LMFDB - Embedded newform 273.2.e.a.209.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (of order $2$, degree $1$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.20
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.633614i q^{2} +(0.915380 + 1.47040i) q^{3} +1.59853 q^{4} -0.119728 q^{5} +(-0.931666 + 0.579998i) q^{6} +(2.16525 - 1.52042i) q^{7} +2.28008i q^{8} +(-1.32416 + 2.69195i) q^{9} +O(q^{10})$	\(q+0.633614i q^{2} +(0.915380 + 1.47040i) q^{3} +1.59853 q^{4} -0.119728 q^{5} +(-0.931666 + 0.579998i) q^{6} +(2.16525 - 1.52042i) q^{7} +2.28008i q^{8} +(-1.32416 + 2.69195i) q^{9} -0.0758615i q^{10} -4.57300i q^{11} +(1.46327 + 2.35048i) q^{12} +1.00000i q^{13} +(0.963362 + 1.37193i) q^{14} +(-0.109597 - 0.176049i) q^{15} +1.75238 q^{16} -6.89311 q^{17} +(-1.70566 - 0.839004i) q^{18} -0.125642i q^{19} -0.191390 q^{20} +(4.21766 + 1.79202i) q^{21} +2.89752 q^{22} -1.84119i q^{23} +(-3.35263 + 2.08714i) q^{24} -4.98567 q^{25} -0.633614 q^{26} +(-5.17036 + 0.517119i) q^{27} +(3.46123 - 2.43045i) q^{28} +3.43711i q^{29} +(0.111547 - 0.0694421i) q^{30} +0.162714i q^{31} +5.67049i q^{32} +(6.72414 - 4.18603i) q^{33} -4.36757i q^{34} +(-0.259242 + 0.182038i) q^{35} +(-2.11671 + 4.30318i) q^{36} -6.26753 q^{37} +0.0796088 q^{38} +(-1.47040 + 0.915380i) q^{39} -0.272990i q^{40} +7.36363 q^{41} +(-1.13545 + 2.67237i) q^{42} +1.26263 q^{43} -7.31009i q^{44} +(0.158539 - 0.322303i) q^{45} +1.16661 q^{46} +2.57710 q^{47} +(1.60409 + 2.57670i) q^{48} +(2.37662 - 6.58420i) q^{49} -3.15899i q^{50} +(-6.30982 - 10.1356i) q^{51} +1.59853i q^{52} -6.10594i q^{53} +(-0.327654 - 3.27601i) q^{54} +0.547517i q^{55} +(3.46669 + 4.93695i) q^{56} +(0.184745 - 0.115011i) q^{57} -2.17780 q^{58} +7.02785 q^{59} +(-0.175194 - 0.281419i) q^{60} -2.09585i q^{61} -0.103098 q^{62} +(1.22578 + 7.84203i) q^{63} -0.0881493 q^{64} -0.119728i q^{65} +(2.65233 + 4.26051i) q^{66} -1.47781 q^{67} -11.0189 q^{68} +(2.70729 - 1.68539i) q^{69} +(-0.115342 - 0.164259i) q^{70} +5.86634i q^{71} +(-6.13787 - 3.01919i) q^{72} -15.5912i q^{73} -3.97119i q^{74} +(-4.56378 - 7.33093i) q^{75} -0.200844i q^{76} +(-6.95290 - 9.90169i) q^{77} +(-0.579998 - 0.931666i) q^{78} -9.95186 q^{79} -0.209809 q^{80} +(-5.49322 - 7.12914i) q^{81} +4.66570i q^{82} -7.28990 q^{83} +(6.74207 + 2.86460i) q^{84} +0.825301 q^{85} +0.800020i q^{86} +(-5.05393 + 3.14626i) q^{87} +10.4268 q^{88} +16.8866 q^{89} +(0.204216 + 0.100453i) q^{90} +(1.52042 + 2.16525i) q^{91} -2.94321i q^{92} +(-0.239255 + 0.148945i) q^{93} +1.63289i q^{94} +0.0150430i q^{95} +(-8.33790 + 5.19066i) q^{96} +5.75147i q^{97} +(4.17184 + 1.50586i) q^{98} +(12.3103 + 6.05537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$			0.633614i			0.448033i	0.974585	+	0.224016i	$0.0719169\pi$
$2$			0.633614i			0.448033i	−0.974585	+	0.224016i	$0.928083\pi$
$3$	0.915380	+	1.47040i	0.528495	+	0.848936i
$3$	0.915380	+	1.47040i	0.528495	+	0.848936i
$4$	1.59853			0.799267
$5$	−0.119728			−0.0535441			−0.0267721	−	0.999642i	$-0.508523\pi$
$5$	−0.119728			−0.0535441			−0.0267721	+	0.999642i	$0.508523\pi$
$6$	−0.931666	+	0.579998i	−0.380351	+	0.236783i
$7$	2.16525	−	1.52042i	0.818388	−	0.574666i
$7$	2.16525	−	1.52042i	0.818388	−	0.574666i
$8$			2.28008i			0.806130i
$9$	−1.32416	+	2.69195i	−0.441386	+	0.897317i
$10$		−	0.0758615i		−	0.0239895i
$11$		−	4.57300i		−	1.37881i	−0.724376	−	0.689406i	$-0.757872\pi$
$11$		−	4.57300i		−	1.37881i	0.724376	−	0.689406i	$-0.242128\pi$
$12$	1.46327	+	2.35048i	0.422409	+	0.678527i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.963362	+	1.37193i	0.257469	+	0.366664i
$15$	−0.109597	−	0.176049i	−0.0282978	−	0.0454555i
$16$	1.75238			0.438094
$17$	−6.89311			−1.67183			−0.835913	−	0.548862i	$-0.815061\pi$
$17$	−6.89311			−1.67183			−0.835913	+	0.548862i	$0.815061\pi$
$18$	−1.70566	−	0.839004i	−0.402028	−	0.197755i
$19$		−	0.125642i		−	0.0288244i	−0.999896	−	0.0144122i	$-0.995412\pi$
$19$		−	0.125642i		−	0.0288244i	0.999896	−	0.0144122i	$-0.00458770\pi$
$20$	−0.191390			−0.0427960
$21$	4.21766	+	1.79202i	0.920369	+	0.391051i
$22$	2.89752			0.617752
$23$		−	1.84119i		−	0.383916i	−0.981403	−	0.191958i	$-0.938516\pi$
$23$		−	1.84119i		−	0.383916i	0.981403	−	0.191958i	$-0.0614837\pi$
$24$	−3.35263	+	2.08714i	−0.684353	+	0.426036i
$25$	−4.98567			−0.997133
$26$	−0.633614			−0.124262
$27$	−5.17036	+	0.517119i	−0.995036	+	0.0995195i
$28$	3.46123	−	2.43045i	0.654110	−	0.459312i
$29$			3.43711i			0.638255i	0.947712	+	0.319127i	$0.103390\pi$
$29$			3.43711i			0.638255i	−0.947712	+	0.319127i	$0.896610\pi$
$30$	0.111547	−	0.0694421i	0.0203656	−	0.0126783i
$31$			0.162714i			0.0292243i	0.999893	+	0.0146121i	$0.00465135\pi$
$31$			0.162714i			0.0292243i	−0.999893	+	0.0146121i	$0.995349\pi$
$32$			5.67049i			1.00241i
$33$	6.72414	−	4.18603i	1.17052	−	0.728695i
$34$		−	4.36757i		−	0.749033i
$35$	−0.259242	+	0.182038i	−0.0438198	+	0.0307700i
$36$	−2.11671	+	4.30318i	−0.352785	+	0.717196i
$37$	−6.26753			−1.03037			−0.515187	−	0.857078i	$-0.672278\pi$
$37$	−6.26753			−1.03037			−0.515187	+	0.857078i	$0.672278\pi$
$38$	0.0796088			0.0129143
$39$	−1.47040	+	0.915380i	−0.235453	+	0.146578i
$40$		−	0.272990i		−	0.0431635i
$41$	7.36363			1.15001			0.575003	−	0.818151i	$-0.305001\pi$
$41$	7.36363			1.15001			0.575003	+	0.818151i	$0.305001\pi$
$42$	−1.13545	+	2.67237i	−0.175204	+	0.412355i
$43$	1.26263			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$43$	1.26263			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$44$		−	7.31009i		−	1.10204i
$45$	0.158539	−	0.322303i	0.0236336	−	0.0480461i
$46$	1.16661			0.172007
$47$	2.57710			0.375909			0.187954	−	0.982178i	$-0.439814\pi$
$47$	2.57710			0.375909			0.187954	+	0.982178i	$0.439814\pi$
$48$	1.60409	+	2.57670i	0.231531	+	0.371914i
$49$	2.37662	−	6.58420i	0.339517	−	0.940600i
$50$		−	3.15899i		−	0.446748i
$51$	−6.30982	−	10.1356i	−0.883552	−	1.41927i
$52$			1.59853i			0.221677i
$53$		−	6.10594i		−	0.838715i	−0.907821	−	0.419357i	$-0.862255\pi$
$53$		−	6.10594i		−	0.838715i	0.907821	−	0.419357i	$-0.137745\pi$
$54$	−0.327654	−	3.27601i	−0.0445880	−	0.445808i
$55$			0.547517i			0.0738272i
$56$	3.46669	+	4.93695i	0.463256	+	0.659727i
$57$	0.184745	−	0.115011i	0.0244700	−	0.0152335i
$58$	−2.17780			−0.285959
$59$	7.02785			0.914948			0.457474	−	0.889223i	$-0.348754\pi$
$59$	7.02785			0.914948			0.457474	+	0.889223i	$0.348754\pi$
$60$	−0.175194	−	0.281419i	−0.0226175	−	0.0363311i
$61$		−	2.09585i		−	0.268346i	−0.990958	−	0.134173i	$-0.957162\pi$
$61$		−	2.09585i		−	0.268346i	0.990958	−	0.134173i	$-0.0428379\pi$
$62$	−0.103098			−0.0130934
$63$	1.22578	+	7.84203i	0.154433	+	0.988003i
$64$	−0.0881493			−0.0110187
$65$		−	0.119728i		−	0.0148505i
$66$	2.65233	+	4.26051i	0.326479	+	0.524432i
$67$	−1.47781			−0.180543			−0.0902715	−	0.995917i	$-0.528773\pi$
$67$	−1.47781			−0.180543			−0.0902715	+	0.995917i	$0.528773\pi$
$68$	−11.0189			−1.33623
$69$	2.70729	−	1.68539i	0.325920	−	0.202897i
$70$	−0.115342	−	0.164259i	−0.0137860	−	0.0196327i
$71$			5.86634i			0.696206i	0.937456	+	0.348103i	$0.113174\pi$
$71$			5.86634i			0.696206i	−0.937456	+	0.348103i	$0.886826\pi$
$72$	−6.13787	−	3.01919i	−0.723355	−	0.355814i
$73$		−	15.5912i		−	1.82481i	−0.409284	−	0.912407i	$-0.634222\pi$
$73$		−	15.5912i		−	1.82481i	0.409284	−	0.912407i	$-0.365778\pi$
$74$		−	3.97119i		−	0.461642i
$75$	−4.56378	−	7.33093i	−0.526980	−	0.846502i
$76$		−	0.200844i		−	0.0230383i
$77$	−6.95290	−	9.90169i	−0.792356	−	1.12840i
$78$	−0.579998	−	0.931666i	−0.0656718	−	0.105490i
$79$	−9.95186			−1.11967			−0.559836	−	0.828604i	$-0.689136\pi$
$79$	−9.95186			−1.11967			−0.559836	+	0.828604i	$0.689136\pi$
$80$	−0.209809			−0.0234574
$81$	−5.49322	−	7.12914i	−0.610357	−	0.792126i
$82$			4.66570i			0.515240i
$83$	−7.28990			−0.800171			−0.400085	−	0.916478i	$-0.631020\pi$
$83$	−7.28990			−0.800171			−0.400085	+	0.916478i	$0.631020\pi$
$84$	6.74207	+	2.86460i	0.735620	+	0.312554i
$85$	0.825301			0.0895164
$86$			0.800020i			0.0862684i
$87$	−5.05393	+	3.14626i	−0.541838	+	0.337315i
$88$	10.4268			1.11150
$89$	16.8866			1.78998			0.894989	−	0.446088i	$-0.147183\pi$
$89$	16.8866			1.78998			0.894989	+	0.446088i	$0.147183\pi$
$90$	0.204216	+	0.100453i	0.0215262	+	0.0105886i
$91$	1.52042	+	2.16525i	0.159384	+	0.226980i
$92$		−	2.94321i		−	0.306851i
$93$	−0.239255	+	0.148945i	−0.0248096	+	0.0154449i
$94$			1.63289i			0.168419i
$95$			0.0150430i			0.00154337i
$96$	−8.33790	+	5.19066i	−0.850983	+	0.529769i
$97$			5.75147i			0.583973i	0.956422	+	0.291986i	$0.0943162\pi$
$97$			5.75147i			0.583973i	−0.956422	+	0.291986i	$0.905684\pi$
$98$	4.17184	+	1.50586i	0.421419	+	0.152115i
$99$	12.3103	+	6.05537i	1.23723	+	0.608588i
$100$	−7.96975			−0.796975
$101$	12.3284			1.22672			0.613362	−	0.789802i	$-0.289817\pi$
$101$	12.3284			1.22672			0.613362	+	0.789802i	$0.289817\pi$
$102$	6.42208	−	3.99799i	0.635881	−	0.395860i
$103$			11.7124i			1.15405i	0.816725	+	0.577027i	$0.195787\pi$
$103$			11.7124i			1.15405i	−0.816725	+	0.577027i	$0.804213\pi$
$104$	−2.28008			−0.223580
$105$	−0.504973	−	0.214555i	−0.0492803	−	0.0209385i
$106$	3.86881			0.375772
$107$		−	0.138293i		−	0.0133693i	−0.999978	−	0.00668463i	$-0.997872\pi$
$107$		−	0.138293i		−	0.0133693i	0.999978	−	0.00668463i	$-0.00212780\pi$
$108$	−8.26499	+	0.826632i	−0.795299	+	0.0795427i
$109$	−2.00736			−0.192270			−0.0961352	−	0.995368i	$-0.530648\pi$
$109$	−2.00736			−0.192270			−0.0961352	+	0.995368i	$0.530648\pi$
$110$	−0.346915			−0.0330770
$111$	−5.73717	−	9.21578i	−0.544548	−	0.874723i
$112$	3.79433	−	2.66436i	0.358531	−	0.251758i
$113$			13.7007i			1.28885i	0.764666	+	0.644427i	$0.222904\pi$
$113$			13.7007i			1.28885i	−0.764666	+	0.644427i	$0.777096\pi$
$114$	0.0728723	+	0.117057i	0.00682512	+	0.0109634i
$115$			0.220443i			0.0205564i
$116$			5.49433i			0.510136i
$117$	−2.69195	−	1.32416i	−0.248871	−	0.122418i
$118$			4.45294i			0.409926i
$119$	−14.9253	+	10.4805i	−1.36820	+	0.960742i
$120$	0.401405	−	0.249890i	0.0366431	−	0.0228117i
$121$	−9.91232			−0.901120
$122$	1.32796			0.120228
$123$	6.74052	+	10.8275i	0.607772	+	0.976281i
$124$			0.260104i			0.0233580i
$125$	1.19557			0.106935
$126$	−4.96882	+	0.776669i	−0.442658	+	0.0691912i
$127$	21.8726			1.94088			0.970440	−	0.241344i	$-0.0775883\pi$
$127$	21.8726			1.94088			0.970440	+	0.241344i	$0.0775883\pi$
$128$			11.2851i			0.997474i
$129$	1.15579	+	1.85657i	0.101761	+	0.163462i
$130$	0.0758615			0.00665349
$131$	−13.4580			−1.17583			−0.587917	−	0.808921i	$-0.700052\pi$
$131$	−13.4580			−1.17583			−0.587917	+	0.808921i	$0.700052\pi$
$132$	10.7488	−	6.69152i	0.935560	−	0.582422i
$133$	−0.191030	−	0.272047i	−0.0165644	−	0.0235895i
$134$		−	0.936360i		−	0.0808892i
$135$	0.619038	−	0.0619137i	0.0532783	−	0.00532869i
$136$		−	15.7169i		−	1.34771i
$137$			6.15902i			0.526200i	0.964769	+	0.263100i	$0.0847450\pi$
$137$			6.15902i			0.526200i	−0.964769	+	0.263100i	$0.915255\pi$
$138$	1.06789	+	1.71538i	0.0909047	+	0.146023i
$139$			19.7701i			1.67688i	0.544997	+	0.838438i	$0.316531\pi$
$139$			19.7701i			1.67688i	−0.544997	+	0.838438i	$0.683469\pi$
$140$	−0.414407	+	0.290993i	−0.0350237	+	0.0245934i
$141$	2.35903	+	3.78937i	0.198666	+	0.319123i
$142$	−3.71699			−0.311923
$143$	4.57300			0.382413
$144$	−2.32042	+	4.71731i	−0.193368	+	0.393109i
$145$		−	0.411519i		−	0.0341748i
$146$	9.87881			0.817576
$147$	11.8569	−	2.53246i	0.977943	−	0.208874i
$148$	−10.0189			−0.823544
$149$		−	20.0372i		−	1.64151i	−0.571277	−	0.820757i	$-0.693552\pi$
$149$		−	20.0372i		−	1.64151i	0.571277	−	0.820757i	$-0.306448\pi$
$150$	4.64498	−	2.89167i	0.379261	−	0.236104i
$151$	−6.70839			−0.545921			−0.272961	−	0.962025i	$-0.588003\pi$
$151$	−6.70839			−0.545921			−0.272961	+	0.962025i	$0.588003\pi$
$152$	0.286475			0.0232362
$153$	9.12757	−	18.5559i	0.737920	−	1.50016i
$154$	6.27385	−	4.40545i	0.505561	−	0.355002i
$155$		−	0.0194815i		−	0.00156479i
$156$	−2.35048	+	1.46327i	−0.188189	+	0.117155i
$157$			15.7882i			1.26004i	0.776580	+	0.630019i	$0.216953\pi$
$157$			15.7882i			1.26004i	−0.776580	+	0.630019i	$0.783047\pi$
$158$		−	6.30564i		−	0.501650i
$159$	8.97817	−	5.58925i	0.712015	−	0.443257i
$160$		−	0.678918i		−	0.0536732i
$161$	−2.79940	−	3.98665i	−0.220623	−	0.314192i
$162$	4.51712	−	3.48058i	0.354898	−	0.273460i
$163$	15.4406			1.20940			0.604701	−	0.796453i	$-0.293293\pi$
$163$	15.4406			1.20940			0.604701	+	0.796453i	$0.293293\pi$
$164$	11.7710			0.919161
$165$	−0.805070	+	0.501187i	−0.0626746	+	0.0390173i
$166$		−	4.61898i		−	0.358503i
$167$	−21.5146			−1.66485			−0.832423	−	0.554141i	$-0.813047\pi$
$167$	−21.5146			−1.66485			−0.832423	+	0.554141i	$0.813047\pi$
$168$	−4.08595	+	9.61661i	−0.315238	+	0.741937i
$169$	−1.00000			−0.0769231
$170$			0.522922i			0.0401063i
$171$	0.338223	+	0.166370i	0.0258646	+	0.0127227i
$172$	2.01836			0.153898
$173$	−14.3637			−1.09205			−0.546027	−	0.837768i	$-0.683860\pi$
$173$	−14.3637			−1.09205			−0.546027	+	0.837768i	$0.683860\pi$
$174$	−1.99352	−	3.20224i	−0.151128	−	0.242761i
$175$	−10.7952	+	7.58033i	−0.816042	+	0.573019i
$176$		−	8.01362i		−	0.604049i
$177$	6.43315	+	10.3338i	0.483545	+	0.776732i
$178$			10.6996i			0.801969i
$179$			24.5716i			1.83656i	0.395926	+	0.918282i	$0.370424\pi$
$179$			24.5716i			1.83656i	−0.395926	+	0.918282i	$0.629576\pi$
$180$	0.253430	−	0.515212i	0.0188896	−	0.0384016i
$181$			5.73703i			0.426430i	0.977005	+	0.213215i	$0.0683935\pi$
$181$			5.73703i			0.426430i	−0.977005	+	0.213215i	$0.931606\pi$
$182$	−1.37193	+	0.963362i	−0.101694	+	0.0714091i
$183$	3.08174	−	1.91850i	0.227809	−	0.141820i
$184$	4.19807			0.309486
$185$	0.750400			0.0551705
$186$	−0.0943737	−	0.151595i	−0.00691982	−	0.0111155i
$187$			31.5222i			2.30513i
$188$	4.11958			0.300451
$189$	−10.4089	+	8.98083i	−0.757135	+	0.653259i
$190$	−0.00953142			−0.000691482
$191$		−	18.8155i		−	1.36144i	−0.732542	−	0.680721i	$-0.761666\pi$
$191$		−	18.8155i		−	1.36144i	0.732542	−	0.680721i	$-0.238334\pi$
$192$	−0.0806902	−	0.129615i	−0.00582331	−	0.00935415i
$193$	−17.5147			−1.26073			−0.630366	−	0.776298i	$-0.717095\pi$
$193$	−17.5147			−1.26073			−0.630366	+	0.776298i	$0.717095\pi$
$194$	−3.64421			−0.261639
$195$	0.176049	−	0.109597i	0.0126071	−	0.00784840i
$196$	3.79911	−	10.5251i	0.271365	−	0.751790i
$197$		−	2.83332i		−	0.201866i	−0.994893	−	0.100933i	$-0.967817\pi$
$197$		−	2.83332i		−	0.201866i	0.994893	−	0.100933i	$-0.0321827\pi$
$198$	−3.83677	+	7.79997i	−0.272667	+	0.554320i
$199$		−	12.3380i		−	0.874615i	−0.899312	−	0.437307i	$-0.855932\pi$
$199$		−	12.3380i		−	0.874615i	0.899312	−	0.437307i	$-0.144068\pi$
$200$		−	11.3677i		−	0.803819i
$201$	−1.35276	−	2.17297i	−0.0954161	−	0.153270i
$202$			7.81146i			0.549613i
$203$	5.22586	+	7.44220i	0.366784	+	0.522340i
$204$	−10.0865	−	16.2022i	−0.706194	−	1.13438i
$205$	−0.881634			−0.0615760
$206$	−7.42111			−0.517054
$207$	4.95641	+	2.43803i	0.344494	+	0.169455i
$208$			1.75238i			0.121505i
$209$	−0.574563			−0.0397433
$210$	0.135945	−	0.319958i	0.00938112	−	0.0220792i
$211$	−2.91111			−0.200409			−0.100205	−	0.994967i	$-0.531950\pi$
$211$	−2.91111			−0.200409			−0.100205	+	0.994967i	$0.531950\pi$
$212$		−	9.76054i		−	0.670357i
$213$	−8.62587	+	5.36993i	−0.591035	+	0.367942i
$214$	0.0876242			0.00598987
$215$	−0.151172			−0.0103099
$216$	−1.17907	−	11.7888i	−0.0802257	−	0.802128i
$217$	0.247394	+	0.352316i	0.0167942	+	0.0239168i
$218$		−	1.27189i		−	0.0861434i
$219$	22.9253	−	14.2719i	1.54915	−	0.964405i
$220$			0.875225i			0.0590076i
$221$		−	6.89311i		−	0.463681i
$222$	5.83924	−	3.63515i	0.391904	−	0.243975i
$223$			18.1740i			1.21702i	0.793545	+	0.608512i	$0.208233\pi$
$223$			18.1740i			1.21702i	−0.793545	+	0.608512i	$0.791767\pi$
$224$	8.62155	+	12.2780i	0.576052	+	0.820361i
$225$	6.60180	−	13.4212i	0.440120	−	0.894745i
$226$	−8.68095			−0.577448
$227$	7.92865			0.526243			0.263122	−	0.964763i	$-0.415248\pi$
$227$	7.92865			0.526243			0.263122	+	0.964763i	$0.415248\pi$
$228$	0.295321	−	0.183848i	0.0195581	−	0.0121757i
$229$		−	7.07438i		−	0.467489i	−0.972298	−	0.233744i	$-0.924902\pi$
$229$		−	7.07438i		−	0.467489i	0.972298	−	0.233744i	$-0.0750978\pi$
$230$	−0.139676			−0.00920994
$231$	8.19491	−	19.2874i	0.539185	−	1.26902i
$232$	−7.83688			−0.514517
$233$			12.6727i			0.830214i	0.909773	+	0.415107i	$0.136256\pi$
$233$			12.6727i			0.830214i	−0.909773	+	0.415107i	$0.863744\pi$
$234$	0.839004	−	1.70566i	0.0548474	−	0.111502i
$235$	−0.308552			−0.0201277
$236$	11.2342			0.731287
$237$	−9.10974	−	14.6332i	−0.591741	−	0.950530i
$238$	−6.64056	−	9.45689i	−0.430444	−	0.612999i
$239$		−	5.77260i		−	0.373398i	−0.982417	−	0.186699i	$-0.940221\pi$
$239$		−	5.77260i		−	0.373398i	0.982417	−	0.186699i	$-0.0597790\pi$
$240$	−0.192055	−	0.308503i	−0.0123971	−	0.0199138i
$241$		−	18.1983i		−	1.17225i	−0.810220	−	0.586126i	$-0.800652\pi$
$241$		−	18.1983i		−	1.17225i	0.810220	−	0.586126i	$-0.199348\pi$
$242$		−	6.28059i		−	0.403731i
$243$	5.45431	−	14.6031i	0.349894	−	0.936789i
$244$		−	3.35029i		−	0.214480i
$245$	−0.284549	+	0.788315i	−0.0181792	+	0.0503636i
$246$	−6.86044	+	4.27089i	−0.437406	+	0.272302i
$247$	0.125642			0.00799444
$248$	−0.371001			−0.0235586
$249$	−6.67303	−	10.7191i	−0.422886	−	0.679294i
$250$			0.757527i			0.0479102i
$251$	22.0524			1.39194			0.695968	−	0.718072i	$-0.254975\pi$
$251$	22.0524			1.39194			0.695968	+	0.718072i	$0.254975\pi$
$252$	1.95945	+	12.5358i	0.123433	+	0.789678i
$253$	−8.41978			−0.529347
$254$			13.8588i			0.869577i
$255$	0.755464	+	1.21352i	0.0473090	+	0.0759937i
$256$	−7.32671			−0.457920
$257$	7.24002			0.451620			0.225810	−	0.974171i	$-0.427497\pi$
$257$	7.24002			0.451620			0.225810	+	0.974171i	$0.427497\pi$
$258$	−1.17635	+	0.732323i	−0.0732363	+	0.0455924i
$259$	−13.5708	+	9.52930i	−0.843246	+	0.592122i
$260$		−	0.191390i		−	0.0118695i
$261$	−9.25253	−	4.55127i	−0.572717	−	0.281717i
$262$		−	8.52720i		−	0.526812i
$263$		−	22.8020i		−	1.40603i	−0.711173	−	0.703017i	$-0.751836\pi$
$263$		−	22.8020i		−	1.40603i	0.711173	−	0.703017i	$-0.248164\pi$
$264$	9.54450	+	15.3316i	0.587423	+	0.943594i
$265$			0.731053i			0.0449082i
$266$	0.172373	−	0.121039i	0.0105689	−	0.00742138i
$267$	15.4577	+	24.8301i	0.945995	+	1.51958i
$268$	−2.36233			−0.144302
$269$	−21.5698			−1.31513			−0.657567	−	0.753396i	$-0.728414\pi$
$269$	−21.5698			−1.31513			−0.657567	+	0.753396i	$0.728414\pi$
$270$	0.0392294	+	0.392231i	0.00238743	+	0.0238704i
$271$		−	25.3261i		−	1.53845i	−0.638979	−	0.769224i	$-0.720643\pi$
$271$		−	25.3261i		−	1.53845i	0.638979	−	0.769224i	$-0.279357\pi$
$272$	−12.0793			−0.732417
$273$	−1.79202	+	4.21766i	−0.108458	+	0.255264i
$274$	−3.90244			−0.235755
$275$			22.7994i			1.37486i
$276$	4.32770	−	2.69416i	0.260497	−	0.162169i
$277$	−20.2770			−1.21832			−0.609162	−	0.793046i	$-0.708494\pi$
$277$	−20.2770			−1.21832			−0.609162	+	0.793046i	$0.708494\pi$
$278$	−12.5266			−0.751295
$279$	−0.438018	−	0.215459i	−0.0262235	−	0.0128992i
$280$	−0.415061	−	0.591092i	−0.0248046	−	0.0353245i
$281$		−	19.3613i		−	1.15500i	−0.816391	−	0.577500i	$-0.804028\pi$
$281$		−	19.3613i		−	1.15500i	0.816391	−	0.577500i	$-0.195972\pi$
$282$	−2.40100	+	1.49471i	−0.142977	+	0.0890088i
$283$			1.36591i			0.0811951i	0.999176	+	0.0405975i	$0.0129262\pi$
$283$			1.36591i			0.0811951i	−0.999176	+	0.0405975i	$0.987074\pi$
$284$			9.37754i			0.556455i
$285$	−0.0221192	+	0.0137700i	−0.00131023	+	0.000815666i
$286$			2.89752i			0.171334i
$287$	15.9441	−	11.1958i	0.941151	−	0.660869i
$288$	−15.2647	−	7.50862i	−0.899481	−	0.442450i
$289$	30.5150			1.79500
$290$	0.260744			0.0153114
$291$	−8.45696	+	5.26478i	−0.495756	+	0.308627i
$292$		−	24.9231i		−	1.45851i
$293$	12.0163			0.702001			0.351000	−	0.936375i	$-0.385842\pi$
$293$	12.0163			0.702001			0.351000	+	0.936375i	$0.385842\pi$
$294$	1.60460	+	7.51271i	0.0935823	+	0.438150i
$295$	−0.841432			−0.0489901
$296$		−	14.2905i		−	0.830616i
$297$	2.36478	+	23.6440i	0.137219	+	1.37197i
$298$	12.6959			0.735452
$299$	1.84119			0.106479
$300$	−7.29536	−	11.7187i	−0.421198	−	0.676581i
$301$	2.73391	−	1.91973i	0.157580	−	0.110652i
$302$		−	4.25053i		−	0.244591i
$303$	11.2852	+	18.1277i	0.648318	+	1.04141i
$304$		−	0.220173i		−	0.0126278i
$305$			0.250933i			0.0143684i
$306$	11.7573	+	5.78335i	0.672120	+	0.330612i
$307$			1.39288i			0.0794961i	0.999210	+	0.0397480i	$0.0126555\pi$
$307$			1.39288i			0.0794961i	−0.999210	+	0.0397480i	$0.987344\pi$
$308$	−11.1144	−	15.8282i	−0.633304	−	0.901894i
$309$	−17.2219	+	10.7213i	−0.979718	+	0.609912i
$310$	0.0123437			0.000701076
$311$	−0.809851			−0.0459224			−0.0229612	−	0.999736i	$-0.507309\pi$
$311$	−0.809851			−0.0459224			−0.0229612	+	0.999736i	$0.507309\pi$
$312$	−2.08714	−	3.35263i	−0.118161	−	0.189805i
$313$			9.68818i			0.547609i	0.961785	+	0.273804i	$0.0882820\pi$
$313$			9.68818i			0.547609i	−0.961785	+	0.273804i	$0.911718\pi$
$314$	−10.0036			−0.564538
$315$	−0.146760	−	0.938913i	−0.00826900	−	0.0529017i
$316$	−15.9084			−0.894916
$317$			24.9857i			1.40333i	0.712505	+	0.701667i	$0.247561\pi$
$317$			24.9857i			1.40333i	−0.712505	+	0.701667i	$0.752439\pi$
$318$	3.54143	+	5.68869i	0.198593	+	0.319006i
$319$	15.7179			0.880033
$320$	0.0105540			0.000589985
$321$	0.203346	−	0.126590i	0.0113497	−	0.00706559i
$322$	2.52599	−	1.77374i	0.140768	−	0.0988464i
$323$			0.866068i			0.0481893i
$324$	−8.78109	−	11.3962i	−0.487838	−	0.633120i
$325$		−	4.98567i		−	0.276555i
$326$			9.78339i			0.541852i
$327$	−1.83750	−	2.95163i	−0.101614	−	0.163225i
$328$			16.7897i			0.927054i
$329$	5.58007	−	3.91829i	0.307639	−	0.216022i
$330$	−0.317559	−	0.510103i	−0.0174810	−	0.0280803i
$331$	−1.65209			−0.0908071			−0.0454036	−	0.998969i	$-0.514457\pi$
$331$	−1.65209			−0.0908071			−0.0454036	+	0.998969i	$0.514457\pi$
$332$	−11.6532			−0.639550
$333$	8.29919	−	16.8719i	0.454793	−	0.924573i
$334$		−	13.6319i		−	0.745905i
$335$	0.176935			0.00966702
$336$	7.39093	+	3.14029i	0.403208	+	0.171317i
$337$	15.4904			0.843817			0.421908	−	0.906638i	$-0.361360\pi$
$337$	15.4904			0.843817			0.421908	+	0.906638i	$0.361360\pi$
$338$		−	0.633614i		−	0.0344641i
$339$	−20.1455	+	12.5414i	−1.09415	+	0.681153i
$340$	1.31927			0.0715475
$341$	0.744091			0.0402948
$342$	−0.105415	+	0.214303i	−0.00570017	+	0.0115882i
$343$	−4.86479	−	17.8699i	−0.262674	−	0.964885i
$344$			2.87890i			0.155220i
$345$	−0.324140	+	0.201789i	−0.0174511	+	0.0108640i
$346$		−	9.10106i		−	0.489276i
$347$			21.5189i			1.15520i	0.816321	+	0.577599i	$0.196010\pi$
$347$			21.5189i			1.15520i	−0.816321	+	0.577599i	$0.803990\pi$
$348$	−8.07887	+	5.02940i	−0.433073	+	0.269604i
$349$			9.92806i			0.531437i	0.964051	+	0.265719i	$0.0856092\pi$
$349$			9.92806i			0.531437i	−0.964051	+	0.265719i	$0.914391\pi$
$350$	−4.80300	−	6.84000i	−0.256731	−	0.365613i
$351$	−0.517119	−	5.17036i	−0.0276018	−	0.275973i
$352$	25.9312			1.38214
$353$	−9.57187			−0.509459			−0.254729	−	0.967012i	$-0.581986\pi$
$353$	−9.57187			−0.509459			−0.254729	+	0.967012i	$0.581986\pi$
$354$	−6.54761	+	4.07613i	−0.348001	+	0.216644i
$355$		−	0.702367i		−	0.0372777i
$356$	26.9938			1.43067
$357$	−29.0728	−	12.3526i	−1.53870	−	0.653769i
$358$	−15.5689			−0.822841
$359$			19.6454i			1.03685i	0.855124	+	0.518423i	$0.173481\pi$
$359$			19.6454i			1.03685i	−0.855124	+	0.518423i	$0.826519\pi$
$360$	0.734876	+	0.361482i	0.0387314	+	0.0190518i
$361$	18.9842			0.999169
$362$	−3.63506			−0.191055
$363$	−9.07355	−	14.5751i	−0.476238	−	0.764994i
$364$	2.43045	+	3.46123i	0.127390	+	0.181418i
$365$			1.86671i			0.0977080i
$366$	1.21559	+	1.95264i	0.0635399	+	0.102066i
$367$			1.61873i			0.0844973i	0.999107	+	0.0422486i	$0.0134522\pi$
$367$			1.61873i			0.0844973i	−0.999107	+	0.0422486i	$0.986548\pi$
$368$		−	3.22646i		−	0.168191i
$369$	−9.75060	+	19.8225i	−0.507596	+	1.03192i
$370$			0.475464i			0.0247182i
$371$	−9.28361	−	13.2209i	−0.481981	−	0.686394i
$372$	−0.382457	+	0.238094i	−0.0198295	+	0.0123446i
$373$	15.4579			0.800381			0.400190	−	0.916432i	$-0.368944\pi$
$373$	15.4579			0.800381			0.400190	+	0.916432i	$0.368944\pi$
$374$	−19.9729			−1.03277
$375$	1.09440	+	1.75796i	0.0565145	+	0.0907808i
$376$			5.87600i			0.303031i
$377$	−3.43711			−0.177020
$378$	−5.69038	−	6.59521i	−0.292681	−	0.339221i
$379$	24.2403			1.24514			0.622571	−	0.782563i	$-0.286088\pi$
$379$	24.2403			1.24514			0.622571	+	0.782563i	$0.286088\pi$
$380$			0.0240467i			0.00123357i
$381$	20.0217	+	32.1615i	1.02575	+	1.64768i
$382$	11.9218			0.609971
$383$	9.47184			0.483988			0.241994	−	0.970278i	$-0.422198\pi$
$383$	9.47184			0.483988			0.241994	+	0.970278i	$0.422198\pi$
$384$	−16.5937	+	10.3302i	−0.846792	+	0.527160i
$385$	0.832458	+	1.18551i	0.0424260	+	0.0604193i
$386$		−	11.0975i		−	0.564849i
$387$	−1.67192	+	3.39894i	−0.0849885	+	0.172778i
$388$			9.19391i			0.466750i
$389$			15.8959i			0.805954i	0.915210	+	0.402977i	$0.132025\pi$
$389$			15.8959i			0.805954i	−0.915210	+	0.402977i	$0.867975\pi$
$390$	0.0694421	+	0.111547i	0.00351634	+	0.00564839i
$391$			12.6916i			0.641840i
$392$	15.0125	+	5.41889i	0.758246	+	0.273695i
$393$	−12.3192	−	19.7887i	−0.621423	−	0.998208i
$394$	1.79523			0.0904424
$395$	1.19152			0.0599518
$396$	19.6784	+	9.67971i	0.988878	+	0.486424i
$397$		−	22.2658i		−	1.11749i	−0.829339	−	0.558745i	$-0.811283\pi$
$397$		−	22.2658i		−	1.11749i	0.829339	−	0.558745i	$-0.188717\pi$
$398$	7.81750			0.391856
$399$	0.225154	−	0.529917i	0.0112718	−	0.0265290i
$400$	−8.73676			−0.436838
$401$			4.84319i			0.241858i	0.992661	+	0.120929i	$0.0385873\pi$
$401$			4.84319i			0.241858i	−0.992661	+	0.120929i	$0.961413\pi$
$402$	1.37682	−	0.857126i	0.0686698	−	0.0427495i
$403$	−0.162714			−0.00810536
$404$	19.7074			0.980480
$405$	0.657693	+	0.853559i	0.0326810	+	0.0424137i
$406$	−4.71548	+	3.31118i	−0.234025	+	0.164331i
$407$			28.6614i			1.42069i
$408$	23.1101	−	14.3869i	1.14412	−	0.712258i
$409$		−	3.03190i		−	0.149918i	−0.997187	−	0.0749590i	$-0.976117\pi$
$409$		−	3.03190i		−	0.149918i	0.997187	−	0.0749590i	$-0.0238826\pi$
$410$		−	0.558616i		−	0.0275881i
$411$	−9.05623	+	5.63785i	−0.446711	+	0.278094i
$412$			18.7226i			0.922396i
$413$	15.2170	−	10.6853i	0.748782	−	0.525790i
$414$	−1.54477	+	3.14045i	−0.0759213	+	0.154345i
$415$	0.872807			0.0428444
$416$	−5.67049			−0.278019
$417$	−29.0699	+	18.0971i	−1.42356	+	0.886221i
$418$		−	0.364051i		−	0.0178063i
$419$	−22.1050			−1.07990			−0.539950	−	0.841697i	$-0.681557\pi$
$419$	−22.1050			−1.07990			−0.539950	+	0.841697i	$0.681557\pi$
$420$	−0.807217	−	0.342974i	−0.0393881	−	0.0167354i
$421$	3.78179			0.184313			0.0921566	−	0.995745i	$-0.470624\pi$
$421$	3.78179			0.184313			0.0921566	+	0.995745i	$0.470624\pi$
$422$		−	1.84452i		−	0.0897898i
$423$	−3.41249	+	6.93743i	−0.165921	+	0.337309i
$424$	13.9220			0.676113
$425$	34.3668			1.66703
$426$	−3.40246	−	5.46547i	−0.164850	−	0.264803i
$427$	−3.18659	−	4.53805i	−0.154210	−	0.219612i
$428$		−	0.221066i		−	0.0106856i
$429$	4.18603	+	6.72414i	0.202104	+	0.324645i
$430$		−	0.0957850i		−	0.00461916i
$431$		−	17.5538i		−	0.845537i	−0.906238	−	0.422768i	$-0.861058\pi$
$431$		−	17.5538i		−	0.845537i	0.906238	−	0.422768i	$-0.138942\pi$
$432$	−9.06041	+	0.906187i	−0.435919	+	0.0435989i
$433$		−	31.9918i		−	1.53743i	−0.639592	−	0.768714i	$-0.720897\pi$
$433$		−	31.9918i		−	1.53743i	0.639592	−	0.768714i	$-0.279103\pi$
$434$	−0.223233	+	0.156752i	−0.0107155	+	0.00752435i
$435$	0.605098	−	0.376696i	0.0290122	−	0.0180612i
$436$	−3.20883			−0.153675
$437$	−0.231332			−0.0110661
$438$	9.04287	+	14.5258i	0.432085	+	0.694070i
$439$			41.0533i			1.95937i	0.200553	+	0.979683i	$0.435726\pi$
$439$			41.0533i			1.95937i	−0.200553	+	0.979683i	$0.564274\pi$
$440$	−1.24838			−0.0595144
$441$	14.5773	+	15.1163i	0.694159	+	0.719822i
$442$	4.36757			0.207744
$443$		−	9.29574i		−	0.441654i	−0.975313	−	0.220827i	$-0.929124\pi$
$443$		−	9.29574i		−	0.441654i	0.975313	−	0.220827i	$-0.0708756\pi$
$444$	−9.17106	−	14.7317i	−0.435239	−	0.699137i
$445$	−2.02181			−0.0958428
$446$	−11.5153			−0.545267
$447$	29.4628	−	18.3417i	1.39354	−	0.867532i
$448$	−0.190865	+	0.134024i	−0.00901754	+	0.00633206i
$449$		−	20.0028i		−	0.943989i	−0.881601	−	0.471995i	$-0.843534\pi$
$449$		−	20.0028i		−	0.943989i	0.881601	−	0.471995i	$-0.156466\pi$
$450$	8.50384	+	4.18299i	0.400875	+	0.197188i
$451$		−	33.6739i		−	1.58564i
$452$			21.9010i			1.03014i
$453$	−6.14073	−	9.86403i	−0.288517	−	0.463452i
$454$			5.02371i			0.235774i
$455$	−0.182038	−	0.259242i	−0.00853406	−	0.0121534i
$456$	0.262234	+	0.421233i	0.0122802	+	0.0197260i
$457$	26.7949			1.25341			0.626707	−	0.779255i	$-0.284402\pi$
$457$	26.7949			1.25341			0.626707	+	0.779255i	$0.284402\pi$
$458$	4.48243			0.209450
$459$	35.6399	−	3.56456i	1.66353	−	0.166379i
$460$			0.352385i			0.0164301i
$461$	−30.5567			−1.42317			−0.711584	−	0.702601i	$-0.752022\pi$
$461$	−30.5567			−1.42317			−0.711584	+	0.702601i	$0.752022\pi$
$462$	12.2207	+	5.19241i	0.568560	+	0.241573i
$463$	−31.4417			−1.46122			−0.730610	−	0.682795i	$-0.760764\pi$
$463$	−31.4417			−1.46122			−0.730610	+	0.682795i	$0.760764\pi$
$464$			6.02311i			0.279616i
$465$	0.0286455	−	0.0178329i	0.00132841	−	0.000826983i
$466$	−8.02958			−0.371963
$467$	−12.8549			−0.594856			−0.297428	−	0.954744i	$-0.596129\pi$
$467$	−12.8549			−0.594856			−0.297428	+	0.954744i	$0.596129\pi$
$468$	−4.30318	−	2.11671i	−0.198914	−	0.0978449i
$469$	−3.19983	+	2.24690i	−0.147754	+	0.103752i
$470$		−	0.195503i		−	0.00901787i
$471$	−23.2150	+	14.4522i	−1.06969	+	0.665924i
$472$			16.0241i			0.737567i
$473$		−	5.77401i		−	0.265489i
$474$	9.27181	−	5.77206i	0.425868	−	0.265119i
$475$			0.626411i			0.0287417i
$476$	−23.8586	+	16.7534i	−1.09356	+	0.767889i
$477$	16.4369	+	8.08522i	0.752593	+	0.370197i
$478$	3.65760			0.167295
$479$	26.2134			1.19772			0.598860	−	0.800853i	$-0.295620\pi$
$479$	26.2134			1.19772			0.598860	+	0.800853i	$0.295620\pi$
$480$	0.998282	−	0.621468i	0.0455651	−	0.0283660i
$481$		−	6.26753i		−	0.285775i
$482$	11.5307			0.525207
$483$	3.29946	−	7.76553i	0.150130	−	0.353344i
$484$	−15.8452			−0.720236
$485$		−	0.688613i		−	0.0312683i
$486$	9.25273	+	3.45592i	0.419712	+	0.156764i
$487$	14.5112			0.657564			0.328782	−	0.944406i	$-0.393362\pi$
$487$	14.5112			0.657564			0.328782	+	0.944406i	$0.393362\pi$
$488$	4.77871			0.216322
$489$	14.1340	+	22.7039i	0.639163	+	1.02671i
$490$	−0.499487	−	0.180294i	−0.0225645	−	0.00814485i
$491$			5.10409i			0.230344i	0.993346	+	0.115172i	$0.0367420\pi$
$491$			5.10409i			0.230344i	−0.993346	+	0.115172i	$0.963258\pi$
$492$	10.7749	+	17.3081i	0.485772	+	0.780309i
$493$		−	23.6924i		−	1.06705i
$494$			0.0796088i			0.00358177i
$495$	−1.47389	−	0.724999i	−0.0662464	−	0.0325863i
$496$			0.285136i			0.0128030i
$497$	8.91932	+	12.7021i	0.400086	+	0.569767i
$498$	6.79176	−	4.22813i	0.304346	−	0.189467i
$499$	2.62946			0.117711			0.0588554	−	0.998267i	$-0.481255\pi$
$499$	2.62946			0.117711			0.0588554	+	0.998267i	$0.481255\pi$
$500$	1.91115			0.0854694
$501$	−19.6940	−	31.6350i	−0.879863	−	1.41335i
$502$			13.9727i			0.623633i
$503$	7.42470			0.331051			0.165526	−	0.986205i	$-0.447068\pi$
$503$	7.42470			0.331051			0.165526	+	0.986205i	$0.447068\pi$
$504$	−17.8805	+	2.79487i	−0.796459	+	0.124493i
$505$	−1.47606			−0.0656839
$506$		−	5.33489i		−	0.237165i
$507$	−0.915380	−	1.47040i	−0.0406535	−	0.0653028i
$508$	34.9641			1.55128
$509$	−2.58678			−0.114657			−0.0573285	−	0.998355i	$-0.518258\pi$
$509$	−2.58678			−0.114657			−0.0573285	+	0.998355i	$0.518258\pi$
$510$	−0.768905	+	0.478673i	−0.0340477	+	0.0211960i
$511$	−23.7053	−	33.7589i	−1.04866	−	1.49341i
$512$			17.9280i			0.792311i
$513$	0.0649721	+	0.649616i	0.00286859	+	0.0286813i
$514$			4.58738i			0.202341i
$515$		−	1.40230i		−	0.0617928i
$516$	1.84756	+	2.96779i	0.0813345	+	0.130650i
$517$		−	11.7851i		−	0.518307i
$518$	−6.03790	−	8.59863i	−0.265290	−	0.377802i
$519$	−13.1483	−	21.1204i	−0.577145	−	0.927084i
$520$	0.272990			0.0119714
$521$	−25.1071			−1.09996			−0.549981	−	0.835177i	$-0.685365\pi$
$521$	−25.1071			−1.09996			−0.549981	+	0.835177i	$0.685365\pi$
$522$	2.88375	−	5.86253i	0.126218	−	0.256596i
$523$			28.2219i			1.23406i	0.786940	+	0.617029i	$0.211664\pi$
$523$			28.2219i			1.23406i	−0.786940	+	0.617029i	$0.788336\pi$
$524$	−21.5131			−0.939805
$525$	−21.0278	−	8.93441i	−0.917730	−	0.389930i
$526$	14.4477			0.629949
$527$		−	1.12161i		−	0.0488579i
$528$	11.7832	−	7.33551i	0.512799	−	0.319237i
$529$	19.6100			0.852609
$530$	−0.463205			−0.0201204
$531$	−9.30597	+	18.9186i	−0.403845	+	0.820998i
$532$	−0.305368	−	0.434877i	−0.0132394	−	0.0188543i
$533$			7.36363i			0.318954i
$534$	−15.7327	+	9.79420i	−0.680820	+	0.423837i
$535$			0.0165575i			0.000715845i
$536$		−	3.36952i		−	0.145541i
$537$	−36.1300	+	22.4923i	−1.55913	+	0.970616i
$538$		−	13.6669i		−	0.589223i
$539$	−30.1095	−	10.8683i	−1.29691	−	0.468130i
$540$	0.989553	−	0.0989712i	0.0425836	−	0.00425904i
$541$	−12.6681			−0.544644			−0.272322	−	0.962206i	$-0.587792\pi$
$541$	−12.6681			−0.544644			−0.272322	+	0.962206i	$0.587792\pi$
$542$	16.0469			0.689275
$543$	−8.43573	+	5.25157i	−0.362012	+	0.225366i
$544$		−	39.0873i		−	1.67586i
$545$	0.240338			0.0102949
$546$	−2.67237	−	1.13545i	−0.114367	−	0.0485927i
$547$	−14.7159			−0.629206			−0.314603	−	0.949223i	$-0.601871\pi$
$547$	−14.7159			−0.629206			−0.314603	+	0.949223i	$0.601871\pi$
$548$			9.84540i			0.420575i
$549$	5.64194	+	2.77524i	0.240792	+	0.118444i
$550$	−14.4460			−0.615981
$551$	0.431847			0.0183973
$552$	3.84283	+	6.17285i	0.163562	+	0.262734i
$553$	−21.5483	+	15.1310i	−0.916326	+	0.643438i
$554$		−	12.8478i		−	0.545849i
$555$	0.686902	+	1.10339i	0.0291573	+	0.0468362i
$556$			31.6031i			1.34027i
$557$		−	38.3581i		−	1.62528i	−0.582763	−	0.812642i	$-0.698028\pi$
$557$		−	38.3581i		−	1.62528i	0.582763	−	0.812642i	$-0.301972\pi$
$558$	0.136518	−	0.277534i	0.00577925	−	0.0117490i
$559$			1.26263i			0.0534036i
$560$	−0.454289	+	0.318999i	−0.0191972	+	0.0134802i
$561$	−46.3503	+	28.8548i	−1.95691	+	1.21825i
$562$	12.2676			0.517478
$563$	19.1867			0.808622			0.404311	−	0.914622i	$-0.367511\pi$
$563$	19.1867			0.808622			0.404311	+	0.914622i	$0.367511\pi$
$564$	3.77098	+	6.05744i	0.158787	+	0.255064i
$565$		−	1.64036i		−	0.0690105i
$566$	−0.865461			−0.0363780
$567$	−22.7335	−	7.08435i	−0.954717	−	0.297515i
$568$	−13.3757			−0.561233
$569$		−	22.1461i		−	0.928414i	−0.885727	−	0.464207i	$-0.846339\pi$
$569$		−	22.1461i		−	0.928414i	0.885727	−	0.464207i	$-0.153661\pi$
$570$	−0.00872488	−	0.0140150i	−0.000365445	−	0.000587024i
$571$	−1.21279			−0.0507539			−0.0253769	−	0.999678i	$-0.508079\pi$
$571$	−1.21279			−0.0507539			−0.0253769	+	0.999678i	$0.508079\pi$
$572$	7.31009			0.305650
$573$	27.6663	−	17.2234i	1.15578	−	0.719516i
$574$	7.09384	+	10.1024i	0.296091	+	0.421666i
$575$			9.17958i			0.382815i
$576$	0.116724	−	0.237294i	0.00486348	−	0.00988724i
$577$		−	23.6799i		−	0.985806i	−0.870084	−	0.492903i	$-0.835936\pi$
$577$		−	23.6799i		−	0.985806i	0.870084	−	0.492903i	$-0.164064\pi$
$578$			19.3347i			0.804219i
$579$	−16.0326	−	25.7536i	−0.666291	−	1.07028i
$580$		−	0.657827i		−	0.0273148i
$581$	−15.7845	+	11.0837i	−0.654850	+	0.459831i
$582$	−3.33584	−	5.35845i	−0.138275	−	0.222115i
$583$	−27.9224			−1.15643
$584$	35.5492			1.47104
$585$	0.322303	+	0.158539i	0.0133256	+	0.00655478i
$586$			7.61371i			0.314519i
$587$	0.550629			0.0227269			0.0113635	−	0.999935i	$-0.496383\pi$
$587$	0.550629			0.0227269			0.0113635	+	0.999935i	$0.496383\pi$
$588$	18.9537	−	4.04822i	0.781637	−	0.166946i
$589$	0.0204438			0.000842371
$590$		−	0.533143i		−	0.0219491i
$591$	4.16611	−	2.59356i	0.171371	−	0.106685i
$592$	−10.9831			−0.451401
$593$	−22.5784			−0.927182			−0.463591	−	0.886049i	$-0.653439\pi$
$593$	−22.5784			−0.927182			−0.463591	+	0.886049i	$0.653439\pi$
$594$	−14.9812	+	1.49836i	−0.614686	+	0.0614784i
$595$	1.78698	−	1.25481i	0.0732592	−	0.0514421i
$596$		−	32.0302i		−	1.31201i
$597$	18.1417	−	11.2939i	0.742492	−	0.462230i
$598$			1.16661i			0.0477061i
$599$		−	32.1468i		−	1.31348i	−0.754117	−	0.656740i	$-0.771935\pi$
$599$		−	32.1468i		−	1.31348i	0.754117	−	0.656740i	$-0.228065\pi$
$600$	16.7151	−	10.4058i	0.682391	−	0.424815i
$601$		−	36.6473i		−	1.49488i	−0.664332	−	0.747438i	$-0.731284\pi$
$601$		−	36.6473i		−	1.49488i	0.664332	−	0.747438i	$-0.268716\pi$
$602$	1.21637	+	1.73224i	0.0495755	+	0.0706010i
$603$	1.95685	−	3.97819i	0.0796891	−	0.162004i
$604$	−10.7236			−0.436337
$605$	1.18679			0.0482497
$606$	−11.4860	+	7.15046i	−0.466586	+	0.290468i
$607$		−	39.0958i		−	1.58685i	−0.608669	−	0.793424i	$-0.708296\pi$
$607$		−	39.0958i		−	1.58685i	0.608669	−	0.793424i	$-0.291704\pi$
$608$	0.712454			0.0288938
$609$	−6.15937	+	14.4966i	−0.249590	+	0.587430i
$610$	−0.158995			−0.00643750
$611$			2.57710i			0.104258i
$612$	14.5907	−	29.6623i	0.589795	−	1.19903i
$613$	−30.8788			−1.24718			−0.623591	−	0.781751i	$-0.714327\pi$
$613$	−30.8788			−1.24718			−0.623591	+	0.781751i	$0.714327\pi$
$614$	−0.882550			−0.0356168
$615$	−0.807031	−	1.29636i	−0.0325426	−	0.0522741i
$616$	22.5767	−	15.8532i	0.909639	−	0.638742i
$617$			6.82629i			0.274816i	0.990515	+	0.137408i	$0.0438771\pi$
$617$			6.82629i			0.274816i	−0.990515	+	0.137408i	$0.956123\pi$
$618$	−6.79314	−	10.9120i	−0.273260	−	0.438946i
$619$			7.66630i			0.308135i	0.988060	+	0.154067i	$0.0492373\pi$
$619$			7.66630i			0.308135i	−0.988060	+	0.154067i	$0.950763\pi$
$620$		−	0.0311418i		−	0.00125068i
$621$	0.952116	+	9.51963i	0.0382071	+	0.382010i
$622$		−	0.513133i		−	0.0205748i
$623$	36.5638	−	25.6748i	1.46490	−	1.02864i
$624$	−2.57670	+	1.60409i	−0.103150	+	0.0642150i
$625$	24.7852			0.991407
$626$	−6.13857			−0.245346
$627$	−0.525944	−	0.844838i	−0.0210042	−	0.0337396i
$628$			25.2380i			1.00711i
$629$	43.2028			1.72261
$630$	0.594908	−	0.0929893i	0.0237017	−	0.00370478i
$631$	−19.9944			−0.795965			−0.397983	−	0.917393i	$-0.630290\pi$
$631$	−19.9944			−0.795965			−0.397983	+	0.917393i	$0.630290\pi$
$632$		−	22.6910i		−	0.902601i
$633$	−2.66477	−	4.28050i	−0.105915	−	0.170135i
$634$	−15.8313			−0.628739
$635$	−2.61877			−0.103923
$636$	14.3519	−	8.93461i	0.569090	−	0.354280i
$637$	6.58420	+	2.37662i	0.260875	+	0.0941652i
$638$			9.95908i			0.394284i
$639$	−15.7919	−	7.76796i	−0.624718	−	0.307296i
$640$		−	1.35115i		−	0.0534089i
$641$			1.28003i			0.0505581i	0.999680	+	0.0252791i	$0.00804743\pi$
$641$			1.28003i			0.0505581i	−0.999680	+	0.0252791i	$0.991953\pi$
$642$	0.0802095	+	0.128843i	0.00316562	+	0.00508501i
$643$			36.5207i			1.44023i	0.693852	+	0.720117i	$0.255912\pi$
$643$			36.5207i			1.44023i	−0.693852	+	0.720117i	$0.744088\pi$
$644$	−4.47493	−	6.37279i	−0.176337	−	0.251123i
$645$	−0.138380	−	0.222284i	−0.00544872	−	0.00875243i
$646$	−0.548753			−0.0215904
$647$	−14.5584			−0.572351			−0.286176	−	0.958177i	$-0.592384\pi$
$647$	−14.5584			−0.572351			−0.286176	+	0.958177i	$0.592384\pi$
$648$	16.2550	−	12.5250i	0.638557	−	0.492027i
$649$		−	32.1383i		−	1.26154i
$650$	3.15899			0.123906
$651$	−0.291587	+	0.686272i	−0.0114282	+	0.0268971i
$652$	24.6823			0.966635
$653$			19.8121i			0.775308i	0.921805	+	0.387654i	$0.126715\pi$
$653$			19.8121i			0.775308i	−0.921805	+	0.387654i	$0.873285\pi$
$654$	1.87019	−	1.16427i	0.0731303	−	0.0455264i
$655$	1.61131			0.0629590
$656$	12.9038			0.503811
$657$	41.9708	+	20.6452i	1.63744	+	0.805447i
$658$	2.48268	+	3.53561i	0.0967849	+	0.137832i
$659$			7.02108i			0.273502i	0.990605	+	0.136751i	$0.0436661\pi$
$659$			7.02108i			0.273502i	−0.990605	+	0.136751i	$0.956334\pi$
$660$	−1.28693	+	0.801164i	−0.0500937	+	0.0311853i
$661$		−	13.1060i		−	0.509763i	−0.966972	−	0.254881i	$-0.917964\pi$
$661$		−	13.1060i		−	0.509763i	0.966972	−	0.254881i	$-0.0820364\pi$
$662$		−	1.04679i		−	0.0406846i
$663$	10.1356	−	6.30982i	0.393636	−	0.245053i
$664$		−	16.6216i		−	0.645042i
$665$	0.0228717	+	0.0325718i	0.000886925	+	0.00126308i
$666$	10.6903	+	5.25848i	0.414239	+	0.203762i
$667$	6.32838			0.245036
$668$	−34.3917			−1.33066
$669$	−26.7231	+	16.6362i	−1.03318	+	0.643191i
$670$			0.112109i			0.00433114i
$671$	−9.58433			−0.369999
$672$	−10.1616	+	23.9162i	−0.391994	+	0.922588i
$673$	8.45650			0.325974			0.162987	−	0.986628i	$-0.447887\pi$
$673$	8.45650			0.325974			0.162987	+	0.986628i	$0.447887\pi$
$674$			9.81494i			0.378057i
$675$	25.7777	−	2.57818i	0.992183	−	0.0992342i
$676$	−1.59853			−0.0614821
$677$	−9.23176			−0.354805			−0.177403	−	0.984138i	$-0.556769\pi$
$677$	−9.23176			−0.354805			−0.177403	+	0.984138i	$0.556769\pi$
$678$	−7.94637	−	12.7645i	−0.305179	−	0.490217i
$679$	8.74467	+	12.4534i	0.335589	+	0.477916i
$680$			1.88175i			0.0721619i
$681$	7.25774	+	11.6583i	0.278117	+	0.446747i
$682$			0.471466i			0.0180534i
$683$			23.1656i			0.886406i	0.896421	+	0.443203i	$0.146158\pi$
$683$			23.1656i			0.886406i	−0.896421	+	0.443203i	$0.853842\pi$
$684$	0.540662	+	0.265949i	0.0206727	+	0.0101688i
$685$		−	0.737409i		−	0.0281749i
$686$	11.3226	−	3.08240i	0.432300	−	0.117687i
$687$	10.4022	−	6.47575i	0.396868	−	0.247065i
$688$	2.21260			0.0843547
$689$	6.10594			0.232618
$690$	−0.127856	−	0.205379i	−0.00486741	−	0.00781866i
$691$			43.0049i			1.63599i	0.575229	+	0.817993i	$0.304913\pi$
$691$			43.0049i			1.63599i	−0.575229	+	0.817993i	$0.695087\pi$
$692$	−22.9609			−0.872842
$693$	35.8616	−	5.60548i	1.36227	−	0.212934i
$694$	−13.6347			−0.517566
$695$		−	2.36704i		−	0.0897868i
$696$	−7.17373	−	11.5234i	−0.271920	−	0.436792i
$697$	−50.7583			−1.92261
$698$	−6.29056			−0.238101
$699$	−18.6339	+	11.6003i	−0.704799	+	0.438764i
$700$	−17.2565	+	12.1174i	−0.652235	+	0.457995i
$701$			15.1280i			0.571378i	0.958322	+	0.285689i	$0.0922225\pi$
$701$			15.1280i			0.571378i	−0.958322	+	0.285689i	$0.907778\pi$
$702$	3.27601	−	0.327654i	0.123645	−	0.0123665i
$703$			0.787467i			0.0296999i
$704$			0.403107i			0.0151927i
$705$	−0.282442	−	0.453695i	−0.0106374	−	0.0170871i
$706$		−	6.06487i		−	0.228254i
$707$	26.6941	−	18.7444i	1.00394	−	0.704957i
$708$	10.2836	+	16.5188i	0.386482	+	0.620816i
$709$	10.4225			0.391425			0.195712	−	0.980661i	$-0.437298\pi$
$709$	10.4225			0.391425			0.195712	+	0.980661i	$0.437298\pi$
$710$	0.445029			0.0167016
$711$	13.1778	−	26.7899i	0.494207	−	1.00470i
$712$			38.5029i			1.44296i
$713$	0.299588			0.0112197
$714$	7.82678	−	18.4209i	0.292910	−	0.689386i
$715$	−0.547517			−0.0204760
$716$			39.2785i			1.46791i
$717$	8.48803	−	5.28412i	0.316991	−	0.197339i
$718$	−12.4476			−0.464541
$719$	−6.06868			−0.226324			−0.113162	−	0.993577i	$-0.536098\pi$
$719$	−6.06868			−0.226324			−0.113162	+	0.993577i	$0.536098\pi$
$720$	0.277820	−	0.564796i	0.0103537	−	0.0210487i
$721$	17.8078	+	25.3602i	0.663196	+	0.944463i
$722$			12.0287i			0.447660i
$723$	26.7587	−	16.6583i	0.995168	−	0.619530i
$724$			9.17084i			0.340831i
$725$		−	17.1363i		−	0.636425i
$726$	9.23498	−	5.74913i	0.342742	−	0.213370i
$727$		−	28.9908i		−	1.07521i	−0.843197	−	0.537605i	$-0.819329\pi$
$727$		−	28.9908i		−	1.07521i	0.843197	−	0.537605i	$-0.180671\pi$
$728$	−4.93695	+	3.46669i	−0.182975	+	0.128484i
$729$	26.4652	−	5.34738i	0.980192	−	0.198051i
$730$	−1.18277			−0.0437764
$731$	−8.70345			−0.321909
$732$	4.92627	−	3.06679i	0.182080	−	0.113352i
$733$			41.5404i			1.53433i	0.641450	+	0.767165i	$0.278333\pi$
$733$			41.5404i			1.53433i	−0.641450	+	0.767165i	$0.721667\pi$
$734$	−1.02565			−0.0378575
$735$	−1.41961	+	0.303207i	−0.0523631	+	0.0111840i
$736$	10.4405			0.384841
$737$			6.75802i			0.248935i
$738$	−12.5598	−	6.17812i	−0.462334	−	0.227420i
$739$	5.65278			0.207941			0.103970	−	0.994580i	$-0.466845\pi$
$739$	5.65278			0.207941			0.103970	+	0.994580i	$0.466845\pi$
$740$	1.19954			0.0440960
$741$	0.115011	+	0.184745i	0.00422502	+	0.00678677i
$742$	8.37693	−	5.88222i	0.307527	−	0.215943i
$743$		−	44.2037i		−	1.62168i	−0.585271	−	0.810838i	$-0.699012\pi$
$743$		−	44.2037i		−	1.62168i	0.585271	−	0.810838i	$-0.300988\pi$
$744$	−0.339607	−	0.545520i	−0.0124506	−	0.0199997i
$745$			2.39902i			0.0878934i
$746$			9.79435i			0.358597i
$747$	9.65298	−	19.6241i	0.353184	−	0.718007i
$748$			50.3893i			1.84242i
$749$	−0.210264	−	0.299438i	−0.00768286	−	0.0109412i
$750$	−1.11387	+	0.693426i	−0.0406727	+	0.0253203i
$751$	−34.2389			−1.24940			−0.624698	−	0.780866i	$-0.714778\pi$
$751$	−34.2389			−1.24940			−0.624698	+	0.780866i	$0.714778\pi$
$752$	4.51605			0.164683
$753$	20.1864	+	32.4259i	0.735632	+	1.18167i
$754$		−	2.17780i		−	0.0793108i
$755$	0.803184			0.0292309
$756$	−16.6389	+	14.3562i	−0.605152	+	0.522128i
$757$	46.2552			1.68117			0.840586	−	0.541678i	$-0.182211\pi$
$757$	46.2552			1.68117			0.840586	+	0.541678i	$0.182211\pi$
$758$			15.3590i			0.557865i
$759$	−7.70730	−	12.3805i	−0.279757	−	0.449382i
$760$	−0.0342991			−0.00124416
$761$	20.7970			0.753890			0.376945	−	0.926236i	$-0.376975\pi$
$761$	20.7970			0.753890			0.376945	+	0.926236i	$0.376975\pi$
$762$	−20.3780	+	12.6861i	−0.738216	+	0.459567i
$763$	−4.34644	+	3.05204i	−0.157352	+	0.110491i
$764$		−	30.0772i		−	1.08816i
$765$	−1.09283	+	2.22167i	−0.0395113	+	0.0803246i
$766$			6.00149i			0.216843i
$767$			7.02785i			0.253761i
$768$	−6.70673	−	10.7732i	−0.242008	−	0.388745i
$769$			32.3646i			1.16710i	0.812078	+	0.583548i	$0.198336\pi$
$769$			32.3646i			1.16710i	−0.812078	+	0.583548i	$0.801664\pi$
$770$	−0.751157	+	0.527457i	−0.0270698	+	0.0190082i
$771$	6.62738	+	10.6457i	0.238679	+	0.383397i
$772$	−27.9978			−1.00766
$773$	10.4387			0.375454			0.187727	−	0.982221i	$-0.439888\pi$
$773$	10.4387			0.375454			0.187727	+	0.982221i	$0.439888\pi$
$774$	−2.15362	−	1.05935i	−0.0774101	−	0.0380776i
$775$		−	0.811237i		−	0.0291405i
$776$	−13.1138			−0.470758
$777$	−26.4343	−	11.2315i	−0.948325	−	0.402929i
$778$	−10.0719			−0.361094
$779$		−	0.925184i		−	0.0331482i
$780$	0.281419	−	0.175194i	0.0100764	−	0.00627296i
$781$	26.8268			0.959937
$782$	−8.04155			−0.287565
$783$	−1.77739	−	17.7711i	−0.0635188	−	0.635086i
$784$	4.16473	−	11.5380i	0.148741	−	0.412071i
$785$		−	1.89030i		−	0.0674676i
$786$	12.5384	−	7.80563i	0.447230	−	0.278418i
$787$			15.3737i			0.548012i	0.961728	+	0.274006i	$0.0883488\pi$
$787$			15.3737i			0.548012i	−0.961728	+	0.274006i	$0.911651\pi$
$788$		−	4.52915i		−	0.161344i
$789$	33.5281	−	20.8725i	1.19363	−	0.743082i
$790$			0.754963i			0.0268604i
$791$	20.8309	+	29.6654i	0.740661	+	1.05478i
$792$	−13.8067	+	28.0685i	−0.490601	+	0.997370i
$793$	2.09585			0.0744259
$794$	14.1079			0.500672
$795$	−1.07494	+	0.669192i	−0.0381242	+	0.0237338i
$796$		−	19.7226i		−	0.699051i
$797$	6.13347			0.217259			0.108629	−	0.994082i	$-0.465354\pi$
$797$	6.13347			0.217259			0.108629	+	0.994082i	$0.465354\pi$
$798$	0.335763	+	0.142661i	0.0118859	+	0.00505013i
$799$	−17.7642			−0.628454
$800$		−	28.2712i		−	0.999537i
$801$	−22.3605	+	45.4580i	−0.790071	+	1.60618i
$802$	−3.06871			−0.108360
$803$	−71.2986			−2.51607
$804$	−2.16243	−	3.47357i	−0.0762629	−	0.122503i
$805$	0.335167	+	0.477314i	0.0118131	+	0.0168231i
$806$		−	0.103098i		−	0.00363146i
$807$	−19.7446	−	31.7162i	−0.695042	−	1.11646i
$808$			28.1098i			0.988900i
$809$			19.7160i			0.693177i	0.938017	+	0.346588i	$0.112660\pi$
$809$			19.7160i			0.693177i	−0.938017	+	0.346588i	$0.887340\pi$
$810$	−0.540827	+	0.416723i	−0.0190027	+	0.0146422i
$811$		−	46.3131i		−	1.62627i	−0.582074	−	0.813136i	$-0.697759\pi$
$811$		−	46.3131i		−	1.62627i	0.582074	−	0.813136i	$-0.302241\pi$
$812$	8.35372	+	11.8966i	0.293158	+	0.417489i
$813$	37.2395	−	23.1830i	1.30604	−	0.813063i
$814$	−18.1603			−0.636517
$815$	−1.84868			−0.0647564
$816$	−11.0572	−	17.7615i	−0.387079	−	0.621775i
$817$		−	0.158640i		−	0.00555011i
$818$	1.92106			0.0671681
$819$	−7.84203	+	1.22578i	−0.274023	+	0.0428321i
$820$	−1.40932			−0.0492157
$821$		−	13.0756i		−	0.456341i	−0.973621	−	0.228171i	$-0.926726\pi$
$821$		−	13.0756i		−	0.456341i	0.973621	−	0.228171i	$-0.0732744\pi$
$822$	−3.57222	−	5.73815i	−0.124595	−	0.200141i
$823$	−3.68739			−0.128534			−0.0642671	−	0.997933i	$-0.520471\pi$
$823$	−3.68739			−0.128534			−0.0642671	+	0.997933i	$0.520471\pi$
$824$	−26.7051			−0.930317
$825$	−33.5243	+	20.8702i	−1.16717	+	0.726606i
$826$	6.77036	+	9.64173i	0.235571	+	0.335479i
$827$		−	0.368907i		−	0.0128281i	−0.999979	−	0.00641407i	$-0.997958\pi$
$827$		−	0.368907i		−	0.0128281i	0.999979	−	0.00641407i	$-0.00204168\pi$
$828$	7.92298	+	3.89727i	0.275343	+	0.135440i
$829$			15.4787i			0.537599i	0.963196	+	0.268799i	$0.0866269\pi$
$829$			15.4787i			0.537599i	−0.963196	+	0.268799i	$0.913373\pi$
$830$			0.553023i			0.0191957i
$831$	−18.5611	−	29.8152i	−0.643878	−	1.03428i
$832$		−	0.0881493i		−	0.00305603i
$833$	−16.3823	+	45.3856i	−0.567614	+	1.57252i
$834$	−11.4666	−	18.4191i	−0.397056	−	0.637802i
$835$	2.57590			0.0891427
$836$	−0.918458			−0.0317655
$837$	−0.0841424	−	0.841289i	−0.00290839	−	0.0290792i
$838$		−	14.0060i		−	0.483831i
$839$	−20.9200			−0.722239			−0.361119	−	0.932520i	$-0.617605\pi$
$839$	−20.9200			−0.722239			−0.361119	+	0.932520i	$0.617605\pi$
$840$	0.489204	−	1.15138i	0.0168791	−	0.0397264i
$841$	17.1863			0.592631
$842$			2.39620i			0.0825783i
$843$	28.4689	−	17.7230i	0.980521	−	0.610412i
$844$	−4.65351			−0.160180
$845$	0.119728			0.00411878
$846$	−4.39565	−	2.16220i	−0.151126	−	0.0743379i
$847$	−21.4627	+	15.0709i	−0.737466	+	0.517843i
$848$		−	10.6999i		−	0.367436i
$849$	−2.00844	+	1.25033i	−0.0689295	+	0.0429112i
$850$			21.7753i			0.746885i
$851$			11.5397i			0.395577i
$852$	−13.7887	+	8.58402i	−0.472395	+	0.294084i
$853$			3.42051i			0.117116i	0.998284	+	0.0585580i	$0.0186503\pi$
$853$			3.42051i			0.117116i	−0.998284	+	0.0585580i	$0.981350\pi$
$854$	2.87537	−	2.01906i	0.0983931	−	0.0690910i
$855$	−0.0404949	−	0.0199192i	−0.00138490	−	0.000681223i
$856$	0.315319			0.0107774
$857$	−20.0897			−0.686251			−0.343125	−	0.939290i	$-0.611486\pi$
$857$	−20.0897			−0.686251			−0.343125	+	0.939290i	$0.611486\pi$
$858$	−4.26051	+	2.65233i	−0.145451	+	0.0905490i
$859$			24.6455i			0.840894i	0.907317	+	0.420447i	$0.138127\pi$
$859$			24.6455i			0.840894i	−0.907317	+	0.420447i	$0.861873\pi$
$860$	−0.241654			−0.00824034
$861$	31.0573	+	13.1958i	1.05843	+	0.449711i
$862$	11.1223			0.378828
$863$		−	16.3444i		−	0.556370i	−0.960527	−	0.278185i	$-0.910267\pi$
$863$		−	16.3444i		−	0.556370i	0.960527	−	0.278185i	$-0.0897329\pi$
$864$	−2.93232	−	29.3185i	−0.0997595	−	0.997434i
$865$	1.71974			0.0584731
$866$	20.2705			0.688818
$867$	27.9329	+	44.8693i	0.948650	+	1.52384i
$868$	0.395468	+	0.563190i	0.0134231	+	0.0191159i
$869$			45.5099i			1.54382i
$870$	0.238680	+	0.383398i	0.00809201	+	0.0129984i
$871$		−	1.47781i		−	0.0500736i
$872$		−	4.57695i		−	0.154995i
$873$	−15.4827	−	7.61584i	−0.524009	−	0.257757i
$874$		−	0.146575i		−	0.00495798i
$875$	2.58870	−	1.81777i	0.0875141	−	0.0614518i
$876$	36.6469	−	22.8141i	1.23818	−	0.770817i
$877$	−23.8471			−0.805261			−0.402630	−	0.915363i	$-0.631904\pi$
$877$	−23.8471			−0.805261			−0.402630	+	0.915363i	$0.631904\pi$
$878$	−26.0119			−0.877860
$879$	10.9995	+	17.6688i	0.371004	+	0.595954i
$880$			0.959456i			0.0323433i
$881$	−0.646145			−0.0217692			−0.0108846	−	0.999941i	$-0.503465\pi$
$881$	−0.646145			−0.0217692			−0.0108846	+	0.999941i	$0.503465\pi$
$882$	−9.57788	+	9.23640i	−0.322504	+	0.311006i
$883$	31.8653			1.07235			0.536176	−	0.844106i	$-0.319868\pi$
$883$	31.8653			1.07235			0.536176	+	0.844106i	$0.319868\pi$
$884$		−	11.0189i		−	0.370605i
$885$	−0.770230	−	1.23724i	−0.0258910	−	0.0415894i
$886$	5.88991			0.197875
$887$	41.7532			1.40194			0.700968	−	0.713193i	$-0.252752\pi$
$887$	41.7532			1.40194			0.700968	+	0.713193i	$0.252752\pi$
$888$	21.0127	−	13.0812i	0.705140	−	0.438977i
$889$	47.3597	−	33.2556i	1.58839	−	1.11536i
$890$		−	1.28104i		−	0.0429407i
$891$	−32.6015	+	25.1205i	−1.09219	+	0.841567i
$892$			29.0518i			0.972727i
$893$		−	0.323793i		−	0.0108353i
$894$	11.6216	+	18.6680i	0.388683	+	0.624352i
$895$		−	2.94191i		−	0.0983372i
$896$	17.1582	+	24.4351i	0.573215	+	0.816321i
$897$	1.68539	+	2.70729i	0.0562736	+	0.0903939i
$898$	12.6740			0.422938
$899$	−0.559265			−0.0186525
$900$	10.5532	−	21.4542i	0.351774	−	0.715140i
$901$			42.0889i			1.40218i
$902$	21.3362			0.710419
$903$	5.32535	+	2.26266i	0.177216	+	0.0752965i
$904$	−31.2387			−1.03898
$905$		−	0.686885i		−	0.0228328i
$906$	6.24998	−	3.89085i	0.207642	−	0.129265i
$907$	6.84528			0.227294			0.113647	−	0.993521i	$-0.463747\pi$
$907$	6.84528			0.227294			0.113647	+	0.993521i	$0.463747\pi$
$908$	12.6742			0.420609
$909$	−16.3248	+	33.1875i	−0.541459	+	1.10076i
$910$	0.164259	−	0.115342i	0.00544514	−	0.00382354i
$911$			18.5194i			0.613574i	0.951778	+	0.306787i	$0.0992539\pi$
$911$			18.5194i			0.613574i	−0.951778	+	0.306787i	$0.900746\pi$
$912$	0.323742	−	0.201542i	0.0107202	−	0.00667372i
$913$			33.3367i			1.10328i
$914$			16.9777i			0.561571i
$915$	−0.368972	+	0.229699i	−0.0121978	+	0.00759362i
$916$		−	11.3086i		−	0.373648i
$917$	−29.1400	+	20.4619i	−0.962288	+	0.675712i
$918$	2.25855	+	22.5819i	0.0745434	+	0.745314i
$919$	−37.9353			−1.25137			−0.625685	−	0.780075i	$-0.715181\pi$
$919$	−37.9353			−1.25137			−0.625685	+	0.780075i	$0.715181\pi$
$920$	−0.502628			−0.0165711
$921$	−2.04810	+	1.27502i	−0.0674871	+	0.0420133i
$922$		−	19.3612i		−	0.637626i
$923$	−5.86634			−0.193093
$924$	13.0998	−	30.8315i	0.430953	−	1.01428i
$925$	31.2478			1.02742
$926$		−	19.9219i		−	0.654674i
$927$	−31.5291	−	15.5090i	−1.03555	−	0.509383i
$928$	−19.4901			−0.639794
$929$	44.2758			1.45264			0.726321	−	0.687356i	$-0.241229\pi$
$929$	44.2758			1.45264			0.726321	+	0.687356i	$0.241229\pi$
$930$	0.0112992	+	0.0181502i	0.000370515	+	0.000595169i
$931$	−0.827255	−	0.298604i	−0.0271122	−	0.00978637i
$932$			20.2577i			0.663563i
$933$	−0.741322	−	1.19081i	−0.0242698	−	0.0389852i
$934$		−	8.14507i		−	0.266515i
$935$		−	3.77410i		−	0.123426i
$936$	3.01919	−	6.13787i	0.0986852	−	0.200623i
$937$		−	37.7206i		−	1.23228i	−0.787638	−	0.616138i	$-0.788696\pi$
$937$		−	37.7206i		−	1.23228i	0.787638	−	0.616138i	$-0.211304\pi$
$938$	−1.42366	−	2.02745i	−0.0464843	−	0.0661987i
$939$	−14.2455	+	8.86837i	−0.464885	+	0.289408i
$940$	−0.493230			−0.0160874
$941$	−13.5463			−0.441597			−0.220799	−	0.975319i	$-0.570866\pi$
$941$	−13.5463			−0.441597			−0.220799	+	0.975319i	$0.570866\pi$
$942$	−9.15714	−	14.7094i	−0.298356	−	0.479257i
$943$		−	13.5579i		−	0.441505i
$944$	12.3154			0.400833
$945$	1.24624	−	1.07526i	0.0405401	−	0.0349782i
$946$	3.65849			0.118948
$947$		−	11.4312i		−	0.371464i	−0.982600	−	0.185732i	$-0.940534\pi$
$947$		−	11.4312i		−	0.371464i	0.982600	−	0.185732i	$-0.0594656\pi$
$948$	−14.5622	−	23.3917i	−0.472959	−	0.759727i
$949$	15.5912			0.506112
$950$	−0.396903			−0.0128772
$951$	−36.7389	+	22.8714i	−1.19134	+	0.741655i
$952$	−23.8963	−	34.0309i	−0.774483	−	1.10295i
$953$		−	41.3326i		−	1.33889i	−0.742860	−	0.669447i	$-0.766531\pi$
$953$		−	41.3326i		−	1.33889i	0.742860	−	0.669447i	$-0.233469\pi$
$954$	−5.12291	+	10.4146i	−0.165860	+	0.337186i
$955$			2.25275i			0.0728972i
$956$		−	9.22769i		−	0.298445i
$957$	14.3879	+	23.1116i	0.465093	+	0.747092i
$958$			16.6092i			0.536618i
$959$	9.36432	+	13.3358i	0.302390	+	0.430636i
$960$	0.00966089	+	0.0155186i	0.000311804	+	0.000500859i
$961$	30.9735			0.999146
$962$	3.97119			0.128036
$963$	0.372277	+	0.183121i	0.0119965	+	0.00590100i
$964$		−	29.0905i		−	0.936943i
$965$	2.09700			0.0675048
$966$	4.92035	+	2.09058i	0.158310	+	0.0672634i
$967$	29.5411			0.949977			0.474989	−	0.879992i	$-0.342452\pi$
$967$	29.5411			0.949977			0.474989	+	0.879992i	$0.342452\pi$
$968$		−	22.6009i		−	0.726420i
$969$	−1.27347	+	0.792781i	−0.0409096	+	0.0254678i
$970$	0.436315			0.0140092
$971$	51.8492			1.66392			0.831961	−	0.554835i	$-0.187219\pi$
$971$	51.8492			1.66392			0.831961	+	0.554835i	$0.187219\pi$
$972$	8.71889	−	23.3435i	0.279659	−	0.748745i
$973$	30.0589	+	42.8072i	0.963644	+	1.37233i
$974$			9.19449i			0.294610i
$975$	7.33093	−	4.56378i	0.234778	−	0.146158i
$976$		−	3.67272i		−	0.117561i
$977$		−	24.1686i		−	0.773221i	−0.922243	−	0.386611i	$-0.873646\pi$
$977$		−	24.1686i		−	0.773221i	0.922243	−	0.386611i	$-0.126354\pi$
$978$	−14.3855	+	8.95552i	−0.459998	+	0.286366i
$979$		−	77.2225i		−	2.46804i
$980$	−0.454861	+	1.26015i	−0.0145300	+	0.0402539i
$981$	2.65806	−	5.40372i	0.0848654	−	0.172528i
$982$	−3.23402			−0.103202
$983$	−44.0222			−1.40409			−0.702045	−	0.712133i	$-0.747729\pi$
$983$	−44.0222			−1.40409			−0.702045	+	0.712133i	$0.747729\pi$
$984$	−24.6875	+	15.3689i	−0.787010	+	0.489944i
$985$			0.339228i			0.0108087i
$986$	15.0118			0.478074
$987$	10.8693	+	4.61822i	0.345975	+	0.146999i
$988$	0.200844			0.00638969
$989$		−	2.32475i		−	0.0739227i
$990$	0.459369	−	0.933877i	0.0145997	−	0.0296806i
$991$	14.3694			0.456459			0.228229	−	0.973607i	$-0.426706\pi$
$991$	14.3694			0.456459			0.228229	+	0.973607i	$0.426706\pi$
$992$	−0.922668			−0.0292947
$993$	−1.51229	−	2.42924i	−0.0479911	−	0.0770895i
$994$	−8.04822	+	5.65141i	−0.255274	+	0.179252i
$995$			1.47720i			0.0468305i
$996$	−10.6671	−	17.1348i	−0.337999	−	0.542937i
$997$		−	29.1670i		−	0.923730i	−0.886950	−	0.461865i	$-0.847181\pi$
$997$		−	29.1670i		−	0.923730i	0.886950	−	0.461865i	$-0.152819\pi$
$998$			1.66606i			0.0527383i
$999$	32.4053	−	3.24106i	1.02526	−	0.102542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.20	yes	32
3.2	odd	2	inner	273.2.e.a.209.13	✓	32
7.6	odd	2	inner	273.2.e.a.209.19	yes	32
21.20	even	2	inner	273.2.e.a.209.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.13	✓	32	3.2	odd	2	inner
273.2.e.a.209.14	yes	32	21.20	even	2	inner
273.2.e.a.209.19	yes	32	7.6	odd	2	inner
273.2.e.a.209.20	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.633614i q^{2} +(0.915380 + 1.47040i) q^{3} +1.59853 q^{4} -0.119728 q^{5} +(-0.931666 + 0.579998i) q^{6} +(2.16525 - 1.52042i) q^{7} +2.28008i q^{8} +(-1.32416 + 2.69195i) q^{9} +O(q^{10})\)	\(q+0.633614i q^{2} +(0.915380 + 1.47040i) q^{3} +1.59853 q^{4} -0.119728 q^{5} +(-0.931666 + 0.579998i) q^{6} +(2.16525 - 1.52042i) q^{7} +2.28008i q^{8} +(-1.32416 + 2.69195i) q^{9} -0.0758615i q^{10} -4.57300i q^{11} +(1.46327 + 2.35048i) q^{12} +1.00000i q^{13} +(0.963362 + 1.37193i) q^{14} +(-0.109597 - 0.176049i) q^{15} +1.75238 q^{16} -6.89311 q^{17} +(-1.70566 - 0.839004i) q^{18} -0.125642i q^{19} -0.191390 q^{20} +(4.21766 + 1.79202i) q^{21} +2.89752 q^{22} -1.84119i q^{23} +(-3.35263 + 2.08714i) q^{24} -4.98567 q^{25} -0.633614 q^{26} +(-5.17036 + 0.517119i) q^{27} +(3.46123 - 2.43045i) q^{28} +3.43711i q^{29} +(0.111547 - 0.0694421i) q^{30} +0.162714i q^{31} +5.67049i q^{32} +(6.72414 - 4.18603i) q^{33} -4.36757i q^{34} +(-0.259242 + 0.182038i) q^{35} +(-2.11671 + 4.30318i) q^{36} -6.26753 q^{37} +0.0796088 q^{38} +(-1.47040 + 0.915380i) q^{39} -0.272990i q^{40} +7.36363 q^{41} +(-1.13545 + 2.67237i) q^{42} +1.26263 q^{43} -7.31009i q^{44} +(0.158539 - 0.322303i) q^{45} +1.16661 q^{46} +2.57710 q^{47} +(1.60409 + 2.57670i) q^{48} +(2.37662 - 6.58420i) q^{49} -3.15899i q^{50} +(-6.30982 - 10.1356i) q^{51} +1.59853i q^{52} -6.10594i q^{53} +(-0.327654 - 3.27601i) q^{54} +0.547517i q^{55} +(3.46669 + 4.93695i) q^{56} +(0.184745 - 0.115011i) q^{57} -2.17780 q^{58} +7.02785 q^{59} +(-0.175194 - 0.281419i) q^{60} -2.09585i q^{61} -0.103098 q^{62} +(1.22578 + 7.84203i) q^{63} -0.0881493 q^{64} -0.119728i q^{65} +(2.65233 + 4.26051i) q^{66} -1.47781 q^{67} -11.0189 q^{68} +(2.70729 - 1.68539i) q^{69} +(-0.115342 - 0.164259i) q^{70} +5.86634i q^{71} +(-6.13787 - 3.01919i) q^{72} -15.5912i q^{73} -3.97119i q^{74} +(-4.56378 - 7.33093i) q^{75} -0.200844i q^{76} +(-6.95290 - 9.90169i) q^{77} +(-0.579998 - 0.931666i) q^{78} -9.95186 q^{79} -0.209809 q^{80} +(-5.49322 - 7.12914i) q^{81} +4.66570i q^{82} -7.28990 q^{83} +(6.74207 + 2.86460i) q^{84} +0.825301 q^{85} +0.800020i q^{86} +(-5.05393 + 3.14626i) q^{87} +10.4268 q^{88} +16.8866 q^{89} +(0.204216 + 0.100453i) q^{90} +(1.52042 + 2.16525i) q^{91} -2.94321i q^{92} +(-0.239255 + 0.148945i) q^{93} +1.63289i q^{94} +0.0150430i q^{95} +(-8.33790 + 5.19066i) q^{96} +5.75147i q^{97} +(4.17184 + 1.50586i) q^{98} +(12.3103 + 6.05537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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