LMFDB - Embedded newform 819.2.db.a.209.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(209,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.db (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$96$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.14
Character	$\chi$	$=$	819.209
Dual form			819.2.db.a.482.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86466 - 1.07656i) q^{2} +(1.44952 - 0.948095i) q^{3} +(1.31797 + 2.28279i) q^{4} +(1.11192 + 1.92591i) q^{5} +(-3.72355 + 0.207373i) q^{6} +(-2.49537 + 0.879275i) q^{7} -1.36926i q^{8} +(1.20223 - 2.74857i) q^{9} -4.78822i q^{10} +(-4.06985 - 2.34973i) q^{11} +(4.07473 + 2.05940i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(5.59961 + 1.04687i) q^{14} +(3.43770 + 1.73744i) q^{15} +(1.16185 - 2.01238i) q^{16} -3.36629 q^{17} +(-5.20076 + 3.83087i) q^{18} +0.00383473i q^{19} +(-2.93097 + 5.07658i) q^{20} +(-2.78346 + 3.64038i) q^{21} +(5.05926 + 8.76289i) q^{22} +(0.381370 - 0.220184i) q^{23} +(-1.29819 - 1.98477i) q^{24} +(0.0272490 - 0.0471966i) q^{25} +2.15312 q^{26} +(-0.863241 - 5.12395i) q^{27} +(-5.29603 - 4.53755i) q^{28} +(-8.07506 - 4.66214i) q^{29} +(-4.53969 - 6.94063i) q^{30} +(3.76093 - 2.17137i) q^{31} +(-6.70453 + 3.87086i) q^{32} +(-8.12711 + 0.452618i) q^{33} +(6.27699 + 3.62402i) q^{34} +(-4.46807 - 3.82817i) q^{35} +(7.85892 - 0.878087i) q^{36} -6.02534 q^{37} +(0.00412832 - 0.00715046i) q^{38} +(-0.781276 + 1.54584i) q^{39} +(2.63707 - 1.52251i) q^{40} +(-4.88387 - 8.45911i) q^{41} +(9.10930 - 3.79150i) q^{42} +(4.15883 - 7.20331i) q^{43} -12.3875i q^{44} +(6.63029 - 0.740810i) q^{45} -0.948166 q^{46} +(-3.00173 + 5.19915i) q^{47} +(-0.223802 - 4.01853i) q^{48} +(5.45375 - 4.38823i) q^{49} +(-0.101620 + 0.0586704i) q^{50} +(-4.87952 + 3.19157i) q^{51} +(-2.28279 - 1.31797i) q^{52} -0.750786i q^{53} +(-3.90659 + 10.4837i) q^{54} -10.4509i q^{55} +(1.20396 + 3.41681i) q^{56} +(0.00363568 + 0.00555852i) q^{57} +(10.0382 + 17.3866i) q^{58} +(-5.22720 - 9.05377i) q^{59} +(0.564579 + 10.1375i) q^{60} +(-2.32694 - 1.34346i) q^{61} -9.35047 q^{62} +(-0.583269 + 7.91579i) q^{63} +12.0215 q^{64} +(-1.92591 - 1.11192i) q^{65} +(15.6416 + 7.90535i) q^{66} +(6.45287 + 11.1767i) q^{67} +(-4.43668 - 7.68455i) q^{68} +(0.344049 - 0.680736i) q^{69} +(4.21016 + 11.9484i) q^{70} +13.9073i q^{71} +(-3.76351 - 1.64617i) q^{72} -10.3225i q^{73} +(11.2352 + 6.48666i) q^{74} +(-0.00524885 - 0.0942472i) q^{75} +(-0.00875388 + 0.00505406i) q^{76} +(12.2218 + 2.28493i) q^{77} +(3.12100 - 2.04137i) q^{78} +(-6.88967 + 11.9333i) q^{79} +5.16755 q^{80} +(-6.10927 - 6.60884i) q^{81} +21.0312i q^{82} +(6.53796 - 11.3241i) q^{83} +(-11.9787 - 1.55615i) q^{84} +(-3.74306 - 6.48318i) q^{85} +(-15.5096 + 8.95448i) q^{86} +(-16.1251 + 0.898046i) q^{87} +(-3.21739 + 5.57268i) q^{88} -8.85482 q^{89} +(-13.1608 - 5.75656i) q^{90} +(1.72142 - 2.00916i) q^{91} +(1.00527 + 0.580392i) q^{92} +(3.39289 - 6.71317i) q^{93} +(11.1944 - 6.46309i) q^{94} +(-0.00738534 + 0.00426393i) q^{95} +(-6.04843 + 11.9674i) q^{96} +(7.62278 + 4.40101i) q^{97} +(-14.8936 + 2.31126i) q^{98} +(-11.3513 + 8.36135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 96 q^{4} + 8 q^{9} + 18 q^{14} + 12 q^{15} - 96 q^{16} + 20 q^{18} + 22 q^{21} - 36 q^{23} - 96 q^{25} - 72 q^{29} - 52 q^{30} + 60 q^{32} - 12 q^{36} - 78 q^{42} + 48 q^{46} - 12 q^{49} + 96 q^{50}+ \cdots + 28 q^{99}+O(q^{100}) $ 192 * q + 96 * q^4 + 8 * q^9 + 18 * q^14 + 12 * q^15 - 96 * q^16 + 20 * q^18 + 22 * q^21 - 36 * q^23 - 96 * q^25 - 72 * q^29 - 52 * q^30 + 60 * q^32 - 12 * q^36 - 78 * q^42 + 48 * q^46 - 12 * q^49 + 96 * q^50 + 44 * q^51 - 60 * q^56 + 28 * q^57 - 24 * q^58 + 112 * q^60 - 68 * q^63 - 192 * q^64 + 56 * q^72 + 90 * q^77 - 20 * q^78 + 24 * q^79 - 32 * q^81 + 66 * q^84 + 60 * q^86 - 84 * q^92 - 116 * q^93 - 96 * q^95 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	−1.86466	−	1.07656i	−1.31851	−	0.761244i	−0.335024	−	0.942210i	$-0.608744\pi$
$2$	−1.86466	−	1.07656i	−1.31851	−	0.761244i	−0.983489	+	0.180965i	$0.942078\pi$
$3$	1.44952	−	0.948095i	0.836882	−	0.547383i
$3$	1.44952	−	0.948095i	0.836882	−	0.547383i
$4$	1.31797	+	2.28279i	0.658985	+	1.14140i
$5$	1.11192	+	1.92591i	0.497268	+	0.861293i	0.999995	−	0.00315219i	$-0.00100338\pi$
$5$	1.11192	+	1.92591i	0.497268	+	0.861293i	−0.502727	+	0.864445i	$0.667670\pi$
$6$	−3.72355	+	0.207373i	−1.52013	+	0.0846598i
$7$	−2.49537	+	0.879275i	−0.943162	+	0.332335i
$7$	−2.49537	+	0.879275i	−0.943162	+	0.332335i
$8$		−	1.36926i		−	0.484106i
$9$	1.20223	−	2.74857i	0.400744	−	0.916190i
$10$		−	4.78822i		−	1.51417i
$11$	−4.06985	−	2.34973i	−1.22711	−	0.708470i	−0.260682	−	0.965425i	$-0.583948\pi$
$11$	−4.06985	−	2.34973i	−1.22711	−	0.708470i	−0.966423	+	0.256955i	$0.917281\pi$
$12$	4.07473	+	2.05940i	1.17627	+	0.594497i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i
$14$	5.59961	+	1.04687i	1.49656	+	0.279789i
$15$	3.43770	+	1.73744i	0.887611	+	0.448605i
$16$	1.16185	−	2.01238i	0.290462	−	0.503095i
$17$	−3.36629			−0.816446			−0.408223	−	0.912882i	$-0.633851\pi$
$17$	−3.36629			−0.816446			−0.408223	+	0.912882i	$0.633851\pi$
$18$	−5.20076	+	3.83087i	−1.22583	+	0.902945i
$19$			0.00383473i			0.000879747i	1.00000		0.000439873i	$0.000140016\pi$
$19$			0.00383473i			0.000879747i	−1.00000		0.000439873i	$0.999860\pi$
$20$	−2.93097	+	5.07658i	−0.655384	+	1.13516i
$21$	−2.78346	+	3.64038i	−0.607401	+	0.794395i
$22$	5.05926	+	8.76289i	1.07864	+	1.86825i
$23$	0.381370	−	0.220184i	0.0795210	−	0.0459115i	−0.459712	−	0.888068i	$-0.652047\pi$
$23$	0.381370	−	0.220184i	0.0795210	−	0.0459115i	0.539233	+	0.842156i	$0.318714\pi$
$24$	−1.29819	−	1.98477i	−0.264992	−	0.405140i
$25$	0.0272490	−	0.0471966i	0.00544980	−	0.00943932i
$26$	2.15312			0.422262
$27$	−0.863241	−	5.12395i	−0.166131	−	0.986104i
$28$	−5.29603	−	4.53755i	−1.00085	−	0.857517i
$29$	−8.07506	−	4.66214i	−1.49950	−	0.865737i	−0.499501	−	0.866313i	$-0.666483\pi$
$29$	−8.07506	−	4.66214i	−1.49950	−	0.865737i	−1.00000		0.000576132i	$0.999817\pi$
$30$	−4.53969	−	6.94063i	−0.828830	−	1.26718i
$31$	3.76093	−	2.17137i	0.675483	−	0.389990i	−0.122668	−	0.992448i	$-0.539145\pi$
$31$	3.76093	−	2.17137i	0.675483	−	0.389990i	0.798151	+	0.602458i	$0.205812\pi$
$32$	−6.70453	+	3.87086i	−1.18520	+	0.684278i
$33$	−8.12711	+	0.452618i	−1.41475	+	0.0787906i
$34$	6.27699	+	3.62402i	1.07650	+	0.621515i
$35$	−4.46807	−	3.82817i	−0.755241	−	0.647079i
$36$	7.85892	−	0.878087i	1.30982	−	0.146348i
$37$	−6.02534			−0.990561			−0.495280	−	0.868733i	$-0.664935\pi$
$37$	−6.02534			−0.990561			−0.495280	+	0.868733i	$0.664935\pi$
$38$	0.00412832	−	0.00715046i	0.000669702	−	0.00115996i
$39$	−0.781276	+	1.54584i	−0.125104	+	0.247532i
$40$	2.63707	−	1.52251i	0.416957	−	0.240730i
$41$	−4.88387	−	8.45911i	−0.762732	−	1.32109i	−0.941437	−	0.337188i	$-0.890524\pi$
$41$	−4.88387	−	8.45911i	−0.762732	−	1.32109i	0.178705	−	0.983903i	$-0.442809\pi$
$42$	9.10930	−	3.79150i	1.40560	−	0.585040i
$43$	4.15883	−	7.20331i	0.634216	−	1.09849i	−0.352465	−	0.935825i	$-0.614656\pi$
$43$	4.15883	−	7.20331i	0.634216	−	1.09849i	0.986681	−	0.162669i	$-0.0520102\pi$
$44$		−	12.3875i		−	1.86748i
$45$	6.63029	−	0.740810i	0.988385	−	0.110433i
$46$	−0.948166			−0.139799
$47$	−3.00173	+	5.19915i	−0.437847	+	0.758374i	−0.997523	−	0.0703379i	$-0.977592\pi$
$47$	−3.00173	+	5.19915i	−0.437847	+	0.758374i	0.559676	+	0.828711i	$0.310926\pi$
$48$	−0.223802	−	4.01853i	−0.0323030	−	0.580025i
$49$	5.45375	−	4.38823i	0.779107	−	0.626890i
$50$	−0.101620	+	0.0586704i	−0.0143713	+	0.00829725i
$51$	−4.87952	+	3.19157i	−0.683269	+	0.446909i
$52$	−2.28279	−	1.31797i	−0.316566	−	0.182770i
$53$		−	0.750786i		−	0.103128i	−0.998670	−	0.0515642i	$-0.983579\pi$
$53$		−	0.750786i		−	0.103128i	0.998670	−	0.0515642i	$-0.0164207\pi$
$54$	−3.90659	+	10.4837i	−0.531620	+	1.42666i
$55$		−	10.4509i		−	1.40920i
$56$	1.20396	+	3.41681i	0.160885	+	0.456591i
$57$	0.00363568	+	0.00555852i	0.000481558	+	0.000736244i
$58$	10.0382	+	17.3866i	1.31807	+	2.28297i
$59$	−5.22720	−	9.05377i	−0.680523	−	1.17870i	−0.974821	−	0.222987i	$-0.928419\pi$
$59$	−5.22720	−	9.05377i	−0.680523	−	1.17870i	0.294298	−	0.955714i	$-0.404914\pi$
$60$	0.564579	+	10.1375i	0.0728868	+	1.30874i
$61$	−2.32694	−	1.34346i	−0.297934	−	0.172012i	0.343581	−	0.939123i	$-0.388360\pi$
$61$	−2.32694	−	1.34346i	−0.297934	−	0.172012i	−0.641514	+	0.767111i	$0.721693\pi$
$62$	−9.35047			−1.18751
$63$	−0.583269	+	7.91579i	−0.0734850	+	0.997296i
$64$	12.0215			1.50269
$65$	−1.92591	−	1.11192i	−0.238880	−	0.137917i
$66$	15.6416	+	7.90535i	1.92534	+	0.973082i
$67$	6.45287	+	11.1767i	0.788343	+	1.36545i	0.926981	+	0.375107i	$0.122394\pi$
$67$	6.45287	+	11.1767i	0.788343	+	1.36545i	−0.138638	+	0.990343i	$0.544272\pi$
$68$	−4.43668	−	7.68455i	−0.538026	−	0.931888i
$69$	0.344049	−	0.680736i	0.0414186	−	0.0819510i
$70$	4.21016	+	11.9484i	0.503210	+	1.42811i
$71$			13.9073i			1.65050i	0.564769	+	0.825249i	$0.308965\pi$
$71$			13.9073i			1.65050i	−0.564769	+	0.825249i	$0.691035\pi$
$72$	−3.76351	−	1.64617i	−0.443533	−	0.194003i
$73$		−	10.3225i		−	1.20816i	−0.796923	−	0.604081i	$-0.793540\pi$
$73$		−	10.3225i		−	1.20816i	0.796923	−	0.604081i	$-0.206460\pi$
$74$	11.2352	+	6.48666i	1.30607	+	0.754058i
$75$	−0.00524885	−	0.0942472i	−0.000606085	−	0.0108827i
$76$	−0.00875388	+	0.00505406i	−0.00100414	+	0.000579740i
$77$	12.2218	+	2.28493i	1.39281	+	0.260392i
$78$	3.12100	−	2.04137i	0.353384	−	0.231139i
$79$	−6.88967	+	11.9333i	−0.775148	+	1.34260i	0.159563	+	0.987188i	$0.448991\pi$
$79$	−6.88967	+	11.9333i	−0.775148	+	1.34260i	−0.934711	+	0.355408i	$0.884342\pi$
$80$	5.16755			0.577750
$81$	−6.10927	−	6.60884i	−0.678808	−	0.734316i
$82$			21.0312i			2.32250i
$83$	6.53796	−	11.3241i	0.717635	−	1.24298i	−0.244300	−	0.969700i	$-0.578558\pi$
$83$	6.53796	−	11.3241i	0.717635	−	1.24298i	0.961934	−	0.273280i	$-0.0881086\pi$
$84$	−11.9787	−	1.55615i	−1.30699	−	0.169790i
$85$	−3.74306	−	6.48318i	−0.405992	−	0.703199i
$86$	−15.5096	+	8.95448i	−1.67244	+	0.965586i
$87$	−16.1251	+	0.898046i	−1.72880	+	0.0962807i
$88$	−3.21739	+	5.57268i	−0.342975	+	0.594050i
$89$	−8.85482			−0.938609			−0.469305	−	0.883036i	$-0.655495\pi$
$89$	−8.85482			−0.938609			−0.469305	+	0.883036i	$0.655495\pi$
$90$	−13.1608	−	5.75656i	−1.38727	−	0.606794i
$91$	1.72142	−	2.00916i	0.180454	−	0.210617i
$92$	1.00527	+	0.580392i	0.104806	+	0.0605100i
$93$	3.39289	−	6.71317i	0.351826	−	0.696124i
$94$	11.1944	−	6.46309i	1.15461	−	0.666617i
$95$	−0.00738534	+	0.00426393i	−0.000757719	+	0.000437470i
$96$	−6.04843	+	11.9674i	−0.617315	+	1.22142i
$97$	7.62278	+	4.40101i	0.773976	+	0.446855i	0.834291	−	0.551324i	$-0.185877\pi$
$97$	7.62278	+	4.40101i	0.773976	+	0.446855i	−0.0603150	+	0.998179i	$0.519211\pi$
$98$	−14.8936	+	2.31126i	−1.50448	+	0.233472i
$99$	−11.3513	+	8.36135i	−1.14085	+	0.840347i
$100$	0.143653			0.0143653
$101$	−1.40591	+	2.43510i	−0.139893	+	0.242302i	−0.927456	−	0.373932i	$-0.878009\pi$
$101$	−1.40591	+	2.43510i	−0.139893	+	0.242302i	0.787563	+	0.616234i	$0.211343\pi$
$102$	12.5346	−	0.698079i	1.24111	−	0.0691201i
$103$	−10.2099	+	5.89469i	−1.00601	+	0.580821i	−0.910021	−	0.414561i	$-0.863935\pi$
$103$	−10.2099	+	5.89469i	−1.00601	+	0.580821i	−0.0959900	+	0.995382i	$0.530602\pi$
$104$	0.684630	+	1.18581i	0.0671335	+	0.116279i
$105$	−10.1060	−	1.31287i	−0.986248	−	0.128123i
$106$	−0.808268	+	1.39996i	−0.0785059	+	0.135976i
$107$			14.3631i			1.38854i	0.719716	+	0.694268i	$0.244272\pi$
$107$			14.3631i			1.38854i	−0.719716	+	0.694268i	$0.755728\pi$
$108$	10.5592	−	8.72381i	1.01606	−	0.839449i
$109$	−5.07639			−0.486230			−0.243115	−	0.969998i	$-0.578169\pi$
$109$	−5.07639			−0.486230			−0.243115	+	0.969998i	$0.578169\pi$
$110$	−11.2510	+	19.4873i	−1.07274	+	1.85804i
$111$	−8.73387	+	5.71260i	−0.828983	+	0.542216i
$112$	−1.12981	+	6.04322i	−0.106757	+	0.571031i
$113$	4.07064	−	2.35019i	0.382934	−	0.221087i	−0.296160	−	0.955138i	$-0.595706\pi$
$113$	4.07064	−	2.35019i	0.382934	−	0.221087i	0.679094	+	0.734051i	$0.262373\pi$
$114$	−0.000795220	−	0.0142788i	−7.44791e−5	−	0.00133733i
$115$	0.848108	+	0.489655i	0.0790865	+	0.0456606i
$116$		−	24.5782i		−	2.28203i
$117$	0.333121	+	2.98145i	0.0307970	+	0.275635i
$118$			22.5096i			2.07218i
$119$	8.40015	−	2.95990i	0.770041	−	0.271333i
$120$	2.37901	−	4.70711i	0.217173	−	0.429698i
$121$	5.54245	+	9.59981i	0.503859	+	0.872710i
$122$	2.89263	+	5.01018i	0.261886	+	0.453600i
$123$	−15.0993	−	7.63130i	−1.36146	−	0.688091i
$124$	9.91359	+	5.72361i	0.890267	+	0.513996i
$125$	11.2404			1.00538
$126$	9.60944	−	14.1323i	0.856077	−	1.25901i
$127$	−0.498157			−0.0442043			−0.0221022	−	0.999756i	$-0.507036\pi$
$127$	−0.498157			−0.0442043			−0.0221022	+	0.999756i	$0.507036\pi$
$128$	−9.00694	−	5.20016i	−0.796109	−	0.459634i
$129$	−0.801097	−	14.3843i	−0.0705326	−	1.26647i
$130$	2.39411	+	4.14672i	0.209977	+	0.363691i
$131$	5.13685	+	8.89728i	0.448808	+	0.777359i	0.998309	−	0.0581346i	$-0.0185152\pi$
$131$	5.13685	+	8.89728i	0.448808	+	0.777359i	−0.549500	+	0.835493i	$0.685182\pi$
$132$	−11.7445	−	17.9560i	−1.02223	−	1.56287i
$133$	−0.00337178	−	0.00956907i	−0.000292370	−	0.000829743i
$134$		−	27.7876i		−	2.40049i
$135$	8.90840	−	7.35996i	0.766713	−	0.633445i
$136$			4.60933i			0.395247i
$137$	−0.552499	−	0.318986i	−0.0472032	−	0.0272528i	0.476213	−	0.879330i	$-0.342009\pi$
$137$	−0.552499	−	0.318986i	−0.0472032	−	0.0272528i	−0.523416	+	0.852077i	$0.675343\pi$
$138$	−1.37439	+	0.898951i	−0.116996	+	0.0765238i
$139$	6.77020	−	3.90877i	0.574241	−	0.331538i	−0.184601	−	0.982814i	$-0.559099\pi$
$139$	6.77020	−	3.90877i	0.574241	−	0.331538i	0.758841	+	0.651276i	$0.225766\pi$
$140$	2.85014	−	15.2451i	0.240881	−	1.28844i
$141$	0.578209	+	10.3822i	0.0486940	+	0.874339i
$142$	14.9721	−	25.9325i	1.25643	−	2.17620i
$143$	4.69946			0.392988
$144$	−4.13436	−	5.61277i	−0.344530	−	0.467731i
$145$		−	20.7358i		−	1.72201i
$146$	−11.1129	+	19.2480i	−0.919707	+	1.59298i
$147$	3.74488	−	11.5315i	0.308872	−	0.951104i
$148$	−7.94123	−	13.7546i	−0.652765	−	1.13062i
$149$	−8.77493	+	5.06621i	−0.718870	+	0.415040i	−0.814337	−	0.580393i	$-0.802899\pi$
$149$	−8.77493	+	5.06621i	−0.718870	+	0.415040i	0.0954666	+	0.995433i	$0.469566\pi$
$150$	−0.0916756	+	0.181390i	−0.00748528	+	0.0148104i
$151$	−3.75744	+	6.50807i	−0.305776	+	0.529620i	−0.977434	−	0.211242i	$-0.932249\pi$
$151$	−3.75744	+	6.50807i	−0.305776	+	0.529620i	0.671658	+	0.740862i	$0.265583\pi$
$152$	0.00525074			0.000425891
$153$	−4.04707	+	9.25249i	−0.327186	+	0.748020i
$154$	−20.3297	−	17.4182i	−1.63821	−	1.40360i
$155$	8.36374	+	4.82881i	0.671792	+	0.387859i
$156$	−4.55852	+	0.253875i	−0.364974	+	0.0203262i
$157$	0.238198	−	0.137524i	0.0190103	−	0.0109756i	−0.490465	−	0.871461i	$-0.663173\pi$
$157$	0.238198	−	0.137524i	0.0190103	−	0.0109756i	0.509475	+	0.860485i	$0.329840\pi$
$158$	25.6938	−	14.8343i	2.04409	−	1.18015i
$159$	−0.711817	−	1.08828i	−0.0564507	−	0.0863064i
$160$	−14.9099	−	8.60821i	−1.17873	−	0.680539i
$161$	−0.758056	+	0.884769i	−0.0597432	+	0.0697295i
$162$	4.27689	+	18.9002i	0.336024	+	1.48494i
$163$	8.65590			0.677982			0.338991	−	0.940790i	$-0.389914\pi$
$163$	8.65590			0.677982			0.338991	+	0.940790i	$0.389914\pi$
$164$	12.8736	−	22.2977i	1.00526	−	1.74116i
$165$	−9.90843	−	15.1488i	−0.771370	−	1.17933i
$166$	−24.3822	+	14.0770i	−1.89242	+	1.09259i
$167$	9.90700	+	17.1594i	0.766627	+	1.32784i	0.939382	+	0.342872i	$0.111400\pi$
$167$	9.90700	+	17.1594i	0.766627	+	1.32784i	−0.172756	+	0.984965i	$0.555267\pi$
$168$	4.98462	+	3.81128i	0.384572	+	0.294047i
$169$	0.500000	−	0.866025i	0.0384615	−	0.0666173i
$170$			16.1186i			1.23624i
$171$	0.0105400	+	0.00461023i	0.000806015	+	0.000352553i
$172$	21.9249			1.67176
$173$	11.8289	−	20.4883i	0.899335	−	1.55769i	0.0709891	−	0.997477i	$-0.477384\pi$
$173$	11.8289	−	20.4883i	0.899335	−	1.55769i	0.828346	−	0.560217i	$-0.189282\pi$
$174$	31.0347	+	15.6851i	2.35273	+	1.18909i
$175$	−0.0264975	+	0.141732i	−0.00200302	+	0.0107140i
$176$	−9.45710	+	5.46006i	−0.712855	+	0.411567i
$177$	−16.1608	−	8.16777i	−1.21472	−	0.613927i
$178$	16.5112	+	9.53276i	1.23757	+	0.714511i
$179$			7.91402i			0.591522i	0.955262	+	0.295761i	$0.0955732\pi$
$179$			7.91402i			0.591522i	−0.955262	+	0.295761i	$0.904427\pi$
$180$	10.4296	+	14.1592i	0.777379	+	1.05536i
$181$			4.72412i			0.351141i	0.984467	+	0.175570i	$0.0561770\pi$
$181$			4.72412i			0.351141i	−0.984467	+	0.175570i	$0.943823\pi$
$182$	−5.37284	+	1.89319i	−0.398262	+	0.140332i
$183$	−4.64667	+	0.258784i	−0.343492	+	0.0191299i
$184$	−0.301489	−	0.522194i	−0.0222261	−	0.0384967i
$185$	−6.69973	−	11.6043i	−0.492574	−	0.853163i
$186$	−13.5537	+	8.86513i	−0.993807	+	0.650023i
$187$	13.7003	+	7.90988i	1.00187	+	0.578427i
$188$	−15.8248			−1.15414
$189$	6.65946	+	12.0271i	0.484405	+	0.874844i
$190$	0.0183615			0.00133208
$191$	2.07485	+	1.19791i	0.150131	+	0.0866780i	0.573184	−	0.819427i	$-0.305708\pi$
$191$	2.07485	+	1.19791i	0.150131	+	0.0866780i	−0.423053	+	0.906105i	$0.639042\pi$
$192$	17.4254	−	11.3975i	1.25757	−	0.822545i
$193$	1.75901	+	3.04669i	0.126616	+	0.219305i	0.922363	−	0.386323i	$-0.126255\pi$
$193$	1.75901	+	3.04669i	0.126616	+	0.219305i	−0.795747	+	0.605629i	$0.792922\pi$
$194$	−9.47593	−	16.4128i	−0.680332	−	1.17837i
$195$	−3.84586	+	0.214185i	−0.275408	+	0.0153381i
$196$	17.2053	+	6.66622i	1.22895	+	0.476159i
$197$		−	17.6672i		−	1.25874i	−0.777107	−	0.629369i	$-0.783314\pi$
$197$		−	17.6672i		−	1.25874i	0.777107	−	0.629369i	$-0.216686\pi$
$198$	30.1678	−	3.37069i	2.14393	−	0.239544i
$199$		−	23.4454i		−	1.66200i	−0.556274	−	0.830999i	$-0.687769\pi$
$199$		−	23.4454i		−	1.66200i	0.556274	−	0.830999i	$-0.312231\pi$
$200$	−0.0646244	−	0.0373109i	−0.00456964	−	0.00263828i
$201$	19.9501	+	10.0829i	1.40717	+	0.711196i
$202$	5.24308	−	3.02709i	0.368902	−	0.212986i
$203$	24.2496	+	4.53357i	1.70199	+	0.318194i
$204$	−13.7167	−	6.93254i	−0.960364	−	0.485375i
$205$	10.8610	−	18.8118i	0.758564	−	1.31387i
$206$	25.3840			1.76859
$207$	−0.146696	−	1.31293i	−0.0101961	−	0.0912551i
$208$			2.32370i			0.161119i
$209$	0.00901057	−	0.0156068i	0.000623274	−	0.00107954i
$210$	17.4309	+	13.3278i	1.20285	+	0.919707i
$211$	−11.9023	−	20.6153i	−0.819386	−	1.41922i	−0.906136	−	0.422987i	$-0.860981\pi$
$211$	−11.9023	−	20.6153i	−0.819386	−	1.41922i	0.0867500	−	0.996230i	$-0.472352\pi$
$212$	1.71389	−	0.989514i	0.117710	−	0.0679601i
$213$	13.1855	+	20.1590i	0.903454	+	1.38127i
$214$	15.4628	−	26.7824i	1.05702	−	1.83080i
$215$	18.4972			1.26150
$216$	−7.01601	+	1.18200i	−0.477379	+	0.0804250i
$217$	−7.47568	+	8.72527i	−0.507482	+	0.592310i
$218$	9.46573	+	5.46504i	0.641100	+	0.370139i
$219$	−9.78675	−	14.9628i	−0.661327	−	1.01109i
$220$	23.8572	−	13.7740i	1.60845	−	0.928640i
$221$	2.91530	−	1.68315i	0.196104	−	0.113221i
$222$	22.4357	−	1.24950i	1.50578	−	0.0838606i
$223$	−9.31186	−	5.37621i	−0.623569	−	0.360017i	0.154689	−	0.987963i	$-0.450563\pi$
$223$	−9.31186	−	5.37621i	−0.623569	−	0.360017i	−0.778257	+	0.627946i	$0.783896\pi$
$224$	13.3267	−	15.5544i	0.890430	−	1.03927i
$225$	−0.0969636	−	0.131637i	−0.00646424	−	0.00877580i
$226$	−10.1205			−0.673204
$227$	5.69051	−	9.85625i	0.377692	−	0.654182i	−0.613034	−	0.790057i	$-0.710051\pi$
$227$	5.69051	−	9.85625i	0.377692	−	0.654182i	0.990726	+	0.135875i	$0.0433844\pi$
$228$	−0.00789723	+	0.0156255i	−0.000523007	+	0.00103482i
$229$	−17.4111	+	10.0523i	−1.15056	+	0.664277i	−0.949024	−	0.315204i	$-0.897927\pi$
$229$	−17.4111	+	10.0523i	−1.15056	+	0.664277i	−0.201537	+	0.979481i	$0.564594\pi$
$230$	−1.05429	−	1.82608i	−0.0695177	−	0.120408i
$231$	19.8822	−	8.27541i	1.30815	−	0.544482i
$232$	−6.38368	+	11.0569i	−0.419109	+	0.725918i
$233$			18.4648i			1.20967i	0.796351	+	0.604834i	$0.206761\pi$
$233$			18.4648i			1.20967i	−0.796351	+	0.604834i	$0.793239\pi$
$234$	2.58856	−	5.91801i	0.169219	−	0.386872i
$235$	−13.3508			−0.870909
$236$	13.7786	−	23.8652i	0.896910	−	1.55349i
$237$	1.32713	+	23.8296i	0.0862061	+	1.54790i
$238$	−18.8499	−	3.52408i	−1.22186	−	0.228432i
$239$	−5.87937	+	3.39446i	−0.380305	+	0.219569i	−0.677951	−	0.735107i	$-0.737132\pi$
$239$	−5.87937	+	3.39446i	−0.380305	+	0.219569i	0.297646	+	0.954676i	$0.403799\pi$
$240$	7.49048	−	4.89933i	0.483508	−	0.316250i
$241$	1.58372	+	0.914359i	0.102016	+	0.0588990i	0.550140	−	0.835072i	$-0.314574\pi$
$241$	1.58372	+	0.914359i	0.102016	+	0.0588990i	−0.448124	+	0.893971i	$0.647908\pi$
$242$		−	23.8672i		−	1.53424i
$243$	−15.1213	−	3.78750i	−0.970034	−	0.242968i
$244$		−	7.08255i		−	0.453414i
$245$	14.5155	+	5.62405i	0.927361	+	0.359307i
$246$	19.9395	+	30.4851i	1.27130	+	1.94366i
$247$	−0.00191736	−	0.00332097i	−0.000121999	−	0.000211308i
$248$	−2.97317	−	5.14969i	−0.188797	−	0.327006i
$249$	−1.25938	−	22.6131i	−0.0798099	−	1.43305i
$250$	−20.9596	−	12.1010i	−1.32560	−	0.765336i
$251$	10.9775			0.692895			0.346448	−	0.938069i	$-0.387388\pi$
$251$	10.9775			0.692895			0.346448	+	0.938069i	$0.387388\pi$
$252$	−18.8388	+	9.10130i	−1.18674	+	0.573328i
$253$	−2.06949			−0.130108
$254$	0.928894	+	0.536297i	0.0582840	+	0.0336503i
$255$	−11.5723	−	5.84873i	−0.724687	−	0.366262i
$256$	−0.824911	−	1.42879i	−0.0515569	−	0.0892992i
$257$	−4.05500	−	7.02346i	−0.252944	−	0.438111i	0.711391	−	0.702796i	$-0.248065\pi$
$257$	−4.05500	−	7.02346i	−0.252944	−	0.438111i	−0.964335	+	0.264685i	$0.914732\pi$
$258$	−13.9918	+	27.6843i	−0.871094	+	1.72355i
$259$	15.0355	−	5.29793i	0.934259	−	0.329197i
$260$		−	5.86193i		−	0.363542i
$261$	−22.5223	+	16.5899i	−1.39410	+	1.02689i
$262$		−	22.1205i		−	1.36661i
$263$	24.5369	+	14.1664i	1.51301	+	0.873536i	0.999884	+	0.0152221i	$0.00484554\pi$
$263$	24.5369	+	14.1664i	1.51301	+	0.873536i	0.513125	+	0.858314i	$0.328488\pi$
$264$	0.619751	+	11.1281i	0.0381430	+	0.684888i
$265$	1.44595	−	0.834818i	0.0888238	−	0.0512824i
$266$	−0.00401447	+	0.0214730i	−0.000246143	+	0.00131659i
$267$	−12.8353	+	8.39521i	−0.785506	+	0.513779i
$268$	−17.0094	+	29.4611i	−1.03901	+	1.79962i
$269$	7.80387			0.475810			0.237905	−	0.971288i	$-0.423539\pi$
$269$	7.80387			0.475810			0.237905	+	0.971288i	$0.423539\pi$
$270$	−24.5346	+	4.13339i	−1.49313	+	0.251550i
$271$		−	6.58967i		−	0.400294i	−0.979766	−	0.200147i	$-0.935858\pi$
$271$		−	6.58967i		−	0.400294i	0.979766	−	0.200147i	$-0.0641420\pi$
$272$	−3.91112	+	6.77426i	−0.237147	+	0.410750i
$273$	0.590360	−	4.54439i	0.0357302	−	0.275039i
$274$	0.686815	+	1.18960i	0.0414920	+	0.0718663i
$275$	−0.221799	+	0.128055i	−0.0133750	+	0.00772203i
$276$	2.00742	−	0.111798i	0.120833	−	0.00672946i
$277$	1.34109	−	2.32284i	0.0805786	−	0.139566i	−0.822920	−	0.568157i	$-0.807657\pi$
$277$	1.34109	−	2.32284i	0.0805786	−	0.139566i	0.903499	+	0.428591i	$0.140990\pi$
$278$	−16.8322			−1.00953
$279$	−1.44666	−	12.9477i	−0.0866093	−	0.775157i
$280$	−5.24176	+	6.11794i	−0.313255	+	0.365617i
$281$	−18.6199	−	10.7502i	−1.11077	−	0.641304i	−0.171742	−	0.985142i	$-0.554940\pi$
$281$	−18.6199	−	10.7502i	−1.11077	−	0.641304i	−0.939029	+	0.343838i	$0.888273\pi$
$282$	10.0989	−	19.9818i	0.601382	−	1.18990i
$283$	−13.1903	+	7.61540i	−0.784079	+	0.452688i	−0.837874	−	0.545864i	$-0.816202\pi$
$283$	−13.1903	+	7.61540i	−0.784079	+	0.452688i	0.0537947	+	0.998552i	$0.482868\pi$
$284$	−31.7476	+	18.3295i	−1.88387	+	1.08765i
$285$	−0.00666261	+	0.0131827i	−0.000394659	+	0.000780873i
$286$	−8.76289	−	5.05926i	−0.518161	−	0.299160i
$287$	19.6249	+	16.8144i	1.15842	+	0.992520i
$288$	2.57893	+	23.0816i	0.151965	+	1.36009i
$289$	−5.66807			−0.333416
$290$	−22.3233	+	38.6652i	−1.31087	+	2.27050i
$291$	15.2220	−	0.847748i	0.892328	−	0.0496958i
$292$	23.5642	−	13.6048i	1.37899	−	0.796161i
$293$	−10.9950	−	19.0439i	−0.642334	−	1.11255i	−0.984910	−	0.173065i	$-0.944633\pi$
$293$	−10.9950	−	19.0439i	−0.642334	−	1.11255i	0.342577	−	0.939490i	$-0.388700\pi$
$294$	−19.3973	+	17.4708i	−1.13127	+	1.01892i
$295$	11.6245	−	20.1342i	0.676804	−	1.17226i
$296$			8.25026i			0.479537i
$297$	−8.52662	+	22.8821i	−0.494765	+	1.32775i
$298$	21.8163			1.26379
$299$	−0.220184	+	0.381370i	−0.0127336	+	0.0220552i
$300$	0.208229	−	0.136197i	0.0120221	−	0.00786334i
$301$	−4.04414	+	21.6317i	−0.233100	+	1.24683i
$302$	14.0127	−	8.09023i	0.806340	−	0.465540i
$303$	0.270814	+	4.86267i	0.0155578	+	0.279353i
$304$	0.00771693	+	0.00445537i	0.000442596	+	0.000255533i
$305$		−	5.97529i		−	0.342144i
$306$	17.5073	−	12.8958i	1.00082	−	0.737206i
$307$			1.08149i			0.0617237i	0.999524	+	0.0308619i	$0.00982519\pi$
$307$			1.08149i			0.0617237i	−0.999524	+	0.0308619i	$0.990175\pi$
$308$	10.8920	+	30.9114i	0.620630	+	1.76134i
$309$	−9.21076	+	18.2244i	−0.523982	+	1.03675i
$310$	−10.3970	−	18.0082i	−0.590511	−	1.02279i
$311$	−14.8204	−	25.6696i	−0.840386	−	1.45559i	−0.889568	−	0.456802i	$-0.848995\pi$
$311$	−14.8204	−	25.6696i	−0.840386	−	1.45559i	0.0491819	−	0.998790i	$-0.484339\pi$
$312$	2.11665	+	1.06977i	0.119832	+	0.0605638i
$313$	−13.9828	−	8.07296i	−0.790353	−	0.456310i	0.0497339	−	0.998763i	$-0.484163\pi$
$313$	−13.9828	−	8.07296i	−0.790353	−	0.456310i	−0.840087	+	0.542452i	$0.817496\pi$
$314$	−0.592210			−0.0334204
$315$	−15.8937	+	7.67844i	−0.895506	+	0.432631i
$316$	−36.3215			−2.04324
$317$	5.40525	+	3.12072i	0.303589	+	0.175277i	0.644054	−	0.764980i	$-0.277251\pi$
$317$	5.40525	+	3.12072i	0.303589	+	0.175277i	−0.340465	+	0.940257i	$0.610585\pi$
$318$	0.155693	+	2.79559i	0.00873083	+	0.156769i
$319$	21.9095	+	37.9484i	1.22670	+	2.12470i
$320$	13.3670	+	23.1523i	0.747238	+	1.29425i
$321$	13.6176	+	20.8197i	0.760061	+	1.16204i
$322$	2.36603	−	0.833698i	0.131853	−	0.0464602i
$323$		−	0.0129088i		−	0.000718266i
$324$	7.03477	−	22.6565i	0.390820	−	1.25869i
$325$			0.0544980i			0.00302300i
$326$	−16.1403	−	9.31861i	−0.893929	−	0.516110i
$327$	−7.35834	+	4.81289i	−0.406917	+	0.266154i
$328$	−11.5827	+	6.68729i	−0.639549	+	0.369244i
$329$	2.91895	−	15.6131i	0.160927	−	0.860781i
$330$	2.16723	+	38.9144i	0.119302	+	2.14217i
$331$	5.22359	−	9.04753i	0.287115	−	0.497297i	−0.686005	−	0.727597i	$-0.740637\pi$
$331$	5.22359	−	9.04753i	0.287115	−	0.497297i	0.973120	+	0.230299i	$0.0739706\pi$
$332$	34.4674			1.89164
$333$	−7.24387	+	16.5611i	−0.396961	+	0.907542i
$334$		−	42.6620i		−	2.33436i
$335$	−14.3502	+	24.8553i	−0.784035	+	1.35799i
$336$	4.09186	+	9.83095i	0.223229	+	0.536322i
$337$	−7.32222	−	12.6825i	−0.398867	−	0.690857i	0.594720	−	0.803933i	$-0.297263\pi$
$337$	−7.32222	−	12.6825i	−0.398867	−	0.690857i	−0.993586	+	0.113076i	$0.963930\pi$
$338$	−1.86466	+	1.07656i	−0.101424	+	0.0585572i
$339$	3.67229	−	7.26600i	0.199451	−	0.394635i
$340$	9.86649	−	17.0893i	0.535086	−	0.926796i
$341$	−20.4086			−1.10519
$342$	−0.0146903	−	0.0199435i	−0.000794363	−	0.00107842i
$343$	−9.75067	+	15.7456i	−0.526487	+	0.850183i
$344$	−9.86320	−	5.69452i	−0.531788	−	0.307028i
$345$	1.69359	−	0.0943201i	0.0911799	−	0.00507802i
$346$	−44.1138	+	25.4691i	−2.37157	+	1.36923i
$347$	−14.1233	+	8.15406i	−0.758176	+	0.437733i	−0.828640	−	0.559781i	$-0.810885\pi$
$347$	−14.1233	+	8.15406i	−0.758176	+	0.437733i	0.0704646	+	0.997514i	$0.477552\pi$
$348$	−23.3025	−	35.6267i	−1.24915	−	1.90979i
$349$	−7.55278	−	4.36060i	−0.404291	−	0.233417i	0.284043	−	0.958812i	$-0.408324\pi$
$349$	−7.55278	−	4.36060i	−0.404291	−	0.233417i	−0.688334	+	0.725394i	$0.741658\pi$
$350$	0.201993	−	0.235756i	0.0107970	−	0.0126017i
$351$	3.30956	+	4.00585i	0.176651	+	0.213816i
$352$	36.3819			1.93916
$353$	2.18267	−	3.78049i	0.116172	−	0.201215i	−0.802076	−	0.597222i	$-0.796271\pi$
$353$	2.18267	−	3.78049i	0.116172	−	0.201215i	0.918248	+	0.396007i	$0.129604\pi$
$354$	21.3412	+	32.6282i	1.13427	+	1.73417i
$355$	−26.7843	+	15.4639i	−1.42156	+	0.820740i
$356$	−11.6704	−	20.2137i	−0.618530	−	1.07132i
$357$	9.36995	−	12.2546i	0.495910	−	0.648581i
$358$	8.51993	−	14.7570i	0.450292	−	0.779929i
$359$		−	14.6917i		−	0.775396i	−0.921786	−	0.387698i	$-0.873270\pi$
$359$		−	14.6917i		−	0.775396i	0.921786	−	0.387698i	$-0.126730\pi$
$360$	−1.01436	−	9.07859i	−0.0534616	−	0.478484i
$361$	19.0000			0.999999
$362$	5.08580	−	8.80887i	0.267304	−	0.462984i
$363$	17.1354	+	8.66037i	0.899377	+	0.454552i
$364$	6.85527	+	1.28162i	0.359314	+	0.0671754i
$365$	19.8803	−	11.4779i	1.04058	−	0.600780i
$366$	8.94306	+	4.51989i	0.467461	+	0.236258i
$367$	6.02255	+	3.47712i	0.314374	+	0.181504i	0.648882	−	0.760889i	$-0.275237\pi$
$367$	6.02255	+	3.47712i	0.314374	+	0.181504i	−0.334508	+	0.942393i	$0.608570\pi$
$368$		−	1.02328i		−	0.0533422i
$369$	−29.1220	+	3.25384i	−1.51603	+	0.169388i
$370$			28.8507i			1.49988i
$371$	0.660147	+	1.87349i	0.0342731	+	0.0972668i
$372$	19.7965	−	1.10251i	1.02640	−	0.0571627i
$373$	11.7815	+	20.4061i	0.610020	+	1.05659i	0.991236	+	0.132100i	$0.0421721\pi$
$373$	11.7815	+	20.4061i	0.610020	+	1.05659i	−0.381216	+	0.924486i	$0.624495\pi$
$374$	−17.0309	−	29.4985i	−0.880649	−	1.52533i
$375$	16.2933	−	10.6570i	0.841381	−	0.550325i
$376$	7.11898	+	4.11015i	0.367134	+	0.211965i
$377$	9.32427			0.480225
$378$	0.530307	−	29.5958i	0.0272760	−	1.52224i
$379$	7.31920			0.375962			0.187981	−	0.982173i	$-0.439806\pi$
$379$	7.31920			0.375962			0.187981	+	0.982173i	$0.439806\pi$
$380$	−0.0194673	−	0.0112395i	−0.000998652	−	0.000576572i
$381$	−0.722091	+	0.472300i	−0.0369938	+	0.0241967i
$382$	−2.57926	−	4.46740i	−0.131966	−	0.228572i
$383$	−1.16538	−	2.01850i	−0.0595481	−	0.103140i	0.834715	−	0.550683i	$-0.185633\pi$
$383$	−1.16538	−	2.01850i	−0.0595481	−	0.103140i	−0.894263	+	0.447543i	$0.852299\pi$
$384$	−17.9860	+	1.00168i	−0.917845	+	0.0511169i
$385$	9.18920	+	26.0788i	0.468325	+	1.32910i
$386$		−	7.57472i		−	0.385543i
$387$	−14.7989	−	20.0909i	−0.752271	−	1.02128i
$388$			23.2016i			1.17788i
$389$	−22.9865	−	13.2713i	−1.16546	−	0.672881i	−0.212856	−	0.977084i	$-0.568277\pi$
$389$	−22.9865	−	13.2713i	−1.16546	−	0.672881i	−0.952607	+	0.304203i	$0.901610\pi$
$390$	7.40180	+	3.74092i	0.374805	+	0.189429i
$391$	−1.28380	+	0.741203i	−0.0649246	+	0.0374843i
$392$	−6.00863	−	7.46760i	−0.303482	−	0.377171i
$393$	15.8814	+	8.02659i	0.801113	+	0.404888i
$394$	−19.0199	+	32.9434i	−0.958206	+	1.65966i
$395$	−30.6431			−1.54182
$396$	−34.0479	−	14.8927i	−1.71097	−	0.748384i
$397$		−	3.78160i		−	0.189793i	−0.995487	−	0.0948966i	$-0.969748\pi$
$397$		−	3.78160i		−	0.189793i	0.995487	−	0.0948966i	$-0.0302520\pi$
$398$	−25.2404	+	43.7176i	−1.26519	+	2.19137i
$399$	−0.0139599	−	0.0106738i	−0.000698867	−	0.000534359i
$400$	−0.0633184	−	0.109671i	−0.00316592	−	0.00548353i
$401$	−0.711849	+	0.410986i	−0.0355481	+	0.0205237i	−0.517669	−	0.855581i	$-0.673200\pi$
$401$	−0.711849	+	0.410986i	−0.0355481	+	0.0205237i	0.482121	+	0.876105i	$0.339867\pi$
$402$	−26.3453	−	40.2788i	−1.31399	−	2.00893i
$403$	−2.17137	+	3.76093i	−0.108164	+	0.187345i
$404$	−7.41178			−0.368750
$405$	5.93498	−	19.1144i	0.294912	−	0.949804i
$406$	−40.3365	−	34.5597i	−2.00187	−	1.71517i
$407$	24.5222	+	14.1579i	1.21552	+	0.701782i
$408$	4.37008	+	6.68133i	0.216351	+	0.330775i
$409$	12.2834	−	7.09182i	0.607375	−	0.350668i	−0.164563	−	0.986367i	$-0.552621\pi$
$409$	12.2834	−	7.09182i	0.607375	−	0.350668i	0.771937	+	0.635699i	$0.219288\pi$
$410$	−40.5041	+	23.3850i	−2.00035	+	1.15491i
$411$	−1.10329	+	0.0614447i	−0.0544212	+	0.00303085i
$412$	−26.9127	−	15.5381i	−1.32589	−	0.765505i
$413$	21.0046	+	17.9964i	1.03357	+	0.885544i
$414$	−1.13992	+	2.60610i	−0.0560238	+	0.128083i
$415$	29.0789			1.42743
$416$	3.87086	−	6.70453i	0.189785	−	0.328717i
$417$	6.10767	−	12.0846i	0.299094	−	0.591788i
$418$	−0.0336033	+	0.0194009i	−0.00164359	+	0.000948927i
$419$	−7.59044	−	13.1470i	−0.370817	−	0.642274i	0.618874	−	0.785490i	$-0.287589\pi$
$419$	−7.59044	−	13.1470i	−0.370817	−	0.642274i	−0.989691	+	0.143216i	$0.954256\pi$
$420$	−10.3224	−	24.8003i	−0.503684	−	1.21013i
$421$	0.499774	−	0.865634i	0.0243575	−	0.0421884i	−0.853590	−	0.520946i	$-0.825579\pi$
$421$	0.499774	−	0.865634i	0.0243575	−	0.0421884i	0.877947	+	0.478757i	$0.158913\pi$
$422$			51.2541i			2.49501i
$423$	10.6814	+	14.5010i	0.519350	+	0.705065i
$424$	−1.02802			−0.0499251
$425$	−0.0917281	+	0.158878i	−0.00444946	+	0.00770670i
$426$	−2.88401	−	51.7847i	−0.139731	−	2.50898i
$427$	6.98784	+	1.30641i	0.338165	+	0.0632215i
$428$	−32.7880	+	18.9302i	−1.58487	+	0.915025i
$429$	6.81197	−	4.45553i	0.328885	−	0.215115i
$430$	−34.4910	−	19.9134i	−1.66330	−	0.960309i
$431$		−	26.0532i		−	1.25494i	−0.778642	−	0.627468i	$-0.784091\pi$
$431$		−	26.0532i		−	1.25494i	0.778642	−	0.627468i	$-0.215909\pi$
$432$	−11.3143	−	4.21608i	−0.544359	−	0.202846i
$433$			15.7438i			0.756598i	0.925683	+	0.378299i	$0.123491\pi$
$433$			15.7438i			0.756598i	−0.925683	+	0.378299i	$0.876509\pi$
$434$	23.3329	−	8.22163i	1.12001	−	0.394651i
$435$	−19.6595	−	30.0570i	−0.942600	−	1.44112i
$436$	−6.69053	−	11.5883i	−0.320418	−	0.554980i
$437$	0.000844345		0.00146245i	4.03905e−5		6.99584e-5i
$438$	2.14062	+	38.4365i	0.102283	+	1.83657i
$439$	30.4402	+	17.5746i	1.45283	+	0.838792i	0.998641	−	0.0521133i	$-0.0165957\pi$
$439$	30.4402	+	17.5746i	1.45283	+	0.838792i	0.454189	+	0.890905i	$0.349929\pi$
$440$	−14.3100			−0.682201
$441$	−5.50468	−	20.2657i	−0.262128	−	0.965033i
$442$	−7.24805			−0.344754
$443$	26.6438	+	15.3828i	1.26589	+	0.730860i	0.974207	−	0.225657i	$-0.0724528\pi$
$443$	26.6438	+	15.3828i	1.26589	+	0.730860i	0.291679	+	0.956516i	$0.405786\pi$
$444$	−24.5517	−	12.4086i	−1.16517	−	0.588885i
$445$	−9.84589	−	17.0536i	−0.466740	−	0.808417i
$446$	11.5756	+	20.0496i	0.548122	+	0.949376i
$447$	−7.91621	+	15.6630i	−0.374424	+	0.740837i
$448$	−29.9981	+	10.5702i	−1.41728	+	0.499395i
$449$		−	17.0230i		−	0.803364i	−0.915779	−	0.401682i	$-0.868426\pi$
$449$		−	17.0230i		−	0.803364i	0.915779	−	0.401682i	$-0.131574\pi$
$450$	0.0390887	+	0.349846i	0.00184266	+	0.0164919i
$451$			45.9031i			2.16149i
$452$	10.7300	+	6.19495i	0.504695	+	0.291386i
$453$	0.723778	+	12.9960i	0.0340061	+	0.610606i
$454$	−21.2217	+	12.2524i	−0.995984	+	0.575032i
$455$	5.78354	+	1.08126i	0.271137	+	0.0506903i
$456$	0.00761106	−	0.00497820i	0.000356421	−	0.000233125i
$457$	−2.89325	+	5.01126i	−0.135341	+	0.234417i	−0.925728	−	0.378191i	$-0.876546\pi$
$457$	−2.89325	+	5.01126i	−0.135341	+	0.234417i	0.790387	+	0.612608i	$0.209880\pi$
$458$	43.2878			2.02271
$459$	2.90592	+	17.2487i	0.135637	+	0.805101i
$460$			2.58141i			0.120359i
$461$	−10.7913	+	18.6911i	−0.502603	+	0.870533i	0.497393	+	0.867525i	$0.334291\pi$
$461$	−10.7913	+	18.6911i	−0.502603	+	0.870533i	−0.999995	+	0.00300782i	$0.999043\pi$
$462$	−45.9825	−	5.97357i	−2.13930	−	0.277915i
$463$	−12.6314	−	21.8783i	−0.587033	−	1.01677i	−0.994619	−	0.103604i	$-0.966963\pi$
$463$	−12.6314	−	21.8783i	−0.587033	−	1.01677i	0.407586	−	0.913167i	$-0.366371\pi$
$464$	−18.7640	+	10.8334i	−0.871096	+	0.502928i
$465$	16.7016	−	0.930151i	0.774518	−	0.0431347i
$466$	19.8785	−	34.4305i	0.920853	−	1.59496i
$467$	−4.98275			−0.230574			−0.115287	−	0.993332i	$-0.536779\pi$
$467$	−4.98275			−0.230574			−0.115287	+	0.993332i	$0.536779\pi$
$468$	−6.36698	+	4.68991i	−0.294314	+	0.216791i
$469$	−25.9297	−	22.2162i	−1.19732	−	1.02585i
$470$	24.8947	+	14.3729i	1.14831	+	0.662974i
$471$	0.214888	−	0.425178i	0.00990150	−	0.0195911i
$472$	−12.3970	+	7.15739i	−0.570617	+	0.329446i
$473$	−33.8516	+	19.5442i	−1.55650	+	0.898645i
$474$	23.1794	−	45.8628i	1.06466	−	2.10655i
$475$	0.000180986	0	0.000104492i	8.30421e−6	0	4.79444e-6i
$476$	17.8280	+	15.2747i	0.817144	+	0.700117i
$477$	−2.06359	−	0.902620i	−0.0944852	−	0.0413281i
$478$	14.6174			0.668583
$479$	−1.26772	+	2.19576i	−0.0579236	+	0.100327i	−0.893533	−	0.448997i	$-0.851781\pi$
$479$	−1.26772	+	2.19576i	−0.0579236	+	0.100327i	0.835610	+	0.549324i	$0.185115\pi$
$480$	−29.7736	+	1.65816i	−1.35897	+	0.0756843i
$481$	5.21810	−	3.01267i	0.237925	−	0.137366i
$482$	−1.96873	−	3.40994i	−0.0896731	−	0.155318i
$483$	−0.259975	+	2.00120i	−0.0118293	+	0.0910578i
$484$	−14.6096	+	25.3045i	−0.664072	+	1.15021i
$485$			19.5744i			0.888827i
$486$	24.1187	+	23.3414i	1.09405	+	1.05879i
$487$	4.36876			0.197968			0.0989838	−	0.995089i	$-0.468441\pi$
$487$	4.36876			0.197968			0.0989838	+	0.995089i	$0.468441\pi$
$488$	−1.83954	+	3.18618i	−0.0832722	+	0.144232i
$489$	12.5469	−	8.20661i	0.567391	−	0.371116i
$490$	−21.0118	−	26.1138i	−0.949218	−	1.17970i
$491$	11.4198	−	6.59322i	0.515368	−	0.297548i	−0.219669	−	0.975574i	$-0.570498\pi$
$491$	11.4198	−	6.59322i	0.515368	−	0.297548i	0.735038	+	0.678026i	$0.237165\pi$
$492$	−2.47978	−	44.5264i	−0.111797	−	2.00741i
$493$	27.1830	+	15.6941i	1.22426	+	0.706828i
$494$			0.00825664i			0.000371484i
$495$	−28.7250	−	12.5644i	−1.29109	−	0.564727i
$496$		−	10.0912i		−	0.453110i
$497$	−12.2284	−	34.7040i	−0.548518	−	1.55669i
$498$	−21.9961	+	43.5216i	−0.985670	+	1.95025i
$499$	−16.9332	−	29.3292i	−0.758035	−	1.31296i	−0.943851	−	0.330371i	$-0.892826\pi$
$499$	−16.9332	−	29.3292i	−0.758035	−	1.31296i	0.185816	−	0.982585i	$-0.440507\pi$
$500$	14.8146	+	25.6596i	0.662528	+	1.14753i
$501$	30.6292	+	15.4802i	1.36841	+	0.691605i
$502$	−20.4693	−	11.8180i	−0.913592	−	0.527462i
$503$	11.6017			0.517295			0.258647	−	0.965972i	$-0.416723\pi$
$503$	11.6017			0.517295			0.258647	+	0.965972i	$0.416723\pi$
$504$	10.8388	+	0.798647i	0.482798	+	0.0355745i
$505$	−6.25305			−0.278257
$506$	3.85889	+	2.22793i	0.171549	+	0.0990437i
$507$	−0.0963127	−	1.72937i	−0.00427740	−	0.0768041i
$508$	−0.656557	−	1.13719i	−0.0291300	−	0.0504546i
$509$	9.37798	+	16.2431i	0.415671	+	0.719964i	0.995499	−	0.0947753i	$-0.0302133\pi$
$509$	9.37798	+	16.2431i	0.415671	+	0.719964i	−0.579827	+	0.814739i	$0.696880\pi$
$510$	15.2819	+	23.3642i	0.676695	+	1.03458i
$511$	9.07635	+	25.7586i	0.401514	+	1.13949i
$512$			24.3529i			1.07626i
$513$	0.0196489	−	0.00331029i	0.000867521	−	0.000146153i
$514$			17.4618i			0.770208i
$515$	−22.7053	−	13.1089i	−1.00051	−	0.577647i
$516$	31.7806	−	20.7868i	1.39906	−	0.915090i
$517$	24.4332	−	14.1065i	1.07457	−	0.620403i
$518$	−33.7396	−	6.30777i	−1.48243	−	0.277148i
$519$	−2.27855	−	40.9131i	−0.100017	−	1.79589i
$520$	−1.52251	+	2.63707i	−0.0667666	+	0.115643i
$521$	14.5837			0.638922			0.319461	−	0.947599i	$-0.396498\pi$
$521$	14.5837			0.638922			0.319461	+	0.947599i	$0.396498\pi$
$522$	59.8565	−	6.68784i	2.61985	−	0.292719i
$523$		−	26.8062i		−	1.17216i	−0.810255	−	0.586078i	$-0.800671\pi$
$523$		−	26.8062i		−	1.17216i	0.810255	−	0.586078i	$-0.199329\pi$
$524$	−13.5404	+	23.4527i	−0.591516	+	1.02454i
$525$	0.0959670	+	0.230567i	0.00418834	+	0.0100627i
$526$	−30.5020	−	52.8309i	−1.32995	−	2.30354i
$527$	−12.6604	+	7.30948i	−0.551495	+	0.318406i
$528$	−8.53163	+	16.8807i	−0.371291	+	0.734638i
$529$	−11.4030	+	19.7506i	−0.495784	+	0.858724i
$530$	−3.59493			−0.156154
$531$	−31.1692	+	3.48258i	−1.35263	+	0.151131i
$532$	0.0174003	−	0.0203088i	0.000754398	−	0.000880499i
$533$	8.45911	+	4.88387i	0.366405	+	0.211544i
$534$	32.9714	−	1.83625i	1.42681	−	0.0794624i
$535$	−27.6621	+	15.9707i	−1.19594	+	0.690474i
$536$	15.3038	−	8.83565i	0.661023	−	0.381642i
$537$	7.50324	+	11.4716i	0.323789	+	0.495034i
$538$	−14.5516	−	8.40135i	−0.627362	−	0.362208i
$539$	−32.5071	+	5.04461i	−1.40018	+	0.217287i
$540$	28.5423	+	10.6358i	1.22826	+	0.457692i
$541$	25.2624			1.08612			0.543058	−	0.839695i	$-0.317267\pi$
$541$	25.2624			1.08612			0.543058	+	0.839695i	$0.317267\pi$
$542$	−7.09419	+	12.2875i	−0.304722	+	0.527793i
$543$	4.47891	+	6.84771i	0.192208	+	0.293864i
$544$	22.5694	−	13.0305i	0.967656	−	0.558676i
$545$	−5.64456	−	9.77666i	−0.241786	−	0.418786i
$546$	−5.99314	+	7.83818i	−0.256483	+	0.335443i
$547$	−7.55082	+	13.0784i	−0.322850	+	0.559192i	−0.981075	−	0.193629i	$-0.937974\pi$
$547$	−7.55082	+	13.0784i	−0.322850	+	0.559192i	0.658225	+	0.752821i	$0.271307\pi$
$548$		−	1.68165i		−	0.0718367i
$549$	−6.49011	+	4.78060i	−0.276991	+	0.204031i
$550$	0.551438			0.0235134
$551$	0.0178780	−	0.0309656i	0.000761629	−	0.00131918i
$552$	−0.932104	−	0.471092i	−0.0396730	−	0.0200510i
$553$	6.69967	−	35.8358i	0.284899	−	1.52389i
$554$	−5.00137	+	2.88754i	−0.212488	+	0.122680i
$555$	−20.7134	−	10.4687i	−0.879233	−	0.444370i
$556$	17.8458	+	10.3033i	0.756832	+	0.436957i
$557$		−	8.75103i		−	0.370793i	−0.982664	−	0.185397i	$-0.940643\pi$
$557$		−	8.75103i		−	0.370793i	0.982664	−	0.185397i	$-0.0593570\pi$
$558$	−11.2414	+	25.7004i	−0.475888	+	1.08799i
$559$			8.31766i			0.351800i
$560$	−12.8950	+	4.54369i	−0.544911	+	0.192006i
$561$	27.3582	−	1.52364i	1.15507	−	0.0643283i
$562$	23.1465	+	40.0910i	0.976378	+	1.69114i
$563$	8.11034	+	14.0475i	0.341810	+	0.592032i	0.984769	−	0.173868i	$-0.0556268\pi$
$563$	8.11034	+	14.0475i	0.341810	+	0.592032i	−0.642959	+	0.765901i	$0.722293\pi$
$564$	−22.9384	+	15.0034i	−0.965879	+	0.631756i
$565$	9.05249	+	5.22646i	0.380841	+	0.219879i
$566$	32.7938			1.37843
$567$	21.0559	+	11.1198i	0.884264	+	0.466987i
$568$	19.0428			0.799017
$569$	8.29263	+	4.78775i	0.347645	+	0.200713i	0.663648	−	0.748045i	$-0.269007\pi$
$569$	8.29263	+	4.78775i	0.347645	+	0.200713i	−0.316003	+	0.948758i	$0.602341\pi$
$570$	0.0266154	−	0.0174085i	0.00111480	−	0.000729160i
$571$	18.8468	+	32.6437i	0.788716	+	1.36610i	0.926754	+	0.375669i	$0.122587\pi$
$571$	18.8468	+	32.6437i	0.788716	+	1.36610i	−0.138039	+	0.990427i	$0.544080\pi$
$572$	6.19375	+	10.7279i	0.258974	+	0.448555i
$573$	4.14327	−	0.230749i	0.173088	−	0.00963967i
$574$	−18.4922	−	52.4805i	−0.771848	−	2.19049i
$575$		−	0.0239991i		−	0.00100083i
$576$	14.4526	−	33.0419i	0.602193	−	1.37675i
$577$		−	12.1637i		−	0.506380i	−0.967417	−	0.253190i	$-0.918520\pi$
$577$		−	12.1637i		−	0.506380i	0.967417	−	0.253190i	$-0.0814797\pi$
$578$	10.5690	+	6.10203i	0.439613	+	0.253811i
$579$	5.43827	+	2.74854i	0.226007	+	0.114225i
$580$	47.3355	−	27.3291i	1.96550	−	1.13478i
$581$	−6.35766	+	34.0065i	−0.263760	+	1.41083i
$582$	−29.2965	−	14.8066i	−1.21438	−	0.613755i
$583$	−1.76414	+	3.05559i	−0.0730634	+	0.126550i
$584$	−14.1342			−0.584879
$585$	−5.37159	+	3.95670i	−0.222088	+	0.163590i
$586$			47.3471i			1.95589i
$587$	18.5424	−	32.1163i	0.765325	−	1.32558i	−0.174749	−	0.984613i	$-0.555911\pi$
$587$	18.5424	−	32.1163i	0.765325	−	1.32558i	0.940074	−	0.340969i	$-0.110755\pi$
$588$	31.2597	−	6.64942i	1.28913	−	0.274218i
$589$	0.00832663	+	0.0144221i	0.000343093	+	0.000594254i
$590$	−43.3515	+	25.0290i	−1.78475	+	1.03043i
$591$	−16.7502	−	25.6090i	−0.689011	−	1.05342i
$592$	−7.00054	+	12.1253i	−0.287720	+	0.498346i
$593$	−4.93572			−0.202686			−0.101343	−	0.994852i	$-0.532314\pi$
$593$	−4.93572			−0.202686			−0.101343	+	0.994852i	$0.532314\pi$
$594$	40.5332	−	33.4878i	1.66310	−	1.37402i
$595$	15.0408	+	12.8867i	0.616614	+	0.528305i
$596$	−23.1302	−	13.3542i	−0.947450	−	0.547010i
$597$	−22.2284	−	33.9846i	−0.909749	−	1.39090i
$598$	0.821136	−	0.474083i	0.0335787	−	0.0193867i
$599$	27.6103	−	15.9408i	1.12813	−	0.651324i	0.184663	−	0.982802i	$-0.440881\pi$
$599$	27.6103	−	15.9408i	1.12813	−	0.651324i	0.943463	+	0.331478i	$0.107547\pi$
$600$	−0.129049	+	0.00718704i	−0.00526840	+	0.000293410i
$601$	−28.3481	−	16.3668i	−1.15634	−	0.667616i	−0.205919	−	0.978569i	$-0.566018\pi$
$601$	−28.3481	−	16.3668i	−1.15634	−	0.667616i	−0.950425	+	0.310953i	$0.899352\pi$
$602$	30.8288	−	35.9819i	1.25649	−	1.46651i
$603$	38.4778	−	4.29917i	1.56694	−	0.175076i
$604$	−19.8088			−0.806008
$605$	−12.3256	+	21.3485i	−0.501106	+	0.867941i
$606$	4.72999	−	9.35878i	0.192143	−	0.380174i
$607$	5.40085	−	3.11818i	0.219214	−	0.126563i	−0.386372	−	0.922343i	$-0.626272\pi$
$607$	5.40085	−	3.11818i	0.219214	−	0.126563i	0.605586	+	0.795780i	$0.292939\pi$
$608$	−0.0148437	−	0.0257100i	−0.000601992	−	0.00104268i
$609$	39.4486	−	16.4194i	1.59854	−	0.665347i
$610$	−6.43277	+	11.1419i	−0.260455	+	0.451122i
$611$		−	6.00346i		−	0.242874i
$612$	−26.4554	+	2.95590i	−1.06940	+	0.119485i
$613$	18.0931			0.730773			0.365387	−	0.930856i	$-0.380937\pi$
$613$	18.0931			0.730773			0.365387	+	0.930856i	$0.380937\pi$
$614$	1.16429	−	2.01660i	0.0469868	−	0.0813835i
$615$	−2.09210	−	37.5653i	−0.0843617	−	1.51478i
$616$	3.12866	−	16.7349i	0.126057	−	0.674267i
$617$	23.4240	−	13.5238i	0.943014	−	0.544450i	0.0521105	−	0.998641i	$-0.483405\pi$
$617$	23.4240	−	13.5238i	0.943014	−	0.544450i	0.890904	+	0.454192i	$0.150072\pi$
$618$	36.7947	−	24.0664i	1.48010	−	0.968094i
$619$	0.246076	+	0.142072i	0.00989064	+	0.00571036i	0.504937	−	0.863156i	$-0.331516\pi$
$619$	0.246076	+	0.142072i	0.00989064	+	0.00571036i	−0.495047	+	0.868866i	$0.664849\pi$
$620$			25.4569i			1.02237i
$621$	−1.45742	−	1.76404i	−0.0584844	−	0.0707887i
$622$			63.8202i			2.55896i
$623$	22.0961	−	7.78582i	0.885260	−	0.311932i
$624$	2.20308	+	3.36825i	0.0881940	+	0.134838i
$625$	12.3623	+	21.4121i	0.494491	+	0.856483i
$626$	17.3821	+	30.1066i	0.694727	+	1.20330i
$627$	−0.00173566	−	0.0311652i	−6.93158e−5	−	0.00124462i
$628$	0.627875	+	0.362504i	0.0250550	+	0.0144655i
$629$	20.2831			0.808739
$630$	37.9026	+	2.79282i	1.51007	+	0.111269i
$631$	−31.2146			−1.24263			−0.621316	−	0.783560i	$-0.713402\pi$
$631$	−31.2146			−1.24263			−0.621316	+	0.783560i	$0.713402\pi$
$632$	16.3397	+	9.43374i	0.649959	+	0.375254i
$633$	−36.7979	−	18.5979i	−1.46258	−	0.739201i
$634$	−6.71930	−	11.6382i	−0.266857	−	0.462211i
$635$	−0.553913	−	0.959406i	−0.0219814	−	0.0380729i
$636$	1.54617	−	3.05925i	0.0613096	−	0.121307i
$637$	−2.52897	+	6.52720i	−0.100202	+	0.258617i
$638$		−	94.3478i		−	3.73527i
$639$	38.2253	+	16.7199i	1.51217	+	0.661428i
$640$		−	23.1287i		−	0.914244i
$641$	−5.54553	−	3.20172i	−0.219035	−	0.126460i	0.386468	−	0.922303i	$-0.373695\pi$
$641$	−5.54553	−	3.20172i	−0.219035	−	0.126460i	−0.605504	+	0.795843i	$0.707028\pi$
$642$	−2.97853	−	53.4818i	−0.117553	−	2.11076i
$643$	−12.3749	+	7.14465i	−0.488018	+	0.281758i	−0.723752	−	0.690060i	$-0.757584\pi$
$643$	−12.3749	+	7.14465i	−0.488018	+	0.281758i	0.235734	+	0.971818i	$0.424251\pi$
$644$	−3.01884	−	0.564386i	−0.118959	−	0.0222399i
$645$	26.8121	−	17.5371i	1.05573	−	0.690523i
$646$	−0.0138971	+	0.0240705i	−0.000546776	+	0.000947043i
$647$	−41.4756			−1.63058			−0.815288	−	0.579056i	$-0.803421\pi$
$647$	−41.4756			−1.63058			−0.815288	+	0.579056i	$0.803421\pi$
$648$	−9.04922	+	8.36518i	−0.355487	+	0.328615i
$649$			49.1300i			1.92852i
$650$	0.0586704	−	0.101620i	0.00230124	−	0.00398587i
$651$	−2.56378	+	19.7351i	−0.100483	+	0.773481i
$652$	11.4082	+	19.7596i	0.446780	+	0.773846i
$653$	8.41898	−	4.86070i	0.329460	−	0.190214i	−0.326141	−	0.945321i	$-0.605749\pi$
$653$	8.41898	−	4.86070i	0.329460	−	0.190214i	0.655601	+	0.755107i	$0.272415\pi$
$654$	18.9022	−	1.05271i	0.739133	−	0.0411641i
$655$	−11.4236	+	19.7862i	−0.446356	+	0.773111i
$656$	−22.6973			−0.886179
$657$	−28.3722	−	12.4101i	−1.10691	−	0.484164i
$658$	−22.2514	+	25.9708i	−0.867448	+	1.01245i
$659$	21.9711	+	12.6850i	0.855874	+	0.494139i	0.862628	−	0.505838i	$-0.168817\pi$
$659$	21.9711	+	12.6850i	0.855874	+	0.494139i	−0.00675465	+	0.999977i	$0.502150\pi$
$660$	21.5225	−	42.5845i	0.837763	−	1.65760i
$661$	41.1454	−	23.7553i	1.60037	−	0.923974i	0.608957	−	0.793204i	$-0.291588\pi$
$661$	41.1454	−	23.7553i	1.60037	−	0.923974i	0.991413	−	0.130770i	$-0.0417450\pi$
$662$	−19.4805	+	11.2470i	−0.757129	+	0.437129i
$663$	2.63000	−	5.20374i	0.102141	−	0.202096i
$664$	−15.5056	−	8.95217i	−0.601735	−	0.347412i
$665$	0.0146800	−	0.0171338i	0.000569266	−	0.000664421i
$666$	31.3364	−	23.0823i	1.21426	−	0.894421i
$667$	−4.10611			−0.158989
$668$	−26.1143	+	45.2312i	−1.01039	+	1.75005i
$669$	−18.5949	+	1.03559i	−0.718921	+	0.0400384i
$670$	53.5165	−	30.8978i	2.06752	−	1.19368i
$671$	6.31352	+	10.9353i	0.243731	+	0.422154i
$672$	4.57041	−	35.1814i	0.176307	−	1.35715i
$673$	−10.2735	+	17.7941i	−0.396012	+	0.685914i	−0.993230	−	0.116166i	$-0.962940\pi$
$673$	−10.2735	+	17.7941i	−0.396012	+	0.685914i	0.597217	+	0.802079i	$0.296273\pi$
$674$			31.5313i			1.21454i
$675$	−0.265355	−	0.0988802i	−0.0102135	−	0.00380590i
$676$	2.63594			0.101382
$677$	15.0596	−	26.0840i	0.578787	−	1.00249i	−0.416831	−	0.908984i	$-0.636859\pi$
$677$	15.0596	−	26.0840i	0.578787	−	1.00249i	0.995619	−	0.0935052i	$-0.0298072\pi$
$678$	−14.6699	+	9.59518i	−0.563393	+	0.368500i
$679$	−22.8914	−	4.27965i	−0.878490	−	0.164238i
$680$	−8.87715	+	5.12523i	−0.340423	+	0.196543i
$681$	−1.09614	−	19.6820i	−0.0420040	−	0.754216i
$682$	38.0550	+	21.9711i	1.45720	+	0.841316i
$683$			18.1845i			0.695811i	0.937530	+	0.347905i	$0.113107\pi$
$683$			18.1845i			0.695811i	−0.937530	+	0.347905i	$0.886893\pi$
$684$	0.00336722	+	0.0301368i	0.000128749	+	0.00115231i
$685$		−	1.41875i		−	0.0542077i
$686$	35.1328	−	18.8630i	1.34138	−	0.720193i
$687$	−15.7073	+	31.0785i	−0.599271	+	1.18572i
$688$	−9.66386	−	16.7383i	−0.368431	−	0.638142i
$689$	0.375393	+	0.650200i	0.0143013	+	0.0247707i
$690$	−3.25951	−	1.64738i	−0.124088	−	0.0627147i
$691$	7.36505	+	4.25221i	0.280180	+	0.161762i	0.633505	−	0.773739i	$-0.281616\pi$
$691$	7.36505	+	4.25221i	0.280180	+	0.161762i	−0.353325	+	0.935501i	$0.614949\pi$
$692$	62.3606			2.37059
$693$	20.9738	−	30.8456i	0.796728	−	1.17173i
$694$	35.1134			1.33289
$695$	15.0559	+	8.69252i	0.571103	+	0.329726i
$696$	1.22966	+	22.0795i	0.0466101	+	0.836921i
$697$	16.4405	+	28.4758i	0.622730	+	1.07860i
$698$	9.38891	+	16.2621i	0.355375	+	0.615528i
$699$	17.5064	+	26.7651i	0.662152	+	1.01235i
$700$	−0.358469	+	0.126311i	−0.0135488	+	0.00477410i
$701$			29.7631i			1.12414i	0.827091	+	0.562068i	$0.189994\pi$
$701$			29.7631i			1.12414i	−0.827091	+	0.562068i	$0.810006\pi$
$702$	−1.85866	−	11.0325i	−0.0701508	−	0.416394i
$703$		−	0.0231056i		−	0.000871442i
$704$	−48.9257	−	28.2473i	−1.84396	−	1.06461i
$705$	−19.3523	+	12.6578i	−0.728848	+	0.476721i
$706$	−8.13987	+	4.69955i	−0.306348	+	0.176870i
$707$	1.36714	−	7.31267i	0.0514165	−	0.275021i
$708$	−2.65411	−	47.6566i	−0.0997474	−	1.79104i
$709$	14.6761	−	25.4197i	0.551172	−	0.954659i	−0.447018	−	0.894525i	$-0.647514\pi$
$709$	14.6761	−	25.4197i	0.551172	−	0.954659i	0.998190	−	0.0601336i	$-0.0191527\pi$
$710$	66.5914			2.49913
$711$	24.5164	+	33.2833i	0.919437	+	1.24822i
$712$			12.1246i			0.454387i
$713$	0.956203	−	1.65619i	0.0358101	−	0.0620249i
$714$	−30.6646	+	12.7633i	−1.14759	+	0.477654i
$715$	5.22544	+	9.05073i	0.195420	+	0.338478i
$716$	−18.0661	+	10.4304i	−0.675161	+	0.389804i
$717$	−5.30402	+	10.4945i	−0.198082	+	0.391926i
$718$	−15.8165	+	27.3949i	−0.590266	+	1.02237i
$719$	8.11675			0.302704			0.151352	−	0.988480i	$-0.451637\pi$
$719$	8.11675			0.302704			0.151352	+	0.988480i	$0.451637\pi$
$720$	6.21260	−	14.2034i	0.231530	−	0.529328i
$721$	20.2944	−	23.6867i	0.755804	−	0.882140i
$722$	−35.4285	−	20.4547i	−1.31851	−	0.761244i
$723$	3.16253	−	0.176129i	0.117616	−	0.00655030i
$724$	−10.7842	+	6.22625i	−0.400791	+	0.231397i
$725$	−0.440074	+	0.254077i	−0.0163439	+	0.00943618i
$726$	−22.6283	−	34.5960i	−0.839816	−	1.28398i
$727$	19.5753	+	11.3018i	0.726007	+	0.419161i	0.816960	−	0.576695i	$-0.195658\pi$
$727$	19.5753	+	11.3018i	0.726007	+	0.419161i	−0.0909523	+	0.995855i	$0.528991\pi$
$728$	−2.75106	−	2.35707i	−0.101961	−	0.0873587i
$729$	−25.5096	+	8.84640i	−0.944801	+	0.327644i
$730$	−49.4266			−1.82936
$731$	−13.9998	+	24.2484i	−0.517803	+	0.896861i
$732$	−6.71493	−	10.2663i	−0.248191	−	0.379454i
$733$	−9.71595	+	5.60951i	−0.358867	+	0.207192i	−0.668584	−	0.743637i	$-0.733099\pi$
$733$	−9.71595	+	5.60951i	−0.358867	+	0.207192i	0.309717	+	0.950829i	$0.399766\pi$
$734$	−7.48667	−	12.9673i	−0.276338	−	0.478631i
$735$	26.3727	−	5.60988i	0.972771	−	0.206923i
$736$	−1.70460	+	2.95246i	−0.0628325	+	0.108829i
$737$		−	60.6500i		−	2.23407i
$738$	57.8056	+	25.2843i	2.12785	+	0.930729i
$739$	−43.6346			−1.60512			−0.802562	−	0.596568i	$-0.796531\pi$
$739$	−43.6346			−1.60512			−0.802562	+	0.596568i	$0.796531\pi$
$740$	17.6601	−	30.5882i	0.649198	−	1.12444i
$741$	−0.00592786	−	0.00299598i	−0.000217765	−	0.000110060i
$742$	0.785978	−	4.20411i	0.0288542	−	0.154338i
$743$	−19.9401	+	11.5124i	−0.731532	+	0.422350i	−0.818983	−	0.573818i	$-0.805462\pi$
$743$	−19.9401	+	11.5124i	−0.731532	+	0.422350i	0.0874501	+	0.996169i	$0.472128\pi$
$744$	−9.19208	−	4.64574i	−0.336998	−	0.170321i
$745$	−19.5141	−	11.2665i	−0.714942	−	0.412772i
$746$		−	50.7338i		−	1.85750i
$747$	−23.2649	−	31.5842i	−0.851218	−	1.15561i
$748$			41.6999i			1.52470i
$749$	−12.6291	−	35.8413i	−0.461459	−	1.30961i
$750$	−41.8543	+	2.33097i	−1.52830	+	0.0851148i
$751$	−6.53715	−	11.3227i	−0.238544	−	0.413170i	0.721753	−	0.692151i	$-0.243337\pi$
$751$	−6.53715	−	11.3227i	−0.238544	−	0.413170i	−0.960297	+	0.278981i	$0.910003\pi$
$752$	6.97511	+	12.0812i	0.254356	+	0.440558i
$753$	15.9122	−	10.4077i	0.579872	−	0.379279i
$754$	−17.3866	−	10.0382i	−0.633183	−	0.365568i
$755$	−16.7119			−0.608210
$756$	−18.6784	+	31.0536i	−0.679328	+	1.12941i
$757$	−23.4401			−0.851947			−0.425973	−	0.904736i	$-0.640068\pi$
$757$	−23.4401			−0.851947			−0.425973	+	0.904736i	$0.640068\pi$
$758$	−13.6478	−	7.87957i	−0.495711	−	0.286199i
$759$	−2.99977	+	1.96207i	−0.108885	+	0.0712187i
$760$	0.00583842	+	0.0101124i	0.000211782	+	0.000366817i
$761$	10.7885	+	18.6863i	0.391084	+	0.677377i	0.992593	−	0.121489i	$-0.0387668\pi$
$761$	10.7885	+	18.6863i	0.391084	+	0.677377i	−0.601509	+	0.798866i	$0.705433\pi$
$762$	1.85491	−	0.103305i	0.0671964	−	0.00374233i
$763$	12.6675	−	4.46354i	0.458593	−	0.161591i
$764$			6.31526i			0.228478i
$765$	−22.3195	+	2.49379i	−0.806963	+	0.0901630i
$766$			5.01841i			0.181322i
$767$	9.05377	+	5.22720i	0.326913	+	0.188743i
$768$	−2.55035	−	1.28897i	−0.0920279	−	0.0465116i
$769$	42.4682	−	24.5190i	1.53144	−	0.884178i	0.532145	−	0.846653i	$-0.321386\pi$
$769$	42.4682	−	24.5190i	1.53144	−	0.884178i	0.999296	−	0.0375246i	$-0.0119472\pi$
$770$	10.9407	−	58.5209i	0.394277	−	2.10895i
$771$	−12.5367	−	6.33614i	−0.451499	−	0.228191i
$772$	−4.63664	+	8.03089i	−0.166876	+	0.289038i
$773$	−40.1144			−1.44282			−0.721408	−	0.692511i	$-0.756505\pi$
$773$	−40.1144			−1.44282			−0.721408	+	0.692511i	$0.756505\pi$
$774$	5.96585	+	53.3946i	0.214438	+	1.91923i
$775$		−	0.236671i		−	0.00850147i
$776$	6.02613	−	10.4376i	0.216326	−	0.374687i
$777$	16.7713	−	21.9345i	0.601668	−	0.786897i
$778$	28.5747	+	49.4928i	1.02445	+	1.77440i
$779$	0.0324384	−	0.0187283i	0.00116223	−	0.000671011i
$780$	−5.55767	−	8.49701i	−0.198996	−	0.304242i
$781$	32.6785	−	56.6008i	1.16933	−	2.02534i
$782$	3.19180			0.114139
$783$	−16.9178	+	45.4007i	−0.604593	+	1.62249i
$784$	−2.49436	−	16.0735i	−0.0890843	−	0.574053i
$785$	0.529716	+	0.305832i	0.0189064	+	0.0109156i
$786$	−20.9724	−	32.0642i	−0.748059	−	1.14369i
$787$	−20.9624	+	12.1026i	−0.747228	+	0.431412i	−0.824691	−	0.565583i	$-0.808651\pi$
$787$	−20.9624	+	12.1026i	−0.747228	+	0.431412i	0.0774635	+	0.996995i	$0.475318\pi$
$788$	40.3306	−	23.2849i	1.43672	−	0.829489i
$789$	48.9978	−	2.72880i	1.74437	−	0.0971480i
$790$	57.1390	+	32.9892i	2.03292	+	1.17370i
$791$	−8.09130	+	9.44380i	−0.287694	+	0.335783i
$792$	11.4489	+	15.5429i	0.406817	+	0.552292i
$793$	2.68691			0.0954151
$794$	−4.07113	+	7.05140i	−0.144479	+	0.250245i
$795$	1.30445	−	2.58098i	0.0462639	−	0.0915380i
$796$	53.5209	−	30.9003i	1.89700	−	1.09523i
$797$	8.34555	+	14.4549i	0.295614	+	0.512019i	0.975128	−	0.221644i	$-0.0711423\pi$
$797$	8.34555	+	14.4549i	0.295614	+	0.512019i	−0.679513	+	0.733663i	$0.737809\pi$
$798$	0.0145393	+	0.0349317i	0.000514687	+	0.00123657i
$799$	10.1047	−	17.5019i	0.357479	−	0.619171i
$800$			0.421908i			0.0149167i
$801$	−10.6456	+	24.3381i	−0.376142	+	0.859944i
$802$	1.76981			0.0624941
$803$	−24.2552	+	42.0112i	−0.855947	+	1.48254i
$804$	3.27644	+	58.8311i	0.115551	+	2.07481i
$805$	−2.54689	−	0.476152i	−0.0897659	−	0.0167822i
$806$	8.09775	−	4.67524i	0.285231	−	0.164678i
$807$	11.3119	−	7.39881i	0.398197	−	0.260450i
$808$	3.33429	+	1.92505i	0.117300	+	0.0677231i
$809$		−	37.1781i		−	1.30711i	−0.756878	−	0.653556i	$-0.773276\pi$
$809$		−	37.1781i		−	1.30711i	0.756878	−	0.653556i	$-0.226724\pi$
$810$	−31.6446	+	29.2525i	−1.11188	+	1.02783i
$811$		−	9.84045i		−	0.345545i	−0.984962	−	0.172773i	$-0.944727\pi$
$811$		−	9.84045i		−	0.345545i	0.984962	−	0.172773i	$-0.0552725\pi$
$812$	21.6110	+	61.3318i	0.758398	+	2.15233i
$813$	−6.24763	−	9.55188i	−0.219114	−	0.334999i
$814$	−30.4838	−	52.7994i	−1.06846	−	1.85062i
$815$	9.62470	+	16.6705i	0.337139	+	0.583941i
$816$	0.753382	+	13.5276i	0.0263736	+	0.473559i
$817$	0.0276227	+	0.0159480i	0.000966396	+	0.000557949i
$818$	−30.5391			−1.06778
$819$	−3.45277	−	7.14691i	−0.120650	−	0.249733i
$820$	57.2578			1.99953
$821$	−33.0394	−	19.0753i	−1.15308	−	0.665732i	−0.203446	−	0.979086i	$-0.565214\pi$
$821$	−33.0394	−	19.0753i	−1.15308	−	0.665732i	−0.949636	+	0.313354i	$0.898547\pi$
$822$	2.12341	+	1.07318i	0.0740623	+	0.0374316i
$823$	6.49129	+	11.2432i	0.226272	+	0.391915i	0.956700	−	0.291075i	$-0.0940128\pi$
$823$	6.49129	+	11.2432i	0.226272	+	0.391915i	−0.730428	+	0.682990i	$0.760679\pi$
$824$	8.07136	+	13.9800i	0.281179	+	0.487017i
$825$	−0.200093	+	0.395905i	−0.00696635	+	0.0137837i
$826$	−19.7921	−	56.1698i	−0.688656	−	1.95440i
$827$			37.6941i			1.31075i	0.755303	+	0.655376i	$0.227490\pi$
$827$			37.6941i			1.31075i	−0.755303	+	0.655376i	$0.772510\pi$
$828$	2.80381	−	2.06528i	0.0974392	−	0.0717735i
$829$		−	20.9279i		−	0.726856i	−0.931622	−	0.363428i	$-0.881606\pi$
$829$		−	20.9279i		−	0.726856i	0.931622	−	0.363428i	$-0.118394\pi$
$830$	−54.2222	−	31.3052i	−1.88208	−	1.08662i
$831$	−0.258329	−	4.63850i	−0.00896133	−	0.160908i
$832$	−10.4109	+	6.01075i	−0.360934	+	0.208385i
$833$	−18.3589	+	14.7721i	−0.636099	+	0.511822i
$834$	−24.3986	+	15.9585i	−0.844854	+	0.552597i
$835$	−22.0317	+	38.1600i	−0.762437	+	1.32058i
$836$	0.0475027			0.00164291
$837$	−14.3726	−	17.3964i	−0.496789	−	0.601307i
$838$			32.6863i			1.12913i
$839$	17.4735	−	30.2650i	0.603253	−	1.04487i	−0.389072	−	0.921207i	$-0.627204\pi$
$839$	17.4735	−	30.2650i	0.603253	−	1.04487i	0.992325	−	0.123658i	$-0.0394625\pi$
$840$	−1.79766	+	13.8378i	−0.0620252	+	0.477449i
$841$	28.9711	+	50.1793i	0.999002	+	1.73032i
$842$	−1.86382	+	1.07608i	−0.0642314	+	0.0370840i
$843$	−37.1822	+	2.07076i	−1.28062	+	0.0713209i
$844$	31.3737	−	54.3408i	1.07993	−	1.87049i
$845$	2.22385			0.0765027
$846$	−4.30598	−	38.5387i	−0.148043	−	1.32499i
$847$	−22.2713	−	19.0817i	−0.765252	−	0.655657i
$848$	−1.51087	−	0.872300i	−0.0518834	−	0.0299549i
$849$	−11.8995	+	23.5443i	−0.408388	+	0.808039i
$850$	0.342083	−	0.197502i	0.0117334	−	0.00677426i
$851$	−2.29788	+	1.32668i	−0.0787704	+	0.0454781i
$852$	−28.6408	+	56.6687i	−0.981216	+	1.94144i
$853$	−48.4492	−	27.9721i	−1.65887	−	0.957748i	−0.973238	−	0.229797i	$-0.926194\pi$
$853$	−48.4492	−	27.9721i	−1.65887	−	0.957748i	−0.685630	−	0.727951i	$-0.740473\pi$
$854$	−11.6235	−	9.95885i	−0.397748	−	0.340785i
$855$	0.00284081	+	0.0254253i	9.71535e−5	+	0.000869528i
$856$	19.6669			0.672199
$857$	−4.49737	+	7.78968i	−0.153627	+	0.266090i	−0.932558	−	0.361019i	$-0.882429\pi$
$857$	−4.49737	+	7.78968i	−0.153627	+	0.266090i	0.778931	+	0.627110i	$0.215762\pi$
$858$	−17.4987	+	0.974542i	−0.597395	+	0.0332703i
$859$	−17.2074	+	9.93470i	−0.587109	+	0.338968i	−0.763954	−	0.645271i	$-0.776744\pi$
$859$	−17.2074	+	9.93470i	−0.587109	+	0.338968i	0.176844	+	0.984239i	$0.443411\pi$
$860$	24.3788	+	42.2253i	0.831310	+	1.43987i
$861$	44.3884	+	5.76648i	1.51275	+	0.196521i
$862$	−28.0478	+	48.5803i	−0.955313	+	1.65465i
$863$		−	33.4907i		−	1.14004i	−0.821632	−	0.570018i	$-0.806936\pi$
$863$		−	33.4907i		−	1.14004i	0.821632	−	0.570018i	$-0.193064\pi$
$864$	25.6217	+	31.0122i	0.871668	+	1.05506i
$865$	52.6114			1.78884
$866$	16.9492	−	29.3568i	0.575956	−	0.997585i
$867$	−8.21599	+	5.37387i	−0.279030	+	0.182506i
$868$	−29.7707	−	5.56577i	−1.01048	−	0.188915i
$869$	56.0798	−	32.3777i	1.90238	−	1.09834i
$870$	4.30004	+	77.2107i	0.145785	+	2.61769i
$871$	−11.1767	−	6.45287i	−0.378708	−	0.218647i
$872$			6.95089i			0.235387i
$873$	21.2609	−	15.6607i	0.719571	−	0.530034i
$874$		−	0.00363596i		−	0.000122988i
$875$	−28.0491	+	9.88343i	−0.948231	+	0.334121i
$876$	21.2582	−	42.0616i	0.718249	−	1.42113i
$877$	20.4062	+	35.3446i	0.689069	+	1.19350i	0.972139	+	0.234404i	$0.0753137\pi$
$877$	20.4062	+	35.3446i	0.689069	+	1.19350i	−0.283070	+	0.959099i	$0.591353\pi$
$878$	−37.8404	−	65.5415i	−1.27705	−	2.21192i
$879$	−33.9929	−	17.1802i	−1.14655	−	0.579475i
$880$	−21.0311	−	12.1423i	−0.708960	−	0.409318i
$881$	−17.8319			−0.600773			−0.300387	−	0.953818i	$-0.597116\pi$
$881$	−17.8319			−0.600773			−0.300387	+	0.953818i	$0.597116\pi$
$882$	−11.5529	+	43.7148i	−0.389007	+	1.47195i
$883$	−39.9694			−1.34508			−0.672539	−	0.740062i	$-0.734796\pi$
$883$	−39.9694			−1.34508			−0.672539	+	0.740062i	$0.734796\pi$
$884$	7.68455	+	4.43668i	0.258459	+	0.149222i
$885$	−2.23917	−	40.2061i	−0.0752690	−	1.35151i
$886$	−33.1211	−	57.3674i	−1.11273	−	1.92730i
$887$	25.0861	+	43.4504i	0.842309	+	1.45892i	0.887938	+	0.459963i	$0.152137\pi$
$887$	25.0861	+	43.4504i	0.842309	+	1.45892i	−0.0456292	+	0.998958i	$0.514529\pi$
$888$	7.82203	+	11.9589i	0.262490	+	0.401316i
$889$	1.24309	−	0.438017i	0.0416918	−	0.0146906i
$890$			42.3988i			1.42121i
$891$	9.33484	+	41.2521i	0.312729	+	1.38200i
$892$		−	28.3427i		−	0.948985i
$893$	−0.0199373	−	0.0115108i	−0.000667177	−	0.000385195i
$894$	31.6233	−	20.6840i	1.05764	−	0.691775i
$895$	−15.2417	+	8.79979i	−0.509473	+	0.294145i
$896$	27.0480	+	5.05675i	0.903611	+	0.168934i
$897$	0.0424130	+	0.761559i	0.00141613	+	0.0254277i
$898$	−18.3263	+	31.7421i	−0.611556	+	1.05925i
$899$	−40.4930			−1.35052
$900$	0.172705	−	0.394841i	0.00575683	−	0.0131614i
$901$			2.52737i			0.0841988i
$902$	49.4175	−	85.5936i	1.64542	−	2.84996i
$903$	14.6468	+	35.1898i	0.487415	+	1.17104i
$904$	−3.21802	−	5.57377i	−0.107030	−	0.185381i
$905$	−9.09822	+	5.25286i	−0.302435	+	0.174611i
$906$	12.6414	−	25.0123i	0.419983	−	0.830979i
$907$	10.8676	−	18.8232i	0.360853	−	0.625016i	−0.627248	−	0.778819i	$-0.715819\pi$
$907$	10.8676	−	18.8232i	0.360853	−	0.625016i	0.988101	+	0.153804i	$0.0491523\pi$
$908$	29.9997			0.995574
$909$	5.00283	+	6.79180i	0.165933	+	0.225270i
$910$	−9.62030	−	8.24253i	−0.318910	−	0.273237i
$911$	3.97213	+	2.29331i	0.131603	+	0.0759808i	0.564356	−	0.825532i	$-0.309125\pi$
$911$	3.97213	+	2.29331i	0.131603	+	0.0759808i	−0.432753	+	0.901512i	$0.642458\pi$
$912$	0.0154100		0.000858218i	0.000510275		2.84184e-5i
$913$	−53.2171	+	30.7249i	−1.76123	+	1.01685i
$914$	10.7899	−	6.22953i	0.356897	−	0.206054i
$915$	−5.66514	−	8.66132i	−0.187284	−	0.286334i
$916$	−45.8948	−	26.4974i	−1.51641	−	0.875497i
$917$	−20.6415	−	17.6853i	−0.681642	−	0.584020i
$918$	13.1507	−	35.2914i	0.434039	−	1.16479i
$919$	−39.8097			−1.31320			−0.656600	−	0.754239i	$-0.728006\pi$
$919$	−39.8097			−1.31320			−0.656600	+	0.754239i	$0.728006\pi$
$920$	0.670465	−	1.16128i	0.0221046	−	0.0382863i
$921$	1.02535	+	1.56764i	0.0337865	+	0.0516555i
$922$	40.2443	−	23.2351i	1.32538	−	0.765207i
$923$	−6.95367	−	12.0441i	−0.228883	−	0.396437i
$924$	45.0951	+	34.4801i	1.48352	+	1.13431i
$925$	−0.164184	+	0.284376i	−0.00539835	+	0.00935022i
$926$			54.3941i			1.78750i
$927$	3.92729	+	35.1494i	0.128989	+	1.15446i
$928$	72.1860			2.36962
$929$	5.56532	−	9.63942i	0.182592	−	0.316259i	−0.760170	−	0.649724i	$-0.774885\pi$
$929$	5.56532	−	9.63942i	0.182592	−	0.316259i	0.942763	+	0.333465i	$0.108218\pi$
$930$	−32.1442	−	16.2459i	−1.05405	−	0.532723i
$931$	0.0168277	+	0.0209137i	0.000551505	+	0.000685417i
$932$	−42.1513	+	24.3360i	−1.38071	+	0.797154i
$933$	−45.8197	−	23.1576i	−1.50007	−	0.758146i
$934$	9.29114	+	5.36424i	0.304015	+	0.175523i
$935$			35.1807i			1.15053i
$936$	4.08238	−	0.456129i	0.133437	−	0.0149090i
$937$		−	57.0125i		−	1.86252i	−0.364358	−	0.931259i	$-0.618711\pi$
$937$		−	57.0125i		−	1.86252i	0.364358	−	0.931259i	$-0.381289\pi$
$938$	24.4330	+	69.3405i	0.797765	+	2.26405i
$939$	−27.9223	+	1.55506i	−0.911209	+	0.0507474i
$940$	−17.5959	−	30.4771i	−0.573916	−	0.994052i
$941$	20.7785	+	35.9895i	0.677360	+	1.17322i	0.975773	+	0.218786i	$0.0702096\pi$
$941$	20.7785	+	35.9895i	0.677360	+	1.17322i	−0.298413	+	0.954437i	$0.596457\pi$
$942$	−0.858422	+	0.561472i	−0.0279689	+	0.0182937i
$943$	−3.72512	−	2.15070i	−0.121307	−	0.0700364i
$944$	−24.2928			−0.790665
$945$	−15.7583	+	26.1988i	−0.512618	+	0.852246i
$946$	84.1624			2.73635
$947$	−44.5517	−	25.7219i	−1.44773	−	0.835850i	−0.449388	−	0.893336i	$-0.648358\pi$
$947$	−44.5517	−	25.7219i	−1.44773	−	0.835850i	−0.998346	+	0.0574864i	$0.981691\pi$
$948$	−52.6489	+	34.4362i	−1.70996	+	1.11844i
$949$	5.16127	+	8.93959i	0.167542	+	0.290191i
$950$	−0.000224985	0	0.000389686i	−7.29948e−6	0	1.26431e-5i
$951$	10.7938	−	0.601130i	0.350012	−	0.0194930i
$952$	−4.05287	−	11.5020i	−0.131354	−	0.372782i
$953$			31.8965i			1.03323i	0.856219	+	0.516614i	$0.172808\pi$
$953$			31.8965i			1.03323i	−0.856219	+	0.516614i	$0.827192\pi$
$954$	2.87616	+	3.90466i	0.0931193	+	0.126418i
$955$			5.32796i			0.172409i
$956$	−15.4977	−	8.94759i	−0.501231	−	0.289386i
$957$	67.7370	+	34.2348i	2.18963	+	1.10665i
$958$	4.72773	−	2.72956i	0.152746	−	0.0881880i
$959$	1.65917	+	0.310189i	0.0535773	+	0.0100165i
$960$	41.3264	+	20.8866i	1.33380	+	0.674113i
$961$	−6.07027	+	10.5140i	−0.195815	+	0.339162i
$962$	−12.9733			−0.418276
$963$	39.4781	+	17.2678i	1.27216	+	0.556448i
$964$			4.82039i			0.155254i
$965$	−3.91176	+	6.77538i	−0.125924	+	0.218107i
$966$	2.63918	−	3.45168i	0.0849143	−	0.111056i
$967$	−16.9829	−	29.4153i	−0.546134	−	0.945933i	−0.998535	−	0.0541176i	$-0.982765\pi$
$967$	−16.9829	−	29.4153i	−0.546134	−	0.945933i	0.452400	−	0.891815i	$-0.350568\pi$
$968$	13.1446	−	7.58906i	0.422484	−	0.243922i
$969$	−0.0122388	−	0.0187116i	−0.000393166	−	0.000601104i
$970$	21.0730	−	36.4996i	0.676614	−	1.17193i
$971$	−55.6967			−1.78739			−0.893695	−	0.448674i	$-0.851896\pi$
$971$	−55.6967			−1.78739			−0.893695	+	0.448674i	$0.851896\pi$
$972$	−11.2834	−	39.5107i	−0.361916	−	1.26731i
$973$	−13.4573	+	15.7067i	−0.431420	+	0.503534i
$974$	−8.14626	−	4.70324i	−0.261023	−	0.150702i
$975$	0.0516692	+	0.0789960i	0.00165474	+	0.00252990i
$976$	−5.40709	+	3.12179i	−0.173077	+	0.0999260i
$977$	−8.84266	+	5.10531i	−0.282902	+	0.163333i	−0.634736	−	0.772729i	$-0.718891\pi$
$977$	−8.84266	+	5.10531i	−0.282902	+	0.163333i	0.351835	+	0.936062i	$0.385558\pi$
$978$	−32.2307	+	1.79500i	−1.03062	+	0.0573978i
$979$	36.0378	+	20.8064i	1.15177	+	0.664976i
$980$	6.29246	+	40.5482i	0.201005	+	1.29526i
$981$	−6.10300	+	13.9528i	−0.194854	+	0.445479i
$982$	−28.3920			−0.906027
$983$	12.3386	−	21.3711i	0.393540	−	0.681631i	−0.599374	−	0.800469i	$-0.704584\pi$
$983$	12.3386	−	21.3711i	0.393540	−	0.681631i	0.992914	+	0.118838i	$0.0379169\pi$
$984$	−10.4492	+	20.6749i	−0.333109	+	0.659091i
$985$	34.0255	−	19.6446i	1.08414	−	0.625929i
$986$	−33.7914	−	58.5284i	−1.07614	−	1.86392i
$987$	−10.5717	−	25.3990i	−0.336500	−	0.808461i
$988$	0.00505406	−	0.00875388i	0.000160791	−	0.000278498i
$989$		−	3.66283i		−	0.116471i
$990$	40.0360	+	54.3525i	1.27243	+	1.72744i
$991$	−14.7173			−0.467510			−0.233755	−	0.972296i	$-0.575101\pi$
$991$	−14.7173			−0.467510			−0.233755	+	0.972296i	$0.575101\pi$
$992$	−16.8102	+	29.1161i	−0.533724	+	0.924437i
$993$	−1.00620	−	18.0671i	−0.0319307	−	0.573341i
$994$	−14.5592	+	77.8757i	−0.461791	+	2.47007i
$995$	45.1537	−	26.0695i	1.43147	−	0.826458i
$996$	49.9612	−	32.6783i	1.58308	−	1.03545i
$997$	−24.5805	−	14.1916i	−0.778472	−	0.449451i	0.0574163	−	0.998350i	$-0.481714\pi$
$997$	−24.5805	−	14.1916i	−0.778472	−	0.449451i	−0.835889	+	0.548899i	$0.815047\pi$
$998$			72.9187i			2.30820i
$999$	5.20132	+	30.8735i	0.164563	+	0.976795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.db.a.209.14	yes	192
7.6	odd	2	inner	819.2.db.a.209.13	✓	192
9.5	odd	6	inner	819.2.db.a.482.13	yes	192
63.41	even	6	inner	819.2.db.a.482.14	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.db.a.209.13	✓	192	7.6	odd	2	inner
819.2.db.a.209.14	yes	192	1.1	even	1	trivial
819.2.db.a.482.13	yes	192	9.5	odd	6	inner
819.2.db.a.482.14	yes	192	63.41	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86466 - 1.07656i) q^{2} +(1.44952 - 0.948095i) q^{3} +(1.31797 + 2.28279i) q^{4} +(1.11192 + 1.92591i) q^{5} +(-3.72355 + 0.207373i) q^{6} +(-2.49537 + 0.879275i) q^{7} -1.36926i q^{8} +(1.20223 - 2.74857i) q^{9} -4.78822i q^{10} +(-4.06985 - 2.34973i) q^{11} +(4.07473 + 2.05940i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(5.59961 + 1.04687i) q^{14} +(3.43770 + 1.73744i) q^{15} +(1.16185 - 2.01238i) q^{16} -3.36629 q^{17} +(-5.20076 + 3.83087i) q^{18} +0.00383473i q^{19} +(-2.93097 + 5.07658i) q^{20} +(-2.78346 + 3.64038i) q^{21} +(5.05926 + 8.76289i) q^{22} +(0.381370 - 0.220184i) q^{23} +(-1.29819 - 1.98477i) q^{24} +(0.0272490 - 0.0471966i) q^{25} +2.15312 q^{26} +(-0.863241 - 5.12395i) q^{27} +(-5.29603 - 4.53755i) q^{28} +(-8.07506 - 4.66214i) q^{29} +(-4.53969 - 6.94063i) q^{30} +(3.76093 - 2.17137i) q^{31} +(-6.70453 + 3.87086i) q^{32} +(-8.12711 + 0.452618i) q^{33} +(6.27699 + 3.62402i) q^{34} +(-4.46807 - 3.82817i) q^{35} +(7.85892 - 0.878087i) q^{36} -6.02534 q^{37} +(0.00412832 - 0.00715046i) q^{38} +(-0.781276 + 1.54584i) q^{39} +(2.63707 - 1.52251i) q^{40} +(-4.88387 - 8.45911i) q^{41} +(9.10930 - 3.79150i) q^{42} +(4.15883 - 7.20331i) q^{43} -12.3875i q^{44} +(6.63029 - 0.740810i) q^{45} -0.948166 q^{46} +(-3.00173 + 5.19915i) q^{47} +(-0.223802 - 4.01853i) q^{48} +(5.45375 - 4.38823i) q^{49} +(-0.101620 + 0.0586704i) q^{50} +(-4.87952 + 3.19157i) q^{51} +(-2.28279 - 1.31797i) q^{52} -0.750786i q^{53} +(-3.90659 + 10.4837i) q^{54} -10.4509i q^{55} +(1.20396 + 3.41681i) q^{56} +(0.00363568 + 0.00555852i) q^{57} +(10.0382 + 17.3866i) q^{58} +(-5.22720 - 9.05377i) q^{59} +(0.564579 + 10.1375i) q^{60} +(-2.32694 - 1.34346i) q^{61} -9.35047 q^{62} +(-0.583269 + 7.91579i) q^{63} +12.0215 q^{64} +(-1.92591 - 1.11192i) q^{65} +(15.6416 + 7.90535i) q^{66} +(6.45287 + 11.1767i) q^{67} +(-4.43668 - 7.68455i) q^{68} +(0.344049 - 0.680736i) q^{69} +(4.21016 + 11.9484i) q^{70} +13.9073i q^{71} +(-3.76351 - 1.64617i) q^{72} -10.3225i q^{73} +(11.2352 + 6.48666i) q^{74} +(-0.00524885 - 0.0942472i) q^{75} +(-0.00875388 + 0.00505406i) q^{76} +(12.2218 + 2.28493i) q^{77} +(3.12100 - 2.04137i) q^{78} +(-6.88967 + 11.9333i) q^{79} +5.16755 q^{80} +(-6.10927 - 6.60884i) q^{81} +21.0312i q^{82} +(6.53796 - 11.3241i) q^{83} +(-11.9787 - 1.55615i) q^{84} +(-3.74306 - 6.48318i) q^{85} +(-15.5096 + 8.95448i) q^{86} +(-16.1251 + 0.898046i) q^{87} +(-3.21739 + 5.57268i) q^{88} -8.85482 q^{89} +(-13.1608 - 5.75656i) q^{90} +(1.72142 - 2.00916i) q^{91} +(1.00527 + 0.580392i) q^{92} +(3.39289 - 6.71317i) q^{93} +(11.1944 - 6.46309i) q^{94} +(-0.00738534 + 0.00426393i) q^{95} +(-6.04843 + 11.9674i) q^{96} +(7.62278 + 4.40101i) q^{97} +(-14.8936 + 2.31126i) q^{98} +(-11.3513 + 8.36135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 96 q^{4} + 8 q^{9} + 18 q^{14} + 12 q^{15} - 96 q^{16} + 20 q^{18} + 22 q^{21} - 36 q^{23} - 96 q^{25} - 72 q^{29} - 52 q^{30} + 60 q^{32} - 12 q^{36} - 78 q^{42} + 48 q^{46} - 12 q^{49} + 96 q^{50}+ \cdots + 28 q^{99}+O(q^{100}) \) 192 * q + 96 * q^4 + 8 * q^9 + 18 * q^14 + 12 * q^15 - 96 * q^16 + 20 * q^18 + 22 * q^21 - 36 * q^23 - 96 * q^25 - 72 * q^29 - 52 * q^30 + 60 * q^32 - 12 * q^36 - 78 * q^42 + 48 * q^46 - 12 * q^49 + 96 * q^50 + 44 * q^51 - 60 * q^56 + 28 * q^57 - 24 * q^58 + 112 * q^60 - 68 * q^63 - 192 * q^64 + 56 * q^72 + 90 * q^77 - 20 * q^78 + 24 * q^79 - 32 * q^81 + 66 * q^84 + 60 * q^86 - 84 * q^92 - 116 * q^93 - 96 * q^95 + 28 * q^99

Introduction

L-functions

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