LMFDB - Embedded newform 189.2.w.a.25.16

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			25.16
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17974 - 0.429388i) q^{2} +(-1.72810 - 0.116945i) q^{3} +(-0.324689 + 0.272446i) q^{4} +(3.35074 + 1.21957i) q^{5} +(-2.08891 + 0.604061i) q^{6} +(1.13056 - 2.39204i) q^{7} +(-1.52151 + 2.63533i) q^{8} +(2.97265 + 0.404186i) q^{9} +O(q^{10})$	\(q+(1.17974 - 0.429388i) q^{2} +(-1.72810 - 0.116945i) q^{3} +(-0.324689 + 0.272446i) q^{4} +(3.35074 + 1.21957i) q^{5} +(-2.08891 + 0.604061i) q^{6} +(1.13056 - 2.39204i) q^{7} +(-1.52151 + 2.63533i) q^{8} +(2.97265 + 0.404186i) q^{9} +4.47665 q^{10} +(4.35747 - 1.58599i) q^{11} +(0.592955 - 0.432843i) q^{12} +(0.293837 + 1.66643i) q^{13} +(0.306643 - 3.30742i) q^{14} +(-5.64778 - 2.49939i) q^{15} +(-0.516195 + 2.92749i) q^{16} -7.16716 q^{17} +(3.68049 - 0.799589i) q^{18} -2.21349 q^{19} +(-1.42021 + 0.516915i) q^{20} +(-2.23345 + 4.00146i) q^{21} +(4.45966 - 3.74210i) q^{22} +(-0.389540 - 2.20919i) q^{23} +(2.93751 - 4.37618i) q^{24} +(5.90986 + 4.95897i) q^{25} +(1.06220 + 1.83978i) q^{26} +(-5.08976 - 1.04611i) q^{27} +(0.284623 + 1.08468i) q^{28} +(0.632390 - 3.58646i) q^{29} +(-7.73609 - 0.523523i) q^{30} +(-2.88220 + 2.41846i) q^{31} +(-0.408773 - 2.31827i) q^{32} +(-7.71561 + 2.23116i) q^{33} +(-8.45534 + 3.07749i) q^{34} +(6.70545 - 6.63630i) q^{35} +(-1.07530 + 0.678652i) q^{36} +(-2.18550 + 3.78539i) q^{37} +(-2.61134 + 0.950449i) q^{38} +(-0.312898 - 2.91412i) q^{39} +(-8.31214 + 6.97472i) q^{40} +(0.0778798 + 0.441679i) q^{41} +(-0.916696 + 5.67968i) q^{42} +(0.648959 + 0.544541i) q^{43} +(-0.982725 + 1.70213i) q^{44} +(9.46763 + 4.97967i) q^{45} +(-1.40816 - 2.43900i) q^{46} +(-6.09243 - 5.11215i) q^{47} +(1.23439 - 4.99862i) q^{48} +(-4.44369 - 5.40866i) q^{49} +(9.10140 + 3.31264i) q^{50} +(12.3855 + 0.838165i) q^{51} +(-0.549419 - 0.461017i) q^{52} +(-0.476236 + 0.824865i) q^{53} +(-6.45376 + 0.951352i) q^{54} +16.5350 q^{55} +(4.58366 + 6.61890i) q^{56} +(3.82514 + 0.258858i) q^{57} +(-0.793933 - 4.50262i) q^{58} +(-2.06424 - 11.7069i) q^{59} +(2.51472 - 0.727193i) q^{60} +(4.99716 + 4.19312i) q^{61} +(-2.36178 + 4.09072i) q^{62} +(4.32757 - 6.65373i) q^{63} +(-4.45033 - 7.70820i) q^{64} +(-1.04776 + 5.94213i) q^{65} +(-8.14434 + 5.94517i) q^{66} +(-3.24731 - 1.18193i) q^{67} +(2.32709 - 1.95266i) q^{68} +(0.414809 + 3.86325i) q^{69} +(5.06110 - 10.7083i) q^{70} +(-0.833011 - 1.44282i) q^{71} +(-5.58807 + 7.21894i) q^{72} +(5.40056 + 9.35404i) q^{73} +(-0.952903 + 5.40418i) q^{74} +(-9.63290 - 9.26071i) q^{75} +(0.718696 - 0.603058i) q^{76} +(1.13262 - 12.2163i) q^{77} +(-1.62043 - 3.30354i) q^{78} +(5.88576 - 2.14224i) q^{79} +(-5.29990 + 9.17970i) q^{80} +(8.67327 + 2.40300i) q^{81} +(0.281529 + 0.487623i) q^{82} +(-2.02405 + 11.4790i) q^{83} +(-0.365008 - 1.90772i) q^{84} +(-24.0152 - 8.74084i) q^{85} +(0.999419 + 0.363759i) q^{86} +(-1.51225 + 6.12380i) q^{87} +(-2.45032 + 13.8965i) q^{88} -0.580255 q^{89} +(13.3075 + 1.80940i) q^{90} +(4.31837 + 1.18113i) q^{91} +(0.728365 + 0.611171i) q^{92} +(5.26356 - 3.84227i) q^{93} +(-9.38255 - 3.41497i) q^{94} +(-7.41684 - 2.69951i) q^{95} +(0.435290 + 4.05400i) q^{96} +(-0.291305 - 0.244434i) q^{97} +(-7.56479 - 4.47272i) q^{98} +(13.5943 - 2.95336i) 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 $

$2$	1.17974	−	0.429388i	0.834199	−	0.303623i	0.110618	−	0.993863i	$-0.464717\pi$
$2$	1.17974	−	0.429388i	0.834199	−	0.303623i	0.723581	+	0.690240i	$0.242495\pi$
$3$	−1.72810	−	0.116945i	−0.997718	−	0.0675184i
$3$	−1.72810	−	0.116945i	−0.997718	−	0.0675184i
$4$	−0.324689	+	0.272446i	−0.162344	+	0.136223i
$5$	3.35074	+	1.21957i	1.49849	+	0.545408i	0.955670	−	0.294439i	$-0.0951327\pi$
$5$	3.35074	+	1.21957i	1.49849	+	0.545408i	0.542824	+	0.839846i	$0.317355\pi$
$6$	−2.08891	+	0.604061i	−0.852795	+	0.246607i
$7$	1.13056	−	2.39204i	0.427310	−	0.904105i
$7$	1.13056	−	2.39204i	0.427310	−	0.904105i
$8$	−1.52151	+	2.63533i	−0.537935	+	0.931730i
$9$	2.97265	+	0.404186i	0.990883	+	0.134729i
$10$	4.47665			1.41564
$11$	4.35747	−	1.58599i	1.31383	−	0.478194i	0.412352	−	0.911025i	$-0.364707\pi$
$11$	4.35747	−	1.58599i	1.31383	−	0.478194i	0.901475	+	0.432831i	$0.142485\pi$
$12$	0.592955	−	0.432843i	0.171171	−	0.124951i
$13$	0.293837	+	1.66643i	0.0814958	+	0.462185i	0.998058	+	0.0622932i	$0.0198414\pi$
$13$	0.293837	+	1.66643i	0.0814958	+	0.462185i	−0.916562	+	0.399892i	$0.869048\pi$
$14$	0.306643	−	3.30742i	0.0819537	−	0.883945i
$15$	−5.64778	−	2.49939i	−1.45825	−	0.645339i
$16$	−0.516195	+	2.92749i	−0.129049	+	0.731872i
$17$	−7.16716			−1.73829			−0.869145	−	0.494557i	$-0.835330\pi$
$17$	−7.16716			−1.73829			−0.869145	+	0.494557i	$0.835330\pi$
$18$	3.68049	−	0.799589i	0.867500	−	0.188465i
$19$	−2.21349			−0.507810			−0.253905	−	0.967229i	$-0.581715\pi$
$19$	−2.21349			−0.507810			−0.253905	+	0.967229i	$0.581715\pi$
$20$	−1.42021	+	0.516915i	−0.317569	+	0.115586i
$21$	−2.23345	+	4.00146i	−0.487378	+	0.873191i
$22$	4.45966	−	3.74210i	0.950802	−	0.797817i
$23$	−0.389540	−	2.20919i	−0.0812247	−	0.460648i	−0.998108	−	0.0614919i	$-0.980414\pi$
$23$	−0.389540	−	2.20919i	−0.0812247	−	0.460648i	0.916883	−	0.399156i	$-0.130697\pi$
$24$	2.93751	−	4.37618i	0.599616	−	0.893284i
$25$	5.90986	+	4.95897i	1.18197	+	0.991793i
$26$	1.06220	+	1.83978i	0.208314	+	0.360810i
$27$	−5.08976	−	1.04611i	−0.979525	−	0.201324i
$28$	0.284623	+	1.08468i	0.0537886	+	0.204986i
$29$	0.632390	−	3.58646i	0.117432	−	0.665989i	−0.868085	−	0.496415i	$-0.834650\pi$
$29$	0.632390	−	3.58646i	0.117432	−	0.665989i	0.985517	−	0.169575i	$-0.0542394\pi$
$30$	−7.73609	−	0.523523i	−1.41241	−	0.0955817i
$31$	−2.88220	+	2.41846i	−0.517659	+	0.434368i	−0.863815	−	0.503809i	$-0.831931\pi$
$31$	−2.88220	+	2.41846i	−0.517659	+	0.434368i	0.346156	+	0.938177i	$0.387487\pi$
$32$	−0.408773	−	2.31827i	−0.0722616	−	0.409816i
$33$	−7.71561	+	2.23116i	−1.34312	+	0.388395i
$34$	−8.45534	+	3.07749i	−1.45008	+	0.527786i
$35$	6.70545	−	6.63630i	1.13343	−	1.12174i
$36$	−1.07530	+	0.678652i	−0.179217	+	0.113109i
$37$	−2.18550	+	3.78539i	−0.359293	+	0.622314i	−0.987843	−	0.155455i	$-0.950316\pi$
$37$	−2.18550	+	3.78539i	−0.359293	+	0.622314i	0.628550	+	0.777769i	$0.283649\pi$
$38$	−2.61134	+	0.950449i	−0.423615	+	0.154183i
$39$	−0.312898	−	2.91412i	−0.0501038	−	0.466633i
$40$	−8.31214	+	6.97472i	−1.31427	+	1.10280i
$41$	0.0778798	+	0.441679i	0.0121628	+	0.0689786i	0.990285	−	0.139052i	$-0.0444056\pi$
$41$	0.0778798	+	0.441679i	0.0121628	+	0.0689786i	−0.978122	+	0.208031i	$0.933295\pi$
$42$	−0.916696	+	5.67968i	−0.141449	+	0.876394i
$43$	0.648959	+	0.544541i	0.0989653	+	0.0830417i	0.690928	−	0.722924i	$-0.257202\pi$
$43$	0.648959	+	0.544541i	0.0989653	+	0.0830417i	−0.591963	+	0.805965i	$0.701647\pi$
$44$	−0.982725	+	1.70213i	−0.148151	+	0.256606i
$45$	9.46763	+	4.97967i	1.41135	+	0.742325i
$46$	−1.40816	−	2.43900i	−0.207621	−	0.359610i
$47$	−6.09243	−	5.11215i	−0.888672	−	0.745684i	0.0792716	−	0.996853i	$-0.474741\pi$
$47$	−6.09243	−	5.11215i	−0.888672	−	0.745684i	−0.967943	+	0.251169i	$0.919185\pi$
$48$	1.23439	−	4.99862i	0.178169	−	0.721489i
$49$	−4.44369	−	5.40866i	−0.634813	−	0.772666i
$50$	9.10140	+	3.31264i	1.28713	+	0.468478i
$51$	12.3855	+	0.838165i	1.73432	+	0.117367i
$52$	−0.549419	−	0.461017i	−0.0761907	−	0.0639316i
$53$	−0.476236	+	0.824865i	−0.0654160	+	0.113304i	−0.896878	−	0.442277i	$-0.854171\pi$
$53$	−0.476236	+	0.824865i	−0.0654160	+	0.113304i	0.831462	+	0.555581i	$0.187504\pi$
$54$	−6.45376	+	0.951352i	−0.878245	+	0.129463i
$55$	16.5350			2.22957
$56$	4.58366	+	6.61890i	0.612517	+	0.884487i
$57$	3.82514	+	0.258858i	0.506652	+	0.0342865i
$58$	−0.793933	−	4.50262i	−0.104248	−	0.591222i
$59$	−2.06424	−	11.7069i	−0.268741	−	1.52411i	−0.758166	−	0.652062i	$-0.773904\pi$
$59$	−2.06424	−	11.7069i	−0.268741	−	1.52411i	0.489424	−	0.872046i	$-0.337207\pi$
$60$	2.51472	−	0.727193i	0.324649	−	0.0938802i
$61$	4.99716	+	4.19312i	0.639821	+	0.536874i	0.903963	−	0.427610i	$-0.140644\pi$
$61$	4.99716	+	4.19312i	0.639821	+	0.536874i	−0.264142	+	0.964484i	$0.585089\pi$
$62$	−2.36178	+	4.09072i	−0.299946	+	0.519522i
$63$	4.32757	−	6.65373i	0.545223	−	0.838291i
$64$	−4.45033	−	7.70820i	−0.556291	−	0.963525i
$65$	−1.04776	+	5.94213i	−0.129958	+	0.737031i
$66$	−8.14434	+	5.94517i	−1.00250	+	0.731800i
$67$	−3.24731	−	1.18193i	−0.396722	−	0.144395i	0.135952	−	0.990715i	$-0.456591\pi$
$67$	−3.24731	−	1.18193i	−0.396722	−	0.144395i	−0.532674	+	0.846320i	$0.678813\pi$
$68$	2.32709	−	1.95266i	0.282202	−	0.236795i
$69$	0.414809	+	3.86325i	0.0499372	+	0.465081i
$70$	5.06110	−	10.7083i	0.604917	−	1.27989i
$71$	−0.833011	−	1.44282i	−0.0988603	−	0.171231i	0.812353	−	0.583166i	$-0.198186\pi$
$71$	−0.833011	−	1.44282i	−0.0988603	−	0.171231i	−0.911213	+	0.411935i	$0.864853\pi$
$72$	−5.58807	+	7.21894i	−0.658561	+	0.850760i
$73$	5.40056	+	9.35404i	0.632087	+	1.09481i	0.987124	+	0.159955i	$0.0511349\pi$
$73$	5.40056	+	9.35404i	0.632087	+	1.09481i	−0.355037	+	0.934852i	$0.615532\pi$
$74$	−0.952903	+	5.40418i	−0.110773	+	0.628223i
$75$	−9.63290	−	9.26071i	−1.11231	−	1.06933i
$76$	0.718696	−	0.603058i	0.0824401	−	0.0691755i
$77$	1.13262	−	12.2163i	0.129074	−	1.39217i
$78$	−1.62043	−	3.30354i	−0.183477	−	0.374052i
$79$	5.88576	−	2.14224i	0.662200	−	0.241021i	0.0110139	−	0.999939i	$-0.496494\pi$
$79$	5.88576	−	2.14224i	0.662200	−	0.241021i	0.651186	+	0.758918i	$0.274272\pi$
$80$	−5.29990	+	9.17970i	−0.592547	+	1.02632i
$81$	8.67327	+	2.40300i	0.963696	+	0.267000i
$82$	0.281529	+	0.487623i	0.0310897	+	0.0538489i
$83$	−2.02405	+	11.4790i	−0.222168	+	1.25998i	0.645856	+	0.763459i	$0.276501\pi$
$83$	−2.02405	+	11.4790i	−0.222168	+	1.25998i	−0.868025	+	0.496521i	$0.834611\pi$
$84$	−0.365008	−	1.90772i	−0.0398256	−	0.208150i
$85$	−24.0152	−	8.74084i	−2.60482	−	0.948077i
$86$	0.999419	+	0.363759i	0.107770	+	0.0392251i
$87$	−1.51225	+	6.12380i	−0.162130	+	0.656541i
$88$	−2.45032	+	13.8965i	−0.261205	+	1.48137i
$89$	−0.580255			−0.0615069			−0.0307534	−	0.999527i	$-0.509791\pi$
$89$	−0.580255			−0.0615069			−0.0307534	+	0.999527i	$0.509791\pi$
$90$	13.3075	+	1.80940i	1.40273	+	0.190727i
$91$	4.31837	+	1.18113i	0.452688	+	0.123816i
$92$	0.728365	+	0.611171i	0.0759373	+	0.0637189i
$93$	5.26356	−	3.84227i	0.545806	−	0.398425i
$94$	−9.38255	−	3.41497i	−0.967736	−	0.352227i
$95$	−7.41684	−	2.69951i	−0.760951	−	0.276964i
$96$	0.435290	+	4.05400i	0.0444266	+	0.413760i
$97$	−0.291305	−	0.244434i	−0.0295775	−	0.0248185i	0.627879	−	0.778311i	$-0.283923\pi$
$97$	−0.291305	−	0.244434i	−0.0295775	−	0.0248185i	−0.657457	+	0.753492i	$0.728368\pi$
$98$	−7.56479	−	4.47272i	−0.764159	−	0.451813i
$99$	13.5943	−	2.95336i	1.36627	−	0.296824i
$100$	−3.26992			−0.326992
$101$	2.80379	−	15.9011i	0.278988	−	1.58222i	−0.447015	−	0.894527i	$-0.647513\pi$
$101$	2.80379	−	15.9011i	0.278988	−	1.58222i	0.726003	−	0.687692i	$-0.241376\pi$
$102$	14.9716	−	4.32940i	1.48241	−	0.428674i
$103$	4.62715	+	1.68414i	0.455926	+	0.165944i	0.559766	−	0.828650i	$-0.310891\pi$
$103$	4.62715	+	1.68414i	0.455926	+	0.165944i	−0.103840	+	0.994594i	$0.533113\pi$
$104$	−4.83868	−	1.76114i	−0.474472	−	0.172694i
$105$	−12.3638	+	10.6840i	−1.20658	+	1.04265i
$106$	−0.207645	+	1.17761i	−0.0201682	+	0.114380i
$107$	−1.34021	−	2.32130i	−0.129563	−	0.224409i	0.793945	−	0.607990i	$-0.208024\pi$
$107$	−1.34021	−	2.32130i	−0.129563	−	0.224409i	−0.923507	+	0.383581i	$0.874691\pi$
$108$	1.93760	−	1.04703i	0.186445	−	0.100750i
$109$	−0.666665	+	1.15470i	−0.0638549	+	0.110600i	−0.896185	−	0.443680i	$-0.853673\pi$
$109$	−0.666665	+	1.15470i	−0.0638549	+	0.110600i	0.832331	+	0.554280i	$0.187006\pi$
$110$	19.5069	−	7.09992i	1.85991	−	0.676951i
$111$	4.21943	−	6.28594i	0.400491	−	0.596635i
$112$	6.41907	+	4.54445i	0.606545	+	0.429410i
$113$	−6.81143	+	5.71547i	−0.640766	+	0.537666i	−0.904253	−	0.426997i	$-0.859572\pi$
$113$	−6.81143	+	5.71547i	−0.640766	+	0.537666i	0.263488	+	0.964663i	$0.415127\pi$
$114$	4.62380	−	1.33709i	0.433058	−	0.125230i
$115$	1.38901	−	7.87749i	0.129526	−	0.734580i
$116$	0.771788	+	1.33678i	0.0716587	+	0.124116i
$117$	0.199926	+	5.07248i	0.0184832	+	0.468951i
$118$	−7.46206	−	12.9247i	−0.686938	−	1.18981i
$119$	−8.10287	+	17.1441i	−0.742789	+	1.57160i
$120$	15.1799	−	11.0809i	1.38573	−	1.01155i
$121$	8.04571	−	6.75115i	0.731428	−	0.613741i
$122$	7.69580	+	2.80104i	0.696745	+	0.253595i
$123$	−0.0829318	−	0.772372i	−0.00747771	−	0.0696424i
$124$	0.276920	−	1.57049i	0.0248681	−	0.141034i
$125$	4.84015	+	8.38339i	0.432916	+	0.749833i
$126$	2.24835	−	9.70785i	0.200299	−	0.864844i
$127$	−7.52897	+	13.0406i	−0.668088	+	1.15716i	0.310350	+	0.950622i	$0.399554\pi$
$127$	−7.52897	+	13.0406i	−0.668088	+	1.15716i	−0.978438	+	0.206540i	$0.933780\pi$
$128$	−4.95344	−	4.15643i	−0.437826	−	0.367380i
$129$	−1.05778	−	1.01691i	−0.0931326	−	0.0895342i
$130$	1.31541	+	7.46004i	0.115369	+	0.654289i
$131$	2.22576	+	12.6229i	0.194466	+	1.10287i	0.913178	+	0.407561i	$0.133621\pi$
$131$	2.22576	+	12.6229i	0.194466	+	1.10287i	−0.718712	+	0.695308i	$0.755268\pi$
$132$	1.89730	−	2.82652i	0.165139	−	0.246017i
$133$	−2.50248	+	5.29476i	−0.216992	+	0.459114i
$134$	−4.33847			−0.374787
$135$	−15.7786	−	9.71255i	−1.35801	−	0.835923i
$136$	10.9049	−	18.8878i	0.935087	−	1.61962i
$137$	13.3506	+	11.2025i	1.14062	+	0.957096i	0.999459	−	0.0328902i	$-0.0104712\pi$
$137$	13.3506	+	11.2025i	1.14062	+	0.957096i	0.141164	+	0.989986i	$0.454916\pi$
$138$	2.14820	+	4.37950i	0.182867	+	0.372808i
$139$	17.5718	+	6.39560i	1.49042	+	0.542468i	0.953560	−	0.301204i	$-0.0973884\pi$
$139$	17.5718	+	6.39560i	1.49042	+	0.542468i	0.536859	+	0.843672i	$0.319611\pi$
$140$	−0.369149	+	3.98160i	−0.0311988	+	0.336507i
$141$	9.93047	+	9.54678i	0.836296	+	0.803984i
$142$	−1.60226	−	1.34446i	−0.134459	−	0.112824i
$143$	3.92333	+	6.79541i	0.328086	+	0.568261i
$144$	−2.71771	+	8.49375i	−0.226476	+	0.707813i
$145$	6.49291	−	11.2460i	0.539207	−	0.933933i
$146$	10.3877	+	8.71635i	0.859695	+	0.721370i
$147$	7.04661	+	9.86637i	0.581195	+	0.813764i
$148$	−0.321709	−	1.82450i	−0.0264443	−	0.149973i
$149$	−12.8094	+	10.7484i	−1.04939	+	0.880543i	−0.993029	−	0.117868i	$-0.962394\pi$
$149$	−12.8094	+	10.7484i	−1.04939	+	0.880543i	−0.0563607	+	0.998410i	$0.517950\pi$
$150$	−15.3407	−	6.78893i	−1.25256	−	0.554314i
$151$	−18.2544	+	6.64407i	−1.48552	+	0.540687i	−0.952267	−	0.305267i	$-0.901254\pi$
$151$	−18.2544	+	6.64407i	−1.48552	+	0.540687i	−0.533257	+	0.845953i	$0.679032\pi$
$152$	3.36785	−	5.83329i	0.273169	−	0.473142i
$153$	−21.3054	−	2.89686i	−1.72244	−	0.234197i
$154$	−3.90934	−	14.8983i	−0.315024	−	1.20054i
$155$	−12.6070	+	4.58857i	−1.01262	+	0.368562i
$156$	0.895536	+	0.860935i	0.0717003	+	0.0689300i
$157$	−2.23616	−	12.6819i	−0.178465	−	1.01212i	−0.934068	−	0.357095i	$-0.883767\pi$
$157$	−2.23616	−	12.6819i	−0.178465	−	1.01212i	0.755603	−	0.655029i	$-0.227344\pi$
$158$	6.02378	−	5.05455i	0.479226	−	0.402119i
$159$	0.919447	−	1.36975i	0.0729169	−	0.108629i
$160$	1.45759	−	8.26643i	0.115233	−	0.653519i
$161$	−5.72487	−	1.56582i	−0.451183	−	0.123404i
$162$	11.2640	−	0.889294i	0.884982	−	0.0698695i
$163$	−5.54639	−	9.60664i	−0.434427	−	0.752450i	0.562822	−	0.826578i	$-0.309716\pi$
$163$	−5.54639	−	9.60664i	−0.434427	−	0.752450i	−0.997249	+	0.0741286i	$0.976382\pi$
$164$	−0.145620	−	0.122190i	−0.0113710	−	0.00954143i
$165$	−28.5740	−	1.93368i	−2.22449	−	0.150537i
$166$	2.54109	+	14.4112i	0.197227	+	1.11853i
$167$	1.01189	−	0.849074i	0.0783022	−	0.0657033i	−0.602796	−	0.797895i	$-0.705947\pi$
$167$	1.01189	−	0.849074i	0.0783022	−	0.0657033i	0.681099	+	0.732192i	$0.261502\pi$
$168$	−7.14697	−	11.9741i	−0.551401	−	0.923825i
$169$	9.52534	−	3.46694i	0.732719	−	0.266688i
$170$	−32.0848			−2.46080
$171$	−6.57994	−	0.894663i	−0.503180	−	0.0684166i
$172$	−0.359068			−0.0273786
$173$	2.71681	−	15.4078i	0.206556	−	1.17143i	−0.688418	−	0.725315i	$-0.741694\pi$
$173$	2.71681	−	15.4078i	0.206556	−	1.17143i	0.894973	−	0.446120i	$-0.147195\pi$
$174$	0.845434	+	7.87381i	0.0640922	+	0.596912i
$175$	18.5435	−	8.53023i	1.40175	−	0.644825i
$176$	2.39366	+	13.5751i	0.180429	+	1.02326i
$177$	2.19815	+	20.4721i	0.165223	+	1.53877i
$178$	−0.684547	+	0.249155i	−0.0513090	+	0.0186749i
$179$	11.4277			0.854144			0.427072	−	0.904218i	$-0.359545\pi$
$179$	11.4277			0.854144			0.427072	+	0.904218i	$0.359545\pi$
$180$	−4.43072	+	0.962577i	−0.330246	+	0.0717462i
$181$	−5.01063	+	8.67866i	−0.372437	+	0.645080i	−0.989940	−	0.141489i	$-0.954811\pi$
$181$	−5.01063	+	8.67866i	−0.372437	+	0.645080i	0.617503	+	0.786569i	$0.288144\pi$
$182$	5.60170	−	0.460843i	0.415225	−	0.0341599i
$183$	−8.14522	−	7.83051i	−0.602112	−	0.578848i
$184$	6.41464	+	2.33474i	0.472893	+	0.172119i
$185$	−11.9396	+	10.0185i	−0.877814	+	0.736573i
$186$	4.55978	−	6.79297i	0.334339	−	0.498085i
$187$	−31.2307	+	11.3670i	−2.28381	+	0.831240i
$188$	3.37093			0.245850
$189$	−8.25659	+	10.9922i	−0.600579	+	0.799566i
$190$	−9.90904			−0.718877
$191$	14.3219	−	5.21275i	1.03630	−	0.377182i	0.232822	−	0.972519i	$-0.425204\pi$
$191$	14.3219	−	5.21275i	1.03630	−	0.377182i	0.803476	+	0.595338i	$0.202982\pi$
$192$	6.78917	+	13.8410i	0.489966	+	0.998886i
$193$	8.61263	−	7.22685i	0.619951	−	0.520200i	−0.277837	−	0.960628i	$-0.589618\pi$
$193$	8.61263	−	7.22685i	0.619951	−	0.520200i	0.897788	+	0.440428i	$0.145173\pi$
$194$	−0.448619	−	0.163284i	−0.0322090	−	0.0117231i
$195$	2.50553	−	10.1461i	0.179425	−	0.726574i
$196$	2.91638	+	0.545466i	0.208313	+	0.0389618i
$197$	10.1443	−	17.5705i	0.722754	−	1.25185i	−0.237138	−	0.971476i	$-0.576209\pi$
$197$	10.1443	−	17.5705i	0.722754	−	1.25185i	0.959892	−	0.280371i	$-0.0904574\pi$
$198$	14.7695	−	9.32140i	1.04962	−	0.662443i
$199$	9.59686			0.680303			0.340152	−	0.940371i	$-0.389522\pi$
$199$	9.59686			0.680303			0.340152	+	0.940371i	$0.389522\pi$
$200$	−22.0604	+	8.02934i	−1.55991	+	0.567760i
$201$	5.47346	+	2.42224i	0.386068	+	0.170852i
$202$	−3.52002	−	19.9630i	−0.247667	−	1.40459i
$203$	−7.86400	−	5.56740i	−0.551945	−	0.390755i
$204$	−4.24980	+	3.10225i	−0.297546	+	0.217201i
$205$	−0.277702	+	1.57493i	−0.0193956	+	0.109998i
$206$	6.18196			0.430717
$207$	−0.265042	−	6.72459i	−0.0184217	−	0.467392i
$208$	−5.03014			−0.348777
$209$	−9.64524	+	3.51058i	−0.667175	+	0.242832i
$210$	−9.99837	+	17.9131i	−0.689953	+	1.23612i
$211$	−17.7553	+	14.8985i	−1.22233	+	1.02565i	−0.223626	+	0.974675i	$0.571789\pi$
$211$	−17.7553	+	14.8985i	−1.22233	+	1.02565i	−0.998700	+	0.0509776i	$0.983766\pi$
$212$	−0.0701028	−	0.397573i	−0.00481468	−	0.0273054i
$213$	1.27079	+	2.59075i	0.0870734	+	0.177515i
$214$	−2.57783	−	2.16305i	−0.176217	−	0.147863i
$215$	1.51038	+	2.61606i	0.103007	+	0.178414i
$216$	10.5010	−	11.8215i	0.714500	−	0.804354i
$217$	2.52655	+	9.62854i	0.171513	+	0.653628i
$218$	−0.290674	+	1.64850i	−0.0196869	+	0.111650i
$219$	−8.23878	−	16.7963i	−0.556725	−	1.13499i
$220$	−5.36871	+	4.50489i	−0.361959	+	0.303719i
$221$	−2.10598	−	11.9436i	−0.141663	−	0.803413i
$222$	2.27870	−	9.22752i	0.152937	−	0.619311i
$223$	−13.1365	+	4.78129i	−0.879685	+	0.320179i	−0.742083	−	0.670308i	$-0.766162\pi$
$223$	−13.1365	+	4.78129i	−0.879685	+	0.320179i	−0.137602	+	0.990488i	$0.543940\pi$
$224$	−6.00753	−	1.64313i	−0.401395	−	0.109786i
$225$	15.5636	+	17.1299i	1.03757	+	1.14200i
$226$	−5.58153	+	9.66749i	−0.371278	+	0.643072i
$227$	−0.311571	+	0.113403i	−0.0206797	+	0.00752679i	−0.352339	−	0.935872i	$-0.614614\pi$
$227$	−0.311571	+	0.113403i	−0.0206797	+	0.00752679i	0.331660	+	0.943399i	$0.392391\pi$
$228$	−1.31250	+	0.958095i	−0.0869226	+	0.0634514i
$229$	2.89553	−	2.42964i	0.191342	−	0.160555i	−0.542084	−	0.840324i	$-0.682365\pi$
$229$	2.89553	−	2.42964i	0.191342	−	0.160555i	0.733426	+	0.679769i	$0.237920\pi$
$230$	−1.74383	−	9.88977i	−0.114985	−	0.652112i
$231$	−3.38591	+	20.9785i	−0.222776	+	1.38028i
$232$	8.48933	+	7.12339i	0.557352	+	0.467674i
$233$	2.61966	−	4.53739i	0.171620	−	0.297254i	−0.767367	−	0.641209i	$-0.778433\pi$
$233$	2.61966	−	4.53739i	0.171620	−	0.297254i	0.938986	+	0.343955i	$0.111767\pi$
$234$	2.41393	+	5.89834i	0.157803	+	0.385587i
$235$	−14.1795	−	24.5596i	−0.924968	−	1.60209i
$236$	3.85973	+	3.23870i	0.251247	+	0.210821i
$237$	−10.4217	+	3.01369i	−0.676962	+	0.195760i
$238$	−2.19776	+	23.7048i	−0.142459	+	1.53655i
$239$	4.02467	+	1.46486i	0.260334	+	0.0947540i	0.468890	−	0.883257i	$-0.344654\pi$
$239$	4.02467	+	1.46486i	0.260334	+	0.0947540i	−0.208556	+	0.978010i	$0.566876\pi$
$240$	10.2323	−	15.2436i	0.660491	−	0.983972i
$241$	15.9966	+	13.4227i	1.03043	+	0.864635i	0.990902	−	0.134584i	$-0.0429697\pi$
$241$	15.9966	+	13.4227i	1.03043	+	0.864635i	0.0395292	+	0.999218i	$0.487414\pi$
$242$	6.59294	−	11.4193i	0.423810	−	0.734060i
$243$	−14.7072	−	5.16692i	−0.943470	−	0.331458i
$244$	−2.76492			−0.177006
$245$	−8.29339	−	23.5424i	−0.529845	−	1.50407i
$246$	−0.429485	−	0.875584i	−0.0273830	−	0.0558252i
$247$	−0.650407	−	3.68864i	−0.0413844	−	0.234703i
$248$	−1.98813	−	11.2753i	−0.126247	−	0.715980i
$249$	4.84017	−	19.6001i	0.306733	−	1.24210i
$250$	9.30983	+	7.81187i	0.588805	+	0.494066i
$251$	2.16310	−	3.74660i	0.136534	−	0.236483i	−0.789649	−	0.613559i	$-0.789737\pi$
$251$	2.16310	−	3.74660i	0.136534	−	0.236483i	0.926182	+	0.377076i	$0.123070\pi$
$252$	0.407670	+	3.33942i	0.0256808	+	0.210364i
$253$	−5.20116	−	9.00868i	−0.326994	−	0.566371i
$254$	−3.28272	+	18.6172i	−0.205976	+	1.16815i
$255$	40.4785	+	17.9135i	2.53486	+	1.12179i
$256$	9.09931	+	3.31188i	0.568707	+	0.206992i
$257$	14.4483	−	12.1235i	0.901258	−	0.756246i	−0.0691776	−	0.997604i	$-0.522038\pi$
$257$	14.4483	−	12.1235i	0.901258	−	0.756246i	0.970436	+	0.241359i	$0.0775931\pi$
$258$	−1.68455	−	0.745488i	−0.104876	−	0.0464121i
$259$	6.58397	+	9.50738i	0.409108	+	0.590760i
$260$	−1.27872	−	2.21480i	−0.0793026	−	0.137356i
$261$	3.32947	−	10.4057i	0.206089	−	0.644096i
$262$	8.04594	+	13.9360i	0.497080	+	0.860968i
$263$	2.24631	−	12.7394i	0.138513	−	0.785547i	−0.833835	−	0.552013i	$-0.813860\pi$
$263$	2.24631	−	12.7394i	0.138513	−	0.785547i	0.972349	−	0.233534i	$-0.0750291\pi$
$264$	5.85953	−	23.7279i	0.360629	−	1.46035i
$265$	−2.60172	+	2.18310i	−0.159822	+	0.134107i
$266$	−0.678752	+	7.32095i	−0.0416170	+	0.448876i
$267$	1.00274	+	0.0678580i	0.0613665	+	0.00415284i
$268$	1.37638	−	0.500960i	0.0840756	−	0.0306010i
$269$	−0.492114	+	0.852367i	−0.0300047	+	0.0519697i	−0.880638	−	0.473790i	$-0.842886\pi$
$269$	−0.492114	+	0.852367i	−0.0300047	+	0.0519697i	0.850633	+	0.525760i	$0.176219\pi$
$270$	−22.7851	−	4.68307i	−1.38666	−	0.285002i
$271$	12.6511	+	21.9124i	0.768500	+	1.33108i	0.938376	+	0.345616i	$0.112330\pi$
$271$	12.6511	+	21.9124i	0.768500	+	1.33108i	−0.169876	+	0.985465i	$0.554337\pi$
$272$	3.69965	−	20.9818i	0.224324	−	1.27221i
$273$	−7.32444	−	2.54611i	−0.443295	−	0.154098i
$274$	20.5605	+	7.48339i	1.24210	+	0.452088i
$275$	33.6169	+	12.2356i	2.02718	+	0.737832i
$276$	−1.18721	−	1.14134i	−0.0714618	−	0.0687007i
$277$	0.140238	−	0.795327i	0.00842606	−	0.0477866i	−0.980305	−	0.197490i	$-0.936721\pi$
$277$	0.140238	−	0.795327i	0.00842606	−	0.0477866i	0.988731	+	0.149704i	$0.0478320\pi$
$278$	23.4762			1.40801
$279$	−9.54528	+	6.02427i	−0.571461	+	0.360664i
$280$	7.28644	+	27.7683i	0.435448	+	1.65947i
$281$	10.6846	+	8.96543i	0.637388	+	0.534832i	0.903215	−	0.429188i	$-0.141200\pi$
$281$	10.6846	+	8.96543i	0.637388	+	0.534832i	−0.265826	+	0.964021i	$0.585645\pi$
$282$	15.8146	+	6.99864i	0.941746	+	0.416763i
$283$	1.04668	+	0.380960i	0.0622185	+	0.0226457i	0.372942	−	0.927855i	$-0.378349\pi$
$283$	1.04668	+	0.380960i	0.0622185	+	0.0226457i	−0.310723	+	0.950500i	$0.600571\pi$
$284$	0.663559	+	0.241516i	0.0393750	+	0.0143313i
$285$	12.5013	+	5.53238i	0.740515	+	0.327710i
$286$	7.54637	+	6.33215i	0.446226	+	0.374428i
$287$	1.14456	+	0.313051i	0.0675612	+	0.0184788i
$288$	−0.278128	−	7.05661i	−0.0163889	−	0.415815i
$289$	34.3681			2.02165
$290$	2.83099	−	16.0553i	0.166241	−	0.942802i
$291$	0.474818	+	0.456472i	0.0278343	+	0.0267589i
$292$	−4.30197	−	1.56579i	−0.251754	−	0.0916309i
$293$	1.20610	+	0.438986i	0.0704614	+	0.0256458i	0.377010	−	0.926209i	$-0.376952\pi$
$293$	1.20610	+	0.438986i	0.0704614	+	0.0256458i	−0.306549	+	0.951855i	$0.599174\pi$
$294$	12.5496	+	8.61397i	0.731910	+	0.502377i
$295$	7.36063	−	41.7442i	0.428552	−	2.43044i
$296$	−6.65050	−	11.5190i	−0.386553	−	0.669529i
$297$	−23.8376	+	3.51392i	−1.38320	+	0.203898i
$298$	−10.4965	+	18.1805i	−0.608046	+	1.05317i
$299$	3.56701	−	1.29829i	0.206285	−	0.0750818i
$300$	5.65074	+	0.382401i	0.326245	+	0.0220779i
$301$	2.03625	−	0.936700i	0.117367	−	0.0539905i
$302$	−18.6825	+	15.6765i	−1.07506	+	0.902080i
$303$	−6.70479	+	27.1508i	−0.385180	+	1.55977i
$304$	1.14259	−	6.47998i	0.0655323	−	0.371652i
$305$	11.6304	+	20.1444i	0.665954	+	1.15347i
$306$	−26.3786	+	5.73078i	−1.50797	+	0.327607i
$307$	−3.87477	−	6.71129i	−0.221145	−	0.383034i	0.734011	−	0.679137i	$-0.237646\pi$
$307$	−3.87477	−	6.71129i	−0.221145	−	0.383034i	−0.955156	+	0.296104i	$0.904313\pi$
$308$	2.96053	+	4.27507i	0.168692	+	0.243594i
$309$	−7.79921	−	3.45149i	−0.443682	−	0.196348i
$310$	−12.9026	+	10.8266i	−0.732820	+	0.614909i
$311$	−6.69121	−	2.43540i	−0.379424	−	0.138099i	0.145266	−	0.989393i	$-0.453596\pi$
$311$	−6.69121	−	2.43540i	−0.379424	−	0.138099i	−0.524689	+	0.851294i	$0.675819\pi$
$312$	8.15576	+	3.60928i	0.461729	+	0.204335i
$313$	1.45894	−	8.27405i	0.0824641	−	0.467677i	−0.915411	−	0.402520i	$-0.868134\pi$
$313$	1.45894	−	8.27405i	0.0824641	−	0.467677i	0.997875	−	0.0651565i	$-0.0207547\pi$
$314$	−8.08353	−	14.0011i	−0.456180	−	0.790126i
$315$	22.6152	−	17.0171i	1.27422	−	0.958807i
$316$	−1.32739	+	2.29911i	−0.0746717	+	0.129335i
$317$	−2.41234	−	2.02419i	−0.135490	−	0.113690i	0.572524	−	0.819888i	$-0.305964\pi$
$317$	−2.41234	−	2.02419i	−0.135490	−	0.113690i	−0.708014	+	0.706198i	$0.750409\pi$
$318$	0.496547	−	2.01075i	0.0278450	−	0.112757i
$319$	−2.93247	−	16.6309i	−0.164187	−	0.931150i
$320$	−5.51121	−	31.2556i	−0.308086	−	1.74724i
$321$	2.04454	+	4.16817i	0.114115	+	0.232645i
$322$	−7.42617	+	0.610939i	−0.413844	+	0.0340463i
$323$	15.8645			0.882722
$324$	−3.47080	+	1.58277i	−0.192822	+	0.0879317i
$325$	−6.52725	+	11.3055i	−0.362067	+	0.627118i
$326$	−10.6683	−	8.95173i	−0.590860	−	0.495790i
$327$	1.28710	−	1.91747i	0.0711767	−	0.106036i
$328$	−1.28246	−	0.466779i	−0.0708122	−	0.0257735i
$329$	−19.1163	+	8.79374i	−1.05392	+	0.484815i
$330$	−34.5401	+	9.98813i	−1.90137	+	0.549828i
$331$	−25.9190	−	21.7486i	−1.42464	−	1.19541i	−0.948800	−	0.315878i	$-0.897701\pi$
$331$	−25.9190	−	21.7486i	−1.42464	−	1.19541i	−0.475837	−	0.879534i	$-0.657855\pi$
$332$	−2.47021	−	4.27853i	−0.135571	−	0.234815i
$333$	−8.02671	+	10.3693i	−0.439861	+	0.568233i
$334$	0.829176	−	1.43618i	0.0453705	−	0.0785840i
$335$	−9.43945	−	7.92064i	−0.515732	−	0.432751i
$336$	−10.5613	−	8.60393i	−0.576168	−	0.469383i
$337$	5.44479	+	30.8790i	0.296597	+	1.68208i	0.660641	+	0.750702i	$0.270285\pi$
$337$	5.44479	+	30.8790i	0.296597	+	1.68208i	−0.364044	+	0.931382i	$0.618604\pi$
$338$	9.74872	−	8.18014i	0.530260	−	0.444941i
$339$	12.4392	−	9.08033i	0.675606	−	0.493176i
$340$	10.1789	−	3.70481i	0.552027	−	0.200922i
$341$	−8.72348	+	15.1095i	−0.472403	+	0.818225i
$342$	−8.14674	+	1.76988i	−0.440525	+	0.0957044i
$343$	−17.9616	+	4.51467i	−0.969833	+	0.243770i
$344$	−2.42244	+	0.881697i	−0.130609	+	0.0475379i
$345$	−3.32159	+	13.4506i	−0.178828	+	0.724158i
$346$	−3.41082	−	19.3437i	−0.183367	−	1.03992i
$347$	−6.85734	+	5.75399i	−0.368122	+	0.308891i	−0.808018	−	0.589158i	$-0.799460\pi$
$347$	−6.85734	+	5.75399i	−0.368122	+	0.308891i	0.439896	+	0.898049i	$0.355015\pi$
$348$	−1.17740	−	2.40034i	−0.0631150	−	0.128672i
$349$	−0.736679	+	4.17792i	−0.0394335	+	0.223639i	−0.998156	−	0.0607058i	$-0.980665\pi$
$349$	−0.736679	+	4.17792i	−0.0394335	+	0.223639i	0.958722	+	0.284345i	$0.0917760\pi$
$350$	18.2136	−	18.0258i	0.973557	−	0.963517i
$351$	0.247711	−	8.78913i	0.0132218	−	0.469129i
$352$	−5.45797	−	9.45348i	−0.290911	−	0.503872i
$353$	−4.85639	−	4.07500i	−0.258480	−	0.216890i	0.504334	−	0.863509i	$-0.331738\pi$
$353$	−4.85639	−	4.07500i	−0.258480	−	0.216890i	−0.762814	+	0.646619i	$0.776183\pi$
$354$	11.3837	+	23.2078i	0.605037	+	1.23348i
$355$	−1.03159	−	5.85042i	−0.0547509	−	0.310508i
$356$	0.188402	−	0.158088i	0.00998529	−	0.00837866i
$357$	16.0075	−	28.6791i	0.847205	−	1.51786i
$358$	13.4816	−	4.90691i	0.712526	−	0.259338i
$359$	32.1860			1.69871			0.849355	−	0.527822i	$-0.176991\pi$
$359$	32.1860			1.69871			0.849355	+	0.527822i	$0.176991\pi$
$360$	−27.5281	+	17.3737i	−1.45086	+	0.915676i
$361$	−14.1004			−0.742129
$362$	−2.18470	+	12.3900i	−0.114825	+	0.651206i
$363$	−14.6933	+	10.7257i	−0.771197	+	0.562955i
$364$	−1.72392	+	0.793025i	−0.0903579	+	0.0415658i
$365$	6.68795	+	37.9293i	0.350063	+	1.98531i
$366$	−12.9715	−	5.74047i	−0.678033	−	0.300059i
$367$	−17.9896	+	6.54768i	−0.939050	+	0.341786i	−0.765791	−	0.643090i	$-0.777652\pi$
$367$	−17.9896	+	6.54768i	−0.939050	+	0.341786i	−0.173259	+	0.984876i	$0.555430\pi$
$368$	6.66846			0.347617
$369$	0.0529892	+	1.34443i	0.00275851	+	0.0699884i
$370$	−9.78370	+	16.9459i	−0.508630	+	0.880973i
$371$	1.43470	+	2.07173i	0.0744857	+	0.107559i
$372$	−0.662206	+	2.68158i	−0.0343338	+	0.139033i
$373$	22.3080	+	8.11944i	1.15506	+	0.420408i	0.847331	−	0.531065i	$-0.178208\pi$
$373$	22.3080	+	8.11944i	1.15506	+	0.420408i	0.307731	+	0.951473i	$0.400430\pi$
$374$	−31.9630	+	26.8202i	−1.65277	+	1.38684i
$375$	−7.38386	−	15.0534i	−0.381301	−	0.777352i
$376$	22.7419	−	8.27737i	1.17282	−	0.426873i
$377$	6.16242			0.317381
$378$	−5.02066	+	16.5132i	−0.258235	+	0.849346i
$379$	−12.8379			−0.659438			−0.329719	−	0.944079i	$-0.606954\pi$
$379$	−12.8379			−0.659438			−0.329719	+	0.944079i	$0.606954\pi$
$380$	3.14363	−	1.14419i	0.161265	−	0.0586956i
$381$	14.5358	−	21.6549i	0.744693	−	1.10941i
$382$	14.6578	−	12.2993i	0.749957	−	0.629289i
$383$	14.5954	+	5.31229i	0.745790	+	0.271445i	0.686833	−	0.726815i	$-0.259000\pi$
$383$	14.5954	+	5.31229i	0.745790	+	0.271445i	0.0589567	+	0.998261i	$0.481223\pi$
$384$	8.07395	+	7.76200i	0.412022	+	0.396103i
$385$	18.6937	−	39.5522i	0.952719	−	2.01577i
$386$	7.05749	−	12.2239i	0.359217	−	0.622182i
$387$	1.70903	+	1.88103i	0.0868749	+	0.0956180i
$388$	0.161178			0.00818259
$389$	−23.2106	+	8.44798i	−1.17683	+	0.428329i	−0.855080	−	0.518497i	$-0.826492\pi$
$389$	−23.2106	+	8.44798i	−1.17683	+	0.428329i	−0.321746	+	0.946826i	$0.604270\pi$
$390$	−1.40074	−	13.0455i	−0.0709290	−	0.660585i
$391$	2.79189	+	15.8336i	0.141192	+	0.800740i
$392$	21.0147	−	3.48126i	1.06140	−	0.175830i
$393$	−2.37014	−	22.0739i	−0.119558	−	1.11348i
$394$	4.42306	−	25.0844i	0.222830	−	1.26373i
$395$	22.3342			1.12376
$396$	−3.60927	+	4.66263i	−0.181373	+	0.234306i
$397$	30.9939			1.55554			0.777769	−	0.628551i	$-0.216352\pi$
$397$	30.9939			1.55554			0.777769	+	0.628551i	$0.216352\pi$
$398$	11.3217	−	4.12078i	0.567508	−	0.206556i
$399$	4.94373	−	8.85722i	0.247496	−	0.443415i
$400$	−17.5680	+	14.7413i	−0.878398	+	0.737063i
$401$	−4.20480	−	23.8466i	−0.209978	−	1.19084i	−0.889412	−	0.457106i	$-0.848886\pi$
$401$	−4.20480	−	23.8466i	−0.209978	−	1.19084i	0.679434	−	0.733736i	$-0.262225\pi$
$402$	7.49731	+	0.507364i	0.373932	+	0.0253050i
$403$	−4.87710	−	4.09237i	−0.242945	−	0.203855i
$404$	3.42183	+	5.92679i	0.170243	+	0.294869i
$405$	26.1312	+	18.6295i	1.29847	+	0.925706i
$406$	−11.6680	−	3.19134i	−0.579074	−	0.158384i
$407$	−3.51964	+	19.9609i	−0.174462	+	0.989425i
$408$	−21.0536	+	31.3647i	−1.04231	+	1.55279i
$409$	5.25230	−	4.40721i	0.259710	−	0.217922i	−0.503630	−	0.863919i	$-0.668003\pi$
$409$	5.25230	−	4.40721i	0.259710	−	0.217922i	0.763340	+	0.645997i	$0.223558\pi$
$410$	0.348641	+	1.97724i	0.0172181	+	0.0976489i
$411$	−21.7611	−	20.9204i	−1.07340	−	1.03192i
$412$	−1.96122	+	0.713825i	−0.0966223	+	0.0351677i
$413$	−30.3371	−	8.29755i	−1.49279	−	0.408296i
$414$	−3.20014	−	7.81943i	−0.157278	−	0.384304i
$415$	−20.7814	+	35.9945i	−1.02012	+	1.76690i
$416$	3.74313	−	1.36239i	0.183522	−	0.0667965i
$417$	−29.6178	−	13.1072i	−1.45039	−	0.641861i
$418$	−9.87142	+	8.28311i	−0.482827	+	0.405140i
$419$	−4.48591	−	25.4408i	−0.219151	−	1.24287i	−0.873556	−	0.486723i	$-0.838192\pi$
$419$	−4.48591	−	25.4408i	−0.219151	−	1.24287i	0.654406	−	0.756144i	$-0.272919\pi$
$420$	1.10355	−	6.83743i	0.0538480	−	0.333632i
$421$	11.7983	+	9.89997i	0.575015	+	0.482495i	0.883306	−	0.468797i	$-0.155313\pi$
$421$	11.7983	+	9.89997i	0.575015	+	0.482495i	−0.308291	+	0.951292i	$0.599757\pi$
$422$	−14.5493	+	25.2002i	−0.708250	+	1.22672i
$423$	−16.0444	−	17.6591i	−0.780104	−	0.858615i
$424$	−1.44919	−	2.51008i	−0.0703791	−	0.121900i
$425$	−42.3569	−	35.5417i	−2.05461	−	1.72402i
$426$	2.61164	+	2.51073i	0.126534	+	0.121645i
$427$	15.6797	−	7.21285i	0.758792	−	0.349054i
$428$	1.06758	+	0.388567i	0.0516034	+	0.0187821i
$429$	−5.98522	−	12.2020i	−0.288969	−	0.589116i
$430$	2.90516	+	2.43772i	0.140099	+	0.117557i
$431$	−12.9773	+	22.4774i	−0.625096	+	1.08270i	0.363426	+	0.931623i	$0.381607\pi$
$431$	−12.9773	+	22.4774i	−0.625096	+	1.08270i	−0.988522	+	0.151075i	$0.951726\pi$
$432$	5.68978	−	14.3602i	0.273750	−	0.690906i
$433$	1.89970			0.0912937			0.0456469	−	0.998958i	$-0.485465\pi$
$433$	1.89970			0.0912937			0.0456469	+	0.998958i	$0.485465\pi$
$434$	7.11504	+	10.2743i	0.341533	+	0.493180i
$435$	−12.5356	+	18.6750i	−0.601034	+	0.895396i
$436$	−0.0981343	−	0.556547i	−0.00469978	−	0.0266538i
$437$	0.862245	+	4.89003i	0.0412468	+	0.233922i
$438$	−16.9317	−	16.2775i	−0.809028	−	0.777769i
$439$	11.1956	+	9.39421i	0.534336	+	0.448361i	0.869596	−	0.493765i	$-0.164380\pi$
$439$	11.1956	+	9.39421i	0.534336	+	0.448361i	−0.335260	+	0.942126i	$0.608824\pi$
$440$	−25.1581	+	43.5751i	−1.19937	+	2.07736i
$441$	−11.0234	−	17.8741i	−0.524925	−	0.851149i
$442$	−7.61293	−	13.1860i	−0.362110	−	0.627193i
$443$	−0.468142	+	2.65497i	−0.0222421	+	0.126141i	−0.993907	−	0.110221i	$-0.964844\pi$
$443$	−0.468142	+	2.65497i	−0.0222421	+	0.126141i	0.971665	+	0.236362i	$0.0759552\pi$
$444$	0.342578	+	3.19054i	0.0162580	+	0.151416i
$445$	−1.94428	−	0.707660i	−0.0921678	−	0.0335463i
$446$	−13.4446	+	11.2813i	−0.636618	+	0.534186i
$447$	23.3929	−	17.0763i	1.10645	−	0.807680i
$448$	−23.4696	+	1.93081i	−1.10884	+	0.0912222i
$449$	1.75265	+	3.03568i	0.0827126	+	0.143263i	0.904414	−	0.426655i	$-0.140308\pi$
$449$	1.75265	+	3.03568i	0.0827126	+	0.143263i	−0.821702	+	0.569918i	$0.806975\pi$
$450$	25.7163	+	13.5260i	1.21228	+	0.637620i
$451$	1.03986	+	1.80109i	0.0489650	+	0.0848098i
$452$	0.654437	−	3.71150i	0.0307821	−	0.174574i
$453$	32.3224	−	9.34683i	1.51864	−	0.439153i
$454$	−0.318877	+	0.267570i	−0.0149657	+	0.0125577i
$455$	13.0293	+	9.22419i	0.610821	+	0.432437i
$456$	−6.50215	+	9.68665i	−0.304491	+	0.453619i
$457$	−26.4549	+	9.62880i	−1.23751	+	0.450416i	−0.876163	−	0.482015i	$-0.839905\pi$
$457$	−26.4549	+	9.62880i	−1.23751	+	0.450416i	−0.361346	+	0.932432i	$0.617683\pi$
$458$	2.37270	−	4.10964i	0.110869	−	0.192031i
$459$	36.4791	+	7.49763i	1.70270	+	0.349959i
$460$	1.69519	+	2.93616i	0.0790388	+	0.136899i
$461$	5.05284	−	28.6561i	0.235334	−	1.33465i	−0.606575	−	0.795027i	$-0.707457\pi$
$461$	5.05284	−	28.6561i	0.235334	−	1.33465i	0.841909	−	0.539620i	$-0.181432\pi$
$462$	5.01345	+	26.2029i	0.233247	+	1.21907i
$463$	−4.70977	−	1.71422i	−0.218882	−	0.0796664i	0.230252	−	0.973131i	$-0.426045\pi$
$463$	−4.70977	−	1.71422i	−0.218882	−	0.0796664i	−0.449133	+	0.893465i	$0.648267\pi$
$464$	10.1729	+	3.70263i	0.472264	+	0.171890i
$465$	22.3227	−	6.45517i	1.03519	−	0.299351i
$466$	1.14221	−	6.47777i	0.0529116	−	0.300077i
$467$	−18.5357			−0.857728			−0.428864	−	0.903369i	$-0.641086\pi$
$467$	−18.5357			−0.857728			−0.428864	+	0.903369i	$0.641086\pi$
$468$	−1.44689	−	1.59251i	−0.0668826	−	0.0736137i
$469$	−6.49848	+	6.43146i	−0.300072	+	0.296977i
$470$	−27.2737	−	22.8853i	−1.25804	−	1.05562i
$471$	2.38121	+	22.1770i	0.109721	+	1.02186i
$472$	33.9923	+	12.3722i	1.56462	+	0.569476i
$473$	3.69146	+	1.34358i	0.169733	+	0.0617779i
$474$	−11.0008	+	8.03031i	−0.505283	+	0.368845i
$475$	−13.0815	−	10.9766i	−0.600218	−	0.503643i
$476$	−2.03994	−	7.77409i	−0.0935003	−	0.356325i
$477$	−1.74908	+	2.25954i	−0.0800849	+	0.103457i
$478$	5.37704			0.245940
$479$	0.488458	−	2.77018i	0.0223182	−	0.126573i	−0.971613	−	0.236576i	$-0.923975\pi$
$479$	0.488458	−	2.77018i	0.0223182	−	0.126573i	0.993931	+	0.110003i	$0.0350860\pi$
$480$	−3.48559	+	14.1147i	−0.159095	+	0.644247i
$481$	−6.95028	−	2.52969i	−0.316905	−	0.115344i
$482$	24.6353	+	8.96652i	1.12211	+	0.408414i
$483$	9.71002	+	3.37539i	0.441821	+	0.153585i
$484$	−0.773025	+	4.38404i	−0.0351375	+	0.199275i
$485$	−0.677982	−	1.17430i	−0.0307856	−	0.0533222i
$486$	−19.5693	+	0.219519i	−0.887680	+	0.00995759i
$487$	−2.86962	+	4.97033i	−0.130035	+	0.225227i	−0.923690	−	0.383141i	$-0.874842\pi$
$487$	−2.86962	+	4.97033i	−0.130035	+	0.225227i	0.793655	+	0.608368i	$0.208176\pi$
$488$	−18.6535	+	6.78931i	−0.844403	+	0.307338i
$489$	8.46126	+	17.2498i	0.382632	+	0.780065i
$490$	−19.8928	−	24.2127i	−0.898667	−	1.09382i
$491$	−10.9103	+	9.15480i	−0.492374	+	0.413150i	−0.854876	−	0.518832i	$-0.826367\pi$
$491$	−10.9103	+	9.15480i	−0.492374	+	0.413150i	0.362502	+	0.931983i	$0.381922\pi$
$492$	0.237357	+	0.228186i	0.0107009	+	0.0102874i
$493$	−4.53244	+	25.7047i	−0.204131	+	1.15768i
$494$	−2.35117	−	4.07234i	−0.105784	−	0.183223i
$495$	49.1526	+	6.68319i	2.20925	+	0.300387i
$496$	−5.59222	−	9.68601i	−0.251098	−	0.434915i
$497$	−4.39304	+	0.361409i	−0.197055	+	0.0162114i
$498$	−2.70593	−	25.2012i	−0.121256	−	1.12929i
$499$	4.93739	−	4.14296i	0.221028	−	0.185464i	−0.525550	−	0.850763i	$-0.676140\pi$
$499$	4.93739	−	4.14296i	0.221028	−	0.185464i	0.746577	+	0.665299i	$0.231696\pi$
$500$	−3.85556	−	1.40331i	−0.172426	−	0.0627580i
$501$	−1.84794	+	1.34895i	−0.0825597	+	0.0602666i
$502$	0.943139	−	5.34880i	0.0420943	−	0.238729i
$503$	7.22900	+	12.5210i	0.322325	+	0.558284i	0.980967	−	0.194173i	$-0.0622022\pi$
$503$	7.22900	+	12.5210i	0.322325	+	0.558284i	−0.658642	+	0.752456i	$0.728869\pi$
$504$	10.9503	+	21.5283i	0.487767	+	0.958946i
$505$	28.7872	−	49.8610i	1.28102	−	2.21878i
$506$	−10.0042	−	8.39454i	−0.444742	−	0.373183i
$507$	−16.8662	+	4.87727i	−0.749053	+	0.216607i
$508$	−1.10828	−	6.28536i	−0.0491719	−	0.278868i
$509$	7.58145	+	42.9965i	0.336042	+	1.90579i	0.416697	+	0.909046i	$0.363188\pi$
$509$	7.58145	+	42.9965i	0.336042	+	1.90579i	−0.0806550	+	0.996742i	$0.525701\pi$
$510$	55.4458	+	3.75217i	2.45518	+	0.166149i
$511$	28.4808	−	2.34307i	1.25992	−	0.103651i
$512$	25.0894			1.10880
$513$	11.2662	+	2.31556i	0.497413	+	0.102234i
$514$	11.8394	−	20.5065i	0.522215	−	0.904502i
$515$	13.4504	+	11.2862i	0.592696	+	0.497331i
$516$	0.620504	+	0.0419912i	0.0273162	+	0.00184856i
$517$	−34.6554	−	12.6135i	−1.52414	−	0.554743i
$518$	11.8497	+	8.38911i	0.520646	+	0.368596i
$519$	−6.49679	+	26.3085i	−0.285178	+	1.15482i
$520$	−14.0653	−	11.8022i	−0.616805	−	0.517561i
$521$	7.88539	+	13.6579i	0.345465	+	0.598363i	0.985438	−	0.170034i	$-0.0543878\pi$
$521$	7.88539	+	13.6579i	0.345465	+	0.598363i	−0.639973	+	0.768397i	$0.721054\pi$
$522$	−0.540189	−	13.7056i	−0.0236434	−	0.599877i
$523$	10.7810	−	18.6732i	0.471419	−	0.816521i	−0.528047	−	0.849215i	$-0.677075\pi$
$523$	10.7810	−	18.6732i	0.471419	−	0.816521i	0.999465	+	0.0326942i	$0.0104087\pi$
$524$	−4.16174	−	3.49212i	−0.181807	−	0.152554i
$525$	−33.0425	+	12.5725i	−1.44209	+	0.548709i
$526$	−2.82012	−	15.9937i	−0.122963	−	0.697358i
$527$	20.6572	−	17.3335i	0.899842	−	0.755057i
$528$	−2.54894	−	23.7391i	−0.110928	−	1.03311i
$529$	16.8841	−	6.14533i	0.734093	−	0.267188i
$530$	−2.13194	+	3.69263i	−0.0926056	+	0.160398i
$531$	−1.40450	−	35.6348i	−0.0609502	−	1.54642i
$532$	−0.630011	−	2.40094i	−0.0273144	−	0.104094i
$533$	−0.713144	+	0.259563i	−0.0308897	+	0.0112429i
$534$	1.21210	−	0.350509i	0.0524528	−	0.0151680i
$535$	−1.65969	−	9.41255i	−0.0717545	−	0.406940i
$536$	8.05558	−	6.75944i	0.347948	−	0.291963i
$537$	−19.7481	−	1.33641i	−0.852195	−	0.0576704i
$538$	−0.214568	+	1.21688i	−0.00925068	+	0.0524632i
$539$	−27.9413	−	16.5205i	−1.20352	−	0.711586i
$540$	7.76929	−	1.14528i	0.334337	−	0.0492848i
$541$	−8.55828	−	14.8234i	−0.367949	−	0.637307i	0.621296	−	0.783576i	$-0.286607\pi$
$541$	−8.55828	−	14.8234i	−0.367949	−	0.637307i	−0.989245	+	0.146270i	$0.953273\pi$
$542$	24.3339	+	20.4185i	1.04523	+	0.877052i
$543$	9.67379	−	14.4116i	0.415142	−	0.618462i
$544$	2.92974	+	16.6154i	0.125612	+	0.712379i
$545$	−3.64205	+	3.05604i	−0.156008	+	0.130906i
$546$	−9.73417	+	0.141290i	−0.416584	+	0.00604665i
$547$	−8.99048	+	3.27227i	−0.384405	+	0.139912i	−0.526992	−	0.849870i	$-0.676680\pi$
$547$	−8.99048	+	3.27227i	−0.384405	+	0.139912i	0.142587	+	0.989782i	$0.454458\pi$
$548$	−7.38689			−0.315552
$549$	13.1600	+	14.4844i	0.561655	+	0.618181i
$550$	44.9129			1.91509
$551$	−1.39979	+	7.93861i	−0.0596331	+	0.338196i
$552$	−10.8121	−	4.78482i	−0.460193	−	0.203655i
$553$	1.52986	−	16.5009i	0.0650561	−	0.701689i
$554$	−0.176061	−	0.998491i	−0.00748011	−	0.0424218i
$555$	21.8043	−	15.9166i	0.925543	−	0.675624i
$556$	−7.44781	+	2.71078i	−0.315858	+	0.114963i
$557$	21.4229			0.907717			0.453859	−	0.891074i	$-0.350047\pi$
$557$	21.4229			0.907717			0.453859	+	0.891074i	$0.350047\pi$
$558$	−8.67415	+	11.2057i	−0.367206	+	0.474374i
$559$	−0.716753	+	1.24145i	−0.0303154	+	0.0525079i
$560$	15.9664	+	23.0557i	0.674702	+	0.974283i
$561$	55.2990	−	15.9911i	2.33473	−	0.675144i
$562$	16.4546	+	5.98899i	0.694096	+	0.252630i
$563$	−9.74747	+	8.17910i	−0.410807	+	0.344708i	−0.824653	−	0.565639i	$-0.808630\pi$
$563$	−9.74747	+	8.17910i	−0.410807	+	0.344708i	0.413846	+	0.910347i	$0.364185\pi$
$564$	−5.82529	−	0.394214i	−0.245289	−	0.0165994i
$565$	−29.7937	+	10.8440i	−1.25343	+	0.456212i
$566$	1.39838			0.0587784
$567$	15.5537	−	18.0301i	0.653193	−	0.757191i
$568$	5.06974			0.212721
$569$	−28.3196	+	10.3075i	−1.18722	+	0.432112i	−0.858746	−	0.512401i	$-0.828756\pi$
$569$	−28.3196	+	10.3075i	−1.18722	+	0.432112i	−0.328473	+	0.944513i	$0.606534\pi$
$570$	17.1238	+	1.15881i	0.717237	+	0.0485374i
$571$	−26.2631	+	22.0374i	−1.09908	+	0.922236i	−0.997363	−	0.0725777i	$-0.976877\pi$
$571$	−26.2631	+	22.0374i	−1.09908	+	0.922236i	−0.101715	+	0.994814i	$0.532433\pi$
$572$	−3.12525	−	1.13750i	−0.130673	−	0.0475611i
$573$	−25.3593	+	7.33327i	−1.05940	+	0.306352i
$574$	1.48470	−	0.122144i	0.0619701	−	0.00509818i
$575$	8.65317	−	14.9877i	0.360862	−	0.625032i
$576$	−10.1137	−	24.7125i	−0.421405	−	1.02969i
$577$	−21.4672			−0.893690			−0.446845	−	0.894611i	$-0.647452\pi$
$577$	−21.4672			−0.893690			−0.446845	+	0.894611i	$0.647452\pi$
$578$	40.5453	−	14.7573i	1.68646	−	0.613822i
$579$	−15.7286	+	11.4815i	−0.653659	+	0.477155i
$580$	0.955768	+	5.42043i	0.0396861	+	0.225071i
$581$	25.1698	+	17.8192i	1.04422	+	0.739266i
$582$	0.756163	+	0.334635i	0.0313440	+	0.0138711i
$583$	−0.766957	+	4.34963i	−0.0317641	+	0.180143i
$584$	−32.8680			−1.36009
$585$	−5.51634	+	17.2404i	−0.228073	+	0.712802i
$586$	1.61138			0.0665654
$587$	10.9730	−	3.99384i	0.452903	−	0.164843i	−0.105489	−	0.994420i	$-0.533641\pi$
$587$	10.9730	−	3.99384i	0.452903	−	0.164843i	0.558392	+	0.829577i	$0.311418\pi$
$588$	−4.97601	−	1.28368i	−0.205207	−	0.0529379i
$589$	6.37974	−	5.35324i	0.262873	−	0.220576i
$590$	−9.24088	−	52.4077i	−0.380441	−	2.15759i
$591$	−19.5852	+	29.1772i	−0.805627	+	1.20019i
$592$	−9.95354	−	8.35201i	−0.409088	−	0.343265i
$593$	−6.22019	−	10.7737i	−0.255432	−	0.442422i	0.709580	−	0.704624i	$-0.248885\pi$
$593$	−6.22019	−	10.7737i	−0.255432	−	0.442422i	−0.965013	+	0.262202i	$0.915551\pi$
$594$	−26.6132	+	14.3811i	−1.09195	+	0.590063i
$595$	−48.0590	+	47.5634i	−1.97023	+	1.94991i
$596$	1.23072	−	6.97976i	0.0504123	−	0.285902i
$597$	−16.5843	−	1.12231i	−0.678751	−	0.0459329i
$598$	3.65066	−	3.06326i	0.149286	−	0.125266i
$599$	6.28923	+	35.6680i	0.256971	+	1.45736i	0.790962	+	0.611865i	$0.209581\pi$
$599$	6.28923	+	35.6680i	0.256971	+	1.45736i	−0.533991	+	0.845490i	$0.679308\pi$
$600$	39.0616	−	11.2956i	1.59468	−	0.461142i
$601$	8.68262	−	3.16021i	0.354171	−	0.128908i	−0.158806	−	0.987310i	$-0.550765\pi$
$601$	8.68262	−	3.16021i	0.354171	−	0.128908i	0.512978	+	0.858402i	$0.328542\pi$
$602$	2.00002	−	1.97940i	0.0815149	−	0.0806742i
$603$	−9.17540	−	4.82597i	−0.373651	−	0.196529i
$604$	4.11685	−	7.13060i	0.167512	−	0.290140i
$605$	35.1925	−	12.8090i	1.43078	−	0.520761i
$606$	3.74836	+	34.9097i	0.152267	+	1.41811i
$607$	−14.9778	+	12.5679i	−0.607931	+	0.510115i	−0.893984	−	0.448099i	$-0.852101\pi$
$607$	−14.9778	+	12.5679i	−0.607931	+	0.510115i	0.286053	+	0.958214i	$0.407657\pi$
$608$	0.904817	+	5.13147i	0.0366952	+	0.208109i
$609$	12.9387	+	10.5407i	0.524302	+	0.427129i
$610$	22.3705	+	18.7711i	0.905757	+	0.760020i
$611$	6.72888	−	11.6548i	0.272221	−	0.471501i
$612$	7.70687	−	4.86400i	0.311532	−	0.196616i
$613$	12.1945	+	21.1215i	0.492530	+	0.853087i	0.999963	−	0.00860397i	$-0.00273876\pi$
$613$	12.1945	+	21.1215i	0.492530	+	0.853087i	−0.507433	+	0.861691i	$0.669405\pi$
$614$	−7.45295	−	6.25377i	−0.300777	−	0.252382i
$615$	0.664077	−	2.68915i	0.0267782	−	0.108437i
$616$	30.4707	+	21.5720i	1.22770	+	0.869161i
$617$	−42.4798	−	15.4614i	−1.71017	−	0.622452i	−0.713255	−	0.700905i	$-0.752780\pi$
$617$	−42.4798	−	15.4614i	−1.71017	−	0.622452i	−0.996918	+	0.0784527i	$0.975002\pi$
$618$	−10.6830	−	0.722950i	−0.429734	−	0.0290813i
$619$	−20.0020	−	16.7837i	−0.803948	−	0.674592i	0.145207	−	0.989401i	$-0.453615\pi$
$619$	−20.0020	−	16.7837i	−0.803948	−	0.674592i	−0.949155	+	0.314809i	$0.898060\pi$
$620$	2.84321	−	4.92458i	0.114186	−	0.197776i
$621$	−0.328391	+	11.6518i	−0.0131779	+	0.467569i
$622$	−8.93959			−0.358445
$623$	−0.656010	+	1.38799i	−0.0262825	+	0.0556087i
$624$	8.69258	+	0.588251i	0.347982	+	0.0235489i
$625$	−0.704329	−	3.99445i	−0.0281732	−	0.159778i
$626$	−1.83162	−	10.3876i	−0.0732063	−	0.415174i
$627$	17.0785	−	4.93866i	0.682048	−	0.197231i
$628$	4.18118	+	3.50843i	0.166847	+	0.140002i
$629$	15.6638	−	27.1305i	0.624556	−	1.08176i
$630$	19.3730	−	29.7864i	0.771839	−	1.18672i
$631$	4.86953	+	8.43428i	0.193853	+	0.335763i	0.946524	−	0.322634i	$-0.104568\pi$
$631$	4.86953	+	8.43428i	0.193853	+	0.335763i	−0.752671	+	0.658397i	$0.771235\pi$
$632$	−3.30972	+	18.7704i	−0.131654	+	0.746645i
$633$	32.4252	−	23.6696i	1.28879	−	0.940783i
$634$	−3.71509	−	1.35218i	−0.147545	−	0.0537020i
$635$	−41.1314	+	34.5134i	−1.63225	+	1.36962i
$636$	0.0746503	+	0.695243i	0.00296008	+	0.0275682i
$637$	7.70746	−	8.99438i	0.305381	−	0.356370i
$638$	−10.6006	−	18.3609i	−0.419683	−	0.726913i
$639$	−1.89308	−	4.62568i	−0.0748892	−	0.182989i
$640$	−11.5286	−	19.9681i	−0.455708	−	0.789310i
$641$	−0.336943	+	1.91090i	−0.0133084	+	0.0754760i	−0.990739	−	0.135783i	$-0.956645\pi$
$641$	−0.336943	+	1.91090i	−0.0133084	+	0.0754760i	0.977430	+	0.211259i	$0.0677562\pi$
$642$	4.20178	+	4.03944i	0.165831	+	0.159424i
$643$	21.3616	−	17.9245i	0.842419	−	0.706874i	−0.115687	−	0.993286i	$-0.536907\pi$
$643$	21.3616	−	17.9245i	0.842419	−	0.706874i	0.958107	+	0.286412i	$0.0924626\pi$
$644$	2.28540	−	1.05131i	0.0900574	−	0.0414276i
$645$	−2.30416	−	4.69745i	−0.0907261	−	0.184962i
$646$	18.7159	−	6.81201i	0.736366	−	0.268015i
$647$	−6.80251	+	11.7823i	−0.267434	+	0.463210i	−0.968198	−	0.250183i	$-0.919509\pi$
$647$	−6.80251	+	11.7823i	−0.267434	+	0.463210i	0.700764	+	0.713393i	$0.252842\pi$
$648$	−19.5292	+	19.2007i	−0.767178	+	0.754276i
$649$	−27.5619	−	47.7386i	−1.08190	−	1.87390i
$650$	−2.84596	+	16.1402i	−0.111628	+	0.633073i
$651$	−3.24011	−	16.9345i	−0.126990	−	0.663717i
$652$	4.41814	+	1.60807i	0.173028	+	0.0629770i
$653$	−37.0190	−	13.4738i	−1.44867	−	0.527271i	−0.506447	−	0.862271i	$-0.669041\pi$
$653$	−37.0190	−	13.4738i	−1.44867	−	0.527271i	−0.942218	+	0.335000i	$0.891264\pi$
$654$	0.695097	−	2.81477i	0.0271804	−	0.110066i
$655$	−7.93657	+	45.0105i	−0.310107	+	1.75871i
$656$	−1.33321			−0.0520531
$657$	12.2732	+	29.9891i	0.478822	+	1.16999i
$658$	−18.7762	+	18.5826i	−0.731973	+	0.724425i
$659$	−15.8314	−	13.2841i	−0.616704	−	0.517476i	0.280062	−	0.959982i	$-0.409645\pi$
$659$	−15.8314	−	13.2841i	−0.616704	−	0.517476i	−0.896766	+	0.442506i	$0.854090\pi$
$660$	9.80449	−	7.15704i	0.381639	−	0.278587i
$661$	−17.4374	−	6.34668i	−0.678235	−	0.246857i	−0.0201454	−	0.999797i	$-0.506413\pi$
$661$	−17.4374	−	6.34668i	−0.678235	−	0.246857i	−0.658089	+	0.752940i	$0.728635\pi$
$662$	−39.9161	−	14.5283i	−1.55138	−	0.564658i
$663$	2.24259	+	20.8860i	0.0870950	+	0.811144i
$664$	−27.1713	−	22.7994i	−1.05445	−	0.884788i
$665$	−14.8425	+	14.6894i	−0.575566	+	0.569631i
$666$	−5.01694	+	15.6796i	−0.194402	+	0.607571i
$667$	−8.16952			−0.316325
$668$	−0.0972213	+	0.551370i	−0.00376161	+	0.0213331i
$669$	23.2603	−	6.72630i	0.899295	−	0.260054i
$670$	−14.5371	−	5.29107i	−0.561617	−	0.204412i
$671$	28.4252	+	10.3459i	1.09734	+	0.399401i
$672$	10.1894	+	3.54204i	0.393066	+	0.136637i
$673$	4.34944	−	24.6669i	0.167659	−	0.950839i	−0.778622	−	0.627493i	$-0.784081\pi$
$673$	4.34944	−	24.6669i	0.167659	−	0.950839i	0.946281	−	0.323346i	$-0.104808\pi$
$674$	19.6825	+	34.0910i	0.758141	+	1.31314i
$675$	−24.8922	−	31.4223i	−0.958100	−	1.20945i
$676$	−2.14822	+	3.72082i	−0.0826237	+	0.143108i
$677$	3.04284	−	1.10750i	0.116946	−	0.0425647i	−0.282885	−	0.959154i	$-0.591291\pi$
$677$	3.04284	−	1.10750i	0.116946	−	0.0425647i	0.399830	+	0.916589i	$0.369069\pi$
$678$	10.7760	−	16.0536i	0.413850	−	0.616536i
$679$	−0.914031	+	0.420466i	−0.0350773	+	0.0161360i
$680$	59.5744	−	49.9889i	2.28457	−	1.91699i
$681$	0.551687	−	0.159534i	0.0211407	−	0.00611336i
$682$	−3.80354	+	21.5710i	−0.145645	+	0.825995i
$683$	−5.65588	−	9.79627i	−0.216416	−	0.374844i	0.737293	−	0.675573i	$-0.236103\pi$
$683$	−5.65588	−	9.79627i	−0.216416	−	0.374844i	−0.953710	+	0.300729i	$0.902770\pi$
$684$	2.38018	−	1.50219i	0.0910084	−	0.0574377i
$685$	31.0723	+	53.8187i	1.18721	+	2.05631i
$686$	−19.2513	+	13.0386i	−0.735019	+	0.497816i
$687$	−5.28790	+	3.86004i	−0.201746	+	0.147270i
$688$	−1.92913	+	1.61873i	−0.0735472	+	0.0617135i
$689$	−1.51452	−	0.551240i	−0.0576986	−	0.0210006i
$690$	1.85696	+	17.2944i	0.0706931	+	0.658388i
$691$	6.70403	−	38.0205i	0.255033	−	1.44637i	−0.540953	−	0.841053i	$-0.681936\pi$
$691$	6.70403	−	38.0205i	0.255033	−	1.44637i	0.795987	−	0.605314i	$-0.206952\pi$
$692$	3.31568	+	5.74293i	0.126043	+	0.218313i
$693$	8.30452	−	35.8569i	0.315462	−	1.36209i
$694$	−5.61915	+	9.73265i	−0.213300	+	0.369446i
$695$	51.0785	+	42.8600i	1.93752	+	1.62577i
$696$	−13.8373	−	13.3027i	−0.524503	−	0.504238i
$697$	−0.558177	−	3.16558i	−0.0211425	−	0.119905i
$698$	0.924862	+	5.24516i	0.0350066	+	0.198532i
$699$	−5.05766	+	7.53470i	−0.191298	+	0.284988i
$700$	−3.69682	+	7.82176i	−0.139727	+	0.295635i
$701$	−0.253150			−0.00956134			−0.00478067	−	0.999989i	$-0.501522\pi$
$701$	−0.253150			−0.00956134			−0.00478067	+	0.999989i	$0.501522\pi$
$702$	−3.48172	−	10.4752i	−0.131409	−	0.395361i
$703$	4.83758	−	8.37894i	0.182453	−	0.316018i
$704$	−31.6173	−	26.5301i	−1.19162	−	0.999890i
$705$	21.6314	+	44.0996i	0.814687	+	1.66089i
$706$	−7.47901	−	2.72214i	−0.281476	−	0.102449i
$707$	−34.8662	−	24.6839i	−1.31128	−	0.928332i
$708$	−6.29125	−	6.04817i	−0.236440	−	0.227304i
$709$	3.22893	+	2.70939i	0.121265	+	0.101753i	0.701403	−	0.712764i	$-0.252557\pi$
$709$	3.22893	+	2.70939i	0.121265	+	0.101753i	−0.580139	+	0.814518i	$0.697002\pi$
$710$	−3.72910	−	6.45899i	−0.139951	−	0.242402i
$711$	18.3622	−	3.98919i	0.688634	−	0.149606i
$712$	0.882863	−	1.52916i	0.0330867	−	0.0573078i
$713$	6.46557	+	5.42526i	0.242137	+	0.203177i
$714$	6.57010	−	40.7072i	0.245880	−	1.52343i
$715$	4.85859	+	27.5544i	0.181701	+	1.03048i
$716$	−3.71043	+	3.11342i	−0.138665	+	0.116354i
$717$	−6.78372	−	3.00209i	−0.253343	−	0.112115i
$718$	37.9709	−	13.8203i	1.41706	−	0.515768i
$719$	6.33090	−	10.9654i	0.236103	−	0.408942i	−0.723490	−	0.690335i	$-0.757463\pi$
$719$	6.33090	−	10.9654i	0.236103	−	0.408942i	0.959593	+	0.281393i	$0.0907964\pi$
$720$	−19.4651	+	25.1459i	−0.725420	+	0.937132i
$721$	9.25978	−	9.16429i	0.344852	−	0.341296i
$722$	−16.6348	+	6.05457i	−0.619083	+	0.225328i
$723$	−26.0740	−	25.0665i	−0.969701	−	0.932235i
$724$	−0.737574	−	4.18299i	−0.0274117	−	0.155460i
$725$	21.5225	−	18.0595i	0.799325	−	0.670713i
$726$	−12.7287	+	18.9627i	−0.472405	+	0.703770i
$727$	−5.93941	+	33.6840i	−0.220280	+	1.24927i	0.651225	+	0.758885i	$0.274256\pi$
$727$	−5.93941	+	33.6840i	−0.220280	+	1.24927i	−0.871505	+	0.490387i	$0.836855\pi$
$728$	−9.68310	+	9.58324i	−0.358880	+	0.355179i
$729$	24.8113	+	10.6489i	0.918937	+	0.394403i
$730$	24.1764	+	41.8747i	0.894808	+	1.54985i
$731$	−4.65119	−	3.90281i	−0.172030	−	0.144351i
$732$	4.77805	+	0.323344i	0.176602	+	0.0119511i
$733$	0.737647	+	4.18341i	0.0272456	+	0.154518i	0.995395	−	0.0958542i	$-0.0305583\pi$
$733$	0.737647	+	4.18341i	0.0272456	+	0.154518i	−0.968150	+	0.250372i	$0.919447\pi$
$734$	−18.4115	+	15.4491i	−0.679580	+	0.570235i
$735$	11.5786	+	41.6534i	0.427084	+	1.53641i
$736$	−4.96226	+	1.80612i	−0.182911	+	0.0665743i
$737$	−16.0246			−0.590274
$738$	0.639797	+	1.56332i	0.0235513	+	0.0575467i
$739$	27.3264			1.00522			0.502609	−	0.864514i	$-0.332373\pi$
$739$	27.3264			1.00522			0.502609	+	0.864514i	$0.332373\pi$
$740$	1.14714	−	6.50577i	0.0421698	−	0.239157i
$741$	0.692598	+	6.45040i	0.0254432	+	0.236961i
$742$	2.58214	+	1.82805i	0.0947933	+	0.0671098i
$743$	3.00151	+	17.0224i	0.110115	+	0.624491i	0.989054	+	0.147557i	$0.0471409\pi$
$743$	3.00151	+	17.0224i	0.110115	+	0.624491i	−0.878939	+	0.476934i	$0.841748\pi$
$744$	2.11710	+	19.7173i	0.0776167	+	0.722870i
$745$	−56.0294	+	20.3931i	−2.05276	+	0.747144i
$746$	29.8039			1.09120
$747$	−10.6564	+	33.3048i	−0.389898	+	1.21856i
$748$	7.04334	−	12.1994i	0.257530	−	0.446055i
$749$	−7.06782	+	0.581459i	−0.258253	+	0.0212460i
$750$	−15.1747	−	14.5884i	−0.554103	−	0.532694i
$751$	−29.6046	−	10.7752i	−1.08029	−	0.393192i	−0.260273	−	0.965535i	$-0.583813\pi$
$751$	−29.6046	−	10.7752i	−1.08029	−	0.393192i	−0.820015	+	0.572343i	$0.806035\pi$
$752$	18.1106	−	15.1966i	0.660427	−	0.554164i
$753$	−4.17620	+	6.22153i	−0.152189	+	0.226725i
$754$	7.27002	−	2.64607i	0.264759	−	0.0963643i
$755$	−69.2687			−2.52094
$756$	−0.313965	−	5.81852i	−0.0114188	−	0.211618i
$757$	−8.24761			−0.299764			−0.149882	−	0.988704i	$-0.547889\pi$
$757$	−8.24761			−0.299764			−0.149882	+	0.988704i	$0.547889\pi$
$758$	−15.1453	+	5.51244i	−0.550102	+	0.200221i
$759$	7.93460	+	16.1761i	0.288008	+	0.587157i
$760$	18.3989	−	15.4385i	0.667397	−	0.560013i
$761$	−6.19527	−	2.25489i	−0.224578	−	0.0817398i	0.227280	−	0.973829i	$-0.427017\pi$
$761$	−6.19527	−	2.25489i	−0.224578	−	0.0817398i	−0.451859	+	0.892090i	$0.649239\pi$
$762$	7.85007	−	31.7885i	0.284378	−	1.15158i
$763$	2.00838	+	2.90014i	0.0727082	+	0.104992i
$764$	−3.22997	+	5.59447i	−0.116856	+	0.202401i
$765$	−67.8559	−	35.6900i	−2.45334	−	1.29038i
$766$	19.4997			0.704554
$767$	18.9022	−	6.87984i	0.682519	−	0.248417i
$768$	−15.3372	−	6.78737i	−0.553433	−	0.244918i
$769$	−2.53815	−	14.3946i	−0.0915279	−	0.519081i	−0.995756	−	0.0920311i	$-0.970664\pi$
$769$	−2.53815	−	14.3946i	−0.0915279	−	0.519081i	0.904228	−	0.427050i	$-0.140447\pi$
$770$	5.07033	−	54.6880i	0.182722	−	1.97082i
$771$	−26.3858	+	19.2610i	−0.950262	+	0.693668i
$772$	−0.827494	+	4.69295i	−0.0297822	+	0.168903i
$773$	28.7879			1.03543			0.517714	−	0.855554i	$-0.326783\pi$
$773$	28.7879			1.03543			0.517714	+	0.855554i	$0.326783\pi$
$774$	2.82389	+	1.48528i	0.101503	+	0.0533872i
$775$	−29.0265			−1.04266
$776$	1.08739	−	0.395776i	0.0390349	−	0.0142075i
$777$	−10.2659	−	17.1997i	−0.368287	−	0.617034i
$778$	−23.7549	+	19.9327i	−0.851655	+	0.714624i
$779$	−0.172387	−	0.977653i	−0.00617639	−	0.0350281i
$780$	1.95074	+	3.97693i	0.0698476	+	0.142397i
$781$	−5.91812	−	4.96589i	−0.211767	−	0.177694i
$782$	10.0925	+	17.4807i	0.360906	+	0.625107i
$783$	−6.97055	+	17.5927i	−0.249107	+	0.628711i
$784$	18.1276	−	10.2169i	0.647414	−	0.364890i
$785$	7.97364	−	45.2208i	0.284592	−	1.61400i
$786$	−12.2744	−	25.0237i	−0.437814	−	0.892565i
$787$	7.14689	−	5.99696i	0.254759	−	0.213768i	−0.506459	−	0.862264i	$-0.669046\pi$
$787$	7.14689	−	5.99696i	0.254759	−	0.213768i	0.761218	+	0.648496i	$0.224601\pi$
$788$	1.49326	+	8.46873i	0.0531954	+	0.301686i
$789$	−5.37166	+	21.7523i	−0.191236	+	0.774403i
$790$	26.3485	−	9.59006i	0.937437	−	0.341199i
$791$	5.97092	+	22.7549i	0.212301	+	0.809070i
$792$	−12.9007	+	40.3189i	−0.458407	+	1.43267i
$793$	−5.51920	+	9.55953i	−0.195993	+	0.339469i
$794$	36.5645	−	13.3084i	1.29763	−	0.472298i
$795$	4.75133	−	3.46836i	0.168512	−	0.123010i
$796$	−3.11599	+	2.61463i	−0.110443	+	0.0926729i
$797$	−8.10911	−	45.9890i	−0.287239	−	1.62901i	−0.697175	−	0.716901i	$-0.745560\pi$
$797$	−8.10911	−	45.9890i	−0.287239	−	1.62901i	0.409936	−	0.912114i	$-0.365551\pi$
$798$	2.02910	−	12.5719i	0.0718294	−	0.445042i
$799$	43.6654	+	36.6396i	1.54477	+	1.29622i
$800$	9.08042	−	15.7277i	0.321041	−	0.556060i
$801$	−1.72489	−	0.234531i	−0.0609461	−	0.00828674i
$802$	−15.2000	−	26.3272i	−0.536731	−	0.929645i
$803$	38.3682	+	32.1947i	1.35398	+	1.13613i
$804$	−2.43710	+	0.704748i	−0.0859499	+	0.0248545i
$805$	−17.2729	−	12.2285i	−0.608789	−	0.430998i
$806$	−7.51090	−	2.73374i	−0.264560	−	0.0962920i
$807$	0.950102	−	1.41542i	0.0334452	−	0.0498253i
$808$	37.6387	+	31.5826i	1.32412	+	1.11107i
$809$	−7.42526	+	12.8609i	−0.261058	+	0.452166i	−0.966523	−	0.256579i	$-0.917405\pi$
$809$	−7.42526	+	12.8609i	−0.261058	+	0.452166i	0.705465	+	0.708745i	$0.250738\pi$
$810$	38.8272	+	10.7574i	1.36425	+	0.377977i
$811$	46.2839			1.62525			0.812623	−	0.582789i	$-0.198039\pi$
$811$	46.2839			1.62525			0.812623	+	0.582789i	$0.198039\pi$
$812$	4.07017	−	0.334846i	0.142835	−	0.0117508i
$813$	−19.2998	−	39.3462i	−0.676874	−	1.37993i
$814$	4.41873	+	25.0599i	0.154876	+	0.878348i
$815$	−6.86856	−	38.9535i	−0.240595	−	1.36448i
$816$	−8.84708	+	35.8259i	−0.309710	+	1.25416i
$817$	−1.43647	−	1.20534i	−0.0502556	−	0.0421694i
$818$	4.30392	−	7.45461i	0.150483	−	0.260644i
$819$	12.3596	+	5.25650i	0.431879	+	0.183677i
$820$	−0.338916	−	0.587020i	−0.0118355	−	0.0204996i
$821$	0.176050	−	0.998429i	0.00614419	−	0.0348454i	−0.981582	−	0.191044i	$-0.938813\pi$
$821$	0.176050	−	0.998429i	0.00614419	−	0.0348454i	0.987726	+	0.156198i	$0.0499239\pi$
$822$	−34.6553	−	15.3365i	−1.20874	−	0.534921i
$823$	−4.83004	−	1.75799i	−0.168365	−	0.0612798i	0.256463	−	0.966554i	$-0.417443\pi$
$823$	−4.83004	−	1.75799i	−0.168365	−	0.0612798i	−0.424827	+	0.905274i	$0.639665\pi$
$824$	−11.4785	+	9.63162i	−0.399873	+	0.335533i
$825$	−56.6625	−	25.0756i	−1.97273	−	0.873020i
$826$	−39.3526	+	3.23747i	−1.36925	+	0.112646i
$827$	−4.70173	−	8.14364i	−0.163495	−	0.283182i	0.772625	−	0.634863i	$-0.218944\pi$
$827$	−4.70173	−	8.14364i	−0.163495	−	0.283182i	−0.936120	+	0.351681i	$0.885610\pi$
$828$	1.91815	+	2.11119i	0.0666602	+	0.0733689i
$829$	−15.4152	−	26.6999i	−0.535392	−	0.927327i	−0.999144	−	0.0413616i	$-0.986830\pi$
$829$	−15.4152	−	26.6999i	−0.535392	−	0.927327i	0.463752	−	0.885965i	$-0.346503\pi$
$830$	−9.06097	+	51.3873i	−0.314511	+	1.78368i
$831$	−0.335354	+	1.35800i	−0.0116333	+	0.0471086i
$832$	11.5375	−	9.68113i	0.399992	−	0.335633i
$833$	31.8486	+	38.7647i	1.10349	+	1.34312i
$834$	−40.5693	−	2.74543i	−1.40480	−	0.0950666i
$835$	4.42607	−	1.61096i	0.153171	−	0.0557495i
$836$	2.17526	−	3.76765i	0.0752328	−	0.130307i
$837$	17.1997	−	9.29426i	0.594509	−	0.321257i
$838$	−16.2162	−	28.0873i	−0.560179	−	0.970258i
$839$	−9.97808	+	56.5885i	−0.344482	+	1.95365i	−0.0471155	+	0.998889i	$0.515003\pi$
$839$	−9.97808	+	56.5885i	−0.344482	+	1.95365i	−0.297366	+	0.954763i	$0.596108\pi$
$840$	−9.34432	−	48.8384i	−0.322410	−	1.68508i
$841$	14.7883	+	5.38250i	0.509941	+	0.185603i
$842$	18.1698	+	6.61328i	0.626174	+	0.227909i
$843$	−17.4155	−	16.7426i	−0.599823	−	0.576647i
$844$	1.70591	−	9.67472i	0.0587200	−	0.333018i
$845$	36.1451			1.24343
$846$	−26.5107	−	13.9438i	−0.911458	−	0.479397i
$847$	−7.05288	−	26.8782i	−0.242340	−	0.923545i
$848$	−2.16895	−	1.81997i	−0.0744821	−	0.0624979i
$849$	−1.76421	−	0.780740i	−0.0605476	−	0.0267949i
$850$	−65.2311	−	23.7422i	−2.23741	−	0.814350i
$851$	9.21399	+	3.35362i	0.315851	+	0.114961i
$852$	−1.11845	−	0.494963i	−0.0383175	−	0.0169572i
$853$	35.7342	+	29.9846i	1.22352	+	1.02665i	0.998633	+	0.0522665i	$0.0166445\pi$
$853$	35.7342	+	29.9846i	1.22352	+	1.02665i	0.224883	+	0.974386i	$0.427800\pi$
$854$	15.4007	−	15.2419i	0.527002	−	0.521568i
$855$	−20.9565	−	11.0225i	−0.716698	−	0.376960i
$856$	8.15654			0.278785
$857$	−8.18912	+	46.4428i	−0.279735	+	1.58646i	0.443772	+	0.896140i	$0.353640\pi$
$857$	−8.18912	+	46.4428i	−0.279735	+	1.58646i	−0.723507	+	0.690317i	$0.757471\pi$
$858$	−12.3003	−	11.8251i	−0.419927	−	0.403702i
$859$	8.09163	+	2.94511i	0.276083	+	0.100486i	0.476351	−	0.879255i	$-0.341959\pi$
$859$	8.09163	+	2.94511i	0.276083	+	0.100486i	−0.200268	+	0.979741i	$0.564181\pi$
$860$	−1.20314	−	0.437907i	−0.0410267	−	0.0149325i
$861$	−1.94130	−	0.674833i	−0.0661594	−	0.0229982i
$862$	−5.65828	+	32.0897i	−0.192722	+	1.09298i
$863$	−13.7630	−	23.8381i	−0.468496	−	0.811460i	0.530855	−	0.847462i	$-0.321871\pi$
$863$	−13.7630	−	23.8381i	−0.468496	−	0.811460i	−0.999352	+	0.0360029i	$0.988537\pi$
$864$	−0.344605	+	12.2270i	−0.0117237	+	0.415973i
$865$	27.8942	−	48.3142i	0.948432	−	1.64273i
$866$	2.24114	−	0.815709i	0.0761571	−	0.0277189i
$867$	−59.3915	−	4.01919i	−2.01704	−	0.136499i
$868$	−3.44360	−	2.43793i	−0.116883	−	0.0827487i
$869$	22.2495	−	18.6695i	0.754761	−	0.633320i
$870$	−6.76982	+	27.4141i	−0.229518	+	0.929426i
$871$	1.01542	−	5.75873i	0.0344061	−	0.195127i
$872$	−2.02867	−	3.51376i	−0.0686995	−	0.118991i
$873$	−0.767150	−	0.844356i	−0.0259641	−	0.0285771i
$874$	3.11694	+	5.39870i	0.105432	+	0.182614i
$875$	25.5254	−	2.09994i	0.862918	−	0.0709909i
$876$	7.25111	+	3.20893i	0.244992	+	0.108420i
$877$	38.2565	−	32.1010i	1.29183	−	1.08398i	0.300336	−	0.953833i	$-0.402901\pi$
$877$	38.2565	−	32.1010i	1.29183	−	1.08398i	0.991495	−	0.130142i	$-0.0415433\pi$
$878$	17.2416	+	6.27543i	0.581875	+	0.211785i
$879$	−2.03293	−	0.899659i	−0.0685690	−	0.0303447i
$880$	−8.53526	+	48.4059i	−0.287724	+	1.63176i
$881$	−10.0377	−	17.3859i	−0.338180	−	0.585744i	0.645911	−	0.763413i	$-0.276478\pi$
$881$	−10.0377	−	17.3859i	−0.338180	−	0.585744i	−0.984090	+	0.177669i	$0.943144\pi$
$882$	−20.6797	−	16.3534i	−0.696320	−	0.550648i
$883$	−12.0043	+	20.7920i	−0.403976	+	0.699706i	−0.994202	−	0.107532i	$-0.965705\pi$
$883$	−12.0043	+	20.7920i	−0.403976	+	0.699706i	0.590226	+	0.807238i	$0.299039\pi$
$884$	3.93777	+	3.30418i	0.132442	+	0.111132i
$885$	−17.6017	+	71.2773i	−0.591674	+	2.39596i
$886$	0.587728	+	3.33317i	0.0197451	+	0.111980i
$887$	−8.21436	−	46.5859i	−0.275811	−	1.56420i	−0.736374	−	0.676575i	$-0.763463\pi$
$887$	−8.21436	−	46.5859i	−0.275811	−	1.56420i	0.460562	−	0.887627i	$-0.347648\pi$
$888$	10.1456	+	20.6837i	0.340465	+	0.694100i
$889$	22.6816	+	32.7526i	0.760716	+	1.09849i
$890$	−2.59760			−0.0870717
$891$	41.6047	−	3.28470i	1.39381	−	0.110042i
$892$	2.96263	−	5.13142i	0.0991961	−	0.171813i
$893$	13.4856	+	11.3157i	0.451277	+	0.378666i
$894$	20.2651	−	30.1901i	0.677767	−	1.00971i
$895$	38.2911	+	13.9368i	1.27993	+	0.465857i
$896$	−15.5425	+	7.14974i	−0.519237	+	0.238856i
$897$	−6.31597	+	1.82642i	−0.210884	+	0.0609824i
$898$	3.37115	+	2.82873i	0.112497	+	0.0943959i
$899$	6.85103	+	11.8663i	0.228495	+	0.395764i
$900$	−9.72031	−	1.32165i	−0.324010	−	0.0440551i
$901$	3.41326	−	5.91194i	0.113712	−	0.196955i
$902$	2.00012	+	1.67830i	0.0665967	+	0.0558813i
$903$	−3.62838	+	1.38058i	−0.120745	+	0.0459428i
$904$	−4.69850	−	26.6465i	−0.156270	−	0.886250i
$905$	−27.3735	+	22.9691i	−0.909927	+	0.763519i
$906$	34.1185	−	24.9057i	1.13351	−	0.827435i
$907$	−1.11780	+	0.406845i	−0.0371159	+	0.0135091i	−0.360511	−	0.932755i	$-0.617398\pi$
$907$	−1.11780	+	0.406845i	−0.0371159	+	0.0135091i	0.323395	+	0.946264i	$0.395176\pi$
$908$	0.0702675	−	0.121707i	0.00233191	−	0.00403898i
$909$	14.7617	−	46.1351i	0.489614	−	1.53021i
$910$	19.3318	+	5.28749i	0.640844	+	0.175279i
$911$	−1.56578	+	0.569897i	−0.0518765	+	0.0188815i	−0.367828	−	0.929894i	$-0.619899\pi$
$911$	−1.56578	+	0.569897i	−0.0518765	+	0.0188815i	0.315952	+	0.948775i	$0.397676\pi$
$912$	−2.73232	+	11.0644i	−0.0904761	+	0.366379i
$913$	9.38578	+	53.2294i	0.310624	+	1.76164i
$914$	−27.0753	+	22.7189i	−0.895571	+	0.751474i
$915$	−17.7427	−	36.1716i	−0.586554	−	1.19580i
$916$	−0.278200	+	1.57775i	−0.00919199	+	0.0521304i
$917$	32.7108	+	8.94680i	1.08021	+	0.295450i
$918$	46.2551	−	6.81849i	1.52664	−	0.225044i
$919$	−0.624035	−	1.08086i	−0.0205850	−	0.0356543i	0.855549	−	0.517721i	$-0.173220\pi$
$919$	−0.624035	−	1.08086i	−0.0205850	−	0.0356543i	−0.876134	+	0.482067i	$0.839886\pi$
$920$	18.6464	+	15.6462i	0.614753	+	0.515839i
$921$	5.91112	+	12.0509i	0.194778	+	0.397091i
$922$	−6.34358	−	35.9762i	−0.208915	−	1.18481i
$923$	2.15959	−	1.81211i	0.0710838	−	0.0596464i
$924$	−4.61614	−	7.73395i	−0.151860	−	0.254428i
$925$	−31.6876	+	11.5333i	−1.04188	+	0.379214i
$926$	−6.29235			−0.206779
$927$	13.0742	+	6.87659i	0.429412	+	0.225857i
$928$	−8.57288			−0.281419
$929$	6.46549	−	36.6676i	0.212126	−	1.20303i	−0.673699	−	0.739006i	$-0.735296\pi$
$929$	6.46549	−	36.6676i	0.212126	−	1.20303i	0.885825	−	0.464020i	$-0.153593\pi$
$930$	23.5631	−	17.2005i	0.772665	−	0.564027i
$931$	9.83608	+	11.9720i	0.322364	+	0.392368i
$932$	0.385619	+	2.18695i	0.0126314	+	0.0716361i
$933$	11.2783	+	4.99112i	0.369234	+	0.163402i
$934$	−21.8672	+	7.95899i	−0.715515	+	0.260426i
$935$	−118.509			−3.87565
$936$	−13.6719	−	7.19096i	−0.446879	−	0.235044i
$937$	6.48389	−	11.2304i	0.211820	−	0.366882i	−0.740464	−	0.672096i	$-0.765394\pi$
$937$	6.48389	−	11.2304i	0.211820	−	0.366882i	0.952284	+	0.305213i	$0.0987278\pi$
$938$	−4.90489	+	10.3778i	−0.160150	+	0.338847i
$939$	−3.48880	+	14.1278i	−0.113853	+	0.461042i
$940$	11.2951	+	4.11108i	0.368405	+	0.134089i
$941$	−20.3420	+	17.0689i	−0.663129	+	0.556431i	−0.911023	−	0.412356i	$-0.864706\pi$
$941$	−20.3420	+	17.0689i	−0.663129	+	0.556431i	0.247894	+	0.968787i	$0.420262\pi$
$942$	12.3318	+	25.1406i	0.401791	+	0.819124i
$943$	0.945415	−	0.344103i	0.0307870	−	0.0112055i
$944$	35.3373			1.15013
$945$	−41.0714	+	26.7625i	−1.33605	+	0.870585i
$946$	4.93186			0.160348
$947$	22.8621	−	8.32113i	0.742919	−	0.270400i	0.0572958	−	0.998357i	$-0.481752\pi$
$947$	22.8621	−	8.32113i	0.742919	−	0.270400i	0.685623	+	0.727957i	$0.259530\pi$
$948$	2.56274	−	3.81786i	0.0832338	−	0.123998i
$949$	−14.0010	+	11.7482i	−0.454492	+	0.381364i
$950$	−20.1459	−	7.33250i	−0.653619	−	0.237898i
$951$	3.93204	+	3.78012i	0.127505	+	0.122579i
$952$	−32.8518	−	47.4387i	−1.06473	−	1.53750i
$953$	21.9931	−	38.0932i	0.712427	−	1.23396i	−0.251517	−	0.967853i	$-0.580929\pi$
$953$	21.9931	−	38.0932i	0.712427	−	1.23396i	0.963944	−	0.266107i	$-0.0857374\pi$
$954$	−1.09323	+	3.41670i	−0.0353946	+	0.110620i
$955$	54.3463			1.75860
$956$	−1.70586	+	0.620882i	−0.0551715	+	0.0200808i
$957$	3.12270	+	29.0827i	0.100942	+	0.940111i
$958$	−0.613234	−	3.47782i	−0.0198127	−	0.112363i
$959$	41.8905	−	19.2702i	1.35271	−	0.622266i
$960$	5.86872	+	54.6573i	0.189412	+	1.76406i
$961$	−2.92492	+	16.5881i	−0.0943524	+	0.535099i
$962$	−9.28571			−0.299383
$963$	−3.04572	−	7.44211i	−0.0981470	−	0.239819i
$964$	−8.85088			−0.285068
$965$	37.6723	−	13.7116i	1.21271	−	0.441392i
$966$	12.9046	−	0.187308i	0.415199	−	0.00602654i
$967$	34.6014	−	29.0340i	1.11271	−	0.933672i	0.114494	−	0.993424i	$-0.463475\pi$
$967$	34.6014	−	29.0340i	1.11271	−	0.933672i	0.998213	+	0.0597521i	$0.0190310\pi$
$968$	5.54990	+	31.4750i	0.178380	+	1.01165i
$969$	−27.4153	−	1.85527i	−0.880708	−	0.0595999i
$970$	−1.30407	−	1.09424i	−0.0418711	−	0.0351341i
$971$	−14.4627	−	25.0502i	−0.464131	−	0.803899i	0.535031	−	0.844833i	$-0.320300\pi$
$971$	−14.4627	−	25.0502i	−0.464131	−	0.803899i	−0.999162	+	0.0409338i	$0.986967\pi$
$972$	6.18298	−	2.32929i	0.198319	−	0.0747120i
$973$	35.1644	−	34.8018i	1.12732	−	1.11569i
$974$	−1.25119	+	7.09585i	−0.0400907	+	0.227366i
$975$	12.6019	−	18.7737i	0.403582	−	0.601240i
$976$	−14.8548	+	12.4647i	−0.475491	+	0.398984i
$977$	−8.79593	−	49.8842i	−0.281407	−	1.59594i	−0.717845	−	0.696203i	$-0.754871\pi$
$977$	−8.79593	−	49.8842i	−0.281407	−	1.59594i	0.436438	−	0.899734i	$-0.356240\pi$
$978$	17.3889	+	16.7171i	0.556037	+	0.534553i
$979$	−2.52844	+	0.920278i	−0.0808094	+	0.0294122i
$980$	9.10680	+	5.38444i	0.290906	+	0.172000i
$981$	−2.44847	+	3.16305i	−0.0781737	+	0.100988i
$982$	−8.94026	+	15.4850i	−0.285295	+	0.494146i
$983$	−1.37131	+	0.499115i	−0.0437379	+	0.0159193i	−0.363796	−	0.931478i	$-0.618520\pi$
$983$	−1.37131	+	0.499115i	−0.0437379	+	0.0159193i	0.320059	+	0.947398i	$0.396297\pi$
$984$	2.16164	+	0.956618i	0.0689105	+	0.0304959i
$985$	55.4194	−	46.5024i	1.76581	−	1.48169i
$986$	5.69024	+	32.2710i	0.181214	+	1.02772i
$987$	34.0632	−	12.9609i	1.08424	−	0.412550i
$988$	1.21614	+	1.02046i	0.0386904	+	0.0324651i
$989$	0.950200	−	1.64579i	0.0302146	−	0.0523332i
$990$	60.8567	−	13.2212i	1.93415	−	0.420196i
$991$	25.9421	+	44.9331i	0.824079	+	1.42735i	0.902621	+	0.430435i	$0.141640\pi$
$991$	25.9421	+	44.9331i	0.824079	+	1.42735i	−0.0785429	+	0.996911i	$0.525027\pi$
$992$	6.78480	+	5.69312i	0.215418	+	0.180757i
$993$	42.2472	+	40.6148i	1.34067	+	1.28887i
$994$	−5.02744	+	2.31269i	−0.159461	+	0.0733540i
$995$	32.1565	+	11.7040i	1.01943	+	0.371042i
$996$	3.76842	+	7.68261i	0.119407	+	0.243433i
$997$	12.9863	+	10.8968i	0.411281	+	0.345105i	0.824834	−	0.565374i	$-0.191268\pi$
$997$	12.9863	+	10.8968i	0.411281	+	0.345105i	−0.413554	+	0.910480i	$0.635713\pi$
$998$	4.04587	−	7.00765i	0.128070	−	0.221823i
$999$	15.0836	−	16.9805i	0.477223	−	0.537238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.16	yes	132
3.2	odd	2		567.2.w.a.235.7		132
7.2	even	3		189.2.u.a.79.7	yes	132
21.2	odd	6		567.2.u.a.478.16		132
27.13	even	9		189.2.u.a.67.7	✓	132
27.14	odd	18		567.2.u.a.172.16		132
189.121	even	9	inner	189.2.w.a.121.16	yes	132
189.149	odd	18		567.2.w.a.415.7		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.7	✓	132	27.13	even	9
189.2.u.a.79.7	yes	132	7.2	even	3
189.2.w.a.25.16	yes	132	1.1	even	1	trivial
189.2.w.a.121.16	yes	132	189.121	even	9	inner
567.2.u.a.172.16		132	27.14	odd	18
567.2.u.a.478.16		132	21.2	odd	6
567.2.w.a.235.7		132	3.2	odd	2
567.2.w.a.415.7		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)

\(f(q)\)	\(=\)	\(q+(1.17974 - 0.429388i) q^{2} +(-1.72810 - 0.116945i) q^{3} +(-0.324689 + 0.272446i) q^{4} +(3.35074 + 1.21957i) q^{5} +(-2.08891 + 0.604061i) q^{6} +(1.13056 - 2.39204i) q^{7} +(-1.52151 + 2.63533i) q^{8} +(2.97265 + 0.404186i) q^{9} +O(q^{10})\)	\(q+(1.17974 - 0.429388i) q^{2} +(-1.72810 - 0.116945i) q^{3} +(-0.324689 + 0.272446i) q^{4} +(3.35074 + 1.21957i) q^{5} +(-2.08891 + 0.604061i) q^{6} +(1.13056 - 2.39204i) q^{7} +(-1.52151 + 2.63533i) q^{8} +(2.97265 + 0.404186i) q^{9} +4.47665 q^{10} +(4.35747 - 1.58599i) q^{11} +(0.592955 - 0.432843i) q^{12} +(0.293837 + 1.66643i) q^{13} +(0.306643 - 3.30742i) q^{14} +(-5.64778 - 2.49939i) q^{15} +(-0.516195 + 2.92749i) q^{16} -7.16716 q^{17} +(3.68049 - 0.799589i) q^{18} -2.21349 q^{19} +(-1.42021 + 0.516915i) q^{20} +(-2.23345 + 4.00146i) q^{21} +(4.45966 - 3.74210i) q^{22} +(-0.389540 - 2.20919i) q^{23} +(2.93751 - 4.37618i) q^{24} +(5.90986 + 4.95897i) q^{25} +(1.06220 + 1.83978i) q^{26} +(-5.08976 - 1.04611i) q^{27} +(0.284623 + 1.08468i) q^{28} +(0.632390 - 3.58646i) q^{29} +(-7.73609 - 0.523523i) q^{30} +(-2.88220 + 2.41846i) q^{31} +(-0.408773 - 2.31827i) q^{32} +(-7.71561 + 2.23116i) q^{33} +(-8.45534 + 3.07749i) q^{34} +(6.70545 - 6.63630i) q^{35} +(-1.07530 + 0.678652i) q^{36} +(-2.18550 + 3.78539i) q^{37} +(-2.61134 + 0.950449i) q^{38} +(-0.312898 - 2.91412i) q^{39} +(-8.31214 + 6.97472i) q^{40} +(0.0778798 + 0.441679i) q^{41} +(-0.916696 + 5.67968i) q^{42} +(0.648959 + 0.544541i) q^{43} +(-0.982725 + 1.70213i) q^{44} +(9.46763 + 4.97967i) q^{45} +(-1.40816 - 2.43900i) q^{46} +(-6.09243 - 5.11215i) q^{47} +(1.23439 - 4.99862i) q^{48} +(-4.44369 - 5.40866i) q^{49} +(9.10140 + 3.31264i) q^{50} +(12.3855 + 0.838165i) q^{51} +(-0.549419 - 0.461017i) q^{52} +(-0.476236 + 0.824865i) q^{53} +(-6.45376 + 0.951352i) q^{54} +16.5350 q^{55} +(4.58366 + 6.61890i) q^{56} +(3.82514 + 0.258858i) q^{57} +(-0.793933 - 4.50262i) q^{58} +(-2.06424 - 11.7069i) q^{59} +(2.51472 - 0.727193i) q^{60} +(4.99716 + 4.19312i) q^{61} +(-2.36178 + 4.09072i) q^{62} +(4.32757 - 6.65373i) q^{63} +(-4.45033 - 7.70820i) q^{64} +(-1.04776 + 5.94213i) q^{65} +(-8.14434 + 5.94517i) q^{66} +(-3.24731 - 1.18193i) q^{67} +(2.32709 - 1.95266i) q^{68} +(0.414809 + 3.86325i) q^{69} +(5.06110 - 10.7083i) q^{70} +(-0.833011 - 1.44282i) q^{71} +(-5.58807 + 7.21894i) q^{72} +(5.40056 + 9.35404i) q^{73} +(-0.952903 + 5.40418i) q^{74} +(-9.63290 - 9.26071i) q^{75} +(0.718696 - 0.603058i) q^{76} +(1.13262 - 12.2163i) q^{77} +(-1.62043 - 3.30354i) q^{78} +(5.88576 - 2.14224i) q^{79} +(-5.29990 + 9.17970i) q^{80} +(8.67327 + 2.40300i) q^{81} +(0.281529 + 0.487623i) q^{82} +(-2.02405 + 11.4790i) q^{83} +(-0.365008 - 1.90772i) q^{84} +(-24.0152 - 8.74084i) q^{85} +(0.999419 + 0.363759i) q^{86} +(-1.51225 + 6.12380i) q^{87} +(-2.45032 + 13.8965i) q^{88} -0.580255 q^{89} +(13.3075 + 1.80940i) q^{90} +(4.31837 + 1.18113i) q^{91} +(0.728365 + 0.611171i) q^{92} +(5.26356 - 3.84227i) q^{93} +(-9.38255 - 3.41497i) q^{94} +(-7.41684 - 2.69951i) q^{95} +(0.435290 + 4.05400i) q^{96} +(-0.291305 - 0.244434i) q^{97} +(-7.56479 - 4.47272i) q^{98} +(13.5943 - 2.95336i) 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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