LMFDB - Embedded newform 189.2.u.a.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (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			79.4
Character	$\chi$	$=$	189.79
Dual form			189.2.u.a.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55519 - 1.30496i) q^{2} +(1.19925 + 1.24972i) q^{3} +(0.368398 + 2.08929i) q^{4} +(0.441461 + 2.50365i) q^{5} +(-0.234236 - 3.50852i) q^{6} +(-0.472815 - 2.60316i) q^{7} +(0.123353 - 0.213653i) q^{8} +(-0.123586 + 2.99745i) q^{9} +O(q^{10})$	\(q+(-1.55519 - 1.30496i) q^{2} +(1.19925 + 1.24972i) q^{3} +(0.368398 + 2.08929i) q^{4} +(0.441461 + 2.50365i) q^{5} +(-0.234236 - 3.50852i) q^{6} +(-0.472815 - 2.60316i) q^{7} +(0.123353 - 0.213653i) q^{8} +(-0.123586 + 2.99745i) q^{9} +(2.58060 - 4.46974i) q^{10} +(-0.994702 + 5.64123i) q^{11} +(-2.16922 + 2.96598i) q^{12} +(0.494719 + 2.80569i) q^{13} +(-2.66170 + 4.66541i) q^{14} +(-2.59943 + 3.55421i) q^{15} +(3.51651 - 1.27990i) q^{16} +(2.41871 - 4.18933i) q^{17} +(4.10375 - 4.50033i) q^{18} +(-0.277852 - 0.481253i) q^{19} +(-5.06822 + 1.84468i) q^{20} +(2.68619 - 3.71273i) q^{21} +(8.90852 - 7.47513i) q^{22} +(2.10296 - 1.76459i) q^{23} +(0.414937 - 0.102068i) q^{24} +(-1.37492 + 0.500430i) q^{25} +(2.89193 - 5.00897i) q^{26} +(-3.89418 + 3.44026i) q^{27} +(5.26457 - 1.94685i) q^{28} +(0.164033 - 0.930279i) q^{29} +(8.68070 - 2.13532i) q^{30} +(0.867833 + 4.92173i) q^{31} +(-7.60271 - 2.76716i) q^{32} +(-8.24285 + 5.52217i) q^{33} +(-9.22845 + 3.35888i) q^{34} +(6.30868 - 2.33296i) q^{35} +(-6.30808 + 0.846050i) q^{36} +8.16114 q^{37} +(-0.195903 + 1.11102i) q^{38} +(-2.91303 + 3.98299i) q^{39} +(0.589368 + 0.214513i) q^{40} +(-1.92050 - 10.8917i) q^{41} +(-9.02249 + 2.26863i) q^{42} +(-4.80243 - 4.02972i) q^{43} -12.1526 q^{44} +(-7.55914 + 1.01384i) q^{45} -5.57321 q^{46} +(-0.517743 + 2.93627i) q^{47} +(5.81670 + 2.85971i) q^{48} +(-6.55289 + 2.46163i) q^{49} +(2.79130 + 1.01595i) q^{50} +(8.13612 - 2.00136i) q^{51} +(-5.67965 + 2.06722i) q^{52} +(3.07682 + 5.32920i) q^{53} +(10.5456 - 0.268508i) q^{54} -14.5628 q^{55} +(-0.614496 - 0.220088i) q^{56} +(0.268216 - 0.924380i) q^{57} +(-1.46908 + 1.23270i) q^{58} +(-8.92291 - 3.24767i) q^{59} +(-8.38341 - 4.12160i) q^{60} +(0.889765 - 5.04611i) q^{61} +(5.07300 - 8.78669i) q^{62} +(7.86129 - 1.09553i) q^{63} +(4.47042 + 7.74299i) q^{64} +(-6.80608 + 2.47721i) q^{65} +(20.0254 + 2.16855i) q^{66} +(7.29506 - 6.12129i) q^{67} +(9.64378 + 3.51005i) q^{68} +(4.72722 + 0.511912i) q^{69} +(-12.8556 - 4.60437i) q^{70} +(-5.28149 - 9.14782i) q^{71} +(0.625171 + 0.396148i) q^{72} -0.456492 q^{73} +(-12.6921 - 10.6499i) q^{74} +(-2.27427 - 1.11812i) q^{75} +(0.903117 - 0.757805i) q^{76} +(15.1553 - 0.0778908i) q^{77} +(9.72794 - 2.39292i) q^{78} +(2.52613 + 2.11967i) q^{79} +(4.75684 + 8.23909i) q^{80} +(-8.96945 - 0.740884i) q^{81} +(-11.2265 + 19.4448i) q^{82} +(0.441119 - 2.50171i) q^{83} +(8.74656 + 4.24447i) q^{84} +(11.5564 + 4.20618i) q^{85} +(2.21007 + 12.5339i) q^{86} +(1.35930 - 0.910645i) q^{87} +(1.08257 + 0.908382i) q^{88} +(3.34817 + 5.79919i) q^{89} +(13.0789 + 8.28763i) q^{90} +(7.06976 - 2.61441i) q^{91} +(4.46147 + 3.74362i) q^{92} +(-5.11001 + 6.98694i) q^{93} +(4.63689 - 3.89081i) q^{94} +(1.08223 - 0.908098i) q^{95} +(-5.65940 - 12.8198i) q^{96} +(4.52344 + 3.79562i) q^{97} +(13.4033 + 4.72295i) q^{98} +(-16.7864 - 3.67875i) 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} - 15 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 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.55519	−	1.30496i	−1.09968	−	0.922744i	−0.102280	−	0.994756i	$-0.532614\pi$
$2$	−1.55519	−	1.30496i	−1.09968	−	0.922744i	−0.997404	+	0.0720117i	$0.977058\pi$
$3$	1.19925	+	1.24972i	0.692389	+	0.721524i
$3$	1.19925	+	1.24972i	0.692389	+	0.721524i
$4$	0.368398	+	2.08929i	0.184199	+	1.04464i
$5$	0.441461	+	2.50365i	0.197427	+	1.11967i	0.908919	+	0.416972i	$0.136909\pi$
$5$	0.441461	+	2.50365i	0.197427	+	1.11967i	−0.711492	+	0.702695i	$0.751980\pi$
$6$	−0.234236	−	3.50852i	−0.0956263	−	1.43235i
$7$	−0.472815	−	2.60316i	−0.178707	−	0.983902i
$7$	−0.472815	−	2.60316i	−0.178707	−	0.983902i
$8$	0.123353	−	0.213653i	0.0436118	−	0.0755378i
$9$	−0.123586	+	2.99745i	−0.0411952	+	0.999151i
$10$	2.58060	−	4.46974i	0.816058	−	1.41345i
$11$	−0.994702	+	5.64123i	−0.299914	+	1.70090i	0.346616	+	0.938007i	$0.387331\pi$
$11$	−0.994702	+	5.64123i	−0.299914	+	1.70090i	−0.646530	+	0.762889i	$0.723780\pi$
$12$	−2.16922	+	2.96598i	−0.626200	+	0.856205i
$13$	0.494719	+	2.80569i	0.137210	+	0.778159i	0.973295	+	0.229558i	$0.0737282\pi$
$13$	0.494719	+	2.80569i	0.137210	+	0.778159i	−0.836084	+	0.548601i	$0.815161\pi$
$14$	−2.66170	+	4.66541i	−0.711369	+	1.24688i
$15$	−2.59943	+	3.55421i	−0.671171	+	0.917694i
$16$	3.51651	−	1.27990i	0.879127	−	0.319976i
$17$	2.41871	−	4.18933i	0.586624	−	1.01606i	−0.408047	−	0.912961i	$-0.633790\pi$
$17$	2.41871	−	4.18933i	0.586624	−	1.01606i	0.994671	−	0.103101i	$-0.0328765\pi$
$18$	4.10375	−	4.50033i	0.967262	−	1.06074i
$19$	−0.277852	−	0.481253i	−0.0637435	−	0.110407i	0.832392	−	0.554187i	$-0.186971\pi$
$19$	−0.277852	−	0.481253i	−0.0637435	−	0.110407i	−0.896136	+	0.443780i	$0.853637\pi$
$20$	−5.06822	+	1.84468i	−1.13329	+	0.412483i
$21$	2.68619	−	3.71273i	0.586175	−	0.810185i
$22$	8.90852	−	7.47513i	1.89930	−	1.59370i
$23$	2.10296	−	1.76459i	0.438497	−	0.367943i	−0.396649	−	0.917970i	$-0.629827\pi$
$23$	2.10296	−	1.76459i	0.438497	−	0.367943i	0.835147	+	0.550027i	$0.185383\pi$
$24$	0.414937	−	0.102068i	0.0846987	−	0.0208346i
$25$	−1.37492	+	0.500430i	−0.274984	+	0.100086i
$26$	2.89193	−	5.00897i	0.567154	−	0.982339i
$27$	−3.89418	+	3.44026i	−0.749435	+	0.662078i
$28$	5.26457	−	1.94685i	0.994911	−	0.367920i
$29$	0.164033	−	0.930279i	0.0304602	−	0.172749i	−0.965783	−	0.259353i	$-0.916491\pi$
$29$	0.164033	−	0.930279i	0.0304602	−	0.172749i	0.996243	+	0.0866047i	$0.0276017\pi$
$30$	8.68070	−	2.13532i	1.58487	−	0.389854i
$31$	0.867833	+	4.92173i	0.155867	+	0.883968i	0.957989	+	0.286807i	$0.0925937\pi$
$31$	0.867833	+	4.92173i	0.155867	+	0.883968i	−0.802121	+	0.597161i	$0.796295\pi$
$32$	−7.60271	−	2.76716i	−1.34398	−	0.489169i
$33$	−8.24285	+	5.52217i	−1.43490	+	0.961286i
$34$	−9.22845	+	3.35888i	−1.58267	+	0.576043i
$35$	6.30868	−	2.33296i	1.06636	−	0.394342i
$36$	−6.30808	+	0.846050i	−1.05135	+	0.141008i
$37$	8.16114			1.34168			0.670841	−	0.741601i	$-0.265933\pi$
$37$	8.16114			1.34168			0.670841	+	0.741601i	$0.265933\pi$
$38$	−0.195903	+	1.11102i	−0.0317797	+	0.180232i
$39$	−2.91303	+	3.98299i	−0.466458	+	0.637790i
$40$	0.589368	+	0.214513i	0.0931873	+	0.0339174i
$41$	−1.92050	−	10.8917i	−0.299932	−	1.70100i	−0.646452	−	0.762955i	$-0.723748\pi$
$41$	−1.92050	−	10.8917i	−0.299932	−	1.70100i	0.346520	−	0.938043i	$-0.387363\pi$
$42$	−9.02249	+	2.26863i	−1.39220	+	0.350058i
$43$	−4.80243	−	4.02972i	−0.732364	−	0.614526i	0.198411	−	0.980119i	$-0.436422\pi$
$43$	−4.80243	−	4.02972i	−0.732364	−	0.614526i	−0.930775	+	0.365593i	$0.880866\pi$
$44$	−12.1526			−1.83208
$45$	−7.55914	+	1.01384i	−1.12685	+	0.151135i
$46$	−5.57321			−0.821725
$47$	−0.517743	+	2.93627i	−0.0755206	+	0.428299i	0.923482	+	0.383642i	$0.125330\pi$
$47$	−0.517743	+	2.93627i	−0.0755206	+	0.428299i	−0.999002	+	0.0446563i	$0.985781\pi$
$48$	5.81670	+	2.85971i	0.839569	+	0.412764i
$49$	−6.55289	+	2.46163i	−0.936127	+	0.351661i
$50$	2.79130	+	1.01595i	0.394749	+	0.143677i
$51$	8.13612	−	2.00136i	1.13929	−	0.280247i
$52$	−5.67965	+	2.06722i	−0.787626	+	0.286672i
$53$	3.07682	+	5.32920i	0.422633	+	0.732022i	0.996196	−	0.0871392i	$-0.0277725\pi$
$53$	3.07682	+	5.32920i	0.422633	+	0.732022i	−0.573563	+	0.819162i	$0.694439\pi$
$54$	10.5456	−	0.268508i	1.43507	−	0.0365393i
$55$	−14.5628			−1.96365
$56$	−0.614496	−	0.220088i	−0.0821155	−	0.0294106i
$57$	0.268216	−	0.924380i	0.0355261	−	0.122437i
$58$	−1.46908	+	1.23270i	−0.192899	+	0.161862i
$59$	−8.92291	−	3.24767i	−1.16166	−	0.422811i	−0.311972	−	0.950091i	$-0.600990\pi$
$59$	−8.92291	−	3.24767i	−1.16166	−	0.422811i	−0.849691	+	0.527280i	$0.823212\pi$
$60$	−8.38341	−	4.12160i	−1.08229	−	0.532097i
$61$	0.889765	−	5.04611i	0.113923	−	0.646088i	−0.873355	−	0.487084i	$-0.838061\pi$
$61$	0.889765	−	5.04611i	0.113923	−	0.646088i	0.987278	−	0.159004i	$-0.0508283\pi$
$62$	5.07300	−	8.78669i	0.644271	−	1.11591i
$63$	7.86129	−	1.09553i	0.990429	−	0.138024i
$64$	4.47042	+	7.74299i	0.558802	+	0.967874i
$65$	−6.80608	+	2.47721i	−0.844190	+	0.307260i
$66$	20.0254	+	2.16855i	2.46495	+	0.266930i
$67$	7.29506	−	6.12129i	0.891234	−	0.747834i	−0.0772232	−	0.997014i	$-0.524605\pi$
$67$	7.29506	−	6.12129i	0.891234	−	0.747834i	0.968457	+	0.249180i	$0.0801610\pi$
$68$	9.64378	+	3.51005i	1.16948	+	0.425656i
$69$	4.72722	+	0.511912i	0.569090	+	0.0616269i
$70$	−12.8556	−	4.60437i	−1.53654	−	0.550327i
$71$	−5.28149	−	9.14782i	−0.626798	−	1.08565i	−0.988190	−	0.153232i	$-0.951032\pi$
$71$	−5.28149	−	9.14782i	−0.626798	−	1.08565i	0.361392	−	0.932414i	$-0.382302\pi$
$72$	0.625171	+	0.396148i	0.0736771	+	0.0466865i
$73$	−0.456492			−0.0534283			−0.0267141	−	0.999643i	$-0.508504\pi$
$73$	−0.456492			−0.0534283			−0.0267141	+	0.999643i	$0.508504\pi$
$74$	−12.6921	−	10.6499i	−1.47543	−	1.23803i
$75$	−2.27427	−	1.11812i	−0.262610	−	0.129109i
$76$	0.903117	−	0.757805i	0.103595	−	0.0869262i
$77$	15.1553	−	0.0778908i	1.72711	−	0.00887648i
$78$	9.72794	−	2.39292i	1.10147	−	0.270945i
$79$	2.52613	+	2.11967i	0.284212	+	0.238482i	0.773737	−	0.633507i	$-0.218385\pi$
$79$	2.52613	+	2.11967i	0.284212	+	0.238482i	−0.489525	+	0.871989i	$0.662830\pi$
$80$	4.75684	+	8.23909i	0.531831	+	0.921158i
$81$	−8.96945	−	0.740884i	−0.996606	−	0.0823204i
$82$	−11.2265	+	19.4448i	−1.23976	+	2.14732i
$83$	0.441119	−	2.50171i	0.0484190	−	0.274598i	−0.950980	−	0.309251i	$-0.899922\pi$
$83$	0.441119	−	2.50171i	0.0484190	−	0.274598i	0.999399	+	0.0346532i	$0.0110327\pi$
$84$	8.74656	+	4.24447i	0.954328	+	0.463109i
$85$	11.5564	+	4.20618i	1.25347	+	0.456225i
$86$	2.21007	+	12.5339i	0.238318	+	1.35157i
$87$	1.35930	−	0.910645i	0.145733	−	0.0976314i
$88$	1.08257	+	0.908382i	0.115402	+	0.0968339i
$89$	3.34817	+	5.79919i	0.354905	+	0.614713i	0.987102	−	0.160095i	$-0.0511799\pi$
$89$	3.34817	+	5.79919i	0.354905	+	0.614713i	−0.632197	+	0.774808i	$0.717847\pi$
$90$	13.0789	+	8.28763i	1.37864	+	0.873593i
$91$	7.06976	−	2.61441i	0.741112	−	0.274064i
$92$	4.46147	+	3.74362i	0.465140	+	0.390299i
$93$	−5.11001	+	6.98694i	−0.529884	+	0.724512i
$94$	4.63689	−	3.89081i	0.478259	−	0.401307i
$95$	1.08223	−	0.908098i	0.111034	−	0.0931689i
$96$	−5.65940	−	12.8198i	−0.577610	−	1.30841i
$97$	4.52344	+	3.79562i	0.459286	+	0.385387i	0.842868	−	0.538120i	$-0.180865\pi$
$97$	4.52344	+	3.79562i	0.459286	+	0.385387i	−0.383582	+	0.923507i	$0.625310\pi$
$98$	13.4033	+	4.72295i	1.35394	+	0.477090i
$99$	−16.7864	−	3.67875i	−1.68710	−	0.369728i
$100$	−1.55206	−	2.68825i	−0.155206	−	0.268825i
$101$	2.38567	+	2.00182i	0.237383	+	0.199188i	0.753717	−	0.657199i	$-0.228259\pi$
$101$	2.38567	+	2.00182i	0.237383	+	0.199188i	−0.516334	+	0.856388i	$0.672704\pi$
$102$	−15.2649	−	7.50480i	−1.51145	−	0.743086i
$103$	−2.15981	−	12.2489i	−0.212812	−	1.20692i	−0.884663	−	0.466232i	$-0.845611\pi$
$103$	−2.15981	−	12.2489i	−0.212812	−	1.20692i	0.671850	−	0.740687i	$-0.265500\pi$
$104$	0.660470	+	0.240391i	0.0647644	+	0.0235723i
$105$	10.4812	+	5.08626i	1.02286	+	0.496368i
$106$	2.16936	−	12.3030i	0.210706	−	1.19498i
$107$	3.72902	−	6.45885i	0.360498	−	0.624401i	−0.627545	−	0.778580i	$-0.715940\pi$
$107$	3.72902	−	6.45885i	0.360498	−	0.624401i	0.988043	+	0.154180i	$0.0492734\pi$
$108$	−8.62230	−	6.86868i	−0.829682	−	0.660939i
$109$	7.64451	+	13.2407i	0.732211	+	1.26823i	0.955936	+	0.293574i	$0.0948447\pi$
$109$	7.64451	+	13.2407i	0.732211	+	1.26823i	−0.223726	+	0.974652i	$0.571822\pi$
$110$	22.6479	+	19.0038i	2.15939	+	1.81194i
$111$	9.78727	+	10.1991i	0.928966	+	0.968057i
$112$	−4.99446	−	8.54888i	−0.471932	−	0.807793i
$113$	13.2747	−	11.1388i	1.24878	−	1.04785i	0.251998	−	0.967728i	$-0.418912\pi$
$113$	13.2747	−	11.1388i	1.24878	−	1.04785i	0.996785	−	0.0801258i	$-0.0255322\pi$
$114$	−1.62340	+	1.08757i	−0.152046	+	0.101861i
$115$	5.34630	+	4.48608i	0.498545	+	0.418329i
$116$	2.00405			0.186072
$117$	−8.47107	+	1.13616i	−0.783151	+	0.105038i
$118$	9.63872	+	16.6948i	0.887316	+	1.53688i
$119$	−12.0491	−	4.31552i	−1.10454	−	0.395603i
$120$	0.438722	+	0.993798i	0.0400496	+	0.0907210i
$121$	−20.4975	−	7.46047i	−1.86341	−	0.678224i
$122$	−7.96871	+	6.68654i	−0.721453	+	0.605371i
$123$	11.3084	−	15.4620i	1.01964	−	1.39416i
$124$	−9.96320	+	3.62631i	−0.894722	+	0.325652i
$125$	4.49581	+	7.78697i	0.402117	+	0.696488i
$126$	−13.6554	−	8.55489i	−1.21652	−	0.762130i
$127$	2.09524	−	3.62907i	0.185923	−	0.322027i	−0.757964	−	0.652296i	$-0.773806\pi$
$127$	2.09524	−	3.62907i	0.185923	−	0.322027i	0.943887	+	0.330268i	$0.107139\pi$
$128$	0.342087	−	1.94007i	0.0302365	−	0.171480i
$129$	−0.723321	−	10.8343i	−0.0636849	−	0.953910i
$130$	13.8174	+	5.02911i	1.21186	+	0.441083i
$131$	−2.06049	+	1.72895i	−0.180026	+	0.151059i	−0.728347	−	0.685208i	$-0.759711\pi$
$131$	−2.06049	+	1.72895i	−0.180026	+	0.151059i	0.548322	+	0.836267i	$0.315267\pi$
$132$	−14.5741	−	15.1873i	−1.26851	−	1.32189i
$133$	−1.12141	+	0.950836i	−0.0972383	+	0.0824479i
$134$	−19.3332			−1.67013
$135$	−10.3323	−	8.23093i	−0.889266	−	0.708405i
$136$	−0.596709	−	1.03353i	−0.0511674	−	0.0886245i
$137$	−2.15297	+	0.783616i	−0.183940	+	0.0669489i	−0.432348	−	0.901707i	$-0.642315\pi$
$137$	−2.15297	+	0.783616i	−0.183940	+	0.0669489i	0.248408	+	0.968656i	$0.420093\pi$
$138$	−6.68369	−	6.96494i	−0.568953	−	0.592895i
$139$	2.00556	+	0.729963i	0.170109	+	0.0619147i	0.425671	−	0.904878i	$-0.360038\pi$
$139$	2.00556	+	0.729963i	0.170109	+	0.0619147i	−0.255562	+	0.966793i	$0.582260\pi$
$140$	7.19833	+	12.3212i	0.608370	+	1.04133i
$141$	−4.29041	+	2.87429i	−0.361317	+	0.242059i
$142$	−3.72380	+	21.1187i	−0.312494	+	1.77224i
$143$	−16.3197			−1.36472
$144$	3.40187	+	10.6988i	0.283489	+	0.891563i
$145$	2.40151			0.199435
$146$	0.709930	+	0.595702i	0.0587542	+	0.0493006i
$147$	−10.9349	−	5.23715i	−0.901896	−	0.431953i
$148$	3.00655	+	17.0510i	0.247137	+	1.40158i
$149$	7.63172	+	2.77772i	0.625215	+	0.227560i	0.635147	−	0.772391i	$-0.280939\pi$
$149$	7.63172	+	2.77772i	0.625215	+	0.227560i	−0.00993237	+	0.999951i	$0.503162\pi$
$150$	2.07782	+	4.70671i	0.169653	+	0.384301i
$151$	−2.79284	+	15.8390i	−0.227278	+	1.28896i	0.631005	+	0.775779i	$0.282643\pi$
$151$	−2.79284	+	15.8390i	−0.227278	+	1.28896i	−0.858283	+	0.513177i	$0.828468\pi$
$152$	−0.137095			−0.0111199
$153$	12.2584	+	7.76771i	0.991033	+	0.627983i
$154$	−23.6711	−	19.6559i	−1.90747	−	1.58392i
$155$	−11.9392	+	4.34550i	−0.958977	+	0.349039i
$156$	−9.39478	−	4.61883i	−0.752185	−	0.369803i
$157$	−5.28662	−	1.92417i	−0.421918	−	0.153566i	0.122331	−	0.992489i	$-0.460963\pi$
$157$	−5.28662	−	1.92417i	−0.421918	−	0.153566i	−0.544249	+	0.838924i	$0.683185\pi$
$158$	−1.16252	−	6.59298i	−0.0924851	−	0.524509i
$159$	−2.97012	+	10.2362i	−0.235545	+	0.811785i
$160$	3.57170	−	20.2561i	0.282368	−	1.60139i
$161$	−5.58783	−	4.64001i	−0.440382	−	0.365684i
$162$	12.9824	+	12.8570i	1.01999	+	1.01014i
$163$	−0.362739	+	0.628282i	−0.0284119	+	0.0492108i	−0.879882	−	0.475193i	$-0.842378\pi$
$163$	−0.362739	+	0.628282i	−0.0284119	+	0.0492108i	0.851470	+	0.524404i	$0.175712\pi$
$164$	22.0484	−	8.02496i	1.72169	−	0.626644i
$165$	−17.4645	−	18.1994i	−1.35961	−	1.41682i
$166$	−3.95064	+	3.31498i	−0.306629	+	0.257293i
$167$	−4.91108	+	4.12088i	−0.380030	+	0.318883i	−0.812714	−	0.582662i	$-0.802011\pi$
$167$	−4.91108	+	4.12088i	−0.380030	+	0.318883i	0.432684	+	0.901546i	$0.357567\pi$
$168$	−0.461888	−	1.03189i	−0.0356354	−	0.0796119i
$169$	4.58884	−	1.67020i	0.352988	−	0.128477i
$170$	−12.4835	−	21.6220i	−0.957438	−	1.65833i
$171$	1.47687	−	0.773371i	0.112939	−	0.0591412i
$172$	6.65004	−	11.5182i	0.507061	−	0.878256i
$173$	16.9804	−	6.18036i	1.29100	−	0.469884i	0.396942	−	0.917844i	$-0.370071\pi$
$173$	16.9804	−	6.18036i	1.29100	−	0.469884i	0.894054	+	0.447959i	$0.147849\pi$
$174$	−3.30232	−	0.357609i	−0.250349	−	0.0271103i
$175$	1.95278	+	3.34253i	0.147616	+	0.252671i
$176$	3.72236	+	21.1106i	0.280584	+	1.59127i
$177$	−6.64215	−	15.0459i	−0.499255	−	1.13092i
$178$	2.36067	−	13.3880i	0.176940	−	1.00348i
$179$	6.06566	−	10.5060i	0.453369	−	0.785257i	−0.545224	−	0.838290i	$-0.683555\pi$
$179$	6.06566	−	10.5060i	0.453369	−	0.785257i	0.998593	+	0.0530329i	$0.0168888\pi$
$180$	−4.90299	−	15.4197i	−0.365447	−	1.14932i
$181$	−1.82583	+	3.16242i	−0.135713	+	0.235061i	−0.925869	−	0.377844i	$-0.876666\pi$
$181$	−1.82583	+	3.16242i	−0.135713	+	0.235061i	0.790157	+	0.612905i	$0.209999\pi$
$182$	−14.4065	−	5.15984i	−1.06788	−	0.382473i
$183$	7.37326	−	4.93960i	0.545047	−	0.365146i
$184$	−0.117605	−	0.666971i	−0.00866995	−	0.0491697i
$185$	3.60283	+	20.4326i	0.264885	+	1.50224i
$186$	17.0647	−	4.19765i	1.25124	−	0.307787i
$187$	21.2271	+	17.8117i	1.55228	+	1.30252i
$188$	−6.32545			−0.461331
$189$	10.7968	+	8.51057i	0.785349	+	0.619053i
$190$	−2.86810			−0.208074
$191$	−1.26218	−	1.05909i	−0.0913281	−	0.0766334i	0.595981	−	0.802999i	$-0.296764\pi$
$191$	−1.26218	−	1.05909i	−0.0913281	−	0.0766334i	−0.687309	+	0.726366i	$0.741208\pi$
$192$	−4.31539	+	14.8726i	−0.311436	+	1.07333i
$193$	−1.30894	−	7.42335i	−0.0942194	−	0.534345i	−0.994984	−	0.100037i	$-0.968104\pi$
$193$	−1.30894	−	7.42335i	−0.0942194	−	0.534345i	0.900764	−	0.434308i	$-0.143007\pi$
$194$	−2.08168	−	11.8058i	−0.149456	−	0.847607i
$195$	−11.2580	−	5.53487i	−0.806204	−	0.396360i
$196$	−7.55712	−	12.7840i	−0.539795	−	0.913145i
$197$	−3.93907	+	6.82267i	−0.280647	+	0.486095i	−0.971544	−	0.236858i	$-0.923882\pi$
$197$	−3.93907	+	6.82267i	−0.280647	+	0.486095i	0.690897	+	0.722953i	$0.257216\pi$
$198$	21.3054	+	27.6267i	1.51411	+	1.96334i
$199$	−0.493723	+	0.855154i	−0.0349991	+	0.0606202i	−0.882994	−	0.469384i	$-0.844476\pi$
$199$	−0.493723	+	0.855154i	−0.0349991	+	0.0606202i	0.847995	+	0.530004i	$0.177810\pi$
$200$	−0.0626816	+	0.355485i	−0.00443226	+	0.0251366i
$201$	16.3985	+	1.77580i	1.15666	+	0.125255i
$202$	−1.09788	−	6.22640i	−0.0772467	−	0.438088i
$203$	−2.49922	+	0.0128447i	−0.175411	+	0.000901525i
$204$	7.17876	+	16.2614i	0.502614	+	1.13853i
$205$	26.4212	−	9.61653i	1.84534	−	0.671647i
$206$	−12.6254	+	21.8678i	−0.879651	+	1.52360i
$207$	5.02939	+	6.52160i	0.349566	+	0.453282i
$208$	5.33071	+	9.23305i	0.369618	+	0.640197i
$209$	2.99124	−	1.08872i	0.206908	−	0.0753085i
$210$	−9.66294	−	21.5876i	−0.666806	−	1.48969i
$211$	−12.2920	+	10.3142i	−0.846215	+	0.710059i	−0.958953	−	0.283566i	$-0.908482\pi$
$211$	−12.2920	+	10.3142i	−0.846215	+	0.710059i	0.112738	+	0.993625i	$0.464038\pi$
$212$	−10.0008	+	8.39163i	−0.686855	+	0.576340i
$213$	5.09834	−	17.5709i	0.349332	−	1.20394i
$214$	−14.2279	+	5.17851i	−0.972596	+	0.353996i
$215$	7.96892	−	13.8026i	0.543476	−	0.941328i
$216$	0.254664	+	1.25637i	0.0173277	+	0.0854850i
$217$	12.4017	−	4.58617i	0.841883	−	0.311330i
$218$	5.38987	−	30.5675i	0.365048	−	2.07029i
$219$	−0.547449	−	0.570485i	−0.0369932	−	0.0385498i
$220$	−5.36491	−	30.4259i	−0.361702	−	2.05132i
$221$	12.9506	+	4.71362i	0.871149	+	0.317072i
$222$	−1.91163	−	28.6335i	−0.128300	−	1.92175i
$223$	5.45194	−	1.98434i	0.365089	−	0.132881i	−0.152960	−	0.988232i	$-0.548881\pi$
$223$	5.45194	−	1.98434i	0.365089	−	0.132881i	0.518049	+	0.855351i	$0.326658\pi$
$224$	−3.60869	+	21.0994i	−0.241116	+	1.40976i
$225$	−1.33009	−	4.18310i	−0.0886730	−	0.278874i
$226$	−35.1804			−2.34017
$227$	−4.38402	+	24.8630i	−0.290978	+	1.65022i	0.392138	+	0.919907i	$0.371736\pi$
$227$	−4.38402	+	24.8630i	−0.290978	+	1.65022i	−0.683115	+	0.730310i	$0.739375\pi$
$228$	2.03011	+	0.219841i	0.134447	+	0.0145593i
$229$	−19.3442	−	7.04070i	−1.27830	−	0.465263i	−0.388429	−	0.921478i	$-0.626982\pi$
$229$	−19.3442	−	7.04070i	−1.27830	−	0.465263i	−0.889869	+	0.456216i	$0.849205\pi$
$230$	−2.46036	−	13.9534i	−0.162231	−	0.920058i
$231$	18.2724	+	18.8465i	1.20224	+	1.24001i
$232$	−0.178523	−	0.149799i	−0.0117206	−	0.00983476i
$233$	28.9197			1.89460			0.947298	−	0.320355i	$-0.103802\pi$
$233$	28.9197			1.89460			0.947298	+	0.320355i	$0.103802\pi$
$234$	14.6567	+	9.28745i	0.958141	+	0.607140i
$235$	−7.57995			−0.494462
$236$	3.49815	−	19.8390i	0.227710	−	1.29141i
$237$	0.380474	+	5.69897i	0.0247145	+	0.370188i
$238$	13.1071	+	22.4350i	0.849604	+	1.45425i
$239$	−13.0309	−	4.74288i	−0.842902	−	0.306791i	−0.115759	−	0.993277i	$-0.536930\pi$
$239$	−13.0309	−	4.74288i	−0.842902	−	0.306791i	−0.727143	+	0.686486i	$0.759152\pi$
$240$	−4.59187	+	15.8255i	−0.296404	+	1.02153i
$241$	−7.61509	+	2.77167i	−0.490531	+	0.178539i	−0.575430	−	0.817851i	$-0.695165\pi$
$241$	−7.61509	+	2.77167i	−0.490531	+	0.178539i	0.0848993	+	0.996390i	$0.472943\pi$
$242$	22.1418	+	38.3507i	1.42333	+	2.46528i
$243$	−9.83075	−	12.0978i	−0.630643	−	0.776073i
$244$	10.8706			0.695917
$245$	−9.05590	−	15.3194i	−0.578560	−	0.978723i
$246$	−37.7639	+	9.28933i	−2.40774	+	0.592266i
$247$	1.21279	−	1.01765i	0.0771680	−	0.0647516i
$248$	1.15859	+	0.421693i	0.0735706	+	0.0267775i
$249$	3.65544	−	2.44891i	0.231654	−	0.155193i
$250$	3.16984	−	17.9770i	0.200478	−	1.13697i
$251$	1.46517	−	2.53775i	0.0924809	−	0.160182i	−0.816074	−	0.577948i	$-0.803854\pi$
$251$	1.46517	−	2.53775i	0.0924809	−	0.160182i	0.908554	+	0.417766i	$0.137187\pi$
$252$	5.18496	+	16.0209i	0.326622	+	1.00922i
$253$	7.86266	+	13.6185i	0.494321	+	0.856189i
$254$	−7.99427	+	2.90968i	−0.501605	+	0.182569i
$255$	8.60250	+	19.4865i	0.538709	+	1.22029i
$256$	10.6344	−	8.92335i	0.664652	−	0.557709i
$257$	−16.2975	−	5.93181i	−1.01661	−	0.370016i	−0.220643	−	0.975355i	$-0.570816\pi$
$257$	−16.2975	−	5.93181i	−1.01661	−	0.370016i	−0.795968	+	0.605339i	$0.793038\pi$
$258$	−13.0134	+	17.7933i	−0.810181	+	1.10776i
$259$	−3.85871	−	21.2448i	−0.239768	−	1.32008i
$260$	−7.68296	−	13.3073i	−0.476477	−	0.825282i
$261$	2.76820	+	0.606651i	0.171347	+	0.0375508i
$262$	5.46065			0.337360
$263$	−11.2893	−	9.47281i	−0.696125	−	0.584119i	0.224543	−	0.974464i	$-0.427911\pi$
$263$	−11.2893	−	9.47281i	−0.696125	−	0.584119i	−0.920668	+	0.390346i	$0.872356\pi$
$264$	0.163052	+	2.44228i	0.0100351	+	0.150312i
$265$	−11.9842	+	10.0559i	−0.736182	+	0.617730i
$266$	2.98480	−	0.0153404i	0.183010	−	0.000940577i
$267$	−3.23205	+	11.1390i	−0.197798	+	0.681693i
$268$	15.4766	+	12.9864i	0.945386	+	0.793273i
$269$	−15.0329	−	26.0378i	−0.916573	−	1.58755i	−0.804582	−	0.593842i	$-0.797610\pi$
$269$	−15.0329	−	26.0378i	−0.916573	−	1.58755i	−0.111992	−	0.993709i	$-0.535723\pi$
$270$	5.32771	+	26.2839i	0.324234	+	1.59959i
$271$	−9.41096	+	16.3003i	−0.571675	+	0.990170i	0.424719	+	0.905325i	$0.360373\pi$
$271$	−9.41096	+	16.3003i	−0.571675	+	0.990170i	−0.996394	+	0.0848450i	$0.972960\pi$
$272$	3.14348	−	17.8275i	0.190601	−	1.08095i
$273$	11.7457	+	5.69986i	0.710882	+	0.344971i
$274$	4.37085	+	1.59086i	0.264053	+	0.0961074i
$275$	−1.45541	−	8.25402i	−0.0877643	−	0.497736i
$276$	0.671967	+	10.0651i	0.0404477	+	0.605849i
$277$	23.2185	+	19.4826i	1.39506	+	1.17060i	0.963242	+	0.268637i	$0.0865732\pi$
$277$	23.2185	+	19.4826i	1.39506	+	1.17060i	0.431821	+	0.901959i	$0.357871\pi$
$278$	−2.16645	−	3.75240i	−0.129935	−	0.225054i
$279$	−14.8599	+	1.99303i	−0.889639	+	0.119320i
$280$	0.279748	−	1.63565i	0.0167182	−	0.0977485i
$281$	−3.64722	−	3.06038i	−0.217575	−	0.182567i	0.527486	−	0.849564i	$-0.323135\pi$
$281$	−3.64722	−	3.06038i	−0.217575	−	0.182567i	−0.745060	+	0.666997i	$0.767579\pi$
$282$	10.4232	+	1.12873i	0.620694	+	0.0672150i
$283$	−7.53211	+	6.32019i	−0.447738	+	0.375696i	−0.838596	−	0.544755i	$-0.816623\pi$
$283$	−7.53211	+	6.32019i	−0.447738	+	0.375696i	0.390858	+	0.920451i	$0.372178\pi$
$284$	17.1667	−	14.4046i	1.01866	−	0.854756i
$285$	2.43273	+	0.263441i	0.144103	+	0.0156049i
$286$	25.3801	+	21.2965i	1.50076	+	1.25929i
$287$	−27.4448	+	10.1491i	−1.62002	+	0.599084i
$288$	9.23401	−	22.4468i	0.544120	−	1.32269i
$289$	−3.20033	−	5.54313i	−0.188255	−	0.326067i
$290$	−3.73480	−	3.13387i	−0.219315	−	0.184027i
$291$	0.681301	+	10.2049i	0.0399386	+	0.598224i
$292$	−0.168171	−	0.953743i	−0.00984144	−	0.0558136i
$293$	−19.5850	−	7.12836i	−1.14417	−	0.416443i	−0.300751	−	0.953703i	$-0.597237\pi$
$293$	−19.5850	−	7.12836i	−1.14417	−	0.416443i	−0.843417	+	0.537260i	$0.819460\pi$
$294$	10.1716	+	22.4143i	0.593219	+	1.30723i
$295$	4.19192	−	23.7736i	0.244063	−	1.38415i
$296$	1.00670	−	1.74365i	0.0585131	−	0.101348i
$297$	−15.5337	−	25.3900i	−0.901360	−	1.47328i
$298$	−8.24395	−	14.2789i	−0.477559	−	0.827157i
$299$	5.99128	+	5.02728i	0.346484	+	0.290735i
$300$	1.49824	−	5.16353i	0.0865007	−	0.298116i
$301$	−8.21934	+	14.4068i	−0.473755	+	0.830395i
$302$	25.0125	−	20.9880i	1.43931	−	1.20772i
$303$	0.359319	+	5.38210i	0.0206424	+	0.309193i
$304$	−1.59303	−	1.33671i	−0.0913663	−	0.0766654i
$305$	13.0265			0.745895
$306$	−8.92758	−	28.0769i	−0.510356	−	1.60505i
$307$	−16.2647	−	28.1714i	−0.928278	−	1.60782i	−0.786203	−	0.617968i	$-0.787956\pi$
$307$	−16.2647	−	28.1714i	−0.928278	−	1.60782i	−0.142075	−	0.989856i	$-0.545377\pi$
$308$	5.74594	+	31.6352i	0.327405	+	1.80258i
$309$	12.7175	−	17.3887i	0.723472	−	0.989206i
$310$	24.2383	+	8.82203i	1.37665	+	0.501058i
$311$	−4.85696	+	4.07547i	−0.275413	+	0.231099i	−0.770023	−	0.638016i	$-0.779755\pi$
$311$	−4.85696	+	4.07547i	−0.275413	+	0.231099i	0.494610	+	0.869115i	$0.335311\pi$
$312$	0.491649	+	1.11369i	0.0278342	+	0.0630503i
$313$	−25.5353	+	9.29409i	−1.44334	+	0.525333i	−0.940723	−	0.339176i	$-0.889852\pi$
$313$	−25.5353	+	9.29409i	−1.44334	+	0.525333i	−0.502617	+	0.864509i	$0.667630\pi$
$314$	5.71072	+	9.89125i	0.322274	+	0.558196i
$315$	6.21327	+	19.1983i	0.350078	+	1.08170i
$316$	−3.49799	+	6.05870i	−0.196777	+	0.340828i
$317$	−0.676743	+	3.83800i	−0.0380097	+	0.215564i	−0.997897	−	0.0648232i	$-0.979352\pi$
$317$	−0.676743	+	3.83800i	−0.0380097	+	0.215564i	0.959887	+	0.280387i	$0.0904628\pi$
$318$	17.9769	−	12.0434i	1.00809	−	0.675358i
$319$	5.08476	+	1.85070i	0.284692	+	0.103619i
$320$	−17.4122	+	14.6106i	−0.973373	+	0.816757i
$321$	12.5438	−	3.08558i	0.700125	−	0.172220i
$322$	2.63510	+	14.5080i	0.146848	+	0.808497i
$323$	−2.68817			−0.149574
$324$	−1.75641	−	19.0127i	−0.0975783	−	1.05626i
$325$	−2.08425	−	3.61003i	−0.115613	−	0.200248i
$326$	1.38401	−	0.503737i	0.0766531	−	0.0278994i
$327$	−7.37940	+	25.4324i	−0.408082	+	1.40641i
$328$	−2.56394	−	0.933199i	−0.141570	−	0.0515273i
$329$	7.88837	−	0.0405422i	0.434900	−	0.00223517i
$330$	3.41113	+	51.0939i	0.187776	+	2.81262i
$331$	4.84703	−	27.4889i	0.266417	−	1.51092i	−0.498554	−	0.866859i	$-0.666135\pi$
$331$	4.84703	−	27.4889i	0.266417	−	1.51092i	0.764971	−	0.644065i	$-0.222754\pi$
$332$	5.38930			0.295776
$333$	−1.00860	+	24.4626i	−0.0552709	+	1.34054i
$334$	13.0152			0.712161
$335$	18.5461	+	15.5620i	1.01328	+	0.850242i
$336$	4.69407	−	16.4939i	0.256082	−	0.899818i
$337$	−0.429872	−	2.43793i	−0.0234166	−	0.132802i	0.970858	−	0.239654i	$-0.0770341\pi$
$337$	−0.429872	−	2.43793i	−0.0234166	−	0.132802i	−0.994275	+	0.106852i	$0.965923\pi$
$338$	−9.31604	−	3.39076i	−0.506726	−	0.184433i
$339$	29.8402	+	3.23140i	1.62070	+	0.175505i
$340$	−4.53058	+	25.6942i	−0.245705	+	1.39346i
$341$	−28.6278			−1.55028
$342$	−3.30603	−	0.724518i	−0.178770	−	0.0391774i
$343$	9.50631	+	15.8943i	0.513293	+	0.858214i
$344$	−1.45335	+	0.528978i	−0.0783596	+	0.0285206i
$345$	0.805236	+	12.0613i	0.0433525	+	0.649358i
$346$	−34.4728	−	12.5471i	−1.85327	−	0.674535i
$347$	−3.76942	−	21.3774i	−0.202353	−	1.14760i	−0.901551	−	0.432673i	$-0.857571\pi$
$347$	−3.76942	−	21.3774i	−0.202353	−	1.14760i	0.699198	−	0.714928i	$-0.253541\pi$
$348$	2.40337	+	2.50450i	0.128834	+	0.134255i
$349$	−2.32120	+	13.1642i	−0.124251	+	0.704661i	0.857499	+	0.514485i	$0.172017\pi$
$349$	−2.32120	+	13.1642i	−0.124251	+	0.704661i	−0.981750	+	0.190176i	$0.939094\pi$
$350$	1.32491	−	7.74655i	0.0708195	−	0.414071i
$351$	−11.5788	−	9.22391i	−0.618032	−	0.492336i
$352$	23.1726	−	40.1361i	1.23510	−	2.13926i
$353$	8.39653	−	3.05609i	0.446902	−	0.162659i	−0.108758	−	0.994068i	$-0.534688\pi$
$353$	8.39653	−	3.05609i	0.446902	−	0.162659i	0.555661	+	0.831409i	$0.312465\pi$
$354$	−9.30446	+	32.0669i	−0.494526	+	1.70434i
$355$	20.5714	−	17.2614i	1.09181	−	0.916141i
$356$	−10.8827	+	9.13170i	−0.576784	+	0.483979i
$357$	−9.05675	−	20.2334i	−0.479334	−	1.07086i
$358$	−23.1431	+	8.42342i	−1.22315	+	0.445191i
$359$	6.48945	+	11.2401i	0.342500	+	0.593228i	0.984896	−	0.173145i	$-0.0553930\pi$
$359$	6.48945	+	11.2401i	0.342500	+	0.593228i	−0.642396	+	0.766373i	$0.722060\pi$
$360$	−0.715829	+	1.74009i	−0.0377275	+	0.0917110i
$361$	9.34560	−	16.1870i	0.491874	−	0.851950i
$362$	6.96633	−	2.53554i	0.366142	−	0.133265i
$363$	−15.2582	−	34.5630i	−0.800846	−	1.81409i
$364$	8.06674	+	13.8076i	0.422812	+	0.723717i
$365$	−0.201523	−	1.14290i	−0.0105482	−	0.0598219i
$366$	−17.9128	−	1.93978i	−0.936316	−	0.101394i
$367$	1.21615	−	6.89713i	0.0634825	−	0.360027i	−0.936474	−	0.350736i	$-0.885931\pi$
$367$	1.21615	−	6.89713i	0.0634825	−	0.360027i	0.999957	−	0.00929108i	$-0.00295749\pi$
$368$	5.13656	−	8.89679i	0.267762	−	0.463777i
$369$	32.8847	−	4.41055i	1.71191	−	0.229604i
$370$	21.0607	−	36.4781i	1.09489	−	1.89641i
$371$	12.4180	−	10.5292i	0.644711	−	0.546648i
$372$	−16.4803	−	8.10232i	−0.854462	−	0.420086i
$373$	−0.110958	−	0.629272i	−0.00574517	−	0.0325825i	0.981800	−	0.189916i	$-0.0608215\pi$
$373$	−0.110958	−	0.629272i	−0.00574517	−	0.0325825i	−0.987546	+	0.157333i	$0.949710\pi$
$374$	−9.76867	−	55.4009i	−0.505126	−	2.86471i
$375$	−4.33990	+	14.9570i	−0.224111	+	0.772378i
$376$	0.563477	+	0.472814i	0.0290591	+	0.0243835i
$377$	2.69123			0.138605
$378$	−5.68507	−	27.3248i	−0.292408	−	1.40544i
$379$	5.13223			0.263625			0.131813	−	0.991275i	$-0.457920\pi$
$379$	5.13223			0.263625			0.131813	+	0.991275i	$0.457920\pi$
$380$	2.29597	+	1.92655i	0.117781	+	0.0988299i
$381$	7.04803	−	1.73371i	0.361081	−	0.0888205i
$382$	0.580853	+	3.29418i	0.0297190	+	0.168545i
$383$	0.138926	+	0.787888i	0.00709878	+	0.0402592i	0.988151	−	0.153482i	$-0.0490488\pi$
$383$	0.138926	+	0.787888i	0.00709878	+	0.0402592i	−0.981053	+	0.193741i	$0.937938\pi$
$384$	2.83479	−	1.89912i	0.144662	−	0.0969142i
$385$	6.88551	+	37.9093i	0.350918	+	1.93204i
$386$	−7.65152	+	13.2528i	−0.389452	+	0.674550i
$387$	12.6724	−	13.8971i	0.644175	−	0.706427i
$388$	−6.26372	+	10.8491i	−0.317992	+	0.550779i
$389$	−3.85385	+	21.8563i	−0.195398	+	1.10816i	0.716453	+	0.697635i	$0.245764\pi$
$389$	−3.85385	+	21.8563i	−0.195398	+	1.10816i	−0.911851	+	0.410521i	$0.865347\pi$
$390$	10.2856	+	23.2990i	0.520830	+	1.17979i
$391$	−2.30601	−	13.0780i	−0.116620	−	0.661384i
$392$	−0.282383	+	1.70369i	−0.0142625	+	0.0860495i
$393$	−4.63175	−	0.501573i	−0.233641	−	0.0253010i
$394$	15.0293	−	5.47021i	0.757164	−	0.275585i
$395$	−4.19173	+	7.26030i	−0.210909	+	0.365305i
$396$	1.50189	−	36.4269i	0.0754727	−	1.83052i
$397$	0.0990744	+	0.171602i	0.00497240	+	0.00861246i	0.868501	−	0.495688i	$-0.165084\pi$
$397$	0.0990744	+	0.171602i	0.00497240	+	0.00861246i	−0.863528	+	0.504300i	$0.831751\pi$
$398$	1.88377	−	0.685637i	0.0944249	−	0.0343679i
$399$	−2.53313	−	0.261148i	−0.126815	−	0.0130738i
$400$	−4.19442	+	3.51953i	−0.209721	+	0.175977i
$401$	−10.4032	+	8.72931i	−0.519510	+	0.435921i	−0.864461	−	0.502700i	$-0.832340\pi$
$401$	−10.4032	+	8.72931i	−0.519510	+	0.435921i	0.344951	+	0.938621i	$0.387896\pi$
$402$	−23.1854	−	24.1610i	−1.15638	−	1.20504i
$403$	−13.3795	+	4.86975i	−0.666481	+	0.242579i
$404$	−3.30350	+	5.72182i	−0.164355	+	0.284671i
$405$	−2.10475	−	22.7835i	−0.104586	−	1.13212i
$406$	3.90352	+	3.24140i	0.193729	+	0.160868i
$407$	−8.11790	+	46.0389i	−0.402389	+	2.28206i
$408$	0.576016	−	1.98518i	0.0285170	−	0.0982811i
$409$	1.40459	+	7.96584i	0.0694526	+	0.393885i	0.999641	+	0.0268022i	$0.00853244\pi$
$409$	1.40459	+	7.96584i	0.0694526	+	0.393885i	−0.930188	+	0.367083i	$0.880356\pi$
$410$	−53.6390	−	19.5230i	−2.64904	−	0.964173i
$411$	−3.56125	−	1.75085i	−0.175664	−	0.0863629i
$412$	24.7958	−	9.02493i	1.22160	−	0.444627i
$413$	−4.23533	+	24.7633i	−0.208407	+	1.21852i
$414$	0.688768	−	16.7054i	0.0338511	−	0.821028i
$415$	6.45814			0.317018
$416$	4.00259	−	22.6998i	0.196243	−	1.11295i
$417$	1.49292	+	3.38179i	0.0731088	+	0.165607i
$418$	−6.07268	−	2.21027i	−0.297024	−	0.108108i
$419$	3.04268	+	17.2559i	0.148644	+	0.843005i	0.964368	+	0.264563i	$0.0852278\pi$
$419$	3.04268	+	17.2559i	0.148644	+	0.843005i	−0.815724	+	0.578442i	$0.803661\pi$
$420$	−6.76539	+	23.7721i	−0.330117	+	1.15996i
$421$	14.4084	+	12.0901i	0.702223	+	0.589235i	0.922405	−	0.386223i	$-0.126221\pi$
$421$	14.4084	+	12.0901i	0.702223	+	0.589235i	−0.220182	+	0.975459i	$0.570665\pi$
$422$	32.5759			1.58577
$423$	−8.73734	−	1.91479i	−0.424824	−	0.0931003i
$424$	1.51813			0.0737271
$425$	−1.22907	+	6.97039i	−0.0596185	+	0.338113i
$426$	−30.8582	+	20.6730i	−1.49508	+	1.00161i
$427$	−13.5565	+	0.0696737i	−0.656046	+	0.00337175i
$428$	14.8682	+	5.41158i	0.718681	+	0.261578i
$429$	−19.5714	−	20.3950i	−0.944916	−	0.984678i
$430$	−30.4049	+	11.0665i	−1.46626	+	0.533674i
$431$	−1.50044	−	2.59884i	−0.0722736	−	0.125182i	0.827624	−	0.561283i	$-0.189692\pi$
$431$	−1.50044	−	2.59884i	−0.0722736	−	0.125182i	−0.899897	+	0.436102i	$0.856359\pi$
$432$	−9.29072	+	17.0819i	−0.447000	+	0.821852i
$433$	−25.9071			−1.24502			−0.622508	−	0.782613i	$-0.713886\pi$
$433$	−25.9071			−1.24502			−0.622508	+	0.782613i	$0.713886\pi$
$434$	−25.2718	−	9.05135i	−1.21308	−	0.434479i
$435$	2.88002	+	3.00121i	0.138086	+	0.143897i
$436$	−24.8474	+	20.8494i	−1.18997	+	0.998506i
$437$	−1.43353	−	0.521761i	−0.0685748	−	0.0249592i
$438$	0.106927	+	1.60161i	0.00510915	+	0.0765278i
$439$	4.24499	−	24.0745i	0.202602	−	1.14901i	−0.698566	−	0.715546i	$-0.746178\pi$
$439$	4.24499	−	24.0745i	0.202602	−	1.14901i	0.901168	−	0.433469i	$-0.142711\pi$
$440$	−1.79636	+	3.11139i	−0.0856382	+	0.148330i
$441$	−6.56877	−	19.9462i	−0.312798	−	0.949820i
$442$	−13.9895	−	24.2305i	−0.665412	−	1.15253i
$443$	−4.17871	+	1.52093i	−0.198537	+	0.0722614i	−0.439375	−	0.898304i	$-0.644800\pi$
$443$	−4.17871	+	1.52093i	−0.198537	+	0.0722614i	0.240838	+	0.970565i	$0.422578\pi$
$444$	−17.7033	+	24.2058i	−0.840161	+	1.14876i
$445$	−13.0411	+	10.9428i	−0.618206	+	0.518736i
$446$	−11.0683	−	4.02852i	−0.524097	−	0.190756i
$447$	5.68100	+	12.8687i	0.268702	+	0.608668i
$448$	18.0426	−	15.2982i	0.852431	−	0.722773i
$449$	−2.20153	−	3.81316i	−0.103896	−	0.179954i	0.809390	−	0.587271i	$-0.199798\pi$
$449$	−2.20153	−	3.81316i	−0.103896	−	0.179954i	−0.913287	+	0.407317i	$0.866464\pi$
$450$	−3.39022	+	8.24123i	−0.159817	+	0.388495i
$451$	63.3529			2.98317
$452$	28.1626	+	23.6313i	1.32466	+	1.11152i
$453$	−23.1435	+	15.5047i	−1.08738	+	0.728473i
$454$	39.2632	−	32.9457i	1.84271	−	1.54622i
$455$	9.66659	+	16.5461i	0.453177	+	0.775691i
$456$	−0.164412	−	0.171330i	−0.00769927	−	0.00802326i
$457$	−31.8323	−	26.7105i	−1.48905	−	1.24946i	−0.895810	−	0.444438i	$-0.853404\pi$
$457$	−31.8323	−	26.7105i	−1.48905	−	1.24946i	−0.593241	−	0.805025i	$-0.702152\pi$
$458$	20.8960	+	36.1929i	0.976406	+	1.69118i
$459$	4.99348	+	24.6350i	0.233076	+	1.14986i
$460$	−7.40315	+	12.8226i	−0.345174	+	0.597858i
$461$	−4.35940	+	24.7234i	−0.203037	+	1.15148i	0.697461	+	0.716623i	$0.254313\pi$
$461$	−4.35940	+	24.7234i	−0.203037	+	1.15148i	−0.900499	+	0.434859i	$0.856798\pi$
$462$	−3.82320	−	53.1546i	−0.177871	−	2.47297i
$463$	21.8134	+	7.93944i	1.01376	+	0.368977i	0.794874	−	0.606774i	$-0.207537\pi$
$463$	21.8134	+	7.93944i	1.01376	+	0.368977i	0.218882	+	0.975751i	$0.429759\pi$
$464$	−0.613844	−	3.48128i	−0.0284970	−	0.161615i
$465$	−19.7487	−	9.70923i	−0.915825	−	0.450255i
$466$	−44.9756	−	37.7390i	−2.08346	−	1.74823i
$467$	3.42146	+	5.92613i	0.158326	+	0.274229i	0.934265	−	0.356579i	$-0.116057\pi$
$467$	3.42146	+	5.92613i	0.158326	+	0.274229i	−0.775939	+	0.630808i	$0.782724\pi$
$468$	−5.49449	−	17.2800i	−0.253983	−	0.798767i
$469$	−19.3839	−	16.0960i	−0.895066	−	0.743244i
$470$	11.7882	+	9.89151i	0.543751	+	0.456261i
$471$	−3.93532	−	8.91434i	−0.181330	−	0.410751i
$472$	−1.79454	+	1.50580i	−0.0826004	+	0.0693100i
$473$	27.5096	−	23.0833i	1.26489	−	1.06137i
$474$	6.84520	−	9.35946i	0.314410	−	0.429894i
$475$	0.622857	+	0.522639i	0.0285786	+	0.0239803i
$476$	4.57750	−	26.7639i	0.209809	−	1.22672i
$477$	−16.3543	+	8.56400i	−0.748811	+	0.392119i
$478$	14.0763	+	24.3809i	0.643836	+	1.11516i
$479$	−6.31239	−	5.29673i	−0.288421	−	0.242014i	0.487085	−	0.873355i	$-0.338060\pi$
$479$	−6.31239	−	5.29673i	−0.288421	−	0.242014i	−0.775505	+	0.631341i	$0.782505\pi$
$480$	29.5978	−	19.8286i	1.35095	−	0.905047i
$481$	4.03747	+	22.8976i	0.184093	+	1.04404i
$482$	15.4598	+	5.62690i	0.704174	+	0.256298i
$483$	−0.902511	−	12.5478i	−0.0410657	−	0.570942i
$484$	8.03585	−	45.5736i	0.365266	−	2.07153i
$485$	−7.50598	+	13.0007i	−0.340829	+	0.590333i
$486$	−0.498439	+	31.6430i	−0.0226096	+	1.43536i
$487$	−18.6466	−	32.2969i	−0.844958	−	1.46351i	−0.885658	−	0.464339i	$-0.846292\pi$
$487$	−18.6466	−	32.2969i	−0.844958	−	1.46351i	0.0406993	−	0.999171i	$-0.487041\pi$
$488$	−0.968362	−	0.812552i	−0.0438357	−	0.0367825i
$489$	−1.22019	+	0.300148i	−0.0551789	+	0.0135732i
$490$	−5.90759	+	35.6422i	−0.266878	+	1.61015i
$491$	3.56990	−	2.99550i	0.161107	−	0.135185i	−0.558670	−	0.829390i	$-0.688688\pi$
$491$	3.56990	−	2.99550i	0.161107	−	0.135185i	0.719778	+	0.694205i	$0.244244\pi$
$492$	36.4705	+	17.9303i	1.64422	+	0.808361i
$493$	−3.50050	−	2.93727i	−0.157655	−	0.132288i
$494$	−3.21411			−0.144610
$495$	1.79975	−	43.6513i	0.0808928	−	1.96198i
$496$	9.35108	+	16.1966i	0.419876	+	0.727247i
$497$	−21.3161	+	18.0738i	−0.956156	+	0.810721i
$498$	−8.88061	−	0.961683i	−0.397950	−	0.0430941i
$499$	2.08470	+	0.758770i	0.0933241	+	0.0339672i	0.388260	−	0.921550i	$-0.373076\pi$
$499$	2.08470	+	0.758770i	0.0933241	+	0.0339672i	−0.294936	+	0.955517i	$0.595298\pi$
$500$	−14.6130	+	12.2618i	−0.653513	+	0.548362i
$501$	−11.0396	−	1.19548i	−0.493211	−	0.0534099i
$502$	−5.59028	+	2.03469i	−0.249506	+	0.0908129i
$503$	6.91864	+	11.9834i	0.308487	+	0.534315i	0.978032	−	0.208457i	$-0.0668441\pi$
$503$	6.91864	+	11.9834i	0.308487	+	0.534315i	−0.669545	+	0.742772i	$0.733511\pi$
$504$	0.735648	−	1.81472i	0.0327684	−	0.0808342i
$505$	−3.95867	+	6.85661i	−0.176158	+	0.305115i
$506$	5.54368	−	31.4398i	0.246447	−	1.39767i
$507$	7.59046	+	3.73176i	0.337104	+	0.165733i
$508$	8.35405	+	3.04063i	0.370651	+	0.134906i
$509$	1.52005	−	1.27547i	0.0673751	−	0.0565344i	−0.608478	−	0.793571i	$-0.708220\pi$
$509$	1.52005	−	1.27547i	0.0673751	−	0.0565344i	0.675853	+	0.737036i	$0.263775\pi$
$510$	12.0505	−	41.5310i	0.533607	−	1.83903i
$511$	0.215836	+	1.18832i	0.00954802	+	0.0525682i
$512$	−32.1231			−1.41966
$513$	2.73764	+	0.918205i	0.120870	+	0.0405397i
$514$	17.6049	+	30.4926i	0.776520	+	1.34497i
$515$	29.7135	−	10.8148i	1.30933	−	0.476558i
$516$	22.3696	−	5.50258i	0.984766	−	0.242237i
$517$	−16.0492	−	5.84142i	−0.705842	−	0.256905i
$518$	−21.7225	+	38.0750i	−0.954431	+	1.67292i
$519$	28.0875	+	13.8089i	1.23290	+	0.606143i
$520$	−0.310284	+	1.75971i	−0.0136069	+	0.0771684i
$521$	28.4951			1.24839			0.624196	−	0.781268i	$-0.285427\pi$
$521$	28.4951			1.24839			0.624196	+	0.781268i	$0.285427\pi$
$522$	−3.51341	−	4.55583i	−0.153778	−	0.199403i
$523$	−41.5117			−1.81518			−0.907590	−	0.419857i	$-0.862080\pi$
$523$	−41.5117			−1.81518			−0.907590	+	0.419857i	$0.862080\pi$
$524$	−4.37137	−	3.66801i	−0.190964	−	0.160238i
$525$	−1.83533	+	6.44896i	−0.0801005	+	0.281456i
$526$	5.19530	+	29.4640i	0.226526	+	1.28469i
$527$	22.7178	+	8.26859i	0.989602	+	0.360186i
$528$	−21.9182	+	29.9688i	−0.953867	+	1.30423i
$529$	−2.68526	+	15.2289i	−0.116750	+	0.662124i
$530$	31.7602			1.37957
$531$	10.8375	−	26.3446i	0.470307	−	1.14326i
$532$	−2.39970	−	1.99266i	−0.104040	−	0.0863927i
$533$	29.6086	−	10.7767i	1.28249	−	0.466789i
$534$	19.5623	−	13.1055i	0.846544	−	0.567129i
$535$	17.8169	+	6.48483i	0.770293	+	0.280364i
$536$	−0.407966	−	2.31369i	−0.0176214	−	0.0999362i
$537$	20.4038	−	5.01903i	0.880490	−	0.216587i
$538$	−10.5992	+	60.1109i	−0.456963	+	2.59157i
$539$	−7.36844	−	39.4150i	−0.317381	−	1.69772i
$540$	13.3904	−	24.6195i	0.576230	−	1.05945i
$541$	6.73979	−	11.6737i	0.289766	−	0.501890i	−0.683987	−	0.729494i	$-0.739756\pi$
$541$	6.73979	−	11.6737i	0.289766	−	0.501890i	0.973754	+	0.227604i	$0.0730891\pi$
$542$	35.9069	−	13.0691i	1.54234	−	0.561364i
$543$	−6.14176	+	1.51078i	−0.263568	+	0.0648338i
$544$	−29.9813	+	25.1573i	−1.28544	+	1.07861i
$545$	−29.7753	+	24.9844i	−1.27543	+	1.07022i
$546$	−10.8287	−	24.1920i	−0.463425	−	1.03532i
$547$	−38.5140	+	14.0180i	−1.64674	+	0.599365i	−0.988199	−	0.153178i	$-0.951049\pi$
$547$	−38.5140	+	14.0180i	−1.64674	+	0.599365i	−0.658543	+	0.752543i	$0.728827\pi$
$548$	−2.43035	−	4.20949i	−0.103819	−	0.179821i
$549$	15.0155	+	3.29066i	0.640846	+	0.140442i
$550$	−8.50771	+	14.7358i	−0.362770	+	0.628336i
$551$	−0.493277	+	0.179538i	−0.0210143	+	0.00764858i
$552$	0.692487	−	0.946839i	0.0294742	−	0.0403002i
$553$	4.32346	−	7.57813i	0.183852	−	0.322255i
$554$	−10.6851	−	60.5982i	−0.453966	−	2.57457i
$555$	−21.2143	+	29.0064i	−0.900498	+	1.23125i
$556$	−0.786261	+	4.45911i	−0.0333449	+	0.189108i
$557$	2.11105	−	3.65645i	0.0894482	−	0.154929i	−0.817830	−	0.575460i	$-0.804823\pi$
$557$	2.11105	−	3.65645i	0.0894482	−	0.154929i	0.907278	+	0.420531i	$0.138156\pi$
$558$	25.7107	+	16.2920i	1.08842	+	0.689695i
$559$	8.93030	−	15.4677i	0.377711	−	0.654215i
$560$	19.1986	−	16.2784i	0.811287	−	0.687887i
$561$	3.19713	+	47.8885i	0.134983	+	2.02186i
$562$	1.67844	+	9.51893i	0.0708009	+	0.401532i
$563$	−5.09575	−	28.8994i	−0.214760	−	1.21797i	−0.881322	−	0.472516i	$-0.843346\pi$
$563$	−5.09575	−	28.8994i	−0.214760	−	1.21797i	0.666562	−	0.745450i	$-0.267765\pi$
$564$	−7.58581	−	7.90502i	−0.319420	−	0.332861i
$565$	33.7480	+	28.3180i	1.41979	+	1.19135i
$566$	19.9614			0.839041
$567$	2.31225	+	23.6992i	0.0971054	+	0.995274i
$568$	−2.60595			−0.109343
$569$	−8.40773	−	7.05492i	−0.352470	−	0.295758i	0.449311	−	0.893376i	$-0.351670\pi$
$569$	−8.40773	−	7.05492i	−0.352470	−	0.295758i	−0.801781	+	0.597618i	$0.796114\pi$
$570$	−3.43958	−	3.58431i	−0.144068	−	0.150130i
$571$	−1.29682	−	7.35465i	−0.0542704	−	0.307783i	0.945574	−	0.325406i	$-0.105501\pi$
$571$	−1.29682	−	7.35465i	−0.0542704	−	0.307783i	−0.999845	+	0.0176236i	$0.994390\pi$
$572$	−6.01214	−	34.0965i	−0.251380	−	1.42565i
$573$	−0.190104	−	2.84749i	−0.00794171	−	0.118956i
$574$	55.9260	+	20.0305i	2.33431	+	0.836056i
$575$	−2.00834	+	3.47855i	−0.0837538	+	0.145066i
$576$	−23.7617	+	12.4429i	−0.990072	+	0.518456i
$577$	−3.85645	+	6.67956i	−0.160546	+	0.278074i	−0.935065	−	0.354477i	$-0.884659\pi$
$577$	−3.85645	+	6.67956i	−0.160546	+	0.278074i	0.774519	+	0.632551i	$0.217992\pi$
$578$	−2.25644	+	12.7969i	−0.0938555	+	0.532281i
$579$	7.70735	−	10.5383i	0.320306	−	0.437956i
$580$	0.884712	+	5.01745i	0.0367357	+	0.208338i
$581$	−6.72091	+	0.0345421i	−0.278831	+	0.00143305i
$582$	12.2574	−	16.7596i	0.508088	−	0.694710i
$583$	−33.1238	+	12.0561i	−1.37185	+	0.499312i
$584$	−0.0563095	+	0.0975308i	−0.00233010	+	0.00403585i
$585$	−6.58419	−	20.7070i	−0.272223	−	0.856131i
$586$	21.1561	+	36.6435i	0.873952	+	1.51373i
$587$	−11.7083	+	4.26146i	−0.483252	+	0.175889i	−0.572146	−	0.820152i	$-0.693889\pi$
$587$	−11.7083	+	4.26146i	−0.483252	+	0.175889i	0.0888943	+	0.996041i	$0.471667\pi$
$588$	6.91352	−	24.7756i	0.285109	−	1.02173i
$589$	2.12747	−	1.78516i	0.0876607	−	0.0735561i
$590$	−37.5427	+	31.5021i	−1.54561	+	1.29692i
$591$	−13.2504	+	3.25938i	−0.545047	+	0.134073i
$592$	28.6987	−	10.4455i	1.17951	−	0.429307i
$593$	8.24951	−	14.2886i	0.338767	−	0.586761i	−0.645434	−	0.763816i	$-0.723324\pi$
$593$	8.24951	−	14.2886i	0.338767	−	0.586761i	0.984201	+	0.177055i	$0.0566569\pi$
$594$	−8.97498	+	59.7571i	−0.368248	+	2.45186i
$595$	5.48534	−	32.0719i	0.224877	−	1.31482i
$596$	−2.99195	+	16.9682i	−0.122555	+	0.695044i
$597$	−1.66080	+	0.408531i	−0.0679720	+	0.0167201i
$598$	−2.75718	−	15.6367i	−0.112749	−	0.639433i
$599$	41.2606	+	15.0176i	1.68586	+	0.613604i	0.994095	−	0.108514i	$-0.0346092\pi$
$599$	41.2606	+	15.0176i	1.68586	+	0.613604i	0.691769	+	0.722118i	$0.256831\pi$
$600$	−0.519427	+	0.347982i	−0.0212055	+	0.0142063i
$601$	−30.4547	+	11.0846i	−1.24227	+	0.452151i	−0.877784	−	0.479057i	$-0.840979\pi$
$601$	−30.4547	+	11.0846i	−1.24227	+	0.452151i	−0.364490	+	0.931207i	$0.618757\pi$
$602$	31.5829	−	11.6794i	1.28722	−	0.476017i
$603$	17.4467	+	22.6231i	0.710485	+	0.921285i
$604$	−34.1211			−1.38837
$605$	9.62957	−	54.6120i	0.391498	−	2.22029i
$606$	6.46460	−	8.83906i	0.262606	−	0.359062i
$607$	39.2272	+	14.2775i	1.59218	+	0.579507i	0.977807	−	0.209506i	$-0.0671855\pi$
$607$	39.2272	+	14.2775i	1.59218	+	0.579507i	0.614376	+	0.789013i	$0.289408\pi$
$608$	0.780721	+	4.42769i	0.0316624	+	0.179566i
$609$	−3.01325	−	3.10792i	−0.122103	−	0.125939i
$610$	−20.2586	−	16.9990i	−0.820248	−	0.688270i
$611$	−8.49440			−0.343647
$612$	−11.7130	+	28.4730i	−0.473471	+	1.15095i
$613$	−38.2771			−1.54600			−0.772999	−	0.634408i	$-0.781244\pi$
$613$	−38.2771			−1.54600			−0.772999	+	0.634408i	$0.781244\pi$
$614$	−11.4677	+	65.0365i	−0.462799	+	2.62466i
$615$	43.7036	+	21.4864i	1.76230	+	0.866414i
$616$	1.85281	−	3.24760i	0.0746519	−	0.130849i
$617$	31.1195	+	11.3266i	1.25282	+	0.455990i	0.881355	−	0.472455i	$-0.156632\pi$
$617$	31.1195	+	11.3266i	1.25282	+	0.455990i	0.371469	+	0.928445i	$0.378854\pi$
$618$	−42.4695	+	10.4469i	−1.70837	+	0.420234i
$619$	−9.82447	+	3.57581i	−0.394879	+	0.143724i	−0.531825	−	0.846854i	$-0.678494\pi$
$619$	−9.82447	+	3.57581i	−0.394879	+	0.143724i	0.136946	+	0.990579i	$0.456271\pi$
$620$	−13.4774	−	23.3435i	−0.541265	−	0.937498i
$621$	−2.11865	+	14.1064i	−0.0850184	+	0.566068i
$622$	12.8718			0.516112
$623$	13.5132	−	11.4578i	0.541394	−	0.459045i
$624$	−5.14584	+	17.7346i	−0.205998	+	0.709954i
$625$	−23.1154	+	19.3961i	−0.924614	+	0.775844i
$626$	51.8406	+	18.8684i	2.07197	+	0.754134i
$627$	4.94785	+	2.43255i	0.197598	+	0.0971467i
$628$	2.07257	−	11.7541i	0.0827046	−	0.469041i
$629$	19.7394	−	34.1897i	0.787063	−	1.36323i
$630$	15.3901	−	37.9650i	0.613158	−	1.51256i
$631$	3.39863	+	5.88659i	0.135297	+	0.234342i	0.925711	−	0.378232i	$-0.123468\pi$
$631$	3.39863	+	5.88659i	0.135297	+	0.234342i	−0.790414	+	0.612573i	$0.790134\pi$
$632$	0.764479	−	0.278248i	0.0304093	−	0.0110681i
$633$	−27.6310	−	2.99217i	−1.09823	−	0.118928i
$634$	6.06089	−	5.08569i	0.240709	−	0.201979i
$635$	10.0109	+	3.64366i	0.397270	+	0.144594i
$636$	−22.4806	−	2.43443i	−0.891414	−	0.0965314i
$637$	−10.1484	−	17.1676i	−0.402095	−	0.680205i
$638$	−5.49267	−	9.51358i	−0.217457	−	0.376646i
$639$	28.0729	−	14.7005i	1.11055	−	0.581543i
$640$	5.00828			0.197970
$641$	−3.75248	−	3.14871i	−0.148214	−	0.124367i	0.565666	−	0.824635i	$-0.308619\pi$
$641$	−3.75248	−	3.14871i	−0.148214	−	0.124367i	−0.713880	+	0.700268i	$0.753064\pi$
$642$	−23.5345	−	11.5704i	−0.928831	−	0.456649i
$643$	−16.7039	+	14.0162i	−0.658736	+	0.552745i	−0.909708	−	0.415249i	$-0.863694\pi$
$643$	−16.7039	+	14.0162i	−0.658736	+	0.552745i	0.250972	+	0.967994i	$0.419250\pi$
$644$	7.63579	−	13.3840i	0.300892	−	0.527402i
$645$	26.8061	−	6.59388i	1.05549	−	0.259634i
$646$	4.18061	+	3.50795i	0.164484	+	0.138018i
$647$	20.0922	+	34.8007i	0.789906	+	1.36816i	0.926024	+	0.377465i	$0.123204\pi$
$647$	20.0922	+	34.8007i	0.789906	+	1.36816i	−0.136118	+	0.990693i	$0.543462\pi$
$648$	−1.26470	+	1.82496i	−0.0496820	+	0.0716913i
$649$	27.1965	−	47.1058i	1.06756	−	1.84906i
$650$	−1.46953	+	8.33413i	−0.0576398	+	0.326892i
$651$	20.6042	+	9.99866i	0.807543	+	0.391878i
$652$	−1.44629	−	0.526408i	−0.0566413	−	0.0206157i
$653$	−0.728550	−	4.13181i	−0.0285104	−	0.161690i	0.967229	−	0.253907i	$-0.0817158\pi$
$653$	−0.728550	−	4.13181i	−0.0285104	−	0.161690i	−0.995739	+	0.0922169i	$0.970605\pi$
$654$	44.6645	−	29.9223i	1.74652	−	1.17006i
$655$	−5.23832	−	4.39548i	−0.204678	−	0.171745i
$656$	−20.6938	−	35.8427i	−0.807957	−	1.39942i
$657$	0.0564157	−	1.36831i	0.00220099	−	0.0533829i
$658$	−12.3208	−	10.2309i	−0.480315	−	0.398843i
$659$	−2.95798	−	2.48204i	−0.115226	−	0.0966864i	0.583354	−	0.812218i	$-0.301740\pi$
$659$	−2.95798	−	2.48204i	−0.115226	−	0.0966864i	−0.698580	+	0.715532i	$0.746185\pi$
$660$	31.5899	−	43.1930i	1.22964	−	1.68129i
$661$	−1.93691	+	1.62526i	−0.0753372	+	0.0632155i	−0.679679	−	0.733510i	$-0.737881\pi$
$661$	−1.93691	+	1.62526i	−0.0753372	+	0.0632155i	0.604341	+	0.796725i	$0.293436\pi$
$662$	−43.4098	+	36.4252i	−1.68717	+	1.41570i
$663$	9.64031	+	21.8374i	0.374398	+	0.848093i
$664$	−0.480084	−	0.402839i	−0.0186309	−	0.0156332i
$665$	−2.87562	−	2.38785i	−0.111512	−	0.0925970i
$666$	33.4912	−	36.7278i	1.29776	−	1.42317i
$667$	−1.29661	−	2.24579i	−0.0502049	−	0.0869574i
$668$	−10.4189	−	8.74253i	−0.403121	−	0.338259i
$669$	9.01812	+	4.43365i	0.348660	+	0.171415i
$670$	−8.53486	−	48.4036i	−0.329731	−	1.86999i
$671$	27.5812	+	10.0387i	1.06476	+	0.387541i
$672$	−30.6960	+	20.7937i	−1.18413	+	0.802135i
$673$	5.48831	−	31.1257i	0.211559	−	1.19981i	−0.675220	−	0.737616i	$-0.735952\pi$
$673$	5.48831	−	31.1257i	0.211559	−	1.19981i	0.886779	−	0.462193i	$-0.152937\pi$
$674$	−2.51286	+	4.35240i	−0.0967917	+	0.167648i
$675$	3.63258	−	6.67884i	0.139818	−	0.257069i
$676$	5.18005	+	8.97211i	0.199233	+	0.345081i
$677$	−34.7742	−	29.1790i	−1.33648	−	1.12144i	−0.982516	−	0.186181i	$-0.940389\pi$
$677$	−34.7742	−	29.1790i	−1.33648	−	1.12144i	−0.353964	−	0.935259i	$-0.615167\pi$
$678$	−42.1902	−	43.9656i	−1.62031	−	1.68849i
$679$	7.74186	−	13.5699i	0.297105	−	0.520764i
$680$	2.32418	−	1.95021i	0.0891281	−	0.0747873i
$681$	−36.3293	+	24.3383i	−1.39214	+	0.932644i
$682$	44.5217	+	37.3581i	1.70482	+	1.43052i
$683$	−34.2783			−1.31162			−0.655811	−	0.754925i	$-0.727673\pi$
$683$	−34.2783			−1.31162			−0.655811	+	0.754925i	$0.727673\pi$
$684$	2.15987	+	2.80071i	0.0825848	+	0.107088i
$685$	−2.91235	−	5.04434i	−0.111275	−	0.192735i
$686$	5.95733	−	37.1240i	0.227452	−	1.41740i
$687$	−14.3997	−	32.6183i	−0.549381	−	1.24447i
$688$	−22.0455	−	8.02389i	−0.840475	−	0.305908i
$689$	−13.4299	+	11.2691i	−0.511640	+	0.429317i
$690$	14.4872	−	19.8084i	0.551518	−	0.754092i
$691$	16.9571	−	6.17189i	0.645080	−	0.234790i	0.00129822	−	0.999999i	$-0.499587\pi$
$691$	16.9571	−	6.17189i	0.645080	−	0.234790i	0.643782	+	0.765209i	$0.277365\pi$
$692$	19.1681	+	33.2001i	0.728662	+	1.26208i
$693$	−1.63951	+	45.4371i	−0.0622797	+	1.72601i
$694$	−22.0345	+	38.1648i	−0.836417	+	1.44872i
$695$	−0.942198	+	5.34347i	−0.0357396	+	0.202689i
$696$	−0.0268884	−	0.402750i	−0.00101920	−	0.0152662i
$697$	−50.2741	−	18.2983i	−1.90427	−	0.693096i
$698$	20.7885	−	17.4437i	0.786858	−	0.660252i
$699$	34.6821	+	36.1415i	1.31180	+	1.36700i
$700$	−6.26410	+	5.31131i	−0.236761	+	0.200749i
$701$	22.9450			0.866620			0.433310	−	0.901245i	$-0.357345\pi$
$701$	22.9450			0.866620			0.433310	+	0.901245i	$0.357345\pi$
$702$	5.97045	+	29.4548i	0.225340	+	1.11170i
$703$	−2.26759	−	3.92757i	−0.0855236	−	0.148131i
$704$	−48.1268	+	17.5167i	−1.81385	+	0.660186i
$705$	−9.09028	−	9.47280i	−0.342360	−	0.356766i
$706$	−17.0462	−	6.20433i	−0.641544	−	0.233503i
$707$	4.08307	−	7.15677i	0.153560	−	0.269158i
$708$	28.9883	−	19.4203i	1.08945	−	0.729858i
$709$	−2.63518	+	14.9449i	−0.0989664	+	0.561266i	0.894493	+	0.447082i	$0.147537\pi$
$709$	−2.63518	+	14.9449i	−0.0989664	+	0.561266i	−0.993460	+	0.114185i	$0.963574\pi$
$710$	−54.5178			−2.04601
$711$	−6.66581	+	7.30999i	−0.249987	+	0.274146i
$712$	1.65202			0.0619121
$713$	10.5099	+	8.81881i	0.393597	+	0.330267i
$714$	−12.3187	+	43.2853i	−0.461017	+	1.61991i
$715$	−7.20450	−	40.8588i	−0.269433	−	1.52803i
$716$	24.1847	+	8.80252i	0.903825	+	0.328965i
$717$	−9.70015	−	21.9729i	−0.362259	−	0.820593i
$718$	4.57548	−	25.9488i	0.170755	−	0.968402i
$719$	−42.4405			−1.58276			−0.791381	−	0.611323i	$-0.790638\pi$
$719$	−42.4405			−1.58276			−0.791381	+	0.611323i	$0.790638\pi$
$720$	−25.2842	+	13.2402i	−0.942285	+	0.493432i
$721$	−30.8646	+	11.4138i	−1.14946	+	0.425072i
$722$	−35.6576	+	12.9783i	−1.32704	+	0.483002i
$723$	−12.5962	−	6.19278i	−0.468458	−	0.230312i
$724$	−7.27985	−	2.64965i	−0.270554	−	0.0984735i
$725$	0.240007	+	1.36115i	0.00891363	+	0.0505517i
$726$	−21.3740	+	73.6632i	−0.793262	+	2.73390i
$727$	1.22040	−	6.92123i	0.0452621	−	0.256694i	−0.953777	−	0.300514i	$-0.902842\pi$
$727$	1.22040	−	6.92123i	0.0452621	−	0.256694i	0.999039	+	0.0438200i	$0.0139528\pi$
$728$	0.313497	−	1.83297i	0.0116190	−	0.0679344i
$729$	3.32926	−	26.7940i	0.123306	−	0.992369i
$730$	−1.17802	+	2.04040i	−0.0436006	+	0.0755185i
$731$	−28.4975	+	10.3722i	−1.05402	+	0.383632i
$732$	13.0366	+	13.5851i	0.481845	+	0.502121i
$733$	25.1453	−	21.0994i	0.928763	−	0.779325i	−0.0468316	−	0.998903i	$-0.514912\pi$
$733$	25.1453	−	21.0994i	0.928763	−	0.779325i	0.975595	+	0.219578i	$0.0704680\pi$
$734$	−10.8918	+	9.13930i	−0.402024	+	0.337338i
$735$	8.28466	−	29.6892i	0.305584	−	1.09510i
$736$	−20.8711	+	7.59645i	−0.769318	+	0.280009i
$737$	27.2752	+	47.2420i	1.00469	+	1.74018i
$738$	−56.8974	−	36.0539i	−2.09442	−	1.32716i
$739$	−2.89676	+	5.01734i	−0.106559	+	0.184566i	−0.914374	−	0.404870i	$-0.867317\pi$
$739$	−2.89676	+	5.01734i	−0.106559	+	0.184566i	0.807815	+	0.589436i	$0.200650\pi$
$740$	−41.3624	+	15.0547i	−1.52051	+	0.553422i
$741$	2.72622	+	0.295223i	0.100150	+	0.0108453i
$742$	−33.0525	+	0.169873i	−1.21339	+	0.00623623i
$743$	3.82255	+	21.6788i	0.140236	+	0.795317i	0.971070	+	0.238797i	$0.0767529\pi$
$743$	3.82255	+	21.6788i	0.140236	+	0.795317i	−0.830834	+	0.556521i	$0.812136\pi$
$744$	0.862447	+	1.95363i	0.0316188	+	0.0716235i
$745$	−3.58533	+	20.3334i	−0.131356	+	0.744959i
$746$	−0.648613	+	1.12343i	−0.0237474	+	0.0411317i
$747$	7.44424	+	1.63141i	0.272370	+	0.0596901i
$748$	−29.3937	+	50.9113i	−1.07474	+	1.86150i
$749$	−18.5766	−	6.65340i	−0.678773	−	0.243110i
$750$	26.2676	−	17.5976i	0.959159	−	0.642574i
$751$	5.94584	+	33.7206i	0.216967	+	1.23048i	0.877461	+	0.479649i	$0.159236\pi$
$751$	5.94584	+	33.7206i	0.216967	+	1.23048i	−0.660494	+	0.750832i	$0.729653\pi$
$752$	1.93749	+	10.9881i	0.0706531	+	0.400694i
$753$	4.92859	−	1.21236i	0.179608	−	0.0441807i
$754$	−4.18536	−	3.51194i	−0.152422	−	0.127897i
$755$	−40.8882			−1.48807
$756$	−13.8035	+	25.6929i	−0.502030	+	0.934440i
$757$	7.63111			0.277357			0.138679	−	0.990337i	$-0.455714\pi$
$757$	7.63111			0.277357			0.138679	+	0.990337i	$0.455714\pi$
$758$	−7.98158	−	6.69734i	−0.289904	−	0.243259i
$759$	−7.58999	+	26.1581i	−0.275499	+	0.949481i
$760$	−0.0605221	−	0.343238i	−0.00219537	−	0.0124506i
$761$	8.38957	+	47.5796i	0.304122	+	1.72476i	0.627611	+	0.778527i	$0.284033\pi$
$761$	8.38957	+	47.5796i	0.304122	+	1.72476i	−0.323489	+	0.946232i	$0.604856\pi$
$762$	−13.2234	−	6.50114i	−0.479034	−	0.235511i
$763$	30.8532	−	26.1603i	1.11696	−	0.947065i
$764$	1.74777	−	3.02723i	0.0632321	−	0.109521i
$765$	−14.0360	+	34.1199i	−0.507474	+	1.23361i
$766$	0.812104	−	1.40661i	0.0293425	−	0.0508227i
$767$	4.69764	−	26.6416i	0.169622	−	0.961974i
$768$	23.9050	+	2.58868i	0.862599	+	0.0934110i
$769$	−4.98810	−	28.2889i	−0.179875	−	1.02012i	−0.932365	−	0.361519i	$-0.882258\pi$
$769$	−4.98810	−	28.2889i	−0.179875	−	1.02012i	0.752489	−	0.658604i	$-0.228853\pi$
$770$	38.7618	−	67.9414i	1.39688	−	2.44844i
$771$	−12.1318	−	27.4810i	−0.436914	−	0.989705i
$772$	15.0273	−	5.46950i	0.540845	−	0.196852i
$773$	−0.858660	+	1.48724i	−0.0308839	+	0.0534924i	−0.881054	−	0.473015i	$-0.843166\pi$
$773$	−0.858660	+	1.48724i	−0.0308839	+	0.0534924i	0.850170	+	0.526508i	$0.176499\pi$
$774$	−37.8430	+	5.07557i	−1.36024	+	0.182438i
$775$	−3.65618	−	6.33269i	−0.131334	−	0.227477i
$776$	1.36892	−	0.498248i	0.0491415	−	0.0178861i
$777$	21.9224	−	30.3001i	0.786461	−	1.08701i
$778$	34.5149	−	28.9615i	1.23742	−	1.03832i
$779$	−4.70805	+	3.95052i	−0.168683	+	0.141542i
$780$	7.41652	−	25.5603i	0.265554	−	0.915206i
$781$	56.8585	−	20.6948i	2.03456	−	0.740518i
$782$	−13.4800	+	23.3480i	−0.482043	+	0.834924i
$783$	2.56163	+	4.18699i	0.0915450	+	0.149631i
$784$	−19.8927	+	17.0434i	−0.710452	+	0.608693i
$785$	2.48362	−	14.0853i	0.0886441	−	0.502726i
$786$	6.54871	+	6.82427i	0.233585	+	0.243414i
$787$	−4.68669	−	26.5795i	−0.167062	−	0.947457i	−0.946913	−	0.321491i	$-0.895816\pi$
$787$	−4.68669	−	26.5795i	−0.167062	−	0.947457i	0.779850	−	0.625966i	$-0.215295\pi$
$788$	−15.7057	−	5.71640i	−0.559492	−	0.203638i
$789$	−1.70034	−	25.4687i	−0.0605337	−	0.906709i
$790$	15.9933	−	5.82109i	0.569016	−	0.207105i
$791$	−35.2727	−	29.2897i	−1.25415	−	1.04142i
$792$	−2.85662	+	3.13268i	−0.101506	+	0.111315i
$793$	14.5980			0.518391
$794$	0.0698539	−	0.396161i	0.00247902	−	0.0140592i
$795$	−26.9391	−	2.91724i	−0.955431	−	0.103464i
$796$	−1.96855	−	0.716494i	−0.0697734	−	0.0253955i
$797$	−2.90591	−	16.4802i	−0.102933	−	0.583760i	−0.992026	−	0.126034i	$-0.959775\pi$
$797$	−2.90591	−	16.4802i	−0.102933	−	0.583760i	0.889093	−	0.457726i	$-0.151336\pi$
$798$	3.59870	+	3.71176i	0.127393	+	0.131395i
$799$	11.0487	+	9.27098i	0.390876	+	0.327984i
$800$	11.8379			0.418532
$801$	−17.7966	+	9.31927i	−0.628812	+	0.329280i
$802$	27.5703			0.973540
$803$	0.454073	−	2.57518i	0.0160239	−	0.0908760i
$804$	2.33102	+	34.9154i	0.0822088	+	1.23137i
$805$	9.15017	−	16.0384i	0.322501	−	0.565278i
$806$	27.1625	+	9.88633i	0.956757	+	0.348231i
$807$	14.5116	−	50.0128i	0.510832	−	1.76053i
$808$	0.721973	−	0.262777i	0.0253989	−	0.00924445i
$809$	−3.95309	−	6.84695i	−0.138983	−	0.240726i	0.788129	−	0.615510i	$-0.211050\pi$
$809$	−3.95309	−	6.84695i	−0.138983	−	0.240726i	−0.927112	+	0.374784i	$0.877717\pi$
$810$	−26.4581	+	38.1792i	−0.929645	+	1.34148i
$811$	35.7609			1.25574			0.627868	−	0.778320i	$-0.283928\pi$
$811$	35.7609			1.25574			0.627868	+	0.778320i	$0.283928\pi$
$812$	−0.947546	−	5.21687i	−0.0332523	−	0.183076i
$813$	−31.6568	+	7.78709i	−1.11025	+	0.273105i
$814$	72.7036	−	61.0056i	2.54826	−	2.13824i
$815$	−1.73313	−	0.630809i	−0.0607090	−	0.0220963i
$816$	26.0492	−	17.4513i	0.911905	−	0.610917i
$817$	−0.604951	+	3.43085i	−0.0211646	+	0.120030i
$818$	8.21067	−	14.2213i	0.287079	−	0.497236i
$819$	6.96284	+	21.5144i	0.243301	+	0.751773i
$820$	29.8252	+	51.6588i	1.04154	+	1.80400i
$821$	30.5943	−	11.1354i	1.06775	−	0.388629i	0.252414	−	0.967619i	$-0.418776\pi$
$821$	30.5943	−	11.1354i	1.06775	−	0.388629i	0.815334	+	0.578991i	$0.196553\pi$
$822$	3.25363	+	7.37017i	0.113483	+	0.257064i
$823$	16.6425	−	13.9647i	0.580120	−	0.486778i	−0.304867	−	0.952395i	$-0.598612\pi$
$823$	16.6425	−	13.9647i	0.580120	−	0.486778i	0.884987	+	0.465617i	$0.154167\pi$
$824$	−2.88343	−	1.04948i	−0.100449	−	0.0365605i
$825$	8.56979	−	11.7175i	0.298362	−	0.407951i
$826$	38.9018	−	32.9847i	1.35357	−	1.14768i
$827$	−8.58158	−	14.8637i	−0.298411	−	0.516863i	0.677362	−	0.735650i	$-0.263123\pi$
$827$	−8.58158	−	14.8637i	−0.298411	−	0.516863i	−0.975773	+	0.218787i	$0.929790\pi$
$828$	−11.7727	+	12.9104i	−0.409129	+	0.448667i
$829$	−12.7054			−0.441276			−0.220638	−	0.975356i	$-0.570814\pi$
$829$	−12.7054			−0.441276			−0.220638	+	0.975356i	$0.570814\pi$
$830$	−10.0436	−	8.42760i	−0.348619	−	0.292526i
$831$	3.49706	+	52.3811i	0.121312	+	1.81708i
$832$	−19.5129	+	16.3732i	−0.676486	+	0.567640i
$833$	−5.53699	+	33.4062i	−0.191845	+	1.15746i
$834$	2.09132	−	7.20752i	0.0724164	−	0.249576i
$835$	−12.4853	−	10.4764i	−0.432072	−	0.362551i
$836$	3.37663	+	5.84849i	0.116783	+	0.202274i
$837$	−20.3115	−	16.1805i	−0.702068	−	0.559280i
$838$	17.7862	−	30.8067i	0.614416	−	1.06420i
$839$	3.40606	−	19.3167i	0.117590	−	0.666887i	−0.867845	−	0.496835i	$-0.834495\pi$
$839$	3.40606	−	19.3167i	0.117590	−	0.666887i	0.985435	−	0.170052i	$-0.0543936\pi$
$840$	2.37958	−	1.61195i	0.0821034	−	0.0556174i
$841$	26.4126	+	9.61339i	0.910778	+	0.331496i
$842$	−6.63073	−	37.6047i	−0.228510	−	1.29594i
$843$	−0.549328	−	8.22816i	−0.0189199	−	0.283393i
$844$	−26.0777	−	21.8818i	−0.897631	−	0.753202i
$845$	6.20739	+	10.7515i	0.213541	+	0.369864i
$846$	11.0895	+	14.3797i	0.381264	+	0.494385i
$847$	−9.72929	+	56.8856i	−0.334302	+	1.95461i
$848$	17.6405	+	14.8022i	0.605778	+	0.508308i
$849$	−16.9314	−	1.83350i	−0.581083	−	0.0629256i
$850$	11.0075	−	9.23638i	0.377554	−	0.316805i
$851$	17.1625	−	14.4011i	0.588324	−	0.493663i
$852$	38.5890	+	4.17881i	1.32204	+	0.143164i
$853$	−26.1797	−	21.9674i	−0.896376	−	0.752149i	0.0731024	−	0.997324i	$-0.476710\pi$
$853$	−26.1797	−	21.9674i	−0.896376	−	0.752149i	−0.969479	+	0.245175i	$0.921154\pi$
$854$	21.1739	+	17.5823i	0.724554	+	0.601655i
$855$	2.58823	+	3.35616i	0.0885157	+	0.114778i
$856$	−0.919969	−	1.59343i	−0.0314439	−	0.0544624i
$857$	1.99806	+	1.67657i	0.0682524	+	0.0572706i	0.676276	−	0.736649i	$-0.263593\pi$
$857$	1.99806	+	1.67657i	0.0682524	+	0.0572706i	−0.608023	+	0.793919i	$0.708037\pi$
$858$	3.82265	+	57.2578i	0.130503	+	1.95475i
$859$	0.897983	+	5.09272i	0.0306388	+	0.173761i	0.996287	−	0.0860905i	$-0.0274374\pi$
$859$	0.897983	+	5.09272i	0.0306388	+	0.173761i	−0.965649	+	0.259852i	$0.916326\pi$
$860$	31.7733	+	11.5645i	1.08346	+	0.394348i
$861$	−45.5968	−	22.1269i	−1.55393	−	0.754081i
$862$	−1.05791	+	5.99969i	−0.0360324	+	0.204350i
$863$	21.0794	−	36.5106i	0.717552	−	1.24284i	−0.244415	−	0.969671i	$-0.578596\pi$
$863$	21.0794	−	36.5106i	0.717552	−	1.24284i	0.961967	−	0.273166i	$-0.0880707\pi$
$864$	39.1260	−	15.3795i	1.33109	−	0.523220i
$865$	22.9697	+	39.7846i	0.780992	+	1.35272i
$866$	40.2904	+	33.8077i	1.36912	+	1.14883i
$867$	3.08934	−	10.6471i	0.104920	−	0.361595i
$868$	14.1506	+	24.2212i	0.480303	+	0.822123i
$869$	−14.4703	+	12.1420i	−0.490872	+	0.411890i
$870$	−0.562519	−	8.42574i	−0.0190712	−	0.285659i
$871$	20.7835	+	17.4394i	0.704221	+	0.590911i
$872$	3.77188			0.127732
$873$	−11.9362	+	13.0897i	−0.403980	+	0.443020i
$874$	1.54853	+	2.68213i	0.0523797	+	0.0907242i
$875$	18.1451	−	15.3851i	0.613415	−	0.520112i
$876$	0.990230	−	1.35394i	0.0334568	−	0.0457456i
$877$	41.7115	+	15.1817i	1.40850	+	0.512651i	0.930688	−	0.365814i	$-0.119209\pi$
$877$	41.7115	+	15.1817i	1.40850	+	0.512651i	0.477808	+	0.878464i	$0.341432\pi$
$878$	−38.0180	+	31.9009i	−1.28304	+	1.07660i
$879$	−14.5789	−	33.0244i	−0.491735	−	1.11389i
$880$	−51.2103	+	18.6390i	−1.72630	+	0.628321i
$881$	−10.1994	−	17.6658i	−0.343625	−	0.595176i	0.641478	−	0.767141i	$-0.278322\pi$
$881$	−10.1994	−	17.6658i	−0.343625	−	0.595176i	−0.985103	+	0.171966i	$0.944988\pi$
$882$	−15.8133	+	39.5921i	−0.532461	+	1.33313i
$883$	−11.3979	+	19.7418i	−0.383571	+	0.664364i	−0.991570	−	0.129574i	$-0.958639\pi$
$883$	−11.3979	+	19.7418i	−0.383571	+	0.664364i	0.607999	+	0.793938i	$0.291972\pi$
$884$	−5.07715	+	28.7940i	−0.170763	+	0.968446i
$885$	34.7374	−	23.2718i	1.16769	−	0.782273i
$886$	8.48342	+	3.08771i	0.285006	+	0.103734i
$887$	−6.02600	+	5.05642i	−0.202333	+	0.169778i	−0.738324	−	0.674446i	$-0.764383\pi$
$887$	−6.02600	+	5.05642i	−0.202333	+	0.169778i	0.535991	+	0.844224i	$0.319938\pi$
$888$	3.38636	−	0.832992i	0.113639	−	0.0279534i
$889$	−10.4377	−	3.73838i	−0.350069	−	0.125381i
$890$	34.5611			1.15849
$891$	13.1014	−	49.8618i	0.438914	−	1.67043i
$892$	6.15435	+	10.6596i	0.206063	+	0.356911i
$893$	1.55694	−	0.566681i	0.0521011	−	0.0189633i
$894$	7.95806	−	27.4267i	0.266157	−	0.917285i
$895$	28.9812	+	10.5483i	0.968734	+	0.352590i
$896$	−5.21206	+	0.0267874i	−0.174123	+	0.000894903i
$897$	0.902380	+	13.5164i	0.0301296	+	0.451299i
$898$	−1.55222	+	8.80307i	−0.0517982	+	0.293762i
$899$	4.72093			0.157452
$900$	8.24971	−	4.32000i	0.274990	−	0.144000i
$901$	29.7677			0.991707
$902$	−98.5257	−	82.6729i	−3.28055	−	2.75271i
$903$	−27.8615	+	7.00556i	−0.927173	+	0.233130i
$904$	−0.742371	−	4.21020i	−0.0246909	−	0.140029i
$905$	−8.72364	−	3.17515i	−0.289984	−	0.105545i
$906$	56.2255	+	6.08867i	1.86797	+	0.202282i
$907$	−9.55243	+	54.1745i	−0.317183	+	1.79884i	0.242524	+	0.970145i	$0.422025\pi$
$907$	−9.55243	+	54.1745i	−0.317183	+	1.79884i	−0.559707	+	0.828690i	$0.689086\pi$
$908$	−53.5611			−1.77749
$909$	−6.29518	+	6.90354i	−0.208798	+	0.228976i
$910$	6.55853	−	38.3467i	0.217413	−	1.27118i
$911$	−19.5461	+	7.11419i	−0.647590	+	0.235704i	−0.644869	−	0.764293i	$-0.723088\pi$
$911$	−19.5461	+	7.11419i	−0.647590	+	0.235704i	−0.00272069	+	0.999996i	$0.500866\pi$
$912$	−0.239935	−	3.59388i	−0.00794503	−	0.119005i
$913$	13.6739	+	4.97691i	0.452541	+	0.164712i
$914$	14.6492	+	83.0795i	0.484551	+	2.74803i
$915$	15.6221	+	16.2794i	0.516449	+	0.538181i
$916$	7.58371	−	43.0094i	0.250573	−	1.42107i
$917$	5.47497	+	4.54630i	0.180800	+	0.150132i
$918$	24.3818	−	44.8283i	0.804720	−	1.47955i
$919$	−13.8544	+	23.9965i	−0.457014	+	0.791571i	−0.998802	−	0.0489442i	$-0.984414\pi$
$919$	−13.8544	+	23.9965i	−0.457014	+	0.791571i	0.541788	+	0.840515i	$0.317748\pi$
$920$	1.61794	−	0.588883i	0.0533420	−	0.0194149i
$921$	15.7007	−	54.1109i	0.517355	−	1.78301i
$922$	39.0426	−	32.7606i	1.28580	−	1.07891i
$923$	23.0531	−	19.3439i	0.758802	−	0.636711i
$924$	−32.6442	+	45.1194i	−1.07392	+	1.48432i
$925$	−11.2209	+	4.08408i	−0.368941	+	0.134284i
$926$	−23.5634	−	40.8129i	−0.774340	−	1.34120i
$927$	36.9824	−	4.96014i	1.21466	−	0.162912i
$928$	−3.82133	+	6.61873i	−0.125441	+	0.217271i
$929$	30.6315	−	11.1490i	1.00499	−	0.365785i	0.213481	−	0.976947i	$-0.431520\pi$
$929$	30.6315	−	11.1490i	1.00499	−	0.365785i	0.791506	+	0.611162i	$0.209298\pi$
$930$	18.0428	+	40.8709i	0.591648	+	1.34021i
$931$	3.00540	+	2.46963i	0.0984979	+	0.0809390i
$932$	10.6540	+	60.4217i	0.348983	+	1.97918i
$933$	−10.9179	−	1.18230i	−0.357436	−	0.0387069i
$934$	2.41235	−	13.6811i	0.0789344	−	0.447659i
$935$	−35.2232	+	61.0084i	−1.15192	+	1.99519i
$936$	−0.802187	+	1.95002i	−0.0262203	+	0.0637384i
$937$	14.2370	−	24.6593i	0.465104	−	0.805583i	−0.534102	−	0.845420i	$-0.679350\pi$
$937$	14.2370	−	24.6593i	0.465104	−	0.805583i	0.999206	+	0.0398364i	$0.0126837\pi$
$938$	9.14103	+	50.3274i	0.298465	+	1.64325i
$939$	−42.2383	−	20.7659i	−1.37839	−	0.677671i
$940$	−2.79244	−	15.8367i	−0.0910794	−	0.516537i
$941$	−6.88134	−	39.0260i	−0.224325	−	1.27221i	−0.863971	−	0.503542i	$-0.832030\pi$
$941$	−6.88134	−	39.0260i	−0.224325	−	1.27221i	0.639645	−	0.768670i	$-0.279081\pi$
$942$	−5.51267	+	18.9989i	−0.179613	+	0.619017i
$943$	−23.2581	−	19.5159i	−0.757389	−	0.635525i
$944$	−35.5342			−1.15654
$945$	−16.5411	+	30.7884i	−0.538083	+	1.00155i
$946$	−72.9052			−2.37035
$947$	5.14758	+	4.31933i	0.167274	+	0.140359i	0.722582	−	0.691285i	$-0.242955\pi$
$947$	5.14758	+	4.31933i	0.167274	+	0.140359i	−0.555308	+	0.831645i	$0.687400\pi$
$948$	−11.7666	+	2.89441i	−0.382162	+	0.0940061i
$949$	−0.225835	−	1.28078i	−0.00733092	−	0.0415757i
$950$	−0.286638	−	1.62560i	−0.00929976	−	0.0527415i
$951$	−5.60800	+	3.75700i	−0.181852	+	0.121829i
$952$	−2.40831	+	2.04200i	−0.0780539	+	0.0661815i
$953$	6.10269	−	10.5702i	0.197685	−	0.342401i	−0.750092	−	0.661333i	$-0.769991\pi$
$953$	6.10269	−	10.5702i	0.197685	−	0.342401i	0.947778	+	0.318932i	$0.103324\pi$
$954$	36.6096	+	8.02302i	1.18528	+	0.259755i
$955$	2.09440	−	3.62761i	0.0677732	−	0.117387i
$956$	5.10867	−	28.9727i	0.165226	−	0.937044i
$957$	3.78506	+	8.57397i	0.122354	+	0.277157i
$958$	2.90495	+	16.4748i	0.0938548	+	0.532277i
$959$	3.05783	+	5.23402i	0.0987426	+	0.169015i
$960$	−39.1408	−	4.23856i	−1.26326	−	0.136799i
$961$	5.66023	−	2.06015i	0.182588	−	0.0664566i
$962$	23.6014	−	40.8789i	0.760940	−	1.31799i
$963$	18.8993	+	11.9758i	0.609020	+	0.385914i
$964$	−8.59620	−	14.8891i	−0.276865	−	0.479544i
$965$	18.0076	−	6.55425i	0.579687	−	0.210989i
$966$	−14.9707	+	20.6918i	−0.481674	+	0.665749i
$967$	−7.93227	+	6.65596i	−0.255084	+	0.214041i	−0.761358	−	0.648332i	$-0.775467\pi$
$967$	−7.93227	+	6.65596i	−0.255084	+	0.214041i	0.506274	+	0.862373i	$0.331023\pi$
$968$	−4.12237	+	3.45908i	−0.132498	+	0.111179i
$969$	−3.22380	−	3.35945i	−0.103563	−	0.107921i
$970$	28.6386	−	10.4236i	0.919531	−	0.334682i
$971$	−18.0985	+	31.3475i	−0.580808	+	1.00599i	0.414575	+	0.910015i	$0.363930\pi$
$971$	−18.0985	+	31.3475i	−0.580808	+	1.00599i	−0.995384	+	0.0959748i	$0.969403\pi$
$972$	21.6542	−	24.9961i	0.694557	−	0.801750i
$973$	0.951954	−	5.56593i	0.0305183	−	0.178435i
$974$	−13.1471	+	74.5607i	−0.421259	+	2.38908i
$975$	2.01197	−	6.93406i	0.0644347	−	0.222068i
$976$	−3.32967	−	18.8835i	−0.106580	−	0.604446i
$977$	−39.0034	−	14.1961i	−1.24783	−	0.454173i	−0.368162	−	0.929762i	$-0.620013\pi$
$977$	−39.0034	−	14.1961i	−1.24783	−	0.454173i	−0.879668	+	0.475589i	$0.842235\pi$
$978$	2.28930	+	1.12551i	0.0732038	+	0.0359898i
$979$	−36.0450	+	13.1193i	−1.15200	+	0.419295i
$980$	28.6706	−	24.5641i	0.915848	−	0.784670i
$981$	−40.6330	+	21.2777i	−1.29731	+	0.679344i
$982$	−9.46086			−0.301908
$983$	−3.31834	+	18.8192i	−0.105838	+	0.600240i	0.885044	+	0.465508i	$0.154128\pi$
$983$	−3.31834	+	18.8192i	−0.105838	+	0.600240i	−0.990882	+	0.134732i	$0.956983\pi$
$984$	−1.90858	−	4.32335i	−0.0608434	−	0.137823i
$985$	−18.8205	−	6.85012i	−0.599672	−	0.218263i
$986$	1.61092	+	9.13600i	0.0513023	+	0.290950i
$987$	9.51082	+	9.80961i	0.302733	+	0.312243i
$988$	2.57296	+	2.15897i	0.0818567	+	0.0686859i
$989$	−17.2101			−0.547250
$990$	−59.7621	+	65.5374i	−1.89936	+	2.08292i
$991$	29.3668			0.932868			0.466434	−	0.884556i	$-0.345539\pi$
$991$	29.3668			0.932868			0.466434	+	0.884556i	$0.345539\pi$
$992$	7.02132	−	39.8199i	0.222927	−	1.26428i
$993$	40.1661	−	26.9087i	1.27463	−	0.853921i
$994$	56.7360	−	0.291594i	1.79956	−	0.00924881i
$995$	−2.35897	−	0.858594i	−0.0747843	−	0.0272193i
$996$	6.46313	+	6.73510i	0.204792	+	0.213410i
$997$	−33.7574	+	12.2867i	−1.06911	+	0.389124i	−0.815843	−	0.578273i	$-0.803727\pi$
$997$	−33.7574	+	12.2867i	−1.06911	+	0.389124i	−0.253265	+	0.967397i	$0.581505\pi$
$998$	−2.25194	−	3.90048i	−0.0712840	−	0.123467i
$999$	−31.7809	+	28.0764i	−1.00550	+	0.888299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.79.4	yes	132
3.2	odd	2		567.2.u.a.478.19		132
7.4	even	3		189.2.w.a.25.19	yes	132
21.11	odd	6		567.2.w.a.235.4		132
27.13	even	9		189.2.w.a.121.19	yes	132
27.14	odd	18		567.2.w.a.415.4		132
189.67	even	9	inner	189.2.u.a.67.4	✓	132
189.95	odd	18		567.2.u.a.172.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.4	✓	132	189.67	even	9	inner
189.2.u.a.79.4	yes	132	1.1	even	1	trivial
189.2.w.a.25.19	yes	132	7.4	even	3
189.2.w.a.121.19	yes	132	27.13	even	9
567.2.u.a.172.19		132	189.95	odd	18
567.2.u.a.478.19		132	3.2	odd	2
567.2.w.a.235.4		132	21.11	odd	6
567.2.w.a.415.4		132	27.14	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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55519 - 1.30496i) q^{2} +(1.19925 + 1.24972i) q^{3} +(0.368398 + 2.08929i) q^{4} +(0.441461 + 2.50365i) q^{5} +(-0.234236 - 3.50852i) q^{6} +(-0.472815 - 2.60316i) q^{7} +(0.123353 - 0.213653i) q^{8} +(-0.123586 + 2.99745i) q^{9} +O(q^{10})\)	\(q+(-1.55519 - 1.30496i) q^{2} +(1.19925 + 1.24972i) q^{3} +(0.368398 + 2.08929i) q^{4} +(0.441461 + 2.50365i) q^{5} +(-0.234236 - 3.50852i) q^{6} +(-0.472815 - 2.60316i) q^{7} +(0.123353 - 0.213653i) q^{8} +(-0.123586 + 2.99745i) q^{9} +(2.58060 - 4.46974i) q^{10} +(-0.994702 + 5.64123i) q^{11} +(-2.16922 + 2.96598i) q^{12} +(0.494719 + 2.80569i) q^{13} +(-2.66170 + 4.66541i) q^{14} +(-2.59943 + 3.55421i) q^{15} +(3.51651 - 1.27990i) q^{16} +(2.41871 - 4.18933i) q^{17} +(4.10375 - 4.50033i) q^{18} +(-0.277852 - 0.481253i) q^{19} +(-5.06822 + 1.84468i) q^{20} +(2.68619 - 3.71273i) q^{21} +(8.90852 - 7.47513i) q^{22} +(2.10296 - 1.76459i) q^{23} +(0.414937 - 0.102068i) q^{24} +(-1.37492 + 0.500430i) q^{25} +(2.89193 - 5.00897i) q^{26} +(-3.89418 + 3.44026i) q^{27} +(5.26457 - 1.94685i) q^{28} +(0.164033 - 0.930279i) q^{29} +(8.68070 - 2.13532i) q^{30} +(0.867833 + 4.92173i) q^{31} +(-7.60271 - 2.76716i) q^{32} +(-8.24285 + 5.52217i) q^{33} +(-9.22845 + 3.35888i) q^{34} +(6.30868 - 2.33296i) q^{35} +(-6.30808 + 0.846050i) q^{36} +8.16114 q^{37} +(-0.195903 + 1.11102i) q^{38} +(-2.91303 + 3.98299i) q^{39} +(0.589368 + 0.214513i) q^{40} +(-1.92050 - 10.8917i) q^{41} +(-9.02249 + 2.26863i) q^{42} +(-4.80243 - 4.02972i) q^{43} -12.1526 q^{44} +(-7.55914 + 1.01384i) q^{45} -5.57321 q^{46} +(-0.517743 + 2.93627i) q^{47} +(5.81670 + 2.85971i) q^{48} +(-6.55289 + 2.46163i) q^{49} +(2.79130 + 1.01595i) q^{50} +(8.13612 - 2.00136i) q^{51} +(-5.67965 + 2.06722i) q^{52} +(3.07682 + 5.32920i) q^{53} +(10.5456 - 0.268508i) q^{54} -14.5628 q^{55} +(-0.614496 - 0.220088i) q^{56} +(0.268216 - 0.924380i) q^{57} +(-1.46908 + 1.23270i) q^{58} +(-8.92291 - 3.24767i) q^{59} +(-8.38341 - 4.12160i) q^{60} +(0.889765 - 5.04611i) q^{61} +(5.07300 - 8.78669i) q^{62} +(7.86129 - 1.09553i) q^{63} +(4.47042 + 7.74299i) q^{64} +(-6.80608 + 2.47721i) q^{65} +(20.0254 + 2.16855i) q^{66} +(7.29506 - 6.12129i) q^{67} +(9.64378 + 3.51005i) q^{68} +(4.72722 + 0.511912i) q^{69} +(-12.8556 - 4.60437i) q^{70} +(-5.28149 - 9.14782i) q^{71} +(0.625171 + 0.396148i) q^{72} -0.456492 q^{73} +(-12.6921 - 10.6499i) q^{74} +(-2.27427 - 1.11812i) q^{75} +(0.903117 - 0.757805i) q^{76} +(15.1553 - 0.0778908i) q^{77} +(9.72794 - 2.39292i) q^{78} +(2.52613 + 2.11967i) q^{79} +(4.75684 + 8.23909i) q^{80} +(-8.96945 - 0.740884i) q^{81} +(-11.2265 + 19.4448i) q^{82} +(0.441119 - 2.50171i) q^{83} +(8.74656 + 4.24447i) q^{84} +(11.5564 + 4.20618i) q^{85} +(2.21007 + 12.5339i) q^{86} +(1.35930 - 0.910645i) q^{87} +(1.08257 + 0.908382i) q^{88} +(3.34817 + 5.79919i) q^{89} +(13.0789 + 8.28763i) q^{90} +(7.06976 - 2.61441i) q^{91} +(4.46147 + 3.74362i) q^{92} +(-5.11001 + 6.98694i) q^{93} +(4.63689 - 3.89081i) q^{94} +(1.08223 - 0.908098i) q^{95} +(-5.65940 - 12.8198i) q^{96} +(4.52344 + 3.79562i) q^{97} +(13.4033 + 4.72295i) q^{98} +(-16.7864 - 3.67875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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