LMFDB - Embedded newform 560.2.bb.c.29.18

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			29.18
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.c.309.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.168286 - 1.40417i) q^{2} +(0.0271728 - 0.0271728i) q^{3} +(-1.94336 - 0.472603i) q^{4} +(1.37117 + 1.76632i) q^{5} +(-0.0335823 - 0.0427279i) q^{6} -1.00000 q^{7} +(-0.990653 + 2.64927i) q^{8} +2.99852i q^{9} +O(q^{10})$	\(q+(0.168286 - 1.40417i) q^{2} +(0.0271728 - 0.0271728i) q^{3} +(-1.94336 - 0.472603i) q^{4} +(1.37117 + 1.76632i) q^{5} +(-0.0335823 - 0.0427279i) q^{6} -1.00000 q^{7} +(-0.990653 + 2.64927i) q^{8} +2.99852i q^{9} +(2.71096 - 1.62810i) q^{10} +(0.129379 - 0.129379i) q^{11} +(-0.0656484 + 0.0399646i) q^{12} +(-3.72874 + 3.72874i) q^{13} +(-0.168286 + 1.40417i) q^{14} +(0.0852544 + 0.0107374i) q^{15} +(3.55329 + 1.83687i) q^{16} +1.74547i q^{17} +(4.21042 + 0.504610i) q^{18} +(1.43141 + 1.43141i) q^{19} +(-1.82991 - 4.08062i) q^{20} +(-0.0271728 + 0.0271728i) q^{21} +(-0.159897 - 0.203443i) q^{22} -4.38453 q^{23} +(0.0450691 + 0.0989067i) q^{24} +(-1.23979 + 4.84386i) q^{25} +(4.60828 + 5.86327i) q^{26} +(0.162997 + 0.162997i) q^{27} +(1.94336 + 0.472603i) q^{28} +(0.897874 + 0.897874i) q^{29} +(0.0294242 - 0.117904i) q^{30} +9.67014 q^{31} +(3.17724 - 4.68029i) q^{32} -0.00703119i q^{33} +(2.45092 + 0.293738i) q^{34} +(-1.37117 - 1.76632i) q^{35} +(1.41711 - 5.82721i) q^{36} +(-5.50019 - 5.50019i) q^{37} +(2.25082 - 1.76905i) q^{38} +0.202641i q^{39} +(-6.03781 + 1.88278i) q^{40} -0.275981i q^{41} +(0.0335823 + 0.0427279i) q^{42} +(4.02033 + 4.02033i) q^{43} +(-0.312576 + 0.190286i) q^{44} +(-5.29636 + 4.11149i) q^{45} +(-0.737855 + 6.15661i) q^{46} -4.55481i q^{47} +(0.146466 - 0.0466399i) q^{48} +1.00000 q^{49} +(6.59293 + 2.55602i) q^{50} +(0.0474292 + 0.0474292i) q^{51} +(9.00851 - 5.48408i) q^{52} +(4.87624 + 4.87624i) q^{53} +(0.256304 - 0.201444i) q^{54} +(0.405927 + 0.0511245i) q^{55} +(0.990653 - 2.64927i) q^{56} +0.0777908 q^{57} +(1.41186 - 1.10966i) q^{58} +(7.07161 - 7.07161i) q^{59} +(-0.160605 - 0.0611580i) q^{60} +(-3.88321 - 3.88321i) q^{61} +(1.62735 - 13.5785i) q^{62} -2.99852i q^{63} +(-6.03721 - 5.24900i) q^{64} +(-11.6989 - 1.47342i) q^{65} +(-0.00987296 - 0.00118325i) q^{66} +(-7.33615 + 7.33615i) q^{67} +(0.824913 - 3.39207i) q^{68} +(-0.119140 + 0.119140i) q^{69} +(-2.71096 + 1.62810i) q^{70} -0.762807i q^{71} +(-7.94388 - 2.97050i) q^{72} +11.0968 q^{73} +(-8.64877 + 6.79756i) q^{74} +(0.0979326 + 0.165309i) q^{75} +(-2.10526 - 3.45824i) q^{76} +(-0.129379 + 0.129379i) q^{77} +(0.284541 + 0.0341016i) q^{78} +1.50228 q^{79} +(1.62766 + 8.79493i) q^{80} -8.98671 q^{81} +(-0.387523 - 0.0464437i) q^{82} +(-6.02356 + 6.02356i) q^{83} +(0.0656484 - 0.0399646i) q^{84} +(-3.08306 + 2.39333i) q^{85} +(6.32178 - 4.96865i) q^{86} +0.0487954 q^{87} +(0.214590 + 0.470930i) q^{88} -2.39026i q^{89} +(4.88190 + 8.12887i) q^{90} +(3.72874 - 3.72874i) q^{91} +(8.52072 + 2.07214i) q^{92} +(0.262765 - 0.262765i) q^{93} +(-6.39570 - 0.766511i) q^{94} +(-0.565625 + 4.49104i) q^{95} +(-0.0408419 - 0.213511i) q^{96} -9.67479i q^{97} +(0.168286 - 1.40417i) q^{98} +(0.387947 + 0.387947i) 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 $

$2$	0.168286	−	1.40417i	0.118996	−	0.992895i
$2$	0.168286	−	1.40417i	0.118996	−	0.992895i
$3$	0.0271728	−	0.0271728i	0.0156882	−	0.0156882i	−0.699219	−	0.714907i	$-0.746469\pi$
$3$	0.0271728	−	0.0271728i	0.0156882	−	0.0156882i	0.714907	+	0.699219i	$0.246469\pi$
$4$	−1.94336	−	0.472603i	−0.971680	−	0.236301i
$5$	1.37117	+	1.76632i	0.613206	+	0.789923i
$5$	1.37117	+	1.76632i	0.613206	+	0.789923i
$6$	−0.0335823	−	0.0427279i	−0.0137099	−	0.0174436i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.990653	+	2.64927i	−0.350249	+	0.936657i
$9$			2.99852i			0.999508i
$10$	2.71096	−	1.62810i	0.857280	−	0.514851i
$11$	0.129379	−	0.129379i	0.0390093	−	0.0390093i	−0.687333	−	0.726342i	$-0.741219\pi$
$11$	0.129379	−	0.129379i	0.0390093	−	0.0390093i	0.726342	+	0.687333i	$0.241219\pi$
$12$	−0.0656484	+	0.0399646i	−0.0189511	+	0.0115368i
$13$	−3.72874	+	3.72874i	−1.03417	+	1.03417i	−0.0347722	+	0.999395i	$0.511071\pi$
$13$	−3.72874	+	3.72874i	−1.03417	+	1.03417i	−0.999395	+	0.0347722i	$0.988929\pi$
$14$	−0.168286	+	1.40417i	−0.0449763	+	0.375279i
$15$	0.0852544	+	0.0107374i	0.0220126	+	0.00277238i
$16$	3.55329	+	1.83687i	0.888323	+	0.459219i
$17$			1.74547i			0.423338i	0.977341	+	0.211669i	$0.0678899\pi$
$17$			1.74547i			0.423338i	−0.977341	+	0.211669i	$0.932110\pi$
$18$	4.21042	+	0.504610i	0.992406	+	0.118938i
$19$	1.43141	+	1.43141i	0.328388	+	0.328388i	0.851973	−	0.523585i	$-0.175406\pi$
$19$	1.43141	+	1.43141i	0.328388	+	0.328388i	−0.523585	+	0.851973i	$0.675406\pi$
$20$	−1.82991	−	4.08062i	−0.409180	−	0.912454i
$21$	−0.0271728	+	0.0271728i	−0.00592959	+	0.00592959i
$22$	−0.159897	−	0.203443i	−0.0340902	−	0.0433741i
$23$	−4.38453			−0.914238			−0.457119	−	0.889406i	$-0.651119\pi$
$23$	−4.38453			−0.914238			−0.457119	+	0.889406i	$0.651119\pi$
$24$	0.0450691	+	0.0989067i	0.00919970	+	0.0201892i
$25$	−1.23979	+	4.84386i	−0.247957	+	0.968771i
$26$	4.60828	+	5.86327i	0.903757	+	1.14988i
$27$	0.162997	+	0.162997i	0.0313687	+	0.0313687i
$28$	1.94336	+	0.472603i	0.367260	+	0.0893135i
$29$	0.897874	+	0.897874i	0.166731	+	0.166731i	0.785541	−	0.618810i	$-0.212385\pi$
$29$	0.897874	+	0.897874i	0.166731	+	0.166731i	−0.618810	+	0.785541i	$0.712385\pi$
$30$	0.0294242	−	0.117904i	0.00537209	−	0.0215263i
$31$	9.67014			1.73681			0.868405	−	0.495856i	$-0.165146\pi$
$31$	9.67014			1.73681			0.868405	+	0.495856i	$0.165146\pi$
$32$	3.17724	−	4.68029i	0.561663	−	0.827366i
$33$		−	0.00703119i		−	0.00122397i
$34$	2.45092	+	0.293738i	0.420330	+	0.0503756i
$35$	−1.37117	−	1.76632i	−0.231770	−	0.298563i
$36$	1.41711	−	5.82721i	0.236185	−	0.971202i
$37$	−5.50019	−	5.50019i	−0.904225	−	0.904225i	0.0915734	−	0.995798i	$-0.470810\pi$
$37$	−5.50019	−	5.50019i	−0.904225	−	0.904225i	−0.995798	+	0.0915734i	$0.970810\pi$
$38$	2.25082	−	1.76905i	0.365132	−	0.286978i
$39$			0.202641i			0.0324485i
$40$	−6.03781	+	1.88278i	−0.954661	+	0.297694i
$41$		−	0.275981i		−	0.0431010i	−0.999768	−	0.0215505i	$-0.993140\pi$
$41$		−	0.275981i		−	0.0431010i	0.999768	−	0.0215505i	$-0.00686026\pi$
$42$	0.0335823	+	0.0427279i	0.00518186	+	0.00659305i
$43$	4.02033	+	4.02033i	0.613095	+	0.613095i	0.943751	−	0.330656i	$-0.107270\pi$
$43$	4.02033	+	4.02033i	0.613095	+	0.613095i	−0.330656	+	0.943751i	$0.607270\pi$
$44$	−0.312576	+	0.190286i	−0.0471225	+	0.0286866i
$45$	−5.29636	+	4.11149i	−0.789534	+	0.612904i
$46$	−0.737855	+	6.15661i	−0.108791	+	0.907742i
$47$		−	4.55481i		−	0.664387i	−0.943211	−	0.332194i	$-0.892211\pi$
$47$		−	4.55481i		−	0.664387i	0.943211	−	0.332194i	$-0.107789\pi$
$48$	0.146466	−	0.0466399i	0.0211405	−	0.00673189i
$49$	1.00000			0.142857
$50$	6.59293	+	2.55602i	0.932382	+	0.361475i
$51$	0.0474292	+	0.0474292i	0.00664142	+	0.00664142i
$52$	9.00851	−	5.48408i	1.24925	−	0.760504i
$53$	4.87624	+	4.87624i	0.669803	+	0.669803i	0.957670	−	0.287867i	$-0.0929462\pi$
$53$	4.87624	+	4.87624i	0.669803	+	0.669803i	−0.287867	+	0.957670i	$0.592946\pi$
$54$	0.256304	−	0.201444i	0.0348786	−	0.0274131i
$55$	0.405927	+	0.0511245i	0.0547351	+	0.00689362i
$56$	0.990653	−	2.64927i	0.132382	−	0.354023i
$57$	0.0777908			0.0103036
$58$	1.41186	−	1.10966i	0.185387	−	0.145706i
$59$	7.07161	−	7.07161i	0.920645	−	0.920645i	−0.0764296	−	0.997075i	$-0.524352\pi$
$59$	7.07161	−	7.07161i	0.920645	−	0.920645i	0.997075	+	0.0764296i	$0.0243521\pi$
$60$	−0.160605	−	0.0611580i	−0.0207341	−	0.00789547i
$61$	−3.88321	−	3.88321i	−0.497194	−	0.497194i	0.413369	−	0.910563i	$-0.364352\pi$
$61$	−3.88321	−	3.88321i	−0.497194	−	0.497194i	−0.910563	+	0.413369i	$0.864352\pi$
$62$	1.62735	−	13.5785i	0.206674	−	1.72447i
$63$		−	2.99852i		−	0.377778i
$64$	−6.03721	−	5.24900i	−0.754652	−	0.656125i
$65$	−11.6989	−	1.47342i	−1.45107	−	0.182755i
$66$	−0.00987296	−	0.00118325i	−0.00121528	−	0.000145648i
$67$	−7.33615	+	7.33615i	−0.896254	+	0.896254i	−0.995102	−	0.0988486i	$-0.968484\pi$
$67$	−7.33615	+	7.33615i	−0.896254	+	0.896254i	0.0988486	+	0.995102i	$0.468484\pi$
$68$	0.824913	−	3.39207i	0.100035	−	0.411349i
$69$	−0.119140	+	0.119140i	−0.0143428	+	0.0143428i
$70$	−2.71096	+	1.62810i	−0.324021	+	0.194595i
$71$		−	0.762807i		−	0.0905286i	−0.998975	−	0.0452643i	$-0.985587\pi$
$71$		−	0.762807i		−	0.0905286i	0.998975	−	0.0452643i	$-0.0144130\pi$
$72$	−7.94388	−	2.97050i	−0.936196	−	0.350076i
$73$	11.0968			1.29878			0.649392	−	0.760454i	$-0.275024\pi$
$73$	11.0968			1.29878			0.649392	+	0.760454i	$0.275024\pi$
$74$	−8.64877	+	6.79756i	−1.00540	+	0.790201i
$75$	0.0979326	+	0.165309i	0.0113083	+	0.0190883i
$76$	−2.10526	−	3.45824i	−0.241490	−	0.396687i
$77$	−0.129379	+	0.129379i	−0.0147441	+	0.0147441i
$78$	0.284541	+	0.0341016i	0.0322179	+	0.00386125i
$79$	1.50228			0.169020			0.0845098	−	0.996423i	$-0.473068\pi$
$79$	1.50228			0.169020			0.0845098	+	0.996423i	$0.473068\pi$
$80$	1.62766	+	8.79493i	0.181978	+	0.983303i
$81$	−8.98671			−0.998524
$82$	−0.387523	−	0.0464437i	−0.0427947	−	0.00512885i
$83$	−6.02356	+	6.02356i	−0.661171	+	0.661171i	−0.955656	−	0.294485i	$-0.904852\pi$
$83$	−6.02356	+	6.02356i	−0.661171	+	0.661171i	0.294485	+	0.955656i	$0.404852\pi$
$84$	0.0656484	−	0.0399646i	0.00716283	−	0.00436049i
$85$	−3.08306	+	2.39333i	−0.334404	+	0.259593i
$86$	6.32178	−	4.96865i	0.681695	−	0.535783i
$87$	0.0487954			0.00523142
$88$	0.214590	+	0.470930i	0.0228754	+	0.0502013i
$89$		−	2.39026i		−	0.253367i	−0.991943	−	0.126683i	$-0.959567\pi$
$89$		−	2.39026i		−	0.253367i	0.991943	−	0.126683i	$-0.0404332\pi$
$90$	4.88190	+	8.12887i	0.514598	+	0.856858i
$91$	3.72874	−	3.72874i	0.390879	−	0.390879i
$92$	8.52072	+	2.07214i	0.888347	+	0.216036i
$93$	0.262765	−	0.262765i	0.0272474	−	0.0272474i
$94$	−6.39570	−	0.766511i	−0.659667	−	0.0790596i
$95$	−0.565625	+	4.49104i	−0.0580319	+	0.460771i
$96$	−0.0408419	−	0.213511i	−0.00416841	−	0.0217914i
$97$		−	9.67479i		−	0.982326i	−0.871068	−	0.491163i	$-0.836572\pi$
$97$		−	9.67479i		−	0.982326i	0.871068	−	0.491163i	$-0.163428\pi$
$98$	0.168286	−	1.40417i	0.0169995	−	0.141842i
$99$	0.387947	+	0.387947i	0.0389901	+	0.0389901i
$100$	4.69857	−	8.82743i	0.469857	−	0.882743i
$101$	−3.25404	+	3.25404i	−0.323789	+	0.323789i	−0.850219	−	0.526430i	$-0.823530\pi$
$101$	−3.25404	+	3.25404i	−0.323789	+	0.323789i	0.526430	+	0.850219i	$0.323530\pi$
$102$	0.0745801	−	0.0586168i	0.00738453	−	0.00580392i
$103$	−13.0843			−1.28924			−0.644618	−	0.764505i	$-0.722983\pi$
$103$	−13.0843			−1.28924			−0.644618	+	0.764505i	$0.722983\pi$
$104$	−6.18454	−	13.5723i	−0.606444	−	1.33088i
$105$	−0.0852544	−	0.0107374i	−0.00831998	−	0.00104786i
$106$	7.66765	−	6.02644i	0.744748	−	0.585340i
$107$	4.08369	+	4.08369i	0.394786	+	0.394786i	0.876389	−	0.481604i	$-0.159945\pi$
$107$	4.08369	+	4.08369i	0.394786	+	0.394786i	−0.481604	+	0.876389i	$0.659945\pi$
$108$	−0.239728	−	0.393794i	−0.0230679	−	0.0378928i
$109$	7.36243	+	7.36243i	0.705193	+	0.705193i	0.965520	−	0.260327i	$-0.0838305\pi$
$109$	7.36243	+	7.36243i	0.705193	+	0.705193i	−0.260327	+	0.965520i	$0.583831\pi$
$110$	0.140099	−	0.561384i	0.0133579	−	0.0535259i
$111$	−0.298911			−0.0283713
$112$	−3.55329	−	1.83687i	−0.335755	−	0.173568i
$113$			6.72734i			0.632855i	0.948617	+	0.316427i	$0.102483\pi$
$113$			6.72734i			0.632855i	−0.948617	+	0.316427i	$0.897517\pi$
$114$	0.0130911	−	0.109231i	0.00122609	−	0.0102304i
$115$	−6.01194	−	7.74449i	−0.560616	−	0.722178i
$116$	−1.32055	−	2.16923i	−0.122610	−	0.201408i
$117$	−11.1807	−	11.1807i	−1.03366	−	1.03366i
$118$	−8.73966	−	11.1198i	−0.804551	−	1.02366i
$119$		−	1.74547i		−	0.160007i
$120$	−0.112904	+	0.215224i	−0.0103066	+	0.0196472i
$121$			10.9665i			0.996957i
$122$	−6.10616	+	4.79918i	−0.552826	+	0.434497i
$123$	−0.00749917	−	0.00749917i	−0.000676177	−	0.000676177i
$124$	−18.7926	−	4.57014i	−1.68762	−	0.410410i
$125$	−10.2558	+	4.45189i	−0.917303	+	0.398189i
$126$	−4.21042	−	0.504610i	−0.375094	−	0.0449542i
$127$		−	12.4488i		−	1.10466i	−0.833627	−	0.552328i	$-0.813740\pi$
$127$		−	12.4488i		−	1.10466i	0.833627	−	0.552328i	$-0.186260\pi$
$128$	−8.38645	+	7.59391i	−0.741264	+	0.671213i
$129$	0.218487			0.0192367
$130$	−4.03769	+	16.1792i	−0.354129	+	1.41901i
$131$	4.93684	+	4.93684i	0.431334	+	0.431334i	0.889082	−	0.457748i	$-0.151344\pi$
$131$	4.93684	+	4.93684i	0.431334	+	0.431334i	−0.457748	+	0.889082i	$0.651344\pi$
$132$	−0.00332296	+	0.0136641i	−0.000289227	+	0.00118931i
$133$	−1.43141	−	1.43141i	−0.124119	−	0.124119i
$134$	9.06660	+	11.5357i	0.783235	+	0.996537i
$135$	−0.0644084	+	0.511400i	−0.00554339	+	0.0440143i
$136$	−4.62421	−	1.72915i	−0.396522	−	0.148274i
$137$	18.7120			1.59867			0.799335	−	0.600885i	$-0.205185\pi$
$137$	18.7120			1.59867			0.799335	+	0.600885i	$0.205185\pi$
$138$	0.147243	+	0.187342i	0.0125341	+	0.0159476i
$139$	7.31276	−	7.31276i	0.620260	−	0.620260i	−0.325338	−	0.945598i	$-0.605478\pi$
$139$	7.31276	−	7.31276i	0.620260	−	0.620260i	0.945598	+	0.325338i	$0.105478\pi$
$140$	1.82991	+	4.08062i	0.154655	+	0.344875i
$141$	−0.123767	−	0.123767i	−0.0104230	−	0.0104230i
$142$	−1.07111	−	0.128370i	−0.0898854	−	0.0107726i
$143$			0.964845i			0.0806844i
$144$	−5.50791	+	10.6546i	−0.458993	+	0.887886i
$145$	−0.354796	+	2.81707i	−0.0294642	+	0.233945i
$146$	1.86744	−	15.5818i	0.154550	−	1.28955i
$147$	0.0271728	−	0.0271728i	0.00224117	−	0.00224117i
$148$	8.08944	+	13.2882i	0.664948	+	1.09229i
$149$	−15.0882	+	15.0882i	−1.23607	+	1.23607i	−0.274477	+	0.961594i	$0.588505\pi$
$149$	−15.0882	+	15.0882i	−1.23607	+	1.23607i	−0.961594	+	0.274477i	$0.911495\pi$
$150$	0.248602	−	0.109694i	0.0202983	−	0.00895650i
$151$		−	19.0428i		−	1.54968i	−0.632156	−	0.774841i	$-0.717830\pi$
$151$		−	19.0428i		−	1.54968i	0.632156	−	0.774841i	$-0.282170\pi$
$152$	−5.21022	+	2.37416i	−0.422605	+	0.192570i
$153$	−5.23382			−0.423130
$154$	0.159897	+	0.203443i	0.0128849	+	0.0163939i
$155$	13.2594	+	17.0806i	1.06502	+	1.37195i
$156$	0.0957685	−	0.393804i	0.00766762	−	0.0315295i
$157$	−8.58699	+	8.58699i	−0.685317	+	0.685317i	−0.961193	−	0.275876i	$-0.911032\pi$
$157$	−8.58699	+	8.58699i	−0.685317	+	0.685317i	0.275876	+	0.961193i	$0.411032\pi$
$158$	0.252813	−	2.10945i	0.0201127	−	0.167819i
$159$	0.265002			0.0210160
$160$	12.6234	−	0.805437i	0.997971	−	0.0636754i
$161$	4.38453			0.345549
$162$	−1.51234	+	12.6188i	−0.118821	+	0.991429i
$163$	3.89049	−	3.89049i	0.304727	−	0.304727i	−0.538133	−	0.842860i	$-0.680870\pi$
$163$	3.89049	−	3.89049i	0.304727	−	0.304727i	0.842860	+	0.538133i	$0.180870\pi$
$164$	−0.130429	+	0.536330i	−0.0101848	+	0.0418803i
$165$	0.0124193	−	0.00964096i	0.000966845	−	0.000750548i
$166$	7.44439	+	9.47175i	0.577796	+	0.735150i
$167$	11.7741			0.911111			0.455555	−	0.890207i	$-0.349441\pi$
$167$	11.7741			0.911111			0.455555	+	0.890207i	$0.349441\pi$
$168$	−0.0450691	−	0.0989067i	−0.00347716	−	0.00763082i
$169$		−	14.8071i		−	1.13900i
$170$	2.84180	+	4.73189i	0.217956	+	0.362919i
$171$	−4.29212	+	4.29212i	−0.328227	+	0.328227i
$172$	−5.91293	−	9.71298i	−0.450857	−	0.740607i
$173$	0.249964	−	0.249964i	0.0190044	−	0.0190044i	−0.697541	−	0.716545i	$-0.745722\pi$
$173$	0.249964	−	0.249964i	0.0190044	−	0.0190044i	0.716545	+	0.697541i	$0.245722\pi$
$174$	0.00821159	−	0.0685169i	0.000622519	−	0.00519425i
$175$	1.23979	−	4.84386i	0.0937190	−	0.366161i
$176$	0.697376	−	0.222069i	0.0525667	−	0.0167391i
$177$		−	0.384311i		−	0.0288866i
$178$	−3.35632	−	0.402247i	−0.251567	−	0.0301497i
$179$	11.5314	+	11.5314i	0.861895	+	0.861895i	0.991558	−	0.129663i	$-0.0413896\pi$
$179$	11.5314	+	11.5314i	0.861895	+	0.861895i	−0.129663	+	0.991558i	$0.541390\pi$
$180$	12.2358	−	5.48702i	0.912005	−	0.408978i
$181$	−9.02180	+	9.02180i	−0.670585	+	0.670585i	−0.957851	−	0.287266i	$-0.907254\pi$
$181$	−9.02180	+	9.02180i	−0.670585	+	0.670585i	0.287266	+	0.957851i	$0.407254\pi$
$182$	−4.60828	−	5.86327i	−0.341588	−	0.434614i
$183$	−0.211035			−0.0156002
$184$	4.34355	−	11.6158i	0.320211	−	0.856327i
$185$	2.17341	−	17.2568i	0.159792	−	1.26874i
$186$	−0.324745	−	0.413185i	−0.0238115	−	0.0302962i
$187$	0.225827	+	0.225827i	0.0165141	+	0.0165141i
$188$	−2.15262	+	8.85163i	−0.156996	+	0.645572i
$189$	−0.162997	−	0.162997i	−0.0118563	−	0.0118563i
$190$	6.21098	+	1.55001i	0.450592	+	0.112450i
$191$	−16.9269			−1.22479			−0.612394	−	0.790553i	$-0.709793\pi$
$191$	−16.9269			−1.22479			−0.612394	+	0.790553i	$0.709793\pi$
$192$	−0.306678	+	0.0214179i	−0.0221326	+	0.00154570i
$193$		−	13.3847i		−	0.963450i	−0.876322	−	0.481725i	$-0.840010\pi$
$193$		−	13.3847i		−	0.963450i	0.876322	−	0.481725i	$-0.159990\pi$
$194$	−13.5850	−	1.62813i	−0.975347	−	0.116893i
$195$	−0.357929	+	0.277855i	−0.0256318	+	0.0198976i
$196$	−1.94336	−	0.472603i	−0.138811	−	0.0337573i
$197$	13.8284	+	13.8284i	0.985230	+	0.985230i	0.999892	−	0.0146629i	$-0.00466750\pi$
$197$	13.8284	+	13.8284i	0.985230	+	0.985230i	−0.0146629	+	0.999892i	$0.504667\pi$
$198$	0.610028	−	0.479456i	0.0433528	−	0.0340734i
$199$		−	16.8574i		−	1.19499i	−0.801872	−	0.597496i	$-0.796162\pi$
$199$		−	16.8574i		−	1.19499i	0.801872	−	0.597496i	$-0.203838\pi$
$200$	−11.6045	−	8.08310i	−0.820559	−	0.571561i
$201$			0.398687i			0.0281212i
$202$	4.02160	+	5.11682i	0.282959	+	0.360018i
$203$	−0.897874	−	0.897874i	−0.0630184	−	0.0630184i
$204$	−0.0697568	−	0.114587i	−0.00488395	−	0.00802271i
$205$	0.487471	−	0.378417i	0.0340464	−	0.0264298i
$206$	−2.20191	+	18.3725i	−0.153414	+	1.28008i
$207$		−	13.1471i		−	0.913788i
$208$	−20.0986	+	6.40009i	−1.39358	+	0.443766i
$209$	0.370390			0.0256204
$210$	−0.0294242	+	0.117904i	−0.00203046	+	0.00813617i
$211$	−3.94014	−	3.94014i	−0.271251	−	0.271251i	0.558353	−	0.829604i	$-0.311434\pi$
$211$	−3.94014	−	3.94014i	−0.271251	−	0.271251i	−0.829604	+	0.558353i	$0.811434\pi$
$212$	−7.17176	−	11.7808i	−0.492559	−	0.809109i
$213$	−0.0207276	−	0.0207276i	−0.00142023	−	0.00142023i
$214$	6.42141	−	5.04695i	0.438959	−	0.345003i
$215$	−1.58864	+	12.6138i	−0.108344	+	0.860252i
$216$	−0.593294	+	0.270348i	−0.0403686	+	0.0183949i
$217$	−9.67014			−0.656452
$218$	11.5771	−	9.09907i	0.784098	−	0.616267i
$219$	0.301531	−	0.301531i	0.0203756	−	0.0203756i
$220$	−0.764700	−	0.291195i	−0.0515560	−	0.0196324i
$221$	−6.50840	−	6.50840i	−0.437802	−	0.437802i
$222$	−0.0503025	+	0.419720i	−0.00337608	+	0.0281698i
$223$		−	26.3996i		−	1.76785i	−0.467633	−	0.883923i	$-0.654893\pi$
$223$		−	26.3996i		−	1.76785i	0.467633	−	0.883923i	$-0.345107\pi$
$224$	−3.17724	+	4.68029i	−0.212289	+	0.312715i
$225$	−14.5244	−	3.71753i	−0.968294	−	0.247835i
$226$	9.44630	+	1.13212i	0.628358	+	0.0753073i
$227$	15.9828	−	15.9828i	1.06081	−	1.06081i	0.0627865	−	0.998027i	$-0.480001\pi$
$227$	15.9828	−	15.9828i	1.06081	−	1.06081i	0.998027	−	0.0627865i	$-0.0199987\pi$
$228$	−0.151176	−	0.0367642i	−0.0100118	−	0.00243477i
$229$	19.0004	−	19.0004i	1.25558	−	1.25558i	0.302406	−	0.953179i	$-0.402210\pi$
$229$	19.0004	−	19.0004i	1.25558	−	1.25558i	0.953179	−	0.302406i	$-0.0977897\pi$
$230$	−11.8863	+	7.13846i	−0.783758	+	0.470696i
$231$			0.00703119i			0.000462618i
$232$	−3.26819	+	1.48922i	−0.214567	+	0.0977724i
$233$	28.1512			1.84425			0.922124	−	0.386893i	$-0.126452\pi$
$233$	28.1512			1.84425			0.922124	+	0.386893i	$0.126452\pi$
$234$	−17.5811	+	13.8180i	−1.14932	+	0.903313i
$235$	8.04526	−	6.24542i	0.524815	−	0.407406i
$236$	−17.0847	+	10.4006i	−1.11212	+	0.677023i
$237$	0.0408211	−	0.0408211i	0.00265161	−	0.00265161i
$238$	−2.45092	−	0.293738i	−0.158870	−	0.0190402i
$239$	15.7384			1.01804			0.509018	−	0.860756i	$-0.330009\pi$
$239$	15.7384			1.01804			0.509018	+	0.860756i	$0.330009\pi$
$240$	0.283211	+	0.194755i	0.0182812	+	0.0125714i
$241$	14.1919			0.914182			0.457091	−	0.889420i	$-0.348891\pi$
$241$	14.1919			0.914182			0.457091	+	0.889420i	$0.348891\pi$
$242$	15.3988	+	1.84551i	0.989873	+	0.118634i
$243$	−0.733184	+	0.733184i	−0.0470337	+	0.0470337i
$244$	5.71126	+	9.38169i	0.365626	+	0.600601i
$245$	1.37117	+	1.76632i	0.0876008	+	0.112846i
$246$	−0.0117921	+	0.00926806i	−0.000751835	+	0.000590910i
$247$	−10.6747			−0.679217
$248$	−9.57975	+	25.6188i	−0.608315	+	1.62679i
$249$			0.327354i			0.0207452i
$250$	4.52529	+	15.1500i	0.286204	+	0.958169i
$251$	−6.97991	+	6.97991i	−0.440568	+	0.440568i	−0.892203	−	0.451635i	$-0.850841\pi$
$251$	−6.97991	+	6.97991i	−0.440568	+	0.440568i	0.451635	+	0.892203i	$0.350841\pi$
$252$	−1.41711	+	5.82721i	−0.0892696	+	0.367080i
$253$	−0.567268	+	0.567268i	−0.0356638	+	0.0356638i
$254$	−17.4802	−	2.09497i	−1.09681	−	0.131450i
$255$	−0.0187417	+	0.148809i	−0.00117365	+	0.00931876i
$256$	9.25179	+	13.0539i	0.578237	+	0.815869i
$257$		−	23.3129i		−	1.45422i	−0.686522	−	0.727109i	$-0.740863\pi$
$257$		−	23.3129i		−	1.45422i	0.686522	−	0.727109i	$-0.259137\pi$
$258$	0.0367684	−	0.306792i	0.00228910	−	0.0191001i
$259$	5.50019	+	5.50019i	0.341765	+	0.341765i
$260$	22.0388	+	8.39232i	1.36679	+	0.520470i
$261$	−2.69230	+	2.69230i	−0.166649	+	0.166649i
$262$	7.76294	−	6.10134i	0.479596	−	0.376942i
$263$	−22.1287			−1.36451			−0.682257	−	0.731113i	$-0.739001\pi$
$263$	−22.1287			−1.36451			−0.682257	+	0.731113i	$0.739001\pi$
$264$	0.0186275	+	0.00696547i	0.00114644	+	0.000428695i
$265$	−1.92685	+	15.2992i	−0.118366	+	0.939820i
$266$	−2.25082	+	1.76905i	−0.138007	+	0.108467i
$267$	−0.0649499	−	0.0649499i	−0.00397487	−	0.00397487i
$268$	17.7239	−	10.7897i	1.08266	−	0.659086i
$269$	16.5362	+	16.5362i	1.00823	+	1.00823i	0.999966	+	0.00826106i	$0.00262961\pi$
$269$	16.5362	+	16.5362i	1.00823	+	1.00823i	0.00826106	+	0.999966i	$0.497370\pi$
$270$	0.707252	+	0.176502i	0.0430420	+	0.0107415i
$271$	−6.13633			−0.372755			−0.186378	−	0.982478i	$-0.559675\pi$
$271$	−6.13633			−0.372755			−0.186378	+	0.982478i	$0.559675\pi$
$272$	−3.20620	+	6.20216i	−0.194405	+	0.376061i
$273$		−	0.202641i		−	0.0122644i
$274$	3.14896	−	26.2747i	0.190236	−	1.58731i
$275$	0.466292	+	0.787097i	0.0281185	+	0.0474638i
$276$	0.287838	−	0.175226i	0.0173258	−	0.0105474i
$277$	−0.539558	−	0.539558i	−0.0324189	−	0.0324189i	0.690712	−	0.723130i	$-0.257297\pi$
$277$	−0.539558	−	0.539558i	−0.0324189	−	0.0324189i	−0.723130	+	0.690712i	$0.757297\pi$
$278$	−9.03769	−	11.4990i	−0.542045	−	0.689662i
$279$			28.9962i			1.73595i
$280$	6.03781	−	1.88278i	0.360828	−	0.112518i
$281$			1.42389i			0.0849424i	0.999098	+	0.0424712i	$0.0135231\pi$
$281$			1.42389i			0.0849424i	−0.999098	+	0.0424712i	$0.986477\pi$
$282$	−0.194617	+	0.152961i	−0.0115893	+	0.00910869i
$283$	3.44122	+	3.44122i	0.204559	+	0.204559i	0.801950	−	0.597391i	$-0.203796\pi$
$283$	3.44122	+	3.44122i	0.204559	+	0.204559i	−0.597391	+	0.801950i	$0.703796\pi$
$284$	−0.360505	+	1.48241i	−0.0213920	+	0.0879648i
$285$	0.106664	+	0.137404i	0.00631826	+	0.00813909i
$286$	1.35480	+	0.162370i	0.0801111	+	0.00960113i
$287$			0.275981i			0.0162906i
$288$	14.0340	+	9.52704i	0.826959	+	0.561386i
$289$	13.9533			0.820785
$290$	3.89593	+	0.972266i	0.228777	+	0.0570935i
$291$	−0.262891	−	0.262891i	−0.0154109	−	0.0154109i
$292$	−21.5651	−	5.24438i	−1.26200	−	0.306904i
$293$	6.26698	+	6.26698i	0.366121	+	0.366121i	0.866060	−	0.499940i	$-0.166644\pi$
$293$	6.26698	+	6.26698i	0.366121	+	0.366121i	−0.499940	+	0.866060i	$0.666644\pi$
$294$	−0.0335823	−	0.0427279i	−0.00195856	−	0.00249194i
$295$	22.1871	+	2.79436i	1.29178	+	0.162694i
$296$	20.0202	−	9.12268i	1.16365	−	0.530245i
$297$	0.0421768			0.00244734
$298$	18.6471	+	23.7254i	1.08020	+	1.37438i
$299$	16.3488	−	16.3488i	0.945475	−	0.945475i
$300$	−0.112193	−	0.367539i	−0.00647744	−	0.0212199i
$301$	−4.02033	−	4.02033i	−0.231728	−	0.231728i
$302$	−26.7392	−	3.20464i	−1.53867	−	0.184406i
$303$			0.176843i			0.0101593i
$304$	2.45690	+	7.71555i	0.140913	+	0.442517i
$305$	1.53446	−	12.1835i	0.0878628	−	0.697628i
$306$	−0.880779	+	7.34915i	−0.0503508	+	0.420123i
$307$	20.6430	−	20.6430i	1.17816	−	1.17816i	0.197945	−	0.980213i	$-0.436573\pi$
$307$	20.6430	−	20.6430i	1.17816	−	1.17816i	0.980213	−	0.197945i	$-0.0634268\pi$
$308$	0.312576	−	0.190286i	0.0178106	−	0.0108425i
$309$	−0.355537	+	0.355537i	−0.0202258	+	0.0202258i
$310$	26.2153	−	15.7440i	1.48893	−	0.894198i
$311$			2.25549i			0.127897i	0.997953	+	0.0639485i	$0.0203694\pi$
$311$			2.25549i			0.127897i	−0.997953	+	0.0639485i	$0.979631\pi$
$312$	−0.536849	−	0.200747i	−0.0303931	−	0.0113650i
$313$	29.2014			1.65056			0.825279	−	0.564725i	$-0.191018\pi$
$313$	29.2014			1.65056			0.825279	+	0.564725i	$0.191018\pi$
$314$	10.6125	+	13.5026i	0.598897	+	0.761997i
$315$	5.29636	−	4.11149i	0.298416	−	0.231656i
$316$	−2.91947	−	0.709981i	−0.164233	−	0.0399396i
$317$	−9.42890	+	9.42890i	−0.529580	+	0.529580i	−0.920447	−	0.390867i	$-0.872175\pi$
$317$	−9.42890	+	9.42890i	−0.529580	+	0.529580i	0.390867	+	0.920447i	$0.372175\pi$
$318$	0.0445961	−	0.372106i	0.00250083	−	0.0208667i
$319$	0.232333			0.0130081
$320$	0.993382	−	17.8609i	0.0555317	−	0.998457i
$321$	0.221931			0.0123870
$322$	0.737855	−	6.15661i	0.0411191	−	0.343094i
$323$	−2.49848	+	2.49848i	−0.139019	+	0.139019i
$324$	17.4644	+	4.24714i	0.970245	+	0.235952i
$325$	−13.4387	−	22.6843i	−0.745442	−	1.25830i
$326$	−4.80818	−	6.11761i	−0.266300	−	0.338823i
$327$	0.400115			0.0221264
$328$	0.731146	+	0.273401i	0.0403708	+	0.0150961i
$329$			4.55481i			0.251115i
$330$	−0.0114475	−	0.0190613i	−0.000630164	−	0.00104929i
$331$	−15.3003	+	15.3003i	−0.840981	+	0.840981i	−0.988986	−	0.148006i	$-0.952715\pi$
$331$	−15.3003	+	15.3003i	−0.840981	+	0.840981i	0.148006	+	0.988986i	$0.452715\pi$
$332$	14.5527	−	8.85919i	0.798682	−	0.486211i
$333$	16.4924	−	16.4924i	0.903780	−	0.903780i
$334$	1.98142	−	16.5328i	0.108419	−	0.904637i
$335$	−23.0171	−	2.89889i	−1.25756	−	0.158384i
$336$	−0.146466	+	0.0466399i	−0.00799037	+	0.00254441i
$337$			6.28699i			0.342474i	0.985230	+	0.171237i	$0.0547764\pi$
$337$			6.28699i			0.342474i	−0.985230	+	0.171237i	$0.945224\pi$
$338$	−20.7916	−	2.49182i	−1.13091	−	0.135537i
$339$	0.182801	+	0.182801i	0.00992836	+	0.00992836i
$340$	7.12258	−	3.19404i	0.386276	−	0.173221i
$341$	1.25112	−	1.25112i	0.0677518	−	0.0677518i
$342$	5.30454	+	6.74915i	0.286837	+	0.364952i
$343$	−1.00000			−0.0539949
$344$	−14.6337	+	6.66818i	−0.788995	+	0.359524i
$345$	−0.373801	−	0.0470783i	−0.0201247	−	0.00253461i
$346$	−0.308925	−	0.393056i	−0.0166079	−	0.0211308i
$347$	17.3247	+	17.3247i	0.930037	+	0.930037i	0.997708	−	0.0676707i	$-0.0215567\pi$
$347$	17.3247	+	17.3247i	0.930037	+	0.930037i	−0.0676707	+	0.997708i	$0.521557\pi$
$348$	−0.0948271	−	0.0230609i	−0.00508327	−	0.00123619i
$349$	1.87300	+	1.87300i	0.100260	+	0.100260i	0.755457	−	0.655198i	$-0.227415\pi$
$349$	1.87300	+	1.87300i	0.100260	+	0.100260i	−0.655198	+	0.755457i	$0.727415\pi$
$350$	−6.59293	−	2.55602i	−0.352407	−	0.136625i
$351$	−1.21554			−0.0648810
$352$	−0.194463	−	1.01660i	−0.0103649	−	0.0541851i
$353$			7.20372i			0.383416i	0.981452	+	0.191708i	$0.0614026\pi$
$353$			7.20372i			0.383416i	−0.981452	+	0.191708i	$0.938597\pi$
$354$	−0.539636	−	0.0646741i	−0.0286813	−	0.00343739i
$355$	1.34736	−	1.04594i	0.0715106	−	0.0555127i
$356$	−1.12964	+	4.64513i	−0.0598709	+	0.246191i
$357$	−0.0474292	−	0.0474292i	−0.00251022	−	0.00251022i
$358$	18.1325	−	14.2514i	0.958333	−	0.753209i
$359$			30.8851i			1.63005i	0.579425	+	0.815025i	$0.303277\pi$
$359$			30.8851i			1.63005i	−0.579425	+	0.815025i	$0.696723\pi$
$360$	−5.64557	−	18.1045i	−0.297547	−	0.954191i
$361$		−	14.9021i		−	0.784322i
$362$	11.1499	+	14.1863i	0.586023	+	0.745618i
$363$	0.297991	+	0.297991i	0.0156405	+	0.0156405i
$364$	−9.00851	+	5.48408i	−0.472174	+	0.287444i
$365$	15.2156	+	19.6005i	0.796421	+	1.02594i
$366$	−0.0355143	+	0.296328i	−0.00185636	+	0.0154893i
$367$			6.59027i			0.344009i	0.985096	+	0.172005i	$0.0550244\pi$
$367$			6.59027i			0.344009i	−0.985096	+	0.172005i	$0.944976\pi$
$368$	−15.5795	−	8.05383i	−0.812139	−	0.419835i
$369$	0.827535			0.0430797
$370$	−23.8656	−	5.95590i	−1.24071	−	0.309633i
$371$	−4.87624	−	4.87624i	−0.253162	−	0.253162i
$372$	−0.634830	+	0.386463i	−0.0329144	+	0.0200372i
$373$	4.84548	+	4.84548i	0.250889	+	0.250889i	0.821335	−	0.570446i	$-0.193230\pi$
$373$	4.84548	+	4.84548i	0.250889	+	0.250889i	−0.570446	+	0.821335i	$0.693230\pi$
$374$	0.355103	−	0.279095i	0.0183619	−	0.0144317i
$375$	−0.157707	+	0.399648i	−0.00814398	+	0.0206377i
$376$	12.0669	+	4.51223i	0.622303	+	0.232701i
$377$	−6.69588			−0.344855
$378$	−0.256304	+	0.201444i	−0.0131829	+	0.0103612i
$379$	−14.6047	+	14.6047i	−0.750195	+	0.750195i	−0.974516	−	0.224320i	$-0.927984\pi$
$379$	−14.6047	+	14.6047i	−0.750195	+	0.750195i	0.224320	+	0.974516i	$0.427984\pi$
$380$	3.22169	−	8.46039i	0.165269	−	0.434009i
$381$	−0.338270	−	0.338270i	−0.0173301	−	0.0173301i
$382$	−2.84856	+	23.7682i	−0.145745	+	1.21609i
$383$			8.39845i			0.429141i	0.976709	+	0.214570i	$0.0688351\pi$
$383$			8.39845i			0.429141i	−0.976709	+	0.214570i	$0.931165\pi$
$384$	−0.0215354	+	0.434231i	−0.00109897	+	0.0221592i
$385$	−0.405927	−	0.0511245i	−0.0206879	−	0.00260554i
$386$	−18.7943	−	2.25245i	−0.956604	−	0.114647i
$387$	−12.0551	+	12.0551i	−0.612793	+	0.612793i
$388$	−4.57233	+	18.8016i	−0.232125	+	0.954507i
$389$	22.6704	−	22.6704i	1.14944	−	1.14944i	0.162774	−	0.986663i	$-0.447956\pi$
$389$	22.6704	−	22.6704i	1.14944	−	1.14944i	0.986663	−	0.162774i	$-0.0520441\pi$
$390$	0.329920	+	0.549350i	0.0167061	+	0.0278174i
$391$		−	7.65306i		−	0.387032i
$392$	−0.990653	+	2.64927i	−0.0500355	+	0.133808i
$393$	0.268295			0.0135337
$394$	21.7444	−	17.0902i	1.09547	−	0.860991i
$395$	2.05988	+	2.65351i	0.103644	+	0.133512i
$396$	−0.570576	−	0.937265i	−0.0286725	−	0.0470993i
$397$	−7.74441	+	7.74441i	−0.388681	+	0.388681i	−0.874217	−	0.485536i	$-0.838625\pi$
$397$	−7.74441	+	7.74441i	−0.388681	+	0.388681i	0.485536	+	0.874217i	$0.338625\pi$
$398$	−23.6706	−	2.83687i	−1.18650	−	0.142200i
$399$	−0.0777908			−0.00389441
$400$	−13.3029	+	14.9343i	−0.665144	+	0.746715i
$401$	−8.54246			−0.426590			−0.213295	−	0.976988i	$-0.568420\pi$
$401$	−8.54246			−0.426590			−0.213295	+	0.976988i	$0.568420\pi$
$402$	0.559823	+	0.0670935i	0.0279214	+	0.00334632i
$403$	−36.0575	+	36.0575i	−1.79615	+	1.79615i
$404$	7.86163	−	4.78590i	0.391131	−	0.238107i
$405$	−12.3223	−	15.8734i	−0.612300	−	0.788757i
$406$	−1.41186	+	1.10966i	−0.0700696	+	0.0550717i
$407$	−1.42322			−0.0705464
$408$	−0.172638	+	0.0786667i	−0.00854687	+	0.00389458i
$409$			7.94314i			0.392763i	0.980528	+	0.196382i	$0.0629191\pi$
$409$			7.94314i			0.392763i	−0.980528	+	0.196382i	$0.937081\pi$
$410$	−0.449325	−	0.748172i	−0.0221906	−	0.0369496i
$411$	0.508456	−	0.508456i	0.0250803	−	0.0250803i
$412$	25.4275	+	6.18368i	1.25272	+	0.304648i
$413$	−7.07161	+	7.07161i	−0.347971	+	0.347971i
$414$	−18.4607	−	2.21248i	−0.907295	−	0.108737i
$415$	−18.8989	−	2.38022i	−0.927708	−	0.116840i
$416$	5.60447	+	29.2987i	0.274782	+	1.43649i
$417$		−	0.397416i		−	0.0194616i
$418$	0.0623315	−	0.520089i	0.00304873	−	0.0254384i
$419$	−13.6717	−	13.6717i	−0.667908	−	0.667908i	0.289323	−	0.957231i	$-0.406570\pi$
$419$	−13.6717	−	13.6717i	−0.667908	−	0.667908i	−0.957231	+	0.289323i	$0.906570\pi$
$420$	0.160605	+	0.0611580i	0.00783674	+	0.00298421i
$421$	−6.30725	+	6.30725i	−0.307397	+	0.307397i	−0.843899	−	0.536502i	$-0.819745\pi$
$421$	−6.30725	+	6.30725i	−0.307397	+	0.307397i	0.536502	+	0.843899i	$0.319745\pi$
$422$	−6.19568	+	4.86954i	−0.301601	+	0.237046i
$423$	13.6577			0.664060
$424$	−17.7491	+	8.08779i	−0.861973	+	0.392778i
$425$	−8.45479	−	2.16400i	−0.410118	−	0.104970i
$426$	−0.0325931	+	0.0256168i	−0.00157914	+	0.00124114i
$427$	3.88321	+	3.88321i	0.187922	+	0.187922i
$428$	−6.00612	−	9.86605i	−0.290317	−	0.476894i
$429$	0.0262175	+	0.0262175i	0.00126579	+	0.00126579i
$430$	17.4445	+	4.35344i	0.841247	+	0.209941i
$431$	22.0509			1.06215			0.531077	−	0.847324i	$-0.321788\pi$
$431$	22.0509			1.06215			0.531077	+	0.847324i	$0.321788\pi$
$432$	0.279770	+	0.878579i	0.0134605	+	0.0422706i
$433$			6.57436i			0.315944i	0.987444	+	0.157972i	$0.0504955\pi$
$433$			6.57436i			0.315944i	−0.987444	+	0.157972i	$0.949504\pi$
$434$	−1.62735	+	13.5785i	−0.0781153	+	0.651788i
$435$	0.0669069	+	0.0861885i	0.00320794	+	0.00413242i
$436$	−10.8283	−	17.7874i	−0.518584	−	0.851860i
$437$	−6.27607	−	6.27607i	−0.300225	−	0.300225i
$438$	−0.372656	−	0.474143i	−0.0178062	−	0.0226554i
$439$		−	31.5095i		−	1.50386i	−0.659240	−	0.751932i	$-0.729122\pi$
$439$		−	31.5095i		−	1.50386i	0.659240	−	0.751932i	$-0.270878\pi$
$440$	−0.537575	+	1.02476i	−0.0256279	+	0.0488535i
$441$			2.99852i			0.142787i
$442$	−10.2341	+	8.04360i	−0.486788	+	0.382595i
$443$	−10.9153	−	10.9153i	−0.518602	−	0.518602i	0.398546	−	0.917148i	$-0.369515\pi$
$443$	−10.9153	−	10.9153i	−0.518602	−	0.518602i	−0.917148	+	0.398546i	$0.869515\pi$
$444$	0.580891	+	0.141266i	0.0275679	+	0.00670419i
$445$	4.22196	−	3.27745i	0.200140	−	0.155366i
$446$	−37.0693	−	4.44268i	−1.75528	−	0.210367i
$447$			0.819975i			0.0387835i
$448$	6.03721	+	5.24900i	0.285232	+	0.247992i
$449$	−1.26792			−0.0598370			−0.0299185	−	0.999552i	$-0.509525\pi$
$449$	−1.26792			−0.0598370			−0.0299185	+	0.999552i	$0.509525\pi$
$450$	−7.66428	+	19.7691i	−0.361297	+	0.931923i
$451$	−0.0357062	−	0.0357062i	−0.00168134	−	0.00168134i
$452$	3.17936	−	13.0736i	0.149544	−	0.614932i
$453$	−0.517446	−	0.517446i	−0.0243117	−	0.0243117i
$454$	−19.7528	−	25.1321i	−0.927043	−	1.17951i
$455$	11.6989	+	1.47342i	0.548453	+	0.0690750i
$456$	−0.0770637	+	0.206089i	−0.00360884	+	0.00965098i
$457$	−8.67635			−0.405863			−0.202931	−	0.979193i	$-0.565047\pi$
$457$	−8.67635			−0.405863			−0.202931	+	0.979193i	$0.565047\pi$
$458$	−23.4823	−	29.8773i	−1.09725	−	1.39607i
$459$	−0.284505	+	0.284505i	−0.0132796	+	0.0132796i
$460$	8.02329	+	17.8916i	0.374088	+	0.834200i
$461$	−26.5321	−	26.5321i	−1.23572	−	1.23572i	−0.961733	−	0.273988i	$-0.911657\pi$
$461$	−26.5321	−	26.5321i	−1.23572	−	1.23572i	−0.273988	−	0.961733i	$-0.588343\pi$
$462$	0.00987296	+	0.00118325i	0.000459331	+	5.50498e-5i
$463$			1.22464i			0.0569139i	0.999595	+	0.0284570i	$0.00905935\pi$
$463$			1.22464i			0.0569139i	−0.999595	+	0.0284570i	$0.990941\pi$
$464$	1.54113	+	4.83969i	0.0715450	+	0.224677i
$465$	0.824422	+	0.103832i	0.0382317	+	0.00481509i
$466$	4.73746	−	39.5290i	0.219459	−	1.83114i
$467$	−18.6019	+	18.6019i	−0.860792	+	0.860792i	−0.991430	−	0.130638i	$-0.958297\pi$
$467$	−18.6019	+	18.6019i	−0.860792	+	0.860792i	0.130638	+	0.991430i	$0.458297\pi$
$468$	16.4441	+	27.0122i	0.760130	+	1.24864i
$469$	7.33615	−	7.33615i	0.338752	−	0.338752i
$470$	−7.41569	−	12.3479i	−0.342060	−	0.569566i
$471$			0.466665i			0.0215028i
$472$	11.7291	+	25.7401i	0.539874	+	1.18478i
$473$	1.04030			0.0478329
$474$	−0.0504499	−	0.0641892i	−0.00231724	−	0.00294831i
$475$	−8.70819	+	5.15891i	−0.399559	+	0.236707i
$476$	−0.824913	+	3.39207i	−0.0378098	+	0.155475i
$477$	−14.6215	+	14.6215i	−0.669473	+	0.669473i
$478$	2.64856	−	22.0994i	0.121142	−	1.01080i
$479$	23.9956			1.09639			0.548193	−	0.836352i	$-0.315316\pi$
$479$	23.9956			1.09639			0.548193	+	0.836352i	$0.315316\pi$
$480$	0.321128	−	0.364900i	0.0146574	−	0.0166553i
$481$	41.0176			1.87024
$482$	2.38830	−	19.9278i	0.108784	−	0.907686i
$483$	0.119140	−	0.119140i	0.00542105	−	0.00542105i
$484$	5.18281	−	21.3119i	0.235582	−	0.968723i
$485$	17.0888	−	13.2658i	0.775962	−	0.602368i
$486$	0.906126	+	1.15290i	0.0411027	+	0.0522964i
$487$	−16.4007			−0.743185			−0.371593	−	0.928396i	$-0.621188\pi$
$487$	−16.4007			−0.743185			−0.371593	+	0.928396i	$0.621188\pi$
$488$	14.1346	−	6.44074i	0.639842	−	0.291559i
$489$		−	0.211431i		−	0.00956124i
$490$	2.71096	−	1.62810i	0.122469	−	0.0735501i
$491$	−31.0310	+	31.0310i	−1.40041	+	1.40041i	−0.601653	+	0.798757i	$0.705491\pi$
$491$	−31.0310	+	31.0310i	−1.40041	+	1.40041i	−0.798757	+	0.601653i	$0.794509\pi$
$492$	0.0110294	+	0.0181177i	0.000497246	+	0.000816809i
$493$	−1.56721	+	1.56721i	−0.0705835	+	0.0705835i
$494$	−1.79641	+	14.9891i	−0.0808242	+	0.674391i
$495$	−0.153298	+	1.21718i	−0.00689023	+	0.0547082i
$496$	34.3609	+	17.7628i	1.54285	+	0.797575i
$497$			0.762807i			0.0342166i
$498$	0.459658	+	0.0550890i	0.0205978	+	0.00246860i
$499$	−12.6748	−	12.6748i	−0.567402	−	0.567402i	0.363998	−	0.931400i	$-0.381411\pi$
$499$	−12.6748	−	12.6748i	−0.567402	−	0.567402i	−0.931400	+	0.363998i	$0.881411\pi$
$500$	22.0346	−	3.80472i	0.985418	−	0.170152i
$501$	0.319936	−	0.319936i	0.0142937	−	0.0142937i
$502$	8.62632	+	10.9756i	0.385012	+	0.489863i
$503$	−21.8526			−0.974360			−0.487180	−	0.873302i	$-0.661974\pi$
$503$	−21.8526			−0.974360			−0.487180	+	0.873302i	$0.661974\pi$
$504$	7.94388	+	2.97050i	0.353849	+	0.132316i
$505$	−10.2095	−	1.28584i	−0.454318	−	0.0572191i
$506$	0.701074	+	0.892001i	0.0311666	+	0.0396543i
$507$	−0.402349	−	0.402349i	−0.0178689	−	0.0178689i
$508$	−5.88336	+	24.1926i	−0.261032	+	1.07337i
$509$	−18.9072	−	18.9072i	−0.838048	−	0.838048i	0.150554	−	0.988602i	$-0.451894\pi$
$509$	−18.9072	−	18.9072i	−0.838048	−	0.838048i	−0.988602	+	0.150554i	$0.951894\pi$
$510$	0.205798	+	0.0513589i	0.00911289	+	0.00227421i
$511$	−11.0968			−0.490894
$512$	19.8868	−	10.7942i	0.878880	−	0.477043i
$513$			0.466630i			0.0206022i
$514$	−32.7352	−	3.92323i	−1.44389	−	0.173046i
$515$	−17.9408	−	23.1111i	−0.790567	−	1.01840i
$516$	−0.424599	−	0.103258i	−0.0186919	−	0.00454567i
$517$	−0.589298	−	0.589298i	−0.0259173	−	0.0259173i
$518$	8.64877	−	6.79756i	0.380005	−	0.298668i
$519$		−	0.0135844i		−	0.000596290i
$520$	15.4930	−	29.5339i	0.679414	−	1.29515i
$521$		−	33.3380i		−	1.46057i	−0.683145	−	0.730283i	$-0.739388\pi$
$521$		−	33.3380i		−	1.46057i	0.683145	−	0.730283i	$-0.260612\pi$
$522$	3.32735	+	4.23350i	0.145634	+	0.185295i
$523$	−7.27884	−	7.27884i	−0.318281	−	0.318281i	0.529825	−	0.848107i	$-0.322257\pi$
$523$	−7.27884	−	7.27884i	−0.318281	−	0.318281i	−0.848107	+	0.529825i	$0.822257\pi$
$524$	−7.26089	−	11.9272i	−0.317193	−	0.521043i
$525$	−0.0979326	−	0.165309i	−0.00427413	−	0.00721469i
$526$	−3.72395	+	31.0723i	−0.162372	+	1.35482i
$527$			16.8789i			0.735257i
$528$	0.0129154	−	0.0249839i	0.000562071	−	0.00108728i
$529$	−3.77588			−0.164169
$530$	21.1583	+	5.28026i	0.919057	+	0.229360i
$531$	21.2044	+	21.2044i	0.920192	+	0.920192i
$532$	2.10526	+	3.45824i	0.0912745	+	0.149934i
$533$	1.02906	+	1.02906i	0.0445736	+	0.0445736i
$534$	−0.102131	+	0.0802703i	−0.00441962	+	0.00347363i
$535$	−1.61368	+	12.8126i	−0.0697654	+	0.553935i
$536$	−12.1678	−	26.7030i	−0.525571	−	1.15339i
$537$	0.626679			0.0270432
$538$	26.0023	−	20.4367i	1.12104	−	0.881088i
$539$	0.129379	−	0.129379i	0.00557276	−	0.00557276i
$540$	0.366858	−	0.963395i	0.0157870	−	0.0414579i
$541$	−14.7726	−	14.7726i	−0.635123	−	0.635123i	0.314225	−	0.949348i	$-0.398255\pi$
$541$	−14.7726	−	14.7726i	−0.635123	−	0.635123i	−0.949348	+	0.314225i	$0.898255\pi$
$542$	−1.03266	+	8.61642i	−0.0443565	+	0.370107i
$543$			0.490295i			0.0210406i
$544$	8.16929	+	5.54578i	0.350256	+	0.237773i
$545$	−2.90928	+	23.0996i	−0.124620	+	0.989477i
$546$	−0.284541	−	0.0341016i	−0.0121772	−	0.00145941i
$547$	−1.87629	+	1.87629i	−0.0802242	+	0.0802242i	−0.746080	−	0.665856i	$-0.768066\pi$
$547$	−1.87629	+	1.87629i	−0.0802242	+	0.0802242i	0.665856	+	0.746080i	$0.268066\pi$
$548$	−36.3641	−	8.84333i	−1.55340	−	0.377768i
$549$	11.6439	−	11.6439i	0.496949	−	0.496949i
$550$	1.18369	−	0.522294i	0.0504725	−	0.0222707i
$551$			2.57045i			0.109505i
$552$	−0.197607	−	0.433660i	−0.00841071	−	0.0184578i
$553$	−1.50228			−0.0638834
$554$	−0.848429	+	0.666829i	−0.0360463	+	0.0283308i
$555$	−0.409857	−	0.527972i	−0.0173975	−	0.0224112i
$556$	−17.6674	+	10.7553i	−0.749263	+	0.456126i
$557$	28.2329	−	28.2329i	1.19627	−	1.19627i	0.220992	−	0.975276i	$-0.429070\pi$
$557$	28.2329	−	28.2329i	1.19627	−	1.19627i	0.975276	−	0.220992i	$-0.0709296\pi$
$558$	40.7154	+	4.87965i	1.72362	+	0.206572i
$559$	−29.9816			−1.26809
$560$	−1.62766	−	8.79493i	−0.0687811	−	0.371653i
$561$	0.0122727			0.000518154
$562$	1.99938	+	0.239622i	0.0843389	+	0.0101078i
$563$	21.5008	−	21.5008i	0.906149	−	0.906149i	−0.0898100	−	0.995959i	$-0.528626\pi$
$563$	21.5008	−	21.5008i	0.906149	−	0.906149i	0.995959	+	0.0898100i	$0.0286260\pi$
$564$	0.182031	+	0.299016i	0.00766488	+	0.0125908i
$565$	−11.8826	+	9.22433i	−0.499907	+	0.388070i
$566$	5.41115	−	4.25293i	0.227447	−	0.178764i
$567$	8.98671			0.377406
$568$	2.02088	+	0.755677i	0.0847942	+	0.0317075i
$569$			17.9313i			0.751718i	0.926677	+	0.375859i	$0.122652\pi$
$569$			17.9313i			0.751718i	−0.926677	+	0.375859i	$0.877348\pi$
$570$	0.210888	−	0.126651i	0.00883311	−	0.00530484i
$571$	−12.3175	+	12.3175i	−0.515472	+	0.515472i	−0.916198	−	0.400726i	$-0.868758\pi$
$571$	−12.3175	+	12.3175i	−0.515472	+	0.515472i	0.400726	+	0.916198i	$0.368758\pi$
$572$	0.455988	−	1.87504i	0.0190658	−	0.0783994i
$573$	−0.459951	+	0.459951i	−0.0192147	+	0.0192147i
$574$	0.387523	+	0.0464437i	0.0161749	+	0.00193852i
$575$	5.43588	−	21.2380i	0.226692	−	0.885687i
$576$	15.7393	−	18.1027i	0.655802	−	0.754280i
$577$			18.4189i			0.766789i	0.923585	+	0.383394i	$0.125245\pi$
$577$			18.4189i			0.766789i	−0.923585	+	0.383394i	$0.874755\pi$
$578$	2.34815	−	19.5928i	0.0976703	−	0.814953i
$579$	−0.363699	−	0.363699i	−0.0151148	−	0.0151148i
$580$	2.02085	−	5.30690i	0.0839113	−	0.220357i
$581$	6.02356	−	6.02356i	0.249899	−	0.249899i
$582$	−0.413383	+	0.324902i	−0.0171353	+	0.0134676i
$583$	1.26177			0.0522571
$584$	−10.9931	+	29.3984i	−0.454897	+	1.21651i
$585$	4.41808	−	35.0794i	0.182665	−	1.45036i
$586$	9.85452	−	7.74523i	0.407086	−	0.319952i
$587$	23.9577	+	23.9577i	0.988842	+	0.988842i	0.999938	−	0.0110968i	$-0.00353228\pi$
$587$	23.9577	+	23.9577i	0.988842	+	0.988842i	−0.0110968	+	0.999938i	$0.503532\pi$
$588$	−0.0656484	+	0.0399646i	−0.00270729	+	0.00164811i
$589$	13.8420	+	13.8420i	0.570348	+	0.570348i
$590$	7.65753	−	30.6841i	0.315255	−	1.26325i
$591$	0.751510			0.0309130
$592$	−9.44062	−	29.6469i	−0.388007	−	1.21848i
$593$		−	3.45172i		−	0.141745i	−0.997485	−	0.0708726i	$-0.977422\pi$
$593$		−	3.45172i		−	0.141745i	0.997485	−	0.0708726i	$-0.0225784\pi$
$594$	0.00709776	−	0.0592232i	0.000291225	−	0.00242996i
$595$	3.08306	−	2.39333i	0.126393	−	0.0981171i
$596$	36.4524	−	22.1910i	1.49315	−	0.908980i
$597$	−0.458063	−	0.458063i	−0.0187473	−	0.0187473i
$598$	−20.2051	−	25.7077i	−0.826249	−	1.05127i
$599$			33.4491i			1.36669i	0.730093	+	0.683347i	$0.239477\pi$
$599$			33.4491i			1.36669i	−0.730093	+	0.683347i	$0.760523\pi$
$600$	−0.534966	+	0.0956852i	−0.0218399	+	0.00390633i
$601$			40.3198i			1.64468i	0.568997	+	0.822340i	$0.307332\pi$
$601$			40.3198i			1.64468i	−0.568997	+	0.822340i	$0.692668\pi$
$602$	−6.32178	+	4.96865i	−0.257656	+	0.202507i
$603$	−21.9976	−	21.9976i	−0.895813	−	0.895813i
$604$	−8.99968	+	37.0070i	−0.366192	+	1.50579i
$605$	−19.3704	+	15.0370i	−0.787519	+	0.611340i
$606$	0.248316	+	0.0297601i	0.0100872	+	0.00120892i
$607$			35.5147i			1.44150i	0.693197	+	0.720748i	$0.256202\pi$
$607$			35.5147i			1.44150i	−0.693197	+	0.720748i	$0.743798\pi$
$608$	11.2474	−	2.15148i	0.456141	−	0.0872539i
$609$	−0.0487954			−0.00197729
$610$	−16.8495	−	4.20495i	−0.682215	−	0.170254i
$611$	16.9837	+	16.9837i	0.687088	+	0.687088i
$612$	10.1712	+	2.47352i	0.411146	+	0.0999861i
$613$	4.26441	+	4.26441i	0.172238	+	0.172238i	0.787962	−	0.615724i	$-0.211136\pi$
$613$	4.26441	+	4.26441i	0.172238	+	0.172238i	−0.615724	+	0.787962i	$0.711136\pi$
$614$	−25.5123	−	32.4601i	−1.02959	−	1.30998i
$615$	0.00296331	−	0.0235286i	0.000119492	−	0.000948764i
$616$	−0.214590	−	0.470930i	−0.00864609	−	0.0189743i
$617$	−28.2795			−1.13849			−0.569244	−	0.822168i	$-0.692764\pi$
$617$	−28.2795			−1.13849			−0.569244	+	0.822168i	$0.692764\pi$
$618$	0.439401	+	0.559065i	0.0176753	+	0.0224889i
$619$	−16.9726	+	16.9726i	−0.682187	+	0.682187i	−0.960492	−	0.278306i	$-0.910227\pi$
$619$	−16.9726	+	16.9726i	−0.682187	+	0.682187i	0.278306	+	0.960492i	$0.410227\pi$
$620$	−17.6955	−	39.4602i	−0.710667	−	1.58476i
$621$	−0.714664	−	0.714664i	−0.0286785	−	0.0286785i
$622$	3.16708	+	0.379567i	0.126988	+	0.0152193i
$623$			2.39026i			0.0957636i
$624$	−0.372225	+	0.720042i	−0.0149009	+	0.0288247i
$625$	−21.9259	−	12.0107i	−0.877035	−	0.480427i
$626$	4.91418	−	41.0035i	0.196410	−	1.63883i
$627$	0.0100645	−	0.0100645i	0.000401938	−	0.000401938i
$628$	20.7459	−	12.6294i	0.827850	−	0.503967i
$629$	9.60039	−	9.60039i	0.382793	−	0.382793i
$630$	−4.88190	−	8.12887i	−0.194500	−	0.323862i
$631$		−	45.3629i		−	1.80587i	−0.429778	−	0.902934i	$-0.641408\pi$
$631$		−	45.3629i		−	1.80587i	0.429778	−	0.902934i	$-0.358592\pi$
$632$	−1.48824	+	3.97994i	−0.0591989	+	0.158313i
$633$	−0.214129			−0.00851087
$634$	11.6530	+	14.8265i	0.462799	+	0.588835i
$635$	21.9887	−	17.0695i	0.872593	−	0.677382i
$636$	−0.514994	−	0.125241i	−0.0204208	−	0.00496611i
$637$	−3.72874	+	3.72874i	−0.147738	+	0.147738i
$638$	0.0390983	−	0.326233i	0.00154792	−	0.0129157i
$639$	2.28730			0.0904840
$640$	−24.9125	−	4.40062i	−0.984755	−	0.173950i
$641$	43.5357			1.71956			0.859778	−	0.510669i	$-0.170602\pi$
$641$	43.5357			1.71956			0.859778	+	0.510669i	$0.170602\pi$
$642$	0.0373478	−	0.311627i	0.00147400	−	0.0122989i
$643$	−8.04362	+	8.04362i	−0.317210	+	0.317210i	−0.847694	−	0.530485i	$-0.822010\pi$
$643$	−8.04362	+	8.04362i	−0.317210	+	0.317210i	0.530485	+	0.847694i	$0.322010\pi$
$644$	−8.52072	−	2.07214i	−0.335763	−	0.0816538i
$645$	0.299583	+	0.385919i	0.0117961	+	0.0151955i
$646$	3.08782	+	3.92874i	0.121489	+	0.154574i
$647$	−8.30734			−0.326595			−0.163298	−	0.986577i	$-0.552213\pi$
$647$	−8.30734			−0.326595			−0.163298	+	0.986577i	$0.552213\pi$
$648$	8.90271	−	23.8082i	0.349731	−	0.935274i
$649$		−	1.82984i		−	0.0718275i
$650$	−34.1141	+	15.0526i	−1.33806	+	0.590413i
$651$	−0.262765	+	0.262765i	−0.0102986	+	0.0102986i
$652$	−9.39928	+	5.72197i	−0.368104	+	0.224090i
$653$	−0.221791	+	0.221791i	−0.00867936	+	0.00867936i	−0.711433	−	0.702754i	$-0.751954\pi$
$653$	−0.221791	+	0.221791i	−0.00867936	+	0.00867936i	0.702754	+	0.711433i	$0.251954\pi$
$654$	0.0673338	−	0.561828i	0.00263296	−	0.0219692i
$655$	−1.95080	+	15.4893i	−0.0762241	+	0.605217i
$656$	0.506942	−	0.980641i	0.0197928	−	0.0382876i
$657$			33.2740i			1.29814i
$658$	6.39570	+	0.766511i	0.249331	+	0.0298817i
$659$	−12.9745	−	12.9745i	−0.505415	−	0.505415i	0.407700	−	0.913116i	$-0.366331\pi$
$659$	−12.9745	−	12.9745i	−0.505415	−	0.505415i	−0.913116	+	0.407700i	$0.866331\pi$
$660$	−0.0286916	+	0.0128664i	−0.00111682	+	0.000500825i
$661$	−2.72672	+	2.72672i	−0.106057	+	0.106057i	−0.758144	−	0.652087i	$-0.773894\pi$
$661$	−2.72672	+	2.72672i	−0.106057	+	0.106057i	0.652087	+	0.758144i	$0.273894\pi$
$662$	18.9093	+	24.0590i	0.734932	+	0.935079i
$663$	−0.353703			−0.0137367
$664$	−9.99075	−	21.9252i	−0.387716	−	0.850865i
$665$	0.565625	−	4.49104i	0.0219340	−	0.174155i
$666$	−20.3827	−	25.9335i	−0.789812	−	1.00490i
$667$	−3.93676	−	3.93676i	−0.152432	−	0.152432i
$668$	−22.8814	−	5.56449i	−0.885308	−	0.215297i
$669$	−0.717350	−	0.717350i	−0.0277343	−	0.0277343i
$670$	−7.94399	+	31.8320i	−0.306903	+	1.22978i
$671$	−1.00481			−0.0387904
$672$	0.0408419	+	0.213511i	0.00157551	+	0.00823637i
$673$		−	11.3799i		−	0.438664i	−0.975650	−	0.219332i	$-0.929612\pi$
$673$		−	11.3799i		−	0.438664i	0.975650	−	0.219332i	$-0.0703878\pi$
$674$	8.82797	+	1.05801i	0.340041	+	0.0407531i
$675$	−0.991612	+	0.587451i	−0.0381672	+	0.0226110i
$676$	−6.99786	+	28.7754i	−0.269148	+	1.10675i
$677$	23.5306	+	23.5306i	0.904353	+	0.904353i	0.995809	−	0.0914561i	$-0.0291521\pi$
$677$	23.5306	+	23.5306i	0.904353	+	0.904353i	−0.0914561	+	0.995809i	$0.529152\pi$
$678$	0.287445	−	0.225919i	0.0110393	−	0.00867638i
$679$			9.67479i			0.371284i
$680$	−3.28633	−	10.5388i	−0.126025	−	0.404144i
$681$		−	0.868592i		−	0.0332845i
$682$	−1.54623	−	1.96732i	−0.0592082	−	0.0753326i
$683$	−25.9912	−	25.9912i	−0.994524	−	0.994524i	0.00546131	−	0.999985i	$-0.498262\pi$
$683$	−25.9912	−	25.9912i	−0.994524	−	0.994524i	−0.999985	+	0.00546131i	$0.998262\pi$
$684$	10.3696	−	6.31266i	0.396492	−	0.241371i
$685$	25.6573	+	33.0514i	0.980314	+	1.26283i
$686$	−0.168286	+	1.40417i	−0.00642519	+	0.0536113i
$687$		−	1.03259i		−	0.0393958i
$688$	6.90058	+	21.6703i	0.263082	+	0.826171i
$689$	−36.3645			−1.38538
$690$	−0.129011	+	0.516955i	−0.00491137	+	0.0196801i
$691$	−7.46397	−	7.46397i	−0.283943	−	0.283943i	0.550737	−	0.834679i	$-0.314347\pi$
$691$	−7.46397	−	7.46397i	−0.283943	−	0.283943i	−0.834679	+	0.550737i	$0.814347\pi$
$692$	−0.603903	+	0.367636i	−0.0229570	+	0.0139754i
$693$	−0.387947	−	0.387947i	−0.0147369	−	0.0147369i
$694$	27.2422	−	21.4112i	1.03410	−	0.812758i
$695$	22.9437	+	2.88965i	0.870305	+	0.109611i
$696$	−0.0483393	+	0.129272i	−0.00183230	+	0.00490005i
$697$	0.481715			0.0182463
$698$	2.94521	−	2.31481i	0.111478	−	0.0876167i
$699$	0.764947	−	0.764947i	0.0289330	−	0.0289330i
$700$	−4.69857	+	8.82743i	−0.177589	+	0.333645i
$701$	28.5285	+	28.5285i	1.07751	+	1.07751i	0.996732	+	0.0807753i	$0.0257396\pi$
$701$	28.5285	+	28.5285i	1.07751	+	1.07751i	0.0807753	+	0.996732i	$0.474260\pi$
$702$	−0.204559	+	1.70683i	−0.00772059	+	0.0644200i
$703$		−	15.7461i		−	0.593874i
$704$	−1.46020	+	0.101978i	−0.0550335	+	0.00384345i
$705$	0.0489067	−	0.388317i	0.00184193	−	0.0146249i
$706$	10.1152	+	1.21229i	0.380691	+	0.0456250i
$707$	3.25404	−	3.25404i	0.122381	−	0.122381i
$708$	−0.181626	+	0.746854i	−0.00682593	+	0.0280685i
$709$	−17.9860	+	17.9860i	−0.675477	+	0.675477i	−0.958973	−	0.283497i	$-0.908506\pi$
$709$	−17.9860	+	17.9860i	−0.675477	+	0.675477i	0.283497	+	0.958973i	$0.408506\pi$
$710$	−1.24193	−	2.06794i	−0.0466087	−	0.0776083i
$711$			4.50462i			0.168936i
$712$	6.33243	+	2.36791i	0.237318	+	0.0887414i
$713$	−42.3991			−1.58786
$714$	−0.0745801	+	0.0586168i	−0.00279109	+	0.00219368i
$715$	−1.70423	+	1.32297i	−0.0637345	+	0.0494761i
$716$	−16.9598	−	27.8594i	−0.633819	−	1.04115i
$717$	0.427657	−	0.427657i	0.0159712	−	0.0159712i
$718$	43.3677	+	5.19752i	1.61847	+	0.193970i
$719$	−15.8716			−0.591912			−0.295956	−	0.955202i	$-0.595638\pi$
$719$	−15.8716			−0.591912			−0.295956	+	0.955202i	$0.595638\pi$
$720$	−26.3718	+	4.88057i	−0.982819	+	0.181888i
$721$	13.0843			0.487285
$722$	−20.9250	−	2.50782i	−0.778750	−	0.0933314i
$723$	0.385634	−	0.385634i	0.0143419	−	0.0143419i
$724$	21.7963	−	13.2689i	0.810054	−	0.493134i
$725$	−5.46234	+	3.23600i	−0.202866	+	0.120182i
$726$	0.468576	−	0.368281i	0.0173905	−	0.0136682i
$727$	43.0744			1.59754			0.798771	−	0.601635i	$-0.205484\pi$
$727$	43.0744			1.59754			0.798771	+	0.601635i	$0.205484\pi$
$728$	6.18454	+	13.5723i	0.229214	+	0.503024i
$729$		−	26.9203i		−	0.997048i
$730$	30.0830	−	18.0667i	1.11342	−	0.668680i
$731$	−7.01736	+	7.01736i	−0.259546	+	0.259546i
$732$	0.410117	+	0.0997358i	0.0151584	+	0.00368634i
$733$	26.9953	−	26.9953i	0.997095	−	0.997095i	−0.00290057	−	0.999996i	$-0.500923\pi$
$733$	26.9953	−	26.9953i	0.997095	−	0.997095i	0.999996	+	0.00290057i	$0.000923281\pi$
$734$	9.25383	+	1.10905i	0.341565	+	0.0409358i
$735$	0.0852544	+	0.0107374i	0.00314466	+	0.000396054i
$736$	−13.9307	+	20.5209i	−0.513493	+	0.756410i
$737$			1.89829i			0.0699245i
$738$	0.139263	−	1.16200i	0.00512633	−	0.0427736i
$739$	−9.04264	−	9.04264i	−0.332639	−	0.332639i	0.520949	−	0.853588i	$-0.325578\pi$
$739$	−9.04264	−	9.04264i	−0.332639	−	0.332639i	−0.853588	+	0.520949i	$0.825578\pi$
$740$	−12.3793	+	32.5090i	−0.455073	+	1.19505i
$741$	−0.290062	+	0.290062i	−0.0106557	+	0.0106557i
$742$	−7.66765	+	6.02644i	−0.281488	+	0.221238i
$743$	−25.0004			−0.917174			−0.458587	−	0.888649i	$-0.651644\pi$
$743$	−25.0004			−0.917174			−0.458587	+	0.888649i	$0.651644\pi$
$744$	0.435825	+	0.956442i	0.0159781	+	0.0350649i
$745$	−47.3390	−	5.96211i	−1.73437	−	0.218435i
$746$	7.61928	−	5.98842i	0.278962	−	0.219252i
$747$	−18.0618	−	18.0618i	−0.660846	−	0.660846i
$748$	−0.332137	−	0.545590i	−0.0121441	−	0.0199488i
$749$	−4.08369	−	4.08369i	−0.149215	−	0.149215i
$750$	0.534632	+	0.288702i	0.0195220	+	0.0105419i
$751$	−10.6715			−0.389408			−0.194704	−	0.980862i	$-0.562375\pi$
$751$	−10.6715			−0.389408			−0.194704	+	0.980862i	$0.562375\pi$
$752$	8.36661	−	16.1846i	0.305099	−	0.590191i
$753$			0.379327i			0.0138234i
$754$	−1.12682	+	9.40212i	−0.0410365	+	0.342405i
$755$	33.6357	−	26.1109i	1.22413	−	0.950274i
$756$	0.239728	+	0.393794i	0.00871883	+	0.0143221i
$757$	−21.7018	−	21.7018i	−0.788767	−	0.788767i	0.192525	−	0.981292i	$-0.438332\pi$
$757$	−21.7018	−	21.7018i	−0.788767	−	0.788767i	−0.981292	+	0.192525i	$0.938332\pi$
$758$	18.0497	+	22.9652i	0.655595	+	0.834135i
$759$			0.0308285i			0.00111900i
$760$	−11.3376	−	5.94755i	−0.411259	−	0.215740i
$761$			41.0678i			1.48871i	0.667787	+	0.744353i	$0.267242\pi$
$761$			41.0678i			1.48871i	−0.667787	+	0.744353i	$0.732758\pi$
$762$	−0.531912	+	0.418060i	−0.0192692	+	0.0151447i
$763$	−7.36243	−	7.36243i	−0.266538	−	0.266538i
$764$	32.8951	+	7.99970i	1.19010	+	0.289419i
$765$	−7.17646	−	9.24462i	−0.259466	−	0.334240i
$766$	11.7928	+	1.41334i	0.426092	+	0.0510661i
$767$			52.7365i			1.90420i
$768$	0.606108	+	0.103314i	0.0218710	+	0.00372803i
$769$	25.3146			0.912867			0.456433	−	0.889758i	$-0.349127\pi$
$769$	25.3146			0.912867			0.456433	+	0.889758i	$0.349127\pi$
$770$	−0.140099	+	0.561384i	−0.00504882	+	0.0202309i
$771$	−0.633476	−	0.633476i	−0.0228141	−	0.0228141i
$772$	−6.32564	+	26.0112i	−0.227665	+	0.936165i
$773$	24.9648	+	24.9648i	0.897922	+	0.897922i	0.995252	−	0.0973304i	$-0.0310304\pi$
$773$	24.9648	+	24.9648i	0.897922	+	0.897922i	−0.0973304	+	0.995252i	$0.531030\pi$
$774$	14.8986	+	18.9560i	0.535519	+	0.681359i
$775$	−11.9889	+	46.8408i	−0.430654	+	1.68257i
$776$	25.6311	+	9.58436i	0.920103	+	0.344058i
$777$	0.298911			0.0107234
$778$	−28.0179	−	35.6482i	−1.00449	−	1.27805i
$779$	0.395042	−	0.395042i	0.0141538	−	0.0141538i
$780$	0.826899	−	0.370814i	0.0296077	−	0.0132773i
$781$	−0.0986915	−	0.0986915i	−0.00353146	−	0.00353146i
$782$	−10.7462	−	1.28790i	−0.384282	−	0.0460553i
$783$			0.292701i			0.0104603i
$784$	3.55329	+	1.83687i	0.126903	+	0.0656027i
$785$	−26.9416	−	3.39317i	−0.961588	−	0.121107i
$786$	0.0451504	−	0.376731i	0.00161046	−	0.0134375i
$787$	−9.75332	+	9.75332i	−0.347668	+	0.347668i	−0.859240	−	0.511572i	$-0.829063\pi$
$787$	−9.75332	+	9.75332i	−0.347668	+	0.347668i	0.511572	+	0.859240i	$0.329063\pi$
$788$	−20.3382	−	33.4088i	−0.724517	−	1.19014i
$789$	−0.601298	+	0.601298i	−0.0214068	+	0.0214068i
$790$	4.07261	−	2.44586i	0.144897	−	0.0870199i
$791$		−	6.72734i		−	0.239197i
$792$	−1.41210	+	0.643454i	−0.0501766	+	0.0228641i
$793$	28.9590			1.02836
$794$	9.57116	+	12.1777i	0.339668	+	0.432171i
$795$	0.363363	+	0.468079i	0.0128871	+	0.0166010i
$796$	−7.96687	+	32.7601i	−0.282378	+	1.16115i
$797$	−9.64269	+	9.64269i	−0.341561	+	0.341561i	−0.856954	−	0.515393i	$-0.827646\pi$
$797$	−9.64269	+	9.64269i	−0.341561	+	0.341561i	0.515393	+	0.856954i	$0.327646\pi$
$798$	−0.0130911	+	0.109231i	−0.000463420	+	0.00386674i
$799$	7.95027			0.281260
$800$	18.7315	+	21.1927i	0.662260	+	0.749274i
$801$	7.16724			0.253242
$802$	−1.43758	+	11.9950i	−0.0507626	+	0.423559i
$803$	1.43570	−	1.43570i	0.0506647	−	0.0506647i
$804$	0.188421	−	0.774793i	0.00664509	−	0.0273248i
$805$	6.01194	+	7.74449i	0.211893	+	0.272958i
$806$	44.5627	+	56.6986i	1.56965	+	1.99712i
$807$	0.898666			0.0316346
$808$	−5.39719	−	11.8444i	−0.189872	−	0.416686i
$809$		−	7.49404i		−	0.263477i	−0.991285	−	0.131738i	$-0.957944\pi$
$809$		−	7.49404i		−	0.263477i	0.991285	−	0.131738i	$-0.0420558\pi$
$810$	−24.3626	+	14.6313i	−0.856014	+	0.514091i
$811$	34.2145	−	34.2145i	1.20143	−	1.20143i	0.227702	−	0.973731i	$-0.426879\pi$
$811$	34.2145	−	34.2145i	1.20143	−	1.20143i	0.973731	−	0.227702i	$-0.0731212\pi$
$812$	1.32055	+	2.16923i	0.0463424	+	0.0761250i
$813$	−0.166741	+	0.166741i	−0.00584786	+	0.00584786i
$814$	−0.239508	+	1.99844i	−0.00839476	+	0.0700452i
$815$	12.2064	+	1.53733i	0.427571	+	0.0538505i
$816$	0.0814084	+	0.255651i	0.00284986	+	0.00894959i
$817$			11.5095i			0.402666i
$818$	11.1535	+	1.33672i	0.389972	+	0.0467373i
$819$	11.1807	+	11.1807i	0.390686	+	0.390686i
$820$	−1.12617	+	0.505019i	−0.0393276	+	0.0176360i
$821$	10.5755	−	10.5755i	0.369086	−	0.369086i	−0.498058	−	0.867144i	$-0.665953\pi$
$821$	10.5755	−	10.5755i	0.369086	−	0.369086i	0.867144	+	0.498058i	$0.165953\pi$
$822$	−0.628390	−	0.799522i	−0.0219176	−	0.0278865i
$823$	−25.9368			−0.904099			−0.452049	−	0.891993i	$-0.649307\pi$
$823$	−25.9368			−0.904099			−0.452049	+	0.891993i	$0.649307\pi$
$824$	12.9620	−	34.6638i	0.451553	−	1.20757i
$825$	0.0340581	+	0.00871717i	0.00118575	+	0.000303493i
$826$	8.73966	+	11.1198i	0.304092	+	0.386906i
$827$	−0.822468	−	0.822468i	−0.0286000	−	0.0286000i	0.692662	−	0.721262i	$-0.256438\pi$
$827$	−0.822468	−	0.822468i	−0.0286000	−	0.0286000i	−0.721262	+	0.692662i	$0.756438\pi$
$828$	−6.21337	+	25.5496i	−0.215929	+	0.887909i
$829$	25.3332	+	25.3332i	0.879858	+	0.879858i	0.993520	−	0.113662i	$-0.0362580\pi$
$829$	25.3332	+	25.3332i	0.879858	+	0.879858i	−0.113662	+	0.993520i	$0.536258\pi$
$830$	−6.52263	+	26.1366i	−0.226404	+	0.907213i
$831$	−0.0293226			−0.00101719
$832$	42.0834	−	2.93904i	1.45898	−	0.101893i
$833$			1.74547i			0.0604769i
$834$	−0.558038	−	0.0668796i	−0.0193233	−	0.00231585i
$835$	16.1444	+	20.7969i	0.558698	+	0.719707i
$836$	−0.719801	−	0.175047i	−0.0248948	−	0.00605414i
$837$	1.57620	+	1.57620i	0.0544814	+	0.0544814i
$838$	−21.4981	+	16.8966i	−0.742641	+	0.583684i
$839$		−	19.4127i		−	0.670199i	−0.942183	−	0.335100i	$-0.891230\pi$
$839$		−	19.4127i		−	0.670199i	0.942183	−	0.335100i	$-0.108770\pi$
$840$	0.112904	−	0.215224i	0.00389555	−	0.00742595i
$841$		−	27.3876i		−	0.944402i
$842$	7.79500	+	9.91784i	0.268633	+	0.341791i
$843$	0.0386912	+	0.0386912i	0.00133259	+	0.00133259i
$844$	5.79499	+	9.51924i	0.199472	+	0.327666i
$845$	26.1540	−	20.3030i	0.899726	−	0.698444i
$846$	2.29840	−	19.1777i	0.0790206	−	0.659342i
$847$		−	10.9665i		−	0.376814i
$848$	8.36967	+	26.2837i	0.287416	+	0.902587i
$849$	0.187015			0.00641833
$850$	−4.46144	+	11.5077i	−0.153026	+	0.394713i
$851$	24.1157	+	24.1157i	0.826677	+	0.826677i
$852$	0.0304853	+	0.0500771i	0.00104441	+	0.00171561i
$853$	18.5604	+	18.5604i	0.635495	+	0.635495i	0.949441	−	0.313946i	$-0.101651\pi$
$853$	18.5604	+	18.5604i	0.635495	+	0.635495i	−0.313946	+	0.949441i	$0.601651\pi$
$854$	6.10616	−	4.79918i	0.208948	−	0.164225i
$855$	−13.4665	−	1.69604i	−0.460544	−	0.0580033i
$856$	−14.8643	+	6.77327i	−0.508052	+	0.231506i
$857$	−29.1511			−0.995783			−0.497892	−	0.867239i	$-0.665892\pi$
$857$	−29.1511			−0.995783			−0.497892	+	0.867239i	$0.665892\pi$
$858$	0.0412258	−	0.0324017i	0.00140742	−	0.00110618i
$859$	31.7734	−	31.7734i	1.08409	−	1.08409i	0.0879710	−	0.996123i	$-0.471962\pi$
$859$	31.7734	−	31.7734i	1.08409	−	1.08409i	0.996123	−	0.0879710i	$-0.0280383\pi$
$860$	9.04860	−	23.7623i	0.308555	−	0.810287i
$861$	0.00749917	+	0.00749917i	0.000255571	+	0.000255571i
$862$	3.71085	−	30.9631i	0.126392	−	1.05461i
$863$			52.8089i			1.79764i	0.438323	+	0.898818i	$0.355573\pi$
$863$			52.8089i			1.79764i	−0.438323	+	0.898818i	$0.644427\pi$
$864$	1.28075	−	0.244991i	0.0435720	−	0.00833477i
$865$	0.784259	+	0.0987736i	0.0266656	+	0.00335840i
$866$	9.23149	+	1.10637i	0.313699	+	0.0375961i
$867$	0.379151	−	0.379151i	0.0128766	−	0.0128766i
$868$	18.7926	+	4.57014i	0.637861	+	0.155121i
$869$	0.194364	−	0.194364i	0.00659334	−	0.00659334i
$870$	0.132282	−	0.0794440i	0.00448479	−	0.00269340i
$871$		−	54.7093i		−	1.85375i
$872$	−26.7986	+	12.2114i	−0.907517	+	0.413531i
$873$	29.0101			0.981843
$874$	−9.86881	+	7.75646i	−0.333817	+	0.262366i
$875$	10.2558	−	4.45189i	0.346708	−	0.150501i
$876$	−0.728488	+	0.443479i	−0.0246133	+	0.0149838i
$877$	31.4657	−	31.4657i	1.06252	−	1.06252i	0.0646098	−	0.997911i	$-0.479420\pi$
$877$	31.4657	−	31.4657i	1.06252	−	1.06252i	0.997911	−	0.0646098i	$-0.0205803\pi$
$878$	−44.2445	−	5.30260i	−1.49318	−	0.178954i
$879$	0.340582			0.0114876
$880$	1.34847	+	0.927296i	0.0454568	+	0.0312592i
$881$	−4.25662			−0.143409			−0.0717045	−	0.997426i	$-0.522844\pi$
$881$	−4.25662			−0.143409			−0.0717045	+	0.997426i	$0.522844\pi$
$882$	4.21042	+	0.504610i	0.141772	+	0.0169911i
$883$	14.7583	−	14.7583i	0.496658	−	0.496658i	−0.413738	−	0.910396i	$-0.635777\pi$
$883$	14.7583	−	14.7583i	0.496658	−	0.496658i	0.910396	+	0.413738i	$0.135777\pi$
$884$	9.57227	+	15.7240i	0.321950	+	0.528857i
$885$	0.678816	−	0.526955i	0.0228182	−	0.0177134i
$886$	−17.1638	+	13.4900i	−0.576629	+	0.453205i
$887$	19.1016			0.641368			0.320684	−	0.947186i	$-0.396087\pi$
$887$	19.1016			0.641368			0.320684	+	0.947186i	$0.396087\pi$
$888$	0.296117	−	0.791894i	0.00993702	−	0.0265742i
$889$			12.4488i			0.417521i
$890$	−3.89158	−	6.47988i	−0.130446	−	0.217206i
$891$	−1.16269	+	1.16269i	−0.0389517	+	0.0389517i
$892$	−12.4765	+	51.3038i	−0.417744	+	1.71778i
$893$	6.51980	−	6.51980i	0.218177	−	0.218177i
$894$	1.15138	+	0.137990i	0.0385079	+	0.00461509i
$895$	−4.55664	+	36.1796i	−0.152312	+	1.20935i
$896$	8.38645	−	7.59391i	0.280172	−	0.253695i
$897$		−	0.888484i		−	0.0296656i
$898$	−0.213374	+	1.78037i	−0.00712037	+	0.0594118i
$899$	8.68257	+	8.68257i	0.289580	+	0.289580i
$900$	26.4692	+	14.0888i	0.882308	+	0.469626i
$901$	−8.51131	+	8.51131i	−0.283553	+	0.283553i
$902$	−0.0561463	+	0.0441286i	−0.00186947	+	0.00146932i
$903$	−0.218487			−0.00727080
$904$	−17.8225	−	6.66446i	−0.592768	−	0.221657i
$905$	−28.3058	−	3.56498i	−0.940918	−	0.118504i
$906$	−0.813659	+	0.639501i	−0.0270320	+	0.0212460i
$907$	−23.1102	−	23.1102i	−0.767360	−	0.767360i	0.210281	−	0.977641i	$-0.432562\pi$
$907$	−23.1102	−	23.1102i	−0.767360	−	0.767360i	−0.977641	+	0.210281i	$0.932562\pi$
$908$	−38.6138	+	23.5068i	−1.28144	+	0.780099i
$909$	−9.75731	−	9.75731i	−0.323629	−	0.323629i
$910$	4.03769	−	16.1792i	0.133848	−	0.536336i
$911$	39.4577			1.30729			0.653646	−	0.756800i	$-0.273239\pi$
$911$	39.4577			1.30729			0.653646	+	0.756800i	$0.273239\pi$
$912$	0.276414	+	0.142892i	0.00915297	+	0.00473163i
$913$			1.55865i			0.0515837i
$914$	−1.46011	+	12.1830i	−0.0482961	+	0.402979i
$915$	−0.289365	−	0.372756i	−0.00956612	−	0.0123229i
$916$	−45.9044	+	27.9450i	−1.51672	+	0.923330i
$917$	−4.93684	−	4.93684i	−0.163029	−	0.163029i
$918$	0.351614	+	0.447370i	0.0116050	+	0.0147654i
$919$			41.6623i			1.37431i	0.726510	+	0.687156i	$0.241141\pi$
$919$			41.6623i			1.37431i	−0.726510	+	0.687156i	$0.758859\pi$
$920$	26.4730	−	8.25512i	0.872788	−	0.272163i
$921$		−	1.12186i		−	0.0369664i
$922$	−41.7204	+	32.7904i	−1.37399	+	1.07989i
$923$	2.84431	+	2.84431i	0.0936217	+	0.0936217i
$924$	0.00332296	−	0.0136641i	0.000109317	−	0.000449517i
$925$	33.4612	−	19.8231i	1.10020	−	0.651778i
$926$	1.71960	+	0.206090i	0.0565095	+	0.00677254i
$927$		−	39.2336i		−	1.28860i
$928$	7.05507	−	1.34955i	0.231594	−	0.0443010i
$929$	−14.1648			−0.464732			−0.232366	−	0.972628i	$-0.574647\pi$
$929$	−14.1648			−0.464732			−0.232366	+	0.972628i	$0.574647\pi$
$930$	0.284536	−	1.14015i	0.00933030	−	0.0373870i
$931$	1.43141	+	1.43141i	0.0469126	+	0.0469126i
$932$	−54.7080	−	13.3044i	−1.79202	−	0.435799i
$933$	0.0612879	+	0.0612879i	0.00200648	+	0.00200648i
$934$	22.9897	+	29.2505i	0.752245	+	0.957107i
$935$	−0.0892361	+	0.708532i	−0.00291833	+	0.0231715i
$936$	40.6969	−	18.5445i	1.33022	−	0.606146i
$937$	38.7680			1.26650			0.633248	−	0.773949i	$-0.281722\pi$
$937$	38.7680			1.26650			0.633248	+	0.773949i	$0.281722\pi$
$938$	−9.06660	−	11.5357i	−0.296035	−	0.376655i
$939$	0.793482	−	0.793482i	0.0258943	−	0.0258943i
$940$	−18.5864	+	8.33488i	−0.606223	+	0.271854i
$941$	−24.2309	−	24.2309i	−0.789904	−	0.789904i	0.191574	−	0.981478i	$-0.438641\pi$
$941$	−24.2309	−	24.2309i	−0.789904	−	0.789904i	−0.981478	+	0.191574i	$0.938641\pi$
$942$	0.655275	+	0.0785332i	0.0213500	+	0.00255875i
$943$			1.21005i			0.0394045i
$944$	38.1172	−	12.1378i	1.24061	−	0.395053i
$945$	0.0644084	−	0.511400i	0.00209520	−	0.0166359i
$946$	0.175067	−	1.46075i	0.00569193	−	0.0474930i
$947$	11.2552	−	11.2552i	0.365745	−	0.365745i	−0.500178	−	0.865923i	$-0.666732\pi$
$947$	11.2552	−	11.2552i	0.365745	−	0.365745i	0.865923	+	0.500178i	$0.166732\pi$
$948$	−0.0986222	+	0.0600379i	−0.00320310	+	0.00194994i
$949$	−41.3772	+	41.3772i	−1.34316	+	1.34316i
$950$	5.77849	+	13.0959i	0.187479	+	0.424887i
$951$			0.512419i			0.0166163i
$952$	4.62421	+	1.72915i	0.149871	+	0.0560421i
$953$	−33.7855			−1.09442			−0.547210	−	0.836996i	$-0.684310\pi$
$953$	−33.7855			−1.09442			−0.547210	+	0.836996i	$0.684310\pi$
$954$	18.0704	+	22.9916i	0.585052	+	0.744381i
$955$	−23.2097	−	29.8984i	−0.751047	−	0.967488i
$956$	−30.5855	−	7.43803i	−0.989204	−	0.240563i
$957$	0.00631312	−	0.00631312i	0.000204074	−	0.000204074i
$958$	4.03812	−	33.6937i	0.130466	−	1.08860i
$959$	−18.7120			−0.604241
$960$	−0.458338	−	0.512324i	−0.0147928	−	0.0165352i
$961$	62.5117			2.01651
$962$	6.90268	−	57.5954i	0.222551	−	1.85695i
$963$	−12.2451	+	12.2451i	−0.394591	+	0.394591i
$964$	−27.5800	−	6.70714i	−0.888292	−	0.216022i
$965$	23.6416	−	18.3527i	0.761051	−	0.590793i
$966$	−0.147243	−	0.187342i	−0.00473745	−	0.00602762i
$967$	49.1382			1.58018			0.790089	−	0.612993i	$-0.210034\pi$
$967$	49.1382			1.58018			0.790089	+	0.612993i	$0.210034\pi$
$968$	−29.0532	−	10.8640i	−0.933806	−	0.349183i
$969$			0.135781i			0.00436193i
$970$	−15.7515	−	26.2279i	−0.505752	−	0.842128i
$971$	−5.83095	+	5.83095i	−0.187124	+	0.187124i	−0.794452	−	0.607328i	$-0.792242\pi$
$971$	−5.83095	+	5.83095i	−0.187124	+	0.187124i	0.607328	+	0.794452i	$0.292242\pi$
$972$	1.77134	−	1.07833i	0.0568159	−	0.0345876i
$973$	−7.31276	+	7.31276i	−0.234436	+	0.234436i
$974$	−2.76000	+	23.0293i	−0.0884362	+	0.737905i
$975$	−0.981562	−	0.251231i	−0.0314351	−	0.00804583i
$976$	−6.66522	−	20.9312i	−0.213348	−	0.669990i
$977$		−	16.1183i		−	0.515670i	−0.966189	−	0.257835i	$-0.916991\pi$
$977$		−	16.1183i		−	0.515670i	0.966189	−	0.257835i	$-0.0830091\pi$
$978$	−0.296884	−	0.0355809i	−0.00949330	−	0.00113775i
$979$	−0.309250	−	0.309250i	−0.00988367	−	0.00988367i
$980$	−1.82991	−	4.08062i	−0.0584543	−	0.130351i
$981$	−22.0764	+	22.0764i	−0.704846	+	0.704846i
$982$	38.3506	+	48.7948i	1.22382	+	1.55710i
$983$	34.4978			1.10031			0.550155	−	0.835063i	$-0.314569\pi$
$983$	34.4978			1.10031			0.550155	+	0.835063i	$0.314569\pi$
$984$	0.0272963	−	0.0124382i	0.000870176	−	0.000396516i
$985$	−5.46430	+	43.3864i	−0.174107	+	1.38240i
$986$	1.93688	+	2.46436i	0.0616829	+	0.0784812i
$987$	0.123767	+	0.123767i	0.00393954	+	0.00393954i
$988$	20.7448	+	5.04491i	0.659981	+	0.160500i
$989$	−17.6273	−	17.6273i	−0.560515	−	0.560515i
$990$	1.68332	+	0.420090i	0.0534996	+	0.0133513i
$991$	25.1516			0.798967			0.399484	−	0.916740i	$-0.369189\pi$
$991$	25.1516			0.798967			0.399484	+	0.916740i	$0.369189\pi$
$992$	30.7244	−	45.2591i	0.975501	−	1.43698i
$993$			0.831504i			0.0263870i
$994$	1.07111	+	0.128370i	0.0339735	+	0.00407164i
$995$	29.7757	−	23.1144i	0.943952	−	0.732776i
$996$	0.154708	−	0.636166i	0.00490212	−	0.0201577i
$997$	−19.7693	−	19.7693i	−0.626101	−	0.626101i	0.320984	−	0.947085i	$-0.395987\pi$
$997$	−19.7693	−	19.7693i	−0.626101	−	0.626101i	−0.947085	+	0.320984i	$0.895987\pi$
$998$	−19.9305	+	15.6645i	−0.630889	+	0.495851i
$999$		−	1.79302i		−	0.0567287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.c.29.18	✓	70
5.4	even	2		560.2.bb.d.29.18	yes	70
16.5	even	4		560.2.bb.d.309.18	yes	70
80.69	even	4	inner	560.2.bb.c.309.18	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.18	✓	70	1.1	even	1	trivial
560.2.bb.c.309.18	yes	70	80.69	even	4	inner
560.2.bb.d.29.18	yes	70	5.4	even	2
560.2.bb.d.309.18	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)

\(f(q)\)	\(=\)	\(q+(0.168286 - 1.40417i) q^{2} +(0.0271728 - 0.0271728i) q^{3} +(-1.94336 - 0.472603i) q^{4} +(1.37117 + 1.76632i) q^{5} +(-0.0335823 - 0.0427279i) q^{6} -1.00000 q^{7} +(-0.990653 + 2.64927i) q^{8} +2.99852i q^{9} +O(q^{10})\)	\(q+(0.168286 - 1.40417i) q^{2} +(0.0271728 - 0.0271728i) q^{3} +(-1.94336 - 0.472603i) q^{4} +(1.37117 + 1.76632i) q^{5} +(-0.0335823 - 0.0427279i) q^{6} -1.00000 q^{7} +(-0.990653 + 2.64927i) q^{8} +2.99852i q^{9} +(2.71096 - 1.62810i) q^{10} +(0.129379 - 0.129379i) q^{11} +(-0.0656484 + 0.0399646i) q^{12} +(-3.72874 + 3.72874i) q^{13} +(-0.168286 + 1.40417i) q^{14} +(0.0852544 + 0.0107374i) q^{15} +(3.55329 + 1.83687i) q^{16} +1.74547i q^{17} +(4.21042 + 0.504610i) q^{18} +(1.43141 + 1.43141i) q^{19} +(-1.82991 - 4.08062i) q^{20} +(-0.0271728 + 0.0271728i) q^{21} +(-0.159897 - 0.203443i) q^{22} -4.38453 q^{23} +(0.0450691 + 0.0989067i) q^{24} +(-1.23979 + 4.84386i) q^{25} +(4.60828 + 5.86327i) q^{26} +(0.162997 + 0.162997i) q^{27} +(1.94336 + 0.472603i) q^{28} +(0.897874 + 0.897874i) q^{29} +(0.0294242 - 0.117904i) q^{30} +9.67014 q^{31} +(3.17724 - 4.68029i) q^{32} -0.00703119i q^{33} +(2.45092 + 0.293738i) q^{34} +(-1.37117 - 1.76632i) q^{35} +(1.41711 - 5.82721i) q^{36} +(-5.50019 - 5.50019i) q^{37} +(2.25082 - 1.76905i) q^{38} +0.202641i q^{39} +(-6.03781 + 1.88278i) q^{40} -0.275981i q^{41} +(0.0335823 + 0.0427279i) q^{42} +(4.02033 + 4.02033i) q^{43} +(-0.312576 + 0.190286i) q^{44} +(-5.29636 + 4.11149i) q^{45} +(-0.737855 + 6.15661i) q^{46} -4.55481i q^{47} +(0.146466 - 0.0466399i) q^{48} +1.00000 q^{49} +(6.59293 + 2.55602i) q^{50} +(0.0474292 + 0.0474292i) q^{51} +(9.00851 - 5.48408i) q^{52} +(4.87624 + 4.87624i) q^{53} +(0.256304 - 0.201444i) q^{54} +(0.405927 + 0.0511245i) q^{55} +(0.990653 - 2.64927i) q^{56} +0.0777908 q^{57} +(1.41186 - 1.10966i) q^{58} +(7.07161 - 7.07161i) q^{59} +(-0.160605 - 0.0611580i) q^{60} +(-3.88321 - 3.88321i) q^{61} +(1.62735 - 13.5785i) q^{62} -2.99852i q^{63} +(-6.03721 - 5.24900i) q^{64} +(-11.6989 - 1.47342i) q^{65} +(-0.00987296 - 0.00118325i) q^{66} +(-7.33615 + 7.33615i) q^{67} +(0.824913 - 3.39207i) q^{68} +(-0.119140 + 0.119140i) q^{69} +(-2.71096 + 1.62810i) q^{70} -0.762807i q^{71} +(-7.94388 - 2.97050i) q^{72} +11.0968 q^{73} +(-8.64877 + 6.79756i) q^{74} +(0.0979326 + 0.165309i) q^{75} +(-2.10526 - 3.45824i) q^{76} +(-0.129379 + 0.129379i) q^{77} +(0.284541 + 0.0341016i) q^{78} +1.50228 q^{79} +(1.62766 + 8.79493i) q^{80} -8.98671 q^{81} +(-0.387523 - 0.0464437i) q^{82} +(-6.02356 + 6.02356i) q^{83} +(0.0656484 - 0.0399646i) q^{84} +(-3.08306 + 2.39333i) q^{85} +(6.32178 - 4.96865i) q^{86} +0.0487954 q^{87} +(0.214590 + 0.470930i) q^{88} -2.39026i q^{89} +(4.88190 + 8.12887i) q^{90} +(3.72874 - 3.72874i) q^{91} +(8.52072 + 2.07214i) q^{92} +(0.262765 - 0.262765i) q^{93} +(-6.39570 - 0.766511i) q^{94} +(-0.565625 + 4.49104i) q^{95} +(-0.0408419 - 0.213511i) q^{96} -9.67479i q^{97} +(0.168286 - 1.40417i) q^{98} +(0.387947 + 0.387947i) 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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