LMFDB - Embedded newform 189.2.w.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06527 + 0.751697i) q^{2} +(-0.131292 + 1.72707i) q^{3} +(2.16820 - 1.81934i) q^{4} +(-1.77012 - 0.644271i) q^{5} +(-1.02708 - 3.66555i) q^{6} +(-0.610341 - 2.57439i) q^{7} +(-0.912517 + 1.58053i) q^{8} +(-2.96552 - 0.453502i) q^{9} +O(q^{10})$	\(q+(-2.06527 + 0.751697i) q^{2} +(-0.131292 + 1.72707i) q^{3} +(2.16820 - 1.81934i) q^{4} +(-1.77012 - 0.644271i) q^{5} +(-1.02708 - 3.66555i) q^{6} +(-0.610341 - 2.57439i) q^{7} +(-0.912517 + 1.58053i) q^{8} +(-2.96552 - 0.453502i) q^{9} +4.14007 q^{10} +(-0.327911 + 0.119350i) q^{11} +(2.85745 + 3.98350i) q^{12} +(-0.602948 - 3.41949i) q^{13} +(3.19568 + 4.85802i) q^{14} +(1.34510 - 2.97253i) q^{15} +(-0.286465 + 1.62463i) q^{16} -0.361781 q^{17} +(6.46550 - 1.29257i) q^{18} +5.69812 q^{19} +(-5.01012 + 1.82354i) q^{20} +(4.52628 - 0.716103i) q^{21} +(0.587510 - 0.492979i) q^{22} +(-1.04537 - 5.92860i) q^{23} +(-2.60987 - 1.78349i) q^{24} +(-1.11198 - 0.933063i) q^{25} +(3.81566 + 6.60892i) q^{26} +(1.17258 - 5.06212i) q^{27} +(-6.00703 - 4.47138i) q^{28} +(1.01351 - 5.74790i) q^{29} +(-0.543560 + 7.15018i) q^{30} +(-4.32980 + 3.63313i) q^{31} +(-1.26342 - 7.16524i) q^{32} +(-0.163073 - 0.581994i) q^{33} +(0.747174 - 0.271949i) q^{34} +(-0.578228 + 4.95021i) q^{35} +(-7.25493 + 4.41201i) q^{36} +(-2.03435 + 3.52360i) q^{37} +(-11.7682 + 4.28326i) q^{38} +(5.98484 - 0.592379i) q^{39} +(2.63355 - 2.20981i) q^{40} +(1.73529 + 9.84132i) q^{41} +(-8.80969 + 4.88133i) q^{42} +(-7.48894 - 6.28397i) q^{43} +(-0.493839 + 0.855355i) q^{44} +(4.95716 + 2.71335i) q^{45} +(6.61549 + 11.4584i) q^{46} +(-1.77971 - 1.49336i) q^{47} +(-2.76823 - 0.708046i) q^{48} +(-6.25497 + 3.14251i) q^{49} +(2.99792 + 1.09115i) q^{50} +(0.0474990 - 0.624819i) q^{51} +(-7.52851 - 6.31717i) q^{52} +(2.00143 - 3.46658i) q^{53} +(1.38349 + 11.3361i) q^{54} +0.657336 q^{55} +(4.62584 + 1.38451i) q^{56} +(-0.748120 + 9.84104i) q^{57} +(2.22751 + 12.6328i) q^{58} +(-1.53680 - 8.71562i) q^{59} +(-2.49158 - 8.89224i) q^{60} +(-8.09969 - 6.79644i) q^{61} +(6.21119 - 10.7581i) q^{62} +(0.642492 + 7.91121i) q^{63} +(6.34571 + 10.9911i) q^{64} +(-1.13579 + 6.44136i) q^{65} +(0.774273 + 1.07939i) q^{66} +(-3.99124 - 1.45269i) q^{67} +(-0.784413 + 0.658201i) q^{68} +(10.3764 - 1.02705i) q^{69} +(-2.52686 - 10.6582i) q^{70} +(-5.31461 - 9.20518i) q^{71} +(3.42286 - 4.27326i) q^{72} +(1.59326 + 2.75961i) q^{73} +(1.55281 - 8.80641i) q^{74} +(1.75746 - 1.79796i) q^{75} +(12.3547 - 10.3668i) q^{76} +(0.507391 + 0.771327i) q^{77} +(-11.9150 + 5.72221i) q^{78} +(11.9365 - 4.34452i) q^{79} +(1.55378 - 2.69122i) q^{80} +(8.58867 + 2.68974i) q^{81} +(-10.9815 - 19.0206i) q^{82} +(-2.06563 + 11.7148i) q^{83} +(8.51105 - 9.78748i) q^{84} +(0.640395 + 0.233085i) q^{85} +(20.1903 + 7.34867i) q^{86} +(9.79395 + 2.50506i) q^{87} +(0.110589 - 0.627180i) q^{88} +11.2861 q^{89} +(-12.2775 - 1.87753i) q^{90} +(-8.43508 + 3.63927i) q^{91} +(-13.0527 - 10.9525i) q^{92} +(-5.70620 - 7.95486i) q^{93} +(4.79814 + 1.74638i) q^{94} +(-10.0864 - 3.67113i) q^{95} +(12.5407 - 1.24128i) q^{96} +(4.66375 + 3.91335i) q^{97} +(10.5560 - 11.1920i) q^{98} +(1.02655 - 0.205227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.06527	+	0.751697i	−1.46037	+	0.531530i	−0.945466	−	0.325721i	$-0.894393\pi$
$2$	−2.06527	+	0.751697i	−1.46037	+	0.531530i	−0.514900	+	0.857250i	$0.672171\pi$
$3$	−0.131292	+	1.72707i	−0.0758017	+	0.997123i
$3$	−0.131292	+	1.72707i	−0.0758017	+	0.997123i
$4$	2.16820	−	1.81934i	1.08410	−	0.909668i
$5$	−1.77012	−	0.644271i	−0.791622	−	0.288127i	−0.0856118	−	0.996329i	$-0.527284\pi$
$5$	−1.77012	−	0.644271i	−0.791622	−	0.288127i	−0.706010	+	0.708202i	$0.749507\pi$
$6$	−1.02708	−	3.66555i	−0.419302	−	1.49646i
$7$	−0.610341	−	2.57439i	−0.230687	−	0.973028i
$7$	−0.610341	−	2.57439i	−0.230687	−	0.973028i
$8$	−0.912517	+	1.58053i	−0.322623	+	0.558800i
$9$	−2.96552	−	0.453502i	−0.988508	−	0.151167i
$10$	4.14007			1.30921
$11$	−0.327911	+	0.119350i	−0.0988689	+	0.0359853i	−0.390981	−	0.920399i	$-0.627864\pi$
$11$	−0.327911	+	0.119350i	−0.0988689	+	0.0359853i	0.292112	+	0.956384i	$0.405642\pi$
$12$	2.85745	+	3.98350i	0.824875	+	1.14994i
$13$	−0.602948	−	3.41949i	−0.167228	−	0.948395i	−0.946738	−	0.322005i	$-0.895643\pi$
$13$	−0.602948	−	3.41949i	−0.167228	−	0.948395i	0.779510	−	0.626389i	$-0.215468\pi$
$14$	3.19568	+	4.85802i	0.854081	+	1.29836i
$15$	1.34510	−	2.97253i	0.347304	−	0.767504i
$16$	−0.286465	+	1.62463i	−0.0716163	+	0.406156i
$17$	−0.361781			−0.0877447			−0.0438723	−	0.999037i	$-0.513969\pi$
$17$	−0.361781			−0.0877447			−0.0438723	+	0.999037i	$0.513969\pi$
$18$	6.46550	−	1.29257i	1.52393	−	0.304662i
$19$	5.69812			1.30724			0.653619	−	0.756824i	$-0.273250\pi$
$19$	5.69812			1.30724			0.653619	+	0.756824i	$0.273250\pi$
$20$	−5.01012	+	1.82354i	−1.12030	+	0.407755i
$21$	4.52628	−	0.716103i	0.987715	−	0.156266i
$22$	0.587510	−	0.492979i	0.125257	−	0.105103i
$23$	−1.04537	−	5.92860i	−0.217975	−	1.23620i	−0.875668	−	0.482913i	$-0.839579\pi$
$23$	−1.04537	−	5.92860i	−0.217975	−	1.23620i	0.657693	−	0.753286i	$-0.271532\pi$
$24$	−2.60987	−	1.78349i	−0.532737	−	0.364053i
$25$	−1.11198	−	0.933063i	−0.222396	−	0.186613i
$26$	3.81566	+	6.60892i	0.748313	+	1.29612i
$27$	1.17258	−	5.06212i	0.225663	−	0.974205i
$28$	−6.00703	−	4.47138i	−1.13522	−	0.845011i
$29$	1.01351	−	5.74790i	0.188204	−	1.06736i	−0.733565	−	0.679619i	$-0.762145\pi$
$29$	1.01351	−	5.74790i	0.188204	−	1.06736i	0.921769	−	0.387739i	$-0.126744\pi$
$30$	−0.543560	+	7.15018i	−0.0992400	+	1.30544i
$31$	−4.32980	+	3.63313i	−0.777655	+	0.652530i	−0.942657	−	0.333763i	$-0.891681\pi$
$31$	−4.32980	+	3.63313i	−0.777655	+	0.652530i	0.165002	+	0.986293i	$0.447237\pi$
$32$	−1.26342	−	7.16524i	−0.223344	−	1.26665i
$33$	−0.163073	−	0.581994i	−0.0283874	−	0.101312i
$34$	0.747174	−	0.271949i	0.128139	−	0.0466389i
$35$	−0.578228	+	4.95021i	−0.0977384	+	0.836737i
$36$	−7.25493	+	4.41201i	−1.20915	+	0.735334i
$37$	−2.03435	+	3.52360i	−0.334446	+	0.579277i	−0.983378	−	0.181569i	$-0.941882\pi$
$37$	−2.03435	+	3.52360i	−0.334446	+	0.579277i	0.648933	+	0.760846i	$0.275216\pi$
$38$	−11.7682	+	4.28326i	−1.90905	+	0.694836i
$39$	5.98484	−	0.592379i	0.958342	−	0.0948565i
$40$	2.63355	−	2.20981i	0.416401	−	0.349402i
$41$	1.73529	+	9.84132i	0.271007	+	1.53696i	0.751367	+	0.659884i	$0.229395\pi$
$41$	1.73529	+	9.84132i	0.271007	+	1.53696i	−0.480361	+	0.877071i	$0.659494\pi$
$42$	−8.80969	+	4.88133i	−1.35937	+	0.753206i
$43$	−7.48894	−	6.28397i	−1.14205	−	0.958296i	−0.142548	−	0.989788i	$-0.545530\pi$
$43$	−7.48894	−	6.28397i	−1.14205	−	0.958296i	−0.999504	+	0.0314920i	$0.989974\pi$
$44$	−0.493839	+	0.855355i	−0.0744491	+	0.128950i
$45$	4.95716	+	2.71335i	0.738969	+	0.404483i
$46$	6.61549	+	11.4584i	0.975401	+	1.68944i
$47$	−1.77971	−	1.49336i	−0.259598	−	0.217828i	0.503694	−	0.863882i	$-0.331974\pi$
$47$	−1.77971	−	1.49336i	−0.259598	−	0.217828i	−0.763292	+	0.646054i	$0.776418\pi$
$48$	−2.76823	−	0.708046i	−0.399559	−	0.102198i
$49$	−6.25497	+	3.14251i	−0.893567	+	0.448930i
$50$	2.99792	+	1.09115i	0.423970	+	0.154313i
$51$	0.0474990	−	0.624819i	0.00665119	−	0.0874922i
$52$	−7.52851	−	6.31717i	−1.04402	−	0.876034i
$53$	2.00143	−	3.46658i	0.274918	−	0.476172i	−0.695197	−	0.718820i	$-0.744683\pi$
$53$	2.00143	−	3.46658i	0.274918	−	0.476172i	0.970114	+	0.242648i	$0.0780160\pi$
$54$	1.38349	+	11.3361i	0.188269	+	1.54264i
$55$	0.657336			0.0886351
$56$	4.62584	+	1.38451i	0.618153	+	0.185014i
$57$	−0.748120	+	9.84104i	−0.0990909	+	1.30348i
$58$	2.22751	+	12.6328i	0.292486	+	1.65877i
$59$	−1.53680	−	8.71562i	−0.200074	−	1.13468i	−0.905005	−	0.425401i	$-0.860133\pi$
$59$	−1.53680	−	8.71562i	−0.200074	−	1.13468i	0.704931	−	0.709276i	$-0.250978\pi$
$60$	−2.49158	−	8.89224i	−0.321661	−	1.14798i
$61$	−8.09969	−	6.79644i	−1.03706	−	0.870195i	−0.0453845	−	0.998970i	$-0.514451\pi$
$61$	−8.09969	−	6.79644i	−1.03706	−	0.870195i	−0.991674	+	0.128774i	$0.958896\pi$
$62$	6.21119	−	10.7581i	0.788822	−	1.36628i
$63$	0.642492	+	7.91121i	0.0809463	+	0.996718i
$64$	6.34571	+	10.9911i	0.793214	+	1.37389i
$65$	−1.13579	+	6.44136i	−0.140877	+	0.798953i
$66$	0.774273	+	1.07939i	0.0953064	+	0.132864i
$67$	−3.99124	−	1.45269i	−0.487608	−	0.177475i	0.0865040	−	0.996252i	$-0.472430\pi$
$67$	−3.99124	−	1.45269i	−0.487608	−	0.177475i	−0.574112	+	0.818777i	$0.694653\pi$
$68$	−0.784413	+	0.658201i	−0.0951240	+	0.0798186i
$69$	10.3764	−	1.02705i	1.24917	−	0.123642i
$70$	−2.52686	−	10.6582i	−0.302017	−	1.27389i
$71$	−5.31461	−	9.20518i	−0.630728	−	1.09245i	−0.987403	−	0.158225i	$-0.949423\pi$
$71$	−5.31461	−	9.20518i	−0.630728	−	1.09245i	0.356675	−	0.934229i	$-0.383910\pi$
$72$	3.42286	−	4.27326i	0.403388	−	0.503608i
$73$	1.59326	+	2.75961i	0.186477	+	0.322988i	0.944073	−	0.329736i	$-0.106960\pi$
$73$	1.59326	+	2.75961i	0.186477	+	0.322988i	−0.757596	+	0.652724i	$0.773626\pi$
$74$	1.55281	−	8.80641i	0.180510	−	1.02372i
$75$	1.75746	−	1.79796i	0.202934	−	0.207611i
$76$	12.3547	−	10.3668i	1.41718	−	1.18915i
$77$	0.507391	+	0.771327i	0.0578225	+	0.0879008i
$78$	−11.9150	+	5.72221i	−1.34911	+	0.647913i
$79$	11.9365	−	4.34452i	1.34296	−	0.488796i	0.432214	−	0.901771i	$-0.357732\pi$
$79$	11.9365	−	4.34452i	1.34296	−	0.488796i	0.910743	+	0.412975i	$0.135510\pi$
$80$	1.55378	−	2.69122i	0.173718	−	0.300888i
$81$	8.58867	+	2.68974i	0.954297	+	0.298860i
$82$	−10.9815	−	19.0206i	−1.21271	−	2.10047i
$83$	−2.06563	+	11.7148i	−0.226733	+	1.28587i	0.632612	+	0.774469i	$0.281983\pi$
$83$	−2.06563	+	11.7148i	−0.226733	+	1.28587i	−0.859345	+	0.511397i	$0.829128\pi$
$84$	8.51105	−	9.78748i	0.928632	−	1.06790i
$85$	0.640395	+	0.233085i	0.0694606	+	0.0252816i
$86$	20.1903	+	7.34867i	2.17718	+	0.792428i
$87$	9.79395	+	2.50506i	1.05002	+	0.268570i
$88$	0.110589	−	0.627180i	0.0117888	−	0.0668576i
$89$	11.2861			1.19633			0.598164	−	0.801374i	$-0.295897\pi$
$89$	11.2861			1.19633			0.598164	+	0.801374i	$0.295897\pi$
$90$	−12.2775	−	1.87753i	−1.29416	−	0.197909i
$91$	−8.43508	+	3.63927i	−0.884237	+	0.381500i
$92$	−13.0527	−	10.9525i	−1.36084	−	1.14188i
$93$	−5.70620	−	7.95486i	−0.591705	−	0.824881i
$94$	4.79814	+	1.74638i	0.494890	+	0.180125i
$95$	−10.0864	−	3.67113i	−1.03484	−	0.376650i
$96$	12.5407	−	1.24128i	1.27993	−	0.126688i
$97$	4.66375	+	3.91335i	0.473532	+	0.397341i	0.848081	−	0.529867i	$-0.177758\pi$
$97$	4.66375	+	3.91335i	0.473532	+	0.397341i	−0.374549	+	0.927207i	$0.622202\pi$
$98$	10.5560	−	11.1920i	1.06631	−	1.13056i
$99$	1.02655	−	0.205227i	0.103172	−	0.0206261i
$100$	−4.10856			−0.410856
$101$	−0.965700	+	5.47676i	−0.0960907	+	0.544958i	0.898317	+	0.439348i	$0.144790\pi$
$101$	−0.965700	+	5.47676i	−0.0960907	+	0.544958i	−0.994408	+	0.105610i	$0.966321\pi$
$102$	0.371576	+	1.32613i	0.0367915	+	0.131306i
$103$	2.74281	+	0.998301i	0.270257	+	0.0983656i	0.473594	−	0.880743i	$-0.342956\pi$
$103$	2.74281	+	0.998301i	0.270257	+	0.0983656i	−0.203337	+	0.979109i	$0.565179\pi$
$104$	5.95478	+	2.16736i	0.583914	+	0.212527i
$105$	−8.47342	−	1.64856i	−0.826921	−	0.160883i
$106$	−1.52768	+	8.66389i	−0.148381	+	0.841512i
$107$	−5.43491	−	9.41354i	−0.525413	−	0.910041i	−0.999562	−	0.0295969i	$-0.990578\pi$
$107$	−5.43491	−	9.41354i	−0.525413	−	0.910041i	0.474149	−	0.880444i	$-0.342756\pi$
$108$	−6.66732	−	13.1090i	−0.641563	−	1.26142i
$109$	−7.02338	+	12.1648i	−0.672717	+	1.16518i	0.304413	+	0.952540i	$0.401540\pi$
$109$	−7.02338	+	12.1648i	−0.672717	+	1.16518i	−0.977130	+	0.212641i	$0.931794\pi$
$110$	−1.35757	+	0.494117i	−0.129440	+	0.0471122i
$111$	−5.81841	−	3.97609i	−0.552259	−	0.377394i
$112$	4.35726	−	0.254102i	0.411722	−	0.0240104i
$113$	−2.06095	+	1.72934i	−0.193877	+	0.162682i	−0.734559	−	0.678545i	$-0.762611\pi$
$113$	−2.06095	+	1.72934i	−0.193877	+	0.162682i	0.540681	+	0.841227i	$0.318166\pi$
$114$	−5.85241	−	20.8868i	−0.548128	−	1.95622i
$115$	−1.96919	+	11.1678i	−0.183628	+	1.04141i
$116$	−8.25988	−	14.3065i	−0.766910	−	1.32833i
$117$	0.237314	+	10.4140i	0.0219397	+	0.962775i
$118$	9.72540	+	16.8449i	0.895296	+	1.55070i
$119$	0.220810	+	0.931364i	0.0202416	+	0.0853780i
$120$	3.47073	+	4.83845i	0.316833	+	0.441688i
$121$	−8.33321	+	6.99239i	−0.757564	+	0.635672i
$122$	21.8369	+	7.94798i	1.97702	+	0.719576i
$123$	−17.2244	+	1.70487i	−1.55308	+	0.153723i
$124$	−2.77798	+	15.7547i	−0.249470	+	1.41482i
$125$	6.07650	+	10.5248i	0.543499	+	0.941368i
$126$	−7.27375	−	15.8558i	−0.647997	−	1.41255i
$127$	5.56161	−	9.63300i	0.493513	−	0.854790i	−0.506459	−	0.862264i	$-0.669046\pi$
$127$	5.56161	−	9.63300i	0.493513	−	0.854790i	0.999972	+	0.00747384i	$0.00237902\pi$
$128$	−10.2204	−	8.57597i	−0.903368	−	0.758015i
$129$	11.8361	−	12.1089i	1.04211	−	1.06613i
$130$	−2.49625	−	14.1569i	−0.218935	−	1.24164i
$131$	−0.0349241	−	0.198064i	−0.00305133	−	0.0173050i	0.983244	−	0.182294i	$-0.0583522\pi$
$131$	−0.0349241	−	0.198064i	−0.00305133	−	0.0173050i	−0.986295	+	0.164989i	$0.947241\pi$
$132$	−1.41242	−	0.965196i	−0.122935	−	0.0840095i
$133$	−3.47780	−	14.6692i	−0.301563	−	1.27198i
$134$	9.33498			0.806420
$135$	−5.33698	+	8.20510i	−0.459334	+	0.706183i
$136$	0.330131	−	0.571803i	0.0283085	−	0.0490317i
$137$	13.6440	+	11.4487i	1.16569	+	0.978126i	0.999968	−	0.00804738i	$-0.00256159\pi$
$137$	13.6440	+	11.4487i	1.16569	+	0.978126i	0.165717	+	0.986173i	$0.447006\pi$
$138$	−20.6579	+	9.92100i	−1.75852	+	0.844532i
$139$	16.2672	+	5.92079i	1.37977	+	0.502195i	0.922108	−	0.386932i	$-0.126465\pi$
$139$	16.2672	+	5.92079i	1.37977	+	0.502195i	0.457661	+	0.889127i	$0.348687\pi$
$140$	7.75238	+	11.7850i	0.655195	+	0.996017i
$141$	2.81279	−	2.87762i	0.236880	−	0.242339i
$142$	17.8956	+	15.0162i	1.50177	+	1.26013i
$143$	0.605828	+	1.04932i	0.0506619	+	0.0877490i
$144$	1.58629	−	4.68795i	0.132191	−	0.390663i
$145$	−5.49724	+	9.52150i	−0.456521	+	0.790718i
$146$	−5.36490	−	4.50169i	−0.444003	−	0.372562i
$147$	−4.60610	−	11.2153i	−0.379905	−	0.925026i
$148$	1.99973	+	11.3411i	0.164377	+	0.932229i
$149$	1.31294	−	1.10169i	0.107560	−	0.0902538i	−0.587421	−	0.809281i	$-0.699857\pi$
$149$	1.31294	−	1.10169i	0.107560	−	0.0902538i	0.694982	+	0.719027i	$0.255412\pi$
$150$	−2.27810	+	5.03435i	−0.186006	+	0.411053i
$151$	11.6671	−	4.24646i	0.949451	−	0.345572i	0.179560	−	0.983747i	$-0.442533\pi$
$151$	11.6671	−	4.24646i	0.949451	−	0.345572i	0.769891	+	0.638175i	$0.220310\pi$
$152$	−5.19963	+	9.00602i	−0.421746	+	0.730485i
$153$	1.07287	+	0.164068i	0.0867363	+	0.0132641i
$154$	−1.62770	−	1.21159i	−0.131164	−	0.0976330i
$155$	10.0050	−	3.64152i	0.803620	−	0.292494i
$156$	11.8986	−	12.1728i	0.952651	−	0.974608i
$157$	0.626075	+	3.55065i	0.0499662	+	0.283373i	0.999545	−	0.0301553i	$-0.00960018\pi$
$157$	0.626075	+	3.55065i	0.0499662	+	0.283373i	−0.949579	+	0.313528i	$0.898489\pi$
$158$	−21.3863	+	17.9452i	−1.70140	+	1.42764i
$159$	5.72425	+	3.91174i	0.453962	+	0.310221i
$160$	−2.37994	+	13.4973i	−0.188151	+	1.06706i
$161$	−14.6245	+	6.30967i	−1.15257	+	0.497272i
$162$	−19.7598	+	0.901039i	−1.55248	+	0.0707923i
$163$	−8.21388	−	14.2269i	−0.643361	−	1.11433i	−0.984678	−	0.174385i	$-0.944206\pi$
$163$	−8.21388	−	14.2269i	−0.643361	−	1.11433i	0.341317	−	0.939948i	$-0.389127\pi$
$164$	21.6671	+	18.1809i	1.69192	+	1.41969i
$165$	−0.0863031	+	1.13526i	−0.00671869	+	0.0883801i
$166$	−4.53988	−	25.7469i	−0.352363	−	1.99835i
$167$	−15.9292	+	13.3662i	−1.23264	+	1.03430i	−0.234573	+	0.972099i	$0.575369\pi$
$167$	−15.9292	+	13.3662i	−1.23264	+	1.03430i	−0.998063	+	0.0622059i	$0.980186\pi$
$168$	−2.99849	+	7.80735i	−0.231338	+	0.602350i
$169$	0.886670	−	0.322722i	0.0682054	−	0.0248247i
$170$	−1.49780			−0.114876
$171$	−16.8979	−	2.58411i	−1.29222	−	0.197612i
$172$	−27.6702			−2.10983
$173$	−1.19602	+	6.78297i	−0.0909318	+	0.515700i	0.904987	+	0.425440i	$0.139881\pi$
$173$	−1.19602	+	6.78297i	−0.0909318	+	0.515700i	−0.995918	+	0.0902595i	$0.971230\pi$
$174$	−22.1102	+	2.18846i	−1.67617	+	0.165907i
$175$	−1.72338	+	3.43216i	−0.130275	+	0.259447i
$176$	−0.0999636	−	0.566922i	−0.00753504	−	0.0427334i
$177$	15.2542	−	1.50986i	1.14658	−	0.113488i
$178$	−23.3089	+	8.48375i	−1.74708	+	0.635884i
$179$	−18.6502			−1.39398			−0.696992	−	0.717079i	$-0.745479\pi$
$179$	−18.6502			−1.39398			−0.696992	+	0.717079i	$0.745479\pi$
$180$	15.6846	−	3.13564i	1.16906	−	0.233717i
$181$	8.76519	−	15.1817i	0.651511	−	1.12845i	−0.331245	−	0.943545i	$-0.607469\pi$
$181$	8.76519	−	15.1817i	0.651511	−	1.12845i	0.982756	−	0.184906i	$-0.0591980\pi$
$182$	14.6851	−	13.8567i	1.08853	−	1.02713i
$183$	12.8013	−	13.0964i	0.946303	−	0.968112i
$184$	10.3242	+	3.75771i	0.761112	+	0.277022i
$185$	5.87121	−	4.92653i	0.431660	−	0.362206i
$186$	17.7645	+	12.1396i	1.30255	+	0.890119i
$187$	0.118632	−	0.0431784i	0.00867522	−	0.00315752i
$188$	−6.57569			−0.479582
$189$	−13.7475	+	0.0709455i	−0.999987	+	0.00516053i
$190$	23.5906			1.71144
$191$	6.77625	−	2.46635i	0.490312	−	0.178459i	−0.0850194	−	0.996379i	$-0.527095\pi$
$191$	6.77625	−	2.46635i	0.490312	−	0.178459i	0.575332	+	0.817920i	$0.304873\pi$
$192$	−19.8155	+	9.51642i	−1.43006	+	0.686789i
$193$	14.4164	−	12.0968i	1.03772	−	0.870749i	0.0459690	−	0.998943i	$-0.485362\pi$
$193$	14.4164	−	12.0968i	1.03772	−	0.870749i	0.991749	+	0.128194i	$0.0409180\pi$
$194$	−12.5736	−	4.57640i	−0.902728	−	0.328566i
$195$	−10.9755	−	2.80728i	−0.785975	−	0.201034i
$196$	−7.84474	+	18.1935i	−0.560339	+	1.29954i
$197$	0.976617	−	1.69155i	0.0695811	−	0.120518i	−0.829136	−	0.559047i	$-0.811167\pi$
$197$	0.976617	−	1.69155i	0.0695811	−	0.120518i	0.898717	+	0.438529i	$0.144500\pi$
$198$	−1.96584	+	1.19551i	−0.139706	+	0.0849609i
$199$	−6.33128			−0.448813			−0.224406	−	0.974496i	$-0.572044\pi$
$199$	−6.33128			−0.448813			−0.224406	+	0.974496i	$0.572044\pi$
$200$	2.48943	−	0.906079i	0.176029	−	0.0640695i
$201$	3.03292	−	6.70242i	0.213926	−	0.472752i
$202$	−2.12243	−	12.0369i	−0.149334	−	0.846913i
$203$	−15.4159	+	0.899010i	−1.08199	+	0.0630981i
$204$	−1.03377	−	1.44115i	−0.0723783	−	0.100901i
$205$	3.26880	−	18.5383i	0.228303	−	1.29477i
$206$	−6.41506			−0.446959
$207$	0.411448	+	18.0555i	0.0285976	+	1.25494i
$208$	5.72811			0.397173
$209$	−1.86848	+	0.680070i	−0.129245	+	0.0470414i
$210$	18.7391	−	2.96472i	1.29312	−	0.204585i
$211$	−16.4153	+	13.7741i	−1.13008	+	0.948246i	−0.999069	−	0.0431356i	$-0.986265\pi$
$211$	−16.4153	+	13.7741i	−1.13008	+	0.948246i	−0.131006	+	0.991382i	$0.541821\pi$
$212$	−1.96737	−	11.1575i	−0.135120	−	0.766302i
$213$	16.5957	−	7.97012i	1.13712	−	0.546104i
$214$	18.3007	+	15.3561i	1.25101	+	1.04972i
$215$	9.20775	+	15.9483i	0.627963	+	1.08766i
$216$	6.93081	+	6.47256i	0.471582	+	0.440402i
$217$	11.9958	+	8.92915i	0.814325	+	0.606150i
$218$	5.36089	−	30.4031i	0.363085	−	2.05916i
$219$	−4.97522	+	2.38935i	−0.336194	+	0.161458i
$220$	1.42524	−	1.19591i	0.0960894	−	0.0806286i
$221$	0.218135	+	1.23710i	0.0146733	+	0.0832166i
$222$	15.0054	+	3.83802i	1.00710	+	0.257591i
$223$	2.01624	−	0.733850i	0.135017	−	0.0491423i	−0.273628	−	0.961836i	$-0.588224\pi$
$223$	2.01624	−	0.733850i	0.135017	−	0.0491423i	0.408645	+	0.912693i	$0.366001\pi$
$224$	−17.6750	+	7.62579i	−1.18096	+	0.509519i
$225$	2.87446	+	3.27131i	0.191631	+	0.218087i
$226$	2.95647	−	5.12076i	0.196661	−	0.340628i
$227$	16.0434	−	5.83931i	1.06484	−	0.387569i	0.250593	−	0.968093i	$-0.419374\pi$
$227$	16.0434	−	5.83931i	1.06484	−	0.387569i	0.814243	+	0.580524i	$0.197152\pi$
$228$	16.2821	+	22.6984i	1.07831	+	1.50324i
$229$	19.8594	−	16.6641i	1.31235	−	1.10119i	0.324482	−	0.945892i	$-0.394810\pi$
$229$	19.8594	−	16.6641i	1.31235	−	1.10119i	0.987867	−	0.155300i	$-0.0496344\pi$
$230$	−4.32792	−	24.5448i	−0.285375	−	1.61844i
$231$	−1.39875	+	0.775028i	−0.0920310	+	0.0509931i
$232$	8.15986	+	6.84694i	0.535721	+	0.449523i
$233$	−6.96108	+	12.0569i	−0.456035	+	0.789876i	−0.998747	−	0.0500427i	$-0.984064\pi$
$233$	−6.96108	+	12.0569i	−0.456035	+	0.789876i	0.542712	+	0.839919i	$0.317398\pi$
$234$	−8.31829	−	21.3293i	−0.543784	−	1.39434i
$235$	2.18818	+	3.79004i	0.142741	+	0.247235i
$236$	−19.1887	−	16.1013i	−1.24908	−	1.04810i
$237$	5.93611	+	21.1855i	0.385592	+	1.37614i
$238$	−1.15613	−	1.75754i	−0.0749411	−	0.113924i
$239$	9.46671	+	3.44560i	0.612351	+	0.222877i	0.629531	−	0.776975i	$-0.283247\pi$
$239$	9.46671	+	3.44560i	0.612351	+	0.222877i	−0.0171808	+	0.999852i	$0.505469\pi$
$240$	4.44392	+	3.03681i	0.286854	+	0.196026i
$241$	−7.47641	−	6.27346i	−0.481598	−	0.404109i	0.369406	−	0.929268i	$-0.379561\pi$
$241$	−7.47641	−	6.27346i	−0.481598	−	0.404109i	−0.851004	+	0.525159i	$0.824006\pi$
$242$	11.9542	−	20.7052i	0.768443	−	1.33098i
$243$	−5.77299	+	14.4801i	−0.370337	+	0.928897i
$244$	−29.9268			−1.91587
$245$	13.0967	−	1.53273i	0.836716	−	0.0979225i
$246$	34.2916	−	16.4686i	2.18635	−	1.05000i
$247$	−3.43567	−	19.4846i	−0.218606	−	1.23978i
$248$	−1.79125	−	10.1587i	−0.113744	−	0.645075i
$249$	−19.9610	−	5.10555i	−1.26498	−	0.323551i
$250$	−20.4611	−	17.1689i	−1.29407	−	1.08586i
$251$	13.8849	−	24.0493i	0.876404	−	1.51798i	0.0211447	−	0.999776i	$-0.493269\pi$
$251$	13.8849	−	24.0493i	0.876404	−	1.51798i	0.855259	−	0.518200i	$-0.173398\pi$
$252$	15.7862	+	15.9842i	0.994437	+	1.00691i
$253$	1.05037	+	1.81929i	0.0660360	+	0.114378i
$254$	−4.24514	+	24.0754i	−0.266364	+	1.51062i
$255$	−0.486632	+	1.07540i	−0.0304741	+	0.0673444i
$256$	3.70241	+	1.34757i	0.231401	+	0.0842230i
$257$	10.0071	−	8.39695i	0.624226	−	0.523788i	−0.274903	−	0.961472i	$-0.588646\pi$
$257$	10.0071	−	8.39695i	0.624226	−	0.523788i	0.899129	+	0.437684i	$0.144201\pi$
$258$	−15.3425	+	33.9052i	−0.955182	+	2.11085i
$259$	10.3128	+	3.08662i	0.640805	+	0.191793i
$260$	9.25640	+	16.0325i	0.574057	+	0.994296i
$261$	−5.61227	+	16.5859i	−0.347391	+	1.02664i
$262$	0.221012	+	0.382804i	0.0136542	+	0.0236497i
$263$	−1.35582	+	7.68924i	−0.0836035	+	0.474139i	0.914046	+	0.405611i	$0.132941\pi$
$263$	−1.35582	+	7.68924i	−0.0836035	+	0.474139i	−0.997649	+	0.0685277i	$0.978170\pi$
$264$	1.06866	+	0.273338i	0.0657717	+	0.0168228i
$265$	−5.77619	+	4.84680i	−0.354829	+	0.297737i
$266$	18.2094	+	27.6816i	1.11649	+	1.69727i
$267$	−1.48178	+	19.4919i	−0.0906836	+	1.19289i
$268$	−11.2968	+	4.11169i	−0.690060	+	0.251161i
$269$	−2.31323	+	4.00663i	−0.141040	+	0.244288i	−0.927889	−	0.372858i	$-0.878378\pi$
$269$	−2.31323	+	4.00663i	−0.141040	+	0.244288i	0.786849	+	0.617146i	$0.211711\pi$
$270$	4.85456	−	20.9575i	0.295439	−	1.27544i
$271$	−2.63491	−	4.56381i	−0.160060	−	0.277232i	0.774830	−	0.632169i	$-0.217835\pi$
$271$	−2.63491	−	4.56381i	−0.160060	−	0.277232i	−0.934890	+	0.354938i	$0.884502\pi$
$272$	0.103638	−	0.587758i	0.00628395	−	0.0356380i
$273$	−5.17781	−	15.0458i	−0.313375	−	0.910611i
$274$	−36.7845	−	13.3884i	−2.22223	−	0.808826i
$275$	0.475992	+	0.173247i	0.0287034	+	0.0104472i
$276$	20.6295	−	21.1049i	1.24175	−	1.27037i
$277$	3.47076	−	19.6837i	0.208538	−	1.18268i	−0.683236	−	0.730197i	$-0.739428\pi$
$277$	3.47076	−	19.6837i	0.208538	−	1.18268i	0.891774	−	0.452480i	$-0.149461\pi$
$278$	−38.0469			−2.28190
$279$	14.4878	−	8.81058i	0.867360	−	0.527476i
$280$	−7.29628	−	5.43105i	−0.436036	−	0.324567i
$281$	−3.12783	−	2.62456i	−0.186590	−	0.156568i	0.544708	−	0.838626i	$-0.316641\pi$
$281$	−3.12783	−	2.62456i	−0.186590	−	0.156568i	−0.731298	+	0.682058i	$0.761085\pi$
$282$	−3.64607	+	8.05742i	−0.217121	+	0.479812i
$283$	3.96128	+	1.44179i	0.235474	+	0.0857054i	0.457062	−	0.889435i	$-0.348902\pi$
$283$	3.96128	+	1.44179i	0.235474	+	0.0857054i	−0.221588	+	0.975140i	$0.571124\pi$
$284$	−28.2705	−	10.2896i	−1.67754	−	0.610576i
$285$	7.66456	−	16.9378i	0.454009	−	1.00331i
$286$	−2.03997	−	1.71174i	−0.120626	−	0.101217i
$287$	24.2763	−	10.4739i	1.43298	−	0.618253i
$288$	0.497271	+	21.8217i	0.0293020	+	1.28585i
$289$	−16.8691			−0.992301
$290$	4.19601	−	23.7967i	0.246398	−	1.39739i
$291$	−7.37093	+	7.54082i	−0.432092	+	0.442051i
$292$	8.47517	+	3.08471i	0.495972	+	0.180519i
$293$	−15.2863	−	5.56375i	−0.893034	−	0.325038i	−0.145576	−	0.989347i	$-0.546504\pi$
$293$	−15.2863	−	5.56375i	−0.893034	−	0.325038i	−0.747458	+	0.664309i	$0.768726\pi$
$294$	17.9434	+	19.7003i	1.04648	+	1.14895i
$295$	−2.89490	+	16.4178i	−0.168548	+	0.955882i
$296$	−3.71276	−	6.43070i	−0.215800	−	0.373777i
$297$	0.219662	+	1.79987i	0.0127461	+	0.104439i
$298$	−1.88344	+	3.26222i	−0.109105	+	0.188975i
$299$	−19.6425	+	7.14927i	−1.13595	+	0.413453i
$300$	0.539422	−	7.09575i	0.0311435	−	0.409674i
$301$	−11.6066	+	23.1148i	−0.668992	+	1.33232i
$302$	−20.9036	+	17.5402i	−1.20286	+	1.00932i
$303$	−9.33194	−	2.38689i	−0.536106	−	0.137123i
$304$	−1.63231	+	9.25731i	−0.0936196	+	0.530943i
$305$	9.95867	+	17.2489i	0.570232	+	0.987670i
$306$	−2.33909	+	0.467627i	−0.133717	+	0.0267325i
$307$	−8.15085	−	14.1177i	−0.465193	−	0.805739i	0.534017	−	0.845474i	$-0.320682\pi$
$307$	−8.15085	−	14.1177i	−0.465193	−	0.805739i	−0.999210	+	0.0397351i	$0.987349\pi$
$308$	2.50343	+	0.749277i	0.142646	+	0.0426940i
$309$	−2.08424	+	4.60595i	−0.118569	+	0.262023i
$310$	−17.9257	+	15.0414i	−1.01811	+	0.854296i
$311$	−4.15496	−	1.51228i	−0.235606	−	0.0857536i	0.221519	−	0.975156i	$-0.428899\pi$
$311$	−4.15496	−	1.51228i	−0.235606	−	0.0857536i	−0.457125	+	0.889402i	$0.651121\pi$
$312$	−4.52500	+	9.99975i	−0.256178	+	0.566125i
$313$	−2.02994	+	11.5124i	−0.114739	+	0.650717i	0.872140	+	0.489256i	$0.162732\pi$
$313$	−2.02994	+	11.5124i	−0.114739	+	0.650717i	−0.986879	+	0.161461i	$0.948379\pi$
$314$	−3.96202	−	6.86243i	−0.223590	−	0.387269i
$315$	3.95967	−	14.4177i	0.223102	−	0.812347i
$316$	17.9765	−	31.1362i	1.01126	−	1.75155i
$317$	6.00702	+	5.04049i	0.337388	+	0.283102i	0.795702	−	0.605688i	$-0.207102\pi$
$317$	6.00702	+	5.04049i	0.337388	+	0.283102i	−0.458314	+	0.888790i	$0.651547\pi$
$318$	−14.7626	−	3.77591i	−0.827843	−	0.211742i
$319$	0.353670	+	2.00576i	0.0198017	+	0.112301i
$320$	−4.15143	−	23.5439i	−0.232072	−	1.31614i
$321$	16.9714	−	8.15053i	0.947250	−	0.454918i
$322$	25.4606	−	24.0244i	1.41886	−	1.33883i
$323$	−2.06147			−0.114703
$324$	23.5155	−	9.79379i	1.30642	−	0.544100i
$325$	−2.52013	+	4.36499i	−0.139792	+	0.242126i
$326$	27.6582	+	23.2080i	1.53184	+	1.28537i
$327$	−20.0874	−	13.7270i	−1.11084	−	0.759105i
$328$	−17.1379	−	6.23770i	−0.946284	−	0.344419i
$329$	−2.75825	+	5.49313i	−0.152067	+	0.302846i
$330$	−0.675134	−	2.40950i	−0.0371649	−	0.132638i
$331$	−7.30625	−	6.13067i	−0.401588	−	0.336972i	0.419519	−	0.907746i	$-0.362199\pi$
$331$	−7.30625	−	6.13067i	−0.401588	−	0.336972i	−0.821107	+	0.570774i	$0.806643\pi$
$332$	16.8344	+	29.1581i	0.923910	+	1.60026i
$333$	7.63089	−	9.52675i	0.418170	−	0.522063i
$334$	22.8507	−	39.5786i	1.25034	−	2.16565i
$335$	6.12905	+	5.14289i	0.334866	+	0.280986i
$336$	−0.133223	+	7.55864i	−0.00726793	+	0.412358i
$337$	−1.11913	−	6.34690i	−0.0609628	−	0.345737i	−0.999998	−	0.00191675i	$-0.999390\pi$
$337$	−1.11913	−	6.34690i	−0.0609628	−	0.345737i	0.939035	−	0.343821i	$-0.111721\pi$
$338$	−1.58862	+	1.33301i	−0.0864098	+	0.0725064i
$339$	−2.71610	−	3.78644i	−0.147518	−	0.205651i
$340$	1.81257	−	0.659720i	0.0983001	−	0.0357783i
$341$	0.986175	−	1.70811i	0.0534044	−	0.0924991i
$342$	36.8412	−	7.36523i	1.99214	−	0.398266i
$343$	11.9077	+	14.1847i	0.642956	+	0.765903i
$344$	16.7657	−	6.10223i	0.903949	−	0.329010i
$345$	−19.0291	−	4.86718i	−1.02449	−	0.262040i
$346$	−2.62863	−	14.9077i	−0.141316	−	0.801443i
$347$	17.1501	−	14.3906i	0.920666	−	0.772530i	−0.0534523	−	0.998570i	$-0.517022\pi$
$347$	17.1501	−	14.3906i	0.920666	−	0.772530i	0.974118	+	0.226040i	$0.0725781\pi$
$348$	25.7928	−	12.3870i	1.38264	−	0.664014i
$349$	−0.293026	+	1.66183i	−0.0156853	+	0.0889560i	−0.991646	−	0.128993i	$-0.958826\pi$
$349$	−0.293026	+	1.66183i	−0.0156853	+	0.0889560i	0.975960	+	0.217949i	$0.0699366\pi$
$350$	0.979302	−	8.38380i	0.0523459	−	0.448133i
$351$	−18.0168	−	0.957422i	−0.961668	−	0.0511034i
$352$	1.26946	+	2.19877i	0.0676625	+	0.117195i
$353$	−5.87354	−	4.92849i	−0.312617	−	0.262317i	0.472956	−	0.881086i	$-0.343187\pi$
$353$	−5.87354	−	4.92849i	−0.312617	−	0.262317i	−0.785573	+	0.618769i	$0.787632\pi$
$354$	−30.3691	+	14.5848i	−1.61410	+	0.775175i
$355$	3.47687	+	19.7183i	0.184533	+	1.04654i
$356$	24.4706	−	20.5333i	1.29694	−	1.08826i
$357$	−1.63752	+	0.259072i	−0.0866667	+	0.0137115i
$358$	38.5178	−	14.0193i	2.03573	−	0.740944i
$359$	14.7113			0.776435			0.388218	−	0.921568i	$-0.373091\pi$
$359$	14.7113			0.776435			0.388218	+	0.921568i	$0.373091\pi$
$360$	−8.81201	+	5.35893i	−0.464434	+	0.282441i
$361$	13.4686			0.708873
$362$	−6.69040	+	37.9432i	−0.351640	+	1.99425i
$363$	−10.9822	−	15.3101i	−0.576418	−	0.803570i
$364$	−11.6679	+	23.2369i	−0.611564	+	1.21795i
$365$	−1.04233	−	5.91133i	−0.0545579	−	0.309413i
$366$	−16.5937	+	36.6703i	−0.867367	+	1.91679i
$367$	19.4515	−	7.07977i	1.01536	−	0.369561i	0.219871	−	0.975529i	$-0.429436\pi$
$367$	19.4515	−	7.07977i	1.01536	−	0.369561i	0.795489	+	0.605968i	$0.207214\pi$
$368$	9.93122			0.517701
$369$	−0.682992	−	29.9716i	−0.0355551	−	1.56026i
$370$	−8.42237	+	14.5880i	−0.437858	+	0.758393i
$371$	−10.1459	−	3.03667i	−0.526748	−	0.157656i
$372$	−26.8448	−	6.86624i	−1.39184	−	0.355998i
$373$	6.70146	+	2.43913i	0.346989	+	0.126294i	0.509635	−	0.860391i	$-0.329781\pi$
$373$	6.70146	+	2.43913i	0.346989	+	0.126294i	−0.162646	+	0.986685i	$0.552003\pi$
$374$	−0.212550	+	0.178350i	−0.0109907	+	0.00922227i
$375$	−18.9749	+	9.11270i	−0.979857	+	0.470578i
$376$	3.98431	−	1.45017i	0.205475	−	0.0747867i
$377$	−20.2660			−1.04375
$378$	28.3391	−	10.4805i	1.45760	−	0.539059i
$379$	17.0792			0.877298			0.438649	−	0.898658i	$-0.355457\pi$
$379$	17.0792			0.877298			0.438649	+	0.898658i	$0.355457\pi$
$380$	−28.5483	+	10.3907i	−1.46450	+	0.533033i
$381$	15.9066	+	10.8700i	0.814922	+	0.556888i
$382$	−12.1408	+	10.1874i	−0.621179	+	0.521231i
$383$	−8.77081	−	3.19231i	−0.448167	−	0.163120i	0.108070	−	0.994143i	$-0.465533\pi$
$383$	−8.77081	−	3.19231i	−0.448167	−	0.163120i	−0.556237	+	0.831024i	$0.687755\pi$
$384$	16.1531	−	16.5254i	0.824311	−	0.843310i
$385$	−0.401199	−	1.69224i	−0.0204470	−	0.0862444i
$386$	−20.6807	+	35.8200i	−1.05262	+	1.82319i
$387$	19.3588	+	22.0315i	0.984065	+	1.11992i
$388$	17.2316			0.874804
$389$	−16.6672	+	6.06635i	−0.845059	+	0.307576i	−0.728024	−	0.685552i	$-0.759561\pi$
$389$	−16.6672	+	6.06635i	−0.845059	+	0.307576i	−0.117035	+	0.993128i	$0.537339\pi$
$390$	24.7777	−	2.45249i	1.25467	−	0.124187i
$391$	0.378196	+	2.14485i	0.0191262	+	0.108470i
$392$	0.740943	−	12.7537i	0.0374233	−	0.644161i
$393$	0.346656	−	0.0343119i	0.0174865	−	0.00173081i
$394$	−0.745444	+	4.22763i	−0.0375549	+	0.212985i
$395$	−23.9280			−1.20395
$396$	1.85240	−	2.31262i	0.0930865	−	0.116213i
$397$	−31.5262			−1.58225			−0.791126	−	0.611653i	$-0.790505\pi$
$397$	−31.5262			−1.58225			−0.791126	+	0.611653i	$0.790505\pi$
$398$	13.0758	−	4.75920i	0.655431	−	0.238557i
$399$	25.7913	−	4.08044i	1.29118	−	0.204277i
$400$	1.83442	−	1.53926i	0.0917211	−	0.0769631i
$401$	3.85409	+	21.8576i	0.192464	+	1.09152i	0.915984	+	0.401215i	$0.131412\pi$
$401$	3.85409	+	21.8576i	0.192464	+	1.09152i	−0.723520	+	0.690303i	$0.757477\pi$
$402$	−1.22561	+	16.1221i	−0.0611280	+	0.804099i
$403$	15.0341	+	12.6151i	0.748901	+	0.628403i
$404$	7.87023	+	13.6316i	0.391559	+	0.678200i
$405$	−13.4701	−	10.2946i	−0.669333	−	0.511543i
$406$	31.1623	−	13.4448i	1.54656	−	0.667254i
$407$	0.246545	−	1.39823i	0.0122208	−	0.0693076i
$408$	0.944199	+	0.645232i	0.0467448	+	0.0319437i
$409$	5.70872	−	4.79018i	0.282278	−	0.236859i	−0.490644	−	0.871360i	$-0.663239\pi$
$409$	5.70872	−	4.79018i	0.282278	−	0.236859i	0.772922	+	0.634501i	$0.218794\pi$
$410$	7.18422	+	40.7438i	0.354804	+	2.01219i
$411$	−21.5640	+	22.0610i	−1.06367	+	1.08819i
$412$	7.76321	−	2.82558i	0.382466	−	0.139206i
$413$	−21.4994	+	9.27582i	−1.05792	+	0.456433i
$414$	−14.4220	−	36.9802i	−0.708803	−	1.81748i
$415$	11.2039	−	19.4058i	0.549979	−	0.952591i
$416$	−23.7396	+	8.64053i	−1.16393	+	0.423637i
$417$	−12.3614	+	27.3173i	−0.605339	+	1.33773i
$418$	3.34770	−	2.80905i	0.163741	−	0.137395i
$419$	−2.38606	−	13.5320i	−0.116567	−	0.661082i	−0.985963	−	0.166966i	$-0.946603\pi$
$419$	−2.38606	−	13.5320i	−0.116567	−	0.661082i	0.869396	−	0.494116i	$-0.164508\pi$
$420$	−21.3714	+	11.8416i	−1.04282	+	0.577811i
$421$	−0.831436	−	0.697658i	−0.0405217	−	0.0340018i	0.622302	−	0.782777i	$-0.286198\pi$
$421$	−0.831436	−	0.697658i	−0.0405217	−	0.0340018i	−0.662824	+	0.748776i	$0.730642\pi$
$422$	23.5481	−	40.7865i	1.14630	−	1.98545i
$423$	4.60054	+	5.23569i	0.223686	+	0.254568i
$424$	3.65268	+	6.32663i	0.177390	+	0.307248i
$425$	0.402293	+	0.337564i	0.0195141	+	0.0163743i
$426$	−28.2835	+	28.9354i	−1.37034	+	1.40193i
$427$	−12.5531	+	24.9999i	−0.607488	+	1.20983i
$428$	−28.9104	−	10.5225i	−1.39744	−	0.508625i
$429$	−1.89180	+	0.908538i	−0.0913368	+	0.0438646i
$430$	−31.0047	−	26.0161i	−1.49518	−	1.25461i
$431$	3.85657	−	6.67978i	0.185765	−	0.321754i	−0.758069	−	0.652174i	$-0.773857\pi$
$431$	3.85657	−	6.67978i	0.185765	−	0.321754i	0.943834	+	0.330420i	$0.107190\pi$
$432$	7.88815	+	3.35512i	0.379519	+	0.161423i
$433$	−6.88273			−0.330763			−0.165381	−	0.986230i	$-0.552886\pi$
$433$	−6.88273			−0.330763			−0.165381	+	0.986230i	$0.552886\pi$
$434$	−31.4865	−	9.42392i	−1.51140	−	0.452363i
$435$	−15.7225	−	10.7442i	−0.753838	−	0.515145i
$436$	6.90386	+	39.1537i	0.330635	+	1.87512i
$437$	−5.95666	−	33.7819i	−0.284946	−	1.61601i
$438$	8.47909	−	8.67452i	0.405147	−	0.414484i
$439$	3.85792	+	3.23718i	0.184128	+	0.154502i	0.730193	−	0.683241i	$-0.239430\pi$
$439$	3.85792	+	3.23718i	0.184128	+	0.154502i	−0.546065	+	0.837743i	$0.683875\pi$
$440$	−0.599830	+	1.03894i	−0.0285958	+	0.0495293i
$441$	19.9744	−	6.48256i	0.951162	−	0.308693i
$442$	−1.38043	−	2.39098i	−0.0656605	−	0.113727i
$443$	4.61237	−	26.1581i	0.219141	−	1.24281i	−0.654435	−	0.756118i	$-0.727093\pi$
$443$	4.61237	−	26.1581i	0.219141	−	1.24281i	0.873575	−	0.486689i	$-0.161796\pi$
$444$	−19.8493	+	1.96468i	−0.942007	+	0.0932397i
$445$	−19.9778	−	7.27133i	−0.947039	−	0.344694i
$446$	−3.61244	+	3.03120i	−0.171054	+	0.143531i
$447$	1.73031	+	2.41218i	0.0818409	+	0.114092i
$448$	24.4223	−	23.0446i	1.15385	−	1.08876i
$449$	6.26326	+	10.8483i	0.295582	+	0.511963i	0.975120	−	0.221677i	$-0.0711532\pi$
$449$	6.26326	+	10.8483i	0.295582	+	0.511963i	−0.679538	+	0.733640i	$0.737820\pi$
$450$	−8.39557	−	4.59541i	−0.395771	−	0.216630i
$451$	−1.74358	−	3.01997i	−0.0821020	−	0.142205i
$452$	−1.32229	+	7.49911i	−0.0621955	+	0.352728i
$453$	5.80213	+	20.7073i	0.272608	+	0.972914i
$454$	−28.7445	+	24.1195i	−1.34905	+	1.13198i
$455$	17.2758	−	1.00747i	0.809902	−	0.0472310i
$456$	−14.8713	−	10.1625i	−0.696414	−	0.475904i
$457$	−24.0078	+	8.73812i	−1.12304	+	0.408752i	−0.835760	−	0.549095i	$-0.814972\pi$
$457$	−24.0078	+	8.73812i	−1.12304	+	0.408752i	−0.287278	+	0.957847i	$0.592750\pi$
$458$	−28.4888	+	49.3440i	−1.33119	+	2.30570i
$459$	−0.424216	+	1.83138i	−0.0198007	+	0.0854813i
$460$	16.0485	+	27.7968i	0.748264	+	1.29603i
$461$	−2.43070	+	13.7852i	−0.113209	+	0.642041i	0.874412	+	0.485184i	$0.161247\pi$
$461$	−2.43070	+	13.7852i	−0.113209	+	0.642041i	−0.987621	+	0.156857i	$0.949864\pi$
$462$	2.30621	−	2.65208i	0.107295	−	0.123386i
$463$	29.4497	+	10.7188i	1.36864	+	0.498146i	0.918716	−	0.394919i	$-0.129227\pi$
$463$	29.4497	+	10.7188i	1.36864	+	0.498146i	0.449929	+	0.893065i	$0.351449\pi$
$464$	9.04785	+	3.29315i	0.420036	+	0.152881i
$465$	4.97557	+	17.7574i	0.230737	+	0.823480i
$466$	5.31334	−	30.1334i	0.246136	−	1.39590i
$467$	15.7151			0.727208			0.363604	−	0.931554i	$-0.381546\pi$
$467$	15.7151			0.727208			0.363604	+	0.931554i	$0.381546\pi$
$468$	19.4611	+	22.1479i	0.899591	+	1.02379i
$469$	−1.30378	+	11.1617i	−0.0602030	+	0.515398i
$470$	−7.36814	−	6.18260i	−0.339867	−	0.285182i
$471$	−6.21441	+	0.615101i	−0.286345	+	0.0283424i
$472$	15.1776	+	5.52420i	0.698606	+	0.254272i
$473$	3.20570	+	1.16678i	0.147398	+	0.0536485i
$474$	−28.1847	−	39.2916i	−1.29457	−	1.80472i
$475$	−6.33620	−	5.31671i	−0.290725	−	0.243947i
$476$	2.17322	+	1.61766i	0.0996096	+	0.0741452i
$477$	−7.50739	+	9.37258i	−0.343740	+	0.429141i
$478$	−22.1414			−1.01272
$479$	2.72158	−	15.4348i	0.124352	−	0.705236i	−0.857338	−	0.514753i	$-0.827884\pi$
$479$	2.72158	−	15.4348i	0.124352	−	0.705236i	0.981691	−	0.190483i	$-0.0610053\pi$
$480$	−22.9983	−	5.88242i	−1.04972	−	0.268494i
$481$	13.2755	+	4.83189i	0.605312	+	0.220315i
$482$	20.1565	+	7.33638i	0.918105	+	0.334163i
$483$	−8.97714	−	26.0859i	−0.408474	−	1.18695i
$484$	−5.34656	+	30.3218i	−0.243025	+	1.37826i
$485$	−5.73414	−	9.93182i	−0.260374	−	0.450981i
$486$	1.03816	−	34.2448i	0.0470917	−	1.55338i
$487$	3.59178	−	6.22115i	0.162759	−	0.281907i	−0.773098	−	0.634286i	$-0.781294\pi$
$487$	3.59178	−	6.22115i	0.162759	−	0.281907i	0.935857	+	0.352379i	$0.114627\pi$
$488$	18.1330	−	6.59989i	0.820845	−	0.298763i
$489$	25.6492	−	12.3180i	1.15990	−	0.557041i
$490$	−25.8960	+	13.0102i	−1.16986	+	0.587742i
$491$	19.0066	−	15.9485i	0.857757	−	0.719744i	−0.103727	−	0.994606i	$-0.533077\pi$
$491$	19.0066	−	15.9485i	0.857757	−	0.719744i	0.961484	+	0.274862i	$0.0886323\pi$
$492$	−34.2443	+	35.0336i	−1.54385	+	1.57944i
$493$	−0.366668	+	2.07948i	−0.0165139	+	0.0936550i
$494$	21.7421	+	37.6585i	0.978224	+	1.69433i
$495$	−1.94934	−	0.298103i	−0.0876165	−	0.0133987i
$496$	−4.66214	−	8.07507i	−0.209336	−	0.362581i
$497$	−20.4540	+	19.3002i	−0.917487	+	0.865731i
$498$	45.0627	−	4.46030i	2.01931	−	0.199871i
$499$	26.3237	−	22.0882i	1.17841	−	0.988804i	0.178423	−	0.983954i	$-0.442900\pi$
$499$	26.3237	−	22.0882i	1.17841	−	0.988804i	0.999988	−	0.00485045i	$-0.00154395\pi$
$500$	32.3233	+	11.7647i	1.44554	+	0.526134i
$501$	−20.9929	−	29.2656i	−0.937893	−	1.30749i
$502$	−10.5982	+	60.1054i	−0.473021	+	2.68264i
$503$	12.4451	+	21.5555i	0.554898	+	0.961111i	0.997911	+	0.0645965i	$0.0205760\pi$
$503$	12.4451	+	21.5555i	0.554898	+	0.961111i	−0.443014	+	0.896515i	$0.646091\pi$
$504$	−13.0901	−	6.20363i	−0.583082	−	0.276332i
$505$	5.23792	−	9.07235i	0.233084	−	0.403714i
$506$	−3.53684	−	2.96777i	−0.157232	−	0.131933i
$507$	0.440949	+	1.57371i	0.0195832	+	0.0698909i
$508$	−5.46697	−	31.0047i	−0.242558	−	1.37561i
$509$	−5.41551	−	30.7129i	−0.240038	−	1.36132i	−0.831739	−	0.555167i	$-0.812654\pi$
$509$	−5.41551	−	30.7129i	−0.240038	−	1.36132i	0.591701	−	0.806158i	$-0.298457\pi$
$510$	0.196649	−	2.58680i	0.00870778	−	0.114545i
$511$	6.13188	−	5.78598i	0.271258	−	0.255957i
$512$	18.0242			0.796566
$513$	6.68149	−	28.8446i	0.294995	−	1.27352i
$514$	−14.3554	+	24.8643i	−0.633189	+	1.09672i
$515$	−4.21193	−	3.53423i	−0.185600	−	0.155737i
$516$	3.63288	−	47.7883i	0.159929	−	2.10376i
$517$	0.761819	+	0.277280i	0.0335048	+	0.0121947i
$518$	−23.6189	+	1.37738i	−1.03775	+	0.0605186i
$519$	−11.5576	−	2.95616i	−0.507323	−	0.129761i
$520$	−9.14431	−	7.67299i	−0.401005	−	0.336483i
$521$	−12.5867	−	21.8008i	−0.551434	−	0.955112i	−0.998171	−	0.0604465i	$-0.980748\pi$
$521$	−12.5867	−	21.8008i	−0.551434	−	0.955112i	0.446738	−	0.894665i	$-0.352586\pi$
$522$	−0.876724	−	38.4731i	−0.0383732	−	1.68392i
$523$	−2.01825	+	3.49570i	−0.0882517	+	0.152856i	−0.906772	−	0.421621i	$-0.861461\pi$
$523$	−2.01825	+	3.49570i	−0.0882517	+	0.152856i	0.818520	+	0.574477i	$0.194795\pi$
$524$	−0.436068	−	0.365905i	−0.0190497	−	0.0159846i
$525$	−5.70131	−	3.42701i	−0.248825	−	0.149567i
$526$	−2.97984	−	16.8995i	−0.129927	−	0.736854i
$527$	1.56644	−	1.31440i	0.0682351	−	0.0572560i
$528$	0.992237	−	0.0982114i	0.0431816	−	0.00427410i
$529$	−12.4426	+	4.52874i	−0.540983	+	0.196902i
$530$	8.28607	−	14.3519i	0.359924	−	0.623407i
$531$	0.604868	+	26.5433i	0.0262490	+	1.15188i
$532$	−34.2288	−	25.4785i	−1.48400	−	1.10463i
$533$	32.6059	−	11.8676i	1.41232	−	0.514043i
$534$	−11.5917	−	41.3699i	−0.501623	−	1.79025i
$535$	3.55557	+	20.1647i	0.153721	+	0.871794i
$536$	5.93810	−	4.98266i	0.256487	−	0.215218i
$537$	2.44863	−	32.2102i	0.105666	−	1.38997i
$538$	1.76567	−	10.0136i	0.0761234	−	0.431717i
$539$	1.67601	−	1.77699i	0.0721910	−	0.0765405i
$540$	3.35619	+	27.5001i	0.144428	+	1.18342i
$541$	18.6655	+	32.3295i	0.802491	+	1.38995i	0.917972	+	0.396645i	$0.129826\pi$
$541$	18.6655	+	32.3295i	0.802491	+	1.38995i	−0.115482	+	0.993310i	$0.536841\pi$
$542$	8.87241	+	7.44483i	0.381103	+	0.319783i
$543$	25.0691	+	17.1313i	1.07582	+	0.735175i
$544$	0.457082	+	2.59224i	0.0195972	+	0.111142i
$545$	20.2697	−	17.0083i	0.868258	−	0.728555i
$546$	22.0034	+	27.1814i	0.941660	+	1.16326i
$547$	14.0195	−	5.10267i	0.599429	−	0.218174i	−0.0244427	−	0.999701i	$-0.507781\pi$
$547$	14.0195	−	5.10267i	0.599429	−	0.218174i	0.623871	+	0.781527i	$0.285559\pi$
$548$	50.4119			2.15349
$549$	20.9376	+	23.8282i	0.893596	+	1.01696i
$550$	−1.11328			−0.0474704
$551$	5.77510	−	32.7522i	0.246028	−	1.39529i
$552$	−7.84532	+	17.3373i	−0.333919	+	0.737924i
$553$	−18.4698	−	28.0775i	−0.785416	−	1.19398i
$554$	7.62809	+	43.2611i	0.324087	+	1.83799i
$555$	7.73760	+	10.7868i	0.328443	+	0.457874i
$556$	46.0425	−	16.7581i	1.95264	−	0.710702i
$557$	−22.3851			−0.948486			−0.474243	−	0.880394i	$-0.657278\pi$
$557$	−22.3851			−0.948486			−0.474243	+	0.880394i	$0.657278\pi$
$558$	−23.2983	+	29.0866i	−0.986294	+	1.23133i
$559$	−16.9725	+	29.3972i	−0.717860	+	1.24337i
$560$	−7.87659	−	2.35747i	−0.332847	−	0.0996211i
$561$	0.0589966	+	0.210554i	0.00249084	+	0.00888960i
$562$	8.43267	+	3.06924i	0.355711	+	0.129468i
$563$	−22.4299	+	18.8209i	−0.945308	+	0.793207i	−0.978501	−	0.206241i	$-0.933877\pi$
$563$	−22.4299	+	18.8209i	−0.945308	+	0.793207i	0.0331933	+	0.999449i	$0.489432\pi$
$564$	0.863338	−	11.3567i	0.0363531	−	0.478202i
$565$	4.76228	−	1.73333i	0.200351	−	0.0729217i
$566$	−9.26490			−0.389433
$567$	1.68242	−	23.7523i	0.0706550	−	0.997501i
$568$	19.3987			0.813951
$569$	35.8359	−	13.0432i	1.50232	−	0.546800i	0.545660	−	0.838006i	$-0.316279\pi$
$569$	35.8359	−	13.0432i	1.50232	−	0.546800i	0.956660	+	0.291206i	$0.0940566\pi$
$570$	−3.09727	+	40.7426i	−0.129730	+	1.70652i
$571$	−2.57728	+	2.16259i	−0.107856	+	0.0905017i	−0.695121	−	0.718893i	$-0.744649\pi$
$571$	−2.57728	+	2.16259i	−0.107856	+	0.0905017i	0.587265	+	0.809395i	$0.300205\pi$
$572$	3.22263	+	1.17294i	0.134745	+	0.0490432i
$573$	3.36989	+	12.0269i	0.140779	+	0.502429i
$574$	−42.2639	+	39.8798i	−1.76406	+	1.66455i
$575$	−4.36933	+	7.56790i	−0.182214	+	0.315603i
$576$	−13.8339	−	35.4721i	−0.576412	−	1.47801i
$577$	−9.06294			−0.377295			−0.188647	−	0.982045i	$-0.560410\pi$
$577$	−9.06294			−0.377295			−0.188647	+	0.982045i	$0.560410\pi$
$578$	34.8393	−	12.6805i	1.44912	−	0.527437i
$579$	18.9993	+	26.4864i	0.789583	+	1.10074i
$580$	5.40369	+	30.6459i	0.224376	+	1.27250i
$581$	31.4192	−	1.83227i	1.30349	−	0.0760154i
$582$	9.55456	−	21.1145i	0.396049	−	0.875225i
$583$	−0.242555	+	1.37560i	−0.0100456	+	0.0569716i
$584$	−5.81551			−0.240648
$585$	6.28937	−	18.5869i	0.260033	−	0.768475i
$586$	35.7525			1.47692
$587$	0.717654	−	0.261205i	0.0296208	−	0.0107811i	−0.327167	−	0.944966i	$-0.606094\pi$
$587$	0.717654	−	0.261205i	0.0296208	−	0.0107811i	0.356788	+	0.934185i	$0.383872\pi$
$588$	−30.3914	−	15.9371i	−1.25332	−	0.657233i
$589$	−24.6717	+	20.7020i	−1.01658	+	0.853013i
$590$	−6.36246	−	36.0833i	−0.261938	−	1.48553i
$591$	2.79320	+	1.90877i	0.114897	+	0.0785163i
$592$	−5.14176	−	4.31445i	−0.211325	−	0.177323i
$593$	16.7359	+	28.9874i	0.687259	+	1.19037i	0.972721	+	0.231978i	$0.0745197\pi$
$593$	16.7359	+	28.9874i	0.687259	+	1.19037i	−0.285462	+	0.958390i	$0.592147\pi$
$594$	−1.80662	−	3.55210i	−0.0741264	−	0.145744i
$595$	0.209192	−	1.79089i	0.00857602	−	0.0734192i
$596$	0.842378	−	4.77736i	0.0345052	−	0.195688i
$597$	0.831249	−	10.9346i	0.0340208	−	0.447521i
$598$	35.1929	−	29.5304i	1.43915	−	1.20759i
$599$	−5.22398	−	29.6266i	−0.213446	−	1.21051i	−0.883583	−	0.468275i	$-0.844876\pi$
$599$	−5.22398	−	29.6266i	−0.213446	−	1.21051i	0.670137	−	0.742237i	$-0.266235\pi$
$600$	1.23802	+	4.41838i	0.0505418	+	0.180380i
$601$	−11.1403	+	4.05472i	−0.454421	+	0.165396i	−0.559082	−	0.829112i	$-0.688846\pi$
$601$	−11.1403	+	4.05472i	−0.454421	+	0.165396i	0.104661	+	0.994508i	$0.466624\pi$
$602$	6.59537	−	56.4629i	0.268807	−	2.30126i
$603$	11.1773	+	6.11804i	0.455176	+	0.249146i
$604$	17.5708	−	30.4335i	0.714945	−	1.23832i
$605$	19.2558	−	7.00853i	0.782859	−	0.284937i
$606$	21.0672	−	2.08523i	0.855796	−	0.0847065i
$607$	−17.1749	+	14.4115i	−0.697108	+	0.584943i	−0.920949	−	0.389683i	$-0.872585\pi$
$607$	−17.1749	+	14.4115i	−0.697108	+	0.584943i	0.223841	+	0.974626i	$0.428140\pi$
$608$	−7.19915	−	40.8284i	−0.291964	−	1.65581i
$609$	0.471342	−	26.7424i	0.0190998	−	1.08366i
$610$	−33.5333	−	28.1378i	−1.35772	−	1.13926i
$611$	−4.03344	+	6.98612i	−0.163175	+	0.282628i
$612$	2.62469	−	1.59618i	0.106097	−	0.0645217i
$613$	−0.939159	−	1.62667i	−0.0379323	−	0.0657006i	0.846436	−	0.532490i	$-0.178744\pi$
$613$	−0.939159	−	1.62667i	−0.0379323	−	0.0657006i	−0.884368	+	0.466790i	$0.845410\pi$
$614$	27.4459	+	23.0299i	1.10763	+	0.929409i
$615$	31.5877	+	8.07938i	1.27374	+	0.325792i
$616$	−1.68210	+	0.0980952i	−0.0677739	+	0.00395237i
$617$	−37.6560	−	13.7057i	−1.51597	−	0.551770i	−0.555835	−	0.831292i	$-0.687602\pi$
$617$	−37.6560	−	13.7057i	−1.51597	−	0.551770i	−0.960139	+	0.279523i	$0.909824\pi$
$618$	0.842249	−	11.0792i	0.0338802	−	0.445673i
$619$	−26.6863	−	22.3924i	−1.07261	−	0.900028i	−0.0773254	−	0.997006i	$-0.524638\pi$
$619$	−26.6863	−	22.3924i	−1.07261	−	0.900028i	−0.995287	+	0.0969776i	$0.969082\pi$
$620$	15.0677	−	26.0980i	0.605133	−	1.04812i
$621$	−31.2371	−	1.65995i	−1.25350	−	0.0666115i
$622$	9.71789			0.389652
$623$	−6.88839	−	29.0549i	−0.275977	−	1.16406i
$624$	−0.752056	+	9.89283i	−0.0301064	+	0.396030i
$625$	−2.71498	−	15.3974i	−0.108599	−	0.615897i
$626$	−4.46143	−	25.3020i	−0.178315	−	1.01127i
$627$	−0.929210	−	3.31627i	−0.0371091	−	0.132439i
$628$	7.81728	+	6.55948i	0.311944	+	0.261752i
$629$	0.735990	−	1.27477i	0.0293458	−	0.0508285i
$630$	2.65996	+	32.7530i	0.105975	+	1.30491i
$631$	−4.20962	−	7.29128i	−0.167582	−	0.290261i	0.769987	−	0.638060i	$-0.220263\pi$
$631$	−4.20962	−	7.29128i	−0.167582	−	0.290261i	−0.937569	+	0.347798i	$0.886929\pi$
$632$	−4.02560	+	22.8303i	−0.160130	+	0.908142i
$633$	−21.6335	−	30.1588i	−0.859856	−	1.19870i
$634$	−16.1950	−	5.89451i	−0.643187	−	0.234101i
$635$	−16.0510	+	13.4684i	−0.636964	+	0.534476i
$636$	19.5281	−	1.93289i	0.774340	−	0.0766440i
$637$	14.5172	+	19.4940i	0.575192	+	0.772380i
$638$	−2.23815	−	3.87659i	−0.0886092	−	0.153476i
$639$	11.5860	+	29.7084i	0.458337	+	1.17524i
$640$	12.5662	+	21.7652i	0.496721	+	0.860346i
$641$	0.906208	−	5.13936i	0.0357931	−	0.202993i	−0.961667	−	0.274220i	$-0.911580\pi$
$641$	0.906208	−	5.13936i	0.0357931	−	0.202993i	0.997460	+	0.0712272i	$0.0226915\pi$
$642$	−28.9238	+	29.5904i	−1.14153	+	1.16784i
$643$	21.0433	−	17.6574i	0.829866	−	0.696340i	−0.125395	−	0.992107i	$-0.540020\pi$
$643$	21.0433	−	17.6574i	0.829866	−	0.696340i	0.955260	+	0.295767i	$0.0955752\pi$
$644$	−20.2295	+	40.2875i	−0.797152	+	1.58755i
$645$	−28.7527	+	13.8085i	−1.13214	+	0.543710i
$646$	4.25749	−	1.54960i	0.167509	−	0.0609682i
$647$	16.0780	−	27.8479i	0.632090	−	1.09481i	−0.355033	−	0.934854i	$-0.615530\pi$
$647$	16.0780	−	27.8479i	0.632090	−	1.09481i	0.987124	−	0.159959i	$-0.0511362\pi$
$648$	−12.0885	+	11.1202i	−0.474882	+	0.436842i
$649$	1.54414	+	2.67453i	0.0606128	+	0.104984i
$650$	1.92360	−	10.9093i	0.0754497	−	0.427896i
$651$	−16.9962	+	19.5452i	−0.666133	+	0.766035i
$652$	−43.6928	−	15.9029i	−1.71114	−	0.622805i
$653$	14.3302	+	5.21577i	0.560785	+	0.204109i	0.606832	−	0.794830i	$-0.292440\pi$
$653$	14.3302	+	5.21577i	0.560785	+	0.204109i	−0.0460470	+	0.998939i	$0.514662\pi$
$654$	51.8044	+	13.2503i	2.02571	+	0.518129i
$655$	−0.0657873	+	0.373098i	−0.00257052	+	0.0145782i
$656$	−16.4856			−0.643653
$657$	−3.47337	−	8.90624i	−0.135509	−	0.347465i
$658$	1.56736	−	13.4182i	0.0611021	−	0.523095i
$659$	10.5049	+	8.81463i	0.409211	+	0.343369i	0.824041	−	0.566530i	$-0.191714\pi$
$659$	10.5049	+	8.81463i	0.409211	+	0.343369i	−0.414830	+	0.909899i	$0.636159\pi$
$660$	1.87830	+	2.61849i	0.0731128	+	0.101925i
$661$	15.2048	+	5.53410i	0.591399	+	0.215252i	0.620345	−	0.784329i	$-0.286993\pi$
$661$	15.2048	+	5.53410i	0.591399	+	0.215252i	−0.0289456	+	0.999581i	$0.509215\pi$
$662$	19.6978	+	7.16940i	0.765576	+	0.278647i
$663$	−2.16520	+	0.214311i	−0.0840894	+	0.00832315i
$664$	−16.6306	−	13.9547i	−0.645392	−	0.541549i
$665$	−3.29481	+	28.2069i	−0.127767	+	1.09382i
$666$	−8.59861	+	25.4114i	−0.333189	+	0.984673i
$667$	−35.1365			−1.36049
$668$	−10.2201	+	57.9610i	−0.395427	+	2.24258i
$669$	1.00269	+	3.57853i	0.0387663	+	0.138354i
$670$	−16.5240	−	6.01426i	−0.638379	−	0.232351i
$671$	3.46713	+	1.26193i	0.133847	+	0.0487163i
$672$	−10.8497	−	31.5271i	−0.418535	−	1.21619i
$673$	−6.01131	+	34.0918i	−0.231719	+	1.31414i	0.617695	+	0.786417i	$0.288066\pi$
$673$	−6.01131	+	34.0918i	−0.231719	+	1.31414i	−0.849414	+	0.527726i	$0.823045\pi$
$674$	7.08224	+	12.2668i	0.272798	+	0.472500i
$675$	−6.02716	+	4.53489i	−0.231986	+	0.174548i
$676$	1.33534	−	2.31288i	0.0513593	−	0.0889568i
$677$	17.6787	−	6.43452i	0.679448	−	0.247299i	0.0208373	−	0.999783i	$-0.493367\pi$
$677$	17.6787	−	6.43452i	0.679448	−	0.247299i	0.658610	+	0.752484i	$0.271145\pi$
$678$	8.45573	+	5.77834i	0.324740	+	0.221916i
$679$	7.22801	−	14.3948i	0.277386	−	0.552421i
$680$	−0.952768	+	0.799467i	−0.0365370	+	0.0306582i
$681$	7.97851	+	28.4747i	0.305737	+	1.09115i
$682$	−0.752740	+	4.26900i	−0.0288239	+	0.163469i
$683$	−14.1594	−	24.5248i	−0.541794	−	0.938415i	−0.998801	−	0.0489520i	$-0.984412\pi$
$683$	−14.1594	−	24.5248i	−0.541794	−	0.938415i	0.457007	−	0.889463i	$-0.348921\pi$
$684$	−41.3394	+	25.1401i	−1.58065	+	0.961257i
$685$	−16.7755	−	29.0560i	−0.640958	−	1.11017i
$686$	−35.2552	−	20.3443i	−1.34605	−	0.776748i
$687$	26.1726	+	36.4865i	0.998545	+	1.39205i
$688$	12.3544	−	10.3666i	0.471007	−	0.395222i
$689$	−13.0607	−	4.75370i	−0.497572	−	0.181102i
$690$	42.9588	−	4.25206i	1.63541	−	0.161873i
$691$	−7.30143	+	41.4084i	−0.277759	+	1.57525i	0.452299	+	0.891866i	$0.350604\pi$
$691$	−7.30143	+	41.4084i	−0.277759	+	1.57525i	−0.730058	+	0.683385i	$0.760507\pi$
$692$	9.74730	+	16.8828i	0.370537	+	0.641788i
$693$	−1.15488	−	2.51749i	−0.0438703	−	0.0956316i
$694$	−24.6022	+	42.6122i	−0.933886	+	1.61754i
$695$	−24.9804	−	20.9610i	−0.947559	−	0.795097i
$696$	−12.8964	+	13.1937i	−0.488839	+	0.500105i
$697$	−0.627794	−	3.56040i	−0.0237794	−	0.134860i
$698$	−0.644017	−	3.65240i	−0.0243764	−	0.138245i
$699$	−19.9092	−	13.6052i	−0.753035	−	0.514597i
$700$	2.50762	+	10.5770i	0.0947791	+	0.399774i
$701$	−32.0463			−1.21037			−0.605187	−	0.796084i	$-0.706901\pi$
$701$	−32.0463			−1.21037			−0.605187	+	0.796084i	$0.706901\pi$
$702$	37.9293	−	11.5659i	1.43155	−	0.436526i
$703$	−11.5920	+	20.0779i	−0.437200	+	0.757253i
$704$	−3.39261	−	2.84674i	−0.127864	−	0.107291i
$705$	−6.83294	+	3.28153i	−0.257344	+	0.123590i
$706$	15.8352	+	5.76353i	0.595965	+	0.216913i
$707$	14.6887	−	0.856601i	0.552426	−	0.0322158i
$708$	30.3273	−	31.0263i	1.13977	−	1.16604i
$709$	21.0722	+	17.6817i	0.791384	+	0.664050i	0.946087	−	0.323911i	$-0.104998\pi$
$709$	21.0722	+	17.6817i	0.791384	+	0.664050i	−0.154704	+	0.987961i	$0.549442\pi$
$710$	−22.0029	−	38.1101i	−0.825753	−	1.43025i
$711$	−37.3681	+	7.47057i	−1.40141	+	0.280168i
$712$	−10.2988	+	17.8380i	−0.385963	+	0.668508i
$713$	26.0657	+	21.8717i	0.976167	+	0.819102i
$714$	3.18718	−	1.76597i	0.119277	−	0.0660898i
$715$	−0.396339	−	2.24775i	−0.0148222	−	0.0840610i
$716$	−40.4375	+	33.9311i	−1.51122	+	1.26806i
$717$	−7.19369	+	15.8973i	−0.268653	+	0.593694i
$718$	−30.3829	+	11.0585i	−1.13388	+	0.412698i
$719$	−5.00397	+	8.66714i	−0.186617	+	0.323230i	−0.944120	−	0.329602i	$-0.893086\pi$
$719$	−5.00397	+	8.66714i	−0.186617	+	0.323230i	0.757503	+	0.652831i	$0.226419\pi$
$720$	−5.82824	+	7.27624i	−0.217206	+	0.271170i
$721$	0.895967	−	7.67037i	0.0333676	−	0.285659i
$722$	−27.8162	+	10.1243i	−1.03521	+	0.376787i
$723$	11.8163	−	12.0886i	0.439452	−	0.449580i
$724$	−8.61603	−	48.8639i	−0.320212	−	1.81601i
$725$	−6.49016	+	5.44589i	−0.241039	+	0.202255i
$726$	34.1898	+	23.3641i	1.26890	+	0.867122i
$727$	−1.02367	+	5.80555i	−0.0379660	+	0.215316i	−0.997889	−	0.0649495i	$-0.979311\pi$
$727$	−1.02367	+	5.80555i	−0.0379660	+	0.215316i	0.959923	+	0.280265i	$0.0904225\pi$
$728$	1.94519	−	16.6528i	0.0720936	−	0.617193i
$729$	−24.2501	−	11.8715i	−0.898153	−	0.439684i
$730$	6.59622	+	11.4250i	0.244137	+	0.422858i
$731$	2.70935	+	2.27342i	0.100209	+	0.0840853i
$732$	3.92916	−	51.6856i	0.145226	−	1.91035i
$733$	2.87334	+	16.2955i	0.106129	+	0.601888i	0.990763	+	0.135602i	$0.0432970\pi$
$733$	2.87334	+	16.2955i	0.106129	+	0.601888i	−0.884634	+	0.466286i	$0.845592\pi$
$734$	−34.8507	+	29.2432i	−1.28636	+	1.07939i
$735$	0.927634	+	22.8201i	0.0342163	+	0.841731i
$736$	−41.1591	+	14.9807i	−1.51715	+	0.552196i
$737$	1.48215			0.0545958
$738$	23.9401	+	61.3861i	0.881248	+	2.25965i
$739$	36.6820			1.34937			0.674685	−	0.738106i	$-0.264280\pi$
$739$	36.6820			1.34937			0.674685	+	0.738106i	$0.264280\pi$
$740$	3.76695	−	21.3634i	0.138476	−	0.785335i
$741$	34.1024	−	3.37545i	1.25278	−	0.124000i
$742$	23.2366	−	1.35509i	0.853044	−	0.0497469i
$743$	6.45820	+	36.6263i	0.236928	+	1.34369i	0.838514	+	0.544880i	$0.183425\pi$
$743$	6.45820	+	36.6263i	0.236928	+	1.34369i	−0.601586	+	0.798808i	$0.705464\pi$
$744$	17.7799	−	1.75985i	0.651841	−	0.0645191i
$745$	−3.03385	+	1.10423i	−0.111152	+	0.0404559i
$746$	−15.6738			−0.573859
$747$	11.4384	−	33.8037i	0.418508	−	1.23681i
$748$	0.178661	−	0.309451i	0.00653251	−	0.0113146i
$749$	−20.9170	+	19.7370i	−0.764290	+	0.721176i
$750$	32.3382	−	33.0835i	1.18082	−	1.20804i
$751$	−19.2815	−	7.01791i	−0.703593	−	0.256087i	−0.0346491	−	0.999400i	$-0.511031\pi$
$751$	−19.2815	−	7.01791i	−0.703593	−	0.256087i	−0.668944	+	0.743312i	$0.733254\pi$
$752$	2.93597	−	2.46357i	0.107064	−	0.0898372i
$753$	39.7117	+	27.1376i	1.44718	+	0.988948i
$754$	41.8547	−	15.2339i	1.52426	−	0.554784i
$755$	−23.3880			−0.851175
$756$	−29.6784	+	25.1652i	−1.07939	+	0.915251i
$757$	−22.7486			−0.826813			−0.413407	−	0.910547i	$-0.635661\pi$
$757$	−22.7486			−0.826813			−0.413407	+	0.910547i	$0.635661\pi$
$758$	−35.2731	+	12.8384i	−1.28118	+	0.466310i
$759$	−3.27994	+	1.57520i	−0.119054	+	0.0571760i
$760$	15.0063	−	12.5918i	0.544335	−	0.456752i
$761$	35.9318	+	13.0781i	1.30253	+	0.474080i	0.897818	−	0.440366i	$-0.145151\pi$
$761$	35.9318	+	13.0781i	1.30253	+	0.474080i	0.404707	+	0.914446i	$0.367374\pi$
$762$	−41.0225	−	10.4926i	−1.48609	−	0.380105i
$763$	35.6037	+	10.6562i	1.28894	+	0.385780i
$764$	10.2051	−	17.6758i	0.369209	−	0.639489i
$765$	−1.79340	−	0.981639i	−0.0648406	−	0.0354912i
$766$	20.5137			0.741191
$767$	−28.8763	+	10.5101i	−1.04266	+	0.379498i
$768$	−2.81344	+	6.21739i	−0.101521	+	0.224351i
$769$	0.455481	+	2.58316i	0.0164251	+	0.0931513i	0.991918	−	0.126878i	$-0.0404957\pi$
$769$	0.455481	+	2.58316i	0.0164251	+	0.0931513i	−0.975493	+	0.220029i	$0.929385\pi$
$770$	2.10063	+	3.19335i	0.0757016	+	0.115080i
$771$	13.1882	+	18.3854i	0.474963	+	0.662134i
$772$	9.24954	−	52.4567i	0.332898	−	1.88796i
$773$	−11.8251			−0.425319			−0.212660	−	0.977126i	$-0.568213\pi$
$773$	−11.8251			−0.425319			−0.212660	+	0.977126i	$0.568213\pi$
$774$	−56.5422	−	30.9490i	−2.03237	−	1.11244i
$775$	8.20460			0.294718
$776$	−10.4409	+	3.80018i	−0.374806	+	0.136418i
$777$	−6.68479	+	17.4056i	−0.239815	+	0.624423i
$778$	29.8621	−	25.0573i	1.07061	−	0.898348i
$779$	9.88789	+	56.0770i	0.354270	+	2.00917i
$780$	−28.9046	+	13.8815i	−1.03495	+	0.497036i
$781$	2.84136	+	2.38418i	0.101672	+	0.0853127i
$782$	−2.39335	−	4.14541i	−0.0855862	−	0.148240i
$783$	−27.9082	−	11.8704i	−0.997356	−	0.424213i
$784$	−3.31357	−	11.0622i	−0.118342	−	0.395079i
$785$	1.17935	−	6.68844i	0.0420929	−	0.238721i
$786$	−0.690145	+	0.331443i	−0.0246167	+	0.0118222i
$787$	2.06927	−	1.73632i	0.0737615	−	0.0618932i	−0.605162	−	0.796103i	$-0.706891\pi$
$787$	2.06927	−	1.73632i	0.0737615	−	0.0618932i	0.678923	+	0.734210i	$0.262447\pi$
$788$	−0.959997	−	5.44442i	−0.0341985	−	0.193949i
$789$	−13.1018	−	3.35113i	−0.466437	−	0.119303i
$790$	49.4178	−	17.9866i	1.75821	−	0.639935i
$791$	5.70987	+	4.25019i	0.203020	+	0.151119i
$792$	−0.612381	+	1.80977i	−0.0217600	+	0.0643072i
$793$	−18.3567	+	31.7947i	−0.651864	+	1.12906i
$794$	65.1100	−	23.6981i	2.31067	−	0.841014i
$795$	−7.61238	−	10.6122i	−0.269983	−	0.376377i
$796$	−13.7275	+	11.5187i	−0.486558	+	0.408271i
$797$	3.59169	+	20.3695i	0.127224	+	0.721524i	0.979962	+	0.199185i	$0.0638295\pi$
$797$	3.59169	+	20.3695i	0.127224	+	0.721524i	−0.852738	+	0.522339i	$0.825059\pi$
$798$	−50.1987	+	27.8144i	−1.77701	+	0.984620i
$799$	0.643865	+	0.540267i	0.0227783	+	0.0191133i
$800$	−5.28072	+	9.14647i	−0.186701	+	0.323376i
$801$	−33.4693	−	5.11828i	−1.18258	−	0.180845i
$802$	−24.3900	−	42.2448i	−0.861242	−	1.49172i
$803$	−0.851807	−	0.714751i	−0.0300596	−	0.0252230i
$804$	−5.61798	−	20.0501i	−0.198131	−	0.707113i
$805$	29.9523	−	1.74673i	1.05568	−	0.0615640i
$806$	−40.5322	−	14.7525i	−1.42769	−	0.519635i
$807$	−6.61601	−	4.52114i	−0.232895	−	0.159152i
$808$	−7.77494	−	6.52395i	−0.273521	−	0.229512i
$809$	17.2348	−	29.8515i	0.605942	−	1.04952i	−0.385960	−	0.922515i	$-0.626130\pi$
$809$	17.2348	−	29.8515i	0.605942	−	1.04952i	0.991902	−	0.127007i	$-0.0405369\pi$
$810$	35.5577	+	11.1357i	1.24937	+	0.391269i
$811$	−0.756699			−0.0265713			−0.0132856	−	0.999912i	$-0.504229\pi$
$811$	−0.756699			−0.0265713			−0.0132856	+	0.999912i	$0.504229\pi$
$812$	−31.7892	+	29.9960i	−1.11558	+	1.05265i
$813$	8.22795	−	3.95148i	0.288567	−	0.138585i
$814$	0.541861	+	3.07305i	0.0189922	+	0.107710i
$815$	5.37360	+	30.4752i	0.188229	+	1.06750i
$816$	1.00149	+	0.256157i	0.0350592	+	0.00896729i
$817$	−42.6729	−	35.8068i	−1.49293	−	1.25272i
$818$	−8.18928	+	14.1842i	−0.286331	+	0.495940i
$819$	26.6649	−	6.96703i	0.931746	−	0.243448i
$820$	−26.6400	−	46.1418i	−0.930309	−	1.61134i
$821$	7.89769	−	44.7900i	0.275631	−	1.56318i	−0.461319	−	0.887234i	$-0.652624\pi$
$821$	7.89769	−	44.7900i	0.275631	−	1.56318i	0.736950	−	0.675947i	$-0.236265\pi$
$822$	27.9523	−	61.7714i	0.974947	−	2.15453i
$823$	31.5612	+	11.4873i	1.10015	+	0.400423i	0.827373	−	0.561654i	$-0.189835\pi$
$823$	31.5612	+	11.4873i	1.10015	+	0.400423i	0.272780	+	0.962076i	$0.412057\pi$
$824$	−4.08070	+	3.42412i	−0.142158	+	0.119285i
$825$	−0.361703	+	0.799324i	−0.0125929	+	0.0278289i
$826$	37.4295	−	35.3181i	1.30234	−	1.22887i
$827$	8.70359	+	15.0751i	0.302654	+	0.524211i	0.976736	−	0.214445i	$-0.0687941\pi$
$827$	8.70359	+	15.0751i	0.302654	+	0.524211i	−0.674083	+	0.738656i	$0.735461\pi$
$828$	33.7411	+	38.3994i	1.17259	+	1.33447i
$829$	−12.6867	−	21.9741i	−0.440628	−	0.763191i	0.557108	−	0.830440i	$-0.311911\pi$
$829$	−12.6867	−	21.9741i	−0.440628	−	0.763191i	−0.997736	+	0.0672494i	$0.978578\pi$
$830$	−8.55187	+	48.5001i	−0.296840	+	1.68346i
$831$	33.5394	+	8.57856i	1.16347	+	0.297587i
$832$	33.7577	−	28.3261i	1.17034	−	0.982031i
$833$	2.26293	−	1.13690i	0.0784057	−	0.0393912i
$834$	4.99526	−	65.7095i	0.172972	−	2.27533i
$835$	36.8080	−	13.3970i	1.27379	−	0.463623i
$836$	−2.81396	+	4.87392i	−0.0973227	+	0.168568i
$837$	13.3143	+	26.1781i	0.460211	+	0.904848i
$838$	15.0998	+	26.1536i	0.521614	+	0.903463i
$839$	−6.27482	+	35.5863i	−0.216631	+	1.22857i	0.661423	+	0.750013i	$0.269953\pi$
$839$	−6.27482	+	35.5863i	−0.216631	+	1.22857i	−0.878054	+	0.478562i	$0.841158\pi$
$840$	10.3377	−	11.8881i	0.356686	−	0.410179i
$841$	−4.76009	−	1.73253i	−0.164141	−	0.0597425i
$842$	2.24157	+	0.815864i	0.0772495	+	0.0281165i
$843$	4.94345	−	5.05738i	0.170261	−	0.174185i
$844$	−10.5320	+	59.7299i	−0.362526	+	2.05599i
$845$	−1.77743			−0.0611456
$846$	−13.4370	−	7.35489i	−0.461974	−	0.252866i
$847$	23.0872	+	17.1852i	0.793287	+	0.590490i
$848$	5.05855	+	4.24463i	0.173711	+	0.145761i
$849$	−3.01015	+	6.65210i	−0.103308	+	0.228300i
$850$	−1.08459	−	0.394758i	−0.0372011	−	0.0135401i
$851$	23.0167	+	8.37740i	0.789003	+	0.287174i
$852$	21.4825	−	47.4741i	0.735980	−	1.62643i
$853$	−35.3963	−	29.7010i	−1.21195	−	1.01694i	−0.999206	−	0.0398344i	$-0.987317\pi$
$853$	−35.3963	−	29.7010i	−1.21195	−	1.01694i	−0.212740	−	0.977109i	$-0.568239\pi$
$854$	7.13325	−	61.0677i	0.244095	−	2.08969i
$855$	28.2465	+	15.4610i	0.966009	+	0.528756i
$856$	19.8378			0.678042
$857$	−1.70555	+	9.67266i	−0.0582605	+	0.330412i	−0.999982	−	0.00598150i	$-0.998096\pi$
$857$	−1.70555	+	9.67266i	−0.0582605	+	0.330412i	0.941722	+	0.336393i	$0.109207\pi$
$858$	3.22412	−	3.29843i	0.110070	−	0.112607i
$859$	−20.5950	−	7.49595i	−0.702691	−	0.255759i	−0.0341314	−	0.999417i	$-0.510866\pi$
$859$	−20.5950	−	7.49595i	−0.702691	−	0.255759i	−0.668559	+	0.743659i	$0.733089\pi$
$860$	48.9795	+	17.8271i	1.67019	+	0.607899i
$861$	14.9018	+	43.3019i	0.507852	+	1.47572i
$862$	−2.94370	+	16.6945i	−0.100263	+	0.568618i
$863$	−10.6666	−	18.4750i	−0.363094	−	0.628897i	0.625375	−	0.780325i	$-0.284946\pi$
$863$	−10.6666	−	18.4750i	−0.363094	−	0.628897i	−0.988468	+	0.151428i	$0.951613\pi$
$864$	−37.7528	−	2.00620i	−1.28438	−	0.0682522i
$865$	6.48717	−	11.2361i	0.220571	−	0.382039i
$866$	14.2147	−	5.17373i	0.483035	−	0.175810i
$867$	2.21479	−	29.1341i	0.0752181	−	0.989446i
$868$	42.2543	−	2.46415i	1.43421	−	0.0836385i
$869$	−3.39558	+	2.84923i	−0.115187	+	0.0966535i
$870$	40.5477	+	10.3711i	1.37469	+	0.351614i
$871$	−2.56096	+	14.5239i	−0.0867747	+	0.492124i
$872$	−12.8179	−	22.2012i	−0.434069	−	0.751829i
$873$	−12.0558	−	13.7202i	−0.408025	−	0.464357i
$874$	37.6959	+	65.2911i	1.27508	+	2.20851i
$875$	23.3862	−	22.0670i	0.790599	−	0.746001i
$876$	−6.44023	+	14.2322i	−0.217595	+	0.480861i
$877$	39.1696	−	32.8672i	1.32266	−	1.10985i	0.336929	−	0.941530i	$-0.390612\pi$
$877$	39.1696	−	32.8672i	1.32266	−	1.10985i	0.985733	−	0.168316i	$-0.0538328\pi$
$878$	−10.4010	−	3.78566i	−0.351017	−	0.127760i
$879$	11.6159	−	25.6700i	0.391796	−	0.865826i
$880$	−0.188304	+	1.06792i	−0.00634772	+	0.0359997i
$881$	−9.07914	−	15.7255i	−0.305884	−	0.529807i	0.671574	−	0.740938i	$-0.265619\pi$
$881$	−9.07914	−	15.7255i	−0.305884	−	0.529807i	−0.977458	+	0.211131i	$0.932285\pi$
$882$	−36.3796	+	28.4029i	−1.22496	+	0.956376i
$883$	4.33888	−	7.51516i	0.146015	−	0.252905i	−0.783736	−	0.621094i	$-0.786689\pi$
$883$	4.33888	−	7.51516i	0.146015	−	0.252905i	0.929751	+	0.368189i	$0.120022\pi$
$884$	2.72367	+	2.28543i	0.0916068	+	0.0768673i
$885$	−27.9746	−	7.15522i	−0.940355	−	0.240520i
$886$	10.1371	+	57.4906i	0.340564	+	1.93143i
$887$	5.20268	+	29.5058i	0.174689	+	0.990709i	0.938502	+	0.345273i	$0.112214\pi$
$887$	5.20268	+	29.5058i	0.174689	+	0.990709i	−0.763814	+	0.645437i	$0.776675\pi$
$888$	11.5937	−	5.56789i	0.389059	−	0.186846i
$889$	−28.1936	−	8.43835i	−0.945582	−	0.283013i
$890$	46.7254			1.56624
$891$	−3.13734	+	0.143061i	−0.105105	+	0.00479274i
$892$	3.03649	−	5.25935i	0.101669	−	0.176096i
$893$	−10.1410	−	8.50933i	−0.339356	−	0.284754i
$894$	−5.38679	−	3.68113i	−0.180161	−	0.123116i
$895$	33.0132	+	12.0158i	1.10351	+	0.401644i
$896$	−15.8399	+	31.5457i	−0.529175	+	1.05387i
$897$	−9.76837	−	34.8625i	−0.326157	−	1.16403i
$898$	−21.0900	−	17.6966i	−0.703781	−	0.590542i
$899$	16.4946	+	28.5695i	0.550126	+	0.952846i
$900$	12.1840	+	1.86324i	0.406134	+	0.0621079i
$901$	−0.724079	+	1.25414i	−0.0241226	+	0.0417815i
$902$	5.87106	+	4.92641i	0.195485	+	0.164031i
$903$	−38.3970	−	23.0801i	−1.27777	−	0.768059i
$904$	−0.852616	−	4.83543i	−0.0283576	−	0.160824i
$905$	−25.2966	+	21.2264i	−0.840887	+	0.705588i
$906$	−27.5486	−	38.4047i	−0.915240	−	1.27591i
$907$	−26.2997	+	9.57231i	−0.873267	+	0.317843i	−0.739489	−	0.673168i	$-0.764933\pi$
$907$	−26.2997	+	9.57231i	−0.873267	+	0.317843i	−0.133778	+	0.991011i	$0.542711\pi$
$908$	24.1616	−	41.8491i	0.801831	−	1.38881i
$909$	5.34752	−	15.8035i	0.177366	−	0.524169i
$910$	−34.9219	+	15.0669i	−1.15765	+	0.499461i
$911$	−37.9020	+	13.7952i	−1.25575	+	0.457055i	−0.882340	−	0.470612i	$-0.844033\pi$
$911$	−37.9020	+	13.7952i	−1.25575	+	0.457055i	−0.373409	+	0.927667i	$0.621811\pi$
$912$	−15.7737	−	4.03453i	−0.522319	−	0.133597i
$913$	−0.720814	−	4.08794i	−0.0238555	−	0.135291i
$914$	43.0142	−	36.0932i	1.42278	−	1.19386i
$915$	−31.0975	+	14.9346i	−1.02805	+	0.493724i
$916$	12.7418	−	72.2621i	0.420999	−	2.38761i
$917$	−0.488579	+	0.210795i	−0.0161343	+	0.00696106i
$918$	−0.500519	−	4.10117i	−0.0165196	−	0.135359i
$919$	−14.8126	−	25.6561i	−0.488621	−	0.846317i	0.511293	−	0.859406i	$-0.329167\pi$
$919$	−14.8126	−	25.6561i	−0.488621	−	0.846317i	−0.999914	+	0.0130897i	$0.995833\pi$
$920$	−15.8541	−	13.3032i	−0.522696	−	0.438594i
$921$	25.4523	−	12.2235i	0.838683	−	0.402779i
$922$	−5.34224	−	30.2973i	−0.175937	−	0.997789i
$923$	−28.2725	+	23.7235i	−0.930602	+	0.780868i
$924$	−1.62273	+	4.22521i	−0.0533840	+	0.138999i
$925$	5.54991	−	2.02000i	0.182480	−	0.0664172i
$926$	−68.8789			−2.26350
$927$	−7.68114	−	4.20436i	−0.252282	−	0.138089i
$928$	−42.4656			−1.39400
$929$	0.707495	−	4.01240i	0.0232122	−	0.131643i	−0.971000	−	0.239081i	$-0.923154\pi$
$929$	0.707495	−	4.01240i	0.0232122	−	0.131643i	0.994212	+	0.107439i	$0.0342649\pi$
$930$	−23.6241	−	32.9337i	−0.774664	−	1.07994i
$931$	−35.6416	+	17.9064i	−1.16810	+	0.586859i
$932$	6.84262	+	38.8064i	0.224137	+	1.27115i
$933$	3.15733	−	6.97734i	0.103366	−	0.228428i
$934$	−32.4559	+	11.8130i	−1.06199	+	0.386533i
$935$	−0.237811			−0.00777726
$936$	−16.6762	−	9.12787i	−0.545077	−	0.298354i
$937$	−8.88493	+	15.3891i	−0.290258	+	0.502741i	−0.973871	−	0.227104i	$-0.927074\pi$
$937$	−8.88493	+	15.3891i	−0.290258	+	0.502741i	0.683613	+	0.729845i	$0.260408\pi$
$938$	−5.69752	−	24.0319i	−0.186031	−	0.784669i
$939$	−19.6161	−	5.01733i	−0.640148	−	0.163734i
$940$	11.6398	+	4.23653i	0.379647	+	0.138180i
$941$	−5.68015	+	4.76621i	−0.185168	+	0.155374i	−0.730660	−	0.682742i	$-0.760787\pi$
$941$	−5.68015	+	4.76621i	−0.185168	+	0.155374i	0.545492	+	0.838116i	$0.316343\pi$
$942$	12.3721	−	5.94170i	0.403104	−	0.193591i
$943$	56.5312	−	20.5757i	1.84091	−	0.670037i
$944$	14.5999			0.475185
$945$	24.3805	+	8.73156i	0.793098	+	0.284038i
$946$	−7.49769			−0.243771
$947$	−55.0398	+	20.0329i	−1.78855	+	0.650980i	−0.789234	+	0.614092i	$0.789522\pi$
$947$	−55.0398	+	20.0329i	−1.78855	+	0.650980i	−0.999319	+	0.0368881i	$0.988255\pi$
$948$	51.4142	+	35.1346i	1.66986	+	1.14112i
$949$	8.47579	−	7.11204i	0.275136	−	0.230866i
$950$	17.0825	+	6.21753i	0.554230	+	0.201723i
$951$	−9.49394	+	9.71275i	−0.307862	+	0.314957i
$952$	−1.67354	−	0.500890i	−0.0542396	−	0.0162339i
$953$	8.82226	−	15.2806i	0.285781	−	0.494988i	−0.687017	−	0.726641i	$-0.741080\pi$
$953$	8.82226	−	15.2806i	0.285781	−	0.494988i	0.972798	+	0.231654i	$0.0744136\pi$
$954$	8.45946	−	25.0002i	0.273885	−	0.809411i
$955$	−13.5838			−0.439561
$956$	26.7944	−	9.75238i	0.866594	−	0.315415i
$957$	−3.51052	+	0.347471i	−0.113479	+	0.0112321i
$958$	5.98152	+	33.9229i	0.193254	+	1.09600i
$959$	21.1459	−	42.1126i	0.682835	−	1.35989i
$960$	41.2070	−	4.07866i	1.32995	−	0.131638i
$961$	0.164417	−	0.932457i	0.00530378	−	0.0300793i
$962$	−31.0496			−1.00108
$963$	11.8483	+	30.3808i	0.381806	+	0.979008i
$964$	−27.6239			−0.889706
$965$	−33.3125	+	12.1247i	−1.07237	+	0.390309i
$966$	38.1489	+	47.1264i	1.22742	+	1.51627i
$967$	7.51004	−	6.30167i	0.241507	−	0.202648i	−0.513998	−	0.857791i	$-0.671836\pi$
$967$	7.51004	−	6.30167i	0.241507	−	0.202648i	0.755505	+	0.655143i	$0.227392\pi$
$968$	−3.44746	−	19.5515i	−0.110806	−	0.628410i
$969$	0.270655	−	3.56030i	0.00869469	−	0.114373i
$970$	19.3083	+	16.2016i	0.619951	+	0.520200i
$971$	−21.6004	−	37.4129i	−0.693189	−	1.20064i	−0.970787	−	0.239941i	$-0.922872\pi$
$971$	−21.6004	−	37.4129i	−0.693189	−	1.20064i	0.277598	−	0.960697i	$-0.410462\pi$
$972$	13.8271	+	41.8987i	0.443505	+	1.34390i
$973$	5.31386	−	45.4919i	0.170354	−	1.45840i
$974$	−2.74158	+	15.5483i	−0.0878459	+	0.498199i
$975$	−7.20776	−	4.92552i	−0.230833	−	0.157743i
$976$	13.3620	−	11.2120i	0.427706	−	0.358888i
$977$	4.92856	+	27.9512i	0.157679	+	0.894239i	0.956296	+	0.292400i	$0.0944540\pi$
$977$	4.92856	+	27.9512i	0.157679	+	0.894239i	−0.798617	+	0.601839i	$0.794435\pi$
$978$	−43.7130	+	44.7205i	−1.39779	+	1.43000i
$979$	−3.70085	+	1.34700i	−0.118280	+	0.0430502i
$980$	25.6077	−	27.1505i	0.818007	−	0.867292i
$981$	26.3448	−	32.8900i	0.841124	−	1.05010i
$982$	−27.2654	+	47.2251i	−0.870074	+	1.50701i
$983$	−28.7006	+	10.4461i	−0.915405	+	0.333180i	−0.756409	−	0.654099i	$-0.773048\pi$
$983$	−28.7006	+	10.4461i	−0.915405	+	0.333180i	−0.158996	+	0.987279i	$0.550826\pi$
$984$	13.0230	−	28.7794i	0.415158	−	0.917454i
$985$	−2.81855	+	2.36504i	−0.0898063	+	0.0753565i
$986$	−0.805869	−	4.57031i	−0.0256641	−	0.145548i
$987$	−9.12487	−	5.48489i	−0.290448	−	0.174586i
$988$	−42.8983	−	35.9960i	−1.36478	−	1.14518i
$989$	−29.4264	+	50.9680i	−0.935706	+	1.62069i
$990$	4.25000	−	0.849653i	0.135074	−	0.0270038i
$991$	14.8609	+	25.7399i	0.472072	+	0.817654i	0.999489	−	0.0319531i	$-0.0101727\pi$
$991$	14.8609	+	25.7399i	0.472072	+	0.817654i	−0.527417	+	0.849607i	$0.676839\pi$
$992$	31.5027	+	26.4339i	1.00021	+	0.839276i
$993$	11.5473	−	11.8135i	0.366444	−	0.374889i
$994$	27.7351	−	55.2353i	0.879705	−	1.75196i
$995$	11.2071	+	4.07906i	0.355290	+	0.129315i
$996$	−52.5683	+	25.2460i	−1.66569	+	0.799950i
$997$	39.7516	+	33.3555i	1.25894	+	1.05638i	0.995794	+	0.0916257i	$0.0292063\pi$
$997$	39.7516	+	33.3555i	1.25894	+	1.05638i	0.263151	+	0.964755i	$0.415238\pi$
$998$	−37.7619	+	65.4056i	−1.19533	+	2.07038i
$999$	15.4515	+	14.4298i	0.488863	+	0.456540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.4	yes	132
3.2	odd	2		567.2.w.a.235.19		132
7.2	even	3		189.2.u.a.79.19	yes	132
21.2	odd	6		567.2.u.a.478.4		132
27.13	even	9		189.2.u.a.67.19	✓	132
27.14	odd	18		567.2.u.a.172.4		132
189.121	even	9	inner	189.2.w.a.121.4	yes	132
189.149	odd	18		567.2.w.a.415.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.19	✓	132	27.13	even	9
189.2.u.a.79.19	yes	132	7.2	even	3
189.2.w.a.25.4	yes	132	1.1	even	1	trivial
189.2.w.a.121.4	yes	132	189.121	even	9	inner
567.2.u.a.172.4		132	27.14	odd	18
567.2.u.a.478.4		132	21.2	odd	6
567.2.w.a.235.19		132	3.2	odd	2
567.2.w.a.415.19		132	189.149	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06527 + 0.751697i) q^{2} +(-0.131292 + 1.72707i) q^{3} +(2.16820 - 1.81934i) q^{4} +(-1.77012 - 0.644271i) q^{5} +(-1.02708 - 3.66555i) q^{6} +(-0.610341 - 2.57439i) q^{7} +(-0.912517 + 1.58053i) q^{8} +(-2.96552 - 0.453502i) q^{9} +O(q^{10})\)	\(q+(-2.06527 + 0.751697i) q^{2} +(-0.131292 + 1.72707i) q^{3} +(2.16820 - 1.81934i) q^{4} +(-1.77012 - 0.644271i) q^{5} +(-1.02708 - 3.66555i) q^{6} +(-0.610341 - 2.57439i) q^{7} +(-0.912517 + 1.58053i) q^{8} +(-2.96552 - 0.453502i) q^{9} +4.14007 q^{10} +(-0.327911 + 0.119350i) q^{11} +(2.85745 + 3.98350i) q^{12} +(-0.602948 - 3.41949i) q^{13} +(3.19568 + 4.85802i) q^{14} +(1.34510 - 2.97253i) q^{15} +(-0.286465 + 1.62463i) q^{16} -0.361781 q^{17} +(6.46550 - 1.29257i) q^{18} +5.69812 q^{19} +(-5.01012 + 1.82354i) q^{20} +(4.52628 - 0.716103i) q^{21} +(0.587510 - 0.492979i) q^{22} +(-1.04537 - 5.92860i) q^{23} +(-2.60987 - 1.78349i) q^{24} +(-1.11198 - 0.933063i) q^{25} +(3.81566 + 6.60892i) q^{26} +(1.17258 - 5.06212i) q^{27} +(-6.00703 - 4.47138i) q^{28} +(1.01351 - 5.74790i) q^{29} +(-0.543560 + 7.15018i) q^{30} +(-4.32980 + 3.63313i) q^{31} +(-1.26342 - 7.16524i) q^{32} +(-0.163073 - 0.581994i) q^{33} +(0.747174 - 0.271949i) q^{34} +(-0.578228 + 4.95021i) q^{35} +(-7.25493 + 4.41201i) q^{36} +(-2.03435 + 3.52360i) q^{37} +(-11.7682 + 4.28326i) q^{38} +(5.98484 - 0.592379i) q^{39} +(2.63355 - 2.20981i) q^{40} +(1.73529 + 9.84132i) q^{41} +(-8.80969 + 4.88133i) q^{42} +(-7.48894 - 6.28397i) q^{43} +(-0.493839 + 0.855355i) q^{44} +(4.95716 + 2.71335i) q^{45} +(6.61549 + 11.4584i) q^{46} +(-1.77971 - 1.49336i) q^{47} +(-2.76823 - 0.708046i) q^{48} +(-6.25497 + 3.14251i) q^{49} +(2.99792 + 1.09115i) q^{50} +(0.0474990 - 0.624819i) q^{51} +(-7.52851 - 6.31717i) q^{52} +(2.00143 - 3.46658i) q^{53} +(1.38349 + 11.3361i) q^{54} +0.657336 q^{55} +(4.62584 + 1.38451i) q^{56} +(-0.748120 + 9.84104i) q^{57} +(2.22751 + 12.6328i) q^{58} +(-1.53680 - 8.71562i) q^{59} +(-2.49158 - 8.89224i) q^{60} +(-8.09969 - 6.79644i) q^{61} +(6.21119 - 10.7581i) q^{62} +(0.642492 + 7.91121i) q^{63} +(6.34571 + 10.9911i) q^{64} +(-1.13579 + 6.44136i) q^{65} +(0.774273 + 1.07939i) q^{66} +(-3.99124 - 1.45269i) q^{67} +(-0.784413 + 0.658201i) q^{68} +(10.3764 - 1.02705i) q^{69} +(-2.52686 - 10.6582i) q^{70} +(-5.31461 - 9.20518i) q^{71} +(3.42286 - 4.27326i) q^{72} +(1.59326 + 2.75961i) q^{73} +(1.55281 - 8.80641i) q^{74} +(1.75746 - 1.79796i) q^{75} +(12.3547 - 10.3668i) q^{76} +(0.507391 + 0.771327i) q^{77} +(-11.9150 + 5.72221i) q^{78} +(11.9365 - 4.34452i) q^{79} +(1.55378 - 2.69122i) q^{80} +(8.58867 + 2.68974i) q^{81} +(-10.9815 - 19.0206i) q^{82} +(-2.06563 + 11.7148i) q^{83} +(8.51105 - 9.78748i) q^{84} +(0.640395 + 0.233085i) q^{85} +(20.1903 + 7.34867i) q^{86} +(9.79395 + 2.50506i) q^{87} +(0.110589 - 0.627180i) q^{88} +11.2861 q^{89} +(-12.2775 - 1.87753i) q^{90} +(-8.43508 + 3.63927i) q^{91} +(-13.0527 - 10.9525i) q^{92} +(-5.70620 - 7.95486i) q^{93} +(4.79814 + 1.74638i) q^{94} +(-10.0864 - 3.67113i) q^{95} +(12.5407 - 1.24128i) q^{96} +(4.66375 + 3.91335i) q^{97} +(10.5560 - 11.1920i) q^{98} +(1.02655 - 0.205227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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