LMFDB - Embedded newform 560.2.bb.c.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.c.309.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32540 + 0.493263i) q^{2} +(-2.08897 + 2.08897i) q^{3} +(1.51338 - 1.30754i) q^{4} +(-2.21442 - 0.310380i) q^{5} +(1.73832 - 3.79914i) q^{6} -1.00000 q^{7} +(-1.36088 + 2.47952i) q^{8} -5.72761i q^{9} +O(q^{10})$	\(q+(-1.32540 + 0.493263i) q^{2} +(-2.08897 + 2.08897i) q^{3} +(1.51338 - 1.30754i) q^{4} +(-2.21442 - 0.310380i) q^{5} +(1.73832 - 3.79914i) q^{6} -1.00000 q^{7} +(-1.36088 + 2.47952i) q^{8} -5.72761i q^{9} +(3.08810 - 0.680914i) q^{10} +(-4.43987 + 4.43987i) q^{11} +(-0.429989 + 5.89284i) q^{12} +(0.101184 - 0.101184i) q^{13} +(1.32540 - 0.493263i) q^{14} +(5.27424 - 3.97749i) q^{15} +(0.580654 - 3.95763i) q^{16} -4.38194i q^{17} +(2.82522 + 7.59139i) q^{18} +(-3.97870 - 3.97870i) q^{19} +(-3.75710 + 2.42573i) q^{20} +(2.08897 - 2.08897i) q^{21} +(3.69459 - 8.07463i) q^{22} +1.06402 q^{23} +(-2.33681 - 8.02248i) q^{24} +(4.80733 + 1.37463i) q^{25} +(-0.0841988 + 0.184019i) q^{26} +(5.69790 + 5.69790i) q^{27} +(-1.51338 + 1.30754i) q^{28} +(2.74592 + 2.74592i) q^{29} +(-5.02854 + 7.87336i) q^{30} +1.33653 q^{31} +(1.18255 + 5.53187i) q^{32} -18.5495i q^{33} +(2.16145 + 5.80784i) q^{34} +(2.21442 + 0.310380i) q^{35} +(-7.48911 - 8.66806i) q^{36} +(2.01303 + 2.01303i) q^{37} +(7.23593 + 3.31083i) q^{38} +0.422739i q^{39} +(3.78315 - 5.06831i) q^{40} +6.25989i q^{41} +(-1.73832 + 3.79914i) q^{42} +(4.41676 + 4.41676i) q^{43} +(-0.913892 + 12.5245i) q^{44} +(-1.77774 + 12.6833i) q^{45} +(-1.41026 + 0.524843i) q^{46} +9.69091i q^{47} +(7.05441 + 9.48035i) q^{48} +1.00000 q^{49} +(-7.04970 + 0.549347i) q^{50} +(9.15376 + 9.15376i) q^{51} +(0.0208274 - 0.285432i) q^{52} +(-4.50422 - 4.50422i) q^{53} +(-10.3626 - 4.74144i) q^{54} +(11.2098 - 8.45369i) q^{55} +(1.36088 - 2.47952i) q^{56} +16.6228 q^{57} +(-4.99391 - 2.28499i) q^{58} +(6.66322 - 6.66322i) q^{59} +(2.78120 - 12.9158i) q^{60} +(-6.31967 - 6.31967i) q^{61} +(-1.77144 + 0.659263i) q^{62} +5.72761i q^{63} +(-4.29603 - 6.74864i) q^{64} +(-0.255469 + 0.192658i) q^{65} +(9.14979 + 24.5856i) q^{66} +(8.40678 - 8.40678i) q^{67} +(-5.72959 - 6.63156i) q^{68} +(-2.22271 + 2.22271i) q^{69} +(-3.08810 + 0.680914i) q^{70} +0.145220i q^{71} +(14.2017 + 7.79457i) q^{72} -5.54317 q^{73} +(-3.66103 - 1.67512i) q^{74} +(-12.9139 + 7.17082i) q^{75} +(-11.2236 - 0.818968i) q^{76} +(4.43987 - 4.43987i) q^{77} +(-0.208522 - 0.560300i) q^{78} +9.69338 q^{79} +(-2.51418 + 8.58364i) q^{80} -6.62268 q^{81} +(-3.08778 - 8.29688i) q^{82} +(2.13962 - 2.13962i) q^{83} +(0.429989 - 5.89284i) q^{84} +(-1.36007 + 9.70347i) q^{85} +(-8.03261 - 3.67536i) q^{86} -11.4723 q^{87} +(-4.96662 - 17.0508i) q^{88} -12.6158i q^{89} +(-3.90001 - 17.6874i) q^{90} +(-0.101184 + 0.101184i) q^{91} +(1.61027 - 1.39126i) q^{92} +(-2.79198 + 2.79198i) q^{93} +(-4.78017 - 12.8444i) q^{94} +(7.57562 + 10.0454i) q^{95} +(-14.0262 - 9.08559i) q^{96} +1.50782i q^{97} +(-1.32540 + 0.493263i) q^{98} +(25.4298 + 25.4298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) $ 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * q^10 - 2 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 + 18 * q^18 + 14 * q^19 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * q^50 + 8 * q^51 - 28 * q^52 + 30 * q^53 - 32 * q^54 - 6 * q^55 + 8 * q^56 + 76 * q^57 - 56 * q^58 + 2 * q^59 - 64 * q^60 + 30 * q^61 - 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 - 6 * q^67 + 36 * q^68 - 16 * q^69 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * q^80 - 82 * q^81 - 24 * q^82 - 10 * q^83 - 4 * q^84 - 32 * q^85 + 32 * q^86 + 4 * q^87 - 32 * q^88 + 158 * q^90 + 6 * q^91 + 92 * q^92 + 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 - 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.32540	+	0.493263i	−0.937201	+	0.348790i
$2$	−1.32540	+	0.493263i	−0.937201	+	0.348790i
$3$	−2.08897	+	2.08897i	−1.20607	+	1.20607i	−0.233779	+	0.972290i	$0.575109\pi$
$3$	−2.08897	+	2.08897i	−1.20607	+	1.20607i	−0.972290	+	0.233779i	$0.924891\pi$
$4$	1.51338	−	1.30754i	0.756691	−	0.653772i
$5$	−2.21442	−	0.310380i	−0.990320	−	0.138806i
$5$	−2.21442	−	0.310380i	−0.990320	−	0.138806i
$6$	1.73832	−	3.79914i	0.709664	−	1.55099i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.36088	+	2.47952i	−0.481143	+	0.876642i
$9$		−	5.72761i		−	1.90920i
$10$	3.08810	−	0.680914i	0.976543	−	0.215324i
$11$	−4.43987	+	4.43987i	−1.33867	+	1.33867i	−0.441320	+	0.897350i	$0.645490\pi$
$11$	−4.43987	+	4.43987i	−1.33867	+	1.33867i	−0.897350	+	0.441320i	$0.854510\pi$
$12$	−0.429989	+	5.89284i	−0.124127	+	1.70112i
$13$	0.101184	−	0.101184i	0.0280633	−	0.0280633i	−0.692936	−	0.720999i	$-0.743683\pi$
$13$	0.101184	−	0.101184i	0.0280633	−	0.0280633i	0.720999	+	0.692936i	$0.243683\pi$
$14$	1.32540	−	0.493263i	0.354229	−	0.131830i
$15$	5.27424	−	3.97749i	1.36180	−	1.02698i
$16$	0.580654	−	3.95763i	0.145163	−	0.989408i
$17$		−	4.38194i		−	1.06278i	−0.847128	−	0.531389i	$-0.821670\pi$
$17$		−	4.38194i		−	1.06278i	0.847128	−	0.531389i	$-0.178330\pi$
$18$	2.82522	+	7.59139i	0.665911	+	1.78931i
$19$	−3.97870	−	3.97870i	−0.912777	−	0.912777i	0.0837127	−	0.996490i	$-0.473322\pi$
$19$	−3.97870	−	3.97870i	−0.912777	−	0.912777i	−0.996490	+	0.0837127i	$0.973322\pi$
$20$	−3.75710	+	2.42573i	−0.840114	+	0.542410i
$21$	2.08897	−	2.08897i	0.455851	−	0.455851i
$22$	3.69459	−	8.07463i	0.787688	−	1.72152i
$23$	1.06402			0.221864			0.110932	−	0.993828i	$-0.464616\pi$
$23$	1.06402			0.221864			0.110932	+	0.993828i	$0.464616\pi$
$24$	−2.33681	−	8.02248i	−0.477000	−	1.63758i
$25$	4.80733	+	1.37463i	0.961466	+	0.274925i
$26$	−0.0841988	+	0.184019i	−0.0165127	+	0.0360891i
$27$	5.69790	+	5.69790i	1.09656	+	1.09656i
$28$	−1.51338	+	1.30754i	−0.286002	+	0.247103i
$29$	2.74592	+	2.74592i	0.509905	+	0.509905i	0.914497	−	0.404592i	$-0.132587\pi$
$29$	2.74592	+	2.74592i	0.509905	+	0.509905i	−0.404592	+	0.914497i	$0.632587\pi$
$30$	−5.02854	+	7.87336i	−0.918082	+	1.43747i
$31$	1.33653			0.240048			0.120024	−	0.992771i	$-0.461703\pi$
$31$	1.33653			0.240048			0.120024	+	0.992771i	$0.461703\pi$
$32$	1.18255	+	5.53187i	0.209048	+	0.977905i
$33$		−	18.5495i		−	3.22906i
$34$	2.16145	+	5.80784i	0.370686	+	0.996036i
$35$	2.21442	+	0.310380i	0.374306	+	0.0524638i
$36$	−7.48911	−	8.66806i	−1.24818	−	1.44468i
$37$	2.01303	+	2.01303i	0.330940	+	0.330940i	0.852944	−	0.522003i	$-0.174815\pi$
$37$	2.01303	+	2.01303i	0.330940	+	0.330940i	−0.522003	+	0.852944i	$0.674815\pi$
$38$	7.23593	+	3.31083i	1.17382	+	0.537088i
$39$			0.422739i			0.0676925i
$40$	3.78315	−	5.06831i	0.598168	−	0.801370i
$41$			6.25989i			0.977631i	0.872387	+	0.488815i	$0.162571\pi$
$41$			6.25989i			0.977631i	−0.872387	+	0.488815i	$0.837429\pi$
$42$	−1.73832	+	3.79914i	−0.268228	+	0.586220i
$43$	4.41676	+	4.41676i	0.673549	+	0.673549i	0.958533	−	0.284983i	$-0.0919880\pi$
$43$	4.41676	+	4.41676i	0.673549	+	0.673549i	−0.284983	+	0.958533i	$0.591988\pi$
$44$	−0.913892	+	12.5245i	−0.137774	+	1.88815i
$45$	−1.77774	+	12.6833i	−0.265009	+	1.89072i
$46$	−1.41026	+	0.524843i	−0.207931	+	0.0773839i
$47$			9.69091i			1.41356i	0.707431	+	0.706782i	$0.249854\pi$
$47$			9.69091i			1.41356i	−0.707431	+	0.706782i	$0.750146\pi$
$48$	7.05441	+	9.48035i	1.01822	+	1.36837i
$49$	1.00000			0.142857
$50$	−7.04970	+	0.549347i	−0.996978	+	0.0776894i
$51$	9.15376	+	9.15376i	1.28178	+	1.28178i
$52$	0.0208274	−	0.285432i	0.00288824	−	0.0395822i
$53$	−4.50422	−	4.50422i	−0.618702	−	0.618702i	0.326497	−	0.945198i	$-0.394132\pi$
$53$	−4.50422	−	4.50422i	−0.618702	−	0.618702i	−0.945198	+	0.326497i	$0.894132\pi$
$54$	−10.3626	−	4.74144i	−1.41017	−	0.645229i
$55$	11.2098	−	8.45369i	1.51153	−	1.13990i
$56$	1.36088	−	2.47952i	0.181855	−	0.331340i
$57$	16.6228			2.20174
$58$	−4.99391	−	2.28499i	−0.655733	−	0.300034i
$59$	6.66322	−	6.66322i	0.867478	−	0.867478i	−0.124715	−	0.992193i	$-0.539802\pi$
$59$	6.66322	−	6.66322i	0.867478	−	0.867478i	0.992193	+	0.124715i	$0.0398017\pi$
$60$	2.78120	−	12.9158i	0.359051	−	1.66742i
$61$	−6.31967	−	6.31967i	−0.809151	−	0.809151i	0.175354	−	0.984505i	$-0.443893\pi$
$61$	−6.31967	−	6.31967i	−0.809151	−	0.809151i	−0.984505	+	0.175354i	$0.943893\pi$
$62$	−1.77144	+	0.659263i	−0.224974	+	0.0837265i
$63$			5.72761i			0.721611i
$64$	−4.29603	−	6.74864i	−0.537004	−	0.843580i
$65$	−0.255469	+	0.192658i	−0.0316870	+	0.0238963i
$66$	9.14979	+	24.5856i	1.12626	+	3.02627i
$67$	8.40678	−	8.40678i	1.02705	−	1.02705i	0.0274279	−	0.999624i	$-0.491268\pi$
$67$	8.40678	−	8.40678i	1.02705	−	1.02705i	0.999624	−	0.0274279i	$-0.00873166\pi$
$68$	−5.72959	−	6.63156i	−0.694814	−	0.804194i
$69$	−2.22271	+	2.22271i	−0.267583	+	0.267583i
$70$	−3.08810	+	0.680914i	−0.369098	+	0.0813848i
$71$			0.145220i			0.0172344i	0.999963	+	0.00861720i	$0.00274297\pi$
$71$			0.145220i			0.0172344i	−0.999963	+	0.00861720i	$0.997257\pi$
$72$	14.2017	+	7.79457i	1.67369	+	0.918599i
$73$	−5.54317			−0.648779			−0.324390	−	0.945924i	$-0.605159\pi$
$73$	−5.54317			−0.648779			−0.324390	+	0.945924i	$0.605159\pi$
$74$	−3.66103	−	1.67512i	−0.425586	−	0.194729i
$75$	−12.9139	+	7.17082i	−1.49117	+	0.828015i
$76$	−11.2236	−	0.818968i	−1.28744	−	0.0939420i
$77$	4.43987	−	4.43987i	0.505970	−	0.505970i
$78$	−0.208522	−	0.560300i	−0.0236105	−	0.0634415i
$79$	9.69338			1.09059			0.545295	−	0.838244i	$-0.316418\pi$
$79$	9.69338			1.09059			0.545295	+	0.838244i	$0.316418\pi$
$80$	−2.51418	+	8.58364i	−0.281094	+	0.959680i
$81$	−6.62268			−0.735853
$82$	−3.08778	−	8.29688i	−0.340988	−	0.916237i
$83$	2.13962	−	2.13962i	0.234854	−	0.234854i	−0.579861	−	0.814715i	$-0.696893\pi$
$83$	2.13962	−	2.13962i	0.234854	−	0.234854i	0.814715	+	0.579861i	$0.196893\pi$
$84$	0.429989	−	5.89284i	0.0469157	−	0.642961i
$85$	−1.36007	+	9.70347i	−0.147520	+	1.05249i
$86$	−8.03261	−	3.67536i	−0.866178	−	0.396324i
$87$	−11.4723			−1.22996
$88$	−4.96662	−	17.0508i	−0.529444	−	1.81763i
$89$		−	12.6158i		−	1.33727i	−0.743591	−	0.668634i	$-0.766879\pi$
$89$		−	12.6158i		−	1.33727i	0.743591	−	0.668634i	$-0.233121\pi$
$90$	−3.90001	−	17.6874i	−0.411097	−	1.86442i
$91$	−0.101184	+	0.101184i	−0.0106069	+	0.0106069i
$92$	1.61027	−	1.39126i	0.167882	−	0.145048i
$93$	−2.79198	+	2.79198i	−0.289515	+	0.289515i
$94$	−4.78017	−	12.8444i	−0.493037	−	1.32479i
$95$	7.57562	+	10.0454i	0.777242	+	1.03064i
$96$	−14.0262	−	9.08559i	−1.43155	−	0.927295i
$97$			1.50782i			0.153096i	0.997066	+	0.0765480i	$0.0243898\pi$
$97$			1.50782i			0.153096i	−0.997066	+	0.0765480i	$0.975610\pi$
$98$	−1.32540	+	0.493263i	−0.133886	+	0.0498271i
$99$	25.4298	+	25.4298i	2.55579	+	2.55579i
$100$	9.07271	−	4.20546i	0.907271	−	0.420546i
$101$	7.47618	−	7.47618i	0.743908	−	0.743908i	−0.229419	−	0.973328i	$-0.573683\pi$
$101$	7.47618	−	7.47618i	0.743908	−	0.743908i	0.973328	+	0.229419i	$0.0736828\pi$
$102$	−16.6476	−	7.61720i	−1.64836	−	0.754215i
$103$	−17.6853			−1.74258			−0.871290	−	0.490769i	$-0.836716\pi$
$103$	−17.6853			−1.74258			−0.871290	+	0.490769i	$0.836716\pi$
$104$	0.113188	+	0.388585i	0.0110990	+	0.0381039i
$105$	−5.27424	+	3.97749i	−0.514713	+	0.388163i
$106$	8.19166	+	3.74813i	0.795645	+	0.364051i
$107$	−5.67558	−	5.67558i	−0.548679	−	0.548679i	0.377379	−	0.926059i	$-0.376825\pi$
$107$	−5.67558	−	5.67558i	−0.548679	−	0.548679i	−0.926059	+	0.377379i	$0.876825\pi$
$108$	16.0734	+	1.17284i	1.54666	+	0.112857i
$109$	13.9375	+	13.9375i	1.33497	+	1.33497i	0.900857	+	0.434115i	$0.142939\pi$
$109$	13.9375	+	13.9375i	1.33497	+	1.33497i	0.434115	+	0.900857i	$0.357061\pi$
$110$	−10.6876	+	16.7339i	−1.01902	+	1.59552i
$111$	−8.41034			−0.798274
$112$	−0.580654	+	3.95763i	−0.0548666	+	0.373961i
$113$		−	14.3005i		−	1.34528i	−0.739972	−	0.672638i	$-0.765161\pi$
$113$		−	14.3005i		−	1.34528i	0.739972	−	0.672638i	$-0.234839\pi$
$114$	−22.0319	+	8.19942i	−2.06348	+	0.767946i
$115$	−2.35619	−	0.330251i	−0.219716	−	0.0307961i
$116$	7.74604	+	0.565214i	0.719202	+	0.0524788i
$117$	−0.579540	−	0.579540i	−0.0535785	−	0.0535785i
$118$	−5.54473	+	12.1182i	−0.510433	+	1.11557i
$119$			4.38194i			0.401692i
$120$	2.68467	+	18.4905i	0.245076	+	1.68794i
$121$		−	28.4248i		−	2.58407i
$122$	11.4934	+	5.25885i	1.04056	+	0.476114i
$123$	−13.0767	−	13.0767i	−1.17909	−	1.17909i
$124$	2.02269	−	1.74758i	0.181643	−	0.156937i
$125$	−10.2188	−	4.53610i	−0.913997	−	0.405721i
$126$	−2.82522	−	7.59139i	−0.251691	−	0.676294i
$127$		−	5.46991i		−	0.485376i	−0.970104	−	0.242688i	$-0.921971\pi$
$127$		−	5.46991i		−	0.485376i	0.970104	−	0.242688i	$-0.0780291\pi$
$128$	9.02282	+	6.82559i	0.797512	+	0.603303i
$129$	−18.4530			−1.62469
$130$	0.243568	−	0.381362i	0.0213623	−	0.0334477i
$131$	0.0735407	+	0.0735407i	0.00642528	+	0.00642528i	0.710312	−	0.703887i	$-0.248554\pi$
$131$	0.0735407	+	0.0735407i	0.00642528	+	0.00642528i	−0.703887	+	0.710312i	$0.748554\pi$
$132$	−24.2543	−	28.0725i	−2.11107	−	2.44340i
$133$	3.97870	+	3.97870i	0.344997	+	0.344997i
$134$	−6.99561	+	15.2891i	−0.604329	+	1.32078i
$135$	−10.8490	−	14.3861i	−0.933737	−	1.23816i
$136$	10.8651	+	5.96329i	0.931676	+	0.511347i
$137$	8.23795			0.703816			0.351908	−	0.936035i	$-0.385533\pi$
$137$	8.23795			0.703816			0.351908	+	0.936035i	$0.385533\pi$
$138$	1.84961	−	4.04237i	0.157449	−	0.344109i
$139$	2.48265	−	2.48265i	0.210575	−	0.210575i	−0.593936	−	0.804512i	$-0.702427\pi$
$139$	2.48265	−	2.48265i	0.210575	−	0.210575i	0.804512	+	0.593936i	$0.202427\pi$
$140$	3.75710	−	2.42573i	0.317533	−	0.205012i
$141$	−20.2440	−	20.2440i	−1.70486	−	1.70486i
$142$	−0.0716315	−	0.192474i	−0.00601118	−	0.0161521i
$143$			0.898483i			0.0751349i
$144$	−22.6678	−	3.32576i	−1.88898	−	0.277146i
$145$	−5.22835	−	6.93291i	−0.434191	−	0.575747i
$146$	7.34693	−	2.73424i	0.608036	−	0.226288i
$147$	−2.08897	+	2.08897i	−0.172296	+	0.172296i
$148$	5.67862	+	0.414358i	0.466779	+	0.0340600i
$149$	−9.59491	+	9.59491i	−0.786046	+	0.786046i	−0.980843	−	0.194798i	$-0.937595\pi$
$149$	−9.59491	+	9.59491i	−0.786046	+	0.786046i	0.194798	+	0.980843i	$0.437595\pi$
$150$	13.5790	−	15.8742i	1.10872	−	1.29612i
$151$		−	0.477885i		−	0.0388897i	−0.999811	−	0.0194449i	$-0.993810\pi$
$151$		−	0.477885i		−	0.0388897i	0.999811	−	0.0194449i	$-0.00618988\pi$
$152$	15.2798	−	4.45075i	1.23936	−	0.361003i
$153$	−25.0981			−2.02906
$154$	−3.69459	+	8.07463i	−0.297718	+	0.650672i
$155$	−2.95965	−	0.414833i	−0.237725	−	0.0333202i
$156$	0.552751	+	0.639766i	0.0442555	+	0.0512223i
$157$	12.6286	−	12.6286i	1.00787	−	1.00787i	0.00790521	−	0.999969i	$-0.497484\pi$
$157$	12.6286	−	12.6286i	1.00787	−	1.00787i	0.999969	−	0.00790521i	$-0.00251633\pi$
$158$	−12.8476	+	4.78139i	−1.02210	+	0.380387i
$159$	18.8184			1.49239
$160$	−0.901693	−	12.6169i	−0.0712851	−	0.997456i
$161$	−1.06402			−0.0838567
$162$	8.77771	−	3.26672i	0.689642	−	0.256658i
$163$	−2.61436	+	2.61436i	−0.204772	+	0.204772i	−0.802041	−	0.597269i	$-0.796253\pi$
$163$	−2.61436	+	2.61436i	−0.204772	+	0.204772i	0.597269	+	0.802041i	$0.296253\pi$
$164$	8.18509	+	9.47361i	0.639148	+	0.739765i
$165$	−5.75740	+	41.0764i	−0.448213	+	3.19780i
$166$	−1.78046	+	3.89126i	−0.138191	+	0.302020i
$167$	−5.95070			−0.460479			−0.230240	−	0.973134i	$-0.573951\pi$
$167$	−5.95070			−0.460479			−0.230240	+	0.973134i	$0.573951\pi$
$168$	2.33681	+	8.02248i	0.180289	+	0.618948i
$169$			12.9795i			0.998425i
$170$	−2.98373	−	13.5319i	−0.228842	−	1.03785i
$171$	−22.7885	+	22.7885i	−1.74268	+	1.74268i
$172$	12.4594	+	0.909136i	0.950017	+	0.0693210i
$173$	−8.60406	+	8.60406i	−0.654155	+	0.654155i	−0.953991	−	0.299836i	$-0.903068\pi$
$173$	−8.60406	+	8.60406i	−0.654155	+	0.654155i	0.299836	+	0.953991i	$0.403068\pi$
$174$	15.2054	−	5.65887i	1.15272	−	0.428998i
$175$	−4.80733	−	1.37463i	−0.363400	−	0.103912i
$176$	14.9933	+	20.1494i	1.13016	+	1.51882i
$177$			27.8386i			2.09247i
$178$	6.22289	+	16.7210i	0.466426	+	1.25329i
$179$	−14.0070	−	14.0070i	−1.04693	−	1.04693i	−0.998843	−	0.0480913i	$-0.984686\pi$
$179$	−14.0070	−	14.0070i	−1.04693	−	1.04693i	−0.0480913	−	0.998843i	$-0.515314\pi$
$180$	13.8936	+	21.5192i	1.03557	+	1.60395i
$181$	−0.174053	+	0.174053i	−0.0129373	+	0.0129373i	−0.713546	−	0.700609i	$-0.752912\pi$
$181$	−0.174053	+	0.174053i	−0.0129373	+	0.0129373i	0.700609	+	0.713546i	$0.252912\pi$
$182$	0.0841988	−	0.184019i	0.00624123	−	0.0136404i
$183$	26.4032			1.95178
$184$	−1.44800	+	2.63826i	−0.106748	+	0.194495i
$185$	−3.83290	−	5.08251i	−0.281800	−	0.373673i
$186$	2.32332	−	5.07768i	0.170354	−	0.372313i
$187$	19.4552	+	19.4552i	1.42271	+	1.42271i
$188$	12.6713	+	14.6661i	0.924150	+	1.06963i
$189$	−5.69790	−	5.69790i	−0.414461	−	0.414461i
$190$	−14.9958	−	9.57747i	−1.08791	−	0.694823i
$191$	−4.86788			−0.352228			−0.176114	−	0.984370i	$-0.556353\pi$
$191$	−4.86788			−0.352228			−0.176114	+	0.984370i	$0.556353\pi$
$192$	23.0720	+	5.12344i	1.66508	+	0.369752i
$193$		−	7.45125i		−	0.536353i	−0.963370	−	0.268176i	$-0.913579\pi$
$193$		−	7.45125i		−	0.536353i	0.963370	−	0.268176i	$-0.0864210\pi$
$194$	−0.743753	−	1.99847i	−0.0533983	−	0.143482i
$195$	0.131210	−	0.936123i	0.00939614	−	0.0670372i
$196$	1.51338	−	1.30754i	0.108099	−	0.0933961i
$197$	2.51329	+	2.51329i	0.179064	+	0.179064i	0.790948	−	0.611884i	$-0.209588\pi$
$197$	2.51329	+	2.51329i	0.179064	+	0.179064i	−0.611884	+	0.790948i	$0.709588\pi$
$198$	−46.2483	−	21.1611i	−3.28673	−	1.50386i
$199$		−	22.4709i		−	1.59292i	−0.604693	−	0.796458i	$-0.706704\pi$
$199$		−	22.4709i		−	1.59292i	0.604693	−	0.796458i	$-0.293296\pi$
$200$	−9.95059	+	10.0492i	−0.703613	+	0.710583i
$201$			35.1231i			2.47739i
$202$	−6.22122	+	13.5967i	−0.437724	+	0.956659i
$203$	−2.74592	−	2.74592i	−0.192726	−	0.192726i
$204$	25.8221	+	1.88419i	1.80791	+	0.131920i
$205$	1.94295	−	13.8620i	0.135701	−	0.968167i
$206$	23.4401	−	8.72349i	1.63315	−	0.607794i
$207$		−	6.09430i		−	0.423583i
$208$	−0.341695	−	0.459200i	−0.0236923	−	0.0318398i
$209$	35.3298			2.44381
$210$	5.02854	−	7.87336i	0.347002	−	0.543314i
$211$	−9.74909	−	9.74909i	−0.671155	−	0.671155i	0.286827	−	0.957982i	$-0.407399\pi$
$211$	−9.74909	−	9.74909i	−0.671155	−	0.671155i	−0.957982	+	0.286827i	$0.907399\pi$
$212$	−12.7061	−	0.927138i	−0.872656	−	0.0636761i
$213$	−0.303360	−	0.303360i	−0.0207859	−	0.0207859i
$214$	10.3220	+	4.72287i	0.705597	+	0.322849i
$215$	−8.40969	−	11.1514i	−0.573536	−	0.760522i
$216$	−21.8822	+	6.37391i	−1.48889	+	0.433690i
$217$	−1.33653			−0.0907298
$218$	−25.3477	−	11.5980i	−1.71676	−	0.785513i
$219$	11.5795	−	11.5795i	0.782472	−	0.782472i
$220$	5.91111	−	27.4510i	0.398527	−	1.85074i
$221$	−0.443381	−	0.443381i	−0.0298250	−	0.0298250i
$222$	11.1471	−	4.14851i	0.748143	−	0.278430i
$223$		−	4.86788i		−	0.325977i	−0.986628	−	0.162989i	$-0.947887\pi$
$223$		−	4.86788i		−	0.325977i	0.986628	−	0.162989i	$-0.0521134\pi$
$224$	−1.18255	−	5.53187i	−0.0790128	−	0.369613i
$225$	7.87332	−	27.5345i	0.524888	−	1.83563i
$226$	7.05390	+	18.9539i	0.469218	+	1.26079i
$227$	12.2070	−	12.2070i	0.810207	−	0.810207i	−0.174458	−	0.984665i	$-0.555817\pi$
$227$	12.2070	−	12.2070i	0.810207	−	0.810207i	0.984665	+	0.174458i	$0.0558172\pi$
$228$	25.1567	−	21.7351i	1.66604	−	1.43944i
$229$	−13.2949	+	13.2949i	−0.878549	+	0.878549i	−0.993385	−	0.114835i	$-0.963366\pi$
$229$	−13.2949	+	13.2949i	−0.878549	+	0.878549i	0.114835	+	0.993385i	$0.463366\pi$
$230$	3.28580	−	0.724508i	0.216660	−	0.0477726i
$231$			18.5495i			1.22047i
$232$	−10.5454	+	3.07170i	−0.692341	+	0.201667i
$233$	18.3113			1.19962			0.599808	−	0.800144i	$-0.295244\pi$
$233$	18.3113			1.19962			0.599808	+	0.800144i	$0.295244\pi$
$234$	1.05399	+	0.482258i	0.0689015	+	0.0315262i
$235$	3.00787	−	21.4598i	0.196212	−	1.39988i
$236$	1.37154	−	18.7965i	0.0892798	−	1.22355i
$237$	−20.2492	+	20.2492i	−1.31533	+	1.31533i
$238$	−2.16145	−	5.80784i	−0.140106	−	0.376466i
$239$	−11.3768			−0.735903			−0.367951	−	0.929845i	$-0.619941\pi$
$239$	−11.3768			−0.735903			−0.367951	+	0.929845i	$0.619941\pi$
$240$	−12.6789	−	23.1830i	−0.818421	−	1.49646i
$241$	−1.64574			−0.106012			−0.0530058	−	0.998594i	$-0.516880\pi$
$241$	−1.64574			−0.106012			−0.0530058	+	0.998594i	$0.516880\pi$
$242$	14.0209	+	37.6743i	0.901299	+	2.42180i
$243$	−3.25911	+	3.25911i	−0.209072	+	0.209072i
$244$	−17.8273	−	1.30083i	−1.14128	−	0.0832770i
$245$	−2.21442	−	0.310380i	−0.141474	−	0.0198295i
$246$	23.7822	+	10.8817i	1.51630	+	0.693790i
$247$	−0.805159			−0.0512310
$248$	−1.81886	+	3.31396i	−0.115498	+	0.210437i
$249$			8.93922i			0.566500i
$250$	15.7815	+	0.971600i	0.998110	+	0.0614494i
$251$	13.7976	−	13.7976i	0.870899	−	0.870899i	−0.121671	−	0.992570i	$-0.538825\pi$
$251$	13.7976	−	13.7976i	0.870899	−	0.870899i	0.992570	+	0.121671i	$0.0388253\pi$
$252$	7.48911	+	8.66806i	0.471769	+	0.546037i
$253$	−4.72411	+	4.72411i	−0.297002	+	0.297002i
$254$	2.69810	+	7.24983i	0.169294	+	0.454895i
$255$	−17.4291	−	23.1114i	−1.09145	−	1.44729i
$256$	−15.3257	−	4.59602i	−0.957855	−	0.287252i
$257$			16.8443i			1.05072i	0.850880	+	0.525359i	$0.176069\pi$
$257$			16.8443i			1.05072i	−0.850880	+	0.525359i	$0.823931\pi$
$258$	24.4576	−	9.10217i	1.52266	−	0.566677i
$259$	−2.01303	−	2.01303i	−0.125084	−	0.125084i
$260$	−0.134713	+	0.625602i	−0.00835454	+	0.0387982i
$261$	15.7276	−	15.7276i	0.973512	−	0.973512i
$262$	−0.133746	−	0.0611961i	−0.00826285	−	0.00378071i
$263$	−12.2930			−0.758018			−0.379009	−	0.925393i	$-0.623735\pi$
$263$	−12.2930			−0.758018			−0.379009	+	0.925393i	$0.623735\pi$
$264$	45.9939	+	25.2436i	2.83073	+	1.55364i
$265$	8.57622	+	11.3723i	0.526833	+	0.698592i
$266$	−7.23593	−	3.31083i	−0.443663	−	0.203000i
$267$	26.3540	+	26.3540i	1.61284	+	1.61284i
$268$	1.73043	−	23.7149i	0.105703	−	1.44862i
$269$	−0.0755647	−	0.0755647i	−0.00460726	−	0.00460726i	0.704799	−	0.709407i	$-0.251037\pi$
$269$	−0.0755647	−	0.0755647i	−0.00460726	−	0.00460726i	−0.709407	+	0.704799i	$0.751037\pi$
$270$	21.4755	+	13.7159i	1.30695	+	0.834723i
$271$	26.8585			1.63154			0.815768	−	0.578379i	$-0.196315\pi$
$271$	26.8585			1.63154			0.815768	+	0.578379i	$0.196315\pi$
$272$	−17.3421	−	2.54439i	−1.05152	−	0.154276i
$273$		−	0.422739i		−	0.0255854i
$274$	−10.9186	+	4.06348i	−0.659617	+	0.245484i
$275$	−27.4470	+	15.2407i	−1.65512	+	0.919051i
$276$	−0.457518	+	6.27011i	−0.0275394	+	0.377416i
$277$	−1.16938	−	1.16938i	−0.0702613	−	0.0702613i	0.671103	−	0.741364i	$-0.265821\pi$
$277$	−1.16938	−	1.16938i	−0.0702613	−	0.0702613i	−0.741364	+	0.671103i	$0.765821\pi$
$278$	−2.06591	+	4.51511i	−0.123905	+	0.270798i
$279$		−	7.65514i		−	0.458301i
$280$	−3.78315	+	5.06831i	−0.226086	+	0.302890i
$281$		−	11.4253i		−	0.681575i	−0.940140	−	0.340788i	$-0.889306\pi$
$281$		−	11.4253i		−	0.681575i	0.940140	−	0.340788i	$-0.110694\pi$
$282$	36.8172	+	16.8459i	2.19243	+	1.00316i
$283$	12.8444	+	12.8444i	0.763522	+	0.763522i	0.976957	−	0.213435i	$-0.0684651\pi$
$283$	12.8444	+	12.8444i	0.763522	+	0.763522i	−0.213435	+	0.976957i	$0.568465\pi$
$284$	0.189881	+	0.219773i	0.0112674	+	0.0130411i
$285$	−36.8099	−	5.15939i	−2.18043	−	0.305616i
$286$	−0.443189	−	1.19085i	−0.0262063	−	0.0704165i
$287$		−	6.25989i		−	0.369510i
$288$	31.6844	−	6.77321i	1.86702	−	0.399115i
$289$	−2.20143			−0.129496
$290$	10.3494	+	6.60994i	0.607739	+	0.388149i
$291$	−3.14980	−	3.14980i	−0.184644	−	0.184644i
$292$	−8.38894	+	7.24794i	−0.490925	+	0.424154i
$293$	−0.754637	−	0.754637i	−0.0440864	−	0.0440864i	0.684720	−	0.728806i	$-0.259925\pi$
$293$	−0.754637	−	0.754637i	−0.0440864	−	0.0440864i	−0.728806	+	0.684720i	$0.759925\pi$
$294$	1.73832	−	3.79914i	0.101381	−	0.221570i
$295$	−16.8233	+	12.6871i	−0.979491	+	0.738669i
$296$	−7.73084	+	2.25186i	−0.449346	+	0.130887i
$297$	−50.5958			−2.93587
$298$	7.98430	−	17.4499i	0.462518	−	1.01085i
$299$	0.107662	−	0.107662i	0.00622623	−	0.00622623i
$300$	−10.1675	+	27.7377i	−0.587024	+	1.60144i
$301$	−4.41676	−	4.41676i	−0.254578	−	0.254578i
$302$	0.235723	+	0.633390i	0.0135643	+	0.0364475i
$303$			31.2351i			1.79441i
$304$	−18.0565	+	13.4360i	−1.03561	+	0.770607i
$305$	12.0329	+	15.9559i	0.689003	+	0.913634i
$306$	33.2650	−	12.3800i	1.90163	−	0.707715i
$307$	18.8786	−	18.8786i	1.07746	−	1.07746i	0.0807196	−	0.996737i	$-0.474278\pi$
$307$	18.8786	−	18.8786i	1.07746	−	1.07746i	0.996737	−	0.0807196i	$-0.0257218\pi$
$308$	0.913892	−	12.5245i	0.0520738	−	0.713652i
$309$	36.9440	−	36.9440i	2.10167	−	2.10167i
$310$	4.12735	−	0.910065i	0.234418	−	0.0516882i
$311$			22.2707i			1.26285i	0.775436	+	0.631426i	$0.217530\pi$
$311$			22.2707i			1.26285i	−0.775436	+	0.631426i	$0.782470\pi$
$312$	−1.04819	−	0.575296i	−0.0593421	−	0.0325697i
$313$	17.1679			0.970386			0.485193	−	0.874407i	$-0.338749\pi$
$313$	17.1679			0.970386			0.485193	+	0.874407i	$0.338749\pi$
$314$	−10.5088	+	22.9672i	−0.593044	+	1.29612i
$315$	1.77774	−	12.6833i	0.100164	−	0.714625i
$316$	14.6698	−	12.6745i	0.825240	−	0.712998i
$317$	20.5541	−	20.5541i	1.15443	−	1.15443i	0.168780	−	0.985654i	$-0.446017\pi$
$317$	20.5541	−	20.5541i	1.15443	−	1.15443i	0.985654	−	0.168780i	$-0.0539828\pi$
$318$	−24.9419	+	9.28241i	−1.39867	+	0.520532i
$319$	−24.3830			−1.36519
$320$	7.41858	+	16.2777i	0.414711	+	0.909953i
$321$	23.7123			1.32349
$322$	1.41026	−	0.524843i	0.0785905	−	0.0292484i
$323$	−17.4345	+	17.4345i	−0.970079	+	0.970079i
$324$	−10.0226	+	8.65945i	−0.556814	+	0.481081i
$325$	0.625512	−	0.347333i	0.0346972	−	0.0192666i
$326$	2.17551	−	4.75464i	0.120490	−	0.263335i
$327$	−58.2302			−3.22014
$328$	−15.5215	−	8.51894i	−0.857033	−	0.470380i
$329$		−	9.69091i		−	0.534277i
$330$	−12.6306	−	57.2827i	−0.695293	−	3.15331i
$331$	3.24816	−	3.24816i	0.178535	−	0.178535i	−0.612182	−	0.790717i	$-0.709708\pi$
$331$	3.24816	−	3.24816i	0.178535	−	0.178535i	0.790717	+	0.612182i	$0.209708\pi$
$332$	0.440415	−	6.03572i	0.0241709	−	0.331253i
$333$	11.5299	−	11.5299i	0.631832	−	0.631832i
$334$	7.88708	−	2.93526i	0.431562	−	0.160611i
$335$	−21.2255	+	16.0069i	−1.15967	+	0.874548i
$336$	−7.05441	−	9.48035i	−0.384850	−	0.517195i
$337$			0.227615i			0.0123990i	0.999981	+	0.00619950i	$0.00197337\pi$
$337$			0.227615i			0.0123990i	−0.999981	+	0.00619950i	$0.998027\pi$
$338$	−6.40232	−	17.2031i	−0.348240	−	0.935725i
$339$	29.8733	+	29.8733i	1.62249	+	1.62249i
$340$	10.6294	+	16.4634i	0.576461	+	0.892854i
$341$	−5.93403	+	5.93403i	−0.321346	+	0.321346i
$342$	18.9632	−	41.4446i	1.02541	−	2.24107i
$343$	−1.00000			−0.0539949
$344$	−16.9621	+	4.94077i	−0.914535	+	0.266389i
$345$	5.61191	−	4.23214i	0.302135	−	0.227851i
$346$	7.15977	−	15.6479i	0.384912	−	0.841237i
$347$	−12.4747	−	12.4747i	−0.669679	−	0.669679i	0.287962	−	0.957642i	$-0.407022\pi$
$347$	−12.4747	−	12.4747i	−0.669679	−	0.669679i	−0.957642	+	0.287962i	$0.907022\pi$
$348$	−17.3620	+	15.0006i	−0.930700	+	0.804114i
$349$	−12.1224	−	12.1224i	−0.648900	−	0.648900i	0.303827	−	0.952727i	$-0.401735\pi$
$349$	−12.1224	−	12.1224i	−0.648900	−	0.648900i	−0.952727	+	0.303827i	$0.901735\pi$
$350$	7.04970	−	0.549347i	0.376822	−	0.0293638i
$351$	1.15307			0.0615462
$352$	−29.8111	−	19.3104i	−1.58894	−	1.02925i
$353$			3.35886i			0.178774i	0.995997	+	0.0893870i	$0.0284908\pi$
$353$			3.35886i			0.178774i	−0.995997	+	0.0893870i	$0.971509\pi$
$354$	−13.7317	−	36.8973i	−0.729834	−	1.96107i
$355$	0.0450733	−	0.321577i	0.00239224	−	0.0170676i
$356$	−16.4957	−	19.0925i	−0.874269	−	1.01190i
$357$	−9.15376	−	9.15376i	−0.484468	−	0.484468i
$358$	25.4741	+	11.6558i	1.34635	+	0.616028i
$359$		−	11.2212i		−	0.592230i	−0.955152	−	0.296115i	$-0.904309\pi$
$359$		−	11.2212i		−	0.592230i	0.955152	−	0.296115i	$-0.0956911\pi$
$360$	−29.0293	−	21.6684i	−1.52998	−	1.14202i
$361$			12.6602i			0.666325i
$362$	0.144836	−	0.316545i	0.00761243	−	0.0166372i
$363$	59.3787	+	59.3787i	3.11657	+	3.11657i
$364$	−0.0208274	+	0.285432i	−0.00109165	+	0.0149607i
$365$	12.2749	+	1.72049i	0.642499	+	0.0900546i
$366$	−34.9949	+	13.0238i	−1.82921	+	0.680762i
$367$			25.4272i			1.32729i	0.748049	+	0.663644i	$0.230991\pi$
$367$			25.4272i			1.32729i	−0.748049	+	0.663644i	$0.769009\pi$
$368$	0.617828	−	4.21101i	0.0322065	−	0.219514i
$369$	35.8542			1.86650
$370$	7.58714	+	4.84574i	0.394437	+	0.251918i
$371$	4.50422	+	4.50422i	0.233847	+	0.233847i
$372$	−0.574695	+	7.87597i	−0.0297966	+	0.408350i
$373$	4.29994	+	4.29994i	0.222643	+	0.222643i	0.809610	−	0.586968i	$-0.199678\pi$
$373$	4.29994	+	4.29994i	0.222643	+	0.222643i	−0.586968	+	0.809610i	$0.699678\pi$
$374$	−35.3826	−	16.1895i	−1.82959	−	0.837137i
$375$	30.8226	−	11.8710i	1.59167	−	0.613016i
$376$	−24.0288	−	13.1881i	−1.23919	−	0.680126i
$377$	0.555684			0.0286192
$378$	10.3626	+	4.74144i	0.532993	+	0.243874i
$379$	−17.9256	+	17.9256i	−0.920774	+	0.920774i	−0.997084	−	0.0763103i	$-0.975686\pi$
$379$	−17.9256	+	17.9256i	−0.920774	+	0.920774i	0.0763103	+	0.997084i	$0.475686\pi$
$380$	24.5997	+	5.29713i	1.26194	+	0.271737i
$381$	11.4265	+	11.4265i	0.585396	+	0.585396i
$382$	6.45190	−	2.40115i	0.330108	−	0.122853i
$383$		−	29.6546i		−	1.51528i	−0.652675	−	0.757638i	$-0.726353\pi$
$383$		−	29.6546i		−	1.51528i	0.652675	−	0.757638i	$-0.273647\pi$
$384$	−33.1069	+	4.58996i	−1.68948	+	0.234230i
$385$	−11.2098	+	8.45369i	−0.571303	+	0.430840i
$386$	3.67543	+	9.87590i	0.187074	+	0.502670i
$387$	25.2975	−	25.2975i	1.28594	−	1.28594i
$388$	1.97154	+	2.28191i	0.100090	+	0.115846i
$389$	4.29343	−	4.29343i	0.217686	−	0.217686i	−0.589837	−	0.807522i	$-0.700808\pi$
$389$	4.29343	−	4.29343i	0.217686	−	0.217686i	0.807522	+	0.589837i	$0.200808\pi$
$390$	0.287849	+	1.30546i	0.0145758	+	0.0661046i
$391$		−	4.66248i		−	0.235792i
$392$	−1.36088	+	2.47952i	−0.0687347	+	0.125235i
$393$	−0.307249			−0.0154987
$394$	−4.57083	−	2.09140i	−0.230275	−	0.105363i
$395$	−21.4652	−	3.00863i	−1.08003	−	0.151381i
$396$	71.7357	+	5.23442i	3.60485	+	0.263039i
$397$	2.26941	−	2.26941i	0.113899	−	0.113899i	−0.647860	−	0.761759i	$-0.724336\pi$
$397$	2.26941	−	2.26941i	0.113899	−	0.113899i	0.761759	+	0.647860i	$0.224336\pi$
$398$	11.0840	+	29.7829i	0.555593	+	1.49288i
$399$	−16.6228			−0.832181
$400$	8.23165	−	18.2274i	0.411583	−	0.911372i
$401$	10.3479			0.516748			0.258374	−	0.966045i	$-0.416813\pi$
$401$	10.3479			0.516748			0.258374	+	0.966045i	$0.416813\pi$
$402$	−17.3249	−	46.5522i	−0.864088	−	2.32181i
$403$	0.135235	−	0.135235i	0.00673655	−	0.00673655i
$404$	1.53888	−	21.0898i	0.0765622	−	1.04926i
$405$	14.6654	+	2.05555i	0.728730	+	0.102141i
$406$	4.99391	+	2.28499i	0.247844	+	0.113402i
$407$	−17.8752			−0.886040
$408$	−35.1541	+	10.2398i	−1.74038	+	0.506945i
$409$			16.6187i			0.821742i	0.911693	+	0.410871i	$0.134775\pi$
$409$			16.6187i			0.821742i	−0.911693	+	0.410871i	$0.865225\pi$
$410$	4.26245	+	19.3312i	0.210507	+	0.954698i
$411$	−17.2089	+	17.2089i	−0.848850	+	0.848850i
$412$	−26.7645	+	23.1243i	−1.31859	+	1.13925i
$413$	−6.66322	+	6.66322i	−0.327876	+	0.327876i
$414$	3.00609	+	8.07740i	0.147742	+	0.396983i
$415$	−5.40212	+	4.07393i	−0.265180	+	0.199981i
$416$	0.679389	+	0.440079i	0.0333098	+	0.0215767i
$417$			10.3724i			0.507937i
$418$	−46.8262	+	17.4269i	−2.29035	+	0.852378i
$419$	−4.85684	−	4.85684i	−0.237272	−	0.237272i	0.578448	−	0.815720i	$-0.303659\pi$
$419$	−4.85684	−	4.85684i	−0.237272	−	0.237272i	−0.815720	+	0.578448i	$0.803659\pi$
$420$	−2.78120	+	12.9158i	−0.135709	+	0.630225i
$421$	−5.52650	+	5.52650i	−0.269345	+	0.269345i	−0.828836	−	0.559491i	$-0.810997\pi$
$421$	−5.52650	+	5.52650i	−0.269345	+	0.269345i	0.559491	+	0.828836i	$0.310997\pi$
$422$	17.7303	+	8.11259i	0.863099	+	0.394915i
$423$	55.5058			2.69878
$424$	17.2980	−	5.03861i	0.840064	−	0.244696i
$425$	6.02353	−	21.0654i	0.292184	−	1.02182i
$426$	0.551710	+	0.252437i	0.0267304	+	0.0122306i
$427$	6.31967	+	6.31967i	0.305830	+	0.305830i
$428$	−16.0104	−	1.16825i	−0.773892	−	0.0564695i
$429$	−1.87691	−	1.87691i	−0.0906179	−	0.0906179i
$430$	16.6468	+	10.6320i	0.802781	+	0.512718i
$431$	−9.79700			−0.471905			−0.235953	−	0.971765i	$-0.575821\pi$
$431$	−9.79700			−0.471905			−0.235953	+	0.971765i	$0.575821\pi$
$432$	25.8587	−	19.2417i	1.24413	−	0.925766i
$433$			10.9167i			0.524624i	0.964983	+	0.262312i	$0.0844849\pi$
$433$			10.9167i			0.524624i	−0.964983	+	0.262312i	$0.915515\pi$
$434$	1.77144	−	0.659263i	0.0850320	−	0.0316456i
$435$	25.4045	+	3.56078i	1.21805	+	0.170726i
$436$	39.3167	+	2.86887i	1.88293	+	0.137394i
$437$	−4.23343	−	4.23343i	−0.202512	−	0.202512i
$438$	−9.63578	+	21.0593i	−0.460415	+	1.00625i
$439$			9.50628i			0.453710i	0.973929	+	0.226855i	$0.0728444\pi$
$439$			9.50628i			0.453710i	−0.973929	+	0.226855i	$0.927156\pi$
$440$	5.70595	+	39.2993i	0.272021	+	1.87352i
$441$		−	5.72761i		−	0.272743i
$442$	0.806361	+	0.368954i	0.0383547	+	0.0175494i
$443$	0.583476	+	0.583476i	0.0277218	+	0.0277218i	0.720832	−	0.693110i	$-0.243760\pi$
$443$	0.583476	+	0.583476i	0.0277218	+	0.0277218i	−0.693110	+	0.720832i	$0.743760\pi$
$444$	−12.7281	+	10.9969i	−0.604047	+	0.521889i
$445$	−3.91568	+	27.9366i	−0.185621	+	1.32432i
$446$	2.40115	+	6.45190i	0.113698	+	0.305506i
$447$		−	40.0870i		−	1.89605i
$448$	4.29603	+	6.74864i	0.202968	+	0.318843i
$449$	41.7242			1.96909			0.984544	−	0.175138i	$-0.0560370\pi$
$449$	41.7242			1.96909			0.984544	+	0.175138i	$0.0560370\pi$
$450$	3.14645	+	40.3779i	0.148325	+	1.90343i
$451$	−27.7931	−	27.7931i	−1.30873	−	1.30873i
$452$	−18.6985	−	21.6421i	−0.879504	−	1.01796i
$453$	0.998288	+	0.998288i	0.0469037	+	0.0469037i
$454$	−10.1579	+	22.2005i	−0.476735	+	1.04192i
$455$	0.255469	−	0.192658i	0.0119766	−	0.00903194i
$456$	−22.6216	+	41.2166i	−1.05935	+	1.93014i
$457$	−15.7261			−0.735637			−0.367819	−	0.929898i	$-0.619895\pi$
$457$	−15.7261			−0.735637			−0.367819	+	0.929898i	$0.619895\pi$
$458$	11.0632	−	24.1789i	0.516948	−	1.12981i
$459$	24.9679	−	24.9679i	1.16540	−	1.16540i
$460$	−3.99764	+	2.58103i	−0.186391	+	0.120341i
$461$	20.8457	+	20.8457i	0.970880	+	0.970880i	0.999588	−	0.0287077i	$-0.00913920\pi$
$461$	20.8457	+	20.8457i	0.970880	+	0.970880i	−0.0287077	+	0.999588i	$0.509139\pi$
$462$	−9.14979	−	24.5856i	−0.425687	−	1.14382i
$463$			42.0725i			1.95527i	0.210298	+	0.977637i	$0.432557\pi$
$463$			42.0725i			1.95527i	−0.210298	+	0.977637i	$0.567443\pi$
$464$	12.4618	−	9.27291i	0.578523	−	0.430484i
$465$	7.04920	−	5.31605i	0.326899	−	0.246526i
$466$	−24.2699	+	9.03232i	−1.12428	+	0.418414i
$467$	6.45091	−	6.45091i	0.298513	−	0.298513i	−0.541918	−	0.840431i	$-0.682302\pi$
$467$	6.45091	−	6.45091i	0.298513	−	0.298513i	0.840431	+	0.541918i	$0.182302\pi$
$468$	−1.63484	−	0.119291i	−0.0755705	−	0.00551424i
$469$	−8.40678	+	8.40678i	−0.388189	+	0.388189i
$470$	6.59868	+	29.9265i	0.304375	+	1.38041i
$471$			52.7617i			2.43113i
$472$	7.45376	+	25.5894i	0.343087	+	1.17785i
$473$	−39.2196			−1.80332
$474$	16.8501	−	36.8265i	0.773953	−	1.69150i
$475$	−13.6577	−	24.5962i	−0.626659	−	1.12855i
$476$	5.72959	+	6.63156i	0.262615	+	0.303957i
$477$	−25.7984	+	25.7984i	−1.18123	+	1.18123i
$478$	15.0788	−	5.61175i	0.689689	−	0.256675i
$479$	16.3497			0.747039			0.373519	−	0.927622i	$-0.378151\pi$
$479$	16.3497			0.747039			0.373519	+	0.927622i	$0.378151\pi$
$480$	28.2400	+	24.4728i	1.28898	+	1.11703i
$481$	0.407372			0.0185745
$482$	2.18127	−	0.811784i	0.0993542	−	0.0369758i
$483$	2.22271	−	2.22271i	0.101137	−	0.101137i
$484$	−37.1667	−	43.0176i	−1.68940	−	1.95535i
$485$	0.467998	−	3.33895i	0.0212507	−	0.151614i
$486$	2.71203	−	5.92723i	0.123020	−	0.268864i
$487$	−25.8407			−1.17096			−0.585478	−	0.810689i	$-0.699093\pi$
$487$	−25.8407			−1.17096			−0.585478	+	0.810689i	$0.699093\pi$
$488$	24.2700	−	7.06945i	1.09865	−	0.320019i
$489$		−	10.9226i		−	0.493939i
$490$	3.08810	−	0.680914i	0.139506	−	0.0307606i
$491$	−14.2112	+	14.2112i	−0.641344	+	0.641344i	−0.950886	−	0.309542i	$-0.899824\pi$
$491$	−14.2112	+	14.2112i	−0.641344	+	0.641344i	0.309542	+	0.950886i	$0.399824\pi$
$492$	−36.8885	−	2.69169i	−1.66306	−	0.121351i
$493$	12.0325	−	12.0325i	0.541915	−	0.541915i
$494$	1.06716	−	0.397155i	0.0480138	−	0.0178689i
$495$	−48.4194	−	64.2053i	−2.17629	−	2.88581i
$496$	0.776063	−	5.28950i	0.0348462	−	0.237506i
$497$		−	0.145220i		−	0.00651399i
$498$	−4.40939	−	11.8481i	−0.197590	−	0.530925i
$499$	−22.5762	−	22.5762i	−1.01065	−	1.01065i	−0.999943	−	0.0107075i	$-0.996592\pi$
$499$	−22.5762	−	22.5762i	−1.01065	−	1.01065i	−0.0107075	−	0.999943i	$-0.503408\pi$
$500$	−21.3961	+	6.49668i	−0.956863	+	0.290540i
$501$	12.4309	−	12.4309i	0.555370	−	0.555370i
$502$	−11.4816	+	25.0933i	−0.512447	+	1.11997i
$503$	−21.5887			−0.962593			−0.481296	−	0.876558i	$-0.659834\pi$
$503$	−21.5887			−0.962593			−0.481296	+	0.876558i	$0.659834\pi$
$504$	−14.2017	−	7.79457i	−0.632595	−	0.347198i
$505$	−18.8759	+	14.2350i	−0.839966	+	0.633448i
$506$	3.93112	−	8.59158i	0.174760	−	0.381942i
$507$	−27.1139	−	27.1139i	−1.20417	−	1.20417i
$508$	−7.15215	−	8.27806i	−0.317325	−	0.367280i
$509$	−8.83029	−	8.83029i	−0.391396	−	0.391396i	0.483789	−	0.875185i	$-0.339260\pi$
$509$	−8.83029	−	8.83029i	−0.391396	−	0.391396i	−0.875185	+	0.483789i	$0.839260\pi$
$510$	34.5006	+	22.0348i	1.52771	+	0.975717i
$511$	5.54317			0.245215
$512$	22.5797	−	1.46802i	0.997893	−	0.0648778i
$513$		−	45.3405i		−	2.00183i
$514$	−8.30868	−	22.3255i	−0.366480	−	0.984734i
$515$	39.1626	+	5.48915i	1.72571	+	0.241881i
$516$	−27.9264	+	24.1281i	−1.22939	+	1.06218i
$517$	−43.0264	−	43.0264i	−1.89230	−	1.89230i
$518$	3.66103	+	1.67512i	0.160857	+	0.0736007i
$519$		−	35.9473i		−	1.57791i
$520$	−0.130037	−	0.895623i	−0.00570252	−	0.0392757i
$521$		−	21.3484i		−	0.935290i	−0.883916	−	0.467645i	$-0.845103\pi$
$521$		−	21.3484i		−	0.935290i	0.883916	−	0.467645i	$-0.154897\pi$
$522$	−13.0875	+	28.6032i	−0.572825	+	1.25193i
$523$	22.2678	+	22.2678i	0.973701	+	0.973701i	0.999663	−	0.0259622i	$-0.00826495\pi$
$523$	22.2678	+	22.2678i	0.973701	+	0.973701i	−0.0259622	+	0.999663i	$0.508265\pi$
$524$	0.207453	+	0.0151375i	0.00906263	+	0.000661283i
$525$	12.9139	−	7.17082i	0.563610	−	0.312960i
$526$	16.2932	−	6.06368i	0.710416	−	0.264389i
$527$		−	5.85661i		−	0.255118i
$528$	−73.4121	−	10.7708i	−3.19485	−	0.468741i
$529$	−21.8679			−0.950776
$530$	−16.9765	−	10.8425i	−0.737410	−	0.470967i
$531$	−38.1643	−	38.1643i	−1.65619	−	1.65619i
$532$	11.2236	+	0.818968i	0.486606	+	0.0355068i
$533$	0.633398	+	0.633398i	0.0274355	+	0.0274355i
$534$	−47.9291	−	21.9302i	−2.07409	−	0.949012i
$535$	10.8065	+	14.3297i	0.467208	+	0.619528i
$536$	9.40418	+	32.2854i	0.406199	+	1.39452i
$537$	58.5206			2.52535
$538$	0.137427	+	0.0628804i	0.00592490	+	0.00271096i
$539$	−4.43987	+	4.43987i	−0.191239	+	0.191239i
$540$	−35.2292	−	7.58602i	−1.51602	−	0.326450i
$541$	20.6802	+	20.6802i	0.889110	+	0.889110i	0.994438	−	0.105328i	$-0.0335891\pi$
$541$	20.6802	+	20.6802i	0.889110	+	0.889110i	−0.105328	+	0.994438i	$0.533589\pi$
$542$	−35.5983	+	13.2483i	−1.52908	+	0.569063i
$543$		−	0.727184i		−	0.0312065i
$544$	24.2403	−	5.18189i	1.03930	−	0.222172i
$545$	−26.5376	−	35.1895i	−1.13675	−	1.50735i
$546$	0.208522	+	0.560300i	0.00892391	+	0.0239786i
$547$	17.2754	−	17.2754i	0.738644	−	0.738644i	−0.233672	−	0.972316i	$-0.575074\pi$
$547$	17.2754	−	17.2754i	0.738644	−	0.738644i	0.972316	+	0.233672i	$0.0750741\pi$
$548$	12.4672	−	10.7715i	0.532571	−	0.460135i
$549$	−36.1966	+	36.1966i	−1.54483	+	1.54483i
$550$	28.8607	−	33.7387i	1.23062	−	1.43862i
$551$		−	21.8504i		−	0.930859i
$552$	−2.48642	−	8.53609i	−0.105829	−	0.363320i
$553$	−9.69338			−0.412204
$554$	2.12671	+	0.973088i	0.0903554	+	0.0413426i
$555$	18.6240	+	2.61040i	0.790546	+	0.110805i
$556$	0.511023	−	7.00337i	0.0216722	−	0.297009i
$557$	21.7726	−	21.7726i	0.922536	−	0.922536i	−0.0746722	−	0.997208i	$-0.523791\pi$
$557$	21.7726	−	21.7726i	0.922536	−	0.922536i	0.997208	+	0.0746722i	$0.0237910\pi$
$558$	3.77600	+	10.1461i	0.159851	+	0.429520i
$559$	0.893807			0.0378040
$560$	2.51418	−	8.58364i	0.106244	−	0.362725i
$561$	−81.2829			−3.43177
$562$	5.63568	+	15.1431i	0.237727	+	0.638773i
$563$	11.4423	−	11.4423i	0.482234	−	0.482234i	−0.423611	−	0.905844i	$-0.639238\pi$
$563$	11.4423	−	11.4423i	0.482234	−	0.482234i	0.905844	+	0.423611i	$0.139238\pi$
$564$	−57.1070	−	4.16699i	−2.40464	−	0.175462i
$565$	−4.43858	+	31.6673i	−0.186733	+	1.33225i
$566$	−23.3597	−	10.6884i	−0.981883	−	0.449265i
$567$	6.62268			0.278126
$568$	−0.360075	−	0.197626i	−0.0151084	−	0.00829220i
$569$		−	9.59398i		−	0.402201i	−0.979571	−	0.201100i	$-0.935548\pi$
$569$		−	9.59398i		−	0.402201i	0.979571	−	0.201100i	$-0.0644517\pi$
$570$	51.3329	−	11.3187i	2.15010	−	0.474088i
$571$	26.2869	−	26.2869i	1.10007	−	1.10007i	0.105672	−	0.994401i	$-0.466301\pi$
$571$	26.2869	−	26.2869i	1.10007	−	1.10007i	0.994401	−	0.105672i	$-0.0336993\pi$
$572$	1.17481	+	1.35975i	0.0491212	+	0.0568540i
$573$	10.1689	−	10.1689i	0.424811	−	0.424811i
$574$	3.08778	+	8.29688i	0.128881	+	0.346305i
$575$	5.11510	+	1.46263i	0.213314	+	0.0609959i
$576$	−38.6536	+	24.6060i	−1.61057	+	1.02525i
$577$		−	7.25880i		−	0.302188i	−0.988519	−	0.151094i	$-0.951720\pi$
$577$		−	7.25880i		−	0.302188i	0.988519	−	0.151094i	$-0.0482796\pi$
$578$	2.91778	−	1.08588i	0.121363	−	0.0451668i
$579$	15.5655	+	15.5655i	0.646878	+	0.646878i
$580$	−16.9776	−	3.65584i	−0.704956	−	0.151801i
$581$	−2.13962	+	2.13962i	−0.0887665	+	0.0887665i
$582$	5.72843	+	2.62107i	0.237451	+	0.108647i
$583$	39.9962			1.65647
$584$	7.54357	−	13.7444i	0.312155	−	0.568747i
$585$	1.10347	+	1.46322i	0.0456228	+	0.0604969i
$586$	1.37243	+	0.627963i	0.0566947	+	0.0259409i
$587$	−18.8514	−	18.8514i	−0.778079	−	0.778079i	0.201425	−	0.979504i	$-0.435443\pi$
$587$	−18.8514	−	18.8514i	−0.778079	−	0.778079i	−0.979504	+	0.201425i	$0.935443\pi$
$588$	−0.429989	+	5.89284i	−0.0177325	+	0.243017i
$589$	−5.31767	−	5.31767i	−0.219111	−	0.219111i
$590$	16.0396	−	25.1138i	0.660340	−	1.03392i
$591$	−10.5004			−0.431927
$592$	9.13571	−	6.79796i	0.375475	−	0.279395i
$593$		−	26.8657i		−	1.10324i	−0.834095	−	0.551621i	$-0.814010\pi$
$593$		−	26.8657i		−	1.10324i	0.834095	−	0.551621i	$-0.185990\pi$
$594$	67.0598	−	24.9571i	2.75150	−	1.02400i
$595$	1.36007	−	9.70347i	0.0557574	−	0.397804i
$596$	−1.97500	+	27.0665i	−0.0808990	+	1.10869i
$597$	46.9410	+	46.9410i	1.92117	+	1.92117i
$598$	−0.0895894	+	0.195800i	−0.00366358	+	0.00800687i
$599$			32.8284i			1.34133i	0.741760	+	0.670666i	$0.233992\pi$
$599$			32.8284i			1.34133i	−0.741760	+	0.670666i	$0.766008\pi$
$600$	−0.205919	−	41.7789i	−0.00840662	−	1.70562i
$601$			18.0401i			0.735870i	0.929851	+	0.367935i	$0.119935\pi$
$601$			18.0401i			0.735870i	−0.929851	+	0.367935i	$0.880065\pi$
$602$	8.03261	+	3.67536i	0.327385	+	0.149796i
$603$	−48.1508	−	48.1508i	−1.96085	−	1.96085i
$604$	−0.624856	−	0.723223i	−0.0254250	−	0.0294275i
$605$	−8.82250	+	62.9445i	−0.358686	+	2.55906i
$606$	−15.4071	−	41.3990i	−0.625872	−	1.68172i
$607$		−	7.89411i		−	0.320412i	−0.987084	−	0.160206i	$-0.948784\pi$
$607$		−	7.89411i		−	0.320412i	0.987084	−	0.160206i	$-0.0512159\pi$
$608$	17.3046	−	26.7147i	0.701795	−	1.08342i
$609$	11.4723			0.464881
$610$	−23.8189	−	15.2126i	−0.964400	−	0.615941i
$611$	0.980561	+	0.980561i	0.0396693	+	0.0396693i
$612$	−37.9830	+	32.8168i	−1.53537	+	1.32654i
$613$	4.65601	+	4.65601i	0.188054	+	0.188054i	0.794854	−	0.606800i	$-0.207547\pi$
$613$	4.65601	+	4.65601i	0.188054	+	0.188054i	−0.606800	+	0.794854i	$0.707547\pi$
$614$	−15.7096	+	34.3338i	−0.633987	+	1.38560i
$615$	24.8987	+	33.0162i	1.00401	+	1.33134i
$616$	4.96662	+	17.0508i	0.200111	+	0.686998i
$617$	−4.68774			−0.188721			−0.0943607	−	0.995538i	$-0.530081\pi$
$617$	−4.68774			−0.188721			−0.0943607	+	0.995538i	$0.530081\pi$
$618$	−30.7425	+	67.1888i	−1.23665	+	2.70273i
$619$	−33.1883	+	33.1883i	−1.33395	+	1.33395i	−0.432151	+	0.901801i	$0.642245\pi$
$619$	−33.1883	+	33.1883i	−1.33395	+	1.33395i	−0.901801	+	0.432151i	$0.857755\pi$
$620$	−5.02149	+	3.24207i	−0.201668	+	0.130205i
$621$	6.06269	+	6.06269i	0.243287	+	0.243287i
$622$	−10.9853	−	29.5176i	−0.440470	−	1.18355i
$623$			12.6158i			0.505440i
$624$	1.67305	+	0.245465i	0.0669755	+	0.00982647i
$625$	21.2208	+	13.2166i	0.848832	+	0.528662i
$626$	−22.7543	+	8.46828i	−0.909446	+	0.338461i
$627$	−73.8030	+	73.8030i	−2.94741	+	2.94741i
$628$	2.59945	−	35.6244i	0.103729	−	1.42157i
$629$	8.82099	−	8.82099i	0.351716	−	0.351716i
$630$	3.90001	+	17.6874i	0.155380	+	0.704684i
$631$		−	40.6288i		−	1.61741i	−0.588217	−	0.808703i	$-0.700170\pi$
$631$		−	40.6288i		−	1.61741i	0.588217	−	0.808703i	$-0.299830\pi$
$632$	−13.1915	+	24.0349i	−0.524730	+	0.956058i
$633$	40.7311			1.61892
$634$	−17.1039	+	37.3811i	−0.679282	+	1.48459i
$635$	−1.69775	+	12.1127i	−0.0673732	+	0.480677i
$636$	28.4794	−	24.6059i	1.12928	−	0.975686i
$637$	0.101184	−	0.101184i	0.00400904	−	0.00400904i
$638$	32.3173	−	12.0273i	1.27946	−	0.476164i
$639$	0.831761			0.0329040
$640$	−17.8618	−	17.9152i	−0.706050	−	0.708162i
$641$	−17.3299			−0.684491			−0.342246	−	0.939611i	$-0.611187\pi$
$641$	−17.3299			−0.684491			−0.342246	+	0.939611i	$0.611187\pi$
$642$	−31.4283	+	11.6964i	−1.24038	+	0.461620i
$643$	7.65082	−	7.65082i	0.301719	−	0.301719i	−0.539967	−	0.841686i	$-0.681563\pi$
$643$	7.65082	−	7.65082i	0.301719	−	0.301719i	0.841686	+	0.539967i	$0.181563\pi$
$644$	−1.61027	+	1.39126i	−0.0634536	+	0.0548232i
$645$	40.8627	+	5.72744i	1.60897	+	0.225518i
$646$	14.5079	−	31.7074i	0.570805	−	1.24751i
$647$	24.5069			0.963465			0.481732	−	0.876318i	$-0.340008\pi$
$647$	24.5069			0.963465			0.481732	+	0.876318i	$0.340008\pi$
$648$	9.01265	−	16.4211i	0.354050	−	0.645080i
$649$			59.1676i			2.32253i
$650$	−0.657729	+	0.768899i	−0.0257982	+	0.0301587i
$651$	2.79198	−	2.79198i	0.109426	−	0.109426i
$652$	−0.538133	+	7.37491i	−0.0210749	+	0.288824i
$653$	20.6822	−	20.6822i	0.809357	−	0.809357i	−0.175179	−	0.984537i	$-0.556050\pi$
$653$	20.6822	−	20.6822i	0.809357	−	0.809357i	0.984537	+	0.175179i	$0.0560505\pi$
$654$	77.1784	−	28.7228i	3.01792	−	1.12315i
$655$	−0.140025	−	0.185676i	−0.00547121	−	0.00725495i
$656$	24.7743	+	3.63483i	0.967276	+	0.141916i
$657$			31.7491i			1.23865i
$658$	4.78017	+	12.8444i	0.186350	+	0.500725i
$659$	−1.30963	−	1.30963i	−0.0510161	−	0.0510161i	0.681138	−	0.732155i	$-0.261485\pi$
$659$	−1.30963	−	1.30963i	−0.0510161	−	0.0510161i	−0.732155	+	0.681138i	$0.761485\pi$
$660$	44.9961	+	69.6924i	1.75147	+	2.71277i
$661$	11.3116	−	11.3116i	0.439968	−	0.439968i	−0.452033	−	0.892001i	$-0.649301\pi$
$661$	11.3116	−	11.3116i	0.439968	−	0.439968i	0.892001	+	0.452033i	$0.149301\pi$
$662$	−2.70292	+	5.90732i	−0.105052	+	0.229594i
$663$	1.85242			0.0719420
$664$	2.39347	+	8.21700i	0.0928847	+	0.318881i
$665$	−7.57562	−	10.0454i	−0.293770	−	0.389545i
$666$	−9.59445	+	20.9690i	−0.371777	+	0.812531i
$667$	2.92172	+	2.92172i	0.113129	+	0.113129i
$668$	−9.00569	+	7.78081i	−0.348441	+	0.301049i
$669$	10.1689	+	10.1689i	0.393151	+	0.393151i
$670$	20.2367	−	31.6853i	0.781811	−	1.22411i
$671$	56.1170			2.16637
$672$	14.0262	+	9.08559i	0.541074	+	0.350484i
$673$		−	29.7376i		−	1.14630i	−0.819450	−	0.573151i	$-0.805721\pi$
$673$		−	29.7376i		−	1.14630i	0.819450	−	0.573151i	$-0.194279\pi$
$674$	−0.112274	−	0.301682i	−0.00432465	−	0.0116204i
$675$	19.5592	+	35.2242i	0.752834	+	1.35578i
$676$	16.9713	+	19.6430i	0.652743	+	0.755499i
$677$	−20.2977	−	20.2977i	−0.780103	−	0.780103i	0.199745	−	0.979848i	$-0.435989\pi$
$677$	−20.2977	−	20.2977i	−0.780103	−	0.780103i	−0.979848	+	0.199745i	$0.935989\pi$
$678$	−54.3295	−	24.8587i	−2.08651	−	0.954694i
$679$		−	1.50782i		−	0.0578649i
$680$	−22.2091	−	16.5775i	−0.851678	−	0.635720i
$681$			51.0002i			1.95433i
$682$	4.93794	−	10.7920i	0.189083	−	0.413248i
$683$	−24.2836	−	24.2836i	−0.929186	−	0.929186i	0.0684674	−	0.997653i	$-0.478189\pi$
$683$	−24.2836	−	24.2836i	−0.929186	−	0.929186i	−0.997653	+	0.0684674i	$0.978189\pi$
$684$	−4.69073	+	64.2846i	−0.179354	+	2.45798i
$685$	−18.2423	−	2.55690i	−0.697002	−	0.0976940i
$686$	1.32540	−	0.493263i	0.0506041	−	0.0188329i
$687$		−	55.5452i		−	2.11918i
$688$	20.0445	−	14.9153i	0.764190	−	0.568640i
$689$	−0.911506			−0.0347256
$690$	−5.35048	+	8.37743i	−0.203689	+	0.318923i
$691$	−3.93339	−	3.93339i	−0.149633	−	0.149633i	0.628321	−	0.777954i	$-0.283742\pi$
$691$	−3.93339	−	3.93339i	−0.149633	−	0.149633i	−0.777954	+	0.628321i	$0.783742\pi$
$692$	−1.77104	+	24.2714i	−0.0673249	+	0.922661i
$693$	−25.4298	−	25.4298i	−0.965999	−	0.965999i
$694$	22.6874	+	10.3807i	0.861201	+	0.394047i
$695$	−6.26820	+	4.72707i	−0.237766	+	0.179308i
$696$	15.6124	−	28.4458i	0.591786	−	1.07824i
$697$	27.4305			1.03900
$698$	22.0467	+	10.0876i	0.834479	+	0.381820i
$699$	−38.2519	+	38.2519i	−1.44682	+	1.44682i
$700$	−9.07271	+	4.20546i	−0.342916	+	0.158952i
$701$	5.87475	+	5.87475i	0.221886	+	0.221886i	0.809292	−	0.587406i	$-0.199851\pi$
$701$	5.87475	+	5.87475i	0.221886	+	0.221886i	−0.587406	+	0.809292i	$0.699851\pi$
$702$	−1.52828	+	0.568766i	−0.0576812	+	0.0214667i
$703$		−	16.0185i		−	0.604150i
$704$	49.0368	+	10.8893i	1.84815	+	0.410405i
$705$	38.5455	+	51.1122i	1.45171	+	1.92500i
$706$	−1.65680	−	4.45184i	−0.0623546	−	0.167547i
$707$	−7.47618	+	7.47618i	−0.281171	+	0.281171i
$708$	36.4002	+	42.1304i	1.36800	+	1.58336i
$709$	17.1706	−	17.1706i	0.644854	−	0.644854i	−0.306891	−	0.951745i	$-0.599289\pi$
$709$	17.1706	−	17.1706i	0.644854	−	0.644854i	0.951745	+	0.306891i	$0.0992885\pi$
$710$	0.0988821	+	0.448452i	0.00371098	+	0.0168301i
$711$		−	55.5199i		−	2.08216i
$712$	31.2810	+	17.1685i	1.17231	+	0.643417i
$713$	1.42210			0.0532581
$714$	16.6476	+	7.61720i	0.623022	+	0.285066i
$715$	0.278871	−	1.98962i	0.0104292	−	0.0744076i
$716$	−39.5128	−	2.88318i	−1.47666	−	0.107749i
$717$	23.7658	−	23.7658i	0.887549	−	0.887549i
$718$	5.53498	+	14.8725i	0.206564	+	0.555038i
$719$	5.39352			0.201144			0.100572	−	0.994930i	$-0.467933\pi$
$719$	5.39352			0.201144			0.100572	+	0.994930i	$0.467933\pi$
$720$	49.1637	+	14.4003i	1.83222	+	0.536666i
$721$	17.6853			0.658633
$722$	−6.24480	−	16.7798i	−0.232407	−	0.624480i
$723$	3.43791	−	3.43791i	0.127857	−	0.127857i
$724$	−0.0358267	+	0.490991i	−0.00133149	+	0.0182476i
$725$	9.42593	+	16.9752i	0.350070	+	0.630442i
$726$	−107.990	−	49.4113i	−4.00788	−	1.83383i
$727$	14.6985			0.545135			0.272568	−	0.962137i	$-0.412127\pi$
$727$	14.6985			0.545135			0.272568	+	0.962137i	$0.412127\pi$
$728$	−0.113188	−	0.388585i	−0.00419504	−	0.0144019i
$729$		−	33.4844i		−	1.24016i
$730$	−17.1179	+	3.77443i	−0.633560	+	0.139698i
$731$	19.3540	−	19.3540i	0.715833	−	0.715833i
$732$	39.9582	−	34.5234i	1.47690	−	1.27602i
$733$	−29.0523	+	29.0523i	−1.07307	+	1.07307i	−0.0759605	+	0.997111i	$0.524202\pi$
$733$	−29.0523	+	29.0523i	−1.07307	+	1.07307i	−0.997111	+	0.0759605i	$0.975798\pi$
$734$	−12.5423	−	33.7012i	−0.462945	−	1.24394i
$735$	5.27424	−	3.97749i	0.194543	−	0.146712i
$736$	1.25826	+	5.88603i	0.0463802	+	0.216962i
$737$			74.6500i			2.74977i
$738$	−47.5213	+	17.6856i	−1.74928	+	0.651015i
$739$	−6.69096	−	6.69096i	−0.246131	−	0.246131i	0.573250	−	0.819381i	$-0.305682\pi$
$739$	−6.69096	−	6.69096i	−0.246131	−	0.246131i	−0.819381	+	0.573250i	$0.805682\pi$
$740$	−12.4462	−	2.68009i	−0.457533	−	0.0985222i
$741$	1.68195	−	1.68195i	0.0617882	−	0.0617882i
$742$	−8.19166	−	3.74813i	−0.300725	−	0.137598i
$743$	−5.66114			−0.207687			−0.103844	−	0.994594i	$-0.533114\pi$
$743$	−5.66114			−0.207687			−0.103844	+	0.994594i	$0.533114\pi$
$744$	−3.12323	−	10.7223i	−0.114503	−	0.393099i
$745$	24.2252	−	18.2691i	0.887544	−	0.669328i
$746$	−7.82016	−	3.57815i	−0.286316	−	0.131005i
$747$	−12.2549	−	12.2549i	−0.448384	−	0.448384i
$748$	54.8818	+	4.00462i	2.00668	+	0.146424i
$749$	5.67558	+	5.67558i	0.207381	+	0.207381i
$750$	−34.9968	+	30.9375i	−1.27790	+	1.12968i
$751$	50.9440			1.85897			0.929487	−	0.368855i	$-0.120250\pi$
$751$	50.9440			1.85897			0.929487	+	0.368855i	$0.120250\pi$
$752$	38.3531	+	5.62706i	1.39859	+	0.205198i
$753$			57.6458i			2.10073i
$754$	−0.736505	+	0.274099i	−0.0268219	+	0.00998209i
$755$	−0.148326	+	1.05824i	−0.00539814	+	0.0385132i
$756$	−16.0734	−	1.17284i	−0.584582	−	0.0426559i
$757$	−1.62825	−	1.62825i	−0.0591798	−	0.0591798i	0.676897	−	0.736077i	$-0.263324\pi$
$757$	−1.62825	−	1.62825i	−0.0591798	−	0.0591798i	−0.736077	+	0.676897i	$0.763324\pi$
$758$	14.9166	−	32.6006i	0.541794	−	1.18411i
$759$		−	19.7371i		−	0.716411i
$760$	−35.2173	+	5.11328i	−1.27747	+	0.185478i
$761$			20.1532i			0.730552i	0.930899	+	0.365276i	$0.119025\pi$
$761$			20.1532i			0.730552i	−0.930899	+	0.365276i	$0.880975\pi$
$762$	−20.7810	−	9.50842i	−0.752815	−	0.344454i
$763$	−13.9375	−	13.9375i	−0.504572	−	0.504572i
$764$	−7.36697	+	6.36497i	−0.266528	+	0.230277i
$765$	55.5777	+	7.78994i	2.00942	+	0.281646i
$766$	14.6275	+	39.3042i	0.528513	+	1.42012i
$767$		−	1.34842i		−	0.0486885i
$768$	41.6159	−	22.4140i	1.50168	−	0.808794i
$769$	17.6941			0.638066			0.319033	−	0.947744i	$-0.396642\pi$
$769$	17.6941			0.638066			0.319033	+	0.947744i	$0.396642\pi$
$770$	10.6876	−	16.7339i	0.385154	−	0.603048i
$771$	−35.1873	−	35.1873i	−1.26724	−	1.26724i
$772$	−9.74284	−	11.2766i	−0.350653	−	0.405853i
$773$	−13.0695	−	13.0695i	−0.470077	−	0.470077i	0.431862	−	0.901940i	$-0.357857\pi$
$773$	−13.0695	−	13.0695i	−0.470077	−	0.470077i	−0.901940	+	0.431862i	$0.857857\pi$
$774$	−21.0510	+	46.0076i	−0.756663	+	1.65371i
$775$	6.42515	+	1.83723i	0.230798	+	0.0659953i
$776$	−3.73867	−	2.05196i	−0.134210	−	0.0736610i
$777$	8.41034			0.301719
$778$	−3.57273	+	7.80832i	−0.128089	+	0.279942i
$779$	24.9063	−	24.9063i	0.892359	−	0.892359i
$780$	−1.02545	−	1.58828i	−0.0367171	−	0.0568694i
$781$	−0.644755	−	0.644755i	−0.0230712	−	0.0230712i
$782$	2.29983	+	6.17967i	0.0822418	+	0.220984i
$783$			31.2920i			1.11828i
$784$	0.580654	−	3.95763i	0.0207376	−	0.141344i
$785$	−31.8848	+	24.0454i	−1.13802	+	0.858218i
$786$	0.407229	−	0.151555i	0.0145254	−	0.00540578i
$787$	−19.4112	+	19.4112i	−0.691935	+	0.691935i	−0.962657	−	0.270723i	$-0.912737\pi$
$787$	−19.4112	+	19.4112i	−0.691935	+	0.691935i	0.270723	+	0.962657i	$0.412737\pi$
$788$	7.08980	+	0.517329i	0.252564	+	0.0184291i
$789$	25.6797	−	25.6797i	0.914222	−	0.914222i
$790$	29.9341	−	6.60036i	1.06501	−	0.234830i
$791$			14.3005i			0.508466i
$792$	−97.6606	+	28.4469i	−3.47022	+	1.01082i
$793$	−1.27889			−0.0454149
$794$	−1.88847	+	4.12731i	−0.0670192	+	0.146473i
$795$	−41.6718	−	5.84085i	−1.47795	−	0.207154i
$796$	−29.3816	−	34.0070i	−1.04140	−	1.20535i
$797$	−12.0403	+	12.0403i	−0.426490	+	0.426490i	−0.887431	−	0.460941i	$-0.847512\pi$
$797$	−12.0403	+	12.0403i	−0.426490	+	0.426490i	0.460941	+	0.887431i	$0.347512\pi$
$798$	22.0319	−	8.19942i	0.779921	−	0.290256i
$799$	42.4650			1.50230
$800$	−1.91932	+	28.2191i	−0.0678581	+	0.997695i
$801$	−72.2582			−2.55312
$802$	−13.7151	+	5.10422i	−0.484296	+	0.180236i
$803$	24.6109	−	24.6109i	0.868501	−	0.868501i
$804$	45.9250	+	53.1546i	1.61965	+	1.87462i
$805$	2.35619	+	0.330251i	0.0830449	+	0.0116398i
$806$	−0.112535	+	0.245948i	−0.00396386	+	0.00866314i
$807$	0.315705			0.0111134
$808$	8.36317	+	28.7115i	0.294215	+	1.01007i
$809$		−	18.0865i		−	0.635887i	−0.948110	−	0.317943i	$-0.897008\pi$
$809$		−	18.0865i		−	0.635887i	0.948110	−	0.317943i	$-0.102992\pi$
$810$	−20.4515	+	4.50948i	−0.718592	+	0.158447i
$811$	−11.8195	+	11.8195i	−0.415038	+	0.415038i	−0.883489	−	0.468452i	$-0.844812\pi$
$811$	−11.8195	+	11.8195i	−0.415038	+	0.415038i	0.468452	+	0.883489i	$0.344812\pi$
$812$	−7.74604	−	0.565214i	−0.271833	−	0.0198351i
$813$	−56.1066	+	56.1066i	−1.96774	+	1.96774i
$814$	23.6918	−	8.81717i	0.830398	−	0.309042i
$815$	6.60073	−	4.97784i	0.231214	−	0.174366i
$816$	41.5424	−	30.9120i	1.45427	−	1.08214i
$817$		−	35.1460i		−	1.22960i
$818$	−8.19740	−	22.0265i	−0.286615	−	0.770138i
$819$	0.579540	+	0.579540i	0.0202508	+	0.0202508i
$820$	−15.1848	−	23.5191i	−0.530277	−	0.821321i
$821$	8.16806	−	8.16806i	0.285067	−	0.285067i	−0.550059	−	0.835126i	$-0.685395\pi$
$821$	8.16806	−	8.16806i	0.285067	−	0.285067i	0.835126	+	0.550059i	$0.185395\pi$
$822$	14.3202	−	31.2971i	0.499473	−	1.09161i
$823$	−1.53460			−0.0534928			−0.0267464	−	0.999642i	$-0.508515\pi$
$823$	−1.53460			−0.0534928			−0.0267464	+	0.999642i	$0.508515\pi$
$824$	24.0674	−	43.8509i	0.838429	−	1.52762i
$825$	25.4986	−	89.1736i	0.887748	−	3.10463i
$826$	5.54473	−	12.1182i	0.192926	−	0.421645i
$827$	−12.6155	−	12.6155i	−0.438683	−	0.438683i	0.452886	−	0.891568i	$-0.350395\pi$
$827$	−12.6155	−	12.6155i	−0.438683	−	0.438683i	−0.891568	+	0.452886i	$0.850395\pi$
$828$	−7.96857	−	9.22301i	−0.276927	−	0.320522i
$829$	13.7265	+	13.7265i	0.476742	+	0.476742i	0.904088	−	0.427346i	$-0.140551\pi$
$829$	13.7265	+	13.7265i	0.476742	+	0.476742i	−0.427346	+	0.904088i	$0.640551\pi$
$830$	5.15047	−	8.06427i	0.178775	−	0.279915i
$831$	4.88561			0.169480
$832$	−1.11754	−	0.248164i	−0.0387437	−	0.00860354i
$833$		−	4.38194i		−	0.151825i
$834$	−5.11631	−	13.7476i	−0.177163	−	0.476039i
$835$	13.1774	+	1.84698i	0.456022	+	0.0639174i
$836$	53.4675	−	46.1953i	1.84921	−	1.59770i
$837$	7.61543	+	7.61543i	0.263228	+	0.263228i
$838$	8.83297	+	4.04156i	0.305130	+	0.139614i
$839$			22.1803i			0.765751i	0.923800	+	0.382875i	$0.125066\pi$
$839$			22.1803i			0.765751i	−0.923800	+	0.382875i	$0.874934\pi$
$840$	−2.68467	−	18.4905i	−0.0926299	−	0.637981i
$841$		−	13.9198i		−	0.479994i
$842$	4.59882	−	10.0509i	0.158486	−	0.346376i
$843$	23.8671	+	23.8671i	0.822027	+	0.822027i
$844$	−27.5015	−	2.00673i	−0.946639	−	0.0690745i
$845$	4.02859	−	28.7421i	0.138588	−	0.988760i
$846$	−73.5675	+	27.3790i	−2.52930	+	0.941308i
$847$			28.4248i			0.976688i
$848$	−20.4414	+	15.2106i	−0.701961	+	0.522335i
$849$	−53.6633			−1.84172
$850$	2.40721	+	30.8914i	0.0825666	+	1.05957i
$851$	2.14191	+	2.14191i	0.0734237	+	0.0734237i
$852$	−0.855755	−	0.0624429i	−0.0293177	−	0.00213926i
$853$	−2.64300	−	2.64300i	−0.0904945	−	0.0904945i	0.660410	−	0.750905i	$-0.270382\pi$
$853$	−2.64300	−	2.64300i	−0.0904945	−	0.0904945i	−0.750905	+	0.660410i	$0.770382\pi$
$854$	−11.4934	−	5.25885i	−0.393295	−	0.179954i
$855$	57.5363	−	43.3902i	1.96770	−	1.48391i
$856$	21.7965	−	6.34895i	0.744989	−	0.217003i
$857$	−8.47448			−0.289483			−0.144741	−	0.989470i	$-0.546235\pi$
$857$	−8.47448			−0.289483			−0.144741	+	0.989470i	$0.546235\pi$
$858$	3.41347	+	1.56185i	0.116534	+	0.0533206i
$859$	14.9964	−	14.9964i	0.511672	−	0.511672i	−0.403367	−	0.915038i	$-0.632160\pi$
$859$	14.9964	−	14.9964i	0.511672	−	0.511672i	0.915038	+	0.403367i	$0.132160\pi$
$860$	−27.3081	−	5.88035i	−0.931198	−	0.200518i
$861$	13.0767	+	13.0767i	0.445654	+	0.445654i
$862$	12.9850	−	4.83250i	0.442270	−	0.164596i
$863$			27.6715i			0.941948i	0.882147	+	0.470974i	$0.156098\pi$
$863$			27.6715i			0.941948i	−0.882147	+	0.470974i	$0.843902\pi$
$864$	−24.7820	+	38.2581i	−0.843099	+	1.30157i
$865$	21.7235	−	16.3825i	0.738623	−	0.557021i
$866$	−5.38481	−	14.4690i	−0.182983	−	0.491678i
$867$	4.59872	−	4.59872i	0.156181	−	0.156181i
$868$	−2.02269	+	1.74758i	−0.0686544	+	0.0593166i
$869$	−43.0373	+	43.0373i	−1.45994	+	1.45994i
$870$	−35.4276	+	7.81166i	−1.20111	+	0.264840i
$871$		−	1.70126i		−	0.0576449i
$872$	−53.5256	+	15.5911i	−1.81261	+	0.527981i
$873$	8.63621			0.292291
$874$	7.69919	+	3.52280i	0.260429	+	0.119160i
$875$	10.2188	+	4.53610i	0.345458	+	0.153348i
$876$	2.38351	−	32.6650i	0.0805312	−	1.10365i
$877$	−31.8910	+	31.8910i	−1.07688	+	1.07688i	−0.0800964	+	0.996787i	$0.525523\pi$
$877$	−31.8910	+	31.8910i	−1.07688	+	1.07688i	−0.996787	+	0.0800964i	$0.974477\pi$
$878$	−4.68910	−	12.5996i	−0.158249	−	0.425217i
$879$	3.15283			0.106342
$880$	−26.9476	−	49.2728i	−0.908403	−	1.66099i
$881$	−4.53041			−0.152633			−0.0763167	−	0.997084i	$-0.524316\pi$
$881$	−4.53041			−0.152633			−0.0763167	+	0.997084i	$0.524316\pi$
$882$	2.82522	+	7.59139i	0.0951301	+	0.255615i
$883$	−26.5399	+	26.5399i	−0.893139	+	0.893139i	−0.994817	−	0.101679i	$-0.967579\pi$
$883$	−26.5399	+	26.5399i	−0.893139	+	0.893139i	0.101679	+	0.994817i	$0.467579\pi$
$884$	−1.25074	−	0.0912645i	−0.0420671	−	0.00306956i
$885$	8.64054	−	61.6463i	0.290449	−	2.07222i
$886$	−1.06115	−	0.485533i	−0.0356499	−	0.0163118i
$887$	−9.63489			−0.323508			−0.161754	−	0.986831i	$-0.551715\pi$
$887$	−9.63489			−0.323508			−0.161754	+	0.986831i	$0.551715\pi$
$888$	11.4454	−	20.8536i	0.384084	−	0.699801i
$889$			5.46991i			0.183455i
$890$	−8.59026	−	38.9587i	−0.287946	−	1.30590i
$891$	29.4038	−	29.4038i	0.985065	−	0.985065i
$892$	−6.36497	−	7.36696i	−0.213115	−	0.246664i
$893$	38.5573	−	38.5573i	1.29027	−	1.29027i
$894$	19.7734	+	53.1314i	0.661323	+	1.77698i
$895$	26.6700	+	35.3650i	0.891478	+	1.18212i
$896$	−9.02282	−	6.82559i	−0.301431	−	0.228027i
$897$			0.449804i			0.0150185i
$898$	−55.3014	+	20.5810i	−1.84543	+	0.686798i
$899$	3.67001	+	3.67001i	0.122402	+	0.122402i
$900$	−24.0872	−	51.9649i	−0.802908	−	1.73216i
$901$	−19.7372	+	19.7372i	−0.657542	+	0.657542i
$902$	50.5463	+	23.1277i	1.68301	+	0.770068i
$903$	18.4530			0.614076
$904$	35.4583	+	19.4612i	1.17933	+	0.647269i
$905$	0.439450	−	0.331405i	0.0146078	−	0.0110163i
$906$	−1.81555	−	0.830714i	−0.0603177	−	0.0275986i
$907$	−7.30276	−	7.30276i	−0.242484	−	0.242484i	0.575393	−	0.817877i	$-0.304849\pi$
$907$	−7.30276	−	7.30276i	−0.242484	−	0.242484i	−0.817877	+	0.575393i	$0.804849\pi$
$908$	2.51266	−	34.4351i	0.0833856	−	1.14277i
$909$	−42.8207	−	42.8207i	−1.42027	−	1.42027i
$910$	−0.243568	+	0.381362i	−0.00807419	+	0.0126420i
$911$	−1.26732			−0.0419883			−0.0209942	−	0.999780i	$-0.506683\pi$
$911$	−1.26732			−0.0419883			−0.0209942	+	0.999780i	$0.506683\pi$
$912$	9.65209	−	65.7869i	0.319613	−	2.17842i
$913$			18.9993i			0.628784i
$914$	20.8434	−	7.75712i	0.689440	−	0.256583i
$915$	−58.4679	−	8.19504i	−1.93289	−	0.270920i
$916$	−2.73658	+	37.5038i	−0.0904193	+	1.23916i
$917$	−0.0735407	−	0.0735407i	−0.00242853	−	0.00242853i
$918$	−20.7767	+	45.4082i	−0.685735	+	1.49869i
$919$			6.44861i			0.212720i	0.994328	+	0.106360i	$0.0339196\pi$
$919$			6.44861i			0.212720i	−0.994328	+	0.106360i	$0.966080\pi$
$920$	4.02535	−	5.39279i	0.132712	−	0.177795i
$921$			78.8736i			2.59897i
$922$	−37.9113	−	17.3465i	−1.24854	−	0.571277i
$923$	0.0146938	+	0.0146938i	0.000483654	+	0.000483654i
$924$	24.2543	+	28.0725i	0.797908	+	0.923518i
$925$	6.91014	+	12.4445i	0.227204	+	0.409172i
$926$	−20.7528	−	55.7630i	−0.681980	−	1.83249i
$927$			101.294i			3.32694i
$928$	−11.9429	+	18.4373i	−0.392044	+	0.605233i
$929$	−16.3142			−0.535252			−0.267626	−	0.963523i	$-0.586239\pi$
$929$	−16.3142			−0.535252			−0.267626	+	0.963523i	$0.586239\pi$
$930$	−6.72081	+	10.5230i	−0.220384	+	0.345063i
$931$	−3.97870	−	3.97870i	−0.130397	−	0.130397i
$932$	27.7121	−	23.9429i	0.907739	−	0.784276i
$933$	−46.5228	−	46.5228i	−1.52309	−	1.52309i
$934$	−5.36806	+	11.7321i	−0.175648	+	0.383885i
$935$	−37.0436	−	49.1206i	−1.21145	−	1.60642i
$936$	2.22566	−	0.648298i	0.0727481	−	0.0211903i
$937$	4.87282			0.159188			0.0795940	−	0.996827i	$-0.474638\pi$
$937$	4.87282			0.159188			0.0795940	+	0.996827i	$0.474638\pi$
$938$	6.99561	−	15.2891i	0.228415	−	0.499208i
$939$	−35.8632	+	35.8632i	−1.17035	+	1.17035i
$940$	−23.5076	−	36.4098i	−0.766732	−	1.18756i
$941$	5.56001	+	5.56001i	0.181251	+	0.181251i	0.791901	−	0.610650i	$-0.209092\pi$
$941$	5.56001	+	5.56001i	0.181251	+	0.181251i	−0.610650	+	0.791901i	$0.709092\pi$
$942$	−26.0254	−	69.9305i	−0.847954	−	2.27846i
$943$			6.66066i			0.216901i
$944$	−22.5015	−	30.2396i	−0.732363	−	0.984215i
$945$	10.8490	+	14.3861i	0.352919	+	0.467979i
$946$	51.9818	−	19.3456i	1.69007	−	0.628980i
$947$	32.8826	−	32.8826i	1.06854	−	1.06854i	0.0710710	−	0.997471i	$-0.477358\pi$
$947$	32.8826	−	32.8826i	1.06854	−	1.06854i	0.997471	−	0.0710710i	$-0.0226417\pi$
$948$	−4.16805	+	57.1215i	−0.135372	+	1.85522i
$949$	−0.560878	+	0.560878i	−0.0182069	+	0.0182069i
$950$	30.2343	+	25.8630i	0.980932	+	0.839105i
$951$			85.8739i			2.78465i
$952$	−10.8651	−	5.96329i	−0.352140	−	0.193271i
$953$	−24.0199			−0.778079			−0.389040	−	0.921221i	$-0.627193\pi$
$953$	−24.0199			−0.778079			−0.389040	+	0.921221i	$0.627193\pi$
$954$	21.4678	−	46.9186i	0.695047	−	1.51905i
$955$	10.7795	+	1.51089i	0.348818	+	0.0488914i
$956$	−17.2174	+	14.8757i	−0.556851	+	0.481113i
$957$	50.9355	−	50.9355i	1.64651	−	1.64651i
$958$	−21.6700	+	8.06473i	−0.700125	+	0.260559i
$959$	−8.23795			−0.266017
$960$	−49.5009	−	18.5065i	−1.59764	−	0.597296i
$961$	−29.2137			−0.942377
$962$	−0.539931	+	0.200942i	−0.0174081	+	0.00647861i
$963$	−32.5075	+	32.5075i	−1.04754	+	1.04754i
$964$	−2.49064	+	2.15188i	−0.0802180	+	0.0693074i
$965$	−2.31272	+	16.5002i	−0.0744491	+	0.531161i
$966$	−1.84961	+	4.04237i	−0.0595101	+	0.130061i
$967$	58.7494			1.88925			0.944626	−	0.328148i	$-0.106424\pi$
$967$	58.7494			1.88925			0.944626	+	0.328148i	$0.106424\pi$
$968$	70.4799	+	38.6827i	2.26531	+	1.24331i
$969$		−	72.8402i		−	2.33996i
$970$	1.02670	+	4.65630i	0.0329653	+	0.149505i
$971$	24.6303	−	24.6303i	0.790423	−	0.790423i	−0.191140	−	0.981563i	$-0.561218\pi$
$971$	24.6303	−	24.6303i	0.790423	−	0.790423i	0.981563	+	0.191140i	$0.0612184\pi$
$972$	−0.670847	+	9.19370i	−0.0215174	+	0.294888i
$973$	−2.48265	+	2.48265i	−0.0795900	+	0.0795900i
$974$	34.2494	−	12.7463i	1.09742	−	0.408417i
$975$	−0.581108	+	2.03225i	−0.0186104	+	0.0650840i
$976$	−28.6805	+	21.3414i	−0.918040	+	0.683121i
$977$		−	48.2488i		−	1.54362i	−0.635855	−	0.771808i	$-0.719353\pi$
$977$		−	48.2488i		−	1.54362i	0.635855	−	0.771808i	$-0.280647\pi$
$978$	5.38774	+	14.4769i	0.172281	+	0.462920i
$979$	56.0123	+	56.0123i	1.79016	+	1.79016i
$980$	−3.75710	+	2.42573i	−0.120016	+	0.0774872i
$981$	79.8287	−	79.8287i	2.54873	−	2.54873i
$982$	11.8257	−	25.8455i	0.377374	−	0.824762i
$983$	7.70564			0.245772			0.122886	−	0.992421i	$-0.460785\pi$
$983$	7.70564			0.245772			0.122886	+	0.992421i	$0.460785\pi$
$984$	50.2199	−	14.6282i	1.60095	−	0.466330i
$985$	−4.78540	−	6.34555i	−0.152476	−	0.202186i
$986$	−10.0127	+	21.8830i	−0.318869	+	0.696898i
$987$	20.2440	+	20.2440i	0.644375	+	0.644375i
$988$	−1.21851	+	1.05278i	−0.0387661	+	0.0334934i
$989$	4.69953	+	4.69953i	0.149436	+	0.149436i
$990$	95.8453	+	61.2143i	3.04616	+	1.94552i
$991$	−40.0412			−1.27195			−0.635975	−	0.771709i	$-0.719402\pi$
$991$	−40.0412			−1.27195			−0.635975	+	0.771709i	$0.719402\pi$
$992$	1.58052	+	7.39352i	0.0501817	+	0.234745i
$993$			13.5706i			0.430651i
$994$	0.0716315	+	0.192474i	0.00227201	+	0.00610492i
$995$	−6.97451	+	49.7600i	−0.221107	+	1.57750i
$996$	11.6884	+	13.5285i	0.370362	+	0.428666i
$997$	2.49869	+	2.49869i	0.0791342	+	0.0791342i	0.745566	−	0.666432i	$-0.232179\pi$
$997$	2.49869	+	2.49869i	0.0791342	+	0.0791342i	−0.666432	+	0.745566i	$0.732179\pi$
$998$	41.0586	+	18.7865i	1.29969	+	0.594678i
$999$			22.9401i			0.725793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.c.29.4	✓	70
5.4	even	2		560.2.bb.d.29.32	yes	70
16.5	even	4		560.2.bb.d.309.32	yes	70
80.69	even	4	inner	560.2.bb.c.309.4	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.4	✓	70	1.1	even	1	trivial
560.2.bb.c.309.4	yes	70	80.69	even	4	inner
560.2.bb.d.29.32	yes	70	5.4	even	2
560.2.bb.d.309.32	yes	70	16.5	even	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32540 + 0.493263i) q^{2} +(-2.08897 + 2.08897i) q^{3} +(1.51338 - 1.30754i) q^{4} +(-2.21442 - 0.310380i) q^{5} +(1.73832 - 3.79914i) q^{6} -1.00000 q^{7} +(-1.36088 + 2.47952i) q^{8} -5.72761i q^{9} +O(q^{10})\)	\(q+(-1.32540 + 0.493263i) q^{2} +(-2.08897 + 2.08897i) q^{3} +(1.51338 - 1.30754i) q^{4} +(-2.21442 - 0.310380i) q^{5} +(1.73832 - 3.79914i) q^{6} -1.00000 q^{7} +(-1.36088 + 2.47952i) q^{8} -5.72761i q^{9} +(3.08810 - 0.680914i) q^{10} +(-4.43987 + 4.43987i) q^{11} +(-0.429989 + 5.89284i) q^{12} +(0.101184 - 0.101184i) q^{13} +(1.32540 - 0.493263i) q^{14} +(5.27424 - 3.97749i) q^{15} +(0.580654 - 3.95763i) q^{16} -4.38194i q^{17} +(2.82522 + 7.59139i) q^{18} +(-3.97870 - 3.97870i) q^{19} +(-3.75710 + 2.42573i) q^{20} +(2.08897 - 2.08897i) q^{21} +(3.69459 - 8.07463i) q^{22} +1.06402 q^{23} +(-2.33681 - 8.02248i) q^{24} +(4.80733 + 1.37463i) q^{25} +(-0.0841988 + 0.184019i) q^{26} +(5.69790 + 5.69790i) q^{27} +(-1.51338 + 1.30754i) q^{28} +(2.74592 + 2.74592i) q^{29} +(-5.02854 + 7.87336i) q^{30} +1.33653 q^{31} +(1.18255 + 5.53187i) q^{32} -18.5495i q^{33} +(2.16145 + 5.80784i) q^{34} +(2.21442 + 0.310380i) q^{35} +(-7.48911 - 8.66806i) q^{36} +(2.01303 + 2.01303i) q^{37} +(7.23593 + 3.31083i) q^{38} +0.422739i q^{39} +(3.78315 - 5.06831i) q^{40} +6.25989i q^{41} +(-1.73832 + 3.79914i) q^{42} +(4.41676 + 4.41676i) q^{43} +(-0.913892 + 12.5245i) q^{44} +(-1.77774 + 12.6833i) q^{45} +(-1.41026 + 0.524843i) q^{46} +9.69091i q^{47} +(7.05441 + 9.48035i) q^{48} +1.00000 q^{49} +(-7.04970 + 0.549347i) q^{50} +(9.15376 + 9.15376i) q^{51} +(0.0208274 - 0.285432i) q^{52} +(-4.50422 - 4.50422i) q^{53} +(-10.3626 - 4.74144i) q^{54} +(11.2098 - 8.45369i) q^{55} +(1.36088 - 2.47952i) q^{56} +16.6228 q^{57} +(-4.99391 - 2.28499i) q^{58} +(6.66322 - 6.66322i) q^{59} +(2.78120 - 12.9158i) q^{60} +(-6.31967 - 6.31967i) q^{61} +(-1.77144 + 0.659263i) q^{62} +5.72761i q^{63} +(-4.29603 - 6.74864i) q^{64} +(-0.255469 + 0.192658i) q^{65} +(9.14979 + 24.5856i) q^{66} +(8.40678 - 8.40678i) q^{67} +(-5.72959 - 6.63156i) q^{68} +(-2.22271 + 2.22271i) q^{69} +(-3.08810 + 0.680914i) q^{70} +0.145220i q^{71} +(14.2017 + 7.79457i) q^{72} -5.54317 q^{73} +(-3.66103 - 1.67512i) q^{74} +(-12.9139 + 7.17082i) q^{75} +(-11.2236 - 0.818968i) q^{76} +(4.43987 - 4.43987i) q^{77} +(-0.208522 - 0.560300i) q^{78} +9.69338 q^{79} +(-2.51418 + 8.58364i) q^{80} -6.62268 q^{81} +(-3.08778 - 8.29688i) q^{82} +(2.13962 - 2.13962i) q^{83} +(0.429989 - 5.89284i) q^{84} +(-1.36007 + 9.70347i) q^{85} +(-8.03261 - 3.67536i) q^{86} -11.4723 q^{87} +(-4.96662 - 17.0508i) q^{88} -12.6158i q^{89} +(-3.90001 - 17.6874i) q^{90} +(-0.101184 + 0.101184i) q^{91} +(1.61027 - 1.39126i) q^{92} +(-2.79198 + 2.79198i) q^{93} +(-4.78017 - 12.8444i) q^{94} +(7.57562 + 10.0454i) q^{95} +(-14.0262 - 9.08559i) q^{96} +1.50782i q^{97} +(-1.32540 + 0.493263i) q^{98} +(25.4298 + 25.4298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * q^10 - 2 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 + 18 * q^18 + 14 * q^19 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * q^50 + 8 * q^51 - 28 * q^52 + 30 * q^53 - 32 * q^54 - 6 * q^55 + 8 * q^56 + 76 * q^57 - 56 * q^58 + 2 * q^59 - 64 * q^60 + 30 * q^61 - 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 - 6 * q^67 + 36 * q^68 - 16 * q^69 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * q^80 - 82 * q^81 - 24 * q^82 - 10 * q^83 - 4 * q^84 - 32 * q^85 + 32 * q^86 + 4 * q^87 - 32 * q^88 + 158 * q^90 + 6 * q^91 + 92 * q^92 + 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 - 2 * q^98 - 34 * q^99

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