LMFDB - Embedded newform 592.2.bl.a.51.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(51,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 11]))

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

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

chi := DirichletCharacter("592.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bl (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$296$
Relative dimension:	$74$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			51.11
Character	$\chi$	$=$	592.51
Dual form			592.2.bl.a.267.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27069 - 0.620773i) q^{2} +(0.166554 - 0.621587i) q^{3} +(1.22928 + 1.57761i) q^{4} +(1.08801 - 0.628166i) q^{5} +(-0.597501 + 0.686449i) q^{6} +(0.442359 + 0.766189i) q^{7} +(-0.582689 - 2.76776i) q^{8} +(2.23945 + 1.29295i) q^{9} +(-1.77247 + 0.122790i) q^{10} +(0.581266 - 0.581266i) q^{11} +(1.18537 - 0.501347i) q^{12} +(-2.57947 - 4.46778i) q^{13} +(-0.0864699 - 1.24819i) q^{14} +(-0.209247 - 0.780919i) q^{15} +(-0.977734 + 3.87866i) q^{16} +(1.74360 + 6.50722i) q^{17} +(-2.04301 - 3.03311i) q^{18} +(5.98256 - 3.45403i) q^{19} +(2.32848 + 0.944276i) q^{20} +(0.549929 - 0.147353i) q^{21} +(-1.09944 + 0.377772i) q^{22} +(-0.734026 + 0.734026i) q^{23} +(-1.81745 - 0.0987881i) q^{24} +(-1.71082 + 2.96322i) q^{25} +(0.504221 + 7.27840i) q^{26} +(2.54176 - 2.54176i) q^{27} +(-0.664966 + 1.63973i) q^{28} +3.99909i q^{29} +(-0.218887 + 1.12220i) q^{30} +(5.62257 - 5.62257i) q^{31} +(3.65016 - 4.32161i) q^{32} +(-0.264495 - 0.458119i) q^{33} +(1.82394 - 9.35101i) q^{34} +(0.962587 + 0.555750i) q^{35} +(0.713141 + 5.12238i) q^{36} +(4.33668 - 4.26535i) q^{37} +(-9.74612 + 0.675175i) q^{38} +(-3.20673 + 0.859241i) q^{39} +(-2.37258 - 2.64533i) q^{40} +(0.999834 + 1.73176i) q^{41} +(-0.790259 - 0.154142i) q^{42} -10.3415 q^{43} +(1.63155 + 0.202474i) q^{44} +3.24874 q^{45} +(1.38838 - 0.477052i) q^{46} -1.74303i q^{47} +(2.24808 + 1.25375i) q^{48} +(3.10864 - 5.38432i) q^{49} +(4.01340 - 2.70329i) q^{50} +4.33521 q^{51} +(3.87753 - 9.56156i) q^{52} +(1.72926 + 6.45368i) q^{53} +(-4.80764 + 1.65192i) q^{54} +(0.267295 - 0.997558i) q^{55} +(1.86287 - 1.67079i) q^{56} +(-1.15056 - 4.29396i) q^{57} +(2.48253 - 5.08159i) q^{58} +(3.79636 - 6.57548i) q^{59} +(0.974766 - 1.29008i) q^{60} +(8.78495 - 5.07200i) q^{61} +(-10.6349 + 3.65418i) q^{62} +2.28778i q^{63} +(-7.32095 + 3.22548i) q^{64} +(-5.61301 - 3.24067i) q^{65} +(0.0517021 + 0.746317i) q^{66} +(-1.11761 + 4.17099i) q^{67} +(-8.12251 + 10.7499i) q^{68} +(0.334006 + 0.578515i) q^{69} +(-0.878150 - 1.30373i) q^{70} +(-4.13731 - 7.16603i) q^{71} +(2.27366 - 6.95163i) q^{72} -5.89407 q^{73} +(-8.15837 + 2.72783i) q^{74} +(1.55695 + 1.55695i) q^{75} +(12.8034 + 5.19219i) q^{76} +(0.702488 + 0.188231i) q^{77} +(4.60814 + 0.898827i) q^{78} +(2.55760 - 9.54511i) q^{79} +(1.37265 + 4.83422i) q^{80} +(2.72225 + 4.71507i) q^{81} +(-0.195442 - 2.82120i) q^{82} +(-2.99440 - 11.1752i) q^{83} +(0.908484 + 0.686438i) q^{84} +(5.98468 + 5.98468i) q^{85} +(13.1408 + 6.41974i) q^{86} +(2.48578 + 0.666063i) q^{87} +(-1.94750 - 1.27011i) q^{88} +(1.84295 + 6.87799i) q^{89} +(-4.12812 - 2.01673i) q^{90} +(2.28211 - 3.95272i) q^{91} +(-2.06033 - 0.255685i) q^{92} +(-2.55846 - 4.43137i) q^{93} +(-1.08203 + 2.21485i) q^{94} +(4.33941 - 7.51608i) q^{95} +(-2.07831 - 2.98867i) q^{96} +(8.53878 - 8.53878i) q^{97} +(-7.29254 + 4.91201i) q^{98} +(2.05326 - 0.550169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 296 q - 6 q^{3} - 12 q^{4} - 6 q^{5} - 4 q^{7} - 8 q^{10} + 8 q^{11} + 28 q^{12} - 2 q^{13} - 12 q^{14} - 12 q^{15} - 12 q^{16} - 8 q^{17} - 14 q^{18} - 6 q^{19} + 2 q^{20} - 6 q^{21} - 30 q^{22} + 30 q^{24}+ \cdots - 48 q^{99}+O(q^{100}) $ 296 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 - 4 * q^7 - 8 * q^10 + 8 * q^11 + 28 * q^12 - 2 * q^13 - 12 * q^14 - 12 * q^15 - 12 * q^16 - 8 * q^17 - 14 * q^18 - 6 * q^19 + 2 * q^20 - 6 * q^21 - 30 * q^22 + 30 * q^24 + 132 * q^25 - 8 * q^26 - 32 * q^28 - 70 * q^30 - 10 * q^32 - 4 * q^33 - 18 * q^34 - 6 * q^35 - 32 * q^36 - 20 * q^37 + 20 * q^38 - 8 * q^39 + 4 * q^40 + 10 * q^42 - 24 * q^43 + 40 * q^44 - 16 * q^45 - 32 * q^46 + 28 * q^48 - 128 * q^49 + 32 * q^50 + 60 * q^51 + 14 * q^52 - 26 * q^53 + 50 * q^54 - 8 * q^55 - 74 * q^56 - 12 * q^57 + 12 * q^58 - 2 * q^59 - 68 * q^60 - 6 * q^61 - 34 * q^62 - 24 * q^64 - 36 * q^65 - 116 * q^66 - 6 * q^67 - 28 * q^68 + 4 * q^69 + 14 * q^70 - 4 * q^71 - 86 * q^72 + 32 * q^73 + 40 * q^74 + 4 * q^75 + 14 * q^76 + 12 * q^77 - 18 * q^78 + 40 * q^79 - 12 * q^80 + 112 * q^81 + 84 * q^82 + 58 * q^83 + 132 * q^84 - 20 * q^85 - 46 * q^86 + 104 * q^87 - 56 * q^88 + 16 * q^89 + 4 * q^90 + 26 * q^91 - 76 * q^92 - 8 * q^93 + 86 * q^94 - 40 * q^95 - 144 * q^96 - 8 * q^97 + 26 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.27069	−	0.620773i	−0.898510	−	0.438953i
$2$	−1.27069	−	0.620773i	−0.898510	−	0.438953i
$3$	0.166554	−	0.621587i	0.0961598	−	0.358873i	−0.901033	−	0.433751i	$-0.857190\pi$
$3$	0.166554	−	0.621587i	0.0961598	−	0.358873i	0.997193	+	0.0748774i	$0.0238566\pi$
$4$	1.22928	+	1.57761i	0.614641	+	0.788807i
$5$	1.08801	−	0.628166i	0.486575	−	0.280924i	−0.236577	−	0.971613i	$-0.576026\pi$
$5$	1.08801	−	0.628166i	0.486575	−	0.280924i	0.723153	+	0.690688i	$0.242692\pi$
$6$	−0.597501	+	0.686449i	−0.243929	+	0.280242i
$7$	0.442359	+	0.766189i	0.167196	+	0.289592i	0.937433	−	0.348166i	$-0.113195\pi$
$7$	0.442359	+	0.766189i	0.167196	+	0.289592i	−0.770237	+	0.637758i	$0.779862\pi$
$8$	−0.582689	−	2.76776i	−0.206012	−	0.978550i
$9$	2.23945	+	1.29295i	0.746482	+	0.430982i
$10$	−1.77247	+	0.122790i	−0.560505	+	0.0388297i
$11$	0.581266	−	0.581266i	0.175258	−	0.175258i	−0.614027	−	0.789285i	$-0.710451\pi$
$11$	0.581266	−	0.581266i	0.175258	−	0.175258i	0.789285	+	0.614027i	$0.210451\pi$
$12$	1.18537	−	0.501347i	0.342185	−	0.144727i
$13$	−2.57947	−	4.46778i	−0.715417	−	1.23914i	−0.962799	−	0.270220i	$-0.912904\pi$
$13$	−2.57947	−	4.46778i	−0.715417	−	1.23914i	0.247382	−	0.968918i	$-0.420430\pi$
$14$	−0.0864699	−	1.24819i	−0.0231101	−	0.333593i
$15$	−0.209247	−	0.780919i	−0.0540272	−	0.201632i
$16$	−0.977734	+	3.87866i	−0.244434	+	0.969666i
$17$	1.74360	+	6.50722i	0.422886	+	1.57823i	0.768496	+	0.639855i	$0.221005\pi$
$17$	1.74360	+	6.50722i	0.422886	+	1.57823i	−0.345610	+	0.938378i	$0.612328\pi$
$18$	−2.04301	−	3.03311i	−0.481541	−	0.714912i
$19$	5.98256	−	3.45403i	1.37249	−	0.792409i	0.381252	−	0.924471i	$-0.375493\pi$
$19$	5.98256	−	3.45403i	1.37249	−	0.792409i	0.991241	+	0.132062i	$0.0421598\pi$
$20$	2.32848	+	0.944276i	0.520664	+	0.211146i
$21$	0.549929	−	0.147353i	0.120004	−	0.0321551i
$22$	−1.09944	+	0.377772i	−0.234402	+	0.0805412i
$23$	−0.734026	+	0.734026i	−0.153055	+	0.153055i	−0.779481	−	0.626426i	$-0.784517\pi$
$23$	−0.734026	+	0.734026i	−0.153055	+	0.153055i	0.626426	+	0.779481i	$0.284517\pi$
$24$	−1.81745	−	0.0987881i	−0.370985	−	0.0201650i
$25$	−1.71082	+	2.96322i	−0.342163	+	0.592644i
$26$	0.504221	+	7.27840i	0.0988859	+	1.42741i
$27$	2.54176	−	2.54176i	0.489163	−	0.489163i
$28$	−0.664966	+	1.63973i	−0.125667	+	0.309880i
$29$			3.99909i			0.742613i	0.928510	+	0.371306i	$0.121090\pi$
$29$			3.99909i			0.742613i	−0.928510	+	0.371306i	$0.878910\pi$
$30$	−0.218887	+	1.12220i	−0.0399631	+	0.204884i
$31$	5.62257	−	5.62257i	1.00984	−	1.00984i	0.00989265	−	0.999951i	$-0.496851\pi$
$31$	5.62257	−	5.62257i	1.00984	−	1.00984i	0.999951	−	0.00989265i	$-0.00314898\pi$
$32$	3.65016	−	4.32161i	0.645264	−	0.763960i
$33$	−0.264495	−	0.458119i	−0.0460427	−	0.0797483i
$34$	1.82394	−	9.35101i	0.312802	−	1.60369i
$35$	0.962587	+	0.555750i	0.162707	+	0.0939388i
$36$	0.713141	+	5.12238i	0.118857	+	0.853729i
$37$	4.33668	−	4.26535i	0.712945	−	0.701220i
$37$	4.33668	−	4.26535i	0.712945	−	0.701220i
$38$	−9.74612	+	0.675175i	−1.58103	+	0.109528i
$39$	−3.20673	+	0.859241i	−0.513488	+	0.137589i
$40$	−2.37258	−	2.64533i	−0.375138	−	0.418264i
$41$	0.999834	+	1.73176i	0.156148	+	0.270456i	0.933476	−	0.358639i	$-0.116759\pi$
$41$	0.999834	+	1.73176i	0.156148	+	0.270456i	−0.777329	+	0.629095i	$0.783426\pi$
$42$	−0.790259	−	0.154142i	−0.121940	−	0.0237846i
$43$	−10.3415			−1.57707			−0.788534	−	0.614991i	$-0.789160\pi$
$43$	−10.3415			−1.57707			−0.788534	+	0.614991i	$0.789160\pi$
$44$	1.63155	+	0.202474i	0.245966	+	0.0305241i
$45$	3.24874			0.484293
$46$	1.38838	−	0.477052i	0.204705	−	0.0703375i
$47$		−	1.74303i		−	0.254247i	−0.991887	−	0.127124i	$-0.959425\pi$
$47$		−	1.74303i		−	0.254247i	0.991887	−	0.127124i	$-0.0405745\pi$
$48$	2.24808	+	1.25375i	0.324482	+	0.180964i
$49$	3.10864	−	5.38432i	0.444091	−	0.769188i
$50$	4.01340	−	2.70329i	0.567580	−	0.382303i
$51$	4.33521			0.607050
$52$	3.87753	−	9.56156i	0.537717	−	1.32595i
$53$	1.72926	+	6.45368i	0.237532	+	0.886482i	0.976991	+	0.213280i	$0.0684147\pi$
$53$	1.72926	+	6.45368i	0.237532	+	0.886482i	−0.739459	+	0.673202i	$0.764919\pi$
$54$	−4.80764	+	1.65192i	−0.654237	+	0.224798i
$55$	0.267295	−	0.997558i	0.0360420	−	0.134511i
$56$	1.86287	−	1.67079i	0.248936	−	0.223269i
$57$	−1.15056	−	4.29396i	−0.152396	−	0.568749i
$58$	2.48253	−	5.08159i	0.325972	−	0.667245i
$59$	3.79636	−	6.57548i	0.494244	−	0.856055i	−0.505734	−	0.862689i	$-0.668778\pi$
$59$	3.79636	−	6.57548i	0.494244	−	0.856055i	0.999978	+	0.00663408i	$0.00211171\pi$
$60$	0.974766	−	1.29008i	0.125842	−	0.166549i
$61$	8.78495	−	5.07200i	1.12480	−	0.649402i	0.182177	−	0.983266i	$-0.441686\pi$
$61$	8.78495	−	5.07200i	1.12480	−	0.649402i	0.942621	+	0.333863i	$0.108352\pi$
$62$	−10.6349	+	3.65418i	−1.35063	+	0.464081i
$63$			2.28778i			0.288234i
$64$	−7.32095	+	3.22548i	−0.915118	+	0.403185i
$65$	−5.61301	−	3.24067i	−0.696208	−	0.401956i
$66$	0.0517021	+	0.746317i	0.00636409	+	0.0918652i
$67$	−1.11761	+	4.17099i	−0.136538	+	0.509567i	0.863449	+	0.504437i	$0.168300\pi$
$67$	−1.11761	+	4.17099i	−0.136538	+	0.509567i	−0.999987	+	0.00513045i	$0.998367\pi$
$68$	−8.12251	+	10.7499i	−0.984998	+	1.30362i
$69$	0.334006	+	0.578515i	0.0402096	+	0.0696451i
$70$	−0.878150	−	1.30373i	−0.104959	−	0.155826i
$71$	−4.13731	−	7.16603i	−0.491008	−	0.850451i	0.508938	−	0.860803i	$-0.330038\pi$
$71$	−4.13731	−	7.16603i	−0.491008	−	0.850451i	−0.999946	+	0.0103517i	$0.996705\pi$
$72$	2.27366	−	6.95163i	0.267953	−	0.819257i
$73$	−5.89407			−0.689849			−0.344924	−	0.938631i	$-0.612095\pi$
$73$	−5.89407			−0.689849			−0.344924	+	0.938631i	$0.612095\pi$
$74$	−8.15837	+	2.72783i	−0.948391	+	0.317103i
$75$	1.55695	+	1.55695i	0.179782	+	0.179782i
$76$	12.8034	+	5.19219i	1.46865	+	0.595585i
$77$	0.702488	+	0.188231i	0.0800559	+	0.0214509i
$78$	4.60814	+	0.898827i	0.521769	+	0.101772i
$79$	2.55760	−	9.54511i	0.287753	−	1.07391i	−0.659051	−	0.752098i	$-0.729042\pi$
$79$	2.55760	−	9.54511i	0.287753	−	1.07391i	0.946804	−	0.321811i	$-0.104291\pi$
$80$	1.37265	+	4.83422i	0.153467	+	0.540483i
$81$	2.72225	+	4.71507i	0.302472	+	0.523897i
$82$	−0.195442	−	2.82120i	−0.0215830	−	0.311549i
$83$	−2.99440	−	11.1752i	−0.328678	−	1.22664i	−0.910563	−	0.413371i	$-0.864351\pi$
$83$	−2.99440	−	11.1752i	−0.328678	−	1.22664i	0.581885	−	0.813271i	$-0.302315\pi$
$84$	0.908484	+	0.686438i	0.0991237	+	0.0748965i
$85$	5.98468	+	5.98468i	0.649130	+	0.649130i
$86$	13.1408	+	6.41974i	1.41701	+	0.692259i
$87$	2.48578	+	0.666063i	0.266504	+	0.0714095i
$88$	−1.94750	−	1.27011i	−0.207604	−	0.135394i
$89$	1.84295	+	6.87799i	0.195352	+	0.729065i	0.992175	+	0.124852i	$0.0398457\pi$
$89$	1.84295	+	6.87799i	0.195352	+	0.729065i	−0.796823	+	0.604213i	$0.793488\pi$
$90$	−4.12812	−	2.01673i	−0.435142	−	0.212582i
$91$	2.28211	−	3.95272i	0.239230	−	0.414358i
$92$	−2.06033	−	0.255685i	−0.214805	−	0.0266570i
$93$	−2.55846	−	4.43137i	−0.265299	−	0.459512i
$94$	−1.08203	+	2.21485i	−0.111603	+	0.228444i
$95$	4.33941	−	7.51608i	0.445214	−	0.771133i
$96$	−2.07831	−	2.98867i	−0.212116	−	0.305030i
$97$	8.53878	−	8.53878i	0.866981	−	0.866981i	−0.125156	−	0.992137i	$-0.539943\pi$
$97$	8.53878	−	8.53878i	0.866981	−	0.866981i	0.992137	+	0.125156i	$0.0399430\pi$
$98$	−7.29254	+	4.91201i	−0.736658	+	0.496188i
$99$	2.05326	−	0.550169i	0.206360	−	0.0552941i
$100$	−6.77789	+	0.943623i	−0.677789	+	0.0943623i
$101$	−7.38620	−	7.38620i	−0.734954	−	0.734954i	0.236643	−	0.971597i	$-0.423953\pi$
$101$	−7.38620	−	7.38620i	−0.734954	−	0.734954i	−0.971597	+	0.236643i	$0.923953\pi$
$102$	−5.50868	−	2.69118i	−0.545441	−	0.266466i
$103$	6.74126	+	6.74126i	0.664236	+	0.664236i	0.956376	−	0.292140i	$-0.0943672\pi$
$103$	6.74126	+	6.74126i	0.664236	+	0.664236i	−0.292140	+	0.956376i	$0.594367\pi$
$104$	−10.8627	+	9.74267i	−1.06517	+	0.955347i
$105$	0.505769	−	0.505769i	0.0493580	−	0.0493580i
$106$	1.80893	−	9.27408i	0.175699	−	0.900778i
$107$	−3.14049	+	11.7205i	−0.303603	+	1.13306i	0.630538	+	0.776158i	$0.282834\pi$
$107$	−3.14049	+	11.7205i	−0.303603	+	1.13306i	−0.934141	+	0.356904i	$0.883832\pi$
$108$	7.13447	+	0.885380i	0.686514	+	0.0851958i
$109$	−8.30586	+	14.3862i	−0.795557	+	1.37794i	0.126928	+	0.991912i	$0.459488\pi$
$109$	−8.30586	+	14.3862i	−0.795557	+	1.37794i	−0.922485	+	0.386033i	$0.873845\pi$
$110$	−0.958905	+	1.10165i	−0.0914280	+	0.105038i
$111$	−1.92900	−	3.40603i	−0.183092	−	0.323286i
$112$	−3.40430	+	0.966634i	−0.321676	+	0.0913383i
$113$	−12.6100	+	3.37884i	−1.18625	+	0.317854i	−0.797402	−	0.603448i	$-0.793793\pi$
$113$	−12.6100	+	3.37884i	−1.18625	+	0.317854i	−0.388846	+	0.921303i	$0.627126\pi$
$114$	−1.20357	+	6.17051i	−0.112725	+	0.577921i
$115$	−0.337541	+	1.25972i	−0.0314759	+	0.117470i
$116$	−6.30902	+	4.91601i	−0.585778	+	0.456440i
$117$		−	13.3405i		−	1.23333i
$118$	−8.90586	+	5.99869i	−0.819851	+	0.552225i
$119$	−4.21446	+	4.21446i	−0.386339	+	0.386339i
$120$	−2.03947	+	1.03418i	−0.186177	+	0.0944069i
$121$			10.3243i			0.938569i
$122$	−14.3115	+	0.991446i	−1.29570	+	0.0897613i
$123$	1.24297	−	0.333052i	0.112075	−	0.0300303i
$124$	15.7820	+	1.95853i	1.41726	+	0.175881i
$125$			10.5804i			0.946336i
$126$	1.42019	−	2.90705i	0.126521	−	0.258981i
$127$	−1.83655	−	1.06033i	−0.162967	−	0.0940892i	0.416298	−	0.909228i	$-0.363327\pi$
$127$	−1.83655	−	1.06033i	−0.162967	−	0.0940892i	−0.579265	+	0.815139i	$0.696661\pi$
$128$	11.3049	+	0.446075i	0.999222	+	0.0394279i
$129$	−1.72242	+	6.42816i	−0.151651	+	0.565968i
$130$	5.12064	+	7.60228i	0.449110	+	0.666764i
$131$	−9.00336	+	15.5943i	−0.786627	+	1.36248i	0.141395	+	0.989953i	$0.454841\pi$
$131$	−9.00336	+	15.5943i	−0.786627	+	1.36248i	−0.928022	+	0.372525i	$0.878492\pi$
$132$	0.397596	−	0.980429i	0.0346063	−	0.0853354i
$133$	5.29288	+	3.05585i	0.458951	+	0.264975i
$134$	4.00937	−	4.60623i	0.346357	−	0.397917i
$135$	1.16883	−	4.36213i	0.100597	−	0.375432i
$136$	16.9944	−	8.61756i	1.45726	−	0.738950i
$137$			22.9450i			1.96033i	0.198191	+	0.980163i	$0.436493\pi$
$137$			22.9450i			1.96033i	−0.198191	+	0.980163i	$0.563507\pi$
$138$	−0.0652897	−	0.942453i	−0.00555782	−	0.0802269i
$139$	3.80330	+	14.1941i	0.322592	+	1.20393i	0.916710	+	0.399552i	$0.130834\pi$
$139$	3.80330	+	14.1941i	0.322592	+	1.20393i	−0.594118	+	0.804378i	$0.702499\pi$
$140$	0.306531	+	2.20176i	0.0259066	+	0.186083i
$141$	−1.08345	−	0.290308i	−0.0912426	−	0.0244484i
$142$	0.808739	+	11.6741i	0.0678678	+	0.979669i
$143$	−4.09633	−	1.09761i	−0.342552	−	0.0917865i
$144$	−7.20448	+	7.42190i	−0.600374	+	0.618492i
$145$	2.51209	+	4.35107i	0.208618	+	0.361337i
$146$	7.48951	+	3.65888i	0.619836	+	0.302811i
$147$	−2.82906	−	2.82906i	−0.233337	−	0.233337i
$148$	12.0601	+	1.59829i	0.991332	+	0.131378i
$149$	11.9822	−	11.9822i	0.981618	−	0.981618i	−0.0182164	−	0.999834i	$-0.505799\pi$
$149$	11.9822	−	11.9822i	0.981618	−	0.981618i	0.999834	+	0.0182164i	$0.00579877\pi$
$150$	−1.01188	−	2.94492i	−0.0826200	−	0.240451i
$151$	−18.6358	+	10.7594i	−1.51656	+	0.875588i	−0.516752	+	0.856135i	$0.672859\pi$
$151$	−18.6358	+	10.7594i	−1.51656	+	0.875588i	−0.999811	+	0.0194533i	$0.993807\pi$
$152$	−13.0459	−	14.5456i	−1.05816	−	1.17981i
$153$	−4.50877	+	16.8270i	−0.364512	+	1.36038i
$154$	−0.775792	−	0.675268i	−0.0625151	−	0.0544146i
$155$	2.58554	−	9.64935i	0.207675	−	0.775054i
$156$	−5.29752	−	4.00273i	−0.424141	−	0.320475i
$157$	−17.7062	+	4.74437i	−1.41311	+	0.378642i	−0.883034	−	0.469309i	$-0.844503\pi$
$157$	−17.7062	+	4.74437i	−1.41311	+	0.378642i	−0.530076	+	0.847950i	$0.677837\pi$
$158$	−9.17526	+	10.5411i	−0.729944	+	0.838608i
$159$	4.29954			0.340976
$160$	1.25674	−	6.99488i	0.0993544	−	0.552994i
$161$	−0.887105	−	0.237699i	−0.0699137	−	0.0187333i
$162$	−0.532130	−	7.68127i	−0.0418081	−	0.603498i
$163$	8.30613	−	14.3866i	0.650586	−	1.12685i	−0.332395	−	0.943140i	$-0.607857\pi$
$163$	8.30613	−	14.3866i	0.650586	−	1.12685i	0.982981	−	0.183708i	$-0.0588100\pi$
$164$	−1.50298	+	3.70618i	−0.117363	+	0.289404i
$165$	−0.575550	−	0.332294i	−0.0448065	−	0.0258690i
$166$	−3.13235	+	16.0591i	−0.243118	+	1.24642i
$167$	−7.45822	−	1.99842i	−0.577134	−	0.154643i	−0.0415677	−	0.999136i	$-0.513235\pi$
$167$	−7.45822	−	1.99842i	−0.577134	−	0.154643i	−0.535567	+	0.844493i	$0.679902\pi$
$168$	−0.728275	−	1.43621i	−0.0561876	−	0.110806i
$169$	−6.80734	+	11.7907i	−0.523642	+	0.906974i
$170$	−3.88952	−	11.3198i	−0.298312	−	0.868187i
$171$	17.8635			1.36606
$172$	−12.7127	−	16.3149i	−0.969331	−	1.24400i
$173$	1.30486	+	4.86981i	0.0992069	+	0.370245i	0.997624	−	0.0688987i	$-0.0219485\pi$
$173$	1.30486	+	4.86981i	0.0992069	+	0.370245i	−0.898417	+	0.439144i	$0.855282\pi$
$174$	−2.74517	−	2.38946i	−0.208111	−	0.181145i
$175$	−3.02718			−0.228833
$176$	1.68621	+	2.82286i	0.127103	+	0.212781i
$177$	−3.45494	−	3.45494i	−0.259689	−	0.259689i
$178$	1.92786	−	9.88381i	0.144499	−	0.740823i
$179$	7.17888			0.536575			0.268287	−	0.963339i	$-0.413542\pi$
$179$	7.17888			0.536575			0.268287	+	0.963339i	$0.413542\pi$
$180$	3.99361	+	5.12525i	0.297666	+	0.382014i
$181$	−10.9637	−	2.93771i	−0.814925	−	0.218359i	−0.172799	−	0.984957i	$-0.555281\pi$
$181$	−10.9637	−	2.93771i	−0.814925	−	0.218359i	−0.642127	+	0.766599i	$0.721948\pi$
$182$	−5.35358	+	3.60600i	−0.396834	+	0.267294i
$183$	−1.68952	−	6.30537i	−0.124893	−	0.466106i
$184$	2.45931	+	1.60390i	0.181303	+	0.118241i
$185$	2.03902	−	7.36492i	0.149912	−	0.541480i
$186$	0.500113	+	7.21910i	0.0366701	+	0.529330i
$187$	4.79593	+	2.76893i	0.350713	+	0.202484i
$188$	2.74983	−	2.14268i	0.200552	−	0.156271i
$189$	3.07184	+	0.823098i	0.223444	+	0.0598716i
$190$	−10.1798	+	6.85678i	−0.738520	+	0.497443i
$191$	−12.5356	−	12.5356i	−0.907046	−	0.907046i	0.0889870	−	0.996033i	$-0.471637\pi$
$191$	−12.5356	−	12.5356i	−0.907046	−	0.907046i	−0.996033	+	0.0889870i	$0.971637\pi$
$192$	0.785586	+	5.08782i	0.0566948	+	0.367182i
$193$	2.36960	−	2.36960i	0.170568	−	0.170568i	−0.616661	−	0.787229i	$-0.711515\pi$
$193$	2.36960	−	2.36960i	0.170568	−	0.170568i	0.787229	+	0.616661i	$0.211515\pi$
$194$	−16.1507	+	5.54945i	−1.15956	+	0.398428i
$195$	−2.94922	+	2.94922i	−0.211198	+	0.211198i
$196$	12.3158	−	1.71461i	0.879698	−	0.122472i
$197$	0.307672	+	1.14825i	0.0219207	+	0.0818092i	0.976020	−	0.217682i	$-0.0698497\pi$
$197$	0.307672	+	1.14825i	0.0219207	+	0.0818092i	−0.954099	+	0.299491i	$0.903183\pi$
$198$	−2.95058	−	0.575516i	−0.209688	−	0.0409002i
$199$	−4.58334	−	4.58334i	−0.324904	−	0.324904i	0.525741	−	0.850645i	$-0.323788\pi$
$199$	−4.58334	−	4.58334i	−0.324904	−	0.324904i	−0.850645	+	0.525741i	$0.823788\pi$
$200$	9.19834	+	3.00848i	0.650421	+	0.212732i
$201$	2.40649	+	1.38939i	0.169740	+	0.0979997i
$202$	4.80038	+	13.9707i	0.337753	+	0.982974i
$203$	−3.06406	+	1.76903i	−0.215055	+	0.124162i
$204$	5.32919	+	6.83928i	0.373118	+	0.478846i
$205$	2.17567	+	1.25612i	0.151955	+	0.0877314i
$206$	−4.38123	−	12.7508i	−0.305255	−	0.888391i
$207$	−2.59287	+	0.694757i	−0.180217	+	0.0482889i
$208$	19.8510	−	5.63661i	1.37642	−	0.390828i
$209$	1.46975	−	5.48517i	0.101665	−	0.379417i
$210$	−0.956641	+	0.328705i	−0.0660145	+	0.0226828i
$211$	11.7821	−	11.7821i	0.811114	−	0.811114i	−0.173687	−	0.984801i	$-0.555568\pi$
$211$	11.7821	−	11.7821i	0.811114	−	0.811114i	0.984801	+	0.173687i	$0.0555682\pi$
$212$	−8.05568	+	10.6615i	−0.553266	+	0.732235i
$213$	−5.14339	+	1.37817i	−0.352419	+	0.0944305i
$214$	11.2663	−	12.9435i	0.770151	−	0.884800i
$215$	−11.2517	+	6.49620i	−0.767362	+	0.443037i
$216$	−8.51604	−	5.55392i	−0.579443	−	0.377897i
$217$	6.79515	+	1.82075i	0.461285	+	0.123601i
$218$	19.4847	−	13.1242i	1.31967	−	0.888885i
$219$	−0.981679	+	3.66367i	−0.0663357	+	0.247568i
$220$	1.90234	−	0.804591i	0.128256	−	0.0542455i
$221$	24.5752	−	24.5752i	1.65311	−	1.65311i
$222$	0.336775	+	5.52546i	0.0226029	+	0.370845i
$223$			4.91961i			0.329441i	0.986340	+	0.164721i	$0.0526723\pi$
$223$			4.91961i			0.329441i	−0.986340	+	0.164721i	$0.947328\pi$
$224$	4.92585	+	0.885009i	0.329122	+	0.0591322i
$225$	−7.66256	+	4.42398i	−0.510837	+	0.294932i
$226$	18.1208	+	3.53451i	1.20538	+	0.235112i
$227$	−14.0490	+	8.11117i	−0.932462	+	0.538357i	−0.887589	−	0.460635i	$-0.847622\pi$
$227$	−14.0490	+	8.11117i	−0.932462	+	0.538357i	−0.0448727	+	0.998993i	$0.514288\pi$
$228$	5.35985	−	7.09363i	0.354965	−	0.469787i
$229$	−0.564661	−	0.151301i	−0.0373139	−	0.00999822i	0.240114	−	0.970745i	$-0.422815\pi$
$229$	−0.564661	−	0.151301i	−0.0373139	−	0.00999822i	−0.277428	+	0.960747i	$0.589482\pi$
$230$	1.21091	−	1.39117i	0.0798450	−	0.0917312i
$231$	0.234004	−	0.405306i	0.0153963	−	0.0266672i
$232$	11.0685	−	2.33023i	0.726683	−	0.152987i
$233$	−9.53947			−0.624951			−0.312476	−	0.949926i	$-0.601158\pi$
$233$	−9.53947			−0.624951			−0.312476	+	0.949926i	$0.601158\pi$
$234$	−8.28140	+	16.9515i	−0.541372	+	1.10816i
$235$	−1.09491	−	1.89645i	−0.0714243	−	0.123710i
$236$	15.0404	−	2.09393i	0.979045	−	0.136303i
$237$	−5.50713	−	3.17955i	−0.357727	−	0.206534i
$238$	7.97147	−	2.73903i	0.516714	−	0.177545i
$239$	16.6814	−	4.46978i	1.07903	−	0.289126i	0.324834	−	0.945771i	$-0.394692\pi$
$239$	16.6814	−	4.46978i	1.07903	−	0.289126i	0.754200	+	0.656645i	$0.228025\pi$
$240$	3.23351	−	0.0480660i	0.208722	−	0.00310265i
$241$	−22.4220	−	6.00794i	−1.44433	−	0.387006i	−0.550279	−	0.834981i	$-0.685479\pi$
$241$	−22.4220	−	6.00794i	−1.44433	−	0.387006i	−0.894046	+	0.447975i	$0.852145\pi$
$242$	6.40902	−	13.1189i	0.411988	−	0.843314i
$243$	13.8006	−	3.69785i	0.885307	−	0.237217i
$244$	18.8008	+	7.62436i	1.20360	+	0.488100i
$245$		−	7.81096i		−	0.499024i
$246$	−1.78617	−	0.348396i	−0.113882	−	0.0222129i
$247$	−30.8637	−	17.8192i	−1.96381	−	1.13381i
$248$	−18.8381	−	12.2857i	−1.19622	−	0.780143i
$249$	−7.44511			−0.471815
$250$	6.56800	−	13.4443i	0.415397	−	0.850293i
$251$			26.2625i			1.65767i	0.559492	+	0.828836i	$0.310996\pi$
$251$			26.2625i			1.65767i	−0.559492	+	0.828836i	$0.689004\pi$
$252$	−3.60924	+	2.81233i	−0.227361	+	0.177160i
$253$			0.853329i			0.0536483i
$254$	1.67545	+	2.48743i	0.105127	+	0.156075i
$255$	4.71677	−	2.72323i	0.295375	−	0.170535i
$256$	−14.0881	−	7.58461i	−0.880504	−	0.474038i
$257$	−0.663208	−	2.47513i	−0.0413698	−	0.154394i	0.942151	−	0.335188i	$-0.108800\pi$
$257$	−0.663208	−	2.47513i	−0.0413698	−	0.154394i	−0.983521	+	0.180794i	$0.942133\pi$
$258$	6.17908	−	7.09893i	0.384693	−	0.441960i
$259$	5.18643	+	1.43589i	0.322269	+	0.0892222i
$260$	−1.78744	−	12.8389i	−0.110852	−	0.796232i
$261$	−5.17061	+	8.95575i	−0.320052	+	0.554347i
$262$	21.1209	−	14.2264i	1.30486	−	0.878908i
$263$	−10.1664	+	5.86956i	−0.626886	+	0.361933i	−0.779545	−	0.626346i	$-0.784550\pi$
$263$	−10.1664	+	5.86956i	−0.626886	+	0.361933i	0.152659	+	0.988279i	$0.451216\pi$
$264$	−1.11384	+	0.998999i	−0.0685523	+	0.0614842i
$265$	5.93544	+	5.93544i	0.364611	+	0.364611i
$266$	−4.82860	−	7.16869i	−0.296060	−	0.439541i
$267$	4.58221			0.280427
$268$	−7.95407	+	3.36415i	−0.485872	+	0.205498i
$269$	7.57229	+	7.57229i	0.461691	+	0.461691i	0.899209	−	0.437519i	$-0.144143\pi$
$269$	7.57229	+	7.57229i	0.461691	+	0.461691i	−0.437519	+	0.899209i	$0.644143\pi$
$270$	−4.19310	+	4.81731i	−0.255184	+	0.293172i
$271$	1.94346	+	1.12206i	0.118057	+	0.0681601i	0.557866	−	0.829931i	$-0.311620\pi$
$271$	1.94346	+	1.12206i	0.118057	+	0.0681601i	−0.439809	+	0.898091i	$0.644954\pi$
$272$	−26.9441	+	0.400523i	−1.63373	+	0.0242853i
$273$	−2.07687	−	2.07687i	−0.125698	−	0.125698i
$274$	14.2437	−	29.1559i	0.860491	−	1.76137i
$275$	0.727980	+	2.71686i	0.0438988	+	0.163833i
$276$	−0.502087	+	1.23809i	−0.0302221	+	0.0745243i
$277$	2.70575	+	4.68649i	0.162573	+	0.281584i	0.935791	−	0.352556i	$-0.114687\pi$
$277$	2.70575	+	4.68649i	0.162573	+	0.281584i	−0.773218	+	0.634140i	$0.781354\pi$
$278$	3.97853	−	20.3972i	0.238616	−	1.22335i
$279$	19.8611	−	5.32177i	1.18905	−	0.318606i
$280$	0.977291	−	2.98803i	0.0584043	−	0.178569i
$281$	−19.5437	+	5.23671i	−1.16588	+	0.312396i	−0.789311	−	0.613993i	$-0.789562\pi$
$281$	−19.5437	+	5.23671i	−1.16588	+	0.312396i	−0.376567	+	0.926389i	$0.622895\pi$
$282$	1.19650	+	1.04146i	0.0712507	+	0.0620183i
$283$	−1.96159	+	1.13253i	−0.116605	+	0.0673217i	−0.557168	−	0.830400i	$-0.688112\pi$
$283$	−1.96159	+	1.13253i	−0.116605	+	0.0673217i	0.440563	+	0.897722i	$0.354779\pi$
$284$	6.21932	−	15.3361i	0.369048	−	0.910033i
$285$	−3.94915	−	3.94915i	−0.233927	−	0.233927i
$286$	4.52377	+	3.93760i	0.267496	+	0.232835i
$287$	−0.884571	+	1.53212i	−0.0522146	+	0.0904383i
$288$	13.7619	−	4.95855i	0.810931	−	0.292186i
$289$	−24.5813	+	14.1920i	−1.44596	+	0.834826i
$290$	−0.491050	−	7.08828i	−0.0288354	−	0.416238i
$291$	−3.88542	−	6.72975i	−0.227768	−	0.394505i
$292$	−7.24547	−	9.29857i	−0.424009	−	0.544158i
$293$	−2.27178	−	0.608721i	−0.132719	−	0.0355618i	0.191848	−	0.981425i	$-0.438552\pi$
$293$	−2.27178	−	0.608721i	−0.132719	−	0.0355618i	−0.324567	+	0.945863i	$0.605219\pi$
$294$	1.83864	+	5.35106i	0.107232	+	0.312080i
$295$		−	9.53897i		−	0.555380i
$296$	−14.3324	−	9.51749i	−0.833053	−	0.553193i
$297$		−	2.95488i		−	0.171460i
$298$	−22.6638	+	7.78736i	−1.31288	+	0.451109i
$299$	5.17286	+	1.38606i	0.299154	+	0.0801581i
$300$	−0.542339	+	4.37021i	−0.0313119	+	0.252314i
$301$	−4.57467	−	7.92356i	−0.263680	−	0.456707i
$302$	30.3594	−	2.10319i	1.74699	−	0.121025i
$303$	−5.82136	+	3.36096i	−0.334428	+	0.193082i
$304$	7.54768	+	26.5815i	0.432889	+	1.52455i
$305$	6.37211	−	11.0368i	0.364866	−	0.631966i
$306$	16.1750	−	18.5828i	0.924660	−	1.06231i
$307$	−14.7387	−	14.7387i	−0.841181	−	0.841181i	0.147832	−	0.989013i	$-0.452771\pi$
$307$	−14.7387	−	14.7387i	−0.841181	−	0.841181i	−0.989013	+	0.147832i	$0.952771\pi$
$308$	0.566599	+	1.33964i	0.0322850	+	0.0763333i
$309$	5.31306	−	3.06750i	0.302249	−	0.174504i
$310$	−9.27546	+	10.6563i	−0.526811	+	0.605235i
$311$	13.7849	−	3.69365i	0.781669	−	0.209448i	0.154148	−	0.988048i	$-0.450737\pi$
$311$	13.7849	−	3.69365i	0.781669	−	0.209448i	0.627520	+	0.778600i	$0.284070\pi$
$312$	4.24669	+	8.37477i	0.240422	+	0.474128i
$313$	14.5559	−	3.90025i	0.822750	−	0.220455i	0.177202	−	0.984175i	$-0.443295\pi$
$313$	14.5559	−	3.90025i	0.822750	−	0.220455i	0.645549	+	0.763719i	$0.276629\pi$
$314$	25.4442	+	4.96295i	1.43590	+	0.280075i
$315$	1.43711	+	2.48914i	0.0809718	+	0.140247i
$316$	18.2025	−	7.69871i	1.02397	−	0.433086i
$317$	−4.08907	−	15.2606i	−0.229665	−	0.857123i	−0.980482	−	0.196611i	$-0.937006\pi$
$317$	−4.08907	−	15.2606i	−0.229665	−	0.857123i	0.750816	−	0.660511i	$-0.229660\pi$
$318$	−5.46336	−	2.66904i	−0.306370	−	0.149672i
$319$	2.32454	+	2.32454i	0.130149	+	0.130149i
$320$	−5.93916	+	8.10814i	−0.332009	+	0.453259i
$321$	6.76223	+	3.90418i	0.377431	+	0.217910i
$322$	0.979674	+	0.852732i	0.0545951	+	0.0475209i
$323$	32.9074	+	32.9074i	1.83101	+	1.83101i
$324$	−4.09216	+	10.0908i	−0.227342	+	0.560601i
$325$	17.6520			0.979157
$326$	−19.4853	+	13.1247i	−1.07919	+	0.726908i
$327$	7.55888	+	7.55888i	0.418007	+	0.418007i
$328$	4.21051	−	3.77638i	0.232486	−	0.208515i
$329$	1.33549	−	0.771047i	0.0736280	−	0.0425092i
$330$	0.525063	+	0.779526i	0.0289038	+	0.0429115i
$331$	3.11601	−	5.39709i	0.171272	−	0.296651i	−0.767593	−	0.640937i	$-0.778546\pi$
$331$	3.11601	−	5.39709i	0.171272	−	0.296651i	0.938865	+	0.344286i	$0.111879\pi$
$332$	13.9493	−	18.4615i	0.765565	−	1.01321i
$333$	15.2266	−	3.94494i	0.834414	−	0.216182i
$334$	8.23648	+	7.16923i	0.450680	+	0.392283i
$335$	1.40409	+	5.24014i	0.0767137	+	0.286299i
$336$	0.0338484	+	2.27706i	0.00184658	+	0.124224i
$337$	10.1106	−	5.83736i	0.550760	−	0.317981i	−0.198668	−	0.980067i	$-0.563662\pi$
$337$	10.1106	−	5.83736i	0.550760	−	0.317981i	0.749428	+	0.662085i	$0.230328\pi$
$338$	15.9693	−	10.7564i	0.868616	−	0.585071i
$339$			8.40096i			0.456278i
$340$	−2.08466	+	16.7984i	−0.113057	+	0.911020i
$341$		−	6.53642i		−	0.353967i
$342$	−22.6989	−	11.0892i	−1.22741	−	0.599634i
$343$	11.6936			0.631393
$344$	6.02590	+	28.6228i	0.324895	+	1.54324i
$345$	0.726807	+	0.419622i	0.0391300	+	0.0225917i
$346$	1.36498	−	6.99802i	0.0733818	−	0.376216i
$347$		−	16.1646i		−	0.867763i	−0.900970	−	0.433881i	$-0.857144\pi$
$347$		−	16.1646i		−	0.867763i	0.900970	−	0.433881i	$-0.142856\pi$
$348$	2.00493	+	4.74038i	0.107476	+	0.254111i
$349$	−22.6966	+	6.08153i	−1.21492	+	0.325537i	−0.808691	−	0.588234i	$-0.799823\pi$
$349$	−22.6966	+	6.08153i	−1.21492	+	0.325537i	−0.406230	+	0.913771i	$0.633157\pi$
$350$	3.84659	+	1.87919i	0.205609	+	0.100447i
$351$	−17.9124	−	4.79962i	−0.956095	−	0.256185i
$352$	−0.390289	−	4.63372i	−0.0208025	−	0.246978i
$353$	−8.07062	+	2.16252i	−0.429556	+	0.115099i	−0.467118	−	0.884195i	$-0.654708\pi$
$353$	−8.07062	+	2.16252i	−0.429556	+	0.115099i	0.0375619	+	0.999294i	$0.488041\pi$
$354$	2.24540	+	6.53487i	0.119342	+	0.347324i
$355$	−9.00291	−	5.19783i	−0.477825	−	0.275872i
$356$	−8.58530	+	11.3624i	−0.455020	+	0.602208i
$357$	1.91772	+	3.32158i	0.101496	+	0.175797i
$358$	−9.12209	−	4.45645i	−0.482118	−	0.235531i
$359$	−32.8876			−1.73574			−0.867871	−	0.496790i	$-0.834512\pi$
$359$	−32.8876			−1.73574			−0.867871	+	0.496790i	$0.834512\pi$
$360$	−1.89300	−	8.99171i	−0.0997700	−	0.473905i
$361$	14.3607	−	24.8734i	0.755825	−	1.30913i
$362$	12.1078	+	10.5389i	0.636369	+	0.553911i
$363$	6.41742	+	1.71954i	0.336827	+	0.0902526i
$364$	9.04122	−	1.25873i	0.473889	−	0.0659752i
$365$	−6.41284	+	3.70245i	−0.335663	+	0.193795i
$366$	−1.76736	+	9.06095i	−0.0923813	+	0.473623i
$367$	7.68135	−	4.43483i	0.400963	−	0.231496i	−0.285936	−	0.958249i	$-0.592305\pi$
$367$	7.68135	−	4.43483i	0.400963	−	0.231496i	0.686899	+	0.726753i	$0.258971\pi$
$368$	−2.12936	−	3.56472i	−0.111000	−	0.185824i
$369$			5.17092i			0.269187i
$370$	−7.16290	+	8.09272i	−0.372381	+	0.420721i
$371$	−4.17979	+	4.17979i	−0.217004	+	0.217004i
$372$	3.84594	−	9.48366i	0.199403	−	0.491705i
$373$	6.87323	−	25.6513i	0.355882	−	1.32817i	−0.523488	−	0.852033i	$-0.675369\pi$
$373$	6.87323	−	25.6513i	0.355882	−	1.32817i	0.879370	−	0.476138i	$-0.157964\pi$
$374$	−4.37523	−	6.49562i	−0.226238	−	0.335880i
$375$	6.57661	+	1.76220i	0.339615	+	0.0909995i
$376$	−4.82429	+	1.01565i	−0.248794	+	0.0523779i
$377$	17.8670	−	10.3155i	0.920199	−	0.531277i
$378$	−3.39239	−	2.95282i	−0.174486	−	0.151876i
$379$	−17.0581	+	4.57070i	−0.876214	+	0.234781i	−0.668773	−	0.743467i	$-0.733180\pi$
$379$	−17.0581	+	4.57070i	−0.876214	+	0.234781i	−0.207441	+	0.978247i	$0.566514\pi$
$380$	17.1918	−	2.39346i	0.881922	−	0.122782i
$381$	−0.964971	+	0.964971i	−0.0494370	+	0.0494370i
$382$	8.14705	+	23.7106i	0.416839	+	1.21314i
$383$	−9.71715	+	36.2649i	−0.496523	+	1.85305i	0.0248038	+	0.999692i	$0.492104\pi$
$383$	−9.71715	+	36.2649i	−0.496523	+	1.85305i	−0.521327	+	0.853357i	$0.674563\pi$
$384$	2.16015	−	6.95269i	0.110235	−	0.354803i
$385$	0.882558	−	0.236481i	0.0449793	−	0.0120522i
$386$	−4.48201	+	1.54003i	−0.228128	+	0.0783857i
$387$	−23.1593	−	13.3710i	−1.17725	−	0.679688i
$388$	23.9675	+	2.97434i	1.21676	+	0.150999i
$389$	6.17385	−	3.56447i	0.313027	−	0.180726i	−0.335253	−	0.942128i	$-0.608822\pi$
$389$	6.17385	−	3.56447i	0.313027	−	0.180726i	0.648280	+	0.761402i	$0.275489\pi$
$390$	5.57833	−	1.91674i	0.282470	−	0.0970577i
$391$	−6.05632	−	3.49662i	−0.306281	−	0.176832i
$392$	−16.7138	−	5.46657i	−0.844177	−	0.276103i
$393$	8.19365	+	8.19365i	0.413315	+	0.413315i
$394$	0.321847	−	1.65005i	0.0162144	−	0.0831285i
$395$	−3.21320	−	11.9918i	−0.161674	−	0.603374i
$396$	3.39199	+	2.56294i	0.170454	+	0.128793i
$397$	10.6449	−	10.6449i	0.534251	−	0.534251i	−0.387584	−	0.921834i	$-0.626690\pi$
$397$	10.6449	−	10.6449i	0.534251	−	0.534251i	0.921834	+	0.387584i	$0.126690\pi$
$398$	2.97877	+	8.66919i	0.149312	+	0.434547i
$399$	2.78102	−	2.78102i	0.139225	−	0.139225i
$400$	−9.82061	−	9.53292i	−0.491031	−	0.476646i
$401$	7.12805	+	7.12805i	0.355958	+	0.355958i	0.862321	−	0.506363i	$-0.169010\pi$
$401$	7.12805	+	7.12805i	0.355958	+	0.355958i	−0.506363	+	0.862321i	$0.669010\pi$
$402$	−2.19539	−	3.25935i	−0.109496	−	0.162562i
$403$	−39.6236	−	10.6171i	−1.97379	−	0.528877i
$404$	2.57286	−	20.7323i	0.128004	−	1.03147i
$405$	5.92369	+	3.42005i	0.294351	+	0.169943i
$406$	4.99162	−	0.345801i	0.247730	−	0.0171618i
$407$	0.0414589	−	5.00007i	0.00205504	−	0.247844i
$408$	−2.52608	−	11.9988i	−0.125059	−	0.594029i
$409$	5.25485	+	19.6114i	0.259836	+	0.969720i	0.965336	+	0.261011i	$0.0840558\pi$
$409$	5.25485	+	19.6114i	0.259836	+	0.969720i	−0.705500	+	0.708710i	$0.749278\pi$
$410$	−1.98482	−	2.94673i	−0.0980234	−	0.145529i
$411$	14.2623	+	3.82158i	0.703509	+	0.188505i
$412$	−2.34820	+	18.9220i	−0.115688	+	0.932221i
$413$	6.71741			0.330542
$414$	3.72600	+	0.726765i	0.183123	+	0.0357186i
$415$	−10.2779	−	10.2779i	−0.504520	−	0.504520i
$416$	−28.7235	−	5.16064i	−1.40828	−	0.253021i
$417$	9.45633			0.463078
$418$	−5.27263	+	6.05755i	−0.257893	+	0.296284i
$419$	6.64410	+	24.7961i	0.324585	+	1.21137i	0.914728	+	0.404070i	$0.132405\pi$
$419$	6.64410	+	24.7961i	0.324585	+	1.21137i	−0.590143	+	0.807299i	$0.700929\pi$
$420$	1.41964	+	0.176176i	0.0692714	+	0.00859651i
$421$	−5.90760			−0.287919			−0.143959	−	0.989584i	$-0.545983\pi$
$421$	−5.90760			−0.287919			−0.143959	+	0.989584i	$0.545983\pi$
$422$	−22.2854	+	7.65733i	−1.08483	+	0.372753i
$423$	2.25365	−	3.90343i	0.109576	−	0.189791i
$424$	16.8546	−	8.54666i	0.818532	−	0.415062i
$425$	−22.2653	−	5.96597i	−1.08003	−	0.289392i
$426$	7.39116	+	1.44166i	0.358103	+	0.0698488i
$427$	7.77221	+	4.48729i	0.376124	+	0.217155i
$428$	−22.3510	+	9.45328i	−1.08037	+	0.456942i
$429$	−1.36452	+	2.36341i	−0.0658794	+	0.114107i
$430$	18.3301	−	1.26984i	0.883955	−	0.0612372i
$431$	7.99513	+	2.14229i	0.385112	+	0.103190i	0.446180	−	0.894943i	$-0.352784\pi$
$431$	7.99513	+	2.14229i	0.385112	+	0.103190i	−0.0610684	+	0.998134i	$0.519451\pi$
$432$	7.37348	+	12.3438i	0.354757	+	0.593892i
$433$	18.3193			0.880368			0.440184	−	0.897908i	$-0.354913\pi$
$433$	18.3193			0.880368			0.440184	+	0.897908i	$0.354913\pi$
$434$	−7.50422	−	6.53185i	−0.360214	−	0.313539i
$435$	3.12297	−	0.836796i	0.149735	−	0.0401213i
$436$	−32.9061	+	4.58121i	−1.57591	+	0.219400i
$437$	−1.85600	+	6.92670i	−0.0887847	+	0.331349i
$438$	3.52171	−	4.04598i	0.168274	−	0.193324i
$439$	−7.42879	+	27.7246i	−0.354557	+	1.32322i	0.526484	+	0.850185i	$0.323510\pi$
$439$	−7.42879	+	27.7246i	−0.354557	+	1.32322i	−0.881041	+	0.473040i	$0.843157\pi$
$440$	−2.91675	−	0.158541i	−0.139050	−	0.00755814i
$441$	13.9233	−	8.03859i	0.663012	−	0.382790i
$442$	−46.4830	+	15.9717i	−2.21097	+	0.759698i
$443$	−15.3646	+	15.3646i	−0.729993	+	0.729993i	−0.970618	−	0.240625i	$-0.922648\pi$
$443$	−15.3646	+	15.3646i	−0.729993	+	0.729993i	0.240625	+	0.970618i	$0.422648\pi$
$444$	3.00212	−	7.23018i	0.142474	−	0.343129i
$445$	6.32567	+	6.32567i	0.299866	+	0.299866i
$446$	3.05396	−	6.25128i	0.144609	−	0.296006i
$447$	−5.45228	−	9.44363i	−0.257884	−	0.446668i
$448$	−5.70982	−	4.18240i	−0.269763	−	0.197600i
$449$	−6.41493	−	1.71888i	−0.302739	−	0.0811187i	0.104252	−	0.994551i	$-0.466755\pi$
$449$	−6.41493	−	1.71888i	−0.302739	−	0.0811187i	−0.406991	+	0.913432i	$0.633422\pi$
$450$	12.4830	−	0.864776i	0.588454	−	0.0407659i
$451$	1.58778	+	0.425446i	0.0747659	+	0.0200335i
$452$	−20.8317	−	15.7402i	−0.979842	−	0.740355i
$453$	3.58404	+	13.3758i	0.168393	+	0.628450i
$454$	22.8870	−	1.58553i	1.07414	−	0.0744125i
$455$		−	5.73416i		−	0.268822i
$456$	−11.2142	+	5.68652i	−0.525154	+	0.266296i
$457$	5.95584	−	22.2275i	0.278603	−	1.03976i	−0.674786	−	0.738014i	$-0.735764\pi$
$457$	5.95584	−	22.2275i	0.278603	−	1.03976i	0.953389	−	0.301746i	$-0.0975693\pi$
$458$	0.623584	+	0.542782i	0.0291381	+	0.0253625i
$459$	20.9717	+	12.1080i	0.978873	+	0.565153i
$460$	−2.40229	+	1.01604i	−0.112007	+	0.0473732i
$461$	−3.58265	+	6.20533i	−0.166861	+	0.289011i	−0.937314	−	0.348485i	$-0.886696\pi$
$461$	−3.58265	+	6.20533i	−0.166861	+	0.289011i	0.770454	+	0.637496i	$0.220030\pi$
$462$	−0.548948	+	0.369754i	−0.0255394	+	0.0172025i
$463$	−4.25652	+	15.8855i	−0.197817	+	0.738264i	0.793702	+	0.608306i	$0.208151\pi$
$463$	−4.25652	+	15.8855i	−0.197817	+	0.738264i	−0.991520	+	0.129957i	$0.958516\pi$
$464$	−15.5111	−	3.91005i	−0.720086	−	0.181519i
$465$	−5.56728	−	3.21427i	−0.258176	−	0.149058i
$466$	12.1217	+	5.92185i	0.561525	+	0.274324i
$467$		−	27.6427i		−	1.27915i	−0.768728	−	0.639575i	$-0.779110\pi$
$467$		−	27.6427i		−	1.27915i	0.768728	−	0.639575i	$-0.220890\pi$
$468$	21.0461	−	16.3992i	0.972856	−	0.758052i
$469$	−3.69015	+	0.988772i	−0.170395	+	0.0456572i
$470$	0.214028	+	3.08948i	0.00987236	+	0.142507i
$471$			11.7961i			0.543537i
$472$	−20.4114	−	6.67593i	−0.939512	−	0.307285i
$473$	−6.01118	+	6.01118i	−0.276394	+	0.276394i
$474$	5.02406	+	7.45888i	0.230763	+	0.342598i
$475$			23.6368i			1.08453i
$476$	−11.8295	−	1.46803i	−0.542206	−	0.0672873i
$477$	−4.47167	+	16.6885i	−0.204744	+	0.764115i
$478$	−23.9716	−	4.67571i	−1.09643	−	0.213862i
$479$	−31.1961	+	8.35897i	−1.42539	+	0.381931i	−0.887391	−	0.461017i	$-0.847485\pi$
$479$	−31.1961	+	8.35897i	−1.42539	+	0.381931i	−0.537995	+	0.842948i	$0.680818\pi$
$480$	−4.13861	−	1.94620i	−0.188901	−	0.0888314i
$481$	−30.2430	−	8.37295i	−1.37896	−	0.381773i
$482$	24.7617	+	21.5532i	1.12786	+	0.981719i
$483$	−0.295501	+	0.511823i	−0.0134458	+	0.0232888i
$484$	−16.2877	+	12.6914i	−0.740350	+	0.576883i
$485$	3.92655	−	14.6541i	0.178295	−	0.665408i
$486$	−19.8317	−	3.86822i	−0.899584	−	0.175466i
$487$	5.29187	−	5.29187i	0.239798	−	0.239798i	−0.576969	−	0.816766i	$-0.695765\pi$
$487$	5.29187	−	5.29187i	0.239798	−	0.239798i	0.816766	+	0.576969i	$0.195765\pi$
$488$	−19.1569	−	21.3592i	−0.867194	−	0.966886i
$489$	−7.55912	−	7.55912i	−0.341835	−	0.341835i
$490$	−4.84883	+	9.92527i	−0.219048	+	0.448378i
$491$	23.8915	+	23.8915i	1.07821	+	1.07821i	0.996670	+	0.0815393i	$0.0259836\pi$
$491$	23.8915	+	23.8915i	1.07821	+	1.07821i	0.0815393	+	0.996670i	$0.474016\pi$
$492$	2.05338	+	1.55151i	0.0925737	+	0.0699474i
$493$	−26.0230	+	6.97283i	−1.17202	+	0.314041i
$494$	28.1564	+	41.8019i	1.26681	+	1.88076i
$495$	1.88838	−	1.88838i	0.0848763	−	0.0848763i
$496$	16.3107	+	27.3054i	0.732371	+	1.22605i
$497$	3.66035	−	6.33992i	0.164189	−	0.284384i
$498$	9.46039	+	4.62172i	0.423930	+	0.207104i
$499$	−1.60411	−	2.77840i	−0.0718098	−	0.124378i	0.827885	−	0.560898i	$-0.189544\pi$
$499$	−1.60411	−	2.77840i	−0.0718098	−	0.124378i	−0.899695	+	0.436520i	$0.856211\pi$
$500$	−16.6917	+	13.0062i	−0.746477	+	0.581657i
$501$	−2.48439	+	4.30308i	−0.110994	+	0.192248i
$502$	16.3030	−	33.3713i	0.727640	−	1.48944i
$503$	−7.45009	−	27.8041i	−0.332183	−	1.23972i	−0.906891	−	0.421366i	$-0.861551\pi$
$503$	−7.45009	−	27.8041i	−0.332183	−	1.23972i	0.574708	−	0.818359i	$-0.305116\pi$
$504$	6.33203	−	1.33307i	0.282051	−	0.0593795i
$505$	−12.6760	−	3.39654i	−0.564077	−	0.151144i
$506$	0.529724	−	1.08431i	0.0235491	−	0.0482036i
$507$	6.19513	+	6.19513i	0.275135	+	0.275135i
$508$	−0.584840	−	4.20081i	−0.0259481	−	0.186381i
$509$	−8.80667	−	32.8669i	−0.390349	−	1.45680i	−0.829560	−	0.558418i	$-0.811409\pi$
$509$	−8.80667	−	32.8669i	−0.390349	−	1.45680i	0.439211	−	0.898384i	$-0.355258\pi$
$510$	−7.68403	+	0.532322i	−0.340255	+	0.0235716i
$511$	−2.60730	−	4.51597i	−0.115340	−	0.199775i
$512$	13.1932	+	18.3831i	0.583062	+	0.812428i
$513$	6.42692	−	23.9856i	0.283755	−	1.05899i
$514$	−0.693763	+	3.55681i	−0.0306006	+	0.156884i
$515$	11.5692	+	3.09996i	0.509801	+	0.136601i
$516$	−12.2585	+	5.18470i	−0.539650	+	0.228244i
$517$	−1.01317	−	1.01317i	−0.0445590	−	0.0445590i
$518$	−5.69896	−	5.04417i	−0.250398	−	0.221628i
$519$	3.24434			0.142411
$520$	−5.69875	+	17.4237i	−0.249907	+	0.764081i
$521$	−15.3234	−	26.5409i	−0.671330	−	1.16278i	−0.977527	−	0.210810i	$-0.932390\pi$
$521$	−15.3234	−	26.5409i	−0.671330	−	1.16278i	0.306197	−	0.951968i	$-0.400943\pi$
$522$	12.1297	−	8.17017i	0.530903	−	0.357598i
$523$	−12.3531	−	21.3961i	−0.540161	−	0.935587i	−0.998894	−	0.0470126i	$-0.985030\pi$
$523$	−12.3531	−	21.3961i	−0.540161	−	0.935587i	0.458733	−	0.888574i	$-0.348303\pi$
$524$	−35.6694	+	4.96592i	−1.55823	+	0.216937i
$525$	−0.504188	+	1.88165i	−0.0220046	+	0.0821221i
$526$	16.5619	−	1.14735i	0.722135	−	0.0500268i
$527$	46.3909	+	26.7838i	2.02082	+	1.16672i
$528$	2.03550	−	0.577969i	0.0885836	−	0.0251529i
$529$			21.9224i			0.953148i
$530$	−3.85752	−	11.2266i	−0.167560	−	0.487654i
$531$	17.0035	−	9.81696i	0.737888	−	0.426020i
$532$	1.68549	+	12.1066i	0.0730754	+	0.524888i
$533$	5.15809	−	8.93407i	0.223421	−	0.386977i
$534$	−5.82255	−	2.84452i	−0.251966	−	0.123094i
$535$	3.94550	+	14.7248i	0.170579	+	0.636609i
$536$	12.1955	+	0.662891i	0.526765	+	0.0286325i
$537$	1.19567	−	4.46229i	0.0515969	−	0.192562i
$538$	−4.92132	−	14.3227i	−0.212173	−	0.617494i
$539$	−1.32278	−	4.93667i	−0.0569760	−	0.212637i
$540$	8.31857	−	3.51832i	0.357974	−	0.151404i
$541$	−31.4280			−1.35120			−0.675598	−	0.737270i	$-0.736114\pi$
$541$	−31.4280			−1.35120			−0.675598	+	0.737270i	$0.736114\pi$
$542$	−1.77298	−	2.63223i	−0.0761561	−	0.113064i
$543$	−3.65209	+	6.32560i	−0.156726	+	0.271457i
$544$	34.4861	+	16.2172i	1.47858	+	0.695308i
$545$			20.8698i			0.893965i
$546$	1.34978	+	3.92831i	0.0577653	+	0.168116i
$547$	14.1621			0.605526			0.302763	−	0.953066i	$-0.402091\pi$
$547$	14.1621			0.605526			0.302763	+	0.953066i	$0.402091\pi$
$548$	−36.1984	+	28.2059i	−1.54632	+	1.20490i
$549$	26.2312			1.11952
$550$	0.761519	−	3.90418i	0.0324713	−	0.166475i
$551$	13.8130	+	23.9248i	0.588453	+	1.01923i
$552$	1.40657	−	1.26154i	0.0598675	−	0.0536948i
$553$	8.44473	−	2.26276i	0.359107	−	0.0962223i
$554$	−0.528905	−	7.63471i	−0.0224710	−	0.324368i
$555$	−4.23833	−	2.49408i	−0.179907	−	0.105868i
$556$	−17.7175	+	23.4487i	−0.751390	+	0.994447i
$557$	10.5022	+	6.06346i	0.444993	+	0.256917i	0.705713	−	0.708497i	$-0.250627\pi$
$557$	10.5022	+	6.06346i	0.444993	+	0.256917i	−0.260720	+	0.965414i	$0.583960\pi$
$558$	−28.5408	−	5.56696i	−1.20823	−	0.235668i
$559$	26.6757	+	46.2036i	1.12826	+	1.95421i
$560$	−3.09672	+	3.19018i	−0.130860	+	0.134810i
$561$	2.51991	−	2.51991i	0.106391	−	0.106391i
$562$	28.0847	+	5.47798i	1.18468	+	0.231074i
$563$			5.29546i			0.223177i	0.993754	+	0.111589i	$0.0355939\pi$
$563$			5.29546i			0.223177i	−0.993754	+	0.111589i	$0.964406\pi$
$564$	−0.873865	−	2.06613i	−0.0367964	−	0.0869998i
$565$	−11.5974	+	11.5974i	−0.487906	+	0.487906i
$566$	3.19561	−	0.221380i	0.134321	−	0.00930529i
$567$	−2.40842	+	4.17151i	−0.101144	+	0.175187i
$568$	−17.4231	+	15.6266i	−0.731055	+	0.655679i
$569$	21.0112	−	21.0112i	0.880835	−	0.880835i	−0.112784	−	0.993620i	$-0.535977\pi$
$569$	21.0112	−	21.0112i	0.880835	−	0.880835i	0.993620	+	0.112784i	$0.0359769\pi$
$570$	2.56660	+	7.46965i	0.107503	+	0.312869i
$571$	−25.0958	+	6.72439i	−1.05023	+	0.281407i	−0.742345	−	0.670018i	$-0.766286\pi$
$571$	−25.0958	+	6.72439i	−1.05023	+	0.281407i	−0.307880	+	0.951425i	$0.599620\pi$
$572$	−3.30394	−	7.81169i	−0.138145	−	0.326623i
$573$	−9.87983	+	5.70412i	−0.412736	+	0.238293i
$574$	2.07511	−	1.39773i	0.0866135	−	0.0583400i
$575$	−0.919297	−	3.43086i	−0.0383373	−	0.143077i
$576$	−20.5652	−	2.24229i	−0.856885	−	0.0934287i
$577$	0.913995	+	3.41107i	0.0380501	+	0.142005i	0.982338	−	0.187116i	$-0.0599142\pi$
$577$	0.913995	+	3.41107i	0.0380501	+	0.142005i	−0.944288	+	0.329121i	$0.893247\pi$
$578$	40.0452	−	2.77418i	1.66566	−	0.115391i
$579$	−1.07825	−	1.86758i	−0.0448105	−	0.0776140i
$580$	−3.77624	+	9.31180i	−0.156800	+	0.386652i
$581$	7.23774	−	7.23774i	0.300272	−	0.300272i
$582$	0.759502	+	10.9634i	0.0314824	+	0.454446i
$583$	4.75647	+	2.74615i	0.196993	+	0.113734i
$584$	3.43441	+	16.3133i	0.142117	+	0.675051i
$585$	−8.38002	−	14.5146i	−0.346471	−	0.600106i
$586$	2.50884	+	2.18375i	0.103639	+	0.0902099i
$587$	5.09716	−	2.94285i	0.210382	−	0.121464i	−0.391107	−	0.920345i	$-0.627908\pi$
$587$	5.09716	−	2.94285i	0.210382	−	0.121464i	0.601489	+	0.798881i	$0.294574\pi$
$588$	0.985456	−	7.94089i	0.0406395	−	0.327477i
$589$	14.2168	−	53.0579i	0.585794	−	2.18621i
$590$	−5.92154	+	12.1210i	−0.243786	+	0.499015i
$591$	0.764978			0.0314670
$592$	12.3038	+	20.9909i	0.505681	+	0.862721i
$593$	26.3672			1.08277			0.541386	−	0.840774i	$-0.317900\pi$
$593$	26.3672			1.08277			0.541386	+	0.840774i	$0.317900\pi$
$594$	−1.83431	+	3.75473i	−0.0752627	+	0.154058i
$595$	−1.93802	+	7.23277i	−0.0794509	+	0.296515i
$596$	33.6327	+	4.17379i	1.37765	+	0.170965i
$597$	−3.61231	+	2.08557i	−0.147842	+	0.0853567i
$598$	−5.71265	−	4.97242i	−0.233607	−	0.203338i
$599$	15.0951	+	26.1455i	0.616769	+	1.06828i	0.990071	+	0.140566i	$0.0448923\pi$
$599$	15.0951	+	26.1455i	0.616769	+	1.06828i	−0.373302	+	0.927710i	$0.621774\pi$
$600$	3.40205	−	5.21649i	0.138888	−	0.212962i
$601$	27.7497	+	16.0213i	1.13193	+	0.653522i	0.944420	−	0.328740i	$-0.106624\pi$
$601$	27.7497	+	16.0213i	1.13193	+	0.653522i	0.187513	+	0.982262i	$0.439957\pi$
$602$	0.894232	+	12.9082i	0.0364462	+	0.526098i
$603$	−7.89569	+	7.89569i	−0.321537	+	0.321537i
$604$	−39.8829	−	16.1738i	−1.62281	−	0.658104i
$605$	6.48535	+	11.2329i	0.263667	+	0.456684i
$606$	9.48351	−	0.656983i	0.385241	−	0.0266881i
$607$	−3.81756	−	14.2473i	−0.154950	−	0.578281i	−0.999110	−	0.0421893i	$-0.986567\pi$
$607$	−3.81756	−	14.2473i	−0.154950	−	0.578281i	0.844160	−	0.536092i	$-0.180100\pi$
$608$	6.91034	−	38.4621i	0.280251	−	1.55984i
$609$	0.589278	+	2.19922i	0.0238788	+	0.0891167i
$610$	−14.9483	+	10.0687i	−0.605239	+	0.407669i
$611$	−7.78748	+	4.49610i	−0.315048	+	0.181893i
$612$	−32.0890	+	13.5720i	−1.29712	+	0.548614i
$613$	−18.6174	+	4.98852i	−0.751950	+	0.201484i	−0.614383	−	0.789008i	$-0.710595\pi$
$613$	−18.6174	+	4.98852i	−0.751950	+	0.201484i	−0.137567	+	0.990492i	$0.543928\pi$
$614$	9.57885	+	27.8776i	0.386571	+	1.12505i
$615$	1.14315	−	1.14315i	0.0460964	−	0.0460964i
$616$	0.111646	−	2.05399i	0.00449833	−	0.0827578i
$617$	−7.72020	+	13.3718i	−0.310803	+	0.538327i	−0.978537	−	0.206073i	$-0.933931\pi$
$617$	−7.72020	+	13.3718i	−0.310803	+	0.538327i	0.667733	+	0.744401i	$0.267265\pi$
$618$	−8.65544	+	0.599617i	−0.348173	+	0.0241201i
$619$	−7.45949	+	7.45949i	−0.299822	+	0.299822i	−0.840944	−	0.541122i	$-0.818000\pi$
$619$	−7.45949	+	7.45949i	−0.299822	+	0.299822i	0.541122	+	0.840944i	$0.318000\pi$
$620$	18.4013	−	7.78279i	0.739014	−	0.312564i
$621$			3.73144i			0.149738i
$622$	−19.8092	−	3.86382i	−0.794275	−	0.154925i
$623$	−4.45459	+	4.45459i	−0.178469	+	0.178469i
$624$	−0.197376	−	13.2779i	−0.00790136	−	0.531543i
$625$	−1.90786	−	3.30451i	−0.0763143	−	0.132180i
$626$	−20.9172	−	4.07994i	−0.836019	−	0.163067i
$627$	−3.16472	−	1.82715i	−0.126387	−	0.0729693i
$628$	−29.2507	−	22.1014i	−1.16723	−	0.881943i
$629$	35.3170	+	20.7826i	1.40818	+	0.828658i
$630$	−0.280918	−	4.05504i	−0.0111920	−	0.161556i
$631$	17.3003	−	4.63560i	0.688713	−	0.184540i	0.102544	−	0.994729i	$-0.467302\pi$
$631$	17.3003	−	4.63560i	0.688713	−	0.184540i	0.586170	+	0.810188i	$0.300635\pi$
$632$	−27.9088	−	1.51700i	−1.11015	−	0.0603428i
$633$	−5.36125	−	9.28595i	−0.213090	−	0.369083i
$634$	−4.27747	+	21.9298i	−0.169880	+	0.870945i
$635$	−2.66425			−0.105728
$636$	5.28534	+	6.78301i	0.209577	+	0.268964i
$637$	−32.0746			−1.27084
$638$	−1.51074	−	4.39676i	−0.0598109	−	0.174070i
$639$		−	21.3973i		−	0.846462i
$640$	12.5801	−	6.61602i	0.497273	−	0.261521i
$641$	15.7675	−	27.3101i	0.622778	−	1.07868i	−0.366188	−	0.930541i	$-0.619337\pi$
$641$	15.7675	−	27.3101i	0.622778	−	1.07868i	0.988966	−	0.148142i	$-0.0473292\pi$
$642$	−6.16906	−	9.15879i	−0.243473	−	0.361469i
$643$	12.8634			0.507284			0.253642	−	0.967298i	$-0.418371\pi$
$643$	12.8634			0.507284			0.253642	+	0.967298i	$0.418371\pi$
$644$	−0.715504	−	1.69171i	−0.0281948	−	0.0666627i
$645$	2.16393	+	8.07590i	0.0852047	+	0.317988i
$646$	−21.3869	−	62.2429i	−0.841456	−	2.44891i
$647$	6.11236	−	22.8117i	0.240302	−	0.896819i	−0.735385	−	0.677649i	$-0.762999\pi$
$647$	6.11236	−	22.8117i	0.240302	−	0.896819i	0.975687	−	0.219169i	$-0.0703347\pi$
$648$	11.4639	−	10.2819i	0.450346	−	0.403913i
$649$	−1.61541	−	6.02880i	−0.0634105	−	0.236651i
$650$	−22.4301	−	10.9579i	−0.879782	−	0.429804i
$651$	2.26351	−	3.92052i	0.0887140	−	0.153657i
$652$	32.9071	−	4.58136i	1.28874	−	0.179420i
$653$	29.6731	−	17.1318i	1.16120	−	0.670418i	0.209607	−	0.977786i	$-0.432782\pi$
$653$	29.6731	−	17.1318i	1.16120	−	0.670418i	0.951591	+	0.307368i	$0.0994483\pi$
$654$	−4.91261	−	14.2973i	−0.192098	−	0.559069i
$655$			22.6224i			0.883931i
$656$	−7.69450	+	2.18482i	−0.300420	+	0.0853027i
$657$	−13.1995	−	7.62071i	−0.514960	−	0.297312i
$658$	−2.17563	+	0.150720i	−0.0848151	+	0.00587568i
$659$	−1.11127	+	4.14731i	−0.0432888	+	0.161556i	−0.984187	−	0.177134i	$-0.943317\pi$
$659$	−1.11127	+	4.14731i	−0.0432888	+	0.161556i	0.940898	+	0.338690i	$0.109984\pi$
$660$	−0.183281	−	1.31648i	−0.00713421	−	0.0512438i
$661$	−11.2587	−	19.5006i	−0.437911	−	0.758484i	0.559617	−	0.828751i	$-0.310948\pi$
$661$	−11.2587	−	19.5006i	−0.437911	−	0.758484i	−0.997528	+	0.0702673i	$0.977615\pi$
$662$	−7.30984	+	4.92367i	−0.284105	+	0.191364i
$663$	−11.1825	−	19.3687i	−0.434294	−	0.752219i
$664$	−29.1855	+	14.7995i	−1.13262	+	0.574330i
$665$	7.67831			0.297752
$666$	−21.7972	−	4.43950i	−0.844623	−	0.172027i
$667$	−2.93544	−	2.93544i	−0.113661	−	0.113661i
$668$	−6.01551	−	14.2228i	−0.232747	−	0.550297i
$669$	3.05796	+	0.819379i	0.118228	+	0.0316790i
$670$	1.46878	−	7.53019i	0.0567439	−	0.290917i
$671$	2.15822	−	8.05457i	0.0833170	−	0.310943i
$672$	1.37053	−	2.91444i	0.0528693	−	0.112427i
$673$	11.0909	+	19.2101i	0.427525	+	0.740494i	0.996652	−	0.0817547i	$-0.0260524\pi$
$673$	11.0909	+	19.2101i	0.427525	+	0.740494i	−0.569128	+	0.822249i	$0.692719\pi$
$674$	−16.4711	+	1.14106i	−0.634442	+	0.0439518i
$675$	3.18332	+	11.8803i	0.122526	+	0.457273i
$676$	−26.9693	+	3.75468i	−1.03728	+	0.144411i
$677$	−10.6535	−	10.6535i	−0.409448	−	0.409448i	0.472098	−	0.881546i	$-0.343497\pi$
$677$	−10.6535	−	10.6535i	−0.409448	−	0.409448i	−0.881546	+	0.472098i	$0.843497\pi$
$678$	5.21509	−	10.6750i	0.200284	−	0.409970i
$679$	10.3195	+	2.76511i	0.396027	+	0.106115i
$680$	13.0769	−	20.0513i	0.501477	−	0.768934i
$681$	2.70189	+	10.0836i	0.103537	+	0.386404i
$682$	−4.05763	+	8.30573i	−0.155375	+	0.318043i
$683$	−2.91904	+	5.05593i	−0.111694	+	0.193460i	−0.916453	−	0.400141i	$-0.868961\pi$
$683$	−2.91904	+	5.05593i	−0.111694	+	0.193460i	0.804759	+	0.593601i	$0.202294\pi$
$684$	21.9593	+	28.1817i	0.839633	+	1.07755i
$685$	14.4133	+	24.9645i	0.550703	+	0.953846i
$686$	−14.8588	−	7.25905i	−0.567313	−	0.277152i
$687$	−0.188093	+	0.325786i	−0.00717619	+	0.0124295i
$688$	10.1113	−	40.1113i	0.385489	−	1.52923i
$689$	24.3730	−	24.3730i	0.928539	−	0.928539i
$690$	−0.663053	−	0.984390i	−0.0252420	−	0.0374751i
$691$	4.52918	−	1.21359i	0.172298	−	0.0461672i	−0.171638	−	0.985160i	$-0.554906\pi$
$691$	4.52918	−	1.21359i	0.172298	−	0.0461672i	0.343937	+	0.938993i	$0.388239\pi$
$692$	−6.07865	+	8.04494i	−0.231075	+	0.305823i
$693$	1.32981	+	1.32981i	0.0505154	+	0.0505154i
$694$	−10.0346	+	20.5401i	−0.380907	+	0.779693i
$695$	13.0543	+	13.0543i	0.495178	+	0.495178i
$696$	0.395063	−	7.26814i	0.0149748	−	0.275498i
$697$	−9.52565	+	9.52565i	−0.360810	+	0.360810i
$698$	32.6155	+	6.36172i	1.23451	+	0.240795i
$699$	−1.58883	+	5.92961i	−0.0600952	+	0.224278i
$700$	−3.72126	−	4.77572i	−0.140650	−	0.180505i
$701$	15.8922	−	27.5262i	0.600242	−	1.03965i	−0.392542	−	0.919734i	$-0.628404\pi$
$701$	15.8922	−	27.5262i	0.600242	−	1.03965i	0.992784	−	0.119916i	$-0.0382624\pi$
$702$	19.7816	+	17.2184i	0.746608	+	0.649865i
$703$	11.2118	−	40.4967i	0.422860	−	1.52736i
$704$	−2.38056	+	6.13028i	−0.0897205	+	0.231044i
$705$	−1.36117	+	0.364724i	−0.0512645	+	0.0137363i
$706$	11.5976	+	2.26215i	0.436483	+	0.0851370i
$707$	2.39187	−	8.92657i	0.0899554	−	0.335718i
$708$	1.20347	−	9.69765i	0.0452291	−	0.364460i
$709$			24.6900i			0.927251i	0.886031	+	0.463625i	$0.153452\pi$
$709$			24.6900i			0.927251i	−0.886031	+	0.463625i	$0.846548\pi$
$710$	8.21319	+	12.1936i	0.308235	+	0.457617i
$711$	18.0689	−	18.0689i	0.677638	−	0.677638i
$712$	17.9627	−	9.10857i	0.673181	−	0.341358i
$713$			8.25423i			0.309123i
$714$	−0.374865	−	5.41116i	−0.0140290	−	0.202507i
$715$	−5.14634	+	1.37896i	−0.192462	+	0.0515701i
$716$	8.82486	+	11.3255i	0.329801	+	0.423254i
$717$		−	11.1134i		−	0.415038i
$718$	41.7898	+	20.4157i	1.55958	+	0.761909i
$719$	−34.9069	−	20.1535i	−1.30181	−	0.751600i	−0.321095	−	0.947047i	$-0.604051\pi$
$719$	−34.9069	−	20.1535i	−1.30181	−	0.751600i	−0.980714	+	0.195447i	$0.937384\pi$
$720$	−3.17640	+	12.6008i	−0.118377	+	0.469602i
$721$	−2.18302	+	8.14714i	−0.0812999	+	0.303415i
$722$	−33.6886	+	22.6916i	−1.25376	+	0.844492i
$723$	−7.46892	+	12.9365i	−0.277772	+	0.481115i
$724$	−8.84289	−	20.9078i	−0.328643	−	0.777031i
$725$	−11.8502	−	6.84171i	−0.440105	−	0.254095i
$726$	−7.08708	−	6.16876i	−0.263026	−	0.228944i
$727$	1.68057	−	6.27196i	0.0623287	−	0.232614i	−0.927734	−	0.373243i	$-0.878246\pi$
$727$	1.68057	−	6.27196i	0.0623287	−	0.232614i	0.990062	+	0.140629i	$0.0449125\pi$
$728$	−12.2699	−	4.01310i	−0.454754	−	0.148735i
$729$			7.13935i			0.264420i
$730$	10.4471	−	0.723735i	0.386664	−	0.0267866i
$731$	−18.0315	−	67.2946i	−0.666921	−	2.48898i
$732$	7.87055	−	10.4165i	0.290904	−	0.385004i
$733$	−3.85655	−	1.03336i	−0.142445	−	0.0381680i	0.186892	−	0.982380i	$-0.440159\pi$
$733$	−3.85655	−	1.03336i	−0.142445	−	0.0381680i	−0.329337	+	0.944212i	$0.606825\pi$
$734$	−12.5136	+	0.866896i	−0.461885	+	0.0319977i
$735$	−4.85519	−	1.30094i	−0.179086	−	0.0479860i
$736$	0.492859	+	5.85149i	0.0181670	+	0.215689i
$737$	1.77482	+	3.07408i	0.0653764	+	0.113235i
$738$	3.20997	−	6.57061i	0.118161	−	0.241868i
$739$	−4.33895	−	4.33895i	−0.159611	−	0.159611i	0.622783	−	0.782394i	$-0.286002\pi$
$739$	−4.33895	−	4.33895i	−0.159611	−	0.159611i	−0.782394	+	0.622783i	$0.786002\pi$
$740$	14.1255	−	5.83677i	0.519265	−	0.214564i
$741$	−16.2166	+	16.2166i	−0.595732	+	0.595732i
$742$	7.90589	−	2.71649i	0.290234	−	0.0997256i
$743$	27.8324	−	16.0691i	1.02107	−	0.589516i	0.106658	−	0.994296i	$-0.465985\pi$
$743$	27.8324	−	16.0691i	1.02107	−	0.589516i	0.914414	+	0.404779i	$0.132652\pi$
$744$	−10.7742	+	9.66329i	−0.395001	+	0.354274i
$745$	5.50999	−	20.5636i	0.201870	−	0.753391i
$746$	−24.6573	+	28.3279i	−0.902769	+	1.03716i
$747$	7.74318	−	28.8979i	0.283308	−	1.05732i
$748$	1.52724	+	10.9699i	0.0558414	+	0.401100i
$749$	−10.3693	+	2.77845i	−0.378887	+	0.101522i
$750$	−7.26288	−	6.32178i	−0.265203	−	0.230839i
$751$	7.65582			0.279365			0.139682	−	0.990196i	$-0.455392\pi$
$751$	7.65582			0.279365			0.139682	+	0.990196i	$0.455392\pi$
$752$	6.76064	+	1.70422i	0.246535	+	0.0621466i
$753$	16.3244	+	4.37411i	0.594894	+	0.159401i
$754$	−29.1070	+	2.01643i	−1.06001	+	0.0734339i
$755$	−13.5174	+	23.4128i	−0.491948	+	0.852079i
$756$	2.47763	+	5.85800i	0.0901105	+	0.213053i
$757$	18.2258	+	10.5227i	0.662429	+	0.382454i	0.793202	−	0.608959i	$-0.208412\pi$
$757$	18.2258	+	10.5227i	0.662429	+	0.382454i	−0.130773	+	0.991412i	$0.541746\pi$
$758$	24.5128	+	4.78128i	0.890345	+	0.173664i
$759$	0.530418	+	0.142125i	0.0192529	+	0.00515881i
$760$	−23.3312	−	7.63089i	−0.846311	−	0.276801i
$761$	8.03458	−	13.9163i	0.291253	−	0.504466i	−0.682853	−	0.730556i	$-0.739261\pi$
$761$	8.03458	−	13.9163i	0.291253	−	0.504466i	0.974106	+	0.226090i	$0.0725944\pi$
$762$	1.82520	−	0.627146i	0.0661201	−	0.0227191i
$763$	−14.6967			−0.532056
$764$	4.36657	−	35.1862i	0.157977	−	1.27299i
$765$	5.66451	+	21.1402i	0.204801	+	0.764327i
$766$	34.8597	−	40.0491i	1.25953	−	1.44703i
$767$	−39.1704			−1.41436
$768$	−7.06091	+	7.49371i	−0.254789	+	0.270406i
$769$	−9.31156	−	9.31156i	−0.335783	−	0.335783i	0.518994	−	0.854778i	$-0.326307\pi$
$769$	−9.31156	−	9.31156i	−0.335783	−	0.335783i	−0.854778	+	0.518994i	$0.826307\pi$
$770$	−1.26825	−	0.247376i	−0.0457047	−	0.00891480i
$771$	−1.64896			−0.0593860
$772$	6.65123	+	0.825411i	0.239383	+	0.0297072i
$773$	−1.97182	−	0.528348i	−0.0709216	−	0.0190034i	0.223184	−	0.974776i	$-0.428355\pi$
$773$	−1.97182	−	0.528348i	−0.0709216	−	0.0190034i	−0.294105	+	0.955773i	$0.595022\pi$
$774$	21.1278	+	31.3670i	0.759423	+	1.12747i
$775$	7.04173	+	26.2801i	0.252946	+	0.944009i
$776$	−28.6087	−	18.6578i	−1.02699	−	0.669776i
$777$	1.75635	−	2.98466i	0.0630088	−	0.107074i
$778$	−10.0578	+	0.696764i	−0.360588	+	0.0249802i
$779$	11.9631	+	6.90692i	0.428624	+	0.247466i
$780$	−8.27816	−	1.02731i	−0.296406	−	0.0367837i
$781$	−6.57025	−	1.76049i	−0.235102	−	0.0629954i
$782$	5.52507	+	8.20270i	0.197576	+	0.293328i
$783$	10.1647	+	10.1647i	0.363258	+	0.363258i
$784$	17.8445	+	17.3218i	0.637305	+	0.618635i
$785$	−16.2844	+	16.2844i	−0.581215	+	0.581215i
$786$	−5.32515	−	15.4979i	−0.189942	−	0.552794i
$787$	−1.90649	+	1.90649i	−0.0679590	+	0.0679590i	−0.740269	−	0.672310i	$-0.765302\pi$
$787$	−1.90649	+	1.90649i	−0.0679590	+	0.0679590i	0.672310	+	0.740269i	$0.265302\pi$
$788$	−1.43328	+	1.89691i	−0.0510583	+	0.0675745i
$789$	1.95519	+	7.29688i	0.0696068	+	0.259776i
$790$	−3.36124	+	17.2325i	−0.119587	+	0.613105i
$791$	−8.16697	−	8.16697i	−0.290384	−	0.290384i
$792$	−2.71915	−	5.36234i	−0.0966206	−	0.190543i
$793$	−45.3211	−	26.1661i	−1.60940	−	0.929187i
$794$	−20.1343	+	6.91823i	−0.714541	+	0.245519i
$795$	4.67796	−	2.70082i	0.165910	−	0.0957883i
$796$	1.59653	−	12.8650i	0.0565874	−	0.455986i
$797$	43.8559	+	25.3202i	1.55345	+	0.896887i	0.997857	+	0.0654363i	$0.0208439\pi$
$797$	43.8559	+	25.3202i	1.55345	+	0.896887i	0.555598	+	0.831451i	$0.312489\pi$
$798$	−5.26018	+	1.80742i	−0.186209	+	0.0639819i
$799$	11.3423	−	3.03916i	0.401262	−	0.107518i
$800$	6.56112	+	18.2097i	0.231971	+	0.643811i
$801$	−4.76567	+	17.7857i	−0.168387	+	0.628427i
$802$	−4.63260	−	13.4824i	−0.163583	−	0.476080i
$803$	−3.42602	+	3.42602i	−0.120902	+	0.120902i
$804$	0.766334	+	5.50445i	0.0270265	+	0.194127i
$805$	−1.11450	+	0.298629i	−0.0392809	+	0.0105253i
$806$	43.7584	+	38.0883i	1.54132	+	1.34160i
$807$	5.96803	−	3.44564i	0.210084	−	0.121292i
$808$	−16.1393	+	24.7470i	−0.567780	+	0.870598i
$809$	13.3864	+	3.58688i	0.470641	+	0.126108i	0.486341	−	0.873769i	$-0.338331\pi$
$809$	13.3864	+	3.58688i	0.470641	+	0.126108i	−0.0157004	+	0.999877i	$0.504998\pi$
$810$	−5.40408	−	8.02307i	−0.189880	−	0.281902i
$811$	11.0641	−	41.2917i	0.388512	−	1.44995i	−0.444043	−	0.896006i	$-0.646456\pi$
$811$	11.0641	−	41.2917i	0.388512	−	1.44995i	0.832555	−	0.553942i	$-0.186877\pi$
$812$	−6.55744	−	2.65926i	−0.230121	−	0.0933217i
$813$	1.02115	−	1.02115i	0.0358132	−	0.0358132i
$814$	−3.15659	+	6.32778i	−0.110638	+	0.221788i
$815$		−	20.8705i		−	0.731062i
$816$	−4.23868	+	16.8148i	−0.148383	+	0.588636i
$817$	−61.8688	+	35.7200i	−2.16452	+	1.24968i
$818$	5.49695	−	28.1820i	0.192196	−	0.985359i
$819$	10.2213	−	5.90127i	0.357161	−	0.206207i
$820$	0.692831	+	4.97649i	0.0241947	+	0.173787i
$821$	−16.9088	−	4.53070i	−0.590122	−	0.158123i	−0.0486128	−	0.998818i	$-0.515480\pi$
$821$	−16.9088	−	4.53070i	−0.590122	−	0.158123i	−0.541509	+	0.840695i	$0.682147\pi$
$822$	−15.7506	−	13.7097i	−0.549365	−	0.478180i
$823$	−22.7987	+	39.4885i	−0.794712	+	1.37648i	0.128310	+	0.991734i	$0.459045\pi$
$823$	−22.7987	+	39.4885i	−0.794712	+	1.37648i	−0.923022	+	0.384747i	$0.874289\pi$
$824$	14.7301	−	22.5862i	0.513148	−	0.786828i
$825$	1.81001			0.0630165
$826$	−8.53572	−	4.16999i	−0.296996	−	0.145093i
$827$	−6.81654	−	11.8066i	−0.237034	−	0.410555i	0.722828	−	0.691028i	$-0.242842\pi$
$827$	−6.81654	−	11.8066i	−0.237034	−	0.410555i	−0.959862	+	0.280473i	$0.909509\pi$
$828$	−4.28342	−	3.23649i	−0.148859	−	0.112476i
$829$	−5.97565	−	3.45004i	−0.207543	−	0.119825i	0.392626	−	0.919698i	$-0.371567\pi$
$829$	−5.97565	−	3.45004i	−0.207543	−	0.119825i	−0.600169	+	0.799873i	$0.704900\pi$
$830$	6.67970	+	19.4401i	0.231856	+	0.674777i
$831$	3.36371	−	0.901304i	0.116686	−	0.0312659i
$832$	33.2949	+	24.3883i	1.15429	+	0.845512i
$833$	40.4572	+	10.8405i	1.40176	+	0.375600i
$834$	−12.0160	−	5.87024i	−0.416081	−	0.203270i
$835$	−9.36999	+	2.51068i	−0.324262	+	0.0868857i
$836$	10.4602	−	4.42412i	0.361774	−	0.153012i
$837$		−	28.5825i		−	0.987956i
$838$	6.95020	−	35.6325i	0.240091	−	1.23090i
$839$	43.0617	+	24.8617i	1.48666	+	0.858321i	0.999884	−	0.0152083i	$-0.00484115\pi$
$839$	43.0617	+	24.8617i	1.48666	+	0.858321i	0.486771	+	0.873529i	$0.338174\pi$
$840$	−1.69455	−	1.10514i	−0.0584676	−	0.0381309i
$841$	13.0073			0.448527
$842$	7.50669	+	3.66728i	0.258698	+	0.126383i
$843$			13.0203i			0.448442i
$844$	33.0711	+	4.10410i	1.13836	+	0.141269i
$845$			17.1046i			0.588415i
$846$	−5.28682	+	3.56103i	−0.181765	+	0.122431i
$847$	−7.91033	+	4.56703i	−0.271802	+	0.156925i
$848$	−26.7224	+	0.397228i	−0.917652	+	0.0136409i
$849$	0.377252	+	1.40793i	0.0129473	+	0.0483199i
$850$	24.5887	+	21.4026i	0.843385	+	0.734102i
$851$	−0.0523545	+	6.31411i	−0.00179469	+	0.216445i
$852$	−8.49689	−	6.42013i	−0.291099	−	0.219950i
$853$	4.03070	−	6.98138i	0.138009	−	0.239038i	−0.788734	−	0.614734i	$-0.789263\pi$
$853$	4.03070	−	6.98138i	0.138009	−	0.239038i	0.926743	+	0.375697i	$0.122597\pi$
$854$	−7.09044	−	10.5267i	−0.242630	−	0.360217i
$855$	19.4357	−	11.2212i	0.664689	−	0.383758i
$856$	34.2694	+	1.86272i	1.17130	+	0.0636666i
$857$	−13.6459	−	13.6459i	−0.466136	−	0.466136i	0.434524	−	0.900660i	$-0.356917\pi$
$857$	−13.6459	−	13.6459i	−0.466136	−	0.466136i	−0.900660	+	0.434524i	$0.856917\pi$
$858$	3.20101	−	2.15610i	0.109281	−	0.0736079i
$859$	33.9956			1.15992			0.579958	−	0.814647i	$-0.303069\pi$
$859$	33.9956			1.15992			0.579958	+	0.814647i	$0.303069\pi$
$860$	−24.0800	−	9.76526i	−0.821123	−	0.332992i
$861$	0.805018	+	0.805018i	0.0274349	+	0.0274349i
$862$	−8.82941	−	7.68533i	−0.300731	−	0.261763i
$863$	13.9659	+	8.06324i	0.475406	+	0.274476i	0.718500	−	0.695527i	$-0.244829\pi$
$863$	13.9659	+	8.06324i	0.475406	+	0.274476i	−0.243094	+	0.970003i	$0.578162\pi$
$864$	−1.70666	−	20.2624i	−0.0580617	−	0.689340i
$865$	4.47876	+	4.47876i	0.152282	+	0.152282i
$866$	−23.2780	−	11.3721i	−0.791019	−	0.386440i
$867$	4.72747	+	17.6432i	0.160553	+	0.599193i
$868$	5.48070	+	12.9583i	0.186027	+	0.439835i
$869$	−4.06160	−	7.03490i	−0.137780	−	0.238643i
$870$	−4.48777	−	0.875349i	−0.152150	−	0.0296771i
$871$	21.5179	−	5.76570i	0.729105	−	0.195363i
$872$	44.6571	+	14.6059i	1.51228	+	0.494619i
$873$	30.1623	−	8.08196i	1.02084	−	0.273533i
$874$	6.65831	−	7.64950i	0.225221	−	0.258748i
$875$	−8.10655	+	4.68032i	−0.274051	+	0.158224i
$876$	−6.98662	+	2.95498i	−0.236056	+	0.0998394i
$877$	−17.6890	−	17.6890i	−0.597317	−	0.597317i	0.342281	−	0.939598i	$-0.388801\pi$
$877$	−17.6890	−	17.6890i	−0.597317	−	0.597317i	−0.939598	+	0.342281i	$0.888801\pi$
$878$	26.6504	−	30.6177i	0.899406	−	1.03330i
$879$	−0.756745	+	1.31072i	−0.0255244	+	0.0442095i
$880$	3.60785	+	2.01209i	0.121621	+	0.0678276i
$881$	6.67641	−	3.85463i	0.224934	−	0.129866i	−0.383299	−	0.923624i	$-0.625212\pi$
$881$	6.67641	−	3.85463i	0.224934	−	0.129866i	0.608233	+	0.793759i	$0.291879\pi$
$882$	−22.6822	+	1.57134i	−0.763750	+	0.0529098i
$883$	−10.6637	−	18.4701i	−0.358863	−	0.621568i	0.628909	−	0.777479i	$-0.283502\pi$
$883$	−10.6637	−	18.4701i	−0.358863	−	0.621568i	−0.987771	+	0.155911i	$0.950169\pi$
$884$	68.9801	+	8.56036i	2.32005	+	0.287916i
$885$	−5.92929	−	1.58875i	−0.199311	−	0.0534052i
$886$	29.0615	−	9.98562i	0.976339	−	0.335474i
$887$			8.87337i			0.297938i	0.988842	+	0.148969i	$0.0475955\pi$
$887$			8.87337i			0.297938i	−0.988842	+	0.148969i	$0.952404\pi$
$888$	−8.30306	+	7.32365i	−0.278632	+	0.245766i
$889$		−	1.87619i		−	0.0629253i
$890$	−4.11113	−	11.9647i	−0.137805	−	0.401059i
$891$	4.32306	+	1.15836i	0.144828	+	0.0388066i
$892$	−7.76125	+	6.04759i	−0.259866	+	0.202488i
$893$	−6.02049	−	10.4278i	−0.201468	−	0.348953i
$894$	1.06578	+	15.3845i	0.0356451	+	0.514535i
$895$	7.81073	−	4.50953i	0.261084	−	0.150737i
$896$	4.65905	+	8.85902i	0.155648	+	0.295959i
$897$	1.72312	−	2.98453i	0.0575332	−	0.0996505i
$898$	7.08432	+	6.16637i	0.236407	+	0.205774i
$899$	22.4852	+	22.4852i	0.749923	+	0.749923i
$900$	−16.3988	−	6.65025i	−0.546626	−	0.221675i
$901$	−38.9804	+	22.5053i	−1.29863	+	0.749762i
$902$	−1.75347	−	1.52626i	−0.0583841	−	0.0508189i
$903$	−5.68711	+	1.52386i	−0.189255	+	0.0507108i
$904$	16.6995	+	32.9326i	0.555417	+	1.09532i
$905$	−13.7740	+	3.69074i	−0.457864	+	0.122684i
$906$	3.74916	−	19.2213i	0.124557	−	0.638585i
$907$	−15.3928	−	26.6612i	−0.511111	−	0.885270i	−0.999917	−	0.0128777i	$-0.995901\pi$
$907$	−15.3928	−	26.6612i	−0.511111	−	0.885270i	0.488806	−	0.872392i	$-0.337433\pi$
$908$	−30.0664	−	12.1929i	−0.997789	−	0.404637i
$909$	−6.99105	−	26.0909i	−0.231878	−	0.865382i
$910$	−3.55961	+	7.28631i	−0.118000	+	0.241539i
$911$	8.45265	+	8.45265i	0.280049	+	0.280049i	0.833128	−	0.553080i	$-0.186547\pi$
$911$	8.45265	+	8.45265i	0.280049	+	0.280049i	−0.553080	+	0.833128i	$0.686547\pi$
$912$	17.7798	−	0.264296i	0.588747	−	0.00875170i
$913$	−8.23633	−	4.75525i	−0.272583	−	0.157376i
$914$	−21.3662	+	24.5469i	−0.706732	+	0.811941i
$915$	−5.79904	−	5.79904i	−0.191710	−	0.191710i
$916$	−0.455434	−	1.07681i	−0.0150480	−	0.0355788i
$917$	−15.9309			−0.526084
$918$	−19.1321	−	28.4041i	−0.631452	−	0.937474i
$919$	−27.3002	−	27.3002i	−0.900551	−	0.900551i	0.0949330	−	0.995484i	$-0.469736\pi$
$919$	−27.3002	−	27.3002i	−0.900551	−	0.900551i	−0.995484	+	0.0949330i	$0.969736\pi$
$920$	3.68328	+	0.200206i	0.121434	+	0.00660060i
$921$	−11.6161	+	6.70659i	−0.382765	+	0.220990i
$922$	8.40452	−	5.66101i	0.276788	−	0.186435i
$923$	−21.3441	+	36.9691i	−0.702551	+	1.21685i
$924$	0.927074	−	0.129068i	0.0304985	−	0.00424602i
$925$	5.21992	+	20.1478i	0.171630	+	0.662454i
$926$	15.2700	−	17.5432i	0.501804	−	0.576505i
$927$	6.38061	+	23.8128i	0.209567	+	0.782114i
$928$	17.2825	+	14.5973i	0.567326	+	0.479181i
$929$	3.09652	−	1.78778i	0.101593	−	0.0586550i	−0.448342	−	0.893862i	$-0.647985\pi$
$929$	3.09652	−	1.78778i	0.101593	−	0.0586550i	0.549936	+	0.835207i	$0.314652\pi$
$930$	5.07892	+	7.54034i	0.166544	+	0.247257i
$931$		−	42.9493i		−	1.40761i
$932$	−11.7267	−	15.0496i	−0.384121	−	0.492966i
$933$		−	9.18369i		−	0.300660i
$934$	−17.1598	+	35.1251i	−0.561487	+	1.14933i
$935$	6.95739			0.227531
$936$	−36.9231	+	7.77334i	−1.20687	+	0.254079i
$937$	−6.61176	−	3.81730i	−0.215997	−	0.124706i	0.388099	−	0.921618i	$-0.373132\pi$
$937$	−6.61176	−	3.81730i	−0.215997	−	0.124706i	−0.604095	+	0.796912i	$0.706465\pi$
$938$	5.30282	+	1.03433i	0.173143	+	0.0337720i
$939$		−	9.69738i		−	0.316462i
$940$	1.64590	−	4.05862i	0.0536834	−	0.132377i
$941$	−1.04093	+	0.278917i	−0.0339334	+	0.00909244i	−0.275746	−	0.961231i	$-0.588925\pi$
$941$	−1.04093	+	0.278917i	−0.0339334	+	0.00909244i	0.241812	+	0.970323i	$0.422258\pi$
$942$	7.32273	−	14.9892i	0.238587	−	0.488374i
$943$	−2.00506	−	0.537255i	−0.0652938	−	0.0174954i
$944$	21.7923	+	21.1539i	0.709278	+	0.688500i
$945$	3.85925	−	1.03408i	0.125542	−	0.0336387i
$946$	11.3699	−	3.90674i	0.369667	−	0.127019i
$947$	9.25735	+	5.34473i	0.300823	+	0.173680i	0.642813	−	0.766023i	$-0.277767\pi$
$947$	9.25735	+	5.34473i	0.300823	+	0.173680i	−0.341989	+	0.939704i	$0.611101\pi$
$948$	−1.75372	−	12.5967i	−0.0569582	−	0.409122i
$949$	15.2036	+	26.3334i	0.493529	+	0.854818i
$950$	14.6731	−	30.0350i	0.476059	−	0.974464i
$951$	−10.1669			−0.329683
$952$	14.1203	+	9.20888i	0.457642	+	0.298461i
$953$	2.51539	−	4.35678i	0.0814813	−	0.141130i	−0.822405	−	0.568902i	$-0.807368\pi$
$953$	2.51539	−	4.35678i	0.0814813	−	0.141130i	0.903886	+	0.427773i	$0.140702\pi$
$954$	16.0419	−	18.4300i	0.519375	−	0.596692i
$955$	−21.5134	−	5.76450i	−0.696157	−	0.186535i
$956$	27.5578	+	20.8223i	0.891283	+	0.673441i
$957$	1.83206	−	1.05774i	0.0592221	−	0.0341919i
$958$	44.8294	+	8.74408i	1.44837	+	0.282508i
$959$	−17.5802	+	10.1499i	−0.567695	+	0.327759i
$960$	4.05072	+	5.04214i	0.130737	+	0.162735i
$961$		−	32.2266i		−	1.03957i
$962$	33.2316	+	29.4134i	1.07143	+	0.948326i
$963$	−22.1869	+	22.1869i	−0.714963	+	0.714963i
$964$	−18.0847	−	42.7587i	−0.582468	−	1.37716i
$965$	1.08966	−	4.06667i	0.0350774	−	0.130911i
$966$	0.693215	−	0.466927i	0.0223038	−	0.0150231i
$967$	1.46474	+	0.392475i	0.0471028	+	0.0126211i	0.282293	−	0.959328i	$-0.408905\pi$
$967$	1.46474	+	0.392475i	0.0471028	+	0.0126211i	−0.235191	+	0.971949i	$0.575571\pi$
$968$	28.5750	−	6.01583i	0.918436	−	0.193356i
$969$	25.9356	−	14.9739i	0.833172	−	0.481032i
$970$	−14.0863	+	16.1832i	−0.452283	+	0.519612i
$971$	−14.7938	+	3.96399i	−0.474756	+	0.127210i	−0.488260	−	0.872698i	$-0.662368\pi$
$971$	−14.7938	+	3.96399i	−0.474756	+	0.127210i	0.0135038	+	0.999909i	$0.495701\pi$
$972$	22.7986	+	17.2263i	0.731264	+	0.552533i
$973$	−9.19295	+	9.19295i	−0.294712	+	0.294712i
$974$	−10.0094	+	3.43925i	−0.320720	+	0.110201i
$975$	2.94000	−	10.9722i	0.0941555	−	0.351393i
$976$	11.0832	+	39.0329i	0.354765	+	1.24941i
$977$	−2.15614	+	0.577736i	−0.0689810	+	0.0184834i	−0.293144	−	0.956068i	$-0.594702\pi$
$977$	−2.15614	+	0.577736i	−0.0689810	+	0.0184834i	0.224163	+	0.974552i	$0.428035\pi$
$978$	4.91276	+	14.2978i	0.157093	+	0.457192i
$979$	5.06919	+	2.92670i	0.162012	+	0.0935376i
$980$	12.3227	−	9.60186i	0.393633	−	0.306720i
$981$	−37.2010	+	21.4780i	−1.18774	+	0.685741i
$982$	−15.5274	−	45.1898i	−0.495499	−	1.44207i
$983$	−20.0335	−	11.5664i	−0.638970	−	0.368910i	0.145248	−	0.989395i	$-0.453602\pi$
$983$	−20.0335	−	11.5664i	−0.638970	−	0.368910i	−0.784218	+	0.620486i	$0.786935\pi$
$984$	−1.64607	−	3.24616i	−0.0524748	−	0.103484i
$985$	1.05604	+	1.05604i	0.0336483	+	0.0336483i
$986$	37.3956	+	7.29409i	1.19092	+	0.232291i
$987$	−0.256841	−	0.958544i	−0.00817534	−	0.0305108i
$988$	−9.82839	−	70.5957i	−0.312683	−	2.24595i
$989$	7.59095	−	7.59095i	0.241378	−	0.241378i
$990$	−3.57179	+	1.22728i	−0.113519	+	0.0390055i
$991$	−8.43333	+	8.43333i	−0.267894	+	0.267894i	−0.828251	−	0.560357i	$-0.810664\pi$
$991$	−8.43333	+	8.43333i	−0.267894	+	0.267894i	0.560357	+	0.828251i	$0.310664\pi$
$992$	−3.77526	−	44.8219i	−0.119865	−	1.42310i
$993$	−2.83578	−	2.83578i	−0.0899907	−	0.0899907i
$994$	−8.58681	+	5.78379i	−0.272357	+	0.183451i
$995$	−7.86584	−	2.10764i	−0.249364	−	0.0668168i
$996$	−9.15213	−	11.7455i	−0.289996	−	0.372171i
$997$	15.4025	+	8.89263i	0.487802	+	0.281632i	0.723662	−	0.690155i	$-0.242457\pi$
$997$	15.4025	+	8.89263i	0.487802	+	0.281632i	−0.235860	+	0.971787i	$0.575791\pi$
$998$	0.313563	+	4.52626i	0.00992565	+	0.143276i
$999$	0.181292	−	21.8643i	0.00573581	−	0.691757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bl.a.51.11	yes	296
16.11	odd	4		592.2.bf.a.347.24	✓	296
37.8	odd	12		592.2.bf.a.563.24	yes	296
592.267	even	12	inner	592.2.bl.a.267.11	yes	296

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.bf.a.347.24	✓	296	16.11	odd	4
592.2.bf.a.563.24	yes	296	37.8	odd	12
592.2.bl.a.51.11	yes	296	1.1	even	1	trivial
592.2.bl.a.267.11	yes	296	592.267	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27069 - 0.620773i) q^{2} +(0.166554 - 0.621587i) q^{3} +(1.22928 + 1.57761i) q^{4} +(1.08801 - 0.628166i) q^{5} +(-0.597501 + 0.686449i) q^{6} +(0.442359 + 0.766189i) q^{7} +(-0.582689 - 2.76776i) q^{8} +(2.23945 + 1.29295i) q^{9} +(-1.77247 + 0.122790i) q^{10} +(0.581266 - 0.581266i) q^{11} +(1.18537 - 0.501347i) q^{12} +(-2.57947 - 4.46778i) q^{13} +(-0.0864699 - 1.24819i) q^{14} +(-0.209247 - 0.780919i) q^{15} +(-0.977734 + 3.87866i) q^{16} +(1.74360 + 6.50722i) q^{17} +(-2.04301 - 3.03311i) q^{18} +(5.98256 - 3.45403i) q^{19} +(2.32848 + 0.944276i) q^{20} +(0.549929 - 0.147353i) q^{21} +(-1.09944 + 0.377772i) q^{22} +(-0.734026 + 0.734026i) q^{23} +(-1.81745 - 0.0987881i) q^{24} +(-1.71082 + 2.96322i) q^{25} +(0.504221 + 7.27840i) q^{26} +(2.54176 - 2.54176i) q^{27} +(-0.664966 + 1.63973i) q^{28} +3.99909i q^{29} +(-0.218887 + 1.12220i) q^{30} +(5.62257 - 5.62257i) q^{31} +(3.65016 - 4.32161i) q^{32} +(-0.264495 - 0.458119i) q^{33} +(1.82394 - 9.35101i) q^{34} +(0.962587 + 0.555750i) q^{35} +(0.713141 + 5.12238i) q^{36} +(4.33668 - 4.26535i) q^{37} +(-9.74612 + 0.675175i) q^{38} +(-3.20673 + 0.859241i) q^{39} +(-2.37258 - 2.64533i) q^{40} +(0.999834 + 1.73176i) q^{41} +(-0.790259 - 0.154142i) q^{42} -10.3415 q^{43} +(1.63155 + 0.202474i) q^{44} +3.24874 q^{45} +(1.38838 - 0.477052i) q^{46} -1.74303i q^{47} +(2.24808 + 1.25375i) q^{48} +(3.10864 - 5.38432i) q^{49} +(4.01340 - 2.70329i) q^{50} +4.33521 q^{51} +(3.87753 - 9.56156i) q^{52} +(1.72926 + 6.45368i) q^{53} +(-4.80764 + 1.65192i) q^{54} +(0.267295 - 0.997558i) q^{55} +(1.86287 - 1.67079i) q^{56} +(-1.15056 - 4.29396i) q^{57} +(2.48253 - 5.08159i) q^{58} +(3.79636 - 6.57548i) q^{59} +(0.974766 - 1.29008i) q^{60} +(8.78495 - 5.07200i) q^{61} +(-10.6349 + 3.65418i) q^{62} +2.28778i q^{63} +(-7.32095 + 3.22548i) q^{64} +(-5.61301 - 3.24067i) q^{65} +(0.0517021 + 0.746317i) q^{66} +(-1.11761 + 4.17099i) q^{67} +(-8.12251 + 10.7499i) q^{68} +(0.334006 + 0.578515i) q^{69} +(-0.878150 - 1.30373i) q^{70} +(-4.13731 - 7.16603i) q^{71} +(2.27366 - 6.95163i) q^{72} -5.89407 q^{73} +(-8.15837 + 2.72783i) q^{74} +(1.55695 + 1.55695i) q^{75} +(12.8034 + 5.19219i) q^{76} +(0.702488 + 0.188231i) q^{77} +(4.60814 + 0.898827i) q^{78} +(2.55760 - 9.54511i) q^{79} +(1.37265 + 4.83422i) q^{80} +(2.72225 + 4.71507i) q^{81} +(-0.195442 - 2.82120i) q^{82} +(-2.99440 - 11.1752i) q^{83} +(0.908484 + 0.686438i) q^{84} +(5.98468 + 5.98468i) q^{85} +(13.1408 + 6.41974i) q^{86} +(2.48578 + 0.666063i) q^{87} +(-1.94750 - 1.27011i) q^{88} +(1.84295 + 6.87799i) q^{89} +(-4.12812 - 2.01673i) q^{90} +(2.28211 - 3.95272i) q^{91} +(-2.06033 - 0.255685i) q^{92} +(-2.55846 - 4.43137i) q^{93} +(-1.08203 + 2.21485i) q^{94} +(4.33941 - 7.51608i) q^{95} +(-2.07831 - 2.98867i) q^{96} +(8.53878 - 8.53878i) q^{97} +(-7.29254 + 4.91201i) q^{98} +(2.05326 - 0.550169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 296 q - 6 q^{3} - 12 q^{4} - 6 q^{5} - 4 q^{7} - 8 q^{10} + 8 q^{11} + 28 q^{12} - 2 q^{13} - 12 q^{14} - 12 q^{15} - 12 q^{16} - 8 q^{17} - 14 q^{18} - 6 q^{19} + 2 q^{20} - 6 q^{21} - 30 q^{22} + 30 q^{24}+ \cdots - 48 q^{99}+O(q^{100}) \) 296 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 - 4 * q^7 - 8 * q^10 + 8 * q^11 + 28 * q^12 - 2 * q^13 - 12 * q^14 - 12 * q^15 - 12 * q^16 - 8 * q^17 - 14 * q^18 - 6 * q^19 + 2 * q^20 - 6 * q^21 - 30 * q^22 + 30 * q^24 + 132 * q^25 - 8 * q^26 - 32 * q^28 - 70 * q^30 - 10 * q^32 - 4 * q^33 - 18 * q^34 - 6 * q^35 - 32 * q^36 - 20 * q^37 + 20 * q^38 - 8 * q^39 + 4 * q^40 + 10 * q^42 - 24 * q^43 + 40 * q^44 - 16 * q^45 - 32 * q^46 + 28 * q^48 - 128 * q^49 + 32 * q^50 + 60 * q^51 + 14 * q^52 - 26 * q^53 + 50 * q^54 - 8 * q^55 - 74 * q^56 - 12 * q^57 + 12 * q^58 - 2 * q^59 - 68 * q^60 - 6 * q^61 - 34 * q^62 - 24 * q^64 - 36 * q^65 - 116 * q^66 - 6 * q^67 - 28 * q^68 + 4 * q^69 + 14 * q^70 - 4 * q^71 - 86 * q^72 + 32 * q^73 + 40 * q^74 + 4 * q^75 + 14 * q^76 + 12 * q^77 - 18 * q^78 + 40 * q^79 - 12 * q^80 + 112 * q^81 + 84 * q^82 + 58 * q^83 + 132 * q^84 - 20 * q^85 - 46 * q^86 + 104 * q^87 - 56 * q^88 + 16 * q^89 + 4 * q^90 + 26 * q^91 - 76 * q^92 - 8 * q^93 + 86 * q^94 - 40 * q^95 - 144 * q^96 - 8 * q^97 + 26 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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