LMFDB - Embedded newform 207.2.o.a.11.13

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			11.13
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.13

$q$-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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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	0.0917824	−	0.995779i	$-0.470744\pi$
$2$	0.392874	−	0.0187149i	0.277804	−	0.0132334i	0.186022	+	0.982546i	$0.440441\pi$
$3$	−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	0.179341	−	0.983787i	$-0.442603\pi$
$5$	−1.77722	−	1.69458i	−0.794798	−	0.757838i	−0.974139	+	0.225948i	$0.927452\pi$
$6$	−0.413625	−	0.541309i	−0.168862	−	0.220988i
$7$	0.708274	+	3.67488i	0.267703	+	1.38897i	0.828022	+	0.560696i	$0.189466\pi$
$7$	0.708274	+	3.67488i	0.267703	+	1.38897i	−0.560319	+	0.828277i	$0.689322\pi$
$8$	−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	−0.628756	−	0.777603i	$-0.716435\pi$
$11$	−1.19416	+	0.615633i	−0.360053	+	0.185620i	0.268703	+	0.963223i	$0.413405\pi$
$12$	2.05921	+	2.44439i	0.594442	+	0.705636i
$13$	−4.80127	−	0.925369i	−1.33163	−	0.256651i	−0.526717	−	0.850041i	$-0.676577\pi$
$13$	−4.80127	−	0.925369i	−1.33163	−	0.256651i	−0.804916	+	0.593389i	$0.797789\pi$
$14$	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	0.692543	−	0.721377i	$-0.256490\pi$
$17$	−1.26232	−	2.76408i	−0.306156	−	0.670389i	−0.998699	+	0.0509877i	$0.983763\pi$
$18$	−0.363822	+	1.12247i	−0.0857537	+	0.264569i
$19$	−4.64144	−	2.11967i	−1.06482	−	0.486286i	−0.195584	−	0.980687i	$-0.562660\pi$
$19$	−4.64144	−	2.11967i	−1.06482	−	0.486286i	−0.869234	+	0.494401i	$0.835388\pi$
$20$	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	−0.974953	−	0.222413i	$-0.928607\pi$
$29$	0.131792	−	1.38019i	0.0244732	−	0.256295i	0.999426	−	0.0338825i	$-0.0107872\pi$
$30$	−0.182186	+	1.66295i	−0.0332625	+	0.303611i
$31$	−0.267693	+	0.210516i	−0.0480791	+	0.0378098i	−0.641909	−	0.766780i	$-0.721857\pi$
$31$	−0.267693	+	0.210516i	−0.0480791	+	0.0378098i	0.593830	+	0.804590i	$0.297615\pi$
$32$	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	0.418371	+	0.908276i	$0.362601\pi$
$37$	−2.58296	+	8.79676i	−0.424636	+	1.44618i	−0.843007	+	0.537902i	$0.819217\pi$
$38$	−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	−0.932310	−	0.361659i	$-0.882210\pi$
$41$	−3.37252	+	3.53700i	−0.526700	+	0.552387i	0.405611	+	0.914046i	$0.367059\pi$
$42$	1.69628	−	1.90342i	0.261742	−	0.293704i
$43$	−3.52572	+	4.48332i	−0.537668	+	0.683700i	−0.976660	−	0.214791i	$-0.931093\pi$
$43$	−3.52572	+	4.48332i	−0.537668	+	0.683700i	0.438992	+	0.898491i	$0.355335\pi$
$44$	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	0.0628202	−	0.998025i	$-0.479991\pi$
$47$	−5.27943	−	3.04808i	−0.770085	−	0.444609i	−0.832905	+	0.553416i	$0.813324\pi$
$48$	−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	0.696579	−	0.717481i	$-0.254705\pi$
$53$	−0.820706	−	0.947145i	−0.112733	−	0.130100i	−0.809311	+	0.587380i	$0.800159\pi$
$54$	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	−0.380794	−	0.924660i	$-0.624349\pi$
$59$	2.43019	−	12.6090i	0.316384	−	1.64156i	0.697178	−	0.716898i	$-0.254439\pi$
$60$	0.482547	−	7.83372i	0.0622966	−	1.01133i
$61$	0.0847140	−	0.211605i	0.0108465	−	0.0270933i	−0.922846	−	0.385170i	$-0.874143\pi$
$61$	0.0847140	−	0.211605i	0.0108465	−	0.0270933i	0.933692	+	0.358076i	$0.116567\pi$
$62$	−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	−0.720565	−	0.693387i	$-0.756118\pi$
$67$	2.14636	−	4.16336i	0.262220	−	0.508635i	0.982785	+	0.184751i	$0.0591480\pi$
$68$	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	0.946689	+	0.322150i	$0.104405\pi$
$71$	7.13238	+	11.0982i	0.846458	+	1.31711i	−0.100231	+	0.994964i	$0.531958\pi$
$72$	0.982386	−	4.42967i	0.115775	−	0.522042i
$73$	−1.37981	+	3.02136i	−0.161495	+	0.353624i	−0.973030	−	0.230680i	$-0.925905\pi$
$73$	−1.37981	+	3.02136i	−0.161495	+	0.353624i	0.811535	+	0.584304i	$0.198632\pi$
$74$	−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	0.425850	−	0.904794i	$-0.359975\pi$
$79$	11.7315	−	4.06031i	1.31990	−	0.456821i	0.894047	+	0.447973i	$0.147854\pi$
$80$	−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	−0.358701	−	0.933452i	$-0.616780\pi$
$83$	5.07110	−	4.83529i	0.556626	−	0.530742i	0.915327	+	0.402711i	$0.131932\pi$
$84$	−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	0.159000	+	0.987279i	$0.449173\pi$
$89$	−2.56329	+	17.8281i	−0.271708	+	1.88977i	−0.430708	+	0.902491i	$0.641736\pi$
$90$	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	−0.143238	−	0.989688i	$-0.545751\pi$
$97$	−7.13111	−	1.72999i	−0.724054	−	0.175654i	−0.580816	+	0.814035i	$0.697267\pi$
$98$	−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	−0.999644	−	0.0266874i	$-0.991504\pi$
$101$	−9.83618	−	10.3159i	−0.978736	−	1.02647i	0.0209078	−	0.999781i	$-0.493344\pi$
$102$	−0.974098	+	1.82660i	−0.0964501	+	0.180860i
$103$	−8.66645	−	0.412834i	−0.853930	−	0.0406777i	−0.383949	−	0.923354i	$-0.625436\pi$
$103$	−8.66645	−	0.412834i	−0.853930	−	0.0406777i	−0.469981	+	0.882676i	$0.655739\pi$
$104$	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	−0.993296	−	0.115598i	$-0.963121\pi$
$107$	−0.753083	−	5.23781i	−0.0728033	−	0.506358i	0.920493	−	0.390760i	$-0.127788\pi$
$108$	−9.04264	+	3.18891i	−0.870129	+	0.306853i
$109$	13.3881	−	6.11415i	1.28235	−	0.585629i	0.346507	−	0.938047i	$-0.387368\pi$
$109$	13.3881	−	6.11415i	1.28235	−	0.585629i	0.935843	+	0.352418i	$0.114640\pi$
$110$	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	0.164449	−	0.986386i	$-0.447415\pi$
$113$	−5.77904	−	2.97930i	−0.543647	−	0.280269i	−0.708096	+	0.706116i	$0.750446\pi$
$114$	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	0.283564	−	0.958953i	$-0.408483\pi$
$127$	−5.30715	−	3.41070i	−0.470933	−	0.302650i	−0.754498	+	0.656303i	$0.772119\pi$
$128$	−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	−0.617326	−	0.786707i	$-0.711784\pi$
$131$	−18.1856	−	6.29411i	−1.58889	−	0.549919i	−0.971561	+	0.236788i	$0.923905\pi$
$132$	−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	−0.991892	−	0.127083i	$-0.959439\pi$
$137$	−4.51672	+	7.82319i	−0.385889	+	0.668380i	0.606003	+	0.795462i	$0.292772\pi$
$138$	−3.20505	+	0.634025i	−0.272832	+	0.0539718i
$139$	9.15903	+	15.8639i	0.776859	+	1.34556i	0.933744	+	0.357942i	$0.116521\pi$
$139$	9.15903	+	15.8639i	0.776859	+	1.34556i	−0.156885	+	0.987617i	$0.550145\pi$
$140$	−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	0.484213	+	0.874950i	$0.339106\pi$
$149$	−0.988447	+	20.7501i	−0.0809767	+	1.69991i	−0.565190	+	0.824961i	$0.691197\pi$
$150$	0.536706	−	0.452132i	0.0438219	−	0.0369164i
$151$	2.88856	+	8.34595i	0.235068	+	0.679183i	0.999409	+	0.0343717i	$0.0109430\pi$
$151$	2.88856	+	8.34595i	0.235068	+	0.679183i	−0.764341	+	0.644812i	$0.776936\pi$
$152$	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	0.984851	−	0.173405i	$-0.0554771\pi$
$157$	−0.188196	−	1.97088i	−0.0150197	−	0.157293i	−0.999870	+	0.0161124i	$0.994871\pi$
$158$	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	−0.438677	−	0.898645i	$-0.644553\pi$
$163$	2.50907	−	1.61248i	0.196526	−	0.126299i	0.635203	+	0.772345i	$0.280916\pi$
$164$	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	0.172141	−	0.985072i	$-0.444931\pi$
$167$	−9.07766	−	6.46418i	−0.702451	−	0.500213i	−0.874592	+	0.484859i	$0.838871\pi$
$168$	−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	0.911009	−	0.412387i	$-0.135305\pi$
$173$	0.613597	+	1.19021i	0.0466509	+	0.0904902i	−0.864358	+	0.502878i	$0.832275\pi$
$174$	−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	−0.928666	−	0.370916i	$-0.879044\pi$
$179$	−4.65532	−	15.8546i	−0.347955	−	1.18503i	0.580712	−	0.814109i	$-0.302774\pi$
$180$	−11.6363	+	7.02832i	−0.867316	+	0.523860i
$181$	10.0022	+	1.43811i	0.743461	+	0.106894i	0.503628	−	0.863921i	$-0.331998\pi$
$181$	10.0022	+	1.43811i	0.743461	+	0.106894i	0.239833	+	0.970814i	$0.422907\pi$
$182$	−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	0.0984083	−	0.995146i	$-0.468625\pi$
$191$	7.73418	−	1.49064i	0.559626	−	0.107859i	0.461218	+	0.887287i	$0.347413\pi$
$192$	6.08972	+	4.92774i	0.439488	+	0.355629i
$193$	−6.03906	−	24.8933i	−0.434701	−	1.79186i	−0.593816	−	0.804601i	$-0.702379\pi$
$193$	−6.03906	−	24.8933i	−0.434701	−	1.79186i	0.159115	−	0.987260i	$-0.449136\pi$
$194$	−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	−0.846293	−	0.532718i	$-0.821171\pi$
$197$	−20.9697	−	18.1703i	−1.49403	−	1.29458i	−0.647736	−	0.761865i	$-0.724284\pi$
$198$	−0.256567	−	1.56439i	−0.0182334	−	0.111176i
$199$	14.1918	−	2.04047i	1.00603	−	0.144645i	0.380447	−	0.924803i	$-0.375770\pi$
$199$	14.1918	−	2.04047i	1.00603	−	0.144645i	0.625583	+	0.780157i	$0.284861\pi$
$200$	−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	−0.525744	−	0.850643i	$-0.676213\pi$
$211$	−12.7973	+	1.22199i	−0.881002	+	0.0841255i	−0.355258	+	0.934768i	$0.615607\pi$
$212$	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	0.204587	−	0.978848i	$-0.434415\pi$
$223$	11.3241	−	2.18255i	0.758320	−	0.146154i	0.553733	+	0.832694i	$0.313203\pi$
$224$	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	0.670614	−	0.741807i	$-0.266031\pi$
$227$	1.62448	+	1.27751i	0.107821	+	0.0847910i	−0.562793	+	0.826598i	$0.690273\pi$
$228$	−4.37636	−	15.7103i	−0.289832	−	1.04044i
$229$	10.8821	−	6.28278i	0.719109	−	0.415178i	−0.0953158	−	0.995447i	$-0.530386\pi$
$229$	10.8821	−	6.28278i	0.719109	−	0.415178i	0.814425	+	0.580269i	$0.197053\pi$
$230$	−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	−0.601499	−	0.798873i	$-0.705430\pi$
$233$	−21.4266	−	3.08068i	−1.40370	−	0.201822i	−0.802203	+	0.597052i	$0.796339\pi$
$234$	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	−0.481611	−	0.876385i	$-0.659948\pi$
$239$	−7.85504	+	1.90561i	−0.508100	+	0.123264i	−0.0264897	+	0.999649i	$0.508433\pi$
$240$	0.443364	+	13.1595i	0.0286190	+	0.849443i
$241$	−2.30926	−	4.47934i	−0.148752	−	0.288539i	0.802673	−	0.596420i	$-0.203411\pi$
$241$	−2.30926	−	4.47934i	−0.148752	−	0.288539i	−0.951425	+	0.307880i	$0.900380\pi$
$242$	−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	−0.318687	−	0.947860i	$-0.603242\pi$
$251$	6.51350	−	4.18597i	0.411129	−	0.264216i	0.729816	+	0.683644i	$0.239606\pi$
$252$	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	0.941968	+	0.335704i	$0.108974\pi$
$257$	1.29139	+	13.5241i	0.0805549	+	0.843609i	−0.861413	+	0.507906i	$0.830420\pi$
$258$	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	−0.951096	−	0.308894i	$-0.900041\pi$
$263$	−6.39658	−	18.4817i	−0.394430	−	1.13963i	0.556667	−	0.830736i	$-0.312080\pi$
$264$	−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	−0.765359	−	0.643603i	$-0.777439\pi$
$269$	−3.89084	+	3.37143i	−0.237229	+	0.205560i	0.528130	+	0.849163i	$0.322893\pi$
$270$	−4.47414	−	2.27362i	−0.272287	−	0.138368i
$271$	−8.42993	+	2.47525i	−0.512082	+	0.150361i	−0.527557	−	0.849519i	$-0.676892\pi$
$271$	−8.42993	+	2.47525i	−0.512082	+	0.150361i	0.0154755	+	0.999880i	$0.495074\pi$
$272$	−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	−0.996595	−	0.0824500i	$-0.973726\pi$
$277$	−7.10493	+	12.3061i	−0.426894	+	0.739402i	0.569701	+	0.821852i	$0.307059\pi$
$278$	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	−0.982909	−	0.184094i	$-0.941065\pi$
$281$	−0.417536	+	1.72110i	−0.0249081	+	0.102673i	0.958001	+	0.286766i	$0.0925802\pi$
$282$	0.533754	+	4.11857i	0.0317846	+	0.245257i
$283$	−0.264061	−	0.0913925i	−0.0156968	−	0.00543272i	0.319208	−	0.947685i	$-0.396583\pi$
$283$	−0.264061	−	0.0913925i	−0.0156968	−	0.00543272i	−0.334905	+	0.942252i	$0.608704\pi$
$284$	−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	0.0150546	−	0.999887i	$-0.495208\pi$
$293$	16.3474	−	22.9567i	0.955024	−	1.34114i	0.939970	−	0.341257i	$-0.110853\pi$
$294$	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	0.992499	+	0.122254i	$0.0390123\pi$
$307$	1.30791	+	9.09669i	0.0746462	+	0.519176i	−0.917853	+	0.396921i	$0.870079\pi$
$308$	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	0.260390	−	0.965504i	$-0.416149\pi$
$311$	7.54475	+	0.359401i	0.427824	+	0.0203797i	0.167434	+	0.985883i	$0.446452\pi$
$312$	−6.77436	−	10.8709i	−0.383522	−	0.615444i
$313$	−13.3445	−	13.9953i	−0.754277	−	0.791063i	0.228952	−	0.973438i	$-0.426470\pi$
$313$	−13.3445	−	13.9953i	−0.754277	−	0.791063i	−0.983229	+	0.182375i	$0.941622\pi$
$314$	−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	−0.0862197	−	0.996276i	$-0.527479\pi$
$317$	−11.0277	−	2.67528i	−0.619375	−	0.150259i	−0.533155	+	0.846017i	$0.678994\pi$
$318$	−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	−0.948081	−	0.318030i	$-0.896979\pi$
$331$	−12.2901	+	11.7185i	−0.675522	+	0.644109i	0.272558	+	0.962139i	$0.412130\pi$
$332$	−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	0.429336	−	0.903145i	$-0.358748\pi$
$337$	−10.0888	−	12.8289i	−0.549571	−	0.698836i	−0.978906	+	0.204309i	$0.934505\pi$
$338$	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	−0.782370	−	0.622814i	$-0.785989\pi$
$347$	3.33027	−	6.45983i	0.178779	−	0.346782i	0.961148	+	0.276032i	$0.0890196\pi$
$348$	3.64512	−	2.51995i	0.195399	−	0.135083i
$349$	−2.99532	−	4.20633i	−0.160336	−	0.225160i	0.726591	−	0.687070i	$-0.241104\pi$
$349$	−2.99532	−	4.20633i	−0.160336	−	0.225160i	−0.886927	+	0.461910i	$0.847164\pi$
$350$	−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	−0.559022	−	0.829153i	$-0.688823\pi$
$353$	7.84866	−	19.6050i	0.417742	−	1.04347i	0.976764	−	0.214316i	$-0.0687523\pi$
$354$	−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	0.820896	−	0.571078i	$-0.193475\pi$
$359$	22.7885	+	6.69129i	1.20273	+	0.353153i	0.381833	+	0.924231i	$0.375293\pi$
$360$	−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	0.968018	−	0.250882i	$-0.0807206\pi$
$367$	23.6545	+	13.6569i	1.23476	+	0.712887i	0.266739	+	0.963769i	$0.414054\pi$
$368$	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	−0.532992	−	0.846120i	$-0.678932\pi$
$373$	6.51881	−	6.83673i	0.337531	−	0.353993i	0.870523	+	0.492128i	$0.163781\pi$
$374$	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	−0.0688530	+	0.997627i	$0.521934\pi$
$379$	−18.4502	+	28.7091i	−0.947724	+	1.47469i	−0.878871	+	0.477060i	$0.841702\pi$
$380$	−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	−0.872236	−	0.489085i	$-0.837331\pi$
$383$	−11.7926	+	9.27384i	−0.602576	+	0.473871i	0.269661	+	0.962955i	$0.413089\pi$
$384$	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	0.947777	+	0.318933i	$0.103325\pi$
$389$	0.682579	+	14.3291i	0.0346081	+	0.726514i	−0.913169	+	0.407581i	$0.866372\pi$
$390$	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	0.917502	−	0.397730i	$-0.130202\pi$
$397$	0.320425	+	0.701633i	0.0160817	+	0.0352139i	−0.901421	+	0.432944i	$0.857475\pi$
$398$	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	0.0809688	−	0.996717i	$-0.474199\pi$
$401$	−4.29144	−	0.827108i	−0.214304	−	0.0413038i	−0.295273	+	0.955413i	$0.595411\pi$
$402$	−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	0.760146	−	0.649752i	$-0.225127\pi$
$409$	2.97895	+	2.84042i	0.147300	+	0.140450i	−0.612847	+	0.790202i	$0.709976\pi$
$410$	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	0.967531	−	0.252753i	$-0.0813359\pi$
$419$	15.5794	+	14.8549i	0.761101	+	0.725709i	−0.206429	+	0.978461i	$0.566184\pi$
$420$	29.1297	−	3.77512i	1.42138	−	0.184207i
$421$	5.96934	+	30.9719i	0.290928	+	1.50948i	0.773599	+	0.633676i	$0.218455\pi$
$421$	5.96934	+	30.9719i	0.290928	+	1.50948i	−0.482671	+	0.875802i	$0.660333\pi$
$422$	−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	−0.982417	−	0.186701i	$-0.940220\pi$
$431$	−9.96858	−	21.8282i	−0.480170	−	1.05143i	0.502247	−	0.864724i	$-0.332507\pi$
$432$	14.5930	−	6.76760i	0.702105	−	0.325607i
$433$	1.08449	+	0.495269i	0.0521172	+	0.0238011i	0.441303	−	0.897358i	$-0.354516\pi$
$433$	1.08449	+	0.495269i	0.0521172	+	0.0238011i	−0.389186	+	0.921159i	$0.627244\pi$
$434$	−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	−0.676835	−	0.736135i	$-0.736649\pi$
$439$	−1.53033	−	32.1257i	−0.0730388	−	1.53327i	0.603796	−	0.797139i	$-0.293654\pi$
$440$	−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	0.918359	+	0.395748i	$0.129515\pi$
$443$	−1.22707	+	12.8505i	−0.0582999	+	0.610544i	−0.976659	+	0.214796i	$0.931091\pi$
$444$	−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	0.254048	+	0.967192i	$0.418238\pi$
$449$	−15.4954	+	24.1114i	−0.731275	+	1.13789i	−0.985324	+	0.170695i	$0.945399\pi$
$450$	−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	−0.802683	−	0.596406i	$-0.796595\pi$
$457$	−0.723619	+	0.920156i	−0.0338495	+	0.0430431i	0.768834	+	0.639449i	$0.220837\pi$
$458$	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	0.348729	−	0.937223i	$-0.386613\pi$
$461$	−6.19576	−	3.57712i	−0.288565	−	0.166603i	−0.637295	+	0.770620i	$0.719947\pi$
$462$	−0.853829	+	3.31728i	−0.0397237	+	0.154334i
$463$	−1.73662	+	0.695239i	−0.0807078	+	0.0323105i	−0.411665	−	0.911335i	$-0.635053\pi$
$463$	−1.73662	+	0.695239i	−0.0807078	+	0.0323105i	0.330957	+	0.943646i	$0.392628\pi$
$464$	−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	0.479669	−	0.877450i	$-0.340757\pi$
$467$	−9.87831	−	11.4002i	−0.457114	−	0.527537i	−0.936782	+	0.349912i	$0.886211\pi$
$468$	−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	0.940726	−	0.339168i	$-0.110146\pi$
$479$	6.84005	+	9.60551i	0.312530	+	0.438887i	−0.628196	+	0.778055i	$0.716206\pi$
$480$	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	−0.0807024	−	0.996738i	$-0.525716\pi$
$487$	16.0089	−	35.0545i	0.725431	−	1.58847i	0.806133	−	0.591734i	$-0.201556\pi$
$488$	−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	0.663093	−	0.748537i	$-0.269243\pi$
$491$	−4.88980	−	6.21789i	−0.220674	−	0.280609i	−0.883767	+	0.467927i	$0.845001\pi$
$492$	−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	−0.198956	−	0.980008i	$-0.563755\pi$
$499$	12.5817	−	36.3525i	0.563235	−	1.62736i	0.762191	−	0.647352i	$-0.224124\pi$
$500$	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	−0.948733	−	0.316077i	$-0.897634\pi$
$503$	1.13526	−	7.89593i	0.0506189	−	0.352062i	0.999352	−	0.0359849i	$-0.0114568\pi$
$504$	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	0.998442	−	0.0558008i	$-0.0177712\pi$
$509$	5.35438	+	13.3746i	0.237329	+	0.592818i	−0.761113	+	0.648619i	$0.775347\pi$
$510$	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	0.998257	+	0.0590110i	$0.0187947\pi$
$521$	1.30246	+	9.05880i	0.0570618	+	0.396873i	−0.941196	+	0.337862i	$0.890296\pi$
$522$	1.50128	+	0.650077i	0.0657090	+	0.0284531i
$523$	−1.84322	+	0.841770i	−0.0805983	+	0.0368080i	−0.455306	−	0.890335i	$-0.650470\pi$
$523$	−1.84322	+	0.841770i	−0.0805983	+	0.0368080i	0.374708	+	0.927143i	$0.377743\pi$
$524$	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	0.777251	−	0.629190i	$-0.216613\pi$
$541$	12.2763	+	7.88953i	0.527801	+	0.339197i	−0.249450	+	0.968388i	$0.580250\pi$
$542$	−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	−0.917781	−	0.397087i	$-0.870021\pi$
$547$	1.86943	−	7.70589i	0.0799310	−	0.329480i	0.997712	+	0.0676067i	$0.0215363\pi$
$548$	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	−0.777178	−	0.629281i	$-0.783350\pi$
$557$	−25.7430	+	7.55883i	−1.09077	+	0.320278i	−0.313589	+	0.949559i	$0.601531\pi$
$558$	−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	0.622785	+	0.782393i	$0.286001\pi$
$563$	−1.69774	+	35.6399i	−0.0715512	+	1.50204i	−0.694336	+	0.719651i	$0.744302\pi$
$564$	−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	0.164455	−	0.986385i	$-0.447413\pi$
$569$	3.32196	+	0.317209i	0.139264	+	0.0132981i	−0.0251913	+	0.999683i	$0.508019\pi$
$570$	4.37051	−	7.33229i	0.183060	−	0.307116i
$571$	−0.812591	−	8.50983i	−0.0340059	−	0.356125i	−0.996420	−	0.0845397i	$-0.973058\pi$
$571$	−0.812591	−	8.50983i	−0.0340059	−	0.356125i	0.962414	−	0.271586i	$-0.0875481\pi$
$572$	−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	−0.704482	−	0.709722i	$-0.748820\pi$
$577$	−8.44447	+	5.42693i	−0.351548	+	0.225926i	0.352934	+	0.935648i	$0.385184\pi$
$578$	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	0.794565	−	0.607179i	$-0.207699\pi$
$587$	−3.89880	−	7.56262i	−0.160921	−	0.312143i	−0.955486	+	0.295036i	$0.904668\pi$
$588$	−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	0.989478	−	0.144682i	$-0.0462158\pi$
$593$	1.92025	+	6.53979i	0.0788554	+	0.268557i	−0.910623	+	0.413238i	$0.864398\pi$
$594$	−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	0.148465	−	0.988918i	$-0.452567\pi$
$599$	26.4110	−	15.2484i	1.07913	−	0.623033i	0.930660	+	0.365884i	$0.119233\pi$
$600$	−1.88919	+	1.92689i	−0.0771257	+	0.0786648i
$601$	−9.17554	−	7.21572i	−0.374278	−	0.294335i	0.413246	−	0.910619i	$-0.364395\pi$
$601$	−9.17554	−	7.21572i	−0.374278	−	0.294335i	−0.787524	+	0.616284i	$0.788637\pi$
$602$	−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	0.686905	+	0.726747i	$0.258969\pi$
$607$	10.0859	+	41.5747i	0.409374	+	1.68746i	−0.277531	+	0.960717i	$0.589516\pi$
$608$	−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	0.210751	−	0.977540i	$-0.432409\pi$
$613$	17.0432	−	2.45045i	0.688369	−	0.0989725i	0.477619	+	0.878567i	$0.341500\pi$
$614$	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	0.0794655	−	0.996838i	$-0.474679\pi$
$617$	8.59813	−	0.821022i	0.346148	−	0.0330531i	0.266682	+	0.963785i	$0.414073\pi$
$618$	3.36119	+	4.86198i	0.135207	+	0.195578i
$619$	−33.4403	+	1.59296i	−1.34408	+	0.0640265i	−0.707243	−	0.706971i	$-0.750061\pi$
$619$	−33.4403	+	1.59296i	−1.34408	+	0.0640265i	−0.636838	+	0.770997i	$0.719758\pi$
$620$	−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	0.934859	−	0.355019i	$-0.115526\pi$
$631$	17.9982	+	15.5955i	0.716498	+	0.620849i	−0.218361	+	0.975868i	$0.570071\pi$
$632$	−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	0.995520	−	0.0945549i	$-0.0301428\pi$
$641$	28.8203	+	22.6645i	1.13833	+	0.895195i	0.142813	+	0.989750i	$0.454385\pi$
$642$	−2.52378	+	2.57414i	−0.0996056	+	0.101593i
$643$	−40.8998	+	23.6135i	−1.61293	+	0.931225i	−0.624243	+	0.781231i	$0.714592\pi$
$643$	−40.8998	+	23.6135i	−1.61293	+	0.931225i	−0.988687	+	0.149995i	$0.952074\pi$
$644$	−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	0.509068	−	0.860726i	$-0.329990\pi$
$647$	19.2048	+	2.76124i	0.755020	+	0.108555i	0.245952	+	0.969282i	$0.420899\pi$
$648$	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	−0.684037	−	0.729447i	$-0.739777\pi$
$653$	−24.4750	+	5.93758i	−0.957782	+	0.232355i	−0.273745	+	0.961802i	$0.588262\pi$
$654$	−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	−0.277391	−	0.960757i	$-0.589470\pi$
$659$	−29.2944	−	11.7277i	−1.14115	−	0.456846i	−0.863755	+	0.503911i	$0.831894\pi$
$660$	4.24646	+	9.65180i	0.165293	+	0.375696i
$661$	−4.48158	−	3.19132i	−0.174313	−	0.124128i	0.489570	−	0.871964i	$-0.337154\pi$
$661$	−4.48158	−	3.19132i	−0.174313	−	0.124128i	−0.663884	+	0.747836i	$0.731093\pi$
$662$	−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	−0.335345	−	0.942095i	$-0.608853\pi$
$673$	−21.8673	−	2.08808i	−0.842923	−	0.0804894i	−0.507578	+	0.861606i	$0.669459\pi$
$674$	−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	0.984697	−	0.174274i	$-0.0557579\pi$
$677$	2.67852	+	7.73907i	0.102944	+	0.297437i	−0.881753	+	0.471711i	$0.843637\pi$
$678$	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	−0.879041	−	0.476746i	$-0.841816\pi$
$683$	−13.9099	+	12.0530i	−0.532248	+	0.461195i	0.346793	+	0.937942i	$0.387271\pi$
$684$	−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	−0.985090	−	0.172042i	$-0.944963\pi$
$691$	−9.03090	+	15.6420i	−0.343552	+	0.595049i	0.641538	+	0.767091i	$0.278297\pi$
$692$	−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	0.536308	−	0.844022i	$-0.319818\pi$
$701$	−0.229034	−	0.147191i	−0.00865049	−	0.00555933i	−0.544959	+	0.838463i	$0.683455\pi$
$702$	−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	−0.0358884	−	0.999356i	$-0.511426\pi$
$709$	23.8782	−	17.0036i	0.896766	−	0.638584i	0.932654	+	0.360772i	$0.117487\pi$
$710$	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	0.0951793	−	0.995460i	$-0.469658\pi$
$719$	24.3963	−	11.1414i	0.909827	−	0.415504i	0.814648	+	0.579956i	$0.196930\pi$
$720$	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	0.506534	−	0.862220i	$-0.330926\pi$
$727$	−10.2139	−	10.7120i	−0.378811	−	0.397286i	−0.885345	+	0.464934i	$0.846078\pi$
$728$	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	0.998792	−	0.0491472i	$-0.0156503\pi$
$733$	6.55235	+	16.3670i	0.242017	+	0.604528i	−0.756775	+	0.653676i	$0.773226\pi$
$734$	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	−0.950809	−	0.309778i	$-0.899745\pi$
$739$	1.32552	−	9.21921i	0.0487601	−	0.339134i	0.999569	−	0.0293561i	$-0.00934569\pi$
$740$	−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	−0.842355	−	0.538922i	$-0.818832\pi$
$743$	4.16831	−	12.0435i	0.152920	−	0.441834i	0.995276	+	0.0970879i	$0.0309528\pi$
$744$	−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	0.482524	−	0.875883i	$-0.339720\pi$
$751$	−13.2207	−	16.8114i	−0.482429	−	0.613458i	−0.964952	+	0.262425i	$0.915478\pi$
$752$	−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	0.669040	−	0.743226i	$-0.266705\pi$
$757$	−7.84006	−	12.1994i	−0.284952	−	0.443394i	−0.953992	+	0.299833i	$0.903069\pi$
$758$	−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	−0.105973	−	0.994369i	$-0.533796\pi$
$761$	21.1169	−	40.9610i	0.765486	−	1.48484i	0.871460	−	0.490467i	$-0.163174\pi$
$762$	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	0.868319	+	0.496006i	$0.165201\pi$
$769$	−3.38725	+	17.5747i	−0.122147	+	0.633761i	−0.990466	+	0.137755i	$0.956011\pi$
$770$	−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	−0.212461	−	0.977169i	$-0.568148\pi$
$773$	−25.5646	−	7.50643i	−0.919493	−	0.269988i	−0.707032	+	0.707182i	$0.749966\pi$
$774$	−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	−0.969356	−	0.245662i	$-0.920995\pi$
$787$	−19.0160	+	19.9434i	−0.677848	+	0.710907i	0.291507	+	0.956569i	$0.405843\pi$
$788$	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	−0.632849	−	0.774276i	$-0.718114\pi$
$797$	−0.835596	+	0.657120i	−0.0295983	+	0.0232764i	0.603250	+	0.797552i	$0.293872\pi$
$798$	−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	0.684719	−	0.728807i	$-0.259925\pi$
$809$	16.5628	+	7.56400i	0.582319	+	0.265936i	−0.102400	+	0.994743i	$0.532652\pi$
$810$	1.16749	+	8.61387i	0.0410214	+	0.302661i
$811$	9.37690	+	20.5325i	0.329268	+	0.720995i	0.999782	−	0.0209016i	$-0.00665366\pi$
$811$	9.37690	+	20.5325i	0.329268	+	0.720995i	−0.670514	+	0.741897i	$0.733926\pi$
$812$	−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	−0.999805	−	0.0197292i	$-0.993720\pi$
$821$	−2.26218	−	11.7373i	−0.0789507	−	0.409635i	0.920855	−	0.389906i	$-0.127493\pi$
$822$	6.10299	−	0.790929i	0.212866	−	0.0275868i
$823$	−27.9871	−	26.6857i	−0.975569	−	0.930204i	0.0220087	−	0.999758i	$-0.492994\pi$
$823$	−27.9871	−	26.6857i	−0.975569	−	0.930204i	−0.997578	+	0.0695542i	$0.977842\pi$
$824$	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	0.635012	−	0.772502i	$-0.280995\pi$
$839$	47.2896	−	24.3795i	1.63262	−	0.841673i	0.997605	−	0.0691706i	$-0.0220353\pi$
$840$	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	−0.776254	−	0.630421i	$-0.782882\pi$
$853$	−1.85285	−	38.8960i	−0.0634402	−	1.33177i	0.712813	−	0.701354i	$-0.247421\pi$
$854$	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	−0.589707	−	0.807617i	$-0.700757\pi$
$857$	4.16243	−	43.5909i	0.142186	−	1.48904i	0.731893	−	0.681420i	$-0.238637\pi$
$858$	−3.60900	−	2.64644i	−0.123209	−	0.0903479i
$859$	−7.03823	+	5.53492i	−0.240141	+	0.188849i	−0.730975	−	0.682404i	$-0.760935\pi$
$859$	−7.03823	+	5.53492i	−0.240141	+	0.188849i	0.490834	+	0.871253i	$0.336692\pi$
$860$	−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	−0.964774	−	0.263080i	$-0.915262\pi$
$863$	−9.53827	+	14.8418i	−0.324687	+	0.505222i	0.640087	+	0.768302i	$0.278898\pi$
$864$	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	−0.469488	−	0.882939i	$-0.655561\pi$
$877$	−5.92207	+	2.37084i	−0.199974	+	0.0800575i	0.269514	+	0.962997i	$0.413137\pi$
$878$	−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	0.994614	−	0.103652i	$-0.0330527\pi$
$881$	22.2751	+	25.7069i	0.750469	+	0.866087i	−0.244145	+	0.969739i	$0.578507\pi$
$882$	−0.556440	−	8.24849i	−0.0187363	−	0.277741i
$883$	40.5705	+	11.9126i	1.36531	+	0.400890i	0.880631	−	0.473803i	$-0.157119\pi$
$883$	40.5705	+	11.9126i	1.36531	+	0.400890i	0.484677	+	0.874693i	$0.338937\pi$
$884$	−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	−0.999950	−	0.0100473i	$-0.996802\pi$
$887$	−2.02206	+	10.4915i	−0.0678942	+	0.352269i	0.932055	+	0.362316i	$0.118014\pi$
$888$	−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	0.0669283	−	0.997758i	$-0.478680\pi$
$907$	22.1751	−	7.67486i	0.736310	−	0.254840i	0.669382	+	0.742918i	$0.266559\pi$
$908$	−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	−0.470720	−	0.882283i	$-0.656006\pi$
$911$	11.7159	−	11.1711i	0.388166	−	0.370115i	0.858886	+	0.512167i	$0.171157\pi$
$912$	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	$-0.793986\pi$
$919$		−	36.5577i		−	1.20593i	0.797769	−	0.602964i	$-0.206014\pi$
$920$	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	0.0536494	−	0.998560i	$-0.482915\pi$
$929$	−28.8437	−	30.2504i	−0.946332	−	0.992485i	−0.999982	+	0.00607524i	$0.998066\pi$
$930$	−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	−0.772503	−	0.635011i	$-0.780995\pi$
$937$	−24.4417	+	11.1621i	−0.798475	+	0.364651i	−0.0259723	+	0.999663i	$0.508268\pi$
$938$	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	0.317602	−	0.948224i	$-0.397122\pi$
$941$	−8.29998	−	4.27894i	−0.270572	−	0.139489i	−0.588173	+	0.808735i	$0.700153\pi$
$942$	−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	−0.505391	−	0.862891i	$-0.668652\pi$
$947$	4.45427	−	3.17187i	0.144744	−	0.103072i	0.650135	+	0.759819i	$0.274712\pi$
$948$	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	−0.803616	−	0.595148i	$-0.797094\pi$
$953$	−3.09201	+	3.56836i	−0.100160	+	0.115591i	0.703456	+	0.710738i	$0.251639\pi$
$954$	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	0.968221	−	0.250095i	$-0.0804620\pi$
$967$	8.31902	+	14.4090i	0.267522	+	0.463361i	−0.700700	+	0.713456i	$0.747129\pi$
$968$	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	−0.178933	−	0.983861i	$-0.557265\pi$
$971$	6.30866	−	1.85239i	0.202454	−	0.0594460i	0.381387	+	0.924415i	$0.375446\pi$
$972$	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	0.934409	+	0.356201i	$0.115928\pi$
$977$	−0.926081	+	19.4408i	−0.0296280	+	0.621968i	−0.964037	+	0.265767i	$0.914375\pi$
$978$	−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	0.177550	−	0.984112i	$-0.443183\pi$
$983$	5.19349	+	0.495919i	0.165647	+	0.0158173i	−0.0119031	+	0.999929i	$0.503789\pi$
$984$	−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	−0.349975	−	0.936759i	$-0.613810\pi$
$991$	11.2304	−	7.21735i	0.356746	−	0.229267i	0.706721	+	0.707492i	$0.250174\pi$
$992$	−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	0.710099	−	0.704102i	$-0.248650\pi$
$997$	23.3068	+	9.33065i	0.738135	+	0.295505i	0.0280364	+	0.999607i	$0.491075\pi$
$998$	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.11.13	✓	440
3.2	odd	2		621.2.s.a.494.10		440
9.4	even	3		621.2.s.a.287.10		440
9.5	odd	6	inner	207.2.o.a.149.13	yes	440
23.21	odd	22	inner	207.2.o.a.182.13	yes	440
69.44	even	22		621.2.s.a.251.10		440
207.67	odd	66		621.2.s.a.44.10		440
207.113	even	66	inner	207.2.o.a.113.13	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.13	✓	440	1.1	even	1	trivial
207.2.o.a.113.13	yes	440	207.113	even	66	inner
207.2.o.a.149.13	yes	440	9.5	odd	6	inner
207.2.o.a.182.13	yes	440	23.21	odd	22	inner
621.2.s.a.44.10		440	207.67	odd	66
621.2.s.a.251.10		440	69.44	even	22
621.2.s.a.287.10		440	9.4	even	3
621.2.s.a.494.10		440	3.2	odd	2

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

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