LMFDB - Embedded newform 273.2.e.a.209.9

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			209.9
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71574i q^{2} +(-1.66803 - 0.466569i) q^{3} -0.943779 q^{4} +2.59497 q^{5} +(-0.800512 + 2.86191i) q^{6} +(2.59496 + 0.515930i) q^{7} -1.81221i q^{8} +(2.56463 + 1.55650i) q^{9} +O(q^{10})$	\(q-1.71574i q^{2} +(-1.66803 - 0.466569i) q^{3} -0.943779 q^{4} +2.59497 q^{5} +(-0.800512 + 2.86191i) q^{6} +(2.59496 + 0.515930i) q^{7} -1.81221i q^{8} +(2.56463 + 1.55650i) q^{9} -4.45230i q^{10} -3.05204i q^{11} +(1.57425 + 0.440338i) q^{12} +1.00000i q^{13} +(0.885205 - 4.45229i) q^{14} +(-4.32848 - 1.21073i) q^{15} -4.99684 q^{16} -2.57699 q^{17} +(2.67055 - 4.40025i) q^{18} +0.733175i q^{19} -2.44908 q^{20} +(-4.08775 - 2.07131i) q^{21} -5.23651 q^{22} +5.99021i q^{23} +(-0.845518 + 3.02281i) q^{24} +1.73386 q^{25} +1.71574 q^{26} +(-3.55165 - 3.79286i) q^{27} +(-2.44907 - 0.486924i) q^{28} +0.420393i q^{29} +(-2.07730 + 7.42656i) q^{30} -10.3445i q^{31} +4.94889i q^{32} +(-1.42398 + 5.09088i) q^{33} +4.42145i q^{34} +(6.73384 + 1.33882i) q^{35} +(-2.42044 - 1.46899i) q^{36} +2.32273 q^{37} +1.25794 q^{38} +(0.466569 - 1.66803i) q^{39} -4.70262i q^{40} +10.4619 q^{41} +(-3.55384 + 7.01353i) q^{42} -10.0212 q^{43} +2.88045i q^{44} +(6.65513 + 4.03906i) q^{45} +10.2777 q^{46} -2.63047 q^{47} +(8.33486 + 2.33137i) q^{48} +(6.46763 + 2.67764i) q^{49} -2.97486i q^{50} +(4.29849 + 1.20234i) q^{51} -0.943779i q^{52} +12.1389i q^{53} +(-6.50757 + 6.09373i) q^{54} -7.91993i q^{55} +(0.934972 - 4.70260i) q^{56} +(0.342076 - 1.22296i) q^{57} +0.721287 q^{58} -5.06888 q^{59} +(4.08512 + 1.14266i) q^{60} +9.31982i q^{61} -17.7486 q^{62} +(5.85206 + 5.36222i) q^{63} -1.50265 q^{64} +2.59497i q^{65} +(8.73464 + 2.44319i) q^{66} +2.59536 q^{67} +2.43211 q^{68} +(2.79484 - 9.99183i) q^{69} +(2.29708 - 11.5535i) q^{70} +4.49399i q^{71} +(2.82069 - 4.64763i) q^{72} +3.93686i q^{73} -3.98521i q^{74} +(-2.89212 - 0.808964i) q^{75} -0.691955i q^{76} +(1.57464 - 7.91991i) q^{77} +(-2.86191 - 0.800512i) q^{78} +8.55165 q^{79} -12.9666 q^{80} +(4.15463 + 7.98367i) q^{81} -17.9499i q^{82} +1.25121 q^{83} +(3.85793 + 1.95486i) q^{84} -6.68720 q^{85} +17.1938i q^{86} +(0.196142 - 0.701227i) q^{87} -5.53092 q^{88} +7.71703 q^{89} +(6.93000 - 11.4185i) q^{90} +(-0.515930 + 2.59496i) q^{91} -5.65343i q^{92} +(-4.82644 + 17.2550i) q^{93} +4.51321i q^{94} +1.90256i q^{95} +(2.30900 - 8.25488i) q^{96} +8.62720i q^{97} +(4.59414 - 11.0968i) q^{98} +(4.75049 - 7.82733i) 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 $

$2$		−	1.71574i		−	1.21321i	−0.795002	−	0.606607i	$-0.792530\pi$
$2$		−	1.71574i		−	1.21321i	0.795002	−	0.606607i	$-0.207470\pi$
$3$	−1.66803	−	0.466569i	−0.963036	−	0.269374i
$3$	−1.66803	−	0.466569i	−0.963036	−	0.269374i
$4$	−0.943779			−0.471889
$5$	2.59497			1.16050			0.580252	−	0.814437i	$-0.302954\pi$
$5$	2.59497			1.16050			0.580252	+	0.814437i	$0.302954\pi$
$6$	−0.800512	+	2.86191i	−0.326808	+	1.16837i
$7$	2.59496	+	0.515930i	0.980803	+	0.195003i
$7$	2.59496	+	0.515930i	0.980803	+	0.195003i
$8$		−	1.81221i		−	0.640711i
$9$	2.56463	+	1.55650i	0.854876	+	0.518833i
$10$		−	4.45230i		−	1.40794i
$11$		−	3.05204i		−	0.920223i	−0.887861	−	0.460112i	$-0.847809\pi$
$11$		−	3.05204i		−	0.920223i	0.887861	−	0.460112i	$-0.152191\pi$
$12$	1.57425	+	0.440338i	0.454446	+	0.127114i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.885205	−	4.45229i	0.236581	−	1.18992i
$15$	−4.32848	−	1.21073i	−1.11761	−	0.312609i
$16$	−4.99684			−1.24921
$17$	−2.57699			−0.625012			−0.312506	−	0.949916i	$-0.601168\pi$
$17$	−2.57699			−0.625012			−0.312506	+	0.949916i	$0.601168\pi$
$18$	2.67055	−	4.40025i	0.629455	−	1.03715i
$19$			0.733175i			0.168202i	0.996457	+	0.0841009i	$0.0268018\pi$
$19$			0.733175i			0.168202i	−0.996457	+	0.0841009i	$0.973198\pi$
$20$	−2.44908			−0.547630
$21$	−4.08775	−	2.07131i	−0.892019	−	0.451997i
$22$	−5.23651			−1.11643
$23$			5.99021i			1.24904i	0.781007	+	0.624522i	$0.214706\pi$
$23$			5.99021i			1.24904i	−0.781007	+	0.624522i	$0.785294\pi$
$24$	−0.845518	+	3.02281i	−0.172591	+	0.617028i
$25$	1.73386			0.346772
$26$	1.71574			0.336485
$27$	−3.55165	−	3.79286i	−0.683516	−	0.729935i
$28$	−2.44907	−	0.486924i	−0.462830	−	0.0920200i
$29$			0.420393i			0.0780650i	0.999238	+	0.0390325i	$0.0124276\pi$
$29$			0.420393i			0.0780650i	−0.999238	+	0.0390325i	$0.987572\pi$
$30$	−2.07730	+	7.42656i	−0.379262	+	1.35590i
$31$		−	10.3445i		−	1.85794i	−0.370161	−	0.928968i	$-0.620697\pi$
$31$		−	10.3445i		−	1.85794i	0.370161	−	0.928968i	$-0.379303\pi$
$32$			4.94889i			0.874848i
$33$	−1.42398	+	5.09088i	−0.247884	+	0.886208i
$34$			4.42145i			0.758273i
$35$	6.73384	+	1.33882i	1.13823	+	0.226302i
$36$	−2.42044	−	1.46899i	−0.403407	−	0.244832i
$37$	2.32273			0.381854			0.190927	−	0.981604i	$-0.438851\pi$
$37$	2.32273			0.381854			0.190927	+	0.981604i	$0.438851\pi$
$38$	1.25794			0.204065
$39$	0.466569	−	1.66803i	0.0747108	−	0.267098i
$40$		−	4.70262i		−	0.743549i
$41$	10.4619			1.63387			0.816935	−	0.576730i	$-0.195671\pi$
$41$	10.4619			1.63387			0.816935	+	0.576730i	$0.195671\pi$
$42$	−3.55384	+	7.01353i	−0.548370	+	1.08221i
$43$	−10.0212			−1.52821			−0.764107	−	0.645089i	$-0.776820\pi$
$43$	−10.0212			−1.52821			−0.764107	+	0.645089i	$0.776820\pi$
$44$			2.88045i			0.434244i
$45$	6.65513	+	4.03906i	0.992088	+	0.602108i
$46$	10.2777			1.51536
$47$	−2.63047			−0.383693			−0.191847	−	0.981425i	$-0.561448\pi$
$47$	−2.63047			−0.383693			−0.191847	+	0.981425i	$0.561448\pi$
$48$	8.33486	+	2.33137i	1.20303	+	0.336504i
$49$	6.46763	+	2.67764i	0.923947	+	0.382520i
$50$		−	2.97486i		−	0.420708i
$51$	4.29849	+	1.20234i	0.601908	+	0.168362i
$52$		−	0.943779i		−	0.130879i
$53$			12.1389i			1.66740i	0.552216	+	0.833701i	$0.313782\pi$
$53$			12.1389i			1.66740i	−0.552216	+	0.833701i	$0.686218\pi$
$54$	−6.50757	+	6.09373i	−0.885568	+	0.829252i
$55$		−	7.91993i		−	1.06792i
$56$	0.934972	−	4.70260i	0.124941	−	0.628411i
$57$	0.342076	−	1.22296i	0.0453091	−	0.161984i
$58$	0.721287			0.0947096
$59$	−5.06888			−0.659912			−0.329956	−	0.943996i	$-0.607034\pi$
$59$	−5.06888			−0.659912			−0.329956	+	0.943996i	$0.607034\pi$
$60$	4.08512	+	1.14266i	0.527387	+	0.147517i
$61$			9.31982i			1.19328i	0.802509	+	0.596640i	$0.203498\pi$
$61$			9.31982i			1.19328i	−0.802509	+	0.596640i	$0.796502\pi$
$62$	−17.7486			−2.25407
$63$	5.85206	+	5.36222i	0.737290	+	0.675576i
$64$	−1.50265			−0.187832
$65$			2.59497i			0.321866i
$66$	8.73464	+	2.44319i	1.07516	+	0.300736i
$67$	2.59536			0.317074			0.158537	−	0.987353i	$-0.449322\pi$
$67$	2.59536			0.317074			0.158537	+	0.987353i	$0.449322\pi$
$68$	2.43211			0.294936
$69$	2.79484	−	9.99183i	0.336460	−	1.20287i
$70$	2.29708	−	11.5535i	0.274553	−	1.38091i
$71$			4.49399i			0.533338i	0.963788	+	0.266669i	$0.0859230\pi$
$71$			4.49399i			0.533338i	−0.963788	+	0.266669i	$0.914077\pi$
$72$	2.82069	−	4.64763i	0.332422	−	0.547729i
$73$			3.93686i			0.460774i	0.973099	+	0.230387i	$0.0739993\pi$
$73$			3.93686i			0.460774i	−0.973099	+	0.230387i	$0.926001\pi$
$74$		−	3.98521i		−	0.463271i
$75$	−2.89212	−	0.808964i	−0.333954	−	0.0934111i
$76$		−	0.691955i		−	0.0793726i
$77$	1.57464	−	7.91991i	0.179447	−	0.902557i
$78$	−2.86191	−	0.800512i	−0.324047	−	0.0906402i
$79$	8.55165			0.962135			0.481068	−	0.876683i	$-0.340249\pi$
$79$	8.55165			0.962135			0.481068	+	0.876683i	$0.340249\pi$
$80$	−12.9666			−1.44971
$81$	4.15463	+	7.98367i	0.461625	+	0.887075i
$82$		−	17.9499i		−	1.98224i
$83$	1.25121			0.137338			0.0686690	−	0.997640i	$-0.478125\pi$
$83$	1.25121			0.137338			0.0686690	+	0.997640i	$0.478125\pi$
$84$	3.85793	+	1.95486i	0.420934	+	0.213293i
$85$	−6.68720			−0.725329
$86$			17.1938i			1.85405i
$87$	0.196142	−	0.701227i	0.0210286	−	0.0751794i
$88$	−5.53092			−0.589598
$89$	7.71703			0.818004			0.409002	−	0.912533i	$-0.365877\pi$
$89$	7.71703			0.818004			0.409002	+	0.912533i	$0.365877\pi$
$90$	6.93000	−	11.4185i	0.730486	−	1.20362i
$91$	−0.515930	+	2.59496i	−0.0540842	+	0.272026i
$92$		−	5.65343i		−	0.589411i
$93$	−4.82644	+	17.2550i	−0.500479	+	1.78926i
$94$			4.51321i			0.465502i
$95$			1.90256i			0.195199i
$96$	2.30900	−	8.25488i	0.235661	−	0.842510i
$97$			8.62720i			0.875959i	0.898985	+	0.437980i	$0.144306\pi$
$97$			8.62720i			0.875959i	−0.898985	+	0.437980i	$0.855694\pi$
$98$	4.59414	−	11.0968i	0.464078	−	1.12095i
$99$	4.75049	−	7.82733i	0.477442	−	0.786677i
$100$	−1.63638			−0.163638
$101$	−14.4904			−1.44185			−0.720924	−	0.693015i	$-0.756282\pi$
$101$	−14.4904			−1.44185			−0.720924	+	0.693015i	$0.756282\pi$
$102$	2.06291	−	7.37510i	0.204259	−	0.730244i
$103$			1.09027i			0.107427i	0.998556	+	0.0537136i	$0.0171058\pi$
$103$			1.09027i			0.107427i	−0.998556	+	0.0537136i	$0.982894\pi$
$104$	1.81221			0.177701
$105$	−10.6076	−	5.37499i	−1.03519	−	0.524545i
$106$	20.8272			2.02292
$107$		−	11.0685i		−	1.07003i	−0.844843	−	0.535014i	$-0.820306\pi$
$107$		−	11.0685i		−	1.07003i	0.844843	−	0.535014i	$-0.179694\pi$
$108$	3.35198	+	3.57962i	0.322544	+	0.344449i
$109$	−7.44325			−0.712934			−0.356467	−	0.934308i	$-0.616019\pi$
$109$	−7.44325			−0.712934			−0.356467	+	0.934308i	$0.616019\pi$
$110$	−13.5886			−1.29562
$111$	−3.87438	−	1.08371i	−0.367739	−	0.102861i
$112$	−12.9666	−	2.57802i	−1.22523	−	0.243600i
$113$		−	2.60664i		−	0.245212i	−0.992455	−	0.122606i	$-0.960875\pi$
$113$		−	2.60664i		−	0.245212i	0.992455	−	0.122606i	$-0.0391252\pi$
$114$	−2.09828	−	0.586915i	−0.196522	−	0.0549697i
$115$			15.5444i			1.44952i
$116$		−	0.396758i		−	0.0368381i
$117$	−1.55650	+	2.56463i	−0.143898	+	0.237100i
$118$			8.69691i			0.800615i
$119$	−6.68718	−	1.32955i	−0.613013	−	0.121879i
$120$	−2.19409	+	7.84409i	−0.200292	+	0.716064i
$121$	1.68508			0.153189
$122$	15.9904			1.44771
$123$	−17.4507	−	4.88118i	−1.57348	−	0.440121i
$124$			9.76296i			0.876740i
$125$	−8.47553			−0.758075
$126$	9.20020	−	10.0406i	0.819619	−	0.894491i
$127$	−10.3052			−0.914438			−0.457219	−	0.889354i	$-0.651154\pi$
$127$	−10.3052			−0.914438			−0.457219	+	0.889354i	$0.651154\pi$
$128$			12.4759i			1.10273i
$129$	16.7156	+	4.67556i	1.47173	+	0.411660i
$130$	4.45230			0.390493
$131$	16.4118			1.43391			0.716954	−	0.697120i	$-0.245536\pi$
$131$	16.4118			1.43391			0.716954	+	0.697120i	$0.245536\pi$
$132$	1.34393	−	4.80466i	0.116974	−	0.418192i
$133$	−0.378267	+	1.90256i	−0.0327999	+	0.164973i
$134$		−	4.45297i		−	0.384678i
$135$	−9.21643	−	9.84234i	−0.793224	−	0.847094i
$136$			4.67003i			0.400452i
$137$			15.6821i			1.33981i	0.742446	+	0.669906i	$0.233666\pi$
$137$			15.6821i			1.33981i	−0.742446	+	0.669906i	$0.766334\pi$
$138$	−17.1434	−	4.79524i	−1.45934	−	0.408198i
$139$			17.9897i			1.52587i	0.646476	+	0.762934i	$0.276242\pi$
$139$			17.9897i			1.52587i	−0.646476	+	0.762934i	$0.723758\pi$
$140$	−6.35525	−	1.26355i	−0.537117	−	0.106790i
$141$	4.38769	+	1.22729i	0.369510	+	0.103357i
$142$	7.71053			0.647053
$143$	3.05204			0.255224
$144$	−12.8150	−	7.77757i	−1.06792	−	0.648131i
$145$			1.09091i			0.0905948i
$146$	6.75464			0.559018
$147$	−9.53888	−	7.48396i	−0.786754	−	0.617267i
$148$	−2.19214			−0.180193
$149$		−	17.0065i		−	1.39323i	−0.717447	−	0.696613i	$-0.754689\pi$
$149$		−	17.0065i		−	1.39323i	0.717447	−	0.696613i	$-0.245311\pi$
$150$	−1.38798	+	4.96214i	−0.113328	+	0.405157i
$151$	−4.27119			−0.347584			−0.173792	−	0.984782i	$-0.555602\pi$
$151$	−4.27119			−0.347584			−0.173792	+	0.984782i	$0.555602\pi$
$152$	1.32866			0.107769
$153$	−6.60902	−	4.01108i	−0.534307	−	0.324276i
$154$	−13.5885	−	2.70168i	−1.09500	−	0.217707i
$155$		−	26.8438i		−	2.15614i
$156$	−0.440338	+	1.57425i	−0.0352552	+	0.126041i
$157$		−	18.2365i		−	1.45543i	−0.685880	−	0.727715i	$-0.740583\pi$
$157$		−	18.2365i		−	1.45543i	0.685880	−	0.727715i	$-0.259417\pi$
$158$		−	14.6724i		−	1.16728i
$159$	5.66362	−	20.2480i	0.449154	−	1.60577i
$160$			12.8422i			1.01527i
$161$	−3.09053	+	15.5443i	−0.243568	+	1.22507i
$162$	13.6979	−	7.12828i	1.07621	−	0.560051i
$163$	−15.7225			−1.23148			−0.615742	−	0.787948i	$-0.711144\pi$
$163$	−15.7225			−1.23148			−0.615742	+	0.787948i	$0.711144\pi$
$164$	−9.87369			−0.771006
$165$	−3.69519	+	13.2107i	−0.287670	+	1.02845i
$166$		−	2.14675i		−	0.166620i
$167$	−2.34956			−0.181815			−0.0909073	−	0.995859i	$-0.528977\pi$
$167$	−2.34956			−0.181815			−0.0909073	+	0.995859i	$0.528977\pi$
$168$	−3.75364	+	7.40784i	−0.289600	+	0.571527i
$169$	−1.00000			−0.0769231
$170$			11.4735i			0.879980i
$171$	−1.14118	+	1.88032i	−0.0872686	+	0.143792i
$172$	9.45777			0.721148
$173$	11.7367			0.892321			0.446161	−	0.894953i	$-0.352791\pi$
$173$	11.7367			0.892321			0.446161	+	0.894953i	$0.352791\pi$
$174$	−1.20313	−	0.336530i	−0.0912087	−	0.0255123i
$175$	4.49929	+	0.894550i	0.340115	+	0.0676217i
$176$			15.2505i			1.14955i
$177$	8.45503	+	2.36498i	0.635519	+	0.177763i
$178$		−	13.2405i		−	0.992414i
$179$		−	5.67909i		−	0.424475i	−0.977218	−	0.212237i	$-0.931925\pi$
$179$		−	5.67909i		−	0.424475i	0.977218	−	0.212237i	$-0.0680750\pi$
$180$	−6.28097	−	3.81198i	−0.468156	−	0.284128i
$181$		−	18.9665i		−	1.40977i	−0.709322	−	0.704885i	$-0.750999\pi$
$181$		−	18.9665i		−	1.40977i	0.709322	−	0.704885i	$-0.249001\pi$
$182$	4.45229	+	0.885205i	0.330026	+	0.0656157i
$183$	4.34834	−	15.5457i	0.321438	−	1.14917i
$184$	10.8555			0.800277
$185$	6.02741			0.443144
$186$	29.6051	+	8.28094i	2.17075	+	0.607188i
$187$			7.86506i			0.575150i
$188$	2.48258			0.181061
$189$	−7.25955	−	11.6747i	−0.528055	−	0.849210i
$190$	3.26431			0.236818
$191$			2.23991i			0.162074i	0.996711	+	0.0810369i	$0.0258232\pi$
$191$			2.23991i			0.162074i	−0.996711	+	0.0810369i	$0.974177\pi$
$192$	2.50647	+	0.701091i	0.180889	+	0.0505969i
$193$	−2.18224			−0.157081			−0.0785405	−	0.996911i	$-0.525026\pi$
$193$	−2.18224			−0.157081			−0.0785405	+	0.996911i	$0.525026\pi$
$194$	14.8021			1.06273
$195$	1.21073	−	4.32848i	0.0867022	−	0.309969i
$196$	−6.10401	−	2.52710i	−0.436001	−	0.180507i
$197$		−	16.9270i		−	1.20600i	−0.797741	−	0.603001i	$-0.793972\pi$
$197$		−	16.9270i		−	1.20600i	0.797741	−	0.603001i	$-0.206028\pi$
$198$	−13.4297	−	8.15062i	−0.954407	−	0.579239i
$199$		−	2.98186i		−	0.211378i	−0.994399	−	0.105689i	$-0.966295\pi$
$199$		−	2.98186i		−	0.211378i	0.994399	−	0.105689i	$-0.0337049\pi$
$200$		−	3.14211i		−	0.222181i
$201$	−4.32913	−	1.21091i	−0.305353	−	0.0854112i
$202$			24.8618i			1.74927i
$203$	−0.216894	+	1.09090i	−0.0152229	+	0.0765664i
$204$	−4.05682	−	1.13474i	−0.284034	−	0.0794480i
$205$	27.1482			1.89611
$206$	1.87062			0.130332
$207$	−9.32375	+	15.3627i	−0.648045	+	1.06778i
$208$		−	4.99684i		−	0.346468i
$209$	2.23767			0.154783
$210$	−9.22211	+	18.1999i	−0.636386	+	1.25591i
$211$	27.1711			1.87054			0.935268	−	0.353941i	$-0.115159\pi$
$211$	27.1711			1.87054			0.935268	+	0.353941i	$0.115159\pi$
$212$		−	11.4564i		−	0.786829i
$213$	2.09675	−	7.49609i	0.143667	−	0.513624i
$214$	−18.9906			−1.29817
$215$	−26.0046			−1.77350
$216$	−6.87343	+	6.43633i	−0.467678	+	0.437937i
$217$	5.33707	−	26.8437i	0.362304	−	1.82227i
$218$			12.7707i			0.864942i
$219$	1.83681	−	6.56679i	0.124120	−	0.443742i
$220$			7.47466i			0.503942i
$221$		−	2.57699i		−	0.173347i
$222$	−1.85937	+	6.64744i	−0.124793	+	0.446147i
$223$			22.7088i			1.52069i	0.649518	+	0.760346i	$0.274971\pi$
$223$			22.7088i			1.52069i	−0.649518	+	0.760346i	$0.725029\pi$
$224$	−2.55328	+	12.8422i	−0.170598	+	0.858053i
$225$	4.44670	+	2.69875i	0.296447	+	0.179916i
$226$	−4.47233			−0.297495
$227$	5.03879			0.334436			0.167218	−	0.985920i	$-0.446522\pi$
$227$	5.03879			0.334436			0.167218	+	0.985920i	$0.446522\pi$
$228$	−0.322844	+	1.15420i	−0.0213809	+	0.0764387i
$229$			18.8658i			1.24669i	0.781948	+	0.623344i	$0.214226\pi$
$229$			18.8658i			1.24669i	−0.781948	+	0.623344i	$0.785774\pi$
$230$	26.6702			1.75858
$231$	−6.32172	+	12.4759i	−0.415939	+	0.820857i
$232$	0.761839			0.0500172
$233$			8.32302i			0.545259i	0.962119	+	0.272629i	$0.0878933\pi$
$233$			8.32302i			0.545259i	−0.962119	+	0.272629i	$0.912107\pi$
$234$	4.40025	+	2.67055i	0.287653	+	0.174579i
$235$	−6.82598			−0.445278
$236$	4.78390			0.311406
$237$	−14.2644	−	3.98993i	−0.926571	−	0.259174i
$238$	−2.28116	+	11.4735i	−0.147866	+	0.743716i
$239$			11.3856i			0.736471i	0.929733	+	0.368235i	$0.120038\pi$
$239$			11.3856i			0.736471i	−0.929733	+	0.368235i	$0.879962\pi$
$240$	21.6287	+	6.04983i	1.39613	+	0.390515i
$241$		−	14.8620i		−	0.957347i	−0.877993	−	0.478673i	$-0.841118\pi$
$241$		−	14.8620i		−	0.957347i	0.877993	−	0.478673i	$-0.158882\pi$
$242$		−	2.89117i		−	0.185851i
$243$	−3.20510	−	15.2554i	−0.205607	−	0.978635i
$244$		−	8.79585i		−	0.563097i
$245$	16.7833	+	6.94838i	1.07225	+	0.443916i
$246$	−8.37486	+	29.9409i	−0.533962	+	1.90896i
$247$	−0.733175			−0.0466508
$248$	−18.7464			−1.19040
$249$	−2.08705	−	0.583774i	−0.132261	−	0.0369952i
$250$			14.5418i			0.919707i
$251$	−16.9071			−1.06717			−0.533583	−	0.845748i	$-0.679155\pi$
$251$	−16.9071			−1.06717			−0.533583	+	0.845748i	$0.679155\pi$
$252$	−5.52305	−	5.06075i	−0.347919	−	0.318797i
$253$	18.2823			1.14940
$254$			17.6811i			1.10941i
$255$	11.1544	+	3.12004i	0.698518	+	0.195384i
$256$	18.4002			1.15001
$257$	1.57678			0.0983571			0.0491786	−	0.998790i	$-0.484340\pi$
$257$	1.57678			0.0983571			0.0491786	+	0.998790i	$0.484340\pi$
$258$	8.02207	−	28.6797i	0.499432	−	1.78552i
$259$	6.02739	+	1.19837i	0.374524	+	0.0744629i
$260$		−	2.44908i		−	0.151885i
$261$	−0.654341	+	1.07815i	−0.0405027	+	0.0667359i
$262$		−	28.1585i		−	1.73964i
$263$		−	25.4487i		−	1.56924i	−0.619979	−	0.784618i	$-0.712859\pi$
$263$		−	25.4487i		−	1.56924i	0.619979	−	0.784618i	$-0.287141\pi$
$264$	9.22572	+	2.58055i	0.567804	+	0.158822i
$265$			31.5000i			1.93503i
$266$	3.26430	+	0.649010i	0.200147	+	0.0397933i
$267$	−12.8722	−	3.60053i	−0.787767	−	0.220349i
$268$	−2.44944			−0.149624
$269$	−22.6417			−1.38049			−0.690245	−	0.723576i	$-0.742497\pi$
$269$	−22.6417			−1.38049			−0.690245	+	0.723576i	$0.742497\pi$
$270$	−16.8869	+	15.8130i	−1.02771	+	0.962351i
$271$			3.37865i			0.205238i	0.994721	+	0.102619i	$0.0327223\pi$
$271$			3.37865i			0.205238i	−0.994721	+	0.102619i	$0.967278\pi$
$272$	12.8768			0.780771
$273$	2.07131	−	4.08775i	0.125362	−	0.247402i
$274$	26.9065			1.62548
$275$		−	5.29180i		−	0.319107i
$276$	−2.63771	+	9.43007i	−0.158772	+	0.567624i
$277$	−20.8446			−1.25243			−0.626216	−	0.779650i	$-0.715397\pi$
$277$	−20.8446			−1.25243			−0.626216	+	0.779650i	$0.715397\pi$
$278$	30.8658			1.85121
$279$	16.1013	−	26.5299i	0.963958	−	1.58830i
$280$	2.42622	−	12.2031i	0.144995	−	0.729275i
$281$			3.38843i			0.202137i	0.994879	+	0.101069i	$0.0322261\pi$
$281$			3.38843i			0.202137i	−0.994879	+	0.101069i	$0.967774\pi$
$282$	2.10572	−	7.52816i	0.125394	−	0.448295i
$283$			28.2948i			1.68195i	0.541074	+	0.840975i	$0.318018\pi$
$283$			28.2948i			1.68195i	−0.541074	+	0.840975i	$0.681982\pi$
$284$		−	4.24133i		−	0.251676i
$285$	0.887677	−	3.17353i	0.0525814	−	0.187984i
$286$		−	5.23651i		−	0.309641i
$287$	27.1481	+	5.39760i	1.60250	+	0.318610i
$288$	−7.70293	+	12.6921i	−0.453900	+	0.747886i
$289$	−10.3591			−0.609361
$290$	1.87172			0.109911
$291$	4.02518	−	14.3904i	0.235960	−	0.843580i
$292$		−	3.71552i		−	0.217435i
$293$	6.57320			0.384010			0.192005	−	0.981394i	$-0.438501\pi$
$293$	6.57320			0.384010			0.192005	+	0.981394i	$0.438501\pi$
$294$	−12.8406	+	16.3663i	−0.748877	+	0.954501i
$295$	−13.1536			−0.765831
$296$		−	4.20926i		−	0.244659i
$297$	−11.5759	+	10.8398i	−0.671703	+	0.628987i
$298$	−29.1788			−1.69028
$299$	−5.99021			−0.346423
$300$	2.72952	+	0.763483i	0.157589	+	0.0440797i
$301$	−26.0045	−	5.17023i	−1.49888	−	0.298007i
$302$			7.32826i			0.421694i
$303$	24.1704	+	6.76076i	1.38855	+	0.388395i
$304$		−	3.66356i		−	0.210119i
$305$			24.1846i			1.38481i
$306$	−6.88198	+	11.3394i	−0.393417	+	0.648229i
$307$		−	6.47195i		−	0.369373i	−0.982797	−	0.184687i	$-0.940873\pi$
$307$		−	6.47195i		−	0.369373i	0.982797	−	0.184687i	$-0.0591270\pi$
$308$	−1.48611	+	7.47464i	−0.0846790	+	0.425907i
$309$	0.508684	−	1.81859i	0.0289380	−	0.103456i
$310$	−46.0570			−2.61586
$311$	0.370213			0.0209929			0.0104964	−	0.999945i	$-0.496659\pi$
$311$	0.370213			0.0209929			0.0104964	+	0.999945i	$0.496659\pi$
$312$	−3.02281	−	0.845518i	−0.171133	−	0.0478680i
$313$			2.83228i			0.160090i	0.996791	+	0.0800450i	$0.0255064\pi$
$313$			2.83228i			0.160090i	−0.996791	+	0.0800450i	$0.974494\pi$
$314$	−31.2891			−1.76575
$315$	15.1859	+	13.9148i	0.855629	+	0.784009i
$316$	−8.07086			−0.454021
$317$		−	13.0738i		−	0.734299i	−0.930162	−	0.367149i	$-0.880334\pi$
$317$		−	13.0738i		−	0.734299i	0.930162	−	0.367149i	$-0.119666\pi$
$318$	−34.7403	−	9.71732i	−1.94814	−	0.544920i
$319$	1.28305			0.0718372
$320$	−3.89934			−0.217980
$321$	−5.16420	+	18.4625i	−0.288237	+	1.03048i
$322$	26.6701	+	5.30256i	1.48627	+	0.295500i
$323$		−	1.88938i		−	0.105128i
$324$	−3.92105	−	7.53482i	−0.217836	−	0.418601i
$325$			1.73386i			0.0961772i
$326$			26.9758i			1.49405i
$327$	12.4155	+	3.47279i	0.686581	+	0.192046i
$328$		−	18.9591i		−	1.04684i
$329$	−6.82596	−	1.35714i	−0.376327	−	0.0748215i
$330$	22.6661	+	6.34001i	1.24773	+	0.349006i
$331$	0.549743			0.0302166			0.0151083	−	0.999886i	$-0.495191\pi$
$331$	0.549743			0.0302166			0.0151083	+	0.999886i	$0.495191\pi$
$332$	−1.18086			−0.0648083
$333$	5.95694	+	3.61532i	0.326438	+	0.198119i
$334$			4.03125i			0.220580i
$335$	6.73487			0.367965
$336$	20.4258	+	10.3500i	1.11432	+	0.564640i
$337$	−4.72754			−0.257525			−0.128763	−	0.991675i	$-0.541101\pi$
$337$	−4.72754			−0.257525			−0.128763	+	0.991675i	$0.541101\pi$
$338$			1.71574i			0.0933242i
$339$	−1.21618	+	4.34795i	−0.0660536	+	0.236148i
$340$	6.31124			0.342275
$341$	−31.5719			−1.70972
$342$	3.22615	+	1.95798i	0.174450	+	0.105876i
$343$	15.4018	+	10.2852i	0.831617	+	0.555349i
$344$			18.1604i			0.979145i
$345$	7.25253	−	25.9285i	0.390463	−	1.39594i
$346$		−	20.1371i		−	1.08258i
$347$		−	20.1509i		−	1.08176i	−0.841101	−	0.540878i	$-0.818092\pi$
$347$		−	20.1509i		−	1.08176i	0.841101	−	0.540878i	$-0.181908\pi$
$348$	−0.185115	+	0.661803i	−0.00992320	+	0.0354764i
$349$		−	32.3305i		−	1.73061i	−0.501244	−	0.865306i	$-0.667124\pi$
$349$		−	32.3305i		−	1.73061i	0.501244	−	0.865306i	$-0.332876\pi$
$350$	1.53482	−	7.71964i	0.0820396	−	0.412632i
$351$	3.79286	−	3.55165i	0.202448	−	0.189573i
$352$	15.1042			0.805055
$353$	4.91786			0.261751			0.130876	−	0.991399i	$-0.458221\pi$
$353$	4.91786			0.261751			0.130876	+	0.991399i	$0.458221\pi$
$354$	4.05770	−	14.5067i	0.215665	−	0.771021i
$355$			11.6617i			0.618941i
$356$	−7.28317			−0.386007
$357$	10.5341	+	5.33775i	0.557522	+	0.282504i
$358$	−9.74386			−0.514979
$359$		−	2.99417i		−	0.158026i	−0.996874	−	0.0790132i	$-0.974823\pi$
$359$		−	2.99417i		−	0.158026i	0.996874	−	0.0790132i	$-0.0251769\pi$
$360$	7.31961	−	12.0605i	0.385777	−	0.635642i
$361$	18.4625			0.971708
$362$	−32.5417			−1.71035
$363$	−2.81076	−	0.786206i	−0.147527	−	0.0412651i
$364$	0.486924	−	2.44907i	0.0255218	−	0.128366i
$365$			10.2160i			0.534731i
$366$	−26.6725	−	7.46063i	−1.39419	−	0.389974i
$367$			9.50327i			0.496067i	0.968751	+	0.248033i	$0.0797843\pi$
$367$			9.50327i			0.496067i	−0.968751	+	0.248033i	$0.920216\pi$
$368$		−	29.9321i		−	1.56032i
$369$	26.8308	+	16.2839i	1.39676	+	0.847705i
$370$		−	10.3415i		−	0.537629i
$371$	−6.26281	+	31.4999i	−0.325149	+	1.63539i
$372$	4.55509	−	16.2849i	0.236171	−	0.844332i
$373$	1.28860			0.0667214			0.0333607	−	0.999443i	$-0.489379\pi$
$373$	1.28860			0.0667214			0.0333607	+	0.999443i	$0.489379\pi$
$374$	13.4944			0.697780
$375$	14.1374	+	3.95442i	0.730053	+	0.204205i
$376$			4.76695i			0.245837i
$377$	−0.420393			−0.0216513
$378$	−20.0308	+	12.4555i	−1.03027	+	0.640644i
$379$	15.0342			0.772256			0.386128	−	0.922445i	$-0.373812\pi$
$379$	15.0342			0.772256			0.386128	+	0.922445i	$0.373812\pi$
$380$		−	1.79560i		−	0.0921123i
$381$	17.1893	+	4.80808i	0.880636	+	0.246325i
$382$	3.84310			0.196630
$383$	−16.6524			−0.850897			−0.425449	−	0.904983i	$-0.639884\pi$
$383$	−16.6524			−0.850897			−0.425449	+	0.904983i	$0.639884\pi$
$384$	5.82088	−	20.8102i	0.297046	−	1.06197i
$385$	4.08613	−	20.5519i	0.208249	−	1.04742i
$386$			3.74416i			0.190573i
$387$	−25.7006	−	15.5979i	−1.30643	−	0.792888i
$388$		−	8.14217i		−	0.413356i
$389$			10.6804i			0.541518i	0.962647	+	0.270759i	$0.0872746\pi$
$389$			10.6804i			0.541518i	−0.962647	+	0.270759i	$0.912725\pi$
$390$	−7.42656	−	2.07730i	−0.376058	−	0.105188i
$391$		−	15.4367i		−	0.780667i
$392$	4.85243	−	11.7207i	0.245085	−	0.591984i
$393$	−27.3754	−	7.65725i	−1.38091	−	0.386257i
$394$	−29.0425			−1.46314
$395$	22.1912			1.11656
$396$	−4.48341	+	7.38727i	−0.225300	+	0.371224i
$397$		−	28.0511i		−	1.40784i	−0.710278	−	0.703922i	$-0.751431\pi$
$397$		−	28.0511i		−	1.40784i	0.710278	−	0.703922i	$-0.248569\pi$
$398$	−5.11611			−0.256447
$399$	1.51863	−	2.99703i	0.0760268	−	0.150039i
$400$	−8.66381			−0.433191
$401$		−	23.5615i		−	1.17661i	−0.808641	−	0.588303i	$-0.799796\pi$
$401$		−	23.5615i		−	1.17661i	0.808641	−	0.588303i	$-0.200204\pi$
$402$	−2.07762	+	7.42768i	−0.103622	+	0.370459i
$403$	10.3445			0.515299
$404$	13.6757			0.680392
$405$	10.7811	+	20.7174i	0.535718	+	1.02945i
$406$	1.87171	+	0.372134i	0.0928914	+	0.0184687i
$407$		−	7.08905i		−	0.351391i
$408$	2.17889	−	7.78974i	0.107871	−	0.385650i
$409$		−	37.0914i		−	1.83405i	−0.398827	−	0.917026i	$-0.630583\pi$
$409$		−	37.0914i		−	1.83405i	0.398827	−	0.917026i	$-0.369417\pi$
$410$		−	46.5794i		−	2.30039i
$411$	7.31678	−	26.1582i	0.360910	−	1.29029i
$412$		−	1.02897i		−	0.0506937i
$413$	−13.1535	−	2.61519i	−0.647244	−	0.128685i
$414$	26.3584	+	15.9972i	1.29544	+	0.786218i
$415$	3.24684			0.159381
$416$	−4.94889			−0.242639
$417$	8.39344	−	30.0074i	0.411029	−	1.46947i
$418$		−	3.83928i		−	0.187785i
$419$	−18.4391			−0.900807			−0.450404	−	0.892825i	$-0.648720\pi$
$419$	−18.4391			−0.900807			−0.450404	+	0.892825i	$0.648720\pi$
$420$	10.0112	+	5.07280i	0.488496	+	0.247527i
$421$	−10.1576			−0.495050			−0.247525	−	0.968881i	$-0.579617\pi$
$421$	−10.1576			−0.495050			−0.247525	+	0.968881i	$0.579617\pi$
$422$		−	46.6187i		−	2.26936i
$423$	−6.74617	−	4.09432i	−0.328010	−	0.199073i
$424$	21.9981			1.06832
$425$	−4.46813			−0.216736
$426$	−12.8614	−	3.59749i	−0.623135	−	0.174299i
$427$	−4.80838	+	24.1846i	−0.232694	+	1.17037i
$428$			10.4462i			0.504935i
$429$	−5.09088	−	1.42398i	−0.245790	−	0.0687506i
$430$			44.6173i			2.15164i
$431$			17.1864i			0.827842i	0.910313	+	0.413921i	$0.135841\pi$
$431$			17.1864i			0.827842i	−0.910313	+	0.413921i	$0.864159\pi$
$432$	17.7470	+	18.9523i	0.853855	+	0.911842i
$433$			21.6473i			1.04030i	0.854074	+	0.520152i	$0.174125\pi$
$433$			21.6473i			1.04030i	−0.854074	+	0.520152i	$0.825875\pi$
$434$	−46.0569	−	9.15704i	−2.21080	−	0.439552i
$435$	0.508983	−	1.81966i	0.0244039	−	0.0872461i
$436$	7.02478			0.336426
$437$	−4.39187			−0.210092
$438$	−11.2669	−	3.15150i	−0.538355	−	0.150585i
$439$		−	6.65071i		−	0.317421i	−0.987325	−	0.158711i	$-0.949266\pi$
$439$		−	6.65071i		−	0.317421i	0.987325	−	0.158711i	$-0.0507337\pi$
$440$	−14.3525			−0.684231
$441$	12.4193	+	16.9340i	0.591397	+	0.806381i
$442$	−4.42145			−0.210307
$443$		−	31.0647i		−	1.47593i	−0.674840	−	0.737964i	$-0.735788\pi$
$443$		−	31.0647i		−	1.47593i	0.674840	−	0.737964i	$-0.264212\pi$
$444$	3.65655	+	1.02279i	0.173532	+	0.0485392i
$445$	20.0255			0.949298
$446$	38.9624			1.84493
$447$	−7.93470	+	28.3673i	−0.375298	+	1.34173i
$448$	−3.89932	−	0.775265i	−0.184226	−	0.0366278i
$449$		−	9.60903i		−	0.453478i	−0.973956	−	0.226739i	$-0.927194\pi$
$449$		−	9.60903i		−	0.453478i	0.973956	−	0.226739i	$-0.0728065\pi$
$450$	4.63036	−	7.62940i	0.218277	−	0.359654i
$451$		−	31.9300i		−	1.50353i
$452$			2.46009i			0.115713i
$453$	7.12445	+	1.99280i	0.334736	+	0.0936300i
$454$		−	8.64527i		−	0.405743i
$455$	−1.33882	+	6.73384i	−0.0627650	+	0.315687i
$456$	−2.21625	−	0.619913i	−0.103785	−	0.0290301i
$457$	−9.05741			−0.423688			−0.211844	−	0.977304i	$-0.567947\pi$
$457$	−9.05741			−0.423688			−0.211844	+	0.977304i	$0.567947\pi$
$458$	32.3689			1.51250
$459$	9.15257	+	9.77414i	0.427206	+	0.456218i
$460$		−	14.6705i		−	0.684014i
$461$	37.1625			1.73083			0.865415	−	0.501056i	$-0.167055\pi$
$461$	37.1625			1.73083			0.865415	+	0.501056i	$0.167055\pi$
$462$	21.4055	+	10.8465i	0.995875	+	0.504623i
$463$	−23.6898			−1.10096			−0.550478	−	0.834850i	$-0.685555\pi$
$463$	−23.6898			−1.10096			−0.550478	+	0.834850i	$0.685555\pi$
$464$		−	2.10064i		−	0.0975196i
$465$	−12.5245	+	44.7761i	−0.580808	+	2.07644i
$466$	14.2802			0.661516
$467$	−31.2672			−1.44688			−0.723438	−	0.690390i	$-0.757439\pi$
$467$	−31.2672			−1.44688			−0.723438	+	0.690390i	$0.757439\pi$
$468$	1.46899	−	2.42044i	0.0679041	−	0.111885i
$469$	6.73485	+	1.33902i	0.310987	+	0.0618304i
$470$			11.7116i			0.540218i
$471$	−8.50857	+	30.4189i	−0.392054	+	1.40163i
$472$			9.18586i			0.422813i
$473$			30.5850i			1.40630i
$474$	−6.84570	+	24.4740i	−0.314433	+	1.12413i
$475$			1.27122i			0.0583276i
$476$	6.31122	+	1.25480i	0.289274	+	0.0575136i
$477$	−18.8941	+	31.1317i	−0.865103	+	1.42542i
$478$	19.5347			0.893497
$479$	−10.1389			−0.463257			−0.231629	−	0.972804i	$-0.574405\pi$
$479$	−10.1389			−0.463257			−0.231629	+	0.972804i	$0.574405\pi$
$480$	5.99177	−	21.4211i	0.273486	−	0.977737i
$481$			2.32273i			0.105907i
$482$	−25.4994			−1.16147
$483$	12.4076	−	24.4864i	0.564565	−	1.11417i
$484$	−1.59034			−0.0722884
$485$			22.3873i			1.01656i
$486$	−26.1744	+	5.49913i	−1.18729	+	0.249446i
$487$	−34.8841			−1.58075			−0.790374	−	0.612625i	$-0.790114\pi$
$487$	−34.8841			−1.58075			−0.790374	+	0.612625i	$0.790114\pi$
$488$	16.8894			0.764549
$489$	26.2256	+	7.33564i	1.18596	+	0.331729i
$490$	11.9216	−	28.7958i	0.538565	−	1.30086i
$491$			9.88521i			0.446113i	0.974805	+	0.223057i	$0.0716035\pi$
$491$			9.88521i			0.446113i	−0.974805	+	0.223057i	$0.928396\pi$
$492$	16.4696	+	4.60676i	0.742506	+	0.207689i
$493$		−	1.08335i		−	0.0487915i
$494$			1.25794i			0.0565974i
$495$	12.3274	−	20.3117i	0.554074	−	0.912942i
$496$			51.6900i			2.32095i
$497$	−2.31858	+	11.6617i	−0.104003	+	0.523099i
$498$	−1.00161	+	3.58084i	−0.0448831	+	0.160461i
$499$	5.22157			0.233750			0.116875	−	0.993147i	$-0.462712\pi$
$499$	5.22157			0.233750			0.116875	+	0.993147i	$0.462712\pi$
$500$	7.99903			0.357727
$501$	3.91913	+	1.09623i	0.175094	+	0.0489760i
$502$			29.0083i			1.29470i
$503$	5.14174			0.229259			0.114629	−	0.993408i	$-0.463432\pi$
$503$	5.14174			0.229259			0.114629	+	0.993408i	$0.463432\pi$
$504$	9.71744	−	10.6051i	0.432849	−	0.472390i
$505$	−37.6021			−1.67327
$506$		−	31.3678i		−	1.39447i
$507$	1.66803	+	0.466569i	0.0740797	+	0.0207210i
$508$	9.72582			0.431513
$509$	−17.9037			−0.793567			−0.396784	−	0.917912i	$-0.629874\pi$
$509$	−17.9037			−0.793567			−0.396784	+	0.917912i	$0.629874\pi$
$510$	5.35319	−	19.1382i	0.237043	−	0.847452i
$511$	−2.03115	+	10.2160i	−0.0898526	+	0.451929i
$512$		−	6.61819i		−	0.292485i
$513$	2.78083	−	2.60398i	0.122776	−	0.114969i
$514$		−	2.70536i		−	0.119328i
$515$			2.82921i			0.124670i
$516$	−15.7758	−	4.41270i	−0.694491	−	0.194258i
$517$			8.02828i			0.353083i
$518$	2.05609	−	10.3415i	0.0903395	−	0.454378i
$519$	−19.5770	−	5.47595i	−0.859337	−	0.240368i
$520$	4.70262			0.206223
$521$	14.3929			0.630563			0.315282	−	0.948998i	$-0.397901\pi$
$521$	14.3929			0.630563			0.315282	+	0.948998i	$0.397901\pi$
$522$	1.84983	+	1.12268i	0.0809650	+	0.0491384i
$523$		−	35.8357i		−	1.56699i	−0.621400	−	0.783493i	$-0.713436\pi$
$523$		−	35.8357i		−	1.56699i	0.621400	−	0.783493i	$-0.286564\pi$
$524$	−15.4891			−0.676646
$525$	−7.08757	−	3.59136i	−0.309327	−	0.156740i
$526$	−43.6635			−1.90382
$527$			26.6578i			1.16123i
$528$	7.11542	−	25.4383i	0.309659	−	1.10706i
$529$	−12.8826			−0.560112
$530$	54.0459			2.34760
$531$	−12.9998	−	7.88971i	−0.564143	−	0.342384i
$532$	0.357000	−	1.79559i	0.0154779	−	0.0778489i
$533$			10.4619i			0.453154i
$534$	−6.17758	+	22.0854i	−0.267330	+	0.955731i
$535$		−	28.7223i		−	1.24177i
$536$		−	4.70332i		−	0.203153i
$537$	−2.64968	+	9.47287i	−0.114342	+	0.408785i
$538$			38.8474i			1.67483i
$539$	8.17224	−	19.7394i	0.352003	−	0.850238i
$540$	8.69827	+	9.28899i	0.374314	+	0.399734i
$541$	−36.7113			−1.57834			−0.789171	−	0.614173i	$-0.789490\pi$
$541$	−36.7113			−1.57834			−0.789171	+	0.614173i	$0.789490\pi$
$542$	5.79690			0.248998
$543$	−8.84918	+	31.6367i	−0.379755	+	1.35766i
$544$		−	12.7532i		−	0.546790i
$545$	−19.3150			−0.827364
$546$	−7.01353	−	3.55384i	−0.300151	−	0.152090i
$547$	−19.7408			−0.844058			−0.422029	−	0.906582i	$-0.638682\pi$
$547$	−19.7408			−0.844058			−0.422029	+	0.906582i	$0.638682\pi$
$548$		−	14.8004i		−	0.632243i
$549$	−14.5063	+	23.9019i	−0.619113	+	1.02011i
$550$	−9.07937			−0.387146
$551$	−0.308221			−0.0131307
$552$	−18.1072	−	5.06483i	−0.770696	−	0.215573i
$553$	22.1912	+	4.41205i	0.943665	+	0.187620i
$554$			35.7640i			1.51947i
$555$	−10.0539	−	2.81220i	−0.426763	−	0.119371i
$556$		−	16.9783i		−	0.720041i
$557$			19.4559i			0.824372i	0.911100	+	0.412186i	$0.135235\pi$
$557$			19.4559i			0.824372i	−0.911100	+	0.412186i	$0.864765\pi$
$558$	−45.5185	−	27.6257i	−1.92695	−	1.16949i
$559$		−	10.0212i		−	0.423850i
$560$	−33.6479	−	6.68988i	−1.42188	−	0.282699i
$561$	3.66959	−	13.1191i	0.154930	−	0.553890i
$562$	5.81369			0.245236
$563$	−8.46238			−0.356647			−0.178323	−	0.983972i	$-0.557067\pi$
$563$	−8.46238			−0.356647			−0.178323	+	0.983972i	$0.557067\pi$
$564$	−4.14101	−	1.15829i	−0.174368	−	0.0487730i
$565$		−	6.76415i		−	0.284570i
$566$	48.5466			2.04057
$567$	6.66207	+	22.8608i	0.279781	+	0.960064i
$568$	8.14403			0.341716
$569$		−	23.7664i		−	0.996339i	−0.867080	−	0.498169i	$-0.834006\pi$
$569$		−	23.7664i		−	0.996339i	0.867080	−	0.498169i	$-0.165994\pi$
$570$	−5.44496	−	1.52303i	−0.228064	−	0.0637926i
$571$	14.2965			0.598290			0.299145	−	0.954208i	$-0.403299\pi$
$571$	14.2965			0.598290			0.299145	+	0.954208i	$0.403299\pi$
$572$	−2.88045			−0.120437
$573$	1.04507	−	3.73622i	0.0436584	−	0.156083i
$574$	9.26090	−	46.5793i	0.386543	−	1.94418i
$575$			10.3862i			0.433133i
$576$	−3.85375	−	2.33888i	−0.160573	−	0.0974532i
$577$		−	23.4326i		−	0.975512i	−0.872980	−	0.487756i	$-0.837816\pi$
$577$		−	23.4326i		−	0.975512i	0.872980	−	0.487756i	$-0.162184\pi$
$578$			17.7736i			0.739285i
$579$	3.64003	+	1.01816i	0.151275	+	0.0423135i
$580$		−	1.02957i		−	0.0427507i
$581$	3.24683	+	0.645536i	0.134701	+	0.0267814i
$582$	−24.6903	−	6.90618i	−1.02344	−	0.286270i
$583$	37.0483			1.53438
$584$	7.13440			0.295223
$585$	−4.03906	+	6.65513i	−0.166995	+	0.275156i
$586$		−	11.2779i		−	0.465887i
$587$	43.1928			1.78276			0.891380	−	0.453258i	$-0.149738\pi$
$587$	43.1928			1.78276			0.891380	+	0.453258i	$0.149738\pi$
$588$	9.00259	+	7.06321i	0.371261	+	0.291282i
$589$	7.58436			0.312508
$590$			22.5682i			0.929118i
$591$	−7.89762	+	28.2348i	−0.324865	+	1.16142i
$592$	−11.6063			−0.477016
$593$	19.4621			0.799214			0.399607	−	0.916687i	$-0.369147\pi$
$593$	19.4621			0.799214			0.399607	+	0.916687i	$0.369147\pi$
$594$	18.5983	+	19.8613i	0.763097	+	0.814920i
$595$	−17.3530	−	3.45013i	−0.711405	−	0.141442i
$596$			16.0504i			0.657449i
$597$	−1.39124	+	4.97382i	−0.0569397	+	0.203565i
$598$			10.2777i			0.420285i
$599$		−	10.1945i		−	0.416535i	−0.978072	−	0.208267i	$-0.933218\pi$
$599$		−	10.1945i		−	0.416535i	0.978072	−	0.208267i	$-0.0667824\pi$
$600$	−1.46601	+	5.24112i	−0.0598496	+	0.213968i
$601$		−	33.0367i		−	1.34759i	−0.738916	−	0.673797i	$-0.764662\pi$
$601$		−	33.0367i		−	1.34759i	0.738916	−	0.673797i	$-0.235338\pi$
$602$	−8.87079	+	44.6171i	−0.361546	+	1.81846i
$603$	6.65613	+	4.03967i	0.271059	+	0.164508i
$604$	4.03105			0.164021
$605$	4.37273			0.177777
$606$	11.5997	−	41.4701i	0.471207	−	1.68461i
$607$			40.8934i			1.65981i	0.557903	+	0.829906i	$0.311606\pi$
$607$			40.8934i			1.65981i	−0.557903	+	0.829906i	$0.688394\pi$
$608$	−3.62840			−0.147151
$609$	0.870765	−	1.71846i	0.0352852	−	0.0696355i
$610$	41.4947			1.68007
$611$		−	2.63047i		−	0.106417i
$612$	6.23745	+	3.78557i	0.252134	+	0.153023i
$613$	46.7817			1.88950			0.944748	−	0.327797i	$-0.106306\pi$
$613$	46.7817			1.88950			0.944748	+	0.327797i	$0.106306\pi$
$614$	−11.1042			−0.448129
$615$	−45.2840	−	12.6665i	−1.82603	−	0.510763i
$616$	−14.3525	−	2.85357i	−0.578279	−	0.114974i
$617$			1.23541i			0.0497359i	0.999691	+	0.0248679i	$0.00791653\pi$
$617$			1.23541i			0.0497359i	−0.999691	+	0.0248679i	$0.992083\pi$
$618$	−3.12024	−	0.872772i	−0.125515	−	0.0351080i
$619$			31.1847i			1.25342i	0.779254	+	0.626709i	$0.215598\pi$
$619$			31.1847i			1.25342i	−0.779254	+	0.626709i	$0.784402\pi$
$620$			25.3346i			1.01746i
$621$	22.7200	−	21.2751i	0.911722	−	0.853742i
$622$		−	0.635192i		−	0.0254689i
$623$	20.0254	+	3.98145i	0.802300	+	0.159514i
$624$	−2.33137	+	8.33486i	−0.0933294	+	0.333662i
$625$	−30.6630			−1.22652
$626$	4.85947			0.194223
$627$	−3.73250	−	1.04403i	−0.149062	−	0.0416945i
$628$			17.2112i			0.686801i
$629$	−5.98565			−0.238663
$630$	23.8742	−	26.0551i	0.951172	−	1.03806i
$631$	30.5729			1.21709			0.608544	−	0.793520i	$-0.291754\pi$
$631$	30.5729			1.21709			0.608544	+	0.793520i	$0.291754\pi$
$632$		−	15.4973i		−	0.616451i
$633$	−45.3221	−	12.6772i	−1.80139	−	0.503873i
$634$	−22.4313			−0.890862
$635$	−26.7416			−1.06121
$636$	−5.34520	+	19.1096i	−0.211951	+	0.757745i
$637$	−2.67764	+	6.46763i	−0.106092	+	0.256257i
$638$		−	2.20139i		−	0.0871540i
$639$	−6.99488	+	11.5254i	−0.276713	+	0.455938i
$640$			32.3747i			1.27972i
$641$		−	12.4066i		−	0.490032i	−0.969519	−	0.245016i	$-0.921207\pi$
$641$		−	12.4066i		−	0.490032i	0.969519	−	0.245016i	$-0.0787932\pi$
$642$	31.6769	+	8.86044i	1.25019	+	0.349694i
$643$			1.52341i			0.0600773i	0.999549	+	0.0300387i	$0.00956304\pi$
$643$			1.52341i			0.0600773i	−0.999549	+	0.0300387i	$0.990437\pi$
$644$	2.91678	−	14.6704i	0.114937	−	0.578096i
$645$	43.3764	+	12.1329i	1.70794	+	0.477734i
$646$	−3.24170			−0.127543
$647$	43.4797			1.70936			0.854682	−	0.519152i	$-0.173752\pi$
$647$	43.4797			1.70936			0.854682	+	0.519152i	$0.173752\pi$
$648$	14.4681	−	7.52904i	0.568359	−	0.295769i
$649$			15.4704i			0.607267i
$650$	2.97486			0.116684
$651$	−21.4268	+	42.2859i	−0.839782	+	1.65731i
$652$	14.8386			0.581124
$653$			20.4120i			0.798783i	0.916780	+	0.399392i	$0.130779\pi$
$653$			20.4120i			0.798783i	−0.916780	+	0.399392i	$0.869221\pi$
$654$	5.95842	−	21.3019i	0.232992	−	0.832970i
$655$	42.5882			1.66406
$656$	−52.2763			−2.04105
$657$	−6.12771	+	10.0966i	−0.239065	+	0.393905i
$658$	−2.32850	+	11.7116i	−0.0907745	+	0.456566i
$659$		−	6.29533i		−	0.245231i	−0.992454	−	0.122616i	$-0.960872\pi$
$659$		−	6.29533i		−	0.245231i	0.992454	−	0.122616i	$-0.0391282\pi$
$660$	3.48744	−	12.4679i	0.135749	−	0.485314i
$661$			19.0363i			0.740425i	0.928947	+	0.370213i	$0.120715\pi$
$661$			19.0363i			0.740425i	−0.928947	+	0.370213i	$0.879285\pi$
$662$		−	0.943218i		−	0.0366592i
$663$	−1.20234	+	4.29849i	−0.0466951	+	0.166939i
$664$		−	2.26745i		−	0.0879940i
$665$	−0.981591	+	4.93708i	−0.0380645	+	0.191452i
$666$	6.20297	−	10.2206i	0.240360	−	0.396039i
$667$	−2.51824			−0.0975067
$668$	2.21747			0.0857963
$669$	10.5952	−	37.8788i	0.409634	−	1.46448i
$670$		−	11.5553i		−	0.446421i
$671$	28.4444			1.09808
$672$	10.2507	−	20.2298i	0.395429	−	0.780381i
$673$	35.9421			1.38546			0.692732	−	0.721195i	$-0.256407\pi$
$673$	35.9421			1.38546			0.692732	+	0.721195i	$0.256407\pi$
$674$			8.11124i			0.312433i
$675$	−6.15807	−	6.57627i	−0.237024	−	0.253121i
$676$	0.943779			0.0362992
$677$	11.4136			0.438658			0.219329	−	0.975651i	$-0.429613\pi$
$677$	11.4136			0.438658			0.219329	+	0.975651i	$0.429613\pi$
$678$	7.45996	+	2.08665i	0.286498	+	0.0801372i
$679$	−4.45103	+	22.3872i	−0.170815	+	0.859143i
$680$			12.1186i			0.464727i
$681$	−8.40483	−	2.35094i	−0.322074	−	0.0900882i
$682$			54.1693i			2.07425i
$683$		−	32.0602i		−	1.22675i	−0.789792	−	0.613375i	$-0.789812\pi$
$683$		−	32.0602i		−	1.22675i	0.789792	−	0.613375i	$-0.210188\pi$
$684$	1.07703	−	1.77461i	0.0411811	−	0.0678537i
$685$			40.6946i			1.55486i
$686$	17.6468	−	26.4255i	0.673758	−	1.00893i
$687$	8.80220	−	31.4687i	0.335825	−	1.20061i
$688$	50.0742			1.90906
$689$	−12.1389			−0.462454
$690$	−44.4866	−	12.4435i	−1.69358	−	0.473715i
$691$		−	2.31381i		−	0.0880216i	−0.999031	−	0.0440108i	$-0.985986\pi$
$691$		−	2.31381i		−	0.0880216i	0.999031	−	0.0440108i	$-0.0140136\pi$
$692$	−11.0768			−0.421077
$693$	16.3657	−	17.8607i	0.621681	−	0.678472i
$694$	−34.5737			−1.31240
$695$			46.6828i			1.77078i
$696$	−1.27077	−	0.355450i	−0.0481683	−	0.0134733i
$697$	−26.9601			−1.02119
$698$	−55.4709			−2.09960
$699$	3.88326	−	13.8830i	0.146878	−	0.525104i
$700$	−4.24634	−	0.844258i	−0.160496	−	0.0319099i
$701$		−	9.15259i		−	0.345689i	−0.984949	−	0.172844i	$-0.944704\pi$
$701$		−	9.15259i		−	0.345689i	0.984949	−	0.172844i	$-0.0552957\pi$
$702$	−6.09373	−	6.50757i	−0.229993	−	0.245612i
$703$			1.70297i			0.0642286i
$704$			4.58615i			0.172847i
$705$	11.3859	+	3.18479i	0.428819	+	0.119946i
$706$		−	8.43778i		−	0.317560i
$707$	−37.6020	−	7.47603i	−1.41417	−	0.281165i
$708$	−7.97968	−	2.23202i	−0.299895	−	0.0838844i
$709$	−9.28551			−0.348725			−0.174362	−	0.984682i	$-0.555786\pi$
$709$	−9.28551			−0.348725			−0.174362	+	0.984682i	$0.555786\pi$
$710$	20.0086			0.750909
$711$	21.9318	+	13.3106i	0.822506	+	0.499187i
$712$		−	13.9849i		−	0.524105i
$713$	61.9660			2.32064
$714$	9.15821	−	18.0738i	0.342737	−	0.676394i
$715$	7.91993			0.296189
$716$			5.35980i			0.200305i
$717$	5.31215	−	18.9914i	0.198386	−	0.709248i
$718$	−5.13724			−0.191720
$719$	10.5091			0.391922			0.195961	−	0.980612i	$-0.437217\pi$
$719$	10.5091			0.391922			0.195961	+	0.980612i	$0.437217\pi$
$720$	−33.2546	−	20.1825i	−1.23933	−	0.752159i
$721$	−0.562502	+	2.82920i	−0.0209487	+	0.105365i
$722$		−	31.6769i		−	1.17889i
$723$	−6.93415	+	24.7902i	−0.257884	+	0.921959i
$724$			17.9002i			0.665255i
$725$			0.728902i			0.0270707i
$726$	−1.34893	+	4.82255i	−0.0500635	+	0.178982i
$727$		−	5.54496i		−	0.205651i	−0.994699	−	0.102826i	$-0.967212\pi$
$727$		−	5.54496i		−	0.205651i	0.994699	−	0.102826i	$-0.0327884\pi$
$728$	4.70260	+	0.934972i	0.174290	+	0.0346524i
$729$	−1.77150	+	26.9418i	−0.0656111	+	0.997845i
$730$	17.5281			0.648743
$731$	25.8244			0.955152
$732$	−4.10387	+	14.6717i	−0.151683	+	0.542282i
$733$		−	20.1559i		−	0.744474i	−0.928138	−	0.372237i	$-0.878591\pi$
$733$		−	20.1559i		−	0.744474i	0.928138	−	0.372237i	$-0.121409\pi$
$734$	16.3052			0.601835
$735$	−24.7531	−	19.4206i	−0.913032	−	0.716341i
$736$	−29.6449			−1.09272
$737$		−	7.92113i		−	0.291778i
$738$	27.9390	−	46.0348i	1.02845	−	1.69456i
$739$	−18.5892			−0.683815			−0.341907	−	0.939734i	$-0.611073\pi$
$739$	−18.5892			−0.683815			−0.341907	+	0.939734i	$0.611073\pi$
$740$	−5.68854			−0.209115
$741$	1.22296	+	0.342076i	0.0449264	+	0.0125665i
$742$	54.0457	+	10.7454i	1.98408	+	0.394476i
$743$			11.8117i			0.433329i	0.976246	+	0.216665i	$0.0695178\pi$
$743$			11.8117i			0.433329i	−0.976246	+	0.216665i	$0.930482\pi$
$744$	31.2696	+	8.74650i	1.14640	+	0.320662i
$745$		−	44.1313i		−	1.61685i
$746$		−	2.21092i		−	0.0809474i
$747$	3.20888	+	1.94750i	0.117407	+	0.0712554i
$748$		−	7.42288i		−	0.271407i
$749$	5.71055	−	28.7222i	0.208659	−	1.04949i
$750$	6.78477	−	24.2562i	0.247745	−	0.885711i
$751$	−12.8603			−0.469278			−0.234639	−	0.972083i	$-0.575391\pi$
$751$	−12.8603			−0.469278			−0.234639	+	0.972083i	$0.575391\pi$
$752$	13.1440			0.479313
$753$	28.2015	+	7.88832i	1.02772	+	0.287466i
$754$			0.721287i			0.0262677i
$755$	−11.0836			−0.403373
$756$	6.85141	+	11.0183i	0.249183	+	0.400733i
$757$	−5.92750			−0.215439			−0.107719	−	0.994181i	$-0.534355\pi$
$757$	−5.92750			−0.215439			−0.107719	+	0.994181i	$0.534355\pi$
$758$		−	25.7949i		−	0.936912i
$759$	−30.4954	−	8.52996i	−1.10691	−	0.309618i
$760$	3.44784			0.125066
$761$	−33.1297			−1.20095			−0.600476	−	0.799643i	$-0.705022\pi$
$761$	−33.1297			−1.20095			−0.600476	+	0.799643i	$0.705022\pi$
$762$	8.24943	−	29.4925i	0.298845	−	1.06840i
$763$	−19.3149	−	3.84020i	−0.699248	−	0.139025i
$764$		−	2.11397i		−	0.0764809i
$765$	−17.1502	−	10.4086i	−0.620066	−	0.376324i
$766$			28.5712i			1.03232i
$767$		−	5.06888i		−	0.183027i
$768$	−30.6921	−	8.58497i	−1.10750	−	0.309783i
$769$			6.36015i			0.229353i	0.993403	+	0.114677i	$0.0365831\pi$
$769$			6.36015i			0.229353i	−0.993403	+	0.114677i	$0.963417\pi$
$770$	−35.2618	−	7.01076i	−1.27075	−	0.252650i
$771$	−2.63012	−	0.735678i	−0.0947214	−	0.0264948i
$772$	2.05955			0.0741248
$773$	49.7761			1.79032			0.895161	−	0.445743i	$-0.147060\pi$
$773$	49.7761			1.79032			0.895161	+	0.445743i	$0.147060\pi$
$774$	−26.7621	+	44.0956i	−0.961943	+	1.58498i
$775$		−	17.9360i		−	0.644280i
$776$	15.6343			0.561237
$777$	−9.49473	−	4.81110i	−0.340621	−	0.172597i
$778$	18.3248			0.656977
$779$			7.67038i			0.274820i
$780$	−1.14266	+	4.08512i	−0.0409139	+	0.146271i
$781$	13.7158			0.490790
$782$	−26.4854			−0.947117
$783$	1.59449	−	1.49309i	0.0569824	−	0.0533587i
$784$	−32.3177	−	13.3797i	−1.15420	−	0.477847i
$785$		−	47.3231i		−	1.68903i
$786$	−13.1379	+	46.9692i	−0.468613	+	1.67533i
$787$		−	4.09669i		−	0.146031i	−0.997331	−	0.0730156i	$-0.976738\pi$
$787$		−	4.09669i		−	0.146031i	0.997331	−	0.0730156i	$-0.0232623\pi$
$788$			15.9754i			0.569099i
$789$	−11.8736	+	42.4492i	−0.422711	+	1.51123i
$790$		−	38.0745i		−	1.35463i
$791$	1.34484	−	6.76413i	0.0478172	−	0.240505i
$792$	−14.1847	−	8.60886i	−0.504033	−	0.305902i
$793$	−9.31982			−0.330957
$794$	−48.1285			−1.70802
$795$	14.6969	−	52.5428i	0.521245	−	1.86350i
$796$			2.81421i			0.0997472i
$797$	−19.5674			−0.693113			−0.346556	−	0.938029i	$-0.612649\pi$
$797$	−19.5674			−0.693113			−0.346556	+	0.938029i	$0.612649\pi$
$798$	−5.14214	−	2.60559i	−0.182030	−	0.0922368i
$799$	6.77869			0.239813
$800$			8.58067i			0.303373i
$801$	19.7913	+	12.0115i	0.699292	+	0.424407i
$802$	−40.4255			−1.42747
$803$	12.0154			0.424015
$804$	4.08574	+	1.14283i	0.144093	+	0.0403046i
$805$	−8.01983	+	40.3371i	−0.282662	+	1.42170i
$806$		−	17.7486i		−	0.625168i
$807$	37.7670	+	10.5639i	1.32946	+	0.371868i
$808$			26.2596i			0.923808i
$809$		−	4.57893i		−	0.160987i	−0.996755	−	0.0804933i	$-0.974350\pi$
$809$		−	4.57893i		−	0.160987i	0.996755	−	0.0804933i	$-0.0256496\pi$
$810$	35.5457	−	18.4977i	1.24895	−	0.649941i
$811$		−	8.43946i		−	0.296350i	−0.988961	−	0.148175i	$-0.952660\pi$
$811$		−	8.43946i		−	0.296350i	0.988961	−	0.148175i	$-0.0473398\pi$
$812$	0.204700	−	1.02957i	0.00718354	−	0.0361309i
$813$	1.57637	−	5.63568i	0.0552858	−	0.197652i
$814$	−12.1630			−0.426313
$815$	−40.7995			−1.42914
$816$	−21.4788	−	6.00791i	−0.751910	−	0.210319i
$817$		−	7.34727i		−	0.257048i
$818$	−63.6394			−2.22510
$819$	−5.36222	+	5.85206i	−0.187371	+	0.204488i
$820$	−25.6219			−0.894756
$821$			4.08300i			0.142498i	0.997459	+	0.0712489i	$0.0226985\pi$
$821$			4.08300i			0.142498i	−0.997459	+	0.0712489i	$0.977302\pi$
$822$	−44.8807	−	12.5537i	−1.56540	−	0.437861i
$823$	−26.0927			−0.909535			−0.454767	−	0.890610i	$-0.650278\pi$
$823$	−26.0927			−0.909535			−0.454767	+	0.890610i	$0.650278\pi$
$824$	1.97579			0.0688298
$825$	−2.46899	+	8.82686i	−0.0859591	+	0.307312i
$826$	−4.48700	+	22.5681i	−0.156123	+	0.785245i
$827$		−	28.0383i		−	0.974987i	−0.873127	−	0.487494i	$-0.837911\pi$
$827$		−	28.0383i		−	0.974987i	0.873127	−	0.487494i	$-0.162089\pi$
$828$	8.79955	−	14.4989i	0.305806	−	0.503873i
$829$		−	6.47349i		−	0.224834i	−0.993661	−	0.112417i	$-0.964141\pi$
$829$		−	6.47349i		−	0.224834i	0.993661	−	0.112417i	$-0.0358592\pi$
$830$		−	5.57075i		−	0.193364i
$831$	34.7694	+	9.72545i	1.20614	+	0.337372i
$832$		−	1.50265i		−	0.0520951i
$833$	−16.6670	−	6.90024i	−0.577478	−	0.239079i
$834$	−51.4849	−	14.4010i	−1.78278	−	0.498666i
$835$	−6.09704			−0.210997
$836$	−2.11187			−0.0730405
$837$	−39.2354	+	36.7403i	−1.35617	+	1.26993i
$838$			31.6367i			1.09287i
$839$	−7.42432			−0.256316			−0.128158	−	0.991754i	$-0.540906\pi$
$839$	−7.42432			−0.256316			−0.128158	+	0.991754i	$0.540906\pi$
$840$	−9.74059	+	19.2231i	−0.336082	+	0.663260i
$841$	28.8233			0.993906
$842$			17.4278i			0.600602i
$843$	1.58094	−	5.65200i	0.0544504	−	0.194665i
$844$	−25.6435			−0.882686
$845$	−2.59497			−0.0892696
$846$	−7.02480	+	11.5747i	−0.241518	+	0.397947i
$847$	4.37272	+	0.869385i	0.150248	+	0.0298724i
$848$		−	60.6560i		−	2.08294i
$849$	13.2015	−	47.1965i	0.453073	−	1.61978i
$850$			7.66618i			0.262948i
$851$			13.9136i			0.476953i
$852$	−1.97887	+	7.07465i	−0.0677950	+	0.242373i
$853$		−	24.2591i		−	0.830617i	−0.909681	−	0.415309i	$-0.863674\pi$
$853$		−	24.2591i		−	0.830617i	0.909681	−	0.415309i	$-0.136326\pi$
$854$	41.4945	+	8.24995i	1.41991	+	0.282308i
$855$	−2.96134	+	4.87937i	−0.101276	+	0.166871i
$856$	−20.0583			−0.685579
$857$	−27.5486			−0.941043			−0.470521	−	0.882389i	$-0.655934\pi$
$857$	−27.5486			−0.941043			−0.470521	+	0.882389i	$0.655934\pi$
$858$	−2.44319	+	8.73464i	−0.0834092	+	0.298196i
$859$			7.15559i			0.244146i	0.992521	+	0.122073i	$0.0389541\pi$
$859$			7.15559i			0.244146i	−0.992521	+	0.122073i	$0.961046\pi$
$860$	24.5426			0.836896
$861$	−42.7655	−	21.6698i	−1.45744	−	0.738505i
$862$	29.4875			1.00435
$863$			26.5850i			0.904964i	0.891774	+	0.452482i	$0.149461\pi$
$863$			26.5850i			0.904964i	−0.891774	+	0.452482i	$0.850539\pi$
$864$	18.7704	−	17.5767i	0.638582	−	0.597973i
$865$	30.4562			1.03554
$866$	37.1413			1.26211
$867$	17.2793	+	4.83325i	0.586836	+	0.164146i
$868$	−5.03701	+	25.3345i	−0.170967	+	0.859909i
$869$		−	26.0999i		−	0.885379i
$870$	−3.12207	−	0.873284i	−0.105848	−	0.0296071i
$871$			2.59536i			0.0879404i
$872$			13.4887i			0.456785i
$873$	−13.4282	+	22.1256i	−0.454476	+	0.748837i
$874$			7.53532i			0.254886i
$875$	−21.9937	−	4.37278i	−0.743522	−	0.147827i
$876$	−1.73355	+	6.19759i	−0.0585711	+	0.209397i
$877$	24.1956			0.817027			0.408513	−	0.912752i	$-0.366047\pi$
$877$	24.1956			0.817027			0.408513	+	0.912752i	$0.366047\pi$
$878$	−11.4109			−0.385100
$879$	−10.9643	−	3.06685i	−0.369816	−	0.103442i
$880$			39.5746i			1.33406i
$881$	−38.5732			−1.29956			−0.649782	−	0.760121i	$-0.725140\pi$
$881$	−38.5732			−1.29956			−0.649782	+	0.760121i	$0.725140\pi$
$882$	29.0544	−	21.3084i	0.978313	−	0.717491i
$883$	16.6212			0.559348			0.279674	−	0.960095i	$-0.409774\pi$
$883$	16.6212			0.559348			0.279674	+	0.960095i	$0.409774\pi$
$884$			2.43211i			0.0818006i
$885$	21.9405	+	6.13705i	0.737523	+	0.206295i
$886$	−53.2990			−1.79062
$887$	37.3655			1.25461			0.627306	−	0.778773i	$-0.284157\pi$
$887$	37.3655			1.25461			0.627306	+	0.778773i	$0.284157\pi$
$888$	−1.96391	+	7.02117i	−0.0659045	+	0.235615i
$889$	−26.7415	−	5.31676i	−0.896883	−	0.178318i
$890$		−	34.3586i		−	1.15170i
$891$	24.3665	−	12.6801i	0.816307	−	0.424798i
$892$		−	21.4321i		−	0.717598i
$893$		−	1.92859i		−	0.0645379i
$894$	48.6710	+	13.6139i	1.62780	+	0.455317i
$895$		−	14.7370i		−	0.492605i
$896$	−6.43672	+	32.3746i	−0.215036	+	1.08156i
$897$	9.99183	+	2.79484i	0.333617	+	0.0933171i
$898$	−16.4866			−0.550167
$899$	4.34878			0.145040
$900$	−4.19670	−	2.54702i	−0.139890	−	0.0849007i
$901$		−	31.2817i		−	1.04215i
$902$	−54.7837			−1.82410
$903$	40.9640	+	20.7570i	1.36320	+	0.690749i
$904$	−4.72377			−0.157110
$905$		−	49.2175i		−	1.63604i
$906$	3.41914	−	12.2237i	0.113593	−	0.406106i
$907$	2.73858			0.0909331			0.0454666	−	0.998966i	$-0.485523\pi$
$907$	2.73858			0.0909331			0.0454666	+	0.998966i	$0.485523\pi$
$908$	−4.75550			−0.157817
$909$	−37.1624	−	22.5543i	−1.23260	−	0.748077i
$910$	11.5535	+	2.29708i	0.382996	+	0.0761474i
$911$			17.7532i			0.588189i	0.955776	+	0.294095i	$0.0950181\pi$
$911$			17.7532i			0.588189i	−0.955776	+	0.294095i	$0.904982\pi$
$912$	−1.70930	+	6.11091i	−0.0566006	+	0.202352i
$913$		−	3.81873i		−	0.126382i
$914$			15.5402i			0.514024i
$915$	11.2838	−	40.3406i	0.373031	−	1.33362i
$916$		−	17.8052i		−	0.588299i
$917$	42.5881	+	8.46737i	1.40638	+	0.279617i
$918$	16.7699	−	15.7035i	0.553490	−	0.518292i
$919$	49.3436			1.62770			0.813848	−	0.581078i	$-0.197369\pi$
$919$	49.3436			1.62770			0.813848	+	0.581078i	$0.197369\pi$
$920$	28.1696			0.928726
$921$	−3.01961	+	10.7954i	−0.0994994	+	0.355720i
$922$		−	63.7614i		−	2.09987i
$923$	−4.49399			−0.147921
$924$	5.96630	−	11.7745i	0.196277	−	0.387354i
$925$	4.02729			0.132416
$926$			40.6456i			1.33570i
$927$	−1.69700	+	2.79613i	−0.0557367	+	0.0918369i
$928$	−2.08048			−0.0682950
$929$	−3.21484			−0.105475			−0.0527377	−	0.998608i	$-0.516795\pi$
$929$	−3.21484			−0.105475			−0.0527377	+	0.998608i	$0.516795\pi$
$930$	76.8244	+	21.4888i	2.51917	+	0.704645i
$931$	−1.96318	+	4.74190i	−0.0643405	+	0.155410i
$932$		−	7.85509i		−	0.257302i
$933$	−0.617526	−	0.172730i	−0.0202169	−	0.00565492i
$934$			53.6466i			1.75537i
$935$			20.4096i			0.667465i
$936$	4.64763	+	2.82069i	0.151913	+	0.0921973i
$937$		−	3.32509i		−	0.108626i	−0.998524	−	0.0543130i	$-0.982703\pi$
$937$		−	3.32509i		−	0.108626i	0.998524	−	0.0543130i	$-0.0172969\pi$
$938$	2.29742	−	11.5553i	0.0750135	−	0.377293i
$939$	1.32145	−	4.72432i	0.0431240	−	0.154172i
$940$	6.44222			0.210122
$941$	−41.0375			−1.33778			−0.668892	−	0.743360i	$-0.733231\pi$
$941$	−41.0375			−1.33778			−0.668892	+	0.743360i	$0.733231\pi$
$942$	52.1911	+	14.5985i	1.70048	+	0.475646i
$943$			62.6688i			2.04078i
$944$	25.3284			0.824369
$945$	−18.8383	−	30.2955i	−0.612810	−	0.985513i
$946$	52.4760			1.70614
$947$			41.1006i			1.33559i	0.744346	+	0.667795i	$0.232762\pi$
$947$			41.1006i			1.33559i	−0.744346	+	0.667795i	$0.767238\pi$
$948$	13.4624	+	3.76561i	0.437239	+	0.122301i
$949$	−3.93686			−0.127796
$950$	2.18109			0.0707639
$951$	−6.09983	+	21.8075i	−0.197801	+	0.707156i
$952$	−2.40941	+	12.1185i	−0.0780895	+	0.392764i
$953$			28.7942i			0.932737i	0.884591	+	0.466368i	$0.154438\pi$
$953$			28.7942i			0.932737i	−0.884591	+	0.466368i	$0.845562\pi$
$954$	53.4140	+	32.4175i	1.72934	+	1.04956i
$955$			5.81248i			0.188088i
$956$		−	10.7454i		−	0.347533i
$957$	−2.14017	−	0.598633i	−0.0691818	−	0.0193511i
$958$			17.3957i			0.562030i
$959$	−8.09087	+	40.6944i	−0.261268	+	1.31409i
$960$	6.50420	+	1.81931i	0.209922	+	0.0587179i
$961$	−76.0097			−2.45192
$962$	3.98521			0.128488
$963$	17.2280	−	28.3865i	0.555166	−	0.914741i
$964$			14.0265i			0.451762i
$965$	−5.66284			−0.182293
$966$	−42.0125	−	21.2883i	−1.35173	−	0.684938i
$967$	13.1084			0.421539			0.210769	−	0.977536i	$-0.432403\pi$
$967$	13.1084			0.421539			0.210769	+	0.977536i	$0.432403\pi$
$968$		−	3.05372i		−	0.0981501i
$969$	−0.881527	+	3.15154i	−0.0283187	+	0.101242i
$970$	38.4109			1.23330
$971$	−54.6974			−1.75532			−0.877662	−	0.479280i	$-0.840898\pi$
$971$	−54.6974			−1.75532			−0.877662	+	0.479280i	$0.840898\pi$
$972$	3.02490	+	14.3977i	0.0970239	+	0.461807i
$973$	−9.28145	+	46.6826i	−0.297550	+	1.49658i
$974$			59.8521i			1.91779i
$975$	0.808964	−	2.89212i	0.0259076	−	0.0926221i
$976$		−	46.5697i		−	1.49066i
$977$			15.6475i			0.500606i	0.968168	+	0.250303i	$0.0805303\pi$
$977$			15.6475i			0.500606i	−0.968168	+	0.250303i	$0.919470\pi$
$978$	12.5861	−	44.9964i	0.402459	−	1.43883i
$979$		−	23.5527i		−	0.752746i
$980$	−15.8397	−	6.55774i	−0.505981	−	0.209479i
$981$	−19.0892	−	11.5854i	−0.609470	−	0.369894i
$982$	16.9605			0.541231
$983$	−45.6063			−1.45461			−0.727307	−	0.686312i	$-0.759228\pi$
$983$	−45.6063			−1.45461			−0.727307	+	0.686312i	$0.759228\pi$
$984$	−8.84571	+	31.6242i	−0.281991	+	1.00814i
$985$		−	43.9251i		−	1.39957i
$986$	−1.85875			−0.0591946
$987$	10.7527	+	5.44852i	0.342262	+	0.173428i
$988$	0.691955			0.0220140
$989$		−	60.0289i		−	1.90881i
$990$	−34.8496	−	21.1506i	−1.10759	−	0.672210i
$991$	5.34493			0.169787			0.0848936	−	0.996390i	$-0.472945\pi$
$991$	5.34493			0.169787			0.0848936	+	0.996390i	$0.472945\pi$
$992$	51.1940			1.62541
$993$	−0.916986	−	0.256493i	−0.0290997	−	0.00813955i
$994$	20.0085	+	3.97810i	0.634632	+	0.126178i
$995$		−	7.73783i		−	0.245306i
$996$	1.96971	+	0.550954i	0.0624127	+	0.0174576i
$997$		−	18.2247i		−	0.577182i	−0.957453	−	0.288591i	$-0.906813\pi$
$997$		−	18.2247i		−	0.577182i	0.957453	−	0.288591i	$-0.0931867\pi$
$998$		−	8.95888i		−	0.283588i
$999$	−8.24953	−	8.80978i	−0.261004	−	0.278729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.9	✓	32
3.2	odd	2	inner	273.2.e.a.209.24	yes	32
7.6	odd	2	inner	273.2.e.a.209.10	yes	32
21.20	even	2	inner	273.2.e.a.209.23	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.9	✓	32	1.1	even	1	trivial
273.2.e.a.209.10	yes	32	7.6	odd	2	inner
273.2.e.a.209.23	yes	32	21.20	even	2	inner
273.2.e.a.209.24	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.71574i q^{2} +(-1.66803 - 0.466569i) q^{3} -0.943779 q^{4} +2.59497 q^{5} +(-0.800512 + 2.86191i) q^{6} +(2.59496 + 0.515930i) q^{7} -1.81221i q^{8} +(2.56463 + 1.55650i) q^{9} +O(q^{10})\)	\(q-1.71574i q^{2} +(-1.66803 - 0.466569i) q^{3} -0.943779 q^{4} +2.59497 q^{5} +(-0.800512 + 2.86191i) q^{6} +(2.59496 + 0.515930i) q^{7} -1.81221i q^{8} +(2.56463 + 1.55650i) q^{9} -4.45230i q^{10} -3.05204i q^{11} +(1.57425 + 0.440338i) q^{12} +1.00000i q^{13} +(0.885205 - 4.45229i) q^{14} +(-4.32848 - 1.21073i) q^{15} -4.99684 q^{16} -2.57699 q^{17} +(2.67055 - 4.40025i) q^{18} +0.733175i q^{19} -2.44908 q^{20} +(-4.08775 - 2.07131i) q^{21} -5.23651 q^{22} +5.99021i q^{23} +(-0.845518 + 3.02281i) q^{24} +1.73386 q^{25} +1.71574 q^{26} +(-3.55165 - 3.79286i) q^{27} +(-2.44907 - 0.486924i) q^{28} +0.420393i q^{29} +(-2.07730 + 7.42656i) q^{30} -10.3445i q^{31} +4.94889i q^{32} +(-1.42398 + 5.09088i) q^{33} +4.42145i q^{34} +(6.73384 + 1.33882i) q^{35} +(-2.42044 - 1.46899i) q^{36} +2.32273 q^{37} +1.25794 q^{38} +(0.466569 - 1.66803i) q^{39} -4.70262i q^{40} +10.4619 q^{41} +(-3.55384 + 7.01353i) q^{42} -10.0212 q^{43} +2.88045i q^{44} +(6.65513 + 4.03906i) q^{45} +10.2777 q^{46} -2.63047 q^{47} +(8.33486 + 2.33137i) q^{48} +(6.46763 + 2.67764i) q^{49} -2.97486i q^{50} +(4.29849 + 1.20234i) q^{51} -0.943779i q^{52} +12.1389i q^{53} +(-6.50757 + 6.09373i) q^{54} -7.91993i q^{55} +(0.934972 - 4.70260i) q^{56} +(0.342076 - 1.22296i) q^{57} +0.721287 q^{58} -5.06888 q^{59} +(4.08512 + 1.14266i) q^{60} +9.31982i q^{61} -17.7486 q^{62} +(5.85206 + 5.36222i) q^{63} -1.50265 q^{64} +2.59497i q^{65} +(8.73464 + 2.44319i) q^{66} +2.59536 q^{67} +2.43211 q^{68} +(2.79484 - 9.99183i) q^{69} +(2.29708 - 11.5535i) q^{70} +4.49399i q^{71} +(2.82069 - 4.64763i) q^{72} +3.93686i q^{73} -3.98521i q^{74} +(-2.89212 - 0.808964i) q^{75} -0.691955i q^{76} +(1.57464 - 7.91991i) q^{77} +(-2.86191 - 0.800512i) q^{78} +8.55165 q^{79} -12.9666 q^{80} +(4.15463 + 7.98367i) q^{81} -17.9499i q^{82} +1.25121 q^{83} +(3.85793 + 1.95486i) q^{84} -6.68720 q^{85} +17.1938i q^{86} +(0.196142 - 0.701227i) q^{87} -5.53092 q^{88} +7.71703 q^{89} +(6.93000 - 11.4185i) q^{90} +(-0.515930 + 2.59496i) q^{91} -5.65343i q^{92} +(-4.82644 + 17.2550i) q^{93} +4.51321i q^{94} +1.90256i q^{95} +(2.30900 - 8.25488i) q^{96} +8.62720i q^{97} +(4.59414 - 11.0968i) q^{98} +(4.75049 - 7.82733i) 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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