LMFDB - Embedded newform 990.2.t.b.131.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] 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, 0, 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("990.131"); 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.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.7
Character	$\chi$	$=$	990.131
Dual form			990.2.t.b.461.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.21393 - 1.23547i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.462983 - 1.66903i) q^{6} +(1.10421 - 0.637517i) q^{7} -1.00000 q^{8} +(-0.0527607 + 2.99954i) q^{9} +1.00000i q^{10} +(-2.15908 + 2.51761i) q^{11} +(1.67691 - 0.433558i) q^{12} +(-1.12883 - 0.651729i) q^{13} +(1.10421 + 0.637517i) q^{14} +(-0.433558 - 1.67691i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.37485 q^{17} +(-2.62405 + 1.45408i) q^{18} +5.39364i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-2.12807 - 0.590319i) q^{21} +(-3.25986 - 0.611015i) q^{22} +(1.82924 + 1.05611i) q^{23} +(1.21393 + 1.23547i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.30346i q^{26} +(3.76988 - 3.57603i) q^{27} +1.27503i q^{28} +(2.37826 + 4.11927i) q^{29} +(1.23547 - 1.21393i) q^{30} +(1.73590 - 3.00666i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.73140 - 0.388719i) q^{33} +(-1.68743 - 2.92271i) q^{34} +1.27503 q^{35} +(-2.57129 - 1.54546i) q^{36} +9.60655 q^{37} +(-4.67103 + 2.69682i) q^{38} +(0.565125 + 2.18578i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-4.86110 + 8.41967i) q^{41} +(-0.552802 - 2.13812i) q^{42} +(-8.29679 + 4.79015i) q^{43} +(-1.10077 - 3.12863i) q^{44} +(-1.54546 + 2.57129i) q^{45} +2.11222i q^{46} +(-6.51661 + 3.76236i) q^{47} +(-0.462983 + 1.66903i) q^{48} +(-2.68714 + 4.65427i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(4.09682 + 4.16952i) q^{51} +(1.12883 - 0.651729i) q^{52} +5.11769i q^{53} +(4.98188 + 1.47679i) q^{54} +(-3.12863 + 1.10077i) q^{55} +(-1.10421 + 0.637517i) q^{56} +(6.66367 - 6.54749i) q^{57} +(-2.37826 + 4.11927i) q^{58} +(-2.49884 - 1.44271i) q^{59} +(1.66903 + 0.462983i) q^{60} +(-4.52899 + 2.61481i) q^{61} +3.47179 q^{62} +(1.85400 + 3.34576i) q^{63} +1.00000 q^{64} +(-0.651729 - 1.12883i) q^{65} +(3.20234 + 4.76917i) q^{66} +(3.12011 - 5.40419i) q^{67} +(1.68743 - 2.92271i) q^{68} +(-0.915772 - 3.54201i) q^{69} +(0.637517 + 1.10421i) q^{70} -10.3735i q^{71} +(0.0527607 - 2.99954i) q^{72} +14.1623i q^{73} +(4.80327 + 8.31951i) q^{74} +(0.462983 - 1.66903i) q^{75} +(-4.67103 - 2.69682i) q^{76} +(-0.779066 + 4.15643i) q^{77} +(-1.61038 + 1.58230i) q^{78} +(5.22002 - 3.01378i) q^{79} -1.00000i q^{80} +(-8.99443 - 0.316515i) q^{81} -9.72220 q^{82} +(0.809702 + 1.40244i) q^{83} +(1.57526 - 1.54780i) q^{84} +(-2.92271 - 1.68743i) q^{85} +(-8.29679 - 4.79015i) q^{86} +(2.20219 - 7.93877i) q^{87} +(2.15908 - 2.51761i) q^{88} +8.53513i q^{89} +(-2.99954 - 0.0527607i) q^{90} -1.66195 q^{91} +(-1.82924 + 1.05611i) q^{92} +(-5.82188 + 1.50522i) q^{93} +(-6.51661 - 3.76236i) q^{94} +(-2.69682 + 4.67103i) q^{95} +(-1.67691 + 0.433558i) q^{96} +(5.59811 + 9.69621i) q^{97} -5.37429 q^{98} +(-7.43775 - 6.60908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * 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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.21393	−	1.23547i	−0.700861	−	0.713298i
$3$	−1.21393	−	1.23547i	−0.700861	−	0.713298i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	0.462983	−	1.66903i	0.189012	−	0.681377i
$7$	1.10421	−	0.637517i	0.417353	−	0.240959i	−0.276591	−	0.960988i	$-0.589205\pi$
$7$	1.10421	−	0.637517i	0.417353	−	0.240959i	0.693944	+	0.720029i	$0.255871\pi$
$8$	−1.00000			−0.353553
$9$	−0.0527607	+	2.99954i	−0.0175869	+	0.999845i
$10$			1.00000i			0.316228i
$11$	−2.15908	+	2.51761i	−0.650988	+	0.759088i
$11$	−2.15908	+	2.51761i	−0.650988	+	0.759088i
$12$	1.67691	−	0.433558i	0.484082	−	0.125157i
$13$	−1.12883	−	0.651729i	−0.313080	−	0.180757i	0.335224	−	0.942139i	$-0.391188\pi$
$13$	−1.12883	−	0.651729i	−0.313080	−	0.180757i	−0.648304	+	0.761381i	$0.724521\pi$
$14$	1.10421	+	0.637517i	0.295113	+	0.170384i
$15$	−0.433558	−	1.67691i	−0.111944	−	0.432976i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.37485			−0.818521			−0.409261	−	0.912417i	$-0.634213\pi$
$17$	−3.37485			−0.818521			−0.409261	+	0.912417i	$0.634213\pi$
$18$	−2.62405	+	1.45408i	−0.618496	+	0.342729i
$19$			5.39364i			1.23739i	0.785633	+	0.618693i	$0.212338\pi$
$19$			5.39364i			1.23739i	−0.785633	+	0.618693i	$0.787662\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−2.12807	−	0.590319i	−0.464382	−	0.128818i
$22$	−3.25986	−	0.611015i	−0.695004	−	0.130269i
$23$	1.82924	+	1.05611i	0.381423	+	0.220215i	0.678437	−	0.734658i	$-0.262658\pi$
$23$	1.82924	+	1.05611i	0.381423	+	0.220215i	−0.297014	+	0.954873i	$0.595991\pi$
$24$	1.21393	+	1.23547i	0.247792	+	0.252189i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	1.30346i		−	0.255629i
$27$	3.76988	−	3.57603i	0.725513	−	0.688208i
$28$			1.27503i			0.240959i
$29$	2.37826	+	4.11927i	0.441633	+	0.764930i	0.997811	−	0.0661329i	$-0.0210661\pi$
$29$	2.37826	+	4.11927i	0.441633	+	0.764930i	−0.556178	+	0.831063i	$0.687733\pi$
$30$	1.23547	−	1.21393i	0.225565	−	0.221632i
$31$	1.73590	−	3.00666i	0.311776	−	0.540012i	−0.666971	−	0.745084i	$-0.732409\pi$
$31$	1.73590	−	3.00666i	0.311776	−	0.540012i	0.978747	+	0.205072i	$0.0657428\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.73140	−	0.388719i	0.997708	−	0.0676673i
$34$	−1.68743	−	2.92271i	−0.289391	−	0.501240i
$35$	1.27503			0.215520
$36$	−2.57129	−	1.54546i	−0.428549	−	0.257577i
$37$	9.60655			1.57931			0.789653	−	0.613553i	$-0.210260\pi$
$37$	9.60655			1.57931			0.789653	+	0.613553i	$0.210260\pi$
$38$	−4.67103	+	2.69682i	−0.757741	+	0.437482i
$39$	0.565125	+	2.18578i	0.0904924	+	0.350005i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	−4.86110	+	8.41967i	−0.759176	+	1.31493i	0.184095	+	0.982908i	$0.441065\pi$
$41$	−4.86110	+	8.41967i	−0.759176	+	1.31493i	−0.943271	+	0.332023i	$0.892269\pi$
$42$	−0.552802	−	2.13812i	−0.0852991	−	0.329919i
$43$	−8.29679	+	4.79015i	−1.26525	+	0.730492i	−0.974085	−	0.226182i	$-0.927376\pi$
$43$	−8.29679	+	4.79015i	−1.26525	+	0.730492i	−0.291164	+	0.956673i	$0.594042\pi$
$44$	−1.10077	−	3.12863i	−0.165948	−	0.471658i
$45$	−1.54546	+	2.57129i	−0.230384	+	0.383306i
$46$			2.11222i			0.311430i
$47$	−6.51661	+	3.76236i	−0.950545	+	0.548797i	−0.893250	−	0.449560i	$-0.851581\pi$
$47$	−6.51661	+	3.76236i	−0.950545	+	0.548797i	−0.0572947	+	0.998357i	$0.518247\pi$
$48$	−0.462983	+	1.66903i	−0.0668258	+	0.240903i
$49$	−2.68714	+	4.65427i	−0.383878	+	0.664896i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	4.09682	+	4.16952i	0.573670	+	0.583849i
$52$	1.12883	−	0.651729i	0.156540	−	0.0903785i
$53$			5.11769i			0.702969i	0.936194	+	0.351485i	$0.114323\pi$
$53$			5.11769i			0.702969i	−0.936194	+	0.351485i	$0.885677\pi$
$54$	4.98188	+	1.47679i	0.677947	+	0.200966i
$55$	−3.12863	+	1.10077i	−0.421864	+	0.148428i
$56$	−1.10421	+	0.637517i	−0.147557	+	0.0851918i
$57$	6.66367	−	6.54749i	0.882624	−	0.867236i
$58$	−2.37826	+	4.11927i	−0.312281	+	0.540887i
$59$	−2.49884	−	1.44271i	−0.325321	−	0.187824i	0.328441	−	0.944525i	$-0.393477\pi$
$59$	−2.49884	−	1.44271i	−0.325321	−	0.187824i	−0.653762	+	0.756700i	$0.726810\pi$
$60$	1.66903	+	0.462983i	0.215470	+	0.0597708i
$61$	−4.52899	+	2.61481i	−0.579878	+	0.334793i	−0.761085	−	0.648652i	$-0.775333\pi$
$61$	−4.52899	+	2.61481i	−0.579878	+	0.334793i	0.181207	+	0.983445i	$0.442000\pi$
$62$	3.47179			0.440918
$63$	1.85400	+	3.34576i	0.233582	+	0.421526i
$64$	1.00000			0.125000
$65$	−0.651729	−	1.12883i	−0.0808370	−	0.140014i
$66$	3.20234	+	4.76917i	0.394181	+	0.587045i
$67$	3.12011	−	5.40419i	0.381182	−	0.660227i	−0.610049	−	0.792363i	$-0.708850\pi$
$67$	3.12011	−	5.40419i	0.381182	−	0.660227i	0.991232	+	0.132137i	$0.0421838\pi$
$68$	1.68743	−	2.92271i	0.204630	−	0.354430i
$69$	−0.915772	−	3.54201i	−0.110246	−	0.426408i
$70$	0.637517	+	1.10421i	0.0761979	+	0.131979i
$71$		−	10.3735i		−	1.23111i	−0.788094	−	0.615555i	$-0.788932\pi$
$71$		−	10.3735i		−	1.23111i	0.788094	−	0.615555i	$-0.211068\pi$
$72$	0.0527607	−	2.99954i	0.00621791	−	0.353499i
$73$			14.1623i			1.65757i	0.559568	+	0.828785i	$0.310967\pi$
$73$			14.1623i			1.65757i	−0.559568	+	0.828785i	$0.689033\pi$
$74$	4.80327	+	8.31951i	0.558369	+	0.967124i
$75$	0.462983	−	1.66903i	0.0534606	−	0.192722i
$76$	−4.67103	−	2.69682i	−0.535804	−	0.309346i
$77$	−0.779066	+	4.15643i	−0.0887828	+	0.473669i
$78$	−1.61038	+	1.58230i	−0.182340	+	0.179161i
$79$	5.22002	−	3.01378i	0.587298	−	0.339077i	−0.176730	−	0.984259i	$-0.556552\pi$
$79$	5.22002	−	3.01378i	0.587298	−	0.339077i	0.764028	+	0.645183i	$0.223219\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−8.99443	−	0.316515i	−0.999381	−	0.0351684i
$82$	−9.72220			−1.07364
$83$	0.809702	+	1.40244i	0.0888763	+	0.153938i	0.907036	−	0.421052i	$-0.138339\pi$
$83$	0.809702	+	1.40244i	0.0888763	+	0.153938i	−0.818160	+	0.574990i	$0.805006\pi$
$84$	1.57526	−	1.54780i	0.171875	−	0.168879i
$85$	−2.92271	−	1.68743i	−0.317012	−	0.183027i
$86$	−8.29679	−	4.79015i	−0.894666	−	0.516536i
$87$	2.20219	−	7.93877i	0.236100	−	0.851125i
$88$	2.15908	−	2.51761i	0.230159	−	0.268378i
$89$			8.53513i			0.904722i	0.891835	+	0.452361i	$0.149418\pi$
$89$			8.53513i			0.904722i	−0.891835	+	0.452361i	$0.850582\pi$
$90$	−2.99954	−	0.0527607i	−0.316179	−	0.00556147i
$91$	−1.66195			−0.174220
$92$	−1.82924	+	1.05611i	−0.190711	+	0.110107i
$93$	−5.82188	+	1.50522i	−0.603701	+	0.156084i
$94$	−6.51661	−	3.76236i	−0.672137	−	0.388058i
$95$	−2.69682	+	4.67103i	−0.276688	+	0.479238i
$96$	−1.67691	+	0.433558i	−0.171149	+	0.0442498i
$97$	5.59811	+	9.69621i	0.568402	+	0.984501i	0.996724	+	0.0808752i	$0.0257715\pi$
$97$	5.59811	+	9.69621i	0.568402	+	0.984501i	−0.428322	+	0.903626i	$0.640895\pi$
$98$	−5.37429			−0.542885
$99$	−7.43775	−	6.60908i	−0.747522	−	0.664237i
$100$	−1.00000			−0.100000
$101$	6.56252	+	11.3666i	0.652995	+	1.13102i	0.982392	+	0.186830i	$0.0598212\pi$
$101$	6.56252	+	11.3666i	0.652995	+	1.13102i	−0.329397	+	0.944192i	$0.606845\pi$
$102$	−1.56250	+	5.63271i	−0.154710	+	0.557722i
$103$	8.51528	−	14.7489i	0.839035	−	1.45325i	−0.0516668	−	0.998664i	$-0.516453\pi$
$103$	8.51528	−	14.7489i	0.839035	−	1.45325i	0.890702	−	0.454587i	$-0.150213\pi$
$104$	1.12883	+	0.651729i	0.110691	+	0.0639073i
$105$	−1.54780	−	1.57526i	−0.151050	−	0.153730i
$106$	−4.43205	+	2.55885i	−0.430479	+	0.248537i
$107$	7.85693			0.759558			0.379779	−	0.925077i	$-0.376000\pi$
$107$	7.85693			0.759558			0.379779	+	0.925077i	$0.376000\pi$
$108$	1.21200	+	5.05283i	0.116625	+	0.486209i
$109$		−	4.20234i		−	0.402511i	−0.979539	−	0.201255i	$-0.935498\pi$
$109$		−	4.20234i		−	0.402511i	0.979539	−	0.201255i	$-0.0645021\pi$
$110$	−2.51761	−	2.15908i	−0.240045	−	0.205860i
$111$	−11.6616	−	11.8686i	−1.10687	−	1.12652i
$112$	−1.10421	−	0.637517i	−0.104338	−	0.0602397i
$113$	−3.80120	−	2.19462i	−0.357587	−	0.206453i	0.310435	−	0.950595i	$-0.399525\pi$
$113$	−3.80120	−	2.19462i	−0.357587	−	0.206453i	−0.668022	+	0.744142i	$0.732859\pi$
$114$	9.00212	+	2.49716i	0.843126	+	0.233881i
$115$	1.05611	+	1.82924i	0.0984829	+	0.170577i
$116$	−4.75653			−0.441633
$117$	2.01444	−	3.35157i	0.186235	−	0.309853i
$118$		−	2.88541i		−	0.265624i
$119$	−3.72655	+	2.15153i	−0.341612	+	0.197230i
$120$	0.433558	+	1.67691i	0.0395783	+	0.153080i
$121$	−1.67672	−	10.8715i	−0.152429	−	0.988314i
$122$	−4.52899	−	2.61481i	−0.410036	−	0.236734i
$123$	16.3033	−	4.21514i	1.47001	−	0.380066i
$124$	1.73590	+	3.00666i	0.155888	+	0.270006i
$125$			1.00000i			0.0894427i
$126$	−1.97052	+	3.27849i	−0.175547	+	0.292071i
$127$		−	20.1509i		−	1.78810i	−0.447962	−	0.894052i	$-0.647850\pi$
$127$		−	20.1509i		−	1.78810i	0.447962	−	0.894052i	$-0.352150\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	15.9898	+	4.43552i	1.40782	+	0.390526i
$130$	0.651729	−	1.12883i	0.0571604	−	0.0990047i
$131$	−6.46311	+	11.1944i	−0.564684	+	0.978062i	0.432395	+	0.901684i	$0.357669\pi$
$131$	−6.46311	+	11.1944i	−0.564684	+	0.978062i	−0.997079	+	0.0763773i	$0.975665\pi$
$132$	−2.52906	+	5.15789i	−0.220126	+	0.448937i
$133$	3.43854	+	5.95572i	0.298159	+	0.516427i
$134$	6.24022			0.539073
$135$	5.05283	−	1.21200i	0.434878	−	0.104312i
$136$	3.37485			0.289391
$137$	3.20650	−	1.85128i	0.273950	−	0.158165i	−0.356731	−	0.934207i	$-0.616109\pi$
$137$	3.20650	−	1.85128i	0.273950	−	0.158165i	0.630681	+	0.776042i	$0.282775\pi$
$138$	2.60958	−	2.56409i	0.222143	−	0.218269i
$139$	−20.0545	−	11.5785i	−1.70100	−	0.982075i	−0.944747	−	0.327799i	$-0.893693\pi$
$139$	−20.0545	−	11.5785i	−1.70100	−	0.982075i	−0.756256	−	0.654276i	$-0.772974\pi$
$140$	−0.637517	+	1.10421i	−0.0538800	+	0.0933230i
$141$	12.5590	+	3.48382i	1.05766	+	0.293391i
$142$	8.98373	−	5.18676i	0.753898	−	0.435263i
$143$	4.07803	−	1.43481i	0.341022	−	0.119985i
$144$	2.62405	−	1.45408i	0.218671	−	0.121173i
$145$			4.75653i			0.395008i
$146$	−12.2649	+	7.08114i	−1.01505	+	0.586039i
$147$	9.01220	−	2.33007i	0.743313	−	0.192181i
$148$	−4.80327	+	8.31951i	−0.394827	+	0.683860i
$149$	4.27677	−	7.40758i	0.350367	−	0.606853i	−0.635947	−	0.771733i	$-0.719390\pi$
$149$	4.27677	−	7.40758i	0.350367	−	0.606853i	0.986314	+	0.164880i	$0.0527236\pi$
$150$	1.67691	−	0.433558i	0.136919	−	0.0353999i
$151$	10.0587	−	5.80738i	0.818564	−	0.472598i	−0.0313571	−	0.999508i	$-0.509983\pi$
$151$	10.0587	−	5.80738i	0.818564	−	0.472598i	0.849921	+	0.526910i	$0.176650\pi$
$152$		−	5.39364i		−	0.437482i
$153$	0.178060	−	10.1230i	0.0143953	−	0.818395i
$154$	−3.98911	+	1.40352i	−0.321451	+	0.113099i
$155$	3.00666	−	1.73590i	0.241501	−	0.139430i
$156$	−2.17550	−	0.603478i	−0.174180	−	0.0483169i
$157$	7.53844	−	13.0570i	0.601633	−	1.04206i	−0.390941	−	0.920416i	$-0.627850\pi$
$157$	7.53844	−	13.0570i	0.601633	−	1.04206i	0.992574	−	0.121643i	$-0.0388162\pi$
$158$	5.22002	+	3.01378i	0.415282	+	0.239763i
$159$	6.32274	−	6.21251i	0.501426	−	0.492684i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	2.69316			0.212251
$162$	−4.22311	−	7.94766i	−0.331799	−	0.624428i
$163$	20.1959			1.58186			0.790931	−	0.611906i	$-0.209597\pi$
$163$	20.1959			1.58186			0.790931	+	0.611906i	$0.209597\pi$
$164$	−4.86110	−	8.41967i	−0.379588	−	0.657466i
$165$	5.15789	+	2.52906i	0.401541	+	0.196887i
$166$	−0.809702	+	1.40244i	−0.0628450	+	0.108851i
$167$	1.71895	−	2.97731i	0.133016	−	0.230391i	−0.791822	−	0.610752i	$-0.790867\pi$
$167$	1.71895	−	2.97731i	0.133016	−	0.230391i	0.924838	+	0.380361i	$0.124200\pi$
$168$	2.12807	+	0.590319i	0.164184	+	0.0455441i
$169$	−5.65050	−	9.78695i	−0.434654	−	0.752842i
$170$		−	3.37485i		−	0.258839i
$171$	−16.1784	−	0.284572i	−1.23719	−	0.0217618i
$172$		−	9.58031i		−	0.730492i
$173$	0.930545	+	1.61175i	0.0707480	+	0.122539i	0.899229	−	0.437478i	$-0.144128\pi$
$173$	0.930545	+	1.61175i	0.0707480	+	0.122539i	−0.828481	+	0.560017i	$0.810795\pi$
$174$	7.97627	−	2.06223i	0.604680	−	0.156337i
$175$	1.10421	+	0.637517i	0.0834706	+	0.0481918i
$176$	3.25986	+	0.611015i	0.245721	+	0.0460570i
$177$	1.25099	+	4.83857i	0.0940304	+	0.363690i
$178$	−7.39164	+	4.26757i	−0.554027	+	0.319868i
$179$			8.67688i			0.648540i	0.945965	+	0.324270i	$0.105119\pi$
$179$			8.67688i			0.648540i	−0.945965	+	0.324270i	$0.894881\pi$
$180$	−1.45408	−	2.62405i	−0.108380	−	0.195585i
$181$	12.1761			0.905045			0.452523	−	0.891753i	$-0.350524\pi$
$181$	12.1761			0.905045			0.452523	+	0.891753i	$0.350524\pi$
$182$	−0.830977	−	1.43929i	−0.0615961	−	0.106688i
$183$	8.72838	+	2.42123i	0.645221	+	0.178982i
$184$	−1.82924	−	1.05611i	−0.134853	−	0.0778576i
$185$	8.31951	+	4.80327i	0.611663	+	0.353144i
$186$	−4.21450	−	4.28929i	−0.309022	−	0.314506i
$187$	7.28658	−	8.49656i	0.532848	−	0.621330i
$188$		−	7.52473i		−	0.548797i
$189$	1.88296	−	6.35206i	0.136965	−	0.462045i
$190$	−5.39364			−0.391296
$191$	5.40786	−	3.12223i	0.391299	−	0.225917i	−0.291424	−	0.956594i	$-0.594129\pi$
$191$	5.40786	−	3.12223i	0.391299	−	0.225917i	0.682723	+	0.730677i	$0.260796\pi$
$192$	−1.21393	−	1.23547i	−0.0876077	−	0.0891622i
$193$	−20.3959	−	11.7756i	−1.46813	−	0.847625i	−0.468766	−	0.883322i	$-0.655301\pi$
$193$	−20.3959	−	11.7756i	−1.46813	−	0.847625i	−0.999363	+	0.0356977i	$0.988635\pi$
$194$	−5.59811	+	9.69621i	−0.401921	+	0.696148i
$195$	−0.603478	+	2.17550i	−0.0432160	+	0.155791i
$196$	−2.68714	−	4.65427i	−0.191939	−	0.332448i
$197$	−4.66350			−0.332261			−0.166130	−	0.986104i	$-0.553127\pi$
$197$	−4.66350			−0.332261			−0.166130	+	0.986104i	$0.553127\pi$
$198$	2.00476	−	9.74582i	0.142472	−	0.692605i
$199$	−14.4153			−1.02187			−0.510936	−	0.859619i	$-0.670701\pi$
$199$	−14.4153			−1.02187			−0.510936	+	0.859619i	$0.670701\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−10.4643	+	2.70550i	−0.738094	+	0.190831i
$202$	−6.56252	+	11.3666i	−0.461737	+	0.799753i
$203$	5.25222	+	3.03237i	0.368633	+	0.212831i
$204$	−5.65932	+	1.46319i	−0.396232	+	0.102444i
$205$	−8.41967	+	4.86110i	−0.588055	+	0.339514i
$206$	17.0306			1.18658
$207$	−3.26436	+	5.43115i	−0.226889	+	0.377491i
$208$			1.30346i			0.0903785i
$209$	−13.5791	−	11.6453i	−0.939285	−	0.805523i
$210$	0.590319	−	2.12807i	0.0407359	−	0.146850i
$211$	−9.37866	−	5.41477i	−0.645653	−	0.372768i	0.141136	−	0.989990i	$-0.454925\pi$
$211$	−9.37866	−	5.41477i	−0.645653	−	0.372768i	−0.786789	+	0.617222i	$0.788258\pi$
$212$	−4.43205	−	2.55885i	−0.304395	−	0.175742i
$213$	−12.8161	+	12.5927i	−0.878147	+	0.862837i
$214$	3.92846	+	6.80430i	0.268544	+	0.465132i
$215$	−9.58031			−0.653372
$216$	−3.76988	+	3.57603i	−0.256508	+	0.243318i
$217$		−	4.42665i		−	0.300501i
$218$	3.63933	−	2.10117i	0.246487	−	0.142309i
$219$	17.4970	−	17.1920i	1.18234	−	1.16173i
$220$	0.611015	−	3.25986i	0.0411947	−	0.219779i
$221$	3.80962	+	2.19949i	0.256263	+	0.147954i
$222$	4.44766	−	16.0336i	0.298508	−	1.07610i
$223$	−1.95126	−	3.37969i	−0.130666	−	0.226320i	0.793267	−	0.608873i	$-0.208378\pi$
$223$	−1.95126	−	3.37969i	−0.130666	−	0.226320i	−0.923934	+	0.382553i	$0.875045\pi$
$224$		−	1.27503i		−	0.0851918i
$225$	−2.62405	+	1.45408i	−0.174937	+	0.0969384i
$226$		−	4.38925i		−	0.291968i
$227$	9.33836	+	16.1745i	0.619809	+	1.07354i	0.989520	+	0.144394i	$0.0461232\pi$
$227$	9.33836	+	16.1745i	0.619809	+	1.07354i	−0.369711	+	0.929147i	$0.620543\pi$
$228$	2.33846	+	9.04465i	0.154868	+	0.598997i
$229$	7.83446	−	13.5697i	0.517715	−	0.896709i	−0.482073	−	0.876131i	$-0.660116\pi$
$229$	7.83446	−	13.5697i	0.517715	−	0.896709i	0.999788	−	0.0205783i	$-0.00655073\pi$
$230$	−1.05611	+	1.82924i	−0.0696379	+	0.120616i
$231$	6.08086	−	4.08309i	0.400091	−	0.268648i
$232$	−2.37826	−	4.11927i	−0.156141	−	0.270444i
$233$	−15.6597			−1.02590			−0.512951	−	0.858418i	$-0.671448\pi$
$233$	−15.6597			−1.02590			−0.512951	+	0.858418i	$0.671448\pi$
$234$	3.90977	+	0.0687714i	0.255590	+	0.00449573i
$235$	−7.52473			−0.490859
$236$	2.49884	−	1.44271i	0.162661	−	0.0939121i
$237$	−10.0602	−	2.79066i	−0.653477	−	0.181273i
$238$	−3.72655	−	2.15153i	−0.241556	−	0.139463i
$239$	−4.30431	+	7.45528i	−0.278422	+	0.482242i	−0.970993	−	0.239108i	$-0.923145\pi$
$239$	−4.30431	+	7.45528i	−0.278422	+	0.482242i	0.692570	+	0.721350i	$0.256478\pi$
$240$	−1.23547	+	1.21393i	−0.0797491	+	0.0783587i
$241$	2.66362	−	1.53784i	0.171579	−	0.0990612i	−0.411751	−	0.911296i	$-0.635083\pi$
$241$	2.66362	−	1.53784i	0.171579	−	0.0990612i	0.583330	+	0.812235i	$0.301749\pi$
$242$	8.57660	−	6.88781i	0.551325	−	0.442765i
$243$	10.5275	+	11.4966i	0.675342	+	0.737504i
$244$		−	5.22963i		−	0.334793i
$245$	−4.65427	+	2.68714i	−0.297350	+	0.171675i
$246$	11.8020	+	12.0115i	0.752471	+	0.765823i
$247$	3.51519	−	6.08849i	0.223666	−	0.387401i
$248$	−1.73590	+	3.00666i	−0.110229	+	0.190923i
$249$	0.749756	−	2.70283i	0.0475138	−	0.171285i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$			6.03992i			0.381236i	0.981664	+	0.190618i	$0.0610492\pi$
$251$			6.03992i			0.381236i	−0.981664	+	0.190618i	$0.938951\pi$
$252$	−3.82451	−	0.0672717i	−0.240922	−	0.00423772i
$253$	−6.60836	+	2.32508i	−0.415464	+	0.146176i
$254$	17.4512	−	10.0755i	1.09499	−	0.632191i
$255$	1.46319	+	5.65932i	0.0916287	+	0.354400i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.4999	+	8.94889i	0.966859	+	0.558216i	0.898277	−	0.439429i	$-0.144819\pi$
$257$	15.4999	+	8.94889i	0.966859	+	0.558216i	0.0685820	+	0.997645i	$0.478153\pi$
$258$	4.15362	+	16.0653i	0.258593	+	1.00018i
$259$	10.6077	−	6.12434i	0.659128	−	0.380548i
$260$	1.30346			0.0808370
$261$	−12.4814	+	6.91635i	−0.772579	+	0.428112i
$262$	−12.9262			−0.798584
$263$	−12.6011	−	21.8257i	−0.777016	−	1.34583i	−0.933654	−	0.358175i	$-0.883399\pi$
$263$	−12.6011	−	21.8257i	−0.777016	−	1.34583i	0.156638	−	0.987656i	$-0.449934\pi$
$264$	−5.73140	+	0.388719i	−0.352743	+	0.0239240i
$265$	−2.55885	+	4.43205i	−0.157189	+	0.272259i
$266$	−3.43854	+	5.95572i	−0.210830	+	0.365169i
$267$	10.5449	−	10.3610i	0.645336	−	0.634085i
$268$	3.12011	+	5.40419i	0.190591	+	0.330113i
$269$			14.1266i			0.861314i	0.902516	+	0.430657i	$0.141718\pi$
$269$			14.1266i			0.861314i	−0.902516	+	0.430657i	$0.858282\pi$
$270$	3.57603	+	3.76988i	0.217631	+	0.229427i
$271$			13.7320i			0.834157i	0.908870	+	0.417079i	$0.136946\pi$
$271$			13.7320i			0.834157i	−0.908870	+	0.417079i	$0.863054\pi$
$272$	1.68743	+	2.92271i	0.102315	+	0.177215i
$273$	2.01749	+	2.05329i	0.122104	+	0.124271i
$274$	3.20650	+	1.85128i	0.193712	+	0.111840i
$275$	−3.25986	−	0.611015i	−0.196577	−	0.0368456i
$276$	3.52536	+	0.977923i	0.212201	+	0.0588640i
$277$	11.1494	−	6.43710i	0.669902	−	0.386768i	−0.126138	−	0.992013i	$-0.540258\pi$
$277$	11.1494	−	6.43710i	0.669902	−	0.386768i	0.796039	+	0.605245i	$0.206925\pi$
$278$		−	23.1570i		−	1.38886i
$279$	8.92699	+	5.36551i	0.534445	+	0.321225i
$280$	−1.27503			−0.0761979
$281$	5.05524	+	8.75593i	0.301570	+	0.522335i	0.976492	−	0.215554i	$-0.0691559\pi$
$281$	5.05524	+	8.75593i	0.301570	+	0.522335i	−0.674922	+	0.737890i	$0.735823\pi$
$282$	3.26241	+	12.6183i	0.194274	+	0.751408i
$283$	17.2491	+	9.95876i	1.02535	+	0.591987i	0.915649	−	0.401978i	$-0.131677\pi$
$283$	17.2491	+	9.95876i	1.02535	+	0.591987i	0.109702	+	0.993965i	$0.465010\pi$
$284$	8.98373	+	5.18676i	0.533086	+	0.307777i
$285$	9.04465	−	2.33846i	0.535759	−	0.138518i
$286$	3.28160	+	2.81427i	0.194045	+	0.166411i
$287$			12.3961i			0.731721i
$288$	2.57129	+	1.54546i	0.151515	+	0.0910671i
$289$	−5.61039			−0.330023
$290$	−4.11927	+	2.37826i	−0.241892	+	0.139656i
$291$	5.18366	−	18.6868i	0.303871	−	1.09544i
$292$	−12.2649	−	7.08114i	−0.717749	−	0.414392i
$293$	9.53347	−	16.5125i	0.556951	−	0.964668i	−0.440798	−	0.897606i	$-0.645304\pi$
$293$	9.53347	−	16.5125i	0.556951	−	0.964668i	0.997749	−	0.0670612i	$-0.0213623\pi$
$294$	6.52399	+	6.63976i	0.380487	+	0.387239i
$295$	−1.44271	−	2.49884i	−0.0839976	−	0.145488i
$296$	−9.60655			−0.558369
$297$	0.863584	+	17.2120i	0.0501102	+	0.998744i
$298$	8.55354			0.495493
$299$	−1.37660	−	2.38434i	−0.0796107	−	0.137890i
$300$	1.21393	+	1.23547i	0.0700861	+	0.0713298i
$301$	−6.10761	+	10.5787i	−0.352037	+	0.609746i
$302$	10.0587	+	5.80738i	0.578812	+	0.334177i
$303$	6.07667	−	21.9060i	0.349096	−	1.25847i
$304$	4.67103	−	2.69682i	0.267902	−	0.154673i
$305$	−5.22963			−0.299448
$306$	8.85579	−	4.90729i	0.506252	−	0.280531i
$307$			30.0696i			1.71616i	0.513516	+	0.858080i	$0.328343\pi$
$307$			30.0696i			1.71616i	−0.513516	+	0.858080i	$0.671657\pi$
$308$	−3.21004	−	2.75291i	−0.182909	−	0.156861i
$309$	−28.5587	+	7.38374i	−1.62465	+	0.420046i
$310$	3.00666	+	1.73590i	0.170767	+	0.0985922i
$311$	−20.3268	−	11.7357i	−1.15263	−	0.665469i	−0.203100	−	0.979158i	$-0.565102\pi$
$311$	−20.3268	−	11.7357i	−1.15263	−	0.665469i	−0.949526	+	0.313690i	$0.898435\pi$
$312$	−0.565125	−	2.18578i	−0.0319939	−	0.123746i
$313$	−5.64926	−	9.78481i	−0.319315	−	0.553070i	0.661030	−	0.750359i	$-0.270119\pi$
$313$	−5.64926	−	9.78481i	−0.319315	−	0.553070i	−0.980345	+	0.197289i	$0.936786\pi$
$314$	15.0769			0.850837
$315$	−0.0672717	+	3.82451i	−0.00379033	+	0.215487i
$316$			6.02756i			0.339077i
$317$	2.70791	−	1.56341i	0.152092	−	0.0878101i	−0.422023	−	0.906585i	$-0.638680\pi$
$317$	2.70791	−	1.56341i	0.152092	−	0.0878101i	0.574114	+	0.818775i	$0.305346\pi$
$318$	8.54156	+	2.36940i	0.478987	+	0.132870i
$319$	−15.5056	−	2.90631i	−0.868147	−	0.162722i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−9.53774	−	9.70698i	−0.532345	−	0.541791i
$322$	1.34658	+	2.33234i	0.0750419	+	0.129976i
$323$		−	18.2027i		−	1.01283i
$324$	4.77133	−	7.63115i	0.265074	−	0.423953i
$325$		−	1.30346i		−	0.0723028i
$326$	10.0979	+	17.4901i	0.559272	+	0.968688i
$327$	−5.19185	+	5.10133i	−0.287110	+	0.282104i
$328$	4.86110	−	8.41967i	0.268409	−	0.464899i
$329$	−4.79715	+	8.30890i	−0.264475	+	0.458084i
$330$	0.388719	+	5.73140i	0.0213983	+	0.315503i
$331$	−0.0462278	−	0.0800689i	−0.00254091	−	0.00440098i	0.864752	−	0.502199i	$-0.167475\pi$
$331$	−0.0462278	−	0.0800689i	−0.00254091	−	0.00440098i	−0.867293	+	0.497798i	$0.834142\pi$
$332$	−1.61940			−0.0888763
$333$	−0.506848	+	28.8152i	−0.0277751	+	1.57906i
$334$	3.43790			0.188113
$335$	5.40419	−	3.12011i	0.295262	−	0.170470i
$336$	0.552802	+	2.13812i	0.0301578	+	0.116644i
$337$	19.5264	+	11.2736i	1.06367	+	0.614111i	0.926445	−	0.376429i	$-0.122848\pi$
$337$	19.5264	+	11.2736i	1.06367	+	0.614111i	0.137225	+	0.990540i	$0.456182\pi$
$338$	5.65050	−	9.78695i	0.307347	−	0.532340i
$339$	1.90299	+	7.36037i	0.103356	+	0.399761i
$340$	2.92271	−	1.68743i	0.158506	−	0.0915135i
$341$	3.82165	+	10.8619i	0.206954	+	0.588207i
$342$	−7.84276	−	14.1532i	−0.424088	−	0.765318i
$343$			15.7776i			0.851913i
$344$	8.29679	−	4.79015i	0.447333	−	0.258268i
$345$	0.977923	−	3.52536i	0.0526496	−	0.189799i
$346$	−0.930545	+	1.61175i	−0.0500264	+	0.0866482i
$347$	10.0556	−	17.4168i	0.539813	−	0.934984i	−0.459101	−	0.888384i	$-0.651828\pi$
$347$	10.0556	−	17.4168i	0.539813	−	0.934984i	0.998914	−	0.0465993i	$-0.0148384\pi$
$348$	5.77408	+	5.87654i	0.309523	+	0.315015i
$349$	14.2019	−	8.19949i	0.760212	−	0.438909i	−0.0691596	−	0.997606i	$-0.522032\pi$
$349$	14.2019	−	8.19949i	0.760212	−	0.438909i	0.829372	+	0.558697i	$0.188698\pi$
$350$			1.27503i			0.0681535i
$351$	−6.58615	+	1.57979i	−0.351543	+	0.0843229i
$352$	1.10077	+	3.12863i	0.0586714	+	0.166756i
$353$	−8.17582	+	4.72031i	−0.435155	+	0.251237i	−0.701540	−	0.712630i	$-0.747504\pi$
$353$	−8.17582	+	4.72031i	−0.435155	+	0.251237i	0.266385	+	0.963867i	$0.414171\pi$
$354$	−3.56483	+	3.50268i	−0.189469	+	0.186165i
$355$	5.18676	−	8.98373i	0.275284	−	0.476807i
$356$	−7.39164	−	4.26757i	−0.391756	−	0.226181i
$357$	7.18190	+	1.99224i	0.380107	+	0.105440i
$358$	−7.51440	+	4.33844i	−0.397148	+	0.229294i
$359$	18.5687			0.980021			0.490010	−	0.871717i	$-0.336993\pi$
$359$	18.5687			0.980021			0.490010	+	0.871717i	$0.336993\pi$
$360$	1.54546	−	2.57129i	0.0814529	−	0.135519i
$361$	−10.0914			−0.531124
$362$	6.08807	+	10.5448i	0.319982	+	0.554225i
$363$	−11.3959	+	15.2687i	−0.598130	+	0.801399i
$364$	0.830977	−	1.43929i	0.0435550	−	0.0754395i
$365$	−7.08114	+	12.2649i	−0.370644	+	0.641974i
$366$	2.26735	+	8.76962i	0.118516	+	0.458395i
$367$	13.6592	+	23.6584i	0.713005	+	1.23496i	0.963724	+	0.266900i	$0.0859995\pi$
$367$	13.6592	+	23.6584i	0.713005	+	1.23496i	−0.250719	+	0.968060i	$0.580667\pi$
$368$		−	2.11222i		−	0.110107i
$369$	−24.9986	−	15.0253i	−1.30138	−	0.782184i
$370$			9.60655i			0.499421i
$371$	3.26262	+	5.65102i	0.169387	+	0.293386i
$372$	1.60738	−	5.79451i	0.0833387	−	0.300431i
$373$	5.63218	+	3.25174i	0.291623	+	0.168369i	0.638674	−	0.769478i	$-0.279483\pi$
$373$	5.63218	+	3.25174i	0.291623	+	0.168369i	−0.347051	+	0.937846i	$0.612817\pi$
$374$	11.0015	+	2.06209i	0.568875	+	0.106628i
$375$	1.23547	−	1.21393i	0.0637993	−	0.0626869i
$376$	6.51661	−	3.76236i	0.336068	−	0.194029i
$377$		−	6.19994i		−	0.319313i
$378$	6.44253	−	1.54534i	0.331368	−	0.0794837i
$379$	−7.08548			−0.363957			−0.181978	−	0.983303i	$-0.558250\pi$
$379$	−7.08548			−0.363957			−0.181978	+	0.983303i	$0.558250\pi$
$380$	−2.69682	−	4.67103i	−0.138344	−	0.239619i
$381$	−24.8958	+	24.4618i	−1.27545	+	1.25321i
$382$	5.40786	+	3.12223i	0.276690	+	0.159747i
$383$	−18.6989	−	10.7958i	−0.955471	−	0.551641i	−0.0606948	−	0.998156i	$-0.519332\pi$
$383$	−18.6989	−	10.7958i	−0.955471	−	0.551641i	−0.894776	+	0.446515i	$0.852665\pi$
$384$	0.462983	−	1.66903i	0.0236265	−	0.0851721i
$385$	−2.75291	+	3.21004i	−0.140301	+	0.163599i
$386$		−	23.5512i		−	1.19872i
$387$	−13.9305	−	25.1393i	−0.708127	−	1.27790i
$388$	−11.1962			−0.568402
$389$	1.43162	−	0.826544i	0.0725858	−	0.0419075i	−0.463268	−	0.886218i	$-0.653323\pi$
$389$	1.43162	−	0.826544i	0.0725858	−	0.0419075i	0.535854	+	0.844311i	$0.319990\pi$
$390$	−2.18578	+	0.565125i	−0.110681	+	0.0286162i
$391$	−6.17341	−	3.56422i	−0.312203	−	0.180250i
$392$	2.68714	−	4.65427i	0.135721	−	0.235076i
$393$	21.6761	−	5.60426i	1.09341	−	0.282698i
$394$	−2.33175	−	4.03871i	−0.117472	−	0.203467i
$395$	6.02756			0.303279
$396$	9.44250	−	3.13674i	0.474504	−	0.157627i
$397$	3.84040			0.192744			0.0963721	−	0.995345i	$-0.469276\pi$
$397$	3.84040			0.192744			0.0963721	+	0.995345i	$0.469276\pi$
$398$	−7.20764	−	12.4840i	−0.361286	−	0.625766i
$399$	3.18397	−	11.4780i	0.159398	−	0.574620i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	14.7239	+	8.50085i	0.735276	+	0.424512i	0.820349	−	0.571863i	$-0.193779\pi$
$401$	14.7239	+	8.50085i	0.735276	+	0.424512i	−0.0850730	+	0.996375i	$0.527112\pi$
$402$	−7.57517	−	7.70959i	−0.377815	−	0.384519i
$403$	−3.91905	+	2.26267i	−0.195222	+	0.112711i
$404$	−13.1250			−0.652995
$405$	−7.63115	−	4.77133i	−0.379195	−	0.237089i
$406$			6.06474i			0.300988i
$407$	−20.7413	+	24.1855i	−1.02811	+	1.19883i
$408$	−4.09682	−	4.16952i	−0.202823	−	0.206422i
$409$	3.55993	+	2.05533i	0.176027	+	0.101629i	0.585425	−	0.810727i	$-0.300928\pi$
$409$	3.55993	+	2.05533i	0.176027	+	0.101629i	−0.409398	+	0.912356i	$0.634261\pi$
$410$	−8.41967	−	4.86110i	−0.415818	−	0.240073i
$411$	−6.17965	−	1.71422i	−0.304820	−	0.0845561i
$412$	8.51528	+	14.7489i	0.419518	+	0.726626i
$413$	−3.67900			−0.181032
$414$	−6.33569	−	0.111442i	−0.311382	−	0.00547710i
$415$			1.61940i			0.0794934i
$416$	−1.12883	+	0.651729i	−0.0553453	+	0.0319536i
$417$	10.0399	+	38.8322i	0.491656	+	1.90162i
$418$	3.29560	−	17.5825i	0.161193	−	0.859988i
$419$	17.3548	+	10.0198i	0.847839	+	0.489500i	0.859921	−	0.510427i	$-0.170513\pi$
$419$	17.3548	+	10.0198i	0.847839	+	0.489500i	−0.0120824	+	0.999927i	$0.503846\pi$
$420$	2.13812	−	0.552802i	0.104329	−	0.0269740i
$421$	−1.74631	−	3.02470i	−0.0851100	−	0.147415i	0.820328	−	0.571893i	$-0.193791\pi$
$421$	−1.74631	−	3.02470i	−0.0851100	−	0.147415i	−0.905438	+	0.424478i	$0.860458\pi$
$422$		−	10.8295i		−	0.527174i
$423$	−10.9415	−	19.7453i	−0.531995	−	0.960049i
$424$		−	5.11769i		−	0.248537i
$425$	−1.68743	−	2.92271i	−0.0818521	−	0.141772i
$426$	−17.3137	−	4.80276i	−0.838850	−	0.232694i
$427$	−3.33398	+	5.77462i	−0.161343	+	0.279453i
$428$	−3.92846	+	6.80430i	−0.189890	+	0.328898i
$429$	−6.72310	−	3.29652i	−0.324594	−	0.159157i
$430$	−4.79015	−	8.29679i	−0.231002	−	0.400107i
$431$	5.82803			0.280726			0.140363	−	0.990100i	$-0.455173\pi$
$431$	5.82803			0.280726			0.140363	+	0.990100i	$0.455173\pi$
$432$	−4.98188	−	1.47679i	−0.239691	−	0.0710522i
$433$	−18.0147			−0.865729			−0.432865	−	0.901459i	$-0.642497\pi$
$433$	−18.0147			−0.865729			−0.432865	+	0.901459i	$0.642497\pi$
$434$	3.83359	−	2.21333i	0.184018	−	0.106243i
$435$	5.87654	−	5.77408i	0.281758	−	0.276846i
$436$	3.63933	+	2.10117i	0.174292	+	0.100628i
$437$	−5.69629	+	9.86626i	−0.272490	+	0.471967i
$438$	23.6372	+	6.55689i	1.12943	+	0.313300i
$439$	0.710007	−	0.409923i	0.0338868	−	0.0195645i	−0.482961	−	0.875642i	$-0.660439\pi$
$439$	0.710007	−	0.409923i	0.0338868	−	0.0195645i	0.516848	+	0.856077i	$0.327105\pi$
$440$	3.12863	−	1.10077i	0.149151	−	0.0524773i
$441$	−13.8189	−	8.30575i	−0.658042	−	0.395512i
$442$			4.39898i			0.209238i
$443$	20.9407	−	12.0901i	0.994924	−	0.574420i	0.0881814	−	0.996104i	$-0.471894\pi$
$443$	20.9407	−	12.0901i	0.994924	−	0.574420i	0.906742	+	0.421685i	$0.138561\pi$
$444$	16.1093	−	4.16500i	0.764514	−	0.197662i
$445$	−4.26757	+	7.39164i	−0.202302	+	0.350398i
$446$	1.95126	−	3.37969i	0.0923949	−	0.160033i
$447$	−14.3435	+	3.70846i	−0.678425	+	0.175404i
$448$	1.10421	−	0.637517i	0.0521691	−	0.0301199i
$449$			8.84226i			0.417292i	0.977991	+	0.208646i	$0.0669057\pi$
$449$			8.84226i			0.417292i	−0.977991	+	0.208646i	$0.933094\pi$
$450$	−2.57129	−	1.54546i	−0.121212	−	0.0728537i
$451$	−10.7019	−	30.4171i	−0.503934	−	1.43229i
$452$	3.80120	−	2.19462i	0.178793	−	0.103226i
$453$	−19.3853	−	5.37744i	−0.910803	−	0.252654i
$454$	−9.33836	+	16.1745i	−0.438271	+	0.759108i
$455$	−1.43929	−	0.830977i	−0.0674752	−	0.0389568i
$456$	−6.66367	+	6.54749i	−0.312055	+	0.306614i
$457$	13.0231	−	7.51886i	0.609193	−	0.351718i	−0.163457	−	0.986550i	$-0.552264\pi$
$457$	13.0231	−	7.51886i	0.609193	−	0.351718i	0.772649	+	0.634833i	$0.218931\pi$
$458$	15.6689			0.732160
$459$	−12.7228	+	12.0686i	−0.593848	+	0.563313i
$460$	−2.11222			−0.0984829
$461$	−4.80589	−	8.32404i	−0.223833	−	0.387689i	0.732136	−	0.681158i	$-0.238524\pi$
$461$	−4.80589	−	8.32404i	−0.223833	−	0.387689i	−0.955969	+	0.293469i	$0.905190\pi$
$462$	6.57649	+	3.22464i	0.305966	+	0.150024i
$463$	−13.3284	+	23.0854i	−0.619422	+	1.07287i	0.370169	+	0.928964i	$0.379300\pi$
$463$	−13.3284	+	23.0854i	−0.619422	+	1.07287i	−0.989591	+	0.143906i	$0.954034\pi$
$464$	2.37826	−	4.11927i	0.110408	−	0.191233i
$465$	−5.79451	−	1.60738i	−0.268714	−	0.0745404i
$466$	−7.82986	−	13.5617i	−0.362711	−	0.628234i
$467$		−	6.89050i		−	0.318855i	−0.987210	−	0.159427i	$-0.949035\pi$
$467$		−	6.89050i		−	0.318855i	0.987210	−	0.159427i	$-0.0509647\pi$
$468$	1.89533	+	3.42035i	0.0876115	+	0.158106i
$469$		−	7.95649i		−	0.367397i
$470$	−3.76236	−	6.51661i	−0.173545	−	0.300589i
$471$	−25.2826	+	6.53670i	−1.16496	+	0.301195i
$472$	2.49884	+	1.44271i	0.115018	+	0.0664059i
$473$	5.85372	−	31.2304i	0.269154	−	1.43598i
$474$	−2.61330	−	10.1077i	−0.120033	−	0.464261i
$475$	−4.67103	+	2.69682i	−0.214322	+	0.123739i
$476$		−	4.30305i		−	0.197230i
$477$	−15.3507	−	0.270013i	−0.702861	−	0.0123631i
$478$	−8.60861			−0.393749
$479$	−6.23709	−	10.8030i	−0.284980	−	0.493600i	0.687624	−	0.726067i	$-0.258654\pi$
$479$	−6.23709	−	10.8030i	−0.284980	−	0.493600i	−0.972604	+	0.232467i	$0.925320\pi$
$480$	−1.66903	−	0.462983i	−0.0761803	−	0.0211322i
$481$	−10.8441	−	6.26086i	−0.494450	−	0.285471i
$482$	2.66362	+	1.53784i	0.121325	+	0.0700469i
$483$	−3.26930	−	3.32731i	−0.148758	−	0.151398i
$484$	10.2533	+	3.98364i	0.466060	+	0.181075i
$485$			11.1962i			0.508394i
$486$	−4.69254	+	14.8654i	−0.212858	+	0.674308i
$487$	21.3546			0.967669			0.483835	−	0.875160i	$-0.339244\pi$
$487$	21.3546			0.967669			0.483835	+	0.875160i	$0.339244\pi$
$488$	4.52899	−	2.61481i	0.205018	−	0.118367i
$489$	−24.5163	−	24.9513i	−1.10867	−	1.12834i
$490$	−4.65427	−	2.68714i	−0.210258	−	0.121393i
$491$	−10.2802	+	17.8058i	−0.463939	+	0.803565i	−0.999153	−	0.0411511i	$-0.986897\pi$
$491$	−10.2802	+	17.8058i	−0.463939	+	0.803565i	0.535214	+	0.844716i	$0.320231\pi$
$492$	−4.50121	+	16.2266i	−0.202930	+	0.731552i
$493$	−8.02629	−	13.9019i	−0.361486	−	0.626112i
$494$	7.03038			0.316312
$495$	−3.13674	−	9.44250i	−0.140986	−	0.424409i
$496$	−3.47179			−0.155888
$497$	−6.61329	−	11.4546i	−0.296647	−	0.513807i
$498$	2.71559	−	0.702105i	0.121689	−	0.0314621i
$499$	−8.47693	+	14.6825i	−0.379480	+	0.657278i	−0.990987	−	0.133961i	$-0.957230\pi$
$499$	−8.47693	+	14.6825i	−0.379480	+	0.657278i	0.611507	+	0.791239i	$0.290564\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−5.76504	+	1.49053i	−0.257563	+	0.0665919i
$502$	−5.23072	+	3.01996i	−0.233459	+	0.134787i
$503$	−24.5268			−1.09360			−0.546799	−	0.837264i	$-0.684154\pi$
$503$	−24.5268			−1.09360			−0.546799	+	0.837264i	$0.684154\pi$
$504$	−1.85400	−	3.34576i	−0.0825836	−	0.149032i
$505$			13.1250i			0.584057i
$506$	−5.31776	−	4.56047i	−0.236403	−	0.202737i
$507$	−5.23217	+	18.8617i	−0.232369	+	0.837676i
$508$	17.4512	+	10.0755i	0.774272	+	0.447026i
$509$	7.97673	+	4.60537i	0.353562	+	0.204129i	0.666253	−	0.745726i	$-0.267897\pi$
$509$	7.97673	+	4.60537i	0.353562	+	0.204129i	−0.312691	+	0.949855i	$0.601230\pi$
$510$	−4.16952	+	4.09682i	−0.184629	+	0.181410i
$511$	9.02870	+	15.6382i	0.399406	+	0.691792i
$512$	−1.00000			−0.0441942
$513$	19.2878	+	20.3334i	0.851579	+	0.897740i
$514$			17.8978i			0.789437i
$515$	14.7489	−	8.51528i	0.649914	−	0.375228i
$516$	−11.8362	+	11.6298i	−0.521058	+	0.511973i
$517$	4.59773	−	24.5295i	0.202208	−	1.07881i
$518$	10.6077	+	6.12434i	0.466074	+	0.269088i
$519$	0.861652	−	3.10621i	0.0378223	−	0.136347i
$520$	0.651729	+	1.12883i	0.0285802	+	0.0495024i
$521$			23.9155i			1.04776i	0.851793	+	0.523879i	$0.175516\pi$
$521$			23.9155i			1.04776i	−0.851793	+	0.523879i	$0.824484\pi$
$522$	−12.2304	−	7.35103i	−0.535312	−	0.321746i
$523$			11.5018i			0.502939i	0.967865	+	0.251469i	$0.0809138\pi$
$523$			11.5018i			0.502939i	−0.967865	+	0.251469i	$0.919086\pi$
$524$	−6.46311	−	11.1944i	−0.282342	−	0.489031i
$525$	−0.552802	−	2.13812i	−0.0241262	−	0.0933151i
$526$	12.6011	−	21.8257i	0.549433	−	0.951647i
$527$	−5.85839	+	10.1470i	−0.255195	+	0.442011i
$528$	−3.20234	−	4.76917i	−0.139364	−	0.207552i
$529$	−9.26926	−	16.0548i	−0.403011	−	0.698036i
$530$	−5.11769			−0.222298
$531$	4.45929	−	7.41924i	0.193517	−	0.321968i
$532$	−6.87708			−0.298159
$533$	10.9747	−	6.33624i	0.475366	−	0.274453i
$534$	14.2454	+	3.95162i	0.616457	+	0.171003i
$535$	6.80430	+	3.92846i	0.294176	+	0.169842i
$536$	−3.12011	+	5.40419i	−0.134768	+	0.233425i
$537$	10.7200	−	10.5331i	0.462602	−	0.454537i
$538$	−12.2340	+	7.06330i	−0.527445	+	0.304520i
$539$	−5.91587	−	16.8141i	−0.254815	−	0.724236i
$540$	−1.47679	+	4.98188i	−0.0635510	+	0.214386i
$541$			17.3878i			0.747562i	0.927517	+	0.373781i	$0.121939\pi$
$541$			17.3878i			0.747562i	−0.927517	+	0.373781i	$0.878061\pi$
$542$	−11.8922	+	6.86598i	−0.510815	+	0.294919i
$543$	−14.7809	−	15.0432i	−0.634311	−	0.645567i
$544$	−1.68743	+	2.92271i	−0.0723478	+	0.125310i
$545$	2.10117	−	3.63933i	0.0900042	−	0.155892i
$546$	−0.769456	+	2.77384i	−0.0329297	+	0.118710i
$547$	−7.28532	+	4.20618i	−0.311498	+	0.179843i	−0.647597	−	0.761983i	$-0.724226\pi$
$547$	−7.28532	+	4.20618i	−0.311498	+	0.179843i	0.336099	+	0.941827i	$0.390892\pi$
$548$			3.70255i			0.158165i
$549$	−7.60428	−	13.7228i	−0.324543	−	0.585676i
$550$	−1.10077	−	3.12863i	−0.0469371	−	0.133405i
$551$	−22.2179	+	12.8275i	−0.946514	+	0.546470i
$552$	0.915772	+	3.54201i	0.0389778	+	0.150758i
$553$	3.84267	−	6.65570i	0.163407	−	0.283029i
$554$	11.1494	+	6.43710i	0.473692	+	0.273486i
$555$	−4.16500	−	16.1093i	−0.176794	−	0.683802i
$556$	20.0545	−	11.5785i	0.850502	−	0.491037i
$557$	25.5098			1.08089			0.540443	−	0.841380i	$-0.318256\pi$
$557$	25.5098			1.08089			0.540443	+	0.841380i	$0.318256\pi$
$558$	−0.183174	+	10.4138i	−0.00775438	+	0.440850i
$559$	12.4875			0.528166
$560$	−0.637517	−	1.10421i	−0.0269400	−	0.0466615i
$561$	−19.3426	+	1.31187i	−0.816645	+	0.0553871i
$562$	−5.05524	+	8.75593i	−0.213242	+	0.369347i
$563$	13.1690	−	22.8093i	0.555006	−	0.961299i	−0.442897	−	0.896573i	$-0.646049\pi$
$563$	13.1690	−	22.8093i	0.555006	−	0.961299i	0.997903	−	0.0647264i	$-0.0206175\pi$
$564$	−9.29656	+	9.13447i	−0.391456	+	0.384631i
$565$	−2.19462	−	3.80120i	−0.0923285	−	0.159918i
$566$			19.9175i			0.837195i
$567$	−10.1335	+	5.38461i	−0.425569	+	0.226132i
$568$			10.3735i			0.435263i
$569$	14.2692	+	24.7150i	0.598197	+	1.03611i	0.993087	+	0.117380i	$0.0374495\pi$
$569$	14.2692	+	24.7150i	0.598197	+	1.03611i	−0.394890	+	0.918729i	$0.629217\pi$
$570$	6.54749	+	6.66367i	0.274244	+	0.279110i
$571$	32.0431	+	18.5001i	1.34096	+	0.774205i	0.986949	−	0.161036i	$-0.0514834\pi$
$571$	32.0431	+	18.5001i	1.34096	+	0.774205i	0.354013	+	0.935240i	$0.384817\pi$
$572$	−0.796433	+	4.24908i	−0.0333005	+	0.177663i
$573$	−10.4222	−	2.89108i	−0.435392	−	0.120777i
$574$	−10.7354	+	6.19807i	−0.448086	+	0.258702i
$575$			2.11222i			0.0880858i
$576$	−0.0527607	+	2.99954i	−0.00219836	+	0.124981i
$577$	−27.7269			−1.15429			−0.577144	−	0.816643i	$-0.695833\pi$
$577$	−27.7269			−1.15429			−0.577144	+	0.816643i	$0.695833\pi$
$578$	−2.80519	−	4.85874i	−0.116681	−	0.202097i
$579$	10.2108	+	39.4932i	0.424346	+	1.64128i
$580$	−4.11927	−	2.37826i	−0.171044	−	0.0987521i
$581$	1.78816	+	1.03240i	0.0741856	+	0.0428311i
$582$	18.7751	−	4.85421i	0.778251	−	0.201214i
$583$	−12.8844	−	11.0495i	−0.533616	−	0.457625i
$584$		−	14.1623i		−	0.586039i
$585$	3.42035	−	1.89533i	0.141414	−	0.0783621i
$586$	19.0669			0.787648
$587$	13.5447	−	7.82004i	0.559050	−	0.322768i	−0.193714	−	0.981058i	$-0.562053\pi$
$587$	13.5447	−	7.82004i	0.559050	−	0.322768i	0.752764	+	0.658290i	$0.228720\pi$
$588$	−2.48820	+	8.96982i	−0.102612	+	0.369909i
$589$	16.2168	+	9.36279i	0.668203	+	0.385787i
$590$	1.44271	−	2.49884i	0.0593952	−	0.102876i
$591$	5.66115	+	5.76161i	0.232869	+	0.237001i
$592$	−4.80327	−	8.31951i	−0.197413	−	0.341930i
$593$	−40.5045			−1.66332			−0.831660	−	0.555286i	$-0.812609\pi$
$593$	−40.5045			−1.66332			−0.831660	+	0.555286i	$0.812609\pi$
$594$	−14.4743	+	9.35390i	−0.593886	+	0.383795i
$595$	−4.30305			−0.176408
$596$	4.27677	+	7.40758i	0.175183	+	0.303426i
$597$	17.4991	+	17.8096i	0.716190	+	0.728899i
$598$	1.37660	−	2.38434i	0.0562932	−	0.0975028i
$599$	−23.7343	−	13.7030i	−0.969757	−	0.559890i	−0.0705950	−	0.997505i	$-0.522490\pi$
$599$	−23.7343	−	13.7030i	−0.969757	−	0.559890i	−0.899162	+	0.437615i	$0.855823\pi$
$600$	−0.462983	+	1.66903i	−0.0189012	+	0.0681377i
$601$	26.3874	−	15.2348i	1.07636	−	0.621438i	0.146450	−	0.989218i	$-0.453215\pi$
$601$	26.3874	−	15.2348i	1.07636	−	0.621438i	0.929913	+	0.367780i	$0.119882\pi$
$602$	−12.2152			−0.497855
$603$	16.0454	+	9.64401i	0.653421	+	0.392734i
$604$			11.6148i			0.472598i
$605$	3.98364	−	10.2533i	0.161958	−	0.416857i
$606$	22.0095	−	5.69047i	0.894076	−	0.231160i
$607$	−15.9618	−	9.21558i	−0.647871	−	0.374049i	0.139769	−	0.990184i	$-0.455364\pi$
$607$	−15.9618	−	9.21558i	−0.647871	−	0.374049i	−0.787640	+	0.616135i	$0.788697\pi$
$608$	4.67103	+	2.69682i	0.189435	+	0.109370i
$609$	−2.62942	−	10.1700i	−0.106549	−	0.412110i
$610$	−2.61481	−	4.52899i	−0.105871	−	0.183373i
$611$	9.80817			0.396796
$612$	8.67773	+	5.21570i	0.350777	+	0.210832i
$613$			42.1721i			1.70332i	0.524097	+	0.851659i	$0.324403\pi$
$613$			42.1721i			1.70332i	−0.524097	+	0.851659i	$0.675597\pi$
$614$	−26.0410	+	15.0348i	−1.05093	+	0.606754i
$615$	16.2266	+	4.50121i	0.654320	+	0.181506i
$616$	0.779066	−	4.15643i	0.0313895	−	0.167467i
$617$	−22.2411	−	12.8409i	−0.895394	−	0.516956i	−0.0196907	−	0.999806i	$-0.506268\pi$
$617$	−22.2411	−	12.8409i	−0.895394	−	0.516956i	−0.875703	+	0.482850i	$0.839601\pi$
$618$	−20.6739	−	21.0407i	−0.831625	−	0.846381i
$619$	−13.8445	−	23.9795i	−0.556459	−	0.963816i	−0.997788	−	0.0664705i	$-0.978826\pi$
$619$	−13.8445	−	23.9795i	−0.556459	−	0.963816i	0.441329	−	0.897345i	$-0.354507\pi$
$620$			3.47179i			0.139430i
$621$	10.6727	−	2.56001i	0.428281	−	0.102730i
$622$		−	23.4713i		−	0.941115i
$623$	5.44130	+	9.42460i	0.218001	+	0.377589i
$624$	1.61038	−	1.58230i	0.0644668	−	0.0633428i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.64926	−	9.78481i	0.225790	−	0.391080i
$627$	2.09661	+	30.9131i	0.0837305	+	1.23455i
$628$	7.53844	+	13.0570i	0.300816	+	0.521029i
$629$	−32.4207			−1.29270
$630$	−3.34576	+	1.85400i	−0.133298	+	0.0738650i
$631$	23.6658			0.942119			0.471060	−	0.882101i	$-0.343872\pi$
$631$	23.6658			0.942119			0.471060	+	0.882101i	$0.343872\pi$
$632$	−5.22002	+	3.01378i	−0.207641	+	0.119882i
$633$	4.69523	+	18.1602i	0.186619	+	0.721802i
$634$	2.70791	+	1.56341i	0.107545	+	0.0620911i
$635$	10.0755	−	17.4512i	0.399832	−	0.692530i
$636$	2.21882	+	8.58191i	0.0879818	+	0.340295i
$637$	6.06664	−	3.50258i	0.240369	−	0.138777i
$638$	−5.23586	−	14.8814i	−0.207290	−	0.589160i
$639$	31.1157	+	0.547314i	1.23092	+	0.0216514i
$640$			1.00000i			0.0395285i
$641$	16.7978	−	9.69820i	0.663472	−	0.383056i	−0.130126	−	0.991497i	$-0.541538\pi$
$641$	16.7978	−	9.69820i	0.663472	−	0.383056i	0.793599	+	0.608442i	$0.208205\pi$
$642$	3.63762	−	13.1134i	0.143566	−	0.517545i
$643$	5.73872	−	9.93976i	0.226313	−	0.391986i	−0.730399	−	0.683020i	$-0.760666\pi$
$643$	5.73872	−	9.93976i	0.226313	−	0.391986i	0.956713	+	0.291034i	$0.0939994\pi$
$644$	−1.34658	+	2.33234i	−0.0530626	+	0.0919072i
$645$	11.6298	+	11.8362i	0.457923	+	0.466048i
$646$	15.7640	−	9.10136i	0.620227	−	0.358088i
$647$			2.45185i			0.0963924i	0.998838	+	0.0481962i	$0.0153473\pi$
$647$			2.45185i			0.0963924i	−0.998838	+	0.0481962i	$0.984653\pi$
$648$	8.99443	+	0.316515i	0.353335	+	0.0124339i
$649$	9.02737	−	3.17618i	0.354355	−	0.124676i
$650$	1.12883	−	0.651729i	0.0442763	−	0.0255629i
$651$	−5.46899	+	5.37364i	−0.214346	+	0.210609i
$652$	−10.0979	+	17.4901i	−0.395465	+	0.684966i
$653$	−20.5412	−	11.8594i	−0.803838	−	0.464096i	0.0409734	−	0.999160i	$-0.486954\pi$
$653$	−20.5412	−	11.8594i	−0.803838	−	0.464096i	−0.844811	+	0.535064i	$0.820287\pi$
$654$	−7.01381	−	1.94561i	−0.274262	−	0.0760794i
$655$	−11.1944	+	6.46311i	−0.437402	+	0.252534i
$656$	9.72220			0.379588
$657$	−42.4803	−	0.747212i	−1.65731	−	0.0291515i
$658$	−9.59429			−0.374024
$659$	−12.4162	−	21.5054i	−0.483665	−	0.837732i	0.516159	−	0.856493i	$-0.327361\pi$
$659$	−12.4162	−	21.5054i	−0.483665	−	0.837732i	−0.999824	+	0.0187609i	$0.994028\pi$
$660$	−4.76917	+	3.20234i	−0.185640	+	0.124651i
$661$	−16.4988	+	28.5768i	−0.641729	+	1.11151i	0.343318	+	0.939219i	$0.388449\pi$
$661$	−16.4988	+	28.5768i	−0.641729	+	1.11151i	−0.985047	+	0.172288i	$0.944884\pi$
$662$	0.0462278	−	0.0800689i	0.00179669	−	0.00311197i
$663$	−1.90721	−	7.37669i	−0.0740700	−	0.286487i
$664$	−0.809702	−	1.40244i	−0.0314225	−	0.0544254i
$665$			6.87708i			0.266682i
$666$	−25.2081	+	13.9686i	−0.976794	+	0.541274i
$667$			10.0469i			0.389016i
$668$	1.71895	+	2.97731i	0.0665081	+	0.115195i
$669$	−1.80680	+	6.51341i	−0.0698550	+	0.251823i
$670$	5.40419	+	3.12011i	0.208782	+	0.120540i
$671$	3.19538	−	17.0478i	0.123356	−	0.658124i
$672$	−1.57526	+	1.54780i	−0.0607671	+	0.0597077i
$673$	24.5268	−	14.1605i	0.945438	−	0.545849i	0.0537768	−	0.998553i	$-0.482874\pi$
$673$	24.5268	−	14.1605i	0.945438	−	0.545849i	0.891661	+	0.452704i	$0.149541\pi$
$674$			22.5471i			0.868484i
$675$	4.98188	+	1.47679i	0.191752	+	0.0568418i
$676$	11.3010			0.434654
$677$	−5.30072	−	9.18112i	−0.203723	−	0.352859i	0.746002	−	0.665944i	$-0.231971\pi$
$677$	−5.30072	−	9.18112i	−0.203723	−	0.352859i	−0.949725	+	0.313085i	$0.898638\pi$
$678$	−5.42277	+	5.32823i	−0.208260	+	0.204629i
$679$	12.3630	+	7.13779i	0.474449	+	0.273923i
$680$	2.92271	+	1.68743i	0.112081	+	0.0647098i
$681$	8.64700	−	31.1719i	0.331354	−	1.19451i
$682$	−7.49588	+	8.74062i	−0.287032	+	0.334695i
$683$		−	7.15826i		−	0.273903i	−0.990578	−	0.136952i	$-0.956269\pi$
$683$		−	7.15826i		−	0.273903i	0.990578	−	0.136952i	$-0.0437305\pi$
$684$	8.33566	−	13.8686i	0.318722	−	0.530281i
$685$	3.70255			0.141467
$686$	−13.6638	+	7.88882i	−0.521688	+	0.301197i
$687$	−26.2754	+	6.79338i	−1.00247	+	0.259184i
$688$	8.29679	+	4.79015i	0.316312	+	0.182623i
$689$	3.33535	−	5.77699i	0.127067	−	0.220086i
$690$	3.54201	−	0.915772i	0.134842	−	0.0348628i
$691$	24.5817	+	42.5767i	0.935132	+	1.61970i	0.774399	+	0.632697i	$0.218052\pi$
$691$	24.5817	+	42.5767i	0.935132	+	1.61970i	0.160732	+	0.986998i	$0.448614\pi$
$692$	−1.86109			−0.0707480
$693$	−12.4263	−	2.55613i	−0.472034	−	0.0970994i
$694$	20.1112			0.763411
$695$	−11.5785	−	20.0545i	−0.439197	−	0.760712i
$696$	−2.20219	+	7.93877i	−0.0834738	+	0.300918i
$697$	16.4055	−	28.4151i	0.621402	−	1.07630i
$698$	14.2019	+	8.19949i	0.537551	+	0.310355i
$699$	19.0098	+	19.3471i	0.719015	+	0.731774i
$700$	−1.10421	+	0.637517i	−0.0417353	+	0.0240959i
$701$	6.48029			0.244757			0.122379	−	0.992483i	$-0.460948\pi$
$701$	6.48029			0.244757			0.122379	+	0.992483i	$0.460948\pi$
$702$	−4.66121	−	4.91388i	−0.175926	−	0.185462i
$703$			51.8143i			1.95421i
$704$	−2.15908	+	2.51761i	−0.0813735	+	0.0948860i
$705$	9.13447	+	9.29656i	0.344024	+	0.350129i
$706$	−8.17582	−	4.72031i	−0.307701	−	0.177651i
$707$	14.4928	+	8.36744i	0.545059	+	0.314690i
$708$	−4.81582	−	1.33590i	−0.180990	−	0.0502060i
$709$	25.2075	+	43.6606i	0.946686	+	1.63971i	0.752340	+	0.658775i	$0.228925\pi$
$709$	25.2075	+	43.6606i	0.946686	+	1.63971i	0.194346	+	0.980933i	$0.437741\pi$
$710$	10.3735			0.389311
$711$	8.76453	+	15.8166i	0.328695	+	0.593170i
$712$		−	8.53513i		−	0.319868i
$713$	6.35074	−	3.66660i	0.237837	−	0.137315i
$714$	1.86562	+	7.21583i	0.0698192	+	0.270046i
$715$	4.24908	+	0.796433i	0.158907	+	0.0297849i
$716$	−7.51440	−	4.33844i	−0.280826	−	0.162135i
$717$	14.4359	−	3.73233i	0.539117	−	0.139387i
$718$	9.28437	+	16.0810i	0.346490	+	0.600138i
$719$			27.7203i			1.03379i	0.856048	+	0.516896i	$0.172913\pi$
$719$			27.7203i			1.03379i	−0.856048	+	0.516896i	$0.827087\pi$
$720$	2.99954	+	0.0527607i	0.111786	+	0.00196628i
$721$		−	21.7145i		−	0.808692i
$722$	−5.04568	−	8.73937i	−0.187781	−	0.325246i
$723$	−5.13340	−	1.42399i	−0.190913	−	0.0529588i
$724$	−6.08807	+	10.5448i	−0.226261	+	0.391896i
$725$	−2.37826	+	4.11927i	−0.0883265	+	0.152986i
$726$	−18.9210	−	2.23480i	−0.702226	−	0.0829413i
$727$	11.8138	+	20.4620i	0.438148	+	0.758895i	0.997547	−	0.0700040i	$-0.0223012\pi$
$727$	11.8138	+	20.4620i	0.438148	+	0.758895i	−0.559399	+	0.828899i	$0.688968\pi$
$728$	1.66195			0.0615961
$729$	1.42395	−	26.9624i	0.0527390	−	0.998608i
$730$	−14.1623			−0.524169
$731$	28.0004	−	16.1661i	1.03563	−	0.597923i
$732$	−6.46104	+	6.34839i	−0.238807	+	0.234643i
$733$	−21.4597	−	12.3898i	−0.792634	−	0.457627i	0.0482553	−	0.998835i	$-0.484634\pi$
$733$	−21.4597	−	12.3898i	−0.792634	−	0.457627i	−0.840889	+	0.541208i	$0.817967\pi$
$734$	−13.6592	+	23.6584i	−0.504170	+	0.873249i
$735$	8.96982	+	2.48820i	0.330857	+	0.0917787i
$736$	1.82924	−	1.05611i	0.0674267	−	0.0389288i
$737$	6.86906	+	19.5233i	0.253025	+	0.719150i
$738$	0.512950	−	29.1621i	0.0188820	−	1.07347i
$739$			13.2395i			0.487021i	0.969898	+	0.243511i	$0.0782991\pi$
$739$			13.2395i			0.487021i	−0.969898	+	0.243511i	$0.921701\pi$
$740$	−8.31951	+	4.80327i	−0.305831	+	0.176572i
$741$	−11.7893	+	3.04808i	−0.433092	+	0.111974i
$742$	−3.26262	+	5.65102i	−0.119774	+	0.207455i
$743$	15.3959	−	26.6664i	0.564819	−	0.978296i	−0.432247	−	0.901755i	$-0.642279\pi$
$743$	15.3959	−	26.6664i	0.564819	−	0.978296i	0.997066	−	0.0765407i	$-0.0243875\pi$
$744$	5.82188	−	1.50522i	0.213440	−	0.0551842i
$745$	7.40758	−	4.27677i	0.271393	−	0.156689i
$746$			6.50348i			0.238109i
$747$	−4.24940	+	2.35474i	−0.155478	+	0.0861552i
$748$	3.71494	+	10.5586i	0.135832	+	0.386062i
$749$	8.67572	−	5.00893i	0.317004	−	0.183022i
$750$	1.66903	+	0.462983i	0.0609442	+	0.0169057i
$751$	−7.84780	+	13.5928i	−0.286370	+	0.496008i	−0.972941	−	0.231056i	$-0.925782\pi$
$751$	−7.84780	+	13.5928i	−0.286370	+	0.496008i	0.686570	+	0.727063i	$0.259115\pi$
$752$	6.51661	+	3.76236i	0.237636	+	0.137199i
$753$	7.46213	−	7.33202i	0.271935	−	0.267194i
$754$	5.36930	−	3.09997i	0.195538	−	0.112894i
$755$	11.6148			0.422705
$756$	4.55957	+	4.80672i	0.165830	+	0.174819i
$757$	12.4907			0.453982			0.226991	−	0.973897i	$-0.427111\pi$
$757$	12.4907			0.453982			0.226991	+	0.973897i	$0.427111\pi$
$758$	−3.54274	−	6.13621i	−0.128678	−	0.222877i
$759$	10.8946	+	5.34193i	0.395450	+	0.193900i
$760$	2.69682	−	4.67103i	0.0978239	−	0.169436i
$761$	−15.4599	+	26.7773i	−0.560421	+	0.970678i	0.437039	+	0.899443i	$0.356027\pi$
$761$	−15.4599	+	26.7773i	−0.560421	+	0.970678i	−0.997460	+	0.0712348i	$0.977306\pi$
$762$	−33.6324	−	9.32953i	−1.21837	−	0.337973i
$763$	−2.67906	−	4.64027i	−0.0969886	−	0.167989i
$764$			6.24446i			0.225917i
$765$	5.21570	−	8.67773i	0.188574	−	0.313744i
$766$		−	21.5917i		−	0.780139i
$767$	1.88051	+	3.25713i	0.0679011	+	0.117608i
$768$	1.67691	−	0.433558i	0.0605103	−	0.0156447i
$769$	36.0224	+	20.7976i	1.29900	+	0.749979i	0.980232	−	0.197853i	$-0.0633968\pi$
$769$	36.0224	+	20.7976i	1.29900	+	0.749979i	0.318770	+	0.947832i	$0.396730\pi$
$770$	−4.15643	−	0.779066i	−0.149787	−	0.0280756i
$771$	−7.75973	−	30.0130i	−0.279460	−	1.08089i
$772$	20.3959	−	11.7756i	0.734064	−	0.423812i
$773$			39.4393i			1.41853i	0.704940	+	0.709267i	$0.250974\pi$
$773$			39.4393i			1.41853i	−0.704940	+	0.709267i	$0.749026\pi$
$774$	14.8060	−	24.6338i	0.532190	−	0.885443i
$775$	3.47179			0.124710
$776$	−5.59811	−	9.69621i	−0.200961	−	0.348074i
$777$	−20.4434	−	5.67093i	−0.733401	−	0.203443i
$778$	1.43162	+	0.826544i	0.0513259	+	0.0296330i
$779$	−45.4127	−	26.2190i	−1.62708	−	0.939394i
$780$	−1.58230	−	1.61038i	−0.0566555	−	0.0576609i
$781$	26.1165	+	22.3973i	0.934521	+	0.801437i
$782$		−	7.12844i		−	0.254912i
$783$	23.6964	+	7.02441i	0.846841	+	0.251032i
$784$	5.37429			0.191939
$785$	13.0570	−	7.53844i	0.466023	−	0.269058i
$786$	15.6915	+	15.9699i	0.559697	+	0.569628i
$787$	−18.1102	−	10.4559i	−0.645560	−	0.372714i	0.141193	−	0.989982i	$-0.454906\pi$
$787$	−18.1102	−	10.4559i	−0.645560	−	0.372714i	−0.786753	+	0.617268i	$0.788240\pi$
$788$	2.33175	−	4.03871i	0.0830652	−	0.143873i
$789$	−11.6682	+	42.0631i	−0.415398	+	1.49748i
$790$	3.01378	+	5.22002i	0.107225	+	0.185720i
$791$	−5.59644			−0.198987
$792$	7.43775	+	6.60908i	0.264289	+	0.234843i
$793$	6.81660			0.242065
$794$	1.92020	+	3.32589i	0.0681454	+	0.118031i
$795$	8.58191	−	2.21882i	0.304369	−	0.0786933i
$796$	7.20764	−	12.4840i	0.255468	−	0.442483i
$797$	10.1775	+	5.87596i	0.360504	+	0.208137i	0.669302	−	0.742991i	$-0.266593\pi$
$797$	10.1775	+	5.87596i	0.360504	+	0.208137i	−0.308798	+	0.951128i	$0.599927\pi$
$798$	11.5322	−	2.98161i	0.408237	−	0.105548i
$799$	21.9926	−	12.6974i	0.778041	−	0.449202i
$800$	1.00000			0.0353553
$801$	−25.6014	−	0.450320i	−0.904583	−	0.0159113i
$802$			17.0017i			0.600351i
$803$	−35.6551	−	30.5775i	−1.25824	−	1.07906i
$804$	2.88911	−	10.4151i	0.101891	−	0.367312i
$805$	2.33234	+	1.34658i	0.0822043	+	0.0474607i
$806$	−3.91905	−	2.26267i	−0.138043	−	0.0796990i
$807$	17.4530	−	17.1487i	0.614373	−	0.603662i
$808$	−6.56252	−	11.3666i	−0.230869	−	0.399876i
$809$	50.3042			1.76860			0.884300	−	0.466919i	$-0.154636\pi$
$809$	50.3042			1.76860			0.884300	+	0.466919i	$0.154636\pi$
$810$	0.316515	−	8.99443i	0.0111212	−	0.316032i
$811$		−	35.9519i		−	1.26244i	−0.775603	−	0.631220i	$-0.782554\pi$
$811$		−	35.9519i		−	1.26244i	0.775603	−	0.631220i	$-0.217446\pi$
$812$	−5.25222	+	3.03237i	−0.184317	+	0.106415i
$813$	16.9654	−	16.6696i	0.595002	−	0.584628i
$814$	−31.3160	−	5.86975i	−1.09762	−	0.205735i
$815$	17.4901	+	10.0979i	0.612652	+	0.353715i
$816$	1.56250	−	5.63271i	0.0546983	−	0.197184i
$817$	−25.8364	−	44.7499i	−0.903900	−	1.56560i
$818$			4.11065i			0.143726i
$819$	0.0876859	−	4.98509i	0.00306399	−	0.174193i
$820$		−	9.72220i		−	0.339514i
$821$	24.1294	+	41.7934i	0.842123	+	1.45860i	0.888096	+	0.459657i	$0.152028\pi$
$821$	24.1294	+	41.7934i	0.842123	+	1.45860i	−0.0459732	+	0.998943i	$0.514639\pi$
$822$	−1.60527	−	6.20885i	−0.0559903	−	0.216558i
$823$	−10.8929	+	18.8670i	−0.379702	+	0.657663i	−0.991019	−	0.133723i	$-0.957307\pi$
$823$	−10.8929	+	18.8670i	−0.379702	+	0.657663i	0.611317	+	0.791386i	$0.290640\pi$
$824$	−8.51528	+	14.7489i	−0.296644	+	0.513802i
$825$	3.20234	+	4.76917i	0.111491	+	0.166041i
$826$	−1.83950	−	3.18611i	−0.0640044	−	0.110859i
$827$	−39.9482			−1.38914			−0.694568	−	0.719427i	$-0.744404\pi$
$827$	−39.9482			−1.38914			−0.694568	+	0.719427i	$0.744404\pi$
$828$	−3.07133	−	5.54259i	−0.106736	−	0.192618i
$829$	13.3365			0.463197			0.231599	−	0.972811i	$-0.425604\pi$
$829$	13.3365			0.463197			0.231599	+	0.972811i	$0.425604\pi$
$830$	−1.40244	+	0.809702i	−0.0486796	+	0.0281052i
$831$	−21.4874	−	5.96053i	−0.745389	−	0.206769i
$832$	−1.12883	−	0.651729i	−0.0391351	−	0.0225946i
$833$	9.06871	−	15.7075i	0.314212	−	0.544231i
$834$	−28.6097	+	28.1109i	−0.990673	+	0.973401i
$835$	2.97731	−	1.71895i	0.103034	−	0.0594867i
$836$	16.8747	−	5.93717i	0.583623	−	0.205341i
$837$	−4.20780	−	17.5424i	−0.145443	−	0.606353i
$838$			20.0396i			0.692257i
$839$	−39.3269	+	22.7054i	−1.35772	+	0.783878i	−0.989316	−	0.145789i	$-0.953428\pi$
$839$	−39.3269	+	22.7054i	−1.35772	+	0.783878i	−0.368401	+	0.929667i	$0.620095\pi$
$840$	1.54780	+	1.57526i	0.0534042	+	0.0543518i
$841$	3.18772	−	5.52129i	0.109921	−	0.190389i
$842$	1.74631	−	3.02470i	0.0601819	−	0.104238i
$843$	4.68098	−	16.8747i	0.161221	−	0.581194i
$844$	9.37866	−	5.41477i	0.322827	−	0.186384i
$845$		−	11.3010i		−	0.388766i
$846$	11.6292	−	19.3483i	0.399819	−	0.665208i
$847$	−8.78220	−	10.9355i	−0.301760	−	0.375747i
$848$	4.43205	−	2.55885i	0.152197	−	0.0878712i
$849$	−8.63540	−	33.3999i	−0.296366	−	1.14628i
$850$	1.68743	−	2.92271i	0.0578782	−	0.100248i
$851$	17.5727	+	10.1456i	0.602383	+	0.347786i
$852$	−4.49752	−	17.3954i	−0.154083	−	0.595958i
$853$	−10.0615	+	5.80903i	−0.344500	+	0.198897i	−0.662260	−	0.749274i	$-0.730403\pi$
$853$	−10.0615	+	5.80903i	−0.344500	+	0.198897i	0.317760	+	0.948171i	$0.397069\pi$
$854$	−6.66796			−0.228173
$855$	−13.8686	−	8.33566i	−0.474297	−	0.285073i
$856$	−7.85693			−0.268544
$857$	7.32841	+	12.6932i	0.250334	+	0.433591i	0.963618	−	0.267284i	$-0.0861263\pi$
$857$	7.32841	+	12.6932i	0.250334	+	0.433591i	−0.713284	+	0.700875i	$0.752793\pi$
$858$	−0.506679	−	7.47063i	−0.0172977	−	0.255043i
$859$	−12.3209	+	21.3405i	−0.420385	+	0.728128i	−0.995977	−	0.0896090i	$-0.971438\pi$
$859$	−12.3209	+	21.3405i	−0.420385	+	0.728128i	0.575592	+	0.817737i	$0.304772\pi$
$860$	4.79015	−	8.29679i	0.163343	−	0.282918i
$861$	15.3150	−	15.0480i	0.521935	−	0.512835i
$862$	2.91401	+	5.04722i	0.0992517	+	0.171909i
$863$		−	43.3057i		−	1.47414i	−0.675816	−	0.737071i	$-0.736208\pi$
$863$		−	43.3057i		−	1.47414i	0.675816	−	0.737071i	$-0.263792\pi$
$864$	−1.21200	−	5.05283i	−0.0412330	−	0.171901i
$865$			1.86109i			0.0632789i
$866$	−9.00733	−	15.6012i	−0.306081	−	0.530149i
$867$	6.81060	+	6.93145i	0.231300	+	0.235404i
$868$	3.83359	+	2.21333i	0.130121	+	0.0751252i
$869$	−3.68293	+	19.6490i	−0.124935	+	0.666546i
$870$	7.93877	+	2.20219i	0.269149	+	0.0746613i
$871$	−7.04413	+	4.06693i	−0.238681	+	0.137803i
$872$			4.20234i			0.142309i
$873$	−29.3795	+	16.2802i	−0.994346	+	0.551000i
$874$	−11.3926			−0.385360
$875$	0.637517	+	1.10421i	0.0215520	+	0.0373292i
$876$	6.14017	+	23.7489i	0.207457	+	0.802400i
$877$	−9.65616	−	5.57499i	−0.326065	−	0.188254i	0.328028	−	0.944668i	$-0.393616\pi$
$877$	−9.65616	−	5.57499i	−0.326065	−	0.188254i	−0.654093	+	0.756414i	$0.726949\pi$
$878$	0.710007	+	0.409923i	0.0239616	+	0.0138342i
$879$	−31.9735	+	8.26662i	−1.07844	+	0.278826i
$880$	2.51761	+	2.15908i	0.0848686	+	0.0727827i
$881$			4.07884i			0.137419i	0.997637	+	0.0687097i	$0.0218882\pi$
$881$			4.07884i			0.137419i	−0.997637	+	0.0687097i	$0.978112\pi$
$882$	0.283551	−	16.1204i	0.00954767	−	0.542801i
$883$	16.7916			0.565081			0.282541	−	0.959255i	$-0.408823\pi$
$883$	16.7916			0.565081			0.282541	+	0.959255i	$0.408823\pi$
$884$	−3.80962	+	2.19949i	−0.128132	+	0.0739768i
$885$	−1.33590	+	4.81582i	−0.0449056	+	0.161882i
$886$	20.9407	+	12.0901i	0.703517	+	0.406176i
$887$	27.5638	−	47.7419i	0.925503	−	1.60302i	0.134752	−	0.990879i	$-0.456976\pi$
$887$	27.5638	−	47.7419i	0.925503	−	1.60302i	0.790751	−	0.612138i	$-0.209690\pi$
$888$	11.6616	+	11.8686i	0.391339	+	0.398283i
$889$	−12.8466	−	22.2509i	−0.430860	−	0.746271i
$890$	−8.53513			−0.286098
$891$	20.2166	−	21.9611i	0.677281	−	0.735724i
$892$	3.90252			0.130666
$893$	−20.2928	−	35.1482i	−0.679074	−	1.17619i
$894$	−10.3834	−	10.5676i	−0.347272	−	0.353434i
$895$	−4.33844	+	7.51440i	−0.145018	+	0.251179i
$896$	1.10421	+	0.637517i	0.0368891	+	0.0212980i
$897$	−1.27468	+	4.59515i	−0.0425604	+	0.153428i
$898$	−7.65762	+	4.42113i	−0.255538	+	0.147535i
$899$	16.5137			0.550762
$900$	0.0527607	−	2.99954i	0.00175869	−	0.0999845i
$901$		−	17.2714i		−	0.575395i
$902$	20.9910	−	24.4767i	0.698925	−	0.814985i
$903$	20.4838	−	5.29601i	0.681659	−	0.176240i
$904$	3.80120	+	2.19462i	0.126426	+	0.0729921i
$905$	10.5448	+	6.08807i	0.350522	+	0.202374i
$906$	−5.03568	−	19.4769i	−0.167299	−	0.647077i
$907$	23.9876	+	41.5477i	0.796494	+	1.37957i	0.921886	+	0.387461i	$0.126648\pi$
$907$	23.9876	+	41.5477i	0.796494	+	1.37957i	−0.125392	+	0.992107i	$0.540019\pi$
$908$	−18.6767			−0.619809
$909$	−34.4408	+	19.0848i	−1.14233	+	0.633003i
$910$		−	1.66195i		−	0.0550932i
$911$	−12.6947	+	7.32930i	−0.420595	+	0.242830i	−0.695332	−	0.718689i	$-0.744743\pi$
$911$	−12.6947	+	7.32930i	−0.420595	+	0.242830i	0.274737	+	0.961519i	$0.411409\pi$
$912$	−9.00212	−	2.49716i	−0.298090	−	0.0826893i
$913$	−5.27902	−	0.989480i	−0.174710	−	0.0327470i
$914$	13.0231	+	7.51886i	0.430764	+	0.248702i
$915$	6.34839	+	6.46104i	0.209871	+	0.213595i
$916$	7.83446	+	13.5697i	0.258858	+	0.448355i
$917$			16.4814i			0.544263i
$918$	−16.8131	−	4.98395i	−0.554914	−	0.164495i
$919$		−	4.48996i		−	0.148110i	−0.997254	−	0.0740551i	$-0.976406\pi$
$919$		−	4.48996i		−	0.148110i	0.997254	−	0.0740551i	$-0.0235941\pi$
$920$	−1.05611	−	1.82924i	−0.0348190	−	0.0603082i
$921$	37.1500	−	36.5023i	1.22413	−	1.20279i
$922$	4.80589	−	8.32404i	0.158273	−	0.274138i
$923$	−6.76072	+	11.7099i	−0.222532	+	0.385436i
$924$	0.495630	+	7.30773i	0.0163050	+	0.240407i
$925$	4.80327	+	8.31951i	0.157931	+	0.273544i
$926$	−26.6568			−0.875995
$927$	43.7906	+	26.3200i	1.43827	+	0.864464i
$928$	4.75653			0.156141
$929$	43.8038	−	25.2902i	1.43716	−	0.829743i	0.439506	−	0.898240i	$-0.355153\pi$
$929$	43.8038	−	25.2902i	1.43716	−	0.829743i	0.997651	+	0.0684962i	$0.0218201\pi$
$930$	−1.50522	−	5.82188i	−0.0493582	−	0.190907i
$931$	−25.1035	−	14.4935i	−0.822732	−	0.475005i
$932$	7.82986	−	13.5617i	0.256476	−	0.444229i
$933$	10.1762	+	39.3593i	0.333153	+	1.28857i
$934$	5.96735	−	3.44525i	0.195258	−	0.112732i
$935$	10.5586	−	3.71494i	0.345305	−	0.121492i
$936$	−2.01444	+	3.35157i	−0.0658441	+	0.109550i
$937$		−	26.2722i		−	0.858277i	−0.903239	−	0.429138i	$-0.858817\pi$
$937$		−	26.2722i		−	0.858277i	0.903239	−	0.429138i	$-0.141183\pi$
$938$	6.89053	−	3.97825i	0.224984	−	0.129894i
$939$	−5.23102	+	18.8575i	−0.170708	+	0.615392i
$940$	3.76236	−	6.51661i	0.122715	−	0.212548i
$941$	24.7419	−	42.8542i	0.806562	−	1.39701i	−0.108670	−	0.994078i	$-0.534659\pi$
$941$	24.7419	−	42.8542i	0.806562	−	1.39701i	0.915232	−	0.402928i	$-0.132007\pi$
$942$	−18.3022	−	18.6270i	−0.596319	−	0.606900i
$943$	−17.7842	+	10.2677i	−0.579134	+	0.334363i
$944$			2.88541i			0.0939121i
$945$	4.80672	−	4.55957i	0.156363	−	0.148323i
$946$	29.9732	−	10.5457i	0.974513	−	0.342872i
$947$	16.5015	−	9.52717i	0.536228	−	0.309592i	−0.207321	−	0.978273i	$-0.566474\pi$
$947$	16.5015	−	9.52717i	0.536228	−	0.309592i	0.743549	+	0.668681i	$0.233141\pi$
$948$	7.44685	−	7.31702i	0.241863	−	0.237646i
$949$	9.22997	−	15.9868i	0.299617	−	0.518953i
$950$	−4.67103	−	2.69682i	−0.151548	−	0.0874964i
$951$	−5.21876	−	1.44767i	−0.169230	−	0.0469439i
$952$	3.72655	−	2.15153i	0.120778	−	0.0697313i
$953$	−37.2153			−1.20552			−0.602760	−	0.797922i	$-0.705933\pi$
$953$	−37.2153			−1.20552			−0.602760	+	0.797922i	$0.705933\pi$
$954$	−7.44151	−	13.4291i	−0.240928	−	0.434783i
$955$	6.24446			0.202066
$956$	−4.30431	−	7.45528i	−0.139211	−	0.241121i
$957$	15.2320	+	22.6847i	0.492381	+	0.733293i
$958$	6.23709	−	10.8030i	0.201511	−	0.349028i
$959$	2.36044	−	4.08840i	0.0762226	−	0.132021i
$960$	−0.433558	−	1.67691i	−0.0139930	−	0.0541220i
$961$	9.47333	+	16.4083i	0.305591	+	0.529300i
$962$		−	12.5217i		−	0.403717i
$963$	−0.414537	+	23.5671i	−0.0133583	+	0.759441i
$964$			3.07569i			0.0990612i
$965$	−11.7756	−	20.3959i	−0.379069	−	0.656567i
$966$	1.24689	−	4.49495i	0.0401179	−	0.144623i
$967$	51.8749	+	29.9500i	1.66818	+	0.963127i	0.968616	+	0.248562i	$0.0799579\pi$
$967$	51.8749	+	29.9500i	1.66818	+	0.963127i	0.699569	+	0.714565i	$0.253375\pi$
$968$	1.67672	+	10.8715i	0.0538919	+	0.349422i
$969$	−22.4889	+	22.0968i	−0.722447	+	0.709851i
$970$	−9.69621	+	5.59811i	−0.311327	+	0.179745i
$971$		−	21.4402i		−	0.688049i	−0.938961	−	0.344024i	$-0.888210\pi$
$971$		−	21.4402i		−	0.688049i	0.938961	−	0.344024i	$-0.111790\pi$
$972$	−15.2201	+	3.36884i	−0.488184	+	0.108056i
$973$	−29.5260			−0.946559
$974$	10.6773	+	18.4936i	0.342123	+	0.592574i
$975$	−1.61038	+	1.58230i	−0.0515734	+	0.0506743i
$976$	4.52899	+	2.61481i	0.144969	+	0.0836982i
$977$	−39.4138	−	22.7556i	−1.26096	−	0.728015i	−0.287699	−	0.957721i	$-0.592890\pi$
$977$	−39.4138	−	22.7556i	−1.26096	−	0.728015i	−0.973260	+	0.229705i	$0.926224\pi$
$978$	9.35033	−	33.7074i	0.298991	−	1.07784i
$979$	−21.4881	−	18.4281i	−0.686764	−	0.588963i
$980$		−	5.37429i		−	0.171675i
$981$	12.6051	+	0.221718i	0.402449	+	0.00707892i
$982$	−20.5604			−0.656108
$983$	3.55891	−	2.05474i	0.113512	−	0.0655360i	−0.442169	−	0.896932i	$-0.645791\pi$
$983$	3.55891	−	2.05474i	0.113512	−	0.0655360i	0.555681	+	0.831396i	$0.312458\pi$
$984$	−16.3033	+	4.21514i	−0.519729	+	0.134374i
$985$	−4.03871	−	2.33175i	−0.128684	−	0.0742958i
$986$	8.02629	−	13.9019i	0.255609	−	0.442728i
$987$	16.0888	−	4.15968i	0.512111	−	0.132404i
$988$	3.51519	+	6.08849i	0.111833	+	0.193701i
$989$	−20.2358			−0.643460
$990$	6.60908	−	7.43775i	0.210050	−	0.236387i
$991$	4.65948			0.148013			0.0740066	−	0.997258i	$-0.476421\pi$
$991$	4.65948			0.148013			0.0740066	+	0.997258i	$0.476421\pi$
$992$	−1.73590	−	3.00666i	−0.0551147	−	0.0954615i
$993$	−0.0428053	+	0.154311i	−0.00135839	+	0.00489690i
$994$	6.61329	−	11.4546i	0.209761	−	0.363317i
$995$	−12.4840	−	7.20764i	−0.395769	−	0.228497i
$996$	1.96584	+	2.00072i	0.0622900	+	0.0633952i
$997$	−7.97296	+	4.60319i	−0.252506	+	0.145784i	−0.620911	−	0.783881i	$-0.713237\pi$
$997$	−7.97296	+	4.60319i	−0.252506	+	0.145784i	0.368405	+	0.929665i	$0.379904\pi$
$998$	−16.9539			−0.536665
$999$	36.2155	−	34.3533i	1.14581	−	1.08689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.131.7	yes	48
3.2	odd	2		2970.2.t.a.2771.7		48
9.2	odd	6		990.2.t.a.461.7	yes	48
9.7	even	3		2970.2.t.b.791.7		48
11.10	odd	2		990.2.t.a.131.7	✓	48
33.32	even	2		2970.2.t.b.2771.7		48
99.43	odd	6		2970.2.t.a.791.7		48
99.65	even	6	inner	990.2.t.b.461.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.7	✓	48	11.10	odd	2
990.2.t.a.461.7	yes	48	9.2	odd	6
990.2.t.b.131.7	yes	48	1.1	even	1	trivial
990.2.t.b.461.7	yes	48	99.65	even	6	inner
2970.2.t.a.791.7		48	99.43	odd	6
2970.2.t.a.2771.7		48	3.2	odd	2
2970.2.t.b.791.7		48	9.7	even	3
2970.2.t.b.2771.7		48	33.32	even	2

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.21393 - 1.23547i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.462983 - 1.66903i) q^{6} +(1.10421 - 0.637517i) q^{7} -1.00000 q^{8} +(-0.0527607 + 2.99954i) q^{9} +1.00000i q^{10} +(-2.15908 + 2.51761i) q^{11} +(1.67691 - 0.433558i) q^{12} +(-1.12883 - 0.651729i) q^{13} +(1.10421 + 0.637517i) q^{14} +(-0.433558 - 1.67691i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.37485 q^{17} +(-2.62405 + 1.45408i) q^{18} +5.39364i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-2.12807 - 0.590319i) q^{21} +(-3.25986 - 0.611015i) q^{22} +(1.82924 + 1.05611i) q^{23} +(1.21393 + 1.23547i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.30346i q^{26} +(3.76988 - 3.57603i) q^{27} +1.27503i q^{28} +(2.37826 + 4.11927i) q^{29} +(1.23547 - 1.21393i) q^{30} +(1.73590 - 3.00666i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.73140 - 0.388719i) q^{33} +(-1.68743 - 2.92271i) q^{34} +1.27503 q^{35} +(-2.57129 - 1.54546i) q^{36} +9.60655 q^{37} +(-4.67103 + 2.69682i) q^{38} +(0.565125 + 2.18578i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-4.86110 + 8.41967i) q^{41} +(-0.552802 - 2.13812i) q^{42} +(-8.29679 + 4.79015i) q^{43} +(-1.10077 - 3.12863i) q^{44} +(-1.54546 + 2.57129i) q^{45} +2.11222i q^{46} +(-6.51661 + 3.76236i) q^{47} +(-0.462983 + 1.66903i) q^{48} +(-2.68714 + 4.65427i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(4.09682 + 4.16952i) q^{51} +(1.12883 - 0.651729i) q^{52} +5.11769i q^{53} +(4.98188 + 1.47679i) q^{54} +(-3.12863 + 1.10077i) q^{55} +(-1.10421 + 0.637517i) q^{56} +(6.66367 - 6.54749i) q^{57} +(-2.37826 + 4.11927i) q^{58} +(-2.49884 - 1.44271i) q^{59} +(1.66903 + 0.462983i) q^{60} +(-4.52899 + 2.61481i) q^{61} +3.47179 q^{62} +(1.85400 + 3.34576i) q^{63} +1.00000 q^{64} +(-0.651729 - 1.12883i) q^{65} +(3.20234 + 4.76917i) q^{66} +(3.12011 - 5.40419i) q^{67} +(1.68743 - 2.92271i) q^{68} +(-0.915772 - 3.54201i) q^{69} +(0.637517 + 1.10421i) q^{70} -10.3735i q^{71} +(0.0527607 - 2.99954i) q^{72} +14.1623i q^{73} +(4.80327 + 8.31951i) q^{74} +(0.462983 - 1.66903i) q^{75} +(-4.67103 - 2.69682i) q^{76} +(-0.779066 + 4.15643i) q^{77} +(-1.61038 + 1.58230i) q^{78} +(5.22002 - 3.01378i) q^{79} -1.00000i q^{80} +(-8.99443 - 0.316515i) q^{81} -9.72220 q^{82} +(0.809702 + 1.40244i) q^{83} +(1.57526 - 1.54780i) q^{84} +(-2.92271 - 1.68743i) q^{85} +(-8.29679 - 4.79015i) q^{86} +(2.20219 - 7.93877i) q^{87} +(2.15908 - 2.51761i) q^{88} +8.53513i q^{89} +(-2.99954 - 0.0527607i) q^{90} -1.66195 q^{91} +(-1.82924 + 1.05611i) q^{92} +(-5.82188 + 1.50522i) q^{93} +(-6.51661 - 3.76236i) q^{94} +(-2.69682 + 4.67103i) q^{95} +(-1.67691 + 0.433558i) q^{96} +(5.59811 + 9.69621i) q^{97} -5.37429 q^{98} +(-7.43775 - 6.60908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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