77437	+	4.48853i	−0.416152	+	0.240266i	0.277277	+	0.960790i	$0.410568\pi$
$350$	7.24510	+	0.968582i	0.387267	+	0.0517729i
$351$	5.40960	+	2.41902i	0.288743	+	0.129118i
$352$	1.88907	−	2.72606i	0.100688	−	0.145300i
$353$	−2.56258	−	4.43852i	−0.136392	−	0.236239i	0.789736	−	0.613447i	$-0.210217\pi$
$353$	−2.56258	−	4.43852i	−0.136392	−	0.236239i	−0.926129	+	0.377208i	$0.876884\pi$
$354$	15.4352	−	9.63341i	0.820373	−	0.512010i
$355$	−5.87336	+	1.16218i	−0.311726	+	0.0616820i
$356$	−10.5845	−	6.11095i	−0.560976	−	0.323879i
$357$	−8.75353	+	16.4416i	−0.463286	+	0.870180i
$358$	0.134142	+	0.232340i	0.00708962	+	0.0122796i
$359$	30.8653			1.62901			0.814504	−	0.580158i	$-0.197009\pi$
$359$	30.8653			1.62901			0.814504	+	0.580158i	$0.197009\pi$
$360$	−1.72142	+	6.48357i	−0.0907266	+	0.341714i
$361$	18.0881			0.952006
$362$	11.0469	−	6.37795i	0.580614	−	0.335218i
$363$	17.5987	−	7.29960i	0.923695	−	0.383130i
$364$	0.833601	−	1.44384i	0.0436926	−	0.0756777i
$365$	0.804200	+	4.06422i	0.0420937	+	0.212731i
$366$	−0.555407	−	16.1550i	−0.0290316	−	0.844437i
$367$	−11.5770	+	6.68396i	−0.604312	+	0.348900i	−0.770736	−	0.637155i	$-0.780111\pi$
$367$	−11.5770	+	6.68396i	−0.604312	+	0.348900i	0.166424	+	0.986054i	$0.446778\pi$
$368$	−8.65879			−0.451371
$369$	−8.58724	−	12.7608i	−0.447034	−	0.664302i
$370$	0.0998037	−	0.0873491i	0.00518855	−	0.00454106i
$371$	−4.26265	−	7.38312i	−0.221306	−	0.383312i
$372$	−11.0053	−	5.85923i	−0.570596	−	0.303787i
$373$	13.6536	−	23.6487i	0.706955	−	1.22448i	−0.259026	−	0.965870i	$-0.583402\pi$
$373$	13.6536	−	23.6487i	0.706955	−	1.22448i	0.965981	−	0.258612i	$-0.0832650\pi$
$374$	22.0612	−	10.4186i	1.14076	−	0.538730i
$375$	17.6279	+	8.01600i	0.910302	+	0.413944i
$376$	0.120097	−	0.0693378i	0.00619351	−	0.00357582i
$377$	−7.26825			−0.374334
$378$	3.10094	−	6.93456i	0.159495	−	0.356675i
$379$	3.26559			0.167742			0.0838711	−	0.996477i	$-0.473272\pi$
$379$	3.26559			0.167742			0.0838711	+	0.996477i	$0.473272\pi$
$380$	−0.688383	+	2.02127i	−0.0353133	+	0.103689i
$381$	−0.0208091	+	0.0129873i	−0.00106608	+	0.000665361i
$382$	3.18981	−	5.52490i	0.163205	−	0.282679i
$383$	15.6478	−	27.1028i	0.799566	−	1.38489i	−0.120332	−	0.992734i	$-0.538396\pi$
$383$	15.6478	−	27.1028i	0.799566	−	1.38489i	0.919899	−	0.392156i	$-0.128271\pi$
$384$	−0.813975	+	1.52887i	−0.0415380	+	0.0780198i
$385$	6.44471	+	8.71843i	0.328453	+	0.444332i
$386$			26.4377i			1.34564i
$387$	−36.1708	+	2.49004i	−1.83867	+	0.126576i
$388$		−	2.49244i		−	0.126535i
$389$	23.2375	−	13.4162i	1.17819	−	0.680228i	0.222595	−	0.974911i	$-0.428547\pi$
$389$	23.2375	−	13.4162i	1.17819	−	0.680228i	0.955595	+	0.294683i	$0.0952140\pi$
$390$	3.22176	−	3.02139i	0.163140	−	0.152994i
$391$	−55.1619	−	31.8477i	−2.78966	−	1.61061i
$392$	4.21132	+	2.43141i	0.212704	+	0.122805i
$393$	0.0741358	+	2.15638i	0.00373966	+	0.108775i
$394$	−5.08371	−	8.80524i	−0.256114	−	0.443602i
$395$	−8.12011	−	9.27791i	−0.408567	−	0.466822i
$396$	−8.68399	+	4.85678i	−0.436387	+	0.244062i
$397$		−	21.4734i		−	1.07772i	−0.842396	−	0.538859i	$-0.818856\pi$
$397$		−	21.4734i		−	1.07772i	0.842396	−	0.538859i	$-0.181144\pi$
$398$	18.6800	−	10.7849i	0.936346	−	0.540600i
$399$	1.13632	−	2.13432i	0.0568871	−	0.106850i
$400$	3.96067	+	3.05174i	0.198034	+	0.152587i
$401$	−4.01966	−	2.32075i	−0.200732	−	0.115893i	0.396265	−	0.918136i	$-0.370306\pi$
$401$	−4.01966	−	2.32075i	−0.200732	−	0.115893i	−0.596997	+	0.802243i	$0.703640\pi$
$402$	17.4629	−	10.8989i	0.870972	−	0.543590i
$403$	4.10456	+	7.10931i	0.204463	+	0.354140i
$404$	1.49255			0.0742572
$405$	13.1847	−	15.2041i	0.655151	−	0.755498i
$406$			9.31717i			0.462403i
$407$	0.196054	+	0.0161899i	0.00971805	+	0.000802502i
$408$	−10.8088	+	6.74599i	−0.535117	+	0.333976i
$409$	2.65115	+	1.53064i	0.131091	+	0.0756855i	0.564111	−	0.825699i	$-0.309219\pi$
$409$	2.65115	+	1.53064i	0.131091	+	0.0756855i	−0.433020	+	0.901384i	$0.642552\pi$
$410$	−11.2464	+	2.22535i	−0.555418	+	0.109902i
$411$	16.1645	+	8.60602i	0.797336	+	0.424504i
$412$	−2.01805	+	1.16512i	−0.0994222	+	0.0574014i
$413$			15.3570i			0.755669i
$414$	23.3351	+	11.4125i	1.14686	+	0.560895i
$415$	1.15880	+	1.32403i	0.0568834	+	0.0649941i
$416$	0.987638	−	0.570213i	0.0484229	−	0.0279570i
$417$	−5.81041	+	0.199761i	−0.284537	+	0.00978234i
$418$	−2.86383	+	1.35246i	−0.140074	+	0.0661510i
$419$	−13.0397	−	7.52847i	−0.637030	−	0.367790i	0.146439	−	0.989220i	$-0.453219\pi$
$419$	−13.0397	−	7.52847i	−0.637030	−	0.367790i	−0.783470	+	0.621430i	$0.786552\pi$
$420$	−3.87312	−	4.12998i	−0.188989	−	0.201522i
$421$	0.0446411	+	0.0773206i	0.00217567	+	0.00376838i	0.867111	−	0.498115i	$-0.165974\pi$
$421$	0.0446411	+	0.0773206i	0.00217567	+	0.00376838i	−0.864936	+	0.501883i	$0.832641\pi$
$422$	−0.111180			−0.00541217
$423$	−0.415044	+	0.0285721i	−0.0201801	+	0.00138922i
$424$		−	5.83161i		−	0.283208i
$425$	14.0074	+	34.0091i	0.679459	+	1.64968i
$426$	4.09366	+	2.17948i	0.198339	+	0.105596i
$427$	11.8156	+	6.82174i	0.571797	+	0.330127i
$428$	13.6069	+	7.85596i	0.657715	+	0.379732i
$429$	6.54369	+	0.314504i	0.315932	+	0.0151844i
$430$	−8.71215	+	25.5811i	−0.420137	+	1.23363i
$431$	−34.6664			−1.66982			−0.834910	−	0.550386i	$-0.814480\pi$
$431$	−34.6664			−1.66982			−0.834910	+	0.550386i	$0.814480\pi$
$432$	4.20872	−	3.04740i	0.202492	−	0.146618i
$433$			7.56002i			0.363312i	0.983362	+	0.181656i	$0.0581457\pi$
$433$			7.56002i			0.363312i	−0.983362	+	0.181656i	$0.941854\pi$
$434$	9.11342	−	5.26164i	0.437458	−	0.252567i
$435$	−7.15012	+	23.6253i	−0.342822	+	1.13275i
$436$	12.2333	+	7.06293i	0.585871	+	0.338253i
$437$	7.16072	+	4.13424i	0.342543	+	0.197768i
$438$	1.50815	−	2.83272i	0.0720620	−	0.135352i
$439$	5.47237	−	3.15947i	0.261182	−	0.150794i	−0.363692	−	0.931519i	$-0.618484\pi$
$439$	5.47237	−	3.15947i	0.261182	−	0.150794i	0.624874	+	0.780726i	$0.285150\pi$
$440$	0.835938	+	7.36894i	0.0398518	+	0.351300i
$441$	−8.14468	−	12.1032i	−0.387842	−	0.576342i
$442$	8.38915			0.399031
$443$	20.0960	+	34.8073i	0.954789	+	1.65374i	0.734850	+	0.678230i	$0.237253\pi$
$443$	20.0960	+	34.8073i	0.954789	+	1.65374i	0.219939	+	0.975514i	$0.429414\pi$
$444$	−0.102674	+	0.00352991i	−0.00487269	+	0.000167522i
$445$	26.8092	−	5.30481i	1.27088	−	0.251472i
$446$	−5.34313	+	9.25457i	−0.253004	+	0.438217i
$447$	0.462132	+	13.4420i	0.0218581	+	0.635782i
$448$	−0.730956	−	1.26605i	−0.0345344	−	0.0598154i
$449$		−	8.49626i		−	0.400963i	−0.979697	−	0.200482i	$-0.935749\pi$
$449$		−	8.49626i		−	0.400963i	0.979697	−	0.200482i	$-0.0642507\pi$
$450$	−6.65158	−	13.4446i	−0.313558	−	0.633783i
$451$	−13.9766	−	9.68535i	−0.658134	−	0.456065i
$452$	−2.02683	−	3.51058i	−0.0953342	−	0.165124i
$453$	8.35597	−	15.6948i	0.392598	−	0.737407i
$454$	5.81600	−	10.0736i	0.272959	−	0.472778i
$455$	0.723635	+	3.65707i	0.0339245	+	0.171446i
$456$	1.40312	−	0.875715i	0.0657073	−	0.0410091i
$457$	5.73480	+	9.93297i	0.268263	+	0.464645i	0.968413	−	0.249351i	$-0.0802172\pi$
$457$	5.73480	+	9.93297i	0.268263	+	0.464645i	−0.700151	+	0.713995i	$0.746884\pi$
$458$		−	12.5377i		−	0.585850i
$459$	38.0208	−	3.93384i	1.77466	−	0.183616i
$460$	14.5696	−	12.7515i	0.679312	−	0.594540i
$461$	14.8727	+	25.7603i	0.692691	+	1.19978i	0.970953	+	0.239270i	$0.0769082\pi$
$461$	14.8727	+	25.7603i	0.692691	+	1.19978i	−0.278262	+	0.960505i	$0.589758\pi$
$462$	0.403163	−	8.38836i	0.0187568	−	0.390262i
$463$	−8.08876	−	4.67005i	−0.375917	−	0.217036i	0.300124	−	0.953900i	$-0.402972\pi$
$463$	−8.08876	−	4.67005i	−0.375917	−	0.217036i	−0.676040	+	0.736865i	$0.736305\pi$
$464$	−3.18664	+	5.51942i	−0.147936	+	0.256233i
$465$	27.1465	−	6.34804i	1.25889	−	0.294383i
$466$	10.4445	+	18.0904i	0.483832	+	0.838022i
$467$	19.4955			0.902146			0.451073	−	0.892487i	$-0.351041\pi$
$467$	19.4955			0.902146			0.451073	+	0.892487i	$0.351041\pi$
$468$	−3.41320	+	0.234968i	−0.157775	+	0.0108614i
$469$			17.3744i			0.802277i
$470$	−0.0999681	+	0.293532i	−0.00461119	+	0.0135396i
$471$	−23.5825	+	0.810764i	−1.08663	+	0.0373580i
$472$	−5.25237	+	9.09738i	−0.241760	+	0.418741i
$473$	−36.2445	+	17.1167i	−1.66652	+	0.787027i
$474$	0.328146	+	9.54473i	0.0150722	+	0.438404i
$475$	−1.81834	−	4.41481i	−0.0834311	−	0.202566i
$476$		−	10.7541i		−	0.492911i
$477$	−7.68621	+	15.7159i	−0.351927	+	0.719583i
$478$		−	22.4019i		−	1.02464i
$479$	−13.6727	−	23.6817i	−0.624720	−	1.08205i	−0.988595	−	0.150599i	$-0.951880\pi$
$479$	−13.6727	−	23.6817i	−0.624720	−	1.08205i	0.363875	−	0.931448i	$-0.381454\pi$
$480$	−0.881881	−	3.77124i	−0.0402522	−	0.172133i
$481$	0.0585805	+	0.0338215i	0.00267104	+	0.00154213i
$482$	−12.5298	+	21.7023i	−0.570718	+	0.988512i
$483$	−18.5997	+	11.6084i	−0.846316	+	0.528201i
$484$	−6.98817	+	8.49503i	−0.317644	+	0.386138i
$485$	3.67052	+	4.19388i	0.166670	+	0.190434i
$486$	−15.3589	+	2.66542i	−0.696693	+	0.120906i
$487$		−	2.20630i		−	0.0999768i	−0.998750	−	0.0499884i	$-0.984082\pi$
$487$		−	2.20630i		−	0.0999768i	0.998750	−	0.0499884i	$-0.0159184\pi$
$488$	4.66631	+	8.08229i	0.211234	+	0.365868i
$489$	21.2963	+	34.1222i	0.963052	+	1.54306i
$490$	−10.6668	+	2.11066i	−0.481875	+	0.0953501i
$491$	10.4872	−	18.1643i	0.473280	−	0.819745i	−0.526252	−	0.850328i	$-0.676403\pi$
$491$	10.4872	−	18.1643i	0.473280	−	0.819745i	0.999532	+	0.0305838i	$0.00973666\pi$
$492$	7.83859	+	4.17328i	0.353391	+	0.188146i
$493$	−40.6017	+	23.4414i	−1.82861	+	1.05575i
$494$	−1.08902			−0.0489973
$495$	7.45963	−	20.9608i	0.335285	−	0.942117i
$496$	7.19830			0.323213
$497$	−3.38995	+	1.95719i	−0.152060	+	0.0877919i
$498$	−0.0468290	−	1.36211i	−0.00209846	−	0.0610375i
$499$	16.2274	−	28.1067i	0.726438	−	1.25823i	−0.231941	−	0.972730i	$-0.574508\pi$
$499$	16.2274	−	28.1067i	0.726438	−	1.25823i	0.958379	−	0.285498i	$-0.0921590\pi$
$500$	−11.1585	+	0.697755i	−0.499025	+	0.0312045i
$501$	−28.2362	+	0.970754i	−1.26150	+	0.0433701i
$502$	9.49802	+	16.4510i	0.423917	+	0.734246i
$503$			19.5918i			0.873556i	0.899569	+	0.436778i	$0.143881\pi$
$503$			19.5918i			0.873556i	−0.899569	+	0.436778i	$0.856119\pi$
$504$	0.301206	+	4.37538i	0.0134168	+	0.194895i
$505$	−2.51143	+	2.19802i	−0.111757	+	0.0978107i
$506$	28.6206	+	2.36344i	1.27234	+	0.105068i
$507$	−17.8869	−	9.52304i	−0.794386	−	0.422933i
$508$	0.00708101	−	0.0122647i	0.000314169	−	0.000544157i
$509$	6.23985	+	3.60258i	0.276576	+	0.159681i	0.631872	−	0.775072i	$-0.282287\pi$
$509$	6.23985	+	3.60258i	0.276576	+	0.159681i	−0.355296	+	0.934754i	$0.615620\pi$
$510$	8.25281	−	27.2688i	0.365440	−	1.20748i
$511$	1.35433	+	2.34576i	0.0599119	+	0.103770i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.93558	+	0.510663i	−0.217911	+	0.0225463i
$514$			18.7170i			0.825571i
$515$	1.67982	−	4.93238i	0.0740217	−	0.217347i
$516$	17.7579	−	11.0830i	0.781748	−	0.487903i
$517$	−0.415890	+	0.196407i	−0.0182908	+	0.00863795i
$518$	0.0433558	−	0.0750944i	0.00190494	−	0.00329946i
$519$	18.7675	−	35.2506i	0.823803	−	1.54733i
$520$	−0.822107	+	2.41392i	−0.0360518	+	0.105857i
$521$			17.2391i			0.755258i	0.925957	+	0.377629i	$0.123261\pi$
$521$			17.2391i			0.755258i	−0.925957	+	0.377629i	$0.876739\pi$
$522$	15.8626	−	10.6745i	0.694287	−	0.467212i
$523$	11.4358			0.500051			0.250025	−	0.968239i	$-0.419561\pi$
$523$	11.4358			0.500051			0.250025	+	0.968239i	$0.419561\pi$
$524$	−0.622860	−	1.07883i	−0.0272098	−	0.0471287i
$525$	12.5991	+	1.24547i	0.549871	+	0.0543567i
$526$	8.38350	−	14.5206i	0.365538	−	0.633130i
$527$	45.8576	+	26.4759i	1.99759	+	1.15331i
$528$	3.10780	−	4.83131i	0.135250	−	0.210256i
$529$	−25.9874	−	45.0114i	−1.12989	−	1.95702i
$530$	8.58797	+	9.81248i	0.373038	+	0.426227i
$531$	26.1455	−	17.5943i	1.13462	−	0.763527i
$532$			1.39601i			0.0605248i
$533$	−2.92351	−	5.06366i	−0.126631	−	0.219332i
$534$	−18.6857	−	9.94831i	−0.808609	−	0.430506i
$535$	−34.4647	+	6.81963i	−1.49004	+	0.294838i
$536$	−5.94237	+	10.2925i	−0.256671	+	0.444568i
$537$	0.246030	+	0.394205i	0.0106170	+	0.0170112i
$538$	2.67028	+	4.62506i	0.115124	+	0.199400i
$539$	−13.2563	−	9.18620i	−0.570991	−	0.395678i
$540$	−2.59397	+	11.3257i	−0.111627	+	0.487380i
$541$		−	24.8969i		−	1.07040i	−0.844724	−	0.535201i	$-0.820236\pi$
$541$		−	24.8969i		−	1.07040i	0.844724	−	0.535201i	$-0.179764\pi$
$542$	−0.744718	−	1.28989i	−0.0319884	−	0.0554055i
$543$	18.7430	−	11.6978i	0.804338	−	0.502002i
$544$	3.67808	−	6.37062i	0.157696	−	0.273138i
$545$	−30.9856	+	6.13121i	−1.32728	+	0.262632i
$546$	1.35706	−	2.54894i	0.0580768	−	0.109084i
$547$	2.51541	+	4.35681i	0.107551	+	0.186284i	0.914778	−	0.403958i	$-0.132366\pi$
$547$	2.51541	+	4.35681i	0.107551	+	0.186284i	−0.807227	+	0.590242i	$0.799032\pi$
$548$	−10.5728			−0.451649
$549$	−1.92285	−	27.9318i	−0.0820653	−	1.19210i
$550$	−12.2585	−	11.1682i	−0.522705	−	0.476214i
$551$	5.27062	−	3.04299i	0.224536	−	0.129636i
$552$	−14.9886	+	0.515306i	−0.637958	+	0.0219329i
$553$	−6.98090	−	4.03042i	−0.296858	−	0.171391i
$554$	−14.7345	−	8.50699i	−0.626011	−	0.361428i
$555$	0.167565	−	0.157143i	0.00711272	−	0.00667036i
$556$	2.90692	−	1.67831i	0.123281	−	0.0711763i
$557$		−	35.0008i		−	1.48303i	−0.670936	−	0.741516i	$-0.734107\pi$
$557$		−	35.0008i		−	1.48303i	0.670936	−	0.741516i	$-0.265893\pi$
$558$	−19.3991	−	9.48754i	−0.821230	−	0.401640i
$559$	−13.7826			−0.582941
$560$	3.09440	+	1.05386i	0.130762	+	0.0445337i
$561$	37.5686	−	19.3477i	1.58615	−	0.816861i
$562$	20.3640	+	11.7572i	0.859003	+	0.495946i
$563$	26.3612	+	15.2197i	1.11099	+	0.641432i	0.939086	−	0.343681i	$-0.111674\pi$
$563$	26.3612	+	15.2197i	1.11099	+	0.641432i	0.171907	+	0.985113i	$0.445007\pi$
$564$	0.203764	−	0.127173i	0.00858001	−	0.00535494i
$565$	8.58031	+	2.92220i	0.360976	+	0.122938i
$566$		−	11.5587i		−	0.485849i
$567$	4.95513	−	12.1885i	0.208096	−	0.511868i
$568$	−2.67757			−0.112349
$569$	−7.98391	−	13.8285i	−0.334703	−	0.579723i	0.648725	−	0.761023i	$-0.275303\pi$
$569$	−7.98391	−	13.8285i	−0.334703	−	0.579723i	−0.983428	+	0.181300i	$0.941969\pi$
$570$	−1.07132	+	3.53984i	−0.0448726	+	0.148267i
$571$	11.5381	+	6.66150i	0.482853	+	0.278775i	0.721605	−	0.692305i	$-0.243405\pi$
$571$	11.5381	+	6.66150i	0.482853	+	0.278775i	−0.238752	+	0.971081i	$0.576738\pi$
$572$	−3.42015	+	1.61519i	−0.143004	+	0.0675344i
$573$	5.19284	−	9.75360i	0.216934	−	0.407462i
$574$	−6.49111	+	3.74764i	−0.270934	+	0.156424i
$575$	−5.73684	+	42.9122i	−0.239243	+	1.78956i
$576$	−1.31803	+	2.69496i	−0.0549178	+	0.112290i
$577$			27.6397i			1.15065i	0.817923	+	0.575327i	$0.195125\pi$
$577$			27.6397i			1.15065i	−0.817923	+	0.575327i	$0.804875\pi$
$578$	32.1409	−	18.5565i	1.33688	−	0.771850i
$579$	1.57337	+	45.7644i	0.0653870	+	1.90190i
$580$	−2.76627	−	13.9800i	−0.114863	−	0.580489i
$581$	0.996229	+	0.575173i	0.0413305	+	0.0238622i
$582$	−0.148331	−	4.31449i	−0.00614853	−	0.178841i
$583$	−1.59175	+	19.2756i	−0.0659236	+	0.798315i
$584$			1.85282i			0.0766701i
$585$	5.39715	−	5.42185i	0.223145	−	0.224166i
$586$	13.8578			0.572458
$587$	−13.9183	−	24.1072i	−0.574469	−	0.995009i	−0.996099	−	0.0882412i	$-0.971875\pi$
$587$	−13.9183	−	24.1072i	−0.574469	−	0.995009i	0.421630	−	0.906768i	$-0.361458\pi$
$588$	7.43461	+	3.95821i	0.306598	+	0.163234i
$589$	−5.95290	−	3.43691i	−0.245285	−	0.141615i
$590$	−4.55950	−	23.0426i	−0.187712	−	0.948647i
$591$	−9.32407	−	14.9396i	−0.383541	−	0.614532i
$592$	0.0513673	−	0.0296569i	0.00211118	−	0.00121889i
$593$			17.2575i			0.708681i	0.935117	+	0.354340i	$0.115295\pi$
$593$			17.2575i			0.708681i	−0.935117	+	0.354340i	$0.884705\pi$
$594$	−14.7432	+	8.92403i	−0.604921	+	0.366157i
$595$	15.8371	+	18.0952i	0.649257	+	0.741830i
$596$	−3.88265	−	6.72495i	−0.159040	−	0.275465i
$597$	31.6939	−	19.7807i	1.29714	−	0.809571i
$598$	8.55175	+	4.93736i	0.349707	+	0.201904i
$599$	−10.1226	−	5.84426i	−0.413596	−	0.238790i	0.278737	−	0.960367i	$-0.410084\pi$
$599$	−10.1226	−	5.84426i	−0.413596	−	0.238790i	−0.692334	+	0.721577i	$0.743417\pi$
$600$	7.03765	+	5.04693i	0.287311	+	0.206040i
$601$	3.26378	−	1.88435i	0.133133	−	0.0768641i	−0.431955	−	0.901895i	$-0.642176\pi$
$601$	3.26378	−	1.88435i	0.133133	−	0.0768641i	0.565087	+	0.825031i	$0.308843\pi$
$602$			17.6679i			0.720090i
$603$	29.5802	−	19.9056i	1.20460	−	0.810620i
$604$			10.2656i			0.417703i
$605$	−0.751718	−	24.5853i	−0.0305617	−	0.999533i
$606$	2.58365	−	0.0888254i	0.104954	−	0.00360828i
$607$	21.4411	−	37.1370i	0.870267	−	1.50735i	0.00854594	−	0.999963i	$-0.497280\pi$
$607$	21.4411	−	37.1370i	0.870267	−	1.50735i	0.861721	−	0.507383i	$-0.169387\pi$
$608$	−0.477461	+	0.826988i	−0.0193636	+	0.0335388i
$609$	0.554487	+	16.1283i	0.0224690	+	0.653551i
$610$	−19.7542	−	6.72768i	−0.799824	−	0.272396i
$611$	−0.158149			−0.00639803
$612$	−18.3089	+	12.3208i	−0.740094	+	0.498037i
$613$	−3.52322			−0.142302			−0.0711508	−	0.997466i	$-0.522667\pi$
$613$	−3.52322			−0.142302			−0.0711508	+	0.997466i	$0.522667\pi$
$614$	−7.29134	+	4.20965i	−0.294254	+	0.169888i
$615$	−19.3353	+	4.52144i	−0.779676	+	0.182322i
$616$	2.07051	+	4.38429i	0.0834232	+	0.176648i
$617$	−20.9499	+	36.2863i	−0.843411	+	1.46083i	0.0435826	+	0.999050i	$0.486123\pi$
$617$	−20.9499	+	36.2863i	−0.843411	+	1.46083i	−0.886994	+	0.461781i	$0.847211\pi$
$618$	−3.42396	+	2.13696i	−0.137732	+	0.0859610i
$619$	−0.990042	−	1.71480i	−0.0397931	−	0.0689238i	0.845443	−	0.534066i	$-0.179337\pi$
$619$	−0.990042	−	1.71480i	−0.0397931	−	0.0689238i	−0.885236	+	0.465142i	$0.846003\pi$
$620$	−12.1121	+	10.6006i	−0.486435	+	0.425732i
$621$	41.0729	+	18.3667i	1.64820	+	0.737029i
$622$	−11.8087			−0.473487
$623$	15.4736	−	8.93366i	0.619935	−	0.357920i
$624$	1.67569	−	1.04583i	0.0670814	−	0.0418668i
$625$	17.7482	−	17.6068i	0.709930	−	0.704273i
$626$	−3.94968	+	6.84104i	−0.157861	+	0.273423i
$627$	−4.87688	+	2.51158i	−0.194764	+	0.100303i
$628$	11.7982	−	6.81172i	0.470801	−	0.271817i
$629$	0.436322			0.0173973
$630$	−6.95027	−	6.91861i	−0.276905	−	0.275644i
$631$	−14.8826			−0.592465			−0.296233	−	0.955116i	$-0.595730\pi$
$631$	−14.8826			−0.592465			−0.296233	+	0.955116i	$0.595730\pi$
$632$	−2.75695	−	4.77518i	−0.109666	−	0.189947i
$633$	−0.192456	+	0.00661661i	−0.00764945	+	0.000262987i
$634$	−18.7110	−	10.8028i	−0.743110	−	0.429035i
$635$	0.00614691	+	0.0310649i	0.000243933	+	0.00123277i
$636$	−0.347053	−	10.0947i	−0.0137615	−	0.400280i
$637$	−2.77284	−	4.80270i	−0.109864	−	0.190290i
$638$	12.0396	−	17.3739i	0.476651	−	0.687841i
$639$	7.21595	+	3.52911i	0.285459	+	0.139610i
$640$	1.47266	+	1.68264i	0.0582120	+	0.0665121i
$641$	−18.5182	+	10.6915i	−0.731426	+	0.422289i	−0.818944	−	0.573874i	$-0.805440\pi$
$641$	−18.5182	+	10.6915i	−0.731426	+	0.422289i	0.0875173	+	0.996163i	$0.472107\pi$
$642$	24.0215	+	12.7891i	0.948052	+	0.504745i
$643$	12.5876	+	7.26745i	0.496406	+	0.286600i	0.727228	−	0.686396i	$-0.240808\pi$
$643$	12.5876	+	7.26745i	0.496406	+	0.286600i	−0.230822	+	0.972996i	$0.574141\pi$
$644$	6.32920	−	10.9625i	0.249405	−	0.431983i
$645$	−13.5586	+	44.8001i	−0.533869	+	1.76400i
$646$	−6.08345	+	3.51228i	−0.239350	+	0.138189i
$647$	17.6122			0.692407			0.346203	−	0.938159i	$-0.387471\pi$
$647$	17.6122			0.692407			0.346203	+	0.938159i	$0.387471\pi$
$648$	7.10406	−	5.52561i	0.279074	−	0.217067i
$649$	19.8442	−	28.6366i	0.778953	−	1.12408i
$650$	−2.17157	−	5.27243i	−0.0851759	−	0.206802i
$651$	15.4625	−	9.65040i	0.606021	−	0.378229i
$652$	−20.1113	−	11.6113i	−0.787619	−	0.454732i
$653$	−13.1267	+	22.7361i	−0.513688	+	0.889734i	0.486186	+	0.873856i	$0.338388\pi$
$653$	−13.1267	+	22.7361i	−0.513688	+	0.889734i	−0.999874	+	0.0158787i	$0.994945\pi$
$654$	21.5966	+	11.4981i	0.844494	+	0.449611i
$655$	2.63679	+	0.898012i	0.103028	+	0.0350882i
$656$	−5.12704			−0.200177
$657$	2.44206	−	4.99327i	0.0952739	−	0.194806i
$658$			0.202731i			0.00790329i
$659$	−6.80581	−	11.7880i	−0.265117	−	0.459196i	0.702477	−	0.711706i	$-0.252077\pi$
$659$	−6.80581	−	11.7880i	−0.265117	−	0.459196i	−0.967594	+	0.252510i	$0.918744\pi$
$660$	1.88558	+	12.7061i	0.0733959	+	0.494584i
$661$	9.20969	−	15.9517i	0.358215	−	0.620447i	−0.629447	−	0.777043i	$-0.716719\pi$
$661$	9.20969	−	15.9517i	0.358215	−	0.620447i	0.987663	+	0.156596i	$0.0500520\pi$
$662$	−9.73058	−	5.61795i	−0.378190	−	0.218348i
$663$	14.5219	−	0.499259i	0.563982	−	0.0193896i
$664$	0.393439	+	0.681456i	0.0152684	+	0.0264456i
$665$	−2.05585	−	2.34899i	−0.0797225	−	0.0910897i
$666$	−0.177521	+	0.0122207i	−0.00687881	+	0.000473544i
$667$	−55.1849			−2.13677
$668$	14.1264	−	8.15590i	0.546568	−	0.315561i
$669$	−8.69834	+	16.3379i	−0.336297	+	0.631660i
$670$	−5.15847	−	26.0696i	−0.199289	−	1.00716i
$671$	−13.2178	−	27.9887i	−0.510269	−	1.08049i
$672$	−1.34065	−	2.14807i	−0.0517167	−	0.0828637i
$673$	−4.57955	−	7.93202i	−0.176529	−	0.305757i	0.764160	−	0.645026i	$-0.223154\pi$
$673$	−4.57955	−	7.93202i	−0.176529	−	0.305757i	−0.940689	+	0.339269i	$0.889820\pi$
$674$		−	17.0494i		−	0.656719i
$675$	−12.3142	−	22.8771i	−0.473973	−	0.880539i
$676$	11.6994			0.449978
$677$	22.1933	−	12.8133i	0.852959	−	0.492456i	−0.00868918	−	0.999962i	$-0.502766\pi$
$677$	22.1933	−	12.8133i	0.852959	−	0.492456i	0.861648	+	0.507506i	$0.169433\pi$
$678$	−3.71743	−	5.95628i	−0.142767	−	0.228750i
$679$	3.15556	+	1.82187i	0.121099	+	0.0699168i
$680$	3.19288	+	16.1360i	0.122441	+	0.618788i
$681$	9.46816	−	17.7838i	0.362821	−	0.681478i
$682$	−23.7931	−	1.96479i	−0.911083	−	0.0752358i
$683$	−37.4611			−1.43341			−0.716704	−	0.697378i	$-0.754350\pi$
$683$	−37.4611			−1.43341			−0.716704	+	0.697378i	$0.754350\pi$
$684$	2.37673	−	1.59939i	0.0908766	−	0.0611542i
$685$	17.7903	−	15.5702i	0.679731	−	0.594906i
$686$	−15.0189	+	8.67119i	−0.573426	+	0.331068i
$687$	−0.746151	−	21.7032i	−0.0284675	−	0.828028i
$688$	−6.04274	+	10.4663i	−0.230377	+	0.399025i
$689$	−3.32526	+	5.75951i	−0.126682	+	0.219420i
$690$	24.4616	−	22.9402i	0.931235	−	0.873319i
$691$	11.5002	+	19.9189i	0.437488	+	0.757751i	0.997495	−	0.0707364i	$-0.0225349\pi$
$691$	11.5002	+	19.9189i	0.437488	+	0.757751i	−0.560007	+	0.828488i	$0.689202\pi$
$692$			23.0566i			0.876482i
$693$	0.198675	−	14.5445i	0.00754703	−	0.552499i
$694$	−8.84354			−0.335696
$695$	−2.41972	+	7.10491i	−0.0917851	+	0.269504i
$696$	−5.18769	+	9.74392i	−0.196639	+	0.369342i
$697$	−32.6625	−	18.8577i	−1.23718	−	0.714285i
$698$	4.48853	−	7.77437i	0.169893	−	0.294264i
$699$	19.1563	+	30.6934i	0.724559	+	1.16093i
$700$	−6.75873	+	2.78373i	−0.255456	+	0.105215i
$701$	4.41091			0.166598			0.0832988	−	0.996525i	$-0.473454\pi$
$701$	4.41091			0.166598			0.0832988	+	0.996525i	$0.473454\pi$
$702$	−5.89436	+	0.609864i	−0.222468	+	0.0230178i
$703$	−0.0566401			−0.00213622
$704$	−0.272953	+	3.30537i	−0.0102873	+	0.124576i
$705$	−0.155579	+	0.514061i	−0.00585944	+	0.0193607i
$706$	4.43852	+	2.56258i	0.167046	+	0.0964440i
$707$	−1.09099	+	1.88965i	−0.0410309	+	0.0710676i
$708$	−8.55060	+	16.0604i	−0.321351	+	0.603587i
$709$	0.417874	+	0.723778i	0.0156936	+	0.0271821i	0.873766	−	0.486347i	$-0.161671\pi$
$709$	0.417874	+	0.723778i	0.0156936	+	0.0271821i	−0.858072	+	0.513529i	$0.828338\pi$
$710$	4.50539	−	3.94316i	0.169084	−	0.147984i
$711$	1.13606	+	16.5027i	0.0426056	+	0.618898i
$712$	12.2219			0.458035
$713$	31.1643	+	53.9781i	1.16711	+	2.02150i
$714$	−0.640000	−	18.6156i	−0.0239514	−	0.696670i
$715$	3.37626	−	7.75450i	0.126265	−	0.290002i
$716$	−0.232340	−	0.134142i	−0.00868297	−	0.00501312i
$717$	−1.33319	−	38.7783i	−0.0497889	−	1.44820i
$718$	−26.7301	+	15.4327i	−0.997560	+	0.575941i
$719$		−	52.0135i		−	1.93978i	−0.243550	−	0.969888i	$-0.578312\pi$
$719$		−	52.0135i		−	1.93978i	0.243550	−	0.969888i	$-0.421688\pi$
$720$	−1.75100	−	6.47565i	−0.0652558	−	0.241333i
$721$		−	3.40661i		−	0.126869i
$722$	−15.6648	+	9.04406i	−0.582982	+	0.336585i
$723$	−20.3979	+	38.3129i	−0.758606	+	1.42487i
$724$	−6.37795	+	11.0469i	−0.237035	+	0.410556i
$725$	25.2425	+	19.4496i	0.937481	+	0.722338i
$726$	−11.5912	+	15.1210i	−0.430188	+	0.561193i
$727$	20.5699	−	11.8760i	0.762894	−	0.440457i	−0.0674396	−	0.997723i	$-0.521483\pi$
$727$	20.5699	−	11.8760i	0.762894	−	0.440457i	0.830334	+	0.557266i	$0.188150\pi$
$728$			1.66720i			0.0617906i
$729$	−26.4280	+	5.52797i	−0.978816	+	0.204740i
$730$	−2.72857	−	3.11762i	−0.100989	−	0.115388i
$731$	−76.9920	+	44.4514i	−2.84765	+	1.64409i
$732$	8.55852	+	13.7130i	0.316332	+	0.506846i
$733$	−14.8009	+	25.6359i	−0.546683	+	0.946883i	0.451816	+	0.892111i	$0.350776\pi$
$733$	−14.8009	+	25.6359i	−0.546683	+	0.946883i	−0.998499	+	0.0547716i	$0.982557\pi$
$734$	6.68396	−	11.5770i	0.246709	−	0.427313i
$735$	−18.3389	+	4.28842i	−0.676439	+	0.158181i
$736$	7.49874	−	4.32940i	0.276407	−	0.159584i
$737$	22.4511	−	32.3985i	0.826998	−	1.19342i
$738$	13.8172	+	6.75758i	0.508617	+	0.248750i
$739$			46.2352i			1.70079i	0.526146	+	0.850394i	$0.323637\pi$
$739$			46.2352i			1.70079i	−0.526146	+	0.850394i	$0.676363\pi$
$740$	−0.0427580	+	0.125548i	−0.00157181	+	0.00461525i
$741$	−1.88512	+	0.0648101i	−0.0692517	+	0.00238086i
$742$	7.38312	+	4.26265i	0.271043	+	0.156487i
$743$	−12.2306	−	7.06132i	−0.448696	−	0.259055i	0.258584	−	0.965989i	$-0.416744\pi$
$743$	−12.2306	−	7.06132i	−0.448696	−	0.259055i	−0.707279	+	0.706934i	$0.750078\pi$
$744$	12.4605	−	0.428388i	0.456822	−	0.0157055i
$745$	16.4367	+	5.59783i	0.602192	+	0.205089i
$746$			27.3071i			0.999785i
$747$	−0.162125	−	2.35506i	−0.00593183	−	0.0861671i
$748$	−13.8963	+	20.0533i	−0.508099	+	0.733223i
$749$	−19.8921	+	11.4847i	−0.726842	+	0.419642i
$750$	−19.2742	+	1.87190i	−0.703795	+	0.0683523i
$751$	−4.52529	+	7.83803i	−0.165130	+	0.286014i	−0.936702	−	0.350129i	$-0.886138\pi$
$751$	−4.52529	+	7.83803i	−0.165130	+	0.286014i	0.771571	+	0.636143i	$0.219471\pi$
$752$	−0.0693378	+	0.120097i	−0.00252849	+	0.00437947i
$753$	17.4204	+	27.9120i	0.634834	+	1.01717i
$754$	6.29449	−	3.63412i	0.229232	−	0.132347i
$755$	−15.1178	−	17.2734i	−0.550193	−	0.628642i
$756$	0.781785	+	7.55598i	0.0284332	+	0.274808i
$757$		−	3.27023i		−	0.118859i	−0.998233	−	0.0594293i	$-0.981072\pi$
$757$		−	3.27023i		−	0.118859i	0.998233	−	0.0594293i	$-0.0189281\pi$
$758$	−2.82809	+	1.63280i	−0.102721	+	0.0593058i
$759$	49.6836	+	2.38790i	1.80340	+	0.0866754i
$760$	−0.414476	−	2.09466i	−0.0150346	−	0.0759813i
$761$	−11.5767	+	20.0515i	−0.419657	+	0.726866i	−0.995905	−	0.0904083i	$-0.971183\pi$
$761$	−11.5767	+	20.0515i	−0.419657	+	0.726866i	0.576248	+	0.817275i	$0.304516\pi$
$762$	0.0115275	−	0.0216519i	0.000417598	−	0.000784366i
$763$	−17.8841	+	10.3254i	−0.647447	+	0.373804i
$764$			6.37961i			0.230806i
$765$	12.6630	−	47.6942i	0.457832	−	1.72439i
$766$			31.2956i			1.13076i
$767$	10.3749	−	5.98994i	0.374615	−	0.216284i
$768$	−0.0595124	−	1.73103i	−0.00214747	−	0.0624631i
$769$	12.6831	+	7.32261i	0.457365	+	0.264060i	0.710936	−	0.703257i	$-0.248272\pi$
$769$	12.6831	+	7.32261i	0.457365	+	0.264060i	−0.253571	+	0.967317i	$0.581605\pi$
$770$	−9.94049	−	4.32802i	−0.358231	−	0.155971i
$771$	1.11389	+	32.3996i	0.0401159	+	1.16684i
$772$	−13.2188	−	22.8957i	−0.475756	−	0.824034i
$773$	17.5929			0.632774			0.316387	−	0.948630i	$-0.397530\pi$
$773$	17.5929			0.632774			0.316387	+	0.948630i	$0.397530\pi$
$774$	30.0798	−	20.2418i	1.08120	−	0.727578i
$775$	4.76919	−	35.6741i	0.171314	−	1.28145i
$776$	1.24622	+	2.15852i	0.0447367	+	0.0774863i
$777$	0.0705810	−	0.132571i	0.00253208	−	0.00475595i
$778$	−13.4162	+	23.2375i	−0.480994	+	0.833106i
$779$	4.24000	+	2.44797i	0.151914	+	0.0877075i
$780$	−1.27943	+	4.22748i	−0.0458111	+	0.151368i
$781$	8.85038	+	0.730851i	0.316692	+	0.0261519i
$782$	63.6955			2.27775
$783$	26.8233	−	19.4220i	0.958588	−	0.694084i
$784$	−4.86281			−0.173672
$785$	−9.82083	+	28.8365i	−0.350520	+	1.02922i
$786$	−1.14239	−	1.83041i	−0.0407478	−	0.0652885i
$787$	−17.2224	+	29.8301i	−0.613913	+	1.06333i	0.376661	+	0.926351i	$0.377072\pi$
$787$	−17.2224	+	29.8301i	−0.613913	+	1.06333i	−0.990574	+	0.136978i	$0.956261\pi$
$788$	8.80524	+	5.08371i	0.313674	+	0.181100i
$789$	13.6479	−	25.6346i	0.485879	−	0.912615i
$790$	11.6712	+	3.97485i	0.415242	+	0.141419i
$791$	5.92610			0.210708
$792$	5.09217	−	8.54809i	0.180942	−	0.303743i
$793$		−	10.6432i		−	0.377950i
$794$	10.7367	+	18.5965i	0.381031	+	0.659964i
$795$	15.4500	+	16.4746i	0.547955	+	0.584294i
$796$	−10.7849	+	18.6800i	−0.382262	+	0.662097i
$797$	−2.21157	+	3.83055i	−0.0783377	+	0.135685i	−0.902533	−	0.430621i	$-0.858295\pi$
$797$	−2.21157	+	3.83055i	−0.0783377	+	0.135685i	0.824195	+	0.566306i	$0.191628\pi$
$798$	0.0830801	+	2.41654i	0.00294100	+	0.0855445i
$799$	−0.883450	+	0.510060i	−0.0312542	+	0.0180446i
$800$	−4.95591	−	0.662545i	−0.175218	−	0.0234245i
$801$	−32.9375	−	16.1088i	−1.16379	−	0.569176i
$802$	4.64150			0.163897
$803$	0.505731	−	6.12425i	0.0178469	−	0.216120i
$804$	−9.67388	+	18.1702i	−0.341171	+	0.640815i
$805$	5.49427	+	27.7667i	0.193648	+	0.978646i
$806$	−7.10931	−	4.10456i	−0.250415	−	0.144577i
$807$	4.89758	+	7.84719i	0.172403	+	0.276234i
$808$	−1.29259	+	0.746276i	−0.0454731	+	0.0262539i
$809$	−22.2674			−0.782880			−0.391440	−	0.920204i	$-0.628023\pi$
$809$	−22.2674			−0.782880			−0.391440	+	0.920204i	$0.628023\pi$
$810$	−3.81621	+	19.7595i	−0.134088	+	0.694277i
$811$			10.8059i			0.379448i	0.981837	+	0.189724i	$0.0607593\pi$
$811$			10.8059i			0.379448i	−0.981837	+	0.189724i	$0.939241\pi$
$812$	−4.65858	−	8.06890i	−0.163484	−	0.283163i
$813$	−1.36589	−	2.18852i	−0.0479039	−	0.0767546i
$814$	−0.177883	+	0.0840063i	−0.00623479	+	0.00294442i
$815$	50.9395	−	10.0795i	1.78433	−	0.353071i
$816$	5.98773	−	11.2466i	0.209612	−	0.393710i
$817$	9.99454	−	5.77035i	0.349665	−	0.201879i
$818$	−3.06129			−0.107035
$819$	2.19742	−	4.49304i	0.0767839	−	0.157000i
$820$	8.62696	−	7.55039i	0.301267	−	0.263671i
$821$	22.2395	+	38.5200i	0.776164	+	1.34436i	0.934138	+	0.356913i	$0.116171\pi$
$821$	22.2395	+	38.5200i	0.776164	+	1.34436i	−0.157974	+	0.987443i	$0.550496\pi$
$822$	−18.3019	+	0.629215i	−0.638351	+	0.0219464i
$823$	−25.0244	−	14.4479i	−0.872297	−	0.503621i	−0.00418628	−	0.999991i	$-0.501333\pi$
$823$	−25.0244	−	14.4479i	−0.872297	−	0.503621i	−0.868111	+	0.496370i	$0.834666\pi$
$824$	1.16512	−	2.01805i	0.0405889	−	0.0703021i
$825$	−21.8845	−	18.6029i	−0.761920	−	0.647671i
$826$	−7.67850	−	13.2996i	−0.267169	−	0.462751i
$827$		−	1.85307i		−	0.0644377i	−0.999481	−	0.0322189i	$-0.989743\pi$
$827$		−	1.85307i		−	0.0644377i	0.999481	−	0.0322189i	$-0.0102574\pi$
$828$	−25.9151	+	1.78402i	−0.900610	+	0.0619989i
$829$	−27.6166			−0.959163			−0.479582	−	0.877497i	$-0.659212\pi$
$829$	−27.6166			−0.959163			−0.479582	+	0.877497i	$0.659212\pi$
$830$	−1.66557	−	0.567243i	−0.0578127	−	0.0196893i
$831$	−26.0122	−	13.8490i	−0.902353	−	0.480415i
$832$	−0.570213	+	0.987638i	−0.0197686	+	0.0342402i
$833$	−30.9791	−	17.8858i	−1.07336	−	0.619707i
$834$	4.93209	−	3.07821i	0.170784	−	0.106590i
$835$	−11.7588	+	34.5269i	−0.406930	+	1.19485i
$836$	1.80392	−	2.60318i	0.0623898	−	0.0900328i
$837$	−34.1450	−	15.2687i	−1.18023	−	0.527764i
$838$	15.0569			0.520133
$839$	13.2197	−	7.63238i	0.456394	−	0.263499i	−0.254133	−	0.967169i	$-0.581790\pi$
$839$	13.2197	−	7.63238i	0.456394	−	0.263499i	0.710527	+	0.703670i	$0.248457\pi$
$840$	5.41921	+	1.64011i	0.186981	+	0.0565890i
$841$	−5.80933	+	10.0621i	−0.200322	+	0.346968i
$842$	−0.0773206	−	0.0446411i	−0.00266464	−	0.00153843i
$843$	35.9503	+	19.1401i	1.23820	+	0.659219i
$844$	0.0962850	−	0.0555901i	0.00331426	−	0.00191349i
$845$	−19.6859	+	17.2293i	−0.677216	+	0.592705i
$846$	0.345153	−	0.232266i	0.0118666	−	0.00798548i
$847$	−5.64710	−	15.0569i	−0.194037	−	0.517361i
$848$	2.91580	+	5.05032i	0.100129	+	0.173429i
$849$	−0.687887	−	20.0084i	−0.0236082	−	0.686688i
$850$	−29.1353	−	22.4491i	−0.999333	−	0.769996i
$851$	0.444779	+	0.256793i	0.0152468	+	0.00880275i
$852$	−4.63496	+	0.159349i	−0.158791	+	0.00545920i
$853$	7.02386	+	12.1657i	0.240493	+	0.416545i	0.960855	−	0.277053i	$-0.0893577\pi$
$853$	7.02386	+	12.1657i	0.240493	+	0.416545i	−0.720362	+	0.693598i	$0.756024\pi$
$854$	−13.6435			−0.466870
$855$	−1.64382	+	6.19131i	−0.0562174	+	0.211738i
$856$	−15.7119			−0.537022
$857$	−36.7764	+	21.2329i	−1.25626	+	0.725302i	−0.972345	−	0.233548i	$-0.924966\pi$
$857$	−36.7764	+	21.2329i	−1.25626	+	0.725302i	−0.283914	+	0.958850i	$0.591633\pi$
$858$	−5.82426	+	2.99948i	−0.198837	+	0.102400i
$859$	21.4247	−	37.1087i	0.731002	−	1.26613i	−0.225454	−	0.974254i	$-0.572386\pi$
$859$	21.4247	−	37.1087i	0.731002	−	1.26613i	0.956456	−	0.291878i	$-0.0942802\pi$
$860$	−5.24560	−	26.5100i	−0.178874	−	0.903982i
$861$	−11.0133	+	6.87358i	−0.375331	+	0.234251i
$862$	30.0220	−	17.3332i	1.02255	−	0.590371i
$863$	−24.7626			−0.842927			−0.421464	−	0.906845i	$-0.638483\pi$
$863$	−24.7626			−0.842927			−0.421464	+	0.906845i	$0.638483\pi$
$864$	−2.12116	+	4.74349i	−0.0721632	+	0.161377i
$865$	−33.9546	−	38.7960i	−1.15449	−	1.31910i
$866$	−3.78001	−	6.54717i	−0.128450	−	0.222482i
$867$	54.5324	−	34.0347i	1.85202	−	1.15588i
$868$	−5.26164	+	9.11342i	−0.178592	+	0.309330i
$869$	7.80936	+	16.5363i	0.264914	+	0.560955i
$870$	−5.62047	−	24.0352i	−0.190552	−	0.814869i
$871$	11.7378	−	6.77683i	0.397721	−	0.229624i
$872$	−14.1259			−0.478362
$873$	−0.513531	−	7.45967i	−0.0173804	−	0.252472i
$874$	−8.26848			−0.279686
$875$	7.27301	−	14.6373i	0.245873	−	0.494832i
$876$	0.110266	+	3.20728i	0.00372553	+	0.108364i
$877$	−4.56759	+	7.91130i	−0.154237	+	0.267146i	−0.932781	−	0.360444i	$-0.882625\pi$
$877$	−4.56759	+	7.91130i	−0.154237	+	0.267146i	0.778544	+	0.627590i	$0.215958\pi$
$878$	−3.15947	+	5.47237i	−0.106627	+	0.184684i
$879$	23.9882	−	0.824708i	0.809100	−	0.0278167i
$880$	−4.40841	−	5.96372i	−0.148608	−	0.201037i
$881$			10.0533i			0.338703i	0.985556	+	0.169352i	$0.0541673\pi$
$881$			10.0533i			0.338703i	−0.985556	+	0.169352i	$0.945833\pi$
$882$	13.1051	+	6.40932i	0.441271	+	0.215813i
$883$			20.9142i			0.703820i	0.936034	+	0.351910i	$0.114468\pi$
$883$			20.9142i			0.703820i	−0.936034	+	0.351910i	$0.885532\pi$
$884$	−7.26522	+	4.19458i	−0.244356	+	0.141079i
$885$	−9.26394	−	39.6160i	−0.311404	−	1.33168i
$886$	−34.8073	−	20.0960i	−1.16937	−	0.675138i
$887$	−2.94687	−	1.70137i	−0.0989461	−	0.0571265i	0.449710	−	0.893174i	$-0.351527\pi$
$887$	−2.94687	−	1.70137i	−0.0989461	−	0.0571265i	−0.548657	+	0.836048i	$0.684861\pi$
$888$	0.0871532	−	0.0543939i	0.00292467	−	0.00182534i
$889$	0.0103518	+	0.0179299i	0.000347189	+	0.000601349i
$890$	−20.5650	+	17.9987i	−0.689341	+	0.603317i
$891$	−24.9898	+	16.3251i	−0.837189	+	0.546913i
$892$		−	10.6863i		−	0.357802i
$893$	0.114683	−	0.0662122i	0.00383772	−	0.00221571i
$894$	−7.12119	−	11.4100i	−0.238168	−	0.381608i
$895$	0.588490	−	0.116446i	0.0196711	−	0.00389237i
$896$	1.26605	+	0.730956i	0.0422959	+	0.0244195i
$897$	15.0972	+	8.03777i	0.504079	+	0.268373i
$898$	4.24813	+	7.35798i	0.141762	+	0.245539i
$899$	45.8767			1.53007
$900$	12.4827	+	8.31755i	0.416091	+	0.277252i
$901$			42.8982i			1.42915i
$902$	16.9468	+	1.39944i	0.564267	+	0.0465963i
$903$	1.05146	+	30.5836i	0.0349904	+	1.01776i
$904$	3.51058	+	2.02683i	0.116760	+	0.0674114i
$905$	−5.53659	−	27.9805i	−0.184043	−	0.930105i
$906$	0.610933	+	17.7701i	0.0202969	+	0.590372i
$907$	−42.1495	+	24.3350i	−1.39955	+	0.808031i	−0.994345	−	0.106195i	$-0.966133\pi$
$907$	−42.1495	+	24.3350i	−1.39955	+	0.808031i	−0.405205	+	0.914226i	$0.632800\pi$
$908$			11.6320i			0.386022i
$909$	4.46708	−	0.307518i	0.148164	−	0.0101997i
$910$	−2.45522	−	2.80530i	−0.0813898	−	0.0929947i
$911$	−8.52046	+	4.91929i	−0.282295	+	0.162983i	−0.634462	−	0.772954i	$-0.718778\pi$
$911$	−8.52046	+	4.91929i	−0.282295	+	0.162983i	0.352167	+	0.935937i	$0.385445\pi$
$912$	−0.777283	+	1.45995i	−0.0257384	+	0.0483439i
$913$	−1.11446	−	2.35986i	−0.0368832	−	0.0780999i
$914$	−9.93297	−	5.73480i	−0.328553	−	0.189690i
$915$	−34.5954	−	10.4702i	−1.14369	−	0.346134i
$916$	6.26887	+	10.8580i	0.207129	+	0.358759i
$917$	1.82113			0.0601391
$918$	−30.9600	+	22.4172i	−1.02183	+	0.739878i
$919$			56.9449i			1.87844i	0.343317	+	0.939219i	$0.388449\pi$
$919$			56.9449i			1.87844i	−0.343317	+	0.939219i	$0.611551\pi$
$920$	−6.24193	+	18.3279i	−0.205790	+	0.604253i
$921$	−12.3710	+	7.72096i	−0.407638	+	0.254414i
$922$	−25.7603	−	14.8727i	−0.848369	−	0.489806i
$923$	2.64447	+	1.52679i	0.0870439	+	0.0502548i
$924$	3.84503	+	7.46611i	0.126492	+	0.245617i
$925$	−0.112944	−	0.274220i	−0.00371357	−	0.00901631i
$926$	9.34010			0.306935
$927$	−5.79980	+	3.90290i	−0.190490	+	0.128188i
$928$		−	6.37328i		−	0.209213i
$929$	28.7309	−	16.5878i	0.942630	−	0.544228i	0.0518461	−	0.998655i	$-0.483489\pi$
$929$	28.7309	−	16.5878i	0.942630	−	0.544228i	0.890784	+	0.454428i	$0.150156\pi$
$930$	−20.3356	+	19.0708i	−0.666829	+	0.625357i
$931$	4.02149	+	2.32181i	0.131799	+	0.0760941i
$932$	−18.0904	−	10.4445i	−0.592571	−	0.342121i
$933$	−20.4412	+	0.702766i	−0.669216	+	0.0230075i
$934$	−16.8836	+	9.74777i	−0.552449	+	0.318957i
$935$	−6.14930	−	54.2071i	−0.201103	−	1.77276i
$936$	2.83843	−	1.91009i	0.0927771	−	0.0624332i
$937$	−49.3597			−1.61251			−0.806256	−	0.591567i	$-0.798509\pi$
$937$	−49.3597			−1.61251			−0.806256	+	0.591567i	$0.798509\pi$
$938$	−8.68722	−	15.0467i	−0.283648	−	0.491292i
$939$	−6.42988	+	12.0771i	−0.209831	+	0.394121i
$940$	−0.0601910	−	0.304190i	−0.00196321	−	0.00992159i
$941$	−21.1192	+	36.5795i	−0.688465	+	1.19246i	0.283869	+	0.958863i	$0.408382\pi$
$941$	−21.1192	+	36.5795i	−0.688465	+	1.19246i	−0.972334	+	0.233593i	$0.924952\pi$
$942$	20.0177	−	12.4934i	0.652212	−	0.407057i
$943$	−22.1970	−	38.4463i	−0.722834	−	1.25199i
$944$		−	10.5047i		−	0.341900i
$945$	−12.4429	−	11.5627i	−0.404766	−	0.376134i
$946$	22.8303	−	32.9458i	0.742278	−	1.07116i
$947$	−9.50351	−	16.4606i	−0.308823	−	0.534896i	0.669283	−	0.743008i	$-0.266602\pi$
$947$	−9.50351	−	16.4606i	−0.308823	−	0.534896i	−0.978105	+	0.208112i	$0.933268\pi$
$948$	−5.05655	−	8.10190i	−0.164229	−	0.263138i
$949$	1.05650	−	1.82991i	0.0342954	−	0.0594014i
$950$	3.78214	+	2.91417i	0.122709	+	0.0945482i
$951$	−33.0322	−	17.5865i	−1.07114	−	0.570280i
$952$	5.37703	+	9.31329i	0.174270	+	0.301845i
$953$		−	4.95060i		−	0.160366i	−0.996780	−	0.0801828i	$-0.974450\pi$
$953$		−	4.95060i		−	0.160366i	0.996780	−	0.0801828i	$-0.0255504\pi$
$954$	−1.20152	−	17.4535i	−0.0389005	−	0.565078i
$955$	−9.39500	−	10.7346i	−0.304015	−	0.347363i
$956$	11.2009	+	19.4006i	0.362265	+	0.627461i
$957$	19.8069	−	30.7913i	0.640265	−	0.995341i
$958$	23.6817	+	13.6727i	0.765122	+	0.441744i
$959$	7.72828	−	13.3858i	0.249559	−	0.432249i
$960$	2.64935	+	2.82505i	0.0855075	+	0.0911782i
$961$	−10.4077	−	18.0267i	−0.335733	−	0.581507i
$962$	−0.0676430			−0.00218090
$963$	42.3430	+	20.7087i	1.36448	+	0.667329i
$964$		−	25.0596i		−	0.807117i
$965$	55.9601	+	19.0583i	1.80142	+	0.613509i
$966$	10.3036	−	19.3530i	0.331513	−	0.622674i
$967$	13.3319	−	23.0916i	0.428726	−	0.742575i	−0.568035	−	0.823005i	$-0.692296\pi$
$967$	13.3319	−	23.0916i	0.428726	−	0.742575i	0.996760	+	0.0804301i	$0.0256294\pi$
$968$	1.80442	−	10.8510i	0.0579963	−	0.348764i
$969$	−10.3216	+	6.44190i	−0.331578	+	0.206944i
$970$	−5.27570	−	1.79675i	−0.169393	−	0.0576900i
$971$			0.621197i			0.0199351i	0.999950	+	0.00996757i	$0.00317283\pi$
$971$			0.621197i			0.0199351i	−0.999950	+	0.00996757i	$0.996827\pi$
$972$	11.9685	−	9.98777i	0.383889	−	0.320358i
$973$			4.90709i			0.157314i
$974$	1.10315	+	1.91071i	0.0353471	+	0.0612231i
$975$	−4.07282	−	8.99750i	−0.130435	−	0.288150i
$976$	−8.08229	−	4.66631i	−0.258708	−	0.149365i
$977$	−3.65941	+	6.33829i	−0.117075	+	0.202780i	−0.918607	−	0.395172i	$-0.870685\pi$
$977$	−3.65941	+	6.33829i	−0.117075	+	0.202780i	0.801532	+	0.597951i	$0.204018\pi$
$978$	−35.5042	−	18.9026i	−1.13530	−	0.604437i
$979$	−40.3979	−	3.33600i	−1.29112	−	0.106619i
$980$	8.18236	−	7.16127i	0.261376	−	0.228758i
$981$	38.0686	+	18.6182i	1.21544	+	0.594435i
$982$			20.9744i			0.669319i
$983$	5.72046	+	9.90812i	0.182454	+	0.316020i	0.942716	−	0.333597i	$-0.108263\pi$
$983$	5.72046	+	9.90812i	0.182454	+	0.316020i	−0.760262	+	0.649617i	$0.774929\pi$
$984$	−8.87506	+	0.305123i	−0.282926	+	0.00972696i
$985$	−22.3026	+	4.41308i	−0.710620	+	0.140613i
$986$	23.4414	−	40.6017i	0.746527	−	1.29302i
$987$	0.0120650	+	0.350934i	0.000384034	+	0.0111703i
$988$	0.943118	−	0.544509i	0.0300046	−	0.0173231i
$989$	−104.646			−3.32754
$990$	4.02015	+	21.8824i	0.127769	+	0.695468i
$991$	43.0732			1.36826			0.684132	−	0.729358i	$-0.260181\pi$
$991$	43.0732			1.36826			0.684132	+	0.729358i	$0.260181\pi$
$992$	−6.23391	+	3.59915i	−0.197927	+	0.114273i
$993$	−17.1782	−	9.14575i	−0.545135	−	0.290231i
$994$	1.95719	−	3.38995i	0.0620782	−	0.107523i
$995$	−9.36222	−	47.3143i	−0.296802	−	1.49996i
$996$	0.721609	+	1.15621i	0.0228651	+	0.0366358i
$997$	19.0820	+	33.0509i	0.604332	+	1.04673i	0.992157	+	0.125000i	$0.0398932\pi$
$997$	19.0820	+	33.0509i	0.604332	+	1.04673i	−0.387825	+	0.921733i	$0.626774\pi$
$998$			32.4548i			1.02734i
$999$	−0.306567	+	0.0317192i	−0.00969935	+	0.00100355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.7	✓	144
5.4	even	2	inner	990.2.o.a.329.66	yes	144
9.2	odd	6	inner	990.2.o.a.659.30	yes	144
11.10	odd	2	inner	990.2.o.a.329.43	yes	144
45.29	odd	6	inner	990.2.o.a.659.43	yes	144
55.54	odd	2	inner	990.2.o.a.329.30	yes	144
99.65	even	6	inner	990.2.o.a.659.66	yes	144
495.164	even	6	inner	990.2.o.a.659.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.7	✓	144	1.1	even	1	trivial
990.2.o.a.329.30	yes	144	55.54	odd	2	inner
990.2.o.a.329.43	yes	144	11.10	odd	2	inner
990.2.o.a.329.66	yes	144	5.4	even	2	inner
990.2.o.a.659.7	yes	144	495.164	even	6	inner
990.2.o.a.659.30	yes	144	9.2	odd	6	inner
990.2.o.a.659.43	yes	144	45.29	odd	6	inner
990.2.o.a.659.66	yes	144	99.65	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.46936 + 0.917053i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.434042 + 2.19354i) q^{5} +(0.813975 - 1.52887i) q^{6} +(0.730956 + 1.26605i) q^{7} +1.00000i q^{8} +(1.31803 - 2.69496i) q^{9} +(-1.47266 - 1.68264i) q^{10} +(0.272953 - 3.30537i) q^{11} +(0.0595124 + 1.73103i) q^{12} +(0.570213 - 0.987638i) q^{13} +(-1.26605 - 0.730956i) q^{14} +(-2.64935 - 2.82505i) q^{15} +(-0.500000 - 0.866025i) q^{16} -7.35616i q^{17} +(0.206035 + 2.99292i) q^{18} +0.954923i q^{19} +(2.11668 + 0.720878i) q^{20} +(-2.23507 - 1.18996i) q^{21} +(1.41630 + 2.99901i) q^{22} +(4.32940 - 7.49874i) q^{23} +(-0.917053 - 1.46936i) q^{24} +(-4.62322 + 1.90417i) q^{25} +1.14043i q^{26} +(0.534769 + 5.16856i) q^{27} +1.46191 q^{28} +(-3.18664 - 5.51942i) q^{29} +(3.70693 + 1.12189i) q^{30} +(-3.59915 + 6.23391i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.63014 + 5.10709i) q^{33} +(3.67808 + 6.37062i) q^{34} +(-2.45987 + 2.15290i) q^{35} +(-1.67489 - 2.48892i) q^{36} +0.0593138i q^{37} +(-0.477461 - 0.826988i) q^{38} +(0.0678695 + 1.97411i) q^{39} +(-2.19354 + 0.434042i) q^{40} +(2.56352 - 4.44015i) q^{41} +(2.53061 - 0.0870019i) q^{42} +(-6.04274 - 10.4663i) q^{43} +(-2.72606 - 1.88907i) q^{44} +(6.48357 + 1.72142i) q^{45} +8.65879i q^{46} +(-0.0693378 - 0.120097i) q^{47} +(1.52887 + 0.813975i) q^{48} +(2.43141 - 4.21132i) q^{49} +(3.05174 - 3.96067i) q^{50} +(6.74599 + 10.8088i) q^{51} +(-0.570213 - 0.987638i) q^{52} -5.83161 q^{53} +(-3.04740 - 4.20872i) q^{54} +(7.36894 - 0.835938i) q^{55} +(-1.26605 + 0.730956i) q^{56} +(-0.875715 - 1.40312i) q^{57} +(5.51942 + 3.18664i) q^{58} +(9.09738 + 5.25237i) q^{59} +(-3.77124 + 0.881881i) q^{60} +(8.08229 - 4.66631i) q^{61} -7.19830i q^{62} +(4.37538 - 0.301206i) q^{63} -1.00000 q^{64} +(2.41392 + 0.822107i) q^{65} +(-4.83131 - 3.10780i) q^{66} +(10.2925 + 5.94237i) q^{67} +(-6.37062 - 3.67808i) q^{68} +(0.515306 + 14.9886i) q^{69} +(1.05386 - 3.09440i) q^{70} +2.67757i q^{71} +(2.69496 + 1.31803i) q^{72} +1.85282 q^{73} +(-0.0296569 - 0.0513673i) q^{74} +(5.04693 - 7.03765i) q^{75} +(0.826988 + 0.477461i) q^{76} +(4.38429 - 2.07051i) q^{77} +(-1.04583 - 1.67569i) q^{78} +(-4.77518 + 2.75695i) q^{79} +(1.68264 - 1.47266i) q^{80} +(-5.52561 - 7.10406i) q^{81} +5.12704i q^{82} +(0.681456 - 0.393439i) q^{83} +(-2.14807 + 1.34065i) q^{84} +(16.1360 - 3.19288i) q^{85} +(10.4663 + 6.04274i) q^{86} +(9.74392 + 5.18769i) q^{87} +(3.30537 + 0.272953i) q^{88} -12.2219i q^{89} +(-6.47565 + 1.75100i) q^{90} +1.66720 q^{91} +(-4.32940 - 7.49874i) q^{92} +(-0.428388 - 12.4605i) q^{93} +(0.120097 + 0.0693378i) q^{94} +(-2.09466 + 0.414476i) q^{95} +(-1.73103 + 0.0595124i) q^{96} +(2.15852 - 1.24622i) q^{97} +4.86281i q^{98} +(-8.54809 - 5.09217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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