LMFDB - Embedded newform 189.2.u.a.4.8

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			4.8
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.203963 - 1.15673i) q^{2} +(-1.51129 - 0.846167i) q^{3} +(0.582964 - 0.212181i) q^{4} +(-3.41115 + 1.24156i) q^{5} +(-0.670539 + 1.92074i) q^{6} +(-1.99948 + 1.73265i) q^{7} +(-1.53891 - 2.66548i) q^{8} +(1.56800 + 2.55761i) q^{9} +O(q^{10})$	\(q+(-0.203963 - 1.15673i) q^{2} +(-1.51129 - 0.846167i) q^{3} +(0.582964 - 0.212181i) q^{4} +(-3.41115 + 1.24156i) q^{5} +(-0.670539 + 1.92074i) q^{6} +(-1.99948 + 1.73265i) q^{7} +(-1.53891 - 2.66548i) q^{8} +(1.56800 + 2.55761i) q^{9} +(2.13189 + 3.69255i) q^{10} +(0.000515903 + 0.000187773i) q^{11} +(-1.06057 - 0.172616i) q^{12} +(-2.69743 + 0.981783i) q^{13} +(2.41202 + 1.95947i) q^{14} +(6.20581 + 1.01005i) q^{15} +(-1.81888 + 1.52622i) q^{16} +(-2.53989 - 4.39921i) q^{17} +(2.63865 - 2.33541i) q^{18} +(1.08055 - 1.87157i) q^{19} +(-1.72514 + 1.44757i) q^{20} +(4.48791 - 0.926635i) q^{21} +(0.000111978 - 0.000635059i) q^{22} +(-1.20838 + 6.85309i) q^{23} +(0.0703100 + 5.33049i) q^{24} +(6.26426 - 5.25634i) q^{25} +(1.68583 + 2.91995i) q^{26} +(-0.205549 - 5.19209i) q^{27} +(-0.797992 + 1.43432i) q^{28} +(-7.97979 - 2.90441i) q^{29} +(-0.0974020 - 7.38445i) q^{30} +(-1.25345 + 0.456219i) q^{31} +(-2.57909 - 2.16412i) q^{32} +(-0.000620793 - 0.000720320i) q^{33} +(-4.57065 + 3.83523i) q^{34} +(4.66936 - 8.39279i) q^{35} +(1.45677 + 1.15829i) q^{36} -4.25405 q^{37} +(-2.38529 - 0.868174i) q^{38} +(4.90735 + 0.798712i) q^{39} +(8.55880 + 7.18169i) q^{40} +(3.15472 - 1.14822i) q^{41} +(-1.98723 - 5.00230i) q^{42} +(-1.87937 - 10.6584i) q^{43} +0.000340595 q^{44} +(-8.52411 - 6.77762i) q^{45} +8.17363 q^{46} +(6.51821 + 2.37243i) q^{47} +(4.04029 - 0.767490i) q^{48} +(0.995880 - 6.92880i) q^{49} +(-7.35783 - 6.17395i) q^{50} +(0.116042 + 8.79765i) q^{51} +(-1.36419 + 1.14469i) q^{52} +(2.44073 - 4.22748i) q^{53} +(-5.96391 + 1.29676i) q^{54} -0.00199295 q^{55} +(7.69536 + 2.66319i) q^{56} +(-3.21668 + 1.91416i) q^{57} +(-1.73203 + 9.82285i) q^{58} +(5.33053 + 4.47285i) q^{59} +(3.83207 - 0.727936i) q^{60} +(-1.54932 - 0.563906i) q^{61} +(0.783379 + 1.35685i) q^{62} +(-7.56663 - 2.39710i) q^{63} +(-4.35164 + 7.53726i) q^{64} +(7.98239 - 6.69802i) q^{65} +(-0.000706597 + 0.000865007i) q^{66} +(-2.57130 + 14.5826i) q^{67} +(-2.41409 - 2.02566i) q^{68} +(7.62507 - 9.33452i) q^{69} +(-10.6606 - 3.68938i) q^{70} +(-4.45552 + 7.71718i) q^{71} +(4.40422 - 8.11541i) q^{72} -3.56587 q^{73} +(0.867667 + 4.92078i) q^{74} +(-13.9149 + 2.64325i) q^{75} +(0.232810 - 1.32033i) q^{76} +(-0.00135689 + 0.000518427i) q^{77} +(-0.0770224 - 5.83938i) q^{78} +(-0.856561 - 4.85780i) q^{79} +(4.30958 - 7.46441i) q^{80} +(-4.08273 + 8.02068i) q^{81} +(-1.97163 - 3.41496i) q^{82} +(4.35490 + 1.58505i) q^{83} +(2.41967 - 1.49245i) q^{84} +(14.1258 + 11.8530i) q^{85} +(-11.9456 + 4.34783i) q^{86} +(9.60218 + 11.1416i) q^{87} +(-0.000293425 - 0.00166409i) q^{88} +(-0.167028 + 0.289300i) q^{89} +(-6.10127 + 11.2425i) q^{90} +(3.69238 - 6.63674i) q^{91} +(0.749654 + 4.25150i) q^{92} +(2.28037 + 0.371149i) q^{93} +(1.41479 - 8.02369i) q^{94} +(-1.36226 + 7.72576i) q^{95} +(2.06656 + 5.45296i) q^{96} +(1.55231 + 8.80360i) q^{97} +(-8.21786 + 0.261251i) q^{98} +(0.000328687 + 0.00161391i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.203963	−	1.15673i	−0.144223	−	0.817931i	−0.967987	−	0.250998i	$-0.919241\pi$
$2$	−0.203963	−	1.15673i	−0.144223	−	0.817931i	0.823764	−	0.566933i	$-0.191870\pi$
$3$	−1.51129	−	0.846167i	−0.872545	−	0.488534i
$3$	−1.51129	−	0.846167i	−0.872545	−	0.488534i
$4$	0.582964	−	0.212181i	0.291482	−	0.106091i
$5$	−3.41115	+	1.24156i	−1.52551	+	0.555241i	−0.962518	−	0.271219i	$-0.912573\pi$
$5$	−3.41115	+	1.24156i	−1.52551	+	0.555241i	−0.562995	+	0.826460i	$0.690351\pi$
$6$	−0.670539	+	1.92074i	−0.273746	+	0.784139i
$7$	−1.99948	+	1.73265i	−0.755734	+	0.654878i
$7$	−1.99948	+	1.73265i	−0.755734	+	0.654878i
$8$	−1.53891	−	2.66548i	−0.544088	−	0.942388i
$9$	1.56800	+	2.55761i	0.522668	+	0.852536i
$10$	2.13189	+	3.69255i	0.674163	+	1.16769i
$11$	0.000515903	0	0.000187773i	0.000155551	0	5.66158e-5i	0.342098	−	0.939664i	$-0.388863\pi$
$11$	0.000515903	0	0.000187773i	0.000155551	0	5.66158e-5i	−0.341942	+	0.939721i	$0.611085\pi$
$12$	−1.06057	−	0.172616i	−0.306160	−	0.0498301i
$13$	−2.69743	+	0.981783i	−0.748132	+	0.272298i	−0.687819	−	0.725882i	$-0.741432\pi$
$13$	−2.69743	+	0.981783i	−0.748132	+	0.272298i	−0.0603123	+	0.998180i	$0.519210\pi$
$14$	2.41202	+	1.95947i	0.644640	+	0.523690i
$15$	6.20581	+	1.01005i	1.60233	+	0.260793i
$16$	−1.81888	+	1.52622i	−0.454720	+	0.381555i
$17$	−2.53989	−	4.39921i	−0.616013	−	1.06697i	−0.990206	−	0.139614i	$-0.955414\pi$
$17$	−2.53989	−	4.39921i	−0.616013	−	1.06697i	0.374193	−	0.927351i	$-0.377920\pi$
$18$	2.63865	−	2.33541i	0.621935	−	0.550462i
$19$	1.08055	−	1.87157i	0.247895	−	0.429367i	−0.715046	−	0.699077i	$-0.753594\pi$
$19$	1.08055	−	1.87157i	0.247895	−	0.429367i	0.962942	+	0.269710i	$0.0869278\pi$
$20$	−1.72514	+	1.44757i	−0.385753	+	0.323685i
$21$	4.48791	−	0.926635i	0.979343	−	0.202208i
$22$	0.000111978	0	0.000635059i	2.38738e−5	0	0.000135395i
$23$	−1.20838	+	6.85309i	−0.251966	+	1.42897i	0.551778	+	0.833991i	$0.313950\pi$
$23$	−1.20838	+	6.85309i	−0.251966	+	1.42897i	−0.803743	+	0.594976i	$0.797161\pi$
$24$	0.0703100	+	5.33049i	0.0143520	+	1.08808i
$25$	6.26426	−	5.25634i	1.25285	−	1.05127i
$26$	1.68583	+	2.91995i	0.330619	+	0.572648i
$27$	−0.205549	−	5.19209i	−0.0395579	−	0.999217i
$28$	−0.797992	+	1.43432i	−0.150806	+	0.271062i
$29$	−7.97979	−	2.90441i	−1.48181	−	0.539335i	−0.530531	−	0.847665i	$-0.678008\pi$
$29$	−7.97979	−	2.90441i	−1.48181	−	0.539335i	−0.951279	+	0.308330i	$0.900230\pi$
$30$	−0.0974020	−	7.38445i	−0.0177831	−	1.34821i
$31$	−1.25345	+	0.456219i	−0.225126	+	0.0819393i	−0.452121	−	0.891957i	$-0.649332\pi$
$31$	−1.25345	+	0.456219i	−0.225126	+	0.0819393i	0.226994	+	0.973896i	$0.427110\pi$
$32$	−2.57909	−	2.16412i	−0.455924	−	0.382566i
$33$	−0.000620793	0	0.000720320i	−0.000108066	0	0.000125392i
$34$	−4.57065	+	3.83523i	−0.783861	+	0.657737i
$35$	4.66936	−	8.39279i	0.789267	−	1.41864i
$36$	1.45677	+	1.15829i	0.242794	+	0.193049i
$37$	−4.25405			−0.699362			−0.349681	−	0.936869i	$-0.613710\pi$
$37$	−4.25405			−0.699362			−0.349681	+	0.936869i	$0.613710\pi$
$38$	−2.38529	−	0.868174i	−0.386945	−	0.140836i
$39$	4.90735	+	0.798712i	0.785805	+	0.127896i
$40$	8.55880	+	7.18169i	1.35327	+	1.13552i
$41$	3.15472	−	1.14822i	0.492684	−	0.179322i	−0.0837167	−	0.996490i	$-0.526679\pi$
$41$	3.15472	−	1.14822i	0.492684	−	0.179322i	0.576400	+	0.817167i	$0.304457\pi$
$42$	−1.98723	−	5.00230i	−0.306636	−	0.771871i
$43$	−1.87937	−	10.6584i	−0.286601	−	1.62539i	−0.699512	−	0.714621i	$-0.746599\pi$
$43$	−1.87937	−	10.6584i	−0.286601	−	1.62539i	0.412911	−	0.910771i	$-0.364512\pi$
$44$	0.000340595	0		5.13466e−5	0
$45$	−8.52411	−	6.77762i	−1.27070	−	1.01035i
$46$	8.17363			1.20514
$47$	6.51821	+	2.37243i	0.950779	+	0.346055i	0.770413	−	0.637545i	$-0.220050\pi$
$47$	6.51821	+	2.37243i	0.950779	+	0.346055i	0.180365	+	0.983600i	$0.442272\pi$
$48$	4.04029	−	0.767490i	0.583166	−	0.110778i
$49$	0.995880	−	6.92880i	0.142269	−	0.989828i
$50$	−7.35783	−	6.17395i	−1.04055	−	0.873129i
$51$	0.116042	+	8.79765i	0.0162492	+	1.23192i
$52$	−1.36419	+	1.14469i	−0.189179	+	0.158740i
$53$	2.44073	−	4.22748i	0.335261	−	0.580689i	−0.648274	−	0.761407i	$-0.724509\pi$
$53$	2.44073	−	4.22748i	0.335261	−	0.580689i	0.983535	+	0.180718i	$0.0578423\pi$
$54$	−5.96391	+	1.29676i	−0.811586	+	0.176466i
$55$	−0.00199295			−0.000268730
$56$	7.69536	+	2.66319i	1.02834	+	0.355883i
$57$	−3.21668	+	1.91416i	−0.426060	+	0.253537i
$58$	−1.73203	+	9.82285i	−0.227427	+	1.28980i
$59$	5.33053	+	4.47285i	0.693976	+	0.582315i	0.920053	−	0.391794i	$-0.128145\pi$
$59$	5.33053	+	4.47285i	0.693976	+	0.582315i	−0.226077	+	0.974110i	$0.572590\pi$
$60$	3.83207	−	0.727936i	0.494718	−	0.0939762i
$61$	−1.54932	−	0.563906i	−0.198370	−	0.0722007i	0.240925	−	0.970544i	$-0.422549\pi$
$61$	−1.54932	−	0.563906i	−0.198370	−	0.0722007i	−0.439295	+	0.898343i	$0.644772\pi$
$62$	0.783379	+	1.35685i	0.0994892	+	0.172320i
$63$	−7.56663	−	2.39710i	−0.953306	−	0.302007i
$64$	−4.35164	+	7.53726i	−0.543955	+	0.942157i
$65$	7.98239	−	6.69802i	0.990093	−	0.830787i
$66$	−0.000706597	0	0.000865007i	−8.69761e−5	0	0.000106475i
$67$	−2.57130	+	14.5826i	−0.314134	+	1.78154i	0.262900	+	0.964823i	$0.415321\pi$
$67$	−2.57130	+	14.5826i	−0.314134	+	1.78154i	−0.577034	+	0.816720i	$0.695790\pi$
$68$	−2.41409	−	2.02566i	−0.292752	−	0.245648i
$69$	7.62507	−	9.33452i	0.917951	−	1.12374i
$70$	−10.6606	−	3.68938i	−1.27418	−	0.440965i
$71$	−4.45552	+	7.71718i	−0.528773	+	0.915861i	0.470664	+	0.882312i	$0.344014\pi$
$71$	−4.45552	+	7.71718i	−0.528773	+	0.915861i	−0.999437	+	0.0335489i	$0.989319\pi$
$72$	4.40422	−	8.11541i	0.519042	−	0.956411i
$73$	−3.56587			−0.417354			−0.208677	−	0.977985i	$-0.566916\pi$
$73$	−3.56587			−0.417354			−0.208677	+	0.977985i	$0.566916\pi$
$74$	0.867667	+	4.92078i	0.100864	+	0.572029i
$75$	−13.9149	+	2.64325i	−1.60675	+	0.305216i
$76$	0.232810	−	1.32033i	0.0267051	−	0.151452i
$77$	−0.00135689		0.000518427i	−0.000154631		5.90803e-5i
$78$	−0.0770224	−	5.83938i	−0.00872107	−	0.661180i
$79$	−0.856561	−	4.85780i	−0.0963706	−	0.546545i	−0.994319	−	0.106444i	$-0.966054\pi$
$79$	−0.856561	−	4.85780i	−0.0963706	−	0.546545i	0.897948	−	0.440101i	$-0.145057\pi$
$80$	4.30958	−	7.46441i	0.481826	−	0.834547i
$81$	−4.08273	+	8.02068i	−0.453636	+	0.891187i
$82$	−1.97163	−	3.41496i	−0.217730	−	0.377119i
$83$	4.35490	+	1.58505i	0.478013	+	0.173982i	0.569779	−	0.821798i	$-0.307029\pi$
$83$	4.35490	+	1.58505i	0.478013	+	0.173982i	−0.0917660	+	0.995781i	$0.529251\pi$
$84$	2.41967	−	1.49245i	0.264008	−	0.162839i
$85$	14.1258	+	11.8530i	1.53216	+	1.28563i
$86$	−11.9456	+	4.34783i	−1.28812	+	0.468839i
$87$	9.60218	+	11.1416i	1.02946	+	1.19451i
$88$	−0.000293425	−	0.00166409i	−3.12792e−5	−	0.000177393i
$89$	−0.167028	+	0.289300i	−0.0177049	+	0.0306658i	−0.874742	−	0.484589i	$-0.838969\pi$
$89$	−0.167028	+	0.289300i	−0.0177049	+	0.0306658i	0.857037	+	0.515255i	$0.172303\pi$
$90$	−6.10127	+	11.2425i	−0.643130	+	1.18506i
$91$	3.69238	−	6.63674i	0.387067	−	0.695720i
$92$	0.749654	+	4.25150i	0.0781568	+	0.443249i
$93$	2.28037	+	0.371149i	0.236463	+	0.0384863i
$94$	1.41479	−	8.02369i	0.145925	−	0.827581i
$95$	−1.36226	+	7.72576i	−0.139765	+	0.792646i
$96$	2.06656	+	5.45296i	0.210917	+	0.556540i
$97$	1.55231	+	8.80360i	0.157614	+	0.893871i	0.956357	+	0.292199i	$0.0943871\pi$
$97$	1.55231	+	8.80360i	0.157614	+	0.893871i	−0.798744	+	0.601671i	$0.794502\pi$
$98$	−8.21786	+	0.261251i	−0.830130	+	0.0263904i
$99$	0.000328687		0.00161391i	3.30343e−5		0.000162204i
$100$	2.53654	−	4.39341i	0.253654	−	0.439341i
$101$	0.734363	+	4.16478i	0.0730718	+	0.414411i	0.999299	+	0.0374443i	$0.0119217\pi$
$101$	0.734363	+	4.16478i	0.0730718	+	0.414411i	−0.926227	+	0.376966i	$0.876967\pi$
$102$	10.1528	−	1.92862i	1.00528	−	0.190962i
$103$	−5.28422	+	1.92330i	−0.520670	+	0.189508i	−0.588967	−	0.808157i	$-0.700465\pi$
$103$	−5.28422	+	1.92330i	−0.520670	+	0.189508i	0.0682979	+	0.997665i	$0.478243\pi$
$104$	6.76802	+	5.67905i	0.663659	+	0.556876i
$105$	−14.1585	+	8.73289i	−1.38172	+	0.852243i
$106$	−5.38786	−	1.96102i	−0.523316	−	0.190471i
$107$	1.16415	+	2.01637i	0.112543	+	0.194929i	0.916795	−	0.399359i	$-0.130767\pi$
$107$	1.16415	+	2.01637i	0.112543	+	0.194929i	−0.804252	+	0.594288i	$0.797434\pi$
$108$	−1.22149	−	2.98318i	−0.117538	−	0.287057i
$109$	6.34077	−	10.9825i	0.607336	−	1.05194i	−0.384342	−	0.923191i	$-0.625572\pi$
$109$	6.34077	−	10.9825i	0.607336	−	1.05194i	0.991678	−	0.128746i	$-0.0410951\pi$
$110$	0.000406488		0.00230531i	3.87571e−5		0.000219803i
$111$	6.42911	+	3.59963i	0.610224	+	0.341662i
$112$	0.992422	−	6.20313i	0.0937751	−	0.586141i
$113$	1.25181	−	7.09938i	0.117761	−	0.667854i	−0.867586	−	0.497288i	$-0.834329\pi$
$113$	1.25181	−	7.09938i	0.117761	−	0.667854i	0.985346	−	0.170566i	$-0.0545596\pi$
$114$	2.87025	+	3.33042i	0.268823	+	0.311922i
$115$	−4.38652	−	24.8772i	−0.409045	−	2.31981i
$116$	−5.26819			−0.489139
$117$	−6.74059	−	5.35952i	−0.623168	−	0.495488i
$118$	4.08665	−	7.07828i	0.376206	−	0.651608i
$119$	12.7007	+	4.39543i	1.16427	+	0.402929i
$120$	−6.85794	−	18.0958i	−0.626041	−	1.65191i
$121$	−8.42649	−	7.07066i	−0.766044	−	0.642788i
$122$	−0.336283	+	1.90716i	−0.0304457	+	0.172666i
$123$	−5.73928	−	0.934116i	−0.517494	−	0.0842264i
$124$	−0.633915	+	0.531918i	−0.0569273	+	0.0477676i
$125$	−5.76711	+	9.98892i	−0.515826	+	0.893436i
$126$	−1.22949	+	9.24146i	−0.109532	+	0.823295i
$127$	2.42965	+	4.20828i	0.215597	+	0.373425i	0.953457	−	0.301529i	$-0.0974969\pi$
$127$	2.42965	+	4.20828i	0.215597	+	0.373425i	−0.737860	+	0.674954i	$0.764164\pi$
$128$	3.27868	+	1.19334i	0.289797	+	0.105478i
$129$	−6.17852	+	17.6982i	−0.543989	+	1.55824i
$130$	−9.37590	−	7.86732i	−0.822321	−	0.690009i
$131$	−2.27814	+	12.9200i	−0.199042	+	1.12882i	0.707501	+	0.706712i	$0.249822\pi$
$131$	−2.27814	+	12.9200i	−0.199042	+	1.12882i	−0.906544	+	0.422112i	$0.861289\pi$
$132$	−0.000514738	0	0.000288200i	−4.48022e−5	0	2.50846e-5i
$133$	1.08222	+	5.61438i	0.0938403	+	0.486829i
$134$	17.3925			1.50248
$135$	7.14743	+	17.4558i	0.615153	+	1.50235i
$136$	−7.81732	+	13.5400i	−0.670330	+	1.16105i
$137$	0.752660	−	0.631556i	0.0643040	−	0.0539575i	−0.610069	−	0.792348i	$-0.708858\pi$
$137$	0.752660	−	0.631556i	0.0643040	−	0.0539575i	0.674373	+	0.738391i	$0.264414\pi$
$138$	−12.3527	−	6.91625i	−1.05153	−	0.588751i
$139$	−12.7170	−	10.6708i	−1.07864	−	0.905089i	−0.0828359	−	0.996563i	$-0.526398\pi$
$139$	−12.7170	−	10.6708i	−1.07864	−	0.905089i	−0.995807	+	0.0914740i	$0.970842\pi$
$140$	0.941277	−	5.88344i	0.0795524	−	0.497242i
$141$	−7.84344	−	9.10093i	−0.660537	−	0.766437i
$142$	9.83545	+	3.57981i	0.825373	+	0.300411i
$143$	−0.00157596			−0.000131789
$144$	−6.75549	−	2.25886i	−0.562957	−	0.188238i
$145$	30.8263			2.55998
$146$	0.727304	+	4.12475i	0.0601921	+	0.341366i
$147$	−7.36798	+	9.62875i	−0.607701	+	0.794166i
$148$	−2.47996	+	0.902630i	−0.203851	+	0.0741958i
$149$	−10.1419	−	8.51010i	−0.830860	−	0.697174i	0.124628	−	0.992204i	$-0.460226\pi$
$149$	−10.1419	−	8.51010i	−0.830860	−	0.697174i	−0.955488	+	0.295029i	$0.904671\pi$
$150$	5.89563	+	15.5566i	0.481377	+	1.27019i
$151$	11.6208	+	4.22964i	0.945690	+	0.344203i	0.768410	−	0.639957i	$-0.221048\pi$
$151$	11.6208	+	4.22964i	0.945690	+	0.344203i	0.177280	+	0.984161i	$0.443270\pi$
$152$	−6.65149			−0.539507
$153$	7.26891	−	13.3940i	0.587656	−	1.08284i
$154$	0.000876434		0.00146381i	7.06250e−5		0.000117957i
$155$	3.70929	−	3.11246i	0.297937	−	0.249999i
$156$	3.03028	−	0.575629i	0.242616	−	0.0460872i
$157$	−9.27592	−	7.78342i	−0.740299	−	0.621185i	0.192619	−	0.981274i	$-0.438302\pi$
$157$	−9.27592	−	7.78342i	−0.740299	−	0.621185i	−0.932918	+	0.360089i	$0.882746\pi$
$158$	−5.44445	+	1.98162i	−0.433137	+	0.157649i
$159$	−7.26581	+	4.32368i	−0.576216	+	0.342890i
$160$	11.4846	+	4.18004i	0.907934	+	0.330461i
$161$	−9.45782	−	15.7963i	−0.745381	−	1.24493i
$162$	10.1105	+	3.08669i	0.794354	+	0.242513i
$163$	−5.48069	−	9.49283i	−0.429281	−	0.743536i	0.567529	−	0.823354i	$-0.307900\pi$
$163$	−5.48069	−	9.49283i	−0.429281	−	0.743536i	−0.996809	+	0.0798174i	$0.974566\pi$
$164$	1.59545	−	1.33874i	0.124584	−	0.104538i
$165$	0.00301194	+	0.00168637i	0.000234479	+	0.000131284i
$166$	0.945242	−	5.36073i	0.0733650	−	0.416074i
$167$	0.770807	−	4.37146i	0.0596468	−	0.338274i	−0.940351	−	0.340205i	$-0.889504\pi$
$167$	0.770807	−	4.37146i	0.0596468	−	0.338274i	0.999998	+	0.00193094i	$0.000614637\pi$
$168$	−9.37643	−	10.5364i	−0.723407	−	0.812901i
$169$	−3.64636	+	3.05966i	−0.280490	+	0.235359i
$170$	10.8295	−	18.7573i	0.830586	−	1.43862i
$171$	6.48104	−	0.171002i	0.495618	−	0.0130768i
$172$	−3.35712	−	5.81470i	−0.255978	−	0.443367i
$173$	−1.77823	+	1.49211i	−0.135196	+	0.113443i	−0.707878	−	0.706335i	$-0.750347\pi$
$173$	−1.77823	+	1.49211i	−0.135196	+	0.113443i	0.572682	+	0.819778i	$0.305903\pi$
$174$	10.9294	−	13.3796i	0.828554	−	1.01431i
$175$	−3.41792	+	21.3637i	−0.258371	+	1.61494i
$176$	−0.00122495		0.000445845i	−9.23340e−5		3.36068e-5i
$177$	−4.27122	−	11.2703i	−0.321044	−	0.847127i
$178$	0.368709	+	0.134199i	0.0276359	+	0.0100587i
$179$	1.56939	+	2.71826i	0.117302	+	0.203172i	0.918697	−	0.394962i	$-0.129242\pi$
$179$	1.56939	+	2.71826i	0.117302	+	0.203172i	−0.801396	+	0.598134i	$0.795909\pi$
$180$	−6.40733	−	2.14245i	−0.477575	−	0.159689i
$181$	−1.69438	−	2.93476i	−0.125942	−	0.218139i	0.796158	−	0.605088i	$-0.206862\pi$
$181$	−1.69438	−	2.93476i	−0.125942	−	0.218139i	−0.922101	+	0.386949i	$0.873529\pi$
$182$	−8.43002	−	2.91744i	−0.624875	−	0.216255i
$183$	1.86431	+	2.16321i	0.137814	+	0.159909i
$184$	20.1263	−	7.32539i	1.48373	−	0.540035i
$185$	14.5112	−	5.28165i	1.06688	−	0.388314i
$186$	−0.0357911	−	2.71347i	−0.00262433	−	0.198961i
$187$	−0.000484280	−	0.00274649i	−3.54141e−5	−	0.000200843i
$188$	4.30327			0.313848
$189$	9.40703	+	10.0254i	0.684261	+	0.729237i
$190$	9.21446			0.668487
$191$	−0.188414	−	1.06855i	−0.0136332	−	0.0773176i	0.977232	−	0.212173i	$-0.0680541\pi$
$191$	−0.188414	−	1.06855i	−0.0136332	−	0.0773176i	−0.990865	+	0.134856i	$0.956943\pi$
$192$	12.9544	−	7.70878i	0.934901	−	0.556333i
$193$	9.37963	−	3.41391i	0.675161	−	0.245738i	0.0183924	−	0.999831i	$-0.494145\pi$
$193$	9.37963	−	3.41391i	0.675161	−	0.245738i	0.656768	+	0.754092i	$0.271923\pi$
$194$	9.86677	−	3.59121i	0.708393	−	0.257834i
$195$	−17.7314	+	3.36823i	−1.26977	+	0.241204i
$196$	−0.889600	−	4.25054i	−0.0635429	−	0.303610i
$197$	−4.71108	−	8.15983i	−0.335650	−	0.581364i	0.647959	−	0.761675i	$-0.275623\pi$
$197$	−4.71108	−	8.15983i	−0.335650	−	0.581364i	−0.983610	+	0.180311i	$0.942289\pi$
$198$	0.00179981		0.000709379i	0.000127907		5.04134e-5i
$199$	−1.32014	−	2.28655i	−0.0935822	−	0.162089i	0.815434	−	0.578850i	$-0.196498\pi$
$199$	−1.32014	−	2.28655i	−0.0935822	−	0.162089i	−0.909016	+	0.416761i	$0.863165\pi$
$200$	−23.6508	−	8.60818i	−1.67236	−	0.608690i
$201$	16.2253	−	19.8627i	1.14444	−	1.40101i
$202$	4.66774	−	1.69892i	0.328421	−	0.119535i
$203$	20.9878	−	8.01883i	1.47305	−	0.562812i
$204$	1.93435	+	5.10409i	0.135431	+	0.357358i
$205$	−9.33562	+	7.83352i	−0.652028	+	0.547117i
$206$	3.30252	+	5.72013i	0.230097	+	0.398540i
$207$	−19.4223	+	7.65510i	−1.34994	+	0.532066i
$208$	3.40788	−	5.90261i	0.236294	−	0.409273i
$209$	0.000908890	0	0.000762649i	6.28692e−5	0	5.27535e-5i
$210$	12.9894	+	14.5963i	0.896353	+	1.00724i
$211$	−4.06625	+	23.0609i	−0.279932	+	1.58758i	0.442912	+	0.896565i	$0.353945\pi$
$211$	−4.06625	+	23.0609i	−0.279932	+	1.58758i	−0.722844	+	0.691011i	$0.757166\pi$
$212$	0.525868	−	2.98234i	0.0361167	−	0.204828i
$213$	13.2636	−	7.89280i	0.908808	−	0.540806i
$214$	2.09495	−	1.75787i	0.143208	−	0.120165i
$215$	19.6438	+	34.0241i	1.33970	+	2.32042i
$216$	−13.5231	+	8.53805i	−0.920127	+	0.580941i
$217$	1.71579	−	3.08399i	0.116475	−	0.209355i
$218$	−13.9971	−	5.09453i	−0.948004	−	0.345045i
$219$	5.38907	+	3.01732i	0.364160	+	0.203892i
$220$	−0.00116182		0.000422868i	−7.83299e−5		2.85097e-5i
$221$	11.1702	+	9.37293i	0.751391	+	0.630492i
$222$	2.85250	−	8.17093i	0.191448	−	0.548397i
$223$	0.440602	−	0.369709i	0.0295049	−	0.0247576i	−0.627916	−	0.778281i	$-0.716092\pi$
$223$	0.440602	−	0.369709i	0.0295049	−	0.0247576i	0.657421	+	0.753524i	$0.271647\pi$
$224$	8.90651	−	0.141536i	0.595091	−	0.00945678i
$225$	23.2660	+	7.77956i	1.55107	+	0.518637i
$226$	−8.46738			−0.563242
$227$	−0.578975	−	0.210730i	−0.0384279	−	0.0139866i	0.322735	−	0.946489i	$-0.395398\pi$
$227$	−0.578975	−	0.210730i	−0.0384279	−	0.0139866i	−0.361163	+	0.932503i	$0.617620\pi$
$228$	−1.46906	+	1.79841i	−0.0972909	+	0.119102i
$229$	−21.5720	−	18.1011i	−1.42552	−	1.19615i	−0.948302	−	0.317370i	$-0.897200\pi$
$229$	−21.5720	−	18.1011i	−1.42552	−	1.19615i	−0.477219	−	0.878784i	$-0.658355\pi$
$230$	−27.8815	+	10.1480i	−1.83845	+	0.669141i
$231$	0.00248932		0.000364656i	0.000163786		2.39926e-5i
$232$	4.53858	+	25.7396i	0.297972	+	1.68989i
$233$	−26.9066			−1.76271			−0.881355	−	0.472454i	$-0.843368\pi$
$233$	−26.9066			−1.76271			−0.881355	+	0.472454i	$0.843368\pi$
$234$	−4.82469	+	8.89018i	−0.315400	+	0.581169i
$235$	−25.1801			−1.64257
$236$	4.05656	+	1.47647i	0.264060	+	0.0961099i
$237$	−2.81599	+	8.06634i	−0.182918	+	0.523965i
$238$	2.49385	−	15.5878i	0.161652	−	1.01041i
$239$	−8.20393	−	6.88392i	−0.530668	−	0.445283i	0.337664	−	0.941267i	$-0.390363\pi$
$239$	−8.20393	−	6.88392i	−0.530668	−	0.445283i	−0.868332	+	0.495983i	$0.834808\pi$
$240$	−12.8292	+	7.63428i	−0.828119	+	0.492791i
$241$	−16.8377	+	14.1285i	−1.08461	+	0.910096i	−0.996295	−	0.0859963i	$-0.972593\pi$
$241$	−16.8377	+	14.1285i	−1.08461	+	0.910096i	−0.0883151	+	0.996093i	$0.528148\pi$
$242$	−6.46015	+	11.1893i	−0.415274	+	0.719276i
$243$	12.9570	−	8.66693i	0.831193	−	0.555984i
$244$	−1.02285			−0.0654810
$245$	5.20540	+	24.8716i	0.332561	+	1.58899i
$246$	0.0900798	+	6.82932i	0.00574328	+	0.435421i
$247$	−1.07723	+	6.10928i	−0.0685426	+	0.388724i
$248$	3.14499	+	2.63896i	0.199707	+	0.167574i
$249$	−5.24031	−	6.08045i	−0.332091	−	0.385333i
$250$	12.7307	+	4.63361i	0.805163	+	0.293055i
$251$	−14.7977	−	25.6303i	−0.934019	−	1.61777i	−0.776373	−	0.630274i	$-0.782943\pi$
$251$	−14.7977	−	25.6303i	−0.934019	−	1.61777i	−0.157646	−	0.987496i	$-0.550391\pi$
$252$	−4.91969	+	0.208073i	−0.309911	+	0.0131074i
$253$	−0.00191024	+	0.00330863i	−0.000120096	+	0.000208012i
$254$	4.37229	−	3.66878i	0.274342	−	0.230200i
$255$	−11.3186	−	29.8660i	−0.708800	−	1.87028i
$256$	−2.31097	+	13.1062i	−0.144436	+	0.819135i
$257$	5.97570	+	5.01421i	0.372754	+	0.312778i	0.809850	−	0.586637i	$-0.199549\pi$
$257$	5.97570	+	5.01421i	0.372754	+	0.312778i	−0.437096	+	0.899415i	$0.643993\pi$
$258$	21.7322	+	3.53710i	1.35299	+	0.220210i
$259$	8.50591	−	7.37076i	0.528531	−	0.457997i
$260$	3.23225	−	5.59842i	0.200455	−	0.347199i
$261$	−5.08401	−	24.9633i	−0.314693	−	1.54519i
$262$	15.4096			0.952007
$263$	−2.36049	−	13.3870i	−0.145554	−	0.825477i	−0.966921	−	0.255077i	$-0.917899\pi$
$263$	−2.36049	−	13.3870i	−0.145554	−	0.825477i	0.821367	−	0.570400i	$-0.193212\pi$
$264$	−0.000964650		0.00276322i	−5.93701e−5		0.000170064i
$265$	−3.07706	+	17.4509i	−0.189022	+	1.07200i
$266$	6.27359	−	2.39696i	0.384658	−	0.146967i
$267$	0.497223	−	0.295884i	0.0304296	−	0.0181078i
$268$	1.59517	+	9.04668i	0.0974408	+	0.552614i
$269$	−10.0377	+	17.3859i	−0.612011	+	1.06003i	0.378890	+	0.925442i	$0.376306\pi$
$269$	−10.0377	+	17.3859i	−0.612011	+	1.06003i	−0.990901	+	0.134592i	$0.957028\pi$
$270$	18.7338	−	11.8280i	1.14010	−	0.719827i
$271$	5.18251	+	8.97638i	0.314815	+	0.545276i	0.979398	−	0.201938i	$-0.0647241\pi$
$271$	5.18251	+	8.97638i	0.314815	+	0.545276i	−0.664583	+	0.747215i	$0.731391\pi$
$272$	11.3339	+	4.12521i	0.687219	+	0.250127i
$273$	−11.1961	+	6.90569i	−0.677616	+	0.417951i
$274$	−0.884054	−	0.741809i	−0.0534077	−	0.0448143i
$275$	0.00421875	−	0.00153550i	0.000254400	−	9.25941e-5i
$276$	2.46453	−	7.05958i	0.148347	−	0.424937i
$277$	0.235573	+	1.33600i	0.0141542	+	0.0802724i	0.991067	−	0.133368i	$-0.0425791\pi$
$277$	0.235573	+	1.33600i	0.0141542	+	0.0802724i	−0.976912	+	0.213640i	$0.931468\pi$
$278$	−9.74948	+	16.8866i	−0.584735	+	1.01279i
$279$	−3.13225	−	2.49048i	−0.187523	−	0.149101i
$280$	−29.5565	+	0.469692i	−1.76634	+	0.0280695i
$281$	5.12956	+	29.0912i	0.306004	+	1.73544i	0.618740	+	0.785596i	$0.287643\pi$
$281$	5.12956	+	29.0912i	0.306004	+	1.73544i	−0.312736	+	0.949840i	$0.601246\pi$
$282$	−8.92754	+	10.9290i	−0.531628	+	0.650812i
$283$	1.92121	−	10.8957i	0.114204	−	0.647684i	−0.872937	−	0.487833i	$-0.837787\pi$
$283$	1.92121	−	10.8957i	0.114204	−	0.647684i	0.987141	−	0.159851i	$-0.0511015\pi$
$284$	−0.959962	+	5.44422i	−0.0569633	+	0.323055i
$285$	8.59605	−	10.5232i	0.509186	−	0.623339i
$286$	0.000321438		0.00182296i	1.90070e−5		0.000107794i
$287$	−4.31834	+	7.76186i	−0.254904	+	0.458168i
$288$	1.49093	−	9.98966i	0.0878541	−	0.588646i
$289$	−4.40203	+	7.62454i	−0.258943	+	0.448503i
$290$	−6.28740	−	35.6576i	−0.369209	−	2.09389i
$291$	5.10332	−	14.6183i	0.299162	−	0.856942i
$292$	−2.07877	+	0.756612i	−0.121651	+	0.0442773i
$293$	−11.9832	−	10.0551i	−0.700064	−	0.587424i	0.221728	−	0.975109i	$-0.428830\pi$
$293$	−11.9832	−	10.0551i	−0.700064	−	0.587424i	−0.921792	+	0.387685i	$0.873275\pi$
$294$	12.6406	+	6.55885i	0.737218	+	0.382520i
$295$	−23.7365	−	8.63940i	−1.38200	−	0.503005i
$296$	6.54661	+	11.3391i	0.380514	+	0.659070i
$297$	0.000868892	−	0.00271721i	5.04182e−5	−	0.000157668i
$298$	−7.77530	+	13.4672i	−0.450411	+	0.780135i
$299$	−3.46872	−	19.6721i	−0.200601	−	1.13767i
$300$	−7.55101	+	4.49339i	−0.435958	+	0.259426i
$301$	22.2250	+	18.0551i	1.28103	+	1.04068i
$302$	2.52233	−	14.3048i	0.145144	−	0.823151i
$303$	2.41426	−	6.91558i	0.138696	−	0.397290i
$304$	0.891035	+	5.05331i	0.0511044	+	0.289827i
$305$	5.98508			0.342705
$306$	−16.9758	−	5.67628i	−0.970444	−	0.324491i
$307$	−12.4569	+	21.5759i	−0.710951	+	1.23140i	0.253550	+	0.967322i	$0.418402\pi$
$307$	−12.4569	+	21.5759i	−0.710951	+	1.23140i	−0.964501	+	0.264081i	$0.914931\pi$
$308$	−0.000681014	0	0.000590130i	−3.88044e−5	0	3.36258e-5i
$309$	9.61343	+	1.56466i	0.546889	+	0.0890107i
$310$	−4.35683	−	3.65582i	−0.247451	−	0.207636i
$311$	3.72042	−	21.0996i	0.210966	−	1.19645i	−0.676806	−	0.736162i	$-0.736636\pi$
$311$	3.72042	−	21.0996i	0.210966	−	1.19645i	0.887771	−	0.460284i	$-0.152253\pi$
$312$	−5.42304	−	14.3096i	−0.307019	−	0.810120i
$313$	20.0098	−	16.7902i	1.13102	−	0.949038i	0.131912	−	0.991261i	$-0.457888\pi$
$313$	20.0098	−	16.7902i	1.13102	−	0.949038i	0.999108	+	0.0422231i	$0.0134440\pi$
$314$	−7.11137	+	12.3173i	−0.401318	+	0.695103i
$315$	28.7871	−	1.21752i	1.62197	−	0.0685994i
$316$	−1.53008	−	2.65017i	−0.0860736	−	0.149084i
$317$	21.2806	+	7.74551i	1.19524	+	0.435031i	0.861560	−	0.507656i	$-0.169488\pi$
$317$	21.2806	+	7.74551i	1.19524	+	0.435031i	0.333679	+	0.942687i	$0.391710\pi$
$318$	6.48328	+	7.52271i	0.363564	+	0.421852i
$319$	−0.00357143	−	0.00299679i	−0.000199962	−	0.000167788i
$320$	5.48615	−	31.1135i	0.306685	−	1.73930i
$321$	−0.0531877	−	4.03238i	−0.00296865	−	0.225066i
$322$	−16.3431	+	14.1620i	−0.910763	+	0.789218i
$323$	−10.9779			−0.610826
$324$	−0.678240	+	5.54205i	−0.0376800	+	0.307891i
$325$	−11.7368	+	20.3287i	−0.651040	+	1.12763i
$326$	−9.86278	+	8.27586i	−0.546249	+	0.458357i
$327$	−18.8758	+	11.2325i	−1.04383	+	0.621157i
$328$	−7.91539	−	6.64180i	−0.437054	−	0.366732i
$329$	−17.1436	+	6.55010i	−0.945160	+	0.361119i
$330$	0.00133635	−	0.00382795i	7.35638e−5	−	0.000210722i
$331$	14.9869	+	5.45480i	0.823757	+	0.299823i	0.719294	−	0.694706i	$-0.244465\pi$
$331$	14.9869	+	5.45480i	0.823757	+	0.299823i	0.104463	+	0.994529i	$0.466688\pi$
$332$	2.87507			0.157790
$333$	−6.67037	−	10.8802i	−0.365534	−	0.596231i
$334$	−5.21382			−0.285287
$335$	−9.33399	−	52.9357i	−0.509970	−	2.89219i
$336$	−6.74872	+	8.53498i	−0.368173	+	0.465621i
$337$	14.8992	−	5.42286i	0.811610	−	0.295402i	0.0973215	−	0.995253i	$-0.468972\pi$
$337$	14.8992	−	5.42286i	0.811610	−	0.295402i	0.714289	+	0.699851i	$0.246750\pi$
$338$	4.28292	+	3.59380i	0.232960	+	0.195477i
$339$	−7.89911	+	9.66999i	−0.429021	+	0.525202i
$340$	10.7498	+	3.91261i	0.582990	+	0.212191i
$341$	−0.000732325	0		−3.96576e−5	0
$342$	−1.51969	−	7.46193i	−0.0821756	−	0.403495i
$343$	10.0139	+	15.5795i	0.540700	+	0.841216i
$344$	−25.5176	+	21.4118i	−1.37581	+	1.15445i
$345$	−14.4209	+	41.3084i	−0.776397	+	2.22397i
$346$	2.08866	+	1.75259i	0.112287	+	0.0942200i
$347$	−3.27600	+	1.19236i	−0.175865	+	0.0640095i	−0.428452	−	0.903565i	$-0.640941\pi$
$347$	−3.27600	+	1.19236i	−0.175865	+	0.0640095i	0.252587	+	0.967574i	$0.418719\pi$
$348$	7.96177	+	4.45777i	0.426796	+	0.238961i
$349$	4.72842	+	1.72101i	0.253107	+	0.0921233i	0.465458	−	0.885070i	$-0.345890\pi$
$349$	4.72842	+	1.72101i	0.253107	+	0.0921233i	−0.212351	+	0.977193i	$0.568112\pi$
$350$	25.4091	−	0.403785i	1.35818	−	0.0215832i
$351$	5.65195	+	13.8035i	0.301679	+	0.736774i
$352$	−0.000924199	−	0.00160076i	−4.92600e−5	−	8.53208e-5i
$353$	4.79087	−	4.02002i	0.254992	−	0.213964i	−0.506326	−	0.862342i	$-0.668997\pi$
$353$	4.79087	−	4.02002i	0.254992	−	0.213964i	0.761319	+	0.648378i	$0.224552\pi$
$354$	−12.1655	+	7.23936i	−0.646590	+	0.384768i
$355$	5.61712	−	31.8562i	0.298126	−	1.69075i
$356$	−0.0359869	+	0.204092i	−0.00190730	+	0.0108168i
$357$	−15.4752	−	17.3897i	−0.819037	−	0.920361i
$358$	2.82420	−	2.36978i	0.149263	−	0.125247i
$359$	1.12942	−	1.95621i	0.0596084	−	0.103245i	−0.834681	−	0.550733i	$-0.814348\pi$
$359$	1.12942	−	1.95621i	0.0596084	−	0.103245i	0.894290	+	0.447489i	$0.147681\pi$
$360$	−4.94771	+	33.1510i	−0.260767	+	1.74721i
$361$	7.16482	+	12.4098i	0.377096	+	0.653149i
$362$	−3.04913	+	2.55852i	−0.160259	+	0.134473i
$363$	6.75192	+	17.8160i	0.354384	+	0.935100i
$364$	0.744331	−	4.65244i	0.0390135	−	0.243854i
$365$	12.1637	−	4.42723i	0.636678	−	0.231732i
$366$	2.12199	−	2.59772i	0.110918	−	0.135785i
$367$	19.7427	+	7.18576i	1.03056	+	0.375094i	0.801295	−	0.598270i	$-0.204145\pi$
$367$	19.7427	+	7.18576i	1.03056	+	0.375094i	0.229267	+	0.973364i	$0.426367\pi$
$368$	−8.26142	−	14.3092i	−0.430656	−	0.745919i
$369$	7.88331	+	6.26811i	0.410389	+	0.326305i
$370$	−9.06918	−	15.7083i	−0.471484	−	0.816634i
$371$	2.44451	+	12.6817i	0.126912	+	0.658401i
$372$	1.40812	−	0.267485i	0.0730077	−	0.0138685i
$373$	10.5114	−	3.82582i	0.544258	−	0.198094i	−0.0552355	−	0.998473i	$-0.517591\pi$
$373$	10.5114	−	3.82582i	0.544258	−	0.198094i	0.599493	+	0.800380i	$0.295369\pi$
$374$	−0.00307817	+	0.00112036i	−0.000159168	+	5.79325e-5i
$375$	17.1681	−	10.2162i	0.886555	−	0.527564i
$376$	−3.70729	−	21.0251i	−0.191189	−	1.08429i
$377$	24.3764			1.25545
$378$	9.67794	−	12.9262i	0.497779	−	0.664851i
$379$	25.6070			1.31535			0.657673	−	0.753304i	$-0.271541\pi$
$379$	25.6070			1.31535			0.657673	+	0.753304i	$0.271541\pi$
$380$	0.845115	+	4.79288i	0.0433535	+	0.245870i
$381$	−0.111006	−	8.41584i	−0.00568702	−	0.431156i
$382$	−1.19759	+	0.435889i	−0.0612743	+	0.0223020i
$383$	−15.7956	+	5.74913i	−0.807118	+	0.293767i	−0.712433	−	0.701740i	$-0.752407\pi$
$383$	−15.7956	+	5.74913i	−0.807118	+	0.293767i	−0.0946850	+	0.995507i	$0.530184\pi$
$384$	−3.94528	−	4.57780i	−0.201331	−	0.233610i
$385$	0.00398488	−	0.00345308i	0.000203088	−	0.000175985i
$386$	−5.86206	−	10.1534i	−0.298371	−	0.516794i
$387$	24.3132	−	21.5191i	1.23591	−	1.09388i
$388$	2.77290	+	4.80281i	0.140773	+	0.243826i
$389$	−3.75763	−	1.36767i	−0.190519	−	0.0693434i	0.244999	−	0.969523i	$-0.421213\pi$
$389$	−3.75763	−	1.36767i	−0.190519	−	0.0693434i	−0.435518	+	0.900180i	$0.643435\pi$
$390$	7.51266	+	19.8234i	0.380418	+	1.00380i
$391$	33.2173	−	12.0901i	1.67987	−	0.611424i
$392$	−20.0011	+	8.00832i	−1.01021	+	0.404481i
$393$	14.3754	−	17.5982i	0.725143	−	0.887711i
$394$	−8.47783	+	7.11374i	−0.427107	+	0.358385i
$395$	8.95309	+	15.5072i	0.450479	+	0.780252i
$396$	0.000534054	0	0.000871108i	2.68372e−5	0	4.37748e-5i
$397$	−11.0773	+	19.1864i	−0.555952	+	0.962937i	0.441877	+	0.897076i	$0.354313\pi$
$397$	−11.0773	+	19.1864i	−0.555952	+	0.962937i	−0.997829	+	0.0658616i	$0.979020\pi$
$398$	−2.37566	+	1.99341i	−0.119081	+	0.0999208i
$399$	3.11515	−	9.40070i	0.155953	−	0.470624i
$400$	−3.37160	+	19.1213i	−0.168580	+	0.956064i
$401$	1.04905	−	5.94943i	0.0523868	−	0.297100i	−0.947346	−	0.320211i	$-0.896246\pi$
$401$	1.04905	−	5.94943i	0.0523868	−	0.297100i	0.999733	+	0.0231111i	$0.00735714\pi$
$402$	−26.2852	−	14.7170i	−1.31098	−	0.734016i
$403$	2.93318	−	2.46123i	0.146112	−	0.122603i
$404$	1.31179	+	2.27210i	0.0652642	+	0.113041i
$405$	3.96865	−	32.4287i	0.197204	−	1.61139i
$406$	−13.5563	−	22.6416i	−0.672790	−	1.12369i
$407$	−0.00219468		0.000798797i	−0.000108786		3.95949e-5i
$408$	23.2714	−	13.8481i	1.15210	−	0.685585i
$409$	−22.4229	+	8.16126i	−1.10874	+	0.403549i	−0.830531	−	0.556972i	$-0.811963\pi$
$409$	−22.4229	+	8.16126i	−1.10874	+	0.403549i	−0.278209	+	0.960521i	$0.589741\pi$
$410$	10.9654	+	9.20104i	0.541541	+	0.454407i
$411$	−1.67189	+	0.317590i	−0.0824682	+	0.0156656i
$412$	−2.67242	+	2.24243i	−0.131661	+	0.110476i
$413$	−18.4082	+	0.292530i	−0.905807	+	0.0143945i
$414$	12.8163	+	20.9049i	0.629886	+	1.02742i
$415$	−16.8232			−0.825816
$416$	9.08161	+	3.30544i	0.445263	+	0.162062i
$417$	10.1898	+	26.8875i	0.498997	+	1.31669i
$418$	−0.00106756		0.000895787i	−5.22160e−5		4.38144e-5i
$419$	26.4887	−	9.64110i	1.29406	−	0.470998i	0.399001	−	0.916951i	$-0.369357\pi$
$419$	26.4887	−	9.64110i	1.29406	−	0.470998i	0.895057	+	0.445952i	$0.147135\pi$
$420$	−6.40092	+	8.09512i	−0.312333	+	0.395001i
$421$	−6.16048	−	34.9378i	−0.300243	−	1.70277i	−0.645090	−	0.764106i	$-0.723180\pi$
$421$	−6.16048	−	34.9378i	−0.300243	−	1.70277i	0.344847	−	0.938659i	$-0.387931\pi$
$422$	27.5045			1.33890
$423$	4.15282	+	20.3910i	0.201917	+	0.991445i
$424$	−15.0243			−0.729645
$425$	−39.0342	−	14.2073i	−1.89344	−	0.689155i
$426$	−11.8351	−	13.7326i	−0.573413	−	0.665345i
$427$	4.07489	−	1.55690i	0.197198	−	0.0753436i
$428$	1.10649	+	0.928457i	0.0534843	+	0.0448787i
$429$	0.00238174	+	0.00133353i	0.000114992	+	6.43833e-5i
$430$	35.3501	−	29.6622i	1.70473	−	1.43044i
$431$	6.23650	−	10.8019i	0.300402	−	0.520311i	−0.675825	−	0.737062i	$-0.736213\pi$
$431$	6.23650	−	10.8019i	0.300402	−	0.520311i	0.976227	+	0.216751i	$0.0695459\pi$
$432$	8.29814	+	9.13006i	0.399244	+	0.439270i
$433$	9.78672			0.470320			0.235160	−	0.971957i	$-0.424439\pi$
$433$	9.78672			0.470320			0.235160	+	0.971957i	$0.424439\pi$
$434$	−3.91730	−	1.35569i	−0.188036	−	0.0650751i
$435$	−46.5875	−	26.0842i	−2.23370	−	1.25064i
$436$	1.36615	−	7.74782i	0.0654267	−	0.371053i
$437$	11.5203	+	9.66668i	0.551090	+	0.462420i
$438$	2.39105	−	6.84911i	0.114249	−	0.327263i
$439$	−6.19971	−	2.25651i	−0.295896	−	0.107697i	0.189806	−	0.981822i	$-0.439214\pi$
$439$	−6.19971	−	2.25651i	−0.295896	−	0.107697i	−0.485703	+	0.874124i	$0.661436\pi$
$440$	0.00306698	+	0.00531217i	0.000146213	+	0.000253248i
$441$	19.2827	−	8.31731i	0.918224	−	0.396062i
$442$	8.56363	−	14.8327i	0.407331	−	0.705517i
$443$	−28.3117	+	23.7563i	−1.34513	+	1.12870i	−0.364852	+	0.931065i	$0.618880\pi$
$443$	−28.3117	+	23.7563i	−1.34513	+	1.12870i	−0.980276	+	0.197631i	$0.936675\pi$
$444$	4.51171	+	0.734319i	0.214116	+	0.0348492i
$445$	0.210573	−	1.19422i	0.00998213	−	0.0566115i
$446$	−0.517520	−	0.434251i	−0.0245053	−	0.0205624i
$447$	8.12647	+	21.4430i	0.384369	+	1.01422i
$448$	−4.35836	−	22.6105i	−0.205913	−	1.06824i
$449$	−2.25488	+	3.90556i	−0.106414	+	0.184315i	−0.914315	−	0.405003i	$-0.867270\pi$
$449$	−2.25488	+	3.90556i	−0.106414	+	0.184315i	0.807901	+	0.589318i	$0.200604\pi$
$450$	4.25345	−	28.4992i	0.200509	−	1.34347i
$451$	0.00184313			8.67897e−5
$452$	−0.776596	−	4.40429i	−0.0365280	−	0.207160i
$453$	−13.9835	−	16.2254i	−0.657002	−	0.762335i
$454$	−0.125668	+	0.712698i	−0.00589789	+	0.0334486i
$455$	−4.35537	+	27.2232i	−0.204183	+	1.27624i
$456$	10.0523	+	5.62827i	0.470744	+	0.263568i
$457$	3.66043	+	20.7593i	0.171228	+	0.971079i	0.942409	+	0.334464i	$0.108555\pi$
$457$	3.66043	+	20.7593i	0.171228	+	0.971079i	−0.771181	+	0.636616i	$0.780334\pi$
$458$	−16.5382	+	28.6450i	−0.772778	+	1.33849i
$459$	−22.3190	+	14.0916i	−1.04176	+	0.657737i
$460$	−7.83566	−	13.5718i	−0.365339	−	0.632786i
$461$	−20.9179	−	7.61348i	−0.974242	−	0.354595i	−0.194643	−	0.980874i	$-0.562355\pi$
$461$	−20.9179	−	7.61348i	−0.974242	−	0.354595i	−0.779599	+	0.626279i	$0.784577\pi$
$462$	−8.59204e−5	−	0.00295385i	−3.99738e−6	−	0.000137426i
$463$	−14.0481	−	11.7877i	−0.652869	−	0.547822i	0.255071	−	0.966922i	$-0.417901\pi$
$463$	−14.0481	−	11.7877i	−0.652869	−	0.547822i	−0.907940	+	0.419100i	$0.862346\pi$
$464$	18.9471	−	6.89616i	0.879595	−	0.320146i
$465$	−8.23948	+	1.56516i	−0.382097	+	0.0725827i
$466$	5.48794	+	31.1237i	0.254224	+	1.44178i
$467$	9.06683	−	15.7042i	0.419563	−	0.726704i	−0.576333	−	0.817215i	$-0.695517\pi$
$467$	9.06683	−	15.7042i	0.419563	−	0.726704i	0.995895	+	0.0905111i	$0.0288501\pi$
$468$	−5.06671	−	1.69418i	−0.234209	−	0.0783134i
$469$	−20.1251	−	33.6128i	−0.929292	−	1.55209i
$470$	5.13580	+	29.1266i	0.236897	+	1.34351i
$471$	7.43255	+	19.6120i	0.342474	+	0.903673i
$472$	3.71904	−	21.0917i	0.171183	−	0.970825i
$473$	0.00103180	−	0.00585160i	4.74420e−5	−	0.000269057i
$474$	9.90493	+	1.61211i	0.454949	+	0.0740467i
$475$	−3.06874	−	17.4037i	−0.140804	−	0.798537i
$476$	8.33670	−	0.132481i	0.382112	−	0.00607226i
$477$	14.6393	−	0.386257i	0.670288	−	0.0176855i
$478$	−6.28953	+	10.8938i	−0.287676	+	0.498270i
$479$	−5.50485	−	31.2196i	−0.251523	−	1.42646i	−0.804842	−	0.593489i	$-0.797750\pi$
$479$	−5.50485	−	31.2196i	−0.251523	−	1.42646i	0.553319	−	0.832970i	$-0.313361\pi$
$480$	−13.8195	−	16.0351i	−0.630771	−	0.731899i
$481$	11.4750	−	4.17655i	0.523214	−	0.190434i
$482$	19.7771	+	16.5950i	0.900822	+	0.755879i
$483$	0.927189	+	31.8758i	0.0421886	+	1.45040i
$484$	−6.41260	−	2.33400i	−0.291482	−	0.106091i
$485$	−16.2253	−	28.1031i	−0.736755	−	1.27610i
$486$	−12.6680	−	13.2200i	−0.574634	−	0.599673i
$487$	5.37973	−	9.31796i	0.243779	−	0.422237i	−0.718009	−	0.696034i	$-0.754946\pi$
$487$	5.37973	−	9.31796i	0.243779	−	0.422237i	0.961788	+	0.273797i	$0.0882796\pi$
$488$	0.881189	+	4.99747i	0.0398895	+	0.226225i
$489$	0.250402	+	18.9840i	0.0113236	+	0.858487i
$490$	27.7080	−	11.0941i	1.25172	−	0.501181i
$491$	−0.0307042	+	0.174132i	−0.00138566	+	0.00785848i	−0.985493	−	0.169718i	$-0.945714\pi$
$491$	−0.0307042	+	0.174132i	−0.00138566	+	0.00785848i	0.984107	+	0.177576i	$0.0568256\pi$
$492$	−3.54399	+	0.673213i	−0.159776	+	0.0303508i
$493$	7.49066	+	42.4817i	0.337362	+	1.91328i
$494$	7.28650			0.327835
$495$	−0.00312496	−	0.00509720i	−0.000140457	−	0.000229102i
$496$	1.58359	−	2.74285i	0.0711051	−	0.123158i
$497$	−4.46240	−	23.1502i	−0.200166	−	1.03843i
$498$	−5.96461	+	7.30180i	−0.267281	+	0.327201i
$499$	−21.9278	−	18.3996i	−0.981623	−	0.823679i	0.00271052	−	0.999996i	$-0.499137\pi$
$499$	−21.9278	−	18.3996i	−0.981623	−	0.823679i	−0.984333	+	0.176317i	$0.943582\pi$
$500$	−1.24255	+	7.04685i	−0.0555685	+	0.315145i
$501$	−4.86390	+	5.95433i	−0.217303	+	0.266020i
$502$	−26.6291	+	22.3445i	−1.18852	+	0.997284i
$503$	12.4042	−	21.4846i	0.553074	−	0.957953i	−0.444976	−	0.895542i	$-0.646788\pi$
$503$	12.4042	−	21.4846i	0.553074	−	0.957953i	0.998051	−	0.0624107i	$-0.0198788\pi$
$504$	5.25496	+	23.8576i	0.234075	+	1.06270i
$505$	−7.67583	−	13.2949i	−0.341570	−	0.591616i
$506$	0.00421680	+	0.00153479i	0.000187460	+	6.82298e-5i
$507$	8.09970	−	1.53861i	0.359721	−	0.0683321i
$508$	2.30932	+	1.93775i	0.102460	+	0.0859737i
$509$	−0.431902	+	2.44944i	−0.0191437	+	0.108569i	−0.992882	−	0.119099i	$-0.961999\pi$
$509$	−0.431902	+	2.44944i	−0.0191437	+	0.108569i	0.973739	+	0.227669i	$0.0731104\pi$
$510$	−32.2383	+	19.1841i	−1.42754	+	0.849488i
$511$	7.12990	−	6.17839i	0.315408	−	0.273316i
$512$	22.6098			0.999223
$513$	−9.93944	−	5.22561i	−0.438837	−	0.230716i
$514$	4.58126	−	7.93498i	0.202071	−	0.349997i
$515$	15.6374	−	13.1213i	0.689065	−	0.578194i
$516$	0.153380	+	11.6284i	0.00675219	+	0.511911i
$517$	0.00291728	+	0.00244789i	0.000128302	+	0.000107658i
$518$	−10.2609	−	8.33567i	−0.450836	−	0.366248i
$519$	3.94999	−	0.750337i	0.173385	−	0.0329361i
$520$	−30.1376	−	10.9692i	−1.32162	−	0.481031i
$521$	−36.8596			−1.61485			−0.807424	−	0.589971i	$-0.799139\pi$
$521$	−36.8596			−1.61485			−0.807424	+	0.589971i	$0.799139\pi$
$522$	−27.8388	+	10.9724i	−1.21847	+	0.480249i
$523$	35.3235			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$523$	35.3235			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$524$	1.41331	+	8.01526i	0.0617406	+	0.350148i
$525$	23.2427	−	29.3946i	1.01440	−	1.28289i
$526$	−15.0037	+	5.46089i	−0.654191	+	0.238106i
$527$	5.19062	+	4.35545i	0.226107	+	0.189726i
$528$	0.00222851		0.000362709i	9.69837e−5		1.57849e-5i
$529$	−23.8917	−	8.69586i	−1.03877	−	0.378081i
$530$	20.8135			0.904082
$531$	−3.08150	+	20.6469i	−0.133726	+	0.895998i
$532$	1.82216	+	3.04335i	0.0790007	+	0.131946i
$533$	−7.38231	+	6.19449i	−0.319763	+	0.268313i
$534$	−0.443672	−	0.514804i	−0.0191996	−	0.0222777i
$535$	−6.47452	−	5.43277i	−0.279918	−	0.234879i
$536$	42.8264	−	15.5876i	1.84982	−	0.673280i
$537$	−0.0717023	−	5.43605i	−0.00309418	−	0.234583i
$538$	22.1580	+	8.06487i	0.955301	+	0.347701i
$539$	0.00181482	−	0.00338759i	7.81699e−5	−	0.000145914i
$540$	7.87048	+	8.65953i	0.338692	+	0.372647i
$541$	15.6446	+	27.0972i	0.672613	+	1.16500i	0.977160	+	0.212503i	$0.0681617\pi$
$541$	15.6446	+	27.0972i	0.672613	+	1.16500i	−0.304547	+	0.952497i	$0.598505\pi$
$542$	9.32620	−	7.82561i	0.400595	−	0.336139i
$543$	0.0774131	+	5.86900i	0.00332211	+	0.251863i
$544$	−2.96980	+	16.8426i	−0.127329	+	0.722120i
$545$	−7.99388	+	45.3355i	−0.342420	+	1.94196i
$546$	10.2716	+	11.5423i	0.439583	+	0.493965i
$547$	−11.0496	+	9.27171i	−0.472446	+	0.396430i	−0.847686	−	0.530498i	$-0.822005\pi$
$547$	−11.0496	+	9.27171i	−0.472446	+	0.396430i	0.375240	+	0.926928i	$0.377560\pi$
$548$	0.304769	−	0.527875i	0.0130191	−	0.0225497i
$549$	−0.987087	−	4.84676i	−0.0421279	−	0.206855i
$550$	−0.00263662	−	0.00456677i	−0.000112426	−	0.000194728i
$551$	−14.0584	+	11.7964i	−0.598906	+	0.502542i
$552$	−36.6152	−	5.95944i	−1.55845	−	0.253650i
$553$	10.1295	+	8.22898i	0.430751	+	0.349932i
$554$	1.49734	−	0.544988i	0.0636160	−	0.0231543i
$555$	−26.3998	−	4.29679i	−1.12061	−	0.182388i
$556$	−9.67771	−	3.52240i	−0.410427	−	0.149383i
$557$	11.7685	+	20.3837i	0.498649	+	0.863685i	0.999999	−	0.00155960i	$-0.000496438\pi$
$557$	11.7685	+	20.3837i	0.498649	+	0.863685i	−0.501350	+	0.865245i	$0.667163\pi$
$558$	−2.24195	+	4.13113i	−0.0949095	+	0.174884i
$559$	15.5337	+	26.9052i	0.657006	+	1.13797i
$560$	4.31624	+	22.3920i	0.182394	+	0.946233i
$561$	−0.00159210	+	0.00456053i	−6.72185e−5	+	0.000192546i
$562$	32.6044	−	11.8670i	1.37533	−	0.500581i
$563$	23.1219	−	8.41568i	0.974471	−	0.354678i	0.194783	−	0.980846i	$-0.437600\pi$
$563$	23.1219	−	8.41568i	0.974471	−	0.354678i	0.779688	+	0.626168i	$0.215378\pi$
$564$	−6.50349	−	3.64128i	−0.273846	−	0.153326i
$565$	4.54417	+	25.7712i	0.191175	+	1.08420i
$566$	−12.9953			−0.546232
$567$	−5.73365	−	23.1111i	−0.240791	−	0.970577i
$568$	27.4266			1.15080
$569$	−5.04404	−	28.6062i	−0.211457	−	1.19923i	−0.886949	−	0.461867i	$-0.847180\pi$
$569$	−5.04404	−	28.6062i	−0.211457	−	1.19923i	0.675492	−	0.737367i	$-0.263931\pi$
$570$	−13.9257	−	7.79697i	−0.583285	−	0.326579i
$571$	−20.9568	+	7.62766i	−0.877016	+	0.319208i	−0.741005	−	0.671500i	$-0.765650\pi$
$571$	−20.9568	+	7.62766i	−0.877016	+	0.319208i	−0.136011	+	0.990707i	$0.543428\pi$
$572$	−0.000918730	0	0.000334390i	−3.84140e−5	0	1.39816e-5i
$573$	−0.619423	+	1.77432i	−0.0258768	+	0.0741234i
$574$	9.85915	+	3.41203i	0.411513	+	0.142415i
$575$	28.4525	+	49.2812i	1.18655	+	2.05517i
$576$	−26.1007	+	0.688666i	−1.08753	+	0.0286944i
$577$	−9.61429	−	16.6524i	−0.400248	−	0.693250i	0.593507	−	0.804828i	$-0.297743\pi$
$577$	−9.61429	−	16.6524i	−0.400248	−	0.693250i	−0.993756	+	0.111578i	$0.964409\pi$
$578$	9.71738	+	3.53684i	0.404190	+	0.147113i
$579$	−17.0641	−	2.77732i	−0.709159	−	0.115422i
$580$	17.9706	−	6.54076i	0.746188	−	0.271590i
$581$	−11.4539	+	4.37621i	−0.475188	+	0.181556i
$582$	−17.9503	−	2.92157i	−0.744065	−	0.121103i
$583$	0.00205299	−	0.00172266i	8.50262e−5	−	7.13454e-5i
$584$	5.48756	+	9.50474i	0.227077	+	0.393309i
$585$	29.6473	+	9.91330i	1.22577	+	0.409865i
$586$	−9.18688	+	15.9121i	−0.379507	+	0.657325i
$587$	−4.54497	+	3.81368i	−0.187591	+	0.157407i	−0.731747	−	0.681577i	$-0.761295\pi$
$587$	−4.54497	+	3.81368i	−0.187591	+	0.157407i	0.544156	+	0.838984i	$0.316850\pi$
$588$	−2.25222	+	7.17656i	−0.0928801	+	0.295956i
$589$	−0.500572	+	2.83889i	−0.0206257	+	0.116974i
$590$	−5.15207	+	29.2189i	−0.212108	+	1.20292i
$591$	0.215240	+	16.3182i	0.00885379	+	0.671243i
$592$	7.73760	−	6.49262i	0.318014	−	0.266845i
$593$	1.27815	+	2.21382i	0.0524873	+	0.0909107i	0.891075	−	0.453855i	$-0.149952\pi$
$593$	1.27815	+	2.21382i	0.0524873	+	0.0909107i	−0.838588	+	0.544766i	$0.816618\pi$
$594$	−0.00332030		0.000450864i	−0.000136233		1.84992e-5i
$595$	−48.7813	+	0.775199i	−1.99984	+	0.0317801i
$596$	−7.71807	−	2.80915i	−0.316144	−	0.115067i
$597$	0.0603146	+	4.57270i	0.00246851	+	0.187148i
$598$	−22.0478	+	8.02473i	−0.901600	+	0.328156i
$599$	20.7922	+	17.4468i	0.849548	+	0.712855i	0.959690	−	0.281061i	$-0.0906862\pi$
$599$	20.7922	+	17.4468i	0.849548	+	0.712855i	−0.110142	+	0.993916i	$0.535131\pi$
$600$	28.4593	+	33.0220i	1.16184	+	1.34812i
$601$	13.2745	−	11.1387i	0.541480	−	0.454356i	−0.330564	−	0.943784i	$-0.607239\pi$
$601$	13.2745	−	11.1387i	0.541480	−	0.454356i	0.872044	+	0.489428i	$0.162794\pi$
$602$	16.3517	−	29.3909i	0.666447	−	1.19788i
$603$	−41.3283	+	16.2891i	−1.68302	+	0.663345i
$604$	7.67197			0.312168
$605$	37.5226	+	13.6571i	1.52551	+	0.555241i
$606$	−8.49188	−	1.38212i	−0.344959	−	0.0561449i
$607$	9.24077	+	7.75393i	0.375071	+	0.314722i	0.810764	−	0.585373i	$-0.199052\pi$
$607$	9.24077	+	7.75393i	0.375071	+	0.314722i	−0.435693	+	0.900096i	$0.643497\pi$
$608$	−6.83713	+	2.48851i	−0.277282	+	0.100923i
$609$	−38.5039	−	5.64037i	−1.56026	−	0.228559i
$610$	−1.22073	−	6.92311i	−0.0494260	−	0.280309i
$611$	−19.9116			−0.805537
$612$	1.39555	−	9.35055i	0.0564117	−	0.377974i
$613$	11.3649			0.459025			0.229512	−	0.973306i	$-0.426287\pi$
$613$	11.3649			0.459025			0.229512	+	0.973306i	$0.426287\pi$
$614$	27.4982	+	10.0085i	1.10974	+	0.403912i
$615$	20.7373	−	3.93924i	0.836209	−	0.158845i
$616$	0.00346998	+	0.00281893i	0.000139810	+	0.000113578i
$617$	−15.1612	−	12.7218i	−0.610368	−	0.512159i	0.284391	−	0.958708i	$-0.408208\pi$
$617$	−15.1612	−	12.7218i	−0.610368	−	0.512159i	−0.894759	+	0.446549i	$0.852653\pi$
$618$	−0.150886	−	11.4393i	−0.00606951	−	0.460155i
$619$	19.5590	−	16.4119i	0.786142	−	0.659651i	−0.158646	−	0.987336i	$-0.550713\pi$
$619$	19.5590	−	16.4119i	0.786142	−	0.659651i	0.944787	+	0.327684i	$0.106268\pi$
$620$	1.50197	−	2.60149i	0.0603207	−	0.104479i
$621$	35.8302	+	4.86539i	1.43782	+	0.195241i
$622$	−25.1653			−1.00904
$623$	−0.167286	−	0.867851i	−0.00670215	−	0.0347697i
$624$	−10.1449	+	6.03694i	−0.406121	+	0.241671i
$625$	0.170688	−	0.968020i	0.00682752	−	0.0387208i
$626$	−23.5030	−	19.7213i	−0.939367	−	0.788223i
$627$	−0.00201893		0.000383513i	−8.06281e−5		1.53160e-5i
$628$	−7.05902	−	2.56927i	−0.281686	−	0.102525i
$629$	10.8048	+	18.7145i	0.430816	+	0.746194i
$630$	−7.27982	−	33.0505i	−0.290035	−	1.31676i
$631$	−2.70425	+	4.68389i	−0.107654	+	0.186463i	−0.914820	−	0.403863i	$-0.867667\pi$
$631$	−2.70425	+	4.68389i	−0.107654	+	0.186463i	0.807165	+	0.590326i	$0.201001\pi$
$632$	−11.6302	+	9.75887i	−0.462623	+	0.388187i
$633$	25.6586	−	31.4110i	1.01984	−	1.24847i
$634$	4.61901	−	26.1957i	0.183444	−	1.04036i
$635$	−13.5127	−	11.3385i	−0.536237	−	0.449956i
$636$	−3.31830	+	4.06222i	−0.131579	+	0.161077i
$637$	4.11626	+	19.6677i	0.163092	+	0.779261i
$638$	−0.00273803	+	0.00474241i	−0.000108400	+	0.000187754i
$639$	−26.7238	+	0.705105i	−1.05718	+	0.0278935i
$640$	−12.6657			−0.500655
$641$	2.11785	+	12.0109i	0.0836499	+	0.474402i	0.997640	+	0.0686652i	$0.0218740\pi$
$641$	2.11785	+	12.0109i	0.0836499	+	0.474402i	−0.913990	+	0.405737i	$0.867015\pi$
$642$	−4.65352	+	0.883978i	−0.183660	+	0.0348878i
$643$	−4.22738	+	23.9747i	−0.166712	+	0.945469i	0.780570	+	0.625068i	$0.214929\pi$
$643$	−4.22738	+	23.9747i	−0.166712	+	0.945469i	−0.947282	+	0.320401i	$0.896182\pi$
$644$	−8.86526	−	7.20192i	−0.349340	−	0.283795i
$645$	−0.897488	−	68.0423i	−0.0353386	−	2.67916i
$646$	2.23908	+	12.6984i	0.0880954	+	0.499614i
$647$	−7.42195	+	12.8552i	−0.291787	+	0.505390i	−0.974232	−	0.225547i	$-0.927583\pi$
$647$	−7.42195	+	12.8552i	−0.291787	+	0.505390i	0.682445	+	0.730937i	$0.260916\pi$
$648$	27.6619	−	1.46073i	1.08666	−	0.0573829i
$649$	0.00191016	+	0.00330849i	7.49802e−5	+	0.000129870i
$650$	25.9087	+	9.42999i	1.01622	+	0.369875i
$651$	−5.20263	+	3.20896i	−0.203907	+	0.125769i
$652$	−5.20925	−	4.37108i	−0.204010	−	0.171185i
$653$	0.368323	−	0.134058i	0.0144136	−	0.00524611i	−0.334803	−	0.942288i	$-0.608670\pi$
$653$	0.368323	−	0.134058i	0.0144136	−	0.00524611i	0.349217	+	0.937042i	$0.386448\pi$
$654$	16.8429	+	19.5432i	0.658609	+	0.764200i
$655$	−8.26981	−	46.9004i	−0.323128	−	1.83255i
$656$	−3.98561	+	6.90327i	−0.155612	+	0.269527i
$657$	−5.59130	−	9.12010i	−0.218137	−	0.355809i
$658$	11.0734	+	18.4946i	0.431684	+	0.720994i
$659$	−5.91682	−	33.5559i	−0.230487	−	1.30715i	−0.851914	−	0.523682i	$-0.824558\pi$
$659$	−5.91682	−	33.5559i	−0.230487	−	1.30715i	0.621427	−	0.783472i	$-0.286553\pi$
$660$	0.00211367		0.000344017i	8.22743e−5		1.33908e-5i
$661$	0.516014	−	2.92646i	0.0200706	−	0.113826i	−0.973127	−	0.230271i	$-0.926039\pi$
$661$	0.516014	−	2.92646i	0.0200706	−	0.113826i	0.993197	+	0.116445i	$0.0371498\pi$
$662$	3.25295	−	18.4484i	0.126430	−	0.717018i
$663$	−8.95040	−	23.6171i	−0.347605	−	0.917212i
$664$	−2.47689	−	14.0471i	−0.0961220	−	0.545135i
$665$	−10.6622	−	17.8079i	−0.413462	−	0.690559i
$666$	−11.2249	+	9.93496i	−0.434957	+	0.384972i
$667$	29.5468	−	51.1766i	1.14406	−	1.98157i
$668$	−0.478191	−	2.71196i	−0.0185018	−	0.104929i
$669$	−0.978714	+	0.185915i	−0.0378393	+	0.00718791i
$670$	−59.3285	+	21.5938i	−2.29206	+	0.834241i
$671$	−0.000693412	0	0.000581841i	−2.67689e−5	0	2.24617e-5i
$672$	−13.5801	−	7.32249i	−0.523864	−	0.282471i
$673$	−25.9552	−	9.44691i	−1.00050	−	0.364151i	−0.210721	−	0.977546i	$-0.567581\pi$
$673$	−25.9552	−	9.44691i	−1.00050	−	0.364151i	−0.789777	+	0.613395i	$0.789804\pi$
$674$	−9.31166	−	16.1283i	−0.358672	−	0.621237i
$675$	−28.5790	−	31.4441i	−1.10000	−	1.21028i
$676$	−1.47649	+	2.55736i	−0.0567882	+	0.0983601i
$677$	4.85983	+	27.5615i	0.186779	+	1.05927i	0.923649	+	0.383240i	$0.125192\pi$
$677$	4.85983	+	27.5615i	0.186779	+	1.05927i	−0.736870	+	0.676034i	$0.763697\pi$
$678$	12.7967	+	7.16482i	0.491454	+	0.275163i
$679$	−18.3574	−	14.9131i	−0.704490	−	0.572311i
$680$	9.85538	−	55.8926i	0.377936	−	2.14338i
$681$	0.696687	+	0.808383i	0.0266971	+	0.0309773i
$682$	0.000149367	0	0.000847102i	5.71955e−6	0	3.24372e-5i
$683$	31.9759			1.22353			0.611763	−	0.791041i	$-0.290461\pi$
$683$	31.9759			1.22353			0.611763	+	0.791041i	$0.290461\pi$
$684$	3.74193	−	1.47484i	0.143076	−	0.0563921i
$685$	−1.78332	+	3.08880i	−0.0681372	+	0.118017i
$686$	15.9788	−	14.7610i	0.610075	−	0.563578i
$687$	17.2851	+	45.6096i	0.659468	+	1.74011i
$688$	19.6854	+	16.5180i	0.750500	+	0.629744i
$689$	−2.43324	+	13.7996i	−0.0926990	+	0.525722i
$690$	50.7240	+	8.25575i	1.93103	+	0.314291i
$691$	−10.7975	+	9.06021i	−0.410758	+	0.344667i	−0.824634	−	0.565666i	$-0.808619\pi$
$691$	−10.7975	+	9.06021i	−0.410758	+	0.344667i	0.413876	+	0.910333i	$0.364175\pi$
$692$	−0.720044	+	1.24715i	−0.0273720	+	0.0474096i
$693$	−0.00345354	−	0.00265749i	−0.000131189	−	0.000100950i
$694$	2.04742	+	3.54624i	0.0777191	+	0.134614i
$695$	56.6281	+	20.6109i	2.14803	+	0.781818i
$696$	14.9208	−	42.7404i	0.565573	−	1.62007i
$697$	−13.0639	−	10.9619i	−0.494830	−	0.415212i
$698$	1.02632	−	5.82053i	0.0388466	−	0.220310i
$699$	40.6637	+	22.7675i	1.53804	+	0.861145i
$700$	2.54046	+	13.1795i	0.0960202	+	0.498138i
$701$	24.3039			0.917945			0.458973	−	0.888450i	$-0.348218\pi$
$701$	24.3039			0.917945			0.458973	+	0.888450i	$0.348218\pi$
$702$	14.8141	−	9.35317i	0.559122	−	0.353013i
$703$	−4.59671	+	7.96174i	−0.173368	+	0.300283i
$704$	−0.00366032	+	0.00307137i	−0.000137953	+	0.000115757i
$705$	38.0545	+	21.3066i	1.43321	+	0.802452i
$706$	−5.62723	−	4.72181i	−0.211784	−	0.177708i
$707$	−8.68443	−	7.05502i	−0.326612	−	0.265331i
$708$	−4.88131	−	5.66390i	−0.183451	−	0.212862i
$709$	−10.7228	−	3.90279i	−0.402704	−	0.146572i	0.132724	−	0.991153i	$-0.457628\pi$
$709$	−10.7228	−	3.90279i	−0.402704	−	0.146572i	−0.535428	+	0.844581i	$0.679850\pi$
$710$	−37.9947			−1.42592
$711$	11.0813	−	9.80780i	0.415580	−	0.367821i
$712$	1.02816			0.0385320
$713$	−1.61186	−	9.14130i	−0.0603645	−	0.342344i
$714$	−16.9588	+	21.4475i	−0.634668	+	0.802653i
$715$	0.00537585	−	0.00195665i	0.000201045	−	7.31745e-5i
$716$	1.49166	+	1.25165i	0.0557460	+	0.0467764i
$717$	6.57359	+	17.3455i	0.245495	+	0.647779i
$718$	−2.49316	−	0.907437i	−0.0930440	−	0.0338653i
$719$	−33.4073			−1.24588			−0.622941	−	0.782269i	$-0.714062\pi$
$719$	−33.4073			−1.24588			−0.622941	+	0.782269i	$0.714062\pi$
$720$	25.8485	−	0.682010i	0.963316	−	0.0254170i
$721$	7.23332	−	13.0013i	0.269383	−	0.484193i
$722$	12.8935	−	10.8189i	0.479845	−	0.402638i
$723$	37.4017	−	7.10479i	1.39098	−	0.264230i
$724$	−1.61046	−	1.35134i	−0.0598524	−	0.0502222i
$725$	−65.2540	+	23.7505i	−2.42347	+	0.882072i
$726$	19.2312	−	11.4440i	0.713737	−	0.424725i
$727$	−16.5355	−	6.01843i	−0.613268	−	0.223211i	0.0166646	−	0.999861i	$-0.494695\pi$
$727$	−16.5355	−	6.01843i	−0.613268	−	0.223211i	−0.629933	+	0.776650i	$0.716917\pi$
$728$	−23.3723	+	0.371417i	−0.866236	+	0.0137656i
$729$	−26.9155	+	2.13445i	−0.996870	+	0.0790538i
$730$	−7.60205	−	13.1671i	−0.281365	−	0.487338i
$731$	−42.1152	+	35.3389i	−1.55769	+	1.30706i
$732$	1.54582	+	0.865499i	0.0571351	+	0.0319897i
$733$	−5.73093	+	32.5017i	−0.211677	+	1.20048i	0.674905	+	0.737905i	$0.264185\pi$
$733$	−5.73093	+	32.5017i	−0.211677	+	1.20048i	−0.886581	+	0.462573i	$0.846926\pi$
$734$	4.28521	−	24.3026i	0.158170	−	0.897026i
$735$	13.1786	−	41.9929i	0.486102	−	1.54893i
$736$	17.9474	−	15.0597i	0.661551	−	0.555107i
$737$	−0.00406476	+	0.00704037i	−0.000149727	+	0.000259335i
$738$	5.64260	−	10.3973i	0.207707	−	0.382730i
$739$	3.00468	+	5.20426i	0.110529	+	0.191442i	0.915984	−	0.401215i	$-0.131412\pi$
$739$	3.00468	+	5.20426i	0.110529	+	0.191442i	−0.805455	+	0.592657i	$0.798079\pi$
$740$	7.33884	−	6.15802i	0.269781	−	0.226373i
$741$	6.79748	−	8.32139i	0.249712	−	0.305694i
$742$	14.1707	−	5.41422i	0.520223	−	0.198762i
$743$	6.49525	−	2.36408i	0.238288	−	0.0867297i	−0.220116	−	0.975474i	$-0.570644\pi$
$743$	6.49525	−	2.36408i	0.238288	−	0.0867297i	0.458404	+	0.888744i	$0.348421\pi$
$744$	−2.52000	−	6.64943i	−0.0923876	−	0.243780i
$745$	45.1614	+	16.4374i	1.65459	+	0.602220i
$746$	−6.56937	−	11.3785i	−0.240522	−	0.416596i
$747$	2.77456	+	13.6235i	0.101516	+	0.498458i
$748$	−0.000865072	−	0.00149835i	−3.16302e−5	−	5.47850e-5i
$749$	−5.82135	−	2.01463i	−0.212707	−	0.0736132i
$750$	−15.3191	−	17.7751i	−0.559373	−	0.649054i
$751$	17.0287	−	6.19793i	0.621385	−	0.226166i	−0.0120925	−	0.999927i	$-0.503849\pi$
$751$	17.0287	−	6.19793i	0.621385	−	0.226166i	0.633477	+	0.773761i	$0.281627\pi$
$752$	−15.4767	+	5.63306i	−0.564377	+	0.205416i
$753$	0.676076	+	51.2561i	0.0246376	+	1.86788i
$754$	−4.97187	−	28.1969i	−0.181065	−	1.02687i
$755$	−44.8917			−1.63378
$756$	7.61115	+	3.84842i	0.276815	+	0.139966i
$757$	22.8031			0.828791			0.414396	−	0.910097i	$-0.363993\pi$
$757$	22.8031			0.828791			0.414396	+	0.910097i	$0.363993\pi$
$758$	−5.22288	−	29.6204i	−0.189703	−	1.07586i
$759$	0.00568657	−	0.00338392i	0.000206410	−	0.000122829i
$760$	22.6892	−	8.25820i	0.823025	−	0.299556i
$761$	17.2717	−	6.28639i	0.626099	−	0.227881i	−0.00943366	−	0.999956i	$-0.503003\pi$
$761$	17.2717	−	6.28639i	0.626099	−	0.227881i	0.635532	+	0.772074i	$0.280781\pi$
$762$	−9.71220	+	1.84492i	−0.351836	+	0.0668344i
$763$	6.35057	+	32.9457i	0.229906	+	1.19272i
$764$	−0.336565	−	0.582948i	−0.0121765	−	0.0210903i
$765$	−8.16590	+	54.7137i	−0.295239	+	1.97818i
$766$	9.87190	+	17.0986i	0.356686	+	0.617799i
$767$	−18.7701	−	6.83175i	−0.677749	−	0.246680i
$768$	14.5825	−	17.8518i	0.526202	−	0.644170i
$769$	−24.0640	+	8.75859i	−0.867771	+	0.315843i	−0.737264	−	0.675604i	$-0.763883\pi$
$769$	−24.0640	+	8.75859i	−0.867771	+	0.315843i	−0.130507	+	0.991447i	$0.541661\pi$
$770$	−0.00480705	−	0.00390513i	−0.000173234	−	0.000140731i
$771$	−4.78817	−	12.6344i	−0.172442	−	0.455016i
$772$	4.74362	−	3.98037i	0.170726	−	0.143257i
$773$	−8.20965	−	14.2195i	−0.295281	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$773$	−8.20965	−	14.2195i	−0.295281	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$774$	−29.8508	−	23.7347i	−1.07296	−	0.853126i
$775$	−5.45390	+	9.44643i	−0.195910	+	0.339326i
$776$	21.0769	−	17.6856i	0.756617	−	0.634877i
$777$	−19.0918	+	3.94195i	−0.684914	+	0.141417i
$778$	−0.815603	+	4.62551i	−0.0292408	+	0.165833i
$779$	1.25985	−	7.14497i	0.0451389	−	0.255995i
$780$	−9.62206	+	5.72582i	−0.344525	+	0.205017i
$781$	−0.00374770	+	0.00314469i	−0.000134103	+	0.000112526i
$782$	−20.7601	−	35.9575i	−0.742379	−	1.28584i
$783$	−13.4397	+	42.0288i	−0.480296	+	1.50199i
$784$	8.76349	+	14.1226i	0.312982	+	0.504378i
$785$	41.3051	+	15.0338i	1.47424	+	0.536581i
$786$	−23.2884	−	13.0391i	−0.830668	−	0.465088i
$787$	−31.3943	+	11.4266i	−1.11909	+	0.407314i	−0.834318	−	0.551283i	$-0.814138\pi$
$787$	−31.3943	+	11.4266i	−1.11909	+	0.407314i	−0.284767	+	0.958597i	$0.591916\pi$
$788$	−4.47775	−	3.75728i	−0.159513	−	0.133848i
$789$	−7.76023	+	22.2290i	−0.276272	+	0.791373i
$790$	16.1115	−	13.5192i	0.573223	−	0.480991i
$791$	9.79773	+	16.3641i	0.348367	+	0.581839i
$792$	0.00379601	−	0.00335977i	0.000134885	−	0.000119384i
$793$	4.73281			0.168067
$794$	24.4528	+	8.90009i	0.867798	+	0.315853i
$795$	19.4167	−	23.7696i	0.688638	−	0.843022i
$796$	−1.25476	−	1.05287i	−0.0444737	−	0.0373178i
$797$	−50.6567	+	18.4375i	−1.79435	+	0.653090i	−0.795460	+	0.606006i	$0.792771\pi$
$797$	−50.6567	+	18.4375i	−1.79435	+	0.653090i	−0.998891	+	0.0470845i	$0.985007\pi$
$798$	−11.5094	−	1.68600i	−0.407430	−	0.0596836i
$799$	−6.11867	−	34.7007i	−0.216463	−	1.22762i
$800$	−27.5314			−0.973383
$801$	−1.00182	+	0.0264328i	−0.0353975	+	0.000933958i
$802$	−7.09585			−0.250563
$803$	−0.00183964		0.000669576i	−6.49196e−5		2.36288e-5i
$804$	5.24423	−	15.0220i	0.184950	−	0.529784i
$805$	51.8741	+	42.1413i	1.82832	+	1.48528i
$806$	−3.44524	−	2.89090i	−0.121353	−	0.101828i
$807$	29.8813	−	17.7815i	1.05187	−	0.625938i
$808$	9.97099	−	8.36665i	0.350778	−	0.294338i
$809$	14.9497	−	25.8936i	0.525604	−	0.910372i	−0.473952	−	0.880551i	$-0.657173\pi$
$809$	14.9497	−	25.8936i	0.525604	−	0.910372i	0.999555	−	0.0298213i	$-0.00949382\pi$
$810$	−38.3207	+	2.02358i	−1.34645	+	0.0711015i
$811$	−8.26277			−0.290145			−0.145073	−	0.989421i	$-0.546342\pi$
$811$	−8.26277			−0.290145			−0.145073	+	0.989421i	$0.546342\pi$
$812$	10.5337	−	9.12791i	0.369659	−	0.320327i
$813$	−0.236779	−	17.9512i	−0.00830420	−	0.629576i
$814$	−0.000476360		0.00270157i	−1.66964e−5		9.46901e-5i
$815$	30.4814	+	25.5769i	1.06772	+	0.895919i
$816$	−13.6382	−	15.8248i	−0.477434	−	0.553978i
$817$	−21.9787	−	7.99959i	−0.768937	−	0.279870i
$818$	14.0138	+	24.2726i	0.489981	+	0.848672i
$819$	22.7639	−	0.962774i	0.795434	−	0.0336420i
$820$	−3.78020	+	6.54750i	−0.132010	+	0.228649i
$821$	−7.11731	+	5.97213i	−0.248396	+	0.208429i	−0.758481	−	0.651695i	$-0.774058\pi$
$821$	−7.11731	+	5.97213i	−0.248396	+	0.208429i	0.510085	+	0.860124i	$0.329614\pi$
$822$	0.708369	+	1.86915i	0.0247072	+	0.0651940i
$823$	−3.38291	+	19.1854i	−0.117921	+	0.668762i	0.867342	+	0.497713i	$0.165827\pi$
$823$	−3.38291	+	19.1854i	−0.117921	+	0.668762i	−0.985263	+	0.171049i	$0.945284\pi$
$824$	13.2585	+	11.1252i	0.461880	+	0.387563i
$825$	−0.00767505	−	0.00124918i	−0.000267211	−	4.34908e-5i
$826$	4.09296	+	21.2336i	0.142412	+	0.738812i
$827$	3.20511	−	5.55142i	0.111453	−	0.193042i	−0.804904	−	0.593406i	$-0.797783\pi$
$827$	3.20511	−	5.55142i	0.111453	−	0.193042i	0.916356	+	0.400364i	$0.131116\pi$
$828$	−9.69821	+	8.58369i	−0.337036	+	0.298304i
$829$	45.7862			1.59022			0.795109	−	0.606466i	$-0.207413\pi$
$829$	45.7862			1.59022			0.795109	+	0.606466i	$0.207413\pi$
$830$	3.43129	+	19.4598i	0.119102	+	0.675461i
$831$	0.774459	−	2.21842i	0.0268657	−	0.0769561i
$832$	4.33827	−	24.6036i	0.150403	−	0.852975i
$833$	−33.0107	+	13.2173i	−1.14375	+	0.457951i
$834$	29.0232	−	17.2709i	1.00499	−	0.598042i
$835$	2.79808	+	15.8687i	0.0968317	+	0.549160i
$836$	0.000368030	0	0.000637446i	1.27286e−5	0	2.20465e-5i
$837$	2.62637	+	6.41425i	0.0907807	+	0.221709i
$838$	−16.5548	−	28.6738i	−0.571877	−	0.990521i
$839$	22.1960	+	8.07869i	0.766292	+	0.278907i	0.695445	−	0.718580i	$-0.255207\pi$
$839$	22.1960	+	8.07869i	0.766292	+	0.278907i	0.0708472	+	0.997487i	$0.477430\pi$
$840$	45.0659	+	24.2999i	1.55492	+	0.838426i
$841$	33.0262	+	27.7123i	1.13884	+	0.955597i
$842$	−39.1571	+	14.2520i	−1.34944	+	0.491157i
$843$	16.8637	−	48.3058i	0.580818	−	1.66374i
$844$	2.52261	+	14.3064i	0.0868318	+	0.492448i
$845$	8.63955	−	14.9641i	0.297210	−	0.514782i
$846$	22.7399	−	8.96269i	0.781813	−	0.308144i
$847$	29.0996	−	0.462431i	0.999874	−	0.0158893i
$848$	2.01266	+	11.4144i	0.0691151	+	0.391971i
$849$	−12.1231	+	14.8410i	−0.416064	+	0.509341i
$850$	−8.47247	+	48.0498i	−0.290603	+	1.64809i
$851$	5.14053	−	29.1534i	0.176215	−	0.999365i
$852$	6.05750	−	7.41551i	0.207526	−	0.254051i
$853$	9.58605	+	54.3652i	0.328220	+	1.86143i	0.486005	+	0.873956i	$0.338454\pi$
$853$	9.58605	+	54.3652i	0.328220	+	1.86143i	−0.157785	+	0.987474i	$0.550435\pi$
$854$	−2.63203	−	4.39599i	−0.0900663	−	0.150428i
$855$	−21.8955	+	8.62990i	−0.748810	+	0.295136i
$856$	3.58305	−	6.20602i	0.122466	−	0.212117i
$857$	−5.98862	−	33.9632i	−0.204567	−	1.16016i	−0.898119	−	0.439753i	$-0.855066\pi$
$857$	−5.98862	−	33.9632i	−0.204567	−	1.16016i	0.693552	−	0.720407i	$-0.256045\pi$
$858$	0.00105674	−	0.00302702i	3.60767e−5	−	0.000103341i
$859$	−27.8562	+	10.1388i	−0.950442	+	0.345932i	−0.770281	−	0.637705i	$-0.779884\pi$
$859$	−27.8562	+	10.1388i	−0.950442	+	0.345932i	−0.180161	+	0.983637i	$0.557662\pi$
$860$	18.6709	+	15.6668i	0.636673	+	0.534232i
$861$	13.0941	−	8.07639i	0.446246	−	0.275243i
$862$	−13.7669	−	5.01075i	−0.468904	−	0.170667i
$863$	−5.52665	−	9.57243i	−0.188129	−	0.325849i	0.756497	−	0.653997i	$-0.226909\pi$
$863$	−5.52665	−	9.57243i	−0.188129	−	0.325849i	−0.944627	+	0.328147i	$0.893576\pi$
$864$	−10.7062	+	13.8357i	−0.364231	+	0.470700i
$865$	4.21326	−	7.29758i	0.143255	−	0.248125i
$866$	−1.99612	−	11.3206i	−0.0678310	−	0.384689i
$867$	13.1044	−	7.79806i	0.445048	−	0.264836i
$868$	0.345879	−	2.16191i	0.0117399	−	0.0733801i
$869$	0.000470263	−	0.00266699i	1.59526e−5	−	9.04715e-5i
$870$	−20.6702	+	59.2093i	−0.700785	+	2.00738i
$871$	−7.38102	−	41.8598i	−0.250096	−	1.41837i
$872$	−39.0316			−1.32178
$873$	−20.0821	+	17.7743i	−0.679678	+	0.601569i
$874$	8.83202	−	15.2975i	0.298747	−	0.517446i
$875$	−5.77601	−	29.9650i	−0.195265	−	1.01300i
$876$	3.78185	+	0.615528i	0.127777	+	0.0207968i
$877$	1.33109	+	1.11692i	0.0449478	+	0.0377157i	0.664985	−	0.746857i	$-0.268438\pi$
$877$	1.33109	+	1.11692i	0.0449478	+	0.0377157i	−0.620037	+	0.784573i	$0.712882\pi$
$878$	−1.34566	+	7.63163i	−0.0454139	+	0.257555i
$879$	9.60180	+	25.3359i	0.323861	+	0.854559i
$880$	0.00362494	−	0.00304169i	0.000122197	−	0.000102535i
$881$	18.6860	−	32.3651i	0.629548	−	1.09041i	−0.358095	−	0.933685i	$-0.616573\pi$
$881$	18.6860	−	32.3651i	0.629548	−	1.09041i	0.987642	−	0.156724i	$-0.0500932\pi$
$882$	−13.5538	−	20.6084i	−0.456381	−	0.693922i
$883$	−22.1563	−	38.3758i	−0.745619	−	1.29145i	−0.949905	−	0.312538i	$-0.898821\pi$
$883$	−22.1563	−	38.3758i	−0.745619	−	1.29145i	0.204287	−	0.978911i	$-0.434513\pi$
$884$	8.50060	+	3.09396i	0.285906	+	0.104061i
$885$	28.5625	+	33.1417i	0.960117	+	1.11405i
$886$	33.2542	+	27.9035i	1.11720	+	0.937438i
$887$	5.89959	−	33.4582i	0.198089	−	1.12342i	−0.709862	−	0.704341i	$-0.751243\pi$
$887$	5.89959	−	33.4582i	0.198089	−	1.12342i	0.907951	−	0.419076i	$-0.137646\pi$
$888$	−0.299102	−	22.6762i	−0.0100372	−	0.760962i
$889$	−12.1495	−	4.20467i	−0.407482	−	0.141020i
$890$	−1.42434			−0.0477439
$891$	−0.00361236	+	0.00337127i	−0.000121019	+	0.000112942i
$892$	0.178410	−	0.309015i	0.00597360	−	0.0103466i
$893$	11.4834	−	9.63573i	0.384278	−	0.322448i
$894$	23.1463	−	13.7737i	0.774127	−	0.460661i
$895$	−8.72830	−	7.32391i	−0.291755	−	0.244811i
$896$	−8.62331	+	3.29472i	−0.288085	+	0.110069i
$897$	−11.4036	+	32.6653i	−0.380755	+	1.09066i
$898$	4.97759	+	1.81169i	0.166104	+	0.0604570i
$899$	11.3273			0.377787
$900$	15.2139	−	0.401418i	0.507131	−	0.0133806i
$901$	−24.7967			−0.826099
$902$	−0.000375930	−	0.00213201i	−1.25171e−5	−	7.09880e-5i
$903$	−18.3109	−	46.0925i	−0.609348	−	1.53386i
$904$	−20.8497	+	7.58865i	−0.693449	+	0.252395i
$905$	9.42346	+	7.90722i	0.313246	+	0.262845i
$906$	−15.9163	+	19.4845i	−0.528782	+	0.647328i
$907$	23.1796	+	8.43669i	0.769666	+	0.280136i	0.696857	−	0.717210i	$-0.254581\pi$
$907$	23.1796	+	8.43669i	0.769666	+	0.280136i	0.0728094	+	0.997346i	$0.476804\pi$
$908$	−0.382234			−0.0126849
$909$	−9.50039	+	8.40860i	−0.315108	+	0.278896i
$910$	32.3782	−	0.514533i	1.07333	−	0.0170566i
$911$	−5.01971	+	4.21204i	−0.166311	+	0.139551i	−0.722145	−	0.691742i	$-0.756843\pi$
$911$	−5.01971	+	4.21204i	−0.166311	+	0.139551i	0.555834	+	0.831293i	$0.312399\pi$
$912$	2.92933	−	8.39099i	0.0969998	−	0.277854i
$913$	0.00194908	+	0.00163547i	6.45050e−5	+	5.41261e-5i
$914$	23.2663	−	8.46824i	0.769581	−	0.280105i
$915$	−9.04520	−	5.06437i	−0.299025	−	0.167423i
$916$	−16.4164	−	5.97509i	−0.542414	−	0.197423i
$917$	−17.8306	−	29.7805i	−0.588820	−	0.983440i
$918$	20.8523	+	22.9429i	0.688230	+	0.757228i
$919$	−8.95848	−	15.5165i	−0.295513	−	0.511844i	0.679591	−	0.733591i	$-0.262157\pi$
$919$	−8.95848	−	15.5165i	−0.295513	−	0.511844i	−0.975104	+	0.221747i	$0.928824\pi$
$920$	−59.5590	+	49.9760i	−1.96360	+	1.64766i
$921$	37.0828	−	22.0669i	1.22192	−	0.727130i
$922$	−4.54027	+	25.7492i	−0.149526	+	0.848003i
$923$	4.44183	−	25.1909i	0.146205	−	0.829168i
$924$	0.00152856		0.000315607i	5.02859e−5		1.03827e-5i
$925$	−26.6485	+	22.3607i	−0.876196	+	0.735216i
$926$	−10.7699	+	18.6541i	−0.353922	+	0.613010i
$927$	−13.2047	−	10.4992i	−0.433700	−	0.344840i
$928$	14.2952	+	24.7600i	0.469262	+	0.812785i
$929$	12.2952	−	10.3169i	0.403393	−	0.338487i	−0.418410	−	0.908258i	$-0.637413\pi$
$929$	12.2952	−	10.3169i	0.403393	−	0.338487i	0.821803	+	0.569771i	$0.192968\pi$
$930$	3.49101	+	9.21161i	0.114475	+	0.302061i
$931$	−11.8916	−	9.35077i	−0.389732	−	0.306459i
$932$	−15.6856	+	5.70908i	−0.513798	+	0.187007i
$933$	−23.4764	+	28.7395i	−0.768582	+	0.940889i
$934$	−20.0148	−	7.28479i	−0.654905	−	0.238366i
$935$	0.00506187	+	0.00876742i	0.000165541	+	0.000286725i
$936$	−3.91249	+	26.2147i	−0.127884	+	0.856855i
$937$	−15.6496	−	27.1059i	−0.511249	−	0.885510i	−0.999915	−	0.0130386i	$-0.995850\pi$
$937$	−15.6496	−	27.1059i	−0.511249	−	0.885510i	0.488666	−	0.872471i	$-0.337484\pi$
$938$	−34.7761	+	30.1351i	−1.13548	+	0.983945i
$939$	−44.4479	+	8.44328i	−1.45050	+	0.275536i
$940$	−14.6791	+	5.34275i	−0.478779	+	0.174261i
$941$	−25.7548	+	9.37399i	−0.839583	+	0.305583i	−0.725786	−	0.687921i	$-0.758524\pi$
$941$	−25.7548	+	9.37399i	−0.839583	+	0.305583i	−0.113797	+	0.993504i	$0.536302\pi$
$942$	21.1698	−	12.5976i	0.689750	−	0.410451i
$943$	4.05676	+	23.0070i	0.132106	+	0.749212i
$944$	−16.5222			−0.537750
$945$	−44.5359	−	22.5186i	−1.44875	−	0.732531i
$946$	−0.00697917			−0.000226912
$947$	5.33872	+	30.2774i	0.173485	+	0.983883i	0.939878	+	0.341511i	$0.110939\pi$
$947$	5.33872	+	30.2774i	0.173485	+	0.983883i	−0.766393	+	0.642372i	$0.777950\pi$
$948$	0.0699063	+	5.29989i	0.00227045	+	0.172132i
$949$	9.61867	−	3.50091i	0.312235	−	0.113644i
$950$	−19.5055	+	7.09941i	−0.632841	+	0.230335i
$951$	−25.6072	−	29.7127i	−0.830371	−	0.963499i
$952$	−7.82940	−	40.6177i	−0.253752	−	1.31643i
$953$	15.6355	+	27.0815i	0.506484	+	0.877256i	0.999972	+	0.00750321i	$0.00238837\pi$
$953$	15.6355	+	27.0815i	0.506484	+	0.877256i	−0.493488	+	0.869753i	$0.664278\pi$
$954$	−3.43267	−	16.8549i	−0.111137	−	0.545699i
$955$	1.96938	+	3.41106i	0.0637275	+	0.110379i
$956$	−6.24323	−	2.27235i	−0.201921	−	0.0734931i
$957$	0.00286169	+	0.00755104i	9.25054e−5	+	0.000244091i
$958$	−34.9898	+	12.7352i	−1.13047	+	0.411457i
$959$	−0.410668	+	2.56688i	−0.0132612	+	0.0828889i
$960$	−34.6184	+	42.3794i	−1.11730	+	1.36779i
$961$	−22.3844	+	18.7827i	−0.722077	+	0.605894i
$962$	−7.17161	−	12.4216i	−0.231222	−	0.400488i
$963$	−3.33168	+	6.13911i	−0.107362	+	0.197830i
$964$	−6.81795	+	11.8090i	−0.219592	+	0.380344i
$965$	−27.7568	+	23.2907i	−0.893522	+	0.749754i
$966$	36.6825	−	7.57397i	1.18024	−	0.243689i
$967$	1.64826	−	9.34777i	0.0530046	−	0.300604i	−0.946768	−	0.321916i	$-0.895673\pi$
$967$	1.64826	−	9.34777i	0.0530046	−	0.300604i	0.999773	+	0.0213118i	$0.00678426\pi$
$968$	−5.87905	+	33.3417i	−0.188960	+	1.07164i
$969$	16.5908	+	9.28912i	0.532973	+	0.298410i
$970$	−29.1983	+	24.5003i	−0.937502	+	0.786658i
$971$	−2.41464	−	4.18227i	−0.0774893	−	0.134215i	0.824677	−	0.565604i	$-0.191357\pi$
$971$	−2.41464	−	4.18227i	−0.0774893	−	0.134215i	−0.902166	+	0.431389i	$0.858024\pi$
$972$	5.71451	−	7.80174i	0.183293	−	0.250241i
$973$	43.9163	−	0.697888i	1.40789	−	0.0223732i
$974$	−11.8756	−	4.32237i	−0.380519	−	0.138498i
$975$	34.9392	−	20.7913i	1.11895	−	0.665856i
$976$	3.67867	−	1.33893i	0.117751	−	0.0428580i
$977$	−43.9709	−	36.8959i	−1.40675	−	1.18041i	−0.958007	−	0.286746i	$-0.907426\pi$
$977$	−43.9709	−	36.8959i	−1.40675	−	1.18041i	−0.448746	−	0.893660i	$-0.648129\pi$
$978$	21.9083	−	4.16168i	0.700550	−	0.133076i
$979$	−0.000140493	0	0.000117888i	−4.49017e−6	0	3.76770e-6i
$980$	8.31185	+	13.3948i	0.265512	+	0.427880i
$981$	38.0314	−	1.00345i	1.21425	−	0.0320378i
$982$	0.207686			0.00662754
$983$	−7.54652	−	2.74671i	−0.240696	−	0.0876063i	0.218855	−	0.975757i	$-0.429768\pi$
$983$	−7.54652	−	2.74671i	−0.240696	−	0.0876063i	−0.459552	+	0.888151i	$0.651990\pi$
$984$	6.34239	+	16.7354i	0.202188	+	0.533506i
$985$	26.2011	+	21.9853i	0.834836	+	0.700511i
$986$	47.6119	−	17.3293i	1.51627	−	0.551878i
$987$	31.4515	+	4.60727i	1.00111	+	0.146651i
$988$	0.668289	+	3.79006i	0.0212611	+	0.120578i
$989$	75.3140			2.39485
$990$	−0.00525870	+	0.00465437i	−0.000167133	+	0.000147926i
$991$	27.5912			0.876462			0.438231	−	0.898862i	$-0.355605\pi$
$991$	27.5912			0.876462			0.438231	+	0.898862i	$0.355605\pi$
$992$	4.22008	+	1.53598i	0.133988	+	0.0487675i
$993$	−18.0340	−	20.9252i	−0.572291	−	0.664043i
$994$	−25.8684	+	9.88357i	−0.820495	+	0.313488i
$995$	7.34208	+	6.16073i	0.232759	+	0.195308i
$996$	−4.34507	−	2.43279i	−0.137679	−	0.0770858i
$997$	−5.70443	+	4.78659i	−0.180661	+	0.151593i	−0.728634	−	0.684904i	$-0.759844\pi$
$997$	−5.70443	+	4.78659i	−0.180661	+	0.151593i	0.547972	+	0.836496i	$0.315400\pi$
$998$	−16.8109	+	29.1174i	−0.532140	+	0.921694i
$999$	0.874414	+	22.0874i	0.0276652	+	0.698814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.8	✓	132
3.2	odd	2		567.2.u.a.550.15		132
7.2	even	3		189.2.w.a.58.8	yes	132
21.2	odd	6		567.2.w.a.226.15		132
27.7	even	9		189.2.w.a.88.8	yes	132
27.20	odd	18		567.2.w.a.424.15		132
189.128	odd	18		567.2.u.a.100.15		132
189.142	even	9	inner	189.2.u.a.142.8	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.8	✓	132	1.1	even	1	trivial
189.2.u.a.142.8	yes	132	189.142	even	9	inner
189.2.w.a.58.8	yes	132	7.2	even	3
189.2.w.a.88.8	yes	132	27.7	even	9
567.2.u.a.100.15		132	189.128	odd	18
567.2.u.a.550.15		132	3.2	odd	2
567.2.w.a.226.15		132	21.2	odd	6
567.2.w.a.424.15		132	27.20	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)

\(f(q)\)	\(=\)	\(q+(-0.203963 - 1.15673i) q^{2} +(-1.51129 - 0.846167i) q^{3} +(0.582964 - 0.212181i) q^{4} +(-3.41115 + 1.24156i) q^{5} +(-0.670539 + 1.92074i) q^{6} +(-1.99948 + 1.73265i) q^{7} +(-1.53891 - 2.66548i) q^{8} +(1.56800 + 2.55761i) q^{9} +O(q^{10})\)	\(q+(-0.203963 - 1.15673i) q^{2} +(-1.51129 - 0.846167i) q^{3} +(0.582964 - 0.212181i) q^{4} +(-3.41115 + 1.24156i) q^{5} +(-0.670539 + 1.92074i) q^{6} +(-1.99948 + 1.73265i) q^{7} +(-1.53891 - 2.66548i) q^{8} +(1.56800 + 2.55761i) q^{9} +(2.13189 + 3.69255i) q^{10} +(0.000515903 + 0.000187773i) q^{11} +(-1.06057 - 0.172616i) q^{12} +(-2.69743 + 0.981783i) q^{13} +(2.41202 + 1.95947i) q^{14} +(6.20581 + 1.01005i) q^{15} +(-1.81888 + 1.52622i) q^{16} +(-2.53989 - 4.39921i) q^{17} +(2.63865 - 2.33541i) q^{18} +(1.08055 - 1.87157i) q^{19} +(-1.72514 + 1.44757i) q^{20} +(4.48791 - 0.926635i) q^{21} +(0.000111978 - 0.000635059i) q^{22} +(-1.20838 + 6.85309i) q^{23} +(0.0703100 + 5.33049i) q^{24} +(6.26426 - 5.25634i) q^{25} +(1.68583 + 2.91995i) q^{26} +(-0.205549 - 5.19209i) q^{27} +(-0.797992 + 1.43432i) q^{28} +(-7.97979 - 2.90441i) q^{29} +(-0.0974020 - 7.38445i) q^{30} +(-1.25345 + 0.456219i) q^{31} +(-2.57909 - 2.16412i) q^{32} +(-0.000620793 - 0.000720320i) q^{33} +(-4.57065 + 3.83523i) q^{34} +(4.66936 - 8.39279i) q^{35} +(1.45677 + 1.15829i) q^{36} -4.25405 q^{37} +(-2.38529 - 0.868174i) q^{38} +(4.90735 + 0.798712i) q^{39} +(8.55880 + 7.18169i) q^{40} +(3.15472 - 1.14822i) q^{41} +(-1.98723 - 5.00230i) q^{42} +(-1.87937 - 10.6584i) q^{43} +0.000340595 q^{44} +(-8.52411 - 6.77762i) q^{45} +8.17363 q^{46} +(6.51821 + 2.37243i) q^{47} +(4.04029 - 0.767490i) q^{48} +(0.995880 - 6.92880i) q^{49} +(-7.35783 - 6.17395i) q^{50} +(0.116042 + 8.79765i) q^{51} +(-1.36419 + 1.14469i) q^{52} +(2.44073 - 4.22748i) q^{53} +(-5.96391 + 1.29676i) q^{54} -0.00199295 q^{55} +(7.69536 + 2.66319i) q^{56} +(-3.21668 + 1.91416i) q^{57} +(-1.73203 + 9.82285i) q^{58} +(5.33053 + 4.47285i) q^{59} +(3.83207 - 0.727936i) q^{60} +(-1.54932 - 0.563906i) q^{61} +(0.783379 + 1.35685i) q^{62} +(-7.56663 - 2.39710i) q^{63} +(-4.35164 + 7.53726i) q^{64} +(7.98239 - 6.69802i) q^{65} +(-0.000706597 + 0.000865007i) q^{66} +(-2.57130 + 14.5826i) q^{67} +(-2.41409 - 2.02566i) q^{68} +(7.62507 - 9.33452i) q^{69} +(-10.6606 - 3.68938i) q^{70} +(-4.45552 + 7.71718i) q^{71} +(4.40422 - 8.11541i) q^{72} -3.56587 q^{73} +(0.867667 + 4.92078i) q^{74} +(-13.9149 + 2.64325i) q^{75} +(0.232810 - 1.32033i) q^{76} +(-0.00135689 + 0.000518427i) q^{77} +(-0.0770224 - 5.83938i) q^{78} +(-0.856561 - 4.85780i) q^{79} +(4.30958 - 7.46441i) q^{80} +(-4.08273 + 8.02068i) q^{81} +(-1.97163 - 3.41496i) q^{82} +(4.35490 + 1.58505i) q^{83} +(2.41967 - 1.49245i) q^{84} +(14.1258 + 11.8530i) q^{85} +(-11.9456 + 4.34783i) q^{86} +(9.60218 + 11.1416i) q^{87} +(-0.000293425 - 0.00166409i) q^{88} +(-0.167028 + 0.289300i) q^{89} +(-6.10127 + 11.2425i) q^{90} +(3.69238 - 6.63674i) q^{91} +(0.749654 + 4.25150i) q^{92} +(2.28037 + 0.371149i) q^{93} +(1.41479 - 8.02369i) q^{94} +(-1.36226 + 7.72576i) q^{95} +(2.06656 + 5.45296i) q^{96} +(1.55231 + 8.80360i) q^{97} +(-8.21786 + 0.261251i) q^{98} +(0.000328687 + 0.00161391i) 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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