LMFDB - Embedded newform 560.2.bb.d.29.7

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			29.7
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17664 - 0.784556i) q^{2} +(-0.0419138 + 0.0419138i) q^{3} +(0.768944 + 1.84627i) q^{4} +(0.673232 + 2.13231i) q^{5} +(0.0822009 - 0.0164335i) q^{6} +1.00000 q^{7} +(0.543737 - 2.77567i) q^{8} +2.99649i q^{9} +O(q^{10})$	\(q+(-1.17664 - 0.784556i) q^{2} +(-0.0419138 + 0.0419138i) q^{3} +(0.768944 + 1.84627i) q^{4} +(0.673232 + 2.13231i) q^{5} +(0.0822009 - 0.0164335i) q^{6} +1.00000 q^{7} +(0.543737 - 2.77567i) q^{8} +2.99649i q^{9} +(0.880770 - 3.03714i) q^{10} +(-2.53433 + 2.53433i) q^{11} +(-0.109614 - 0.0451549i) q^{12} +(1.58083 - 1.58083i) q^{13} +(-1.17664 - 0.784556i) q^{14} +(-0.117591 - 0.0611556i) q^{15} +(-2.81745 + 2.83936i) q^{16} -0.0619836i q^{17} +(2.35091 - 3.52577i) q^{18} +(0.275189 + 0.275189i) q^{19} +(-3.41915 + 2.88260i) q^{20} +(-0.0419138 + 0.0419138i) q^{21} +(4.97031 - 0.993660i) q^{22} -7.89979 q^{23} +(0.0935487 + 0.139129i) q^{24} +(-4.09352 + 2.87108i) q^{25} +(-3.10031 + 0.619812i) q^{26} +(-0.251335 - 0.251335i) q^{27} +(0.768944 + 1.84627i) q^{28} +(0.644284 + 0.644284i) q^{29} +(0.0903818 + 0.164214i) q^{30} -2.33937 q^{31} +(5.54275 - 1.13045i) q^{32} -0.212447i q^{33} +(-0.0486296 + 0.0729321i) q^{34} +(0.673232 + 2.13231i) q^{35} +(-5.53233 + 2.30413i) q^{36} +(0.912703 + 0.912703i) q^{37} +(-0.107896 - 0.539699i) q^{38} +0.132517i q^{39} +(6.28466 - 0.709253i) q^{40} +3.67993i q^{41} +(0.0822009 - 0.0164335i) q^{42} +(-1.75313 - 1.75313i) q^{43} +(-6.62782 - 2.73031i) q^{44} +(-6.38945 + 2.01733i) q^{45} +(9.29518 + 6.19783i) q^{46} +10.7157i q^{47} +(-0.000918450 - 0.237098i) q^{48} +1.00000 q^{49} +(7.06910 - 0.166626i) q^{50} +(0.00259797 + 0.00259797i) q^{51} +(4.13421 + 1.70307i) q^{52} +(7.11440 + 7.11440i) q^{53} +(0.0985435 + 0.492917i) q^{54} +(-7.11018 - 3.69779i) q^{55} +(0.543737 - 2.77567i) q^{56} -0.0230684 q^{57} +(-0.252611 - 1.26356i) q^{58} +(5.76751 - 5.76751i) q^{59} +(0.0224890 - 0.264130i) q^{60} +(7.45281 + 7.45281i) q^{61} +(2.75258 + 1.83536i) q^{62} +2.99649i q^{63} +(-7.40870 - 3.01847i) q^{64} +(4.43509 + 2.30656i) q^{65} +(-0.166676 + 0.249972i) q^{66} +(8.97977 - 8.97977i) q^{67} +(0.114439 - 0.0476619i) q^{68} +(0.331110 - 0.331110i) q^{69} +(0.880770 - 3.03714i) q^{70} -5.82385i q^{71} +(8.31726 + 1.62930i) q^{72} -3.69118 q^{73} +(-0.357853 - 1.78999i) q^{74} +(0.0512368 - 0.291913i) q^{75} +(-0.296469 + 0.719680i) q^{76} +(-2.53433 + 2.53433i) q^{77} +(0.103967 - 0.155924i) q^{78} +15.3579 q^{79} +(-7.95121 - 4.09613i) q^{80} -8.96839 q^{81} +(2.88711 - 4.32994i) q^{82} +(-7.39047 + 7.39047i) q^{83} +(-0.109614 - 0.0451549i) q^{84} +(0.132168 - 0.0417293i) q^{85} +(0.687369 + 3.43823i) q^{86} -0.0540087 q^{87} +(5.65646 + 8.41247i) q^{88} +9.78411i q^{89} +(9.10076 + 2.63921i) q^{90} +(1.58083 - 1.58083i) q^{91} +(-6.07450 - 14.5852i) q^{92} +(0.0980517 - 0.0980517i) q^{93} +(8.40704 - 12.6084i) q^{94} +(-0.401524 + 0.772056i) q^{95} +(-0.184936 + 0.279699i) q^{96} -8.28186i q^{97} +(-1.17664 - 0.784556i) q^{98} +(-7.59408 - 7.59408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 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} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 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} - 8 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} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 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} + 18 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 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * 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 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * 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 - 8 * 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 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * 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 + 18 * 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 $

$2$	−1.17664	−	0.784556i	−0.832007	−	0.554765i
$2$	−1.17664	−	0.784556i	−0.832007	−	0.554765i
$3$	−0.0419138	+	0.0419138i	−0.0241989	+	0.0241989i	−0.719103	−	0.694904i	$-0.755447\pi$
$3$	−0.0419138	+	0.0419138i	−0.0241989	+	0.0241989i	0.694904	+	0.719103i	$0.255447\pi$
$4$	0.768944	+	1.84627i	0.384472	+	0.923137i
$5$	0.673232	+	2.13231i	0.301079	+	0.953599i
$5$	0.673232	+	2.13231i	0.301079	+	0.953599i
$6$	0.0822009	−	0.0164335i	0.0335584	−	0.00670897i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.543737	−	2.77567i	0.192240	−	0.981348i
$9$			2.99649i			0.998829i
$10$	0.880770	−	3.03714i	0.278524	−	0.960429i
$11$	−2.53433	+	2.53433i	−0.764129	+	0.764129i	−0.977066	−	0.212937i	$-0.931697\pi$
$11$	−2.53433	+	2.53433i	−0.764129	+	0.764129i	0.212937	+	0.977066i	$0.431697\pi$
$12$	−0.109614	−	0.0451549i	−0.0316427	−	0.0130351i
$13$	1.58083	−	1.58083i	0.438443	−	0.438443i	−0.453045	−	0.891488i	$-0.649662\pi$
$13$	1.58083	−	1.58083i	0.438443	−	0.438443i	0.891488	+	0.453045i	$0.149662\pi$
$14$	−1.17664	−	0.784556i	−0.314469	−	0.209681i
$15$	−0.117591	−	0.0611556i	−0.0303618	−	0.0157903i
$16$	−2.81745	+	2.83936i	−0.704362	+	0.709841i
$17$		−	0.0619836i		−	0.0150332i	−0.999972	−	0.00751661i	$-0.997607\pi$
$17$		−	0.0619836i		−	0.0150332i	0.999972	−	0.00751661i	$-0.00239264\pi$
$18$	2.35091	−	3.52577i	0.554115	−	0.831033i
$19$	0.275189	+	0.275189i	0.0631328	+	0.0631328i	0.737968	−	0.674835i	$-0.235785\pi$
$19$	0.275189	+	0.275189i	0.0631328	+	0.0631328i	−0.674835	+	0.737968i	$0.735785\pi$
$20$	−3.41915	+	2.88260i	−0.764546	+	0.644569i
$21$	−0.0419138	+	0.0419138i	−0.00914633	+	0.00914633i
$22$	4.97031	−	0.993660i	1.05967	−	0.211849i
$23$	−7.89979			−1.64722			−0.823610	−	0.567156i	$-0.808044\pi$
$23$	−7.89979			−1.64722			−0.823610	+	0.567156i	$0.808044\pi$
$24$	0.0935487	+	0.139129i	0.0190956	+	0.0283996i
$25$	−4.09352	+	2.87108i	−0.818703	+	0.574217i
$26$	−3.10031	+	0.619812i	−0.608021	+	0.121555i
$27$	−0.251335	−	0.251335i	−0.0483695	−	0.0483695i
$28$	0.768944	+	1.84627i	0.145317	+	0.348913i
$29$	0.644284	+	0.644284i	0.119641	+	0.119641i	0.764392	−	0.644752i	$-0.223039\pi$
$29$	0.644284	+	0.644284i	0.119641	+	0.119641i	−0.644752	+	0.764392i	$0.723039\pi$
$30$	0.0903818	+	0.164214i	0.0165014	+	0.0299813i
$31$	−2.33937			−0.420163			−0.210081	−	0.977684i	$-0.567373\pi$
$31$	−2.33937			−0.420163			−0.210081	+	0.977684i	$0.567373\pi$
$32$	5.54275	−	1.13045i	0.979829	−	0.199837i
$33$		−	0.212447i		−	0.0369822i
$34$	−0.0486296	+	0.0729321i	−0.00833991	+	0.0125078i
$35$	0.673232	+	2.13231i	0.113797	+	0.360427i
$36$	−5.53233	+	2.30413i	−0.922055	+	0.384022i
$37$	0.912703	+	0.912703i	0.150047	+	0.150047i	0.778139	−	0.628092i	$-0.216164\pi$
$37$	0.912703	+	0.912703i	0.150047	+	0.150047i	−0.628092	+	0.778139i	$0.716164\pi$
$38$	−0.107896	−	0.539699i	−0.0175031	−	0.0875508i
$39$			0.132517i			0.0212197i
$40$	6.28466	−	0.709253i	0.993692	−	0.112143i
$41$			3.67993i			0.574709i	0.957824	+	0.287354i	$0.0927757\pi$
$41$			3.67993i			0.574709i	−0.957824	+	0.287354i	$0.907224\pi$
$42$	0.0822009	−	0.0164335i	0.0126839	−	0.00253575i
$43$	−1.75313	−	1.75313i	−0.267350	−	0.267350i	0.560681	−	0.828032i	$-0.310539\pi$
$43$	−1.75313	−	1.75313i	−0.267350	−	0.267350i	−0.828032	+	0.560681i	$0.810539\pi$
$44$	−6.62782	−	2.73031i	−0.999182	−	0.411609i
$45$	−6.38945	+	2.01733i	−0.952483	+	0.300726i
$46$	9.29518	+	6.19783i	1.37050	+	0.913820i
$47$			10.7157i			1.56304i	0.623880	+	0.781520i	$0.285555\pi$
$47$			10.7157i			1.56304i	−0.623880	+	0.781520i	$0.714445\pi$
$48$	−0.000918450	−	0.237098i	−0.000132567	−	0.0342222i
$49$	1.00000			0.142857
$50$	7.06910	−	0.166626i	0.999722	−	0.0235645i
$51$	0.00259797	+	0.00259797i	0.000363788	+	0.000363788i
$52$	4.13421	+	1.70307i	0.573312	+	0.236174i
$53$	7.11440	+	7.11440i	0.977238	+	0.977238i	0.999747	−	0.0225085i	$-0.00716528\pi$
$53$	7.11440	+	7.11440i	0.977238	+	0.977238i	−0.0225085	+	0.999747i	$0.507165\pi$
$54$	0.0985435	+	0.492917i	0.0134101	+	0.0670775i
$55$	−7.11018	−	3.69779i	−0.958736	−	0.498610i
$56$	0.543737	−	2.77567i	0.0726599	−	0.370915i
$57$	−0.0230684			−0.00305549
$58$	−0.252611	−	1.26356i	−0.0331695	−	0.165914i
$59$	5.76751	−	5.76751i	0.750865	−	0.750865i	−0.223775	−	0.974641i	$-0.571838\pi$
$59$	5.76751	−	5.76751i	0.750865	−	0.750865i	0.974641	+	0.223775i	$0.0718382\pi$
$60$	0.0224890	−	0.264130i	0.00290332	−	0.0340991i
$61$	7.45281	+	7.45281i	0.954235	+	0.954235i	0.998998	−	0.0447631i	$-0.0142533\pi$
$61$	7.45281	+	7.45281i	0.954235	+	0.954235i	−0.0447631	+	0.998998i	$0.514253\pi$
$62$	2.75258	+	1.83536i	0.349579	+	0.233092i
$63$			2.99649i			0.377522i
$64$	−7.40870	−	3.01847i	−0.926088	−	0.377309i
$65$	4.43509	+	2.30656i	0.550105	+	0.286093i
$66$	−0.166676	+	0.249972i	−0.0205164	+	0.0307695i
$67$	8.97977	−	8.97977i	1.09705	−	1.09705i	0.102300	−	0.994754i	$-0.467380\pi$
$67$	8.97977	−	8.97977i	1.09705	−	1.09705i	0.994754	−	0.102300i	$-0.0326200\pi$
$68$	0.114439	−	0.0476619i	0.0138777	−	0.00577986i
$69$	0.331110	−	0.331110i	0.0398610	−	0.0398610i
$70$	0.880770	−	3.03714i	0.105272	−	0.363008i
$71$		−	5.82385i		−	0.691164i	−0.938389	−	0.345582i	$-0.887682\pi$
$71$		−	5.82385i		−	0.691164i	0.938389	−	0.345582i	$-0.112318\pi$
$72$	8.31726	+	1.62930i	0.980199	+	0.192015i
$73$	−3.69118			−0.432020			−0.216010	−	0.976391i	$-0.569304\pi$
$73$	−3.69118			−0.432020			−0.216010	+	0.976391i	$0.569304\pi$
$74$	−0.357853	−	1.78999i	−0.0415995	−	0.208082i
$75$	0.0512368	−	0.291913i	0.00591632	−	0.0337072i
$76$	−0.296469	+	0.719680i	−0.0340074	+	0.0825530i
$77$	−2.53433	+	2.53433i	−0.288814	+	0.288814i
$78$	0.103967	−	0.155924i	0.0117719	−	0.0176549i
$79$	15.3579			1.72790			0.863952	−	0.503575i	$-0.167982\pi$
$79$	15.3579			1.72790			0.863952	+	0.503575i	$0.167982\pi$
$80$	−7.95121	−	4.09613i	−0.888972	−	0.457962i
$81$	−8.96839			−0.996488
$82$	2.88711	−	4.32994i	0.318828	−	0.478162i
$83$	−7.39047	+	7.39047i	−0.811210	+	0.811210i	−0.984815	−	0.173605i	$-0.944458\pi$
$83$	−7.39047	+	7.39047i	−0.811210	+	0.811210i	0.173605	+	0.984815i	$0.444458\pi$
$84$	−0.109614	−	0.0451549i	−0.0119598	−	0.00492680i
$85$	0.132168	−	0.0417293i	0.0143357	−	0.00452618i
$86$	0.687369	+	3.43823i	0.0741209	+	0.370754i
$87$	−0.0540087			−0.00579034
$88$	5.65646	+	8.41247i	0.602980	+	0.896773i
$89$			9.78411i			1.03711i	0.855043	+	0.518557i	$0.173531\pi$
$89$			9.78411i			1.03711i	−0.855043	+	0.518557i	$0.826469\pi$
$90$	9.10076	+	2.63921i	0.959304	+	0.278198i
$91$	1.58083	−	1.58083i	0.165716	−	0.165716i
$92$	−6.07450	−	14.5852i	−0.633311	−	1.52061i
$93$	0.0980517	−	0.0980517i	0.0101675	−	0.0101675i
$94$	8.40704	−	12.6084i	0.867120	−	1.30046i
$95$	−0.401524	+	0.772056i	−0.0411954	+	0.0792113i
$96$	−0.184936	+	0.279699i	−0.0188750	+	0.0285466i
$97$		−	8.28186i		−	0.840895i	−0.907317	−	0.420448i	$-0.861873\pi$
$97$		−	8.28186i		−	0.840895i	0.907317	−	0.420448i	$-0.138127\pi$
$98$	−1.17664	−	0.784556i	−0.118858	−	0.0792521i
$99$	−7.59408	−	7.59408i	−0.763234	−	0.763234i
$100$	−8.44849	−	5.35005i	−0.844849	−	0.535005i
$101$	−12.6324	+	12.6324i	−1.25697	+	1.25697i	−0.304437	+	0.952532i	$0.598468\pi$
$101$	−12.6324	+	12.6324i	−1.25697	+	1.25697i	−0.952532	+	0.304437i	$0.901532\pi$
$102$	−0.00101861	−	0.00509511i	−0.000100857	−	0.000504491i
$103$	−11.8204			−1.16470			−0.582351	−	0.812937i	$-0.697867\pi$
$103$	−11.8204			−1.16470			−0.582351	+	0.812937i	$0.697867\pi$
$104$	−3.52831	−	5.24742i	−0.345979	−	0.514552i
$105$	−0.117591	−	0.0611556i	−0.0114757	−	0.00596817i
$106$	−2.78942	−	13.9527i	−0.270932	−	1.35521i
$107$	−2.77296	−	2.77296i	−0.268072	−	0.268072i	0.560251	−	0.828323i	$-0.310705\pi$
$107$	−2.77296	−	2.77296i	−0.268072	−	0.268072i	−0.828323	+	0.560251i	$0.810705\pi$
$108$	0.270771	−	0.657296i	0.0260549	−	0.0632484i
$109$	10.3465	+	10.3465i	0.991017	+	0.991017i	0.999960	−	0.00894285i	$-0.00284664\pi$
$109$	10.3465	+	10.3465i	0.991017	+	0.991017i	−0.00894285	+	0.999960i	$0.502847\pi$
$110$	5.46496	+	9.92929i	0.521064	+	0.946720i
$111$	−0.0765096			−0.00726197
$112$	−2.81745	+	2.83936i	−0.266224	+	0.268295i
$113$		−	13.7947i		−	1.29770i	−0.760917	−	0.648849i	$-0.775251\pi$
$113$		−	13.7947i		−	1.29770i	0.760917	−	0.648849i	$-0.224749\pi$
$114$	0.0271432	+	0.0180985i	0.00254219	+	0.00169508i
$115$	−5.31839	−	16.8448i	−0.495943	−	1.57079i
$116$	−0.694106	+	1.68494i	−0.0644461	+	0.156443i
$117$	4.73694	+	4.73694i	0.437930	+	0.437930i
$118$	−11.3112	+	2.26132i	−1.04128	+	0.208172i
$119$		−	0.0619836i		−	0.00568203i
$120$	−0.233686	+	0.293141i	−0.0213325	+	0.0267600i
$121$		−	1.84565i		−	0.167787i
$122$	−2.92210	−	14.6164i	−0.264554	−	1.32331i
$123$	−0.154240	−	0.154240i	−0.0139073	−	0.0139073i
$124$	−1.79884	−	4.31911i	−0.161541	−	0.387868i
$125$	−8.87793	−	6.79575i	−0.794067	−	0.607831i
$126$	2.35091	−	3.52577i	0.209436	−	0.314101i
$127$		−	1.44411i		−	0.128144i	−0.997945	−	0.0640718i	$-0.979591\pi$
$127$		−	1.44411i		−	0.128144i	0.997945	−	0.0640718i	$-0.0204087\pi$
$128$	6.34918	+	9.36418i	0.561194	+	0.827684i
$129$	0.146961			0.0129392
$130$	−3.40886	−	6.19355i	−0.298977	−	0.543211i
$131$	−3.89852	−	3.89852i	−0.340616	−	0.340616i	0.515983	−	0.856599i	$-0.327427\pi$
$131$	−3.89852	−	3.89852i	−0.340616	−	0.340616i	−0.856599	+	0.515983i	$0.827427\pi$
$132$	0.392234	−	0.163360i	0.0341396	−	0.0142186i
$133$	0.275189	+	0.275189i	0.0238619	+	0.0238619i
$134$	−17.6110	+	3.52079i	−1.52136	+	0.304150i
$135$	0.366718	−	0.705132i	0.0315621	−	0.0606881i
$136$	−0.172046	−	0.0337028i	−0.0147528	−	0.00288999i
$137$	−4.15386			−0.354888			−0.177444	−	0.984131i	$-0.556783\pi$
$137$	−4.15386			−0.354888			−0.177444	+	0.984131i	$0.556783\pi$
$138$	−0.649370	+	0.129822i	−0.0552781	+	0.0110512i
$139$	7.80296	−	7.80296i	0.661838	−	0.661838i	−0.293975	−	0.955813i	$-0.594978\pi$
$139$	7.80296	−	7.80296i	0.661838	−	0.661838i	0.955813	+	0.293975i	$0.0949782\pi$
$140$	−3.41915	+	2.88260i	−0.288971	+	0.243624i
$141$	−0.449134	−	0.449134i	−0.0378239	−	0.0378239i
$142$	−4.56913	+	6.85255i	−0.383433	+	0.575053i
$143$			8.01269i			0.670055i
$144$	−8.50811	−	8.44245i	−0.709009	−	0.703537i
$145$	−0.940063	+	1.80757i	−0.0780680	+	0.150110i
$146$	4.34317	+	2.89593i	0.359443	+	0.239669i
$147$	−0.0419138	+	0.0419138i	−0.00345699	+	0.00345699i
$148$	−0.983281	+	2.38692i	−0.0808252	+	0.196203i
$149$	15.4231	−	15.4231i	1.26351	−	1.26351i	0.314135	−	0.949378i	$-0.398286\pi$
$149$	15.4231	−	15.4231i	1.26351	−	1.26351i	0.949378	−	0.314135i	$-0.101714\pi$
$150$	−0.289309	+	0.303277i	−0.0236220	+	0.0247624i
$151$		−	5.42820i		−	0.441741i	−0.975303	−	0.220870i	$-0.929110\pi$
$151$		−	5.42820i		−	0.441741i	0.975303	−	0.220870i	$-0.0708898\pi$
$152$	0.913466	−	0.614204i	0.0740919	−	0.0498186i
$153$	0.185733			0.0150156
$154$	4.97031	−	0.993660i	0.400519	−	0.0800714i
$155$	−1.57494	−	4.98826i	−0.126502	−	0.400667i
$156$	−0.244663	+	0.101898i	−0.0195887	+	0.00815839i
$157$	17.0956	−	17.0956i	1.36438	−	1.36438i	0.496130	−	0.868248i	$-0.334754\pi$
$157$	17.0956	−	17.0956i	1.36438	−	1.36438i	0.868248	−	0.496130i	$-0.165246\pi$
$158$	−18.0707	−	12.0492i	−1.43763	−	0.958580i
$159$	−0.596382			−0.0472962
$160$	6.14203	+	11.0578i	0.485570	+	0.874198i
$161$	−7.89979			−0.622591
$162$	10.5525	+	7.03620i	0.829085	+	0.552816i
$163$	4.70913	−	4.70913i	0.368847	−	0.368847i	−0.498209	−	0.867057i	$-0.666009\pi$
$163$	4.70913	−	4.70913i	0.368847	−	0.368847i	0.867057	+	0.498209i	$0.166009\pi$
$164$	−6.79416	+	2.82966i	−0.530534	+	0.220959i
$165$	0.453003	−	0.143026i	0.0352662	−	0.0111345i
$166$	14.4941	−	2.89766i	1.12496	−	0.224902i
$167$	2.61011			0.201976			0.100988	−	0.994888i	$-0.467800\pi$
$167$	2.61011			0.201976			0.100988	+	0.994888i	$0.467800\pi$
$168$	0.0935487	+	0.139129i	0.00721744	+	0.0107340i
$169$			8.00195i			0.615535i
$170$	−0.188253	−	0.0545933i	−0.0144384	−	0.00418711i
$171$	−0.824601	+	0.824601i	−0.0630588	+	0.0630588i
$172$	1.88870	−	4.58482i	0.144012	−	0.349590i
$173$	5.95264	−	5.95264i	0.452571	−	0.452571i	−0.443636	−	0.896207i	$-0.646312\pi$
$173$	5.95264	−	5.95264i	0.452571	−	0.452571i	0.896207	+	0.443636i	$0.146312\pi$
$174$	0.0635486	+	0.0423729i	0.00481761	+	0.00321228i
$175$	−4.09352	+	2.87108i	−0.309441	+	0.217033i
$176$	−0.0555344	−	14.3362i	−0.00418606	−	1.08063i
$177$			0.483476i			0.0363402i
$178$	7.67618	−	11.5123i	0.575354	−	0.862886i
$179$	−1.32312	−	1.32312i	−0.0988945	−	0.0988945i	0.655928	−	0.754823i	$-0.272277\pi$
$179$	−1.32312	−	1.32312i	−0.0988945	−	0.0988945i	−0.754823	+	0.655928i	$0.772277\pi$
$180$	−8.63767	−	10.2454i	−0.643814	−	0.763651i
$181$	13.0703	−	13.0703i	0.971507	−	0.971507i	−0.0280983	−	0.999605i	$-0.508945\pi$
$181$	13.0703	−	13.0703i	0.971507	−	0.971507i	0.999605	+	0.0280983i	$0.00894514\pi$
$182$	−3.10031	+	0.619812i	−0.229810	+	0.0459435i
$183$	−0.624750			−0.0461829
$184$	−4.29541	+	21.9272i	−0.316662	+	1.61650i
$185$	−1.33171	+	2.56063i	−0.0979091	+	0.188261i
$186$	−0.192298	+	0.0384441i	−0.0141000	+	0.00281886i
$187$	0.157087	+	0.157087i	0.0114873	+	0.0114873i
$188$	−19.7840	+	8.23975i	−1.44290	+	0.600946i
$189$	−0.251335	−	0.251335i	−0.0182819	−	0.0182819i
$190$	1.07817	−	0.593411i	0.0782185	−	0.0430506i
$191$	4.73266			0.342443			0.171222	−	0.985233i	$-0.445229\pi$
$191$	4.73266			0.342443			0.171222	+	0.985233i	$0.445229\pi$
$192$	0.437042	−	0.184011i	0.0315408	−	0.0132799i
$193$			4.05514i			0.291895i	0.989292	+	0.145948i	$0.0466231\pi$
$193$			4.05514i			0.291895i	−0.989292	+	0.145948i	$0.953377\pi$
$194$	−6.49758	+	9.74473i	−0.466499	+	0.699631i
$195$	−0.282568	+	0.0892147i	−0.0202351	+	0.00638880i
$196$	0.768944	+	1.84627i	0.0549246	+	0.131877i
$197$	7.30355	+	7.30355i	0.520357	+	0.520357i	0.917679	−	0.397322i	$-0.130061\pi$
$197$	7.30355	+	7.30355i	0.520357	+	0.520357i	−0.397322	+	0.917679i	$0.630061\pi$
$198$	2.97749	+	14.8935i	0.211601	+	1.05843i
$199$			19.1148i			1.35502i	0.735516	+	0.677508i	$0.236940\pi$
$199$			19.1148i			1.35502i	−0.735516	+	0.677508i	$0.763060\pi$
$200$	5.74339	+	12.9234i	0.406119	+	0.913820i
$201$			0.752752i			0.0530950i
$202$	24.7745	−	4.95291i	1.74313	−	0.348485i
$203$	0.644284	+	0.644284i	0.0452199	+	0.0452199i
$204$	−0.00279886	+	0.00679424i	−0.000195960	+	0.000475692i
$205$	−7.84676	+	2.47745i	−0.548042	+	0.173032i
$206$	13.9084	+	9.27380i	0.969041	+	0.646136i
$207$		−	23.6716i		−	1.64529i
$208$	0.0346405	+	8.94246i	0.00240189	+	0.620048i
$209$	−1.39484			−0.0964832
$210$	0.0903818	+	0.164214i	0.00623693	+	0.0113319i
$211$	−3.10376	−	3.10376i	−0.213671	−	0.213671i	0.592154	−	0.805825i	$-0.298278\pi$
$211$	−3.10376	−	3.10376i	−0.213671	−	0.213671i	−0.805825	+	0.592154i	$0.798278\pi$
$212$	−7.66455	+	18.6057i	−0.526403	+	1.27785i
$213$	0.244099	+	0.244099i	0.0167254	+	0.0167254i
$214$	1.08722	+	5.43830i	0.0743209	+	0.371754i
$215$	2.55796	−	4.91849i	0.174452	−	0.335439i
$216$	−0.834284	+	0.560964i	−0.0567659	+	0.0381687i
$217$	−2.33937			−0.158807
$218$	−4.05667	−	20.2915i	−0.274752	−	1.37431i
$219$	0.154711	−	0.154711i	0.0104544	−	0.0104544i
$220$	1.35981	−	15.9707i	0.0916781	−	1.07675i
$221$	−0.0979855	−	0.0979855i	−0.00659122	−	0.00659122i
$222$	0.0900239	+	0.0600261i	0.00604201	+	0.00402869i
$223$			19.3889i			1.29837i	0.760629	+	0.649187i	$0.224891\pi$
$223$			19.3889i			1.29837i	−0.760629	+	0.649187i	$0.775109\pi$
$224$	5.54275	−	1.13045i	0.370341	−	0.0755313i
$225$	−8.60316	−	12.2662i	−0.573544	−	0.817745i
$226$	−10.8227	+	16.2314i	−0.719917	+	1.07969i
$227$	4.18360	−	4.18360i	0.277675	−	0.277675i	−0.554505	−	0.832180i	$-0.687092\pi$
$227$	4.18360	−	4.18360i	0.277675	−	0.277675i	0.832180	+	0.554505i	$0.187092\pi$
$228$	−0.0177383	−	0.0425906i	−0.00117475	−	0.00282063i
$229$	−0.976961	+	0.976961i	−0.0645594	+	0.0645594i	−0.738649	−	0.674090i	$-0.764536\pi$
$229$	−0.976961	+	0.976961i	−0.0645594	+	0.0645594i	0.674090	+	0.738649i	$0.264536\pi$
$230$	−6.95790	+	23.9928i	−0.458790	+	1.58204i
$231$		−	0.212447i		−	0.0139780i
$232$	2.13864	−	1.43800i	0.140409	−	0.0944093i
$233$	−1.12520			−0.0737143			−0.0368572	−	0.999321i	$-0.511735\pi$
$233$	−1.12520			−0.0737143			−0.0368572	+	0.999321i	$0.511735\pi$
$234$	−1.85726	−	9.29004i	−0.121413	−	0.607309i
$235$	−22.8492	+	7.21413i	−1.49051	+	0.470598i
$236$	15.0833	+	6.21350i	0.981838	+	0.404464i
$237$	−0.643709	+	0.643709i	−0.0418134	+	0.0418134i
$238$	−0.0486296	+	0.0729321i	−0.00315219	+	0.00472749i
$239$	18.8058			1.21644			0.608222	−	0.793767i	$-0.291883\pi$
$239$	18.8058			1.21644			0.608222	+	0.793767i	$0.291883\pi$
$240$	0.504949	−	0.161581i	0.0325943	−	0.0104300i
$241$	0.974531			0.0627750			0.0313875	−	0.999507i	$-0.490007\pi$
$241$	0.974531			0.0627750			0.0313875	+	0.999507i	$0.490007\pi$
$242$	−1.44802	+	2.17166i	−0.0930822	+	0.139600i
$243$	1.12990	−	1.12990i	0.0724834	−	0.0724834i
$244$	−8.02913	+	19.4907i	−0.514012	+	1.24777i
$245$	0.673232	+	2.13231i	0.0430112	+	0.136228i
$246$	0.0604743	+	0.302494i	0.00385570	+	0.0192863i
$247$	0.870055			0.0553603
$248$	−1.27200	+	6.49332i	−0.0807721	+	0.412326i
$249$		−	0.619525i		−	0.0392608i
$250$	5.11445	+	14.9614i	0.323466	+	0.946240i
$251$	3.79847	−	3.79847i	0.239757	−	0.239757i	−0.576992	−	0.816750i	$-0.695774\pi$
$251$	3.79847	−	3.79847i	0.239757	−	0.239757i	0.816750	+	0.576992i	$0.195774\pi$
$252$	−5.53233	+	2.30413i	−0.348504	+	0.145147i
$253$	20.0207	−	20.0207i	1.25869	−	1.25869i
$254$	−1.13298	+	1.69919i	−0.0710896	+	0.106616i
$255$	−0.00379064	+	0.00728871i	−0.000237379	+	0.000456437i
$256$	−0.123957	−	15.9995i	−0.00774731	−	0.999970i
$257$			19.5636i			1.22034i	0.792270	+	0.610171i	$0.208899\pi$
$257$			19.5636i			1.22034i	−0.792270	+	0.610171i	$0.791101\pi$
$258$	−0.172919	−	0.115299i	−0.0107655	−	0.00717820i
$259$	0.912703	+	0.912703i	0.0567126	+	0.0567126i
$260$	−0.848201	+	9.96200i	−0.0526032	+	0.617817i
$261$	−1.93059	+	1.93059i	−0.119500	+	0.119500i
$262$	1.52853	+	7.64575i	0.0944331	+	0.472356i
$263$	8.02063			0.494573			0.247287	−	0.968942i	$-0.420461\pi$
$263$	8.02063			0.494573			0.247287	+	0.968942i	$0.420461\pi$
$264$	−0.589682	−	0.115515i	−0.0362924	−	0.00710946i
$265$	−10.3805	+	19.9598i	−0.637668	+	1.22612i
$266$	−0.107896	−	0.539699i	−0.00661554	−	0.0330911i
$267$	−0.410089	−	0.410089i	−0.0250970	−	0.0250970i
$268$	23.4840	+	9.67416i	1.43452	+	0.590944i
$269$	−14.0484	−	14.0484i	−0.856546	−	0.856546i	0.134384	−	0.990929i	$-0.457095\pi$
$269$	−14.0484	−	14.0484i	−0.856546	−	0.856546i	−0.990929	+	0.134384i	$0.957095\pi$
$270$	−0.984710	+	0.541973i	−0.0599275	+	0.0329834i
$271$	−27.2687			−1.65646			−0.828228	−	0.560391i	$-0.810651\pi$
$271$	−27.2687			−1.65646			−0.828228	+	0.560391i	$0.810651\pi$
$272$	0.175994	+	0.174636i	0.0106712	+	0.0105888i
$273$			0.132517i			0.00802029i
$274$	4.88758	+	3.25894i	0.295270	+	0.196880i
$275$	3.09805	−	17.6506i	0.186820	−	1.06437i
$276$	0.865925	+	0.356714i	0.0521225	+	0.0214717i
$277$	13.1042	+	13.1042i	0.787358	+	0.787358i	0.981060	−	0.193703i	$-0.0620497\pi$
$277$	13.1042	+	13.1042i	0.787358	+	0.787358i	−0.193703	+	0.981060i	$0.562050\pi$
$278$	−15.3031	+	3.05938i	−0.917819	+	0.183490i
$279$		−	7.00988i		−	0.419671i
$280$	6.28466	−	0.709253i	0.375580	−	0.0423860i
$281$		−	21.2564i		−	1.26805i	−0.773313	−	0.634025i	$-0.781402\pi$
$281$		−	21.2564i		−	1.26805i	0.773313	−	0.634025i	$-0.218598\pi$
$282$	0.176096	+	0.880838i	0.0104864	+	0.0524531i
$283$	2.82839	+	2.82839i	0.168130	+	0.168130i	0.786157	−	0.618027i	$-0.212068\pi$
$283$	2.82839	+	2.82839i	0.168130	+	0.168130i	−0.618027	+	0.786157i	$0.712068\pi$
$284$	10.7524	−	4.47821i	0.638038	−	0.265733i
$285$	−0.0155304	−	0.0491891i	−0.000919942	−	0.00291371i
$286$	6.28640	−	9.42802i	0.371723	−	0.557490i
$287$			3.67993i			0.217219i
$288$	3.38738	+	16.6088i	0.199603	+	0.978682i
$289$	16.9962			0.999774
$290$	2.52425	−	1.38932i	0.148229	−	0.0815836i
$291$	0.347124	+	0.347124i	0.0203488	+	0.0203488i
$292$	−2.83831	−	6.81492i	−0.166099	−	0.398813i
$293$	11.9217	+	11.9217i	0.696476	+	0.696476i	0.963649	−	0.267173i	$-0.0860895\pi$
$293$	11.9217	+	11.9217i	0.696476	+	0.696476i	−0.267173	+	0.963649i	$0.586090\pi$
$294$	0.0822009	−	0.0164335i	0.00479405	−	0.000958424i
$295$	16.1810	+	8.41526i	0.942094	+	0.489955i
$296$	3.02963	−	2.03709i	0.176094	−	0.118404i
$297$	1.27393			0.0739211
$298$	−30.2477	+	6.04711i	−1.75220	+	0.350300i
$299$	−12.4882	+	12.4882i	−0.722213	+	0.722213i
$300$	0.578349	−	0.129867i	0.0333910	−	0.00749789i
$301$	−1.75313	−	1.75313i	−0.101049	−	0.101049i
$302$	−4.25873	+	6.38702i	−0.245062	+	0.367532i
$303$		−	1.05894i		−	0.0608346i
$304$	−1.55669	+	0.00603019i	−0.0892825	+	0.000345855i
$305$	−10.8743	+	20.9092i	−0.622658	+	1.19726i
$306$	−0.218540	−	0.145718i	−0.0124931	−	0.00833014i
$307$	13.7165	−	13.7165i	0.782839	−	0.782839i	−0.197470	−	0.980309i	$-0.563272\pi$
$307$	13.7165	−	13.7165i	0.782839	−	0.782839i	0.980309	+	0.197470i	$0.0632724\pi$
$308$	−6.62782	−	2.73031i	−0.377655	−	0.155574i
$309$	0.495439	−	0.495439i	0.0281845	−	0.0281845i
$310$	−2.06044	+	7.10500i	−0.117025	+	0.403537i
$311$			25.9318i			1.47046i	0.677818	+	0.735229i	$0.262926\pi$
$311$			25.9318i			1.47046i	−0.677818	+	0.735229i	$0.737074\pi$
$312$	0.367824	+	0.0720544i	0.0208239	+	0.00407928i
$313$	3.45264			0.195155			0.0975773	−	0.995228i	$-0.468891\pi$
$313$	3.45264			0.195155			0.0975773	+	0.995228i	$0.468891\pi$
$314$	−33.5278	+	6.70285i	−1.89208	+	0.378264i
$315$	−6.38945	+	2.01733i	−0.360005	+	0.113664i
$316$	11.8094	+	28.3549i	0.664331	+	1.59509i
$317$	−2.28866	+	2.28866i	−0.128544	+	0.128544i	−0.768452	−	0.639908i	$-0.778973\pi$
$317$	−2.28866	+	2.28866i	−0.128544	+	0.128544i	0.639908	+	0.768452i	$0.278973\pi$
$318$	0.701725	+	0.467895i	0.0393508	+	0.0262383i
$319$	−3.26566			−0.182842
$320$	1.44855	−	17.8298i	0.0809763	−	0.996716i
$321$	0.232450			0.0129741
$322$	9.29518	+	6.19783i	0.518000	+	0.345392i
$323$	0.0170572	−	0.0170572i	0.000949089	−	0.000949089i
$324$	−6.89619	−	16.5581i	−0.383122	−	0.919894i
$325$	−1.93246	+	11.0098i	−0.107194	+	0.610716i
$326$	−9.23550	+	1.84636i	−0.511507	+	0.102260i
$327$	−0.867323			−0.0479631
$328$	10.2143	+	2.00091i	0.563989	+	0.110482i
$329$			10.7157i			0.590774i
$330$	−0.645231	−	0.187116i	−0.0355188	−	0.0103004i
$331$	20.9506	−	20.9506i	1.15155	−	1.15155i	0.165308	−	0.986242i	$-0.447138\pi$
$331$	20.9506	−	20.9506i	1.15155	−	1.15155i	0.986242	−	0.165308i	$-0.0528619\pi$
$332$	−19.3277	−	7.96197i	−1.06075	−	0.436970i
$333$	−2.73490	+	2.73490i	−0.149872	+	0.149872i
$334$	−3.07115	−	2.04778i	−0.168046	−	0.112049i
$335$	25.1931	+	13.1022i	1.37645	+	0.715850i
$336$	−0.000918450	−	0.237098i	−5.01056e−5	−	0.0129348i
$337$		−	22.7142i		−	1.23732i	−0.785658	−	0.618661i	$-0.787675\pi$
$337$		−	22.7142i		−	1.23732i	0.785658	−	0.618661i	$-0.212325\pi$
$338$	6.27798	−	9.41539i	0.341477	−	0.512130i
$339$	0.578188	+	0.578188i	0.0314029	+	0.0314029i
$340$	0.178674	+	0.211931i	0.00968995	+	0.0114936i
$341$	5.92873	−	5.92873i	0.321059	−	0.321059i
$342$	1.61720	−	0.323310i	0.0874482	−	0.0174826i
$343$	1.00000			0.0539949
$344$	−5.81936	+	3.91288i	−0.313759	+	0.210968i
$345$	0.928944	+	0.483116i	0.0500127	+	0.0260101i
$346$	−11.6743	+	2.33391i	−0.627613	+	0.125472i
$347$	−1.16850	−	1.16850i	−0.0627282	−	0.0627282i	0.675047	−	0.737775i	$-0.264123\pi$
$347$	−1.16850	−	1.16850i	−0.0627282	−	0.0627282i	−0.737775	+	0.675047i	$0.764123\pi$
$348$	−0.0415297	−	0.0997149i	−0.00222623	−	0.00534528i
$349$	17.3485	+	17.3485i	0.928643	+	0.928643i	0.997618	−	0.0689754i	$-0.0219730\pi$
$349$	17.3485	+	17.3485i	0.928643	+	0.928643i	−0.0689754	+	0.997618i	$0.521973\pi$
$350$	7.06910	−	0.166626i	0.377860	−	0.00890656i
$351$	−0.794636			−0.0424146
$352$	−11.1822	+	16.9121i	−0.596015	+	0.901417i
$353$		−	20.6875i		−	1.10109i	−0.834806	−	0.550544i	$-0.814421\pi$
$353$		−	20.6875i		−	1.10109i	0.834806	−	0.550544i	$-0.185579\pi$
$354$	0.379314	−	0.568875i	0.0201603	−	0.0302354i
$355$	12.4183	−	3.92080i	0.659093	−	0.208095i
$356$	−18.0641	+	7.52344i	−0.957398	+	0.398741i
$357$	0.00259797	+	0.00259797i	0.000137499	+	0.000137499i
$358$	0.518769	+	2.59489i	0.0274178	+	0.137144i
$359$		−	13.8414i		−	0.730522i	−0.930905	−	0.365261i	$-0.880980\pi$
$359$		−	13.8414i		−	0.730522i	0.930905	−	0.365261i	$-0.119020\pi$
$360$	2.12527	+	18.8319i	0.112011	+	0.992528i
$361$		−	18.8485i		−	0.992029i
$362$	−25.6333	+	5.12460i	−1.34726	+	0.269343i
$363$	0.0773583	+	0.0773583i	0.00406026	+	0.00406026i
$364$	4.13421	+	1.70307i	0.216692	+	0.0892653i
$365$	−2.48502	−	7.87074i	−0.130072	−	0.411974i
$366$	0.735104	+	0.490152i	0.0384245	+	0.0256206i
$367$			19.9940i			1.04368i	0.853044	+	0.521839i	$0.174754\pi$
$367$			19.9940i			1.04368i	−0.853044	+	0.521839i	$0.825246\pi$
$368$	22.2573	−	22.4304i	1.16024	−	1.16926i
$369$	−11.0269			−0.574035
$370$	3.57589	−	1.96813i	0.185902	−	0.102318i
$371$	7.11440	+	7.11440i	0.369361	+	0.369361i
$372$	0.256426	+	0.105634i	0.0132951	+	0.00547686i
$373$	−17.0954	−	17.0954i	−0.885164	−	0.885164i	0.108890	−	0.994054i	$-0.465270\pi$
$373$	−17.0954	−	17.0954i	−0.885164	−	0.885164i	−0.994054	+	0.108890i	$0.965270\pi$
$374$	−0.0615906	−	0.308077i	−0.00318478	−	0.0159303i
$375$	0.656943	−	0.0872720i	0.0339244	−	0.00450670i
$376$	29.7432	+	5.82650i	1.53389	+	0.300479i
$377$	2.03701			0.104911
$378$	0.0985435	+	0.492917i	0.00506853	+	0.0253529i
$379$	−16.5259	+	16.5259i	−0.848880	+	0.848880i	−0.989993	−	0.141114i	$-0.954932\pi$
$379$	−16.5259	+	16.5259i	−0.848880	+	0.848880i	0.141114	+	0.989993i	$0.454932\pi$
$380$	−1.73418	−	0.147654i	−0.0889613	−	0.00757449i
$381$	0.0605279	+	0.0605279i	0.00310094	+	0.00310094i
$382$	−5.56862	−	3.71303i	−0.284915	−	0.189975i
$383$			6.08457i			0.310907i	0.987843	+	0.155453i	$0.0496838\pi$
$383$			6.08457i			0.310907i	−0.987843	+	0.155453i	$0.950316\pi$
$384$	−0.658606	−	0.126370i	−0.0336093	−	0.00644878i
$385$	−7.11018	−	3.69779i	−0.362368	−	0.188457i
$386$	3.18148	−	4.77142i	0.161933	−	0.242859i
$387$	5.25324	−	5.25324i	0.267037	−	0.267037i
$388$	15.2906	−	6.36829i	0.776261	−	0.323301i
$389$	10.8348	−	10.8348i	0.549345	−	0.549345i	−0.376906	−	0.926251i	$-0.623012\pi$
$389$	10.8348	−	10.8348i	0.549345	−	0.549345i	0.926251	+	0.376906i	$0.123012\pi$
$390$	0.402473	+	0.116717i	0.0203800	+	0.00591019i
$391$			0.489658i			0.0247631i
$392$	0.543737	−	2.77567i	0.0274629	−	0.140193i
$393$	0.326804			0.0164851
$394$	−2.86358	−	14.3237i	−0.144265	−	0.721616i
$395$	10.3395	+	32.7479i	0.520234	+	1.64773i
$396$	8.18133	−	19.8602i	0.411127	−	0.998012i
$397$	−20.6348	+	20.6348i	−1.03563	+	1.03563i	−0.0362893	+	0.999341i	$0.511554\pi$
$397$	−20.6348	+	20.6348i	−1.03563	+	1.03563i	−0.999341	+	0.0362893i	$0.988446\pi$
$398$	14.9967	−	22.4912i	0.751715	−	1.12738i
$399$	−0.0230684			−0.00115487
$400$	3.38123	−	19.7121i	0.169062	−	0.985605i
$401$	0.535707			0.0267519			0.0133760	−	0.999911i	$-0.495742\pi$
$401$	0.535707			0.0267519			0.0133760	+	0.999911i	$0.495742\pi$
$402$	0.590576	−	0.885714i	0.0294552	−	0.0441754i
$403$	−3.69814	+	3.69814i	−0.184218	+	0.184218i
$404$	−33.0364	−	13.6092i	−1.64362	−	0.677085i
$405$	−6.03781	−	19.1234i	−0.300021	−	0.950250i
$406$	−0.252611	−	1.26356i	−0.0125369	−	0.0627097i
$407$	−4.62618			−0.229311
$408$	0.00862371	−	0.00579849i	0.000426937	−	0.000287068i
$409$		−	13.6159i		−	0.673261i	−0.941637	−	0.336630i	$-0.890713\pi$
$409$		−	13.6159i		−	0.673261i	0.941637	−	0.336630i	$-0.109287\pi$
$410$	11.1765	+	3.24117i	0.551967	+	0.160070i
$411$	0.174104	−	0.174104i	0.00858791	−	0.00858791i
$412$	−9.08926	−	21.8238i	−0.447796	−	1.07518i
$413$	5.76751	−	5.76751i	0.283800	−	0.283800i
$414$	−18.5717	+	27.8529i	−0.912750	+	1.36889i
$415$	−20.7343	−	10.7833i	−1.01781	−	0.529331i
$416$	6.97510	−	10.5492i	0.341982	−	0.517217i
$417$			0.654102i			0.0320315i
$418$	1.64122	+	1.09433i	0.0802747	+	0.0535255i
$419$	23.5899	+	23.5899i	1.15244	+	1.15244i	0.986062	+	0.166381i	$0.0532081\pi$
$419$	23.5899	+	23.5899i	1.15244	+	1.15244i	0.166381	+	0.986062i	$0.446792\pi$
$420$	0.0224890	−	0.264130i	0.00109735	−	0.0128882i
$421$	−15.5499	+	15.5499i	−0.757857	+	0.757857i	−0.975932	−	0.218075i	$-0.930022\pi$
$421$	−15.5499	+	15.5499i	−0.757857	+	0.757857i	0.218075	+	0.975932i	$0.430022\pi$
$422$	1.21692	+	6.08706i	0.0592388	+	0.296314i
$423$	−32.1094			−1.56121
$424$	23.6156	−	15.8789i	1.14687	−	0.771146i
$425$	0.177960	+	0.253731i	0.00863233	+	0.0123078i
$426$	−0.0957065	−	0.478726i	−0.00463699	−	0.0231943i
$427$	7.45281	+	7.45281i	0.360667	+	0.360667i
$428$	2.98739	−	7.25188i	0.144401	−	0.350533i
$429$	−0.335842	−	0.335842i	−0.0162146	−	0.0162146i
$430$	−6.86862	+	3.78041i	−0.331235	+	0.182308i
$431$	−19.4166			−0.935267			−0.467633	−	0.883923i	$-0.654893\pi$
$431$	−19.4166			−0.935267			−0.467633	+	0.883923i	$0.654893\pi$
$432$	1.42176	−	0.00550747i	0.0684043	−	0.000264978i
$433$		−	37.7820i		−	1.81569i	−0.419310	−	0.907843i	$-0.637728\pi$
$433$		−	37.7820i		−	1.81569i	0.419310	−	0.907843i	$-0.362272\pi$
$434$	2.75258	+	1.83536i	0.132128	+	0.0881003i
$435$	−0.0363604	−	0.115164i	−0.00174335	−	0.00552167i
$436$	−11.1466	+	27.0584i	−0.533826	+	1.29586i
$437$	−2.17394	−	2.17394i	−0.103994	−	0.103994i
$438$	−0.303418	+	0.0606591i	−0.0144979	+	0.00289841i
$439$			14.9531i			0.713673i	0.934167	+	0.356836i	$0.116145\pi$
$439$			14.9531i			0.713673i	−0.934167	+	0.356836i	$0.883855\pi$
$440$	−14.1299	+	17.7249i	−0.673618	+	0.845001i
$441$			2.99649i			0.142690i
$442$	0.0384182	+	0.192168i	0.00182737	+	0.00914052i
$443$	−8.56210	−	8.56210i	−0.406797	−	0.406797i	0.473823	−	0.880620i	$-0.342874\pi$
$443$	−8.56210	−	8.56210i	−0.406797	−	0.406797i	−0.880620	+	0.473823i	$0.842874\pi$
$444$	−0.0588316	−	0.141258i	−0.00279203	−	0.00670379i
$445$	−20.8628	+	6.58698i	−0.988991	+	0.312253i
$446$	15.2116	−	22.8136i	0.720292	−	1.08026i
$447$			1.29288i			0.0611513i
$448$	−7.40870	−	3.01847i	−0.350028	−	0.142609i
$449$	6.70481			0.316419			0.158210	−	0.987406i	$-0.449428\pi$
$449$	6.70481			0.316419			0.158210	+	0.987406i	$0.449428\pi$
$450$	0.499294	+	21.1825i	0.0235369	+	0.998551i
$451$	−9.32616	−	9.32616i	−0.439152	−	0.439152i
$452$	25.4688	−	10.6074i	1.19795	−	0.498929i
$453$	0.227516	+	0.227516i	0.0106896	+	0.0106896i
$454$	−8.20484	+	1.64031i	−0.385072	+	0.0769834i
$455$	4.43509	+	2.30656i	0.207920	+	0.108133i
$456$	−0.0125432	+	0.0640304i	−0.000587387	+	0.00299850i
$457$	−32.0083			−1.49728			−0.748642	−	0.662974i	$-0.769294\pi$
$457$	−32.0083			−1.49728			−0.748642	+	0.662974i	$0.769294\pi$
$458$	1.91601	−	0.383047i	0.0895292	−	0.0178986i
$459$	−0.0155787	+	0.0155787i	−0.000727150	+	0.000727150i
$460$	27.0106	−	22.7719i	1.25938	−	1.06175i
$461$	−5.36837	−	5.36837i	−0.250030	−	0.250030i	0.570953	−	0.820983i	$-0.306574\pi$
$461$	−5.36837	−	5.36837i	−0.250030	−	0.250030i	−0.820983	+	0.570953i	$0.806574\pi$
$462$	−0.166676	+	0.249972i	−0.00775448	+	0.0116298i
$463$			7.70916i			0.358275i	0.983824	+	0.179137i	$0.0573307\pi$
$463$			7.70916i			0.358275i	−0.983824	+	0.179137i	$0.942669\pi$
$464$	−3.64459	+	0.0141181i	−0.169196	+	0.000655417i
$465$	0.275088	+	0.143065i	0.0127569	+	0.00663450i
$466$	1.32395	+	0.882783i	0.0613309	+	0.0408941i
$467$	12.4910	−	12.4910i	0.578013	−	0.578013i	−0.356343	−	0.934355i	$-0.615976\pi$
$467$	12.4910	−	12.4910i	0.578013	−	0.578013i	0.934355	+	0.356343i	$0.115976\pi$
$468$	−5.10324	+	12.3881i	−0.235897	+	0.572641i
$469$	8.97977	−	8.97977i	0.414647	−	0.414647i
$470$	32.5450	+	9.43803i	1.50119	+	0.435344i
$471$			1.43308i			0.0660329i
$472$	−12.8727	−	19.1447i	−0.592514	−	0.881206i
$473$	8.88604			0.408580
$474$	1.26244	−	0.252385i	0.0579856	−	0.0115924i
$475$	−1.91658	−	0.336401i	−0.0879389	−	0.0154351i
$476$	0.114439	−	0.0476619i	0.00524529	−	0.00218458i
$477$	−21.3182	+	21.3182i	−0.976094	+	0.976094i
$478$	−22.1275	−	14.7542i	−1.01209	−	0.674840i
$479$	32.4112			1.48090			0.740452	−	0.672110i	$-0.234612\pi$
$479$	32.4112			1.48090			0.740452	+	0.672110i	$0.234612\pi$
$480$	−0.720910	−	0.206039i	−0.0329049	−	0.00940437i
$481$	2.88566			0.131575
$482$	−1.14667	−	0.764574i	−0.0522293	−	0.0348254i
$483$	0.331110	−	0.331110i	0.0150660	−	0.0150660i
$484$	3.40758	−	1.41921i	0.154890	−	0.0645093i
$485$	17.6595	−	5.57561i	0.801877	−	0.253175i
$486$	−2.21596	+	0.443013i	−0.100518	+	0.0200955i
$487$	−11.9176			−0.540038			−0.270019	−	0.962855i	$-0.587030\pi$
$487$	−11.9176			−0.540038			−0.270019	+	0.962855i	$0.587030\pi$
$488$	24.7389	−	16.6342i	1.11988	−	0.752994i
$489$			0.394754i			0.0178514i
$490$	0.880770	−	3.03714i	0.0397891	−	0.137204i
$491$	17.2770	−	17.2770i	0.779701	−	0.779701i	−0.200079	−	0.979780i	$-0.564120\pi$
$491$	17.2770	−	17.2770i	0.779701	−	0.779701i	0.979780	+	0.200079i	$0.0641199\pi$
$492$	0.166167	−	0.403370i	0.00749138	−	0.0181853i
$493$	0.0399351	−	0.0399351i	0.00179858	−	0.00179858i
$494$	−1.02374	−	0.682607i	−0.0460601	−	0.0307119i
$495$	11.0804	−	21.3055i	0.498026	−	0.957613i
$496$	6.59105	−	6.64231i	0.295947	−	0.298249i
$497$		−	5.82385i		−	0.261235i
$498$	−0.486052	+	0.728955i	−0.0217805	+	0.0326653i
$499$	9.71866	+	9.71866i	0.435067	+	0.435067i	0.890348	−	0.455281i	$-0.150461\pi$
$499$	9.71866	+	9.71866i	0.435067	+	0.435067i	−0.455281	+	0.890348i	$0.650461\pi$
$500$	5.72018	−	21.6166i	0.255814	−	0.966726i
$501$	−0.109400	+	0.109400i	−0.00488761	+	0.00488761i
$502$	−7.44953	+	1.48931i	−0.332489	+	0.0664709i
$503$	10.2265			0.455978			0.227989	−	0.973664i	$-0.426785\pi$
$503$	10.2265			0.455978			0.227989	+	0.973664i	$0.426785\pi$
$504$	8.31726	+	1.62930i	0.370480	+	0.0725748i
$505$	−35.4407	−	18.4317i	−1.57709	−	0.820199i
$506$	−39.2644	+	7.84971i	−1.74552	+	0.348962i
$507$	−0.335392	−	0.335392i	−0.0148953	−	0.0148953i
$508$	2.66621	−	1.11044i	0.118294	−	0.0492677i
$509$	−27.9975	−	27.9975i	−1.24097	−	1.24097i	−0.959601	−	0.281366i	$-0.909213\pi$
$509$	−27.9975	−	27.9975i	−1.24097	−	1.24097i	−0.281366	−	0.959601i	$-0.590787\pi$
$510$	0.0101786	−	0.00560219i	0.000450716	−	0.000248069i
$511$	−3.69118			−0.163288
$512$	−12.4067	+	18.9229i	−0.548302	+	0.836280i
$513$		−	0.138330i		−	0.00610740i
$514$	15.3487	−	23.0192i	0.677002	−	1.01533i
$515$	−7.95790	−	25.2049i	−0.350667	−	1.11066i
$516$	0.113005	+	0.271330i	0.00497475	+	0.0119446i
$517$	−27.1570	−	27.1570i	−1.19436	−	1.19436i
$518$	−0.357853	−	1.78999i	−0.0157231	−	0.0786474i
$519$			0.498995i			0.0219035i
$520$	8.81377	−	11.0562i	0.386509	−	0.484846i
$521$		−	3.38598i		−	0.148342i	−0.997246	−	0.0741712i	$-0.976369\pi$
$521$		−	3.38598i		−	0.148342i	0.997246	−	0.0741712i	$-0.0236311\pi$
$522$	3.78626	−	0.756945i	0.165720	−	0.0331306i
$523$	0.511939	+	0.511939i	0.0223855	+	0.0223855i	0.718211	−	0.695825i	$-0.244961\pi$
$523$	0.511939	+	0.511939i	0.0223855	+	0.0223855i	−0.695825	+	0.718211i	$0.744961\pi$
$524$	4.19999	−	10.1955i	0.183478	−	0.445392i
$525$	0.0512368	−	0.291913i	0.00223616	−	0.0127401i
$526$	−9.43736	−	6.29263i	−0.411489	−	0.274372i
$527$			0.145002i			0.00631641i
$528$	0.603213	+	0.598557i	0.0262515	+	0.0260489i
$529$	39.4067			1.71334
$530$	27.8736	−	15.3413i	1.21075	−	0.666384i
$531$	17.2823	+	17.2823i	0.749986	+	0.749986i
$532$	−0.296469	+	0.719680i	−0.0128536	+	0.0312021i
$533$	5.81734	+	5.81734i	0.251977	+	0.251977i
$534$	0.160788	+	0.804263i	0.00695796	+	0.0348039i
$535$	4.04597	−	7.77965i	0.174922	−	0.336344i
$536$	−20.0423	−	29.8075i	−0.865693	−	1.28749i
$537$	0.110914			0.00478628
$538$	5.50810	+	27.5516i	0.237471	+	1.18783i
$539$	−2.53433	+	2.53433i	−0.109161	+	0.109161i
$540$	1.58385	+	0.134855i	0.0681582	+	0.00580323i
$541$	8.21572	+	8.21572i	0.353221	+	0.353221i	0.861307	−	0.508085i	$-0.169647\pi$
$541$	8.21572	+	8.21572i	0.353221	+	0.353221i	−0.508085	+	0.861307i	$0.669647\pi$
$542$	32.0853	+	21.3938i	1.37818	+	0.918944i
$543$			1.09565i			0.0470188i
$544$	−0.0700693	−	0.343560i	−0.00300420	−	0.0147300i
$545$	−15.0964	+	29.0276i	−0.646659	+	1.24341i
$546$	0.103967	−	0.155924i	0.00444938	−	0.00667294i
$547$	−27.4399	+	27.4399i	−1.17324	+	1.17324i	−0.191813	+	0.981431i	$0.561437\pi$
$547$	−27.4399	+	27.4399i	−1.17324	+	1.17324i	−0.981431	+	0.191813i	$0.938563\pi$
$548$	−3.19409	−	7.66916i	−0.136445	−	0.327610i
$549$	−22.3322	+	22.3322i	−0.953117	+	0.953117i
$550$	−17.4932	+	18.3377i	−0.745911	+	0.781923i
$551$			0.354600i			0.0151065i
$552$	−0.739016	−	1.09909i	−0.0314546	−	0.0467803i
$553$	15.3579			0.653086
$554$	−5.13791	−	25.6999i	−0.218289	−	1.09189i
$555$	−0.0515087	−	0.163142i	−0.00218642	−	0.00692501i
$556$	20.4064	+	8.40635i	0.865425	+	0.356509i
$557$	−21.6270	+	21.6270i	−0.916366	+	0.916366i	−0.996763	−	0.0803965i	$-0.974381\pi$
$557$	−21.6270	+	21.6270i	−0.916366	+	0.916366i	0.0803965	+	0.996763i	$0.474381\pi$
$558$	−5.49965	+	8.24808i	−0.232819	+	0.349169i
$559$	−5.54281			−0.234436
$560$	−7.95121	−	4.09613i	−0.336000	−	0.173093i
$561$	−0.0131682			−0.000555962
$562$	−16.6768	+	25.0110i	−0.703469	+	1.05503i
$563$	−27.9765	+	27.9765i	−1.17907	+	1.17907i	−0.199087	+	0.979982i	$0.563798\pi$
$563$	−27.9765	+	27.9765i	−1.17907	+	1.17907i	−0.979982	+	0.199087i	$0.936202\pi$
$564$	0.483865	−	1.17458i	0.0203744	−	0.0494588i
$565$	29.4147	−	9.28705i	1.23748	−	0.390709i
$566$	−1.10896	−	5.54702i	−0.0466129	−	0.233159i
$567$	−8.96839			−0.376637
$568$	−16.1651	−	3.16664i	−0.678272	−	0.132869i
$569$		−	23.8230i		−	0.998714i	−0.866396	−	0.499357i	$-0.833570\pi$
$569$		−	23.8230i		−	0.998714i	0.866396	−	0.499357i	$-0.166430\pi$
$570$	−0.0203180	+	0.0700622i	−0.000851026	+	0.00293458i
$571$	−7.51603	+	7.51603i	−0.314536	+	0.314536i	−0.846664	−	0.532128i	$-0.821393\pi$
$571$	−7.51603	+	7.51603i	−0.314536	+	0.314536i	0.532128	+	0.846664i	$0.321393\pi$
$572$	−14.7936	+	6.16131i	−0.618552	+	0.257617i
$573$	−0.198363	+	0.198363i	−0.00828675	+	0.00828675i
$574$	2.88711	−	4.32994i	0.120506	−	0.180728i
$575$	32.3379	−	22.6810i	1.34859	−	0.945862i
$576$	9.04480	−	22.2001i	0.376867	−	0.925003i
$577$			23.0240i			0.958501i	0.877678	+	0.479250i	$0.159091\pi$
$577$			23.0240i			0.958501i	−0.877678	+	0.479250i	$0.840909\pi$
$578$	−19.9983	−	13.3344i	−0.831819	−	0.554639i
$579$	−0.169966	−	0.169966i	−0.00706355	−	0.00706355i
$580$	−4.06012	−	0.345693i	−0.168587	−	0.0143541i
$581$	−7.39047	+	7.39047i	−0.306608	+	0.306608i
$582$	−0.136100	−	0.680776i	−0.00564154	−	0.0282191i
$583$	−36.0605			−1.49347
$584$	−2.00703	+	10.2455i	−0.0830515	+	0.423961i
$585$	−6.91157	+	13.2897i	−0.285758	+	0.549461i
$586$	−4.67428	−	23.3808i	−0.193093	−	0.965853i
$587$	10.5406	+	10.5406i	0.435056	+	0.435056i	0.890344	−	0.455288i	$-0.150464\pi$
$587$	10.5406	+	10.5406i	0.435056	+	0.435056i	−0.455288	+	0.890344i	$0.650464\pi$
$588$	−0.109614	−	0.0451549i	−0.00452039	−	0.00186216i
$589$	−0.643769	−	0.643769i	−0.0265260	−	0.0265260i
$590$	−12.4369	−	22.5966i	−0.512019	−	0.930287i
$591$	−0.612239			−0.0251841
$592$	−5.16299	+	0.0199999i	−0.212198	+	0.000821992i
$593$			28.1030i			1.15405i	0.816726	+	0.577025i	$0.195787\pi$
$593$			28.1030i			1.15405i	−0.816726	+	0.577025i	$0.804213\pi$
$594$	−1.49896	−	0.999471i	−0.0615029	−	0.0410088i
$595$	0.132168	−	0.0417293i	0.00541838	−	0.00171074i
$596$	40.3349	+	16.6158i	1.65218	+	0.680610i
$597$	−0.801175	−	0.801175i	−0.0327899	−	0.0327899i
$598$	24.4918	−	4.89639i	1.00154	−	0.200228i
$599$		−	9.32620i		−	0.381058i	−0.981682	−	0.190529i	$-0.938980\pi$
$599$		−	9.32620i		−	0.381058i	0.981682	−	0.190529i	$-0.0610204\pi$
$600$	−0.782394	−	0.300940i	−0.0319411	−	0.0122858i
$601$		−	39.2357i		−	1.60046i	−0.599695	−	0.800229i	$-0.704711\pi$
$601$		−	39.2357i		−	1.60046i	0.599695	−	0.800229i	$-0.295289\pi$
$602$	0.687369	+	3.43823i	0.0280151	+	0.140132i
$603$	26.9078	+	26.9078i	1.09577	+	1.09577i
$604$	10.0219	−	4.17398i	0.407787	−	0.169837i
$605$	3.93551	−	1.24255i	0.160001	−	0.0505170i
$606$	−0.830799	+	1.24599i	−0.0337489	+	0.0506148i
$607$		−	4.58924i		−	0.186272i	−0.995653	−	0.0931358i	$-0.970311\pi$
$607$		−	4.58924i		−	0.186272i	0.995653	−	0.0931358i	$-0.0296891\pi$
$608$	1.83639	+	1.21422i	0.0744756	+	0.0492431i
$609$	−0.0540087			−0.00218854
$610$	29.1995	−	16.0711i	1.18225	−	0.650698i
$611$	16.9396	+	16.9396i	0.685305	+	0.685305i
$612$	0.142818	+	0.342914i	0.00577309	+	0.0138615i
$613$	23.1267	+	23.1267i	0.934079	+	0.934079i	0.997958	−	0.0638790i	$-0.0203472\pi$
$613$	23.1267	+	23.1267i	0.934079	+	0.934079i	−0.0638790	+	0.997958i	$0.520347\pi$
$614$	−26.9006	+	5.37795i	−1.08562	+	0.217036i
$615$	0.225048	−	0.432726i	0.00907482	−	0.0174492i
$616$	5.65646	+	8.41247i	0.227905	+	0.338948i
$617$	−17.1948			−0.692236			−0.346118	−	0.938191i	$-0.612500\pi$
$617$	−17.1948			−0.692236			−0.346118	+	0.938191i	$0.612500\pi$
$618$	−0.971651	+	0.194252i	−0.0390855	+	0.00781395i
$619$	−5.38682	+	5.38682i	−0.216515	+	0.216515i	−0.807028	−	0.590513i	$-0.798925\pi$
$619$	−5.38682	+	5.38682i	−0.216515	+	0.216515i	0.590513	+	0.807028i	$0.298925\pi$
$620$	7.99866	−	6.74346i	0.321234	−	0.270824i
$621$	1.98550	+	1.98550i	0.0796752	+	0.0796752i
$622$	20.3450	−	30.5123i	0.815759	−	1.22343i
$623$			9.78411i			0.391992i
$624$	−0.376264	−	0.373360i	−0.0150626	−	0.0149464i
$625$	8.51377	−	23.5057i	0.340551	−	0.940226i
$626$	−4.06250	−	2.70879i	−0.162370	−	0.108265i
$627$	0.0584630	−	0.0584630i	0.00233479	−	0.00233479i
$628$	44.7087	+	18.4176i	1.78407	+	0.734942i
$629$	0.0565726	−	0.0565726i	0.00225570	−	0.00225570i
$630$	9.10076	+	2.63921i	0.362583	+	0.105149i
$631$			29.2838i			1.16577i	0.812555	+	0.582884i	$0.198076\pi$
$631$			29.2838i			1.16577i	−0.812555	+	0.582884i	$0.801924\pi$
$632$	8.35068	−	42.6286i	0.332172	−	1.69567i
$633$	0.260180			0.0103412
$634$	4.48850	−	0.897338i	0.178261	−	0.0356378i
$635$	3.07928	−	0.972218i	0.122198	−	0.0385813i
$636$	−0.458585	−	1.10109i	−0.0181841	−	0.0436609i
$637$	1.58083	−	1.58083i	0.0626348	−	0.0626348i
$638$	3.84249	+	2.56209i	0.152126	+	0.101434i
$639$	17.4511			0.690354
$640$	−15.6929	+	19.8427i	−0.620316	+	0.784352i
$641$	14.5914			0.576327			0.288163	−	0.957581i	$-0.406955\pi$
$641$	14.5914			0.576327			0.288163	+	0.957581i	$0.406955\pi$
$642$	−0.273509	−	0.182370i	−0.0107945	−	0.00719757i
$643$	−17.6612	+	17.6612i	−0.696489	+	0.696489i	−0.963652	−	0.267162i	$-0.913914\pi$
$643$	−17.6612	+	17.6612i	−0.696489	+	0.696489i	0.267162	+	0.963652i	$0.413914\pi$
$644$	−6.07450	−	14.5852i	−0.239369	−	0.574737i
$645$	0.0989387	+	0.313366i	0.00389571	+	0.0123388i
$646$	−0.0334525	+	0.00668780i	−0.00131617	+	0.000263128i
$647$	49.4413			1.94374			0.971869	−	0.235522i	$-0.0756799\pi$
$647$	49.4413			1.94374			0.971869	+	0.235522i	$0.0756799\pi$
$648$	−4.87645	+	24.8933i	−0.191565	+	0.977901i
$649$			29.2335i			1.14752i
$650$	10.9116	−	11.4385i	0.427990	−	0.448653i
$651$	0.0980517	−	0.0980517i	0.00384295	−	0.00384295i
$652$	12.3154	+	5.07328i	0.482308	+	0.198685i
$653$	17.1424	−	17.1424i	0.670834	−	0.670834i	−0.287074	−	0.957908i	$-0.592683\pi$
$653$	17.1424	−	17.1424i	0.670834	−	0.670834i	0.957908	+	0.287074i	$0.0926826\pi$
$654$	1.02052	+	0.680463i	0.0399056	+	0.0266082i
$655$	5.68826	−	10.9375i	0.222259	−	0.427363i
$656$	−10.4487	−	10.3680i	−0.407951	−	0.404803i
$657$		−	11.0606i		−	0.431514i
$658$	8.40704	−	12.6084i	0.327741	−	0.491528i
$659$	−3.89445	−	3.89445i	−0.151706	−	0.151706i	0.627173	−	0.778880i	$-0.284212\pi$
$659$	−3.89445	−	3.89445i	−0.151706	−	0.151706i	−0.778880	+	0.627173i	$0.784212\pi$
$660$	0.612398	+	0.726388i	0.0238376	+	0.0282746i
$661$	−5.17053	+	5.17053i	−0.201110	+	0.201110i	−0.800476	−	0.599365i	$-0.795420\pi$
$661$	−5.17053	+	5.17053i	−0.201110	+	0.201110i	0.599365	+	0.800476i	$0.295420\pi$
$662$	−41.0882	+	8.21432i	−1.59694	+	0.319259i
$663$	0.00821388			0.000319001
$664$	16.4950	+	24.5320i	0.640132	+	0.952026i
$665$	−0.401524	+	0.772056i	−0.0155704	+	0.0299391i
$666$	5.36367	−	1.07230i	0.207838	−	0.0415508i
$667$	−5.08971	−	5.08971i	−0.197074	−	0.197074i
$668$	2.00703	+	4.81898i	0.0776543	+	0.186452i
$669$	−0.812660	−	0.812660i	−0.0314193	−	0.0314193i
$670$	−19.3637	−	35.1820i	−0.748087	−	1.35920i
$671$	−37.7758			−1.45832
$672$	−0.184936	+	0.279699i	−0.00713407	+	0.0107896i
$673$			24.0007i			0.925160i	0.886578	+	0.462580i	$0.153076\pi$
$673$			24.0007i			0.925160i	−0.886578	+	0.462580i	$0.846924\pi$
$674$	−17.8206	+	26.7264i	−0.686423	+	1.02946i
$675$	1.75045	+	0.307241i	0.0673748	+	0.0118257i
$676$	−14.7738	+	6.15306i	−0.568223	+	0.236656i
$677$	−16.7685	−	16.7685i	−0.644467	−	0.644467i	0.307183	−	0.951650i	$-0.400614\pi$
$677$	−16.7685	−	16.7685i	−0.644467	−	0.644467i	−0.951650	+	0.307183i	$0.900614\pi$
$678$	−0.226696	−	1.13394i	−0.00870621	−	0.0435486i
$679$		−	8.28186i		−	0.317829i
$680$	−0.0439621	−	0.389546i	−0.00168587	−	0.0149384i
$681$			0.350701i			0.0134389i
$682$	−11.6274	+	2.32454i	−0.445235	+	0.0890111i
$683$	−30.3310	−	30.3310i	−1.16058	−	1.16058i	−0.984348	−	0.176237i	$-0.943607\pi$
$683$	−30.3310	−	30.3310i	−1.16058	−	1.16058i	−0.176237	−	0.984348i	$-0.556393\pi$
$684$	−2.15651	−	0.888367i	−0.0824563	−	0.0339675i
$685$	−2.79651	−	8.85733i	−0.106849	−	0.338421i
$686$	−1.17664	−	0.784556i	−0.0449242	−	0.0299545i
$687$		−	0.0818962i		−	0.00312454i
$688$	9.91714	−	0.0384162i	0.378088	−	0.00146460i
$689$	22.4933			0.856927
$690$	−0.713997	−	1.29726i	−0.0271814	−	0.0493859i
$691$	27.0205	+	27.0205i	1.02791	+	1.02791i	0.999599	+	0.0283094i	$0.00901237\pi$
$691$	27.0205	+	27.0205i	1.02791	+	1.02791i	0.0283094	+	0.999599i	$0.490988\pi$
$692$	15.5675	+	6.41295i	0.591786	+	0.243784i
$693$	−7.59408	−	7.59408i	−0.288475	−	0.288475i
$694$	0.458144	+	2.29165i	0.0173909	+	0.0869897i
$695$	21.8915	+	11.3851i	0.830394	+	0.431863i
$696$	−0.0293665	+	0.149910i	−0.00111314	+	0.00568234i
$697$	0.228095			0.00863973
$698$	−6.80199	−	34.0237i	−0.257459	−	1.28782i
$699$	0.0471614	−	0.0471614i	0.00178381	−	0.00178381i
$700$	−8.44849	−	5.35005i	−0.319323	−	0.202213i
$701$	30.3439	+	30.3439i	1.14607	+	1.14607i	0.987318	+	0.158755i	$0.0507481\pi$
$701$	30.3439	+	30.3439i	1.14607	+	1.14607i	0.158755	+	0.987318i	$0.449252\pi$
$702$	0.934998	+	0.623437i	0.0352892	+	0.0235301i
$703$			0.502332i			0.0189458i
$704$	26.4259	−	11.1263i	0.995963	−	0.419338i
$705$	0.655323	−	1.26007i	0.0246809	−	0.0474568i
$706$	−16.2305	+	24.3417i	−0.610844	+	0.916112i
$707$	−12.6324	+	12.6324i	−0.475090	+	0.475090i
$708$	−0.892628	+	0.371766i	−0.0335470	+	0.0139718i
$709$	17.7738	−	17.7738i	0.667509	−	0.667509i	−0.289629	−	0.957139i	$-0.593532\pi$
$709$	17.7738	−	17.7738i	0.667509	−	0.667509i	0.957139	+	0.289629i	$0.0935321\pi$
$710$	−17.6879	−	5.12947i	−0.663814	−	0.192506i
$711$			46.0199i			1.72588i
$712$	27.1575	+	5.31998i	1.01777	+	0.199375i
$713$	18.4805			0.692101
$714$	−0.00101861	−	0.00509511i	−3.81205e−5	−	0.000190680i
$715$	−17.0856	+	5.39440i	−0.638964	+	0.201739i
$716$	1.42543	−	3.46024i	0.0532710	−	0.129315i
$717$	−0.788220	+	0.788220i	−0.0294366	+	0.0294366i
$718$	−10.8594	+	16.2863i	−0.405268	+	0.607800i
$719$	−44.4866			−1.65907			−0.829536	−	0.558454i	$-0.811395\pi$
$719$	−44.4866			−1.65907			−0.829536	+	0.558454i	$0.811395\pi$
$720$	12.2740	−	23.8257i	0.457425	−	0.887931i
$721$	−11.8204			−0.440216
$722$	−14.7877	+	22.1779i	−0.550342	+	0.825375i
$723$	−0.0408462	+	0.0408462i	−0.00151909	+	0.00151909i
$724$	34.1816	+	14.0810i	1.27035	+	0.523316i
$725$	−4.48718	−	0.787595i	−0.166650	−	0.0292505i
$726$	−0.0303307	−	0.151714i	−0.00112568	−	0.00563065i
$727$	−21.4617			−0.795969			−0.397984	−	0.917392i	$-0.630290\pi$
$727$	−21.4617			−0.795969			−0.397984	+	0.917392i	$0.630290\pi$
$728$	−3.52831	−	5.24742i	−0.130768	−	0.194482i
$729$		−	26.8105i		−	0.992980i
$730$	−3.25108	+	11.2106i	−0.120328	+	0.414924i
$731$	−0.108666	+	0.108666i	−0.00401914	+	0.00401914i
$732$	−0.480398	−	1.15346i	−0.0177560	−	0.0426331i
$733$	−5.57990	+	5.57990i	−0.206098	+	0.206098i	−0.802607	−	0.596508i	$-0.796554\pi$
$733$	−5.57990	+	5.57990i	−0.206098	+	0.206098i	0.596508	+	0.802607i	$0.296554\pi$
$734$	15.6864	−	23.5257i	0.578996	−	0.868348i
$735$	−0.117591	−	0.0611556i	−0.00433741	−	0.00225576i
$736$	−43.7866	+	8.93032i	−1.61400	+	0.329176i
$737$			45.5154i			1.67658i
$738$	12.9746	+	8.65119i	0.477602	+	0.318455i
$739$	−18.4472	−	18.4472i	−0.678593	−	0.678593i	0.281089	−	0.959682i	$-0.409304\pi$
$739$	−18.4472	−	18.4472i	−0.678593	−	0.678593i	−0.959682	+	0.281089i	$0.909304\pi$
$740$	−5.75163	−	0.489715i	−0.211434	−	0.0180023i
$741$	−0.0364673	+	0.0364673i	−0.00133966	+	0.00133966i
$742$	−2.78942	−	13.9527i	−0.102403	−	0.512220i
$743$	26.0352			0.955139			0.477570	−	0.878594i	$-0.341518\pi$
$743$	26.0352			0.955139			0.477570	+	0.878594i	$0.341518\pi$
$744$	−0.218845	−	0.325474i	−0.00802324	−	0.0119324i
$745$	43.2703	+	22.5036i	1.58530	+	0.824469i
$746$	6.70275	+	33.5273i	0.245405	+	1.22752i
$747$	−22.1455	−	22.1455i	−0.810260	−	0.810260i
$748$	−0.169234	+	0.410816i	−0.00618782	+	0.0150209i
$749$	−2.77296	−	2.77296i	−0.101322	−	0.101322i
$750$	−0.841453	−	0.412721i	−0.0307255	−	0.0150704i
$751$	−49.2368			−1.79668			−0.898339	−	0.439303i	$-0.855225\pi$
$751$	−49.2368			−1.79668			−0.898339	+	0.439303i	$0.855225\pi$
$752$	−30.4257	−	30.1908i	−1.10951	−	1.10095i
$753$			0.318416i			0.0116037i
$754$	−2.39682	−	1.59815i	−0.0872869	−	0.0582010i
$755$	11.5746	−	3.65444i	0.421244	−	0.132999i
$756$	0.270771	−	0.657296i	0.00984784	−	0.0239056i
$757$	−7.39773	−	7.39773i	−0.268875	−	0.268875i	0.559772	−	0.828647i	$-0.310889\pi$
$757$	−7.39773	−	7.39773i	−0.268875	−	0.268875i	−0.828647	+	0.559772i	$0.810889\pi$
$758$	32.4105	−	6.47949i	1.17720	−	0.235346i
$759$			1.67828i			0.0609178i
$760$	1.92465	+	1.53429i	0.0698144	+	0.0556546i
$761$		−	2.03189i		−	0.0736561i	−0.999322	−	0.0368280i	$-0.988275\pi$
$761$		−	2.03189i		−	0.0736561i	0.999322	−	0.0368280i	$-0.0117254\pi$
$762$	−0.0237318	−	0.118707i	−0.000859712	−	0.00430029i
$763$	10.3465	+	10.3465i	0.374569	+	0.374569i
$764$	3.63915	+	8.73778i	0.131660	+	0.316122i
$765$	0.125041	+	0.396041i	0.00452088	+	0.0143189i
$766$	4.77368	−	7.15932i	0.172480	−	0.258677i
$767$		−	18.2349i		−	0.658424i
$768$	0.675795	+	0.665404i	0.0243857	+	0.0240107i
$769$	−50.2517			−1.81212			−0.906061	−	0.423146i	$-0.860926\pi$
$769$	−50.2517			−1.81212			−0.906061	+	0.423146i	$0.860926\pi$
$770$	5.46496	+	9.92929i	0.196944	+	0.357827i
$771$	−0.819982	−	0.819982i	−0.0295309	−	0.0295309i
$772$	−7.48689	+	3.11818i	−0.269459	+	0.112226i
$773$	−27.3398	−	27.3398i	−0.983343	−	0.983343i	0.0165204	−	0.999864i	$-0.494741\pi$
$773$	−27.3398	−	27.3398i	−0.983343	−	0.983343i	−0.999864	+	0.0165204i	$0.994741\pi$
$774$	−10.3026	+	2.05969i	−0.370320	+	0.0740341i
$775$	9.57624	−	6.71652i	0.343989	−	0.241265i
$776$	−22.9877	−	4.50315i	−0.825211	−	0.161654i
$777$	−0.0765096			−0.00274477
$778$	−21.2491	+	4.24810i	−0.761816	+	0.152302i
$779$	−1.01268	+	1.01268i	−0.0362829	+	0.0362829i
$780$	−0.381994	−	0.453096i	−0.0136776	−	0.0162234i
$781$	14.7596	+	14.7596i	0.528138	+	0.528138i
$782$	0.384164	−	0.576149i	0.0137377	−	0.0206030i
$783$		−	0.323863i		−	0.0115739i
$784$	−2.81745	+	2.83936i	−0.100623	+	0.101406i
$785$	47.9625	+	24.9439i	1.71186	+	0.890285i
$786$	−0.384529	−	0.256396i	−0.0137157	−	0.00914533i
$787$	−21.3681	+	21.3681i	−0.761689	+	0.761689i	−0.976628	−	0.214939i	$-0.931045\pi$
$787$	−21.3681	+	21.3681i	−0.761689	+	0.761689i	0.214939	+	0.976628i	$0.431045\pi$
$788$	−7.86833	+	19.1004i	−0.280298	+	0.680423i
$789$	−0.336175	+	0.336175i	−0.0119681	+	0.0119681i
$790$	13.5268	−	46.6443i	0.481262	−	1.65953i
$791$		−	13.7947i		−	0.490484i
$792$	−25.2079	+	16.9495i	−0.895723	+	0.602274i
$793$	23.5632			0.836755
$794$	40.4688	−	8.09049i	1.43618	−	0.287121i
$795$	−0.401504	−	1.27167i	−0.0142399	−	0.0451016i
$796$	−35.2912	+	14.6982i	−1.25086	+	0.520966i
$797$	27.3451	−	27.3451i	0.968614	−	0.968614i	−0.0309085	−	0.999522i	$-0.509840\pi$
$797$	27.3451	−	27.3451i	0.968614	−	0.968614i	0.999522	+	0.0309085i	$0.00984004\pi$
$798$	0.0271432	+	0.0180985i	0.000960857	+	0.000640679i
$799$	0.664196			0.0234975
$800$	−19.4437	+	20.5412i	−0.687440	+	0.726241i
$801$	−29.3180			−1.03590
$802$	−0.630332	−	0.420292i	−0.0222578	−	0.0148410i
$803$	9.35466	−	9.35466i	0.330119	−	0.330119i
$804$	−1.38978	+	0.578824i	−0.0490139	+	0.0204135i
$805$	−5.31839	−	16.8448i	−0.187449	−	0.593702i
$806$	7.25277	−	1.44997i	0.255468	−	0.0510729i
$807$	1.17764			0.0414550
$808$	28.1947	+	41.9321i	0.991885	+	1.47516i
$809$			19.9373i			0.700957i	0.936571	+	0.350478i	$0.113981\pi$
$809$			19.9373i			0.700957i	−0.936571	+	0.350478i	$0.886019\pi$
$810$	−7.89909	+	27.2383i	−0.277546	+	0.957056i
$811$	−8.14617	+	8.14617i	−0.286051	+	0.286051i	−0.835516	−	0.549466i	$-0.814831\pi$
$811$	−8.14617	+	8.14617i	−0.286051	+	0.286051i	0.549466	+	0.835516i	$0.314831\pi$
$812$	−0.694106	+	1.68494i	−0.0243583	+	0.0591299i
$813$	1.14293	−	1.14293i	0.0400844	−	0.0400844i
$814$	5.44333	+	3.62950i	0.190789	+	0.127214i
$815$	13.2117	+	6.87100i	0.462785	+	0.240681i
$816$	−0.0146962		5.69288e-5i	−0.000514470		1.99291e-6i
$817$		−	0.964887i		−	0.0337571i
$818$	−10.6824	+	16.0209i	−0.373501	+	0.560158i
$819$	4.73694	+	4.73694i	0.165522	+	0.165522i
$820$	−10.6078	−	12.5822i	−0.370439	−	0.439391i
$821$	−13.3312	+	13.3312i	−0.465262	+	0.465262i	−0.900376	−	0.435114i	$-0.856708\pi$
$821$	−13.3312	+	13.3312i	−0.465262	+	0.465262i	0.435114	+	0.900376i	$0.356708\pi$
$822$	−0.341451	+	0.0682627i	−0.0119095	+	0.00238093i
$823$	30.7628			1.07232			0.536162	−	0.844115i	$-0.319874\pi$
$823$	30.7628			1.07232			0.536162	+	0.844115i	$0.319874\pi$
$824$	−6.42721	+	32.8097i	−0.223903	+	1.14298i
$825$	0.609952	+	0.869654i	0.0212358	+	0.0302775i
$826$	−11.3112	+	2.26132i	−0.393566	+	0.0786815i
$827$	8.00868	+	8.00868i	0.278489	+	0.278489i	0.832506	−	0.554017i	$-0.186906\pi$
$827$	8.00868	+	8.00868i	0.278489	+	0.278489i	−0.554017	+	0.832506i	$0.686906\pi$
$828$	43.7043	−	18.2022i	1.51883	−	0.632569i
$829$	6.49766	+	6.49766i	0.225673	+	0.225673i	0.810882	−	0.585209i	$-0.198988\pi$
$829$	6.49766	+	6.49766i	0.225673	+	0.225673i	−0.585209	+	0.810882i	$0.698988\pi$
$830$	15.9366	+	28.9552i	0.553168	+	1.00505i
$831$	−1.09850			−0.0381064
$832$	−16.4836	+	6.94021i	−0.571465	+	0.240608i
$833$		−	0.0619836i		−	0.00214760i
$834$	0.513180	−	0.769640i	0.0177700	−	0.0266505i
$835$	1.75721	+	5.56557i	0.0608108	+	0.192605i
$836$	−1.07256	−	2.57526i	−0.0370951	−	0.0890672i
$837$	0.587966	+	0.587966i	0.0203231	+	0.0203231i
$838$	−9.24913	−	46.2643i	−0.319506	−	1.59817i
$839$		−	34.1728i		−	1.17978i	−0.807485	−	0.589888i	$-0.799172\pi$
$839$		−	34.1728i		−	1.17978i	0.807485	−	0.589888i	$-0.200828\pi$
$840$	−0.233686	+	0.293141i	−0.00806294	+	0.0101143i
$841$		−	28.1698i		−	0.971372i
$842$	30.4964	−	6.09682i	1.05098	−	0.210110i
$843$	0.890935	+	0.890935i	0.0306854	+	0.0306854i
$844$	3.34377	−	8.11700i	0.115097	−	0.279399i
$845$	−17.0627	+	5.38717i	−0.586974	+	0.185324i
$846$	37.7810	+	25.1916i	1.29894	+	0.866104i
$847$		−	1.84565i		−	0.0634174i
$848$	−40.2448	+	0.155897i	−1.38201	+	0.00535352i
$849$	−0.237097			−0.00813715
$850$	−0.0103281	−	0.438168i	−0.000354251	−	0.0150291i
$851$	−7.21016	−	7.21016i	−0.247161	−	0.247161i
$852$	−0.262975	+	0.638373i	−0.00900938	+	0.0218703i
$853$	−33.1881	−	33.1881i	−1.13634	−	1.13634i	−0.989101	−	0.147236i	$-0.952962\pi$
$853$	−33.1881	−	33.1881i	−1.13634	−	1.13634i	−0.147236	−	0.989101i	$-0.547038\pi$
$854$	−2.92210	−	14.6164i	−0.0999921	−	0.500163i
$855$	−2.31346	−	1.20316i	−0.0791185	−	0.0411472i
$856$	−9.20457	+	6.18905i	−0.314606	+	0.211538i
$857$	−43.3054			−1.47928			−0.739641	−	0.673001i	$-0.765005\pi$
$857$	−43.3054			−1.47928			−0.739641	+	0.673001i	$0.765005\pi$
$858$	0.131677	+	0.658650i	0.00449537	+	0.0224859i
$859$	−14.0265	+	14.0265i	−0.478576	+	0.478576i	−0.904676	−	0.426100i	$-0.859887\pi$
$859$	−14.0265	+	14.0265i	−0.478576	+	0.478576i	0.426100	+	0.904676i	$0.359887\pi$
$860$	11.0478	+	0.940651i	0.376727	+	0.0320759i
$861$	−0.154240	−	0.154240i	−0.00525647	−	0.00525647i
$862$	22.8463	+	15.2334i	0.778149	+	0.518853i
$863$			12.0198i			0.409159i	0.978850	+	0.204580i	$0.0655827\pi$
$863$			12.0198i			0.409159i	−0.978850	+	0.204580i	$0.934417\pi$
$864$	−1.67721	−	1.10897i	−0.0570599	−	0.0377278i
$865$	16.7004	+	8.68539i	0.567831	+	0.295312i
$866$	−29.6421	+	44.4556i	−1.00728	+	1.51066i
$867$	−0.712373	+	0.712373i	−0.0241934	+	0.0241934i
$868$	−1.79884	−	4.31911i	−0.0610567	−	0.146600i
$869$	−38.9221	+	38.9221i	−1.32034	+	1.32034i
$870$	−0.0475693	+	0.164032i	−0.00161275	+	0.00556122i
$871$		−	28.3910i		−	0.961991i
$872$	34.3443	−	23.0928i	1.16305	−	0.782019i
$873$	24.8165			0.839910
$874$	0.852358	+	4.26351i	0.0288314	+	0.144215i
$875$	−8.87793	−	6.79575i	−0.300129	−	0.229738i
$876$	0.404603	+	0.166675i	0.0136703	+	0.00563142i
$877$	9.62972	−	9.62972i	0.325173	−	0.325173i	−0.525575	−	0.850747i	$-0.676150\pi$
$877$	9.62972	−	9.62972i	0.325173	−	0.325173i	0.850747	+	0.525575i	$0.176150\pi$
$878$	11.7315	−	17.5944i	0.395921	−	0.593781i
$879$	−0.999370			−0.0337079
$880$	30.5319	−	9.77002i	1.02923	−	0.329347i
$881$	2.30646			0.0777067			0.0388533	−	0.999245i	$-0.487629\pi$
$881$	2.30646			0.0777067			0.0388533	+	0.999245i	$0.487629\pi$
$882$	2.35091	−	3.52577i	0.0791593	−	0.118719i
$883$	−23.0076	+	23.0076i	−0.774269	+	0.774269i	−0.978850	−	0.204581i	$-0.934417\pi$
$883$	−23.0076	+	23.0076i	−0.774269	+	0.774269i	0.204581	+	0.978850i	$0.434417\pi$
$884$	0.105563	−	0.256253i	0.00355046	−	0.00861874i
$885$	−1.03092	+	0.325491i	−0.0346540	+	0.0109413i
$886$	3.35703	+	16.7919i	0.112782	+	0.564135i
$887$	36.5975			1.22882			0.614412	−	0.788986i	$-0.289393\pi$
$887$	36.5975			1.22882			0.614412	+	0.788986i	$0.289393\pi$
$888$	−0.0416011	+	0.212365i	−0.00139604	+	0.00712652i
$889$		−	1.44411i		−	0.0484337i
$890$	29.7158	+	8.61755i	0.996075	+	0.288861i
$891$	22.7289	−	22.7289i	0.761445	−	0.761445i
$892$	−35.7971	+	14.9090i	−1.19858	+	0.499189i
$893$	−2.94884	+	2.94884i	−0.0986791	+	0.0986791i
$894$	1.01434	−	1.52125i	0.0339246	−	0.0508783i
$895$	1.93054	−	3.71207i	0.0645308	−	0.124081i
$896$	6.34918	+	9.36418i	0.212111	+	0.312835i
$897$		−	1.04686i		−	0.0349535i
$898$	−7.88911	−	5.26029i	−0.263263	−	0.175538i
$899$	−1.50722	−	1.50722i	−0.0502685	−	0.0502685i
$900$	16.0313	−	25.3158i	0.534378	−	0.843860i
$901$	0.440976	−	0.440976i	0.0146910	−	0.0146910i
$902$	3.65660	+	18.2904i	0.121751	+	0.609003i
$903$	0.146961			0.00489055
$904$	−38.2896	−	7.50070i	−1.27349	−	0.249469i
$905$	36.6693	+	19.0706i	1.21893	+	0.633928i
$906$	−0.0892046	−	0.446203i	−0.00296362	−	0.0148241i
$907$	3.70656	+	3.70656i	0.123074	+	0.123074i	0.765961	−	0.642887i	$-0.222263\pi$
$907$	3.70656	+	3.70656i	0.123074	+	0.123074i	−0.642887	+	0.765961i	$0.722263\pi$
$908$	10.9410	+	4.50711i	0.363091	+	0.149574i
$909$	−37.8528	−	37.8528i	−1.25550	−	1.25550i
$910$	−3.40886	−	6.19355i	−0.113003	−	0.205314i
$911$	59.9156			1.98509			0.992546	−	0.121871i	$-0.0388896\pi$
$911$	59.9156			1.98509			0.992546	+	0.121871i	$0.0388896\pi$
$912$	0.0649942	−	0.0654996i	0.00215217	−	0.00216891i
$913$		−	37.4598i		−	1.23974i
$914$	37.6621	+	25.1123i	1.24575	+	0.830641i
$915$	−0.420602	−	1.33216i	−0.0139047	−	0.0440400i
$916$	−2.55497	−	1.05251i	−0.0844185	−	0.0347759i
$917$	−3.89852	−	3.89852i	−0.128741	−	0.128741i
$918$	0.0305527	−	0.00610808i	0.00100839	−	0.000201597i
$919$		−	4.43723i		−	0.146371i	−0.997318	−	0.0731853i	$-0.976684\pi$
$919$		−	4.43723i		−	0.146371i	0.997318	−	0.0731853i	$-0.0233165\pi$
$920$	−49.6475	+	5.60296i	−1.63683	+	0.184724i
$921$			1.14982i			0.0378877i
$922$	2.10483	+	10.5284i	0.0693189	+	0.346734i
$923$	−9.20651	−	9.20651i	−0.303036	−	0.303036i
$924$	0.392234	−	0.163360i	0.0129036	−	0.00537413i
$925$	−6.35661	−	1.11572i	−0.209004	−	0.0366846i
$926$	6.04826	−	9.07087i	0.198758	−	0.298087i
$927$		−	35.4198i		−	1.16334i
$928$	4.29944	+	2.84278i	0.141136	+	0.0933187i
$929$	−34.5403			−1.13323			−0.566615	−	0.823983i	$-0.691747\pi$
$929$	−34.5403			−1.13323			−0.566615	+	0.823983i	$0.691747\pi$
$930$	−0.211436	−	0.384158i	−0.00693327	−	0.0125970i
$931$	0.275189	+	0.275189i	0.00901897	+	0.00901897i
$932$	−0.865216	−	2.07743i	−0.0283411	−	0.0680484i
$933$	−1.08690	−	1.08690i	−0.0355835	−	0.0355835i
$934$	−24.4972	+	4.89746i	−0.801572	+	0.160250i
$935$	−0.229202	+	0.440714i	−0.00749572	+	0.0144129i
$936$	15.7238	−	10.5725i	0.513949	−	0.345574i
$937$	37.2032			1.21538			0.607688	−	0.794176i	$-0.292097\pi$
$937$	37.2032			1.21538			0.607688	+	0.794176i	$0.292097\pi$
$938$	−17.6110	+	3.52079i	−0.575021	+	0.114958i
$939$	−0.144713	+	0.144713i	−0.00472253	+	0.00472253i
$940$	−30.8890	−	36.6385i	−1.00749	−	1.19502i
$941$	23.5957	+	23.5957i	0.769197	+	0.769197i	0.977965	−	0.208768i	$-0.0669453\pi$
$941$	23.5957	+	23.5957i	0.769197	+	0.769197i	−0.208768	+	0.977965i	$0.566945\pi$
$942$	1.12433	−	1.68622i	0.0366328	−	0.0549399i
$943$		−	29.0707i		−	0.946672i
$944$	0.126383	+	32.6257i	0.00411340	+	1.06188i
$945$	0.366718	−	0.705132i	0.0119294	−	0.0229380i
$946$	−10.4556	−	6.97159i	−0.339942	−	0.226666i
$947$	−18.7281	+	18.7281i	−0.608581	+	0.608581i	−0.942575	−	0.333994i	$-0.891604\pi$
$947$	−18.7281	+	18.7281i	−0.608581	+	0.608581i	0.333994	+	0.942575i	$0.391604\pi$
$948$	−1.68344	−	0.693486i	−0.0546755	−	0.0225234i
$949$	−5.83512	+	5.83512i	−0.189416	+	0.189416i
$950$	1.99120	+	1.89949i	0.0646029	+	0.0616275i
$951$		−	0.191853i		−	0.00622125i
$952$	−0.172046	−	0.0337028i	−0.00557605	−	0.00109231i
$953$	14.2577			0.461852			0.230926	−	0.972971i	$-0.425824\pi$
$953$	14.2577			0.461852			0.230926	+	0.972971i	$0.425824\pi$
$954$	41.8091	−	8.35844i	1.35362	−	0.270615i
$955$	3.18618	+	10.0915i	0.103102	+	0.326554i
$956$	14.4606	+	34.7206i	0.467689	+	1.12294i
$957$	0.136876	−	0.136876i	0.00442457	−	0.00442457i
$958$	−38.1361	−	25.4284i	−1.23212	−	0.821553i
$959$	−4.15386			−0.134135
$960$	0.686600	+	0.808028i	0.0221599	+	0.0260790i
$961$	−25.5274			−0.823463
$962$	−3.39537	−	2.26396i	−0.109471	−	0.0729929i
$963$	8.30912	−	8.30912i	0.267758	−	0.267758i
$964$	0.749360	+	1.79925i	0.0241352	+	0.0579499i
$965$	−8.64682	+	2.73005i	−0.278351	+	0.0878834i
$966$	−0.649370	+	0.129822i	−0.0208931	+	0.00417694i
$967$	−2.70451			−0.0869713			−0.0434856	−	0.999054i	$-0.513846\pi$
$967$	−2.70451			−0.0869713			−0.0434856	+	0.999054i	$0.513846\pi$
$968$	−5.12293	−	1.00355i	−0.164657	−	0.0322553i
$969$			0.00142986i			4.59339e-5i
$970$	−25.1532	−	7.29441i	−0.807620	−	0.234209i
$971$	30.3259	−	30.3259i	0.973203	−	0.973203i	−0.0264473	−	0.999650i	$-0.508419\pi$
$971$	30.3259	−	30.3259i	0.973203	−	0.973203i	0.999650	+	0.0264473i	$0.00841941\pi$
$972$	2.95495	+	1.21728i	0.0947799	+	0.0390442i
$973$	7.80296	−	7.80296i	0.250151	−	0.250151i
$974$	14.0227	+	9.35002i	0.449315	+	0.299594i
$975$	−0.380467	−	0.542461i	−0.0121847	−	0.0173726i
$976$	−42.1591	+	0.163312i	−1.34948	+	0.00522750i
$977$			35.9872i			1.15133i	0.817684	+	0.575667i	$0.195257\pi$
$977$			35.9872i			1.15133i	−0.817684	+	0.575667i	$0.804743\pi$
$978$	0.309707	−	0.464482i	0.00990333	−	0.0148525i
$979$	−24.7962	−	24.7962i	−0.792489	−	0.792489i
$980$	−3.41915	+	2.88260i	−0.109221	+	0.0920813i
$981$	−31.0032	+	31.0032i	−0.989857	+	0.989857i
$982$	−33.8835	+	6.77397i	−1.08127	+	0.216166i
$983$	−6.57572			−0.209733			−0.104866	−	0.994486i	$-0.533441\pi$
$983$	−6.57572			−0.209733			−0.104866	+	0.994486i	$0.533441\pi$
$984$	−0.511984	+	0.344253i	−0.0163215	+	0.0109744i
$985$	−10.6565	+	20.4904i	−0.339544	+	0.652880i
$986$	−0.0783203	+	0.0156577i	−0.00249423	+	0.000498644i
$987$	−0.449134	−	0.449134i	−0.0142961	−	0.0142961i
$988$	0.669024	+	1.60636i	0.0212845	+	0.0511051i
$989$	13.8494	+	13.8494i	0.440385	+	0.440385i
$990$	−29.7530	+	16.3757i	−0.945611	+	0.520454i
$991$	−39.9535			−1.26916			−0.634582	−	0.772855i	$-0.718828\pi$
$991$	−39.9535			−1.26916			−0.634582	+	0.772855i	$0.718828\pi$
$992$	−12.9665	+	2.64454i	−0.411688	+	0.0839641i
$993$			1.75624i			0.0557325i
$994$	−4.56913	+	6.85255i	−0.144924	+	0.217350i
$995$	−40.7588	+	12.8687i	−1.29214	+	0.407966i
$996$	1.14381	−	0.476380i	0.0362431	−	0.0150947i
$997$	12.5849	+	12.5849i	0.398568	+	0.398568i	0.877728	−	0.479160i	$-0.159058\pi$
$997$	12.5849	+	12.5849i	0.398568	+	0.398568i	−0.479160	+	0.877728i	$0.659058\pi$
$998$	−3.81049	−	19.0602i	−0.120619	−	0.603339i
$999$		−	0.458789i		−	0.0145154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.7	yes	70
5.4	even	2		560.2.bb.c.29.29	✓	70
16.5	even	4		560.2.bb.c.309.29	yes	70
80.69	even	4	inner	560.2.bb.d.309.7	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.29	✓	70	5.4	even	2
560.2.bb.c.309.29	yes	70	16.5	even	4
560.2.bb.d.29.7	yes	70	1.1	even	1	trivial
560.2.bb.d.309.7	yes	70	80.69	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17664 - 0.784556i) q^{2} +(-0.0419138 + 0.0419138i) q^{3} +(0.768944 + 1.84627i) q^{4} +(0.673232 + 2.13231i) q^{5} +(0.0822009 - 0.0164335i) q^{6} +1.00000 q^{7} +(0.543737 - 2.77567i) q^{8} +2.99649i q^{9} +O(q^{10})\)	\(q+(-1.17664 - 0.784556i) q^{2} +(-0.0419138 + 0.0419138i) q^{3} +(0.768944 + 1.84627i) q^{4} +(0.673232 + 2.13231i) q^{5} +(0.0822009 - 0.0164335i) q^{6} +1.00000 q^{7} +(0.543737 - 2.77567i) q^{8} +2.99649i q^{9} +(0.880770 - 3.03714i) q^{10} +(-2.53433 + 2.53433i) q^{11} +(-0.109614 - 0.0451549i) q^{12} +(1.58083 - 1.58083i) q^{13} +(-1.17664 - 0.784556i) q^{14} +(-0.117591 - 0.0611556i) q^{15} +(-2.81745 + 2.83936i) q^{16} -0.0619836i q^{17} +(2.35091 - 3.52577i) q^{18} +(0.275189 + 0.275189i) q^{19} +(-3.41915 + 2.88260i) q^{20} +(-0.0419138 + 0.0419138i) q^{21} +(4.97031 - 0.993660i) q^{22} -7.89979 q^{23} +(0.0935487 + 0.139129i) q^{24} +(-4.09352 + 2.87108i) q^{25} +(-3.10031 + 0.619812i) q^{26} +(-0.251335 - 0.251335i) q^{27} +(0.768944 + 1.84627i) q^{28} +(0.644284 + 0.644284i) q^{29} +(0.0903818 + 0.164214i) q^{30} -2.33937 q^{31} +(5.54275 - 1.13045i) q^{32} -0.212447i q^{33} +(-0.0486296 + 0.0729321i) q^{34} +(0.673232 + 2.13231i) q^{35} +(-5.53233 + 2.30413i) q^{36} +(0.912703 + 0.912703i) q^{37} +(-0.107896 - 0.539699i) q^{38} +0.132517i q^{39} +(6.28466 - 0.709253i) q^{40} +3.67993i q^{41} +(0.0822009 - 0.0164335i) q^{42} +(-1.75313 - 1.75313i) q^{43} +(-6.62782 - 2.73031i) q^{44} +(-6.38945 + 2.01733i) q^{45} +(9.29518 + 6.19783i) q^{46} +10.7157i q^{47} +(-0.000918450 - 0.237098i) q^{48} +1.00000 q^{49} +(7.06910 - 0.166626i) q^{50} +(0.00259797 + 0.00259797i) q^{51} +(4.13421 + 1.70307i) q^{52} +(7.11440 + 7.11440i) q^{53} +(0.0985435 + 0.492917i) q^{54} +(-7.11018 - 3.69779i) q^{55} +(0.543737 - 2.77567i) q^{56} -0.0230684 q^{57} +(-0.252611 - 1.26356i) q^{58} +(5.76751 - 5.76751i) q^{59} +(0.0224890 - 0.264130i) q^{60} +(7.45281 + 7.45281i) q^{61} +(2.75258 + 1.83536i) q^{62} +2.99649i q^{63} +(-7.40870 - 3.01847i) q^{64} +(4.43509 + 2.30656i) q^{65} +(-0.166676 + 0.249972i) q^{66} +(8.97977 - 8.97977i) q^{67} +(0.114439 - 0.0476619i) q^{68} +(0.331110 - 0.331110i) q^{69} +(0.880770 - 3.03714i) q^{70} -5.82385i q^{71} +(8.31726 + 1.62930i) q^{72} -3.69118 q^{73} +(-0.357853 - 1.78999i) q^{74} +(0.0512368 - 0.291913i) q^{75} +(-0.296469 + 0.719680i) q^{76} +(-2.53433 + 2.53433i) q^{77} +(0.103967 - 0.155924i) q^{78} +15.3579 q^{79} +(-7.95121 - 4.09613i) q^{80} -8.96839 q^{81} +(2.88711 - 4.32994i) q^{82} +(-7.39047 + 7.39047i) q^{83} +(-0.109614 - 0.0451549i) q^{84} +(0.132168 - 0.0417293i) q^{85} +(0.687369 + 3.43823i) q^{86} -0.0540087 q^{87} +(5.65646 + 8.41247i) q^{88} +9.78411i q^{89} +(9.10076 + 2.63921i) q^{90} +(1.58083 - 1.58083i) q^{91} +(-6.07450 - 14.5852i) q^{92} +(0.0980517 - 0.0980517i) q^{93} +(8.40704 - 12.6084i) q^{94} +(-0.401524 + 0.772056i) q^{95} +(-0.184936 + 0.279699i) q^{96} -8.28186i q^{97} +(-1.17664 - 0.784556i) q^{98} +(-7.59408 - 7.59408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * 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 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * 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 - 8 * 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 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * 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 + 18 * 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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