LMFDB - Embedded newform 209.2.e.b.45.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.9
Root			$1.31818 + 2.28316i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31818 + 2.28316i) q^{2} +(0.631607 + 1.09397i) q^{3} +(-2.47522 + 4.28721i) q^{4} +(-0.759439 - 1.31539i) q^{5} +(-1.66515 + 2.88412i) q^{6} +1.94612 q^{7} -7.77846 q^{8} +(0.702146 - 1.21615i) q^{9} +O(q^{10})$	\(q+(1.31818 + 2.28316i) q^{2} +(0.631607 + 1.09397i) q^{3} +(-2.47522 + 4.28721i) q^{4} +(-0.759439 - 1.31539i) q^{5} +(-1.66515 + 2.88412i) q^{6} +1.94612 q^{7} -7.77846 q^{8} +(0.702146 - 1.21615i) q^{9} +(2.00216 - 3.46785i) q^{10} -1.00000 q^{11} -6.25347 q^{12} +(1.57502 - 2.72802i) q^{13} +(2.56535 + 4.44331i) q^{14} +(0.959333 - 1.66161i) q^{15} +(-5.30301 - 9.18508i) q^{16} +(0.682242 + 1.18168i) q^{17} +3.70223 q^{18} +(-3.37174 + 2.76249i) q^{19} +7.51912 q^{20} +(1.22918 + 2.12901i) q^{21} +(-1.31818 - 2.28316i) q^{22} +(-0.194995 + 0.337741i) q^{23} +(-4.91293 - 8.50944i) q^{24} +(1.34651 - 2.33222i) q^{25} +8.30468 q^{26} +5.56356 q^{27} +(-4.81709 + 8.34344i) q^{28} +(-0.909673 + 1.57560i) q^{29} +5.05831 q^{30} -7.22870 q^{31} +(6.20223 - 10.7426i) q^{32} +(-0.631607 - 1.09397i) q^{33} +(-1.79864 + 3.11534i) q^{34} +(-1.47796 - 2.55990i) q^{35} +(3.47594 + 6.02050i) q^{36} +10.8549 q^{37} +(-10.7518 - 4.05676i) q^{38} +3.97918 q^{39} +(5.90727 + 10.2317i) q^{40} +(-5.02001 - 8.69492i) q^{41} +(-3.24058 + 5.61285i) q^{42} +(0.249376 + 0.431931i) q^{43} +(2.47522 - 4.28721i) q^{44} -2.13295 q^{45} -1.02816 q^{46} +(-5.73507 + 9.93343i) q^{47} +(6.69883 - 11.6027i) q^{48} -3.21261 q^{49} +7.09977 q^{50} +(-0.861817 + 1.49271i) q^{51} +(7.79706 + 13.5049i) q^{52} +(-0.490633 + 0.849801i) q^{53} +(7.33380 + 12.7025i) q^{54} +(0.759439 + 1.31539i) q^{55} -15.1378 q^{56} +(-5.15171 - 1.94379i) q^{57} -4.79647 q^{58} +(-2.98509 - 5.17032i) q^{59} +(4.74913 + 8.22573i) q^{60} +(2.22817 - 3.85930i) q^{61} +(-9.52876 - 16.5043i) q^{62} +(1.36646 - 2.36678i) q^{63} +11.4907 q^{64} -4.78453 q^{65} +(1.66515 - 2.88412i) q^{66} +(6.90453 - 11.9590i) q^{67} -6.75480 q^{68} -0.492639 q^{69} +(3.89645 - 6.74885i) q^{70} +(-3.53176 - 6.11720i) q^{71} +(-5.46162 + 9.45980i) q^{72} +(4.27226 + 7.39977i) q^{73} +(14.3088 + 24.7836i) q^{74} +3.40185 q^{75} +(-3.49758 - 21.2931i) q^{76} -1.94612 q^{77} +(5.24529 + 9.08511i) q^{78} +(7.58446 + 13.1367i) q^{79} +(-8.05462 + 13.9510i) q^{80} +(1.40754 + 2.43793i) q^{81} +(13.2346 - 22.9230i) q^{82} +7.70997 q^{83} -12.1700 q^{84} +(1.03624 - 1.79482i) q^{85} +(-0.657447 + 1.13873i) q^{86} -2.29822 q^{87} +7.77846 q^{88} +(-0.833231 + 1.44320i) q^{89} +(-2.81162 - 4.86987i) q^{90} +(3.06519 - 5.30906i) q^{91} +(-0.965310 - 1.67197i) q^{92} +(-4.56569 - 7.90801i) q^{93} -30.2395 q^{94} +(6.19438 + 2.33720i) q^{95} +15.6695 q^{96} +(-8.72755 - 15.1166i) q^{97} +(-4.23481 - 7.33491i) q^{98} +(-0.702146 + 1.21615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.31818	+	2.28316i	0.932097	+	1.61444i	0.779730	+	0.626116i	$0.215356\pi$
$2$	1.31818	+	2.28316i	0.932097	+	1.61444i	0.152368	+	0.988324i	$0.451310\pi$
$3$	0.631607	+	1.09397i	0.364658	+	0.631607i	0.988721	−	0.149767i	$-0.0478525\pi$
$3$	0.631607	+	1.09397i	0.364658	+	0.631607i	−0.624063	+	0.781374i	$0.714519\pi$
$4$	−2.47522	+	4.28721i	−1.23761	+	2.14361i
$5$	−0.759439	−	1.31539i	−0.339631	−	0.588259i	0.644732	−	0.764409i	$-0.276969\pi$
$5$	−0.759439	−	1.31539i	−0.339631	−	0.588259i	−0.984363	+	0.176150i	$0.943636\pi$
$6$	−1.66515	+	2.88412i	−0.679794	+	1.17744i
$7$	1.94612			0.735565			0.367783	−	0.929912i	$-0.380117\pi$
$7$	1.94612			0.735565			0.367783	+	0.929912i	$0.380117\pi$
$8$	−7.77846			−2.75010
$9$	0.702146	−	1.21615i	0.234049	−	0.405384i
$10$	2.00216	−	3.46785i	0.633139	−	1.09663i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−6.25347			−1.80522
$13$	1.57502	−	2.72802i	0.436832	−	0.756616i	−0.560611	−	0.828079i	$-0.689434\pi$
$13$	1.57502	−	2.72802i	0.436832	−	0.756616i	0.997443	+	0.0714634i	$0.0227669\pi$
$14$	2.56535	+	4.44331i	0.685618	+	1.18753i
$15$	0.959333	−	1.66161i	0.247699	−	0.429027i
$16$	−5.30301	−	9.18508i	−1.32575	−	2.29627i
$17$	0.682242	+	1.18168i	0.165468	+	0.286599i	0.936821	−	0.349808i	$-0.113753\pi$
$17$	0.682242	+	1.18168i	0.165468	+	0.286599i	−0.771353	+	0.636407i	$0.780420\pi$
$18$	3.70223			0.872625
$19$	−3.37174	+	2.76249i	−0.773530	+	0.633759i
$19$	−3.37174	+	2.76249i	−0.773530	+	0.633759i
$20$	7.51912			1.68133
$21$	1.22918	+	2.12901i	0.268230	+	0.464588i
$22$	−1.31818	−	2.28316i	−0.281038	−	0.486772i
$23$	−0.194995	+	0.337741i	−0.0406592	+	0.0704238i	−0.885639	−	0.464375i	$-0.846279\pi$
$23$	−0.194995	+	0.337741i	−0.0406592	+	0.0704238i	0.844980	+	0.534798i	$0.179612\pi$
$24$	−4.91293	−	8.50944i	−1.00285	−	1.73698i
$25$	1.34651	−	2.33222i	0.269301	−	0.466443i
$26$	8.30468			1.62868
$27$	5.56356			1.07071
$28$	−4.81709	+	8.34344i	−0.910344	+	1.57676i
$29$	−0.909673	+	1.57560i	−0.168922	+	0.292582i	−0.938041	−	0.346524i	$-0.887362\pi$
$29$	−0.909673	+	1.57560i	−0.168922	+	0.292582i	0.769119	+	0.639106i	$0.220695\pi$
$30$	5.05831			0.923517
$31$	−7.22870			−1.29831			−0.649156	−	0.760655i	$-0.724878\pi$
$31$	−7.22870			−1.29831			−0.649156	+	0.760655i	$0.724878\pi$
$32$	6.20223	−	10.7426i	1.09641	−	1.89904i
$33$	−0.631607	−	1.09397i	−0.109949	−	0.190437i
$34$	−1.79864	+	3.11534i	−0.308465	+	0.534276i
$35$	−1.47796	−	2.55990i	−0.249821	−	0.432703i
$36$	3.47594	+	6.02050i	0.579323	+	1.00342i
$37$	10.8549			1.78454			0.892271	−	0.451499i	$-0.149111\pi$
$37$	10.8549			1.78454			0.892271	+	0.451499i	$0.149111\pi$
$38$	−10.7518	−	4.05676i	−1.74417	−	0.658093i
$39$	3.97918			0.637178
$40$	5.90727	+	10.2317i	0.934021	+	1.61777i
$41$	−5.02001	−	8.69492i	−0.783994	−	1.35792i	−0.929598	−	0.368575i	$-0.879846\pi$
$41$	−5.02001	−	8.69492i	−0.783994	−	1.35792i	0.145604	−	0.989343i	$-0.453487\pi$
$42$	−3.24058	+	5.61285i	−0.500033	+	0.866082i
$43$	0.249376	+	0.431931i	0.0380294	+	0.0658689i	0.884414	−	0.466704i	$-0.154559\pi$
$43$	0.249376	+	0.431931i	0.0380294	+	0.0658689i	−0.846384	+	0.532573i	$0.821225\pi$
$44$	2.47522	−	4.28721i	0.373154	−	0.646321i
$45$	−2.13295			−0.317961
$46$	−1.02816			−0.151593
$47$	−5.73507	+	9.93343i	−0.836546	+	1.44894i	0.0562195	+	0.998418i	$0.482095\pi$
$47$	−5.73507	+	9.93343i	−0.836546	+	1.44894i	−0.892765	+	0.450522i	$0.851238\pi$
$48$	6.69883	−	11.6027i	0.966893	−	1.67471i
$49$	−3.21261			−0.458944
$50$	7.09977			1.00406
$51$	−0.861817	+	1.49271i	−0.120679	+	0.209021i
$52$	7.79706	+	13.5049i	1.08126	+	1.87279i
$53$	−0.490633	+	0.849801i	−0.0673936	+	0.116729i	−0.897753	−	0.440499i	$-0.854802\pi$
$53$	−0.490633	+	0.849801i	−0.0673936	+	0.116729i	0.830360	+	0.557228i	$0.188135\pi$
$54$	7.33380	+	12.7025i	0.998004	+	1.72859i
$55$	0.759439	+	1.31539i	0.102403	+	0.177367i
$56$	−15.1378			−2.02288
$57$	−5.15171	−	1.94379i	−0.682361	−	0.257461i
$58$	−4.79647			−0.629807
$59$	−2.98509	−	5.17032i	−0.388625	−	0.673118i	0.603640	−	0.797257i	$-0.293716\pi$
$59$	−2.98509	−	5.17032i	−0.388625	−	0.673118i	−0.992265	+	0.124139i	$0.960383\pi$
$60$	4.74913	+	8.22573i	0.613109	+	1.06194i
$61$	2.22817	−	3.85930i	0.285288	−	0.494133i	−0.687391	−	0.726287i	$-0.741244\pi$
$61$	2.22817	−	3.85930i	0.285288	−	0.494133i	0.972679	+	0.232154i	$0.0745775\pi$
$62$	−9.52876	−	16.5043i	−1.21015	−	2.09605i
$63$	1.36646	−	2.36678i	0.172158	−	0.298187i
$64$	11.4907			1.43634
$65$	−4.78453			−0.593448
$66$	1.66515	−	2.88412i	0.204966	−	0.355011i
$67$	6.90453	−	11.9590i	0.843523	−	1.46102i	−0.0433749	−	0.999059i	$-0.513811\pi$
$67$	6.90453	−	11.9590i	0.843523	−	1.46102i	0.886898	−	0.461966i	$-0.152856\pi$
$68$	−6.75480			−0.819140
$69$	−0.492639			−0.0593068
$70$	3.89645	−	6.74885i	0.465715	−	0.806642i
$71$	−3.53176	−	6.11720i	−0.419143	−	0.725978i	0.576710	−	0.816949i	$-0.304336\pi$
$71$	−3.53176	−	6.11720i	−0.419143	−	0.725978i	−0.995854	+	0.0909712i	$0.971003\pi$
$72$	−5.46162	+	9.45980i	−0.643658	+	1.11485i
$73$	4.27226	+	7.39977i	0.500030	+	0.866077i	1.00000		3.46937e-5i	$1.10433e-5\pi$
$73$	4.27226	+	7.39977i	0.500030	+	0.866077i	−0.499970	+	0.866043i	$0.666656\pi$
$74$	14.3088	+	24.7836i	1.66337	+	2.88104i
$75$	3.40185			0.392811
$76$	−3.49758	−	21.2931i	−0.401200	−	2.44249i
$77$	−1.94612			−0.221781
$78$	5.24529	+	9.08511i	0.593912	+	1.02869i
$79$	7.58446	+	13.1367i	0.853318	+	1.47799i	0.878197	+	0.478300i	$0.158747\pi$
$79$	7.58446	+	13.1367i	0.853318	+	1.47799i	−0.0248787	+	0.999690i	$0.507920\pi$
$80$	−8.05462	+	13.9510i	−0.900534	+	1.55977i
$81$	1.40754	+	2.43793i	0.156394	+	0.270882i
$82$	13.2346	−	22.9230i	1.46152	−	2.53142i
$83$	7.70997			0.846279			0.423140	−	0.906064i	$-0.360928\pi$
$83$	7.70997			0.846279			0.423140	+	0.906064i	$0.360928\pi$
$84$	−12.1700			−1.32786
$85$	1.03624	−	1.79482i	0.112396	−	0.194676i
$86$	−0.657447	+	1.13873i	−0.0708943	+	0.122793i
$87$	−2.29822			−0.246395
$88$	7.77846			0.829187
$89$	−0.833231	+	1.44320i	−0.0883224	+	0.152979i	−0.906802	−	0.421557i	$-0.861484\pi$
$89$	−0.833231	+	1.44320i	−0.0883224	+	0.152979i	0.818480	+	0.574535i	$0.194817\pi$
$90$	−2.81162	−	4.86987i	−0.296371	−	0.513329i
$91$	3.06519	−	5.30906i	0.321319	−	0.556540i
$92$	−0.965310	−	1.67197i	−0.100641	−	0.174315i
$93$	−4.56569	−	7.90801i	−0.473440	−	0.820023i
$94$	−30.2395			−3.11897
$95$	6.19438	+	2.33720i	0.635530	+	0.239791i
$96$	15.6695			1.59926
$97$	−8.72755	−	15.1166i	−0.886149	−	1.53485i	−0.844391	−	0.535727i	$-0.820038\pi$
$97$	−8.72755	−	15.1166i	−0.886149	−	1.53485i	−0.0417576	−	0.999128i	$-0.513296\pi$
$98$	−4.23481	−	7.33491i	−0.427780	−	0.740938i
$99$	−0.702146	+	1.21615i	−0.0705684	+	0.122228i
$100$	6.66580	+	11.5455i	0.666580	+	1.15455i
$101$	0.959776	−	1.66238i	0.0955013	−	0.165413i	−0.814316	−	0.580421i	$-0.802888\pi$
$101$	0.959776	−	1.66238i	0.0955013	−	0.165413i	0.909818	+	0.415008i	$0.136221\pi$
$102$	−4.54414			−0.449937
$103$	−9.07557			−0.894243			−0.447121	−	0.894473i	$-0.647551\pi$
$103$	−9.07557			−0.894243			−0.447121	+	0.894473i	$0.647551\pi$
$104$	−12.2513	+	21.2198i	−1.20133	+	2.08077i
$105$	1.86698	−	3.23370i	0.182199	−	0.315577i
$106$	−2.58698			−0.251270
$107$	−14.5422			−1.40584			−0.702922	−	0.711267i	$-0.748122\pi$
$107$	−14.5422			−1.40584			−0.702922	+	0.711267i	$0.748122\pi$
$108$	−13.7710	+	23.8522i	−1.32512	+	2.29517i
$109$	3.00131	+	5.19841i	0.287473	+	0.497918i	0.973206	−	0.229935i	$-0.0738515\pi$
$109$	3.00131	+	5.19841i	0.287473	+	0.497918i	−0.685733	+	0.727853i	$0.740518\pi$
$110$	−2.00216	+	3.46785i	−0.190899	+	0.330646i
$111$	6.85606	+	11.8750i	0.650748	+	1.12713i
$112$	−10.3203	−	17.8753i	−0.975177	−	1.68906i
$113$	−18.4997			−1.74030			−0.870151	−	0.492785i	$-0.835979\pi$
$113$	−18.4997			−1.74030			−0.870151	+	0.492785i	$0.835979\pi$
$114$	−2.35292	−	14.3245i	−0.220371	−	1.34161i
$115$	0.592346			0.0552365
$116$	−4.50329	−	7.79992i	−0.418120	−	0.724205i
$117$	−2.21179	−	3.83094i	−0.204480	−	0.354170i
$118$	7.86979	−	13.6309i	0.724473	−	1.25482i
$119$	1.32773	+	2.29969i	0.121712	+	0.210812i
$120$	−7.46214	+	12.9248i	−0.681197	+	1.17987i
$121$	1.00000			0.0909091
$122$	11.7486			1.06366
$123$	6.34134	−	10.9835i	0.571780	−	0.990352i
$124$	17.8926	−	30.9910i	1.60681	−	2.78307i
$125$	−11.6847			−1.04512
$126$	7.20500			0.641873
$127$	−4.12262	+	7.14059i	−0.365824	+	0.633625i	−0.988908	−	0.148529i	$-0.952546\pi$
$127$	−4.12262	+	7.14059i	−0.365824	+	0.633625i	0.623084	+	0.782155i	$0.285879\pi$
$128$	2.74240	+	4.74998i	0.242396	+	0.419842i
$129$	−0.315015	+	0.545621i	−0.0277355	+	0.0480393i
$130$	−6.30690	−	10.9239i	−0.553151	−	0.958086i
$131$	9.28093	+	16.0750i	0.810878	+	1.40448i	0.912250	+	0.409634i	$0.134343\pi$
$131$	9.28093	+	16.0750i	0.810878	+	1.40448i	−0.101372	+	0.994849i	$0.532323\pi$
$132$	6.25347			0.544294
$133$	−6.56182	+	5.37615i	−0.568982	+	0.466171i
$134$	36.4058			3.14498
$135$	−4.22518	−	7.31823i	−0.363646	−	0.629853i
$136$	−5.30679	−	9.19164i	−0.455054	−	0.788176i
$137$	−7.39677	+	12.8116i	−0.631949	+	1.09457i	0.355204	+	0.934789i	$0.384411\pi$
$137$	−7.39677	+	12.8116i	−0.631949	+	1.09457i	−0.987153	+	0.159779i	$0.948922\pi$
$138$	−0.649390	−	1.12478i	−0.0552797	−	0.0957473i
$139$	0.150171	−	0.260104i	0.0127374	−	0.0220618i	−0.859586	−	0.510990i	$-0.829279\pi$
$139$	0.150171	−	0.260104i	0.0127374	−	0.0220618i	0.872324	+	0.488929i	$0.162612\pi$
$140$	14.6331			1.23673
$141$	−14.4892			−1.22021
$142$	9.31104	−	16.1272i	0.781365	−	1.35336i
$143$	−1.57502	+	2.72802i	−0.131710	+	0.228128i
$144$	−14.8940			−1.24116
$145$	2.76336			0.229485
$146$	−11.2633	+	19.5085i	−0.932153	+	1.61454i
$147$	−2.02910	−	3.51451i	−0.167358	−	0.289872i
$148$	−26.8684	+	46.5375i	−2.20857	+	3.82536i
$149$	3.35821	+	5.81659i	0.275115	+	0.476513i	0.970164	−	0.242449i	$-0.0779507\pi$
$149$	3.35821	+	5.81659i	0.275115	+	0.476513i	−0.695049	+	0.718962i	$0.744617\pi$
$150$	4.48426	+	7.76697i	0.366139	+	0.634171i
$151$	11.8291			0.962635			0.481318	−	0.876546i	$-0.340158\pi$
$151$	11.8291			0.962635			0.481318	+	0.876546i	$0.340158\pi$
$152$	26.2270	−	21.4880i	2.12729	−	1.74290i
$153$	1.91613			0.154910
$154$	−2.56535	−	4.44331i	−0.206722	−	0.358053i
$155$	5.48975	+	9.50853i	0.440948	+	0.763744i
$156$	−9.84935	+	17.0596i	−0.788579	+	1.36586i
$157$	−0.597509	−	1.03492i	−0.0476864	−	0.0825953i	0.841197	−	0.540729i	$-0.181851\pi$
$157$	−0.597509	−	1.03492i	−0.0476864	−	0.0825953i	−0.888883	+	0.458134i	$0.848518\pi$
$158$	−19.9954	+	34.6331i	−1.59075	+	2.75526i
$159$	−1.23955			−0.0983025
$160$	−18.8408			−1.48950
$161$	−0.379483	+	0.657284i	−0.0299075	+	0.0518013i
$162$	−3.71080	+	6.42730i	−0.291548	+	0.504976i
$163$	20.9191			1.63851			0.819255	−	0.573430i	$-0.194387\pi$
$163$	20.9191			1.63851			0.819255	+	0.573430i	$0.194387\pi$
$164$	49.7026			3.88112
$165$	−0.959333	+	1.66161i	−0.0746840	+	0.129356i
$166$	10.1632	+	17.6031i	0.788815	+	1.36627i
$167$	2.29240	−	3.97055i	0.177391	−	0.307251i	−0.763595	−	0.645696i	$-0.776568\pi$
$167$	2.29240	−	3.97055i	0.177391	−	0.307251i	0.940986	+	0.338445i	$0.109901\pi$
$168$	−9.56116	−	16.5604i	−0.737660	−	1.27766i
$169$	1.53861	+	2.66496i	0.118355	+	0.204997i
$170$	5.46383			0.419057
$171$	0.992160	+	6.04023i	0.0758724	+	0.461908i
$172$	−2.46904			−0.188263
$173$	−3.95436	−	6.84915i	−0.300644	−	0.520731i	0.675638	−	0.737234i	$-0.263868\pi$
$173$	−3.95436	−	6.84915i	−0.300644	−	0.520731i	−0.976282	+	0.216503i	$0.930535\pi$
$174$	−3.02948	−	5.24722i	−0.229664	−	0.397790i
$175$	2.62046	−	4.53878i	0.198089	−	0.343099i
$176$	5.30301	+	9.18508i	0.399729	+	0.692351i
$177$	3.77080	−	6.53121i	0.283431	−	0.490916i
$178$	−4.39341			−0.329300
$179$	0.863418			0.0645349			0.0322674	−	0.999479i	$-0.489727\pi$
$179$	0.863418			0.0645349			0.0322674	+	0.999479i	$0.489727\pi$
$180$	5.27952	−	9.14440i	0.393512	−	0.681583i
$181$	−4.13351	+	7.15944i	−0.307241	+	0.532157i	−0.977758	−	0.209737i	$-0.932739\pi$
$181$	−4.13351	+	7.15944i	−0.307241	+	0.532157i	0.670517	+	0.741894i	$0.266072\pi$
$182$	16.1619			1.19800
$183$	5.62930			0.416130
$184$	1.51676	−	2.62710i	0.111817	−	0.193673i
$185$	−8.24367	−	14.2785i	−0.606087	−	1.04977i
$186$	12.0369	−	20.8484i	0.882585	−	1.52868i
$187$	−0.682242	−	1.18168i	−0.0498905	−	0.0864128i
$188$	−28.3911	−	49.1749i	−2.07064	−	3.58645i
$189$	10.8274			0.787575
$190$	2.82913	+	17.2236i	0.205247	+	1.24953i
$191$	−0.995039			−0.0719985			−0.0359992	−	0.999352i	$-0.511461\pi$
$191$	−0.995039			−0.0719985			−0.0359992	+	0.999352i	$0.511461\pi$
$192$	7.25759	+	12.5705i	0.523772	+	0.907199i
$193$	8.65056	+	14.9832i	0.622681	+	1.07852i	0.988984	+	0.148020i	$0.0472900\pi$
$193$	8.65056	+	14.9832i	0.622681	+	1.07852i	−0.366303	+	0.930496i	$0.619377\pi$
$194$	23.0091	−	39.8529i	1.65195	−	2.86127i
$195$	−3.02194	−	5.23415i	−0.216406	−	0.374826i
$196$	7.95192	−	13.7731i	0.567994	−	0.983795i
$197$	10.3579			0.737970			0.368985	−	0.929435i	$-0.379705\pi$
$197$	10.3579			0.737970			0.368985	+	0.929435i	$0.379705\pi$
$198$	−3.70223			−0.263106
$199$	−3.37004	+	5.83708i	−0.238896	+	0.413779i	−0.960398	−	0.278633i	$-0.910119\pi$
$199$	−3.37004	+	5.83708i	−0.238896	+	0.413779i	0.721502	+	0.692412i	$0.243452\pi$
$200$	−10.4737	+	18.1411i	−0.740606	+	1.28277i
$201$	17.4438			1.23039
$202$	5.06065			0.356066
$203$	−1.77034	+	3.06631i	−0.124253	+	0.215213i
$204$	−4.26638	−	7.38958i	−0.298706	−	0.517374i
$205$	−7.62478	+	13.2065i	−0.532538	+	0.922383i
$206$	−11.9633	−	20.7210i	−0.833521	−	1.44370i
$207$	0.273830	+	0.474287i	0.0190325	+	0.0329652i
$208$	−33.4094			−2.31653
$209$	3.37174	−	2.76249i	0.233228	−	0.191086i
$210$	9.84410			0.679307
$211$	7.70026	+	13.3372i	0.530108	+	0.918174i	0.999383	+	0.0351217i	$0.0111819\pi$
$211$	7.70026	+	13.3372i	0.530108	+	0.918174i	−0.469275	+	0.883052i	$0.655485\pi$
$212$	−2.42885	−	4.20689i	−0.166814	−	0.288931i
$213$	4.46137	−	7.72732i	0.305688	−	0.529467i
$214$	−19.1693	−	33.2021i	−1.31038	−	2.26965i
$215$	0.378771	−	0.656051i	0.0258320	−	0.0447423i
$216$	−43.2760			−2.94456
$217$	−14.0679			−0.954993
$218$	−7.91255	+	13.7049i	−0.535906	+	0.928216i
$219$	−5.39677	+	9.34748i	−0.364680	+	0.631644i
$220$	−7.51912			−0.506939
$221$	4.29818			0.289127
$222$	−18.0751	+	31.3070i	−1.21312	+	2.10119i
$223$	−0.786741	−	1.36268i	−0.0526841	−	0.0912515i	0.838481	−	0.544931i	$-0.183444\pi$
$223$	−0.786741	−	1.36268i	−0.0526841	−	0.0912515i	−0.891165	+	0.453680i	$0.850111\pi$
$224$	12.0703	−	20.9064i	0.806480	−	1.39686i
$225$	−1.89089	−	3.27511i	−0.126059	−	0.218341i
$226$	−24.3860	−	42.2378i	−1.62213	−	2.80961i
$227$	8.65140			0.574214			0.287107	−	0.957899i	$-0.407307\pi$
$227$	8.65140			0.574214			0.287107	+	0.957899i	$0.407307\pi$
$228$	21.0851	−	17.2752i	1.39639	−	1.14408i
$229$	−20.4306			−1.35009			−0.675045	−	0.737777i	$-0.735876\pi$
$229$	−20.4306			−1.35009			−0.675045	+	0.737777i	$0.735876\pi$
$230$	0.780821	+	1.35242i	0.0514858	+	0.0891761i
$231$	−1.22918	−	2.12901i	−0.0808743	−	0.140078i
$232$	7.07586	−	12.2557i	0.464553	−	0.804629i
$233$	4.57802	+	7.92936i	0.299916	+	0.519470i	0.976116	−	0.217248i	$-0.0697080\pi$
$233$	4.57802	+	7.92936i	0.299916	+	0.519470i	−0.676200	+	0.736718i	$0.736375\pi$
$234$	5.83110	−	10.0998i	0.381191	−	0.660242i
$235$	17.4217			1.13647
$236$	29.5550			1.92387
$237$	−9.58078	+	16.5944i	−0.622339	+	1.07792i
$238$	−3.50038	+	6.06283i	−0.226896	+	0.392995i
$239$	−18.0613			−1.16829			−0.584143	−	0.811651i	$-0.698569\pi$
$239$	−18.0613			−1.16829			−0.584143	+	0.811651i	$0.698569\pi$
$240$	−20.3494			−1.31355
$241$	11.2550	−	19.4942i	0.724997	−	1.25573i	−0.233978	−	0.972242i	$-0.575174\pi$
$241$	11.2550	−	19.4942i	0.724997	−	1.25573i	0.958975	−	0.283490i	$-0.0914923\pi$
$242$	1.31818	+	2.28316i	0.0847361	+	0.146767i
$243$	6.56732	−	11.3749i	0.421293	−	0.729702i
$244$	11.0304	+	19.1053i	0.706151	+	1.22309i
$245$	2.43978	+	4.22582i	0.155872	+	0.269978i
$246$	33.4363			2.13182
$247$	2.22557	+	13.5492i	0.141609	+	0.862112i
$248$	56.2282			3.57049
$249$	4.86967	+	8.43451i	0.308603	+	0.534516i
$250$	−15.4026	−	26.6782i	−0.974149	−	1.68728i
$251$	6.17190	−	10.6901i	0.389567	−	0.674750i	−0.602824	−	0.797874i	$-0.705958\pi$
$251$	6.17190	−	10.6901i	0.389567	−	0.674750i	0.992391	+	0.123124i	$0.0392913\pi$
$252$	6.76460	+	11.7166i	0.426130	+	0.738078i
$253$	0.194995	−	0.337741i	0.0122592	−	0.0212336i
$254$	−21.7375			−1.36393
$255$	2.61799			0.163945
$256$	4.26071	−	7.37977i	0.266294	−	0.461235i
$257$	−4.84678	+	8.39487i	−0.302334	+	0.523658i	−0.976664	−	0.214772i	$-0.931099\pi$
$257$	−4.84678	+	8.39487i	−0.302334	+	0.523658i	0.674330	+	0.738430i	$0.264432\pi$
$258$	−1.66099			−0.103409
$259$	21.1251			1.31265
$260$	11.8428	−	20.5123i	0.734458	−	1.27212i
$261$	1.27745	+	2.21260i	0.0790720	+	0.136957i
$262$	−24.4679	+	42.3797i	−1.51163	+	2.61823i
$263$	13.8969	+	24.0701i	0.856918	+	1.48422i	0.874855	+	0.484386i	$0.160957\pi$
$263$	13.8969	+	24.0701i	0.856918	+	1.48422i	−0.0179369	+	0.999839i	$0.505710\pi$
$264$	4.91293	+	8.50944i	0.302370	+	0.523720i
$265$	1.49042			0.0915559
$266$	−20.9243	−	7.89494i	−1.28295	−	0.484070i
$267$	−2.10510			−0.128830
$268$	34.1805	+	59.2024i	2.08791	+	3.61636i
$269$	15.9074	+	27.5524i	0.969892	+	1.67990i	0.695854	+	0.718184i	$0.255026\pi$
$269$	15.9074	+	27.5524i	0.969892	+	1.67990i	0.274038	+	0.961719i	$0.411640\pi$
$270$	11.1391	−	19.2936i	0.677907	−	1.17417i
$271$	1.44483	+	2.50251i	0.0877670	+	0.152017i	0.906567	−	0.422062i	$-0.138694\pi$
$271$	1.44483	+	2.50251i	0.0877670	+	0.152017i	−0.818800	+	0.574079i	$0.805360\pi$
$272$	7.23587	−	12.5329i	0.438739	−	0.759918i
$273$	7.74396			0.468686
$274$	−39.0013			−2.35615
$275$	−1.34651	+	2.33222i	−0.0811973	+	0.140638i
$276$	1.21939	−	2.11205i	0.0733988	−	0.127130i
$277$	−8.78095			−0.527596			−0.263798	−	0.964578i	$-0.584975\pi$
$277$	−8.78095			−0.527596			−0.263798	+	0.964578i	$0.584975\pi$
$278$	0.791814			0.0474899
$279$	−5.07560	+	8.79120i	−0.303868	+	0.526316i
$280$	11.4963	+	19.9121i	0.687033	+	1.18998i
$281$	10.3350	−	17.9008i	0.616536	−	1.06787i	−0.373576	−	0.927599i	$-0.621869\pi$
$281$	10.3350	−	17.9008i	0.616536	−	1.06787i	0.990113	−	0.140273i	$-0.0447981\pi$
$282$	−19.0995	−	33.0813i	−1.13736	−	1.96996i
$283$	−6.92308	−	11.9911i	−0.411534	−	0.712798i	0.583523	−	0.812096i	$-0.301674\pi$
$283$	−6.92308	−	11.9911i	−0.411534	−	0.712798i	−0.995058	+	0.0992980i	$0.968340\pi$
$284$	34.9676			2.07495
$285$	1.35557	+	8.25268i	0.0802973	+	0.488847i
$286$	−8.30468			−0.491066
$287$	−9.76956	−	16.9214i	−0.576679	−	0.998837i
$288$	−8.70974	−	15.0857i	−0.513226	−	0.888934i
$289$	7.56909	−	13.1101i	0.445241	−	0.771179i
$290$	3.64262	+	6.30921i	0.213902	+	0.370490i
$291$	11.0248	−	19.0954i	0.646283	−	1.11939i
$292$	−42.2992			−2.47537
$293$	−22.2198			−1.29810			−0.649049	−	0.760747i	$-0.724833\pi$
$293$	−22.2198			−1.29810			−0.649049	+	0.760747i	$0.724833\pi$
$294$	5.34947	−	9.26555i	0.311987	−	0.540378i
$295$	−4.53398	+	7.85308i	−0.263978	+	0.457224i
$296$	−84.4348			−4.90768
$297$	−5.56356			−0.322831
$298$	−8.85348	+	15.3347i	−0.512868	+	0.888314i
$299$	0.614242	+	1.06390i	0.0355225	+	0.0615268i
$300$	−8.42033	+	14.5844i	−0.486148	+	0.842033i
$301$	0.485316	+	0.840591i	0.0279731	+	0.0484509i
$302$	15.5929	+	27.0077i	0.897270	+	1.55412i
$303$	2.42480			0.139301
$304$	43.2541	+	16.3202i	2.48079	+	0.936026i
$305$	−6.76863			−0.387571
$306$	2.52582	+	4.37485i	0.144392	+	0.250093i
$307$	2.21573	+	3.83775i	0.126458	+	0.219032i	0.922302	−	0.386470i	$-0.126306\pi$
$307$	2.21573	+	3.83775i	0.126458	+	0.219032i	−0.795844	+	0.605502i	$0.792972\pi$
$308$	4.81709	−	8.34344i	0.274479	−	0.475411i
$309$	−5.73219	−	9.92845i	−0.326093	−	0.564810i
$310$	−14.4730	+	25.0680i	−0.822012	+	1.42377i
$311$	3.17169			0.179850			0.0899252	−	0.995949i	$-0.471337\pi$
$311$	3.17169			0.179850			0.0899252	+	0.995949i	$0.471337\pi$
$312$	−30.9519			−1.75231
$313$	−2.36985	+	4.10469i	−0.133952	+	0.232011i	−0.925196	−	0.379488i	$-0.876100\pi$
$313$	−2.36985	+	4.10469i	−0.133952	+	0.232011i	0.791245	+	0.611499i	$0.209433\pi$
$314$	1.57525	−	2.72842i	0.0888968	−	0.153974i
$315$	−4.15098			−0.233881
$316$	−75.0929			−4.22430
$317$	−6.57441	+	11.3872i	−0.369256	+	0.639569i	−0.989449	−	0.144879i	$-0.953721\pi$
$317$	−6.57441	+	11.3872i	−0.369256	+	0.639569i	0.620194	+	0.784449i	$0.287054\pi$
$318$	−1.63395	−	2.83009i	−0.0916275	−	0.158704i
$319$	0.909673	−	1.57560i	0.0509319	−	0.0882167i
$320$	−8.72647	−	15.1147i	−0.487825	−	0.844937i
$321$	−9.18492	−	15.9088i	−0.512652	−	0.887940i
$322$	−2.00092			−0.111507
$323$	−5.56472	−	2.09962i	−0.309629	−	0.116826i
$324$	−13.9359			−0.774218
$325$	−4.24155	−	7.34658i	−0.235279	−	0.407515i
$326$	27.5752	+	47.7617i	1.52725	+	2.64528i
$327$	−3.79129	+	6.56670i	−0.209659	+	0.363140i
$328$	39.0480	+	67.6331i	2.15606	+	3.73441i
$329$	−11.1611	+	19.3317i	−0.615334	+	1.06579i
$330$	−5.05831			−0.278451
$331$	21.3690			1.17455			0.587273	−	0.809389i	$-0.300202\pi$
$331$	21.3690			1.17455			0.587273	+	0.809389i	$0.300202\pi$
$332$	−19.0839	+	33.0543i	−1.04736	+	1.81409i
$333$	7.62176	−	13.2013i	0.417670	−	0.723426i
$334$	12.0872			0.661384
$335$	−20.9743			−1.14595
$336$	13.0367	−	22.5803i	0.711213	−	1.23186i
$337$	−2.34281	−	4.05786i	−0.127621	−	0.221046i	0.795134	−	0.606434i	$-0.207401\pi$
$337$	−2.34281	−	4.05786i	−0.127621	−	0.221046i	−0.922754	+	0.385389i	$0.874067\pi$
$338$	−4.05635	+	7.02581i	−0.220636	+	0.382154i
$339$	−11.6845	−	20.2382i	−0.634615	−	1.09919i
$340$	5.12986	+	8.88518i	0.278206	+	0.481866i
$341$	7.22870			0.391456
$342$	−12.4830	+	10.2274i	−0.675002	+	0.553034i
$343$	−19.8750			−1.07315
$344$	−1.93976	−	3.35976i	−0.104585	−	0.181146i
$345$	0.374130	+	0.648011i	0.0201425	+	0.0348878i
$346$	10.4252	−	18.0569i	0.560460	−	0.970745i
$347$	−3.36803	−	5.83360i	−0.180805	−	0.313164i	0.761350	−	0.648342i	$-0.224537\pi$
$347$	−3.36803	−	5.83360i	−0.180805	−	0.313164i	−0.942155	+	0.335177i	$0.891204\pi$
$348$	5.68861	−	9.85296i	0.304942	−	0.528174i
$349$	21.5879			1.15557			0.577787	−	0.816188i	$-0.303916\pi$
$349$	21.5879			1.15557			0.577787	+	0.816188i	$0.303916\pi$
$350$	13.8170			0.738551
$351$	8.76273	−	15.1775i	0.467720	−	0.810115i
$352$	−6.20223	+	10.7426i	−0.330580	+	0.572581i
$353$	5.88791			0.313382			0.156691	−	0.987648i	$-0.449917\pi$
$353$	5.88791			0.313382			0.156691	+	0.987648i	$0.449917\pi$
$354$	19.8824			1.05674
$355$	−5.36432	+	9.29127i	−0.284708	+	0.493130i
$356$	−4.12487	−	7.14448i	−0.218617	−	0.378657i
$357$	−1.67720	+	2.90500i	−0.0887669	+	0.153749i
$358$	1.13814	+	1.97132i	0.0601528	+	0.104188i
$359$	3.94098	+	6.82598i	0.207997	+	0.360261i	0.951083	−	0.308934i	$-0.0999723\pi$
$359$	3.94098	+	6.82598i	0.207997	+	0.360261i	−0.743087	+	0.669195i	$0.766639\pi$
$360$	16.5911			0.874426
$361$	3.73726	−	18.6288i	0.196698	−	0.980464i
$362$	−21.7949			−1.14551
$363$	0.631607	+	1.09397i	0.0331507	+	0.0574188i
$364$	15.1740	+	26.2822i	0.795335	+	1.37756i
$365$	6.48904	−	11.2393i	0.339652	−	0.588294i
$366$	7.42046	+	12.8526i	0.387874	+	0.671817i
$367$	−0.854525	+	1.48008i	−0.0446058	+	0.0772596i	−0.887466	−	0.460873i	$-0.847537\pi$
$367$	−0.854525	+	1.48008i	−0.0446058	+	0.0772596i	0.842861	+	0.538132i	$0.180870\pi$
$368$	4.13623			0.215616
$369$	−14.0991			−0.733972
$370$	21.7334	−	37.6433i	1.12986	−	1.95698i
$371$	−0.954832	+	1.65382i	−0.0495724	+	0.0858619i
$372$	45.2044			2.34374
$373$	6.90319			0.357434			0.178717	−	0.983901i	$-0.442805\pi$
$373$	6.90319			0.357434			0.178717	+	0.983901i	$0.442805\pi$
$374$	1.79864	−	3.11534i	0.0930056	−	0.161090i
$375$	−7.38016	−	12.7828i	−0.381110	−	0.660102i
$376$	44.6100	−	77.2668i	2.30059	−	3.98473i
$377$	2.86551	+	4.96321i	0.147581	+	0.255618i
$378$	14.2725	+	24.7206i	0.734097	+	1.27149i
$379$	−27.8405			−1.43007			−0.715036	−	0.699087i	$-0.753590\pi$
$379$	−27.8405			−1.43007			−0.715036	+	0.699087i	$0.753590\pi$
$380$	−25.3525	+	20.7715i	−1.30056	+	1.06556i
$381$	−10.4155			−0.533602
$382$	−1.31164	−	2.27184i	−0.0671096	−	0.116237i
$383$	−15.3913	−	26.6585i	−0.786458	−	1.36218i	−0.928124	−	0.372270i	$-0.878579\pi$
$383$	−15.3913	−	26.6585i	−0.786458	−	1.36218i	0.141667	−	0.989914i	$-0.454754\pi$
$384$	−3.46423	+	6.00023i	−0.176783	+	0.306198i
$385$	1.47796	+	2.55990i	0.0753239	+	0.130465i
$386$	−22.8061	+	39.5013i	−1.16080	+	2.01056i
$387$	0.700393			0.0356030
$388$	86.4106			4.38683
$389$	7.75729	−	13.4360i	0.393310	−	0.681233i	−0.599574	−	0.800320i	$-0.704663\pi$
$389$	7.75729	−	13.4360i	0.393310	−	0.681233i	0.992884	+	0.119086i	$0.0379965\pi$
$390$	7.96695	−	13.7992i	0.403422	−	0.698748i
$391$	−0.532134			−0.0269112
$392$	24.9892			1.26214
$393$	−11.7238	+	20.3062i	−0.591387	+	1.02431i
$394$	13.6536	+	23.6488i	0.687860	+	1.19141i
$395$	11.5199	−	19.9530i	0.579627	−	1.00394i
$396$	−3.47594	−	6.02050i	−0.174672	−	0.302541i
$397$	−5.09314	−	8.82157i	−0.255617	−	0.442742i	0.709446	−	0.704760i	$-0.248945\pi$
$397$	−5.09314	−	8.82157i	−0.255617	−	0.442742i	−0.965063	+	0.262018i	$0.915612\pi$
$398$	−17.7693			−0.890696
$399$	−10.0259	−	3.78285i	−0.501921	−	0.189379i
$400$	−28.5621			−1.42811
$401$	−8.76329	−	15.1785i	−0.437618	−	0.757976i	0.559888	−	0.828569i	$-0.310844\pi$
$401$	−8.76329	−	15.1785i	−0.437618	−	0.757976i	−0.997505	+	0.0705925i	$0.977511\pi$
$402$	22.9941	+	39.8270i	1.14684	+	1.98639i
$403$	−11.3854	+	19.7200i	−0.567145	+	0.982324i
$404$	4.75132	+	8.22953i	0.236387	+	0.409434i
$405$	2.13788	−	3.70292i	0.106232	−	0.184000i
$406$	−9.33452			−0.463264
$407$	−10.8549			−0.538060
$408$	6.70361	−	11.6110i	0.331878	−	0.574830i
$409$	9.79585	−	16.9669i	0.484374	−	0.838960i	−0.515465	−	0.856910i	$-0.672381\pi$
$409$	9.79585	−	16.9669i	0.484374	−	0.838960i	0.999839	+	0.0179509i	$0.00571424\pi$
$410$	−40.2035			−1.98551
$411$	−18.6874			−0.921781
$412$	22.4641	−	38.9089i	1.10672	−	1.91690i
$413$	−5.80934	−	10.0621i	−0.285859	−	0.495122i
$414$	−0.721916	+	1.25039i	−0.0354802	+	0.0614536i
$415$	−5.85525	−	10.1416i	−0.287423	−	0.497831i
$416$	−19.5373	−	33.8396i	−0.957894	−	1.65912i
$417$	0.379397			0.0185791
$418$	10.7518	+	4.05676i	0.525888	+	0.198422i
$419$	−6.12240			−0.299099			−0.149549	−	0.988754i	$-0.547782\pi$
$419$	−6.12240			−0.299099			−0.149549	+	0.988754i	$0.547782\pi$
$420$	9.24238	+	16.0083i	0.450982	+	0.781124i
$421$	5.04761	+	8.74271i	0.246005	+	0.426094i	0.962414	−	0.271587i	$-0.0875486\pi$
$421$	5.04761	+	8.74271i	0.246005	+	0.426094i	−0.716408	+	0.697681i	$0.754215\pi$
$422$	−20.3007	+	35.1619i	−0.988224	+	1.71165i
$423$	8.05372	+	13.9494i	0.391585	+	0.678245i
$424$	3.81637	−	6.61015i	0.185339	−	0.321017i
$425$	3.67457			0.178243
$426$	23.5236			1.13972
$427$	4.33629	−	7.51067i	0.209848	−	0.363467i
$428$	35.9951	−	62.3453i	1.73989	−	3.01357i
$429$	−3.97918			−0.192116
$430$	1.99716			0.0963117
$431$	−4.56170	+	7.90110i	−0.219729	+	0.380583i	−0.954725	−	0.297489i	$-0.903851\pi$
$431$	−4.56170	+	7.90110i	−0.219729	+	0.380583i	0.734996	+	0.678072i	$0.237184\pi$
$432$	−29.5036	−	51.1017i	−1.41949	−	2.45863i
$433$	17.7484	−	30.7412i	0.852935	−	1.47733i	−0.0256125	−	0.999672i	$-0.508154\pi$
$433$	17.7484	−	30.7412i	0.852935	−	1.47733i	0.878548	−	0.477655i	$-0.158513\pi$
$434$	−18.5441	−	32.1194i	−0.890147	−	1.54178i
$435$	1.74536	+	3.02305i	0.0836836	+	0.144944i
$436$	−29.7156			−1.42312
$437$	−0.275535	−	1.67744i	−0.0131806	−	0.0802431i
$438$	−28.4558			−1.35967
$439$	6.72370	+	11.6458i	0.320905	+	0.555823i	0.980675	−	0.195644i	$-0.0626798\pi$
$439$	6.72370	+	11.6458i	0.320905	+	0.555823i	−0.659770	+	0.751467i	$0.729346\pi$
$440$	−5.90727	−	10.2317i	−0.281618	−	0.487777i
$441$	−2.25572	+	3.90702i	−0.107415	+	0.186049i
$442$	5.66580	+	9.81346i	0.269495	+	0.466778i
$443$	18.2585	−	31.6246i	0.867486	−	1.50253i	0.00292890	−	0.999996i	$-0.499068\pi$
$443$	18.2585	−	31.6246i	0.867486	−	1.50253i	0.864557	−	0.502534i	$-0.167599\pi$
$444$	−67.8811			−3.22149
$445$	2.53115			0.119988
$446$	2.07414	−	3.59252i	0.0982134	−	0.170111i
$447$	−4.24213	+	7.34759i	−0.200646	+	0.347529i
$448$	22.3623			1.05652
$449$	−23.5707			−1.11237			−0.556186	−	0.831058i	$-0.687736\pi$
$449$	−23.5707			−1.11237			−0.556186	+	0.831058i	$0.687736\pi$
$450$	4.98508	−	8.63441i	0.234999	−	0.407030i
$451$	5.02001	+	8.69492i	0.236383	+	0.409428i
$452$	45.7908	−	79.3120i	2.15382	−	3.73052i
$453$	7.47131	+	12.9407i	0.351033	+	0.608007i
$454$	11.4041	+	19.7526i	0.535223	+	0.927034i
$455$	−9.31128			−0.436520
$456$	40.0724	+	15.1197i	1.87656	+	0.708045i
$457$	−26.7896			−1.25316			−0.626581	−	0.779356i	$-0.715546\pi$
$457$	−26.7896			−1.25316			−0.626581	+	0.779356i	$0.715546\pi$
$458$	−26.9312	−	46.6463i	−1.25841	−	2.17964i
$459$	3.79569	+	6.57434i	0.177168	+	0.306864i
$460$	−1.46619	+	2.53951i	−0.0683614	+	0.118405i
$461$	−3.93570	−	6.81684i	−0.183304	−	0.317492i	0.759700	−	0.650274i	$-0.225346\pi$
$461$	−3.93570	−	6.81684i	−0.183304	−	0.317492i	−0.943004	+	0.332782i	$0.892013\pi$
$462$	3.24058	−	5.61285i	0.150766	−	0.261134i
$463$	28.5684			1.32769			0.663843	−	0.747872i	$-0.268924\pi$
$463$	28.5684			1.32769			0.663843	+	0.747872i	$0.268924\pi$
$464$	19.2960			0.895795
$465$	−6.93473	+	12.0113i	−0.321590	+	0.557011i
$466$	−12.0694	+	20.9047i	−0.559102	+	0.968393i
$467$	19.7852			0.915548			0.457774	−	0.889069i	$-0.348647\pi$
$467$	19.7852			0.915548			0.457774	+	0.889069i	$0.348647\pi$
$468$	21.8987			1.01227
$469$	13.4371	−	23.2737i	0.620466	−	1.07468i
$470$	22.9651	+	39.7767i	1.05930	+	1.83476i
$471$	0.754781	−	1.30732i	0.0347785	−	0.0602381i
$472$	23.2194	+	40.2171i	1.06876	+	1.85114i
$473$	−0.249376	−	0.431931i	−0.0114663	−	0.0198602i
$474$	−50.5170			−2.32032
$475$	1.90266	+	11.5833i	0.0873002	+	0.531480i
$476$	−13.1457			−0.602531
$477$	0.688992	+	1.19337i	0.0315468	+	0.0546406i
$478$	−23.8081	−	41.2368i	−1.08896	−	1.88613i
$479$	−11.9806	+	20.7510i	−0.547407	+	0.948137i	0.451044	+	0.892502i	$0.351052\pi$
$479$	−11.9806	+	20.7510i	−0.547407	+	0.948137i	−0.998451	+	0.0556352i	$0.982282\pi$
$480$	−11.9000	−	20.6114i	−0.543158	−	0.940778i
$481$	17.0968	−	29.6125i	0.779546	−	1.35021i
$482$	59.3446			2.70307
$483$	−0.958737			−0.0436240
$484$	−2.47522	+	4.28721i	−0.112510	+	0.194873i
$485$	−13.2561	+	22.9602i	−0.601928	+	1.04257i
$486$	34.6277			1.57075
$487$	−25.1424			−1.13931			−0.569655	−	0.821884i	$-0.692923\pi$
$487$	−25.1424			−1.13931			−0.569655	+	0.821884i	$0.692923\pi$
$488$	−17.3317	+	30.0194i	−0.784571	+	1.35892i
$489$	13.2126	+	22.8850i	0.597496	+	1.03489i
$490$	−6.43216	+	11.1408i	−0.290575	+	0.503291i
$491$	−0.486402	−	0.842474i	−0.0219510	−	0.0380203i	0.854841	−	0.518890i	$-0.173654\pi$
$491$	−0.486402	−	0.842474i	−0.0219510	−	0.0380203i	−0.876792	+	0.480869i	$0.840321\pi$
$492$	31.3925	+	54.3734i	1.41528	+	2.45134i
$493$	−2.48247			−0.111805
$494$	−28.0012	+	22.9416i	−1.25983	+	1.03219i
$495$	2.13295			0.0958689
$496$	38.3338	+	66.3962i	1.72124	+	2.98128i
$497$	−6.87325	−	11.9048i	−0.308307	−	0.534004i
$498$	−12.8382	+	22.2365i	−0.575296	+	0.996441i
$499$	−16.9544	−	29.3659i	−0.758983	−	1.31460i	−0.943370	−	0.331744i	$-0.892363\pi$
$499$	−16.9544	−	29.3659i	−0.758983	−	1.31460i	0.184386	−	0.982854i	$-0.440970\pi$
$500$	28.9223	−	50.0950i	1.29345	−	2.24031i
$501$	5.79158			0.258749
$502$	32.5428			1.45246
$503$	10.8953	−	18.8712i	0.485797	−	0.841426i	−0.514069	−	0.857749i	$-0.671863\pi$
$503$	10.8953	−	18.8712i	0.485797	−	0.841426i	0.999867	+	0.0163228i	$0.00519595\pi$
$504$	−10.6290	+	18.4099i	−0.473452	+	0.820044i
$505$	−2.91557			−0.129741
$506$	1.02816			0.0457071
$507$	−1.94360	+	3.36641i	−0.0863181	+	0.149507i
$508$	−20.4088	−	35.3491i	−0.905495	−	1.56836i
$509$	1.28979	−	2.23398i	0.0571688	−	0.0990192i	−0.836025	−	0.548692i	$-0.815126\pi$
$509$	1.28979	−	2.23398i	0.0571688	−	0.0990192i	0.893193	+	0.449673i	$0.148459\pi$
$510$	3.45099	+	5.97730i	0.152813	+	0.264679i
$511$	8.31434	+	14.4009i	0.367805	+	0.637056i
$512$	33.4352			1.47764
$513$	−18.7589	+	15.3693i	−0.828225	+	0.678571i
$514$	−25.5558			−1.12722
$515$	6.89234	+	11.9379i	0.303713	+	0.526046i
$516$	−1.55946	−	2.70107i	−0.0686515	−	0.118908i
$517$	5.73507	−	9.93343i	0.252228	−	0.436872i
$518$	27.8467	+	48.2320i	1.22352	+	2.11919i
$519$	4.99520	−	8.65194i	0.219265	−	0.379778i
$520$	37.2163			1.63204
$521$	14.4202			0.631762			0.315881	−	0.948799i	$-0.397700\pi$
$521$	14.4202			0.631762			0.315881	+	0.948799i	$0.397700\pi$
$522$	−3.36782	+	5.83324i	−0.147406	+	0.255314i
$523$	9.28479	−	16.0817i	0.405996	−	0.703205i	−0.588441	−	0.808540i	$-0.700258\pi$
$523$	9.28479	−	16.0817i	0.405996	−	0.703205i	0.994437	+	0.105335i	$0.0335915\pi$
$524$	−91.8894			−4.01421
$525$	6.62041			0.288938
$526$	−36.6373	+	63.4576i	−1.59746	+	2.76688i
$527$	−4.93172	−	8.54199i	−0.214829	−	0.372095i
$528$	−6.69883	+	11.6027i	−0.291529	+	0.504943i
$529$	11.4240	+	19.7869i	0.496694	+	0.860299i
$530$	1.96465	+	3.40288i	0.0853391	+	0.147812i
$531$	−8.38387			−0.363829
$532$	−6.80673	−	41.4391i	−0.295109	−	1.79661i
$533$	−31.6265			−1.36990
$534$	−2.77491	−	4.80628i	−0.120082	−	0.207988i
$535$	11.0439	+	19.1286i	0.477469	+	0.827000i
$536$	−53.7067	+	93.0227i	−2.31977	+	4.01797i
$537$	0.545340	+	0.944557i	0.0235332	+	0.0407606i
$538$	−41.9378	+	72.6384i	−1.80807	+	3.13167i
$539$	3.21261			0.138377
$540$	41.8331			1.80021
$541$	3.23581	−	5.60458i	0.139118	−	0.240960i	−0.788045	−	0.615618i	$-0.788907\pi$
$541$	3.23581	−	5.60458i	0.139118	−	0.240960i	0.927163	+	0.374658i	$0.122240\pi$
$542$	−3.80910	+	6.59755i	−0.163615	+	0.283389i
$543$	−10.4430			−0.448152
$544$	16.9257			0.725682
$545$	4.55862	−	7.89575i	0.195270	−	0.338217i
$546$	10.2080	+	17.6807i	0.436861	+	0.756666i
$547$	−19.2013	+	33.2576i	−0.820987	+	1.42199i	0.0839609	+	0.996469i	$0.473243\pi$
$547$	−19.2013	+	33.2576i	−0.820987	+	1.42199i	−0.904948	+	0.425522i	$0.860090\pi$
$548$	−36.6173	−	63.4230i	−1.56421	−	2.70930i
$549$	−3.12900	−	5.41959i	−0.133543	−	0.231302i
$550$	−7.09977			−0.302735
$551$	−1.28540	−	7.82548i	−0.0547600	−	0.333377i
$552$	3.83198			0.163100
$553$	14.7603	+	25.5656i	0.627671	+	1.08716i
$554$	−11.5749	−	20.0483i	−0.491771	−	0.851772i
$555$	10.4135	−	18.0367i	0.442029	−	0.765617i
$556$	0.743415	+	1.28763i	0.0315278	+	0.0546078i
$557$	1.70938	−	2.96074i	0.0724289	−	0.125451i	−0.827536	−	0.561412i	$-0.810258\pi$
$557$	1.70938	−	2.96074i	0.0724289	−	0.125451i	0.899965	+	0.435961i	$0.143592\pi$
$558$	−26.7623			−1.13294
$559$	1.57109			0.0664500
$560$	−15.6753	+	27.1504i	−0.662401	+	1.14731i
$561$	0.861817	−	1.49271i	0.0363859	−	0.0630223i
$562$	54.4939			2.29869
$563$	9.99944			0.421426			0.210713	−	0.977548i	$-0.432421\pi$
$563$	9.99944			0.421426			0.210713	+	0.977548i	$0.432421\pi$
$564$	35.8641	−	62.1184i	1.51015	−	2.61566i
$565$	14.0494	+	24.3342i	0.591061	+	1.02375i
$566$	18.2518	−	31.6130i	0.767180	−	1.32879i
$567$	2.73925	+	4.74452i	0.115038	+	0.199251i
$568$	27.4717	+	47.5824i	1.15269	+	1.99651i
$569$	35.1243			1.47249			0.736244	−	0.676716i	$-0.236598\pi$
$569$	35.1243			1.47249			0.736244	+	0.676716i	$0.236598\pi$
$570$	−17.0553	+	13.9736i	−0.714369	+	0.585288i
$571$	3.64459			0.152521			0.0762607	−	0.997088i	$-0.475702\pi$
$571$	3.64459			0.152521			0.0762607	+	0.997088i	$0.475702\pi$
$572$	−7.79706	−	13.5049i	−0.326011	−	0.564668i
$573$	−0.628473	−	1.08855i	−0.0262548	−	0.0454747i
$574$	25.7562	−	44.6110i	1.07504	−	1.86203i
$575$	0.525123	+	0.909539i	0.0218991	+	0.0379304i
$576$	8.06815	−	13.9744i	0.336173	−	0.582268i
$577$	9.34461			0.389021			0.194511	−	0.980900i	$-0.437688\pi$
$577$	9.34461			0.389021			0.194511	+	0.980900i	$0.437688\pi$
$578$	39.9098			1.66003
$579$	−10.9275	+	18.9270i	−0.454132	+	0.786579i
$580$	−6.83994	+	11.8471i	−0.284013	+	0.491925i
$581$	15.0046			0.622494
$582$	58.1307			2.40959
$583$	0.490633	−	0.849801i	0.0203199	−	0.0351952i
$584$	−33.2316	−	57.5588i	−1.37513	−	2.38180i
$585$	−3.35944	+	5.81872i	−0.138896	+	0.240575i
$586$	−29.2899	−	50.7315i	−1.20995	−	2.09570i
$587$	−11.5043	−	19.9260i	−0.474831	−	0.822432i	0.524753	−	0.851254i	$-0.324158\pi$
$587$	−11.5043	−	19.9260i	−0.474831	−	0.822432i	−0.999585	+	0.0288223i	$0.990824\pi$
$588$	20.0899			0.828495
$589$	24.3733	−	19.9692i	1.00428	−	0.822818i
$590$	−23.9065			−0.984215
$591$	6.54212	+	11.3313i	0.269107	+	0.466107i
$592$	−57.5639	−	99.7036i	−2.36586	−	4.09779i
$593$	3.24908	−	5.62758i	0.133424	−	0.231097i	−0.791570	−	0.611078i	$-0.790736\pi$
$593$	3.24908	−	5.62758i	0.133424	−	0.231097i	0.924994	+	0.379981i	$0.124069\pi$
$594$	−7.33380	−	12.7025i	−0.300909	−	0.521191i
$595$	2.01665	−	3.49295i	0.0826747	−	0.143197i
$596$	−33.2493			−1.36194
$597$	−8.51415			−0.348461
$598$	−1.61937	+	2.80483i	−0.0662209	+	0.114698i
$599$	2.29285	−	3.97132i	0.0936831	−	0.162264i	−0.815375	−	0.578933i	$-0.803469\pi$
$599$	2.29285	−	3.97132i	0.0936831	−	0.162264i	0.909058	+	0.416669i	$0.136803\pi$
$600$	−26.4611			−1.08027
$601$	12.9027			0.526314			0.263157	−	0.964753i	$-0.415236\pi$
$601$	12.9027			0.526314			0.263157	+	0.964753i	$0.415236\pi$
$602$	−1.27947	+	2.21611i	−0.0521474	+	0.0903219i
$603$	−9.69598	−	16.7939i	−0.394851	−	0.683902i
$604$	−29.2796	+	50.7137i	−1.19137	+	2.06351i
$605$	−0.759439	−	1.31539i	−0.0308756	−	0.0534781i
$606$	3.19634	+	5.53622i	0.129842	+	0.224894i
$607$	−45.6759			−1.85393			−0.926963	−	0.375153i	$-0.877590\pi$
$607$	−45.6759			−1.85393			−0.926963	+	0.375153i	$0.877590\pi$
$608$	8.76398	+	53.3548i	0.355426	+	2.16382i
$609$	−4.47262			−0.181240
$610$	−8.92231	−	15.4539i	−0.361254	−	0.625710i
$611$	18.0657	+	31.2907i	0.730861	+	1.26589i
$612$	−4.74286	+	8.21488i	−0.191719	+	0.332067i
$613$	21.0345	+	36.4329i	0.849576	+	1.47151i	0.881587	+	0.472022i	$0.156476\pi$
$613$	21.0345	+	36.4329i	0.849576	+	1.47151i	−0.0320107	+	0.999488i	$0.510191\pi$
$614$	−5.84148	+	10.1177i	−0.235743	+	0.408319i
$615$	−19.2635			−0.776777
$616$	15.1378			0.609921
$617$	11.3633	−	19.6819i	0.457471	−	0.792363i	−0.541355	−	0.840794i	$-0.682089\pi$
$617$	11.3633	−	19.6819i	0.457471	−	0.792363i	0.998827	+	0.0484306i	$0.0154220\pi$
$618$	15.1122	−	26.1751i	0.607901	−	1.05292i
$619$	−40.6982			−1.63580			−0.817900	−	0.575361i	$-0.804862\pi$
$619$	−40.6982			−1.63580			−0.817900	+	0.575361i	$0.804862\pi$
$620$	−54.3534			−2.18289
$621$	−1.08486	+	1.87904i	−0.0435341	+	0.0754033i
$622$	4.18088	+	7.24150i	0.167638	+	0.290358i
$623$	−1.62157	+	2.80864i	−0.0649668	+	0.112526i
$624$	−21.1016	−	36.5491i	−0.844740	−	1.46313i
$625$	2.14132	+	3.70887i	0.0856527	+	0.148355i
$626$	−12.4956			−0.499424
$627$	5.15171	+	1.94379i	0.205739	+	0.0776275i
$628$	5.91587			0.236069
$629$	7.40570	+	12.8271i	0.295285	+	0.511448i
$630$	−5.47176	−	9.47736i	−0.218000	−	0.377587i
$631$	9.22777	−	15.9830i	0.367352	−	0.636272i	−0.621799	−	0.783177i	$-0.713598\pi$
$631$	9.22777	−	15.9830i	0.367352	−	0.636272i	0.989151	+	0.146905i	$0.0469312\pi$
$632$	−58.9954	−	102.183i	−2.34671	−	4.06462i
$633$	−9.72707	+	16.8478i	−0.386616	+	0.669639i
$634$	−34.6651			−1.37673
$635$	12.5235			0.496981
$636$	3.06816	−	5.31420i	0.121660	−	0.210722i
$637$	−5.05993	+	8.76405i	−0.200482	+	0.347244i
$638$	4.79647			0.189894
$639$	−9.91926			−0.392400
$640$	4.16537	−	7.21463i	0.164651	−	0.285183i
$641$	14.9442	+	25.8840i	0.590259	+	1.02236i	0.994197	+	0.107572i	$0.0343076\pi$
$641$	14.9442	+	25.8840i	0.590259	+	1.02236i	−0.403939	+	0.914786i	$0.632359\pi$
$642$	24.2148	−	41.9414i	0.955684	−	1.65529i
$643$	7.05455	+	12.2188i	0.278204	+	0.481864i	0.970939	−	0.239329i	$-0.0769274\pi$
$643$	7.05455	+	12.2188i	0.278204	+	0.481864i	−0.692734	+	0.721193i	$0.743594\pi$
$644$	−1.87861	−	3.25385i	−0.0740277	−	0.128220i
$645$	0.956937			0.0376794
$646$	−2.54155	−	15.4729i	−0.0999960	−	0.608771i
$647$	14.8277			0.582936			0.291468	−	0.956581i	$-0.405856\pi$
$647$	14.8277			0.582936			0.291468	+	0.956581i	$0.405856\pi$
$648$	−10.9485	−	18.9634i	−0.430098	−	0.744952i
$649$	2.98509	+	5.17032i	0.117175	+	0.202953i
$650$	11.1823	−	19.3683i	0.438606	−	0.759687i
$651$	−8.88540	−	15.3900i	−0.348246	−	0.603180i
$652$	−51.7794	+	89.6845i	−2.02784	+	3.51232i
$653$	45.2237			1.76974			0.884870	−	0.465838i	$-0.154247\pi$
$653$	45.2237			1.76974			0.884870	+	0.465838i	$0.154247\pi$
$654$	−19.9905			−0.781690
$655$	14.0966	−	24.4160i	0.550799	−	0.954012i
$656$	−53.2423	+	92.2184i	−2.07876	+	3.60052i
$657$	11.9990			0.468126
$658$	−58.8498			−2.29421
$659$	10.3377	−	17.9055i	0.402701	−	0.697499i	−0.591350	−	0.806415i	$-0.701405\pi$
$659$	10.3377	−	17.9055i	0.402701	−	0.697499i	0.994051	+	0.108916i	$0.0347381\pi$
$660$	−4.74913	−	8.22573i	−0.184859	−	0.320186i
$661$	−3.57633	+	6.19438i	−0.139103	+	0.240934i	−0.927157	−	0.374672i	$-0.877755\pi$
$661$	−3.57633	+	6.19438i	−0.139103	+	0.240934i	0.788054	+	0.615606i	$0.211089\pi$
$662$	28.1683	+	48.7889i	1.09479	+	1.89623i
$663$	2.71476	+	4.70210i	0.105433	+	0.182615i
$664$	−59.9717			−2.32736
$665$	12.0550	+	4.54847i	0.467473	+	0.176382i
$666$	40.1876			1.55724
$667$	−0.354763	−	0.614467i	−0.0137365	−	0.0237923i
$668$	11.3484	+	19.6560i	0.439083	+	0.760514i
$669$	0.993822	−	1.72135i	0.0384234	−	0.0665512i
$670$	−27.6480	−	47.8877i	−1.06813	−	1.85006i
$671$	−2.22817	+	3.85930i	−0.0860175	+	0.148987i
$672$	30.4947			1.17636
$673$	−13.5419			−0.522003			−0.261002	−	0.965338i	$-0.584053\pi$
$673$	−13.5419			−0.522003			−0.261002	+	0.965338i	$0.584053\pi$
$674$	6.17650	−	10.6980i	0.237910	−	0.412072i
$675$	7.49136	−	12.9754i	0.288343	−	0.499424i
$676$	−15.2336			−0.585909
$677$	−30.9201			−1.18836			−0.594179	−	0.804333i	$-0.702523\pi$
$677$	−30.9201			−1.18836			−0.594179	+	0.804333i	$0.702523\pi$
$678$	30.8047	−	53.3553i	1.18305	−	2.04910i
$679$	−16.9849	−	29.4187i	−0.651820	−	1.12899i
$680$	−8.06037	+	13.9610i	−0.309101	+	0.535379i
$681$	5.46428	+	9.46441i	0.209392	+	0.362677i
$682$	9.52876	+	16.5043i	0.364875	+	0.631982i
$683$	10.5045			0.401943			0.200972	−	0.979597i	$-0.435590\pi$
$683$	10.5045			0.401943			0.200972	+	0.979597i	$0.435590\pi$
$684$	−28.3515	−	10.6973i	−1.08405	−	0.409022i
$685$	22.4696			0.858519
$686$	−26.1989	−	45.3778i	−1.00028	−	1.73253i
$687$	−12.9041	−	22.3505i	−0.492321	−	0.852725i
$688$	2.64488	−	4.58107i	0.100835	−	0.174652i
$689$	1.54552	+	2.67691i	0.0588794	+	0.101982i
$690$	−0.986344	+	1.70840i	−0.0375495	+	0.0650376i
$691$	9.99026			0.380048			0.190024	−	0.981779i	$-0.439143\pi$
$691$	9.99026			0.380048			0.190024	+	0.981779i	$0.439143\pi$
$692$	39.1517			1.48832
$693$	−1.36646	+	2.36678i	−0.0519076	+	0.0899067i
$694$	8.87938	−	15.3795i	0.337057	−	0.583799i
$695$	−0.456184			−0.0173040
$696$	17.8766			0.677612
$697$	6.84973	−	11.8641i	0.259452	−	0.449384i
$698$	28.4569	+	49.2887i	1.07711	+	1.86561i
$699$	−5.78301	+	10.0165i	−0.218734	+	0.378858i
$700$	12.9725	+	22.4690i	0.490313	+	0.849247i
$701$	−4.86603	−	8.42820i	−0.183787	−	0.318329i	0.759380	−	0.650647i	$-0.225502\pi$
$701$	−4.86603	−	8.42820i	−0.183787	−	0.318329i	−0.943167	+	0.332319i	$0.892169\pi$
$702$	46.2036			1.74384
$703$	−36.6001	+	29.9867i	−1.38040	+	1.13097i
$704$	−11.4907			−0.433072
$705$	11.0037	+	19.0589i	0.414423	+	0.717801i
$706$	7.76135	+	13.4431i	0.292102	+	0.505936i
$707$	1.86784	−	3.23520i	0.0702474	−	0.121672i
$708$	18.6671	+	32.3324i	0.701554	+	1.21513i
$709$	9.11964	−	15.7957i	0.342495	−	0.593219i	−0.642400	−	0.766369i	$-0.722061\pi$
$709$	9.11964	−	15.7957i	0.342495	−	0.593219i	0.984895	+	0.173150i	$0.0553946\pi$
$710$	−28.2847			−1.06150
$711$	21.3016			0.798872
$712$	6.48126	−	11.2259i	0.242896	−	0.420707i
$713$	1.40956	−	2.44142i	0.0527883	−	0.0914321i
$714$	−8.84345			−0.330958
$715$	4.78453			0.178931
$716$	−2.13715	+	3.70165i	−0.0798691	+	0.138337i
$717$	−11.4076	−	19.7586i	−0.426025	−	0.737897i
$718$	−10.3899	+	17.9958i	−0.387747	+	0.671597i
$719$	14.4268	+	24.9879i	0.538028	+	0.931892i	0.999010	+	0.0444823i	$0.0141638\pi$
$719$	14.4268	+	24.9879i	0.538028	+	0.931892i	−0.460982	+	0.887409i	$0.652503\pi$
$720$	11.3110	+	19.5913i	0.421538	+	0.730125i
$721$	−17.6622			−0.657774
$722$	47.4590	−	16.0234i	1.76624	−	0.596331i
$723$	28.4349			1.05750
$724$	−20.4627	−	35.4424i	−0.760490	−	1.31721i
$725$	2.44976	+	4.24311i	0.0909818	+	0.157585i
$726$	−1.66515	+	2.88412i	−0.0617995	+	0.107040i
$727$	−5.51369	−	9.55000i	−0.204492	−	0.354190i	0.745479	−	0.666529i	$-0.232221\pi$
$727$	−5.51369	−	9.55000i	−0.204492	−	0.354190i	−0.949971	+	0.312339i	$0.898887\pi$
$728$	−23.8424	+	41.2963i	−0.883659	+	1.53054i
$729$	25.0371			0.927300
$730$	34.2150			1.26635
$731$	−0.340269	+	0.589363i	−0.0125853	+	0.0217984i
$732$	−13.9338	+	24.1340i	−0.515007	+	0.892019i
$733$	6.59161			0.243467			0.121733	−	0.992563i	$-0.461155\pi$
$733$	6.59161			0.243467			0.121733	+	0.992563i	$0.461155\pi$
$734$	−4.50569			−0.166308
$735$	−3.08196	+	5.33811i	−0.113680	+	0.196899i
$736$	2.41880	+	4.18949i	0.0891582	+	0.154427i
$737$	−6.90453	+	11.9590i	−0.254332	+	0.440515i
$738$	−18.5853	−	32.1906i	−0.684133	−	1.18495i
$739$	6.37097	+	11.0348i	0.234360	+	0.405923i	0.959086	−	0.283113i	$-0.0913673\pi$
$739$	6.37097	+	11.0348i	0.234360	+	0.405923i	−0.724727	+	0.689036i	$0.758034\pi$
$740$	81.6197			3.00040
$741$	−13.4167	+	10.9924i	−0.492877	+	0.403818i
$742$	−5.03458			−0.184825
$743$	−0.790159	−	1.36860i	−0.0289881	−	0.0502089i	0.851167	−	0.524894i	$-0.175895\pi$
$743$	−0.790159	−	1.36860i	−0.0289881	−	0.0502089i	−0.880156	+	0.474685i	$0.842562\pi$
$744$	35.5141	+	61.5122i	1.30201	+	2.25515i
$745$	5.10071	−	8.83468i	0.186875	−	0.323678i
$746$	9.09969	+	15.7611i	0.333163	+	0.577055i
$747$	5.41353	−	9.37651i	0.198071	−	0.343068i
$748$	6.75480			0.246980
$749$	−28.3008			−1.03409
$750$	19.4568	−	33.7002i	0.710463	−	1.23056i
$751$	−18.6386	+	32.2830i	−0.680131	+	1.17802i	0.294809	+	0.955556i	$0.404744\pi$
$751$	−18.6386	+	32.2830i	−0.680131	+	1.17802i	−0.974940	+	0.222466i	$0.928589\pi$
$752$	121.652			4.43621
$753$	15.5929			0.568235
$754$	−7.55454	+	13.0849i	−0.275120	+	0.476522i
$755$	−8.98345	−	15.5598i	−0.326941	−	0.566279i
$756$	−26.8001	+	46.4192i	−0.974712	+	1.68825i
$757$	6.61745	+	11.4618i	0.240515	+	0.416585i	0.960861	−	0.277030i	$-0.0893503\pi$
$757$	6.61745	+	11.4618i	0.240515	+	0.416585i	−0.720346	+	0.693615i	$0.756017\pi$
$758$	−36.6990	−	63.5645i	−1.33297	−	2.30877i
$759$	0.492639			0.0178817
$760$	−48.1827	−	18.1798i	−1.74777	−	0.659451i
$761$	41.3446			1.49874			0.749370	−	0.662152i	$-0.230357\pi$
$761$	41.3446			1.49874			0.749370	+	0.662152i	$0.230357\pi$
$762$	−13.7296	−	23.7803i	−0.497369	−	0.861469i
$763$	5.84091	+	10.1168i	0.211455	+	0.366251i
$764$	2.46294	−	4.26594i	0.0891061	−	0.154336i
$765$	−1.45519	−	2.52046i	−0.0526124	−	0.0911274i
$766$	40.5771	−	70.2816i	1.46611	−	2.53938i
$767$	−18.8063			−0.679056
$768$	10.7644			0.388426
$769$	−6.24777	+	10.8214i	−0.225300	+	0.390231i	−0.956409	−	0.292029i	$-0.905670\pi$
$769$	−6.24777	+	10.8214i	−0.225300	+	0.390231i	0.731109	+	0.682260i	$0.239003\pi$
$770$	−3.89645	+	6.74885i	−0.140418	+	0.243212i
$771$	−12.2450			−0.440994

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31818 + 2.28316i) q^{2} +(0.631607 + 1.09397i) q^{3} +(-2.47522 + 4.28721i) q^{4} +(-0.759439 - 1.31539i) q^{5} +(-1.66515 + 2.88412i) q^{6} +1.94612 q^{7} -7.77846 q^{8} +(0.702146 - 1.21615i) q^{9} +O(q^{10})\)	\(q+(1.31818 + 2.28316i) q^{2} +(0.631607 + 1.09397i) q^{3} +(-2.47522 + 4.28721i) q^{4} +(-0.759439 - 1.31539i) q^{5} +(-1.66515 + 2.88412i) q^{6} +1.94612 q^{7} -7.77846 q^{8} +(0.702146 - 1.21615i) q^{9} +(2.00216 - 3.46785i) q^{10} -1.00000 q^{11} -6.25347 q^{12} +(1.57502 - 2.72802i) q^{13} +(2.56535 + 4.44331i) q^{14} +(0.959333 - 1.66161i) q^{15} +(-5.30301 - 9.18508i) q^{16} +(0.682242 + 1.18168i) q^{17} +3.70223 q^{18} +(-3.37174 + 2.76249i) q^{19} +7.51912 q^{20} +(1.22918 + 2.12901i) q^{21} +(-1.31818 - 2.28316i) q^{22} +(-0.194995 + 0.337741i) q^{23} +(-4.91293 - 8.50944i) q^{24} +(1.34651 - 2.33222i) q^{25} +8.30468 q^{26} +5.56356 q^{27} +(-4.81709 + 8.34344i) q^{28} +(-0.909673 + 1.57560i) q^{29} +5.05831 q^{30} -7.22870 q^{31} +(6.20223 - 10.7426i) q^{32} +(-0.631607 - 1.09397i) q^{33} +(-1.79864 + 3.11534i) q^{34} +(-1.47796 - 2.55990i) q^{35} +(3.47594 + 6.02050i) q^{36} +10.8549 q^{37} +(-10.7518 - 4.05676i) q^{38} +3.97918 q^{39} +(5.90727 + 10.2317i) q^{40} +(-5.02001 - 8.69492i) q^{41} +(-3.24058 + 5.61285i) q^{42} +(0.249376 + 0.431931i) q^{43} +(2.47522 - 4.28721i) q^{44} -2.13295 q^{45} -1.02816 q^{46} +(-5.73507 + 9.93343i) q^{47} +(6.69883 - 11.6027i) q^{48} -3.21261 q^{49} +7.09977 q^{50} +(-0.861817 + 1.49271i) q^{51} +(7.79706 + 13.5049i) q^{52} +(-0.490633 + 0.849801i) q^{53} +(7.33380 + 12.7025i) q^{54} +(0.759439 + 1.31539i) q^{55} -15.1378 q^{56} +(-5.15171 - 1.94379i) q^{57} -4.79647 q^{58} +(-2.98509 - 5.17032i) q^{59} +(4.74913 + 8.22573i) q^{60} +(2.22817 - 3.85930i) q^{61} +(-9.52876 - 16.5043i) q^{62} +(1.36646 - 2.36678i) q^{63} +11.4907 q^{64} -4.78453 q^{65} +(1.66515 - 2.88412i) q^{66} +(6.90453 - 11.9590i) q^{67} -6.75480 q^{68} -0.492639 q^{69} +(3.89645 - 6.74885i) q^{70} +(-3.53176 - 6.11720i) q^{71} +(-5.46162 + 9.45980i) q^{72} +(4.27226 + 7.39977i) q^{73} +(14.3088 + 24.7836i) q^{74} +3.40185 q^{75} +(-3.49758 - 21.2931i) q^{76} -1.94612 q^{77} +(5.24529 + 9.08511i) q^{78} +(7.58446 + 13.1367i) q^{79} +(-8.05462 + 13.9510i) q^{80} +(1.40754 + 2.43793i) q^{81} +(13.2346 - 22.9230i) q^{82} +7.70997 q^{83} -12.1700 q^{84} +(1.03624 - 1.79482i) q^{85} +(-0.657447 + 1.13873i) q^{86} -2.29822 q^{87} +7.77846 q^{88} +(-0.833231 + 1.44320i) q^{89} +(-2.81162 - 4.86987i) q^{90} +(3.06519 - 5.30906i) q^{91} +(-0.965310 - 1.67197i) q^{92} +(-4.56569 - 7.90801i) q^{93} -30.2395 q^{94} +(6.19438 + 2.33720i) q^{95} +15.6695 q^{96} +(-8.72755 - 15.1166i) q^{97} +(-4.23481 - 7.33491i) q^{98} +(-0.702146 + 1.21615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

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