LMFDB - Embedded newform 99.2.g.b.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(32,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15x^{14} + 150x^{12} + 837x^{10} + 3372x^{8} + 8010x^{6} + 13761x^{4} + 13392x^{2} + 8649 $ x^16 + 15x^14 + 150x^12 + 837x^10 + 3372x^8 + 8010x^6 + 13761x^4 + 13392*x^2 + 8649
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.1
Root			$-1.29716 - 2.24675i$ of defining polynomial
Character	$\chi$	$=$	99.32
Dual form			99.2.g.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29716 - 2.24675i) q^{2} +(-1.72785 + 0.120512i) q^{3} +(-2.36526 + 4.09675i) q^{4} +(-0.137404 - 0.0793301i) q^{5} +(2.51207 + 3.72573i) q^{6} +(-2.91814 + 1.68479i) q^{7} +7.08384 q^{8} +(2.97095 - 0.416454i) q^{9} +O(q^{10})$	\(q+(-1.29716 - 2.24675i) q^{2} +(-1.72785 + 0.120512i) q^{3} +(-2.36526 + 4.09675i) q^{4} +(-0.137404 - 0.0793301i) q^{5} +(2.51207 + 3.72573i) q^{6} +(-2.91814 + 1.68479i) q^{7} +7.08384 q^{8} +(2.97095 - 0.416454i) q^{9} +0.411616i q^{10} +(-3.29820 + 0.349105i) q^{11} +(3.59311 - 7.36362i) q^{12} +(-0.897990 - 0.518455i) q^{13} +(7.57060 + 4.37089i) q^{14} +(0.246974 + 0.120512i) q^{15} +(-4.45837 - 7.72212i) q^{16} -5.02413 q^{17} +(-4.78948 - 6.13478i) q^{18} +5.11879i q^{19} +(0.649990 - 0.375272i) q^{20} +(4.83908 - 3.26274i) q^{21} +(5.06265 + 6.95739i) q^{22} +(-4.02970 - 2.32655i) q^{23} +(-12.2398 + 0.853687i) q^{24} +(-2.48741 - 4.30833i) q^{25} +2.69008i q^{26} +(-5.08318 + 1.07761i) q^{27} -15.9398i q^{28} +(0.673383 + 1.16633i) q^{29} +(-0.0496046 - 0.711212i) q^{30} +(1.62482 - 2.81427i) q^{31} +(-4.48261 + 7.76411i) q^{32} +(5.65673 - 1.00067i) q^{33} +(6.51711 + 11.2880i) q^{34} +0.534618 q^{35} +(-5.32096 + 13.1563i) q^{36} +3.04356 q^{37} +(11.5007 - 6.63990i) q^{38} +(1.61408 + 0.787595i) q^{39} +(-0.973346 - 0.561961i) q^{40} +(0.940692 - 1.62933i) q^{41} +(-13.6076 - 6.63990i) q^{42} +(8.24914 - 4.76264i) q^{43} +(6.37090 - 14.3376i) q^{44} +(-0.441257 - 0.178464i) q^{45} +12.0716i q^{46} +(-0.996127 + 0.575114i) q^{47} +(8.63401 + 12.8054i) q^{48} +(2.17703 - 3.77072i) q^{49} +(-6.45316 + 11.1772i) q^{50} +(8.68096 - 0.605468i) q^{51} +(4.24795 - 2.45256i) q^{52} +9.36720i q^{53} +(9.01482 + 10.0228i) q^{54} +(0.480880 + 0.213678i) q^{55} +(-20.6716 + 11.9348i) q^{56} +(-0.616876 - 8.84452i) q^{57} +(1.74697 - 3.02585i) q^{58} +(-4.69477 - 2.71052i) q^{59} +(-1.07786 + 0.726747i) q^{60} +(-9.61807 + 5.55299i) q^{61} -8.43060 q^{62} +(-7.96802 + 6.22070i) q^{63} +5.42521 q^{64} +(0.0822581 + 0.142475i) q^{65} +(-9.58597 - 11.4112i) q^{66} +(-2.67969 + 4.64135i) q^{67} +(11.8834 - 20.5826i) q^{68} +(7.24310 + 3.53430i) q^{69} +(-0.693486 - 1.20115i) q^{70} -0.558344i q^{71} +(21.0457 - 2.95009i) q^{72} -6.24053i q^{73} +(-3.94799 - 6.83812i) q^{74} +(4.81709 + 7.14439i) q^{75} +(-20.9704 - 12.1073i) q^{76} +(9.03644 - 6.57551i) q^{77} +(-0.324187 - 4.64806i) q^{78} +(-3.72007 + 2.14778i) q^{79} +1.41473i q^{80} +(8.65313 - 2.47453i) q^{81} -4.88092 q^{82} +(4.61447 + 7.99250i) q^{83} +(1.92094 + 27.5417i) q^{84} +(0.690334 + 0.398565i) q^{85} +(-21.4009 - 12.3558i) q^{86} +(-1.30406 - 1.93410i) q^{87} +(-23.3639 + 2.47300i) q^{88} -1.98314i q^{89} +(0.171419 + 1.22289i) q^{90} +3.49395 q^{91} +(19.0625 - 11.0058i) q^{92} +(-2.46829 + 5.05845i) q^{93} +(2.58428 + 1.49203i) q^{94} +(0.406074 - 0.703341i) q^{95} +(6.80962 - 13.9554i) q^{96} +(0.917466 + 1.58910i) q^{97} -11.2958 q^{98} +(-9.65341 + 2.41072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.29716	−	2.24675i	−0.917232	−	1.58869i	−0.803600	−	0.595169i	$-0.797085\pi$
$2$	−1.29716	−	2.24675i	−0.917232	−	1.58869i	−0.113631	−	0.993523i	$-0.536248\pi$
$3$	−1.72785	+	0.120512i	−0.997577	+	0.0695776i
$3$	−1.72785	+	0.120512i	−0.997577	+	0.0695776i
$4$	−2.36526	+	4.09675i	−1.18263	+	2.04837i
$5$	−0.137404	−	0.0793301i	−0.0614488	−	0.0354775i	0.468961	−	0.883219i	$-0.344629\pi$
$5$	−0.137404	−	0.0793301i	−0.0614488	−	0.0354775i	−0.530410	+	0.847741i	$0.677962\pi$
$6$	2.51207	+	3.72573i	1.02555	+	1.52102i
$7$	−2.91814	+	1.68479i	−1.10295	+	0.636790i	−0.936995	−	0.349343i	$-0.886405\pi$
$7$	−2.91814	+	1.68479i	−1.10295	+	0.636790i	−0.165958	+	0.986133i	$0.553072\pi$
$8$	7.08384			2.50451
$9$	2.97095	−	0.416454i	0.990318	−	0.138818i
$10$			0.411616i			0.130164i
$11$	−3.29820	+	0.349105i	−0.994445	+	0.105259i
$11$	−3.29820	+	0.349105i	−0.994445	+	0.105259i
$12$	3.59311	−	7.36362i	1.03724	−	2.12569i
$13$	−0.897990	−	0.518455i	−0.249058	−	0.143794i	0.370275	−	0.928922i	$-0.379263\pi$
$13$	−0.897990	−	0.518455i	−0.249058	−	0.143794i	−0.619333	+	0.785129i	$0.712597\pi$
$14$	7.57060	+	4.37089i	2.02333	+	1.16817i
$15$	0.246974	+	0.120512i	0.0637683	+	0.0311161i
$16$	−4.45837	−	7.72212i	−1.11459	−	1.93053i
$17$	−5.02413			−1.21853			−0.609265	−	0.792966i	$-0.708536\pi$
$17$	−5.02413			−1.21853			−0.609265	+	0.792966i	$0.708536\pi$
$18$	−4.78948	−	6.13478i	−1.12889	−	1.44598i
$19$			5.11879i			1.17433i	0.809467	+	0.587166i	$0.199756\pi$
$19$			5.11879i			1.17433i	−0.809467	+	0.587166i	$0.800244\pi$
$20$	0.649990	−	0.375272i	0.145342	−	0.0839134i
$21$	4.83908	−	3.26274i	1.05597	−	0.711988i
$22$	5.06265	+	6.95739i	1.07936	+	1.48332i
$23$	−4.02970	−	2.32655i	−0.840250	−	0.485118i	0.0170993	−	0.999854i	$-0.494557\pi$
$23$	−4.02970	−	2.32655i	−0.840250	−	0.485118i	−0.857349	+	0.514735i	$0.827890\pi$
$24$	−12.2398	+	0.853687i	−2.49844	+	0.174258i
$25$	−2.48741	−	4.30833i	−0.497483	−	0.861665i
$26$			2.69008i			0.527568i
$27$	−5.08318	+	1.07761i	−0.978259	+	0.207385i
$28$		−	15.9398i		−	3.01235i
$29$	0.673383	+	1.16633i	0.125044	+	0.216583i	0.921750	−	0.387784i	$-0.126759\pi$
$29$	0.673383	+	1.16633i	0.125044	+	0.216583i	−0.796706	+	0.604367i	$0.793426\pi$
$30$	−0.0496046	−	0.711212i	−0.00905652	−	0.129849i
$31$	1.62482	−	2.81427i	0.291826	−	0.505457i	−0.682416	−	0.730964i	$-0.739071\pi$
$31$	1.62482	−	2.81427i	0.291826	−	0.505457i	0.974242	+	0.225507i	$0.0724039\pi$
$32$	−4.48261	+	7.76411i	−0.792421	+	1.37251i
$33$	5.65673	−	1.00067i	0.984711	−	0.174195i
$34$	6.51711	+	11.2880i	1.11768	+	1.93587i
$35$	0.534618			0.0903669
$36$	−5.32096	+	13.1563i	−0.886827	+	2.19271i
$37$	3.04356			0.500359			0.250179	−	0.968200i	$-0.419510\pi$
$37$	3.04356			0.500359			0.250179	+	0.968200i	$0.419510\pi$
$38$	11.5007	−	6.63990i	1.86565	−	1.07713i
$39$	1.61408	+	0.787595i	0.258459	+	0.126116i
$40$	−0.973346	−	0.561961i	−0.153899	−	0.0888539i
$41$	0.940692	−	1.62933i	0.146911	−	0.254458i	−0.783173	−	0.621804i	$-0.786400\pi$
$41$	0.940692	−	1.62933i	0.146911	−	0.254458i	0.930084	+	0.367346i	$0.119733\pi$
$42$	−13.6076	−	6.63990i	−2.09970	−	1.02456i
$43$	8.24914	−	4.76264i	1.25798	−	0.726296i	0.285300	−	0.958438i	$-0.407907\pi$
$43$	8.24914	−	4.76264i	1.25798	−	0.726296i	0.972682	+	0.232143i	$0.0745736\pi$
$44$	6.37090	−	14.3376i	0.960449	−	2.16148i
$45$	−0.441257	−	0.178464i	−0.0657788	−	0.0266038i
$46$			12.0716i			1.77986i
$47$	−0.996127	+	0.575114i	−0.145300	+	0.0838890i	−0.570888	−	0.821028i	$-0.693401\pi$
$47$	−0.996127	+	0.575114i	−0.145300	+	0.0838890i	0.425588	+	0.904917i	$0.360067\pi$
$48$	8.63401	+	12.8054i	1.24621	+	1.84830i
$49$	2.17703	−	3.77072i	0.311004	−	0.538674i
$50$	−6.45316	+	11.1772i	−0.912614	+	1.58069i
$51$	8.68096	−	0.605468i	1.21558	−	0.0847824i
$52$	4.24795	−	2.45256i	0.589085	−	0.340109i
$53$			9.36720i			1.28668i	0.765579	+	0.643342i	$0.222453\pi$
$53$			9.36720i			1.28668i	−0.765579	+	0.643342i	$0.777547\pi$
$54$	9.01482	+	10.0228i	1.22676	+	1.36393i
$55$	0.480880	+	0.213678i	0.0648418	+	0.0288124i
$56$	−20.6716	+	11.9348i	−2.76236	+	1.59485i
$57$	−0.616876	−	8.84452i	−0.0817072	−	1.17149i
$58$	1.74697	−	3.02585i	0.229389	−	0.397313i
$59$	−4.69477	−	2.71052i	−0.611206	−	0.352880i	0.162231	−	0.986753i	$-0.448131\pi$
$59$	−4.69477	−	2.71052i	−0.611206	−	0.352880i	−0.773437	+	0.633873i	$0.781464\pi$
$60$	−1.07786	+	0.726747i	−0.139152	+	0.0938226i
$61$	−9.61807	+	5.55299i	−1.23147	+	0.710988i	−0.967336	−	0.253498i	$-0.918419\pi$
$61$	−9.61807	+	5.55299i	−1.23147	+	0.710988i	−0.264132	+	0.964487i	$0.585085\pi$
$62$	−8.43060			−1.07069
$63$	−7.96802	+	6.22070i	−1.00388	+	0.783735i
$64$	5.42521			0.678152
$65$	0.0822581	+	0.142475i	0.0102029	+	0.0176719i
$66$	−9.58597	−	11.4112i	−1.17995	−	1.40463i
$67$	−2.67969	+	4.64135i	−0.327376	+	0.567032i	−0.981990	−	0.188931i	$-0.939498\pi$
$67$	−2.67969	+	4.64135i	−0.327376	+	0.567032i	0.654614	+	0.755963i	$0.272831\pi$
$68$	11.8834	−	20.5826i	1.44107	−	2.49600i
$69$	7.24310	+	3.53430i	0.871967	+	0.425480i
$70$	−0.693486	−	1.20115i	−0.0828874	−	0.143565i
$71$		−	0.558344i		−	0.0662633i	−0.999451	−	0.0331316i	$-0.989452\pi$
$71$		−	0.558344i		−	0.0662633i	0.999451	−	0.0331316i	$-0.0105481\pi$
$72$	21.0457	−	2.95009i	2.48027	−	0.347672i
$73$		−	6.24053i		−	0.730398i	−0.930929	−	0.365199i	$-0.881001\pi$
$73$		−	6.24053i		−	0.730398i	0.930929	−	0.365199i	$-0.118999\pi$
$74$	−3.94799	−	6.83812i	−0.458945	−	0.794916i
$75$	4.81709	+	7.14439i	0.556230	+	0.824963i
$76$	−20.9704	−	12.1073i	−2.40547	−	1.38880i
$77$	9.03644	−	6.57551i	1.02980	−	0.749349i
$78$	−0.324187	−	4.64806i	−0.0367069	−	0.526289i
$79$	−3.72007	+	2.14778i	−0.418540	+	0.241644i	−0.694453	−	0.719539i	$-0.744353\pi$
$79$	−3.72007	+	2.14778i	−0.418540	+	0.241644i	0.275912	+	0.961183i	$0.411020\pi$
$80$			1.41473i			0.158172i
$81$	8.65313	−	2.47453i	0.961459	−	0.274948i
$82$	−4.88092			−0.539007
$83$	4.61447	+	7.99250i	0.506504	+	0.877291i	0.999972	+	0.00752676i	$0.00239586\pi$
$83$	4.61447	+	7.99250i	0.506504	+	0.877291i	−0.493467	+	0.869764i	$0.664271\pi$
$84$	1.92094	+	27.5417i	0.209592	+	3.00504i
$85$	0.690334	+	0.398565i	0.0748773	+	0.0432304i
$86$	−21.4009	−	12.3558i	−2.30772	−	1.33236i
$87$	−1.30406	−	1.93410i	−0.139810	−	0.207358i
$88$	−23.3639	+	2.47300i	−2.49060	+	0.263623i
$89$		−	1.98314i		−	0.210212i	−0.994461	−	0.105106i	$-0.966482\pi$
$89$		−	1.98314i		−	0.210212i	0.994461	−	0.105106i	$-0.0335182\pi$
$90$	0.171419	+	1.22289i	0.0180691	+	0.128904i
$91$	3.49395			0.366265
$92$	19.0625	−	11.0058i	1.98741	−	1.14743i
$93$	−2.46829	+	5.05845i	−0.255950	+	0.524537i
$94$	2.58428	+	1.49203i	0.266548	+	0.153891i
$95$	0.406074	−	0.703341i	0.0416623	−	0.0721613i
$96$	6.80962	−	13.9554i	0.695004	−	1.42432i
$97$	0.917466	+	1.58910i	0.0931545	+	0.161348i	0.908837	−	0.417152i	$-0.136972\pi$
$97$	0.917466	+	1.58910i	0.0931545	+	0.161348i	−0.815682	+	0.578500i	$0.803638\pi$
$98$	−11.2958			−1.14105
$99$	−9.65341	+	2.41072i	−0.970205	+	0.242287i
$100$	23.5335			2.35335
$101$	8.92252	+	15.4543i	0.887824	+	1.53776i	0.842443	+	0.538786i	$0.181117\pi$
$101$	8.92252	+	15.4543i	0.887824	+	1.53776i	0.0453812	+	0.998970i	$0.485550\pi$
$102$	−12.6209	−	18.7186i	−1.24966	−	1.85341i
$103$	−4.40350	+	7.62708i	−0.433890	+	0.751519i	−0.997204	−	0.0747237i	$-0.976193\pi$
$103$	−4.40350	+	7.62708i	−0.433890	+	0.751519i	0.563315	+	0.826242i	$0.309526\pi$
$104$	−6.36122	−	3.67265i	−0.623768	−	0.360133i
$105$	−0.923741	+	0.0644278i	−0.0901479	+	0.00628751i
$106$	21.0457	−	12.1508i	2.04414	−	1.18019i
$107$	−14.3322			−1.38554			−0.692772	−	0.721156i	$-0.743611\pi$
$107$	−14.3322			−1.38554			−0.692772	+	0.721156i	$0.743611\pi$
$108$	7.60836	−	23.3733i	0.732115	−	2.24910i
$109$		−	7.45146i		−	0.713721i	−0.934158	−	0.356860i	$-0.883847\pi$
$109$		−	7.45146i		−	0.713721i	0.934158	−	0.356860i	$-0.116153\pi$
$110$	−0.143697	−	1.35759i	−0.0137010	−	0.129441i
$111$	−5.25883	+	0.366786i	−0.499146	+	0.0348137i
$112$	26.0203	+	15.0228i	2.45868	+	1.41952i
$113$	−0.0916620	−	0.0529211i	−0.00862284	−	0.00497840i	0.495682	−	0.868504i	$-0.334918\pi$
$113$	−0.0916620	−	0.0529211i	−0.00862284	−	0.00497840i	−0.504305	+	0.863525i	$0.668251\pi$
$114$	−19.0712	+	12.8587i	−1.78619	+	1.20433i
$115$	0.369130	+	0.639352i	0.0344216	+	0.0596199i
$116$	−6.37090			−0.591523
$117$	−2.88380	−	1.16633i	−0.266607	−	0.107828i
$118$			14.0640i			1.29469i
$119$	14.6611	−	8.46460i	1.34398	−	0.775948i
$120$	1.74952	+	0.853687i	0.159709	+	0.0779306i
$121$	10.7563	−	2.30284i	0.977841	−	0.209349i
$122$	24.9524	+	14.4063i	2.25908	+	1.30428i
$123$	−1.42902	+	2.92860i	−0.128851	+	0.264063i
$124$	7.68622	+	13.3129i	0.690243	+	1.19554i
$125$			1.58261i			0.141553i
$126$	24.3122	+	9.83290i	2.16590	+	0.875984i
$127$		−	13.7812i		−	1.22288i	−0.791290	−	0.611441i	$-0.790590\pi$
$127$		−	13.7812i		−	1.22288i	0.791290	−	0.611441i	$-0.209410\pi$
$128$	1.92784	+	3.33912i	0.170399	+	0.295139i
$129$	−13.6793	+	9.22326i	−1.20440	+	0.812063i
$130$	0.213404	−	0.369627i	0.0187168	−	0.0324184i
$131$	1.24756	−	2.16083i	0.109000	−	0.188793i	−0.806366	−	0.591417i	$-0.798569\pi$
$131$	1.24756	−	2.16083i	0.109000	−	0.188793i	0.915365	+	0.402625i	$0.131902\pi$
$132$	−9.28012	+	25.5411i	−0.807731	+	2.22306i
$133$	−8.62409	−	14.9374i	−0.747803	−	1.29523i
$134$	13.9039			1.20112
$135$	0.783935	+	0.255182i	0.0674704	+	0.0219626i
$136$	−35.5901			−3.05183
$137$	−9.87123	+	5.69916i	−0.843356	+	0.486912i	−0.858404	−	0.512975i	$-0.828543\pi$
$137$	−9.87123	+	5.69916i	−0.843356	+	0.486912i	0.0150476	+	0.999887i	$0.495210\pi$
$138$	−1.45478	−	20.8580i	−0.123839	−	1.77555i
$139$	−10.4200	−	6.01599i	−0.883812	−	0.510269i	−0.0118989	−	0.999929i	$-0.503788\pi$
$139$	−10.4200	−	6.01599i	−0.883812	−	0.510269i	−0.871914	+	0.489660i	$0.837121\pi$
$140$	−1.26451	+	2.19019i	−0.106870	+	0.185105i
$141$	1.65185	−	1.11376i	0.139111	−	0.0937953i
$142$	−1.25446	+	0.724263i	−0.105272	+	0.0607788i
$143$	3.14275	+	1.39648i	0.262810	+	0.116779i
$144$	−16.4615	−	21.0854i	−1.37179	−	1.75711i
$145$		−	0.213678i		−	0.0177450i
$146$	−14.0209	+	8.09497i	−1.16038	+	0.669945i
$147$	−3.30716	+	6.77761i	−0.272770	+	0.559008i
$148$	−7.19881	+	12.4687i	−0.591738	+	1.02492i
$149$	−1.16530	+	2.01836i	−0.0954650	+	0.165350i	−0.909803	−	0.415041i	$-0.863767\pi$
$149$	−1.16530	+	2.01836i	−0.0954650	+	0.165350i	0.814338	+	0.580392i	$0.197100\pi$
$150$	9.80312	−	20.0902i	0.800421	−	1.64036i
$151$	6.60387	−	3.81274i	0.537415	−	0.310277i	−0.206616	−	0.978422i	$-0.566245\pi$
$151$	6.60387	−	3.81274i	0.537415	−	0.310277i	0.744031	+	0.668146i	$0.232912\pi$
$152$			36.2607i			2.94113i
$153$	−14.9265	+	2.09232i	−1.20673	+	0.169154i
$154$	−26.4952	−	11.7731i	−2.13505	−	0.948706i
$155$	−0.446512	+	0.257794i	−0.0358647	+	0.0207065i
$156$	−7.04428	+	4.74959i	−0.563994	+	0.380271i
$157$	−8.15839	+	14.1307i	−0.651110	+	1.12776i	0.331744	+	0.943370i	$0.392363\pi$
$157$	−8.15839	+	14.1307i	−0.651110	+	1.12776i	−0.982854	+	0.184386i	$0.940970\pi$
$158$	9.65105	+	5.57204i	0.767797	+	0.443288i
$159$	−1.12886	−	16.1851i	−0.0895244	−	1.28357i
$160$	1.23185	−	0.711212i	0.0973867	−	0.0562262i
$161$	15.6790			1.23567
$162$	−16.7842	−	16.2316i	−1.31869	−	1.27527i
$163$	15.5456			1.21762			0.608812	−	0.793314i	$-0.291646\pi$
$163$	15.5456			1.21762			0.608812	+	0.793314i	$0.291646\pi$
$164$	4.44996	+	7.70755i	0.347483	+	0.601859i
$165$	−0.856640	−	0.311253i	−0.0666893	−	0.0242310i
$166$	11.9714	−	20.7351i	0.929164	−	1.60936i
$167$	−5.69751	+	9.86838i	−0.440887	+	0.763638i	−0.997756	−	0.0669621i	$-0.978669\pi$
$167$	−5.69751	+	9.86838i	−0.440887	+	0.763638i	0.556869	+	0.830601i	$0.312003\pi$
$168$	34.2792	−	23.1127i	2.64470	−	1.78318i
$169$	−5.96241	−	10.3272i	−0.458647	−	0.794400i
$170$		−	2.06801i		−	0.158609i
$171$	2.13174	+	15.2077i	0.163018	+	1.16296i
$172$			45.0595i			3.43575i
$173$	−1.55757	−	2.69779i	−0.118420	−	0.205109i	0.800722	−	0.599036i	$-0.204449\pi$
$173$	−1.55757	−	2.69779i	−0.118420	−	0.205109i	−0.919142	+	0.393927i	$0.871116\pi$
$174$	−2.65386	+	5.43875i	−0.201189	+	0.412311i
$175$	14.5172	+	8.38153i	1.09740	+	0.633584i
$176$	17.4004	+	23.9127i	1.31161	+	1.80248i
$177$	8.43852	+	4.11761i	0.634278	+	0.309499i
$178$	−4.45561	+	2.57245i	−0.333962	+	0.192813i
$179$		−	15.9590i		−	1.19283i	−0.802676	−	0.596415i	$-0.796591\pi$
$179$		−	15.9590i		−	1.19283i	0.802676	−	0.596415i	$-0.203409\pi$
$180$	1.77481	−	1.38561i	0.132286	−	0.103277i
$181$	−10.2550			−0.762245			−0.381122	−	0.924525i	$-0.624462\pi$
$181$	−10.2550			−0.762245			−0.381122	+	0.924525i	$0.624462\pi$
$182$	−4.53221	−	7.85003i	−0.335950	−	0.581883i
$183$	15.9494	−	10.7539i	1.17901	−	0.794948i
$184$	−28.5457	−	16.4809i	−2.10442	−	1.21499i
$185$	−0.418197	−	0.241446i	−0.0307464	−	0.0177515i
$186$	14.5668	−	1.01599i	1.06809	−	0.0744959i
$187$	16.5706	−	1.75395i	1.21176	−	0.128261i
$188$		−	5.44117i		−	0.396838i
$189$	13.0179	−	11.7087i	0.946913	−	0.851682i
$190$	−2.10698			−0.152856
$191$	7.29468	−	4.21159i	0.527824	−	0.304740i	−0.212306	−	0.977203i	$-0.568097\pi$
$191$	7.29468	−	4.21159i	0.527824	−	0.304740i	0.740130	+	0.672464i	$0.234764\pi$
$192$	−9.37397	+	0.653803i	−0.676508	+	0.0471842i
$193$	7.93368	+	4.58051i	0.571079	+	0.329713i	0.757580	−	0.652742i	$-0.226382\pi$
$193$	7.93368	+	4.58051i	0.571079	+	0.329713i	−0.186501	+	0.982455i	$0.559715\pi$
$194$	2.38020	−	4.12263i	0.170889	−	0.295988i
$195$	−0.159300	−	0.236263i	−0.0114077	−	0.0169192i
$196$	10.2985	+	17.8374i	0.735604	+	1.27410i
$197$	6.82011			0.485913			0.242956	−	0.970037i	$-0.421883\pi$
$197$	6.82011			0.485913			0.242956	+	0.970037i	$0.421883\pi$
$198$	17.9383	+	18.5617i	1.27482	+	1.31912i
$199$	−11.6395			−0.825102			−0.412551	−	0.910934i	$-0.635362\pi$
$199$	−11.6395			−0.825102			−0.412551	+	0.910934i	$0.635362\pi$
$200$	−17.6204	−	30.5195i	−1.24595	−	2.15805i
$201$	4.07077	−	8.34251i	0.287130	−	0.588435i
$202$	23.1479	−	40.0933i	1.62868	−	2.82096i
$203$	−3.93005	−	2.26902i	−0.275836	−	0.159254i
$204$	−18.0523	+	36.9958i	−1.26391	+	2.59022i
$205$	−0.258509	+	0.149250i	−0.0180551	+	0.0104241i
$206$	22.8482			1.59191
$207$	−12.9409	−	5.23388i	−0.899458	−	0.363780i
$208$			9.24585i			0.641084i
$209$	−1.78700	−	16.8828i	−0.123609	−	1.16781i
$210$	1.34299	+	1.99184i	0.0926754	+	0.137450i
$211$	−16.6264	−	9.59924i	−1.14461	−	0.660839i	−0.197040	−	0.980396i	$-0.563133\pi$
$211$	−16.6264	−	9.59924i	−1.14461	−	0.660839i	−0.947567	+	0.319556i	$0.896466\pi$
$212$	−38.3750	−	22.1558i	−2.63561	−	1.52167i
$213$	0.0672871	+	0.964737i	0.00461044	+	0.0661027i
$214$	18.5912	+	32.2008i	1.27087	+	2.20120i
$215$	−1.51128			−0.103069
$216$	−36.0084	+	7.63359i	−2.45006	+	0.519400i
$217$			10.9499i			0.743327i
$218$	−16.7416	+	9.66575i	−1.13388	+	0.654647i
$219$	0.752058	+	10.7827i	0.0508194	+	0.728628i
$220$	−2.01279	+	1.46464i	−0.135702	+	0.0987458i
$221$	4.51162	+	2.60478i	0.303484	+	0.175217i
$222$	7.64563	+	11.3395i	0.513141	+	0.761057i
$223$	7.35920	+	12.7465i	0.492809	+	0.853570i	0.999966	−	0.00828390i	$-0.00263688\pi$
$223$	7.35920	+	12.7465i	0.492809	+	0.853570i	−0.507157	+	0.861854i	$0.669304\pi$
$224$		−	30.2090i		−	2.01842i
$225$	−9.18421	−	11.7639i	−0.612281	−	0.784263i
$226$			0.274589i			0.0182654i
$227$	1.47531	+	2.55531i	0.0979197	+	0.169602i	0.910823	−	0.412796i	$-0.135448\pi$
$227$	1.47531	+	2.55531i	0.0979197	+	0.169602i	−0.812904	+	0.582398i	$0.802114\pi$
$228$	37.6928	+	18.3924i	2.49627	+	1.21807i
$229$	−5.54107	+	9.59742i	−0.366164	+	0.634215i	−0.988962	−	0.148168i	$-0.952662\pi$
$229$	−5.54107	+	9.59742i	−0.366164	+	0.634215i	0.622798	+	0.782383i	$0.285996\pi$
$230$	0.957643	−	1.65869i	0.0631451	−	0.109371i
$231$	−14.8212	+	12.4505i	−0.975164	+	0.819184i
$232$	4.77014	+	8.26212i	0.313175	+	0.542435i
$233$	−7.80394			−0.511253			−0.255627	−	0.966776i	$-0.582282\pi$
$233$	−7.80394			−0.511253			−0.255627	+	0.966776i	$0.582282\pi$
$234$	1.12029	+	7.99210i	0.0732359	+	0.522460i
$235$	0.182495			0.0119047
$236$	22.2087	−	12.8222i	1.44566	−	0.834652i
$237$	6.16890	−	4.15936i	0.400713	−	0.270180i
$238$	−38.0357	−	21.9599i	−2.46549	−	1.42345i
$239$	7.95608	−	13.7803i	0.514636	−	0.891375i	−0.485220	−	0.874392i	$-0.661260\pi$
$239$	7.95608	−	13.7803i	0.514636	−	0.891375i	0.999856	−	0.0169832i	$-0.00540617\pi$
$240$	−0.170492	−	2.44445i	−0.0110052	−	0.157788i
$241$	−12.0653	+	6.96588i	−0.777192	+	0.448712i	−0.835434	−	0.549590i	$-0.814784\pi$
$241$	−12.0653	+	6.96588i	−0.777192	+	0.448712i	0.0582422	+	0.998302i	$0.481450\pi$
$242$	−19.1265	−	21.1795i	−1.22950	−	1.36147i
$243$	−14.6531	+	5.31843i	−0.939999	+	0.341178i
$244$		−	52.5370i		−	3.36334i
$245$	−0.598263	+	0.345407i	−0.0382216	+	0.0220673i
$246$	8.43351	−	0.588209i	0.537701	−	0.0375028i
$247$	2.65386	−	4.59663i	0.168861	−	0.292476i
$248$	11.5099	−	19.9358i	0.730882	−	1.26592i
$249$	−8.93632	−	13.2538i	−0.566317	−	0.839924i
$250$	3.55572	−	2.05290i	0.224884	−	0.129837i
$251$		−	7.70054i		−	0.486054i	−0.970020	−	0.243027i	$-0.921860\pi$
$251$		−	7.70054i		−	0.486054i	0.970020	−	0.243027i	$-0.0781403\pi$
$252$	−6.63821	−	47.3565i	−0.418168	−	2.98318i
$253$	14.1030	+	6.26663i	0.886645	+	0.393980i
$254$	−30.9629	+	17.8764i	−1.94278	+	1.12167i
$255$	−1.24083	−	0.605468i	−0.0777037	−	0.0379159i
$256$	10.4267	−	18.0595i	0.651666	−	1.12872i
$257$	−4.87372	−	2.81384i	−0.304014	−	0.175523i	0.340231	−	0.940342i	$-0.389495\pi$
$257$	−4.87372	−	2.81384i	−0.304014	−	0.175523i	−0.644245	+	0.764819i	$0.722828\pi$
$258$	38.4667	+	18.7700i	2.39483	+	1.16857i
$259$	−8.88154	+	5.12776i	−0.551872	+	0.318623i
$260$	−0.778246			−0.0482648
$261$	2.48631	+	3.18469i	0.153899	+	0.197127i
$262$	−6.47313			−0.399912
$263$	−13.0451	−	22.5947i	−0.804394	−	1.39325i	−0.916700	−	0.399577i	$-0.869157\pi$
$263$	−13.0451	−	22.5947i	−0.804394	−	1.39325i	0.112306	−	0.993674i	$-0.464176\pi$
$264$	40.0714	−	7.08862i	2.46622	−	0.436274i
$265$	0.743100	−	1.28709i	0.0456483	−	0.0790652i
$266$	−22.3737	+	38.7523i	−1.37182	+	2.37606i
$267$	0.238992	+	3.42657i	0.0146260	+	0.209703i
$268$	−12.6763	−	21.9560i	−0.774328	−	1.34118i
$269$			18.1739i			1.10808i	0.832489	+	0.554042i	$0.186915\pi$
$269$			18.1739i			1.10808i	−0.832489	+	0.554042i	$0.813085\pi$
$270$	−0.443560	−	2.09232i	−0.0269942	−	0.127334i
$271$			17.8451i			1.08402i	0.840374	+	0.542008i	$0.182336\pi$
$271$			17.8451i			1.08402i	−0.840374	+	0.542008i	$0.817664\pi$
$272$	22.3994	+	38.7969i	1.35816	+	2.35241i
$273$	−6.03703	+	0.421062i	−0.365378	+	0.0254839i
$274$	25.6092	+	14.7855i	1.54711	+	0.893222i
$275$	9.70805	+	13.3414i	0.585417	+	0.804514i
$276$	−31.6109	+	21.3136i	−1.90275	+	1.28293i
$277$	−15.9596	+	9.21430i	−0.958921	+	0.553633i	−0.895841	−	0.444375i	$-0.853426\pi$
$277$	−15.9596	+	9.21430i	−0.958921	+	0.553633i	−0.0630804	+	0.998008i	$0.520092\pi$
$278$			31.2148i			1.87214i
$279$	3.65524	−	9.03772i	0.218834	−	0.541074i
$280$	3.78714			0.226325
$281$	−6.61767	−	11.4621i	−0.394777	−	0.683774i	0.598296	−	0.801276i	$-0.295845\pi$
$281$	−6.61767	−	11.4621i	−0.394777	−	0.683774i	−0.993073	+	0.117501i	$0.962512\pi$
$282$	−4.64506	−	2.26658i	−0.276609	−	0.134973i
$283$	14.7366	+	8.50820i	0.876002	+	0.505760i	0.869338	−	0.494218i	$-0.164546\pi$
$283$	14.7366	+	8.50820i	0.876002	+	0.505760i	0.00666371	+	0.999978i	$0.497879\pi$
$284$	2.28739	+	1.32063i	0.135732	+	0.0783648i
$285$	−0.616876	+	1.26421i	−0.0365406	+	0.0748852i
$286$	−0.939120	−	8.87242i	−0.0555313	−	0.524637i
$287$			6.33947i			0.374207i
$288$	−10.0842	+	24.9336i	−0.594219	+	1.46923i
$289$	8.24189			0.484817
$290$	−0.480081	+	0.277175i	−0.0281914	+	0.0162763i
$291$	−1.77675	−	2.63516i	−0.104155	−	0.154476i
$292$	25.5658	+	14.7604i	1.49613	+	0.863790i
$293$	−13.2439	+	22.9392i	−0.773719	+	1.34012i	0.161793	+	0.986825i	$0.448272\pi$
$293$	−13.2439	+	22.9392i	−0.773719	+	1.34012i	−0.935512	+	0.353295i	$0.885061\pi$
$294$	19.5175	−	1.36128i	1.13828	−	0.0793915i
$295$	0.430052	+	0.744872i	0.0250386	+	0.0433681i
$296$	21.5601			1.25316
$297$	16.3892	−	5.32873i	0.950996	−	0.309204i
$298$	6.04632			0.350254
$299$	2.41242	+	4.17843i	0.139514	+	0.241645i
$300$	−40.6624	+	2.83607i	−2.34765	+	0.163740i
$301$	−16.0481	+	27.7961i	−0.924996	+	1.60214i
$302$	−17.1326	−	9.89149i	−0.985868	−	0.569191i
$303$	−17.2792	−	25.6274i	−0.992666	−	1.47226i
$304$	39.5279	−	22.8215i	2.26708	−	1.30890i
$305$	1.76208			0.100896
$306$	24.0629	+	30.8219i	1.37559	+	1.76197i
$307$			0.641034i			0.0365858i	0.999833	+	0.0182929i	$0.00582313\pi$
$307$			0.641034i			0.0365858i	−0.999833	+	0.0182929i	$0.994177\pi$
$308$	5.56468	+	52.5728i	0.317077	+	2.99561i
$309$	6.68944	−	13.7092i	0.380549	−	0.779886i
$310$	1.15840	+	0.668800i	0.0657925	+	0.0379853i
$311$	10.5744	+	6.10513i	0.599619	+	0.346190i	0.768892	−	0.639379i	$-0.220809\pi$
$311$	10.5744	+	6.10513i	0.599619	+	0.346190i	−0.169273	+	0.985569i	$0.554142\pi$
$312$	11.4338	+	5.57920i	0.647314	+	0.315860i
$313$	−13.3275	−	23.0839i	−0.753315	−	1.30478i	−0.946208	−	0.323560i	$-0.895120\pi$
$313$	−13.3275	−	23.0839i	−0.753315	−	1.30478i	0.192893	−	0.981220i	$-0.438213\pi$
$314$	42.3310			2.38888
$315$	1.58832	−	0.222644i	0.0894919	−	0.0125445i
$316$		−	20.3202i		−	1.14310i
$317$	−15.1631	+	8.75445i	−0.851647	+	0.491699i	−0.861206	−	0.508256i	$-0.830291\pi$
$317$	−15.1631	+	8.75445i	−0.851647	+	0.491699i	0.00955915	+	0.999954i	$0.496957\pi$
$318$	−34.8997	+	23.5310i	−1.95708	+	1.31955i
$319$	−2.62813	−	3.61172i	−0.147147	−	0.202218i
$320$	−0.745444	−	0.430382i	−0.0416716	−	0.0240591i
$321$	24.7639	−	1.72720i	1.38219	−	0.0964029i
$322$	−20.3381	−	35.2267i	−1.13340	−	1.96311i
$323$		−	25.7175i		−	1.43096i
$324$	−10.3294	+	41.3026i	−0.573853	+	2.29459i
$325$			5.15845i			0.286139i
$326$	−20.1651	−	34.9271i	−1.11684	−	1.93443i
$327$	0.897990	+	12.8750i	0.0496590	+	0.711991i
$328$	6.66371	−	11.5419i	0.367942	−	0.637294i
$329$	1.93789	−	3.35653i	0.106839	−	0.185051i
$330$	0.411894	+	2.32840i	0.0226740	+	0.128174i
$331$	12.5699	+	21.7716i	0.690902	+	1.19668i	0.971543	+	0.236865i	$0.0761199\pi$
$331$	12.5699	+	21.7716i	0.690902	+	1.19668i	−0.280640	+	0.959813i	$0.590547\pi$
$332$	−43.6577			−2.39603
$333$	9.04228	−	1.26750i	0.495514	−	0.0694588i
$334$	29.5624			1.61758
$335$	0.736398	−	0.425159i	0.0402337	−	0.0232289i
$336$	−46.7696	−	22.8215i	−2.55149	−	1.24501i
$337$	−9.87559	−	5.70168i	−0.537958	−	0.310590i	0.206293	−	0.978490i	$-0.433860\pi$
$337$	−9.87559	−	5.70168i	−0.537958	−	0.310590i	−0.744251	+	0.667900i	$0.767193\pi$
$338$	−15.4684	+	26.7921i	−0.841371	+	1.45730i
$339$	0.164756	+	0.0803935i	0.00894833	+	0.00436638i
$340$	−3.26564	+	1.88542i	−0.177104	+	0.102251i
$341$	−4.37650	+	9.84924i	−0.237001	+	0.533367i
$342$	31.4027	−	24.5163i	1.69806	−	1.32569i
$343$		−	8.91573i		−	0.481404i
$344$	58.4355	−	33.7378i	3.15063	−	1.81902i
$345$	−0.714852	−	1.06022i	−0.0384864	−	0.0570804i
$346$	−4.04083	+	6.99893i	−0.217237	+	0.376265i
$347$	4.94187	−	8.55957i	0.265294	−	0.459502i	−0.702347	−	0.711835i	$-0.747864\pi$
$347$	4.94187	−	8.55957i	0.265294	−	0.459502i	0.967641	+	0.252333i	$0.0811978\pi$
$348$	11.0080	−	0.767769i	0.590089	−	0.0411567i
$349$	31.3513	−	18.1007i	1.67820	−	0.968906i	0.715384	−	0.698732i	$-0.246252\pi$
$349$	31.3513	−	18.1007i	1.67820	−	0.968906i	0.962811	−	0.270175i	$-0.0870814\pi$
$350$		−	43.4888i		−	2.32457i
$351$	5.12334	+	1.66772i	0.273464	+	0.0890164i
$352$	12.0741	−	27.1725i	0.643549	−	1.44830i
$353$	13.3548	−	7.71038i	0.710803	−	0.410382i	−0.100556	−	0.994931i	$-0.532062\pi$
$353$	13.3548	−	7.71038i	0.710803	−	0.410382i	0.811358	+	0.584549i	$0.198729\pi$
$354$	−1.69487	−	24.3004i	−0.0900815	−	1.29155i
$355$	−0.0442935	+	0.0767186i	−0.00235085	+	0.00407180i
$356$	8.12440	+	4.69063i	0.430592	+	0.248603i
$357$	−24.3122	+	16.3924i	−1.28674	+	0.867579i
$358$	−35.8558	+	20.7014i	−1.89504	+	1.09410i
$359$	−22.5845			−1.19196			−0.595981	−	0.802998i	$-0.703237\pi$
$359$	−22.5845			−1.19196			−0.595981	+	0.802998i	$0.703237\pi$
$360$	−3.12580	−	1.26421i	−0.164744	−	0.0666296i
$361$	−7.20205			−0.379055
$362$	13.3023	+	23.0403i	0.699155	+	1.21097i
$363$	−18.3077	+	5.27522i	−0.960905	+	0.276877i
$364$	−8.26408	+	14.3138i	−0.433156	+	0.750248i
$365$	−0.495061	+	0.857472i	−0.0259127	+	0.0448821i
$366$	−44.8502	−	21.8849i	−2.34436	−	1.14394i
$367$	10.4584	+	18.1144i	0.545922	+	0.945565i	0.998548	+	0.0538647i	$0.0171540\pi$
$367$	10.4584	+	18.1144i	0.545922	+	0.945565i	−0.452626	+	0.891700i	$0.649513\pi$
$368$			41.4904i			2.16284i
$369$	2.11621	−	5.23241i	0.110166	−	0.272388i
$370$			1.25278i			0.0651288i
$371$	−15.7817	−	27.3348i	−0.819348	−	1.41915i
$372$	−14.8850	−	22.0765i	−0.771753	−	1.14461i
$373$	21.2836	+	12.2881i	1.10202	+	0.636252i	0.936751	−	0.349997i	$-0.113817\pi$
$373$	21.2836	+	12.2881i	1.10202	+	0.636252i	0.165270	+	0.986248i	$0.447151\pi$
$374$	−25.4354	−	34.9548i	−1.31523	−	1.80747i
$375$	−0.190723	−	2.73451i	−0.00984890	−	0.141210i
$376$	−7.05640	+	4.07401i	−0.363906	+	0.210101i
$377$		−	1.39648i		−	0.0719221i
$378$	−43.1928	−	14.0599i	−2.22160	−	0.723163i
$379$	26.7013			1.37155			0.685777	−	0.727811i	$-0.259462\pi$
$379$	26.7013			1.37155			0.685777	+	0.727811i	$0.259462\pi$
$380$	1.92094	+	3.32717i	0.0985422	+	0.170680i
$381$	1.66080	+	23.8119i	0.0850853	+	1.21992i
$382$	−18.9248	−	10.9262i	−0.968275	−	0.559034i
$383$	24.3065	+	14.0334i	1.24201	+	0.717072i	0.969502	−	0.245082i	$-0.0788150\pi$
$383$	24.3065	+	14.0334i	1.24201	+	0.717072i	0.272504	+	0.962155i	$0.412148\pi$
$384$	−3.73343	−	5.53718i	−0.190521	−	0.282568i
$385$	−1.76328	+	0.186638i	−0.0898649	+	0.00951194i
$386$		−	23.7667i		−	1.20969i
$387$	22.5244	−	17.5850i	1.14498	−	0.893894i
$388$	−8.68017			−0.440669
$389$	−22.3706	+	12.9157i	−1.13423	+	0.654850i	−0.944996	−	0.327081i	$-0.893935\pi$
$389$	−22.3706	+	12.9157i	−1.13423	+	0.654850i	−0.189237	+	0.981931i	$0.560602\pi$
$390$	−0.324187	+	0.664379i	−0.0164158	+	0.0336421i
$391$	20.2457	+	11.6889i	1.02387	+	0.591132i
$392$	15.4217	−	26.7112i	0.778913	−	1.34912i
$393$	−1.89519	+	3.88395i	−0.0955997	+	0.195919i
$394$	−8.84679	−	15.3231i	−0.445695	−	0.771966i
$395$	0.681535			0.0342917
$396$	12.9567	−	45.2496i	0.651098	−	2.27388i
$397$	6.26174			0.314268			0.157134	−	0.987577i	$-0.449775\pi$
$397$	6.26174			0.314268			0.157134	+	0.987577i	$0.449775\pi$
$398$	15.0983	+	26.1511i	0.756810	+	1.31083i
$399$	16.7013	+	24.7703i	0.836110	+	1.24006i
$400$	−22.1796	+	38.4162i	−1.10898	+	1.92081i
$401$	21.0664	+	12.1627i	1.05201	+	0.607376i	0.923210	−	0.384295i	$-0.125555\pi$
$401$	21.0664	+	12.1627i	1.05201	+	0.607376i	0.128796	+	0.991671i	$0.458889\pi$
$402$	−24.0240	+	1.67559i	−1.19821	+	0.0835709i
$403$	−2.91814	+	1.68479i	−0.145363	+	0.0839253i
$404$	−84.4162			−4.19986
$405$	−1.38528	−	0.346444i	−0.0688350	−	0.0172149i
$406$			11.7731i			0.584290i
$407$	−10.0383	+	1.06252i	−0.497579	+	0.0526673i
$408$	61.4945	−	4.28903i	3.04443	−	0.212339i
$409$	−31.1436	−	17.9808i	−1.53995	−	0.889092i	−0.998841	−	0.0481417i	$-0.984670\pi$
$409$	−31.1436	−	17.9808i	−1.53995	−	0.889092i	−0.541112	−	0.840950i	$-0.681997\pi$
$410$	0.670656	+	0.387204i	0.0331214	+	0.0191226i
$411$	16.3692	−	11.0369i	0.807434	−	0.544410i
$412$	−20.8308	−	36.0800i	−1.02626	−	1.77753i
$413$	18.2666			0.898843
$414$	5.02728	+	35.8642i	0.247077	+	1.76263i
$415$		−	1.46427i		−	0.0718780i
$416$	8.05068	−	4.64806i	0.394717	−	0.227890i
$417$	18.7292	+	9.13901i	0.917174	+	0.447539i
$418$	−35.6134	+	25.9147i	−1.74191	+	1.26753i
$419$	−32.8419	−	18.9613i	−1.60443	−	0.926318i	−0.990586	−	0.136891i	$-0.956289\pi$
$419$	−32.8419	−	18.9613i	−1.60443	−	0.926318i	−0.613844	−	0.789427i	$-0.710378\pi$
$420$	1.92094	−	3.93672i	0.0937323	−	0.192092i
$421$	−3.52098	−	6.09852i	−0.171602	−	0.297224i	0.767378	−	0.641195i	$-0.221561\pi$
$421$	−3.52098	−	6.09852i	−0.171602	−	0.297224i	−0.938980	+	0.343971i	$0.888228\pi$
$422$			49.8071i			2.42457i
$423$	−2.71994	+	2.12348i	−0.132248	+	0.103247i
$424$			66.3557i			3.22252i
$425$	12.4971	+	21.6456i	0.606198	+	1.04997i
$426$	2.08024	−	1.40260i	0.100788	−	0.0679561i
$427$	18.7112	−	32.4088i	0.905501	−	1.56837i
$428$	33.8993	−	58.7153i	1.63858	−	2.83811i
$429$	−5.59850	−	2.03417i	−0.270298	−	0.0982104i
$430$	1.96038	+	3.39547i	0.0945378	+	0.163744i
$431$	38.2910			1.84441			0.922207	−	0.386696i	$-0.126384\pi$
$431$	38.2910			1.84441			0.922207	+	0.386696i	$0.126384\pi$
$432$	30.9841	+	34.4486i	1.49072	+	1.65741i
$433$	−22.1866			−1.06622			−0.533109	−	0.846047i	$-0.678976\pi$
$433$	−22.1866			−1.06622			−0.533109	+	0.846047i	$0.678976\pi$
$434$	24.6017	−	14.2038i	1.18092	−	0.681803i
$435$	0.0257508	+	0.369204i	0.00123465	+	0.0177020i
$436$	30.5267	+	17.6246i	1.46197	+	0.844066i
$437$	11.9091	−	20.6272i	0.569690	−	0.986732i
$438$	23.2505	−	15.6766i	1.11095	−	0.749057i
$439$	−19.1579	+	11.0608i	−0.914357	+	0.527904i	−0.881830	−	0.471567i	$-0.843689\pi$
$439$	−19.1579	+	11.0608i	−0.914357	+	0.527904i	−0.0325264	+	0.999471i	$0.510355\pi$
$440$	3.40647	+	1.51366i	0.162397	+	0.0721610i
$441$	4.89751	−	12.1093i	0.233215	−	0.576632i
$442$		−	13.5153i		−	0.642858i
$443$	16.1301	−	9.31270i	0.766363	−	0.442460i	−0.0652128	−	0.997871i	$-0.520773\pi$
$443$	16.1301	−	9.31270i	0.766363	−	0.442460i	0.831576	+	0.555412i	$0.187439\pi$
$444$	10.9359	−	22.4116i	0.518993	−	1.06361i
$445$	−0.157322	+	0.272490i	−0.00745779	+	0.0129173i
$446$	19.0922	−	33.0686i	0.904040	−	1.56584i
$447$	1.77023	−	3.62786i	0.0837290	−	0.171592i
$448$	−15.8315	+	9.14034i	−0.747969	+	0.431840i
$449$			17.9495i			0.847088i	0.905876	+	0.423544i	$0.139214\pi$
$449$			17.9495i			0.847088i	−0.905876	+	0.423544i	$0.860786\pi$
$450$	−14.5172	+	35.8944i	−0.684349	+	1.69208i
$451$	−2.53378	+	5.70225i	−0.119311	+	0.268508i
$452$	0.433609	−	0.250344i	0.0203952	−	0.0117752i
$453$	−10.9510	+	7.38371i	−0.514524	+	0.346917i
$454$	3.82743	−	6.62930i	0.179630	−	0.311129i
$455$	−0.480081	−	0.277175i	−0.0225066	−	0.0129942i
$456$	−4.36985	−	62.6532i	−0.204637	−	2.93400i
$457$	−5.18506	+	2.99360i	−0.242547	+	0.140035i	−0.616347	−	0.787475i	$-0.711388\pi$
$457$	−5.18506	+	2.99360i	−0.242547	+	0.140035i	0.373800	+	0.927509i	$0.378055\pi$
$458$	28.7507			1.34343
$459$	25.5386	−	5.41404i	1.19204	−	0.252706i
$460$	−3.49235			−0.162832
$461$	−4.80832	−	8.32826i	−0.223946	−	0.387886i	0.732057	−	0.681244i	$-0.238561\pi$
$461$	−4.80832	−	8.32826i	−0.223946	−	0.387886i	−0.956003	+	0.293358i	$0.905227\pi$
$462$	47.1987	+	17.1492i	2.19588	+	0.797855i
$463$	−4.99782	+	8.65648i	−0.232268	+	0.402301i	−0.958475	−	0.285176i	$-0.907948\pi$
$463$	−4.99782	+	8.65648i	−0.232268	+	0.402301i	0.726207	+	0.687476i	$0.241281\pi$
$464$	6.00438	−	10.3999i	0.278746	−	0.482803i
$465$	0.740440	−	0.499240i	0.0343371	−	0.0231517i
$466$	10.1230	+	17.5335i	0.468938	+	0.812224i
$467$		−	18.1972i		−	0.842066i	−0.907045	−	0.421033i	$-0.861668\pi$
$467$		−	18.1972i		−	0.842066i	0.907045	−	0.421033i	$-0.138332\pi$
$468$	11.5991	−	9.05551i	0.536169	−	0.418591i
$469$		−	18.0588i		−	0.833879i
$470$	−0.236726	−	0.410021i	−0.0109194	−	0.0189129i
$471$	12.3936	−	25.3990i	0.571066	−	1.17033i
$472$	−33.2569	−	19.2009i	−1.53078	−	0.883793i
$473$	−25.5446	+	18.5880i	−1.17454	+	0.854675i
$474$	−17.3471	−	8.46460i	−0.796779	−	0.388792i
$475$	22.0534	−	12.7326i	1.01188	−	0.584210i
$476$			80.0838i			3.67064i
$477$	3.90101	+	27.8295i	0.178615	+	1.27423i
$478$	−41.2813			−1.88816
$479$	9.41443	+	16.3063i	0.430156	+	0.745053i	0.996886	−	0.0788507i	$-0.0251250\pi$
$479$	9.41443	+	16.3063i	0.430156	+	0.745053i	−0.566730	+	0.823904i	$0.691792\pi$
$480$	−2.04275	+	1.37732i	−0.0932386	+	0.0628659i
$481$	−2.73309	−	1.57795i	−0.124618	−	0.0719483i
$482$	31.3012	+	18.0718i	1.42573	+	0.823146i
$483$	−27.0909	+	1.88950i	−1.23268	+	0.0859753i
$484$	−16.0072	+	49.5124i	−0.727598	+	2.25056i
$485$		−	0.291130i		−	0.0132196i
$486$	30.9567	+	26.0231i	1.40422	+	1.18043i
$487$	−40.2338			−1.82317			−0.911585	−	0.411112i	$-0.865140\pi$
$487$	−40.2338			−1.82317			−0.911585	+	0.411112i	$0.865140\pi$
$488$	−68.1328	+	39.3365i	−3.08423	+	1.78068i
$489$	−26.8605	+	1.87343i	−1.21467	+	0.0847194i
$490$	1.55209	+	0.896098i	0.0701162	+	0.0404816i
$491$	−4.10919	+	7.11732i	−0.185445	+	0.321200i	−0.943726	−	0.330727i	$-0.892706\pi$
$491$	−4.10919	+	7.11732i	−0.185445	+	0.321200i	0.758281	+	0.651927i	$0.226039\pi$
$492$	−8.61772	−	12.7812i	−0.388517	−	0.576223i
$493$	−3.38316	−	5.85981i	−0.152370	−	0.263913i
$494$	−13.7700			−0.619540
$495$	1.51766	+	0.434564i	0.0682137	+	0.0195322i
$496$	−28.9761			−1.30107
$497$	0.940692	+	1.62933i	0.0421958	+	0.0730853i
$498$	−18.1861	+	37.2700i	−0.814936	+	1.67011i
$499$	15.2562	−	26.4246i	0.682963	−	1.18293i	−0.291109	−	0.956690i	$-0.594024\pi$
$499$	15.2562	−	26.4246i	0.682963	−	1.18293i	0.974072	−	0.226237i	$-0.0726423\pi$
$500$	−6.48354	−	3.74327i	−0.289953	−	0.167404i
$501$	8.65521	−	17.7377i	0.386686	−	0.792464i
$502$	−17.3012	+	9.98884i	−0.772190	+	0.445824i
$503$	16.3781			0.730263			0.365131	−	0.930956i	$-0.381024\pi$
$503$	16.3781			0.730263			0.365131	+	0.930956i	$0.381024\pi$
$504$	−56.4442	+	44.0664i	−2.51422	+	1.96287i
$505$		−	2.83130i		−	0.125991i
$506$	−4.21427	−	39.8146i	−0.187347	−	1.76998i
$507$	11.5467	+	17.1253i	0.512808	+	0.760563i
$508$	56.4580	+	32.5961i	2.50492	+	1.44622i
$509$	−14.4224	−	8.32681i	−0.639264	−	0.369079i	0.145067	−	0.989422i	$-0.453660\pi$
$509$	−14.4224	−	8.32681i	−0.639264	−	0.369079i	−0.784331	+	0.620343i	$0.786994\pi$
$510$	0.249220	+	3.57322i	0.0110357	+	0.158225i
$511$	10.5140	+	18.2107i	0.465111	+	0.805595i
$512$	−46.3889			−2.05012
$513$	−5.51605	−	26.0198i	−0.243539	−	1.14880i
$514$			14.6000i			0.643980i
$515$	1.21011	−	0.698660i	0.0533240	−	0.0307866i
$516$	−5.43020	−	77.8562i	−0.239051	−	3.42743i
$517$	3.08465	−	2.24459i	0.135663	−	0.0987171i
$518$	23.0416	+	13.3031i	1.01239	+	0.584503i
$519$	3.01636	+	4.47367i	0.132404	+	0.196372i
$520$	0.582703	+	1.00927i	0.0255532	+	0.0442595i
$521$		−	41.8433i		−	1.83319i	−0.399818	−	0.916595i	$-0.630927\pi$
$521$		−	41.8433i		−	1.83319i	0.399818	−	0.916595i	$-0.369073\pi$
$522$	3.93005	−	9.71719i	0.172014	−	0.425310i
$523$		−	39.5791i		−	1.73067i	−0.501192	−	0.865336i	$-0.667105\pi$
$523$		−	39.5791i		−	1.73067i	0.501192	−	0.865336i	$-0.332895\pi$
$524$	5.90159	+	10.2218i	0.257812	+	0.446543i
$525$	−26.0937	−	12.7326i	−1.13882	−	0.555694i
$526$	−33.8431	+	58.6180i	−1.47563	+	2.55587i
$527$	−8.16329	+	14.1392i	−0.355599	+	0.615915i
$528$	−32.9471	−	39.2206i	−1.43384	−	1.70686i
$529$	−0.674365	−	1.16803i	−0.0293202	−	0.0507841i
$530$	−3.85569			−0.167480
$531$	−15.0767	−	6.09769i	−0.654275	−	0.264617i
$532$	81.5927			3.53749
$533$	−1.68946	+	0.975413i	−0.0731788	+	0.0422498i
$534$	7.38863	−	4.98177i	0.319737	−	0.215582i
$535$	1.96930	+	1.13697i	0.0851401	+	0.0491557i
$536$	−18.9825	+	32.8786i	−0.819917	+	1.42014i
$537$	1.92325	+	27.5748i	0.0829943	+	1.18994i
$538$	40.8323	−	23.5745i	1.76040	−	1.01637i
$539$	−5.86389	+	13.1966i	−0.252576	+	0.568418i
$540$	−2.89962	+	2.60801i	−0.124780	+	0.112231i
$541$			29.7471i			1.27893i	0.768821	+	0.639464i	$0.220844\pi$
$541$			29.7471i			1.27893i	−0.768821	+	0.639464i	$0.779156\pi$
$542$	40.0936	−	23.1480i	1.72217	−	0.994293i
$543$	17.7191	−	1.23584i	0.760398	−	0.0530352i
$544$	22.5212	−	39.0079i	0.965589	−	1.67245i
$545$	−0.591125	+	1.02386i	−0.0253210	+	0.0438573i
$546$	8.77702	+	13.0175i	0.375622	+	0.557098i
$547$	−0.0889871	+	0.0513767i	−0.00380481	+	0.00219671i	−0.501901	−	0.864925i	$-0.667366\pi$
$547$	−0.0889871	+	0.0513767i	−0.00380481	+	0.00219671i	0.498096	+	0.867122i	$0.334033\pi$
$548$		−	53.9199i		−	2.30334i
$549$	−26.2623	+	20.5032i	−1.12085	+	0.875054i
$550$	17.3818	−	39.1174i	0.741162	−	1.66797i
$551$	−5.97022	+	3.44691i	−0.254340	+	0.146843i
$552$	51.3089	+	25.0364i	2.18385	+	1.06562i
$553$	7.23711	−	12.5351i	0.307753	−	0.533045i
$554$	41.4044	+	23.9049i	1.75911	+	1.01562i
$555$	0.751680	+	0.366786i	0.0319070	+	0.0155692i
$556$	49.2919	−	28.4587i	2.09044	−	1.20692i
$557$	21.3570			0.904926			0.452463	−	0.891783i	$-0.350546\pi$
$557$	21.3570			0.904926			0.452463	+	0.891783i	$0.350546\pi$
$558$	−25.0469	+	3.51096i	−1.06032	+	0.148631i
$559$	−9.87686			−0.417746
$560$	−2.38352	−	4.12838i	−0.100722	−	0.174456i
$561$	−28.4202	+	5.02752i	−1.19990	+	0.212262i
$562$	−17.1684	+	29.7365i	−0.724204	+	1.25436i
$563$	−18.9075	+	32.7488i	−0.796858	+	1.38020i	0.124795	+	0.992183i	$0.460173\pi$
$563$	−18.9075	+	32.7488i	−0.796858	+	1.38020i	−0.921653	+	0.388016i	$0.873161\pi$
$564$	0.655726	+	9.40154i	0.0276110	+	0.395876i
$565$	0.00839647	+	0.0145431i	0.000353242	+	0.000611833i
$566$		−	44.1460i		−	1.85560i
$567$	−21.0820	+	21.7997i	−0.885360	+	0.915502i
$568$		−	3.95522i		−	0.165957i
$569$	8.58131	+	14.8633i	0.359747	+	0.623101i	0.987918	−	0.154975i	$-0.0495295\pi$
$569$	8.58131	+	14.8633i	0.359747	+	0.623101i	−0.628171	+	0.778075i	$0.716196\pi$
$570$	3.64055	−	0.253916i	0.152486	−	0.0106354i
$571$	−32.6430	−	18.8464i	−1.36607	−	0.788698i	−0.375642	−	0.926765i	$-0.622578\pi$
$571$	−32.6430	−	18.8464i	−1.36607	−	0.788698i	−0.990423	+	0.138067i	$0.955911\pi$
$572$	−13.1544	+	9.57201i	−0.550013	+	0.400226i
$573$	−12.0966	+	8.15610i	−0.505342	+	0.340726i
$574$	14.2432	−	8.22332i	0.594500	−	0.343235i
$575$			23.1483i			0.965352i
$576$	16.1181	−	2.25935i	0.671586	−	0.0941396i
$577$	18.2232			0.758642			0.379321	−	0.925265i	$-0.376158\pi$
$577$	18.2232			0.758642			0.379321	+	0.925265i	$0.376158\pi$
$578$	−10.6911	−	18.5175i	−0.444690	−	0.770225i
$579$	−14.2602	−	6.95835i	−0.592635	−	0.289179i
$580$	0.875385	+	0.505404i	0.0363484	+	0.0209857i
$581$	−26.9314	−	15.5488i	−1.11730	−	0.645074i
$582$	−3.61581	+	7.41015i	−0.149880	+	0.307160i
$583$	−3.27014	−	30.8949i	−0.135435	−	1.27954i
$584$		−	44.2069i		−	1.82929i
$585$	0.303719	+	0.389031i	0.0125573	+	0.0160844i
$586$	68.7181			2.83872
$587$	−0.250861	+	0.144835i	−0.0103541	+	0.00597797i	−0.505168	−	0.863021i	$-0.668570\pi$
$587$	−0.250861	+	0.144835i	−0.0103541	+	0.00597797i	0.494814	+	0.868999i	$0.335236\pi$
$588$	−19.9438	−	29.5794i	−0.822470	−	1.21983i
$589$	14.4056	+	8.31710i	0.593574	+	0.342700i
$590$	1.11569	−	1.93244i	0.0459324	−	0.0795573i
$591$	−11.7842	+	0.821905i	−0.484735	+	0.0338086i
$592$	−13.5693	−	23.5027i	−0.557696	−	0.965957i
$593$	−10.5590			−0.433606			−0.216803	−	0.976215i	$-0.569563\pi$
$593$	−10.5590			−0.433606			−0.216803	+	0.976215i	$0.569563\pi$
$594$	−33.2317	−	29.9101i	−1.36351	−	1.22723i
$595$	−2.68599			−0.110115
$596$	−5.51246	−	9.54787i	−0.225799	−	0.391096i
$597$	20.1114	−	1.40270i	0.823103	−	0.0574086i
$598$	6.25859	−	10.8402i	0.255933	−	0.443289i
$599$	11.0356	+	6.37143i	0.450904	+	0.260330i	0.708212	−	0.706000i	$-0.249502\pi$
$599$	11.0356	+	6.37143i	0.450904	+	0.260330i	−0.257308	+	0.966330i	$0.582835\pi$
$600$	34.1235	+	50.6097i	1.39309	+	2.06613i
$601$	−15.4925	+	8.94459i	−0.631952	+	0.364857i	−0.781507	−	0.623896i	$-0.785549\pi$
$601$	−15.4925	+	8.94459i	−0.631952	+	0.364857i	0.149556	+	0.988753i	$0.452216\pi$
$602$	83.2678			3.39374
$603$	−6.02832	+	14.9052i	−0.245492	+	0.606987i
$604$			36.0725i			1.46777i
$605$	−1.66063	−	0.536876i	−0.0675143	−	0.0218271i
$606$	−35.1644	+	72.0650i	−1.42846	+	2.92744i
$607$	−21.3132	−	12.3052i	−0.865077	−	0.499453i	0.000631871	−	1.00000i	$-0.499799\pi$
$607$	−21.3132	−	12.3052i	−0.865077	−	0.499453i	−0.865709	+	0.500547i	$0.833132\pi$
$608$	−39.7429	−	22.9456i	−1.61179	−	0.930565i
$609$	7.06400	+	3.44691i	0.286248	+	0.139676i
$610$	−2.28570	−	3.95895i	−0.0925453	−	0.160293i
$611$	1.19268			0.0482508
$612$	26.7332	−	66.0988i	1.08063	−	2.67188i
$613$		−	15.3836i		−	0.621339i	−0.950518	−	0.310669i	$-0.899447\pi$
$613$		−	15.3836i		−	0.621339i	0.950518	−	0.310669i	$-0.100553\pi$
$614$	1.44024	−	0.831525i	0.0581235	−	0.0335576i
$615$	0.428679	−	0.289036i	0.0172860	−	0.0116551i
$616$	64.0127	−	46.5798i	2.57914	−	1.87675i
$617$	2.83696	+	1.63792i	0.114212	+	0.0659402i	0.556018	−	0.831170i	$-0.312329\pi$
$617$	2.83696	+	1.63792i	0.114212	+	0.0659402i	−0.441806	+	0.897111i	$0.645662\pi$
$618$	−39.4783	+	2.75348i	−1.58805	+	0.110761i
$619$	−4.01397	−	6.95240i	−0.161335	−	0.279440i	0.774013	−	0.633170i	$-0.218247\pi$
$619$	−4.01397	−	6.95240i	−0.161335	−	0.279440i	−0.935348	+	0.353730i	$0.884913\pi$
$620$		−	2.43899i		−	0.0979524i
$621$	22.9908	+	7.48384i	0.922589	+	0.300316i
$622$		−	31.6773i		−	1.27015i
$623$	3.34117	+	5.78707i	0.133861	+	0.231854i
$624$	−1.11424	−	15.9755i	−0.0446051	−	0.639531i
$625$	−12.3115	+	21.3242i	−0.492461	+	0.852967i
$626$	−34.5758	+	59.8871i	−1.38193	+	2.39357i
$627$	5.12225	+	28.9557i	0.204563	+	1.15638i
$628$	−38.5934	−	66.8457i	−1.54004	−	2.66743i
$629$	−15.2913			−0.609702
$630$	−2.56054	−	3.27976i	−0.102014	−	0.130669i
$631$	−40.1130			−1.59687			−0.798436	−	0.602080i	$-0.794339\pi$
$631$	−40.1130			−1.59687			−0.798436	+	0.602080i	$0.794339\pi$
$632$	−26.3523	+	15.2145i	−1.04824	+	0.605202i
$633$	29.8848	+	14.5824i	1.18781	+	0.579599i
$634$	39.3381	+	22.7119i	1.56232	+	0.902003i
$635$	−1.09326	+	1.89359i	−0.0433848	+	0.0751447i
$636$	68.9764	+	33.6574i	2.73509	+	1.33460i
$637$	−3.90990	+	2.25738i	−0.154916	+	0.0894406i
$638$	−4.70553	+	10.5897i	−0.186294	+	0.419251i
$639$	−0.232525	−	1.65881i	−0.00919853	−	0.0656217i
$640$		−	0.611744i		−	0.0241813i
$641$	−1.91439	+	1.10527i	−0.0756137	+	0.0436556i	−0.537330	−	0.843372i	$-0.680567\pi$
$641$	−1.91439	+	1.10527i	−0.0756137	+	0.0436556i	0.461716	+	0.887028i	$0.347234\pi$
$642$	−36.0034	−	53.3979i	−1.42094	−	2.10745i
$643$	11.3784	−	19.7080i	0.448720	−	0.777206i	−0.549583	−	0.835439i	$-0.685213\pi$
$643$	11.3784	−	19.7080i	0.448720	−	0.777206i	0.998303	+	0.0582333i	$0.0185467\pi$
$644$	−37.0848	+	64.2327i	−1.46134	+	2.53112i
$645$	2.61127	−	0.182128i	0.102819	−	0.00717127i
$646$	−57.7808	+	33.3597i	−2.27335	+	1.31252i
$647$			12.2576i			0.481897i	0.970538	+	0.240948i	$0.0774584\pi$
$647$			12.2576i			0.481897i	−0.970538	+	0.240948i	$0.922542\pi$
$648$	61.2974	−	17.5292i	2.40799	−	0.688611i
$649$	16.4305	+	7.30088i	0.644955	+	0.286585i
$650$	11.5897	−	6.69134i	0.454587	−	0.262456i
$651$	−1.31959	−	18.9198i	−0.0517189	−	0.741526i
$652$	−36.7693	+	63.6863i	−1.44000	+	2.49415i
$653$	19.6458	+	11.3425i	0.768798	+	0.443866i	0.832446	−	0.554107i	$-0.186940\pi$
$653$	19.6458	+	11.3425i	0.768798	+	0.443866i	−0.0636475	+	0.997972i	$0.520273\pi$
$654$	27.7621	−	18.7186i	1.08559	−	0.731954i
$655$	−0.342838	+	0.197938i	−0.0133958	+	0.00773406i
$656$	−16.7758			−0.654985
$657$	−2.59889	−	18.5403i	−0.101392	−	0.723327i
$658$	−10.0550			−0.391986
$659$	12.3240	+	21.3458i	0.480074	+	0.831513i	0.999739	−	0.0228574i	$-0.00727637\pi$
$659$	12.3240	+	21.3458i	0.480074	+	0.831513i	−0.519664	+	0.854370i	$0.673943\pi$
$660$	3.30130	−	2.77324i	0.128503	−	0.107948i
$661$	12.8269	−	22.2168i	0.498907	−	0.864133i	−0.501092	−	0.865394i	$-0.667068\pi$
$661$	12.8269	−	22.2168i	0.498907	−	0.864133i	0.999999	+	0.00126123i	$0.000401463\pi$
$662$	32.6103	−	56.4827i	1.26744	−	2.19526i
$663$	−8.10932	−	3.95698i	−0.314940	−	0.153676i
$664$	32.6882	+	56.6176i	1.26855	+	2.19719i
$665$			2.73660i			0.106121i
$666$	−14.5771	−	18.6716i	−0.564850	−	0.723509i
$667$		−	6.26663i		−	0.242645i
$668$	−26.9522	−	46.6825i	−1.04281	−	1.80620i
$669$	−14.2517	−	21.1372i	−0.551004	−	0.817213i
$670$	−1.91045	−	1.10300i	−0.0738073	−	0.0426127i
$671$	29.7837	−	21.6726i	1.14979	−	0.836662i
$672$	3.64055	+	52.1967i	0.140437	+	2.01353i
$673$	27.3002	−	15.7618i	1.05235	−	0.607572i	0.129041	−	0.991639i	$-0.458810\pi$
$673$	27.3002	−	15.7618i	1.05235	−	0.607572i	0.923305	+	0.384067i	$0.125477\pi$
$674$			29.5840i			1.13953i
$675$	17.2867	+	19.2196i	0.665364	+	0.739761i
$676$	56.4105			2.16964
$677$	−4.38509	−	7.59519i	−0.168533	−	0.291907i	0.769372	−	0.638802i	$-0.220570\pi$
$677$	−4.38509	−	7.59519i	−0.168533	−	0.291907i	−0.937904	+	0.346895i	$0.887236\pi$
$678$	−0.0330912	−	0.474449i	−0.00127086	−	0.0182211i
$679$	−5.35459	−	3.09147i	−0.205490	−	0.118640i
$680$	4.89021	+	2.82337i	0.187531	+	0.108271i
$681$	−2.85706	−	4.23741i	−0.109483	−	0.162378i
$682$	27.8058	−	2.94317i	1.06474	−	0.112700i
$683$			22.5674i			0.863516i	0.901990	+	0.431758i	$0.142106\pi$
$683$			22.5674i			0.863516i	−0.901990	+	0.431758i	$0.857894\pi$
$684$	−67.3442	−	27.2369i	−2.57497	−	1.04143i
$685$	1.80846			0.0690976
$686$	−20.0314	+	11.5651i	−0.764803	+	0.441559i
$687$	8.41755	−	17.2507i	0.321150	−	0.658155i
$688$	−73.5553	−	42.4672i	−2.80427	−	1.61905i
$689$	4.85647	−	8.41165i	0.185017	−	0.320458i
$690$	−1.45478	+	2.98137i	−0.0553823	+	0.113499i
$691$	−9.54293	−	16.5288i	−0.363030	−	0.628787i	0.625428	−	0.780282i	$-0.284925\pi$
$691$	−9.54293	−	16.5288i	−0.363030	−	0.628787i	−0.988458	+	0.151495i	$0.951591\pi$
$692$	14.7362			0.560186
$693$	24.1085	−	23.2988i	0.915804	−	0.885048i
$694$	−25.6416			−0.973343
$695$	0.954497	+	1.65324i	0.0362062	+	0.0627109i
$696$	−9.23778	−	13.7009i	−0.350157	−	0.519330i
$697$	−4.72616	+	8.18595i	−0.179016	+	0.310065i
$698$	−81.3353	−	46.9590i	−3.07859	−	1.77742i
$699$	13.4841	−	0.940468i	0.510014	−	0.0355718i
$700$	−68.6740	+	39.6490i	−2.59563	+	1.49859i
$701$	−18.2771			−0.690315			−0.345158	−	0.938545i	$-0.612175\pi$
$701$	−18.2771			−0.690315			−0.345158	+	0.938545i	$0.612175\pi$
$702$	−2.89885	−	13.6742i	−0.109410	−	0.516098i
$703$			15.5794i			0.587587i
$704$	−17.8934	+	1.89397i	−0.674384	+	0.0713816i
$705$	−0.315325	+	0.0219929i	−0.0118758	+	0.000828300i
$706$	−34.6466	−	20.0032i	−1.30394	−	0.752831i
$707$	−52.0743	−	30.0651i	−1.95846	−	1.13072i
$708$	−36.8281	+	24.8312i	−1.38408	+	0.933215i
$709$	−6.09028	−	10.5487i	−0.228725	−	0.396164i	0.728705	−	0.684827i	$-0.240122\pi$
$709$	−6.09028	−	10.5487i	−0.228725	−	0.396164i	−0.957431	+	0.288664i	$0.906789\pi$
$710$	0.229823			0.00862511
$711$	−10.1577	+	7.93019i	−0.380943	+	0.297406i
$712$		−	14.0482i		−	0.526479i
$713$	−13.0950	+	7.56042i	−0.490413	+	0.283140i
$714$	68.3665	+	33.3597i	2.55855	+	1.24846i
$715$	−0.321043	−	0.441195i	−0.0120063	−	0.0164998i
$716$	65.3799	+	37.7471i	2.44336	+	1.41067i
$717$	−12.0862	+	24.7692i	−0.451369	+	0.925022i
$718$	29.2957	+	50.7417i	1.09331	+	1.89366i
$719$		−	8.08637i		−	0.301571i	−0.988567	−	0.150785i	$-0.951820\pi$
$719$		−	8.08637i		−	0.301571i	0.988567	−	0.150785i	$-0.0481802\pi$
$720$	0.589170	+	4.20310i	0.0219571	+	0.156640i
$721$		−	29.6759i		−	1.10519i
$722$	9.34222	+	16.1812i	0.347682	+	0.602202i
$723$	20.0075	−	13.4900i	0.744088	−	0.501700i
$724$	24.2556	−	42.0119i	0.901452	−	1.56136i
$725$	3.34996	−	5.80231i	0.124415	−	0.215492i
$726$	35.6002	+	34.2900i	1.32125	+	1.27262i
$727$	−0.752397	−	1.30319i	−0.0279049	−	0.0483326i	0.851736	−	0.523972i	$-0.175550\pi$
$727$	−0.752397	−	1.30319i	−0.0279049	−	0.0483326i	−0.879641	+	0.475639i	$0.842217\pi$
$728$	24.7506			0.917316
$729$	24.6775	−	10.9553i	0.913983	−	0.405754i
$730$	2.56870			0.0950718
$731$	−41.4447	+	23.9281i	−1.53289	+	0.885014i
$732$	6.33134	+	90.7763i	0.234013	+	3.35519i
$733$	2.84468	+	1.64238i	0.105071	+	0.0606626i	0.551615	−	0.834099i	$-0.314012\pi$
$733$	2.84468	+	1.64238i	0.105071	+	0.0606626i	−0.446544	+	0.894762i	$0.647345\pi$
$734$	27.1324	−	46.9947i	1.00147	−	1.73461i
$735$	0.992085	−	0.668911i	0.0365936	−	0.0246732i
$736$	36.1271	−	20.8580i	1.33166	−	0.768836i
$737$	7.21782	−	16.2436i	0.265872	−	0.598341i
$738$	−14.5010	+	2.03268i	−0.533789	+	0.0748239i
$739$			45.1813i			1.66202i	0.556257	+	0.831010i	$0.312237\pi$
$739$			45.1813i			1.66202i	−0.556257	+	0.831010i	$0.687763\pi$
$740$	1.97829	−	1.14216i	0.0727232	−	0.0419868i
$741$	−4.03154	+	8.26212i	−0.148102	+	0.303516i
$742$	−40.9430	+	70.9153i	−1.50306	+	2.60338i
$743$	−3.06363	+	5.30637i	−0.112394	+	0.194672i	−0.916735	−	0.399496i	$-0.869185\pi$
$743$	−3.06363	+	5.30637i	−0.112394	+	0.194672i	0.804341	+	0.594168i	$0.202518\pi$
$744$	−17.4850	+	35.8332i	−0.641031	+	1.31371i
$745$	0.320233	−	0.184887i	0.0117324	−	0.00677372i
$746$		−	63.7584i		−	2.33436i
$747$	17.0379	+	21.8236i	0.623384	+	0.798485i
$748$	−32.0082	+	72.0340i	−1.17034	+	2.63382i
$749$	41.8233	−	24.1467i	1.52819	−	0.882302i
$750$	−5.89637	+	3.97561i	−0.215305	+	0.145169i
$751$	−10.0212	+	17.3573i	−0.365679	+	0.633375i	−0.988885	−	0.148683i	$-0.952497\pi$
$751$	−10.0212	+	17.3573i	−0.365679	+	0.633375i	0.623205	+	0.782058i	$0.285830\pi$
$752$	8.88220	+	5.12814i	0.323900	+	0.187004i
$753$	0.928007	+	13.3054i	0.0338184	+	0.484876i
$754$	−3.13753	+	1.81145i	−0.114262	+	0.0659693i
$755$	−1.20986			−0.0440314
$756$	17.1769	+	81.0251i	0.624717	+	2.94685i
$757$	38.1828			1.38778			0.693889	−	0.720082i	$-0.255896\pi$
$757$	38.1828			1.38778			0.693889	+	0.720082i	$0.255896\pi$
$758$	−34.6359	−	59.9912i	−1.25803	−	2.17898i
$759$	−25.1230	−	9.12824i	−0.911909	−	0.331334i
$760$	2.87656	−	4.98236i	0.104344	−	0.180729i
$761$	18.8711	−	32.6858i	0.684078	−	1.18486i	−0.289648	−	0.957133i	$-0.593538\pi$
$761$	18.8711	−	32.6858i	0.684078	−	1.18486i	0.973726	−	0.227725i	$-0.0731286\pi$
$762$	51.3450	−	34.6193i	1.86003	−	1.25412i
$763$	12.5541	+	21.7444i	0.454490	+	0.787200i
$764$			39.8459i			1.44158i
$765$	2.21693	+	0.896625i	0.0801535	+	0.0324175i
$766$		−	72.8143i		−	2.63089i
$767$	2.81057	+	4.86805i	0.101484	+	0.175775i
$768$	−15.8394	+	32.4607i	−0.571553	+	1.17133i
$769$	21.6668	+	12.5093i	0.781326	+	0.451099i	0.836900	−	0.547356i	$-0.184366\pi$
$769$	21.6668	+	12.5093i	0.781326	+	0.451099i	−0.0555743	+	0.998455i	$0.517699\pi$
$770$	2.70658	+	3.71954i	0.0975385	+	0.134043i
$771$	8.76018	+	4.27457i	0.315490	+	0.153945i
$772$	−37.5304	+	21.6682i	−1.35075	+	0.779855i
$773$		−	55.3377i		−	1.99036i	−0.0980708	−	0.995179i	$-0.531267\pi$
$773$		−	55.3377i		−	1.99036i	0.0980708	−	0.995179i	$-0.468733\pi$
$774$	−68.7268	−	27.7961i	−2.47033	−	0.999110i
$775$	−16.1664			−0.580713
$776$	6.49918	+	11.2569i	0.233307	+	0.404099i
$777$	14.7280	−	9.93035i	0.528366	−	0.356249i
$778$	58.0365	+	33.5074i	2.08071	+	1.20130i
$779$	8.34019	+	4.81521i	0.298818	+	0.172523i
$780$	1.34470	−	0.0937880i	0.0481478	−	0.00335815i
$781$	0.194921	+	1.84153i	0.00697481	+	0.0658952i
$782$		−	60.6494i		−	2.16882i
$783$	−4.67978	−	5.20305i	−0.167242	−	0.185942i
$784$	−38.8239			−1.38657
$785$	2.24199	−	1.29441i	0.0800199	−	0.0461995i
$786$	11.1846	−	0.780090i	0.398942	−	0.0278249i
$787$	−15.5326	−	8.96774i	−0.553677	−	0.319665i	0.196927	−	0.980418i	$-0.436904\pi$
$787$	−15.5326	−	8.96774i	−0.553677	−	0.319665i	−0.750604	+	0.660753i	$0.770237\pi$
$788$	−16.1313	+	27.9403i	−0.574654	+	0.995330i
$789$	25.2629	+	37.4683i	0.899383	+	1.33391i
$790$	−0.884061	−	1.53124i	−0.0314535	−	0.0544790i
$791$	0.356643			0.0126808
$792$	−68.3832	+	17.0772i	−2.42989	+	0.606811i
$793$	11.5159			0.408942
$794$	−8.12249	−	14.0686i	−0.288256	−	0.499275i
$795$	−1.12886	+	2.31345i	−0.0400365	+	0.0820497i
$796$	27.5304	−	47.6841i	0.975790	−	1.69012i
$797$	29.9676	+	17.3018i	1.06151	+	0.612862i	0.925849	−	0.377893i	$-0.123351\pi$
$797$	29.9676	+	17.3018i	1.06151	+	0.612862i	0.135659	+	0.990756i	$0.456685\pi$
$798$	33.9883	−	69.6546i	1.20317	−	2.46575i
$799$	5.00467	−	2.88945i	0.177053	−	0.102221i
$800$	44.6004			1.57686
$801$	−0.825885	−	5.89181i	−0.0291812	−	0.208177i
$802$		−	63.1079i		−	2.22842i
$803$	2.17860	+	20.5825i	0.0768811	+	0.726341i
$804$	24.5487	+	36.4091i	0.865767	+	1.28405i
$805$	−2.15435	−	1.24381i	−0.0759308	−	0.0438386i
$806$	7.57060	+	4.37089i	0.266663	+	0.153958i
$807$	−2.19017	−	31.4019i	−0.0770978	−	1.10540i
$808$	63.2057	+	109.475i	2.22357	+	3.85133i
$809$	−6.72470			−0.236428			−0.118214	−	0.992988i	$-0.537717\pi$
$809$	−6.72470			−0.236428			−0.118214	+	0.992988i	$0.537717\pi$
$810$	1.01856	+	3.56177i	0.0357884	+	0.125148i
$811$			26.0937i			0.916275i	0.888881	+	0.458137i	$0.151483\pi$
$811$			26.0937i			0.916275i	−0.888881	+	0.458137i	$0.848517\pi$
$812$	18.5912	−	10.7336i	0.652422	−	0.376676i
$813$	−2.15055	−	30.8338i	−0.0754232	−	1.08139i
$814$	15.4085	+	21.1752i	0.540067	+	0.742192i
$815$	−2.13602	−	1.23323i	−0.0748216	−	0.0431983i
$816$	−43.3784	−	64.3360i	−1.51855	−	2.25221i
$817$	24.3790	+	42.2256i	0.852912	+	1.47729i
$818$			93.2959i			3.26201i
$819$	10.3804	−	1.45507i	0.362719	−	0.0508442i
$820$		−	1.41206i		−	0.0493113i
$821$	−19.5583	−	33.8760i	−0.682590	−	1.18228i	−0.974188	−	0.225740i	$-0.927520\pi$
$821$	−19.5583	−	33.8760i	−0.682590	−	1.18228i	0.291598	−	0.956541i	$-0.405813\pi$
$822$	−46.0307	−	22.4609i	−1.60550	−	0.783413i
$823$	15.3692	−	26.6203i	0.535737	−	0.927924i	−0.463390	−	0.886154i	$-0.653367\pi$
$823$	15.3692	−	26.6203i	0.535737	−	0.927924i	0.999127	−	0.0417697i	$-0.0132996\pi$
$824$	−31.1937	+	54.0290i	−1.08668	+	1.88219i
$825$	−18.3819	−	21.8820i	−0.639975	−	0.761832i
$826$	−23.6948	−	41.0406i	−0.824447	−	1.42798i
$827$	−22.0427			−0.766499			−0.383250	−	0.923645i	$-0.625195\pi$
$827$	−22.0427			−0.766499			−0.383250	+	0.923645i	$0.625195\pi$
$828$	52.0505	−	40.6363i	1.80888	−	1.41221i
$829$	13.2009			0.458486			0.229243	−	0.973369i	$-0.426375\pi$
$829$	13.2009			0.458486			0.229243	+	0.973369i	$0.426375\pi$
$830$	−3.28984	+	1.89939i	−0.114192	+	0.0659288i
$831$	26.4655	−	17.8443i	0.918077	−	0.619011i
$832$	−4.87179	−	2.81273i	−0.168899	−	0.0975138i
$833$	−10.9377	+	18.9446i	−0.378968	+	0.656391i
$834$	−3.76176	−	53.9347i	−0.130259	−	1.86760i
$835$	1.56572	−	0.903968i	0.0541839	−	0.0312831i
$836$	73.3913	+	32.6113i	2.53829	+	1.12789i
$837$	−5.22657	+	16.0563i	−0.180657	+	0.554989i
$838$			98.3833i			3.39859i
$839$	−35.2755	+	20.3663i	−1.21785	+	0.703124i	−0.964457	−	0.264240i	$-0.914879\pi$
$839$	−35.2755	+	20.3663i	−1.21785	+	0.703124i	−0.253390	+	0.967364i	$0.581545\pi$
$840$	−6.54363	+	0.456396i	−0.225777	+	0.0157472i
$841$	13.5931	−	23.5440i	0.468728	−	0.811861i
$842$	−9.13457	+	15.8215i	−0.314798	+	0.545246i
$843$	12.8157	+	19.0074i	0.441396	+	0.654649i
$844$	78.6513	−	45.4094i	2.70729	−	1.56305i
$845$			1.89199i			0.0650866i
$846$	8.29912	+	3.35653i	0.285330	+	0.115400i
$847$	−27.5084	+	24.8420i	−0.945202	+	0.853582i
$848$	72.3346	−	41.7624i	2.48398	−	1.43413i
$849$	−26.4881	−	12.9250i	−0.909068	−	0.443584i
$850$	32.4215	−	56.1557i	1.11205	−	1.92612i
$851$	−12.2646	−	7.08099i	−0.420426	−	0.242733i
$852$	−4.11143	−	2.00619i	−0.140855	−	0.0687310i
$853$	−23.8885	+	13.7921i	−0.817928	+	0.472231i	−0.849701	−	0.527264i	$-0.823218\pi$
$853$	−23.8885	+	13.7921i	−0.817928	+	0.472231i	0.0317735	+	0.999495i	$0.489884\pi$
$854$	−97.0860			−3.32222
$855$	0.913519	−	2.25871i	0.0312417	−	0.0772461i
$856$	−101.527			−3.47012
$857$	9.73781	+	16.8664i	0.332637	+	0.576145i	0.983028	−	0.183455i	$-0.0587282\pi$
$857$	9.73781	+	16.8664i	0.332637	+	0.576145i	−0.650391	+	0.759600i	$0.725395\pi$
$858$	2.69189	+	15.2171i	0.0918998	+	0.519502i
$859$	2.28915	−	3.96493i	0.0781050	−	0.135282i	−0.824327	−	0.566113i	$-0.808446\pi$
$859$	2.28915	−	3.96493i	0.0781050	−	0.135282i	0.902432	+	0.430832i	$0.141780\pi$
$860$	3.57457	−	6.19134i	0.121892	−	0.211123i
$861$	−0.763982	−	10.9537i	−0.0260364	−	0.373300i
$862$	−49.6697	−	86.0304i	−1.69176	−	2.93021i
$863$			47.3061i			1.61032i	0.593059	+	0.805159i	$0.297920\pi$
$863$			47.3061i			1.61032i	−0.593059	+	0.805159i	$0.702080\pi$
$864$	14.4193	−	44.2969i	0.490554	−	1.50701i
$865$			0.494248i			0.0168049i
$866$	28.7796	+	49.8476i	0.977969	+	1.69389i
$867$	−14.2408	+	0.993246i	−0.483642	+	0.0337324i
$868$	−44.8589	−	25.8993i	−1.52261	−	0.879080i
$869$	11.5197	−	8.38251i	0.390780	−	0.284357i
$870$	0.796107	−	0.536773i	0.0269906	−	0.0181983i
$871$	4.81266	−	2.77859i	0.163071	−	0.0941490i
$872$		−	52.7849i		−	1.78752i
$873$	3.38753	+	4.33905i	0.114651	+	0.146855i
$874$	−61.7922			−2.09015
$875$	−2.66636	−	4.61827i	−0.0901394	−	0.156126i
$876$	−45.9528	−	22.4229i	−1.55260	−	0.757600i
$877$	−4.42115	−	2.55255i	−0.149292	−	0.0861936i	0.423493	−	0.905899i	$-0.360804\pi$
$877$	−4.42115	−	2.55255i	−0.149292	−	0.0861936i	−0.572785	+	0.819706i	$0.694137\pi$
$878$	49.7018	+	28.6953i	1.67735	+	0.968421i
$879$	20.1191	−	41.2316i	0.678601	−	1.39071i
$880$	−0.493890	−	4.66606i	−0.0166490	−	0.157293i
$881$			46.1405i			1.55451i	0.629184	+	0.777257i	$0.283389\pi$
$881$			46.1405i			1.55451i	−0.629184	+	0.777257i	$0.716611\pi$
$882$	−33.5594	+	4.70419i	−1.13000	+	0.158398i
$883$	−27.9137			−0.939370			−0.469685	−	0.882834i	$-0.655633\pi$
$883$	−27.9137			−0.939370			−0.469685	+	0.882834i	$0.655633\pi$
$884$	−21.3423	+	12.3220i	−0.717819	+	0.414433i
$885$	−0.832833	−	1.23520i	−0.0279954	−	0.0415209i
$886$	−41.8466	−	24.1602i	−1.40586	−	0.811676i
$887$	20.7680	−	35.9712i	0.697320	−	1.20779i	−0.272073	−	0.962277i	$-0.587709\pi$
$887$	20.7680	−	35.9712i	0.697320	−	1.20779i	0.969392	−	0.245516i	$-0.0789575\pi$
$888$	−37.2527	+	2.59825i	−1.25012	+	0.0871915i
$889$	23.2184	+	40.2154i	0.778720	+	1.34878i
$890$	0.816290			0.0273621
$891$	−27.6759	+	11.1824i	−0.927177	+	0.374623i
$892$	−69.6256			−2.33124
$893$	−2.94389	−	5.09897i	−0.0985135	−	0.170630i
$894$	−10.4472	+	0.728654i	−0.349405	+	0.0243698i
$895$	−1.26603	+	2.19282i	−0.0423186	+	0.0732980i
$896$	−11.2514	−	6.49602i	−0.375884	−	0.217017i
$897$	−4.67186	−	6.92899i	−0.155989	−	0.231352i
$898$	40.3280	−	23.2834i	1.34576	−	0.776976i
$899$	4.37650			0.145964
$900$	69.9169	−	9.80061i	2.33056	−	0.326687i
$901$		−	47.0620i		−	1.56786i
$902$	16.0982	−	1.70395i	0.536013	−	0.0567354i
$903$	24.3790	−	49.9616i	0.811281	−	1.66262i
$904$	−0.649319	−	0.374884i	−0.0215960	−	0.0124685i
$905$	1.40907	+	0.813526i	0.0468390	+	0.0270425i
$906$	30.7946	+	15.0264i	1.02308	+	0.499218i
$907$	3.43330	+	5.94664i	0.114001	+	0.197455i	0.917380	−	0.398013i	$-0.130300\pi$
$907$	3.43330	+	5.94664i	0.114001	+	0.197455i	−0.803379	+	0.595468i	$0.796967\pi$
$908$	−13.9579			−0.463211
$909$	32.9444	+	42.1981i	1.09270	+	1.39962i
$910$			1.43816i			0.0476747i
$911$	29.0235	−	16.7567i	0.961591	−	0.555175i	0.0649284	−	0.997890i	$-0.479318\pi$
$911$	29.0235	−	16.7567i	0.961591	−	0.555175i	0.896662	+	0.442715i	$0.145985\pi$
$912$	−65.5482	+	44.1957i	−2.17052	+	1.46347i
$913$	−18.0097	−	24.7499i	−0.596033	−	0.819103i
$914$	13.4517	+	7.76636i	0.444944	+	0.256888i
$915$	−3.04461	+	0.212351i	−0.100652	+	0.00702012i
$916$	−26.2121	−	45.4007i	−0.866073	−	1.50008i
$917$			8.40748i			0.277639i
$918$	−45.2917	−	50.3559i	−1.49485	−	1.66199i
$919$			46.0840i			1.52017i	0.649824	+	0.760085i	$0.274843\pi$
$919$			46.0840i			1.52017i	−0.649824	+	0.760085i	$0.725157\pi$
$920$	2.61486	+	4.52907i	0.0862093	+	0.149319i
$921$	−0.0772523	−	1.10761i	−0.00254555	−	0.0364971i
$922$	−12.4743	+	21.6062i	−0.410821	+	0.711562i
$923$	−0.289476	+	0.501388i	−0.00952823	+	0.0165034i
$924$	−15.9506	−	90.1674i	−0.524736	−	2.96629i
$925$	−7.57060	−	13.1127i	−0.248920	−	0.431142i
$926$	25.9319			0.852176
$927$	−9.90626	+	24.4936i	−0.325364	+	0.804474i
$928$	−12.0741			−0.396350
$929$	50.3776	−	29.0855i	1.65283	−	0.954265i	0.676936	−	0.736042i	$-0.263308\pi$
$929$	50.3776	−	29.0855i	1.65283	−	0.954265i	0.975899	−	0.218222i	$-0.0700258\pi$
$930$	−2.08214	−	1.01599i	−0.0682760	−	0.0333156i
$931$	19.3015	+	11.1437i	0.632582	+	0.365222i
$932$	18.4583	−	31.9708i	0.604623	−	1.04724i
$933$	−19.0067	−	9.27442i	−0.622253	−	0.303631i
$934$	−40.8845	+	23.6047i	−1.33778	+	0.772370i
$935$	−2.41600	−	1.07355i	−0.0790117	−	0.0351087i
$936$	−20.4284	−	8.26212i	−0.667722	−	0.270056i
$937$			6.36938i			0.208079i	0.994573	+	0.104039i	$0.0331768\pi$
$937$			6.36938i			0.208079i	−0.994573	+	0.104039i	$0.966823\pi$
$938$	−40.5737	+	23.4252i	−1.32478	+	0.764860i
$939$	25.8098	+	38.2795i	0.842272	+	1.24920i
$940$	−0.431648	+	0.747637i	−0.0140788	+	0.0243852i
$941$	−6.87117	+	11.9012i	−0.223994	+	0.387969i	−0.956017	−	0.293311i	$-0.905243\pi$
$941$	−6.87117	+	11.9012i	−0.223994	+	0.387969i	0.732023	+	0.681280i	$0.238576\pi$
$942$	−73.1417	+	5.10139i	−2.38309	+	0.166212i
$943$	−7.58141	+	4.37713i	−0.246885	+	0.142539i
$944$			48.3380i			1.57327i
$945$	−2.71756	+	0.576108i	−0.0884022	+	0.0187408i
$946$	74.8980	+	33.2808i	2.43514	+	1.08205i
$947$	−9.90101	+	5.71635i	−0.321739	+	0.185756i	−0.652168	−	0.758075i	$-0.726140\pi$
$947$	−9.90101	+	5.71635i	−0.321739	+	0.185756i	0.330428	+	0.943831i	$0.392807\pi$
$948$	2.44883	+	35.1104i	0.0795343	+	1.14033i
$949$	−3.23543	+	5.60393i	−0.105027	+	0.181911i
$950$	−57.2137	−	33.0324i	−1.85626	−	1.07171i
$951$	25.1447	−	16.9537i	0.815372	−	0.549763i
$952$	103.857	−	59.9618i	3.36602	−	1.94337i
$953$	−39.5826			−1.28221			−0.641103	−	0.767455i	$-0.721523\pi$
$953$	−39.5826			−1.28221			−0.641103	+	0.767455i	$0.721523\pi$
$954$	57.4657	−	44.8640i	1.86052	−	1.45252i
$955$	−1.33642			−0.0432456
$956$	37.6363	+	65.1880i	1.21725	+	2.10833i
$957$	4.97627	+	5.92380i	0.160860	+	0.191489i
$958$	24.4241	−	42.3038i	0.789106	−	1.36677i
$959$	19.2037	−	33.2619i	0.620121	−	1.07408i
$960$	1.33988	+	0.653803i	0.0432446	+	0.0211014i
$961$	10.2199	+	17.7015i	0.329675	+	0.571015i
$962$			8.18742i			0.263973i
$963$	−42.5803	+	5.96870i	−1.37213	+	0.192339i
$964$		−	65.9044i		−	2.12264i
$965$	−0.726745	−	1.25876i	−0.0233947	−	0.0405209i
$966$	39.3866	+	58.4156i	1.26724	+	1.87949i
$967$	32.1259	+	18.5479i	1.03310	+	0.596461i	0.917871	−	0.396878i	$-0.129906\pi$
$967$	32.1259	+	18.5479i	1.03310	+	0.596461i	0.115229	+	0.993339i	$0.463240\pi$
$968$	76.1955	−	16.3129i	2.44902	−	0.524317i
$969$	3.09926	+	44.4360i	0.0995627	+	1.42749i
$970$	−0.654097	+	0.377643i	−0.0210018	+	0.0121254i
$971$			31.6598i			1.01601i	0.861354	+	0.508005i	$0.169617\pi$
$971$			31.6598i			1.01601i	−0.861354	+	0.508005i	$0.830383\pi$
$972$	12.8702	−	72.6096i	0.412811	−	2.32895i
$973$	40.5427			1.29974
$974$	52.1898	+	90.3954i	1.67227	+	2.89646i
$975$	−0.621654	−	8.91304i	−0.0199089	−	0.285446i
$976$	85.7618	+	49.5146i	2.74517	+	1.58492i
$977$	−28.4797	−	16.4427i	−0.911145	−	0.526050i	−0.0303458	−	0.999539i	$-0.509661\pi$
$977$	−28.4797	−	16.4427i	−0.911145	−	0.526050i	−0.880799	+	0.473489i	$0.842994\pi$
$978$	39.0515	+	57.9187i	1.24873	+	1.85204i
$979$	0.692323	+	6.54078i	0.0221267	+	0.209044i
$980$		−	3.26791i		−	0.104389i
$981$	−3.10319	−	22.1379i	−0.0990772	−	0.706810i
$982$	21.3211			0.680385
$983$	24.9856	−	14.4254i	0.796916	−	0.460100i	−0.0454757	−	0.998965i	$-0.514480\pi$
$983$	24.9856	−	14.4254i	0.796916	−	0.460100i	0.842392	+	0.538866i	$0.181147\pi$
$984$	−10.1230	+	20.7457i	−0.322709	+	0.661350i
$985$	−0.937109	−	0.541040i	−0.0298588	−	0.0172390i
$986$	−8.77702	+	15.2023i	−0.279517	+	0.484138i
$987$	−2.94389	+	6.03312i	−0.0937051	+	0.192036i
$988$	12.5541	+	21.7444i	0.399400	+	0.691782i
$989$	−44.3220			−1.40936
$990$	−0.992292	−	3.97350i	−0.0315371	−	0.126286i
$991$	−11.8746			−0.377209			−0.188605	−	0.982053i	$-0.560396\pi$
$991$	−11.8746			−0.377209			−0.188605	+	0.982053i	$0.560396\pi$
$992$	14.5668	+	25.2305i	0.462498	+	0.801070i
$993$	−24.3426	−	36.1034i	−0.772490	−	1.14571i
$994$	2.44046	−	4.22700i	0.0774067	−	0.134072i
$995$	1.59931	+	0.923363i	0.0507016	+	0.0292726i
$996$	75.4340	−	5.26127i	2.39022	−	0.166710i
$997$	−3.56706	+	2.05944i	−0.112970	+	0.0652232i	−0.555420	−	0.831570i	$-0.687443\pi$
$997$	−3.56706	+	2.05944i	−0.112970	+	0.0652232i	0.442450	+	0.896793i	$0.354109\pi$
$998$	−79.1592			−2.50574
$999$	−15.4710	+	3.27976i	−0.489480	+	0.103767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.g.b.32.1	✓	16
3.2	odd	2		297.2.g.b.98.8		16
9.2	odd	6	inner	99.2.g.b.65.8	yes	16
9.4	even	3		891.2.d.b.890.16		16
9.5	odd	6		891.2.d.b.890.1		16
9.7	even	3		297.2.g.b.197.1		16
11.10	odd	2	inner	99.2.g.b.32.8	yes	16
33.32	even	2		297.2.g.b.98.1		16
99.32	even	6		891.2.d.b.890.15		16
99.43	odd	6		297.2.g.b.197.8		16
99.65	even	6	inner	99.2.g.b.65.1	yes	16
99.76	odd	6		891.2.d.b.890.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.1	✓	16	1.1	even	1	trivial
99.2.g.b.32.8	yes	16	11.10	odd	2	inner
99.2.g.b.65.1	yes	16	99.65	even	6	inner
99.2.g.b.65.8	yes	16	9.2	odd	6	inner
297.2.g.b.98.1		16	33.32	even	2
297.2.g.b.98.8		16	3.2	odd	2
297.2.g.b.197.1		16	9.7	even	3
297.2.g.b.197.8		16	99.43	odd	6
891.2.d.b.890.1		16	9.5	odd	6
891.2.d.b.890.2		16	99.76	odd	6
891.2.d.b.890.15		16	99.32	even	6
891.2.d.b.890.16		16	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29716 - 2.24675i) q^{2} +(-1.72785 + 0.120512i) q^{3} +(-2.36526 + 4.09675i) q^{4} +(-0.137404 - 0.0793301i) q^{5} +(2.51207 + 3.72573i) q^{6} +(-2.91814 + 1.68479i) q^{7} +7.08384 q^{8} +(2.97095 - 0.416454i) q^{9} +O(q^{10})\)	\(q+(-1.29716 - 2.24675i) q^{2} +(-1.72785 + 0.120512i) q^{3} +(-2.36526 + 4.09675i) q^{4} +(-0.137404 - 0.0793301i) q^{5} +(2.51207 + 3.72573i) q^{6} +(-2.91814 + 1.68479i) q^{7} +7.08384 q^{8} +(2.97095 - 0.416454i) q^{9} +0.411616i q^{10} +(-3.29820 + 0.349105i) q^{11} +(3.59311 - 7.36362i) q^{12} +(-0.897990 - 0.518455i) q^{13} +(7.57060 + 4.37089i) q^{14} +(0.246974 + 0.120512i) q^{15} +(-4.45837 - 7.72212i) q^{16} -5.02413 q^{17} +(-4.78948 - 6.13478i) q^{18} +5.11879i q^{19} +(0.649990 - 0.375272i) q^{20} +(4.83908 - 3.26274i) q^{21} +(5.06265 + 6.95739i) q^{22} +(-4.02970 - 2.32655i) q^{23} +(-12.2398 + 0.853687i) q^{24} +(-2.48741 - 4.30833i) q^{25} +2.69008i q^{26} +(-5.08318 + 1.07761i) q^{27} -15.9398i q^{28} +(0.673383 + 1.16633i) q^{29} +(-0.0496046 - 0.711212i) q^{30} +(1.62482 - 2.81427i) q^{31} +(-4.48261 + 7.76411i) q^{32} +(5.65673 - 1.00067i) q^{33} +(6.51711 + 11.2880i) q^{34} +0.534618 q^{35} +(-5.32096 + 13.1563i) q^{36} +3.04356 q^{37} +(11.5007 - 6.63990i) q^{38} +(1.61408 + 0.787595i) q^{39} +(-0.973346 - 0.561961i) q^{40} +(0.940692 - 1.62933i) q^{41} +(-13.6076 - 6.63990i) q^{42} +(8.24914 - 4.76264i) q^{43} +(6.37090 - 14.3376i) q^{44} +(-0.441257 - 0.178464i) q^{45} +12.0716i q^{46} +(-0.996127 + 0.575114i) q^{47} +(8.63401 + 12.8054i) q^{48} +(2.17703 - 3.77072i) q^{49} +(-6.45316 + 11.1772i) q^{50} +(8.68096 - 0.605468i) q^{51} +(4.24795 - 2.45256i) q^{52} +9.36720i q^{53} +(9.01482 + 10.0228i) q^{54} +(0.480880 + 0.213678i) q^{55} +(-20.6716 + 11.9348i) q^{56} +(-0.616876 - 8.84452i) q^{57} +(1.74697 - 3.02585i) q^{58} +(-4.69477 - 2.71052i) q^{59} +(-1.07786 + 0.726747i) q^{60} +(-9.61807 + 5.55299i) q^{61} -8.43060 q^{62} +(-7.96802 + 6.22070i) q^{63} +5.42521 q^{64} +(0.0822581 + 0.142475i) q^{65} +(-9.58597 - 11.4112i) q^{66} +(-2.67969 + 4.64135i) q^{67} +(11.8834 - 20.5826i) q^{68} +(7.24310 + 3.53430i) q^{69} +(-0.693486 - 1.20115i) q^{70} -0.558344i q^{71} +(21.0457 - 2.95009i) q^{72} -6.24053i q^{73} +(-3.94799 - 6.83812i) q^{74} +(4.81709 + 7.14439i) q^{75} +(-20.9704 - 12.1073i) q^{76} +(9.03644 - 6.57551i) q^{77} +(-0.324187 - 4.64806i) q^{78} +(-3.72007 + 2.14778i) q^{79} +1.41473i q^{80} +(8.65313 - 2.47453i) q^{81} -4.88092 q^{82} +(4.61447 + 7.99250i) q^{83} +(1.92094 + 27.5417i) q^{84} +(0.690334 + 0.398565i) q^{85} +(-21.4009 - 12.3558i) q^{86} +(-1.30406 - 1.93410i) q^{87} +(-23.3639 + 2.47300i) q^{88} -1.98314i q^{89} +(0.171419 + 1.22289i) q^{90} +3.49395 q^{91} +(19.0625 - 11.0058i) q^{92} +(-2.46829 + 5.05845i) q^{93} +(2.58428 + 1.49203i) q^{94} +(0.406074 - 0.703341i) q^{95} +(6.80962 - 13.9554i) q^{96} +(0.917466 + 1.58910i) q^{97} -11.2958 q^{98} +(-9.65341 + 2.41072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

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