LMFDB - Embedded newform 209.2.e.b.144.9

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			144.9
Root			$1.31818 - 2.28316i$ of defining polynomial
Character	$\chi$	$=$	209.144
Dual form			209.2.e.b.45.9

$q$-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 $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.152368	−	0.988324i	$-0.451310\pi$
$2$	1.31818	−	2.28316i	0.932097	−	1.61444i	0.779730	−	0.626116i	$-0.215356\pi$
$3$	0.631607	−	1.09397i	0.364658	−	0.631607i	−0.624063	−	0.781374i	$-0.714519\pi$
$3$	0.631607	−	1.09397i	0.364658	−	0.631607i	0.988721	+	0.149767i	$0.0478525\pi$
$4$	−2.47522	−	4.28721i	−1.23761	−	2.14361i
$5$	−0.759439	+	1.31539i	−0.339631	+	0.588259i	−0.984363	−	0.176150i	$-0.943636\pi$
$5$	−0.759439	+	1.31539i	−0.339631	+	0.588259i	0.644732	+	0.764409i	$0.276969\pi$
$6$	−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	0.997443	−	0.0714634i	$-0.0227669\pi$
$13$	1.57502	+	2.72802i	0.436832	+	0.756616i	−0.560611	+	0.828079i	$0.689434\pi$
$14$	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	−0.771353	−	0.636407i	$-0.780420\pi$
$17$	0.682242	−	1.18168i	0.165468	−	0.286599i	0.936821	+	0.349808i	$0.113753\pi$
$18$	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	0.844980	−	0.534798i	$-0.179612\pi$
$23$	−0.194995	−	0.337741i	−0.0406592	−	0.0704238i	−0.885639	+	0.464375i	$0.846279\pi$
$24$	−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	0.769119	−	0.639106i	$-0.220695\pi$
$29$	−0.909673	−	1.57560i	−0.168922	−	0.292582i	−0.938041	+	0.346524i	$0.887362\pi$
$30$	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	0.145604	+	0.989343i	$0.453487\pi$
$41$	−5.02001	+	8.69492i	−0.783994	+	1.35792i	−0.929598	+	0.368575i	$0.879846\pi$
$42$	−3.24058	−	5.61285i	−0.500033	−	0.866082i
$43$	0.249376	−	0.431931i	0.0380294	−	0.0658689i	−0.846384	−	0.532573i	$-0.821225\pi$
$43$	0.249376	−	0.431931i	0.0380294	−	0.0658689i	0.884414	+	0.466704i	$0.154559\pi$
$44$	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	−0.892765	−	0.450522i	$-0.851238\pi$
$47$	−5.73507	−	9.93343i	−0.836546	−	1.44894i	0.0562195	−	0.998418i	$-0.482095\pi$
$48$	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	0.830360	−	0.557228i	$-0.188135\pi$
$53$	−0.490633	−	0.849801i	−0.0673936	−	0.116729i	−0.897753	+	0.440499i	$0.854802\pi$
$54$	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	−0.992265	−	0.124139i	$-0.960383\pi$
$59$	−2.98509	+	5.17032i	−0.388625	+	0.673118i	0.603640	+	0.797257i	$0.293716\pi$
$60$	4.74913	−	8.22573i	0.613109	−	1.06194i
$61$	2.22817	+	3.85930i	0.285288	+	0.494133i	0.972679	−	0.232154i	$-0.0745775\pi$
$61$	2.22817	+	3.85930i	0.285288	+	0.494133i	−0.687391	+	0.726287i	$0.741244\pi$
$62$	−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	0.886898	+	0.461966i	$0.152856\pi$
$67$	6.90453	+	11.9590i	0.843523	+	1.46102i	−0.0433749	+	0.999059i	$0.513811\pi$
$68$	−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	−0.995854	−	0.0909712i	$-0.971003\pi$
$71$	−3.53176	+	6.11720i	−0.419143	+	0.725978i	0.576710	+	0.816949i	$0.304336\pi$
$72$	−5.46162	−	9.45980i	−0.643658	−	1.11485i
$73$	4.27226	−	7.39977i	0.500030	−	0.866077i	−0.499970	−	0.866043i	$-0.666656\pi$
$73$	4.27226	−	7.39977i	0.500030	−	0.866077i	1.00000		3.46937e-5i	$-1.10433e-5\pi$
$74$	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	−0.0248787	−	0.999690i	$-0.507920\pi$
$79$	7.58446	−	13.1367i	0.853318	−	1.47799i	0.878197	−	0.478300i	$-0.158747\pi$
$80$	−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	0.818480	−	0.574535i	$-0.194817\pi$
$89$	−0.833231	−	1.44320i	−0.0883224	−	0.152979i	−0.906802	+	0.421557i	$0.861484\pi$
$90$	−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	−0.0417576	+	0.999128i	$0.513296\pi$
$97$	−8.72755	+	15.1166i	−0.886149	+	1.53485i	−0.844391	+	0.535727i	$0.820038\pi$
$98$	−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	0.909818	−	0.415008i	$-0.136221\pi$
$101$	0.959776	+	1.66238i	0.0955013	+	0.165413i	−0.814316	+	0.580421i	$0.802888\pi$
$102$	−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	−0.685733	−	0.727853i	$-0.740518\pi$
$109$	3.00131	−	5.19841i	0.287473	−	0.497918i	0.973206	+	0.229935i	$0.0738515\pi$
$110$	−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	0.623084	−	0.782155i	$-0.285879\pi$
$127$	−4.12262	−	7.14059i	−0.365824	−	0.633625i	−0.988908	+	0.148529i	$0.952546\pi$
$128$	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	−0.101372	−	0.994849i	$-0.532323\pi$
$131$	9.28093	−	16.0750i	0.810878	−	1.40448i	0.912250	−	0.409634i	$-0.134343\pi$
$132$	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	−0.987153	−	0.159779i	$-0.948922\pi$
$137$	−7.39677	−	12.8116i	−0.631949	−	1.09457i	0.355204	−	0.934789i	$-0.384411\pi$
$138$	−0.649390	+	1.12478i	−0.0552797	+	0.0957473i
$139$	0.150171	+	0.260104i	0.0127374	+	0.0220618i	0.872324	−	0.488929i	$-0.162612\pi$
$139$	0.150171	+	0.260104i	0.0127374	+	0.0220618i	−0.859586	+	0.510990i	$0.829279\pi$
$140$	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	−0.695049	−	0.718962i	$-0.744617\pi$
$149$	3.35821	−	5.81659i	0.275115	−	0.476513i	0.970164	+	0.242449i	$0.0779507\pi$
$150$	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	−0.888883	−	0.458134i	$-0.848518\pi$
$157$	−0.597509	+	1.03492i	−0.0476864	+	0.0825953i	0.841197	+	0.540729i	$0.181851\pi$
$158$	−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	0.940986	−	0.338445i	$-0.109901\pi$
$167$	2.29240	+	3.97055i	0.177391	+	0.307251i	−0.763595	+	0.645696i	$0.776568\pi$
$168$	−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	−0.976282	−	0.216503i	$-0.930535\pi$
$173$	−3.95436	+	6.84915i	−0.300644	+	0.520731i	0.675638	+	0.737234i	$0.263868\pi$
$174$	−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	0.670517	−	0.741894i	$-0.266072\pi$
$181$	−4.13351	−	7.15944i	−0.307241	−	0.532157i	−0.977758	+	0.209737i	$0.932739\pi$
$182$	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	−0.366303	−	0.930496i	$-0.619377\pi$
$193$	8.65056	−	14.9832i	0.622681	−	1.07852i	0.988984	−	0.148020i	$-0.0472900\pi$
$194$	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	0.721502	−	0.692412i	$-0.243452\pi$
$199$	−3.37004	−	5.83708i	−0.238896	−	0.413779i	−0.960398	+	0.278633i	$0.910119\pi$
$200$	−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	−0.469275	−	0.883052i	$-0.655485\pi$
$211$	7.70026	−	13.3372i	0.530108	−	0.918174i	0.999383	−	0.0351217i	$-0.0111819\pi$
$212$	−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	−0.891165	−	0.453680i	$-0.850111\pi$
$223$	−0.786741	+	1.36268i	−0.0526841	+	0.0912515i	0.838481	+	0.544931i	$0.183444\pi$
$224$	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	−0.676200	−	0.736718i	$-0.736375\pi$
$233$	4.57802	−	7.92936i	0.299916	−	0.519470i	0.976116	+	0.217248i	$0.0697080\pi$
$234$	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	0.958975	+	0.283490i	$0.0914923\pi$
$241$	11.2550	+	19.4942i	0.724997	+	1.25573i	−0.233978	+	0.972242i	$0.575174\pi$
$242$	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	0.992391	−	0.123124i	$-0.0392913\pi$
$251$	6.17190	+	10.6901i	0.389567	+	0.674750i	−0.602824	+	0.797874i	$0.705958\pi$
$252$	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	0.674330	−	0.738430i	$-0.264432\pi$
$257$	−4.84678	−	8.39487i	−0.302334	−	0.523658i	−0.976664	+	0.214772i	$0.931099\pi$
$258$	−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	−0.0179369	−	0.999839i	$-0.505710\pi$
$263$	13.8969	−	24.0701i	0.856918	−	1.48422i	0.874855	−	0.484386i	$-0.160957\pi$
$264$	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	0.274038	−	0.961719i	$-0.411640\pi$
$269$	15.9074	−	27.5524i	0.969892	−	1.67990i	0.695854	−	0.718184i	$-0.255026\pi$
$270$	11.1391	+	19.2936i	0.677907	+	1.17417i
$271$	1.44483	−	2.50251i	0.0877670	−	0.152017i	−0.818800	−	0.574079i	$-0.805360\pi$
$271$	1.44483	−	2.50251i	0.0877670	−	0.152017i	0.906567	+	0.422062i	$0.138694\pi$
$272$	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	0.990113	+	0.140273i	$0.0447981\pi$
$281$	10.3350	+	17.9008i	0.616536	+	1.06787i	−0.373576	+	0.927599i	$0.621869\pi$
$282$	−19.0995	+	33.0813i	−1.13736	+	1.96996i
$283$	−6.92308	+	11.9911i	−0.411534	+	0.712798i	−0.995058	−	0.0992980i	$-0.968340\pi$
$283$	−6.92308	+	11.9911i	−0.411534	+	0.712798i	0.583523	+	0.812096i	$0.301674\pi$
$284$	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	−0.795844	−	0.605502i	$-0.792972\pi$
$307$	2.21573	−	3.83775i	0.126458	−	0.219032i	0.922302	+	0.386470i	$0.126306\pi$
$308$	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	0.791245	−	0.611499i	$-0.209433\pi$
$313$	−2.36985	−	4.10469i	−0.133952	−	0.232011i	−0.925196	+	0.379488i	$0.876100\pi$
$314$	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	0.620194	−	0.784449i	$-0.287054\pi$
$317$	−6.57441	−	11.3872i	−0.369256	−	0.639569i	−0.989449	+	0.144879i	$0.953721\pi$
$318$	−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	−0.922754	−	0.385389i	$-0.874067\pi$
$337$	−2.34281	+	4.05786i	−0.127621	+	0.221046i	0.795134	+	0.606434i	$0.207401\pi$
$338$	−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	−0.942155	−	0.335177i	$-0.891204\pi$
$347$	−3.36803	+	5.83360i	−0.180805	+	0.313164i	0.761350	+	0.648342i	$0.224537\pi$
$348$	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	−0.743087	−	0.669195i	$-0.766639\pi$
$359$	3.94098	−	6.82598i	0.207997	−	0.360261i	0.951083	+	0.308934i	$0.0999723\pi$
$360$	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	0.842861	−	0.538132i	$-0.180870\pi$
$367$	−0.854525	−	1.48008i	−0.0446058	−	0.0772596i	−0.887466	+	0.460873i	$0.847537\pi$
$368$	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	0.141667	+	0.989914i	$0.454754\pi$
$383$	−15.3913	+	26.6585i	−0.786458	+	1.36218i	−0.928124	+	0.372270i	$0.878579\pi$
$384$	−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	0.992884	−	0.119086i	$-0.0379965\pi$
$389$	7.75729	+	13.4360i	0.393310	+	0.681233i	−0.599574	+	0.800320i	$0.704663\pi$
$390$	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	−0.965063	−	0.262018i	$-0.915612\pi$
$397$	−5.09314	+	8.82157i	−0.255617	+	0.442742i	0.709446	+	0.704760i	$0.248945\pi$
$398$	−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	−0.997505	−	0.0705925i	$-0.977511\pi$
$401$	−8.76329	+	15.1785i	−0.437618	+	0.757976i	0.559888	+	0.828569i	$0.310844\pi$
$402$	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	0.999839	−	0.0179509i	$-0.00571424\pi$
$409$	9.79585	+	16.9669i	0.484374	+	0.838960i	−0.515465	+	0.856910i	$0.672381\pi$
$410$	−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	−0.716408	−	0.697681i	$-0.754215\pi$
$421$	5.04761	−	8.74271i	0.246005	−	0.426094i	0.962414	+	0.271587i	$0.0875486\pi$
$422$	−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	0.734996	−	0.678072i	$-0.237184\pi$
$431$	−4.56170	−	7.90110i	−0.219729	−	0.380583i	−0.954725	+	0.297489i	$0.903851\pi$
$432$	−29.5036	+	51.1017i	−1.41949	+	2.45863i
$433$	17.7484	+	30.7412i	0.852935	+	1.47733i	0.878548	+	0.477655i	$0.158513\pi$
$433$	17.7484	+	30.7412i	0.852935	+	1.47733i	−0.0256125	+	0.999672i	$0.508154\pi$
$434$	−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	−0.659770	−	0.751467i	$-0.729346\pi$
$439$	6.72370	−	11.6458i	0.320905	−	0.555823i	0.980675	+	0.195644i	$0.0626798\pi$
$440$	−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	0.864557	+	0.502534i	$0.167599\pi$
$443$	18.2585	+	31.6246i	0.867486	+	1.50253i	0.00292890	+	0.999996i	$0.499068\pi$
$444$	−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	−0.943004	−	0.332782i	$-0.892013\pi$
$461$	−3.93570	+	6.81684i	−0.183304	+	0.317492i	0.759700	+	0.650274i	$0.225346\pi$
$462$	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	−0.998451	−	0.0556352i	$-0.982282\pi$
$479$	−11.9806	−	20.7510i	−0.547407	−	0.948137i	0.451044	−	0.892502i	$-0.351052\pi$
$480$	−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	−0.876792	−	0.480869i	$-0.840321\pi$
$491$	−0.486402	+	0.842474i	−0.0219510	+	0.0380203i	0.854841	+	0.518890i	$0.173654\pi$
$492$	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	0.184386	+	0.982854i	$0.440970\pi$
$499$	−16.9544	+	29.3659i	−0.758983	+	1.31460i	−0.943370	+	0.331744i	$0.892363\pi$
$500$	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	0.999867	−	0.0163228i	$-0.00519595\pi$
$503$	10.8953	+	18.8712i	0.485797	+	0.841426i	−0.514069	+	0.857749i	$0.671863\pi$
$504$	−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	0.893193	−	0.449673i	$-0.148459\pi$
$509$	1.28979	+	2.23398i	0.0571688	+	0.0990192i	−0.836025	+	0.548692i	$0.815126\pi$
$510$	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	0.994437	−	0.105335i	$-0.0335915\pi$
$523$	9.28479	+	16.0817i	0.405996	+	0.703205i	−0.588441	+	0.808540i	$0.700258\pi$
$524$	−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	0.927163	−	0.374658i	$-0.122240\pi$
$541$	3.23581	+	5.60458i	0.139118	+	0.240960i	−0.788045	+	0.615618i	$0.788907\pi$
$542$	−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	−0.904948	−	0.425522i	$-0.860090\pi$
$547$	−19.2013	−	33.2576i	−0.820987	−	1.42199i	0.0839609	−	0.996469i	$-0.473243\pi$
$548$	−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	0.899965	−	0.435961i	$-0.143592\pi$
$557$	1.70938	+	2.96074i	0.0724289	+	0.125451i	−0.827536	+	0.561412i	$0.810258\pi$
$558$	−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	−0.999585	−	0.0288223i	$-0.990824\pi$
$587$	−11.5043	+	19.9260i	−0.474831	+	0.822432i	0.524753	+	0.851254i	$0.324158\pi$
$588$	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	0.924994	−	0.379981i	$-0.124069\pi$
$593$	3.24908	+	5.62758i	0.133424	+	0.231097i	−0.791570	+	0.611078i	$0.790736\pi$
$594$	−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	0.909058	−	0.416669i	$-0.136803\pi$
$599$	2.29285	+	3.97132i	0.0936831	+	0.162264i	−0.815375	+	0.578933i	$0.803469\pi$
$600$	−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	−0.0320107	−	0.999488i	$-0.510191\pi$
$613$	21.0345	−	36.4329i	0.849576	−	1.47151i	0.881587	−	0.472022i	$-0.156476\pi$
$614$	−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	0.998827	−	0.0484306i	$-0.0154220\pi$
$617$	11.3633	+	19.6819i	0.457471	+	0.792363i	−0.541355	+	0.840794i	$0.682089\pi$
$618$	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	0.989151	−	0.146905i	$-0.0469312\pi$
$631$	9.22777	+	15.9830i	0.367352	+	0.636272i	−0.621799	+	0.783177i	$0.713598\pi$
$632$	−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	−0.403939	−	0.914786i	$-0.632359\pi$
$641$	14.9442	−	25.8840i	0.590259	−	1.02236i	0.994197	−	0.107572i	$-0.0343076\pi$
$642$	24.2148	+	41.9414i	0.955684	+	1.65529i
$643$	7.05455	−	12.2188i	0.278204	−	0.481864i	−0.692734	−	0.721193i	$-0.743594\pi$
$643$	7.05455	−	12.2188i	0.278204	−	0.481864i	0.970939	+	0.239329i	$0.0769274\pi$
$644$	−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	0.994051	−	0.108916i	$-0.0347381\pi$
$659$	10.3377	+	17.9055i	0.402701	+	0.697499i	−0.591350	+	0.806415i	$0.701405\pi$
$660$	−4.74913	+	8.22573i	−0.184859	+	0.320186i
$661$	−3.57633	−	6.19438i	−0.139103	−	0.240934i	0.788054	−	0.615606i	$-0.211089\pi$
$661$	−3.57633	−	6.19438i	−0.139103	−	0.240934i	−0.927157	+	0.374672i	$0.877755\pi$
$662$	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	−0.943167	−	0.332319i	$-0.892169\pi$
$701$	−4.86603	+	8.42820i	−0.183787	+	0.318329i	0.759380	+	0.650647i	$0.225502\pi$
$702$	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	0.984895	−	0.173150i	$-0.0553946\pi$
$709$	9.11964	+	15.7957i	0.342495	+	0.593219i	−0.642400	+	0.766369i	$0.722061\pi$
$710$	−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	−0.460982	−	0.887409i	$-0.652503\pi$
$719$	14.4268	−	24.9879i	0.538028	−	0.931892i	0.999010	−	0.0444823i	$-0.0141638\pi$
$720$	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	−0.949971	−	0.312339i	$-0.898887\pi$
$727$	−5.51369	+	9.55000i	−0.204492	+	0.354190i	0.745479	+	0.666529i	$0.232221\pi$
$728$	−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	−0.724727	−	0.689036i	$-0.758034\pi$
$739$	6.37097	−	11.0348i	0.234360	−	0.405923i	0.959086	+	0.283113i	$0.0913673\pi$
$740$	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	−0.880156	−	0.474685i	$-0.842562\pi$
$743$	−0.790159	+	1.36860i	−0.0289881	+	0.0502089i	0.851167	+	0.524894i	$0.175895\pi$
$744$	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	−0.974940	−	0.222466i	$-0.928589\pi$
$751$	−18.6386	−	32.2830i	−0.680131	−	1.17802i	0.294809	−	0.955556i	$-0.404744\pi$
$752$	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	−0.720346	−	0.693615i	$-0.756017\pi$
$757$	6.61745	−	11.4618i	0.240515	−	0.416585i	0.960861	+	0.277030i	$0.0893503\pi$
$758$	−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	0.731109	−	0.682260i	$-0.239003\pi$
$769$	−6.24777	−	10.8214i	−0.225300	−	0.390231i	−0.956409	+	0.292029i	$0.905670\pi$
$770$	−3.89645	−	6.74885i	−0.140418	−	0.243212i
$771$	−12.2450

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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