LMFDB - Embedded newform 209.2.e.b.144.7

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			144.7
Root			$0.797832 - 1.38189i$ of defining polynomial
Character	$\chi$	$=$	209.144
Dual form			209.2.e.b.45.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797832 - 1.38189i) q^{2} +(-0.583506 + 1.01066i) q^{3} +(-0.273072 - 0.472974i) q^{4} +(0.206639 - 0.357909i) q^{5} +(0.931080 + 1.61268i) q^{6} +2.20560 q^{7} +2.31987 q^{8} +(0.819041 + 1.41862i) q^{9} +O(q^{10})$	\(q+(0.797832 - 1.38189i) q^{2} +(-0.583506 + 1.01066i) q^{3} +(-0.273072 - 0.472974i) q^{4} +(0.206639 - 0.357909i) q^{5} +(0.931080 + 1.61268i) q^{6} +2.20560 q^{7} +2.31987 q^{8} +(0.819041 + 1.41862i) q^{9} +(-0.329727 - 0.571103i) q^{10} -1.00000 q^{11} +0.637357 q^{12} +(-2.41770 - 4.18759i) q^{13} +(1.75970 - 3.04788i) q^{14} +(0.241150 + 0.417685i) q^{15} +(2.39701 - 4.15174i) q^{16} +(0.827285 - 1.43290i) q^{17} +2.61383 q^{18} +(-1.15945 + 4.20187i) q^{19} -0.225709 q^{20} +(-1.28698 + 2.22911i) q^{21} +(-0.797832 + 1.38189i) q^{22} +(-2.50635 - 4.34113i) q^{23} +(-1.35366 + 2.34460i) q^{24} +(2.41460 + 4.18221i) q^{25} -7.71569 q^{26} -5.41270 q^{27} +(-0.602287 - 1.04319i) q^{28} +(2.48706 + 4.30771i) q^{29} +0.769590 q^{30} -7.24422 q^{31} +(-1.50495 - 2.60665i) q^{32} +(0.583506 - 1.01066i) q^{33} +(-1.32007 - 2.28643i) q^{34} +(0.455763 - 0.789404i) q^{35} +(0.447314 - 0.774771i) q^{36} -7.83371 q^{37} +(4.88145 + 4.95461i) q^{38} +5.64298 q^{39} +(0.479375 - 0.830302i) q^{40} +(3.12797 - 5.41780i) q^{41} +(2.05359 + 3.55692i) q^{42} +(-2.74610 + 4.75638i) q^{43} +(0.273072 + 0.472974i) q^{44} +0.676984 q^{45} -7.99859 q^{46} +(0.790657 + 1.36946i) q^{47} +(2.79734 + 4.84513i) q^{48} -2.13534 q^{49} +7.70578 q^{50} +(0.965452 + 1.67221i) q^{51} +(-1.32041 + 2.28702i) q^{52} +(-6.20873 - 10.7538i) q^{53} +(-4.31843 + 7.47973i) q^{54} +(-0.206639 + 0.357909i) q^{55} +5.11669 q^{56} +(-3.57012 - 3.62363i) q^{57} +7.93702 q^{58} +(-0.812097 + 1.40659i) q^{59} +(0.131703 - 0.228116i) q^{60} +(-2.46108 - 4.26271i) q^{61} +(-5.77967 + 10.0107i) q^{62} +(1.80647 + 3.12890i) q^{63} +4.78523 q^{64} -1.99837 q^{65} +(-0.931080 - 1.61268i) q^{66} +(7.71973 + 13.3710i) q^{67} -0.903633 q^{68} +5.84989 q^{69} +(-0.727244 - 1.25962i) q^{70} +(6.30910 - 10.9277i) q^{71} +(1.90007 + 3.29101i) q^{72} +(3.75791 - 6.50889i) q^{73} +(-6.24999 + 10.8253i) q^{74} -5.63574 q^{75} +(2.30399 - 0.599020i) q^{76} -2.20560 q^{77} +(4.50215 - 7.79796i) q^{78} +(-3.84096 + 6.65273i) q^{79} +(-0.990631 - 1.71582i) q^{80} +(0.701222 - 1.21455i) q^{81} +(-4.99118 - 8.64498i) q^{82} +6.46812 q^{83} +1.40575 q^{84} +(-0.341899 - 0.592186i) q^{85} +(4.38185 + 7.58959i) q^{86} -5.80486 q^{87} -2.31987 q^{88} +(-1.80018 - 3.11800i) q^{89} +(0.540119 - 0.935514i) q^{90} +(-5.33248 - 9.23613i) q^{91} +(-1.36883 + 2.37088i) q^{92} +(4.22705 - 7.32146i) q^{93} +2.52325 q^{94} +(1.26430 + 1.28325i) q^{95} +3.51260 q^{96} +(7.45250 - 12.9081i) q^{97} +(-1.70364 + 2.95080i) q^{98} +(-0.819041 - 1.41862i) 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 $

$2$	0.797832	−	1.38189i	0.564152	−	0.977141i	−0.432976	−	0.901406i	$-0.642536\pi$
$2$	0.797832	−	1.38189i	0.564152	−	0.977141i	0.997128	−	0.0757350i	$-0.0241303\pi$
$3$	−0.583506	+	1.01066i	−0.336888	+	0.583506i	−0.983846	−	0.179019i	$-0.942708\pi$
$3$	−0.583506	+	1.01066i	−0.336888	+	0.583506i	0.646958	+	0.762526i	$0.276041\pi$
$4$	−0.273072	−	0.472974i	−0.136536	−	0.236487i
$5$	0.206639	−	0.357909i	0.0924118	−	0.160062i	−0.816114	−	0.577891i	$-0.803876\pi$
$5$	0.206639	−	0.357909i	0.0924118	−	0.160062i	0.908525	+	0.417829i	$0.137209\pi$
$6$	0.931080	+	1.61268i	0.380112	+	0.658373i
$7$	2.20560			0.833637			0.416819	−	0.908990i	$-0.363145\pi$
$7$	2.20560			0.833637			0.416819	+	0.908990i	$0.363145\pi$
$8$	2.31987			0.820197
$9$	0.819041	+	1.41862i	0.273014	+	0.472873i
$10$	−0.329727	−	0.571103i	−0.104269	−	0.180599i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.637357			0.183989
$13$	−2.41770	−	4.18759i	−0.670550	−	1.16143i	−0.977748	−	0.209782i	$-0.932725\pi$
$13$	−2.41770	−	4.18759i	−0.670550	−	1.16143i	0.307198	−	0.951646i	$-0.400609\pi$
$14$	1.75970	−	3.04788i	0.470299	−	0.814581i
$15$	0.241150	+	0.417685i	0.0622648	+	0.107846i
$16$	2.39701	−	4.15174i	0.599252	−	1.03793i
$17$	0.827285	−	1.43290i	0.200646	−	0.347529i	−0.748091	−	0.663596i	$-0.769029\pi$
$17$	0.827285	−	1.43290i	0.200646	−	0.347529i	0.948737	+	0.316067i	$0.102363\pi$
$18$	2.61383			0.616085
$19$	−1.15945	+	4.20187i	−0.265997	+	0.963974i
$19$	−1.15945	+	4.20187i	−0.265997	+	0.963974i
$20$	−0.225709			−0.0504701
$21$	−1.28698	+	2.22911i	−0.280842	+	0.486433i
$22$	−0.797832	+	1.38189i	−0.170098	+	0.294619i
$23$	−2.50635	−	4.34113i	−0.522610	−	0.905188i	−0.999654	−	0.0263079i	$-0.991625\pi$
$23$	−2.50635	−	4.34113i	−0.522610	−	0.905188i	0.477044	−	0.878880i	$-0.341708\pi$
$24$	−1.35366	+	2.34460i	−0.276314	+	0.478590i
$25$	2.41460	+	4.18221i	0.482920	+	0.836442i
$26$	−7.71569			−1.51317
$27$	−5.41270			−1.04167
$28$	−0.602287	−	1.04319i	−0.113821	−	0.197145i
$29$	2.48706	+	4.30771i	0.461835	+	0.799922i	0.999052	−	0.0435219i	$-0.0138578\pi$
$29$	2.48706	+	4.30771i	0.461835	+	0.799922i	−0.537217	+	0.843444i	$0.680524\pi$
$30$	0.769590			0.140507
$31$	−7.24422			−1.30110			−0.650550	−	0.759464i	$-0.725462\pi$
$31$	−7.24422			−1.30110			−0.650550	+	0.759464i	$0.725462\pi$
$32$	−1.50495	−	2.60665i	−0.266040	−	0.460796i
$33$	0.583506	−	1.01066i	0.101575	−	0.175934i
$34$	−1.32007	−	2.28643i	−0.226390	−	0.392119i
$35$	0.455763	−	0.789404i	0.0770379	−	0.133434i
$36$	0.447314	−	0.774771i	0.0745523	−	0.129128i
$37$	−7.83371			−1.28785			−0.643927	−	0.765087i	$-0.722696\pi$
$37$	−7.83371			−1.28785			−0.643927	+	0.765087i	$0.722696\pi$
$38$	4.88145	+	4.95461i	0.791876	+	0.803744i
$39$	5.64298			0.903600
$40$	0.479375	−	0.830302i	0.0757959	−	0.131282i
$41$	3.12797	−	5.41780i	0.488506	−	0.846118i	−0.511406	−	0.859339i	$-0.670875\pi$
$41$	3.12797	−	5.41780i	0.488506	−	0.846118i	0.999913	+	0.0132214i	$0.00420861\pi$
$42$	2.05359	+	3.55692i	0.316875	+	0.548844i
$43$	−2.74610	+	4.75638i	−0.418776	+	0.725341i	−0.995817	−	0.0913741i	$-0.970874\pi$
$43$	−2.74610	+	4.75638i	−0.418776	+	0.725341i	0.577041	+	0.816715i	$0.304207\pi$
$44$	0.273072	+	0.472974i	0.0411671	+	0.0713036i
$45$	0.676984			0.100919
$46$	−7.99859			−1.17933
$47$	0.790657	+	1.36946i	0.115329	+	0.199756i	0.917911	−	0.396786i	$-0.129874\pi$
$47$	0.790657	+	1.36946i	0.115329	+	0.199756i	−0.802582	+	0.596542i	$0.796541\pi$
$48$	2.79734	+	4.84513i	0.403761	+	0.699334i
$49$	−2.13534			−0.305049
$50$	7.70578			1.08976
$51$	0.965452	+	1.67221i	0.135190	+	0.234156i
$52$	−1.32041	+	2.28702i	−0.183108	+	0.317153i
$53$	−6.20873	−	10.7538i	−0.852835	−	1.47715i	−0.878639	−	0.477486i	$-0.841548\pi$
$53$	−6.20873	−	10.7538i	−0.852835	−	1.47715i	0.0258041	−	0.999667i	$-0.491785\pi$
$54$	−4.31843	+	7.47973i	−0.587663	+	1.01786i
$55$	−0.206639	+	0.357909i	−0.0278632	+	0.0482605i
$56$	5.11669			0.683746
$57$	−3.57012	−	3.62363i	−0.472874	−	0.479961i
$58$	7.93702			1.04218
$59$	−0.812097	+	1.40659i	−0.105726	+	0.183123i	−0.914035	−	0.405636i	$-0.867050\pi$
$59$	−0.812097	+	1.40659i	−0.105726	+	0.183123i	0.808309	+	0.588759i	$0.200383\pi$
$60$	0.131703	−	0.228116i	0.0170028	−	0.0294496i
$61$	−2.46108	−	4.26271i	−0.315108	−	0.545784i	0.664352	−	0.747420i	$-0.268708\pi$
$61$	−2.46108	−	4.26271i	−0.315108	−	0.545784i	−0.979461	+	0.201636i	$0.935374\pi$
$62$	−5.77967	+	10.0107i	−0.734019	+	1.27136i
$63$	1.80647	+	3.12890i	0.227594	+	0.394205i
$64$	4.78523			0.598154
$65$	−1.99837			−0.247867
$66$	−0.931080	−	1.61268i	−0.114608	−	0.198507i
$67$	7.71973	+	13.3710i	0.943115	+	1.63352i	0.759483	+	0.650527i	$0.225452\pi$
$67$	7.71973	+	13.3710i	0.943115	+	1.63352i	0.183632	+	0.982995i	$0.441215\pi$
$68$	−0.903633			−0.109582
$69$	5.84989			0.704243
$70$	−0.727244	−	1.25962i	−0.0869223	−	0.150554i
$71$	6.30910	−	10.9277i	0.748753	−	1.29688i	−0.199668	−	0.979864i	$-0.563986\pi$
$71$	6.30910	−	10.9277i	0.748753	−	1.29688i	0.948421	−	0.317014i	$-0.102680\pi$
$72$	1.90007	+	3.29101i	0.223925	+	0.387849i
$73$	3.75791	−	6.50889i	0.439830	−	0.761807i	−0.557846	−	0.829944i	$-0.688372\pi$
$73$	3.75791	−	6.50889i	0.439830	−	0.761807i	0.997676	+	0.0681368i	$0.0217054\pi$
$74$	−6.24999	+	10.8253i	−0.726546	+	1.25842i
$75$	−5.63574			−0.650759
$76$	2.30399	−	0.599020i	0.264286	−	0.0687123i
$77$	−2.20560			−0.251351
$78$	4.50215	−	7.79796i	0.509768	−	0.882945i
$79$	−3.84096	+	6.65273i	−0.432141	+	0.748491i	−0.997057	−	0.0766576i	$-0.975575\pi$
$79$	−3.84096	+	6.65273i	−0.432141	+	0.748491i	0.564916	+	0.825148i	$0.308909\pi$
$80$	−0.990631	−	1.71582i	−0.110756	−	0.191835i
$81$	0.701222	−	1.21455i	0.0779135	−	0.134950i
$82$	−4.99118	−	8.64498i	−0.551184	−	0.954679i
$83$	6.46812			0.709968			0.354984	−	0.934872i	$-0.384486\pi$
$83$	6.46812			0.709968			0.354984	+	0.934872i	$0.384486\pi$
$84$	1.40575			0.153380
$85$	−0.341899	−	0.592186i	−0.0370841	−	0.0642316i
$86$	4.38185	+	7.58959i	0.472507	+	0.818406i
$87$	−5.80486			−0.622346
$88$	−2.31987			−0.247299
$89$	−1.80018	−	3.11800i	−0.190819	−	0.330508i	0.754703	−	0.656066i	$-0.227781\pi$
$89$	−1.80018	−	3.11800i	−0.190819	−	0.330508i	−0.945522	+	0.325559i	$0.894448\pi$
$90$	0.540119	−	0.935514i	0.0569336	−	0.0986118i
$91$	−5.33248	−	9.23613i	−0.558996	−	0.968209i
$92$	−1.36883	+	2.37088i	−0.142710	+	0.247181i
$93$	4.22705	−	7.32146i	0.438324	−	0.759200i
$94$	2.52325			0.260253
$95$	1.26430	+	1.28325i	0.129714	+	0.131659i
$96$	3.51260			0.358503
$97$	7.45250	−	12.9081i	0.756687	−	1.31062i	−0.187844	−	0.982199i	$-0.560150\pi$
$97$	7.45250	−	12.9081i	0.756687	−	1.31062i	0.944531	−	0.328422i	$-0.106517\pi$
$98$	−1.70364	+	2.95080i	−0.172094	+	0.298076i
$99$	−0.819041	−	1.41862i	−0.0823167	−	0.142577i
$100$	1.31872	−	2.28409i	0.131872	−	0.228409i
$101$	−1.23228	−	2.13438i	−0.122617	−	0.212378i	0.798182	−	0.602416i	$-0.205795\pi$
$101$	−1.23228	−	2.13438i	−0.122617	−	0.212378i	−0.920799	+	0.390038i	$0.872462\pi$
$102$	3.08107			0.305072
$103$	−13.7785			−1.35763			−0.678816	−	0.734308i	$-0.737507\pi$
$103$	−13.7785			−1.35763			−0.678816	+	0.734308i	$0.737507\pi$
$104$	−5.60875	−	9.71464i	−0.549983	−	0.952599i
$105$	0.531881	+	0.921244i	0.0519062	+	0.0899043i
$106$	−19.8141			−1.92452
$107$	0.873251			0.0844203			0.0422102	−	0.999109i	$-0.486560\pi$
$107$	0.873251			0.0844203			0.0422102	+	0.999109i	$0.486560\pi$
$108$	1.47806	+	2.56007i	0.142226	+	0.246343i
$109$	−4.51921	+	7.82750i	−0.432862	+	0.749739i	−0.997118	−	0.0758606i	$-0.975830\pi$
$109$	−4.51921	+	7.82750i	−0.432862	+	0.749739i	0.564256	+	0.825600i	$0.309163\pi$
$110$	0.329727	+	0.571103i	0.0314382	+	0.0544526i
$111$	4.57102	−	7.91724i	0.433862	−	0.751471i
$112$	5.28683	−	9.15706i	0.499559	−	0.865261i
$113$	15.3143			1.44065			0.720324	−	0.693638i	$-0.243993\pi$
$113$	15.3143			1.44065			0.720324	+	0.693638i	$0.243993\pi$
$114$	−7.85580	+	2.04245i	−0.735763	+	0.191293i
$115$	−2.07164			−0.193181
$116$	1.35829	−	2.35263i	0.126114	−	0.218436i
$117$	3.96040	−	6.85961i	0.366139	−	0.634171i
$118$	1.29583	+	2.24445i	0.119291	+	0.206618i
$119$	1.82466	−	3.16040i	0.167266	−	0.289713i
$120$	0.559437	+	0.968973i	0.0510694	+	0.0884547i
$121$	1.00000			0.0909091
$122$	−7.85410			−0.711077
$123$	3.65038	+	6.32264i	0.329143	+	0.570093i
$124$	1.97819	+	3.42633i	0.177647	+	0.307693i
$125$	4.06220			0.363334
$126$	5.76505			0.513592
$127$	0.748191	+	1.29590i	0.0663912	+	0.114993i	0.897310	−	0.441400i	$-0.145518\pi$
$127$	0.748191	+	1.29590i	0.0663912	+	0.114993i	−0.830919	+	0.556393i	$0.812185\pi$
$128$	6.82772	−	11.8260i	0.603491	−	1.04528i
$129$	−3.20473	−	5.55076i	−0.282161	−	0.488717i
$130$	−1.59436	+	2.76152i	−0.139835	+	0.242201i
$131$	−6.22412	+	10.7805i	−0.543804	+	0.941896i	0.454877	+	0.890554i	$0.349683\pi$
$131$	−6.22412	+	10.7805i	−0.543804	+	0.941896i	−0.998681	+	0.0513419i	$0.983650\pi$
$132$	−0.637357			−0.0554748
$133$	−2.55728	+	9.26762i	−0.221745	+	0.803605i
$134$	24.6362			2.12824
$135$	−1.11848	+	1.93726i	−0.0962630	+	0.166732i
$136$	1.91919	−	3.32413i	0.164569	−	0.285042i
$137$	9.09737	+	15.7571i	0.777241	+	1.34622i	0.933527	+	0.358508i	$0.116715\pi$
$137$	9.09737	+	15.7571i	0.777241	+	1.34622i	−0.156286	+	0.987712i	$0.549952\pi$
$138$	4.66723	−	8.08387i	0.397301	−	0.688145i
$139$	7.60506	+	13.1723i	0.645052	+	1.11726i	0.984289	+	0.176563i	$0.0564978\pi$
$139$	7.60506	+	13.1723i	0.645052	+	1.11726i	−0.339237	+	0.940701i	$0.610169\pi$
$140$	−0.497824			−0.0420738
$141$	−1.84541			−0.155412
$142$	−10.0672	−	17.4369i	−0.844822	−	1.46327i
$143$	2.41770	+	4.18759i	0.202179	+	0.350184i
$144$	7.85299			0.654416
$145$	2.05569			0.170716
$146$	−5.99636	−	10.3860i	−0.496262	−	0.859551i
$147$	1.24599	−	2.15811i	0.102767	−	0.177998i
$148$	2.13917	+	3.70515i	0.175838	+	0.304561i
$149$	−4.29530	+	7.43967i	−0.351884	+	0.609482i	−0.986580	−	0.163281i	$-0.947792\pi$
$149$	−4.29530	+	7.43967i	−0.351884	+	0.609482i	0.634695	+	0.772763i	$0.281126\pi$
$150$	−4.49637	+	7.78795i	−0.367127	+	0.635883i
$151$	−2.67243			−0.217479			−0.108740	−	0.994070i	$-0.534681\pi$
$151$	−2.67243			−0.217479			−0.108740	+	0.994070i	$0.534681\pi$
$152$	−2.68977	+	9.74776i	−0.218169	+	0.790648i
$153$	2.71032			0.219116
$154$	−1.75970	+	3.04788i	−0.141800	+	0.245605i
$155$	−1.49694	+	2.59277i	−0.120237	+	0.208257i
$156$	−1.54094	−	2.66899i	−0.123374	−	0.213690i
$157$	3.30744	−	5.72866i	0.263963	−	0.457197i	−0.703329	−	0.710865i	$-0.748304\pi$
$157$	3.30744	−	5.72866i	0.263963	−	0.457197i	0.967291	+	0.253668i	$0.0816370\pi$
$158$	6.12888	+	10.6155i	0.487587	+	0.844526i
$159$	14.4913			1.14924
$160$	−1.24393			−0.0983411
$161$	−5.52800	−	9.57478i	−0.435667	−	0.754598i
$162$	−1.11891	−	1.93802i	−0.0879102	−	0.152265i
$163$	8.88161			0.695661			0.347831	−	0.937557i	$-0.386918\pi$
$163$	8.88161			0.695661			0.347831	+	0.937557i	$0.386918\pi$
$164$	−3.41664			−0.266795
$165$	−0.241150	−	0.417685i	−0.0187735	−	0.0325167i
$166$	5.16047	−	8.93820i	0.400530	−	0.693739i
$167$	8.48524	+	14.6969i	0.656607	+	1.13728i	0.981488	+	0.191522i	$0.0613424\pi$
$167$	8.48524	+	14.6969i	0.656607	+	1.13728i	−0.324881	+	0.945755i	$0.605324\pi$
$168$	−2.98562	+	5.17125i	−0.230346	+	0.398970i
$169$	−5.19059	+	8.99036i	−0.399276	+	0.691566i
$170$	−1.09111			−0.0836844
$171$	−6.91049	+	1.79668i	−0.528458	+	0.137395i
$172$	2.99953			0.228712
$173$	−0.141689	+	0.245412i	−0.0107724	+	0.0186583i	−0.871361	−	0.490642i	$-0.836762\pi$
$173$	−0.141689	+	0.245412i	−0.0107724	+	0.0186583i	0.860589	+	0.509300i	$0.170096\pi$
$174$	−4.63130	+	8.02165i	−0.351098	+	0.608120i
$175$	5.32564	+	9.22427i	0.402580	+	0.697289i
$176$	−2.39701	+	4.15174i	−0.180681	+	0.312949i
$177$	−0.947727	−	1.64151i	−0.0712355	−	0.123384i
$178$	−5.74496			−0.430603
$179$	−11.3672			−0.849622			−0.424811	−	0.905282i	$-0.639659\pi$
$179$	−11.3672			−0.849622			−0.424811	+	0.905282i	$0.639659\pi$
$180$	−0.184865	−	0.320196i	−0.0137790	−	0.0238660i
$181$	−4.20561	−	7.28433i	−0.312601	−	0.541440i	0.666324	−	0.745662i	$-0.267867\pi$
$181$	−4.20561	−	7.28433i	−0.312601	−	0.541440i	−0.978925	+	0.204222i	$0.934533\pi$
$182$	−17.0177			−1.26144
$183$	5.74421			0.424624
$184$	−5.81440	−	10.0708i	−0.428643	−	0.742432i
$185$	−1.61875	+	2.80376i	−0.119013	+	0.206137i
$186$	−6.74495	−	11.6826i	−0.494563	−	0.856609i
$187$	−0.827285	+	1.43290i	−0.0604971	+	0.104784i
$188$	0.431813	−	0.747921i	0.0314932	−	0.0545478i
$189$	−11.9382			−0.868379
$190$	2.78200	−	0.723300i	0.201828	−	0.0524737i
$191$	9.83023			0.711290			0.355645	−	0.934621i	$-0.384261\pi$
$191$	9.83023			0.711290			0.355645	+	0.934621i	$0.384261\pi$
$192$	−2.79221	+	4.83626i	−0.201511	+	0.349027i
$193$	6.74566	−	11.6838i	0.485563	−	0.841020i	−0.514299	−	0.857611i	$-0.671948\pi$
$193$	6.74566	−	11.6838i	0.485563	−	0.841020i	0.999862	+	0.0165909i	$0.00528129\pi$
$194$	−11.8917	−	20.5970i	−0.853774	−	1.47878i
$195$	1.16606	−	2.01968i	0.0835034	−	0.144632i
$196$	0.583102	+	1.00996i	0.0416501	+	0.0721401i
$197$	5.29868			0.377515			0.188758	−	0.982024i	$-0.439554\pi$
$197$	5.29868			0.377515			0.188758	+	0.982024i	$0.439554\pi$
$198$	−2.61383			−0.185757
$199$	4.49865	+	7.79188i	0.318901	+	0.552352i	0.980259	−	0.197718i	$-0.0633530\pi$
$199$	4.49865	+	7.79188i	0.318901	+	0.552352i	−0.661358	+	0.750070i	$0.730020\pi$
$200$	5.60155	+	9.70217i	0.396089	+	0.686047i
$201$	−18.0180			−1.27089
$202$	−3.93262			−0.276698
$203$	5.48545	+	9.50108i	0.385003	+	0.666845i
$204$	0.527275	−	0.913268i	0.0369167	−	0.0639415i
$205$	−1.29272	−	2.23906i	−0.0902875	−	0.156383i
$206$	−10.9929	+	19.0403i	−0.765911	+	1.32660i
$207$	4.10561	−	7.11112i	0.285359	−	0.494257i
$208$	−23.1810			−1.60731
$209$	1.15945	−	4.20187i	0.0802010	−	0.290649i
$210$	1.69741			0.117132
$211$	5.13867	−	8.90044i	0.353761	−	0.612731i	−0.633144	−	0.774034i	$-0.718236\pi$
$211$	5.13867	−	8.90044i	0.353761	−	0.612731i	0.986905	+	0.161302i	$0.0515694\pi$
$212$	−3.39086	+	5.87314i	−0.232885	+	0.403369i
$213$	7.36280	+	12.7527i	0.504491	+	0.873804i
$214$	0.696708	−	1.20673i	0.0476259	−	0.0824906i
$215$	1.13490	+	1.96571i	0.0773997	+	0.134060i
$216$	−12.5567			−0.854378
$217$	−15.9778			−1.08465
$218$	7.21114	+	12.4901i	0.488400	+	0.845934i
$219$	4.38552	+	7.59595i	0.296346	+	0.513287i
$220$	0.225709			0.0152173
$221$	−8.00052			−0.538173
$222$	−7.29381	−	12.6333i	−0.489529	−	0.847889i
$223$	−6.12388	+	10.6069i	−0.410085	+	0.710288i	−0.994899	−	0.100880i	$-0.967834\pi$
$223$	−6.12388	+	10.6069i	−0.410085	+	0.710288i	0.584814	+	0.811168i	$0.301168\pi$
$224$	−3.31932	−	5.74923i	−0.221781	−	0.384136i
$225$	−3.95531	+	6.85080i	−0.263688	+	0.456720i
$226$	12.2182	−	21.1626i	0.812745	−	1.40772i
$227$	−5.38317			−0.357294			−0.178647	−	0.983913i	$-0.557172\pi$
$227$	−5.38317			−0.357294			−0.178647	+	0.983913i	$0.557172\pi$
$228$	−0.738984	+	2.67809i	−0.0489404	+	0.177361i
$229$	−5.34294			−0.353071			−0.176536	−	0.984294i	$-0.556489\pi$
$229$	−5.34294			−0.353071			−0.176536	+	0.984294i	$0.556489\pi$
$230$	−1.65282	+	2.86277i	−0.108984	+	0.188765i
$231$	1.28698	−	2.22911i	0.0846771	−	0.146665i
$232$	5.76964	+	9.99331i	0.378796	+	0.656093i
$233$	2.94957	−	5.10880i	0.193233	−	0.334689i	−0.753087	−	0.657921i	$-0.771436\pi$
$233$	2.94957	−	5.10880i	0.193233	−	0.334689i	0.946320	+	0.323232i	$0.104769\pi$
$234$	−6.31946	−	10.9456i	−0.413116	−	0.715538i
$235$	0.653523			0.0426311
$236$	0.887043			0.0577416
$237$	−4.48244	−	7.76382i	−0.291166	−	0.504314i
$238$	−2.91154	−	5.04293i	−0.188727	−	0.326885i
$239$	0.636360			0.0411627			0.0205814	−	0.999788i	$-0.493448\pi$
$239$	0.636360			0.0411627			0.0205814	+	0.999788i	$0.493448\pi$
$240$	2.31216			0.149249
$241$	4.07766	+	7.06271i	0.262665	+	0.454949i	0.966949	−	0.254969i	$-0.0820653\pi$
$241$	4.07766	+	7.06271i	0.262665	+	0.454949i	−0.704284	+	0.709918i	$0.748732\pi$
$242$	0.797832	−	1.38189i	0.0512866	−	0.0888310i
$243$	−7.30071	−	12.6452i	−0.468341	−	0.811191i
$244$	−1.34410	+	2.32805i	−0.0860473	+	0.149038i
$245$	−0.441245	+	0.764259i	−0.0281901	+	0.0488267i
$246$	11.6495			0.742748
$247$	20.3989	−	5.30356i	1.29795	−	0.337458i
$248$	−16.8056			−1.06716
$249$	−3.77419	+	6.53708i	−0.239179	+	0.414271i
$250$	3.24095	−	5.61349i	0.204976	−	0.355028i
$251$	−6.19906	−	10.7371i	−0.391281	−	0.677719i	0.601338	−	0.798995i	$-0.294635\pi$
$251$	−6.19906	−	10.7371i	−0.391281	−	0.677719i	−0.992619	+	0.121276i	$0.961301\pi$
$252$	0.986595	−	1.70883i	0.0621496	−	0.107646i
$253$	2.50635	+	4.34113i	0.157573	+	0.272924i
$254$	2.38772			0.149819
$255$	0.798000			0.0499727
$256$	−6.10951	−	10.5820i	−0.381844	−	0.661374i
$257$	−1.39827	−	2.42187i	−0.0872216	−	0.151072i	0.819114	−	0.573631i	$-0.194465\pi$
$257$	−1.39827	−	2.42187i	−0.0872216	−	0.151072i	−0.906336	+	0.422558i	$0.861132\pi$
$258$	−10.2273			−0.636727
$259$	−17.2780			−1.07360
$260$	0.545698	+	0.945177i	0.0338428	+	0.0586174i
$261$	−4.07400	+	7.05638i	−0.252175	+	0.436779i
$262$	9.93161	+	17.2020i	0.613577	+	1.06275i
$263$	2.93763	−	5.08813i	0.181142	−	0.313747i	−0.761128	−	0.648602i	$-0.775354\pi$
$263$	2.93763	−	5.08813i	0.181142	−	0.313747i	0.942270	+	0.334855i	$0.108687\pi$
$264$	1.35366	−	2.34460i	0.0833118	−	0.144300i
$265$	−5.13187			−0.315248
$266$	10.7665	+	10.9279i	0.660137	+	0.670031i
$267$	4.20166			0.257138
$268$	4.21608	−	7.30246i	0.257538	−	0.446069i
$269$	7.82445	−	13.5523i	0.477065	−	0.826301i	−0.522589	−	0.852584i	$-0.675034\pi$
$269$	7.82445	−	13.5523i	0.477065	−	0.826301i	0.999655	+	0.0262835i	$0.00836726\pi$
$270$	1.78471	+	3.09121i	0.108614	+	0.188125i
$271$	−13.7883	+	23.8820i	−0.837577	+	1.45073i	0.0543377	+	0.998523i	$0.482695\pi$
$271$	−13.7883	+	23.8820i	−0.837577	+	1.45073i	−0.891915	+	0.452203i	$0.850638\pi$
$272$	−3.96602	−	6.86934i	−0.240475	−	0.416515i
$273$	12.4461			0.753275
$274$	29.0327			1.75393
$275$	−2.41460	−	4.18221i	−0.145606	−	0.252197i
$276$	−1.59744	−	2.76685i	−0.0961545	−	0.166545i
$277$	23.6510			1.42105			0.710525	−	0.703672i	$-0.248457\pi$
$277$	23.6510			1.42105			0.710525	+	0.703672i	$0.248457\pi$
$278$	24.2702			1.45563
$279$	−5.93331	−	10.2768i	−0.355218	−	0.615255i
$280$	1.05731	−	1.83131i	0.0631863	−	0.109442i
$281$	14.3290	+	24.8185i	0.854794	+	1.48055i	0.876836	+	0.480790i	$0.159650\pi$
$281$	14.3290	+	24.8185i	0.854794	+	1.48055i	−0.0220416	+	0.999757i	$0.507017\pi$
$282$	−1.47233	+	2.55015i	−0.0876760	+	0.151859i
$283$	10.3771	−	17.9737i	0.616856	−	1.06843i	−0.373200	−	0.927751i	$-0.621739\pi$
$283$	10.3771	−	17.9737i	0.616856	−	1.06843i	0.990056	−	0.140675i	$-0.0449273\pi$
$284$	−6.89136			−0.408927
$285$	−2.03466	+	0.528996i	−0.120523	+	0.0313350i
$286$	7.71569			0.456238
$287$	6.89903	−	11.9495i	0.407237	−	0.705355i
$288$	2.46523	−	4.26991i	0.145265	−	0.251607i
$289$	7.13120	+	12.3516i	0.419482	+	0.726565i
$290$	1.64010	−	2.84073i	0.0963099	−	0.166814i
$291$	8.69717	+	15.0639i	0.509837	+	0.883063i
$292$	−4.10472			−0.240210
$293$	−6.05799			−0.353912			−0.176956	−	0.984219i	$-0.556625\pi$
$293$	−6.05799			−0.353912			−0.176956	+	0.984219i	$0.556625\pi$
$294$	−1.98817	−	3.44362i	−0.115953	−	0.200836i
$295$	0.335622	+	0.581314i	0.0195407	+	0.0338454i
$296$	−18.1732			−1.05629
$297$	5.41270			0.314077
$298$	6.85385	+	11.8712i	0.397033	+	0.687681i
$299$	−12.1192	+	20.9911i	−0.700873	+	1.21395i
$300$	1.53896	+	2.66556i	0.0888520	+	0.153896i
$301$	−6.05679	+	10.4907i	−0.349107	+	0.604672i
$302$	−2.13215	+	3.69299i	−0.122691	+	0.212508i
$303$	2.87618			0.165232
$304$	14.6658	+	14.8856i	0.841143	+	0.853750i
$305$	−2.03422			−0.116479
$306$	2.16238	−	3.74535i	0.123615	−	0.214108i
$307$	15.7235	−	27.2339i	0.897389	−	1.55432i	0.0665682	−	0.997782i	$-0.478795\pi$
$307$	15.7235	−	27.2339i	0.897389	−	1.55432i	0.830820	−	0.556541i	$-0.187872\pi$
$308$	0.602287	+	1.04319i	0.0343185	+	0.0594413i
$309$	8.03982	−	13.9254i	0.457369	−	0.792187i
$310$	2.38861	+	4.13720i	0.135664	+	0.234977i
$311$	10.8262			0.613897			0.306948	−	0.951726i	$-0.400692\pi$
$311$	10.8262			0.613897			0.306948	+	0.951726i	$0.400692\pi$
$312$	13.0910			0.741130
$313$	10.3198	+	17.8744i	0.583310	+	1.01032i	0.995084	+	0.0990363i	$0.0315760\pi$
$313$	10.3198	+	17.8744i	0.583310	+	1.01032i	−0.411774	+	0.911286i	$0.635091\pi$
$314$	−5.27757	−	9.14102i	−0.297831	−	0.515858i
$315$	1.49315			0.0841296
$316$	4.19543			0.236011
$317$	−17.0473	−	29.5268i	−0.957471	−	1.65839i	−0.728610	−	0.684929i	$-0.759833\pi$
$317$	−17.0473	−	29.5268i	−0.957471	−	1.65839i	−0.228861	−	0.973459i	$-0.573500\pi$
$318$	11.5617	−	20.0254i	0.648345	−	1.12297i
$319$	−2.48706	−	4.30771i	−0.139249	−	0.241186i
$320$	0.988816	−	1.71268i	0.0552765	−	0.0957417i
$321$	−0.509547	+	0.882562i	−0.0284402	+	0.0492598i
$322$	−17.6417			−0.983131
$323$	5.06165	+	5.13752i	0.281638	+	0.285859i
$324$	−0.765936			−0.0425520
$325$	11.6756	−	20.2227i	0.647645	−	1.12175i
$326$	7.08603	−	12.2734i	0.392459	−	0.679759i
$327$	−5.27398	−	9.13480i	−0.291652	−	0.505155i
$328$	7.25646	−	12.5686i	0.400671	−	0.693983i
$329$	1.74387	+	3.02047i	0.0961428	+	0.166524i
$330$	−0.769590			−0.0423645
$331$	−16.3637			−0.899432			−0.449716	−	0.893172i	$-0.648475\pi$
$331$	−16.3637			−0.899432			−0.449716	+	0.893172i	$0.648475\pi$
$332$	−1.76626	−	3.05925i	−0.0969362	−	0.167898i
$333$	−6.41613	−	11.1131i	−0.351602	−	0.608992i
$334$	27.0792			1.48171
$335$	6.38079			0.348620
$336$	6.16980	+	10.6864i	0.336590	+	0.582991i
$337$	4.55688	−	7.89274i	0.248229	−	0.429945i	−0.714806	−	0.699323i	$-0.753485\pi$
$337$	4.55688	−	7.89274i	0.248229	−	0.429945i	0.963034	+	0.269378i	$0.0868182\pi$
$338$	8.28243	+	14.3456i	0.450505	+	0.780297i
$339$	−8.93599	+	15.4776i	−0.485336	+	0.840627i
$340$	−0.186726	+	0.323419i	−0.0101266	+	0.0175398i
$341$	7.24422			0.392296
$342$	−3.03061	+	10.9830i	−0.163877	+	0.593890i
$343$	−20.1489			−1.08794
$344$	−6.37058	+	11.0342i	−0.343479	+	0.594923i
$345$	1.20882	−	2.09373i	0.0650804	−	0.112723i
$346$	0.226088	+	0.391595i	0.0121545	+	0.0210523i
$347$	−7.63150	+	13.2181i	−0.409680	+	0.709587i	−0.994854	−	0.101321i	$-0.967693\pi$
$347$	−7.63150	+	13.2181i	−0.409680	+	0.709587i	0.585173	+	0.810908i	$0.301026\pi$
$348$	1.58514	+	2.74555i	0.0849726	+	0.147177i
$349$	−13.0663			−0.699426			−0.349713	−	0.936857i	$-0.613721\pi$
$349$	−13.0663			−0.699426			−0.349713	+	0.936857i	$0.613721\pi$
$350$	16.9959			0.908466
$351$	13.0863	+	22.6661i	0.698495	+	1.20983i
$352$	1.50495	+	2.60665i	0.0802142	+	0.138935i
$353$	−15.6514			−0.833038			−0.416519	−	0.909127i	$-0.636750\pi$
$353$	−15.6514			−0.833038			−0.416519	+	0.909127i	$0.636750\pi$
$354$	−3.02451			−0.160751
$355$	−2.60742	−	4.51618i	−0.138387	−	0.239694i
$356$	−0.983157	+	1.70288i	−0.0521072	+	0.0902523i
$357$	2.12940	+	3.68822i	0.112700	+	0.195202i
$358$	−9.06909	+	15.7081i	−0.479316	+	0.830200i
$359$	18.3775	−	31.8308i	0.969927	−	1.67996i	0.274178	−	0.961679i	$-0.411594\pi$
$359$	18.3775	−	31.8308i	0.969927	−	1.67996i	0.695749	−	0.718285i	$-0.255073\pi$
$360$	1.57051			0.0827732
$361$	−16.3113	−	9.74372i	−0.858492	−	0.512827i
$362$	−13.4215			−0.705417
$363$	−0.583506	+	1.01066i	−0.0306261	+	0.0530460i
$364$	−2.91230	+	5.04425i	−0.152646	+	0.264391i
$365$	−1.55306	−	2.68998i	−0.0812909	−	0.140800i
$366$	4.58292	−	7.93784i	0.239553	−	0.414918i
$367$	−8.38353	−	14.5207i	−0.437617	−	0.757975i	0.559888	−	0.828568i	$-0.310844\pi$
$367$	−8.38353	−	14.5207i	−0.437617	−	0.757975i	−0.997505	+	0.0705935i	$0.977511\pi$
$368$	−24.0310			−1.25270
$369$	10.2477			0.533475
$370$	2.58298	+	4.47386i	0.134283	+	0.232585i
$371$	−13.6940	−	23.7186i	−0.710955	−	1.23141i
$372$	−4.61715			−0.239388
$373$	22.0884			1.14369			0.571847	−	0.820360i	$-0.306227\pi$
$373$	22.0884			1.14369			0.571847	+	0.820360i	$0.306227\pi$
$374$	1.32007	+	2.28643i	0.0682591	+	0.118228i
$375$	−2.37032	+	4.10551i	−0.122403	+	0.212008i
$376$	1.83422	+	3.17696i	0.0945926	+	0.163839i
$377$	12.0259	−	20.8295i	0.619368	−	1.07278i
$378$	−9.52471	+	16.4973i	−0.489898	+	0.848528i
$379$	−4.76307			−0.244662			−0.122331	−	0.992489i	$-0.539037\pi$
$379$	−4.76307			−0.244662			−0.122331	+	0.992489i	$0.539037\pi$
$380$	0.261699	−	0.948400i	0.0134249	−	0.0486519i
$381$	−1.74630			−0.0894655
$382$	7.84287	−	13.5842i	0.401276	−	0.695031i
$383$	−2.37393	+	4.11177i	−0.121302	+	0.210102i	−0.920281	−	0.391257i	$-0.872040\pi$
$383$	−2.37393	+	4.11177i	−0.121302	+	0.210102i	0.798979	+	0.601359i	$0.205374\pi$
$384$	7.96803	+	13.8010i	0.406617	+	0.704281i
$385$	−0.455763	+	0.789404i	−0.0232278	+	0.0402318i
$386$	−10.7638	−	18.6435i	−0.547863	−	0.948927i
$387$	−8.99667			−0.457326
$388$	−8.14028			−0.413260
$389$	−11.2176	−	19.4295i	−0.568756	−	0.985114i	−0.996689	−	0.0813039i	$-0.974092\pi$
$389$	−11.2176	−	19.4295i	−0.568756	−	0.985114i	0.427933	−	0.903810i	$-0.359242\pi$
$390$	−1.86064	−	3.22273i	−0.0942172	−	0.163189i
$391$	−8.29386			−0.419439
$392$	−4.95371			−0.250200
$393$	−7.26363	−	12.5810i	−0.366402	−	0.634626i
$394$	4.22745	−	7.32217i	0.212976	−	0.368885i
$395$	1.58738	+	2.74943i	0.0798699	+	0.138339i
$396$	−0.447314	+	0.774771i	−0.0224784	+	0.0389337i
$397$	−19.6159	+	33.9757i	−0.984494	+	1.70519i	−0.340330	+	0.940306i	$0.610539\pi$
$397$	−19.6159	+	33.9757i	−0.984494	+	1.70519i	−0.644164	+	0.764888i	$0.722794\pi$
$398$	14.3567			0.719634
$399$	−7.87425	−	7.99227i	−0.394205	−	0.400114i
$400$	23.1513			1.15756
$401$	−2.99155	+	5.18151i	−0.149391	+	0.258752i	−0.931002	−	0.365013i	$-0.881065\pi$
$401$	−2.99155	+	5.18151i	−0.149391	+	0.258752i	0.781612	+	0.623765i	$0.214398\pi$
$402$	−14.3754	+	24.8989i	−0.716978	+	1.24184i
$403$	17.5144	+	30.3358i	0.872453	+	1.51113i
$404$	−0.673003	+	1.16568i	−0.0334832	+	0.0579945i
$405$	−0.289800	−	0.501948i	−0.0144003	−	0.0249420i
$406$	17.5059			0.868802
$407$	7.83371			0.388303
$408$	2.23972	+	3.87931i	0.110883	+	0.192054i
$409$	−3.06231	−	5.30407i	−0.151421	−	0.262270i	0.780329	−	0.625369i	$-0.215052\pi$
$409$	−3.06231	−	5.30407i	−0.151421	−	0.262270i	−0.931750	+	0.363100i	$0.881718\pi$
$410$	−4.12550			−0.203744
$411$	−21.2335			−1.04737
$412$	3.76251	+	6.51686i	0.185366	+	0.321063i
$413$	−1.79116	+	3.10238i	−0.0881371	+	0.152658i
$414$	−6.55117	−	11.3470i	−0.321972	−	0.557673i
$415$	1.33657	−	2.31500i	0.0656094	−	0.113639i
$416$	−7.27706	+	12.6042i	−0.356787	+	0.617973i
$417$	−17.7504			−0.869240
$418$	−4.88145	−	4.95461i	−0.238759	−	0.242338i
$419$	−1.36783			−0.0668231			−0.0334115	−	0.999442i	$-0.510637\pi$
$419$	−1.36783			−0.0668231			−0.0334115	+	0.999442i	$0.510637\pi$
$420$	0.290483	−	0.503132i	0.0141741	−	0.0245503i
$421$	−15.6469	+	27.1013i	−0.762584	+	1.32083i	0.178930	+	0.983862i	$0.442736\pi$
$421$	−15.6469	+	27.1013i	−0.762584	+	1.32083i	−0.941514	+	0.336973i	$0.890597\pi$
$422$	−8.19959	−	14.2021i	−0.399150	−	0.691348i
$423$	−1.29516	+	2.24329i	−0.0629729	+	0.109072i
$424$	−14.4034	−	24.9475i	−0.699492	−	1.21156i
$425$	7.99025			0.387584
$426$	23.4971			1.13844
$427$	−5.42814	−	9.40182i	−0.262686	−	0.454986i
$428$	−0.238460	−	0.413025i	−0.0115264	−	0.0199643i
$429$	−5.64298			−0.272446
$430$	3.62185			0.174661
$431$	−6.48920	−	11.2396i	−0.312574	−	0.541393i	0.666345	−	0.745643i	$-0.267858\pi$
$431$	−6.48920	−	11.2396i	−0.312574	−	0.541393i	−0.978919	+	0.204250i	$0.934524\pi$
$432$	−12.9743	+	22.4721i	−0.624225	+	1.08119i
$433$	13.9273	+	24.1227i	0.669302	+	1.15926i	0.978100	+	0.208137i	$0.0667401\pi$
$433$	13.9273	+	24.1227i	0.669302	+	1.15926i	−0.308798	+	0.951128i	$0.599927\pi$
$434$	−12.7476	+	22.0795i	−0.611905	+	1.05985i
$435$	−1.19951	+	2.07761i	−0.0575121	+	0.0996139i
$436$	4.93628			0.236405
$437$	21.1468	−	5.49802i	1.01159	−	0.263006i
$438$	13.9956			0.668738
$439$	11.4040	−	19.7524i	0.544285	−	0.942730i	−0.454366	−	0.890815i	$-0.650134\pi$
$439$	11.4040	−	19.7524i	0.544285	−	0.942730i	0.998652	−	0.0519150i	$-0.0165325\pi$
$440$	−0.479375	+	0.830302i	−0.0228533	+	0.0395831i
$441$	−1.74893	−	3.02924i	−0.0832825	−	0.144249i
$442$	−6.38307	+	11.0558i	−0.303612	+	0.525871i
$443$	−4.16308	−	7.21066i	−0.197794	−	0.342589i	0.750019	−	0.661416i	$-0.230044\pi$
$443$	−4.16308	−	7.21066i	−0.197794	−	0.342589i	−0.947813	+	0.318827i	$0.896711\pi$
$444$	−4.99287			−0.236951
$445$	−1.48795			−0.0705356
$446$	9.77165	+	16.9250i	0.462701	+	0.801422i
$447$	−5.01267	−	8.68219i	−0.237091	−	0.410654i
$448$	10.5543			0.498644
$449$	−42.0027			−1.98223			−0.991115	−	0.133006i	$-0.957537\pi$
$449$	−42.0027			−1.98223			−0.991115	+	0.133006i	$0.957537\pi$
$450$	6.31135	+	10.9316i	0.297520	+	0.515320i
$451$	−3.12797	+	5.41780i	−0.147290	+	0.255114i
$452$	−4.18190	−	7.24327i	−0.196700	−	0.340695i
$453$	1.55938	−	2.70092i	0.0732660	−	0.126900i
$454$	−4.29487	+	7.43893i	−0.201568	+	0.349126i
$455$	−4.40760			−0.206631
$456$	−8.28220	−	8.40634i	−0.387850	−	0.393663i
$457$	−19.5851			−0.916152			−0.458076	−	0.888913i	$-0.651461\pi$
$457$	−19.5851			−0.916152			−0.458076	+	0.888913i	$0.651461\pi$
$458$	−4.26276	+	7.38333i	−0.199186	+	0.345000i
$459$	−4.47784	+	7.75585i	−0.209008	+	0.362012i
$460$	0.565707	+	0.979833i	0.0263762	+	0.0456849i
$461$	11.5781	−	20.0539i	0.539247	−	0.934004i	−0.459697	−	0.888076i	$-0.652042\pi$
$461$	11.5781	−	20.0539i	0.539247	−	0.934004i	0.998945	−	0.0459283i	$-0.0146246\pi$
$462$	−2.05359	−	3.55692i	−0.0955415	−	0.165483i
$463$	27.3013			1.26880			0.634399	−	0.773005i	$-0.281247\pi$
$463$	27.3013			1.26880			0.634399	+	0.773005i	$0.281247\pi$
$464$	23.8460			1.10702
$465$	−1.74695	−	3.02580i	−0.0810127	−	0.140318i
$466$	−4.70652	−	8.15193i	−0.218025	−	0.377631i
$467$	−41.8946			−1.93865			−0.969326	−	0.245777i	$-0.920957\pi$
$467$	−41.8946			−1.93865			−0.969326	+	0.245777i	$0.920957\pi$
$468$	−4.32589			−0.199964
$469$	17.0266	+	29.4909i	0.786216	+	1.36177i
$470$	0.521402	−	0.903094i	0.0240505	−	0.0416566i
$471$	3.85983	+	6.68542i	0.177852	+	0.308048i
$472$	−1.88396	+	3.26311i	−0.0867161	+	0.150197i
$473$	2.74610	−	4.75638i	0.126266	−	0.218699i
$474$	−14.3050			−0.657048
$475$	−20.3727	+	5.29675i	−0.934764	+	0.243032i
$476$	−1.99305			−0.0913513
$477$	10.1704	−	17.6157i	0.465671	−	0.806566i
$478$	0.507709	−	0.879377i	0.0232221	−	0.0402218i
$479$	2.02880	+	3.51399i	0.0926983	+	0.160558i	0.908646	−	0.417568i	$-0.137117\pi$
$479$	2.02880	+	3.51399i	0.0926983	+	0.160558i	−0.815947	+	0.578126i	$0.803784\pi$
$480$	0.725840	−	1.25719i	0.0331299	−	0.0573827i
$481$	18.9396	+	32.8044i	0.863571	+	1.49575i
$482$	13.0131			0.592732
$483$	12.9025			0.587084
$484$	−0.273072	−	0.472974i	−0.0124124	−	0.0214988i
$485$	−3.07996	−	5.33464i	−0.139854	−	0.242234i
$486$	−23.2990			−1.05686
$487$	10.2039			0.462381			0.231190	−	0.972909i	$-0.425738\pi$
$487$	10.2039			0.462381			0.231190	+	0.972909i	$0.425738\pi$
$488$	−5.70937	−	9.88891i	−0.258451	−	0.447650i
$489$	−5.18247	+	8.97631i	−0.234360	+	0.405923i
$490$	0.704079	+	1.21950i	0.0318070	+	0.0550914i
$491$	1.63476	−	2.83149i	0.0737758	−	0.127783i	−0.826777	−	0.562529i	$-0.809828\pi$
$491$	1.63476	−	2.83149i	0.0737758	−	0.127783i	0.900553	+	0.434746i	$0.143162\pi$
$492$	1.99363	−	3.45307i	0.0898798	−	0.155676i
$493$	8.23002			0.370662
$494$	8.94597	−	32.4203i	0.402498	−	1.45866i
$495$	−0.676984			−0.0304281
$496$	−17.3644	+	30.0761i	−0.779686	+	1.35046i
$497$	13.9153	−	24.1021i	0.624188	−	1.08113i
$498$	6.02233	+	10.4310i	0.269867	+	0.467424i
$499$	11.2025	−	19.4033i	0.501494	−	0.868613i	−0.498505	−	0.866887i	$-0.666117\pi$
$499$	11.2025	−	19.4033i	0.501494	−	0.868613i	0.999999	−	0.00172563i	$-0.000549286\pi$
$500$	−1.10927	−	1.92131i	−0.0496081	−	0.0859238i
$501$	−19.8048			−0.884811
$502$	−19.7832			−0.882969
$503$	2.40438	+	4.16451i	0.107206	+	0.185686i	0.914637	−	0.404275i	$-0.132476\pi$
$503$	2.40438	+	4.16451i	0.107206	+	0.185686i	−0.807431	+	0.589962i	$0.799143\pi$
$504$	4.19078	+	7.25864i	0.186672	+	0.323326i
$505$	−1.01855			−0.0453249
$506$	7.99859			0.355581
$507$	−6.05748	−	10.4919i	−0.269022	−	0.465960i
$508$	0.408620	−	0.707750i	0.0181296	−	0.0314013i
$509$	5.76697	+	9.98868i	0.255616	+	0.442741i	0.965063	−	0.262019i	$-0.0843883\pi$
$509$	5.76697	+	9.98868i	0.255616	+	0.442741i	−0.709446	+	0.704759i	$0.751055\pi$
$510$	0.636670	−	1.10275i	0.0281922	−	0.0488304i
$511$	8.28843	−	14.3560i	0.366659	−	0.635071i
$512$	7.81342			0.345308
$513$	6.27577	−	22.7434i	0.277082	−	1.00415i
$514$	−4.46233			−0.196825
$515$	−2.84717	+	4.93144i	−0.125461	+	0.217305i
$516$	−1.75024	+	3.03151i	−0.0770502	+	0.133455i
$517$	−0.790657	−	1.36946i	−0.0347731	−	0.0602287i
$518$	−13.7850	+	23.8762i	−0.605676	+	1.04906i
$519$	−0.165353	−	0.286399i	−0.00725817	−	0.0125715i
$520$	−4.63595			−0.203300
$521$	4.84230			0.212145			0.106072	−	0.994358i	$-0.466172\pi$
$521$	4.84230			0.212145			0.106072	+	0.994358i	$0.466172\pi$
$522$	6.50074	+	11.2596i	0.284530	+	0.492820i
$523$	18.9189	+	32.7685i	0.827265	+	1.43287i	0.900176	+	0.435527i	$0.143438\pi$
$523$	18.9189	+	32.7685i	0.827265	+	1.43287i	−0.0729108	+	0.997338i	$0.523229\pi$
$524$	6.79853			0.296995
$525$	−12.4302			−0.542497
$526$	−4.68747	−	8.11894i	−0.204383	−	0.354003i
$527$	−5.99303	+	10.3802i	−0.261060	+	0.452170i
$528$	−2.79734	−	4.84513i	−0.121738	−	0.210857i
$529$	−1.06359	+	1.84219i	−0.0462430	+	0.0800952i
$530$	−4.09437	+	7.09165i	−0.177848	+	0.308042i
$531$	−2.66056			−0.115459
$532$	5.08167	−	1.32120i	0.220318	−	0.0572812i
$533$	−30.2500			−1.31027
$534$	3.35222	−	5.80622i	0.145065	−	0.251260i
$535$	0.180448	−	0.312545i	0.00780144	−	0.0135125i
$536$	17.9087	+	31.0188i	0.773539	+	1.33981i
$537$	6.63281	−	11.4884i	0.286227	−	0.495760i
$538$	−12.4852	−	21.6250i	−0.538275	−	0.932319i
$539$	2.13534			0.0919757
$540$	1.22170			0.0525735
$541$	0.206473	+	0.357622i	0.00887698	+	0.0153754i	0.870430	−	0.492293i	$-0.163841\pi$
$541$	0.206473	+	0.357622i	0.00887698	+	0.0153754i	−0.861553	+	0.507668i	$0.830508\pi$
$542$	22.0014	+	38.1076i	0.945042	+	1.63686i
$543$	9.81600			0.421245
$544$	−4.98010			−0.213520
$545$	1.86769	+	3.23494i	0.0800031	+	0.138570i
$546$	9.92993	−	17.1991i	0.424962	−	0.736056i
$547$	13.1542	+	22.7837i	0.562432	+	0.974161i	0.997283	+	0.0736591i	$0.0234677\pi$
$547$	13.1542	+	22.7837i	0.562432	+	0.974161i	−0.434851	+	0.900502i	$0.643199\pi$
$548$	4.96847	−	8.60564i	0.212243	−	0.367615i
$549$	4.03144	−	6.98266i	0.172058	−	0.298013i
$550$	−7.70578			−0.328576
$551$	−20.9840	+	5.45570i	−0.893951	+	0.232421i
$552$	13.5710			0.577618
$553$	−8.47160	+	14.6732i	−0.360249	+	0.623970i
$554$	18.8695	−	32.6830i	0.801689	−	1.38857i
$555$	−1.88910	−	3.27202i	−0.0801880	−	0.138890i
$556$	4.15345	−	7.19399i	0.176146	−	0.305093i
$557$	18.0568	+	31.2753i	0.765090	+	1.32517i	0.940199	+	0.340626i	$0.110639\pi$
$557$	18.0568	+	31.2753i	0.765090	+	1.32517i	−0.175109	+	0.984549i	$0.556028\pi$
$558$	−18.9351			−0.801588
$559$	26.5570			1.12324
$560$	−2.18493	−	3.78441i	−0.0923303	−	0.159921i
$561$	−0.965452	−	1.67221i	−0.0407614	−	0.0706008i
$562$	45.7284			1.92894
$563$	−44.9653			−1.89506			−0.947532	−	0.319662i	$-0.896431\pi$
$563$	−44.9653			−1.89506			−0.947532	+	0.319662i	$0.896431\pi$
$564$	0.503931	+	0.872834i	0.0212193	+	0.0367529i
$565$	3.16453	−	5.48113i	0.133133	−	0.230593i
$566$	−16.5584	−	28.6800i	−0.696002	−	1.20551i
$567$	1.54661	−	2.67881i	0.0649516	−	0.112500i
$568$	14.6363	−	25.3508i	0.614125	−	1.06369i
$569$	40.8649			1.71315			0.856574	−	0.516024i	$-0.172589\pi$
$569$	40.8649			1.71315			0.856574	+	0.516024i	$0.172589\pi$
$570$	−0.892303	+	3.23371i	−0.0373745	+	0.135445i
$571$	−31.4841			−1.31757			−0.658784	−	0.752332i	$-0.728929\pi$
$571$	−31.4841			−1.31757			−0.658784	+	0.752332i	$0.728929\pi$
$572$	1.32041	−	2.28702i	0.0552093	−	0.0956253i
$573$	−5.73600	+	9.93504i	−0.239625	+	0.415042i
$574$	−11.0085	−	19.0673i	−0.459488	−	0.795856i
$575$	12.1037	−	20.9642i	0.504758	−	0.874267i
$576$	3.91930	+	6.78843i	0.163304	+	0.282851i
$577$	−32.6849			−1.36069			−0.680345	−	0.732892i	$-0.738170\pi$
$577$	−32.6849			−1.36069			−0.680345	+	0.732892i	$0.738170\pi$
$578$	22.7580			0.946608
$579$	7.87227	+	13.6352i	0.327160	+	0.566658i
$580$	−0.561352	−	0.972291i	−0.0233089	−	0.0403722i
$581$	14.2661			0.591856
$582$	27.7555			1.15050
$583$	6.20873	+	10.7538i	0.257139	+	0.445379i
$584$	8.71784	−	15.0997i	0.360747	−	0.624832i
$585$	−1.63675	−	2.83493i	−0.0676711	−	0.117210i
$586$	−4.83326	+	8.37146i	−0.199660	+	0.345822i
$587$	−1.38822	+	2.40446i	−0.0572979	+	0.0992428i	−0.893252	−	0.449557i	$-0.851582\pi$
$587$	−1.38822	+	2.40446i	−0.0572979	+	0.0992428i	0.835954	+	0.548800i	$0.184915\pi$
$588$	−1.36097			−0.0561256
$589$	8.39932	−	30.4392i	0.346088	−	1.25423i
$590$	1.07108			0.0440956
$591$	−3.09181	+	5.35518i	−0.127180	+	0.220282i
$592$	−18.7775	+	32.5235i	−0.771749	+	1.33671i
$593$	−0.738309	−	1.27879i	−0.0303187	−	0.0525135i	0.850468	−	0.526027i	$-0.176319\pi$
$593$	−0.738309	−	1.27879i	−0.0303187	−	0.0525135i	−0.880787	+	0.473513i	$0.842986\pi$
$594$	4.31843	−	7.47973i	0.177187	−	0.306897i
$595$	−0.754091	−	1.30612i	−0.0309147	−	0.0535459i
$596$	4.69170			0.192179
$597$	−10.5000			−0.429735
$598$	19.3382	+	33.4948i	0.790799	+	1.36970i
$599$	−15.3058	−	26.5104i	−0.625377	−	1.08318i	−0.988468	−	0.151431i	$-0.951612\pi$
$599$	−15.3058	−	26.5104i	−0.625377	−	1.08318i	0.363091	−	0.931754i	$-0.381721\pi$
$600$	−13.0742			−0.533750
$601$	19.2289			0.784362			0.392181	−	0.919888i	$-0.371721\pi$
$601$	19.2289			0.784362			0.392181	+	0.919888i	$0.371721\pi$
$602$	9.66460	+	16.7396i	0.393900	+	0.682254i
$603$	−12.6455	+	21.9027i	−0.514966	+	0.891948i
$604$	0.729765	+	1.26399i	0.0296937	+	0.0514310i
$605$	0.206639	−	0.357909i	0.00840108	−	0.0145511i
$606$	2.29471	−	3.97455i	0.0932161	−	0.161455i
$607$	21.3100			0.864947			0.432474	−	0.901647i	$-0.357641\pi$
$607$	21.3100			0.864947			0.432474	+	0.901647i	$0.357641\pi$
$608$	12.6977	−	3.30132i	0.514961	−	0.133886i
$609$	−12.8032			−0.518811
$610$	−1.62296	+	2.81106i	−0.0657119	+	0.113816i
$611$	3.82315	−	6.62189i	0.154668	−	0.267893i
$612$	−0.740112	−	1.28191i	−0.0299173	−	0.0518182i
$613$	6.88667	−	11.9281i	0.278150	−	0.481770i	−0.692775	−	0.721154i	$-0.743612\pi$
$613$	6.88667	−	11.9281i	0.278150	−	0.481770i	0.970925	+	0.239384i	$0.0769455\pi$
$614$	−25.0895	−	43.4562i	−1.01253	−	1.75375i
$615$	3.01724			0.121667
$616$	−5.11669			−0.206157
$617$	−17.1808	−	29.7581i	−0.691674	−	1.19801i	−0.971289	−	0.237902i	$-0.923540\pi$
$617$	−17.1808	−	29.7581i	−0.691674	−	1.19801i	0.279615	−	0.960112i	$-0.409793\pi$
$618$	−12.8288	−	22.2202i	−0.516052	−	0.893828i
$619$	13.6621			0.549128			0.274564	−	0.961569i	$-0.411466\pi$
$619$	13.6621			0.549128			0.274564	+	0.961569i	$0.411466\pi$
$620$	1.63509			0.0656667
$621$	13.5661	+	23.4972i	0.544390	+	0.942911i
$622$	8.63748	−	14.9606i	0.346331	−	0.599863i
$623$	−3.97047	−	6.87706i	−0.159074	−	0.275523i
$624$	13.5263	−	23.4282i	0.541484	−	0.937878i
$625$	−11.2336	+	19.4572i	−0.449344	+	0.778286i
$626$	32.9339			1.31630
$627$	3.57012	+	3.62363i	0.142577	+	0.144714i
$628$	−3.61268			−0.144162
$629$	−6.48071	+	11.2249i	−0.258403	+	0.447567i
$630$	1.19129	−	2.06337i	0.0474619	−	0.0822065i
$631$	−15.7214	−	27.2303i	−0.625860	−	1.08402i	−0.988374	−	0.152043i	$-0.951415\pi$
$631$	−15.7214	−	27.2303i	−0.625860	−	1.08402i	0.362513	−	0.931979i	$-0.381919\pi$
$632$	−8.91050	+	15.4334i	−0.354441	+	0.613910i
$633$	5.99689	+	10.3869i	0.238355	+	0.412843i
$634$	−54.4035			−2.16064
$635$	0.618422			0.0245413
$636$	−3.95718	−	6.85403i	−0.156912	−	0.271780i
$637$	5.16262	+	8.94193i	0.204551	+	0.354292i
$638$	−7.93702			−0.314230
$639$	20.6697			0.817679
$640$	−2.82175	−	4.88741i	−0.111539	−	0.193192i
$641$	−3.25913	+	5.64498i	−0.128728	+	0.222963i	−0.923184	−	0.384358i	$-0.874423\pi$
$641$	−3.25913	+	5.64498i	−0.128728	+	0.222963i	0.794456	+	0.607322i	$0.207756\pi$
$642$	0.813066	+	1.40827i	0.0320892	+	0.0555801i
$643$	5.22309	−	9.04665i	0.205978	−	0.356765i	−0.744466	−	0.667661i	$-0.767296\pi$
$643$	5.22309	−	9.04665i	0.205978	−	0.356765i	0.950444	+	0.310896i	$0.100629\pi$
$644$	−3.01908	+	5.22920i	−0.118969	+	0.206060i
$645$	−2.64889			−0.104300
$646$	11.1378	−	2.89575i	0.438211	−	0.113932i
$647$	−24.9256			−0.979928			−0.489964	−	0.871743i	$-0.662990\pi$
$647$	−24.9256			−0.979928			−0.489964	+	0.871743i	$0.662990\pi$
$648$	1.62674	−	2.81760i	0.0639044	−	0.110686i
$649$	0.812097	−	1.40659i	0.0318776	−	0.0552136i
$650$	−18.6303	−	32.2686i	−0.730741	−	1.26568i
$651$	9.32316	−	16.1482i	0.365403	−	0.632897i
$652$	−2.42532	−	4.20077i	−0.0949828	−	0.164515i
$653$	17.6003			0.688752			0.344376	−	0.938832i	$-0.388091\pi$
$653$	17.6003			0.688752			0.344376	+	0.938832i	$0.388091\pi$
$654$	−16.8310			−0.658144
$655$	2.57229	+	4.45534i	0.100508	+	0.174085i
$656$	−14.9955	−	25.9730i	−0.585477	−	1.01408i
$657$	12.3115			0.480318
$658$	5.56527			0.216957
$659$	−2.85204	−	4.93988i	−0.111100	−	0.192430i	0.805114	−	0.593120i	$-0.202104\pi$
$659$	−2.85204	−	4.93988i	−0.111100	−	0.192430i	−0.916214	+	0.400690i	$0.868771\pi$
$660$	−0.131703	+	0.228116i	−0.00512653	+	0.00887940i
$661$	17.6095	+	30.5006i	0.684931	+	1.18633i	0.973459	+	0.228863i	$0.0735009\pi$
$661$	17.6095	+	30.5006i	0.684931	+	1.18633i	−0.288528	+	0.957472i	$0.593166\pi$
$662$	−13.0555	+	22.6128i	−0.507417	+	0.878871i
$663$	4.66835	−	8.08582i	0.181304	−	0.314027i
$664$	15.0052			0.582313
$665$	2.78853	+	2.83033i	0.108135	+	0.109755i
$666$	−20.4760			−0.793428
$667$	12.4669	−	21.5933i	0.482720	−	0.836095i
$668$	4.63416	−	8.02660i	0.179301	−	0.310558i
$669$	−7.14664	−	12.3783i	−0.276305	−	0.478574i
$670$	5.09080	−	8.81752i	0.196675	−	0.340651i
$671$	2.46108	+	4.26271i	0.0950088	+	0.164560i
$672$	7.74737			0.298861
$673$	−25.7412			−0.992250			−0.496125	−	0.868251i	$-0.665244\pi$
$673$	−25.7412			−0.992250			−0.496125	+	0.868251i	$0.665244\pi$
$674$	−7.27124	−	12.5942i	−0.280078	−	0.485109i
$675$	−13.0695	−	22.6371i	−0.503046	−	0.871300i
$676$	5.66961			0.218062
$677$	27.5905			1.06039			0.530194	−	0.847876i	$-0.322119\pi$
$677$	27.5905			1.06039			0.530194	+	0.847876i	$0.322119\pi$
$678$	14.2588	+	24.6970i	0.547607	+	0.948484i
$679$	16.4372	−	28.4701i	0.630803	−	1.09258i
$680$	−0.793159	−	1.37379i	−0.0304163	−	0.0526825i
$681$	3.14112	−	5.44057i	0.120368	−	0.208483i
$682$	5.77967	−	10.0107i	0.221315	−	0.383329i
$683$	−0.774825			−0.0296479			−0.0148239	−	0.999890i	$-0.504719\pi$
$683$	−0.774825			−0.0296479			−0.0148239	+	0.999890i	$0.504719\pi$
$684$	2.73684	+	2.77786i	0.104646	+	0.106214i
$685$	7.51949			0.287305
$686$	−16.0754	+	27.8435i	−0.613763	+	1.06307i
$687$	3.11764	−	5.39990i	0.118945	−	0.206019i
$688$	13.1648	+	22.8022i	0.501905	+	0.869324i
$689$	−30.0218	+	51.9992i	−1.14374	+	1.98101i
$690$	−1.92886	−	3.34089i	−0.0734306	−	0.127185i
$691$	26.5487			1.00996			0.504980	−	0.863131i	$-0.331500\pi$
$691$	26.5487			1.00996			0.504980	+	0.863131i	$0.331500\pi$
$692$	0.154765			0.00588328
$693$	−1.80647	−	3.12890i	−0.0686223	−	0.118857i
$694$	12.1773	+	21.0917i	0.462244	+	0.800631i
$695$	6.28601			0.238442
$696$	−13.4665			−0.510446
$697$	−5.17544	−	8.96412i	−0.196034	−	0.339540i
$698$	−10.4248	+	18.0562i	−0.394583	+	0.683437i
$699$	3.44218	+	5.96204i	0.130195	+	0.225505i
$700$	2.90856	−	5.03778i	0.109933	−	0.190410i
$701$	−13.8493	+	23.9876i	−0.523079	+	0.906000i	0.476560	+	0.879142i	$0.341883\pi$
$701$	−13.8493	+	23.9876i	−0.523079	+	0.906000i	−0.999639	+	0.0268578i	$0.991450\pi$
$702$	41.7627			1.57623
$703$	9.08282	−	32.9162i	0.342565	−	1.24146i
$704$	−4.78523			−0.180350
$705$	−0.381335	+	0.660491i	−0.0143619	+	0.0248755i
$706$	−12.4872	+	21.6284i	−0.469960	+	0.813995i
$707$	−2.71792	−	4.70757i	−0.102218	−	0.177046i
$708$	−0.517595	+	0.896501i	−0.0194524	+	0.0336926i
$709$	13.1264	+	22.7356i	0.492972	+	0.853852i	0.999967	−	0.00809658i	$-0.00257725\pi$
$709$	13.1264	+	22.7356i	0.492972	+	0.853852i	−0.506995	+	0.861949i	$0.669244\pi$
$710$	−8.32112			−0.312286
$711$	−12.5836			−0.471922
$712$	−4.17618	−	7.23335i	−0.156509	−	0.271081i
$713$	18.1565	+	31.4481i	0.679968	+	1.17774i
$714$	6.79561			0.254319
$715$	1.99837			0.0747348
$716$	3.10405	+	5.37638i	0.116004	+	0.200925i
$717$	−0.371320	+	0.643146i	−0.0138672	+	0.0240187i
$718$	−29.3243	−	50.7912i	−1.09437	−	1.89551i
$719$	20.6029	−	35.6853i	0.768359	−	1.33084i	−0.170093	−	0.985428i	$-0.554407\pi$
$719$	20.6029	−	35.6853i	0.768359	−	1.33084i	0.938452	−	0.345409i	$-0.112260\pi$
$720$	1.62273	−	2.81066i	0.0604757	−	0.104747i
$721$	−30.3897			−1.13177
$722$	−26.4784	+	14.7666i	−0.985425	+	0.549554i
$723$	−9.51735			−0.353954
$724$	−2.29687	+	3.97829i	−0.0853624	+	0.147852i
$725$	−12.0105	+	20.8028i	−0.446059	+	0.772597i
$726$	0.931080	+	1.61268i	0.0345556	+	0.0598521i
$727$	−4.34274	+	7.52184i	−0.161063	+	0.278970i	−0.935250	−	0.353987i	$-0.884826\pi$
$727$	−4.34274	+	7.52184i	−0.161063	+	0.278970i	0.774187	+	0.632957i	$0.218159\pi$
$728$	−12.3706	−	21.4266i	−0.458486	−	0.794122i
$729$	21.2474			0.786940
$730$	−4.95633			−0.183442
$731$	4.54361	+	7.86976i	0.168051	+	0.291074i
$732$	−1.56858	−	2.71687i	−0.0579765	−	0.100418i
$733$	33.9444			1.25377			0.626883	−	0.779113i	$-0.284330\pi$
$733$	33.9444			1.25377			0.626883	+	0.779113i	$0.284330\pi$
$734$	−26.7546			−0.987530
$735$	−0.514939	−	0.891900i	−0.0189938	−	0.0328982i
$736$	−7.54388	+	13.0664i	−0.278071	+	0.481633i
$737$	−7.71973	−	13.3710i	−0.284360	−	0.492526i
$738$	8.17597	−	14.1612i	0.300961	−	0.521281i
$739$	−17.9896	+	31.1589i	−0.661758	+	1.14620i	0.318395	+	0.947958i	$0.396856\pi$
$739$	−17.9896	+	31.1589i	−0.661758	+	1.14620i	−0.980153	+	0.198241i	$0.936477\pi$
$740$	1.76814			0.0649982
$741$	−6.54277	+	23.7111i	−0.240355	+	0.871047i
$742$	−43.7019			−1.60435
$743$	−23.2294	+	40.2344i	−0.852203	+	1.47606i	0.0270132	+	0.999635i	$0.491400\pi$
$743$	−23.2294	+	40.2344i	−0.852203	+	1.47606i	−0.879216	+	0.476423i	$0.841933\pi$
$744$	9.80618	−	16.9848i	0.359512	−	0.622693i
$745$	1.77515	+	3.07465i	0.0650366	+	0.112647i
$746$	17.6228	−	30.5237i	0.645218	−	1.11755i
$747$	5.29765	+	9.17580i	0.193831	+	0.335725i
$748$	0.903633			0.0330401
$749$	1.92604			0.0703760
$750$	3.78223	+	6.55101i	0.138107	+	0.239209i
$751$	−2.13647	−	3.70048i	−0.0779610	−	0.135032i	0.824409	−	0.565994i	$-0.191508\pi$
$751$	−2.13647	−	3.70048i	−0.0779610	−	0.135032i	−0.902370	+	0.430962i	$0.858174\pi$
$752$	7.58085			0.276445
$753$	14.4688			0.527271
$754$	−19.1894	−	33.2370i	−0.698835	−	1.21042i
$755$	−0.552228	+	0.956487i	−0.0200976	+	0.0348101i
$756$	3.26000	+	5.64648i	0.118565	+	0.205360i
$757$	−5.30317	+	9.18537i	−0.192747	+	0.333848i	−0.946160	−	0.323700i	$-0.895073\pi$
$757$	−5.30317	+	9.18537i	−0.192747	+	0.333848i	0.753413	+	0.657548i	$0.228406\pi$
$758$	−3.80013	+	6.58201i	−0.138027	+	0.239070i
$759$	−5.84989			−0.212337
$760$	2.93300	+	2.97696i	0.106391	+	0.107986i
$761$	36.7869			1.33352			0.666762	−	0.745271i	$-0.267680\pi$
$761$	36.7869			1.33352			0.666762	+	0.745271i	$0.267680\pi$
$762$	−1.39325	+	2.41318i	−0.0504722	+	0.0874204i
$763$	−9.96756	+	17.2643i	−0.360850	+	0.625010i
$764$	−2.68436	−	4.64944i	−0.0971167	−	0.168211i
$765$	0.560058	−	0.970049i	0.0202489	−	0.0350722i
$766$	3.78800	+	6.56101i	0.136866	+	0.237059i
$767$	7.85364			0.283578
$768$	14.2597			0.514554
$769$	−3.87754	−	6.71609i	−0.139828	−	0.242188i	0.787604	−	0.616182i	$-0.211321\pi$
$769$	−3.87754	−	6.71609i	−0.139828	−	0.242188i	−0.927431	+	0.373994i	$0.877988\pi$
$770$	0.727244	+	1.25962i	0.0262081	+	0.0453937i

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)

\(f(q)\)	\(=\)	\(q+(0.797832 - 1.38189i) q^{2} +(-0.583506 + 1.01066i) q^{3} +(-0.273072 - 0.472974i) q^{4} +(0.206639 - 0.357909i) q^{5} +(0.931080 + 1.61268i) q^{6} +2.20560 q^{7} +2.31987 q^{8} +(0.819041 + 1.41862i) q^{9} +O(q^{10})\)	\(q+(0.797832 - 1.38189i) q^{2} +(-0.583506 + 1.01066i) q^{3} +(-0.273072 - 0.472974i) q^{4} +(0.206639 - 0.357909i) q^{5} +(0.931080 + 1.61268i) q^{6} +2.20560 q^{7} +2.31987 q^{8} +(0.819041 + 1.41862i) q^{9} +(-0.329727 - 0.571103i) q^{10} -1.00000 q^{11} +0.637357 q^{12} +(-2.41770 - 4.18759i) q^{13} +(1.75970 - 3.04788i) q^{14} +(0.241150 + 0.417685i) q^{15} +(2.39701 - 4.15174i) q^{16} +(0.827285 - 1.43290i) q^{17} +2.61383 q^{18} +(-1.15945 + 4.20187i) q^{19} -0.225709 q^{20} +(-1.28698 + 2.22911i) q^{21} +(-0.797832 + 1.38189i) q^{22} +(-2.50635 - 4.34113i) q^{23} +(-1.35366 + 2.34460i) q^{24} +(2.41460 + 4.18221i) q^{25} -7.71569 q^{26} -5.41270 q^{27} +(-0.602287 - 1.04319i) q^{28} +(2.48706 + 4.30771i) q^{29} +0.769590 q^{30} -7.24422 q^{31} +(-1.50495 - 2.60665i) q^{32} +(0.583506 - 1.01066i) q^{33} +(-1.32007 - 2.28643i) q^{34} +(0.455763 - 0.789404i) q^{35} +(0.447314 - 0.774771i) q^{36} -7.83371 q^{37} +(4.88145 + 4.95461i) q^{38} +5.64298 q^{39} +(0.479375 - 0.830302i) q^{40} +(3.12797 - 5.41780i) q^{41} +(2.05359 + 3.55692i) q^{42} +(-2.74610 + 4.75638i) q^{43} +(0.273072 + 0.472974i) q^{44} +0.676984 q^{45} -7.99859 q^{46} +(0.790657 + 1.36946i) q^{47} +(2.79734 + 4.84513i) q^{48} -2.13534 q^{49} +7.70578 q^{50} +(0.965452 + 1.67221i) q^{51} +(-1.32041 + 2.28702i) q^{52} +(-6.20873 - 10.7538i) q^{53} +(-4.31843 + 7.47973i) q^{54} +(-0.206639 + 0.357909i) q^{55} +5.11669 q^{56} +(-3.57012 - 3.62363i) q^{57} +7.93702 q^{58} +(-0.812097 + 1.40659i) q^{59} +(0.131703 - 0.228116i) q^{60} +(-2.46108 - 4.26271i) q^{61} +(-5.77967 + 10.0107i) q^{62} +(1.80647 + 3.12890i) q^{63} +4.78523 q^{64} -1.99837 q^{65} +(-0.931080 - 1.61268i) q^{66} +(7.71973 + 13.3710i) q^{67} -0.903633 q^{68} +5.84989 q^{69} +(-0.727244 - 1.25962i) q^{70} +(6.30910 - 10.9277i) q^{71} +(1.90007 + 3.29101i) q^{72} +(3.75791 - 6.50889i) q^{73} +(-6.24999 + 10.8253i) q^{74} -5.63574 q^{75} +(2.30399 - 0.599020i) q^{76} -2.20560 q^{77} +(4.50215 - 7.79796i) q^{78} +(-3.84096 + 6.65273i) q^{79} +(-0.990631 - 1.71582i) q^{80} +(0.701222 - 1.21455i) q^{81} +(-4.99118 - 8.64498i) q^{82} +6.46812 q^{83} +1.40575 q^{84} +(-0.341899 - 0.592186i) q^{85} +(4.38185 + 7.58959i) q^{86} -5.80486 q^{87} -2.31987 q^{88} +(-1.80018 - 3.11800i) q^{89} +(0.540119 - 0.935514i) q^{90} +(-5.33248 - 9.23613i) q^{91} +(-1.36883 + 2.37088i) q^{92} +(4.22705 - 7.32146i) q^{93} +2.52325 q^{94} +(1.26430 + 1.28325i) q^{95} +3.51260 q^{96} +(7.45250 - 12.9081i) q^{97} +(-1.70364 + 2.95080i) q^{98} +(-0.819041 - 1.41862i) 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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