LMFDB - Embedded newform 207.2.o.a.113.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.13
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.392874 + 0.0187149i) q^{2} +(-0.984950 + 1.42474i) q^{3} +(-1.83694 - 0.175407i) q^{4} +(-1.77722 + 1.69458i) q^{5} +(-0.413625 + 0.541309i) q^{6} +(0.708274 - 3.67488i) q^{7} +(-1.49704 - 0.215242i) q^{8} +(-1.05975 - 2.80659i) q^{9} +O(q^{10})$	\(q+(0.392874 + 0.0187149i) q^{2} +(-0.984950 + 1.42474i) q^{3} +(-1.83694 - 0.175407i) q^{4} +(-1.77722 + 1.69458i) q^{5} +(-0.413625 + 0.541309i) q^{6} +(0.708274 - 3.67488i) q^{7} +(-1.49704 - 0.215242i) q^{8} +(-1.05975 - 2.80659i) q^{9} +(-0.729939 + 0.632496i) q^{10} +(-1.19416 - 0.615633i) q^{11} +(2.05921 - 2.44439i) q^{12} +(-4.80127 + 0.925369i) q^{13} +(0.347038 - 1.43051i) q^{14} +(-0.663851 - 4.20115i) q^{15} +(3.03979 + 0.585871i) q^{16} +(-1.26232 + 2.76408i) q^{17} +(-0.363822 - 1.12247i) q^{18} +(-4.64144 + 2.11967i) q^{19} +(3.56190 - 2.80111i) q^{20} +(4.53811 + 4.62867i) q^{21} +(-0.457634 - 0.264215i) q^{22} +(2.11697 + 4.30331i) q^{23} +(1.78117 - 1.92088i) q^{24} +(0.0490149 - 1.02895i) q^{25} +(-1.90361 + 0.273698i) q^{26} +(5.04245 + 1.25449i) q^{27} +(-1.94566 + 6.62631i) q^{28} +(0.131792 + 1.38019i) q^{29} +(-0.182186 - 1.66295i) q^{30} +(-0.267693 - 0.210516i) q^{31} +(4.12289 + 1.00020i) q^{32} +(2.05330 - 1.09500i) q^{33} +(-0.547661 + 1.06231i) q^{34} +(4.96860 + 7.73130i) q^{35} +(1.45440 + 5.34143i) q^{36} +(-2.58296 - 8.79676i) q^{37} +(-1.86317 + 0.745901i) q^{38} +(3.41061 - 7.75199i) q^{39} +(3.02531 - 2.15432i) q^{40} +(-3.37252 - 3.53700i) q^{41} +(1.69628 + 1.90342i) q^{42} +(-3.52572 - 4.48332i) q^{43} +(2.08562 + 1.34035i) q^{44} +(6.63939 + 3.19211i) q^{45} +(0.751165 + 1.73028i) q^{46} +(-5.27943 + 3.04808i) q^{47} +(-3.82875 + 3.75384i) q^{48} +(-6.50449 - 2.60400i) q^{49} +(0.0385134 - 0.403331i) q^{50} +(-2.69477 - 4.52095i) q^{51} +(8.98198 - 0.857675i) q^{52} +(-0.820706 + 0.947145i) q^{53} +(1.95757 + 0.587226i) q^{54} +(3.16553 - 0.929483i) q^{55} +(-1.85130 + 5.34898i) q^{56} +(1.55161 - 8.70059i) q^{57} +(0.0259477 + 0.544709i) q^{58} +(2.43019 + 12.6090i) q^{59} +(0.482547 + 7.83372i) q^{60} +(0.0847140 + 0.211605i) q^{61} +(-0.101230 - 0.0877163i) q^{62} +(-11.0645 + 1.90660i) q^{63} +(-4.33960 - 1.27422i) q^{64} +(6.96482 - 9.78072i) q^{65} +(0.827183 - 0.391769i) q^{66} +(2.14636 + 4.16336i) q^{67} +(2.80364 - 4.85605i) q^{68} +(-8.21618 - 1.22243i) q^{69} +(1.80735 + 3.13042i) q^{70} +(7.13238 - 11.0982i) q^{71} +(0.982386 + 4.42967i) q^{72} +(-1.37981 - 3.02136i) q^{73} +(-0.850149 - 3.50436i) q^{74} +(1.41770 + 1.08330i) q^{75} +(8.89786 - 3.07958i) q^{76} +(-3.10817 + 3.95236i) q^{77} +(1.48502 - 2.98173i) q^{78} +(11.7315 + 4.06031i) q^{79} +(-6.39518 + 4.10993i) q^{80} +(-6.75388 + 5.94854i) q^{81} +(-1.25878 - 1.45271i) q^{82} +(5.07110 + 4.83529i) q^{83} +(-7.52436 - 9.29863i) q^{84} +(-2.44054 - 7.05149i) q^{85} +(-1.30126 - 1.82737i) q^{86} +(-2.09622 - 1.17165i) q^{87} +(1.65520 + 1.17866i) q^{88} +(-2.56329 - 17.8281i) q^{89} +(2.54871 + 1.37835i) q^{90} +18.2995i q^{91} +(-3.13392 - 8.27626i) q^{92} +(0.563594 - 0.174044i) q^{93} +(-2.13120 + 1.09871i) q^{94} +(4.65691 - 11.6324i) q^{95} +(-5.48586 + 4.88888i) q^{96} +(-7.13111 + 1.72999i) q^{97} +(-2.50671 - 1.14478i) q^{98} +(-0.462320 + 4.00393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.392874	+	0.0187149i	0.277804	+	0.0132334i	0.186022	−	0.982546i	$-0.440441\pi$
$2$	0.392874	+	0.0187149i	0.277804	+	0.0132334i	0.0917824	+	0.995779i	$0.470744\pi$
$3$	−0.984950	+	1.42474i	−0.568661	+	0.822572i
$3$	−0.984950	+	1.42474i	−0.568661	+	0.822572i
$4$	−1.83694	−	0.175407i	−0.918472	−	0.0877034i
$5$	−1.77722	+	1.69458i	−0.794798	+	0.757838i	−0.974139	−	0.225948i	$-0.927452\pi$
$5$	−1.77722	+	1.69458i	−0.794798	+	0.757838i	0.179341	+	0.983787i	$0.442603\pi$
$6$	−0.413625	+	0.541309i	−0.168862	+	0.220988i
$7$	0.708274	−	3.67488i	0.267703	−	1.38897i	−0.560319	−	0.828277i	$-0.689322\pi$
$7$	0.708274	−	3.67488i	0.267703	−	1.38897i	0.828022	−	0.560696i	$-0.189466\pi$
$8$	−1.49704	−	0.215242i	−0.529283	−	0.0760994i
$9$	−1.05975	−	2.80659i	−0.353249	−	0.935529i
$10$	−0.729939	+	0.632496i	−0.230827	+	0.200013i
$11$	−1.19416	−	0.615633i	−0.360053	−	0.185620i	0.268703	−	0.963223i	$-0.413405\pi$
$11$	−1.19416	−	0.615633i	−0.360053	−	0.185620i	−0.628756	+	0.777603i	$0.716435\pi$
$12$	2.05921	−	2.44439i	0.594442	−	0.705636i
$13$	−4.80127	+	0.925369i	−1.33163	+	0.256651i	−0.804916	−	0.593389i	$-0.797789\pi$
$13$	−4.80127	+	0.925369i	−1.33163	+	0.256651i	−0.526717	+	0.850041i	$0.676577\pi$
$14$	0.347038	−	1.43051i	0.0927498	−	0.382320i
$15$	−0.663851	−	4.20115i	−0.171406	−	1.08473i
$16$	3.03979	+	0.585871i	0.759946	+	0.146468i
$17$	−1.26232	+	2.76408i	−0.306156	+	0.670389i	−0.998699	−	0.0509877i	$-0.983763\pi$
$17$	−1.26232	+	2.76408i	−0.306156	+	0.670389i	0.692543	+	0.721377i	$0.256490\pi$
$18$	−0.363822	−	1.12247i	−0.0857537	−	0.264569i
$19$	−4.64144	+	2.11967i	−1.06482	+	0.486286i	−0.869234	−	0.494401i	$-0.835388\pi$
$19$	−4.64144	+	2.11967i	−1.06482	+	0.486286i	−0.195584	+	0.980687i	$0.562660\pi$
$20$	3.56190	−	2.80111i	0.796465	−	0.626347i
$21$	4.53811	+	4.62867i	0.990298	+	1.01006i
$22$	−0.457634	−	0.264215i	−0.0975679	−	0.0563308i
$23$	2.11697	+	4.30331i	0.441418	+	0.897302i
$23$	2.11697	+	4.30331i	0.441418	+	0.897302i
$24$	1.78117	−	1.92088i	0.363580	−	0.392098i
$25$	0.0490149	−	1.02895i	0.00980298	−	0.205790i
$26$	−1.90361	+	0.273698i	−0.373329	+	0.0536767i
$27$	5.04245	+	1.25449i	0.970419	+	0.241427i
$28$	−1.94566	+	6.62631i	−0.367695	+	1.25225i
$29$	0.131792	+	1.38019i	0.0244732	+	0.256295i	0.999426	+	0.0338825i	$0.0107872\pi$
$29$	0.131792	+	1.38019i	0.0244732	+	0.256295i	−0.974953	+	0.222413i	$0.928607\pi$
$30$	−0.182186	−	1.66295i	−0.0332625	−	0.303611i
$31$	−0.267693	−	0.210516i	−0.0480791	−	0.0378098i	0.593830	−	0.804590i	$-0.297615\pi$
$31$	−0.267693	−	0.210516i	−0.0480791	−	0.0378098i	−0.641909	+	0.766780i	$0.721857\pi$
$32$	4.12289	+	1.00020i	0.728831	+	0.176812i
$33$	2.05330	−	1.09500i	0.357434	−	0.190615i
$34$	−0.547661	+	1.06231i	−0.0939231	+	0.182185i
$35$	4.96860	+	7.73130i	0.839848	+	1.30683i
$36$	1.45440	+	5.34143i	0.242400	+	0.890239i
$37$	−2.58296	−	8.79676i	−0.424636	−	1.44618i	−0.843007	−	0.537902i	$-0.819217\pi$
$37$	−2.58296	−	8.79676i	−0.424636	−	1.44618i	0.418371	−	0.908276i	$-0.362601\pi$
$38$	−1.86317	+	0.745901i	−0.302246	+	0.121001i
$39$	3.41061	−	7.75199i	0.546134	−	1.24131i
$40$	3.02531	−	2.15432i	0.478344	−	0.340627i
$41$	−3.37252	−	3.53700i	−0.526700	−	0.552387i	0.405611	−	0.914046i	$-0.367059\pi$
$41$	−3.37252	−	3.53700i	−0.526700	−	0.552387i	−0.932310	+	0.361659i	$0.882210\pi$
$42$	1.69628	+	1.90342i	0.261742	+	0.293704i
$43$	−3.52572	−	4.48332i	−0.537668	−	0.683700i	0.438992	−	0.898491i	$-0.355335\pi$
$43$	−3.52572	−	4.48332i	−0.537668	−	0.683700i	−0.976660	+	0.214791i	$0.931093\pi$
$44$	2.08562	+	1.34035i	0.314419	+	0.202065i
$45$	6.63939	+	3.19211i	0.989742	+	0.475852i
$46$	0.751165	+	1.73028i	0.110753	+	0.255116i
$47$	−5.27943	+	3.04808i	−0.770085	+	0.444609i	−0.832905	−	0.553416i	$-0.813324\pi$
$47$	−5.27943	+	3.04808i	−0.770085	+	0.444609i	0.0628202	+	0.998025i	$0.479991\pi$
$48$	−3.82875	+	3.75384i	−0.552632	+	0.541820i
$49$	−6.50449	−	2.60400i	−0.929213	−	0.372001i
$50$	0.0385134	−	0.403331i	0.00544662	−	0.0570396i
$51$	−2.69477	−	4.52095i	−0.377344	−	0.633060i
$52$	8.98198	−	0.857675i	1.24558	−	0.118938i
$53$	−0.820706	+	0.947145i	−0.112733	+	0.130100i	−0.809311	−	0.587380i	$-0.800159\pi$
$53$	−0.820706	+	0.947145i	−0.112733	+	0.130100i	0.696579	+	0.717481i	$0.254705\pi$
$54$	1.95757	+	0.587226i	0.266391	+	0.0799114i
$55$	3.16553	−	0.929483i	0.426840	−	0.125331i
$56$	−1.85130	+	5.34898i	−0.247390	+	0.714788i
$57$	1.55161	−	8.70059i	0.205516	−	1.15242i
$58$	0.0259477	+	0.544709i	0.00340710	+	0.0715238i
$59$	2.43019	+	12.6090i	0.316384	+	1.64156i	0.697178	+	0.716898i	$0.254439\pi$
$59$	2.43019	+	12.6090i	0.316384	+	1.64156i	−0.380794	+	0.924660i	$0.624349\pi$
$60$	0.482547	+	7.83372i	0.0622966	+	1.01133i
$61$	0.0847140	+	0.211605i	0.0108465	+	0.0270933i	0.933692	−	0.358076i	$-0.116567\pi$
$61$	0.0847140	+	0.211605i	0.0108465	+	0.0270933i	−0.922846	+	0.385170i	$0.874143\pi$
$62$	−0.101230	−	0.0877163i	−0.0128562	−	0.0111400i
$63$	−11.0645	+	1.90660i	−1.39399	+	0.240209i
$64$	−4.33960	−	1.27422i	−0.542450	−	0.159278i
$65$	6.96482	−	9.78072i	0.863879	−	1.21315i
$66$	0.827183	−	0.391769i	0.101819	−	0.0482234i
$67$	2.14636	+	4.16336i	0.262220	+	0.508635i	0.982785	−	0.184751i	$-0.0591480\pi$
$67$	2.14636	+	4.16336i	0.262220	+	0.508635i	−0.720565	+	0.693387i	$0.756118\pi$
$68$	2.80364	−	4.85605i	0.339991	−	0.588883i
$69$	−8.21618	−	1.22243i	−0.989112	−	0.147163i
$70$	1.80735	+	3.13042i	0.216019	+	0.374156i
$71$	7.13238	−	11.0982i	0.846458	−	1.31711i	−0.100231	−	0.994964i	$-0.531958\pi$
$71$	7.13238	−	11.0982i	0.846458	−	1.31711i	0.946689	−	0.322150i	$-0.104405\pi$
$72$	0.982386	+	4.42967i	0.115775	+	0.522042i
$73$	−1.37981	−	3.02136i	−0.161495	−	0.353624i	0.811535	−	0.584304i	$-0.198632\pi$
$73$	−1.37981	−	3.02136i	−0.161495	−	0.353624i	−0.973030	+	0.230680i	$0.925905\pi$
$74$	−0.850149	−	3.50436i	−0.0988278	−	0.407374i
$75$	1.41770	+	1.08330i	0.163702	+	0.125088i
$76$	8.89786	−	3.07958i	1.02065	−	0.353252i
$77$	−3.10817	+	3.95236i	−0.354209	+	0.450413i
$78$	1.48502	−	2.98173i	0.168145	−	0.337614i
$79$	11.7315	+	4.06031i	1.31990	+	0.456821i	0.894047	−	0.447973i	$-0.147854\pi$
$79$	11.7315	+	4.06031i	1.31990	+	0.456821i	0.425850	+	0.904794i	$0.359975\pi$
$80$	−6.39518	+	4.10993i	−0.715003	+	0.459504i
$81$	−6.75388	+	5.94854i	−0.750431	+	0.660949i
$82$	−1.25878	−	1.45271i	−0.139009	−	0.160425i
$83$	5.07110	+	4.83529i	0.556626	+	0.530742i	0.915327	−	0.402711i	$-0.131932\pi$
$83$	5.07110	+	4.83529i	0.556626	+	0.530742i	−0.358701	+	0.933452i	$0.616780\pi$
$84$	−7.52436	−	9.29863i	−0.820975	−	1.01456i
$85$	−2.44054	−	7.05149i	−0.264714	−	0.764841i
$86$	−1.30126	−	1.82737i	−0.140319	−	0.197050i
$87$	−2.09622	−	1.17165i	−0.224738	−	0.125614i
$88$	1.65520	+	1.17866i	0.176444	+	0.125645i
$89$	−2.56329	−	17.8281i	−0.271708	−	1.88977i	−0.430708	−	0.902491i	$-0.641736\pi$
$89$	−2.56329	−	17.8281i	−0.271708	−	1.88977i	0.159000	−	0.987279i	$-0.449173\pi$
$90$	2.54871	+	1.37835i	0.268657	+	0.145291i
$91$			18.2995i			1.91831i
$92$	−3.13392	−	8.27626i	−0.326733	−	0.862860i
$93$	0.563594	−	0.174044i	0.0584420	−	0.0180475i
$94$	−2.13120	+	1.09871i	−0.219816	+	0.113323i
$95$	4.65691	−	11.6324i	0.477789	−	1.19346i
$96$	−5.48586	+	4.88888i	−0.559899	+	0.498969i
$97$	−7.13111	+	1.72999i	−0.724054	+	0.175654i	−0.580816	−	0.814035i	$-0.697267\pi$
$97$	−7.13111	+	1.72999i	−0.724054	+	0.175654i	−0.143238	+	0.989688i	$0.545751\pi$
$98$	−2.50671	−	1.14478i	−0.253216	−	0.115640i
$99$	−0.462320	+	4.00393i	−0.0464649	+	0.402410i
$100$	−0.270522	+	1.88153i	−0.0270522	+	0.188153i
$101$	−9.83618	+	10.3159i	−0.978736	+	1.02647i	0.0209078	+	0.999781i	$0.493344\pi$
$101$	−9.83618	+	10.3159i	−0.978736	+	1.02647i	−0.999644	+	0.0266874i	$0.991504\pi$
$102$	−0.974098	−	1.82660i	−0.0964501	−	0.180860i
$103$	−8.66645	+	0.412834i	−0.853930	+	0.0406777i	−0.469981	−	0.882676i	$-0.655739\pi$
$103$	−8.66645	+	0.412834i	−0.853930	+	0.0406777i	−0.383949	+	0.923354i	$0.625436\pi$
$104$	7.38686	−	0.351880i	0.724341	−	0.0345046i
$105$	−15.9089	−	0.535995i	−1.55255	−	0.0523077i
$106$	−0.340160	+	0.356749i	−0.0330392	+	0.0346506i
$107$	−0.753083	+	5.23781i	−0.0728033	+	0.506358i	0.920493	+	0.390760i	$0.127788\pi$
$107$	−0.753083	+	5.23781i	−0.0728033	+	0.506358i	−0.993296	+	0.115598i	$0.963121\pi$
$108$	−9.04264	−	3.18891i	−0.870129	−	0.306853i
$109$	13.3881	+	6.11415i	1.28235	+	0.585629i	0.935843	−	0.352418i	$-0.114640\pi$
$109$	13.3881	+	6.11415i	1.28235	+	0.585629i	0.346507	+	0.938047i	$0.387368\pi$
$110$	1.26105	−	0.305927i	0.120236	−	0.0291690i
$111$	15.0771	+	4.98433i	1.43106	+	0.473092i
$112$	4.30600	−	10.7559i	0.406879	−	1.01634i
$113$	−5.77904	+	2.97930i	−0.543647	+	0.280269i	−0.708096	−	0.706116i	$-0.750446\pi$
$113$	−5.77904	+	2.97930i	−0.543647	+	0.280269i	0.164449	+	0.986386i	$0.447415\pi$
$114$	0.772418	−	3.38920i	0.0723436	−	0.317428i
$115$	−11.0546	−	4.06057i	−1.03085	−	0.378650i
$116$		−	2.55845i		−	0.237546i
$117$	7.68526	+	12.4945i	0.710502	+	1.15512i
$118$	0.718784	+	4.99925i	0.0661694	+	0.460218i
$119$	9.26360	+	6.59658i	0.849193	+	0.604708i
$120$	0.0895487	+	6.43217i	0.00817464	+	0.587174i
$121$	−5.33361	−	7.49001i	−0.484874	−	0.680910i
$122$	0.0293218	+	0.0847197i	0.00265467	+	0.00767016i
$123$	8.36106	−	1.32119i	0.753892	−	0.119127i
$124$	0.454811	+	0.433662i	0.0408433	+	0.0389440i
$125$	−6.38395	−	7.36747i	−0.570998	−	0.658967i
$126$	−4.38262	+	0.541985i	−0.390435	+	0.0482838i
$127$	−5.30715	+	3.41070i	−0.470933	+	0.302650i	−0.754498	−	0.656303i	$-0.772119\pi$
$127$	−5.30715	+	3.41070i	−0.470933	+	0.302650i	0.283564	+	0.958953i	$0.408483\pi$
$128$	−9.69936	−	3.35698i	−0.857310	−	0.296718i
$129$	9.86021	−	0.607377i	0.868143	−	0.0534765i
$130$	2.91934	−	3.71225i	0.256043	−	0.325586i
$131$	−18.1856	+	6.29411i	−1.58889	+	0.549919i	−0.971561	−	0.236788i	$-0.923905\pi$
$131$	−18.1856	+	6.29411i	−1.58889	+	0.549919i	−0.617326	+	0.786707i	$0.711784\pi$
$132$	−3.96387	+	1.65128i	−0.345011	+	0.143726i
$133$	4.50213	+	18.5580i	0.390384	+	1.60918i
$134$	0.765333	+	1.67585i	0.0661147	+	0.144771i
$135$	−11.0874	+	6.31531i	−0.954250	+	0.543535i
$136$	2.48468	−	3.86624i	0.213060	−	0.331527i
$137$	−4.51672	−	7.82319i	−0.385889	−	0.668380i	0.606003	−	0.795462i	$-0.292772\pi$
$137$	−4.51672	−	7.82319i	−0.385889	−	0.668380i	−0.991892	+	0.127083i	$0.959439\pi$
$138$	−3.20505	−	0.634025i	−0.272832	−	0.0539718i
$139$	9.15903	−	15.8639i	0.776859	−	1.34556i	−0.156885	−	0.987617i	$-0.550145\pi$
$139$	9.15903	−	15.8639i	0.776859	−	1.34556i	0.933744	−	0.357942i	$-0.116521\pi$
$140$	−7.77093	−	15.0735i	−0.656763	−	1.27394i
$141$	0.857266	−	10.5240i	0.0721948	−	0.886282i
$142$	3.00983	−	4.22672i	0.252579	−	0.354698i
$143$	6.30318	+	1.85078i	0.527098	+	0.154770i
$144$	−1.57710	−	9.15230i	−0.131425	−	0.762692i
$145$	−2.57307	−	2.22958i	−0.213682	−	0.185156i
$146$	−0.485548	−	1.21284i	−0.0401842	−	0.100375i
$147$	10.1166	−	6.70237i	0.834405	−	0.552802i
$148$	3.20174	+	16.6122i	0.263182	+	1.36552i
$149$	−0.988447	−	20.7501i	−0.0809767	−	1.69991i	−0.565190	−	0.824961i	$-0.691197\pi$
$149$	−0.988447	−	20.7501i	−0.0809767	−	1.69991i	0.484213	−	0.874950i	$-0.339106\pi$
$150$	0.536706	+	0.452132i	0.0438219	+	0.0369164i
$151$	2.88856	−	8.34595i	0.235068	−	0.679183i	−0.764341	−	0.644812i	$-0.776936\pi$
$151$	2.88856	−	8.34595i	0.235068	−	0.679183i	0.999409	−	0.0343717i	$-0.0109430\pi$
$152$	7.40465	−	2.17420i	0.600596	−	0.176351i
$153$	9.09538	+	0.613571i	0.735318	+	0.0496043i
$154$	−1.29509	+	1.49461i	−0.104361	+	0.120439i
$155$	0.832487	−	0.0794928i	0.0668669	−	0.00638502i
$156$	−7.62484	+	13.6417i	−0.610476	+	1.09221i
$157$	−0.188196	+	1.97088i	−0.0150197	+	0.157293i	−0.999870	−	0.0161124i	$-0.994871\pi$
$157$	−0.188196	+	1.97088i	−0.0150197	+	0.157293i	0.984851	+	0.173405i	$0.0554771\pi$
$158$	4.53302	+	1.81475i	0.360628	+	0.144374i
$159$	−0.541077	−	2.10218i	−0.0429102	−	0.166714i
$160$	−9.02221	+	5.20898i	−0.713268	+	0.411806i
$161$	17.3135	−	4.73166i	1.36450	−	0.372907i
$162$	−2.76475	+	2.21063i	−0.217219	+	0.173684i
$163$	2.50907	+	1.61248i	0.196526	+	0.126299i	0.635203	−	0.772345i	$-0.280916\pi$
$163$	2.50907	+	1.61248i	0.196526	+	0.126299i	−0.438677	+	0.898645i	$0.644553\pi$
$164$	5.57472	+	7.08884i	0.435313	+	0.553545i
$165$	−1.79362	+	5.42554i	−0.139633	+	0.422378i
$166$	1.90181	+	1.99457i	0.147609	+	0.154808i
$167$	−9.07766	+	6.46418i	−0.702451	+	0.500213i	−0.874592	−	0.484859i	$-0.838871\pi$
$167$	−9.07766	+	6.46418i	−0.702451	+	0.500213i	0.172141	+	0.985072i	$0.444931\pi$
$168$	−5.79745	−	7.90609i	−0.447283	−	0.609968i
$169$	10.1271	−	4.05428i	0.779008	−	0.311868i
$170$	−0.826859	−	2.81602i	−0.0634172	−	0.215979i
$171$	10.8678	+	10.7803i	0.831081	+	0.824389i
$172$	5.69015	+	8.85405i	0.433870	+	0.675115i
$173$	0.613597	−	1.19021i	0.0466509	−	0.0904902i	−0.864358	−	0.502878i	$-0.832275\pi$
$173$	0.613597	−	1.19021i	0.0466509	−	0.0904902i	0.911009	+	0.412387i	$0.135305\pi$
$174$	−0.801623	−	0.499542i	−0.0607709	−	0.0378702i
$175$	−3.74655	−	0.908902i	−0.283212	−	0.0687066i
$176$	−3.26931	−	2.57102i	−0.246434	−	0.193798i
$177$	−20.3582	−	8.95690i	−1.53021	−	0.673241i
$178$	−0.673399	−	7.05216i	−0.0504734	−	0.528581i
$179$	−4.65532	+	15.8546i	−0.347955	+	1.18503i	0.580712	+	0.814109i	$0.302774\pi$
$179$	−4.65532	+	15.8546i	−0.347955	+	1.18503i	−0.928666	+	0.370916i	$0.879044\pi$
$180$	−11.6363	−	7.02832i	−0.867316	−	0.523860i
$181$	10.0022	−	1.43811i	0.743461	−	0.106894i	0.239833	−	0.970814i	$-0.422907\pi$
$181$	10.0022	−	1.43811i	0.743461	−	0.106894i	0.503628	+	0.863921i	$0.331998\pi$
$182$	−0.342473	+	7.18940i	−0.0253858	+	0.532914i
$183$	−0.384921	−	0.0877256i	−0.0284542	−	0.00648486i
$184$	−2.24293	−	6.89787i	−0.165351	−	0.508518i
$185$	19.4973	+	11.2568i	1.43347	+	0.827614i
$186$	0.224679	−	0.0578298i	0.0164743	−	0.00424029i
$187$	3.20907	−	2.52364i	0.234670	−	0.184547i
$188$	10.2327	−	4.67311i	0.746295	−	0.340821i
$189$	8.18153	−	17.6418i	0.595119	−	1.28325i
$190$	2.04728	−	4.48292i	0.148525	−	0.325225i
$191$	7.73418	+	1.49064i	0.559626	+	0.107859i	0.461218	−	0.887287i	$-0.347413\pi$
$191$	7.73418	+	1.49064i	0.559626	+	0.107859i	0.0984083	+	0.995146i	$0.468625\pi$
$192$	6.08972	−	4.92774i	0.439488	−	0.355629i
$193$	−6.03906	+	24.8933i	−0.434701	+	1.79186i	0.159115	+	0.987260i	$0.449136\pi$
$193$	−6.03906	+	24.8933i	−0.434701	+	1.79186i	−0.593816	+	0.804601i	$0.702379\pi$
$194$	−2.83401	+	0.546210i	−0.203470	+	0.0392156i
$195$	7.07494	+	19.5565i	0.506647	+	1.40047i
$196$	11.4916	+	5.92434i	0.820830	+	0.423167i
$197$	−20.9697	+	18.1703i	−1.49403	+	1.29458i	−0.647736	+	0.761865i	$0.724284\pi$
$197$	−20.9697	+	18.1703i	−1.49403	+	1.29458i	−0.846293	+	0.532718i	$0.821171\pi$
$198$	−0.256567	+	1.56439i	−0.0182334	+	0.111176i
$199$	14.1918	+	2.04047i	1.00603	+	0.144645i	0.625583	−	0.780157i	$-0.284861\pi$
$199$	14.1918	+	2.04047i	1.00603	+	0.144645i	0.380447	+	0.924803i	$0.375770\pi$
$200$	−0.294850	+	1.52983i	−0.0208490	+	0.108175i
$201$	−8.04575	−	1.04270i	−0.567503	−	0.0735467i
$202$	−4.05744	+	3.86876i	−0.285481	+	0.272205i
$203$	5.16538	+	0.493234i	0.362539	+	0.0346183i
$204$	4.15714	+	8.77742i	0.291058	+	0.614542i
$205$	11.9875	+	0.571033i	0.837240	+	0.0398827i
$206$	−3.41255			−0.237764
$207$	9.83417	−	10.5019i	0.683522	−	0.729930i
$208$	−15.1370			−1.04956
$209$	6.84756	+	0.326190i	0.473656	+	0.0225630i
$210$	−6.24016	−	0.508312i	−0.430612	−	0.0350769i
$211$	−12.7973	−	1.22199i	−0.881002	−	0.0841255i	−0.355258	−	0.934768i	$-0.615607\pi$
$211$	−12.7973	−	1.22199i	−0.881002	−	0.0841255i	−0.525744	+	0.850643i	$0.676213\pi$
$212$	1.67373	−	1.59589i	0.114952	−	0.109606i
$213$	8.78697	+	21.0929i	0.602073	+	1.44526i
$214$	−0.393892	+	2.04371i	−0.0269259	+	0.139705i
$215$	13.8633	+	1.99325i	0.945472	+	0.135938i
$216$	−7.27871	−	2.96337i	−0.495254	−	0.201631i
$217$	−0.963221	+	0.834636i	−0.0653877	+	0.0566588i
$218$	5.14542	+	2.65265i	0.348492	+	0.179660i
$219$	5.66369	+	1.01003i	0.382717	+	0.0682513i
$220$	−5.97794	+	1.15215i	−0.403032	+	0.0776781i
$221$	3.50292	−	14.4392i	0.235632	−	0.971287i
$222$	5.83014	+	2.24038i	0.391294	+	0.150365i
$223$	11.3241	+	2.18255i	0.758320	+	0.146154i	0.553733	−	0.832694i	$-0.313203\pi$
$223$	11.3241	+	2.18255i	0.758320	+	0.146154i	0.204587	+	0.978848i	$0.434415\pi$
$224$	6.59575	−	14.4427i	0.440697	−	0.964993i
$225$	−2.93978	+	0.952861i	−0.195985	+	0.0635240i
$226$	−2.32620	+	1.06234i	−0.154736	+	0.0706657i
$227$	1.62448	−	1.27751i	0.107821	−	0.0847910i	−0.562793	−	0.826598i	$-0.690273\pi$
$227$	1.62448	−	1.27751i	0.107821	−	0.0847910i	0.670614	+	0.741807i	$0.266031\pi$
$228$	−4.37636	+	15.7103i	−0.289832	+	1.04044i
$229$	10.8821	+	6.28278i	0.719109	+	0.415178i	0.814425	−	0.580269i	$-0.197053\pi$
$229$	10.8821	+	6.28278i	0.719109	+	0.415178i	−0.0953158	+	0.995447i	$0.530386\pi$
$230$	−4.26708	−	1.80218i	−0.281363	−	0.118832i
$231$	−2.56968	−	8.32120i	−0.169072	−	0.547495i
$232$	0.0997766	−	2.09457i	0.00655065	−	0.137515i
$233$	−21.4266	+	3.08068i	−1.40370	+	0.201822i	−0.802203	−	0.597052i	$-0.796339\pi$
$233$	−21.4266	+	3.08068i	−1.40370	+	0.201822i	−0.601499	+	0.798873i	$0.705430\pi$
$234$	2.78551	+	5.05261i	0.182094	+	0.330299i
$235$	4.21751	−	14.3635i	0.275120	−	0.936974i
$236$	−2.25242	−	23.5884i	−0.146620	−	1.53547i
$237$	−17.3398	+	12.7151i	−1.12634	+	0.825934i
$238$	3.51598	+	2.76500i	0.227907	+	0.179228i
$239$	−7.85504	−	1.90561i	−0.508100	−	0.123264i	−0.0264897	−	0.999649i	$-0.508433\pi$
$239$	−7.85504	−	1.90561i	−0.508100	−	0.123264i	−0.481611	+	0.876385i	$0.659948\pi$
$240$	0.443364	−	13.1595i	0.0286190	−	0.849443i
$241$	−2.30926	+	4.47934i	−0.148752	+	0.288539i	−0.951425	−	0.307880i	$-0.900380\pi$
$241$	−2.30926	+	4.47934i	−0.148752	+	0.288539i	0.802673	+	0.596420i	$0.203411\pi$
$242$	−1.95526	−	3.04245i	−0.125689	−	0.195576i
$243$	−1.82287	−	15.4815i	−0.116937	−	0.993139i
$244$	−0.118498	−	0.403566i	−0.00758604	−	0.0258357i
$245$	15.9726	−	6.39447i	1.02045	−	0.408528i
$246$	3.30957	−	0.362584i	0.211011	−	0.0231175i
$247$	20.3233	−	14.4722i	1.29314	−	0.920842i
$248$	0.355435	+	0.372769i	0.0225701	+	0.0236709i
$249$	−11.8838	+	2.46247i	−0.753105	+	0.156053i
$250$	−2.37021	−	3.01397i	−0.149905	−	0.190620i
$251$	6.51350	+	4.18597i	0.411129	+	0.264216i	0.729816	−	0.683644i	$-0.239606\pi$
$251$	6.51350	+	4.18597i	0.411129	+	0.264216i	−0.318687	+	0.947860i	$0.603242\pi$
$252$	20.6592	−	1.56154i	1.30141	−	0.0983677i
$253$	0.121259	−	6.44212i	0.00762352	−	0.405012i
$254$	−2.14887	+	1.24065i	−0.134832	+	0.0778455i
$255$	12.4503	+	3.46823i	0.779669	+	0.217189i
$256$	4.64986	+	1.86152i	0.290616	+	0.116345i
$257$	1.29139	−	13.5241i	0.0805549	−	0.843609i	−0.861413	−	0.507906i	$-0.830420\pi$
$257$	1.29139	−	13.5241i	0.0805549	−	0.843609i	0.941968	−	0.335704i	$-0.108974\pi$
$258$	3.88519	−	0.0540897i	0.241881	−	0.00336748i
$259$	−34.1564	+	3.26154i	−2.12238	+	0.202663i
$260$	−14.5096	+	16.7449i	−0.899846	+	1.03848i
$261$	3.73397	−	1.83254i	0.231127	−	0.113431i
$262$	−7.26247	+	2.13245i	−0.448677	+	0.131743i
$263$	−6.39658	+	18.4817i	−0.394430	+	1.13963i	0.556667	+	0.830736i	$0.312080\pi$
$263$	−6.39658	+	18.4817i	−0.394430	+	1.13963i	−0.951096	+	0.308894i	$0.900041\pi$
$264$	−3.30956	+	1.19730i	−0.203690	+	0.0736885i
$265$	−0.146434	−	3.07404i	−0.00899539	−	0.188837i
$266$	1.42146	+	7.37522i	0.0871552	+	0.452204i
$267$	27.9250	+	13.9077i	1.70898	+	0.851140i
$268$	−3.21246	−	8.02435i	−0.196232	−	0.490165i
$269$	−3.89084	−	3.37143i	−0.237229	−	0.205560i	0.528130	−	0.849163i	$-0.322893\pi$
$269$	−3.89084	−	3.37143i	−0.237229	−	0.205560i	−0.765359	+	0.643603i	$0.777439\pi$
$270$	−4.47414	+	2.27362i	−0.272287	+	0.138368i
$271$	−8.42993	−	2.47525i	−0.512082	−	0.150361i	0.0154755	−	0.999880i	$-0.495074\pi$
$271$	−8.42993	−	2.47525i	−0.512082	−	0.150361i	−0.527557	+	0.849519i	$0.676892\pi$
$272$	−5.45656	+	7.66267i	−0.330853	+	0.464618i
$273$	−26.0719	−	18.0241i	−1.57795	−	1.09087i
$274$	−1.62809	−	3.15806i	−0.0983567	−	0.190785i
$275$	−0.691987	+	1.19856i	−0.0417284	+	0.0722757i
$276$	14.8782	+	3.68670i	0.895565	+	0.221913i
$277$	−7.10493	−	12.3061i	−0.426894	−	0.739402i	0.569701	−	0.821852i	$-0.307059\pi$
$277$	−7.10493	−	12.3061i	−0.426894	−	0.739402i	−0.996595	+	0.0824500i	$0.973726\pi$
$278$	3.89524	−	6.06111i	0.233621	−	0.363521i
$279$	−0.307146	+	0.974398i	−0.0183883	+	0.0583357i
$280$	−5.77409	−	12.6435i	−0.345068	−	0.755594i
$281$	−0.417536	−	1.72110i	−0.0249081	−	0.102673i	0.958001	−	0.286766i	$-0.0925802\pi$
$281$	−0.417536	−	1.72110i	−0.0249081	−	0.102673i	−0.982909	+	0.184094i	$0.941065\pi$
$282$	0.533754	−	4.11857i	0.0317846	−	0.245257i
$283$	−0.264061	+	0.0913925i	−0.0156968	+	0.00543272i	−0.334905	−	0.942252i	$-0.608704\pi$
$283$	−0.264061	+	0.0913925i	−0.0156968	+	0.00543272i	0.319208	+	0.947685i	$0.396583\pi$
$284$	−15.0485	+	19.1357i	−0.892963	+	1.13549i
$285$	11.9863	+	18.0922i	0.710006	+	1.07169i
$286$	2.44172	+	0.845087i	0.144382	+	0.0499711i
$287$	−15.3867	+	9.88844i	−0.908249	+	0.583696i
$288$	−1.56206	−	12.6312i	−0.0920453	−	0.744301i
$289$	5.08591	+	5.86945i	0.299171	+	0.345262i
$290$	−0.969167	−	0.924098i	−0.0569114	−	0.0542649i
$291$	4.55901	−	11.8639i	0.267254	−	0.695474i
$292$	2.00467	+	5.79210i	0.117314	+	0.338957i
$293$	16.3474	+	22.9567i	0.955024	+	1.34114i	0.939970	+	0.341257i	$0.110853\pi$
$293$	16.3474	+	22.9567i	0.955024	+	1.34114i	0.0150546	+	0.999887i	$0.495208\pi$
$294$	4.09999	−	2.44386i	0.239116	−	0.142529i
$295$	−25.6860	−	18.2909i	−1.49550	−	1.06494i
$296$	1.97336	+	13.7250i	0.114699	+	0.797752i
$297$	−5.24919	−	4.60236i	−0.304589	−	0.267056i
$298$		−	8.17066i		−	0.473314i
$299$	−14.1463	−	18.7024i	−0.818100	−	1.08159i
$300$	−2.41423	−	2.23863i	−0.139385	−	0.129247i
$301$	−18.9728	+	9.78117i	−1.09358	+	0.563778i
$302$	1.29103	−	3.22485i	0.0742907	−	0.185569i
$303$	−5.00927	−	24.1746i	−0.287775	−	1.38879i
$304$	−15.3508	+	3.72407i	−0.880430	+	0.213590i
$305$	−0.509137	−	0.232515i	−0.0291531	−	0.0133138i
$306$	3.56186	+	0.411276i	0.203618	+	0.0235111i
$307$	1.30791	−	9.09669i	0.0746462	−	0.519176i	−0.917853	−	0.396921i	$-0.870079\pi$
$307$	1.30791	−	9.09669i	0.0746462	−	0.519176i	0.992499	−	0.122254i	$-0.0390123\pi$
$308$	6.40280	−	6.71507i	0.364834	−	0.382626i
$309$	7.94784	−	12.7540i	0.452137	−	0.725551i
$310$	0.328550	−	0.0156508i	0.0186604	−	0.000888905i
$311$	7.54475	−	0.359401i	0.427824	−	0.0203797i	0.167434	−	0.985883i	$-0.446452\pi$
$311$	7.54475	−	0.359401i	0.427824	−	0.0203797i	0.260390	+	0.965504i	$0.416149\pi$
$312$	−6.77436	+	10.8709i	−0.383522	+	0.615444i
$313$	−13.3445	+	13.9953i	−0.754277	+	0.791063i	−0.983229	−	0.182375i	$-0.941622\pi$
$313$	−13.3445	+	13.9953i	−0.754277	+	0.791063i	0.228952	+	0.973438i	$0.426470\pi$
$314$	−0.110822	+	0.770784i	−0.00625405	+	0.0434979i
$315$	16.4331	−	22.1380i	0.925901	−	1.24734i
$316$	−20.8379	−	9.51636i	−1.17222	−	0.535337i
$317$	−11.0277	+	2.67528i	−0.619375	+	0.150259i	−0.533155	−	0.846017i	$-0.678994\pi$
$317$	−11.0277	+	2.67528i	−0.619375	+	0.150259i	−0.0862197	+	0.996276i	$0.527479\pi$
$318$	−0.173233	−	0.836018i	−0.00971444	−	0.0468816i
$319$	0.692311	−	1.72931i	0.0387620	−	0.0968227i
$320$	9.87171	−	5.08922i	0.551845	−	0.284496i
$321$	−6.72074	−	6.23192i	−0.375115	−	0.347832i
$322$	6.89059	−	1.53493i	0.383998	−	0.0855382i
$323$		−	15.5050i		−	0.862722i
$324$	13.4499	−	9.74246i	0.747217	−	0.541248i
$325$	0.716824	+	4.98562i	0.0397623	+	0.276553i
$326$	0.955573	+	0.680460i	0.0529243	+	0.0376872i
$327$	−21.8977	+	13.0524i	−1.21094	+	0.721800i
$328$	4.28749	+	6.02094i	0.236737	+	0.332451i
$329$	7.46204	+	21.5601i	0.411396	+	1.18865i
$330$	−0.806206	+	2.09799i	−0.0443802	+	0.115490i
$331$	−12.2901	−	11.7185i	−0.675522	−	0.644109i	0.272558	−	0.962139i	$-0.412130\pi$
$331$	−12.2901	−	11.7185i	−0.675522	−	0.644109i	−0.948081	+	0.318030i	$0.896979\pi$
$332$	−8.46719	−	9.77166i	−0.464697	−	0.536289i
$333$	−21.9516	+	16.5716i	−1.20294	+	0.908120i
$334$	−3.68736	+	2.36972i	−0.201763	+	0.129665i
$335$	−10.8697	−	3.76204i	−0.593875	−	0.205542i
$336$	11.0831	+	16.7289i	0.604632	+	0.912638i
$337$	−10.0888	+	12.8289i	−0.549571	+	0.698836i	−0.978906	−	0.204309i	$-0.934505\pi$
$337$	−10.0888	+	12.8289i	−0.549571	+	0.698836i	0.429336	+	0.903145i	$0.358748\pi$
$338$	4.05455	−	1.40330i	0.220539	−	0.0763292i
$339$	1.44735	−	11.1681i	0.0786092	−	0.606567i
$340$	3.24626	+	13.3813i	0.176053	+	0.725701i
$341$	0.190068	+	0.416191i	0.0102928	+	0.0225380i
$342$	4.06792	+	4.43869i	0.219968	+	0.240017i
$343$	−0.0128878	+	0.0200538i	−0.000695877	+	0.00108281i
$344$	4.31314	+	7.47059i	0.232549	+	0.402787i
$345$	16.6735	−	11.7504i	0.897670	−	0.632623i
$346$	0.263341	−	0.456120i	0.0141573	−	0.0245212i
$347$	3.33027	+	6.45983i	0.178779	+	0.346782i	0.961148	−	0.276032i	$-0.0890196\pi$
$347$	3.33027	+	6.45983i	0.178779	+	0.346782i	−0.782370	+	0.622814i	$0.785989\pi$
$348$	3.64512	+	2.51995i	0.195399	+	0.135083i
$349$	−2.99532	+	4.20633i	−0.160336	+	0.225160i	−0.886927	−	0.461910i	$-0.847164\pi$
$349$	−2.99532	+	4.20633i	−0.160336	+	0.225160i	0.726591	+	0.687070i	$0.241104\pi$
$350$	−1.45491	−	0.427201i	−0.0777683	−	0.0228348i
$351$	−25.3710	−	1.35703i	−1.35420	−	0.0724328i
$352$	−4.30764	−	3.73259i	−0.229598	−	0.198948i
$353$	7.84866	+	19.6050i	0.417742	+	1.04347i	0.976764	+	0.214316i	$0.0687523\pi$
$353$	7.84866	+	19.6050i	0.417742	+	1.04347i	−0.559022	+	0.829153i	$0.688823\pi$
$354$	−7.83058	−	3.89994i	−0.416191	−	0.207279i
$355$	6.13094	+	31.8103i	0.325397	+	1.68832i
$356$	1.58145	+	33.1988i	0.0838168	+	1.75953i
$357$	−18.5226	+	6.70089i	−0.980319	+	0.354649i
$358$	−2.12567	+	6.14172i	−0.112345	+	0.324600i
$359$	22.7885	−	6.69129i	1.20273	−	0.353153i	0.381833	−	0.924231i	$-0.375293\pi$
$359$	22.7885	−	6.69129i	1.20273	−	0.353153i	0.820896	+	0.571078i	$0.193475\pi$
$360$	−9.25234	−	6.20778i	−0.487641	−	0.327179i
$361$	4.60756	−	5.31741i	0.242503	−	0.279864i
$362$	3.95654	−	0.377804i	0.207951	−	0.0198569i
$363$	15.9246	−	0.221703i	0.835826	−	0.0116364i
$364$	3.20986	−	33.6151i	0.168242	−	1.76191i
$365$	7.57217	+	3.03144i	0.396345	+	0.158673i
$366$	−0.149584	−	0.0416689i	−0.00781887	−	0.00217807i
$367$	23.6545	−	13.6569i	1.23476	−	0.712887i	0.266739	−	0.963769i	$-0.414054\pi$
$367$	23.6545	−	13.6569i	1.23476	−	0.712887i	0.968018	+	0.250882i	$0.0807206\pi$
$368$	3.91394	+	14.3214i	0.204028	+	0.746555i
$369$	−6.35289	+	13.2136i	−0.330718	+	0.687873i
$370$	7.44932	+	4.78739i	0.387272	+	0.248884i
$371$	2.89935	+	3.68683i	0.150527	+	0.191411i
$372$	−1.06582	+	0.220851i	−0.0552602	+	0.0114506i
$373$	6.51881	+	6.83673i	0.337531	+	0.353993i	0.870523	−	0.492128i	$-0.163781\pi$
$373$	6.51881	+	6.83673i	0.337531	+	0.353993i	−0.532992	+	0.846120i	$0.678932\pi$
$374$	1.30799	−	0.931416i	0.0676346	−	0.0481624i
$375$	16.7846	−	1.83885i	0.866752	−	0.0949579i
$376$	8.55959	−	3.42674i	0.441427	−	0.176721i
$377$	−1.90996	−	6.50472i	−0.0983679	−	0.335010i
$378$	3.54448	−	6.77791i	0.182308	−	0.348618i
$379$	−18.4502	−	28.7091i	−0.947724	−	1.47469i	−0.878871	−	0.477060i	$-0.841702\pi$
$379$	−18.4502	−	28.7091i	−0.947724	−	1.47469i	−0.0688530	−	0.997627i	$-0.521934\pi$
$380$	−10.5949	+	20.5512i	−0.543507	+	1.05426i
$381$	0.367933	−	10.9207i	0.0188498	−	0.559482i
$382$	3.01067	+	0.730379i	0.154039	+	0.0373695i
$383$	−11.7926	−	9.27384i	−0.602576	−	0.473871i	0.269661	−	0.962955i	$-0.413089\pi$
$383$	−11.7926	−	9.27384i	−0.602576	−	0.473871i	−0.872236	+	0.489085i	$0.837331\pi$
$384$	14.3362	−	10.5126i	0.731591	−	0.536467i
$385$	−1.17367	−	12.2913i	−0.0598159	−	0.626420i
$386$	−2.83847	+	9.66693i	−0.144474	+	0.492034i
$387$	−8.84647	+	14.6464i	−0.449691	+	0.744520i
$388$	13.4029	−	1.92705i	0.680429	−	0.0978309i
$389$	0.682579	−	14.3291i	0.0346081	−	0.726514i	−0.913169	−	0.407581i	$-0.866372\pi$
$389$	0.682579	−	14.3291i	0.0346081	−	0.726514i	0.947777	−	0.318933i	$-0.103325\pi$
$390$	2.41356	+	7.81567i	0.122216	+	0.395762i
$391$	−14.5670	+	0.419342i	−0.736684	+	0.0212070i
$392$	9.17698	+	5.29833i	0.463507	+	0.267606i
$393$	8.94451	−	32.1091i	0.451191	−	1.61969i
$394$	−8.57851	+	6.74621i	−0.432179	+	0.339869i
$395$	−27.7300	+	12.6639i	−1.39525	+	0.637189i
$396$	1.55157	−	7.27391i	0.0779695	−	0.365528i
$397$	0.320425	−	0.701633i	0.0160817	−	0.0352139i	−0.901421	−	0.432944i	$-0.857475\pi$
$397$	0.320425	−	0.701633i	0.0160817	−	0.0352139i	0.917502	+	0.397730i	$0.130202\pi$
$398$	5.53741	+	1.06725i	0.277565	+	0.0534963i
$399$	−30.8746	−	11.8644i	−1.54567	−	0.593962i
$400$	0.751826	−	3.09907i	0.0375913	−	0.154953i
$401$	−4.29144	+	0.827108i	−0.214304	+	0.0413038i	−0.295273	−	0.955413i	$-0.595411\pi$
$401$	−4.29144	+	0.827108i	−0.214304	+	0.0413038i	0.0809688	+	0.996717i	$0.474199\pi$
$402$	−3.14145	−	0.560227i	−0.156681	−	0.0279416i
$403$	1.48007	+	0.763030i	0.0737276	+	0.0380092i
$404$	19.8780	−	17.2244i	0.988966	−	0.856944i
$405$	1.92287	−	22.0169i	0.0955482	−	1.09403i
$406$	2.02012	+	0.290449i	0.100257	+	0.0144147i
$407$	−2.33110	+	12.0949i	−0.115548	+	0.599522i
$408$	3.06108	+	7.34807i	0.151546	+	0.363783i
$409$	2.97895	−	2.84042i	0.147300	−	0.140450i	−0.612847	−	0.790202i	$-0.709976\pi$
$409$	2.97895	−	2.84042i	0.147300	−	0.140450i	0.760146	+	0.649752i	$0.225127\pi$
$410$	4.69888	+	0.448688i	0.232061	+	0.0221591i
$411$	15.5947	+	1.27032i	0.769231	+	0.0626601i
$412$	15.9922	+	0.761802i	0.787879	+	0.0375313i
$413$	48.0579			2.36478
$414$	4.06013	−	3.94187i	0.199545	−	0.193732i
$415$	−17.2063			−0.844622
$416$	−20.7207	−	0.987046i	−1.01591	−	0.0483939i
$417$	13.5807	+	28.6744i	0.665049	+	1.40419i
$418$	2.68413	+	0.256303i	0.131285	+	0.0125362i
$419$	15.5794	−	14.8549i	0.761101	−	0.725709i	−0.206429	−	0.978461i	$-0.566184\pi$
$419$	15.5794	−	14.8549i	0.761101	−	0.725709i	0.967531	+	0.252753i	$0.0813359\pi$
$420$	29.1297	+	3.77512i	1.42138	+	0.184207i
$421$	5.96934	−	30.9719i	0.290928	−	1.50948i	−0.482671	−	0.875802i	$-0.660333\pi$
$421$	5.96934	−	30.9719i	0.290928	−	1.50948i	0.773599	−	0.633676i	$-0.218455\pi$
$422$	−5.00486	−	0.719590i	−0.243633	−	0.0350291i
$423$	14.1496	+	11.5870i	0.687976	+	0.563379i
$424$	1.43249	−	1.24126i	0.0695680	−	0.0602810i
$425$	2.78223	+	1.43434i	0.134958	+	0.0695757i
$426$	3.05742	+	8.45132i	0.148133	+	0.409468i
$427$	0.837624	−	0.161439i	0.0405355	−	0.00781257i
$428$	2.30212	−	9.48946i	0.111277	−	0.458690i
$429$	−8.84519	+	7.15744i	−0.427050	+	0.345564i
$430$	5.40924	+	1.04255i	0.260857	+	0.0502761i
$431$	−9.96858	+	21.8282i	−0.480170	+	1.05143i	0.502247	+	0.864724i	$0.332507\pi$
$431$	−9.96858	+	21.8282i	−0.480170	+	1.05143i	−0.982417	+	0.186701i	$0.940220\pi$
$432$	14.5930	+	6.76760i	0.702105	+	0.325607i
$433$	1.08449	−	0.495269i	0.0521172	−	0.0238011i	−0.389186	−	0.921159i	$-0.627244\pi$
$433$	1.08449	−	0.495269i	0.0521172	−	0.0238011i	0.441303	+	0.897358i	$0.354516\pi$
$434$	−0.394045	+	0.309880i	−0.0189148	+	0.0148747i
$435$	5.71090	−	1.46992i	0.273817	−	0.0704774i
$436$	−23.5208	−	13.5797i	−1.12644	−	0.650351i
$437$	−18.9474	−	15.4863i	−0.906375	−	0.740808i
$438$	2.20622	+	0.502809i	0.105417	+	0.0240251i
$439$	−1.53033	+	32.1257i	−0.0730388	+	1.53327i	0.603796	+	0.797139i	$0.293654\pi$
$439$	−1.53033	+	32.1257i	−0.0730388	+	1.53327i	−0.676835	+	0.736135i	$0.736649\pi$
$440$	−4.93898	+	0.710118i	−0.235457	+	0.0338536i
$441$	−0.415262	+	21.0150i	−0.0197744	+	1.00071i
$442$	1.64644	−	5.60724i	0.0783129	−	0.266709i
$443$	−1.22707	−	12.8505i	−0.0582999	−	0.610544i	−0.976659	−	0.214796i	$-0.931091\pi$
$443$	−1.22707	−	12.8505i	−0.0582999	−	0.610544i	0.918359	−	0.395748i	$-0.129515\pi$
$444$	−26.8216	−	11.8006i	−1.27290	−	0.560030i
$445$	34.7666	+	27.3407i	1.64809	+	1.29607i
$446$	4.40811	+	1.06940i	0.208730	+	0.0506374i
$447$	30.5369	+	19.0295i	1.44435	+	0.900064i
$448$	−7.75624	+	15.0450i	−0.366448	+	0.710810i
$449$	−15.4954	−	24.1114i	−0.731275	−	1.13789i	−0.985324	−	0.170695i	$-0.945399\pi$
$449$	−15.4954	−	24.1114i	−0.731275	−	1.13789i	0.254048	−	0.967192i	$-0.418238\pi$
$450$	−1.17280	+	0.319337i	−0.0552862	+	0.0150537i
$451$	1.84984	+	6.29999i	0.0871057	+	0.296655i
$452$	11.1384	−	4.45913i	0.523905	−	0.209740i
$453$	9.04568	+	12.3358i	0.425003	+	0.579585i
$454$	0.662125	−	0.471497i	0.0310751	−	0.0221285i
$455$	−31.0099	−	32.5223i	−1.45377	−	1.52467i
$456$	−4.19555	+	12.6911i	−0.196475	+	0.594318i
$457$	−0.723619	−	0.920156i	−0.0338495	−	0.0430431i	0.768834	−	0.639449i	$-0.220837\pi$
$457$	−0.723619	−	0.920156i	−0.0338495	−	0.0430431i	−0.802683	+	0.596406i	$0.796595\pi$
$458$	4.15771	+	2.67200i	0.194277	+	0.124854i
$459$	−9.83268	+	12.3542i	−0.458950	+	0.576644i
$460$	19.5944	+	9.39810i	0.913596	+	0.438189i
$461$	−6.19576	+	3.57712i	−0.288565	+	0.166603i	−0.637295	−	0.770620i	$-0.719947\pi$
$461$	−6.19576	+	3.57712i	−0.288565	+	0.166603i	0.348729	+	0.937223i	$0.386613\pi$
$462$	−0.853829	−	3.31728i	−0.0397237	−	0.154334i
$463$	−1.73662	−	0.695239i	−0.0807078	−	0.0323105i	0.330957	−	0.943646i	$-0.392628\pi$
$463$	−1.73662	−	0.695239i	−0.0807078	−	0.0323105i	−0.411665	+	0.911335i	$0.635053\pi$
$464$	−0.407994	+	4.27270i	−0.0189406	+	0.198355i
$465$	−0.706701	+	1.26437i	−0.0327725	+	0.0586338i
$466$	−8.47561	+	0.809322i	−0.392625	+	0.0374911i
$467$	−9.87831	+	11.4002i	−0.457114	+	0.527537i	−0.936782	−	0.349912i	$-0.886211\pi$
$467$	−9.87831	+	11.4002i	−0.457114	+	0.527537i	0.479669	+	0.877450i	$0.340757\pi$
$468$	−11.9258	−	24.2998i	−0.551268	−	1.12326i
$469$	16.8200	−	4.93881i	0.776678	−	0.228053i
$470$	1.92577	−	5.56413i	0.0888289	−	0.256654i
$471$	−2.62261	−	2.20934i	−0.120844	−	0.101801i
$472$	−0.924103	−	19.3993i	−0.0425353	−	0.892925i
$473$	1.45020	+	7.52436i	0.0666803	+	0.345970i
$474$	−7.05033	+	4.67092i	−0.323833	+	0.214543i
$475$	1.95354	+	4.87970i	0.0896344	+	0.223896i
$476$	−15.8596	−	13.7425i	−0.726925	−	0.629884i
$477$	3.52798	+	1.29965i	0.161535	+	0.0595069i
$478$	−3.05038	−	0.895673i	−0.139521	−	0.0409671i
$479$	6.84005	−	9.60551i	0.312530	−	0.438887i	−0.628196	−	0.778055i	$-0.716206\pi$
$479$	6.84005	−	9.60551i	0.312530	−	0.438887i	0.940726	+	0.339168i	$0.110146\pi$
$480$	1.46501	−	17.9849i	0.0668684	−	0.820892i
$481$	20.5417	+	39.8454i	0.936623	+	1.81679i
$482$	−0.991079	+	1.71660i	−0.0451424	+	0.0781889i
$483$	−10.3116	+	29.3276i	−0.469193	+	1.33445i
$484$	8.48374	+	14.6943i	0.385625	+	0.667921i
$485$	9.74197	−	15.1588i	0.442360	−	0.688326i
$486$	−0.426424	−	6.11640i	−0.0193430	−	0.277446i
$487$	16.0089	+	35.0545i	0.725431	+	1.58847i	0.806133	+	0.591734i	$0.201556\pi$
$487$	16.0089	+	35.0545i	0.725431	+	1.58847i	−0.0807024	+	0.996738i	$0.525716\pi$
$488$	−0.0812738	−	0.335015i	−0.00367909	−	0.0151654i
$489$	−4.76867	+	1.98655i	−0.215647	+	0.0898349i
$490$	6.39490	−	2.21330i	0.288892	−	0.0999866i
$491$	−4.88980	+	6.21789i	−0.220674	+	0.280609i	−0.883767	−	0.467927i	$-0.845001\pi$
$491$	−4.88980	+	6.21789i	−0.220674	+	0.280609i	0.663093	+	0.748537i	$0.269243\pi$
$492$	−15.5906	+	0.960358i	−0.702876	+	0.0432963i
$493$	−3.98133	−	1.37795i	−0.179310	−	0.0620599i
$494$	8.25535	−	5.30539i	0.371426	−	0.238701i
$495$	−5.96333	−	7.89932i	−0.268032	−	0.355048i
$496$	−0.690394	−	0.796758i	−0.0309996	−	0.0357755i
$497$	−35.7328	−	34.0712i	−1.60284	−	1.52830i
$498$	−4.71492	+	0.745036i	−0.211281	+	0.0333859i
$499$	12.5817	+	36.3525i	0.563235	+	1.62736i	0.762191	+	0.647352i	$0.224124\pi$
$499$	12.5817	+	36.3525i	0.563235	+	1.62736i	−0.198956	+	0.980008i	$0.563755\pi$
$500$	10.4347	+	14.6534i	0.466652	+	0.655321i
$501$	−0.268697	−	19.3002i	−0.0120045	−	0.862268i
$502$	2.48065	+	1.76646i	0.110717	+	0.0788410i
$503$	1.13526	+	7.89593i	0.0506189	+	0.352062i	0.999352	+	0.0359849i	$0.0114568\pi$
$503$	1.13526	+	7.89593i	0.0506189	+	0.352062i	−0.948733	+	0.316077i	$0.897634\pi$
$504$	16.9743	−	0.472724i	0.756095	−	0.0210568i
$505$		−	35.0018i		−	1.55756i
$506$	0.168203	−	2.52867i	0.00747755	−	0.112413i
$507$	−4.19841	+	18.4217i	−0.186458	+	0.818137i
$508$	10.3472	−	5.33435i	0.459082	−	0.236673i
$509$	5.35438	−	13.3746i	0.237329	−	0.592818i	−0.761113	−	0.648619i	$-0.775347\pi$
$509$	5.35438	−	13.3746i	0.237329	−	0.592818i	0.998442	+	0.0558008i	$0.0177712\pi$
$510$	4.82650	+	1.59559i	0.213721	+	0.0706538i
$511$	−12.0804	+	2.93068i	−0.534406	+	0.129646i
$512$	20.4646	+	9.34589i	0.904418	+	0.413034i
$513$	−26.0633	+	4.86569i	−1.15072	+	0.214826i
$514$	0.760458	−	5.28910i	0.0335423	−	0.233292i
$515$	14.7026	−	15.4197i	0.647875	−	0.679472i
$516$	−18.2192	−	0.613832i	−0.802055	−	0.0270225i
$517$	8.18100	−	0.389709i	0.359800	−	0.0171394i
$518$	−13.4802	+	0.642142i	−0.592287	+	0.0282141i
$519$	1.09138	+	2.04651i	0.0479061	+	0.0898320i
$520$	−12.5318	+	13.1430i	−0.549556	+	0.576358i
$521$	1.30246	−	9.05880i	0.0570618	−	0.396873i	−0.941196	−	0.337862i	$-0.890296\pi$
$521$	1.30246	−	9.05880i	0.0570618	−	0.396873i	0.998257	−	0.0590110i	$-0.0187947\pi$
$522$	1.50128	−	0.650077i	0.0657090	−	0.0284531i
$523$	−1.84322	−	0.841770i	−0.0805983	−	0.0368080i	0.374708	−	0.927143i	$-0.377743\pi$
$523$	−1.84322	−	0.841770i	−0.0805983	−	0.0368080i	−0.455306	+	0.890335i	$0.650470\pi$
$524$	34.5100	−	8.37205i	1.50758	−	0.365735i
$525$	4.98511	−	4.44262i	0.217568	−	0.193892i
$526$	−2.85893	+	7.14127i	−0.124655	+	0.311374i
$527$	0.919798	−	0.474189i	0.0400670	−	0.0206560i
$528$	6.88313	−	2.12559i	0.299550	−	0.0925042i
$529$	−14.0369	+	18.2199i	−0.610301	+	0.792170i
$530$		−	1.21045i		−	0.0525786i
$531$	32.8130	−	20.1829i	1.42396	−	0.875865i
$532$	−5.01495	−	34.8797i	−0.217426	−	1.51223i
$533$	19.4654	+	13.8613i	0.843142	+	0.600398i
$534$	10.7107	+	5.98661i	0.463498	+	0.259066i
$535$	−7.53748	−	10.5849i	−0.325874	−	0.457625i
$536$	−2.31706	−	6.69470i	−0.100082	−	0.289167i
$537$	−18.0033	−	22.2485i	−0.776900	−	0.960096i
$538$	−1.46552	−	1.39737i	−0.0631829	−	0.0602447i
$539$	6.16430	+	7.11398i	0.265515	+	0.306421i
$540$	21.4746	−	9.65606i	0.924122	−	0.415531i
$541$	12.2763	−	7.88953i	0.527801	−	0.339197i	−0.249450	−	0.968388i	$-0.580250\pi$
$541$	12.2763	−	7.88953i	0.527801	−	0.339197i	0.777251	+	0.629190i	$0.216613\pi$
$542$	−3.26558	−	1.13023i	−0.140269	−	0.0485474i
$543$	−7.80279	+	15.6670i	−0.334850	+	0.672336i
$544$	−7.96903	+	10.1334i	−0.341669	+	0.434468i
$545$	−34.1546	+	11.8210i	−1.46302	+	0.506357i
$546$	−9.90568	−	7.56914i	−0.423924	−	0.323929i
$547$	1.86943	+	7.70589i	0.0799310	+	0.329480i	0.997712	−	0.0676067i	$-0.0215363\pi$
$547$	1.86943	+	7.70589i	0.0799310	+	0.329480i	−0.917781	+	0.397087i	$0.870021\pi$
$548$	6.92472	+	15.1630i	0.295809	+	0.647732i
$549$	0.504114	−	0.462005i	0.0215150	−	0.0197179i
$550$	−0.294295	+	0.457932i	−0.0125488	+	0.0195263i
$551$	−3.53726	−	6.12672i	−0.150692	−	0.261007i
$552$	12.0368	+	3.59848i	0.512321	+	0.153162i
$553$	23.2303	−	40.2360i	0.987852	−	1.71101i
$554$	−2.56104	−	4.96772i	−0.108808	−	0.211058i
$555$	−35.2418	+	16.6911i	−1.49593	+	0.708500i
$556$	−19.6073	+	27.5345i	−0.831533	+	1.16772i
$557$	−25.7430	−	7.55883i	−1.09077	−	0.320278i	−0.313589	−	0.949559i	$-0.601531\pi$
$557$	−25.7430	−	7.55883i	−1.09077	−	0.320278i	−0.777178	+	0.629281i	$0.783350\pi$
$558$	−0.138905	+	0.377068i	−0.00588033	+	0.0159626i
$559$	21.0767	+	18.2630i	0.891448	+	0.772444i
$560$	10.5740	+	26.4125i	0.446831	+	1.11613i
$561$	0.434748	+	7.05774i	0.0183551	+	0.297978i
$562$	−0.131829	−	0.683992i	−0.00556086	−	0.0288525i
$563$	−1.69774	−	35.6399i	−0.0715512	−	1.50204i	−0.694336	−	0.719651i	$-0.744302\pi$
$563$	−1.69774	−	35.6399i	−0.0715512	−	1.50204i	0.622785	−	0.782393i	$-0.286001\pi$
$564$	−3.42073	+	19.1816i	−0.144039	+	0.807693i
$565$	5.22198	−	15.0879i	0.219690	−	0.634754i
$566$	−0.105453	+	0.0309639i	−0.00443253	+	0.00130151i
$567$	17.0766	+	29.0329i	0.717148	+	1.21927i
$568$	−13.0662	+	15.0792i	−0.548247	+	0.632711i
$569$	3.32196	−	0.317209i	0.139264	−	0.0132981i	−0.0251913	−	0.999683i	$-0.508019\pi$
$569$	3.32196	−	0.317209i	0.139264	−	0.0132981i	0.164455	+	0.986385i	$0.447413\pi$
$570$	4.37051	+	7.33229i	0.183060	+	0.307116i
$571$	−0.812591	+	8.50983i	−0.0340059	+	0.356125i	0.962414	+	0.271586i	$0.0875481\pi$
$571$	−0.812591	+	8.50983i	−0.0340059	+	0.356125i	−0.996420	+	0.0845397i	$0.973058\pi$
$572$	−11.2539	−	4.50540i	−0.470551	−	0.188380i
$573$	−9.74156	+	9.55096i	−0.406959	+	0.398997i
$574$	−6.23011	+	3.59695i	−0.260040	+	0.150134i
$575$	4.53165	−	1.96732i	0.188983	−	0.0820431i
$576$	1.02266	+	13.5298i	0.0426108	+	0.563743i
$577$	−8.44447	−	5.42693i	−0.351548	−	0.225926i	0.352934	−	0.935648i	$-0.385184\pi$
$577$	−8.44447	−	5.42693i	−0.351548	−	0.225926i	−0.704482	+	0.709722i	$0.748820\pi$
$578$	1.88828	+	2.40114i	0.0785419	+	0.0998742i
$579$	−29.5183	−	33.1228i	−1.22674	−	1.37653i
$580$	4.33550	+	4.54694i	0.180022	+	0.188801i
$581$	21.3608	−	15.2110i	0.886196	−	0.631057i
$582$	2.01315	−	4.57570i	0.0834478	−	0.189669i
$583$	1.56315	−	0.625790i	0.0647390	−	0.0259176i
$584$	1.41531	+	4.82009i	0.0585658	+	0.199457i
$585$	−34.8314	−	9.18230i	−1.44010	−	0.379641i
$586$	5.99284	+	9.32503i	0.247562	+	0.385214i
$587$	−3.89880	+	7.56262i	−0.160921	+	0.312143i	−0.955486	−	0.295036i	$-0.904668\pi$
$587$	−3.89880	+	7.56262i	−0.160921	+	0.312143i	0.794565	+	0.607179i	$0.207699\pi$
$588$	−19.7593	+	10.5373i	−0.814860	+	0.434553i
$589$	1.68871	+	0.409676i	0.0695819	+	0.0168804i
$590$	−9.74906	−	7.66675i	−0.401363	−	0.315635i
$591$	−5.23384	−	47.7732i	−0.215291	−	1.96513i
$592$	−2.69789	−	28.2535i	−0.110882	−	1.16121i
$593$	1.92025	−	6.53979i	0.0788554	−	0.268557i	−0.910623	−	0.413238i	$-0.864398\pi$
$593$	1.92025	−	6.53979i	0.0788554	−	0.268557i	0.989478	+	0.144682i	$0.0462158\pi$
$594$	−1.97614	−	1.90639i	−0.0810819	−	0.0782200i
$595$	−27.6419	+	3.97431i	−1.13321	+	0.162931i
$596$	−1.82398	+	38.2901i	−0.0747132	+	1.56842i
$597$	−16.8854	+	18.2098i	−0.691072	+	0.745278i
$598$	−5.20769	−	7.61243i	−0.212958	−	0.311295i
$599$	26.4110	+	15.2484i	1.07913	+	0.623033i	0.930660	−	0.365884i	$-0.119233\pi$
$599$	26.4110	+	15.2484i	1.07913	+	0.623033i	0.148465	+	0.988918i	$0.452567\pi$
$600$	−1.88919	−	1.92689i	−0.0771257	−	0.0786648i
$601$	−9.17554	+	7.21572i	−0.374278	+	0.294335i	−0.787524	−	0.616284i	$-0.788637\pi$
$601$	−9.17554	+	7.21572i	−0.374278	+	0.294335i	0.413246	+	0.910619i	$0.364395\pi$
$602$	−7.63699	+	3.48770i	−0.311261	+	0.142148i
$603$	9.41024	−	10.4361i	0.383215	−	0.424989i
$604$	−6.77006	+	14.8244i	−0.275470	+	0.603195i
$605$	22.1714	+	4.27319i	0.901396	+	0.173730i
$606$	−1.51559	−	9.59132i	−0.0615666	−	0.389621i
$607$	10.0859	−	41.5747i	0.409374	−	1.68746i	−0.277531	−	0.960717i	$-0.589516\pi$
$607$	10.0859	−	41.5747i	0.409374	−	1.68746i	0.686905	−	0.726747i	$-0.258969\pi$
$608$	−21.2562	+	4.09680i	−0.862054	+	0.166147i
$609$	−5.79037	+	6.87350i	−0.234638	+	0.278528i
$610$	−0.195675	−	0.100878i	−0.00792267	−	0.00408442i
$611$	22.5274	−	19.5201i	0.911361	−	0.789698i
$612$	−16.6001	−	2.72249i	−0.671019	−	0.110050i
$613$	17.0432	+	2.45045i	0.688369	+	0.0989725i	0.477619	−	0.878567i	$-0.341500\pi$
$613$	17.0432	+	2.45045i	0.688369	+	0.0989725i	0.210751	+	0.977540i	$0.432409\pi$
$614$	0.684087	−	3.54938i	0.0276075	−	0.143241i
$615$	−12.6206	+	16.5165i	−0.508912	+	0.666010i
$616$	5.50376	−	5.24782i	0.221753	−	0.211441i
$617$	8.59813	+	0.821022i	0.346148	+	0.0330531i	0.266682	−	0.963785i	$-0.414073\pi$
$617$	8.59813	+	0.821022i	0.346148	+	0.0330531i	0.0794655	+	0.996838i	$0.474679\pi$
$618$	3.36119	−	4.86198i	0.135207	−	0.195578i
$619$	−33.4403	−	1.59296i	−1.34408	−	0.0640265i	−0.636838	−	0.770997i	$-0.719758\pi$
$619$	−33.4403	−	1.59296i	−1.34408	−	0.0640265i	−0.707243	+	0.706971i	$0.750061\pi$
$620$	−1.54317			−0.0619754
$621$	5.27622	+	24.3549i	0.211727	+	0.977329i
$622$	2.97086			0.119121
$623$	−67.3314	−	3.20739i	−2.69758	−	0.128501i
$624$	14.9092	−	21.5662i	0.596844	−	0.863339i
$625$	28.9577	+	2.76513i	1.15831	+	0.110605i
$626$	−5.50464	+	5.24867i	−0.220010	+	0.209779i
$627$	−7.20924	+	9.43469i	−0.287909	+	0.376785i
$628$	0.691410	−	3.58738i	0.0275903	−	0.143152i
$629$	27.5755	+	3.96476i	1.09951	+	0.158085i
$630$	6.87046	−	8.38993i	0.273726	−	0.334263i
$631$	17.9982	−	15.5955i	0.716498	−	0.620849i	−0.218361	−	0.975868i	$-0.570071\pi$
$631$	17.9982	−	15.5955i	0.716498	−	0.620849i	0.934859	+	0.355019i	$0.115526\pi$
$632$	−16.6886	−	8.60355i	−0.663836	−	0.342231i
$633$	14.3457	−	17.0292i	0.570191	−	0.676849i
$634$	−4.38255	+	0.844668i	−0.174053	+	0.0335460i
$635$	3.65229	−	15.0549i	0.144937	−	0.597437i
$636$	0.625192	+	3.95649i	0.0247905	+	0.156885i
$637$	33.6395	+	6.48348i	1.33284	+	0.256885i
$638$	0.304355	−	0.666444i	0.0120495	−	0.0263848i
$639$	−38.7066	−	8.25638i	−1.53121	−	0.326617i
$640$	22.9266	−	10.4702i	0.906253	−	0.413872i
$641$	28.8203	−	22.6645i	1.13833	−	0.895195i	0.142813	−	0.989750i	$-0.454385\pi$
$641$	28.8203	−	22.6645i	1.13833	−	0.895195i	0.995520	+	0.0945549i	$0.0301428\pi$
$642$	−2.52378	−	2.57414i	−0.0996056	−	0.101593i
$643$	−40.8998	−	23.6135i	−1.61293	−	0.931225i	−0.988687	−	0.149995i	$-0.952074\pi$
$643$	−40.8998	−	23.6135i	−1.61293	−	0.931225i	−0.624243	−	0.781231i	$-0.714592\pi$
$644$	−32.6339	+	5.65489i	−1.28596	+	0.222834i
$645$	−16.4945	+	17.7883i	−0.649472	+	0.700415i
$646$	0.290175	−	6.09152i	0.0114168	−	0.239668i
$647$	19.2048	−	2.76124i	0.755020	−	0.108555i	0.245952	−	0.969282i	$-0.420899\pi$
$647$	19.2048	−	2.76124i	0.755020	−	0.108555i	0.509068	+	0.860726i	$0.329990\pi$
$648$	11.3912	−	7.45148i	0.447488	−	0.292722i
$649$	4.86050	−	16.5533i	0.190791	−	0.649775i
$650$	0.188316	+	1.97214i	0.00738638	+	0.0773536i
$651$	−0.240411	−	2.19441i	−0.00942245	−	0.0860057i
$652$	−4.32619	−	3.40215i	−0.169426	−	0.133238i
$653$	−24.4750	−	5.93758i	−0.957782	−	0.232355i	−0.273745	−	0.961802i	$-0.588262\pi$
$653$	−24.4750	−	5.93758i	−0.957782	−	0.232355i	−0.684037	+	0.729447i	$0.739777\pi$
$654$	−8.84731	+	4.71814i	−0.345957	+	0.184494i
$655$	21.6541	−	42.0030i	0.846095	−	1.64119i
$656$	−8.17953	−	12.7276i	−0.319357	−	0.496929i
$657$	−7.01748	+	7.07444i	−0.273778	+	0.276000i
$658$	2.52815	+	8.61008i	0.0985575	+	0.335656i
$659$	−29.2944	+	11.7277i	−1.14115	+	0.456846i	−0.863755	−	0.503911i	$-0.831894\pi$
$659$	−29.2944	+	11.7277i	−1.14115	+	0.456846i	−0.277391	+	0.960757i	$0.589470\pi$
$660$	4.24646	−	9.65180i	0.165293	−	0.375696i
$661$	−4.48158	+	3.19132i	−0.174313	+	0.124128i	−0.663884	−	0.747836i	$-0.731093\pi$
$661$	−4.48158	+	3.19132i	−0.174313	+	0.124128i	0.489570	+	0.871964i	$0.337154\pi$
$662$	−4.60913	−	4.83392i	−0.179139	−	0.187876i
$663$	17.1219	+	19.2127i	0.664959	+	0.746158i
$664$	−6.55088	−	8.33012i	−0.254224	−	0.323271i
$665$	−39.4493	−	25.3525i	−1.52978	−	0.983128i
$666$	−8.93436	+	6.09975i	−0.346199	+	0.236360i
$667$	−5.66039	+	3.48896i	−0.219171	+	0.135093i
$668$	17.8090	−	10.2820i	0.689052	−	0.397824i
$669$	−14.2633	+	13.9842i	−0.551449	+	0.540660i
$670$	−4.20002	−	1.68143i	−0.162261	−	0.0649595i
$671$	0.0291090	−	0.304844i	0.00112374	−	0.0117684i
$672$	14.0805	+	23.6225i	0.543168	+	0.911259i
$673$	−21.8673	+	2.08808i	−0.842923	+	0.0804894i	−0.507578	−	0.861606i	$-0.669459\pi$
$673$	−21.8673	+	2.08808i	−0.842923	+	0.0804894i	−0.335345	+	0.942095i	$0.608853\pi$
$674$	−4.20371	+	4.85134i	−0.161921	+	0.186867i
$675$	1.53796	−	5.12693i	0.0591962	−	0.197336i
$676$	−19.3141	+	5.67112i	−0.742849	+	0.218120i
$677$	2.67852	−	7.73907i	0.102944	−	0.297437i	−0.881753	−	0.471711i	$-0.843637\pi$
$677$	2.67852	−	7.73907i	0.102944	−	0.297437i	0.984697	+	0.174274i	$0.0557579\pi$
$678$	0.777636	−	4.36056i	0.0298649	−	0.167466i
$679$	1.30671	+	27.4312i	0.0501470	+	1.05271i
$680$	2.13581	+	11.0817i	0.0819047	+	0.424962i
$681$	0.220076	+	3.57274i	0.00843333	+	0.136908i
$682$	0.0668839	+	0.167068i	0.00256112	+	0.00639736i
$683$	−13.9099	−	12.0530i	−0.532248	−	0.461195i	0.346793	−	0.937942i	$-0.387271\pi$
$683$	−13.9099	−	12.0530i	−0.532248	−	0.461195i	−0.879041	+	0.476746i	$0.841816\pi$
$684$	−18.0726	−	21.7091i	−0.691023	−	0.830067i
$685$	21.2842	+	6.24961i	0.813228	+	0.238785i
$686$	−0.00543860	+	0.00763744i	−0.000207647	+	0.000291599i
$687$	−19.6696	+	9.31588i	−0.750443	+	0.355423i
$688$	−8.09079	−	15.6940i	−0.308459	−	0.598326i
$689$	3.06397	−	5.30695i	0.116728	−	0.202179i
$690$	6.77049	−	4.30440i	0.257748	−	0.163866i
$691$	−9.03090	−	15.6420i	−0.343552	−	0.595049i	0.641538	−	0.767091i	$-0.278297\pi$
$691$	−9.03090	−	15.6420i	−0.343552	−	0.595049i	−0.985090	+	0.172042i	$0.944963\pi$
$692$	−1.33591	+	2.07872i	−0.0507839	+	0.0790212i
$693$	14.3865	+	4.53485i	0.546498	+	0.172265i
$694$	1.18748	+	2.60023i	0.0450763	+	0.0987033i
$695$	10.6050	+	43.7144i	0.402270	+	1.65818i
$696$	2.88593	+	2.20520i	0.109391	+	0.0835879i
$697$	14.0338	−	4.85713i	0.531567	−	0.183977i
$698$	−1.25550	+	1.59650i	−0.0475215	+	0.0604286i
$699$	16.7150	−	33.5615i	0.632218	−	1.26941i
$700$	6.72277	+	2.32677i	0.254097	+	0.0879437i
$701$	−0.229034	+	0.147191i	−0.00865049	+	0.00555933i	−0.544959	−	0.838463i	$-0.683455\pi$
$701$	−0.229034	+	0.147191i	−0.00865049	+	0.00555933i	0.536308	+	0.844022i	$0.319818\pi$
$702$	−9.94222	−	1.00796i	−0.375245	−	0.0380429i
$703$	30.6349	+	35.3546i	1.15542	+	1.33342i
$704$	4.39773	+	4.19323i	0.165746	+	0.158038i
$705$	16.3102	+	20.1562i	0.614278	+	0.759127i
$706$	2.71663	+	7.84919i	0.102242	+	0.295408i
$707$	30.9429	+	43.4532i	1.16373	+	1.63423i
$708$	35.8257	+	20.0243i	1.34641	+	0.752558i
$709$	23.8782	+	17.0036i	0.896766	+	0.638584i	0.932654	−	0.360772i	$-0.117487\pi$
$709$	23.8782	+	17.0036i	0.896766	+	0.638584i	−0.0358884	+	0.999356i	$0.511426\pi$
$710$	1.81336	+	12.6122i	0.0680542	+	0.473328i
$711$	−1.03679	−	37.2284i	−0.0388826	−	1.39617i
$712$			27.2410i			1.02090i
$713$	0.339219	−	1.59762i	0.0127038	−	0.0598314i
$714$	−7.40245	+	2.28596i	−0.277030	+	0.0855498i
$715$	−14.3384	+	7.39198i	−0.536227	+	0.276444i
$716$	11.3326	−	28.3074i	0.423517	−	1.05790i
$717$	10.4518	−	9.31443i	0.390330	−	0.347854i
$718$	9.07823	−	2.20235i	0.338796	−	0.0821911i
$719$	24.3963	+	11.1414i	0.909827	+	0.415504i	0.814648	−	0.579956i	$-0.196930\pi$
$719$	24.3963	+	11.1414i	0.909827	+	0.415504i	0.0951793	+	0.995460i	$0.469658\pi$
$720$	18.3122	+	13.5932i	0.682454	+	0.506587i
$721$	−4.62111	+	32.1405i	−0.172099	+	1.19698i
$722$	1.90971	−	2.00284i	0.0710719	−	0.0745381i
$723$	−4.10737	−	7.70201i	−0.152755	−	0.286441i
$724$	−18.6258	+	0.887257i	−0.692223	+	0.0329746i
$725$	1.42661	−	0.0679577i	0.0529829	−	0.00252389i
$726$	6.26052	+	0.210927i	0.232350	+	0.00782822i
$727$	−10.2139	+	10.7120i	−0.378811	+	0.397286i	−0.885345	−	0.464934i	$-0.846078\pi$
$727$	−10.2139	+	10.7120i	−0.378811	+	0.397286i	0.506534	+	0.862220i	$0.330926\pi$
$728$	3.93881	−	27.3950i	0.145982	−	1.01533i
$729$	23.8525	+	12.6514i	0.883426	+	0.468571i
$730$	2.91818	+	1.33269i	0.108007	+	0.0493250i
$731$	16.8429	−	4.08603i	0.622955	−	0.151127i
$732$	0.691690	+	0.228665i	0.0255656	+	0.00845169i
$733$	6.55235	−	16.3670i	0.242017	−	0.604528i	−0.756775	−	0.653676i	$-0.773226\pi$
$733$	6.55235	−	16.3670i	0.242017	−	0.604528i	0.998792	+	0.0491472i	$0.0156503\pi$
$734$	9.54885	−	4.92277i	0.352454	−	0.181703i
$735$	−6.62180	+	29.0550i	−0.244249	+	1.07171i
$736$	4.42384	+	19.8594i	0.163065	+	0.732029i
$737$		−	6.29309i		−	0.231809i
$738$	−2.74318	+	5.07240i	−0.100978	+	0.186717i
$739$	1.32552	+	9.21921i	0.0487601	+	0.339134i	0.999569	+	0.0293561i	$0.00934569\pi$
$739$	1.32552	+	9.21921i	0.0487601	+	0.339134i	−0.950809	+	0.309778i	$0.899745\pi$
$740$	−33.8409	−	24.0980i	−1.24402	−	0.885860i
$741$	0.601566	+	43.2097i	0.0220991	+	1.58735i
$742$	1.07008	+	1.50272i	0.0392840	+	0.0551667i
$743$	4.16831	+	12.0435i	0.152920	+	0.441834i	0.995276	−	0.0970879i	$-0.0309528\pi$
$743$	4.16831	+	12.0435i	0.152920	+	0.441834i	−0.842355	+	0.538922i	$0.818832\pi$
$744$	−0.881184	+	0.139242i	−0.0323058	+	0.00510485i
$745$	36.9193	+	35.2025i	1.35262	+	1.28972i
$746$	2.43312	+	2.80798i	0.0890830	+	0.102807i
$747$	8.19658	−	19.3567i	0.299897	−	0.708224i
$748$	−6.33754	+	4.07289i	−0.231724	+	0.148920i
$749$	18.7149	+	6.47729i	0.683828	+	0.236675i
$750$	6.62864	−	0.408316i	0.242044	−	0.0149096i
$751$	−13.2207	+	16.8114i	−0.482429	+	0.613458i	−0.964952	−	0.262425i	$-0.915478\pi$
$751$	−13.2207	+	16.8114i	−0.482429	+	0.613458i	0.482524	+	0.875883i	$0.339720\pi$
$752$	−17.8341	+	6.17245i	−0.650344	+	0.225086i
$753$	−12.3794	+	5.15705i	−0.451130	+	0.187933i
$754$	−0.628638	−	2.59128i	−0.0228937	−	0.0943690i
$755$	9.00924	+	19.7275i	0.327880	+	0.717957i
$756$	−18.1235	+	30.9720i	−0.659146	+	1.12644i
$757$	−7.84006	+	12.1994i	−0.284952	+	0.443394i	−0.953992	−	0.299833i	$-0.903069\pi$
$757$	−7.84006	+	12.1994i	−0.284952	+	0.443394i	0.669040	+	0.743226i	$0.266705\pi$
$758$	−6.71133	−	11.6244i	−0.243766	−	0.422216i
$759$	9.05888	+	6.51793i	0.328817	+	0.236586i
$760$	−9.47536	+	16.4118i	−0.343707	+	0.595318i
$761$	21.1169	+	40.9610i	0.765486	+	1.48484i	0.871460	+	0.490467i	$0.163174\pi$
$761$	21.1169	+	40.9610i	0.765486	+	1.48484i	−0.105973	+	0.994369i	$0.533796\pi$
$762$	0.348931	−	4.28356i	0.0126404	−	0.155177i
$763$	31.9512	−	44.8692i	1.15671	−	1.62437i
$764$	−13.9458	−	4.09485i	−0.504541	−	0.148147i
$765$	−17.2043	+	14.3224i	−0.622021	+	0.517827i
$766$	−4.45947	−	3.86415i	−0.161127	−	0.139617i
$767$	−23.3360	−	58.2906i	−0.842615	−	2.10475i
$768$	−7.23205	+	4.79131i	−0.260964	+	0.172892i
$769$	−3.38725	−	17.5747i	−0.122147	−	0.633761i	−0.990466	−	0.137755i	$-0.956011\pi$
$769$	−3.38725	−	17.5747i	−0.122147	−	0.633761i	0.868319	−	0.496006i	$-0.165201\pi$
$770$	−0.231076	−	4.85088i	−0.00832740	−	0.174814i
$771$	17.9963	+	15.1604i	0.648121	+	0.545990i
$772$	15.4599	−	44.6684i	0.556413	−	1.60765i
$773$	−25.5646	+	7.50643i	−0.919493	+	0.269988i	−0.707032	−	0.707182i	$-0.749966\pi$
$773$	−25.5646	+	7.50643i	−0.919493	+	0.269988i	−0.212461	+	0.977169i	$0.568148\pi$
$774$	−3.74966	+	5.58865i	−0.134779	+	0.200880i
$775$	−0.229732	+	0.265124i	−0.00825220	+	0.00952355i
$776$	11.0479	−	1.05495i	0.396597	−	0.0378704i
$777$	28.9956	−	51.8764i	1.04021	−	1.86105i
$778$	0.536336	−	5.61676i	0.0192286	−	0.201371i
$779$	23.1506	+	9.26812i	0.829458	+	0.332065i
$780$	−9.56592	−	37.1653i	−0.342515	−	1.33073i
$781$	−15.3496	+	8.86211i	−0.549253	+	0.317111i
$782$	−5.73084	−	0.107871i	−0.204935	−	0.00385747i
$783$	−1.06688	+	7.12488i	−0.0381273	+	0.254622i
$784$	−18.2466	−	11.7264i	−0.651666	−	0.418800i
$785$	−3.00534	−	3.82160i	−0.107265	−	0.136399i
$786$	4.11499	−	12.4475i	0.146777	−	0.443986i
$787$	−19.0160	−	19.9434i	−0.677848	−	0.710907i	0.291507	−	0.956569i	$-0.405843\pi$
$787$	−19.0160	−	19.9434i	−0.677848	−	0.710907i	−0.969356	+	0.245662i	$0.920995\pi$
$788$	41.7073	−	29.6997i	1.48576	−	1.05801i
$789$	−20.0312	−	27.3170i	−0.713130	−	0.972510i
$790$	−11.1314	+	4.45635i	−0.396038	+	0.158550i
$791$	6.85543	+	23.3474i	0.243751	+	0.830139i
$792$	1.55392	−	5.89453i	0.0552163	−	0.209453i
$793$	−0.602548	−	0.937582i	−0.0213971	−	0.0332945i
$794$	0.139018	−	0.269657i	0.00493356	−	0.00956976i
$795$	4.52392	+	2.81914i	0.160447	+	0.0999847i
$796$	−25.7116	−	6.23758i	−0.911325	−	0.221085i
$797$	−0.835596	−	0.657120i	−0.0295983	−	0.0232764i	0.603250	−	0.797552i	$-0.293872\pi$
$797$	−0.835596	−	0.657120i	−0.0295983	−	0.0232764i	−0.632849	+	0.774276i	$0.718114\pi$
$798$	−11.9078	−	5.23903i	−0.421532	−	0.185460i
$799$	−1.76085	−	18.4404i	−0.0622944	−	0.652376i
$800$	1.23124	−	4.19322i	0.0435309	−	0.148253i
$801$	−47.3196	+	26.0873i	−1.67195	+	0.921750i
$802$	−1.70148	+	0.244635i	−0.0600812	+	0.00863838i
$803$	−0.212335	+	4.45745i	−0.00749313	+	0.157300i
$804$	14.5967	+	3.32667i	0.514786	+	0.117323i
$805$	−22.7518	+	37.7483i	−0.801895	+	1.33045i
$806$	0.567202	+	0.327474i	0.0199789	+	0.0115348i
$807$	8.63569	−	2.22273i	0.303991	−	0.0782437i
$808$	16.9455	−	13.3261i	0.596142	−	0.468811i
$809$	16.5628	−	7.56400i	0.582319	−	0.265936i	−0.102400	−	0.994743i	$-0.532652\pi$
$809$	16.5628	−	7.56400i	0.582319	−	0.265936i	0.684719	+	0.728807i	$0.259925\pi$
$810$	1.16749	−	8.61387i	0.0410214	−	0.302661i
$811$	9.37690	−	20.5325i	0.329268	−	0.720995i	−0.670514	−	0.741897i	$-0.733926\pi$
$811$	9.37690	−	20.5325i	0.329268	−	0.720995i	0.999782	+	0.0209016i	$0.00665366\pi$
$812$	−9.40200	−	1.81209i	−0.329946	−	0.0635918i
$813$	11.8296	−	9.57243i	0.414884	−	0.335720i
$814$	−1.14219	+	4.70815i	−0.0400336	+	0.165021i
$815$	−7.19166	+	1.38608i	−0.251913	+	0.0485522i
$816$	−5.54284	−	15.3215i	−0.194038	−	0.536360i
$817$	25.8676	+	13.3357i	0.904992	+	0.466556i
$818$	1.22351	−	1.06018i	0.0427791	−	0.0370683i
$819$	51.3591	−	19.3928i	1.79463	−	0.677640i
$820$	−21.9201	−	3.15164i	−0.765484	−	0.110060i
$821$	−2.26218	+	11.7373i	−0.0789507	+	0.409635i	0.920855	+	0.389906i	$0.127493\pi$
$821$	−2.26218	+	11.7373i	−0.0789507	+	0.409635i	−0.999805	+	0.0197292i	$0.993720\pi$
$822$	6.10299	+	0.790929i	0.212866	+	0.0275868i
$823$	−27.9871	+	26.6857i	−0.975569	+	0.930204i	−0.997578	−	0.0695542i	$-0.977842\pi$
$823$	−27.9871	+	26.6857i	−0.975569	+	0.930204i	0.0220087	+	0.999758i	$0.492994\pi$
$824$	13.0629	+	1.24735i	0.455066	+	0.0434536i
$825$	−1.02605	−	2.16642i	−0.0357226	−	0.0754250i
$826$	18.8807	+	0.899400i	0.656944	+	0.0312941i
$827$	−16.0543			−0.558263			−0.279132	−	0.960253i	$-0.590047\pi$
$827$	−16.0543			−0.558263			−0.279132	+	0.960253i	$0.590047\pi$
$828$	−19.9069	+	17.5664i	−0.691813	+	0.610473i
$829$	−25.7840			−0.895517			−0.447758	−	0.894155i	$-0.647778\pi$
$829$	−25.7840			−0.895517			−0.447758	+	0.894155i	$0.647778\pi$
$830$	−6.75990	−	0.322014i	−0.234639	−	0.0111773i
$831$	24.5309	+	1.99824i	0.850969	+	0.0693183i
$832$	22.0147	+	2.10215i	0.763223	+	0.0728790i
$833$	15.4084	−	14.6919i	0.533870	−	0.509044i
$834$	4.79887	+	11.5196i	0.166171	+	0.398890i
$835$	5.17898	−	26.8711i	0.179226	−	0.929912i
$836$	−12.5214	−	1.80030i	−0.433061	−	0.0622647i
$837$	−1.08574	−	1.39734i	−0.0375286	−	0.0482990i
$838$	6.39874	−	5.54454i	0.221041	−	0.191533i
$839$	47.2896	+	24.3795i	1.63262	+	0.841673i	0.997605	+	0.0691706i	$0.0220353\pi$
$839$	47.2896	+	24.3795i	1.63262	+	0.841673i	0.635012	+	0.772502i	$0.280995\pi$
$840$	23.7008	+	4.22666i	0.817757	+	0.145834i
$841$	26.5884	−	5.12449i	0.916840	−	0.176706i
$842$	2.92484	−	12.0563i	0.100797	−	0.415489i
$843$	2.86337	+	1.10032i	0.0986198	+	0.0378972i
$844$	23.2936	+	4.48947i	0.801798	+	0.154534i
$845$	−11.1278	+	24.3665i	−0.382809	+	0.838234i
$846$	5.34215	+	4.81704i	0.183667	+	0.165613i
$847$	−31.3025	+	14.2954i	−1.07557	+	0.491195i
$848$	−3.04967	+	2.39829i	−0.104726	+	0.0823576i
$849$	0.129877	−	0.466235i	0.00445737	−	0.0160011i
$850$	1.06622	+	0.615585i	0.0365712	+	0.0211144i
$851$	32.3871	−	29.7377i	1.11022	−	1.01940i
$852$	−12.4413	−	40.2878i	−0.426233	−	1.38024i
$853$	−1.85285	+	38.8960i	−0.0634402	+	1.33177i	0.712813	+	0.701354i	$0.247421\pi$
$853$	−1.85285	+	38.8960i	−0.0634402	+	1.33177i	−0.776254	+	0.630421i	$0.782882\pi$
$854$	0.332102	−	0.0477491i	0.0113643	−	0.00163394i
$855$	−37.5825	−	0.742640i	−1.28530	−	0.0253977i
$856$	2.25479	−	7.67910i	0.0770671	−	0.262466i
$857$	4.16243	+	43.5909i	0.142186	+	1.48904i	0.731893	+	0.681420i	$0.238637\pi$
$857$	4.16243	+	43.5909i	0.142186	+	1.48904i	−0.589707	+	0.807617i	$0.700757\pi$
$858$	−3.60900	+	2.64644i	−0.123209	+	0.0903479i
$859$	−7.03823	−	5.53492i	−0.240141	−	0.188849i	0.490834	−	0.871253i	$-0.336692\pi$
$859$	−7.03823	−	5.53492i	−0.240141	−	0.188849i	−0.730975	+	0.682404i	$0.760935\pi$
$860$	−25.1165	−	6.09321i	−0.856467	−	0.207777i
$861$	1.06673	−	31.6616i	0.0363540	−	1.07903i
$862$	−4.32491	+	8.38916i	−0.147307	+	0.285736i
$863$	−9.53827	−	14.8418i	−0.324687	−	0.505222i	0.640087	−	0.768302i	$-0.278898\pi$
$863$	−9.53827	−	14.8418i	−0.324687	−	0.505222i	−0.964774	+	0.263080i	$0.915262\pi$
$864$	19.5347	+	10.2156i	0.664584	+	0.347541i
$865$	0.926409	+	3.15506i	0.0314989	+	0.107275i
$866$	0.435336	−	0.174282i	0.0147933	−	0.00592236i
$867$	−13.3718	+	1.46496i	−0.454130	+	0.0497527i
$868$	1.91578	−	1.36422i	0.0650260	−	0.0463048i
$869$	−11.5096	−	12.0710i	−0.390438	−	0.409480i
$870$	2.27118	−	0.470616i	0.0770001	−	0.0159554i
$871$	−14.1579	−	18.0032i	−0.479722	−	0.610017i
$872$	−18.7265	−	12.0348i	−0.634160	−	0.407550i
$873$	12.4125	+	18.1807i	0.420100	+	0.615325i
$874$	−7.15411	−	6.43875i	−0.241991	−	0.217794i
$875$	−31.5961	+	18.2420i	−1.06814	+	0.616694i
$876$	−10.2267	−	2.84881i	−0.345529	−	0.0962525i
$877$	−5.92207	−	2.37084i	−0.199974	−	0.0800575i	0.269514	−	0.962997i	$-0.413137\pi$
$877$	−5.92207	−	2.37084i	−0.199974	−	0.0800575i	−0.469488	+	0.882939i	$0.655561\pi$
$878$	−1.20246	+	12.5927i	−0.0405810	+	0.424983i
$879$	−48.8086	+	0.679514i	−1.64627	+	0.0229194i
$880$	10.1671	−	0.970839i	0.342732	−	0.0327270i
$881$	22.2751	−	25.7069i	0.750469	−	0.866087i	−0.244145	−	0.969739i	$-0.578507\pi$
$881$	22.2751	−	25.7069i	0.750469	−	0.866087i	0.994614	+	0.103652i	$0.0330527\pi$
$882$	−0.556440	+	8.24849i	−0.0187363	+	0.277741i
$883$	40.5705	−	11.9126i	1.36531	−	0.400890i	0.484677	−	0.874693i	$-0.338937\pi$
$883$	40.5705	−	11.9126i	1.36531	−	0.400890i	0.880631	+	0.473803i	$0.157119\pi$
$884$	−8.96740	+	25.9096i	−0.301606	+	0.871434i
$885$	51.3592	−	18.5801i	1.72642	−	0.624564i
$886$	−0.241589	−	5.07159i	−0.00811635	−	0.170383i
$887$	−2.02206	−	10.4915i	−0.0678942	−	0.352269i	0.932055	−	0.362316i	$-0.118014\pi$
$887$	−2.02206	−	10.4915i	−0.0678942	−	0.352269i	−0.999950	+	0.0100473i	$0.996802\pi$
$888$	−21.4982	−	10.7070i	−0.721433	−	0.359302i
$889$	8.77497	+	21.9188i	0.294303	+	0.735134i
$890$	13.1472	+	11.3921i	0.440696	+	0.381865i
$891$	11.7273	−	2.94561i	0.392881	−	0.0986817i
$892$	−20.4189	−	5.99554i	−0.683677	−	0.200746i
$893$	18.0432	−	25.3382i	0.603793	−	0.847909i
$894$	11.6410	+	8.04770i	0.389335	+	0.269155i
$895$	−18.5933	−	36.0659i	−0.621504	−	1.20555i
$896$	−19.2063	+	33.2663i	−0.641637	+	1.11135i
$897$	40.5793	−	1.73380i	1.35490	−	0.0578900i
$898$	−5.63652	−	9.76274i	−0.188093	−	0.325787i
$899$	0.255273	−	0.397213i	0.00851383	−	0.0132478i
$900$	5.56735	−	1.23469i	0.185578	−	0.0411565i
$901$	−1.58200	−	3.46409i	−0.0527040	−	0.115406i
$902$	0.608852	+	2.50972i	0.0202726	+	0.0835647i
$903$	4.75170	−	36.6652i	0.158127	−	1.22014i
$904$	9.29272	−	3.21624i	0.309071	−	0.106971i
$905$	−15.3392	+	19.5054i	−0.509893	+	0.648382i
$906$	3.32295	+	5.01570i	0.110398	+	0.166635i
$907$	22.1751	+	7.67486i	0.736310	+	0.254840i	0.669382	−	0.742918i	$-0.266559\pi$
$907$	22.1751	+	7.67486i	0.736310	+	0.254840i	0.0669283	+	0.997758i	$0.478680\pi$
$908$	−3.20816	+	2.06176i	−0.106467	+	0.0684220i
$909$	39.3763	+	16.6739i	1.30603	+	0.553038i
$910$	−11.5744	−	13.3575i	−0.383686	−	0.442797i
$911$	11.7159	+	11.1711i	0.388166	+	0.370115i	0.858886	−	0.512167i	$-0.171157\pi$
$911$	11.7159	+	11.1711i	0.388166	+	0.370115i	−0.470720	+	0.882283i	$0.656006\pi$
$912$	9.81398	−	25.5389i	0.324973	−	0.845677i
$913$	−3.07895	−	8.89605i	−0.101898	−	0.294416i
$914$	−0.267071	−	0.375048i	−0.00883391	−	0.0124055i
$915$	0.832748	−	0.496370i	0.0275298	−	0.0164095i
$916$	−18.8877	−	13.4499i	−0.624069	−	0.444397i
$917$	10.2497	+	71.2880i	0.338474	+	2.35414i
$918$	−4.09421	+	4.66962i	−0.135129	+	0.154121i
$919$			36.5577i			1.20593i	0.797769	+	0.602964i	$0.206014\pi$
$919$			36.5577i			1.20593i	−0.797769	+	0.602964i	$0.793986\pi$
$920$	15.6752	+	8.45824i	0.516795	+	0.278860i
$921$	11.6722	+	10.8232i	0.384611	+	0.356637i
$922$	−2.50110	+	1.28941i	−0.0823693	+	0.0424643i
$923$	−23.9745	+	59.8855i	−0.789132	+	1.97116i
$924$	3.26076	+	15.7363i	0.107271	+	0.517687i
$925$	−9.17802	+	2.22656i	−0.301772	+	0.0732090i
$926$	−0.669264	−	0.305643i	−0.0219934	−	0.0100440i
$927$	10.3429	+	23.8857i	0.339705	+	0.784508i
$928$	−0.837106	+	5.82220i	−0.0274793	+	0.191123i
$929$	−28.8437	+	30.2504i	−0.946332	+	0.992485i	−0.999982	−	0.00607524i	$-0.998066\pi$
$929$	−28.8437	+	30.2504i	−0.946332	+	0.992485i	0.0536494	+	0.998560i	$0.482915\pi$
$930$	−0.301307	+	0.483513i	−0.00988026	+	0.0158550i
$931$	35.7098	−	1.70107i	1.17034	−	0.0557502i
$932$	39.8998	−	1.90066i	1.30696	−	0.0622582i
$933$	−6.91915	+	11.1033i	−0.226523	+	0.363505i
$934$	−4.09429	+	4.29397i	−0.133969	+	0.140503i
$935$	−1.42673	+	9.92309i	−0.0466589	+	0.324520i
$936$	−8.81578	−	20.3590i	−0.288153	−	0.665454i
$937$	−24.4417	−	11.1621i	−0.798475	−	0.364651i	−0.0259723	−	0.999663i	$-0.508268\pi$
$937$	−24.4417	−	11.1621i	−0.798475	−	0.364651i	−0.772503	+	0.635011i	$0.780995\pi$
$938$	6.70059	−	1.62555i	0.218782	−	0.0530760i
$939$	−6.79597	−	32.7971i	−0.221778	−	1.07029i
$940$	−10.2668	+	25.6452i	−0.334866	+	0.836455i
$941$	−8.29998	+	4.27894i	−0.270572	+	0.139489i	−0.588173	−	0.808735i	$-0.700153\pi$
$941$	−8.29998	+	4.27894i	−0.270572	+	0.139489i	0.317602	+	0.948224i	$0.397122\pi$
$942$	−0.989010	−	0.917076i	−0.0322237	−	0.0298800i
$943$	8.08129	−	22.0007i	0.263163	−	0.716442i
$944$			39.7526i			1.29384i
$945$	15.3551	+	45.2177i	0.499500	+	1.47093i
$946$	0.428929	+	2.98327i	0.0139457	+	0.0969944i
$947$	4.45427	+	3.17187i	0.144744	+	0.103072i	0.650135	−	0.759819i	$-0.274712\pi$
$947$	4.45427	+	3.17187i	0.144744	+	0.103072i	−0.505391	+	0.862891i	$0.668652\pi$
$948$	34.0826	−	20.3154i	1.10695	−	0.659813i
$949$	9.42072	+	13.2295i	0.305809	+	0.429449i
$950$	0.676171	+	1.95367i	0.0219379	+	0.0633854i
$951$	7.05013	−	18.3465i	0.228616	−	0.594927i
$952$	−12.4481	−	11.8692i	−0.403446	−	0.384685i
$953$	−3.09201	−	3.56836i	−0.100160	−	0.115591i	0.703456	−	0.710738i	$-0.251639\pi$
$953$	−3.09201	−	3.56836i	−0.100160	−	0.115591i	−0.803616	+	0.595148i	$0.797094\pi$
$954$	1.36173	+	0.576625i	0.0440877	+	0.0186689i
$955$	−16.2714	+	10.4570i	−0.526529	+	0.338380i
$956$	14.0950	+	4.87833i	0.455865	+	0.157777i
$957$	1.78192	+	2.68964i	0.0576012	+	0.0869438i
$958$	2.86705	−	3.64575i	0.0926301	−	0.117789i
$959$	−31.9483	+	11.0574i	−1.03167	+	0.357063i
$960$	−2.47235	+	19.0772i	−0.0797947	+	0.615714i
$961$	−7.28118	−	30.0135i	−0.234877	−	0.968176i
$962$	7.32462	+	16.0387i	0.236155	+	0.517108i
$963$	15.4984	−	3.43715i	0.499430	−	0.110761i
$964$	5.02768	−	7.82323i	0.161931	−	0.251969i
$965$	−31.4510	−	54.4746i	−1.01244	−	1.75360i
$966$	−4.60002	+	11.3291i	−0.148003	+	0.364508i
$967$	8.31902	−	14.4090i	0.267522	−	0.463361i	−0.700700	−	0.713456i	$-0.747129\pi$
$967$	8.31902	−	14.4090i	0.267522	−	0.463361i	0.968221	+	0.250095i	$0.0804620\pi$
$968$	6.37246	+	12.3608i	0.204818	+	0.397292i
$969$	22.0906	+	15.2717i	0.709651	+	0.490597i
$970$	4.11106	−	5.77318i	0.131998	−	0.185366i
$971$	6.30866	+	1.85239i	0.202454	+	0.0594460i	0.381387	−	0.924415i	$-0.375446\pi$
$971$	6.30866	+	1.85239i	0.202454	+	0.0594460i	−0.178933	+	0.983861i	$0.557265\pi$
$972$	0.632950	+	28.7584i	0.0203019	+	0.922426i
$973$	−51.8108	−	44.8943i	−1.66098	−	1.43924i
$974$	5.63343	+	14.0716i	0.180507	+	0.450884i
$975$	−7.80923	−	3.88930i	−0.250096	−	0.124557i
$976$	0.133539	+	0.692866i	0.00427448	+	0.0221781i
$977$	−0.926081	−	19.4408i	−0.0296280	−	0.621968i	−0.964037	−	0.265767i	$-0.914375\pi$
$977$	−0.926081	−	19.4408i	−0.0296280	−	0.621968i	0.934409	−	0.356201i	$-0.115928\pi$
$978$	−1.91067	+	0.691220i	−0.0610964	+	0.0221028i
$979$	−7.91456	+	22.8676i	−0.252950	+	0.730852i
$980$	−30.4624	+	8.94458i	−0.973087	+	0.285724i
$981$	2.97189	−	44.0544i	0.0948852	−	1.40655i
$982$	−2.03744	+	2.35134i	−0.0650175	+	0.0750342i
$983$	5.19349	−	0.495919i	0.165647	−	0.0158173i	−0.0119031	−	0.999929i	$-0.503789\pi$
$983$	5.19349	−	0.495919i	0.165647	−	0.0158173i	0.177550	+	0.984112i	$0.443183\pi$
$984$	−12.8012	+	0.178219i	−0.408088	+	0.00568140i
$985$	6.47674	−	67.8275i	0.206366	−	2.16116i
$986$	−1.53838	−	0.615873i	−0.0489919	−	0.0196134i
$987$	−38.0673	−	10.6042i	−1.21169	−	0.337536i
$988$	−39.8713	+	23.0197i	−1.26847	+	0.732354i
$989$	11.8293	−	24.6633i	0.376149	−	0.784248i
$990$	−2.19501	−	3.21504i	−0.0697619	−	0.102181i
$991$	11.2304	+	7.21735i	0.356746	+	0.229267i	0.706721	−	0.707492i	$-0.250174\pi$
$991$	11.2304	+	7.21735i	0.356746	+	0.229267i	−0.349975	+	0.936759i	$0.613810\pi$
$992$	−0.893110	−	1.13568i	−0.0283563	−	0.0360579i
$993$	28.8009	−	5.96790i	0.913970	−	0.189386i
$994$	−13.4009	−	14.0544i	−0.425050	−	0.445779i
$995$	−28.6797	+	20.4228i	−0.909209	+	0.647445i
$996$	22.2618	−	2.43892i	0.705392	−	0.0772800i
$997$	23.3068	−	9.33065i	0.738135	−	0.295505i	0.0280364	−	0.999607i	$-0.491075\pi$
$997$	23.3068	−	9.33065i	0.738135	−	0.295505i	0.710099	+	0.704102i	$0.248650\pi$
$998$	4.26270	+	14.5174i	0.134933	+	0.459541i
$999$	−1.98899	−	47.5975i	−0.0629287	−	1.50592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.13	yes	440
3.2	odd	2		621.2.s.a.44.10		440
9.2	odd	6	inner	207.2.o.a.182.13	yes	440
9.7	even	3		621.2.s.a.251.10		440
23.11	odd	22	inner	207.2.o.a.149.13	yes	440
69.11	even	22		621.2.s.a.287.10		440
207.11	even	66	inner	207.2.o.a.11.13	✓	440
207.34	odd	66		621.2.s.a.494.10		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.13	✓	440	207.11	even	66	inner
207.2.o.a.113.13	yes	440	1.1	even	1	trivial
207.2.o.a.149.13	yes	440	23.11	odd	22	inner
207.2.o.a.182.13	yes	440	9.2	odd	6	inner
621.2.s.a.44.10		440	3.2	odd	2
621.2.s.a.251.10		440	9.7	even	3
621.2.s.a.287.10		440	69.11	even	22
621.2.s.a.494.10		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.392874 + 0.0187149i) q^{2} +(-0.984950 + 1.42474i) q^{3} +(-1.83694 - 0.175407i) q^{4} +(-1.77722 + 1.69458i) q^{5} +(-0.413625 + 0.541309i) q^{6} +(0.708274 - 3.67488i) q^{7} +(-1.49704 - 0.215242i) q^{8} +(-1.05975 - 2.80659i) q^{9} +O(q^{10})\)	\(q+(0.392874 + 0.0187149i) q^{2} +(-0.984950 + 1.42474i) q^{3} +(-1.83694 - 0.175407i) q^{4} +(-1.77722 + 1.69458i) q^{5} +(-0.413625 + 0.541309i) q^{6} +(0.708274 - 3.67488i) q^{7} +(-1.49704 - 0.215242i) q^{8} +(-1.05975 - 2.80659i) q^{9} +(-0.729939 + 0.632496i) q^{10} +(-1.19416 - 0.615633i) q^{11} +(2.05921 - 2.44439i) q^{12} +(-4.80127 + 0.925369i) q^{13} +(0.347038 - 1.43051i) q^{14} +(-0.663851 - 4.20115i) q^{15} +(3.03979 + 0.585871i) q^{16} +(-1.26232 + 2.76408i) q^{17} +(-0.363822 - 1.12247i) q^{18} +(-4.64144 + 2.11967i) q^{19} +(3.56190 - 2.80111i) q^{20} +(4.53811 + 4.62867i) q^{21} +(-0.457634 - 0.264215i) q^{22} +(2.11697 + 4.30331i) q^{23} +(1.78117 - 1.92088i) q^{24} +(0.0490149 - 1.02895i) q^{25} +(-1.90361 + 0.273698i) q^{26} +(5.04245 + 1.25449i) q^{27} +(-1.94566 + 6.62631i) q^{28} +(0.131792 + 1.38019i) q^{29} +(-0.182186 - 1.66295i) q^{30} +(-0.267693 - 0.210516i) q^{31} +(4.12289 + 1.00020i) q^{32} +(2.05330 - 1.09500i) q^{33} +(-0.547661 + 1.06231i) q^{34} +(4.96860 + 7.73130i) q^{35} +(1.45440 + 5.34143i) q^{36} +(-2.58296 - 8.79676i) q^{37} +(-1.86317 + 0.745901i) q^{38} +(3.41061 - 7.75199i) q^{39} +(3.02531 - 2.15432i) q^{40} +(-3.37252 - 3.53700i) q^{41} +(1.69628 + 1.90342i) q^{42} +(-3.52572 - 4.48332i) q^{43} +(2.08562 + 1.34035i) q^{44} +(6.63939 + 3.19211i) q^{45} +(0.751165 + 1.73028i) q^{46} +(-5.27943 + 3.04808i) q^{47} +(-3.82875 + 3.75384i) q^{48} +(-6.50449 - 2.60400i) q^{49} +(0.0385134 - 0.403331i) q^{50} +(-2.69477 - 4.52095i) q^{51} +(8.98198 - 0.857675i) q^{52} +(-0.820706 + 0.947145i) q^{53} +(1.95757 + 0.587226i) q^{54} +(3.16553 - 0.929483i) q^{55} +(-1.85130 + 5.34898i) q^{56} +(1.55161 - 8.70059i) q^{57} +(0.0259477 + 0.544709i) q^{58} +(2.43019 + 12.6090i) q^{59} +(0.482547 + 7.83372i) q^{60} +(0.0847140 + 0.211605i) q^{61} +(-0.101230 - 0.0877163i) q^{62} +(-11.0645 + 1.90660i) q^{63} +(-4.33960 - 1.27422i) q^{64} +(6.96482 - 9.78072i) q^{65} +(0.827183 - 0.391769i) q^{66} +(2.14636 + 4.16336i) q^{67} +(2.80364 - 4.85605i) q^{68} +(-8.21618 - 1.22243i) q^{69} +(1.80735 + 3.13042i) q^{70} +(7.13238 - 11.0982i) q^{71} +(0.982386 + 4.42967i) q^{72} +(-1.37981 - 3.02136i) q^{73} +(-0.850149 - 3.50436i) q^{74} +(1.41770 + 1.08330i) q^{75} +(8.89786 - 3.07958i) q^{76} +(-3.10817 + 3.95236i) q^{77} +(1.48502 - 2.98173i) q^{78} +(11.7315 + 4.06031i) q^{79} +(-6.39518 + 4.10993i) q^{80} +(-6.75388 + 5.94854i) q^{81} +(-1.25878 - 1.45271i) q^{82} +(5.07110 + 4.83529i) q^{83} +(-7.52436 - 9.29863i) q^{84} +(-2.44054 - 7.05149i) q^{85} +(-1.30126 - 1.82737i) q^{86} +(-2.09622 - 1.17165i) q^{87} +(1.65520 + 1.17866i) q^{88} +(-2.56329 - 17.8281i) q^{89} +(2.54871 + 1.37835i) q^{90} +18.2995i q^{91} +(-3.13392 - 8.27626i) q^{92} +(0.563594 - 0.174044i) q^{93} +(-2.13120 + 1.09871i) q^{94} +(4.65691 - 11.6324i) q^{95} +(-5.48586 + 4.88888i) q^{96} +(-7.13111 + 1.72999i) q^{97} +(-2.50671 - 1.14478i) q^{98} +(-0.462320 + 4.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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